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--git a/2023/Diffusion Video Autoencoders_ Toward Temporally Consistent Face Video Editing via Disentangled Video Encoding/9c72d0e6-e653-459a-87e1-dce2e1570589_content_list.json b/2023/Diffusion Video Autoencoders_ Toward Temporally Consistent Face Video Editing via Disentangled Video Encoding/9c72d0e6-e653-459a-87e1-dce2e1570589_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..a9d7e222b4c8e0f9cf0fe5b96531f2197cec2930 --- /dev/null +++ b/2023/Diffusion Video Autoencoders_ Toward Temporally Consistent Face Video Editing via Disentangled Video Encoding/9c72d0e6-e653-459a-87e1-dce2e1570589_content_list.json @@ -0,0 +1,1277 @@ +[ + { + "type": "text", + "text": "Diffusion Video Autoencoders: Toward Temporally Consistent Face Video Editing via Disentangled Video Encoding", + "text_level": 1, + "bbox": [ + 171, + 130, + 799, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Gyeongman Kim $^{1}$ Hajin Shim $^{1}$ Hyunsu Kim $^{2}$ Yunjay Choi $^{2}$ Junho Kim $^{2}$ Eunho Yang $^{1,3}$", + "bbox": [ + 107, + 200, + 893, + 222 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ Korea Advanced Institute of Science and Technology (KAIST), South Korea", + "bbox": [ + 196, + 224, + 805, + 243 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ NAVER AI Lab $^{3}$ AITRICS, South Korea", + "bbox": [ + 325, + 244, + 676, + 261 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{gmkim, shimazing, eunhoy}@kaist.ac.kr {hyunsull25.kim, yunjey.choi, jhkim.ai}@navercorp.com", + "bbox": [ + 86, + 265, + 910, + 280 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8f7d1da6435946194341ac20bd0ded96f14cdfc6ac3373d51ad7f288ebc5421c.jpg", + "image_caption": [ + "Figure 1. Face video editing. Our editing method shows improvement compared to the baseline [35] in terms of temporal consistency (left, \"eyeglasses\") and robustness to the unusual case such as the hand-occluded face (right, \"beard\")." + ], + "image_footnote": [], + "bbox": [ + 107, + 292, + 493, + 507 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3fe29fd617bd845440db7245378a97db358199992e8aca5e218426dcc808eee6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 496, + 292, + 864, + 508 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 551, + 313, + 566 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Inspired by the impressive performance of recent face image editing methods, several studies have been naturally proposed to extend these methods to the face video editing task. One of the main challenges here is temporal consistency among edited frames, which is still unresolved. To this end, we propose a novel face video editing framework based on diffusion autoencoders that can successfully extract the decomposed features - for the first time as a face video editing model - of identity and motion from a given video. This modeling allows us to edit the video by simply manipulating the temporally invariant feature to the desired direction for the consistency. Another unique strength of our model is that, since our model is based on diffusion models, it can satisfy both reconstruction and edit capabilities at the same time, and is robust to corner cases in wild face videos (e.g. occluded faces) unlike the existing GAN-based methods.1", + "bbox": [ + 75, + 574, + 468, + 816 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 824, + 207, + 838 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "As one of the standard tasks in computer vision to change various face attributes such as hair color, gender, or glasses", + "bbox": [ + 76, + 849, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "of a given face image, face editing has been continuously gaining attention due to its various applications and entertainment. In particular, with the improvement of analysis and manipulation techniques for recent Generative Adversarial Network (GAN) models [8, 11, 22, 29, 30], we simply can do this task by manipulating a given image's latent feature. In addition, very recently, many methods for face image editing also have been proposed based on Diffusion Probabilistic Model (DPM)-based methods that show high-quality and flexible manipulation performance [3, 12, 17, 19, 23, 25].", + "bbox": [ + 500, + 553, + 890, + 718 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Naturally, further studies [2, 35, 41] have been proposed to extend image editing methods to incorporate the temporal axis for videos. Now, given real videos with a human face, these studies try to manipulate some target facial attributes with the other remaining features and motion intact. They all basically edit each frame of a video independently via off-the-shelf StyleGAN-based image editing techniques [22, 29, 41].", + "bbox": [ + 496, + 719, + 890, + 839 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Despite the advantages of StyleGAN in this task such as high-resolution image generation capability and highly disentangled semantic representation space, one harmful drawback of GAN-based editing methods is that the encoded real", + "bbox": [ + 496, + 839, + 890, + 898 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "1Project page: https://diff-video-ae.github.io", + "bbox": [ + 94, + 886, + 330, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "6091", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "images cannot perfectly be recovered by the pretrained generator [1, 26, 34]. Especially, if a face in a given image is unusually decorated or occluded by some objects, the fixed generator cannot synthesize it. For perfect reconstruction, several methods [6, 27] are suggested to further tune the generator for GAN-inversion [26, 34] on one or a few target images, which is computationally expensive. Moreover, after the fine-tuning, the original editability of GANs cannot be guaranteed. This risk could be worse in video domain since we have to finetune the model on the multiple frames.", + "bbox": [ + 75, + 90, + 472, + 242 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Aside from the reconstruction issue of existing GAN-based methods, it is critical in video editing tasks to consider the temporal consistency among edited frames to produce realistic results. To address this, some prior works rely on the smoothness of the latent trajectory of the original frames [35] or smoothen the latent features directly [2] by simply taking the same editing step for all frames. However, smoothness does not ensure temporal consistency. Rather, the same editing step can make different results for different frames because it can be unintentionally entangled with irrelevant motion features. For example, in the middle row of Fig. 1, eyeglasses vary across time and sometimes diminish when the man closes his eyes.", + "bbox": [ + 75, + 244, + 472, + 441 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we propose a novel video editing framework for human face video, termed Diffusion Video Autoencoder, that resolves the limitations of the prior works. First, instead of GAN-based editing methods suffering from imperfect reconstruction quality, we newly introduce diffusion based model for face video editing tasks. As the recently proposed diffusion autoencoder (DiffAE) [23] does, thanks to the expressive latent spaces of the same size as input space, our model learns a semantically meaningful latent space that can perfectly recover the original image back and are directly editable. Not only that, for the first time as a video editing model, encode the decomposed features of the video: 1) identity feature shared by all frames, 2) feature of motion or facial expression in each frame, and 3) background feature that could not have high-level representation due to large variances. Then, for consistent editing, we simply manipulate a single invariant feature for the desired attribute (single editing operation per video), which is also computationally beneficial compared to the prior works that require editing the latent features of all frames.", + "bbox": [ + 75, + 444, + 472, + 746 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We experimentally demonstrate that our model appropriately decomposes videos into time-invariant and per-frame variant features and can provide temporally consistent manipulation. Specifically, we explore two ways of manipulation. The first one is to edit features in the predefined set of attributes by moving semantic features to the target direction found by learning linear classifier in semantic representation space on annotated CelebA-HQ dataset [10]. Additionally, we explore the text-based editing method that optimizes a time-invariant latent feature with CLIP loss [7]. It", + "bbox": [ + 75, + 750, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "is worth noting that since we cannot fully generate edited images for CLIP loss due to the computational cost, we propose the novel strategy that rather uses latent state of intermediate time step for the efficiency.", + "bbox": [ + 496, + 90, + 890, + 150 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To summarize, our contribution is four-fold:", + "bbox": [ + 517, + 152, + 812, + 165 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We devise diffusion video autoencoders based on diffusion autoencoders [23] that decompose the video into a single time-invariant and per-frame time-variant features for temporally consistent editing.", + "- Based on the decomposed representation of diffusion video autoencoder, face video editing can be conducted by editing only the single time-invariant identity feature and decoding it together with the remaining original features.", + "- Owing to the nearly-perfect reconstruction ability of diffusion models, our framework can be utilized to edit exceptional cases such that a face is partially occluded by some objects as well as usual cases.", + "- In addition to the existing predefined attributes editing method, we propose a text-based identity editing method based on the local directional CLIP loss [7,24] for the intermediately generated product of diffusion video autoencoders." + ], + "bbox": [ + 517, + 172, + 890, + 465 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 481, + 640, + 497 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Video editing When editing a given real video, it is essential to preserve temporal consistency. First, Lai et al. [14] consider editing global features of videos such as artistic style transfer, colorization, image enhancement, etc. To encourage temporal consistency, they train sequential image translator with temporal loss defined as the warping error between the output frames.", + "bbox": [ + 496, + 507, + 890, + 612 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Different from this work, our target task is to edit facial attributes of human face video. In other words, we aim to change face-related attributes such as eyeglasses, beards, etc. For this task, Yao et al. [41] are the first that propose the editing pipeline: 1) align and crop the target face area, 2) encode these frames to latent features, manipulate and decode them, and 3) unalign and paste the edited frames to the original video. However, every step of this pipeline is conducted independently for each frame. For the manipulation step, they try to find disentangled editing directions for a desired attribute and take the same step for every frame, while expecting the disentanglement brings consistency automatically. However, the results show inconsistency and we conjecture that both latent space and learned direction are still entangled with many other attributes. Next, Tza-ban et al. [35] additionally fine-tune the pretrained StyleGAN [27] to enhance reconstructability. Meanwhile, they assume that temporal consistency would be preserved when applying the same editing step to the latent features of the", + "bbox": [ + 496, + 613, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "6092", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "original frames. However, their assumption is not always true for all attributes, especially for beards and eyeglasses as shown in Fig. 1. Alauf et al. [2] also try to avoid temporal inconsistency by smoothing latent features.", + "bbox": [ + 75, + 90, + 468, + 151 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "While the methods in the previous paragraph handle inconsistency implicitly, several works [39, 40] try to solve it more directly. After per-frame editing, Xu et al. [40] further optimize latent codes and the pretrained StyleGAN to enhance consistency between the frame pairs defined by involving bi-directional optical flow. On the other hand, Xia et al. [39] propose to learn the dynamics of inverted GAN latent codes of video frames. The learned dynamics are used to generate the subsequent latent features after editing only the first frame.", + "bbox": [ + 75, + 151, + 470, + 301 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Additionally, although Skorokhodov et al. [31] mainly target to generate video, they also demonstrate manipulation results of the generated video. They model the video with a time-invariant content code and per-frame motion codes. Based on this modeling, the generated video can be manipulated with a target text by optimizing its content vector with CLIP loss. However, they cannot edit the real videos due to the absence of an encoding method. In contrast, our proposed method is capable of encoding and manipulating realistic face videos.", + "bbox": [ + 75, + 303, + 468, + 452 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Diffusion models Denoising diffusion probabilistic models (DDPMs) [9] associate image generation with the sequential denoising process of isotropic Gaussian noise. The model is trained to predict the noise from the input image. Unlike other generative models such as GANs and most traditional-style VAEs that encode input data in a low-dimensional space, diffusion models have a latent space that is the same size as the input. Although DDPMs require a lot of feed-forward steps to generate samples, their image fidelity and diversity are superior to other types of generative models. Compared to DDPMs that assume a Markovian noise-injecting forward diffusion process, Denoising diffusion implicit models (DDIMs) [33] assume a non-Markovian forward process that has the same marginal distribution as DDPMs, and use its corresponding reverse denoising process for sampling, which enables acceleration of the rather onerous sampling process of DDPMs. DDIMs also utilize a deterministic forward-backward process and therefore show nearly-perfect reconstruction ability, which is not the case for DDPMs. In this paper, we adopt conditional DDIMs to encode, manipulate and decode real videos.", + "bbox": [ + 75, + 465, + 470, + 797 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Image editing with diffusion models There are various attempts to manipulate images with diffusion models [3, 12, 17, 19, 23, 25] such as text-guided inpainting [3, 19, 25], stroke-based editing [17], and style transfer [12]. Among those, we are especially interested in facial attribute editing tasks. Kim et al. [12] propose text-based image ma", + "bbox": [ + 75, + 809, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "nipulation by optimizing an unconditional diffusion model to minimize local directional CLIP loss [7]. This method is superior to GAN-based methods as it can successfully edit even occluded or overly decorated faces by the excellent reconstruction ability of diffusion models. However, due to the absence of semantically meaningful latent space, there exist some semantic features that are unable to be changed. Another parallel work proposes diffusion autoencoder (DiffAE) [23], which takes a learnable encoder to obtain semantic representations of which the underlying diffusion model is conditioned. The model can perform face attribute manipulation by moving the semantic vector to a target direction. Based on DiffAEs, we design our diffusion video autoencoders to perform temporally-consistent video editing.", + "bbox": [ + 496, + 90, + 890, + 303 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Preliminaries", + "text_level": 1, + "bbox": [ + 500, + 320, + 637, + 335 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Diffusion probabilistic models (DPMs) DPMs [9, 32] are generative models that attempt to approximate the data distribution $q(x_0)$ via $p_{\\theta}(x_0)$ from the reverse prediction of Markovian diffusion process $q(x_{1:T}|x_0) = \\prod_{t=1}^{T} q(x_t|x_{t-1})$ . Here, the forward process of DPM is a Gaussian noise perturbation $q(x_t|x_{t-1}) = \\mathcal{N}(\\sqrt{1 - \\beta_t} x_{t-1}, \\beta_t I)$ where $\\beta_t$ is fixed or learned variance schedule with increasing $\\beta_1 < \\beta_2 < \\dots < \\beta_T$ , adding gradually increasing noise to data $x_0$ , and its reverse process is denoising of $x_t$ step by step in reverse order. From this definition, a noisy image $x_t$ at step $t$ can be expressed as $x_t = \\sqrt{\\alpha_t} x_0 + \\sqrt{1 - \\alpha_t} \\epsilon$ , $\\epsilon \\sim \\mathcal{N}(0, I)$ where $\\alpha_t = \\prod_{s=1}^t (1 - \\beta_s)$ . While the true reverse process $q(x_{t-1}|x_t)$ is intractable, diffusion models approximate $q(x_{t-1}|x_t, x_0)$ with $p_{\\theta}(x_{t-1}|x_t) = \\mathcal{N}(\\mu_{\\theta}(x_t, t), \\sigma_t)$ by minimizing the variational lower bound of negative log-likelihood. Finally, by reparameterizing $\\mu_{\\theta}$ , the objective is given as $\\mathbb{E}_{x_0 \\sim q(x_0), \\epsilon_t \\sim \\mathcal{N}(0, I), t} \\left\\| \\epsilon_{\\theta}(x_t, t) - \\epsilon_t \\right\\|_2^2$ where the parameterized model $\\epsilon_{\\theta}(x_t, t)$ estimates the true Gaussian noise term $\\frac{1}{\\sqrt{1 - \\alpha_t}} (x_t - \\sqrt{\\alpha_t} x_0)$ in the forward process.", + "bbox": [ + 496, + 345, + 890, + 655 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Speeding up a time-consuming sampling process of diffusion models is one of the core research topics related to diffusion models [20, 33]. Among others, Song et al. [33] propose DDIM, which assumes a non-Markovian forward process $q(x_{t}|x_{t - 1},x_{0})$ that has the same marginal distribution $q(x_{t}|x_{0})$ with DDPMs. The corresponding generative process of DDIM is $x_{t - 1} = \\sqrt{\\alpha_{t - 1}} f_{\\theta}(x_t,t) + \\sqrt{1 - \\alpha_{t - 1} - \\sigma_t^2}\\epsilon_\\theta (x_t,t) + \\sigma_t^2 z$ where $z\\sim \\mathcal{N}(0,I)$ , $\\sigma$ is sampling stochasticity and $f_{\\theta}(x_t,t)$ , the estimated value of $x_0$ at time step $t$ , is as follow:", + "bbox": [ + 496, + 656, + 890, + 809 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nf _ {\\theta} (x _ {t}, t) = \\frac {x _ {t} - \\sqrt {1 - \\alpha_ {t}} \\epsilon_ {\\theta} (x _ {t} , t)}{\\sqrt {\\alpha_ {t}}}.\n$$\n", + "text_format": "latex", + "bbox": [ + 575, + 823, + 815, + 858 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "When $\\sigma$ is set to 0, this process becomes deterministic. With deterministic forward and reverse processes, we can obtain", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "6093", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/6d2d9d4d0fe4627368c7e2bd2e4aa9e40bc1af5396b06ba869c3cc069ebc1f1d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 83, + 88, + 408, + 188 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/8a3c0f47368448e904dc292f7c9c39e9c7ccc2fdc056331136b40eeebbe97fda.jpg", + "image_caption": [ + "(a) Video autoencoding and editing pipeline.", + "Figure 2. Overview of our Diffusion Video Autoencoder." + ], + "image_footnote": [], + "bbox": [ + 78, + 190, + 408, + 332 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/b5ca203f0d7b7161828c724bb2986b3397462f495b0bb6cc1c5584ff2c097baf.jpg", + "image_caption": [ + "(b) Training objective." + ], + "image_footnote": [], + "bbox": [ + 428, + 87, + 888, + 329 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the latent code of each original sample, which can reconstruct the original sample through the reverse process.", + "bbox": [ + 75, + 386, + 468, + 417 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Diffusion autoencoders Due to the determinacy of its sampling process, DDIM can reconstruct the original image $x_0$ from $x_T$ obtained through $T$ forward process steps. While $x_T$ can be considered as a latent state with the same size as $x_0$ , it does not contain high-level semantic information [23]. To supplement this, Prechakul et al. propose diffusion autoencoder (DiffAE) [23] based on DDIM. DiffAE utilizes two forms of latent variables: $z_{\\mathrm{sem}}$ for the useful high-level semantic representation and $x_T$ for the remaining low-level stochasticity information. DiffAE introduces a semantic encoder $\\mathsf{Enc}(x_0)$ which extracts $z_{\\mathrm{sem}}$ from an image, and makes a noise estimator $\\epsilon_{\\theta}(x,t,z_{\\mathrm{sem}})$ conditioned on $z_{\\mathrm{sem}}$ . Stochastic latent $x_T$ is calculated through the deterministic DDIM forward process [33] that involves the noise estimator $\\epsilon_{\\theta}$ given $z_{\\mathrm{sem}}$ . Then, $(z_{\\mathrm{sem}},x_T)$ is decoded to reconstruct the corresponding original image $x_0$ with $p_{\\theta}(x_{0:T}|z_{\\mathrm{sem}}) = p(x_T)\\prod_{t = 1}^{T}p_{\\theta}(x_{t - 1}|x_t,z_{\\mathrm{sem}})$ . DiffAE is trained with simple DDPM loss, as done with DDIM. The differences between DiffAE and DDIM are that an additional variable $z_{\\mathrm{sem}}$ is involved as a conditioning variable during the reverse process (and thus the training process) and that the noise estimator $\\epsilon_{\\theta}$ and semantic encoder Enc are jointly trained. As a result, through the training phase, $z_{\\mathrm{sem}}$ is learned to capture the high-level semantic information of the image, and the low-level stochastic variations remain in $x_T$ .", + "bbox": [ + 75, + 424, + 472, + 818 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Diffusion Video Autoencoders", + "text_level": 1, + "bbox": [ + 76, + 830, + 352, + 845 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section, we introduce a video autoencoder, called Diffusion Video Autoencoder, specially designed for face video editing to have 1) superb reconstruction performance", + "bbox": [ + 76, + 854, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "and 2) an editable representation space for the identity feature of the video disentangled with the per-frame features changing over time. The details of the model components and the training procedure are explained in Sec. 4.1 and then two different editing methods based on our model are presented in Sec. 4.2. We provide the overview in Fig. 2.", + "bbox": [ + 496, + 386, + 890, + 477 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Disentangled Video Encoding", + "text_level": 1, + "bbox": [ + 498, + 484, + 764, + 502 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To encode the video with $N$ frames $\\{x_0^{(n)}\\}_{n = 1}^N$ , we consider the time-invariant feature of human face videos as human identity information, and the time-dependent feature for each frame as motion and background information. Among these three, identity or motion information relevant to a face is appropriate to be projected to a low-dimensional space to extract high-level representation. Comparatively, the background shows high variance with arbitrary details and changes more with the head movement by cropping and aligning the face region. Therefore, it could be very difficult to encode the background information into a high-level semantic space. Thus, identity and motion features are encoded in high-level semantic space $z_{\\mathrm{face}}^{(n)}$ , combining identity feature $z_{\\mathrm{id}}$ of the video and motion feature $z_{\\mathrm{land}}^{(n)}$ of each frame, and the background feature is encoded in noise map $x_{T}^{(n)}$ (see Fig. 2a). We denote $z_{\\mathrm{id}}$ without superscript $(n)$ for frame index since it is the time-invariant and shared across all frames of the video.", + "bbox": [ + 496, + 508, + 892, + 787 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To achieve this decomposition, our model consists of two separated semantic encoders - an identity encoder $E_{\\mathrm{id}}$ and a landmark encoder $E_{\\mathrm{land}}$ - and a conditional noise estimator $\\epsilon_{\\theta}$ for diffusion modeling. The encoded features $(z_{\\mathrm{id}}, z_{\\mathrm{land}}^{(n)})$ by the two encoders are concatenated and passed through an MLP to finally get a face-related feature $z_{\\mathrm{face}}^{(n)}$ . Next, to encode noise map $x_{T}^{(n)}$ , we run the deterministic forward", + "bbox": [ + 496, + 789, + 893, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "6094", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "process of DDIM using noise estimator $\\epsilon_{\\theta}$ with conditioned on $z_{\\mathrm{face}}^{(n)}$ . Since noise map $x_{T}^{(n)}$ is a spatial variable with the same size as the image, it is expected that information in the background can be encoded more easily without loss of spatial information. Then, the encoded features $(x_{T}^{(n)}, z_{\\mathrm{face}}^{(n)})$ can be reconstructed to the original frame by running generative reverse process of conditional DDIM in a deterministic manner:", + "bbox": [ + 75, + 90, + 472, + 214 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\theta} (x _ {0: T} | z _ {\\mathrm {f a c e}}) = p (x _ {T}) \\prod_ {t = 1} ^ {T} p _ {\\theta} (x _ {t - 1} | x _ {t}, z _ {\\mathrm {f a c e}}).\n$$\n", + "text_format": "latex", + "bbox": [ + 109, + 215, + 434, + 258 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To obtain the identity feature disentangled with the motion, we choose to leverage a pretrained model for identity detection, named ArcFace [5]. ArcFace is trained to classify human identity in face images regardless of poses or expressions, so we expect it to provide the disentangled property we need. Nevertheless, when an identity feature is extracted for each frame through the pretrained identity encoder, the feature may be slightly different for each frame because some frames may have partial identity features for some reasons (e.g. excessive side view poses). To alleviate this issue, we average the identity features $z_{\\mathrm{id}}^{(n)} = E_{\\mathrm{id}}(x_0^{(n)})$ of all frames in the inference phase. Similarly, we obtain per-frame motion information via a pretrained landmark detection model [4] which outputs the position of face landmarks. Several studies [21,36] have shown that it is possible to have a sufficiently disentangled nature by extracting features through a pretrained encoder without learning. Therefore, diffusion video autoencoders extract an identity and also a landmark feature of the image through the pretrained encoders and map them together to the high-level semantic space for face features through an additional learnable MLP.", + "bbox": [ + 75, + 267, + 468, + 585 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Next, we explain how the learnable part of our model is trained. Fig. 2b summarizes our training process. For simplicity, from now on, we drop the superscript of frame index. Our objective consists of two parts. The first one is the simple version of DDPM loss [9] as", + "bbox": [ + 75, + 587, + 470, + 662 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {s i m p l e}} = \\mathbb {E} _ {x _ {0} \\sim q (x _ {0}), \\epsilon_ {t} \\sim \\mathcal {N} (0, I), t} \\left\\| \\epsilon_ {\\theta} (x _ {t}, t, z _ {\\mathrm {f a c e}}) - \\epsilon_ {t} \\right\\| _ {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 83, + 674, + 460, + 694 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $z_{\\mathrm{face}}$ is an encoded high-level feature of input image $x_0$ . It encourages the useful information of the image to be well contained in the semantic latent $z_{\\mathrm{face}}$ and exploited by $\\epsilon_{\\theta}$ for denoising. Secondly, we devise a regularization loss to hinder face information (identity and motion) from leaking to $x_{T}$ but contained in $z_{\\mathrm{face}}$ as much as possible for clear decomposition between background and face information. If some face information is lost in $z_{\\mathrm{face}}$ , the lost information would remain in the noise latent $x_{T}$ unintentionally. To avoid it, we sample two different Gaussian noises $\\epsilon_1$ and $\\epsilon_2$ to obtain different noisy samples $x_{t,1}$ and $x_{t,2}$ , respectively. Then, we minimize the difference between the estimated original images $f_{\\theta,1}$ and $f_{\\theta,2}$ except for the back", + "bbox": [ + 75, + 704, + 472, + 902 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/182bf31164a7bfe9b585dc0235394436b4fbb5234f9f82f3fb771f272ab0b3d9.jpg", + "image_caption": [ + "1. Conditional sampling with $z_{id}$ for prediction of each noise level", + "Figure 3. Process of computing noisy CLIP loss." + ], + "image_footnote": [ + "2. Conditional sampling with trainable $z_{\\mathrm{id}}^{\\mathrm{opt}}$ and optimize with $\\mathcal{L}_{\\mathrm{CLIP}}$" + ], + "bbox": [ + 519, + 114, + 869, + 323 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "ground part as:", + "bbox": [ + 500, + 376, + 604, + 390 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {r e g}} = \\mathbb {E} _ {x _ {0} \\sim q (x _ {0}), \\epsilon_ {1}, \\epsilon_ {2} \\sim \\mathcal {N} (0, I), t} \\left\\| f _ {\\theta , 1} \\odot m - f _ {\\theta , 2} \\odot m \\right\\| _ {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 503, + 398, + 885, + 419 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $m$ is a segmentation mask of a face region in the original image $x_0$ and $f_{\\theta ,i} = f_{\\theta}(x_{t,i},t,z_{\\mathrm{face}})$ . As a result, the effect of noise in $x_{t}$ on the face region will be reduced and $z_{\\mathrm{face}}$ will be responsible for face features for the generation (See Fig. 7). In Sec. 5.5, we demonstrate the desired effect of $\\mathcal{L}_{\\mathrm{reg}}$ . The final loss of diffusion video autoencoders is as follows: $\\mathcal{L}_{\\mathrm{dva}} = \\mathcal{L}_{\\mathrm{simple}} + \\mathcal{L}_{\\mathrm{reg}}$ .", + "bbox": [ + 498, + 425, + 892, + 532 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Video Editing Framework", + "text_level": 1, + "bbox": [ + 500, + 540, + 736, + 556 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We now describe our video editing framework with our diffusion video autoencoders. First, all video frames $\\{I_n\\}_{n=1}^N$ are aligned and cropped for interesting face regions as in [35]. The cropped frames $\\{x_0^{(n)}\\}_{n=1}^N$ are then encoded to latent features using our diffusion video autoencoder. To extract the representative identity feature of the video, we average identity features of each frame as", + "bbox": [ + 498, + 563, + 890, + 672 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nz _ {\\mathrm {i d , r e p}} = \\frac {1}{N} \\sum_ {n = 1} ^ {N} (z _ {\\mathrm {i d}} ^ {(n)}),\n$$\n", + "text_format": "latex", + "bbox": [ + 612, + 680, + 779, + 720 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $z_{\\mathrm{id}}^{(n)} = E_{\\mathrm{id}}(x_0^{(n)})$ . Similarly, the per-frame landmark feature is computed as $z_{\\mathrm{lnd}}^{(n)} = E_{\\mathrm{lnd}}(x_0^{(n)})$ to finally obtain per-frame face features $z_{\\mathrm{face}}^{(n)} = MLP(z_{\\mathrm{id,rep}},z_{\\mathrm{lnd}}^{(n)})$ After that, we compute $x_{T}^{(n)}$ with DDIM forward process conditioning $z_{\\mathrm{face}}^{(n)}$ . Thereafter, manipulation is conducted by editing $z_{\\mathrm{id,rep}}$ to $z_{\\mathrm{id,rep}}^{\\mathrm{edit}}$ using a pretrained linear attribute-classifier of the identity space or text-based optimization which we will discuss in more detail later. After modifying the representative identity feature $z_{\\mathrm{id,rep}}^{\\mathrm{edit}}$ the edited frame $\\hat{x}_0^{(n),\\mathrm{edit}}$ is generated by the conditional", + "bbox": [ + 496, + 731, + 893, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "6095", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/a80446c6e986344b6f9b5b186bdd007b1e66e7e75e75ecfcc6b74f5333cb0611.jpg", + "image_caption": [ + "Figure 4. Comparison of temporal consistency to the previous video editing methods for 'beard'." + ], + "image_footnote": [], + "bbox": [ + 112, + 88, + 854, + 489 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "reverse process with $(z_{\\mathrm{face}}^{(n),\\mathrm{edit}},x_T^{(n)})$ where $z_{\\mathrm{face}}^{(n),\\mathrm{edit}} = MLP(z_{\\mathrm{id,rep}}^{\\mathrm{edit}},z_{\\mathrm{nd}}^{(n)})$ . Afterward, as with all previous work, the face part of the edited frame is pasted to the corresponding area of the original frame to create a clean final result. For this process, we segment face regions using a pretrained segmentation network [42]. Below, we explore two editing methods for our video editing framework.", + "bbox": [ + 75, + 525, + 472, + 638 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Classifier-based editing First, as in DiffAE [23], we train a linear classifier $C_{\\text{attr}}(z_{\\text{id}}) = \\text{sigmoid}(w_{\\text{attr}}^{\\top} z_{\\text{id}})$ for each attribute attr on CelebA-HQ's [10] with its attribute annotation in the identity feature space. To change attr, we move the identity feature $z_{\\text{id}}$ to $\\ell_2 \\text{Norm}(z_{\\text{id}} + sw_{\\text{attr}})$ with a scale hyperparameter $s$ .", + "bbox": [ + 75, + 647, + 468, + 739 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "CLIP-based editing Since the pretrained classifier allows editing only for several predefined attributes, we additionally devise the CLIP-guidance identity feature optimization method. Directional CLIP loss [7] requires two images corresponding to one for neutral text and one for target text, respectively. It implies that we need the synthesized images with our diffusion model, which is costly with full generative process. Therefore, to reduce the computational cost, we use the drastically reduced number of steps $S$ ( $\\ll T$ ) for image sampling. In other words, we consider the time", + "bbox": [ + 75, + 750, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "steps $t_1, t_2, \\ldots, t_S$ where $0 = t_0 < t_1 < \\ldots < t_S \\leq T$ and evenly split $T$ . Thereafter, we compute $x_{t_s}$ from the given image $x_0$ that we want to edit (normally chosen as the first frame $x_0^{(1)}$ of the video) through $S$ -step of forward process with $z_{\\mathrm{id}} = E_{\\mathrm{id}}(x_0)$ . Through the sequential reverse steps from $x_{t_S}$ , we recover $\\hat{x}_{t_s}$ for each time $t_s$ where $s = (S - 1), \\ldots, 0$ with the original $z_{\\mathrm{id}}$ . Meanwhile, $x_{t_s}^{\\mathrm{edit}}$ are obtained by the single reverse step from $\\hat{x}_{t_{s+1}}$ but with variable $z_{\\mathrm{id}}^{\\mathrm{opt}}$ being optimized initialized to $z_{\\mathrm{id}}$ (See Fig. 3). Finally, we minimize the directional CLIP loss [7] between intermediate images $\\hat{x}_{t_s}$ and $x_{t_s}^{\\mathrm{edit}}$ , which are still noisy, for all $s$ with a neutral (e.g. \"face\") and a target text (e.g. \"face with eyeglasses\"). We choose intermediate images $x_{t_s}^{\\mathrm{edit}}$ , $\\hat{x}_{t_s}$ from $\\hat{x}_{t_{s+1}}$ instead of estimated $x_0$ to compute CLIP loss because to estimate $x_0$ directly from $x_{t_s}$ is incomplete and erroneous for large $t_s$ . Therefore, we expect that conservatively choosing intermediate images will help to find the edit direction more reliably. We refer the reader to Appendix B for the ablation study of our noisy CLIP loss. In addition to the CLIP loss, to preserve the remaining attributes, we also use ID loss (cosine distance between $z_{\\mathrm{id}}$ and $z_{\\mathrm{id}}^{\\mathrm{opt}}$ ) and $\\ell_1$ loss between face parts of $\\hat{x}_{t_s}$ and $x_{t_s}^{\\mathrm{edit}}$ for all $s$ . After all, the learned editing step $\\Delta z_{\\mathrm{id}} = z_{\\mathrm{id}}^{\\mathrm{opt}} - z_{\\mathrm{id}}$ is applied to $z_{\\mathrm{id},\\mathrm{rep}}$ .", + "bbox": [ + 496, + 527, + 893, + 895 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "6096", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/b770392dfbadc03845032b9a65a16f1adaa843cde7624a59954b3f237ded2245.jpg", + "table_caption": [ + "Table 1. Quantitative reconstruction results on the randomly chosen 20 videos in VoxCeleb1 test set. The reported values are the mean of the averaged per-frame measurements for each video." + ], + "table_footnote": [], + "table_body": "
MethodSSIM ↑MS-SSIM ↑LPIPS ↓MSE ↓
e4e [34]0.5090.7610.1570.037
PTI [27]0.7650.9390.0630.007
Ours (T=20)0.5400.9050.2280.016
Ours (T=100)0.9220.9890.0450.002
", + "bbox": [ + 81, + 138, + 465, + 213 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/ad71b8be527c1e37c09723c2a04d003d33e80cc29e11af902a5d661ff37f0da2.jpg", + "table_caption": [ + "Table 2. Quantitative results to evaluate temporal consistency. Ours show the best global coherency and comparable local consistency to the baselines." + ], + "table_footnote": [], + "table_body": "
MethodTL-IDTG-ID
Yao et al. [41]0.9890.920
Tzaban et al. [35]0.9970.961
Xu et al. [40]1.0020.983
Ours0.9950.996
", + "bbox": [ + 150, + 277, + 395, + 357 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 76, + 378, + 207, + 396 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we present the experimental results to confirm reconstruction performance (Sec. 5.1), temporally consistent editing ability (Sec. 5.2), robustness to the unusual samples (Sec. 5.3), and disentanglement of the encoded features (Sec. 5.4) with further ablation study (Sec. 5.5). For this purpose, we train our diffusion video autoencoder on 77294 videos of the VoxCeleb1 dataset [18]. As preprocessing, frames of the video are aligned and cropped as in [35] like the FFHQ dataset. Next, they are resized to the size of $256^2$ . For the noise estimator $\\epsilon_{\\theta}$ , the UNet improved by [20] is used, and we train diffusion video autoencoder for 1 million steps with a batch size of 16. Please see more details in Appendix A.", + "bbox": [ + 75, + 407, + 467, + 602 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.1. Reconstruction", + "text_level": 1, + "bbox": [ + 76, + 618, + 228, + 633 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For video editing, the ability to reconstruct the original video from the encoded one must be preceded. Otherwise, we will lose the original one before we even edit the video. To compare this ability with baselines quantitatively, we measure frequently used metrics for reconstruction - SSIM [37], Multi-scaled (MS) SSIM [38], LPIPS [43], and MSE - on randomly selected 20 videos in the test set of VoxCeleb1. As baselines, we compared our model with the GAN-based inversion method e4e [34] and PTI [27] used by Yao et al. [41] and Tzaban et al. [35], respectively. Since StyleGAN-based methods handle the higher resolution images with the size of $1024^2$ , we resize the reconstructed results to $256^2$ for comparison. For our method, we vary the number of diffusion steps $T$ to observe computational cost and image quality trade-offs. In Tab. 1, our diffusion video autoencoder with $T = 100$ shows the best reconstruction ability and still outperforms e4e with only $T = 20$ .", + "bbox": [ + 75, + 643, + 467, + 900 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0b00644279b3a0a8e29abd98582847f2b4df2382d2fce9a3cf184d9422f48412.jpg", + "image_caption": [ + "Figure 5. Editing wild face videos that GAN-based prior works struggled with. Classifier-based editing is used to make the person \"young\" (up) or change a \"gender\" (below)." + ], + "image_footnote": [], + "bbox": [ + 501, + 89, + 890, + 255 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Temporal Consistency", + "text_level": 1, + "bbox": [ + 500, + 311, + 705, + 329 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In Fig. 4, a visual comparison is conducted to evaluate the video editing performance of our diffusion video autoencoder qualitatively. We edit the given video to generate a beard through text-based guidance except for Yao et al. [41], which only allows to edit predefined attributes, by moving to the opposite direction of \"no_peat\". As a result, we demonstrate that only our diffusion video autoencoder successfully produces the consistent result. Specifically, Yao et al. [41] fail to preserve the original identity due to the limitations of GAN inversion. In the result of Tzaban et al. [35], the shape and the amount of beard constantly changes according to the lip motion. Although Xu et al. [40] show better but not perfect consistency, the motions unintentionally change as a side effect. The inconsistency can be observed more clearly between the second and the fifth column except for ours showing a reliable result.", + "bbox": [ + 496, + 335, + 890, + 578 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Furthermore, we quantitatively evaluate the temporal consistency of Fig. 4 in Tab. 2. Although there is no perfect metric for temporal consistency of videos, TL-ID and TG-ID [35] imply the local and global consistency of identity between adjacent frames and across all frames, respectively, compared to the original. These metrics can be interpreted as being consistent as the original is when their values are close to 1. We emphasize that we greatly improve global consistency. TL-ID of Xu et al. [40] is larger than 1 because the motion of the editing results shrinks so that the adjacent frames become closer to each other than the original. Additional quantitative comparisons of temporal consistency, editing quality, and time cost are summarized in Appendix C.", + "bbox": [ + 496, + 579, + 890, + 790 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Editing Wild Face Videos", + "text_level": 1, + "bbox": [ + 500, + 800, + 730, + 816 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Owing to the reconstructability of diffusion models, editing wild videos that are difficult to inversion by GAN-based methods becomes possible. As shown in Fig. 5, unlike others, our method robustly reconstructs and edits the given images effectively.", + "bbox": [ + 496, + 824, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "6097", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b04f9ef57cadcf76dd754609c1035a8b7467c0ec6df1b0096a3eebb2573a7619.jpg", + "image_caption": [ + "Figure 6. Demonstration of the disentangled video encoding." + ], + "image_footnote": [], + "bbox": [ + 80, + 88, + 467, + 357 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.4. Decomposed Features Analysis", + "text_level": 1, + "bbox": [ + 76, + 398, + 349, + 416 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To demonstrate whether the diffusion video autoencoder decomposes the features adequately, we examine the synthesized images by changing each element of the decomposed features. To this end, we encode the frames of two different videos and then generate samples with a random noise or exchange the respective elements with each other in Fig. 6. When we decode the semantic latent $z_{\\text{face}}$ with a Gaussian noise instead of the original noise latent $x_{T}$ , it has a blurry background that is different from the original one, while identity and head pose are preserved considerably. This result implies that $x_{T}$ contains only the background information, as we intended. Moreover, the generated images with switched identity, motion, and background feature confirm that the features are properly decomposed and the diffusion video autoencoder can produce a realistic image even with the new combination of the features. However, with extreme changes in the head position, the background occluded by the face is not properly generated because the taken $x_{T}$ has no information about background in that area (See the last column of the lower example in Fig. 6).", + "bbox": [ + 75, + 426, + 472, + 731 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.5. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 751, + 230, + 768 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We further conduct an ablation study on our proposed regularization loss $\\mathcal{L}_{\\mathrm{reg}}$ . First, we train the model with the same setting but ablating $\\mathcal{L}_{\\mathrm{reg}}$ . As shown in Fig. 7, neither model has a problem with reconstruction. However, without the regularization loss, the identity changes significantly according to the random noise. Thus we can conclude that the regularization loss helps the model to decompose features effectively.", + "bbox": [ + 75, + 780, + 468, + 902 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9b255761ec131f226c7a91e11e65ca0a5f42bbf35a5d624795df8c9e4f48857f.jpg", + "image_caption": [ + "Figure 7. Ablation of using regularization loss for training. Regularization loss helps the model to contain identity and motion information in $z_{\\text{face}}$ as much as possible." + ], + "image_footnote": [], + "bbox": [ + 506, + 88, + 890, + 328 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusions", + "text_level": 1, + "bbox": [ + 500, + 400, + 627, + 416 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To tackle the temporal consistency problem in editing human face video, we have proposed a novel framework with the newly designed video diffusion autoencoder which encodes the identity, motion, and background information in a disentangled manner and decodes after editing a single identity feature. Through the disentanglement, the most valuable strength of our framework is that we can search the desired editing direction for only one frame and then edit the remaining frames with temporal consistency by moving the representative video identity feature. Additionally, the wild face video can be reliably edited by the advantage of the diffusion model that is superior in reconstruction to GAN. Finally, we have explored to optimize the semantic identity feature with CLIP loss for text-based video editing. Please refer to the Appendix D for the limitations and further discussion.", + "bbox": [ + 496, + 431, + 890, + 674 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement This work was supported by Institute of Information & communications Technology Planning & Evaluation (IITP) grant (No.2019-0-00075, Artificial Intelligence Graduate School Program(KAIST), No.2021-0-02068, Artificial Intelligence Innovation Hub, No.2022-0-00713, Meta-learning applicable to real-world problems, No.2022-0-00984, Development of Artificial Intelligence Technology for Personalized Plug-and-Play Explanation and Verification of Explanation) and the National Research Foundation of Korea (NRF) grants (No.2018R1A5A1059921) funded by the Korea government (MSIT). This work was also supported by KAIST-NAVER Hypercreative AI Center.", + "bbox": [ + 496, + 703, + 892, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "6098", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Yuval Alaluf, Or Patashnik, and Daniel Cohen-Or. Restyle: A residual-based stylegan encoder via iterative refinement. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 6711–6720, 2021. 2", + "[2] Yuval Alaluf, Or Patashnik, Zongze Wu, Asif Zamir, Eli Shechtman, Dani Lischinski, and Daniel Cohen-Or. Third time's the charm? image and video editing with stylegan3. arXiv preprint arXiv:2201.13433, 2022. 1, 2, 3", + "[3] Omri Avrahami, Dani Lischinski, and Ohad Fried. 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In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 586-595, 2018. 7" + ], + "bbox": [ + 501, + 90, + 893, + 204 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "6100", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Diffusion Video Autoencoders_ Toward Temporally Consistent Face Video Editing via Disentangled Video Encoding/9c72d0e6-e653-459a-87e1-dce2e1570589_model.json b/2023/Diffusion Video Autoencoders_ Toward Temporally Consistent Face Video Editing via Disentangled Video Encoding/9c72d0e6-e653-459a-87e1-dce2e1570589_model.json new file mode 100644 index 0000000000000000000000000000000000000000..8849cbdcac6cf7c93243d0465a74bc9c8c4c3c3f --- /dev/null +++ b/2023/Diffusion Video Autoencoders_ Toward Temporally Consistent Face Video Editing via Disentangled Video Encoding/9c72d0e6-e653-459a-87e1-dce2e1570589_model.json @@ -0,0 +1,1859 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.131, + 0.8, + 0.177 + ], + "angle": 0, + "content": "Diffusion Video Autoencoders: Toward Temporally Consistent Face Video Editing via Disentangled Video Encoding" + }, + { + "type": "text", + "bbox": [ + 0.108, + 0.202, + 0.895, + 0.223 + ], + "angle": 0, + "content": "Gyeongman Kim\\(^{1}\\) Hajin Shim\\(^{1}\\) Hyunsu Kim\\(^{2}\\) Yunjay Choi\\(^{2}\\) Junho Kim\\(^{2}\\) Eunho Yang\\(^{1,3}\\)" + }, + { + "type": "text", + "bbox": [ + 0.197, + 0.226, + 0.807, + 0.244 + ], + "angle": 0, + "content": "\\(^{1}\\)Korea Advanced Institute of Science and Technology (KAIST), South Korea" + }, + { + "type": "text", + "bbox": [ + 0.326, + 0.245, + 0.678, + 0.262 + ], + "angle": 0, + "content": "\\(^{2}\\)NAVER AI Lab \\(^{3}\\)AITRICS, South Korea" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.266, + 0.911, + 0.281 + ], + "angle": 0, + "content": "{gmkim, shimazing, eunhoy}@kaist.ac.kr {hyunsull25.kim, yunjey.choi, jhkim.ai}@navercorp.com" + }, + { + "type": "image", + "bbox": [ + 0.108, + 0.293, + 0.495, + 0.508 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.497, + 0.293, + 0.865, + 0.509 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.1, + 0.511, + 0.868, + 0.54 + ], + "angle": 0, + "content": "Figure 1. Face video editing. Our editing method shows improvement compared to the baseline [35] in terms of temporal consistency (left, \"eyeglasses\") and robustness to the unusual case such as the hand-occluded face (right, \"beard\")." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.552, + 0.314, + 0.568 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.575, + 0.47, + 0.817 + ], + "angle": 0, + "content": "Inspired by the impressive performance of recent face image editing methods, several studies have been naturally proposed to extend these methods to the face video editing task. One of the main challenges here is temporal consistency among edited frames, which is still unresolved. To this end, we propose a novel face video editing framework based on diffusion autoencoders that can successfully extract the decomposed features - for the first time as a face video editing model - of identity and motion from a given video. This modeling allows us to edit the video by simply manipulating the temporally invariant feature to the desired direction for the consistency. Another unique strength of our model is that, since our model is based on diffusion models, it can satisfy both reconstruction and edit capabilities at the same time, and is robust to corner cases in wild face videos (e.g. occluded faces) unlike the existing GAN-based methods.1" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.825, + 0.209, + 0.839 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.85, + 0.469, + 0.88 + ], + "angle": 0, + "content": "As one of the standard tasks in computer vision to change various face attributes such as hair color, gender, or glasses" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.554, + 0.892, + 0.719 + ], + "angle": 0, + "content": "of a given face image, face editing has been continuously gaining attention due to its various applications and entertainment. In particular, with the improvement of analysis and manipulation techniques for recent Generative Adversarial Network (GAN) models [8, 11, 22, 29, 30], we simply can do this task by manipulating a given image's latent feature. In addition, very recently, many methods for face image editing also have been proposed based on Diffusion Probabilistic Model (DPM)-based methods that show high-quality and flexible manipulation performance [3, 12, 17, 19, 23, 25]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.84 + ], + "angle": 0, + "content": "Naturally, further studies [2, 35, 41] have been proposed to extend image editing methods to incorporate the temporal axis for videos. Now, given real videos with a human face, these studies try to manipulate some target facial attributes with the other remaining features and motion intact. They all basically edit each frame of a video independently via off-the-shelf StyleGAN-based image editing techniques [22, 29, 41]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Despite the advantages of StyleGAN in this task such as high-resolution image generation capability and highly disentangled semantic representation space, one harmful drawback of GAN-based editing methods is that the encoded real" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.331, + 0.9 + ], + "angle": 0, + "content": "1Project page: https://diff-video-ae.github.io" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "6091" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.243 + ], + "angle": 0, + "content": "images cannot perfectly be recovered by the pretrained generator [1, 26, 34]. Especially, if a face in a given image is unusually decorated or occluded by some objects, the fixed generator cannot synthesize it. For perfect reconstruction, several methods [6, 27] are suggested to further tune the generator for GAN-inversion [26, 34] on one or a few target images, which is computationally expensive. Moreover, after the fine-tuning, the original editability of GANs cannot be guaranteed. This risk could be worse in video domain since we have to finetune the model on the multiple frames." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.246, + 0.473, + 0.442 + ], + "angle": 0, + "content": "Aside from the reconstruction issue of existing GAN-based methods, it is critical in video editing tasks to consider the temporal consistency among edited frames to produce realistic results. To address this, some prior works rely on the smoothness of the latent trajectory of the original frames [35] or smoothen the latent features directly [2] by simply taking the same editing step for all frames. However, smoothness does not ensure temporal consistency. Rather, the same editing step can make different results for different frames because it can be unintentionally entangled with irrelevant motion features. For example, in the middle row of Fig. 1, eyeglasses vary across time and sometimes diminish when the man closes his eyes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.445, + 0.473, + 0.747 + ], + "angle": 0, + "content": "In this paper, we propose a novel video editing framework for human face video, termed Diffusion Video Autoencoder, that resolves the limitations of the prior works. First, instead of GAN-based editing methods suffering from imperfect reconstruction quality, we newly introduce diffusion based model for face video editing tasks. As the recently proposed diffusion autoencoder (DiffAE) [23] does, thanks to the expressive latent spaces of the same size as input space, our model learns a semantically meaningful latent space that can perfectly recover the original image back and are directly editable. Not only that, for the first time as a video editing model, encode the decomposed features of the video: 1) identity feature shared by all frames, 2) feature of motion or facial expression in each frame, and 3) background feature that could not have high-level representation due to large variances. Then, for consistent editing, we simply manipulate a single invariant feature for the desired attribute (single editing operation per video), which is also computationally beneficial compared to the prior works that require editing the latent features of all frames." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.473, + 0.903 + ], + "angle": 0, + "content": "We experimentally demonstrate that our model appropriately decomposes videos into time-invariant and per-frame variant features and can provide temporally consistent manipulation. Specifically, we explore two ways of manipulation. The first one is to edit features in the predefined set of attributes by moving semantic features to the target direction found by learning linear classifier in semantic representation space on annotated CelebA-HQ dataset [10]. Additionally, we explore the text-based editing method that optimizes a time-invariant latent feature with CLIP loss [7]. It" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.151 + ], + "angle": 0, + "content": "is worth noting that since we cannot fully generate edited images for CLIP loss due to the computational cost, we propose the novel strategy that rather uses latent state of intermediate time step for the efficiency." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.153, + 0.813, + 0.166 + ], + "angle": 0, + "content": "To summarize, our contribution is four-fold:" + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.174, + 0.892, + 0.235 + ], + "angle": 0, + "content": "- We devise diffusion video autoencoders based on diffusion autoencoders [23] that decompose the video into a single time-invariant and per-frame time-variant features for temporally consistent editing." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.242, + 0.892, + 0.317 + ], + "angle": 0, + "content": "- Based on the decomposed representation of diffusion video autoencoder, face video editing can be conducted by editing only the single time-invariant identity feature and decoding it together with the remaining original features." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.324, + 0.892, + 0.384 + ], + "angle": 0, + "content": "- Owing to the nearly-perfect reconstruction ability of diffusion models, our framework can be utilized to edit exceptional cases such that a face is partially occluded by some objects as well as usual cases." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.392, + 0.892, + 0.466 + ], + "angle": 0, + "content": "- In addition to the existing predefined attributes editing method, we propose a text-based identity editing method based on the local directional CLIP loss [7,24] for the intermediately generated product of diffusion video autoencoders." + }, + { + "type": "list", + "bbox": [ + 0.519, + 0.174, + 0.892, + 0.466 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.482, + 0.642, + 0.498 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.508, + 0.892, + 0.613 + ], + "angle": 0, + "content": "Video editing When editing a given real video, it is essential to preserve temporal consistency. First, Lai et al. [14] consider editing global features of videos such as artistic style transfer, colorization, image enhancement, etc. To encourage temporal consistency, they train sequential image translator with temporal loss defined as the warping error between the output frames." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Different from this work, our target task is to edit facial attributes of human face video. In other words, we aim to change face-related attributes such as eyeglasses, beards, etc. For this task, Yao et al. [41] are the first that propose the editing pipeline: 1) align and crop the target face area, 2) encode these frames to latent features, manipulate and decode them, and 3) unalign and paste the edited frames to the original video. However, every step of this pipeline is conducted independently for each frame. For the manipulation step, they try to find disentangled editing directions for a desired attribute and take the same step for every frame, while expecting the disentanglement brings consistency automatically. However, the results show inconsistency and we conjecture that both latent space and learned direction are still entangled with many other attributes. Next, Tza-ban et al. [35] additionally fine-tune the pretrained StyleGAN [27] to enhance reconstructability. Meanwhile, they assume that temporal consistency would be preserved when applying the same editing step to the latent features of the" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6092" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.152 + ], + "angle": 0, + "content": "original frames. However, their assumption is not always true for all attributes, especially for beards and eyeglasses as shown in Fig. 1. Alauf et al. [2] also try to avoid temporal inconsistency by smoothing latent features." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.152, + 0.471, + 0.302 + ], + "angle": 0, + "content": "While the methods in the previous paragraph handle inconsistency implicitly, several works [39, 40] try to solve it more directly. After per-frame editing, Xu et al. [40] further optimize latent codes and the pretrained StyleGAN to enhance consistency between the frame pairs defined by involving bi-directional optical flow. On the other hand, Xia et al. [39] propose to learn the dynamics of inverted GAN latent codes of video frames. The learned dynamics are used to generate the subsequent latent features after editing only the first frame." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.304, + 0.47, + 0.453 + ], + "angle": 0, + "content": "Additionally, although Skorokhodov et al. [31] mainly target to generate video, they also demonstrate manipulation results of the generated video. They model the video with a time-invariant content code and per-frame motion codes. Based on this modeling, the generated video can be manipulated with a target text by optimizing its content vector with CLIP loss. However, they cannot edit the real videos due to the absence of an encoding method. In contrast, our proposed method is capable of encoding and manipulating realistic face videos." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.467, + 0.471, + 0.799 + ], + "angle": 0, + "content": "Diffusion models Denoising diffusion probabilistic models (DDPMs) [9] associate image generation with the sequential denoising process of isotropic Gaussian noise. The model is trained to predict the noise from the input image. Unlike other generative models such as GANs and most traditional-style VAEs that encode input data in a low-dimensional space, diffusion models have a latent space that is the same size as the input. Although DDPMs require a lot of feed-forward steps to generate samples, their image fidelity and diversity are superior to other types of generative models. Compared to DDPMs that assume a Markovian noise-injecting forward diffusion process, Denoising diffusion implicit models (DDIMs) [33] assume a non-Markovian forward process that has the same marginal distribution as DDPMs, and use its corresponding reverse denoising process for sampling, which enables acceleration of the rather onerous sampling process of DDPMs. DDIMs also utilize a deterministic forward-backward process and therefore show nearly-perfect reconstruction ability, which is not the case for DDPMs. In this paper, we adopt conditional DDIMs to encode, manipulate and decode real videos." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Image editing with diffusion models There are various attempts to manipulate images with diffusion models [3, 12, 17, 19, 23, 25] such as text-guided inpainting [3, 19, 25], stroke-based editing [17], and style transfer [12]. Among those, we are especially interested in facial attribute editing tasks. Kim et al. [12] propose text-based image ma" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.304 + ], + "angle": 0, + "content": "nipulation by optimizing an unconditional diffusion model to minimize local directional CLIP loss [7]. This method is superior to GAN-based methods as it can successfully edit even occluded or overly decorated faces by the excellent reconstruction ability of diffusion models. However, due to the absence of semantically meaningful latent space, there exist some semantic features that are unable to be changed. Another parallel work proposes diffusion autoencoder (DiffAE) [23], which takes a learnable encoder to obtain semantic representations of which the underlying diffusion model is conditioned. The model can perform face attribute manipulation by moving the semantic vector to a target direction. Based on DiffAEs, we design our diffusion video autoencoders to perform temporally-consistent video editing." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.321, + 0.638, + 0.337 + ], + "angle": 0, + "content": "3. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.347, + 0.892, + 0.656 + ], + "angle": 0, + "content": "Diffusion probabilistic models (DPMs) DPMs [9, 32] are generative models that attempt to approximate the data distribution \\(q(x_0)\\) via \\(p_{\\theta}(x_0)\\) from the reverse prediction of Markovian diffusion process \\(q(x_{1:T}|x_0) = \\prod_{t=1}^{T} q(x_t|x_{t-1})\\). Here, the forward process of DPM is a Gaussian noise perturbation \\(q(x_t|x_{t-1}) = \\mathcal{N}(\\sqrt{1 - \\beta_t} x_{t-1}, \\beta_t I)\\) where \\(\\beta_t\\) is fixed or learned variance schedule with increasing \\(\\beta_1 < \\beta_2 < \\dots < \\beta_T\\), adding gradually increasing noise to data \\(x_0\\), and its reverse process is denoising of \\(x_t\\) step by step in reverse order. From this definition, a noisy image \\(x_t\\) at step \\(t\\) can be expressed as \\(x_t = \\sqrt{\\alpha_t} x_0 + \\sqrt{1 - \\alpha_t} \\epsilon\\), \\(\\epsilon \\sim \\mathcal{N}(0, I)\\) where \\(\\alpha_t = \\prod_{s=1}^t (1 - \\beta_s)\\). While the true reverse process \\(q(x_{t-1}|x_t)\\) is intractable, diffusion models approximate \\(q(x_{t-1}|x_t, x_0)\\) with \\(p_{\\theta}(x_{t-1}|x_t) = \\mathcal{N}(\\mu_{\\theta}(x_t, t), \\sigma_t)\\) by minimizing the variational lower bound of negative log-likelihood. Finally, by reparameterizing \\(\\mu_{\\theta}\\), the objective is given as \\(\\mathbb{E}_{x_0 \\sim q(x_0), \\epsilon_t \\sim \\mathcal{N}(0, I), t} \\left\\| \\epsilon_{\\theta}(x_t, t) - \\epsilon_t \\right\\|_2^2\\) where the parameterized model \\(\\epsilon_{\\theta}(x_t, t)\\) estimates the true Gaussian noise term \\(\\frac{1}{\\sqrt{1 - \\alpha_t}} (x_t - \\sqrt{\\alpha_t} x_0)\\) in the forward process." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.657, + 0.892, + 0.81 + ], + "angle": 0, + "content": "Speeding up a time-consuming sampling process of diffusion models is one of the core research topics related to diffusion models [20, 33]. Among others, Song et al. [33] propose DDIM, which assumes a non-Markovian forward process \\( q(x_{t}|x_{t - 1},x_{0}) \\) that has the same marginal distribution \\( q(x_{t}|x_{0}) \\) with DDPMs. The corresponding generative process of DDIM is \\( x_{t - 1} = \\sqrt{\\alpha_{t - 1}} f_{\\theta}(x_t,t) + \\sqrt{1 - \\alpha_{t - 1} - \\sigma_t^2}\\epsilon_\\theta (x_t,t) + \\sigma_t^2 z \\) where \\( z\\sim \\mathcal{N}(0,I) \\), \\( \\sigma \\) is sampling stochasticity and \\( f_{\\theta}(x_t,t) \\), the estimated value of \\( x_0 \\) at time step \\( t \\), is as follow:" + }, + { + "type": "equation", + "bbox": [ + 0.576, + 0.824, + 0.816, + 0.859 + ], + "angle": 0, + "content": "\\[\nf _ {\\theta} (x _ {t}, t) = \\frac {x _ {t} - \\sqrt {1 - \\alpha_ {t}} \\epsilon_ {\\theta} (x _ {t} , t)}{\\sqrt {\\alpha_ {t}}}.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "When \\(\\sigma\\) is set to 0, this process becomes deterministic. With deterministic forward and reverse processes, we can obtain" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6093" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.089, + 0.41, + 0.189 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.191, + 0.409, + 0.333 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.125, + 0.335, + 0.361, + 0.348 + ], + "angle": 0, + "content": "(a) Video autoencoding and editing pipeline." + }, + { + "type": "image", + "bbox": [ + 0.429, + 0.088, + 0.889, + 0.33 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.599, + 0.334, + 0.719, + 0.347 + ], + "angle": 0, + "content": "(b) Training objective." + }, + { + "type": "image_caption", + "bbox": [ + 0.315, + 0.355, + 0.654, + 0.37 + ], + "angle": 0, + "content": "Figure 2. Overview of our Diffusion Video Autoencoder." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.387, + 0.47, + 0.418 + ], + "angle": 0, + "content": "the latent code of each original sample, which can reconstruct the original sample through the reverse process." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.425, + 0.473, + 0.819 + ], + "angle": 0, + "content": "Diffusion autoencoders Due to the determinacy of its sampling process, DDIM can reconstruct the original image \\( x_0 \\) from \\( x_T \\) obtained through \\( T \\) forward process steps. While \\( x_T \\) can be considered as a latent state with the same size as \\( x_0 \\), it does not contain high-level semantic information [23]. To supplement this, Prechakul et al. propose diffusion autoencoder (DiffAE) [23] based on DDIM. DiffAE utilizes two forms of latent variables: \\( z_{\\mathrm{sem}} \\) for the useful high-level semantic representation and \\( x_T \\) for the remaining low-level stochasticity information. DiffAE introduces a semantic encoder \\( \\mathsf{Enc}(x_0) \\) which extracts \\( z_{\\mathrm{sem}} \\) from an image, and makes a noise estimator \\( \\epsilon_{\\theta}(x,t,z_{\\mathrm{sem}}) \\) conditioned on \\( z_{\\mathrm{sem}} \\). Stochastic latent \\( x_T \\) is calculated through the deterministic DDIM forward process [33] that involves the noise estimator \\( \\epsilon_{\\theta} \\) given \\( z_{\\mathrm{sem}} \\). Then, \\( (z_{\\mathrm{sem}},x_T) \\) is decoded to reconstruct the corresponding original image \\( x_0 \\) with \\( p_{\\theta}(x_{0:T}|z_{\\mathrm{sem}}) = p(x_T)\\prod_{t = 1}^{T}p_{\\theta}(x_{t - 1}|x_t,z_{\\mathrm{sem}}) \\). DiffAE is trained with simple DDPM loss, as done with DDIM. The differences between DiffAE and DDIM are that an additional variable \\( z_{\\mathrm{sem}} \\) is involved as a conditioning variable during the reverse process (and thus the training process) and that the noise estimator \\( \\epsilon_{\\theta} \\) and semantic encoder Enc are jointly trained. As a result, through the training phase, \\( z_{\\mathrm{sem}} \\) is learned to capture the high-level semantic information of the image, and the low-level stochastic variations remain in \\( x_T \\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.831, + 0.353, + 0.847 + ], + "angle": 0, + "content": "4. Diffusion Video Autoencoders" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.47, + 0.903 + ], + "angle": 0, + "content": "In this section, we introduce a video autoencoder, called Diffusion Video Autoencoder, specially designed for face video editing to have 1) superb reconstruction performance" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.387, + 0.892, + 0.478 + ], + "angle": 0, + "content": "and 2) an editable representation space for the identity feature of the video disentangled with the per-frame features changing over time. The details of the model components and the training procedure are explained in Sec. 4.1 and then two different editing methods based on our model are presented in Sec. 4.2. We provide the overview in Fig. 2." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.486, + 0.765, + 0.503 + ], + "angle": 0, + "content": "4.1. Disentangled Video Encoding" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.51, + 0.893, + 0.789 + ], + "angle": 0, + "content": "To encode the video with \\(N\\) frames \\(\\{x_0^{(n)}\\}_{n = 1}^N\\), we consider the time-invariant feature of human face videos as human identity information, and the time-dependent feature for each frame as motion and background information. Among these three, identity or motion information relevant to a face is appropriate to be projected to a low-dimensional space to extract high-level representation. Comparatively, the background shows high variance with arbitrary details and changes more with the head movement by cropping and aligning the face region. Therefore, it could be very difficult to encode the background information into a high-level semantic space. Thus, identity and motion features are encoded in high-level semantic space \\(z_{\\mathrm{face}}^{(n)}\\), combining identity feature \\(z_{\\mathrm{id}}\\) of the video and motion feature \\(z_{\\mathrm{land}}^{(n)}\\) of each frame, and the background feature is encoded in noise map \\(x_{T}^{(n)}\\) (see Fig. 2a). We denote \\(z_{\\mathrm{id}}\\) without superscript \\((n)\\) for frame index since it is the time-invariant and shared across all frames of the video." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.79, + 0.894, + 0.903 + ], + "angle": 0, + "content": "To achieve this decomposition, our model consists of two separated semantic encoders - an identity encoder \\( E_{\\mathrm{id}} \\) and a landmark encoder \\( E_{\\mathrm{land}} \\) - and a conditional noise estimator \\( \\epsilon_{\\theta} \\) for diffusion modeling. The encoded features \\( (z_{\\mathrm{id}}, z_{\\mathrm{land}}^{(n)}) \\) by the two encoders are concatenated and passed through an MLP to finally get a face-related feature \\( z_{\\mathrm{face}}^{(n)} \\). Next, to encode noise map \\( x_{T}^{(n)} \\), we run the deterministic forward" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6094" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.215 + ], + "angle": 0, + "content": "process of DDIM using noise estimator \\(\\epsilon_{\\theta}\\) with conditioned on \\(z_{\\mathrm{face}}^{(n)}\\). Since noise map \\(x_{T}^{(n)}\\) is a spatial variable with the same size as the image, it is expected that information in the background can be encoded more easily without loss of spatial information. Then, the encoded features \\((x_{T}^{(n)}, z_{\\mathrm{face}}^{(n)})\\) can be reconstructed to the original frame by running generative reverse process of conditional DDIM in a deterministic manner:" + }, + { + "type": "equation", + "bbox": [ + 0.111, + 0.217, + 0.436, + 0.259 + ], + "angle": 0, + "content": "\\[\np _ {\\theta} (x _ {0: T} | z _ {\\mathrm {f a c e}}) = p (x _ {T}) \\prod_ {t = 1} ^ {T} p _ {\\theta} (x _ {t - 1} | x _ {t}, z _ {\\mathrm {f a c e}}).\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.268, + 0.47, + 0.587 + ], + "angle": 0, + "content": "To obtain the identity feature disentangled with the motion, we choose to leverage a pretrained model for identity detection, named ArcFace [5]. ArcFace is trained to classify human identity in face images regardless of poses or expressions, so we expect it to provide the disentangled property we need. Nevertheless, when an identity feature is extracted for each frame through the pretrained identity encoder, the feature may be slightly different for each frame because some frames may have partial identity features for some reasons (e.g. excessive side view poses). To alleviate this issue, we average the identity features \\( z_{\\mathrm{id}}^{(n)} = E_{\\mathrm{id}}(x_0^{(n)}) \\) of all frames in the inference phase. Similarly, we obtain per-frame motion information via a pretrained landmark detection model [4] which outputs the position of face landmarks. Several studies [21,36] have shown that it is possible to have a sufficiently disentangled nature by extracting features through a pretrained encoder without learning. Therefore, diffusion video autoencoders extract an identity and also a landmark feature of the image through the pretrained encoders and map them together to the high-level semantic space for face features through an additional learnable MLP." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.588, + 0.471, + 0.663 + ], + "angle": 0, + "content": "Next, we explain how the learnable part of our model is trained. Fig. 2b summarizes our training process. For simplicity, from now on, we drop the superscript of frame index. Our objective consists of two parts. The first one is the simple version of DDPM loss [9] as" + }, + { + "type": "equation", + "bbox": [ + 0.084, + 0.675, + 0.462, + 0.695 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {s i m p l e}} = \\mathbb {E} _ {x _ {0} \\sim q (x _ {0}), \\epsilon_ {t} \\sim \\mathcal {N} (0, I), t} \\left\\| \\epsilon_ {\\theta} (x _ {t}, t, z _ {\\mathrm {f a c e}}) - \\epsilon_ {t} \\right\\| _ {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.473, + 0.903 + ], + "angle": 0, + "content": "where \\( z_{\\mathrm{face}} \\) is an encoded high-level feature of input image \\( x_0 \\). It encourages the useful information of the image to be well contained in the semantic latent \\( z_{\\mathrm{face}} \\) and exploited by \\( \\epsilon_{\\theta} \\) for denoising. Secondly, we devise a regularization loss to hinder face information (identity and motion) from leaking to \\( x_{T} \\) but contained in \\( z_{\\mathrm{face}} \\) as much as possible for clear decomposition between background and face information. If some face information is lost in \\( z_{\\mathrm{face}} \\), the lost information would remain in the noise latent \\( x_{T} \\) unintentionally. To avoid it, we sample two different Gaussian noises \\( \\epsilon_1 \\) and \\( \\epsilon_2 \\) to obtain different noisy samples \\( x_{t,1} \\) and \\( x_{t,2} \\), respectively. Then, we minimize the difference between the estimated original images \\( f_{\\theta,1} \\) and \\( f_{\\theta,2} \\) except for the back" + }, + { + "type": "image_caption", + "bbox": [ + 0.533, + 0.093, + 0.862, + 0.107 + ], + "angle": 0, + "content": "1. Conditional sampling with \\( z_{id} \\) for prediction of each noise level" + }, + { + "type": "image", + "bbox": [ + 0.52, + 0.116, + 0.87, + 0.324 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.528, + 0.329, + 0.862, + 0.343 + ], + "angle": 0, + "content": "2. Conditional sampling with trainable \\( z_{\\mathrm{id}}^{\\mathrm{opt}} \\) and optimize with \\( \\mathcal{L}_{\\mathrm{CLIP}} \\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.55, + 0.355, + 0.842, + 0.37 + ], + "angle": 0, + "content": "Figure 3. Process of computing noisy CLIP loss." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.377, + 0.605, + 0.391 + ], + "angle": 0, + "content": "ground part as:" + }, + { + "type": "equation", + "bbox": [ + 0.504, + 0.4, + 0.887, + 0.42 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {r e g}} = \\mathbb {E} _ {x _ {0} \\sim q (x _ {0}), \\epsilon_ {1}, \\epsilon_ {2} \\sim \\mathcal {N} (0, I), t} \\left\\| f _ {\\theta , 1} \\odot m - f _ {\\theta , 2} \\odot m \\right\\| _ {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.426, + 0.893, + 0.533 + ], + "angle": 0, + "content": "where \\(m\\) is a segmentation mask of a face region in the original image \\(x_0\\) and \\(f_{\\theta ,i} = f_{\\theta}(x_{t,i},t,z_{\\mathrm{face}})\\). As a result, the effect of noise in \\(x_{t}\\) on the face region will be reduced and \\(z_{\\mathrm{face}}\\) will be responsible for face features for the generation (See Fig. 7). In Sec. 5.5, we demonstrate the desired effect of \\(\\mathcal{L}_{\\mathrm{reg}}\\). The final loss of diffusion video autoencoders is as follows: \\(\\mathcal{L}_{\\mathrm{dva}} = \\mathcal{L}_{\\mathrm{simple}} + \\mathcal{L}_{\\mathrm{reg}}\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.541, + 0.738, + 0.557 + ], + "angle": 0, + "content": "4.2. Video Editing Framework" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.564, + 0.892, + 0.673 + ], + "angle": 0, + "content": "We now describe our video editing framework with our diffusion video autoencoders. First, all video frames \\(\\{I_n\\}_{n=1}^N\\) are aligned and cropped for interesting face regions as in [35]. The cropped frames \\(\\{x_0^{(n)}\\}_{n=1}^N\\) are then encoded to latent features using our diffusion video autoencoder. To extract the representative identity feature of the video, we average identity features of each frame as" + }, + { + "type": "equation", + "bbox": [ + 0.613, + 0.681, + 0.78, + 0.722 + ], + "angle": 0, + "content": "\\[\nz _ {\\mathrm {i d , r e p}} = \\frac {1}{N} \\sum_ {n = 1} ^ {N} (z _ {\\mathrm {i d}} ^ {(n)}),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.732, + 0.895, + 0.903 + ], + "angle": 0, + "content": "where \\(z_{\\mathrm{id}}^{(n)} = E_{\\mathrm{id}}(x_0^{(n)})\\) . Similarly, the per-frame landmark feature is computed as \\(z_{\\mathrm{lnd}}^{(n)} = E_{\\mathrm{lnd}}(x_0^{(n)})\\) to finally obtain per-frame face features \\(z_{\\mathrm{face}}^{(n)} = MLP(z_{\\mathrm{id,rep}},z_{\\mathrm{lnd}}^{(n)})\\) After that, we compute \\(x_{T}^{(n)}\\) with DDIM forward process conditioning \\(z_{\\mathrm{face}}^{(n)}\\) . Thereafter, manipulation is conducted by editing \\(z_{\\mathrm{id,rep}}\\) to \\(z_{\\mathrm{id,rep}}^{\\mathrm{edit}}\\) using a pretrained linear attribute-classifier of the identity space or text-based optimization which we will discuss in more detail later. After modifying the representative identity feature \\(z_{\\mathrm{id,rep}}^{\\mathrm{edit}}\\) the edited frame \\(\\hat{x}_0^{(n),\\mathrm{edit}}\\) is generated by the conditional" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6095" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.113, + 0.089, + 0.855, + 0.491 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.198, + 0.497, + 0.772, + 0.513 + ], + "angle": 0, + "content": "Figure 4. Comparison of temporal consistency to the previous video editing methods for 'beard'." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.526, + 0.473, + 0.64 + ], + "angle": 0, + "content": "reverse process with \\((z_{\\mathrm{face}}^{(n),\\mathrm{edit}},x_T^{(n)})\\) where \\(z_{\\mathrm{face}}^{(n),\\mathrm{edit}} = MLP(z_{\\mathrm{id,rep}}^{\\mathrm{edit}},z_{\\mathrm{nd}}^{(n)})\\). Afterward, as with all previous work, the face part of the edited frame is pasted to the corresponding area of the original frame to create a clean final result. For this process, we segment face regions using a pretrained segmentation network [42]. Below, we explore two editing methods for our video editing framework." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.648, + 0.47, + 0.741 + ], + "angle": 0, + "content": "Classifier-based editing First, as in DiffAE [23], we train a linear classifier \\( C_{\\text{attr}}(z_{\\text{id}}) = \\text{sigmoid}(w_{\\text{attr}}^{\\top} z_{\\text{id}}) \\) for each attribute attr on CelebA-HQ's [10] with its attribute annotation in the identity feature space. To change attr, we move the identity feature \\( z_{\\text{id}} \\) to \\( \\ell_2 \\text{Norm}(z_{\\text{id}} + sw_{\\text{attr}}) \\) with a scale hyperparameter \\( s \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.903 + ], + "angle": 0, + "content": "CLIP-based editing Since the pretrained classifier allows editing only for several predefined attributes, we additionally devise the CLIP-guidance identity feature optimization method. Directional CLIP loss [7] requires two images corresponding to one for neutral text and one for target text, respectively. It implies that we need the synthesized images with our diffusion model, which is costly with full generative process. Therefore, to reduce the computational cost, we use the drastically reduced number of steps \\( S \\) (\\( \\ll T \\)) for image sampling. In other words, we consider the time" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.529, + 0.895, + 0.896 + ], + "angle": 0, + "content": "steps \\( t_1, t_2, \\ldots, t_S \\) where \\( 0 = t_0 < t_1 < \\ldots < t_S \\leq T \\) and evenly split \\( T \\). Thereafter, we compute \\( x_{t_s} \\) from the given image \\( x_0 \\) that we want to edit (normally chosen as the first frame \\( x_0^{(1)} \\) of the video) through \\( S \\)-step of forward process with \\( z_{\\mathrm{id}} = E_{\\mathrm{id}}(x_0) \\). Through the sequential reverse steps from \\( x_{t_S} \\), we recover \\( \\hat{x}_{t_s} \\) for each time \\( t_s \\) where \\( s = (S - 1), \\ldots, 0 \\) with the original \\( z_{\\mathrm{id}} \\). Meanwhile, \\( x_{t_s}^{\\mathrm{edit}} \\) are obtained by the single reverse step from \\( \\hat{x}_{t_{s+1}} \\) but with variable \\( z_{\\mathrm{id}}^{\\mathrm{opt}} \\) being optimized initialized to \\( z_{\\mathrm{id}} \\) (See Fig. 3). Finally, we minimize the directional CLIP loss [7] between intermediate images \\( \\hat{x}_{t_s} \\) and \\( x_{t_s}^{\\mathrm{edit}} \\), which are still noisy, for all \\( s \\) with a neutral (e.g. \"face\") and a target text (e.g. \"face with eyeglasses\"). We choose intermediate images \\( x_{t_s}^{\\mathrm{edit}} \\), \\( \\hat{x}_{t_s} \\) from \\( \\hat{x}_{t_{s+1}} \\) instead of estimated \\( x_0 \\) to compute CLIP loss because to estimate \\( x_0 \\) directly from \\( x_{t_s} \\) is incomplete and erroneous for large \\( t_s \\). Therefore, we expect that conservatively choosing intermediate images will help to find the edit direction more reliably. We refer the reader to Appendix B for the ablation study of our noisy CLIP loss. In addition to the CLIP loss, to preserve the remaining attributes, we also use ID loss (cosine distance between \\( z_{\\mathrm{id}} \\) and \\( z_{\\mathrm{id}}^{\\mathrm{opt}} \\)) and \\( \\ell_1 \\) loss between face parts of \\( \\hat{x}_{t_s} \\) and \\( x_{t_s}^{\\mathrm{edit}} \\) for all \\( s \\). After all, the learned editing step \\( \\Delta z_{\\mathrm{id}} = z_{\\mathrm{id}}^{\\mathrm{opt}} - z_{\\mathrm{id}} \\) is applied to \\( z_{\\mathrm{id},\\mathrm{rep}} \\)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6096" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.09, + 0.47, + 0.132 + ], + "angle": 0, + "content": "Table 1. Quantitative reconstruction results on the randomly chosen 20 videos in VoxCeleb1 test set. The reported values are the mean of the averaged per-frame measurements for each video." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.139, + 0.466, + 0.214 + ], + "angle": 0, + "content": "
MethodSSIM ↑MS-SSIM ↑LPIPS ↓MSE ↓
e4e [34]0.5090.7610.1570.037
PTI [27]0.7650.9390.0630.007
Ours (T=20)0.5400.9050.2280.016
Ours (T=100)0.9220.9890.0450.002
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.231, + 0.468, + 0.271 + ], + "angle": 0, + "content": "Table 2. Quantitative results to evaluate temporal consistency. Ours show the best global coherency and comparable local consistency to the baselines." + }, + { + "type": "table", + "bbox": [ + 0.151, + 0.278, + 0.396, + 0.358 + ], + "angle": 0, + "content": "
MethodTL-IDTG-ID
Yao et al. [41]0.9890.920
Tzaban et al. [35]0.9970.961
Xu et al. [40]1.0020.983
Ours0.9950.996
" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.38, + 0.208, + 0.397 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.408, + 0.468, + 0.603 + ], + "angle": 0, + "content": "In this section, we present the experimental results to confirm reconstruction performance (Sec. 5.1), temporally consistent editing ability (Sec. 5.2), robustness to the unusual samples (Sec. 5.3), and disentanglement of the encoded features (Sec. 5.4) with further ablation study (Sec. 5.5). For this purpose, we train our diffusion video autoencoder on 77294 videos of the VoxCeleb1 dataset [18]. As preprocessing, frames of the video are aligned and cropped as in [35] like the FFHQ dataset. Next, they are resized to the size of \\(256^2\\). For the noise estimator \\(\\epsilon_{\\theta}\\), the UNet improved by [20] is used, and we train diffusion video autoencoder for 1 million steps with a batch size of 16. Please see more details in Appendix A." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.619, + 0.23, + 0.634 + ], + "angle": 0, + "content": "5.1. Reconstruction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.644, + 0.468, + 0.901 + ], + "angle": 0, + "content": "For video editing, the ability to reconstruct the original video from the encoded one must be preceded. Otherwise, we will lose the original one before we even edit the video. To compare this ability with baselines quantitatively, we measure frequently used metrics for reconstruction - SSIM [37], Multi-scaled (MS) SSIM [38], LPIPS [43], and MSE - on randomly selected 20 videos in the test set of VoxCeleb1. As baselines, we compared our model with the GAN-based inversion method e4e [34] and PTI [27] used by Yao et al. [41] and Tzaban et al. [35], respectively. Since StyleGAN-based methods handle the higher resolution images with the size of \\(1024^2\\), we resize the reconstructed results to \\(256^2\\) for comparison. For our method, we vary the number of diffusion steps \\(T\\) to observe computational cost and image quality trade-offs. In Tab. 1, our diffusion video autoencoder with \\(T = 100\\) shows the best reconstruction ability and still outperforms e4e with only \\(T = 20\\)." + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.09, + 0.892, + 0.256 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.263, + 0.892, + 0.306 + ], + "angle": 0, + "content": "Figure 5. Editing wild face videos that GAN-based prior works struggled with. Classifier-based editing is used to make the person \"young\" (up) or change a \"gender\" (below)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.313, + 0.706, + 0.33 + ], + "angle": 0, + "content": "5.2. Temporal Consistency" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.337, + 0.892, + 0.579 + ], + "angle": 0, + "content": "In Fig. 4, a visual comparison is conducted to evaluate the video editing performance of our diffusion video autoencoder qualitatively. We edit the given video to generate a beard through text-based guidance except for Yao et al. [41], which only allows to edit predefined attributes, by moving to the opposite direction of \"no_peat\". As a result, we demonstrate that only our diffusion video autoencoder successfully produces the consistent result. Specifically, Yao et al. [41] fail to preserve the original identity due to the limitations of GAN inversion. In the result of Tzaban et al. [35], the shape and the amount of beard constantly changes according to the lip motion. Although Xu et al. [40] show better but not perfect consistency, the motions unintentionally change as a side effect. The inconsistency can be observed more clearly between the second and the fifth column except for ours showing a reliable result." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.58, + 0.892, + 0.791 + ], + "angle": 0, + "content": "Furthermore, we quantitatively evaluate the temporal consistency of Fig. 4 in Tab. 2. Although there is no perfect metric for temporal consistency of videos, TL-ID and TG-ID [35] imply the local and global consistency of identity between adjacent frames and across all frames, respectively, compared to the original. These metrics can be interpreted as being consistent as the original is when their values are close to 1. We emphasize that we greatly improve global consistency. TL-ID of Xu et al. [40] is larger than 1 because the motion of the editing results shrinks so that the adjacent frames become closer to each other than the original. Additional quantitative comparisons of temporal consistency, editing quality, and time cost are summarized in Appendix C." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.801, + 0.731, + 0.817 + ], + "angle": 0, + "content": "5.3. Editing Wild Face Videos" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.891, + 0.901 + ], + "angle": 0, + "content": "Owing to the reconstructability of diffusion models, editing wild videos that are difficult to inversion by GAN-based methods becomes possible. As shown in Fig. 5, unlike others, our method robustly reconstructs and edits the given images effectively." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.515, + 0.957 + ], + "angle": 0, + "content": "6097" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.468, + 0.358 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.092, + 0.364, + 0.454, + 0.379 + ], + "angle": 0, + "content": "Figure 6. Demonstration of the disentangled video encoding." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.399, + 0.351, + 0.417 + ], + "angle": 0, + "content": "5.4. Decomposed Features Analysis" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.428, + 0.473, + 0.732 + ], + "angle": 0, + "content": "To demonstrate whether the diffusion video autoencoder decomposes the features adequately, we examine the synthesized images by changing each element of the decomposed features. To this end, we encode the frames of two different videos and then generate samples with a random noise or exchange the respective elements with each other in Fig. 6. When we decode the semantic latent \\( z_{\\text{face}} \\) with a Gaussian noise instead of the original noise latent \\( x_{T} \\), it has a blurry background that is different from the original one, while identity and head pose are preserved considerably. This result implies that \\( x_{T} \\) contains only the background information, as we intended. Moreover, the generated images with switched identity, motion, and background feature confirm that the features are properly decomposed and the diffusion video autoencoder can produce a realistic image even with the new combination of the features. However, with extreme changes in the head position, the background occluded by the face is not properly generated because the taken \\( x_{T} \\) has no information about background in that area (See the last column of the lower example in Fig. 6)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.752, + 0.231, + 0.769 + ], + "angle": 0, + "content": "5.5. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.47, + 0.903 + ], + "angle": 0, + "content": "We further conduct an ablation study on our proposed regularization loss \\(\\mathcal{L}_{\\mathrm{reg}}\\). First, we train the model with the same setting but ablating \\(\\mathcal{L}_{\\mathrm{reg}}\\). As shown in Fig. 7, neither model has a problem with reconstruction. However, without the regularization loss, the identity changes significantly according to the random noise. Thus we can conclude that the regularization loss helps the model to decompose features effectively." + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.089, + 0.892, + 0.329 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.336, + 0.892, + 0.379 + ], + "angle": 0, + "content": "Figure 7. Ablation of using regularization loss for training. Regularization loss helps the model to contain identity and motion information in \\( z_{\\text{face}} \\) as much as possible." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.401, + 0.628, + 0.417 + ], + "angle": 0, + "content": "6. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.432, + 0.892, + 0.675 + ], + "angle": 0, + "content": "To tackle the temporal consistency problem in editing human face video, we have proposed a novel framework with the newly designed video diffusion autoencoder which encodes the identity, motion, and background information in a disentangled manner and decodes after editing a single identity feature. Through the disentanglement, the most valuable strength of our framework is that we can search the desired editing direction for only one frame and then edit the remaining frames with temporal consistency by moving the representative video identity feature. Additionally, the wild face video can be reliably edited by the advantage of the diffusion model that is superior in reconstruction to GAN. Finally, we have explored to optimize the semantic identity feature with CLIP loss for text-based video editing. Please refer to the Appendix D for the limitations and further discussion." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.893, + 0.903 + ], + "angle": 0, + "content": "Acknowledgement This work was supported by Institute of Information & communications Technology Planning & Evaluation (IITP) grant (No.2019-0-00075, Artificial Intelligence Graduate School Program(KAIST), No.2021-0-02068, Artificial Intelligence Innovation Hub, No.2022-0-00713, Meta-learning applicable to real-world problems, No.2022-0-00984, Development of Artificial Intelligence Technology for Personalized Plug-and-Play Explanation and Verification of Explanation) and the National Research Foundation of Korea (NRF) grants (No.2018R1A5A1059921) funded by the Korea government (MSIT). 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In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 586-595, 2018. 7" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.092, + 0.894, + 0.205 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.956 + ], + "angle": 0, + "content": "6100" + } + ] +] \ No newline at end of file diff --git a/2023/Diffusion Video Autoencoders_ Toward Temporally Consistent Face Video Editing via Disentangled Video Encoding/9c72d0e6-e653-459a-87e1-dce2e1570589_origin.pdf b/2023/Diffusion Video Autoencoders_ Toward Temporally Consistent Face Video Editing via Disentangled Video Encoding/9c72d0e6-e653-459a-87e1-dce2e1570589_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..3470ba41ad15c285b554feebb3354d88e2fed390 --- /dev/null +++ b/2023/Diffusion Video Autoencoders_ Toward Temporally Consistent Face Video Editing via Disentangled Video Encoding/9c72d0e6-e653-459a-87e1-dce2e1570589_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:1b677f5319c18066b735f3652956b07de13ebdc63913c6172dc6cd1a3580444b +size 2315226 diff --git a/2023/Diffusion Video Autoencoders_ Toward Temporally Consistent Face Video Editing via Disentangled Video Encoding/full.md b/2023/Diffusion Video Autoencoders_ Toward Temporally Consistent Face Video Editing via Disentangled Video Encoding/full.md new file mode 100644 index 0000000000000000000000000000000000000000..54df91c24b7aed09c66fc547bc67c50793dfb1b3 --- /dev/null +++ b/2023/Diffusion Video Autoencoders_ Toward Temporally Consistent Face Video Editing via Disentangled Video Encoding/full.md @@ -0,0 +1,251 @@ +# Diffusion Video Autoencoders: Toward Temporally Consistent Face Video Editing via Disentangled Video Encoding + +Gyeongman Kim $^{1}$ Hajin Shim $^{1}$ Hyunsu Kim $^{2}$ Yunjay Choi $^{2}$ Junho Kim $^{2}$ Eunho Yang $^{1,3}$ + +$^{1}$ Korea Advanced Institute of Science and Technology (KAIST), South Korea + +$^{2}$ NAVER AI Lab $^{3}$ AITRICS, South Korea + +{gmkim, shimazing, eunhoy}@kaist.ac.kr {hyunsull25.kim, yunjey.choi, jhkim.ai}@navercorp.com + +![](images/8f7d1da6435946194341ac20bd0ded96f14cdfc6ac3373d51ad7f288ebc5421c.jpg) +Figure 1. Face video editing. Our editing method shows improvement compared to the baseline [35] in terms of temporal consistency (left, "eyeglasses") and robustness to the unusual case such as the hand-occluded face (right, "beard"). + +![](images/3fe29fd617bd845440db7245378a97db358199992e8aca5e218426dcc808eee6.jpg) + +# Abstract + +Inspired by the impressive performance of recent face image editing methods, several studies have been naturally proposed to extend these methods to the face video editing task. One of the main challenges here is temporal consistency among edited frames, which is still unresolved. To this end, we propose a novel face video editing framework based on diffusion autoencoders that can successfully extract the decomposed features - for the first time as a face video editing model - of identity and motion from a given video. This modeling allows us to edit the video by simply manipulating the temporally invariant feature to the desired direction for the consistency. Another unique strength of our model is that, since our model is based on diffusion models, it can satisfy both reconstruction and edit capabilities at the same time, and is robust to corner cases in wild face videos (e.g. occluded faces) unlike the existing GAN-based methods.1 + +# 1. Introduction + +As one of the standard tasks in computer vision to change various face attributes such as hair color, gender, or glasses + +of a given face image, face editing has been continuously gaining attention due to its various applications and entertainment. In particular, with the improvement of analysis and manipulation techniques for recent Generative Adversarial Network (GAN) models [8, 11, 22, 29, 30], we simply can do this task by manipulating a given image's latent feature. In addition, very recently, many methods for face image editing also have been proposed based on Diffusion Probabilistic Model (DPM)-based methods that show high-quality and flexible manipulation performance [3, 12, 17, 19, 23, 25]. + +Naturally, further studies [2, 35, 41] have been proposed to extend image editing methods to incorporate the temporal axis for videos. Now, given real videos with a human face, these studies try to manipulate some target facial attributes with the other remaining features and motion intact. They all basically edit each frame of a video independently via off-the-shelf StyleGAN-based image editing techniques [22, 29, 41]. + +Despite the advantages of StyleGAN in this task such as high-resolution image generation capability and highly disentangled semantic representation space, one harmful drawback of GAN-based editing methods is that the encoded real + +images cannot perfectly be recovered by the pretrained generator [1, 26, 34]. Especially, if a face in a given image is unusually decorated or occluded by some objects, the fixed generator cannot synthesize it. For perfect reconstruction, several methods [6, 27] are suggested to further tune the generator for GAN-inversion [26, 34] on one or a few target images, which is computationally expensive. Moreover, after the fine-tuning, the original editability of GANs cannot be guaranteed. This risk could be worse in video domain since we have to finetune the model on the multiple frames. + +Aside from the reconstruction issue of existing GAN-based methods, it is critical in video editing tasks to consider the temporal consistency among edited frames to produce realistic results. To address this, some prior works rely on the smoothness of the latent trajectory of the original frames [35] or smoothen the latent features directly [2] by simply taking the same editing step for all frames. However, smoothness does not ensure temporal consistency. Rather, the same editing step can make different results for different frames because it can be unintentionally entangled with irrelevant motion features. For example, in the middle row of Fig. 1, eyeglasses vary across time and sometimes diminish when the man closes his eyes. + +In this paper, we propose a novel video editing framework for human face video, termed Diffusion Video Autoencoder, that resolves the limitations of the prior works. First, instead of GAN-based editing methods suffering from imperfect reconstruction quality, we newly introduce diffusion based model for face video editing tasks. As the recently proposed diffusion autoencoder (DiffAE) [23] does, thanks to the expressive latent spaces of the same size as input space, our model learns a semantically meaningful latent space that can perfectly recover the original image back and are directly editable. Not only that, for the first time as a video editing model, encode the decomposed features of the video: 1) identity feature shared by all frames, 2) feature of motion or facial expression in each frame, and 3) background feature that could not have high-level representation due to large variances. Then, for consistent editing, we simply manipulate a single invariant feature for the desired attribute (single editing operation per video), which is also computationally beneficial compared to the prior works that require editing the latent features of all frames. + +We experimentally demonstrate that our model appropriately decomposes videos into time-invariant and per-frame variant features and can provide temporally consistent manipulation. Specifically, we explore two ways of manipulation. The first one is to edit features in the predefined set of attributes by moving semantic features to the target direction found by learning linear classifier in semantic representation space on annotated CelebA-HQ dataset [10]. Additionally, we explore the text-based editing method that optimizes a time-invariant latent feature with CLIP loss [7]. It + +is worth noting that since we cannot fully generate edited images for CLIP loss due to the computational cost, we propose the novel strategy that rather uses latent state of intermediate time step for the efficiency. + +To summarize, our contribution is four-fold: + +- We devise diffusion video autoencoders based on diffusion autoencoders [23] that decompose the video into a single time-invariant and per-frame time-variant features for temporally consistent editing. +- Based on the decomposed representation of diffusion video autoencoder, face video editing can be conducted by editing only the single time-invariant identity feature and decoding it together with the remaining original features. +- Owing to the nearly-perfect reconstruction ability of diffusion models, our framework can be utilized to edit exceptional cases such that a face is partially occluded by some objects as well as usual cases. +- In addition to the existing predefined attributes editing method, we propose a text-based identity editing method based on the local directional CLIP loss [7,24] for the intermediately generated product of diffusion video autoencoders. + +# 2. Related Work + +Video editing When editing a given real video, it is essential to preserve temporal consistency. First, Lai et al. [14] consider editing global features of videos such as artistic style transfer, colorization, image enhancement, etc. To encourage temporal consistency, they train sequential image translator with temporal loss defined as the warping error between the output frames. + +Different from this work, our target task is to edit facial attributes of human face video. In other words, we aim to change face-related attributes such as eyeglasses, beards, etc. For this task, Yao et al. [41] are the first that propose the editing pipeline: 1) align and crop the target face area, 2) encode these frames to latent features, manipulate and decode them, and 3) unalign and paste the edited frames to the original video. However, every step of this pipeline is conducted independently for each frame. For the manipulation step, they try to find disentangled editing directions for a desired attribute and take the same step for every frame, while expecting the disentanglement brings consistency automatically. However, the results show inconsistency and we conjecture that both latent space and learned direction are still entangled with many other attributes. Next, Tza-ban et al. [35] additionally fine-tune the pretrained StyleGAN [27] to enhance reconstructability. Meanwhile, they assume that temporal consistency would be preserved when applying the same editing step to the latent features of the + +original frames. However, their assumption is not always true for all attributes, especially for beards and eyeglasses as shown in Fig. 1. Alauf et al. [2] also try to avoid temporal inconsistency by smoothing latent features. + +While the methods in the previous paragraph handle inconsistency implicitly, several works [39, 40] try to solve it more directly. After per-frame editing, Xu et al. [40] further optimize latent codes and the pretrained StyleGAN to enhance consistency between the frame pairs defined by involving bi-directional optical flow. On the other hand, Xia et al. [39] propose to learn the dynamics of inverted GAN latent codes of video frames. The learned dynamics are used to generate the subsequent latent features after editing only the first frame. + +Additionally, although Skorokhodov et al. [31] mainly target to generate video, they also demonstrate manipulation results of the generated video. They model the video with a time-invariant content code and per-frame motion codes. Based on this modeling, the generated video can be manipulated with a target text by optimizing its content vector with CLIP loss. However, they cannot edit the real videos due to the absence of an encoding method. In contrast, our proposed method is capable of encoding and manipulating realistic face videos. + +Diffusion models Denoising diffusion probabilistic models (DDPMs) [9] associate image generation with the sequential denoising process of isotropic Gaussian noise. The model is trained to predict the noise from the input image. Unlike other generative models such as GANs and most traditional-style VAEs that encode input data in a low-dimensional space, diffusion models have a latent space that is the same size as the input. Although DDPMs require a lot of feed-forward steps to generate samples, their image fidelity and diversity are superior to other types of generative models. Compared to DDPMs that assume a Markovian noise-injecting forward diffusion process, Denoising diffusion implicit models (DDIMs) [33] assume a non-Markovian forward process that has the same marginal distribution as DDPMs, and use its corresponding reverse denoising process for sampling, which enables acceleration of the rather onerous sampling process of DDPMs. DDIMs also utilize a deterministic forward-backward process and therefore show nearly-perfect reconstruction ability, which is not the case for DDPMs. In this paper, we adopt conditional DDIMs to encode, manipulate and decode real videos. + +Image editing with diffusion models There are various attempts to manipulate images with diffusion models [3, 12, 17, 19, 23, 25] such as text-guided inpainting [3, 19, 25], stroke-based editing [17], and style transfer [12]. Among those, we are especially interested in facial attribute editing tasks. Kim et al. [12] propose text-based image ma + +nipulation by optimizing an unconditional diffusion model to minimize local directional CLIP loss [7]. This method is superior to GAN-based methods as it can successfully edit even occluded or overly decorated faces by the excellent reconstruction ability of diffusion models. However, due to the absence of semantically meaningful latent space, there exist some semantic features that are unable to be changed. Another parallel work proposes diffusion autoencoder (DiffAE) [23], which takes a learnable encoder to obtain semantic representations of which the underlying diffusion model is conditioned. The model can perform face attribute manipulation by moving the semantic vector to a target direction. Based on DiffAEs, we design our diffusion video autoencoders to perform temporally-consistent video editing. + +# 3. Preliminaries + +Diffusion probabilistic models (DPMs) DPMs [9, 32] are generative models that attempt to approximate the data distribution $q(x_0)$ via $p_{\theta}(x_0)$ from the reverse prediction of Markovian diffusion process $q(x_{1:T}|x_0) = \prod_{t=1}^{T} q(x_t|x_{t-1})$ . Here, the forward process of DPM is a Gaussian noise perturbation $q(x_t|x_{t-1}) = \mathcal{N}(\sqrt{1 - \beta_t} x_{t-1}, \beta_t I)$ where $\beta_t$ is fixed or learned variance schedule with increasing $\beta_1 < \beta_2 < \dots < \beta_T$ , adding gradually increasing noise to data $x_0$ , and its reverse process is denoising of $x_t$ step by step in reverse order. From this definition, a noisy image $x_t$ at step $t$ can be expressed as $x_t = \sqrt{\alpha_t} x_0 + \sqrt{1 - \alpha_t} \epsilon$ , $\epsilon \sim \mathcal{N}(0, I)$ where $\alpha_t = \prod_{s=1}^t (1 - \beta_s)$ . While the true reverse process $q(x_{t-1}|x_t)$ is intractable, diffusion models approximate $q(x_{t-1}|x_t, x_0)$ with $p_{\theta}(x_{t-1}|x_t) = \mathcal{N}(\mu_{\theta}(x_t, t), \sigma_t)$ by minimizing the variational lower bound of negative log-likelihood. Finally, by reparameterizing $\mu_{\theta}$ , the objective is given as $\mathbb{E}_{x_0 \sim q(x_0), \epsilon_t \sim \mathcal{N}(0, I), t} \left\| \epsilon_{\theta}(x_t, t) - \epsilon_t \right\|_2^2$ where the parameterized model $\epsilon_{\theta}(x_t, t)$ estimates the true Gaussian noise term $\frac{1}{\sqrt{1 - \alpha_t}} (x_t - \sqrt{\alpha_t} x_0)$ in the forward process. + +Speeding up a time-consuming sampling process of diffusion models is one of the core research topics related to diffusion models [20, 33]. Among others, Song et al. [33] propose DDIM, which assumes a non-Markovian forward process $q(x_{t}|x_{t - 1},x_{0})$ that has the same marginal distribution $q(x_{t}|x_{0})$ with DDPMs. The corresponding generative process of DDIM is $x_{t - 1} = \sqrt{\alpha_{t - 1}} f_{\theta}(x_t,t) + \sqrt{1 - \alpha_{t - 1} - \sigma_t^2}\epsilon_\theta (x_t,t) + \sigma_t^2 z$ where $z\sim \mathcal{N}(0,I)$ , $\sigma$ is sampling stochasticity and $f_{\theta}(x_t,t)$ , the estimated value of $x_0$ at time step $t$ , is as follow: + +$$ +f _ {\theta} (x _ {t}, t) = \frac {x _ {t} - \sqrt {1 - \alpha_ {t}} \epsilon_ {\theta} (x _ {t} , t)}{\sqrt {\alpha_ {t}}}. +$$ + +When $\sigma$ is set to 0, this process becomes deterministic. With deterministic forward and reverse processes, we can obtain + +![](images/6d2d9d4d0fe4627368c7e2bd2e4aa9e40bc1af5396b06ba869c3cc069ebc1f1d.jpg) + +![](images/8a3c0f47368448e904dc292f7c9c39e9c7ccc2fdc056331136b40eeebbe97fda.jpg) +(a) Video autoencoding and editing pipeline. +Figure 2. Overview of our Diffusion Video Autoencoder. + +![](images/b5ca203f0d7b7161828c724bb2986b3397462f495b0bb6cc1c5584ff2c097baf.jpg) +(b) Training objective. + +the latent code of each original sample, which can reconstruct the original sample through the reverse process. + +Diffusion autoencoders Due to the determinacy of its sampling process, DDIM can reconstruct the original image $x_0$ from $x_T$ obtained through $T$ forward process steps. While $x_T$ can be considered as a latent state with the same size as $x_0$ , it does not contain high-level semantic information [23]. To supplement this, Prechakul et al. propose diffusion autoencoder (DiffAE) [23] based on DDIM. DiffAE utilizes two forms of latent variables: $z_{\mathrm{sem}}$ for the useful high-level semantic representation and $x_T$ for the remaining low-level stochasticity information. DiffAE introduces a semantic encoder $\mathsf{Enc}(x_0)$ which extracts $z_{\mathrm{sem}}$ from an image, and makes a noise estimator $\epsilon_{\theta}(x,t,z_{\mathrm{sem}})$ conditioned on $z_{\mathrm{sem}}$ . Stochastic latent $x_T$ is calculated through the deterministic DDIM forward process [33] that involves the noise estimator $\epsilon_{\theta}$ given $z_{\mathrm{sem}}$ . Then, $(z_{\mathrm{sem}},x_T)$ is decoded to reconstruct the corresponding original image $x_0$ with $p_{\theta}(x_{0:T}|z_{\mathrm{sem}}) = p(x_T)\prod_{t = 1}^{T}p_{\theta}(x_{t - 1}|x_t,z_{\mathrm{sem}})$ . DiffAE is trained with simple DDPM loss, as done with DDIM. The differences between DiffAE and DDIM are that an additional variable $z_{\mathrm{sem}}$ is involved as a conditioning variable during the reverse process (and thus the training process) and that the noise estimator $\epsilon_{\theta}$ and semantic encoder Enc are jointly trained. As a result, through the training phase, $z_{\mathrm{sem}}$ is learned to capture the high-level semantic information of the image, and the low-level stochastic variations remain in $x_T$ . + +# 4. Diffusion Video Autoencoders + +In this section, we introduce a video autoencoder, called Diffusion Video Autoencoder, specially designed for face video editing to have 1) superb reconstruction performance + +and 2) an editable representation space for the identity feature of the video disentangled with the per-frame features changing over time. The details of the model components and the training procedure are explained in Sec. 4.1 and then two different editing methods based on our model are presented in Sec. 4.2. We provide the overview in Fig. 2. + +# 4.1. Disentangled Video Encoding + +To encode the video with $N$ frames $\{x_0^{(n)}\}_{n = 1}^N$ , we consider the time-invariant feature of human face videos as human identity information, and the time-dependent feature for each frame as motion and background information. Among these three, identity or motion information relevant to a face is appropriate to be projected to a low-dimensional space to extract high-level representation. Comparatively, the background shows high variance with arbitrary details and changes more with the head movement by cropping and aligning the face region. Therefore, it could be very difficult to encode the background information into a high-level semantic space. Thus, identity and motion features are encoded in high-level semantic space $z_{\mathrm{face}}^{(n)}$ , combining identity feature $z_{\mathrm{id}}$ of the video and motion feature $z_{\mathrm{land}}^{(n)}$ of each frame, and the background feature is encoded in noise map $x_{T}^{(n)}$ (see Fig. 2a). We denote $z_{\mathrm{id}}$ without superscript $(n)$ for frame index since it is the time-invariant and shared across all frames of the video. + +To achieve this decomposition, our model consists of two separated semantic encoders - an identity encoder $E_{\mathrm{id}}$ and a landmark encoder $E_{\mathrm{land}}$ - and a conditional noise estimator $\epsilon_{\theta}$ for diffusion modeling. The encoded features $(z_{\mathrm{id}}, z_{\mathrm{land}}^{(n)})$ by the two encoders are concatenated and passed through an MLP to finally get a face-related feature $z_{\mathrm{face}}^{(n)}$ . Next, to encode noise map $x_{T}^{(n)}$ , we run the deterministic forward + +process of DDIM using noise estimator $\epsilon_{\theta}$ with conditioned on $z_{\mathrm{face}}^{(n)}$ . Since noise map $x_{T}^{(n)}$ is a spatial variable with the same size as the image, it is expected that information in the background can be encoded more easily without loss of spatial information. Then, the encoded features $(x_{T}^{(n)}, z_{\mathrm{face}}^{(n)})$ can be reconstructed to the original frame by running generative reverse process of conditional DDIM in a deterministic manner: + +$$ +p _ {\theta} (x _ {0: T} | z _ {\mathrm {f a c e}}) = p (x _ {T}) \prod_ {t = 1} ^ {T} p _ {\theta} (x _ {t - 1} | x _ {t}, z _ {\mathrm {f a c e}}). +$$ + +To obtain the identity feature disentangled with the motion, we choose to leverage a pretrained model for identity detection, named ArcFace [5]. ArcFace is trained to classify human identity in face images regardless of poses or expressions, so we expect it to provide the disentangled property we need. Nevertheless, when an identity feature is extracted for each frame through the pretrained identity encoder, the feature may be slightly different for each frame because some frames may have partial identity features for some reasons (e.g. excessive side view poses). To alleviate this issue, we average the identity features $z_{\mathrm{id}}^{(n)} = E_{\mathrm{id}}(x_0^{(n)})$ of all frames in the inference phase. Similarly, we obtain per-frame motion information via a pretrained landmark detection model [4] which outputs the position of face landmarks. Several studies [21,36] have shown that it is possible to have a sufficiently disentangled nature by extracting features through a pretrained encoder without learning. Therefore, diffusion video autoencoders extract an identity and also a landmark feature of the image through the pretrained encoders and map them together to the high-level semantic space for face features through an additional learnable MLP. + +Next, we explain how the learnable part of our model is trained. Fig. 2b summarizes our training process. For simplicity, from now on, we drop the superscript of frame index. Our objective consists of two parts. The first one is the simple version of DDPM loss [9] as + +$$ +\mathcal {L} _ {\mathrm {s i m p l e}} = \mathbb {E} _ {x _ {0} \sim q (x _ {0}), \epsilon_ {t} \sim \mathcal {N} (0, I), t} \left\| \epsilon_ {\theta} (x _ {t}, t, z _ {\mathrm {f a c e}}) - \epsilon_ {t} \right\| _ {1} +$$ + +where $z_{\mathrm{face}}$ is an encoded high-level feature of input image $x_0$ . It encourages the useful information of the image to be well contained in the semantic latent $z_{\mathrm{face}}$ and exploited by $\epsilon_{\theta}$ for denoising. Secondly, we devise a regularization loss to hinder face information (identity and motion) from leaking to $x_{T}$ but contained in $z_{\mathrm{face}}$ as much as possible for clear decomposition between background and face information. If some face information is lost in $z_{\mathrm{face}}$ , the lost information would remain in the noise latent $x_{T}$ unintentionally. To avoid it, we sample two different Gaussian noises $\epsilon_1$ and $\epsilon_2$ to obtain different noisy samples $x_{t,1}$ and $x_{t,2}$ , respectively. Then, we minimize the difference between the estimated original images $f_{\theta,1}$ and $f_{\theta,2}$ except for the back + +1. Conditional sampling with $z_{id}$ for prediction of each noise level +Figure 3. Process of computing noisy CLIP loss. +![](images/182bf31164a7bfe9b585dc0235394436b4fbb5234f9f82f3fb771f272ab0b3d9.jpg) +2. Conditional sampling with trainable $z_{\mathrm{id}}^{\mathrm{opt}}$ and optimize with $\mathcal{L}_{\mathrm{CLIP}}$ + +ground part as: + +$$ +\mathcal {L} _ {\mathrm {r e g}} = \mathbb {E} _ {x _ {0} \sim q (x _ {0}), \epsilon_ {1}, \epsilon_ {2} \sim \mathcal {N} (0, I), t} \left\| f _ {\theta , 1} \odot m - f _ {\theta , 2} \odot m \right\| _ {1} +$$ + +where $m$ is a segmentation mask of a face region in the original image $x_0$ and $f_{\theta ,i} = f_{\theta}(x_{t,i},t,z_{\mathrm{face}})$ . As a result, the effect of noise in $x_{t}$ on the face region will be reduced and $z_{\mathrm{face}}$ will be responsible for face features for the generation (See Fig. 7). In Sec. 5.5, we demonstrate the desired effect of $\mathcal{L}_{\mathrm{reg}}$ . The final loss of diffusion video autoencoders is as follows: $\mathcal{L}_{\mathrm{dva}} = \mathcal{L}_{\mathrm{simple}} + \mathcal{L}_{\mathrm{reg}}$ . + +# 4.2. Video Editing Framework + +We now describe our video editing framework with our diffusion video autoencoders. First, all video frames $\{I_n\}_{n=1}^N$ are aligned and cropped for interesting face regions as in [35]. The cropped frames $\{x_0^{(n)}\}_{n=1}^N$ are then encoded to latent features using our diffusion video autoencoder. To extract the representative identity feature of the video, we average identity features of each frame as + +$$ +z _ {\mathrm {i d , r e p}} = \frac {1}{N} \sum_ {n = 1} ^ {N} (z _ {\mathrm {i d}} ^ {(n)}), +$$ + +where $z_{\mathrm{id}}^{(n)} = E_{\mathrm{id}}(x_0^{(n)})$ . Similarly, the per-frame landmark feature is computed as $z_{\mathrm{lnd}}^{(n)} = E_{\mathrm{lnd}}(x_0^{(n)})$ to finally obtain per-frame face features $z_{\mathrm{face}}^{(n)} = MLP(z_{\mathrm{id,rep}},z_{\mathrm{lnd}}^{(n)})$ After that, we compute $x_{T}^{(n)}$ with DDIM forward process conditioning $z_{\mathrm{face}}^{(n)}$ . Thereafter, manipulation is conducted by editing $z_{\mathrm{id,rep}}$ to $z_{\mathrm{id,rep}}^{\mathrm{edit}}$ using a pretrained linear attribute-classifier of the identity space or text-based optimization which we will discuss in more detail later. After modifying the representative identity feature $z_{\mathrm{id,rep}}^{\mathrm{edit}}$ the edited frame $\hat{x}_0^{(n),\mathrm{edit}}$ is generated by the conditional + +![](images/a80446c6e986344b6f9b5b186bdd007b1e66e7e75e75ecfcc6b74f5333cb0611.jpg) +Figure 4. Comparison of temporal consistency to the previous video editing methods for 'beard'. + +reverse process with $(z_{\mathrm{face}}^{(n),\mathrm{edit}},x_T^{(n)})$ where $z_{\mathrm{face}}^{(n),\mathrm{edit}} = MLP(z_{\mathrm{id,rep}}^{\mathrm{edit}},z_{\mathrm{nd}}^{(n)})$ . Afterward, as with all previous work, the face part of the edited frame is pasted to the corresponding area of the original frame to create a clean final result. For this process, we segment face regions using a pretrained segmentation network [42]. Below, we explore two editing methods for our video editing framework. + +Classifier-based editing First, as in DiffAE [23], we train a linear classifier $C_{\text{attr}}(z_{\text{id}}) = \text{sigmoid}(w_{\text{attr}}^{\top} z_{\text{id}})$ for each attribute attr on CelebA-HQ's [10] with its attribute annotation in the identity feature space. To change attr, we move the identity feature $z_{\text{id}}$ to $\ell_2 \text{Norm}(z_{\text{id}} + sw_{\text{attr}})$ with a scale hyperparameter $s$ . + +CLIP-based editing Since the pretrained classifier allows editing only for several predefined attributes, we additionally devise the CLIP-guidance identity feature optimization method. Directional CLIP loss [7] requires two images corresponding to one for neutral text and one for target text, respectively. It implies that we need the synthesized images with our diffusion model, which is costly with full generative process. Therefore, to reduce the computational cost, we use the drastically reduced number of steps $S$ ( $\ll T$ ) for image sampling. In other words, we consider the time + +steps $t_1, t_2, \ldots, t_S$ where $0 = t_0 < t_1 < \ldots < t_S \leq T$ and evenly split $T$ . Thereafter, we compute $x_{t_s}$ from the given image $x_0$ that we want to edit (normally chosen as the first frame $x_0^{(1)}$ of the video) through $S$ -step of forward process with $z_{\mathrm{id}} = E_{\mathrm{id}}(x_0)$ . Through the sequential reverse steps from $x_{t_S}$ , we recover $\hat{x}_{t_s}$ for each time $t_s$ where $s = (S - 1), \ldots, 0$ with the original $z_{\mathrm{id}}$ . Meanwhile, $x_{t_s}^{\mathrm{edit}}$ are obtained by the single reverse step from $\hat{x}_{t_{s+1}}$ but with variable $z_{\mathrm{id}}^{\mathrm{opt}}$ being optimized initialized to $z_{\mathrm{id}}$ (See Fig. 3). Finally, we minimize the directional CLIP loss [7] between intermediate images $\hat{x}_{t_s}$ and $x_{t_s}^{\mathrm{edit}}$ , which are still noisy, for all $s$ with a neutral (e.g. "face") and a target text (e.g. "face with eyeglasses"). We choose intermediate images $x_{t_s}^{\mathrm{edit}}$ , $\hat{x}_{t_s}$ from $\hat{x}_{t_{s+1}}$ instead of estimated $x_0$ to compute CLIP loss because to estimate $x_0$ directly from $x_{t_s}$ is incomplete and erroneous for large $t_s$ . Therefore, we expect that conservatively choosing intermediate images will help to find the edit direction more reliably. We refer the reader to Appendix B for the ablation study of our noisy CLIP loss. In addition to the CLIP loss, to preserve the remaining attributes, we also use ID loss (cosine distance between $z_{\mathrm{id}}$ and $z_{\mathrm{id}}^{\mathrm{opt}}$ ) and $\ell_1$ loss between face parts of $\hat{x}_{t_s}$ and $x_{t_s}^{\mathrm{edit}}$ for all $s$ . After all, the learned editing step $\Delta z_{\mathrm{id}} = z_{\mathrm{id}}^{\mathrm{opt}} - z_{\mathrm{id}}$ is applied to $z_{\mathrm{id},\mathrm{rep}}$ . + +Table 1. Quantitative reconstruction results on the randomly chosen 20 videos in VoxCeleb1 test set. The reported values are the mean of the averaged per-frame measurements for each video. + +
MethodSSIM ↑MS-SSIM ↑LPIPS ↓MSE ↓
e4e [34]0.5090.7610.1570.037
PTI [27]0.7650.9390.0630.007
Ours (T=20)0.5400.9050.2280.016
Ours (T=100)0.9220.9890.0450.002
+ +Table 2. Quantitative results to evaluate temporal consistency. Ours show the best global coherency and comparable local consistency to the baselines. + +
MethodTL-IDTG-ID
Yao et al. [41]0.9890.920
Tzaban et al. [35]0.9970.961
Xu et al. [40]1.0020.983
Ours0.9950.996
+ +# 5. Experiments + +In this section, we present the experimental results to confirm reconstruction performance (Sec. 5.1), temporally consistent editing ability (Sec. 5.2), robustness to the unusual samples (Sec. 5.3), and disentanglement of the encoded features (Sec. 5.4) with further ablation study (Sec. 5.5). For this purpose, we train our diffusion video autoencoder on 77294 videos of the VoxCeleb1 dataset [18]. As preprocessing, frames of the video are aligned and cropped as in [35] like the FFHQ dataset. Next, they are resized to the size of $256^2$ . For the noise estimator $\epsilon_{\theta}$ , the UNet improved by [20] is used, and we train diffusion video autoencoder for 1 million steps with a batch size of 16. Please see more details in Appendix A. + +# 5.1. Reconstruction + +For video editing, the ability to reconstruct the original video from the encoded one must be preceded. Otherwise, we will lose the original one before we even edit the video. To compare this ability with baselines quantitatively, we measure frequently used metrics for reconstruction - SSIM [37], Multi-scaled (MS) SSIM [38], LPIPS [43], and MSE - on randomly selected 20 videos in the test set of VoxCeleb1. As baselines, we compared our model with the GAN-based inversion method e4e [34] and PTI [27] used by Yao et al. [41] and Tzaban et al. [35], respectively. Since StyleGAN-based methods handle the higher resolution images with the size of $1024^2$ , we resize the reconstructed results to $256^2$ for comparison. For our method, we vary the number of diffusion steps $T$ to observe computational cost and image quality trade-offs. In Tab. 1, our diffusion video autoencoder with $T = 100$ shows the best reconstruction ability and still outperforms e4e with only $T = 20$ . + +![](images/0b00644279b3a0a8e29abd98582847f2b4df2382d2fce9a3cf184d9422f48412.jpg) +Figure 5. Editing wild face videos that GAN-based prior works struggled with. Classifier-based editing is used to make the person "young" (up) or change a "gender" (below). + +# 5.2. Temporal Consistency + +In Fig. 4, a visual comparison is conducted to evaluate the video editing performance of our diffusion video autoencoder qualitatively. We edit the given video to generate a beard through text-based guidance except for Yao et al. [41], which only allows to edit predefined attributes, by moving to the opposite direction of "no_peat". As a result, we demonstrate that only our diffusion video autoencoder successfully produces the consistent result. Specifically, Yao et al. [41] fail to preserve the original identity due to the limitations of GAN inversion. In the result of Tzaban et al. [35], the shape and the amount of beard constantly changes according to the lip motion. Although Xu et al. [40] show better but not perfect consistency, the motions unintentionally change as a side effect. The inconsistency can be observed more clearly between the second and the fifth column except for ours showing a reliable result. + +Furthermore, we quantitatively evaluate the temporal consistency of Fig. 4 in Tab. 2. Although there is no perfect metric for temporal consistency of videos, TL-ID and TG-ID [35] imply the local and global consistency of identity between adjacent frames and across all frames, respectively, compared to the original. These metrics can be interpreted as being consistent as the original is when their values are close to 1. We emphasize that we greatly improve global consistency. TL-ID of Xu et al. [40] is larger than 1 because the motion of the editing results shrinks so that the adjacent frames become closer to each other than the original. Additional quantitative comparisons of temporal consistency, editing quality, and time cost are summarized in Appendix C. + +# 5.3. Editing Wild Face Videos + +Owing to the reconstructability of diffusion models, editing wild videos that are difficult to inversion by GAN-based methods becomes possible. As shown in Fig. 5, unlike others, our method robustly reconstructs and edits the given images effectively. + +![](images/b04f9ef57cadcf76dd754609c1035a8b7467c0ec6df1b0096a3eebb2573a7619.jpg) +Figure 6. Demonstration of the disentangled video encoding. + +# 5.4. Decomposed Features Analysis + +To demonstrate whether the diffusion video autoencoder decomposes the features adequately, we examine the synthesized images by changing each element of the decomposed features. To this end, we encode the frames of two different videos and then generate samples with a random noise or exchange the respective elements with each other in Fig. 6. When we decode the semantic latent $z_{\text{face}}$ with a Gaussian noise instead of the original noise latent $x_{T}$ , it has a blurry background that is different from the original one, while identity and head pose are preserved considerably. This result implies that $x_{T}$ contains only the background information, as we intended. Moreover, the generated images with switched identity, motion, and background feature confirm that the features are properly decomposed and the diffusion video autoencoder can produce a realistic image even with the new combination of the features. However, with extreme changes in the head position, the background occluded by the face is not properly generated because the taken $x_{T}$ has no information about background in that area (See the last column of the lower example in Fig. 6). + +# 5.5. Ablation Study + +We further conduct an ablation study on our proposed regularization loss $\mathcal{L}_{\mathrm{reg}}$ . First, we train the model with the same setting but ablating $\mathcal{L}_{\mathrm{reg}}$ . As shown in Fig. 7, neither model has a problem with reconstruction. However, without the regularization loss, the identity changes significantly according to the random noise. Thus we can conclude that the regularization loss helps the model to decompose features effectively. + +![](images/9b255761ec131f226c7a91e11e65ca0a5f42bbf35a5d624795df8c9e4f48857f.jpg) +Figure 7. Ablation of using regularization loss for training. Regularization loss helps the model to contain identity and motion information in $z_{\text{face}}$ as much as possible. + +# 6. Conclusions + +To tackle the temporal consistency problem in editing human face video, we have proposed a novel framework with the newly designed video diffusion autoencoder which encodes the identity, motion, and background information in a disentangled manner and decodes after editing a single identity feature. Through the disentanglement, the most valuable strength of our framework is that we can search the desired editing direction for only one frame and then edit the remaining frames with temporal consistency by moving the representative video identity feature. Additionally, the wild face video can be reliably edited by the advantage of the diffusion model that is superior in reconstruction to GAN. Finally, we have explored to optimize the semantic identity feature with CLIP loss for text-based video editing. Please refer to the Appendix D for the limitations and further discussion. + +Acknowledgement This work was supported by Institute of Information & communications Technology Planning & Evaluation (IITP) grant (No.2019-0-00075, Artificial Intelligence Graduate School Program(KAIST), No.2021-0-02068, Artificial Intelligence Innovation Hub, No.2022-0-00713, Meta-learning applicable to real-world problems, No.2022-0-00984, Development of Artificial Intelligence Technology for Personalized Plug-and-Play Explanation and Verification of Explanation) and the National Research Foundation of Korea (NRF) grants (No.2018R1A5A1059921) funded by the Korea government (MSIT). This work was also supported by KAIST-NAVER Hypercreative AI Center. + +# References + +[1] Yuval Alaluf, Or Patashnik, and Daniel Cohen-Or. Restyle: A residual-based stylegan encoder via iterative refinement. 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Face video editing. Our editing method shows improvement compared to the baseline [35] in terms of temporal consistency (left, \"eyeglasses\") and robustness to the unusual case such as the hand-occluded face (right, \"beard\")." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 304, + 232, + 529, + 403 + ], + "blocks": [ + { + "bbox": [ + 304, + 232, + 529, + 403 + ], + "lines": [ + { + "bbox": [ + 304, + 232, + 529, + 403 + ], + "spans": [ + { + "bbox": [ + 304, + 232, + 529, + 403 + ], + "type": "image", + "image_path": "3fe29fd617bd845440db7245378a97db358199992e8aca5e218426dcc808eee6.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 143, + 437, + 192, + 449 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 437, + 192, + 449 + ], + "spans": [ + { + "bbox": [ + 143, + 437, + 192, + 449 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 455, + 287, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 455, + 287, + 647 + ], + "spans": [ + { + "bbox": [ + 46, + 455, + 287, + 647 + ], + "type": "text", + "content": "Inspired by the impressive performance of recent face image editing methods, several studies have been naturally proposed to extend these methods to the face video editing task. One of the main challenges here is temporal consistency among edited frames, which is still unresolved. To this end, we propose a novel face video editing framework based on diffusion autoencoders that can successfully extract the decomposed features - for the first time as a face video editing model - of identity and motion from a given video. This modeling allows us to edit the video by simply manipulating the temporally invariant feature to the desired direction for the consistency. Another unique strength of our model is that, since our model is based on diffusion models, it can satisfy both reconstruction and edit capabilities at the same time, and is robust to corner cases in wild face videos (e.g. occluded faces) unlike the existing GAN-based methods.1" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 653, + 127, + 664 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 653, + 127, + 664 + ], + "spans": [ + { + "bbox": [ + 47, + 653, + 127, + 664 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 673, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 673, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 47, + 673, + 287, + 696 + ], + "type": "text", + "content": "As one of the standard tasks in computer vision to change various face attributes such as hair color, gender, or glasses" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 438, + 545, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 438, + 545, + 569 + ], + "spans": [ + { + "bbox": [ + 306, + 438, + 545, + 569 + ], + "type": "text", + "content": "of a given face image, face editing has been continuously gaining attention due to its various applications and entertainment. In particular, with the improvement of analysis and manipulation techniques for recent Generative Adversarial Network (GAN) models [8, 11, 22, 29, 30], we simply can do this task by manipulating a given image's latent feature. In addition, very recently, many methods for face image editing also have been proposed based on Diffusion Probabilistic Model (DPM)-based methods that show high-quality and flexible manipulation performance [3, 12, 17, 19, 23, 25]." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 570, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 665 + ], + "type": "text", + "content": "Naturally, further studies [2, 35, 41] have been proposed to extend image editing methods to incorporate the temporal axis for videos. Now, given real videos with a human face, these studies try to manipulate some target facial attributes with the other remaining features and motion intact. They all basically edit each frame of a video independently via off-the-shelf StyleGAN-based image editing techniques [22, 29, 41]." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 665, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 712 + ], + "type": "text", + "content": "Despite the advantages of StyleGAN in this task such as high-resolution image generation capability and highly disentangled semantic representation space, one harmful drawback of GAN-based editing methods is that the encoded real" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 202, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 202, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 202, + 712 + ], + "type": "text", + "content": "1Project page: https://diff-video-ae.github.io" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "6091" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "type": "text", + "content": "images cannot perfectly be recovered by the pretrained generator [1, 26, 34]. Especially, if a face in a given image is unusually decorated or occluded by some objects, the fixed generator cannot synthesize it. For perfect reconstruction, several methods [6, 27] are suggested to further tune the generator for GAN-inversion [26, 34] on one or a few target images, which is computationally expensive. Moreover, after the fine-tuning, the original editability of GANs cannot be guaranteed. This risk could be worse in video domain since we have to finetune the model on the multiple frames." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "spans": [ + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "text", + "content": "Aside from the reconstruction issue of existing GAN-based methods, it is critical in video editing tasks to consider the temporal consistency among edited frames to produce realistic results. To address this, some prior works rely on the smoothness of the latent trajectory of the original frames [35] or smoothen the latent features directly [2] by simply taking the same editing step for all frames. However, smoothness does not ensure temporal consistency. Rather, the same editing step can make different results for different frames because it can be unintentionally entangled with irrelevant motion features. For example, in the middle row of Fig. 1, eyeglasses vary across time and sometimes diminish when the man closes his eyes." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 352, + 289, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 352, + 289, + 591 + ], + "spans": [ + { + "bbox": [ + 46, + 352, + 289, + 591 + ], + "type": "text", + "content": "In this paper, we propose a novel video editing framework for human face video, termed Diffusion Video Autoencoder, that resolves the limitations of the prior works. First, instead of GAN-based editing methods suffering from imperfect reconstruction quality, we newly introduce diffusion based model for face video editing tasks. As the recently proposed diffusion autoencoder (DiffAE) [23] does, thanks to the expressive latent spaces of the same size as input space, our model learns a semantically meaningful latent space that can perfectly recover the original image back and are directly editable. Not only that, for the first time as a video editing model, encode the decomposed features of the video: 1) identity feature shared by all frames, 2) feature of motion or facial expression in each frame, and 3) background feature that could not have high-level representation due to large variances. Then, for consistent editing, we simply manipulate a single invariant feature for the desired attribute (single editing operation per video), which is also computationally beneficial compared to the prior works that require editing the latent features of all frames." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": "We experimentally demonstrate that our model appropriately decomposes videos into time-invariant and per-frame variant features and can provide temporally consistent manipulation. Specifically, we explore two ways of manipulation. The first one is to edit features in the predefined set of attributes by moving semantic features to the target direction found by learning linear classifier in semantic representation space on annotated CelebA-HQ dataset [10]. Additionally, we explore the text-based editing method that optimizes a time-invariant latent feature with CLIP loss [7]. It" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 545, + 119 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 119 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 119 + ], + "type": "text", + "content": "is worth noting that since we cannot fully generate edited images for CLIP loss due to the computational cost, we propose the novel strategy that rather uses latent state of intermediate time step for the efficiency." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 317, + 121, + 497, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 121, + 497, + 131 + ], + "spans": [ + { + "bbox": [ + 317, + 121, + 497, + 131 + ], + "type": "text", + "content": "To summarize, our contribution is four-fold:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 317, + 137, + 545, + 369 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 317, + 137, + 545, + 186 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 137, + 545, + 186 + ], + "spans": [ + { + "bbox": [ + 317, + 137, + 545, + 186 + ], + "type": "text", + "content": "- We devise diffusion video autoencoders based on diffusion autoencoders [23] that decompose the video into a single time-invariant and per-frame time-variant features for temporally consistent editing." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 191, + 545, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 191, + 545, + 251 + ], + "spans": [ + { + "bbox": [ + 317, + 191, + 545, + 251 + ], + "type": "text", + "content": "- Based on the decomposed representation of diffusion video autoencoder, face video editing can be conducted by editing only the single time-invariant identity feature and decoding it together with the remaining original features." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 317, + 256, + 545, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 256, + 545, + 304 + ], + "spans": [ + { + "bbox": [ + 317, + 256, + 545, + 304 + ], + "type": "text", + "content": "- Owing to the nearly-perfect reconstruction ability of diffusion models, our framework can be utilized to edit exceptional cases such that a face is partially occluded by some objects as well as usual cases." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 317, + 310, + 545, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 310, + 545, + 369 + ], + "spans": [ + { + "bbox": [ + 317, + 310, + 545, + 369 + ], + "type": "text", + "content": "- In addition to the existing predefined attributes editing method, we propose a text-based identity editing method based on the local directional CLIP loss [7,24] for the intermediately generated product of diffusion video autoencoders." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 381, + 392, + 394 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 381, + 392, + 394 + ], + "spans": [ + { + "bbox": [ + 306, + 381, + 392, + 394 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 402, + 545, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 402, + 545, + 485 + ], + "spans": [ + { + "bbox": [ + 304, + 402, + 545, + 485 + ], + "type": "text", + "content": "Video editing When editing a given real video, it is essential to preserve temporal consistency. First, Lai et al. [14] consider editing global features of videos such as artistic style transfer, colorization, image enhancement, etc. To encourage temporal consistency, they train sequential image translator with temporal loss defined as the warping error between the output frames." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 486, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 545, + 713 + ], + "type": "text", + "content": "Different from this work, our target task is to edit facial attributes of human face video. In other words, we aim to change face-related attributes such as eyeglasses, beards, etc. For this task, Yao et al. [41] are the first that propose the editing pipeline: 1) align and crop the target face area, 2) encode these frames to latent features, manipulate and decode them, and 3) unalign and paste the edited frames to the original video. However, every step of this pipeline is conducted independently for each frame. For the manipulation step, they try to find disentangled editing directions for a desired attribute and take the same step for every frame, while expecting the disentanglement brings consistency automatically. However, the results show inconsistency and we conjecture that both latent space and learned direction are still entangled with many other attributes. Next, Tza-ban et al. [35] additionally fine-tune the pretrained StyleGAN [27] to enhance reconstructability. Meanwhile, they assume that temporal consistency would be preserved when applying the same editing step to the latent features of the" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6092" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": "original frames. However, their assumption is not always true for all attributes, especially for beards and eyeglasses as shown in Fig. 1. Alauf et al. [2] also try to avoid temporal inconsistency by smoothing latent features." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 120, + 288, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 120, + 288, + 239 + ], + "spans": [ + { + "bbox": [ + 46, + 120, + 288, + 239 + ], + "type": "text", + "content": "While the methods in the previous paragraph handle inconsistency implicitly, several works [39, 40] try to solve it more directly. After per-frame editing, Xu et al. [40] further optimize latent codes and the pretrained StyleGAN to enhance consistency between the frame pairs defined by involving bi-directional optical flow. On the other hand, Xia et al. [39] propose to learn the dynamics of inverted GAN latent codes of video frames. The learned dynamics are used to generate the subsequent latent features after editing only the first frame." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 240, + 287, + 358 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 240, + 287, + 358 + ], + "spans": [ + { + "bbox": [ + 46, + 240, + 287, + 358 + ], + "type": "text", + "content": "Additionally, although Skorokhodov et al. [31] mainly target to generate video, they also demonstrate manipulation results of the generated video. They model the video with a time-invariant content code and per-frame motion codes. Based on this modeling, the generated video can be manipulated with a target text by optimizing its content vector with CLIP loss. However, they cannot edit the real videos due to the absence of an encoding method. In contrast, our proposed method is capable of encoding and manipulating realistic face videos." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 369, + 288, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 369, + 288, + 632 + ], + "spans": [ + { + "bbox": [ + 46, + 369, + 288, + 632 + ], + "type": "text", + "content": "Diffusion models Denoising diffusion probabilistic models (DDPMs) [9] associate image generation with the sequential denoising process of isotropic Gaussian noise. The model is trained to predict the noise from the input image. Unlike other generative models such as GANs and most traditional-style VAEs that encode input data in a low-dimensional space, diffusion models have a latent space that is the same size as the input. Although DDPMs require a lot of feed-forward steps to generate samples, their image fidelity and diversity are superior to other types of generative models. Compared to DDPMs that assume a Markovian noise-injecting forward diffusion process, Denoising diffusion implicit models (DDIMs) [33] assume a non-Markovian forward process that has the same marginal distribution as DDPMs, and use its corresponding reverse denoising process for sampling, which enables acceleration of the rather onerous sampling process of DDPMs. DDIMs also utilize a deterministic forward-backward process and therefore show nearly-perfect reconstruction ability, which is not the case for DDPMs. In this paper, we adopt conditional DDIMs to encode, manipulate and decode real videos." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "type": "text", + "content": "Image editing with diffusion models There are various attempts to manipulate images with diffusion models [3, 12, 17, 19, 23, 25] such as text-guided inpainting [3, 19, 25], stroke-based editing [17], and style transfer [12]. Among those, we are especially interested in facial attribute editing tasks. Kim et al. [12] propose text-based image ma" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 545, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 240 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 240 + ], + "type": "text", + "content": "nipulation by optimizing an unconditional diffusion model to minimize local directional CLIP loss [7]. This method is superior to GAN-based methods as it can successfully edit even occluded or overly decorated faces by the excellent reconstruction ability of diffusion models. However, due to the absence of semantically meaningful latent space, there exist some semantic features that are unable to be changed. Another parallel work proposes diffusion autoencoder (DiffAE) [23], which takes a learnable encoder to obtain semantic representations of which the underlying diffusion model is conditioned. The model can perform face attribute manipulation by moving the semantic vector to a target direction. Based on DiffAEs, we design our diffusion video autoencoders to perform temporally-consistent video editing." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 254, + 390, + 266 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 254, + 390, + 266 + ], + "spans": [ + { + "bbox": [ + 306, + 254, + 390, + 266 + ], + "type": "text", + "content": "3. Preliminaries" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 274, + 545, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 274, + 545, + 519 + ], + "spans": [ + { + "bbox": [ + 304, + 274, + 545, + 519 + ], + "type": "text", + "content": "Diffusion probabilistic models (DPMs) DPMs [9, 32] are generative models that attempt to approximate the data distribution " + }, + { + "bbox": [ + 304, + 274, + 545, + 519 + ], + "type": "inline_equation", + "content": "q(x_0)" + }, + { + "bbox": [ + 304, + 274, + 545, + 519 + ], + "type": "text", + "content": " via " + }, + { + "bbox": [ + 304, + 274, + 545, + 519 + ], + "type": "inline_equation", + "content": "p_{\\theta}(x_0)" + }, + { + "bbox": [ + 304, + 274, + 545, + 519 + ], + "type": "text", + "content": " from the reverse prediction of Markovian diffusion process " + }, + { + "bbox": [ + 304, + 274, + 545, + 519 + ], + "type": "inline_equation", + "content": "q(x_{1:T}|x_0) = \\prod_{t=1}^{T} q(x_t|x_{t-1})" + }, + { + "bbox": [ + 304, + 274, + 545, + 519 + ], + "type": "text", + "content": ". Here, the forward process of DPM is a Gaussian noise perturbation " + }, + { + "bbox": [ + 304, + 274, + 545, + 519 + ], + "type": "inline_equation", + "content": "q(x_t|x_{t-1}) = \\mathcal{N}(\\sqrt{1 - \\beta_t} x_{t-1}, \\beta_t I)" + }, + { + "bbox": [ + 304, + 274, + 545, + 519 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 274, + 545, + 519 + ], + "type": "inline_equation", + "content": "\\beta_t" + }, + { + "bbox": [ + 304, + 274, + 545, + 519 + ], + "type": "text", + "content": " is fixed or learned variance schedule with increasing " + }, + { + "bbox": [ + 304, + 274, + 545, + 519 + ], + "type": "inline_equation", + "content": "\\beta_1 < \\beta_2 < \\dots < \\beta_T" + }, + { + "bbox": [ + 304, + 274, + 545, + 519 + ], + "type": "text", + "content": ", adding gradually increasing noise to data " + }, + { + "bbox": [ + 304, + 274, + 545, + 519 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 304, + 274, + 545, + 519 + ], + "type": "text", + "content": ", and its reverse process is denoising of " + }, + { + "bbox": [ + 304, + 274, + 545, + 519 + ], + "type": "inline_equation", + "content": "x_t" + }, + { + "bbox": [ + 304, + 274, + 545, + 519 + ], + "type": "text", + "content": " step by step in reverse order. From this definition, a noisy image " + }, + { + "bbox": [ + 304, + 274, + 545, + 519 + ], + "type": "inline_equation", + "content": "x_t" + }, + { + "bbox": [ + 304, + 274, + 545, + 519 + ], + "type": "text", + "content": " at step " + }, + { + "bbox": [ + 304, + 274, + 545, + 519 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 274, + 545, + 519 + ], + "type": "text", + "content": " can be expressed as " + }, + { + "bbox": [ + 304, + 274, + 545, + 519 + ], + "type": "inline_equation", + "content": "x_t = \\sqrt{\\alpha_t} x_0 + \\sqrt{1 - \\alpha_t} \\epsilon" + }, + { + "bbox": [ + 304, + 274, + 545, + 519 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 274, + 545, + 519 + ], + "type": "inline_equation", + "content": "\\epsilon \\sim \\mathcal{N}(0, I)" + }, + { + "bbox": [ + 304, + 274, + 545, + 519 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 274, + 545, + 519 + ], + "type": "inline_equation", + "content": "\\alpha_t = \\prod_{s=1}^t (1 - \\beta_s)" + }, + { + "bbox": [ + 304, + 274, + 545, + 519 + ], + "type": "text", + "content": ". While the true reverse process " + }, + { + "bbox": [ + 304, + 274, + 545, + 519 + ], + "type": "inline_equation", + "content": "q(x_{t-1}|x_t)" + }, + { + "bbox": [ + 304, + 274, + 545, + 519 + ], + "type": "text", + "content": " is intractable, diffusion models approximate " + }, + { + "bbox": [ + 304, + 274, + 545, + 519 + ], + "type": "inline_equation", + "content": "q(x_{t-1}|x_t, x_0)" + }, + { + "bbox": [ + 304, + 274, + 545, + 519 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 274, + 545, + 519 + ], + "type": "inline_equation", + "content": "p_{\\theta}(x_{t-1}|x_t) = \\mathcal{N}(\\mu_{\\theta}(x_t, t), \\sigma_t)" + }, + { + "bbox": [ + 304, + 274, + 545, + 519 + ], + "type": "text", + "content": " by minimizing the variational lower bound of negative log-likelihood. Finally, by reparameterizing " + }, + { + "bbox": [ + 304, + 274, + 545, + 519 + ], + "type": "inline_equation", + "content": "\\mu_{\\theta}" + }, + { + "bbox": [ + 304, + 274, + 545, + 519 + ], + "type": "text", + "content": ", the objective is given as " + }, + { + "bbox": [ + 304, + 274, + 545, + 519 + ], + "type": "inline_equation", + "content": "\\mathbb{E}_{x_0 \\sim q(x_0), \\epsilon_t \\sim \\mathcal{N}(0, I), t} \\left\\| \\epsilon_{\\theta}(x_t, t) - \\epsilon_t \\right\\|_2^2" + }, + { + "bbox": [ + 304, + 274, + 545, + 519 + ], + "type": "text", + "content": " where the parameterized model " + }, + { + "bbox": [ + 304, + 274, + 545, + 519 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(x_t, t)" + }, + { + "bbox": [ + 304, + 274, + 545, + 519 + ], + "type": "text", + "content": " estimates the true Gaussian noise term " + }, + { + "bbox": [ + 304, + 274, + 545, + 519 + ], + "type": "inline_equation", + "content": "\\frac{1}{\\sqrt{1 - \\alpha_t}} (x_t - \\sqrt{\\alpha_t} x_0)" + }, + { + "bbox": [ + 304, + 274, + 545, + 519 + ], + "type": "text", + "content": " in the forward process." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 520, + 545, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 520, + 545, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 520, + 545, + 641 + ], + "type": "text", + "content": "Speeding up a time-consuming sampling process of diffusion models is one of the core research topics related to diffusion models [20, 33]. Among others, Song et al. [33] propose DDIM, which assumes a non-Markovian forward process " + }, + { + "bbox": [ + 304, + 520, + 545, + 641 + ], + "type": "inline_equation", + "content": "q(x_{t}|x_{t - 1},x_{0})" + }, + { + "bbox": [ + 304, + 520, + 545, + 641 + ], + "type": "text", + "content": " that has the same marginal distribution " + }, + { + "bbox": [ + 304, + 520, + 545, + 641 + ], + "type": "inline_equation", + "content": "q(x_{t}|x_{0})" + }, + { + "bbox": [ + 304, + 520, + 545, + 641 + ], + "type": "text", + "content": " with DDPMs. The corresponding generative process of DDIM is " + }, + { + "bbox": [ + 304, + 520, + 545, + 641 + ], + "type": "inline_equation", + "content": "x_{t - 1} = \\sqrt{\\alpha_{t - 1}} f_{\\theta}(x_t,t) + \\sqrt{1 - \\alpha_{t - 1} - \\sigma_t^2}\\epsilon_\\theta (x_t,t) + \\sigma_t^2 z" + }, + { + "bbox": [ + 304, + 520, + 545, + 641 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 520, + 545, + 641 + ], + "type": "inline_equation", + "content": "z\\sim \\mathcal{N}(0,I)" + }, + { + "bbox": [ + 304, + 520, + 545, + 641 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 520, + 545, + 641 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 304, + 520, + 545, + 641 + ], + "type": "text", + "content": " is sampling stochasticity and " + }, + { + "bbox": [ + 304, + 520, + 545, + 641 + ], + "type": "inline_equation", + "content": "f_{\\theta}(x_t,t)" + }, + { + "bbox": [ + 304, + 520, + 545, + 641 + ], + "type": "text", + "content": ", the estimated value of " + }, + { + "bbox": [ + 304, + 520, + 545, + 641 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 304, + 520, + 545, + 641 + ], + "type": "text", + "content": " at time step " + }, + { + "bbox": [ + 304, + 520, + 545, + 641 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 520, + 545, + 641 + ], + "type": "text", + "content": ", is as follow:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 352, + 652, + 499, + 680 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 352, + 652, + 499, + 680 + ], + "spans": [ + { + "bbox": [ + 352, + 652, + 499, + 680 + ], + "type": "interline_equation", + "content": "f _ {\\theta} (x _ {t}, t) = \\frac {x _ {t} - \\sqrt {1 - \\alpha_ {t}} \\epsilon_ {\\theta} (x _ {t} , t)}{\\sqrt {\\alpha_ {t}}}.", + "image_path": "84c8427999145c1fc9b4425acd3f14784c998dc16495e8a797e44f90594dd8e9.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "When " + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": " is set to 0, this process becomes deterministic. With deterministic forward and reverse processes, we can obtain" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6093" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 70, + 250, + 149 + ], + "blocks": [ + { + "bbox": [ + 51, + 70, + 250, + 149 + ], + "lines": [ + { + "bbox": [ + 51, + 70, + 250, + 149 + ], + "spans": [ + { + "bbox": [ + 51, + 70, + 250, + 149 + ], + "type": "image", + "image_path": "6d2d9d4d0fe4627368c7e2bd2e4aa9e40bc1af5396b06ba869c3cc069ebc1f1d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 48, + 151, + 250, + 263 + ], + "blocks": [ + { + "bbox": [ + 48, + 151, + 250, + 263 + ], + "lines": [ + { + "bbox": [ + 48, + 151, + 250, + 263 + ], + "spans": [ + { + "bbox": [ + 48, + 151, + 250, + 263 + ], + "type": "image", + "image_path": "8a3c0f47368448e904dc292f7c9c39e9c7ccc2fdc056331136b40eeebbe97fda.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 76, + 265, + 220, + 275 + ], + "lines": [ + { + "bbox": [ + 76, + 265, + 220, + 275 + ], + "spans": [ + { + "bbox": [ + 76, + 265, + 220, + 275 + ], + "type": "text", + "content": "(a) Video autoencoding and editing pipeline." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 192, + 281, + 400, + 293 + ], + "lines": [ + { + "bbox": [ + 192, + 281, + 400, + 293 + ], + "spans": [ + { + "bbox": [ + 192, + 281, + 400, + 293 + ], + "type": "text", + "content": "Figure 2. Overview of our Diffusion Video Autoencoder." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 262, + 69, + 544, + 261 + ], + "blocks": [ + { + "bbox": [ + 262, + 69, + 544, + 261 + ], + "lines": [ + { + "bbox": [ + 262, + 69, + 544, + 261 + ], + "spans": [ + { + "bbox": [ + 262, + 69, + 544, + 261 + ], + "type": "image", + "image_path": "b5ca203f0d7b7161828c724bb2986b3397462f495b0bb6cc1c5584ff2c097baf.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 366, + 264, + 440, + 274 + ], + "lines": [ + { + "bbox": [ + 366, + 264, + 440, + 274 + ], + "spans": [ + { + "bbox": [ + 366, + 264, + 440, + 274 + ], + "type": "text", + "content": "(b) Training objective." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 306, + 287, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 306, + 287, + 331 + ], + "spans": [ + { + "bbox": [ + 46, + 306, + 287, + 331 + ], + "type": "text", + "content": "the latent code of each original sample, which can reconstruct the original sample through the reverse process." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 336, + 289, + 648 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 336, + 289, + 648 + ], + "spans": [ + { + "bbox": [ + 46, + 336, + 289, + 648 + ], + "type": "text", + "content": "Diffusion autoencoders Due to the determinacy of its sampling process, DDIM can reconstruct the original image " + }, + { + "bbox": [ + 46, + 336, + 289, + 648 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 46, + 336, + 289, + 648 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 46, + 336, + 289, + 648 + ], + "type": "inline_equation", + "content": "x_T" + }, + { + "bbox": [ + 46, + 336, + 289, + 648 + ], + "type": "text", + "content": " obtained through " + }, + { + "bbox": [ + 46, + 336, + 289, + 648 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 336, + 289, + 648 + ], + "type": "text", + "content": " forward process steps. While " + }, + { + "bbox": [ + 46, + 336, + 289, + 648 + ], + "type": "inline_equation", + "content": "x_T" + }, + { + "bbox": [ + 46, + 336, + 289, + 648 + ], + "type": "text", + "content": " can be considered as a latent state with the same size as " + }, + { + "bbox": [ + 46, + 336, + 289, + 648 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 46, + 336, + 289, + 648 + ], + "type": "text", + "content": ", it does not contain high-level semantic information [23]. To supplement this, Prechakul et al. propose diffusion autoencoder (DiffAE) [23] based on DDIM. DiffAE utilizes two forms of latent variables: " + }, + { + "bbox": [ + 46, + 336, + 289, + 648 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{sem}}" + }, + { + "bbox": [ + 46, + 336, + 289, + 648 + ], + "type": "text", + "content": " for the useful high-level semantic representation and " + }, + { + "bbox": [ + 46, + 336, + 289, + 648 + ], + "type": "inline_equation", + "content": "x_T" + }, + { + "bbox": [ + 46, + 336, + 289, + 648 + ], + "type": "text", + "content": " for the remaining low-level stochasticity information. DiffAE introduces a semantic encoder " + }, + { + "bbox": [ + 46, + 336, + 289, + 648 + ], + "type": "inline_equation", + "content": "\\mathsf{Enc}(x_0)" + }, + { + "bbox": [ + 46, + 336, + 289, + 648 + ], + "type": "text", + "content": " which extracts " + }, + { + "bbox": [ + 46, + 336, + 289, + 648 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{sem}}" + }, + { + "bbox": [ + 46, + 336, + 289, + 648 + ], + "type": "text", + "content": " from an image, and makes a noise estimator " + }, + { + "bbox": [ + 46, + 336, + 289, + 648 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(x,t,z_{\\mathrm{sem}})" + }, + { + "bbox": [ + 46, + 336, + 289, + 648 + ], + "type": "text", + "content": " conditioned on " + }, + { + "bbox": [ + 46, + 336, + 289, + 648 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{sem}}" + }, + { + "bbox": [ + 46, + 336, + 289, + 648 + ], + "type": "text", + "content": ". Stochastic latent " + }, + { + "bbox": [ + 46, + 336, + 289, + 648 + ], + "type": "inline_equation", + "content": "x_T" + }, + { + "bbox": [ + 46, + 336, + 289, + 648 + ], + "type": "text", + "content": " is calculated through the deterministic DDIM forward process [33] that involves the noise estimator " + }, + { + "bbox": [ + 46, + 336, + 289, + 648 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 46, + 336, + 289, + 648 + ], + "type": "text", + "content": " given " + }, + { + "bbox": [ + 46, + 336, + 289, + 648 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{sem}}" + }, + { + "bbox": [ + 46, + 336, + 289, + 648 + ], + "type": "text", + "content": ". Then, " + }, + { + "bbox": [ + 46, + 336, + 289, + 648 + ], + "type": "inline_equation", + "content": "(z_{\\mathrm{sem}},x_T)" + }, + { + "bbox": [ + 46, + 336, + 289, + 648 + ], + "type": "text", + "content": " is decoded to reconstruct the corresponding original image " + }, + { + "bbox": [ + 46, + 336, + 289, + 648 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 46, + 336, + 289, + 648 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 46, + 336, + 289, + 648 + ], + "type": "inline_equation", + "content": "p_{\\theta}(x_{0:T}|z_{\\mathrm{sem}}) = p(x_T)\\prod_{t = 1}^{T}p_{\\theta}(x_{t - 1}|x_t,z_{\\mathrm{sem}})" + }, + { + "bbox": [ + 46, + 336, + 289, + 648 + ], + "type": "text", + "content": ". DiffAE is trained with simple DDPM loss, as done with DDIM. The differences between DiffAE and DDIM are that an additional variable " + }, + { + "bbox": [ + 46, + 336, + 289, + 648 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{sem}}" + }, + { + "bbox": [ + 46, + 336, + 289, + 648 + ], + "type": "text", + "content": " is involved as a conditioning variable during the reverse process (and thus the training process) and that the noise estimator " + }, + { + "bbox": [ + 46, + 336, + 289, + 648 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 46, + 336, + 289, + 648 + ], + "type": "text", + "content": " and semantic encoder Enc are jointly trained. As a result, through the training phase, " + }, + { + "bbox": [ + 46, + 336, + 289, + 648 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{sem}}" + }, + { + "bbox": [ + 46, + 336, + 289, + 648 + ], + "type": "text", + "content": " is learned to capture the high-level semantic information of the image, and the low-level stochastic variations remain in " + }, + { + "bbox": [ + 46, + 336, + 289, + 648 + ], + "type": "inline_equation", + "content": "x_T" + }, + { + "bbox": [ + 46, + 336, + 289, + 648 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 658, + 216, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 216, + 670 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 216, + 670 + ], + "type": "text", + "content": "4. Diffusion Video Autoencoders" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "content": "In this section, we introduce a video autoencoder, called Diffusion Video Autoencoder, specially designed for face video editing to have 1) superb reconstruction performance" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 306, + 545, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 306, + 545, + 378 + ], + "spans": [ + { + "bbox": [ + 304, + 306, + 545, + 378 + ], + "type": "text", + "content": "and 2) an editable representation space for the identity feature of the video disentangled with the per-frame features changing over time. The details of the model components and the training procedure are explained in Sec. 4.1 and then two different editing methods based on our model are presented in Sec. 4.2. We provide the overview in Fig. 2." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 384, + 468, + 398 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 384, + 468, + 398 + ], + "spans": [ + { + "bbox": [ + 305, + 384, + 468, + 398 + ], + "type": "text", + "content": "4.1. Disentangled Video Encoding" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 403, + 546, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 403, + 546, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 403, + 546, + 624 + ], + "type": "text", + "content": "To encode the video with " + }, + { + "bbox": [ + 304, + 403, + 546, + 624 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 403, + 546, + 624 + ], + "type": "text", + "content": " frames " + }, + { + "bbox": [ + 304, + 403, + 546, + 624 + ], + "type": "inline_equation", + "content": "\\{x_0^{(n)}\\}_{n = 1}^N" + }, + { + "bbox": [ + 304, + 403, + 546, + 624 + ], + "type": "text", + "content": ", we consider the time-invariant feature of human face videos as human identity information, and the time-dependent feature for each frame as motion and background information. Among these three, identity or motion information relevant to a face is appropriate to be projected to a low-dimensional space to extract high-level representation. Comparatively, the background shows high variance with arbitrary details and changes more with the head movement by cropping and aligning the face region. Therefore, it could be very difficult to encode the background information into a high-level semantic space. Thus, identity and motion features are encoded in high-level semantic space " + }, + { + "bbox": [ + 304, + 403, + 546, + 624 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{face}}^{(n)}" + }, + { + "bbox": [ + 304, + 403, + 546, + 624 + ], + "type": "text", + "content": ", combining identity feature " + }, + { + "bbox": [ + 304, + 403, + 546, + 624 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{id}}" + }, + { + "bbox": [ + 304, + 403, + 546, + 624 + ], + "type": "text", + "content": " of the video and motion feature " + }, + { + "bbox": [ + 304, + 403, + 546, + 624 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{land}}^{(n)}" + }, + { + "bbox": [ + 304, + 403, + 546, + 624 + ], + "type": "text", + "content": " of each frame, and the background feature is encoded in noise map " + }, + { + "bbox": [ + 304, + 403, + 546, + 624 + ], + "type": "inline_equation", + "content": "x_{T}^{(n)}" + }, + { + "bbox": [ + 304, + 403, + 546, + 624 + ], + "type": "text", + "content": " (see Fig. 2a). We denote " + }, + { + "bbox": [ + 304, + 403, + 546, + 624 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{id}}" + }, + { + "bbox": [ + 304, + 403, + 546, + 624 + ], + "type": "text", + "content": " without superscript " + }, + { + "bbox": [ + 304, + 403, + 546, + 624 + ], + "type": "inline_equation", + "content": "(n)" + }, + { + "bbox": [ + 304, + 403, + 546, + 624 + ], + "type": "text", + "content": " for frame index since it is the time-invariant and shared across all frames of the video." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 625, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 625, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 625, + 547, + 715 + ], + "type": "text", + "content": "To achieve this decomposition, our model consists of two separated semantic encoders - an identity encoder " + }, + { + "bbox": [ + 304, + 625, + 547, + 715 + ], + "type": "inline_equation", + "content": "E_{\\mathrm{id}}" + }, + { + "bbox": [ + 304, + 625, + 547, + 715 + ], + "type": "text", + "content": " and a landmark encoder " + }, + { + "bbox": [ + 304, + 625, + 547, + 715 + ], + "type": "inline_equation", + "content": "E_{\\mathrm{land}}" + }, + { + "bbox": [ + 304, + 625, + 547, + 715 + ], + "type": "text", + "content": " - and a conditional noise estimator " + }, + { + "bbox": [ + 304, + 625, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 304, + 625, + 547, + 715 + ], + "type": "text", + "content": " for diffusion modeling. The encoded features " + }, + { + "bbox": [ + 304, + 625, + 547, + 715 + ], + "type": "inline_equation", + "content": "(z_{\\mathrm{id}}, z_{\\mathrm{land}}^{(n)})" + }, + { + "bbox": [ + 304, + 625, + 547, + 715 + ], + "type": "text", + "content": " by the two encoders are concatenated and passed through an MLP to finally get a face-related feature " + }, + { + "bbox": [ + 304, + 625, + 547, + 715 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{face}}^{(n)}" + }, + { + "bbox": [ + 304, + 625, + 547, + 715 + ], + "type": "text", + "content": ". Next, to encode noise map " + }, + { + "bbox": [ + 304, + 625, + 547, + 715 + ], + "type": "inline_equation", + "content": "x_{T}^{(n)}" + }, + { + "bbox": [ + 304, + 625, + 547, + 715 + ], + "type": "text", + "content": ", we run the deterministic forward" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6094" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 170 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 170 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 170 + ], + "type": "text", + "content": "process of DDIM using noise estimator " + }, + { + "bbox": [ + 46, + 72, + 289, + 170 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 46, + 72, + 289, + 170 + ], + "type": "text", + "content": " with conditioned on " + }, + { + "bbox": [ + 46, + 72, + 289, + 170 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{face}}^{(n)}" + }, + { + "bbox": [ + 46, + 72, + 289, + 170 + ], + "type": "text", + "content": ". Since noise map " + }, + { + "bbox": [ + 46, + 72, + 289, + 170 + ], + "type": "inline_equation", + "content": "x_{T}^{(n)}" + }, + { + "bbox": [ + 46, + 72, + 289, + 170 + ], + "type": "text", + "content": " is a spatial variable with the same size as the image, it is expected that information in the background can be encoded more easily without loss of spatial information. Then, the encoded features " + }, + { + "bbox": [ + 46, + 72, + 289, + 170 + ], + "type": "inline_equation", + "content": "(x_{T}^{(n)}, z_{\\mathrm{face}}^{(n)})" + }, + { + "bbox": [ + 46, + 72, + 289, + 170 + ], + "type": "text", + "content": " can be reconstructed to the original frame by running generative reverse process of conditional DDIM in a deterministic manner:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 67, + 171, + 266, + 205 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 171, + 266, + 205 + ], + "spans": [ + { + "bbox": [ + 67, + 171, + 266, + 205 + ], + "type": "interline_equation", + "content": "p _ {\\theta} (x _ {0: T} | z _ {\\mathrm {f a c e}}) = p (x _ {T}) \\prod_ {t = 1} ^ {T} p _ {\\theta} (x _ {t - 1} | x _ {t}, z _ {\\mathrm {f a c e}}).", + "image_path": "cbe38871905638ab6b4ea4500ca0c5f8ce67a343fd4d7f63b5fab125c028ba2a.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 212, + 287, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 212, + 287, + 464 + ], + "spans": [ + { + "bbox": [ + 46, + 212, + 287, + 464 + ], + "type": "text", + "content": "To obtain the identity feature disentangled with the motion, we choose to leverage a pretrained model for identity detection, named ArcFace [5]. ArcFace is trained to classify human identity in face images regardless of poses or expressions, so we expect it to provide the disentangled property we need. Nevertheless, when an identity feature is extracted for each frame through the pretrained identity encoder, the feature may be slightly different for each frame because some frames may have partial identity features for some reasons (e.g. excessive side view poses). To alleviate this issue, we average the identity features " + }, + { + "bbox": [ + 46, + 212, + 287, + 464 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{id}}^{(n)} = E_{\\mathrm{id}}(x_0^{(n)})" + }, + { + "bbox": [ + 46, + 212, + 287, + 464 + ], + "type": "text", + "content": " of all frames in the inference phase. Similarly, we obtain per-frame motion information via a pretrained landmark detection model [4] which outputs the position of face landmarks. Several studies [21,36] have shown that it is possible to have a sufficiently disentangled nature by extracting features through a pretrained encoder without learning. Therefore, diffusion video autoencoders extract an identity and also a landmark feature of the image through the pretrained encoders and map them together to the high-level semantic space for face features through an additional learnable MLP." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 465, + 288, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 465, + 288, + 525 + ], + "spans": [ + { + "bbox": [ + 46, + 465, + 288, + 525 + ], + "type": "text", + "content": "Next, we explain how the learnable part of our model is trained. Fig. 2b summarizes our training process. For simplicity, from now on, we drop the superscript of frame index. Our objective consists of two parts. The first one is the simple version of DDPM loss [9] as" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 51, + 534, + 282, + 550 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 534, + 282, + 550 + ], + "spans": [ + { + "bbox": [ + 51, + 534, + 282, + 550 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {s i m p l e}} = \\mathbb {E} _ {x _ {0} \\sim q (x _ {0}), \\epsilon_ {t} \\sim \\mathcal {N} (0, I), t} \\left\\| \\epsilon_ {\\theta} (x _ {t}, t, z _ {\\mathrm {f a c e}}) - \\epsilon_ {t} \\right\\| _ {1}", + "image_path": "bc98cf506834e047b815104b4473bd8d464e1825ecaa70608cf872030aa191a4.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{face}}" + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "text", + "content": " is an encoded high-level feature of input image " + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "text", + "content": ". It encourages the useful information of the image to be well contained in the semantic latent " + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{face}}" + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "text", + "content": " and exploited by " + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "text", + "content": " for denoising. Secondly, we devise a regularization loss to hinder face information (identity and motion) from leaking to " + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "inline_equation", + "content": "x_{T}" + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "text", + "content": " but contained in " + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{face}}" + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "text", + "content": " as much as possible for clear decomposition between background and face information. If some face information is lost in " + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{face}}" + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "text", + "content": ", the lost information would remain in the noise latent " + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "inline_equation", + "content": "x_{T}" + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "text", + "content": " unintentionally. To avoid it, we sample two different Gaussian noises " + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\epsilon_1" + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\epsilon_2" + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "text", + "content": " to obtain different noisy samples " + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "inline_equation", + "content": "x_{t,1}" + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "inline_equation", + "content": "x_{t,2}" + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "text", + "content": ", respectively. Then, we minimize the difference between the estimated original images " + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "inline_equation", + "content": "f_{\\theta,1}" + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "inline_equation", + "content": "f_{\\theta,2}" + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "text", + "content": " except for the back" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 318, + 91, + 532, + 256 + ], + "blocks": [ + { + "bbox": [ + 326, + 73, + 527, + 84 + ], + "lines": [ + { + "bbox": [ + 326, + 73, + 527, + 84 + ], + "spans": [ + { + "bbox": [ + 326, + 73, + 527, + 84 + ], + "type": "text", + "content": "1. Conditional sampling with " + }, + { + "bbox": [ + 326, + 73, + 527, + 84 + ], + "type": "inline_equation", + "content": "z_{id}" + }, + { + "bbox": [ + 326, + 73, + 527, + 84 + ], + "type": "text", + "content": " for prediction of each noise level" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 318, + 91, + 532, + 256 + ], + "lines": [ + { + "bbox": [ + 318, + 91, + 532, + 256 + ], + "spans": [ + { + "bbox": [ + 318, + 91, + 532, + 256 + ], + "type": "image", + "image_path": "182bf31164a7bfe9b585dc0235394436b4fbb5234f9f82f3fb771f272ab0b3d9.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 323, + 260, + 527, + 271 + ], + "lines": [ + { + "bbox": [ + 323, + 260, + 527, + 271 + ], + "spans": [ + { + "bbox": [ + 323, + 260, + 527, + 271 + ], + "type": "text", + "content": "2. Conditional sampling with trainable " + }, + { + "bbox": [ + 323, + 260, + 527, + 271 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{id}}^{\\mathrm{opt}}" + }, + { + "bbox": [ + 323, + 260, + 527, + 271 + ], + "type": "text", + "content": " and optimize with " + }, + { + "bbox": [ + 323, + 260, + 527, + 271 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{CLIP}}" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 336, + 281, + 515, + 293 + ], + "lines": [ + { + "bbox": [ + 336, + 281, + 515, + 293 + ], + "spans": [ + { + "bbox": [ + 336, + 281, + 515, + 293 + ], + "type": "text", + "content": "Figure 3. Process of computing noisy CLIP loss." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 298, + 370, + 309 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 298, + 370, + 309 + ], + "spans": [ + { + "bbox": [ + 306, + 298, + 370, + 309 + ], + "type": "text", + "content": "ground part as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 308, + 316, + 542, + 332 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 316, + 542, + 332 + ], + "spans": [ + { + "bbox": [ + 308, + 316, + 542, + 332 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {r e g}} = \\mathbb {E} _ {x _ {0} \\sim q (x _ {0}), \\epsilon_ {1}, \\epsilon_ {2} \\sim \\mathcal {N} (0, I), t} \\left\\| f _ {\\theta , 1} \\odot m - f _ {\\theta , 2} \\odot m \\right\\| _ {1}", + "image_path": "5a5e50093799a0176c2438e041ff871a068175bc5d958b13c0c7ec5f68709c0c.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 337, + 546, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 337, + 546, + 422 + ], + "spans": [ + { + "bbox": [ + 305, + 337, + 546, + 422 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 337, + 546, + 422 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 305, + 337, + 546, + 422 + ], + "type": "text", + "content": " is a segmentation mask of a face region in the original image " + }, + { + "bbox": [ + 305, + 337, + 546, + 422 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 305, + 337, + 546, + 422 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 337, + 546, + 422 + ], + "type": "inline_equation", + "content": "f_{\\theta ,i} = f_{\\theta}(x_{t,i},t,z_{\\mathrm{face}})" + }, + { + "bbox": [ + 305, + 337, + 546, + 422 + ], + "type": "text", + "content": ". As a result, the effect of noise in " + }, + { + "bbox": [ + 305, + 337, + 546, + 422 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 305, + 337, + 546, + 422 + ], + "type": "text", + "content": " on the face region will be reduced and " + }, + { + "bbox": [ + 305, + 337, + 546, + 422 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{face}}" + }, + { + "bbox": [ + 305, + 337, + 546, + 422 + ], + "type": "text", + "content": " will be responsible for face features for the generation (See Fig. 7). In Sec. 5.5, we demonstrate the desired effect of " + }, + { + "bbox": [ + 305, + 337, + 546, + 422 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{reg}}" + }, + { + "bbox": [ + 305, + 337, + 546, + 422 + ], + "type": "text", + "content": ". The final loss of diffusion video autoencoders is as follows: " + }, + { + "bbox": [ + 305, + 337, + 546, + 422 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{dva}} = \\mathcal{L}_{\\mathrm{simple}} + \\mathcal{L}_{\\mathrm{reg}}" + }, + { + "bbox": [ + 305, + 337, + 546, + 422 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 428, + 451, + 441 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 428, + 451, + 441 + ], + "spans": [ + { + "bbox": [ + 306, + 428, + 451, + 441 + ], + "type": "text", + "content": "4.2. Video Editing Framework" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 446, + 545, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 446, + 545, + 533 + ], + "spans": [ + { + "bbox": [ + 305, + 446, + 545, + 533 + ], + "type": "text", + "content": "We now describe our video editing framework with our diffusion video autoencoders. First, all video frames " + }, + { + "bbox": [ + 305, + 446, + 545, + 533 + ], + "type": "inline_equation", + "content": "\\{I_n\\}_{n=1}^N" + }, + { + "bbox": [ + 305, + 446, + 545, + 533 + ], + "type": "text", + "content": " are aligned and cropped for interesting face regions as in [35]. The cropped frames " + }, + { + "bbox": [ + 305, + 446, + 545, + 533 + ], + "type": "inline_equation", + "content": "\\{x_0^{(n)}\\}_{n=1}^N" + }, + { + "bbox": [ + 305, + 446, + 545, + 533 + ], + "type": "text", + "content": " are then encoded to latent features using our diffusion video autoencoder. To extract the representative identity feature of the video, we average identity features of each frame as" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 375, + 539, + 477, + 571 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 375, + 539, + 477, + 571 + ], + "spans": [ + { + "bbox": [ + 375, + 539, + 477, + 571 + ], + "type": "interline_equation", + "content": "z _ {\\mathrm {i d , r e p}} = \\frac {1}{N} \\sum_ {n = 1} ^ {N} (z _ {\\mathrm {i d}} ^ {(n)}),", + "image_path": "be3aba724d3c6c0942e5916a7f07adb71e41b00f6ba946c225bf1ad08600ae39.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 579, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 579, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 579, + 547, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 579, + 547, + 715 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{id}}^{(n)} = E_{\\mathrm{id}}(x_0^{(n)})" + }, + { + "bbox": [ + 304, + 579, + 547, + 715 + ], + "type": "text", + "content": " . Similarly, the per-frame landmark feature is computed as " + }, + { + "bbox": [ + 304, + 579, + 547, + 715 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{lnd}}^{(n)} = E_{\\mathrm{lnd}}(x_0^{(n)})" + }, + { + "bbox": [ + 304, + 579, + 547, + 715 + ], + "type": "text", + "content": " to finally obtain per-frame face features " + }, + { + "bbox": [ + 304, + 579, + 547, + 715 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{face}}^{(n)} = MLP(z_{\\mathrm{id,rep}},z_{\\mathrm{lnd}}^{(n)})" + }, + { + "bbox": [ + 304, + 579, + 547, + 715 + ], + "type": "text", + "content": " After that, we compute " + }, + { + "bbox": [ + 304, + 579, + 547, + 715 + ], + "type": "inline_equation", + "content": "x_{T}^{(n)}" + }, + { + "bbox": [ + 304, + 579, + 547, + 715 + ], + "type": "text", + "content": " with DDIM forward process conditioning " + }, + { + "bbox": [ + 304, + 579, + 547, + 715 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{face}}^{(n)}" + }, + { + "bbox": [ + 304, + 579, + 547, + 715 + ], + "type": "text", + "content": " . Thereafter, manipulation is conducted by editing " + }, + { + "bbox": [ + 304, + 579, + 547, + 715 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{id,rep}}" + }, + { + "bbox": [ + 304, + 579, + 547, + 715 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 579, + 547, + 715 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{id,rep}}^{\\mathrm{edit}}" + }, + { + "bbox": [ + 304, + 579, + 547, + 715 + ], + "type": "text", + "content": " using a pretrained linear attribute-classifier of the identity space or text-based optimization which we will discuss in more detail later. After modifying the representative identity feature " + }, + { + "bbox": [ + 304, + 579, + 547, + 715 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{id,rep}}^{\\mathrm{edit}}" + }, + { + "bbox": [ + 304, + 579, + 547, + 715 + ], + "type": "text", + "content": " the edited frame " + }, + { + "bbox": [ + 304, + 579, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\hat{x}_0^{(n),\\mathrm{edit}}" + }, + { + "bbox": [ + 304, + 579, + 547, + 715 + ], + "type": "text", + "content": " is generated by the conditional" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6095" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 69, + 70, + 523, + 388 + ], + "blocks": [ + { + "bbox": [ + 69, + 70, + 523, + 388 + ], + "lines": [ + { + "bbox": [ + 69, + 70, + 523, + 388 + ], + "spans": [ + { + "bbox": [ + 69, + 70, + 523, + 388 + ], + "type": "image", + "image_path": "a80446c6e986344b6f9b5b186bdd007b1e66e7e75e75ecfcc6b74f5333cb0611.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 121, + 393, + 472, + 406 + ], + "lines": [ + { + "bbox": [ + 121, + 393, + 472, + 406 + ], + "spans": [ + { + "bbox": [ + 121, + 393, + 472, + 406 + ], + "type": "text", + "content": "Figure 4. Comparison of temporal consistency to the previous video editing methods for 'beard'." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 416, + 289, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 416, + 289, + 506 + ], + "spans": [ + { + "bbox": [ + 46, + 416, + 289, + 506 + ], + "type": "text", + "content": "reverse process with " + }, + { + "bbox": [ + 46, + 416, + 289, + 506 + ], + "type": "inline_equation", + "content": "(z_{\\mathrm{face}}^{(n),\\mathrm{edit}},x_T^{(n)})" + }, + { + "bbox": [ + 46, + 416, + 289, + 506 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 46, + 416, + 289, + 506 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{face}}^{(n),\\mathrm{edit}} = MLP(z_{\\mathrm{id,rep}}^{\\mathrm{edit}},z_{\\mathrm{nd}}^{(n)})" + }, + { + "bbox": [ + 46, + 416, + 289, + 506 + ], + "type": "text", + "content": ". Afterward, as with all previous work, the face part of the edited frame is pasted to the corresponding area of the original frame to create a clean final result. For this process, we segment face regions using a pretrained segmentation network [42]. Below, we explore two editing methods for our video editing framework." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 513, + 287, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 513, + 287, + 586 + ], + "spans": [ + { + "bbox": [ + 46, + 513, + 287, + 586 + ], + "type": "text", + "content": "Classifier-based editing First, as in DiffAE [23], we train a linear classifier " + }, + { + "bbox": [ + 46, + 513, + 287, + 586 + ], + "type": "inline_equation", + "content": "C_{\\text{attr}}(z_{\\text{id}}) = \\text{sigmoid}(w_{\\text{attr}}^{\\top} z_{\\text{id}})" + }, + { + "bbox": [ + 46, + 513, + 287, + 586 + ], + "type": "text", + "content": " for each attribute attr on CelebA-HQ's [10] with its attribute annotation in the identity feature space. To change attr, we move the identity feature " + }, + { + "bbox": [ + 46, + 513, + 287, + 586 + ], + "type": "inline_equation", + "content": "z_{\\text{id}}" + }, + { + "bbox": [ + 46, + 513, + 287, + 586 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 513, + 287, + 586 + ], + "type": "inline_equation", + "content": "\\ell_2 \\text{Norm}(z_{\\text{id}} + sw_{\\text{attr}})" + }, + { + "bbox": [ + 46, + 513, + 287, + 586 + ], + "type": "text", + "content": " with a scale hyperparameter " + }, + { + "bbox": [ + 46, + 513, + 287, + 586 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 513, + 287, + 586 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "content": "CLIP-based editing Since the pretrained classifier allows editing only for several predefined attributes, we additionally devise the CLIP-guidance identity feature optimization method. Directional CLIP loss [7] requires two images corresponding to one for neutral text and one for target text, respectively. It implies that we need the synthesized images with our diffusion model, which is costly with full generative process. Therefore, to reduce the computational cost, we use the drastically reduced number of steps " + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\ll T" + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "content": ") for image sampling. In other words, we consider the time" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "spans": [ + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "text", + "content": "steps " + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "inline_equation", + "content": "t_1, t_2, \\ldots, t_S" + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "inline_equation", + "content": "0 = t_0 < t_1 < \\ldots < t_S \\leq T" + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "text", + "content": " and evenly split " + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "text", + "content": ". Thereafter, we compute " + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "inline_equation", + "content": "x_{t_s}" + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "text", + "content": " from the given image " + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "text", + "content": " that we want to edit (normally chosen as the first frame " + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "inline_equation", + "content": "x_0^{(1)}" + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "text", + "content": " of the video) through " + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "text", + "content": "-step of forward process with " + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{id}} = E_{\\mathrm{id}}(x_0)" + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "text", + "content": ". Through the sequential reverse steps from " + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "inline_equation", + "content": "x_{t_S}" + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "text", + "content": ", we recover " + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "inline_equation", + "content": "\\hat{x}_{t_s}" + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "text", + "content": " for each time " + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "inline_equation", + "content": "t_s" + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "inline_equation", + "content": "s = (S - 1), \\ldots, 0" + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "text", + "content": " with the original " + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{id}}" + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "text", + "content": ". Meanwhile, " + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "inline_equation", + "content": "x_{t_s}^{\\mathrm{edit}}" + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "text", + "content": " are obtained by the single reverse step from " + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "inline_equation", + "content": "\\hat{x}_{t_{s+1}}" + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "text", + "content": " but with variable " + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{id}}^{\\mathrm{opt}}" + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "text", + "content": " being optimized initialized to " + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{id}}" + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "text", + "content": " (See Fig. 3). Finally, we minimize the directional CLIP loss [7] between intermediate images " + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "inline_equation", + "content": "\\hat{x}_{t_s}" + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "inline_equation", + "content": "x_{t_s}^{\\mathrm{edit}}" + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "text", + "content": ", which are still noisy, for all " + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "text", + "content": " with a neutral (e.g. \"face\") and a target text (e.g. \"face with eyeglasses\"). We choose intermediate images " + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "inline_equation", + "content": "x_{t_s}^{\\mathrm{edit}}" + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "inline_equation", + "content": "\\hat{x}_{t_s}" + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "inline_equation", + "content": "\\hat{x}_{t_{s+1}}" + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "text", + "content": " instead of estimated " + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "text", + "content": " to compute CLIP loss because to estimate " + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "text", + "content": " directly from " + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "inline_equation", + "content": "x_{t_s}" + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "text", + "content": " is incomplete and erroneous for large " + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "inline_equation", + "content": "t_s" + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "text", + "content": ". Therefore, we expect that conservatively choosing intermediate images will help to find the edit direction more reliably. We refer the reader to Appendix B for the ablation study of our noisy CLIP loss. In addition to the CLIP loss, to preserve the remaining attributes, we also use ID loss (cosine distance between " + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{id}}" + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{id}}^{\\mathrm{opt}}" + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "text", + "content": ") and " + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "inline_equation", + "content": "\\ell_1" + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "text", + "content": " loss between face parts of " + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "inline_equation", + "content": "\\hat{x}_{t_s}" + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "inline_equation", + "content": "x_{t_s}^{\\mathrm{edit}}" + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "text", + "content": " for all " + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "text", + "content": ". After all, the learned editing step " + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "inline_equation", + "content": "\\Delta z_{\\mathrm{id}} = z_{\\mathrm{id}}^{\\mathrm{opt}} - z_{\\mathrm{id}}" + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "text", + "content": " is applied to " + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{id},\\mathrm{rep}}" + }, + { + "bbox": [ + 304, + 418, + 547, + 709 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6096" + } + ] + } + ], + "index": 6 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 110, + 285, + 169 + ], + "blocks": [ + { + "bbox": [ + 47, + 71, + 287, + 104 + ], + "lines": [ + { + "bbox": [ + 47, + 71, + 287, + 104 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 287, + 104 + ], + "type": "text", + "content": "Table 1. Quantitative reconstruction results on the randomly chosen 20 videos in VoxCeleb1 test set. The reported values are the mean of the averaged per-frame measurements for each video." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 110, + 285, + 169 + ], + "lines": [ + { + "bbox": [ + 50, + 110, + 285, + 169 + ], + "spans": [ + { + "bbox": [ + 50, + 110, + 285, + 169 + ], + "type": "table", + "html": "
MethodSSIM ↑MS-SSIM ↑LPIPS ↓MSE ↓
e4e [34]0.5090.7610.1570.037
PTI [27]0.7650.9390.0630.007
Ours (T=20)0.5400.9050.2280.016
Ours (T=100)0.9220.9890.0450.002
", + "image_path": "b770392dfbadc03845032b9a65a16f1adaa843cde7624a59954b3f237ded2245.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 92, + 220, + 242, + 283 + ], + "blocks": [ + { + "bbox": [ + 47, + 182, + 286, + 214 + ], + "lines": [ + { + "bbox": [ + 47, + 182, + 286, + 214 + ], + "spans": [ + { + "bbox": [ + 47, + 182, + 286, + 214 + ], + "type": "text", + "content": "Table 2. Quantitative results to evaluate temporal consistency. Ours show the best global coherency and comparable local consistency to the baselines." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 92, + 220, + 242, + 283 + ], + "lines": [ + { + "bbox": [ + 92, + 220, + 242, + 283 + ], + "spans": [ + { + "bbox": [ + 92, + 220, + 242, + 283 + ], + "type": "table", + "html": "
MethodTL-IDTG-ID
Yao et al. [41]0.9890.920
Tzaban et al. [35]0.9970.961
Xu et al. [40]1.0020.983
Ours0.9950.996
", + "image_path": "ad71b8be527c1e37c09723c2a04d003d33e80cc29e11af902a5d661ff37f0da2.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 300, + 127, + 314 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 300, + 127, + 314 + ], + "spans": [ + { + "bbox": [ + 47, + 300, + 127, + 314 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 323, + 286, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 323, + 286, + 477 + ], + "spans": [ + { + "bbox": [ + 46, + 323, + 286, + 477 + ], + "type": "text", + "content": "In this section, we present the experimental results to confirm reconstruction performance (Sec. 5.1), temporally consistent editing ability (Sec. 5.2), robustness to the unusual samples (Sec. 5.3), and disentanglement of the encoded features (Sec. 5.4) with further ablation study (Sec. 5.5). For this purpose, we train our diffusion video autoencoder on 77294 videos of the VoxCeleb1 dataset [18]. As preprocessing, frames of the video are aligned and cropped as in [35] like the FFHQ dataset. Next, they are resized to the size of " + }, + { + "bbox": [ + 46, + 323, + 286, + 477 + ], + "type": "inline_equation", + "content": "256^2" + }, + { + "bbox": [ + 46, + 323, + 286, + 477 + ], + "type": "text", + "content": ". For the noise estimator " + }, + { + "bbox": [ + 46, + 323, + 286, + 477 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 46, + 323, + 286, + 477 + ], + "type": "text", + "content": ", the UNet improved by [20] is used, and we train diffusion video autoencoder for 1 million steps with a batch size of 16. Please see more details in Appendix A." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 490, + 140, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 490, + 140, + 502 + ], + "spans": [ + { + "bbox": [ + 47, + 490, + 140, + 502 + ], + "type": "text", + "content": "5.1. Reconstruction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 510, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 286, + 713 + ], + "type": "text", + "content": "For video editing, the ability to reconstruct the original video from the encoded one must be preceded. Otherwise, we will lose the original one before we even edit the video. To compare this ability with baselines quantitatively, we measure frequently used metrics for reconstruction - SSIM [37], Multi-scaled (MS) SSIM [38], LPIPS [43], and MSE - on randomly selected 20 videos in the test set of VoxCeleb1. As baselines, we compared our model with the GAN-based inversion method e4e [34] and PTI [27] used by Yao et al. [41] and Tzaban et al. [35], respectively. Since StyleGAN-based methods handle the higher resolution images with the size of " + }, + { + "bbox": [ + 46, + 510, + 286, + 713 + ], + "type": "inline_equation", + "content": "1024^2" + }, + { + "bbox": [ + 46, + 510, + 286, + 713 + ], + "type": "text", + "content": ", we resize the reconstructed results to " + }, + { + "bbox": [ + 46, + 510, + 286, + 713 + ], + "type": "inline_equation", + "content": "256^2" + }, + { + "bbox": [ + 46, + 510, + 286, + 713 + ], + "type": "text", + "content": " for comparison. For our method, we vary the number of diffusion steps " + }, + { + "bbox": [ + 46, + 510, + 286, + 713 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 510, + 286, + 713 + ], + "type": "text", + "content": " to observe computational cost and image quality trade-offs. In Tab. 1, our diffusion video autoencoder with " + }, + { + "bbox": [ + 46, + 510, + 286, + 713 + ], + "type": "inline_equation", + "content": "T = 100" + }, + { + "bbox": [ + 46, + 510, + 286, + 713 + ], + "type": "text", + "content": " shows the best reconstruction ability and still outperforms e4e with only " + }, + { + "bbox": [ + 46, + 510, + 286, + 713 + ], + "type": "inline_equation", + "content": "T = 20" + }, + { + "bbox": [ + 46, + 510, + 286, + 713 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 307, + 71, + 545, + 202 + ], + "blocks": [ + { + "bbox": [ + 307, + 71, + 545, + 202 + ], + "lines": [ + { + "bbox": [ + 307, + 71, + 545, + 202 + ], + "spans": [ + { + "bbox": [ + 307, + 71, + 545, + 202 + ], + "type": "image", + "image_path": "0b00644279b3a0a8e29abd98582847f2b4df2382d2fce9a3cf184d9422f48412.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 208, + 545, + 242 + ], + "lines": [ + { + "bbox": [ + 305, + 208, + 545, + 242 + ], + "spans": [ + { + "bbox": [ + 305, + 208, + 545, + 242 + ], + "type": "text", + "content": "Figure 5. Editing wild face videos that GAN-based prior works struggled with. Classifier-based editing is used to make the person \"young\" (up) or change a \"gender\" (below)." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 247, + 432, + 261 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 247, + 432, + 261 + ], + "spans": [ + { + "bbox": [ + 306, + 247, + 432, + 261 + ], + "type": "text", + "content": "5.2. Temporal Consistency" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 266, + 545, + 458 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 266, + 545, + 458 + ], + "spans": [ + { + "bbox": [ + 304, + 266, + 545, + 458 + ], + "type": "text", + "content": "In Fig. 4, a visual comparison is conducted to evaluate the video editing performance of our diffusion video autoencoder qualitatively. We edit the given video to generate a beard through text-based guidance except for Yao et al. [41], which only allows to edit predefined attributes, by moving to the opposite direction of \"no_peat\". As a result, we demonstrate that only our diffusion video autoencoder successfully produces the consistent result. Specifically, Yao et al. [41] fail to preserve the original identity due to the limitations of GAN inversion. In the result of Tzaban et al. [35], the shape and the amount of beard constantly changes according to the lip motion. Although Xu et al. [40] show better but not perfect consistency, the motions unintentionally change as a side effect. The inconsistency can be observed more clearly between the second and the fifth column except for ours showing a reliable result." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 459, + 545, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 459, + 545, + 626 + ], + "spans": [ + { + "bbox": [ + 304, + 459, + 545, + 626 + ], + "type": "text", + "content": "Furthermore, we quantitatively evaluate the temporal consistency of Fig. 4 in Tab. 2. Although there is no perfect metric for temporal consistency of videos, TL-ID and TG-ID [35] imply the local and global consistency of identity between adjacent frames and across all frames, respectively, compared to the original. These metrics can be interpreted as being consistent as the original is when their values are close to 1. We emphasize that we greatly improve global consistency. TL-ID of Xu et al. [40] is larger than 1 because the motion of the editing results shrinks so that the adjacent frames become closer to each other than the original. Additional quantitative comparisons of temporal consistency, editing quality, and time cost are summarized in Appendix C." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 634, + 447, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 634, + 447, + 647 + ], + "spans": [ + { + "bbox": [ + 306, + 634, + 447, + 647 + ], + "type": "text", + "content": "5.3. Editing Wild Face Videos" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": "Owing to the reconstructability of diffusion models, editing wild videos that are difficult to inversion by GAN-based methods becomes possible. As shown in Fig. 5, unlike others, our method robustly reconstructs and edits the given images effectively." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6097" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 286, + 283 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 286, + 283 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 286, + 283 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 286, + 283 + ], + "type": "image", + "image_path": "b04f9ef57cadcf76dd754609c1035a8b7467c0ec6df1b0096a3eebb2573a7619.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 56, + 288, + 277, + 300 + ], + "lines": [ + { + "bbox": [ + 56, + 288, + 277, + 300 + ], + "spans": [ + { + "bbox": [ + 56, + 288, + 277, + 300 + ], + "type": "text", + "content": "Figure 6. Demonstration of the disentangled video encoding." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 316, + 214, + 330 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 316, + 214, + 330 + ], + "spans": [ + { + "bbox": [ + 47, + 316, + 214, + 330 + ], + "type": "text", + "content": "5.4. Decomposed Features Analysis" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 338, + 289, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 338, + 289, + 579 + ], + "spans": [ + { + "bbox": [ + 46, + 338, + 289, + 579 + ], + "type": "text", + "content": "To demonstrate whether the diffusion video autoencoder decomposes the features adequately, we examine the synthesized images by changing each element of the decomposed features. To this end, we encode the frames of two different videos and then generate samples with a random noise or exchange the respective elements with each other in Fig. 6. When we decode the semantic latent " + }, + { + "bbox": [ + 46, + 338, + 289, + 579 + ], + "type": "inline_equation", + "content": "z_{\\text{face}}" + }, + { + "bbox": [ + 46, + 338, + 289, + 579 + ], + "type": "text", + "content": " with a Gaussian noise instead of the original noise latent " + }, + { + "bbox": [ + 46, + 338, + 289, + 579 + ], + "type": "inline_equation", + "content": "x_{T}" + }, + { + "bbox": [ + 46, + 338, + 289, + 579 + ], + "type": "text", + "content": ", it has a blurry background that is different from the original one, while identity and head pose are preserved considerably. This result implies that " + }, + { + "bbox": [ + 46, + 338, + 289, + 579 + ], + "type": "inline_equation", + "content": "x_{T}" + }, + { + "bbox": [ + 46, + 338, + 289, + 579 + ], + "type": "text", + "content": " contains only the background information, as we intended. Moreover, the generated images with switched identity, motion, and background feature confirm that the features are properly decomposed and the diffusion video autoencoder can produce a realistic image even with the new combination of the features. However, with extreme changes in the head position, the background occluded by the face is not properly generated because the taken " + }, + { + "bbox": [ + 46, + 338, + 289, + 579 + ], + "type": "inline_equation", + "content": "x_{T}" + }, + { + "bbox": [ + 46, + 338, + 289, + 579 + ], + "type": "text", + "content": " has no information about background in that area (See the last column of the lower example in Fig. 6)." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 595, + 141, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 595, + 141, + 609 + ], + "spans": [ + { + "bbox": [ + 47, + 595, + 141, + 609 + ], + "type": "text", + "content": "5.5. Ablation Study" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 618, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 287, + 715 + ], + "type": "text", + "content": "We further conduct an ablation study on our proposed regularization loss " + }, + { + "bbox": [ + 46, + 618, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{reg}}" + }, + { + "bbox": [ + 46, + 618, + 287, + 715 + ], + "type": "text", + "content": ". First, we train the model with the same setting but ablating " + }, + { + "bbox": [ + 46, + 618, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{reg}}" + }, + { + "bbox": [ + 46, + 618, + 287, + 715 + ], + "type": "text", + "content": ". As shown in Fig. 7, neither model has a problem with reconstruction. However, without the regularization loss, the identity changes significantly according to the random noise. Thus we can conclude that the regularization loss helps the model to decompose features effectively." + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 310, + 70, + 545, + 260 + ], + "blocks": [ + { + "bbox": [ + 310, + 70, + 545, + 260 + ], + "lines": [ + { + "bbox": [ + 310, + 70, + 545, + 260 + ], + "spans": [ + { + "bbox": [ + 310, + 70, + 545, + 260 + ], + "type": "image", + "image_path": "9b255761ec131f226c7a91e11e65ca0a5f42bbf35a5d624795df8c9e4f48857f.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 266, + 545, + 300 + ], + "lines": [ + { + "bbox": [ + 305, + 266, + 545, + 300 + ], + "spans": [ + { + "bbox": [ + 305, + 266, + 545, + 300 + ], + "type": "text", + "content": "Figure 7. Ablation of using regularization loss for training. Regularization loss helps the model to contain identity and motion information in " + }, + { + "bbox": [ + 305, + 266, + 545, + 300 + ], + "type": "inline_equation", + "content": "z_{\\text{face}}" + }, + { + "bbox": [ + 305, + 266, + 545, + 300 + ], + "type": "text", + "content": " as much as possible." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 317, + 384, + 330 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 317, + 384, + 330 + ], + "spans": [ + { + "bbox": [ + 306, + 317, + 384, + 330 + ], + "type": "text", + "content": "6. Conclusions" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 342, + 545, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 342, + 545, + 534 + ], + "spans": [ + { + "bbox": [ + 304, + 342, + 545, + 534 + ], + "type": "text", + "content": "To tackle the temporal consistency problem in editing human face video, we have proposed a novel framework with the newly designed video diffusion autoencoder which encodes the identity, motion, and background information in a disentangled manner and decodes after editing a single identity feature. Through the disentanglement, the most valuable strength of our framework is that we can search the desired editing direction for only one frame and then edit the remaining frames with temporal consistency by moving the representative video identity feature. Additionally, the wild face video can be reliably edited by the advantage of the diffusion model that is superior in reconstruction to GAN. Finally, we have explored to optimize the semantic identity feature with CLIP loss for text-based video editing. Please refer to the Appendix D for the limitations and further discussion." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 557, + 546, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 546, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 546, + 715 + ], + "type": "text", + "content": "Acknowledgement This work was supported by Institute of Information & communications Technology Planning & Evaluation (IITP) grant (No.2019-0-00075, Artificial Intelligence Graduate School Program(KAIST), No.2021-0-02068, Artificial Intelligence Innovation Hub, No.2022-0-00713, Meta-learning applicable to real-world problems, No.2022-0-00984, Development of Artificial Intelligence Technology for Personalized Plug-and-Play Explanation and Verification of Explanation) and the National Research Foundation of Korea (NRF) grants (No.2018R1A5A1059921) funded by the Korea government (MSIT). This work was also supported by KAIST-NAVER Hypercreative AI Center." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6098" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "text", + "content": "[1] Yuval Alaluf, Or Patashnik, and Daniel Cohen-Or. 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Illustration of the SceneDiffuser, applicable to various scene-conditioned 3D tasks: (a) human pose generation, (b) human motion generation, (c) dexterous grasp generation, (d) path planning for 3D navigation with goals, and (e) motion planning for robot arms." + ], + "image_footnote": [], + "bbox": [ + 78, + 321, + 895, + 577 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 619, + 313, + 635 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We introduce the SceneDiffuser, a conditional generative model for 3D scene understanding. SceneDiffuser provides a unified model for solving scene-conditioned generation, optimization, and planning. In contrast to prior work, SceneDiffuser is intrinsically scene-aware, physics-based, and goal-oriented. With an iterative sampling strategy, SceneDiffuser jointly formulates the scene-aware generation, physics-based optimization, and goal-oriented planning via a diffusion-based denoising process in a fully differentiable fashion. Such a design alleviates the discrepancies among different modules and the posterior collapse of previous scene-conditioned generative models. We evaluate the SceneDiffuser on various 3D scene understanding tasks, including human pose and motion generation, dexterous grasp", + "bbox": [ + 75, + 643, + 473, + 854 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "generation, path planning for 3D navigation, and motion planning for robot arms. The results show significant improvements compared with previous models, demonstrating the tremendous potential of the SceneDiffuser for the broad community of 3D scene understanding.", + "bbox": [ + 500, + 621, + 893, + 696 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 709, + 632, + 724 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The ability to generate, optimize, and plan in 3D scenes is a long-standing goal across computer vision, graphics, and robotics. Various tasks have been devised to achieve these goals, fostering downstream applications in motion generation [32, 69, 73, 90], motion planning [42, 43, 60, 75], grasp generation [25, 31, 34], navigation [1, 95], scene synthesis [24, 47, 72, 82], embodied perception and manipulation [30, 39, 61], and autonomous driving [3, 52].", + "bbox": [ + 496, + 734, + 893, + 854 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Despite rich applications and great successes, existing models designed for these tasks exhibit two fundamental limitations for real-world 3D scene understanding.", + "bbox": [ + 498, + 854, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* These authors contributed equally to this work.", + "bbox": [ + 99, + 862, + 362, + 875 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "Corresponding authors: Siyuan Huang (syhuang@bigai.ai) and Wei Liang (liangwei@bit.edu.cn).", + "bbox": [ + 76, + 875, + 468, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "16750", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "First, most prior work [8, 14, 32, 49, 60, 68-70, 73] leverages the conditional Variational Autoencoder (cVAE) for the conditional generation in 3D scenes. cVAE model utilizes an encoder-decoder structure to learn the posterior distribution and relies on the learned latent variables to sample. Although cVAE is easy to train and sample due to its simple architecture and one-step sampling procedure, it suffers from the posterior collapse problem [12, 17, 26, 64, 69, 84, 93]; the learned latent variable is ignored by a strong decoder, leading to limited generation diversity from these collapsed modes. Such collapse is further magnified in 3D tasks with stronger 3D decoders and more complex and noisy input conditions, e.g., the natural 3D scans [9].", + "bbox": [ + 75, + 90, + 472, + 287 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Second, despite the close relations among generation, optimization, and planning in 3D scenes, there lacks a unified framework that could address existing discrepancies among these models. Previous work [15, 34, 69] applies off-the-shelf physics-based post-optimization methods over outputs of generative models and often produces inconsistent and implausible generations, especially when transferring to novel scenes. Similarly, planners are usually standalone modules over results of generative model [8, 14] for trajectory planning or learned separately with the reinforcement learning (RL) [95], leading to gaps between planning and other modules (e.g., generation) during inference, especially in novel scenes where explorations are limited.", + "bbox": [ + 75, + 290, + 472, + 487 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To tackle the above limitations, we introduce the SceneDiffuser, a conditional generative model based on the diffusion process. SceneDiffuser eliminates the discrepancies and provides a single home for scene-conditioned generation, optimization, and planning. Specifically, with a denoising process, it learns a diffusion model for scene-conditioned generation during training. In inference, SceneDiffuser jointly solves the scene-aware generation, physics-based optimization, and goal-oriented planning through a unified iterative guided-sampling framework. Such a design equips the SceneDiffuser with the following three superiority:", + "bbox": [ + 75, + 489, + 472, + 656 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. Generation: Building upon the diffusion model, SceneDiffuser solves the posterior collapse problem of scene-conditioned generative models. Since the forward diffusion process can be treated as data augmentation in 3D scenes, it helps traverse sufficient scene-conditioned distribution modes.", + "2. Optimization: SceneDiffuser integrates the physics-based objective into each step of the sampling process as conditional guidance, enabling the differentiable physics-based optimization during both the learning and sampling process. This design facilitates the physically-plausible generation, which is critical for tasks in 3D scenes.", + "3. Planning: Based on the scene-conditioned trajectory-level generator, SceneDiffuser possesses a physics- and goal-aware trajectory planner, generalizing better to long-horizon trajectories and novel 3D scenes." + ], + "bbox": [ + 76, + 657, + 472, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "As illustrated in Fig. 1, we evaluate the SceneDiffuser on diverse 3D scene understanding tasks. The human pose, motion, and dexterous grasp generation results significantly improve, demonstrating plausible and diverse generations with the 3D scene and object conditions. The results on path planning for 3D navigation and motion planning for robot arms reveal the generalizable and long-horizon planning capability of the SceneDiffuser.", + "bbox": [ + 496, + 90, + 893, + 212 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 224, + 640, + 242 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Conditional Generation in 3D Scenes Generating diverse contents and rich interactions in 3D scenes is essential for understanding the 3D scene affordances. Several applications have emerged on conditional scene generation [24,47,71,81,88], human pose [16,32,87,90,92] and motion generation [14,32,49,60,68-70,73] in furnished 3D indoor scenes, and object-conditioned grasp pose generation [25,31,34,62,78]. However, most previous methods [6,14,16,25,31,62,68,73,75] rely on cVAE and suffer from the posterior collapse problem [12,17,26,64,69,84,93], especially when the 3D scene is natural and complex. In this work, SceneDiffuser addresses the posterior collapse with the diffusion-based denoising process.", + "bbox": [ + 496, + 251, + 895, + 446 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Physics-based Optimization in 3D Scenes Producing physically plausible generations compatible with 3D scenes is challenging in the scene-conditioned generation. Previous work uses physics-based post-optimization [15, 34, 69] or differentiable objective [25, 73, 90] to integrate collision and contact constraints into the generation framework. However, post-optimization approaches [15, 34, 69] cannot be learned jointly with the generative models, yielding inconsistent generation results. Similarly, differentiable approaches [25, 73, 90] impose constraints on the final objective and cannot optimize the physical interactions during sampling, resulting in implausible generations, particularly when adapting to novel scenes. In this work, SceneDiffuser avoids such inconsistency by integrating differentiable physics-based optimization into each step of the sampling process.", + "bbox": [ + 496, + 448, + 895, + 674 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Planning in 3D Scenes The ability to act and plan in 3D scenes is critical for an intelligent agent and has led to the recent culmination of embodied AI research [28, 30, 33, 36, 54, 55, 79]. Among all tasks, visual navigation has been most studied in the vision and robotics community [4, 13, 21, 40, 76, 77, 94, 95]. However, existing work relies heavily on model-based planners with the single-step dynamic model [5,11,48,67,74,80], lacking a trajectory-level optimization for long-horizon planning. Further, these planners lack explicit modeling of physical interactions, making it difficult to generalize to natural scenes with limited exploration, where rapid learning and adaptation are required. Compared with the global trajectory planner based on a trajectory-level generator, SceneDiffuser exhibits superior generalization in long-horizon plans and novel 3D scenes.", + "bbox": [ + 496, + 674, + 895, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "16751", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Diffusion-based Models Diffusion model [19,22,57, 59] has come forth into a promising class of generative model for learning and sampling data distributions with an iterative denoising process, facilitating the image [10, 58], text [83], and shape generation [35]. With flexible conditioning, it is further extended to the language-conditioned image [41, 51, 53], video [18, 56], and 3D generation [44, 63, 85]. Notably, Janner et al. [23] integrate the generation and planning into the same sampling framework for behavior synthesis. To our best knowledge, SceneDiffuser is the first framework that models the 3D scene-conditioned generation with a diffusion model and integrates the generation, optimization, and planning into a unified framework.", + "bbox": [ + 76, + 90, + 472, + 287 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Background", + "text_level": 1, + "bbox": [ + 76, + 299, + 205, + 316 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem Definition", + "text_level": 1, + "bbox": [ + 76, + 323, + 259, + 338 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a 3D scene $S$ , we aim to generate the optimal solution for completing the tasks (e.g., navigation, manipulation) given the goal $\\mathcal{G}$ in the scene. We denote the state and action of an agent as $(\\mathbf{s},\\mathbf{a})$ . The dynamic model defines the state transition as $p(\\mathbf{s}_{i + 1}|\\mathbf{s}_i,\\mathbf{a}_i)$ , which is often deterministic in scene understanding (i.e., $f(\\mathbf{s}_i,\\mathbf{a}_i)$ ). The trajectory is defined as $\\boldsymbol{\\tau} = (\\mathbf{s}_0,\\mathbf{a}_0,\\dots ,\\mathbf{s}_i,\\mathbf{a}_i,\\dots ,\\mathbf{s}_N)$ , where $N$ denotes the horizon of task solving in discrete time.", + "bbox": [ + 76, + 345, + 472, + 467 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Planning with Trajectory Optimization", + "text_level": 1, + "bbox": [ + 76, + 474, + 413, + 491 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The scene-conditional trajectory optimization is defined as maximizing the task objective:", + "bbox": [ + 76, + 498, + 468, + 527 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\tau} ^ {*} = \\underset {\\boldsymbol {\\tau}} {\\arg \\max } \\mathcal {J} (\\boldsymbol {\\tau} | \\mathcal {S}, \\mathcal {G}). \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 532, + 468, + 555 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The dynamic model is usually known for trajectory optimization. Considering the future actions and states with predictable dynamics, the entire trajectory $\\tau$ can be optimized jointly and non-progressively with traditional [29] or data-driven [7] planning algorithms. Trajectory-based optimization benefits from its global awareness of history and future states, thus can better model the long-horizon tasks compared with single-step models in RL, where $\\mathbf{a}_{0:N}^{*} =$", + "bbox": [ + 76, + 560, + 472, + 681 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\underset {\\mathbf {a} _ {0: N}} {\\arg \\max } \\sum_ {i = 0} ^ {N} r (\\mathbf {s} _ {i}, \\mathbf {a} _ {i} | \\mathcal {S}, \\mathcal {G}).\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 681, + 256, + 720 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Diffusion Model", + "text_level": 1, + "bbox": [ + 76, + 726, + 238, + 739 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Diffusion model [19,22,57] is a class of generative models representing the data generation with an iterative denoising process from Gaussian noise. It consists of a forward and a reverse process. The forward process $q(\\tau^t |\\tau^{t - 1})$ gradually destroys data $\\tau^0\\sim q(\\tau^0)$ into Gaussian noise. The parametrized reverse process $p_{\\theta}(\\tau^{t - 1}|\\tau^t)$ recovers the data from noise with the learned normal distribution from a fixed timestep. The training objective for $\\theta$ is denoising score matching over multiple noise scale [22,66]. Please refer to the Appendix A for details of diffusion model and variants.", + "bbox": [ + 76, + 750, + 472, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. SceneDiffuser", + "text_level": 1, + "bbox": [ + 500, + 89, + 640, + 104 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "SceneDiffuser models planning as trajectory optimization and solves the aforementioned problem with the spirit of planning as sampling, where the trajectory optimization is achieved by sampling trajectory-level distribution learned by the model. Leveraging the diffusion model with gradient-based sampling and flexible conditioning, SceneDiffuser models the scene-conditioned goal-oriented trajectory $p(\\tau^0 | S, \\mathcal{G})$ :", + "bbox": [ + 496, + 114, + 893, + 236 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} p \\left(\\boldsymbol {\\tau} ^ {0} | \\mathcal {S}, \\mathcal {G}\\right) = \\frac {p _ {\\theta} \\left(\\boldsymbol {\\tau} ^ {0} | \\mathcal {S}\\right) p _ {\\phi} \\left(\\mathcal {G} \\mid \\boldsymbol {\\tau} ^ {0} , \\mathcal {S}\\right)}{p \\left(\\mathcal {G} \\mid \\mathcal {S}\\right)} \\tag {2} \\\\ \\propto p _ {\\theta} (\\tau^ {0} | \\mathcal {S}) p _ {\\phi} (\\mathcal {G} | \\tau^ {0}, \\mathcal {S}). \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 580, + 242, + 890, + 292 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Generation $p_{\\theta}(\\pmb{\\tau}^{0}|\\mathcal{S})$ characterizes the probability of generating certain trajectories with the scene condition. It can be modeled using a conditional diffusion model [19, 57] with an iterative denoising process:", + "bbox": [ + 496, + 300, + 893, + 361 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\theta} \\left(\\boldsymbol {\\tau} ^ {0} \\mid \\mathcal {S}\\right) = p \\left(\\boldsymbol {\\tau} ^ {T}\\right) \\prod_ {t = 1} ^ {T} p \\left(\\boldsymbol {\\tau} ^ {t - 1} \\mid \\boldsymbol {\\tau} ^ {t}, \\mathcal {S}\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 549, + 369, + 890, + 404 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\np (\\boldsymbol {\\tau} ^ {t - 1} | \\boldsymbol {\\tau} ^ {t}, \\mathcal {S}) = \\mathcal {N} (\\boldsymbol {\\tau} ^ {t - 1}; \\boldsymbol {\\mu} _ {\\theta} (\\boldsymbol {\\tau} ^ {t}, t, \\mathcal {S}), \\boldsymbol {\\Sigma} _ {\\theta} (\\boldsymbol {\\tau} ^ {t}, t, \\mathcal {S})).\n$$\n", + "text_format": "latex", + "bbox": [ + 521, + 406, + 852, + 424 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Optimization and Planning $p_{\\phi}(\\mathcal{G}|\\boldsymbol{\\tau}^0,\\mathcal{S})$ represents the probability of reaching the goal with the sampled trajectory, where the goal can be flexibly defined by customized objective functions in various tasks. As shown in Eq. (4), the precise definition of this probability is $p_{\\phi}(\\mathcal{O} = 1|\\boldsymbol{\\tau}^0,\\mathcal{S},\\mathcal{G})$ where $O$ is an optimality indicator that represents if the goal were achieved. Intuitively, the trajectory objective in Eq. (1) can indicate such optimality. We therefore expand $p_{\\phi}(\\mathcal{G}|\\boldsymbol{\\tau}^t,\\mathcal{S})$ as its exponential in Eq. (5):", + "bbox": [ + 496, + 431, + 893, + 568 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\phi} (\\mathcal {G} | \\boldsymbol {\\tau} ^ {t}, \\mathcal {S}) = p _ {\\phi} \\left(\\mathcal {O} = 1 | \\boldsymbol {\\tau} ^ {t}, \\mathcal {S}, \\mathcal {G}\\right) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 547, + 577, + 890, + 594 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\propto \\exp (\\mathcal {J} (\\boldsymbol {\\tau} ^ {t} | \\mathcal {S}, \\mathcal {G})) \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 627, + 598, + 890, + 614 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n= \\exp \\left(\\varphi_ {p} \\left(\\boldsymbol {\\tau} ^ {t} | \\mathcal {S}, \\mathcal {G}\\right) + \\varphi_ {o} \\left(\\boldsymbol {\\tau} ^ {t} | \\mathcal {S}\\right), \\right. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 627, + 617, + 890, + 635 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\varphi_{o}(\\pmb{\\tau}^{t}|\\mathcal{S})$ denotes the objective for optimizing the trajectory with scene condition and is independent of task goal $\\mathcal{G}$ . In scene understanding, $\\varphi_{o}$ usually denotes plausible physical relationships (e.g., collision, contact, and intersection). $\\varphi_{p}(\\pmb{\\tau}^{t}|\\mathcal{S},\\mathcal{G})$ indicates the objective for planning (i.e., goal-reaching) with scene condition. Both $\\varphi_{o}$ and $\\varphi_{p}$ can be explicitly defined or implicitly learned from observed trajectories with proper parametrization.", + "bbox": [ + 496, + 643, + 893, + 765 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Learning", + "text_level": 1, + "bbox": [ + 500, + 773, + 607, + 789 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$p_{\\theta}(\\tau^0 |S)$ is the scene-conditioned generator, which can be learned by the conditional diffusion model with the simplified objective of estimating the noise $\\epsilon$ [10, 19, 20], where", + "bbox": [ + 496, + 796, + 893, + 842 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\theta} \\left(\\boldsymbol {\\tau} ^ {0} \\mid \\mathcal {S}\\right) = \\mathbb {E} _ {t, \\epsilon , \\boldsymbol {\\tau} ^ {0}} \\left[ \\| \\boldsymbol {\\epsilon} - \\boldsymbol {\\epsilon} _ {\\theta} \\left(\\sqrt {\\hat {\\alpha} ^ {t}} \\boldsymbol {\\tau} ^ {0} + \\sqrt {1 - \\hat {\\alpha} ^ {t}} \\boldsymbol {\\epsilon}, t, \\mathcal {S}\\right) \\| ^ {2} \\right] \\tag {7} \\\\ = \\mathbb {E} _ {t, \\epsilon , \\tau^ {0}} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} (\\tau^ {t}, t, S) \\| ^ {2} \\right], \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 513, + 859, + 890, + 904 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "16752", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\hat{\\alpha}^t$ is the pre-determined function in the forward process. With the learned $p_{\\theta}(\\tau^0 |S)$ , we sample $p(\\tau^0 |S,\\mathcal{G})$ by taking the advantage of the diffusion model's flexible conditioning [10, 23]. Specifically, we approximate $p_{\\phi}(\\mathcal{G}|\\boldsymbol{\\tau}^{t},\\mathcal{S})$ using the Taylor expansion around $\\boldsymbol{\\tau}^{t} = \\boldsymbol{\\mu}$ at timestep $t$ as", + "bbox": [ + 75, + 90, + 472, + 167 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\log p _ {\\phi} (\\mathcal {G} | \\boldsymbol {\\tau} ^ {t}, \\mathcal {S}) \\approx (\\boldsymbol {\\tau} ^ {t} - \\boldsymbol {\\mu}) \\mathbf {g} + C, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 166, + 174, + 468, + 191 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $C$ is a constant, $\\pmb{\\mu} = \\pmb{\\mu}_{\\theta}(\\pmb{\\tau}^t,t,\\mathcal{S})$ and $\\Sigma = \\Sigma_{\\theta}(\\pmb{\\tau}^{t},t,\\mathcal{S})$ are the inferred parameters of original diffusion process, and", + "bbox": [ + 76, + 200, + 470, + 246 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathbf {g} = \\nabla_ {\\boldsymbol {\\tau} ^ {t}} \\log p _ {\\phi} (\\mathcal {G} | \\boldsymbol {\\tau} ^ {t}, \\mathcal {S}) | _ {\\boldsymbol {\\tau} ^ {t} = \\boldsymbol {\\mu}} \\tag {9} \\\\ = \\nabla_ {\\tau^ {t}} \\left(\\varphi_ {o} \\left(\\tau^ {t} | \\mathcal {S}\\right) + \\varphi_ {p} \\left(\\tau^ {t} | \\mathcal {S}, \\mathcal {G}\\right)\\right) | _ {\\tau^ {t} = \\mu}. \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 143, + 253, + 468, + 291 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Therefore, we have", + "bbox": [ + 76, + 299, + 207, + 311 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np \\left(\\boldsymbol {\\tau} ^ {t - 1} \\mid \\boldsymbol {\\tau} ^ {t}, \\mathcal {S}, \\mathcal {G}\\right) = \\mathcal {N} \\left(\\boldsymbol {\\tau} ^ {t - 1}; \\boldsymbol {\\mu} + \\lambda \\boldsymbol {\\Sigma} \\mathbf {g}, \\boldsymbol {\\Sigma}\\right), \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 321, + 468, + 338 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\lambda$ is the scaling factor for the guidance. With Eq. (10), we can sample $\\pmb{\\tau}^t$ with the guidance of optimizing and planning objectives.", + "bbox": [ + 75, + 348, + 470, + 392 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Of note, $\\varphi_{p}$ and $\\varphi_{o}$ serve as the pre-defined guidance for tilting the original trajectory with physical and goal constraints. However, they can also be learned from the observed trajectories. During training, we first fix the learned base model of $p_{\\theta}(\\tau^0 |S)$ , followed by learning $\\phi_{o}$ and $\\phi_{p}$ for optimization and planning with the following objective:", + "bbox": [ + 75, + 393, + 470, + 484 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\phi} \\left(\\boldsymbol {\\tau} ^ {0} \\mid \\mathcal {S}, \\mathcal {G}\\right) = \\mathbb {E} _ {t, \\epsilon , \\boldsymbol {\\tau} ^ {0}} \\left[ \\left\\| \\boldsymbol {\\epsilon} - \\boldsymbol {\\epsilon} _ {\\theta} \\left(\\boldsymbol {\\tau} ^ {t}, t, \\mathcal {S}\\right) - \\boldsymbol {\\Sigma} \\mathbf {g} \\right\\| ^ {2} \\right]. \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 106, + 491, + 468, + 510 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Alg. 1 summarizes the training procedure.", + "bbox": [ + 76, + 518, + 354, + 532 + ], + "page_idx": 3 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1: Training SceneDiffuser" + ], + "code_body": "1 // train base generation model \nInput: Trajectory in 3D scene $(\\tau^0, S)$ \n2 repeat \n3 $\\tau^0 \\sim p(\\tau^0 | S)$ \n4 $\\epsilon \\sim \\mathcal{N}(0, I), t \\sim \\mathcal{U}(\\{1, \\dots, T\\})$ \n5 $\\pmb{\\tau}^t = \\sqrt{\\hat{\\alpha}_t} \\pmb{\\tau}_0 + \\sqrt{1 - \\hat{\\alpha}_t} \\pmb{\\epsilon}$ \n6 $\\theta = \\theta - \\eta \\nabla_\\theta \\| \\pmb{\\epsilon} - \\pmb{\\epsilon}_\\theta (\\pmb{\\tau}^t, t, S) \\|_2^2$ \n7 until converged; \n8 // (optional) train optimization and planning model \nInput: Trajectory in 3D scene with goal $(\\tau^0, S, G)$ , learned $\\theta$ for $p_\\theta(\\tau^0 | S)$ \n9 repeat \n10 $\\pmb{\\tau}^0 \\sim p(\\pmb{\\tau}^0 | S, G)$ \n11 $\\epsilon \\sim \\mathcal{N}(0, I), t \\sim \\mathcal{U}(\\{1, \\dots, T\\})$ \n12 $\\pmb{\\mu} = \\pmb{\\mu}_\\theta(\\pmb{\\tau}^t, t, S), \\pmb{\\Sigma} = \\pmb{\\Sigma}_\\theta(\\pmb{\\tau}^t, t, S)$ \n13 $\\mathbf{g} = \\nabla_{\\pmb{\\tau}^t} \\log p_\\phi(\\mathcal{G} | \\pmb{\\tau}^t, S) |_{\\pmb{\\tau}^t = \\pmb{\\mu}}$ \n14 $\\pmb{\\tau}^t = \\sqrt{\\hat{\\alpha}_t} \\pmb{\\tau}_0 + \\sqrt{1 - \\hat{\\alpha}_t} \\pmb{\\epsilon}$ \n15 $\\phi = \\phi - \\eta \\nabla_\\phi \\| \\pmb{\\epsilon} - \\pmb{\\epsilon}_\\theta(\\pmb{\\tau}^t, t, S) - \\lambda \\pmb{\\Sigma} \\mathbf{g} \\|_2^2$ \n16 until converged;", + "bbox": [ + 81, + 556, + 468, + 797 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Sampling", + "text_level": 1, + "bbox": [ + 76, + 816, + 186, + 832 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "With different sampling strategies, SceneDiffuser can generate, optimize, and plan the trajectory in 3D scenes under a unified framework of guided sampling. Alg. 2 summarizes the detailed sampling algorithm.", + "bbox": [ + 75, + 839, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 2: Sampling SceneDiffuser for generation, optimization, and planning" + ], + "code_body": "Modules: Model $p_{\\theta}(\\cdot |\\mathcal{S})$ , optimization objective $\\varphi_o(\\cdot |\\mathcal{S})$ , and planner objective $\\varphi_p(\\cdot |\\mathcal{S},\\mathcal{G})$ \n1 // one-step guided sampling \n2 function sample $(\\tau^t,\\mathcal{J})$ .. \n3 $\\mu = \\mu_{\\theta}(\\tau^{t},t,\\mathcal{S}),\\Sigma = \\Sigma_{\\theta}(\\tau^{t},t,\\mathcal{S})$ \n4 $\\tau^{t - 1} = \\mathcal{N}(\\tau^{t - 1};\\mu +\\lambda \\Sigma \\nabla_{\\tau^t}(\\mathcal{J}(\\tau^t |\\mathcal{S},\\mathcal{G}))|_{\\tau^t = \\mu},\\Sigma)$ \n5 return $\\tau^{t - 1}$ \n6 // physics-based generation Input: initial trajectory $\\tau^T\\sim \\mathcal{N}(0,\\mathbf{I})$ \n7 for $t = T,\\dots ,1$ do \n8 // sampling with optimization \n9 $\\tau^{t - 1} = \\mathrm{sample}(\\tau^t,\\varphi_o(\\cdot |\\mathcal{S}))$ \n10 return $\\tau^0$ \n11 // goal-oriented planning Input: planning steps $N$ starting state $\\hat{\\mathbf{s}}_0$ , initial plan $\\tau_0^T\\sim \\mathcal{N}(0,\\mathbf{I})$ \n12 $i = 1$ \n13 while not done and planning step $i < N$ do \n14 for $t = T,\\dots ,1$ do \n15 $\\tau_i^{t - 1} = \\mathrm{sample}(\\tau_i^t,\\varphi_o(\\cdot |\\mathcal{S}) + \\varphi_p(\\cdot |\\mathcal{S},\\mathcal{G}))$ \n16 // planning as inpainting \n17 $\\tau_i^{t - 1}[0:i] = \\hat{\\mathbf{s}}_{0:i}$ \n18 Act $\\hat{a}_{i - 1}$ to reach $\\hat{\\mathbf{s}}_i = \\boldsymbol {\\tau}_i^0 [i],\\hat{\\mathbf{s}}_{0:i} = \\hat{\\mathbf{s}}_{0:i - 1}\\cup \\hat{\\mathbf{s}}_i$ \n19 Increment planning step $i = i + 1$", + "bbox": [ + 506, + 126, + 890, + 426 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Scene-aware Generation Sampling $\\pmb{\\tau}^{0}$ from the distribution $p_{\\theta}(\\pmb{\\tau}^{0}|\\mathcal{S})$ in Eq. (3) directly solves the conditional generation tasks. The sampled trajectories represent diverse modes and possible interactions with the 3D scenes.", + "bbox": [ + 496, + 441, + 893, + 501 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Physics-based Optimization In a differentiable manner, the physical relations between each state and the environment are defined by $\\varphi_{o}$ in Eq. (4). For general optimization without the planning objective, the task goal $\\mathcal{G}$ is to sample a plausible trajectory in 3D scenes. Therefore, we can draw physically plausible trajectories in 3D scenes by sampling from $p(\\tau^0 |S,\\mathcal{G})$ with Eq. (10).", + "bbox": [ + 496, + 502, + 893, + 608 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Goal-oriented Planning This can be formulated as motion inpainting under the sampling framework. Given the start state $\\hat{\\mathbf{s}}_s$ and the goal state $\\hat{\\mathbf{s}}_g$ , the planning module returns trajectory $\\hat{\\boldsymbol{\\tau}} = (\\hat{\\mathbf{s}}_0, \\hat{\\mathbf{a}}_0, \\dots, \\hat{\\mathbf{s}}_i, \\hat{\\mathbf{a}}_i, \\dots, \\hat{\\mathbf{s}}_g)$ that can reach the goal state. We set the first state as $\\hat{\\mathbf{s}}_0 = \\hat{\\mathbf{s}}_s$ and define the goal state and reward of goal-reaching in $\\varphi_p$ . For each step $i$ , we first keep the previous states and inpaint the remaining trajectory by sampling the goal-oriented SceneDiffuser with an iterative denoising process. Next, we take the action that can reach the next sampled state with $(\\hat{\\mathbf{a}}_{i-1}, \\hat{\\mathbf{s}}_i)$ . As illustrated in Alg. 2, we repeat the planning steps until the goal or maximal planning step is reached. Our planner leverages the trajectory-level generator, thus more generalizable to long-horizon trajectories and novel scenes.", + "bbox": [ + 496, + 609, + 893, + 820 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.3. Implementation", + "text_level": 1, + "bbox": [ + 500, + 830, + 658, + 847 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Model Architecture The design of SceneDiffuser follows the practices of conditional diffusion model [20,51,53]. Specifically, we augment the time-conditional diffusion", + "bbox": [ + 496, + 854, + 893, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "16753", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/68fa2e81625f8035f9003dff5d110a55349c4fcbe275317a61698eb4977b5392.jpg", + "image_caption": [ + "Figure 2. Model architecture of the SceneDiffuser. We use cross-attention to learn the relation between the input trajectory and scene condition. The optimizer and planner serve as the guidance for physically-plausible and goal-oriented trajectories." + ], + "image_footnote": [], + "bbox": [ + 80, + 89, + 467, + 422 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "model with cross-attention [65] for flexible conditioning. As shown in Fig. 2, for each sampling step, the model computes the cross-attention between the 3D scene condition and input trajectory, wherein the key and value are learned from the condition, and the query is learned from the input trajectory. The computed vector is fed into a feed-forward layer to estimate the noise $\\epsilon$ . The 3D scene is processed by a scene encoder [45, 91]); please refer to Appendix B.", + "bbox": [ + 75, + 484, + 470, + 604 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Objective Design We consider two types of trajectory objectives for optimization and planning: (i) trajectory-level objective, and (ii) the accumulation of step-wise objective. For optimization, we consider step-wise collision, contact objective, and trajectory level smoothness objective, $\\{\\varphi_o^{\\mathrm{collision}},\\varphi_o^{\\mathrm{contact}},\\varphi_o^{\\mathrm{smoothness}}\\}$ . For planning, we consider the accumulation of simple step-wise distance, $\\varphi_p^{L_2}$ . Please refer to the Appendix C for details. Empirically, we observe that parameterizing the objectives with timestep $t$ and increasing the guidance during the last several diffusion steps will enhance the effect of guidance.", + "bbox": [ + 75, + 604, + 470, + 772 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 76, + 784, + 209, + 801 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To demonstrate SceneDiffuser is general and applicable to various scenarios, we evaluate the SceneDiffuser on five scene understanding tasks. For generation, we evaluate the scene-conditioned human pose and motion generation and object-conditioned dexterous grasp generation. For planning, we evaluate the path planning for 3D navigation and motion", + "bbox": [ + 75, + 809, + 470, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "planning for robot arms. Below we first introduce baseline methods, followed by detailed settings, results analyses, and ablative studies for each task. We provide detailed implementation and experimental settings in Appendix D, additional ablative studies in Appendix E, additional experiments in Appendix F, and additional qualitative results in Appendix G.", + "bbox": [ + 496, + 90, + 893, + 181 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Baseline Methods For conditional generation tasks, we primarily compare SceneDiffuser with the widely-adopted cVAE model [25, 31, 32, 73, 90] and its variants. We also compare with strategies for optimizing the physics of the trajectory in the cVAE, including integrating into training as loss and plugging upon as the post-optimization. For planning, we compare with a stochastic planner learned by imitation learning using Behavior Cloning (BC) and a simple heuristic-based deterministic planner guided by $L_{2}$ distance.", + "bbox": [ + 496, + 181, + 893, + 319 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Task 1: Human Pose Generation", + "text_level": 1, + "bbox": [ + 498, + 330, + 784, + 345 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Setup Scene-conditioned human pose generation aims to generate semantically plausible and physically feasible single-frame human bodies within the given 3D scenes. We evaluate the task on the 12 indoor scenes provided by PROX [15] and the refined version of PROX'S per-frame SMPL-X parameters from LEMO [86]. The input is the colored point cloud extracted by randomly downsampling the scene meshes provided in PROX. Training/testing splits are created following the literature [69, 90], resulting in $\\sim 53\\mathrm{k}$ frames in 8 scenes for training and others for testing.", + "bbox": [ + 496, + 354, + 893, + 506 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Metrics We evaluate the physical plausibility of generated poses with both direct human evaluations and indirect collision and contact scores. We randomly selected 1000 frames in the four test scenes for the direct measure and instructed 26 Turkers to decide whether the generated human pose was plausible. We compute the mean percentage of plausible generation and term this metric as the plausible rate. For indirect measures, we report (i) the non-collision score of the generated human bodies by calculating the proportion of the scene vertices with positive SDF to the human body and (ii) the contact score by checking if the body contact with the scene in a distance [15] below a pre-defined threshold. Following the literature [84,90], we evaluate the diversities of global translation, generated SMPL-X parameters, and the marker-based body-mesh representation [89]. Specifically, we calculate the diversity of generated pose with the Average Pairwise Distance (APD) and standard deviation (std).", + "bbox": [ + 496, + 507, + 895, + 763 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Results Tab. 1 quantitatively demonstrates that SceneDiffuser generates significantly better poses while maintaining generation diversity. We further provide qualitative comparisons between baseline models and SceneDiffuser in Fig. 3. While achieving a comparable diversity, collision, and contact performance, our model generates results that contain considerably more physically plausible poses (e.g., floating, severe collision). This is reflected by the significant superiority (i.e., over $28\\%$ ) over", + "bbox": [ + 496, + 763, + 893, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "16754", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/79ebeed5f6404d796eb77541ac30b6a06848874dcbe6cbb1b6ddcfd5e986ae03.jpg", + "table_caption": [ + "Table 1. Quantitative results of human pose generation in 3D scenes. We report metrics for physical plausibility and diversity." + ], + "table_footnote": [], + "table_body": "
modelplausible rate↑non-collision score↑contact score↑APD (trans.)↑std (trans.)↑APD (param)↑std (param)↑APD (marker)↑std (marker)↑
cVAE (w/o. LHS) [90]14.8899.7896.421.2180.4942.8780.1663.6380.172
cVAE (w/ LHS) [90]16.1999.7599.251.0130.4162.9940.1703.6140.169
our (w/o opt.)21.0499.7499.430.7760.3313.2040.1953.4830.167
our (w/ opt.)44.7799.9398.051.0090.4133.2970.1973.6790.177
", + "bbox": [ + 78, + 106, + 890, + 174 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/475d2269c003cb096b542918cc0abca05dd3c04ff8c47765e6c6fe2db6bfad07.jpg", + "table_caption": [ + "Table 2. Quantitative results of human motion generation in 3D scenes. We report model variants with and without the start pose." + ], + "table_footnote": [], + "table_body": "
modelplausible rate↑non-collision score↑contact score↑APD (trans.)↑std (trans.)↑APD (param)↑std (param)↑APD (marker)↑std (marker)↑
cVAE (w/o start) [73]7.7299.8686.261.6280.6132.7660.1553.2750.150
ours (w/o start)21.6799.7197.920.5680.2372.3390.1263.2990.151
ours (w/o start & w/ opt.)25.8399.9398.910.4730.1962.4050.1273.3850.154
cVAE (w/ start) [73]17.6599.8895.440.4780.1881.7470.0912.3080.105
ours (w/ start)36.5699.8598.470.1930.0811.3720.0651.5680.072
ours (w/ start & w/ opt.)38.4499.9498.430.1680.0701.3890.0651.5750.072
", + "bbox": [ + 78, + 204, + 892, + 297 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e79cc5529bfd0233010d2e22d73d9942728496456417c8bc9dd41bf7870b3772.jpg", + "image_caption": [ + "Figure 3. Qualitative results of human pose generation in 3D scenes. From left to right: (a) cVAE generation, (b) SceneDiffuser generation without optimization, and poses generated (c) with and (d) without applying our optimization-guided sampling." + ], + "image_footnote": [], + "bbox": [ + 78, + 313, + 890, + 563 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "cVAE-based baselines on plausible rates. We observe this large improvement both quantitatively from the plausible rate and non-collision score and qualitatively in Fig. 3. Notably, our optimization-guided sampling improves the generator with $23\\%$ on the plausible rate, showing the efficacy of the proposed optimization-guided sampling strategy and its potential for a broader range of 3D tasks with physic-based constraints or objectives.", + "bbox": [ + 75, + 601, + 470, + 723 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Task 2: Human Motion Generation", + "text_level": 1, + "bbox": [ + 76, + 738, + 382, + 753 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Setup We consider generating human motion sequences under two different settings: (1) condition solely on the 3D scene, and (2) condition on both the starting pose and the 3D scene. We use the same human and scene representation as in Sec. 5.1 and clip the original LEMO motion sequence into segments with a fixed duration (60 frames). In total, we obtain 28k motion segments, with the distance between each start and end pose being longer than 0.2 meters. We follow the same split in Sec. 5.1 for training/testing and the same", + "bbox": [ + 75, + 763, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "evaluation metrics for the pose generation. We report the average values of pose metrics over motion sequence as our performance measure.", + "bbox": [ + 496, + 601, + 892, + 647 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results As quantitatively shown in Tab. 2, SceneDiffuser consistently generates high-quality motion sequences compared to cVAE baselines. Specifically, our generated motion outperforms baseline models on plausible rate, non-collision score, and contact score. This performance gain indicates better coverage of motion that involves rich interaction with the scene while remaining physically plausible. It also causes lower diversity in metrics (e.g., translation variance) since the plausible space for the motion is limited compared with cVAE. Empirically, we observe that providing the start position of motion as a condition constrains possible future motion sequences and leads to a drop in generation diversity for all models. We also note only a marginal performance improvement after applying optimization-guided sampling. One potential reason is that the generated motions are already plausible", + "bbox": [ + 496, + 657, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "16755", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/14b9bea5a5732ccd4cfb5b291b509ac3b7fedf2151434f7c8e59e0fadaa91390.jpg", + "image_caption": [ + "Figure 4. Human motions generated by SceneDiffuser. Each row shows sampled human motions from the same start pose." + ], + "image_footnote": [], + "bbox": [ + 76, + 87, + 472, + 204 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "and receive small guidance from the optimization. As qualitatively shown in Fig. 4, SceneDiffuser generates diverse motions (e.g., \"sit,\" \"walk\") from the same start position in unseen 3D scenes.", + "bbox": [ + 75, + 236, + 470, + 297 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Task 3: Dexterous Grasp Generation", + "text_level": 1, + "bbox": [ + 76, + 305, + 393, + 321 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Setup Dexterous grasp generation aims to generate diverse and stable grasping poses for the given object with a human-like dexterous hand. We use the Shadowhand subset of the MultiDex [31] dataset, which contains diverse dexterous grasping poses for 58 daily objects. We represent the pose of Shadowhand as $q \\coloneqq (t,R,\\theta) \\in \\mathbb{R}^{33}$ , where $t \\in \\mathbb{R}^3$ and $R \\in \\mathbb{R}^6$ denote the global translation and orientation respectively, and $\\theta \\in \\mathbb{R}^{24}$ describes the rotation angles of the revolute joints. An object is represented by its point cloud $\\mathcal{O} \\in \\mathbb{R}^{2048 \\times 3}$ . We split the dataset into 48 seen objects and 10 unseen objects for training and testing, respectively.", + "bbox": [ + 75, + 329, + 470, + 494 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Metrics We evaluate models in terms of success rate, diversity, and collision depth. We test if a grasp is successful in IsaacGym [37] by applying external forces to the object and measuring the movement of the object. To measure how learned models capture the diversity of successful grasping pose in the training data, we report the success rate of generated poses that lies at different variance levels from the mean pose of training data. We measure the collision depth as the maximum depth that the hand penetrates the object in each successful grasp for testing models' performance on physically correct grasps. In all cases, we ignore the root transformation of the hand as it does not contribute to the diversity of grasping types.", + "bbox": [ + 75, + 494, + 468, + 690 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results Tab. 3 quantitatively demonstrates that SceneDiffuser generates significantly better grasp poses in", + "bbox": [ + 76, + 691, + 468, + 720 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/87e1bd62fee85e97dcb3858853ad4781725e8792becf8f6a6b0bc67c4562a78d.jpg", + "table_caption": [ + "Table 3. Quantitative results of dexterous grasp generation on MultiDex [31] dataset. We measure the success rates under different diversities and depth collisions. TTA. denotes test-time optimization with physics and contact." + ], + "table_footnote": [], + "table_body": "
modelsucc. rate (%)↑depth coll. (mm)↓
σ2σall
cVAE [25]0.0010.0914.0622.98
cVAE (w/ TTA.) [25]0.0021.9117.9715.19
ours (w/o opt.)70.6571.2571.2517.34
ours (w/ opt.)71.2769.8469.8414.61
", + "bbox": [ + 501, + 148, + 890, + 238 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "terms of success rate while correctly balancing the diversity of generation and grasp success. This result indicates that the SceneDiffuser achieves a consistently high success rate without much performance drop when the generated pose diverges from the mean pose in the training data. We also show that, by applying optimizer upon SceneDiffuser, the guided sampling process can reduce the violation of physically implausible grasping poses, outperforming the state-of-the-art baseline [25] without additional training or intermediate representation (i.e., contact maps). We provide qualitative results in Fig. 5 for visualization.", + "bbox": [ + 496, + 250, + 893, + 416 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.4. Task 4: Path Planning for Navigation", + "text_level": 1, + "bbox": [ + 500, + 434, + 820, + 450 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Setup We selected 61 indoor scenes from ScanNet [9] to construct room-level scenarios for navigational path planning and annotated these scenes with navigation graphs. As shown in Fig. 6b, these annotations are more spatially dense and physically plausible compared to previous methods [1]. We represent the physical robot with a cylinder to simulate physically plausible trajectories; see Fig. 6a. In total, we collected around 6k trajectories by searching the shortest paths between the randomly selected start and target nodes on the graph. We use trajectories in 46 scenes for training and the rest 15 scenes for evaluation. Models take the input as the scene point cloud $S \\in \\mathbb{R}^{32768 \\times 3}$ , a given start position $\\hat{\\mathbf{s}}_0 \\in \\mathbb{R}^2$ , and a target position $\\mathcal{G} \\in \\mathbb{R}^2$ on the floor plane.", + "bbox": [ + 496, + 460, + 893, + 657 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Metrics We evaluate the planned results by checking if the \"robot\" can move from the start to the target without collision along the planned trajectory. We report the average success rate and planning steps over all test cases.", + "bbox": [ + 496, + 660, + 890, + 720 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ecdf21466045ddcdca6b10e7f290b7ab88290d45e33c5c9b92ffda51c9fc189a.jpg", + "image_caption": [ + "Figure 5. Qualitative results of dexterous grasp generation. Compared to grasps generated by cVAE (first row), SceneDiffuser (second row) generates fewer colliding or floating poses, which helps to achieve a higher success rate." + ], + "image_footnote": [], + "bbox": [ + 76, + 720, + 890, + 866 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "16756", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/767ec50fd0823393797124f48f8cc5857d7a97e0192ddd6ca70e2a35929383a5.jpg", + "image_caption": [ + "(a) path planning" + ], + "image_footnote": [], + "bbox": [ + 80, + 88, + 274, + 239 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b2459c2db352f7f0f2e2099adec59589c3d14e695111005ab0125e5a1ba584d2.jpg", + "image_caption": [ + "(b) navigation graph" + ], + "image_footnote": [], + "bbox": [ + 276, + 88, + 468, + 239 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Results As shown in Tab. 4, SceneDiffuser outperforms both the BC and the deterministic planner baseline. These results indicate the efficacy of guided sampling with the planning objective, especially given that all test scenes are unseen during training. Crucially, as simple heuristics (like $L_{2}$ ) oftentimes lead to dead-ends in path planning, SceneDiffuser can correctly combine past knowledge on the scene-conditioned trajectory distribution and planning objective under specific unseen scenes to redirect planning direction, which helps to avoid obstacles and dead-ends to reach the goal successfully. Compared with the baseline models, our model also requires fewer planning steps while maintaining a higher success rate. This suggests that SceneDiffuser successfully navigates to the target without diverging even in long-horizon tasks, where classic RL-based stochastic planners suffer (i.e., the low performance of BC).", + "bbox": [ + 75, + 291, + 472, + 532 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/65ade80f537aa2008cc5624dd3e58a423c5362d4e58c1209964f060556d9abda.jpg", + "table_caption": [ + "Table 4. Quantitative results of path planning in 3D navigation and motion planning for robot arms." + ], + "table_footnote": [], + "table_body": "
taskmodelsucc. rate(%)↑planning steps↓
path planBC0150
deterministic(L2)13.50137.98
ours73.7590.38
arm motionBC0.31299.08
deterministic(L2)72.87141.28
ours78.59147.60
", + "bbox": [ + 78, + 564, + 468, + 671 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.5. Task 5: Motion Planning for Robot Arms", + "text_level": 1, + "bbox": [ + 76, + 680, + 429, + 698 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Setup Aiming to generate valid robot arm motion trajectories in cluttered scenes, we used the Franka Emika arm with seven revolute joints and collected 19,800 trajectories over 200 randomly generated cluttered scenes using the MoveIt 2.0 [50], as shown in Fig. 7. We represent the scene with point clouds $S \\in \\mathbb{R}^{4096 \\times 3}$ and the robot arm trajectory with a sequence of joint angles $\\mathcal{R} \\in [-\\pi, \\pi]$ . We train our model on 160 scenes and test on 40 unseen scenes.", + "bbox": [ + 75, + 704, + 470, + 824 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Metrics Similar to Sec. 5.4, we evaluate the generated trajectories by success rate on unseen scenes and the average number of planning steps. We consider a trajectory successful if the robot arm reaches the goal pose by a certain distance threshold within a limited number of steps.", + "bbox": [ + 75, + 824, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0682f30c22fb2638a4bf30be7724d65d6eaa05f0f61983c948e7a79dddbf4f97.jpg", + "image_caption": [ + "Figure 6. Path planning for 3D scene navigation. SceneDiffuser generates trajectories in long-horizon tasks.", + "(a) motion planning" + ], + "image_footnote": [], + "bbox": [ + 501, + 88, + 694, + 239 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ba49770ba11451363882036a29ab93ccfc52cd6bceabd7fc50065078a9b35317.jpg", + "image_caption": [ + "(b) cluttered scenes", + "Figure 7. Motion planning for robot arms. SceneDiffuser generates arm motions in tabletop scenes with obstacles." + ], + "image_footnote": [], + "bbox": [ + 694, + 88, + 893, + 241 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Results We observe similar overall performance as in Sec. 5.4. Tab. 4 shows that SceneDiffuser consistently outperforms both the RL-based BC and the deterministic planner baseline. SceneDiffuser's planning steps for successful trials are also comparable with the deterministic planner, showing the efficacy of the planner in long-horizon scenarios.", + "bbox": [ + 496, + 292, + 893, + 383 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.6. Ablation Analyses", + "text_level": 1, + "bbox": [ + 500, + 392, + 676, + 407 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We explore how the scaling coefficient $\\lambda$ influences the human pose generation results. We report the diversity and physics metrics of sampling results under different $\\lambda$ s, ranging from 0.1 to 100. As shown in Tab. 5, $\\lambda$ balances generation collision/contact and diversity in human pose generation. Specifically, $\\lambda = 1.0$ leads to the best physical plausibility, while larger $\\lambda$ values lead to diverse generation results. We attribute this effect to the optimization as with bigger $\\lambda$ s; the optimization will draw poses away from the scene.", + "bbox": [ + 496, + 415, + 893, + 551 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/b98a3cc5434462f849a710a3e5d5570957420847293b8417a29b0447202819ee.jpg", + "table_caption": [ + "Table 5. Ablation of the scale coefficient for optimization." + ], + "table_footnote": [], + "table_body": "
metricλ = 0.1λ = 1.0λ = 10.0λ = 100.0
plausible rate ↑28.7552.521.250
APD (trans.) ↑0.7640.8861.56423.96
APD (param) ↑3.2063.2439.040573.6
non-collison score ↑99.7699.8799.8574.9
contact score ↑99.7099.6581.750.0
", + "bbox": [ + 501, + 569, + 893, + 662 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 679, + 617, + 694 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We propose the SceneDiffuser as a general conditional generative model for generation, optimization, and planning in 3D scenes. SceneDiffuser is designed with appealing properties, including scene-aware, physics-based, and goal-oriented. We demonstrate that the SceneDiffuser outperforms previous models by a large margin on various tasks, establishing its efficacy and flexibility.", + "bbox": [ + 496, + 703, + 893, + 809 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments and disclosure of funding We thank Ruiqi Gao and Ying Nian Wu for their helpful discussions and suggestions. This work is supported in part by the National Key R&D Program of China (2021ZD0150200), the Beijing Nova Program, and the National Natural Science Foundation of China (NSFC) (62172043).", + "bbox": [ + 496, + 810, + 893, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "16757", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 106 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Peter Anderson, Qi Wu, Damien Teney, Jake Bruce, Mark Johnson, Niko Sunderhauf, Ian Reid, Stephen Gould, and Anton Van Den Hengel. Vision-and-language navigation: Interpreting visually-grounded navigation instructions in real environments. 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In International Conference on Robotics and Automation (ICRA), 2017. 1, 2" + ], + "bbox": [ + 501, + 92, + 893, + 445 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "16761", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 11 + } +] \ No newline at end of file diff --git a/2023/Diffusion-Based Generation, Optimization, and Planning in 3D Scenes/2c0ff292-024d-4fa0-9487-b60809586e2a_model.json b/2023/Diffusion-Based Generation, Optimization, and Planning in 3D Scenes/2c0ff292-024d-4fa0-9487-b60809586e2a_model.json new file mode 100644 index 0000000000000000000000000000000000000000..b03e2b507f208429d64a7fc0e0bc412a846df7be --- /dev/null +++ b/2023/Diffusion-Based Generation, Optimization, and Planning in 3D Scenes/2c0ff292-024d-4fa0-9487-b60809586e2a_model.json @@ -0,0 +1,2886 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.134, + 0.131, + 0.838, + 0.154 + ], + "angle": 0, + "content": "Diffusion-based Generation, Optimization, and Planning in 3D Scenes" + }, + { + "type": "text", + "bbox": [ + 0.236, + 0.165, + 0.728, + 0.203 + ], + "angle": 0, + "content": "Siyuan Huang\\(^{1*}\\), Zan Wang\\(^{1,2*}\\), Puhao Li\\(^{1,3}\\), Baoxiong Jia\\(^{1}\\), Tengyu Liu\\(^{1}\\), Yixin Zhu\\(^{4}\\), Wei Liang\\(^{2,5}\\), Song-Chun Zhu\\(^{1,3,4}\\)" + }, + { + "type": "text", + "bbox": [ + 0.282, + 0.211, + 0.688, + 0.226 + ], + "angle": 0, + "content": "\\(^{1}\\) National Key Laboratory of General Artificial Intelligence, BIGAI" + }, + { + "type": "text", + "bbox": [ + 0.255, + 0.228, + 0.715, + 0.244 + ], + "angle": 0, + "content": "\\(^{2}\\) School of Computer Science & Technology, Beijing Institute of Technology" + }, + { + "type": "text", + "bbox": [ + 0.239, + 0.246, + 0.731, + 0.262 + ], + "angle": 0, + "content": "\\(^{3}\\) Dept. of Automation, Tsinghua University \\(^{4}\\) Institute for AI, Peking University" + }, + { + "type": "text", + "bbox": [ + 0.255, + 0.264, + 0.71, + 0.28 + ], + "angle": 0, + "content": "5 Yangtze Delta Region Academy of Beijing Institute of Technology, Jiaxing" + }, + { + "type": "list", + "bbox": [ + 0.239, + 0.211, + 0.731, + 0.28 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.364, + 0.288, + 0.601, + 0.305 + ], + "angle": 0, + "content": "https://scenediffuser.github.io" + }, + { + "type": "image", + "bbox": [ + 0.079, + 0.323, + 0.896, + 0.578 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.579, + 0.893, + 0.608 + ], + "angle": 0, + "content": "Figure 1. Illustration of the SceneDiffuser, applicable to various scene-conditioned 3D tasks: (a) human pose generation, (b) human motion generation, (c) dexterous grasp generation, (d) path planning for 3D navigation with goals, and (e) motion planning for robot arms." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.62, + 0.314, + 0.636 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.644, + 0.474, + 0.856 + ], + "angle": 0, + "content": "We introduce the SceneDiffuser, a conditional generative model for 3D scene understanding. SceneDiffuser provides a unified model for solving scene-conditioned generation, optimization, and planning. In contrast to prior work, SceneDiffuser is intrinsically scene-aware, physics-based, and goal-oriented. With an iterative sampling strategy, SceneDiffuser jointly formulates the scene-aware generation, physics-based optimization, and goal-oriented planning via a diffusion-based denoising process in a fully differentiable fashion. Such a design alleviates the discrepancies among different modules and the posterior collapse of previous scene-conditioned generative models. We evaluate the SceneDiffuser on various 3D scene understanding tasks, including human pose and motion generation, dexterous grasp" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.622, + 0.895, + 0.698 + ], + "angle": 0, + "content": "generation, path planning for 3D navigation, and motion planning for robot arms. The results show significant improvements compared with previous models, demonstrating the tremendous potential of the SceneDiffuser for the broad community of 3D scene understanding." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.71, + 0.633, + 0.725 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.895, + 0.856 + ], + "angle": 0, + "content": "The ability to generate, optimize, and plan in 3D scenes is a long-standing goal across computer vision, graphics, and robotics. Various tasks have been devised to achieve these goals, fostering downstream applications in motion generation [32, 69, 73, 90], motion planning [42, 43, 60, 75], grasp generation [25, 31, 34], navigation [1, 95], scene synthesis [24, 47, 72, 82], embodied perception and manipulation [30, 39, 61], and autonomous driving [3, 52]." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Despite rich applications and great successes, existing models designed for these tasks exhibit two fundamental limitations for real-world 3D scene understanding." + }, + { + "type": "page_footnote", + "bbox": [ + 0.1, + 0.863, + 0.364, + 0.876 + ], + "angle": 0, + "content": "* These authors contributed equally to this work." + }, + { + "type": "page_footnote", + "bbox": [ + 0.078, + 0.876, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Corresponding authors: Siyuan Huang (syhuang@bigai.ai) and Wei Liang (liangwei@bit.edu.cn)." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.863, + 0.47, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "16750" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.289 + ], + "angle": 0, + "content": "First, most prior work [8, 14, 32, 49, 60, 68-70, 73] leverages the conditional Variational Autoencoder (cVAE) for the conditional generation in 3D scenes. cVAE model utilizes an encoder-decoder structure to learn the posterior distribution and relies on the learned latent variables to sample. Although cVAE is easy to train and sample due to its simple architecture and one-step sampling procedure, it suffers from the posterior collapse problem [12, 17, 26, 64, 69, 84, 93]; the learned latent variable is ignored by a strong decoder, leading to limited generation diversity from these collapsed modes. Such collapse is further magnified in 3D tasks with stronger 3D decoders and more complex and noisy input conditions, e.g., the natural 3D scans [9]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.291, + 0.473, + 0.488 + ], + "angle": 0, + "content": "Second, despite the close relations among generation, optimization, and planning in 3D scenes, there lacks a unified framework that could address existing discrepancies among these models. Previous work [15, 34, 69] applies off-the-shelf physics-based post-optimization methods over outputs of generative models and often produces inconsistent and implausible generations, especially when transferring to novel scenes. Similarly, planners are usually standalone modules over results of generative model [8, 14] for trajectory planning or learned separately with the reinforcement learning (RL) [95], leading to gaps between planning and other modules (e.g., generation) during inference, especially in novel scenes where explorations are limited." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.49, + 0.473, + 0.657 + ], + "angle": 0, + "content": "To tackle the above limitations, we introduce the SceneDiffuser, a conditional generative model based on the diffusion process. SceneDiffuser eliminates the discrepancies and provides a single home for scene-conditioned generation, optimization, and planning. Specifically, with a denoising process, it learns a diffusion model for scene-conditioned generation during training. In inference, SceneDiffuser jointly solves the scene-aware generation, physics-based optimization, and goal-oriented planning through a unified iterative guided-sampling framework. Such a design equips the SceneDiffuser with the following three superiority:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.659, + 0.472, + 0.749 + ], + "angle": 0, + "content": "1. Generation: Building upon the diffusion model, SceneDiffuser solves the posterior collapse problem of scene-conditioned generative models. Since the forward diffusion process can be treated as data augmentation in 3D scenes, it helps traverse sufficient scene-conditioned distribution modes." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.75, + 0.472, + 0.84 + ], + "angle": 0, + "content": "2. Optimization: SceneDiffuser integrates the physics-based objective into each step of the sampling process as conditional guidance, enabling the differentiable physics-based optimization during both the learning and sampling process. This design facilitates the physically-plausible generation, which is critical for tasks in 3D scenes." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.84, + 0.473, + 0.902 + ], + "angle": 0, + "content": "3. Planning: Based on the scene-conditioned trajectory-level generator, SceneDiffuser possesses a physics- and goal-aware trajectory planner, generalizing better to long-horizon trajectories and novel 3D scenes." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.659, + 0.473, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.213 + ], + "angle": 0, + "content": "As illustrated in Fig. 1, we evaluate the SceneDiffuser on diverse 3D scene understanding tasks. The human pose, motion, and dexterous grasp generation results significantly improve, demonstrating plausible and diverse generations with the 3D scene and object conditions. The results on path planning for 3D navigation and motion planning for robot arms reveal the generalizable and long-horizon planning capability of the SceneDiffuser." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.226, + 0.642, + 0.243 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.252, + 0.897, + 0.448 + ], + "angle": 0, + "content": "Conditional Generation in 3D Scenes Generating diverse contents and rich interactions in 3D scenes is essential for understanding the 3D scene affordances. Several applications have emerged on conditional scene generation [24,47,71,81,88], human pose [16,32,87,90,92] and motion generation [14,32,49,60,68-70,73] in furnished 3D indoor scenes, and object-conditioned grasp pose generation [25,31,34,62,78]. However, most previous methods [6,14,16,25,31,62,68,73,75] rely on cVAE and suffer from the posterior collapse problem [12,17,26,64,69,84,93], especially when the 3D scene is natural and complex. In this work, SceneDiffuser addresses the posterior collapse with the diffusion-based denoising process." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.449, + 0.897, + 0.675 + ], + "angle": 0, + "content": "Physics-based Optimization in 3D Scenes Producing physically plausible generations compatible with 3D scenes is challenging in the scene-conditioned generation. Previous work uses physics-based post-optimization [15, 34, 69] or differentiable objective [25, 73, 90] to integrate collision and contact constraints into the generation framework. However, post-optimization approaches [15, 34, 69] cannot be learned jointly with the generative models, yielding inconsistent generation results. Similarly, differentiable approaches [25, 73, 90] impose constraints on the final objective and cannot optimize the physical interactions during sampling, resulting in implausible generations, particularly when adapting to novel scenes. In this work, SceneDiffuser avoids such inconsistency by integrating differentiable physics-based optimization into each step of the sampling process." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.897, + 0.903 + ], + "angle": 0, + "content": "Planning in 3D Scenes The ability to act and plan in 3D scenes is critical for an intelligent agent and has led to the recent culmination of embodied AI research [28, 30, 33, 36, 54, 55, 79]. Among all tasks, visual navigation has been most studied in the vision and robotics community [4, 13, 21, 40, 76, 77, 94, 95]. However, existing work relies heavily on model-based planners with the single-step dynamic model [5,11,48,67,74,80], lacking a trajectory-level optimization for long-horizon planning. Further, these planners lack explicit modeling of physical interactions, making it difficult to generalize to natural scenes with limited exploration, where rapid learning and adaptation are required. Compared with the global trajectory planner based on a trajectory-level generator, SceneDiffuser exhibits superior generalization in long-horizon plans and novel 3D scenes." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "16751" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.091, + 0.473, + 0.288 + ], + "angle": 0, + "content": "Diffusion-based Models Diffusion model [19,22,57, 59] has come forth into a promising class of generative model for learning and sampling data distributions with an iterative denoising process, facilitating the image [10, 58], text [83], and shape generation [35]. With flexible conditioning, it is further extended to the language-conditioned image [41, 51, 53], video [18, 56], and 3D generation [44, 63, 85]. Notably, Janner et al. [23] integrate the generation and planning into the same sampling framework for behavior synthesis. To our best knowledge, SceneDiffuser is the first framework that models the 3D scene-conditioned generation with a diffusion model and integrates the generation, optimization, and planning into a unified framework." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.3, + 0.206, + 0.317 + ], + "angle": 0, + "content": "3. Background" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.324, + 0.26, + 0.339 + ], + "angle": 0, + "content": "3.1. Problem Definition" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.347, + 0.473, + 0.468 + ], + "angle": 0, + "content": "Given a 3D scene \\(S\\), we aim to generate the optimal solution for completing the tasks (e.g., navigation, manipulation) given the goal \\(\\mathcal{G}\\) in the scene. We denote the state and action of an agent as \\((\\mathbf{s},\\mathbf{a})\\). The dynamic model defines the state transition as \\(p(\\mathbf{s}_{i + 1}|\\mathbf{s}_i,\\mathbf{a}_i)\\), which is often deterministic in scene understanding (i.e., \\(f(\\mathbf{s}_i,\\mathbf{a}_i)\\)). The trajectory is defined as \\(\\boldsymbol{\\tau} = (\\mathbf{s}_0,\\mathbf{a}_0,\\dots ,\\mathbf{s}_i,\\mathbf{a}_i,\\dots ,\\mathbf{s}_N)\\), where \\(N\\) denotes the horizon of task solving in discrete time." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.476, + 0.414, + 0.492 + ], + "angle": 0, + "content": "3.2. Planning with Trajectory Optimization" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.499, + 0.47, + 0.529 + ], + "angle": 0, + "content": "The scene-conditional trajectory optimization is defined as maximizing the task objective:" + }, + { + "type": "equation", + "bbox": [ + 0.191, + 0.534, + 0.47, + 0.556 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\tau} ^ {*} = \\underset {\\boldsymbol {\\tau}} {\\arg \\max } \\mathcal {J} (\\boldsymbol {\\tau} | \\mathcal {S}, \\mathcal {G}). \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.561, + 0.473, + 0.683 + ], + "angle": 0, + "content": "The dynamic model is usually known for trajectory optimization. Considering the future actions and states with predictable dynamics, the entire trajectory \\(\\tau\\) can be optimized jointly and non-progressively with traditional [29] or data-driven [7] planning algorithms. Trajectory-based optimization benefits from its global awareness of history and future states, thus can better model the long-horizon tasks compared with single-step models in RL, where \\(\\mathbf{a}_{0:N}^{*} =\\)" + }, + { + "type": "equation", + "bbox": [ + 0.078, + 0.682, + 0.258, + 0.721 + ], + "angle": 0, + "content": "\\[\n\\underset {\\mathbf {a} _ {0: N}} {\\arg \\max } \\sum_ {i = 0} ^ {N} r (\\mathbf {s} _ {i}, \\mathbf {a} _ {i} | \\mathcal {S}, \\mathcal {G}).\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.727, + 0.239, + 0.741 + ], + "angle": 0, + "content": "3.3. Diffusion Model" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.75, + 0.473, + 0.901 + ], + "angle": 0, + "content": "Diffusion model [19,22,57] is a class of generative models representing the data generation with an iterative denoising process from Gaussian noise. It consists of a forward and a reverse process. The forward process \\( q(\\tau^t |\\tau^{t - 1}) \\) gradually destroys data \\( \\tau^0\\sim q(\\tau^0) \\) into Gaussian noise. The parametrized reverse process \\( p_{\\theta}(\\tau^{t - 1}|\\tau^t) \\) recovers the data from noise with the learned normal distribution from a fixed timestep. The training objective for \\( \\theta \\) is denoising score matching over multiple noise scale [22,66]. Please refer to the Appendix A for details of diffusion model and variants." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.09, + 0.642, + 0.106 + ], + "angle": 0, + "content": "4. SceneDiffuser" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.115, + 0.895, + 0.237 + ], + "angle": 0, + "content": "SceneDiffuser models planning as trajectory optimization and solves the aforementioned problem with the spirit of planning as sampling, where the trajectory optimization is achieved by sampling trajectory-level distribution learned by the model. Leveraging the diffusion model with gradient-based sampling and flexible conditioning, SceneDiffuser models the scene-conditioned goal-oriented trajectory \\( p(\\tau^0 | S, \\mathcal{G}) \\):" + }, + { + "type": "equation", + "bbox": [ + 0.581, + 0.243, + 0.892, + 0.293 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} p \\left(\\boldsymbol {\\tau} ^ {0} | \\mathcal {S}, \\mathcal {G}\\right) = \\frac {p _ {\\theta} \\left(\\boldsymbol {\\tau} ^ {0} | \\mathcal {S}\\right) p _ {\\phi} \\left(\\mathcal {G} \\mid \\boldsymbol {\\tau} ^ {0} , \\mathcal {S}\\right)}{p \\left(\\mathcal {G} \\mid \\mathcal {S}\\right)} \\tag {2} \\\\ \\propto p _ {\\theta} (\\tau^ {0} | \\mathcal {S}) p _ {\\phi} (\\mathcal {G} | \\tau^ {0}, \\mathcal {S}). \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.301, + 0.894, + 0.362 + ], + "angle": 0, + "content": "Generation \\( p_{\\theta}(\\pmb{\\tau}^{0}|\\mathcal{S}) \\) characterizes the probability of generating certain trajectories with the scene condition. It can be modeled using a conditional diffusion model [19, 57] with an iterative denoising process:" + }, + { + "type": "equation", + "bbox": [ + 0.55, + 0.37, + 0.892, + 0.405 + ], + "angle": 0, + "content": "\\[\np _ {\\theta} \\left(\\boldsymbol {\\tau} ^ {0} \\mid \\mathcal {S}\\right) = p \\left(\\boldsymbol {\\tau} ^ {T}\\right) \\prod_ {t = 1} ^ {T} p \\left(\\boldsymbol {\\tau} ^ {t - 1} \\mid \\boldsymbol {\\tau} ^ {t}, \\mathcal {S}\\right), \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.522, + 0.407, + 0.854, + 0.425 + ], + "angle": 0, + "content": "\\[\np (\\boldsymbol {\\tau} ^ {t - 1} | \\boldsymbol {\\tau} ^ {t}, \\mathcal {S}) = \\mathcal {N} (\\boldsymbol {\\tau} ^ {t - 1}; \\boldsymbol {\\mu} _ {\\theta} (\\boldsymbol {\\tau} ^ {t}, t, \\mathcal {S}), \\boldsymbol {\\Sigma} _ {\\theta} (\\boldsymbol {\\tau} ^ {t}, t, \\mathcal {S})).\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.433, + 0.895, + 0.569 + ], + "angle": 0, + "content": "Optimization and Planning \\(p_{\\phi}(\\mathcal{G}|\\boldsymbol{\\tau}^0,\\mathcal{S})\\) represents the probability of reaching the goal with the sampled trajectory, where the goal can be flexibly defined by customized objective functions in various tasks. As shown in Eq. (4), the precise definition of this probability is \\(p_{\\phi}(\\mathcal{O} = 1|\\boldsymbol{\\tau}^0,\\mathcal{S},\\mathcal{G})\\) where \\(O\\) is an optimality indicator that represents if the goal were achieved. Intuitively, the trajectory objective in Eq. (1) can indicate such optimality. We therefore expand \\(p_{\\phi}(\\mathcal{G}|\\boldsymbol{\\tau}^t,\\mathcal{S})\\) as its exponential in Eq. (5):" + }, + { + "type": "equation", + "bbox": [ + 0.549, + 0.578, + 0.892, + 0.595 + ], + "angle": 0, + "content": "\\[\np _ {\\phi} (\\mathcal {G} | \\boldsymbol {\\tau} ^ {t}, \\mathcal {S}) = p _ {\\phi} \\left(\\mathcal {O} = 1 | \\boldsymbol {\\tau} ^ {t}, \\mathcal {S}, \\mathcal {G}\\right) \\tag {4}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.628, + 0.599, + 0.892, + 0.615 + ], + "angle": 0, + "content": "\\[\n\\propto \\exp (\\mathcal {J} (\\boldsymbol {\\tau} ^ {t} | \\mathcal {S}, \\mathcal {G})) \\tag {5}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.628, + 0.618, + 0.892, + 0.636 + ], + "angle": 0, + "content": "\\[\n= \\exp \\left(\\varphi_ {p} \\left(\\boldsymbol {\\tau} ^ {t} | \\mathcal {S}, \\mathcal {G}\\right) + \\varphi_ {o} \\left(\\boldsymbol {\\tau} ^ {t} | \\mathcal {S}\\right), \\right. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.895, + 0.766 + ], + "angle": 0, + "content": "where \\(\\varphi_{o}(\\pmb{\\tau}^{t}|\\mathcal{S})\\) denotes the objective for optimizing the trajectory with scene condition and is independent of task goal \\(\\mathcal{G}\\). In scene understanding, \\(\\varphi_{o}\\) usually denotes plausible physical relationships (e.g., collision, contact, and intersection). \\(\\varphi_{p}(\\pmb{\\tau}^{t}|\\mathcal{S},\\mathcal{G})\\) indicates the objective for planning (i.e., goal-reaching) with scene condition. Both \\(\\varphi_{o}\\) and \\(\\varphi_{p}\\) can be explicitly defined or implicitly learned from observed trajectories with proper parametrization." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.774, + 0.608, + 0.79 + ], + "angle": 0, + "content": "4.1. Learning" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.797, + 0.894, + 0.843 + ], + "angle": 0, + "content": "\\(p_{\\theta}(\\tau^0 |S)\\) is the scene-conditioned generator, which can be learned by the conditional diffusion model with the simplified objective of estimating the noise \\(\\epsilon\\) [10, 19, 20], where" + }, + { + "type": "equation", + "bbox": [ + 0.514, + 0.861, + 0.892, + 0.905 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\theta} \\left(\\boldsymbol {\\tau} ^ {0} \\mid \\mathcal {S}\\right) = \\mathbb {E} _ {t, \\epsilon , \\boldsymbol {\\tau} ^ {0}} \\left[ \\| \\boldsymbol {\\epsilon} - \\boldsymbol {\\epsilon} _ {\\theta} \\left(\\sqrt {\\hat {\\alpha} ^ {t}} \\boldsymbol {\\tau} ^ {0} + \\sqrt {1 - \\hat {\\alpha} ^ {t}} \\boldsymbol {\\epsilon}, t, \\mathcal {S}\\right) \\| ^ {2} \\right] \\tag {7} \\\\ = \\mathbb {E} _ {t, \\epsilon , \\tau^ {0}} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} (\\tau^ {t}, t, S) \\| ^ {2} \\right], \\\\ \\end{array}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16752" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.473, + 0.168 + ], + "angle": 0, + "content": "where \\(\\hat{\\alpha}^t\\) is the pre-determined function in the forward process. With the learned \\(p_{\\theta}(\\tau^0 |S)\\), we sample \\(p(\\tau^0 |S,\\mathcal{G})\\) by taking the advantage of the diffusion model's flexible conditioning [10, 23]. Specifically, we approximate \\(p_{\\phi}(\\mathcal{G}|\\boldsymbol{\\tau}^{t},\\mathcal{S})\\) using the Taylor expansion around \\(\\boldsymbol{\\tau}^{t} = \\boldsymbol{\\mu}\\) at timestep \\(t\\) as" + }, + { + "type": "equation", + "bbox": [ + 0.168, + 0.175, + 0.47, + 0.192 + ], + "angle": 0, + "content": "\\[\n\\log p _ {\\phi} (\\mathcal {G} | \\boldsymbol {\\tau} ^ {t}, \\mathcal {S}) \\approx (\\boldsymbol {\\tau} ^ {t} - \\boldsymbol {\\mu}) \\mathbf {g} + C, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.201, + 0.472, + 0.247 + ], + "angle": 0, + "content": "where \\(C\\) is a constant, \\(\\pmb{\\mu} = \\pmb{\\mu}_{\\theta}(\\pmb{\\tau}^t,t,\\mathcal{S})\\) and \\(\\Sigma = \\Sigma_{\\theta}(\\pmb{\\tau}^{t},t,\\mathcal{S})\\) are the inferred parameters of original diffusion process, and" + }, + { + "type": "equation", + "bbox": [ + 0.144, + 0.255, + 0.47, + 0.292 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathbf {g} = \\nabla_ {\\boldsymbol {\\tau} ^ {t}} \\log p _ {\\phi} (\\mathcal {G} | \\boldsymbol {\\tau} ^ {t}, \\mathcal {S}) | _ {\\boldsymbol {\\tau} ^ {t} = \\boldsymbol {\\mu}} \\tag {9} \\\\ = \\nabla_ {\\tau^ {t}} \\left(\\varphi_ {o} \\left(\\tau^ {t} | \\mathcal {S}\\right) + \\varphi_ {p} \\left(\\tau^ {t} | \\mathcal {S}, \\mathcal {G}\\right)\\right) | _ {\\tau^ {t} = \\mu}. \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.3, + 0.208, + 0.313 + ], + "angle": 0, + "content": "Therefore, we have" + }, + { + "type": "equation", + "bbox": [ + 0.139, + 0.322, + 0.47, + 0.339 + ], + "angle": 0, + "content": "\\[\np \\left(\\boldsymbol {\\tau} ^ {t - 1} \\mid \\boldsymbol {\\tau} ^ {t}, \\mathcal {S}, \\mathcal {G}\\right) = \\mathcal {N} \\left(\\boldsymbol {\\tau} ^ {t - 1}; \\boldsymbol {\\mu} + \\lambda \\boldsymbol {\\Sigma} \\mathbf {g}, \\boldsymbol {\\Sigma}\\right), \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.349, + 0.472, + 0.393 + ], + "angle": 0, + "content": "where \\(\\lambda\\) is the scaling factor for the guidance. With Eq. (10), we can sample \\(\\pmb{\\tau}^t\\) with the guidance of optimizing and planning objectives." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.395, + 0.472, + 0.485 + ], + "angle": 0, + "content": "Of note, \\(\\varphi_{p}\\) and \\(\\varphi_{o}\\) serve as the pre-defined guidance for tilting the original trajectory with physical and goal constraints. However, they can also be learned from the observed trajectories. During training, we first fix the learned base model of \\(p_{\\theta}(\\tau^0 |S)\\), followed by learning \\(\\phi_{o}\\) and \\(\\phi_{p}\\) for optimization and planning with the following objective:" + }, + { + "type": "equation", + "bbox": [ + 0.107, + 0.492, + 0.47, + 0.511 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\phi} \\left(\\boldsymbol {\\tau} ^ {0} \\mid \\mathcal {S}, \\mathcal {G}\\right) = \\mathbb {E} _ {t, \\epsilon , \\boldsymbol {\\tau} ^ {0}} \\left[ \\left\\| \\boldsymbol {\\epsilon} - \\boldsymbol {\\epsilon} _ {\\theta} \\left(\\boldsymbol {\\tau} ^ {t}, t, \\mathcal {S}\\right) - \\boldsymbol {\\Sigma} \\mathbf {g} \\right\\| ^ {2} \\right]. \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.519, + 0.356, + 0.534 + ], + "angle": 0, + "content": "Alg. 1 summarizes the training procedure." + }, + { + "type": "code_caption", + "bbox": [ + 0.088, + 0.541, + 0.339, + 0.555 + ], + "angle": 0, + "content": "Algorithm 1: Training SceneDiffuser" + }, + { + "type": "algorithm", + "bbox": [ + 0.082, + 0.557, + 0.47, + 0.799 + ], + "angle": 0, + "content": "1 // train base generation model \nInput: Trajectory in 3D scene \\((\\tau^0, S)\\) \n2 repeat \n3 \\(\\tau^0 \\sim p(\\tau^0 | S)\\) \n4 \\(\\epsilon \\sim \\mathcal{N}(0, I), t \\sim \\mathcal{U}(\\{1, \\dots, T\\})\\) \n5 \\(\\pmb{\\tau}^t = \\sqrt{\\hat{\\alpha}_t} \\pmb{\\tau}_0 + \\sqrt{1 - \\hat{\\alpha}_t} \\pmb{\\epsilon}\\) \n6 \\(\\theta = \\theta - \\eta \\nabla_\\theta \\| \\pmb{\\epsilon} - \\pmb{\\epsilon}_\\theta (\\pmb{\\tau}^t, t, S) \\|_2^2\\) \n7 until converged; \n8 // (optional) train optimization and planning model \nInput: Trajectory in 3D scene with goal \\((\\tau^0, S, G)\\), learned \\(\\theta\\) for \\(p_\\theta(\\tau^0 | S)\\) \n9 repeat \n10 \\(\\pmb{\\tau}^0 \\sim p(\\pmb{\\tau}^0 | S, G)\\) \n11 \\(\\epsilon \\sim \\mathcal{N}(0, I), t \\sim \\mathcal{U}(\\{1, \\dots, T\\})\\) \n12 \\(\\pmb{\\mu} = \\pmb{\\mu}_\\theta(\\pmb{\\tau}^t, t, S), \\pmb{\\Sigma} = \\pmb{\\Sigma}_\\theta(\\pmb{\\tau}^t, t, S)\\) \n13 \\(\\mathbf{g} = \\nabla_{\\pmb{\\tau}^t} \\log p_\\phi(\\mathcal{G} | \\pmb{\\tau}^t, S) |_{\\pmb{\\tau}^t = \\pmb{\\mu}}\\) \n14 \\(\\pmb{\\tau}^t = \\sqrt{\\hat{\\alpha}_t} \\pmb{\\tau}_0 + \\sqrt{1 - \\hat{\\alpha}_t} \\pmb{\\epsilon}\\) \n15 \\(\\phi = \\phi - \\eta \\nabla_\\phi \\| \\pmb{\\epsilon} - \\pmb{\\epsilon}_\\theta(\\pmb{\\tau}^t, t, S) - \\lambda \\pmb{\\Sigma} \\mathbf{g} \\|_2^2\\) \n16 until converged;" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.818, + 0.187, + 0.833 + ], + "angle": 0, + "content": "4.2. Sampling" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.472, + 0.902 + ], + "angle": 0, + "content": "With different sampling strategies, SceneDiffuser can generate, optimize, and plan the trajectory in 3D scenes under a unified framework of guided sampling. Alg. 2 summarizes the detailed sampling algorithm." + }, + { + "type": "code_caption", + "bbox": [ + 0.509, + 0.095, + 0.85, + 0.125 + ], + "angle": 0, + "content": "Algorithm 2: Sampling SceneDiffuser for generation, optimization, and planning" + }, + { + "type": "algorithm", + "bbox": [ + 0.507, + 0.127, + 0.892, + 0.427 + ], + "angle": 0, + "content": "Modules: Model \\(p_{\\theta}(\\cdot |\\mathcal{S})\\) , optimization objective \\(\\varphi_o(\\cdot |\\mathcal{S})\\) , and planner objective \\(\\varphi_p(\\cdot |\\mathcal{S},\\mathcal{G})\\) \n1 // one-step guided sampling \n2 function sample \\((\\tau^t,\\mathcal{J})\\) .. \n3 \\(\\mu = \\mu_{\\theta}(\\tau^{t},t,\\mathcal{S}),\\Sigma = \\Sigma_{\\theta}(\\tau^{t},t,\\mathcal{S})\\) \n4 \\(\\tau^{t - 1} = \\mathcal{N}(\\tau^{t - 1};\\mu +\\lambda \\Sigma \\nabla_{\\tau^t}(\\mathcal{J}(\\tau^t |\\mathcal{S},\\mathcal{G}))|_{\\tau^t = \\mu},\\Sigma)\\) \n5 return \\(\\tau^{t - 1}\\) \n6 // physics-based generation Input: initial trajectory \\(\\tau^T\\sim \\mathcal{N}(0,\\mathbf{I})\\) \n7 for \\(t = T,\\dots ,1\\) do \n8 // sampling with optimization \n9 \\(\\tau^{t - 1} = \\mathrm{sample}(\\tau^t,\\varphi_o(\\cdot |\\mathcal{S}))\\) \n10 return \\(\\tau^0\\) \n11 // goal-oriented planning Input: planning steps \\(N\\) starting state \\(\\hat{\\mathbf{s}}_0\\) , initial plan \\(\\tau_0^T\\sim \\mathcal{N}(0,\\mathbf{I})\\) \n12 \\(i = 1\\) \n13 while not done and planning step \\(i < N\\) do \n14 for \\(t = T,\\dots ,1\\) do \n15 \\(\\tau_i^{t - 1} = \\mathrm{sample}(\\tau_i^t,\\varphi_o(\\cdot |\\mathcal{S}) + \\varphi_p(\\cdot |\\mathcal{S},\\mathcal{G}))\\) \n16 // planning as inpainting \n17 \\(\\tau_i^{t - 1}[0:i] = \\hat{\\mathbf{s}}_{0:i}\\) \n18 Act \\(\\hat{a}_{i - 1}\\) to reach \\(\\hat{\\mathbf{s}}_i = \\boldsymbol {\\tau}_i^0 [i],\\hat{\\mathbf{s}}_{0:i} = \\hat{\\mathbf{s}}_{0:i - 1}\\cup \\hat{\\mathbf{s}}_i\\) \n19 Increment planning step \\(i = i + 1\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.442, + 0.894, + 0.502 + ], + "angle": 0, + "content": "Scene-aware Generation Sampling \\(\\pmb{\\tau}^{0}\\) from the distribution \\(p_{\\theta}(\\pmb{\\tau}^{0}|\\mathcal{S})\\) in Eq. (3) directly solves the conditional generation tasks. The sampled trajectories represent diverse modes and possible interactions with the 3D scenes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.503, + 0.894, + 0.609 + ], + "angle": 0, + "content": "Physics-based Optimization In a differentiable manner, the physical relations between each state and the environment are defined by \\(\\varphi_{o}\\) in Eq. (4). For general optimization without the planning objective, the task goal \\(\\mathcal{G}\\) is to sample a plausible trajectory in 3D scenes. Therefore, we can draw physically plausible trajectories in 3D scenes by sampling from \\(p(\\tau^0 |S,\\mathcal{G})\\) with Eq. (10)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.61, + 0.895, + 0.821 + ], + "angle": 0, + "content": "Goal-oriented Planning This can be formulated as motion inpainting under the sampling framework. Given the start state \\(\\hat{\\mathbf{s}}_s\\) and the goal state \\(\\hat{\\mathbf{s}}_g\\), the planning module returns trajectory \\(\\hat{\\boldsymbol{\\tau}} = (\\hat{\\mathbf{s}}_0, \\hat{\\mathbf{a}}_0, \\dots, \\hat{\\mathbf{s}}_i, \\hat{\\mathbf{a}}_i, \\dots, \\hat{\\mathbf{s}}_g)\\) that can reach the goal state. We set the first state as \\(\\hat{\\mathbf{s}}_0 = \\hat{\\mathbf{s}}_s\\) and define the goal state and reward of goal-reaching in \\(\\varphi_p\\). For each step \\(i\\), we first keep the previous states and inpaint the remaining trajectory by sampling the goal-oriented SceneDiffuser with an iterative denoising process. Next, we take the action that can reach the next sampled state with \\((\\hat{\\mathbf{a}}_{i-1}, \\hat{\\mathbf{s}}_i)\\). As illustrated in Alg. 2, we repeat the planning steps until the goal or maximal planning step is reached. Our planner leverages the trajectory-level generator, thus more generalizable to long-horizon trajectories and novel scenes." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.832, + 0.66, + 0.848 + ], + "angle": 0, + "content": "4.3. Implementation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Model Architecture The design of SceneDiffuser follows the practices of conditional diffusion model [20,51,53]. Specifically, we augment the time-conditional diffusion" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16753" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.09, + 0.468, + 0.423 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.426, + 0.472, + 0.482 + ], + "angle": 0, + "content": "Figure 2. Model architecture of the SceneDiffuser. We use cross-attention to learn the relation between the input trajectory and scene condition. The optimizer and planner serve as the guidance for physically-plausible and goal-oriented trajectories." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.485, + 0.472, + 0.606 + ], + "angle": 0, + "content": "model with cross-attention [65] for flexible conditioning. As shown in Fig. 2, for each sampling step, the model computes the cross-attention between the 3D scene condition and input trajectory, wherein the key and value are learned from the condition, and the query is learned from the input trajectory. The computed vector is fed into a feed-forward layer to estimate the noise \\(\\epsilon\\). The 3D scene is processed by a scene encoder [45, 91]); please refer to Appendix B." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.606, + 0.472, + 0.773 + ], + "angle": 0, + "content": "Objective Design We consider two types of trajectory objectives for optimization and planning: (i) trajectory-level objective, and (ii) the accumulation of step-wise objective. For optimization, we consider step-wise collision, contact objective, and trajectory level smoothness objective, \\(\\{\\varphi_o^{\\mathrm{collision}},\\varphi_o^{\\mathrm{contact}},\\varphi_o^{\\mathrm{smoothness}}\\}\\). For planning, we consider the accumulation of simple step-wise distance, \\(\\varphi_p^{L_2}\\). Please refer to the Appendix C for details. Empirically, we observe that parameterizing the objectives with timestep \\(t\\) and increasing the guidance during the last several diffusion steps will enhance the effect of guidance." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.785, + 0.21, + 0.803 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.471, + 0.903 + ], + "angle": 0, + "content": "To demonstrate SceneDiffuser is general and applicable to various scenarios, we evaluate the SceneDiffuser on five scene understanding tasks. For generation, we evaluate the scene-conditioned human pose and motion generation and object-conditioned dexterous grasp generation. For planning, we evaluate the path planning for 3D navigation and motion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.183 + ], + "angle": 0, + "content": "planning for robot arms. Below we first introduce baseline methods, followed by detailed settings, results analyses, and ablative studies for each task. We provide detailed implementation and experimental settings in Appendix D, additional ablative studies in Appendix E, additional experiments in Appendix F, and additional qualitative results in Appendix G." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.183, + 0.895, + 0.32 + ], + "angle": 0, + "content": "Baseline Methods For conditional generation tasks, we primarily compare SceneDiffuser with the widely-adopted cVAE model [25, 31, 32, 73, 90] and its variants. We also compare with strategies for optimizing the physics of the trajectory in the cVAE, including integrating into training as loss and plugging upon as the post-optimization. For planning, we compare with a stochastic planner learned by imitation learning using Behavior Cloning (BC) and a simple heuristic-based deterministic planner guided by \\( L_{2} \\) distance." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.331, + 0.785, + 0.346 + ], + "angle": 0, + "content": "5.1. Task 1: Human Pose Generation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.356, + 0.895, + 0.507 + ], + "angle": 0, + "content": "Setup Scene-conditioned human pose generation aims to generate semantically plausible and physically feasible single-frame human bodies within the given 3D scenes. We evaluate the task on the 12 indoor scenes provided by PROX [15] and the refined version of PROX'S per-frame SMPL-X parameters from LEMO [86]. The input is the colored point cloud extracted by randomly downsampling the scene meshes provided in PROX. Training/testing splits are created following the literature [69, 90], resulting in \\(\\sim 53\\mathrm{k}\\) frames in 8 scenes for training and others for testing." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.508, + 0.896, + 0.764 + ], + "angle": 0, + "content": "Metrics We evaluate the physical plausibility of generated poses with both direct human evaluations and indirect collision and contact scores. We randomly selected 1000 frames in the four test scenes for the direct measure and instructed 26 Turkers to decide whether the generated human pose was plausible. We compute the mean percentage of plausible generation and term this metric as the plausible rate. For indirect measures, we report (i) the non-collision score of the generated human bodies by calculating the proportion of the scene vertices with positive SDF to the human body and (ii) the contact score by checking if the body contact with the scene in a distance [15] below a pre-defined threshold. Following the literature [84,90], we evaluate the diversities of global translation, generated SMPL-X parameters, and the marker-based body-mesh representation [89]. Specifically, we calculate the diversity of generated pose with the Average Pairwise Distance (APD) and standard deviation (std)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Results Tab. 1 quantitatively demonstrates that SceneDiffuser generates significantly better poses while maintaining generation diversity. We further provide qualitative comparisons between baseline models and SceneDiffuser in Fig. 3. While achieving a comparable diversity, collision, and contact performance, our model generates results that contain considerably more physically plausible poses (e.g., floating, severe collision). This is reflected by the significant superiority (i.e., over \\(28\\%\\) ) over" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "16754" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.103, + 0.089, + 0.867, + 0.104 + ], + "angle": 0, + "content": "Table 1. Quantitative results of human pose generation in 3D scenes. We report metrics for physical plausibility and diversity." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.107, + 0.892, + 0.175 + ], + "angle": 0, + "content": "
modelplausible rate↑non-collision score↑contact score↑APD (trans.)↑std (trans.)↑APD (param)↑std (param)↑APD (marker)↑std (marker)↑
cVAE (w/o. LHS) [90]14.8899.7896.421.2180.4942.8780.1663.6380.172
cVAE (w/ LHS) [90]16.1999.7599.251.0130.4162.9940.1703.6140.169
our (w/o opt.)21.0499.7499.430.7760.3313.2040.1953.4830.167
our (w/ opt.)44.7799.9398.051.0090.4133.2970.1973.6790.177
" + }, + { + "type": "table_caption", + "bbox": [ + 0.091, + 0.188, + 0.877, + 0.202 + ], + "angle": 0, + "content": "Table 2. Quantitative results of human motion generation in 3D scenes. We report model variants with and without the start pose." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.205, + 0.893, + 0.299 + ], + "angle": 0, + "content": "
modelplausible rate↑non-collision score↑contact score↑APD (trans.)↑std (trans.)↑APD (param)↑std (param)↑APD (marker)↑std (marker)↑
cVAE (w/o start) [73]7.7299.8686.261.6280.6132.7660.1553.2750.150
ours (w/o start)21.6799.7197.920.5680.2372.3390.1263.2990.151
ours (w/o start & w/ opt.)25.8399.9398.910.4730.1962.4050.1273.3850.154
cVAE (w/ start) [73]17.6599.8895.440.4780.1881.7470.0912.3080.105
ours (w/ start)36.5699.8598.470.1930.0811.3720.0651.5680.072
ours (w/ start & w/ opt.)38.4499.9498.430.1680.0701.3890.0651.5750.072
" + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.314, + 0.892, + 0.564 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.57, + 0.893, + 0.598 + ], + "angle": 0, + "content": "Figure 3. Qualitative results of human pose generation in 3D scenes. From left to right: (a) cVAE generation, (b) SceneDiffuser generation without optimization, and poses generated (c) with and (d) without applying our optimization-guided sampling." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.602, + 0.471, + 0.724 + ], + "angle": 0, + "content": "cVAE-based baselines on plausible rates. We observe this large improvement both quantitatively from the plausible rate and non-collision score and qualitatively in Fig. 3. Notably, our optimization-guided sampling improves the generator with \\(23\\%\\) on the plausible rate, showing the efficacy of the proposed optimization-guided sampling strategy and its potential for a broader range of 3D tasks with physic-based constraints or objectives." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.739, + 0.383, + 0.755 + ], + "angle": 0, + "content": "5.2. Task 2: Human Motion Generation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Setup We consider generating human motion sequences under two different settings: (1) condition solely on the 3D scene, and (2) condition on both the starting pose and the 3D scene. We use the same human and scene representation as in Sec. 5.1 and clip the original LEMO motion sequence into segments with a fixed duration (60 frames). In total, we obtain 28k motion segments, with the distance between each start and end pose being longer than 0.2 meters. We follow the same split in Sec. 5.1 for training/testing and the same" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.602, + 0.893, + 0.648 + ], + "angle": 0, + "content": "evaluation metrics for the pose generation. We report the average values of pose metrics over motion sequence as our performance measure." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Results As quantitatively shown in Tab. 2, SceneDiffuser consistently generates high-quality motion sequences compared to cVAE baselines. Specifically, our generated motion outperforms baseline models on plausible rate, non-collision score, and contact score. This performance gain indicates better coverage of motion that involves rich interaction with the scene while remaining physically plausible. It also causes lower diversity in metrics (e.g., translation variance) since the plausible space for the motion is limited compared with cVAE. Empirically, we observe that providing the start position of motion as a condition constrains possible future motion sequences and leads to a drop in generation diversity for all models. We also note only a marginal performance improvement after applying optimization-guided sampling. One potential reason is that the generated motions are already plausible" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16755" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.088, + 0.473, + 0.205 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.206, + 0.47, + 0.233 + ], + "angle": 0, + "content": "Figure 4. Human motions generated by SceneDiffuser. Each row shows sampled human motions from the same start pose." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.237, + 0.471, + 0.298 + ], + "angle": 0, + "content": "and receive small guidance from the optimization. As qualitatively shown in Fig. 4, SceneDiffuser generates diverse motions (e.g., \"sit,\" \"walk\") from the same start position in unseen 3D scenes." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.306, + 0.395, + 0.322 + ], + "angle": 0, + "content": "5.3. Task 3: Dexterous Grasp Generation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.33, + 0.471, + 0.495 + ], + "angle": 0, + "content": "Setup Dexterous grasp generation aims to generate diverse and stable grasping poses for the given object with a human-like dexterous hand. We use the Shadowhand subset of the MultiDex [31] dataset, which contains diverse dexterous grasping poses for 58 daily objects. We represent the pose of Shadowhand as \\( q \\coloneqq (t,R,\\theta) \\in \\mathbb{R}^{33} \\), where \\( t \\in \\mathbb{R}^3 \\) and \\( R \\in \\mathbb{R}^6 \\) denote the global translation and orientation respectively, and \\( \\theta \\in \\mathbb{R}^{24} \\) describes the rotation angles of the revolute joints. An object is represented by its point cloud \\( \\mathcal{O} \\in \\mathbb{R}^{2048 \\times 3} \\). We split the dataset into 48 seen objects and 10 unseen objects for training and testing, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.496, + 0.47, + 0.691 + ], + "angle": 0, + "content": "Metrics We evaluate models in terms of success rate, diversity, and collision depth. We test if a grasp is successful in IsaacGym [37] by applying external forces to the object and measuring the movement of the object. To measure how learned models capture the diversity of successful grasping pose in the training data, we report the success rate of generated poses that lies at different variance levels from the mean pose of training data. We measure the collision depth as the maximum depth that the hand penetrates the object in each successful grasp for testing models' performance on physically correct grasps. In all cases, we ignore the root transformation of the hand as it does not contribute to the diversity of grasping types." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.692, + 0.47, + 0.722 + ], + "angle": 0, + "content": "Results Tab. 3 quantitatively demonstrates that SceneDiffuser generates significantly better grasp poses in" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.09, + 0.894, + 0.146 + ], + "angle": 0, + "content": "Table 3. Quantitative results of dexterous grasp generation on MultiDex [31] dataset. We measure the success rates under different diversities and depth collisions. TTA. denotes test-time optimization with physics and contact." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.149, + 0.892, + 0.239 + ], + "angle": 0, + "content": "
modelsucc. rate (%)↑depth coll. (mm)↓
σ2σall
cVAE [25]0.0010.0914.0622.98
cVAE (w/ TTA.) [25]0.0021.9117.9715.19
ours (w/o opt.)70.6571.2571.2517.34
ours (w/ opt.)71.2769.8469.8414.61
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.251, + 0.895, + 0.417 + ], + "angle": 0, + "content": "terms of success rate while correctly balancing the diversity of generation and grasp success. This result indicates that the SceneDiffuser achieves a consistently high success rate without much performance drop when the generated pose diverges from the mean pose in the training data. We also show that, by applying optimizer upon SceneDiffuser, the guided sampling process can reduce the violation of physically implausible grasping poses, outperforming the state-of-the-art baseline [25] without additional training or intermediate representation (i.e., contact maps). We provide qualitative results in Fig. 5 for visualization." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.435, + 0.821, + 0.452 + ], + "angle": 0, + "content": "5.4. Task 4: Path Planning for Navigation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.462, + 0.894, + 0.658 + ], + "angle": 0, + "content": "Setup We selected 61 indoor scenes from ScanNet [9] to construct room-level scenarios for navigational path planning and annotated these scenes with navigation graphs. As shown in Fig. 6b, these annotations are more spatially dense and physically plausible compared to previous methods [1]. We represent the physical robot with a cylinder to simulate physically plausible trajectories; see Fig. 6a. In total, we collected around 6k trajectories by searching the shortest paths between the randomly selected start and target nodes on the graph. We use trajectories in 46 scenes for training and the rest 15 scenes for evaluation. Models take the input as the scene point cloud \\( S \\in \\mathbb{R}^{32768 \\times 3} \\), a given start position \\( \\hat{\\mathbf{s}}_0 \\in \\mathbb{R}^2 \\), and a target position \\( \\mathcal{G} \\in \\mathbb{R}^2 \\) on the floor plane." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.661, + 0.892, + 0.722 + ], + "angle": 0, + "content": "Metrics We evaluate the planned results by checking if the \"robot\" can move from the start to the target without collision along the planned trajectory. We report the average success rate and planning steps over all test cases." + }, + { + "type": "image", + "bbox": [ + 0.078, + 0.722, + 0.892, + 0.867 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.869, + 0.894, + 0.898 + ], + "angle": 0, + "content": "Figure 5. Qualitative results of dexterous grasp generation. Compared to grasps generated by cVAE (first row), SceneDiffuser (second row) generates fewer colliding or floating poses, which helps to achieve a higher success rate." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "16756" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.276, + 0.241 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.126, + 0.243, + 0.23, + 0.257 + ], + "angle": 0, + "content": "(a) path planning" + }, + { + "type": "image", + "bbox": [ + 0.277, + 0.089, + 0.47, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.309, + 0.243, + 0.432, + 0.257 + ], + "angle": 0, + "content": "(b) navigation graph" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.26, + 0.47, + 0.289 + ], + "angle": 0, + "content": "Figure 6. Path planning for 3D scene navigation. SceneDiffuser generates trajectories in long-horizon tasks." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.292, + 0.473, + 0.534 + ], + "angle": 0, + "content": "Results As shown in Tab. 4, SceneDiffuser outperforms both the BC and the deterministic planner baseline. These results indicate the efficacy of guided sampling with the planning objective, especially given that all test scenes are unseen during training. Crucially, as simple heuristics (like \\( L_{2} \\)) oftentimes lead to dead-ends in path planning, SceneDiffuser can correctly combine past knowledge on the scene-conditioned trajectory distribution and planning objective under specific unseen scenes to redirect planning direction, which helps to avoid obstacles and dead-ends to reach the goal successfully. Compared with the baseline models, our model also requires fewer planning steps while maintaining a higher success rate. This suggests that SceneDiffuser successfully navigates to the target without diverging even in long-horizon tasks, where classic RL-based stochastic planners suffer (i.e., the low performance of BC)." + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.535, + 0.47, + 0.563 + ], + "angle": 0, + "content": "Table 4. Quantitative results of path planning in 3D navigation and motion planning for robot arms." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.565, + 0.47, + 0.672 + ], + "angle": 0, + "content": "
taskmodelsucc. rate(%)↑planning steps↓
path planBC0150
deterministic(L2)13.50137.98
ours73.7590.38
arm motionBC0.31299.08
deterministic(L2)72.87141.28
ours78.59147.60
" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.681, + 0.43, + 0.699 + ], + "angle": 0, + "content": "5.5. Task 5: Motion Planning for Robot Arms" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.471, + 0.825 + ], + "angle": 0, + "content": "Setup Aiming to generate valid robot arm motion trajectories in cluttered scenes, we used the Franka Emika arm with seven revolute joints and collected 19,800 trajectories over 200 randomly generated cluttered scenes using the MoveIt 2.0 [50], as shown in Fig. 7. We represent the scene with point clouds \\( S \\in \\mathbb{R}^{4096 \\times 3} \\) and the robot arm trajectory with a sequence of joint angles \\( \\mathcal{R} \\in [-\\pi, \\pi] \\). We train our model on 160 scenes and test on 40 unseen scenes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Metrics Similar to Sec. 5.4, we evaluate the generated trajectories by success rate on unseen scenes and the average number of planning steps. We consider a trajectory successful if the robot arm reaches the goal pose by a certain distance threshold within a limited number of steps." + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.089, + 0.695, + 0.241 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.541, + 0.243, + 0.661, + 0.258 + ], + "angle": 0, + "content": "(a) motion planning" + }, + { + "type": "image", + "bbox": [ + 0.695, + 0.089, + 0.895, + 0.242 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.734, + 0.243, + 0.852, + 0.256 + ], + "angle": 0, + "content": "(b) cluttered scenes" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.26, + 0.895, + 0.289 + ], + "angle": 0, + "content": "Figure 7. Motion planning for robot arms. SceneDiffuser generates arm motions in tabletop scenes with obstacles." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.293, + 0.895, + 0.385 + ], + "angle": 0, + "content": "Results We observe similar overall performance as in Sec. 5.4. Tab. 4 shows that SceneDiffuser consistently outperforms both the RL-based BC and the deterministic planner baseline. SceneDiffuser's planning steps for successful trials are also comparable with the deterministic planner, showing the efficacy of the planner in long-horizon scenarios." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.393, + 0.677, + 0.409 + ], + "angle": 0, + "content": "5.6. Ablation Analyses" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.416, + 0.895, + 0.552 + ], + "angle": 0, + "content": "We explore how the scaling coefficient \\(\\lambda\\) influences the human pose generation results. We report the diversity and physics metrics of sampling results under different \\(\\lambda\\)s, ranging from 0.1 to 100. As shown in Tab. 5, \\(\\lambda\\) balances generation collision/contact and diversity in human pose generation. Specifically, \\(\\lambda = 1.0\\) leads to the best physical plausibility, while larger \\(\\lambda\\) values lead to diverse generation results. We attribute this effect to the optimization as with bigger \\(\\lambda\\)s; the optimization will draw poses away from the scene." + }, + { + "type": "table_caption", + "bbox": [ + 0.516, + 0.553, + 0.875, + 0.567 + ], + "angle": 0, + "content": "Table 5. Ablation of the scale coefficient for optimization." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.57, + 0.894, + 0.664 + ], + "angle": 0, + "content": "
metricλ = 0.1λ = 1.0λ = 10.0λ = 100.0
plausible rate ↑28.7552.521.250
APD (trans.) ↑0.7640.8861.56423.96
APD (param) ↑3.2063.2439.040573.6
non-collison score ↑99.7699.8799.8574.9
contact score ↑99.7099.6581.750.0
" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.68, + 0.619, + 0.695 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.895, + 0.81 + ], + "angle": 0, + "content": "We propose the SceneDiffuser as a general conditional generative model for generation, optimization, and planning in 3D scenes. SceneDiffuser is designed with appealing properties, including scene-aware, physics-based, and goal-oriented. We demonstrate that the SceneDiffuser outperforms previous models by a large margin on various tasks, establishing its efficacy and flexibility." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Acknowledgments and disclosure of funding We thank Ruiqi Gao and Ying Nian Wu for their helpful discussions and suggestions. This work is supported in part by the National Key R&D Program of China (2021ZD0150200), the Beijing Nova Program, and the National Natural Science Foundation of China (NSFC) (62172043)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16757" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.09, + 0.176, + 0.107 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.473, + 0.198 + ], + "angle": 0, + "content": "[1] Peter Anderson, Qi Wu, Damien Teney, Jake Bruce, Mark Johnson, Niko Sunderhauf, Ian Reid, Stephen Gould, and Anton Van Den Hengel. Vision-and-language navigation: Interpreting visually-grounded navigation instructions in real environments. 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Illustration of the SceneDiffuser, applicable to various scene-conditioned 3D tasks: (a) human pose generation, (b) human motion generation, (c) dexterous grasp generation, (d) path planning for 3D navigation with goals, and (e) motion planning for robot arms. + +# Abstract + +We introduce the SceneDiffuser, a conditional generative model for 3D scene understanding. SceneDiffuser provides a unified model for solving scene-conditioned generation, optimization, and planning. In contrast to prior work, SceneDiffuser is intrinsically scene-aware, physics-based, and goal-oriented. With an iterative sampling strategy, SceneDiffuser jointly formulates the scene-aware generation, physics-based optimization, and goal-oriented planning via a diffusion-based denoising process in a fully differentiable fashion. Such a design alleviates the discrepancies among different modules and the posterior collapse of previous scene-conditioned generative models. We evaluate the SceneDiffuser on various 3D scene understanding tasks, including human pose and motion generation, dexterous grasp + +generation, path planning for 3D navigation, and motion planning for robot arms. The results show significant improvements compared with previous models, demonstrating the tremendous potential of the SceneDiffuser for the broad community of 3D scene understanding. + +# 1. Introduction + +The ability to generate, optimize, and plan in 3D scenes is a long-standing goal across computer vision, graphics, and robotics. Various tasks have been devised to achieve these goals, fostering downstream applications in motion generation [32, 69, 73, 90], motion planning [42, 43, 60, 75], grasp generation [25, 31, 34], navigation [1, 95], scene synthesis [24, 47, 72, 82], embodied perception and manipulation [30, 39, 61], and autonomous driving [3, 52]. + +Despite rich applications and great successes, existing models designed for these tasks exhibit two fundamental limitations for real-world 3D scene understanding. + +First, most prior work [8, 14, 32, 49, 60, 68-70, 73] leverages the conditional Variational Autoencoder (cVAE) for the conditional generation in 3D scenes. cVAE model utilizes an encoder-decoder structure to learn the posterior distribution and relies on the learned latent variables to sample. Although cVAE is easy to train and sample due to its simple architecture and one-step sampling procedure, it suffers from the posterior collapse problem [12, 17, 26, 64, 69, 84, 93]; the learned latent variable is ignored by a strong decoder, leading to limited generation diversity from these collapsed modes. Such collapse is further magnified in 3D tasks with stronger 3D decoders and more complex and noisy input conditions, e.g., the natural 3D scans [9]. + +Second, despite the close relations among generation, optimization, and planning in 3D scenes, there lacks a unified framework that could address existing discrepancies among these models. Previous work [15, 34, 69] applies off-the-shelf physics-based post-optimization methods over outputs of generative models and often produces inconsistent and implausible generations, especially when transferring to novel scenes. Similarly, planners are usually standalone modules over results of generative model [8, 14] for trajectory planning or learned separately with the reinforcement learning (RL) [95], leading to gaps between planning and other modules (e.g., generation) during inference, especially in novel scenes where explorations are limited. + +To tackle the above limitations, we introduce the SceneDiffuser, a conditional generative model based on the diffusion process. SceneDiffuser eliminates the discrepancies and provides a single home for scene-conditioned generation, optimization, and planning. Specifically, with a denoising process, it learns a diffusion model for scene-conditioned generation during training. In inference, SceneDiffuser jointly solves the scene-aware generation, physics-based optimization, and goal-oriented planning through a unified iterative guided-sampling framework. Such a design equips the SceneDiffuser with the following three superiority: + +1. Generation: Building upon the diffusion model, SceneDiffuser solves the posterior collapse problem of scene-conditioned generative models. Since the forward diffusion process can be treated as data augmentation in 3D scenes, it helps traverse sufficient scene-conditioned distribution modes. +2. Optimization: SceneDiffuser integrates the physics-based objective into each step of the sampling process as conditional guidance, enabling the differentiable physics-based optimization during both the learning and sampling process. This design facilitates the physically-plausible generation, which is critical for tasks in 3D scenes. +3. Planning: Based on the scene-conditioned trajectory-level generator, SceneDiffuser possesses a physics- and goal-aware trajectory planner, generalizing better to long-horizon trajectories and novel 3D scenes. + +As illustrated in Fig. 1, we evaluate the SceneDiffuser on diverse 3D scene understanding tasks. The human pose, motion, and dexterous grasp generation results significantly improve, demonstrating plausible and diverse generations with the 3D scene and object conditions. The results on path planning for 3D navigation and motion planning for robot arms reveal the generalizable and long-horizon planning capability of the SceneDiffuser. + +# 2. Related Work + +Conditional Generation in 3D Scenes Generating diverse contents and rich interactions in 3D scenes is essential for understanding the 3D scene affordances. Several applications have emerged on conditional scene generation [24,47,71,81,88], human pose [16,32,87,90,92] and motion generation [14,32,49,60,68-70,73] in furnished 3D indoor scenes, and object-conditioned grasp pose generation [25,31,34,62,78]. However, most previous methods [6,14,16,25,31,62,68,73,75] rely on cVAE and suffer from the posterior collapse problem [12,17,26,64,69,84,93], especially when the 3D scene is natural and complex. In this work, SceneDiffuser addresses the posterior collapse with the diffusion-based denoising process. + +Physics-based Optimization in 3D Scenes Producing physically plausible generations compatible with 3D scenes is challenging in the scene-conditioned generation. Previous work uses physics-based post-optimization [15, 34, 69] or differentiable objective [25, 73, 90] to integrate collision and contact constraints into the generation framework. However, post-optimization approaches [15, 34, 69] cannot be learned jointly with the generative models, yielding inconsistent generation results. Similarly, differentiable approaches [25, 73, 90] impose constraints on the final objective and cannot optimize the physical interactions during sampling, resulting in implausible generations, particularly when adapting to novel scenes. In this work, SceneDiffuser avoids such inconsistency by integrating differentiable physics-based optimization into each step of the sampling process. + +Planning in 3D Scenes The ability to act and plan in 3D scenes is critical for an intelligent agent and has led to the recent culmination of embodied AI research [28, 30, 33, 36, 54, 55, 79]. Among all tasks, visual navigation has been most studied in the vision and robotics community [4, 13, 21, 40, 76, 77, 94, 95]. However, existing work relies heavily on model-based planners with the single-step dynamic model [5,11,48,67,74,80], lacking a trajectory-level optimization for long-horizon planning. Further, these planners lack explicit modeling of physical interactions, making it difficult to generalize to natural scenes with limited exploration, where rapid learning and adaptation are required. Compared with the global trajectory planner based on a trajectory-level generator, SceneDiffuser exhibits superior generalization in long-horizon plans and novel 3D scenes. + +Diffusion-based Models Diffusion model [19,22,57, 59] has come forth into a promising class of generative model for learning and sampling data distributions with an iterative denoising process, facilitating the image [10, 58], text [83], and shape generation [35]. With flexible conditioning, it is further extended to the language-conditioned image [41, 51, 53], video [18, 56], and 3D generation [44, 63, 85]. Notably, Janner et al. [23] integrate the generation and planning into the same sampling framework for behavior synthesis. To our best knowledge, SceneDiffuser is the first framework that models the 3D scene-conditioned generation with a diffusion model and integrates the generation, optimization, and planning into a unified framework. + +# 3. Background + +# 3.1. Problem Definition + +Given a 3D scene $S$ , we aim to generate the optimal solution for completing the tasks (e.g., navigation, manipulation) given the goal $\mathcal{G}$ in the scene. We denote the state and action of an agent as $(\mathbf{s},\mathbf{a})$ . The dynamic model defines the state transition as $p(\mathbf{s}_{i + 1}|\mathbf{s}_i,\mathbf{a}_i)$ , which is often deterministic in scene understanding (i.e., $f(\mathbf{s}_i,\mathbf{a}_i)$ ). The trajectory is defined as $\boldsymbol{\tau} = (\mathbf{s}_0,\mathbf{a}_0,\dots ,\mathbf{s}_i,\mathbf{a}_i,\dots ,\mathbf{s}_N)$ , where $N$ denotes the horizon of task solving in discrete time. + +# 3.2. Planning with Trajectory Optimization + +The scene-conditional trajectory optimization is defined as maximizing the task objective: + +$$ +\boldsymbol {\tau} ^ {*} = \underset {\boldsymbol {\tau}} {\arg \max } \mathcal {J} (\boldsymbol {\tau} | \mathcal {S}, \mathcal {G}). \tag {1} +$$ + +The dynamic model is usually known for trajectory optimization. Considering the future actions and states with predictable dynamics, the entire trajectory $\tau$ can be optimized jointly and non-progressively with traditional [29] or data-driven [7] planning algorithms. Trajectory-based optimization benefits from its global awareness of history and future states, thus can better model the long-horizon tasks compared with single-step models in RL, where $\mathbf{a}_{0:N}^{*} =$ + +$$ +\underset {\mathbf {a} _ {0: N}} {\arg \max } \sum_ {i = 0} ^ {N} r (\mathbf {s} _ {i}, \mathbf {a} _ {i} | \mathcal {S}, \mathcal {G}). +$$ + +# 3.3. Diffusion Model + +Diffusion model [19,22,57] is a class of generative models representing the data generation with an iterative denoising process from Gaussian noise. It consists of a forward and a reverse process. The forward process $q(\tau^t |\tau^{t - 1})$ gradually destroys data $\tau^0\sim q(\tau^0)$ into Gaussian noise. The parametrized reverse process $p_{\theta}(\tau^{t - 1}|\tau^t)$ recovers the data from noise with the learned normal distribution from a fixed timestep. The training objective for $\theta$ is denoising score matching over multiple noise scale [22,66]. Please refer to the Appendix A for details of diffusion model and variants. + +# 4. SceneDiffuser + +SceneDiffuser models planning as trajectory optimization and solves the aforementioned problem with the spirit of planning as sampling, where the trajectory optimization is achieved by sampling trajectory-level distribution learned by the model. Leveraging the diffusion model with gradient-based sampling and flexible conditioning, SceneDiffuser models the scene-conditioned goal-oriented trajectory $p(\tau^0 | S, \mathcal{G})$ : + +$$ +\begin{array}{l} p \left(\boldsymbol {\tau} ^ {0} | \mathcal {S}, \mathcal {G}\right) = \frac {p _ {\theta} \left(\boldsymbol {\tau} ^ {0} | \mathcal {S}\right) p _ {\phi} \left(\mathcal {G} \mid \boldsymbol {\tau} ^ {0} , \mathcal {S}\right)}{p \left(\mathcal {G} \mid \mathcal {S}\right)} \tag {2} \\ \propto p _ {\theta} (\tau^ {0} | \mathcal {S}) p _ {\phi} (\mathcal {G} | \tau^ {0}, \mathcal {S}). \\ \end{array} +$$ + +Generation $p_{\theta}(\pmb{\tau}^{0}|\mathcal{S})$ characterizes the probability of generating certain trajectories with the scene condition. It can be modeled using a conditional diffusion model [19, 57] with an iterative denoising process: + +$$ +p _ {\theta} \left(\boldsymbol {\tau} ^ {0} \mid \mathcal {S}\right) = p \left(\boldsymbol {\tau} ^ {T}\right) \prod_ {t = 1} ^ {T} p \left(\boldsymbol {\tau} ^ {t - 1} \mid \boldsymbol {\tau} ^ {t}, \mathcal {S}\right), \tag {3} +$$ + +$$ +p (\boldsymbol {\tau} ^ {t - 1} | \boldsymbol {\tau} ^ {t}, \mathcal {S}) = \mathcal {N} (\boldsymbol {\tau} ^ {t - 1}; \boldsymbol {\mu} _ {\theta} (\boldsymbol {\tau} ^ {t}, t, \mathcal {S}), \boldsymbol {\Sigma} _ {\theta} (\boldsymbol {\tau} ^ {t}, t, \mathcal {S})). +$$ + +Optimization and Planning $p_{\phi}(\mathcal{G}|\boldsymbol{\tau}^0,\mathcal{S})$ represents the probability of reaching the goal with the sampled trajectory, where the goal can be flexibly defined by customized objective functions in various tasks. As shown in Eq. (4), the precise definition of this probability is $p_{\phi}(\mathcal{O} = 1|\boldsymbol{\tau}^0,\mathcal{S},\mathcal{G})$ where $O$ is an optimality indicator that represents if the goal were achieved. Intuitively, the trajectory objective in Eq. (1) can indicate such optimality. We therefore expand $p_{\phi}(\mathcal{G}|\boldsymbol{\tau}^t,\mathcal{S})$ as its exponential in Eq. (5): + +$$ +p _ {\phi} (\mathcal {G} | \boldsymbol {\tau} ^ {t}, \mathcal {S}) = p _ {\phi} \left(\mathcal {O} = 1 | \boldsymbol {\tau} ^ {t}, \mathcal {S}, \mathcal {G}\right) \tag {4} +$$ + +$$ +\propto \exp (\mathcal {J} (\boldsymbol {\tau} ^ {t} | \mathcal {S}, \mathcal {G})) \tag {5} +$$ + +$$ += \exp \left(\varphi_ {p} \left(\boldsymbol {\tau} ^ {t} | \mathcal {S}, \mathcal {G}\right) + \varphi_ {o} \left(\boldsymbol {\tau} ^ {t} | \mathcal {S}\right), \right. \tag {6} +$$ + +where $\varphi_{o}(\pmb{\tau}^{t}|\mathcal{S})$ denotes the objective for optimizing the trajectory with scene condition and is independent of task goal $\mathcal{G}$ . In scene understanding, $\varphi_{o}$ usually denotes plausible physical relationships (e.g., collision, contact, and intersection). $\varphi_{p}(\pmb{\tau}^{t}|\mathcal{S},\mathcal{G})$ indicates the objective for planning (i.e., goal-reaching) with scene condition. Both $\varphi_{o}$ and $\varphi_{p}$ can be explicitly defined or implicitly learned from observed trajectories with proper parametrization. + +# 4.1. Learning + +$p_{\theta}(\tau^0 |S)$ is the scene-conditioned generator, which can be learned by the conditional diffusion model with the simplified objective of estimating the noise $\epsilon$ [10, 19, 20], where + +$$ +\begin{array}{l} \mathcal {L} _ {\theta} \left(\boldsymbol {\tau} ^ {0} \mid \mathcal {S}\right) = \mathbb {E} _ {t, \epsilon , \boldsymbol {\tau} ^ {0}} \left[ \| \boldsymbol {\epsilon} - \boldsymbol {\epsilon} _ {\theta} \left(\sqrt {\hat {\alpha} ^ {t}} \boldsymbol {\tau} ^ {0} + \sqrt {1 - \hat {\alpha} ^ {t}} \boldsymbol {\epsilon}, t, \mathcal {S}\right) \| ^ {2} \right] \tag {7} \\ = \mathbb {E} _ {t, \epsilon , \tau^ {0}} \left[ \| \epsilon - \epsilon_ {\theta} (\tau^ {t}, t, S) \| ^ {2} \right], \\ \end{array} +$$ + +where $\hat{\alpha}^t$ is the pre-determined function in the forward process. With the learned $p_{\theta}(\tau^0 |S)$ , we sample $p(\tau^0 |S,\mathcal{G})$ by taking the advantage of the diffusion model's flexible conditioning [10, 23]. Specifically, we approximate $p_{\phi}(\mathcal{G}|\boldsymbol{\tau}^{t},\mathcal{S})$ using the Taylor expansion around $\boldsymbol{\tau}^{t} = \boldsymbol{\mu}$ at timestep $t$ as + +$$ +\log p _ {\phi} (\mathcal {G} | \boldsymbol {\tau} ^ {t}, \mathcal {S}) \approx (\boldsymbol {\tau} ^ {t} - \boldsymbol {\mu}) \mathbf {g} + C, \tag {8} +$$ + +where $C$ is a constant, $\pmb{\mu} = \pmb{\mu}_{\theta}(\pmb{\tau}^t,t,\mathcal{S})$ and $\Sigma = \Sigma_{\theta}(\pmb{\tau}^{t},t,\mathcal{S})$ are the inferred parameters of original diffusion process, and + +$$ +\begin{array}{l} \mathbf {g} = \nabla_ {\boldsymbol {\tau} ^ {t}} \log p _ {\phi} (\mathcal {G} | \boldsymbol {\tau} ^ {t}, \mathcal {S}) | _ {\boldsymbol {\tau} ^ {t} = \boldsymbol {\mu}} \tag {9} \\ = \nabla_ {\tau^ {t}} \left(\varphi_ {o} \left(\tau^ {t} | \mathcal {S}\right) + \varphi_ {p} \left(\tau^ {t} | \mathcal {S}, \mathcal {G}\right)\right) | _ {\tau^ {t} = \mu}. \\ \end{array} +$$ + +Therefore, we have + +$$ +p \left(\boldsymbol {\tau} ^ {t - 1} \mid \boldsymbol {\tau} ^ {t}, \mathcal {S}, \mathcal {G}\right) = \mathcal {N} \left(\boldsymbol {\tau} ^ {t - 1}; \boldsymbol {\mu} + \lambda \boldsymbol {\Sigma} \mathbf {g}, \boldsymbol {\Sigma}\right), \tag {10} +$$ + +where $\lambda$ is the scaling factor for the guidance. With Eq. (10), we can sample $\pmb{\tau}^t$ with the guidance of optimizing and planning objectives. + +Of note, $\varphi_{p}$ and $\varphi_{o}$ serve as the pre-defined guidance for tilting the original trajectory with physical and goal constraints. However, they can also be learned from the observed trajectories. During training, we first fix the learned base model of $p_{\theta}(\tau^0 |S)$ , followed by learning $\phi_{o}$ and $\phi_{p}$ for optimization and planning with the following objective: + +$$ +\mathcal {L} _ {\phi} \left(\boldsymbol {\tau} ^ {0} \mid \mathcal {S}, \mathcal {G}\right) = \mathbb {E} _ {t, \epsilon , \boldsymbol {\tau} ^ {0}} \left[ \left\| \boldsymbol {\epsilon} - \boldsymbol {\epsilon} _ {\theta} \left(\boldsymbol {\tau} ^ {t}, t, \mathcal {S}\right) - \boldsymbol {\Sigma} \mathbf {g} \right\| ^ {2} \right]. \tag {11} +$$ + +Alg. 1 summarizes the training procedure. + +Algorithm 1: Training SceneDiffuser +1 // train base generation model +Input: Trajectory in 3D scene $(\tau^0, S)$ +2 repeat +3 $\tau^0 \sim p(\tau^0 | S)$ +4 $\epsilon \sim \mathcal{N}(0, I), t \sim \mathcal{U}(\{1, \dots, T\})$ +5 $\pmb{\tau}^t = \sqrt{\hat{\alpha}_t} \pmb{\tau}_0 + \sqrt{1 - \hat{\alpha}_t} \pmb{\epsilon}$ +6 $\theta = \theta - \eta \nabla_\theta \| \pmb{\epsilon} - \pmb{\epsilon}_\theta (\pmb{\tau}^t, t, S) \|_2^2$ +7 until converged; +8 // (optional) train optimization and planning model +Input: Trajectory in 3D scene with goal $(\tau^0, S, G)$ , learned $\theta$ for $p_\theta(\tau^0 | S)$ +9 repeat +10 $\pmb{\tau}^0 \sim p(\pmb{\tau}^0 | S, G)$ +11 $\epsilon \sim \mathcal{N}(0, I), t \sim \mathcal{U}(\{1, \dots, T\})$ +12 $\pmb{\mu} = \pmb{\mu}_\theta(\pmb{\tau}^t, t, S), \pmb{\Sigma} = \pmb{\Sigma}_\theta(\pmb{\tau}^t, t, S)$ +13 $\mathbf{g} = \nabla_{\pmb{\tau}^t} \log p_\phi(\mathcal{G} | \pmb{\tau}^t, S) |_{\pmb{\tau}^t = \pmb{\mu}}$ +14 $\pmb{\tau}^t = \sqrt{\hat{\alpha}_t} \pmb{\tau}_0 + \sqrt{1 - \hat{\alpha}_t} \pmb{\epsilon}$ +15 $\phi = \phi - \eta \nabla_\phi \| \pmb{\epsilon} - \pmb{\epsilon}_\theta(\pmb{\tau}^t, t, S) - \lambda \pmb{\Sigma} \mathbf{g} \|_2^2$ +16 until converged; + +# 4.2. Sampling + +With different sampling strategies, SceneDiffuser can generate, optimize, and plan the trajectory in 3D scenes under a unified framework of guided sampling. Alg. 2 summarizes the detailed sampling algorithm. + +Algorithm 2: Sampling SceneDiffuser for generation, optimization, and planning +Modules: Model $p_{\theta}(\cdot |\mathcal{S})$ , optimization objective $\varphi_o(\cdot |\mathcal{S})$ , and planner objective $\varphi_p(\cdot |\mathcal{S},\mathcal{G})$ +1 // one-step guided sampling +2 function sample $(\tau^t,\mathcal{J})$ .. +3 $\mu = \mu_{\theta}(\tau^{t},t,\mathcal{S}),\Sigma = \Sigma_{\theta}(\tau^{t},t,\mathcal{S})$ +4 $\tau^{t - 1} = \mathcal{N}(\tau^{t - 1};\mu +\lambda \Sigma \nabla_{\tau^t}(\mathcal{J}(\tau^t |\mathcal{S},\mathcal{G}))|_{\tau^t = \mu},\Sigma)$ +5 return $\tau^{t - 1}$ +6 // physics-based generation Input: initial trajectory $\tau^T\sim \mathcal{N}(0,\mathbf{I})$ +7 for $t = T,\dots ,1$ do +8 // sampling with optimization +9 $\tau^{t - 1} = \mathrm{sample}(\tau^t,\varphi_o(\cdot |\mathcal{S}))$ +10 return $\tau^0$ +11 // goal-oriented planning Input: planning steps $N$ starting state $\hat{\mathbf{s}}_0$ , initial plan $\tau_0^T\sim \mathcal{N}(0,\mathbf{I})$ +12 $i = 1$ +13 while not done and planning step $i < N$ do +14 for $t = T,\dots ,1$ do +15 $\tau_i^{t - 1} = \mathrm{sample}(\tau_i^t,\varphi_o(\cdot |\mathcal{S}) + \varphi_p(\cdot |\mathcal{S},\mathcal{G}))$ +16 // planning as inpainting +17 $\tau_i^{t - 1}[0:i] = \hat{\mathbf{s}}_{0:i}$ +18 Act $\hat{a}_{i - 1}$ to reach $\hat{\mathbf{s}}_i = \boldsymbol {\tau}_i^0 [i],\hat{\mathbf{s}}_{0:i} = \hat{\mathbf{s}}_{0:i - 1}\cup \hat{\mathbf{s}}_i$ +19 Increment planning step $i = i + 1$ + +Scene-aware Generation Sampling $\pmb{\tau}^{0}$ from the distribution $p_{\theta}(\pmb{\tau}^{0}|\mathcal{S})$ in Eq. (3) directly solves the conditional generation tasks. The sampled trajectories represent diverse modes and possible interactions with the 3D scenes. + +Physics-based Optimization In a differentiable manner, the physical relations between each state and the environment are defined by $\varphi_{o}$ in Eq. (4). For general optimization without the planning objective, the task goal $\mathcal{G}$ is to sample a plausible trajectory in 3D scenes. Therefore, we can draw physically plausible trajectories in 3D scenes by sampling from $p(\tau^0 |S,\mathcal{G})$ with Eq. (10). + +Goal-oriented Planning This can be formulated as motion inpainting under the sampling framework. Given the start state $\hat{\mathbf{s}}_s$ and the goal state $\hat{\mathbf{s}}_g$ , the planning module returns trajectory $\hat{\boldsymbol{\tau}} = (\hat{\mathbf{s}}_0, \hat{\mathbf{a}}_0, \dots, \hat{\mathbf{s}}_i, \hat{\mathbf{a}}_i, \dots, \hat{\mathbf{s}}_g)$ that can reach the goal state. We set the first state as $\hat{\mathbf{s}}_0 = \hat{\mathbf{s}}_s$ and define the goal state and reward of goal-reaching in $\varphi_p$ . For each step $i$ , we first keep the previous states and inpaint the remaining trajectory by sampling the goal-oriented SceneDiffuser with an iterative denoising process. Next, we take the action that can reach the next sampled state with $(\hat{\mathbf{a}}_{i-1}, \hat{\mathbf{s}}_i)$ . As illustrated in Alg. 2, we repeat the planning steps until the goal or maximal planning step is reached. Our planner leverages the trajectory-level generator, thus more generalizable to long-horizon trajectories and novel scenes. + +# 4.3. Implementation + +Model Architecture The design of SceneDiffuser follows the practices of conditional diffusion model [20,51,53]. Specifically, we augment the time-conditional diffusion + +![](images/68fa2e81625f8035f9003dff5d110a55349c4fcbe275317a61698eb4977b5392.jpg) +Figure 2. Model architecture of the SceneDiffuser. We use cross-attention to learn the relation between the input trajectory and scene condition. The optimizer and planner serve as the guidance for physically-plausible and goal-oriented trajectories. + +model with cross-attention [65] for flexible conditioning. As shown in Fig. 2, for each sampling step, the model computes the cross-attention between the 3D scene condition and input trajectory, wherein the key and value are learned from the condition, and the query is learned from the input trajectory. The computed vector is fed into a feed-forward layer to estimate the noise $\epsilon$ . The 3D scene is processed by a scene encoder [45, 91]); please refer to Appendix B. + +Objective Design We consider two types of trajectory objectives for optimization and planning: (i) trajectory-level objective, and (ii) the accumulation of step-wise objective. For optimization, we consider step-wise collision, contact objective, and trajectory level smoothness objective, $\{\varphi_o^{\mathrm{collision}},\varphi_o^{\mathrm{contact}},\varphi_o^{\mathrm{smoothness}}\}$ . For planning, we consider the accumulation of simple step-wise distance, $\varphi_p^{L_2}$ . Please refer to the Appendix C for details. Empirically, we observe that parameterizing the objectives with timestep $t$ and increasing the guidance during the last several diffusion steps will enhance the effect of guidance. + +# 5. Experiments + +To demonstrate SceneDiffuser is general and applicable to various scenarios, we evaluate the SceneDiffuser on five scene understanding tasks. For generation, we evaluate the scene-conditioned human pose and motion generation and object-conditioned dexterous grasp generation. For planning, we evaluate the path planning for 3D navigation and motion + +planning for robot arms. Below we first introduce baseline methods, followed by detailed settings, results analyses, and ablative studies for each task. We provide detailed implementation and experimental settings in Appendix D, additional ablative studies in Appendix E, additional experiments in Appendix F, and additional qualitative results in Appendix G. + +Baseline Methods For conditional generation tasks, we primarily compare SceneDiffuser with the widely-adopted cVAE model [25, 31, 32, 73, 90] and its variants. We also compare with strategies for optimizing the physics of the trajectory in the cVAE, including integrating into training as loss and plugging upon as the post-optimization. For planning, we compare with a stochastic planner learned by imitation learning using Behavior Cloning (BC) and a simple heuristic-based deterministic planner guided by $L_{2}$ distance. + +# 5.1. Task 1: Human Pose Generation + +Setup Scene-conditioned human pose generation aims to generate semantically plausible and physically feasible single-frame human bodies within the given 3D scenes. We evaluate the task on the 12 indoor scenes provided by PROX [15] and the refined version of PROX'S per-frame SMPL-X parameters from LEMO [86]. The input is the colored point cloud extracted by randomly downsampling the scene meshes provided in PROX. Training/testing splits are created following the literature [69, 90], resulting in $\sim 53\mathrm{k}$ frames in 8 scenes for training and others for testing. + +Metrics We evaluate the physical plausibility of generated poses with both direct human evaluations and indirect collision and contact scores. We randomly selected 1000 frames in the four test scenes for the direct measure and instructed 26 Turkers to decide whether the generated human pose was plausible. We compute the mean percentage of plausible generation and term this metric as the plausible rate. For indirect measures, we report (i) the non-collision score of the generated human bodies by calculating the proportion of the scene vertices with positive SDF to the human body and (ii) the contact score by checking if the body contact with the scene in a distance [15] below a pre-defined threshold. Following the literature [84,90], we evaluate the diversities of global translation, generated SMPL-X parameters, and the marker-based body-mesh representation [89]. Specifically, we calculate the diversity of generated pose with the Average Pairwise Distance (APD) and standard deviation (std). + +Results Tab. 1 quantitatively demonstrates that SceneDiffuser generates significantly better poses while maintaining generation diversity. We further provide qualitative comparisons between baseline models and SceneDiffuser in Fig. 3. While achieving a comparable diversity, collision, and contact performance, our model generates results that contain considerably more physically plausible poses (e.g., floating, severe collision). This is reflected by the significant superiority (i.e., over $28\%$ ) over + +Table 1. Quantitative results of human pose generation in 3D scenes. We report metrics for physical plausibility and diversity. + +
modelplausible rate↑non-collision score↑contact score↑APD (trans.)↑std (trans.)↑APD (param)↑std (param)↑APD (marker)↑std (marker)↑
cVAE (w/o. LHS) [90]14.8899.7896.421.2180.4942.8780.1663.6380.172
cVAE (w/ LHS) [90]16.1999.7599.251.0130.4162.9940.1703.6140.169
our (w/o opt.)21.0499.7499.430.7760.3313.2040.1953.4830.167
our (w/ opt.)44.7799.9398.051.0090.4133.2970.1973.6790.177
+ +Table 2. Quantitative results of human motion generation in 3D scenes. We report model variants with and without the start pose. + +
modelplausible rate↑non-collision score↑contact score↑APD (trans.)↑std (trans.)↑APD (param)↑std (param)↑APD (marker)↑std (marker)↑
cVAE (w/o start) [73]7.7299.8686.261.6280.6132.7660.1553.2750.150
ours (w/o start)21.6799.7197.920.5680.2372.3390.1263.2990.151
ours (w/o start & w/ opt.)25.8399.9398.910.4730.1962.4050.1273.3850.154
cVAE (w/ start) [73]17.6599.8895.440.4780.1881.7470.0912.3080.105
ours (w/ start)36.5699.8598.470.1930.0811.3720.0651.5680.072
ours (w/ start & w/ opt.)38.4499.9498.430.1680.0701.3890.0651.5750.072
+ +![](images/e79cc5529bfd0233010d2e22d73d9942728496456417c8bc9dd41bf7870b3772.jpg) +Figure 3. Qualitative results of human pose generation in 3D scenes. From left to right: (a) cVAE generation, (b) SceneDiffuser generation without optimization, and poses generated (c) with and (d) without applying our optimization-guided sampling. + +cVAE-based baselines on plausible rates. We observe this large improvement both quantitatively from the plausible rate and non-collision score and qualitatively in Fig. 3. Notably, our optimization-guided sampling improves the generator with $23\%$ on the plausible rate, showing the efficacy of the proposed optimization-guided sampling strategy and its potential for a broader range of 3D tasks with physic-based constraints or objectives. + +# 5.2. Task 2: Human Motion Generation + +Setup We consider generating human motion sequences under two different settings: (1) condition solely on the 3D scene, and (2) condition on both the starting pose and the 3D scene. We use the same human and scene representation as in Sec. 5.1 and clip the original LEMO motion sequence into segments with a fixed duration (60 frames). In total, we obtain 28k motion segments, with the distance between each start and end pose being longer than 0.2 meters. We follow the same split in Sec. 5.1 for training/testing and the same + +evaluation metrics for the pose generation. We report the average values of pose metrics over motion sequence as our performance measure. + +Results As quantitatively shown in Tab. 2, SceneDiffuser consistently generates high-quality motion sequences compared to cVAE baselines. Specifically, our generated motion outperforms baseline models on plausible rate, non-collision score, and contact score. This performance gain indicates better coverage of motion that involves rich interaction with the scene while remaining physically plausible. It also causes lower diversity in metrics (e.g., translation variance) since the plausible space for the motion is limited compared with cVAE. Empirically, we observe that providing the start position of motion as a condition constrains possible future motion sequences and leads to a drop in generation diversity for all models. We also note only a marginal performance improvement after applying optimization-guided sampling. One potential reason is that the generated motions are already plausible + +![](images/14b9bea5a5732ccd4cfb5b291b509ac3b7fedf2151434f7c8e59e0fadaa91390.jpg) +Figure 4. Human motions generated by SceneDiffuser. Each row shows sampled human motions from the same start pose. + +and receive small guidance from the optimization. As qualitatively shown in Fig. 4, SceneDiffuser generates diverse motions (e.g., "sit," "walk") from the same start position in unseen 3D scenes. + +# 5.3. Task 3: Dexterous Grasp Generation + +Setup Dexterous grasp generation aims to generate diverse and stable grasping poses for the given object with a human-like dexterous hand. We use the Shadowhand subset of the MultiDex [31] dataset, which contains diverse dexterous grasping poses for 58 daily objects. We represent the pose of Shadowhand as $q \coloneqq (t,R,\theta) \in \mathbb{R}^{33}$ , where $t \in \mathbb{R}^3$ and $R \in \mathbb{R}^6$ denote the global translation and orientation respectively, and $\theta \in \mathbb{R}^{24}$ describes the rotation angles of the revolute joints. An object is represented by its point cloud $\mathcal{O} \in \mathbb{R}^{2048 \times 3}$ . We split the dataset into 48 seen objects and 10 unseen objects for training and testing, respectively. + +Metrics We evaluate models in terms of success rate, diversity, and collision depth. We test if a grasp is successful in IsaacGym [37] by applying external forces to the object and measuring the movement of the object. To measure how learned models capture the diversity of successful grasping pose in the training data, we report the success rate of generated poses that lies at different variance levels from the mean pose of training data. We measure the collision depth as the maximum depth that the hand penetrates the object in each successful grasp for testing models' performance on physically correct grasps. In all cases, we ignore the root transformation of the hand as it does not contribute to the diversity of grasping types. + +Results Tab. 3 quantitatively demonstrates that SceneDiffuser generates significantly better grasp poses in + +Table 3. Quantitative results of dexterous grasp generation on MultiDex [31] dataset. We measure the success rates under different diversities and depth collisions. TTA. denotes test-time optimization with physics and contact. + +
modelsucc. rate (%)↑depth coll. (mm)↓
σ2σall
cVAE [25]0.0010.0914.0622.98
cVAE (w/ TTA.) [25]0.0021.9117.9715.19
ours (w/o opt.)70.6571.2571.2517.34
ours (w/ opt.)71.2769.8469.8414.61
+ +terms of success rate while correctly balancing the diversity of generation and grasp success. This result indicates that the SceneDiffuser achieves a consistently high success rate without much performance drop when the generated pose diverges from the mean pose in the training data. We also show that, by applying optimizer upon SceneDiffuser, the guided sampling process can reduce the violation of physically implausible grasping poses, outperforming the state-of-the-art baseline [25] without additional training or intermediate representation (i.e., contact maps). We provide qualitative results in Fig. 5 for visualization. + +# 5.4. Task 4: Path Planning for Navigation + +Setup We selected 61 indoor scenes from ScanNet [9] to construct room-level scenarios for navigational path planning and annotated these scenes with navigation graphs. As shown in Fig. 6b, these annotations are more spatially dense and physically plausible compared to previous methods [1]. We represent the physical robot with a cylinder to simulate physically plausible trajectories; see Fig. 6a. In total, we collected around 6k trajectories by searching the shortest paths between the randomly selected start and target nodes on the graph. We use trajectories in 46 scenes for training and the rest 15 scenes for evaluation. Models take the input as the scene point cloud $S \in \mathbb{R}^{32768 \times 3}$ , a given start position $\hat{\mathbf{s}}_0 \in \mathbb{R}^2$ , and a target position $\mathcal{G} \in \mathbb{R}^2$ on the floor plane. + +Metrics We evaluate the planned results by checking if the "robot" can move from the start to the target without collision along the planned trajectory. We report the average success rate and planning steps over all test cases. + +![](images/ecdf21466045ddcdca6b10e7f290b7ab88290d45e33c5c9b92ffda51c9fc189a.jpg) +Figure 5. Qualitative results of dexterous grasp generation. Compared to grasps generated by cVAE (first row), SceneDiffuser (second row) generates fewer colliding or floating poses, which helps to achieve a higher success rate. + +![](images/767ec50fd0823393797124f48f8cc5857d7a97e0192ddd6ca70e2a35929383a5.jpg) +(a) path planning + +![](images/b2459c2db352f7f0f2e2099adec59589c3d14e695111005ab0125e5a1ba584d2.jpg) +(b) navigation graph + +Results As shown in Tab. 4, SceneDiffuser outperforms both the BC and the deterministic planner baseline. These results indicate the efficacy of guided sampling with the planning objective, especially given that all test scenes are unseen during training. Crucially, as simple heuristics (like $L_{2}$ ) oftentimes lead to dead-ends in path planning, SceneDiffuser can correctly combine past knowledge on the scene-conditioned trajectory distribution and planning objective under specific unseen scenes to redirect planning direction, which helps to avoid obstacles and dead-ends to reach the goal successfully. Compared with the baseline models, our model also requires fewer planning steps while maintaining a higher success rate. This suggests that SceneDiffuser successfully navigates to the target without diverging even in long-horizon tasks, where classic RL-based stochastic planners suffer (i.e., the low performance of BC). + +Table 4. Quantitative results of path planning in 3D navigation and motion planning for robot arms. + +
taskmodelsucc. rate(%)↑planning steps↓
path planBC0150
deterministic(L2)13.50137.98
ours73.7590.38
arm motionBC0.31299.08
deterministic(L2)72.87141.28
ours78.59147.60
+ +# 5.5. Task 5: Motion Planning for Robot Arms + +Setup Aiming to generate valid robot arm motion trajectories in cluttered scenes, we used the Franka Emika arm with seven revolute joints and collected 19,800 trajectories over 200 randomly generated cluttered scenes using the MoveIt 2.0 [50], as shown in Fig. 7. We represent the scene with point clouds $S \in \mathbb{R}^{4096 \times 3}$ and the robot arm trajectory with a sequence of joint angles $\mathcal{R} \in [-\pi, \pi]$ . We train our model on 160 scenes and test on 40 unseen scenes. + +Metrics Similar to Sec. 5.4, we evaluate the generated trajectories by success rate on unseen scenes and the average number of planning steps. We consider a trajectory successful if the robot arm reaches the goal pose by a certain distance threshold within a limited number of steps. + +![](images/0682f30c22fb2638a4bf30be7724d65d6eaa05f0f61983c948e7a79dddbf4f97.jpg) +Figure 6. Path planning for 3D scene navigation. SceneDiffuser generates trajectories in long-horizon tasks. +(a) motion planning + +![](images/ba49770ba11451363882036a29ab93ccfc52cd6bceabd7fc50065078a9b35317.jpg) +(b) cluttered scenes +Figure 7. Motion planning for robot arms. SceneDiffuser generates arm motions in tabletop scenes with obstacles. + +Results We observe similar overall performance as in Sec. 5.4. Tab. 4 shows that SceneDiffuser consistently outperforms both the RL-based BC and the deterministic planner baseline. SceneDiffuser's planning steps for successful trials are also comparable with the deterministic planner, showing the efficacy of the planner in long-horizon scenarios. + +# 5.6. Ablation Analyses + +We explore how the scaling coefficient $\lambda$ influences the human pose generation results. We report the diversity and physics metrics of sampling results under different $\lambda$ s, ranging from 0.1 to 100. As shown in Tab. 5, $\lambda$ balances generation collision/contact and diversity in human pose generation. Specifically, $\lambda = 1.0$ leads to the best physical plausibility, while larger $\lambda$ values lead to diverse generation results. We attribute this effect to the optimization as with bigger $\lambda$ s; the optimization will draw poses away from the scene. + +Table 5. Ablation of the scale coefficient for optimization. + +
metricλ = 0.1λ = 1.0λ = 10.0λ = 100.0
plausible rate ↑28.7552.521.250
APD (trans.) ↑0.7640.8861.56423.96
APD (param) ↑3.2063.2439.040573.6
non-collison score ↑99.7699.8799.8574.9
contact score ↑99.7099.6581.750.0
+ +# 6. Conclusion + +We propose the SceneDiffuser as a general conditional generative model for generation, optimization, and planning in 3D scenes. SceneDiffuser is designed with appealing properties, including scene-aware, physics-based, and goal-oriented. We demonstrate that the SceneDiffuser outperforms previous models by a large margin on various tasks, establishing its efficacy and flexibility. + +Acknowledgments and disclosure of funding We thank Ruiqi Gao and Ying Nian Wu for their helpful discussions and suggestions. This work is supported in part by the National Key R&D Program of China (2021ZD0150200), the Beijing Nova Program, and the National Natural Science Foundation of China (NSFC) (62172043). + +# References + +[1] Peter Anderson, Qi Wu, Damien Teney, Jake Bruce, Mark Johnson, Niko Sunderhauf, Ian Reid, Stephen Gould, and Anton Van Den Hengel. Vision-and-language navigation: Interpreting visually-grounded navigation instructions in real environments. 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Illustration of the SceneDiffuser, applicable to various scene-conditioned 3D tasks: (a) human pose generation, (b) human motion generation, (c) dexterous grasp generation, (d) path planning for 3D navigation with goals, and (e) motion planning for robot arms." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 143, + 491, + 192, + 503 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 491, + 192, + 503 + ], + "spans": [ + { + "bbox": [ + 143, + 491, + 192, + 503 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 510, + 290, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 290, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 290, + 677 + ], + "type": "text", + "content": "We introduce the SceneDiffuser, a conditional generative model for 3D scene understanding. SceneDiffuser provides a unified model for solving scene-conditioned generation, optimization, and planning. In contrast to prior work, SceneDiffuser is intrinsically scene-aware, physics-based, and goal-oriented. With an iterative sampling strategy, SceneDiffuser jointly formulates the scene-aware generation, physics-based optimization, and goal-oriented planning via a diffusion-based denoising process in a fully differentiable fashion. Such a design alleviates the discrepancies among different modules and the posterior collapse of previous scene-conditioned generative models. We evaluate the SceneDiffuser on various 3D scene understanding tasks, including human pose and motion generation, dexterous grasp" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 492, + 547, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 492, + 547, + 552 + ], + "spans": [ + { + "bbox": [ + 306, + 492, + 547, + 552 + ], + "type": "text", + "content": "generation, path planning for 3D navigation, and motion planning for robot arms. The results show significant improvements compared with previous models, demonstrating the tremendous potential of the SceneDiffuser for the broad community of 3D scene understanding." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 562, + 387, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 562, + 387, + 574 + ], + "spans": [ + { + "bbox": [ + 306, + 562, + 387, + 574 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 582, + 547, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 677 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 677 + ], + "type": "text", + "content": "The ability to generate, optimize, and plan in 3D scenes is a long-standing goal across computer vision, graphics, and robotics. Various tasks have been devised to achieve these goals, fostering downstream applications in motion generation [32, 69, 73, 90], motion planning [42, 43, 60, 75], grasp generation [25, 31, 34], navigation [1, 95], scene synthesis [24, 47, 72, 82], embodied perception and manipulation [30, 39, 61], and autonomous driving [3, 52]." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 677, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 547, + 714 + ], + "type": "text", + "content": "Despite rich applications and great successes, existing models designed for these tasks exhibit two fundamental limitations for real-world 3D scene understanding." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 61, + 683, + 222, + 693 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 683, + 222, + 693 + ], + "spans": [ + { + "bbox": [ + 61, + 683, + 222, + 693 + ], + "type": "text", + "content": "* These authors contributed equally to this work." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 47, + 693, + 287, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 287, + 713 + ], + "type": "text", + "content": "Corresponding authors: Siyuan Huang (syhuang@bigai.ai) and Wei Liang (liangwei@bit.edu.cn)." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "16750" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": "First, most prior work [8, 14, 32, 49, 60, 68-70, 73] leverages the conditional Variational Autoencoder (cVAE) for the conditional generation in 3D scenes. cVAE model utilizes an encoder-decoder structure to learn the posterior distribution and relies on the learned latent variables to sample. Although cVAE is easy to train and sample due to its simple architecture and one-step sampling procedure, it suffers from the posterior collapse problem [12, 17, 26, 64, 69, 84, 93]; the learned latent variable is ignored by a strong decoder, leading to limited generation diversity from these collapsed modes. Such collapse is further magnified in 3D tasks with stronger 3D decoders and more complex and noisy input conditions, e.g., the natural 3D scans [9]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 230, + 289, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 230, + 289, + 386 + ], + "spans": [ + { + "bbox": [ + 46, + 230, + 289, + 386 + ], + "type": "text", + "content": "Second, despite the close relations among generation, optimization, and planning in 3D scenes, there lacks a unified framework that could address existing discrepancies among these models. Previous work [15, 34, 69] applies off-the-shelf physics-based post-optimization methods over outputs of generative models and often produces inconsistent and implausible generations, especially when transferring to novel scenes. Similarly, planners are usually standalone modules over results of generative model [8, 14] for trajectory planning or learned separately with the reinforcement learning (RL) [95], leading to gaps between planning and other modules (e.g., generation) during inference, especially in novel scenes where explorations are limited." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 388, + 289, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 388, + 289, + 520 + ], + "spans": [ + { + "bbox": [ + 46, + 388, + 289, + 520 + ], + "type": "text", + "content": "To tackle the above limitations, we introduce the SceneDiffuser, a conditional generative model based on the diffusion process. SceneDiffuser eliminates the discrepancies and provides a single home for scene-conditioned generation, optimization, and planning. Specifically, with a denoising process, it learns a diffusion model for scene-conditioned generation during training. In inference, SceneDiffuser jointly solves the scene-aware generation, physics-based optimization, and goal-oriented planning through a unified iterative guided-sampling framework. Such a design equips the SceneDiffuser with the following three superiority:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 521, + 289, + 714 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 47, + 521, + 288, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 521, + 288, + 593 + ], + "spans": [ + { + "bbox": [ + 47, + 521, + 288, + 593 + ], + "type": "text", + "content": "1. Generation: Building upon the diffusion model, SceneDiffuser solves the posterior collapse problem of scene-conditioned generative models. Since the forward diffusion process can be treated as data augmentation in 3D scenes, it helps traverse sufficient scene-conditioned distribution modes." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 594, + 288, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 594, + 288, + 665 + ], + "spans": [ + { + "bbox": [ + 47, + 594, + 288, + 665 + ], + "type": "text", + "content": "2. Optimization: SceneDiffuser integrates the physics-based objective into each step of the sampling process as conditional guidance, enabling the differentiable physics-based optimization during both the learning and sampling process. This design facilitates the physically-plausible generation, which is critical for tasks in 3D scenes." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 665, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 665, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 665, + 289, + 714 + ], + "type": "text", + "content": "3. Planning: Based on the scene-conditioned trajectory-level generator, SceneDiffuser possesses a physics- and goal-aware trajectory planner, generalizing better to long-horizon trajectories and novel 3D scenes." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "text", + "content": "As illustrated in Fig. 1, we evaluate the SceneDiffuser on diverse 3D scene understanding tasks. The human pose, motion, and dexterous grasp generation results significantly improve, demonstrating plausible and diverse generations with the 3D scene and object conditions. The results on path planning for 3D navigation and motion planning for robot arms reveal the generalizable and long-horizon planning capability of the SceneDiffuser." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 178, + 392, + 192 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 178, + 392, + 192 + ], + "spans": [ + { + "bbox": [ + 306, + 178, + 392, + 192 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 199, + 548, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 199, + 548, + 354 + ], + "spans": [ + { + "bbox": [ + 304, + 199, + 548, + 354 + ], + "type": "text", + "content": "Conditional Generation in 3D Scenes Generating diverse contents and rich interactions in 3D scenes is essential for understanding the 3D scene affordances. Several applications have emerged on conditional scene generation [24,47,71,81,88], human pose [16,32,87,90,92] and motion generation [14,32,49,60,68-70,73] in furnished 3D indoor scenes, and object-conditioned grasp pose generation [25,31,34,62,78]. However, most previous methods [6,14,16,25,31,62,68,73,75] rely on cVAE and suffer from the posterior collapse problem [12,17,26,64,69,84,93], especially when the 3D scene is natural and complex. In this work, SceneDiffuser addresses the posterior collapse with the diffusion-based denoising process." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 355, + 548, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 355, + 548, + 534 + ], + "spans": [ + { + "bbox": [ + 304, + 355, + 548, + 534 + ], + "type": "text", + "content": "Physics-based Optimization in 3D Scenes Producing physically plausible generations compatible with 3D scenes is challenging in the scene-conditioned generation. Previous work uses physics-based post-optimization [15, 34, 69] or differentiable objective [25, 73, 90] to integrate collision and contact constraints into the generation framework. However, post-optimization approaches [15, 34, 69] cannot be learned jointly with the generative models, yielding inconsistent generation results. Similarly, differentiable approaches [25, 73, 90] impose constraints on the final objective and cannot optimize the physical interactions during sampling, resulting in implausible generations, particularly when adapting to novel scenes. In this work, SceneDiffuser avoids such inconsistency by integrating differentiable physics-based optimization into each step of the sampling process." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 534, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 548, + 715 + ], + "type": "text", + "content": "Planning in 3D Scenes The ability to act and plan in 3D scenes is critical for an intelligent agent and has led to the recent culmination of embodied AI research [28, 30, 33, 36, 54, 55, 79]. Among all tasks, visual navigation has been most studied in the vision and robotics community [4, 13, 21, 40, 76, 77, 94, 95]. However, existing work relies heavily on model-based planners with the single-step dynamic model [5,11,48,67,74,80], lacking a trajectory-level optimization for long-horizon planning. Further, these planners lack explicit modeling of physical interactions, making it difficult to generalize to natural scenes with limited exploration, where rapid learning and adaptation are required. Compared with the global trajectory planner based on a trajectory-level generator, SceneDiffuser exhibits superior generalization in long-horizon plans and novel 3D scenes." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16751" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 228 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 228 + ], + "type": "text", + "content": "Diffusion-based Models Diffusion model [19,22,57, 59] has come forth into a promising class of generative model for learning and sampling data distributions with an iterative denoising process, facilitating the image [10, 58], text [83], and shape generation [35]. With flexible conditioning, it is further extended to the language-conditioned image [41, 51, 53], video [18, 56], and 3D generation [44, 63, 85]. Notably, Janner et al. [23] integrate the generation and planning into the same sampling framework for behavior synthesis. To our best knowledge, SceneDiffuser is the first framework that models the 3D scene-conditioned generation with a diffusion model and integrates the generation, optimization, and planning into a unified framework." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 237, + 126, + 251 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 237, + 126, + 251 + ], + "spans": [ + { + "bbox": [ + 47, + 237, + 126, + 251 + ], + "type": "text", + "content": "3. Background" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 256, + 159, + 268 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 256, + 159, + 268 + ], + "spans": [ + { + "bbox": [ + 47, + 256, + 159, + 268 + ], + "type": "text", + "content": "3.1. Problem Definition" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 274, + 289, + 370 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 274, + 289, + 370 + ], + "spans": [ + { + "bbox": [ + 47, + 274, + 289, + 370 + ], + "type": "text", + "content": "Given a 3D scene " + }, + { + "bbox": [ + 47, + 274, + 289, + 370 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 47, + 274, + 289, + 370 + ], + "type": "text", + "content": ", we aim to generate the optimal solution for completing the tasks (e.g., navigation, manipulation) given the goal " + }, + { + "bbox": [ + 47, + 274, + 289, + 370 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 47, + 274, + 289, + 370 + ], + "type": "text", + "content": " in the scene. We denote the state and action of an agent as " + }, + { + "bbox": [ + 47, + 274, + 289, + 370 + ], + "type": "inline_equation", + "content": "(\\mathbf{s},\\mathbf{a})" + }, + { + "bbox": [ + 47, + 274, + 289, + 370 + ], + "type": "text", + "content": ". The dynamic model defines the state transition as " + }, + { + "bbox": [ + 47, + 274, + 289, + 370 + ], + "type": "inline_equation", + "content": "p(\\mathbf{s}_{i + 1}|\\mathbf{s}_i,\\mathbf{a}_i)" + }, + { + "bbox": [ + 47, + 274, + 289, + 370 + ], + "type": "text", + "content": ", which is often deterministic in scene understanding (i.e., " + }, + { + "bbox": [ + 47, + 274, + 289, + 370 + ], + "type": "inline_equation", + "content": "f(\\mathbf{s}_i,\\mathbf{a}_i)" + }, + { + "bbox": [ + 47, + 274, + 289, + 370 + ], + "type": "text", + "content": "). The trajectory is defined as " + }, + { + "bbox": [ + 47, + 274, + 289, + 370 + ], + "type": "inline_equation", + "content": "\\boldsymbol{\\tau} = (\\mathbf{s}_0,\\mathbf{a}_0,\\dots ,\\mathbf{s}_i,\\mathbf{a}_i,\\dots ,\\mathbf{s}_N)" + }, + { + "bbox": [ + 47, + 274, + 289, + 370 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 274, + 289, + 370 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 47, + 274, + 289, + 370 + ], + "type": "text", + "content": " denotes the horizon of task solving in discrete time." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 376, + 253, + 389 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 376, + 253, + 389 + ], + "spans": [ + { + "bbox": [ + 47, + 376, + 253, + 389 + ], + "type": "text", + "content": "3.2. Planning with Trajectory Optimization" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 395, + 287, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 395, + 287, + 418 + ], + "spans": [ + { + "bbox": [ + 47, + 395, + 287, + 418 + ], + "type": "text", + "content": "The scene-conditional trajectory optimization is defined as maximizing the task objective:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 116, + 422, + 287, + 440 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 422, + 287, + 440 + ], + "spans": [ + { + "bbox": [ + 116, + 422, + 287, + 440 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\tau} ^ {*} = \\underset {\\boldsymbol {\\tau}} {\\arg \\max } \\mathcal {J} (\\boldsymbol {\\tau} | \\mathcal {S}, \\mathcal {G}). \\tag {1}", + "image_path": "8776e657becd5bbb2e0e2b78f510948c7fe6b8096b9b8dc509c9c3ddce55cc12.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 444, + 289, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 444, + 289, + 540 + ], + "spans": [ + { + "bbox": [ + 47, + 444, + 289, + 540 + ], + "type": "text", + "content": "The dynamic model is usually known for trajectory optimization. Considering the future actions and states with predictable dynamics, the entire trajectory " + }, + { + "bbox": [ + 47, + 444, + 289, + 540 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 47, + 444, + 289, + 540 + ], + "type": "text", + "content": " can be optimized jointly and non-progressively with traditional [29] or data-driven [7] planning algorithms. Trajectory-based optimization benefits from its global awareness of history and future states, thus can better model the long-horizon tasks compared with single-step models in RL, where " + }, + { + "bbox": [ + 47, + 444, + 289, + 540 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_{0:N}^{*} =" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 540, + 157, + 571 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 540, + 157, + 571 + ], + "spans": [ + { + "bbox": [ + 47, + 540, + 157, + 571 + ], + "type": "interline_equation", + "content": "\\underset {\\mathbf {a} _ {0: N}} {\\arg \\max } \\sum_ {i = 0} ^ {N} r (\\mathbf {s} _ {i}, \\mathbf {a} _ {i} | \\mathcal {S}, \\mathcal {G}).", + "image_path": "8f205f0fc44364471cedf80ebb625927e52653268c3748f08858457f0e696ca2.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 575, + 146, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 575, + 146, + 586 + ], + "spans": [ + { + "bbox": [ + 47, + 575, + 146, + 586 + ], + "type": "text", + "content": "3.3. Diffusion Model" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 594, + 289, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 594, + 289, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 594, + 289, + 713 + ], + "type": "text", + "content": "Diffusion model [19,22,57] is a class of generative models representing the data generation with an iterative denoising process from Gaussian noise. It consists of a forward and a reverse process. The forward process " + }, + { + "bbox": [ + 47, + 594, + 289, + 713 + ], + "type": "inline_equation", + "content": "q(\\tau^t |\\tau^{t - 1})" + }, + { + "bbox": [ + 47, + 594, + 289, + 713 + ], + "type": "text", + "content": " gradually destroys data " + }, + { + "bbox": [ + 47, + 594, + 289, + 713 + ], + "type": "inline_equation", + "content": "\\tau^0\\sim q(\\tau^0)" + }, + { + "bbox": [ + 47, + 594, + 289, + 713 + ], + "type": "text", + "content": " into Gaussian noise. The parametrized reverse process " + }, + { + "bbox": [ + 47, + 594, + 289, + 713 + ], + "type": "inline_equation", + "content": "p_{\\theta}(\\tau^{t - 1}|\\tau^t)" + }, + { + "bbox": [ + 47, + 594, + 289, + 713 + ], + "type": "text", + "content": " recovers the data from noise with the learned normal distribution from a fixed timestep. The training objective for " + }, + { + "bbox": [ + 47, + 594, + 289, + 713 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 47, + 594, + 289, + 713 + ], + "type": "text", + "content": " is denoising score matching over multiple noise scale [22,66]. Please refer to the Appendix A for details of diffusion model and variants." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 71, + 392, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 71, + 392, + 83 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 392, + 83 + ], + "type": "text", + "content": "4. SceneDiffuser" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 91, + 547, + 187 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 91, + 547, + 187 + ], + "spans": [ + { + "bbox": [ + 304, + 91, + 547, + 187 + ], + "type": "text", + "content": "SceneDiffuser models planning as trajectory optimization and solves the aforementioned problem with the spirit of planning as sampling, where the trajectory optimization is achieved by sampling trajectory-level distribution learned by the model. Leveraging the diffusion model with gradient-based sampling and flexible conditioning, SceneDiffuser models the scene-conditioned goal-oriented trajectory " + }, + { + "bbox": [ + 304, + 91, + 547, + 187 + ], + "type": "inline_equation", + "content": "p(\\tau^0 | S, \\mathcal{G})" + }, + { + "bbox": [ + 304, + 91, + 547, + 187 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 355, + 192, + 545, + 232 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 355, + 192, + 545, + 232 + ], + "spans": [ + { + "bbox": [ + 355, + 192, + 545, + 232 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} p \\left(\\boldsymbol {\\tau} ^ {0} | \\mathcal {S}, \\mathcal {G}\\right) = \\frac {p _ {\\theta} \\left(\\boldsymbol {\\tau} ^ {0} | \\mathcal {S}\\right) p _ {\\phi} \\left(\\mathcal {G} \\mid \\boldsymbol {\\tau} ^ {0} , \\mathcal {S}\\right)}{p \\left(\\mathcal {G} \\mid \\mathcal {S}\\right)} \\tag {2} \\\\ \\propto p _ {\\theta} (\\tau^ {0} | \\mathcal {S}) p _ {\\phi} (\\mathcal {G} | \\tau^ {0}, \\mathcal {S}). \\\\ \\end{array}", + "image_path": "cf7d4e07a50f9862c30f847c2ed5aa42f772a0a5ef565be918ad25819c021001.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 238, + 547, + 286 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 238, + 547, + 286 + ], + "spans": [ + { + "bbox": [ + 304, + 238, + 547, + 286 + ], + "type": "text", + "content": "Generation " + }, + { + "bbox": [ + 304, + 238, + 547, + 286 + ], + "type": "inline_equation", + "content": "p_{\\theta}(\\pmb{\\tau}^{0}|\\mathcal{S})" + }, + { + "bbox": [ + 304, + 238, + 547, + 286 + ], + "type": "text", + "content": " characterizes the probability of generating certain trajectories with the scene condition. It can be modeled using a conditional diffusion model [19, 57] with an iterative denoising process:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 336, + 293, + 545, + 320 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 336, + 293, + 545, + 320 + ], + "spans": [ + { + "bbox": [ + 336, + 293, + 545, + 320 + ], + "type": "interline_equation", + "content": "p _ {\\theta} \\left(\\boldsymbol {\\tau} ^ {0} \\mid \\mathcal {S}\\right) = p \\left(\\boldsymbol {\\tau} ^ {T}\\right) \\prod_ {t = 1} ^ {T} p \\left(\\boldsymbol {\\tau} ^ {t - 1} \\mid \\boldsymbol {\\tau} ^ {t}, \\mathcal {S}\\right), \\tag {3}", + "image_path": "ba2ae5e5cb2c93e9b19754b99aaf0b83366c2510a0b17895e01b435cbf3ef6d9.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 319, + 322, + 522, + 336 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 322, + 522, + 336 + ], + "spans": [ + { + "bbox": [ + 319, + 322, + 522, + 336 + ], + "type": "interline_equation", + "content": "p (\\boldsymbol {\\tau} ^ {t - 1} | \\boldsymbol {\\tau} ^ {t}, \\mathcal {S}) = \\mathcal {N} (\\boldsymbol {\\tau} ^ {t - 1}; \\boldsymbol {\\mu} _ {\\theta} (\\boldsymbol {\\tau} ^ {t}, t, \\mathcal {S}), \\boldsymbol {\\Sigma} _ {\\theta} (\\boldsymbol {\\tau} ^ {t}, t, \\mathcal {S})).", + "image_path": "08d0485ad134cb065984b7b6fa4e4690329e38e654be2f777819b656c7a941dd.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 342, + 547, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 342, + 547, + 450 + ], + "spans": [ + { + "bbox": [ + 304, + 342, + 547, + 450 + ], + "type": "text", + "content": "Optimization and Planning " + }, + { + "bbox": [ + 304, + 342, + 547, + 450 + ], + "type": "inline_equation", + "content": "p_{\\phi}(\\mathcal{G}|\\boldsymbol{\\tau}^0,\\mathcal{S})" + }, + { + "bbox": [ + 304, + 342, + 547, + 450 + ], + "type": "text", + "content": " represents the probability of reaching the goal with the sampled trajectory, where the goal can be flexibly defined by customized objective functions in various tasks. As shown in Eq. (4), the precise definition of this probability is " + }, + { + "bbox": [ + 304, + 342, + 547, + 450 + ], + "type": "inline_equation", + "content": "p_{\\phi}(\\mathcal{O} = 1|\\boldsymbol{\\tau}^0,\\mathcal{S},\\mathcal{G})" + }, + { + "bbox": [ + 304, + 342, + 547, + 450 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 342, + 547, + 450 + ], + "type": "inline_equation", + "content": "O" + }, + { + "bbox": [ + 304, + 342, + 547, + 450 + ], + "type": "text", + "content": " is an optimality indicator that represents if the goal were achieved. Intuitively, the trajectory objective in Eq. (1) can indicate such optimality. We therefore expand " + }, + { + "bbox": [ + 304, + 342, + 547, + 450 + ], + "type": "inline_equation", + "content": "p_{\\phi}(\\mathcal{G}|\\boldsymbol{\\tau}^t,\\mathcal{S})" + }, + { + "bbox": [ + 304, + 342, + 547, + 450 + ], + "type": "text", + "content": " as its exponential in Eq. (5):" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 335, + 457, + 545, + 471 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 335, + 457, + 545, + 471 + ], + "spans": [ + { + "bbox": [ + 335, + 457, + 545, + 471 + ], + "type": "interline_equation", + "content": "p _ {\\phi} (\\mathcal {G} | \\boldsymbol {\\tau} ^ {t}, \\mathcal {S}) = p _ {\\phi} \\left(\\mathcal {O} = 1 | \\boldsymbol {\\tau} ^ {t}, \\mathcal {S}, \\mathcal {G}\\right) \\tag {4}", + "image_path": "0d6150e4712b344fc53c8f7f1a77aeb82adc111ff4a4e11ce66b281a8d9b0ae7.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 384, + 474, + 545, + 487 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 384, + 474, + 545, + 487 + ], + "spans": [ + { + "bbox": [ + 384, + 474, + 545, + 487 + ], + "type": "interline_equation", + "content": "\\propto \\exp (\\mathcal {J} (\\boldsymbol {\\tau} ^ {t} | \\mathcal {S}, \\mathcal {G})) \\tag {5}", + "image_path": "91e685ef68ba1d477e8c38397108c5fd617f34ca90c68191ba11874773b7d8a1.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 384, + 489, + 545, + 503 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 384, + 489, + 545, + 503 + ], + "spans": [ + { + "bbox": [ + 384, + 489, + 545, + 503 + ], + "type": "interline_equation", + "content": "= \\exp \\left(\\varphi_ {p} \\left(\\boldsymbol {\\tau} ^ {t} | \\mathcal {S}, \\mathcal {G}\\right) + \\varphi_ {o} \\left(\\boldsymbol {\\tau} ^ {t} | \\mathcal {S}\\right), \\right. \\tag {6}", + "image_path": "4ec60020126788c0e294266c68a9b40c43d2402fee9352885612fd0fd258c3df.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 510, + 547, + 606 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 547, + 606 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 547, + 606 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 510, + 547, + 606 + ], + "type": "inline_equation", + "content": "\\varphi_{o}(\\pmb{\\tau}^{t}|\\mathcal{S})" + }, + { + "bbox": [ + 304, + 510, + 547, + 606 + ], + "type": "text", + "content": " denotes the objective for optimizing the trajectory with scene condition and is independent of task goal " + }, + { + "bbox": [ + 304, + 510, + 547, + 606 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 304, + 510, + 547, + 606 + ], + "type": "text", + "content": ". In scene understanding, " + }, + { + "bbox": [ + 304, + 510, + 547, + 606 + ], + "type": "inline_equation", + "content": "\\varphi_{o}" + }, + { + "bbox": [ + 304, + 510, + 547, + 606 + ], + "type": "text", + "content": " usually denotes plausible physical relationships (e.g., collision, contact, and intersection). " + }, + { + "bbox": [ + 304, + 510, + 547, + 606 + ], + "type": "inline_equation", + "content": "\\varphi_{p}(\\pmb{\\tau}^{t}|\\mathcal{S},\\mathcal{G})" + }, + { + "bbox": [ + 304, + 510, + 547, + 606 + ], + "type": "text", + "content": " indicates the objective for planning (i.e., goal-reaching) with scene condition. Both " + }, + { + "bbox": [ + 304, + 510, + 547, + 606 + ], + "type": "inline_equation", + "content": "\\varphi_{o}" + }, + { + "bbox": [ + 304, + 510, + 547, + 606 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 510, + 547, + 606 + ], + "type": "inline_equation", + "content": "\\varphi_{p}" + }, + { + "bbox": [ + 304, + 510, + 547, + 606 + ], + "type": "text", + "content": " can be explicitly defined or implicitly learned from observed trajectories with proper parametrization." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 613, + 372, + 625 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 613, + 372, + 625 + ], + "spans": [ + { + "bbox": [ + 306, + 613, + 372, + 625 + ], + "type": "text", + "content": "4.1. Learning" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 631, + 547, + 667 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 631, + 547, + 667 + ], + "spans": [ + { + "bbox": [ + 304, + 631, + 547, + 667 + ], + "type": "inline_equation", + "content": "p_{\\theta}(\\tau^0 |S)" + }, + { + "bbox": [ + 304, + 631, + 547, + 667 + ], + "type": "text", + "content": " is the scene-conditioned generator, which can be learned by the conditional diffusion model with the simplified objective of estimating the noise " + }, + { + "bbox": [ + 304, + 631, + 547, + 667 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 304, + 631, + 547, + 667 + ], + "type": "text", + "content": " [10, 19, 20], where" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 314, + 681, + 545, + 716 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 681, + 545, + 716 + ], + "spans": [ + { + "bbox": [ + 314, + 681, + 545, + 716 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\theta} \\left(\\boldsymbol {\\tau} ^ {0} \\mid \\mathcal {S}\\right) = \\mathbb {E} _ {t, \\epsilon , \\boldsymbol {\\tau} ^ {0}} \\left[ \\| \\boldsymbol {\\epsilon} - \\boldsymbol {\\epsilon} _ {\\theta} \\left(\\sqrt {\\hat {\\alpha} ^ {t}} \\boldsymbol {\\tau} ^ {0} + \\sqrt {1 - \\hat {\\alpha} ^ {t}} \\boldsymbol {\\epsilon}, t, \\mathcal {S}\\right) \\| ^ {2} \\right] \\tag {7} \\\\ = \\mathbb {E} _ {t, \\epsilon , \\tau^ {0}} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} (\\tau^ {t}, t, S) \\| ^ {2} \\right], \\\\ \\end{array}", + "image_path": "7c8b9bcf936c471981c17c66c1d6853033e7b7eef67e72a791b909b72cb241e4.jpg" + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "16752" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 133 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 133 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 72, + 289, + 133 + ], + "type": "inline_equation", + "content": "\\hat{\\alpha}^t" + }, + { + "bbox": [ + 46, + 72, + 289, + 133 + ], + "type": "text", + "content": " is the pre-determined function in the forward process. With the learned " + }, + { + "bbox": [ + 46, + 72, + 289, + 133 + ], + "type": "inline_equation", + "content": "p_{\\theta}(\\tau^0 |S)" + }, + { + "bbox": [ + 46, + 72, + 289, + 133 + ], + "type": "text", + "content": ", we sample " + }, + { + "bbox": [ + 46, + 72, + 289, + 133 + ], + "type": "inline_equation", + "content": "p(\\tau^0 |S,\\mathcal{G})" + }, + { + "bbox": [ + 46, + 72, + 289, + 133 + ], + "type": "text", + "content": " by taking the advantage of the diffusion model's flexible conditioning [10, 23]. Specifically, we approximate " + }, + { + "bbox": [ + 46, + 72, + 289, + 133 + ], + "type": "inline_equation", + "content": "p_{\\phi}(\\mathcal{G}|\\boldsymbol{\\tau}^{t},\\mathcal{S})" + }, + { + "bbox": [ + 46, + 72, + 289, + 133 + ], + "type": "text", + "content": " using the Taylor expansion around " + }, + { + "bbox": [ + 46, + 72, + 289, + 133 + ], + "type": "inline_equation", + "content": "\\boldsymbol{\\tau}^{t} = \\boldsymbol{\\mu}" + }, + { + "bbox": [ + 46, + 72, + 289, + 133 + ], + "type": "text", + "content": " at timestep " + }, + { + "bbox": [ + 46, + 72, + 289, + 133 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 72, + 289, + 133 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 102, + 138, + 287, + 152 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 138, + 287, + 152 + ], + "spans": [ + { + "bbox": [ + 102, + 138, + 287, + 152 + ], + "type": "interline_equation", + "content": "\\log p _ {\\phi} (\\mathcal {G} | \\boldsymbol {\\tau} ^ {t}, \\mathcal {S}) \\approx (\\boldsymbol {\\tau} ^ {t} - \\boldsymbol {\\mu}) \\mathbf {g} + C, \\tag {8}", + "image_path": "39449e29ed6d55500965134a39b8b4f1554e5195c842c61120f911c6eca26327.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 159, + 288, + 195 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 159, + 288, + 195 + ], + "spans": [ + { + "bbox": [ + 47, + 159, + 288, + 195 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 159, + 288, + 195 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 47, + 159, + 288, + 195 + ], + "type": "text", + "content": " is a constant, " + }, + { + "bbox": [ + 47, + 159, + 288, + 195 + ], + "type": "inline_equation", + "content": "\\pmb{\\mu} = \\pmb{\\mu}_{\\theta}(\\pmb{\\tau}^t,t,\\mathcal{S})" + }, + { + "bbox": [ + 47, + 159, + 288, + 195 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 159, + 288, + 195 + ], + "type": "inline_equation", + "content": "\\Sigma = \\Sigma_{\\theta}(\\pmb{\\tau}^{t},t,\\mathcal{S})" + }, + { + "bbox": [ + 47, + 159, + 288, + 195 + ], + "type": "text", + "content": " are the inferred parameters of original diffusion process, and" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 88, + 201, + 287, + 231 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 201, + 287, + 231 + ], + "spans": [ + { + "bbox": [ + 88, + 201, + 287, + 231 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathbf {g} = \\nabla_ {\\boldsymbol {\\tau} ^ {t}} \\log p _ {\\phi} (\\mathcal {G} | \\boldsymbol {\\tau} ^ {t}, \\mathcal {S}) | _ {\\boldsymbol {\\tau} ^ {t} = \\boldsymbol {\\mu}} \\tag {9} \\\\ = \\nabla_ {\\tau^ {t}} \\left(\\varphi_ {o} \\left(\\tau^ {t} | \\mathcal {S}\\right) + \\varphi_ {p} \\left(\\tau^ {t} | \\mathcal {S}, \\mathcal {G}\\right)\\right) | _ {\\tau^ {t} = \\mu}. \\\\ \\end{array}", + "image_path": "f326b0bca6f3633dcc2dac1b142d17757dc3ccb3c61ba2af3b858d5cbaec4da3.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 237, + 127, + 247 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 237, + 127, + 247 + ], + "spans": [ + { + "bbox": [ + 47, + 237, + 127, + 247 + ], + "type": "text", + "content": "Therefore, we have" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 85, + 255, + 287, + 268 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 255, + 287, + 268 + ], + "spans": [ + { + "bbox": [ + 85, + 255, + 287, + 268 + ], + "type": "interline_equation", + "content": "p \\left(\\boldsymbol {\\tau} ^ {t - 1} \\mid \\boldsymbol {\\tau} ^ {t}, \\mathcal {S}, \\mathcal {G}\\right) = \\mathcal {N} \\left(\\boldsymbol {\\tau} ^ {t - 1}; \\boldsymbol {\\mu} + \\lambda \\boldsymbol {\\Sigma} \\mathbf {g}, \\boldsymbol {\\Sigma}\\right), \\tag {10}", + "image_path": "d7f44beb5c3a13eab6ca6a423306cfe8849b9593229ec745c482e0cac108138d.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 276, + 288, + 311 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 276, + 288, + 311 + ], + "spans": [ + { + "bbox": [ + 46, + 276, + 288, + 311 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 276, + 288, + 311 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 276, + 288, + 311 + ], + "type": "text", + "content": " is the scaling factor for the guidance. With Eq. (10), we can sample " + }, + { + "bbox": [ + 46, + 276, + 288, + 311 + ], + "type": "inline_equation", + "content": "\\pmb{\\tau}^t" + }, + { + "bbox": [ + 46, + 276, + 288, + 311 + ], + "type": "text", + "content": " with the guidance of optimizing and planning objectives." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 312, + 288, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 312, + 288, + 384 + ], + "spans": [ + { + "bbox": [ + 46, + 312, + 288, + 384 + ], + "type": "text", + "content": "Of note, " + }, + { + "bbox": [ + 46, + 312, + 288, + 384 + ], + "type": "inline_equation", + "content": "\\varphi_{p}" + }, + { + "bbox": [ + 46, + 312, + 288, + 384 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 312, + 288, + 384 + ], + "type": "inline_equation", + "content": "\\varphi_{o}" + }, + { + "bbox": [ + 46, + 312, + 288, + 384 + ], + "type": "text", + "content": " serve as the pre-defined guidance for tilting the original trajectory with physical and goal constraints. However, they can also be learned from the observed trajectories. During training, we first fix the learned base model of " + }, + { + "bbox": [ + 46, + 312, + 288, + 384 + ], + "type": "inline_equation", + "content": "p_{\\theta}(\\tau^0 |S)" + }, + { + "bbox": [ + 46, + 312, + 288, + 384 + ], + "type": "text", + "content": ", followed by learning " + }, + { + "bbox": [ + 46, + 312, + 288, + 384 + ], + "type": "inline_equation", + "content": "\\phi_{o}" + }, + { + "bbox": [ + 46, + 312, + 288, + 384 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 312, + 288, + 384 + ], + "type": "inline_equation", + "content": "\\phi_{p}" + }, + { + "bbox": [ + 46, + 312, + 288, + 384 + ], + "type": "text", + "content": " for optimization and planning with the following objective:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 65, + 389, + 287, + 404 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 389, + 287, + 404 + ], + "spans": [ + { + "bbox": [ + 65, + 389, + 287, + 404 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\phi} \\left(\\boldsymbol {\\tau} ^ {0} \\mid \\mathcal {S}, \\mathcal {G}\\right) = \\mathbb {E} _ {t, \\epsilon , \\boldsymbol {\\tau} ^ {0}} \\left[ \\left\\| \\boldsymbol {\\epsilon} - \\boldsymbol {\\epsilon} _ {\\theta} \\left(\\boldsymbol {\\tau} ^ {t}, t, \\mathcal {S}\\right) - \\boldsymbol {\\Sigma} \\mathbf {g} \\right\\| ^ {2} \\right]. \\tag {11}", + "image_path": "f426569c231b30a80f2bea1d8e7fbb37b420c038ec41b5d4a43db7d9a2e1e97f.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 411, + 217, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 411, + 217, + 422 + ], + "spans": [ + { + "bbox": [ + 47, + 411, + 217, + 422 + ], + "type": "text", + "content": "Alg. 1 summarizes the training procedure." + } + ] + } + ], + "index": 9 + }, + { + "type": "code", + "bbox": [ + 50, + 441, + 287, + 632 + ], + "blocks": [ + { + "bbox": [ + 53, + 428, + 207, + 439 + ], + "lines": [ + { + "bbox": [ + 53, + 428, + 207, + 439 + ], + "spans": [ + { + "bbox": [ + 53, + 428, + 207, + 439 + ], + "type": "text", + "content": "Algorithm 1: Training SceneDiffuser" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 50, + 441, + 287, + 632 + ], + "lines": [ + { + "bbox": [ + 50, + 441, + 287, + 632 + ], + "spans": [ + { + "bbox": [ + 50, + 441, + 287, + 632 + ], + "type": "text", + "content": "1 // train base generation model \nInput: Trajectory in 3D scene " + }, + { + "bbox": [ + 50, + 441, + 287, + 632 + ], + "type": "inline_equation", + "content": "(\\tau^0, S)" + }, + { + "bbox": [ + 50, + 441, + 287, + 632 + ], + "type": "text", + "content": " \n2 repeat \n3 " + }, + { + "bbox": [ + 50, + 441, + 287, + 632 + ], + "type": "inline_equation", + "content": "\\tau^0 \\sim p(\\tau^0 | S)" + }, + { + "bbox": [ + 50, + 441, + 287, + 632 + ], + "type": "text", + "content": " \n4 " + }, + { + "bbox": [ + 50, + 441, + 287, + 632 + ], + "type": "inline_equation", + "content": "\\epsilon \\sim \\mathcal{N}(0, I), t \\sim \\mathcal{U}(\\{1, \\dots, T\\})" + }, + { + "bbox": [ + 50, + 441, + 287, + 632 + ], + "type": "text", + "content": " \n5 " + }, + { + "bbox": [ + 50, + 441, + 287, + 632 + ], + "type": "inline_equation", + "content": "\\pmb{\\tau}^t = \\sqrt{\\hat{\\alpha}_t} \\pmb{\\tau}_0 + \\sqrt{1 - \\hat{\\alpha}_t} \\pmb{\\epsilon}" + }, + { + "bbox": [ + 50, + 441, + 287, + 632 + ], + "type": "text", + "content": " \n6 " + }, + { + "bbox": [ + 50, + 441, + 287, + 632 + ], + "type": "inline_equation", + "content": "\\theta = \\theta - \\eta \\nabla_\\theta \\| \\pmb{\\epsilon} - \\pmb{\\epsilon}_\\theta (\\pmb{\\tau}^t, t, S) \\|_2^2" + }, + { + "bbox": [ + 50, + 441, + 287, + 632 + ], + "type": "text", + "content": " \n7 until converged; \n8 // (optional) train optimization and planning model \nInput: Trajectory in 3D scene with goal " + }, + { + "bbox": [ + 50, + 441, + 287, + 632 + ], + "type": "inline_equation", + "content": "(\\tau^0, S, G)" + }, + { + "bbox": [ + 50, + 441, + 287, + 632 + ], + "type": "text", + "content": ", learned " + }, + { + "bbox": [ + 50, + 441, + 287, + 632 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 50, + 441, + 287, + 632 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 50, + 441, + 287, + 632 + ], + "type": "inline_equation", + "content": "p_\\theta(\\tau^0 | S)" + }, + { + "bbox": [ + 50, + 441, + 287, + 632 + ], + "type": "text", + "content": " \n9 repeat \n10 " + }, + { + "bbox": [ + 50, + 441, + 287, + 632 + ], + "type": "inline_equation", + "content": "\\pmb{\\tau}^0 \\sim p(\\pmb{\\tau}^0 | S, G)" + }, + { + "bbox": [ + 50, + 441, + 287, + 632 + ], + "type": "text", + "content": " \n11 " + }, + { + "bbox": [ + 50, + 441, + 287, + 632 + ], + "type": "inline_equation", + "content": "\\epsilon \\sim \\mathcal{N}(0, I), t \\sim \\mathcal{U}(\\{1, \\dots, T\\})" + }, + { + "bbox": [ + 50, + 441, + 287, + 632 + ], + "type": "text", + "content": " \n12 " + }, + { + "bbox": [ + 50, + 441, + 287, + 632 + ], + "type": "inline_equation", + "content": "\\pmb{\\mu} = \\pmb{\\mu}_\\theta(\\pmb{\\tau}^t, t, S), \\pmb{\\Sigma} = \\pmb{\\Sigma}_\\theta(\\pmb{\\tau}^t, t, S)" + }, + { + "bbox": [ + 50, + 441, + 287, + 632 + ], + "type": "text", + "content": " \n13 " + }, + { + "bbox": [ + 50, + 441, + 287, + 632 + ], + "type": "inline_equation", + "content": "\\mathbf{g} = \\nabla_{\\pmb{\\tau}^t} \\log p_\\phi(\\mathcal{G} | \\pmb{\\tau}^t, S) |_{\\pmb{\\tau}^t = \\pmb{\\mu}}" + }, + { + "bbox": [ + 50, + 441, + 287, + 632 + ], + "type": "text", + "content": " \n14 " + }, + { + "bbox": [ + 50, + 441, + 287, + 632 + ], + "type": "inline_equation", + "content": "\\pmb{\\tau}^t = \\sqrt{\\hat{\\alpha}_t} \\pmb{\\tau}_0 + \\sqrt{1 - \\hat{\\alpha}_t} \\pmb{\\epsilon}" + }, + { + "bbox": [ + 50, + 441, + 287, + 632 + ], + "type": "text", + "content": " \n15 " + }, + { + "bbox": [ + 50, + 441, + 287, + 632 + ], + "type": "inline_equation", + "content": "\\phi = \\phi - \\eta \\nabla_\\phi \\| \\pmb{\\epsilon} - \\pmb{\\epsilon}_\\theta(\\pmb{\\tau}^t, t, S) - \\lambda \\pmb{\\Sigma} \\mathbf{g} \\|_2^2" + }, + { + "bbox": [ + 50, + 441, + 287, + 632 + ], + "type": "text", + "content": " \n16 until converged;" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "code_body" + } + ], + "index": 11, + "sub_type": "algorithm" + }, + { + "bbox": [ + 47, + 647, + 114, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 114, + 659 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 114, + 659 + ], + "type": "text", + "content": "4.2. Sampling" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": "With different sampling strategies, SceneDiffuser can generate, optimize, and plan the trajectory in 3D scenes under a unified framework of guided sampling. Alg. 2 summarizes the detailed sampling algorithm." + } + ] + } + ], + "index": 13 + }, + { + "type": "code", + "bbox": [ + 310, + 100, + 545, + 338 + ], + "blocks": [ + { + "bbox": [ + 311, + 75, + 520, + 99 + ], + "lines": [ + { + "bbox": [ + 311, + 75, + 520, + 99 + ], + "spans": [ + { + "bbox": [ + 311, + 75, + 520, + 99 + ], + "type": "text", + "content": "Algorithm 2: Sampling SceneDiffuser for generation, optimization, and planning" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 310, + 100, + 545, + 338 + ], + "lines": [ + { + "bbox": [ + 310, + 100, + 545, + 338 + ], + "spans": [ + { + "bbox": [ + 310, + 100, + 545, + 338 + ], + "type": "text", + "content": "Modules: Model " + }, + { + "bbox": [ + 310, + 100, + 545, + 338 + ], + "type": "inline_equation", + "content": "p_{\\theta}(\\cdot |\\mathcal{S})" + }, + { + "bbox": [ + 310, + 100, + 545, + 338 + ], + "type": "text", + "content": " , optimization objective " + }, + { + "bbox": [ + 310, + 100, + 545, + 338 + ], + "type": "inline_equation", + "content": "\\varphi_o(\\cdot |\\mathcal{S})" + }, + { + "bbox": [ + 310, + 100, + 545, + 338 + ], + "type": "text", + "content": " , and planner objective " + }, + { + "bbox": [ + 310, + 100, + 545, + 338 + ], + "type": "inline_equation", + "content": "\\varphi_p(\\cdot |\\mathcal{S},\\mathcal{G})" + }, + { + "bbox": [ + 310, + 100, + 545, + 338 + ], + "type": "text", + "content": " \n1 // one-step guided sampling \n2 function sample " + }, + { + "bbox": [ + 310, + 100, + 545, + 338 + ], + "type": "inline_equation", + "content": "(\\tau^t,\\mathcal{J})" + }, + { + "bbox": [ + 310, + 100, + 545, + 338 + ], + "type": "text", + "content": " .. \n3 " + }, + { + "bbox": [ + 310, + 100, + 545, + 338 + ], + "type": "inline_equation", + "content": "\\mu = \\mu_{\\theta}(\\tau^{t},t,\\mathcal{S}),\\Sigma = \\Sigma_{\\theta}(\\tau^{t},t,\\mathcal{S})" + }, + { + "bbox": [ + 310, + 100, + 545, + 338 + ], + "type": "text", + "content": " \n4 " + }, + { + "bbox": [ + 310, + 100, + 545, + 338 + ], + "type": "inline_equation", + "content": "\\tau^{t - 1} = \\mathcal{N}(\\tau^{t - 1};\\mu +\\lambda \\Sigma \\nabla_{\\tau^t}(\\mathcal{J}(\\tau^t |\\mathcal{S},\\mathcal{G}))|_{\\tau^t = \\mu},\\Sigma)" + }, + { + "bbox": [ + 310, + 100, + 545, + 338 + ], + "type": "text", + "content": " \n5 return " + }, + { + "bbox": [ + 310, + 100, + 545, + 338 + ], + "type": "inline_equation", + "content": "\\tau^{t - 1}" + }, + { + "bbox": [ + 310, + 100, + 545, + 338 + ], + "type": "text", + "content": " \n6 // physics-based generation Input: initial trajectory " + }, + { + "bbox": [ + 310, + 100, + 545, + 338 + ], + "type": "inline_equation", + "content": "\\tau^T\\sim \\mathcal{N}(0,\\mathbf{I})" + }, + { + "bbox": [ + 310, + 100, + 545, + 338 + ], + "type": "text", + "content": " \n7 for " + }, + { + "bbox": [ + 310, + 100, + 545, + 338 + ], + "type": "inline_equation", + "content": "t = T,\\dots ,1" + }, + { + "bbox": [ + 310, + 100, + 545, + 338 + ], + "type": "text", + "content": " do \n8 // sampling with optimization \n9 " + }, + { + "bbox": [ + 310, + 100, + 545, + 338 + ], + "type": "inline_equation", + "content": "\\tau^{t - 1} = \\mathrm{sample}(\\tau^t,\\varphi_o(\\cdot |\\mathcal{S}))" + }, + { + "bbox": [ + 310, + 100, + 545, + 338 + ], + "type": "text", + "content": " \n10 return " + }, + { + "bbox": [ + 310, + 100, + 545, + 338 + ], + "type": "inline_equation", + "content": "\\tau^0" + }, + { + "bbox": [ + 310, + 100, + 545, + 338 + ], + "type": "text", + "content": " \n11 // goal-oriented planning Input: planning steps " + }, + { + "bbox": [ + 310, + 100, + 545, + 338 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 310, + 100, + 545, + 338 + ], + "type": "text", + "content": " starting state " + }, + { + "bbox": [ + 310, + 100, + 545, + 338 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{s}}_0" + }, + { + "bbox": [ + 310, + 100, + 545, + 338 + ], + "type": "text", + "content": " , initial plan " + }, + { + "bbox": [ + 310, + 100, + 545, + 338 + ], + "type": "inline_equation", + "content": "\\tau_0^T\\sim \\mathcal{N}(0,\\mathbf{I})" + }, + { + "bbox": [ + 310, + 100, + 545, + 338 + ], + "type": "text", + "content": " \n12 " + }, + { + "bbox": [ + 310, + 100, + 545, + 338 + ], + "type": "inline_equation", + "content": "i = 1" + }, + { + "bbox": [ + 310, + 100, + 545, + 338 + ], + "type": "text", + "content": " \n13 while not done and planning step " + }, + { + "bbox": [ + 310, + 100, + 545, + 338 + ], + "type": "inline_equation", + "content": "i < N" + }, + { + "bbox": [ + 310, + 100, + 545, + 338 + ], + "type": "text", + "content": " do \n14 for " + }, + { + "bbox": [ + 310, + 100, + 545, + 338 + ], + "type": "inline_equation", + "content": "t = T,\\dots ,1" + }, + { + "bbox": [ + 310, + 100, + 545, + 338 + ], + "type": "text", + "content": " do \n15 " + }, + { + "bbox": [ + 310, + 100, + 545, + 338 + ], + "type": "inline_equation", + "content": "\\tau_i^{t - 1} = \\mathrm{sample}(\\tau_i^t,\\varphi_o(\\cdot |\\mathcal{S}) + \\varphi_p(\\cdot |\\mathcal{S},\\mathcal{G}))" + }, + { + "bbox": [ + 310, + 100, + 545, + 338 + ], + "type": "text", + "content": " \n16 // planning as inpainting \n17 " + }, + { + "bbox": [ + 310, + 100, + 545, + 338 + ], + "type": "inline_equation", + "content": "\\tau_i^{t - 1}[0:i] = \\hat{\\mathbf{s}}_{0:i}" + }, + { + "bbox": [ + 310, + 100, + 545, + 338 + ], + "type": "text", + "content": " \n18 Act " + }, + { + "bbox": [ + 310, + 100, + 545, + 338 + ], + "type": "inline_equation", + "content": "\\hat{a}_{i - 1}" + }, + { + "bbox": [ + 310, + 100, + 545, + 338 + ], + "type": "text", + "content": " to reach " + }, + { + "bbox": [ + 310, + 100, + 545, + 338 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{s}}_i = \\boldsymbol {\\tau}_i^0 [i],\\hat{\\mathbf{s}}_{0:i} = \\hat{\\mathbf{s}}_{0:i - 1}\\cup \\hat{\\mathbf{s}}_i" + }, + { + "bbox": [ + 310, + 100, + 545, + 338 + ], + "type": "text", + "content": " \n19 Increment planning step " + }, + { + "bbox": [ + 310, + 100, + 545, + 338 + ], + "type": "inline_equation", + "content": "i = i + 1" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "code_body" + } + ], + "index": 15, + "sub_type": "algorithm" + }, + { + "bbox": [ + 304, + 350, + 547, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 350, + 547, + 397 + ], + "spans": [ + { + "bbox": [ + 304, + 350, + 547, + 397 + ], + "type": "text", + "content": "Scene-aware Generation Sampling " + }, + { + "bbox": [ + 304, + 350, + 547, + 397 + ], + "type": "inline_equation", + "content": "\\pmb{\\tau}^{0}" + }, + { + "bbox": [ + 304, + 350, + 547, + 397 + ], + "type": "text", + "content": " from the distribution " + }, + { + "bbox": [ + 304, + 350, + 547, + 397 + ], + "type": "inline_equation", + "content": "p_{\\theta}(\\pmb{\\tau}^{0}|\\mathcal{S})" + }, + { + "bbox": [ + 304, + 350, + 547, + 397 + ], + "type": "text", + "content": " in Eq. (3) directly solves the conditional generation tasks. The sampled trajectories represent diverse modes and possible interactions with the 3D scenes." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 398, + 547, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 398, + 547, + 482 + ], + "spans": [ + { + "bbox": [ + 304, + 398, + 547, + 482 + ], + "type": "text", + "content": "Physics-based Optimization In a differentiable manner, the physical relations between each state and the environment are defined by " + }, + { + "bbox": [ + 304, + 398, + 547, + 482 + ], + "type": "inline_equation", + "content": "\\varphi_{o}" + }, + { + "bbox": [ + 304, + 398, + 547, + 482 + ], + "type": "text", + "content": " in Eq. (4). For general optimization without the planning objective, the task goal " + }, + { + "bbox": [ + 304, + 398, + 547, + 482 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 304, + 398, + 547, + 482 + ], + "type": "text", + "content": " is to sample a plausible trajectory in 3D scenes. Therefore, we can draw physically plausible trajectories in 3D scenes by sampling from " + }, + { + "bbox": [ + 304, + 398, + 547, + 482 + ], + "type": "inline_equation", + "content": "p(\\tau^0 |S,\\mathcal{G})" + }, + { + "bbox": [ + 304, + 398, + 547, + 482 + ], + "type": "text", + "content": " with Eq. (10)." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 483, + 547, + 650 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 483, + 547, + 650 + ], + "spans": [ + { + "bbox": [ + 304, + 483, + 547, + 650 + ], + "type": "text", + "content": "Goal-oriented Planning This can be formulated as motion inpainting under the sampling framework. Given the start state " + }, + { + "bbox": [ + 304, + 483, + 547, + 650 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{s}}_s" + }, + { + "bbox": [ + 304, + 483, + 547, + 650 + ], + "type": "text", + "content": " and the goal state " + }, + { + "bbox": [ + 304, + 483, + 547, + 650 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{s}}_g" + }, + { + "bbox": [ + 304, + 483, + 547, + 650 + ], + "type": "text", + "content": ", the planning module returns trajectory " + }, + { + "bbox": [ + 304, + 483, + 547, + 650 + ], + "type": "inline_equation", + "content": "\\hat{\\boldsymbol{\\tau}} = (\\hat{\\mathbf{s}}_0, \\hat{\\mathbf{a}}_0, \\dots, \\hat{\\mathbf{s}}_i, \\hat{\\mathbf{a}}_i, \\dots, \\hat{\\mathbf{s}}_g)" + }, + { + "bbox": [ + 304, + 483, + 547, + 650 + ], + "type": "text", + "content": " that can reach the goal state. We set the first state as " + }, + { + "bbox": [ + 304, + 483, + 547, + 650 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{s}}_0 = \\hat{\\mathbf{s}}_s" + }, + { + "bbox": [ + 304, + 483, + 547, + 650 + ], + "type": "text", + "content": " and define the goal state and reward of goal-reaching in " + }, + { + "bbox": [ + 304, + 483, + 547, + 650 + ], + "type": "inline_equation", + "content": "\\varphi_p" + }, + { + "bbox": [ + 304, + 483, + 547, + 650 + ], + "type": "text", + "content": ". For each step " + }, + { + "bbox": [ + 304, + 483, + 547, + 650 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 483, + 547, + 650 + ], + "type": "text", + "content": ", we first keep the previous states and inpaint the remaining trajectory by sampling the goal-oriented SceneDiffuser with an iterative denoising process. Next, we take the action that can reach the next sampled state with " + }, + { + "bbox": [ + 304, + 483, + 547, + 650 + ], + "type": "inline_equation", + "content": "(\\hat{\\mathbf{a}}_{i-1}, \\hat{\\mathbf{s}}_i)" + }, + { + "bbox": [ + 304, + 483, + 547, + 650 + ], + "type": "text", + "content": ". As illustrated in Alg. 2, we repeat the planning steps until the goal or maximal planning step is reached. Our planner leverages the trajectory-level generator, thus more generalizable to long-horizon trajectories and novel scenes." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 658, + 403, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 658, + 403, + 671 + ], + "spans": [ + { + "bbox": [ + 306, + 658, + 403, + 671 + ], + "type": "text", + "content": "4.3. Implementation" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "content": "Model Architecture The design of SceneDiffuser follows the practices of conditional diffusion model [20,51,53]. Specifically, we augment the time-conditional diffusion" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16753" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 71, + 286, + 335 + ], + "blocks": [ + { + "bbox": [ + 49, + 71, + 286, + 335 + ], + "lines": [ + { + "bbox": [ + 49, + 71, + 286, + 335 + ], + "spans": [ + { + "bbox": [ + 49, + 71, + 286, + 335 + ], + "type": "image", + "image_path": "68fa2e81625f8035f9003dff5d110a55349c4fcbe275317a61698eb4977b5392.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 337, + 288, + 381 + ], + "lines": [ + { + "bbox": [ + 46, + 337, + 288, + 381 + ], + "spans": [ + { + "bbox": [ + 46, + 337, + 288, + 381 + ], + "type": "text", + "content": "Figure 2. Model architecture of the SceneDiffuser. We use cross-attention to learn the relation between the input trajectory and scene condition. The optimizer and planner serve as the guidance for physically-plausible and goal-oriented trajectories." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 384, + 288, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 384, + 288, + 479 + ], + "spans": [ + { + "bbox": [ + 46, + 384, + 288, + 479 + ], + "type": "text", + "content": "model with cross-attention [65] for flexible conditioning. As shown in Fig. 2, for each sampling step, the model computes the cross-attention between the 3D scene condition and input trajectory, wherein the key and value are learned from the condition, and the query is learned from the input trajectory. The computed vector is fed into a feed-forward layer to estimate the noise " + }, + { + "bbox": [ + 46, + 384, + 288, + 479 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 46, + 384, + 288, + 479 + ], + "type": "text", + "content": ". The 3D scene is processed by a scene encoder [45, 91]); please refer to Appendix B." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 479, + 288, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 479, + 288, + 612 + ], + "spans": [ + { + "bbox": [ + 46, + 479, + 288, + 612 + ], + "type": "text", + "content": "Objective Design We consider two types of trajectory objectives for optimization and planning: (i) trajectory-level objective, and (ii) the accumulation of step-wise objective. For optimization, we consider step-wise collision, contact objective, and trajectory level smoothness objective, " + }, + { + "bbox": [ + 46, + 479, + 288, + 612 + ], + "type": "inline_equation", + "content": "\\{\\varphi_o^{\\mathrm{collision}},\\varphi_o^{\\mathrm{contact}},\\varphi_o^{\\mathrm{smoothness}}\\}" + }, + { + "bbox": [ + 46, + 479, + 288, + 612 + ], + "type": "text", + "content": ". For planning, we consider the accumulation of simple step-wise distance, " + }, + { + "bbox": [ + 46, + 479, + 288, + 612 + ], + "type": "inline_equation", + "content": "\\varphi_p^{L_2}" + }, + { + "bbox": [ + 46, + 479, + 288, + 612 + ], + "type": "text", + "content": ". Please refer to the Appendix C for details. Empirically, we observe that parameterizing the objectives with timestep " + }, + { + "bbox": [ + 46, + 479, + 288, + 612 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 479, + 288, + 612 + ], + "type": "text", + "content": " and increasing the guidance during the last several diffusion steps will enhance the effect of guidance." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 621, + 128, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 621, + 128, + 635 + ], + "spans": [ + { + "bbox": [ + 47, + 621, + 128, + 635 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "text", + "content": "To demonstrate SceneDiffuser is general and applicable to various scenarios, we evaluate the SceneDiffuser on five scene understanding tasks. For generation, we evaluate the scene-conditioned human pose and motion generation and object-conditioned dexterous grasp generation. For planning, we evaluate the path planning for 3D navigation and motion" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 547, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 144 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 144 + ], + "type": "text", + "content": "planning for robot arms. Below we first introduce baseline methods, followed by detailed settings, results analyses, and ablative studies for each task. We provide detailed implementation and experimental settings in Appendix D, additional ablative studies in Appendix E, additional experiments in Appendix F, and additional qualitative results in Appendix G." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 144, + 547, + 253 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 144, + 547, + 253 + ], + "spans": [ + { + "bbox": [ + 304, + 144, + 547, + 253 + ], + "type": "text", + "content": "Baseline Methods For conditional generation tasks, we primarily compare SceneDiffuser with the widely-adopted cVAE model [25, 31, 32, 73, 90] and its variants. We also compare with strategies for optimizing the physics of the trajectory in the cVAE, including integrating into training as loss and plugging upon as the post-optimization. For planning, we compare with a stochastic planner learned by imitation learning using Behavior Cloning (BC) and a simple heuristic-based deterministic planner guided by " + }, + { + "bbox": [ + 304, + 144, + 547, + 253 + ], + "type": "inline_equation", + "content": "L_{2}" + }, + { + "bbox": [ + 304, + 144, + 547, + 253 + ], + "type": "text", + "content": " distance." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 262, + 480, + 274 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 262, + 480, + 274 + ], + "spans": [ + { + "bbox": [ + 305, + 262, + 480, + 274 + ], + "type": "text", + "content": "5.1. Task 1: Human Pose Generation" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 281, + 547, + 401 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 281, + 547, + 401 + ], + "spans": [ + { + "bbox": [ + 304, + 281, + 547, + 401 + ], + "type": "text", + "content": "Setup Scene-conditioned human pose generation aims to generate semantically plausible and physically feasible single-frame human bodies within the given 3D scenes. We evaluate the task on the 12 indoor scenes provided by PROX [15] and the refined version of PROX'S per-frame SMPL-X parameters from LEMO [86]. The input is the colored point cloud extracted by randomly downsampling the scene meshes provided in PROX. Training/testing splits are created following the literature [69, 90], resulting in " + }, + { + "bbox": [ + 304, + 281, + 547, + 401 + ], + "type": "inline_equation", + "content": "\\sim 53\\mathrm{k}" + }, + { + "bbox": [ + 304, + 281, + 547, + 401 + ], + "type": "text", + "content": " frames in 8 scenes for training and others for testing." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 402, + 548, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 402, + 548, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 402, + 548, + 605 + ], + "type": "text", + "content": "Metrics We evaluate the physical plausibility of generated poses with both direct human evaluations and indirect collision and contact scores. We randomly selected 1000 frames in the four test scenes for the direct measure and instructed 26 Turkers to decide whether the generated human pose was plausible. We compute the mean percentage of plausible generation and term this metric as the plausible rate. For indirect measures, we report (i) the non-collision score of the generated human bodies by calculating the proportion of the scene vertices with positive SDF to the human body and (ii) the contact score by checking if the body contact with the scene in a distance [15] below a pre-defined threshold. Following the literature [84,90], we evaluate the diversities of global translation, generated SMPL-X parameters, and the marker-based body-mesh representation [89]. Specifically, we calculate the diversity of generated pose with the Average Pairwise Distance (APD) and standard deviation (std)." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": "Results Tab. 1 quantitatively demonstrates that SceneDiffuser generates significantly better poses while maintaining generation diversity. We further provide qualitative comparisons between baseline models and SceneDiffuser in Fig. 3. While achieving a comparable diversity, collision, and contact performance, our model generates results that contain considerably more physically plausible poses (e.g., floating, severe collision). This is reflected by the significant superiority (i.e., over " + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "inline_equation", + "content": "28\\%" + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": " ) over" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "16754" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 84, + 545, + 138 + ], + "blocks": [ + { + "bbox": [ + 63, + 70, + 530, + 82 + ], + "lines": [ + { + "bbox": [ + 63, + 70, + 530, + 82 + ], + "spans": [ + { + "bbox": [ + 63, + 70, + 530, + 82 + ], + "type": "text", + "content": "Table 1. Quantitative results of human pose generation in 3D scenes. We report metrics for physical plausibility and diversity." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 84, + 545, + 138 + ], + "lines": [ + { + "bbox": [ + 48, + 84, + 545, + 138 + ], + "spans": [ + { + "bbox": [ + 48, + 84, + 545, + 138 + ], + "type": "table", + "html": "
modelplausible rate↑non-collision score↑contact score↑APD (trans.)↑std (trans.)↑APD (param)↑std (param)↑APD (marker)↑std (marker)↑
cVAE (w/o. LHS) [90]14.8899.7896.421.2180.4942.8780.1663.6380.172
cVAE (w/ LHS) [90]16.1999.7599.251.0130.4162.9940.1703.6140.169
our (w/o opt.)21.0499.7499.430.7760.3313.2040.1953.4830.167
our (w/ opt.)44.7799.9398.051.0090.4133.2970.1973.6790.177
", + "image_path": "79ebeed5f6404d796eb77541ac30b6a06848874dcbe6cbb1b6ddcfd5e986ae03.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 48, + 162, + 546, + 236 + ], + "blocks": [ + { + "bbox": [ + 55, + 148, + 536, + 159 + ], + "lines": [ + { + "bbox": [ + 55, + 148, + 536, + 159 + ], + "spans": [ + { + "bbox": [ + 55, + 148, + 536, + 159 + ], + "type": "text", + "content": "Table 2. Quantitative results of human motion generation in 3D scenes. We report model variants with and without the start pose." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 162, + 546, + 236 + ], + "lines": [ + { + "bbox": [ + 48, + 162, + 546, + 236 + ], + "spans": [ + { + "bbox": [ + 48, + 162, + 546, + 236 + ], + "type": "table", + "html": "
modelplausible rate↑non-collision score↑contact score↑APD (trans.)↑std (trans.)↑APD (param)↑std (param)↑APD (marker)↑std (marker)↑
cVAE (w/o start) [73]7.7299.8686.261.6280.6132.7660.1553.2750.150
ours (w/o start)21.6799.7197.920.5680.2372.3390.1263.2990.151
ours (w/o start & w/ opt.)25.8399.9398.910.4730.1962.4050.1273.3850.154
cVAE (w/ start) [73]17.6599.8895.440.4780.1881.7470.0912.3080.105
ours (w/ start)36.5699.8598.470.1930.0811.3720.0651.5680.072
ours (w/ start & w/ opt.)38.4499.9498.430.1680.0701.3890.0651.5750.072
", + "image_path": "475d2269c003cb096b542918cc0abca05dd3c04ff8c47765e6c6fe2db6bfad07.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 48, + 248, + 545, + 446 + ], + "blocks": [ + { + "bbox": [ + 48, + 248, + 545, + 446 + ], + "lines": [ + { + "bbox": [ + 48, + 248, + 545, + 446 + ], + "spans": [ + { + "bbox": [ + 48, + 248, + 545, + 446 + ], + "type": "image", + "image_path": "e79cc5529bfd0233010d2e22d73d9942728496456417c8bc9dd41bf7870b3772.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 451, + 546, + 473 + ], + "lines": [ + { + "bbox": [ + 46, + 451, + 546, + 473 + ], + "spans": [ + { + "bbox": [ + 46, + 451, + 546, + 473 + ], + "type": "text", + "content": "Figure 3. Qualitative results of human pose generation in 3D scenes. From left to right: (a) cVAE generation, (b) SceneDiffuser generation without optimization, and poses generated (c) with and (d) without applying our optimization-guided sampling." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 476, + 288, + 573 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 476, + 288, + 573 + ], + "spans": [ + { + "bbox": [ + 46, + 476, + 288, + 573 + ], + "type": "text", + "content": "cVAE-based baselines on plausible rates. We observe this large improvement both quantitatively from the plausible rate and non-collision score and qualitatively in Fig. 3. Notably, our optimization-guided sampling improves the generator with " + }, + { + "bbox": [ + 46, + 476, + 288, + 573 + ], + "type": "inline_equation", + "content": "23\\%" + }, + { + "bbox": [ + 46, + 476, + 288, + 573 + ], + "type": "text", + "content": " on the plausible rate, showing the efficacy of the proposed optimization-guided sampling strategy and its potential for a broader range of 3D tasks with physic-based constraints or objectives." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 585, + 234, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 585, + 234, + 597 + ], + "spans": [ + { + "bbox": [ + 47, + 585, + 234, + 597 + ], + "type": "text", + "content": "5.2. Task 2: Human Motion Generation" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": "Setup We consider generating human motion sequences under two different settings: (1) condition solely on the 3D scene, and (2) condition on both the starting pose and the 3D scene. We use the same human and scene representation as in Sec. 5.1 and clip the original LEMO motion sequence into segments with a fixed duration (60 frames). In total, we obtain 28k motion segments, with the distance between each start and end pose being longer than 0.2 meters. We follow the same split in Sec. 5.1 for training/testing and the same" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 476, + 546, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 476, + 546, + 513 + ], + "spans": [ + { + "bbox": [ + 304, + 476, + 546, + 513 + ], + "type": "text", + "content": "evaluation metrics for the pose generation. We report the average values of pose metrics over motion sequence as our performance measure." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 521, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 547, + 715 + ], + "type": "text", + "content": "Results As quantitatively shown in Tab. 2, SceneDiffuser consistently generates high-quality motion sequences compared to cVAE baselines. Specifically, our generated motion outperforms baseline models on plausible rate, non-collision score, and contact score. This performance gain indicates better coverage of motion that involves rich interaction with the scene while remaining physically plausible. It also causes lower diversity in metrics (e.g., translation variance) since the plausible space for the motion is limited compared with cVAE. Empirically, we observe that providing the start position of motion as a condition constrains possible future motion sequences and leads to a drop in generation diversity for all models. We also note only a marginal performance improvement after applying optimization-guided sampling. One potential reason is that the generated motions are already plausible" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16755" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 69, + 289, + 162 + ], + "blocks": [ + { + "bbox": [ + 47, + 69, + 289, + 162 + ], + "lines": [ + { + "bbox": [ + 47, + 69, + 289, + 162 + ], + "spans": [ + { + "bbox": [ + 47, + 69, + 289, + 162 + ], + "type": "image", + "image_path": "14b9bea5a5732ccd4cfb5b291b509ac3b7fedf2151434f7c8e59e0fadaa91390.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 163, + 287, + 184 + ], + "lines": [ + { + "bbox": [ + 46, + 163, + 287, + 184 + ], + "spans": [ + { + "bbox": [ + 46, + 163, + 287, + 184 + ], + "type": "text", + "content": "Figure 4. Human motions generated by SceneDiffuser. Each row shows sampled human motions from the same start pose." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 187, + 288, + 236 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 187, + 288, + 236 + ], + "spans": [ + { + "bbox": [ + 46, + 187, + 288, + 236 + ], + "type": "text", + "content": "and receive small guidance from the optimization. As qualitatively shown in Fig. 4, SceneDiffuser generates diverse motions (e.g., \"sit,\" \"walk\") from the same start position in unseen 3D scenes." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 242, + 241, + 255 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 242, + 241, + 255 + ], + "spans": [ + { + "bbox": [ + 47, + 242, + 241, + 255 + ], + "type": "text", + "content": "5.3. Task 3: Dexterous Grasp Generation" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 261, + 288, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 261, + 288, + 392 + ], + "spans": [ + { + "bbox": [ + 46, + 261, + 288, + 392 + ], + "type": "text", + "content": "Setup Dexterous grasp generation aims to generate diverse and stable grasping poses for the given object with a human-like dexterous hand. We use the Shadowhand subset of the MultiDex [31] dataset, which contains diverse dexterous grasping poses for 58 daily objects. We represent the pose of Shadowhand as " + }, + { + "bbox": [ + 46, + 261, + 288, + 392 + ], + "type": "inline_equation", + "content": "q \\coloneqq (t,R,\\theta) \\in \\mathbb{R}^{33}" + }, + { + "bbox": [ + 46, + 261, + 288, + 392 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 261, + 288, + 392 + ], + "type": "inline_equation", + "content": "t \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 46, + 261, + 288, + 392 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 261, + 288, + 392 + ], + "type": "inline_equation", + "content": "R \\in \\mathbb{R}^6" + }, + { + "bbox": [ + 46, + 261, + 288, + 392 + ], + "type": "text", + "content": " denote the global translation and orientation respectively, and " + }, + { + "bbox": [ + 46, + 261, + 288, + 392 + ], + "type": "inline_equation", + "content": "\\theta \\in \\mathbb{R}^{24}" + }, + { + "bbox": [ + 46, + 261, + 288, + 392 + ], + "type": "text", + "content": " describes the rotation angles of the revolute joints. An object is represented by its point cloud " + }, + { + "bbox": [ + 46, + 261, + 288, + 392 + ], + "type": "inline_equation", + "content": "\\mathcal{O} \\in \\mathbb{R}^{2048 \\times 3}" + }, + { + "bbox": [ + 46, + 261, + 288, + 392 + ], + "type": "text", + "content": ". We split the dataset into 48 seen objects and 10 unseen objects for training and testing, respectively." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 392, + 287, + 547 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 392, + 287, + 547 + ], + "spans": [ + { + "bbox": [ + 46, + 392, + 287, + 547 + ], + "type": "text", + "content": "Metrics We evaluate models in terms of success rate, diversity, and collision depth. We test if a grasp is successful in IsaacGym [37] by applying external forces to the object and measuring the movement of the object. To measure how learned models capture the diversity of successful grasping pose in the training data, we report the success rate of generated poses that lies at different variance levels from the mean pose of training data. We measure the collision depth as the maximum depth that the hand penetrates the object in each successful grasp for testing models' performance on physically correct grasps. In all cases, we ignore the root transformation of the hand as it does not contribute to the diversity of grasping types." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 548, + 287, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 548, + 287, + 571 + ], + "spans": [ + { + "bbox": [ + 47, + 548, + 287, + 571 + ], + "type": "text", + "content": "Results Tab. 3 quantitatively demonstrates that SceneDiffuser generates significantly better grasp poses in" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 307, + 118, + 545, + 189 + ], + "blocks": [ + { + "bbox": [ + 305, + 71, + 547, + 115 + ], + "lines": [ + { + "bbox": [ + 305, + 71, + 547, + 115 + ], + "spans": [ + { + "bbox": [ + 305, + 71, + 547, + 115 + ], + "type": "text", + "content": "Table 3. Quantitative results of dexterous grasp generation on MultiDex [31] dataset. We measure the success rates under different diversities and depth collisions. TTA. denotes test-time optimization with physics and contact." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 118, + 545, + 189 + ], + "lines": [ + { + "bbox": [ + 307, + 118, + 545, + 189 + ], + "spans": [ + { + "bbox": [ + 307, + 118, + 545, + 189 + ], + "type": "table", + "html": "
modelsucc. rate (%)↑depth coll. (mm)↓
σ2σall
cVAE [25]0.0010.0914.0622.98
cVAE (w/ TTA.) [25]0.0021.9117.9715.19
ours (w/o opt.)70.6571.2571.2517.34
ours (w/ opt.)71.2769.8469.8414.61
", + "image_path": "87e1bd62fee85e97dcb3858853ad4781725e8792becf8f6a6b0bc67c4562a78d.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 198, + 547, + 330 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 198, + 547, + 330 + ], + "spans": [ + { + "bbox": [ + 304, + 198, + 547, + 330 + ], + "type": "text", + "content": "terms of success rate while correctly balancing the diversity of generation and grasp success. This result indicates that the SceneDiffuser achieves a consistently high success rate without much performance drop when the generated pose diverges from the mean pose in the training data. We also show that, by applying optimizer upon SceneDiffuser, the guided sampling process can reduce the violation of physically implausible grasping poses, outperforming the state-of-the-art baseline [25] without additional training or intermediate representation (i.e., contact maps). We provide qualitative results in Fig. 5 for visualization." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 344, + 502, + 357 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 344, + 502, + 357 + ], + "spans": [ + { + "bbox": [ + 306, + 344, + 502, + 357 + ], + "type": "text", + "content": "5.4. Task 4: Path Planning for Navigation" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 365, + 547, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 365, + 547, + 521 + ], + "spans": [ + { + "bbox": [ + 304, + 365, + 547, + 521 + ], + "type": "text", + "content": "Setup We selected 61 indoor scenes from ScanNet [9] to construct room-level scenarios for navigational path planning and annotated these scenes with navigation graphs. As shown in Fig. 6b, these annotations are more spatially dense and physically plausible compared to previous methods [1]. We represent the physical robot with a cylinder to simulate physically plausible trajectories; see Fig. 6a. In total, we collected around 6k trajectories by searching the shortest paths between the randomly selected start and target nodes on the graph. We use trajectories in 46 scenes for training and the rest 15 scenes for evaluation. Models take the input as the scene point cloud " + }, + { + "bbox": [ + 304, + 365, + 547, + 521 + ], + "type": "inline_equation", + "content": "S \\in \\mathbb{R}^{32768 \\times 3}" + }, + { + "bbox": [ + 304, + 365, + 547, + 521 + ], + "type": "text", + "content": ", a given start position " + }, + { + "bbox": [ + 304, + 365, + 547, + 521 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{s}}_0 \\in \\mathbb{R}^2" + }, + { + "bbox": [ + 304, + 365, + 547, + 521 + ], + "type": "text", + "content": ", and a target position " + }, + { + "bbox": [ + 304, + 365, + 547, + 521 + ], + "type": "inline_equation", + "content": "\\mathcal{G} \\in \\mathbb{R}^2" + }, + { + "bbox": [ + 304, + 365, + 547, + 521 + ], + "type": "text", + "content": " on the floor plane." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 523, + 545, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 523, + 545, + 571 + ], + "spans": [ + { + "bbox": [ + 304, + 523, + 545, + 571 + ], + "type": "text", + "content": "Metrics We evaluate the planned results by checking if the \"robot\" can move from the start to the target without collision along the planned trajectory. We report the average success rate and planning steps over all test cases." + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 47, + 571, + 545, + 686 + ], + "blocks": [ + { + "bbox": [ + 47, + 571, + 545, + 686 + ], + "lines": [ + { + "bbox": [ + 47, + 571, + 545, + 686 + ], + "spans": [ + { + "bbox": [ + 47, + 571, + 545, + 686 + ], + "type": "image", + "image_path": "ecdf21466045ddcdca6b10e7f290b7ab88290d45e33c5c9b92ffda51c9fc189a.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 688, + 547, + 711 + ], + "lines": [ + { + "bbox": [ + 46, + 688, + 547, + 711 + ], + "spans": [ + { + "bbox": [ + 46, + 688, + 547, + 711 + ], + "type": "text", + "content": "Figure 5. Qualitative results of dexterous grasp generation. Compared to grasps generated by cVAE (first row), SceneDiffuser (second row) generates fewer colliding or floating poses, which helps to achieve a higher success rate." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "16756" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 168, + 190 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 168, + 190 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 168, + 190 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 168, + 190 + ], + "type": "image", + "image_path": "767ec50fd0823393797124f48f8cc5857d7a97e0192ddd6ca70e2a35929383a5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 77, + 192, + 140, + 203 + ], + "lines": [ + { + "bbox": [ + 77, + 192, + 140, + 203 + ], + "spans": [ + { + "bbox": [ + 77, + 192, + 140, + 203 + ], + "type": "text", + "content": "(a) path planning" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 169, + 70, + 287, + 190 + ], + "blocks": [ + { + "bbox": [ + 169, + 70, + 287, + 190 + ], + "lines": [ + { + "bbox": [ + 169, + 70, + 287, + 190 + ], + "spans": [ + { + "bbox": [ + 169, + 70, + 287, + 190 + ], + "type": "image", + "image_path": "b2459c2db352f7f0f2e2099adec59589c3d14e695111005ab0125e5a1ba584d2.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 189, + 192, + 264, + 203 + ], + "lines": [ + { + "bbox": [ + 189, + 192, + 264, + 203 + ], + "spans": [ + { + "bbox": [ + 189, + 192, + 264, + 203 + ], + "type": "text", + "content": "(b) navigation graph" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 231, + 289, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 231, + 289, + 422 + ], + "spans": [ + { + "bbox": [ + 46, + 231, + 289, + 422 + ], + "type": "text", + "content": "Results As shown in Tab. 4, SceneDiffuser outperforms both the BC and the deterministic planner baseline. These results indicate the efficacy of guided sampling with the planning objective, especially given that all test scenes are unseen during training. Crucially, as simple heuristics (like " + }, + { + "bbox": [ + 46, + 231, + 289, + 422 + ], + "type": "inline_equation", + "content": "L_{2}" + }, + { + "bbox": [ + 46, + 231, + 289, + 422 + ], + "type": "text", + "content": ") oftentimes lead to dead-ends in path planning, SceneDiffuser can correctly combine past knowledge on the scene-conditioned trajectory distribution and planning objective under specific unseen scenes to redirect planning direction, which helps to avoid obstacles and dead-ends to reach the goal successfully. Compared with the baseline models, our model also requires fewer planning steps while maintaining a higher success rate. This suggests that SceneDiffuser successfully navigates to the target without diverging even in long-horizon tasks, where classic RL-based stochastic planners suffer (i.e., the low performance of BC)." + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 48, + 447, + 287, + 532 + ], + "blocks": [ + { + "bbox": [ + 47, + 423, + 287, + 445 + ], + "lines": [ + { + "bbox": [ + 47, + 423, + 287, + 445 + ], + "spans": [ + { + "bbox": [ + 47, + 423, + 287, + 445 + ], + "type": "text", + "content": "Table 4. Quantitative results of path planning in 3D navigation and motion planning for robot arms." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 447, + 287, + 532 + ], + "lines": [ + { + "bbox": [ + 48, + 447, + 287, + 532 + ], + "spans": [ + { + "bbox": [ + 48, + 447, + 287, + 532 + ], + "type": "table", + "html": "
taskmodelsucc. rate(%)↑planning steps↓
path planBC0150
deterministic(L2)13.50137.98
ours73.7590.38
arm motionBC0.31299.08
deterministic(L2)72.87141.28
ours78.59147.60
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We represent the scene with point clouds " + }, + { + "bbox": [ + 46, + 558, + 288, + 653 + ], + "type": "inline_equation", + "content": "S \\in \\mathbb{R}^{4096 \\times 3}" + }, + { + "bbox": [ + 46, + 558, + 288, + 653 + ], + "type": "text", + "content": " and the robot arm trajectory with a sequence of joint angles " + }, + { + "bbox": [ + 46, + 558, + 288, + 653 + ], + "type": "inline_equation", + "content": "\\mathcal{R} \\in [-\\pi, \\pi]" + }, + { + "bbox": [ + 46, + 558, + 288, + 653 + ], + "type": "text", + "content": ". We train our model on 160 scenes and test on 40 unseen scenes." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "content": "Metrics Similar to Sec. 5.4, we evaluate the generated trajectories by success rate on unseen scenes and the average number of planning steps. We consider a trajectory successful if the robot arm reaches the goal pose by a certain distance threshold within a limited number of steps." + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 307, + 70, + 425, + 190 + ], + "blocks": [ + { + "bbox": [ + 46, + 205, + 287, + 228 + ], + "lines": [ + { + "bbox": [ + 46, + 205, + 287, + 228 + ], + "spans": [ + { + "bbox": [ + 46, + 205, + 287, + 228 + ], + "type": "text", + "content": "Figure 6. Path planning for 3D scene navigation. SceneDiffuser generates trajectories in long-horizon tasks." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 307, + 70, + 425, + 190 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 425, + 190 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 425, + 190 + ], + "type": "image", + "image_path": "0682f30c22fb2638a4bf30be7724d65d6eaa05f0f61983c948e7a79dddbf4f97.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 331, + 192, + 404, + 204 + ], + "lines": [ + { + "bbox": [ + 331, + 192, + 404, + 204 + ], + "spans": [ + { + "bbox": [ + 331, + 192, + 404, + 204 + ], + "type": "text", + "content": "(a) motion planning" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 425, + 70, + 547, + 191 + ], + "blocks": [ + { + "bbox": [ + 425, + 70, + 547, + 191 + ], + "lines": [ + { + "bbox": [ + 425, + 70, + 547, + 191 + ], + "spans": [ + { + "bbox": [ + 425, + 70, + 547, + 191 + ], + "type": "image", + "image_path": "ba49770ba11451363882036a29ab93ccfc52cd6bceabd7fc50065078a9b35317.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 449, + 192, + 521, + 202 + ], + "lines": [ + { + "bbox": [ + 449, + 192, + 521, + 202 + ], + "spans": [ + { + "bbox": [ + 449, + 192, + 521, + 202 + ], + "type": "text", + "content": "(b) cluttered scenes" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 205, + 547, + 228 + ], + "lines": [ + { + "bbox": [ + 305, + 205, + 547, + 228 + ], + "spans": [ + { + "bbox": [ + 305, + 205, + 547, + 228 + ], + "type": "text", + "content": "Figure 7. Motion planning for robot arms. SceneDiffuser generates arm motions in tabletop scenes with obstacles." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 232, + 547, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 232, + 547, + 304 + ], + "spans": [ + { + "bbox": [ + 304, + 232, + 547, + 304 + ], + "type": "text", + "content": "Results We observe similar overall performance as in Sec. 5.4. Tab. 4 shows that SceneDiffuser consistently outperforms both the RL-based BC and the deterministic planner baseline. SceneDiffuser's planning steps for successful trials are also comparable with the deterministic planner, showing the efficacy of the planner in long-horizon scenarios." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 311, + 414, + 323 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 311, + 414, + 323 + ], + "spans": [ + { + "bbox": [ + 306, + 311, + 414, + 323 + ], + "type": "text", + "content": "5.6. Ablation Analyses" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 329, + 547, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 329, + 547, + 437 + ], + "spans": [ + { + "bbox": [ + 304, + 329, + 547, + 437 + ], + "type": "text", + "content": "We explore how the scaling coefficient " + }, + { + "bbox": [ + 304, + 329, + 547, + 437 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 329, + 547, + 437 + ], + "type": "text", + "content": " influences the human pose generation results. We report the diversity and physics metrics of sampling results under different " + }, + { + "bbox": [ + 304, + 329, + 547, + 437 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 329, + 547, + 437 + ], + "type": "text", + "content": "s, ranging from 0.1 to 100. As shown in Tab. 5, " + }, + { + "bbox": [ + 304, + 329, + 547, + 437 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 329, + 547, + 437 + ], + "type": "text", + "content": " balances generation collision/contact and diversity in human pose generation. Specifically, " + }, + { + "bbox": [ + 304, + 329, + 547, + 437 + ], + "type": "inline_equation", + "content": "\\lambda = 1.0" + }, + { + "bbox": [ + 304, + 329, + 547, + 437 + ], + "type": "text", + "content": " leads to the best physical plausibility, while larger " + }, + { + "bbox": [ + 304, + 329, + 547, + 437 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 329, + 547, + 437 + ], + "type": "text", + "content": " values lead to diverse generation results. We attribute this effect to the optimization as with bigger " + }, + { + "bbox": [ + 304, + 329, + 547, + 437 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 329, + 547, + 437 + ], + "type": "text", + "content": "s; the optimization will draw poses away from the scene." + } + ] + } + ], + "index": 18 + }, + { + "type": "table", + "bbox": [ + 307, + 451, + 547, + 525 + ], + "blocks": [ + { + "bbox": [ + 315, + 437, + 535, + 449 + ], + "lines": [ + { + "bbox": [ + 315, + 437, + 535, + 449 + ], + "spans": [ + { + "bbox": [ + 315, + 437, + 535, + 449 + ], + "type": "text", + "content": "Table 5. Ablation of the scale coefficient for optimization." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 451, + 547, + 525 + ], + "lines": [ + { + "bbox": [ + 307, + 451, + 547, + 525 + ], + "spans": [ + { + "bbox": [ + 307, + 451, + 547, + 525 + ], + "type": "table", + "html": "
metricλ = 0.1λ = 1.0λ = 10.0λ = 100.0
plausible rate ↑28.7552.521.250
APD (trans.) ↑0.7640.8861.56423.96
APD (param) ↑3.2063.2439.040573.6
non-collison score ↑99.7699.8799.8574.9
contact score ↑99.7099.6581.750.0
", + "image_path": "b98a3cc5434462f849a710a3e5d5570957420847293b8417a29b0447202819ee.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "table_body" + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 538, + 378, + 550 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 538, + 378, + 550 + ], + "spans": [ + { + "bbox": [ + 306, + 538, + 378, + 550 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 557, + 547, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 547, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 547, + 641 + ], + "type": "text", + "content": "We propose the SceneDiffuser as a general conditional generative model for generation, optimization, and planning in 3D scenes. SceneDiffuser is designed with appealing properties, including scene-aware, physics-based, and goal-oriented. We demonstrate that the SceneDiffuser outperforms previous models by a large margin on various tasks, establishing its efficacy and flexibility." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 642, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 547, + 713 + ], + "type": "text", + "content": "Acknowledgments and disclosure of funding We thank Ruiqi Gao and Ying Nian Wu for their helpful discussions and suggestions. This work is supported in part by the National Key R&D Program of China (2021ZD0150200), the Beijing Nova Program, and the National Natural Science Foundation of China (NSFC) (62172043)." + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16757" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 289, + 708 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 289, + 156 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 289, + 156 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 289, + 156 + ], + "type": "text", + "content": "[1] Peter Anderson, Qi Wu, Damien Teney, Jake Bruce, Mark Johnson, Niko Sunderhauf, Ian Reid, Stephen Gould, and Anton Van Den Hengel. 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Visualization of 3D shape generation for various categories using SDF-Diffusion. SDF-diffusion gradually removes the Gaussian noise and generates high-resolution 3D shapes in the form of an SDF voxel by a two-stage framework. Unlike previous methods, which use point clouds, we can generate 3D meshes without concern of complex post-processing. For visualization purposes, we show less-noise data instead of the initial Gaussian noise." + ], + "image_footnote": [], + "bbox": [ + 486, + 257, + 799, + 469 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 558, + 313, + 571 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We propose a 3D shape generation framework (SDF-Diffusion in short) that uses denoising diffusion models with continuous 3D representation via signed distance fields (SDF). Unlike most existing methods that depend on discontinuous forms, such as point clouds, SDF-Diffusion generates high-resolution 3D shapes while alleviating memory issues by separating the generative process into two-stage: generation and super-resolution. In the first stage, a diffusion-based generative model generates a low-resolution SDF of 3D shapes. Using the estimated low-resolution SDF as a condition, the second stage diffusion model performs super-resolution to generate high-resolution SDF. Our framework can generate a high-fidelity 3D shape despite the extreme spatial complexity. On the ShapeNet dataset, our model shows competitive performance to the state-of-the-art methods and shows applicability on the shape completion task without modification.", + "bbox": [ + 75, + 589, + 470, + 861 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 501, + 558, + 630, + 571 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The need for generative modeling of 3D shapes has rapidly increased due to high demand in various fields, such as computer vision, graphics, robotics, and content generation. To synthesize a high-quality 3D shape, numerous generative approaches have been actively studied, including generative adversarial networks (GAN) [1, 7, 8, 18, 20, 40, 51, 62, 71, 85], variational auto-encoders (VAE) [13, 27, 35, 45, 67], normalizing flows [26, 30, 60, 77], auto-regressive models [19, 31, 45, 46, 76], and others [61, 74, 75, 80, 84].", + "bbox": [ + 496, + 583, + 890, + 718 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, denoising diffusion models (DDM) have emerged as a promising generative framework in image generation [10, 16, 22, 39, 47, 63] and speech synthesis [5, 32, 54]. DDM achieves a generative process by gradually corrupting data through a diffusion process and denoising through a learned neural network. This network can generate new realistic data by repeating the denoising process from the given pure noise. Based on the success of DDM-based generative models in various domains, several attempts are being made to apply them to the task of 3D shape generation [41, 83, 87]. They have applied DDM to generate new point cloud and have outperformed previous methods.", + "bbox": [ + 496, + 719, + 892, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author.", + "bbox": [ + 101, + 887, + 228, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "20887", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, even though DDM-based 3D generative models have demonstrated their impressive performance, they still have limitations to being adopted for real-world problems. Most previous DDM-based 3D generative models use point clouds to represent 3D shapes, which limits their ability to express continuous surfaces of 3D shapes, unlike mesh representation commonly used in real-world applications. To resolve this issue, intricate post-processing [2, 24, 25, 52] is required to reconstruct continuous meshes from point clouds. They require various parameter tuning or additional information (e.g., surface normal at each point [52]), and a densely sampled point cloud is required to reconstruct high-quality mesh. However, existing DDM-based methods for 3D shape generation are based on sparse point clouds.", + "bbox": [ + 75, + 90, + 472, + 316 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we introduce a new DDM-based generation framework that generates high-quality 3D shapes through signed distance fields (SDF) (see Fig. 1). We can view SDF as a function that takes an arbitrary location as input and returns a signed distance value from the input location to the nearest surface of the mesh, and the sign of the value means whether inside or outside of the shape. We sample SDF values uniformly from a 3D shape to form a voxel-shaped SDF. This form has several advantages over point clouds. It can directly reconstruct mesh through the marching cube algorithm [38] and can utilize convolutional neural network (CNN) because of its dense and fixed structure.", + "bbox": [ + 75, + 318, + 472, + 500 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Based on this voxel-shaped SDF representation, we propose a novel DDM-based generative model in two-stage (see Fig. 2). In the first stage, a diffusion-based SDF generation produces low-resolution SDF for coarse 3D shapes. In the second stage, we propose a diffusion-based SDF superresolution, given the low-resolution SDF of the first stage as a condition. In particular, since the increasing resolution of the voxel comes as a significant burden in terms of computational resources (i.e., due to the curse of the dimension), we approach this problem by super-resolution in patch-based learning. Under this scheme, we can iteratively perform the second stage multiple times with the same structure and generate further higher resolution of SDF, which is a more detailed 3D shape. With various experiments, we achieve state-of-the-art in single-/multi-category 3D shape generative quality, and our method can be directly converted into 3D meshes, unlike other point cloud-based methods that require intricate post-processing.", + "bbox": [ + 75, + 500, + 472, + 773 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our contributions are as follows:", + "bbox": [ + 96, + 773, + 398, + 789 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a novel DDM-based generation method that utilizes a voxel-shaped SDF representation to generate high-quality and continuous 3D shapes.", + "- We represent a memory-efficient two-stage framework composed of low-resolution SDF generation and SDF super-resolution conditioned on the low-resolution SDF." + ], + "bbox": [ + 76, + 795, + 472, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In particular, we can iteratively perform super-resolution to generate higher-resolution SDF.", + "bbox": [ + 511, + 90, + 890, + 121 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- SDF-diffusion can be seamlessly extended into multi-category 3D shape generation and completion, which shows the flexibility of the proposed method.", + "bbox": [ + 500, + 132, + 893, + 178 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 191, + 640, + 207 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3D Shape representation. Numerous in-depth studies have been conducted on the representation of 3D shape [8, 43, 44, 48-50, 64, 73, 78, 79, 81]. We can categorize them into two groups: explicit representations, such as voxels [14, 15, 71], point clouds [1, 55, 56], and implicit functions, such as signed distance fields (SDF) [50, 64].", + "bbox": [ + 496, + 217, + 890, + 306 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Voxels are widely adapted in various neural networks due to their intuitive structure and synergy with 3D CNN [14, 15, 71, 73]. However, it may cause a memory problem according to the increase in resolution. Point clouds, which are compact and readily available, are dominant representations with their well-suitability to learn contextual information in neural networks [1, 55, 56, 79, 81]. However, it requires post-processing to convert the synthesized point clouds into meshes for real-world applications [8, 38, 43, 44, 48-50, 78].", + "bbox": [ + 496, + 306, + 890, + 458 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Implicit functions view the 3D shape as a set of levels for a continuous function, which makes it possible to express a continuous surface [8,44,48-50,64,78]. As a result, despite their slow interference as they require numerous network operations, these methods are growing in popularity. In particular, SDF encoded with distance to the nearest surface has some advantages to express sharper reconstructions [50, 64]. Thus, we exploit SDF voxel representation to obtain sharper meshes without unnecessary procedures.", + "bbox": [ + 496, + 458, + 890, + 595 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3D shape generation. To generate 3D geometry, a variety of frameworks are applied [1, 7, 8, 13, 19, 20, 26, 27, 30, 31, 34, 46, 51, 60, 62, 67, 85]. With such a perspective, several frameworks are applied to model the distribution representing a 3D shape, such as GAN-based models [33], auto-regressive models [66], flow-based models [77], and implicit functions [43, 50].", + "bbox": [ + 496, + 598, + 890, + 703 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "For GAN-based 3D generative method, SDF-StyleGAN [86] extends StyleGAN2 [23] for 3D shape generation by proposing global and local discriminator that enables GAN discriminator on SDF. Generative methods, such as AutoSDF [45], and ShapeFormer [76], propose to utilize a voxel form of implicit representation (e.g., SDF and occupancy) for mesh generation through a two-stage. A two-stage generative strategy reduces required computational resources by compressing data into a tractable form (e.g., latent feature) rather than directly dealing with an original data structure to make a generative model concentrate semantically compressed representation and save computational resources. Motivated by VQ-GAN [12],", + "bbox": [ + 496, + 704, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "footer", + "text": "20888", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "AutoSDF and ShapeFormer apply two-stage generative method and show impressive performance on conditional 3D shape generation. They utilize an auto-encoder to convert voxel into compressed latent space and generate a new shape using the autoregressive model on the latent space. However, they miss fully utilizing the advantage of the two-stage generative method because they use a regression-based auto-encoder unlike VQ-GAN, which uses GAN and perceptual loss [21]. Unlike the 2D image generation, there are insufficient research works in perceptually plausible auto-encoding methods about 3D shapes, especially voxel structures; it has difficulties in applying a two-stage strategy to 3D shape generation.", + "bbox": [ + 75, + 90, + 472, + 287 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "On the other hand, recent research works propose a new two-stage generative method [17, 42, 59]. They use a super-resolution model to up-sample low-resolution data, and the generation model learns low-resolution data distribution. Instead of training an auto-encoder, these methods utilize naturally constructed low-resolution forms. Inspired by this, our method exploits a two-stage framework using voxel-shaped SDF. Instead of learning the auto-encoder, we propose a method of generating a coarse 3D shape that is naturally compressed form in the representation of a low-resolution voxel. We then generate high-quality 3D shapes by refining the details of the coarse shape by upsampling the low-resolution voxel.", + "bbox": [ + 75, + 290, + 472, + 486 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Diffusion-Based 3D shape generation. With the success of DDM-based generative models in image generation [10, 16, 47], diffusion-based 3D shape generations have advanced significantly. In particular, diffusion probabilistic models (DPM) [41] suggest a DDM-based approach with an auto-encoder architecture built on PointNet [55], which compresses point clouds into a latent vector and then generates new shape latent using normalizing flows [6, 11]. Point voxel diffusion (PVD) [87] applies DDM directly on the point clouds by adopting a point voxel CNN-based network architecture [36], which utilizes both the 3D CNN and PointNet. In addition, point diffusion-refinement (PDR) [42] proposes a two-stage generative framework for conditional point cloud generation task. It generates sparse point clouds by PointNet-based DDM in the first stage and up-samples the sparse point clouds to denser ones in a learning-based manner. Motivated by latent diffusion models (LDM) [58], latent point diffusion models (LION) [83] propose a two-stage approach with compressed latent point clouds through VAE [29]. LION converts result point clouds into mesh by shapes as points (SAP) [52]. Despite their great performance, it still requires a pre-trained SAP model or fine-tuning stage. In other words, the usability of the above point clouds-based approaches is limited to be adopted in real-world applications. To address this issue, we propose a diffusion-based generative model upon voxel-shaped SDF representation,", + "bbox": [ + 75, + 493, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/c36185db371aa6497a3108a6fc6be8621f74180fc8d56a683fed62636eed9a9a.jpg", + "image_caption": [ + "Figure 2. Overview of SDF-Diffusion. The proposed method consists of two stages. In the first stage, we take as input voxel-shaped noise $\\mathbf{x}_T^{\\mathrm{LR}} = \\epsilon^{\\mathrm{LR}}$ and generate low-resolution SDF voxel $\\mathbf{x}_0^{\\mathrm{LR}}$ of new coarse 3D shape through DDM. In the second stage, conditioned on $\\mathbf{x}_0^{\\mathrm{LR}}$ , we perform super-resolution through another DDM, which generates high-resolution SDF voxel $\\mathbf{x}_0^{\\mathrm{HR}}$ with fine and detailed 3D shape." + ], + "image_footnote": [], + "bbox": [ + 509, + 89, + 880, + 291 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "which can directly reconstruct 3D mesh using zero isosurface finding methods [38].", + "bbox": [ + 498, + 402, + 890, + 435 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 500, + 448, + 635, + 465 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We propose a generative method for high-resolution 3D shapes in the form of SDF voxels based on the denoising diffusion models [16, 63] (SDF-Diffusion in short). To generate high-resolution samples efficiently, the proposed method involves two stages: diffusion-based SDF generation and diffusion-based patch-wise SDF super-resolution (see Fig. 2 for the overview). In the first stage, the diffusion-based SDF generation model generates a low-resolution coarse 3D shape. Given this low-resolution sample, the diffusion-based SDF super-resolution model progressively produces high-resolution samples in the second stage. In other words, we can consider the first stage as a pure diffusion-based generative model, and the second stage as a conditional diffusion-based super-resolution model. It is worth noting that, ideally, the second stage can be repeated multiple times with the same architecture, which enables us to generate more high-resolution 3D shapes.", + "bbox": [ + 496, + 474, + 890, + 731 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the following, we briefly explain the background on DDM in Sec. 3.1. Then, in Sec. 3.2, we describe our method for generating coarse 3D shapes using a diffusion-based technique. In Sec. 3.3, we explain how we generate high-resolution 3D shapes by super-resolving low-resolution correspondence. Training and inference processes for each diffusion model are listed in Algorithm 1 and Algorithm 2.", + "bbox": [ + 496, + 731, + 890, + 838 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Background on Denoising Diffusion Models", + "text_level": 1, + "bbox": [ + 500, + 845, + 870, + 863 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "DDM is a class of generative models that generates new samples from a given data distribution by learning the in-", + "bbox": [ + 500, + 869, + 890, + 901 + ], + "page_idx": 2 + }, + { + "type": "footer", + "text": "20889", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "verse of the noising process [16, 63]. Concretely, starting from samples from the Gaussian distribution $\\mathbf{x}_T$ , the denoising process gradually produces samples with less noise $\\mathbf{x}_{T - 1},\\mathbf{x}_{T - 2},\\ldots$ , and aims to reach final samples $\\mathbf{x}_0$ , which is the noise-free final output.", + "bbox": [ + 75, + 90, + 468, + 167 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Forward process. The forward process (or diffusion process) gradually adds the Gaussian noise to the clean data, which is the approximate joint posterior $q(\\mathbf{x}_{1:T}|\\mathbf{x}_0)$ . This diffusion process is represented as a Markov chain:", + "bbox": [ + 76, + 170, + 468, + 229 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(\\mathbf {x} _ {0: T}\\right) = q \\left(\\mathbf {x} _ {0}\\right) \\prod_ {t = 1} ^ {T} q \\left(\\mathbf {x} _ {t} \\mid \\mathbf {x} _ {t - 1}\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 155, + 233, + 468, + 273 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(\\mathbf {x} _ {t} \\mid \\mathbf {x} _ {t - 1}\\right) = \\mathcal {N} \\left(\\mathbf {x} _ {t}; \\sqrt {1 - \\beta_ {t}} \\mathbf {x} _ {t - 1}, \\beta_ {t} \\mathbf {I}\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 133, + 277, + 468, + 296 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\beta_{t}$ denotes the noise scheduling hyperparameter.", + "bbox": [ + 76, + 306, + 441, + 320 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "According to [16], the forward process admits sampling $\\mathbf{x}_t$ at an arbitrary time step $t$ by a closed form:", + "bbox": [ + 76, + 320, + 468, + 351 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(\\mathbf {x} _ {t} \\mid \\mathbf {x} _ {0}\\right) = \\mathcal {N} \\left(\\mathbf {x} _ {t}; \\sqrt {\\bar {\\alpha} _ {t}} \\mathbf {x} _ {0}, (1 - \\bar {\\alpha} _ {t}) \\mathbf {I}\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 142, + 361, + 468, + 378 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\alpha_{t} = 1 - \\beta_{t}$ and $\\bar{\\alpha}_{t} = \\Pi_{s=1}^{t} \\alpha_{s}$ . Thus, $\\mathbf{x}_{t}$ can be directly sampled by:", + "bbox": [ + 76, + 388, + 468, + 417 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} _ {t} = \\sqrt {\\bar {\\alpha} _ {t}} \\mathbf {x} _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon , \\epsilon \\sim \\mathcal {N} (\\mathbf {0}, \\mathbf {I}). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 142, + 428, + 468, + 446 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Reverse process. The reverse process (or generative process) aims to generate samples by gradually inverting infinitesimal noise, which is the joint distribution $p_{\\theta}(\\mathbf{x}_{0:T})$ . This reverse process is defined as a Markov chain with the learned Gaussian transitions:", + "bbox": [ + 76, + 455, + 468, + 529 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\theta} \\left(\\mathbf {x} _ {0: T}\\right) = p \\left(\\mathbf {x} _ {T}\\right) \\prod_ {t = 1} ^ {T} p _ {\\theta} \\left(\\mathbf {x} _ {t - 1} \\mid \\mathbf {x} _ {t}\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 158, + 532, + 468, + 571 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\theta} \\left(\\mathbf {x} _ {t - 1} \\mid \\mathbf {x} _ {t}\\right) = \\mathcal {N} \\left(\\mathbf {x} _ {t - 1}; \\mu_ {\\theta} \\left(\\mathbf {x} _ {t}, t\\right), \\sigma_ {t} ^ {2} \\mathbf {I}\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 137, + 575, + 468, + 592 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $p(\\mathbf{x}_T) = \\mathcal{N}(\\mathbf{x}_T;\\mathbf{0},\\mathbf{I})$ is the standard Gaussian distribution, $\\mu_{\\theta}(\\mathbf{x}_t,t)$ indicates a denoising function parameterized by $\\theta$ , $\\sigma_t^2$ is a time-step dependant variance, and we fix $\\sigma_t^2 = \\frac{1 - \\bar{\\alpha}_{t - 1}}{1 - \\bar{\\alpha}_t}\\beta_t$ , following [16]. We can sample from $p(\\mathbf{x}_T)$ and then draw $\\mathbf{x}_{t - 1}\\sim p_{\\theta}(\\mathbf{x}_{t - 1}|\\mathbf{x}_t)$ by Eq. (6) as:", + "bbox": [ + 76, + 602, + 468, + 679 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} _ {t - 1} = \\mu_ {\\theta} \\left(\\mathbf {x} _ {t}, t\\right) + \\sigma_ {t} \\epsilon , \\epsilon \\sim \\mathcal {N} (\\mathbf {0}, \\mathbf {I}). \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 685, + 468, + 702 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "By repeating this process, we can eventually generate $\\mathbf{x}_0$ .", + "bbox": [ + 76, + 712, + 455, + 727 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Training objective. Following [16], we can simplify $\\mu_{\\theta}(\\mathbf{x}_t,t)$ ..", + "bbox": [ + 76, + 729, + 468, + 761 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mu_ {\\theta} \\left(\\mathbf {x} _ {t}, t\\right) = \\frac {1}{\\sqrt {\\alpha_ {t}}} \\left(\\mathbf {x} _ {t} - \\frac {\\beta_ {t}}{\\sqrt {1 - \\bar {\\alpha} _ {t}}} \\epsilon_ {\\theta} \\left(\\mathbf {x} _ {t}, t\\right)\\right), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 119, + 770, + 468, + 804 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\epsilon_{\\theta}(\\mathbf{x}_t,t)$ is a neural network parameterized by $\\theta$ that predicts noise from noisy input $\\mathbf{x}_t$ . Thus, the objective function compares the difference between the predicted noise $\\epsilon_{\\theta}(\\mathbf{x}_t,t)$ and the applied noise $\\epsilon$ [16]:", + "bbox": [ + 76, + 813, + 468, + 875 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\left\\| \\epsilon_ {\\theta} \\left(\\mathbf {x} _ {t}, t\\right) - \\epsilon \\right\\| _ {p} ^ {p}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 197, + 883, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $p\\in \\{1,2\\}$ . On the other hand, according to [16], it is possible to modify $\\mu_{\\theta}(\\mathbf{x}_t,t)$ with a neural network predicting $\\mathbf{x}_0$ instead of noise $\\epsilon$ :", + "bbox": [ + 498, + 90, + 890, + 135 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mu_ {\\theta} \\left(\\mathbf {x} _ {t}, t\\right) = \\gamma_ {t} f _ {\\theta} \\left(\\mathbf {x} _ {t}, t\\right) + \\delta_ {t} \\mathbf {x} _ {t}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 145, + 890, + 162 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\gamma_{t} = \\frac{\\beta_{t}\\sqrt{\\bar{\\alpha}_{t - 1}}}{1 - \\bar{\\alpha}_{t}}$ and $\\delta_t = \\frac{(1 - \\bar{\\alpha}_{t - 1})\\sqrt{\\alpha_t}}{1 - \\bar{\\alpha}_t}$ , and $f_{\\theta}(\\mathbf{x}_t,t)$ is a neural network parameterized by $\\theta$ that predicts noise-free data $\\mathbf{x}_0$ . In that case, the objective function becomes:", + "bbox": [ + 498, + 170, + 890, + 220 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\left\\| f _ {\\theta} \\left(\\mathbf {x} _ {t}, t\\right) - \\mathbf {x} _ {0} \\right\\| _ {p} ^ {p}. \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 614, + 229, + 890, + 248 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Thus, we use Eq. (11) as our objective function in this work.", + "bbox": [ + 500, + 252, + 890, + 267 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Diffusion SDF Generation", + "text_level": 1, + "bbox": [ + 500, + 275, + 736, + 290 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here, we describe a diffusion-based generative model for low-resolution 3D shape represented as SDF voxel $\\mathbf{x}_0^{\\mathrm{LR}}\\sim q(\\mathbf{x}_0^{\\mathrm{LR}})$ sampled from the real data distribution $q(\\mathbf{x}_0^{\\mathrm{LR}})$ .", + "bbox": [ + 498, + 299, + 890, + 345 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Diffusion-based SDF voxel generation. Specifically, given a clean data sample $\\mathbf{x}_0^{\\mathrm{LR}}$ , we corrupt $\\mathbf{x}_0^{\\mathrm{LR}}$ with the same shaped voxel noise $\\epsilon^{\\mathrm{LR}} \\sim \\mathcal{N}(\\mathbf{0}, \\mathbf{I})$ sampled from the standard Gaussian distribution following the forward process in Eq. (4):", + "bbox": [ + 498, + 347, + 890, + 422 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} _ {t} ^ {\\mathrm {L R}} = \\sqrt {\\bar {\\alpha} _ {t}} \\mathbf {x} _ {0} ^ {\\mathrm {L R}} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon^ {\\mathrm {L R}}, \\epsilon^ {\\mathrm {L R}} \\sim \\mathcal {N} (\\mathbf {0}, \\mathbf {I}). \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 527, + 430, + 890, + 449 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Then, a network $f_{\\theta}^{\\mathrm{LR}}$ is trained to predict noise-free data with MSE objective function like Eq. (11):", + "bbox": [ + 498, + 455, + 890, + 488 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} ^ {\\mathrm {L R}} = \\left\\| f _ {\\theta} ^ {\\mathrm {L R}} \\left(\\mathbf {x} _ {t} ^ {\\mathrm {L R}}, t, c\\right) - \\mathbf {x} _ {0} ^ {\\mathrm {L R}} \\right\\| _ {2} ^ {2}, \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 494, + 890, + 513 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $c$ is a category label of given data.", + "bbox": [ + 500, + 521, + 769, + 536 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "During inference, a new SDF voxel is generated by progressively predicting lesser noisy samples $\\mathbf{x}_{t - 1}^{\\mathrm{LR}}$ with the trained neural network $f_{\\theta}^{\\mathrm{LR}}$ as $t = T,\\dots ,1$ ..", + "bbox": [ + 498, + 537, + 890, + 582 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} _ {t - 1} ^ {\\mathrm {L R}} = \\gamma_ {t} f _ {\\theta} ^ {\\mathrm {L R}} \\left(\\mathbf {x} _ {t} ^ {\\mathrm {L R}}, t, c\\right) + \\delta_ {t} \\mathbf {x} _ {t} ^ {\\mathrm {L R}} + \\sigma_ {t} \\epsilon^ {\\mathrm {L R}}. \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 560, + 589, + 890, + 608 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In Eq. (13) and Eq. (14), the category condition $c$ is used only for multi-category generations.", + "bbox": [ + 498, + 616, + 890, + 646 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Network architecture. Our model is built upon a U-shaped network in SR3 [59], which is a DDM-based superresolution method designed for 2D image domain. Thus, we modify and improve this structure for 3D domain. We convert 2D-based U-shaped network of SR3 into 3D-based model by replacing 2D-based convolutional layers with 3D ones. The network has three layers, and each layer is composed of several layers of residual blocks and self-attention [68] and the Swish activation function [57]. The voxel feature resolution is halved for each layer (e.g., $32 \\rightarrow 16 \\rightarrow 8$ ), and the channel is doubled (e.g., $64 \\rightarrow 128 \\rightarrow 256$ ). A more detailed design of the network architecture is in the supplementary material.", + "bbox": [ + 498, + 650, + 890, + 845 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The timestep $t$ and category condition $c$ are embedded into a vector $\\mathbf{z}$ through MLPs following [4,59]:", + "bbox": [ + 498, + 845, + 890, + 875 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {z} = \\operatorname {M L P} \\left(\\operatorname {P o s E n c} \\left(\\sqrt {\\bar {\\alpha} _ {t}}\\right)\\right) + \\operatorname {M L P} (\\text {E m b e d d i n g} (c)), \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 881, + 890, + 897 + ], + "page_idx": 3 + }, + { + "type": "footer", + "text": "20890", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Algorithm 1 Training", + "text_level": 1, + "bbox": [ + 80, + 90, + 225, + 104 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Stage 1: Diffusion SDF Generation", + "text_level": 1, + "bbox": [ + 91, + 109, + 308, + 122 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "repeat", + "bbox": [ + 91, + 125, + 130, + 133 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\left(\\mathbf {x} _ {0} ^ {\\mathrm {L R}}, c\\right) \\sim q \\left(\\mathbf {x} _ {0} ^ {\\mathrm {L R}}, c\\right) \\quad \\triangleright \\text {S a m p l e L R v o x e l a n d c a t e g o r y l a b e l}\n$$\n", + "text_format": "latex", + "bbox": [ + 112, + 133, + 468, + 147 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nt \\sim \\mathcal {U} (\\{1, \\dots T ^ {\\mathrm {L R}} \\})\n$$\n", + "text_format": "latex", + "bbox": [ + 112, + 147, + 227, + 157 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\epsilon^ {\\mathrm {L R}} \\sim \\mathcal {N} (\\mathbf {0}, \\mathbf {I})\n$$\n", + "text_format": "latex", + "bbox": [ + 112, + 157, + 196, + 169 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} _ {t} ^ {\\mathrm {L R}} = \\sqrt {\\bar {\\alpha} _ {t}} \\mathbf {x} _ {0} ^ {\\mathrm {L R}} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon^ {\\mathrm {L R}} \\quad \\triangleright \\text {N o i s y v o x e l a t t i m e s t e p} t\n$$\n", + "text_format": "latex", + "bbox": [ + 112, + 169, + 468, + 181 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\theta^ {t} \\leftarrow \\eta \\nabla_ {\\theta} \\| f _ {\\theta} ^ {\\mathrm {L R}} (\\mathbf {x} _ {t} ^ {\\mathrm {L R}}, t, c) - \\mathbf {x} _ {0} ^ {\\mathrm {L R}} \\| _ {2} ^ {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 112, + 181, + 303, + 195 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "until $f_{\\theta}^{\\mathrm{LR}}$ is converged", + "bbox": [ + 91, + 195, + 212, + 208 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Stage 2: Patch-Based Diffusion SDF Super-Resolution", + "text_level": 1, + "bbox": [ + 91, + 212, + 429, + 224 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "repeat", + "bbox": [ + 91, + 224, + 129, + 234 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\left(\\hat {\\mathbf {x}} _ {0} ^ {\\mathrm {H R}}, c\\right) \\sim q \\left(\\hat {\\mathbf {x}} _ {0} ^ {\\mathrm {H R}}, c\\right) \\triangleright \\text {S a m p l e H R v o x e l p a t c h a n d c a t e g o r y l a b e l} \\\\ \\hat {\\mathbf {x}} _ {0} ^ {\\mathrm {L R}} \\sim q \\left(\\hat {\\mathbf {x}} _ {0} ^ {\\mathrm {L R}}\\right) \\quad \\triangleright \\text {S a m p l e L R c o n d i t i o n a l v o x e l p a t c h} \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 112, + 234, + 468, + 258 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nt \\sim \\mathcal {U} (\\{1, \\dots T ^ {\\mathrm {H R}} \\})\n$$\n", + "text_format": "latex", + "bbox": [ + 112, + 258, + 227, + 271 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\epsilon} ^ {\\mathrm {H R}} \\sim \\tilde {\\mathcal {N}} (\\mathbf {0}, \\mathbf {I})\n$$\n", + "text_format": "latex", + "bbox": [ + 112, + 271, + 196, + 284 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\hat {\\mathbf {x}} _ {t} ^ {\\mathrm {H R}} = \\sqrt {\\bar {\\alpha} _ {t}} \\hat {\\mathbf {x}} _ {0} ^ {\\mathrm {H R}} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon^ {\\mathrm {H R}} \\quad \\triangleright \\mathrm {H R} \\text {n o i s y v o x e l a r t i m e s t e p} t \\\\ \\theta \\leftarrow \\eta \\nabla_ {\\theta} \\| f _ {\\theta} ^ {\\mathrm {H R}} (\\hat {\\mathbf {x}} _ {t} ^ {\\mathrm {H R}}, \\hat {\\mathbf {x}} _ {0} ^ {\\mathrm {L R}}, t, c) - \\hat {\\mathbf {x}} _ {0} ^ {\\mathrm {H R}} \\| _ {1} ^ {1} \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 112, + 284, + 468, + 308 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "until $f_{\\theta}^{\\mathrm{HR}}$ is converged", + "bbox": [ + 91, + 309, + 214, + 321 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where PosEnc is the sinusoidal positional encoding used in Transformer [68] and Embedding is the embedding layer, and the second term is ignored for a single-category generation. The embedding vector $\\mathbf{z}$ is inserted into every residual block using adaptive group normalization layers (AdaGN) following [10]. AdaGN is an extension of group normalization [72] through channel-wise scaling and shifting w.r.t. normalized feature maps $\\mathbf{h} \\in \\mathbb{R}^{k \\times h \\times w \\times d}$ , where $k$ is the number of feature map channels:", + "bbox": [ + 75, + 339, + 468, + 474 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {A d a G N} (\\mathbf {h}, \\mathbf {z}) = \\mathbf {z} _ {s} \\left(\\operatorname {G r o u p N o r m} (\\mathbf {h}) + \\mathbf {z} _ {t}\\right), \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 133, + 487, + 468, + 503 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $(\\mathbf{z}_s,\\mathbf{z}_t)\\in \\mathbb{R}^{2\\times k} = \\mathrm{MLP}(\\mathbf{z})$ is result of an MLP layer. The detailed network architecture is available in the supplementary material.", + "bbox": [ + 75, + 517, + 468, + 565 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Patch-Based Diffusion SDF Super-Resolution", + "text_level": 1, + "bbox": [ + 76, + 578, + 460, + 594 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We aim to train a conditional diffusion-based super-resolution model that generates realistic high-resolution SDF voxel $\\mathbf{x}_0^{\\mathrm{HR}}$ with low-resolution condition $\\mathbf{x}_0^{\\mathrm{LR}}$ .", + "bbox": [ + 75, + 603, + 468, + 650 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Patch-based learning scheme. The increase in demanding memory due to the growth of spatial complexity hinders the learning of high-resolution generative models. Instead of training on the full high-resolution voxel, we train our model based on small cube-shaped patches of given input high-resolution voxel $\\mathbf{x}_0^{\\mathrm{HR}}\\sim q(\\mathbf{x}_0^{\\mathrm{HR}})$ sampled from real data distribution to reduce memory consumption. We denote $\\hat{\\mathbf{x}}_t^{\\mathrm{HR}}$ as a cube-shaped patch extracted from a random location of voxel $\\mathbf{x}_t^{\\mathrm{HR}}$ , and $\\hat{\\mathbf{x}}_t^{\\mathrm{LR}}$ is a patch extracted from the corresponding location of $\\mathbf{x}_t^{\\mathrm{LR}}$ . In addition, $\\epsilon^{\\mathrm{HR}}$ and $\\hat{\\epsilon}^{\\mathrm{HR}}$ are voxel-shaped noises sampled from the standard Gaussian distribution that have the same shape with $\\mathbf{x}_t^{\\mathrm{HR}}$ and $\\hat{\\mathbf{x}}_t^{\\mathrm{HR}}$ respectively. Note that the patch-based operation is optional during the test phase if GPU has enough memory.", + "bbox": [ + 75, + 654, + 468, + 864 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Conditional diffusion-based super-resolution. Similarly to Eq. (12), the diffusion process for SDF super-resolution", + "bbox": [ + 75, + 869, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Algorithm 2 Sampling", + "text_level": 1, + "bbox": [ + 501, + 90, + 656, + 106 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Stage 1: Diffusion-Based 3D Shape Generation", + "text_level": 1, + "bbox": [ + 500, + 109, + 794, + 122 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Input: $c$ : category label (integer)", + "bbox": [ + 501, + 123, + 681, + 135 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Output: $\\mathbf{x}_0^{\\mathrm{LR}}$ : generated coarse shape", + "bbox": [ + 501, + 135, + 705, + 147 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nt = T\n$$\n", + "text_format": "latex", + "bbox": [ + 516, + 147, + 550, + 157 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} _ {t} ^ {\\mathrm {L R}} \\sim \\mathcal {N} (\\mathbf {0}, \\mathbf {I})\n$$\n", + "text_format": "latex", + "bbox": [ + 516, + 157, + 599, + 170 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\text {w h i l e} t \\neq 0 \\mathbf {d o}\n$$\n", + "text_format": "latex", + "bbox": [ + 516, + 170, + 596, + 181 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\epsilon^ {\\mathrm {L R}} \\sim \\mathcal {N} (\\mathbf {0}, \\mathbf {I})\n$$\n", + "text_format": "latex", + "bbox": [ + 535, + 181, + 617, + 193 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} _ {t - 1} ^ {\\mathrm {L R}} \\leftarrow \\gamma_ {t} f _ {\\theta} ^ {\\mathrm {L R}} \\left(\\mathbf {x} _ {t} ^ {\\mathrm {L R}}, t, c\\right) + \\delta_ {t} \\mathbf {x} _ {t} ^ {\\mathrm {L R}} + \\sigma_ {t} \\epsilon^ {\\mathrm {L R}}\n$$\n", + "text_format": "latex", + "bbox": [ + 535, + 193, + 764, + 207 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nt = t - 1\n$$\n", + "text_format": "latex", + "bbox": [ + 535, + 207, + 586, + 218 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "end while", + "bbox": [ + 516, + 219, + 571, + 229 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Stage 2: Patch-Based Diffusion SDF Super-Resolution", + "text_level": 1, + "bbox": [ + 500, + 231, + 838, + 243 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Input: $c$ : category label (integer), $\\mathbf{x}_0^{\\mathrm{LR}}$ : low-resolution condition", + "bbox": [ + 501, + 243, + 844, + 256 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Output: $\\mathbf{x}_0^{\\mathrm{HR}}$ : generated high-resolution shape", + "bbox": [ + 501, + 256, + 751, + 268 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nt = T\n$$\n", + "text_format": "latex", + "bbox": [ + 516, + 268, + 550, + 279 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$\\mathbf{x}_t^{\\mathrm{HR}} \\sim \\mathcal{N}(\\mathbf{0}, \\mathbf{I})$ $>$ Patch is optional during inference phase", + "bbox": [ + 516, + 280, + 890, + 292 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\text {w h i l e} t \\neq 0 \\mathbf {d o}\n$$\n", + "text_format": "latex", + "bbox": [ + 516, + 292, + 596, + 303 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\epsilon^ {\\mathrm {H R}} \\sim \\mathcal {N} (\\mathbf {0}, \\mathbf {I})\n$$\n", + "text_format": "latex", + "bbox": [ + 535, + 303, + 617, + 315 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} _ {t - 1} ^ {\\mathrm {H R}} \\leftarrow \\gamma_ {t} f _ {\\theta} ^ {\\mathrm {H R}} (\\mathbf {x} _ {t} ^ {\\mathrm {H R}}, \\mathbf {x} _ {0} ^ {\\mathrm {L R}}, t, c) + \\delta_ {t} \\mathbf {x} _ {t} ^ {\\mathrm {H R}} + \\sigma_ {t} \\epsilon^ {\\mathrm {H R}}\n$$\n", + "text_format": "latex", + "bbox": [ + 535, + 315, + 795, + 329 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nt = t - 1\n$$\n", + "text_format": "latex", + "bbox": [ + 535, + 329, + 589, + 338 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "end while", + "bbox": [ + 516, + 340, + 571, + 349 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "can be represented as:", + "bbox": [ + 500, + 366, + 647, + 380 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {x}} _ {t} ^ {\\mathrm {H R}} = \\sqrt {\\bar {\\alpha} _ {t}} \\hat {\\mathbf {x}} _ {0} ^ {\\mathrm {H R}} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\hat {\\epsilon} ^ {\\mathrm {H R}}, \\hat {\\epsilon} ^ {\\mathrm {H R}} \\sim \\mathcal {N} (\\mathbf {0}, \\mathbf {I}). \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 388, + 890, + 406 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In the case of the objective function, we use $\\mathcal{L}_1$ for superresolution, followed by SR3 [59], where they empirically find that $\\mathcal{L}_1$ loss is better for super-resolution task compared to MSE loss:", + "bbox": [ + 496, + 415, + 890, + 474 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} ^ {\\mathrm {H R}} = \\left\\| f _ {\\theta} ^ {\\mathrm {H R}} \\left(\\hat {\\mathbf {x}} _ {t} ^ {\\mathrm {H R}}, \\hat {\\mathbf {x}} _ {0} ^ {\\mathrm {L R}}, t, c\\right) - \\hat {\\mathbf {x}} _ {0} ^ {\\mathrm {H R}} \\right\\| _ {1} ^ {1}. \\tag {18}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 483, + 890, + 501 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The low-resolution condition is nearly up-sampled to be the same resolution as the high-resolution side and channelwise concatenation is applied. Sampling is done by repeating a similar process to Eq. (14):", + "bbox": [ + 496, + 510, + 890, + 571 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} _ {t - 1} ^ {\\mathrm {H R}} = \\gamma_ {t} f _ {\\theta} ^ {\\mathrm {H R}} \\left(\\mathbf {x} _ {t} ^ {\\mathrm {H R}}, \\mathbf {x} _ {0} ^ {\\mathrm {L R}}, t, c\\right) + \\delta_ {t} \\mathbf {x} _ {t} ^ {\\mathrm {H R}} + \\sigma_ {t} \\epsilon^ {\\mathrm {H R}}, \\tag {19}\n$$\n", + "text_format": "latex", + "bbox": [ + 532, + 578, + 890, + 597 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In Eqs. (18) and (19), the category condition $c$ is ignored for a single-category generation.", + "bbox": [ + 496, + 604, + 890, + 636 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In addition, our model can generate further higher resolution shapes by iteratively applying the second stage model trained on multiple resolutions (e.g., $32^{3} \\to 64^{3}$ and $64^{3} \\to 128^{3}$ ). We provide this higher-resolution generation in the experiments.", + "bbox": [ + 496, + 636, + 890, + 712 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 724, + 632, + 741 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we evaluate and compare the proposed method with state-of-the-art methods in 3D shape generations. Specifically, we present qualitative and quantitative comparisons of our method for single-/multi-category 3D shape generation tasks in Secs. 4.1 and 4.2, respectively. Additionally, we demonstrate the applicability of the proposed SDF-Diffusion for shape completion in Sec. 4.3. Before diving into the details, we first provide several pieces of information for experiments, such as implementation details, dataset, evaluation metrics, and comparison methods.", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "20891", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/91826733846308effc7b218dd3fa865bacb63225e09336ab73c42338d473516e.jpg", + "image_caption": [ + "Figure 3. Generated 3D shapes with a single-category generative model. Baseline methods generate point clouds with 2,048 points, and SDF-Diffusion produces 3D shapes in the form of T-SDF voxels, which can be converted to meshes directly through zero iso-surface finding algorithms." + ], + "image_footnote": [], + "bbox": [ + 102, + 90, + 442, + 251 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation details. For both generation and superresolution models, we share the same network structure regardless of single-category and multi-category generations except for the category embedding layer (i.e., the same network architecture is shared with all of our experiments). For point cloud input, we use the point cloud encoder from the convolutional occupancy network [53] as our point cloud encoder and combine the resulting features using AdaGN.", + "bbox": [ + 75, + 334, + 467, + 455 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We use the Adam optimizer [28] with $\\beta_{1} = 0.9$ and $\\beta_{2} = 0.999$ , to train all of our models. We train our method with learning rate 0.0001 with learning rate warmup at the first epoch and reduce the learning rate when the validation loss is not decreased for 5 epochs. We fix the patch size to $32^{3}$ for training the super-resolution model regardless of the target resolution. On the other hand, we sample the full resolution of the shape at once without using patches during the inference phase. Following [16], we set diffusion step $T = 1,000$ , and linear noise scheduler with $\\beta_{0} = 0.0001$ and $\\beta_{T} = 0.02$ . We reduce sampling steps to 50 using the denoising diffusion implicit model (DDIM) [65] to accelerate sampling speed. We use the exponential moving average (EMA) following [23] for the first stage model. Flip data augmentation is applied to the super-resolution model.", + "bbox": [ + 75, + 457, + 467, + 683 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Dataset. For evaluation, we use the ShapeNet dataset [3] (especially version 1), which consists of 13-category of 3D shapes in mesh representations. In comparison to prior work, our method requires sampled SDF in the training and evaluation phase. For this reason, we convert meshes in the ShapeNet dataset into voxel-shaped SDF similar to the dual octree graph networks [69]. Concretely, we normalize each of the watertight mesh so that it has zero center and unit scale with 0.1 padding. We then extract SDF voxels at multiple resolutions of 32 for low-resolution and 64 and 128 for high-resolution using Mesh2SDF [70]. While sampling watertight mesh, we manipulate the level set value, which is the parameter of Mesh2SDF, to approximately double cell size (i.e., 0.03125 for voxel resolution of 64). We then clip", + "bbox": [ + 75, + 688, + 467, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "each of the extracted SDF voxel with minimum and maximum thresholds as the same value with double voxel size, and we utilize SDF in the form of truncated signed distance fields (T-SDF) to decrease redundant information. After that, we sample 15K points from the watertight meshes at the resolution of 64, which are used as ground truth for training point cloud-based methods and evaluation purposes. Following [69], the dataset is split into the train, validation, and test datasets. We mainly measure the quality of our method with point clouds sampled from a voxel resolution of 64 in the validation dataset like previous methods.", + "bbox": [ + 496, + 90, + 890, + 257 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation metrics. Following the previous methods [77, 87], we use three metrics (MMD, COV, and 1-NNA [37]) based on both the Chamfer Distance (CD) and the Earth Mover's Distance (EMD) as the main evaluation metrics. MMD, COV, and 1-NNA analyze both quality and variety by quantifying the distributional similarity between the produced forms and the validation set. A detailed explanation of the evaluation method is in the supplementary material.", + "bbox": [ + 496, + 260, + 890, + 381 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparison methods. To evaluate the generative ability of our model, we compare it with various methods, such as DDM-based techniques: point voxel diffusion (PVD) [87] and diffusion point cloud (DPM) [41], as well as flow-based technique, PointFlow [77]. As most of the previous methods have been trained using the ShapeNet dataset preprocessed by PointFlow, which only provides point clouds and not SDF, we re-implemented these methods to compare with our approach. It should be noted that since our dataset and PointFlow's are based on the different versions of ShapeNet, and different pre-processing methods, the results may slightly differ from those of the original papers.", + "bbox": [ + 496, + 385, + 890, + 566 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Single-Category Generation", + "text_level": 1, + "bbox": [ + 500, + 575, + 751, + 590 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Following previous works [41, 77, 87], we evaluate metrics for 3 models trained with each category (airplane, car, and chair) separately. To ensure a fair comparison with point clouds-based baseline methods that used 2,048 points to compute metrics, we sampled the same number of points from meshes reconstructed by our method.", + "bbox": [ + 496, + 598, + 890, + 688 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We show the quantitative comparisons in Table 1. Our method, SDF-Diffusion demonstrated competitive performance in all categories and outperformed other baselines, especially in the 1-NNA (EMD) metric, which is the most important metric designed to overcome the limitations of MMD and COV [77]. In addition, EMD is a more distinctive metric [42] because CD tends to fail to compare point clouds with uneven density, and uniform point cloud density is important to represent 3D shapes well. Since SDF-Diffusion reconstructs continuous meshes first and then samples point clouds from the meshes, the point clouds can be evenly arranged, unlike other methods that generate point clouds directly.", + "bbox": [ + 496, + 689, + 890, + 883 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Figure 3 shows the qualitative comparisons with the", + "bbox": [ + 517, + 885, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "20892", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/39d247d21995bb2c9b726e004359648ce44a7e0c2bb2ecd276a09bf23a14fa41.jpg", + "image_caption": [ + "Figure 4. Generated samples by SDF-Diffusion on 13-category classes of the ShapeNet dataset." + ], + "image_footnote": [], + "bbox": [ + 86, + 89, + 872, + 191 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/8d8e26a56f347f12aa512f49c4aa445008fd8eed8fd406f0bed7868214462695.jpg", + "table_caption": [ + "Table 1. Quantitative evaluation on the ShapeNet dataset about MMD, COV, 1-NNA about 3-category. MMD, 1-NNA scores are the lower, the better, and the higher COV, the better. MMD-CD and MMD-EMD scores are multiplied by ${10}^{3}$ and ${10}^{2}$ ." + ], + "table_footnote": [], + "table_body": "
TrainsetPointFlow [77]DPM [41]PVD [87]ours
AirplaneMMD (CD)1.512.432.242.462.37
COV (CD)56.9350.5050.0045.3050.25
1-NNA (CD)45.9272.2867.4562.6256.56
MMD (EMD)2.331.671.641.551.49
COV (EMD)57.4352.9752.2353.9655.20
1-NNA (EMD)47.4062.5063.3752.7248.14
CarMMD (CD)2.442.612.572.482.48
COV (CD)54.0741.9244.1944.3347.26
1-NNA (CD)49.4774.5075.5758.4858.28
MMD (EMD)1.281.391.391.301.28
COV (EMD)52.3441.9241.9248.3352.47
1-NNA (EMD)50.5371.9071.9051.1353.20
ChairMMD (CD)8.058.277.657.878.00
COV (CD)54.9546.5347.8648.8949.78
1-NNA (CD)52.8870.8366.4055.6153.69
MMD (EMD)3.574.214.083.563.61
COV (EMD)53.4749.6341.6550.3749.31
1-NNA (EMD)48.7474.7476.6653.0351.77
", + "bbox": [ + 78, + 294, + 468, + 503 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "baseline methods. SDF-Diffusion generates plausible 3D shapes like the other approaches; especially, we can directly produce continuous 3D meshes.", + "bbox": [ + 75, + 513, + 468, + 559 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Multi-Category Generation", + "text_level": 1, + "bbox": [ + 76, + 573, + 326, + 589 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In addition to single-category, our SDF-Diffusion is seamlessly extended to multi-category generation using category information. We train and compare our SDF-Diffusion on the 13 categories of the ShapeNet dataset: airplane, bench, cabinet, car, chair, display, lamp, loudspeaker, rifle, sofa, table, telephone, and vessel, by conditioning on the category information $c$ . As shown in Fig. 4, SDF-Diffusion generates multicategory detailed 3D shapes with high-quality and diversity. Furthermore, we can perform the second stage (i.e., super-resolution) multiple times to generate much higher-resolution samples. Figure 5 illustrates the 3D shapes generated using multiple super-resolution stages, allowing us to achieve $128^{3}$ resolution SDF voxels.", + "bbox": [ + 75, + 597, + 468, + 808 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To assess the generation quality of multi-category generation, we compare our model with PVD, which is a diffusion-based state-of-the-art 3D shape generation method. However, PVD and other baselines are designed for only single-category generation. So, we compare ours with the modified version of PVD (PVD* in short) that can", + "bbox": [ + 75, + 810, + 470, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/a1357917a71b370bc6cec239702caf2921abf5f3e7f00b37e769ad82d00951bf.jpg", + "table_caption": [ + "Table 2. Quantitative evaluation on the ShapeNet dataset through 1-NNA about CD and EMD with 13-category. PVD* denotes the modified version of PVD for multi-category." + ], + "table_footnote": [], + "table_body": "
Category1-NNA (CD)1-NNA (EMD)
PVD*ourstrainsetPVD*ourstrainset
Airplane67.2070.7945.9257.9258.0447.40
Bench62.4360.2253.3159.6757.4654.14
Cabinet62.1062.7447.1368.1563.0650.96
Car64.5566.2949.4757.8955.8150.53
Chair61.8963.2352.8859.4059.3348.74
Display61.4744.5051.8358.2653.2152.29
Lamp58.8758.0149.1361.0456.2851.95
Loudspeaker59.3257.1448.1457.4554.7652.17
Rifle61.3960.5450.0058.4453.5949.79
Sofa58.0452.8451.5854.5750.6347.32
Table62.4155.7649.7161.8256.3551.00
Telephone60.0057.1448.5755.7154.7650.95
Vessel59.5959.8451.5558.2954.1550.78
Average61.4859.1649.9459.1255.9650.62
", + "bbox": [ + 501, + 281, + 888, + 489 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "receive a category condition with MLPs with Embedding layers similar to ours but without AdaGN to preserve the timestep embedding method of the original PVD. Quantitative results are shown in Table 2. The results of PVD* and SDF-Diffusion are trained equally for 1,000 epochs for only multi-category case. SDF-Diffusion shows better results in most categories about 1-NNA metric, especially outperforming EMD-based metrics. Additional qualitative comparisons on the mesh domain will be discussed in the supplementary material.", + "bbox": [ + 496, + 500, + 890, + 652 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Application: Shape Completion", + "text_level": 1, + "bbox": [ + 498, + 664, + 779, + 681 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We show the applicability of our SDF-Diffusion on another task: 3D shape completion with voxel condition. Without modification of network architecture, we show that our method can be applied to 3D shape completion. Specifically, the second stage of our method takes a voxel-shaped condition by concatenating the conditional input (i.e., low-resolution SDF generated by the first stage) with noisy data to denoise. In other words, let the SDF voxel be a single-channel, then we can consider the second stage of our model takes two-channel input and returns a single-channel output. Therefore, using the same network architecture, we can seamlessly train a shape completion model by giving a partial SDF voxel instead of a low-resolution condition.", + "bbox": [ + 496, + 688, + 890, + 883 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For partial 3D shapes, we perform a 3D shape comple", + "bbox": [ + 517, + 885, + 890, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "20893", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5c7e6ea64402cf503e4f0ffbed5cc305f2ead9b5a5f65e2f3f26fcb62d14806c.jpg", + "image_caption": [ + "Figure 5. Visualization of generated 3D shapes at different resolutions. The first stage model generates coarse shapes in the resolution of $32^{3}$ . By performing super-resolution using our second stage model multiple times, we can obtain improved shape detail of 3D shapes with the voxel resolutions of $64^{3}$ and $128^{3}$ ." + ], + "image_footnote": [], + "bbox": [ + 84, + 87, + 460, + 292 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "tion based on SDF-Diffision, as shown in Fig. 6. As you can see, we can generate various 3D shapes from given partial 3D shapes, which shows the applicability and flexibility of the proposed SDF-Diffision.", + "bbox": [ + 75, + 387, + 468, + 446 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In addition, we also demonstrate the generality of our SDF-Diffusion by using it for the task of 3D shape completion with a partially observed point cloud as a condition. To generate the partial point cloud input, we randomly sample 200 points from the preprocessed ShapeNet dataset using the same method employed in [82]. For out-of-distribution data, we acquire partial point clouds from depth images of the Redwood 3DScans dataset [9]. As the point cloud has a different format than the voxel feature generated by our SDF-Diffusion, we incorporate an additional layer to extract and voxelize the point cloud. Specifically, we employ the PointNet layer [55] from the encoder of the convolutional occupancy network [53], which transforms the point cloud feature into a voxel and gives this feature to each layer of SDF-Diffusion along with the AdaGN. The completed 3D shapes are visualized in Fig. 7. We show SDF-Diffusion can successfully apply unseen out-of-distribution data.", + "bbox": [ + 75, + 449, + 472, + 720 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 738, + 194, + 753 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we have proposed SDF-Diffusion, a novel diffusion-based SDF generation approach for 3D shapes. SDF-Diffusion composed of two-stage generates low-resolution SDF and then produces high-resolution SDF conditioned on the low-resolution one. For memory efficiency, we learn the second stage of SDF-Diffusion (i.e., super-resolution) in a patch-wise manner, which allows us to perform super-resolution several times in high-resolution. In addition, SDF-Diffusion can be seam-", + "bbox": [ + 75, + 763, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/429be4ce4096abf33a75265f0d5d8521ca7488f7563e92a559c5418ea3c7b88c.jpg", + "image_caption": [ + "Figure 6. Generated 3D shapes by 3D shape completion. SDF-Diffusion can be easily expanded to a 3D shape completion task by modifying only the input head of the network architecture." + ], + "image_footnote": [], + "bbox": [ + 506, + 87, + 887, + 329 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8292048ba36c038f2bb36b39d5d89edf89b7c4d6fdd42c111fcd8e5557cb3b2c.jpg", + "image_caption": [ + "Figure 7. Generated 3D shapes by 3D shape completion on out-of-distribution data. SDF-Diffusion shows various completion candidates from out-of-distribution partial point clouds." + ], + "image_footnote": [], + "bbox": [ + 503, + 429, + 887, + 575 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "lessly extended to multi-category 3D shape generation and 3D shape completion. Experiments demonstrate that the proposed method can generate high-quality 3D shapes in the SDF domain with superior generative power.", + "bbox": [ + 498, + 647, + 890, + 709 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments. This work was supported by Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) (No. 2022-0-00612, Geometric and Physical Commonsense Reasoning based Behavior Intelligence for Embodied AI, No.2022-0-00907, Development of AI Bots Collaboration Platform and Self-organizing AI and No.2020-0-01336, Artificial Intelligence Graduate School Program (UNIST)) and Artificial intelligence industrial convergence cluster development project funded by the Ministry of Science and ICT (MSIT, Korea) & Gwangju Metropolitan City.", + "bbox": [ + 496, + 719, + 892, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "20894", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Panos Achlioptas, Olga Diamanti, Ioannis Mitliagkas, and Leonidas Guibas. 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In CVPR, 2021. 1, 3, 6, 7" + ], + "bbox": [ + 78, + 90, + 467, + 871 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "20897", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Diffusion-Based Signed Distance Fields for 3D Shape Generation/959cbb8a-2f33-407b-925b-14af99929d47_model.json b/2023/Diffusion-Based Signed Distance Fields for 3D Shape Generation/959cbb8a-2f33-407b-925b-14af99929d47_model.json new file mode 100644 index 0000000000000000000000000000000000000000..ce772e58d333406e4d4ee8e1e495069dedc2761f --- /dev/null +++ b/2023/Diffusion-Based Signed Distance Fields for 3D Shape Generation/959cbb8a-2f33-407b-925b-14af99929d47_model.json @@ -0,0 +1,3060 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.159, + 0.131, + 0.812, + 0.152 + ], + "angle": 0, + "content": "Diffusion-Based Signed Distance Fields for 3D Shape Generation" + }, + { + "type": "text", + "bbox": [ + 0.269, + 0.181, + 0.707, + 0.216 + ], + "angle": 0, + "content": "Jaehyeok Shim, Changwoo Kang and Kyungdon Joo* Artificial Intelligence Graduate School, UNIST" + }, + { + "type": "text", + "bbox": [ + 0.296, + 0.219, + 0.674, + 0.234 + ], + "angle": 0, + "content": "{jh.shim,kangchangwoo,kyungdon}@unist.ac.kr" + }, + { + "type": "text", + "bbox": [ + 0.296, + 0.238, + 0.67, + 0.251 + ], + "angle": 0, + "content": "https://kitsunetic.github.io/sdf-diffusion" + }, + { + "type": "image", + "bbox": [ + 0.164, + 0.258, + 0.482, + 0.47 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.205, + 0.472, + 0.462, + 0.482 + ], + "angle": 0, + "content": "Noise LR HR" + }, + { + "type": "image", + "bbox": [ + 0.487, + 0.258, + 0.8, + 0.47 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.516, + 0.472, + 0.768, + 0.482 + ], + "angle": 0, + "content": "Noise LR HR" + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.49, + 0.893, + 0.545 + ], + "angle": 0, + "content": "Figure 1. Visualization of 3D shape generation for various categories using SDF-Diffusion. SDF-diffusion gradually removes the Gaussian noise and generates high-resolution 3D shapes in the form of an SDF voxel by a two-stage framework. Unlike previous methods, which use point clouds, we can generate 3D meshes without concern of complex post-processing. For visualization purposes, we show less-noise data instead of the initial Gaussian noise." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.559, + 0.314, + 0.573 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.59, + 0.471, + 0.862 + ], + "angle": 0, + "content": "We propose a 3D shape generation framework (SDF-Diffusion in short) that uses denoising diffusion models with continuous 3D representation via signed distance fields (SDF). Unlike most existing methods that depend on discontinuous forms, such as point clouds, SDF-Diffusion generates high-resolution 3D shapes while alleviating memory issues by separating the generative process into two-stage: generation and super-resolution. In the first stage, a diffusion-based generative model generates a low-resolution SDF of 3D shapes. Using the estimated low-resolution SDF as a condition, the second stage diffusion model performs super-resolution to generate high-resolution SDF. Our framework can generate a high-fidelity 3D shape despite the extreme spatial complexity. On the ShapeNet dataset, our model shows competitive performance to the state-of-the-art methods and shows applicability on the shape completion task without modification." + }, + { + "type": "title", + "bbox": [ + 0.502, + 0.559, + 0.631, + 0.573 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.892, + 0.719 + ], + "angle": 0, + "content": "The need for generative modeling of 3D shapes has rapidly increased due to high demand in various fields, such as computer vision, graphics, robotics, and content generation. To synthesize a high-quality 3D shape, numerous generative approaches have been actively studied, including generative adversarial networks (GAN) [1, 7, 8, 18, 20, 40, 51, 62, 71, 85], variational auto-encoders (VAE) [13, 27, 35, 45, 67], normalizing flows [26, 30, 60, 77], auto-regressive models [19, 31, 45, 46, 76], and others [61, 74, 75, 80, 84]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Recently, denoising diffusion models (DDM) have emerged as a promising generative framework in image generation [10, 16, 22, 39, 47, 63] and speech synthesis [5, 32, 54]. DDM achieves a generative process by gradually corrupting data through a diffusion process and denoising through a learned neural network. This network can generate new realistic data by repeating the denoising process from the given pure noise. Based on the success of DDM-based generative models in various domains, several attempts are being made to apply them to the task of 3D shape generation [41, 83, 87]. They have applied DDM to generate new point cloud and have outperformed previous methods." + }, + { + "type": "page_footnote", + "bbox": [ + 0.102, + 0.888, + 0.229, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20887" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.317 + ], + "angle": 0, + "content": "However, even though DDM-based 3D generative models have demonstrated their impressive performance, they still have limitations to being adopted for real-world problems. Most previous DDM-based 3D generative models use point clouds to represent 3D shapes, which limits their ability to express continuous surfaces of 3D shapes, unlike mesh representation commonly used in real-world applications. To resolve this issue, intricate post-processing [2, 24, 25, 52] is required to reconstruct continuous meshes from point clouds. They require various parameter tuning or additional information (e.g., surface normal at each point [52]), and a densely sampled point cloud is required to reconstruct high-quality mesh. However, existing DDM-based methods for 3D shape generation are based on sparse point clouds." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.319, + 0.473, + 0.501 + ], + "angle": 0, + "content": "In this work, we introduce a new DDM-based generation framework that generates high-quality 3D shapes through signed distance fields (SDF) (see Fig. 1). We can view SDF as a function that takes an arbitrary location as input and returns a signed distance value from the input location to the nearest surface of the mesh, and the sign of the value means whether inside or outside of the shape. We sample SDF values uniformly from a 3D shape to form a voxel-shaped SDF. This form has several advantages over point clouds. It can directly reconstruct mesh through the marching cube algorithm [38] and can utilize convolutional neural network (CNN) because of its dense and fixed structure." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.501, + 0.473, + 0.775 + ], + "angle": 0, + "content": "Based on this voxel-shaped SDF representation, we propose a novel DDM-based generative model in two-stage (see Fig. 2). In the first stage, a diffusion-based SDF generation produces low-resolution SDF for coarse 3D shapes. In the second stage, we propose a diffusion-based SDF superresolution, given the low-resolution SDF of the first stage as a condition. In particular, since the increasing resolution of the voxel comes as a significant burden in terms of computational resources (i.e., due to the curse of the dimension), we approach this problem by super-resolution in patch-based learning. Under this scheme, we can iteratively perform the second stage multiple times with the same structure and generate further higher resolution of SDF, which is a more detailed 3D shape. With various experiments, we achieve state-of-the-art in single-/multi-category 3D shape generative quality, and our method can be directly converted into 3D meshes, unlike other point cloud-based methods that require intricate post-processing." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.775, + 0.399, + 0.79 + ], + "angle": 0, + "content": "In summary, our contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.796, + 0.47, + 0.842 + ], + "angle": 0, + "content": "- We propose a novel DDM-based generation method that utilizes a voxel-shaped SDF representation to generate high-quality and continuous 3D shapes." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.856, + 0.473, + 0.901 + ], + "angle": 0, + "content": "- We represent a memory-efficient two-stage framework composed of low-resolution SDF generation and SDF super-resolution conditioned on the low-resolution SDF." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.796, + 0.473, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "In particular, we can iteratively perform super-resolution to generate higher-resolution SDF." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.133, + 0.894, + 0.179 + ], + "angle": 0, + "content": "- SDF-diffusion can be seamlessly extended into multi-category 3D shape generation and completion, which shows the flexibility of the proposed method." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.192, + 0.642, + 0.208 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.218, + 0.892, + 0.308 + ], + "angle": 0, + "content": "3D Shape representation. Numerous in-depth studies have been conducted on the representation of 3D shape [8, 43, 44, 48-50, 64, 73, 78, 79, 81]. We can categorize them into two groups: explicit representations, such as voxels [14, 15, 71], point clouds [1, 55, 56], and implicit functions, such as signed distance fields (SDF) [50, 64]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.308, + 0.892, + 0.459 + ], + "angle": 0, + "content": "Voxels are widely adapted in various neural networks due to their intuitive structure and synergy with 3D CNN [14, 15, 71, 73]. However, it may cause a memory problem according to the increase in resolution. Point clouds, which are compact and readily available, are dominant representations with their well-suitability to learn contextual information in neural networks [1, 55, 56, 79, 81]. However, it requires post-processing to convert the synthesized point clouds into meshes for real-world applications [8, 38, 43, 44, 48-50, 78]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.459, + 0.892, + 0.596 + ], + "angle": 0, + "content": "Implicit functions view the 3D shape as a set of levels for a continuous function, which makes it possible to express a continuous surface [8,44,48-50,64,78]. As a result, despite their slow interference as they require numerous network operations, these methods are growing in popularity. In particular, SDF encoded with distance to the nearest surface has some advantages to express sharper reconstructions [50, 64]. Thus, we exploit SDF voxel representation to obtain sharper meshes without unnecessary procedures." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.892, + 0.704 + ], + "angle": 0, + "content": "3D shape generation. To generate 3D geometry, a variety of frameworks are applied [1, 7, 8, 13, 19, 20, 26, 27, 30, 31, 34, 46, 51, 60, 62, 67, 85]. With such a perspective, several frameworks are applied to model the distribution representing a 3D shape, such as GAN-based models [33], auto-regressive models [66], flow-based models [77], and implicit functions [43, 50]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.892, + 0.901 + ], + "angle": 0, + "content": "For GAN-based 3D generative method, SDF-StyleGAN [86] extends StyleGAN2 [23] for 3D shape generation by proposing global and local discriminator that enables GAN discriminator on SDF. Generative methods, such as AutoSDF [45], and ShapeFormer [76], propose to utilize a voxel form of implicit representation (e.g., SDF and occupancy) for mesh generation through a two-stage. A two-stage generative strategy reduces required computational resources by compressing data into a tractable form (e.g., latent feature) rather than directly dealing with an original data structure to make a generative model concentrate semantically compressed representation and save computational resources. Motivated by VQ-GAN [12]," + }, + { + "type": "footer", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "20888" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.289 + ], + "angle": 0, + "content": "AutoSDF and ShapeFormer apply two-stage generative method and show impressive performance on conditional 3D shape generation. They utilize an auto-encoder to convert voxel into compressed latent space and generate a new shape using the autoregressive model on the latent space. However, they miss fully utilizing the advantage of the two-stage generative method because they use a regression-based auto-encoder unlike VQ-GAN, which uses GAN and perceptual loss [21]. Unlike the 2D image generation, there are insufficient research works in perceptually plausible auto-encoding methods about 3D shapes, especially voxel structures; it has difficulties in applying a two-stage strategy to 3D shape generation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.291, + 0.473, + 0.487 + ], + "angle": 0, + "content": "On the other hand, recent research works propose a new two-stage generative method [17, 42, 59]. They use a super-resolution model to up-sample low-resolution data, and the generation model learns low-resolution data distribution. Instead of training an auto-encoder, these methods utilize naturally constructed low-resolution forms. Inspired by this, our method exploits a two-stage framework using voxel-shaped SDF. Instead of learning the auto-encoder, we propose a method of generating a coarse 3D shape that is naturally compressed form in the representation of a low-resolution voxel. We then generate high-quality 3D shapes by refining the details of the coarse shape by upsampling the low-resolution voxel." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.494, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Diffusion-Based 3D shape generation. With the success of DDM-based generative models in image generation [10, 16, 47], diffusion-based 3D shape generations have advanced significantly. In particular, diffusion probabilistic models (DPM) [41] suggest a DDM-based approach with an auto-encoder architecture built on PointNet [55], which compresses point clouds into a latent vector and then generates new shape latent using normalizing flows [6, 11]. Point voxel diffusion (PVD) [87] applies DDM directly on the point clouds by adopting a point voxel CNN-based network architecture [36], which utilizes both the 3D CNN and PointNet. In addition, point diffusion-refinement (PDR) [42] proposes a two-stage generative framework for conditional point cloud generation task. It generates sparse point clouds by PointNet-based DDM in the first stage and up-samples the sparse point clouds to denser ones in a learning-based manner. Motivated by latent diffusion models (LDM) [58], latent point diffusion models (LION) [83] propose a two-stage approach with compressed latent point clouds through VAE [29]. LION converts result point clouds into mesh by shapes as points (SAP) [52]. Despite their great performance, it still requires a pre-trained SAP model or fine-tuning stage. In other words, the usability of the above point clouds-based approaches is limited to be adopted in real-world applications. To address this issue, we propose a diffusion-based generative model upon voxel-shaped SDF representation," + }, + { + "type": "image", + "bbox": [ + 0.511, + 0.09, + 0.882, + 0.292 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.295, + 0.895, + 0.394 + ], + "angle": 0, + "content": "Figure 2. Overview of SDF-Diffusion. The proposed method consists of two stages. In the first stage, we take as input voxel-shaped noise \\(\\mathbf{x}_T^{\\mathrm{LR}} = \\epsilon^{\\mathrm{LR}}\\) and generate low-resolution SDF voxel \\(\\mathbf{x}_0^{\\mathrm{LR}}\\) of new coarse 3D shape through DDM. In the second stage, conditioned on \\(\\mathbf{x}_0^{\\mathrm{LR}}\\), we perform super-resolution through another DDM, which generates high-resolution SDF voxel \\(\\mathbf{x}_0^{\\mathrm{HR}}\\) with fine and detailed 3D shape." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.404, + 0.892, + 0.436 + ], + "angle": 0, + "content": "which can directly reconstruct 3D mesh using zero isosurface finding methods [38]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.449, + 0.637, + 0.466 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.475, + 0.892, + 0.732 + ], + "angle": 0, + "content": "We propose a generative method for high-resolution 3D shapes in the form of SDF voxels based on the denoising diffusion models [16, 63] (SDF-Diffusion in short). To generate high-resolution samples efficiently, the proposed method involves two stages: diffusion-based SDF generation and diffusion-based patch-wise SDF super-resolution (see Fig. 2 for the overview). In the first stage, the diffusion-based SDF generation model generates a low-resolution coarse 3D shape. Given this low-resolution sample, the diffusion-based SDF super-resolution model progressively produces high-resolution samples in the second stage. In other words, we can consider the first stage as a pure diffusion-based generative model, and the second stage as a conditional diffusion-based super-resolution model. It is worth noting that, ideally, the second stage can be repeated multiple times with the same architecture, which enables us to generate more high-resolution 3D shapes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.732, + 0.892, + 0.839 + ], + "angle": 0, + "content": "In the following, we briefly explain the background on DDM in Sec. 3.1. Then, in Sec. 3.2, we describe our method for generating coarse 3D shapes using a diffusion-based technique. In Sec. 3.3, we explain how we generate high-resolution 3D shapes by super-resolving low-resolution correspondence. Training and inference processes for each diffusion model are listed in Algorithm 1 and Algorithm 2." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.847, + 0.871, + 0.864 + ], + "angle": 0, + "content": "3.1. Background on Denoising Diffusion Models" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "DDM is a class of generative models that generates new samples from a given data distribution by learning the in-" + }, + { + "type": "footer", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20889" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.168 + ], + "angle": 0, + "content": "verse of the noising process [16, 63]. Concretely, starting from samples from the Gaussian distribution \\(\\mathbf{x}_T\\), the denoising process gradually produces samples with less noise \\(\\mathbf{x}_{T - 1},\\mathbf{x}_{T - 2},\\ldots\\), and aims to reach final samples \\(\\mathbf{x}_0\\), which is the noise-free final output." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.171, + 0.469, + 0.231 + ], + "angle": 0, + "content": "Forward process. The forward process (or diffusion process) gradually adds the Gaussian noise to the clean data, which is the approximate joint posterior \\( q(\\mathbf{x}_{1:T}|\\mathbf{x}_0) \\). This diffusion process is represented as a Markov chain:" + }, + { + "type": "equation", + "bbox": [ + 0.156, + 0.234, + 0.47, + 0.275 + ], + "angle": 0, + "content": "\\[\nq \\left(\\mathbf {x} _ {0: T}\\right) = q \\left(\\mathbf {x} _ {0}\\right) \\prod_ {t = 1} ^ {T} q \\left(\\mathbf {x} _ {t} \\mid \\mathbf {x} _ {t - 1}\\right), \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.135, + 0.279, + 0.469, + 0.297 + ], + "angle": 0, + "content": "\\[\nq \\left(\\mathbf {x} _ {t} \\mid \\mathbf {x} _ {t - 1}\\right) = \\mathcal {N} \\left(\\mathbf {x} _ {t}; \\sqrt {1 - \\beta_ {t}} \\mathbf {x} _ {t - 1}, \\beta_ {t} \\mathbf {I}\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.307, + 0.442, + 0.321 + ], + "angle": 0, + "content": "where \\(\\beta_{t}\\) denotes the noise scheduling hyperparameter." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.321, + 0.469, + 0.352 + ], + "angle": 0, + "content": "According to [16], the forward process admits sampling \\(\\mathbf{x}_t\\) at an arbitrary time step \\(t\\) by a closed form:" + }, + { + "type": "equation", + "bbox": [ + 0.143, + 0.362, + 0.469, + 0.38 + ], + "angle": 0, + "content": "\\[\nq \\left(\\mathbf {x} _ {t} \\mid \\mathbf {x} _ {0}\\right) = \\mathcal {N} \\left(\\mathbf {x} _ {t}; \\sqrt {\\bar {\\alpha} _ {t}} \\mathbf {x} _ {0}, (1 - \\bar {\\alpha} _ {t}) \\mathbf {I}\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.389, + 0.469, + 0.419 + ], + "angle": 0, + "content": "where \\(\\alpha_{t} = 1 - \\beta_{t}\\) and \\(\\bar{\\alpha}_{t} = \\Pi_{s=1}^{t} \\alpha_{s}\\). Thus, \\(\\mathbf{x}_{t}\\) can be directly sampled by:" + }, + { + "type": "equation", + "bbox": [ + 0.143, + 0.429, + 0.469, + 0.447 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} _ {t} = \\sqrt {\\bar {\\alpha} _ {t}} \\mathbf {x} _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon , \\epsilon \\sim \\mathcal {N} (\\mathbf {0}, \\mathbf {I}). \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.457, + 0.469, + 0.53 + ], + "angle": 0, + "content": "Reverse process. The reverse process (or generative process) aims to generate samples by gradually inverting infinitesimal noise, which is the joint distribution \\( p_{\\theta}(\\mathbf{x}_{0:T}) \\). This reverse process is defined as a Markov chain with the learned Gaussian transitions:" + }, + { + "type": "equation", + "bbox": [ + 0.16, + 0.533, + 0.469, + 0.573 + ], + "angle": 0, + "content": "\\[\np _ {\\theta} \\left(\\mathbf {x} _ {0: T}\\right) = p \\left(\\mathbf {x} _ {T}\\right) \\prod_ {t = 1} ^ {T} p _ {\\theta} \\left(\\mathbf {x} _ {t - 1} \\mid \\mathbf {x} _ {t}\\right), \\tag {5}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.138, + 0.576, + 0.469, + 0.593 + ], + "angle": 0, + "content": "\\[\np _ {\\theta} \\left(\\mathbf {x} _ {t - 1} \\mid \\mathbf {x} _ {t}\\right) = \\mathcal {N} \\left(\\mathbf {x} _ {t - 1}; \\mu_ {\\theta} \\left(\\mathbf {x} _ {t}, t\\right), \\sigma_ {t} ^ {2} \\mathbf {I}\\right), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.603, + 0.469, + 0.68 + ], + "angle": 0, + "content": "where \\(p(\\mathbf{x}_T) = \\mathcal{N}(\\mathbf{x}_T;\\mathbf{0},\\mathbf{I})\\) is the standard Gaussian distribution, \\(\\mu_{\\theta}(\\mathbf{x}_t,t)\\) indicates a denoising function parameterized by \\(\\theta\\), \\(\\sigma_t^2\\) is a time-step dependant variance, and we fix \\(\\sigma_t^2 = \\frac{1 - \\bar{\\alpha}_{t - 1}}{1 - \\bar{\\alpha}_t}\\beta_t\\), following [16]. We can sample from \\(p(\\mathbf{x}_T)\\) and then draw \\(\\mathbf{x}_{t - 1}\\sim p_{\\theta}(\\mathbf{x}_{t - 1}|\\mathbf{x}_t)\\) by Eq. (6) as:" + }, + { + "type": "equation", + "bbox": [ + 0.15, + 0.686, + 0.469, + 0.703 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} _ {t - 1} = \\mu_ {\\theta} \\left(\\mathbf {x} _ {t}, t\\right) + \\sigma_ {t} \\epsilon , \\epsilon \\sim \\mathcal {N} (\\mathbf {0}, \\mathbf {I}). \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.713, + 0.456, + 0.728 + ], + "angle": 0, + "content": "By repeating this process, we can eventually generate \\(\\mathbf{x}_0\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.731, + 0.469, + 0.762 + ], + "angle": 0, + "content": "Training objective. Following [16], we can simplify \\(\\mu_{\\theta}(\\mathbf{x}_t,t)\\) .." + }, + { + "type": "equation", + "bbox": [ + 0.12, + 0.771, + 0.469, + 0.805 + ], + "angle": 0, + "content": "\\[\n\\mu_ {\\theta} \\left(\\mathbf {x} _ {t}, t\\right) = \\frac {1}{\\sqrt {\\alpha_ {t}}} \\left(\\mathbf {x} _ {t} - \\frac {\\beta_ {t}}{\\sqrt {1 - \\bar {\\alpha} _ {t}}} \\epsilon_ {\\theta} \\left(\\mathbf {x} _ {t}, t\\right)\\right), \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.814, + 0.469, + 0.875 + ], + "angle": 0, + "content": "where \\(\\epsilon_{\\theta}(\\mathbf{x}_t,t)\\) is a neural network parameterized by \\(\\theta\\) that predicts noise from noisy input \\(\\mathbf{x}_t\\). Thus, the objective function compares the difference between the predicted noise \\(\\epsilon_{\\theta}(\\mathbf{x}_t,t)\\) and the applied noise \\(\\epsilon\\) [16]:" + }, + { + "type": "equation", + "bbox": [ + 0.199, + 0.885, + 0.469, + 0.903 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\left\\| \\epsilon_ {\\theta} \\left(\\mathbf {x} _ {t}, t\\right) - \\epsilon \\right\\| _ {p} ^ {p}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.136 + ], + "angle": 0, + "content": "where \\(p\\in \\{1,2\\}\\). On the other hand, according to [16], it is possible to modify \\(\\mu_{\\theta}(\\mathbf{x}_t,t)\\) with a neural network predicting \\(\\mathbf{x}_0\\) instead of noise \\(\\epsilon\\):" + }, + { + "type": "equation", + "bbox": [ + 0.595, + 0.146, + 0.892, + 0.163 + ], + "angle": 0, + "content": "\\[\n\\mu_ {\\theta} \\left(\\mathbf {x} _ {t}, t\\right) = \\gamma_ {t} f _ {\\theta} \\left(\\mathbf {x} _ {t}, t\\right) + \\delta_ {t} \\mathbf {x} _ {t}, \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.171, + 0.892, + 0.221 + ], + "angle": 0, + "content": "where \\(\\gamma_{t} = \\frac{\\beta_{t}\\sqrt{\\bar{\\alpha}_{t - 1}}}{1 - \\bar{\\alpha}_{t}}\\) and \\(\\delta_t = \\frac{(1 - \\bar{\\alpha}_{t - 1})\\sqrt{\\alpha_t}}{1 - \\bar{\\alpha}_t}\\), and \\(f_{\\theta}(\\mathbf{x}_t,t)\\) is a neural network parameterized by \\(\\theta\\) that predicts noise-free data \\(\\mathbf{x}_0\\). In that case, the objective function becomes:" + }, + { + "type": "equation", + "bbox": [ + 0.616, + 0.231, + 0.891, + 0.249 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\left\\| f _ {\\theta} \\left(\\mathbf {x} _ {t}, t\\right) - \\mathbf {x} _ {0} \\right\\| _ {p} ^ {p}. \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.253, + 0.891, + 0.268 + ], + "angle": 0, + "content": "Thus, we use Eq. (11) as our objective function in this work." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.276, + 0.737, + 0.291 + ], + "angle": 0, + "content": "3.2. Diffusion SDF Generation" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.3, + 0.892, + 0.346 + ], + "angle": 0, + "content": "Here, we describe a diffusion-based generative model for low-resolution 3D shape represented as SDF voxel \\(\\mathbf{x}_0^{\\mathrm{LR}}\\sim q(\\mathbf{x}_0^{\\mathrm{LR}})\\) sampled from the real data distribution \\(q(\\mathbf{x}_0^{\\mathrm{LR}})\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.348, + 0.892, + 0.424 + ], + "angle": 0, + "content": "Diffusion-based SDF voxel generation. Specifically, given a clean data sample \\(\\mathbf{x}_0^{\\mathrm{LR}}\\), we corrupt \\(\\mathbf{x}_0^{\\mathrm{LR}}\\) with the same shaped voxel noise \\(\\epsilon^{\\mathrm{LR}} \\sim \\mathcal{N}(\\mathbf{0}, \\mathbf{I})\\) sampled from the standard Gaussian distribution following the forward process in Eq. (4):" + }, + { + "type": "equation", + "bbox": [ + 0.528, + 0.431, + 0.891, + 0.45 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} _ {t} ^ {\\mathrm {L R}} = \\sqrt {\\bar {\\alpha} _ {t}} \\mathbf {x} _ {0} ^ {\\mathrm {L R}} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon^ {\\mathrm {L R}}, \\epsilon^ {\\mathrm {L R}} \\sim \\mathcal {N} (\\mathbf {0}, \\mathbf {I}). \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.457, + 0.891, + 0.489 + ], + "angle": 0, + "content": "Then, a network \\( f_{\\theta}^{\\mathrm{LR}} \\) is trained to predict noise-free data with MSE objective function like Eq. (11):" + }, + { + "type": "equation", + "bbox": [ + 0.587, + 0.495, + 0.891, + 0.514 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} ^ {\\mathrm {L R}} = \\left\\| f _ {\\theta} ^ {\\mathrm {L R}} \\left(\\mathbf {x} _ {t} ^ {\\mathrm {L R}}, t, c\\right) - \\mathbf {x} _ {0} ^ {\\mathrm {L R}} \\right\\| _ {2} ^ {2}, \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.522, + 0.771, + 0.537 + ], + "angle": 0, + "content": "where \\(c\\) is a category label of given data." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.538, + 0.892, + 0.583 + ], + "angle": 0, + "content": "During inference, a new SDF voxel is generated by progressively predicting lesser noisy samples \\(\\mathbf{x}_{t - 1}^{\\mathrm{LR}}\\) with the trained neural network \\(f_{\\theta}^{\\mathrm{LR}}\\) as \\(t = T,\\dots ,1\\) .." + }, + { + "type": "equation", + "bbox": [ + 0.561, + 0.59, + 0.891, + 0.609 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} _ {t - 1} ^ {\\mathrm {L R}} = \\gamma_ {t} f _ {\\theta} ^ {\\mathrm {L R}} \\left(\\mathbf {x} _ {t} ^ {\\mathrm {L R}}, t, c\\right) + \\delta_ {t} \\mathbf {x} _ {t} ^ {\\mathrm {L R}} + \\sigma_ {t} \\epsilon^ {\\mathrm {L R}}. \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.617, + 0.891, + 0.647 + ], + "angle": 0, + "content": "In Eq. (13) and Eq. (14), the category condition \\( c \\) is used only for multi-category generations." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.651, + 0.892, + 0.846 + ], + "angle": 0, + "content": "Network architecture. Our model is built upon a U-shaped network in SR3 [59], which is a DDM-based superresolution method designed for 2D image domain. Thus, we modify and improve this structure for 3D domain. We convert 2D-based U-shaped network of SR3 into 3D-based model by replacing 2D-based convolutional layers with 3D ones. The network has three layers, and each layer is composed of several layers of residual blocks and self-attention [68] and the Swish activation function [57]. The voxel feature resolution is halved for each layer (e.g., \\(32 \\rightarrow 16 \\rightarrow 8\\)), and the channel is doubled (e.g., \\(64 \\rightarrow 128 \\rightarrow 256\\)). A more detailed design of the network architecture is in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.847, + 0.891, + 0.875 + ], + "angle": 0, + "content": "The timestep \\(t\\) and category condition \\(c\\) are embedded into a vector \\(\\mathbf{z}\\) through MLPs following [4,59]:" + }, + { + "type": "equation", + "bbox": [ + 0.521, + 0.882, + 0.891, + 0.898 + ], + "angle": 0, + "content": "\\[\n\\mathbf {z} = \\operatorname {M L P} \\left(\\operatorname {P o s E n c} \\left(\\sqrt {\\bar {\\alpha} _ {t}}\\right)\\right) + \\operatorname {M L P} (\\text {E m b e d d i n g} (c)), \\tag {15}\n\\]" + }, + { + "type": "footer", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20890" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.081, + 0.092, + 0.227, + 0.106 + ], + "angle": 0, + "content": "Algorithm 1 Training" + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.111, + 0.309, + 0.123 + ], + "angle": 0, + "content": "Stage 1: Diffusion SDF Generation" + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.125, + 0.131, + 0.135 + ], + "angle": 0, + "content": "repeat" + }, + { + "type": "equation", + "bbox": [ + 0.114, + 0.135, + 0.469, + 0.148 + ], + "angle": 0, + "content": "\\[\n\\left(\\mathbf {x} _ {0} ^ {\\mathrm {L R}}, c\\right) \\sim q \\left(\\mathbf {x} _ {0} ^ {\\mathrm {L R}}, c\\right) \\quad \\triangleright \\text {S a m p l e L R v o x e l a n d c a t e g o r y l a b e l}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.114, + 0.148, + 0.228, + 0.159 + ], + "angle": 0, + "content": "\\[\nt \\sim \\mathcal {U} (\\{1, \\dots T ^ {\\mathrm {L R}} \\})\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.114, + 0.159, + 0.197, + 0.17 + ], + "angle": 0, + "content": "\\[\n\\epsilon^ {\\mathrm {L R}} \\sim \\mathcal {N} (\\mathbf {0}, \\mathbf {I})\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.114, + 0.17, + 0.469, + 0.182 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} _ {t} ^ {\\mathrm {L R}} = \\sqrt {\\bar {\\alpha} _ {t}} \\mathbf {x} _ {0} ^ {\\mathrm {L R}} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon^ {\\mathrm {L R}} \\quad \\triangleright \\text {N o i s y v o x e l a t t i m e s t e p} t\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.114, + 0.182, + 0.305, + 0.196 + ], + "angle": 0, + "content": "\\[\n\\theta^ {t} \\leftarrow \\eta \\nabla_ {\\theta} \\| f _ {\\theta} ^ {\\mathrm {L R}} (\\mathbf {x} _ {t} ^ {\\mathrm {L R}}, t, c) - \\mathbf {x} _ {0} ^ {\\mathrm {L R}} \\| _ {2} ^ {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.196, + 0.214, + 0.209 + ], + "angle": 0, + "content": "until \\(f_{\\theta}^{\\mathrm{LR}}\\) is converged" + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.213, + 0.43, + 0.225 + ], + "angle": 0, + "content": "Stage 2: Patch-Based Diffusion SDF Super-Resolution" + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.226, + 0.13, + 0.236 + ], + "angle": 0, + "content": "repeat" + }, + { + "type": "equation", + "bbox": [ + 0.114, + 0.236, + 0.469, + 0.259 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\left(\\hat {\\mathbf {x}} _ {0} ^ {\\mathrm {H R}}, c\\right) \\sim q \\left(\\hat {\\mathbf {x}} _ {0} ^ {\\mathrm {H R}}, c\\right) \\triangleright \\text {S a m p l e H R v o x e l p a t c h a n d c a t e g o r y l a b e l} \\\\ \\hat {\\mathbf {x}} _ {0} ^ {\\mathrm {L R}} \\sim q \\left(\\hat {\\mathbf {x}} _ {0} ^ {\\mathrm {L R}}\\right) \\quad \\triangleright \\text {S a m p l e L R c o n d i t i o n a l v o x e l p a t c h} \\end{array}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.114, + 0.26, + 0.228, + 0.272 + ], + "angle": 0, + "content": "\\[\nt \\sim \\mathcal {U} (\\{1, \\dots T ^ {\\mathrm {H R}} \\})\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.114, + 0.272, + 0.197, + 0.285 + ], + "angle": 0, + "content": "\\[\n\\hat {\\epsilon} ^ {\\mathrm {H R}} \\sim \\tilde {\\mathcal {N}} (\\mathbf {0}, \\mathbf {I})\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.114, + 0.285, + 0.469, + 0.309 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\hat {\\mathbf {x}} _ {t} ^ {\\mathrm {H R}} = \\sqrt {\\bar {\\alpha} _ {t}} \\hat {\\mathbf {x}} _ {0} ^ {\\mathrm {H R}} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon^ {\\mathrm {H R}} \\quad \\triangleright \\mathrm {H R} \\text {n o i s y v o x e l a r t i m e s t e p} t \\\\ \\theta \\leftarrow \\eta \\nabla_ {\\theta} \\| f _ {\\theta} ^ {\\mathrm {H R}} (\\hat {\\mathbf {x}} _ {t} ^ {\\mathrm {H R}}, \\hat {\\mathbf {x}} _ {0} ^ {\\mathrm {L R}}, t, c) - \\hat {\\mathbf {x}} _ {0} ^ {\\mathrm {H R}} \\| _ {1} ^ {1} \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.31, + 0.215, + 0.322 + ], + "angle": 0, + "content": "until \\(f_{\\theta}^{\\mathrm{HR}}\\) is converged" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.34, + 0.47, + 0.476 + ], + "angle": 0, + "content": "where PosEnc is the sinusoidal positional encoding used in Transformer [68] and Embedding is the embedding layer, and the second term is ignored for a single-category generation. The embedding vector \\(\\mathbf{z}\\) is inserted into every residual block using adaptive group normalization layers (AdaGN) following [10]. AdaGN is an extension of group normalization [72] through channel-wise scaling and shifting w.r.t. normalized feature maps \\(\\mathbf{h} \\in \\mathbb{R}^{k \\times h \\times w \\times d}\\), where \\(k\\) is the number of feature map channels:" + }, + { + "type": "equation", + "bbox": [ + 0.134, + 0.488, + 0.469, + 0.504 + ], + "angle": 0, + "content": "\\[\n\\operatorname {A d a G N} (\\mathbf {h}, \\mathbf {z}) = \\mathbf {z} _ {s} \\left(\\operatorname {G r o u p N o r m} (\\mathbf {h}) + \\mathbf {z} _ {t}\\right), \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.518, + 0.469, + 0.566 + ], + "angle": 0, + "content": "where \\((\\mathbf{z}_s,\\mathbf{z}_t)\\in \\mathbb{R}^{2\\times k} = \\mathrm{MLP}(\\mathbf{z})\\) is result of an MLP layer. The detailed network architecture is available in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.579, + 0.461, + 0.595 + ], + "angle": 0, + "content": "3.3. Patch-Based Diffusion SDF Super-Resolution" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.604, + 0.469, + 0.651 + ], + "angle": 0, + "content": "We aim to train a conditional diffusion-based super-resolution model that generates realistic high-resolution SDF voxel \\(\\mathbf{x}_0^{\\mathrm{HR}}\\) with low-resolution condition \\(\\mathbf{x}_0^{\\mathrm{LR}}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.655, + 0.469, + 0.866 + ], + "angle": 0, + "content": "Patch-based learning scheme. The increase in demanding memory due to the growth of spatial complexity hinders the learning of high-resolution generative models. Instead of training on the full high-resolution voxel, we train our model based on small cube-shaped patches of given input high-resolution voxel \\(\\mathbf{x}_0^{\\mathrm{HR}}\\sim q(\\mathbf{x}_0^{\\mathrm{HR}})\\) sampled from real data distribution to reduce memory consumption. We denote \\(\\hat{\\mathbf{x}}_t^{\\mathrm{HR}}\\) as a cube-shaped patch extracted from a random location of voxel \\(\\mathbf{x}_t^{\\mathrm{HR}}\\), and \\(\\hat{\\mathbf{x}}_t^{\\mathrm{LR}}\\) is a patch extracted from the corresponding location of \\(\\mathbf{x}_t^{\\mathrm{LR}}\\). In addition, \\(\\epsilon^{\\mathrm{HR}}\\) and \\(\\hat{\\epsilon}^{\\mathrm{HR}}\\) are voxel-shaped noises sampled from the standard Gaussian distribution that have the same shape with \\(\\mathbf{x}_t^{\\mathrm{HR}}\\) and \\(\\hat{\\mathbf{x}}_t^{\\mathrm{HR}}\\) respectively. Note that the patch-based operation is optional during the test phase if GPU has enough memory." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Conditional diffusion-based super-resolution. Similarly to Eq. (12), the diffusion process for SDF super-resolution" + }, + { + "type": "title", + "bbox": [ + 0.502, + 0.092, + 0.657, + 0.107 + ], + "angle": 0, + "content": "Algorithm 2 Sampling" + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.111, + 0.795, + 0.123 + ], + "angle": 0, + "content": "Stage 1: Diffusion-Based 3D Shape Generation" + }, + { + "type": "text", + "bbox": [ + 0.502, + 0.124, + 0.682, + 0.136 + ], + "angle": 0, + "content": "Input: \\(c\\): category label (integer)" + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.136, + 0.706, + 0.148 + ], + "angle": 0, + "content": "Output: \\(\\mathbf{x}_0^{\\mathrm{LR}}\\): generated coarse shape" + }, + { + "type": "equation", + "bbox": [ + 0.517, + 0.148, + 0.551, + 0.158 + ], + "angle": 0, + "content": "\\[\nt = T\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.517, + 0.159, + 0.6, + 0.171 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} _ {t} ^ {\\mathrm {L R}} \\sim \\mathcal {N} (\\mathbf {0}, \\mathbf {I})\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.517, + 0.171, + 0.598, + 0.182 + ], + "angle": 0, + "content": "\\[\n\\text {w h i l e} t \\neq 0 \\mathbf {d o}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.536, + 0.182, + 0.618, + 0.194 + ], + "angle": 0, + "content": "\\[\n\\epsilon^ {\\mathrm {L R}} \\sim \\mathcal {N} (\\mathbf {0}, \\mathbf {I})\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.536, + 0.194, + 0.765, + 0.208 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} _ {t - 1} ^ {\\mathrm {L R}} \\leftarrow \\gamma_ {t} f _ {\\theta} ^ {\\mathrm {L R}} \\left(\\mathbf {x} _ {t} ^ {\\mathrm {L R}}, t, c\\right) + \\delta_ {t} \\mathbf {x} _ {t} ^ {\\mathrm {L R}} + \\sigma_ {t} \\epsilon^ {\\mathrm {L R}}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.536, + 0.208, + 0.588, + 0.219 + ], + "angle": 0, + "content": "\\[\nt = t - 1\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.22, + 0.572, + 0.23 + ], + "angle": 0, + "content": "end while" + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.232, + 0.839, + 0.244 + ], + "angle": 0, + "content": "Stage 2: Patch-Based Diffusion SDF Super-Resolution" + }, + { + "type": "text", + "bbox": [ + 0.502, + 0.244, + 0.845, + 0.257 + ], + "angle": 0, + "content": "Input: \\(c\\): category label (integer), \\(\\mathbf{x}_0^{\\mathrm{LR}}\\): low-resolution condition" + }, + { + "type": "text", + "bbox": [ + 0.502, + 0.257, + 0.753, + 0.269 + ], + "angle": 0, + "content": "Output: \\(\\mathbf{x}_0^{\\mathrm{HR}}\\): generated high-resolution shape" + }, + { + "type": "equation", + "bbox": [ + 0.517, + 0.27, + 0.551, + 0.28 + ], + "angle": 0, + "content": "\\[\nt = T\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.281, + 0.891, + 0.293 + ], + "angle": 0, + "content": "\\(\\mathbf{x}_t^{\\mathrm{HR}} \\sim \\mathcal{N}(\\mathbf{0}, \\mathbf{I})\\) \\(>\\) Patch is optional during inference phase" + }, + { + "type": "equation", + "bbox": [ + 0.517, + 0.293, + 0.598, + 0.304 + ], + "angle": 0, + "content": "\\[\n\\text {w h i l e} t \\neq 0 \\mathbf {d o}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.536, + 0.304, + 0.619, + 0.316 + ], + "angle": 0, + "content": "\\[\n\\epsilon^ {\\mathrm {H R}} \\sim \\mathcal {N} (\\mathbf {0}, \\mathbf {I})\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.536, + 0.316, + 0.796, + 0.33 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} _ {t - 1} ^ {\\mathrm {H R}} \\leftarrow \\gamma_ {t} f _ {\\theta} ^ {\\mathrm {H R}} (\\mathbf {x} _ {t} ^ {\\mathrm {H R}}, \\mathbf {x} _ {0} ^ {\\mathrm {L R}}, t, c) + \\delta_ {t} \\mathbf {x} _ {t} ^ {\\mathrm {H R}} + \\sigma_ {t} \\epsilon^ {\\mathrm {H R}}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.536, + 0.33, + 0.59, + 0.339 + ], + "angle": 0, + "content": "\\[\nt = t - 1\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.341, + 0.572, + 0.351 + ], + "angle": 0, + "content": "end while" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.367, + 0.648, + 0.381 + ], + "angle": 0, + "content": "can be represented as:" + }, + { + "type": "equation", + "bbox": [ + 0.525, + 0.389, + 0.891, + 0.407 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {x}} _ {t} ^ {\\mathrm {H R}} = \\sqrt {\\bar {\\alpha} _ {t}} \\hat {\\mathbf {x}} _ {0} ^ {\\mathrm {H R}} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\hat {\\epsilon} ^ {\\mathrm {H R}}, \\hat {\\epsilon} ^ {\\mathrm {H R}} \\sim \\mathcal {N} (\\mathbf {0}, \\mathbf {I}). \\tag {17}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.416, + 0.892, + 0.476 + ], + "angle": 0, + "content": "In the case of the objective function, we use \\(\\mathcal{L}_1\\) for superresolution, followed by SR3 [59], where they empirically find that \\(\\mathcal{L}_1\\) loss is better for super-resolution task compared to MSE loss:" + }, + { + "type": "equation", + "bbox": [ + 0.568, + 0.484, + 0.891, + 0.502 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} ^ {\\mathrm {H R}} = \\left\\| f _ {\\theta} ^ {\\mathrm {H R}} \\left(\\hat {\\mathbf {x}} _ {t} ^ {\\mathrm {H R}}, \\hat {\\mathbf {x}} _ {0} ^ {\\mathrm {L R}}, t, c\\right) - \\hat {\\mathbf {x}} _ {0} ^ {\\mathrm {H R}} \\right\\| _ {1} ^ {1}. \\tag {18}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.511, + 0.892, + 0.573 + ], + "angle": 0, + "content": "The low-resolution condition is nearly up-sampled to be the same resolution as the high-resolution side and channelwise concatenation is applied. Sampling is done by repeating a similar process to Eq. (14):" + }, + { + "type": "equation", + "bbox": [ + 0.533, + 0.579, + 0.891, + 0.598 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} _ {t - 1} ^ {\\mathrm {H R}} = \\gamma_ {t} f _ {\\theta} ^ {\\mathrm {H R}} \\left(\\mathbf {x} _ {t} ^ {\\mathrm {H R}}, \\mathbf {x} _ {0} ^ {\\mathrm {L R}}, t, c\\right) + \\delta_ {t} \\mathbf {x} _ {t} ^ {\\mathrm {H R}} + \\sigma_ {t} \\epsilon^ {\\mathrm {H R}}, \\tag {19}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.606, + 0.891, + 0.637 + ], + "angle": 0, + "content": "In Eqs. (18) and (19), the category condition \\( c \\) is ignored for a single-category generation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.637, + 0.892, + 0.713 + ], + "angle": 0, + "content": "In addition, our model can generate further higher resolution shapes by iteratively applying the second stage model trained on multiple resolutions (e.g., \\(32^{3} \\to 64^{3}\\) and \\(64^{3} \\to 128^{3}\\)). We provide this higher-resolution generation in the experiments." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.725, + 0.633, + 0.742 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In this section, we evaluate and compare the proposed method with state-of-the-art methods in 3D shape generations. Specifically, we present qualitative and quantitative comparisons of our method for single-/multi-category 3D shape generation tasks in Secs. 4.1 and 4.2, respectively. Additionally, we demonstrate the applicability of the proposed SDF-Diffusion for shape completion in Sec. 4.3. Before diving into the details, we first provide several pieces of information for experiments, such as implementation details, dataset, evaluation metrics, and comparison methods." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "20891" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.104, + 0.091, + 0.443, + 0.252 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.254, + 0.47, + 0.325 + ], + "angle": 0, + "content": "Figure 3. Generated 3D shapes with a single-category generative model. Baseline methods generate point clouds with 2,048 points, and SDF-Diffusion produces 3D shapes in the form of T-SDF voxels, which can be converted to meshes directly through zero iso-surface finding algorithms." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.335, + 0.468, + 0.456 + ], + "angle": 0, + "content": "Implementation details. For both generation and superresolution models, we share the same network structure regardless of single-category and multi-category generations except for the category embedding layer (i.e., the same network architecture is shared with all of our experiments). For point cloud input, we use the point cloud encoder from the convolutional occupancy network [53] as our point cloud encoder and combine the resulting features using AdaGN." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.458, + 0.468, + 0.684 + ], + "angle": 0, + "content": "We use the Adam optimizer [28] with \\(\\beta_{1} = 0.9\\) and \\(\\beta_{2} = 0.999\\), to train all of our models. We train our method with learning rate 0.0001 with learning rate warmup at the first epoch and reduce the learning rate when the validation loss is not decreased for 5 epochs. We fix the patch size to \\(32^{3}\\) for training the super-resolution model regardless of the target resolution. On the other hand, we sample the full resolution of the shape at once without using patches during the inference phase. Following [16], we set diffusion step \\(T = 1,000\\), and linear noise scheduler with \\(\\beta_{0} = 0.0001\\) and \\(\\beta_{T} = 0.02\\). We reduce sampling steps to 50 using the denoising diffusion implicit model (DDIM) [65] to accelerate sampling speed. We use the exponential moving average (EMA) following [23] for the first stage model. Flip data augmentation is applied to the super-resolution model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Dataset. For evaluation, we use the ShapeNet dataset [3] (especially version 1), which consists of 13-category of 3D shapes in mesh representations. In comparison to prior work, our method requires sampled SDF in the training and evaluation phase. For this reason, we convert meshes in the ShapeNet dataset into voxel-shaped SDF similar to the dual octree graph networks [69]. Concretely, we normalize each of the watertight mesh so that it has zero center and unit scale with 0.1 padding. We then extract SDF voxels at multiple resolutions of 32 for low-resolution and 64 and 128 for high-resolution using Mesh2SDF [70]. While sampling watertight mesh, we manipulate the level set value, which is the parameter of Mesh2SDF, to approximately double cell size (i.e., 0.03125 for voxel resolution of 64). We then clip" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.258 + ], + "angle": 0, + "content": "each of the extracted SDF voxel with minimum and maximum thresholds as the same value with double voxel size, and we utilize SDF in the form of truncated signed distance fields (T-SDF) to decrease redundant information. After that, we sample 15K points from the watertight meshes at the resolution of 64, which are used as ground truth for training point cloud-based methods and evaluation purposes. Following [69], the dataset is split into the train, validation, and test datasets. We mainly measure the quality of our method with point clouds sampled from a voxel resolution of 64 in the validation dataset like previous methods." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.261, + 0.892, + 0.382 + ], + "angle": 0, + "content": "Evaluation metrics. Following the previous methods [77, 87], we use three metrics (MMD, COV, and 1-NNA [37]) based on both the Chamfer Distance (CD) and the Earth Mover's Distance (EMD) as the main evaluation metrics. MMD, COV, and 1-NNA analyze both quality and variety by quantifying the distributional similarity between the produced forms and the validation set. A detailed explanation of the evaluation method is in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.386, + 0.892, + 0.567 + ], + "angle": 0, + "content": "Comparison methods. To evaluate the generative ability of our model, we compare it with various methods, such as DDM-based techniques: point voxel diffusion (PVD) [87] and diffusion point cloud (DPM) [41], as well as flow-based technique, PointFlow [77]. As most of the previous methods have been trained using the ShapeNet dataset preprocessed by PointFlow, which only provides point clouds and not SDF, we re-implemented these methods to compare with our approach. It should be noted that since our dataset and PointFlow's are based on the different versions of ShapeNet, and different pre-processing methods, the results may slightly differ from those of the original papers." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.576, + 0.753, + 0.592 + ], + "angle": 0, + "content": "4.1. Single-Category Generation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.891, + 0.689 + ], + "angle": 0, + "content": "Following previous works [41, 77, 87], we evaluate metrics for 3 models trained with each category (airplane, car, and chair) separately. To ensure a fair comparison with point clouds-based baseline methods that used 2,048 points to compute metrics, we sampled the same number of points from meshes reconstructed by our method." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.69, + 0.892, + 0.885 + ], + "angle": 0, + "content": "We show the quantitative comparisons in Table 1. Our method, SDF-Diffusion demonstrated competitive performance in all categories and outperformed other baselines, especially in the 1-NNA (EMD) metric, which is the most important metric designed to overcome the limitations of MMD and COV [77]. In addition, EMD is a more distinctive metric [42] because CD tends to fail to compare point clouds with uneven density, and uniform point cloud density is important to represent 3D shapes well. Since SDF-Diffusion reconstructs continuous meshes first and then samples point clouds from the meshes, the point clouds can be evenly arranged, unlike other methods that generate point clouds directly." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.886, + 0.891, + 0.901 + ], + "angle": 0, + "content": "Figure 3 shows the qualitative comparisons with the" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20892" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.09, + 0.873, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.176, + 0.196, + 0.793, + 0.212 + ], + "angle": 0, + "content": "Figure 4. Generated samples by SDF-Diffusion on 13-category classes of the ShapeNet dataset." + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.228, + 0.47, + 0.284 + ], + "angle": 0, + "content": "Table 1. Quantitative evaluation on the ShapeNet dataset about MMD, COV, 1-NNA about 3-category. MMD, 1-NNA scores are the lower, the better, and the higher COV, the better. MMD-CD and MMD-EMD scores are multiplied by \\( {10}^{3} \\) and \\( {10}^{2} \\) ." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.295, + 0.469, + 0.504 + ], + "angle": 0, + "content": "
TrainsetPointFlow [77]DPM [41]PVD [87]ours
AirplaneMMD (CD)1.512.432.242.462.37
COV (CD)56.9350.5050.0045.3050.25
1-NNA (CD)45.9272.2867.4562.6256.56
MMD (EMD)2.331.671.641.551.49
COV (EMD)57.4352.9752.2353.9655.20
1-NNA (EMD)47.4062.5063.3752.7248.14
CarMMD (CD)2.442.612.572.482.48
COV (CD)54.0741.9244.1944.3347.26
1-NNA (CD)49.4774.5075.5758.4858.28
MMD (EMD)1.281.391.391.301.28
COV (EMD)52.3441.9241.9248.3352.47
1-NNA (EMD)50.5371.9071.9051.1353.20
ChairMMD (CD)8.058.277.657.878.00
COV (CD)54.9546.5347.8648.8949.78
1-NNA (CD)52.8870.8366.4055.6153.69
MMD (EMD)3.574.214.083.563.61
COV (EMD)53.4749.6341.6550.3749.31
1-NNA (EMD)48.7474.7476.6653.0351.77
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.515, + 0.47, + 0.56 + ], + "angle": 0, + "content": "baseline methods. SDF-Diffusion generates plausible 3D shapes like the other approaches; especially, we can directly produce continuous 3D meshes." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.574, + 0.327, + 0.59 + ], + "angle": 0, + "content": "4.2. Multi-Category Generation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.598, + 0.47, + 0.809 + ], + "angle": 0, + "content": "In addition to single-category, our SDF-Diffusion is seamlessly extended to multi-category generation using category information. We train and compare our SDF-Diffusion on the 13 categories of the ShapeNet dataset: airplane, bench, cabinet, car, chair, display, lamp, loudspeaker, rifle, sofa, table, telephone, and vessel, by conditioning on the category information \\( c \\). As shown in Fig. 4, SDF-Diffusion generates multicategory detailed 3D shapes with high-quality and diversity. Furthermore, we can perform the second stage (i.e., super-resolution) multiple times to generate much higher-resolution samples. Figure 5 illustrates the 3D shapes generated using multiple super-resolution stages, allowing us to achieve \\( 128^{3} \\) resolution SDF voxels." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.471, + 0.901 + ], + "angle": 0, + "content": "To assess the generation quality of multi-category generation, we compare our model with PVD, which is a diffusion-based state-of-the-art 3D shape generation method. However, PVD and other baselines are designed for only single-category generation. So, we compare ours with the modified version of PVD (PVD* in short) that can" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.228, + 0.892, + 0.271 + ], + "angle": 0, + "content": "Table 2. Quantitative evaluation on the ShapeNet dataset through 1-NNA about CD and EMD with 13-category. PVD* denotes the modified version of PVD for multi-category." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.282, + 0.89, + 0.491 + ], + "angle": 0, + "content": "
Category1-NNA (CD)1-NNA (EMD)
PVD*ourstrainsetPVD*ourstrainset
Airplane67.2070.7945.9257.9258.0447.40
Bench62.4360.2253.3159.6757.4654.14
Cabinet62.1062.7447.1368.1563.0650.96
Car64.5566.2949.4757.8955.8150.53
Chair61.8963.2352.8859.4059.3348.74
Display61.4744.5051.8358.2653.2152.29
Lamp58.8758.0149.1361.0456.2851.95
Loudspeaker59.3257.1448.1457.4554.7652.17
Rifle61.3960.5450.0058.4453.5949.79
Sofa58.0452.8451.5854.5750.6347.32
Table62.4155.7649.7161.8256.3551.00
Telephone60.0057.1448.5755.7154.7650.95
Vessel59.5959.8451.5558.2954.1550.78
Average61.4859.1649.9459.1255.9650.62
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.501, + 0.892, + 0.653 + ], + "angle": 0, + "content": "receive a category condition with MLPs with Embedding layers similar to ours but without AdaGN to preserve the timestep embedding method of the original PVD. Quantitative results are shown in Table 2. The results of PVD* and SDF-Diffusion are trained equally for 1,000 epochs for only multi-category case. SDF-Diffusion shows better results in most categories about 1-NNA metric, especially outperforming EMD-based metrics. Additional qualitative comparisons on the mesh domain will be discussed in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.665, + 0.78, + 0.682 + ], + "angle": 0, + "content": "4.3. Application: Shape Completion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.892, + 0.884 + ], + "angle": 0, + "content": "We show the applicability of our SDF-Diffusion on another task: 3D shape completion with voxel condition. Without modification of network architecture, we show that our method can be applied to 3D shape completion. Specifically, the second stage of our method takes a voxel-shaped condition by concatenating the conditional input (i.e., low-resolution SDF generated by the first stage) with noisy data to denoise. In other words, let the SDF voxel be a single-channel, then we can consider the second stage of our model takes two-channel input and returns a single-channel output. Therefore, using the same network architecture, we can seamlessly train a shape completion model by giving a partial SDF voxel instead of a low-resolution condition." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "For partial 3D shapes, we perform a 3D shape comple" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20893" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.088, + 0.462, + 0.294 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.306, + 0.47, + 0.376 + ], + "angle": 0, + "content": "Figure 5. Visualization of generated 3D shapes at different resolutions. The first stage model generates coarse shapes in the resolution of \\(32^{3}\\). By performing super-resolution using our second stage model multiple times, we can obtain improved shape detail of 3D shapes with the voxel resolutions of \\(64^{3}\\) and \\(128^{3}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.388, + 0.47, + 0.448 + ], + "angle": 0, + "content": "tion based on SDF-Diffision, as shown in Fig. 6. As you can see, we can generate various 3D shapes from given partial 3D shapes, which shows the applicability and flexibility of the proposed SDF-Diffision." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.45, + 0.473, + 0.721 + ], + "angle": 0, + "content": "In addition, we also demonstrate the generality of our SDF-Diffusion by using it for the task of 3D shape completion with a partially observed point cloud as a condition. To generate the partial point cloud input, we randomly sample 200 points from the preprocessed ShapeNet dataset using the same method employed in [82]. For out-of-distribution data, we acquire partial point clouds from depth images of the Redwood 3DScans dataset [9]. As the point cloud has a different format than the voxel feature generated by our SDF-Diffusion, we incorporate an additional layer to extract and voxelize the point cloud. Specifically, we employ the PointNet layer [55] from the encoder of the convolutional occupancy network [53], which transforms the point cloud feature into a voxel and gives this feature to each layer of SDF-Diffusion along with the AdaGN. The completed 3D shapes are visualized in Fig. 7. We show SDF-Diffusion can successfully apply unseen out-of-distribution data." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.739, + 0.196, + 0.755 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.47, + 0.901 + ], + "angle": 0, + "content": "In this work, we have proposed SDF-Diffusion, a novel diffusion-based SDF generation approach for 3D shapes. SDF-Diffusion composed of two-stage generates low-resolution SDF and then produces high-resolution SDF conditioned on the low-resolution one. For memory efficiency, we learn the second stage of SDF-Diffusion (i.e., super-resolution) in a patch-wise manner, which allows us to perform super-resolution several times in high-resolution. In addition, SDF-Diffusion can be seam-" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.088, + 0.888, + 0.33 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.344, + 0.892, + 0.399 + ], + "angle": 0, + "content": "Figure 6. Generated 3D shapes by 3D shape completion. SDF-Diffusion can be easily expanded to a 3D shape completion task by modifying only the input head of the network architecture." + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.43, + 0.888, + 0.576 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.594, + 0.892, + 0.637 + ], + "angle": 0, + "content": "Figure 7. Generated 3D shapes by 3D shape completion on out-of-distribution data. SDF-Diffusion shows various completion candidates from out-of-distribution partial point clouds." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.648, + 0.892, + 0.71 + ], + "angle": 0, + "content": "lessly extended to multi-category 3D shape generation and 3D shape completion. Experiments demonstrate that the proposed method can generate high-quality 3D shapes in the SDF domain with superior generative power." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Acknowledgments. This work was supported by Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) (No. 2022-0-00612, Geometric and Physical Commonsense Reasoning based Behavior Intelligence for Embodied AI, No.2022-0-00907, Development of AI Bots Collaboration Platform and Self-organizing AI and No.2020-0-01336, Artificial Intelligence Graduate School Program (UNIST)) and Artificial intelligence industrial convergence cluster development project funded by the Ministry of Science and ICT (MSIT, Korea) & Gwangju Metropolitan City." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20894" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.117, + 0.47, + 0.158 + ], + "angle": 0, + "content": "[1] Panos Achlioptas, Olga Diamanti, Ioannis Mitliagkas, and Leonidas Guibas. 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Visualization of 3D shape generation for various categories using SDF-Diffusion. SDF-diffusion gradually removes the Gaussian noise and generates high-resolution 3D shapes in the form of an SDF voxel by a two-stage framework. Unlike previous methods, which use point clouds, we can generate 3D meshes without concern of complex post-processing. For visualization purposes, we show less-noise data instead of the initial Gaussian noise. + +# Abstract + +We propose a 3D shape generation framework (SDF-Diffusion in short) that uses denoising diffusion models with continuous 3D representation via signed distance fields (SDF). Unlike most existing methods that depend on discontinuous forms, such as point clouds, SDF-Diffusion generates high-resolution 3D shapes while alleviating memory issues by separating the generative process into two-stage: generation and super-resolution. In the first stage, a diffusion-based generative model generates a low-resolution SDF of 3D shapes. Using the estimated low-resolution SDF as a condition, the second stage diffusion model performs super-resolution to generate high-resolution SDF. Our framework can generate a high-fidelity 3D shape despite the extreme spatial complexity. On the ShapeNet dataset, our model shows competitive performance to the state-of-the-art methods and shows applicability on the shape completion task without modification. + +# 1. Introduction + +The need for generative modeling of 3D shapes has rapidly increased due to high demand in various fields, such as computer vision, graphics, robotics, and content generation. To synthesize a high-quality 3D shape, numerous generative approaches have been actively studied, including generative adversarial networks (GAN) [1, 7, 8, 18, 20, 40, 51, 62, 71, 85], variational auto-encoders (VAE) [13, 27, 35, 45, 67], normalizing flows [26, 30, 60, 77], auto-regressive models [19, 31, 45, 46, 76], and others [61, 74, 75, 80, 84]. + +Recently, denoising diffusion models (DDM) have emerged as a promising generative framework in image generation [10, 16, 22, 39, 47, 63] and speech synthesis [5, 32, 54]. DDM achieves a generative process by gradually corrupting data through a diffusion process and denoising through a learned neural network. This network can generate new realistic data by repeating the denoising process from the given pure noise. Based on the success of DDM-based generative models in various domains, several attempts are being made to apply them to the task of 3D shape generation [41, 83, 87]. They have applied DDM to generate new point cloud and have outperformed previous methods. + +However, even though DDM-based 3D generative models have demonstrated their impressive performance, they still have limitations to being adopted for real-world problems. Most previous DDM-based 3D generative models use point clouds to represent 3D shapes, which limits their ability to express continuous surfaces of 3D shapes, unlike mesh representation commonly used in real-world applications. To resolve this issue, intricate post-processing [2, 24, 25, 52] is required to reconstruct continuous meshes from point clouds. They require various parameter tuning or additional information (e.g., surface normal at each point [52]), and a densely sampled point cloud is required to reconstruct high-quality mesh. However, existing DDM-based methods for 3D shape generation are based on sparse point clouds. + +In this work, we introduce a new DDM-based generation framework that generates high-quality 3D shapes through signed distance fields (SDF) (see Fig. 1). We can view SDF as a function that takes an arbitrary location as input and returns a signed distance value from the input location to the nearest surface of the mesh, and the sign of the value means whether inside or outside of the shape. We sample SDF values uniformly from a 3D shape to form a voxel-shaped SDF. This form has several advantages over point clouds. It can directly reconstruct mesh through the marching cube algorithm [38] and can utilize convolutional neural network (CNN) because of its dense and fixed structure. + +Based on this voxel-shaped SDF representation, we propose a novel DDM-based generative model in two-stage (see Fig. 2). In the first stage, a diffusion-based SDF generation produces low-resolution SDF for coarse 3D shapes. In the second stage, we propose a diffusion-based SDF superresolution, given the low-resolution SDF of the first stage as a condition. In particular, since the increasing resolution of the voxel comes as a significant burden in terms of computational resources (i.e., due to the curse of the dimension), we approach this problem by super-resolution in patch-based learning. Under this scheme, we can iteratively perform the second stage multiple times with the same structure and generate further higher resolution of SDF, which is a more detailed 3D shape. With various experiments, we achieve state-of-the-art in single-/multi-category 3D shape generative quality, and our method can be directly converted into 3D meshes, unlike other point cloud-based methods that require intricate post-processing. + +In summary, our contributions are as follows: + +- We propose a novel DDM-based generation method that utilizes a voxel-shaped SDF representation to generate high-quality and continuous 3D shapes. +- We represent a memory-efficient two-stage framework composed of low-resolution SDF generation and SDF super-resolution conditioned on the low-resolution SDF. + +In particular, we can iteratively perform super-resolution to generate higher-resolution SDF. + +- SDF-diffusion can be seamlessly extended into multi-category 3D shape generation and completion, which shows the flexibility of the proposed method. + +# 2. Related Work + +3D Shape representation. Numerous in-depth studies have been conducted on the representation of 3D shape [8, 43, 44, 48-50, 64, 73, 78, 79, 81]. We can categorize them into two groups: explicit representations, such as voxels [14, 15, 71], point clouds [1, 55, 56], and implicit functions, such as signed distance fields (SDF) [50, 64]. + +Voxels are widely adapted in various neural networks due to their intuitive structure and synergy with 3D CNN [14, 15, 71, 73]. However, it may cause a memory problem according to the increase in resolution. Point clouds, which are compact and readily available, are dominant representations with their well-suitability to learn contextual information in neural networks [1, 55, 56, 79, 81]. However, it requires post-processing to convert the synthesized point clouds into meshes for real-world applications [8, 38, 43, 44, 48-50, 78]. + +Implicit functions view the 3D shape as a set of levels for a continuous function, which makes it possible to express a continuous surface [8,44,48-50,64,78]. As a result, despite their slow interference as they require numerous network operations, these methods are growing in popularity. In particular, SDF encoded with distance to the nearest surface has some advantages to express sharper reconstructions [50, 64]. Thus, we exploit SDF voxel representation to obtain sharper meshes without unnecessary procedures. + +3D shape generation. To generate 3D geometry, a variety of frameworks are applied [1, 7, 8, 13, 19, 20, 26, 27, 30, 31, 34, 46, 51, 60, 62, 67, 85]. With such a perspective, several frameworks are applied to model the distribution representing a 3D shape, such as GAN-based models [33], auto-regressive models [66], flow-based models [77], and implicit functions [43, 50]. + +For GAN-based 3D generative method, SDF-StyleGAN [86] extends StyleGAN2 [23] for 3D shape generation by proposing global and local discriminator that enables GAN discriminator on SDF. Generative methods, such as AutoSDF [45], and ShapeFormer [76], propose to utilize a voxel form of implicit representation (e.g., SDF and occupancy) for mesh generation through a two-stage. A two-stage generative strategy reduces required computational resources by compressing data into a tractable form (e.g., latent feature) rather than directly dealing with an original data structure to make a generative model concentrate semantically compressed representation and save computational resources. Motivated by VQ-GAN [12], + +AutoSDF and ShapeFormer apply two-stage generative method and show impressive performance on conditional 3D shape generation. They utilize an auto-encoder to convert voxel into compressed latent space and generate a new shape using the autoregressive model on the latent space. However, they miss fully utilizing the advantage of the two-stage generative method because they use a regression-based auto-encoder unlike VQ-GAN, which uses GAN and perceptual loss [21]. Unlike the 2D image generation, there are insufficient research works in perceptually plausible auto-encoding methods about 3D shapes, especially voxel structures; it has difficulties in applying a two-stage strategy to 3D shape generation. + +On the other hand, recent research works propose a new two-stage generative method [17, 42, 59]. They use a super-resolution model to up-sample low-resolution data, and the generation model learns low-resolution data distribution. Instead of training an auto-encoder, these methods utilize naturally constructed low-resolution forms. Inspired by this, our method exploits a two-stage framework using voxel-shaped SDF. Instead of learning the auto-encoder, we propose a method of generating a coarse 3D shape that is naturally compressed form in the representation of a low-resolution voxel. We then generate high-quality 3D shapes by refining the details of the coarse shape by upsampling the low-resolution voxel. + +Diffusion-Based 3D shape generation. With the success of DDM-based generative models in image generation [10, 16, 47], diffusion-based 3D shape generations have advanced significantly. In particular, diffusion probabilistic models (DPM) [41] suggest a DDM-based approach with an auto-encoder architecture built on PointNet [55], which compresses point clouds into a latent vector and then generates new shape latent using normalizing flows [6, 11]. Point voxel diffusion (PVD) [87] applies DDM directly on the point clouds by adopting a point voxel CNN-based network architecture [36], which utilizes both the 3D CNN and PointNet. In addition, point diffusion-refinement (PDR) [42] proposes a two-stage generative framework for conditional point cloud generation task. It generates sparse point clouds by PointNet-based DDM in the first stage and up-samples the sparse point clouds to denser ones in a learning-based manner. Motivated by latent diffusion models (LDM) [58], latent point diffusion models (LION) [83] propose a two-stage approach with compressed latent point clouds through VAE [29]. LION converts result point clouds into mesh by shapes as points (SAP) [52]. Despite their great performance, it still requires a pre-trained SAP model or fine-tuning stage. In other words, the usability of the above point clouds-based approaches is limited to be adopted in real-world applications. To address this issue, we propose a diffusion-based generative model upon voxel-shaped SDF representation, + +![](images/c36185db371aa6497a3108a6fc6be8621f74180fc8d56a683fed62636eed9a9a.jpg) +Figure 2. Overview of SDF-Diffusion. The proposed method consists of two stages. In the first stage, we take as input voxel-shaped noise $\mathbf{x}_T^{\mathrm{LR}} = \epsilon^{\mathrm{LR}}$ and generate low-resolution SDF voxel $\mathbf{x}_0^{\mathrm{LR}}$ of new coarse 3D shape through DDM. In the second stage, conditioned on $\mathbf{x}_0^{\mathrm{LR}}$ , we perform super-resolution through another DDM, which generates high-resolution SDF voxel $\mathbf{x}_0^{\mathrm{HR}}$ with fine and detailed 3D shape. + +which can directly reconstruct 3D mesh using zero isosurface finding methods [38]. + +# 3. Methodology + +We propose a generative method for high-resolution 3D shapes in the form of SDF voxels based on the denoising diffusion models [16, 63] (SDF-Diffusion in short). To generate high-resolution samples efficiently, the proposed method involves two stages: diffusion-based SDF generation and diffusion-based patch-wise SDF super-resolution (see Fig. 2 for the overview). In the first stage, the diffusion-based SDF generation model generates a low-resolution coarse 3D shape. Given this low-resolution sample, the diffusion-based SDF super-resolution model progressively produces high-resolution samples in the second stage. In other words, we can consider the first stage as a pure diffusion-based generative model, and the second stage as a conditional diffusion-based super-resolution model. It is worth noting that, ideally, the second stage can be repeated multiple times with the same architecture, which enables us to generate more high-resolution 3D shapes. + +In the following, we briefly explain the background on DDM in Sec. 3.1. Then, in Sec. 3.2, we describe our method for generating coarse 3D shapes using a diffusion-based technique. In Sec. 3.3, we explain how we generate high-resolution 3D shapes by super-resolving low-resolution correspondence. Training and inference processes for each diffusion model are listed in Algorithm 1 and Algorithm 2. + +# 3.1. Background on Denoising Diffusion Models + +DDM is a class of generative models that generates new samples from a given data distribution by learning the in- + +verse of the noising process [16, 63]. Concretely, starting from samples from the Gaussian distribution $\mathbf{x}_T$ , the denoising process gradually produces samples with less noise $\mathbf{x}_{T - 1},\mathbf{x}_{T - 2},\ldots$ , and aims to reach final samples $\mathbf{x}_0$ , which is the noise-free final output. + +Forward process. The forward process (or diffusion process) gradually adds the Gaussian noise to the clean data, which is the approximate joint posterior $q(\mathbf{x}_{1:T}|\mathbf{x}_0)$ . This diffusion process is represented as a Markov chain: + +$$ +q \left(\mathbf {x} _ {0: T}\right) = q \left(\mathbf {x} _ {0}\right) \prod_ {t = 1} ^ {T} q \left(\mathbf {x} _ {t} \mid \mathbf {x} _ {t - 1}\right), \tag {1} +$$ + +$$ +q \left(\mathbf {x} _ {t} \mid \mathbf {x} _ {t - 1}\right) = \mathcal {N} \left(\mathbf {x} _ {t}; \sqrt {1 - \beta_ {t}} \mathbf {x} _ {t - 1}, \beta_ {t} \mathbf {I}\right), \tag {2} +$$ + +where $\beta_{t}$ denotes the noise scheduling hyperparameter. + +According to [16], the forward process admits sampling $\mathbf{x}_t$ at an arbitrary time step $t$ by a closed form: + +$$ +q \left(\mathbf {x} _ {t} \mid \mathbf {x} _ {0}\right) = \mathcal {N} \left(\mathbf {x} _ {t}; \sqrt {\bar {\alpha} _ {t}} \mathbf {x} _ {0}, (1 - \bar {\alpha} _ {t}) \mathbf {I}\right), \tag {3} +$$ + +where $\alpha_{t} = 1 - \beta_{t}$ and $\bar{\alpha}_{t} = \Pi_{s=1}^{t} \alpha_{s}$ . Thus, $\mathbf{x}_{t}$ can be directly sampled by: + +$$ +\mathbf {x} _ {t} = \sqrt {\bar {\alpha} _ {t}} \mathbf {x} _ {0} + \sqrt {1 - \bar {\alpha} _ {t}} \epsilon , \epsilon \sim \mathcal {N} (\mathbf {0}, \mathbf {I}). \tag {4} +$$ + +Reverse process. The reverse process (or generative process) aims to generate samples by gradually inverting infinitesimal noise, which is the joint distribution $p_{\theta}(\mathbf{x}_{0:T})$ . This reverse process is defined as a Markov chain with the learned Gaussian transitions: + +$$ +p _ {\theta} \left(\mathbf {x} _ {0: T}\right) = p \left(\mathbf {x} _ {T}\right) \prod_ {t = 1} ^ {T} p _ {\theta} \left(\mathbf {x} _ {t - 1} \mid \mathbf {x} _ {t}\right), \tag {5} +$$ + +$$ +p _ {\theta} \left(\mathbf {x} _ {t - 1} \mid \mathbf {x} _ {t}\right) = \mathcal {N} \left(\mathbf {x} _ {t - 1}; \mu_ {\theta} \left(\mathbf {x} _ {t}, t\right), \sigma_ {t} ^ {2} \mathbf {I}\right), \tag {6} +$$ + +where $p(\mathbf{x}_T) = \mathcal{N}(\mathbf{x}_T;\mathbf{0},\mathbf{I})$ is the standard Gaussian distribution, $\mu_{\theta}(\mathbf{x}_t,t)$ indicates a denoising function parameterized by $\theta$ , $\sigma_t^2$ is a time-step dependant variance, and we fix $\sigma_t^2 = \frac{1 - \bar{\alpha}_{t - 1}}{1 - \bar{\alpha}_t}\beta_t$ , following [16]. We can sample from $p(\mathbf{x}_T)$ and then draw $\mathbf{x}_{t - 1}\sim p_{\theta}(\mathbf{x}_{t - 1}|\mathbf{x}_t)$ by Eq. (6) as: + +$$ +\mathbf {x} _ {t - 1} = \mu_ {\theta} \left(\mathbf {x} _ {t}, t\right) + \sigma_ {t} \epsilon , \epsilon \sim \mathcal {N} (\mathbf {0}, \mathbf {I}). \tag {7} +$$ + +By repeating this process, we can eventually generate $\mathbf{x}_0$ . + +Training objective. Following [16], we can simplify $\mu_{\theta}(\mathbf{x}_t,t)$ .. + +$$ +\mu_ {\theta} \left(\mathbf {x} _ {t}, t\right) = \frac {1}{\sqrt {\alpha_ {t}}} \left(\mathbf {x} _ {t} - \frac {\beta_ {t}}{\sqrt {1 - \bar {\alpha} _ {t}}} \epsilon_ {\theta} \left(\mathbf {x} _ {t}, t\right)\right), \tag {8} +$$ + +where $\epsilon_{\theta}(\mathbf{x}_t,t)$ is a neural network parameterized by $\theta$ that predicts noise from noisy input $\mathbf{x}_t$ . Thus, the objective function compares the difference between the predicted noise $\epsilon_{\theta}(\mathbf{x}_t,t)$ and the applied noise $\epsilon$ [16]: + +$$ +\mathcal {L} = \left\| \epsilon_ {\theta} \left(\mathbf {x} _ {t}, t\right) - \epsilon \right\| _ {p} ^ {p}, \tag {9} +$$ + +where $p\in \{1,2\}$ . On the other hand, according to [16], it is possible to modify $\mu_{\theta}(\mathbf{x}_t,t)$ with a neural network predicting $\mathbf{x}_0$ instead of noise $\epsilon$ : + +$$ +\mu_ {\theta} \left(\mathbf {x} _ {t}, t\right) = \gamma_ {t} f _ {\theta} \left(\mathbf {x} _ {t}, t\right) + \delta_ {t} \mathbf {x} _ {t}, \tag {10} +$$ + +where $\gamma_{t} = \frac{\beta_{t}\sqrt{\bar{\alpha}_{t - 1}}}{1 - \bar{\alpha}_{t}}$ and $\delta_t = \frac{(1 - \bar{\alpha}_{t - 1})\sqrt{\alpha_t}}{1 - \bar{\alpha}_t}$ , and $f_{\theta}(\mathbf{x}_t,t)$ is a neural network parameterized by $\theta$ that predicts noise-free data $\mathbf{x}_0$ . In that case, the objective function becomes: + +$$ +\mathcal {L} = \left\| f _ {\theta} \left(\mathbf {x} _ {t}, t\right) - \mathbf {x} _ {0} \right\| _ {p} ^ {p}. \tag {11} +$$ + +Thus, we use Eq. (11) as our objective function in this work. + +# 3.2. Diffusion SDF Generation + +Here, we describe a diffusion-based generative model for low-resolution 3D shape represented as SDF voxel $\mathbf{x}_0^{\mathrm{LR}}\sim q(\mathbf{x}_0^{\mathrm{LR}})$ sampled from the real data distribution $q(\mathbf{x}_0^{\mathrm{LR}})$ . + +Diffusion-based SDF voxel generation. Specifically, given a clean data sample $\mathbf{x}_0^{\mathrm{LR}}$ , we corrupt $\mathbf{x}_0^{\mathrm{LR}}$ with the same shaped voxel noise $\epsilon^{\mathrm{LR}} \sim \mathcal{N}(\mathbf{0}, \mathbf{I})$ sampled from the standard Gaussian distribution following the forward process in Eq. (4): + +$$ +\mathbf {x} _ {t} ^ {\mathrm {L R}} = \sqrt {\bar {\alpha} _ {t}} \mathbf {x} _ {0} ^ {\mathrm {L R}} + \sqrt {1 - \bar {\alpha} _ {t}} \epsilon^ {\mathrm {L R}}, \epsilon^ {\mathrm {L R}} \sim \mathcal {N} (\mathbf {0}, \mathbf {I}). \tag {12} +$$ + +Then, a network $f_{\theta}^{\mathrm{LR}}$ is trained to predict noise-free data with MSE objective function like Eq. (11): + +$$ +\mathcal {L} ^ {\mathrm {L R}} = \left\| f _ {\theta} ^ {\mathrm {L R}} \left(\mathbf {x} _ {t} ^ {\mathrm {L R}}, t, c\right) - \mathbf {x} _ {0} ^ {\mathrm {L R}} \right\| _ {2} ^ {2}, \tag {13} +$$ + +where $c$ is a category label of given data. + +During inference, a new SDF voxel is generated by progressively predicting lesser noisy samples $\mathbf{x}_{t - 1}^{\mathrm{LR}}$ with the trained neural network $f_{\theta}^{\mathrm{LR}}$ as $t = T,\dots ,1$ .. + +$$ +\mathbf {x} _ {t - 1} ^ {\mathrm {L R}} = \gamma_ {t} f _ {\theta} ^ {\mathrm {L R}} \left(\mathbf {x} _ {t} ^ {\mathrm {L R}}, t, c\right) + \delta_ {t} \mathbf {x} _ {t} ^ {\mathrm {L R}} + \sigma_ {t} \epsilon^ {\mathrm {L R}}. \tag {14} +$$ + +In Eq. (13) and Eq. (14), the category condition $c$ is used only for multi-category generations. + +Network architecture. Our model is built upon a U-shaped network in SR3 [59], which is a DDM-based superresolution method designed for 2D image domain. Thus, we modify and improve this structure for 3D domain. We convert 2D-based U-shaped network of SR3 into 3D-based model by replacing 2D-based convolutional layers with 3D ones. The network has three layers, and each layer is composed of several layers of residual blocks and self-attention [68] and the Swish activation function [57]. The voxel feature resolution is halved for each layer (e.g., $32 \rightarrow 16 \rightarrow 8$ ), and the channel is doubled (e.g., $64 \rightarrow 128 \rightarrow 256$ ). A more detailed design of the network architecture is in the supplementary material. + +The timestep $t$ and category condition $c$ are embedded into a vector $\mathbf{z}$ through MLPs following [4,59]: + +$$ +\mathbf {z} = \operatorname {M L P} \left(\operatorname {P o s E n c} \left(\sqrt {\bar {\alpha} _ {t}}\right)\right) + \operatorname {M L P} (\text {E m b e d d i n g} (c)), \tag {15} +$$ + +# Algorithm 1 Training + +# Stage 1: Diffusion SDF Generation + +repeat + +$$ +\left(\mathbf {x} _ {0} ^ {\mathrm {L R}}, c\right) \sim q \left(\mathbf {x} _ {0} ^ {\mathrm {L R}}, c\right) \quad \triangleright \text {S a m p l e L R v o x e l a n d c a t e g o r y l a b e l} +$$ + +$$ +t \sim \mathcal {U} (\{1, \dots T ^ {\mathrm {L R}} \}) +$$ + +$$ +\epsilon^ {\mathrm {L R}} \sim \mathcal {N} (\mathbf {0}, \mathbf {I}) +$$ + +$$ +\mathbf {x} _ {t} ^ {\mathrm {L R}} = \sqrt {\bar {\alpha} _ {t}} \mathbf {x} _ {0} ^ {\mathrm {L R}} + \sqrt {1 - \bar {\alpha} _ {t}} \epsilon^ {\mathrm {L R}} \quad \triangleright \text {N o i s y v o x e l a t t i m e s t e p} t +$$ + +$$ +\theta^ {t} \leftarrow \eta \nabla_ {\theta} \| f _ {\theta} ^ {\mathrm {L R}} (\mathbf {x} _ {t} ^ {\mathrm {L R}}, t, c) - \mathbf {x} _ {0} ^ {\mathrm {L R}} \| _ {2} ^ {2} +$$ + +until $f_{\theta}^{\mathrm{LR}}$ is converged + +# Stage 2: Patch-Based Diffusion SDF Super-Resolution + +repeat + +$$ +\begin{array}{l} \left(\hat {\mathbf {x}} _ {0} ^ {\mathrm {H R}}, c\right) \sim q \left(\hat {\mathbf {x}} _ {0} ^ {\mathrm {H R}}, c\right) \triangleright \text {S a m p l e H R v o x e l p a t c h a n d c a t e g o r y l a b e l} \\ \hat {\mathbf {x}} _ {0} ^ {\mathrm {L R}} \sim q \left(\hat {\mathbf {x}} _ {0} ^ {\mathrm {L R}}\right) \quad \triangleright \text {S a m p l e L R c o n d i t i o n a l v o x e l p a t c h} \end{array} +$$ + +$$ +t \sim \mathcal {U} (\{1, \dots T ^ {\mathrm {H R}} \}) +$$ + +$$ +\hat {\epsilon} ^ {\mathrm {H R}} \sim \tilde {\mathcal {N}} (\mathbf {0}, \mathbf {I}) +$$ + +$$ +\begin{array}{l} \hat {\mathbf {x}} _ {t} ^ {\mathrm {H R}} = \sqrt {\bar {\alpha} _ {t}} \hat {\mathbf {x}} _ {0} ^ {\mathrm {H R}} + \sqrt {1 - \bar {\alpha} _ {t}} \epsilon^ {\mathrm {H R}} \quad \triangleright \mathrm {H R} \text {n o i s y v o x e l a r t i m e s t e p} t \\ \theta \leftarrow \eta \nabla_ {\theta} \| f _ {\theta} ^ {\mathrm {H R}} (\hat {\mathbf {x}} _ {t} ^ {\mathrm {H R}}, \hat {\mathbf {x}} _ {0} ^ {\mathrm {L R}}, t, c) - \hat {\mathbf {x}} _ {0} ^ {\mathrm {H R}} \| _ {1} ^ {1} \end{array} +$$ + +until $f_{\theta}^{\mathrm{HR}}$ is converged + +where PosEnc is the sinusoidal positional encoding used in Transformer [68] and Embedding is the embedding layer, and the second term is ignored for a single-category generation. The embedding vector $\mathbf{z}$ is inserted into every residual block using adaptive group normalization layers (AdaGN) following [10]. AdaGN is an extension of group normalization [72] through channel-wise scaling and shifting w.r.t. normalized feature maps $\mathbf{h} \in \mathbb{R}^{k \times h \times w \times d}$ , where $k$ is the number of feature map channels: + +$$ +\operatorname {A d a G N} (\mathbf {h}, \mathbf {z}) = \mathbf {z} _ {s} \left(\operatorname {G r o u p N o r m} (\mathbf {h}) + \mathbf {z} _ {t}\right), \tag {16} +$$ + +where $(\mathbf{z}_s,\mathbf{z}_t)\in \mathbb{R}^{2\times k} = \mathrm{MLP}(\mathbf{z})$ is result of an MLP layer. The detailed network architecture is available in the supplementary material. + +# 3.3. Patch-Based Diffusion SDF Super-Resolution + +We aim to train a conditional diffusion-based super-resolution model that generates realistic high-resolution SDF voxel $\mathbf{x}_0^{\mathrm{HR}}$ with low-resolution condition $\mathbf{x}_0^{\mathrm{LR}}$ . + +Patch-based learning scheme. The increase in demanding memory due to the growth of spatial complexity hinders the learning of high-resolution generative models. Instead of training on the full high-resolution voxel, we train our model based on small cube-shaped patches of given input high-resolution voxel $\mathbf{x}_0^{\mathrm{HR}}\sim q(\mathbf{x}_0^{\mathrm{HR}})$ sampled from real data distribution to reduce memory consumption. We denote $\hat{\mathbf{x}}_t^{\mathrm{HR}}$ as a cube-shaped patch extracted from a random location of voxel $\mathbf{x}_t^{\mathrm{HR}}$ , and $\hat{\mathbf{x}}_t^{\mathrm{LR}}$ is a patch extracted from the corresponding location of $\mathbf{x}_t^{\mathrm{LR}}$ . In addition, $\epsilon^{\mathrm{HR}}$ and $\hat{\epsilon}^{\mathrm{HR}}$ are voxel-shaped noises sampled from the standard Gaussian distribution that have the same shape with $\mathbf{x}_t^{\mathrm{HR}}$ and $\hat{\mathbf{x}}_t^{\mathrm{HR}}$ respectively. Note that the patch-based operation is optional during the test phase if GPU has enough memory. + +Conditional diffusion-based super-resolution. Similarly to Eq. (12), the diffusion process for SDF super-resolution + +# Algorithm 2 Sampling + +# Stage 1: Diffusion-Based 3D Shape Generation + +Input: $c$ : category label (integer) + +Output: $\mathbf{x}_0^{\mathrm{LR}}$ : generated coarse shape + +$$ +t = T +$$ + +$$ +\mathbf {x} _ {t} ^ {\mathrm {L R}} \sim \mathcal {N} (\mathbf {0}, \mathbf {I}) +$$ + +$$ +\text {w h i l e} t \neq 0 \mathbf {d o} +$$ + +$$ +\epsilon^ {\mathrm {L R}} \sim \mathcal {N} (\mathbf {0}, \mathbf {I}) +$$ + +$$ +\mathbf {x} _ {t - 1} ^ {\mathrm {L R}} \leftarrow \gamma_ {t} f _ {\theta} ^ {\mathrm {L R}} \left(\mathbf {x} _ {t} ^ {\mathrm {L R}}, t, c\right) + \delta_ {t} \mathbf {x} _ {t} ^ {\mathrm {L R}} + \sigma_ {t} \epsilon^ {\mathrm {L R}} +$$ + +$$ +t = t - 1 +$$ + +end while + +# Stage 2: Patch-Based Diffusion SDF Super-Resolution + +Input: $c$ : category label (integer), $\mathbf{x}_0^{\mathrm{LR}}$ : low-resolution condition + +Output: $\mathbf{x}_0^{\mathrm{HR}}$ : generated high-resolution shape + +$$ +t = T +$$ + +$\mathbf{x}_t^{\mathrm{HR}} \sim \mathcal{N}(\mathbf{0}, \mathbf{I})$ $>$ Patch is optional during inference phase + +$$ +\text {w h i l e} t \neq 0 \mathbf {d o} +$$ + +$$ +\epsilon^ {\mathrm {H R}} \sim \mathcal {N} (\mathbf {0}, \mathbf {I}) +$$ + +$$ +\mathbf {x} _ {t - 1} ^ {\mathrm {H R}} \leftarrow \gamma_ {t} f _ {\theta} ^ {\mathrm {H R}} (\mathbf {x} _ {t} ^ {\mathrm {H R}}, \mathbf {x} _ {0} ^ {\mathrm {L R}}, t, c) + \delta_ {t} \mathbf {x} _ {t} ^ {\mathrm {H R}} + \sigma_ {t} \epsilon^ {\mathrm {H R}} +$$ + +$$ +t = t - 1 +$$ + +end while + +can be represented as: + +$$ +\hat {\mathbf {x}} _ {t} ^ {\mathrm {H R}} = \sqrt {\bar {\alpha} _ {t}} \hat {\mathbf {x}} _ {0} ^ {\mathrm {H R}} + \sqrt {1 - \bar {\alpha} _ {t}} \hat {\epsilon} ^ {\mathrm {H R}}, \hat {\epsilon} ^ {\mathrm {H R}} \sim \mathcal {N} (\mathbf {0}, \mathbf {I}). \tag {17} +$$ + +In the case of the objective function, we use $\mathcal{L}_1$ for superresolution, followed by SR3 [59], where they empirically find that $\mathcal{L}_1$ loss is better for super-resolution task compared to MSE loss: + +$$ +\mathcal {L} ^ {\mathrm {H R}} = \left\| f _ {\theta} ^ {\mathrm {H R}} \left(\hat {\mathbf {x}} _ {t} ^ {\mathrm {H R}}, \hat {\mathbf {x}} _ {0} ^ {\mathrm {L R}}, t, c\right) - \hat {\mathbf {x}} _ {0} ^ {\mathrm {H R}} \right\| _ {1} ^ {1}. \tag {18} +$$ + +The low-resolution condition is nearly up-sampled to be the same resolution as the high-resolution side and channelwise concatenation is applied. Sampling is done by repeating a similar process to Eq. (14): + +$$ +\mathbf {x} _ {t - 1} ^ {\mathrm {H R}} = \gamma_ {t} f _ {\theta} ^ {\mathrm {H R}} \left(\mathbf {x} _ {t} ^ {\mathrm {H R}}, \mathbf {x} _ {0} ^ {\mathrm {L R}}, t, c\right) + \delta_ {t} \mathbf {x} _ {t} ^ {\mathrm {H R}} + \sigma_ {t} \epsilon^ {\mathrm {H R}}, \tag {19} +$$ + +In Eqs. (18) and (19), the category condition $c$ is ignored for a single-category generation. + +In addition, our model can generate further higher resolution shapes by iteratively applying the second stage model trained on multiple resolutions (e.g., $32^{3} \to 64^{3}$ and $64^{3} \to 128^{3}$ ). We provide this higher-resolution generation in the experiments. + +# 4. Experiments + +In this section, we evaluate and compare the proposed method with state-of-the-art methods in 3D shape generations. Specifically, we present qualitative and quantitative comparisons of our method for single-/multi-category 3D shape generation tasks in Secs. 4.1 and 4.2, respectively. Additionally, we demonstrate the applicability of the proposed SDF-Diffusion for shape completion in Sec. 4.3. Before diving into the details, we first provide several pieces of information for experiments, such as implementation details, dataset, evaluation metrics, and comparison methods. + +![](images/91826733846308effc7b218dd3fa865bacb63225e09336ab73c42338d473516e.jpg) +Figure 3. Generated 3D shapes with a single-category generative model. Baseline methods generate point clouds with 2,048 points, and SDF-Diffusion produces 3D shapes in the form of T-SDF voxels, which can be converted to meshes directly through zero iso-surface finding algorithms. + +Implementation details. For both generation and superresolution models, we share the same network structure regardless of single-category and multi-category generations except for the category embedding layer (i.e., the same network architecture is shared with all of our experiments). For point cloud input, we use the point cloud encoder from the convolutional occupancy network [53] as our point cloud encoder and combine the resulting features using AdaGN. + +We use the Adam optimizer [28] with $\beta_{1} = 0.9$ and $\beta_{2} = 0.999$ , to train all of our models. We train our method with learning rate 0.0001 with learning rate warmup at the first epoch and reduce the learning rate when the validation loss is not decreased for 5 epochs. We fix the patch size to $32^{3}$ for training the super-resolution model regardless of the target resolution. On the other hand, we sample the full resolution of the shape at once without using patches during the inference phase. Following [16], we set diffusion step $T = 1,000$ , and linear noise scheduler with $\beta_{0} = 0.0001$ and $\beta_{T} = 0.02$ . We reduce sampling steps to 50 using the denoising diffusion implicit model (DDIM) [65] to accelerate sampling speed. We use the exponential moving average (EMA) following [23] for the first stage model. Flip data augmentation is applied to the super-resolution model. + +Dataset. For evaluation, we use the ShapeNet dataset [3] (especially version 1), which consists of 13-category of 3D shapes in mesh representations. In comparison to prior work, our method requires sampled SDF in the training and evaluation phase. For this reason, we convert meshes in the ShapeNet dataset into voxel-shaped SDF similar to the dual octree graph networks [69]. Concretely, we normalize each of the watertight mesh so that it has zero center and unit scale with 0.1 padding. We then extract SDF voxels at multiple resolutions of 32 for low-resolution and 64 and 128 for high-resolution using Mesh2SDF [70]. While sampling watertight mesh, we manipulate the level set value, which is the parameter of Mesh2SDF, to approximately double cell size (i.e., 0.03125 for voxel resolution of 64). We then clip + +each of the extracted SDF voxel with minimum and maximum thresholds as the same value with double voxel size, and we utilize SDF in the form of truncated signed distance fields (T-SDF) to decrease redundant information. After that, we sample 15K points from the watertight meshes at the resolution of 64, which are used as ground truth for training point cloud-based methods and evaluation purposes. Following [69], the dataset is split into the train, validation, and test datasets. We mainly measure the quality of our method with point clouds sampled from a voxel resolution of 64 in the validation dataset like previous methods. + +Evaluation metrics. Following the previous methods [77, 87], we use three metrics (MMD, COV, and 1-NNA [37]) based on both the Chamfer Distance (CD) and the Earth Mover's Distance (EMD) as the main evaluation metrics. MMD, COV, and 1-NNA analyze both quality and variety by quantifying the distributional similarity between the produced forms and the validation set. A detailed explanation of the evaluation method is in the supplementary material. + +Comparison methods. To evaluate the generative ability of our model, we compare it with various methods, such as DDM-based techniques: point voxel diffusion (PVD) [87] and diffusion point cloud (DPM) [41], as well as flow-based technique, PointFlow [77]. As most of the previous methods have been trained using the ShapeNet dataset preprocessed by PointFlow, which only provides point clouds and not SDF, we re-implemented these methods to compare with our approach. It should be noted that since our dataset and PointFlow's are based on the different versions of ShapeNet, and different pre-processing methods, the results may slightly differ from those of the original papers. + +# 4.1. Single-Category Generation + +Following previous works [41, 77, 87], we evaluate metrics for 3 models trained with each category (airplane, car, and chair) separately. To ensure a fair comparison with point clouds-based baseline methods that used 2,048 points to compute metrics, we sampled the same number of points from meshes reconstructed by our method. + +We show the quantitative comparisons in Table 1. Our method, SDF-Diffusion demonstrated competitive performance in all categories and outperformed other baselines, especially in the 1-NNA (EMD) metric, which is the most important metric designed to overcome the limitations of MMD and COV [77]. In addition, EMD is a more distinctive metric [42] because CD tends to fail to compare point clouds with uneven density, and uniform point cloud density is important to represent 3D shapes well. Since SDF-Diffusion reconstructs continuous meshes first and then samples point clouds from the meshes, the point clouds can be evenly arranged, unlike other methods that generate point clouds directly. + +Figure 3 shows the qualitative comparisons with the + +![](images/39d247d21995bb2c9b726e004359648ce44a7e0c2bb2ecd276a09bf23a14fa41.jpg) +Figure 4. Generated samples by SDF-Diffusion on 13-category classes of the ShapeNet dataset. + +Table 1. Quantitative evaluation on the ShapeNet dataset about MMD, COV, 1-NNA about 3-category. MMD, 1-NNA scores are the lower, the better, and the higher COV, the better. MMD-CD and MMD-EMD scores are multiplied by ${10}^{3}$ and ${10}^{2}$ . + +
TrainsetPointFlow [77]DPM [41]PVD [87]ours
AirplaneMMD (CD)1.512.432.242.462.37
COV (CD)56.9350.5050.0045.3050.25
1-NNA (CD)45.9272.2867.4562.6256.56
MMD (EMD)2.331.671.641.551.49
COV (EMD)57.4352.9752.2353.9655.20
1-NNA (EMD)47.4062.5063.3752.7248.14
CarMMD (CD)2.442.612.572.482.48
COV (CD)54.0741.9244.1944.3347.26
1-NNA (CD)49.4774.5075.5758.4858.28
MMD (EMD)1.281.391.391.301.28
COV (EMD)52.3441.9241.9248.3352.47
1-NNA (EMD)50.5371.9071.9051.1353.20
ChairMMD (CD)8.058.277.657.878.00
COV (CD)54.9546.5347.8648.8949.78
1-NNA (CD)52.8870.8366.4055.6153.69
MMD (EMD)3.574.214.083.563.61
COV (EMD)53.4749.6341.6550.3749.31
1-NNA (EMD)48.7474.7476.6653.0351.77
+ +baseline methods. SDF-Diffusion generates plausible 3D shapes like the other approaches; especially, we can directly produce continuous 3D meshes. + +# 4.2. Multi-Category Generation + +In addition to single-category, our SDF-Diffusion is seamlessly extended to multi-category generation using category information. We train and compare our SDF-Diffusion on the 13 categories of the ShapeNet dataset: airplane, bench, cabinet, car, chair, display, lamp, loudspeaker, rifle, sofa, table, telephone, and vessel, by conditioning on the category information $c$ . As shown in Fig. 4, SDF-Diffusion generates multicategory detailed 3D shapes with high-quality and diversity. Furthermore, we can perform the second stage (i.e., super-resolution) multiple times to generate much higher-resolution samples. Figure 5 illustrates the 3D shapes generated using multiple super-resolution stages, allowing us to achieve $128^{3}$ resolution SDF voxels. + +To assess the generation quality of multi-category generation, we compare our model with PVD, which is a diffusion-based state-of-the-art 3D shape generation method. However, PVD and other baselines are designed for only single-category generation. So, we compare ours with the modified version of PVD (PVD* in short) that can + +Table 2. Quantitative evaluation on the ShapeNet dataset through 1-NNA about CD and EMD with 13-category. PVD* denotes the modified version of PVD for multi-category. + +
Category1-NNA (CD)1-NNA (EMD)
PVD*ourstrainsetPVD*ourstrainset
Airplane67.2070.7945.9257.9258.0447.40
Bench62.4360.2253.3159.6757.4654.14
Cabinet62.1062.7447.1368.1563.0650.96
Car64.5566.2949.4757.8955.8150.53
Chair61.8963.2352.8859.4059.3348.74
Display61.4744.5051.8358.2653.2152.29
Lamp58.8758.0149.1361.0456.2851.95
Loudspeaker59.3257.1448.1457.4554.7652.17
Rifle61.3960.5450.0058.4453.5949.79
Sofa58.0452.8451.5854.5750.6347.32
Table62.4155.7649.7161.8256.3551.00
Telephone60.0057.1448.5755.7154.7650.95
Vessel59.5959.8451.5558.2954.1550.78
Average61.4859.1649.9459.1255.9650.62
+ +receive a category condition with MLPs with Embedding layers similar to ours but without AdaGN to preserve the timestep embedding method of the original PVD. Quantitative results are shown in Table 2. The results of PVD* and SDF-Diffusion are trained equally for 1,000 epochs for only multi-category case. SDF-Diffusion shows better results in most categories about 1-NNA metric, especially outperforming EMD-based metrics. Additional qualitative comparisons on the mesh domain will be discussed in the supplementary material. + +# 4.3. Application: Shape Completion + +We show the applicability of our SDF-Diffusion on another task: 3D shape completion with voxel condition. Without modification of network architecture, we show that our method can be applied to 3D shape completion. Specifically, the second stage of our method takes a voxel-shaped condition by concatenating the conditional input (i.e., low-resolution SDF generated by the first stage) with noisy data to denoise. In other words, let the SDF voxel be a single-channel, then we can consider the second stage of our model takes two-channel input and returns a single-channel output. Therefore, using the same network architecture, we can seamlessly train a shape completion model by giving a partial SDF voxel instead of a low-resolution condition. + +For partial 3D shapes, we perform a 3D shape comple + +![](images/5c7e6ea64402cf503e4f0ffbed5cc305f2ead9b5a5f65e2f3f26fcb62d14806c.jpg) +Figure 5. Visualization of generated 3D shapes at different resolutions. The first stage model generates coarse shapes in the resolution of $32^{3}$ . By performing super-resolution using our second stage model multiple times, we can obtain improved shape detail of 3D shapes with the voxel resolutions of $64^{3}$ and $128^{3}$ . + +tion based on SDF-Diffision, as shown in Fig. 6. As you can see, we can generate various 3D shapes from given partial 3D shapes, which shows the applicability and flexibility of the proposed SDF-Diffision. + +In addition, we also demonstrate the generality of our SDF-Diffusion by using it for the task of 3D shape completion with a partially observed point cloud as a condition. To generate the partial point cloud input, we randomly sample 200 points from the preprocessed ShapeNet dataset using the same method employed in [82]. For out-of-distribution data, we acquire partial point clouds from depth images of the Redwood 3DScans dataset [9]. As the point cloud has a different format than the voxel feature generated by our SDF-Diffusion, we incorporate an additional layer to extract and voxelize the point cloud. Specifically, we employ the PointNet layer [55] from the encoder of the convolutional occupancy network [53], which transforms the point cloud feature into a voxel and gives this feature to each layer of SDF-Diffusion along with the AdaGN. The completed 3D shapes are visualized in Fig. 7. We show SDF-Diffusion can successfully apply unseen out-of-distribution data. + +# 5. Conclusion + +In this work, we have proposed SDF-Diffusion, a novel diffusion-based SDF generation approach for 3D shapes. SDF-Diffusion composed of two-stage generates low-resolution SDF and then produces high-resolution SDF conditioned on the low-resolution one. For memory efficiency, we learn the second stage of SDF-Diffusion (i.e., super-resolution) in a patch-wise manner, which allows us to perform super-resolution several times in high-resolution. In addition, SDF-Diffusion can be seam- + +![](images/429be4ce4096abf33a75265f0d5d8521ca7488f7563e92a559c5418ea3c7b88c.jpg) +Figure 6. Generated 3D shapes by 3D shape completion. SDF-Diffusion can be easily expanded to a 3D shape completion task by modifying only the input head of the network architecture. + +![](images/8292048ba36c038f2bb36b39d5d89edf89b7c4d6fdd42c111fcd8e5557cb3b2c.jpg) +Figure 7. Generated 3D shapes by 3D shape completion on out-of-distribution data. SDF-Diffusion shows various completion candidates from out-of-distribution partial point clouds. + +lessly extended to multi-category 3D shape generation and 3D shape completion. Experiments demonstrate that the proposed method can generate high-quality 3D shapes in the SDF domain with superior generative power. + +Acknowledgments. This work was supported by Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) (No. 2022-0-00612, Geometric and Physical Commonsense Reasoning based Behavior Intelligence for Embodied AI, No.2022-0-00907, Development of AI Bots Collaboration Platform and Self-organizing AI and No.2020-0-01336, Artificial Intelligence Graduate School Program (UNIST)) and Artificial intelligence industrial convergence cluster development project funded by the Ministry of Science and ICT (MSIT, Korea) & Gwangju Metropolitan City. + +# References + +[1] Panos Achlioptas, Olga Diamanti, Ioannis Mitliagkas, and Leonidas Guibas. Learning representations and generative models for 3D point clouds. In ICML, 2018. 1, 2 +[2] Fausto Bernardini, Joshua Mittleman, Holly Rushmeier, Cláudio Silva, and Gabriel Taubin. The ball-pivoting algorithm for surface reconstruction. 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Visualization of 3D shape generation for various categories using SDF-Diffusion. SDF-diffusion gradually removes the Gaussian noise and generates high-resolution 3D shapes in the form of an SDF voxel by a two-stage framework. Unlike previous methods, which use point clouds, we can generate 3D meshes without concern of complex post-processing. For visualization purposes, we show less-noise data instead of the initial Gaussian noise." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 143, + 442, + 192, + 453 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 442, + 192, + 453 + ], + "spans": [ + { + "bbox": [ + 143, + 442, + 192, + 453 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 467, + 288, + 682 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 467, + 288, + 682 + ], + "spans": [ + { + "bbox": [ + 46, + 467, + 288, + 682 + ], + "type": "text", + "content": "We propose a 3D shape generation framework (SDF-Diffusion in short) that uses denoising diffusion models with continuous 3D representation via signed distance fields (SDF). Unlike most existing methods that depend on discontinuous forms, such as point clouds, SDF-Diffusion generates high-resolution 3D shapes while alleviating memory issues by separating the generative process into two-stage: generation and super-resolution. In the first stage, a diffusion-based generative model generates a low-resolution SDF of 3D shapes. Using the estimated low-resolution SDF as a condition, the second stage diffusion model performs super-resolution to generate high-resolution SDF. Our framework can generate a high-fidelity 3D shape despite the extreme spatial complexity. On the ShapeNet dataset, our model shows competitive performance to the state-of-the-art methods and shows applicability on the shape completion task without modification." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 307, + 442, + 386, + 453 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 442, + 386, + 453 + ], + "spans": [ + { + "bbox": [ + 307, + 442, + 386, + 453 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 462, + 545, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 545, + 569 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 545, + 569 + ], + "type": "text", + "content": "The need for generative modeling of 3D shapes has rapidly increased due to high demand in various fields, such as computer vision, graphics, robotics, and content generation. To synthesize a high-quality 3D shape, numerous generative approaches have been actively studied, including generative adversarial networks (GAN) [1, 7, 8, 18, 20, 40, 51, 62, 71, 85], variational auto-encoders (VAE) [13, 27, 35, 45, 67], normalizing flows [26, 30, 60, 77], auto-regressive models [19, 31, 45, 46, 76], and others [61, 74, 75, 80, 84]." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "content": "Recently, denoising diffusion models (DDM) have emerged as a promising generative framework in image generation [10, 16, 22, 39, 47, 63] and speech synthesis [5, 32, 54]. DDM achieves a generative process by gradually corrupting data through a diffusion process and denoising through a learned neural network. This network can generate new realistic data by repeating the denoising process from the given pure noise. Based on the success of DDM-based generative models in various domains, several attempts are being made to apply them to the task of 3D shape generation [41, 83, 87]. They have applied DDM to generate new point cloud and have outperformed previous methods." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 62, + 703, + 140, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 703, + 140, + 712 + ], + "spans": [ + { + "bbox": [ + 62, + 703, + 140, + 712 + ], + "type": "text", + "content": "*Corresponding author." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20887" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": "However, even though DDM-based 3D generative models have demonstrated their impressive performance, they still have limitations to being adopted for real-world problems. Most previous DDM-based 3D generative models use point clouds to represent 3D shapes, which limits their ability to express continuous surfaces of 3D shapes, unlike mesh representation commonly used in real-world applications. To resolve this issue, intricate post-processing [2, 24, 25, 52] is required to reconstruct continuous meshes from point clouds. They require various parameter tuning or additional information (e.g., surface normal at each point [52]), and a densely sampled point cloud is required to reconstruct high-quality mesh. However, existing DDM-based methods for 3D shape generation are based on sparse point clouds." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 252, + 289, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 252, + 289, + 396 + ], + "spans": [ + { + "bbox": [ + 46, + 252, + 289, + 396 + ], + "type": "text", + "content": "In this work, we introduce a new DDM-based generation framework that generates high-quality 3D shapes through signed distance fields (SDF) (see Fig. 1). We can view SDF as a function that takes an arbitrary location as input and returns a signed distance value from the input location to the nearest surface of the mesh, and the sign of the value means whether inside or outside of the shape. We sample SDF values uniformly from a 3D shape to form a voxel-shaped SDF. This form has several advantages over point clouds. It can directly reconstruct mesh through the marching cube algorithm [38] and can utilize convolutional neural network (CNN) because of its dense and fixed structure." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 396, + 289, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 396, + 289, + 613 + ], + "spans": [ + { + "bbox": [ + 46, + 396, + 289, + 613 + ], + "type": "text", + "content": "Based on this voxel-shaped SDF representation, we propose a novel DDM-based generative model in two-stage (see Fig. 2). In the first stage, a diffusion-based SDF generation produces low-resolution SDF for coarse 3D shapes. In the second stage, we propose a diffusion-based SDF superresolution, given the low-resolution SDF of the first stage as a condition. In particular, since the increasing resolution of the voxel comes as a significant burden in terms of computational resources (i.e., due to the curse of the dimension), we approach this problem by super-resolution in patch-based learning. Under this scheme, we can iteratively perform the second stage multiple times with the same structure and generate further higher resolution of SDF, which is a more detailed 3D shape. With various experiments, we achieve state-of-the-art in single-/multi-category 3D shape generative quality, and our method can be directly converted into 3D meshes, unlike other point cloud-based methods that require intricate post-processing." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 613, + 244, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 613, + 244, + 625 + ], + "spans": [ + { + "bbox": [ + 59, + 613, + 244, + 625 + ], + "type": "text", + "content": "In summary, our contributions are as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 630, + 289, + 713 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 47, + 630, + 287, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 630, + 287, + 666 + ], + "spans": [ + { + "bbox": [ + 47, + 630, + 287, + 666 + ], + "type": "text", + "content": "- We propose a novel DDM-based generation method that utilizes a voxel-shaped SDF representation to generate high-quality and continuous 3D shapes." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 677, + 289, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 289, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 289, + 713 + ], + "type": "text", + "content": "- We represent a memory-efficient two-stage framework composed of low-resolution SDF generation and SDF super-resolution conditioned on the low-resolution SDF." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 313, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 545, + 96 + ], + "type": "text", + "content": "In particular, we can iteratively perform super-resolution to generate higher-resolution SDF." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 105, + 547, + 141 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 105, + 547, + 141 + ], + "spans": [ + { + "bbox": [ + 306, + 105, + 547, + 141 + ], + "type": "text", + "content": "- SDF-diffusion can be seamlessly extended into multi-category 3D shape generation and completion, which shows the flexibility of the proposed method." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 152, + 392, + 164 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 152, + 392, + 164 + ], + "spans": [ + { + "bbox": [ + 306, + 152, + 392, + 164 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 172, + 545, + 243 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 172, + 545, + 243 + ], + "spans": [ + { + "bbox": [ + 304, + 172, + 545, + 243 + ], + "type": "text", + "content": "3D Shape representation. Numerous in-depth studies have been conducted on the representation of 3D shape [8, 43, 44, 48-50, 64, 73, 78, 79, 81]. We can categorize them into two groups: explicit representations, such as voxels [14, 15, 71], point clouds [1, 55, 56], and implicit functions, such as signed distance fields (SDF) [50, 64]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 243, + 545, + 363 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 243, + 545, + 363 + ], + "spans": [ + { + "bbox": [ + 304, + 243, + 545, + 363 + ], + "type": "text", + "content": "Voxels are widely adapted in various neural networks due to their intuitive structure and synergy with 3D CNN [14, 15, 71, 73]. However, it may cause a memory problem according to the increase in resolution. Point clouds, which are compact and readily available, are dominant representations with their well-suitability to learn contextual information in neural networks [1, 55, 56, 79, 81]. However, it requires post-processing to convert the synthesized point clouds into meshes for real-world applications [8, 38, 43, 44, 48-50, 78]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 363, + 545, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 363, + 545, + 472 + ], + "spans": [ + { + "bbox": [ + 304, + 363, + 545, + 472 + ], + "type": "text", + "content": "Implicit functions view the 3D shape as a set of levels for a continuous function, which makes it possible to express a continuous surface [8,44,48-50,64,78]. As a result, despite their slow interference as they require numerous network operations, these methods are growing in popularity. In particular, SDF encoded with distance to the nearest surface has some advantages to express sharper reconstructions [50, 64]. Thus, we exploit SDF voxel representation to obtain sharper meshes without unnecessary procedures." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 474, + 545, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 545, + 557 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 545, + 557 + ], + "type": "text", + "content": "3D shape generation. To generate 3D geometry, a variety of frameworks are applied [1, 7, 8, 13, 19, 20, 26, 27, 30, 31, 34, 46, 51, 60, 62, 67, 85]. With such a perspective, several frameworks are applied to model the distribution representing a 3D shape, such as GAN-based models [33], auto-regressive models [66], flow-based models [77], and implicit functions [43, 50]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": "For GAN-based 3D generative method, SDF-StyleGAN [86] extends StyleGAN2 [23] for 3D shape generation by proposing global and local discriminator that enables GAN discriminator on SDF. Generative methods, such as AutoSDF [45], and ShapeFormer [76], propose to utilize a voxel form of implicit representation (e.g., SDF and occupancy) for mesh generation through a two-stage. A two-stage generative strategy reduces required computational resources by compressing data into a tractable form (e.g., latent feature) rather than directly dealing with an original data structure to make a generative model concentrate semantically compressed representation and save computational resources. Motivated by VQ-GAN [12]," + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "footer", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "20888" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": "AutoSDF and ShapeFormer apply two-stage generative method and show impressive performance on conditional 3D shape generation. They utilize an auto-encoder to convert voxel into compressed latent space and generate a new shape using the autoregressive model on the latent space. However, they miss fully utilizing the advantage of the two-stage generative method because they use a regression-based auto-encoder unlike VQ-GAN, which uses GAN and perceptual loss [21]. Unlike the 2D image generation, there are insufficient research works in perceptually plausible auto-encoding methods about 3D shapes, especially voxel structures; it has difficulties in applying a two-stage strategy to 3D shape generation." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 230, + 289, + 385 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 230, + 289, + 385 + ], + "spans": [ + { + "bbox": [ + 46, + 230, + 289, + 385 + ], + "type": "text", + "content": "On the other hand, recent research works propose a new two-stage generative method [17, 42, 59]. They use a super-resolution model to up-sample low-resolution data, and the generation model learns low-resolution data distribution. Instead of training an auto-encoder, these methods utilize naturally constructed low-resolution forms. Inspired by this, our method exploits a two-stage framework using voxel-shaped SDF. Instead of learning the auto-encoder, we propose a method of generating a coarse 3D shape that is naturally compressed form in the representation of a low-resolution voxel. We then generate high-quality 3D shapes by refining the details of the coarse shape by upsampling the low-resolution voxel." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 391, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 391, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 391, + 289, + 715 + ], + "type": "text", + "content": "Diffusion-Based 3D shape generation. With the success of DDM-based generative models in image generation [10, 16, 47], diffusion-based 3D shape generations have advanced significantly. In particular, diffusion probabilistic models (DPM) [41] suggest a DDM-based approach with an auto-encoder architecture built on PointNet [55], which compresses point clouds into a latent vector and then generates new shape latent using normalizing flows [6, 11]. Point voxel diffusion (PVD) [87] applies DDM directly on the point clouds by adopting a point voxel CNN-based network architecture [36], which utilizes both the 3D CNN and PointNet. In addition, point diffusion-refinement (PDR) [42] proposes a two-stage generative framework for conditional point cloud generation task. It generates sparse point clouds by PointNet-based DDM in the first stage and up-samples the sparse point clouds to denser ones in a learning-based manner. Motivated by latent diffusion models (LDM) [58], latent point diffusion models (LION) [83] propose a two-stage approach with compressed latent point clouds through VAE [29]. LION converts result point clouds into mesh by shapes as points (SAP) [52]. Despite their great performance, it still requires a pre-trained SAP model or fine-tuning stage. In other words, the usability of the above point clouds-based approaches is limited to be adopted in real-world applications. To address this issue, we propose a diffusion-based generative model upon voxel-shaped SDF representation," + } + ] + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 312, + 71, + 539, + 231 + ], + "blocks": [ + { + "bbox": [ + 312, + 71, + 539, + 231 + ], + "lines": [ + { + "bbox": [ + 312, + 71, + 539, + 231 + ], + "spans": [ + { + "bbox": [ + 312, + 71, + 539, + 231 + ], + "type": "image", + "image_path": "c36185db371aa6497a3108a6fc6be8621f74180fc8d56a683fed62636eed9a9a.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 233, + 547, + 312 + ], + "lines": [ + { + "bbox": [ + 304, + 233, + 547, + 312 + ], + "spans": [ + { + "bbox": [ + 304, + 233, + 547, + 312 + ], + "type": "text", + "content": "Figure 2. Overview of SDF-Diffusion. The proposed method consists of two stages. In the first stage, we take as input voxel-shaped noise " + }, + { + "bbox": [ + 304, + 233, + 547, + 312 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_T^{\\mathrm{LR}} = \\epsilon^{\\mathrm{LR}}" + }, + { + "bbox": [ + 304, + 233, + 547, + 312 + ], + "type": "text", + "content": " and generate low-resolution SDF voxel " + }, + { + "bbox": [ + 304, + 233, + 547, + 312 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0^{\\mathrm{LR}}" + }, + { + "bbox": [ + 304, + 233, + 547, + 312 + ], + "type": "text", + "content": " of new coarse 3D shape through DDM. In the second stage, conditioned on " + }, + { + "bbox": [ + 304, + 233, + 547, + 312 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0^{\\mathrm{LR}}" + }, + { + "bbox": [ + 304, + 233, + 547, + 312 + ], + "type": "text", + "content": ", we perform super-resolution through another DDM, which generates high-resolution SDF voxel " + }, + { + "bbox": [ + 304, + 233, + 547, + 312 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0^{\\mathrm{HR}}" + }, + { + "bbox": [ + 304, + 233, + 547, + 312 + ], + "type": "text", + "content": " with fine and detailed 3D shape." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 305, + 319, + 545, + 345 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 319, + 545, + 345 + ], + "spans": [ + { + "bbox": [ + 305, + 319, + 545, + 345 + ], + "type": "text", + "content": "which can directly reconstruct 3D mesh using zero isosurface finding methods [38]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 355, + 389, + 369 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 355, + 389, + 369 + ], + "spans": [ + { + "bbox": [ + 306, + 355, + 389, + 369 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 376, + 545, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 376, + 545, + 579 + ], + "spans": [ + { + "bbox": [ + 304, + 376, + 545, + 579 + ], + "type": "text", + "content": "We propose a generative method for high-resolution 3D shapes in the form of SDF voxels based on the denoising diffusion models [16, 63] (SDF-Diffusion in short). To generate high-resolution samples efficiently, the proposed method involves two stages: diffusion-based SDF generation and diffusion-based patch-wise SDF super-resolution (see Fig. 2 for the overview). In the first stage, the diffusion-based SDF generation model generates a low-resolution coarse 3D shape. Given this low-resolution sample, the diffusion-based SDF super-resolution model progressively produces high-resolution samples in the second stage. In other words, we can consider the first stage as a pure diffusion-based generative model, and the second stage as a conditional diffusion-based super-resolution model. It is worth noting that, ideally, the second stage can be repeated multiple times with the same architecture, which enables us to generate more high-resolution 3D shapes." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 579, + 545, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 579, + 545, + 664 + ], + "spans": [ + { + "bbox": [ + 304, + 579, + 545, + 664 + ], + "type": "text", + "content": "In the following, we briefly explain the background on DDM in Sec. 3.1. Then, in Sec. 3.2, we describe our method for generating coarse 3D shapes using a diffusion-based technique. In Sec. 3.3, we explain how we generate high-resolution 3D shapes by super-resolving low-resolution correspondence. Training and inference processes for each diffusion model are listed in Algorithm 1 and Algorithm 2." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 670, + 533, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 670, + 533, + 684 + ], + "spans": [ + { + "bbox": [ + 306, + 670, + 533, + 684 + ], + "type": "text", + "content": "3.1. Background on Denoising Diffusion Models" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": "DDM is a class of generative models that generates new samples from a given data distribution by learning the in-" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "footer", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20889" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "content": "verse of the noising process [16, 63]. Concretely, starting from samples from the Gaussian distribution " + }, + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_T" + }, + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "content": ", the denoising process gradually produces samples with less noise " + }, + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{T - 1},\\mathbf{x}_{T - 2},\\ldots" + }, + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "content": ", and aims to reach final samples " + }, + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0" + }, + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "content": ", which is the noise-free final output." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 135, + 287, + 182 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 135, + 287, + 182 + ], + "spans": [ + { + "bbox": [ + 47, + 135, + 287, + 182 + ], + "type": "text", + "content": "Forward process. The forward process (or diffusion process) gradually adds the Gaussian noise to the clean data, which is the approximate joint posterior " + }, + { + "bbox": [ + 47, + 135, + 287, + 182 + ], + "type": "inline_equation", + "content": "q(\\mathbf{x}_{1:T}|\\mathbf{x}_0)" + }, + { + "bbox": [ + 47, + 135, + 287, + 182 + ], + "type": "text", + "content": ". This diffusion process is represented as a Markov chain:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 95, + 185, + 287, + 217 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 95, + 185, + 287, + 217 + ], + "spans": [ + { + "bbox": [ + 95, + 185, + 287, + 217 + ], + "type": "interline_equation", + "content": "q \\left(\\mathbf {x} _ {0: T}\\right) = q \\left(\\mathbf {x} _ {0}\\right) \\prod_ {t = 1} ^ {T} q \\left(\\mathbf {x} _ {t} \\mid \\mathbf {x} _ {t - 1}\\right), \\tag {1}", + "image_path": "79a44b5263d2b684f562cf8bfb03b0ae55e2cd891f3e2df18ec3c8075e5ecd07.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 82, + 220, + 287, + 235 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 220, + 287, + 235 + ], + "spans": [ + { + "bbox": [ + 82, + 220, + 287, + 235 + ], + "type": "interline_equation", + "content": "q \\left(\\mathbf {x} _ {t} \\mid \\mathbf {x} _ {t - 1}\\right) = \\mathcal {N} \\left(\\mathbf {x} _ {t}; \\sqrt {1 - \\beta_ {t}} \\mathbf {x} _ {t - 1}, \\beta_ {t} \\mathbf {I}\\right), \\tag {2}", + "image_path": "19e89e5564b0e619fb7cb7c7106c8cc2acbf245fd52cbda424291aa65e7b7051.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 243, + 270, + 254 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 243, + 270, + 254 + ], + "spans": [ + { + "bbox": [ + 47, + 243, + 270, + 254 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 243, + 270, + 254 + ], + "type": "inline_equation", + "content": "\\beta_{t}" + }, + { + "bbox": [ + 47, + 243, + 270, + 254 + ], + "type": "text", + "content": " denotes the noise scheduling hyperparameter." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 254, + 287, + 278 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 254, + 287, + 278 + ], + "spans": [ + { + "bbox": [ + 47, + 254, + 287, + 278 + ], + "type": "text", + "content": "According to [16], the forward process admits sampling " + }, + { + "bbox": [ + 47, + 254, + 287, + 278 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t" + }, + { + "bbox": [ + 47, + 254, + 287, + 278 + ], + "type": "text", + "content": " at an arbitrary time step " + }, + { + "bbox": [ + 47, + 254, + 287, + 278 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 254, + 287, + 278 + ], + "type": "text", + "content": " by a closed form:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 87, + 286, + 287, + 300 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 286, + 287, + 300 + ], + "spans": [ + { + "bbox": [ + 87, + 286, + 287, + 300 + ], + "type": "interline_equation", + "content": "q \\left(\\mathbf {x} _ {t} \\mid \\mathbf {x} _ {0}\\right) = \\mathcal {N} \\left(\\mathbf {x} _ {t}; \\sqrt {\\bar {\\alpha} _ {t}} \\mathbf {x} _ {0}, (1 - \\bar {\\alpha} _ {t}) \\mathbf {I}\\right), \\tag {3}", + "image_path": "8ddee053cd47e16d6c9b25d9a218afa873784c164bf4d04c582f18f22857ad1f.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 308, + 287, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 308, + 287, + 331 + ], + "spans": [ + { + "bbox": [ + 47, + 308, + 287, + 331 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 308, + 287, + 331 + ], + "type": "inline_equation", + "content": "\\alpha_{t} = 1 - \\beta_{t}" + }, + { + "bbox": [ + 47, + 308, + 287, + 331 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 308, + 287, + 331 + ], + "type": "inline_equation", + "content": "\\bar{\\alpha}_{t} = \\Pi_{s=1}^{t} \\alpha_{s}" + }, + { + "bbox": [ + 47, + 308, + 287, + 331 + ], + "type": "text", + "content": ". Thus, " + }, + { + "bbox": [ + 47, + 308, + 287, + 331 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{t}" + }, + { + "bbox": [ + 47, + 308, + 287, + 331 + ], + "type": "text", + "content": " can be directly sampled by:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 87, + 339, + 287, + 354 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 339, + 287, + 354 + ], + "spans": [ + { + "bbox": [ + 87, + 339, + 287, + 354 + ], + "type": "interline_equation", + "content": "\\mathbf {x} _ {t} = \\sqrt {\\bar {\\alpha} _ {t}} \\mathbf {x} _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon , \\epsilon \\sim \\mathcal {N} (\\mathbf {0}, \\mathbf {I}). \\tag {4}", + "image_path": "26c26971234b37380cf1aa61faf4ed6eada12bd169e44ce8e85b7d708e277e63.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 361, + 287, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 361, + 287, + 419 + ], + "spans": [ + { + "bbox": [ + 47, + 361, + 287, + 419 + ], + "type": "text", + "content": "Reverse process. The reverse process (or generative process) aims to generate samples by gradually inverting infinitesimal noise, which is the joint distribution " + }, + { + "bbox": [ + 47, + 361, + 287, + 419 + ], + "type": "inline_equation", + "content": "p_{\\theta}(\\mathbf{x}_{0:T})" + }, + { + "bbox": [ + 47, + 361, + 287, + 419 + ], + "type": "text", + "content": ". This reverse process is defined as a Markov chain with the learned Gaussian transitions:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 97, + 422, + 287, + 453 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 422, + 287, + 453 + ], + "spans": [ + { + "bbox": [ + 97, + 422, + 287, + 453 + ], + "type": "interline_equation", + "content": "p _ {\\theta} \\left(\\mathbf {x} _ {0: T}\\right) = p \\left(\\mathbf {x} _ {T}\\right) \\prod_ {t = 1} ^ {T} p _ {\\theta} \\left(\\mathbf {x} _ {t - 1} \\mid \\mathbf {x} _ {t}\\right), \\tag {5}", + "image_path": "028f64fcc1ebf3615a65c275a125b3659b32e610d01abef9da6d4faec198f5fe.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 84, + 456, + 287, + 469 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 84, + 456, + 287, + 469 + ], + "spans": [ + { + "bbox": [ + 84, + 456, + 287, + 469 + ], + "type": "interline_equation", + "content": "p _ {\\theta} \\left(\\mathbf {x} _ {t - 1} \\mid \\mathbf {x} _ {t}\\right) = \\mathcal {N} \\left(\\mathbf {x} _ {t - 1}; \\mu_ {\\theta} \\left(\\mathbf {x} _ {t}, t\\right), \\sigma_ {t} ^ {2} \\mathbf {I}\\right), \\tag {6}", + "image_path": "9da0ffd3c376aab6d9514dfb2834762820e6fdabb7faabb7f90d9a718d1658ad.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 477, + 287, + 538 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 477, + 287, + 538 + ], + "spans": [ + { + "bbox": [ + 47, + 477, + 287, + 538 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 477, + 287, + 538 + ], + "type": "inline_equation", + "content": "p(\\mathbf{x}_T) = \\mathcal{N}(\\mathbf{x}_T;\\mathbf{0},\\mathbf{I})" + }, + { + "bbox": [ + 47, + 477, + 287, + 538 + ], + "type": "text", + "content": " is the standard Gaussian distribution, " + }, + { + "bbox": [ + 47, + 477, + 287, + 538 + ], + "type": "inline_equation", + "content": "\\mu_{\\theta}(\\mathbf{x}_t,t)" + }, + { + "bbox": [ + 47, + 477, + 287, + 538 + ], + "type": "text", + "content": " indicates a denoising function parameterized by " + }, + { + "bbox": [ + 47, + 477, + 287, + 538 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 47, + 477, + 287, + 538 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 477, + 287, + 538 + ], + "type": "inline_equation", + "content": "\\sigma_t^2" + }, + { + "bbox": [ + 47, + 477, + 287, + 538 + ], + "type": "text", + "content": " is a time-step dependant variance, and we fix " + }, + { + "bbox": [ + 47, + 477, + 287, + 538 + ], + "type": "inline_equation", + "content": "\\sigma_t^2 = \\frac{1 - \\bar{\\alpha}_{t - 1}}{1 - \\bar{\\alpha}_t}\\beta_t" + }, + { + "bbox": [ + 47, + 477, + 287, + 538 + ], + "type": "text", + "content": ", following [16]. We can sample from " + }, + { + "bbox": [ + 47, + 477, + 287, + 538 + ], + "type": "inline_equation", + "content": "p(\\mathbf{x}_T)" + }, + { + "bbox": [ + 47, + 477, + 287, + 538 + ], + "type": "text", + "content": " and then draw " + }, + { + "bbox": [ + 47, + 477, + 287, + 538 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{t - 1}\\sim p_{\\theta}(\\mathbf{x}_{t - 1}|\\mathbf{x}_t)" + }, + { + "bbox": [ + 47, + 477, + 287, + 538 + ], + "type": "text", + "content": " by Eq. (6) as:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 91, + 543, + 287, + 556 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 543, + 287, + 556 + ], + "spans": [ + { + "bbox": [ + 91, + 543, + 287, + 556 + ], + "type": "interline_equation", + "content": "\\mathbf {x} _ {t - 1} = \\mu_ {\\theta} \\left(\\mathbf {x} _ {t}, t\\right) + \\sigma_ {t} \\epsilon , \\epsilon \\sim \\mathcal {N} (\\mathbf {0}, \\mathbf {I}). \\tag {7}", + "image_path": "d99537024632c688e6e0ac2ca27d8299238b0c1915200cdf01e4e29ea91c5b48.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 564, + 279, + 576 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 564, + 279, + 576 + ], + "spans": [ + { + "bbox": [ + 47, + 564, + 279, + 576 + ], + "type": "text", + "content": "By repeating this process, we can eventually generate " + }, + { + "bbox": [ + 47, + 564, + 279, + 576 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0" + }, + { + "bbox": [ + 47, + 564, + 279, + 576 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 47, + 578, + 287, + 603 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 578, + 287, + 603 + ], + "spans": [ + { + "bbox": [ + 47, + 578, + 287, + 603 + ], + "type": "text", + "content": "Training objective. Following [16], we can simplify " + }, + { + "bbox": [ + 47, + 578, + 287, + 603 + ], + "type": "inline_equation", + "content": "\\mu_{\\theta}(\\mathbf{x}_t,t)" + }, + { + "bbox": [ + 47, + 578, + 287, + 603 + ], + "type": "text", + "content": " .." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 73, + 610, + 287, + 637 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 73, + 610, + 287, + 637 + ], + "spans": [ + { + "bbox": [ + 73, + 610, + 287, + 637 + ], + "type": "interline_equation", + "content": "\\mu_ {\\theta} \\left(\\mathbf {x} _ {t}, t\\right) = \\frac {1}{\\sqrt {\\alpha_ {t}}} \\left(\\mathbf {x} _ {t} - \\frac {\\beta_ {t}}{\\sqrt {1 - \\bar {\\alpha} _ {t}}} \\epsilon_ {\\theta} \\left(\\mathbf {x} _ {t}, t\\right)\\right), \\tag {8}", + "image_path": "a0088915a7a937ffebafcdaecb4e3346ef95e00300f348e8d5171699217b51ab.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 47, + 644, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 644, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 47, + 644, + 287, + 693 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 644, + 287, + 693 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(\\mathbf{x}_t,t)" + }, + { + "bbox": [ + 47, + 644, + 287, + 693 + ], + "type": "text", + "content": " is a neural network parameterized by " + }, + { + "bbox": [ + 47, + 644, + 287, + 693 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 47, + 644, + 287, + 693 + ], + "type": "text", + "content": " that predicts noise from noisy input " + }, + { + "bbox": [ + 47, + 644, + 287, + 693 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t" + }, + { + "bbox": [ + 47, + 644, + 287, + 693 + ], + "type": "text", + "content": ". Thus, the objective function compares the difference between the predicted noise " + }, + { + "bbox": [ + 47, + 644, + 287, + 693 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(\\mathbf{x}_t,t)" + }, + { + "bbox": [ + 47, + 644, + 287, + 693 + ], + "type": "text", + "content": " and the applied noise " + }, + { + "bbox": [ + 47, + 644, + 287, + 693 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 47, + 644, + 287, + 693 + ], + "type": "text", + "content": " [16]:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 121, + 700, + 287, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 121, + 700, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 121, + 700, + 287, + 715 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\left\\| \\epsilon_ {\\theta} \\left(\\mathbf {x} _ {t}, t\\right) - \\epsilon \\right\\| _ {p} ^ {p}, \\tag {9}", + "image_path": "1d777987060de4f70c0c66d7ba772a4a479612087f92748c5aae228aace4e698.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 72, + 545, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 107 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 107 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 72, + 545, + 107 + ], + "type": "inline_equation", + "content": "p\\in \\{1,2\\}" + }, + { + "bbox": [ + 305, + 72, + 545, + 107 + ], + "type": "text", + "content": ". On the other hand, according to [16], it is possible to modify " + }, + { + "bbox": [ + 305, + 72, + 545, + 107 + ], + "type": "inline_equation", + "content": "\\mu_{\\theta}(\\mathbf{x}_t,t)" + }, + { + "bbox": [ + 305, + 72, + 545, + 107 + ], + "type": "text", + "content": " with a neural network predicting " + }, + { + "bbox": [ + 305, + 72, + 545, + 107 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0" + }, + { + "bbox": [ + 305, + 72, + 545, + 107 + ], + "type": "text", + "content": " instead of noise " + }, + { + "bbox": [ + 305, + 72, + 545, + 107 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 305, + 72, + 545, + 107 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 364, + 115, + 545, + 129 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 115, + 545, + 129 + ], + "spans": [ + { + "bbox": [ + 364, + 115, + 545, + 129 + ], + "type": "interline_equation", + "content": "\\mu_ {\\theta} \\left(\\mathbf {x} _ {t}, t\\right) = \\gamma_ {t} f _ {\\theta} \\left(\\mathbf {x} _ {t}, t\\right) + \\delta_ {t} \\mathbf {x} _ {t}, \\tag {10}", + "image_path": "bdb882a7818f8b9a9f49925c05935971fabdb58ae98f41d32216f9814d55986e.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 135, + 545, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 135, + 545, + 175 + ], + "spans": [ + { + "bbox": [ + 305, + 135, + 545, + 175 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 135, + 545, + 175 + ], + "type": "inline_equation", + "content": "\\gamma_{t} = \\frac{\\beta_{t}\\sqrt{\\bar{\\alpha}_{t - 1}}}{1 - \\bar{\\alpha}_{t}}" + }, + { + "bbox": [ + 305, + 135, + 545, + 175 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 135, + 545, + 175 + ], + "type": "inline_equation", + "content": "\\delta_t = \\frac{(1 - \\bar{\\alpha}_{t - 1})\\sqrt{\\alpha_t}}{1 - \\bar{\\alpha}_t}" + }, + { + "bbox": [ + 305, + 135, + 545, + 175 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 135, + 545, + 175 + ], + "type": "inline_equation", + "content": "f_{\\theta}(\\mathbf{x}_t,t)" + }, + { + "bbox": [ + 305, + 135, + 545, + 175 + ], + "type": "text", + "content": " is a neural network parameterized by " + }, + { + "bbox": [ + 305, + 135, + 545, + 175 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 305, + 135, + 545, + 175 + ], + "type": "text", + "content": " that predicts noise-free data " + }, + { + "bbox": [ + 305, + 135, + 545, + 175 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0" + }, + { + "bbox": [ + 305, + 135, + 545, + 175 + ], + "type": "text", + "content": ". In that case, the objective function becomes:" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 376, + 182, + 545, + 197 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 376, + 182, + 545, + 197 + ], + "spans": [ + { + "bbox": [ + 376, + 182, + 545, + 197 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\left\\| f _ {\\theta} \\left(\\mathbf {x} _ {t}, t\\right) - \\mathbf {x} _ {0} \\right\\| _ {p} ^ {p}. \\tag {11}", + "image_path": "996ab53130c94075cd698cbc3ac344690263c288d8e995fae60227992e6c6527.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 200, + 545, + 212 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 200, + 545, + 212 + ], + "spans": [ + { + "bbox": [ + 306, + 200, + 545, + 212 + ], + "type": "text", + "content": "Thus, we use Eq. (11) as our objective function in this work." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 218, + 451, + 230 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 218, + 451, + 230 + ], + "spans": [ + { + "bbox": [ + 306, + 218, + 451, + 230 + ], + "type": "text", + "content": "3.2. Diffusion SDF Generation" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 305, + 237, + 545, + 274 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 237, + 545, + 274 + ], + "spans": [ + { + "bbox": [ + 305, + 237, + 545, + 274 + ], + "type": "text", + "content": "Here, we describe a diffusion-based generative model for low-resolution 3D shape represented as SDF voxel " + }, + { + "bbox": [ + 305, + 237, + 545, + 274 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0^{\\mathrm{LR}}\\sim q(\\mathbf{x}_0^{\\mathrm{LR}})" + }, + { + "bbox": [ + 305, + 237, + 545, + 274 + ], + "type": "text", + "content": " sampled from the real data distribution " + }, + { + "bbox": [ + 305, + 237, + 545, + 274 + ], + "type": "inline_equation", + "content": "q(\\mathbf{x}_0^{\\mathrm{LR}})" + }, + { + "bbox": [ + 305, + 237, + 545, + 274 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 305, + 275, + 545, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 275, + 545, + 335 + ], + "spans": [ + { + "bbox": [ + 305, + 275, + 545, + 335 + ], + "type": "text", + "content": "Diffusion-based SDF voxel generation. 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(4):" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 323, + 341, + 545, + 356 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 341, + 545, + 356 + ], + "spans": [ + { + "bbox": [ + 323, + 341, + 545, + 356 + ], + "type": "interline_equation", + "content": "\\mathbf {x} _ {t} ^ {\\mathrm {L R}} = \\sqrt {\\bar {\\alpha} _ {t}} \\mathbf {x} _ {0} ^ {\\mathrm {L R}} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon^ {\\mathrm {L R}}, \\epsilon^ {\\mathrm {L R}} \\sim \\mathcal {N} (\\mathbf {0}, \\mathbf {I}). \\tag {12}", + "image_path": "4f02766f8fe4cb796d1155e5931887307c5f77116e896911bb85c11cdfbb4995.jpg" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 305, + 361, + 545, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 361, + 545, + 387 + ], + "spans": [ + { + "bbox": [ + 305, + 361, + 545, + 387 + ], + "type": "text", + "content": "Then, a network " + }, + { + "bbox": [ + 305, + 361, + 545, + 387 + ], + "type": "inline_equation", + "content": "f_{\\theta}^{\\mathrm{LR}}" + }, + { + "bbox": [ + 305, + 361, + 545, + 387 + ], + "type": "text", + "content": " is trained to predict noise-free data with MSE objective function like Eq. 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AdaGN is an extension of group normalization [72] through channel-wise scaling and shifting w.r.t. normalized feature maps " + }, + { + "bbox": [ + 46, + 269, + 287, + 376 + ], + "type": "inline_equation", + "content": "\\mathbf{h} \\in \\mathbb{R}^{k \\times h \\times w \\times d}" + }, + { + "bbox": [ + 46, + 269, + 287, + 376 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 269, + 287, + 376 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 269, + 287, + 376 + ], + "type": "text", + "content": " is the number of feature map channels:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 82, + 386, + 287, + 399 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 386, + 287, + 399 + ], + "spans": [ + { + "bbox": [ + 82, + 386, + 287, + 399 + ], + "type": "interline_equation", + "content": "\\operatorname {A d a G N} (\\mathbf {h}, \\mathbf {z}) = \\mathbf {z} _ {s} \\left(\\operatorname {G r o u p N o r m} (\\mathbf {h}) + \\mathbf {z} _ {t}\\right), \\tag {16}", + "image_path": "a33ea14cd0ec83ca599d6e7ec362d03faa21cc2b6e9f61c019333df827691526.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 46, + 410, + 287, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 410, + 287, + 448 + ], + "spans": [ + { + "bbox": [ + 46, + 410, + 287, + 448 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 410, + 287, + 448 + ], + "type": "inline_equation", + "content": "(\\mathbf{z}_s,\\mathbf{z}_t)\\in \\mathbb{R}^{2\\times k} = \\mathrm{MLP}(\\mathbf{z})" + }, + { + "bbox": [ + 46, + 410, + 287, + 448 + ], + "type": "text", + "content": " is result of an MLP layer. The detailed network architecture is available in the supplementary material." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 47, + 458, + 282, + 471 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 458, + 282, + 471 + ], + "spans": [ + { + "bbox": [ + 47, + 458, + 282, + 471 + ], + "type": "text", + "content": "3.3. Patch-Based Diffusion SDF Super-Resolution" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 46, + 478, + 287, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 478, + 287, + 515 + ], + "spans": [ + { + "bbox": [ + 46, + 478, + 287, + 515 + ], + "type": "text", + "content": "We aim to train a conditional diffusion-based super-resolution model that generates realistic high-resolution SDF voxel " + }, + { + "bbox": [ + 46, + 478, + 287, + 515 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0^{\\mathrm{HR}}" + }, + { + "bbox": [ + 46, + 478, + 287, + 515 + ], + "type": "text", + "content": " with low-resolution condition " + }, + { + "bbox": [ + 46, + 478, + 287, + 515 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0^{\\mathrm{LR}}" + }, + { + "bbox": [ + 46, + 478, + 287, + 515 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 46, + 518, + 287, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 518, + 287, + 685 + ], + "spans": [ + { + "bbox": [ + 46, + 518, + 287, + 685 + ], + "type": "text", + "content": "Patch-based learning scheme. The increase in demanding memory due to the growth of spatial complexity hinders the learning of high-resolution generative models. Instead of training on the full high-resolution voxel, we train our model based on small cube-shaped patches of given input high-resolution voxel " + }, + { + "bbox": [ + 46, + 518, + 287, + 685 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0^{\\mathrm{HR}}\\sim q(\\mathbf{x}_0^{\\mathrm{HR}})" + }, + { + "bbox": [ + 46, + 518, + 287, + 685 + ], + "type": "text", + "content": " sampled from real data distribution to reduce memory consumption. We denote " + }, + { + "bbox": [ + 46, + 518, + 287, + 685 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{x}}_t^{\\mathrm{HR}}" + }, + { + "bbox": [ + 46, + 518, + 287, + 685 + ], + "type": "text", + "content": " as a cube-shaped patch extracted from a random location of voxel " + }, + { + "bbox": [ + 46, + 518, + 287, + 685 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t^{\\mathrm{HR}}" + }, + { + "bbox": [ + 46, + 518, + 287, + 685 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 518, + 287, + 685 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{x}}_t^{\\mathrm{LR}}" + }, + { + "bbox": [ + 46, + 518, + 287, + 685 + ], + "type": "text", + "content": " is a patch extracted from the corresponding location of " + }, + { + "bbox": [ + 46, + 518, + 287, + 685 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t^{\\mathrm{LR}}" + }, + { + "bbox": [ + 46, + 518, + 287, + 685 + ], + "type": "text", + "content": ". In addition, " + }, + { + "bbox": [ + 46, + 518, + 287, + 685 + ], + "type": "inline_equation", + "content": "\\epsilon^{\\mathrm{HR}}" + }, + { + "bbox": [ + 46, + 518, + 287, + 685 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 518, + 287, + 685 + ], + "type": "inline_equation", + "content": "\\hat{\\epsilon}^{\\mathrm{HR}}" + }, + { + "bbox": [ + 46, + 518, + 287, + 685 + ], + "type": "text", + "content": " are voxel-shaped noises sampled from the standard Gaussian distribution that have the same shape with " + }, + { + "bbox": [ + 46, + 518, + 287, + 685 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t^{\\mathrm{HR}}" + }, + { + "bbox": [ + 46, + 518, + 287, + 685 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 518, + 287, + 685 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{x}}_t^{\\mathrm{HR}}" + }, + { + "bbox": [ + 46, + 518, + 287, + 685 + ], + "type": "text", + "content": " respectively. Note that the patch-based operation is optional during the test phase if GPU has enough memory." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "content": "Conditional diffusion-based super-resolution. Similarly to Eq. 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1} ^ {\\mathrm {H R}} \\leftarrow \\gamma_ {t} f _ {\\theta} ^ {\\mathrm {H R}} (\\mathbf {x} _ {t} ^ {\\mathrm {H R}}, \\mathbf {x} _ {0} ^ {\\mathrm {L R}}, t, c) + \\delta_ {t} \\mathbf {x} _ {t} ^ {\\mathrm {H R}} + \\sigma_ {t} \\epsilon^ {\\mathrm {H R}}", + "image_path": "fdba74788e07053ae5c8e94b336edd685d18d5d90f04b252f721aaf3f7643b5d.jpg" + } + ] + } + ], + "index": 41 + }, + { + "bbox": [ + 328, + 261, + 361, + 268 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 328, + 261, + 361, + 268 + ], + "spans": [ + { + "bbox": [ + 328, + 261, + 361, + 268 + ], + "type": "interline_equation", + "content": "t = t - 1", + "image_path": "e8a9235be97ae06fc53cd7c3362935e157b23e9506198197f3c0c9a66d0b743e.jpg" + } + ] + } + ], + "index": 42 + }, + { + "bbox": [ + 316, + 270, + 350, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 270, + 350, + 277 + ], + "spans": [ + { + "bbox": [ + 316, + 270, + 350, + 277 + ], + "type": "text", + "content": "end while" + } + ] + } + ], + "index": 43 + }, + { + "bbox": [ + 306, + 290, + 396, + 301 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 290, + 396, + 301 + ], + "spans": [ + { + "bbox": [ + 306, + 290, + 396, + 301 + ], + "type": "text", + "content": "can be represented as:" + } + ] + } + ], + "index": 44 + }, + { + "bbox": [ + 321, + 308, + 545, + 322 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 308, + 545, + 322 + ], + "spans": [ + { + "bbox": [ + 321, + 308, + 545, + 322 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {x}} _ {t} ^ {\\mathrm {H R}} = \\sqrt {\\bar {\\alpha} _ {t}} \\hat {\\mathbf {x}} _ {0} ^ {\\mathrm {H R}} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\hat {\\epsilon} ^ {\\mathrm {H R}}, \\hat {\\epsilon} ^ {\\mathrm {H R}} \\sim \\mathcal {N} (\\mathbf {0}, \\mathbf {I}). \\tag {17}", + "image_path": "1533e6eb5286dd6069bddc216b73e88cc8724d7dec30ec0654faa1ffd84a93d1.jpg" + } + ] + } + ], + "index": 45 + }, + { + "bbox": [ + 304, + 329, + 545, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 329, + 545, + 376 + ], + "spans": [ + { + "bbox": [ + 304, + 329, + 545, + 376 + ], + "type": "text", + "content": "In the case of the objective function, we use " + }, + { + "bbox": [ + 304, + 329, + 545, + 376 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_1" + }, + { + "bbox": [ + 304, + 329, + 545, + 376 + ], + "type": "text", + "content": " for superresolution, followed by SR3 [59], where they empirically find that " + }, + { + "bbox": [ + 304, + 329, + 545, + 376 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_1" + }, + { + "bbox": [ + 304, + 329, + 545, + 376 + ], + "type": "text", + "content": " loss is better for super-resolution task compared to MSE loss:" + } + ] + } + ], + "index": 46 + }, + { + "bbox": [ + 347, + 383, + 545, + 397 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 383, + 545, + 397 + ], + "spans": [ + { + "bbox": [ + 347, + 383, + 545, + 397 + ], + "type": "interline_equation", + "content": "\\mathcal {L} ^ {\\mathrm {H R}} = \\left\\| f _ {\\theta} ^ {\\mathrm {H R}} \\left(\\hat {\\mathbf {x}} _ {t} ^ {\\mathrm {H R}}, \\hat {\\mathbf {x}} _ {0} ^ {\\mathrm {L R}}, t, c\\right) - \\hat {\\mathbf {x}} _ {0} ^ {\\mathrm {H R}} \\right\\| _ {1} ^ {1}. \\tag {18}", + "image_path": "7c72143f6e37e250d0d618015aca0dc8369feb126db4e409da256695ea59b4cc.jpg" + } + ] + } + ], + "index": 47 + }, + { + "bbox": [ + 304, + 404, + 545, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 404, + 545, + 453 + ], + "spans": [ + { + "bbox": [ + 304, + 404, + 545, + 453 + ], + "type": "text", + "content": "The low-resolution condition is nearly up-sampled to be the same resolution as the high-resolution side and channelwise concatenation is applied. Sampling is done by repeating a similar process to Eq. (14):" + } + ] + } + ], + "index": 48 + }, + { + "bbox": [ + 326, + 458, + 545, + 473 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 458, + 545, + 473 + ], + "spans": [ + { + "bbox": [ + 326, + 458, + 545, + 473 + ], + "type": "interline_equation", + "content": "\\mathbf {x} _ {t - 1} ^ {\\mathrm {H R}} = \\gamma_ {t} f _ {\\theta} ^ {\\mathrm {H R}} \\left(\\mathbf {x} _ {t} ^ {\\mathrm {H R}}, \\mathbf {x} _ {0} ^ {\\mathrm {L R}}, t, c\\right) + \\delta_ {t} \\mathbf {x} _ {t} ^ {\\mathrm {H R}} + \\sigma_ {t} \\epsilon^ {\\mathrm {H R}}, \\tag {19}", + "image_path": "656f60203db9eb2a6badd3229db44c2dc5380e09a9c2d9b0a52ad27c78bd05b9.jpg" + } + ] + } + ], + "index": 49 + }, + { + "bbox": [ + 304, + 479, + 545, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 479, + 545, + 504 + ], + "spans": [ + { + "bbox": [ + 304, + 479, + 545, + 504 + ], + "type": "text", + "content": "In Eqs. (18) and (19), the category condition " + }, + { + "bbox": [ + 304, + 479, + 545, + 504 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 479, + 545, + 504 + ], + "type": "text", + "content": " is ignored for a single-category generation." + } + ] + } + ], + "index": 50 + }, + { + "bbox": [ + 304, + 504, + 545, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 504, + 545, + 564 + ], + "spans": [ + { + "bbox": [ + 304, + 504, + 545, + 564 + ], + "type": "text", + "content": "In addition, our model can generate further higher resolution shapes by iteratively applying the second stage model trained on multiple resolutions (e.g., " + }, + { + "bbox": [ + 304, + 504, + 545, + 564 + ], + "type": "inline_equation", + "content": "32^{3} \\to 64^{3}" + }, + { + "bbox": [ + 304, + 504, + 545, + 564 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 504, + 545, + 564 + ], + "type": "inline_equation", + "content": "64^{3} \\to 128^{3}" + }, + { + "bbox": [ + 304, + 504, + 545, + 564 + ], + "type": "text", + "content": "). We provide this higher-resolution generation in the experiments." + } + ] + } + ], + "index": 51 + }, + { + "bbox": [ + 306, + 574, + 387, + 587 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 574, + 387, + 587 + ], + "spans": [ + { + "bbox": [ + 306, + 574, + 387, + 587 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 52 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "In this section, we evaluate and compare the proposed method with state-of-the-art methods in 3D shape generations. Specifically, we present qualitative and quantitative comparisons of our method for single-/multi-category 3D shape generation tasks in Secs. 4.1 and 4.2, respectively. Additionally, we demonstrate the applicability of the proposed SDF-Diffusion for shape completion in Sec. 4.3. Before diving into the details, we first provide several pieces of information for experiments, such as implementation details, dataset, evaluation metrics, and comparison methods." + } + ] + } + ], + "index": 53 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20891" + } + ] + } + ], + "index": 54 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 63, + 72, + 271, + 199 + ], + "blocks": [ + { + "bbox": [ + 63, + 72, + 271, + 199 + ], + "lines": [ + { + "bbox": [ + 63, + 72, + 271, + 199 + ], + "spans": [ + { + "bbox": [ + 63, + 72, + 271, + 199 + ], + "type": "image", + "image_path": "91826733846308effc7b218dd3fa865bacb63225e09336ab73c42338d473516e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 201, + 287, + 257 + ], + "lines": [ + { + "bbox": [ + 46, + 201, + 287, + 257 + ], + "spans": [ + { + "bbox": [ + 46, + 201, + 287, + 257 + ], + "type": "text", + "content": "Figure 3. Generated 3D shapes with a single-category generative model. Baseline methods generate point clouds with 2,048 points, and SDF-Diffusion produces 3D shapes in the form of T-SDF voxels, which can be converted to meshes directly through zero iso-surface finding algorithms." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 265, + 286, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 265, + 286, + 361 + ], + "spans": [ + { + "bbox": [ + 46, + 265, + 286, + 361 + ], + "type": "text", + "content": "Implementation details. For both generation and superresolution models, we share the same network structure regardless of single-category and multi-category generations except for the category embedding layer (i.e., the same network architecture is shared with all of our experiments). For point cloud input, we use the point cloud encoder from the convolutional occupancy network [53] as our point cloud encoder and combine the resulting features using AdaGN." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 362, + 286, + 541 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 362, + 286, + 541 + ], + "spans": [ + { + "bbox": [ + 46, + 362, + 286, + 541 + ], + "type": "text", + "content": "We use the Adam optimizer [28] with " + }, + { + "bbox": [ + 46, + 362, + 286, + 541 + ], + "type": "inline_equation", + "content": "\\beta_{1} = 0.9" + }, + { + "bbox": [ + 46, + 362, + 286, + 541 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 362, + 286, + 541 + ], + "type": "inline_equation", + "content": "\\beta_{2} = 0.999" + }, + { + "bbox": [ + 46, + 362, + 286, + 541 + ], + "type": "text", + "content": ", to train all of our models. We train our method with learning rate 0.0001 with learning rate warmup at the first epoch and reduce the learning rate when the validation loss is not decreased for 5 epochs. We fix the patch size to " + }, + { + "bbox": [ + 46, + 362, + 286, + 541 + ], + "type": "inline_equation", + "content": "32^{3}" + }, + { + "bbox": [ + 46, + 362, + 286, + 541 + ], + "type": "text", + "content": " for training the super-resolution model regardless of the target resolution. On the other hand, we sample the full resolution of the shape at once without using patches during the inference phase. Following [16], we set diffusion step " + }, + { + "bbox": [ + 46, + 362, + 286, + 541 + ], + "type": "inline_equation", + "content": "T = 1,000" + }, + { + "bbox": [ + 46, + 362, + 286, + 541 + ], + "type": "text", + "content": ", and linear noise scheduler with " + }, + { + "bbox": [ + 46, + 362, + 286, + 541 + ], + "type": "inline_equation", + "content": "\\beta_{0} = 0.0001" + }, + { + "bbox": [ + 46, + 362, + 286, + 541 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 362, + 286, + 541 + ], + "type": "inline_equation", + "content": "\\beta_{T} = 0.02" + }, + { + "bbox": [ + 46, + 362, + 286, + 541 + ], + "type": "text", + "content": ". We reduce sampling steps to 50 using the denoising diffusion implicit model (DDIM) [65] to accelerate sampling speed. We use the exponential moving average (EMA) following [23] for the first stage model. Flip data augmentation is applied to the super-resolution model." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 545, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 286, + 713 + ], + "type": "text", + "content": "Dataset. For evaluation, we use the ShapeNet dataset [3] (especially version 1), which consists of 13-category of 3D shapes in mesh representations. In comparison to prior work, our method requires sampled SDF in the training and evaluation phase. For this reason, we convert meshes in the ShapeNet dataset into voxel-shaped SDF similar to the dual octree graph networks [69]. Concretely, we normalize each of the watertight mesh so that it has zero center and unit scale with 0.1 padding. We then extract SDF voxels at multiple resolutions of 32 for low-resolution and 64 and 128 for high-resolution using Mesh2SDF [70]. While sampling watertight mesh, we manipulate the level set value, which is the parameter of Mesh2SDF, to approximately double cell size (i.e., 0.03125 for voxel resolution of 64). We then clip" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "content": "each of the extracted SDF voxel with minimum and maximum thresholds as the same value with double voxel size, and we utilize SDF in the form of truncated signed distance fields (T-SDF) to decrease redundant information. After that, we sample 15K points from the watertight meshes at the resolution of 64, which are used as ground truth for training point cloud-based methods and evaluation purposes. Following [69], the dataset is split into the train, validation, and test datasets. We mainly measure the quality of our method with point clouds sampled from a voxel resolution of 64 in the validation dataset like previous methods." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 206, + 545, + 302 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 206, + 545, + 302 + ], + "spans": [ + { + "bbox": [ + 304, + 206, + 545, + 302 + ], + "type": "text", + "content": "Evaluation metrics. Following the previous methods [77, 87], we use three metrics (MMD, COV, and 1-NNA [37]) based on both the Chamfer Distance (CD) and the Earth Mover's Distance (EMD) as the main evaluation metrics. MMD, COV, and 1-NNA analyze both quality and variety by quantifying the distributional similarity between the produced forms and the validation set. A detailed explanation of the evaluation method is in the supplementary material." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 305, + 545, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 305, + 545, + 449 + ], + "spans": [ + { + "bbox": [ + 304, + 305, + 545, + 449 + ], + "type": "text", + "content": "Comparison methods. To evaluate the generative ability of our model, we compare it with various methods, such as DDM-based techniques: point voxel diffusion (PVD) [87] and diffusion point cloud (DPM) [41], as well as flow-based technique, PointFlow [77]. As most of the previous methods have been trained using the ShapeNet dataset preprocessed by PointFlow, which only provides point clouds and not SDF, we re-implemented these methods to compare with our approach. It should be noted that since our dataset and PointFlow's are based on the different versions of ShapeNet, and different pre-processing methods, the results may slightly differ from those of the original papers." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 456, + 460, + 468 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 456, + 460, + 468 + ], + "spans": [ + { + "bbox": [ + 306, + 456, + 460, + 468 + ], + "type": "text", + "content": "4.1. Single-Category Generation" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 474, + 545, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 545, + 545 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 545, + 545 + ], + "type": "text", + "content": "Following previous works [41, 77, 87], we evaluate metrics for 3 models trained with each category (airplane, car, and chair) separately. To ensure a fair comparison with point clouds-based baseline methods that used 2,048 points to compute metrics, we sampled the same number of points from meshes reconstructed by our method." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 546, + 545, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 546, + 545, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 546, + 545, + 700 + ], + "type": "text", + "content": "We show the quantitative comparisons in Table 1. Our method, SDF-Diffusion demonstrated competitive performance in all categories and outperformed other baselines, especially in the 1-NNA (EMD) metric, which is the most important metric designed to overcome the limitations of MMD and COV [77]. In addition, EMD is a more distinctive metric [42] because CD tends to fail to compare point clouds with uneven density, and uniform point cloud density is important to represent 3D shapes well. Since SDF-Diffusion reconstructs continuous meshes first and then samples point clouds from the meshes, the point clouds can be evenly arranged, unlike other methods that generate point clouds directly." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "type": "text", + "content": "Figure 3 shows the qualitative comparisons with the" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20892" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 71, + 534, + 152 + ], + "blocks": [ + { + "bbox": [ + 53, + 71, + 534, + 152 + ], + "lines": [ + { + "bbox": [ + 53, + 71, + 534, + 152 + ], + "spans": [ + { + "bbox": [ + 53, + 71, + 534, + 152 + ], + "type": "image", + "image_path": "39d247d21995bb2c9b726e004359648ce44a7e0c2bb2ecd276a09bf23a14fa41.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 107, + 155, + 485, + 167 + ], + "lines": [ + { + "bbox": [ + 107, + 155, + 485, + 167 + ], + "spans": [ + { + "bbox": [ + 107, + 155, + 485, + 167 + ], + "type": "text", + "content": "Figure 4. Generated samples by SDF-Diffusion on 13-category classes of the ShapeNet dataset." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 48, + 233, + 287, + 399 + ], + "blocks": [ + { + "bbox": [ + 46, + 180, + 287, + 224 + ], + "lines": [ + { + "bbox": [ + 46, + 180, + 287, + 224 + ], + "spans": [ + { + "bbox": [ + 46, + 180, + 287, + 224 + ], + "type": "text", + "content": "Table 1. Quantitative evaluation on the ShapeNet dataset about MMD, COV, 1-NNA about 3-category. MMD, 1-NNA scores are the lower, the better, and the higher COV, the better. MMD-CD and MMD-EMD scores are multiplied by " + }, + { + "bbox": [ + 46, + 180, + 287, + 224 + ], + "type": "inline_equation", + "content": "{10}^{3}" + }, + { + "bbox": [ + 46, + 180, + 287, + 224 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 180, + 287, + 224 + ], + "type": "inline_equation", + "content": "{10}^{2}" + }, + { + "bbox": [ + 46, + 180, + 287, + 224 + ], + "type": "text", + "content": " ." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 233, + 287, + 399 + ], + "lines": [ + { + "bbox": [ + 48, + 233, + 287, + 399 + ], + "spans": [ + { + "bbox": [ + 48, + 233, + 287, + 399 + ], + "type": "table", + "html": "
TrainsetPointFlow [77]DPM [41]PVD [87]ours
AirplaneMMD (CD)1.512.432.242.462.37
COV (CD)56.9350.5050.0045.3050.25
1-NNA (CD)45.9272.2867.4562.6256.56
MMD (EMD)2.331.671.641.551.49
COV (EMD)57.4352.9752.2353.9655.20
1-NNA (EMD)47.4062.5063.3752.7248.14
CarMMD (CD)2.442.612.572.482.48
COV (CD)54.0741.9244.1944.3347.26
1-NNA (CD)49.4774.5075.5758.4858.28
MMD (EMD)1.281.391.391.301.28
COV (EMD)52.3441.9241.9248.3352.47
1-NNA (EMD)50.5371.9071.9051.1353.20
ChairMMD (CD)8.058.277.657.878.00
COV (CD)54.9546.5347.8648.8949.78
1-NNA (CD)52.8870.8366.4055.6153.69
MMD (EMD)3.574.214.083.563.61
COV (EMD)53.4749.6341.6550.3749.31
1-NNA (EMD)48.7474.7476.6653.0351.77
", + "image_path": "8d8e26a56f347f12aa512f49c4aa445008fd8eed8fd406f0bed7868214462695.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 407, + 287, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 407, + 287, + 443 + ], + "spans": [ + { + "bbox": [ + 46, + 407, + 287, + 443 + ], + "type": "text", + "content": "baseline methods. SDF-Diffusion generates plausible 3D shapes like the other approaches; especially, we can directly produce continuous 3D meshes." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 454, + 200, + 467 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 454, + 200, + 467 + ], + "spans": [ + { + "bbox": [ + 47, + 454, + 200, + 467 + ], + "type": "text", + "content": "4.2. Multi-Category Generation" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 473, + 287, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 473, + 287, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 473, + 287, + 640 + ], + "type": "text", + "content": "In addition to single-category, our SDF-Diffusion is seamlessly extended to multi-category generation using category information. We train and compare our SDF-Diffusion on the 13 categories of the ShapeNet dataset: airplane, bench, cabinet, car, chair, display, lamp, loudspeaker, rifle, sofa, table, telephone, and vessel, by conditioning on the category information " + }, + { + "bbox": [ + 46, + 473, + 287, + 640 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 473, + 287, + 640 + ], + "type": "text", + "content": ". As shown in Fig. 4, SDF-Diffusion generates multicategory detailed 3D shapes with high-quality and diversity. Furthermore, we can perform the second stage (i.e., super-resolution) multiple times to generate much higher-resolution samples. Figure 5 illustrates the 3D shapes generated using multiple super-resolution stages, allowing us to achieve " + }, + { + "bbox": [ + 46, + 473, + 287, + 640 + ], + "type": "inline_equation", + "content": "128^{3}" + }, + { + "bbox": [ + 46, + 473, + 287, + 640 + ], + "type": "text", + "content": " resolution SDF voxels." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 642, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 288, + 713 + ], + "type": "text", + "content": "To assess the generation quality of multi-category generation, we compare our model with PVD, which is a diffusion-based state-of-the-art 3D shape generation method. However, PVD and other baselines are designed for only single-category generation. So, we compare ours with the modified version of PVD (PVD* in short) that can" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 307, + 223, + 544, + 388 + ], + "blocks": [ + { + "bbox": [ + 304, + 180, + 545, + 214 + ], + "lines": [ + { + "bbox": [ + 304, + 180, + 545, + 214 + ], + "spans": [ + { + "bbox": [ + 304, + 180, + 545, + 214 + ], + "type": "text", + "content": "Table 2. Quantitative evaluation on the ShapeNet dataset through 1-NNA about CD and EMD with 13-category. PVD* denotes the modified version of PVD for multi-category." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 223, + 544, + 388 + ], + "lines": [ + { + "bbox": [ + 307, + 223, + 544, + 388 + ], + "spans": [ + { + "bbox": [ + 307, + 223, + 544, + 388 + ], + "type": "table", + "html": "
Category1-NNA (CD)1-NNA (EMD)
PVD*ourstrainsetPVD*ourstrainset
Airplane67.2070.7945.9257.9258.0447.40
Bench62.4360.2253.3159.6757.4654.14
Cabinet62.1062.7447.1368.1563.0650.96
Car64.5566.2949.4757.8955.8150.53
Chair61.8963.2352.8859.4059.3348.74
Display61.4744.5051.8358.2653.2152.29
Lamp58.8758.0149.1361.0456.2851.95
Loudspeaker59.3257.1448.1457.4554.7652.17
Rifle61.3960.5450.0058.4453.5949.79
Sofa58.0452.8451.5854.5750.6347.32
Table62.4155.7649.7161.8256.3551.00
Telephone60.0057.1448.5755.7154.7650.95
Vessel59.5959.8451.5558.2954.1550.78
Average61.4859.1649.9459.1255.9650.62
", + "image_path": "a1357917a71b370bc6cec239702caf2921abf5f3e7f00b37e769ad82d00951bf.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 396, + 545, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 396, + 545, + 517 + ], + "spans": [ + { + "bbox": [ + 304, + 396, + 545, + 517 + ], + "type": "text", + "content": "receive a category condition with MLPs with Embedding layers similar to ours but without AdaGN to preserve the timestep embedding method of the original PVD. Quantitative results are shown in Table 2. The results of PVD* and SDF-Diffusion are trained equally for 1,000 epochs for only multi-category case. SDF-Diffusion shows better results in most categories about 1-NNA metric, especially outperforming EMD-based metrics. Additional qualitative comparisons on the mesh domain will be discussed in the supplementary material." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 526, + 477, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 526, + 477, + 540 + ], + "spans": [ + { + "bbox": [ + 305, + 526, + 477, + 540 + ], + "type": "text", + "content": "4.3. Application: Shape Completion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 545, + 545, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 545, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 545, + 700 + ], + "type": "text", + "content": "We show the applicability of our SDF-Diffusion on another task: 3D shape completion with voxel condition. Without modification of network architecture, we show that our method can be applied to 3D shape completion. Specifically, the second stage of our method takes a voxel-shaped condition by concatenating the conditional input (i.e., low-resolution SDF generated by the first stage) with noisy data to denoise. In other words, let the SDF voxel be a single-channel, then we can consider the second stage of our model takes two-channel input and returns a single-channel output. Therefore, using the same network architecture, we can seamlessly train a shape completion model by giving a partial SDF voxel instead of a low-resolution condition." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "text", + "content": "For partial 3D shapes, we perform a 3D shape comple" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20893" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 69, + 282, + 232 + ], + "blocks": [ + { + "bbox": [ + 52, + 69, + 282, + 232 + ], + "lines": [ + { + "bbox": [ + 52, + 69, + 282, + 232 + ], + "spans": [ + { + "bbox": [ + 52, + 69, + 282, + 232 + ], + "type": "image", + "image_path": "5c7e6ea64402cf503e4f0ffbed5cc305f2ead9b5a5f65e2f3f26fcb62d14806c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 242, + 287, + 297 + ], + "lines": [ + { + "bbox": [ + 46, + 242, + 287, + 297 + ], + "spans": [ + { + "bbox": [ + 46, + 242, + 287, + 297 + ], + "type": "text", + "content": "Figure 5. Visualization of generated 3D shapes at different resolutions. The first stage model generates coarse shapes in the resolution of " + }, + { + "bbox": [ + 46, + 242, + 287, + 297 + ], + "type": "inline_equation", + "content": "32^{3}" + }, + { + "bbox": [ + 46, + 242, + 287, + 297 + ], + "type": "text", + "content": ". By performing super-resolution using our second stage model multiple times, we can obtain improved shape detail of 3D shapes with the voxel resolutions of " + }, + { + "bbox": [ + 46, + 242, + 287, + 297 + ], + "type": "inline_equation", + "content": "64^{3}" + }, + { + "bbox": [ + 46, + 242, + 287, + 297 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 242, + 287, + 297 + ], + "type": "inline_equation", + "content": "128^{3}" + }, + { + "bbox": [ + 46, + 242, + 287, + 297 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 307, + 287, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 307, + 287, + 354 + ], + "spans": [ + { + "bbox": [ + 46, + 307, + 287, + 354 + ], + "type": "text", + "content": "tion based on SDF-Diffision, as shown in Fig. 6. As you can see, we can generate various 3D shapes from given partial 3D shapes, which shows the applicability and flexibility of the proposed SDF-Diffision." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 356, + 289, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 356, + 289, + 571 + ], + "spans": [ + { + "bbox": [ + 46, + 356, + 289, + 571 + ], + "type": "text", + "content": "In addition, we also demonstrate the generality of our SDF-Diffusion by using it for the task of 3D shape completion with a partially observed point cloud as a condition. To generate the partial point cloud input, we randomly sample 200 points from the preprocessed ShapeNet dataset using the same method employed in [82]. For out-of-distribution data, we acquire partial point clouds from depth images of the Redwood 3DScans dataset [9]. As the point cloud has a different format than the voxel feature generated by our SDF-Diffusion, we incorporate an additional layer to extract and voxelize the point cloud. Specifically, we employ the PointNet layer [55] from the encoder of the convolutional occupancy network [53], which transforms the point cloud feature into a voxel and gives this feature to each layer of SDF-Diffusion along with the AdaGN. The completed 3D shapes are visualized in Fig. 7. We show SDF-Diffusion can successfully apply unseen out-of-distribution data." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 585, + 119, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 585, + 119, + 597 + ], + "spans": [ + { + "bbox": [ + 47, + 585, + 119, + 597 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": "In this work, we have proposed SDF-Diffusion, a novel diffusion-based SDF generation approach for 3D shapes. SDF-Diffusion composed of two-stage generates low-resolution SDF and then produces high-resolution SDF conditioned on the low-resolution one. For memory efficiency, we learn the second stage of SDF-Diffusion (i.e., super-resolution) in a patch-wise manner, which allows us to perform super-resolution several times in high-resolution. In addition, SDF-Diffusion can be seam-" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 310, + 69, + 543, + 261 + ], + "blocks": [ + { + "bbox": [ + 310, + 69, + 543, + 261 + ], + "lines": [ + { + "bbox": [ + 310, + 69, + 543, + 261 + ], + "spans": [ + { + "bbox": [ + 310, + 69, + 543, + 261 + ], + "type": "image", + "image_path": "429be4ce4096abf33a75265f0d5d8521ca7488f7563e92a559c5418ea3c7b88c.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 272, + 545, + 316 + ], + "lines": [ + { + "bbox": [ + 305, + 272, + 545, + 316 + ], + "spans": [ + { + "bbox": [ + 305, + 272, + 545, + 316 + ], + "type": "text", + "content": "Figure 6. Generated 3D shapes by 3D shape completion. SDF-Diffusion can be easily expanded to a 3D shape completion task by modifying only the input head of the network architecture." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 308, + 340, + 543, + 456 + ], + "blocks": [ + { + "bbox": [ + 308, + 340, + 543, + 456 + ], + "lines": [ + { + "bbox": [ + 308, + 340, + 543, + 456 + ], + "spans": [ + { + "bbox": [ + 308, + 340, + 543, + 456 + ], + "type": "image", + "image_path": "8292048ba36c038f2bb36b39d5d89edf89b7c4d6fdd42c111fcd8e5557cb3b2c.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 470, + 545, + 504 + ], + "lines": [ + { + "bbox": [ + 305, + 470, + 545, + 504 + ], + "spans": [ + { + "bbox": [ + 305, + 470, + 545, + 504 + ], + "type": "text", + "content": "Figure 7. Generated 3D shapes by 3D shape completion on out-of-distribution data. SDF-Diffusion shows various completion candidates from out-of-distribution partial point clouds." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 513, + 545, + 562 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 513, + 545, + 562 + ], + "spans": [ + { + "bbox": [ + 305, + 513, + 545, + 562 + ], + "type": "text", + "content": "lessly extended to multi-category 3D shape generation and 3D shape completion. Experiments demonstrate that the proposed method can generate high-quality 3D shapes in the SDF domain with superior generative power." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "content": "Acknowledgments. This work was supported by Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) (No. 2022-0-00612, Geometric and Physical Commonsense Reasoning based Behavior Intelligence for Embodied AI, No.2022-0-00907, Development of AI Bots Collaboration Platform and Self-organizing AI and No.2020-0-01336, Artificial Intelligence Graduate School Program (UNIST)) and Artificial intelligence industrial convergence cluster development project funded by the Ministry of Science and ICT (MSIT, Korea) & Gwangju Metropolitan City." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20894" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 92, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 18, + "blocks": [ + { + "bbox": [ + 53, + 92, + 287, + 125 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 92, + 287, + 125 + ], + "spans": [ + { + "bbox": [ + 53, + 92, + 287, + 125 + ], + "type": "text", + "content": "[1] Panos Achlioptas, Olga Diamanti, Ioannis Mitliagkas, and Leonidas Guibas. 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In CVPR, 2021. 1, 3, 6, 7" + } + ] + } + ], + "index": 15 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20897" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Diffusion-SDF_ Text-To-Shape via Voxelized Diffusion/a08ad0f7-f625-4886-ac27-deeab3818eeb_content_list.json b/2023/Diffusion-SDF_ Text-To-Shape via Voxelized Diffusion/a08ad0f7-f625-4886-ac27-deeab3818eeb_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..2430b8801bef9d1cab853bb6fff35b95bf035e23 --- /dev/null +++ b/2023/Diffusion-SDF_ Text-To-Shape via Voxelized Diffusion/a08ad0f7-f625-4886-ac27-deeab3818eeb_content_list.json @@ -0,0 +1,1502 @@ +[ + { + "type": "text", + "text": "Diffusion-SDF: Text-to-Shape via Voxelized Diffusion", + "text_level": 1, + "bbox": [ + 215, + 130, + 756, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Muheng Li $^{1}$ , Yueqi Duan $^{\\dagger,2}$ , Jie Zhou $^{1}$ , Jiwen Lu $^{1}$", + "bbox": [ + 285, + 179, + 681, + 198 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ Department of Automation, Tsinghua University", + "bbox": [ + 289, + 198, + 681, + 217 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ Department of Electronic Engineering, Tsinghua University", + "bbox": [ + 245, + 217, + 723, + 234 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/6f39f28fd0259c09807bc049bec6f6c39d108427572e4ac27dfb77e6bcfe045d.jpg", + "image_caption": [ + "Figure 1. We propose a text-to-shape synthesis approach named Diffusion-SDF. Our method is capable of performing various text-to-shape tasks including text-to-shape generation (directly generating 3D shapes from texts), text-guided shape completion (generating the missing part of an incomplete shape under the guidance of texts), and text-guided shape manipulation (modifying a given shape according to texts)." + ], + "image_footnote": [], + "bbox": [ + 81, + 253, + 883, + 420 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 482, + 313, + 498 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "With the rising industrial attention to 3D virtual modeling technology, generating novel 3D content based on specified conditions (e.g. text) has become a hot issue. In this paper, we propose a new generative 3D modeling framework called Diffusion-SDF for the challenging task of text-to-shape synthesis. Previous approaches lack flexibility in both 3D data representation and shape generation, thereby failing to generate highly diversified 3D shapes conforming to the given text descriptions. To address this, we propose a SDF autoencoder together with the Voxelized Diffusion model to learn and generate representations for voxelized signed distance fields (SDFs) of 3D shapes. Specifically, we design a novel UinU-Net architecture that implants a local-focused inner network inside the standard U-Net architecture, which enables better reconstruction of patch-independent SDF representations. We extend our approach to further text-to-shape tasks including text-conditioned shape completion and manipulation. Experimental results show that Diffusion-SDF generates both higher quality and more diversified 3D shapes that conform well to given text descriptions when compared to previous approaches. Code is available at: https://github.com/ttlmh/Diffusion-SDF.", + "bbox": [ + 73, + 513, + 473, + 863 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 501, + 482, + 632, + 497 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Exploring data representations for 3D shapes has been a fundamental and critical issue in 3D computer vision. Explicit 3D representations including point clouds [38, 39], polygon meshes [17, 24] and occupancy voxel grids [9, 53] have been widely applied in various 3D downstream applications [1, 35, 56]. While explicit 3D representations achieve encouraging performance, there are some primary limitations including not being suitable for generating watertight surfaces (e.g. point clouds), or being subject to topological constraints (e.g. meshes). On the other hand, implicit 3D representations have been widely studied more recently [3, 14, 37], with representative works including DeepSDF [37], Occupancy Network [32] and IM-Net [8]. In general, implicit functions encode the shapes by the isosurface of the function, which is a continuous field and can be evaluated at arbitrary resolution.", + "bbox": [ + 496, + 507, + 893, + 748 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In recent years, numerous explorations have been conducted for implicit 3D generative models, which show promising performance on several downstream applications such as single/multi-view 3D reconstruction [23, 54] and shape completion [12, 34]. Besides, several studies have also explored the feasibility of directly generating novel 3D shapes based on implicit representations [15, 21]. However, these approaches are incapable of generating specified 3D shapes that match a given condition, e.g. a short text describing the shape characteristics as shown in Figure 1.", + "bbox": [ + 496, + 750, + 895, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "†Corresponding author.", + "bbox": [ + 102, + 886, + 228, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "12642", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Text-based visual content synthesis has the advantages of the flexibility and generality [41, 42]. Users may generate rich and diverse 3D shapes based on easily obtained natural language descriptors. In addition to generating 3D shapes directly based on text descriptions, manipulating 3D data with text guidance can be further utilized for iterative 3D synthesis and fine-grained 3D editing, which can be beneficial for non-expert users to create 3D visual content.", + "bbox": [ + 75, + 90, + 470, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In the literature, there have been few attempts on the challenging task of text-to-shape generation based on implicit 3D representations [29, 34, 48]. For example, AutoSDF [34] introduced a vector quantized SDF autoencoder together with an autoregressive generator for shape generation. While encouraging progress has been made, the quality and diversity of generated shapes still requires improvement. The current approaches struggle to generate highly diversified 3D shapes that both guarantee generation quality and conform to the semantics of the input text. Motivated by the success of denoising diffusion models in 2D image [13, 19, 36] and even explicit 3D point cloud [31, 58, 59] generation, we find that DMs achieve high-quality and highly diversified generation while being robust to model training. To this end, we aim to design an implicit 3D representation-based generative diffusion process for text-to-shape synthesis that can achieve better generation flexibility and generalization performance.", + "bbox": [ + 75, + 212, + 470, + 484 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we propose the Diffusion-SDF framework for text-to-shape synthesis based on truncated signed distance fields (TSDFs). Considering that 3D shapes share structural similarities at local scales, and the cubic data volume of 3D voxels may lead to slow sampling speed for diffusion models, we propose a two-stage separated generation pipeline. First, we introduce a patch-based SDF autoencoder that maps the original signed distance fields into patch-independent local Gaussian latent representations. Second, we introduce the Voxelized Diffusion model that captures the intra-patch information along with both patch-top-patch and patch-to-global relations. Specifically, we design a novel UinU-Net architecture to replace the standard U-Net [46] for the noise estimator in the reverse process. UinU-Net implants a local-focused inner network inside the outer U-Net backbone, which takes into account the patch-independent prior of SDF representations to better reconstruct local patch features from noise. Our work digs deeper into the further potential of diffusion model-based approaches towards text-conditioned 3D shape synthesis based on voxelized TSDFs. Experiments on the largest existing text-shape dataset [6] show that our Diffusion-SDF approach achieves promising generation performance on text-to-shape tasks compared to existing state-of-the-art approaches, in both qualitative and quantitative evaluations.", + "bbox": [ + 75, + 486, + 470, + 863 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 89, + 640, + 106 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Text-conditioned generative 3D models. In the field of generative 3D modeling, a variety of works have focused on synthesizing 3D visual content unconditionally [1, 32, 52, 56] or conditioned on single/multi-view images [9, 34, 54, 55]. Besides, there has also been a series of works concentrating on the challenging task of text-to-shape generation [6]. Some of them adopted purely explicit 3D data representation-based methods to generate 3D shapes conditioned on input text [6, 33, 58]. In contrast, our focus lies on synthesizing 3D shapes based on implicit 3D data representations. So far, there have also been few existing works focusing on the task of implicit text-to-shape generation [29, 34, 48]. All of these approaches have yielded impressive generation results, but there are still some remained issues to be addressed. Sanghi et al. [48] proposed a normalizing flow [43]-based approach to generate shape voxels using implicit Occupancy Networks [32], and Liu et al. [29] introduced a shape-IMLE [28] generator using implicit IMNET [8] decoder, while these approaches neither employ the more flexible implicit SDFs as data representation nor take into account the constraints for local shape structures. More similar to our work, AutoSDF [34] introduced an autoregressive prior for 3D shape generation based on a discretized SDF autoencoder. The autoregressive model adopts a relatively unnatural way to predict patched 3D tokens in a sequential manner that loses the 3D-specific inductive bias and is also relatively inefficient.", + "bbox": [ + 496, + 122, + 893, + 531 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Diffusion Probabilistic Models. Diffusion Probabilistic Models (DPMs) [19, 49], also known as diffusion models, have currently arisen as a powerful family of generative models. Compared to previous state-of-the-art generative models, including Generative Adversarial Network (GAN) [16], Variational Autoencoder (VAE) [26], and flow-based generative models [43], the diffusion model demonstrates its superiority in both training stability and generative diversity [11]. Diffusion models have achieved promising performance on image [13, 19, 36, 45] and speech [7, 27] synthesis. Especially, fairly impressive results have been achieved with diffusion model-based approaches on the task of text-to-image synthesis [41, 45, 47]. In the field of 3D computer vision, several studies have adopted diffusion models for generative 3D modeling [31, 58, 59]. PVD [59] employed diffusion models to generate 3D shapes based on point-voxel 3D representation. Luo et al. [31] treated points in point clouds as particles in a thermodynamic system with a heat bath. LION [58] introduced a VAE framework with hierarchical diffusion models in latent space. All these approaches have focused on the diffusion process of explicit 3D data representations for shape generation. On the contrary, our work tries to explore the feasibility of diffusion models on implicit 3D data representations.", + "bbox": [ + 496, + 537, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_footnote", + "text": "Strictly speaking, our approach employs a combined explicit-implicit representation in the form of voxelized signed distance fields.", + "bbox": [ + 75, + 875, + 470, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "12643", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/c0ef4f7890d6a75ea23def4e026769d2f0d1dfbea590d0e9ef19f57fa1ff4b77.jpg", + "image_caption": [ + "Figure 2. Overview of Diffusion-SDF. We propose a two-stage pipeline to generate novel 3D shapes from texts. First, we train an autoencoder to learn patch-independent normal-distributed representations for voxelized TSDFs. Then, we propose the Voxelized Diffusion framework together with the UinU-Net denoiser to generate shape representations. Please check Figure 3 for more details of UinU-Net." + ], + "image_footnote": [], + "bbox": [ + 91, + 90, + 885, + 351 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 412, + 169, + 428 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we introduce the methodology design for Diffusion-SDF. In general, we propose a two-stage pipeline as illustrated in Figure 2. Detailed information of each stage will be included in the following sections.", + "bbox": [ + 75, + 439, + 470, + 501 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Autoencoding Signed Distance Fields", + "text_level": 1, + "bbox": [ + 76, + 512, + 397, + 529 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Signed distance fields (SDF) belong to a type of implicit 3D data representation which assigns the scalar signed distance value to the shape surface for each point $p$ in the 3D space $\\mathbb{R}^3$ . Our objective is to generate the signed distance fields for the target 3D shapes that match the given text conditions. Specifically, the 3D data are represented by truncated signed distance functions (TSDF) in a regularly-spaced voxel grid as [3, 22]. Generating voxelized SDFs directly from denoising diffusion models is both cost-expensive and time-consuming. In addition, the local structural information of 3D shapes is not well-emphasized through direct voxel-based generation. To address this, we propose a patch-wise autoencoder to learn the latent representations for voxelized signed distance fields.", + "bbox": [ + 75, + 537, + 468, + 748 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a 3D shape, we first sample its truncated signed distance field $x$ as a voxel grid of size $D^3$ . Before the shape $x$ is encoded, it is first split into $N$ local patches of size $P^3$ , producing a sequence of shape patches $X_p = [x_{p1},\\dots,x_{pN}]$ , where $N = (D / P)^3$ is the resulting number of patches. Then, the local shape encoder $\\mathcal{E}_{loc}$ encodes each shape patches into latent representations $Z_p = [z_{p1},\\dots,z_{pN}]$ , where $z_{pn} = \\mathcal{E}_{loc}(x_{pn}) \\in \\mathbb{R}^c$ , and $c$ is the number of latent channels. Here, since each patch is encoded independently, the local structural information can be", + "bbox": [ + 75, + 750, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "explored well through the local shape encoder. Meanwhile, the input data scale can also be downsampled by the factor $P$ . However, when reconstructing the shape from local patches, it is also necessary to consider the spatial location of each patch in the global shape, and the interrelationship between adjacent patches. To preserve both patch-to-global and patch-to-patch information while decoding the latent embeddings, the patch embeddings are first rearranged into a voxel grid embedding $z$ , and then sent into the patch-joint decoder $\\mathcal{D}$ that reconstructs the SDF field from the latent patches, giving $\\tilde{x} = \\mathcal{D}(z)$ .", + "bbox": [ + 496, + 414, + 893, + 582 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In detail, we adopt a VAE [26, 44]-like autoencoder, which encodes each shape patch into a normal distribution. We utilize a combination of both $\\mathcal{L}_1$ reconstruction loss together with the KL-regularization loss at the training stage for the SDF autoencoder. The latter one forces a mild KL-penalty towards a standard normal distribution on each learned patch latent. The final SDF representations will be in the form of patch-independent Gaussian distributions.", + "bbox": [ + 496, + 589, + 893, + 712 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Voxelized Diffusion Models (VDMs)", + "text_level": 1, + "bbox": [ + 500, + 747, + 812, + 763 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Diffusion models (DMs) [19, 49] are a class of probabilistic generative models that learn to fit a certain distribution by gradually denoising a Gaussian variable through a fixed Markov Chain of length $T$ . Given a data sample $x_0 \\sim q(x_0)$ , DMs describe two different processes in the opposite direction: a forward process $q(\\mathbf{x}_{0:T})$ that gradually transform a data sample into pure Gaussian noise, and a reverse process $p_{\\theta}(\\mathbf{x}_{0:T})$ that gradually denoise a pure", + "bbox": [ + 496, + 779, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "12644", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Gaussian sample into real data,", + "bbox": [ + 76, + 90, + 287, + 107 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(\\boldsymbol {x} _ {0: T}\\right) = q \\left(\\boldsymbol {x} _ {0}\\right) \\Pi_ {t = 1} ^ {T} q \\left(\\boldsymbol {x} _ {t} \\mid \\boldsymbol {x} _ {t - 1}\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 147, + 117, + 468, + 142 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\theta} \\left(\\boldsymbol {x} _ {0: T}\\right) = p \\left(\\boldsymbol {x} _ {T}\\right) \\Pi_ {t = 1} ^ {T} p _ {\\theta} \\left(\\boldsymbol {x} _ {t - 1} | \\boldsymbol {x} _ {t}\\right),\n$$\n", + "text_format": "latex", + "bbox": [ + 142, + 138, + 403, + 156 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $q(\\pmb{x}_t|\\pmb{x}_{t-1})$ and $p_\\theta(\\pmb{x}_{t-1}|\\pmb{x}_t)$ are both Gaussian transition probabilities in the forms of", + "bbox": [ + 76, + 167, + 468, + 198 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(\\boldsymbol {x} _ {t} \\mid \\boldsymbol {x} _ {t - 1}\\right) = \\mathcal {N} \\left(\\boldsymbol {x} _ {t}; \\sqrt {1 - \\beta_ {t}} \\boldsymbol {x} _ {t - 1}, \\beta_ {t} \\boldsymbol {I}\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 125, + 209, + 468, + 238 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\theta} \\left(\\boldsymbol {x} _ {t - 1} | \\boldsymbol {x} _ {t}\\right) = \\mathcal {N} \\left(\\boldsymbol {x} _ {t - 1}; \\boldsymbol {\\mu} _ {\\theta} \\left(\\boldsymbol {x} _ {t}, t\\right), \\beta_ {t} \\boldsymbol {I}\\right).\n$$\n", + "text_format": "latex", + "bbox": [ + 120, + 238, + 406, + 253 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Based on [19], the mean variable $\\pmb{\\mu}_{\\theta}(\\pmb{x}_t,t)$ for the reverse transition $p_{\\theta}\\left(\\pmb{x}_{t - 1}|\\pmb{x}_t\\right)$ can be expressed in the form of", + "bbox": [ + 76, + 265, + 468, + 297 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\mu} _ {\\theta} \\left(\\boldsymbol {x} _ {t}, t\\right) = \\frac {1}{\\sqrt {\\alpha_ {t}}} \\left(\\boldsymbol {x} _ {t} - \\frac {\\beta_ {t}}{\\sqrt {1 - \\bar {\\alpha} _ {t}}} \\boldsymbol {\\epsilon} _ {\\theta} \\left(\\boldsymbol {x} _ {t}, t\\right)\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 104, + 306, + 468, + 342 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\alpha_{t} = 1 - \\beta_{t}$ , $\\bar{\\alpha}_{t} = \\Pi_{i=1}^{t} \\alpha_{i}$ , and $\\beta_{t}$ decreases to 0 gradually as $t$ approaches 0. The evidence lower bound (ELBO) is maximized at the training stage of DMs, eventually leading to the loss function as the form of", + "bbox": [ + 76, + 352, + 468, + 412 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {D M} = \\mathbb {E} _ {\\boldsymbol {x}, t, \\boldsymbol {\\epsilon} \\sim \\mathcal {N} (0, 1)} \\left[ \\| \\boldsymbol {\\epsilon} - \\boldsymbol {\\epsilon} _ {\\theta} (\\boldsymbol {x} _ {t}, t) \\| ^ {2} \\right], \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 127, + 422, + 468, + 450 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\pmb{x}_t = \\sqrt{\\bar{\\alpha}_t}\\pmb{x}_0 + \\sqrt{1 - \\bar{\\alpha}_t}\\pmb{\\epsilon},$ $\\pmb{\\epsilon}$ is a noise variable, and $t$ is uniformly sampled from $\\{1,\\dots,T\\}$ . The neural network-based score estimator $\\pmb{\\epsilon}_{\\theta}(\\pmb{x}_t,t)$ is the core function of denoising diffusion models, which is implemented as a timestep-conditioned denoising autoencoder in [19].", + "bbox": [ + 76, + 460, + 468, + 537 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "UinU-Net Architecture. In our scenario, we are designing a novel diffusion-based architecture to generate latent SDF representations with regard to the target text conditions. The corresponding TSDF fields can be then reconstructed through the patch-joint decoder which is pre-trained in the first stage. As we mentioned in the above section, the key part of generative diffusion models is to estimate the function approximator $\\epsilon_{\\theta}$ from the data distribution of the training set. Since our model is designed to generate latent samples, the score estimator can be expressed as $\\epsilon_{\\theta}(z_t,t)$ , as the loss function becomes", + "bbox": [ + 76, + 537, + 468, + 703 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {D i f f u s i o n - S D F}} = \\mathbb {E} _ {z, t, \\epsilon \\sim \\mathcal {N} (0, 1)} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} (z _ {t}, t) \\| ^ {2} \\right]. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 710, + 468, + 748 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To incorporate the 3D positional prior of different latent shape patches, we adopt a 3D U-Net [10]-based autoencoder as the neural function approximator $\\epsilon_{\\theta}$ that directly learns to denoise the voxel grid embedding $z_{t}$ that is obtained from the pre-trained local shape encoder $\\mathcal{E}_{loc}$ . Besides, another crucial prior for our design is the patch-based encoding process, through which all the shape patches are encoded into independent Gaussian distributions. Thus, when generating the local shape embeddings, an important point is to recover the independent distribution for", + "bbox": [ + 76, + 750, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/df50bd5778b88bd489565e43d60675f0101589c569fe450b87b75060d189167b.jpg", + "image_caption": [ + "Figure 3. Detailed illustration of UinU-Net. To better recover $z$ based on independently distributed patches, we propose to implant an inner network inside the standard U-Net architecture. The inner network is mainly composed of $1 \\times 1 \\times 1$ convolutions, thus it focuses on patch-wise features, while the spatial transformer brings in patch-to-patch information. (Standard U-Net operators include $3 \\times 3 \\times 3$ residual blocks, conditional cross-attention layers, pooling layers and up-scaling layers.)" + ], + "image_footnote": [], + "bbox": [ + 509, + 90, + 883, + 344 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "each shape patch as well. To address this, we propose a novel UinU-Net architecture for the implementation of the autoencoder-based neural score estimator as shown in Figure 3. The standard 3D U-net [10] adopts a series of $3 \\times 3 \\times 3$ convolutional layers to construct a downsampling-upsampling network architecture with the information shared through skip connections. This design takes into account the patch-to-patch and patch-to-global features via hierarchical receptive fields. Given that our input data are compressed 3D latent representations, and each patch is encoded independently, we propose to implant another inner network inside the outer U-Net architecture where the embedded resolution is equal to the original latent resolution $D / P$ . Specifically, we adopt a $1 \\times 1 \\times 1$ convolution-based ResNet [18] structure to learn independent patch-focused information. We also introduce the spatial Transformer [51] network that accepts positional embedded patch representations as input tokens, following self-attention layers to capture the relational information between independent local patch embeddings. The inner synthesis paths are skip-connected to the outer ones, ensuring information transmission from inner to outer networks. This architecture is designed to capture the intra-patch information along with both patch-to-patch and patch-to-global relations.", + "bbox": [ + 496, + 491, + 892, + 868 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Text-Guided Shape Generation So far, we have discussed the generative process without text conditions. To synthe-", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "12645", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "size latent SDF representations based on given conditions, we introduce a conditioning mechanism based on classifier-free guidance diffusion [20]. We adopt a text-conditioned score estimator. In detail, to fit the target conditions into the 3D denoising autoencoder, we utilize the cross-attention mechanism as proposed in [45]. The input caption is first encoded as text embeddings through a pre-trained text encoder $\\tau$ . Thus, the conditioned score can be formed as $\\epsilon_{\\theta}(z_t|\\tau(c))$ , where $c$ is the input caption. Meanwhile, we also obtain an unconditioned score $\\epsilon_{\\theta}(z_t|\\emptyset)$ with an empty sequence as input caption. Within the guided diffusion sampling process, the output of the model is extrapolated further in the direction of $\\epsilon_{\\theta}(z_t|\\tau(c))$ and away from $\\epsilon_{\\theta}(z_t|\\emptyset)$ as:", + "bbox": [ + 75, + 90, + 472, + 287 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\epsilon} _ {\\theta} \\left(z _ {t} | \\tau (c)\\right) = \\epsilon_ {\\theta} \\left(z _ {t} | \\emptyset\\right) + s \\cdot \\left(\\epsilon_ {\\theta} \\left(z _ {t} | \\tau (c)\\right) - \\epsilon_ {\\theta} \\left(z _ {t} | \\emptyset\\right)\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 294, + 468, + 325 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $s \\geq 1$ refers to the guidance scale.", + "bbox": [ + 76, + 325, + 349, + 340 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Text-Guided Shape Completion Current shape completion approaches mainly focused on recovering the full shapes from partial input shapes or single view images [1, 57, 59]. Besides, we have explored the feasibility of text-conditioned shape completion. According to the patch-based design of our SDF encoder, information for the given shape patches can be encoded even if some of the patches are missing. Motivated by the success of diffusion model-based image inpainting [30, 45], we introduce a mask-diffusion strategy to generate the missing shape based on a pre-trained VDM. The core idea is to incorporate known information into each denoising step of the reverse process. For a full shape representation, we transform it into a partial shape representation given the mask $m_z$ . For each estimation step $z_{t-1}$ , we combine the estimated result through the reverse process $\\widetilde{z}_{t-1}$ with the forward sampling result of the unmasked patches $\\hat{z}_{t-1}$ ,", + "bbox": [ + 75, + 340, + 472, + 598 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nz _ {t - 1} = (1 - m) \\odot \\widetilde {z} _ {t - 1} + m \\odot \\hat {z} _ {t - 1}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 145, + 604, + 468, + 622 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\odot$ refers to element-wise product, and", + "bbox": [ + 76, + 628, + 375, + 643 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{c} \\widetilde {z} _ {t - 1} \\sim \\mathcal {N} (\\boldsymbol {\\mu} _ {\\theta} (z _ {t}, t, c), \\beta_ {t} \\boldsymbol {I}) \\\\ \\hat {\\quad} \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\end{array} \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 171, + 651, + 468, + 676 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {z} _ {t - 1} = \\sqrt {\\bar {\\alpha} _ {t}} z _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon .\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 672, + 367, + 688 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "By such a strategy, the unknown region can be recovered based on both the given shape and text conditions.", + "bbox": [ + 76, + 696, + 468, + 724 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Text-Guided Shape Manipulation Visual content editing is one of the most valuable applications for vision-language generation. We propose a diffusion-based text-guided shape manipulation approach. For a given shape representation $z_{init}$ , our goal is to transform it into another shape representation $z_{goal}$ based on text $c$ . Inspired by image manipulation techniques [4, 25], we use a cycle-sampling strategy based on a pre-trained VDM. Firstly, we forward-sample the given shape $z_{init}$ for $t_{mid}$ steps, where $0 < t_{mid} < T$ . This operation will lead to an intermediate output $z_{mid}$", + "bbox": [ + 76, + 726, + 472, + 878 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nz _ {m i d} = \\sqrt {\\bar {\\alpha} _ {t _ {m i d}}} z _ {i n i t} + \\sqrt {1 - \\bar {\\alpha} _ {t _ {m i d}}} \\epsilon . \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 142, + 883, + 468, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Then, the reverse process will start from $z_{mid}$ , and another $t_{mid}$ denoising steps will be conducted conditioned on $c$ . Such a design will make the generated shapes correspond to the target text descriptions while maintaining the original shape characteristics.", + "bbox": [ + 496, + 90, + 893, + 167 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 498, + 179, + 633, + 196 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We extensively experimented with our proposed Diffusion-SDF on various text-conditioned 3D shape synthesis tasks, such as text-to-shape generation, text-conditioned shape completion, and text-guided shape manipulation. The following subsections describe details of experimental settings, results, and analyses.", + "bbox": [ + 496, + 204, + 893, + 294 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Dataset. We mainly trained and evaluated our approach on the current largest text-shape dataset Text2Shape (T2S) [6]. T2S gathered data in the form of shape-text pairs based on two object classes (chairs, tables) in ShapeNet [5]. T2S contains about 75K shape-text pairs in total ( $\\sim$ 30K for chairs, $\\sim$ 40K for tables), with an average of $\\sim$ 16 words per description. T2S was originally designed to contain both color and shape information within the text descriptions, while we mainly focus on text-shape correspondence.", + "bbox": [ + 496, + 295, + 890, + 430 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation details. For the training stage of the SDF autoencoder, to improve the model's generalization ability, we trained the autoencoder across the 13 categories of ShapeNet [5] dataset. For the input data, we sampled the voxelized SDF from original shapes with $64 \\times 64 \\times 64$ grid points, which is also the data size adopted for follow-up operations. For the diffusion stage, to facilitate the generative sampling speed, we adopt the DDIM [50] sampler to reduce the original DDPM sampling steps from $T = 1000$ to 50. For the conditioning mechanism, we adopt a freeze CLIP [40] text encoder $\\tau$ .", + "bbox": [ + 496, + 431, + 893, + 598 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Text-Conditioned Shape Generation", + "text_level": 1, + "bbox": [ + 498, + 604, + 815, + 622 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The most immediate application of our approach involves generating novel shapes that are conditioned on textual descriptions. To showcase the efficacy of our approach, we conduct a comparative evaluation of our generation results against two state-of-the-art supervised text-to-shape synthesis methods that are based on implicit 3D representations [29, 34]. Besides, there are some other works regarding text-to-shape generation, which have different settings compared to our approach. For instance, [48] proposed a zero-shot shape generation approach conditioned on categorical texts, and [15, 33] proposed to generate textured shapes based on provided/pre-generated meshes. As a result, these prior works are not directly compared against our proposed approach.", + "bbox": [ + 496, + 628, + 893, + 840 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Quantitative comparison. To compare the generation performance of our approach to the previous methods quantitatively, we propose to use several metrics to evaluate the generated results:", + "bbox": [ + 496, + 840, + 893, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "12646", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/b7326a862a80c0fa072828e72c19228f4fbf32b0f46c20b63da6ff224431b1ee.jpg", + "image_caption": [ + "The chair is retro and round with little to no arm rest." + ], + "image_footnote": [], + "bbox": [ + 116, + 108, + 205, + 186 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/5d646b81247a9e0b0a07bf6752d6f154e2550e49a1652b89719eba10394ccea6.jpg", + "image_caption": [ + "A sofa with thick legs." + ], + "image_footnote": [], + "bbox": [ + 272, + 106, + 393, + 190 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/fe0a02b11663e8455adbf5e6030af4e36851f719643bb61be16693e03b521668.jpg", + "image_caption": [ + "A solid locking chair made of grey tiles." + ], + "image_footnote": [], + "bbox": [ + 462, + 103, + 545, + 190 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a284aa0bf7608e7740f6590e4a083d3f59f70ec21841576512e7368c48b428ee.jpg", + "image_caption": [ + "Fabric chair with singlepiece gray metal legs." + ], + "image_footnote": [], + "bbox": [ + 606, + 104, + 687, + 186 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b21bc53d8c19e4b0a95b565038c9f79f4754679ab292049c5e26164ced7d9723.jpg", + "image_caption": [ + "An old fashioned rocking chair with very high back." + ], + "image_footnote": [], + "bbox": [ + 754, + 102, + 844, + 186 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e4dcbc6ed55ea589159b9ba90bdbe3e72beddb1bc5864c44386c2903f5f3b6a0.jpg", + "image_caption": [ + "A rectangular table with four curving legs." + ], + "image_footnote": [], + "bbox": [ + 109, + 234, + 212, + 314 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/bfc2b9986b0e8897be41a7358a7367dbcee251d9c8c09f294de1b8f1acdf3cb2.jpg", + "image_caption": [ + "A two layered table with four legs." + ], + "image_footnote": [], + "bbox": [ + 267, + 233, + 390, + 319 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/514e8f6d63dafd65e13193b9959a976a7738612316d0cd1bcebe5aa3e7010627.jpg", + "image_caption": [ + "A wooden round table with very thick legs.", + "Figure 4. Qualitative results of text-to-shape generation. Our approach can generate shapes that conform to diverse text descriptions." + ], + "image_footnote": [], + "bbox": [ + 442, + 237, + 558, + 310 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/9e38e2f5ca0763cad702031ec4a2677e27ed871d42cfb65205a06d947d88fb2a.jpg", + "image_caption": [ + "A tall round table with one thin leg." + ], + "image_footnote": [], + "bbox": [ + 609, + 228, + 689, + 309 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/6259ca67d6af8f02becf570b9b1b8805497833fdc17ffed07c3fcafd468a86c0.jpg", + "image_caption": [ + "A triangular table." + ], + "image_footnote": [], + "bbox": [ + 751, + 244, + 857, + 306 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- IoU (Intersection over Union) measures the occupancy similarity between the generated shape to the ground truth. To compute the IoU score, we downsample all the generated SDFs to occupancy voxel grids of size $32^{3}$ . IoU metric is used to measure the conformity of the generated samples with the ground truth shapes.", + "- Acc (Classification Accuracy) introduces a voxel-based classifier, which is pre-trained to classify the 13 categories in ShapeNet [5] according to [48]. Acc metric is used to measure the semantic authenticity of the generated samples.", + "- CLIP-S (CLIP Similarity Score) introduces the pretrained vision-language model CLIP [40] for further evaluation. The CLIP can be used to measure the correspondence between given images and texts. We render 5 view images for each generated shape, and compute the cosine similarity score between rendered images and the given text. The highest score is reported for each text query. CLIP-S metric is used to measure the semantic conformance between the generated samples and input texts.", + "- TMD (Total Mutual Difference). For each given text description, we generate $k = 10$ different samples. Then, we compute the average IoU score for each generated shape to other $k - 1$ shapes. The average IoU score for all text queries is reported. TMD assesses the generation diversity for each given text query." + ], + "bbox": [ + 76, + 387, + 468, + 814 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To keep consistency with previous approaches, we limit the comparisons to the chair category in Text2Shape [6] dataset. Since the officially released AutoSDF [34] model was trained on another dataset [2], we re-trained the model following the original settings on the training set of", + "bbox": [ + 75, + 824, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/3b734ed5748b0a0335b41db4a8a4c10051308eac8f2956c9231ff0026234325b.jpg", + "table_caption": [ + "Table 1. Quantitative comparisons of text-to-shape generation." + ], + "table_footnote": [], + "table_body": "
MethodsIoU↑Acc↑CLIP-S↑TMD↓
Liu et al. [29]0.16034.7929.940.891
AutoSDF [34]0.18783.8829.100.581
Diffusion-SDF (Ours)0.19488.5630.880.169
", + "bbox": [ + 504, + 404, + 885, + 470 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Text2Shape for the fair comparison. The results are shown in Table 1. From the results, it can be seen that our approach is able to achieve relatively high generation quality with high IoU and Acc scores, and robust text-shape conformance with good CLIP-S performance, while achieving much better generation diversity with a much lower TMD performance.", + "bbox": [ + 496, + 489, + 890, + 594 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Qualitative results. The quantitative experiment shows the generation performance of our approach on the limited given subset from Text2Shape dataset. Due to the generalization of natural language, our approach is capable of generating different forms of shapes based on various text descriptions. Figure 4 shows the generated results of Diffusion-SDF from different text inputs. The results show that our method can generate eligible results from distinguished conditions. Besides, our method is capable of synthesizing various shape outputs from the same input text description. Figure 5 compares our approach with [29, 34] based on same text queries. The results have shown that our method has a great advantage in the diversity of generated samples, while the previous approaches are unable to generate highly-diversified shapes.", + "bbox": [ + 496, + 595, + 892, + 821 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Ablation Studies", + "text_level": 1, + "bbox": [ + 500, + 830, + 663, + 845 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We have conducted extensive ablation studies to demonstrate the effectiveness of our special architecture design for Diffusion-SDF.", + "bbox": [ + 498, + 854, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "12647", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/02ddb923b29588ae6462fd6f0ccf7f57dec96f1ded4376742b1ca91e257942d0.jpg", + "image_caption": [ + "Figure 5. Qualitative comparison of diversified text-to-shape generation. Our approach is capable of generating highly-diversified shapes that conform to the same text query, while also keeping the satisfactory quality of the generated shapes." + ], + "image_footnote": [], + "bbox": [ + 80, + 89, + 500, + 281 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0fa0e6f23b58bfd7c6a05ffc4dd46bc42c6c792bcd844245b3c08862d99008ec.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 531, + 90, + 883, + 281 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e7b9179d84c108d13680a3e9006b8721b1f66ab9c339e862167bd18599b9e2a0.jpg", + "image_caption": [ + "Figure 6. Qualitative comparison of U-Net and $UinU$ -Net. Since $UinU$ -Net-based architecture contains a local-focused inner network, it can better recover the independent patch representations, thereby improving the generation quality compared to conventional U-Net." + ], + "image_footnote": [], + "bbox": [ + 81, + 325, + 486, + 448 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/09287a35eaa799d9c17681f466a6caede630d2d19c952bdde2ec52d44e29b115.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 509, + 325, + 883, + 448 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of the UinU-Net architecture. In order to validate the benefit of our proposed modifications to the conventional U-Net architecture, we additionally compare our proposed UinU-Net architecture to the simpler U-Net architecture used in [45]. The quantitative results for text-to-shape generation are shown in Table 2. Qualitative comparisons are shown in Figure 6. From the results, it can be found that our proposed UinU-Net architecture for Voxelized Diffusion models generally improves the quality of generated shapes. With the UinU-Net architecture, the noise for each step is estimated both patch-mutually and patch-independently. Since the shape representations are repositioned based on separate patch embeddings extracted by the SDF encoders, the key to recovering the authentic shape SDFs from the joint decoder is to ensure that the generated SDF representations are also distributed independently in patches. From the qualitative results, it can be inferred that the inner network is conducive to recovering the independently distributed patch representations.", + "bbox": [ + 75, + 503, + 472, + 790 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Inner network architecture. As for the UinU-Net architecture, we have conducted ablation experiments on several variants for the inner network to validate the effectiveness of the final design. The results have shown in Table 3. According to the results, it can be inferred that the inner outer concatenation mechanism and spatial attention layer can generally improve the generation quality. Without the inner-outer", + "bbox": [ + 75, + 795, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/28da582fcc340d16b37fb90e1e4ac7995b7fa01585598493ec5a4007d69c34a1.jpg", + "table_caption": [ + "Table 2. Evaluating effectiveness of the UinU-Net architecture." + ], + "table_footnote": [], + "table_body": "
IoU↑Acc↑CLIP-S↑TMD↓
U-Net [45]0.18780.9829.350.171
UinU-Net (Ours)0.19488.5630.880.169
", + "bbox": [ + 517, + 518, + 870, + 573 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/ee237119567691a87de2e4d26fbecd8ce5665ad6ecdadba2ac476cb84d50494b.jpg", + "table_caption": [ + "Table 3. Evaluating effectiveness of the inner network design." + ], + "table_footnote": [], + "table_body": "
IoU↑Acc↑CLIP-S↑TMD↓
UinU-Net0.19488.5630.880.169
- w/o in-out concat0.19883.9128.680.181
- w/o spatial attention0.19485.5630.820.161
", + "bbox": [ + 506, + 599, + 883, + 667 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "concatenation mechanism, the accuracy score and CLIP-S have significant decreases, indicating that the information transmission mechanism has affected the semantic authenticity and conformance of the generated shapes. Accuracy score has dropped without the spatial attention module, indicating that the introduction of patch-to-patch information helps preserve the full shape semantics while recovering the patch-wise representations.", + "bbox": [ + 496, + 685, + 890, + 806 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Text-Guided Shape Completion", + "text_level": 1, + "bbox": [ + 498, + 816, + 779, + 832 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we validate the effectiveness of our approach on the text-guided shape completion task. Specifically, given a partial input shape, our goal is to generate the missing part conditioned on the input text descriptions. For", + "bbox": [ + 496, + 839, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "12648", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5a6e07a01fd19d2661def0b2b90315ae8289f103cb47ccd3186506249353f186.jpg", + "image_caption": [ + "Figure 7. Qualitative result of text-guide shape completion. Given a known partial shape, our approach can generate the missing part based on text conditions." + ], + "image_footnote": [], + "bbox": [ + 83, + 92, + 872, + 220 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/be0a8e59a20e3e0fdcf462459e869bf12843ea6b948e6d61c0f8df9b0ec01b85.jpg", + "image_caption": [ + "Figure 8. Qualitative result of text-guide shape manipulation. Given a known shape, our approach is able to manipulate the given shape into the target shape based on the text descriptions." + ], + "image_footnote": [], + "bbox": [ + 96, + 268, + 318, + 391 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/be8085016c16f5b740f52bfa3ee0ba1fede224360874ca7dfac6c5efb7942816.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 348, + 268, + 599, + 393 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/aab811df5b21f58eec47fa06a8549b6d28c79bed5df5a03b1c4380a4f131ff7b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 630, + 268, + 872, + 396 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "instance, we can generate the body of a chair based on the given chair legs or generate the missing chair legs based on the chair body. The qualitative results of our approach are displayed in Figure 7. The results show that our approach is capable of generating the missing part of a shape while being well-blended with the given shape, as evident in the generated examples such as revolving throne, revolving toilet, and revolving sofa. Moreover, our completion performance is not limited by the shape geometry in the training set. The core limitation of our approach is the cut region of patch grids, which can be addressed by increasing resolution and decreasing patch size.", + "bbox": [ + 75, + 450, + 472, + 632 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Text-Guided Shape Manipulation", + "text_level": 1, + "bbox": [ + 76, + 648, + 370, + 665 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We demonstrate our approach's effectiveness for text-guided shape manipulation. Our approach can modify a given shape to match an instructive text description. Figure 8 gives several qualitative illustrations for our proposed approach. From the results, it can be summarized that our approach can handle the shape manipulation of both local shape structures (e.g. the existence/style of arms or legs) or the overall shape characteristics (e.g. sofa or straight chair). In addition, one key issue for our designed approach is the choice for $t_{mid}$ . Since the shape characteristics usually form in the early stage of the reverse process, thus we set $t_{mid}$ to relatively larger step numbers (600~800 step before DDIM's down-sampling). In experiments, we observe that excessively small or large values for $t_{mid}$ result in unchanged or destructed original shape features, respectively.", + "bbox": [ + 75, + 674, + 468, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations. This paper demonstrates the superiority of our approach on the Text2Shape [6] dataset, which is limited to only two categories from ShapeNet, restricting our approach's generalization to other categories. Moreover, the lack of current shape-text datasets prevents us from validating our approach on additional benchmarks. To address this, we propose introducing more datasets and exploring zero-shot text-to-shape generation by leveraging knowledge from 2D vision-language models. While some studies have attempted to tackle this challenge [48], achieving flexible text-to-shape generation remains a significant obstacle. Our future work will seek a possible solution to this problem.", + "bbox": [ + 500, + 474, + 892, + 656 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Conclusion. Our paper presents a framework for text-to-shape synthesis called Diffusion-SDF, which utilizes a diffusion model to generate voxelized SDFs conditioned on texts. The approach comprises a two-stage pipeline: a patch-wise autoencoder for generating Gaussian SDF representations, followed by a Voxelized Diffusion model with UinU-Net denoisers for generating patch-independent SDF representations. We evaluate our approach on various text-to-shape synthesis tasks, and the results demonstrate that it can generate highly diverse and high-quality 3D shapes.", + "bbox": [ + 496, + 657, + 892, + 809 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments This work was supported in part by the National Key Research and Development Program of China under Grant 2017YFA0700802, in part by the National Natural Science Foundation of China under Grant 62206147 and Grant 62125603, and in part by a grant from the Beijing Academy of Artificial Intelligence (BAAI).", + "bbox": [ + 496, + 810, + 893, + 901 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "12649", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Panos Achlioptas, Olga Diamanti, Ioannis Mitliagkas, and Leonidas J. 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In ICCV, pages 5806-5815, 2021. 2, 5" + ], + "bbox": [ + 501, + 90, + 890, + 714 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "12651", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Diffusion-SDF_ Text-To-Shape via Voxelized Diffusion/a08ad0f7-f625-4886-ac27-deeab3818eeb_model.json b/2023/Diffusion-SDF_ Text-To-Shape via Voxelized Diffusion/a08ad0f7-f625-4886-ac27-deeab3818eeb_model.json new file mode 100644 index 0000000000000000000000000000000000000000..3eb14136004dd0e3fb928d69d171709483fd5cf9 --- /dev/null +++ b/2023/Diffusion-SDF_ Text-To-Shape via Voxelized Diffusion/a08ad0f7-f625-4886-ac27-deeab3818eeb_model.json @@ -0,0 +1,2266 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.217, + 0.131, + 0.757, + 0.154 + ], + "angle": 0, + "content": "Diffusion-SDF: Text-to-Shape via Voxelized Diffusion" + }, + { + "type": "text", + "bbox": [ + 0.287, + 0.18, + 0.682, + 0.199 + ], + "angle": 0, + "content": "Muheng Li\\(^{1}\\), Yueqi Duan\\(^{\\dagger,2}\\), Jie Zhou\\(^{1}\\), Jiwen Lu\\(^{1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.29, + 0.199, + 0.682, + 0.218 + ], + "angle": 0, + "content": "\\(^{1}\\)Department of Automation, Tsinghua University" + }, + { + "type": "text", + "bbox": [ + 0.246, + 0.218, + 0.725, + 0.235 + ], + "angle": 0, + "content": "\\(^{2}\\)Department of Electronic Engineering, Tsinghua University" + }, + { + "type": "image", + "bbox": [ + 0.083, + 0.255, + 0.885, + 0.421 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.428, + 0.895, + 0.471 + ], + "angle": 0, + "content": "Figure 1. We propose a text-to-shape synthesis approach named Diffusion-SDF. Our method is capable of performing various text-to-shape tasks including text-to-shape generation (directly generating 3D shapes from texts), text-guided shape completion (generating the missing part of an incomplete shape under the guidance of texts), and text-guided shape manipulation (modifying a given shape according to texts)." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.483, + 0.314, + 0.499 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.515, + 0.474, + 0.864 + ], + "angle": 0, + "content": "With the rising industrial attention to 3D virtual modeling technology, generating novel 3D content based on specified conditions (e.g. text) has become a hot issue. In this paper, we propose a new generative 3D modeling framework called Diffusion-SDF for the challenging task of text-to-shape synthesis. Previous approaches lack flexibility in both 3D data representation and shape generation, thereby failing to generate highly diversified 3D shapes conforming to the given text descriptions. To address this, we propose a SDF autoencoder together with the Voxelized Diffusion model to learn and generate representations for voxelized signed distance fields (SDFs) of 3D shapes. Specifically, we design a novel UinU-Net architecture that implants a local-focused inner network inside the standard U-Net architecture, which enables better reconstruction of patch-independent SDF representations. We extend our approach to further text-to-shape tasks including text-conditioned shape completion and manipulation. Experimental results show that Diffusion-SDF generates both higher quality and more diversified 3D shapes that conform well to given text descriptions when compared to previous approaches. Code is available at: https://github.com/ttlmh/Diffusion-SDF." + }, + { + "type": "title", + "bbox": [ + 0.502, + 0.483, + 0.633, + 0.498 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.508, + 0.895, + 0.749 + ], + "angle": 0, + "content": "Exploring data representations for 3D shapes has been a fundamental and critical issue in 3D computer vision. Explicit 3D representations including point clouds [38, 39], polygon meshes [17, 24] and occupancy voxel grids [9, 53] have been widely applied in various 3D downstream applications [1, 35, 56]. While explicit 3D representations achieve encouraging performance, there are some primary limitations including not being suitable for generating watertight surfaces (e.g. point clouds), or being subject to topological constraints (e.g. meshes). On the other hand, implicit 3D representations have been widely studied more recently [3, 14, 37], with representative works including DeepSDF [37], Occupancy Network [32] and IM-Net [8]. In general, implicit functions encode the shapes by the isosurface of the function, which is a continuous field and can be evaluated at arbitrary resolution." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.896, + 0.902 + ], + "angle": 0, + "content": "In recent years, numerous explorations have been conducted for implicit 3D generative models, which show promising performance on several downstream applications such as single/multi-view 3D reconstruction [23, 54] and shape completion [12, 34]. Besides, several studies have also explored the feasibility of directly generating novel 3D shapes based on implicit representations [15, 21]. However, these approaches are incapable of generating specified 3D shapes that match a given condition, e.g. a short text describing the shape characteristics as shown in Figure 1." + }, + { + "type": "page_footnote", + "bbox": [ + 0.103, + 0.887, + 0.23, + 0.901 + ], + "angle": 0, + "content": "†Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "12642" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.212 + ], + "angle": 0, + "content": "Text-based visual content synthesis has the advantages of the flexibility and generality [41, 42]. Users may generate rich and diverse 3D shapes based on easily obtained natural language descriptors. In addition to generating 3D shapes directly based on text descriptions, manipulating 3D data with text guidance can be further utilized for iterative 3D synthesis and fine-grained 3D editing, which can be beneficial for non-expert users to create 3D visual content." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.213, + 0.471, + 0.485 + ], + "angle": 0, + "content": "In the literature, there have been few attempts on the challenging task of text-to-shape generation based on implicit 3D representations [29, 34, 48]. For example, AutoSDF [34] introduced a vector quantized SDF autoencoder together with an autoregressive generator for shape generation. While encouraging progress has been made, the quality and diversity of generated shapes still requires improvement. The current approaches struggle to generate highly diversified 3D shapes that both guarantee generation quality and conform to the semantics of the input text. Motivated by the success of denoising diffusion models in 2D image [13, 19, 36] and even explicit 3D point cloud [31, 58, 59] generation, we find that DMs achieve high-quality and highly diversified generation while being robust to model training. To this end, we aim to design an implicit 3D representation-based generative diffusion process for text-to-shape synthesis that can achieve better generation flexibility and generalization performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.487, + 0.471, + 0.864 + ], + "angle": 0, + "content": "In this paper, we propose the Diffusion-SDF framework for text-to-shape synthesis based on truncated signed distance fields (TSDFs). Considering that 3D shapes share structural similarities at local scales, and the cubic data volume of 3D voxels may lead to slow sampling speed for diffusion models, we propose a two-stage separated generation pipeline. First, we introduce a patch-based SDF autoencoder that maps the original signed distance fields into patch-independent local Gaussian latent representations. Second, we introduce the Voxelized Diffusion model that captures the intra-patch information along with both patch-top-patch and patch-to-global relations. Specifically, we design a novel UinU-Net architecture to replace the standard U-Net [46] for the noise estimator in the reverse process. UinU-Net implants a local-focused inner network inside the outer U-Net backbone, which takes into account the patch-independent prior of SDF representations to better reconstruct local patch features from noise. Our work digs deeper into the further potential of diffusion model-based approaches towards text-conditioned 3D shape synthesis based on voxelized TSDFs. Experiments on the largest existing text-shape dataset [6] show that our Diffusion-SDF approach achieves promising generation performance on text-to-shape tasks compared to existing state-of-the-art approaches, in both qualitative and quantitative evaluations." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.09, + 0.642, + 0.107 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.123, + 0.895, + 0.532 + ], + "angle": 0, + "content": "Text-conditioned generative 3D models. In the field of generative 3D modeling, a variety of works have focused on synthesizing 3D visual content unconditionally [1, 32, 52, 56] or conditioned on single/multi-view images [9, 34, 54, 55]. Besides, there has also been a series of works concentrating on the challenging task of text-to-shape generation [6]. Some of them adopted purely explicit 3D data representation-based methods to generate 3D shapes conditioned on input text [6, 33, 58]. In contrast, our focus lies on synthesizing 3D shapes based on implicit 3D data representations. So far, there have also been few existing works focusing on the task of implicit text-to-shape generation [29, 34, 48]. All of these approaches have yielded impressive generation results, but there are still some remained issues to be addressed. Sanghi et al. [48] proposed a normalizing flow [43]-based approach to generate shape voxels using implicit Occupancy Networks [32], and Liu et al. [29] introduced a shape-IMLE [28] generator using implicit IMNET [8] decoder, while these approaches neither employ the more flexible implicit SDFs as data representation nor take into account the constraints for local shape structures. More similar to our work, AutoSDF [34] introduced an autoregressive prior for 3D shape generation based on a discretized SDF autoencoder. The autoregressive model adopts a relatively unnatural way to predict patched 3D tokens in a sequential manner that loses the 3D-specific inductive bias and is also relatively inefficient." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.538, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Diffusion Probabilistic Models. Diffusion Probabilistic Models (DPMs) [19, 49], also known as diffusion models, have currently arisen as a powerful family of generative models. Compared to previous state-of-the-art generative models, including Generative Adversarial Network (GAN) [16], Variational Autoencoder (VAE) [26], and flow-based generative models [43], the diffusion model demonstrates its superiority in both training stability and generative diversity [11]. Diffusion models have achieved promising performance on image [13, 19, 36, 45] and speech [7, 27] synthesis. Especially, fairly impressive results have been achieved with diffusion model-based approaches on the task of text-to-image synthesis [41, 45, 47]. In the field of 3D computer vision, several studies have adopted diffusion models for generative 3D modeling [31, 58, 59]. PVD [59] employed diffusion models to generate 3D shapes based on point-voxel 3D representation. Luo et al. [31] treated points in point clouds as particles in a thermodynamic system with a heat bath. LION [58] introduced a VAE framework with hierarchical diffusion models in latent space. All these approaches have focused on the diffusion process of explicit 3D data representations for shape generation. On the contrary, our work tries to explore the feasibility of diffusion models on implicit 3D data representations." + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.875, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Strictly speaking, our approach employs a combined explicit-implicit representation in the form of voxelized signed distance fields." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "12643" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.093, + 0.092, + 0.887, + 0.352 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.353, + 0.895, + 0.396 + ], + "angle": 0, + "content": "Figure 2. Overview of Diffusion-SDF. We propose a two-stage pipeline to generate novel 3D shapes from texts. First, we train an autoencoder to learn patch-independent normal-distributed representations for voxelized TSDFs. Then, we propose the Voxelized Diffusion framework together with the UinU-Net denoiser to generate shape representations. Please check Figure 3 for more details of UinU-Net." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.413, + 0.17, + 0.429 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.44, + 0.471, + 0.502 + ], + "angle": 0, + "content": "In this section, we introduce the methodology design for Diffusion-SDF. In general, we propose a two-stage pipeline as illustrated in Figure 2. Detailed information of each stage will be included in the following sections." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.513, + 0.398, + 0.53 + ], + "angle": 0, + "content": "3.1. Autoencoding Signed Distance Fields" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.538, + 0.47, + 0.749 + ], + "angle": 0, + "content": "Signed distance fields (SDF) belong to a type of implicit 3D data representation which assigns the scalar signed distance value to the shape surface for each point \\( p \\) in the 3D space \\( \\mathbb{R}^3 \\). Our objective is to generate the signed distance fields for the target 3D shapes that match the given text conditions. Specifically, the 3D data are represented by truncated signed distance functions (TSDF) in a regularly-spaced voxel grid as [3, 22]. Generating voxelized SDFs directly from denoising diffusion models is both cost-expensive and time-consuming. In addition, the local structural information of 3D shapes is not well-emphasized through direct voxel-based generation. To address this, we propose a patch-wise autoencoder to learn the latent representations for voxelized signed distance fields." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Given a 3D shape, we first sample its truncated signed distance field \\( x \\) as a voxel grid of size \\( D^3 \\). Before the shape \\( x \\) is encoded, it is first split into \\( N \\) local patches of size \\( P^3 \\), producing a sequence of shape patches \\( X_p = [x_{p1},\\dots,x_{pN}] \\), where \\( N = (D / P)^3 \\) is the resulting number of patches. Then, the local shape encoder \\( \\mathcal{E}_{loc} \\) encodes each shape patches into latent representations \\( Z_p = [z_{p1},\\dots,z_{pN}] \\), where \\( z_{pn} = \\mathcal{E}_{loc}(x_{pn}) \\in \\mathbb{R}^c \\), and \\( c \\) is the number of latent channels. Here, since each patch is encoded independently, the local structural information can be" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.415, + 0.895, + 0.583 + ], + "angle": 0, + "content": "explored well through the local shape encoder. Meanwhile, the input data scale can also be downsampled by the factor \\( P \\). However, when reconstructing the shape from local patches, it is also necessary to consider the spatial location of each patch in the global shape, and the interrelationship between adjacent patches. To preserve both patch-to-global and patch-to-patch information while decoding the latent embeddings, the patch embeddings are first rearranged into a voxel grid embedding \\( z \\), and then sent into the patch-joint decoder \\( \\mathcal{D} \\) that reconstructs the SDF field from the latent patches, giving \\( \\tilde{x} = \\mathcal{D}(z) \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.59, + 0.895, + 0.713 + ], + "angle": 0, + "content": "In detail, we adopt a VAE [26, 44]-like autoencoder, which encodes each shape patch into a normal distribution. We utilize a combination of both \\(\\mathcal{L}_1\\) reconstruction loss together with the KL-regularization loss at the training stage for the SDF autoencoder. The latter one forces a mild KL-penalty towards a standard normal distribution on each learned patch latent. The final SDF representations will be in the form of patch-independent Gaussian distributions." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.748, + 0.813, + 0.765 + ], + "angle": 0, + "content": "3.2. Voxelized Diffusion Models (VDMs)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Diffusion models (DMs) [19, 49] are a class of probabilistic generative models that learn to fit a certain distribution by gradually denoising a Gaussian variable through a fixed Markov Chain of length \\( T \\). Given a data sample \\( x_0 \\sim q(x_0) \\), DMs describe two different processes in the opposite direction: a forward process \\( q(\\mathbf{x}_{0:T}) \\) that gradually transform a data sample into pure Gaussian noise, and a reverse process \\( p_{\\theta}(\\mathbf{x}_{0:T}) \\) that gradually denoise a pure" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "12644" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.078, + 0.092, + 0.289, + 0.108 + ], + "angle": 0, + "content": "Gaussian sample into real data," + }, + { + "type": "equation", + "bbox": [ + 0.148, + 0.118, + 0.47, + 0.143 + ], + "angle": 0, + "content": "\\[\nq \\left(\\boldsymbol {x} _ {0: T}\\right) = q \\left(\\boldsymbol {x} _ {0}\\right) \\Pi_ {t = 1} ^ {T} q \\left(\\boldsymbol {x} _ {t} \\mid \\boldsymbol {x} _ {t - 1}\\right), \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.143, + 0.14, + 0.405, + 0.157 + ], + "angle": 0, + "content": "\\[\np _ {\\theta} \\left(\\boldsymbol {x} _ {0: T}\\right) = p \\left(\\boldsymbol {x} _ {T}\\right) \\Pi_ {t = 1} ^ {T} p _ {\\theta} \\left(\\boldsymbol {x} _ {t - 1} | \\boldsymbol {x} _ {t}\\right),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.168, + 0.47, + 0.199 + ], + "angle": 0, + "content": "where \\(q(\\pmb{x}_t|\\pmb{x}_{t-1})\\) and \\(p_\\theta(\\pmb{x}_{t-1}|\\pmb{x}_t)\\) are both Gaussian transition probabilities in the forms of" + }, + { + "type": "equation", + "bbox": [ + 0.127, + 0.21, + 0.469, + 0.239 + ], + "angle": 0, + "content": "\\[\nq \\left(\\boldsymbol {x} _ {t} \\mid \\boldsymbol {x} _ {t - 1}\\right) = \\mathcal {N} \\left(\\boldsymbol {x} _ {t}; \\sqrt {1 - \\beta_ {t}} \\boldsymbol {x} _ {t - 1}, \\beta_ {t} \\boldsymbol {I}\\right), \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.121, + 0.239, + 0.408, + 0.255 + ], + "angle": 0, + "content": "\\[\np _ {\\theta} \\left(\\boldsymbol {x} _ {t - 1} | \\boldsymbol {x} _ {t}\\right) = \\mathcal {N} \\left(\\boldsymbol {x} _ {t - 1}; \\boldsymbol {\\mu} _ {\\theta} \\left(\\boldsymbol {x} _ {t}, t\\right), \\beta_ {t} \\boldsymbol {I}\\right).\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.266, + 0.469, + 0.299 + ], + "angle": 0, + "content": "Based on [19], the mean variable \\(\\pmb{\\mu}_{\\theta}(\\pmb{x}_t,t)\\) for the reverse transition \\(p_{\\theta}\\left(\\pmb{x}_{t - 1}|\\pmb{x}_t\\right)\\) can be expressed in the form of" + }, + { + "type": "equation", + "bbox": [ + 0.105, + 0.308, + 0.47, + 0.343 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\mu} _ {\\theta} \\left(\\boldsymbol {x} _ {t}, t\\right) = \\frac {1}{\\sqrt {\\alpha_ {t}}} \\left(\\boldsymbol {x} _ {t} - \\frac {\\beta_ {t}}{\\sqrt {1 - \\bar {\\alpha} _ {t}}} \\boldsymbol {\\epsilon} _ {\\theta} \\left(\\boldsymbol {x} _ {t}, t\\right)\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.353, + 0.47, + 0.414 + ], + "angle": 0, + "content": "where \\(\\alpha_{t} = 1 - \\beta_{t}\\), \\(\\bar{\\alpha}_{t} = \\Pi_{i=1}^{t} \\alpha_{i}\\), and \\(\\beta_{t}\\) decreases to 0 gradually as \\(t\\) approaches 0. The evidence lower bound (ELBO) is maximized at the training stage of DMs, eventually leading to the loss function as the form of" + }, + { + "type": "equation", + "bbox": [ + 0.128, + 0.424, + 0.47, + 0.451 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {D M} = \\mathbb {E} _ {\\boldsymbol {x}, t, \\boldsymbol {\\epsilon} \\sim \\mathcal {N} (0, 1)} \\left[ \\| \\boldsymbol {\\epsilon} - \\boldsymbol {\\epsilon} _ {\\theta} (\\boldsymbol {x} _ {t}, t) \\| ^ {2} \\right], \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.462, + 0.469, + 0.538 + ], + "angle": 0, + "content": "where \\(\\pmb{x}_t = \\sqrt{\\bar{\\alpha}_t}\\pmb{x}_0 + \\sqrt{1 - \\bar{\\alpha}_t}\\pmb{\\epsilon},\\) \\(\\pmb{\\epsilon}\\) is a noise variable, and \\(t\\) is uniformly sampled from \\(\\{1,\\dots,T\\}\\). The neural network-based score estimator \\(\\pmb{\\epsilon}_{\\theta}(\\pmb{x}_t,t)\\) is the core function of denoising diffusion models, which is implemented as a timestep-conditioned denoising autoencoder in [19]." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.539, + 0.47, + 0.704 + ], + "angle": 0, + "content": "UinU-Net Architecture. In our scenario, we are designing a novel diffusion-based architecture to generate latent SDF representations with regard to the target text conditions. The corresponding TSDF fields can be then reconstructed through the patch-joint decoder which is pre-trained in the first stage. As we mentioned in the above section, the key part of generative diffusion models is to estimate the function approximator \\(\\epsilon_{\\theta}\\) from the data distribution of the training set. Since our model is designed to generate latent samples, the score estimator can be expressed as \\(\\epsilon_{\\theta}(z_t,t)\\), as the loss function becomes" + }, + { + "type": "equation", + "bbox": [ + 0.091, + 0.712, + 0.469, + 0.749 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {D i f f u s i o n - S D F}} = \\mathbb {E} _ {z, t, \\epsilon \\sim \\mathcal {N} (0, 1)} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} (z _ {t}, t) \\| ^ {2} \\right]. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.75, + 0.47, + 0.901 + ], + "angle": 0, + "content": "To incorporate the 3D positional prior of different latent shape patches, we adopt a 3D U-Net [10]-based autoencoder as the neural function approximator \\(\\epsilon_{\\theta}\\) that directly learns to denoise the voxel grid embedding \\(z_{t}\\) that is obtained from the pre-trained local shape encoder \\(\\mathcal{E}_{loc}\\). Besides, another crucial prior for our design is the patch-based encoding process, through which all the shape patches are encoded into independent Gaussian distributions. Thus, when generating the local shape embeddings, an important point is to recover the independent distribution for" + }, + { + "type": "image", + "bbox": [ + 0.51, + 0.092, + 0.885, + 0.345 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.357, + 0.893, + 0.47 + ], + "angle": 0, + "content": "Figure 3. Detailed illustration of UinU-Net. To better recover \\( z \\) based on independently distributed patches, we propose to implant an inner network inside the standard U-Net architecture. The inner network is mainly composed of \\( 1 \\times 1 \\times 1 \\) convolutions, thus it focuses on patch-wise features, while the spatial transformer brings in patch-to-patch information. (Standard U-Net operators include \\( 3 \\times 3 \\times 3 \\) residual blocks, conditional cross-attention layers, pooling layers and up-scaling layers.)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.492, + 0.893, + 0.869 + ], + "angle": 0, + "content": "each shape patch as well. To address this, we propose a novel UinU-Net architecture for the implementation of the autoencoder-based neural score estimator as shown in Figure 3. The standard 3D U-net [10] adopts a series of \\(3 \\times 3 \\times 3\\) convolutional layers to construct a downsampling-upsampling network architecture with the information shared through skip connections. This design takes into account the patch-to-patch and patch-to-global features via hierarchical receptive fields. Given that our input data are compressed 3D latent representations, and each patch is encoded independently, we propose to implant another inner network inside the outer U-Net architecture where the embedded resolution is equal to the original latent resolution \\(D / P\\). Specifically, we adopt a \\(1 \\times 1 \\times 1\\) convolution-based ResNet [18] structure to learn independent patch-focused information. We also introduce the spatial Transformer [51] network that accepts positional embedded patch representations as input tokens, following self-attention layers to capture the relational information between independent local patch embeddings. The inner synthesis paths are skip-connected to the outer ones, ensuring information transmission from inner to outer networks. This architecture is designed to capture the intra-patch information along with both patch-to-patch and patch-to-global relations." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Text-Guided Shape Generation So far, we have discussed the generative process without text conditions. To synthe-" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12645" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.289 + ], + "angle": 0, + "content": "size latent SDF representations based on given conditions, we introduce a conditioning mechanism based on classifier-free guidance diffusion [20]. We adopt a text-conditioned score estimator. In detail, to fit the target conditions into the 3D denoising autoencoder, we utilize the cross-attention mechanism as proposed in [45]. The input caption is first encoded as text embeddings through a pre-trained text encoder \\(\\tau\\). Thus, the conditioned score can be formed as \\(\\epsilon_{\\theta}(z_t|\\tau(c))\\), where \\(c\\) is the input caption. Meanwhile, we also obtain an unconditioned score \\(\\epsilon_{\\theta}(z_t|\\emptyset)\\) with an empty sequence as input caption. Within the guided diffusion sampling process, the output of the model is extrapolated further in the direction of \\(\\epsilon_{\\theta}(z_t|\\tau(c))\\) and away from \\(\\epsilon_{\\theta}(z_t|\\emptyset)\\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.085, + 0.295, + 0.469, + 0.327 + ], + "angle": 0, + "content": "\\[\n\\hat {\\epsilon} _ {\\theta} \\left(z _ {t} | \\tau (c)\\right) = \\epsilon_ {\\theta} \\left(z _ {t} | \\emptyset\\right) + s \\cdot \\left(\\epsilon_ {\\theta} \\left(z _ {t} | \\tau (c)\\right) - \\epsilon_ {\\theta} \\left(z _ {t} | \\emptyset\\right)\\right), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.327, + 0.351, + 0.341 + ], + "angle": 0, + "content": "where \\(s \\geq 1\\) refers to the guidance scale." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.342, + 0.473, + 0.599 + ], + "angle": 0, + "content": "Text-Guided Shape Completion Current shape completion approaches mainly focused on recovering the full shapes from partial input shapes or single view images [1, 57, 59]. Besides, we have explored the feasibility of text-conditioned shape completion. According to the patch-based design of our SDF encoder, information for the given shape patches can be encoded even if some of the patches are missing. Motivated by the success of diffusion model-based image inpainting [30, 45], we introduce a mask-diffusion strategy to generate the missing shape based on a pre-trained VDM. The core idea is to incorporate known information into each denoising step of the reverse process. For a full shape representation, we transform it into a partial shape representation given the mask \\( m_z \\). For each estimation step \\( z_{t-1} \\), we combine the estimated result through the reverse process \\( \\widetilde{z}_{t-1} \\) with the forward sampling result of the unmasked patches \\( \\hat{z}_{t-1} \\)," + }, + { + "type": "equation", + "bbox": [ + 0.147, + 0.606, + 0.47, + 0.623 + ], + "angle": 0, + "content": "\\[\nz _ {t - 1} = (1 - m) \\odot \\widetilde {z} _ {t - 1} + m \\odot \\hat {z} _ {t - 1}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.63, + 0.376, + 0.645 + ], + "angle": 0, + "content": "where \\(\\odot\\) refers to element-wise product, and" + }, + { + "type": "equation", + "bbox": [ + 0.172, + 0.652, + 0.469, + 0.678 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{c} \\widetilde {z} _ {t - 1} \\sim \\mathcal {N} (\\boldsymbol {\\mu} _ {\\theta} (z _ {t}, t, c), \\beta_ {t} \\boldsymbol {I}) \\\\ \\hat {\\quad} \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\end{array} \\tag {8}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.175, + 0.674, + 0.369, + 0.689 + ], + "angle": 0, + "content": "\\[\n\\hat {z} _ {t - 1} = \\sqrt {\\bar {\\alpha} _ {t}} z _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon .\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.697, + 0.47, + 0.725 + ], + "angle": 0, + "content": "By such a strategy, the unknown region can be recovered based on both the given shape and text conditions." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.727, + 0.473, + 0.879 + ], + "angle": 0, + "content": "Text-Guided Shape Manipulation Visual content editing is one of the most valuable applications for vision-language generation. We propose a diffusion-based text-guided shape manipulation approach. For a given shape representation \\( z_{init} \\), our goal is to transform it into another shape representation \\( z_{goal} \\) based on text \\( c \\). Inspired by image manipulation techniques [4, 25], we use a cycle-sampling strategy based on a pre-trained VDM. Firstly, we forward-sample the given shape \\( z_{init} \\) for \\( t_{mid} \\) steps, where \\( 0 < t_{mid} < T \\). This operation will lead to an intermediate output \\( z_{mid} \\)" + }, + { + "type": "equation", + "bbox": [ + 0.143, + 0.884, + 0.47, + 0.904 + ], + "angle": 0, + "content": "\\[\nz _ {m i d} = \\sqrt {\\bar {\\alpha} _ {t _ {m i d}}} z _ {i n i t} + \\sqrt {1 - \\bar {\\alpha} _ {t _ {m i d}}} \\epsilon . \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.168 + ], + "angle": 0, + "content": "Then, the reverse process will start from \\( z_{mid} \\), and another \\( t_{mid} \\) denoising steps will be conducted conditioned on \\( c \\). Such a design will make the generated shapes correspond to the target text descriptions while maintaining the original shape characteristics." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.18, + 0.634, + 0.198 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.205, + 0.894, + 0.295 + ], + "angle": 0, + "content": "We extensively experimented with our proposed Diffusion-SDF on various text-conditioned 3D shape synthesis tasks, such as text-to-shape generation, text-conditioned shape completion, and text-guided shape manipulation. The following subsections describe details of experimental settings, results, and analyses." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.296, + 0.892, + 0.431 + ], + "angle": 0, + "content": "Dataset. We mainly trained and evaluated our approach on the current largest text-shape dataset Text2Shape (T2S) [6]. T2S gathered data in the form of shape-text pairs based on two object classes (chairs, tables) in ShapeNet [5]. T2S contains about 75K shape-text pairs in total (\\(\\sim\\)30K for chairs, \\(\\sim\\)40K for tables), with an average of \\(\\sim\\)16 words per description. T2S was originally designed to contain both color and shape information within the text descriptions, while we mainly focus on text-shape correspondence." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.432, + 0.895, + 0.599 + ], + "angle": 0, + "content": "Implementation details. For the training stage of the SDF autoencoder, to improve the model's generalization ability, we trained the autoencoder across the 13 categories of ShapeNet [5] dataset. For the input data, we sampled the voxelized SDF from original shapes with \\(64 \\times 64 \\times 64\\) grid points, which is also the data size adopted for follow-up operations. For the diffusion stage, to facilitate the generative sampling speed, we adopt the DDIM [50] sampler to reduce the original DDPM sampling steps from \\(T = 1000\\) to 50. For the conditioning mechanism, we adopt a freeze CLIP [40] text encoder \\(\\tau\\)." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.606, + 0.816, + 0.623 + ], + "angle": 0, + "content": "4.1. Text-Conditioned Shape Generation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.895, + 0.841 + ], + "angle": 0, + "content": "The most immediate application of our approach involves generating novel shapes that are conditioned on textual descriptions. To showcase the efficacy of our approach, we conduct a comparative evaluation of our generation results against two state-of-the-art supervised text-to-shape synthesis methods that are based on implicit 3D representations [29, 34]. Besides, there are some other works regarding text-to-shape generation, which have different settings compared to our approach. For instance, [48] proposed a zero-shot shape generation approach conditioned on categorical texts, and [15, 33] proposed to generate textured shapes based on provided/pre-generated meshes. As a result, these prior works are not directly compared against our proposed approach." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.841, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Quantitative comparison. To compare the generation performance of our approach to the previous methods quantitatively, we propose to use several metrics to evaluate the generated results:" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "12646" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.117, + 0.109, + 0.207, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.086, + 0.194, + 0.24, + 0.219 + ], + "angle": 0, + "content": "The chair is retro and round with little to no arm rest." + }, + { + "type": "image", + "bbox": [ + 0.273, + 0.107, + 0.395, + 0.191 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.265, + 0.194, + 0.39, + 0.207 + ], + "angle": 0, + "content": "A sofa with thick legs." + }, + { + "type": "image", + "bbox": [ + 0.463, + 0.104, + 0.546, + 0.191 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.439, + 0.194, + 0.555, + 0.22 + ], + "angle": 0, + "content": "A solid locking chair made of grey tiles." + }, + { + "type": "image", + "bbox": [ + 0.607, + 0.106, + 0.688, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.577, + 0.194, + 0.713, + 0.22 + ], + "angle": 0, + "content": "Fabric chair with singlepiece gray metal legs." + }, + { + "type": "image", + "bbox": [ + 0.756, + 0.103, + 0.846, + 0.188 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.731, + 0.194, + 0.875, + 0.22 + ], + "angle": 0, + "content": "An old fashioned rocking chair with very high back." + }, + { + "type": "image", + "bbox": [ + 0.111, + 0.235, + 0.213, + 0.315 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.099, + 0.322, + 0.226, + 0.347 + ], + "angle": 0, + "content": "A rectangular table with four curving legs." + }, + { + "type": "image", + "bbox": [ + 0.268, + 0.234, + 0.391, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.273, + 0.322, + 0.382, + 0.347 + ], + "angle": 0, + "content": "A two layered table with four legs." + }, + { + "type": "image", + "bbox": [ + 0.443, + 0.238, + 0.559, + 0.311 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.436, + 0.322, + 0.56, + 0.347 + ], + "angle": 0, + "content": "A wooden round table with very thick legs." + }, + { + "type": "image", + "bbox": [ + 0.611, + 0.229, + 0.69, + 0.31 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.592, + 0.322, + 0.716, + 0.347 + ], + "angle": 0, + "content": "A tall round table with one thin leg." + }, + { + "type": "image", + "bbox": [ + 0.753, + 0.246, + 0.859, + 0.307 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.753, + 0.322, + 0.853, + 0.334 + ], + "angle": 0, + "content": "A triangular table." + }, + { + "type": "image_caption", + "bbox": [ + 0.083, + 0.353, + 0.884, + 0.368 + ], + "angle": 0, + "content": "Figure 4. Qualitative results of text-to-shape generation. Our approach can generate shapes that conform to diverse text descriptions." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.388, + 0.47, + 0.478 + ], + "angle": 0, + "content": "- IoU (Intersection over Union) measures the occupancy similarity between the generated shape to the ground truth. To compute the IoU score, we downsample all the generated SDFs to occupancy voxel grids of size \\(32^{3}\\). IoU metric is used to measure the conformity of the generated samples with the ground truth shapes." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.489, + 0.47, + 0.566 + ], + "angle": 0, + "content": "- Acc (Classification Accuracy) introduces a voxel-based classifier, which is pre-trained to classify the 13 categories in ShapeNet [5] according to [48]. Acc metric is used to measure the semantic authenticity of the generated samples." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.576, + 0.47, + 0.713 + ], + "angle": 0, + "content": "- CLIP-S (CLIP Similarity Score) introduces the pretrained vision-language model CLIP [40] for further evaluation. The CLIP can be used to measure the correspondence between given images and texts. We render 5 view images for each generated shape, and compute the cosine similarity score between rendered images and the given text. The highest score is reported for each text query. CLIP-S metric is used to measure the semantic conformance between the generated samples and input texts." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.723, + 0.47, + 0.815 + ], + "angle": 0, + "content": "- TMD (Total Mutual Difference). For each given text description, we generate \\( k = 10 \\) different samples. Then, we compute the average IoU score for each generated shape to other \\( k - 1 \\) shapes. The average IoU score for all text queries is reported. TMD assesses the generation diversity for each given text query." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.388, + 0.47, + 0.815 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.471, + 0.903 + ], + "angle": 0, + "content": "To keep consistency with previous approaches, we limit the comparisons to the chair category in Text2Shape [6] dataset. Since the officially released AutoSDF [34] model was trained on another dataset [2], we re-trained the model following the original settings on the training set of" + }, + { + "type": "table_caption", + "bbox": [ + 0.51, + 0.386, + 0.882, + 0.4 + ], + "angle": 0, + "content": "Table 1. Quantitative comparisons of text-to-shape generation." + }, + { + "type": "table", + "bbox": [ + 0.506, + 0.405, + 0.887, + 0.472 + ], + "angle": 0, + "content": "
MethodsIoU↑Acc↑CLIP-S↑TMD↓
Liu et al. [29]0.16034.7929.940.891
AutoSDF [34]0.18783.8829.100.581
Diffusion-SDF (Ours)0.19488.5630.880.169
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.49, + 0.892, + 0.595 + ], + "angle": 0, + "content": "Text2Shape for the fair comparison. The results are shown in Table 1. From the results, it can be seen that our approach is able to achieve relatively high generation quality with high IoU and Acc scores, and robust text-shape conformance with good CLIP-S performance, while achieving much better generation diversity with a much lower TMD performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.596, + 0.893, + 0.823 + ], + "angle": 0, + "content": "Qualitative results. The quantitative experiment shows the generation performance of our approach on the limited given subset from Text2Shape dataset. Due to the generalization of natural language, our approach is capable of generating different forms of shapes based on various text descriptions. Figure 4 shows the generated results of Diffusion-SDF from different text inputs. The results show that our method can generate eligible results from distinguished conditions. Besides, our method is capable of synthesizing various shape outputs from the same input text description. Figure 5 compares our approach with [29, 34] based on same text queries. The results have shown that our method has a great advantage in the diversity of generated samples, while the previous approaches are unable to generate highly-diversified shapes." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.832, + 0.665, + 0.847 + ], + "angle": 0, + "content": "4.2. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We have conducted extensive ablation studies to demonstrate the effectiveness of our special architecture design for Diffusion-SDF." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12647" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.09, + 0.5, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.532, + 0.092, + 0.885, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.287, + 0.893, + 0.318 + ], + "angle": 0, + "content": "Figure 5. Qualitative comparison of diversified text-to-shape generation. Our approach is capable of generating highly-diversified shapes that conform to the same text query, while also keeping the satisfactory quality of the generated shapes." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.327, + 0.488, + 0.449 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.511, + 0.327, + 0.884, + 0.449 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.455, + 0.893, + 0.484 + ], + "angle": 0, + "content": "Figure 6. Qualitative comparison of U-Net and \\(UinU\\)-Net. Since \\(UinU\\)-Net-based architecture contains a local-focused inner network, it can better recover the independent patch representations, thereby improving the generation quality compared to conventional U-Net." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.504, + 0.473, + 0.791 + ], + "angle": 0, + "content": "Effectiveness of the UinU-Net architecture. In order to validate the benefit of our proposed modifications to the conventional U-Net architecture, we additionally compare our proposed UinU-Net architecture to the simpler U-Net architecture used in [45]. The quantitative results for text-to-shape generation are shown in Table 2. Qualitative comparisons are shown in Figure 6. From the results, it can be found that our proposed UinU-Net architecture for Voxelized Diffusion models generally improves the quality of generated shapes. With the UinU-Net architecture, the noise for each step is estimated both patch-mutually and patch-independently. Since the shape representations are repositioned based on separate patch embeddings extracted by the SDF encoders, the key to recovering the authentic shape SDFs from the joint decoder is to ensure that the generated SDF representations are also distributed independently in patches. From the qualitative results, it can be inferred that the inner network is conducive to recovering the independently distributed patch representations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Inner network architecture. As for the UinU-Net architecture, we have conducted ablation experiments on several variants for the inner network to validate the effectiveness of the final design. The results have shown in Table 3. According to the results, it can be inferred that the inner outer concatenation mechanism and spatial attention layer can generally improve the generation quality. Without the inner-outer" + }, + { + "type": "table_caption", + "bbox": [ + 0.508, + 0.502, + 0.882, + 0.515 + ], + "angle": 0, + "content": "Table 2. Evaluating effectiveness of the UinU-Net architecture." + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.52, + 0.872, + 0.574 + ], + "angle": 0, + "content": "
IoU↑Acc↑CLIP-S↑TMD↓
U-Net [45]0.18780.9829.350.171
UinU-Net (Ours)0.19488.5630.880.169
" + }, + { + "type": "table_caption", + "bbox": [ + 0.512, + 0.581, + 0.879, + 0.595 + ], + "angle": 0, + "content": "Table 3. Evaluating effectiveness of the inner network design." + }, + { + "type": "table", + "bbox": [ + 0.507, + 0.6, + 0.884, + 0.668 + ], + "angle": 0, + "content": "
IoU↑Acc↑CLIP-S↑TMD↓
UinU-Net0.19488.5630.880.169
- w/o in-out concat0.19883.9128.680.181
- w/o spatial attention0.19485.5630.820.161
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.686, + 0.892, + 0.807 + ], + "angle": 0, + "content": "concatenation mechanism, the accuracy score and CLIP-S have significant decreases, indicating that the information transmission mechanism has affected the semantic authenticity and conformance of the generated shapes. Accuracy score has dropped without the spatial attention module, indicating that the introduction of patch-to-patch information helps preserve the full shape semantics while recovering the patch-wise representations." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.817, + 0.78, + 0.833 + ], + "angle": 0, + "content": "4.3. Text-Guided Shape Completion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.894, + 0.903 + ], + "angle": 0, + "content": "In this section, we validate the effectiveness of our approach on the text-guided shape completion task. Specifically, given a partial input shape, our goal is to generate the missing part conditioned on the input text descriptions. For" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12648" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.093, + 0.874, + 0.222 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.227, + 0.893, + 0.255 + ], + "angle": 0, + "content": "Figure 7. Qualitative result of text-guide shape completion. Given a known partial shape, our approach can generate the missing part based on text conditions." + }, + { + "type": "image", + "bbox": [ + 0.097, + 0.269, + 0.32, + 0.392 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.349, + 0.269, + 0.6, + 0.395 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.631, + 0.269, + 0.874, + 0.397 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.402, + 0.893, + 0.43 + ], + "angle": 0, + "content": "Figure 8. Qualitative result of text-guide shape manipulation. Given a known shape, our approach is able to manipulate the given shape into the target shape based on the text descriptions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.451, + 0.473, + 0.633 + ], + "angle": 0, + "content": "instance, we can generate the body of a chair based on the given chair legs or generate the missing chair legs based on the chair body. The qualitative results of our approach are displayed in Figure 7. The results show that our approach is capable of generating the missing part of a shape while being well-blended with the given shape, as evident in the generated examples such as revolving throne, revolving toilet, and revolving sofa. Moreover, our completion performance is not limited by the shape geometry in the training set. The core limitation of our approach is the cut region of patch grids, which can be addressed by increasing resolution and decreasing patch size." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.649, + 0.371, + 0.666 + ], + "angle": 0, + "content": "4.4. Text-Guided Shape Manipulation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.675, + 0.47, + 0.903 + ], + "angle": 0, + "content": "We demonstrate our approach's effectiveness for text-guided shape manipulation. Our approach can modify a given shape to match an instructive text description. Figure 8 gives several qualitative illustrations for our proposed approach. From the results, it can be summarized that our approach can handle the shape manipulation of both local shape structures (e.g. the existence/style of arms or legs) or the overall shape characteristics (e.g. sofa or straight chair). In addition, one key issue for our designed approach is the choice for \\( t_{mid} \\). Since the shape characteristics usually form in the early stage of the reverse process, thus we set \\( t_{mid} \\) to relatively larger step numbers (600~800 step before DDIM's down-sampling). In experiments, we observe that excessively small or large values for \\( t_{mid} \\) result in unchanged or destructed original shape features, respectively." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.476, + 0.893, + 0.657 + ], + "angle": 0, + "content": "Limitations. This paper demonstrates the superiority of our approach on the Text2Shape [6] dataset, which is limited to only two categories from ShapeNet, restricting our approach's generalization to other categories. Moreover, the lack of current shape-text datasets prevents us from validating our approach on additional benchmarks. To address this, we propose introducing more datasets and exploring zero-shot text-to-shape generation by leveraging knowledge from 2D vision-language models. While some studies have attempted to tackle this challenge [48], achieving flexible text-to-shape generation remains a significant obstacle. Our future work will seek a possible solution to this problem." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.893, + 0.81 + ], + "angle": 0, + "content": "Conclusion. Our paper presents a framework for text-to-shape synthesis called Diffusion-SDF, which utilizes a diffusion model to generate voxelized SDFs conditioned on texts. The approach comprises a two-stage pipeline: a patch-wise autoencoder for generating Gaussian SDF representations, followed by a Voxelized Diffusion model with UinU-Net denoisers for generating patch-independent SDF representations. We evaluate our approach on various text-to-shape synthesis tasks, and the results demonstrate that it can generate highly diverse and high-quality 3D shapes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.894, + 0.902 + ], + "angle": 0, + "content": "Acknowledgments This work was supported in part by the National Key Research and Development Program of China under Grant 2017YFA0700802, in part by the National Natural Science Foundation of China under Grant 62206147 and Grant 62125603, and in part by a grant from the Beijing Academy of Artificial Intelligence (BAAI)." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "12649" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.169 + ], + "angle": 0, + "content": "[1] Panos Achlioptas, Olga Diamanti, Ioannis Mitliagkas, and Leonidas J. 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In ICCV, pages 5806-5815, 2021. 2, 5" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.092, + 0.892, + 0.715 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.518, + 0.957 + ], + "angle": 0, + "content": "12651" + } + ] +] \ No newline at end of file diff --git a/2023/Diffusion-SDF_ Text-To-Shape via Voxelized Diffusion/a08ad0f7-f625-4886-ac27-deeab3818eeb_origin.pdf b/2023/Diffusion-SDF_ Text-To-Shape via Voxelized Diffusion/a08ad0f7-f625-4886-ac27-deeab3818eeb_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..2ee1f95d9c3e8da4be0a6d65d72957b76f2847a9 --- /dev/null +++ b/2023/Diffusion-SDF_ Text-To-Shape via Voxelized Diffusion/a08ad0f7-f625-4886-ac27-deeab3818eeb_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:2a0a10e588aa49e11d23186bced76762e00d9d0c6ec7dd372f8d3ac2cd29c30c +size 2945241 diff --git a/2023/Diffusion-SDF_ Text-To-Shape via Voxelized Diffusion/full.md b/2023/Diffusion-SDF_ Text-To-Shape via Voxelized Diffusion/full.md new file mode 100644 index 0000000000000000000000000000000000000000..79db5ad8e098f666a1c7a8e797b444c1be721b6a --- /dev/null +++ b/2023/Diffusion-SDF_ Text-To-Shape via Voxelized Diffusion/full.md @@ -0,0 +1,316 @@ +# Diffusion-SDF: Text-to-Shape via Voxelized Diffusion + +Muheng Li $^{1}$ , Yueqi Duan $^{\dagger,2}$ , Jie Zhou $^{1}$ , Jiwen Lu $^{1}$ + +$^{1}$ Department of Automation, Tsinghua University + +$^{2}$ Department of Electronic Engineering, Tsinghua University + +![](images/6f39f28fd0259c09807bc049bec6f6c39d108427572e4ac27dfb77e6bcfe045d.jpg) +Figure 1. We propose a text-to-shape synthesis approach named Diffusion-SDF. Our method is capable of performing various text-to-shape tasks including text-to-shape generation (directly generating 3D shapes from texts), text-guided shape completion (generating the missing part of an incomplete shape under the guidance of texts), and text-guided shape manipulation (modifying a given shape according to texts). + +# Abstract + +With the rising industrial attention to 3D virtual modeling technology, generating novel 3D content based on specified conditions (e.g. text) has become a hot issue. In this paper, we propose a new generative 3D modeling framework called Diffusion-SDF for the challenging task of text-to-shape synthesis. Previous approaches lack flexibility in both 3D data representation and shape generation, thereby failing to generate highly diversified 3D shapes conforming to the given text descriptions. To address this, we propose a SDF autoencoder together with the Voxelized Diffusion model to learn and generate representations for voxelized signed distance fields (SDFs) of 3D shapes. Specifically, we design a novel UinU-Net architecture that implants a local-focused inner network inside the standard U-Net architecture, which enables better reconstruction of patch-independent SDF representations. We extend our approach to further text-to-shape tasks including text-conditioned shape completion and manipulation. Experimental results show that Diffusion-SDF generates both higher quality and more diversified 3D shapes that conform well to given text descriptions when compared to previous approaches. Code is available at: https://github.com/ttlmh/Diffusion-SDF. + +# 1. Introduction + +Exploring data representations for 3D shapes has been a fundamental and critical issue in 3D computer vision. Explicit 3D representations including point clouds [38, 39], polygon meshes [17, 24] and occupancy voxel grids [9, 53] have been widely applied in various 3D downstream applications [1, 35, 56]. While explicit 3D representations achieve encouraging performance, there are some primary limitations including not being suitable for generating watertight surfaces (e.g. point clouds), or being subject to topological constraints (e.g. meshes). On the other hand, implicit 3D representations have been widely studied more recently [3, 14, 37], with representative works including DeepSDF [37], Occupancy Network [32] and IM-Net [8]. In general, implicit functions encode the shapes by the isosurface of the function, which is a continuous field and can be evaluated at arbitrary resolution. + +In recent years, numerous explorations have been conducted for implicit 3D generative models, which show promising performance on several downstream applications such as single/multi-view 3D reconstruction [23, 54] and shape completion [12, 34]. Besides, several studies have also explored the feasibility of directly generating novel 3D shapes based on implicit representations [15, 21]. However, these approaches are incapable of generating specified 3D shapes that match a given condition, e.g. a short text describing the shape characteristics as shown in Figure 1. + +Text-based visual content synthesis has the advantages of the flexibility and generality [41, 42]. Users may generate rich and diverse 3D shapes based on easily obtained natural language descriptors. In addition to generating 3D shapes directly based on text descriptions, manipulating 3D data with text guidance can be further utilized for iterative 3D synthesis and fine-grained 3D editing, which can be beneficial for non-expert users to create 3D visual content. + +In the literature, there have been few attempts on the challenging task of text-to-shape generation based on implicit 3D representations [29, 34, 48]. For example, AutoSDF [34] introduced a vector quantized SDF autoencoder together with an autoregressive generator for shape generation. While encouraging progress has been made, the quality and diversity of generated shapes still requires improvement. The current approaches struggle to generate highly diversified 3D shapes that both guarantee generation quality and conform to the semantics of the input text. Motivated by the success of denoising diffusion models in 2D image [13, 19, 36] and even explicit 3D point cloud [31, 58, 59] generation, we find that DMs achieve high-quality and highly diversified generation while being robust to model training. To this end, we aim to design an implicit 3D representation-based generative diffusion process for text-to-shape synthesis that can achieve better generation flexibility and generalization performance. + +In this paper, we propose the Diffusion-SDF framework for text-to-shape synthesis based on truncated signed distance fields (TSDFs). Considering that 3D shapes share structural similarities at local scales, and the cubic data volume of 3D voxels may lead to slow sampling speed for diffusion models, we propose a two-stage separated generation pipeline. First, we introduce a patch-based SDF autoencoder that maps the original signed distance fields into patch-independent local Gaussian latent representations. Second, we introduce the Voxelized Diffusion model that captures the intra-patch information along with both patch-top-patch and patch-to-global relations. Specifically, we design a novel UinU-Net architecture to replace the standard U-Net [46] for the noise estimator in the reverse process. UinU-Net implants a local-focused inner network inside the outer U-Net backbone, which takes into account the patch-independent prior of SDF representations to better reconstruct local patch features from noise. Our work digs deeper into the further potential of diffusion model-based approaches towards text-conditioned 3D shape synthesis based on voxelized TSDFs. Experiments on the largest existing text-shape dataset [6] show that our Diffusion-SDF approach achieves promising generation performance on text-to-shape tasks compared to existing state-of-the-art approaches, in both qualitative and quantitative evaluations. + +# 2. Related Work + +Text-conditioned generative 3D models. In the field of generative 3D modeling, a variety of works have focused on synthesizing 3D visual content unconditionally [1, 32, 52, 56] or conditioned on single/multi-view images [9, 34, 54, 55]. Besides, there has also been a series of works concentrating on the challenging task of text-to-shape generation [6]. Some of them adopted purely explicit 3D data representation-based methods to generate 3D shapes conditioned on input text [6, 33, 58]. In contrast, our focus lies on synthesizing 3D shapes based on implicit 3D data representations. So far, there have also been few existing works focusing on the task of implicit text-to-shape generation [29, 34, 48]. All of these approaches have yielded impressive generation results, but there are still some remained issues to be addressed. Sanghi et al. [48] proposed a normalizing flow [43]-based approach to generate shape voxels using implicit Occupancy Networks [32], and Liu et al. [29] introduced a shape-IMLE [28] generator using implicit IMNET [8] decoder, while these approaches neither employ the more flexible implicit SDFs as data representation nor take into account the constraints for local shape structures. More similar to our work, AutoSDF [34] introduced an autoregressive prior for 3D shape generation based on a discretized SDF autoencoder. The autoregressive model adopts a relatively unnatural way to predict patched 3D tokens in a sequential manner that loses the 3D-specific inductive bias and is also relatively inefficient. + +Diffusion Probabilistic Models. Diffusion Probabilistic Models (DPMs) [19, 49], also known as diffusion models, have currently arisen as a powerful family of generative models. Compared to previous state-of-the-art generative models, including Generative Adversarial Network (GAN) [16], Variational Autoencoder (VAE) [26], and flow-based generative models [43], the diffusion model demonstrates its superiority in both training stability and generative diversity [11]. Diffusion models have achieved promising performance on image [13, 19, 36, 45] and speech [7, 27] synthesis. Especially, fairly impressive results have been achieved with diffusion model-based approaches on the task of text-to-image synthesis [41, 45, 47]. In the field of 3D computer vision, several studies have adopted diffusion models for generative 3D modeling [31, 58, 59]. PVD [59] employed diffusion models to generate 3D shapes based on point-voxel 3D representation. Luo et al. [31] treated points in point clouds as particles in a thermodynamic system with a heat bath. LION [58] introduced a VAE framework with hierarchical diffusion models in latent space. All these approaches have focused on the diffusion process of explicit 3D data representations for shape generation. On the contrary, our work tries to explore the feasibility of diffusion models on implicit 3D data representations. + +![](images/c0ef4f7890d6a75ea23def4e026769d2f0d1dfbea590d0e9ef19f57fa1ff4b77.jpg) +Figure 2. Overview of Diffusion-SDF. We propose a two-stage pipeline to generate novel 3D shapes from texts. First, we train an autoencoder to learn patch-independent normal-distributed representations for voxelized TSDFs. Then, we propose the Voxelized Diffusion framework together with the UinU-Net denoiser to generate shape representations. Please check Figure 3 for more details of UinU-Net. + +# 3. Method + +In this section, we introduce the methodology design for Diffusion-SDF. In general, we propose a two-stage pipeline as illustrated in Figure 2. Detailed information of each stage will be included in the following sections. + +# 3.1. Autoencoding Signed Distance Fields + +Signed distance fields (SDF) belong to a type of implicit 3D data representation which assigns the scalar signed distance value to the shape surface for each point $p$ in the 3D space $\mathbb{R}^3$ . Our objective is to generate the signed distance fields for the target 3D shapes that match the given text conditions. Specifically, the 3D data are represented by truncated signed distance functions (TSDF) in a regularly-spaced voxel grid as [3, 22]. Generating voxelized SDFs directly from denoising diffusion models is both cost-expensive and time-consuming. In addition, the local structural information of 3D shapes is not well-emphasized through direct voxel-based generation. To address this, we propose a patch-wise autoencoder to learn the latent representations for voxelized signed distance fields. + +Given a 3D shape, we first sample its truncated signed distance field $x$ as a voxel grid of size $D^3$ . Before the shape $x$ is encoded, it is first split into $N$ local patches of size $P^3$ , producing a sequence of shape patches $X_p = [x_{p1},\dots,x_{pN}]$ , where $N = (D / P)^3$ is the resulting number of patches. Then, the local shape encoder $\mathcal{E}_{loc}$ encodes each shape patches into latent representations $Z_p = [z_{p1},\dots,z_{pN}]$ , where $z_{pn} = \mathcal{E}_{loc}(x_{pn}) \in \mathbb{R}^c$ , and $c$ is the number of latent channels. Here, since each patch is encoded independently, the local structural information can be + +explored well through the local shape encoder. Meanwhile, the input data scale can also be downsampled by the factor $P$ . However, when reconstructing the shape from local patches, it is also necessary to consider the spatial location of each patch in the global shape, and the interrelationship between adjacent patches. To preserve both patch-to-global and patch-to-patch information while decoding the latent embeddings, the patch embeddings are first rearranged into a voxel grid embedding $z$ , and then sent into the patch-joint decoder $\mathcal{D}$ that reconstructs the SDF field from the latent patches, giving $\tilde{x} = \mathcal{D}(z)$ . + +In detail, we adopt a VAE [26, 44]-like autoencoder, which encodes each shape patch into a normal distribution. We utilize a combination of both $\mathcal{L}_1$ reconstruction loss together with the KL-regularization loss at the training stage for the SDF autoencoder. The latter one forces a mild KL-penalty towards a standard normal distribution on each learned patch latent. The final SDF representations will be in the form of patch-independent Gaussian distributions. + +# 3.2. Voxelized Diffusion Models (VDMs) + +Diffusion models (DMs) [19, 49] are a class of probabilistic generative models that learn to fit a certain distribution by gradually denoising a Gaussian variable through a fixed Markov Chain of length $T$ . Given a data sample $x_0 \sim q(x_0)$ , DMs describe two different processes in the opposite direction: a forward process $q(\mathbf{x}_{0:T})$ that gradually transform a data sample into pure Gaussian noise, and a reverse process $p_{\theta}(\mathbf{x}_{0:T})$ that gradually denoise a pure + +Gaussian sample into real data, + +$$ +q \left(\boldsymbol {x} _ {0: T}\right) = q \left(\boldsymbol {x} _ {0}\right) \Pi_ {t = 1} ^ {T} q \left(\boldsymbol {x} _ {t} \mid \boldsymbol {x} _ {t - 1}\right), \tag {1} +$$ + +$$ +p _ {\theta} \left(\boldsymbol {x} _ {0: T}\right) = p \left(\boldsymbol {x} _ {T}\right) \Pi_ {t = 1} ^ {T} p _ {\theta} \left(\boldsymbol {x} _ {t - 1} | \boldsymbol {x} _ {t}\right), +$$ + +where $q(\pmb{x}_t|\pmb{x}_{t-1})$ and $p_\theta(\pmb{x}_{t-1}|\pmb{x}_t)$ are both Gaussian transition probabilities in the forms of + +$$ +q \left(\boldsymbol {x} _ {t} \mid \boldsymbol {x} _ {t - 1}\right) = \mathcal {N} \left(\boldsymbol {x} _ {t}; \sqrt {1 - \beta_ {t}} \boldsymbol {x} _ {t - 1}, \beta_ {t} \boldsymbol {I}\right), \tag {2} +$$ + +$$ +p _ {\theta} \left(\boldsymbol {x} _ {t - 1} | \boldsymbol {x} _ {t}\right) = \mathcal {N} \left(\boldsymbol {x} _ {t - 1}; \boldsymbol {\mu} _ {\theta} \left(\boldsymbol {x} _ {t}, t\right), \beta_ {t} \boldsymbol {I}\right). +$$ + +Based on [19], the mean variable $\pmb{\mu}_{\theta}(\pmb{x}_t,t)$ for the reverse transition $p_{\theta}\left(\pmb{x}_{t - 1}|\pmb{x}_t\right)$ can be expressed in the form of + +$$ +\boldsymbol {\mu} _ {\theta} \left(\boldsymbol {x} _ {t}, t\right) = \frac {1}{\sqrt {\alpha_ {t}}} \left(\boldsymbol {x} _ {t} - \frac {\beta_ {t}}{\sqrt {1 - \bar {\alpha} _ {t}}} \boldsymbol {\epsilon} _ {\theta} \left(\boldsymbol {x} _ {t}, t\right)\right), \tag {3} +$$ + +where $\alpha_{t} = 1 - \beta_{t}$ , $\bar{\alpha}_{t} = \Pi_{i=1}^{t} \alpha_{i}$ , and $\beta_{t}$ decreases to 0 gradually as $t$ approaches 0. The evidence lower bound (ELBO) is maximized at the training stage of DMs, eventually leading to the loss function as the form of + +$$ +\mathcal {L} _ {D M} = \mathbb {E} _ {\boldsymbol {x}, t, \boldsymbol {\epsilon} \sim \mathcal {N} (0, 1)} \left[ \| \boldsymbol {\epsilon} - \boldsymbol {\epsilon} _ {\theta} (\boldsymbol {x} _ {t}, t) \| ^ {2} \right], \tag {4} +$$ + +where $\pmb{x}_t = \sqrt{\bar{\alpha}_t}\pmb{x}_0 + \sqrt{1 - \bar{\alpha}_t}\pmb{\epsilon},$ $\pmb{\epsilon}$ is a noise variable, and $t$ is uniformly sampled from $\{1,\dots,T\}$ . The neural network-based score estimator $\pmb{\epsilon}_{\theta}(\pmb{x}_t,t)$ is the core function of denoising diffusion models, which is implemented as a timestep-conditioned denoising autoencoder in [19]. + +UinU-Net Architecture. In our scenario, we are designing a novel diffusion-based architecture to generate latent SDF representations with regard to the target text conditions. The corresponding TSDF fields can be then reconstructed through the patch-joint decoder which is pre-trained in the first stage. As we mentioned in the above section, the key part of generative diffusion models is to estimate the function approximator $\epsilon_{\theta}$ from the data distribution of the training set. Since our model is designed to generate latent samples, the score estimator can be expressed as $\epsilon_{\theta}(z_t,t)$ , as the loss function becomes + +$$ +\mathcal {L} _ {\text {D i f f u s i o n - S D F}} = \mathbb {E} _ {z, t, \epsilon \sim \mathcal {N} (0, 1)} \left[ \| \epsilon - \epsilon_ {\theta} (z _ {t}, t) \| ^ {2} \right]. \tag {5} +$$ + +To incorporate the 3D positional prior of different latent shape patches, we adopt a 3D U-Net [10]-based autoencoder as the neural function approximator $\epsilon_{\theta}$ that directly learns to denoise the voxel grid embedding $z_{t}$ that is obtained from the pre-trained local shape encoder $\mathcal{E}_{loc}$ . Besides, another crucial prior for our design is the patch-based encoding process, through which all the shape patches are encoded into independent Gaussian distributions. Thus, when generating the local shape embeddings, an important point is to recover the independent distribution for + +![](images/df50bd5778b88bd489565e43d60675f0101589c569fe450b87b75060d189167b.jpg) +Figure 3. Detailed illustration of UinU-Net. To better recover $z$ based on independently distributed patches, we propose to implant an inner network inside the standard U-Net architecture. The inner network is mainly composed of $1 \times 1 \times 1$ convolutions, thus it focuses on patch-wise features, while the spatial transformer brings in patch-to-patch information. (Standard U-Net operators include $3 \times 3 \times 3$ residual blocks, conditional cross-attention layers, pooling layers and up-scaling layers.) + +each shape patch as well. To address this, we propose a novel UinU-Net architecture for the implementation of the autoencoder-based neural score estimator as shown in Figure 3. The standard 3D U-net [10] adopts a series of $3 \times 3 \times 3$ convolutional layers to construct a downsampling-upsampling network architecture with the information shared through skip connections. This design takes into account the patch-to-patch and patch-to-global features via hierarchical receptive fields. Given that our input data are compressed 3D latent representations, and each patch is encoded independently, we propose to implant another inner network inside the outer U-Net architecture where the embedded resolution is equal to the original latent resolution $D / P$ . Specifically, we adopt a $1 \times 1 \times 1$ convolution-based ResNet [18] structure to learn independent patch-focused information. We also introduce the spatial Transformer [51] network that accepts positional embedded patch representations as input tokens, following self-attention layers to capture the relational information between independent local patch embeddings. The inner synthesis paths are skip-connected to the outer ones, ensuring information transmission from inner to outer networks. This architecture is designed to capture the intra-patch information along with both patch-to-patch and patch-to-global relations. + +Text-Guided Shape Generation So far, we have discussed the generative process without text conditions. To synthe- + +size latent SDF representations based on given conditions, we introduce a conditioning mechanism based on classifier-free guidance diffusion [20]. We adopt a text-conditioned score estimator. In detail, to fit the target conditions into the 3D denoising autoencoder, we utilize the cross-attention mechanism as proposed in [45]. The input caption is first encoded as text embeddings through a pre-trained text encoder $\tau$ . Thus, the conditioned score can be formed as $\epsilon_{\theta}(z_t|\tau(c))$ , where $c$ is the input caption. Meanwhile, we also obtain an unconditioned score $\epsilon_{\theta}(z_t|\emptyset)$ with an empty sequence as input caption. Within the guided diffusion sampling process, the output of the model is extrapolated further in the direction of $\epsilon_{\theta}(z_t|\tau(c))$ and away from $\epsilon_{\theta}(z_t|\emptyset)$ as: + +$$ +\hat {\epsilon} _ {\theta} \left(z _ {t} | \tau (c)\right) = \epsilon_ {\theta} \left(z _ {t} | \emptyset\right) + s \cdot \left(\epsilon_ {\theta} \left(z _ {t} | \tau (c)\right) - \epsilon_ {\theta} \left(z _ {t} | \emptyset\right)\right), \tag {6} +$$ + +where $s \geq 1$ refers to the guidance scale. + +Text-Guided Shape Completion Current shape completion approaches mainly focused on recovering the full shapes from partial input shapes or single view images [1, 57, 59]. Besides, we have explored the feasibility of text-conditioned shape completion. According to the patch-based design of our SDF encoder, information for the given shape patches can be encoded even if some of the patches are missing. Motivated by the success of diffusion model-based image inpainting [30, 45], we introduce a mask-diffusion strategy to generate the missing shape based on a pre-trained VDM. The core idea is to incorporate known information into each denoising step of the reverse process. For a full shape representation, we transform it into a partial shape representation given the mask $m_z$ . For each estimation step $z_{t-1}$ , we combine the estimated result through the reverse process $\widetilde{z}_{t-1}$ with the forward sampling result of the unmasked patches $\hat{z}_{t-1}$ , + +$$ +z _ {t - 1} = (1 - m) \odot \widetilde {z} _ {t - 1} + m \odot \hat {z} _ {t - 1}, \tag {7} +$$ + +where $\odot$ refers to element-wise product, and + +$$ +\begin{array}{c} \widetilde {z} _ {t - 1} \sim \mathcal {N} (\boldsymbol {\mu} _ {\theta} (z _ {t}, t, c), \beta_ {t} \boldsymbol {I}) \\ \hat {\quad} \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \end{array} \tag {8} +$$ + +$$ +\hat {z} _ {t - 1} = \sqrt {\bar {\alpha} _ {t}} z _ {0} + \sqrt {1 - \bar {\alpha} _ {t}} \epsilon . +$$ + +By such a strategy, the unknown region can be recovered based on both the given shape and text conditions. + +Text-Guided Shape Manipulation Visual content editing is one of the most valuable applications for vision-language generation. We propose a diffusion-based text-guided shape manipulation approach. For a given shape representation $z_{init}$ , our goal is to transform it into another shape representation $z_{goal}$ based on text $c$ . Inspired by image manipulation techniques [4, 25], we use a cycle-sampling strategy based on a pre-trained VDM. Firstly, we forward-sample the given shape $z_{init}$ for $t_{mid}$ steps, where $0 < t_{mid} < T$ . This operation will lead to an intermediate output $z_{mid}$ + +$$ +z _ {m i d} = \sqrt {\bar {\alpha} _ {t _ {m i d}}} z _ {i n i t} + \sqrt {1 - \bar {\alpha} _ {t _ {m i d}}} \epsilon . \tag {9} +$$ + +Then, the reverse process will start from $z_{mid}$ , and another $t_{mid}$ denoising steps will be conducted conditioned on $c$ . Such a design will make the generated shapes correspond to the target text descriptions while maintaining the original shape characteristics. + +# 4. Experiments + +We extensively experimented with our proposed Diffusion-SDF on various text-conditioned 3D shape synthesis tasks, such as text-to-shape generation, text-conditioned shape completion, and text-guided shape manipulation. The following subsections describe details of experimental settings, results, and analyses. + +Dataset. We mainly trained and evaluated our approach on the current largest text-shape dataset Text2Shape (T2S) [6]. T2S gathered data in the form of shape-text pairs based on two object classes (chairs, tables) in ShapeNet [5]. T2S contains about 75K shape-text pairs in total ( $\sim$ 30K for chairs, $\sim$ 40K for tables), with an average of $\sim$ 16 words per description. T2S was originally designed to contain both color and shape information within the text descriptions, while we mainly focus on text-shape correspondence. + +Implementation details. For the training stage of the SDF autoencoder, to improve the model's generalization ability, we trained the autoencoder across the 13 categories of ShapeNet [5] dataset. For the input data, we sampled the voxelized SDF from original shapes with $64 \times 64 \times 64$ grid points, which is also the data size adopted for follow-up operations. For the diffusion stage, to facilitate the generative sampling speed, we adopt the DDIM [50] sampler to reduce the original DDPM sampling steps from $T = 1000$ to 50. For the conditioning mechanism, we adopt a freeze CLIP [40] text encoder $\tau$ . + +# 4.1. Text-Conditioned Shape Generation + +The most immediate application of our approach involves generating novel shapes that are conditioned on textual descriptions. To showcase the efficacy of our approach, we conduct a comparative evaluation of our generation results against two state-of-the-art supervised text-to-shape synthesis methods that are based on implicit 3D representations [29, 34]. Besides, there are some other works regarding text-to-shape generation, which have different settings compared to our approach. For instance, [48] proposed a zero-shot shape generation approach conditioned on categorical texts, and [15, 33] proposed to generate textured shapes based on provided/pre-generated meshes. As a result, these prior works are not directly compared against our proposed approach. + +Quantitative comparison. To compare the generation performance of our approach to the previous methods quantitatively, we propose to use several metrics to evaluate the generated results: + +![](images/b7326a862a80c0fa072828e72c19228f4fbf32b0f46c20b63da6ff224431b1ee.jpg) +The chair is retro and round with little to no arm rest. + +![](images/5d646b81247a9e0b0a07bf6752d6f154e2550e49a1652b89719eba10394ccea6.jpg) +A sofa with thick legs. + +![](images/fe0a02b11663e8455adbf5e6030af4e36851f719643bb61be16693e03b521668.jpg) +A solid locking chair made of grey tiles. + +![](images/a284aa0bf7608e7740f6590e4a083d3f59f70ec21841576512e7368c48b428ee.jpg) +Fabric chair with singlepiece gray metal legs. + +![](images/b21bc53d8c19e4b0a95b565038c9f79f4754679ab292049c5e26164ced7d9723.jpg) +An old fashioned rocking chair with very high back. + +![](images/e4dcbc6ed55ea589159b9ba90bdbe3e72beddb1bc5864c44386c2903f5f3b6a0.jpg) +A rectangular table with four curving legs. + +![](images/bfc2b9986b0e8897be41a7358a7367dbcee251d9c8c09f294de1b8f1acdf3cb2.jpg) +A two layered table with four legs. + +![](images/514e8f6d63dafd65e13193b9959a976a7738612316d0cd1bcebe5aa3e7010627.jpg) +A wooden round table with very thick legs. +Figure 4. Qualitative results of text-to-shape generation. Our approach can generate shapes that conform to diverse text descriptions. + +![](images/9e38e2f5ca0763cad702031ec4a2677e27ed871d42cfb65205a06d947d88fb2a.jpg) +A tall round table with one thin leg. + +![](images/6259ca67d6af8f02becf570b9b1b8805497833fdc17ffed07c3fcafd468a86c0.jpg) +A triangular table. + +- IoU (Intersection over Union) measures the occupancy similarity between the generated shape to the ground truth. To compute the IoU score, we downsample all the generated SDFs to occupancy voxel grids of size $32^{3}$ . IoU metric is used to measure the conformity of the generated samples with the ground truth shapes. +- Acc (Classification Accuracy) introduces a voxel-based classifier, which is pre-trained to classify the 13 categories in ShapeNet [5] according to [48]. Acc metric is used to measure the semantic authenticity of the generated samples. +- CLIP-S (CLIP Similarity Score) introduces the pretrained vision-language model CLIP [40] for further evaluation. The CLIP can be used to measure the correspondence between given images and texts. We render 5 view images for each generated shape, and compute the cosine similarity score between rendered images and the given text. The highest score is reported for each text query. CLIP-S metric is used to measure the semantic conformance between the generated samples and input texts. +- TMD (Total Mutual Difference). For each given text description, we generate $k = 10$ different samples. Then, we compute the average IoU score for each generated shape to other $k - 1$ shapes. The average IoU score for all text queries is reported. TMD assesses the generation diversity for each given text query. + +To keep consistency with previous approaches, we limit the comparisons to the chair category in Text2Shape [6] dataset. Since the officially released AutoSDF [34] model was trained on another dataset [2], we re-trained the model following the original settings on the training set of + +Table 1. Quantitative comparisons of text-to-shape generation. + +
MethodsIoU↑Acc↑CLIP-S↑TMD↓
Liu et al. [29]0.16034.7929.940.891
AutoSDF [34]0.18783.8829.100.581
Diffusion-SDF (Ours)0.19488.5630.880.169
+ +Text2Shape for the fair comparison. The results are shown in Table 1. From the results, it can be seen that our approach is able to achieve relatively high generation quality with high IoU and Acc scores, and robust text-shape conformance with good CLIP-S performance, while achieving much better generation diversity with a much lower TMD performance. + +Qualitative results. The quantitative experiment shows the generation performance of our approach on the limited given subset from Text2Shape dataset. Due to the generalization of natural language, our approach is capable of generating different forms of shapes based on various text descriptions. Figure 4 shows the generated results of Diffusion-SDF from different text inputs. The results show that our method can generate eligible results from distinguished conditions. Besides, our method is capable of synthesizing various shape outputs from the same input text description. Figure 5 compares our approach with [29, 34] based on same text queries. The results have shown that our method has a great advantage in the diversity of generated samples, while the previous approaches are unable to generate highly-diversified shapes. + +# 4.2. Ablation Studies + +We have conducted extensive ablation studies to demonstrate the effectiveness of our special architecture design for Diffusion-SDF. + +![](images/02ddb923b29588ae6462fd6f0ccf7f57dec96f1ded4376742b1ca91e257942d0.jpg) +Figure 5. Qualitative comparison of diversified text-to-shape generation. Our approach is capable of generating highly-diversified shapes that conform to the same text query, while also keeping the satisfactory quality of the generated shapes. + +![](images/0fa0e6f23b58bfd7c6a05ffc4dd46bc42c6c792bcd844245b3c08862d99008ec.jpg) + +![](images/e7b9179d84c108d13680a3e9006b8721b1f66ab9c339e862167bd18599b9e2a0.jpg) +Figure 6. Qualitative comparison of U-Net and $UinU$ -Net. Since $UinU$ -Net-based architecture contains a local-focused inner network, it can better recover the independent patch representations, thereby improving the generation quality compared to conventional U-Net. + +![](images/09287a35eaa799d9c17681f466a6caede630d2d19c952bdde2ec52d44e29b115.jpg) + +Effectiveness of the UinU-Net architecture. In order to validate the benefit of our proposed modifications to the conventional U-Net architecture, we additionally compare our proposed UinU-Net architecture to the simpler U-Net architecture used in [45]. The quantitative results for text-to-shape generation are shown in Table 2. Qualitative comparisons are shown in Figure 6. From the results, it can be found that our proposed UinU-Net architecture for Voxelized Diffusion models generally improves the quality of generated shapes. With the UinU-Net architecture, the noise for each step is estimated both patch-mutually and patch-independently. Since the shape representations are repositioned based on separate patch embeddings extracted by the SDF encoders, the key to recovering the authentic shape SDFs from the joint decoder is to ensure that the generated SDF representations are also distributed independently in patches. From the qualitative results, it can be inferred that the inner network is conducive to recovering the independently distributed patch representations. + +Inner network architecture. As for the UinU-Net architecture, we have conducted ablation experiments on several variants for the inner network to validate the effectiveness of the final design. The results have shown in Table 3. According to the results, it can be inferred that the inner outer concatenation mechanism and spatial attention layer can generally improve the generation quality. Without the inner-outer + +Table 2. Evaluating effectiveness of the UinU-Net architecture. + +
IoU↑Acc↑CLIP-S↑TMD↓
U-Net [45]0.18780.9829.350.171
UinU-Net (Ours)0.19488.5630.880.169
+ +Table 3. Evaluating effectiveness of the inner network design. + +
IoU↑Acc↑CLIP-S↑TMD↓
UinU-Net0.19488.5630.880.169
- w/o in-out concat0.19883.9128.680.181
- w/o spatial attention0.19485.5630.820.161
+ +concatenation mechanism, the accuracy score and CLIP-S have significant decreases, indicating that the information transmission mechanism has affected the semantic authenticity and conformance of the generated shapes. Accuracy score has dropped without the spatial attention module, indicating that the introduction of patch-to-patch information helps preserve the full shape semantics while recovering the patch-wise representations. + +# 4.3. Text-Guided Shape Completion + +In this section, we validate the effectiveness of our approach on the text-guided shape completion task. Specifically, given a partial input shape, our goal is to generate the missing part conditioned on the input text descriptions. For + +![](images/5a6e07a01fd19d2661def0b2b90315ae8289f103cb47ccd3186506249353f186.jpg) +Figure 7. Qualitative result of text-guide shape completion. Given a known partial shape, our approach can generate the missing part based on text conditions. + +![](images/be0a8e59a20e3e0fdcf462459e869bf12843ea6b948e6d61c0f8df9b0ec01b85.jpg) +Figure 8. Qualitative result of text-guide shape manipulation. Given a known shape, our approach is able to manipulate the given shape into the target shape based on the text descriptions. + +![](images/be8085016c16f5b740f52bfa3ee0ba1fede224360874ca7dfac6c5efb7942816.jpg) + +![](images/aab811df5b21f58eec47fa06a8549b6d28c79bed5df5a03b1c4380a4f131ff7b.jpg) + +instance, we can generate the body of a chair based on the given chair legs or generate the missing chair legs based on the chair body. The qualitative results of our approach are displayed in Figure 7. The results show that our approach is capable of generating the missing part of a shape while being well-blended with the given shape, as evident in the generated examples such as revolving throne, revolving toilet, and revolving sofa. Moreover, our completion performance is not limited by the shape geometry in the training set. The core limitation of our approach is the cut region of patch grids, which can be addressed by increasing resolution and decreasing patch size. + +# 4.4. Text-Guided Shape Manipulation + +We demonstrate our approach's effectiveness for text-guided shape manipulation. Our approach can modify a given shape to match an instructive text description. Figure 8 gives several qualitative illustrations for our proposed approach. From the results, it can be summarized that our approach can handle the shape manipulation of both local shape structures (e.g. the existence/style of arms or legs) or the overall shape characteristics (e.g. sofa or straight chair). In addition, one key issue for our designed approach is the choice for $t_{mid}$ . Since the shape characteristics usually form in the early stage of the reverse process, thus we set $t_{mid}$ to relatively larger step numbers (600~800 step before DDIM's down-sampling). In experiments, we observe that excessively small or large values for $t_{mid}$ result in unchanged or destructed original shape features, respectively. + +Limitations. This paper demonstrates the superiority of our approach on the Text2Shape [6] dataset, which is limited to only two categories from ShapeNet, restricting our approach's generalization to other categories. Moreover, the lack of current shape-text datasets prevents us from validating our approach on additional benchmarks. To address this, we propose introducing more datasets and exploring zero-shot text-to-shape generation by leveraging knowledge from 2D vision-language models. While some studies have attempted to tackle this challenge [48], achieving flexible text-to-shape generation remains a significant obstacle. Our future work will seek a possible solution to this problem. + +Conclusion. Our paper presents a framework for text-to-shape synthesis called Diffusion-SDF, which utilizes a diffusion model to generate voxelized SDFs conditioned on texts. The approach comprises a two-stage pipeline: a patch-wise autoencoder for generating Gaussian SDF representations, followed by a Voxelized Diffusion model with UinU-Net denoisers for generating patch-independent SDF representations. We evaluate our approach on various text-to-shape synthesis tasks, and the results demonstrate that it can generate highly diverse and high-quality 3D shapes. + +Acknowledgments This work was supported in part by the National Key Research and Development Program of China under Grant 2017YFA0700802, in part by the National Natural Science Foundation of China under Grant 62206147 and Grant 62125603, and in part by a grant from the Beijing Academy of Artificial Intelligence (BAAI). + +# References + +[1] Panos Achlioptas, Olga Diamanti, Ioannis Mitliagkas, and Leonidas J. Guibas. Learning representations and generative models for 3D point clouds. In ICML, pages 40-49, 2018. 1, 2, 5 +[2] Panos Achlioptas, Leonidas J. Guibas, Noah D. Goodman, Judy Fan, and Robert X. D. Hawkins. Shapeplot: Learning language for shape differentiation. In ICCV, pages 8937-8946, 2019. 6 +[3] Rohan Chabra, Jan Eric Lenssen, Eddy Ilg, Tanner Schmidt, Julian Straub, Steven Lovegrove, and Richard A. Newcombe. 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Gomez, Lukasz Kaiser, and Illia Polosukhin. Attention is all you need. In NeurIPS, pages 5998-6008, 2017. 4 +[52] Jiajun Wu, Chengkai Zhang, Tianfan Xue, Bill Freeman, and Josh Tenenbaum. Learning a probabilistic latent space of object shapes via 3D generative-adversarial modeling. In NeurIPS, pages 82–90, 2016. 2 +[53] Zhirong Wu, Shuran Song, Aditya Khosla, Fisher Yu, Linguang Zhang, Xiaou Tang, and Jianxiong Xiao. 3D ShapeNets: A deep representation for volumetric shapes. In CVPR, pages 1912-1920, 2015. 1 +[54] Qiangeng Xu, Weiyue Wang, Duygu Ceylan, Radomir Mech, and Ulrich Neumann. DISN: deep implicit surface network for high-quality single-view 3D reconstruction. In NeurIPS, pages 490-500, 2019. 1, 2 +[55] Xinchen Yan, Jimei Yang, Ersin Yumer, Yijie Guo, and Honglak Lee. Perspective transformer nets: Learning single-view 3D object reconstruction without 3D supervision. In NeurIPS, pages 1696-1704, 2016. 2 +[56] Guandao Yang, Xun Huang, Zekun Hao, Ming-Yu Liu, Serge J. Belongie, and Bharath Hariharan. Pointflow: 3D point cloud generation with continuous normalizing flows. In ICCV, pages 4540-4549, 2019. 1, 2 +[57] Xumin Yu, Yongming Rao, Ziyi Wang, Zuyan Liu, Jiwen Lu, and Jie Zhou. Pointr: Diverse point cloud completion with geometry-aware transformers. In ICCV, pages 12478-12487, 2021. 5 +[58] Xiaohui Zeng, Arash Vahdat, Francis Williams, Zan Gojcic, Or Litany, Sanja Fidler, and Karsten Kreis. LION: latent point diffusion models for 3D shape generation. 2022. 2 +[59] Linqi Zhou, Yilun Du, and Jiajun Wu. 3D shape generation and completion through point-voxel diffusion. In ICCV, pages 5806-5815, 2021. 2, 5 \ No newline at end of file diff --git a/2023/Diffusion-SDF_ Text-To-Shape via Voxelized Diffusion/images.zip b/2023/Diffusion-SDF_ Text-To-Shape via Voxelized Diffusion/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..4f882b6bc1a3e6e40045b77e5cde7872ec526cd0 --- /dev/null +++ b/2023/Diffusion-SDF_ Text-To-Shape via Voxelized Diffusion/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:76d437e24e543662f06d504f9355e110a4571c4d365f65c1caf0cdcb7af2cfd6 +size 543526 diff --git a/2023/Diffusion-SDF_ Text-To-Shape via Voxelized Diffusion/layout.json b/2023/Diffusion-SDF_ Text-To-Shape via Voxelized Diffusion/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..ec58c28490e3d1bb0c40318587342b27ba130e3b --- /dev/null +++ b/2023/Diffusion-SDF_ Text-To-Shape via Voxelized Diffusion/layout.json @@ -0,0 +1,8796 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 132, + 103, + 463, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 132, + 103, + 463, + 121 + ], + "spans": [ + { + "bbox": [ + 132, + 103, + 463, + 121 + ], + "type": "text", + "content": "Diffusion-SDF: Text-to-Shape via Voxelized Diffusion" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 175, + 142, + 417, + 157 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 175, + 142, + 417, + 157 + ], + "spans": [ + { + "bbox": [ + 175, + 142, + 417, + 157 + ], + "type": "text", + "content": "Muheng Li" + }, + { + "bbox": [ + 175, + 142, + 417, + 157 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 175, + 142, + 417, + 157 + ], + "type": "text", + "content": ", Yueqi Duan" + }, + { + "bbox": [ + 175, + 142, + 417, + 157 + ], + "type": "inline_equation", + "content": "^{\\dagger,2}" + }, + { + "bbox": [ + 175, + 142, + 417, + 157 + ], + "type": "text", + "content": ", Jie Zhou" + }, + { + "bbox": [ + 175, + 142, + 417, + 157 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 175, + 142, + 417, + 157 + ], + "type": "text", + "content": ", Jiwen Lu" + }, + { + "bbox": [ + 175, + 142, + 417, + 157 + ], + "type": "inline_equation", + "content": "^{1}" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 177, + 157, + 417, + 172 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 177, + 157, + 417, + 172 + ], + "spans": [ + { + "bbox": [ + 177, + 157, + 417, + 172 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 177, + 157, + 417, + 172 + ], + "type": "text", + "content": "Department of Automation, Tsinghua University" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 150, + 172, + 443, + 186 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 150, + 172, + 443, + 186 + ], + "spans": [ + { + "bbox": [ + 150, + 172, + 443, + 186 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 150, + 172, + 443, + 186 + ], + "type": "text", + "content": "Department of Electronic Engineering, Tsinghua University" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 50, + 201, + 541, + 333 + ], + "blocks": [ + { + "bbox": [ + 50, + 201, + 541, + 333 + ], + "lines": [ + { + "bbox": [ + 50, + 201, + 541, + 333 + ], + "spans": [ + { + "bbox": [ + 50, + 201, + 541, + 333 + ], + "type": "image", + "image_path": "6f39f28fd0259c09807bc049bec6f6c39d108427572e4ac27dfb77e6bcfe045d.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 338, + 547, + 373 + ], + "lines": [ + { + "bbox": [ + 46, + 338, + 547, + 373 + ], + "spans": [ + { + "bbox": [ + 46, + 338, + 547, + 373 + ], + "type": "text", + "content": "Figure 1. We propose a text-to-shape synthesis approach named Diffusion-SDF. Our method is capable of performing various text-to-shape tasks including text-to-shape generation (directly generating 3D shapes from texts), text-guided shape completion (generating the missing part of an incomplete shape under the guidance of texts), and text-guided shape manipulation (modifying a given shape according to texts)." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 143, + 382, + 192, + 395 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 382, + 192, + 395 + ], + "spans": [ + { + "bbox": [ + 143, + 382, + 192, + 395 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 45, + 407, + 290, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 407, + 290, + 684 + ], + "spans": [ + { + "bbox": [ + 45, + 407, + 290, + 684 + ], + "type": "text", + "content": "With the rising industrial attention to 3D virtual modeling technology, generating novel 3D content based on specified conditions (e.g. text) has become a hot issue. In this paper, we propose a new generative 3D modeling framework called Diffusion-SDF for the challenging task of text-to-shape synthesis. Previous approaches lack flexibility in both 3D data representation and shape generation, thereby failing to generate highly diversified 3D shapes conforming to the given text descriptions. To address this, we propose a SDF autoencoder together with the Voxelized Diffusion model to learn and generate representations for voxelized signed distance fields (SDFs) of 3D shapes. Specifically, we design a novel UinU-Net architecture that implants a local-focused inner network inside the standard U-Net architecture, which enables better reconstruction of patch-independent SDF representations. We extend our approach to further text-to-shape tasks including text-conditioned shape completion and manipulation. Experimental results show that Diffusion-SDF generates both higher quality and more diversified 3D shapes that conform well to given text descriptions when compared to previous approaches. Code is available at: https://github.com/ttlmh/Diffusion-SDF." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 307, + 382, + 387, + 394 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 382, + 387, + 394 + ], + "spans": [ + { + "bbox": [ + 307, + 382, + 387, + 394 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 402, + 547, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 402, + 547, + 593 + ], + "spans": [ + { + "bbox": [ + 304, + 402, + 547, + 593 + ], + "type": "text", + "content": "Exploring data representations for 3D shapes has been a fundamental and critical issue in 3D computer vision. Explicit 3D representations including point clouds [38, 39], polygon meshes [17, 24] and occupancy voxel grids [9, 53] have been widely applied in various 3D downstream applications [1, 35, 56]. While explicit 3D representations achieve encouraging performance, there are some primary limitations including not being suitable for generating watertight surfaces (e.g. point clouds), or being subject to topological constraints (e.g. meshes). On the other hand, implicit 3D representations have been widely studied more recently [3, 14, 37], with representative works including DeepSDF [37], Occupancy Network [32] and IM-Net [8]. In general, implicit functions encode the shapes by the isosurface of the function, which is a continuous field and can be evaluated at arbitrary resolution." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 594, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 548, + 714 + ], + "type": "text", + "content": "In recent years, numerous explorations have been conducted for implicit 3D generative models, which show promising performance on several downstream applications such as single/multi-view 3D reconstruction [23, 54] and shape completion [12, 34]. Besides, several studies have also explored the feasibility of directly generating novel 3D shapes based on implicit representations [15, 21]. However, these approaches are incapable of generating specified 3D shapes that match a given condition, e.g. a short text describing the shape characteristics as shown in Figure 1." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 63, + 702, + 140, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 702, + 140, + 713 + ], + "spans": [ + { + "bbox": [ + 63, + 702, + 140, + 713 + ], + "type": "text", + "content": "†Corresponding author." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "12642" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 167 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 167 + ], + "type": "text", + "content": "Text-based visual content synthesis has the advantages of the flexibility and generality [41, 42]. Users may generate rich and diverse 3D shapes based on easily obtained natural language descriptors. In addition to generating 3D shapes directly based on text descriptions, manipulating 3D data with text guidance can be further utilized for iterative 3D synthesis and fine-grained 3D editing, which can be beneficial for non-expert users to create 3D visual content." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 168, + 288, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 168, + 288, + 384 + ], + "spans": [ + { + "bbox": [ + 46, + 168, + 288, + 384 + ], + "type": "text", + "content": "In the literature, there have been few attempts on the challenging task of text-to-shape generation based on implicit 3D representations [29, 34, 48]. For example, AutoSDF [34] introduced a vector quantized SDF autoencoder together with an autoregressive generator for shape generation. While encouraging progress has been made, the quality and diversity of generated shapes still requires improvement. The current approaches struggle to generate highly diversified 3D shapes that both guarantee generation quality and conform to the semantics of the input text. Motivated by the success of denoising diffusion models in 2D image [13, 19, 36] and even explicit 3D point cloud [31, 58, 59] generation, we find that DMs achieve high-quality and highly diversified generation while being robust to model training. To this end, we aim to design an implicit 3D representation-based generative diffusion process for text-to-shape synthesis that can achieve better generation flexibility and generalization performance." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 385, + 288, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 385, + 288, + 684 + ], + "spans": [ + { + "bbox": [ + 46, + 385, + 288, + 684 + ], + "type": "text", + "content": "In this paper, we propose the Diffusion-SDF framework for text-to-shape synthesis based on truncated signed distance fields (TSDFs). Considering that 3D shapes share structural similarities at local scales, and the cubic data volume of 3D voxels may lead to slow sampling speed for diffusion models, we propose a two-stage separated generation pipeline. First, we introduce a patch-based SDF autoencoder that maps the original signed distance fields into patch-independent local Gaussian latent representations. Second, we introduce the Voxelized Diffusion model that captures the intra-patch information along with both patch-top-patch and patch-to-global relations. Specifically, we design a novel UinU-Net architecture to replace the standard U-Net [46] for the noise estimator in the reverse process. UinU-Net implants a local-focused inner network inside the outer U-Net backbone, which takes into account the patch-independent prior of SDF representations to better reconstruct local patch features from noise. Our work digs deeper into the further potential of diffusion model-based approaches towards text-conditioned 3D shape synthesis based on voxelized TSDFs. Experiments on the largest existing text-shape dataset [6] show that our Diffusion-SDF approach achieves promising generation performance on text-to-shape tasks compared to existing state-of-the-art approaches, in both qualitative and quantitative evaluations." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 306, + 71, + 392, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 71, + 392, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 392, + 84 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 97, + 547, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 97, + 547, + 421 + ], + "spans": [ + { + "bbox": [ + 304, + 97, + 547, + 421 + ], + "type": "text", + "content": "Text-conditioned generative 3D models. In the field of generative 3D modeling, a variety of works have focused on synthesizing 3D visual content unconditionally [1, 32, 52, 56] or conditioned on single/multi-view images [9, 34, 54, 55]. Besides, there has also been a series of works concentrating on the challenging task of text-to-shape generation [6]. Some of them adopted purely explicit 3D data representation-based methods to generate 3D shapes conditioned on input text [6, 33, 58]. In contrast, our focus lies on synthesizing 3D shapes based on implicit 3D data representations. So far, there have also been few existing works focusing on the task of implicit text-to-shape generation [29, 34, 48]. All of these approaches have yielded impressive generation results, but there are still some remained issues to be addressed. Sanghi et al. [48] proposed a normalizing flow [43]-based approach to generate shape voxels using implicit Occupancy Networks [32], and Liu et al. [29] introduced a shape-IMLE [28] generator using implicit IMNET [8] decoder, while these approaches neither employ the more flexible implicit SDFs as data representation nor take into account the constraints for local shape structures. More similar to our work, AutoSDF [34] introduced an autoregressive prior for 3D shape generation based on a discretized SDF autoencoder. The autoregressive model adopts a relatively unnatural way to predict patched 3D tokens in a sequential manner that loses the 3D-specific inductive bias and is also relatively inefficient." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 426, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 547, + 715 + ], + "type": "text", + "content": "Diffusion Probabilistic Models. Diffusion Probabilistic Models (DPMs) [19, 49], also known as diffusion models, have currently arisen as a powerful family of generative models. Compared to previous state-of-the-art generative models, including Generative Adversarial Network (GAN) [16], Variational Autoencoder (VAE) [26], and flow-based generative models [43], the diffusion model demonstrates its superiority in both training stability and generative diversity [11]. Diffusion models have achieved promising performance on image [13, 19, 36, 45] and speech [7, 27] synthesis. Especially, fairly impressive results have been achieved with diffusion model-based approaches on the task of text-to-image synthesis [41, 45, 47]. In the field of 3D computer vision, several studies have adopted diffusion models for generative 3D modeling [31, 58, 59]. PVD [59] employed diffusion models to generate 3D shapes based on point-voxel 3D representation. Luo et al. [31] treated points in point clouds as particles in a thermodynamic system with a heat bath. LION [58] introduced a VAE framework with hierarchical diffusion models in latent space. All these approaches have focused on the diffusion process of explicit 3D data representations for shape generation. On the contrary, our work tries to explore the feasibility of diffusion models on implicit 3D data representations." + } + ] + } + ], + "index": 5 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 46, + 693, + 288, + 715 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 693, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 693, + 288, + 715 + ], + "type": "text", + "content": "Strictly speaking, our approach employs a combined explicit-implicit representation in the form of voxelized signed distance fields." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "12643" + } + ] + } + ], + "index": 7 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 72, + 542, + 278 + ], + "blocks": [ + { + "bbox": [ + 56, + 72, + 542, + 278 + ], + "lines": [ + { + "bbox": [ + 56, + 72, + 542, + 278 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 542, + 278 + ], + "type": "image", + "image_path": "c0ef4f7890d6a75ea23def4e026769d2f0d1dfbea590d0e9ef19f57fa1ff4b77.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 279, + 547, + 313 + ], + "lines": [ + { + "bbox": [ + 46, + 279, + 547, + 313 + ], + "spans": [ + { + "bbox": [ + 46, + 279, + 547, + 313 + ], + "type": "text", + "content": "Figure 2. Overview of Diffusion-SDF. We propose a two-stage pipeline to generate novel 3D shapes from texts. First, we train an autoencoder to learn patch-independent normal-distributed representations for voxelized TSDFs. Then, we propose the Voxelized Diffusion framework together with the UinU-Net denoiser to generate shape representations. Please check Figure 3 for more details of UinU-Net." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 327, + 104, + 339 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 327, + 104, + 339 + ], + "spans": [ + { + "bbox": [ + 47, + 327, + 104, + 339 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 348, + 288, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 348, + 288, + 397 + ], + "spans": [ + { + "bbox": [ + 46, + 348, + 288, + 397 + ], + "type": "text", + "content": "In this section, we introduce the methodology design for Diffusion-SDF. In general, we propose a two-stage pipeline as illustrated in Figure 2. Detailed information of each stage will be included in the following sections." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 406, + 243, + 419 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 406, + 243, + 419 + ], + "spans": [ + { + "bbox": [ + 47, + 406, + 243, + 419 + ], + "type": "text", + "content": "3.1. Autoencoding Signed Distance Fields" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 426, + 287, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 426, + 287, + 593 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 287, + 593 + ], + "type": "text", + "content": "Signed distance fields (SDF) belong to a type of implicit 3D data representation which assigns the scalar signed distance value to the shape surface for each point " + }, + { + "bbox": [ + 46, + 426, + 287, + 593 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 426, + 287, + 593 + ], + "type": "text", + "content": " in the 3D space " + }, + { + "bbox": [ + 46, + 426, + 287, + 593 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^3" + }, + { + "bbox": [ + 46, + 426, + 287, + 593 + ], + "type": "text", + "content": ". Our objective is to generate the signed distance fields for the target 3D shapes that match the given text conditions. Specifically, the 3D data are represented by truncated signed distance functions (TSDF) in a regularly-spaced voxel grid as [3, 22]. Generating voxelized SDFs directly from denoising diffusion models is both cost-expensive and time-consuming. In addition, the local structural information of 3D shapes is not well-emphasized through direct voxel-based generation. To address this, we propose a patch-wise autoencoder to learn the latent representations for voxelized signed distance fields." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": "Given a 3D shape, we first sample its truncated signed distance field " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " as a voxel grid of size " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "D^3" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": ". Before the shape " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " is encoded, it is first split into " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " local patches of size " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "P^3" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": ", producing a sequence of shape patches " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "X_p = [x_{p1},\\dots,x_{pN}]" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "N = (D / P)^3" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " is the resulting number of patches. Then, the local shape encoder " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{E}_{loc}" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " encodes each shape patches into latent representations " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "Z_p = [z_{p1},\\dots,z_{pN}]" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "z_{pn} = \\mathcal{E}_{loc}(x_{pn}) \\in \\mathbb{R}^c" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " is the number of latent channels. Here, since each patch is encoded independently, the local structural information can be" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 328, + 547, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 328, + 547, + 461 + ], + "spans": [ + { + "bbox": [ + 304, + 328, + 547, + 461 + ], + "type": "text", + "content": "explored well through the local shape encoder. Meanwhile, the input data scale can also be downsampled by the factor " + }, + { + "bbox": [ + 304, + 328, + 547, + 461 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 328, + 547, + 461 + ], + "type": "text", + "content": ". However, when reconstructing the shape from local patches, it is also necessary to consider the spatial location of each patch in the global shape, and the interrelationship between adjacent patches. To preserve both patch-to-global and patch-to-patch information while decoding the latent embeddings, the patch embeddings are first rearranged into a voxel grid embedding " + }, + { + "bbox": [ + 304, + 328, + 547, + 461 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 304, + 328, + 547, + 461 + ], + "type": "text", + "content": ", and then sent into the patch-joint decoder " + }, + { + "bbox": [ + 304, + 328, + 547, + 461 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 304, + 328, + 547, + 461 + ], + "type": "text", + "content": " that reconstructs the SDF field from the latent patches, giving " + }, + { + "bbox": [ + 304, + 328, + 547, + 461 + ], + "type": "inline_equation", + "content": "\\tilde{x} = \\mathcal{D}(z)" + }, + { + "bbox": [ + 304, + 328, + 547, + 461 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 467, + 547, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 467, + 547, + 564 + ], + "spans": [ + { + "bbox": [ + 304, + 467, + 547, + 564 + ], + "type": "text", + "content": "In detail, we adopt a VAE [26, 44]-like autoencoder, which encodes each shape patch into a normal distribution. We utilize a combination of both " + }, + { + "bbox": [ + 304, + 467, + 547, + 564 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_1" + }, + { + "bbox": [ + 304, + 467, + 547, + 564 + ], + "type": "text", + "content": " reconstruction loss together with the KL-regularization loss at the training stage for the SDF autoencoder. The latter one forces a mild KL-penalty towards a standard normal distribution on each learned patch latent. The final SDF representations will be in the form of patch-independent Gaussian distributions." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 592, + 497, + 605 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 592, + 497, + 605 + ], + "spans": [ + { + "bbox": [ + 306, + 592, + 497, + 605 + ], + "type": "text", + "content": "3.2. Voxelized Diffusion Models (VDMs)" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "type": "text", + "content": "Diffusion models (DMs) [19, 49] are a class of probabilistic generative models that learn to fit a certain distribution by gradually denoising a Gaussian variable through a fixed Markov Chain of length " + }, + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "type": "text", + "content": ". Given a data sample " + }, + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "type": "inline_equation", + "content": "x_0 \\sim q(x_0)" + }, + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "type": "text", + "content": ", DMs describe two different processes in the opposite direction: a forward process " + }, + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "type": "inline_equation", + "content": "q(\\mathbf{x}_{0:T})" + }, + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "type": "text", + "content": " that gradually transform a data sample into pure Gaussian noise, and a reverse process " + }, + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "type": "inline_equation", + "content": "p_{\\theta}(\\mathbf{x}_{0:T})" + }, + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "type": "text", + "content": " that gradually denoise a pure" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "12644" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 176, + 85 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 176, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 176, + 85 + ], + "type": "text", + "content": "Gaussian sample into real data," + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 90, + 93, + 287, + 113 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 90, + 93, + 287, + 113 + ], + "spans": [ + { + "bbox": [ + 90, + 93, + 287, + 113 + ], + "type": "interline_equation", + "content": "q \\left(\\boldsymbol {x} _ {0: T}\\right) = q \\left(\\boldsymbol {x} _ {0}\\right) \\Pi_ {t = 1} ^ {T} q \\left(\\boldsymbol {x} _ {t} \\mid \\boldsymbol {x} _ {t - 1}\\right), \\tag {1}", + "image_path": "bb0b6552efb21d7e9654fc81a9916eb9ac462f42a9c2604536e08ef0cbd6fc9e.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 87, + 110, + 247, + 124 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 110, + 247, + 124 + ], + "spans": [ + { + "bbox": [ + 87, + 110, + 247, + 124 + ], + "type": "interline_equation", + "content": "p _ {\\theta} \\left(\\boldsymbol {x} _ {0: T}\\right) = p \\left(\\boldsymbol {x} _ {T}\\right) \\Pi_ {t = 1} ^ {T} p _ {\\theta} \\left(\\boldsymbol {x} _ {t - 1} | \\boldsymbol {x} _ {t}\\right),", + "image_path": "ac002bb88704fa8aca843eb9d09de9a63d68dfb2897ede23566bdabf38ed17fa.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 133, + 287, + 157 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 133, + 287, + 157 + ], + "spans": [ + { + "bbox": [ + 47, + 133, + 287, + 157 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 133, + 287, + 157 + ], + "type": "inline_equation", + "content": "q(\\pmb{x}_t|\\pmb{x}_{t-1})" + }, + { + "bbox": [ + 47, + 133, + 287, + 157 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 133, + 287, + 157 + ], + "type": "inline_equation", + "content": "p_\\theta(\\pmb{x}_{t-1}|\\pmb{x}_t)" + }, + { + "bbox": [ + 47, + 133, + 287, + 157 + ], + "type": "text", + "content": " are both Gaussian transition probabilities in the forms of" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 77, + 166, + 287, + 189 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 166, + 287, + 189 + ], + "spans": [ + { + "bbox": [ + 77, + 166, + 287, + 189 + ], + "type": "interline_equation", + "content": "q \\left(\\boldsymbol {x} _ {t} \\mid \\boldsymbol {x} _ {t - 1}\\right) = \\mathcal {N} \\left(\\boldsymbol {x} _ {t}; \\sqrt {1 - \\beta_ {t}} \\boldsymbol {x} _ {t - 1}, \\beta_ {t} \\boldsymbol {I}\\right), \\tag {2}", + "image_path": "b9259b36506ffae9072ff0fb594c9ec0c9e852434fdc663677a9986f1c4ce159.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 74, + 189, + 249, + 201 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 74, + 189, + 249, + 201 + ], + "spans": [ + { + "bbox": [ + 74, + 189, + 249, + 201 + ], + "type": "interline_equation", + "content": "p _ {\\theta} \\left(\\boldsymbol {x} _ {t - 1} | \\boldsymbol {x} _ {t}\\right) = \\mathcal {N} \\left(\\boldsymbol {x} _ {t - 1}; \\boldsymbol {\\mu} _ {\\theta} \\left(\\boldsymbol {x} _ {t}, t\\right), \\beta_ {t} \\boldsymbol {I}\\right).", + "image_path": "feed641750205c64e86b4a882592b9527656ad464a3cfd85132c38766c7b9301.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 210, + 287, + 236 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 210, + 287, + 236 + ], + "spans": [ + { + "bbox": [ + 47, + 210, + 287, + 236 + ], + "type": "text", + "content": "Based on [19], the mean variable " + }, + { + "bbox": [ + 47, + 210, + 287, + 236 + ], + "type": "inline_equation", + "content": "\\pmb{\\mu}_{\\theta}(\\pmb{x}_t,t)" + }, + { + "bbox": [ + 47, + 210, + 287, + 236 + ], + "type": "text", + "content": " for the reverse transition " + }, + { + "bbox": [ + 47, + 210, + 287, + 236 + ], + "type": "inline_equation", + "content": "p_{\\theta}\\left(\\pmb{x}_{t - 1}|\\pmb{x}_t\\right)" + }, + { + "bbox": [ + 47, + 210, + 287, + 236 + ], + "type": "text", + "content": " can be expressed in the form of" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 64, + 243, + 287, + 271 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 243, + 287, + 271 + ], + "spans": [ + { + "bbox": [ + 64, + 243, + 287, + 271 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\mu} _ {\\theta} \\left(\\boldsymbol {x} _ {t}, t\\right) = \\frac {1}{\\sqrt {\\alpha_ {t}}} \\left(\\boldsymbol {x} _ {t} - \\frac {\\beta_ {t}}{\\sqrt {1 - \\bar {\\alpha} _ {t}}} \\boldsymbol {\\epsilon} _ {\\theta} \\left(\\boldsymbol {x} _ {t}, t\\right)\\right), \\tag {3}", + "image_path": "b13ca213b37d354103fe62391750fcf79bd73bd5b286bd37107fcbc463b69068.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 279, + 287, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 279, + 287, + 327 + ], + "spans": [ + { + "bbox": [ + 47, + 279, + 287, + 327 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 279, + 287, + 327 + ], + "type": "inline_equation", + "content": "\\alpha_{t} = 1 - \\beta_{t}" + }, + { + "bbox": [ + 47, + 279, + 287, + 327 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 279, + 287, + 327 + ], + "type": "inline_equation", + "content": "\\bar{\\alpha}_{t} = \\Pi_{i=1}^{t} \\alpha_{i}" + }, + { + "bbox": [ + 47, + 279, + 287, + 327 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 279, + 287, + 327 + ], + "type": "inline_equation", + "content": "\\beta_{t}" + }, + { + "bbox": [ + 47, + 279, + 287, + 327 + ], + "type": "text", + "content": " decreases to 0 gradually as " + }, + { + "bbox": [ + 47, + 279, + 287, + 327 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 279, + 287, + 327 + ], + "type": "text", + "content": " approaches 0. The evidence lower bound (ELBO) is maximized at the training stage of DMs, eventually leading to the loss function as the form of" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 78, + 335, + 287, + 357 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 335, + 287, + 357 + ], + "spans": [ + { + "bbox": [ + 78, + 335, + 287, + 357 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {D M} = \\mathbb {E} _ {\\boldsymbol {x}, t, \\boldsymbol {\\epsilon} \\sim \\mathcal {N} (0, 1)} \\left[ \\| \\boldsymbol {\\epsilon} - \\boldsymbol {\\epsilon} _ {\\theta} (\\boldsymbol {x} _ {t}, t) \\| ^ {2} \\right], \\tag {4}", + "image_path": "f9e61169e1b39960921391c18459cb06bae0c12e58208a8c5a03d0883d420cf2.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 365, + 287, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 365, + 287, + 426 + ], + "spans": [ + { + "bbox": [ + 47, + 365, + 287, + 426 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 365, + 287, + 426 + ], + "type": "inline_equation", + "content": "\\pmb{x}_t = \\sqrt{\\bar{\\alpha}_t}\\pmb{x}_0 + \\sqrt{1 - \\bar{\\alpha}_t}\\pmb{\\epsilon}," + }, + { + "bbox": [ + 47, + 365, + 287, + 426 + ], + "type": "inline_equation", + "content": "\\pmb{\\epsilon}" + }, + { + "bbox": [ + 47, + 365, + 287, + 426 + ], + "type": "text", + "content": " is a noise variable, and " + }, + { + "bbox": [ + 47, + 365, + 287, + 426 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 365, + 287, + 426 + ], + "type": "text", + "content": " is uniformly sampled from " + }, + { + "bbox": [ + 47, + 365, + 287, + 426 + ], + "type": "inline_equation", + "content": "\\{1,\\dots,T\\}" + }, + { + "bbox": [ + 47, + 365, + 287, + 426 + ], + "type": "text", + "content": ". The neural network-based score estimator " + }, + { + "bbox": [ + 47, + 365, + 287, + 426 + ], + "type": "inline_equation", + "content": "\\pmb{\\epsilon}_{\\theta}(\\pmb{x}_t,t)" + }, + { + "bbox": [ + 47, + 365, + 287, + 426 + ], + "type": "text", + "content": " is the core function of denoising diffusion models, which is implemented as a timestep-conditioned denoising autoencoder in [19]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 426, + 287, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 426, + 287, + 557 + ], + "spans": [ + { + "bbox": [ + 47, + 426, + 287, + 557 + ], + "type": "text", + "content": "UinU-Net Architecture. In our scenario, we are designing a novel diffusion-based architecture to generate latent SDF representations with regard to the target text conditions. The corresponding TSDF fields can be then reconstructed through the patch-joint decoder which is pre-trained in the first stage. As we mentioned in the above section, the key part of generative diffusion models is to estimate the function approximator " + }, + { + "bbox": [ + 47, + 426, + 287, + 557 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 47, + 426, + 287, + 557 + ], + "type": "text", + "content": " from the data distribution of the training set. Since our model is designed to generate latent samples, the score estimator can be expressed as " + }, + { + "bbox": [ + 47, + 426, + 287, + 557 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(z_t,t)" + }, + { + "bbox": [ + 47, + 426, + 287, + 557 + ], + "type": "text", + "content": ", as the loss function becomes" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 563, + 287, + 593 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 563, + 287, + 593 + ], + "spans": [ + { + "bbox": [ + 55, + 563, + 287, + 593 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {D i f f u s i o n - S D F}} = \\mathbb {E} _ {z, t, \\epsilon \\sim \\mathcal {N} (0, 1)} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} (z _ {t}, t) \\| ^ {2} \\right]. \\tag {5}", + "image_path": "4995fe9c64ae4239474d73c72aea7d82a6ee0376632ae6f4bcdff05252379e6b.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 594, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 594, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 594, + 287, + 713 + ], + "type": "text", + "content": "To incorporate the 3D positional prior of different latent shape patches, we adopt a 3D U-Net [10]-based autoencoder as the neural function approximator " + }, + { + "bbox": [ + 47, + 594, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 47, + 594, + 287, + 713 + ], + "type": "text", + "content": " that directly learns to denoise the voxel grid embedding " + }, + { + "bbox": [ + 47, + 594, + 287, + 713 + ], + "type": "inline_equation", + "content": "z_{t}" + }, + { + "bbox": [ + 47, + 594, + 287, + 713 + ], + "type": "text", + "content": " that is obtained from the pre-trained local shape encoder " + }, + { + "bbox": [ + 47, + 594, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{E}_{loc}" + }, + { + "bbox": [ + 47, + 594, + 287, + 713 + ], + "type": "text", + "content": ". Besides, another crucial prior for our design is the patch-based encoding process, through which all the shape patches are encoded into independent Gaussian distributions. Thus, when generating the local shape embeddings, an important point is to recover the independent distribution for" + } + ] + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 312, + 72, + 541, + 273 + ], + "blocks": [ + { + "bbox": [ + 312, + 72, + 541, + 273 + ], + "lines": [ + { + "bbox": [ + 312, + 72, + 541, + 273 + ], + "spans": [ + { + "bbox": [ + 312, + 72, + 541, + 273 + ], + "type": "image", + "image_path": "df50bd5778b88bd489565e43d60675f0101589c569fe450b87b75060d189167b.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 282, + 546, + 372 + ], + "lines": [ + { + "bbox": [ + 305, + 282, + 546, + 372 + ], + "spans": [ + { + "bbox": [ + 305, + 282, + 546, + 372 + ], + "type": "text", + "content": "Figure 3. Detailed illustration of UinU-Net. To better recover " + }, + { + "bbox": [ + 305, + 282, + 546, + 372 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 305, + 282, + 546, + 372 + ], + "type": "text", + "content": " based on independently distributed patches, we propose to implant an inner network inside the standard U-Net architecture. The inner network is mainly composed of " + }, + { + "bbox": [ + 305, + 282, + 546, + 372 + ], + "type": "inline_equation", + "content": "1 \\times 1 \\times 1" + }, + { + "bbox": [ + 305, + 282, + 546, + 372 + ], + "type": "text", + "content": " convolutions, thus it focuses on patch-wise features, while the spatial transformer brings in patch-to-patch information. (Standard U-Net operators include " + }, + { + "bbox": [ + 305, + 282, + 546, + 372 + ], + "type": "inline_equation", + "content": "3 \\times 3 \\times 3" + }, + { + "bbox": [ + 305, + 282, + 546, + 372 + ], + "type": "text", + "content": " residual blocks, conditional cross-attention layers, pooling layers and up-scaling layers.)" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 389, + 546, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 389, + 546, + 688 + ], + "spans": [ + { + "bbox": [ + 304, + 389, + 546, + 688 + ], + "type": "text", + "content": "each shape patch as well. To address this, we propose a novel UinU-Net architecture for the implementation of the autoencoder-based neural score estimator as shown in Figure 3. The standard 3D U-net [10] adopts a series of " + }, + { + "bbox": [ + 304, + 389, + 546, + 688 + ], + "type": "inline_equation", + "content": "3 \\times 3 \\times 3" + }, + { + "bbox": [ + 304, + 389, + 546, + 688 + ], + "type": "text", + "content": " convolutional layers to construct a downsampling-upsampling network architecture with the information shared through skip connections. This design takes into account the patch-to-patch and patch-to-global features via hierarchical receptive fields. Given that our input data are compressed 3D latent representations, and each patch is encoded independently, we propose to implant another inner network inside the outer U-Net architecture where the embedded resolution is equal to the original latent resolution " + }, + { + "bbox": [ + 304, + 389, + 546, + 688 + ], + "type": "inline_equation", + "content": "D / P" + }, + { + "bbox": [ + 304, + 389, + 546, + 688 + ], + "type": "text", + "content": ". Specifically, we adopt a " + }, + { + "bbox": [ + 304, + 389, + 546, + 688 + ], + "type": "inline_equation", + "content": "1 \\times 1 \\times 1" + }, + { + "bbox": [ + 304, + 389, + 546, + 688 + ], + "type": "text", + "content": " convolution-based ResNet [18] structure to learn independent patch-focused information. We also introduce the spatial Transformer [51] network that accepts positional embedded patch representations as input tokens, following self-attention layers to capture the relational information between independent local patch embeddings. The inner synthesis paths are skip-connected to the outer ones, ensuring information transmission from inner to outer networks. This architecture is designed to capture the intra-patch information along with both patch-to-patch and patch-to-global relations." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "Text-Guided Shape Generation So far, we have discussed the generative process without text conditions. To synthe-" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12645" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": "size latent SDF representations based on given conditions, we introduce a conditioning mechanism based on classifier-free guidance diffusion [20]. We adopt a text-conditioned score estimator. In detail, to fit the target conditions into the 3D denoising autoencoder, we utilize the cross-attention mechanism as proposed in [45]. The input caption is first encoded as text embeddings through a pre-trained text encoder " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": ". Thus, the conditioned score can be formed as " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(z_t|\\tau(c))" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": " is the input caption. Meanwhile, we also obtain an unconditioned score " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(z_t|\\emptyset)" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": " with an empty sequence as input caption. Within the guided diffusion sampling process, the output of the model is extrapolated further in the direction of " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(z_t|\\tau(c))" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": " and away from " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(z_t|\\emptyset)" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 52, + 233, + 287, + 258 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 233, + 287, + 258 + ], + "spans": [ + { + "bbox": [ + 52, + 233, + 287, + 258 + ], + "type": "interline_equation", + "content": "\\hat {\\epsilon} _ {\\theta} \\left(z _ {t} | \\tau (c)\\right) = \\epsilon_ {\\theta} \\left(z _ {t} | \\emptyset\\right) + s \\cdot \\left(\\epsilon_ {\\theta} \\left(z _ {t} | \\tau (c)\\right) - \\epsilon_ {\\theta} \\left(z _ {t} | \\emptyset\\right)\\right), \\tag {6}", + "image_path": "d688ed7ec99e3c57ac92c5bd02fb3cb820877ea20d1d344c9f735daa2a5c79f1.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 258, + 214, + 270 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 258, + 214, + 270 + ], + "spans": [ + { + "bbox": [ + 47, + 258, + 214, + 270 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 258, + 214, + 270 + ], + "type": "inline_equation", + "content": "s \\geq 1" + }, + { + "bbox": [ + 47, + 258, + 214, + 270 + ], + "type": "text", + "content": " refers to the guidance scale." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 270, + 289, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 270, + 289, + 474 + ], + "spans": [ + { + "bbox": [ + 46, + 270, + 289, + 474 + ], + "type": "text", + "content": "Text-Guided Shape Completion Current shape completion approaches mainly focused on recovering the full shapes from partial input shapes or single view images [1, 57, 59]. Besides, we have explored the feasibility of text-conditioned shape completion. According to the patch-based design of our SDF encoder, information for the given shape patches can be encoded even if some of the patches are missing. Motivated by the success of diffusion model-based image inpainting [30, 45], we introduce a mask-diffusion strategy to generate the missing shape based on a pre-trained VDM. The core idea is to incorporate known information into each denoising step of the reverse process. For a full shape representation, we transform it into a partial shape representation given the mask " + }, + { + "bbox": [ + 46, + 270, + 289, + 474 + ], + "type": "inline_equation", + "content": "m_z" + }, + { + "bbox": [ + 46, + 270, + 289, + 474 + ], + "type": "text", + "content": ". For each estimation step " + }, + { + "bbox": [ + 46, + 270, + 289, + 474 + ], + "type": "inline_equation", + "content": "z_{t-1}" + }, + { + "bbox": [ + 46, + 270, + 289, + 474 + ], + "type": "text", + "content": ", we combine the estimated result through the reverse process " + }, + { + "bbox": [ + 46, + 270, + 289, + 474 + ], + "type": "inline_equation", + "content": "\\widetilde{z}_{t-1}" + }, + { + "bbox": [ + 46, + 270, + 289, + 474 + ], + "type": "text", + "content": " with the forward sampling result of the unmasked patches " + }, + { + "bbox": [ + 46, + 270, + 289, + 474 + ], + "type": "inline_equation", + "content": "\\hat{z}_{t-1}" + }, + { + "bbox": [ + 46, + 270, + 289, + 474 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 89, + 479, + 287, + 493 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 89, + 479, + 287, + 493 + ], + "spans": [ + { + "bbox": [ + 89, + 479, + 287, + 493 + ], + "type": "interline_equation", + "content": "z _ {t - 1} = (1 - m) \\odot \\widetilde {z} _ {t - 1} + m \\odot \\hat {z} _ {t - 1}, \\tag {7}", + "image_path": "73c20ffd5960c2dc295cbd924220a3904ff9cf1afcaa0c692700ea2ceec64571.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 498, + 230, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 498, + 230, + 510 + ], + "spans": [ + { + "bbox": [ + 47, + 498, + 230, + 510 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 498, + 230, + 510 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 47, + 498, + 230, + 510 + ], + "type": "text", + "content": " refers to element-wise product, and" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 516, + 287, + 536 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 516, + 287, + 536 + ], + "spans": [ + { + "bbox": [ + 105, + 516, + 287, + 536 + ], + "type": "interline_equation", + "content": "\\begin{array}{c} \\widetilde {z} _ {t - 1} \\sim \\mathcal {N} (\\boldsymbol {\\mu} _ {\\theta} (z _ {t}, t, c), \\beta_ {t} \\boldsymbol {I}) \\\\ \\hat {\\quad} \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\end{array} \\tag {8}", + "image_path": "720749a7a804f914e321e9fb446203aaa5520e393b724b73d758d5b8a8441c12.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 107, + 533, + 225, + 545 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 533, + 225, + 545 + ], + "spans": [ + { + "bbox": [ + 107, + 533, + 225, + 545 + ], + "type": "interline_equation", + "content": "\\hat {z} _ {t - 1} = \\sqrt {\\bar {\\alpha} _ {t}} z _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon .", + "image_path": "10d1d2780572a7b7105cb2efe83a7473d8b6159d0c6195f05b99938516419fe1.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 552, + 287, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 552, + 287, + 574 + ], + "spans": [ + { + "bbox": [ + 47, + 552, + 287, + 574 + ], + "type": "text", + "content": "By such a strategy, the unknown region can be recovered based on both the given shape and text conditions." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 575, + 289, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 575, + 289, + 696 + ], + "spans": [ + { + "bbox": [ + 47, + 575, + 289, + 696 + ], + "type": "text", + "content": "Text-Guided Shape Manipulation Visual content editing is one of the most valuable applications for vision-language generation. We propose a diffusion-based text-guided shape manipulation approach. For a given shape representation " + }, + { + "bbox": [ + 47, + 575, + 289, + 696 + ], + "type": "inline_equation", + "content": "z_{init}" + }, + { + "bbox": [ + 47, + 575, + 289, + 696 + ], + "type": "text", + "content": ", our goal is to transform it into another shape representation " + }, + { + "bbox": [ + 47, + 575, + 289, + 696 + ], + "type": "inline_equation", + "content": "z_{goal}" + }, + { + "bbox": [ + 47, + 575, + 289, + 696 + ], + "type": "text", + "content": " based on text " + }, + { + "bbox": [ + 47, + 575, + 289, + 696 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 47, + 575, + 289, + 696 + ], + "type": "text", + "content": ". Inspired by image manipulation techniques [4, 25], we use a cycle-sampling strategy based on a pre-trained VDM. Firstly, we forward-sample the given shape " + }, + { + "bbox": [ + 47, + 575, + 289, + 696 + ], + "type": "inline_equation", + "content": "z_{init}" + }, + { + "bbox": [ + 47, + 575, + 289, + 696 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 47, + 575, + 289, + 696 + ], + "type": "inline_equation", + "content": "t_{mid}" + }, + { + "bbox": [ + 47, + 575, + 289, + 696 + ], + "type": "text", + "content": " steps, where " + }, + { + "bbox": [ + 47, + 575, + 289, + 696 + ], + "type": "inline_equation", + "content": "0 < t_{mid} < T" + }, + { + "bbox": [ + 47, + 575, + 289, + 696 + ], + "type": "text", + "content": ". This operation will lead to an intermediate output " + }, + { + "bbox": [ + 47, + 575, + 289, + 696 + ], + "type": "inline_equation", + "content": "z_{mid}" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 87, + 700, + 287, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 700, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 87, + 700, + 287, + 715 + ], + "type": "interline_equation", + "content": "z _ {m i d} = \\sqrt {\\bar {\\alpha} _ {t _ {m i d}}} z _ {i n i t} + \\sqrt {1 - \\bar {\\alpha} _ {t _ {m i d}}} \\epsilon . \\tag {9}", + "image_path": "9cdbf771ace6d7f079d7423cd29e81d72d9ac96eaf11fdadcf3c6400eff33ceb.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "content": "Then, the reverse process will start from " + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "inline_equation", + "content": "z_{mid}" + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "content": ", and another " + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "inline_equation", + "content": "t_{mid}" + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "content": " denoising steps will be conducted conditioned on " + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "content": ". Such a design will make the generated shapes correspond to the target text descriptions while maintaining the original shape characteristics." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 142, + 388, + 156 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 142, + 388, + 156 + ], + "spans": [ + { + "bbox": [ + 305, + 142, + 388, + 156 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 162, + 547, + 233 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 162, + 547, + 233 + ], + "spans": [ + { + "bbox": [ + 304, + 162, + 547, + 233 + ], + "type": "text", + "content": "We extensively experimented with our proposed Diffusion-SDF on various text-conditioned 3D shape synthesis tasks, such as text-to-shape generation, text-conditioned shape completion, and text-guided shape manipulation. The following subsections describe details of experimental settings, results, and analyses." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 234, + 545, + 341 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 234, + 545, + 341 + ], + "spans": [ + { + "bbox": [ + 304, + 234, + 545, + 341 + ], + "type": "text", + "content": "Dataset. We mainly trained and evaluated our approach on the current largest text-shape dataset Text2Shape (T2S) [6]. T2S gathered data in the form of shape-text pairs based on two object classes (chairs, tables) in ShapeNet [5]. T2S contains about 75K shape-text pairs in total (" + }, + { + "bbox": [ + 304, + 234, + 545, + 341 + ], + "type": "inline_equation", + "content": "\\sim" + }, + { + "bbox": [ + 304, + 234, + 545, + 341 + ], + "type": "text", + "content": "30K for chairs, " + }, + { + "bbox": [ + 304, + 234, + 545, + 341 + ], + "type": "inline_equation", + "content": "\\sim" + }, + { + "bbox": [ + 304, + 234, + 545, + 341 + ], + "type": "text", + "content": "40K for tables), with an average of " + }, + { + "bbox": [ + 304, + 234, + 545, + 341 + ], + "type": "inline_equation", + "content": "\\sim" + }, + { + "bbox": [ + 304, + 234, + 545, + 341 + ], + "type": "text", + "content": "16 words per description. T2S was originally designed to contain both color and shape information within the text descriptions, while we mainly focus on text-shape correspondence." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 342, + 547, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 342, + 547, + 474 + ], + "spans": [ + { + "bbox": [ + 304, + 342, + 547, + 474 + ], + "type": "text", + "content": "Implementation details. For the training stage of the SDF autoencoder, to improve the model's generalization ability, we trained the autoencoder across the 13 categories of ShapeNet [5] dataset. For the input data, we sampled the voxelized SDF from original shapes with " + }, + { + "bbox": [ + 304, + 342, + 547, + 474 + ], + "type": "inline_equation", + "content": "64 \\times 64 \\times 64" + }, + { + "bbox": [ + 304, + 342, + 547, + 474 + ], + "type": "text", + "content": " grid points, which is also the data size adopted for follow-up operations. For the diffusion stage, to facilitate the generative sampling speed, we adopt the DDIM [50] sampler to reduce the original DDPM sampling steps from " + }, + { + "bbox": [ + 304, + 342, + 547, + 474 + ], + "type": "inline_equation", + "content": "T = 1000" + }, + { + "bbox": [ + 304, + 342, + 547, + 474 + ], + "type": "text", + "content": " to 50. For the conditioning mechanism, we adopt a freeze CLIP [40] text encoder " + }, + { + "bbox": [ + 304, + 342, + 547, + 474 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 342, + 547, + 474 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 479, + 499, + 493 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 479, + 499, + 493 + ], + "spans": [ + { + "bbox": [ + 305, + 479, + 499, + 493 + ], + "type": "text", + "content": "4.1. Text-Conditioned Shape Generation" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 498, + 547, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 547, + 666 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 547, + 666 + ], + "type": "text", + "content": "The most immediate application of our approach involves generating novel shapes that are conditioned on textual descriptions. To showcase the efficacy of our approach, we conduct a comparative evaluation of our generation results against two state-of-the-art supervised text-to-shape synthesis methods that are based on implicit 3D representations [29, 34]. Besides, there are some other works regarding text-to-shape generation, which have different settings compared to our approach. For instance, [48] proposed a zero-shot shape generation approach conditioned on categorical texts, and [15, 33] proposed to generate textured shapes based on provided/pre-generated meshes. As a result, these prior works are not directly compared against our proposed approach." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 666, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 666, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 666, + 547, + 713 + ], + "type": "text", + "content": "Quantitative comparison. To compare the generation performance of our approach to the previous methods quantitatively, we propose to use several metrics to evaluate the generated results:" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "text", + "content": "12646" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 71, + 86, + 126, + 148 + ], + "blocks": [ + { + "bbox": [ + 71, + 86, + 126, + 148 + ], + "lines": [ + { + "bbox": [ + 71, + 86, + 126, + 148 + ], + "spans": [ + { + "bbox": [ + 71, + 86, + 126, + 148 + ], + "type": "image", + "image_path": "b7326a862a80c0fa072828e72c19228f4fbf32b0f46c20b63da6ff224431b1ee.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": 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"Figure 4. Qualitative results of text-to-shape generation. Our approach can generate shapes that conform to diverse text descriptions." + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 373, + 181, + 422, + 245 + ], + "blocks": [ + { + "bbox": [ + 373, + 181, + 422, + 245 + ], + "lines": [ + { + "bbox": [ + 373, + 181, + 422, + 245 + ], + "spans": [ + { + "bbox": [ + 373, + 181, + 422, + 245 + ], + "type": "image", + "image_path": "9e38e2f5ca0763cad702031ec4a2677e27ed871d42cfb65205a06d947d88fb2a.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 362, + 255, + 438, + 274 + ], + "lines": [ + { + "bbox": [ + 362, + 255, + 438, + 274 + ], + "spans": [ + { + "bbox": [ + 362, + 255, + 438, + 274 + ], + "type": "text", + "content": "A tall round table with one thin leg." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 460, + 194, + 525, + 243 + ], + "blocks": [ + { + "bbox": [ + 460, + 194, + 525, + 243 + ], + "lines": [ + { + "bbox": [ + 460, + 194, + 525, + 243 + ], + "spans": [ + { + "bbox": [ + 460, + 194, + 525, + 243 + ], + "type": "image", + "image_path": "6259ca67d6af8f02becf570b9b1b8805497833fdc17ffed07c3fcafd468a86c0.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 460, + 255, + 522, + 264 + ], + "lines": [ + { + "bbox": [ + 460, + 255, + 522, + 264 + ], + "spans": [ + { + "bbox": [ + 460, + 255, + 522, + 264 + ], + "type": "text", + "content": "A triangular table." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "bbox": [ + 47, + 307, + 287, + 645 + ], + "type": "list", + "angle": 0, + "index": 25, + "blocks": [ + { + "bbox": [ + 47, + 307, + 287, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 307, + 287, + 378 + ], + "spans": [ + { + "bbox": [ + 47, + 307, + 287, + 378 + ], + "type": "text", + "content": "- IoU (Intersection over Union) measures the occupancy similarity between the generated shape to the ground truth. To compute the IoU score, we downsample all the generated SDFs to occupancy voxel grids of size " + }, + { + "bbox": [ + 47, + 307, + 287, + 378 + ], + "type": "inline_equation", + "content": "32^{3}" + }, + { + "bbox": [ + 47, + 307, + 287, + 378 + ], + "type": "text", + "content": ". IoU metric is used to measure the conformity of the generated samples with the ground truth shapes." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 47, + 387, + 287, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 387, + 287, + 448 + ], + "spans": [ + { + "bbox": [ + 47, + 387, + 287, + 448 + ], + "type": "text", + "content": "- Acc (Classification Accuracy) introduces a voxel-based classifier, which is pre-trained to classify the 13 categories in ShapeNet [5] according to [48]. Acc metric is used to measure the semantic authenticity of the generated samples." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 47, + 456, + 287, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 456, + 287, + 564 + ], + "spans": [ + { + "bbox": [ + 47, + 456, + 287, + 564 + ], + "type": "text", + "content": "- CLIP-S (CLIP Similarity Score) introduces the pretrained vision-language model CLIP [40] for further evaluation. The CLIP can be used to measure the correspondence between given images and texts. We render 5 view images for each generated shape, and compute the cosine similarity score between rendered images and the given text. The highest score is reported for each text query. CLIP-S metric is used to measure the semantic conformance between the generated samples and input texts." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 47, + 572, + 287, + 645 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 572, + 287, + 645 + ], + "spans": [ + { + "bbox": [ + 47, + 572, + 287, + 645 + ], + "type": "text", + "content": "- TMD (Total Mutual Difference). For each given text description, we generate " + }, + { + "bbox": [ + 47, + 572, + 287, + 645 + ], + "type": "inline_equation", + "content": "k = 10" + }, + { + "bbox": [ + 47, + 572, + 287, + 645 + ], + "type": "text", + "content": " different samples. Then, we compute the average IoU score for each generated shape to other " + }, + { + "bbox": [ + 47, + 572, + 287, + 645 + ], + "type": "inline_equation", + "content": "k - 1" + }, + { + "bbox": [ + 47, + 572, + 287, + 645 + ], + "type": "text", + "content": " shapes. The average IoU score for all text queries is reported. TMD assesses the generation diversity for each given text query." + } + ] + } + ], + "index": 24 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "content": "To keep consistency with previous approaches, we limit the comparisons to the chair category in Text2Shape [6] dataset. Since the officially released AutoSDF [34] model was trained on another dataset [2], we re-trained the model following the original settings on the training set of" + } + ] + } + ], + "index": 26 + }, + { + "type": "table", + "bbox": [ + 309, + 320, + 542, + 373 + ], + "blocks": [ + { + "bbox": [ + 312, + 305, + 539, + 316 + ], + "lines": [ + { + "bbox": [ + 312, + 305, + 539, + 316 + ], + "spans": [ + { + "bbox": [ + 312, + 305, + 539, + 316 + ], + "type": "text", + "content": "Table 1. Quantitative comparisons of text-to-shape generation." + } + ] + } + ], + "index": 27, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 320, + 542, + 373 + ], + "lines": [ + { + "bbox": [ + 309, + 320, + 542, + 373 + ], + "spans": [ + { + "bbox": [ + 309, + 320, + 542, + 373 + ], + "type": "table", + "html": "
MethodsIoU↑Acc↑CLIP-S↑TMD↓
Liu et al. [29]0.16034.7929.940.891
AutoSDF [34]0.18783.8829.100.581
Diffusion-SDF (Ours)0.19488.5630.880.169
", + "image_path": "3b734ed5748b0a0335b41db4a8a4c10051308eac8f2956c9231ff0026234325b.jpg" + } + ] + } + ], + "index": 28, + "angle": 0, + "type": "table_body" + } + ], + "index": 28 + }, + { + "bbox": [ + 304, + 388, + 545, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 388, + 545, + 471 + ], + "spans": [ + { + "bbox": [ + 304, + 388, + 545, + 471 + ], + "type": "text", + "content": "Text2Shape for the fair comparison. The results are shown in Table 1. From the results, it can be seen that our approach is able to achieve relatively high generation quality with high IoU and Acc scores, and robust text-shape conformance with good CLIP-S performance, while achieving much better generation diversity with a much lower TMD performance." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 304, + 472, + 546, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 472, + 546, + 651 + ], + "spans": [ + { + "bbox": [ + 304, + 472, + 546, + 651 + ], + "type": "text", + "content": "Qualitative results. The quantitative experiment shows the generation performance of our approach on the limited given subset from Text2Shape dataset. Due to the generalization of natural language, our approach is capable of generating different forms of shapes based on various text descriptions. Figure 4 shows the generated results of Diffusion-SDF from different text inputs. The results show that our method can generate eligible results from distinguished conditions. Besides, our method is capable of synthesizing various shape outputs from the same input text description. Figure 5 compares our approach with [29, 34] based on same text queries. The results have shown that our method has a great advantage in the diversity of generated samples, while the previous approaches are unable to generate highly-diversified shapes." + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 306, + 658, + 406, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 658, + 406, + 670 + ], + "spans": [ + { + "bbox": [ + 306, + 658, + 406, + 670 + ], + "type": "text", + "content": "4.2. Ablation Studies" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": "We have conducted extensive ablation studies to demonstrate the effectiveness of our special architecture design for Diffusion-SDF." + } + ] + } + ], + "index": 32 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12647" + } + ] + } + ], + "index": 33 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 71, + 306, + 223 + ], + "blocks": [ + { + "bbox": [ + 49, + 71, + 306, + 223 + ], + "lines": [ + { + "bbox": [ + 49, + 71, + 306, + 223 + ], + "spans": [ + { + "bbox": [ + 49, + 71, + 306, + 223 + ], + "type": "image", + "image_path": "02ddb923b29588ae6462fd6f0ccf7f57dec96f1ded4376742b1ca91e257942d0.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 227, + 546, + 251 + ], + "lines": [ + { + "bbox": [ + 46, + 227, + 546, + 251 + ], + "spans": [ + { + "bbox": [ + 46, + 227, + 546, + 251 + ], + "type": "text", + "content": "Figure 5. Qualitative comparison of diversified text-to-shape generation. Our approach is capable of generating highly-diversified shapes that conform to the same text query, while also keeping the satisfactory quality of the generated shapes." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 325, + 72, + 541, + 223 + ], + "blocks": [ + { + "bbox": [ + 325, + 72, + 541, + 223 + ], + "lines": [ + { + "bbox": [ + 325, + 72, + 541, + 223 + ], + "spans": [ + { + "bbox": [ + 325, + 72, + 541, + 223 + ], + "type": "image", + "image_path": "0fa0e6f23b58bfd7c6a05ffc4dd46bc42c6c792bcd844245b3c08862d99008ec.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 50, + 258, + 298, + 355 + ], + "blocks": [ + { + "bbox": [ + 50, + 258, + 298, + 355 + ], + "lines": [ + { + "bbox": [ + 50, + 258, + 298, + 355 + ], + "spans": [ + { + "bbox": [ + 50, + 258, + 298, + 355 + ], + "type": "image", + "image_path": "e7b9179d84c108d13680a3e9006b8721b1f66ab9c339e862167bd18599b9e2a0.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 360, + 546, + 383 + ], + "lines": [ + { + "bbox": [ + 46, + 360, + 546, + 383 + ], + "spans": [ + { + "bbox": [ + 46, + 360, + 546, + 383 + ], + "type": "text", + "content": "Figure 6. Qualitative comparison of U-Net and " + }, + { + "bbox": [ + 46, + 360, + 546, + 383 + ], + "type": "inline_equation", + "content": "UinU" + }, + { + "bbox": [ + 46, + 360, + 546, + 383 + ], + "type": "text", + "content": "-Net. Since " + }, + { + "bbox": [ + 46, + 360, + 546, + 383 + ], + "type": "inline_equation", + "content": "UinU" + }, + { + "bbox": [ + 46, + 360, + 546, + 383 + ], + "type": "text", + "content": "-Net-based architecture contains a local-focused inner network, it can better recover the independent patch representations, thereby improving the generation quality compared to conventional U-Net." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 312, + 258, + 541, + 355 + ], + "blocks": [ + { + "bbox": [ + 312, + 258, + 541, + 355 + ], + "lines": [ + { + "bbox": [ + 312, + 258, + 541, + 355 + ], + "spans": [ + { + "bbox": [ + 312, + 258, + 541, + 355 + ], + "type": "image", + "image_path": "09287a35eaa799d9c17681f466a6caede630d2d19c952bdde2ec52d44e29b115.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 399, + 289, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 399, + 289, + 626 + ], + "spans": [ + { + "bbox": [ + 46, + 399, + 289, + 626 + ], + "type": "text", + "content": "Effectiveness of the UinU-Net architecture. In order to validate the benefit of our proposed modifications to the conventional U-Net architecture, we additionally compare our proposed UinU-Net architecture to the simpler U-Net architecture used in [45]. The quantitative results for text-to-shape generation are shown in Table 2. Qualitative comparisons are shown in Figure 6. From the results, it can be found that our proposed UinU-Net architecture for Voxelized Diffusion models generally improves the quality of generated shapes. With the UinU-Net architecture, the noise for each step is estimated both patch-mutually and patch-independently. Since the shape representations are repositioned based on separate patch embeddings extracted by the SDF encoders, the key to recovering the authentic shape SDFs from the joint decoder is to ensure that the generated SDF representations are also distributed independently in patches. From the qualitative results, it can be inferred that the inner network is conducive to recovering the independently distributed patch representations." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "type": "text", + "content": "Inner network architecture. As for the UinU-Net architecture, we have conducted ablation experiments on several variants for the inner network to validate the effectiveness of the final design. The results have shown in Table 3. According to the results, it can be inferred that the inner outer concatenation mechanism and spatial attention layer can generally improve the generation quality. Without the inner-outer" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 317, + 411, + 533, + 454 + ], + "blocks": [ + { + "bbox": [ + 310, + 397, + 539, + 407 + ], + "lines": [ + { + "bbox": [ + 310, + 397, + 539, + 407 + ], + "spans": [ + { + "bbox": [ + 310, + 397, + 539, + 407 + ], + "type": "text", + "content": "Table 2. Evaluating effectiveness of the UinU-Net architecture." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 317, + 411, + 533, + 454 + ], + "lines": [ + { + "bbox": [ + 317, + 411, + 533, + 454 + ], + "spans": [ + { + "bbox": [ + 317, + 411, + 533, + 454 + ], + "type": "table", + "html": "
IoU↑Acc↑CLIP-S↑TMD↓
U-Net [45]0.18780.9829.350.171
UinU-Net (Ours)0.19488.5630.880.169
", + "image_path": "28da582fcc340d16b37fb90e1e4ac7995b7fa01585598493ec5a4007d69c34a1.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 310, + 475, + 541, + 529 + ], + "blocks": [ + { + "bbox": [ + 313, + 460, + 537, + 471 + ], + "lines": [ + { + "bbox": [ + 313, + 460, + 537, + 471 + ], + "spans": [ + { + "bbox": [ + 313, + 460, + 537, + 471 + ], + "type": "text", + "content": "Table 3. Evaluating effectiveness of the inner network design." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 310, + 475, + 541, + 529 + ], + "lines": [ + { + "bbox": [ + 310, + 475, + 541, + 529 + ], + "spans": [ + { + "bbox": [ + 310, + 475, + 541, + 529 + ], + "type": "table", + "html": "
IoU↑Acc↑CLIP-S↑TMD↓
UinU-Net0.19488.5630.880.169
- w/o in-out concat0.19883.9128.680.181
- w/o spatial attention0.19485.5630.820.161
", + "image_path": "ee237119567691a87de2e4d26fbecd8ce5665ad6ecdadba2ac476cb84d50494b.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 543, + 545, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 543, + 545, + 639 + ], + "spans": [ + { + "bbox": [ + 304, + 543, + 545, + 639 + ], + "type": "text", + "content": "concatenation mechanism, the accuracy score and CLIP-S have significant decreases, indicating that the information transmission mechanism has affected the semantic authenticity and conformance of the generated shapes. Accuracy score has dropped without the spatial attention module, indicating that the introduction of patch-to-patch information helps preserve the full shape semantics while recovering the patch-wise representations." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 647, + 477, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 647, + 477, + 659 + ], + "spans": [ + { + "bbox": [ + 305, + 647, + 477, + 659 + ], + "type": "text", + "content": "4.3. Text-Guided Shape Completion" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": "In this section, we validate the effectiveness of our approach on the text-guided shape completion task. Specifically, given a partial input shape, our goal is to generate the missing part conditioned on the input text descriptions. For" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12648" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 73, + 534, + 175 + ], + "blocks": [ + { + "bbox": [ + 51, + 73, + 534, + 175 + ], + "lines": [ + { + "bbox": [ + 51, + 73, + 534, + 175 + ], + "spans": [ + { + "bbox": [ + 51, + 73, + 534, + 175 + ], + "type": "image", + "image_path": "5a6e07a01fd19d2661def0b2b90315ae8289f103cb47ccd3186506249353f186.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 179, + 546, + 201 + ], + "lines": [ + { + "bbox": [ + 46, + 179, + 546, + 201 + ], + "spans": [ + { + "bbox": [ + 46, + 179, + 546, + 201 + ], + "type": "text", + "content": "Figure 7. Qualitative result of text-guide shape completion. Given a known partial shape, our approach can generate the missing part based on text conditions." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 59, + 213, + 195, + 310 + ], + "blocks": [ + { + "bbox": [ + 59, + 213, + 195, + 310 + ], + "lines": [ + { + "bbox": [ + 59, + 213, + 195, + 310 + ], + "spans": [ + { + "bbox": [ + 59, + 213, + 195, + 310 + ], + "type": "image", + "image_path": "be0a8e59a20e3e0fdcf462459e869bf12843ea6b948e6d61c0f8df9b0ec01b85.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 318, + 546, + 340 + ], + "lines": [ + { + "bbox": [ + 46, + 318, + 546, + 340 + ], + "spans": [ + { + "bbox": [ + 46, + 318, + 546, + 340 + ], + "type": "text", + "content": "Figure 8. Qualitative result of text-guide shape manipulation. Given a known shape, our approach is able to manipulate the given shape into the target shape based on the text descriptions." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 213, + 213, + 367, + 312 + ], + "blocks": [ + { + "bbox": [ + 213, + 213, + 367, + 312 + ], + "lines": [ + { + "bbox": [ + 213, + 213, + 367, + 312 + ], + "spans": [ + { + "bbox": [ + 213, + 213, + 367, + 312 + ], + "type": "image", + "image_path": "be8085016c16f5b740f52bfa3ee0ba1fede224360874ca7dfac6c5efb7942816.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 386, + 213, + 534, + 314 + ], + "blocks": [ + { + "bbox": [ + 386, + 213, + 534, + 314 + ], + "lines": [ + { + "bbox": [ + 386, + 213, + 534, + 314 + ], + "spans": [ + { + "bbox": [ + 386, + 213, + 534, + 314 + ], + "type": "image", + "image_path": "aab811df5b21f58eec47fa06a8549b6d28c79bed5df5a03b1c4380a4f131ff7b.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 357, + 289, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 357, + 289, + 501 + ], + "spans": [ + { + "bbox": [ + 46, + 357, + 289, + 501 + ], + "type": "text", + "content": "instance, we can generate the body of a chair based on the given chair legs or generate the missing chair legs based on the chair body. The qualitative results of our approach are displayed in Figure 7. The results show that our approach is capable of generating the missing part of a shape while being well-blended with the given shape, as evident in the generated examples such as revolving throne, revolving toilet, and revolving sofa. Moreover, our completion performance is not limited by the shape geometry in the training set. The core limitation of our approach is the cut region of patch grids, which can be addressed by increasing resolution and decreasing patch size." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 514, + 227, + 527 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 514, + 227, + 527 + ], + "spans": [ + { + "bbox": [ + 47, + 514, + 227, + 527 + ], + "type": "text", + "content": "4.4. Text-Guided Shape Manipulation" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 534, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 534, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 534, + 287, + 715 + ], + "type": "text", + "content": "We demonstrate our approach's effectiveness for text-guided shape manipulation. Our approach can modify a given shape to match an instructive text description. Figure 8 gives several qualitative illustrations for our proposed approach. From the results, it can be summarized that our approach can handle the shape manipulation of both local shape structures (e.g. the existence/style of arms or legs) or the overall shape characteristics (e.g. sofa or straight chair). In addition, one key issue for our designed approach is the choice for " + }, + { + "bbox": [ + 46, + 534, + 287, + 715 + ], + "type": "inline_equation", + "content": "t_{mid}" + }, + { + "bbox": [ + 46, + 534, + 287, + 715 + ], + "type": "text", + "content": ". Since the shape characteristics usually form in the early stage of the reverse process, thus we set " + }, + { + "bbox": [ + 46, + 534, + 287, + 715 + ], + "type": "inline_equation", + "content": "t_{mid}" + }, + { + "bbox": [ + 46, + 534, + 287, + 715 + ], + "type": "text", + "content": " to relatively larger step numbers (600~800 step before DDIM's down-sampling). In experiments, we observe that excessively small or large values for " + }, + { + "bbox": [ + 46, + 534, + 287, + 715 + ], + "type": "inline_equation", + "content": "t_{mid}" + }, + { + "bbox": [ + 46, + 534, + 287, + 715 + ], + "type": "text", + "content": " result in unchanged or destructed original shape features, respectively." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 376, + 546, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 376, + 546, + 520 + ], + "spans": [ + { + "bbox": [ + 306, + 376, + 546, + 520 + ], + "type": "text", + "content": "Limitations. This paper demonstrates the superiority of our approach on the Text2Shape [6] dataset, which is limited to only two categories from ShapeNet, restricting our approach's generalization to other categories. Moreover, the lack of current shape-text datasets prevents us from validating our approach on additional benchmarks. To address this, we propose introducing more datasets and exploring zero-shot text-to-shape generation by leveraging knowledge from 2D vision-language models. While some studies have attempted to tackle this challenge [48], achieving flexible text-to-shape generation remains a significant obstacle. Our future work will seek a possible solution to this problem." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 521, + 546, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 546, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 546, + 641 + ], + "type": "text", + "content": "Conclusion. Our paper presents a framework for text-to-shape synthesis called Diffusion-SDF, which utilizes a diffusion model to generate voxelized SDFs conditioned on texts. The approach comprises a two-stage pipeline: a patch-wise autoencoder for generating Gaussian SDF representations, followed by a Voxelized Diffusion model with UinU-Net denoisers for generating patch-independent SDF representations. We evaluate our approach on various text-to-shape synthesis tasks, and the results demonstrate that it can generate highly diverse and high-quality 3D shapes." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "type": "text", + "content": "Acknowledgments This work was supported in part by the National Key Research and Development Program of China under Grant 2017YFA0700802, in part by the National Natural Science Foundation of China under Grant 62206147 and Grant 62125603, and in part by a grant from the Beijing Academy of Artificial Intelligence (BAAI)." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "12649" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "type": "text", + "content": "[1] Panos Achlioptas, Olga Diamanti, Ioannis Mitliagkas, and Leonidas J. 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DiffusionRig takes in coarse physical rendering as the condition to \"rig\" the input image with learned personal priors. The edited images respect the rendering conditions, preserve the identity, and exhibit high-frequency facial details." + ], + "image_footnote": [], + "bbox": [ + 80, + 434, + 205, + 530 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d5a5f38acd1ca173d8180451d886fb6d592c01d0bd02b9a307571822afb19152.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 207, + 234, + 431, + 332 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ef90403c3864047854dd8747f839dddd368f79877f21c01a4155f8b4d6b74a4c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 209, + 334, + 431, + 431 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/297ea672a34998154ca752c5a3e047268955f498b22cbd811bc10f31051bbc51.jpg", + "image_caption": [ + "Condition", + "Output", + "Rigging Expression" + ], + "image_footnote": [], + "bbox": [ + 209, + 433, + 431, + 529 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/9dd95c7212a8a8a0c22b358a33098405b6e0cebe8df202c2e1e21234872d8738.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 436, + 234, + 658, + 332 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/dd24d6e0a09e66c969a561b369e6e2cf8a3aa2ba3352c0cb11c5c00bebd81abf.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 437, + 334, + 658, + 431 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/55cfeac15a14d4327038d98077bb56f326f00190385616b718f4dd178a7efa43.jpg", + "image_caption": [ + "Condition", + "Output", + "Rigging Lighting" + ], + "image_footnote": [], + "bbox": [ + 436, + 433, + 656, + 529 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/530dae9c5dd9caef9a9545872c8fb150b0adfb8151c428ff6a1c6f86896c5ff5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 665, + 234, + 888, + 332 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/579dff7d49d2a8f8f790c85ccf19586381c5f2c606e8322930e7dc4c288880c3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 666, + 334, + 754, + 430 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/06d8f6ecc848c03fc60eca68a53160a7983a71d68c911aa669d6155ffd141791.jpg", + "image_caption": [ + "Condition", + "Rigging Pose" + ], + "image_footnote": [], + "bbox": [ + 665, + 431, + 754, + 529 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/04d75601730a6f53cad2fbd7b4002fa7a8d3ae32d962b7987f2cf9e708fa9161.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 763, + 334, + 888, + 430 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/6ee4548fc99592fd831cc158af30419d0c933db3edf093138743494ff8b3e08c.jpg", + "image_caption": [ + "Output" + ], + "image_footnote": [], + "bbox": [ + 763, + 431, + 888, + 529 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 625, + 313, + 640 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We address the problem of learning person-specific facial priors from a small number (e.g., 20) of portrait photos of the same person. This enables us to edit this specific person's facial appearance, such as expression and lighting, while preserving their identity and high-frequency facial details. Key to our approach, which we dub DiffusionRig, is a diffusion model conditioned on, or \"rigged by,\" crude 3D face models estimated from single in-the-wild images by an off-the-shelf estimator. On a high level, DiffusionRig learns to map simplistic renderings of 3D face models to realistic photos of a given person. Specifically, DiffusionRig is trained in two stages: It first learns generic facial priors from a large-scale face dataset and then person-specific priors from a small portrait photo collection of the person of interest. By learning the CGI-to-photo mapping with such personalized priors,", + "bbox": [ + 73, + 648, + 473, + 877 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "DiffusionRig can \"rig\" the lighting, facial expression, head pose, etc. of a portrait photo, conditioned only on coarse 3D models while preserving this person's identity and other high-frequency characteristics. Qualitative and quantitative experiments show that DiffusionRig outperforms existing approaches in both identity preservation and photorealism. Please see the project website: https://diffusionrig.github.io for the supplemental material, video, code, and data.", + "bbox": [ + 496, + 611, + 893, + 733 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 743, + 632, + 758 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "It is a longstanding problem in computer vision and graphics to photorealistically change the lighting, expression, head pose, etc. of a portrait photo while preserving the person's identity and high-frequency facial characteristics. The difficulty of this problem stems from its fundamentally underconstrained nature, and prior work typically addresses this with zero-shot learning, where neural networks were trained on a large-scale dataset of different identities and tested on a new identity. These methods ignore the fact that such", + "bbox": [ + 496, + 763, + 895, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Work done during an internship at Adobe.", + "bbox": [ + 99, + 887, + 334, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "12736", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "generic facial priors often fail to capture the test identity's high-frequency facial characteristics, and multiple photos of the same person are often readily available in the person's personal photo albums, e.g., on a mobile phone. In this work, we demonstrate that one can convincingly edit a person's facial appearance, such as lighting, expression, and head pose, while preserving their identity and other high-frequency facial details. Our key insight is that we can first learn generic facial priors from a large-scale face dataset [19] and then finetune these generic priors into personalized ones using around 20 photos capturing the test identity.", + "bbox": [ + 75, + 90, + 472, + 257 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "When it comes to facial appearance editing, the natural question is what representation one uses to change lighting, expression, head pose, hairstyle, accessories, etc. Off-the-shelf 3D face estimators such as DECA [9] can already extract, from an in-the-wild image, a parametric 3D face model that comprises parameters for lighting (spherical harmonics), expression, and head pose. However, directly rendering these physical properties back into images yields CGI-looking results, as shown in the output columns of Figure 1. The reasons are at least three-fold: (a) The 3D face shape estimated is coarse, with mismatched face contours and misses high-frequency geometric details, (b) the assumptions on reflectance (Lambertian) and lighting (spherical harmonics) are restrictive and insufficient for reproducing the reality, and (c) 3D morphable models (3DMMs) simply cannot model all appearance aspects including hairstyle and accessories. Nonetheless, such 3DMMs provide us with a useful representation that is amenable to \"appearance rigging\" since we can modify the facial expression and head pose by simply changing the 3DMM parameters as well as lighting by varying the spherical harmonics (SH) coefficients.", + "bbox": [ + 75, + 260, + 472, + 575 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "On the other hand, diffusion models [15] have recently gained popularity as an alternative to Generative Adversarial Networks (GANs) [11] for image generation. Diff-AE [33] further shows that when trained on the autoencoding task, diffusion models can provide a latent space for appearance editing. In addition, diffusion models are able to map pixel-aligned features (such as noise maps in the vanilla diffusion model) to photorealistic images. Although Diff-AE is capable of interpolating from, e.g., smile to no smile, after semantic labels are used to find the direction to move towards, it is unable to perform edits that require 3D understanding and that cannot be expressed by simple binary semantic labels. Such 3D edits, including relighting and head pose change, are the focus of our work.", + "bbox": [ + 75, + 580, + 472, + 792 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To combine the best of both worlds, we propose Diffusion-Rig, a model that allows us to edit or \"rig\" the appearance (such as lighting and head pose) of a 3DMM and then produce a photorealistic edited image conditioned on our 3D edits. Specifically, DiffusionRig first extracts rough physical properties from single portrait photos using an off-the-shelf method [9], performs desired 3D edits in the 3DMM space,", + "bbox": [ + 75, + 795, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "and finally uses a diffusion model [15] to map the edited \"physical buffers\" (surface normals, albedo, and Lambertian rendering) to photorealistic images. Since the edited images should preserve the identity and high-frequency facial characteristics, we first train DiffusionRig on the CelebA dataset [27] to learn generic facial priors so that DiffusionRig knows how to map surface normals and the Lambertian rendering to a photorealistic image. Note that because the physical buffers are coarse and do not contain sufficient identity information, this \"Stage 1 model\" provides no guarantee for identity preservation. At the second stage, we finetune DiffusionRig on a tiny dataset of roughly 20 images of one person of interest, producing a person-specific diffusion model mapping physical buffers to photos of just this person. As discussed, there are appearance aspects not modeled by the 3DMM, including but not limited to hairstyle and accessories. To provide our model with this additional information, we add an encoder branch that encodes the input image into a global latent code (\"global\" in contrast to physical buffers that are pixel-aligned with the output image and hence \"local\"). This code is chosen to be low-dimensional in the hope of capturing just the aspects not modeled by the 3DMM, such as hairstyle and eyeglasses.", + "bbox": [ + 496, + 90, + 893, + 438 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our contributions are:", + "bbox": [ + 517, + 439, + 750, + 454 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- A deep learning model for 3D facial appearance editing (that modifies lighting, facial expression, head pose, etc.) trained using just images with no 3D label,", + "- A method to drive portrait photo generation using diffusion models with 3D morphable face models, and", + "- A two-stage training strategy that learns personalized facial priors on top of generic face priors, enabling editing that preserves identity and high-frequency details." + ], + "bbox": [ + 517, + 455, + 890, + 575 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 584, + 640, + 599 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our work is related to generative models, 3D Morphable Face Models (3DMMs), and personalized priors.", + "bbox": [ + 500, + 606, + 890, + 638 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Generative Modeling Since the proposal of early Generative Adversarial Networks (GANs) [11], researchers have made significant progress in generating photorealistic images of constrained classes, such as faces [18, 20, 21]. Recently, denoising diffusion models [16], which learn to denoise random noise images into photorealistic images, have shown impressive synthesis results and gained popularity as an alternative to GANs. Different diffusion models are invented for faster sampling [41] (used in this work), conditional generation [7, 31], and later pixel-aligned conditional generation [37]. Similarly, we use pixel-aligned conditions, specifically surface normal, albedo, and Lambertian rendering images, as the condition that our diffusion model should satisfy. Closely related to DiffusionRig are Diffusion Autoencoders (Diff-AE) that learn a latent space of facial attributes (e.g., +smiling vs. -smiling) via the autoencoding task [34]. Given binary labels of a certain attribute, the authors find the", + "bbox": [ + 496, + 643, + 893, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "12737", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/effdec835022b1dfc0b6b0910025e37bd1304cbe603a4943554151aea9564395.jpg", + "image_caption": [ + "Surface", + "Normals", + "Figure 2. Reconstruction with vs. without personalized priors. Given the input image and its conditions (surface normals, albedo, and Lambertian rendering) automatically extracted using DECA, Stage 1 learns only generic face priors and fails to reconstruct the identity in both of the randomly sampled reconstructions. With Stage 2, DiffusionRig is able to faithfully reconstruct the input image using either of the two stochastically sampled noise maps." + ], + "image_footnote": [], + "bbox": [ + 80, + 94, + 161, + 181 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/d4d1d7febf0a2f0b86c1902106d5554a10796e0bcd47315ce2d811f1e5aa1ae0.jpg", + "image_caption": [ + "Albedo" + ], + "image_footnote": [], + "bbox": [ + 165, + 95, + 246, + 181 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/f1a4725121403ae890cbb32b87de82880af59551f320a28ff23bd8343664f305.jpg", + "image_caption": [ + "Lambertian", + "Render" + ], + "image_footnote": [], + "bbox": [ + 250, + 95, + 331, + 181 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/c3c1d0b64b0db04df9486294c3105f14f7f2927803b9562a3167624a88a657dc.jpg", + "image_caption": [ + "Input" + ], + "image_footnote": [], + "bbox": [ + 333, + 94, + 444, + 180 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/befa565e8017181d1e015b5a0ac8ab00951180d29b5a3ec349c73572f4fc0940.jpg", + "image_caption": [ + "Stage 1", + "Sample 1" + ], + "image_footnote": [], + "bbox": [ + 446, + 94, + 555, + 180 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/615a5b7ab2245e5bc4983b5dbb072dccfb624ffaf990592f50da1420c1de554e.jpg", + "image_caption": [ + "Stage 1", + "Sample 2" + ], + "image_footnote": [], + "bbox": [ + 555, + 94, + 666, + 180 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/d63cf3be8a497b65bc810d19fb8b2fb2f326dfa421558663657eddc66c5dcda2.jpg", + "image_caption": [ + "Stage 2", + "Sample 1" + ], + "image_footnote": [], + "bbox": [ + 666, + 94, + 777, + 180 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/46ea9073adfb7beda8e18b425c08e31ec42475677b83d2d74e717723fc1b32ff.jpg", + "image_caption": [ + "Stage 2", + "Sample 2" + ], + "image_footnote": [], + "bbox": [ + 779, + 94, + 890, + 180 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "direction, along which the latent code should be pushed, to manipulate that attribute. 3D-aware generative models are a recent popular trend to combine 3D controllability with 2D image generation [3, 4, 10, 13, 43, 45, 46, 54].", + "bbox": [ + 75, + 281, + 468, + 340 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Facial Appearance Modeling 3D Morphable Face Models or 3DMMs provide a valuable parameter space to describe (and in turn solve for) 3D facial characteristics [2]. The FLAME face model learned from 4D scans is a widely-used 3DMM that supports shape, pose, and expression change [24]. We refer the reader to a recent survey paper on Morphable Face Models [8].", + "bbox": [ + 75, + 347, + 472, + 453 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "RingNet regresses FLAME parameters from 2D images [38]. Also a learning-based method, DECA additionally predicts albedo and lighting in spherical harmonics (SH) from a single face image [9]. An alternative to using 3DMMs for \"face de-rendering\" is directly predicting surface normals, albedo, and lighting in the image space, as in SfSNet [39]. Although such approaches enjoy the benefit of being able to represent hair, accessories, etc., image-space representations do not provide a physically meaningful parameter space for rigging like 3DMMs do.", + "bbox": [ + 75, + 454, + 472, + 604 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The geometry, albedo, and lighting from 3DMM are still extremely coarse and far from reality. The community has bridged the realism gap between 3DMM rendering and real photos through expensive hardware setups to capture fine-grained facial geometry [48, 50] and reflectance fields [6]. Neural network-based, implicit appearance models have also been proposed to address the infeasibility of explicitly describing the appearance with precise reflectance and lighting [1, 12, 28, 29, 30, 35, 36, 40, 42, 52, 53].", + "bbox": [ + 75, + 606, + 470, + 743 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Personalized Priors Learning personal priors has been more widely discussed in super-resolution, face restoration, and inpainting, by using exemplar imagery [47], personal supplemental attributes [51], an attention module with identity penalty [49], or facial component dictionaries [25]. Conditional portrait image editing also shares the objective of preserving the input identity [26, 44]. However, it remains a challenge how to compute an unbiased identity score, and these approaches do not explicitly learn personalized priors.", + "bbox": [ + 75, + 750, + 472, + 883 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Closer to DiffusionRig that learns a personal prior from a", + "bbox": [ + 96, + 885, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "set of personal album of the person, MyStyle [32] is a method to finetune a pre-trained StyleGAN model to achieve a generative model for a specific identity, while preserving the expressiveness of the latent space. However, it does not support precise 3D rigging to control the generation and requires a much larger personal dataset to obtain a smooth personalized latent space. DiffusionRig, on the other hand, focuses on controllable image editing and achieves the smooth editing naturally with the continuous physical space as conditions.", + "bbox": [ + 496, + 281, + 893, + 417 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Preliminaries", + "text_level": 1, + "bbox": [ + 500, + 429, + 637, + 445 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We provide the background knowledge for the two building blocks—3D Morphable Face Models (3DMMs) and Denoising Diffusion Probabilistic Models (DDPMs).", + "bbox": [ + 498, + 455, + 893, + 501 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. 3D Morphable Face Models", + "text_level": 1, + "bbox": [ + 500, + 508, + 750, + 525 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3D Morphable Face Models or 3DMMs are parametric models that use a compact latent space (handcrafted or learned from scans) to represent the head pose, face geometry, facial expression, etc. [2, 24]. In this paper, we employ FLAME [24], a popular 3DMM using standard vertex-based linear blend skinning with corrective blendshapes and representing a face mesh with pose, shape, and expression parameters. Although FLAME provides a compact and physically meaningful space for face geometry, it does not provide descriptions for appearance. To this end, DECA [9] uses FLAME and additionally models facial appearance with Lambertian reflectance and Spherical Harmonics (SH) lighting. Trained on a large dataset, DECA predicts albedo, SH lighting, and the FLAME parameters from a single portrait image. We utilize DECA to generate rough 3D representations that support easy \"rigging\" by editing the FLAME parameters, albedo, and/or SH lighting. As we show in Figure 2, the realism gap between DECA rendering and real photos is significant, calling for measurements post-editing.", + "bbox": [ + 496, + 532, + 893, + 821 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Denoising Diffusion Probabilistic Models", + "text_level": 1, + "bbox": [ + 500, + 830, + 849, + 847 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Denoising Diffusion Probabilistic Models (DDPMs) [7, 15, 31] are a class of generative models that take random noise images as input and denoise the images progressively", + "bbox": [ + 500, + 854, + 893, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "12738", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/c763a44a9dcf0f326a1eb468bb5890d157562662c8bce4f60b095713e15b751d.jpg", + "image_caption": [ + "Figure 3. DiffusionRig overview. The input to our model is a set of physical buffers reconstructed from the input, a random noise map, and a global latent code that encodes nuance features not modeled by the physical buffers. At Stage 1, we train our model on a large face dataset to learn generic face priors. At Stage 2, we keep the global latent code encoder frozen and fine-tune the diffusion model to learn personalized priors." + ], + "image_footnote": [], + "bbox": [ + 84, + 98, + 883, + 281 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "to produce photorealistic images. This generation process can be seen as the reverse of the diffusion process that gradually adds noise to images. The key component of DDPMs is a denoising network $f_{\\theta}$ . During training, it takes a noisy image $x_{t}$ and a timestep $t$ ( $1 \\leq t \\leq T$ ), and predicts the noise at time $t$ : $\\epsilon_{t}$ . More formally, the predicted noise at time $t$ is $\\hat{\\epsilon}_{t} = f_{\\theta}(x_{t}, t)$ , where $x_{t} = \\alpha_{t} x_{0} + \\sqrt{1 - \\alpha_{t}^{2}} \\epsilon_{t}$ , $\\epsilon_{t}$ is a random, normally distributed noise image, and $\\alpha_{t}$ is a hyperparameter that gradually increases noise level of $x_{t}$ with each step of the forward process. The loss is computed on the distance between $\\epsilon_{t}$ and $\\hat{\\epsilon}_{t}$ . Therefore, the trained model can generate images by taking as input a random noise image and gradually denoising it to a photorealistic one.", + "bbox": [ + 75, + 354, + 472, + 551 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Method", + "text_level": 1, + "bbox": [ + 76, + 556, + 169, + 571 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To enable personalized appearance editing, our model, which we dub DiffusionRig, needs to (a) generate images based on different appearance conditions, such as novel lighting, and (b) learn personal priors so that the person's identity is not altered during editing.", + "bbox": [ + 75, + 582, + 468, + 657 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To this end, we design a two-stage training pipeline as shown in Figure 3. At the first stage, the model learns generic face priors by being trained to reconstruct portrait images given their underlying \"appearance conditions\" represented as physical buffers automatically extracted using an off-the-shelf estimator. At the second stage, we finetune our model using portrait photos of just one person so that the model learns personalized priors, which are necessary to prevent identity shift during appearance editing.", + "bbox": [ + 75, + 657, + 470, + 792 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Learning Generic Face Priors", + "text_level": 1, + "bbox": [ + 76, + 801, + 341, + 816 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our first stage is designed to learn facial priors that enable photorealistic image synthesis conditioned on physical constraints like lighting. For the physical conditioning, we use DECA [9] to produce the physical parameters including the FLAME [24] parameters (shape $\\beta$ , expression $\\psi$ , and", + "bbox": [ + 75, + 825, + 470, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "pose $\\theta$ ), albedo $\\alpha$ , (orthographic) camera $\\mathbf{c}$ , and (spherical harmonics) lighting $\\mathbf{l}$ from the input portrait image. We then use the Lambertian reflectance to render these physical properties into three buffers: surface normals, albedo, and Lambertian rendering. Although these physical buffers provide pixel-aligned descriptions of the facial geometry, albedo, and lighting, they are rather coarse and nowhere close to photorealistic images (see the Lambertian rendering in Figures 1 and 2). Still, using these buffers, we can \"rig\" our generative model in a disentangled, physically meaningful way by changing the DECA parameters. For photorealistic image synthesis, we use a Denoising Diffusion Probabilistic Model (DDPM) as our generator because DDPMs can naturally take pixel-aligned conditions (more advantageous than latent code conditions as shown in Section 5.5) to drive the generation process.", + "bbox": [ + 496, + 354, + 893, + 595 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Besides the pixel-aligned physical buffers, we keep the random noise images in DDPMs to explain the stochasticity during generation. In addition to the pixel-aligned buffers and noise map, we need another condition to encode global appearance information (as opposed to local information such as local surface normals) that is not modeled by the physical buffers, such as hair, hat, glasses, and the image background. Therefore, our diffusion model takes both physical buffers and a learned global latent code as conditions for image synthesis. Formally, our model can be described as $\\hat{\\epsilon}_t = f_\\theta ([x_t,z],t,\\phi_\\theta (x_0))$ where $x_{t}$ is the noisy image at timestep $t$ , $z$ represent the physical buffers, $x_0$ is the original image, $\\hat{\\epsilon}_t$ is the predicted noise, and $f_{\\theta}$ and $\\phi_{\\theta}$ are the denoising model and the global latent encoder, respectively.", + "bbox": [ + 496, + 597, + 895, + 809 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "It is theoretically possible that the global latent code also encodes local geometry, albedo, and/or illumination information, which could lead to the diffusion model ignoring the physical buffers entirely. Empirically, we find that the network learns to use the physical buffers for local information and does not rely on the global latent code, possibly because", + "bbox": [ + 496, + 810, + 893, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "12739", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "these buffers are pixel-aligned with the ground truth and thus more easily leveraged by the model.", + "bbox": [ + 76, + 90, + 468, + 121 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Learning Personalized Priors", + "text_level": 1, + "bbox": [ + 76, + 133, + 339, + 148 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After learning the generic facial priors at the first stage, DiffusionRig is able to generate photorealistic images given coarse physical buffers. The next step is to learn personalized priors for a given person to avoid identity shift during appearance editing. Personal priors are crucial to preserving identity and high-frequency facial characteristics, as shown in Figure 2. We achieve this by finetuning our denoising model on a specific person's photo album of around 20 images. During the finetuning stage, the denoising model learns the person's identity information. We fix the global encoder from the previous stage since it has learned to encode global image information not modeled by the physical buffers (which we want to retain). We show that this approach is simple and yet effective compared with GANs that need careful tuning, as mentioned in MyStyle [32].", + "bbox": [ + 75, + 154, + 472, + 380 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For this small personalized dataset, we also extract the DECA parameters first. However, since DECA is a single-image estimator, its output is sensitive to extreme poses or expressions. Under the assumption that the general shape of a person's face does not change drastically within a reasonable period of time, we compute the mean of the shape parameters in FLAME over all the images in the album and use that mean shape when conditioning DiffusionRig.", + "bbox": [ + 75, + 381, + 472, + 503 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Model Architecture", + "text_level": 1, + "bbox": [ + 76, + 513, + 264, + 529 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "DiffusionRig consists of two trainable parts: a denoising model $f_{\\theta}$ and a global encoder $\\phi_{\\theta}$ . The architecture of our denoising model is based on ADM [7] with modifications to reduce computational cost and take an additional global latent code as input. For the global code, we use the same method that ADM uses for their time embedding: We scale and shift the features in each layer using the global latent code. The encoder is simply a ResNet-18 [14] and we use the output features as the global latent codes.", + "bbox": [ + 75, + 534, + 468, + 670 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our loss function is a P2 weight loss [5] that computes distances between predicted and ground-truth noises: $\\mathcal{L} = \\lambda_t' ||\\hat{\\epsilon}_t - \\epsilon_t||_2^2$ , where $\\lambda_t'$ is a hyperparameter to control the loss weight at different timesteps. We empirically find that the P2 weight loss speeds up the training process and generates high-quality images compared with a constant loss weight.", + "bbox": [ + 76, + 671, + 468, + 763 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.4. Implementation Details", + "text_level": 1, + "bbox": [ + 76, + 773, + 294, + 789 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "During the first stage, we train DiffusionRig on the FFHQ dataset [19], which contains 70,000 images. With Adam [23] as the optimizer with a learning rate of $10^{-4}$ , we train DiffusionRig for 50,000 iterations with a batch size of 256 (so the total number of samples seen by the model is 12,800,000). During the second stage, we use only 10-20 images of a single person. In the following, we show results for four", + "bbox": [ + 75, + 794, + 472, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "celebrities (Obama, Biden, Swift, and Harris) and two noncelebrities. Please see the supplemental material and video for more results including more identities. We use 20 images for each person except for Harris, for whom we use only 10, and for the ablation study on the number of training images. We provide the personal photo album of two identities in the supplemental material. We finetune our model on each small dataset for 5,000 iterations with a batch size of 4 (so the total number of seen samples during finetuning is 20,000). We furthermore decrease the learning rate to $10^{-5}$ for the second stage. Training for the first stage takes around 15 hours using eight A100 GPUs, and the Stage 2 finetuning completes within 30 minutes on a single V100 GPU.", + "bbox": [ + 496, + 90, + 893, + 287 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 500, + 292, + 633, + 310 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We first show how to edit a person's appearance (e.g., facial expression, lighting, and head pose) by modifying the physical buffers that condition the model. We then demonstrate how to rig, with the global latent code, other aspects of a person's appearance not modeled by the physical buffers such as hairstyle and accessories. By swapping in the global latent code from another image, we can transfer portrait characteristics, such as hairstyle, accessories including glasses, and/or the image background, while preserving the physical properties (e.g., identity, pose, expression, and lighting) from the original image. Finally, we show the power of the learned personal priors by conditioning, for example, an Obama model on both the physical buffers and global latent code from a different person (to \"Obama-fy\" that person).", + "bbox": [ + 496, + 316, + 893, + 529 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Rigging Appearance With Physical Buffers", + "text_level": 1, + "bbox": [ + 498, + 532, + 864, + 549 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we use our personalized model to rig the appearance with physical buffers. We show three different types of appearance rigging: relighting, expression change, and pose change. For relighting, we use different Spherical Harmonics (SH) parameters for producing the Lambertian rendering. To change the expression, we modify the expression and jaw rotation parameters of FLAME (the last three parameters of the pose vector). To vary the pose, we modify the head rotation parameters (the first three parameters of the pose vector). The 64-dimensional global latent code is produced by encoding the input image and remains unchanged when editing appearance.", + "bbox": [ + 496, + 553, + 893, + 733 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our results are displayed in Figure 4, where we depict three identities: two celebrities and one daily user. All the images have a resolution of $256 \\times 256$ . Additionally, $512 \\times 512$ results can be found in the supplemental material. We compare our method against DECA [9], HeadNerf [17], GIF [10], and MyStyle [32], of which the first two are 3D face model estimation methods, and the latter two are GAN-based approaches. As Figure 4 shows, while GIF is capable of rigging the appearance by changing the expression and pose, it fails to preserve the individual's identity. DiffusionRig and MyStyle, on the other hand, are both personalized models", + "bbox": [ + 496, + 734, + 895, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "12740", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/4e7ec30e73c5ff3df5d09816f339e4930e642f9795868c719c275f65dbfc6306.jpg", + "image_caption": [ + "Original" + ], + "image_footnote": [], + "bbox": [ + 106, + 89, + 187, + 152 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/1b1e0503cc964b80ccc2a1088e2020d574cbfd0753578429c4eacdd3247ed637.jpg", + "image_caption": [ + "DECA" + ], + "image_footnote": [], + "bbox": [ + 106, + 155, + 187, + 220 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/17af4b50874db34082298c9776c3a71795b8d5424209df93807db7031dd2e9aa.jpg", + "image_caption": [ + "HeadNerf" + ], + "image_footnote": [], + "bbox": [ + 106, + 222, + 187, + 285 + ], + "page_idx": 5 + }, + { + "type": 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Appearance editing. DiffusionRig achieves convincing appearance edits while preserving the individual's identity using only 20 images per identity. GIF creates realistic-looking images but does not use personalized priors, leading to significant identity shifts. MyStyle is unable to make dramatic changes to the expression or pose without artifacts or minor identity shifts. In addition, MyStyle does not trivially support controllable relighting, so the corresponding fields have been left empty." + ], + "image_footnote": [], + "bbox": [ + 449, + 419, + 531, + 484 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/21430bfacb16d053837b387b29d61ca1de03619dd31eaea88b052d36d16c5b37.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 535, + 89, + 614, + 152 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b6f497254c0f3c36d3bdf608db395dace19b911ce33140c4a2e5d79a4c3fa693.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 535, + 155, + 614, + 220 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/48246d07a93a92eefc0d3aaff0c350e8f3336b7e91409e6151c8274e471890b4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 535, + 222, + 614, + 285 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": 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"img_path": "images/3371c015180874e874e7721758014359a8b41d8b999c6e81c1a1c2d370626884.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 792, + 222, + 872, + 285 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/6033af2fac38e7d32e779d287a71a5bb972225e982926a28e3e06a0fb6eeee90.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 792, + 287, + 874, + 351 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/097cd3355a4619ad570a1f7109fc2416d3cdf8d4afd9caf55b6278793424abc8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 792, + 354, + 874, + 417 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/cd2f39d2edd02bc156bb88862dffc9906731ff7e97cc386c1f2f290c60de6943.jpg", + "image_caption": [ + "Pose" + ], + "image_footnote": [], + "bbox": [ + 792, + 419, + 872, + 484 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "that are able to preserve the identity. However, since our method is directly conditioned on physical buffers, we can rig the appearance in a physically-based manner, whereas MyStyle needs to search for and step into a certain direction within the latent space to produce the target appearance, limiting its controllability, interpretability, and capacity for dramatic appearance changes. We also observe more artifacts for MyStyle when doing appearance editing, which is likely due to the use of too few images during finetuning the StyleGAN model.", + "bbox": [ + 75, + 570, + 468, + 720 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Rigging Appearance With Global Latent Code", + "text_level": 1, + "bbox": [ + 76, + 729, + 467, + 744 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "By design, DiffusionRig finds it easier to learn what physical buffers can describe from the pixel-aligned buffers than from the global latent code. The latent code thus encodes what physical buffers cannot describe including background, makeup, and hairstyle. In this part, we change the global latent code to show its effects on the generated images.", + "bbox": [ + 75, + 750, + 468, + 839 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In Figure 5, we show a $2 \\times 3$ matrix of generated images. Along the horizontal axis, we swap in the global latent code from another image of the same person while keeping the physical buffers identical (i.e., same physical buffers but", + "bbox": [ + 75, + 839, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "different global codes). Along the vertical axis, we replace the physical buffers while keeping the same global latent code (i.e., same global code but different physical buffers). We can see that geometry information, such as head pose and expression, is preserved for each row, which shows that only the physical buffers (not the latent code) contain such information. This means that in DiffusionRig these physical properties are well disentangled from each other and from other appearance properties that physical buffers cannot describe. On the other hand, the information hard to model explicitly, including image background, glasses, and hair style/color, is encoded in the global latent code.", + "bbox": [ + 496, + 570, + 890, + 751 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.3. Identity Transfer With Learned Priors", + "text_level": 1, + "bbox": [ + 500, + 758, + 831, + 773 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In previous sections, we saw what information the physical buffers and the global latent code encode. Now, we demonstrate what information is encoded in the personalized diffusion models' weights. Here, we keep both physical buffers and global latent code the same but exchange the personalized model itself with another person's personalized model (i.e., model swapping without code or buffer swapping). The results of this experiment for four identities are", + "bbox": [ + 496, + 780, + 892, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "12741", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e86a61d4b8f92795d3841c4749e7703ed8bfa8cfc4a8916e6bc7ba618a796067.jpg", + "image_caption": [ + "Figure 5. Mix and match of physical buffers and global latent code. We mix the physical buffers from one image and the global latent code from another image to demonstrate how the two conditions encode disentangled information." + ], + "image_footnote": [], + "bbox": [ + 83, + 89, + 472, + 319 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "shown in Figure 6. Each row uses the same physical buffers and latent code but another personalized model. Each column uses the same personalized model but different physical buffers and latent code. For example, the column \"Obama-fy\" shows four images that are generated by Obama's personal model but using the other celebrities' images as input. We see that across each row, while all inputs (physical buffers plus global latent code) are the same, the four different personalized models output different identities. These results further corroborate that our model is able to learn personalized priors from a small dataset.", + "bbox": [ + 75, + 393, + 472, + 559 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.4. Baseline Comparisons & Evaluation Metrics", + "text_level": 1, + "bbox": [ + 76, + 569, + 454, + 585 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We evaluate our DiffusionRig quantitatively in three aspects: rigging quality, identity preservation, and photorealism, since these three qualities are the most important for our personalized appearance editing.", + "bbox": [ + 75, + 588, + 470, + 648 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "DECA Re-Inference Error We follow the same setup as in GIF [10] to compute the DECA re-inference error. To evaluate relighting quality, we directly compute the RMSE on the re-inferred spherical harmonics. We show our results in Table 1. For our model, we also evaluate two ablated versions: \"vector cond.\" and \"feature cond.\" Instead of using pixel-aligned physical buffers as the condition, we use DECA's output parameters and features computed from physical buffers as conditions in our two ablated models. More details can be found in Section 5.5.", + "bbox": [ + 75, + 652, + 470, + 801 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Face Re-Identification Error An important metric for evaluating this work is whether DiffusionRig can preserve the identity after appearance editing, since identity shift is a notorious problem in generative model-based editing. To this end, we run a widely popular face re-identification network [22] to automatically determine if the edited and", + "bbox": [ + 75, + 809, + 470, + 900 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/93eb51dd6ad1d97f838e39abc83a77e40267efcd6892855dbed43fbbe019086c.jpg", + "image_caption": [ + "Figure 6. Swapping personalized models. We demonstrate the power of personalized priors by running one person's model on other identities. This creates the effect of \"adding\" one person's identity to another person. The images with green borders are \"no-swap\" results where the corresponding person's model is used." + ], + "image_footnote": [], + "bbox": [ + 504, + 88, + 890, + 404 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/565afc1fb1f5d4f2073d6b429a9907e6db0e32af8a6bd61807e774665f3fa61b.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Light ↓Shape ↓Exp. ↓Pose ↓
GIF [10]13.83.05.05.6
GIF, vector cond. [10]-3.423.129.7
DiffusionRig (Ours)11.24.32.84.2
DiffusionRig, vector cond.15.510.78.814.0
DiffusionRig, feature cond.27.05.34.121.6
", + "bbox": [ + 506, + 491, + 885, + 568 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 1. RMSE of DECA re-inference. All numbers are multiples of $10^{-3}$ . We generate 1,000 images to compute the RMSE. For shape, expression, and pose, the RMSE is computed on rendered FLAME faces. For lighting, the RMSE is computed on re-inferred spherical harmonics directly. We only use our Stage 1 model since GIF is not a personalized model. Numbers for GIF and its vector-conditioned variant are cited from the original paper [10].", + "bbox": [ + 498, + 571, + 893, + 671 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "original images are of the same person. As Table 2 shows, both MyStyle [32] and DiffusionRig preserve the identity in all 400 expression-edited images of Obama and another 400 of Swift. That said, for dramatic changes such as head pose change, DiffusionRig preserves the identity better than MyStyle, as also demonstrated by Figure 4. One caveat of this error metric, though, is the obvious degenerate solution of not applying any edit at all, thereby achieving a perfect score. We refer the reader to Figure 4 and Table 1, which show that DiffusionRig avoids this degenerate solution.", + "bbox": [ + 496, + 684, + 893, + 835 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "User Study To further evaluate both the photorealism and identity preservation of images from DiffusionRig against MyStyle, we conduct a user study involving Amazon Mechanical Turk. During the study, we show pairs of images,", + "bbox": [ + 498, + 839, + 895, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "12742", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/adf867f78ac03cba2b2db2990c4f3dcb9ce87a2878c011dba70ffe884174089e.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Auto. Face Re-ID ↑User Study ↑
Obama and SwiftObamaSwift
Expr.PoseExpr.PoseExpr.Pose
MyStyle100%97.9%79.4%78.0%64.5%62.5%
Ours100%99.3%87.2%86.5%82.4%80.2%
", + "bbox": [ + 89, + 88, + 455, + 148 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 2. DiffusionRig vs. MyStyle [32] in expression and pose editing, as measured by an automatic face re-ID error [22] (which has an obvious flaw; see text) as well as a user study on both realism and identity preservation.", + "bbox": [ + 75, + 152, + 468, + 209 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "where the left image is an original image from the real image dataset, and the right image is a generated one. We occasionally include some real images on the right, too, for consistency check and quality control. We then ask the users whether the right image is a real image of the person on the left (so both photorealism and identity preservation are probed). We generate images that include either an expression or pose change for both DiffusionRig and MyStyle. We report our results in Table 2.", + "bbox": [ + 75, + 215, + 470, + 352 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.5. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 361, + 230, + 378 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We show several ablation studies to motivate the finetuning stage that injects the personalized prior and the choice of physical, pixel-aligned buffers to condition the model.", + "bbox": [ + 75, + 381, + 470, + 426 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "No Personalized Priors We first show how DiffusionRig performs in the absence of personalized priors (i.e., trained on only the large dataset from Stage 1). Figure 2 shows that our model learns to use the physical buffers as conditions for pose, expression, and lighting, but it is incapable of preserving the person's identity during appearance editing.", + "bbox": [ + 75, + 431, + 468, + 525 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Number of Images Here we explore how the number of images used in Stage 2 affects DiffusionRig's ability of learning personalized priors. We train three models of a non-celebrity with 1, 5, 10, and 20 images and test them on relighting, expression change, and pose change. As Figure 7 demonstrates, using just 1, 5, or 10 images yields worse results than using 20 images (unsurprisingly). With more images, DiffusionRig learns better-personalized priors that capture high-frequency face characteristics, such as the wrinkles in Figure 7.", + "bbox": [ + 75, + 529, + 470, + 680 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2d2e5c5783488e6aa3bc1d1c3045e0e82c6f3f687f807108e6621a7e7f3bc393.jpg", + "image_caption": [ + "Figure 7. Quality w.r.t. number of Stage 2 images. DiffusionRig achieves high-quality relighting and pose change with 20 images for Stage 2. Using fewer may yield blurry results and make them hard to rig with new conditions." + ], + "image_footnote": [], + "bbox": [ + 99, + 688, + 444, + 790 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Different Forms of Conditions There are alternative ways to condition the image synthesis. We demonstrate that pixel", + "bbox": [ + 75, + 869, + 472, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "aligned physical buffers are the most effective form in accurately rigging the appearance. We explore the following two conditioning alternatives. \"Vector cond.\" is when we directly concatenate DECA parameters, a 236-dimensional vector, to the global latent code without using pixel-aligned buffers. \"Feature cond.\" means that we concatenate the physical buffers to the input image and pass them into the encoder to compute a global latent code, which is then used as a non-spatial feature condition. As shown in Figure 8, using pixel-aligned physical guidance is essential for accurate conditional image editing. Both vector and feature conditioning suffer from the generated images not following the desired physical guidance.", + "bbox": [ + 496, + 90, + 893, + 287 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/183d48f117d4e70bd1297aa616acc8e9ed4d10a932dee27672d38e1db75124fd.jpg", + "image_caption": [ + "Rigging Expression: input and src." + ], + "image_footnote": [], + "bbox": [ + 522, + 299, + 694, + 364 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8d0745cd9ad51a92459a55f76c6da2b8a1ef0d6d566e063b6f9990e0014dfb46.jpg", + "image_caption": [ + "Feature Cond." + ], + "image_footnote": [], + "bbox": [ + 696, + 299, + 779, + 363 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8e25e5137f5d0d12d5dfb54311e52ac0063b809492b16de77ed8b56869aeb6d6.jpg", + "image_caption": [ + "DiffusionRig" + ], + "image_footnote": [], + "bbox": [ + 781, + 299, + 864, + 363 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d785af753933884ec1b9a287c9e8f9a5e0323d662dcaa769294674324acf6bd0.jpg", + "image_caption": [ + "Rigging Pose: input and src.", + "Figure 8. Ablation on the form of conditions. Neither feature conditioning nor vector conditioning is able to rig the input image to follow the physical properties of the target image." + ], + "image_footnote": [], + "bbox": [ + 522, + 377, + 691, + 441 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/763937feabce623a112dbc3eb8c0f6d13e1bd4a4c086fe48be0db0005d18939e.jpg", + "image_caption": [ + "Vector Cond." + ], + "image_footnote": [], + "bbox": [ + 694, + 376, + 779, + 441 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1b179c838131a72f360761a63c29da6c7d2867cd03c122e021f741204d5d2c57.jpg", + "image_caption": [ + "DiffusionRig" + ], + "image_footnote": [], + "bbox": [ + 781, + 376, + 864, + 441 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Limitations & Conclusion", + "text_level": 1, + "bbox": [ + 500, + 513, + 741, + 530 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Although DiffusionRig achieves state-of-the-art facial appearance editing, it relies on a small portrait dataset to finetune, which limits its scalability for massive user adoption. Furthermore, when the edit involves dramatic head pose change, DiffusionRig may not stay faithful to the original background, since head pose change sometimes reveals what used to be occluded, therefore requiring background inpainting—a topic beyond the scope of this paper. Additionally, since DiffusionRig relies on DECA to get physical buffers, it will also be affected by DECA's limited estimation capability: for instance, extreme expressions usually cannot be well predicted. and the estimated lighting is sometimes coupled with the skin tone.", + "bbox": [ + 496, + 537, + 893, + 733 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we have presented DiffusionRig, a riggable diffusion model for identity-preserving, personalized editing of facial appearance. We introduced a two-stage method to first learn generic face priors and later personalized priors. Using both explicit conditioning via physical buffers and implicit conditioning via global latent code, we can drive and control our model's facial image synthesis.", + "bbox": [ + 496, + 734, + 893, + 842 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgment We thank Marc Levoy for the valuable feedback and everyone whose photos appear in this paper for their permission.", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "12743", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 106 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Sai Bi, Stephen Lombardi, Shunsuke Saito, Tomas Simon, Shih-En Wei, Kevyn Mcphail, Ravi Ramamoorthi, Yaser Sheikh, and Jason Saragih. 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Springer, 2022." + ], + "bbox": [ + 78, + 90, + 470, + 167 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "12746", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/DiffusionRig_ Learning Personalized Priors for Facial Appearance Editing/d7adefe3-24be-45f5-8e46-305721be8441_model.json b/2023/DiffusionRig_ Learning Personalized Priors for Facial Appearance Editing/d7adefe3-24be-45f5-8e46-305721be8441_model.json new file mode 100644 index 0000000000000000000000000000000000000000..74fd72629f96f9f136a6ecfb4f42320fd1bd419a --- /dev/null +++ b/2023/DiffusionRig_ Learning Personalized Priors for Facial Appearance Editing/d7adefe3-24be-45f5-8e46-305721be8441_model.json @@ -0,0 +1,3346 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.11, + 0.131, + 0.861, + 0.154 + ], + "angle": 0, + "content": "DiffusionRig: Learning Personalized Priors for Facial Appearance Editing" + }, + { + "type": "text", + "bbox": [ + 0.134, + 0.18, + 0.834, + 0.218 + ], + "angle": 0, + "content": "Zheng Ding\\(^{1\\dagger}\\), Xuaner Zhang\\(^{2}\\), Zhihao Xia\\(^{2}\\), Lars Jebe\\(^{2}\\), Zhuowen Tu\\(^{1}\\), Xiuming Zhang\\(^{2}\\) \n\\(^{1}\\)UC San Diego \\(^{2}\\)Adobe" + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.235, + 0.206, + 0.334 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.336, + 0.206, + 0.433 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.435, + 0.206, + 0.531 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.123, + 0.548, + 0.162, + 0.562 + ], + "angle": 0, + "content": "Input" + }, + { + "type": "image", + "bbox": [ + 0.209, + 0.235, + 0.432, + 0.333 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.21, + 0.335, + 0.432, + 0.432 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.21, + 0.434, + 0.432, + 0.53 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.226, + 0.532, + 0.29, + 0.543 + ], + "angle": 0, + "content": "Condition" + }, + { + "type": "image_caption", + "bbox": [ + 0.306, + 0.532, + 0.39, + 0.544 + ], + "angle": 0, + "content": "Output" + }, + { + "type": "image_caption", + "bbox": [ + 0.25, + 0.548, + 0.387, + 0.562 + ], + "angle": 0, + "content": "Rigging Expression" + }, + { + "type": "image", + "bbox": [ + 0.437, + 0.235, + 0.66, + 0.333 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.438, + 0.335, + 0.659, + 0.432 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.437, + 0.434, + 0.658, + 0.53 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.453, + 0.533, + 0.516, + 0.544 + ], + "angle": 0, + "content": "Condition" + }, + { + "type": "image_caption", + "bbox": [ + 0.534, + 0.533, + 0.616, + 0.544 + ], + "angle": 0, + "content": "Output" + }, + { + "type": "image_caption", + "bbox": [ + 0.486, + 0.548, + 0.608, + 0.563 + ], + "angle": 0, + "content": "Rigging Lighting" + }, + { + "type": "image", + "bbox": [ + 0.666, + 0.235, + 0.89, + 0.333 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.667, + 0.335, + 0.755, + 0.431 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.666, + 0.433, + 0.755, + 0.53 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.685, + 0.532, + 0.748, + 0.543 + ], + "angle": 0, + "content": "Condition" + }, + { + "type": "image", + "bbox": [ + 0.764, + 0.335, + 0.889, + 0.431 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.764, + 0.433, + 0.889, + 0.53 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.805, + 0.532, + 0.849, + 0.544 + ], + "angle": 0, + "content": "Output" + }, + { + "type": "image_caption", + "bbox": [ + 0.729, + 0.548, + 0.823, + 0.562 + ], + "angle": 0, + "content": "Rigging Pose" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.569, + 0.893, + 0.598 + ], + "angle": 0, + "content": "Figure 1. DiffusionRig takes in coarse physical rendering as the condition to \"rig\" the input image with learned personal priors. The edited images respect the rendering conditions, preserve the identity, and exhibit high-frequency facial details." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.625, + 0.314, + 0.641 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.65, + 0.474, + 0.878 + ], + "angle": 0, + "content": "We address the problem of learning person-specific facial priors from a small number (e.g., 20) of portrait photos of the same person. This enables us to edit this specific person's facial appearance, such as expression and lighting, while preserving their identity and high-frequency facial details. Key to our approach, which we dub DiffusionRig, is a diffusion model conditioned on, or \"rigged by,\" crude 3D face models estimated from single in-the-wild images by an off-the-shelf estimator. On a high level, DiffusionRig learns to map simplistic renderings of 3D face models to realistic photos of a given person. Specifically, DiffusionRig is trained in two stages: It first learns generic facial priors from a large-scale face dataset and then person-specific priors from a small portrait photo collection of the person of interest. By learning the CGI-to-photo mapping with such personalized priors," + }, + { + "type": "page_footnote", + "bbox": [ + 0.101, + 0.888, + 0.335, + 0.9 + ], + "angle": 0, + "content": "† Work done during an internship at Adobe." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.612, + 0.895, + 0.734 + ], + "angle": 0, + "content": "DiffusionRig can \"rig\" the lighting, facial expression, head pose, etc. of a portrait photo, conditioned only on coarse 3D models while preserving this person's identity and other high-frequency characteristics. Qualitative and quantitative experiments show that DiffusionRig outperforms existing approaches in both identity preservation and photorealism. Please see the project website: https://diffusionrig.github.io for the supplemental material, video, code, and data." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.744, + 0.633, + 0.759 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.896, + 0.903 + ], + "angle": 0, + "content": "It is a longstanding problem in computer vision and graphics to photorealistically change the lighting, expression, head pose, etc. of a portrait photo while preserving the person's identity and high-frequency facial characteristics. The difficulty of this problem stems from its fundamentally underconstrained nature, and prior work typically addresses this with zero-shot learning, where neural networks were trained on a large-scale dataset of different identities and tested on a new identity. These methods ignore the fact that such" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "12736" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.258 + ], + "angle": 0, + "content": "generic facial priors often fail to capture the test identity's high-frequency facial characteristics, and multiple photos of the same person are often readily available in the person's personal photo albums, e.g., on a mobile phone. In this work, we demonstrate that one can convincingly edit a person's facial appearance, such as lighting, expression, and head pose, while preserving their identity and other high-frequency facial details. Our key insight is that we can first learn generic facial priors from a large-scale face dataset [19] and then finetune these generic priors into personalized ones using around 20 photos capturing the test identity." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.261, + 0.473, + 0.577 + ], + "angle": 0, + "content": "When it comes to facial appearance editing, the natural question is what representation one uses to change lighting, expression, head pose, hairstyle, accessories, etc. Off-the-shelf 3D face estimators such as DECA [9] can already extract, from an in-the-wild image, a parametric 3D face model that comprises parameters for lighting (spherical harmonics), expression, and head pose. However, directly rendering these physical properties back into images yields CGI-looking results, as shown in the output columns of Figure 1. The reasons are at least three-fold: (a) The 3D face shape estimated is coarse, with mismatched face contours and misses high-frequency geometric details, (b) the assumptions on reflectance (Lambertian) and lighting (spherical harmonics) are restrictive and insufficient for reproducing the reality, and (c) 3D morphable models (3DMMs) simply cannot model all appearance aspects including hairstyle and accessories. Nonetheless, such 3DMMs provide us with a useful representation that is amenable to \"appearance rigging\" since we can modify the facial expression and head pose by simply changing the 3DMM parameters as well as lighting by varying the spherical harmonics (SH) coefficients." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.581, + 0.473, + 0.793 + ], + "angle": 0, + "content": "On the other hand, diffusion models [15] have recently gained popularity as an alternative to Generative Adversarial Networks (GANs) [11] for image generation. Diff-AE [33] further shows that when trained on the autoencoding task, diffusion models can provide a latent space for appearance editing. In addition, diffusion models are able to map pixel-aligned features (such as noise maps in the vanilla diffusion model) to photorealistic images. Although Diff-AE is capable of interpolating from, e.g., smile to no smile, after semantic labels are used to find the direction to move towards, it is unable to perform edits that require 3D understanding and that cannot be expressed by simple binary semantic labels. Such 3D edits, including relighting and head pose change, are the focus of our work." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.473, + 0.903 + ], + "angle": 0, + "content": "To combine the best of both worlds, we propose Diffusion-Rig, a model that allows us to edit or \"rig\" the appearance (such as lighting and head pose) of a 3DMM and then produce a photorealistic edited image conditioned on our 3D edits. Specifically, DiffusionRig first extracts rough physical properties from single portrait photos using an off-the-shelf method [9], performs desired 3D edits in the 3DMM space," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.439 + ], + "angle": 0, + "content": "and finally uses a diffusion model [15] to map the edited \"physical buffers\" (surface normals, albedo, and Lambertian rendering) to photorealistic images. Since the edited images should preserve the identity and high-frequency facial characteristics, we first train DiffusionRig on the CelebA dataset [27] to learn generic facial priors so that DiffusionRig knows how to map surface normals and the Lambertian rendering to a photorealistic image. Note that because the physical buffers are coarse and do not contain sufficient identity information, this \"Stage 1 model\" provides no guarantee for identity preservation. At the second stage, we finetune DiffusionRig on a tiny dataset of roughly 20 images of one person of interest, producing a person-specific diffusion model mapping physical buffers to photos of just this person. As discussed, there are appearance aspects not modeled by the 3DMM, including but not limited to hairstyle and accessories. To provide our model with this additional information, we add an encoder branch that encodes the input image into a global latent code (\"global\" in contrast to physical buffers that are pixel-aligned with the output image and hence \"local\"). This code is chosen to be low-dimensional in the hope of capturing just the aspects not modeled by the 3DMM, such as hairstyle and eyeglasses." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.44, + 0.751, + 0.455 + ], + "angle": 0, + "content": "In summary, our contributions are:" + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.456, + 0.892, + 0.5 + ], + "angle": 0, + "content": "- A deep learning model for 3D facial appearance editing (that modifies lighting, facial expression, head pose, etc.) trained using just images with no 3D label," + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.501, + 0.892, + 0.531 + ], + "angle": 0, + "content": "- A method to drive portrait photo generation using diffusion models with 3D morphable face models, and" + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.531, + 0.892, + 0.576 + ], + "angle": 0, + "content": "- A two-stage training strategy that learns personalized facial priors on top of generic face priors, enabling editing that preserves identity and high-frequency details." + }, + { + "type": "list", + "bbox": [ + 0.519, + 0.456, + 0.892, + 0.576 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.585, + 0.642, + 0.601 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.607, + 0.892, + 0.639 + ], + "angle": 0, + "content": "Our work is related to generative models, 3D Morphable Face Models (3DMMs), and personalized priors." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Generative Modeling Since the proposal of early Generative Adversarial Networks (GANs) [11], researchers have made significant progress in generating photorealistic images of constrained classes, such as faces [18, 20, 21]. Recently, denoising diffusion models [16], which learn to denoise random noise images into photorealistic images, have shown impressive synthesis results and gained popularity as an alternative to GANs. Different diffusion models are invented for faster sampling [41] (used in this work), conditional generation [7, 31], and later pixel-aligned conditional generation [37]. Similarly, we use pixel-aligned conditions, specifically surface normal, albedo, and Lambertian rendering images, as the condition that our diffusion model should satisfy. Closely related to DiffusionRig are Diffusion Autoencoders (Diff-AE) that learn a latent space of facial attributes (e.g., +smiling vs. -smiling) via the autoencoding task [34]. Given binary labels of a certain attribute, the authors find the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12737" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.095, + 0.163, + 0.182 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.1, + 0.182, + 0.145, + 0.192 + ], + "angle": 0, + "content": "Surface" + }, + { + "type": "image_caption", + "bbox": [ + 0.1, + 0.194, + 0.147, + 0.204 + ], + "angle": 0, + "content": "Normals" + }, + { + "type": "image", + "bbox": [ + 0.166, + 0.096, + 0.248, + 0.182 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.185, + 0.184, + 0.227, + 0.193 + ], + "angle": 0, + "content": "Albedo" + }, + { + "type": "image", + "bbox": [ + 0.25, + 0.096, + 0.332, + 0.182 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.26, + 0.182, + 0.324, + 0.193 + ], + "angle": 0, + "content": "Lambertian" + }, + { + "type": "image_caption", + "bbox": [ + 0.272, + 0.195, + 0.313, + 0.205 + ], + "angle": 0, + "content": "Render" + }, + { + "type": "image", + "bbox": [ + 0.334, + 0.095, + 0.446, + 0.181 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.374, + 0.184, + 0.405, + 0.194 + ], + "angle": 0, + "content": "Input" + }, + { + "type": "image", + "bbox": [ + 0.447, + 0.095, + 0.556, + 0.181 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.479, + 0.182, + 0.525, + 0.193 + ], + "angle": 0, + "content": "Stage 1" + }, + { + "type": "image_caption", + "bbox": [ + 0.476, + 0.195, + 0.528, + 0.206 + ], + "angle": 0, + "content": "Sample 1" + }, + { + "type": "image", + "bbox": [ + 0.557, + 0.095, + 0.668, + 0.181 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.591, + 0.182, + 0.632, + 0.193 + ], + "angle": 0, + "content": "Stage 1" + }, + { + "type": "image_caption", + "bbox": [ + 0.587, + 0.194, + 0.639, + 0.206 + ], + "angle": 0, + "content": "Sample 2" + }, + { + "type": "image", + "bbox": [ + 0.668, + 0.095, + 0.779, + 0.181 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.701, + 0.182, + 0.744, + 0.193 + ], + "angle": 0, + "content": "Stage 2" + }, + { + "type": "image_caption", + "bbox": [ + 0.698, + 0.194, + 0.748, + 0.206 + ], + "angle": 0, + "content": "Sample 1" + }, + { + "type": "image", + "bbox": [ + 0.781, + 0.095, + 0.892, + 0.181 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.813, + 0.182, + 0.856, + 0.193 + ], + "angle": 0, + "content": "Stage 2" + }, + { + "type": "image_caption", + "bbox": [ + 0.81, + 0.194, + 0.862, + 0.205 + ], + "angle": 0, + "content": "Sample 2" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.213, + 0.894, + 0.27 + ], + "angle": 0, + "content": "Figure 2. Reconstruction with vs. without personalized priors. Given the input image and its conditions (surface normals, albedo, and Lambertian rendering) automatically extracted using DECA, Stage 1 learns only generic face priors and fails to reconstruct the identity in both of the randomly sampled reconstructions. With Stage 2, DiffusionRig is able to faithfully reconstruct the input image using either of the two stochastically sampled noise maps." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.282, + 0.47, + 0.342 + ], + "angle": 0, + "content": "direction, along which the latent code should be pushed, to manipulate that attribute. 3D-aware generative models are a recent popular trend to combine 3D controllability with 2D image generation [3, 4, 10, 13, 43, 45, 46, 54]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.348, + 0.473, + 0.454 + ], + "angle": 0, + "content": "Facial Appearance Modeling 3D Morphable Face Models or 3DMMs provide a valuable parameter space to describe (and in turn solve for) 3D facial characteristics [2]. The FLAME face model learned from 4D scans is a widely-used 3DMM that supports shape, pose, and expression change [24]. We refer the reader to a recent survey paper on Morphable Face Models [8]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.455, + 0.473, + 0.606 + ], + "angle": 0, + "content": "RingNet regresses FLAME parameters from 2D images [38]. Also a learning-based method, DECA additionally predicts albedo and lighting in spherical harmonics (SH) from a single face image [9]. An alternative to using 3DMMs for \"face de-rendering\" is directly predicting surface normals, albedo, and lighting in the image space, as in SfSNet [39]. Although such approaches enjoy the benefit of being able to represent hair, accessories, etc., image-space representations do not provide a physically meaningful parameter space for rigging like 3DMMs do." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.607, + 0.472, + 0.744 + ], + "angle": 0, + "content": "The geometry, albedo, and lighting from 3DMM are still extremely coarse and far from reality. The community has bridged the realism gap between 3DMM rendering and real photos through expensive hardware setups to capture fine-grained facial geometry [48, 50] and reflectance fields [6]. Neural network-based, implicit appearance models have also been proposed to address the infeasibility of explicitly describing the appearance with precise reflectance and lighting [1, 12, 28, 29, 30, 35, 36, 40, 42, 52, 53]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.473, + 0.885 + ], + "angle": 0, + "content": "Personalized Priors Learning personal priors has been more widely discussed in super-resolution, face restoration, and inpainting, by using exemplar imagery [47], personal supplemental attributes [51], an attention module with identity penalty [49], or facial component dictionaries [25]. Conditional portrait image editing also shares the objective of preserving the input identity [26, 44]. However, it remains a challenge how to compute an unbiased identity score, and these approaches do not explicitly learn personalized priors." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Closer to DiffusionRig that learns a personal prior from a" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.282, + 0.895, + 0.419 + ], + "angle": 0, + "content": "set of personal album of the person, MyStyle [32] is a method to finetune a pre-trained StyleGAN model to achieve a generative model for a specific identity, while preserving the expressiveness of the latent space. However, it does not support precise 3D rigging to control the generation and requires a much larger personal dataset to obtain a smooth personalized latent space. DiffusionRig, on the other hand, focuses on controllable image editing and achieves the smooth editing naturally with the continuous physical space as conditions." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.43, + 0.638, + 0.446 + ], + "angle": 0, + "content": "3. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.456, + 0.895, + 0.502 + ], + "angle": 0, + "content": "We provide the background knowledge for the two building blocks—3D Morphable Face Models (3DMMs) and Denoising Diffusion Probabilistic Models (DDPMs)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.51, + 0.75, + 0.526 + ], + "angle": 0, + "content": "3.1. 3D Morphable Face Models" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.533, + 0.895, + 0.822 + ], + "angle": 0, + "content": "3D Morphable Face Models or 3DMMs are parametric models that use a compact latent space (handcrafted or learned from scans) to represent the head pose, face geometry, facial expression, etc. [2, 24]. In this paper, we employ FLAME [24], a popular 3DMM using standard vertex-based linear blend skinning with corrective blendshapes and representing a face mesh with pose, shape, and expression parameters. Although FLAME provides a compact and physically meaningful space for face geometry, it does not provide descriptions for appearance. To this end, DECA [9] uses FLAME and additionally models facial appearance with Lambertian reflectance and Spherical Harmonics (SH) lighting. Trained on a large dataset, DECA predicts albedo, SH lighting, and the FLAME parameters from a single portrait image. We utilize DECA to generate rough 3D representations that support easy \"rigging\" by editing the FLAME parameters, albedo, and/or SH lighting. As we show in Figure 2, the realism gap between DECA rendering and real photos is significant, calling for measurements post-editing." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.832, + 0.85, + 0.848 + ], + "angle": 0, + "content": "3.2. Denoising Diffusion Probabilistic Models" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.856, + 0.894, + 0.902 + ], + "angle": 0, + "content": "Denoising Diffusion Probabilistic Models (DDPMs) [7, 15, 31] are a class of generative models that take random noise images as input and denoise the images progressively" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12738" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.099, + 0.885, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.285, + 0.895, + 0.342 + ], + "angle": 0, + "content": "Figure 3. DiffusionRig overview. The input to our model is a set of physical buffers reconstructed from the input, a random noise map, and a global latent code that encodes nuance features not modeled by the physical buffers. At Stage 1, we train our model on a large face dataset to learn generic face priors. At Stage 2, we keep the global latent code encoder frozen and fine-tune the diffusion model to learn personalized priors." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.355, + 0.473, + 0.552 + ], + "angle": 0, + "content": "to produce photorealistic images. This generation process can be seen as the reverse of the diffusion process that gradually adds noise to images. The key component of DDPMs is a denoising network \\( f_{\\theta} \\). During training, it takes a noisy image \\( x_{t} \\) and a timestep \\( t \\) (\\( 1 \\leq t \\leq T \\)), and predicts the noise at time \\( t \\): \\( \\epsilon_{t} \\). More formally, the predicted noise at time \\( t \\) is \\( \\hat{\\epsilon}_{t} = f_{\\theta}(x_{t}, t) \\), where \\( x_{t} = \\alpha_{t} x_{0} + \\sqrt{1 - \\alpha_{t}^{2}} \\epsilon_{t} \\), \\( \\epsilon_{t} \\) is a random, normally distributed noise image, and \\( \\alpha_{t} \\) is a hyperparameter that gradually increases noise level of \\( x_{t} \\) with each step of the forward process. The loss is computed on the distance between \\( \\epsilon_{t} \\) and \\( \\hat{\\epsilon}_{t} \\). Therefore, the trained model can generate images by taking as input a random noise image and gradually denoising it to a photorealistic one." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.558, + 0.17, + 0.573 + ], + "angle": 0, + "content": "4. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.583, + 0.47, + 0.658 + ], + "angle": 0, + "content": "To enable personalized appearance editing, our model, which we dub DiffusionRig, needs to (a) generate images based on different appearance conditions, such as novel lighting, and (b) learn personal priors so that the person's identity is not altered during editing." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.658, + 0.471, + 0.794 + ], + "angle": 0, + "content": "To this end, we design a two-stage training pipeline as shown in Figure 3. At the first stage, the model learns generic face priors by being trained to reconstruct portrait images given their underlying \"appearance conditions\" represented as physical buffers automatically extracted using an off-the-shelf estimator. At the second stage, we finetune our model using portrait photos of just one person so that the model learns personalized priors, which are necessary to prevent identity shift during appearance editing." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.802, + 0.342, + 0.818 + ], + "angle": 0, + "content": "4.1. Learning Generic Face Priors" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Our first stage is designed to learn facial priors that enable photorealistic image synthesis conditioned on physical constraints like lighting. For the physical conditioning, we use DECA [9] to produce the physical parameters including the FLAME [24] parameters (shape \\(\\beta\\), expression \\(\\psi\\), and" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.355, + 0.895, + 0.596 + ], + "angle": 0, + "content": "pose \\(\\theta\\)), albedo \\(\\alpha\\), (orthographic) camera \\(\\mathbf{c}\\), and (spherical harmonics) lighting \\(\\mathbf{l}\\) from the input portrait image. We then use the Lambertian reflectance to render these physical properties into three buffers: surface normals, albedo, and Lambertian rendering. Although these physical buffers provide pixel-aligned descriptions of the facial geometry, albedo, and lighting, they are rather coarse and nowhere close to photorealistic images (see the Lambertian rendering in Figures 1 and 2). Still, using these buffers, we can \"rig\" our generative model in a disentangled, physically meaningful way by changing the DECA parameters. For photorealistic image synthesis, we use a Denoising Diffusion Probabilistic Model (DDPM) as our generator because DDPMs can naturally take pixel-aligned conditions (more advantageous than latent code conditions as shown in Section 5.5) to drive the generation process." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.598, + 0.896, + 0.81 + ], + "angle": 0, + "content": "Besides the pixel-aligned physical buffers, we keep the random noise images in DDPMs to explain the stochasticity during generation. In addition to the pixel-aligned buffers and noise map, we need another condition to encode global appearance information (as opposed to local information such as local surface normals) that is not modeled by the physical buffers, such as hair, hat, glasses, and the image background. Therefore, our diffusion model takes both physical buffers and a learned global latent code as conditions for image synthesis. Formally, our model can be described as \\(\\hat{\\epsilon}_t = f_\\theta ([x_t,z],t,\\phi_\\theta (x_0))\\) where \\(x_{t}\\) is the noisy image at timestep \\(t\\), \\(z\\) represent the physical buffers, \\(x_0\\) is the original image, \\(\\hat{\\epsilon}_t\\) is the predicted noise, and \\(f_{\\theta}\\) and \\(\\phi_{\\theta}\\) are the denoising model and the global latent encoder, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.895, + 0.902 + ], + "angle": 0, + "content": "It is theoretically possible that the global latent code also encodes local geometry, albedo, and/or illumination information, which could lead to the diffusion model ignoring the physical buffers entirely. Empirically, we find that the network learns to use the physical buffers for local information and does not rely on the global latent code, possibly because" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12739" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.122 + ], + "angle": 0, + "content": "these buffers are pixel-aligned with the ground truth and thus more easily leveraged by the model." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.134, + 0.34, + 0.15 + ], + "angle": 0, + "content": "4.2. Learning Personalized Priors" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.155, + 0.473, + 0.381 + ], + "angle": 0, + "content": "After learning the generic facial priors at the first stage, DiffusionRig is able to generate photorealistic images given coarse physical buffers. The next step is to learn personalized priors for a given person to avoid identity shift during appearance editing. Personal priors are crucial to preserving identity and high-frequency facial characteristics, as shown in Figure 2. We achieve this by finetuning our denoising model on a specific person's photo album of around 20 images. During the finetuning stage, the denoising model learns the person's identity information. We fix the global encoder from the previous stage since it has learned to encode global image information not modeled by the physical buffers (which we want to retain). We show that this approach is simple and yet effective compared with GANs that need careful tuning, as mentioned in MyStyle [32]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.382, + 0.473, + 0.504 + ], + "angle": 0, + "content": "For this small personalized dataset, we also extract the DECA parameters first. However, since DECA is a single-image estimator, its output is sensitive to extreme poses or expressions. Under the assumption that the general shape of a person's face does not change drastically within a reasonable period of time, we compute the mean of the shape parameters in FLAME over all the images in the album and use that mean shape when conditioning DiffusionRig." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.515, + 0.266, + 0.53 + ], + "angle": 0, + "content": "4.3. Model Architecture" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.535, + 0.47, + 0.671 + ], + "angle": 0, + "content": "DiffusionRig consists of two trainable parts: a denoising model \\( f_{\\theta} \\) and a global encoder \\( \\phi_{\\theta} \\). The architecture of our denoising model is based on ADM [7] with modifications to reduce computational cost and take an additional global latent code as input. For the global code, we use the same method that ADM uses for their time embedding: We scale and shift the features in each layer using the global latent code. The encoder is simply a ResNet-18 [14] and we use the output features as the global latent codes." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.672, + 0.47, + 0.764 + ], + "angle": 0, + "content": "Our loss function is a P2 weight loss [5] that computes distances between predicted and ground-truth noises: \\(\\mathcal{L} = \\lambda_t' ||\\hat{\\epsilon}_t - \\epsilon_t||_2^2\\), where \\(\\lambda_t'\\) is a hyperparameter to control the loss weight at different timesteps. We empirically find that the P2 weight loss speeds up the training process and generates high-quality images compared with a constant loss weight." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.775, + 0.295, + 0.79 + ], + "angle": 0, + "content": "4.4. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.473, + 0.903 + ], + "angle": 0, + "content": "During the first stage, we train DiffusionRig on the FFHQ dataset [19], which contains 70,000 images. With Adam [23] as the optimizer with a learning rate of \\(10^{-4}\\), we train DiffusionRig for 50,000 iterations with a batch size of 256 (so the total number of samples seen by the model is 12,800,000). During the second stage, we use only 10-20 images of a single person. In the following, we show results for four" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.289 + ], + "angle": 0, + "content": "celebrities (Obama, Biden, Swift, and Harris) and two noncelebrities. Please see the supplemental material and video for more results including more identities. We use 20 images for each person except for Harris, for whom we use only 10, and for the ablation study on the number of training images. We provide the personal photo album of two identities in the supplemental material. We finetune our model on each small dataset for 5,000 iterations with a batch size of 4 (so the total number of seen samples during finetuning is 20,000). We furthermore decrease the learning rate to \\(10^{-5}\\) for the second stage. Training for the first stage takes around 15 hours using eight A100 GPUs, and the Stage 2 finetuning completes within 30 minutes on a single V100 GPU." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.293, + 0.634, + 0.311 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.318, + 0.895, + 0.53 + ], + "angle": 0, + "content": "We first show how to edit a person's appearance (e.g., facial expression, lighting, and head pose) by modifying the physical buffers that condition the model. We then demonstrate how to rig, with the global latent code, other aspects of a person's appearance not modeled by the physical buffers such as hairstyle and accessories. By swapping in the global latent code from another image, we can transfer portrait characteristics, such as hairstyle, accessories including glasses, and/or the image background, while preserving the physical properties (e.g., identity, pose, expression, and lighting) from the original image. Finally, we show the power of the learned personal priors by conditioning, for example, an Obama model on both the physical buffers and global latent code from a different person (to \"Obama-fy\" that person)." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.534, + 0.866, + 0.55 + ], + "angle": 0, + "content": "5.1. Rigging Appearance With Physical Buffers" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.554, + 0.895, + 0.734 + ], + "angle": 0, + "content": "In this section, we use our personalized model to rig the appearance with physical buffers. We show three different types of appearance rigging: relighting, expression change, and pose change. For relighting, we use different Spherical Harmonics (SH) parameters for producing the Lambertian rendering. To change the expression, we modify the expression and jaw rotation parameters of FLAME (the last three parameters of the pose vector). To vary the pose, we modify the head rotation parameters (the first three parameters of the pose vector). The 64-dimensional global latent code is produced by encoding the input image and remains unchanged when editing appearance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.897, + 0.903 + ], + "angle": 0, + "content": "Our results are displayed in Figure 4, where we depict three identities: two celebrities and one daily user. All the images have a resolution of \\(256 \\times 256\\). Additionally, \\(512 \\times 512\\) results can be found in the supplemental material. We compare our method against DECA [9], HeadNerf [17], GIF [10], and MyStyle [32], of which the first two are 3D face model estimation methods, and the latter two are GAN-based approaches. As Figure 4 shows, while GIF is capable of rigging the appearance by changing the expression and pose, it fails to preserve the individual's identity. DiffusionRig and MyStyle, on the other hand, are both personalized models" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "12740" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.086, + 0.096, + 0.104, + 0.14 + ], + "angle": 270, + "content": "Original" + }, + { + "type": "image_caption", + "bbox": [ + 0.088, + 0.166, + 0.104, + 0.201 + ], + "angle": 270, + "content": "DECA" + }, + { + "type": "image_caption", + "bbox": [ + 0.088, + 0.223, + 0.104, + 0.277 + ], + "angle": 270, + "content": "HeadNerf" + }, + { + "type": "image_caption", + "bbox": [ + 0.088, + 0.305, + 0.104, + 0.327 + ], + "angle": 270, + "content": "GIF" + }, + { + "type": "image_caption", + "bbox": [ + 0.087, + 0.356, + 0.104, + 0.407 + ], + "angle": 270, + "content": "MyStyle" + }, + { + "type": "image", + "bbox": [ + 0.107, + 0.09, + 0.189, + 0.154 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.107, + 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"image_caption", + "bbox": [ + 0.076, + 0.507, + 0.892, + 0.562 + ], + "angle": 0, + "content": "Figure 4. Appearance editing. DiffusionRig achieves convincing appearance edits while preserving the individual's identity using only 20 images per identity. GIF creates realistic-looking images but does not use personalized priors, leading to significant identity shifts. MyStyle is unable to make dramatic changes to the expression or pose without artifacts or minor identity shifts. In addition, MyStyle does not trivially support controllable relighting, so the corresponding fields have been left empty." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.571, + 0.47, + 0.722 + ], + "angle": 0, + "content": "that are able to preserve the identity. However, since our method is directly conditioned on physical buffers, we can rig the appearance in a physically-based manner, whereas MyStyle needs to search for and step into a certain direction within the latent space to produce the target appearance, limiting its controllability, interpretability, and capacity for dramatic appearance changes. We also observe more artifacts for MyStyle when doing appearance editing, which is likely due to the use of too few images during finetuning the StyleGAN model." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.73, + 0.468, + 0.746 + ], + "angle": 0, + "content": "5.2. Rigging Appearance With Global Latent Code" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.47, + 0.84 + ], + "angle": 0, + "content": "By design, DiffusionRig finds it easier to learn what physical buffers can describe from the pixel-aligned buffers than from the global latent code. The latent code thus encodes what physical buffers cannot describe including background, makeup, and hairstyle. In this part, we change the global latent code to show its effects on the generated images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.469, + 0.901 + ], + "angle": 0, + "content": "In Figure 5, we show a \\(2 \\times 3\\) matrix of generated images. Along the horizontal axis, we swap in the global latent code from another image of the same person while keeping the physical buffers identical (i.e., same physical buffers but" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.571, + 0.892, + 0.752 + ], + "angle": 0, + "content": "different global codes). Along the vertical axis, we replace the physical buffers while keeping the same global latent code (i.e., same global code but different physical buffers). We can see that geometry information, such as head pose and expression, is preserved for each row, which shows that only the physical buffers (not the latent code) contain such information. This means that in DiffusionRig these physical properties are well disentangled from each other and from other appearance properties that physical buffers cannot describe. On the other hand, the information hard to model explicitly, including image background, glasses, and hair style/color, is encoded in the global latent code." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.759, + 0.833, + 0.774 + ], + "angle": 0, + "content": "5.3. Identity Transfer With Learned Priors" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.781, + 0.893, + 0.901 + ], + "angle": 0, + "content": "In previous sections, we saw what information the physical buffers and the global latent code encode. Now, we demonstrate what information is encoded in the personalized diffusion models' weights. Here, we keep both physical buffers and global latent code the same but exchange the personalized model itself with another person's personalized model (i.e., model swapping without code or buffer swapping). The results of this experiment for four identities are" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "12741" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.09, + 0.473, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.324, + 0.472, + 0.38 + ], + "angle": 0, + "content": "Figure 5. Mix and match of physical buffers and global latent code. We mix the physical buffers from one image and the global latent code from another image to demonstrate how the two conditions encode disentangled information." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.394, + 0.473, + 0.56 + ], + "angle": 0, + "content": "shown in Figure 6. Each row uses the same physical buffers and latent code but another personalized model. Each column uses the same personalized model but different physical buffers and latent code. For example, the column \"Obama-fy\" shows four images that are generated by Obama's personal model but using the other celebrities' images as input. We see that across each row, while all inputs (physical buffers plus global latent code) are the same, the four different personalized models output different identities. These results further corroborate that our model is able to learn personalized priors from a small dataset." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.57, + 0.455, + 0.586 + ], + "angle": 0, + "content": "5.4. Baseline Comparisons & Evaluation Metrics" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.589, + 0.472, + 0.65 + ], + "angle": 0, + "content": "We evaluate our DiffusionRig quantitatively in three aspects: rigging quality, identity preservation, and photorealism, since these three qualities are the most important for our personalized appearance editing." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.653, + 0.472, + 0.803 + ], + "angle": 0, + "content": "DECA Re-Inference Error We follow the same setup as in GIF [10] to compute the DECA re-inference error. To evaluate relighting quality, we directly compute the RMSE on the re-inferred spherical harmonics. We show our results in Table 1. For our model, we also evaluate two ablated versions: \"vector cond.\" and \"feature cond.\" Instead of using pixel-aligned physical buffers as the condition, we use DECA's output parameters and features computed from physical buffers as conditions in our two ablated models. More details can be found in Section 5.5." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.472, + 0.901 + ], + "angle": 0, + "content": "Face Re-Identification Error An important metric for evaluating this work is whether DiffusionRig can preserve the identity after appearance editing, since identity shift is a notorious problem in generative model-based editing. To this end, we run a widely popular face re-identification network [22] to automatically determine if the edited and" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.089, + 0.892, + 0.405 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.409, + 0.895, + 0.48 + ], + "angle": 0, + "content": "Figure 6. Swapping personalized models. We demonstrate the power of personalized priors by running one person's model on other identities. This creates the effect of \"adding\" one person's identity to another person. The images with green borders are \"no-swap\" results where the corresponding person's model is used." + }, + { + "type": "table", + "bbox": [ + 0.508, + 0.492, + 0.887, + 0.569 + ], + "angle": 0, + "content": "
Light ↓Shape ↓Exp. ↓Pose ↓
GIF [10]13.83.05.05.6
GIF, vector cond. [10]-3.423.129.7
DiffusionRig (Ours)11.24.32.84.2
DiffusionRig, vector cond.15.510.78.814.0
DiffusionRig, feature cond.27.05.34.121.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.573, + 0.895, + 0.672 + ], + "angle": 0, + "content": "Table 1. RMSE of DECA re-inference. All numbers are multiples of \\(10^{-3}\\). We generate 1,000 images to compute the RMSE. For shape, expression, and pose, the RMSE is computed on rendered FLAME faces. For lighting, the RMSE is computed on re-inferred spherical harmonics directly. We only use our Stage 1 model since GIF is not a personalized model. Numbers for GIF and its vector-conditioned variant are cited from the original paper [10]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.685, + 0.895, + 0.837 + ], + "angle": 0, + "content": "original images are of the same person. As Table 2 shows, both MyStyle [32] and DiffusionRig preserve the identity in all 400 expression-edited images of Obama and another 400 of Swift. That said, for dramatic changes such as head pose change, DiffusionRig preserves the identity better than MyStyle, as also demonstrated by Figure 4. One caveat of this error metric, though, is the obvious degenerate solution of not applying any edit at all, thereby achieving a perfect score. We refer the reader to Figure 4 and Table 1, which show that DiffusionRig avoids this degenerate solution." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.897, + 0.903 + ], + "angle": 0, + "content": "User Study To further evaluate both the photorealism and identity preservation of images from DiffusionRig against MyStyle, we conduct a user study involving Amazon Mechanical Turk. During the study, we show pairs of images," + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "12742" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.09, + 0.089, + 0.457, + 0.149 + ], + "angle": 0, + "content": "
Auto. Face Re-ID ↑User Study ↑
Obama and SwiftObamaSwift
Expr.PoseExpr.PoseExpr.Pose
MyStyle100%97.9%79.4%78.0%64.5%62.5%
Ours100%99.3%87.2%86.5%82.4%80.2%
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.154, + 0.47, + 0.21 + ], + "angle": 0, + "content": "Table 2. DiffusionRig vs. MyStyle [32] in expression and pose editing, as measured by an automatic face re-ID error [22] (which has an obvious flaw; see text) as well as a user study on both realism and identity preservation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.217, + 0.471, + 0.353 + ], + "angle": 0, + "content": "where the left image is an original image from the real image dataset, and the right image is a generated one. We occasionally include some real images on the right, too, for consistency check and quality control. We then ask the users whether the right image is a real image of the person on the left (so both photorealism and identity preservation are probed). We generate images that include either an expression or pose change for both DiffusionRig and MyStyle. We report our results in Table 2." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.362, + 0.231, + 0.379 + ], + "angle": 0, + "content": "5.5. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.382, + 0.471, + 0.428 + ], + "angle": 0, + "content": "We show several ablation studies to motivate the finetuning stage that injects the personalized prior and the choice of physical, pixel-aligned buffers to condition the model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.433, + 0.47, + 0.526 + ], + "angle": 0, + "content": "No Personalized Priors We first show how DiffusionRig performs in the absence of personalized priors (i.e., trained on only the large dataset from Stage 1). Figure 2 shows that our model learns to use the physical buffers as conditions for pose, expression, and lighting, but it is incapable of preserving the person's identity during appearance editing." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.53, + 0.471, + 0.681 + ], + "angle": 0, + "content": "Number of Images Here we explore how the number of images used in Stage 2 affects DiffusionRig's ability of learning personalized priors. We train three models of a non-celebrity with 1, 5, 10, and 20 images and test them on relighting, expression change, and pose change. As Figure 7 demonstrates, using just 1, 5, or 10 images yields worse results than using 20 images (unsurprisingly). With more images, DiffusionRig learns better-personalized priors that capture high-frequency face characteristics, such as the wrinkles in Figure 7." + }, + { + "type": "image", + "bbox": [ + 0.1, + 0.689, + 0.446, + 0.791 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.798, + 0.47, + 0.854 + ], + "angle": 0, + "content": "Figure 7. Quality w.r.t. number of Stage 2 images. DiffusionRig achieves high-quality relighting and pose change with 20 images for Stage 2. Using fewer may yield blurry results and make them hard to rig with new conditions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Different Forms of Conditions There are alternative ways to condition the image synthesis. We demonstrate that pixel" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.289 + ], + "angle": 0, + "content": "aligned physical buffers are the most effective form in accurately rigging the appearance. We explore the following two conditioning alternatives. \"Vector cond.\" is when we directly concatenate DECA parameters, a 236-dimensional vector, to the global latent code without using pixel-aligned buffers. \"Feature cond.\" means that we concatenate the physical buffers to the input image and pass them into the encoder to compute a global latent code, which is then used as a non-spatial feature condition. As shown in Figure 8, using pixel-aligned physical guidance is essential for accurate conditional image editing. Both vector and feature conditioning suffer from the generated images not following the desired physical guidance." + }, + { + "type": "image", + "bbox": [ + 0.523, + 0.3, + 0.695, + 0.365 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.528, + 0.365, + 0.688, + 0.375 + ], + "angle": 0, + "content": "Rigging Expression: input and src." + }, + { + "type": "image", + "bbox": [ + 0.697, + 0.3, + 0.781, + 0.364 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.705, + 0.365, + 0.771, + 0.374 + ], + "angle": 0, + "content": "Feature Cond." + }, + { + "type": "image", + "bbox": [ + 0.782, + 0.3, + 0.865, + 0.364 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.792, + 0.365, + 0.855, + 0.375 + ], + "angle": 0, + "content": "DiffusionRig" + }, + { + "type": "image", + "bbox": [ + 0.523, + 0.378, + 0.692, + 0.442 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.536, + 0.443, + 0.668, + 0.453 + ], + "angle": 0, + "content": "Rigging Pose: input and src." + }, + { + "type": "image", + "bbox": [ + 0.695, + 0.377, + 0.781, + 0.442 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.706, + 0.443, + 0.77, + 0.452 + ], + "angle": 0, + "content": "Vector Cond." + }, + { + "type": "image", + "bbox": [ + 0.782, + 0.377, + 0.865, + 0.442 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.795, + 0.443, + 0.857, + 0.453 + ], + "angle": 0, + "content": "DiffusionRig" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.459, + 0.892, + 0.502 + ], + "angle": 0, + "content": "Figure 8. Ablation on the form of conditions. Neither feature conditioning nor vector conditioning is able to rig the input image to follow the physical properties of the target image." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.515, + 0.742, + 0.531 + ], + "angle": 0, + "content": "6. Limitations & Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.538, + 0.895, + 0.734 + ], + "angle": 0, + "content": "Although DiffusionRig achieves state-of-the-art facial appearance editing, it relies on a small portrait dataset to finetune, which limits its scalability for massive user adoption. Furthermore, when the edit involves dramatic head pose change, DiffusionRig may not stay faithful to the original background, since head pose change sometimes reveals what used to be occluded, therefore requiring background inpainting—a topic beyond the scope of this paper. Additionally, since DiffusionRig relies on DECA to get physical buffers, it will also be affected by DECA's limited estimation capability: for instance, extreme expressions usually cannot be well predicted. and the estimated lighting is sometimes coupled with the skin tone." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.736, + 0.894, + 0.843 + ], + "angle": 0, + "content": "In this paper, we have presented DiffusionRig, a riggable diffusion model for identity-preserving, personalized editing of facial appearance. We introduced a two-stage method to first learn generic face priors and later personalized priors. Using both explicit conditioning via physical buffers and implicit conditioning via global latent code, we can drive and control our model's facial image synthesis." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgment We thank Marc Levoy for the valuable feedback and everyone whose photos appear in this paper for their permission." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12743" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.09, + 0.176, + 0.107 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.169 + ], + "angle": 0, + "content": "[1] Sai Bi, Stephen Lombardi, Shunsuke Saito, Tomas Simon, Shih-En Wei, Kevyn Mcphail, Ravi Ramamoorthi, Yaser Sheikh, and Jason Saragih. 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DiffusionRig takes in coarse physical rendering as the condition to "rig" the input image with learned personal priors. The edited images respect the rendering conditions, preserve the identity, and exhibit high-frequency facial details. + +![](images/d5a5f38acd1ca173d8180451d886fb6d592c01d0bd02b9a307571822afb19152.jpg) + +![](images/ef90403c3864047854dd8747f839dddd368f79877f21c01a4155f8b4d6b74a4c.jpg) + +![](images/297ea672a34998154ca752c5a3e047268955f498b22cbd811bc10f31051bbc51.jpg) +Condition +Output +Rigging Expression + +![](images/9dd95c7212a8a8a0c22b358a33098405b6e0cebe8df202c2e1e21234872d8738.jpg) + +![](images/dd24d6e0a09e66c969a561b369e6e2cf8a3aa2ba3352c0cb11c5c00bebd81abf.jpg) + +![](images/55cfeac15a14d4327038d98077bb56f326f00190385616b718f4dd178a7efa43.jpg) +Condition +Output +Rigging Lighting + +![](images/530dae9c5dd9caef9a9545872c8fb150b0adfb8151c428ff6a1c6f86896c5ff5.jpg) + +![](images/579dff7d49d2a8f8f790c85ccf19586381c5f2c606e8322930e7dc4c288880c3.jpg) + +![](images/06d8f6ecc848c03fc60eca68a53160a7983a71d68c911aa669d6155ffd141791.jpg) +Condition +Rigging Pose + +![](images/04d75601730a6f53cad2fbd7b4002fa7a8d3ae32d962b7987f2cf9e708fa9161.jpg) + +![](images/6ee4548fc99592fd831cc158af30419d0c933db3edf093138743494ff8b3e08c.jpg) +Output + +# Abstract + +We address the problem of learning person-specific facial priors from a small number (e.g., 20) of portrait photos of the same person. This enables us to edit this specific person's facial appearance, such as expression and lighting, while preserving their identity and high-frequency facial details. Key to our approach, which we dub DiffusionRig, is a diffusion model conditioned on, or "rigged by," crude 3D face models estimated from single in-the-wild images by an off-the-shelf estimator. On a high level, DiffusionRig learns to map simplistic renderings of 3D face models to realistic photos of a given person. Specifically, DiffusionRig is trained in two stages: It first learns generic facial priors from a large-scale face dataset and then person-specific priors from a small portrait photo collection of the person of interest. By learning the CGI-to-photo mapping with such personalized priors, + +DiffusionRig can "rig" the lighting, facial expression, head pose, etc. of a portrait photo, conditioned only on coarse 3D models while preserving this person's identity and other high-frequency characteristics. Qualitative and quantitative experiments show that DiffusionRig outperforms existing approaches in both identity preservation and photorealism. Please see the project website: https://diffusionrig.github.io for the supplemental material, video, code, and data. + +# 1. Introduction + +It is a longstanding problem in computer vision and graphics to photorealistically change the lighting, expression, head pose, etc. of a portrait photo while preserving the person's identity and high-frequency facial characteristics. The difficulty of this problem stems from its fundamentally underconstrained nature, and prior work typically addresses this with zero-shot learning, where neural networks were trained on a large-scale dataset of different identities and tested on a new identity. These methods ignore the fact that such + +generic facial priors often fail to capture the test identity's high-frequency facial characteristics, and multiple photos of the same person are often readily available in the person's personal photo albums, e.g., on a mobile phone. In this work, we demonstrate that one can convincingly edit a person's facial appearance, such as lighting, expression, and head pose, while preserving their identity and other high-frequency facial details. Our key insight is that we can first learn generic facial priors from a large-scale face dataset [19] and then finetune these generic priors into personalized ones using around 20 photos capturing the test identity. + +When it comes to facial appearance editing, the natural question is what representation one uses to change lighting, expression, head pose, hairstyle, accessories, etc. Off-the-shelf 3D face estimators such as DECA [9] can already extract, from an in-the-wild image, a parametric 3D face model that comprises parameters for lighting (spherical harmonics), expression, and head pose. However, directly rendering these physical properties back into images yields CGI-looking results, as shown in the output columns of Figure 1. The reasons are at least three-fold: (a) The 3D face shape estimated is coarse, with mismatched face contours and misses high-frequency geometric details, (b) the assumptions on reflectance (Lambertian) and lighting (spherical harmonics) are restrictive and insufficient for reproducing the reality, and (c) 3D morphable models (3DMMs) simply cannot model all appearance aspects including hairstyle and accessories. Nonetheless, such 3DMMs provide us with a useful representation that is amenable to "appearance rigging" since we can modify the facial expression and head pose by simply changing the 3DMM parameters as well as lighting by varying the spherical harmonics (SH) coefficients. + +On the other hand, diffusion models [15] have recently gained popularity as an alternative to Generative Adversarial Networks (GANs) [11] for image generation. Diff-AE [33] further shows that when trained on the autoencoding task, diffusion models can provide a latent space for appearance editing. In addition, diffusion models are able to map pixel-aligned features (such as noise maps in the vanilla diffusion model) to photorealistic images. Although Diff-AE is capable of interpolating from, e.g., smile to no smile, after semantic labels are used to find the direction to move towards, it is unable to perform edits that require 3D understanding and that cannot be expressed by simple binary semantic labels. Such 3D edits, including relighting and head pose change, are the focus of our work. + +To combine the best of both worlds, we propose Diffusion-Rig, a model that allows us to edit or "rig" the appearance (such as lighting and head pose) of a 3DMM and then produce a photorealistic edited image conditioned on our 3D edits. Specifically, DiffusionRig first extracts rough physical properties from single portrait photos using an off-the-shelf method [9], performs desired 3D edits in the 3DMM space, + +and finally uses a diffusion model [15] to map the edited "physical buffers" (surface normals, albedo, and Lambertian rendering) to photorealistic images. Since the edited images should preserve the identity and high-frequency facial characteristics, we first train DiffusionRig on the CelebA dataset [27] to learn generic facial priors so that DiffusionRig knows how to map surface normals and the Lambertian rendering to a photorealistic image. Note that because the physical buffers are coarse and do not contain sufficient identity information, this "Stage 1 model" provides no guarantee for identity preservation. At the second stage, we finetune DiffusionRig on a tiny dataset of roughly 20 images of one person of interest, producing a person-specific diffusion model mapping physical buffers to photos of just this person. As discussed, there are appearance aspects not modeled by the 3DMM, including but not limited to hairstyle and accessories. To provide our model with this additional information, we add an encoder branch that encodes the input image into a global latent code ("global" in contrast to physical buffers that are pixel-aligned with the output image and hence "local"). This code is chosen to be low-dimensional in the hope of capturing just the aspects not modeled by the 3DMM, such as hairstyle and eyeglasses. + +In summary, our contributions are: + +- A deep learning model for 3D facial appearance editing (that modifies lighting, facial expression, head pose, etc.) trained using just images with no 3D label, +- A method to drive portrait photo generation using diffusion models with 3D morphable face models, and +- A two-stage training strategy that learns personalized facial priors on top of generic face priors, enabling editing that preserves identity and high-frequency details. + +# 2. Related Work + +Our work is related to generative models, 3D Morphable Face Models (3DMMs), and personalized priors. + +Generative Modeling Since the proposal of early Generative Adversarial Networks (GANs) [11], researchers have made significant progress in generating photorealistic images of constrained classes, such as faces [18, 20, 21]. Recently, denoising diffusion models [16], which learn to denoise random noise images into photorealistic images, have shown impressive synthesis results and gained popularity as an alternative to GANs. Different diffusion models are invented for faster sampling [41] (used in this work), conditional generation [7, 31], and later pixel-aligned conditional generation [37]. Similarly, we use pixel-aligned conditions, specifically surface normal, albedo, and Lambertian rendering images, as the condition that our diffusion model should satisfy. Closely related to DiffusionRig are Diffusion Autoencoders (Diff-AE) that learn a latent space of facial attributes (e.g., +smiling vs. -smiling) via the autoencoding task [34]. Given binary labels of a certain attribute, the authors find the + +![](images/effdec835022b1dfc0b6b0910025e37bd1304cbe603a4943554151aea9564395.jpg) +Surface +Normals +Figure 2. Reconstruction with vs. without personalized priors. Given the input image and its conditions (surface normals, albedo, and Lambertian rendering) automatically extracted using DECA, Stage 1 learns only generic face priors and fails to reconstruct the identity in both of the randomly sampled reconstructions. With Stage 2, DiffusionRig is able to faithfully reconstruct the input image using either of the two stochastically sampled noise maps. + +![](images/d4d1d7febf0a2f0b86c1902106d5554a10796e0bcd47315ce2d811f1e5aa1ae0.jpg) +Albedo + +![](images/f1a4725121403ae890cbb32b87de82880af59551f320a28ff23bd8343664f305.jpg) +Lambertian +Render + +![](images/c3c1d0b64b0db04df9486294c3105f14f7f2927803b9562a3167624a88a657dc.jpg) +Input + +![](images/befa565e8017181d1e015b5a0ac8ab00951180d29b5a3ec349c73572f4fc0940.jpg) +Stage 1 +Sample 1 + +![](images/615a5b7ab2245e5bc4983b5dbb072dccfb624ffaf990592f50da1420c1de554e.jpg) +Stage 1 +Sample 2 + +![](images/d63cf3be8a497b65bc810d19fb8b2fb2f326dfa421558663657eddc66c5dcda2.jpg) +Stage 2 +Sample 1 + +![](images/46ea9073adfb7beda8e18b425c08e31ec42475677b83d2d74e717723fc1b32ff.jpg) +Stage 2 +Sample 2 + +direction, along which the latent code should be pushed, to manipulate that attribute. 3D-aware generative models are a recent popular trend to combine 3D controllability with 2D image generation [3, 4, 10, 13, 43, 45, 46, 54]. + +Facial Appearance Modeling 3D Morphable Face Models or 3DMMs provide a valuable parameter space to describe (and in turn solve for) 3D facial characteristics [2]. The FLAME face model learned from 4D scans is a widely-used 3DMM that supports shape, pose, and expression change [24]. We refer the reader to a recent survey paper on Morphable Face Models [8]. + +RingNet regresses FLAME parameters from 2D images [38]. Also a learning-based method, DECA additionally predicts albedo and lighting in spherical harmonics (SH) from a single face image [9]. An alternative to using 3DMMs for "face de-rendering" is directly predicting surface normals, albedo, and lighting in the image space, as in SfSNet [39]. Although such approaches enjoy the benefit of being able to represent hair, accessories, etc., image-space representations do not provide a physically meaningful parameter space for rigging like 3DMMs do. + +The geometry, albedo, and lighting from 3DMM are still extremely coarse and far from reality. The community has bridged the realism gap between 3DMM rendering and real photos through expensive hardware setups to capture fine-grained facial geometry [48, 50] and reflectance fields [6]. Neural network-based, implicit appearance models have also been proposed to address the infeasibility of explicitly describing the appearance with precise reflectance and lighting [1, 12, 28, 29, 30, 35, 36, 40, 42, 52, 53]. + +Personalized Priors Learning personal priors has been more widely discussed in super-resolution, face restoration, and inpainting, by using exemplar imagery [47], personal supplemental attributes [51], an attention module with identity penalty [49], or facial component dictionaries [25]. Conditional portrait image editing also shares the objective of preserving the input identity [26, 44]. However, it remains a challenge how to compute an unbiased identity score, and these approaches do not explicitly learn personalized priors. + +Closer to DiffusionRig that learns a personal prior from a + +set of personal album of the person, MyStyle [32] is a method to finetune a pre-trained StyleGAN model to achieve a generative model for a specific identity, while preserving the expressiveness of the latent space. However, it does not support precise 3D rigging to control the generation and requires a much larger personal dataset to obtain a smooth personalized latent space. DiffusionRig, on the other hand, focuses on controllable image editing and achieves the smooth editing naturally with the continuous physical space as conditions. + +# 3. Preliminaries + +We provide the background knowledge for the two building blocks—3D Morphable Face Models (3DMMs) and Denoising Diffusion Probabilistic Models (DDPMs). + +# 3.1. 3D Morphable Face Models + +3D Morphable Face Models or 3DMMs are parametric models that use a compact latent space (handcrafted or learned from scans) to represent the head pose, face geometry, facial expression, etc. [2, 24]. In this paper, we employ FLAME [24], a popular 3DMM using standard vertex-based linear blend skinning with corrective blendshapes and representing a face mesh with pose, shape, and expression parameters. Although FLAME provides a compact and physically meaningful space for face geometry, it does not provide descriptions for appearance. To this end, DECA [9] uses FLAME and additionally models facial appearance with Lambertian reflectance and Spherical Harmonics (SH) lighting. Trained on a large dataset, DECA predicts albedo, SH lighting, and the FLAME parameters from a single portrait image. We utilize DECA to generate rough 3D representations that support easy "rigging" by editing the FLAME parameters, albedo, and/or SH lighting. As we show in Figure 2, the realism gap between DECA rendering and real photos is significant, calling for measurements post-editing. + +# 3.2. Denoising Diffusion Probabilistic Models + +Denoising Diffusion Probabilistic Models (DDPMs) [7, 15, 31] are a class of generative models that take random noise images as input and denoise the images progressively + +![](images/c763a44a9dcf0f326a1eb468bb5890d157562662c8bce4f60b095713e15b751d.jpg) +Figure 3. DiffusionRig overview. The input to our model is a set of physical buffers reconstructed from the input, a random noise map, and a global latent code that encodes nuance features not modeled by the physical buffers. At Stage 1, we train our model on a large face dataset to learn generic face priors. At Stage 2, we keep the global latent code encoder frozen and fine-tune the diffusion model to learn personalized priors. + +to produce photorealistic images. This generation process can be seen as the reverse of the diffusion process that gradually adds noise to images. The key component of DDPMs is a denoising network $f_{\theta}$ . During training, it takes a noisy image $x_{t}$ and a timestep $t$ ( $1 \leq t \leq T$ ), and predicts the noise at time $t$ : $\epsilon_{t}$ . More formally, the predicted noise at time $t$ is $\hat{\epsilon}_{t} = f_{\theta}(x_{t}, t)$ , where $x_{t} = \alpha_{t} x_{0} + \sqrt{1 - \alpha_{t}^{2}} \epsilon_{t}$ , $\epsilon_{t}$ is a random, normally distributed noise image, and $\alpha_{t}$ is a hyperparameter that gradually increases noise level of $x_{t}$ with each step of the forward process. The loss is computed on the distance between $\epsilon_{t}$ and $\hat{\epsilon}_{t}$ . Therefore, the trained model can generate images by taking as input a random noise image and gradually denoising it to a photorealistic one. + +# 4. Method + +To enable personalized appearance editing, our model, which we dub DiffusionRig, needs to (a) generate images based on different appearance conditions, such as novel lighting, and (b) learn personal priors so that the person's identity is not altered during editing. + +To this end, we design a two-stage training pipeline as shown in Figure 3. At the first stage, the model learns generic face priors by being trained to reconstruct portrait images given their underlying "appearance conditions" represented as physical buffers automatically extracted using an off-the-shelf estimator. At the second stage, we finetune our model using portrait photos of just one person so that the model learns personalized priors, which are necessary to prevent identity shift during appearance editing. + +# 4.1. Learning Generic Face Priors + +Our first stage is designed to learn facial priors that enable photorealistic image synthesis conditioned on physical constraints like lighting. For the physical conditioning, we use DECA [9] to produce the physical parameters including the FLAME [24] parameters (shape $\beta$ , expression $\psi$ , and + +pose $\theta$ ), albedo $\alpha$ , (orthographic) camera $\mathbf{c}$ , and (spherical harmonics) lighting $\mathbf{l}$ from the input portrait image. We then use the Lambertian reflectance to render these physical properties into three buffers: surface normals, albedo, and Lambertian rendering. Although these physical buffers provide pixel-aligned descriptions of the facial geometry, albedo, and lighting, they are rather coarse and nowhere close to photorealistic images (see the Lambertian rendering in Figures 1 and 2). Still, using these buffers, we can "rig" our generative model in a disentangled, physically meaningful way by changing the DECA parameters. For photorealistic image synthesis, we use a Denoising Diffusion Probabilistic Model (DDPM) as our generator because DDPMs can naturally take pixel-aligned conditions (more advantageous than latent code conditions as shown in Section 5.5) to drive the generation process. + +Besides the pixel-aligned physical buffers, we keep the random noise images in DDPMs to explain the stochasticity during generation. In addition to the pixel-aligned buffers and noise map, we need another condition to encode global appearance information (as opposed to local information such as local surface normals) that is not modeled by the physical buffers, such as hair, hat, glasses, and the image background. Therefore, our diffusion model takes both physical buffers and a learned global latent code as conditions for image synthesis. Formally, our model can be described as $\hat{\epsilon}_t = f_\theta ([x_t,z],t,\phi_\theta (x_0))$ where $x_{t}$ is the noisy image at timestep $t$ , $z$ represent the physical buffers, $x_0$ is the original image, $\hat{\epsilon}_t$ is the predicted noise, and $f_{\theta}$ and $\phi_{\theta}$ are the denoising model and the global latent encoder, respectively. + +It is theoretically possible that the global latent code also encodes local geometry, albedo, and/or illumination information, which could lead to the diffusion model ignoring the physical buffers entirely. Empirically, we find that the network learns to use the physical buffers for local information and does not rely on the global latent code, possibly because + +these buffers are pixel-aligned with the ground truth and thus more easily leveraged by the model. + +# 4.2. Learning Personalized Priors + +After learning the generic facial priors at the first stage, DiffusionRig is able to generate photorealistic images given coarse physical buffers. The next step is to learn personalized priors for a given person to avoid identity shift during appearance editing. Personal priors are crucial to preserving identity and high-frequency facial characteristics, as shown in Figure 2. We achieve this by finetuning our denoising model on a specific person's photo album of around 20 images. During the finetuning stage, the denoising model learns the person's identity information. We fix the global encoder from the previous stage since it has learned to encode global image information not modeled by the physical buffers (which we want to retain). We show that this approach is simple and yet effective compared with GANs that need careful tuning, as mentioned in MyStyle [32]. + +For this small personalized dataset, we also extract the DECA parameters first. However, since DECA is a single-image estimator, its output is sensitive to extreme poses or expressions. Under the assumption that the general shape of a person's face does not change drastically within a reasonable period of time, we compute the mean of the shape parameters in FLAME over all the images in the album and use that mean shape when conditioning DiffusionRig. + +# 4.3. Model Architecture + +DiffusionRig consists of two trainable parts: a denoising model $f_{\theta}$ and a global encoder $\phi_{\theta}$ . The architecture of our denoising model is based on ADM [7] with modifications to reduce computational cost and take an additional global latent code as input. For the global code, we use the same method that ADM uses for their time embedding: We scale and shift the features in each layer using the global latent code. The encoder is simply a ResNet-18 [14] and we use the output features as the global latent codes. + +Our loss function is a P2 weight loss [5] that computes distances between predicted and ground-truth noises: $\mathcal{L} = \lambda_t' ||\hat{\epsilon}_t - \epsilon_t||_2^2$ , where $\lambda_t'$ is a hyperparameter to control the loss weight at different timesteps. We empirically find that the P2 weight loss speeds up the training process and generates high-quality images compared with a constant loss weight. + +# 4.4. Implementation Details + +During the first stage, we train DiffusionRig on the FFHQ dataset [19], which contains 70,000 images. With Adam [23] as the optimizer with a learning rate of $10^{-4}$ , we train DiffusionRig for 50,000 iterations with a batch size of 256 (so the total number of samples seen by the model is 12,800,000). During the second stage, we use only 10-20 images of a single person. In the following, we show results for four + +celebrities (Obama, Biden, Swift, and Harris) and two noncelebrities. Please see the supplemental material and video for more results including more identities. We use 20 images for each person except for Harris, for whom we use only 10, and for the ablation study on the number of training images. We provide the personal photo album of two identities in the supplemental material. We finetune our model on each small dataset for 5,000 iterations with a batch size of 4 (so the total number of seen samples during finetuning is 20,000). We furthermore decrease the learning rate to $10^{-5}$ for the second stage. Training for the first stage takes around 15 hours using eight A100 GPUs, and the Stage 2 finetuning completes within 30 minutes on a single V100 GPU. + +# 5. Experiments + +We first show how to edit a person's appearance (e.g., facial expression, lighting, and head pose) by modifying the physical buffers that condition the model. We then demonstrate how to rig, with the global latent code, other aspects of a person's appearance not modeled by the physical buffers such as hairstyle and accessories. By swapping in the global latent code from another image, we can transfer portrait characteristics, such as hairstyle, accessories including glasses, and/or the image background, while preserving the physical properties (e.g., identity, pose, expression, and lighting) from the original image. Finally, we show the power of the learned personal priors by conditioning, for example, an Obama model on both the physical buffers and global latent code from a different person (to "Obama-fy" that person). + +# 5.1. Rigging Appearance With Physical Buffers + +In this section, we use our personalized model to rig the appearance with physical buffers. We show three different types of appearance rigging: relighting, expression change, and pose change. For relighting, we use different Spherical Harmonics (SH) parameters for producing the Lambertian rendering. To change the expression, we modify the expression and jaw rotation parameters of FLAME (the last three parameters of the pose vector). To vary the pose, we modify the head rotation parameters (the first three parameters of the pose vector). The 64-dimensional global latent code is produced by encoding the input image and remains unchanged when editing appearance. + +Our results are displayed in Figure 4, where we depict three identities: two celebrities and one daily user. All the images have a resolution of $256 \times 256$ . Additionally, $512 \times 512$ results can be found in the supplemental material. We compare our method against DECA [9], HeadNerf [17], GIF [10], and MyStyle [32], of which the first two are 3D face model estimation methods, and the latter two are GAN-based approaches. As Figure 4 shows, while GIF is capable of rigging the appearance by changing the expression and pose, it fails to preserve the individual's identity. DiffusionRig and MyStyle, on the other hand, are both personalized models + +![](images/4e7ec30e73c5ff3df5d09816f339e4930e642f9795868c719c275f65dbfc6306.jpg) +Original + +![](images/1b1e0503cc964b80ccc2a1088e2020d574cbfd0753578429c4eacdd3247ed637.jpg) +DECA + +![](images/17af4b50874db34082298c9776c3a71795b8d5424209df93807db7031dd2e9aa.jpg) +HeadNerf + +![](images/6ea7b1b52edbaed975efb8b497c7f6fdd39209a7322292fdf04ba668b3744c2f.jpg) +GIF + +![](images/3050c8eb38e496a5c9e8e84c73aa8c6814b3f4952ec90718264078264cb9ef71.jpg) +MyStyle + +![](images/a2f423aca9a7afcb4def816f663a78e43404de059f035ecdf03c8179ff347ee3.jpg) +Lighting + +![](images/742c6a0b5b691ebd70df4d5676dff3c7aa3a8ce4fb717d9c663651755641eee5.jpg) + +![](images/2256230d40cd445b9ba5314c0fa30c322817926e5ad10457468ac638a06baa54.jpg) + +![](images/989e82f2e976549d8ecd63c6c6ef9d4a867c10acb3922edd6108f71e85d976b8.jpg) + +![](images/e1e7932f6e2a23030d53c142f3b0ebeb836ac7f62bfa0f40171451640d4c0743.jpg) + +![](images/ba52946df6978c37b81a859c84e7c50f33239a504bd95ba0c399ba136af8e8d2.jpg) + +![](images/e34daebc4ce6ce449840a1500690561c935f2ff532d74fb79f07a605c1a4022d.jpg) +Expression + +![](images/165503793f2d2030eb2bd2b146deb1e3987eba6be48cf6db7736e2a60edc2b74.jpg) + +![](images/b29eba72d4e1be584b82d00a3121d9c57fd23258fbf928e49a73b8ce9b26eacb.jpg) + +![](images/1fdb10632dd5a7830c4b143d1c32c1a24e80c94e6268e8f8121d04961c8f6387.jpg) + +![](images/1a376eff9c65ece1c2afac47262f4d47d441716041bbbe4aa52e74a21f30db99.jpg) + +![](images/cd9c25a8966ccdc305ecbfde86d53e488912fd863e9dfbab8a6283f443a2d9df.jpg) + +![](images/907acf95fc17ddd19a9125aee7ebdd77cba46483e62c5e6f5f437a8e89d22aad.jpg) +Pose + +![](images/1ebafc13c28e1caf8008217f379777c9fff0e7f71a6d304d5c56e785cc290cf1.jpg) + +![](images/b7ba36f9536658bd1d0d0deaee3dd123f3ed62c331a00b0d19db6a36ef87c349.jpg) + +![](images/8b2e90071276a1fc3b738a8de6589644feb1c7230068606d5a83350903d0a159.jpg) + +![](images/d05e7f3f6d15433e05176a83787e109b98a1b4701845eea375aeaf179537ee89.jpg) + +![](images/c81269312fe9e8211aca6fce723a4f5eb1ae48afea67d4006a85bd554b862969.jpg) + +![](images/798a5c4e4f561b5c20e8b1d7560d40ddd0bb74248de179f3d25e0d09f79d2c48.jpg) +Lighting + +![](images/a8e021d365e9bb50ebe8c6d6841d46e44b5c1ba50a5f1a1e4e34b70b54c32a09.jpg) + +![](images/ee8d43a5adf6dddbe14e6dd41b0b7372ea2ef6404080ffb474ce1d28d93256c4.jpg) + +![](images/39d67c25670bdf5b651e93c0e1eae87b7cdaea87b19704cd2ff0802d646642df.jpg) + +![](images/f6e931ab104851e1316b8c504c3a23a72f7ab108f6629004685f389ca7a5a92b.jpg) + +![](images/654ddab347c09bd5ef9d2b6ed64e9822a2a58cfd15b3d3bb75c17ae3559295f2.jpg) + +![](images/87afff6dddafdffbdea29ec79867813450333b108d08b9760eae82594d43997f.jpg) +Expression +Figure 4. Appearance editing. DiffusionRig achieves convincing appearance edits while preserving the individual's identity using only 20 images per identity. GIF creates realistic-looking images but does not use personalized priors, leading to significant identity shifts. MyStyle is unable to make dramatic changes to the expression or pose without artifacts or minor identity shifts. In addition, MyStyle does not trivially support controllable relighting, so the corresponding fields have been left empty. + +![](images/21430bfacb16d053837b387b29d61ca1de03619dd31eaea88b052d36d16c5b37.jpg) + +![](images/b6f497254c0f3c36d3bdf608db395dace19b911ce33140c4a2e5d79a4c3fa693.jpg) + +![](images/48246d07a93a92eefc0d3aaff0c350e8f3336b7e91409e6151c8274e471890b4.jpg) + +![](images/a0e32049256ead47484e1087de27586423ef9b6261f5f64f71a43b079b82a4bd.jpg) + +![](images/47c33266abb37a1bf53dcf8c91d6f7a2b5b77e26ec643de740a93bbf6979f784.jpg) + +![](images/79ed49322f52711319277c54dd786c8ad4c42c6a1875e0c8de4fd33b03537cb3.jpg) +Pose + +![](images/51e9405cda918d910bec19dd1f1d50a1c4910a57ad5fe6d01351b4409ba1b9d9.jpg) + +![](images/60186752b3068ab8e17f023e4d3d0c619d05d6d6b865f97f6db49b305a3bef62.jpg) + +![](images/14aef4d7375a923ecf15e8cda19490c6022ee709e3054b5a56db7a976e12bf1b.jpg) + +![](images/712e465a845bc8d1226cd9125d00ff9fdacb3ac0178b46a16d994b4b787cef00.jpg) + +![](images/14c18f85c6d30ef7239b77110ff806a8b50656b5c761c2cda1b3cd27cbdf6d25.jpg) + +![](images/111fa496aaa1b3bc06f252de0957e9f3bf36248e3fccbcce61e78ca6c185b505.jpg) +Lighting + +![](images/978b0c35933017e7fdb1d8ab7831ebc0e5bd1eda095a0f270482f3d0711f8f73.jpg) + +![](images/958a99cff17ab420abfa384e22c3b13b383440622fb520eff11363963a273b7f.jpg) + +![](images/cf09f1bd9b22c4625c60040998ff0b536ad3b4abc9fc25a27417c698e9796a7e.jpg) + +![](images/d11d9be4995357f44020cb13ddecee19c56b45f0a501eb29abe22f60b95df6d8.jpg) + +![](images/68b7fcec55b2d1ac50ecb8d817f5cf142edf1fca831547bb58effa4ef35a69bd.jpg) + +![](images/321e090ef59b6b949cc3e56c1c75c504e26d7924ca56e97d61a4f7b13bf6e340.jpg) +Expression + +![](images/c42f74cb50d74fb11cec6672bf0a5b2b3a05d16383a41a6e7be8471837d3b47f.jpg) + +![](images/ea730fffe8e1f4013bc1a29e6a5b9a25aec7e44dc696e62683987b975c8308d9.jpg) + +![](images/3371c015180874e874e7721758014359a8b41d8b999c6e81c1a1c2d370626884.jpg) + +![](images/6033af2fac38e7d32e779d287a71a5bb972225e982926a28e3e06a0fb6eeee90.jpg) + +![](images/097cd3355a4619ad570a1f7109fc2416d3cdf8d4afd9caf55b6278793424abc8.jpg) + +![](images/cd2f39d2edd02bc156bb88862dffc9906731ff7e97cc386c1f2f290c60de6943.jpg) +Pose + +that are able to preserve the identity. However, since our method is directly conditioned on physical buffers, we can rig the appearance in a physically-based manner, whereas MyStyle needs to search for and step into a certain direction within the latent space to produce the target appearance, limiting its controllability, interpretability, and capacity for dramatic appearance changes. We also observe more artifacts for MyStyle when doing appearance editing, which is likely due to the use of too few images during finetuning the StyleGAN model. + +# 5.2. Rigging Appearance With Global Latent Code + +By design, DiffusionRig finds it easier to learn what physical buffers can describe from the pixel-aligned buffers than from the global latent code. The latent code thus encodes what physical buffers cannot describe including background, makeup, and hairstyle. In this part, we change the global latent code to show its effects on the generated images. + +In Figure 5, we show a $2 \times 3$ matrix of generated images. Along the horizontal axis, we swap in the global latent code from another image of the same person while keeping the physical buffers identical (i.e., same physical buffers but + +different global codes). Along the vertical axis, we replace the physical buffers while keeping the same global latent code (i.e., same global code but different physical buffers). We can see that geometry information, such as head pose and expression, is preserved for each row, which shows that only the physical buffers (not the latent code) contain such information. This means that in DiffusionRig these physical properties are well disentangled from each other and from other appearance properties that physical buffers cannot describe. On the other hand, the information hard to model explicitly, including image background, glasses, and hair style/color, is encoded in the global latent code. + +# 5.3. Identity Transfer With Learned Priors + +In previous sections, we saw what information the physical buffers and the global latent code encode. Now, we demonstrate what information is encoded in the personalized diffusion models' weights. Here, we keep both physical buffers and global latent code the same but exchange the personalized model itself with another person's personalized model (i.e., model swapping without code or buffer swapping). The results of this experiment for four identities are + +![](images/e86a61d4b8f92795d3841c4749e7703ed8bfa8cfc4a8916e6bc7ba618a796067.jpg) +Figure 5. Mix and match of physical buffers and global latent code. We mix the physical buffers from one image and the global latent code from another image to demonstrate how the two conditions encode disentangled information. + +shown in Figure 6. Each row uses the same physical buffers and latent code but another personalized model. Each column uses the same personalized model but different physical buffers and latent code. For example, the column "Obama-fy" shows four images that are generated by Obama's personal model but using the other celebrities' images as input. We see that across each row, while all inputs (physical buffers plus global latent code) are the same, the four different personalized models output different identities. These results further corroborate that our model is able to learn personalized priors from a small dataset. + +# 5.4. Baseline Comparisons & Evaluation Metrics + +We evaluate our DiffusionRig quantitatively in three aspects: rigging quality, identity preservation, and photorealism, since these three qualities are the most important for our personalized appearance editing. + +DECA Re-Inference Error We follow the same setup as in GIF [10] to compute the DECA re-inference error. To evaluate relighting quality, we directly compute the RMSE on the re-inferred spherical harmonics. We show our results in Table 1. For our model, we also evaluate two ablated versions: "vector cond." and "feature cond." Instead of using pixel-aligned physical buffers as the condition, we use DECA's output parameters and features computed from physical buffers as conditions in our two ablated models. More details can be found in Section 5.5. + +Face Re-Identification Error An important metric for evaluating this work is whether DiffusionRig can preserve the identity after appearance editing, since identity shift is a notorious problem in generative model-based editing. To this end, we run a widely popular face re-identification network [22] to automatically determine if the edited and + +![](images/93eb51dd6ad1d97f838e39abc83a77e40267efcd6892855dbed43fbbe019086c.jpg) +Figure 6. Swapping personalized models. We demonstrate the power of personalized priors by running one person's model on other identities. This creates the effect of "adding" one person's identity to another person. The images with green borders are "no-swap" results where the corresponding person's model is used. + +
Light ↓Shape ↓Exp. ↓Pose ↓
GIF [10]13.83.05.05.6
GIF, vector cond. [10]-3.423.129.7
DiffusionRig (Ours)11.24.32.84.2
DiffusionRig, vector cond.15.510.78.814.0
DiffusionRig, feature cond.27.05.34.121.6
+ +Table 1. RMSE of DECA re-inference. All numbers are multiples of $10^{-3}$ . We generate 1,000 images to compute the RMSE. For shape, expression, and pose, the RMSE is computed on rendered FLAME faces. For lighting, the RMSE is computed on re-inferred spherical harmonics directly. We only use our Stage 1 model since GIF is not a personalized model. Numbers for GIF and its vector-conditioned variant are cited from the original paper [10]. + +original images are of the same person. As Table 2 shows, both MyStyle [32] and DiffusionRig preserve the identity in all 400 expression-edited images of Obama and another 400 of Swift. That said, for dramatic changes such as head pose change, DiffusionRig preserves the identity better than MyStyle, as also demonstrated by Figure 4. One caveat of this error metric, though, is the obvious degenerate solution of not applying any edit at all, thereby achieving a perfect score. We refer the reader to Figure 4 and Table 1, which show that DiffusionRig avoids this degenerate solution. + +User Study To further evaluate both the photorealism and identity preservation of images from DiffusionRig against MyStyle, we conduct a user study involving Amazon Mechanical Turk. During the study, we show pairs of images, + +
Auto. Face Re-ID ↑User Study ↑
Obama and SwiftObamaSwift
Expr.PoseExpr.PoseExpr.Pose
MyStyle100%97.9%79.4%78.0%64.5%62.5%
Ours100%99.3%87.2%86.5%82.4%80.2%
+ +Table 2. DiffusionRig vs. MyStyle [32] in expression and pose editing, as measured by an automatic face re-ID error [22] (which has an obvious flaw; see text) as well as a user study on both realism and identity preservation. + +where the left image is an original image from the real image dataset, and the right image is a generated one. We occasionally include some real images on the right, too, for consistency check and quality control. We then ask the users whether the right image is a real image of the person on the left (so both photorealism and identity preservation are probed). We generate images that include either an expression or pose change for both DiffusionRig and MyStyle. We report our results in Table 2. + +# 5.5. Ablation Study + +We show several ablation studies to motivate the finetuning stage that injects the personalized prior and the choice of physical, pixel-aligned buffers to condition the model. + +No Personalized Priors We first show how DiffusionRig performs in the absence of personalized priors (i.e., trained on only the large dataset from Stage 1). Figure 2 shows that our model learns to use the physical buffers as conditions for pose, expression, and lighting, but it is incapable of preserving the person's identity during appearance editing. + +Number of Images Here we explore how the number of images used in Stage 2 affects DiffusionRig's ability of learning personalized priors. We train three models of a non-celebrity with 1, 5, 10, and 20 images and test them on relighting, expression change, and pose change. As Figure 7 demonstrates, using just 1, 5, or 10 images yields worse results than using 20 images (unsurprisingly). With more images, DiffusionRig learns better-personalized priors that capture high-frequency face characteristics, such as the wrinkles in Figure 7. + +![](images/2d2e5c5783488e6aa3bc1d1c3045e0e82c6f3f687f807108e6621a7e7f3bc393.jpg) +Figure 7. Quality w.r.t. number of Stage 2 images. DiffusionRig achieves high-quality relighting and pose change with 20 images for Stage 2. Using fewer may yield blurry results and make them hard to rig with new conditions. + +Different Forms of Conditions There are alternative ways to condition the image synthesis. We demonstrate that pixel + +aligned physical buffers are the most effective form in accurately rigging the appearance. We explore the following two conditioning alternatives. "Vector cond." is when we directly concatenate DECA parameters, a 236-dimensional vector, to the global latent code without using pixel-aligned buffers. "Feature cond." means that we concatenate the physical buffers to the input image and pass them into the encoder to compute a global latent code, which is then used as a non-spatial feature condition. As shown in Figure 8, using pixel-aligned physical guidance is essential for accurate conditional image editing. Both vector and feature conditioning suffer from the generated images not following the desired physical guidance. + +![](images/183d48f117d4e70bd1297aa616acc8e9ed4d10a932dee27672d38e1db75124fd.jpg) +Rigging Expression: input and src. + +![](images/8d0745cd9ad51a92459a55f76c6da2b8a1ef0d6d566e063b6f9990e0014dfb46.jpg) +Feature Cond. + +![](images/8e25e5137f5d0d12d5dfb54311e52ac0063b809492b16de77ed8b56869aeb6d6.jpg) +DiffusionRig + +![](images/d785af753933884ec1b9a287c9e8f9a5e0323d662dcaa769294674324acf6bd0.jpg) +Rigging Pose: input and src. +Figure 8. Ablation on the form of conditions. Neither feature conditioning nor vector conditioning is able to rig the input image to follow the physical properties of the target image. + +![](images/763937feabce623a112dbc3eb8c0f6d13e1bd4a4c086fe48be0db0005d18939e.jpg) +Vector Cond. + +![](images/1b179c838131a72f360761a63c29da6c7d2867cd03c122e021f741204d5d2c57.jpg) +DiffusionRig + +# 6. Limitations & Conclusion + +Although DiffusionRig achieves state-of-the-art facial appearance editing, it relies on a small portrait dataset to finetune, which limits its scalability for massive user adoption. Furthermore, when the edit involves dramatic head pose change, DiffusionRig may not stay faithful to the original background, since head pose change sometimes reveals what used to be occluded, therefore requiring background inpainting—a topic beyond the scope of this paper. Additionally, since DiffusionRig relies on DECA to get physical buffers, it will also be affected by DECA's limited estimation capability: for instance, extreme expressions usually cannot be well predicted. and the estimated lighting is sometimes coupled with the skin tone. + +In this paper, we have presented DiffusionRig, a riggable diffusion model for identity-preserving, personalized editing of facial appearance. We introduced a two-stage method to first learn generic face priors and later personalized priors. Using both explicit conditioning via physical buffers and implicit conditioning via global latent code, we can drive and control our model's facial image synthesis. + +Acknowledgment We thank Marc Levoy for the valuable feedback and everyone whose photos appear in this paper for their permission. + +# References + +[1] Sai Bi, Stephen Lombardi, Shunsuke Saito, Tomas Simon, Shih-En Wei, Kevyn Mcphail, Ravi Ramamoorthi, Yaser Sheikh, and Jason Saragih. 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"type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 495, + 192, + 507 + ], + "spans": [ + { + "bbox": [ + 143, + 495, + 192, + 507 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 45, + 514, + 290, + 695 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 514, + 290, + 695 + ], + "spans": [ + { + "bbox": [ + 45, + 514, + 290, + 695 + ], + "type": "text", + "content": "We address the problem of learning person-specific facial priors from a small number (e.g., 20) of portrait photos of the same person. This enables us to edit this specific person's facial appearance, such as expression and lighting, while preserving their identity and high-frequency facial details. Key to our approach, which we dub DiffusionRig, is a diffusion model conditioned on, or \"rigged by,\" crude 3D face models estimated from single in-the-wild images by an off-the-shelf estimator. On a high level, DiffusionRig learns to map simplistic renderings of 3D face models to realistic photos of a given person. Specifically, DiffusionRig is trained in two stages: It first learns generic facial priors from a large-scale face dataset and then person-specific priors from a small portrait photo collection of the person of interest. By learning the CGI-to-photo mapping with such personalized priors," + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 304, + 484, + 547, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 484, + 547, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 484, + 547, + 581 + ], + "type": "text", + "content": "DiffusionRig can \"rig\" the lighting, facial expression, head pose, etc. of a portrait photo, conditioned only on coarse 3D models while preserving this person's identity and other high-frequency characteristics. Qualitative and quantitative experiments show that DiffusionRig outperforms existing approaches in both identity preservation and photorealism. Please see the project website: https://diffusionrig.github.io for the supplemental material, video, code, and data." + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 306, + 589, + 387, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 589, + 387, + 601 + ], + "spans": [ + { + "bbox": [ + 306, + 589, + 387, + 601 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 304, + 605, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 548, + 715 + ], + "type": "text", + "content": "It is a longstanding problem in computer vision and graphics to photorealistically change the lighting, expression, head pose, etc. of a portrait photo while preserving the person's identity and high-frequency facial characteristics. The difficulty of this problem stems from its fundamentally underconstrained nature, and prior work typically addresses this with zero-shot learning, where neural networks were trained on a large-scale dataset of different identities and tested on a new identity. These methods ignore the fact that such" + } + ] + } + ], + "index": 34 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 61, + 703, + 205, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 703, + 205, + 712 + ], + "spans": [ + { + "bbox": [ + 61, + 703, + 205, + 712 + ], + "type": "text", + "content": "† Work done during an internship at Adobe." + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "12736" + } + ] + } + ], + "index": 35 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": "generic facial priors often fail to capture the test identity's high-frequency facial characteristics, and multiple photos of the same person are often readily available in the person's personal photo albums, e.g., on a mobile phone. In this work, we demonstrate that one can convincingly edit a person's facial appearance, such as lighting, expression, and head pose, while preserving their identity and other high-frequency facial details. Our key insight is that we can first learn generic facial priors from a large-scale face dataset [19] and then finetune these generic priors into personalized ones using around 20 photos capturing the test identity." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 206, + 289, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 206, + 289, + 456 + ], + "spans": [ + { + "bbox": [ + 46, + 206, + 289, + 456 + ], + "type": "text", + "content": "When it comes to facial appearance editing, the natural question is what representation one uses to change lighting, expression, head pose, hairstyle, accessories, etc. Off-the-shelf 3D face estimators such as DECA [9] can already extract, from an in-the-wild image, a parametric 3D face model that comprises parameters for lighting (spherical harmonics), expression, and head pose. However, directly rendering these physical properties back into images yields CGI-looking results, as shown in the output columns of Figure 1. The reasons are at least three-fold: (a) The 3D face shape estimated is coarse, with mismatched face contours and misses high-frequency geometric details, (b) the assumptions on reflectance (Lambertian) and lighting (spherical harmonics) are restrictive and insufficient for reproducing the reality, and (c) 3D morphable models (3DMMs) simply cannot model all appearance aspects including hairstyle and accessories. Nonetheless, such 3DMMs provide us with a useful representation that is amenable to \"appearance rigging\" since we can modify the facial expression and head pose by simply changing the 3DMM parameters as well as lighting by varying the spherical harmonics (SH) coefficients." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 460, + 289, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 460, + 289, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 460, + 289, + 628 + ], + "type": "text", + "content": "On the other hand, diffusion models [15] have recently gained popularity as an alternative to Generative Adversarial Networks (GANs) [11] for image generation. Diff-AE [33] further shows that when trained on the autoencoding task, diffusion models can provide a latent space for appearance editing. In addition, diffusion models are able to map pixel-aligned features (such as noise maps in the vanilla diffusion model) to photorealistic images. Although Diff-AE is capable of interpolating from, e.g., smile to no smile, after semantic labels are used to find the direction to move towards, it is unable to perform edits that require 3D understanding and that cannot be expressed by simple binary semantic labels. Such 3D edits, including relighting and head pose change, are the focus of our work." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 630, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 289, + 715 + ], + "type": "text", + "content": "To combine the best of both worlds, we propose Diffusion-Rig, a model that allows us to edit or \"rig\" the appearance (such as lighting and head pose) of a 3DMM and then produce a photorealistic edited image conditioned on our 3D edits. Specifically, DiffusionRig first extracts rough physical properties from single portrait photos using an off-the-shelf method [9], performs desired 3D edits in the 3DMM space," + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 547, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 347 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 347 + ], + "type": "text", + "content": "and finally uses a diffusion model [15] to map the edited \"physical buffers\" (surface normals, albedo, and Lambertian rendering) to photorealistic images. Since the edited images should preserve the identity and high-frequency facial characteristics, we first train DiffusionRig on the CelebA dataset [27] to learn generic facial priors so that DiffusionRig knows how to map surface normals and the Lambertian rendering to a photorealistic image. Note that because the physical buffers are coarse and do not contain sufficient identity information, this \"Stage 1 model\" provides no guarantee for identity preservation. At the second stage, we finetune DiffusionRig on a tiny dataset of roughly 20 images of one person of interest, producing a person-specific diffusion model mapping physical buffers to photos of just this person. As discussed, there are appearance aspects not modeled by the 3DMM, including but not limited to hairstyle and accessories. To provide our model with this additional information, we add an encoder branch that encodes the input image into a global latent code (\"global\" in contrast to physical buffers that are pixel-aligned with the output image and hence \"local\"). This code is chosen to be low-dimensional in the hope of capturing just the aspects not modeled by the 3DMM, such as hairstyle and eyeglasses." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 317, + 348, + 459, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 348, + 459, + 360 + ], + "spans": [ + { + "bbox": [ + 317, + 348, + 459, + 360 + ], + "type": "text", + "content": "In summary, our contributions are:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 317, + 361, + 545, + 456 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 317, + 361, + 545, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 361, + 545, + 396 + ], + "spans": [ + { + "bbox": [ + 317, + 361, + 545, + 396 + ], + "type": "text", + "content": "- A deep learning model for 3D facial appearance editing (that modifies lighting, facial expression, head pose, etc.) trained using just images with no 3D label," + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 396, + 545, + 420 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 396, + 545, + 420 + ], + "spans": [ + { + "bbox": [ + 317, + 396, + 545, + 420 + ], + "type": "text", + "content": "- A method to drive portrait photo generation using diffusion models with 3D morphable face models, and" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 318, + 420, + 545, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 420, + 545, + 456 + ], + "spans": [ + { + "bbox": [ + 318, + 420, + 545, + 456 + ], + "type": "text", + "content": "- A two-stage training strategy that learns personalized facial priors on top of generic face priors, enabling editing that preserves identity and high-frequency details." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 463, + 392, + 475 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 463, + 392, + 475 + ], + "spans": [ + { + "bbox": [ + 306, + 463, + 392, + 475 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 480, + 545, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 480, + 545, + 506 + ], + "spans": [ + { + "bbox": [ + 306, + 480, + 545, + 506 + ], + "type": "text", + "content": "Our work is related to generative models, 3D Morphable Face Models (3DMMs), and personalized priors." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 510, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 547, + 713 + ], + "type": "text", + "content": "Generative Modeling Since the proposal of early Generative Adversarial Networks (GANs) [11], researchers have made significant progress in generating photorealistic images of constrained classes, such as faces [18, 20, 21]. Recently, denoising diffusion models [16], which learn to denoise random noise images into photorealistic images, have shown impressive synthesis results and gained popularity as an alternative to GANs. Different diffusion models are invented for faster sampling [41] (used in this work), conditional generation [7, 31], and later pixel-aligned conditional generation [37]. Similarly, we use pixel-aligned conditions, specifically surface normal, albedo, and Lambertian rendering images, as the condition that our diffusion model should satisfy. Closely related to DiffusionRig are Diffusion Autoencoders (Diff-AE) that learn a latent space of facial attributes (e.g., +smiling vs. -smiling) via the autoencoding task [34]. Given binary labels of a certain attribute, the authors find the" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12737" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 75, + 99, + 144 + ], + "blocks": [ + { + "bbox": [ + 49, + 75, + 99, + 144 + ], + "lines": [ + { + "bbox": [ + 49, + 75, + 99, + 144 + ], + "spans": [ + { + "bbox": [ + 49, + 75, + 99, + 144 + ], + "type": "image", + "image_path": "effdec835022b1dfc0b6b0910025e37bd1304cbe603a4943554151aea9564395.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 61, + 144, + 88, + 152 + ], + "lines": [ + { + "bbox": [ + 61, + 144, + 88, + 152 + ], + "spans": [ + { + "bbox": [ + 61, + 144, + 88, + 152 + ], + "type": "text", + "content": "Surface" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 61, + 153, + 89, + 161 + ], + "lines": [ + { + "bbox": [ + 61, + 153, + 89, + 161 + ], + "spans": [ + { + "bbox": [ + 61, + 153, + 89, + 161 + ], + "type": "text", + "content": "Normals" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 168, + 547, + 213 + ], + "lines": [ + { + "bbox": [ + 46, + 168, + 547, + 213 + ], + "spans": [ + { + "bbox": [ + 46, + 168, + 547, + 213 + ], + "type": "text", + "content": "Figure 2. Reconstruction with vs. without personalized priors. Given the input image and its conditions (surface normals, albedo, and Lambertian rendering) automatically extracted using DECA, Stage 1 learns only generic face priors and fails to reconstruct the identity in both of the randomly sampled reconstructions. 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"bbox": [ + 46, + 223, + 287, + 270 + ], + "type": "text", + "content": "direction, along which the latent code should be pushed, to manipulate that attribute. 3D-aware generative models are a recent popular trend to combine 3D controllability with 2D image generation [3, 4, 10, 13, 43, 45, 46, 54]." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 46, + 275, + 289, + 359 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 275, + 289, + 359 + ], + "spans": [ + { + "bbox": [ + 46, + 275, + 289, + 359 + ], + "type": "text", + "content": "Facial Appearance Modeling 3D Morphable Face Models or 3DMMs provide a valuable parameter space to describe (and in turn solve for) 3D facial characteristics [2]. The FLAME face model learned from 4D scans is a widely-used 3DMM that supports shape, pose, and expression change [24]. We refer the reader to a recent survey paper on Morphable Face Models [8]." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 46, + 360, + 289, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 360, + 289, + 479 + ], + "spans": [ + { + "bbox": [ + 46, + 360, + 289, + 479 + ], + "type": "text", + "content": "RingNet regresses FLAME parameters from 2D images [38]. Also a learning-based method, DECA additionally predicts albedo and lighting in spherical harmonics (SH) from a single face image [9]. An alternative to using 3DMMs for \"face de-rendering\" is directly predicting surface normals, albedo, and lighting in the image space, as in SfSNet [39]. Although such approaches enjoy the benefit of being able to represent hair, accessories, etc., image-space representations do not provide a physically meaningful parameter space for rigging like 3DMMs do." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 46, + 480, + 288, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 480, + 288, + 589 + ], + "spans": [ + { + "bbox": [ + 46, + 480, + 288, + 589 + ], + "type": "text", + "content": "The geometry, albedo, and lighting from 3DMM are still extremely coarse and far from reality. The community has bridged the realism gap between 3DMM rendering and real photos through expensive hardware setups to capture fine-grained facial geometry [48, 50] and reflectance fields [6]. Neural network-based, implicit appearance models have also been proposed to address the infeasibility of explicitly describing the appearance with precise reflectance and lighting [1, 12, 28, 29, 30, 35, 36, 40, 42, 52, 53]." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 46, + 594, + 289, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 289, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 289, + 700 + ], + "type": "text", + "content": "Personalized Priors Learning personal priors has been more widely discussed in super-resolution, face restoration, and inpainting, by using exemplar imagery [47], personal supplemental attributes [51], an attention module with identity penalty [49], or facial component dictionaries [25]. Conditional portrait image editing also shares the objective of preserving the input identity [26, 44]. However, it remains a challenge how to compute an unbiased identity score, and these approaches do not explicitly learn personalized priors." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "type": "text", + "content": "Closer to DiffusionRig that learns a personal prior from a" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 304, + 223, + 547, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 223, + 547, + 331 + ], + "spans": [ + { + "bbox": [ + 304, + 223, + 547, + 331 + ], + "type": "text", + "content": "set of personal album of the person, MyStyle [32] is a method to finetune a pre-trained StyleGAN model to achieve a generative model for a specific identity, while preserving the expressiveness of the latent space. However, it does not support precise 3D rigging to control the generation and requires a much larger personal dataset to obtain a smooth personalized latent space. DiffusionRig, on the other hand, focuses on controllable image editing and achieves the smooth editing naturally with the continuous physical space as conditions." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 306, + 340, + 390, + 353 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 340, + 390, + 353 + ], + "spans": [ + { + "bbox": [ + 306, + 340, + 390, + 353 + ], + "type": "text", + "content": "3. Preliminaries" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 305, + 361, + 547, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 361, + 547, + 397 + ], + "spans": [ + { + "bbox": [ + 305, + 361, + 547, + 397 + ], + "type": "text", + "content": "We provide the background knowledge for the two building blocks—3D Morphable Face Models (3DMMs) and Denoising Diffusion Probabilistic Models (DDPMs)." + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 306, + 403, + 459, + 416 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 403, + 459, + 416 + ], + "spans": [ + { + "bbox": [ + 306, + 403, + 459, + 416 + ], + "type": "text", + "content": "3.1. 3D Morphable Face Models" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 304, + 422, + 547, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 422, + 547, + 651 + ], + "spans": [ + { + "bbox": [ + 304, + 422, + 547, + 651 + ], + "type": "text", + "content": "3D Morphable Face Models or 3DMMs are parametric models that use a compact latent space (handcrafted or learned from scans) to represent the head pose, face geometry, facial expression, etc. [2, 24]. In this paper, we employ FLAME [24], a popular 3DMM using standard vertex-based linear blend skinning with corrective blendshapes and representing a face mesh with pose, shape, and expression parameters. Although FLAME provides a compact and physically meaningful space for face geometry, it does not provide descriptions for appearance. To this end, DECA [9] uses FLAME and additionally models facial appearance with Lambertian reflectance and Spherical Harmonics (SH) lighting. Trained on a large dataset, DECA predicts albedo, SH lighting, and the FLAME parameters from a single portrait image. We utilize DECA to generate rough 3D representations that support easy \"rigging\" by editing the FLAME parameters, albedo, and/or SH lighting. As we show in Figure 2, the realism gap between DECA rendering and real photos is significant, calling for measurements post-editing." + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 306, + 658, + 520, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 658, + 520, + 671 + ], + "spans": [ + { + "bbox": [ + 306, + 658, + 520, + 671 + ], + "type": "text", + "content": "3.2. Denoising Diffusion Probabilistic Models" + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 306, + 677, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 677, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 677, + 547, + 714 + ], + "type": "text", + "content": "Denoising Diffusion Probabilistic Models (DDPMs) [7, 15, 31] are a class of generative models that take random noise images as input and denoise the images progressively" + } + ] + } + ], + "index": 35 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12738" + } + ] + } + ], + "index": 36 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 78, + 541, + 223 + ], + "blocks": [ + { + "bbox": [ + 52, + 78, + 541, + 223 + ], + "lines": [ + { + "bbox": [ + 52, + 78, + 541, + 223 + ], + "spans": [ + { + "bbox": [ + 52, + 78, + 541, + 223 + ], + "type": "image", + "image_path": "c763a44a9dcf0f326a1eb468bb5890d157562662c8bce4f60b095713e15b751d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 225, + 547, + 270 + ], + "lines": [ + { + "bbox": [ + 46, + 225, + 547, + 270 + ], + "spans": [ + { + "bbox": [ + 46, + 225, + 547, + 270 + ], + "type": "text", + "content": "Figure 3. DiffusionRig overview. The input to our model is a set of physical buffers reconstructed from the input, a random noise map, and a global latent code that encodes nuance features not modeled by the physical buffers. At Stage 1, we train our model on a large face dataset to learn generic face priors. At Stage 2, we keep the global latent code encoder frozen and fine-tune the diffusion model to learn personalized priors." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 281, + 289, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 281, + 289, + 437 + ], + "spans": [ + { + "bbox": [ + 46, + 281, + 289, + 437 + ], + "type": "text", + "content": "to produce photorealistic images. This generation process can be seen as the reverse of the diffusion process that gradually adds noise to images. The key component of DDPMs is a denoising network " + }, + { + "bbox": [ + 46, + 281, + 289, + 437 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 46, + 281, + 289, + 437 + ], + "type": "text", + "content": ". During training, it takes a noisy image " + }, + { + "bbox": [ + 46, + 281, + 289, + 437 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 46, + 281, + 289, + 437 + ], + "type": "text", + "content": " and a timestep " + }, + { + "bbox": [ + 46, + 281, + 289, + 437 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 281, + 289, + 437 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 46, + 281, + 289, + 437 + ], + "type": "inline_equation", + "content": "1 \\leq t \\leq T" + }, + { + "bbox": [ + 46, + 281, + 289, + 437 + ], + "type": "text", + "content": "), and predicts the noise at time " + }, + { + "bbox": [ + 46, + 281, + 289, + 437 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 281, + 289, + 437 + ], + "type": "text", + "content": ": " + }, + { + "bbox": [ + 46, + 281, + 289, + 437 + ], + "type": "inline_equation", + "content": "\\epsilon_{t}" + }, + { + "bbox": [ + 46, + 281, + 289, + 437 + ], + "type": "text", + "content": ". More formally, the predicted noise at time " + }, + { + "bbox": [ + 46, + 281, + 289, + 437 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 281, + 289, + 437 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 46, + 281, + 289, + 437 + ], + "type": "inline_equation", + "content": "\\hat{\\epsilon}_{t} = f_{\\theta}(x_{t}, t)" + }, + { + "bbox": [ + 46, + 281, + 289, + 437 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 281, + 289, + 437 + ], + "type": "inline_equation", + "content": "x_{t} = \\alpha_{t} x_{0} + \\sqrt{1 - \\alpha_{t}^{2}} \\epsilon_{t}" + }, + { + "bbox": [ + 46, + 281, + 289, + 437 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 281, + 289, + 437 + ], + "type": "inline_equation", + "content": "\\epsilon_{t}" + }, + { + "bbox": [ + 46, + 281, + 289, + 437 + ], + "type": "text", + "content": " is a random, normally distributed noise image, and " + }, + { + "bbox": [ + 46, + 281, + 289, + 437 + ], + "type": "inline_equation", + "content": "\\alpha_{t}" + }, + { + "bbox": [ + 46, + 281, + 289, + 437 + ], + "type": "text", + "content": " is a hyperparameter that gradually increases noise level of " + }, + { + "bbox": [ + 46, + 281, + 289, + 437 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 46, + 281, + 289, + 437 + ], + "type": "text", + "content": " with each step of the forward process. The loss is computed on the distance between " + }, + { + "bbox": [ + 46, + 281, + 289, + 437 + ], + "type": "inline_equation", + "content": "\\epsilon_{t}" + }, + { + "bbox": [ + 46, + 281, + 289, + 437 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 281, + 289, + 437 + ], + "type": "inline_equation", + "content": "\\hat{\\epsilon}_{t}" + }, + { + "bbox": [ + 46, + 281, + 289, + 437 + ], + "type": "text", + "content": ". Therefore, the trained model can generate images by taking as input a random noise image and gradually denoising it to a photorealistic one." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 441, + 104, + 453 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 441, + 104, + 453 + ], + "spans": [ + { + "bbox": [ + 47, + 441, + 104, + 453 + ], + "type": "text", + "content": "4. Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 461, + 287, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 461, + 287, + 521 + ], + "spans": [ + { + "bbox": [ + 46, + 461, + 287, + 521 + ], + "type": "text", + "content": "To enable personalized appearance editing, our model, which we dub DiffusionRig, needs to (a) generate images based on different appearance conditions, such as novel lighting, and (b) learn personal priors so that the person's identity is not altered during editing." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 521, + 288, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 288, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 288, + 628 + ], + "type": "text", + "content": "To this end, we design a two-stage training pipeline as shown in Figure 3. At the first stage, the model learns generic face priors by being trained to reconstruct portrait images given their underlying \"appearance conditions\" represented as physical buffers automatically extracted using an off-the-shelf estimator. At the second stage, we finetune our model using portrait photos of just one person so that the model learns personalized priors, which are necessary to prevent identity shift during appearance editing." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 635, + 209, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 635, + 209, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 635, + 209, + 647 + ], + "type": "text", + "content": "4.1. Learning Generic Face Priors" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "type": "text", + "content": "Our first stage is designed to learn facial priors that enable photorealistic image synthesis conditioned on physical constraints like lighting. For the physical conditioning, we use DECA [9] to produce the physical parameters including the FLAME [24] parameters (shape " + }, + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "type": "text", + "content": ", expression " + }, + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\psi" + }, + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "type": "text", + "content": ", and" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 281, + 547, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 281, + 547, + 472 + ], + "spans": [ + { + "bbox": [ + 304, + 281, + 547, + 472 + ], + "type": "text", + "content": "pose " + }, + { + "bbox": [ + 304, + 281, + 547, + 472 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 281, + 547, + 472 + ], + "type": "text", + "content": "), albedo " + }, + { + "bbox": [ + 304, + 281, + 547, + 472 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 281, + 547, + 472 + ], + "type": "text", + "content": ", (orthographic) camera " + }, + { + "bbox": [ + 304, + 281, + 547, + 472 + ], + "type": "inline_equation", + "content": "\\mathbf{c}" + }, + { + "bbox": [ + 304, + 281, + 547, + 472 + ], + "type": "text", + "content": ", and (spherical harmonics) lighting " + }, + { + "bbox": [ + 304, + 281, + 547, + 472 + ], + "type": "inline_equation", + "content": "\\mathbf{l}" + }, + { + "bbox": [ + 304, + 281, + 547, + 472 + ], + "type": "text", + "content": " from the input portrait image. We then use the Lambertian reflectance to render these physical properties into three buffers: surface normals, albedo, and Lambertian rendering. Although these physical buffers provide pixel-aligned descriptions of the facial geometry, albedo, and lighting, they are rather coarse and nowhere close to photorealistic images (see the Lambertian rendering in Figures 1 and 2). Still, using these buffers, we can \"rig\" our generative model in a disentangled, physically meaningful way by changing the DECA parameters. For photorealistic image synthesis, we use a Denoising Diffusion Probabilistic Model (DDPM) as our generator because DDPMs can naturally take pixel-aligned conditions (more advantageous than latent code conditions as shown in Section 5.5) to drive the generation process." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 473, + 548, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 473, + 548, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 473, + 548, + 641 + ], + "type": "text", + "content": "Besides the pixel-aligned physical buffers, we keep the random noise images in DDPMs to explain the stochasticity during generation. In addition to the pixel-aligned buffers and noise map, we need another condition to encode global appearance information (as opposed to local information such as local surface normals) that is not modeled by the physical buffers, such as hair, hat, glasses, and the image background. Therefore, our diffusion model takes both physical buffers and a learned global latent code as conditions for image synthesis. Formally, our model can be described as " + }, + { + "bbox": [ + 304, + 473, + 548, + 641 + ], + "type": "inline_equation", + "content": "\\hat{\\epsilon}_t = f_\\theta ([x_t,z],t,\\phi_\\theta (x_0))" + }, + { + "bbox": [ + 304, + 473, + 548, + 641 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 473, + 548, + 641 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 304, + 473, + 548, + 641 + ], + "type": "text", + "content": " is the noisy image at timestep " + }, + { + "bbox": [ + 304, + 473, + 548, + 641 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 473, + 548, + 641 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 473, + 548, + 641 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 304, + 473, + 548, + 641 + ], + "type": "text", + "content": " represent the physical buffers, " + }, + { + "bbox": [ + 304, + 473, + 548, + 641 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 304, + 473, + 548, + 641 + ], + "type": "text", + "content": " is the original image, " + }, + { + "bbox": [ + 304, + 473, + 548, + 641 + ], + "type": "inline_equation", + "content": "\\hat{\\epsilon}_t" + }, + { + "bbox": [ + 304, + 473, + 548, + 641 + ], + "type": "text", + "content": " is the predicted noise, and " + }, + { + "bbox": [ + 304, + 473, + 548, + 641 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 304, + 473, + 548, + 641 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 473, + 548, + 641 + ], + "type": "inline_equation", + "content": "\\phi_{\\theta}" + }, + { + "bbox": [ + 304, + 473, + 548, + 641 + ], + "type": "text", + "content": " are the denoising model and the global latent encoder, respectively." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "type": "text", + "content": "It is theoretically possible that the global latent code also encodes local geometry, albedo, and/or illumination information, which could lead to the diffusion model ignoring the physical buffers entirely. Empirically, we find that the network learns to use the physical buffers for local information and does not rely on the global latent code, possibly because" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12739" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": "these buffers are pixel-aligned with the ground truth and thus more easily leveraged by the model." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 106, + 208, + 118 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 106, + 208, + 118 + ], + "spans": [ + { + "bbox": [ + 47, + 106, + 208, + 118 + ], + "type": "text", + "content": "4.2. Learning Personalized Priors" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 122, + 289, + 301 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 122, + 289, + 301 + ], + "spans": [ + { + "bbox": [ + 46, + 122, + 289, + 301 + ], + "type": "text", + "content": "After learning the generic facial priors at the first stage, DiffusionRig is able to generate photorealistic images given coarse physical buffers. The next step is to learn personalized priors for a given person to avoid identity shift during appearance editing. Personal priors are crucial to preserving identity and high-frequency facial characteristics, as shown in Figure 2. We achieve this by finetuning our denoising model on a specific person's photo album of around 20 images. During the finetuning stage, the denoising model learns the person's identity information. We fix the global encoder from the previous stage since it has learned to encode global image information not modeled by the physical buffers (which we want to retain). We show that this approach is simple and yet effective compared with GANs that need careful tuning, as mentioned in MyStyle [32]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 302, + 289, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 302, + 289, + 399 + ], + "spans": [ + { + "bbox": [ + 46, + 302, + 289, + 399 + ], + "type": "text", + "content": "For this small personalized dataset, we also extract the DECA parameters first. However, since DECA is a single-image estimator, its output is sensitive to extreme poses or expressions. Under the assumption that the general shape of a person's face does not change drastically within a reasonable period of time, we compute the mean of the shape parameters in FLAME over all the images in the album and use that mean shape when conditioning DiffusionRig." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 407, + 162, + 419 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 407, + 162, + 419 + ], + "spans": [ + { + "bbox": [ + 47, + 407, + 162, + 419 + ], + "type": "text", + "content": "4.3. Model Architecture" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 423, + 287, + 531 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 423, + 287, + 531 + ], + "spans": [ + { + "bbox": [ + 46, + 423, + 287, + 531 + ], + "type": "text", + "content": "DiffusionRig consists of two trainable parts: a denoising model " + }, + { + "bbox": [ + 46, + 423, + 287, + 531 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 46, + 423, + 287, + 531 + ], + "type": "text", + "content": " and a global encoder " + }, + { + "bbox": [ + 46, + 423, + 287, + 531 + ], + "type": "inline_equation", + "content": "\\phi_{\\theta}" + }, + { + "bbox": [ + 46, + 423, + 287, + 531 + ], + "type": "text", + "content": ". The architecture of our denoising model is based on ADM [7] with modifications to reduce computational cost and take an additional global latent code as input. For the global code, we use the same method that ADM uses for their time embedding: We scale and shift the features in each layer using the global latent code. The encoder is simply a ResNet-18 [14] and we use the output features as the global latent codes." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 532, + 287, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 532, + 287, + 605 + ], + "spans": [ + { + "bbox": [ + 47, + 532, + 287, + 605 + ], + "type": "text", + "content": "Our loss function is a P2 weight loss [5] that computes distances between predicted and ground-truth noises: " + }, + { + "bbox": [ + 47, + 532, + 287, + 605 + ], + "type": "inline_equation", + "content": "\\mathcal{L} = \\lambda_t' ||\\hat{\\epsilon}_t - \\epsilon_t||_2^2" + }, + { + "bbox": [ + 47, + 532, + 287, + 605 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 532, + 287, + 605 + ], + "type": "inline_equation", + "content": "\\lambda_t'" + }, + { + "bbox": [ + 47, + 532, + 287, + 605 + ], + "type": "text", + "content": " is a hyperparameter to control the loss weight at different timesteps. We empirically find that the P2 weight loss speeds up the training process and generates high-quality images compared with a constant loss weight." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 613, + 180, + 625 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 613, + 180, + 625 + ], + "spans": [ + { + "bbox": [ + 47, + 613, + 180, + 625 + ], + "type": "text", + "content": "4.4. Implementation Details" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 629, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 289, + 715 + ], + "type": "text", + "content": "During the first stage, we train DiffusionRig on the FFHQ dataset [19], which contains 70,000 images. With Adam [23] as the optimizer with a learning rate of " + }, + { + "bbox": [ + 46, + 629, + 289, + 715 + ], + "type": "inline_equation", + "content": "10^{-4}" + }, + { + "bbox": [ + 46, + 629, + 289, + 715 + ], + "type": "text", + "content": ", we train DiffusionRig for 50,000 iterations with a batch size of 256 (so the total number of samples seen by the model is 12,800,000). During the second stage, we use only 10-20 images of a single person. In the following, we show results for four" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 547, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 228 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 228 + ], + "type": "text", + "content": "celebrities (Obama, Biden, Swift, and Harris) and two noncelebrities. Please see the supplemental material and video for more results including more identities. We use 20 images for each person except for Harris, for whom we use only 10, and for the ablation study on the number of training images. We provide the personal photo album of two identities in the supplemental material. We finetune our model on each small dataset for 5,000 iterations with a batch size of 4 (so the total number of seen samples during finetuning is 20,000). We furthermore decrease the learning rate to " + }, + { + "bbox": [ + 304, + 72, + 547, + 228 + ], + "type": "inline_equation", + "content": "10^{-5}" + }, + { + "bbox": [ + 304, + 72, + 547, + 228 + ], + "type": "text", + "content": " for the second stage. Training for the first stage takes around 15 hours using eight A100 GPUs, and the Stage 2 finetuning completes within 30 minutes on a single V100 GPU." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 232, + 388, + 246 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 232, + 388, + 246 + ], + "spans": [ + { + "bbox": [ + 306, + 232, + 388, + 246 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 251, + 547, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 251, + 547, + 419 + ], + "spans": [ + { + "bbox": [ + 304, + 251, + 547, + 419 + ], + "type": "text", + "content": "We first show how to edit a person's appearance (e.g., facial expression, lighting, and head pose) by modifying the physical buffers that condition the model. We then demonstrate how to rig, with the global latent code, other aspects of a person's appearance not modeled by the physical buffers such as hairstyle and accessories. By swapping in the global latent code from another image, we can transfer portrait characteristics, such as hairstyle, accessories including glasses, and/or the image background, while preserving the physical properties (e.g., identity, pose, expression, and lighting) from the original image. Finally, we show the power of the learned personal priors by conditioning, for example, an Obama model on both the physical buffers and global latent code from a different person (to \"Obama-fy\" that person)." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 422, + 529, + 435 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 422, + 529, + 435 + ], + "spans": [ + { + "bbox": [ + 305, + 422, + 529, + 435 + ], + "type": "text", + "content": "5.1. Rigging Appearance With Physical Buffers" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 438, + 547, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 438, + 547, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 438, + 547, + 581 + ], + "type": "text", + "content": "In this section, we use our personalized model to rig the appearance with physical buffers. We show three different types of appearance rigging: relighting, expression change, and pose change. For relighting, we use different Spherical Harmonics (SH) parameters for producing the Lambertian rendering. To change the expression, we modify the expression and jaw rotation parameters of FLAME (the last three parameters of the pose vector). To vary the pose, we modify the head rotation parameters (the first three parameters of the pose vector). The 64-dimensional global latent code is produced by encoding the input image and remains unchanged when editing appearance." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "type": "text", + "content": "Our results are displayed in Figure 4, where we depict three identities: two celebrities and one daily user. All the images have a resolution of " + }, + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "type": "text", + "content": ". 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Appearance editing. DiffusionRig achieves convincing appearance edits while preserving the individual's identity using only 20 images per identity. GIF creates realistic-looking images but does not use personalized priors, leading to significant identity shifts. MyStyle is unable to make dramatic changes to the expression or pose without artifacts or minor identity shifts. 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+ } + ], + "index": 66, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 485, + 386, + 521, + 397 + ], + "lines": [ + { + "bbox": [ + 485, + 386, + 521, + 397 + ], + "spans": [ + { + "bbox": [ + 485, + 386, + 521, + 397 + ], + "type": "text", + "content": "Pose" + } + ] + } + ], + "index": 67, + "angle": 0, + "type": "image_caption" + } + ], + "index": 66 + }, + { + "bbox": [ + 46, + 452, + 287, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 452, + 287, + 571 + ], + "spans": [ + { + "bbox": [ + 46, + 452, + 287, + 571 + ], + "type": "text", + "content": "that are able to preserve the identity. However, since our method is directly conditioned on physical buffers, we can rig the appearance in a physically-based manner, whereas MyStyle needs to search for and step into a certain direction within the latent space to produce the target appearance, limiting its controllability, interpretability, and capacity for dramatic appearance changes. We also observe more artifacts for MyStyle when doing appearance editing, which is likely due to the use of too few images during finetuning the StyleGAN model." + } + ] + } + ], + "index": 69 + }, + { + "bbox": [ + 47, + 578, + 286, + 590 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 578, + 286, + 590 + ], + "spans": [ + { + "bbox": [ + 47, + 578, + 286, + 590 + ], + "type": "text", + "content": "5.2. Rigging Appearance With Global Latent Code" + } + ] + } + ], + "index": 70 + }, + { + "bbox": [ + 46, + 594, + 287, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 665 + ], + "type": "text", + "content": "By design, DiffusionRig finds it easier to learn what physical buffers can describe from the pixel-aligned buffers than from the global latent code. The latent code thus encodes what physical buffers cannot describe including background, makeup, and hairstyle. In this part, we change the global latent code to show its effects on the generated images." + } + ] + } + ], + "index": 71 + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "content": "In Figure 5, we show a " + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "inline_equation", + "content": "2 \\times 3" + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "content": " matrix of generated images. Along the horizontal axis, we swap in the global latent code from another image of the same person while keeping the physical buffers identical (i.e., same physical buffers but" + } + ] + } + ], + "index": 72 + }, + { + "bbox": [ + 304, + 452, + 545, + 595 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 452, + 545, + 595 + ], + "spans": [ + { + "bbox": [ + 304, + 452, + 545, + 595 + ], + "type": "text", + "content": "different global codes). Along the vertical axis, we replace the physical buffers while keeping the same global latent code (i.e., same global code but different physical buffers). We can see that geometry information, such as head pose and expression, is preserved for each row, which shows that only the physical buffers (not the latent code) contain such information. This means that in DiffusionRig these physical properties are well disentangled from each other and from other appearance properties that physical buffers cannot describe. On the other hand, the information hard to model explicitly, including image background, glasses, and hair style/color, is encoded in the global latent code." + } + ] + } + ], + "index": 73 + }, + { + "bbox": [ + 306, + 601, + 509, + 613 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 601, + 509, + 613 + ], + "spans": [ + { + "bbox": [ + 306, + 601, + 509, + 613 + ], + "type": "text", + "content": "5.3. Identity Transfer With Learned Priors" + } + ] + } + ], + "index": 74 + }, + { + "bbox": [ + 304, + 618, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 618, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 618, + 546, + 713 + ], + "type": "text", + "content": "In previous sections, we saw what information the physical buffers and the global latent code encode. Now, we demonstrate what information is encoded in the personalized diffusion models' weights. Here, we keep both physical buffers and global latent code the same but exchange the personalized model itself with another person's personalized model (i.e., model swapping without code or buffer swapping). The results of this experiment for four identities are" + } + ] + } + ], + "index": 75 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12741" + } + ] + } + ], + "index": 76 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 71, + 289, + 253 + ], + "blocks": [ + { + "bbox": [ + 51, + 71, + 289, + 253 + ], + "lines": [ + { + "bbox": [ + 51, + 71, + 289, + 253 + ], + "spans": [ + { + "bbox": [ + 51, + 71, + 289, + 253 + ], + "type": "image", + "image_path": "e86a61d4b8f92795d3841c4749e7703ed8bfa8cfc4a8916e6bc7ba618a796067.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 256, + 288, + 300 + ], + "lines": [ + { + "bbox": [ + 47, + 256, + 288, + 300 + ], + "spans": [ + { + "bbox": [ + 47, + 256, + 288, + 300 + ], + "type": "text", + "content": "Figure 5. Mix and match of physical buffers and global latent code. We mix the physical buffers from one image and the global latent code from another image to demonstrate how the two conditions encode disentangled information." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 312, + 289, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 312, + 289, + 443 + ], + "spans": [ + { + "bbox": [ + 46, + 312, + 289, + 443 + ], + "type": "text", + "content": "shown in Figure 6. Each row uses the same physical buffers and latent code but another personalized model. Each column uses the same personalized model but different physical buffers and latent code. For example, the column \"Obama-fy\" shows four images that are generated by Obama's personal model but using the other celebrities' images as input. We see that across each row, while all inputs (physical buffers plus global latent code) are the same, the four different personalized models output different identities. These results further corroborate that our model is able to learn personalized priors from a small dataset." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 451, + 278, + 464 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 451, + 278, + 464 + ], + "spans": [ + { + "bbox": [ + 47, + 451, + 278, + 464 + ], + "type": "text", + "content": "5.4. Baseline Comparisons & Evaluation Metrics" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 466, + 288, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 466, + 288, + 514 + ], + "spans": [ + { + "bbox": [ + 46, + 466, + 288, + 514 + ], + "type": "text", + "content": "We evaluate our DiffusionRig quantitatively in three aspects: rigging quality, identity preservation, and photorealism, since these three qualities are the most important for our personalized appearance editing." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 517, + 288, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 517, + 288, + 635 + ], + "spans": [ + { + "bbox": [ + 46, + 517, + 288, + 635 + ], + "type": "text", + "content": "DECA Re-Inference Error We follow the same setup as in GIF [10] to compute the DECA re-inference error. To evaluate relighting quality, we directly compute the RMSE on the re-inferred spherical harmonics. We show our results in Table 1. For our model, we also evaluate two ablated versions: \"vector cond.\" and \"feature cond.\" Instead of using pixel-aligned physical buffers as the condition, we use DECA's output parameters and features computed from physical buffers as conditions in our two ablated models. More details can be found in Section 5.5." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 641, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 288, + 713 + ], + "type": "text", + "content": "Face Re-Identification Error An important metric for evaluating this work is whether DiffusionRig can preserve the identity after appearance editing, since identity shift is a notorious problem in generative model-based editing. To this end, we run a widely popular face re-identification network [22] to automatically determine if the edited and" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 309, + 70, + 545, + 320 + ], + "blocks": [ + { + "bbox": [ + 309, + 70, + 545, + 320 + ], + "lines": [ + { + "bbox": [ + 309, + 70, + 545, + 320 + ], + "spans": [ + { + "bbox": [ + 309, + 70, + 545, + 320 + ], + "type": "image", + "image_path": "93eb51dd6ad1d97f838e39abc83a77e40267efcd6892855dbed43fbbe019086c.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 323, + 547, + 380 + ], + "lines": [ + { + "bbox": [ + 305, + 323, + 547, + 380 + ], + "spans": [ + { + "bbox": [ + 305, + 323, + 547, + 380 + ], + "type": "text", + "content": "Figure 6. Swapping personalized models. We demonstrate the power of personalized priors by running one person's model on other identities. This creates the effect of \"adding\" one person's identity to another person. The images with green borders are \"no-swap\" results where the corresponding person's model is used." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 310, + 389, + 542, + 450 + ], + "blocks": [ + { + "bbox": [ + 310, + 389, + 542, + 450 + ], + "lines": [ + { + "bbox": [ + 310, + 389, + 542, + 450 + ], + "spans": [ + { + "bbox": [ + 310, + 389, + 542, + 450 + ], + "type": "table", + "html": "
Light ↓Shape ↓Exp. ↓Pose ↓
GIF [10]13.83.05.05.6
GIF, vector cond. [10]-3.423.129.7
DiffusionRig (Ours)11.24.32.84.2
DiffusionRig, vector cond.15.510.78.814.0
DiffusionRig, feature cond.27.05.34.121.6
", + "image_path": "565afc1fb1f5d4f2073d6b429a9907e6db0e32af8a6bd61807e774665f3fa61b.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 453, + 547, + 532 + ], + "lines": [ + { + "bbox": [ + 305, + 453, + 547, + 532 + ], + "spans": [ + { + "bbox": [ + 305, + 453, + 547, + 532 + ], + "type": "text", + "content": "Table 1. RMSE of DECA re-inference. All numbers are multiples of " + }, + { + "bbox": [ + 305, + 453, + 547, + 532 + ], + "type": "inline_equation", + "content": "10^{-3}" + }, + { + "bbox": [ + 305, + 453, + 547, + 532 + ], + "type": "text", + "content": ". We generate 1,000 images to compute the RMSE. For shape, expression, and pose, the RMSE is computed on rendered FLAME faces. For lighting, the RMSE is computed on re-inferred spherical harmonics directly. We only use our Stage 1 model since GIF is not a personalized model. Numbers for GIF and its vector-conditioned variant are cited from the original paper [10]." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 542, + 547, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 542, + 547, + 662 + ], + "spans": [ + { + "bbox": [ + 304, + 542, + 547, + 662 + ], + "type": "text", + "content": "original images are of the same person. As Table 2 shows, both MyStyle [32] and DiffusionRig preserve the identity in all 400 expression-edited images of Obama and another 400 of Swift. That said, for dramatic changes such as head pose change, DiffusionRig preserves the identity better than MyStyle, as also demonstrated by Figure 4. One caveat of this error metric, though, is the obvious degenerate solution of not applying any edit at all, thereby achieving a perfect score. We refer the reader to Figure 4 and Table 1, which show that DiffusionRig avoids this degenerate solution." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 665, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 665, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 665, + 548, + 715 + ], + "type": "text", + "content": "User Study To further evaluate both the photorealism and identity preservation of images from DiffusionRig against MyStyle, we conduct a user study involving Amazon Mechanical Turk. During the study, we show pairs of images," + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "12742" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 55, + 70, + 279, + 118 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 279, + 118 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 279, + 118 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 279, + 118 + ], + "type": "table", + "html": "
Auto. Face Re-ID ↑User Study ↑
Obama and SwiftObamaSwift
Expr.PoseExpr.PoseExpr.Pose
MyStyle100%97.9%79.4%78.0%64.5%62.5%
Ours100%99.3%87.2%86.5%82.4%80.2%
", + "image_path": "adf867f78ac03cba2b2db2990c4f3dcb9ce87a2878c011dba70ffe884174089e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 121, + 287, + 166 + ], + "lines": [ + { + "bbox": [ + 46, + 121, + 287, + 166 + ], + "spans": [ + { + "bbox": [ + 46, + 121, + 287, + 166 + ], + "type": "text", + "content": "Table 2. DiffusionRig vs. MyStyle [32] in expression and pose editing, as measured by an automatic face re-ID error [22] (which has an obvious flaw; see text) as well as a user study on both realism and identity preservation." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 171, + 288, + 279 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 171, + 288, + 279 + ], + "spans": [ + { + "bbox": [ + 46, + 171, + 288, + 279 + ], + "type": "text", + "content": "where the left image is an original image from the real image dataset, and the right image is a generated one. We occasionally include some real images on the right, too, for consistency check and quality control. We then ask the users whether the right image is a real image of the person on the left (so both photorealism and identity preservation are probed). We generate images that include either an expression or pose change for both DiffusionRig and MyStyle. We report our results in Table 2." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 286, + 141, + 300 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 286, + 141, + 300 + ], + "spans": [ + { + "bbox": [ + 47, + 286, + 141, + 300 + ], + "type": "text", + "content": "5.5. Ablation Study" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 302, + 288, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 302, + 288, + 338 + ], + "spans": [ + { + "bbox": [ + 46, + 302, + 288, + 338 + ], + "type": "text", + "content": "We show several ablation studies to motivate the finetuning stage that injects the personalized prior and the choice of physical, pixel-aligned buffers to condition the model." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 342, + 287, + 416 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 342, + 287, + 416 + ], + "spans": [ + { + "bbox": [ + 46, + 342, + 287, + 416 + ], + "type": "text", + "content": "No Personalized Priors We first show how DiffusionRig performs in the absence of personalized priors (i.e., trained on only the large dataset from Stage 1). Figure 2 shows that our model learns to use the physical buffers as conditions for pose, expression, and lighting, but it is incapable of preserving the person's identity during appearance editing." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 419, + 288, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 419, + 288, + 539 + ], + "spans": [ + { + "bbox": [ + 46, + 419, + 288, + 539 + ], + "type": "text", + "content": "Number of Images Here we explore how the number of images used in Stage 2 affects DiffusionRig's ability of learning personalized priors. We train three models of a non-celebrity with 1, 5, 10, and 20 images and test them on relighting, expression change, and pose change. As Figure 7 demonstrates, using just 1, 5, or 10 images yields worse results than using 20 images (unsurprisingly). With more images, DiffusionRig learns better-personalized priors that capture high-frequency face characteristics, such as the wrinkles in Figure 7." + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 61, + 545, + 272, + 626 + ], + "blocks": [ + { + "bbox": [ + 61, + 545, + 272, + 626 + ], + "lines": [ + { + "bbox": [ + 61, + 545, + 272, + 626 + ], + "spans": [ + { + "bbox": [ + 61, + 545, + 272, + 626 + ], + "type": "image", + "image_path": "2d2e5c5783488e6aa3bc1d1c3045e0e82c6f3f687f807108e6621a7e7f3bc393.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 632, + 287, + 676 + ], + "lines": [ + { + "bbox": [ + 46, + 632, + 287, + 676 + ], + "spans": [ + { + "bbox": [ + 46, + 632, + 287, + 676 + ], + "type": "text", + "content": "Figure 7. Quality w.r.t. number of Stage 2 images. DiffusionRig achieves high-quality relighting and pose change with 20 images for Stage 2. Using fewer may yield blurry results and make them hard to rig with new conditions." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "text", + "content": "Different Forms of Conditions There are alternative ways to condition the image synthesis. We demonstrate that pixel" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 547, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 228 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 228 + ], + "type": "text", + "content": "aligned physical buffers are the most effective form in accurately rigging the appearance. We explore the following two conditioning alternatives. \"Vector cond.\" is when we directly concatenate DECA parameters, a 236-dimensional vector, to the global latent code without using pixel-aligned buffers. \"Feature cond.\" means that we concatenate the physical buffers to the input image and pass them into the encoder to compute a global latent code, which is then used as a non-spatial feature condition. As shown in Figure 8, using pixel-aligned physical guidance is essential for accurate conditional image editing. Both vector and feature conditioning suffer from the generated images not following the desired physical guidance." + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 320, + 237, + 425, + 289 + ], + "blocks": [ + { + "bbox": [ + 320, + 237, + 425, + 289 + ], + "lines": [ + { + "bbox": [ + 320, + 237, + 425, + 289 + ], + "spans": [ + { + "bbox": [ + 320, + 237, + 425, + 289 + ], + "type": "image", + "image_path": "183d48f117d4e70bd1297aa616acc8e9ed4d10a932dee27672d38e1db75124fd.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 323, + 289, + 421, + 297 + ], + "lines": [ + { + "bbox": [ + 323, + 289, + 421, + 297 + ], + "spans": [ + { + "bbox": [ + 323, + 289, + 421, + 297 + ], + "type": "text", + "content": "Rigging Expression: input and src." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 426, + 237, + 477, + 288 + ], + "blocks": [ + { + "bbox": [ + 426, + 237, + 477, + 288 + ], + "lines": [ + { + "bbox": [ + 426, + 237, + 477, + 288 + ], + "spans": [ + { + "bbox": [ + 426, + 237, + 477, + 288 + ], + "type": "image", + "image_path": "8d0745cd9ad51a92459a55f76c6da2b8a1ef0d6d566e063b6f9990e0014dfb46.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 431, + 289, + 471, + 296 + ], + "lines": [ + { + "bbox": [ + 431, + 289, + 471, + 296 + ], + "spans": [ + { + "bbox": [ + 431, + 289, + 471, + 296 + ], + "type": "text", + "content": "Feature Cond." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 478, + 237, + 529, + 288 + ], + "blocks": [ + { + "bbox": [ + 478, + 237, + 529, + 288 + ], + "lines": [ + { + "bbox": [ + 478, + 237, + 529, + 288 + ], + "spans": [ + { + "bbox": [ + 478, + 237, + 529, + 288 + ], + "type": "image", + "image_path": "8e25e5137f5d0d12d5dfb54311e52ac0063b809492b16de77ed8b56869aeb6d6.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 484, + 289, + 523, + 297 + ], + "lines": [ + { + "bbox": [ + 484, + 289, + 523, + 297 + ], + "spans": [ + { + "bbox": [ + 484, + 289, + 523, + 297 + ], + "type": "text", + "content": "DiffusionRig" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 320, + 299, + 423, + 350 + ], + "blocks": [ + { + "bbox": [ + 320, + 299, + 423, + 350 + ], + "lines": [ + { + "bbox": [ + 320, + 299, + 423, + 350 + ], + "spans": [ + { + "bbox": [ + 320, + 299, + 423, + 350 + ], + "type": "image", + "image_path": "d785af753933884ec1b9a287c9e8f9a5e0323d662dcaa769294674324acf6bd0.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 328, + 350, + 408, + 358 + ], + "lines": [ + { + "bbox": [ + 328, + 350, + 408, + 358 + ], + "spans": [ + { + "bbox": [ + 328, + 350, + 408, + 358 + ], + "type": "text", + "content": "Rigging Pose: input and src." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 304, + 363, + 545, + 397 + ], + "lines": [ + { + "bbox": [ + 304, + 363, + 545, + 397 + ], + "spans": [ + { + "bbox": [ + 304, + 363, + 545, + 397 + ], + "type": "text", + "content": "Figure 8. Ablation on the form of conditions. Neither feature conditioning nor vector conditioning is able to rig the input image to follow the physical properties of the target image." + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 425, + 298, + 477, + 350 + ], + "blocks": [ + { + "bbox": [ + 425, + 298, + 477, + 350 + ], + "lines": [ + { + "bbox": [ + 425, + 298, + 477, + 350 + ], + "spans": [ + { + "bbox": [ + 425, + 298, + 477, + 350 + ], + "type": "image", + "image_path": "763937feabce623a112dbc3eb8c0f6d13e1bd4a4c086fe48be0db0005d18939e.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 432, + 350, + 471, + 357 + ], + "lines": [ + { + "bbox": [ + 432, + 350, + 471, + 357 + ], + "spans": [ + { + "bbox": [ + 432, + 350, + 471, + 357 + ], + "type": "text", + "content": "Vector Cond." + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + } + ], + "index": 19 + }, + { + "type": "image", + "bbox": [ + 478, + 298, + 529, + 350 + ], + "blocks": [ + { + "bbox": [ + 478, + 298, + 529, + 350 + ], + "lines": [ + { + "bbox": [ + 478, + 298, + 529, + 350 + ], + "spans": [ + { + "bbox": [ + 478, + 298, + 529, + 350 + ], + "type": "image", + "image_path": "1b179c838131a72f360761a63c29da6c7d2867cd03c122e021f741204d5d2c57.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 486, + 350, + 524, + 358 + ], + "lines": [ + { + "bbox": [ + 486, + 350, + 524, + 358 + ], + "spans": [ + { + "bbox": [ + 486, + 350, + 524, + 358 + ], + "type": "text", + "content": "DiffusionRig" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 407, + 454, + 420 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 407, + 454, + 420 + ], + "spans": [ + { + "bbox": [ + 306, + 407, + 454, + 420 + ], + "type": "text", + "content": "6. Limitations & Conclusion" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 426, + 547, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 547, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 547, + 581 + ], + "type": "text", + "content": "Although DiffusionRig achieves state-of-the-art facial appearance editing, it relies on a small portrait dataset to finetune, which limits its scalability for massive user adoption. Furthermore, when the edit involves dramatic head pose change, DiffusionRig may not stay faithful to the original background, since head pose change sometimes reveals what used to be occluded, therefore requiring background inpainting—a topic beyond the scope of this paper. Additionally, since DiffusionRig relies on DECA to get physical buffers, it will also be affected by DECA's limited estimation capability: for instance, extreme expressions usually cannot be well predicted. and the estimated lighting is sometimes coupled with the skin tone." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 304, + 582, + 547, + 667 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 667 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 667 + ], + "type": "text", + "content": "In this paper, we have presented DiffusionRig, a riggable diffusion model for identity-preserving, personalized editing of facial appearance. We introduced a two-stage method to first learn generic face priors and later personalized priors. Using both explicit conditioning via physical buffers and implicit conditioning via global latent code, we can drive and control our model's facial image synthesis." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgment We thank Marc Levoy for the valuable feedback and everyone whose photos appear in this paper for their permission." + } + ] + } + ], + "index": 27 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12743" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 704 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "type": "text", + "content": "[1] Sai Bi, Stephen Lombardi, Shunsuke Saito, Tomas Simon, Shih-En Wei, Kevyn Mcphail, Ravi Ramamoorthi, Yaser Sheikh, and Jason Saragih. 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Generative multiplane images: Making a 2d gan 3d-aware. In European Conference on Computer Vision, pages 18-35. 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Synthesized samples on various datasets, including FFHQ (1024 $^2$ and 256 $^2$ ), LSUN Church (256 $^2$ ), LSUN Bedroom (256 $^2$ ), LSUN Cat (256 $^2$ ) and CIFAR10 (32 $^2$ ). All these samples are generated from a 64 $^2$ noise except CIFAR10 from 16 $^2$ , while conventional diffusion models can only start from a noise with the same dimension as the final sample." + ], + "image_footnote": [], + "bbox": [ + 98, + 297, + 867, + 431 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 481, + 313, + 494 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Diffusion models, which learn to reverse a signal destruction process to generate new data, typically require the signal at each step to have the same dimension. We argue that, considering the spatial redundancy in image signals, there is no need to maintain a high dimensionality in the evolution process, especially in the early generation phase. To this end, we make a theoretical generalization of the forward diffusion process via signal decomposition. Concretely, we manage to decompose an image into multiple orthogonal components and control the attenuation of each component when perturbing the image. That way, along with the noise strength increasing, we are able to diminish those inconsequential components and thus use a lower-dimensional signal to represent the source, barely losing information. Such a reformulation allows to vary dimensions in both training and inference of diffusion models. Extensive experiments on a range of datasets suggest that our approach substantially reduces the computational cost and achieves on-par or even better synthesis performance compared to baseline methods. We also show that our strategy facilitates high-resolution image synthesis and improves FID of diffusion model trained on FFHQ at $1024 \\times 1024$ resolution from 52.40 to 10.46. Code is available at https://github.com/damo-vilab/dvdp.", + "bbox": [ + 75, + 502, + 470, + 864 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 501, + 479, + 630, + 494 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Diffusion models [2, 6, 9, 15, 21, 24, 28] have recently shown great potential in image synthesis. Instead of directly learning the observed distribution, it constructs a multistep forward process through gradually adding noise onto the real data (i.e., diffusion). After a sufficiently large number of steps, the source signal could be considered completely destroyed, resulting in a pure noise distribution that naturally supports sampling. In this way, starting from sampled noises, we can expect new instances after reversing the diffusion process step by step.", + "bbox": [ + 496, + 503, + 890, + 655 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "As it can be seen, the above pipeline does not change the dimension of the source signal throughout the entire diffusion process [6,26,28]. It thus requires the reverse process to map a high-dimensional input to a high-dimensional output at every single step, causing heavy computation overheads [10, 22]. However, images present a measure of spatial redundancy [4] from the semantic perspective (e.g., an image pixel could usually be easily predicted according to its neighbours). Given such a fact, when the source signal is attenuated to some extent along with the noise strength growing, it should be possible to get replaced by a lower-dimensional signal. We therefore argue that there is no need to follow the source signal dimension along the entire distribution evolution process, especially at early steps (i.e., steps close to the pure noise distribution) for coarse generation.", + "bbox": [ + 496, + 659, + 892, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* corresponding author. \n† Work performed at Alibaba DAMO Academy.", + "bbox": [ + 93, + 875, + 351, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "14307", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/32e7610b3c4f4a513822f75e6717dcff62f0bb639277a422609e3c53a8d50873.jpg", + "image_caption": [ + "Figure 2. Conceptual comparison between DDPM [6] and our proposed DVDP, where our approach allows using a varying dimension in the diffusion process." + ], + "image_footnote": [], + "bbox": [ + 119, + 88, + 851, + 258 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we propose dimensionality-varying diffusion process (DVDP), which allows dynamically adjusting the signal dimension when constructing the forward path. The varying dimensionality concept is shown in Fig. 2. For this purpose, we first decompose an image into multiple orthogonal components, each of which owns dimension lower than the original data. Then, based on such a decomposition, we theoretically generalize the conventional diffusion process such that we can control the attenuation of each component when adding noise. Thanks to this reformulation, we manage to drop those inconsequential components after the noise strength reaches a certain level, and thus represent the source image using a lower-dimensional signal with little information lost. The remaining diffusion process could inherit this dimension and apply the same technique to further reduce the dimension.", + "bbox": [ + 75, + 306, + 472, + 547 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We evaluate our approach on various datasets, including objects, human faces, animals, indoor scenes, and outdoor scenes. Experimental results suggest that DVDP achieves on-par or even better synthesis performance than baseline models on all datasets. More importantly, DVDP relies on much fewer computations, and hence speeds up both training and inference of diffusion models. We also demonstrate the effectiveness of our approach in learning from high-resolution data. For example, we are able to start from a $64 \\times 64$ noise to produce an image under $1024 \\times 1024$ resolution. With FID [5] as the evaluation metric, our $1024 \\times 1024$ model trained on FFHQ improves the baseline [28] from 52.40 to 10.46. All these advantages benefit from using a lower-dimensional signal, which reduces the computational cost and mitigates the optimization difficulty.", + "bbox": [ + 75, + 550, + 472, + 779 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 797, + 218, + 813 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Diffusion models. [26] proposes diffusion models for the first time that generate samples from a target distribution by reversing a diffusion process in which target distribution is gradually disturbed to an easily sampled standard Gaussian. [6] further proposes DDPM to reverse the diffusion process", + "bbox": [ + 75, + 824, + 470, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "by learning a noise prediction network. [28] considers diffusion models as stochastic differential equations with continuous timesteps and proposes a unified framework.", + "bbox": [ + 496, + 306, + 890, + 352 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Accelerating diffusion models. Diffusion models significantly suffer from the low training and inference speed. There are many methods that speed up sampling from thousands of steps to tens of steps while keeping an acceptable sample quality [1, 14, 17, 19, 25, 27, 30, 31]. Besides improvements only on inference speed, there are other works aiming at speeding up both training and inference. [18] proposes a patch operation to decrease the dimensionality of each channel while accordingly increasing the number of channels, which greatly reduces the complexity of computation. Besides, a trainable forward process [33] is also proven to benefit a faster training and inference speed. However, the price of their acceleration is a poor sampling quality evaluated by FID score. In this work, we accelerate DDPM on both training and inference from a different perspective, i.e., reducing the dimensionality of the early diffusion process, and thus improving the efficiency while obtaining on-par or even better synthesis performance.", + "bbox": [ + 496, + 353, + 892, + 626 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Varying dimensionality of diffusion models. Due to the redundancy in image signals, it is possible to improve the efficiency of diffusion models by varying dimensionality during the generation process. The most relevant work to our proposed model is subspace diffusion [10], which can also vary dimensionality in the diffusion process. However, subspace diffusion suffers from a trade-off between sampling acceleration and sample quality, while our DVDP can relieve this dilemma (see theoretical analysis in Sec. 4.4 and experimental results in Sec. 5.3). Instead of varying dimensionality in one diffusion process, there are works cascading several diffusion processes with growing dimensionality [7, 21, 23, 24], where the subsequent process is conditioned on the previous samples.", + "bbox": [ + 496, + 627, + 893, + 838 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Discussion with latent diffusion. Besides varying dimensionality in image space, there are other methods, which we generally call latent diffusion, that directly apply diffusion models in a low dimensional latent space, obtained by an", + "bbox": [ + 496, + 839, + 893, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "14308", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "autoencoder [3, 8, 20, 22, 29]. Although latent diffusion can also speed up the training and sampling of diffusion models, it decreases dimensionality by an additional model and keeps the diffusion process unchanged. In this paper, however, we focus on the improvement on the diffusion process itself to accelerate training and sampling, which is totally a different route. Besides training and sampling efficiency, another important contribution of this work is to prove that it is unnecessary for diffusion process to keep a fixed dimension along time. By controlling the attenuation of each data component, it is possible to change dimensionality while keeping the process reversible. Thus, we will not further compare our DVDP with latent diffusion.", + "bbox": [ + 75, + 90, + 472, + 287 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Background", + "text_level": 1, + "bbox": [ + 76, + 303, + 205, + 320 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We first introduce the background of Denoising Diffusion Probabilistic Model (DDPM) [6, 26] and some of its extensions which are closely related to our work. DDPM constructs a forward process to perturb the distribution of data $q(\\mathbf{x}_0)$ into a standard Gaussian $\\mathcal{N}(\\mathbf{0};\\mathbf{I})$ . Considering an increasing variance schedule of noises $\\beta_{1},\\ldots ,\\beta_{T}$ , DDPM defines the forward process as a Markov chain", + "bbox": [ + 75, + 329, + 468, + 435 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} _ {t} = \\sqrt {1 - \\beta_ {t}} \\mathbf {x} _ {t - 1} + \\sqrt {\\beta_ {t}} \\epsilon , t = 1, 2, \\dots , T, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 116, + 449, + 468, + 467 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\epsilon$ is a standard Gaussian noise. In order to generate high-fidelity images, DDPM [6] denoises samples from a standard Gaussian iteratively utilizing the reverse process parameterized as", + "bbox": [ + 75, + 473, + 468, + 534 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} _ {t - 1} = \\frac {1}{\\sqrt {\\alpha_ {t}}} \\left(\\mathbf {x} _ {t} - \\frac {\\beta_ {t}}{\\sqrt {1 - \\bar {\\alpha} _ {t}}} \\epsilon_ {\\theta} (\\mathbf {x} _ {t}, t)\\right) + \\sqrt {\\beta_ {t}} \\epsilon , \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 94, + 546, + 468, + 580 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\alpha_{t} = 1 - \\beta_{t}$ , $\\bar{\\alpha}_{t} = \\prod_{s=1}^{t} \\alpha_{s}$ , and $\\epsilon_{\\theta}$ is a neural network used to predict $\\epsilon$ from $\\mathbf{x}_{t}$ . The parameters $\\theta$ are learned by minimizing the following loss function", + "bbox": [ + 76, + 588, + 468, + 635 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nL (\\theta) = \\mathbb {E} _ {t, \\mathbf {x} _ {0}, \\epsilon} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} \\left(\\mathbf {x} _ {t} \\left(\\mathbf {x} _ {0}, \\epsilon\\right), t\\right) \\| ^ {2} \\right]. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 133, + 646, + 468, + 672 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "While the standard diffusion model is implemented directly in the image space, [13] takes the relative importance of different frequency components into consideration, and generalizes the forward diffusion process as", + "bbox": [ + 75, + 678, + 468, + 739 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} _ {t} = \\boldsymbol {U} (\\mathbf {I} - \\mathbf {B} _ {t}) ^ {\\frac {1}{2}} \\boldsymbol {U} ^ {T} \\mathbf {x} _ {t - 1} + \\boldsymbol {U} \\mathbf {B} _ {t} ^ {\\frac {1}{2}} \\boldsymbol {U} ^ {T} \\epsilon , \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 133, + 751, + 468, + 772 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{U}$ is an orthogonal matrix to impose a rotation on $\\mathbf{x}_t$ , and the noise schedule is defined by the diagonal matrix $\\mathbf{B}_t$ . As Eq. (4) is too general to be directly instantiated as an implementation, [13] only discusses one special case called blur diffusion, which owns a clearly different focus from our work. In this work, we extend the generalized framework further and make it possible to vary dimensionality during the diffusion process.", + "bbox": [ + 75, + 780, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Dimensionality-Varying Diffusion Process", + "text_level": 1, + "bbox": [ + 500, + 89, + 872, + 107 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We formulate the dimensionality-varying diffusion process in this section, which progressively decreases the dimension of $\\mathbf{x}_t$ in the forward process, and can be effectively reversed to generate high-dimensional data from a low-dimensional noise. To establish DVDP, we gradually attenuate components of $\\mathbf{x}_0$ in different subspaces and decrease the dimensionality of $\\mathbf{x}_t$ at dimensionality turning points by downsampling operator (Sec. 4.1), which is approximately reversible (Sec. 4.2) with controllable small error caused by the loss of attenuated $\\mathbf{x}_0$ component (Sec. 4.3).", + "bbox": [ + 496, + 114, + 890, + 267 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Forward Process of DVDP", + "text_level": 1, + "bbox": [ + 500, + 277, + 740, + 292 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we will construct the forward process of our DVDP, which decreases the dimensionality as time evolves and can be effectively reversed. To this end, we concatenate multiple diffusion processes with different dimensions into an entire Markov chain by downsampling operations, while we elaborately design each process so that the information loss induced by downsampling is negligible. Fig. 3 illustrates this overall framework. The concatenation of different processes enables us to decrease the dimensionality, and the control on information loss ensures that downsampling operations are approximately reversible, such that the entire process can be reversed (discussed later in Sec. 4.2). To limit the information loss, we decompose the data into orthogonal components and control the attenuation of each component in the forward process of each concatenated diffusion, which we call Attenuated Diffusion Process (ADP). Once the lost data component induced by downsampling is attenuated to be small enough, the information loss will be negligible.", + "bbox": [ + 496, + 301, + 890, + 589 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Notation list. As a prerequisite for constructing each ADP, we first define a sequence of subspaces and other necessary notations as follows:", + "bbox": [ + 496, + 590, + 890, + 635 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- $\\mathbb{S}_0 \\supseteq \\mathbb{S}_1 \\supseteq \\dots \\supseteq \\mathbb{S}_K$ is a sequence of subspaces with decreasing dimensionality $d = \\bar{d}_0 > \\bar{d}_1 > \\dots > \\bar{d}_K$ , where $\\mathbb{S}_0 = \\mathbb{R}^d$ is the original space, $K \\in \\mathbb{N}_+$ . For simplicity, $\\mathbb{S}_{K+1} \\triangleq \\{\\mathbf{0}\\}$ and $\\bar{d}_{K+1} \\triangleq 0$ .", + "- $d_{i} = \\dim (\\mathbb{S}_{i} / \\mathbb{S}_{i + 1})$ , $i = 0,1,\\dots ,K$ . Note that $d_{K} = \\dim (\\mathbb{S}_{K} / \\mathbb{S}_{K + 1}) = \\dim (\\mathbb{S}_{K})$", + "- $\\mathbf{U}_0 = [\\hat{\\mathbf{U}}_0, \\dots, \\hat{\\mathbf{U}}_K] \\in \\mathbb{R}^{d \\times d}$ is an orthogonal matrix, and column vectors of its sub-matrix $\\hat{\\mathbf{U}}_i \\in \\mathbb{R}^{d \\times d_i}$ span subspace $\\mathbb{S}_i / \\mathbb{S}_{i+1}$ for $i = 0, 1, \\dots, K$ .", + "- $\\mathbf{U}_k \\in \\mathbb{R}^{\\bar{d}_k \\times \\bar{d}_k}$ is an orthogonal matrix for $k = 0,1,\\dots,K$ , and can be split as $\\mathbf{U}_k = [N_k, P_k]$ when $k < K$ where $N_k \\in \\mathbb{R}^{\\bar{d}_k \\times d_k}, P_k \\in \\mathbb{R}^{\\bar{d}_k \\times \\bar{d}_{k+1}}$ .", + "- $I_{n} \\in \\mathbb{R}^{n \\times n}$ is an identity matrix.", + "- $O_{n} \\in \\mathbb{R}^{n \\times n}$ is a zero matrix." + ], + "bbox": [ + 517, + 642, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "14309", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/5e086991f38ed0e1da5707e117cb5ce92a3e9c83974101cf3e29a5ee98ea9875.jpg", + "image_caption": [ + "Figure 3. Framework illustration of DVDP. Each row represents an Attenuated Diffusion Process (ADP), which controls the attenuation of each data component while adding noise. All $K + 1$ ADPs ( $K = 2$ here) have different dimensions decreasing from top to bottom, and are concatenated by some simple operations to obtain our DVDP. In the forward process, the concatenation is achieved by downsampling operation, and in reverse process, it is the upsampling operation followed by adding a Gaussian noise." + ], + "image_footnote": [], + "bbox": [ + 125, + 89, + 851, + 270 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "With the above definitions, we can first construct an ADP $\\mathbf{x}_t^0\\in \\mathbb{S}_0$ for $t = 0,1,\\dots ,T$ as", + "bbox": [ + 76, + 352, + 470, + 383 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathbf {x} _ {t} ^ {0} = \\sum_ {i = 0} ^ {K} \\left(\\bar {\\lambda} _ {i, t} \\mathbf {v} _ {i} ^ {0} + \\bar {\\sigma} _ {i, t} \\mathbf {z} _ {i} ^ {0}\\right) \\tag {5} \\\\ = \\boldsymbol {U} _ {0} \\bar {\\boldsymbol {\\Lambda}} _ {0, t} \\boldsymbol {U} _ {0} ^ {T} \\mathbf {x} _ {0} ^ {0} + \\boldsymbol {U} _ {0} \\bar {\\boldsymbol {L}} _ {0, t} \\boldsymbol {U} _ {0} ^ {T} \\epsilon^ {0}, \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 393, + 468, + 455 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{v}_i^0\\in \\mathbb{S}_i / \\mathbb{S}_{i + 1}$ is the component of original data point $\\mathbf{x}_0^0$ in subspace $\\mathbb{S}_i / \\mathbb{S}_{i + 1}$ , $\\bar{\\lambda}_{i,t}$ controls the attenuation of $\\mathbf{v}_i^0$ along timestep $t$ , $\\mathbf{z}_i^0$ is the component of a standard Gaussian noise $\\epsilon^0\\in \\mathbb{R}^{\\bar{d}_0}$ in the same subspace as $\\mathbf{v}_i^0$ (i.e., $\\mathbb{S}_i / \\mathbb{S}_{i + 1}$ ), $\\bar{\\sigma}_{i,t}$ is the standard deviation of $\\mathbf{z}_i^0$ , and $\\bar{\\Lambda}_{0,t}$ , $\\bar{\\pmb{L}}_{0,t}\\in \\mathbb{R}^{\\bar{d}_0\\times \\bar{d}_0}$ are two diagonal matrices defined as $\\bar{\\Lambda}_{0,t} = \\mathrm{diag}(\\bar{\\lambda}_{0,t}\\pmb{I}_{d_0},\\bar{\\lambda}_{1,t}\\pmb{I}_{d_1},\\dots ,\\bar{\\lambda}_{K,t}\\pmb{I}_{d_K})$ and $\\bar{\\pmb{L}}_{0,t} = \\mathrm{diag}(\\bar{\\sigma}_{0,t}\\pmb{I}_{d_0},\\bar{\\sigma}_{1,t}\\pmb{I}_{d_1},\\dots ,\\bar{\\sigma}_{K,t}\\pmb{I}_{d_K})$ . To control the attenuation of each data component $\\mathbf{v}_i^0$ , we require $\\bar{\\lambda}_{i,t}$ to gradually decrease from 1 to approximate 0 for $i = 0,1,\\dots ,K - 1$ as timestep $t$ evolves. As for $\\bar{\\lambda}_{K,t}$ , it is not required to decrease (explained later after Eq. (8)).", + "bbox": [ + 76, + 460, + 468, + 647 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Starting from $\\mathbf{x}_t^0$ , we can recursively construct a dimensionality-decreasing sequence of ADPs", + "bbox": [ + 76, + 647, + 468, + 676 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathbf {x} _ {t} ^ {k} = \\mathcal {D} _ {k} \\mathbf {x} _ {t} ^ {k - 1} = \\sum_ {i = k} ^ {K} \\left(\\bar {\\lambda} _ {i, t} \\mathbf {v} _ {i} ^ {k} + \\bar {\\sigma} _ {i, t} \\mathbf {z} _ {i} ^ {k}\\right) \\tag {6} \\\\ = \\boldsymbol {U} _ {k} \\bar {\\boldsymbol {\\Lambda}} _ {k, t} \\boldsymbol {U} _ {k} ^ {T} \\mathbf {x} _ {0} ^ {k} + \\boldsymbol {U} _ {k} \\bar {\\boldsymbol {\\mathcal {L}}} _ {k, t} \\boldsymbol {U} _ {k} ^ {T} \\epsilon^ {k}, 1 \\leq k \\leq K, \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 688, + 468, + 751 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{D}_k:\\mathbb{R}^{\\bar{d}_{k - 1}}\\to \\mathbb{R}^{\\bar{d}_k}$ is a linear surjection, which we call the $k$ -th downsampling operator as it reduces the dimensionality of the operand (without ambiguity, we also use $\\mathcal{D}_k$ to denote the corresponding matrix in $\\mathbb{R}^{\\bar{d}_k\\times \\bar{d}_{k - 1}}$ $\\mathbf{v}_i^k = \\overline{\\mathcal{D}}_k\\mathbf{v}_i^0\\in \\overline{\\mathcal{D}}_k(\\mathbb{S}_i / \\mathbb{S}_{i + 1})$ is the component of $\\mathbf{x}_0^k = \\overline{\\mathcal{D}}_k\\mathbf{x}_0^0\\in \\mathbb{R}^{\\bar{d}_k}$ $(\\overline{\\mathcal{D}}_k\\triangleq \\prod_{i = 1}^{k}\\mathcal{D}_i)$ $\\mathbf{z}_i^k = \\overline{\\mathcal{D}}_k\\mathbf{z}_i^0\\in \\overline{\\mathcal{D}}_k(\\mathbb{S}_i / \\mathbb{S}_{i + 1})$ is the component of a standard Gaussian noise $\\epsilon^k = \\overline{\\mathcal{D}}_k\\epsilon^0\\in \\mathbb{R}^{\\bar{d}_k}$ $\\bar{\\Lambda}_{k,t} =$ diag( $\\bar{\\lambda}_{k,t}\\pmb {I}_{d_k}$ $\\bar{\\lambda}_{k + 1,t}\\pmb {I}_{d_{k + 1}},\\dots ,\\bar{\\lambda}_{K,t}\\pmb {I}_{d_K})\\in \\mathbb{R}^{\\bar{d}_k\\times \\bar{d}_k},$", + "bbox": [ + 76, + 757, + 470, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\bar{\\pmb{L}}_{k,t} = \\mathrm{diag}(\\bar{\\sigma}_{k,t}\\pmb{I}_{d_k},\\bar{\\sigma}_{k + 1,t}\\pmb{I}_{d_{k + 1}},\\dots ,\\bar{\\sigma}_{K,t}\\pmb{I}_{d_K})\\in$ $\\mathbb{R}^{\\bar{d}_k\\times \\bar{d}_k}$ , and orthogonal matrix $U_{k}\\in \\mathbb{R}^{\\bar{d}_{k}\\times \\bar{d}_{k}}$ consists of the last $\\bar{d}_k$ columns of $\\mathcal{D}_k\\pmb{U}_{k - 1}$ , i.e., $\\pmb {U}_k = \\mathcal{D}_k\\pmb {P}_{k - 1}$ (note that this condition requires further restriction on $\\mathcal{D}_k$", + "bbox": [ + 498, + 351, + 890, + 415 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Both Eqs. (5) and (6) can be derived from Markov chains with Gaussian kernels as (see Supplementary Material for the proof)", + "bbox": [ + 498, + 416, + 890, + 460 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} _ {t} ^ {k} = \\boldsymbol {U} _ {k} \\boldsymbol {\\Lambda} _ {k, t} \\boldsymbol {U} _ {k} ^ {T} \\mathbf {x} _ {t - 1} ^ {k} + \\boldsymbol {U} _ {k} \\boldsymbol {L} _ {k, t} \\boldsymbol {U} _ {k} ^ {T} \\epsilon^ {k}, 0 \\leq k \\leq K, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 506, + 473, + 890, + 492 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\Lambda_{k,t} = \\bar{\\Lambda}_{k,t - 1}^{-1}\\bar{\\Lambda}_{k,t},L_{k,t} = (\\bar{L}_{k,t}^{2} - \\Lambda_{k,t}^{2}\\bar{L}_{k,t - 1}^{2})^{1 / 2}.$", + "bbox": [ + 498, + 503, + 888, + 523 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Now with the ADPs $\\{\\mathbf{x}_t^k\\}_{k = 0}^K$ given by Eq. (7), we can construct the forward process of DVDP by merging different parts of $\\{\\mathbf{x}_t^k\\}_{k = 0}^K$ in the following manner: consider a strictly increasing time sequence $T_{1},\\dots ,T_{K},T_{K + 1} = T,$ if for each $k$ satisfying $1\\leq k\\leq K$ $\\bar{\\lambda}_{k - 1,T_k}$ becomes small enough, then $\\mathbf{x}_{T_k}^{k - 1}$ is downsampled by $\\mathcal{D}_k$ to obtain $\\mathbf{x}_{T_k}^k$ with lower dimensionality, and each $T_{k}$ is a dimensionality turning point. The entire process can be expressed as", + "bbox": [ + 496, + 523, + 890, + 647 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathbf {x} _ {0} ^ {0} \\longrightarrow \\mathbf {x} _ {1} ^ {0} \\quad \\longrightarrow \\dots \\longrightarrow \\mathbf {x} _ {T _ {1}} ^ {0} \\\\ \\xrightarrow {\\mathcal {D} _ {1}} \\mathbf {x} _ {T _ {1}} ^ {1} \\longrightarrow \\mathbf {x} _ {T _ {1} + 1} ^ {1} \\longrightarrow \\dots \\longrightarrow \\mathbf {x} _ {T _ {2}} ^ {1} \\tag {8} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 568, + 657, + 890, + 712 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\begin{array}{c} \\bullet \\\\ \\bullet \\\\ \\bullet \\\\ \\bullet \\end{array} \\\\ \\xrightarrow {\\mathcal {D} _ {K}} \\mathbf {x} _ {T _ {K}} ^ {K} \\longrightarrow \\mathbf {x} _ {T _ {K} + 1} ^ {K} \\longrightarrow \\dots \\longrightarrow \\mathbf {x} _ {T} ^ {K}. \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 570, + 710, + 823, + 753 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Between two adjacent dimensionality turning points $T_{k-1}$ and $T_{k}$ , $\\mathbf{x}_{t}^{k-1}$ diffuses and attenuates data components $\\mathbf{v}_{i}^{k-1}$ , $i \\geq k-1$ , which keeps the dimensionality $\\bar{d}_{k-1}$ . When it comes to $T_{k}$ , $\\mathbf{x}_{T_{k}}^{k-1} \\xrightarrow{\\mathcal{D}_{k}} \\mathbf{x}_{T_{k}}^{k}$ decreases the dimension from $\\bar{d}_{k-1}$ to $\\bar{d}_{k}$ . After the last dimensionality turning point $T_{k}$ , $\\mathbf{x}_{t}^{K}$ can just evolve as conventional diffusion without data component attenuation. Thus, the entire process in Eq. (8) decreases the dimensionality by $K$ times from $\\bar{d}_{0} = d$ to $\\bar{d}_{K}$ . It should be noted that process", + "bbox": [ + 496, + 758, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "14310", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "in Eq. (8) is also Markovian since each diffusion subprocess $\\mathbf{x}_{T_{k - 1}}^{k - 1}\\rightarrow \\mathbf{x}_{T_k}^{k - 1}$ is Markovian, and the result of each downsampling operation $\\mathbf{x}_{T_k}^k$ is uniquely determined by the previous state $\\mathbf{x}_{T_k}^{k - 1}$ . Also note that each downsampling operation $\\mathcal{D}_k$ loses little information because of small $\\bar{\\lambda}_{k - 1,T_k}$ which is a controllable hyperparameter. For better understanding, consider the relationship between $\\mathbf{x}_{T_k}^{k - 1}$ and $\\mathbf{x}_{T_k}^k$ derived from Eq. (6)", + "bbox": [ + 75, + 90, + 472, + 220 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} _ {T _ {k}} ^ {k - 1} = \\mathcal {D} _ {k} ^ {T} \\mathbf {x} _ {T _ {k}} ^ {k} + \\underbrace {\\bar {\\lambda} _ {k - 1 , T _ {k}} \\mathbf {v} _ {k - 1} ^ {k - 1}} _ {\\text {d a t a c o m p o n e n t}} + \\underbrace {\\bar {\\sigma} _ {k - 1 , T _ {k}} \\mathbf {z} _ {k - 1} ^ {k - 1}} _ {\\text {n o i s e c o m p o n e n t}}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 224, + 468, + 263 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{D}_k^T$ is the transpose of matrix $\\mathcal{D}_k$ , named as the $k$ -th upsampling operator. From Eq. (9), it is clear that $\\mathbf{x}_{T_k}^k$ actually loses two terms compared with $\\mathbf{x}_{T_k}^{k-1}$ : 1) data component $\\bar{\\lambda}_{k-1,T_k}\\mathbf{v}_{k-1}^{k-1}$ which is informative but negligible as $\\bar{\\lambda}_{k-1,T_k}$ is set to be small enough, and 2) noise component $\\bar{\\sigma}_{k-1,T_k}\\mathbf{z}_{k-1}^{k-1}$ that is non-informative and can be compensated in the reverse process, as we will discuss in Sec. 4.2.", + "bbox": [ + 75, + 265, + 472, + 390 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Reverse Process Approximating DVDP", + "text_level": 1, + "bbox": [ + 76, + 398, + 411, + 416 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we will derive an approximate reverse process, which induces a data generation process with progressively growing dimensionality. The approximation error will be discussed in Sec. 4.3, and we can find that it actually converges to zero. Loss function will also be given at the end of this section. Implementation details of training and sampling can be found in Supplementary Material.", + "bbox": [ + 75, + 422, + 468, + 527 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Reverse transition. Since DVDP is a sequence of fixed-dimensionality diffusion processes connected by downsampling operations at dimensionality turning points, we consider reverse transition kernels between and at dimensionality turning points separately.", + "bbox": [ + 75, + 527, + 468, + 602 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For reverse transition between two adjacent dimensionality turning points, i.e., $p_{\\theta}(\\mathbf{x}_{t - 1}^{k}|\\mathbf{x}_{t}^{k})$ with $T_{k - 1}\\leq t\\leq T_{k}$ for $k\\in [1,K + 1]$ , it can be defined as a Gaussian kernel $p_{\\theta}(\\mathbf{x}_{t - 1}^{k}|\\mathbf{x}_{t}^{k}) = \\mathcal{N}(\\mathbf{x}_{t - 1}^{k};\\pmb{\\mu}_{\\theta}(\\mathbf{x}_{t}^{k},t),\\pmb{\\Sigma}_{t})$ . As in DDPM [6], the covariance matrices $\\pmb{\\Sigma}_t$ are set to untrained time-dependent constants, and the mean term $\\pmb{\\mu}_{\\theta}(\\mathbf{x}_{t}^{k},t)$ is defined as (see Supplementary Material for details)", + "bbox": [ + 75, + 603, + 468, + 708 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\boldsymbol {\\mu} _ {\\theta} = \\tilde {\\boldsymbol {\\mu}} _ {k, t} \\left(\\mathbf {x} _ {t} ^ {k}, U _ {k} \\bar {\\boldsymbol {\\Lambda}} _ {k, t} ^ {- 1} \\boldsymbol {U} _ {k} ^ {T} \\mathbf {x} _ {t} ^ {k} \\right. \\tag {10} \\\\ - \\boldsymbol {U} _ {k} \\bar {\\boldsymbol {\\Lambda}} _ {k, t} ^ {- 1} \\bar {\\boldsymbol {L}} _ {k, t} \\boldsymbol {U} _ {k} ^ {T} \\boldsymbol {\\epsilon} _ {\\theta} \\left(\\boldsymbol {x} _ {t} ^ {k}, t\\right), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 714, + 468, + 753 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\tilde{\\pmb{\\mu}}_{k,t}(\\cdot ,\\cdot)$ is the mean function of forward process posterior $q(\\mathbf{x}_{t - 1}^k |\\mathbf{x}_t^k,\\mathbf{x}_0^k) = \\mathcal{N}(\\mathbf{x}_{t - 1}^k;\\tilde{\\pmb{\\mu}}_{k,t}(\\mathbf{x}_t^k,\\mathbf{x}_0^k),\\tilde{\\pmb{\\Sigma}}_{k,t})$ and $\\epsilon_{\\theta}$ represents a trainable network.", + "bbox": [ + 75, + 756, + 468, + 801 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For reverse transition at dimensionality turning points, i.e., $p_{\\theta}(\\mathbf{x}_{T_k}^{k - 1}|\\mathbf{x}_{T_k}^k)$ for $k\\in [1,K]$ , the corresponding forward transitions barely lose information as illustrated by Eq. (9) in Sec. 4.1, thus $\\mathbf{x}_{T_k}^k\\to \\mathbf{x}_{T_k}^{k - 1}$ can be approximately achieved without any trainable network as", + "bbox": [ + 76, + 801, + 468, + 878 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} _ {T _ {k}} ^ {k - 1} = \\mathcal {D} _ {k} ^ {T} \\mathbf {x} _ {T _ {k}} ^ {k} + \\boldsymbol {U} _ {k - 1} \\Delta \\boldsymbol {L} _ {k - 1} \\boldsymbol {U} _ {k - 1} ^ {T} \\epsilon^ {k - 1}, \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 112, + 882, + 468, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{D}_k^T\\in \\mathbb{R}^{\\bar{d}_k\\times \\bar{d}_{k - 1}}$ is the upsampling operator, and $\\Delta L_{k - 1} = \\mathrm{diag}(\\bar{\\sigma}_{k - 1,T_k}\\pmb{I}_{d_{k - 1}},\\pmb{O}_{\\bar{d}_k})$ represents the standard deviation of the added Gaussian noise $\\epsilon^{k - 1}\\in \\mathbb{R}^{\\bar{d}_{k - 1}}$ . Eq. (11) can be understood as: we first upsample $\\mathbf{x}_{T_k}^k$ , then add a Gaussian noise in compensation for the lost noise component in the forward downsampling operation, i.e., $\\bar{\\sigma}_{k - 1,T_k}\\mathbf{z}_{k - 1}^{k - 1}$ in Eq. (9). The approximation error comes from neglecting data component $\\bar{\\lambda}_{k - 1,T_k}\\mathbf{v}_{k - 1}^{k - 1}$ , and will be analyzed later in Sec. 4.3.", + "bbox": [ + 496, + 88, + 890, + 231 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Loss function. Similar with DDPM [6], a loss function can be derived from a weighted variational bound as (see Supplementary Material for details)", + "bbox": [ + 496, + 232, + 890, + 277 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL (\\theta) = \\mathbb {E} _ {k} \\mathbb {E} _ {\\mathbf {x} _ {0} ^ {k}, \\epsilon^ {k}, t \\sim \\mathcal {U} _ {k}} \\left[ \\left\\| \\epsilon^ {k} - \\epsilon_ {\\theta} \\left(\\mathbf {x} _ {t} ^ {k} \\left(\\mathbf {x} _ {0} ^ {k}, \\epsilon^ {k}\\right), t\\right) \\right\\| ^ {2} \\right], \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 506, + 287, + 890, + 310 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{U}_k = \\mathcal{U}\\big((T_k,T_{k + 1}]\\big)$ is a discrete uniform distribution between $T_{k}$ (exclusive) and $T_{k + 1}$ (inclusive), and $\\mathbf{x}_t^k (\\mathbf{x}_0^k,\\epsilon^k)$ represents the forward $\\mathbf{x}_t^k$ determined by $\\mathbf{x}_0^k$ and $\\epsilon^k$ given in Eq. (6).", + "bbox": [ + 496, + 320, + 890, + 382 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Error Analysis", + "text_level": 1, + "bbox": [ + 498, + 391, + 651, + 407 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In Sec. 4.2, we mention that the reverse process is just an approximation of the forward DVDP at each dimensionality turning point $T_{k}$ . In this section, we will measure this approximation error in probability sense, i.e., the difference between the real forward distribution $q(\\mathbf{x}_{T_k}^{k - 1})$ and the reverse distribution $p(\\mathbf{x}_{T_k}^{k - 1})$ under proper assumptions, and will find that this difference converges to zero.", + "bbox": [ + 496, + 414, + 890, + 522 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To measure the difference between two distributions, we use Jensen-Shannon Divergence (JSD) as a metric. Under this metric, upper bound of the approximation error can be derived from Proposition 1 (see Supplementary Material for proof):", + "bbox": [ + 496, + 523, + 890, + 598 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Proposition 1 Assume $p_1(\\pmb{x}|\\pmb{x}_0)$ , $p_2(\\pmb{x}|\\pmb{x}_0)$ are two Gaussians such that $p_1(\\pmb{x}|\\pmb{x}_0) = \\mathcal{N}(\\pmb{x};\\pmb{A}_1\\pmb{x}_0,\\pmb{\\Sigma})$ and $p_2(\\pmb{x}|\\pmb{x}_0) = \\mathcal{N}(\\pmb{x};\\pmb{A}_2\\pmb{x}_0,\\pmb{\\Sigma})$ , where positive semi-definite matrices $A_1, A_2$ satisfy $A_1\\succeq A_2\\succeq 0$ , covariance matrix $\\pmb{\\Sigma}$ is positive definite, and the support of distribution $p(\\pmb{x}_0)$ is bounded, then Jensen-Shannon Divergence (JSD) of the two marginal distributions $p_1(\\pmb{x})$ and $p_2(\\pmb{x})$ satisfies", + "bbox": [ + 496, + 604, + 890, + 710 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\operatorname {J S D} \\left(p _ {1} \\mid \\mid p _ {2}\\right) \\leq \\frac {\\sqrt {2}}{2} e ^ {- \\frac {1}{2}} B \\left(2 \\sqrt {2} + \\frac {V _ {d} (r)}{\\left(2 \\pi\\right) ^ {\\frac {d}{2}}}\\right) \\tag {13} \\\\ \\cdot \\left\\| \\boldsymbol {\\Sigma} ^ {- \\frac {1}{2}} \\left(\\boldsymbol {A} _ {1} - \\boldsymbol {A} _ {2}\\right) \\right\\| _ {2}, \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 532, + 715, + 890, + 777 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $B$ is the upper bound of $\\| \\pmb{x}_0\\| _2$ , $V_{d}(\\cdot)$ is the volume of a $d$ -dimensional sphere with respect to the radius, and $r = 2B\\| \\Sigma^{-\\frac{1}{2}}A_1\\| _2$ .", + "bbox": [ + 496, + 787, + 890, + 834 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "With Proposition 1, the upper bound of JSD between the forward distribution $q(\\mathbf{x}_{T_k}^{k - 1})$ and the reverse distribution $p(\\mathbf{x}_{T_k}^{k - 1})$ can be obtained by Theorem 1 (see Supplementary Material for proof)", + "bbox": [ + 496, + 837, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "14311", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Theorem 1 (Reverse Process Error) Assume $0 < k \\leq K$ , $q(\\mathbf{x}_{T_k}^{k-1})$ and $q(\\mathbf{x}_{T_k}^k)$ are defined by Eqs. (5) and (6), $p(\\mathbf{x}_{T_k}^{k-1})$ is the marginal distribution of $q(\\mathbf{x}_{T_k}^k)p(\\mathbf{x}_{T_k}^{k-1}|\\mathbf{x}_{T_k}^k)$ where $p(\\mathbf{x}_{T_k}^{k-1}|\\mathbf{x}_{T_k}^k)$ is defined by Eq. (11), and $\\| \\mathbf{x}_0\\|_2 \\leq \\sqrt{d}$ , then", + "bbox": [ + 76, + 90, + 468, + 174 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\xi_ {1} \\leq \\frac {\\sqrt {2}}{2} e ^ {- \\frac {1}{2}} \\sqrt {d} \\left(2 \\sqrt {2} + \\frac {V _ {d} (r)}{(2 \\pi) ^ {\\frac {d}{2}}}\\right) \\frac {\\bar {\\lambda} _ {k - 1 , T _ {k}}}{\\bar {\\sigma} _ {k - 1 , T _ {k}}} \\tag {14} \\\\ = o \\left(\\bar {\\lambda} _ {k - 1, T _ {k}}\\right), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 109, + 179, + 468, + 239 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\xi_1 \\triangleq \\mathrm{JSD}(q(\\mathbf{x}_{T_k}^{k-1})||p(\\mathbf{x}_{T_k}^{k-1})), \\text{ and } r = 2\\sqrt{d}\\max_{k-1 \\leq i \\leq K} \\frac{\\bar{\\lambda}_{i,T_k}}{\\bar{\\sigma}_{i,T_k}}.$", + "bbox": [ + 76, + 251, + 468, + 294 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Note that the assumption $\\| \\mathbf{x}_0\\| _2\\leq \\sqrt{d}$ can be satisfied for image data, since pixel values can be normalized in $[-1,1]$ . Thus, Theorem 1 claims that $\\xi_{1}$ can be arbitrarily small as $\\bar{\\lambda}_{k - 1,T_k}\\to 0$ if we can get an exact $q(\\mathbf{x}_{T_k}^{k - 1})$ by reverse process. It means that the approximation error caused by stepping over $T_{k}$ can be small enough.", + "bbox": [ + 76, + 297, + 468, + 391 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. Comparison with Subspace Diffusion", + "text_level": 1, + "bbox": [ + 76, + 400, + 397, + 416 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To reduce the dimensionality of latent space in diffusion models, subspace diffusion is proposed to model in a low-dimensional subspace at high noise levels, and keep the original full-dimensional network at low noise levels [10]. This can also be seen as a concatenation of multiple diffusion processes with different dimensionality like our DVDP, but without controllable attenuation on each data component. Each concatenated processes is just conventional isotropic diffusion.", + "bbox": [ + 75, + 422, + 468, + 559 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Thus, subspace diffusion can be seen as a special case of our DVDP with $\\bar{\\lambda}_t \\triangleq \\bar{\\lambda}_{0,t} = \\bar{\\lambda}_{1,t} = \\dots = \\bar{\\lambda}_{K,t}$ and $\\bar{\\sigma}_t \\triangleq \\bar{\\sigma}_{0,t} = \\bar{\\sigma}_{1,t} = \\dots = \\bar{\\sigma}_{K,t}$ , which limits the choice of dimensionality turning points. This limitation can be further explained by Eq. (9): at dimensionality turning point $T_k$ in the forward process, $\\mathbf{x}_{T_k}^{k-1}$ will lose an informative data component $\\bar{\\lambda}_{k-1,T_k} \\mathbf{v}_{k-1}^{k-1}$ and a noninformative noise component $\\bar{\\sigma}_{k-1,T_k} \\mathbf{z}_{k-1}^{k-1}$ . To safely neglect the data component in the reverse transition, it requires that $\\bar{\\lambda}_{k-1,T_k} / \\bar{\\sigma}_{k-1,T_k} \\ll \\| \\mathbf{z}_{k-1}^{k-1} \\| / \\| \\mathbf{v}_{k-1}^{k-1} \\|$ . For subspace diffusion, it means that the consistent $\\bar{\\lambda}_t / \\bar{\\sigma}_t$ for components in all subspaces should be small enough, which usually indicates a large $T_k$ , i.e., a large number of diffusion steps in high dimensional space.", + "bbox": [ + 75, + 561, + 468, + 779 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Therefore, as claimed in [10], the choice of $T_{k}$ should balance two factors: 1) smaller $T_{k}$ reduces the number of reverse diffusion steps occurring at higher dimensionality, whereas 2) larger $T_{k}$ makes the reverse transition at $T_{k}$ more accurate. Although [10] additionally proposes to compensate the loss of data component by adding an extra Gaussian noise besides compensation for the noise component, this trade-off still exists.", + "bbox": [ + 75, + 779, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "However, our DVDP can set much smaller $T_{k}$ with little loss in accuracy, which benefits from the controllable attenuation for each data component. Theorem 1 supports this advantage theoretically, and experimental results in Sec. 5.3 further demonstrate it.", + "bbox": [ + 496, + 90, + 890, + 166 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 500, + 179, + 632, + 196 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we show that our DVDP can speed up both training and inference of diffusion models while achieving competitive performance. Besides, thanks to the varied dimension, DVDP is able to generate high-quality and high-resolution images from a low-dimensional subspace and exceeds existing methods including scoreSDE [28] and Cascaded Diffusion Models (CDM) [7] on FFHQ $1024^{2}$ . Specifically, we first introduce our experimental setup in Sec. 5.1. Then we compare our DVDP with existing alternatives on several widely evaluated datasets in terms of visual quality and modeling efficiency in Sec. 5.2. After that, we compare our DVDP with Subspace Diffusion [10], a closely related work proposed recently, in Sec. 5.3. Finally, we implement necessary ablation studies in the last Sec. 5.4.", + "bbox": [ + 496, + 204, + 890, + 429 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 500, + 439, + 689, + 455 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. In order to verify that DVDP is widely applicable, we use six image datasets covering various classes and a wide range of resolutions from 32 to 1024. To be specific, we implement DVDP on CIFAR10 $32^2$ [12], LSUN Bedroom $256^2$ [32], LSUN Church $256^2$ , LSUN Cat $256^2$ , FFHQ $256^2$ , and FFHQ $1024^2$ [11].", + "bbox": [ + 496, + 462, + 890, + 551 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation details. We adopt the UNet improved by [2] which achieves better performance than the traditional version [6]. Since most baseline methods adopt a single UNet network for all timesteps in the whole diffusion process, our DVDP also keeps this setting, except the comparison with Subspace Diffusion in Sec. 5.3, which takes two networks for different generation stages [10]. In principle, the network structure of our DVDP is kept the same as the corresponding baseline. However, when resolution comes to $1024 \\times 1024$ , the UNet in conventional diffusion models should be deep enough to contain sufficient downsampling blocks, thus to obtain embeddings with proper size (usually $4 \\times 4$ or $8 \\times 8$ ) in the bottleneck layer. On the contrary, our DVDP does not need such a deep network since the generation starts from a low resolution noise ( $64 \\times 64$ in our case). Thus we only maintain a similar amount of parameters but use a different hyperparameter setting on FFHQ $1024^2$ .", + "bbox": [ + 496, + 553, + 890, + 824 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We set the number of timesteps $T = 1,000$ in all of our experiments. For DVDP, we reduce the dimensionality by $\\frac{1}{4}$ (i.e., $h \\times w \\to \\frac{h}{2} \\times \\frac{w}{2}$ for image resolution) when the timestep $t$ reaches a dimensionality turning point. For simplicity, we adopt $\\mathbb{T} \\triangleq \\{T_1, \\dots, T_K\\}$ . For CIFAR10", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "14312", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/9e507874ee5faaa5533477fef881e9390f29f6476036e5e90219b88aaa811283.jpg", + "table_caption": [ + "Table 1. Quantitative comparison between DDPM [6] and our DVDP on various datasets regarding image quality and model efficiency. * indicates our reproduced DDPM. Both ${\\mathrm{{DDMP}}}^{ * }$ and our DVDP adopt the improved UNet [2] for a fair comparison." + ], + "table_footnote": [], + "table_body": "
DatasetMethodFID (50k)↓Training Speed (sec/iter)Training Speed UpSampling Speed (sec/sample)Sampling Speed Up
CIFAR10 32 × 32DDPM3.17----
DDPM*3.160.18-0.34-
DVDP3.240.151.2×0.261.3×
LSUN Bedroom 256 × 256DDPM6.36----
DDPM*5.740.99-12.2-
DVDP4.880.452.2×5.012.4×
LSUN Church 256 × 256DDPM7.89----
DDPM*7.540.99-12.2-
DVDP7.030.452.2×5.012.4×
LSUN Cat 256 × 256DDPM19.75----
DDPM*18.110.99-12.2-
DVDP16.500.452.2×5.012.4×
FFHQ 256 × 256DDPM*8.330.99-12.2-
DVDP8.030.452.2×5.012.4×
", + "bbox": [ + 76, + 123, + 893, + 388 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "$32^{2}$ , we set $\\mathbb{T} = \\{600\\}$ , indicating that the resolution is decreased from $32 \\times 32$ to $16 \\times 16$ when $t = 600$ . Similarly, we set $\\mathbb{T} = \\{300, 600\\}$ for all $256^{2}$ datasets and $\\mathbb{T} = \\{200, 400, 600, 800\\}$ for FFHQ $1024^{2}$ .", + "bbox": [ + 75, + 411, + 468, + 470 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In all of our experiments, the noise schedule of DVDP is an adapted version of linear schedule [6], which is suitable for DVDP and keeps a comparable signal-to-noise ratio (SNR) with the original version (see Supplementary Material for details).", + "bbox": [ + 75, + 473, + 468, + 547 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Evaluation metrics. For sample quality, we calculate the FID score [5] on 50k samples, except for FFHQ $1024^{2}$ with 10k samples due to a much slower sampling. As for training and sampling speed, both of them are evaluated on a single NVIDIA A100. Training speed is measured by the mean time of each iteration (estimated over 4,000 iterations), and sampling speed is measured by the mean time of each sample (estimated over 100 batches). The training batch size and sampling batch size are 128, 256 respectively for CIFAR10 $32^{2}$ , and 24, 64 respectively for other $256^{2}$ datasets.", + "bbox": [ + 75, + 549, + 468, + 715 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Visual Quality and Modeling Efficiency.", + "text_level": 1, + "bbox": [ + 76, + 724, + 418, + 742 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison with existing alternatives. We compare DVDP with other alternatives here to show that DVDP has the capability of acceleration while maintaining a reasonable or even better visual quality. For the sake of fairness, we reproduce DDPM using the same network structure as DVDP with the same hyperparameters, represented as $\\mathrm{DDPM^{*}}$ . Some samples generated by our DVDP are shown in Fig. 1, and Tab. 1 summarizes the quantitative results on CIFAR10, FFHQ $256^{2}$ , and three LSUN datasets. The results show that our proposed DVDP achieves better FID", + "bbox": [ + 75, + 750, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "scores on all of the $256^{2}$ datasets, demonstrating an improved sample quality. Meanwhile, DVDP enjoys improved training and sampling speeds. Specifically, DDPM and $\\mathrm{DDPM}^*$ spend $2.2\\times$ time as DVDP when training the same epochs, and they spend $2.4\\times$ time in sampling. Although the superiority of DVDP is obvious on all $256^{2}$ datasets, it becomes indistinct when it comes to CIFAR10 $32^{2}$ , which is reasonable considering the small pixel redundancy and low resolution of images in CIFAR10.", + "bbox": [ + 496, + 411, + 890, + 547 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Towards high-resolution image synthesis. It is hard for diffusion models to generate high-resolution images directly. This can attribute to the curse of dimensionality: the support of high-dimensional data with large noise can only be visited a small part during training, leading to inaccurate prediction on unseen points [10]. Score-SDE [28] tries this task by directly training a single diffusion model, but the sample quality is far from reasonable. CDM performs better in high-resolution image synthesis and obtains impressive results [21, 24]. It first generates low-resolution images, followed by several conditional diffusion models as superresolution modules. We compare DVDP with score-SDE and CDM on FFHQ $1024^{2}$ in Tab. 2. The FID of score-SDE is evaluated on samples generated from their official code and model weight without acceleration, and CDM is implemented by three cascaded diffusions as in [21]. Our DVDP is sampled by both DDPM method with 1000 steps and DDIM method with 675 steps. The results show that DVDP beats both score-SDE and CDM.", + "bbox": [ + 496, + 547, + 892, + 834 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Comparison with Subspace Diffusion", + "text_level": 1, + "bbox": [ + 500, + 845, + 821, + 863 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Subspace diffusion [10] can also vary dimensionality during the diffusion process. As mentioned in [10] and also", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "14313", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/8bff80bff4f21832320de488bb8c0964c410899932be484258f20895a63590bf.jpg", + "table_caption": [ + "Table 2. Synthesis performance of different models trained on FFHQ ${1024} \\times {1024}$ ." + ], + "table_footnote": [], + "table_body": "
Model#Params (M)NFEFID (10k)↓
Score-SDE100200052.40
CDM98152524.7
165152517.35
286152517.24
DVDP10567512.43
100010.46
", + "bbox": [ + 89, + 119, + 450, + 243 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8b4da43eaa7cf459ac0df1d7937df27726bba25899fe848371489d03184cd7b4.jpg", + "image_caption": [ + "Figure 4. Quantitative comparison between subspace diffusion [10] and our DVDP on CelebA $64 \\times 64$ regarding different dimensionality turning point $T_{1}$ ." + ], + "image_footnote": [], + "bbox": [ + 106, + 252, + 434, + 402 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "discussed in Sec. 4.4, dimensionality turning point $T_{k}$ in subspace diffusion should be large enough to maintain the sample quality. However, large $T_{k}$ means more diffusion steps in high dimensional space, which will impair the advantage of such dimensionality-varying method, e.g., less acceleration in sampling. Thus, $T_{k}$ is expected to be as small as possible while maintaining the sampling quality.", + "bbox": [ + 75, + 470, + 467, + 575 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Considering that the dimensionality decreases only once, i.e., $K = 1$ , and only one dimensionality turning point $T_{1}$ , we compare DVDP with subspace diffusion when the downsampling is carried out at different $T_{1}$ . Since the subspace diffusion is only implemented on continuous timesteps in [10], we reproduce it on discrete timesteps similar as DDPM and use the reproduced version as a baseline. Fig. 4 illustrates that DVDP is consistently better with regard to sample quality on CelebA $64 \\times 64$ [16] when $T_{1}$ varies, where the advantage gets larger when $T_{1}$ gets smaller. In addition, some samples of DVDP and subspace diffusion are shown in Fig. 5, where the sample quality of subspace diffusion is apparently worse than that of DVDP especially when $T_{1}$ is small. In conclusion, DVDP is much more insensitive to the dimensionality turning point than subspace diffusion.", + "bbox": [ + 75, + 577, + 467, + 818 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.4. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 830, + 230, + 847 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We implement ablation study in this section to show that DVDP is able to keep effective when the number of downsampling, i.e., $K$ , grows. Specifically, we train DVDP", + "bbox": [ + 75, + 854, + 467, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/971557c0e03ef95643690ac3f2dbc1ebf5759ff585b1b532900598dfcfee1a42.jpg", + "table_caption": [ + "Table 3. Ablation study on the number of downsampling times on CelebA $128 \\times 128$ ." + ], + "table_footnote": [], + "table_body": "
Downsampling times K0123
FID (50k)6.145.996.106.37
Training Speed Up-1.98×2.24×2.25×
Sampling Speed Up-2.12×2.36×2.43×
", + "bbox": [ + 511, + 117, + 874, + 244 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/40c981e278b0b2ff1d535ac9453aade4a21f1e7bcb1d8da4ae78adc9de7c4e52.jpg", + "image_caption": [ + "Figure 5. Qualitative comparison between subspace diffusion [10] and our DVDP on CelebA $64 \\times 64$ . $T_{1}$ denotes the dimensionality turning point." + ], + "image_footnote": [], + "bbox": [ + 511, + 261, + 870, + 393 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "models on four different settings of dimensionality turning points $\\mathbb{T}$ for $K = 0,1,2,3$ . When $K = 1$ , $\\mathbb{T}$ is set to $\\{250\\}$ . Similarly, when $K = 2$ and $K = 3$ , $\\mathbb{T}$ is set to $\\{250,500\\}$ and $\\{250,500,750\\}$ , respectively. Furthermore, we use the same noise schedule for these four different settings. Tab. 3 shows that when the number of downsampling grows, the sample quality preserves a reasonable level, indicating that DVDP can vary dimensionality for multiple times.", + "bbox": [ + 496, + 470, + 890, + 592 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 607, + 617, + 622 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper generalizes the traditional diffusion process to a dimensionality-varying diffusion process (DVDP). The proposed DVDP has both theoretical and experimental contributions. Theoretically, we carefully decompose the signal in the diffusion process into multiple orthogonal dynamic-attenuated components. With a rigorously deduced approximation strategy, this then leads to a novel reverse process that generates images from much lower dimensional noises compared with the image resolutions. This design allows much higher training and sampling speed of the diffusion models with on-par or even better synthesis performance, and superior performance in synthesizing large-size images of $1024 \\times 1024$ resolution compared with classic methods. The results in this work can promote the understanding and applications of diffusion models in broader scenarios.", + "bbox": [ + 496, + 633, + 890, + 858 + ], + "page_idx": 7 + }, + { + "type": "page_footnote", + "text": "This work was supported in part by the National Key R&D Program of China under Grant 2022YFA1005000, in part by the NSFC under Grant 61701304.", + "bbox": [ + 498, + 862, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "14314", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Fan Bao, Chongxuan Li, Jun Zhu, and Bo Zhang. Analytic-DPM: an analytic estimate of the optimal reverse variance in diffusion probabilistic models. Int. Conf. Learn. Represent., 2022. 2", + "[2] Prafulla Dhariwal and Alexander Nichol. 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Syst., pages 16280-16291, 2021. 2" + ], + "bbox": [ + 78, + 90, + 468, + 189 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "14316", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Dimensionality-Varying Diffusion Process/6d385449-d42c-4da7-84b2-17c8988b13c5_model.json b/2023/Dimensionality-Varying Diffusion Process/6d385449-d42c-4da7-84b2-17c8988b13c5_model.json new file mode 100644 index 0000000000000000000000000000000000000000..7507975267b15ec7e8d670cd30d8aefc314c735a --- /dev/null +++ b/2023/Dimensionality-Varying Diffusion Process/6d385449-d42c-4da7-84b2-17c8988b13c5_model.json @@ -0,0 +1,1936 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.274, + 0.131, + 0.697, + 0.154 + ], + "angle": 0, + "content": "Dimensionality-Varying Diffusion Process" + }, + { + "type": "text", + "bbox": [ + 0.165, + 0.179, + 0.816, + 0.255 + ], + "angle": 0, + "content": "Han Zhang\\(^{1,4\\dagger}\\) Ruili Feng\\(^{2,4}\\) Zhantao Yang\\(^{1,4\\dagger}\\) Lianghua Huang\\(^{4}\\) Yu Liu\\(^{4}\\) Yifei Zhang\\(^{1,4\\dagger}\\) Yujun Shen\\(^{3}\\) Deli Zhao\\(^{4}\\) Jingren Zhou\\(^{4}\\) Fan Cheng\\(^{1*}\\) \n\\(^{1}\\)Shanghai Jiao Tong University \\(^{2}\\)University of Science and Technology of China \\(^{3}\\)Ant Group \\(^{4}\\)Alibaba Group" + }, + { + "type": "text", + "bbox": [ + 0.202, + 0.258, + 0.777, + 0.273 + ], + "angle": 0, + "content": "{hzhang9617, ruilifengustc, ztyangl96, shenyujun0302, zhaodeli}@gmail.com" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.276, + 0.889, + 0.29 + ], + "angle": 0, + "content": "{xuangen.hlh, ly103369, jingren.zhou}@alibaba-inc.com qidouxiong619@sjtu.edu.cn chengfan@sjtu.edu.cn" + }, + { + "type": "image", + "bbox": [ + 0.099, + 0.298, + 0.868, + 0.432 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.433, + 0.893, + 0.475 + ], + "angle": 0, + "content": "Figure 1. Synthesized samples on various datasets, including FFHQ (1024\\(^2\\) and 256\\(^2\\)), LSUN Church (256\\(^2\\)), LSUN Bedroom (256\\(^2\\)), LSUN Cat (256\\(^2\\)) and CIFAR10 (32\\(^2\\)). All these samples are generated from a 64\\(^2\\) noise except CIFAR10 from 16\\(^2\\), while conventional diffusion models can only start from a noise with the same dimension as the final sample." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.482, + 0.314, + 0.496 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.503, + 0.472, + 0.866 + ], + "angle": 0, + "content": "Diffusion models, which learn to reverse a signal destruction process to generate new data, typically require the signal at each step to have the same dimension. We argue that, considering the spatial redundancy in image signals, there is no need to maintain a high dimensionality in the evolution process, especially in the early generation phase. To this end, we make a theoretical generalization of the forward diffusion process via signal decomposition. Concretely, we manage to decompose an image into multiple orthogonal components and control the attenuation of each component when perturbing the image. That way, along with the noise strength increasing, we are able to diminish those inconsequential components and thus use a lower-dimensional signal to represent the source, barely losing information. Such a reformulation allows to vary dimensions in both training and inference of diffusion models. Extensive experiments on a range of datasets suggest that our approach substantially reduces the computational cost and achieves on-par or even better synthesis performance compared to baseline methods. We also show that our strategy facilitates high-resolution image synthesis and improves FID of diffusion model trained on FFHQ at \\(1024 \\times 1024\\) resolution from 52.40 to 10.46. Code is available at https://github.com/damo-vilab/dvdp." + }, + { + "type": "title", + "bbox": [ + 0.502, + 0.481, + 0.631, + 0.496 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.504, + 0.892, + 0.656 + ], + "angle": 0, + "content": "Diffusion models [2, 6, 9, 15, 21, 24, 28] have recently shown great potential in image synthesis. Instead of directly learning the observed distribution, it constructs a multistep forward process through gradually adding noise onto the real data (i.e., diffusion). After a sufficiently large number of steps, the source signal could be considered completely destroyed, resulting in a pure noise distribution that naturally supports sampling. In this way, starting from sampled noises, we can expect new instances after reversing the diffusion process step by step." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.893, + 0.901 + ], + "angle": 0, + "content": "As it can be seen, the above pipeline does not change the dimension of the source signal throughout the entire diffusion process [6,26,28]. It thus requires the reverse process to map a high-dimensional input to a high-dimensional output at every single step, causing heavy computation overheads [10, 22]. However, images present a measure of spatial redundancy [4] from the semantic perspective (e.g., an image pixel could usually be easily predicted according to its neighbours). Given such a fact, when the source signal is attenuated to some extent along with the noise strength growing, it should be possible to get replaced by a lower-dimensional signal. We therefore argue that there is no need to follow the source signal dimension along the entire distribution evolution process, especially at early steps (i.e., steps close to the pure noise distribution) for coarse generation." + }, + { + "type": "page_footnote", + "bbox": [ + 0.094, + 0.876, + 0.352, + 0.901 + ], + "angle": 0, + "content": "* corresponding author. \n† Work performed at Alibaba DAMO Academy." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14307" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.12, + 0.089, + 0.852, + 0.26 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.265, + 0.895, + 0.296 + ], + "angle": 0, + "content": "Figure 2. Conceptual comparison between DDPM [6] and our proposed DVDP, where our approach allows using a varying dimension in the diffusion process." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.308, + 0.473, + 0.549 + ], + "angle": 0, + "content": "In this work, we propose dimensionality-varying diffusion process (DVDP), which allows dynamically adjusting the signal dimension when constructing the forward path. The varying dimensionality concept is shown in Fig. 2. For this purpose, we first decompose an image into multiple orthogonal components, each of which owns dimension lower than the original data. Then, based on such a decomposition, we theoretically generalize the conventional diffusion process such that we can control the attenuation of each component when adding noise. Thanks to this reformulation, we manage to drop those inconsequential components after the noise strength reaches a certain level, and thus represent the source image using a lower-dimensional signal with little information lost. The remaining diffusion process could inherit this dimension and apply the same technique to further reduce the dimension." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.551, + 0.473, + 0.78 + ], + "angle": 0, + "content": "We evaluate our approach on various datasets, including objects, human faces, animals, indoor scenes, and outdoor scenes. Experimental results suggest that DVDP achieves on-par or even better synthesis performance than baseline models on all datasets. More importantly, DVDP relies on much fewer computations, and hence speeds up both training and inference of diffusion models. We also demonstrate the effectiveness of our approach in learning from high-resolution data. For example, we are able to start from a \\(64 \\times 64\\) noise to produce an image under \\(1024 \\times 1024\\) resolution. With FID [5] as the evaluation metric, our \\(1024 \\times 1024\\) model trained on FFHQ improves the baseline [28] from 52.40 to 10.46. All these advantages benefit from using a lower-dimensional signal, which reduces the computational cost and mitigates the optimization difficulty." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.798, + 0.22, + 0.814 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Diffusion models. [26] proposes diffusion models for the first time that generate samples from a target distribution by reversing a diffusion process in which target distribution is gradually disturbed to an easily sampled standard Gaussian. [6] further proposes DDPM to reverse the diffusion process" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.308, + 0.892, + 0.353 + ], + "angle": 0, + "content": "by learning a noise prediction network. [28] considers diffusion models as stochastic differential equations with continuous timesteps and proposes a unified framework." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.354, + 0.893, + 0.627 + ], + "angle": 0, + "content": "Accelerating diffusion models. Diffusion models significantly suffer from the low training and inference speed. There are many methods that speed up sampling from thousands of steps to tens of steps while keeping an acceptable sample quality [1, 14, 17, 19, 25, 27, 30, 31]. Besides improvements only on inference speed, there are other works aiming at speeding up both training and inference. [18] proposes a patch operation to decrease the dimensionality of each channel while accordingly increasing the number of channels, which greatly reduces the complexity of computation. Besides, a trainable forward process [33] is also proven to benefit a faster training and inference speed. However, the price of their acceleration is a poor sampling quality evaluated by FID score. In this work, we accelerate DDPM on both training and inference from a different perspective, i.e., reducing the dimensionality of the early diffusion process, and thus improving the efficiency while obtaining on-par or even better synthesis performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.628, + 0.895, + 0.839 + ], + "angle": 0, + "content": "Varying dimensionality of diffusion models. Due to the redundancy in image signals, it is possible to improve the efficiency of diffusion models by varying dimensionality during the generation process. The most relevant work to our proposed model is subspace diffusion [10], which can also vary dimensionality in the diffusion process. However, subspace diffusion suffers from a trade-off between sampling acceleration and sample quality, while our DVDP can relieve this dilemma (see theoretical analysis in Sec. 4.4 and experimental results in Sec. 5.3). Instead of varying dimensionality in one diffusion process, there are works cascading several diffusion processes with growing dimensionality [7, 21, 23, 24], where the subsequent process is conditioned on the previous samples." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Discussion with latent diffusion. Besides varying dimensionality in image space, there are other methods, which we generally call latent diffusion, that directly apply diffusion models in a low dimensional latent space, obtained by an" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14308" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.473, + 0.288 + ], + "angle": 0, + "content": "autoencoder [3, 8, 20, 22, 29]. Although latent diffusion can also speed up the training and sampling of diffusion models, it decreases dimensionality by an additional model and keeps the diffusion process unchanged. In this paper, however, we focus on the improvement on the diffusion process itself to accelerate training and sampling, which is totally a different route. Besides training and sampling efficiency, another important contribution of this work is to prove that it is unnecessary for diffusion process to keep a fixed dimension along time. By controlling the attenuation of each data component, it is possible to change dimensionality while keeping the process reversible. Thus, we will not further compare our DVDP with latent diffusion." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.304, + 0.206, + 0.321 + ], + "angle": 0, + "content": "3. Background" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.33, + 0.47, + 0.436 + ], + "angle": 0, + "content": "We first introduce the background of Denoising Diffusion Probabilistic Model (DDPM) [6, 26] and some of its extensions which are closely related to our work. DDPM constructs a forward process to perturb the distribution of data \\( q(\\mathbf{x}_0) \\) into a standard Gaussian \\( \\mathcal{N}(\\mathbf{0};\\mathbf{I}) \\). Considering an increasing variance schedule of noises \\( \\beta_{1},\\ldots ,\\beta_{T} \\), DDPM defines the forward process as a Markov chain" + }, + { + "type": "equation", + "bbox": [ + 0.117, + 0.45, + 0.469, + 0.468 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} _ {t} = \\sqrt {1 - \\beta_ {t}} \\mathbf {x} _ {t - 1} + \\sqrt {\\beta_ {t}} \\epsilon , t = 1, 2, \\dots , T, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.474, + 0.47, + 0.535 + ], + "angle": 0, + "content": "where \\(\\epsilon\\) is a standard Gaussian noise. In order to generate high-fidelity images, DDPM [6] denoises samples from a standard Gaussian iteratively utilizing the reverse process parameterized as" + }, + { + "type": "equation", + "bbox": [ + 0.095, + 0.547, + 0.469, + 0.582 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} _ {t - 1} = \\frac {1}{\\sqrt {\\alpha_ {t}}} \\left(\\mathbf {x} _ {t} - \\frac {\\beta_ {t}}{\\sqrt {1 - \\bar {\\alpha} _ {t}}} \\epsilon_ {\\theta} (\\mathbf {x} _ {t}, t)\\right) + \\sqrt {\\beta_ {t}} \\epsilon , \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.589, + 0.47, + 0.636 + ], + "angle": 0, + "content": "where \\(\\alpha_{t} = 1 - \\beta_{t}\\), \\(\\bar{\\alpha}_{t} = \\prod_{s=1}^{t} \\alpha_{s}\\), and \\(\\epsilon_{\\theta}\\) is a neural network used to predict \\(\\epsilon\\) from \\(\\mathbf{x}_{t}\\). The parameters \\(\\theta\\) are learned by minimizing the following loss function" + }, + { + "type": "equation", + "bbox": [ + 0.135, + 0.647, + 0.469, + 0.673 + ], + "angle": 0, + "content": "\\[\nL (\\theta) = \\mathbb {E} _ {t, \\mathbf {x} _ {0}, \\epsilon} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} \\left(\\mathbf {x} _ {t} \\left(\\mathbf {x} _ {0}, \\epsilon\\right), t\\right) \\| ^ {2} \\right]. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.679, + 0.47, + 0.74 + ], + "angle": 0, + "content": "While the standard diffusion model is implemented directly in the image space, [13] takes the relative importance of different frequency components into consideration, and generalizes the forward diffusion process as" + }, + { + "type": "equation", + "bbox": [ + 0.134, + 0.752, + 0.469, + 0.773 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} _ {t} = \\boldsymbol {U} (\\mathbf {I} - \\mathbf {B} _ {t}) ^ {\\frac {1}{2}} \\boldsymbol {U} ^ {T} \\mathbf {x} _ {t - 1} + \\boldsymbol {U} \\mathbf {B} _ {t} ^ {\\frac {1}{2}} \\boldsymbol {U} ^ {T} \\epsilon , \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.47, + 0.901 + ], + "angle": 0, + "content": "where \\(\\mathbf{U}\\) is an orthogonal matrix to impose a rotation on \\(\\mathbf{x}_t\\), and the noise schedule is defined by the diagonal matrix \\(\\mathbf{B}_t\\). As Eq. (4) is too general to be directly instantiated as an implementation, [13] only discusses one special case called blur diffusion, which owns a clearly different focus from our work. In this work, we extend the generalized framework further and make it possible to vary dimensionality during the diffusion process." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.09, + 0.874, + 0.108 + ], + "angle": 0, + "content": "4. Dimensionality-Varying Diffusion Process" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.116, + 0.892, + 0.268 + ], + "angle": 0, + "content": "We formulate the dimensionality-varying diffusion process in this section, which progressively decreases the dimension of \\(\\mathbf{x}_t\\) in the forward process, and can be effectively reversed to generate high-dimensional data from a low-dimensional noise. To establish DVDP, we gradually attenuate components of \\(\\mathbf{x}_0\\) in different subspaces and decrease the dimensionality of \\(\\mathbf{x}_t\\) at dimensionality turning points by downsampling operator (Sec. 4.1), which is approximately reversible (Sec. 4.2) with controllable small error caused by the loss of attenuated \\(\\mathbf{x}_0\\) component (Sec. 4.3)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.279, + 0.741, + 0.294 + ], + "angle": 0, + "content": "4.1. Forward Process of DVDP" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.303, + 0.892, + 0.59 + ], + "angle": 0, + "content": "In this section, we will construct the forward process of our DVDP, which decreases the dimensionality as time evolves and can be effectively reversed. To this end, we concatenate multiple diffusion processes with different dimensions into an entire Markov chain by downsampling operations, while we elaborately design each process so that the information loss induced by downsampling is negligible. Fig. 3 illustrates this overall framework. The concatenation of different processes enables us to decrease the dimensionality, and the control on information loss ensures that downsampling operations are approximately reversible, such that the entire process can be reversed (discussed later in Sec. 4.2). To limit the information loss, we decompose the data into orthogonal components and control the attenuation of each component in the forward process of each concatenated diffusion, which we call Attenuated Diffusion Process (ADP). Once the lost data component induced by downsampling is attenuated to be small enough, the information loss will be negligible." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.591, + 0.892, + 0.636 + ], + "angle": 0, + "content": "Notation list. As a prerequisite for constructing each ADP, we first define a sequence of subspaces and other necessary notations as follows:" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.643, + 0.892, + 0.705 + ], + "angle": 0, + "content": "- \\(\\mathbb{S}_0 \\supseteq \\mathbb{S}_1 \\supseteq \\dots \\supseteq \\mathbb{S}_K\\) is a sequence of subspaces with decreasing dimensionality \\(d = \\bar{d}_0 > \\bar{d}_1 > \\dots > \\bar{d}_K\\), where \\(\\mathbb{S}_0 = \\mathbb{R}^d\\) is the original space, \\(K \\in \\mathbb{N}_+\\). For simplicity, \\(\\mathbb{S}_{K+1} \\triangleq \\{\\mathbf{0}\\}\\) and \\(\\bar{d}_{K+1} \\triangleq 0\\)." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.71, + 0.892, + 0.742 + ], + "angle": 0, + "content": "- \\( d_{i} = \\dim (\\mathbb{S}_{i} / \\mathbb{S}_{i + 1}) \\), \\( i = 0,1,\\dots ,K \\). Note that \\( d_{K} = \\dim (\\mathbb{S}_{K} / \\mathbb{S}_{K + 1}) = \\dim (\\mathbb{S}_{K}) \\)" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.747, + 0.892, + 0.796 + ], + "angle": 0, + "content": "- \\( \\mathbf{U}_0 = [\\hat{\\mathbf{U}}_0, \\dots, \\hat{\\mathbf{U}}_K] \\in \\mathbb{R}^{d \\times d} \\) is an orthogonal matrix, and column vectors of its sub-matrix \\( \\hat{\\mathbf{U}}_i \\in \\mathbb{R}^{d \\times d_i} \\) span subspace \\( \\mathbb{S}_i / \\mathbb{S}_{i+1} \\) for \\( i = 0, 1, \\dots, K \\)." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.802, + 0.892, + 0.853 + ], + "angle": 0, + "content": "- \\( \\mathbf{U}_k \\in \\mathbb{R}^{\\bar{d}_k \\times \\bar{d}_k} \\) is an orthogonal matrix for \\( k = 0,1,\\dots,K \\), and can be split as \\( \\mathbf{U}_k = [N_k, P_k] \\) when \\( k < K \\) where \\( N_k \\in \\mathbb{R}^{\\bar{d}_k \\times d_k}, P_k \\in \\mathbb{R}^{\\bar{d}_k \\times \\bar{d}_{k+1}} \\)." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.863, + 0.752, + 0.88 + ], + "angle": 0, + "content": "- \\(I_{n} \\in \\mathbb{R}^{n \\times n}\\) is an identity matrix." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.886, + 0.727, + 0.901 + ], + "angle": 0, + "content": "- \\(O_{n} \\in \\mathbb{R}^{n \\times n}\\) is a zero matrix." + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.643, + 0.892, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14309" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.126, + 0.09, + 0.852, + 0.271 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.276, + 0.895, + 0.334 + ], + "angle": 0, + "content": "Figure 3. Framework illustration of DVDP. Each row represents an Attenuated Diffusion Process (ADP), which controls the attenuation of each data component while adding noise. All \\( K + 1 \\) ADPs (\\( K = 2 \\) here) have different dimensions decreasing from top to bottom, and are concatenated by some simple operations to obtain our DVDP. In the forward process, the concatenation is achieved by downsampling operation, and in reverse process, it is the upsampling operation followed by adding a Gaussian noise." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.353, + 0.471, + 0.385 + ], + "angle": 0, + "content": "With the above definitions, we can first construct an ADP \\(\\mathbf{x}_t^0\\in \\mathbb{S}_0\\) for \\(t = 0,1,\\dots ,T\\) as" + }, + { + "type": "equation", + "bbox": [ + 0.15, + 0.395, + 0.469, + 0.457 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathbf {x} _ {t} ^ {0} = \\sum_ {i = 0} ^ {K} \\left(\\bar {\\lambda} _ {i, t} \\mathbf {v} _ {i} ^ {0} + \\bar {\\sigma} _ {i, t} \\mathbf {z} _ {i} ^ {0}\\right) \\tag {5} \\\\ = \\boldsymbol {U} _ {0} \\bar {\\boldsymbol {\\Lambda}} _ {0, t} \\boldsymbol {U} _ {0} ^ {T} \\mathbf {x} _ {0} ^ {0} + \\boldsymbol {U} _ {0} \\bar {\\boldsymbol {L}} _ {0, t} \\boldsymbol {U} _ {0} ^ {T} \\epsilon^ {0}, \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.462, + 0.47, + 0.648 + ], + "angle": 0, + "content": "where \\(\\mathbf{v}_i^0\\in \\mathbb{S}_i / \\mathbb{S}_{i + 1}\\) is the component of original data point \\(\\mathbf{x}_0^0\\) in subspace \\(\\mathbb{S}_i / \\mathbb{S}_{i + 1}\\), \\(\\bar{\\lambda}_{i,t}\\) controls the attenuation of \\(\\mathbf{v}_i^0\\) along timestep \\(t\\), \\(\\mathbf{z}_i^0\\) is the component of a standard Gaussian noise \\(\\epsilon^0\\in \\mathbb{R}^{\\bar{d}_0}\\) in the same subspace as \\(\\mathbf{v}_i^0\\) (i.e., \\(\\mathbb{S}_i / \\mathbb{S}_{i + 1}\\)), \\(\\bar{\\sigma}_{i,t}\\) is the standard deviation of \\(\\mathbf{z}_i^0\\), and \\(\\bar{\\Lambda}_{0,t}\\), \\(\\bar{\\pmb{L}}_{0,t}\\in \\mathbb{R}^{\\bar{d}_0\\times \\bar{d}_0}\\) are two diagonal matrices defined as \\(\\bar{\\Lambda}_{0,t} = \\mathrm{diag}(\\bar{\\lambda}_{0,t}\\pmb{I}_{d_0},\\bar{\\lambda}_{1,t}\\pmb{I}_{d_1},\\dots ,\\bar{\\lambda}_{K,t}\\pmb{I}_{d_K})\\) and \\(\\bar{\\pmb{L}}_{0,t} = \\mathrm{diag}(\\bar{\\sigma}_{0,t}\\pmb{I}_{d_0},\\bar{\\sigma}_{1,t}\\pmb{I}_{d_1},\\dots ,\\bar{\\sigma}_{K,t}\\pmb{I}_{d_K})\\). To control the attenuation of each data component \\(\\mathbf{v}_i^0\\), we require \\(\\bar{\\lambda}_{i,t}\\) to gradually decrease from 1 to approximate 0 for \\(i = 0,1,\\dots ,K - 1\\) as timestep \\(t\\) evolves. As for \\(\\bar{\\lambda}_{K,t}\\), it is not required to decrease (explained later after Eq. (8))." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.648, + 0.47, + 0.678 + ], + "angle": 0, + "content": "Starting from \\(\\mathbf{x}_t^0\\), we can recursively construct a dimensionality-decreasing sequence of ADPs" + }, + { + "type": "equation", + "bbox": [ + 0.093, + 0.689, + 0.47, + 0.752 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathbf {x} _ {t} ^ {k} = \\mathcal {D} _ {k} \\mathbf {x} _ {t} ^ {k - 1} = \\sum_ {i = k} ^ {K} \\left(\\bar {\\lambda} _ {i, t} \\mathbf {v} _ {i} ^ {k} + \\bar {\\sigma} _ {i, t} \\mathbf {z} _ {i} ^ {k}\\right) \\tag {6} \\\\ = \\boldsymbol {U} _ {k} \\bar {\\boldsymbol {\\Lambda}} _ {k, t} \\boldsymbol {U} _ {k} ^ {T} \\mathbf {x} _ {0} ^ {k} + \\boldsymbol {U} _ {k} \\bar {\\boldsymbol {\\mathcal {L}}} _ {k, t} \\boldsymbol {U} _ {k} ^ {T} \\epsilon^ {k}, 1 \\leq k \\leq K, \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.758, + 0.471, + 0.904 + ], + "angle": 0, + "content": "where \\(\\mathcal{D}_k:\\mathbb{R}^{\\bar{d}_{k - 1}}\\to \\mathbb{R}^{\\bar{d}_k}\\) is a linear surjection, which we call the \\(k\\) -th downsampling operator as it reduces the dimensionality of the operand (without ambiguity, we also use \\(\\mathcal{D}_k\\) to denote the corresponding matrix in \\(\\mathbb{R}^{\\bar{d}_k\\times \\bar{d}_{k - 1}}\\) \\(\\mathbf{v}_i^k = \\overline{\\mathcal{D}}_k\\mathbf{v}_i^0\\in \\overline{\\mathcal{D}}_k(\\mathbb{S}_i / \\mathbb{S}_{i + 1})\\) is the component of \\(\\mathbf{x}_0^k = \\overline{\\mathcal{D}}_k\\mathbf{x}_0^0\\in \\mathbb{R}^{\\bar{d}_k}\\) \\((\\overline{\\mathcal{D}}_k\\triangleq \\prod_{i = 1}^{k}\\mathcal{D}_i)\\) \\(\\mathbf{z}_i^k = \\overline{\\mathcal{D}}_k\\mathbf{z}_i^0\\in \\overline{\\mathcal{D}}_k(\\mathbb{S}_i / \\mathbb{S}_{i + 1})\\) is the component of a standard Gaussian noise \\(\\epsilon^k = \\overline{\\mathcal{D}}_k\\epsilon^0\\in \\mathbb{R}^{\\bar{d}_k}\\) \\(\\bar{\\Lambda}_{k,t} =\\) diag( \\(\\bar{\\lambda}_{k,t}\\pmb {I}_{d_k}\\) \\(\\bar{\\lambda}_{k + 1,t}\\pmb {I}_{d_{k + 1}},\\dots ,\\bar{\\lambda}_{K,t}\\pmb {I}_{d_K})\\in \\mathbb{R}^{\\bar{d}_k\\times \\bar{d}_k},\\)" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.352, + 0.892, + 0.416 + ], + "angle": 0, + "content": "\\(\\bar{\\pmb{L}}_{k,t} = \\mathrm{diag}(\\bar{\\sigma}_{k,t}\\pmb{I}_{d_k},\\bar{\\sigma}_{k + 1,t}\\pmb{I}_{d_{k + 1}},\\dots ,\\bar{\\sigma}_{K,t}\\pmb{I}_{d_K})\\in\\) \\(\\mathbb{R}^{\\bar{d}_k\\times \\bar{d}_k}\\) , and orthogonal matrix \\(U_{k}\\in \\mathbb{R}^{\\bar{d}_{k}\\times \\bar{d}_{k}}\\) consists of the last \\(\\bar{d}_k\\) columns of \\(\\mathcal{D}_k\\pmb{U}_{k - 1}\\) , i.e., \\(\\pmb {U}_k = \\mathcal{D}_k\\pmb {P}_{k - 1}\\) (note that this condition requires further restriction on \\(\\mathcal{D}_k\\)" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.417, + 0.892, + 0.462 + ], + "angle": 0, + "content": "Both Eqs. (5) and (6) can be derived from Markov chains with Gaussian kernels as (see Supplementary Material for the proof)" + }, + { + "type": "equation", + "bbox": [ + 0.508, + 0.474, + 0.892, + 0.493 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} _ {t} ^ {k} = \\boldsymbol {U} _ {k} \\boldsymbol {\\Lambda} _ {k, t} \\boldsymbol {U} _ {k} ^ {T} \\mathbf {x} _ {t - 1} ^ {k} + \\boldsymbol {U} _ {k} \\boldsymbol {L} _ {k, t} \\boldsymbol {U} _ {k} ^ {T} \\epsilon^ {k}, 0 \\leq k \\leq K, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.505, + 0.889, + 0.524 + ], + "angle": 0, + "content": "where \\(\\Lambda_{k,t} = \\bar{\\Lambda}_{k,t - 1}^{-1}\\bar{\\Lambda}_{k,t},L_{k,t} = (\\bar{L}_{k,t}^{2} - \\Lambda_{k,t}^{2}\\bar{L}_{k,t - 1}^{2})^{1 / 2}.\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.525, + 0.892, + 0.648 + ], + "angle": 0, + "content": "Now with the ADPs \\(\\{\\mathbf{x}_t^k\\}_{k = 0}^K\\) given by Eq. (7), we can construct the forward process of DVDP by merging different parts of \\(\\{\\mathbf{x}_t^k\\}_{k = 0}^K\\) in the following manner: consider a strictly increasing time sequence \\(T_{1},\\dots ,T_{K},T_{K + 1} = T,\\) if for each \\(k\\) satisfying \\(1\\leq k\\leq K\\) \\(\\bar{\\lambda}_{k - 1,T_k}\\) becomes small enough, then \\(\\mathbf{x}_{T_k}^{k - 1}\\) is downsampled by \\(\\mathcal{D}_k\\) to obtain \\(\\mathbf{x}_{T_k}^k\\) with lower dimensionality, and each \\(T_{k}\\) is a dimensionality turning point. The entire process can be expressed as" + }, + { + "type": "equation", + "bbox": [ + 0.57, + 0.658, + 0.892, + 0.713 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathbf {x} _ {0} ^ {0} \\longrightarrow \\mathbf {x} _ {1} ^ {0} \\quad \\longrightarrow \\dots \\longrightarrow \\mathbf {x} _ {T _ {1}} ^ {0} \\\\ \\xrightarrow {\\mathcal {D} _ {1}} \\mathbf {x} _ {T _ {1}} ^ {1} \\longrightarrow \\mathbf {x} _ {T _ {1} + 1} ^ {1} \\longrightarrow \\dots \\longrightarrow \\mathbf {x} _ {T _ {2}} ^ {1} \\tag {8} \\\\ \\end{array}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.571, + 0.712, + 0.824, + 0.754 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\begin{array}{c} \\bullet \\\\ \\bullet \\\\ \\bullet \\\\ \\bullet \\end{array} \\\\ \\xrightarrow {\\mathcal {D} _ {K}} \\mathbf {x} _ {T _ {K}} ^ {K} \\longrightarrow \\mathbf {x} _ {T _ {K} + 1} ^ {K} \\longrightarrow \\dots \\longrightarrow \\mathbf {x} _ {T} ^ {K}. \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.759, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Between two adjacent dimensionality turning points \\( T_{k-1} \\) and \\( T_{k} \\), \\( \\mathbf{x}_{t}^{k-1} \\) diffuses and attenuates data components \\( \\mathbf{v}_{i}^{k-1} \\), \\( i \\geq k-1 \\), which keeps the dimensionality \\( \\bar{d}_{k-1} \\). When it comes to \\( T_{k} \\), \\( \\mathbf{x}_{T_{k}}^{k-1} \\xrightarrow{\\mathcal{D}_{k}} \\mathbf{x}_{T_{k}}^{k} \\) decreases the dimension from \\( \\bar{d}_{k-1} \\) to \\( \\bar{d}_{k} \\). After the last dimensionality turning point \\( T_{k} \\), \\( \\mathbf{x}_{t}^{K} \\) can just evolve as conventional diffusion without data component attenuation. Thus, the entire process in Eq. (8) decreases the dimensionality by \\( K \\) times from \\( \\bar{d}_{0} = d \\) to \\( \\bar{d}_{K} \\). It should be noted that process" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "14310" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.473, + 0.222 + ], + "angle": 0, + "content": "in Eq. (8) is also Markovian since each diffusion subprocess \\(\\mathbf{x}_{T_{k - 1}}^{k - 1}\\rightarrow \\mathbf{x}_{T_k}^{k - 1}\\) is Markovian, and the result of each downsampling operation \\(\\mathbf{x}_{T_k}^k\\) is uniquely determined by the previous state \\(\\mathbf{x}_{T_k}^{k - 1}\\). Also note that each downsampling operation \\(\\mathcal{D}_k\\) loses little information because of small \\(\\bar{\\lambda}_{k - 1,T_k}\\) which is a controllable hyperparameter. For better understanding, consider the relationship between \\(\\mathbf{x}_{T_k}^{k - 1}\\) and \\(\\mathbf{x}_{T_k}^k\\) derived from Eq. (6)" + }, + { + "type": "equation", + "bbox": [ + 0.1, + 0.226, + 0.47, + 0.265 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} _ {T _ {k}} ^ {k - 1} = \\mathcal {D} _ {k} ^ {T} \\mathbf {x} _ {T _ {k}} ^ {k} + \\underbrace {\\bar {\\lambda} _ {k - 1 , T _ {k}} \\mathbf {v} _ {k - 1} ^ {k - 1}} _ {\\text {d a t a c o m p o n e n t}} + \\underbrace {\\bar {\\sigma} _ {k - 1 , T _ {k}} \\mathbf {z} _ {k - 1} ^ {k - 1}} _ {\\text {n o i s e c o m p o n e n t}}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.266, + 0.473, + 0.391 + ], + "angle": 0, + "content": "where \\(\\mathcal{D}_k^T\\) is the transpose of matrix \\(\\mathcal{D}_k\\), named as the \\(k\\)-th upsampling operator. From Eq. (9), it is clear that \\(\\mathbf{x}_{T_k}^k\\) actually loses two terms compared with \\(\\mathbf{x}_{T_k}^{k-1}\\): 1) data component \\(\\bar{\\lambda}_{k-1,T_k}\\mathbf{v}_{k-1}^{k-1}\\) which is informative but negligible as \\(\\bar{\\lambda}_{k-1,T_k}\\) is set to be small enough, and 2) noise component \\(\\bar{\\sigma}_{k-1,T_k}\\mathbf{z}_{k-1}^{k-1}\\) that is non-informative and can be compensated in the reverse process, as we will discuss in Sec. 4.2." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.399, + 0.413, + 0.417 + ], + "angle": 0, + "content": "4.2. Reverse Process Approximating DVDP" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.423, + 0.47, + 0.528 + ], + "angle": 0, + "content": "In this section, we will derive an approximate reverse process, which induces a data generation process with progressively growing dimensionality. The approximation error will be discussed in Sec. 4.3, and we can find that it actually converges to zero. Loss function will also be given at the end of this section. Implementation details of training and sampling can be found in Supplementary Material." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.528, + 0.47, + 0.603 + ], + "angle": 0, + "content": "Reverse transition. Since DVDP is a sequence of fixed-dimensionality diffusion processes connected by downsampling operations at dimensionality turning points, we consider reverse transition kernels between and at dimensionality turning points separately." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.604, + 0.47, + 0.709 + ], + "angle": 0, + "content": "For reverse transition between two adjacent dimensionality turning points, i.e., \\( p_{\\theta}(\\mathbf{x}_{t - 1}^{k}|\\mathbf{x}_{t}^{k}) \\) with \\( T_{k - 1}\\leq t\\leq T_{k} \\) for \\( k\\in [1,K + 1] \\), it can be defined as a Gaussian kernel \\( p_{\\theta}(\\mathbf{x}_{t - 1}^{k}|\\mathbf{x}_{t}^{k}) = \\mathcal{N}(\\mathbf{x}_{t - 1}^{k};\\pmb{\\mu}_{\\theta}(\\mathbf{x}_{t}^{k},t),\\pmb{\\Sigma}_{t}) \\). As in DDPM [6], the covariance matrices \\( \\pmb{\\Sigma}_t \\) are set to untrained time-dependent constants, and the mean term \\( \\pmb{\\mu}_{\\theta}(\\mathbf{x}_{t}^{k},t) \\) is defined as (see Supplementary Material for details)" + }, + { + "type": "equation", + "bbox": [ + 0.154, + 0.715, + 0.47, + 0.755 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\boldsymbol {\\mu} _ {\\theta} = \\tilde {\\boldsymbol {\\mu}} _ {k, t} \\left(\\mathbf {x} _ {t} ^ {k}, U _ {k} \\bar {\\boldsymbol {\\Lambda}} _ {k, t} ^ {- 1} \\boldsymbol {U} _ {k} ^ {T} \\mathbf {x} _ {t} ^ {k} \\right. \\tag {10} \\\\ - \\boldsymbol {U} _ {k} \\bar {\\boldsymbol {\\Lambda}} _ {k, t} ^ {- 1} \\bar {\\boldsymbol {L}} _ {k, t} \\boldsymbol {U} _ {k} ^ {T} \\boldsymbol {\\epsilon} _ {\\theta} \\left(\\boldsymbol {x} _ {t} ^ {k}, t\\right), \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.757, + 0.47, + 0.802 + ], + "angle": 0, + "content": "where \\(\\tilde{\\pmb{\\mu}}_{k,t}(\\cdot ,\\cdot)\\) is the mean function of forward process posterior \\(q(\\mathbf{x}_{t - 1}^k |\\mathbf{x}_t^k,\\mathbf{x}_0^k) = \\mathcal{N}(\\mathbf{x}_{t - 1}^k;\\tilde{\\pmb{\\mu}}_{k,t}(\\mathbf{x}_t^k,\\mathbf{x}_0^k),\\tilde{\\pmb{\\Sigma}}_{k,t})\\) and \\(\\epsilon_{\\theta}\\) represents a trainable network." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.803, + 0.47, + 0.879 + ], + "angle": 0, + "content": "For reverse transition at dimensionality turning points, i.e., \\( p_{\\theta}(\\mathbf{x}_{T_k}^{k - 1}|\\mathbf{x}_{T_k}^k) \\) for \\( k\\in [1,K] \\), the corresponding forward transitions barely lose information as illustrated by Eq. (9) in Sec. 4.1, thus \\( \\mathbf{x}_{T_k}^k\\to \\mathbf{x}_{T_k}^{k - 1} \\) can be approximately achieved without any trainable network as" + }, + { + "type": "equation", + "bbox": [ + 0.113, + 0.883, + 0.47, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} _ {T _ {k}} ^ {k - 1} = \\mathcal {D} _ {k} ^ {T} \\mathbf {x} _ {T _ {k}} ^ {k} + \\boldsymbol {U} _ {k - 1} \\Delta \\boldsymbol {L} _ {k - 1} \\boldsymbol {U} _ {k - 1} ^ {T} \\epsilon^ {k - 1}, \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.089, + 0.892, + 0.232 + ], + "angle": 0, + "content": "where \\(\\mathcal{D}_k^T\\in \\mathbb{R}^{\\bar{d}_k\\times \\bar{d}_{k - 1}}\\) is the upsampling operator, and \\(\\Delta L_{k - 1} = \\mathrm{diag}(\\bar{\\sigma}_{k - 1,T_k}\\pmb{I}_{d_{k - 1}},\\pmb{O}_{\\bar{d}_k})\\) represents the standard deviation of the added Gaussian noise \\(\\epsilon^{k - 1}\\in \\mathbb{R}^{\\bar{d}_{k - 1}}\\). Eq. (11) can be understood as: we first upsample \\(\\mathbf{x}_{T_k}^k\\), then add a Gaussian noise in compensation for the lost noise component in the forward downsampling operation, i.e., \\(\\bar{\\sigma}_{k - 1,T_k}\\mathbf{z}_{k - 1}^{k - 1}\\) in Eq. (9). The approximation error comes from neglecting data component \\(\\bar{\\lambda}_{k - 1,T_k}\\mathbf{v}_{k - 1}^{k - 1}\\), and will be analyzed later in Sec. 4.3." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.233, + 0.892, + 0.278 + ], + "angle": 0, + "content": "Loss function. Similar with DDPM [6], a loss function can be derived from a weighted variational bound as (see Supplementary Material for details)" + }, + { + "type": "equation", + "bbox": [ + 0.508, + 0.288, + 0.892, + 0.311 + ], + "angle": 0, + "content": "\\[\nL (\\theta) = \\mathbb {E} _ {k} \\mathbb {E} _ {\\mathbf {x} _ {0} ^ {k}, \\epsilon^ {k}, t \\sim \\mathcal {U} _ {k}} \\left[ \\left\\| \\epsilon^ {k} - \\epsilon_ {\\theta} \\left(\\mathbf {x} _ {t} ^ {k} \\left(\\mathbf {x} _ {0} ^ {k}, \\epsilon^ {k}\\right), t\\right) \\right\\| ^ {2} \\right], \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.321, + 0.892, + 0.383 + ], + "angle": 0, + "content": "where \\(\\mathcal{U}_k = \\mathcal{U}\\big((T_k,T_{k + 1}]\\big)\\) is a discrete uniform distribution between \\(T_{k}\\) (exclusive) and \\(T_{k + 1}\\) (inclusive), and \\(\\mathbf{x}_t^k (\\mathbf{x}_0^k,\\epsilon^k)\\) represents the forward \\(\\mathbf{x}_t^k\\) determined by \\(\\mathbf{x}_0^k\\) and \\(\\epsilon^k\\) given in Eq. (6)." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.392, + 0.652, + 0.408 + ], + "angle": 0, + "content": "4.3. Error Analysis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.415, + 0.892, + 0.523 + ], + "angle": 0, + "content": "In Sec. 4.2, we mention that the reverse process is just an approximation of the forward DVDP at each dimensionality turning point \\( T_{k} \\). In this section, we will measure this approximation error in probability sense, i.e., the difference between the real forward distribution \\( q(\\mathbf{x}_{T_k}^{k - 1}) \\) and the reverse distribution \\( p(\\mathbf{x}_{T_k}^{k - 1}) \\) under proper assumptions, and will find that this difference converges to zero." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.524, + 0.892, + 0.599 + ], + "angle": 0, + "content": "To measure the difference between two distributions, we use Jensen-Shannon Divergence (JSD) as a metric. Under this metric, upper bound of the approximation error can be derived from Proposition 1 (see Supplementary Material for proof):" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.605, + 0.892, + 0.712 + ], + "angle": 0, + "content": "Proposition 1 Assume \\( p_1(\\pmb{x}|\\pmb{x}_0) \\), \\( p_2(\\pmb{x}|\\pmb{x}_0) \\) are two Gaussians such that \\( p_1(\\pmb{x}|\\pmb{x}_0) = \\mathcal{N}(\\pmb{x};\\pmb{A}_1\\pmb{x}_0,\\pmb{\\Sigma}) \\) and \\( p_2(\\pmb{x}|\\pmb{x}_0) = \\mathcal{N}(\\pmb{x};\\pmb{A}_2\\pmb{x}_0,\\pmb{\\Sigma}) \\), where positive semi-definite matrices \\( A_1, A_2 \\) satisfy \\( A_1\\succeq A_2\\succeq 0 \\), covariance matrix \\( \\pmb{\\Sigma} \\) is positive definite, and the support of distribution \\( p(\\pmb{x}_0) \\) is bounded, then Jensen-Shannon Divergence (JSD) of the two marginal distributions \\( p_1(\\pmb{x}) \\) and \\( p_2(\\pmb{x}) \\) satisfies" + }, + { + "type": "equation", + "bbox": [ + 0.534, + 0.716, + 0.892, + 0.778 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\operatorname {J S D} \\left(p _ {1} \\mid \\mid p _ {2}\\right) \\leq \\frac {\\sqrt {2}}{2} e ^ {- \\frac {1}{2}} B \\left(2 \\sqrt {2} + \\frac {V _ {d} (r)}{\\left(2 \\pi\\right) ^ {\\frac {d}{2}}}\\right) \\tag {13} \\\\ \\cdot \\left\\| \\boldsymbol {\\Sigma} ^ {- \\frac {1}{2}} \\left(\\boldsymbol {A} _ {1} - \\boldsymbol {A} _ {2}\\right) \\right\\| _ {2}, \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.789, + 0.892, + 0.835 + ], + "angle": 0, + "content": "where \\(B\\) is the upper bound of \\(\\| \\pmb{x}_0\\| _2\\), \\(V_{d}(\\cdot)\\) is the volume of a \\(d\\)-dimensional sphere with respect to the radius, and \\(r = 2B\\| \\Sigma^{-\\frac{1}{2}}A_1\\| _2\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.838, + 0.892, + 0.901 + ], + "angle": 0, + "content": "With Proposition 1, the upper bound of JSD between the forward distribution \\( q(\\mathbf{x}_{T_k}^{k - 1}) \\) and the reverse distribution \\( p(\\mathbf{x}_{T_k}^{k - 1}) \\) can be obtained by Theorem 1 (see Supplementary Material for proof)" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "14311" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.175 + ], + "angle": 0, + "content": "Theorem 1 (Reverse Process Error) Assume \\(0 < k \\leq K\\), \\(q(\\mathbf{x}_{T_k}^{k-1})\\) and \\(q(\\mathbf{x}_{T_k}^k)\\) are defined by Eqs. (5) and (6), \\(p(\\mathbf{x}_{T_k}^{k-1})\\) is the marginal distribution of \\(q(\\mathbf{x}_{T_k}^k)p(\\mathbf{x}_{T_k}^{k-1}|\\mathbf{x}_{T_k}^k)\\) where \\(p(\\mathbf{x}_{T_k}^{k-1}|\\mathbf{x}_{T_k}^k)\\) is defined by Eq. (11), and \\(\\| \\mathbf{x}_0\\|_2 \\leq \\sqrt{d}\\), then" + }, + { + "type": "equation", + "bbox": [ + 0.11, + 0.18, + 0.47, + 0.24 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\xi_ {1} \\leq \\frac {\\sqrt {2}}{2} e ^ {- \\frac {1}{2}} \\sqrt {d} \\left(2 \\sqrt {2} + \\frac {V _ {d} (r)}{(2 \\pi) ^ {\\frac {d}{2}}}\\right) \\frac {\\bar {\\lambda} _ {k - 1 , T _ {k}}}{\\bar {\\sigma} _ {k - 1 , T _ {k}}} \\tag {14} \\\\ = o \\left(\\bar {\\lambda} _ {k - 1, T _ {k}}\\right), \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.252, + 0.469, + 0.295 + ], + "angle": 0, + "content": "where \\(\\xi_1 \\triangleq \\mathrm{JSD}(q(\\mathbf{x}_{T_k}^{k-1})||p(\\mathbf{x}_{T_k}^{k-1})), \\text{ and } r = 2\\sqrt{d}\\max_{k-1 \\leq i \\leq K} \\frac{\\bar{\\lambda}_{i,T_k}}{\\bar{\\sigma}_{i,T_k}}.\\)" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.299, + 0.469, + 0.392 + ], + "angle": 0, + "content": "Note that the assumption \\(\\| \\mathbf{x}_0\\| _2\\leq \\sqrt{d}\\) can be satisfied for image data, since pixel values can be normalized in \\([-1,1]\\). Thus, Theorem 1 claims that \\(\\xi_{1}\\) can be arbitrarily small as \\(\\bar{\\lambda}_{k - 1,T_k}\\to 0\\) if we can get an exact \\(q(\\mathbf{x}_{T_k}^{k - 1})\\) by reverse process. It means that the approximation error caused by stepping over \\(T_{k}\\) can be small enough." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.401, + 0.398, + 0.417 + ], + "angle": 0, + "content": "4.4. Comparison with Subspace Diffusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.424, + 0.469, + 0.56 + ], + "angle": 0, + "content": "To reduce the dimensionality of latent space in diffusion models, subspace diffusion is proposed to model in a low-dimensional subspace at high noise levels, and keep the original full-dimensional network at low noise levels [10]. This can also be seen as a concatenation of multiple diffusion processes with different dimensionality like our DVDP, but without controllable attenuation on each data component. Each concatenated processes is just conventional isotropic diffusion." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.562, + 0.469, + 0.78 + ], + "angle": 0, + "content": "Thus, subspace diffusion can be seen as a special case of our DVDP with \\(\\bar{\\lambda}_t \\triangleq \\bar{\\lambda}_{0,t} = \\bar{\\lambda}_{1,t} = \\dots = \\bar{\\lambda}_{K,t}\\) and \\(\\bar{\\sigma}_t \\triangleq \\bar{\\sigma}_{0,t} = \\bar{\\sigma}_{1,t} = \\dots = \\bar{\\sigma}_{K,t}\\), which limits the choice of dimensionality turning points. This limitation can be further explained by Eq. (9): at dimensionality turning point \\(T_k\\) in the forward process, \\(\\mathbf{x}_{T_k}^{k-1}\\) will lose an informative data component \\(\\bar{\\lambda}_{k-1,T_k} \\mathbf{v}_{k-1}^{k-1}\\) and a noninformative noise component \\(\\bar{\\sigma}_{k-1,T_k} \\mathbf{z}_{k-1}^{k-1}\\). To safely neglect the data component in the reverse transition, it requires that \\(\\bar{\\lambda}_{k-1,T_k} / \\bar{\\sigma}_{k-1,T_k} \\ll \\| \\mathbf{z}_{k-1}^{k-1} \\| / \\| \\mathbf{v}_{k-1}^{k-1} \\|\\). For subspace diffusion, it means that the consistent \\(\\bar{\\lambda}_t / \\bar{\\sigma}_t\\) for components in all subspaces should be small enough, which usually indicates a large \\(T_k\\), i.e., a large number of diffusion steps in high dimensional space." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Therefore, as claimed in [10], the choice of \\( T_{k} \\) should balance two factors: 1) smaller \\( T_{k} \\) reduces the number of reverse diffusion steps occurring at higher dimensionality, whereas 2) larger \\( T_{k} \\) makes the reverse transition at \\( T_{k} \\) more accurate. Although [10] additionally proposes to compensate the loss of data component by adding an extra Gaussian noise besides compensation for the noise component, this trade-off still exists." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.167 + ], + "angle": 0, + "content": "However, our DVDP can set much smaller \\( T_{k} \\) with little loss in accuracy, which benefits from the controllable attenuation for each data component. Theorem 1 supports this advantage theoretically, and experimental results in Sec. 5.3 further demonstrate it." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.18, + 0.633, + 0.197 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.205, + 0.892, + 0.43 + ], + "angle": 0, + "content": "In this section, we show that our DVDP can speed up both training and inference of diffusion models while achieving competitive performance. Besides, thanks to the varied dimension, DVDP is able to generate high-quality and high-resolution images from a low-dimensional subspace and exceeds existing methods including scoreSDE [28] and Cascaded Diffusion Models (CDM) [7] on FFHQ \\(1024^{2}\\). Specifically, we first introduce our experimental setup in Sec. 5.1. Then we compare our DVDP with existing alternatives on several widely evaluated datasets in terms of visual quality and modeling efficiency in Sec. 5.2. After that, we compare our DVDP with Subspace Diffusion [10], a closely related work proposed recently, in Sec. 5.3. Finally, we implement necessary ablation studies in the last Sec. 5.4." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.44, + 0.691, + 0.456 + ], + "angle": 0, + "content": "5.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.463, + 0.892, + 0.553 + ], + "angle": 0, + "content": "Datasets. In order to verify that DVDP is widely applicable, we use six image datasets covering various classes and a wide range of resolutions from 32 to 1024. To be specific, we implement DVDP on CIFAR10 \\(32^2\\) [12], LSUN Bedroom \\(256^2\\) [32], LSUN Church \\(256^2\\), LSUN Cat \\(256^2\\), FFHQ \\(256^2\\), and FFHQ \\(1024^2\\) [11]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.554, + 0.892, + 0.825 + ], + "angle": 0, + "content": "Implementation details. We adopt the UNet improved by [2] which achieves better performance than the traditional version [6]. Since most baseline methods adopt a single UNet network for all timesteps in the whole diffusion process, our DVDP also keeps this setting, except the comparison with Subspace Diffusion in Sec. 5.3, which takes two networks for different generation stages [10]. In principle, the network structure of our DVDP is kept the same as the corresponding baseline. However, when resolution comes to \\(1024 \\times 1024\\), the UNet in conventional diffusion models should be deep enough to contain sufficient downsampling blocks, thus to obtain embeddings with proper size (usually \\(4 \\times 4\\) or \\(8 \\times 8\\)) in the bottleneck layer. On the contrary, our DVDP does not need such a deep network since the generation starts from a low resolution noise (\\(64 \\times 64\\) in our case). Thus we only maintain a similar amount of parameters but use a different hyperparameter setting on FFHQ \\(1024^2\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We set the number of timesteps \\( T = 1,000 \\) in all of our experiments. For DVDP, we reduce the dimensionality by \\( \\frac{1}{4} \\) (i.e., \\( h \\times w \\to \\frac{h}{2} \\times \\frac{w}{2} \\) for image resolution) when the timestep \\( t \\) reaches a dimensionality turning point. For simplicity, we adopt \\( \\mathbb{T} \\triangleq \\{T_1, \\dots, T_K\\} \\). For CIFAR10" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14312" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.892, + 0.119 + ], + "angle": 0, + "content": "Table 1. Quantitative comparison between DDPM [6] and our DVDP on various datasets regarding image quality and model efficiency. * indicates our reproduced DDPM. Both \\( {\\mathrm{{DDMP}}}^{ * } \\) and our DVDP adopt the improved UNet [2] for a fair comparison." + }, + { + "type": "table", + "bbox": [ + 0.078, + 0.124, + 0.895, + 0.389 + ], + "angle": 0, + "content": "
DatasetMethodFID (50k)↓Training Speed (sec/iter)Training Speed UpSampling Speed (sec/sample)Sampling Speed Up
CIFAR10 32 × 32DDPM3.17----
DDPM*3.160.18-0.34-
DVDP3.240.151.2×0.261.3×
LSUN Bedroom 256 × 256DDPM6.36----
DDPM*5.740.99-12.2-
DVDP4.880.452.2×5.012.4×
LSUN Church 256 × 256DDPM7.89----
DDPM*7.540.99-12.2-
DVDP7.030.452.2×5.012.4×
LSUN Cat 256 × 256DDPM19.75----
DDPM*18.110.99-12.2-
DVDP16.500.452.2×5.012.4×
FFHQ 256 × 256DDPM*8.330.99-12.2-
DVDP8.030.452.2×5.012.4×
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.412, + 0.469, + 0.472 + ], + "angle": 0, + "content": "\\(32^{2}\\), we set \\(\\mathbb{T} = \\{600\\}\\), indicating that the resolution is decreased from \\(32 \\times 32\\) to \\(16 \\times 16\\) when \\(t = 600\\). Similarly, we set \\(\\mathbb{T} = \\{300, 600\\}\\) for all \\(256^{2}\\) datasets and \\(\\mathbb{T} = \\{200, 400, 600, 800\\}\\) for FFHQ \\(1024^{2}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.474, + 0.47, + 0.548 + ], + "angle": 0, + "content": "In all of our experiments, the noise schedule of DVDP is an adapted version of linear schedule [6], which is suitable for DVDP and keeps a comparable signal-to-noise ratio (SNR) with the original version (see Supplementary Material for details)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.55, + 0.47, + 0.716 + ], + "angle": 0, + "content": "Evaluation metrics. For sample quality, we calculate the FID score [5] on 50k samples, except for FFHQ \\(1024^{2}\\) with 10k samples due to a much slower sampling. As for training and sampling speed, both of them are evaluated on a single NVIDIA A100. Training speed is measured by the mean time of each iteration (estimated over 4,000 iterations), and sampling speed is measured by the mean time of each sample (estimated over 100 batches). The training batch size and sampling batch size are 128, 256 respectively for CIFAR10 \\(32^{2}\\), and 24, 64 respectively for other \\(256^{2}\\) datasets." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.726, + 0.419, + 0.743 + ], + "angle": 0, + "content": "5.2. Visual Quality and Modeling Efficiency." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Comparison with existing alternatives. We compare DVDP with other alternatives here to show that DVDP has the capability of acceleration while maintaining a reasonable or even better visual quality. For the sake of fairness, we reproduce DDPM using the same network structure as DVDP with the same hyperparameters, represented as \\(\\mathrm{DDPM^{*}}\\). Some samples generated by our DVDP are shown in Fig. 1, and Tab. 1 summarizes the quantitative results on CIFAR10, FFHQ \\(256^{2}\\), and three LSUN datasets. The results show that our proposed DVDP achieves better FID" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.412, + 0.892, + 0.548 + ], + "angle": 0, + "content": "scores on all of the \\(256^{2}\\) datasets, demonstrating an improved sample quality. Meanwhile, DVDP enjoys improved training and sampling speeds. Specifically, DDPM and \\(\\mathrm{DDPM}^*\\) spend \\(2.2\\times\\) time as DVDP when training the same epochs, and they spend \\(2.4\\times\\) time in sampling. Although the superiority of DVDP is obvious on all \\(256^{2}\\) datasets, it becomes indistinct when it comes to CIFAR10 \\(32^{2}\\), which is reasonable considering the small pixel redundancy and low resolution of images in CIFAR10." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.549, + 0.893, + 0.835 + ], + "angle": 0, + "content": "Towards high-resolution image synthesis. It is hard for diffusion models to generate high-resolution images directly. This can attribute to the curse of dimensionality: the support of high-dimensional data with large noise can only be visited a small part during training, leading to inaccurate prediction on unseen points [10]. Score-SDE [28] tries this task by directly training a single diffusion model, but the sample quality is far from reasonable. CDM performs better in high-resolution image synthesis and obtains impressive results [21, 24]. It first generates low-resolution images, followed by several conditional diffusion models as superresolution modules. We compare DVDP with score-SDE and CDM on FFHQ \\(1024^{2}\\) in Tab. 2. The FID of score-SDE is evaluated on samples generated from their official code and model weight without acceleration, and CDM is implemented by three cascaded diffusions as in [21]. Our DVDP is sampled by both DDPM method with 1000 steps and DDIM method with 675 steps. The results show that DVDP beats both score-SDE and CDM." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.847, + 0.822, + 0.864 + ], + "angle": 0, + "content": "5.3. Comparison with Subspace Diffusion" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Subspace diffusion [10] can also vary dimensionality during the diffusion process. As mentioned in [10] and also" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14313" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.468, + 0.117 + ], + "angle": 0, + "content": "Table 2. Synthesis performance of different models trained on FFHQ \\( {1024} \\times {1024} \\) ." + }, + { + "type": "table", + "bbox": [ + 0.091, + 0.12, + 0.451, + 0.244 + ], + "angle": 0, + "content": "
Model#Params (M)NFEFID (10k)↓
Score-SDE100200052.40
CDM98152524.7
165152517.35
286152517.24
DVDP10567512.43
100010.46
" + }, + { + "type": "image", + "bbox": [ + 0.107, + 0.253, + 0.435, + 0.404 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.409, + 0.468, + 0.451 + ], + "angle": 0, + "content": "Figure 4. Quantitative comparison between subspace diffusion [10] and our DVDP on CelebA \\(64 \\times 64\\) regarding different dimensionality turning point \\(T_{1}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.471, + 0.468, + 0.577 + ], + "angle": 0, + "content": "discussed in Sec. 4.4, dimensionality turning point \\( T_{k} \\) in subspace diffusion should be large enough to maintain the sample quality. However, large \\( T_{k} \\) means more diffusion steps in high dimensional space, which will impair the advantage of such dimensionality-varying method, e.g., less acceleration in sampling. Thus, \\( T_{k} \\) is expected to be as small as possible while maintaining the sampling quality." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.578, + 0.468, + 0.819 + ], + "angle": 0, + "content": "Considering that the dimensionality decreases only once, i.e., \\( K = 1 \\), and only one dimensionality turning point \\( T_{1} \\), we compare DVDP with subspace diffusion when the downsampling is carried out at different \\( T_{1} \\). Since the subspace diffusion is only implemented on continuous timesteps in [10], we reproduce it on discrete timesteps similar as DDPM and use the reproduced version as a baseline. Fig. 4 illustrates that DVDP is consistently better with regard to sample quality on CelebA \\( 64 \\times 64 \\) [16] when \\( T_{1} \\) varies, where the advantage gets larger when \\( T_{1} \\) gets smaller. In addition, some samples of DVDP and subspace diffusion are shown in Fig. 5, where the sample quality of subspace diffusion is apparently worse than that of DVDP especially when \\( T_{1} \\) is small. In conclusion, DVDP is much more insensitive to the dimensionality turning point than subspace diffusion." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.832, + 0.231, + 0.848 + ], + "angle": 0, + "content": "5.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.468, + 0.901 + ], + "angle": 0, + "content": "We implement ablation study in this section to show that DVDP is able to keep effective when the number of downsampling, i.e., \\( K \\), grows. Specifically, we train DVDP" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.089, + 0.887, + 0.116 + ], + "angle": 0, + "content": "Table 3. Ablation study on the number of downsampling times on CelebA \\(128 \\times 128\\)." + }, + { + "type": "table", + "bbox": [ + 0.512, + 0.118, + 0.875, + 0.245 + ], + "angle": 0, + "content": "
Downsampling times K0123
FID (50k)6.145.996.106.37
Training Speed Up-1.98×2.24×2.25×
Sampling Speed Up-2.12×2.36×2.43×
" + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.262, + 0.872, + 0.395 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.409, + 0.888, + 0.451 + ], + "angle": 0, + "content": "Figure 5. Qualitative comparison between subspace diffusion [10] and our DVDP on CelebA \\(64 \\times 64\\). \\(T_{1}\\) denotes the dimensionality turning point." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.471, + 0.892, + 0.593 + ], + "angle": 0, + "content": "models on four different settings of dimensionality turning points \\(\\mathbb{T}\\) for \\(K = 0,1,2,3\\). When \\(K = 1\\), \\(\\mathbb{T}\\) is set to \\(\\{250\\}\\). Similarly, when \\(K = 2\\) and \\(K = 3\\), \\(\\mathbb{T}\\) is set to \\(\\{250,500\\}\\) and \\(\\{250,500,750\\}\\), respectively. Furthermore, we use the same noise schedule for these four different settings. Tab. 3 shows that when the number of downsampling grows, the sample quality preserves a reasonable level, indicating that DVDP can vary dimensionality for multiple times." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.608, + 0.619, + 0.623 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.634, + 0.892, + 0.859 + ], + "angle": 0, + "content": "This paper generalizes the traditional diffusion process to a dimensionality-varying diffusion process (DVDP). The proposed DVDP has both theoretical and experimental contributions. Theoretically, we carefully decompose the signal in the diffusion process into multiple orthogonal dynamic-attenuated components. With a rigorously deduced approximation strategy, this then leads to a novel reverse process that generates images from much lower dimensional noises compared with the image resolutions. This design allows much higher training and sampling speed of the diffusion models with on-par or even better synthesis performance, and superior performance in synthesizing large-size images of \\(1024 \\times 1024\\) resolution compared with classic methods. The results in this work can promote the understanding and applications of diffusion models in broader scenarios." + }, + { + "type": "page_footnote", + "bbox": [ + 0.499, + 0.863, + 0.892, + 0.899 + ], + "angle": 0, + "content": "This work was supported in part by the National Key R&D Program of China under Grant 2022YFA1005000, in part by the NSFC under Grant 61701304." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14314" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.169 + ], + "angle": 0, + "content": "[1] Fan Bao, Chongxuan Li, Jun Zhu, and Bo Zhang. Analytic-DPM: an analytic estimate of the optimal reverse variance in diffusion probabilistic models. Int. Conf. Learn. 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Syst., pages 16280-16291, 2021. 2" + }, + { + "type": "list", + "bbox": [ + 0.079, + 0.092, + 0.47, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "14316" + } + ] +] \ No newline at end of file diff --git a/2023/Dimensionality-Varying Diffusion Process/6d385449-d42c-4da7-84b2-17c8988b13c5_origin.pdf b/2023/Dimensionality-Varying Diffusion Process/6d385449-d42c-4da7-84b2-17c8988b13c5_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..ce1c6ee7dd15ccadaafaae2c3a71e5abc0bc839d --- /dev/null +++ b/2023/Dimensionality-Varying Diffusion Process/6d385449-d42c-4da7-84b2-17c8988b13c5_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:95d5ba37f196629a5f5990103742f7de9ba0550af882f799507298784cc903af +size 1746340 diff --git a/2023/Dimensionality-Varying Diffusion Process/full.md b/2023/Dimensionality-Varying Diffusion Process/full.md new file mode 100644 index 0000000000000000000000000000000000000000..9f0d482d0b44bade992c5bb8524aeff3bd58b9a0 --- /dev/null +++ b/2023/Dimensionality-Varying Diffusion Process/full.md @@ -0,0 +1,301 @@ +# Dimensionality-Varying Diffusion Process + +Han Zhang $^{1,4\dagger}$ Ruili Feng $^{2,4}$ Zhantao Yang $^{1,4\dagger}$ Lianghua Huang $^{4}$ Yu Liu $^{4}$ Yifei Zhang $^{1,4\dagger}$ Yujun Shen $^{3}$ Deli Zhao $^{4}$ Jingren Zhou $^{4}$ Fan Cheng $^{1*}$ $^{1}$ Shanghai Jiao Tong University $^{2}$ University of Science and Technology of China $^{3}$ Ant Group $^{4}$ Alibaba Group + +{hzhang9617, ruilifengustc, ztyangl96, shenyujun0302, zhaodeli}@gmail.com + +{xuangen.hlh, ly103369, jingren.zhou}@alibaba-inc.com qidouxiong619@sjtu.edu.cn chengfan@sjtu.edu.cn + +![](images/7259c99e9a8a2dcab2a5aa8585e87ef41a3825ac575d578ff728afadc6526dee.jpg) +Figure 1. Synthesized samples on various datasets, including FFHQ (1024 $^2$ and 256 $^2$ ), LSUN Church (256 $^2$ ), LSUN Bedroom (256 $^2$ ), LSUN Cat (256 $^2$ ) and CIFAR10 (32 $^2$ ). All these samples are generated from a 64 $^2$ noise except CIFAR10 from 16 $^2$ , while conventional diffusion models can only start from a noise with the same dimension as the final sample. + +# Abstract + +Diffusion models, which learn to reverse a signal destruction process to generate new data, typically require the signal at each step to have the same dimension. We argue that, considering the spatial redundancy in image signals, there is no need to maintain a high dimensionality in the evolution process, especially in the early generation phase. To this end, we make a theoretical generalization of the forward diffusion process via signal decomposition. Concretely, we manage to decompose an image into multiple orthogonal components and control the attenuation of each component when perturbing the image. That way, along with the noise strength increasing, we are able to diminish those inconsequential components and thus use a lower-dimensional signal to represent the source, barely losing information. Such a reformulation allows to vary dimensions in both training and inference of diffusion models. Extensive experiments on a range of datasets suggest that our approach substantially reduces the computational cost and achieves on-par or even better synthesis performance compared to baseline methods. We also show that our strategy facilitates high-resolution image synthesis and improves FID of diffusion model trained on FFHQ at $1024 \times 1024$ resolution from 52.40 to 10.46. Code is available at https://github.com/damo-vilab/dvdp. + +# 1. Introduction + +Diffusion models [2, 6, 9, 15, 21, 24, 28] have recently shown great potential in image synthesis. Instead of directly learning the observed distribution, it constructs a multistep forward process through gradually adding noise onto the real data (i.e., diffusion). After a sufficiently large number of steps, the source signal could be considered completely destroyed, resulting in a pure noise distribution that naturally supports sampling. In this way, starting from sampled noises, we can expect new instances after reversing the diffusion process step by step. + +As it can be seen, the above pipeline does not change the dimension of the source signal throughout the entire diffusion process [6,26,28]. It thus requires the reverse process to map a high-dimensional input to a high-dimensional output at every single step, causing heavy computation overheads [10, 22]. However, images present a measure of spatial redundancy [4] from the semantic perspective (e.g., an image pixel could usually be easily predicted according to its neighbours). Given such a fact, when the source signal is attenuated to some extent along with the noise strength growing, it should be possible to get replaced by a lower-dimensional signal. We therefore argue that there is no need to follow the source signal dimension along the entire distribution evolution process, especially at early steps (i.e., steps close to the pure noise distribution) for coarse generation. + +![](images/32e7610b3c4f4a513822f75e6717dcff62f0bb639277a422609e3c53a8d50873.jpg) +Figure 2. Conceptual comparison between DDPM [6] and our proposed DVDP, where our approach allows using a varying dimension in the diffusion process. + +In this work, we propose dimensionality-varying diffusion process (DVDP), which allows dynamically adjusting the signal dimension when constructing the forward path. The varying dimensionality concept is shown in Fig. 2. For this purpose, we first decompose an image into multiple orthogonal components, each of which owns dimension lower than the original data. Then, based on such a decomposition, we theoretically generalize the conventional diffusion process such that we can control the attenuation of each component when adding noise. Thanks to this reformulation, we manage to drop those inconsequential components after the noise strength reaches a certain level, and thus represent the source image using a lower-dimensional signal with little information lost. The remaining diffusion process could inherit this dimension and apply the same technique to further reduce the dimension. + +We evaluate our approach on various datasets, including objects, human faces, animals, indoor scenes, and outdoor scenes. Experimental results suggest that DVDP achieves on-par or even better synthesis performance than baseline models on all datasets. More importantly, DVDP relies on much fewer computations, and hence speeds up both training and inference of diffusion models. We also demonstrate the effectiveness of our approach in learning from high-resolution data. For example, we are able to start from a $64 \times 64$ noise to produce an image under $1024 \times 1024$ resolution. With FID [5] as the evaluation metric, our $1024 \times 1024$ model trained on FFHQ improves the baseline [28] from 52.40 to 10.46. All these advantages benefit from using a lower-dimensional signal, which reduces the computational cost and mitigates the optimization difficulty. + +# 2. Related Work + +Diffusion models. [26] proposes diffusion models for the first time that generate samples from a target distribution by reversing a diffusion process in which target distribution is gradually disturbed to an easily sampled standard Gaussian. [6] further proposes DDPM to reverse the diffusion process + +by learning a noise prediction network. [28] considers diffusion models as stochastic differential equations with continuous timesteps and proposes a unified framework. + +Accelerating diffusion models. Diffusion models significantly suffer from the low training and inference speed. There are many methods that speed up sampling from thousands of steps to tens of steps while keeping an acceptable sample quality [1, 14, 17, 19, 25, 27, 30, 31]. Besides improvements only on inference speed, there are other works aiming at speeding up both training and inference. [18] proposes a patch operation to decrease the dimensionality of each channel while accordingly increasing the number of channels, which greatly reduces the complexity of computation. Besides, a trainable forward process [33] is also proven to benefit a faster training and inference speed. However, the price of their acceleration is a poor sampling quality evaluated by FID score. In this work, we accelerate DDPM on both training and inference from a different perspective, i.e., reducing the dimensionality of the early diffusion process, and thus improving the efficiency while obtaining on-par or even better synthesis performance. + +Varying dimensionality of diffusion models. Due to the redundancy in image signals, it is possible to improve the efficiency of diffusion models by varying dimensionality during the generation process. The most relevant work to our proposed model is subspace diffusion [10], which can also vary dimensionality in the diffusion process. However, subspace diffusion suffers from a trade-off between sampling acceleration and sample quality, while our DVDP can relieve this dilemma (see theoretical analysis in Sec. 4.4 and experimental results in Sec. 5.3). Instead of varying dimensionality in one diffusion process, there are works cascading several diffusion processes with growing dimensionality [7, 21, 23, 24], where the subsequent process is conditioned on the previous samples. + +Discussion with latent diffusion. Besides varying dimensionality in image space, there are other methods, which we generally call latent diffusion, that directly apply diffusion models in a low dimensional latent space, obtained by an + +autoencoder [3, 8, 20, 22, 29]. Although latent diffusion can also speed up the training and sampling of diffusion models, it decreases dimensionality by an additional model and keeps the diffusion process unchanged. In this paper, however, we focus on the improvement on the diffusion process itself to accelerate training and sampling, which is totally a different route. Besides training and sampling efficiency, another important contribution of this work is to prove that it is unnecessary for diffusion process to keep a fixed dimension along time. By controlling the attenuation of each data component, it is possible to change dimensionality while keeping the process reversible. Thus, we will not further compare our DVDP with latent diffusion. + +# 3. Background + +We first introduce the background of Denoising Diffusion Probabilistic Model (DDPM) [6, 26] and some of its extensions which are closely related to our work. DDPM constructs a forward process to perturb the distribution of data $q(\mathbf{x}_0)$ into a standard Gaussian $\mathcal{N}(\mathbf{0};\mathbf{I})$ . Considering an increasing variance schedule of noises $\beta_{1},\ldots ,\beta_{T}$ , DDPM defines the forward process as a Markov chain + +$$ +\mathbf {x} _ {t} = \sqrt {1 - \beta_ {t}} \mathbf {x} _ {t - 1} + \sqrt {\beta_ {t}} \epsilon , t = 1, 2, \dots , T, \tag {1} +$$ + +where $\epsilon$ is a standard Gaussian noise. In order to generate high-fidelity images, DDPM [6] denoises samples from a standard Gaussian iteratively utilizing the reverse process parameterized as + +$$ +\mathbf {x} _ {t - 1} = \frac {1}{\sqrt {\alpha_ {t}}} \left(\mathbf {x} _ {t} - \frac {\beta_ {t}}{\sqrt {1 - \bar {\alpha} _ {t}}} \epsilon_ {\theta} (\mathbf {x} _ {t}, t)\right) + \sqrt {\beta_ {t}} \epsilon , \tag {2} +$$ + +where $\alpha_{t} = 1 - \beta_{t}$ , $\bar{\alpha}_{t} = \prod_{s=1}^{t} \alpha_{s}$ , and $\epsilon_{\theta}$ is a neural network used to predict $\epsilon$ from $\mathbf{x}_{t}$ . The parameters $\theta$ are learned by minimizing the following loss function + +$$ +L (\theta) = \mathbb {E} _ {t, \mathbf {x} _ {0}, \epsilon} \left[ \| \epsilon - \epsilon_ {\theta} \left(\mathbf {x} _ {t} \left(\mathbf {x} _ {0}, \epsilon\right), t\right) \| ^ {2} \right]. \tag {3} +$$ + +While the standard diffusion model is implemented directly in the image space, [13] takes the relative importance of different frequency components into consideration, and generalizes the forward diffusion process as + +$$ +\mathbf {x} _ {t} = \boldsymbol {U} (\mathbf {I} - \mathbf {B} _ {t}) ^ {\frac {1}{2}} \boldsymbol {U} ^ {T} \mathbf {x} _ {t - 1} + \boldsymbol {U} \mathbf {B} _ {t} ^ {\frac {1}{2}} \boldsymbol {U} ^ {T} \epsilon , \tag {4} +$$ + +where $\mathbf{U}$ is an orthogonal matrix to impose a rotation on $\mathbf{x}_t$ , and the noise schedule is defined by the diagonal matrix $\mathbf{B}_t$ . As Eq. (4) is too general to be directly instantiated as an implementation, [13] only discusses one special case called blur diffusion, which owns a clearly different focus from our work. In this work, we extend the generalized framework further and make it possible to vary dimensionality during the diffusion process. + +# 4. Dimensionality-Varying Diffusion Process + +We formulate the dimensionality-varying diffusion process in this section, which progressively decreases the dimension of $\mathbf{x}_t$ in the forward process, and can be effectively reversed to generate high-dimensional data from a low-dimensional noise. To establish DVDP, we gradually attenuate components of $\mathbf{x}_0$ in different subspaces and decrease the dimensionality of $\mathbf{x}_t$ at dimensionality turning points by downsampling operator (Sec. 4.1), which is approximately reversible (Sec. 4.2) with controllable small error caused by the loss of attenuated $\mathbf{x}_0$ component (Sec. 4.3). + +# 4.1. Forward Process of DVDP + +In this section, we will construct the forward process of our DVDP, which decreases the dimensionality as time evolves and can be effectively reversed. To this end, we concatenate multiple diffusion processes with different dimensions into an entire Markov chain by downsampling operations, while we elaborately design each process so that the information loss induced by downsampling is negligible. Fig. 3 illustrates this overall framework. The concatenation of different processes enables us to decrease the dimensionality, and the control on information loss ensures that downsampling operations are approximately reversible, such that the entire process can be reversed (discussed later in Sec. 4.2). To limit the information loss, we decompose the data into orthogonal components and control the attenuation of each component in the forward process of each concatenated diffusion, which we call Attenuated Diffusion Process (ADP). Once the lost data component induced by downsampling is attenuated to be small enough, the information loss will be negligible. + +Notation list. As a prerequisite for constructing each ADP, we first define a sequence of subspaces and other necessary notations as follows: + +- $\mathbb{S}_0 \supseteq \mathbb{S}_1 \supseteq \dots \supseteq \mathbb{S}_K$ is a sequence of subspaces with decreasing dimensionality $d = \bar{d}_0 > \bar{d}_1 > \dots > \bar{d}_K$ , where $\mathbb{S}_0 = \mathbb{R}^d$ is the original space, $K \in \mathbb{N}_+$ . For simplicity, $\mathbb{S}_{K+1} \triangleq \{\mathbf{0}\}$ and $\bar{d}_{K+1} \triangleq 0$ . +- $d_{i} = \dim (\mathbb{S}_{i} / \mathbb{S}_{i + 1})$ , $i = 0,1,\dots ,K$ . Note that $d_{K} = \dim (\mathbb{S}_{K} / \mathbb{S}_{K + 1}) = \dim (\mathbb{S}_{K})$ +- $\mathbf{U}_0 = [\hat{\mathbf{U}}_0, \dots, \hat{\mathbf{U}}_K] \in \mathbb{R}^{d \times d}$ is an orthogonal matrix, and column vectors of its sub-matrix $\hat{\mathbf{U}}_i \in \mathbb{R}^{d \times d_i}$ span subspace $\mathbb{S}_i / \mathbb{S}_{i+1}$ for $i = 0, 1, \dots, K$ . +- $\mathbf{U}_k \in \mathbb{R}^{\bar{d}_k \times \bar{d}_k}$ is an orthogonal matrix for $k = 0,1,\dots,K$ , and can be split as $\mathbf{U}_k = [N_k, P_k]$ when $k < K$ where $N_k \in \mathbb{R}^{\bar{d}_k \times d_k}, P_k \in \mathbb{R}^{\bar{d}_k \times \bar{d}_{k+1}}$ . +- $I_{n} \in \mathbb{R}^{n \times n}$ is an identity matrix. +- $O_{n} \in \mathbb{R}^{n \times n}$ is a zero matrix. + +![](images/5e086991f38ed0e1da5707e117cb5ce92a3e9c83974101cf3e29a5ee98ea9875.jpg) +Figure 3. Framework illustration of DVDP. Each row represents an Attenuated Diffusion Process (ADP), which controls the attenuation of each data component while adding noise. All $K + 1$ ADPs ( $K = 2$ here) have different dimensions decreasing from top to bottom, and are concatenated by some simple operations to obtain our DVDP. In the forward process, the concatenation is achieved by downsampling operation, and in reverse process, it is the upsampling operation followed by adding a Gaussian noise. + +With the above definitions, we can first construct an ADP $\mathbf{x}_t^0\in \mathbb{S}_0$ for $t = 0,1,\dots ,T$ as + +$$ +\begin{array}{l} \mathbf {x} _ {t} ^ {0} = \sum_ {i = 0} ^ {K} \left(\bar {\lambda} _ {i, t} \mathbf {v} _ {i} ^ {0} + \bar {\sigma} _ {i, t} \mathbf {z} _ {i} ^ {0}\right) \tag {5} \\ = \boldsymbol {U} _ {0} \bar {\boldsymbol {\Lambda}} _ {0, t} \boldsymbol {U} _ {0} ^ {T} \mathbf {x} _ {0} ^ {0} + \boldsymbol {U} _ {0} \bar {\boldsymbol {L}} _ {0, t} \boldsymbol {U} _ {0} ^ {T} \epsilon^ {0}, \\ \end{array} +$$ + +where $\mathbf{v}_i^0\in \mathbb{S}_i / \mathbb{S}_{i + 1}$ is the component of original data point $\mathbf{x}_0^0$ in subspace $\mathbb{S}_i / \mathbb{S}_{i + 1}$ , $\bar{\lambda}_{i,t}$ controls the attenuation of $\mathbf{v}_i^0$ along timestep $t$ , $\mathbf{z}_i^0$ is the component of a standard Gaussian noise $\epsilon^0\in \mathbb{R}^{\bar{d}_0}$ in the same subspace as $\mathbf{v}_i^0$ (i.e., $\mathbb{S}_i / \mathbb{S}_{i + 1}$ ), $\bar{\sigma}_{i,t}$ is the standard deviation of $\mathbf{z}_i^0$ , and $\bar{\Lambda}_{0,t}$ , $\bar{\pmb{L}}_{0,t}\in \mathbb{R}^{\bar{d}_0\times \bar{d}_0}$ are two diagonal matrices defined as $\bar{\Lambda}_{0,t} = \mathrm{diag}(\bar{\lambda}_{0,t}\pmb{I}_{d_0},\bar{\lambda}_{1,t}\pmb{I}_{d_1},\dots ,\bar{\lambda}_{K,t}\pmb{I}_{d_K})$ and $\bar{\pmb{L}}_{0,t} = \mathrm{diag}(\bar{\sigma}_{0,t}\pmb{I}_{d_0},\bar{\sigma}_{1,t}\pmb{I}_{d_1},\dots ,\bar{\sigma}_{K,t}\pmb{I}_{d_K})$ . To control the attenuation of each data component $\mathbf{v}_i^0$ , we require $\bar{\lambda}_{i,t}$ to gradually decrease from 1 to approximate 0 for $i = 0,1,\dots ,K - 1$ as timestep $t$ evolves. As for $\bar{\lambda}_{K,t}$ , it is not required to decrease (explained later after Eq. (8)). + +Starting from $\mathbf{x}_t^0$ , we can recursively construct a dimensionality-decreasing sequence of ADPs + +$$ +\begin{array}{l} \mathbf {x} _ {t} ^ {k} = \mathcal {D} _ {k} \mathbf {x} _ {t} ^ {k - 1} = \sum_ {i = k} ^ {K} \left(\bar {\lambda} _ {i, t} \mathbf {v} _ {i} ^ {k} + \bar {\sigma} _ {i, t} \mathbf {z} _ {i} ^ {k}\right) \tag {6} \\ = \boldsymbol {U} _ {k} \bar {\boldsymbol {\Lambda}} _ {k, t} \boldsymbol {U} _ {k} ^ {T} \mathbf {x} _ {0} ^ {k} + \boldsymbol {U} _ {k} \bar {\boldsymbol {\mathcal {L}}} _ {k, t} \boldsymbol {U} _ {k} ^ {T} \epsilon^ {k}, 1 \leq k \leq K, \\ \end{array} +$$ + +where $\mathcal{D}_k:\mathbb{R}^{\bar{d}_{k - 1}}\to \mathbb{R}^{\bar{d}_k}$ is a linear surjection, which we call the $k$ -th downsampling operator as it reduces the dimensionality of the operand (without ambiguity, we also use $\mathcal{D}_k$ to denote the corresponding matrix in $\mathbb{R}^{\bar{d}_k\times \bar{d}_{k - 1}}$ $\mathbf{v}_i^k = \overline{\mathcal{D}}_k\mathbf{v}_i^0\in \overline{\mathcal{D}}_k(\mathbb{S}_i / \mathbb{S}_{i + 1})$ is the component of $\mathbf{x}_0^k = \overline{\mathcal{D}}_k\mathbf{x}_0^0\in \mathbb{R}^{\bar{d}_k}$ $(\overline{\mathcal{D}}_k\triangleq \prod_{i = 1}^{k}\mathcal{D}_i)$ $\mathbf{z}_i^k = \overline{\mathcal{D}}_k\mathbf{z}_i^0\in \overline{\mathcal{D}}_k(\mathbb{S}_i / \mathbb{S}_{i + 1})$ is the component of a standard Gaussian noise $\epsilon^k = \overline{\mathcal{D}}_k\epsilon^0\in \mathbb{R}^{\bar{d}_k}$ $\bar{\Lambda}_{k,t} =$ diag( $\bar{\lambda}_{k,t}\pmb {I}_{d_k}$ $\bar{\lambda}_{k + 1,t}\pmb {I}_{d_{k + 1}},\dots ,\bar{\lambda}_{K,t}\pmb {I}_{d_K})\in \mathbb{R}^{\bar{d}_k\times \bar{d}_k},$ + +$\bar{\pmb{L}}_{k,t} = \mathrm{diag}(\bar{\sigma}_{k,t}\pmb{I}_{d_k},\bar{\sigma}_{k + 1,t}\pmb{I}_{d_{k + 1}},\dots ,\bar{\sigma}_{K,t}\pmb{I}_{d_K})\in$ $\mathbb{R}^{\bar{d}_k\times \bar{d}_k}$ , and orthogonal matrix $U_{k}\in \mathbb{R}^{\bar{d}_{k}\times \bar{d}_{k}}$ consists of the last $\bar{d}_k$ columns of $\mathcal{D}_k\pmb{U}_{k - 1}$ , i.e., $\pmb {U}_k = \mathcal{D}_k\pmb {P}_{k - 1}$ (note that this condition requires further restriction on $\mathcal{D}_k$ + +Both Eqs. (5) and (6) can be derived from Markov chains with Gaussian kernels as (see Supplementary Material for the proof) + +$$ +\mathbf {x} _ {t} ^ {k} = \boldsymbol {U} _ {k} \boldsymbol {\Lambda} _ {k, t} \boldsymbol {U} _ {k} ^ {T} \mathbf {x} _ {t - 1} ^ {k} + \boldsymbol {U} _ {k} \boldsymbol {L} _ {k, t} \boldsymbol {U} _ {k} ^ {T} \epsilon^ {k}, 0 \leq k \leq K, \tag {7} +$$ + +where $\Lambda_{k,t} = \bar{\Lambda}_{k,t - 1}^{-1}\bar{\Lambda}_{k,t},L_{k,t} = (\bar{L}_{k,t}^{2} - \Lambda_{k,t}^{2}\bar{L}_{k,t - 1}^{2})^{1 / 2}.$ + +Now with the ADPs $\{\mathbf{x}_t^k\}_{k = 0}^K$ given by Eq. (7), we can construct the forward process of DVDP by merging different parts of $\{\mathbf{x}_t^k\}_{k = 0}^K$ in the following manner: consider a strictly increasing time sequence $T_{1},\dots ,T_{K},T_{K + 1} = T,$ if for each $k$ satisfying $1\leq k\leq K$ $\bar{\lambda}_{k - 1,T_k}$ becomes small enough, then $\mathbf{x}_{T_k}^{k - 1}$ is downsampled by $\mathcal{D}_k$ to obtain $\mathbf{x}_{T_k}^k$ with lower dimensionality, and each $T_{k}$ is a dimensionality turning point. The entire process can be expressed as + +$$ +\begin{array}{l} \mathbf {x} _ {0} ^ {0} \longrightarrow \mathbf {x} _ {1} ^ {0} \quad \longrightarrow \dots \longrightarrow \mathbf {x} _ {T _ {1}} ^ {0} \\ \xrightarrow {\mathcal {D} _ {1}} \mathbf {x} _ {T _ {1}} ^ {1} \longrightarrow \mathbf {x} _ {T _ {1} + 1} ^ {1} \longrightarrow \dots \longrightarrow \mathbf {x} _ {T _ {2}} ^ {1} \tag {8} \\ \end{array} +$$ + +$$ +\begin{array}{l} \begin{array}{c} \bullet \\ \bullet \\ \bullet \\ \bullet \end{array} \\ \xrightarrow {\mathcal {D} _ {K}} \mathbf {x} _ {T _ {K}} ^ {K} \longrightarrow \mathbf {x} _ {T _ {K} + 1} ^ {K} \longrightarrow \dots \longrightarrow \mathbf {x} _ {T} ^ {K}. \\ \end{array} +$$ + +Between two adjacent dimensionality turning points $T_{k-1}$ and $T_{k}$ , $\mathbf{x}_{t}^{k-1}$ diffuses and attenuates data components $\mathbf{v}_{i}^{k-1}$ , $i \geq k-1$ , which keeps the dimensionality $\bar{d}_{k-1}$ . When it comes to $T_{k}$ , $\mathbf{x}_{T_{k}}^{k-1} \xrightarrow{\mathcal{D}_{k}} \mathbf{x}_{T_{k}}^{k}$ decreases the dimension from $\bar{d}_{k-1}$ to $\bar{d}_{k}$ . After the last dimensionality turning point $T_{k}$ , $\mathbf{x}_{t}^{K}$ can just evolve as conventional diffusion without data component attenuation. Thus, the entire process in Eq. (8) decreases the dimensionality by $K$ times from $\bar{d}_{0} = d$ to $\bar{d}_{K}$ . It should be noted that process + +in Eq. (8) is also Markovian since each diffusion subprocess $\mathbf{x}_{T_{k - 1}}^{k - 1}\rightarrow \mathbf{x}_{T_k}^{k - 1}$ is Markovian, and the result of each downsampling operation $\mathbf{x}_{T_k}^k$ is uniquely determined by the previous state $\mathbf{x}_{T_k}^{k - 1}$ . Also note that each downsampling operation $\mathcal{D}_k$ loses little information because of small $\bar{\lambda}_{k - 1,T_k}$ which is a controllable hyperparameter. For better understanding, consider the relationship between $\mathbf{x}_{T_k}^{k - 1}$ and $\mathbf{x}_{T_k}^k$ derived from Eq. (6) + +$$ +\mathbf {x} _ {T _ {k}} ^ {k - 1} = \mathcal {D} _ {k} ^ {T} \mathbf {x} _ {T _ {k}} ^ {k} + \underbrace {\bar {\lambda} _ {k - 1 , T _ {k}} \mathbf {v} _ {k - 1} ^ {k - 1}} _ {\text {d a t a c o m p o n e n t}} + \underbrace {\bar {\sigma} _ {k - 1 , T _ {k}} \mathbf {z} _ {k - 1} ^ {k - 1}} _ {\text {n o i s e c o m p o n e n t}}, \tag {9} +$$ + +where $\mathcal{D}_k^T$ is the transpose of matrix $\mathcal{D}_k$ , named as the $k$ -th upsampling operator. From Eq. (9), it is clear that $\mathbf{x}_{T_k}^k$ actually loses two terms compared with $\mathbf{x}_{T_k}^{k-1}$ : 1) data component $\bar{\lambda}_{k-1,T_k}\mathbf{v}_{k-1}^{k-1}$ which is informative but negligible as $\bar{\lambda}_{k-1,T_k}$ is set to be small enough, and 2) noise component $\bar{\sigma}_{k-1,T_k}\mathbf{z}_{k-1}^{k-1}$ that is non-informative and can be compensated in the reverse process, as we will discuss in Sec. 4.2. + +# 4.2. Reverse Process Approximating DVDP + +In this section, we will derive an approximate reverse process, which induces a data generation process with progressively growing dimensionality. The approximation error will be discussed in Sec. 4.3, and we can find that it actually converges to zero. Loss function will also be given at the end of this section. Implementation details of training and sampling can be found in Supplementary Material. + +Reverse transition. Since DVDP is a sequence of fixed-dimensionality diffusion processes connected by downsampling operations at dimensionality turning points, we consider reverse transition kernels between and at dimensionality turning points separately. + +For reverse transition between two adjacent dimensionality turning points, i.e., $p_{\theta}(\mathbf{x}_{t - 1}^{k}|\mathbf{x}_{t}^{k})$ with $T_{k - 1}\leq t\leq T_{k}$ for $k\in [1,K + 1]$ , it can be defined as a Gaussian kernel $p_{\theta}(\mathbf{x}_{t - 1}^{k}|\mathbf{x}_{t}^{k}) = \mathcal{N}(\mathbf{x}_{t - 1}^{k};\pmb{\mu}_{\theta}(\mathbf{x}_{t}^{k},t),\pmb{\Sigma}_{t})$ . As in DDPM [6], the covariance matrices $\pmb{\Sigma}_t$ are set to untrained time-dependent constants, and the mean term $\pmb{\mu}_{\theta}(\mathbf{x}_{t}^{k},t)$ is defined as (see Supplementary Material for details) + +$$ +\begin{array}{l} \boldsymbol {\mu} _ {\theta} = \tilde {\boldsymbol {\mu}} _ {k, t} \left(\mathbf {x} _ {t} ^ {k}, U _ {k} \bar {\boldsymbol {\Lambda}} _ {k, t} ^ {- 1} \boldsymbol {U} _ {k} ^ {T} \mathbf {x} _ {t} ^ {k} \right. \tag {10} \\ - \boldsymbol {U} _ {k} \bar {\boldsymbol {\Lambda}} _ {k, t} ^ {- 1} \bar {\boldsymbol {L}} _ {k, t} \boldsymbol {U} _ {k} ^ {T} \boldsymbol {\epsilon} _ {\theta} \left(\boldsymbol {x} _ {t} ^ {k}, t\right), \\ \end{array} +$$ + +where $\tilde{\pmb{\mu}}_{k,t}(\cdot ,\cdot)$ is the mean function of forward process posterior $q(\mathbf{x}_{t - 1}^k |\mathbf{x}_t^k,\mathbf{x}_0^k) = \mathcal{N}(\mathbf{x}_{t - 1}^k;\tilde{\pmb{\mu}}_{k,t}(\mathbf{x}_t^k,\mathbf{x}_0^k),\tilde{\pmb{\Sigma}}_{k,t})$ and $\epsilon_{\theta}$ represents a trainable network. + +For reverse transition at dimensionality turning points, i.e., $p_{\theta}(\mathbf{x}_{T_k}^{k - 1}|\mathbf{x}_{T_k}^k)$ for $k\in [1,K]$ , the corresponding forward transitions barely lose information as illustrated by Eq. (9) in Sec. 4.1, thus $\mathbf{x}_{T_k}^k\to \mathbf{x}_{T_k}^{k - 1}$ can be approximately achieved without any trainable network as + +$$ +\mathbf {x} _ {T _ {k}} ^ {k - 1} = \mathcal {D} _ {k} ^ {T} \mathbf {x} _ {T _ {k}} ^ {k} + \boldsymbol {U} _ {k - 1} \Delta \boldsymbol {L} _ {k - 1} \boldsymbol {U} _ {k - 1} ^ {T} \epsilon^ {k - 1}, \tag {11} +$$ + +where $\mathcal{D}_k^T\in \mathbb{R}^{\bar{d}_k\times \bar{d}_{k - 1}}$ is the upsampling operator, and $\Delta L_{k - 1} = \mathrm{diag}(\bar{\sigma}_{k - 1,T_k}\pmb{I}_{d_{k - 1}},\pmb{O}_{\bar{d}_k})$ represents the standard deviation of the added Gaussian noise $\epsilon^{k - 1}\in \mathbb{R}^{\bar{d}_{k - 1}}$ . Eq. (11) can be understood as: we first upsample $\mathbf{x}_{T_k}^k$ , then add a Gaussian noise in compensation for the lost noise component in the forward downsampling operation, i.e., $\bar{\sigma}_{k - 1,T_k}\mathbf{z}_{k - 1}^{k - 1}$ in Eq. (9). The approximation error comes from neglecting data component $\bar{\lambda}_{k - 1,T_k}\mathbf{v}_{k - 1}^{k - 1}$ , and will be analyzed later in Sec. 4.3. + +Loss function. Similar with DDPM [6], a loss function can be derived from a weighted variational bound as (see Supplementary Material for details) + +$$ +L (\theta) = \mathbb {E} _ {k} \mathbb {E} _ {\mathbf {x} _ {0} ^ {k}, \epsilon^ {k}, t \sim \mathcal {U} _ {k}} \left[ \left\| \epsilon^ {k} - \epsilon_ {\theta} \left(\mathbf {x} _ {t} ^ {k} \left(\mathbf {x} _ {0} ^ {k}, \epsilon^ {k}\right), t\right) \right\| ^ {2} \right], \tag {12} +$$ + +where $\mathcal{U}_k = \mathcal{U}\big((T_k,T_{k + 1}]\big)$ is a discrete uniform distribution between $T_{k}$ (exclusive) and $T_{k + 1}$ (inclusive), and $\mathbf{x}_t^k (\mathbf{x}_0^k,\epsilon^k)$ represents the forward $\mathbf{x}_t^k$ determined by $\mathbf{x}_0^k$ and $\epsilon^k$ given in Eq. (6). + +# 4.3. Error Analysis + +In Sec. 4.2, we mention that the reverse process is just an approximation of the forward DVDP at each dimensionality turning point $T_{k}$ . In this section, we will measure this approximation error in probability sense, i.e., the difference between the real forward distribution $q(\mathbf{x}_{T_k}^{k - 1})$ and the reverse distribution $p(\mathbf{x}_{T_k}^{k - 1})$ under proper assumptions, and will find that this difference converges to zero. + +To measure the difference between two distributions, we use Jensen-Shannon Divergence (JSD) as a metric. Under this metric, upper bound of the approximation error can be derived from Proposition 1 (see Supplementary Material for proof): + +Proposition 1 Assume $p_1(\pmb{x}|\pmb{x}_0)$ , $p_2(\pmb{x}|\pmb{x}_0)$ are two Gaussians such that $p_1(\pmb{x}|\pmb{x}_0) = \mathcal{N}(\pmb{x};\pmb{A}_1\pmb{x}_0,\pmb{\Sigma})$ and $p_2(\pmb{x}|\pmb{x}_0) = \mathcal{N}(\pmb{x};\pmb{A}_2\pmb{x}_0,\pmb{\Sigma})$ , where positive semi-definite matrices $A_1, A_2$ satisfy $A_1\succeq A_2\succeq 0$ , covariance matrix $\pmb{\Sigma}$ is positive definite, and the support of distribution $p(\pmb{x}_0)$ is bounded, then Jensen-Shannon Divergence (JSD) of the two marginal distributions $p_1(\pmb{x})$ and $p_2(\pmb{x})$ satisfies + +$$ +\begin{array}{l} \operatorname {J S D} \left(p _ {1} \mid \mid p _ {2}\right) \leq \frac {\sqrt {2}}{2} e ^ {- \frac {1}{2}} B \left(2 \sqrt {2} + \frac {V _ {d} (r)}{\left(2 \pi\right) ^ {\frac {d}{2}}}\right) \tag {13} \\ \cdot \left\| \boldsymbol {\Sigma} ^ {- \frac {1}{2}} \left(\boldsymbol {A} _ {1} - \boldsymbol {A} _ {2}\right) \right\| _ {2}, \\ \end{array} +$$ + +where $B$ is the upper bound of $\| \pmb{x}_0\| _2$ , $V_{d}(\cdot)$ is the volume of a $d$ -dimensional sphere with respect to the radius, and $r = 2B\| \Sigma^{-\frac{1}{2}}A_1\| _2$ . + +With Proposition 1, the upper bound of JSD between the forward distribution $q(\mathbf{x}_{T_k}^{k - 1})$ and the reverse distribution $p(\mathbf{x}_{T_k}^{k - 1})$ can be obtained by Theorem 1 (see Supplementary Material for proof) + +Theorem 1 (Reverse Process Error) Assume $0 < k \leq K$ , $q(\mathbf{x}_{T_k}^{k-1})$ and $q(\mathbf{x}_{T_k}^k)$ are defined by Eqs. (5) and (6), $p(\mathbf{x}_{T_k}^{k-1})$ is the marginal distribution of $q(\mathbf{x}_{T_k}^k)p(\mathbf{x}_{T_k}^{k-1}|\mathbf{x}_{T_k}^k)$ where $p(\mathbf{x}_{T_k}^{k-1}|\mathbf{x}_{T_k}^k)$ is defined by Eq. (11), and $\| \mathbf{x}_0\|_2 \leq \sqrt{d}$ , then + +$$ +\begin{array}{l} \xi_ {1} \leq \frac {\sqrt {2}}{2} e ^ {- \frac {1}{2}} \sqrt {d} \left(2 \sqrt {2} + \frac {V _ {d} (r)}{(2 \pi) ^ {\frac {d}{2}}}\right) \frac {\bar {\lambda} _ {k - 1 , T _ {k}}}{\bar {\sigma} _ {k - 1 , T _ {k}}} \tag {14} \\ = o \left(\bar {\lambda} _ {k - 1, T _ {k}}\right), \\ \end{array} +$$ + +where $\xi_1 \triangleq \mathrm{JSD}(q(\mathbf{x}_{T_k}^{k-1})||p(\mathbf{x}_{T_k}^{k-1})), \text{ and } r = 2\sqrt{d}\max_{k-1 \leq i \leq K} \frac{\bar{\lambda}_{i,T_k}}{\bar{\sigma}_{i,T_k}}.$ + +Note that the assumption $\| \mathbf{x}_0\| _2\leq \sqrt{d}$ can be satisfied for image data, since pixel values can be normalized in $[-1,1]$ . Thus, Theorem 1 claims that $\xi_{1}$ can be arbitrarily small as $\bar{\lambda}_{k - 1,T_k}\to 0$ if we can get an exact $q(\mathbf{x}_{T_k}^{k - 1})$ by reverse process. It means that the approximation error caused by stepping over $T_{k}$ can be small enough. + +# 4.4. Comparison with Subspace Diffusion + +To reduce the dimensionality of latent space in diffusion models, subspace diffusion is proposed to model in a low-dimensional subspace at high noise levels, and keep the original full-dimensional network at low noise levels [10]. This can also be seen as a concatenation of multiple diffusion processes with different dimensionality like our DVDP, but without controllable attenuation on each data component. Each concatenated processes is just conventional isotropic diffusion. + +Thus, subspace diffusion can be seen as a special case of our DVDP with $\bar{\lambda}_t \triangleq \bar{\lambda}_{0,t} = \bar{\lambda}_{1,t} = \dots = \bar{\lambda}_{K,t}$ and $\bar{\sigma}_t \triangleq \bar{\sigma}_{0,t} = \bar{\sigma}_{1,t} = \dots = \bar{\sigma}_{K,t}$ , which limits the choice of dimensionality turning points. This limitation can be further explained by Eq. (9): at dimensionality turning point $T_k$ in the forward process, $\mathbf{x}_{T_k}^{k-1}$ will lose an informative data component $\bar{\lambda}_{k-1,T_k} \mathbf{v}_{k-1}^{k-1}$ and a noninformative noise component $\bar{\sigma}_{k-1,T_k} \mathbf{z}_{k-1}^{k-1}$ . To safely neglect the data component in the reverse transition, it requires that $\bar{\lambda}_{k-1,T_k} / \bar{\sigma}_{k-1,T_k} \ll \| \mathbf{z}_{k-1}^{k-1} \| / \| \mathbf{v}_{k-1}^{k-1} \|$ . For subspace diffusion, it means that the consistent $\bar{\lambda}_t / \bar{\sigma}_t$ for components in all subspaces should be small enough, which usually indicates a large $T_k$ , i.e., a large number of diffusion steps in high dimensional space. + +Therefore, as claimed in [10], the choice of $T_{k}$ should balance two factors: 1) smaller $T_{k}$ reduces the number of reverse diffusion steps occurring at higher dimensionality, whereas 2) larger $T_{k}$ makes the reverse transition at $T_{k}$ more accurate. Although [10] additionally proposes to compensate the loss of data component by adding an extra Gaussian noise besides compensation for the noise component, this trade-off still exists. + +However, our DVDP can set much smaller $T_{k}$ with little loss in accuracy, which benefits from the controllable attenuation for each data component. Theorem 1 supports this advantage theoretically, and experimental results in Sec. 5.3 further demonstrate it. + +# 5. Experiments + +In this section, we show that our DVDP can speed up both training and inference of diffusion models while achieving competitive performance. Besides, thanks to the varied dimension, DVDP is able to generate high-quality and high-resolution images from a low-dimensional subspace and exceeds existing methods including scoreSDE [28] and Cascaded Diffusion Models (CDM) [7] on FFHQ $1024^{2}$ . Specifically, we first introduce our experimental setup in Sec. 5.1. Then we compare our DVDP with existing alternatives on several widely evaluated datasets in terms of visual quality and modeling efficiency in Sec. 5.2. After that, we compare our DVDP with Subspace Diffusion [10], a closely related work proposed recently, in Sec. 5.3. Finally, we implement necessary ablation studies in the last Sec. 5.4. + +# 5.1. Experimental Setup + +Datasets. In order to verify that DVDP is widely applicable, we use six image datasets covering various classes and a wide range of resolutions from 32 to 1024. To be specific, we implement DVDP on CIFAR10 $32^2$ [12], LSUN Bedroom $256^2$ [32], LSUN Church $256^2$ , LSUN Cat $256^2$ , FFHQ $256^2$ , and FFHQ $1024^2$ [11]. + +Implementation details. We adopt the UNet improved by [2] which achieves better performance than the traditional version [6]. Since most baseline methods adopt a single UNet network for all timesteps in the whole diffusion process, our DVDP also keeps this setting, except the comparison with Subspace Diffusion in Sec. 5.3, which takes two networks for different generation stages [10]. In principle, the network structure of our DVDP is kept the same as the corresponding baseline. However, when resolution comes to $1024 \times 1024$ , the UNet in conventional diffusion models should be deep enough to contain sufficient downsampling blocks, thus to obtain embeddings with proper size (usually $4 \times 4$ or $8 \times 8$ ) in the bottleneck layer. On the contrary, our DVDP does not need such a deep network since the generation starts from a low resolution noise ( $64 \times 64$ in our case). Thus we only maintain a similar amount of parameters but use a different hyperparameter setting on FFHQ $1024^2$ . + +We set the number of timesteps $T = 1,000$ in all of our experiments. For DVDP, we reduce the dimensionality by $\frac{1}{4}$ (i.e., $h \times w \to \frac{h}{2} \times \frac{w}{2}$ for image resolution) when the timestep $t$ reaches a dimensionality turning point. For simplicity, we adopt $\mathbb{T} \triangleq \{T_1, \dots, T_K\}$ . For CIFAR10 + +Table 1. Quantitative comparison between DDPM [6] and our DVDP on various datasets regarding image quality and model efficiency. * indicates our reproduced DDPM. Both ${\mathrm{{DDMP}}}^{ * }$ and our DVDP adopt the improved UNet [2] for a fair comparison. + +
DatasetMethodFID (50k)↓Training Speed (sec/iter)Training Speed UpSampling Speed (sec/sample)Sampling Speed Up
CIFAR10 32 × 32DDPM3.17----
DDPM*3.160.18-0.34-
DVDP3.240.151.2×0.261.3×
LSUN Bedroom 256 × 256DDPM6.36----
DDPM*5.740.99-12.2-
DVDP4.880.452.2×5.012.4×
LSUN Church 256 × 256DDPM7.89----
DDPM*7.540.99-12.2-
DVDP7.030.452.2×5.012.4×
LSUN Cat 256 × 256DDPM19.75----
DDPM*18.110.99-12.2-
DVDP16.500.452.2×5.012.4×
FFHQ 256 × 256DDPM*8.330.99-12.2-
DVDP8.030.452.2×5.012.4×
+ +$32^{2}$ , we set $\mathbb{T} = \{600\}$ , indicating that the resolution is decreased from $32 \times 32$ to $16 \times 16$ when $t = 600$ . Similarly, we set $\mathbb{T} = \{300, 600\}$ for all $256^{2}$ datasets and $\mathbb{T} = \{200, 400, 600, 800\}$ for FFHQ $1024^{2}$ . + +In all of our experiments, the noise schedule of DVDP is an adapted version of linear schedule [6], which is suitable for DVDP and keeps a comparable signal-to-noise ratio (SNR) with the original version (see Supplementary Material for details). + +Evaluation metrics. For sample quality, we calculate the FID score [5] on 50k samples, except for FFHQ $1024^{2}$ with 10k samples due to a much slower sampling. As for training and sampling speed, both of them are evaluated on a single NVIDIA A100. Training speed is measured by the mean time of each iteration (estimated over 4,000 iterations), and sampling speed is measured by the mean time of each sample (estimated over 100 batches). The training batch size and sampling batch size are 128, 256 respectively for CIFAR10 $32^{2}$ , and 24, 64 respectively for other $256^{2}$ datasets. + +# 5.2. Visual Quality and Modeling Efficiency. + +Comparison with existing alternatives. We compare DVDP with other alternatives here to show that DVDP has the capability of acceleration while maintaining a reasonable or even better visual quality. For the sake of fairness, we reproduce DDPM using the same network structure as DVDP with the same hyperparameters, represented as $\mathrm{DDPM^{*}}$ . Some samples generated by our DVDP are shown in Fig. 1, and Tab. 1 summarizes the quantitative results on CIFAR10, FFHQ $256^{2}$ , and three LSUN datasets. The results show that our proposed DVDP achieves better FID + +scores on all of the $256^{2}$ datasets, demonstrating an improved sample quality. Meanwhile, DVDP enjoys improved training and sampling speeds. Specifically, DDPM and $\mathrm{DDPM}^*$ spend $2.2\times$ time as DVDP when training the same epochs, and they spend $2.4\times$ time in sampling. Although the superiority of DVDP is obvious on all $256^{2}$ datasets, it becomes indistinct when it comes to CIFAR10 $32^{2}$ , which is reasonable considering the small pixel redundancy and low resolution of images in CIFAR10. + +Towards high-resolution image synthesis. It is hard for diffusion models to generate high-resolution images directly. This can attribute to the curse of dimensionality: the support of high-dimensional data with large noise can only be visited a small part during training, leading to inaccurate prediction on unseen points [10]. Score-SDE [28] tries this task by directly training a single diffusion model, but the sample quality is far from reasonable. CDM performs better in high-resolution image synthesis and obtains impressive results [21, 24]. It first generates low-resolution images, followed by several conditional diffusion models as superresolution modules. We compare DVDP with score-SDE and CDM on FFHQ $1024^{2}$ in Tab. 2. The FID of score-SDE is evaluated on samples generated from their official code and model weight without acceleration, and CDM is implemented by three cascaded diffusions as in [21]. Our DVDP is sampled by both DDPM method with 1000 steps and DDIM method with 675 steps. The results show that DVDP beats both score-SDE and CDM. + +# 5.3. Comparison with Subspace Diffusion + +Subspace diffusion [10] can also vary dimensionality during the diffusion process. As mentioned in [10] and also + +Table 2. Synthesis performance of different models trained on FFHQ ${1024} \times {1024}$ . + +
Model#Params (M)NFEFID (10k)↓
Score-SDE100200052.40
CDM98152524.7
165152517.35
286152517.24
DVDP10567512.43
100010.46
+ +![](images/8b4da43eaa7cf459ac0df1d7937df27726bba25899fe848371489d03184cd7b4.jpg) +Figure 4. Quantitative comparison between subspace diffusion [10] and our DVDP on CelebA $64 \times 64$ regarding different dimensionality turning point $T_{1}$ . + +discussed in Sec. 4.4, dimensionality turning point $T_{k}$ in subspace diffusion should be large enough to maintain the sample quality. However, large $T_{k}$ means more diffusion steps in high dimensional space, which will impair the advantage of such dimensionality-varying method, e.g., less acceleration in sampling. Thus, $T_{k}$ is expected to be as small as possible while maintaining the sampling quality. + +Considering that the dimensionality decreases only once, i.e., $K = 1$ , and only one dimensionality turning point $T_{1}$ , we compare DVDP with subspace diffusion when the downsampling is carried out at different $T_{1}$ . Since the subspace diffusion is only implemented on continuous timesteps in [10], we reproduce it on discrete timesteps similar as DDPM and use the reproduced version as a baseline. Fig. 4 illustrates that DVDP is consistently better with regard to sample quality on CelebA $64 \times 64$ [16] when $T_{1}$ varies, where the advantage gets larger when $T_{1}$ gets smaller. In addition, some samples of DVDP and subspace diffusion are shown in Fig. 5, where the sample quality of subspace diffusion is apparently worse than that of DVDP especially when $T_{1}$ is small. In conclusion, DVDP is much more insensitive to the dimensionality turning point than subspace diffusion. + +# 5.4. Ablation Study + +We implement ablation study in this section to show that DVDP is able to keep effective when the number of downsampling, i.e., $K$ , grows. Specifically, we train DVDP + +Table 3. Ablation study on the number of downsampling times on CelebA $128 \times 128$ . + +
Downsampling times K0123
FID (50k)6.145.996.106.37
Training Speed Up-1.98×2.24×2.25×
Sampling Speed Up-2.12×2.36×2.43×
+ +![](images/40c981e278b0b2ff1d535ac9453aade4a21f1e7bcb1d8da4ae78adc9de7c4e52.jpg) +Figure 5. Qualitative comparison between subspace diffusion [10] and our DVDP on CelebA $64 \times 64$ . $T_{1}$ denotes the dimensionality turning point. + +models on four different settings of dimensionality turning points $\mathbb{T}$ for $K = 0,1,2,3$ . When $K = 1$ , $\mathbb{T}$ is set to $\{250\}$ . Similarly, when $K = 2$ and $K = 3$ , $\mathbb{T}$ is set to $\{250,500\}$ and $\{250,500,750\}$ , respectively. Furthermore, we use the same noise schedule for these four different settings. Tab. 3 shows that when the number of downsampling grows, the sample quality preserves a reasonable level, indicating that DVDP can vary dimensionality for multiple times. + +# 6. Conclusion + +This paper generalizes the traditional diffusion process to a dimensionality-varying diffusion process (DVDP). The proposed DVDP has both theoretical and experimental contributions. Theoretically, we carefully decompose the signal in the diffusion process into multiple orthogonal dynamic-attenuated components. With a rigorously deduced approximation strategy, this then leads to a novel reverse process that generates images from much lower dimensional noises compared with the image resolutions. This design allows much higher training and sampling speed of the diffusion models with on-par or even better synthesis performance, and superior performance in synthesizing large-size images of $1024 \times 1024$ resolution compared with classic methods. The results in this work can promote the understanding and applications of diffusion models in broader scenarios. + +# References + +[1] Fan Bao, Chongxuan Li, Jun Zhu, and Bo Zhang. Analytic-DPM: an analytic estimate of the optimal reverse variance in diffusion probabilistic models. Int. Conf. Learn. Represent., 2022. 2 +[2] Prafulla Dhariwal and Alexander Nichol. Diffusion models beat GANs on image synthesis. Adv. 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We argue that, considering the spatial redundancy in image signals, there is no need to maintain a high dimensionality in the evolution process, especially in the early generation phase. To this end, we make a theoretical generalization of the forward diffusion process via signal decomposition. Concretely, we manage to decompose an image into multiple orthogonal components and control the attenuation of each component when perturbing the image. That way, along with the noise strength increasing, we are able to diminish those inconsequential components and thus use a lower-dimensional signal to represent the source, barely losing information. Such a reformulation allows to vary dimensions in both training and inference of diffusion models. Extensive experiments on a range of datasets suggest that our approach substantially reduces the computational cost and achieves on-par or even better synthesis performance compared to baseline methods. We also show that our strategy facilitates high-resolution image synthesis and improves FID of diffusion model trained on FFHQ at " + }, + { + "bbox": [ + 46, + 398, + 288, + 685 + ], + "type": "inline_equation", + "content": "1024 \\times 1024" + }, + { + "bbox": [ + 46, + 398, + 288, + 685 + ], + "type": "text", + "content": " resolution from 52.40 to 10.46. Code is available at https://github.com/damo-vilab/dvdp." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 307, + 380, + 386, + 392 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 380, + 386, + 392 + ], + "spans": [ + { + "bbox": [ + 307, + 380, + 386, + 392 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 399, + 545, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 399, + 545, + 519 + ], + "spans": [ + { + "bbox": [ + 304, + 399, + 545, + 519 + ], + "type": "text", + "content": "Diffusion models [2, 6, 9, 15, 21, 24, 28] have recently shown great potential in image synthesis. Instead of directly learning the observed distribution, it constructs a multistep forward process through gradually adding noise onto the real data (i.e., diffusion). After a sufficiently large number of steps, the source signal could be considered completely destroyed, resulting in a pure noise distribution that naturally supports sampling. In this way, starting from sampled noises, we can expect new instances after reversing the diffusion process step by step." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "text", + "content": "As it can be seen, the above pipeline does not change the dimension of the source signal throughout the entire diffusion process [6,26,28]. It thus requires the reverse process to map a high-dimensional input to a high-dimensional output at every single step, causing heavy computation overheads [10, 22]. However, images present a measure of spatial redundancy [4] from the semantic perspective (e.g., an image pixel could usually be easily predicted according to its neighbours). Given such a fact, when the source signal is attenuated to some extent along with the noise strength growing, it should be possible to get replaced by a lower-dimensional signal. We therefore argue that there is no need to follow the source signal dimension along the entire distribution evolution process, especially at early steps (i.e., steps close to the pure noise distribution) for coarse generation." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 57, + 693, + 215, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 693, + 215, + 713 + ], + "spans": [ + { + "bbox": [ + 57, + 693, + 215, + 713 + ], + "type": "text", + "content": "* corresponding author. \n† Work performed at Alibaba DAMO Academy." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14307" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 73, + 70, + 521, + 205 + ], + "blocks": [ + { + "bbox": [ + 73, + 70, + 521, + 205 + ], + "lines": [ + { + "bbox": [ + 73, + 70, + 521, + 205 + ], + "spans": [ + { + "bbox": [ + 73, + 70, + 521, + 205 + ], + "type": "image", + "image_path": "32e7610b3c4f4a513822f75e6717dcff62f0bb639277a422609e3c53a8d50873.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 209, + 547, + 234 + ], + "lines": [ + { + "bbox": [ + 46, + 209, + 547, + 234 + ], + "spans": [ + { + "bbox": [ + 46, + 209, + 547, + 234 + ], + "type": "text", + "content": "Figure 2. Conceptual comparison between DDPM [6] and our proposed DVDP, where our approach allows using a varying dimension in the diffusion process." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 243, + 289, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 243, + 289, + 434 + ], + "spans": [ + { + "bbox": [ + 46, + 243, + 289, + 434 + ], + "type": "text", + "content": "In this work, we propose dimensionality-varying diffusion process (DVDP), which allows dynamically adjusting the signal dimension when constructing the forward path. The varying dimensionality concept is shown in Fig. 2. For this purpose, we first decompose an image into multiple orthogonal components, each of which owns dimension lower than the original data. Then, based on such a decomposition, we theoretically generalize the conventional diffusion process such that we can control the attenuation of each component when adding noise. Thanks to this reformulation, we manage to drop those inconsequential components after the noise strength reaches a certain level, and thus represent the source image using a lower-dimensional signal with little information lost. The remaining diffusion process could inherit this dimension and apply the same technique to further reduce the dimension." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 436, + 289, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 436, + 289, + 617 + ], + "spans": [ + { + "bbox": [ + 46, + 436, + 289, + 617 + ], + "type": "text", + "content": "We evaluate our approach on various datasets, including objects, human faces, animals, indoor scenes, and outdoor scenes. Experimental results suggest that DVDP achieves on-par or even better synthesis performance than baseline models on all datasets. More importantly, DVDP relies on much fewer computations, and hence speeds up both training and inference of diffusion models. We also demonstrate the effectiveness of our approach in learning from high-resolution data. For example, we are able to start from a " + }, + { + "bbox": [ + 46, + 436, + 289, + 617 + ], + "type": "inline_equation", + "content": "64 \\times 64" + }, + { + "bbox": [ + 46, + 436, + 289, + 617 + ], + "type": "text", + "content": " noise to produce an image under " + }, + { + "bbox": [ + 46, + 436, + 289, + 617 + ], + "type": "inline_equation", + "content": "1024 \\times 1024" + }, + { + "bbox": [ + 46, + 436, + 289, + 617 + ], + "type": "text", + "content": " resolution. With FID [5] as the evaluation metric, our " + }, + { + "bbox": [ + 46, + 436, + 289, + 617 + ], + "type": "inline_equation", + "content": "1024 \\times 1024" + }, + { + "bbox": [ + 46, + 436, + 289, + 617 + ], + "type": "text", + "content": " model trained on FFHQ improves the baseline [28] from 52.40 to 10.46. All these advantages benefit from using a lower-dimensional signal, which reduces the computational cost and mitigates the optimization difficulty." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 632, + 134, + 644 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 632, + 134, + 644 + ], + "spans": [ + { + "bbox": [ + 47, + 632, + 134, + 644 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "content": "Diffusion models. [26] proposes diffusion models for the first time that generate samples from a target distribution by reversing a diffusion process in which target distribution is gradually disturbed to an easily sampled standard Gaussian. [6] further proposes DDPM to reverse the diffusion process" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 243, + 545, + 279 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 243, + 545, + 279 + ], + "spans": [ + { + "bbox": [ + 304, + 243, + 545, + 279 + ], + "type": "text", + "content": "by learning a noise prediction network. [28] considers diffusion models as stochastic differential equations with continuous timesteps and proposes a unified framework." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 280, + 546, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 280, + 546, + 496 + ], + "spans": [ + { + "bbox": [ + 304, + 280, + 546, + 496 + ], + "type": "text", + "content": "Accelerating diffusion models. Diffusion models significantly suffer from the low training and inference speed. There are many methods that speed up sampling from thousands of steps to tens of steps while keeping an acceptable sample quality [1, 14, 17, 19, 25, 27, 30, 31]. Besides improvements only on inference speed, there are other works aiming at speeding up both training and inference. [18] proposes a patch operation to decrease the dimensionality of each channel while accordingly increasing the number of channels, which greatly reduces the complexity of computation. Besides, a trainable forward process [33] is also proven to benefit a faster training and inference speed. However, the price of their acceleration is a poor sampling quality evaluated by FID score. In this work, we accelerate DDPM on both training and inference from a different perspective, i.e., reducing the dimensionality of the early diffusion process, and thus improving the efficiency while obtaining on-par or even better synthesis performance." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 497, + 547, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 497, + 547, + 664 + ], + "spans": [ + { + "bbox": [ + 304, + 497, + 547, + 664 + ], + "type": "text", + "content": "Varying dimensionality of diffusion models. Due to the redundancy in image signals, it is possible to improve the efficiency of diffusion models by varying dimensionality during the generation process. The most relevant work to our proposed model is subspace diffusion [10], which can also vary dimensionality in the diffusion process. However, subspace diffusion suffers from a trade-off between sampling acceleration and sample quality, while our DVDP can relieve this dilemma (see theoretical analysis in Sec. 4.4 and experimental results in Sec. 5.3). Instead of varying dimensionality in one diffusion process, there are works cascading several diffusion processes with growing dimensionality [7, 21, 23, 24], where the subsequent process is conditioned on the previous samples." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "content": "Discussion with latent diffusion. Besides varying dimensionality in image space, there are other methods, which we generally call latent diffusion, that directly apply diffusion models in a low dimensional latent space, obtained by an" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14308" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": "autoencoder [3, 8, 20, 22, 29]. Although latent diffusion can also speed up the training and sampling of diffusion models, it decreases dimensionality by an additional model and keeps the diffusion process unchanged. In this paper, however, we focus on the improvement on the diffusion process itself to accelerate training and sampling, which is totally a different route. Besides training and sampling efficiency, another important contribution of this work is to prove that it is unnecessary for diffusion process to keep a fixed dimension along time. By controlling the attenuation of each data component, it is possible to change dimensionality while keeping the process reversible. Thus, we will not further compare our DVDP with latent diffusion." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 240, + 126, + 254 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 240, + 126, + 254 + ], + "spans": [ + { + "bbox": [ + 47, + 240, + 126, + 254 + ], + "type": "text", + "content": "3. Background" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 261, + 287, + 345 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 261, + 287, + 345 + ], + "spans": [ + { + "bbox": [ + 46, + 261, + 287, + 345 + ], + "type": "text", + "content": "We first introduce the background of Denoising Diffusion Probabilistic Model (DDPM) [6, 26] and some of its extensions which are closely related to our work. DDPM constructs a forward process to perturb the distribution of data " + }, + { + "bbox": [ + 46, + 261, + 287, + 345 + ], + "type": "inline_equation", + "content": "q(\\mathbf{x}_0)" + }, + { + "bbox": [ + 46, + 261, + 287, + 345 + ], + "type": "text", + "content": " into a standard Gaussian " + }, + { + "bbox": [ + 46, + 261, + 287, + 345 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(\\mathbf{0};\\mathbf{I})" + }, + { + "bbox": [ + 46, + 261, + 287, + 345 + ], + "type": "text", + "content": ". Considering an increasing variance schedule of noises " + }, + { + "bbox": [ + 46, + 261, + 287, + 345 + ], + "type": "inline_equation", + "content": "\\beta_{1},\\ldots ,\\beta_{T}" + }, + { + "bbox": [ + 46, + 261, + 287, + 345 + ], + "type": "text", + "content": ", DDPM defines the forward process as a Markov chain" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 71, + 356, + 287, + 370 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 71, + 356, + 287, + 370 + ], + "spans": [ + { + "bbox": [ + 71, + 356, + 287, + 370 + ], + "type": "interline_equation", + "content": "\\mathbf {x} _ {t} = \\sqrt {1 - \\beta_ {t}} \\mathbf {x} _ {t - 1} + \\sqrt {\\beta_ {t}} \\epsilon , t = 1, 2, \\dots , T, \\tag {1}", + "image_path": "25757e19c87fb144ceb3413e76e0c74d5b5a48f897f4e778721fbcfaafa4fbd5.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 375, + 287, + 423 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 375, + 287, + 423 + ], + "spans": [ + { + "bbox": [ + 46, + 375, + 287, + 423 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 375, + 287, + 423 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 46, + 375, + 287, + 423 + ], + "type": "text", + "content": " is a standard Gaussian noise. In order to generate high-fidelity images, DDPM [6] denoises samples from a standard Gaussian iteratively utilizing the reverse process parameterized as" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 58, + 433, + 287, + 460 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 433, + 287, + 460 + ], + "spans": [ + { + "bbox": [ + 58, + 433, + 287, + 460 + ], + "type": "interline_equation", + "content": "\\mathbf {x} _ {t - 1} = \\frac {1}{\\sqrt {\\alpha_ {t}}} \\left(\\mathbf {x} _ {t} - \\frac {\\beta_ {t}}{\\sqrt {1 - \\bar {\\alpha} _ {t}}} \\epsilon_ {\\theta} (\\mathbf {x} _ {t}, t)\\right) + \\sqrt {\\beta_ {t}} \\epsilon , \\tag {2}", + "image_path": "c9ef9ff7827d4988569464d929d1e02beb72d4bba972a2cf1067732d9ca6c83f.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 466, + 287, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 466, + 287, + 503 + ], + "spans": [ + { + "bbox": [ + 47, + 466, + 287, + 503 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 466, + 287, + 503 + ], + "type": "inline_equation", + "content": "\\alpha_{t} = 1 - \\beta_{t}" + }, + { + "bbox": [ + 47, + 466, + 287, + 503 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 466, + 287, + 503 + ], + "type": "inline_equation", + "content": "\\bar{\\alpha}_{t} = \\prod_{s=1}^{t} \\alpha_{s}" + }, + { + "bbox": [ + 47, + 466, + 287, + 503 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 466, + 287, + 503 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 47, + 466, + 287, + 503 + ], + "type": "text", + "content": " is a neural network used to predict " + }, + { + "bbox": [ + 47, + 466, + 287, + 503 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 47, + 466, + 287, + 503 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 47, + 466, + 287, + 503 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{t}" + }, + { + "bbox": [ + 47, + 466, + 287, + 503 + ], + "type": "text", + "content": ". The parameters " + }, + { + "bbox": [ + 47, + 466, + 287, + 503 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 47, + 466, + 287, + 503 + ], + "type": "text", + "content": " are learned by minimizing the following loss function" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 82, + 512, + 287, + 533 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 512, + 287, + 533 + ], + "spans": [ + { + "bbox": [ + 82, + 512, + 287, + 533 + ], + "type": "interline_equation", + "content": "L (\\theta) = \\mathbb {E} _ {t, \\mathbf {x} _ {0}, \\epsilon} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} \\left(\\mathbf {x} _ {t} \\left(\\mathbf {x} _ {0}, \\epsilon\\right), t\\right) \\| ^ {2} \\right]. \\tag {3}", + "image_path": "ab131b285b13c46af73632bf09ce92fcc772729d94efcbdfc85072ef8e5bf0e7.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 537, + 287, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 537, + 287, + 586 + ], + "spans": [ + { + "bbox": [ + 46, + 537, + 287, + 586 + ], + "type": "text", + "content": "While the standard diffusion model is implemented directly in the image space, [13] takes the relative importance of different frequency components into consideration, and generalizes the forward diffusion process as" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 82, + 595, + 287, + 612 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 595, + 287, + 612 + ], + "spans": [ + { + "bbox": [ + 82, + 595, + 287, + 612 + ], + "type": "interline_equation", + "content": "\\mathbf {x} _ {t} = \\boldsymbol {U} (\\mathbf {I} - \\mathbf {B} _ {t}) ^ {\\frac {1}{2}} \\boldsymbol {U} ^ {T} \\mathbf {x} _ {t - 1} + \\boldsymbol {U} \\mathbf {B} _ {t} ^ {\\frac {1}{2}} \\boldsymbol {U} ^ {T} \\epsilon , \\tag {4}", + "image_path": "837535066561cfd9eb01b263f95dd49f2ed8e0361be6c31c51203eb9e3251c9d.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{U}" + }, + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "type": "text", + "content": " is an orthogonal matrix to impose a rotation on " + }, + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t" + }, + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "type": "text", + "content": ", and the noise schedule is defined by the diagonal matrix " + }, + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{B}_t" + }, + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "type": "text", + "content": ". As Eq. (4) is too general to be directly instantiated as an implementation, [13] only discusses one special case called blur diffusion, which owns a clearly different focus from our work. In this work, we extend the generalized framework further and make it possible to vary dimensionality during the diffusion process." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 71, + 534, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 71, + 534, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 534, + 85 + ], + "type": "text", + "content": "4. Dimensionality-Varying Diffusion Process" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 91, + 545, + 212 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 91, + 545, + 212 + ], + "spans": [ + { + "bbox": [ + 304, + 91, + 545, + 212 + ], + "type": "text", + "content": "We formulate the dimensionality-varying diffusion process in this section, which progressively decreases the dimension of " + }, + { + "bbox": [ + 304, + 91, + 545, + 212 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t" + }, + { + "bbox": [ + 304, + 91, + 545, + 212 + ], + "type": "text", + "content": " in the forward process, and can be effectively reversed to generate high-dimensional data from a low-dimensional noise. To establish DVDP, we gradually attenuate components of " + }, + { + "bbox": [ + 304, + 91, + 545, + 212 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0" + }, + { + "bbox": [ + 304, + 91, + 545, + 212 + ], + "type": "text", + "content": " in different subspaces and decrease the dimensionality of " + }, + { + "bbox": [ + 304, + 91, + 545, + 212 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t" + }, + { + "bbox": [ + 304, + 91, + 545, + 212 + ], + "type": "text", + "content": " at dimensionality turning points by downsampling operator (Sec. 4.1), which is approximately reversible (Sec. 4.2) with controllable small error caused by the loss of attenuated " + }, + { + "bbox": [ + 304, + 91, + 545, + 212 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0" + }, + { + "bbox": [ + 304, + 91, + 545, + 212 + ], + "type": "text", + "content": " component (Sec. 4.3)." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 220, + 453, + 232 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 220, + 453, + 232 + ], + "spans": [ + { + "bbox": [ + 306, + 220, + 453, + 232 + ], + "type": "text", + "content": "4.1. Forward Process of DVDP" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 239, + 545, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 239, + 545, + 467 + ], + "spans": [ + { + "bbox": [ + 304, + 239, + 545, + 467 + ], + "type": "text", + "content": "In this section, we will construct the forward process of our DVDP, which decreases the dimensionality as time evolves and can be effectively reversed. To this end, we concatenate multiple diffusion processes with different dimensions into an entire Markov chain by downsampling operations, while we elaborately design each process so that the information loss induced by downsampling is negligible. Fig. 3 illustrates this overall framework. The concatenation of different processes enables us to decrease the dimensionality, and the control on information loss ensures that downsampling operations are approximately reversible, such that the entire process can be reversed (discussed later in Sec. 4.2). To limit the information loss, we decompose the data into orthogonal components and control the attenuation of each component in the forward process of each concatenated diffusion, which we call Attenuated Diffusion Process (ADP). Once the lost data component induced by downsampling is attenuated to be small enough, the information loss will be negligible." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 468, + 545, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 468, + 545, + 503 + ], + "spans": [ + { + "bbox": [ + 304, + 468, + 545, + 503 + ], + "type": "text", + "content": "Notation list. As a prerequisite for constructing each ADP, we first define a sequence of subspaces and other necessary notations as follows:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 317, + 509, + 545, + 713 + ], + "type": "list", + "angle": 0, + "index": 22, + "blocks": [ + { + "bbox": [ + 317, + 509, + 545, + 558 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 509, + 545, + 558 + ], + "spans": [ + { + "bbox": [ + 317, + 509, + 545, + 558 + ], + "type": "text", + "content": "- " + }, + { + "bbox": [ + 317, + 509, + 545, + 558 + ], + "type": "inline_equation", + "content": "\\mathbb{S}_0 \\supseteq \\mathbb{S}_1 \\supseteq \\dots \\supseteq \\mathbb{S}_K" + }, + { + "bbox": [ + 317, + 509, + 545, + 558 + ], + "type": "text", + "content": " is a sequence of subspaces with decreasing dimensionality " + }, + { + "bbox": [ + 317, + 509, + 545, + 558 + ], + "type": "inline_equation", + "content": "d = \\bar{d}_0 > \\bar{d}_1 > \\dots > \\bar{d}_K" + }, + { + "bbox": [ + 317, + 509, + 545, + 558 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 317, + 509, + 545, + 558 + ], + "type": "inline_equation", + "content": "\\mathbb{S}_0 = \\mathbb{R}^d" + }, + { + "bbox": [ + 317, + 509, + 545, + 558 + ], + "type": "text", + "content": " is the original space, " + }, + { + "bbox": [ + 317, + 509, + 545, + 558 + ], + "type": "inline_equation", + "content": "K \\in \\mathbb{N}_+" + }, + { + "bbox": [ + 317, + 509, + 545, + 558 + ], + "type": "text", + "content": ". For simplicity, " + }, + { + "bbox": [ + 317, + 509, + 545, + 558 + ], + "type": "inline_equation", + "content": "\\mathbb{S}_{K+1} \\triangleq \\{\\mathbf{0}\\}" + }, + { + "bbox": [ + 317, + 509, + 545, + 558 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 317, + 509, + 545, + 558 + ], + "type": "inline_equation", + "content": "\\bar{d}_{K+1} \\triangleq 0" + }, + { + "bbox": [ + 317, + 509, + 545, + 558 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 317, + 562, + 545, + 587 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 562, + 545, + 587 + ], + "spans": [ + { + "bbox": [ + 317, + 562, + 545, + 587 + ], + "type": "text", + "content": "- " + }, + { + "bbox": [ + 317, + 562, + 545, + 587 + ], + "type": "inline_equation", + "content": "d_{i} = \\dim (\\mathbb{S}_{i} / \\mathbb{S}_{i + 1})" + }, + { + "bbox": [ + 317, + 562, + 545, + 587 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 317, + 562, + 545, + 587 + ], + "type": "inline_equation", + "content": "i = 0,1,\\dots ,K" + }, + { + "bbox": [ + 317, + 562, + 545, + 587 + ], + "type": "text", + "content": ". Note that " + }, + { + "bbox": [ + 317, + 562, + 545, + 587 + ], + "type": "inline_equation", + "content": "d_{K} = \\dim (\\mathbb{S}_{K} / \\mathbb{S}_{K + 1}) = \\dim (\\mathbb{S}_{K})" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 317, + 591, + 545, + 630 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 591, + 545, + 630 + ], + "spans": [ + { + "bbox": [ + 317, + 591, + 545, + 630 + ], + "type": "text", + "content": "- " + }, + { + "bbox": [ + 317, + 591, + 545, + 630 + ], + "type": "inline_equation", + "content": "\\mathbf{U}_0 = [\\hat{\\mathbf{U}}_0, \\dots, \\hat{\\mathbf{U}}_K] \\in \\mathbb{R}^{d \\times d}" + }, + { + "bbox": [ + 317, + 591, + 545, + 630 + ], + "type": "text", + "content": " is an orthogonal matrix, and column vectors of its sub-matrix " + }, + { + "bbox": [ + 317, + 591, + 545, + 630 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{U}}_i \\in \\mathbb{R}^{d \\times d_i}" + }, + { + "bbox": [ + 317, + 591, + 545, + 630 + ], + "type": "text", + "content": " span subspace " + }, + { + "bbox": [ + 317, + 591, + 545, + 630 + ], + "type": "inline_equation", + "content": "\\mathbb{S}_i / \\mathbb{S}_{i+1}" + }, + { + "bbox": [ + 317, + 591, + 545, + 630 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 317, + 591, + 545, + 630 + ], + "type": "inline_equation", + "content": "i = 0, 1, \\dots, K" + }, + { + "bbox": [ + 317, + 591, + 545, + 630 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 317, + 635, + 545, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 635, + 545, + 675 + ], + "spans": [ + { + "bbox": [ + 317, + 635, + 545, + 675 + ], + "type": "text", + "content": "- " + }, + { + "bbox": [ + 317, + 635, + 545, + 675 + ], + "type": "inline_equation", + "content": "\\mathbf{U}_k \\in \\mathbb{R}^{\\bar{d}_k \\times \\bar{d}_k}" + }, + { + "bbox": [ + 317, + 635, + 545, + 675 + ], + "type": "text", + "content": " is an orthogonal matrix for " + }, + { + "bbox": [ + 317, + 635, + 545, + 675 + ], + "type": "inline_equation", + "content": "k = 0,1,\\dots,K" + }, + { + "bbox": [ + 317, + 635, + 545, + 675 + ], + "type": "text", + "content": ", and can be split as " + }, + { + "bbox": [ + 317, + 635, + 545, + 675 + ], + "type": "inline_equation", + "content": "\\mathbf{U}_k = [N_k, P_k]" + }, + { + "bbox": [ + 317, + 635, + 545, + 675 + ], + "type": "text", + "content": " when " + }, + { + "bbox": [ + 317, + 635, + 545, + 675 + ], + "type": "inline_equation", + "content": "k < K" + }, + { + "bbox": [ + 317, + 635, + 545, + 675 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 317, + 635, + 545, + 675 + ], + "type": "inline_equation", + "content": "N_k \\in \\mathbb{R}^{\\bar{d}_k \\times d_k}, P_k \\in \\mathbb{R}^{\\bar{d}_k \\times \\bar{d}_{k+1}}" + }, + { + "bbox": [ + 317, + 635, + 545, + 675 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 19 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+ } + ] + } + ], + "index": 21 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14309" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 77, + 71, + 521, + 214 + ], + "blocks": [ + { + "bbox": [ + 77, + 71, + 521, + 214 + ], + "lines": [ + { + "bbox": [ + 77, + 71, + 521, + 214 + ], + "spans": [ + { + "bbox": [ + 77, + 71, + 521, + 214 + ], + "type": "image", + "image_path": "5e086991f38ed0e1da5707e117cb5ce92a3e9c83974101cf3e29a5ee98ea9875.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 218, + 547, + 264 + ], + "lines": [ + { + "bbox": [ + 46, + 218, + 547, + 264 + ], + "spans": [ + { + "bbox": [ + 46, + 218, + 547, + 264 + ], + "type": "text", + "content": "Figure 3. Framework illustration of DVDP. Each row represents an Attenuated Diffusion Process (ADP), which controls the attenuation of each data component while adding noise. All " + }, + { + "bbox": [ + 46, + 218, + 547, + 264 + ], + "type": "inline_equation", + "content": "K + 1" + }, + { + "bbox": [ + 46, + 218, + 547, + 264 + ], + "type": "text", + "content": " ADPs (" + }, + { + "bbox": [ + 46, + 218, + 547, + 264 + ], + "type": "inline_equation", + "content": "K = 2" + }, + { + "bbox": [ + 46, + 218, + 547, + 264 + ], + "type": "text", + "content": " here) have different dimensions decreasing from top to bottom, and are concatenated by some simple operations to obtain our DVDP. In the forward process, the concatenation is achieved by downsampling operation, and in reverse process, it is the upsampling operation followed by adding a Gaussian noise." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 279, + 288, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 279, + 288, + 304 + ], + "spans": [ + { + "bbox": [ + 47, + 279, + 288, + 304 + ], + "type": "text", + "content": "With the above definitions, we can first construct an ADP " + }, + { + "bbox": [ + 47, + 279, + 288, + 304 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t^0\\in \\mathbb{S}_0" + }, + { + "bbox": [ + 47, + 279, + 288, + 304 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 47, + 279, + 288, + 304 + ], + "type": "inline_equation", + "content": "t = 0,1,\\dots ,T" + }, + { + "bbox": [ + 47, + 279, + 288, + 304 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 91, + 312, + 287, + 361 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 312, + 287, + 361 + ], + "spans": [ + { + "bbox": [ + 91, + 312, + 287, + 361 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathbf {x} _ {t} ^ {0} = \\sum_ {i = 0} ^ {K} \\left(\\bar {\\lambda} _ {i, t} \\mathbf {v} _ {i} ^ {0} + \\bar {\\sigma} _ {i, t} \\mathbf {z} _ {i} ^ {0}\\right) \\tag {5} \\\\ = \\boldsymbol {U} _ {0} \\bar {\\boldsymbol {\\Lambda}} _ {0, t} \\boldsymbol {U} _ {0} ^ {T} \\mathbf {x} _ {0} ^ {0} + \\boldsymbol {U} _ {0} \\bar {\\boldsymbol {L}} _ {0, t} \\boldsymbol {U} _ {0} ^ {T} \\epsilon^ {0}, \\\\ \\end{array}", + "image_path": "8fe86e872e909b114b5a795369a52ebbf2c0c8d8993d4397db96367d35a0eecb.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 365, + 287, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 365, + 287, + 513 + ], + "spans": [ + { + "bbox": [ + 47, + 365, + 287, + 513 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 365, + 287, + 513 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_i^0\\in \\mathbb{S}_i / \\mathbb{S}_{i + 1}" + }, + { + "bbox": [ + 47, + 365, + 287, + 513 + ], + "type": "text", + "content": " is the component of original data point " + }, + { + "bbox": [ + 47, + 365, + 287, + 513 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0^0" + }, + { + "bbox": [ + 47, + 365, + 287, + 513 + ], + "type": "text", + "content": " in subspace " + }, + { + "bbox": [ + 47, + 365, + 287, + 513 + ], + "type": "inline_equation", + "content": "\\mathbb{S}_i / \\mathbb{S}_{i + 1}" + }, + { + "bbox": [ + 47, + 365, + 287, + 513 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 365, + 287, + 513 + ], + "type": "inline_equation", + "content": "\\bar{\\lambda}_{i,t}" + }, + { + "bbox": [ + 47, + 365, + 287, + 513 + ], + "type": "text", + "content": " controls the attenuation of " + }, + { + "bbox": [ + 47, + 365, + 287, + 513 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_i^0" + }, + { + "bbox": [ + 47, + 365, + 287, + 513 + ], + "type": "text", + "content": " along timestep " + }, + { + "bbox": [ + 47, + 365, + 287, + 513 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 365, + 287, + 513 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 365, + 287, + 513 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_i^0" + }, + { + "bbox": [ + 47, + 365, + 287, + 513 + ], + "type": "text", + "content": " is the component of a standard Gaussian noise " + }, + { + "bbox": [ + 47, + 365, + 287, + 513 + ], + "type": "inline_equation", + "content": "\\epsilon^0\\in \\mathbb{R}^{\\bar{d}_0}" + }, + { + "bbox": [ + 47, + 365, + 287, + 513 + ], + "type": "text", + "content": " in the same subspace as " + }, + { + "bbox": [ + 47, + 365, + 287, + 513 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_i^0" + }, + { + "bbox": [ + 47, + 365, + 287, + 513 + ], + "type": "text", + "content": " (i.e., " + }, + { + "bbox": [ + 47, + 365, + 287, + 513 + ], + "type": "inline_equation", + "content": "\\mathbb{S}_i / \\mathbb{S}_{i + 1}" + }, + { + "bbox": [ + 47, + 365, + 287, + 513 + ], + "type": "text", + "content": "), " + }, + { + "bbox": [ + 47, + 365, + 287, + 513 + ], + "type": "inline_equation", + "content": "\\bar{\\sigma}_{i,t}" + }, + { + "bbox": [ + 47, + 365, + 287, + 513 + ], + "type": "text", + "content": " is the standard deviation of " + }, + { + "bbox": [ + 47, + 365, + 287, + 513 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_i^0" + }, + { + "bbox": [ + 47, + 365, + 287, + 513 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 365, + 287, + 513 + ], + "type": "inline_equation", + "content": "\\bar{\\Lambda}_{0,t}" + }, + { + "bbox": [ + 47, + 365, + 287, + 513 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 365, + 287, + 513 + ], + "type": "inline_equation", + "content": "\\bar{\\pmb{L}}_{0,t}\\in \\mathbb{R}^{\\bar{d}_0\\times \\bar{d}_0}" + }, + { + "bbox": [ + 47, + 365, + 287, + 513 + ], + "type": "text", + "content": " are two diagonal matrices defined as " + }, + { + "bbox": [ + 47, + 365, + 287, + 513 + ], + "type": "inline_equation", + "content": "\\bar{\\Lambda}_{0,t} = \\mathrm{diag}(\\bar{\\lambda}_{0,t}\\pmb{I}_{d_0},\\bar{\\lambda}_{1,t}\\pmb{I}_{d_1},\\dots ,\\bar{\\lambda}_{K,t}\\pmb{I}_{d_K})" + }, + { + "bbox": [ + 47, + 365, + 287, + 513 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 365, + 287, + 513 + ], + "type": "inline_equation", + "content": "\\bar{\\pmb{L}}_{0,t} = \\mathrm{diag}(\\bar{\\sigma}_{0,t}\\pmb{I}_{d_0},\\bar{\\sigma}_{1,t}\\pmb{I}_{d_1},\\dots ,\\bar{\\sigma}_{K,t}\\pmb{I}_{d_K})" + }, + { + "bbox": [ + 47, + 365, + 287, + 513 + ], + "type": "text", + "content": ". To control the attenuation of each data component " + }, + { + "bbox": [ + 47, + 365, + 287, + 513 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_i^0" + }, + { + "bbox": [ + 47, + 365, + 287, + 513 + ], + "type": "text", + "content": ", we require " + }, + { + "bbox": [ + 47, + 365, + 287, + 513 + ], + "type": "inline_equation", + "content": "\\bar{\\lambda}_{i,t}" + }, + { + "bbox": [ + 47, + 365, + 287, + 513 + ], + "type": "text", + "content": " to gradually decrease from 1 to approximate 0 for " + }, + { + "bbox": [ + 47, + 365, + 287, + 513 + ], + "type": "inline_equation", + "content": "i = 0,1,\\dots ,K - 1" + }, + { + "bbox": [ + 47, + 365, + 287, + 513 + ], + "type": "text", + "content": " as timestep " + }, + { + "bbox": [ + 47, + 365, + 287, + 513 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 365, + 287, + 513 + ], + "type": "text", + "content": " evolves. As for " + }, + { + "bbox": [ + 47, + 365, + 287, + 513 + ], + "type": "inline_equation", + "content": "\\bar{\\lambda}_{K,t}" + }, + { + "bbox": [ + 47, + 365, + 287, + 513 + ], + "type": "text", + "content": ", it is not required to decrease (explained later after Eq. (8))." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 513, + 287, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 513, + 287, + 536 + ], + "spans": [ + { + "bbox": [ + 47, + 513, + 287, + 536 + ], + "type": "text", + "content": "Starting from " + }, + { + "bbox": [ + 47, + 513, + 287, + 536 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t^0" + }, + { + "bbox": [ + 47, + 513, + 287, + 536 + ], + "type": "text", + "content": ", we can recursively construct a dimensionality-decreasing sequence of ADPs" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 56, + 545, + 287, + 595 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 545, + 287, + 595 + ], + "spans": [ + { + "bbox": [ + 56, + 545, + 287, + 595 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathbf {x} _ {t} ^ {k} = \\mathcal {D} _ {k} \\mathbf {x} _ {t} ^ {k - 1} = \\sum_ {i = k} ^ {K} \\left(\\bar {\\lambda} _ {i, t} \\mathbf {v} _ {i} ^ {k} + \\bar {\\sigma} _ {i, t} \\mathbf {z} _ {i} ^ {k}\\right) \\tag {6} \\\\ = \\boldsymbol {U} _ {k} \\bar {\\boldsymbol {\\Lambda}} _ {k, t} \\boldsymbol {U} _ {k} ^ {T} \\mathbf {x} _ {0} ^ {k} + \\boldsymbol {U} _ {k} \\bar {\\boldsymbol {\\mathcal {L}}} _ {k, t} \\boldsymbol {U} _ {k} ^ {T} \\epsilon^ {k}, 1 \\leq k \\leq K, \\\\ \\end{array}", + "image_path": "6f7f44cb6cfcb4663d897445a48abc32ae95bc7806edd948025a08a99bfdb819.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 600, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 600, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 600, + 288, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 600, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_k:\\mathbb{R}^{\\bar{d}_{k - 1}}\\to \\mathbb{R}^{\\bar{d}_k}" + }, + { + "bbox": [ + 47, + 600, + 288, + 715 + ], + "type": "text", + "content": " is a linear surjection, which we call the " + }, + { + "bbox": [ + 47, + 600, + 288, + 715 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 600, + 288, + 715 + ], + "type": "text", + "content": " -th downsampling operator as it reduces the dimensionality of the operand (without ambiguity, we also use " + }, + { + "bbox": [ + 47, + 600, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_k" + }, + { + "bbox": [ + 47, + 600, + 288, + 715 + ], + "type": "text", + "content": " to denote the corresponding matrix in " + }, + { + "bbox": [ + 47, + 600, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{\\bar{d}_k\\times \\bar{d}_{k - 1}}" + }, + { + "bbox": [ + 47, + 600, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_i^k = \\overline{\\mathcal{D}}_k\\mathbf{v}_i^0\\in \\overline{\\mathcal{D}}_k(\\mathbb{S}_i / \\mathbb{S}_{i + 1})" + }, + { + "bbox": [ + 47, + 600, + 288, + 715 + ], + "type": "text", + "content": " is the component of " + }, + { + "bbox": [ + 47, + 600, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0^k = \\overline{\\mathcal{D}}_k\\mathbf{x}_0^0\\in \\mathbb{R}^{\\bar{d}_k}" + }, + { + "bbox": [ + 47, + 600, + 288, + 715 + ], + "type": "inline_equation", + "content": "(\\overline{\\mathcal{D}}_k\\triangleq \\prod_{i = 1}^{k}\\mathcal{D}_i)" + }, + { + "bbox": [ + 47, + 600, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_i^k = \\overline{\\mathcal{D}}_k\\mathbf{z}_i^0\\in \\overline{\\mathcal{D}}_k(\\mathbb{S}_i / \\mathbb{S}_{i + 1})" + }, + { + "bbox": [ + 47, + 600, + 288, + 715 + ], + "type": "text", + "content": " is the component of a standard Gaussian noise " + }, + { + "bbox": [ + 47, + 600, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\epsilon^k = \\overline{\\mathcal{D}}_k\\epsilon^0\\in \\mathbb{R}^{\\bar{d}_k}" + }, + { + "bbox": [ + 47, + 600, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\bar{\\Lambda}_{k,t} =" + }, + { + "bbox": [ + 47, + 600, + 288, + 715 + ], + "type": "text", + "content": " diag( " + }, + { + "bbox": [ + 47, + 600, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\bar{\\lambda}_{k,t}\\pmb {I}_{d_k}" + }, + { + "bbox": [ + 47, + 600, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\bar{\\lambda}_{k + 1,t}\\pmb {I}_{d_{k + 1}},\\dots ,\\bar{\\lambda}_{K,t}\\pmb {I}_{d_K})\\in \\mathbb{R}^{\\bar{d}_k\\times \\bar{d}_k}," + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 278, + 545, + 329 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 278, + 545, + 329 + ], + "spans": [ + { + "bbox": [ + 305, + 278, + 545, + 329 + ], + "type": "inline_equation", + "content": "\\bar{\\pmb{L}}_{k,t} = \\mathrm{diag}(\\bar{\\sigma}_{k,t}\\pmb{I}_{d_k},\\bar{\\sigma}_{k + 1,t}\\pmb{I}_{d_{k + 1}},\\dots ,\\bar{\\sigma}_{K,t}\\pmb{I}_{d_K})\\in" + }, + { + "bbox": [ + 305, + 278, + 545, + 329 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{\\bar{d}_k\\times \\bar{d}_k}" + }, + { + "bbox": [ + 305, + 278, + 545, + 329 + ], + "type": "text", + "content": " , and orthogonal matrix " + }, + { + "bbox": [ + 305, + 278, + 545, + 329 + ], + "type": "inline_equation", + "content": "U_{k}\\in \\mathbb{R}^{\\bar{d}_{k}\\times \\bar{d}_{k}}" + }, + { + "bbox": [ + 305, + 278, + 545, + 329 + ], + "type": "text", + "content": " consists of the last " + }, + { + "bbox": [ + 305, + 278, + 545, + 329 + ], + "type": "inline_equation", + "content": "\\bar{d}_k" + }, + { + "bbox": [ + 305, + 278, + 545, + 329 + ], + "type": "text", + "content": " columns of " + }, + { + "bbox": [ + 305, + 278, + 545, + 329 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_k\\pmb{U}_{k - 1}" + }, + { + "bbox": [ + 305, + 278, + 545, + 329 + ], + "type": "text", + "content": " , i.e., " + }, + { + "bbox": [ + 305, + 278, + 545, + 329 + ], + "type": "inline_equation", + "content": "\\pmb {U}_k = \\mathcal{D}_k\\pmb {P}_{k - 1}" + }, + { + "bbox": [ + 305, + 278, + 545, + 329 + ], + "type": "text", + "content": " (note that this condition requires further restriction on " + }, + { + "bbox": [ + 305, + 278, + 545, + 329 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_k" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 330, + 545, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 330, + 545, + 365 + ], + "spans": [ + { + "bbox": [ + 305, + 330, + 545, + 365 + ], + "type": "text", + "content": "Both Eqs. (5) and (6) can be derived from Markov chains with Gaussian kernels as (see Supplementary Material for the proof)" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 310, + 375, + 545, + 390 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 375, + 545, + 390 + ], + "spans": [ + { + "bbox": [ + 310, + 375, + 545, + 390 + ], + "type": "interline_equation", + "content": "\\mathbf {x} _ {t} ^ {k} = \\boldsymbol {U} _ {k} \\boldsymbol {\\Lambda} _ {k, t} \\boldsymbol {U} _ {k} ^ {T} \\mathbf {x} _ {t - 1} ^ {k} + \\boldsymbol {U} _ {k} \\boldsymbol {L} _ {k, t} \\boldsymbol {U} _ {k} ^ {T} \\epsilon^ {k}, 0 \\leq k \\leq K, \\tag {7}", + "image_path": "cfe3afd928cb8e5ee4fc9fa2ea0ed2dc29f4ff35754d3becda921f6a4afb099e.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 399, + 544, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 399, + 544, + 415 + ], + "spans": [ + { + "bbox": [ + 305, + 399, + 544, + 415 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 399, + 544, + 415 + ], + "type": "inline_equation", + "content": "\\Lambda_{k,t} = \\bar{\\Lambda}_{k,t - 1}^{-1}\\bar{\\Lambda}_{k,t},L_{k,t} = (\\bar{L}_{k,t}^{2} - \\Lambda_{k,t}^{2}\\bar{L}_{k,t - 1}^{2})^{1 / 2}." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 415, + 545, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 415, + 545, + 513 + ], + "spans": [ + { + "bbox": [ + 304, + 415, + 545, + 513 + ], + "type": "text", + "content": "Now with the ADPs " + }, + { + "bbox": [ + 304, + 415, + 545, + 513 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{x}_t^k\\}_{k = 0}^K" + }, + { + "bbox": [ + 304, + 415, + 545, + 513 + ], + "type": "text", + "content": " given by Eq. (7), we can construct the forward process of DVDP by merging different parts of " + }, + { + "bbox": [ + 304, + 415, + 545, + 513 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{x}_t^k\\}_{k = 0}^K" + }, + { + "bbox": [ + 304, + 415, + 545, + 513 + ], + "type": "text", + "content": " in the following manner: consider a strictly increasing time sequence " + }, + { + "bbox": [ + 304, + 415, + 545, + 513 + ], + "type": "inline_equation", + "content": "T_{1},\\dots ,T_{K},T_{K + 1} = T," + }, + { + "bbox": [ + 304, + 415, + 545, + 513 + ], + "type": "text", + "content": " if for each " + }, + { + "bbox": [ + 304, + 415, + 545, + 513 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 415, + 545, + 513 + ], + "type": "text", + "content": " satisfying " + }, + { + "bbox": [ + 304, + 415, + 545, + 513 + ], + "type": "inline_equation", + "content": "1\\leq k\\leq K" + }, + { + "bbox": [ + 304, + 415, + 545, + 513 + ], + "type": "inline_equation", + "content": "\\bar{\\lambda}_{k - 1,T_k}" + }, + { + "bbox": [ + 304, + 415, + 545, + 513 + ], + "type": "text", + "content": " becomes small enough, then " + }, + { + "bbox": [ + 304, + 415, + 545, + 513 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{T_k}^{k - 1}" + }, + { + "bbox": [ + 304, + 415, + 545, + 513 + ], + "type": "text", + "content": " is downsampled by " + }, + { + "bbox": [ + 304, + 415, + 545, + 513 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_k" + }, + { + "bbox": [ + 304, + 415, + 545, + 513 + ], + "type": "text", + "content": " to obtain " + }, + { + "bbox": [ + 304, + 415, + 545, + 513 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{T_k}^k" + }, + { + "bbox": [ + 304, + 415, + 545, + 513 + ], + "type": "text", + "content": " with lower dimensionality, and each " + }, + { + "bbox": [ + 304, + 415, + 545, + 513 + ], + "type": "inline_equation", + "content": "T_{k}" + }, + { + "bbox": [ + 304, + 415, + 545, + 513 + ], + "type": "text", + "content": " is a dimensionality turning point. The entire process can be expressed as" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 348, + 521, + 545, + 564 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 521, + 545, + 564 + ], + "spans": [ + { + "bbox": [ + 348, + 521, + 545, + 564 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathbf {x} _ {0} ^ {0} \\longrightarrow \\mathbf {x} _ {1} ^ {0} \\quad \\longrightarrow \\dots \\longrightarrow \\mathbf {x} _ {T _ {1}} ^ {0} \\\\ \\xrightarrow {\\mathcal {D} _ {1}} \\mathbf {x} _ {T _ {1}} ^ {1} \\longrightarrow \\mathbf {x} _ {T _ {1} + 1} ^ {1} \\longrightarrow \\dots \\longrightarrow \\mathbf {x} _ {T _ {2}} ^ {1} \\tag {8} \\\\ \\end{array}", + "image_path": "59f09471c67c2208f6f33673f4abbb287b577c20634c6e0cc295775821747d93.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 349, + 563, + 504, + 597 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 349, + 563, + 504, + 597 + ], + "spans": [ + { + "bbox": [ + 349, + 563, + 504, + 597 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\begin{array}{c} \\bullet \\\\ \\bullet \\\\ \\bullet \\\\ \\bullet \\end{array} \\\\ \\xrightarrow {\\mathcal {D} _ {K}} \\mathbf {x} _ {T _ {K}} ^ {K} \\longrightarrow \\mathbf {x} _ {T _ {K} + 1} ^ {K} \\longrightarrow \\dots \\longrightarrow \\mathbf {x} _ {T} ^ {K}. \\\\ \\end{array}", + "image_path": "2d6d4bd3e43162bc886e51c28196a3117000ce61fd4036236889c997cd3b7e3c.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 601, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 601, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 601, + 545, + 714 + ], + "type": "text", + "content": "Between two adjacent dimensionality turning points " + }, + { + "bbox": [ + 304, + 601, + 545, + 714 + ], + "type": "inline_equation", + "content": "T_{k-1}" + }, + { + "bbox": [ + 304, + 601, + 545, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 601, + 545, + 714 + ], + "type": "inline_equation", + "content": "T_{k}" + }, + { + "bbox": [ + 304, + 601, + 545, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 601, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{t}^{k-1}" + }, + { + "bbox": [ + 304, + 601, + 545, + 714 + ], + "type": "text", + "content": " diffuses and attenuates data components " + }, + { + "bbox": [ + 304, + 601, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_{i}^{k-1}" + }, + { + "bbox": [ + 304, + 601, + 545, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 601, + 545, + 714 + ], + "type": "inline_equation", + "content": "i \\geq k-1" + }, + { + "bbox": [ + 304, + 601, + 545, + 714 + ], + "type": "text", + "content": ", which keeps the dimensionality " + }, + { + "bbox": [ + 304, + 601, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\bar{d}_{k-1}" + }, + { + "bbox": [ + 304, + 601, + 545, + 714 + ], + "type": "text", + "content": ". When it comes to " + }, + { + "bbox": [ + 304, + 601, + 545, + 714 + ], + "type": "inline_equation", + "content": "T_{k}" + }, + { + "bbox": [ + 304, + 601, + 545, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 601, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{T_{k}}^{k-1} \\xrightarrow{\\mathcal{D}_{k}} \\mathbf{x}_{T_{k}}^{k}" + }, + { + "bbox": [ + 304, + 601, + 545, + 714 + ], + "type": "text", + "content": " decreases the dimension from " + }, + { + "bbox": [ + 304, + 601, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\bar{d}_{k-1}" + }, + { + "bbox": [ + 304, + 601, + 545, + 714 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 601, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\bar{d}_{k}" + }, + { + "bbox": [ + 304, + 601, + 545, + 714 + ], + "type": "text", + "content": ". After the last dimensionality turning point " + }, + { + "bbox": [ + 304, + 601, + 545, + 714 + ], + "type": "inline_equation", + "content": "T_{k}" + }, + { + "bbox": [ + 304, + 601, + 545, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 601, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{t}^{K}" + }, + { + "bbox": [ + 304, + 601, + 545, + 714 + ], + "type": "text", + "content": " can just evolve as conventional diffusion without data component attenuation. Thus, the entire process in Eq. (8) decreases the dimensionality by " + }, + { + "bbox": [ + 304, + 601, + 545, + 714 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 601, + 545, + 714 + ], + "type": "text", + "content": " times from " + }, + { + "bbox": [ + 304, + 601, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\bar{d}_{0} = d" + }, + { + "bbox": [ + 304, + 601, + 545, + 714 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 601, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\bar{d}_{K}" + }, + { + "bbox": [ + 304, + 601, + 545, + 714 + ], + "type": "text", + "content": ". It should be noted that process" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "14310" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 175 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 175 + ], + "type": "text", + "content": "in Eq. (8) is also Markovian since each diffusion subprocess " + }, + { + "bbox": [ + 46, + 72, + 289, + 175 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{T_{k - 1}}^{k - 1}\\rightarrow \\mathbf{x}_{T_k}^{k - 1}" + }, + { + "bbox": [ + 46, + 72, + 289, + 175 + ], + "type": "text", + "content": " is Markovian, and the result of each downsampling operation " + }, + { + "bbox": [ + 46, + 72, + 289, + 175 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{T_k}^k" + }, + { + "bbox": [ + 46, + 72, + 289, + 175 + ], + "type": "text", + "content": " is uniquely determined by the previous state " + }, + { + "bbox": [ + 46, + 72, + 289, + 175 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{T_k}^{k - 1}" + }, + { + "bbox": [ + 46, + 72, + 289, + 175 + ], + "type": "text", + "content": ". Also note that each downsampling operation " + }, + { + "bbox": [ + 46, + 72, + 289, + 175 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_k" + }, + { + "bbox": [ + 46, + 72, + 289, + 175 + ], + "type": "text", + "content": " loses little information because of small " + }, + { + "bbox": [ + 46, + 72, + 289, + 175 + ], + "type": "inline_equation", + "content": "\\bar{\\lambda}_{k - 1,T_k}" + }, + { + "bbox": [ + 46, + 72, + 289, + 175 + ], + "type": "text", + "content": " which is a controllable hyperparameter. For better understanding, consider the relationship between " + }, + { + "bbox": [ + 46, + 72, + 289, + 175 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{T_k}^{k - 1}" + }, + { + "bbox": [ + 46, + 72, + 289, + 175 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 72, + 289, + 175 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{T_k}^k" + }, + { + "bbox": [ + 46, + 72, + 289, + 175 + ], + "type": "text", + "content": " derived from Eq. (6)" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 61, + 178, + 287, + 209 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 178, + 287, + 209 + ], + "spans": [ + { + "bbox": [ + 61, + 178, + 287, + 209 + ], + "type": "interline_equation", + "content": "\\mathbf {x} _ {T _ {k}} ^ {k - 1} = \\mathcal {D} _ {k} ^ {T} \\mathbf {x} _ {T _ {k}} ^ {k} + \\underbrace {\\bar {\\lambda} _ {k - 1 , T _ {k}} \\mathbf {v} _ {k - 1} ^ {k - 1}} _ {\\text {d a t a c o m p o n e n t}} + \\underbrace {\\bar {\\sigma} _ {k - 1 , T _ {k}} \\mathbf {z} _ {k - 1} ^ {k - 1}} _ {\\text {n o i s e c o m p o n e n t}}, \\tag {9}", + "image_path": "94016b431e9c202937be0624de0cd24b44cb7e6dc2275fbba122e5e5629f0005.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 210, + 289, + 309 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 210, + 289, + 309 + ], + "spans": [ + { + "bbox": [ + 46, + 210, + 289, + 309 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 210, + 289, + 309 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_k^T" + }, + { + "bbox": [ + 46, + 210, + 289, + 309 + ], + "type": "text", + "content": " is the transpose of matrix " + }, + { + "bbox": [ + 46, + 210, + 289, + 309 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_k" + }, + { + "bbox": [ + 46, + 210, + 289, + 309 + ], + "type": "text", + "content": ", named as the " + }, + { + "bbox": [ + 46, + 210, + 289, + 309 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 210, + 289, + 309 + ], + "type": "text", + "content": "-th upsampling operator. From Eq. (9), it is clear that " + }, + { + "bbox": [ + 46, + 210, + 289, + 309 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{T_k}^k" + }, + { + "bbox": [ + 46, + 210, + 289, + 309 + ], + "type": "text", + "content": " actually loses two terms compared with " + }, + { + "bbox": [ + 46, + 210, + 289, + 309 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{T_k}^{k-1}" + }, + { + "bbox": [ + 46, + 210, + 289, + 309 + ], + "type": "text", + "content": ": 1) data component " + }, + { + "bbox": [ + 46, + 210, + 289, + 309 + ], + "type": "inline_equation", + "content": "\\bar{\\lambda}_{k-1,T_k}\\mathbf{v}_{k-1}^{k-1}" + }, + { + "bbox": [ + 46, + 210, + 289, + 309 + ], + "type": "text", + "content": " which is informative but negligible as " + }, + { + "bbox": [ + 46, + 210, + 289, + 309 + ], + "type": "inline_equation", + "content": "\\bar{\\lambda}_{k-1,T_k}" + }, + { + "bbox": [ + 46, + 210, + 289, + 309 + ], + "type": "text", + "content": " is set to be small enough, and 2) noise component " + }, + { + "bbox": [ + 46, + 210, + 289, + 309 + ], + "type": "inline_equation", + "content": "\\bar{\\sigma}_{k-1,T_k}\\mathbf{z}_{k-1}^{k-1}" + }, + { + "bbox": [ + 46, + 210, + 289, + 309 + ], + "type": "text", + "content": " that is non-informative and can be compensated in the reverse process, as we will discuss in Sec. 4.2." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 316, + 252, + 330 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 316, + 252, + 330 + ], + "spans": [ + { + "bbox": [ + 47, + 316, + 252, + 330 + ], + "type": "text", + "content": "4.2. Reverse Process Approximating DVDP" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 335, + 287, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 335, + 287, + 418 + ], + "spans": [ + { + "bbox": [ + 46, + 335, + 287, + 418 + ], + "type": "text", + "content": "In this section, we will derive an approximate reverse process, which induces a data generation process with progressively growing dimensionality. The approximation error will be discussed in Sec. 4.3, and we can find that it actually converges to zero. Loss function will also be given at the end of this section. Implementation details of training and sampling can be found in Supplementary Material." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 418, + 287, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 418, + 287, + 477 + ], + "spans": [ + { + "bbox": [ + 46, + 418, + 287, + 477 + ], + "type": "text", + "content": "Reverse transition. Since DVDP is a sequence of fixed-dimensionality diffusion processes connected by downsampling operations at dimensionality turning points, we consider reverse transition kernels between and at dimensionality turning points separately." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 478, + 287, + 561 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 478, + 287, + 561 + ], + "spans": [ + { + "bbox": [ + 46, + 478, + 287, + 561 + ], + "type": "text", + "content": "For reverse transition between two adjacent dimensionality turning points, i.e., " + }, + { + "bbox": [ + 46, + 478, + 287, + 561 + ], + "type": "inline_equation", + "content": "p_{\\theta}(\\mathbf{x}_{t - 1}^{k}|\\mathbf{x}_{t}^{k})" + }, + { + "bbox": [ + 46, + 478, + 287, + 561 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 46, + 478, + 287, + 561 + ], + "type": "inline_equation", + "content": "T_{k - 1}\\leq t\\leq T_{k}" + }, + { + "bbox": [ + 46, + 478, + 287, + 561 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 46, + 478, + 287, + 561 + ], + "type": "inline_equation", + "content": "k\\in [1,K + 1]" + }, + { + "bbox": [ + 46, + 478, + 287, + 561 + ], + "type": "text", + "content": ", it can be defined as a Gaussian kernel " + }, + { + "bbox": [ + 46, + 478, + 287, + 561 + ], + "type": "inline_equation", + "content": "p_{\\theta}(\\mathbf{x}_{t - 1}^{k}|\\mathbf{x}_{t}^{k}) = \\mathcal{N}(\\mathbf{x}_{t - 1}^{k};\\pmb{\\mu}_{\\theta}(\\mathbf{x}_{t}^{k},t),\\pmb{\\Sigma}_{t})" + }, + { + "bbox": [ + 46, + 478, + 287, + 561 + ], + "type": "text", + "content": ". As in DDPM [6], the covariance matrices " + }, + { + "bbox": [ + 46, + 478, + 287, + 561 + ], + "type": "inline_equation", + "content": "\\pmb{\\Sigma}_t" + }, + { + "bbox": [ + 46, + 478, + 287, + 561 + ], + "type": "text", + "content": " are set to untrained time-dependent constants, and the mean term " + }, + { + "bbox": [ + 46, + 478, + 287, + 561 + ], + "type": "inline_equation", + "content": "\\pmb{\\mu}_{\\theta}(\\mathbf{x}_{t}^{k},t)" + }, + { + "bbox": [ + 46, + 478, + 287, + 561 + ], + "type": "text", + "content": " is defined as (see Supplementary Material for details)" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 94, + 566, + 287, + 597 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 566, + 287, + 597 + ], + "spans": [ + { + "bbox": [ + 94, + 566, + 287, + 597 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\boldsymbol {\\mu} _ {\\theta} = \\tilde {\\boldsymbol {\\mu}} _ {k, t} \\left(\\mathbf {x} _ {t} ^ {k}, U _ {k} \\bar {\\boldsymbol {\\Lambda}} _ {k, t} ^ {- 1} \\boldsymbol {U} _ {k} ^ {T} \\mathbf {x} _ {t} ^ {k} \\right. \\tag {10} \\\\ - \\boldsymbol {U} _ {k} \\bar {\\boldsymbol {\\Lambda}} _ {k, t} ^ {- 1} \\bar {\\boldsymbol {L}} _ {k, t} \\boldsymbol {U} _ {k} ^ {T} \\boldsymbol {\\epsilon} _ {\\theta} \\left(\\boldsymbol {x} _ {t} ^ {k}, t\\right), \\\\ \\end{array}", + "image_path": "89da50eaa7778b8d2a4d970885d5ae1dd87e871bfb77dc71ec88d97029d32bb9.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 599, + 287, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 599, + 287, + 635 + ], + "spans": [ + { + "bbox": [ + 46, + 599, + 287, + 635 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 599, + 287, + 635 + ], + "type": "inline_equation", + "content": "\\tilde{\\pmb{\\mu}}_{k,t}(\\cdot ,\\cdot)" + }, + { + "bbox": [ + 46, + 599, + 287, + 635 + ], + "type": "text", + "content": " is the mean function of forward process posterior " + }, + { + "bbox": [ + 46, + 599, + 287, + 635 + ], + "type": "inline_equation", + "content": "q(\\mathbf{x}_{t - 1}^k |\\mathbf{x}_t^k,\\mathbf{x}_0^k) = \\mathcal{N}(\\mathbf{x}_{t - 1}^k;\\tilde{\\pmb{\\mu}}_{k,t}(\\mathbf{x}_t^k,\\mathbf{x}_0^k),\\tilde{\\pmb{\\Sigma}}_{k,t})" + }, + { + "bbox": [ + 46, + 599, + 287, + 635 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 599, + 287, + 635 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 46, + 599, + 287, + 635 + ], + "type": "text", + "content": " represents a trainable network." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 635, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 635, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 47, + 635, + 287, + 696 + ], + "type": "text", + "content": "For reverse transition at dimensionality turning points, i.e., " + }, + { + "bbox": [ + 47, + 635, + 287, + 696 + ], + "type": "inline_equation", + "content": "p_{\\theta}(\\mathbf{x}_{T_k}^{k - 1}|\\mathbf{x}_{T_k}^k)" + }, + { + "bbox": [ + 47, + 635, + 287, + 696 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 47, + 635, + 287, + 696 + ], + "type": "inline_equation", + "content": "k\\in [1,K]" + }, + { + "bbox": [ + 47, + 635, + 287, + 696 + ], + "type": "text", + "content": ", the corresponding forward transitions barely lose information as illustrated by Eq. (9) in Sec. 4.1, thus " + }, + { + "bbox": [ + 47, + 635, + 287, + 696 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{T_k}^k\\to \\mathbf{x}_{T_k}^{k - 1}" + }, + { + "bbox": [ + 47, + 635, + 287, + 696 + ], + "type": "text", + "content": " can be approximately achieved without any trainable network as" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 69, + 699, + 287, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 699, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 69, + 699, + 287, + 715 + ], + "type": "interline_equation", + "content": "\\mathbf {x} _ {T _ {k}} ^ {k - 1} = \\mathcal {D} _ {k} ^ {T} \\mathbf {x} _ {T _ {k}} ^ {k} + \\boldsymbol {U} _ {k - 1} \\Delta \\boldsymbol {L} _ {k - 1} \\boldsymbol {U} _ {k - 1} ^ {T} \\epsilon^ {k - 1}, \\tag {11}", + "image_path": "da1a9e875e5d707b7f4d58fc1b706ccaac59298f99cc4ce2b80d0dcf00e9897f.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 70, + 545, + 183 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 70, + 545, + 183 + ], + "spans": [ + { + "bbox": [ + 304, + 70, + 545, + 183 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 70, + 545, + 183 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_k^T\\in \\mathbb{R}^{\\bar{d}_k\\times \\bar{d}_{k - 1}}" + }, + { + "bbox": [ + 304, + 70, + 545, + 183 + ], + "type": "text", + "content": " is the upsampling operator, and " + }, + { + "bbox": [ + 304, + 70, + 545, + 183 + ], + "type": "inline_equation", + "content": "\\Delta L_{k - 1} = \\mathrm{diag}(\\bar{\\sigma}_{k - 1,T_k}\\pmb{I}_{d_{k - 1}},\\pmb{O}_{\\bar{d}_k})" + }, + { + "bbox": [ + 304, + 70, + 545, + 183 + ], + "type": "text", + "content": " represents the standard deviation of the added Gaussian noise " + }, + { + "bbox": [ + 304, + 70, + 545, + 183 + ], + "type": "inline_equation", + "content": "\\epsilon^{k - 1}\\in \\mathbb{R}^{\\bar{d}_{k - 1}}" + }, + { + "bbox": [ + 304, + 70, + 545, + 183 + ], + "type": "text", + "content": ". Eq. (11) can be understood as: we first upsample " + }, + { + "bbox": [ + 304, + 70, + 545, + 183 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{T_k}^k" + }, + { + "bbox": [ + 304, + 70, + 545, + 183 + ], + "type": "text", + "content": ", then add a Gaussian noise in compensation for the lost noise component in the forward downsampling operation, i.e., " + }, + { + "bbox": [ + 304, + 70, + 545, + 183 + ], + "type": "inline_equation", + "content": "\\bar{\\sigma}_{k - 1,T_k}\\mathbf{z}_{k - 1}^{k - 1}" + }, + { + "bbox": [ + 304, + 70, + 545, + 183 + ], + "type": "text", + "content": " in Eq. (9). The approximation error comes from neglecting data component " + }, + { + "bbox": [ + 304, + 70, + 545, + 183 + ], + "type": "inline_equation", + "content": "\\bar{\\lambda}_{k - 1,T_k}\\mathbf{v}_{k - 1}^{k - 1}" + }, + { + "bbox": [ + 304, + 70, + 545, + 183 + ], + "type": "text", + "content": ", and will be analyzed later in Sec. 4.3." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 184, + 545, + 220 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 184, + 545, + 220 + ], + "spans": [ + { + "bbox": [ + 304, + 184, + 545, + 220 + ], + "type": "text", + "content": "Loss function. Similar with DDPM [6], a loss function can be derived from a weighted variational bound as (see Supplementary Material for details)" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 310, + 228, + 545, + 246 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 228, + 545, + 246 + ], + "spans": [ + { + "bbox": [ + 310, + 228, + 545, + 246 + ], + "type": "interline_equation", + "content": "L (\\theta) = \\mathbb {E} _ {k} \\mathbb {E} _ {\\mathbf {x} _ {0} ^ {k}, \\epsilon^ {k}, t \\sim \\mathcal {U} _ {k}} \\left[ \\left\\| \\epsilon^ {k} - \\epsilon_ {\\theta} \\left(\\mathbf {x} _ {t} ^ {k} \\left(\\mathbf {x} _ {0} ^ {k}, \\epsilon^ {k}\\right), t\\right) \\right\\| ^ {2} \\right], \\tag {12}", + "image_path": "17819b4a8e608db7b5a756b16266537220bd9ead8e5614587a32935b81da3bc3.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 254, + 545, + 303 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 254, + 545, + 303 + ], + "spans": [ + { + "bbox": [ + 304, + 254, + 545, + 303 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 254, + 545, + 303 + ], + "type": "inline_equation", + "content": "\\mathcal{U}_k = \\mathcal{U}\\big((T_k,T_{k + 1}]\\big)" + }, + { + "bbox": [ + 304, + 254, + 545, + 303 + ], + "type": "text", + "content": " is a discrete uniform distribution between " + }, + { + "bbox": [ + 304, + 254, + 545, + 303 + ], + "type": "inline_equation", + "content": "T_{k}" + }, + { + "bbox": [ + 304, + 254, + 545, + 303 + ], + "type": "text", + "content": " (exclusive) and " + }, + { + "bbox": [ + 304, + 254, + 545, + 303 + ], + "type": "inline_equation", + "content": "T_{k + 1}" + }, + { + "bbox": [ + 304, + 254, + 545, + 303 + ], + "type": "text", + "content": " (inclusive), and " + }, + { + "bbox": [ + 304, + 254, + 545, + 303 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t^k (\\mathbf{x}_0^k,\\epsilon^k)" + }, + { + "bbox": [ + 304, + 254, + 545, + 303 + ], + "type": "text", + "content": " represents the forward " + }, + { + "bbox": [ + 304, + 254, + 545, + 303 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t^k" + }, + { + "bbox": [ + 304, + 254, + 545, + 303 + ], + "type": "text", + "content": " determined by " + }, + { + "bbox": [ + 304, + 254, + 545, + 303 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0^k" + }, + { + "bbox": [ + 304, + 254, + 545, + 303 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 254, + 545, + 303 + ], + "type": "inline_equation", + "content": "\\epsilon^k" + }, + { + "bbox": [ + 304, + 254, + 545, + 303 + ], + "type": "text", + "content": " given in Eq. (6)." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 310, + 399, + 323 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 310, + 399, + 323 + ], + "spans": [ + { + "bbox": [ + 305, + 310, + 399, + 323 + ], + "type": "text", + "content": "4.3. Error Analysis" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 328, + 545, + 414 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 328, + 545, + 414 + ], + "spans": [ + { + "bbox": [ + 304, + 328, + 545, + 414 + ], + "type": "text", + "content": "In Sec. 4.2, we mention that the reverse process is just an approximation of the forward DVDP at each dimensionality turning point " + }, + { + "bbox": [ + 304, + 328, + 545, + 414 + ], + "type": "inline_equation", + "content": "T_{k}" + }, + { + "bbox": [ + 304, + 328, + 545, + 414 + ], + "type": "text", + "content": ". In this section, we will measure this approximation error in probability sense, i.e., the difference between the real forward distribution " + }, + { + "bbox": [ + 304, + 328, + 545, + 414 + ], + "type": "inline_equation", + "content": "q(\\mathbf{x}_{T_k}^{k - 1})" + }, + { + "bbox": [ + 304, + 328, + 545, + 414 + ], + "type": "text", + "content": " and the reverse distribution " + }, + { + "bbox": [ + 304, + 328, + 545, + 414 + ], + "type": "inline_equation", + "content": "p(\\mathbf{x}_{T_k}^{k - 1})" + }, + { + "bbox": [ + 304, + 328, + 545, + 414 + ], + "type": "text", + "content": " under proper assumptions, and will find that this difference converges to zero." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 415, + 545, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 415, + 545, + 474 + ], + "spans": [ + { + "bbox": [ + 304, + 415, + 545, + 474 + ], + "type": "text", + "content": "To measure the difference between two distributions, we use Jensen-Shannon Divergence (JSD) as a metric. Under this metric, upper bound of the approximation error can be derived from Proposition 1 (see Supplementary Material for proof):" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 479, + 545, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 479, + 545, + 563 + ], + "spans": [ + { + "bbox": [ + 304, + 479, + 545, + 563 + ], + "type": "text", + "content": "Proposition 1 Assume " + }, + { + "bbox": [ + 304, + 479, + 545, + 563 + ], + "type": "inline_equation", + "content": "p_1(\\pmb{x}|\\pmb{x}_0)" + }, + { + "bbox": [ + 304, + 479, + 545, + 563 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 479, + 545, + 563 + ], + "type": "inline_equation", + "content": "p_2(\\pmb{x}|\\pmb{x}_0)" + }, + { + "bbox": [ + 304, + 479, + 545, + 563 + ], + "type": "text", + "content": " are two Gaussians such that " + }, + { + "bbox": [ + 304, + 479, + 545, + 563 + ], + "type": "inline_equation", + "content": "p_1(\\pmb{x}|\\pmb{x}_0) = \\mathcal{N}(\\pmb{x};\\pmb{A}_1\\pmb{x}_0,\\pmb{\\Sigma})" + }, + { + "bbox": [ + 304, + 479, + 545, + 563 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 479, + 545, + 563 + ], + "type": "inline_equation", + "content": "p_2(\\pmb{x}|\\pmb{x}_0) = \\mathcal{N}(\\pmb{x};\\pmb{A}_2\\pmb{x}_0,\\pmb{\\Sigma})" + }, + { + "bbox": [ + 304, + 479, + 545, + 563 + ], + "type": "text", + "content": ", where positive semi-definite matrices " + }, + { + "bbox": [ + 304, + 479, + 545, + 563 + ], + "type": "inline_equation", + "content": "A_1, A_2" + }, + { + "bbox": [ + 304, + 479, + 545, + 563 + ], + "type": "text", + "content": " satisfy " + }, + { + "bbox": [ + 304, + 479, + 545, + 563 + ], + "type": "inline_equation", + "content": "A_1\\succeq A_2\\succeq 0" + }, + { + "bbox": [ + 304, + 479, + 545, + 563 + ], + "type": "text", + "content": ", covariance matrix " + }, + { + "bbox": [ + 304, + 479, + 545, + 563 + ], + "type": "inline_equation", + "content": "\\pmb{\\Sigma}" + }, + { + "bbox": [ + 304, + 479, + 545, + 563 + ], + "type": "text", + "content": " is positive definite, and the support of distribution " + }, + { + "bbox": [ + 304, + 479, + 545, + 563 + ], + "type": "inline_equation", + "content": "p(\\pmb{x}_0)" + }, + { + "bbox": [ + 304, + 479, + 545, + 563 + ], + "type": "text", + "content": " is bounded, then Jensen-Shannon Divergence (JSD) of the two marginal distributions " + }, + { + "bbox": [ + 304, + 479, + 545, + 563 + ], + "type": "inline_equation", + "content": "p_1(\\pmb{x})" + }, + { + "bbox": [ + 304, + 479, + 545, + 563 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 479, + 545, + 563 + ], + "type": "inline_equation", + "content": "p_2(\\pmb{x})" + }, + { + "bbox": [ + 304, + 479, + 545, + 563 + ], + "type": "text", + "content": " satisfies" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 326, + 567, + 545, + 616 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 567, + 545, + 616 + ], + "spans": [ + { + "bbox": [ + 326, + 567, + 545, + 616 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\operatorname {J S D} \\left(p _ {1} \\mid \\mid p _ {2}\\right) \\leq \\frac {\\sqrt {2}}{2} e ^ {- \\frac {1}{2}} B \\left(2 \\sqrt {2} + \\frac {V _ {d} (r)}{\\left(2 \\pi\\right) ^ {\\frac {d}{2}}}\\right) \\tag {13} \\\\ \\cdot \\left\\| \\boldsymbol {\\Sigma} ^ {- \\frac {1}{2}} \\left(\\boldsymbol {A} _ {1} - \\boldsymbol {A} _ {2}\\right) \\right\\| _ {2}, \\\\ \\end{array}", + "image_path": "1d783b470c2fe7e70841c93284ad9a57e787033d591ef9a3a03c9aea5efb6046.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 624, + 545, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 624, + 545, + 661 + ], + "spans": [ + { + "bbox": [ + 304, + 624, + 545, + 661 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 624, + 545, + 661 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 304, + 624, + 545, + 661 + ], + "type": "text", + "content": " is the upper bound of " + }, + { + "bbox": [ + 304, + 624, + 545, + 661 + ], + "type": "inline_equation", + "content": "\\| \\pmb{x}_0\\| _2" + }, + { + "bbox": [ + 304, + 624, + 545, + 661 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 624, + 545, + 661 + ], + "type": "inline_equation", + "content": "V_{d}(\\cdot)" + }, + { + "bbox": [ + 304, + 624, + 545, + 661 + ], + "type": "text", + "content": " is the volume of a " + }, + { + "bbox": [ + 304, + 624, + 545, + 661 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 624, + 545, + 661 + ], + "type": "text", + "content": "-dimensional sphere with respect to the radius, and " + }, + { + "bbox": [ + 304, + 624, + 545, + 661 + ], + "type": "inline_equation", + "content": "r = 2B\\| \\Sigma^{-\\frac{1}{2}}A_1\\| _2" + }, + { + "bbox": [ + 304, + 624, + 545, + 661 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 663, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 663, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 663, + 545, + 713 + ], + "type": "text", + "content": "With Proposition 1, the upper bound of JSD between the forward distribution " + }, + { + "bbox": [ + 304, + 663, + 545, + 713 + ], + "type": "inline_equation", + "content": "q(\\mathbf{x}_{T_k}^{k - 1})" + }, + { + "bbox": [ + 304, + 663, + 545, + 713 + ], + "type": "text", + "content": " and the reverse distribution " + }, + { + "bbox": [ + 304, + 663, + 545, + 713 + ], + "type": "inline_equation", + "content": "p(\\mathbf{x}_{T_k}^{k - 1})" + }, + { + "bbox": [ + 304, + 663, + 545, + 713 + ], + "type": "text", + "content": " can be obtained by Theorem 1 (see Supplementary Material for proof)" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14311" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 138 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 138 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 138 + ], + "type": "text", + "content": "Theorem 1 (Reverse Process Error) Assume " + }, + { + "bbox": [ + 47, + 72, + 287, + 138 + ], + "type": "inline_equation", + "content": "0 < k \\leq K" + }, + { + "bbox": [ + 47, + 72, + 287, + 138 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 72, + 287, + 138 + ], + "type": "inline_equation", + "content": "q(\\mathbf{x}_{T_k}^{k-1})" + }, + { + "bbox": [ + 47, + 72, + 287, + 138 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 72, + 287, + 138 + ], + "type": "inline_equation", + "content": "q(\\mathbf{x}_{T_k}^k)" + }, + { + "bbox": [ + 47, + 72, + 287, + 138 + ], + "type": "text", + "content": " are defined by Eqs. (5) and (6), " + }, + { + "bbox": [ + 47, + 72, + 287, + 138 + ], + "type": "inline_equation", + "content": "p(\\mathbf{x}_{T_k}^{k-1})" + }, + { + "bbox": [ + 47, + 72, + 287, + 138 + ], + "type": "text", + "content": " is the marginal distribution of " + }, + { + "bbox": [ + 47, + 72, + 287, + 138 + ], + "type": "inline_equation", + "content": "q(\\mathbf{x}_{T_k}^k)p(\\mathbf{x}_{T_k}^{k-1}|\\mathbf{x}_{T_k}^k)" + }, + { + "bbox": [ + 47, + 72, + 287, + 138 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 47, + 72, + 287, + 138 + ], + "type": "inline_equation", + "content": "p(\\mathbf{x}_{T_k}^{k-1}|\\mathbf{x}_{T_k}^k)" + }, + { + "bbox": [ + 47, + 72, + 287, + 138 + ], + "type": "text", + "content": " is defined by Eq. (11), and " + }, + { + "bbox": [ + 47, + 72, + 287, + 138 + ], + "type": "inline_equation", + "content": "\\| \\mathbf{x}_0\\|_2 \\leq \\sqrt{d}" + }, + { + "bbox": [ + 47, + 72, + 287, + 138 + ], + "type": "text", + "content": ", then" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 67, + 142, + 287, + 190 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 142, + 287, + 190 + ], + "spans": [ + { + "bbox": [ + 67, + 142, + 287, + 190 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\xi_ {1} \\leq \\frac {\\sqrt {2}}{2} e ^ {- \\frac {1}{2}} \\sqrt {d} \\left(2 \\sqrt {2} + \\frac {V _ {d} (r)}{(2 \\pi) ^ {\\frac {d}{2}}}\\right) \\frac {\\bar {\\lambda} _ {k - 1 , T _ {k}}}{\\bar {\\sigma} _ {k - 1 , T _ {k}}} \\tag {14} \\\\ = o \\left(\\bar {\\lambda} _ {k - 1, T _ {k}}\\right), \\\\ \\end{array}", + "image_path": "8cd2a2d6ea059100ea14b7bfb0e922a3f4b554d7f9208e1db9e70ab70204b1e7.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 199, + 287, + 233 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 199, + 287, + 233 + ], + "spans": [ + { + "bbox": [ + 47, + 199, + 287, + 233 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 199, + 287, + 233 + ], + "type": "inline_equation", + "content": "\\xi_1 \\triangleq \\mathrm{JSD}(q(\\mathbf{x}_{T_k}^{k-1})||p(\\mathbf{x}_{T_k}^{k-1})), \\text{ and } r = 2\\sqrt{d}\\max_{k-1 \\leq i \\leq K} \\frac{\\bar{\\lambda}_{i,T_k}}{\\bar{\\sigma}_{i,T_k}}." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 236, + 287, + 310 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 236, + 287, + 310 + ], + "spans": [ + { + "bbox": [ + 47, + 236, + 287, + 310 + ], + "type": "text", + "content": "Note that the assumption " + }, + { + "bbox": [ + 47, + 236, + 287, + 310 + ], + "type": "inline_equation", + "content": "\\| \\mathbf{x}_0\\| _2\\leq \\sqrt{d}" + }, + { + "bbox": [ + 47, + 236, + 287, + 310 + ], + "type": "text", + "content": " can be satisfied for image data, since pixel values can be normalized in " + }, + { + "bbox": [ + 47, + 236, + 287, + 310 + ], + "type": "inline_equation", + "content": "[-1,1]" + }, + { + "bbox": [ + 47, + 236, + 287, + 310 + ], + "type": "text", + "content": ". Thus, Theorem 1 claims that " + }, + { + "bbox": [ + 47, + 236, + 287, + 310 + ], + "type": "inline_equation", + "content": "\\xi_{1}" + }, + { + "bbox": [ + 47, + 236, + 287, + 310 + ], + "type": "text", + "content": " can be arbitrarily small as " + }, + { + "bbox": [ + 47, + 236, + 287, + 310 + ], + "type": "inline_equation", + "content": "\\bar{\\lambda}_{k - 1,T_k}\\to 0" + }, + { + "bbox": [ + 47, + 236, + 287, + 310 + ], + "type": "text", + "content": " if we can get an exact " + }, + { + "bbox": [ + 47, + 236, + 287, + 310 + ], + "type": "inline_equation", + "content": "q(\\mathbf{x}_{T_k}^{k - 1})" + }, + { + "bbox": [ + 47, + 236, + 287, + 310 + ], + "type": "text", + "content": " by reverse process. It means that the approximation error caused by stepping over " + }, + { + "bbox": [ + 47, + 236, + 287, + 310 + ], + "type": "inline_equation", + "content": "T_{k}" + }, + { + "bbox": [ + 47, + 236, + 287, + 310 + ], + "type": "text", + "content": " can be small enough." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 317, + 243, + 330 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 317, + 243, + 330 + ], + "spans": [ + { + "bbox": [ + 47, + 317, + 243, + 330 + ], + "type": "text", + "content": "4.4. Comparison with Subspace Diffusion" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 335, + 287, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 335, + 287, + 443 + ], + "spans": [ + { + "bbox": [ + 46, + 335, + 287, + 443 + ], + "type": "text", + "content": "To reduce the dimensionality of latent space in diffusion models, subspace diffusion is proposed to model in a low-dimensional subspace at high noise levels, and keep the original full-dimensional network at low noise levels [10]. This can also be seen as a concatenation of multiple diffusion processes with different dimensionality like our DVDP, but without controllable attenuation on each data component. Each concatenated processes is just conventional isotropic diffusion." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 445, + 287, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 445, + 287, + 617 + ], + "spans": [ + { + "bbox": [ + 46, + 445, + 287, + 617 + ], + "type": "text", + "content": "Thus, subspace diffusion can be seen as a special case of our DVDP with " + }, + { + "bbox": [ + 46, + 445, + 287, + 617 + ], + "type": "inline_equation", + "content": "\\bar{\\lambda}_t \\triangleq \\bar{\\lambda}_{0,t} = \\bar{\\lambda}_{1,t} = \\dots = \\bar{\\lambda}_{K,t}" + }, + { + "bbox": [ + 46, + 445, + 287, + 617 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 445, + 287, + 617 + ], + "type": "inline_equation", + "content": "\\bar{\\sigma}_t \\triangleq \\bar{\\sigma}_{0,t} = \\bar{\\sigma}_{1,t} = \\dots = \\bar{\\sigma}_{K,t}" + }, + { + "bbox": [ + 46, + 445, + 287, + 617 + ], + "type": "text", + "content": ", which limits the choice of dimensionality turning points. This limitation can be further explained by Eq. (9): at dimensionality turning point " + }, + { + "bbox": [ + 46, + 445, + 287, + 617 + ], + "type": "inline_equation", + "content": "T_k" + }, + { + "bbox": [ + 46, + 445, + 287, + 617 + ], + "type": "text", + "content": " in the forward process, " + }, + { + "bbox": [ + 46, + 445, + 287, + 617 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{T_k}^{k-1}" + }, + { + "bbox": [ + 46, + 445, + 287, + 617 + ], + "type": "text", + "content": " will lose an informative data component " + }, + { + "bbox": [ + 46, + 445, + 287, + 617 + ], + "type": "inline_equation", + "content": "\\bar{\\lambda}_{k-1,T_k} \\mathbf{v}_{k-1}^{k-1}" + }, + { + "bbox": [ + 46, + 445, + 287, + 617 + ], + "type": "text", + "content": " and a noninformative noise component " + }, + { + "bbox": [ + 46, + 445, + 287, + 617 + ], + "type": "inline_equation", + "content": "\\bar{\\sigma}_{k-1,T_k} \\mathbf{z}_{k-1}^{k-1}" + }, + { + "bbox": [ + 46, + 445, + 287, + 617 + ], + "type": "text", + "content": ". To safely neglect the data component in the reverse transition, it requires that " + }, + { + "bbox": [ + 46, + 445, + 287, + 617 + ], + "type": "inline_equation", + "content": "\\bar{\\lambda}_{k-1,T_k} / \\bar{\\sigma}_{k-1,T_k} \\ll \\| \\mathbf{z}_{k-1}^{k-1} \\| / \\| \\mathbf{v}_{k-1}^{k-1} \\|" + }, + { + "bbox": [ + 46, + 445, + 287, + 617 + ], + "type": "text", + "content": ". For subspace diffusion, it means that the consistent " + }, + { + "bbox": [ + 46, + 445, + 287, + 617 + ], + "type": "inline_equation", + "content": "\\bar{\\lambda}_t / \\bar{\\sigma}_t" + }, + { + "bbox": [ + 46, + 445, + 287, + 617 + ], + "type": "text", + "content": " for components in all subspaces should be small enough, which usually indicates a large " + }, + { + "bbox": [ + 46, + 445, + 287, + 617 + ], + "type": "inline_equation", + "content": "T_k" + }, + { + "bbox": [ + 46, + 445, + 287, + 617 + ], + "type": "text", + "content": ", i.e., a large number of diffusion steps in high dimensional space." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": "Therefore, as claimed in [10], the choice of " + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "inline_equation", + "content": "T_{k}" + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": " should balance two factors: 1) smaller " + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "inline_equation", + "content": "T_{k}" + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": " reduces the number of reverse diffusion steps occurring at higher dimensionality, whereas 2) larger " + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "inline_equation", + "content": "T_{k}" + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": " makes the reverse transition at " + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "inline_equation", + "content": "T_{k}" + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": " more accurate. Although [10] additionally proposes to compensate the loss of data component by adding an extra Gaussian noise besides compensation for the noise component, this trade-off still exists." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "text", + "content": "However, our DVDP can set much smaller " + }, + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "inline_equation", + "content": "T_{k}" + }, + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "text", + "content": " with little loss in accuracy, which benefits from the controllable attenuation for each data component. Theorem 1 supports this advantage theoretically, and experimental results in Sec. 5.3 further demonstrate it." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 142, + 387, + 156 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 142, + 387, + 156 + ], + "spans": [ + { + "bbox": [ + 306, + 142, + 387, + 156 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 162, + 545, + 340 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 162, + 545, + 340 + ], + "spans": [ + { + "bbox": [ + 304, + 162, + 545, + 340 + ], + "type": "text", + "content": "In this section, we show that our DVDP can speed up both training and inference of diffusion models while achieving competitive performance. Besides, thanks to the varied dimension, DVDP is able to generate high-quality and high-resolution images from a low-dimensional subspace and exceeds existing methods including scoreSDE [28] and Cascaded Diffusion Models (CDM) [7] on FFHQ " + }, + { + "bbox": [ + 304, + 162, + 545, + 340 + ], + "type": "inline_equation", + "content": "1024^{2}" + }, + { + "bbox": [ + 304, + 162, + 545, + 340 + ], + "type": "text", + "content": ". Specifically, we first introduce our experimental setup in Sec. 5.1. Then we compare our DVDP with existing alternatives on several widely evaluated datasets in terms of visual quality and modeling efficiency in Sec. 5.2. After that, we compare our DVDP with Subspace Diffusion [10], a closely related work proposed recently, in Sec. 5.3. Finally, we implement necessary ablation studies in the last Sec. 5.4." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 348, + 422, + 361 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 348, + 422, + 361 + ], + "spans": [ + { + "bbox": [ + 306, + 348, + 422, + 361 + ], + "type": "text", + "content": "5.1. Experimental Setup" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 366, + 545, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 366, + 545, + 437 + ], + "spans": [ + { + "bbox": [ + 304, + 366, + 545, + 437 + ], + "type": "text", + "content": "Datasets. In order to verify that DVDP is widely applicable, we use six image datasets covering various classes and a wide range of resolutions from 32 to 1024. To be specific, we implement DVDP on CIFAR10 " + }, + { + "bbox": [ + 304, + 366, + 545, + 437 + ], + "type": "inline_equation", + "content": "32^2" + }, + { + "bbox": [ + 304, + 366, + 545, + 437 + ], + "type": "text", + "content": " [12], LSUN Bedroom " + }, + { + "bbox": [ + 304, + 366, + 545, + 437 + ], + "type": "inline_equation", + "content": "256^2" + }, + { + "bbox": [ + 304, + 366, + 545, + 437 + ], + "type": "text", + "content": " [32], LSUN Church " + }, + { + "bbox": [ + 304, + 366, + 545, + 437 + ], + "type": "inline_equation", + "content": "256^2" + }, + { + "bbox": [ + 304, + 366, + 545, + 437 + ], + "type": "text", + "content": ", LSUN Cat " + }, + { + "bbox": [ + 304, + 366, + 545, + 437 + ], + "type": "inline_equation", + "content": "256^2" + }, + { + "bbox": [ + 304, + 366, + 545, + 437 + ], + "type": "text", + "content": ", FFHQ " + }, + { + "bbox": [ + 304, + 366, + 545, + 437 + ], + "type": "inline_equation", + "content": "256^2" + }, + { + "bbox": [ + 304, + 366, + 545, + 437 + ], + "type": "text", + "content": ", and FFHQ " + }, + { + "bbox": [ + 304, + 366, + 545, + 437 + ], + "type": "inline_equation", + "content": "1024^2" + }, + { + "bbox": [ + 304, + 366, + 545, + 437 + ], + "type": "text", + "content": " [11]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 438, + 545, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 438, + 545, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 438, + 545, + 653 + ], + "type": "text", + "content": "Implementation details. We adopt the UNet improved by [2] which achieves better performance than the traditional version [6]. Since most baseline methods adopt a single UNet network for all timesteps in the whole diffusion process, our DVDP also keeps this setting, except the comparison with Subspace Diffusion in Sec. 5.3, which takes two networks for different generation stages [10]. In principle, the network structure of our DVDP is kept the same as the corresponding baseline. However, when resolution comes to " + }, + { + "bbox": [ + 304, + 438, + 545, + 653 + ], + "type": "inline_equation", + "content": "1024 \\times 1024" + }, + { + "bbox": [ + 304, + 438, + 545, + 653 + ], + "type": "text", + "content": ", the UNet in conventional diffusion models should be deep enough to contain sufficient downsampling blocks, thus to obtain embeddings with proper size (usually " + }, + { + "bbox": [ + 304, + 438, + 545, + 653 + ], + "type": "inline_equation", + "content": "4 \\times 4" + }, + { + "bbox": [ + 304, + 438, + 545, + 653 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 304, + 438, + 545, + 653 + ], + "type": "inline_equation", + "content": "8 \\times 8" + }, + { + "bbox": [ + 304, + 438, + 545, + 653 + ], + "type": "text", + "content": ") in the bottleneck layer. On the contrary, our DVDP does not need such a deep network since the generation starts from a low resolution noise (" + }, + { + "bbox": [ + 304, + 438, + 545, + 653 + ], + "type": "inline_equation", + "content": "64 \\times 64" + }, + { + "bbox": [ + 304, + 438, + 545, + 653 + ], + "type": "text", + "content": " in our case). Thus we only maintain a similar amount of parameters but use a different hyperparameter setting on FFHQ " + }, + { + "bbox": [ + 304, + 438, + 545, + 653 + ], + "type": "inline_equation", + "content": "1024^2" + }, + { + "bbox": [ + 304, + 438, + 545, + 653 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "We set the number of timesteps " + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "inline_equation", + "content": "T = 1,000" + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": " in all of our experiments. For DVDP, we reduce the dimensionality by " + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\frac{1}{4}" + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": " (i.e., " + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "inline_equation", + "content": "h \\times w \\to \\frac{h}{2} \\times \\frac{w}{2}" + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": " for image resolution) when the timestep " + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": " reaches a dimensionality turning point. For simplicity, we adopt " + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbb{T} \\triangleq \\{T_1, \\dots, T_K\\}" + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": ". For CIFAR10" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14312" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 98, + 547, + 308 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 545, + 94 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 545, + 94 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 545, + 94 + ], + "type": "text", + "content": "Table 1. Quantitative comparison between DDPM [6] and our DVDP on various datasets regarding image quality and model efficiency. * indicates our reproduced DDPM. Both " + }, + { + "bbox": [ + 47, + 70, + 545, + 94 + ], + "type": "inline_equation", + "content": "{\\mathrm{{DDMP}}}^{ * }" + }, + { + "bbox": [ + 47, + 70, + 545, + 94 + ], + "type": "text", + "content": " and our DVDP adopt the improved UNet [2] for a fair comparison." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 47, + 98, + 547, + 308 + ], + "lines": [ + { + "bbox": [ + 47, + 98, + 547, + 308 + ], + "spans": [ + { + "bbox": [ + 47, + 98, + 547, + 308 + ], + "type": "table", + "html": "
DatasetMethodFID (50k)↓Training Speed (sec/iter)Training Speed UpSampling Speed (sec/sample)Sampling Speed Up
CIFAR10 32 × 32DDPM3.17----
DDPM*3.160.18-0.34-
DVDP3.240.151.2×0.261.3×
LSUN Bedroom 256 × 256DDPM6.36----
DDPM*5.740.99-12.2-
DVDP4.880.452.2×5.012.4×
LSUN Church 256 × 256DDPM7.89----
DDPM*7.540.99-12.2-
DVDP7.030.452.2×5.012.4×
LSUN Cat 256 × 256DDPM19.75----
DDPM*18.110.99-12.2-
DVDP16.500.452.2×5.012.4×
FFHQ 256 × 256DDPM*8.330.99-12.2-
DVDP8.030.452.2×5.012.4×
", + "image_path": "9e507874ee5faaa5533477fef881e9390f29f6476036e5e90219b88aaa811283.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 326, + 287, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 326, + 287, + 373 + ], + "spans": [ + { + "bbox": [ + 46, + 326, + 287, + 373 + ], + "type": "inline_equation", + "content": "32^{2}" + }, + { + "bbox": [ + 46, + 326, + 287, + 373 + ], + "type": "text", + "content": ", we set " + }, + { + "bbox": [ + 46, + 326, + 287, + 373 + ], + "type": "inline_equation", + "content": "\\mathbb{T} = \\{600\\}" + }, + { + "bbox": [ + 46, + 326, + 287, + 373 + ], + "type": "text", + "content": ", indicating that the resolution is decreased from " + }, + { + "bbox": [ + 46, + 326, + 287, + 373 + ], + "type": "inline_equation", + "content": "32 \\times 32" + }, + { + "bbox": [ + 46, + 326, + 287, + 373 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 326, + 287, + 373 + ], + "type": "inline_equation", + "content": "16 \\times 16" + }, + { + "bbox": [ + 46, + 326, + 287, + 373 + ], + "type": "text", + "content": " when " + }, + { + "bbox": [ + 46, + 326, + 287, + 373 + ], + "type": "inline_equation", + "content": "t = 600" + }, + { + "bbox": [ + 46, + 326, + 287, + 373 + ], + "type": "text", + "content": ". Similarly, we set " + }, + { + "bbox": [ + 46, + 326, + 287, + 373 + ], + "type": "inline_equation", + "content": "\\mathbb{T} = \\{300, 600\\}" + }, + { + "bbox": [ + 46, + 326, + 287, + 373 + ], + "type": "text", + "content": " for all " + }, + { + "bbox": [ + 46, + 326, + 287, + 373 + ], + "type": "inline_equation", + "content": "256^{2}" + }, + { + "bbox": [ + 46, + 326, + 287, + 373 + ], + "type": "text", + "content": " datasets and " + }, + { + "bbox": [ + 46, + 326, + 287, + 373 + ], + "type": "inline_equation", + "content": "\\mathbb{T} = \\{200, 400, 600, 800\\}" + }, + { + "bbox": [ + 46, + 326, + 287, + 373 + ], + "type": "text", + "content": " for FFHQ " + }, + { + "bbox": [ + 46, + 326, + 287, + 373 + ], + "type": "inline_equation", + "content": "1024^{2}" + }, + { + "bbox": [ + 46, + 326, + 287, + 373 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 375, + 287, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 375, + 287, + 434 + ], + "spans": [ + { + "bbox": [ + 46, + 375, + 287, + 434 + ], + "type": "text", + "content": "In all of our experiments, the noise schedule of DVDP is an adapted version of linear schedule [6], which is suitable for DVDP and keeps a comparable signal-to-noise ratio (SNR) with the original version (see Supplementary Material for details)." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 435, + 287, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 435, + 287, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 435, + 287, + 567 + ], + "type": "text", + "content": "Evaluation metrics. For sample quality, we calculate the FID score [5] on 50k samples, except for FFHQ " + }, + { + "bbox": [ + 46, + 435, + 287, + 567 + ], + "type": "inline_equation", + "content": "1024^{2}" + }, + { + "bbox": [ + 46, + 435, + 287, + 567 + ], + "type": "text", + "content": " with 10k samples due to a much slower sampling. As for training and sampling speed, both of them are evaluated on a single NVIDIA A100. Training speed is measured by the mean time of each iteration (estimated over 4,000 iterations), and sampling speed is measured by the mean time of each sample (estimated over 100 batches). The training batch size and sampling batch size are 128, 256 respectively for CIFAR10 " + }, + { + "bbox": [ + 46, + 435, + 287, + 567 + ], + "type": "inline_equation", + "content": "32^{2}" + }, + { + "bbox": [ + 46, + 435, + 287, + 567 + ], + "type": "text", + "content": ", and 24, 64 respectively for other " + }, + { + "bbox": [ + 46, + 435, + 287, + 567 + ], + "type": "inline_equation", + "content": "256^{2}" + }, + { + "bbox": [ + 46, + 435, + 287, + 567 + ], + "type": "text", + "content": " datasets." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 574, + 256, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 574, + 256, + 588 + ], + "spans": [ + { + "bbox": [ + 47, + 574, + 256, + 588 + ], + "type": "text", + "content": "5.2. Visual Quality and Modeling Efficiency." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "text", + "content": "Comparison with existing alternatives. We compare DVDP with other alternatives here to show that DVDP has the capability of acceleration while maintaining a reasonable or even better visual quality. For the sake of fairness, we reproduce DDPM using the same network structure as DVDP with the same hyperparameters, represented as " + }, + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{DDPM^{*}}" + }, + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "text", + "content": ". Some samples generated by our DVDP are shown in Fig. 1, and Tab. 1 summarizes the quantitative results on CIFAR10, FFHQ " + }, + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "inline_equation", + "content": "256^{2}" + }, + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "text", + "content": ", and three LSUN datasets. The results show that our proposed DVDP achieves better FID" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 326, + 545, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 326, + 545, + 434 + ], + "spans": [ + { + "bbox": [ + 304, + 326, + 545, + 434 + ], + "type": "text", + "content": "scores on all of the " + }, + { + "bbox": [ + 304, + 326, + 545, + 434 + ], + "type": "inline_equation", + "content": "256^{2}" + }, + { + "bbox": [ + 304, + 326, + 545, + 434 + ], + "type": "text", + "content": " datasets, demonstrating an improved sample quality. Meanwhile, DVDP enjoys improved training and sampling speeds. Specifically, DDPM and " + }, + { + "bbox": [ + 304, + 326, + 545, + 434 + ], + "type": "inline_equation", + "content": "\\mathrm{DDPM}^*" + }, + { + "bbox": [ + 304, + 326, + 545, + 434 + ], + "type": "text", + "content": " spend " + }, + { + "bbox": [ + 304, + 326, + 545, + 434 + ], + "type": "inline_equation", + "content": "2.2\\times" + }, + { + "bbox": [ + 304, + 326, + 545, + 434 + ], + "type": "text", + "content": " time as DVDP when training the same epochs, and they spend " + }, + { + "bbox": [ + 304, + 326, + 545, + 434 + ], + "type": "inline_equation", + "content": "2.4\\times" + }, + { + "bbox": [ + 304, + 326, + 545, + 434 + ], + "type": "text", + "content": " time in sampling. Although the superiority of DVDP is obvious on all " + }, + { + "bbox": [ + 304, + 326, + 545, + 434 + ], + "type": "inline_equation", + "content": "256^{2}" + }, + { + "bbox": [ + 304, + 326, + 545, + 434 + ], + "type": "text", + "content": " datasets, it becomes indistinct when it comes to CIFAR10 " + }, + { + "bbox": [ + 304, + 326, + 545, + 434 + ], + "type": "inline_equation", + "content": "32^{2}" + }, + { + "bbox": [ + 304, + 326, + 545, + 434 + ], + "type": "text", + "content": ", which is reasonable considering the small pixel redundancy and low resolution of images in CIFAR10." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 434, + 546, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 434, + 546, + 661 + ], + "spans": [ + { + "bbox": [ + 304, + 434, + 546, + 661 + ], + "type": "text", + "content": "Towards high-resolution image synthesis. It is hard for diffusion models to generate high-resolution images directly. This can attribute to the curse of dimensionality: the support of high-dimensional data with large noise can only be visited a small part during training, leading to inaccurate prediction on unseen points [10]. Score-SDE [28] tries this task by directly training a single diffusion model, but the sample quality is far from reasonable. CDM performs better in high-resolution image synthesis and obtains impressive results [21, 24]. It first generates low-resolution images, followed by several conditional diffusion models as superresolution modules. We compare DVDP with score-SDE and CDM on FFHQ " + }, + { + "bbox": [ + 304, + 434, + 546, + 661 + ], + "type": "inline_equation", + "content": "1024^{2}" + }, + { + "bbox": [ + 304, + 434, + 546, + 661 + ], + "type": "text", + "content": " in Tab. 2. The FID of score-SDE is evaluated on samples generated from their official code and model weight without acceleration, and CDM is implemented by three cascaded diffusions as in [21]. Our DVDP is sampled by both DDPM method with 1000 steps and DDIM method with 675 steps. The results show that DVDP beats both score-SDE and CDM." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 670, + 503, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 670, + 503, + 684 + ], + "spans": [ + { + "bbox": [ + 306, + 670, + 503, + 684 + ], + "type": "text", + "content": "5.3. Comparison with Subspace Diffusion" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "Subspace diffusion [10] can also vary dimensionality during the diffusion process. As mentioned in [10] and also" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14313" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 55, + 95, + 276, + 193 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 286, + 92 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 286, + 92 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 286, + 92 + ], + "type": "text", + "content": "Table 2. Synthesis performance of different models trained on FFHQ " + }, + { + "bbox": [ + 47, + 70, + 286, + 92 + ], + "type": "inline_equation", + "content": "{1024} \\times {1024}" + }, + { + "bbox": [ + 47, + 70, + 286, + 92 + ], + "type": "text", + "content": " ." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 55, + 95, + 276, + 193 + ], + "lines": [ + { + "bbox": [ + 55, + 95, + 276, + 193 + ], + "spans": [ + { + "bbox": [ + 55, + 95, + 276, + 193 + ], + "type": "table", + "html": "
Model#Params (M)NFEFID (10k)↓
Score-SDE100200052.40
CDM98152524.7
165152517.35
286152517.24
DVDP10567512.43
100010.46
", + "image_path": "8bff80bff4f21832320de488bb8c0964c410899932be484258f20895a63590bf.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 65, + 200, + 266, + 319 + ], + "blocks": [ + { + "bbox": [ + 65, + 200, + 266, + 319 + ], + "lines": [ + { + "bbox": [ + 65, + 200, + 266, + 319 + ], + "spans": [ + { + "bbox": [ + 65, + 200, + 266, + 319 + ], + "type": "image", + "image_path": "8b4da43eaa7cf459ac0df1d7937df27726bba25899fe848371489d03184cd7b4.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 323, + 286, + 357 + ], + "lines": [ + { + "bbox": [ + 46, + 323, + 286, + 357 + ], + "spans": [ + { + "bbox": [ + 46, + 323, + 286, + 357 + ], + "type": "text", + "content": "Figure 4. Quantitative comparison between subspace diffusion [10] and our DVDP on CelebA " + }, + { + "bbox": [ + 46, + 323, + 286, + 357 + ], + "type": "inline_equation", + "content": "64 \\times 64" + }, + { + "bbox": [ + 46, + 323, + 286, + 357 + ], + "type": "text", + "content": " regarding different dimensionality turning point " + }, + { + "bbox": [ + 46, + 323, + 286, + 357 + ], + "type": "inline_equation", + "content": "T_{1}" + }, + { + "bbox": [ + 46, + 323, + 286, + 357 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 373, + 286, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 373, + 286, + 456 + ], + "spans": [ + { + "bbox": [ + 46, + 373, + 286, + 456 + ], + "type": "text", + "content": "discussed in Sec. 4.4, dimensionality turning point " + }, + { + "bbox": [ + 46, + 373, + 286, + 456 + ], + "type": "inline_equation", + "content": "T_{k}" + }, + { + "bbox": [ + 46, + 373, + 286, + 456 + ], + "type": "text", + "content": " in subspace diffusion should be large enough to maintain the sample quality. However, large " + }, + { + "bbox": [ + 46, + 373, + 286, + 456 + ], + "type": "inline_equation", + "content": "T_{k}" + }, + { + "bbox": [ + 46, + 373, + 286, + 456 + ], + "type": "text", + "content": " means more diffusion steps in high dimensional space, which will impair the advantage of such dimensionality-varying method, e.g., less acceleration in sampling. Thus, " + }, + { + "bbox": [ + 46, + 373, + 286, + 456 + ], + "type": "inline_equation", + "content": "T_{k}" + }, + { + "bbox": [ + 46, + 373, + 286, + 456 + ], + "type": "text", + "content": " is expected to be as small as possible while maintaining the sampling quality." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 457, + 286, + 648 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 457, + 286, + 648 + ], + "spans": [ + { + "bbox": [ + 46, + 457, + 286, + 648 + ], + "type": "text", + "content": "Considering that the dimensionality decreases only once, i.e., " + }, + { + "bbox": [ + 46, + 457, + 286, + 648 + ], + "type": "inline_equation", + "content": "K = 1" + }, + { + "bbox": [ + 46, + 457, + 286, + 648 + ], + "type": "text", + "content": ", and only one dimensionality turning point " + }, + { + "bbox": [ + 46, + 457, + 286, + 648 + ], + "type": "inline_equation", + "content": "T_{1}" + }, + { + "bbox": [ + 46, + 457, + 286, + 648 + ], + "type": "text", + "content": ", we compare DVDP with subspace diffusion when the downsampling is carried out at different " + }, + { + "bbox": [ + 46, + 457, + 286, + 648 + ], + "type": "inline_equation", + "content": "T_{1}" + }, + { + "bbox": [ + 46, + 457, + 286, + 648 + ], + "type": "text", + "content": ". Since the subspace diffusion is only implemented on continuous timesteps in [10], we reproduce it on discrete timesteps similar as DDPM and use the reproduced version as a baseline. Fig. 4 illustrates that DVDP is consistently better with regard to sample quality on CelebA " + }, + { + "bbox": [ + 46, + 457, + 286, + 648 + ], + "type": "inline_equation", + "content": "64 \\times 64" + }, + { + "bbox": [ + 46, + 457, + 286, + 648 + ], + "type": "text", + "content": " [16] when " + }, + { + "bbox": [ + 46, + 457, + 286, + 648 + ], + "type": "inline_equation", + "content": "T_{1}" + }, + { + "bbox": [ + 46, + 457, + 286, + 648 + ], + "type": "text", + "content": " varies, where the advantage gets larger when " + }, + { + "bbox": [ + 46, + 457, + 286, + 648 + ], + "type": "inline_equation", + "content": "T_{1}" + }, + { + "bbox": [ + 46, + 457, + 286, + 648 + ], + "type": "text", + "content": " gets smaller. In addition, some samples of DVDP and subspace diffusion are shown in Fig. 5, where the sample quality of subspace diffusion is apparently worse than that of DVDP especially when " + }, + { + "bbox": [ + 46, + 457, + 286, + 648 + ], + "type": "inline_equation", + "content": "T_{1}" + }, + { + "bbox": [ + 46, + 457, + 286, + 648 + ], + "type": "text", + "content": " is small. In conclusion, DVDP is much more insensitive to the dimensionality turning point than subspace diffusion." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 658, + 141, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 141, + 671 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 141, + 671 + ], + "type": "text", + "content": "5.4. Ablation Study" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "text", + "content": "We implement ablation study in this section to show that DVDP is able to keep effective when the number of downsampling, i.e., " + }, + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "text", + "content": ", grows. Specifically, we train DVDP" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 313, + 93, + 535, + 194 + ], + "blocks": [ + { + "bbox": [ + 305, + 70, + 542, + 91 + ], + "lines": [ + { + "bbox": [ + 305, + 70, + 542, + 91 + ], + "spans": [ + { + "bbox": [ + 305, + 70, + 542, + 91 + ], + "type": "text", + "content": "Table 3. Ablation study on the number of downsampling times on CelebA " + }, + { + "bbox": [ + 305, + 70, + 542, + 91 + ], + "type": "inline_equation", + "content": "128 \\times 128" + }, + { + "bbox": [ + 305, + 70, + 542, + 91 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 313, + 93, + 535, + 194 + ], + "lines": [ + { + "bbox": [ + 313, + 93, + 535, + 194 + ], + "spans": [ + { + "bbox": [ + 313, + 93, + 535, + 194 + ], + "type": "table", + "html": "
Downsampling times K0123
FID (50k)6.145.996.106.37
Training Speed Up-1.98×2.24×2.25×
Sampling Speed Up-2.12×2.36×2.43×
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Qualitative comparison between subspace diffusion [10] and our DVDP on CelebA " + }, + { + "bbox": [ + 305, + 323, + 543, + 357 + ], + "type": "inline_equation", + "content": "64 \\times 64" + }, + { + "bbox": [ + 305, + 323, + 543, + 357 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 305, + 323, + 543, + 357 + ], + "type": "inline_equation", + "content": "T_{1}" + }, + { + "bbox": [ + 305, + 323, + 543, + 357 + ], + "type": "text", + "content": " denotes the dimensionality turning point." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 373, + 545, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 373, + 545, + 469 + ], + "spans": [ + { + "bbox": [ + 304, + 373, + 545, + 469 + ], + "type": "text", + "content": "models on four different settings of dimensionality turning points " + }, + { + "bbox": [ + 304, + 373, + 545, + 469 + ], + "type": "inline_equation", + "content": "\\mathbb{T}" + }, + { + "bbox": [ + 304, + 373, + 545, + 469 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 304, + 373, + 545, + 469 + ], + "type": "inline_equation", + "content": "K = 0,1,2,3" + }, + { + "bbox": [ + 304, + 373, + 545, + 469 + ], + "type": "text", + "content": ". When " + }, + { + "bbox": [ + 304, + 373, + 545, + 469 + ], + "type": "inline_equation", + "content": "K = 1" + }, + { + "bbox": [ + 304, + 373, + 545, + 469 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 373, + 545, + 469 + ], + "type": "inline_equation", + "content": "\\mathbb{T}" + }, + { + "bbox": [ + 304, + 373, + 545, + 469 + ], + "type": "text", + "content": " is set to " + }, + { + "bbox": [ + 304, + 373, + 545, + 469 + ], + "type": "inline_equation", + "content": "\\{250\\}" + }, + { + "bbox": [ + 304, + 373, + 545, + 469 + ], + "type": "text", + "content": ". Similarly, when " + }, + { + "bbox": [ + 304, + 373, + 545, + 469 + ], + "type": "inline_equation", + "content": "K = 2" + }, + { + "bbox": [ + 304, + 373, + 545, + 469 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 373, + 545, + 469 + ], + "type": "inline_equation", + "content": "K = 3" + }, + { + "bbox": [ + 304, + 373, + 545, + 469 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 373, + 545, + 469 + ], + "type": "inline_equation", + "content": "\\mathbb{T}" + }, + { + "bbox": [ + 304, + 373, + 545, + 469 + ], + "type": "text", + "content": " is set to " + }, + { + "bbox": [ + 304, + 373, + 545, + 469 + ], + "type": "inline_equation", + "content": "\\{250,500\\}" + }, + { + "bbox": [ + 304, + 373, + 545, + 469 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 373, + 545, + 469 + ], + "type": "inline_equation", + "content": "\\{250,500,750\\}" + }, + { + "bbox": [ + 304, + 373, + 545, + 469 + ], + "type": "text", + "content": ", respectively. Furthermore, we use the same noise schedule for these four different settings. Tab. 3 shows that when the number of downsampling grows, the sample quality preserves a reasonable level, indicating that DVDP can vary dimensionality for multiple times." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 481, + 378, + 493 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 481, + 378, + 493 + ], + "spans": [ + { + "bbox": [ + 306, + 481, + 378, + 493 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 502, + 545, + 680 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 502, + 545, + 680 + ], + "spans": [ + { + "bbox": [ + 304, + 502, + 545, + 680 + ], + "type": "text", + "content": "This paper generalizes the traditional diffusion process to a dimensionality-varying diffusion process (DVDP). The proposed DVDP has both theoretical and experimental contributions. Theoretically, we carefully decompose the signal in the diffusion process into multiple orthogonal dynamic-attenuated components. With a rigorously deduced approximation strategy, this then leads to a novel reverse process that generates images from much lower dimensional noises compared with the image resolutions. This design allows much higher training and sampling speed of the diffusion models with on-par or even better synthesis performance, and superior performance in synthesizing large-size images of " + }, + { + "bbox": [ + 304, + 502, + 545, + 680 + ], + "type": "inline_equation", + "content": "1024 \\times 1024" + }, + { + "bbox": [ + 304, + 502, + 545, + 680 + ], + "type": "text", + "content": " resolution compared with classic methods. The results in this work can promote the understanding and applications of diffusion models in broader scenarios." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 305, + 683, + 545, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 683, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 305, + 683, + 545, + 712 + ], + "type": "text", + "content": "This work was supported in part by the National Key R&D Program of China under Grant 2022YFA1005000, in part by the NSFC under Grant 61701304." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14314" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 712 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "type": "text", + "content": "[1] Fan Bao, Chongxuan Li, Jun Zhu, and Bo Zhang. 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However, effectiveness and efficiency are equally crucial in real-world applications, e.g., autonomous driving and augmented reality. We argue that this dilemma comes from wasted resources on valueless depth samples. This paper tackles the problem by proposing a novel learning-based 3D reconstruction framework named Dionysus. Our main contribution is to find out the most promising depth candidates from estimated semantic maps. This strategy simultaneously enables high effectiveness and efficiency by attending to the most reliable nominators. Specifically, we distinguish unreliable depth candidates by checking the cross-view semantic consistency and allow adaptive sampling by redistributing depth nominators among pixels. Experiments on the most popular datasets confirm our proposed framework's effectiveness.", + "bbox": [ + 75, + 376, + 472, + 632 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 662, + 209, + 679 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recovering 3D structures from 2D images is one of the most fundamental computer vision tasks [7, 25, 26, 68] and has wide applications in various scenarios (e.g., autonomous driving, metaverse, and augmented reality). Thanks to the popularity of smartphones, high-quality RGB videos are always obtainable. Since each image describes only a tiny piece of the whole scenario [31, 33], reconstruction from multiple frames [44, 50] is more attractive than from a single image [13, 14]. Although model quality and real-time response are equally essential, the existing 3D reconstruction methods have difficulty performing well in both aspects. For example, multi-view stereo (MVS) models [63, 73] consume seconds on each image, while real-time approaches [9, 57, 64] lead to missing details or large-area", + "bbox": [ + 75, + 688, + 472, + 902 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "mess.", + "bbox": [ + 500, + 348, + 540, + 359 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The mainstream reconstruction methods [15,63,72] generally sample a set of candidate depths or voxels, then use neural networks (e.g., CNNs [21] and transformers [58]) to evaluate each candidate's reliability. The candidate number is generally small because of the evaluation networks' high computational demand. Consequently, the reconstruction quality becomes unsatisfying because the ground truth is less likely to be sampled.", + "bbox": [ + 496, + 364, + 893, + 484 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Pursuing a higher candidate sampling density, CasMVSNet [15] shrinks the depth range in a coarse-to-fine fashion; IS-MVSNet [63] searches for new candidates according to the estimated error distribution; NeuralRecon [57] prunes the voxels thought to be unreliable in the previous predictions. All these methods select candidates according to the initial depth estimations. Notably, small objects and delicate structures are hard to recover in the beginning low-resolution phase because they require a high resolution to distinguish. As a result, the final reconstruction often suffers from missing objects and crude details because the actual depth can be outside the final search range when the initial estimation is unreliable. However, decent reconstruction quality on delicate objects is crucial to many real-world applications. Specifically, traffic accidents may occur if any pedestrian or warning post fails to recover; frequent collisions and even fire disasters might happen if cleaning robots cannot well reconstruct table legs and electric cables. Besides the defects in meticulous structures, coarse-to-fine models also have room to improve efficiency. As mentioned, the mainstream coarse-to-fine methods sample and then evaluate initial candidates multiple times to locate the most valuable candidate depths. Notably, examining the preliminary candidates may be more expensive (usually two times more [15, 78]) than assessing the final nominators.", + "bbox": [ + 496, + 489, + 895, + 867 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In addition to the costly evaluation networks widely adopted in coarse-to-fine architectures, another natural so-", + "bbox": [ + 500, + 869, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "12576", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f83eb7bf3f711219e9ae9f3546d88c1620ddfcf7f842c1733bb521b59d522fe2.jpg", + "image_caption": [ + "Figure 1. The overall architecture of our framework. We first estimate a semantic map for the current frame and then retrieve the former semantic estimations. After that, we locate the most valuable depth candidates through the semantic maps. Finally, we predict the depth map for the current frame by examining each depth candidate." + ], + "image_footnote": [], + "bbox": [ + 125, + 85, + 854, + 392 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "lution is to measure each depth candidate's reliability according to the photometric consistency among RGB images or feature maps from different views. The basic logic behind these methods is that pixels from distinct perspectives should own the same color if they are the correct projections from the same 3D point. However, a 3D point may look distinct in different views due to illumination, transparency, and reflection. Moreover, candidates close to but not precisely coinciding with the ground truth may have different colors for delicate objects, thus leading to low photometric consistency. Consequently, the found candidate may correspond to a pixel distant from the ground truth but of a similar color.", + "bbox": [ + 75, + 470, + 468, + 666 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To get rid of detail defects and keep efficiency, it becomes crucial to accurately and efficiently find the most promising candidate depths. This paper proposes a novel high-quality real-time 3D reconstruction framework named Dionysus, which looks for depth hypotheses based on semantic estimations. Precisely, we distinguish each depth candidate's reliability according to its semantic consistency among warped views. Fig. 1 illustrates the overall architecture of our framework. Our intuition is that two pixels should share the same semantic label if they are projections of the same 3D point. We argue that selecting depth candidates according to the semantic tags results in various benefits:", + "bbox": [ + 75, + 667, + 470, + 863 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "1. Consistent: A 3D point may have distinct colors when observing from different perspectives, but its semantic", + "bbox": [ + 89, + 869, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "label never changes.", + "bbox": [ + 531, + 472, + 669, + 487 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "2. Efficient: Semantic estimation requires a meager cost. A semantic segmentation model may spend only milliseconds on each frame [11,47] while evaluating each cost volume in coarse layers generally takes ten times more cost. In addition, most hierarchical methods shrink the depth range only by half in each stage, while our method may significantly reduce the depth range on delicate objects (e.g., desk legs).", + "3. Dense: Tiny objects always get missing in hierarchical frameworks because the initial samples are too sparse. However, the semantic maps are highly dense, thus retaining fine details.", + "4. Adaptive: Semantics indicate various properties of the pixel. For example, an electric cable may demand highly dense samples to recover, but a wall may not. In other words, we can assign each pixel the most suitable sampling density according to its semantic estimation." + ], + "bbox": [ + 511, + 497, + 893, + 776 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Depth Reassignment: A bed pixel may have much more valid depth candidates than a pen pixel after the semantic-based pruning because there are likely many bed pixels in other views. Consequently, we cannot form a regular cost volume based on the pruned depth candidates because pixels may have different numbers of valid depth candidates. However, most GPUs are not designed for irregular inputs", + "bbox": [ + 496, + 794, + 890, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "12577", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "and are inefficient in such cases. Thus, we further propose reallocating depth samples from pixels with excess valid candidates to those in the opposite. In this way, all pixels finally have the same number of candidates and thus can be conveniently computed by GPUs. Moreover, we sample more densely for delicate structures, otherwise more sparsely, because tiny objects have a narrower depth range after semantic pruning, and all pixels have the same depth number.", + "bbox": [ + 75, + 90, + 472, + 224 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To summarize, this paper has two significant contributions:", + "bbox": [ + 76, + 227, + 468, + 255 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. Instead of densely evaluating all depths or sparsely evaluating limited depths, we efficiently select the most promising depth candidates based on the cross-view semantic consistency.", + "2. We reallocate depth samples among pixels to make our model adaptive to objects and efficient on GPUs." + ], + "bbox": [ + 88, + 266, + 468, + 367 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The mentioned contributions significantly benefit the effectiveness while retaining efficiency. Our extensive experiments on the most popular 3D reconstruction datasets [5] further verify our proposed method's validity.", + "bbox": [ + 76, + 376, + 468, + 436 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 450, + 218, + 465 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We first introduce the development of 3D reconstruction, then present the progress in semantic segmentation, and finally discuss the existing semantic-based 3D reconstruction networks.", + "bbox": [ + 76, + 474, + 468, + 535 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.1.3D Reconstruction", + "text_level": 1, + "bbox": [ + 76, + 545, + 256, + 560 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Recovering 3D structures from images has been widely studied for many decades. Despite the great success of traditional methods [1, 12, 52, 53], most recent solutions [9, 15, 73] are based on neural networks [21, 35-38, 62] because of the latter's popularity [27, 32, 71, 75, 76] in the last decades. Thanks to the popularity of smartphones, continuous video sequences can now be easily captured. Compared to independent images, video sequences [28, 80] contain rich correlations among frames, thus leading to more consistent reconstruction quality. In consequence, learning-based video reconstruction [44, 56, 69] is becoming a hot spot. However, due to their high computation demand, most video reconstruction methods are limited in offline applications.", + "bbox": [ + 75, + 568, + 468, + 763 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Real-time video reconstruction is attracting wide attention from the academy and the industry, considering its vital position in autonomous driving and augmented reality. The mainstream real-time methods can be categorized into depth-based [9, 16, 40, 61] and volume-based [57]. Specifically, the former estimates depth maps and fuses them into 3D representations. In contrast, the latter directly regresses 3D representations from the RGB inputs. Depth-based methods generally lead to lower latency because they", + "bbox": [ + 75, + 765, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "immediately process each new frame without waiting. Conversely, volumetric methods estimate 3D representations from a group of frames, thus cannot respond to new frames at once and are less suitable for online scenarios. The mainstream depth-based approaches usually uniformly sample depth candidates from an overly broad range [9] or gradually shrink the search range by repeated predictions [15,72]. Our main difference from the existing depth-based methods is that we utilize semantics to select depth candidates.", + "bbox": [ + 496, + 90, + 890, + 227 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Semantic Segmentation", + "text_level": 1, + "bbox": [ + 500, + 237, + 718, + 253 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Semantic segmentation focuses on estimating each pixel's object category (e.g., whether it represents a dog). Most semantic segmentation networks [2, 51, 67, 74, 77] inherited a learning-based framework from FCN [39]. Real-time solutions generally put their most effort into designing a lightweight backbone considering its contribution to the whole model's complexity. The existing online methods generally own three backbone types [43]: classification-based [22, 24, 60], segmentation-based [23, 34, 41], and two-branch-based [48, 74, 79].", + "bbox": [ + 496, + 261, + 890, + 412 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The first class encodes features using image classification networks and then decodes to output semantics. The second class designs segmentation-specific backbones considering the task difference between segmentation and classification. The third class processes macro and micro information separately to reduce the overall cost. State-of-the-art segmentation models can infer hundreds of frames per second and retain high quality simultaneously. In comparison, the fastest depth estimation networks are bounded to dozens of frames per second.", + "bbox": [ + 496, + 412, + 890, + 564 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Semantic-based 3D Reconstruction", + "text_level": 1, + "bbox": [ + 500, + 574, + 805, + 589 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Quite a few papers focus on integrating semantics into depth estimation networks. Most related works belong to single-image depth estimation and stereo matching.", + "bbox": [ + 496, + 598, + 890, + 643 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In single-image depth estimation, view correspondence does not exist; thus, semantic information becomes more vital. [66] simultaneously estimates depth and semantic maps by multi-task learning. [65] shares depth weights among pixels of the same semantic label. [10] jointly estimates depth, semantics, and surface normal. [20] introduces a synergy network to share features between the semantic and depth branches. [30] restricts depth predictions by semantic priors (e.g., the sky is distant, and the ground is horizontal). [59] infers invisible regions from semantics.", + "bbox": [ + 496, + 643, + 890, + 794 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In stereo matching, two views with fixed relative poses are given, and the goal is to match pixels in the two views. These papers can be generally divided into two categories. The first class treats semantic maps as additional channels. [8] refines disparities by concatenating semantic and disparity features along the channel dimension. [70] constructs cost volumes for semantics and disparity and then", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "12578", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/ed3a1474d5c41f458e9b48ce5a0baf21b358a2f7901a7a69a230656918cde5ff.jpg", + "image_caption": [ + "Figure 2. Architecture of the semantic head. Former semantic and depth estimations are warped and then integrated with the current frame. After that, we extract hierarchical information from the concatenated feature map. The semantic map for the current frame is inferred from the feature volume composed of spatial and context information." + ], + "image_footnote": [], + "bbox": [ + 86, + 90, + 897, + 330 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "fuses them by summing and global pooling. [3] constructs cost volume using semantic consistency between left and right images and estimates disparity residuals according to semantic category. The second class revises the disparity using priors in semantics. [49] filters depth maps based on semantic priors. For example, ground and water pixels with heights higher than $90\\%$ get pruned. [46] refines edge and texture-less regions using semantic cues. [4] estimates disparity confidence using semantic consistency and refines disparity in each semantic region.", + "bbox": [ + 75, + 417, + 468, + 568 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The related works in multi-view stereo are limited. [18] recovers a segmented 3D representation from 2D images and semantics. [42] augments depth edges and guides cost aggregation using semantics.", + "bbox": [ + 76, + 568, + 468, + 628 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Unlike the mentioned works, we select depth candidates by explicitly exploiting semantic consistency for multi-view inputs. We also balance depth candidates among pixels and adaptively attend to pixels in need.", + "bbox": [ + 76, + 628, + 468, + 690 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 76, + 704, + 210, + 722 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We first introduce the overall architecture of our model in Sec. 3.1, then elaborate on each sub-component in Sec. 3.2 and 3.3. Our model inputs an RGB video sequence divided into frames and the camera parameters of each frame, which are estimated by off-the-shelf tools (e.g., ARKit). The output is expected to be the depth map of each frame.", + "bbox": [ + 76, + 729, + 468, + 821 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1. Overall Architecture", + "text_level": 1, + "bbox": [ + 76, + 830, + 272, + 847 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Fig. 1 exhibits the overall framework. We have a semantic head to predict a semantic map $S_{t}$ for the current frame $I_{t}$ . At the same time, we retrieve the semantic maps", + "bbox": [ + 76, + 854, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\{S_i\\}_{i = t - n}^{t - 1}$ predicted in the previous timestamps from a semantic queue.", + "bbox": [ + 500, + 415, + 888, + 446 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "After that, we look for the most promising depth candidates for each pixel in $I_{t}$ using our novel semantic-based depth candidate selection module, which is our main contribution. Finally, we examine each depth nominator using a depth head to output the final depth estimation. We sum losses from the depth and semantic heads as the overall loss.", + "bbox": [ + 498, + 448, + 890, + 537 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Semantic-based Depth Candidate Selection", + "text_level": 1, + "bbox": [ + 500, + 547, + 864, + 564 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This section introduces our main contributions. Sec. 3.2.1 first shows how to prune unreliable depth candidates using the semantic information, and then Sec. 3.2.2 demonstrates how to concentrate on pixels in need and become efficient on GPUs.", + "bbox": [ + 498, + 571, + 890, + 645 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.1 Semantic-based Depth Pruning", + "text_level": 1, + "bbox": [ + 500, + 665, + 772, + 681 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To estimate the depth of a pixel in the current frame $I_{t}$ , we sample a set of depth candidates and evaluate their reliability one by one. The candidate number must be high enough to hit the ground truth.", + "bbox": [ + 498, + 689, + 890, + 750 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "However, the existing learning-based methods can only examine a small number of samples because they use a giant neural network to assess each candidate. Consequently, small objects distant from the background and delicate structures get defective. The small object problem cannot be solved via coarse-to-fine architectures because significantly wrong predictions in the coarse stages cannot be recovered in finer stages.", + "bbox": [ + 496, + 750, + 890, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Unlike the existing methods, we first predict the semantic labels for each pixel at a low cost; then, we use the se", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "12579", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/9eb71af5d386b186ba95cff4ba18a524693585549d7f8c3d7130ff81f405e586.jpg", + "image_caption": [ + "Figure 3. Illustration of depth pruning. We uniformly sample depth candidates for a given pixel (purple) in the current frame, then evaluate each candidate to determine whether it leads to a pixel of the same semantic label projected on the former frames." + ], + "image_footnote": [], + "bbox": [ + 169, + 85, + 795, + 309 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "mantic maps to restrict the depth candidate sampling only to the most reliable regions.", + "bbox": [ + 75, + 378, + 470, + 409 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "I/O: The inputs include the current frame $I_{t}$ and retrieved previous semantic $\\{S_{i}\\}_{i = t - n}^{t - 1}$ and depth $\\{D_{i}\\}_{i = t - n}^{t - 1}$ estimations. Besides, similar to most existing methods [9, 57, 73], we assume the camera parameters from time $t - n$ to $t$ are available. In fact, the camera parameters can be obtained from off-the-shelf tools (e.g., ARKit).", + "bbox": [ + 75, + 426, + 468, + 516 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The outputs are the most promising depth candidates for each pixel in the current frame $I_{t}$ .", + "bbox": [ + 76, + 517, + 470, + 547 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Semantic Head: Instead of outputting the correct label, semantic consistency among frames is more crucial because we examine depth candidates by cross-view conformity. Thus, we need to consider previous semantic estimations when processing new frames.", + "bbox": [ + 75, + 565, + 468, + 641 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We propose a highly efficient 2D convolutional network to predict the semantic labels for each pixel in $I_{t}$ , as shown in Fig. 2. The inputs of the semantic prediction head include the current frame $I_{t}$ , the semantic and depth maps predicted from timestamp $t - n$ to $t - 1$ , and the corresponding camera parameters.", + "bbox": [ + 75, + 641, + 468, + 731 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The former depth and semantic predictions are warped to the current view according to the relative poses and then fused by concatenating along the channel dimension. Inspired by STDC-Seg [11] and BiSeNet [74], we adopt a two-pathway architecture to efficiently extract spatial and context information, which are then fused to generate the final semantic estimation.", + "bbox": [ + 75, + 731, + 470, + 838 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Depth Pruning: After obtaining the semantic maps, we start to prune depth candidates. According to the camera parameters from time $t - n$ to $t$ , we can draw a straight line", + "bbox": [ + 75, + 854, + 472, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "(i.e., the epipolar line) on each previous frame $\\in \\{I_i\\}_{i = t - n}^{t - 1}$ for each pixel $p_t\\in$ the current frame $I_{t}$ and guarantee that the correct correspondences can only lie on the epipolar line.", + "bbox": [ + 496, + 377, + 890, + 436 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Then, we sample $N_{s}$ (a significant number) depth candidates for each pixel in $I_{t}$ , as shown in Fig. 3. Each depth corresponds to one pixel on the epipolar line in each former frame. After that, we check whether the projected pixel's semantic label is exactly the same as $p_{t}$ . Only the candidate depths leading to a positive answer get retained, otherwise pruned.", + "bbox": [ + 496, + 439, + 892, + 545 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Consequently, each former frame provides a set of reliable depth candidates. These sets of candidate overlap yet may differ due to occlusion and field views. We use the union of all the sets as the aggregated depth candidate set because each pair of matched pixels may imply the existence of a 3D point.", + "bbox": [ + 496, + 547, + 893, + 637 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Since we judge the reliability based on semantics, a question might be whether our framework relies heavily on each pixel's precise prediction. The answer is no because we only require semantics in different frames to be consistent instead of strictly being the ground truth. Moreover, the existing semantic segmentation architectures [11, 47] can provide impressive enough label estimations.", + "bbox": [ + 496, + 638, + 893, + 744 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2.2 Semantic-based Depth Reallocation", + "text_level": 1, + "bbox": [ + 500, + 768, + 802, + 784 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After pruning unreliable candidates, pixels may own inconsistent numbers of depth nominators because different objects might occupy distinct amounts of space, as shown in the left of Fig. 4. Since the initial depth candidates are uniformly sampled, a pixel owning many reliable depth nominators likely belongs to a large object (e.g., walls and floors). These objects usually do not require dense samples", + "bbox": [ + 496, + 795, + 893, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "12580", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/e318bc45c45cf2b94614dfc2b47a9ef086022c87350f8d2d58ecf9e0bb071514.jpg", + "image_caption": [ + "Figure 4. Reassignment among pixels. Pixels may have a different number of candidate depths after semantic pruning. However, the difference disappears after reallocation." + ], + "image_footnote": [], + "bbox": [ + 205, + 85, + 767, + 198 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/1a8b5fd82947b74abd21888d7c93fcb36072fa01a6cf677c48b0d47593fa48b5.jpg", + "image_caption": [ + "Figure 5. Illustration of candidate reallocation. Top: pixel with too many candidates. We reduce the nominator number by down-sampling. Bottom: pixel with too few candidates." + ], + "image_footnote": [], + "bbox": [ + 117, + 253, + 854, + 443 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "because they have smooth surfaces, and their depths can be easily inferred from neighbors. In contrast, coarser sampling may help the network overcome repetitive patterns and non-textured regions by collecting information from a larger field of view.", + "bbox": [ + 75, + 510, + 468, + 585 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "However, delicate objects (e.g., toothbrushes and nail clippers) eagerly demand higher depth resolution for detail recovery. Thus, we should put more effort into pixels holding fewer candidates.", + "bbox": [ + 75, + 585, + 468, + 647 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Reallocate Candidates: We propose to set a unified depth number $N_{u}$ for all pixels by transfer payment, as shown in Fig. 4. Specifically, if a pixel occupies too many candidates, we lower its sampling density; otherwise, we promote.", + "bbox": [ + 75, + 671, + 468, + 746 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As shown in Fig. 5, we uniformly position $N_{u}$ candidates within the depth range bounded by the $N_{v}^{i}$ valid nominators for each pixel $p_{i}$ . Segmented depth ranges may occur when multiple objects of the same semantic label appear in the same image, as shown in Fig. 3. In such cases, candidates in different fragments are reallocated separately, and the quota of new candidates in each fragment is proportional to the number of valid candidates inside the fragment.", + "bbox": [ + 75, + 748, + 468, + 868 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To avoid fractional new candidate numbers, we prioritize the narrowest fragments and offer them slightly more", + "bbox": [ + 75, + 869, + 468, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "candidates by the ceiling function. After that, we assign the remaining quotas for the rest fragments. This way, attention transfers from large surfaces to small objects because fragments containing fewer valid candidates get promoted.", + "bbox": [ + 496, + 510, + 890, + 571 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "A more significant unified depth number $N_{u}$ offers higher effectiveness while lowering the model efficiency. In default, the value of $N_{u}$ is set to ensure the whole model runs as fast as the state-of-the-art real-time methods.", + "bbox": [ + 496, + 571, + 890, + 631 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Efficiency: Our reallocation strategy benefits effectiveness by attending more to delicate structures and contributes to efficiency.", + "bbox": [ + 496, + 655, + 890, + 700 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We take Fig. 4 as an example. Although these three pixels have the same number of initial depth hypotheses, they get different valid candidate numbers after the semantic pruning. Notably, most GPUs are designed to process regular inputs and are inefficient on irregular data.", + "bbox": [ + 496, + 702, + 890, + 777 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Thus, without reassignment, we have to pad pixels 2 and 3 with zeros to form a three (pixel number) by three (the max valid candidate number among pixels: $\\max_i\\{N_v^i\\}$ ) matrix as the input of the depth head. In comparison, a three-by-two matrix is enough after reallocation. The reduction of input matrix size directly lowers the computation demand of the costly depth head.", + "bbox": [ + 496, + 777, + 890, + 883 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Although sparsification may sound like a good solution,", + "bbox": [ + 517, + 885, + 890, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "12581", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e75e74c01d671a77c39570d3b67c78044fb28fbdae5f5e5cae1578aea81ddd29.jpg", + "image_caption": [ + "Figure 6. Architecture of the depth head. The outputs of the semantic-based depth selection module are used to warp the previous video frames to the current view for cost volume calculation. The depth predictions are regressed based on the current cost volume and former estimations." + ], + "image_footnote": [], + "bbox": [ + 84, + 85, + 883, + 338 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "it heavily relies on specialized hardware and is usually less efficient on inputs of irregular zero distributions. In addition, it leads to lower sampling density on small objects.", + "bbox": [ + 75, + 420, + 470, + 467 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Spatial Correlation: Since our samples are pixel-wisely determined, a possible doubt might be whether the spatial correlation still holds. The answer is yes because neighboring pixels generally share the same semantic label. As a result, they should match adjacent pixels in other views, thus leading to similar depth candidates after the semantic pruning.", + "bbox": [ + 75, + 506, + 468, + 612 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Moreover, our candidate reassignment module evenly distributes candidates in the valid depth range; thus, neighboring pixels should have similar final depth samples. The local spatial correlation still holds as illustrated in Fig. 7. In other words, we can exploit convolutions to evaluate the candidate depths.", + "bbox": [ + 75, + 616, + 468, + 708 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c13e3a6914abbd89f112748d5715b8bcbedc06a0a8a9d76582cbf8b288101e26.jpg", + "image_caption": [ + "Figure 7. Spatial correlation after depth selection. Neighboring pixels generally have similar sets of depth candidates." + ], + "image_footnote": [], + "bbox": [ + 86, + 731, + 472, + 835 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "3.3. Depth Head", + "text_level": 1, + "bbox": [ + 500, + 419, + 629, + 436 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "After determining the depth candidates for each pixel, we predict the depth map by assessing each depth candidate. The model starts by extracting image features from the current frame $I_{t}$ using a feature pyramid network (FPN) [29]. After that, we warp the image features from previous time stamps to the current view and then construct a cost volume by measuring the pixel-wise correlation between the current and former features.", + "bbox": [ + 496, + 443, + 890, + 563 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Finally, we send the raw cost volume into a U-shape refining network to regress the depth prediction at time $t$ . Notably, we keep the temporal consistency by introducing a ConvLSTM [54] to update the extracted features and by warping the previous depth estimations to the current viewpoint.", + "bbox": [ + 496, + 564, + 890, + 656 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 671, + 633, + 688 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Our model is implemented using PyTorch [45]. We optimize the model using MADGRAD [6] on eight A100 GPUs. The input image is cropped and scaled to $256 \\times 256$ . The weights for testing are selected according to their losses on the validation set. The depth metrics are borrowed from DeepVideoMVS [9].", + "bbox": [ + 496, + 696, + 890, + 787 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Keyframe Selection: Considering the high similarity between adjacent frames, estimating depth maps for every raw frame is inefficient. Thus, we select the most iconic frames (i.e., keyframes) from the input video sequences. When a new frame comes, we examine its pose distance to the latest keyframe and only adopt the new frames leading to pose", + "bbox": [ + 496, + 809, + 890, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "12582", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/f139d60b3be9882c817eb3c4e62c9a4ed8d987c288c5a1a4cf24b065d61ae850.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ScanNet
Abs Diff↓Abs Rel↓Sq Rel↓δ < 1.05↑δ < 1.25↑Time (ms) ↓
DPSNet [19]0.15480.07890.029249.3993.31308 ms
MVDepthNet [61]0.16430.08440.034146.7392.8046 ms
DELTAS [55]0.14920.07830.027148.6893.8183 ms
GPMVS [16]0.14920.07530.029051.0993.9849 ms
DeepVideoMVS (Fusion) [9]0.11820.05800.018760.2396.7830 ms
Ours0.10690.05060.016561.3497.1330 ms
", + "bbox": [ + 122, + 88, + 848, + 220 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "distances above a threshold. We define the pose distance as Eq. (1) and set the threshold as 0.35, following [9, 17]. Notably, we do not estimate depth for the first frame in a video sequence because it has no predecessors to provide multi-view information.", + "bbox": [ + 75, + 285, + 470, + 359 + ], + "page_idx": 7 + }, + { + "type": "equation", + "text": "\n$$\nD i s _ {p} = \\sqrt {\\left| t r a n s i t i o n \\right| ^ {2} + \\frac {2}{3} T r a c e (I - r o t a t i o n)} \\quad (1)\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 383, + 468, + 419 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Datasets: Following the mainstream settings [9, 57], we train and evaluate our model on ScanNet [5], which is a large-scale real-world video dataset containing 1201 scenes for training, 321 for validation, and 100 for testing.", + "bbox": [ + 75, + 431, + 468, + 494 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Comparison to existing SOTAs Tab. 1 demonstrates that our method outperforms various state-of-the-art depth estimation approaches in effectiveness and efficiency.", + "bbox": [ + 75, + 511, + 468, + 556 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Compared to real-time SOTAs [9], our method shows significant advantages in all effectiveness metrics while retaining comparable time efficiency. Compared to semi-realtime algorithms [16, 55, 61], our method dominates inference time and offers significant competitiveness in reconstruction quality. In addition, our real-time framework even generates more accurate depth maps than some offline solutions [19] while spending one magnitude less cost.", + "bbox": [ + 75, + 556, + 468, + 676 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Moreover, our method benefits relative error more than absolute error and favors $L^1$ difference more than $L^2$ . These results indicate that delicate structures and small objects win more attention.", + "bbox": [ + 75, + 678, + 468, + 738 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Impacts of the Semantic Head To assess the effectiveness of our proposed semantic-based depth selection strategy, we fix all other variables and only examine the semantic head's impacts. Tab. 2 confirms that our semantic-based depth selection module offers significant benefits.", + "bbox": [ + 75, + 756, + 468, + 832 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Limitations", + "text_level": 1, + "bbox": [ + 76, + 844, + 199, + 859 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Like most dense reconstruction models, our pipeline requires the camera parameters to be known, which may not", + "bbox": [ + 75, + 869, + 468, + 902 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/9c289f5c4d44c17fc8dbc3c133d440d12005e4eeed42b6f15aa97d37775dc0e8.jpg", + "table_caption": [ + "Table 1. Depth evaluation results on the ScanNet dataset. The best results are marked in bold. Our model is leading in both effectiveness and efficiency." + ], + "table_footnote": [], + "table_body": "
Abs Diff↓Abs Rel↓Sq Rel↓
No Semantic Head0.12250.06330.0192
+ Semantic Head0.10690.05240.0161
", + "bbox": [ + 504, + 282, + 888, + 339 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 2. Improvements from our semantic head.", + "bbox": [ + 542, + 349, + 846, + 363 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "always be feasible. Besides, our current model may have difficulty with unseen object categories, although we only require adjacent frames to have the same class prediction (even if it is incorrect).", + "bbox": [ + 498, + 392, + 890, + 453 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 469, + 617, + 484 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper proposes a novel 3D reconstruction network that is leading in effectiveness and efficiency. Our core contribution is to locate the most promising depth candidates using semantic maps. Specifically, we prune unreliable candidates according to the cross-view semantic consistency and then resample the candidates to look after pixels in need. Consequently, our method produces highly delicate reconstructions of meticulous structures and generates smooth surfaces for large planes with low overhead. Experimental results on the most popular datasets verify the proposed method's advantages in real scenarios.", + "bbox": [ + 496, + 494, + 890, + 662 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments", + "text_level": 1, + "bbox": [ + 500, + 678, + 658, + 695 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work is partially supported by the National Science Foundation of China (NSFC) under Grant No. U22B2060, the Hong Kong RGC GRF Project 16209519, CRF Project C6030-18G, C2004-21GF, AOE Project AoE/E-603/18, RIF Project R6020-19, Theme-based project TRS T41-603/20R, China NSFC No. 61729201, Guangdong Basic and Applied Basic Research Foundation 2019B151530001, Hong Kong ITC ITF grants MHX/078/21 and PRP/004/22FX, Microsoft Research Asia Collaborative Research Grant, HKUST-Webank joint research lab grant and HKUST Global Strategic Partnership Fund (2021 SJTU-HKUST). In addition, we gratefully acknowledge the generous support from MindSpore.", + "bbox": [ + 496, + 703, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "12583", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 90, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Neill DF Campbell, George Vogiatzis, Carlos Hernández, and Roberto Cipolla. Using multiple hypotheses to improve depth-maps for multi-view stereo. In European Conference on Computer Vision, pages 766-779. Springer, 2008. 3", + "[2] Liang-Chieh Chen, George Papandreou, Iasonas Kokkinos, Kevin Murphy, and Alan L Yuille. Deeplab: Semantic image segmentation with deep convolutional nets, atrous convolution, and fully connected crfs. 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Visual prompt multi-modal tracking. arXiv preprint arXiv:2303.10826, 2023. 3" + ], + "bbox": [ + 78, + 90, + 468, + 303 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "12587", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 11 + } +] \ No newline at end of file diff --git a/2023/Dionysus_ Recovering Scene Structures by Dividing Into Semantic Pieces/13315114-2bd9-46a3-8750-70a0a8a52fb9_model.json b/2023/Dionysus_ Recovering Scene Structures by Dividing Into Semantic Pieces/13315114-2bd9-46a3-8750-70a0a8a52fb9_model.json new file mode 100644 index 0000000000000000000000000000000000000000..9086b4b9f7ed6094da54bdaab2dc743366c6bf14 --- /dev/null +++ b/2023/Dionysus_ Recovering Scene Structures by Dividing Into Semantic Pieces/13315114-2bd9-46a3-8750-70a0a8a52fb9_model.json @@ -0,0 +1,2512 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.272, + 0.131, + 0.7, + 0.175 + ], + "angle": 0, + "content": "Dionysus: Recovering Scene Structures by Dividing into Semantic Pieces" + }, + { + "type": "text", + "bbox": [ + 0.214, + 0.203, + 0.756, + 0.293 + ], + "angle": 0, + "content": "Likang Wang1, Lei Chen1,2 \n1Department of Computer Science and Engineering \nThe Hong Kong University of Science and Technology \n2Data Science and Analytics Thrust \nThe Hong Kong University of Science and Technology (Guangzhou)" + }, + { + "type": "text", + "bbox": [ + 0.294, + 0.296, + 0.673, + 0.31 + ], + "angle": 0, + "content": "lwangcg@connect.ust.hk, leichen@cse.ust.hk" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.345, + 0.314, + 0.361 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.377, + 0.473, + 0.633 + ], + "angle": 0, + "content": "Most existing 3D reconstruction methods result in either detail loss or unsatisfying efficiency. However, effectiveness and efficiency are equally crucial in real-world applications, e.g., autonomous driving and augmented reality. We argue that this dilemma comes from wasted resources on valueless depth samples. This paper tackles the problem by proposing a novel learning-based 3D reconstruction framework named Dionysus. Our main contribution is to find out the most promising depth candidates from estimated semantic maps. This strategy simultaneously enables high effectiveness and efficiency by attending to the most reliable nominators. Specifically, we distinguish unreliable depth candidates by checking the cross-view semantic consistency and allow adaptive sampling by redistributing depth nominators among pixels. Experiments on the most popular datasets confirm our proposed framework's effectiveness." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.664, + 0.21, + 0.68 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Recovering 3D structures from 2D images is one of the most fundamental computer vision tasks [7, 25, 26, 68] and has wide applications in various scenarios (e.g., autonomous driving, metaverse, and augmented reality). Thanks to the popularity of smartphones, high-quality RGB videos are always obtainable. Since each image describes only a tiny piece of the whole scenario [31, 33], reconstruction from multiple frames [44, 50] is more attractive than from a single image [13, 14]. Although model quality and real-time response are equally essential, the existing 3D reconstruction methods have difficulty performing well in both aspects. For example, multi-view stereo (MVS) models [63, 73] consume seconds on each image, while real-time approaches [9, 57, 64] lead to missing details or large-area" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.349, + 0.542, + 0.36 + ], + "angle": 0, + "content": "mess." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.365, + 0.895, + 0.486 + ], + "angle": 0, + "content": "The mainstream reconstruction methods [15,63,72] generally sample a set of candidate depths or voxels, then use neural networks (e.g., CNNs [21] and transformers [58]) to evaluate each candidate's reliability. The candidate number is generally small because of the evaluation networks' high computational demand. Consequently, the reconstruction quality becomes unsatisfying because the ground truth is less likely to be sampled." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.49, + 0.896, + 0.868 + ], + "angle": 0, + "content": "Pursuing a higher candidate sampling density, CasMVSNet [15] shrinks the depth range in a coarse-to-fine fashion; IS-MVSNet [63] searches for new candidates according to the estimated error distribution; NeuralRecon [57] prunes the voxels thought to be unreliable in the previous predictions. All these methods select candidates according to the initial depth estimations. Notably, small objects and delicate structures are hard to recover in the beginning low-resolution phase because they require a high resolution to distinguish. As a result, the final reconstruction often suffers from missing objects and crude details because the actual depth can be outside the final search range when the initial estimation is unreliable. However, decent reconstruction quality on delicate objects is crucial to many real-world applications. Specifically, traffic accidents may occur if any pedestrian or warning post fails to recover; frequent collisions and even fire disasters might happen if cleaning robots cannot well reconstruct table legs and electric cables. Besides the defects in meticulous structures, coarse-to-fine models also have room to improve efficiency. As mentioned, the mainstream coarse-to-fine methods sample and then evaluate initial candidates multiple times to locate the most valuable candidate depths. Notably, examining the preliminary candidates may be more expensive (usually two times more [15, 78]) than assessing the final nominators." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.895, + 0.902 + ], + "angle": 0, + "content": "In addition to the costly evaluation networks widely adopted in coarse-to-fine architectures, another natural so-" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "12576" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.127, + 0.087, + 0.855, + 0.393 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.403, + 0.895, + 0.446 + ], + "angle": 0, + "content": "Figure 1. The overall architecture of our framework. We first estimate a semantic map for the current frame and then retrieve the former semantic estimations. After that, we locate the most valuable depth candidates through the semantic maps. Finally, we predict the depth map for the current frame by examining each depth candidate." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.472, + 0.47, + 0.667 + ], + "angle": 0, + "content": "lution is to measure each depth candidate's reliability according to the photometric consistency among RGB images or feature maps from different views. The basic logic behind these methods is that pixels from distinct perspectives should own the same color if they are the correct projections from the same 3D point. However, a 3D point may look distinct in different views due to illumination, transparency, and reflection. Moreover, candidates close to but not precisely coinciding with the ground truth may have different colors for delicate objects, thus leading to low photometric consistency. Consequently, the found candidate may correspond to a pixel distant from the ground truth but of a similar color." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.669, + 0.471, + 0.864 + ], + "angle": 0, + "content": "To get rid of detail defects and keep efficiency, it becomes crucial to accurately and efficiently find the most promising candidate depths. This paper proposes a novel high-quality real-time 3D reconstruction framework named Dionysus, which looks for depth hypotheses based on semantic estimations. Precisely, we distinguish each depth candidate's reliability according to its semantic consistency among warped views. Fig. 1 illustrates the overall architecture of our framework. Our intuition is that two pixels should share the same semantic label if they are projections of the same 3D point. We argue that selecting depth candidates according to the semantic tags results in various benefits:" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.871, + 0.471, + 0.902 + ], + "angle": 0, + "content": "1. Consistent: A 3D point may have distinct colors when observing from different perspectives, but its semantic" + }, + { + "type": "text", + "bbox": [ + 0.532, + 0.473, + 0.67, + 0.488 + ], + "angle": 0, + "content": "label never changes." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.498, + 0.892, + 0.62 + ], + "angle": 0, + "content": "2. Efficient: Semantic estimation requires a meager cost. A semantic segmentation model may spend only milliseconds on each frame [11,47] while evaluating each cost volume in coarse layers generally takes ten times more cost. In addition, most hierarchical methods shrink the depth range only by half in each stage, while our method may significantly reduce the depth range on delicate objects (e.g., desk legs)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.629, + 0.894, + 0.69 + ], + "angle": 0, + "content": "3. Dense: Tiny objects always get missing in hierarchical frameworks because the initial samples are too sparse. However, the semantic maps are highly dense, thus retaining fine details." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.7, + 0.894, + 0.777 + ], + "angle": 0, + "content": "4. Adaptive: Semantics indicate various properties of the pixel. For example, an electric cable may demand highly dense samples to recover, but a wall may not. In other words, we can assign each pixel the most suitable sampling density according to its semantic estimation." + }, + { + "type": "list", + "bbox": [ + 0.512, + 0.498, + 0.894, + 0.777 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Depth Reassignment: A bed pixel may have much more valid depth candidates than a pen pixel after the semantic-based pruning because there are likely many bed pixels in other views. Consequently, we cannot form a regular cost volume based on the pruned depth candidates because pixels may have different numbers of valid depth candidates. However, most GPUs are not designed for irregular inputs" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12577" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.226 + ], + "angle": 0, + "content": "and are inefficient in such cases. Thus, we further propose reallocating depth samples from pixels with excess valid candidates to those in the opposite. In this way, all pixels finally have the same number of candidates and thus can be conveniently computed by GPUs. Moreover, we sample more densely for delicate structures, otherwise more sparsely, because tiny objects have a narrower depth range after semantic pruning, and all pixels have the same depth number." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.228, + 0.47, + 0.256 + ], + "angle": 0, + "content": "To summarize, this paper has two significant contributions:" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.267, + 0.469, + 0.327 + ], + "angle": 0, + "content": "1. Instead of densely evaluating all depths or sparsely evaluating limited depths, we efficiently select the most promising depth candidates based on the cross-view semantic consistency." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.338, + 0.469, + 0.368 + ], + "angle": 0, + "content": "2. We reallocate depth samples among pixels to make our model adaptive to objects and efficient on GPUs." + }, + { + "type": "list", + "bbox": [ + 0.089, + 0.267, + 0.469, + 0.368 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.377, + 0.469, + 0.438 + ], + "angle": 0, + "content": "The mentioned contributions significantly benefit the effectiveness while retaining efficiency. Our extensive experiments on the most popular 3D reconstruction datasets [5] further verify our proposed method's validity." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.451, + 0.22, + 0.467 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.476, + 0.469, + 0.536 + ], + "angle": 0, + "content": "We first introduce the development of 3D reconstruction, then present the progress in semantic segmentation, and finally discuss the existing semantic-based 3D reconstruction networks." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.546, + 0.257, + 0.561 + ], + "angle": 0, + "content": "2.1.3D Reconstruction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.569, + 0.469, + 0.765 + ], + "angle": 0, + "content": "Recovering 3D structures from images has been widely studied for many decades. Despite the great success of traditional methods [1, 12, 52, 53], most recent solutions [9, 15, 73] are based on neural networks [21, 35-38, 62] because of the latter's popularity [27, 32, 71, 75, 76] in the last decades. Thanks to the popularity of smartphones, continuous video sequences can now be easily captured. Compared to independent images, video sequences [28, 80] contain rich correlations among frames, thus leading to more consistent reconstruction quality. In consequence, learning-based video reconstruction [44, 56, 69] is becoming a hot spot. However, due to their high computation demand, most video reconstruction methods are limited in offline applications." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.766, + 0.469, + 0.902 + ], + "angle": 0, + "content": "Real-time video reconstruction is attracting wide attention from the academy and the industry, considering its vital position in autonomous driving and augmented reality. The mainstream real-time methods can be categorized into depth-based [9, 16, 40, 61] and volume-based [57]. Specifically, the former estimates depth maps and fuses them into 3D representations. In contrast, the latter directly regresses 3D representations from the RGB inputs. Depth-based methods generally lead to lower latency because they" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.228 + ], + "angle": 0, + "content": "immediately process each new frame without waiting. Conversely, volumetric methods estimate 3D representations from a group of frames, thus cannot respond to new frames at once and are less suitable for online scenarios. The mainstream depth-based approaches usually uniformly sample depth candidates from an overly broad range [9] or gradually shrink the search range by repeated predictions [15,72]. Our main difference from the existing depth-based methods is that we utilize semantics to select depth candidates." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.238, + 0.719, + 0.254 + ], + "angle": 0, + "content": "2.2. Semantic Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.262, + 0.892, + 0.413 + ], + "angle": 0, + "content": "Semantic segmentation focuses on estimating each pixel's object category (e.g., whether it represents a dog). Most semantic segmentation networks [2, 51, 67, 74, 77] inherited a learning-based framework from FCN [39]. Real-time solutions generally put their most effort into designing a lightweight backbone considering its contribution to the whole model's complexity. The existing online methods generally own three backbone types [43]: classification-based [22, 24, 60], segmentation-based [23, 34, 41], and two-branch-based [48, 74, 79]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.413, + 0.892, + 0.565 + ], + "angle": 0, + "content": "The first class encodes features using image classification networks and then decodes to output semantics. The second class designs segmentation-specific backbones considering the task difference between segmentation and classification. The third class processes macro and micro information separately to reduce the overall cost. State-of-the-art segmentation models can infer hundreds of frames per second and retain high quality simultaneously. In comparison, the fastest depth estimation networks are bounded to dozens of frames per second." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.575, + 0.806, + 0.59 + ], + "angle": 0, + "content": "2.3. Semantic-based 3D Reconstruction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.891, + 0.644 + ], + "angle": 0, + "content": "Quite a few papers focus on integrating semantics into depth estimation networks. Most related works belong to single-image depth estimation and stereo matching." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.892, + 0.795 + ], + "angle": 0, + "content": "In single-image depth estimation, view correspondence does not exist; thus, semantic information becomes more vital. [66] simultaneously estimates depth and semantic maps by multi-task learning. [65] shares depth weights among pixels of the same semantic label. [10] jointly estimates depth, semantics, and surface normal. [20] introduces a synergy network to share features between the semantic and depth branches. [30] restricts depth predictions by semantic priors (e.g., the sky is distant, and the ground is horizontal). [59] infers invisible regions from semantics." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In stereo matching, two views with fixed relative poses are given, and the goal is to match pixels in the two views. These papers can be generally divided into two categories. The first class treats semantic maps as additional channels. [8] refines disparities by concatenating semantic and disparity features along the channel dimension. [70] constructs cost volumes for semantics and disparity and then" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "12578" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.092, + 0.898, + 0.332 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.349, + 0.895, + 0.392 + ], + "angle": 0, + "content": "Figure 2. Architecture of the semantic head. Former semantic and depth estimations are warped and then integrated with the current frame. After that, we extract hierarchical information from the concatenated feature map. The semantic map for the current frame is inferred from the feature volume composed of spatial and context information." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.418, + 0.47, + 0.569 + ], + "angle": 0, + "content": "fuses them by summing and global pooling. [3] constructs cost volume using semantic consistency between left and right images and estimates disparity residuals according to semantic category. The second class revises the disparity using priors in semantics. [49] filters depth maps based on semantic priors. For example, ground and water pixels with heights higher than \\(90\\%\\) get pruned. [46] refines edge and texture-less regions using semantic cues. [4] estimates disparity confidence using semantic consistency and refines disparity in each semantic region." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.569, + 0.47, + 0.629 + ], + "angle": 0, + "content": "The related works in multi-view stereo are limited. [18] recovers a segmented 3D representation from 2D images and semantics. [42] augments depth edges and guides cost aggregation using semantics." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.63, + 0.47, + 0.691 + ], + "angle": 0, + "content": "Unlike the mentioned works, we select depth candidates by explicitly exploiting semantic consistency for multi-view inputs. We also balance depth candidates among pixels and adaptively attend to pixels in need." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.705, + 0.212, + 0.723 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.731, + 0.47, + 0.822 + ], + "angle": 0, + "content": "We first introduce the overall architecture of our model in Sec. 3.1, then elaborate on each sub-component in Sec. 3.2 and 3.3. Our model inputs an RGB video sequence divided into frames and the camera parameters of each frame, which are estimated by off-the-shelf tools (e.g., ARKit). The output is expected to be the depth map of each frame." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.832, + 0.274, + 0.848 + ], + "angle": 0, + "content": "3.1. Overall Architecture" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Fig. 1 exhibits the overall framework. We have a semantic head to predict a semantic map \\( S_{t} \\) for the current frame \\( I_{t} \\). At the same time, we retrieve the semantic maps" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.416, + 0.89, + 0.448 + ], + "angle": 0, + "content": "\\(\\{S_i\\}_{i = t - n}^{t - 1}\\) predicted in the previous timestamps from a semantic queue." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.449, + 0.892, + 0.539 + ], + "angle": 0, + "content": "After that, we look for the most promising depth candidates for each pixel in \\( I_{t} \\) using our novel semantic-based depth candidate selection module, which is our main contribution. Finally, we examine each depth nominator using a depth head to output the final depth estimation. We sum losses from the depth and semantic heads as the overall loss." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.548, + 0.866, + 0.565 + ], + "angle": 0, + "content": "3.2. Semantic-based Depth Candidate Selection" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.572, + 0.892, + 0.646 + ], + "angle": 0, + "content": "This section introduces our main contributions. Sec. 3.2.1 first shows how to prune unreliable depth candidates using the semantic information, and then Sec. 3.2.2 demonstrates how to concentrate on pixels in need and become efficient on GPUs." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.666, + 0.773, + 0.682 + ], + "angle": 0, + "content": "3.2.1 Semantic-based Depth Pruning" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.69, + 0.892, + 0.75 + ], + "angle": 0, + "content": "To estimate the depth of a pixel in the current frame \\( I_{t} \\), we sample a set of depth candidates and evaluate their reliability one by one. The candidate number must be high enough to hit the ground truth." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.87 + ], + "angle": 0, + "content": "However, the existing learning-based methods can only examine a small number of samples because they use a giant neural network to assess each candidate. Consequently, small objects distant from the background and delicate structures get defective. The small object problem cannot be solved via coarse-to-fine architectures because significantly wrong predictions in the coarse stages cannot be recovered in finer stages." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Unlike the existing methods, we first predict the semantic labels for each pixel at a low cost; then, we use the se" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12579" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.171, + 0.086, + 0.797, + 0.31 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.324, + 0.895, + 0.355 + ], + "angle": 0, + "content": "Figure 3. Illustration of depth pruning. We uniformly sample depth candidates for a given pixel (purple) in the current frame, then evaluate each candidate to determine whether it leads to a pixel of the same semantic label projected on the former frames." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.379, + 0.471, + 0.41 + ], + "angle": 0, + "content": "mantic maps to restrict the depth candidate sampling only to the most reliable regions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.427, + 0.47, + 0.517 + ], + "angle": 0, + "content": "I/O: The inputs include the current frame \\( I_{t} \\) and retrieved previous semantic \\( \\{S_{i}\\}_{i = t - n}^{t - 1} \\) and depth \\( \\{D_{i}\\}_{i = t - n}^{t - 1} \\) estimations. Besides, similar to most existing methods [9, 57, 73], we assume the camera parameters from time \\( t - n \\) to \\( t \\) are available. In fact, the camera parameters can be obtained from off-the-shelf tools (e.g., ARKit)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.518, + 0.471, + 0.549 + ], + "angle": 0, + "content": "The outputs are the most promising depth candidates for each pixel in the current frame \\( I_{t} \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.566, + 0.47, + 0.642 + ], + "angle": 0, + "content": "Semantic Head: Instead of outputting the correct label, semantic consistency among frames is more crucial because we examine depth candidates by cross-view conformity. Thus, we need to consider previous semantic estimations when processing new frames." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.642, + 0.47, + 0.732 + ], + "angle": 0, + "content": "We propose a highly efficient 2D convolutional network to predict the semantic labels for each pixel in \\( I_{t} \\), as shown in Fig. 2. The inputs of the semantic prediction head include the current frame \\( I_{t} \\), the semantic and depth maps predicted from timestamp \\( t - n \\) to \\( t - 1 \\), and the corresponding camera parameters." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.732, + 0.471, + 0.839 + ], + "angle": 0, + "content": "The former depth and semantic predictions are warped to the current view according to the relative poses and then fused by concatenating along the channel dimension. Inspired by STDC-Seg [11] and BiSeNet [74], we adopt a two-pathway architecture to efficiently extract spatial and context information, which are then fused to generate the final semantic estimation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Depth Pruning: After obtaining the semantic maps, we start to prune depth candidates. According to the camera parameters from time \\( t - n \\) to \\( t \\), we can draw a straight line" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.378, + 0.892, + 0.438 + ], + "angle": 0, + "content": "(i.e., the epipolar line) on each previous frame \\(\\in \\{I_i\\}_{i = t - n}^{t - 1}\\) for each pixel \\(p_t\\in\\) the current frame \\(I_{t}\\) and guarantee that the correct correspondences can only lie on the epipolar line." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.44, + 0.893, + 0.546 + ], + "angle": 0, + "content": "Then, we sample \\( N_{s} \\) (a significant number) depth candidates for each pixel in \\( I_{t} \\), as shown in Fig. 3. Each depth corresponds to one pixel on the epipolar line in each former frame. After that, we check whether the projected pixel's semantic label is exactly the same as \\( p_{t} \\). Only the candidate depths leading to a positive answer get retained, otherwise pruned." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.548, + 0.894, + 0.638 + ], + "angle": 0, + "content": "Consequently, each former frame provides a set of reliable depth candidates. These sets of candidate overlap yet may differ due to occlusion and field views. We use the union of all the sets as the aggregated depth candidate set because each pair of matched pixels may imply the existence of a 3D point." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.64, + 0.894, + 0.745 + ], + "angle": 0, + "content": "Since we judge the reliability based on semantics, a question might be whether our framework relies heavily on each pixel's precise prediction. The answer is no because we only require semantics in different frames to be consistent instead of strictly being the ground truth. Moreover, the existing semantic segmentation architectures [11, 47] can provide impressive enough label estimations." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.77, + 0.803, + 0.785 + ], + "angle": 0, + "content": "3.2.2 Semantic-based Depth Reallocation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.894, + 0.903 + ], + "angle": 0, + "content": "After pruning unreliable candidates, pixels may own inconsistent numbers of depth nominators because different objects might occupy distinct amounts of space, as shown in the left of Fig. 4. Since the initial depth candidates are uniformly sampled, a pixel owning many reliable depth nominators likely belongs to a large object (e.g., walls and floors). These objects usually do not require dense samples" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "12580" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.207, + 0.086, + 0.768, + 0.199 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.212, + 0.895, + 0.242 + ], + "angle": 0, + "content": "Figure 4. Reassignment among pixels. Pixels may have a different number of candidate depths after semantic pruning. However, the difference disappears after reallocation." + }, + { + "type": "image", + "bbox": [ + 0.119, + 0.254, + 0.855, + 0.444 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.456, + 0.893, + 0.486 + ], + "angle": 0, + "content": "Figure 5. Illustration of candidate reallocation. Top: pixel with too many candidates. We reduce the nominator number by down-sampling. Bottom: pixel with too few candidates." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.511, + 0.47, + 0.586 + ], + "angle": 0, + "content": "because they have smooth surfaces, and their depths can be easily inferred from neighbors. In contrast, coarser sampling may help the network overcome repetitive patterns and non-textured regions by collecting information from a larger field of view." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.587, + 0.47, + 0.648 + ], + "angle": 0, + "content": "However, delicate objects (e.g., toothbrushes and nail clippers) eagerly demand higher depth resolution for detail recovery. Thus, we should put more effort into pixels holding fewer candidates." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.672, + 0.47, + 0.747 + ], + "angle": 0, + "content": "Reallocate Candidates: We propose to set a unified depth number \\( N_{u} \\) for all pixels by transfer payment, as shown in Fig. 4. Specifically, if a pixel occupies too many candidates, we lower its sampling density; otherwise, we promote." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.749, + 0.47, + 0.869 + ], + "angle": 0, + "content": "As shown in Fig. 5, we uniformly position \\( N_{u} \\) candidates within the depth range bounded by the \\( N_{v}^{i} \\) valid nominators for each pixel \\( p_{i} \\). Segmented depth ranges may occur when multiple objects of the same semantic label appear in the same image, as shown in Fig. 3. In such cases, candidates in different fragments are reallocated separately, and the quota of new candidates in each fragment is proportional to the number of valid candidates inside the fragment." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.47, + 0.902 + ], + "angle": 0, + "content": "To avoid fractional new candidate numbers, we prioritize the narrowest fragments and offer them slightly more" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.511, + 0.892, + 0.572 + ], + "angle": 0, + "content": "candidates by the ceiling function. After that, we assign the remaining quotas for the rest fragments. This way, attention transfers from large surfaces to small objects because fragments containing fewer valid candidates get promoted." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.572, + 0.892, + 0.632 + ], + "angle": 0, + "content": "A more significant unified depth number \\( N_{u} \\) offers higher effectiveness while lowering the model efficiency. In default, the value of \\( N_{u} \\) is set to ensure the whole model runs as fast as the state-of-the-art real-time methods." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.656, + 0.892, + 0.701 + ], + "angle": 0, + "content": "Efficiency: Our reallocation strategy benefits effectiveness by attending more to delicate structures and contributes to efficiency." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.703, + 0.892, + 0.778 + ], + "angle": 0, + "content": "We take Fig. 4 as an example. Although these three pixels have the same number of initial depth hypotheses, they get different valid candidate numbers after the semantic pruning. Notably, most GPUs are designed to process regular inputs and are inefficient on irregular data." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.779, + 0.892, + 0.885 + ], + "angle": 0, + "content": "Thus, without reassignment, we have to pad pixels 2 and 3 with zeros to form a three (pixel number) by three (the max valid candidate number among pixels: \\(\\max_i\\{N_v^i\\}\\)) matrix as the input of the depth head. In comparison, a three-by-two matrix is enough after reallocation. The reduction of input matrix size directly lowers the computation demand of the costly depth head." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Although sparsification may sound like a good solution," + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "12581" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.086, + 0.885, + 0.339 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.352, + 0.895, + 0.395 + ], + "angle": 0, + "content": "Figure 6. Architecture of the depth head. The outputs of the semantic-based depth selection module are used to warp the previous video frames to the current view for cost volume calculation. The depth predictions are regressed based on the current cost volume and former estimations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.421, + 0.471, + 0.468 + ], + "angle": 0, + "content": "it heavily relies on specialized hardware and is usually less efficient on inputs of irregular zero distributions. In addition, it leads to lower sampling density on small objects." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.507, + 0.47, + 0.613 + ], + "angle": 0, + "content": "Spatial Correlation: Since our samples are pixel-wisely determined, a possible doubt might be whether the spatial correlation still holds. The answer is yes because neighboring pixels generally share the same semantic label. As a result, they should match adjacent pixels in other views, thus leading to similar depth candidates after the semantic pruning." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.617, + 0.47, + 0.709 + ], + "angle": 0, + "content": "Moreover, our candidate reassignment module evenly distributes candidates in the valid depth range; thus, neighboring pixels should have similar final depth samples. The local spatial correlation still holds as illustrated in Fig. 7. In other words, we can exploit convolutions to evaluate the candidate depths." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.732, + 0.473, + 0.837 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.849, + 0.47, + 0.88 + ], + "angle": 0, + "content": "Figure 7. Spatial correlation after depth selection. Neighboring pixels generally have similar sets of depth candidates." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.42, + 0.63, + 0.437 + ], + "angle": 0, + "content": "3.3. Depth Head" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.444, + 0.892, + 0.564 + ], + "angle": 0, + "content": "After determining the depth candidates for each pixel, we predict the depth map by assessing each depth candidate. The model starts by extracting image features from the current frame \\( I_{t} \\) using a feature pyramid network (FPN) [29]. After that, we warp the image features from previous time stamps to the current view and then construct a cost volume by measuring the pixel-wise correlation between the current and former features." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.565, + 0.892, + 0.657 + ], + "angle": 0, + "content": "Finally, we send the raw cost volume into a U-shape refining network to regress the depth prediction at time \\( t \\). Notably, we keep the temporal consistency by introducing a ConvLSTM [54] to update the extracted features and by warping the previous depth estimations to the current viewpoint." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.672, + 0.634, + 0.689 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.698, + 0.892, + 0.789 + ], + "angle": 0, + "content": "Our model is implemented using PyTorch [45]. We optimize the model using MADGRAD [6] on eight A100 GPUs. The input image is cropped and scaled to \\(256 \\times 256\\). The weights for testing are selected according to their losses on the validation set. The depth metrics are borrowed from DeepVideoMVS [9]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Keyframe Selection: Considering the high similarity between adjacent frames, estimating depth maps for every raw frame is inefficient. Thus, we select the most iconic frames (i.e., keyframes) from the input video sequences. When a new frame comes, we examine its pose distance to the latest keyframe and only adopt the new frames leading to pose" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "12582" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.124, + 0.089, + 0.849, + 0.222 + ], + "angle": 0, + "content": "
ScanNet
Abs Diff↓Abs Rel↓Sq Rel↓δ < 1.05↑δ < 1.25↑Time (ms) ↓
DPSNet [19]0.15480.07890.029249.3993.31308 ms
MVDepthNet [61]0.16430.08440.034146.7392.8046 ms
DELTAS [55]0.14920.07830.027148.6893.8183 ms
GPMVS [16]0.14920.07530.029051.0993.9849 ms
DeepVideoMVS (Fusion) [9]0.11820.05800.018760.2396.7830 ms
Ours0.10690.05060.016561.3497.1330 ms
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.232, + 0.893, + 0.261 + ], + "angle": 0, + "content": "Table 1. Depth evaluation results on the ScanNet dataset. The best results are marked in bold. Our model is leading in both effectiveness and efficiency." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.286, + 0.471, + 0.361 + ], + "angle": 0, + "content": "distances above a threshold. We define the pose distance as Eq. (1) and set the threshold as 0.35, following [9, 17]. Notably, we do not estimate depth for the first frame in a video sequence because it has no predecessors to provide multi-view information." + }, + { + "type": "equation", + "bbox": [ + 0.091, + 0.385, + 0.47, + 0.42 + ], + "angle": 0, + "content": "\\[\nD i s _ {p} = \\sqrt {\\left| t r a n s i t i o n \\right| ^ {2} + \\frac {2}{3} T r a c e (I - r o t a t i o n)} \\quad (1)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.433, + 0.47, + 0.495 + ], + "angle": 0, + "content": "Datasets: Following the mainstream settings [9, 57], we train and evaluate our model on ScanNet [5], which is a large-scale real-world video dataset containing 1201 scenes for training, 321 for validation, and 100 for testing." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.512, + 0.469, + 0.557 + ], + "angle": 0, + "content": "Comparison to existing SOTAs Tab. 1 demonstrates that our method outperforms various state-of-the-art depth estimation approaches in effectiveness and efficiency." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.558, + 0.469, + 0.678 + ], + "angle": 0, + "content": "Compared to real-time SOTAs [9], our method shows significant advantages in all effectiveness metrics while retaining comparable time efficiency. Compared to semi-realtime algorithms [16, 55, 61], our method dominates inference time and offers significant competitiveness in reconstruction quality. In addition, our real-time framework even generates more accurate depth maps than some offline solutions [19] while spending one magnitude less cost." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.679, + 0.469, + 0.739 + ], + "angle": 0, + "content": "Moreover, our method benefits relative error more than absolute error and favors \\( L^1 \\) difference more than \\( L^2 \\). These results indicate that delicate structures and small objects win more attention." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.757, + 0.469, + 0.833 + ], + "angle": 0, + "content": "Impacts of the Semantic Head To assess the effectiveness of our proposed semantic-based depth selection strategy, we fix all other variables and only examine the semantic head's impacts. Tab. 2 confirms that our semantic-based depth selection module offers significant benefits." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.845, + 0.2, + 0.86 + ], + "angle": 0, + "content": "5. Limitations" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Like most dense reconstruction models, our pipeline requires the camera parameters to be known, which may not" + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.284, + 0.89, + 0.34 + ], + "angle": 0, + "content": "
Abs Diff↓Abs Rel↓Sq Rel↓
No Semantic Head0.12250.06330.0192
+ Semantic Head0.10690.05240.0161
" + }, + { + "type": "table_caption", + "bbox": [ + 0.544, + 0.35, + 0.848, + 0.364 + ], + "angle": 0, + "content": "Table 2. Improvements from our semantic head." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.393, + 0.892, + 0.454 + ], + "angle": 0, + "content": "always be feasible. Besides, our current model may have difficulty with unseen object categories, although we only require adjacent frames to have the same class prediction (even if it is incorrect)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.47, + 0.619, + 0.485 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.496, + 0.892, + 0.663 + ], + "angle": 0, + "content": "This paper proposes a novel 3D reconstruction network that is leading in effectiveness and efficiency. Our core contribution is to locate the most promising depth candidates using semantic maps. Specifically, we prune unreliable candidates according to the cross-view semantic consistency and then resample the candidates to look after pixels in need. Consequently, our method produces highly delicate reconstructions of meticulous structures and generates smooth surfaces for large planes with low overhead. Experimental results on the most popular datasets verify the proposed method's advantages in real scenarios." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.679, + 0.66, + 0.696 + ], + "angle": 0, + "content": "Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.892, + 0.901 + ], + "angle": 0, + "content": "This work is partially supported by the National Science Foundation of China (NSFC) under Grant No. U22B2060, the Hong Kong RGC GRF Project 16209519, CRF Project C6030-18G, C2004-21GF, AOE Project AoE/E-603/18, RIF Project R6020-19, Theme-based project TRS T41-603/20R, China NSFC No. 61729201, Guangdong Basic and Applied Basic Research Foundation 2019B151530001, Hong Kong ITC ITF grants MHX/078/21 and PRP/004/22FX, Microsoft Research Asia Collaborative Research Grant, HKUST-Webank joint research lab grant and HKUST Global Strategic Partnership Fund (2021 SJTU-HKUST). In addition, we gratefully acknowledge the generous support from MindSpore." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12583" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.091, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Neill DF Campbell, George Vogiatzis, Carlos Hernández, and Roberto Cipolla. Using multiple hypotheses to improve depth-maps for multi-view stereo. In European Conference on Computer Vision, pages 766-779. Springer, 2008. 3" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.172, + 0.471, + 0.242 + ], + "angle": 0, + "content": "[2] Liang-Chieh Chen, George Papandreou, Iasonas Kokkinos, Kevin Murphy, and Alan L Yuille. Deeplab: Semantic image segmentation with deep convolutional nets, atrous convolution, and fully connected crfs. 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However, effectiveness and efficiency are equally crucial in real-world applications, e.g., autonomous driving and augmented reality. We argue that this dilemma comes from wasted resources on valueless depth samples. This paper tackles the problem by proposing a novel learning-based 3D reconstruction framework named Dionysus. Our main contribution is to find out the most promising depth candidates from estimated semantic maps. This strategy simultaneously enables high effectiveness and efficiency by attending to the most reliable nominators. Specifically, we distinguish unreliable depth candidates by checking the cross-view semantic consistency and allow adaptive sampling by redistributing depth nominators among pixels. Experiments on the most popular datasets confirm our proposed framework's effectiveness. + +# 1. Introduction + +Recovering 3D structures from 2D images is one of the most fundamental computer vision tasks [7, 25, 26, 68] and has wide applications in various scenarios (e.g., autonomous driving, metaverse, and augmented reality). Thanks to the popularity of smartphones, high-quality RGB videos are always obtainable. Since each image describes only a tiny piece of the whole scenario [31, 33], reconstruction from multiple frames [44, 50] is more attractive than from a single image [13, 14]. Although model quality and real-time response are equally essential, the existing 3D reconstruction methods have difficulty performing well in both aspects. For example, multi-view stereo (MVS) models [63, 73] consume seconds on each image, while real-time approaches [9, 57, 64] lead to missing details or large-area + +mess. + +The mainstream reconstruction methods [15,63,72] generally sample a set of candidate depths or voxels, then use neural networks (e.g., CNNs [21] and transformers [58]) to evaluate each candidate's reliability. The candidate number is generally small because of the evaluation networks' high computational demand. Consequently, the reconstruction quality becomes unsatisfying because the ground truth is less likely to be sampled. + +Pursuing a higher candidate sampling density, CasMVSNet [15] shrinks the depth range in a coarse-to-fine fashion; IS-MVSNet [63] searches for new candidates according to the estimated error distribution; NeuralRecon [57] prunes the voxels thought to be unreliable in the previous predictions. All these methods select candidates according to the initial depth estimations. Notably, small objects and delicate structures are hard to recover in the beginning low-resolution phase because they require a high resolution to distinguish. As a result, the final reconstruction often suffers from missing objects and crude details because the actual depth can be outside the final search range when the initial estimation is unreliable. However, decent reconstruction quality on delicate objects is crucial to many real-world applications. Specifically, traffic accidents may occur if any pedestrian or warning post fails to recover; frequent collisions and even fire disasters might happen if cleaning robots cannot well reconstruct table legs and electric cables. Besides the defects in meticulous structures, coarse-to-fine models also have room to improve efficiency. As mentioned, the mainstream coarse-to-fine methods sample and then evaluate initial candidates multiple times to locate the most valuable candidate depths. Notably, examining the preliminary candidates may be more expensive (usually two times more [15, 78]) than assessing the final nominators. + +In addition to the costly evaluation networks widely adopted in coarse-to-fine architectures, another natural so- + +![](images/f83eb7bf3f711219e9ae9f3546d88c1620ddfcf7f842c1733bb521b59d522fe2.jpg) +Figure 1. The overall architecture of our framework. We first estimate a semantic map for the current frame and then retrieve the former semantic estimations. After that, we locate the most valuable depth candidates through the semantic maps. Finally, we predict the depth map for the current frame by examining each depth candidate. + +lution is to measure each depth candidate's reliability according to the photometric consistency among RGB images or feature maps from different views. The basic logic behind these methods is that pixels from distinct perspectives should own the same color if they are the correct projections from the same 3D point. However, a 3D point may look distinct in different views due to illumination, transparency, and reflection. Moreover, candidates close to but not precisely coinciding with the ground truth may have different colors for delicate objects, thus leading to low photometric consistency. Consequently, the found candidate may correspond to a pixel distant from the ground truth but of a similar color. + +To get rid of detail defects and keep efficiency, it becomes crucial to accurately and efficiently find the most promising candidate depths. This paper proposes a novel high-quality real-time 3D reconstruction framework named Dionysus, which looks for depth hypotheses based on semantic estimations. Precisely, we distinguish each depth candidate's reliability according to its semantic consistency among warped views. Fig. 1 illustrates the overall architecture of our framework. Our intuition is that two pixels should share the same semantic label if they are projections of the same 3D point. We argue that selecting depth candidates according to the semantic tags results in various benefits: + +1. Consistent: A 3D point may have distinct colors when observing from different perspectives, but its semantic + +label never changes. + +2. Efficient: Semantic estimation requires a meager cost. A semantic segmentation model may spend only milliseconds on each frame [11,47] while evaluating each cost volume in coarse layers generally takes ten times more cost. In addition, most hierarchical methods shrink the depth range only by half in each stage, while our method may significantly reduce the depth range on delicate objects (e.g., desk legs). +3. Dense: Tiny objects always get missing in hierarchical frameworks because the initial samples are too sparse. However, the semantic maps are highly dense, thus retaining fine details. +4. Adaptive: Semantics indicate various properties of the pixel. For example, an electric cable may demand highly dense samples to recover, but a wall may not. In other words, we can assign each pixel the most suitable sampling density according to its semantic estimation. + +Depth Reassignment: A bed pixel may have much more valid depth candidates than a pen pixel after the semantic-based pruning because there are likely many bed pixels in other views. Consequently, we cannot form a regular cost volume based on the pruned depth candidates because pixels may have different numbers of valid depth candidates. However, most GPUs are not designed for irregular inputs + +and are inefficient in such cases. Thus, we further propose reallocating depth samples from pixels with excess valid candidates to those in the opposite. In this way, all pixels finally have the same number of candidates and thus can be conveniently computed by GPUs. Moreover, we sample more densely for delicate structures, otherwise more sparsely, because tiny objects have a narrower depth range after semantic pruning, and all pixels have the same depth number. + +To summarize, this paper has two significant contributions: + +1. Instead of densely evaluating all depths or sparsely evaluating limited depths, we efficiently select the most promising depth candidates based on the cross-view semantic consistency. +2. We reallocate depth samples among pixels to make our model adaptive to objects and efficient on GPUs. + +The mentioned contributions significantly benefit the effectiveness while retaining efficiency. Our extensive experiments on the most popular 3D reconstruction datasets [5] further verify our proposed method's validity. + +# 2. Related Work + +We first introduce the development of 3D reconstruction, then present the progress in semantic segmentation, and finally discuss the existing semantic-based 3D reconstruction networks. + +# 2.1.3D Reconstruction + +Recovering 3D structures from images has been widely studied for many decades. Despite the great success of traditional methods [1, 12, 52, 53], most recent solutions [9, 15, 73] are based on neural networks [21, 35-38, 62] because of the latter's popularity [27, 32, 71, 75, 76] in the last decades. Thanks to the popularity of smartphones, continuous video sequences can now be easily captured. Compared to independent images, video sequences [28, 80] contain rich correlations among frames, thus leading to more consistent reconstruction quality. In consequence, learning-based video reconstruction [44, 56, 69] is becoming a hot spot. However, due to their high computation demand, most video reconstruction methods are limited in offline applications. + +Real-time video reconstruction is attracting wide attention from the academy and the industry, considering its vital position in autonomous driving and augmented reality. The mainstream real-time methods can be categorized into depth-based [9, 16, 40, 61] and volume-based [57]. Specifically, the former estimates depth maps and fuses them into 3D representations. In contrast, the latter directly regresses 3D representations from the RGB inputs. Depth-based methods generally lead to lower latency because they + +immediately process each new frame without waiting. Conversely, volumetric methods estimate 3D representations from a group of frames, thus cannot respond to new frames at once and are less suitable for online scenarios. The mainstream depth-based approaches usually uniformly sample depth candidates from an overly broad range [9] or gradually shrink the search range by repeated predictions [15,72]. Our main difference from the existing depth-based methods is that we utilize semantics to select depth candidates. + +# 2.2. Semantic Segmentation + +Semantic segmentation focuses on estimating each pixel's object category (e.g., whether it represents a dog). Most semantic segmentation networks [2, 51, 67, 74, 77] inherited a learning-based framework from FCN [39]. Real-time solutions generally put their most effort into designing a lightweight backbone considering its contribution to the whole model's complexity. The existing online methods generally own three backbone types [43]: classification-based [22, 24, 60], segmentation-based [23, 34, 41], and two-branch-based [48, 74, 79]. + +The first class encodes features using image classification networks and then decodes to output semantics. The second class designs segmentation-specific backbones considering the task difference between segmentation and classification. The third class processes macro and micro information separately to reduce the overall cost. State-of-the-art segmentation models can infer hundreds of frames per second and retain high quality simultaneously. In comparison, the fastest depth estimation networks are bounded to dozens of frames per second. + +# 2.3. Semantic-based 3D Reconstruction + +Quite a few papers focus on integrating semantics into depth estimation networks. Most related works belong to single-image depth estimation and stereo matching. + +In single-image depth estimation, view correspondence does not exist; thus, semantic information becomes more vital. [66] simultaneously estimates depth and semantic maps by multi-task learning. [65] shares depth weights among pixels of the same semantic label. [10] jointly estimates depth, semantics, and surface normal. [20] introduces a synergy network to share features between the semantic and depth branches. [30] restricts depth predictions by semantic priors (e.g., the sky is distant, and the ground is horizontal). [59] infers invisible regions from semantics. + +In stereo matching, two views with fixed relative poses are given, and the goal is to match pixels in the two views. These papers can be generally divided into two categories. The first class treats semantic maps as additional channels. [8] refines disparities by concatenating semantic and disparity features along the channel dimension. [70] constructs cost volumes for semantics and disparity and then + +![](images/ed3a1474d5c41f458e9b48ce5a0baf21b358a2f7901a7a69a230656918cde5ff.jpg) +Figure 2. Architecture of the semantic head. Former semantic and depth estimations are warped and then integrated with the current frame. After that, we extract hierarchical information from the concatenated feature map. The semantic map for the current frame is inferred from the feature volume composed of spatial and context information. + +fuses them by summing and global pooling. [3] constructs cost volume using semantic consistency between left and right images and estimates disparity residuals according to semantic category. The second class revises the disparity using priors in semantics. [49] filters depth maps based on semantic priors. For example, ground and water pixels with heights higher than $90\%$ get pruned. [46] refines edge and texture-less regions using semantic cues. [4] estimates disparity confidence using semantic consistency and refines disparity in each semantic region. + +The related works in multi-view stereo are limited. [18] recovers a segmented 3D representation from 2D images and semantics. [42] augments depth edges and guides cost aggregation using semantics. + +Unlike the mentioned works, we select depth candidates by explicitly exploiting semantic consistency for multi-view inputs. We also balance depth candidates among pixels and adaptively attend to pixels in need. + +# 3. Methodology + +We first introduce the overall architecture of our model in Sec. 3.1, then elaborate on each sub-component in Sec. 3.2 and 3.3. Our model inputs an RGB video sequence divided into frames and the camera parameters of each frame, which are estimated by off-the-shelf tools (e.g., ARKit). The output is expected to be the depth map of each frame. + +# 3.1. Overall Architecture + +Fig. 1 exhibits the overall framework. We have a semantic head to predict a semantic map $S_{t}$ for the current frame $I_{t}$ . At the same time, we retrieve the semantic maps + +$\{S_i\}_{i = t - n}^{t - 1}$ predicted in the previous timestamps from a semantic queue. + +After that, we look for the most promising depth candidates for each pixel in $I_{t}$ using our novel semantic-based depth candidate selection module, which is our main contribution. Finally, we examine each depth nominator using a depth head to output the final depth estimation. We sum losses from the depth and semantic heads as the overall loss. + +# 3.2. Semantic-based Depth Candidate Selection + +This section introduces our main contributions. Sec. 3.2.1 first shows how to prune unreliable depth candidates using the semantic information, and then Sec. 3.2.2 demonstrates how to concentrate on pixels in need and become efficient on GPUs. + +# 3.2.1 Semantic-based Depth Pruning + +To estimate the depth of a pixel in the current frame $I_{t}$ , we sample a set of depth candidates and evaluate their reliability one by one. The candidate number must be high enough to hit the ground truth. + +However, the existing learning-based methods can only examine a small number of samples because they use a giant neural network to assess each candidate. Consequently, small objects distant from the background and delicate structures get defective. The small object problem cannot be solved via coarse-to-fine architectures because significantly wrong predictions in the coarse stages cannot be recovered in finer stages. + +Unlike the existing methods, we first predict the semantic labels for each pixel at a low cost; then, we use the se + +![](images/9eb71af5d386b186ba95cff4ba18a524693585549d7f8c3d7130ff81f405e586.jpg) +Figure 3. Illustration of depth pruning. We uniformly sample depth candidates for a given pixel (purple) in the current frame, then evaluate each candidate to determine whether it leads to a pixel of the same semantic label projected on the former frames. + +mantic maps to restrict the depth candidate sampling only to the most reliable regions. + +I/O: The inputs include the current frame $I_{t}$ and retrieved previous semantic $\{S_{i}\}_{i = t - n}^{t - 1}$ and depth $\{D_{i}\}_{i = t - n}^{t - 1}$ estimations. Besides, similar to most existing methods [9, 57, 73], we assume the camera parameters from time $t - n$ to $t$ are available. In fact, the camera parameters can be obtained from off-the-shelf tools (e.g., ARKit). + +The outputs are the most promising depth candidates for each pixel in the current frame $I_{t}$ . + +Semantic Head: Instead of outputting the correct label, semantic consistency among frames is more crucial because we examine depth candidates by cross-view conformity. Thus, we need to consider previous semantic estimations when processing new frames. + +We propose a highly efficient 2D convolutional network to predict the semantic labels for each pixel in $I_{t}$ , as shown in Fig. 2. The inputs of the semantic prediction head include the current frame $I_{t}$ , the semantic and depth maps predicted from timestamp $t - n$ to $t - 1$ , and the corresponding camera parameters. + +The former depth and semantic predictions are warped to the current view according to the relative poses and then fused by concatenating along the channel dimension. Inspired by STDC-Seg [11] and BiSeNet [74], we adopt a two-pathway architecture to efficiently extract spatial and context information, which are then fused to generate the final semantic estimation. + +Depth Pruning: After obtaining the semantic maps, we start to prune depth candidates. According to the camera parameters from time $t - n$ to $t$ , we can draw a straight line + +(i.e., the epipolar line) on each previous frame $\in \{I_i\}_{i = t - n}^{t - 1}$ for each pixel $p_t\in$ the current frame $I_{t}$ and guarantee that the correct correspondences can only lie on the epipolar line. + +Then, we sample $N_{s}$ (a significant number) depth candidates for each pixel in $I_{t}$ , as shown in Fig. 3. Each depth corresponds to one pixel on the epipolar line in each former frame. After that, we check whether the projected pixel's semantic label is exactly the same as $p_{t}$ . Only the candidate depths leading to a positive answer get retained, otherwise pruned. + +Consequently, each former frame provides a set of reliable depth candidates. These sets of candidate overlap yet may differ due to occlusion and field views. We use the union of all the sets as the aggregated depth candidate set because each pair of matched pixels may imply the existence of a 3D point. + +Since we judge the reliability based on semantics, a question might be whether our framework relies heavily on each pixel's precise prediction. The answer is no because we only require semantics in different frames to be consistent instead of strictly being the ground truth. Moreover, the existing semantic segmentation architectures [11, 47] can provide impressive enough label estimations. + +# 3.2.2 Semantic-based Depth Reallocation + +After pruning unreliable candidates, pixels may own inconsistent numbers of depth nominators because different objects might occupy distinct amounts of space, as shown in the left of Fig. 4. Since the initial depth candidates are uniformly sampled, a pixel owning many reliable depth nominators likely belongs to a large object (e.g., walls and floors). These objects usually do not require dense samples + +![](images/e318bc45c45cf2b94614dfc2b47a9ef086022c87350f8d2d58ecf9e0bb071514.jpg) +Figure 4. Reassignment among pixels. Pixels may have a different number of candidate depths after semantic pruning. However, the difference disappears after reallocation. + +![](images/1a8b5fd82947b74abd21888d7c93fcb36072fa01a6cf677c48b0d47593fa48b5.jpg) +Figure 5. Illustration of candidate reallocation. Top: pixel with too many candidates. We reduce the nominator number by down-sampling. Bottom: pixel with too few candidates. + +because they have smooth surfaces, and their depths can be easily inferred from neighbors. In contrast, coarser sampling may help the network overcome repetitive patterns and non-textured regions by collecting information from a larger field of view. + +However, delicate objects (e.g., toothbrushes and nail clippers) eagerly demand higher depth resolution for detail recovery. Thus, we should put more effort into pixels holding fewer candidates. + +Reallocate Candidates: We propose to set a unified depth number $N_{u}$ for all pixels by transfer payment, as shown in Fig. 4. Specifically, if a pixel occupies too many candidates, we lower its sampling density; otherwise, we promote. + +As shown in Fig. 5, we uniformly position $N_{u}$ candidates within the depth range bounded by the $N_{v}^{i}$ valid nominators for each pixel $p_{i}$ . Segmented depth ranges may occur when multiple objects of the same semantic label appear in the same image, as shown in Fig. 3. In such cases, candidates in different fragments are reallocated separately, and the quota of new candidates in each fragment is proportional to the number of valid candidates inside the fragment. + +To avoid fractional new candidate numbers, we prioritize the narrowest fragments and offer them slightly more + +candidates by the ceiling function. After that, we assign the remaining quotas for the rest fragments. This way, attention transfers from large surfaces to small objects because fragments containing fewer valid candidates get promoted. + +A more significant unified depth number $N_{u}$ offers higher effectiveness while lowering the model efficiency. In default, the value of $N_{u}$ is set to ensure the whole model runs as fast as the state-of-the-art real-time methods. + +Efficiency: Our reallocation strategy benefits effectiveness by attending more to delicate structures and contributes to efficiency. + +We take Fig. 4 as an example. Although these three pixels have the same number of initial depth hypotheses, they get different valid candidate numbers after the semantic pruning. Notably, most GPUs are designed to process regular inputs and are inefficient on irregular data. + +Thus, without reassignment, we have to pad pixels 2 and 3 with zeros to form a three (pixel number) by three (the max valid candidate number among pixels: $\max_i\{N_v^i\}$ ) matrix as the input of the depth head. In comparison, a three-by-two matrix is enough after reallocation. The reduction of input matrix size directly lowers the computation demand of the costly depth head. + +Although sparsification may sound like a good solution, + +![](images/e75e74c01d671a77c39570d3b67c78044fb28fbdae5f5e5cae1578aea81ddd29.jpg) +Figure 6. Architecture of the depth head. The outputs of the semantic-based depth selection module are used to warp the previous video frames to the current view for cost volume calculation. The depth predictions are regressed based on the current cost volume and former estimations. + +it heavily relies on specialized hardware and is usually less efficient on inputs of irregular zero distributions. In addition, it leads to lower sampling density on small objects. + +Spatial Correlation: Since our samples are pixel-wisely determined, a possible doubt might be whether the spatial correlation still holds. The answer is yes because neighboring pixels generally share the same semantic label. As a result, they should match adjacent pixels in other views, thus leading to similar depth candidates after the semantic pruning. + +Moreover, our candidate reassignment module evenly distributes candidates in the valid depth range; thus, neighboring pixels should have similar final depth samples. The local spatial correlation still holds as illustrated in Fig. 7. In other words, we can exploit convolutions to evaluate the candidate depths. + +![](images/c13e3a6914abbd89f112748d5715b8bcbedc06a0a8a9d76582cbf8b288101e26.jpg) +Figure 7. Spatial correlation after depth selection. Neighboring pixels generally have similar sets of depth candidates. + +# 3.3. Depth Head + +After determining the depth candidates for each pixel, we predict the depth map by assessing each depth candidate. The model starts by extracting image features from the current frame $I_{t}$ using a feature pyramid network (FPN) [29]. After that, we warp the image features from previous time stamps to the current view and then construct a cost volume by measuring the pixel-wise correlation between the current and former features. + +Finally, we send the raw cost volume into a U-shape refining network to regress the depth prediction at time $t$ . Notably, we keep the temporal consistency by introducing a ConvLSTM [54] to update the extracted features and by warping the previous depth estimations to the current viewpoint. + +# 4. Experiments + +Our model is implemented using PyTorch [45]. We optimize the model using MADGRAD [6] on eight A100 GPUs. The input image is cropped and scaled to $256 \times 256$ . The weights for testing are selected according to their losses on the validation set. The depth metrics are borrowed from DeepVideoMVS [9]. + +Keyframe Selection: Considering the high similarity between adjacent frames, estimating depth maps for every raw frame is inefficient. Thus, we select the most iconic frames (i.e., keyframes) from the input video sequences. When a new frame comes, we examine its pose distance to the latest keyframe and only adopt the new frames leading to pose + +
ScanNet
Abs Diff↓Abs Rel↓Sq Rel↓δ < 1.05↑δ < 1.25↑Time (ms) ↓
DPSNet [19]0.15480.07890.029249.3993.31308 ms
MVDepthNet [61]0.16430.08440.034146.7392.8046 ms
DELTAS [55]0.14920.07830.027148.6893.8183 ms
GPMVS [16]0.14920.07530.029051.0993.9849 ms
DeepVideoMVS (Fusion) [9]0.11820.05800.018760.2396.7830 ms
Ours0.10690.05060.016561.3497.1330 ms
+ +distances above a threshold. We define the pose distance as Eq. (1) and set the threshold as 0.35, following [9, 17]. Notably, we do not estimate depth for the first frame in a video sequence because it has no predecessors to provide multi-view information. + +$$ +D i s _ {p} = \sqrt {\left| t r a n s i t i o n \right| ^ {2} + \frac {2}{3} T r a c e (I - r o t a t i o n)} \quad (1) +$$ + +Datasets: Following the mainstream settings [9, 57], we train and evaluate our model on ScanNet [5], which is a large-scale real-world video dataset containing 1201 scenes for training, 321 for validation, and 100 for testing. + +Comparison to existing SOTAs Tab. 1 demonstrates that our method outperforms various state-of-the-art depth estimation approaches in effectiveness and efficiency. + +Compared to real-time SOTAs [9], our method shows significant advantages in all effectiveness metrics while retaining comparable time efficiency. Compared to semi-realtime algorithms [16, 55, 61], our method dominates inference time and offers significant competitiveness in reconstruction quality. In addition, our real-time framework even generates more accurate depth maps than some offline solutions [19] while spending one magnitude less cost. + +Moreover, our method benefits relative error more than absolute error and favors $L^1$ difference more than $L^2$ . These results indicate that delicate structures and small objects win more attention. + +Impacts of the Semantic Head To assess the effectiveness of our proposed semantic-based depth selection strategy, we fix all other variables and only examine the semantic head's impacts. Tab. 2 confirms that our semantic-based depth selection module offers significant benefits. + +# 5. Limitations + +Like most dense reconstruction models, our pipeline requires the camera parameters to be known, which may not + +Table 1. Depth evaluation results on the ScanNet dataset. The best results are marked in bold. Our model is leading in both effectiveness and efficiency. + +
Abs Diff↓Abs Rel↓Sq Rel↓
No Semantic Head0.12250.06330.0192
+ Semantic Head0.10690.05240.0161
+ +Table 2. Improvements from our semantic head. + +always be feasible. Besides, our current model may have difficulty with unseen object categories, although we only require adjacent frames to have the same class prediction (even if it is incorrect). + +# 6. Conclusion + +This paper proposes a novel 3D reconstruction network that is leading in effectiveness and efficiency. Our core contribution is to locate the most promising depth candidates using semantic maps. Specifically, we prune unreliable candidates according to the cross-view semantic consistency and then resample the candidates to look after pixels in need. Consequently, our method produces highly delicate reconstructions of meticulous structures and generates smooth surfaces for large planes with low overhead. Experimental results on the most popular datasets verify the proposed method's advantages in real scenarios. + +# Acknowledgments + +This work is partially supported by the National Science Foundation of China (NSFC) under Grant No. U22B2060, the Hong Kong RGC GRF Project 16209519, CRF Project C6030-18G, C2004-21GF, AOE Project AoE/E-603/18, RIF Project R6020-19, Theme-based project TRS T41-603/20R, China NSFC No. 61729201, Guangdong Basic and Applied Basic Research Foundation 2019B151530001, Hong Kong ITC ITF grants MHX/078/21 and PRP/004/22FX, Microsoft Research Asia Collaborative Research Grant, HKUST-Webank joint research lab grant and HKUST Global Strategic Partnership Fund (2021 SJTU-HKUST). In addition, we gratefully acknowledge the generous support from MindSpore. + +# References + +[1] Neill DF Campbell, George Vogiatzis, Carlos Hernández, and Roberto Cipolla. Using multiple hypotheses to improve depth-maps for multi-view stereo. 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Visual prompt multi-modal tracking. arXiv preprint arXiv:2303.10826, 2023. 3 \ No newline at end of file diff --git a/2023/Dionysus_ Recovering Scene Structures by Dividing Into Semantic Pieces/images.zip b/2023/Dionysus_ Recovering Scene Structures by Dividing Into Semantic Pieces/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..3be5d1939cca415334f128b2ade134bf5674f3c7 --- /dev/null +++ b/2023/Dionysus_ Recovering Scene Structures by Dividing Into Semantic Pieces/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:da0d80803e45dd6560fbb30538ed60bc4a3cb4b882ee2042e8a4af0f000105f3 +size 354657 diff --git a/2023/Dionysus_ Recovering Scene Structures by Dividing Into Semantic Pieces/layout.json b/2023/Dionysus_ Recovering Scene Structures by Dividing Into Semantic Pieces/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..2ee99326fbe060e53773325ac250a12230256a05 --- /dev/null +++ b/2023/Dionysus_ Recovering Scene Structures by Dividing Into Semantic Pieces/layout.json @@ -0,0 +1,8246 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 166, + 103, + 428, + 138 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 166, + 103, + 428, + 138 + ], + "spans": [ + { + "bbox": [ + 166, + 103, + 428, + 138 + ], + "type": "text", + "content": "Dionysus: Recovering Scene Structures by Dividing into Semantic Pieces" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 130, + 160, + 462, + 232 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 130, + 160, + 462, + 232 + ], + "spans": [ + { + "bbox": [ + 130, + 160, + 462, + 232 + ], + "type": "text", + "content": "Likang Wang1, Lei Chen1,2 \n1Department of Computer Science and Engineering \nThe Hong Kong University of Science and Technology \n2Data Science and Analytics Thrust \nThe Hong Kong University of Science and Technology (Guangzhou)" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 179, + 234, + 411, + 245 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 179, + 234, + 411, + 245 + ], + "spans": [ + { + "bbox": [ + 179, + 234, + 411, + 245 + ], + "type": "text", + "content": "lwangcg@connect.ust.hk, leichen@cse.ust.hk" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 273, + 192, + 285 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 273, + 192, + 285 + ], + "spans": [ + { + "bbox": [ + 143, + 273, + 192, + 285 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 298, + 289, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 298, + 289, + 501 + ], + "spans": [ + { + "bbox": [ + 46, + 298, + 289, + 501 + ], + "type": "text", + "content": "Most existing 3D reconstruction methods result in either detail loss or unsatisfying efficiency. However, effectiveness and efficiency are equally crucial in real-world applications, e.g., autonomous driving and augmented reality. We argue that this dilemma comes from wasted resources on valueless depth samples. This paper tackles the problem by proposing a novel learning-based 3D reconstruction framework named Dionysus. Our main contribution is to find out the most promising depth candidates from estimated semantic maps. This strategy simultaneously enables high effectiveness and efficiency by attending to the most reliable nominators. Specifically, we distinguish unreliable depth candidates by checking the cross-view semantic consistency and allow adaptive sampling by redistributing depth nominators among pixels. Experiments on the most popular datasets confirm our proposed framework's effectiveness." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 525, + 128, + 538 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 525, + 128, + 538 + ], + "spans": [ + { + "bbox": [ + 47, + 525, + 128, + 538 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 545, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 289, + 715 + ], + "type": "text", + "content": "Recovering 3D structures from 2D images is one of the most fundamental computer vision tasks [7, 25, 26, 68] and has wide applications in various scenarios (e.g., autonomous driving, metaverse, and augmented reality). Thanks to the popularity of smartphones, high-quality RGB videos are always obtainable. Since each image describes only a tiny piece of the whole scenario [31, 33], reconstruction from multiple frames [44, 50] is more attractive than from a single image [13, 14]. Although model quality and real-time response are equally essential, the existing 3D reconstruction methods have difficulty performing well in both aspects. For example, multi-view stereo (MVS) models [63, 73] consume seconds on each image, while real-time approaches [9, 57, 64] lead to missing details or large-area" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 276, + 331, + 285 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 276, + 331, + 285 + ], + "spans": [ + { + "bbox": [ + 306, + 276, + 331, + 285 + ], + "type": "text", + "content": "mess." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 289, + 547, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 289, + 547, + 384 + ], + "spans": [ + { + "bbox": [ + 304, + 289, + 547, + 384 + ], + "type": "text", + "content": "The mainstream reconstruction methods [15,63,72] generally sample a set of candidate depths or voxels, then use neural networks (e.g., CNNs [21] and transformers [58]) to evaluate each candidate's reliability. The candidate number is generally small because of the evaluation networks' high computational demand. Consequently, the reconstruction quality becomes unsatisfying because the ground truth is less likely to be sampled." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 388, + 548, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 388, + 548, + 687 + ], + "spans": [ + { + "bbox": [ + 304, + 388, + 548, + 687 + ], + "type": "text", + "content": "Pursuing a higher candidate sampling density, CasMVSNet [15] shrinks the depth range in a coarse-to-fine fashion; IS-MVSNet [63] searches for new candidates according to the estimated error distribution; NeuralRecon [57] prunes the voxels thought to be unreliable in the previous predictions. All these methods select candidates according to the initial depth estimations. Notably, small objects and delicate structures are hard to recover in the beginning low-resolution phase because they require a high resolution to distinguish. As a result, the final reconstruction often suffers from missing objects and crude details because the actual depth can be outside the final search range when the initial estimation is unreliable. However, decent reconstruction quality on delicate objects is crucial to many real-world applications. Specifically, traffic accidents may occur if any pedestrian or warning post fails to recover; frequent collisions and even fire disasters might happen if cleaning robots cannot well reconstruct table legs and electric cables. Besides the defects in meticulous structures, coarse-to-fine models also have room to improve efficiency. As mentioned, the mainstream coarse-to-fine methods sample and then evaluate initial candidates multiple times to locate the most valuable candidate depths. Notably, examining the preliminary candidates may be more expensive (usually two times more [15, 78]) than assessing the final nominators." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "type": "text", + "content": "In addition to the costly evaluation networks widely adopted in coarse-to-fine architectures, another natural so-" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "12576" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 77, + 68, + 523, + 311 + ], + "blocks": [ + { + "bbox": [ + 77, + 68, + 523, + 311 + ], + "lines": [ + { + "bbox": [ + 77, + 68, + 523, + 311 + ], + "spans": [ + { + "bbox": [ + 77, + 68, + 523, + 311 + ], + "type": "image", + "image_path": "f83eb7bf3f711219e9ae9f3546d88c1620ddfcf7f842c1733bb521b59d522fe2.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 319, + 547, + 353 + ], + "lines": [ + { + "bbox": [ + 46, + 319, + 547, + 353 + ], + "spans": [ + { + "bbox": [ + 46, + 319, + 547, + 353 + ], + "type": "text", + "content": "Figure 1. The overall architecture of our framework. We first estimate a semantic map for the current frame and then retrieve the former semantic estimations. After that, we locate the most valuable depth candidates through the semantic maps. Finally, we predict the depth map for the current frame by examining each depth candidate." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 373, + 287, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 373, + 287, + 528 + ], + "spans": [ + { + "bbox": [ + 46, + 373, + 287, + 528 + ], + "type": "text", + "content": "lution is to measure each depth candidate's reliability according to the photometric consistency among RGB images or feature maps from different views. The basic logic behind these methods is that pixels from distinct perspectives should own the same color if they are the correct projections from the same 3D point. However, a 3D point may look distinct in different views due to illumination, transparency, and reflection. Moreover, candidates close to but not precisely coinciding with the ground truth may have different colors for delicate objects, thus leading to low photometric consistency. Consequently, the found candidate may correspond to a pixel distant from the ground truth but of a similar color." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 529, + 288, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 529, + 288, + 684 + ], + "spans": [ + { + "bbox": [ + 46, + 529, + 288, + 684 + ], + "type": "text", + "content": "To get rid of detail defects and keep efficiency, it becomes crucial to accurately and efficiently find the most promising candidate depths. This paper proposes a novel high-quality real-time 3D reconstruction framework named Dionysus, which looks for depth hypotheses based on semantic estimations. Precisely, we distinguish each depth candidate's reliability according to its semantic consistency among warped views. Fig. 1 illustrates the overall architecture of our framework. Our intuition is that two pixels should share the same semantic label if they are projections of the same 3D point. We argue that selecting depth candidates according to the semantic tags results in various benefits:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 689, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 689, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 689, + 288, + 714 + ], + "type": "text", + "content": "1. Consistent: A 3D point may have distinct colors when observing from different perspectives, but its semantic" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 325, + 374, + 410, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 374, + 410, + 386 + ], + "spans": [ + { + "bbox": [ + 325, + 374, + 410, + 386 + ], + "type": "text", + "content": "label never changes." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 394, + 547, + 615 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 313, + 394, + 545, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 394, + 545, + 491 + ], + "spans": [ + { + "bbox": [ + 313, + 394, + 545, + 491 + ], + "type": "text", + "content": "2. Efficient: Semantic estimation requires a meager cost. A semantic segmentation model may spend only milliseconds on each frame [11,47] while evaluating each cost volume in coarse layers generally takes ten times more cost. In addition, most hierarchical methods shrink the depth range only by half in each stage, while our method may significantly reduce the depth range on delicate objects (e.g., desk legs)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 498, + 547, + 546 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 498, + 547, + 546 + ], + "spans": [ + { + "bbox": [ + 313, + 498, + 547, + 546 + ], + "type": "text", + "content": "3. Dense: Tiny objects always get missing in hierarchical frameworks because the initial samples are too sparse. However, the semantic maps are highly dense, thus retaining fine details." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 554, + 547, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 554, + 547, + 615 + ], + "spans": [ + { + "bbox": [ + 313, + 554, + 547, + 615 + ], + "type": "text", + "content": "4. Adaptive: Semantics indicate various properties of the pixel. For example, an electric cable may demand highly dense samples to recover, but a wall may not. In other words, we can assign each pixel the most suitable sampling density according to its semantic estimation." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 304, + 629, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 715 + ], + "type": "text", + "content": "Depth Reassignment: A bed pixel may have much more valid depth candidates than a pen pixel after the semantic-based pruning because there are likely many bed pixels in other views. Consequently, we cannot form a regular cost volume based on the pruned depth candidates because pixels may have different numbers of valid depth candidates. However, most GPUs are not designed for irregular inputs" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12577" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 178 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 178 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 178 + ], + "type": "text", + "content": "and are inefficient in such cases. Thus, we further propose reallocating depth samples from pixels with excess valid candidates to those in the opposite. In this way, all pixels finally have the same number of candidates and thus can be conveniently computed by GPUs. Moreover, we sample more densely for delicate structures, otherwise more sparsely, because tiny objects have a narrower depth range after semantic pruning, and all pixels have the same depth number." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 180, + 287, + 202 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 180, + 287, + 202 + ], + "spans": [ + { + "bbox": [ + 47, + 180, + 287, + 202 + ], + "type": "text", + "content": "To summarize, this paper has two significant contributions:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 54, + 211, + 287, + 291 + ], + "type": "list", + "angle": 0, + "index": 4, + "blocks": [ + { + "bbox": [ + 55, + 211, + 287, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 211, + 287, + 258 + ], + "spans": [ + { + "bbox": [ + 55, + 211, + 287, + 258 + ], + "type": "text", + "content": "1. Instead of densely evaluating all depths or sparsely evaluating limited depths, we efficiently select the most promising depth candidates based on the cross-view semantic consistency." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 267, + 287, + 291 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 267, + 287, + 291 + ], + "spans": [ + { + "bbox": [ + 54, + 267, + 287, + 291 + ], + "type": "text", + "content": "2. We reallocate depth samples among pixels to make our model adaptive to objects and efficient on GPUs." + } + ] + } + ], + "index": 3 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 298, + 287, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 298, + 287, + 346 + ], + "spans": [ + { + "bbox": [ + 47, + 298, + 287, + 346 + ], + "type": "text", + "content": "The mentioned contributions significantly benefit the effectiveness while retaining efficiency. Our extensive experiments on the most popular 3D reconstruction datasets [5] further verify our proposed method's validity." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 357, + 134, + 369 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 357, + 134, + 369 + ], + "spans": [ + { + "bbox": [ + 47, + 357, + 134, + 369 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 376, + 287, + 424 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 376, + 287, + 424 + ], + "spans": [ + { + "bbox": [ + 47, + 376, + 287, + 424 + ], + "type": "text", + "content": "We first introduce the development of 3D reconstruction, then present the progress in semantic segmentation, and finally discuss the existing semantic-based 3D reconstruction networks." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 432, + 157, + 444 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 432, + 157, + 444 + ], + "spans": [ + { + "bbox": [ + 47, + 432, + 157, + 444 + ], + "type": "text", + "content": "2.1.3D Reconstruction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 450, + 287, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 450, + 287, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 450, + 287, + 605 + ], + "type": "text", + "content": "Recovering 3D structures from images has been widely studied for many decades. Despite the great success of traditional methods [1, 12, 52, 53], most recent solutions [9, 15, 73] are based on neural networks [21, 35-38, 62] because of the latter's popularity [27, 32, 71, 75, 76] in the last decades. Thanks to the popularity of smartphones, continuous video sequences can now be easily captured. Compared to independent images, video sequences [28, 80] contain rich correlations among frames, thus leading to more consistent reconstruction quality. In consequence, learning-based video reconstruction [44, 56, 69] is becoming a hot spot. However, due to their high computation demand, most video reconstruction methods are limited in offline applications." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 606, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 606, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 606, + 287, + 714 + ], + "type": "text", + "content": "Real-time video reconstruction is attracting wide attention from the academy and the industry, considering its vital position in autonomous driving and augmented reality. The mainstream real-time methods can be categorized into depth-based [9, 16, 40, 61] and volume-based [57]. Specifically, the former estimates depth maps and fuses them into 3D representations. In contrast, the latter directly regresses 3D representations from the RGB inputs. Depth-based methods generally lead to lower latency because they" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "content": "immediately process each new frame without waiting. Conversely, volumetric methods estimate 3D representations from a group of frames, thus cannot respond to new frames at once and are less suitable for online scenarios. The mainstream depth-based approaches usually uniformly sample depth candidates from an overly broad range [9] or gradually shrink the search range by repeated predictions [15,72]. Our main difference from the existing depth-based methods is that we utilize semantics to select depth candidates." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 188, + 440, + 201 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 188, + 440, + 201 + ], + "spans": [ + { + "bbox": [ + 306, + 188, + 440, + 201 + ], + "type": "text", + "content": "2.2. Semantic Segmentation" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 207, + 545, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 207, + 545, + 327 + ], + "spans": [ + { + "bbox": [ + 304, + 207, + 545, + 327 + ], + "type": "text", + "content": "Semantic segmentation focuses on estimating each pixel's object category (e.g., whether it represents a dog). Most semantic segmentation networks [2, 51, 67, 74, 77] inherited a learning-based framework from FCN [39]. Real-time solutions generally put their most effort into designing a lightweight backbone considering its contribution to the whole model's complexity. The existing online methods generally own three backbone types [43]: classification-based [22, 24, 60], segmentation-based [23, 34, 41], and two-branch-based [48, 74, 79]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 327, + 545, + 447 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 327, + 545, + 447 + ], + "spans": [ + { + "bbox": [ + 304, + 327, + 545, + 447 + ], + "type": "text", + "content": "The first class encodes features using image classification networks and then decodes to output semantics. The second class designs segmentation-specific backbones considering the task difference between segmentation and classification. The third class processes macro and micro information separately to reduce the overall cost. State-of-the-art segmentation models can infer hundreds of frames per second and retain high quality simultaneously. In comparison, the fastest depth estimation networks are bounded to dozens of frames per second." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 455, + 493, + 467 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 455, + 493, + 467 + ], + "spans": [ + { + "bbox": [ + 306, + 455, + 493, + 467 + ], + "type": "text", + "content": "2.3. Semantic-based 3D Reconstruction" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 474, + 545, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 545, + 510 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 545, + 510 + ], + "type": "text", + "content": "Quite a few papers focus on integrating semantics into depth estimation networks. Most related works belong to single-image depth estimation and stereo matching." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 510, + 545, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 545, + 629 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 545, + 629 + ], + "type": "text", + "content": "In single-image depth estimation, view correspondence does not exist; thus, semantic information becomes more vital. [66] simultaneously estimates depth and semantic maps by multi-task learning. [65] shares depth weights among pixels of the same semantic label. [10] jointly estimates depth, semantics, and surface normal. [20] introduces a synergy network to share features between the semantic and depth branches. [30] restricts depth predictions by semantic priors (e.g., the sky is distant, and the ground is horizontal). [59] infers invisible regions from semantics." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "In stereo matching, two views with fixed relative poses are given, and the goal is to match pixels in the two views. These papers can be generally divided into two categories. The first class treats semantic maps as additional channels. [8] refines disparities by concatenating semantic and disparity features along the channel dimension. [70] constructs cost volumes for semantics and disparity and then" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "12578" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 72, + 549, + 262 + ], + "blocks": [ + { + "bbox": [ + 53, + 72, + 549, + 262 + ], + "lines": [ + { + "bbox": [ + 53, + 72, + 549, + 262 + ], + "spans": [ + { + "bbox": [ + 53, + 72, + 549, + 262 + ], + "type": "image", + "image_path": "ed3a1474d5c41f458e9b48ce5a0baf21b358a2f7901a7a69a230656918cde5ff.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 276, + 547, + 310 + ], + "lines": [ + { + "bbox": [ + 46, + 276, + 547, + 310 + ], + "spans": [ + { + "bbox": [ + 46, + 276, + 547, + 310 + ], + "type": "text", + "content": "Figure 2. Architecture of the semantic head. Former semantic and depth estimations are warped and then integrated with the current frame. After that, we extract hierarchical information from the concatenated feature map. The semantic map for the current frame is inferred from the feature volume composed of spatial and context information." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 331, + 287, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 331, + 287, + 450 + ], + "spans": [ + { + "bbox": [ + 46, + 331, + 287, + 450 + ], + "type": "text", + "content": "fuses them by summing and global pooling. [3] constructs cost volume using semantic consistency between left and right images and estimates disparity residuals according to semantic category. The second class revises the disparity using priors in semantics. [49] filters depth maps based on semantic priors. For example, ground and water pixels with heights higher than " + }, + { + "bbox": [ + 46, + 331, + 287, + 450 + ], + "type": "inline_equation", + "content": "90\\%" + }, + { + "bbox": [ + 46, + 331, + 287, + 450 + ], + "type": "text", + "content": " get pruned. [46] refines edge and texture-less regions using semantic cues. [4] estimates disparity confidence using semantic consistency and refines disparity in each semantic region." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 450, + 287, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 450, + 287, + 498 + ], + "spans": [ + { + "bbox": [ + 47, + 450, + 287, + 498 + ], + "type": "text", + "content": "The related works in multi-view stereo are limited. [18] recovers a segmented 3D representation from 2D images and semantics. [42] augments depth edges and guides cost aggregation using semantics." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 498, + 287, + 547 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 498, + 287, + 547 + ], + "spans": [ + { + "bbox": [ + 47, + 498, + 287, + 547 + ], + "type": "text", + "content": "Unlike the mentioned works, we select depth candidates by explicitly exploiting semantic consistency for multi-view inputs. We also balance depth candidates among pixels and adaptively attend to pixels in need." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 558, + 129, + 572 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 558, + 129, + 572 + ], + "spans": [ + { + "bbox": [ + 47, + 558, + 129, + 572 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 578, + 287, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 578, + 287, + 651 + ], + "spans": [ + { + "bbox": [ + 47, + 578, + 287, + 651 + ], + "type": "text", + "content": "We first introduce the overall architecture of our model in Sec. 3.1, then elaborate on each sub-component in Sec. 3.2 and 3.3. Our model inputs an RGB video sequence divided into frames and the camera parameters of each frame, which are estimated by off-the-shelf tools (e.g., ARKit). The output is expected to be the depth map of each frame." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 658, + 167, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 167, + 671 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 167, + 671 + ], + "type": "text", + "content": "3.1. Overall Architecture" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": "Fig. 1 exhibits the overall framework. We have a semantic head to predict a semantic map " + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "S_{t}" + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": " for the current frame " + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "I_{t}" + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": ". At the same time, we retrieve the semantic maps" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 329, + 544, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 329, + 544, + 354 + ], + "spans": [ + { + "bbox": [ + 306, + 329, + 544, + 354 + ], + "type": "inline_equation", + "content": "\\{S_i\\}_{i = t - n}^{t - 1}" + }, + { + "bbox": [ + 306, + 329, + 544, + 354 + ], + "type": "text", + "content": " predicted in the previous timestamps from a semantic queue." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 355, + 545, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 355, + 545, + 426 + ], + "spans": [ + { + "bbox": [ + 305, + 355, + 545, + 426 + ], + "type": "text", + "content": "After that, we look for the most promising depth candidates for each pixel in " + }, + { + "bbox": [ + 305, + 355, + 545, + 426 + ], + "type": "inline_equation", + "content": "I_{t}" + }, + { + "bbox": [ + 305, + 355, + 545, + 426 + ], + "type": "text", + "content": " using our novel semantic-based depth candidate selection module, which is our main contribution. Finally, we examine each depth nominator using a depth head to output the final depth estimation. We sum losses from the depth and semantic heads as the overall loss." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 434, + 529, + 447 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 434, + 529, + 447 + ], + "spans": [ + { + "bbox": [ + 306, + 434, + 529, + 447 + ], + "type": "text", + "content": "3.2. Semantic-based Depth Candidate Selection" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 453, + 545, + 511 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 453, + 545, + 511 + ], + "spans": [ + { + "bbox": [ + 305, + 453, + 545, + 511 + ], + "type": "text", + "content": "This section introduces our main contributions. Sec. 3.2.1 first shows how to prune unreliable depth candidates using the semantic information, and then Sec. 3.2.2 demonstrates how to concentrate on pixels in need and become efficient on GPUs." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 527, + 473, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 527, + 473, + 540 + ], + "spans": [ + { + "bbox": [ + 306, + 527, + 473, + 540 + ], + "type": "text", + "content": "3.2.1 Semantic-based Depth Pruning" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 546, + 545, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 546, + 545, + 594 + ], + "spans": [ + { + "bbox": [ + 305, + 546, + 545, + 594 + ], + "type": "text", + "content": "To estimate the depth of a pixel in the current frame " + }, + { + "bbox": [ + 305, + 546, + 545, + 594 + ], + "type": "inline_equation", + "content": "I_{t}" + }, + { + "bbox": [ + 305, + 546, + 545, + 594 + ], + "type": "text", + "content": ", we sample a set of depth candidates and evaluate their reliability one by one. The candidate number must be high enough to hit the ground truth." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 594, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 689 + ], + "type": "text", + "content": "However, the existing learning-based methods can only examine a small number of samples because they use a giant neural network to assess each candidate. Consequently, small objects distant from the background and delicate structures get defective. The small object problem cannot be solved via coarse-to-fine architectures because significantly wrong predictions in the coarse stages cannot be recovered in finer stages." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "Unlike the existing methods, we first predict the semantic labels for each pixel at a low cost; then, we use the se" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12579" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 104, + 68, + 487, + 245 + ], + "blocks": [ + { + "bbox": [ + 104, + 68, + 487, + 245 + ], + "lines": [ + { + "bbox": [ + 104, + 68, + 487, + 245 + ], + "spans": [ + { + "bbox": [ + 104, + 68, + 487, + 245 + ], + "type": "image", + "image_path": "9eb71af5d386b186ba95cff4ba18a524693585549d7f8c3d7130ff81f405e586.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 256, + 547, + 281 + ], + "lines": [ + { + "bbox": [ + 46, + 256, + 547, + 281 + ], + "spans": [ + { + "bbox": [ + 46, + 256, + 547, + 281 + ], + "type": "text", + "content": "Figure 3. Illustration of depth pruning. We uniformly sample depth candidates for a given pixel (purple) in the current frame, then evaluate each candidate to determine whether it leads to a pixel of the same semantic label projected on the former frames." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 300, + 288, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 300, + 288, + 324 + ], + "spans": [ + { + "bbox": [ + 46, + 300, + 288, + 324 + ], + "type": "text", + "content": "mantic maps to restrict the depth candidate sampling only to the most reliable regions." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 338, + 287, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 338, + 287, + 409 + ], + "spans": [ + { + "bbox": [ + 46, + 338, + 287, + 409 + ], + "type": "text", + "content": "I/O: The inputs include the current frame " + }, + { + "bbox": [ + 46, + 338, + 287, + 409 + ], + "type": "inline_equation", + "content": "I_{t}" + }, + { + "bbox": [ + 46, + 338, + 287, + 409 + ], + "type": "text", + "content": " and retrieved previous semantic " + }, + { + "bbox": [ + 46, + 338, + 287, + 409 + ], + "type": "inline_equation", + "content": "\\{S_{i}\\}_{i = t - n}^{t - 1}" + }, + { + "bbox": [ + 46, + 338, + 287, + 409 + ], + "type": "text", + "content": " and depth " + }, + { + "bbox": [ + 46, + 338, + 287, + 409 + ], + "type": "inline_equation", + "content": "\\{D_{i}\\}_{i = t - n}^{t - 1}" + }, + { + "bbox": [ + 46, + 338, + 287, + 409 + ], + "type": "text", + "content": " estimations. Besides, similar to most existing methods [9, 57, 73], we assume the camera parameters from time " + }, + { + "bbox": [ + 46, + 338, + 287, + 409 + ], + "type": "inline_equation", + "content": "t - n" + }, + { + "bbox": [ + 46, + 338, + 287, + 409 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 338, + 287, + 409 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 338, + 287, + 409 + ], + "type": "text", + "content": " are available. In fact, the camera parameters can be obtained from off-the-shelf tools (e.g., ARKit)." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 410, + 288, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 410, + 288, + 434 + ], + "spans": [ + { + "bbox": [ + 47, + 410, + 288, + 434 + ], + "type": "text", + "content": "The outputs are the most promising depth candidates for each pixel in the current frame " + }, + { + "bbox": [ + 47, + 410, + 288, + 434 + ], + "type": "inline_equation", + "content": "I_{t}" + }, + { + "bbox": [ + 47, + 410, + 288, + 434 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 448, + 287, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 448, + 287, + 508 + ], + "spans": [ + { + "bbox": [ + 46, + 448, + 287, + 508 + ], + "type": "text", + "content": "Semantic Head: Instead of outputting the correct label, semantic consistency among frames is more crucial because we examine depth candidates by cross-view conformity. Thus, we need to consider previous semantic estimations when processing new frames." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 508, + 287, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 508, + 287, + 579 + ], + "spans": [ + { + "bbox": [ + 46, + 508, + 287, + 579 + ], + "type": "text", + "content": "We propose a highly efficient 2D convolutional network to predict the semantic labels for each pixel in " + }, + { + "bbox": [ + 46, + 508, + 287, + 579 + ], + "type": "inline_equation", + "content": "I_{t}" + }, + { + "bbox": [ + 46, + 508, + 287, + 579 + ], + "type": "text", + "content": ", as shown in Fig. 2. The inputs of the semantic prediction head include the current frame " + }, + { + "bbox": [ + 46, + 508, + 287, + 579 + ], + "type": "inline_equation", + "content": "I_{t}" + }, + { + "bbox": [ + 46, + 508, + 287, + 579 + ], + "type": "text", + "content": ", the semantic and depth maps predicted from timestamp " + }, + { + "bbox": [ + 46, + 508, + 287, + 579 + ], + "type": "inline_equation", + "content": "t - n" + }, + { + "bbox": [ + 46, + 508, + 287, + 579 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 508, + 287, + 579 + ], + "type": "inline_equation", + "content": "t - 1" + }, + { + "bbox": [ + 46, + 508, + 287, + 579 + ], + "type": "text", + "content": ", and the corresponding camera parameters." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 579, + 288, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 579, + 288, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 579, + 288, + 664 + ], + "type": "text", + "content": "The former depth and semantic predictions are warped to the current view according to the relative poses and then fused by concatenating along the channel dimension. Inspired by STDC-Seg [11] and BiSeNet [74], we adopt a two-pathway architecture to efficiently extract spatial and context information, which are then fused to generate the final semantic estimation." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "type": "text", + "content": "Depth Pruning: After obtaining the semantic maps, we start to prune depth candidates. According to the camera parameters from time " + }, + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "type": "inline_equation", + "content": "t - n" + }, + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "type": "text", + "content": ", we can draw a straight line" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 299, + 545, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 299, + 545, + 346 + ], + "spans": [ + { + "bbox": [ + 304, + 299, + 545, + 346 + ], + "type": "text", + "content": "(i.e., the epipolar line) on each previous frame " + }, + { + "bbox": [ + 304, + 299, + 545, + 346 + ], + "type": "inline_equation", + "content": "\\in \\{I_i\\}_{i = t - n}^{t - 1}" + }, + { + "bbox": [ + 304, + 299, + 545, + 346 + ], + "type": "text", + "content": " for each pixel " + }, + { + "bbox": [ + 304, + 299, + 545, + 346 + ], + "type": "inline_equation", + "content": "p_t\\in" + }, + { + "bbox": [ + 304, + 299, + 545, + 346 + ], + "type": "text", + "content": " the current frame " + }, + { + "bbox": [ + 304, + 299, + 545, + 346 + ], + "type": "inline_equation", + "content": "I_{t}" + }, + { + "bbox": [ + 304, + 299, + 545, + 346 + ], + "type": "text", + "content": " and guarantee that the correct correspondences can only lie on the epipolar line." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 348, + 546, + 432 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 348, + 546, + 432 + ], + "spans": [ + { + "bbox": [ + 304, + 348, + 546, + 432 + ], + "type": "text", + "content": "Then, we sample " + }, + { + "bbox": [ + 304, + 348, + 546, + 432 + ], + "type": "inline_equation", + "content": "N_{s}" + }, + { + "bbox": [ + 304, + 348, + 546, + 432 + ], + "type": "text", + "content": " (a significant number) depth candidates for each pixel in " + }, + { + "bbox": [ + 304, + 348, + 546, + 432 + ], + "type": "inline_equation", + "content": "I_{t}" + }, + { + "bbox": [ + 304, + 348, + 546, + 432 + ], + "type": "text", + "content": ", as shown in Fig. 3. Each depth corresponds to one pixel on the epipolar line in each former frame. After that, we check whether the projected pixel's semantic label is exactly the same as " + }, + { + "bbox": [ + 304, + 348, + 546, + 432 + ], + "type": "inline_equation", + "content": "p_{t}" + }, + { + "bbox": [ + 304, + 348, + 546, + 432 + ], + "type": "text", + "content": ". Only the candidate depths leading to a positive answer get retained, otherwise pruned." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 434, + 547, + 505 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 434, + 547, + 505 + ], + "spans": [ + { + "bbox": [ + 304, + 434, + 547, + 505 + ], + "type": "text", + "content": "Consequently, each former frame provides a set of reliable depth candidates. These sets of candidate overlap yet may differ due to occlusion and field views. We use the union of all the sets as the aggregated depth candidate set because each pair of matched pixels may imply the existence of a 3D point." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 506, + 547, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 506, + 547, + 590 + ], + "spans": [ + { + "bbox": [ + 304, + 506, + 547, + 590 + ], + "type": "text", + "content": "Since we judge the reliability based on semantics, a question might be whether our framework relies heavily on each pixel's precise prediction. The answer is no because we only require semantics in different frames to be consistent instead of strictly being the ground truth. Moreover, the existing semantic segmentation architectures [11, 47] can provide impressive enough label estimations." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 609, + 491, + 621 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 609, + 491, + 621 + ], + "spans": [ + { + "bbox": [ + 306, + 609, + 491, + 621 + ], + "type": "text", + "content": "3.2.2 Semantic-based Depth Reallocation" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "type": "text", + "content": "After pruning unreliable candidates, pixels may own inconsistent numbers of depth nominators because different objects might occupy distinct amounts of space, as shown in the left of Fig. 4. Since the initial depth candidates are uniformly sampled, a pixel owning many reliable depth nominators likely belongs to a large object (e.g., walls and floors). These objects usually do not require dense samples" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "12580" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 126, + 68, + 470, + 157 + ], + "blocks": [ + { + "bbox": [ + 126, + 68, + 470, + 157 + ], + "lines": [ + { + "bbox": [ + 126, + 68, + 470, + 157 + ], + "spans": [ + { + "bbox": [ + 126, + 68, + 470, + 157 + ], + "type": "image", + "image_path": "e318bc45c45cf2b94614dfc2b47a9ef086022c87350f8d2d58ecf9e0bb071514.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 167, + 547, + 191 + ], + "lines": [ + { + "bbox": [ + 46, + 167, + 547, + 191 + ], + "spans": [ + { + "bbox": [ + 46, + 167, + 547, + 191 + ], + "type": "text", + "content": "Figure 4. Reassignment among pixels. Pixels may have a different number of candidate depths after semantic pruning. However, the difference disappears after reallocation." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 72, + 201, + 523, + 351 + ], + "blocks": [ + { + "bbox": [ + 72, + 201, + 523, + 351 + ], + "lines": [ + { + "bbox": [ + 72, + 201, + 523, + 351 + ], + "spans": [ + { + "bbox": [ + 72, + 201, + 523, + 351 + ], + "type": "image", + "image_path": "1a8b5fd82947b74abd21888d7c93fcb36072fa01a6cf677c48b0d47593fa48b5.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 361, + 546, + 384 + ], + "lines": [ + { + "bbox": [ + 46, + 361, + 546, + 384 + ], + "spans": [ + { + "bbox": [ + 46, + 361, + 546, + 384 + ], + "type": "text", + "content": "Figure 5. Illustration of candidate reallocation. Top: pixel with too many candidates. We reduce the nominator number by down-sampling. Bottom: pixel with too few candidates." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 404, + 287, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 404, + 287, + 464 + ], + "spans": [ + { + "bbox": [ + 46, + 404, + 287, + 464 + ], + "type": "text", + "content": "because they have smooth surfaces, and their depths can be easily inferred from neighbors. In contrast, coarser sampling may help the network overcome repetitive patterns and non-textured regions by collecting information from a larger field of view." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 464, + 287, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 464, + 287, + 513 + ], + "spans": [ + { + "bbox": [ + 46, + 464, + 287, + 513 + ], + "type": "text", + "content": "However, delicate objects (e.g., toothbrushes and nail clippers) eagerly demand higher depth resolution for detail recovery. Thus, we should put more effort into pixels holding fewer candidates." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 532, + 287, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 532, + 287, + 591 + ], + "spans": [ + { + "bbox": [ + 46, + 532, + 287, + 591 + ], + "type": "text", + "content": "Reallocate Candidates: We propose to set a unified depth number " + }, + { + "bbox": [ + 46, + 532, + 287, + 591 + ], + "type": "inline_equation", + "content": "N_{u}" + }, + { + "bbox": [ + 46, + 532, + 287, + 591 + ], + "type": "text", + "content": " for all pixels by transfer payment, as shown in Fig. 4. Specifically, if a pixel occupies too many candidates, we lower its sampling density; otherwise, we promote." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 593, + 287, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 593, + 287, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 593, + 287, + 688 + ], + "type": "text", + "content": "As shown in Fig. 5, we uniformly position " + }, + { + "bbox": [ + 46, + 593, + 287, + 688 + ], + "type": "inline_equation", + "content": "N_{u}" + }, + { + "bbox": [ + 46, + 593, + 287, + 688 + ], + "type": "text", + "content": " candidates within the depth range bounded by the " + }, + { + "bbox": [ + 46, + 593, + 287, + 688 + ], + "type": "inline_equation", + "content": "N_{v}^{i}" + }, + { + "bbox": [ + 46, + 593, + 287, + 688 + ], + "type": "text", + "content": " valid nominators for each pixel " + }, + { + "bbox": [ + 46, + 593, + 287, + 688 + ], + "type": "inline_equation", + "content": "p_{i}" + }, + { + "bbox": [ + 46, + 593, + 287, + 688 + ], + "type": "text", + "content": ". Segmented depth ranges may occur when multiple objects of the same semantic label appear in the same image, as shown in Fig. 3. In such cases, candidates in different fragments are reallocated separately, and the quota of new candidates in each fragment is proportional to the number of valid candidates inside the fragment." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "content": "To avoid fractional new candidate numbers, we prioritize the narrowest fragments and offer them slightly more" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 404, + 545, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 404, + 545, + 453 + ], + "spans": [ + { + "bbox": [ + 304, + 404, + 545, + 453 + ], + "type": "text", + "content": "candidates by the ceiling function. After that, we assign the remaining quotas for the rest fragments. This way, attention transfers from large surfaces to small objects because fragments containing fewer valid candidates get promoted." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 453, + 545, + 500 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 453, + 545, + 500 + ], + "spans": [ + { + "bbox": [ + 304, + 453, + 545, + 500 + ], + "type": "text", + "content": "A more significant unified depth number " + }, + { + "bbox": [ + 304, + 453, + 545, + 500 + ], + "type": "inline_equation", + "content": "N_{u}" + }, + { + "bbox": [ + 304, + 453, + 545, + 500 + ], + "type": "text", + "content": " offers higher effectiveness while lowering the model efficiency. In default, the value of " + }, + { + "bbox": [ + 304, + 453, + 545, + 500 + ], + "type": "inline_equation", + "content": "N_{u}" + }, + { + "bbox": [ + 304, + 453, + 545, + 500 + ], + "type": "text", + "content": " is set to ensure the whole model runs as fast as the state-of-the-art real-time methods." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 519, + 545, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 519, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 519, + 545, + 555 + ], + "type": "text", + "content": "Efficiency: Our reallocation strategy benefits effectiveness by attending more to delicate structures and contributes to efficiency." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 556, + 545, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 556, + 545, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 556, + 545, + 616 + ], + "type": "text", + "content": "We take Fig. 4 as an example. Although these three pixels have the same number of initial depth hypotheses, they get different valid candidate numbers after the semantic pruning. Notably, most GPUs are designed to process regular inputs and are inefficient on irregular data." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 616, + 545, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 616, + 545, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 616, + 545, + 700 + ], + "type": "text", + "content": "Thus, without reassignment, we have to pad pixels 2 and 3 with zeros to form a three (pixel number) by three (the max valid candidate number among pixels: " + }, + { + "bbox": [ + 304, + 616, + 545, + 700 + ], + "type": "inline_equation", + "content": "\\max_i\\{N_v^i\\}" + }, + { + "bbox": [ + 304, + 616, + 545, + 700 + ], + "type": "text", + "content": ") matrix as the input of the depth head. In comparison, a three-by-two matrix is enough after reallocation. The reduction of input matrix size directly lowers the computation demand of the costly depth head." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "text", + "content": "Although sparsification may sound like a good solution," + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12581" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 68, + 541, + 268 + ], + "blocks": [ + { + "bbox": [ + 52, + 68, + 541, + 268 + ], + "lines": [ + { + "bbox": [ + 52, + 68, + 541, + 268 + ], + "spans": [ + { + "bbox": [ + 52, + 68, + 541, + 268 + ], + "type": "image", + "image_path": "e75e74c01d671a77c39570d3b67c78044fb28fbdae5f5e5cae1578aea81ddd29.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 278, + 547, + 312 + ], + "lines": [ + { + "bbox": [ + 46, + 278, + 547, + 312 + ], + "spans": [ + { + "bbox": [ + 46, + 278, + 547, + 312 + ], + "type": "text", + "content": "Figure 6. Architecture of the depth head. The outputs of the semantic-based depth selection module are used to warp the previous video frames to the current view for cost volume calculation. The depth predictions are regressed based on the current cost volume and former estimations." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 333, + 288, + 370 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 333, + 288, + 370 + ], + "spans": [ + { + "bbox": [ + 46, + 333, + 288, + 370 + ], + "type": "text", + "content": "it heavily relies on specialized hardware and is usually less efficient on inputs of irregular zero distributions. In addition, it leads to lower sampling density on small objects." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 401, + 287, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 401, + 287, + 485 + ], + "spans": [ + { + "bbox": [ + 46, + 401, + 287, + 485 + ], + "type": "text", + "content": "Spatial Correlation: Since our samples are pixel-wisely determined, a possible doubt might be whether the spatial correlation still holds. The answer is yes because neighboring pixels generally share the same semantic label. As a result, they should match adjacent pixels in other views, thus leading to similar depth candidates after the semantic pruning." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 488, + 287, + 561 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 488, + 287, + 561 + ], + "spans": [ + { + "bbox": [ + 46, + 488, + 287, + 561 + ], + "type": "text", + "content": "Moreover, our candidate reassignment module evenly distributes candidates in the valid depth range; thus, neighboring pixels should have similar final depth samples. The local spatial correlation still holds as illustrated in Fig. 7. In other words, we can exploit convolutions to evaluate the candidate depths." + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 53, + 579, + 289, + 662 + ], + "blocks": [ + { + "bbox": [ + 53, + 579, + 289, + 662 + ], + "lines": [ + { + "bbox": [ + 53, + 579, + 289, + 662 + ], + "spans": [ + { + "bbox": [ + 53, + 579, + 289, + 662 + ], + "type": "image", + "image_path": "c13e3a6914abbd89f112748d5715b8bcbedc06a0a8a9d76582cbf8b288101e26.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 672, + 287, + 696 + ], + "lines": [ + { + "bbox": [ + 46, + 672, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 672, + 287, + 696 + ], + "type": "text", + "content": "Figure 7. Spatial correlation after depth selection. Neighboring pixels generally have similar sets of depth candidates." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 332, + 385, + 346 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 332, + 385, + 346 + ], + "spans": [ + { + "bbox": [ + 306, + 332, + 385, + 346 + ], + "type": "text", + "content": "3.3. Depth Head" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 351, + 545, + 446 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 351, + 545, + 446 + ], + "spans": [ + { + "bbox": [ + 304, + 351, + 545, + 446 + ], + "type": "text", + "content": "After determining the depth candidates for each pixel, we predict the depth map by assessing each depth candidate. The model starts by extracting image features from the current frame " + }, + { + "bbox": [ + 304, + 351, + 545, + 446 + ], + "type": "inline_equation", + "content": "I_{t}" + }, + { + "bbox": [ + 304, + 351, + 545, + 446 + ], + "type": "text", + "content": " using a feature pyramid network (FPN) [29]. After that, we warp the image features from previous time stamps to the current view and then construct a cost volume by measuring the pixel-wise correlation between the current and former features." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 447, + 545, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 447, + 545, + 520 + ], + "spans": [ + { + "bbox": [ + 304, + 447, + 545, + 520 + ], + "type": "text", + "content": "Finally, we send the raw cost volume into a U-shape refining network to regress the depth prediction at time " + }, + { + "bbox": [ + 304, + 447, + 545, + 520 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 447, + 545, + 520 + ], + "type": "text", + "content": ". Notably, we keep the temporal consistency by introducing a ConvLSTM [54] to update the extracted features and by warping the previous depth estimations to the current viewpoint." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 532, + 388, + 545 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 532, + 388, + 545 + ], + "spans": [ + { + "bbox": [ + 306, + 532, + 388, + 545 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 552, + 545, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 552, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 552, + 545, + 624 + ], + "type": "text", + "content": "Our model is implemented using PyTorch [45]. We optimize the model using MADGRAD [6] on eight A100 GPUs. The input image is cropped and scaled to " + }, + { + "bbox": [ + 304, + 552, + 545, + 624 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 304, + 552, + 545, + 624 + ], + "type": "text", + "content": ". The weights for testing are selected according to their losses on the validation set. The depth metrics are borrowed from DeepVideoMVS [9]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 641, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 715 + ], + "type": "text", + "content": "Keyframe Selection: Considering the high similarity between adjacent frames, estimating depth maps for every raw frame is inefficient. Thus, we select the most iconic frames (i.e., keyframes) from the input video sequences. When a new frame comes, we examine its pose distance to the latest keyframe and only adopt the new frames leading to pose" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "12582" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 75, + 70, + 519, + 175 + ], + "blocks": [ + { + "bbox": [ + 75, + 70, + 519, + 175 + ], + "lines": [ + { + "bbox": [ + 75, + 70, + 519, + 175 + ], + "spans": [ + { + "bbox": [ + 75, + 70, + 519, + 175 + ], + "type": "table", + "html": "
ScanNet
Abs Diff↓Abs Rel↓Sq Rel↓δ < 1.05↑δ < 1.25↑Time (ms) ↓
DPSNet [19]0.15480.07890.029249.3993.31308 ms
MVDepthNet [61]0.16430.08440.034146.7392.8046 ms
DELTAS [55]0.14920.07830.027148.6893.8183 ms
GPMVS [16]0.14920.07530.029051.0993.9849 ms
DeepVideoMVS (Fusion) [9]0.11820.05800.018760.2396.7830 ms
Ours0.10690.05060.016561.3497.1330 ms
", + "image_path": "f139d60b3be9882c817eb3c4e62c9a4ed8d987c288c5a1a4cf24b065d61ae850.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 226, + 288, + 285 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 226, + 288, + 285 + ], + "spans": [ + { + "bbox": [ + 46, + 226, + 288, + 285 + ], + "type": "text", + "content": "distances above a threshold. We define the pose distance as Eq. (1) and set the threshold as 0.35, following [9, 17]. Notably, we do not estimate depth for the first frame in a video sequence because it has no predecessors to provide multi-view information." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 304, + 287, + 332 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 304, + 287, + 332 + ], + "spans": [ + { + "bbox": [ + 55, + 304, + 287, + 332 + ], + "type": "interline_equation", + "content": "D i s _ {p} = \\sqrt {\\left| t r a n s i t i o n \\right| ^ {2} + \\frac {2}{3} T r a c e (I - r o t a t i o n)} \\quad (1)", + "image_path": "94fd4066dbe1d28fa134117be4c1660b1092d2dfcce5d41ae080eda992312c2b.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 342, + 287, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 342, + 287, + 392 + ], + "spans": [ + { + "bbox": [ + 46, + 342, + 287, + 392 + ], + "type": "text", + "content": "Datasets: Following the mainstream settings [9, 57], we train and evaluate our model on ScanNet [5], which is a large-scale real-world video dataset containing 1201 scenes for training, 321 for validation, and 100 for testing." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 405, + 287, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 405, + 287, + 441 + ], + "spans": [ + { + "bbox": [ + 46, + 405, + 287, + 441 + ], + "type": "text", + "content": "Comparison to existing SOTAs Tab. 1 demonstrates that our method outperforms various state-of-the-art depth estimation approaches in effectiveness and efficiency." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 441, + 287, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 441, + 287, + 536 + ], + "spans": [ + { + "bbox": [ + 46, + 441, + 287, + 536 + ], + "type": "text", + "content": "Compared to real-time SOTAs [9], our method shows significant advantages in all effectiveness metrics while retaining comparable time efficiency. Compared to semi-realtime algorithms [16, 55, 61], our method dominates inference time and offers significant competitiveness in reconstruction quality. In addition, our real-time framework even generates more accurate depth maps than some offline solutions [19] while spending one magnitude less cost." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 537, + 287, + 585 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 537, + 287, + 585 + ], + "spans": [ + { + "bbox": [ + 46, + 537, + 287, + 585 + ], + "type": "text", + "content": "Moreover, our method benefits relative error more than absolute error and favors " + }, + { + "bbox": [ + 46, + 537, + 287, + 585 + ], + "type": "inline_equation", + "content": "L^1" + }, + { + "bbox": [ + 46, + 537, + 287, + 585 + ], + "type": "text", + "content": " difference more than " + }, + { + "bbox": [ + 46, + 537, + 287, + 585 + ], + "type": "inline_equation", + "content": "L^2" + }, + { + "bbox": [ + 46, + 537, + 287, + 585 + ], + "type": "text", + "content": ". These results indicate that delicate structures and small objects win more attention." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 599, + 287, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 599, + 287, + 659 + ], + "spans": [ + { + "bbox": [ + 46, + 599, + 287, + 659 + ], + "type": "text", + "content": "Impacts of the Semantic Head To assess the effectiveness of our proposed semantic-based depth selection strategy, we fix all other variables and only examine the semantic head's impacts. Tab. 2 confirms that our semantic-based depth selection module offers significant benefits." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 669, + 122, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 669, + 122, + 681 + ], + "spans": [ + { + "bbox": [ + 47, + 669, + 122, + 681 + ], + "type": "text", + "content": "5. Limitations" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "type": "text", + "content": "Like most dense reconstruction models, our pipeline requires the camera parameters to be known, which may not" + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 309, + 224, + 544, + 269 + ], + "blocks": [ + { + "bbox": [ + 46, + 183, + 546, + 206 + ], + "lines": [ + { + "bbox": [ + 46, + 183, + 546, + 206 + ], + "spans": [ + { + "bbox": [ + 46, + 183, + 546, + 206 + ], + "type": "text", + "content": "Table 1. Depth evaluation results on the ScanNet dataset. The best results are marked in bold. Our model is leading in both effectiveness and efficiency." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 224, + 544, + 269 + ], + "lines": [ + { + "bbox": [ + 309, + 224, + 544, + 269 + ], + "spans": [ + { + "bbox": [ + 309, + 224, + 544, + 269 + ], + "type": "table", + "html": "
Abs Diff↓Abs Rel↓Sq Rel↓
No Semantic Head0.12250.06330.0192
+ Semantic Head0.10690.05240.0161
", + "image_path": "9c289f5c4d44c17fc8dbc3c133d440d12005e4eeed42b6f15aa97d37775dc0e8.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 332, + 277, + 518, + 288 + ], + "lines": [ + { + "bbox": [ + 332, + 277, + 518, + 288 + ], + "spans": [ + { + "bbox": [ + 332, + 277, + 518, + 288 + ], + "type": "text", + "content": "Table 2. Improvements from our semantic head." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 311, + 545, + 359 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 311, + 545, + 359 + ], + "spans": [ + { + "bbox": [ + 305, + 311, + 545, + 359 + ], + "type": "text", + "content": "always be feasible. Besides, our current model may have difficulty with unseen object categories, although we only require adjacent frames to have the same class prediction (even if it is incorrect)." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 372, + 378, + 384 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 372, + 378, + 384 + ], + "spans": [ + { + "bbox": [ + 306, + 372, + 378, + 384 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 392, + 545, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 392, + 545, + 525 + ], + "spans": [ + { + "bbox": [ + 304, + 392, + 545, + 525 + ], + "type": "text", + "content": "This paper proposes a novel 3D reconstruction network that is leading in effectiveness and efficiency. Our core contribution is to locate the most promising depth candidates using semantic maps. Specifically, we prune unreliable candidates according to the cross-view semantic consistency and then resample the candidates to look after pixels in need. Consequently, our method produces highly delicate reconstructions of meticulous structures and generates smooth surfaces for large planes with low overhead. Experimental results on the most popular datasets verify the proposed method's advantages in real scenarios." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 537, + 403, + 551 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 537, + 403, + 551 + ], + "spans": [ + { + "bbox": [ + 306, + 537, + 403, + 551 + ], + "type": "text", + "content": "Acknowledgments" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "type": "text", + "content": "This work is partially supported by the National Science Foundation of China (NSFC) under Grant No. U22B2060, the Hong Kong RGC GRF Project 16209519, CRF Project C6030-18G, C2004-21GF, AOE Project AoE/E-603/18, RIF Project R6020-19, Theme-based project TRS T41-603/20R, China NSFC No. 61729201, Guangdong Basic and Applied Basic Research Foundation 2019B151530001, Hong Kong ITC ITF grants MHX/078/21 and PRP/004/22FX, Microsoft Research Asia Collaborative Research Grant, HKUST-Webank joint research lab grant and HKUST Global Strategic Partnership Fund (2021 SJTU-HKUST). In addition, we gratefully acknowledge the generous support from MindSpore." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12583" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 72, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 72, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 72, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "text", + "content": "[1] Neill DF Campbell, George Vogiatzis, Carlos Hernández, and Roberto Cipolla. 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Visibility-aware multi-view stereo network. In 31st British Machine Vision Conference 2020, BMVC 2020, Virtual Event, UK, September 7-10, 2020. BMVA Press, 2020. 1" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 48, + 152, + 287, + 205 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 152, + 287, + 205 + ], + "spans": [ + { + "bbox": [ + 48, + 152, + 287, + 205 + ], + "type": "text", + "content": "[79] Hengshuang Zhao, Xiaojuan Qi, Xiaoyong Shen, Jianping Shi, and Jiaya Jia. Icnet for real-time semantic segmentation on high-resolution images. In Proceedings of the European conference on computer vision (ECCV), pages 405-420, 2018. 3" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 48, + 208, + 287, + 240 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 208, + 287, + 240 + ], + "spans": [ + { + "bbox": [ + 48, + 208, + 287, + 240 + ], + "type": "text", + "content": "[80] Jiawen Zhu, Simiao Lai, Xin Chen, Dong Wang, and Huchuan Lu. Visual prompt multi-modal tracking. arXiv preprint arXiv:2303.10826, 2023. 3" + } + ] + } + ], + "index": 3 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "12587" + } + ] + } + ], + "index": 5 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 11 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Directional Connectivity-Based Segmentation of Medical Images/b9c53750-6c7d-4628-8a5d-c4d2ad764a83_content_list.json b/2023/Directional Connectivity-Based Segmentation of Medical Images/b9c53750-6c7d-4628-8a5d-c4d2ad764a83_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..91b1a2ed06cbcc8420d7c893308bab365671d729 --- /dev/null +++ b/2023/Directional Connectivity-Based Segmentation of Medical Images/b9c53750-6c7d-4628-8a5d-c4d2ad764a83_content_list.json @@ -0,0 +1,2227 @@ +[ + { + "type": "text", + "text": "Directional Connectivity-based Segmentation of Medical Images", + "text_level": 1, + "bbox": [ + 205, + 106, + 841, + 128 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Ziyun Yang", + "bbox": [ + 334, + 141, + 433, + 157 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Duke University", + "bbox": [ + 316, + 159, + 452, + 175 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Durham, NC, United States", + "bbox": [ + 274, + 176, + 495, + 191 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ziyun.yang@duke.edu", + "bbox": [ + 279, + 193, + 488, + 209 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Sina Farsiu", + "bbox": [ + 602, + 141, + 697, + 157 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Duke University", + "bbox": [ + 584, + 159, + 718, + 175 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Durham, NC, United States", + "bbox": [ + 540, + 176, + 761, + 191 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "sina.farsiu@duke.edu", + "bbox": [ + 540, + 193, + 761, + 208 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 269, + 268, + 349, + 286 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Anatomical consistency in biomarker segmentation is crucial for many medical image analysis tasks. A promising paradigm for achieving anatomically consistent segmentation via deep networks is incorporating pixel connectivity, a basic concept in digital topology, to model inter-pixel relationships. However, previous works on connectivity modeling have ignored the rich channel-wise directional information in the latent space. In this work, we demonstrate that effective disentanglement of directional sub-space from the shared latent space can significantly enhance the feature representation in the connectivity-based network. To this end, we propose a directional connectivity modeling scheme for segmentation that decouples, tracks, and utilizes the directional information across the network. Experiments on various public medical image segmentation benchmarks show the effectiveness of our model as compared to the state-of-the-art methods. Code is available at https://github.com/Zyun-Y/DconnNet.", + "bbox": [ + 112, + 301, + 504, + 565 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 114, + 594, + 246, + 609 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Maintaining anatomical consistency in the segmentation of medical images is important but challenging, as minor geometric errors may change the global topology [1, 2] and cause functional mistakes in downstream clinical decision-making [3]. Anatomical consistency in images can be expressed with topological properties, such as pixel connectivity and adjacency [4, 5]. As such, by directly modeling the mutual information between pixels or regions, graph-based methods have long been used to correct topological and geometrical errors [6-8]. However, such classic machine vision techniques usually depend on manually defined priors and thus are not easily generalizable for a wide variety of applications.", + "bbox": [ + 112, + 614, + 503, + 804 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Alternative to the classic approaches, deep learning-based segmentation methods utilized an encoder-decoder architecture [9] to learn from a group of pixels in a particular receptive field at each layer. More recently, significant progress has been made in capturing the interpixel dependency inside a network's latent space [10-12];", + "bbox": [ + 112, + 805, + 503, + 893 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/40ba21137e681264752775952d67769fe75f02d01b5b1fd014bc0a3d0a9278da.jpg", + "image_caption": [ + "Figure 1. The latent space differences between traditional pixel-classification-based and connectivity-based models. In the former, only categorical features, e.g., boundaries, are highlighted; while in the latter, the feature map also contains directional information (e.g., the horizontal connections between boundary pixels)." + ], + "image_footnote": [], + "bbox": [ + 578, + 252, + 913, + 407 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/7523ccfec1499837641b23ddc19bf8d9d54e5a792438268750c596d9e8b3f2ab.jpg", + "image_caption": [ + "Figure 2. The flows of the two groups of latent features (categorical and directional) in the latent space of DconnNet, are visualized by T-SNE [13]. They were first disentangled (Sec 3.2) and then effectively fused in a projected shared manifold (Sec 3.3). The colors are rendered based on the results of clustering." + ], + "image_footnote": [], + "bbox": [ + 542, + 478, + 929, + 592 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "however, very few studies have been conducted on the problem modeling side of the networks. A typical segmentation network models the problem as a pure pixelwise classification task and uses a segmentation mask as the only label. Yet, this pixel-wise modeling scheme is suboptimal as it does not directly exploit inter-pixel relationships and geometrical properties [14, 15]. Thus, these models may result in low spatial coherence (i.e., inconsistent predictions for neighboring pixels that share similar spatial features) in their prediction [16]. Especially, when applied to high noise/artifacts medical data, the lower spatial consistency may lead to topological issues [17].", + "bbox": [ + 537, + 665, + 929, + 839 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The concept of pixel connectivity has long been used to ensure the basic topological duality of separation and connectedness in digital images [18]. More recently, in the context of deep learning, the connectivity masks, reviewed", + "bbox": [ + 537, + 839, + 929, + 898 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation.", + "bbox": [ + 236, + 0, + 810, + 18 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "Except for this watermark, it is identical to the accepted version;", + "bbox": [ + 323, + 16, + 723, + 31 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 292, + 31, + 754, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "11525", + "bbox": [ + 480, + 943, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0099ae811e168b8b62f042f2be4ab122fdb96ef7be584fd0dfabf8a20d4c0979.jpg", + "image_caption": [ + "Figure 3. Illustration of generating the connectivity mask from the segmentation mask by traversing 8-neighbor pixel connectivity. For each pixel, channel $C_i$ 's binary value in the converted connectivity vector carries the categorical information (connected or not connected) while $i$ encodes the directional information (direction of connection)." + ], + "image_footnote": [], + "bbox": [ + 119, + 90, + 496, + 214 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "in Section 2.1, have been introduced as a topological extension of the segmentation mask [15]. Using connectivity masks as training labels has several advantages over segmentation masks. In terms of problem modeling, using a connectivity mask inherently changes the problem from pixel-wise classification to connectivity prediction, which models and enhances the topological representation between pixels of interest. In terms of label representation, a connectivity mask is more informative in three ways: first, a connectivity mask stores the categorical information among the connections of pixels and it is inter-pixel relation-aware; second, it sparsely represents edge pixels [16]; third, it contains rich directional information channel-wisely. Thus, a network trained with connectivity masks has both categorical (reflected by connectivity) and directional features in its latent space, each of which forms a specific sub-latent space, as shown in Fig. 1.", + "bbox": [ + 112, + 301, + 503, + 547 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In previous studies [15, 16, 19-22], these two groups of features were learned simultaneously through a shared network path which may result in highly coupled latent space and introduce redundancy [23]. Further, effectively disentangling meaningful subspaces from the shared latent space has been shown effective in accounting for the dependencies/independencies between features [24, 25].", + "bbox": [ + 112, + 549, + 503, + 650 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Inspired by the idea of latent space disentanglement, in this paper, we propose a novel directional connectivity-based segmentation network (DconnNet) to disentangle the directional subspace from the shared latent space and utilize the extracted directional features to enhance the overall data representation, as in Fig. 2. The disentangling process is conducted by a sub-path slicing-based module called Sub-path Direction Excitation (SDE). The directional-based feature enhancement is applied in a coarse-to-fine manner using an Interactive Feature-space Decoder (IFD) with two top-down interactive decoding flows. Finally, we propose a novel Size Density loss (SDL) that alleviates the common data imbalance problem in medical datasets with a label size distribution-based weighting scheme. With experiments on different public medical image analysis benchmarks, we demonstrate the superiority of DconnNet against other state-of-art methods.", + "bbox": [ + 112, + 650, + 503, + 898 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 540, + 90, + 686, + 107 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Deep connectivity modeling", + "text_level": 1, + "bbox": [ + 540, + 114, + 790, + 131 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In topology, pixel connectivity describes how neighboring pixels are related to each other [4]. Following broad utilization in characterizing topological properties in classic image processing methods [26, 27], connectivity has found new applications in deep learning-based image segmentation [15, 16, 19-22]. The connectivity-based segmentation networks use the connectivity mask (Fig. 3) as the label, defined as an 8-channel mask with each channel representing if a pixel on the original image belongs to the same class of interest with one of its neighboring pixels at a specific direction. The connectivity mask was first introduced and applied to image segmentation in [15]. This idea was later extended by other works, including [16] which showed the bilateral property of pixel connectivity in saliency detection, and [28] which modeled the cross-modality connectivity for radar-video data fusion. Meanwhile, the effectiveness of connectivity modeling has been demonstrated in different applications such as remote sensing segmentation [19], path planning [20], and medical image segmentation [21, 22, 29]. Although significant progress has been made in this field, we demonstrate that the rich directional information in the connectivity masks has not yet been fully utilized.", + "bbox": [ + 537, + 137, + 929, + 473 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Interpretation of latent space", + "text_level": 1, + "bbox": [ + 540, + 481, + 803, + 496 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Latent space is an embedding of a set of features in a deep network. Interpretation, alignment, and disentanglement of latent spaces are important in different computer vision techniques such as unsupervised learning [30], multi-modal information fusion [24, 31], generative models [32, 33], knowledge distillation [34, 35], and transfer learning [36]. However, the interpretation of latent space is challenging because it usually requires implicit domain knowledge based on human judgment [37].", + "bbox": [ + 537, + 502, + 929, + 633 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To interpret the latent space, researchers either apply dimension reduction tools such as PCA [38], T-SNE [13], or develop interactive analysis tools [39]. To manipulate latent space, a variation autoencoder (VAE) can be used to map the input to latent space and disentangle/match the different latent spaces [40, 41]. In this work, we utilize the intrinsic property of the connectivity mask and propose a simple yet effective sub-path slicing-based method to disentangle the directional subspace from the shared latent space, followed by a visual demonstration of the effectiveness of our disentanglement process with T-SNE.", + "bbox": [ + 537, + 633, + 929, + 794 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.3. Self-attention mechanism", + "text_level": 1, + "bbox": [ + 540, + 803, + 774, + 819 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Self-attention is widely used in computer vision as it can capture the dependencies between latent features. The self-attention mechanism is defined as:", + "bbox": [ + 537, + 825, + 929, + 871 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {y} = f (\\alpha , g (\\mathbf {x})), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 678, + 878, + 929, + 895 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "11526", + "bbox": [ + 480, + 943, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/d1bd85b28bd12db36e57db595a91c999ca99c3d16dec624dcc06735035c33c0b.jpg", + "image_caption": [ + "Figure 4. The overview of the proposed DconnNet. It contains three parts: a pretrained ResNet encoder, a Sub-path Direction Excitation Module, and an Interactive Feature-space Decoder. The term \"up $N \\times$ \" means upsampling with a stride of $N$ ." + ], + "image_footnote": [], + "bbox": [ + 122, + 88, + 903, + 287 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $x$ is the input feature map, $g$ is a unary function that computes the embedding of input, and $f$ is usually a matrix multiplication [10, 42] or a simple dot product [11, 43, 44], depending on the definition of $\\alpha$ . $\\alpha$ is the attention/relation map which can be a mutual relation map by spatial- or channel-wisely computing the similarity between one pixel with other pixels in a feature map, or between two related feature maps from the same feature space [10, 42]; it can be a contextual-spatial relation map generated by similarity estimation between a feature map and a latent vector with abstract contextual meaning [44, 45]. Broadly speaking, $\\alpha$ can also be a single map [11] or a vector [43, 46] containing special contextual meaning.", + "bbox": [ + 112, + 323, + 503, + 522 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 114, + 537, + 205, + 554 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Directional space in connectivity modeling", + "text_level": 1, + "bbox": [ + 112, + 566, + 478, + 583 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Due to connectivity between different pixel classes and directions, there are two groups of features in the latent space of a connectivity-based network: categorical directional. Each group of features forms its specific subspace in the latent space. In a single-path connectivity network, these two subspaces are highly coupled (Fig. 2), resulting in low-discriminative features. We demonstrate that the efficient disentangling and effective utilization of the direction space can enhance the overall feature representation in the connectivity model.", + "bbox": [ + 112, + 588, + 503, + 733 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In a connectivity mask, different channels represent different directions of the pixel connection. Thus, as the network goes deeper, it naturally stores directional information among channels. Based on this property, the directional features can be captured and manipulated through channel-wise operations. Specifically, we propose SDE to disentangle channel-wise directional features from the latent space, followed by IFD to extract the directional embeddings at different layers and use them to enhance the overall feature representation in a self-attention manner. The overall DconnNet structure is shown in Fig. 4.", + "bbox": [ + 112, + 734, + 503, + 893 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Sub-path Direction Excitation Module", + "text_level": 1, + "bbox": [ + 539, + 323, + 872, + 339 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Directional prior extraction. Taking advantage of the channel-wise directional information in the connectivity mask, a direct way to get distinctive directional embedding is to coarsely supervise the intermediate features and squeeze the channels of the auxiliary connectivity output. We denote the encoder's outputs as $e_n$ , where $n$ is the $n_{th}$ encoder layer. As shown in Fig. 5, we upsample $e_5$ , the last encoder output, to the input size and get a preliminary output called $X_{prior}$ , which will be supervised to learn the connectivity mask in the loss calculation. Therefore, rich, distinctive directional information can be obtained from the channels of $X_{prior}$ . Then, we squeeze [43] $X_{prior}$ through a global average pooling (GAP) and map the vector to the same dimension as the latent feature map $e_5 \\in R^{Ce_5 \\times He_5 \\times We_5}$ with a $1 \\times 1$ convolutional kernel $W_1$ [44]:", + "bbox": [ + 537, + 344, + 929, + 568 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nG A P (X) = \\frac {1}{H \\times W} \\sum_ {i = 1} ^ {H} \\sum_ {j = 1} ^ {W} X (i, j), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 625, + 570, + 928, + 612 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nv _ {p r i o r} = \\delta \\left(W _ {1} G A P \\left(X _ {p r i o r}\\right)\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 627, + 612, + 928, + 636 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathrm{H}$ and $\\mathrm{W}$ are the height and the width of a feature map, $W_{1} \\in R^{C_{e_{5}} \\times C_{k}}$ , $C_{k}$ is the channel of $X_{prior}$ , and $\\delta$ is the ReLu activation. The resulting $v_{prior} \\in R^{C_{e_{5}}}$ has the directional information of a specific direction embedded in each entry. Next, we re-encode $v_{prior}$ with a $1 \\times 1$ convolution $W_{2} \\in R^{C_{e_{5}} \\times C_{e_{5}}}$ and apply a sigmoid gating function $\\sigma$ to normalize the projected vector:", + "bbox": [ + 537, + 638, + 929, + 750 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\alpha_ {p r i o r} = \\sigma \\left(W _ {2} v _ {p r i o r}\\right). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 651, + 752, + 928, + 770 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Since $\\alpha_{prior}$ contains rich element-wise directional information, we call it the directional prior.", + "bbox": [ + 537, + 770, + 926, + 800 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Channel-wise slicing. To early disentangle the categorical and directional subspaces in the hidden layers, we split the latent features $(e_5)$ and the directional prior $(\\alpha_{prior})$ into eight parts by channel-wise slicing. We denote the $i_{th}$ slices as $e_5^i$ and $\\alpha_{prior}^{i}$ .", + "bbox": [ + 537, + 801, + 929, + 878 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Sub-path excitation (SPE). We construct a sub-path for", + "bbox": [ + 539, + 880, + 919, + 896 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "11527", + "bbox": [ + 478, + 943, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/4910310916cd4c502f86ac3a626708c63e5b2a590eb1545c877313387b29421e.jpg", + "image_caption": [ + "Figure 5. The SDE module, including three steps: direction prior extraction, channel-wise slicing, and sub-path excitation." + ], + "image_footnote": [], + "bbox": [ + 133, + 90, + 924, + 301 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/5ceeeb35b134fe49d31d5d85d0ed1572822a3d07f3423d9824b3644887ae9135.jpg", + "image_caption": [ + "Figure 6. The Interactive Feature-space Decoder (IFD)." + ], + "image_footnote": [], + "bbox": [ + 135, + 333, + 514, + 489 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "each pair of these feature-embedding slices. In each subpath, we pass the feature slice $e_5^i$ through spatial and channel attention modules [10] to capture the long-range and inter-channel dependencies, resulting in $e_5^{i\\prime}$ . Next, we channel-wisely multiply the $\\alpha_{prior}^i$ with $e_5^{i\\prime}$ to selectivity highlight or suppress features with specific directional information. Then, we recode the output with a $1\\times 1$ convolution kernel $W_3^i$ and residually output it as:", + "bbox": [ + 112, + 508, + 503, + 633 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ne _ {S D E} ^ {i} = W _ {3} ^ {i} \\left(\\alpha_ {p r i o r} ^ {i} \\cdot e _ {5} ^ {i ^ {\\prime}}\\right) + e _ {5} ^ {i}. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 204, + 636, + 501, + 655 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Finally, we stack all sub-paths outputs $(e_{SDE}^{i})$ into one and recode it, resulting in a new feature map, $e_{SDE}$ .", + "bbox": [ + 112, + 657, + 503, + 688 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Due to the slicing operation, each group of slices will only contain part of the full features. However, the shrink of discriminative contextual information in directional and categorical features differs. Specifically, $\\alpha_{prior}$ is a highly discriminative directional embedding as it is a low-level linear combination of unique directional features. Thus, channel-wise slicing will cause significant shrinkage of directional information in each slice. However, $e_5$ contains a group of high-level but less-discriminative categorical features which usually have low variations with others [47]. As a result, high channel-wise categorical correlation and redundancy [48] exist in $e_5$ . Therefore, a channel-wise slicing will result in less shrinkage [49] of high-discriminative categorical features in $e_5^i$ . By doing this, we", + "bbox": [ + 112, + 686, + 503, + 896 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "contextual-unevernly divide the directional and categorical features in each sub-path and make each sub-path shift its focus to the dominant features. Specifically, inside each sub-path, the network learns how to focus on the dominant class-specific information with less distinctive directional information emphasized in the channels. Between sub-paths, the network learns different distinctive directional information. Then, once we stack the sub-paths back, the direction information will be naturally disentangled from the original latent space and embedded into the channels.", + "bbox": [ + 539, + 320, + 929, + 467 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Interactive Feature-space Decoder", + "text_level": 1, + "bbox": [ + 540, + 476, + 843, + 493 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To ensure that the direction-dependent information can be effectively fused into feature maps in each layer, we propose an Interactive Feature-space Decoder with two top-down dynamically interactive flows, i.e., space flow and feature flow, as in Fig. 6.", + "bbox": [ + 537, + 500, + 929, + 573 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Feature maps. There are two types of feature maps in each layer of IFD: the main feature map $d_{i}$ and the direction-enhanced map $r_{i}$ . At the first decoder layer ( $i = 5$ ), they are both initialized as the outputs of SDE:", + "bbox": [ + 537, + 577, + 929, + 637 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nr _ {5} = d _ {5} = e _ {S D E}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 673, + 638, + 928, + 654 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "and are updated separately in the space and feature flows.", + "bbox": [ + 537, + 655, + 923, + 671 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Space flow. In each space flow, a Space Block (S), which contains the embedding squeezing (ES) module and the manifold projection and enhancement (MPE) module, is used to enhance the directional representation. The ES module takes $r_i$ as the input and outputs a directional embedding $n_i$ , a high-level directional representation as:", + "bbox": [ + 537, + 675, + 929, + 763 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nn _ {i} = G A P \\left(r _ {i}\\right). \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 679, + 765, + 926, + 781 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Then, we use $n_i$ as the input of MPE to enhance the directional representation in the main feature map $d_i$ . In MPE, we first project both the main feature map $d_i \\in R^{C_{d_i} \\times H_{d_i} \\times W_{d_i}}$ and directional embedding $n_i \\in R^{C_{d_i}/2}$ onto a shared manifold $R^{C_{d_i}}$ at the current resolution with two $1 \\times 1$ convolutional projectors:", + "bbox": [ + 537, + 782, + 929, + 876 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nd _ {i} ^ {\\prime} = W _ {d _ {i}} d _ {i}, n _ {i} ^ {\\prime} = W _ {n _ {i}} n _ {i}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 650, + 877, + 928, + 895 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "11528", + "bbox": [ + 480, + 943, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $W_{d_i} \\in R^{C_{d_i} \\times C_{d_i}}$ and $W_{n_i} \\in R^{C_{d_i} \\times C_{d_i}/2}$ . Next, we model the category-direction relation by calculating the similarity between the projected directional embedding $n_i'$ and feature map $d_i'$ with a channel-wise dot product and a sigmoid activation:", + "bbox": [ + 112, + 90, + 504, + 170 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\alpha_ {n d} = \\sigma \\left(d _ {i} ^ {\\prime} \\cdot n _ {i} ^ {\\prime}\\right), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 243, + 172, + 501, + 188 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\alpha_{nd}$ is the normalized category-direction attention map in which the direction-relevant features are enhanced and the irrelevant features are suppressed across channels. Next, we enhance the directional information in the re-encoded original feature map $d^{\\prime \\prime}_i$ with the attention map $\\alpha_{nd}$ using a point-wise inner multiplication:", + "bbox": [ + 112, + 189, + 503, + 277 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nr _ {i - 1} = \\alpha_ {n d} \\cdot d ^ {\\prime \\prime} _ {i}. \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 243, + 280, + 501, + 296 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "By doing this, we effectively fuse the directional information into the feature map, resulting in a new direction-enhanced map $r_{i-1}$ , which will be further used as the input of feature flow and to generate the directional embedding $n_{i-1}$ for the next layer.", + "bbox": [ + 112, + 297, + 503, + 371 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Feature flow. Each feature flow contains a Feature Block (F), including two convolutional layers and an upsampling layer with a skip connection. It takes $r_i$ as the input and outputs the upsampled main feature map $d_i$ .", + "bbox": [ + 112, + 375, + 503, + 434 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This top-down design and dynamic interactions between the two flows are mutually beneficial. Specifically, the embedding $n_i$ extracted by space flow effectively fuses the directional information into the feature map $d_i$ from the feature flow. On the other hand, the $d_i$ generated by feature flow refines the directional representation $n_{i-1}$ by adding supplementary directional information at a higher resolution to the space flow via MPE and ES.", + "bbox": [ + 112, + 434, + 503, + 551 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Connectivity output", + "text_level": 1, + "bbox": [ + 112, + 561, + 307, + 578 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We integrate the main feature maps $d_{1}$ to $d_{4}$ to get the final connectivity output $X$ . Every eight channels of $X$ represent the connectivity of one class. In line with [16], we use the Bilateral Voting (BV) module in (11) and the Region-guided Channel Aggregation (RCA) module in (12) to get the final segmentation map.", + "bbox": [ + 112, + 585, + 503, + 672 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\bar {X} _ {j} (x, y) = \\bar {X} _ {9 - j} (x + a, y + b) \\\\ = X _ {j} (x, y) \\times X _ {9 - j} (x + a, y + b), (11) \\\\ \\tilde {S} (x, y) = \\max \\{\\tilde {X} _ {i} (x, y) \\} _ {i = 1} ^ {8}, (12) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 165, + 675, + 500, + 729 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $j$ is the $j_{th}$ channel, $a,b\\in \\{0,\\pm 1\\}$ represent the location of neighboring pixel, $\\tilde{X}$ is the Bicon map, $\\tilde{S}$ is the final segmentation prediction [16].", + "bbox": [ + 112, + 732, + 503, + 777 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Loss function", + "text_level": 1, + "bbox": [ + 112, + 785, + 254, + 799 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The total loss function of our work is:", + "bbox": [ + 130, + 808, + 383, + 821 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\text {t o t a l}} = L (\\text {m a i n}) + 0. 3 * L (\\text {p r i o r}), \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 184, + 825, + 500, + 840 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where main represents the main output and prior represents the auxiliary output from SDE. Each loss $L$ contains two parts, the Size Density Loss $L_{sd}$ and the", + "bbox": [ + 112, + 844, + 503, + 888 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "original Bicon loss [16] $L_{bicon}$", + "bbox": [ + 540, + 90, + 750, + 107 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL = L _ {s d} + L _ {b i c o n}. \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 666, + 109, + 926, + 126 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Size Density Loss. Considering the imbalanced nature of the medical data, we propose a novel imbalanced loss function based on the label size distribution of the classes of interests in the dataset, called Size Density Loss.", + "bbox": [ + 537, + 128, + 929, + 186 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Before training, we sample all the training images and calculate the size of the label (total positive pixel number) on each image. Based on the extracted size distribution, for each class $j$ , we calculate the probability density function of label size $k$ , i.e., $PDF_{j}(k)$ . Then, in the training phase, for each training image, we calculate its label size for each class $j$ and get its size density weight $P_{j}(k)$ as:", + "bbox": [ + 537, + 188, + 929, + 292 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nP _ {j} (k) = \\left\\{ \\begin{array}{l l} 1, & k = 0, \\\\ - \\log \\left(P D F _ {j} (k)\\right), & k \\neq 0. \\end{array} \\right. \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 616, + 294, + 928, + 332 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We define the $L_{sd}$ as a variant of Dice loss [50]:", + "bbox": [ + 557, + 334, + 877, + 349 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {s d} = \\sum_ {j} ^ {\\text {C l a s s}} P _ {j} (k) \\left(1 - \\frac {2 \\times \\sum \\left(S \\times G _ {s}\\right) + \\varepsilon}{\\sum S + \\sum G _ {s} + \\varepsilon}\\right), \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 578, + 351, + 926, + 392 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $S$ is the final segmentation prediction, $\\varepsilon$ is the stabilization term [51] and is usually set as 1.", + "bbox": [ + 539, + 393, + 929, + 424 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Bicon Loss term. We use the Bicon Loss $L_{bicon}$ for connectivity modeling, as originally defined in [16]:", + "bbox": [ + 539, + 429, + 929, + 458 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {b i c o n} = L _ {d e c o u p l e} + L _ {c o n \\_ c o n s t}. \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 625, + 460, + 926, + 476 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 540, + 497, + 671, + 513 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Datasets and evaluation metrics", + "text_level": 1, + "bbox": [ + 539, + 523, + 823, + 537 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We used three popular and diverse medical benchmark datasets in this paper. Specifically, we used Retouch [52] and ISIC2018 [53] datasets to evaluate the DconnNet performance for large-scale medical segmentation. We used CHASEDB1 [54] dataset to assess the topological performance of the DconnNet.", + "bbox": [ + 537, + 544, + 929, + 633 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Retouch is an OCT retinal fluids segmentation benchmark that has been widely used [55, 56] for assessing computer vision methods. It contains three classes of disease biomarkers: intraretinal fluid (IRF), subretinal fluid (SRF), and pigment epithelial detachment (PED). Retouch contains a training set of 70 OCT volumes from three OCT scanners, with frame sizes spanning from $512 \\times 496$ to $512 \\times 1024$ pixels. Retouch is a two-level balanced dataset: at the image level, biomarkers do not span the whole volume; at the pixel level, each biomarker has a relatively small size compared to the background. Since the testing labels are unavailable, we implemented the volume-level 3-fold cross-validation (CV) for each scanner on the training data set. Following the official guidelines [52], we used volume-level Dice [65] ( $DSC_v$ ), image-level Dice ( $DSC$ ), absolute volume difference ( $AVD$ ), and volume-wise balanced accuracy [66] ( $BACC$ ) to evaluate the results.", + "bbox": [ + 537, + 638, + 929, + 888 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "11529", + "bbox": [ + 478, + 943, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/87ec234d67e748f46f4d29a094996dfc527ad655793c98fbe3a3e6d7865c9429.jpg", + "image_caption": [ + "Figure 7. Visual comparison between the proposed DconnNet and other state-of-the-art methods on Retouch dataset. Different colors of masks represent different biomarker classes. Green: IRF; blue: SRF; red: PED." + ], + "image_footnote": [], + "bbox": [ + 119, + 95, + 919, + 296 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/f6c15b86bfdd100776075bab6135bc11a7a51a82c8e243e3a7aaa9760c60cde2.jpg", + "table_caption": [ + "Table 1. Results on Retouch dataset. Model size (M) and testing speed (FPS) are also reported. The best results are bold." + ], + "table_footnote": [], + "table_body": "
MethodDSCvDSCAVDBACCSize / Speed
DeepLabv3+ [57]60.282.70.02386.559.3 / 38
U-Net [58]66.184.20.02187.413.4 / 38
Att-UNet [59]65.383.40.02286.634.9 / 36
CE-Net [60]67.384.20.02684.629.0 / 37
nnU-Net [61]67.284.30.02386.430.0 / 20
CPFNet [62]69.085.70.02288.043.3 / 37
Curvature [63]68.284.70.02487.143.3 / 37
MsTGANet [64]68.985.00.02387.111.6 / 37
DconnNet78.287.70.02090.536.4 / 40
", + "bbox": [ + 109, + 357, + 508, + 505 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ISIC 2018 is a popular medical segmentation benchmark [67-70] containing 2594 images of various types of skin lesions at different resolutions. Following [71], we used 5-fold CV and evaluated the results with Dice, IOU, accuracy (ACC), and precision (PREC) metrics.", + "bbox": [ + 112, + 512, + 501, + 585 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "CHASEDB1 is a vessel segmentation dataset containing 28 fundus images with a resolution of $999 \\times 960$ pixels and two sets of manual annotations. The first manual annotation is adopted in this work as in [72]. We conducted 5-fold CV and evaluated the results with two volumetric metrics Dice and IOU; and three topology-similarity-based metric clDice, 0- and 1-Betti numbers $(\\beta_0$ and $\\beta_{1}$ ) [73] to measure the topological similarity.", + "bbox": [ + 112, + 590, + 503, + 708 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Experimental details", + "text_level": 1, + "bbox": [ + 114, + 715, + 310, + 729 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We generated the connectivity mask for each image via simple matrix operations [16]. We used the ImageNet [74] pretrained ResNet [75] as our encoder. The hyperparameter setting differed across datasets. For the Retouch dataset, we resized each image to $256 \\times 256$ with no data augmentation and trained DconnNet with a 'poly' learning rate strategy. For ISIC2018, we resized images to $224 \\times 320$ and used the same data augmentation and the parameter settings in [71]. For CHASEDB1, to fully use the limited data, we resized to $960 \\times 960$ pixels and applied the same augmentations as in [60]. Since the CHASEDB1 dataset has a limited sample", + "bbox": [ + 112, + 737, + 503, + 898 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "size, we did not apply SDL loss to this dataset. We did not use any pre-processing for training and no post-processing for evaluation. The framework is built on PyTorch 1.7.0 [76]. All experiments are performed with a GPU NVIDIA GeForce GTX 3090 Ti.", + "bbox": [ + 539, + 329, + 929, + 402 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Results", + "text_level": 1, + "bbox": [ + 540, + 416, + 627, + 431 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Retinal fluid segmentation", + "text_level": 1, + "bbox": [ + 540, + 440, + 782, + 455 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparison of state-of-the-art methods. We compared the proposed DconnNet with eight state-of-the-art models for relevant applications, including DeepLab V3+ [57], U-Net [58], Attention UNet [59], CE-Net [60], nnU-Net [61], CPFNet [62], CPFNet-backboned Curvature Loss [63], and MsTGANet [64] in Table 1, which shows the superior performance of the proposed model. Specifically, the improvements on $DSC_{i}$ and $DSC_{v}$ demonstrate that our model has a consistent prediction on the small fluid regions, while the improvements on AVD and BACC demonstrate that our model has an overall more accurate prediction on the fluid regions, regardless of the target size.", + "bbox": [ + 537, + 463, + 929, + 647 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Qualitative study. In Fig. 7, we compared DconnNet with the top-six baselines. In image (a), all competing methods missed the tiny SRF region, while our DconnNet made an accurate prediction. In (b), all methods, except DconnNet, either made false positive (FP) segmentations of IRF or an incomplete segmentation on PED. In (c), only our DconnNet made the topologically connected prediction for PED and accurately segmented the IRF and SRF regions.", + "bbox": [ + 537, + 648, + 929, + 772 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Skin lesion segmentation", + "text_level": 1, + "bbox": [ + 540, + 779, + 767, + 795 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparison of state-of-the-art methods. In Table 2, we compared our method with U-Net [58], BCDU-Net [77], CE-Net [60], nnU-Net [61], HiFormer [78], CPFNet [62], FATNet [79], and Ms RED [71]. The proposed DconnNet outperformed all competitive models.", + "bbox": [ + 537, + 801, + 928, + 878 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Qualitative study. Due to limited space, in Figs. 8 and 9,", + "bbox": [ + 539, + 882, + 923, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "11530", + "bbox": [ + 480, + 943, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/2bb5774a133196ba33c9d92b9ea1c39471d37a6ba9ad8f474b1e7987f3f49085.jpg", + "table_caption": [ + "Table 2. Results on ISIC2018 dataset. The best results are bold." + ], + "table_footnote": [], + "table_body": "
MethodDSCIOUACCPREC
U-Net [58]88.4181.2395.5390.7
BCDU-Net [77]88.3380.8495.4889.68
CE-Net [60]89.2382.3495.7691.51
nnU-Net [61]89.2482.3595.7991.45
HiFormer [78]88.5481.4595.5991.09
CPFNet [62]89.3482.6495.8991.38
FATNet [79]88.8481.7995.6291.18
Ms RED [71]89.4882.7195.8991.83
DconnNet90.4383.9196.3991.54
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Visualization on ISIC2018 dataset." + ], + "image_footnote": [], + "bbox": [ + 119, + 332, + 183, + 368 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/44b98384f192b3b960ffb8cb6e16a8ae0175ccc39a2c81cad71a57d4a94fbcef.jpg", + "image_caption": [ + "", + "" + ], + "image_footnote": [], + "bbox": [ + 183, + 332, + 245, + 368 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c2456587ac6acc96bbbebe2d5f49136836f880525571fad63a40609c00065136.jpg", + "image_caption": [ + "CPFNet [62]" + ], + "image_footnote": [], + "bbox": [ + 245, + 332, + 308, + 368 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/04b51b61ec96b17e44ef73addfba0516f1aeba430b1c943923475507a0dd3559.jpg", + "image_caption": [ + "Net [79]" + ], + "image_footnote": [], + "bbox": [ + 308, + 332, + 370, + 368 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/09a274ebaa4255452b50460d356837b1b09ff3aa66fbd0a5306693b1b4b091fa.jpg", + "image_caption": [ + "Ms RED [71]" + ], + "image_footnote": [], + "bbox": [ + 370, + 332, + 442, + 368 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/72b2078f40acc6a5a726aee131bfa056ea290ebf25979b7bdded3c20e2c0280e.jpg", + "image_caption": [ + "DconnNet" + ], + "image_footnote": [], + "bbox": [ + 442, + 332, + 500, + 368 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "we only compare the best-performing methods. In Fig. 8, DconnNet can accurately segment the lesion even under strong clinical confounders (e.g., the hairs in the first image). Also, DconnNet could learn the topology of skin lesions and make connected predictions in all cases, while others showed topological errors.", + "bbox": [ + 112, + 404, + 503, + 494 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Topological vessel segmentation", + "text_level": 1, + "bbox": [ + 114, + 503, + 395, + 520 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We used this experiment to demonstrate the topology-preserving ability of DconnNet in vessel segmentation, in which anatomical consistency is crucial. Due to the limited sampling size, we did not use SDL in this experiment.", + "bbox": [ + 112, + 526, + 503, + 585 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison of state-of-the-art methods. We compared the results of DconnNet versus up-to-date leading methods, including U-Net [58], Att-UNet [59], GT-DLA [80], CE-Net [60], cclDiceLoss [73], and Graph Cut Loss [72] in Table 3. Our method surpassed other methods on all metrics. The superior performances of DconnNet on cclDice, $\\beta_0$ , and $\\beta_{1}$ , reflect the topological similarity between predictions and labels.", + "bbox": [ + 112, + 589, + 503, + 705 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Qualitative study on the vessel topology. In Fig. 9, we visually compared different methods. While in part due to limited training data DconnNet could not make perfect predictions across the whole images, it visually outperformed other methods. Our model's predicted vessels are mostly connected and with no significant topological errors. Other models showed more topological issues, e.g., in the form of non-simply connected regions.", + "bbox": [ + 112, + 710, + 503, + 829 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.4. Ablation study", + "text_level": 1, + "bbox": [ + 114, + 835, + 264, + 852 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We conducted ablation studies to compare directional connectivity modeling with the traditional segmentation-", + "bbox": [ + 112, + 858, + 503, + 888 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/954b4c2366b8ee9f65cd3f3b6784cdfb4e9dd3e64cbea00c04a6c79291cfe340.jpg", + "table_caption": [ + "Table 3. Results on CHASEDB1. The best results are bold." + ], + "table_footnote": [], + "table_body": "
MethodclDiceDSCIOUβ0β1
U-Net [58]74.074.759.31.3902.633
Att-UNet [59]75.375.761.01.3302.531
GT-DLA [80]81.080.667.40.7901.969
CE-Net [60]82.081.068.10.3831.670
clDiceLoss [73]82.981.068.10.3451.656
GraphCutLoss [72]82.681.468.80.4371.692
DconnNet83.381.869.40.3411.630
", + "bbox": [ + 532, + 104, + 937, + 215 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/24ee4037a0e82fd143a8422b9b551174ce2dcc7c2fd3b278047169fd06e195f4.jpg", + "image_caption": [ + "Figure 9. Visualization on CHASEDB1 dataset." + ], + "image_footnote": [], + "bbox": [ + 542, + 220, + 609, + 275 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3043361a2241bfb4e6934afc2094da1d3f79f4baf660228c9470d62147f914d4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 609, + 220, + 736, + 275 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/16336ad29e7892b02336a76afc8be69d5d7eb38384db05b8b5a32ef8667babf6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 736, + 220, + 866, + 275 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/960edc1aa50b7d1d3c926e09cad4e994bf4a2777d0d87c95fa21ca797e6a661c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 866, + 220, + 929, + 275 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/f4d9f060ddbf644e1fbbe3862a79d745729a5e9981faa4e9effb5e30cf3d127f.jpg", + "table_caption": [ + "Table 4. Ablation study of the Retouch Dataset. Conn stands for connectivity modeling with $L_{bicon}$ . DS stands for dice loss." + ], + "table_footnote": [], + "table_body": "
ConnModuleLossDSC\\( DSC_v \\)AVDBACC
SDEIFDDSSDL
1√83.265.00.02587.0
2 √√85.870.30.02487.7
3 √√√86.273.70.02387.9
4 √√√√86.775.20.02388.3
5 √√√√87.778.20.02090.5
", + "bbox": [ + 534, + 328, + 937, + 426 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "based modeling and the naive connectivity modeling [16]. All experiments in this section are on the Retouch Dataset.", + "bbox": [ + 539, + 434, + 926, + 464 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Overall ablation study. The overall ablation study is reported in Table 4. The backbone (Exp. 1), a pretrained ResNet [75] encoder with a regular decoder, is from [62]. Exp. 2 is identical to [16] with a different backbone. Both connectivity modeling (Exp. 2) and directional modeling (Exp. 3 and 4) result in significant performance improvements. Especially, the considerable increases in the $DSC$ terms demonstrate that the model is becoming stable when dealing with the small fluid regions. Finally, by adding SDL (Exp. 5), all metrics got improved showing the impact of the distribution-based weighting scheme.", + "bbox": [ + 539, + 468, + 929, + 630 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Directional prior in SDE. The directional prior in the SDE module was designed to provide an initial prior to disentangle the directional features which will later be utilized across the entire network. Thus, Table 5 compares two experiments: the complete DconnNet and the one without directional prior, i.e., only PAM and CAM in each sub-path of SDE. Even when most of the network structure was kept unchanged, the network performed worse without the guidance of an initial directional embedding prior.", + "bbox": [ + 539, + 633, + 929, + 766 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Sub-path attention vs. single-path attention. In SDE, we applied a sub-path attention unit in each slice to capture the dependency between the contextual-unevenly sliced directional and categorical features. To demonstrate the effectiveness of the sub-path attention, we compared our proposed SDE with the alternative single-path attention units. We first compared it with a regular dual attention unit [10] which is the direct alternative to our SDE since", + "bbox": [ + 539, + 768, + 929, + 887 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "11531", + "bbox": [ + 480, + 943, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/8602d4fba45a068f335b04eeef9ece465d25d1f42ac2c305deb33b72197e02ad.jpg", + "table_caption": [ + "Table 5. Ablation study on directional prior." + ], + "table_footnote": [], + "table_body": "
DconnNetDSCDSCvAVDBACC
w/o. prior86.372.30.02389.1
w/. prior87.776.60.02090.5
", + "bbox": [ + 127, + 104, + 490, + 148 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/cf4a251248dd5e3b26e2dd2220a5c69c878c1ffa61ede4f7280aa26b1ac43605.jpg", + "table_caption": [ + "Table 6. Ablation study on Sub-path attention. Backbone_Conn is the connectivity-based modeling on backbone [16], DA is the dual attention, and NL is the non-local module." + ], + "table_footnote": [], + "table_body": "
Backbone_ConnDSC\\( DSC_v \\)AVDBACC
+ DA [10]84.769.50.02786.2
+ NL [42]85.170.00.02887.2
+SDE87.776.60.02090.5
", + "bbox": [ + 114, + 196, + 501, + 258 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "we used the same module in each sub-path. We also conducted an experiment with the non-local unit [42]. The results are shown in Table 6, which shows all metrics increase after introducing the sub-path mechanism.", + "bbox": [ + 112, + 268, + 503, + 327 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Disentanglement of directional subspace. To show that the directional subspace is disentangled from the shared latent space with the proposed sub-path slicing method, we conducted two experiments on the DconnNet's latent space. First, we used T-SNE to visualize the learned patchwise feature maps in the latent spaces before and after the SDE module of a trained DconnNet, as shown in Fig. 2. Applying SDE decoupled the latent space and changed the latent features' centered distribution to a polarized distribution. We interpret this as the decoupling process between the directional subspace and categorical subspace.", + "bbox": [ + 112, + 330, + 503, + 491 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Then, to show the well-structured directional subspace between channels, we visualize the learned channel embeddings in the latent spaces before and after the SDE module of a trained DconnNet, as in Fig. 10. After SDE, the channel embeddings naturally grouped into several distinctive parts, demonstrating the effectiveness of the sub-path excitation.", + "bbox": [ + 112, + 491, + 503, + 593 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Comparison of size density loss. Exp. 4 and 5 in Table 4 demonstrated the superiority of the proposed SDL in connectivity modeling. This subsection further analyzes SDL in a pixel-classification-based segmentation setting.", + "bbox": [ + 112, + 597, + 503, + 656 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In Table 7, we compared SDL with alternative loss functions with a similar idea of weighting the region-based Dice loss, including Exponential Logarithmical Loss [81], Focal Dice Loss [82], Dice loss [50], and Generalised Dice [83] based on two networks: U-Net and CPFNet. Our SDL achieves the highest DSC both image- and volume-wise. Moreover, it shows more stability when dealing with a two-level imbalanced medical dataset compared to feedback-based losses (e.g., Focal-like losses) since it is less sensitive to FP prediction on the negative training images.", + "bbox": [ + 112, + 656, + 503, + 801 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Model size. Table 1 compares different model sizes. DconnNet (36.42M parameters) performed far better than the backbone (33.16M) with only $\\sim 3\\mathrm{M}$ extra parameters. In SDE, due to the channel slicing, we quadratically reduced the size of each sub-path attention (0.196M) from the full-size dual attention [10] (23.35M), resulting in the", + "bbox": [ + 112, + 806, + 503, + 893 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6e8ee6707013eebd630cb2f4846ee37cd46cd345bc881c212ea4ee9f046a01c5.jpg", + "image_caption": [ + "Figure 10. Visualization of latent channel embeddings of DconnNet before and after SDE module using T-SNE. The colors in (b) indicate the unsupervised clustering result. When applied to SDE, the channel embeddings naturally grouped into several distinctive parts." + ], + "image_footnote": [], + "bbox": [ + 553, + 94, + 916, + 224 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/804e8f54de79bbc099cc616e30899af1b651f9ed40d0faa19cde4e4fe52f609e.jpg", + "table_caption": [ + "Table 7. Ablation study on loss function on Retouch Dataset." + ], + "table_footnote": [], + "table_body": "
LossU-NetCPFNet
DSCDSCvDSCDSCv
Exponential [81]Not Converged
Focal [82]
Dice [50]82.965.683.165.2
Generalised [83]80.154.180.955.5
SDL85.169.285.469.1
", + "bbox": [ + 545, + 316, + 924, + 414 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/4c6142fa4e12ebcc3f363ace1507e78f76ba989a9c5df25c9890abe40c46f8ad.jpg", + "table_caption": [ + "Table 8. The components' size of DconnNet." + ], + "table_footnote": [], + "table_body": "
ModuleResNet EncoderSDEIFDFinal DecoderConnect. ModelingTotal
Feature BlockSpace Block
Para. (M)21.801.5711.351.490.180.0336.42
", + "bbox": [ + 540, + 436, + 928, + 492 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "small size of the proposed SDE in Table 8. Also, changing the network to connectivity modeling only takes extra 0.03M parameters. Given the relatively small parameter increase, 3D connectivity modeling is a potential future direction for 3D image segmentation.", + "bbox": [ + 539, + 505, + 929, + 579 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 540, + 592, + 661, + 607 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper proposed a novel directional connectivity modeling network (DconnNet) for medical image segmentation. The core idea is to disentangle the directional subspace from the shared latent space and use the extracted directional features to enhance the overall data representation. We demonstrated the effectiveness of DconnNet in three ways. First, by statistical comparisons to other state-of-the-art methods, we showed the overall better performance of DconnNet. Then, we demonstrated its topology-preserving ability by qualitatively and quantitatively comparing DconnNet to other methods on a topologically sensitive dataset to other methods. Third, by visualizing the latent space of DconnNet, we revealed the disentanglement process of the directional subspace.", + "bbox": [ + 537, + 613, + 929, + 818 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgment", + "text_level": 1, + "bbox": [ + 540, + 830, + 692, + 847 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This research was supported in part by NIH R01 EY030124, U01 EY034687, R01 EY031033, UG1 EY033287, and R01 AG072732.", + "bbox": [ + 539, + 851, + 928, + 895 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "11532", + "bbox": [ + 480, + 943, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 114, + 92, + 210, + 107 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] P. L. Bazin, and D. L. Pham, \"Topology correction of segmented medical images using a fast-marching algorithm,\" Comput. 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Support, pp. 240-248, 2017." + ], + "bbox": [ + 114, + 90, + 503, + 758 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "11535", + "bbox": [ + 480, + 943, + 519, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Directional Connectivity-Based Segmentation of Medical Images/b9c53750-6c7d-4628-8a5d-c4d2ad764a83_model.json b/2023/Directional Connectivity-Based Segmentation of Medical Images/b9c53750-6c7d-4628-8a5d-c4d2ad764a83_model.json new file mode 100644 index 0000000000000000000000000000000000000000..77f301360081b169007df213810bd8cf221a976f --- /dev/null +++ b/2023/Directional Connectivity-Based Segmentation of Medical Images/b9c53750-6c7d-4628-8a5d-c4d2ad764a83_model.json @@ -0,0 +1,3192 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.02 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation." + }, + { + "type": "header", + "bbox": [ + 0.325, + 0.017, + 0.725, + 0.032 + ], + "angle": 0, + "content": "Except for this watermark, it is identical to the accepted version;" + }, + { + "type": "header", + "bbox": [ + 0.293, + 0.032, + 0.756, + 0.047 + ], + "angle": 0, + "content": "the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.207, + 0.107, + 0.842, + 0.13 + ], + "angle": 0, + "content": "Directional Connectivity-based Segmentation of Medical Images" + }, + { + "type": "text", + "bbox": [ + 0.335, + 0.142, + 0.434, + 0.159 + ], + "angle": 0, + "content": "Ziyun Yang" + }, + { + "type": "text", + "bbox": [ + 0.318, + 0.16, + 0.453, + 0.176 + ], + "angle": 0, + "content": "Duke University" + }, + { + "type": "text", + "bbox": [ + 0.275, + 0.177, + 0.496, + 0.193 + ], + "angle": 0, + "content": "Durham, NC, United States" + }, + { + "type": "text", + "bbox": [ + 0.281, + 0.194, + 0.49, + 0.21 + ], + "angle": 0, + "content": "ziyun.yang@duke.edu" + }, + { + "type": "text", + "bbox": [ + 0.604, + 0.142, + 0.699, + 0.158 + ], + "angle": 0, + "content": "Sina Farsiu" + }, + { + "type": "text", + "bbox": [ + 0.585, + 0.16, + 0.719, + 0.176 + ], + "angle": 0, + "content": "Duke University" + }, + { + "type": "text", + "bbox": [ + 0.542, + 0.177, + 0.762, + 0.193 + ], + "angle": 0, + "content": "Durham, NC, United States" + }, + { + "type": "text", + "bbox": [ + 0.542, + 0.194, + 0.762, + 0.209 + ], + "angle": 0, + "content": "sina.farsiu@duke.edu" + }, + { + "type": "title", + "bbox": [ + 0.27, + 0.27, + 0.35, + 0.287 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.303, + 0.506, + 0.566 + ], + "angle": 0, + "content": "Anatomical consistency in biomarker segmentation is crucial for many medical image analysis tasks. A promising paradigm for achieving anatomically consistent segmentation via deep networks is incorporating pixel connectivity, a basic concept in digital topology, to model inter-pixel relationships. However, previous works on connectivity modeling have ignored the rich channel-wise directional information in the latent space. In this work, we demonstrate that effective disentanglement of directional sub-space from the shared latent space can significantly enhance the feature representation in the connectivity-based network. To this end, we propose a directional connectivity modeling scheme for segmentation that decouples, tracks, and utilizes the directional information across the network. Experiments on various public medical image segmentation benchmarks show the effectiveness of our model as compared to the state-of-the-art methods. Code is available at https://github.com/Zyun-Y/DconnNet." + }, + { + "type": "title", + "bbox": [ + 0.116, + 0.595, + 0.248, + 0.61 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.616, + 0.504, + 0.805 + ], + "angle": 0, + "content": "Maintaining anatomical consistency in the segmentation of medical images is important but challenging, as minor geometric errors may change the global topology [1, 2] and cause functional mistakes in downstream clinical decision-making [3]. Anatomical consistency in images can be expressed with topological properties, such as pixel connectivity and adjacency [4, 5]. As such, by directly modeling the mutual information between pixels or regions, graph-based methods have long been used to correct topological and geometrical errors [6-8]. However, such classic machine vision techniques usually depend on manually defined priors and thus are not easily generalizable for a wide variety of applications." + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.806, + 0.504, + 0.894 + ], + "angle": 0, + "content": "Alternative to the classic approaches, deep learning-based segmentation methods utilized an encoder-decoder architecture [9] to learn from a group of pixels in a particular receptive field at each layer. More recently, significant progress has been made in capturing the interpixel dependency inside a network's latent space [10-12];" + }, + { + "type": "image", + "bbox": [ + 0.579, + 0.253, + 0.915, + 0.408 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.54, + 0.408, + 0.932, + 0.476 + ], + "angle": 0, + "content": "Figure 1. The latent space differences between traditional pixel-classification-based and connectivity-based models. In the former, only categorical features, e.g., boundaries, are highlighted; while in the latter, the feature map also contains directional information (e.g., the horizontal connections between boundary pixels)." + }, + { + "type": "image", + "bbox": [ + 0.543, + 0.479, + 0.93, + 0.593 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.54, + 0.595, + 0.931, + 0.662 + ], + "angle": 0, + "content": "Figure 2. The flows of the two groups of latent features (categorical and directional) in the latent space of DconnNet, are visualized by T-SNE [13]. They were first disentangled (Sec 3.2) and then effectively fused in a projected shared manifold (Sec 3.3). The colors are rendered based on the results of clustering." + }, + { + "type": "text", + "bbox": [ + 0.539, + 0.666, + 0.931, + 0.84 + ], + "angle": 0, + "content": "however, very few studies have been conducted on the problem modeling side of the networks. A typical segmentation network models the problem as a pure pixelwise classification task and uses a segmentation mask as the only label. Yet, this pixel-wise modeling scheme is suboptimal as it does not directly exploit inter-pixel relationships and geometrical properties [14, 15]. Thus, these models may result in low spatial coherence (i.e., inconsistent predictions for neighboring pixels that share similar spatial features) in their prediction [16]. Especially, when applied to high noise/artifacts medical data, the lower spatial consistency may lead to topological issues [17]." + }, + { + "type": "text", + "bbox": [ + 0.539, + 0.84, + 0.931, + 0.899 + ], + "angle": 0, + "content": "The concept of pixel connectivity has long been used to ensure the basic topological duality of separation and connectedness in digital images [18]. More recently, in the context of deep learning, the connectivity masks, reviewed" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.944, + 0.52, + 0.956 + ], + "angle": 0, + "content": "11525" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.12, + 0.091, + 0.498, + 0.215 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.114, + 0.218, + 0.504, + 0.298 + ], + "angle": 0, + "content": "Figure 3. Illustration of generating the connectivity mask from the segmentation mask by traversing 8-neighbor pixel connectivity. For each pixel, channel \\( C_i \\)'s binary value in the converted connectivity vector carries the categorical information (connected or not connected) while \\( i \\) encodes the directional information (direction of connection)." + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.302, + 0.504, + 0.549 + ], + "angle": 0, + "content": "in Section 2.1, have been introduced as a topological extension of the segmentation mask [15]. Using connectivity masks as training labels has several advantages over segmentation masks. In terms of problem modeling, using a connectivity mask inherently changes the problem from pixel-wise classification to connectivity prediction, which models and enhances the topological representation between pixels of interest. In terms of label representation, a connectivity mask is more informative in three ways: first, a connectivity mask stores the categorical information among the connections of pixels and it is inter-pixel relation-aware; second, it sparsely represents edge pixels [16]; third, it contains rich directional information channel-wisely. Thus, a network trained with connectivity masks has both categorical (reflected by connectivity) and directional features in its latent space, each of which forms a specific sub-latent space, as shown in Fig. 1." + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.55, + 0.504, + 0.651 + ], + "angle": 0, + "content": "In previous studies [15, 16, 19-22], these two groups of features were learned simultaneously through a shared network path which may result in highly coupled latent space and introduce redundancy [23]. Further, effectively disentangling meaningful subspaces from the shared latent space has been shown effective in accounting for the dependencies/independencies between features [24, 25]." + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.651, + 0.504, + 0.899 + ], + "angle": 0, + "content": "Inspired by the idea of latent space disentanglement, in this paper, we propose a novel directional connectivity-based segmentation network (DconnNet) to disentangle the directional subspace from the shared latent space and utilize the extracted directional features to enhance the overall data representation, as in Fig. 2. The disentangling process is conducted by a sub-path slicing-based module called Sub-path Direction Excitation (SDE). The directional-based feature enhancement is applied in a coarse-to-fine manner using an Interactive Feature-space Decoder (IFD) with two top-down interactive decoding flows. Finally, we propose a novel Size Density loss (SDL) that alleviates the common data imbalance problem in medical datasets with a label size distribution-based weighting scheme. With experiments on different public medical image analysis benchmarks, we demonstrate the superiority of DconnNet against other state-of-art methods." + }, + { + "type": "title", + "bbox": [ + 0.542, + 0.092, + 0.687, + 0.108 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.542, + 0.115, + 0.791, + 0.132 + ], + "angle": 0, + "content": "2.1. Deep connectivity modeling" + }, + { + "type": "text", + "bbox": [ + 0.539, + 0.138, + 0.931, + 0.474 + ], + "angle": 0, + "content": "In topology, pixel connectivity describes how neighboring pixels are related to each other [4]. Following broad utilization in characterizing topological properties in classic image processing methods [26, 27], connectivity has found new applications in deep learning-based image segmentation [15, 16, 19-22]. The connectivity-based segmentation networks use the connectivity mask (Fig. 3) as the label, defined as an 8-channel mask with each channel representing if a pixel on the original image belongs to the same class of interest with one of its neighboring pixels at a specific direction. The connectivity mask was first introduced and applied to image segmentation in [15]. This idea was later extended by other works, including [16] which showed the bilateral property of pixel connectivity in saliency detection, and [28] which modeled the cross-modality connectivity for radar-video data fusion. Meanwhile, the effectiveness of connectivity modeling has been demonstrated in different applications such as remote sensing segmentation [19], path planning [20], and medical image segmentation [21, 22, 29]. Although significant progress has been made in this field, we demonstrate that the rich directional information in the connectivity masks has not yet been fully utilized." + }, + { + "type": "title", + "bbox": [ + 0.541, + 0.482, + 0.804, + 0.497 + ], + "angle": 0, + "content": "2.2. Interpretation of latent space" + }, + { + "type": "text", + "bbox": [ + 0.539, + 0.503, + 0.931, + 0.635 + ], + "angle": 0, + "content": "Latent space is an embedding of a set of features in a deep network. Interpretation, alignment, and disentanglement of latent spaces are important in different computer vision techniques such as unsupervised learning [30], multi-modal information fusion [24, 31], generative models [32, 33], knowledge distillation [34, 35], and transfer learning [36]. However, the interpretation of latent space is challenging because it usually requires implicit domain knowledge based on human judgment [37]." + }, + { + "type": "text", + "bbox": [ + 0.539, + 0.635, + 0.931, + 0.795 + ], + "angle": 0, + "content": "To interpret the latent space, researchers either apply dimension reduction tools such as PCA [38], T-SNE [13], or develop interactive analysis tools [39]. To manipulate latent space, a variation autoencoder (VAE) can be used to map the input to latent space and disentangle/match the different latent spaces [40, 41]. In this work, we utilize the intrinsic property of the connectivity mask and propose a simple yet effective sub-path slicing-based method to disentangle the directional subspace from the shared latent space, followed by a visual demonstration of the effectiveness of our disentanglement process with T-SNE." + }, + { + "type": "title", + "bbox": [ + 0.541, + 0.804, + 0.776, + 0.82 + ], + "angle": 0, + "content": "2.3. Self-attention mechanism" + }, + { + "type": "text", + "bbox": [ + 0.539, + 0.827, + 0.931, + 0.872 + ], + "angle": 0, + "content": "Self-attention is widely used in computer vision as it can capture the dependencies between latent features. The self-attention mechanism is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.679, + 0.88, + 0.93, + 0.896 + ], + "angle": 0, + "content": "\\[\n\\mathbf {y} = f (\\alpha , g (\\mathbf {x})), \\tag {1}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.944, + 0.52, + 0.956 + ], + "angle": 0, + "content": "11526" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.123, + 0.089, + 0.905, + 0.288 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.114, + 0.29, + 0.923, + 0.318 + ], + "angle": 0, + "content": "Figure 4. The overview of the proposed DconnNet. It contains three parts: a pretrained ResNet encoder, a Sub-path Direction Excitation Module, and an Interactive Feature-space Decoder. The term \"up \\(N \\times\\) \" means upsampling with a stride of \\(N\\)." + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.324, + 0.504, + 0.523 + ], + "angle": 0, + "content": "where \\( x \\) is the input feature map, \\( g \\) is a unary function that computes the embedding of input, and \\( f \\) is usually a matrix multiplication [10, 42] or a simple dot product [11, 43, 44], depending on the definition of \\( \\alpha \\). \\( \\alpha \\) is the attention/relation map which can be a mutual relation map by spatial- or channel-wisely computing the similarity between one pixel with other pixels in a feature map, or between two related feature maps from the same feature space [10, 42]; it can be a contextual-spatial relation map generated by similarity estimation between a feature map and a latent vector with abstract contextual meaning [44, 45]. Broadly speaking, \\( \\alpha \\) can also be a single map [11] or a vector [43, 46] containing special contextual meaning." + }, + { + "type": "title", + "bbox": [ + 0.115, + 0.539, + 0.206, + 0.555 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.114, + 0.567, + 0.479, + 0.584 + ], + "angle": 0, + "content": "3.1. Directional space in connectivity modeling" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.589, + 0.504, + 0.734 + ], + "angle": 0, + "content": "Due to connectivity between different pixel classes and directions, there are two groups of features in the latent space of a connectivity-based network: categorical directional. Each group of features forms its specific subspace in the latent space. In a single-path connectivity network, these two subspaces are highly coupled (Fig. 2), resulting in low-discriminative features. We demonstrate that the efficient disentangling and effective utilization of the direction space can enhance the overall feature representation in the connectivity model." + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.735, + 0.504, + 0.895 + ], + "angle": 0, + "content": "In a connectivity mask, different channels represent different directions of the pixel connection. Thus, as the network goes deeper, it naturally stores directional information among channels. Based on this property, the directional features can be captured and manipulated through channel-wise operations. Specifically, we propose SDE to disentangle channel-wise directional features from the latent space, followed by IFD to extract the directional embeddings at different layers and use them to enhance the overall feature representation in a self-attention manner. The overall DconnNet structure is shown in Fig. 4." + }, + { + "type": "title", + "bbox": [ + 0.54, + 0.324, + 0.874, + 0.34 + ], + "angle": 0, + "content": "3.2. Sub-path Direction Excitation Module" + }, + { + "type": "text", + "bbox": [ + 0.539, + 0.345, + 0.931, + 0.569 + ], + "angle": 0, + "content": "Directional prior extraction. Taking advantage of the channel-wise directional information in the connectivity mask, a direct way to get distinctive directional embedding is to coarsely supervise the intermediate features and squeeze the channels of the auxiliary connectivity output. We denote the encoder's outputs as \\( e_n \\), where \\( n \\) is the \\( n_{th} \\) encoder layer. As shown in Fig. 5, we upsample \\( e_5 \\), the last encoder output, to the input size and get a preliminary output called \\( X_{prior} \\), which will be supervised to learn the connectivity mask in the loss calculation. Therefore, rich, distinctive directional information can be obtained from the channels of \\( X_{prior} \\). Then, we squeeze [43] \\( X_{prior} \\) through a global average pooling (GAP) and map the vector to the same dimension as the latent feature map \\( e_5 \\in R^{Ce_5 \\times He_5 \\times We_5} \\) with a \\( 1 \\times 1 \\) convolutional kernel \\( W_1 \\) [44]:" + }, + { + "type": "equation", + "bbox": [ + 0.627, + 0.571, + 0.929, + 0.613 + ], + "angle": 0, + "content": "\\[\nG A P (X) = \\frac {1}{H \\times W} \\sum_ {i = 1} ^ {H} \\sum_ {j = 1} ^ {W} X (i, j), \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.628, + 0.613, + 0.929, + 0.637 + ], + "angle": 0, + "content": "\\[\nv _ {p r i o r} = \\delta \\left(W _ {1} G A P \\left(X _ {p r i o r}\\right)\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.539, + 0.64, + 0.931, + 0.751 + ], + "angle": 0, + "content": "where \\( \\mathrm{H} \\) and \\( \\mathrm{W} \\) are the height and the width of a feature map, \\( W_{1} \\in R^{C_{e_{5}} \\times C_{k}} \\), \\( C_{k} \\) is the channel of \\( X_{prior} \\), and \\( \\delta \\) is the ReLu activation. The resulting \\( v_{prior} \\in R^{C_{e_{5}}} \\) has the directional information of a specific direction embedded in each entry. Next, we re-encode \\( v_{prior} \\) with a \\( 1 \\times 1 \\) convolution \\( W_{2} \\in R^{C_{e_{5}} \\times C_{e_{5}}} \\) and apply a sigmoid gating function \\( \\sigma \\) to normalize the projected vector:" + }, + { + "type": "equation", + "bbox": [ + 0.652, + 0.753, + 0.929, + 0.771 + ], + "angle": 0, + "content": "\\[\n\\alpha_ {p r i o r} = \\sigma \\left(W _ {2} v _ {p r i o r}\\right). \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.539, + 0.771, + 0.928, + 0.801 + ], + "angle": 0, + "content": "Since \\(\\alpha_{prior}\\) contains rich element-wise directional information, we call it the directional prior." + }, + { + "type": "text", + "bbox": [ + 0.539, + 0.803, + 0.931, + 0.88 + ], + "angle": 0, + "content": "Channel-wise slicing. To early disentangle the categorical and directional subspaces in the hidden layers, we split the latent features \\((e_5)\\) and the directional prior \\((\\alpha_{prior})\\) into eight parts by channel-wise slicing. We denote the \\(i_{th}\\) slices as \\(e_5^i\\) and \\(\\alpha_{prior}^{i}\\)." + }, + { + "type": "text", + "bbox": [ + 0.54, + 0.881, + 0.92, + 0.897 + ], + "angle": 0, + "content": "Sub-path excitation (SPE). We construct a sub-path for" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.944, + 0.519, + 0.956 + ], + "angle": 0, + "content": "11527" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.134, + 0.091, + 0.925, + 0.302 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.153, + 0.303, + 0.879, + 0.318 + ], + "angle": 0, + "content": "Figure 5. The SDE module, including three steps: direction prior extraction, channel-wise slicing, and sub-path excitation." + }, + { + "type": "image", + "bbox": [ + 0.137, + 0.334, + 0.516, + 0.491 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.142, + 0.492, + 0.474, + 0.506 + ], + "angle": 0, + "content": "Figure 6. The Interactive Feature-space Decoder (IFD)." + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.51, + 0.504, + 0.635 + ], + "angle": 0, + "content": "each pair of these feature-embedding slices. In each subpath, we pass the feature slice \\( e_5^i \\) through spatial and channel attention modules [10] to capture the long-range and inter-channel dependencies, resulting in \\( e_5^{i\\prime} \\). Next, we channel-wisely multiply the \\( \\alpha_{prior}^i \\) with \\( e_5^{i\\prime} \\) to selectivity highlight or suppress features with specific directional information. Then, we recode the output with a \\( 1\\times 1 \\) convolution kernel \\( W_3^i \\) and residually output it as:" + }, + { + "type": "equation", + "bbox": [ + 0.205, + 0.637, + 0.502, + 0.656 + ], + "angle": 0, + "content": "\\[\ne _ {S D E} ^ {i} = W _ {3} ^ {i} \\left(\\alpha_ {p r i o r} ^ {i} \\cdot e _ {5} ^ {i ^ {\\prime}}\\right) + e _ {5} ^ {i}. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.658, + 0.504, + 0.689 + ], + "angle": 0, + "content": "Finally, we stack all sub-paths outputs \\((e_{SDE}^{i})\\) into one and recode it, resulting in a new feature map, \\(e_{SDE}\\)." + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.688, + 0.504, + 0.897 + ], + "angle": 0, + "content": "Due to the slicing operation, each group of slices will only contain part of the full features. However, the shrink of discriminative contextual information in directional and categorical features differs. Specifically, \\(\\alpha_{prior}\\) is a highly discriminative directional embedding as it is a low-level linear combination of unique directional features. Thus, channel-wise slicing will cause significant shrinkage of directional information in each slice. However, \\(e_5\\) contains a group of high-level but less-discriminative categorical features which usually have low variations with others [47]. As a result, high channel-wise categorical correlation and redundancy [48] exist in \\(e_5\\). Therefore, a channel-wise slicing will result in less shrinkage [49] of high-discriminative categorical features in \\(e_5^i\\). By doing this, we" + }, + { + "type": "text", + "bbox": [ + 0.54, + 0.321, + 0.931, + 0.468 + ], + "angle": 0, + "content": "contextual-unevernly divide the directional and categorical features in each sub-path and make each sub-path shift its focus to the dominant features. Specifically, inside each sub-path, the network learns how to focus on the dominant class-specific information with less distinctive directional information emphasized in the channels. Between sub-paths, the network learns different distinctive directional information. Then, once we stack the sub-paths back, the direction information will be naturally disentangled from the original latent space and embedded into the channels." + }, + { + "type": "title", + "bbox": [ + 0.541, + 0.477, + 0.844, + 0.494 + ], + "angle": 0, + "content": "3.3. Interactive Feature-space Decoder" + }, + { + "type": "text", + "bbox": [ + 0.539, + 0.5, + 0.931, + 0.574 + ], + "angle": 0, + "content": "To ensure that the direction-dependent information can be effectively fused into feature maps in each layer, we propose an Interactive Feature-space Decoder with two top-down dynamically interactive flows, i.e., space flow and feature flow, as in Fig. 6." + }, + { + "type": "text", + "bbox": [ + 0.539, + 0.578, + 0.931, + 0.638 + ], + "angle": 0, + "content": "Feature maps. There are two types of feature maps in each layer of IFD: the main feature map \\( d_{i} \\) and the direction-enhanced map \\( r_{i} \\). At the first decoder layer (\\( i = 5 \\)), they are both initialized as the outputs of SDE:" + }, + { + "type": "equation", + "bbox": [ + 0.674, + 0.64, + 0.929, + 0.655 + ], + "angle": 0, + "content": "\\[\nr _ {5} = d _ {5} = e _ {S D E}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.539, + 0.656, + 0.924, + 0.672 + ], + "angle": 0, + "content": "and are updated separately in the space and feature flows." + }, + { + "type": "text", + "bbox": [ + 0.539, + 0.676, + 0.931, + 0.764 + ], + "angle": 0, + "content": "Space flow. In each space flow, a Space Block (S), which contains the embedding squeezing (ES) module and the manifold projection and enhancement (MPE) module, is used to enhance the directional representation. The ES module takes \\( r_i \\) as the input and outputs a directional embedding \\( n_i \\), a high-level directional representation as:" + }, + { + "type": "equation", + "bbox": [ + 0.681, + 0.766, + 0.928, + 0.782 + ], + "angle": 0, + "content": "\\[\nn _ {i} = G A P \\left(r _ {i}\\right). \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.539, + 0.784, + 0.931, + 0.877 + ], + "angle": 0, + "content": "Then, we use \\( n_i \\) as the input of MPE to enhance the directional representation in the main feature map \\( d_i \\). In MPE, we first project both the main feature map \\( d_i \\in R^{C_{d_i} \\times H_{d_i} \\times W_{d_i}} \\) and directional embedding \\( n_i \\in R^{C_{d_i}/2} \\) onto a shared manifold \\( R^{C_{d_i}} \\) at the current resolution with two \\( 1 \\times 1 \\) convolutional projectors:" + }, + { + "type": "equation", + "bbox": [ + 0.651, + 0.878, + 0.929, + 0.896 + ], + "angle": 0, + "content": "\\[\nd _ {i} ^ {\\prime} = W _ {d _ {i}} d _ {i}, n _ {i} ^ {\\prime} = W _ {n _ {i}} n _ {i}, \\tag {8}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.944, + 0.52, + 0.956 + ], + "angle": 0, + "content": "11528" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.113, + 0.092, + 0.505, + 0.171 + ], + "angle": 0, + "content": "where \\( W_{d_i} \\in R^{C_{d_i} \\times C_{d_i}} \\) and \\( W_{n_i} \\in R^{C_{d_i} \\times C_{d_i}/2} \\). Next, we model the category-direction relation by calculating the similarity between the projected directional embedding \\( n_i' \\) and feature map \\( d_i' \\) with a channel-wise dot product and a sigmoid activation:" + }, + { + "type": "equation", + "bbox": [ + 0.245, + 0.173, + 0.503, + 0.189 + ], + "angle": 0, + "content": "\\[\n\\alpha_ {n d} = \\sigma \\left(d _ {i} ^ {\\prime} \\cdot n _ {i} ^ {\\prime}\\right), \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.19, + 0.504, + 0.279 + ], + "angle": 0, + "content": "where \\(\\alpha_{nd}\\) is the normalized category-direction attention map in which the direction-relevant features are enhanced and the irrelevant features are suppressed across channels. Next, we enhance the directional information in the re-encoded original feature map \\(d^{\\prime \\prime}_i\\) with the attention map \\(\\alpha_{nd}\\) using a point-wise inner multiplication:" + }, + { + "type": "equation", + "bbox": [ + 0.245, + 0.281, + 0.502, + 0.297 + ], + "angle": 0, + "content": "\\[\nr _ {i - 1} = \\alpha_ {n d} \\cdot d ^ {\\prime \\prime} _ {i}. \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.298, + 0.504, + 0.372 + ], + "angle": 0, + "content": "By doing this, we effectively fuse the directional information into the feature map, resulting in a new direction-enhanced map \\( r_{i-1} \\), which will be further used as the input of feature flow and to generate the directional embedding \\( n_{i-1} \\) for the next layer." + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.376, + 0.504, + 0.435 + ], + "angle": 0, + "content": "Feature flow. Each feature flow contains a Feature Block (F), including two convolutional layers and an upsampling layer with a skip connection. It takes \\( r_i \\) as the input and outputs the upsampled main feature map \\( d_i \\)." + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.435, + 0.504, + 0.552 + ], + "angle": 0, + "content": "This top-down design and dynamic interactions between the two flows are mutually beneficial. Specifically, the embedding \\( n_i \\) extracted by space flow effectively fuses the directional information into the feature map \\( d_i \\) from the feature flow. On the other hand, the \\( d_i \\) generated by feature flow refines the directional representation \\( n_{i-1} \\) by adding supplementary directional information at a higher resolution to the space flow via MPE and ES." + }, + { + "type": "title", + "bbox": [ + 0.114, + 0.563, + 0.308, + 0.579 + ], + "angle": 0, + "content": "3.4. Connectivity output" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.586, + 0.504, + 0.674 + ], + "angle": 0, + "content": "We integrate the main feature maps \\( d_{1} \\) to \\( d_{4} \\) to get the final connectivity output \\( X \\). Every eight channels of \\( X \\) represent the connectivity of one class. In line with [16], we use the Bilateral Voting (BV) module in (11) and the Region-guided Channel Aggregation (RCA) module in (12) to get the final segmentation map." + }, + { + "type": "equation", + "bbox": [ + 0.166, + 0.676, + 0.501, + 0.731 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\bar {X} _ {j} (x, y) = \\bar {X} _ {9 - j} (x + a, y + b) \\\\ = X _ {j} (x, y) \\times X _ {9 - j} (x + a, y + b), (11) \\\\ \\tilde {S} (x, y) = \\max \\{\\tilde {X} _ {i} (x, y) \\} _ {i = 1} ^ {8}, (12) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.733, + 0.504, + 0.779 + ], + "angle": 0, + "content": "where \\(j\\) is the \\(j_{th}\\) channel, \\(a,b\\in \\{0,\\pm 1\\}\\) represent the location of neighboring pixel, \\(\\tilde{X}\\) is the Bicon map, \\(\\tilde{S}\\) is the final segmentation prediction [16]." + }, + { + "type": "title", + "bbox": [ + 0.114, + 0.786, + 0.255, + 0.8 + ], + "angle": 0, + "content": "3.5. Loss function" + }, + { + "type": "text", + "bbox": [ + 0.132, + 0.809, + 0.384, + 0.822 + ], + "angle": 0, + "content": "The total loss function of our work is:" + }, + { + "type": "equation", + "bbox": [ + 0.186, + 0.826, + 0.501, + 0.842 + ], + "angle": 0, + "content": "\\[\nL _ {\\text {t o t a l}} = L (\\text {m a i n}) + 0. 3 * L (\\text {p r i o r}), \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.845, + 0.504, + 0.89 + ], + "angle": 0, + "content": "where main represents the main output and prior represents the auxiliary output from SDE. Each loss \\( L \\) contains two parts, the Size Density Loss \\( L_{sd} \\) and the" + }, + { + "type": "text", + "bbox": [ + 0.541, + 0.092, + 0.751, + 0.108 + ], + "angle": 0, + "content": "original Bicon loss [16] \\(L_{bicon}\\)" + }, + { + "type": "equation", + "bbox": [ + 0.668, + 0.111, + 0.928, + 0.127 + ], + "angle": 0, + "content": "\\[\nL = L _ {s d} + L _ {b i c o n}. \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.539, + 0.13, + 0.931, + 0.188 + ], + "angle": 0, + "content": "Size Density Loss. Considering the imbalanced nature of the medical data, we propose a novel imbalanced loss function based on the label size distribution of the classes of interests in the dataset, called Size Density Loss." + }, + { + "type": "text", + "bbox": [ + 0.539, + 0.189, + 0.931, + 0.294 + ], + "angle": 0, + "content": "Before training, we sample all the training images and calculate the size of the label (total positive pixel number) on each image. Based on the extracted size distribution, for each class \\( j \\), we calculate the probability density function of label size \\( k \\), i.e., \\( PDF_{j}(k) \\). Then, in the training phase, for each training image, we calculate its label size for each class \\( j \\) and get its size density weight \\( P_{j}(k) \\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.617, + 0.295, + 0.929, + 0.333 + ], + "angle": 0, + "content": "\\[\nP _ {j} (k) = \\left\\{ \\begin{array}{l l} 1, & k = 0, \\\\ - \\log \\left(P D F _ {j} (k)\\right), & k \\neq 0. \\end{array} \\right. \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.558, + 0.335, + 0.878, + 0.351 + ], + "angle": 0, + "content": "We define the \\(L_{sd}\\) as a variant of Dice loss [50]:" + }, + { + "type": "equation", + "bbox": [ + 0.579, + 0.352, + 0.928, + 0.393 + ], + "angle": 0, + "content": "\\[\nL _ {s d} = \\sum_ {j} ^ {\\text {C l a s s}} P _ {j} (k) \\left(1 - \\frac {2 \\times \\sum \\left(S \\times G _ {s}\\right) + \\varepsilon}{\\sum S + \\sum G _ {s} + \\varepsilon}\\right), \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.54, + 0.395, + 0.931, + 0.425 + ], + "angle": 0, + "content": "where \\(S\\) is the final segmentation prediction, \\(\\varepsilon\\) is the stabilization term [51] and is usually set as 1." + }, + { + "type": "text", + "bbox": [ + 0.54, + 0.43, + 0.931, + 0.459 + ], + "angle": 0, + "content": "Bicon Loss term. We use the Bicon Loss \\( L_{bicon} \\) for connectivity modeling, as originally defined in [16]:" + }, + { + "type": "equation", + "bbox": [ + 0.627, + 0.461, + 0.928, + 0.477 + ], + "angle": 0, + "content": "\\[\nL _ {b i c o n} = L _ {d e c o u p l e} + L _ {c o n \\_ c o n s t}. \\tag {17}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.541, + 0.498, + 0.673, + 0.515 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.54, + 0.524, + 0.824, + 0.539 + ], + "angle": 0, + "content": "4.1. Datasets and evaluation metrics" + }, + { + "type": "text", + "bbox": [ + 0.539, + 0.545, + 0.931, + 0.634 + ], + "angle": 0, + "content": "We used three popular and diverse medical benchmark datasets in this paper. Specifically, we used Retouch [52] and ISIC2018 [53] datasets to evaluate the DconnNet performance for large-scale medical segmentation. We used CHASEDB1 [54] dataset to assess the topological performance of the DconnNet." + }, + { + "type": "text", + "bbox": [ + 0.539, + 0.64, + 0.931, + 0.89 + ], + "angle": 0, + "content": "Retouch is an OCT retinal fluids segmentation benchmark that has been widely used [55, 56] for assessing computer vision methods. It contains three classes of disease biomarkers: intraretinal fluid (IRF), subretinal fluid (SRF), and pigment epithelial detachment (PED). Retouch contains a training set of 70 OCT volumes from three OCT scanners, with frame sizes spanning from \\(512 \\times 496\\) to \\(512 \\times 1024\\) pixels. Retouch is a two-level balanced dataset: at the image level, biomarkers do not span the whole volume; at the pixel level, each biomarker has a relatively small size compared to the background. Since the testing labels are unavailable, we implemented the volume-level 3-fold cross-validation (CV) for each scanner on the training data set. Following the official guidelines [52], we used volume-level Dice [65] (\\(DSC_v\\)), image-level Dice (\\(DSC\\)), absolute volume difference (\\(AVD\\)), and volume-wise balanced accuracy [66] (\\(BACC\\)) to evaluate the results." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.944, + 0.52, + 0.956 + ], + "angle": 0, + "content": "11529" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.12, + 0.096, + 0.921, + 0.297 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.115, + 0.298, + 0.925, + 0.324 + ], + "angle": 0, + "content": "Figure 7. Visual comparison between the proposed DconnNet and other state-of-the-art methods on Retouch dataset. Different colors of masks represent different biomarker classes. Green: IRF; blue: SRF; red: PED." + }, + { + "type": "table_caption", + "bbox": [ + 0.117, + 0.33, + 0.501, + 0.357 + ], + "angle": 0, + "content": "Table 1. Results on Retouch dataset. Model size (M) and testing speed (FPS) are also reported. The best results are bold." + }, + { + "type": "table", + "bbox": [ + 0.11, + 0.358, + 0.509, + 0.506 + ], + "angle": 0, + "content": "
MethodDSCvDSCAVDBACCSize / Speed
DeepLabv3+ [57]60.282.70.02386.559.3 / 38
U-Net [58]66.184.20.02187.413.4 / 38
Att-UNet [59]65.383.40.02286.634.9 / 36
CE-Net [60]67.384.20.02684.629.0 / 37
nnU-Net [61]67.284.30.02386.430.0 / 20
CPFNet [62]69.085.70.02288.043.3 / 37
Curvature [63]68.284.70.02487.143.3 / 37
MsTGANet [64]68.985.00.02387.111.6 / 37
DconnNet78.287.70.02090.536.4 / 40
" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.513, + 0.502, + 0.587 + ], + "angle": 0, + "content": "ISIC 2018 is a popular medical segmentation benchmark [67-70] containing 2594 images of various types of skin lesions at different resolutions. Following [71], we used 5-fold CV and evaluated the results with Dice, IOU, accuracy (ACC), and precision (PREC) metrics." + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.591, + 0.504, + 0.709 + ], + "angle": 0, + "content": "CHASEDB1 is a vessel segmentation dataset containing 28 fundus images with a resolution of \\(999 \\times 960\\) pixels and two sets of manual annotations. The first manual annotation is adopted in this work as in [72]. We conducted 5-fold CV and evaluated the results with two volumetric metrics Dice and IOU; and three topology-similarity-based metric clDice, 0- and 1-Betti numbers \\((\\beta_0\\) and \\(\\beta_{1}\\)) [73] to measure the topological similarity." + }, + { + "type": "title", + "bbox": [ + 0.115, + 0.716, + 0.312, + 0.731 + ], + "angle": 0, + "content": "4.2. Experimental details" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.738, + 0.504, + 0.9 + ], + "angle": 0, + "content": "We generated the connectivity mask for each image via simple matrix operations [16]. We used the ImageNet [74] pretrained ResNet [75] as our encoder. The hyperparameter setting differed across datasets. For the Retouch dataset, we resized each image to \\(256 \\times 256\\) with no data augmentation and trained DconnNet with a 'poly' learning rate strategy. For ISIC2018, we resized images to \\(224 \\times 320\\) and used the same data augmentation and the parameter settings in [71]. For CHASEDB1, to fully use the limited data, we resized to \\(960 \\times 960\\) pixels and applied the same augmentations as in [60]. Since the CHASEDB1 dataset has a limited sample" + }, + { + "type": "text", + "bbox": [ + 0.54, + 0.33, + 0.931, + 0.404 + ], + "angle": 0, + "content": "size, we did not apply SDL loss to this dataset. We did not use any pre-processing for training and no post-processing for evaluation. The framework is built on PyTorch 1.7.0 [76]. All experiments are performed with a GPU NVIDIA GeForce GTX 3090 Ti." + }, + { + "type": "title", + "bbox": [ + 0.541, + 0.417, + 0.628, + 0.432 + ], + "angle": 0, + "content": "5. Results" + }, + { + "type": "title", + "bbox": [ + 0.541, + 0.441, + 0.783, + 0.457 + ], + "angle": 0, + "content": "5.1. Retinal fluid segmentation" + }, + { + "type": "text", + "bbox": [ + 0.539, + 0.464, + 0.93, + 0.648 + ], + "angle": 0, + "content": "Comparison of state-of-the-art methods. We compared the proposed DconnNet with eight state-of-the-art models for relevant applications, including DeepLab V3+ [57], U-Net [58], Attention UNet [59], CE-Net [60], nnU-Net [61], CPFNet [62], CPFNet-backboned Curvature Loss [63], and MsTGANet [64] in Table 1, which shows the superior performance of the proposed model. Specifically, the improvements on \\(DSC_{i}\\) and \\(DSC_{v}\\) demonstrate that our model has a consistent prediction on the small fluid regions, while the improvements on AVD and BACC demonstrate that our model has an overall more accurate prediction on the fluid regions, regardless of the target size." + }, + { + "type": "text", + "bbox": [ + 0.539, + 0.65, + 0.931, + 0.773 + ], + "angle": 0, + "content": "Qualitative study. In Fig. 7, we compared DconnNet with the top-six baselines. In image (a), all competing methods missed the tiny SRF region, while our DconnNet made an accurate prediction. In (b), all methods, except DconnNet, either made false positive (FP) segmentations of IRF or an incomplete segmentation on PED. In (c), only our DconnNet made the topologically connected prediction for PED and accurately segmented the IRF and SRF regions." + }, + { + "type": "title", + "bbox": [ + 0.541, + 0.78, + 0.768, + 0.796 + ], + "angle": 0, + "content": "5.2. Skin lesion segmentation" + }, + { + "type": "text", + "bbox": [ + 0.539, + 0.803, + 0.929, + 0.879 + ], + "angle": 0, + "content": "Comparison of state-of-the-art methods. In Table 2, we compared our method with U-Net [58], BCDU-Net [77], CE-Net [60], nnU-Net [61], HiFormer [78], CPFNet [62], FATNet [79], and Ms RED [71]. The proposed DconnNet outperformed all competitive models." + }, + { + "type": "text", + "bbox": [ + 0.54, + 0.883, + 0.924, + 0.899 + ], + "angle": 0, + "content": "Qualitative study. Due to limited space, in Figs. 8 and 9," + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.944, + 0.519, + 0.956 + ], + "angle": 0, + "content": "11530" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.12, + 0.092, + 0.498, + 0.104 + ], + "angle": 0, + "content": "Table 2. Results on ISIC2018 dataset. The best results are bold." + }, + { + "type": "table", + "bbox": [ + 0.12, + 0.105, + 0.498, + 0.256 + ], + "angle": 0, + "content": "
MethodDSCIOUACCPREC
U-Net [58]88.4181.2395.5390.7
BCDU-Net [77]88.3380.8495.4889.68
CE-Net [60]89.2382.3495.7691.51
nnU-Net [61]89.2482.3595.7991.45
HiFormer [78]88.5481.4595.5991.09
CPFNet [62]89.3482.6495.8991.38
FATNet [79]88.8481.7995.6291.18
Ms RED [71]89.4882.7195.8991.83
DconnNet90.4383.9196.3991.54
" + }, + { + "type": "image", + "bbox": [ + 0.12, + 0.261, + 0.184, + 0.298 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.184, + 0.261, + 0.246, + 0.298 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.246, + 0.261, + 0.31, + 0.298 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.31, + 0.261, + 0.372, + 0.298 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.372, + 0.261, + 0.444, + 0.298 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.444, + 0.261, + 0.5, + 0.298 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.12, + 0.298, + 0.184, + 0.333 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.184, + 0.298, + 0.246, + 0.333 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.246, + 0.298, + 0.31, + 0.333 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.31, + 0.298, + 0.372, + 0.333 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.372, + 0.298, + 0.444, + 0.333 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.444, + 0.298, + 0.5, + 0.333 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.12, + 0.333, + 0.184, + 0.369 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.184, + 0.333, + 0.246, + 0.369 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.246, + 0.333, + 0.31, + 0.369 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.31, + 0.333, + 0.372, + 0.369 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.372, + 0.333, + 0.444, + 0.369 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.444, + 0.333, + 0.5, + 0.369 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.141, + 0.37, + 0.163, + 0.377 + ], + "angle": 0, + "content": "Image" + }, + { + "type": "image_caption", + "bbox": [ + 0.174, + 0.37, + 0.191, + 0.377 + ], + "angle": 0, + "content": "" + }, + { + "type": "image_caption", + "bbox": [ + 0.223, + 0.37, + 0.232, + 0.377 + ], + "angle": 0, + "content": "" + }, + { + "type": "image_caption", + "bbox": [ + 0.255, + 0.37, + 0.299, + 0.377 + ], + "angle": 0, + "content": "CPFNet [62]" + }, + { + "type": "image_caption", + "bbox": [ + 0.335, + 0.37, + 0.362, + 0.377 + ], + "angle": 0, + "content": "Net [79]" + }, + { + "type": "image_caption", + "bbox": [ + 0.385, + 0.37, + 0.433, + 0.377 + ], + "angle": 0, + "content": "Ms RED [71]" + }, + { + "type": "image_caption", + "bbox": [ + 0.45, + 0.37, + 0.486, + 0.377 + ], + "angle": 0, + "content": "DconnNet" + }, + { + "type": "image_caption", + "bbox": [ + 0.174, + 0.381, + 0.442, + 0.395 + ], + "angle": 0, + "content": "Figure 8. Visualization on ISIC2018 dataset." + }, + { + "type": "text", + "bbox": [ + 0.114, + 0.405, + 0.504, + 0.496 + ], + "angle": 0, + "content": "we only compare the best-performing methods. In Fig. 8, DconnNet can accurately segment the lesion even under strong clinical confounders (e.g., the hairs in the first image). Also, DconnNet could learn the topology of skin lesions and make connected predictions in all cases, while others showed topological errors." + }, + { + "type": "title", + "bbox": [ + 0.115, + 0.505, + 0.396, + 0.521 + ], + "angle": 0, + "content": "5.3. Topological vessel segmentation" + }, + { + "type": "text", + "bbox": [ + 0.114, + 0.527, + 0.504, + 0.587 + ], + "angle": 0, + "content": "We used this experiment to demonstrate the topology-preserving ability of DconnNet in vessel segmentation, in which anatomical consistency is crucial. Due to the limited sampling size, we did not use SDL in this experiment." + }, + { + "type": "text", + "bbox": [ + 0.114, + 0.59, + 0.504, + 0.707 + ], + "angle": 0, + "content": "Comparison of state-of-the-art methods. We compared the results of DconnNet versus up-to-date leading methods, including U-Net [58], Att-UNet [59], GT-DLA [80], CE-Net [60], cclDiceLoss [73], and Graph Cut Loss [72] in Table 3. Our method surpassed other methods on all metrics. The superior performances of DconnNet on cclDice, \\(\\beta_0\\), and \\(\\beta_{1}\\), reflect the topological similarity between predictions and labels." + }, + { + "type": "text", + "bbox": [ + 0.114, + 0.712, + 0.504, + 0.83 + ], + "angle": 0, + "content": "Qualitative study on the vessel topology. In Fig. 9, we visually compared different methods. While in part due to limited training data DconnNet could not make perfect predictions across the whole images, it visually outperformed other methods. Our model's predicted vessels are mostly connected and with no significant topological errors. Other models showed more topological issues, e.g., in the form of non-simply connected regions." + }, + { + "type": "title", + "bbox": [ + 0.115, + 0.836, + 0.266, + 0.853 + ], + "angle": 0, + "content": "5.4. Ablation study" + }, + { + "type": "text", + "bbox": [ + 0.114, + 0.859, + 0.504, + 0.89 + ], + "angle": 0, + "content": "We conducted ablation studies to compare directional connectivity modeling with the traditional segmentation-" + }, + { + "type": "table_caption", + "bbox": [ + 0.558, + 0.092, + 0.912, + 0.104 + ], + "angle": 0, + "content": "Table 3. Results on CHASEDB1. The best results are bold." + }, + { + "type": "table", + "bbox": [ + 0.534, + 0.105, + 0.938, + 0.217 + ], + "angle": 0, + "content": "
MethodclDiceDSCIOUβ0β1
U-Net [58]74.074.759.31.3902.633
Att-UNet [59]75.375.761.01.3302.531
GT-DLA [80]81.080.667.40.7901.969
CE-Net [60]82.081.068.10.3831.670
clDiceLoss [73]82.981.068.10.3451.656
GraphCutLoss [72]82.681.468.80.4371.692
DconnNet83.381.869.40.3411.630
" + }, + { + "type": "image", + "bbox": [ + 0.544, + 0.222, + 0.61, + 0.276 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.61, + 0.222, + 0.738, + 0.276 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.738, + 0.222, + 0.867, + 0.276 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.867, + 0.222, + 0.931, + 0.276 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.593, + 0.282, + 0.877, + 0.295 + ], + "angle": 0, + "content": "Figure 9. Visualization on CHASEDB1 dataset." + }, + { + "type": "table_caption", + "bbox": [ + 0.54, + 0.3, + 0.93, + 0.328 + ], + "angle": 0, + "content": "Table 4. Ablation study of the Retouch Dataset. Conn stands for connectivity modeling with \\( L_{bicon} \\). DS stands for dice loss." + }, + { + "type": "table", + "bbox": [ + 0.535, + 0.329, + 0.938, + 0.427 + ], + "angle": 0, + "content": "
ConnModuleLossDSC\\( DSC_v \\)AVDBACC
SDEIFDDSSDL
1√83.265.00.02587.0
2 √√85.870.30.02487.7
3 √√√86.273.70.02387.9
4 √√√√86.775.20.02388.3
5 √√√√87.778.20.02090.5
" + }, + { + "type": "text", + "bbox": [ + 0.54, + 0.435, + 0.928, + 0.465 + ], + "angle": 0, + "content": "based modeling and the naive connectivity modeling [16]. All experiments in this section are on the Retouch Dataset." + }, + { + "type": "text", + "bbox": [ + 0.54, + 0.469, + 0.931, + 0.631 + ], + "angle": 0, + "content": "Overall ablation study. The overall ablation study is reported in Table 4. The backbone (Exp. 1), a pretrained ResNet [75] encoder with a regular decoder, is from [62]. Exp. 2 is identical to [16] with a different backbone. Both connectivity modeling (Exp. 2) and directional modeling (Exp. 3 and 4) result in significant performance improvements. Especially, the considerable increases in the \\(DSC\\) terms demonstrate that the model is becoming stable when dealing with the small fluid regions. Finally, by adding SDL (Exp. 5), all metrics got improved showing the impact of the distribution-based weighting scheme." + }, + { + "type": "text", + "bbox": [ + 0.54, + 0.634, + 0.931, + 0.767 + ], + "angle": 0, + "content": "Directional prior in SDE. The directional prior in the SDE module was designed to provide an initial prior to disentangle the directional features which will later be utilized across the entire network. Thus, Table 5 compares two experiments: the complete DconnNet and the one without directional prior, i.e., only PAM and CAM in each sub-path of SDE. Even when most of the network structure was kept unchanged, the network performed worse without the guidance of an initial directional embedding prior." + }, + { + "type": "text", + "bbox": [ + 0.54, + 0.77, + 0.931, + 0.888 + ], + "angle": 0, + "content": "Sub-path attention vs. single-path attention. In SDE, we applied a sub-path attention unit in each slice to capture the dependency between the contextual-unevenly sliced directional and categorical features. To demonstrate the effectiveness of the sub-path attention, we compared our proposed SDE with the alternative single-path attention units. We first compared it with a regular dual attention unit [10] which is the direct alternative to our SDE since" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.944, + 0.518, + 0.956 + ], + "angle": 0, + "content": "11531" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.185, + 0.092, + 0.449, + 0.105 + ], + "angle": 0, + "content": "Table 5. Ablation study on directional prior." + }, + { + "type": "table", + "bbox": [ + 0.129, + 0.106, + 0.491, + 0.15 + ], + "angle": 0, + "content": "
DconnNetDSCDSCvAVDBACC
w/o. prior86.372.30.02389.1
w/. prior87.776.60.02090.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.115, + 0.157, + 0.503, + 0.197 + ], + "angle": 0, + "content": "Table 6. Ablation study on Sub-path attention. Backbone_Conn is the connectivity-based modeling on backbone [16], DA is the dual attention, and NL is the non-local module." + }, + { + "type": "table", + "bbox": [ + 0.115, + 0.198, + 0.502, + 0.259 + ], + "angle": 0, + "content": "
Backbone_ConnDSC\\( DSC_v \\)AVDBACC
+ DA [10]84.769.50.02786.2
+ NL [42]85.170.00.02887.2
+SDE87.776.60.02090.5
" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.269, + 0.504, + 0.328 + ], + "angle": 0, + "content": "we used the same module in each sub-path. We also conducted an experiment with the non-local unit [42]. The results are shown in Table 6, which shows all metrics increase after introducing the sub-path mechanism." + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.332, + 0.504, + 0.492 + ], + "angle": 0, + "content": "Disentanglement of directional subspace. To show that the directional subspace is disentangled from the shared latent space with the proposed sub-path slicing method, we conducted two experiments on the DconnNet's latent space. First, we used T-SNE to visualize the learned patchwise feature maps in the latent spaces before and after the SDE module of a trained DconnNet, as shown in Fig. 2. Applying SDE decoupled the latent space and changed the latent features' centered distribution to a polarized distribution. We interpret this as the decoupling process between the directional subspace and categorical subspace." + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.492, + 0.504, + 0.594 + ], + "angle": 0, + "content": "Then, to show the well-structured directional subspace between channels, we visualize the learned channel embeddings in the latent spaces before and after the SDE module of a trained DconnNet, as in Fig. 10. After SDE, the channel embeddings naturally grouped into several distinctive parts, demonstrating the effectiveness of the sub-path excitation." + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.598, + 0.504, + 0.657 + ], + "angle": 0, + "content": "Comparison of size density loss. Exp. 4 and 5 in Table 4 demonstrated the superiority of the proposed SDL in connectivity modeling. This subsection further analyzes SDL in a pixel-classification-based segmentation setting." + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.657, + 0.504, + 0.803 + ], + "angle": 0, + "content": "In Table 7, we compared SDL with alternative loss functions with a similar idea of weighting the region-based Dice loss, including Exponential Logarithmical Loss [81], Focal Dice Loss [82], Dice loss [50], and Generalised Dice [83] based on two networks: U-Net and CPFNet. Our SDL achieves the highest DSC both image- and volume-wise. Moreover, it shows more stability when dealing with a two-level imbalanced medical dataset compared to feedback-based losses (e.g., Focal-like losses) since it is less sensitive to FP prediction on the negative training images." + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.807, + 0.504, + 0.895 + ], + "angle": 0, + "content": "Model size. Table 1 compares different model sizes. DconnNet (36.42M parameters) performed far better than the backbone (33.16M) with only \\(\\sim 3\\mathrm{M}\\) extra parameters. In SDE, due to the channel slicing, we quadratically reduced the size of each sub-path attention (0.196M) from the full-size dual attention [10] (23.35M), resulting in the" + }, + { + "type": "image", + "bbox": [ + 0.554, + 0.095, + 0.917, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.54, + 0.229, + 0.93, + 0.296 + ], + "angle": 0, + "content": "Figure 10. Visualization of latent channel embeddings of DconnNet before and after SDE module using T-SNE. The colors in (b) indicate the unsupervised clustering result. When applied to SDE, the channel embeddings naturally grouped into several distinctive parts." + }, + { + "type": "table_caption", + "bbox": [ + 0.552, + 0.303, + 0.917, + 0.316 + ], + "angle": 0, + "content": "Table 7. Ablation study on loss function on Retouch Dataset." + }, + { + "type": "table", + "bbox": [ + 0.547, + 0.317, + 0.925, + 0.415 + ], + "angle": 0, + "content": "
LossU-NetCPFNet
DSCDSCvDSCDSCv
Exponential [81]Not Converged
Focal [82]
Dice [50]82.965.683.165.2
Generalised [83]80.154.180.955.5
SDL85.169.285.469.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.601, + 0.422, + 0.869, + 0.435 + ], + "angle": 0, + "content": "Table 8. The components' size of DconnNet." + }, + { + "type": "table", + "bbox": [ + 0.542, + 0.438, + 0.929, + 0.493 + ], + "angle": 0, + "content": "
ModuleResNet EncoderSDEIFDFinal DecoderConnect. ModelingTotal
Feature BlockSpace Block
Para. (M)21.801.5711.351.490.180.0336.42
" + }, + { + "type": "text", + "bbox": [ + 0.54, + 0.506, + 0.931, + 0.58 + ], + "angle": 0, + "content": "small size of the proposed SDE in Table 8. Also, changing the network to connectivity modeling only takes extra 0.03M parameters. Given the relatively small parameter increase, 3D connectivity modeling is a potential future direction for 3D image segmentation." + }, + { + "type": "title", + "bbox": [ + 0.541, + 0.593, + 0.662, + 0.608 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.539, + 0.614, + 0.931, + 0.819 + ], + "angle": 0, + "content": "This paper proposed a novel directional connectivity modeling network (DconnNet) for medical image segmentation. The core idea is to disentangle the directional subspace from the shared latent space and use the extracted directional features to enhance the overall data representation. We demonstrated the effectiveness of DconnNet in three ways. First, by statistical comparisons to other state-of-the-art methods, we showed the overall better performance of DconnNet. Then, we demonstrated its topology-preserving ability by qualitatively and quantitatively comparing DconnNet to other methods on a topologically sensitive dataset to other methods. Third, by visualizing the latent space of DconnNet, we revealed the disentanglement process of the directional subspace." + }, + { + "type": "title", + "bbox": [ + 0.541, + 0.831, + 0.694, + 0.848 + ], + "angle": 0, + "content": "Acknowledgment" + }, + { + "type": "text", + "bbox": [ + 0.54, + 0.852, + 0.929, + 0.896 + ], + "angle": 0, + "content": "This research was supported in part by NIH R01 EY030124, U01 EY034687, R01 EY031033, UG1 EY033287, and R01 AG072732." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.944, + 0.52, + 0.956 + ], + "angle": 0, + "content": "11532" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.116, + 0.093, + 0.212, + 0.108 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.117, + 0.114, + 0.504, + 0.167 + ], + "angle": 0, + "content": "[1] P. L. Bazin, and D. L. Pham, \"Topology correction of segmented medical images using a fast-marching algorithm,\" Comput. 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A promising paradigm for achieving anatomically consistent segmentation via deep networks is incorporating pixel connectivity, a basic concept in digital topology, to model inter-pixel relationships. However, previous works on connectivity modeling have ignored the rich channel-wise directional information in the latent space. In this work, we demonstrate that effective disentanglement of directional sub-space from the shared latent space can significantly enhance the feature representation in the connectivity-based network. To this end, we propose a directional connectivity modeling scheme for segmentation that decouples, tracks, and utilizes the directional information across the network. Experiments on various public medical image segmentation benchmarks show the effectiveness of our model as compared to the state-of-the-art methods. Code is available at https://github.com/Zyun-Y/DconnNet. + +# 1. Introduction + +Maintaining anatomical consistency in the segmentation of medical images is important but challenging, as minor geometric errors may change the global topology [1, 2] and cause functional mistakes in downstream clinical decision-making [3]. Anatomical consistency in images can be expressed with topological properties, such as pixel connectivity and adjacency [4, 5]. As such, by directly modeling the mutual information between pixels or regions, graph-based methods have long been used to correct topological and geometrical errors [6-8]. However, such classic machine vision techniques usually depend on manually defined priors and thus are not easily generalizable for a wide variety of applications. + +Alternative to the classic approaches, deep learning-based segmentation methods utilized an encoder-decoder architecture [9] to learn from a group of pixels in a particular receptive field at each layer. More recently, significant progress has been made in capturing the interpixel dependency inside a network's latent space [10-12]; + +![](images/40ba21137e681264752775952d67769fe75f02d01b5b1fd014bc0a3d0a9278da.jpg) +Figure 1. The latent space differences between traditional pixel-classification-based and connectivity-based models. In the former, only categorical features, e.g., boundaries, are highlighted; while in the latter, the feature map also contains directional information (e.g., the horizontal connections between boundary pixels). + +![](images/7523ccfec1499837641b23ddc19bf8d9d54e5a792438268750c596d9e8b3f2ab.jpg) +Figure 2. The flows of the two groups of latent features (categorical and directional) in the latent space of DconnNet, are visualized by T-SNE [13]. They were first disentangled (Sec 3.2) and then effectively fused in a projected shared manifold (Sec 3.3). The colors are rendered based on the results of clustering. + +however, very few studies have been conducted on the problem modeling side of the networks. A typical segmentation network models the problem as a pure pixelwise classification task and uses a segmentation mask as the only label. Yet, this pixel-wise modeling scheme is suboptimal as it does not directly exploit inter-pixel relationships and geometrical properties [14, 15]. Thus, these models may result in low spatial coherence (i.e., inconsistent predictions for neighboring pixels that share similar spatial features) in their prediction [16]. Especially, when applied to high noise/artifacts medical data, the lower spatial consistency may lead to topological issues [17]. + +The concept of pixel connectivity has long been used to ensure the basic topological duality of separation and connectedness in digital images [18]. More recently, in the context of deep learning, the connectivity masks, reviewed + +![](images/0099ae811e168b8b62f042f2be4ab122fdb96ef7be584fd0dfabf8a20d4c0979.jpg) +Figure 3. Illustration of generating the connectivity mask from the segmentation mask by traversing 8-neighbor pixel connectivity. For each pixel, channel $C_i$ 's binary value in the converted connectivity vector carries the categorical information (connected or not connected) while $i$ encodes the directional information (direction of connection). + +in Section 2.1, have been introduced as a topological extension of the segmentation mask [15]. Using connectivity masks as training labels has several advantages over segmentation masks. In terms of problem modeling, using a connectivity mask inherently changes the problem from pixel-wise classification to connectivity prediction, which models and enhances the topological representation between pixels of interest. In terms of label representation, a connectivity mask is more informative in three ways: first, a connectivity mask stores the categorical information among the connections of pixels and it is inter-pixel relation-aware; second, it sparsely represents edge pixels [16]; third, it contains rich directional information channel-wisely. Thus, a network trained with connectivity masks has both categorical (reflected by connectivity) and directional features in its latent space, each of which forms a specific sub-latent space, as shown in Fig. 1. + +In previous studies [15, 16, 19-22], these two groups of features were learned simultaneously through a shared network path which may result in highly coupled latent space and introduce redundancy [23]. Further, effectively disentangling meaningful subspaces from the shared latent space has been shown effective in accounting for the dependencies/independencies between features [24, 25]. + +Inspired by the idea of latent space disentanglement, in this paper, we propose a novel directional connectivity-based segmentation network (DconnNet) to disentangle the directional subspace from the shared latent space and utilize the extracted directional features to enhance the overall data representation, as in Fig. 2. The disentangling process is conducted by a sub-path slicing-based module called Sub-path Direction Excitation (SDE). The directional-based feature enhancement is applied in a coarse-to-fine manner using an Interactive Feature-space Decoder (IFD) with two top-down interactive decoding flows. Finally, we propose a novel Size Density loss (SDL) that alleviates the common data imbalance problem in medical datasets with a label size distribution-based weighting scheme. With experiments on different public medical image analysis benchmarks, we demonstrate the superiority of DconnNet against other state-of-art methods. + +# 2. Related Work + +# 2.1. Deep connectivity modeling + +In topology, pixel connectivity describes how neighboring pixels are related to each other [4]. Following broad utilization in characterizing topological properties in classic image processing methods [26, 27], connectivity has found new applications in deep learning-based image segmentation [15, 16, 19-22]. The connectivity-based segmentation networks use the connectivity mask (Fig. 3) as the label, defined as an 8-channel mask with each channel representing if a pixel on the original image belongs to the same class of interest with one of its neighboring pixels at a specific direction. The connectivity mask was first introduced and applied to image segmentation in [15]. This idea was later extended by other works, including [16] which showed the bilateral property of pixel connectivity in saliency detection, and [28] which modeled the cross-modality connectivity for radar-video data fusion. Meanwhile, the effectiveness of connectivity modeling has been demonstrated in different applications such as remote sensing segmentation [19], path planning [20], and medical image segmentation [21, 22, 29]. Although significant progress has been made in this field, we demonstrate that the rich directional information in the connectivity masks has not yet been fully utilized. + +# 2.2. Interpretation of latent space + +Latent space is an embedding of a set of features in a deep network. Interpretation, alignment, and disentanglement of latent spaces are important in different computer vision techniques such as unsupervised learning [30], multi-modal information fusion [24, 31], generative models [32, 33], knowledge distillation [34, 35], and transfer learning [36]. However, the interpretation of latent space is challenging because it usually requires implicit domain knowledge based on human judgment [37]. + +To interpret the latent space, researchers either apply dimension reduction tools such as PCA [38], T-SNE [13], or develop interactive analysis tools [39]. To manipulate latent space, a variation autoencoder (VAE) can be used to map the input to latent space and disentangle/match the different latent spaces [40, 41]. In this work, we utilize the intrinsic property of the connectivity mask and propose a simple yet effective sub-path slicing-based method to disentangle the directional subspace from the shared latent space, followed by a visual demonstration of the effectiveness of our disentanglement process with T-SNE. + +# 2.3. Self-attention mechanism + +Self-attention is widely used in computer vision as it can capture the dependencies between latent features. The self-attention mechanism is defined as: + +$$ +\mathbf {y} = f (\alpha , g (\mathbf {x})), \tag {1} +$$ + +![](images/d1bd85b28bd12db36e57db595a91c999ca99c3d16dec624dcc06735035c33c0b.jpg) +Figure 4. The overview of the proposed DconnNet. It contains three parts: a pretrained ResNet encoder, a Sub-path Direction Excitation Module, and an Interactive Feature-space Decoder. The term "up $N \times$ " means upsampling with a stride of $N$ . + +where $x$ is the input feature map, $g$ is a unary function that computes the embedding of input, and $f$ is usually a matrix multiplication [10, 42] or a simple dot product [11, 43, 44], depending on the definition of $\alpha$ . $\alpha$ is the attention/relation map which can be a mutual relation map by spatial- or channel-wisely computing the similarity between one pixel with other pixels in a feature map, or between two related feature maps from the same feature space [10, 42]; it can be a contextual-spatial relation map generated by similarity estimation between a feature map and a latent vector with abstract contextual meaning [44, 45]. Broadly speaking, $\alpha$ can also be a single map [11] or a vector [43, 46] containing special contextual meaning. + +# 3. Method + +# 3.1. Directional space in connectivity modeling + +Due to connectivity between different pixel classes and directions, there are two groups of features in the latent space of a connectivity-based network: categorical directional. Each group of features forms its specific subspace in the latent space. In a single-path connectivity network, these two subspaces are highly coupled (Fig. 2), resulting in low-discriminative features. We demonstrate that the efficient disentangling and effective utilization of the direction space can enhance the overall feature representation in the connectivity model. + +In a connectivity mask, different channels represent different directions of the pixel connection. Thus, as the network goes deeper, it naturally stores directional information among channels. Based on this property, the directional features can be captured and manipulated through channel-wise operations. Specifically, we propose SDE to disentangle channel-wise directional features from the latent space, followed by IFD to extract the directional embeddings at different layers and use them to enhance the overall feature representation in a self-attention manner. The overall DconnNet structure is shown in Fig. 4. + +# 3.2. Sub-path Direction Excitation Module + +Directional prior extraction. Taking advantage of the channel-wise directional information in the connectivity mask, a direct way to get distinctive directional embedding is to coarsely supervise the intermediate features and squeeze the channels of the auxiliary connectivity output. We denote the encoder's outputs as $e_n$ , where $n$ is the $n_{th}$ encoder layer. As shown in Fig. 5, we upsample $e_5$ , the last encoder output, to the input size and get a preliminary output called $X_{prior}$ , which will be supervised to learn the connectivity mask in the loss calculation. Therefore, rich, distinctive directional information can be obtained from the channels of $X_{prior}$ . Then, we squeeze [43] $X_{prior}$ through a global average pooling (GAP) and map the vector to the same dimension as the latent feature map $e_5 \in R^{Ce_5 \times He_5 \times We_5}$ with a $1 \times 1$ convolutional kernel $W_1$ [44]: + +$$ +G A P (X) = \frac {1}{H \times W} \sum_ {i = 1} ^ {H} \sum_ {j = 1} ^ {W} X (i, j), \tag {2} +$$ + +$$ +v _ {p r i o r} = \delta \left(W _ {1} G A P \left(X _ {p r i o r}\right)\right), \tag {3} +$$ + +where $\mathrm{H}$ and $\mathrm{W}$ are the height and the width of a feature map, $W_{1} \in R^{C_{e_{5}} \times C_{k}}$ , $C_{k}$ is the channel of $X_{prior}$ , and $\delta$ is the ReLu activation. The resulting $v_{prior} \in R^{C_{e_{5}}}$ has the directional information of a specific direction embedded in each entry. Next, we re-encode $v_{prior}$ with a $1 \times 1$ convolution $W_{2} \in R^{C_{e_{5}} \times C_{e_{5}}}$ and apply a sigmoid gating function $\sigma$ to normalize the projected vector: + +$$ +\alpha_ {p r i o r} = \sigma \left(W _ {2} v _ {p r i o r}\right). \tag {4} +$$ + +Since $\alpha_{prior}$ contains rich element-wise directional information, we call it the directional prior. + +Channel-wise slicing. To early disentangle the categorical and directional subspaces in the hidden layers, we split the latent features $(e_5)$ and the directional prior $(\alpha_{prior})$ into eight parts by channel-wise slicing. We denote the $i_{th}$ slices as $e_5^i$ and $\alpha_{prior}^{i}$ . + +Sub-path excitation (SPE). We construct a sub-path for + +![](images/4910310916cd4c502f86ac3a626708c63e5b2a590eb1545c877313387b29421e.jpg) +Figure 5. The SDE module, including three steps: direction prior extraction, channel-wise slicing, and sub-path excitation. + +![](images/5ceeeb35b134fe49d31d5d85d0ed1572822a3d07f3423d9824b3644887ae9135.jpg) +Figure 6. The Interactive Feature-space Decoder (IFD). + +each pair of these feature-embedding slices. In each subpath, we pass the feature slice $e_5^i$ through spatial and channel attention modules [10] to capture the long-range and inter-channel dependencies, resulting in $e_5^{i\prime}$ . Next, we channel-wisely multiply the $\alpha_{prior}^i$ with $e_5^{i\prime}$ to selectivity highlight or suppress features with specific directional information. Then, we recode the output with a $1\times 1$ convolution kernel $W_3^i$ and residually output it as: + +$$ +e _ {S D E} ^ {i} = W _ {3} ^ {i} \left(\alpha_ {p r i o r} ^ {i} \cdot e _ {5} ^ {i ^ {\prime}}\right) + e _ {5} ^ {i}. \tag {5} +$$ + +Finally, we stack all sub-paths outputs $(e_{SDE}^{i})$ into one and recode it, resulting in a new feature map, $e_{SDE}$ . + +Due to the slicing operation, each group of slices will only contain part of the full features. However, the shrink of discriminative contextual information in directional and categorical features differs. Specifically, $\alpha_{prior}$ is a highly discriminative directional embedding as it is a low-level linear combination of unique directional features. Thus, channel-wise slicing will cause significant shrinkage of directional information in each slice. However, $e_5$ contains a group of high-level but less-discriminative categorical features which usually have low variations with others [47]. As a result, high channel-wise categorical correlation and redundancy [48] exist in $e_5$ . Therefore, a channel-wise slicing will result in less shrinkage [49] of high-discriminative categorical features in $e_5^i$ . By doing this, we + +contextual-unevernly divide the directional and categorical features in each sub-path and make each sub-path shift its focus to the dominant features. Specifically, inside each sub-path, the network learns how to focus on the dominant class-specific information with less distinctive directional information emphasized in the channels. Between sub-paths, the network learns different distinctive directional information. Then, once we stack the sub-paths back, the direction information will be naturally disentangled from the original latent space and embedded into the channels. + +# 3.3. Interactive Feature-space Decoder + +To ensure that the direction-dependent information can be effectively fused into feature maps in each layer, we propose an Interactive Feature-space Decoder with two top-down dynamically interactive flows, i.e., space flow and feature flow, as in Fig. 6. + +Feature maps. There are two types of feature maps in each layer of IFD: the main feature map $d_{i}$ and the direction-enhanced map $r_{i}$ . At the first decoder layer ( $i = 5$ ), they are both initialized as the outputs of SDE: + +$$ +r _ {5} = d _ {5} = e _ {S D E}, \tag {6} +$$ + +and are updated separately in the space and feature flows. + +Space flow. In each space flow, a Space Block (S), which contains the embedding squeezing (ES) module and the manifold projection and enhancement (MPE) module, is used to enhance the directional representation. The ES module takes $r_i$ as the input and outputs a directional embedding $n_i$ , a high-level directional representation as: + +$$ +n _ {i} = G A P \left(r _ {i}\right). \tag {7} +$$ + +Then, we use $n_i$ as the input of MPE to enhance the directional representation in the main feature map $d_i$ . In MPE, we first project both the main feature map $d_i \in R^{C_{d_i} \times H_{d_i} \times W_{d_i}}$ and directional embedding $n_i \in R^{C_{d_i}/2}$ onto a shared manifold $R^{C_{d_i}}$ at the current resolution with two $1 \times 1$ convolutional projectors: + +$$ +d _ {i} ^ {\prime} = W _ {d _ {i}} d _ {i}, n _ {i} ^ {\prime} = W _ {n _ {i}} n _ {i}, \tag {8} +$$ + +where $W_{d_i} \in R^{C_{d_i} \times C_{d_i}}$ and $W_{n_i} \in R^{C_{d_i} \times C_{d_i}/2}$ . Next, we model the category-direction relation by calculating the similarity between the projected directional embedding $n_i'$ and feature map $d_i'$ with a channel-wise dot product and a sigmoid activation: + +$$ +\alpha_ {n d} = \sigma \left(d _ {i} ^ {\prime} \cdot n _ {i} ^ {\prime}\right), \tag {9} +$$ + +where $\alpha_{nd}$ is the normalized category-direction attention map in which the direction-relevant features are enhanced and the irrelevant features are suppressed across channels. Next, we enhance the directional information in the re-encoded original feature map $d^{\prime \prime}_i$ with the attention map $\alpha_{nd}$ using a point-wise inner multiplication: + +$$ +r _ {i - 1} = \alpha_ {n d} \cdot d ^ {\prime \prime} _ {i}. \tag {10} +$$ + +By doing this, we effectively fuse the directional information into the feature map, resulting in a new direction-enhanced map $r_{i-1}$ , which will be further used as the input of feature flow and to generate the directional embedding $n_{i-1}$ for the next layer. + +Feature flow. Each feature flow contains a Feature Block (F), including two convolutional layers and an upsampling layer with a skip connection. It takes $r_i$ as the input and outputs the upsampled main feature map $d_i$ . + +This top-down design and dynamic interactions between the two flows are mutually beneficial. Specifically, the embedding $n_i$ extracted by space flow effectively fuses the directional information into the feature map $d_i$ from the feature flow. On the other hand, the $d_i$ generated by feature flow refines the directional representation $n_{i-1}$ by adding supplementary directional information at a higher resolution to the space flow via MPE and ES. + +# 3.4. Connectivity output + +We integrate the main feature maps $d_{1}$ to $d_{4}$ to get the final connectivity output $X$ . Every eight channels of $X$ represent the connectivity of one class. In line with [16], we use the Bilateral Voting (BV) module in (11) and the Region-guided Channel Aggregation (RCA) module in (12) to get the final segmentation map. + +$$ +\begin{array}{l} \bar {X} _ {j} (x, y) = \bar {X} _ {9 - j} (x + a, y + b) \\ = X _ {j} (x, y) \times X _ {9 - j} (x + a, y + b), (11) \\ \tilde {S} (x, y) = \max \{\tilde {X} _ {i} (x, y) \} _ {i = 1} ^ {8}, (12) \\ \end{array} +$$ + +where $j$ is the $j_{th}$ channel, $a,b\in \{0,\pm 1\}$ represent the location of neighboring pixel, $\tilde{X}$ is the Bicon map, $\tilde{S}$ is the final segmentation prediction [16]. + +# 3.5. Loss function + +The total loss function of our work is: + +$$ +L _ {\text {t o t a l}} = L (\text {m a i n}) + 0. 3 * L (\text {p r i o r}), \tag {13} +$$ + +where main represents the main output and prior represents the auxiliary output from SDE. Each loss $L$ contains two parts, the Size Density Loss $L_{sd}$ and the + +original Bicon loss [16] $L_{bicon}$ + +$$ +L = L _ {s d} + L _ {b i c o n}. \tag {14} +$$ + +Size Density Loss. Considering the imbalanced nature of the medical data, we propose a novel imbalanced loss function based on the label size distribution of the classes of interests in the dataset, called Size Density Loss. + +Before training, we sample all the training images and calculate the size of the label (total positive pixel number) on each image. Based on the extracted size distribution, for each class $j$ , we calculate the probability density function of label size $k$ , i.e., $PDF_{j}(k)$ . Then, in the training phase, for each training image, we calculate its label size for each class $j$ and get its size density weight $P_{j}(k)$ as: + +$$ +P _ {j} (k) = \left\{ \begin{array}{l l} 1, & k = 0, \\ - \log \left(P D F _ {j} (k)\right), & k \neq 0. \end{array} \right. \tag {15} +$$ + +We define the $L_{sd}$ as a variant of Dice loss [50]: + +$$ +L _ {s d} = \sum_ {j} ^ {\text {C l a s s}} P _ {j} (k) \left(1 - \frac {2 \times \sum \left(S \times G _ {s}\right) + \varepsilon}{\sum S + \sum G _ {s} + \varepsilon}\right), \tag {16} +$$ + +where $S$ is the final segmentation prediction, $\varepsilon$ is the stabilization term [51] and is usually set as 1. + +Bicon Loss term. We use the Bicon Loss $L_{bicon}$ for connectivity modeling, as originally defined in [16]: + +$$ +L _ {b i c o n} = L _ {d e c o u p l e} + L _ {c o n \_ c o n s t}. \tag {17} +$$ + +# 4. Experiments + +# 4.1. Datasets and evaluation metrics + +We used three popular and diverse medical benchmark datasets in this paper. Specifically, we used Retouch [52] and ISIC2018 [53] datasets to evaluate the DconnNet performance for large-scale medical segmentation. We used CHASEDB1 [54] dataset to assess the topological performance of the DconnNet. + +Retouch is an OCT retinal fluids segmentation benchmark that has been widely used [55, 56] for assessing computer vision methods. It contains three classes of disease biomarkers: intraretinal fluid (IRF), subretinal fluid (SRF), and pigment epithelial detachment (PED). Retouch contains a training set of 70 OCT volumes from three OCT scanners, with frame sizes spanning from $512 \times 496$ to $512 \times 1024$ pixels. Retouch is a two-level balanced dataset: at the image level, biomarkers do not span the whole volume; at the pixel level, each biomarker has a relatively small size compared to the background. Since the testing labels are unavailable, we implemented the volume-level 3-fold cross-validation (CV) for each scanner on the training data set. Following the official guidelines [52], we used volume-level Dice [65] ( $DSC_v$ ), image-level Dice ( $DSC$ ), absolute volume difference ( $AVD$ ), and volume-wise balanced accuracy [66] ( $BACC$ ) to evaluate the results. + +![](images/87ec234d67e748f46f4d29a094996dfc527ad655793c98fbe3a3e6d7865c9429.jpg) +Figure 7. Visual comparison between the proposed DconnNet and other state-of-the-art methods on Retouch dataset. Different colors of masks represent different biomarker classes. Green: IRF; blue: SRF; red: PED. + +Table 1. Results on Retouch dataset. Model size (M) and testing speed (FPS) are also reported. The best results are bold. + +
MethodDSCvDSCAVDBACCSize / Speed
DeepLabv3+ [57]60.282.70.02386.559.3 / 38
U-Net [58]66.184.20.02187.413.4 / 38
Att-UNet [59]65.383.40.02286.634.9 / 36
CE-Net [60]67.384.20.02684.629.0 / 37
nnU-Net [61]67.284.30.02386.430.0 / 20
CPFNet [62]69.085.70.02288.043.3 / 37
Curvature [63]68.284.70.02487.143.3 / 37
MsTGANet [64]68.985.00.02387.111.6 / 37
DconnNet78.287.70.02090.536.4 / 40
+ +ISIC 2018 is a popular medical segmentation benchmark [67-70] containing 2594 images of various types of skin lesions at different resolutions. Following [71], we used 5-fold CV and evaluated the results with Dice, IOU, accuracy (ACC), and precision (PREC) metrics. + +CHASEDB1 is a vessel segmentation dataset containing 28 fundus images with a resolution of $999 \times 960$ pixels and two sets of manual annotations. The first manual annotation is adopted in this work as in [72]. We conducted 5-fold CV and evaluated the results with two volumetric metrics Dice and IOU; and three topology-similarity-based metric clDice, 0- and 1-Betti numbers $(\beta_0$ and $\beta_{1}$ ) [73] to measure the topological similarity. + +# 4.2. Experimental details + +We generated the connectivity mask for each image via simple matrix operations [16]. We used the ImageNet [74] pretrained ResNet [75] as our encoder. The hyperparameter setting differed across datasets. For the Retouch dataset, we resized each image to $256 \times 256$ with no data augmentation and trained DconnNet with a 'poly' learning rate strategy. For ISIC2018, we resized images to $224 \times 320$ and used the same data augmentation and the parameter settings in [71]. For CHASEDB1, to fully use the limited data, we resized to $960 \times 960$ pixels and applied the same augmentations as in [60]. Since the CHASEDB1 dataset has a limited sample + +size, we did not apply SDL loss to this dataset. We did not use any pre-processing for training and no post-processing for evaluation. The framework is built on PyTorch 1.7.0 [76]. All experiments are performed with a GPU NVIDIA GeForce GTX 3090 Ti. + +# 5. Results + +# 5.1. Retinal fluid segmentation + +Comparison of state-of-the-art methods. We compared the proposed DconnNet with eight state-of-the-art models for relevant applications, including DeepLab V3+ [57], U-Net [58], Attention UNet [59], CE-Net [60], nnU-Net [61], CPFNet [62], CPFNet-backboned Curvature Loss [63], and MsTGANet [64] in Table 1, which shows the superior performance of the proposed model. Specifically, the improvements on $DSC_{i}$ and $DSC_{v}$ demonstrate that our model has a consistent prediction on the small fluid regions, while the improvements on AVD and BACC demonstrate that our model has an overall more accurate prediction on the fluid regions, regardless of the target size. + +Qualitative study. In Fig. 7, we compared DconnNet with the top-six baselines. In image (a), all competing methods missed the tiny SRF region, while our DconnNet made an accurate prediction. In (b), all methods, except DconnNet, either made false positive (FP) segmentations of IRF or an incomplete segmentation on PED. In (c), only our DconnNet made the topologically connected prediction for PED and accurately segmented the IRF and SRF regions. + +# 5.2. Skin lesion segmentation + +Comparison of state-of-the-art methods. In Table 2, we compared our method with U-Net [58], BCDU-Net [77], CE-Net [60], nnU-Net [61], HiFormer [78], CPFNet [62], FATNet [79], and Ms RED [71]. The proposed DconnNet outperformed all competitive models. + +Qualitative study. Due to limited space, in Figs. 8 and 9, + +Table 2. Results on ISIC2018 dataset. The best results are bold. + +
MethodDSCIOUACCPREC
U-Net [58]88.4181.2395.5390.7
BCDU-Net [77]88.3380.8495.4889.68
CE-Net [60]89.2382.3495.7691.51
nnU-Net [61]89.2482.3595.7991.45
HiFormer [78]88.5481.4595.5991.09
CPFNet [62]89.3482.6495.8991.38
FATNet [79]88.8481.7995.6291.18
Ms RED [71]89.4882.7195.8991.83
DconnNet90.4383.9196.3991.54
+ +![](images/3bcb37141a9f9518cc4a30cc40dcad9841d87dd85f7aadc82efdab64d96f6f39.jpg) + +![](images/bb93afc200425da96587d58fddb57bf5e0ab4f860e62c82d89ea9d51a7100d51.jpg) + +![](images/12f9c3556cd02d97bc883c7d16fdf440feb559786090feca24909facf3234859.jpg) + +![](images/a3278838612ffb4b8f1bf675cd51d8444f9de28b3a18159c5bb9eba41a26aca7.jpg) + +![](images/475a46d3020e2de17e1f50e730b120ba8ea2e903dae573c765970cba7725fa51.jpg) + +![](images/8ed860d46ec097135b560977d67568d03d6eb8c5e166292d7aa0b9dd8414ff0f.jpg) + +![](images/f2a2b71bf3279819e07e6c00e140f97fc7e01150a1fa0c25d04eaee46e48546b.jpg) + +![](images/552b16226fde58ddf018198e40fda750d5a8b640b1d00f68bcdfcd748f816312.jpg) + +![](images/f3f4cb5f6f3cc63027df3803212e8aa2bf72258aebb98c696b33ee470b382b4e.jpg) + +![](images/1f41edbca8fb25a6c131d61d4c695f4b95c5ffa697793166b11e7a299c29a867.jpg) + +![](images/f8b8482d413e6a586321595952a032027bb02ddff0081b3cbbd05b86bc9a8e38.jpg) + +![](images/8008bc1ecc0a3e495cd861e78190b0f9e64b0559f58cba473cd58b05c0ebc626.jpg) + +![](images/f7af82c2c3f10396ee9e09a20a99dd411c0d182827c5875dc1e47f889b004c32.jpg) +Image +Figure 8. Visualization on ISIC2018 dataset. + +![](images/44b98384f192b3b960ffb8cb6e16a8ae0175ccc39a2c81cad71a57d4a94fbcef.jpg) + +![](images/c2456587ac6acc96bbbebe2d5f49136836f880525571fad63a40609c00065136.jpg) +CPFNet [62] + +![](images/04b51b61ec96b17e44ef73addfba0516f1aeba430b1c943923475507a0dd3559.jpg) +Net [79] + +![](images/09a274ebaa4255452b50460d356837b1b09ff3aa66fbd0a5306693b1b4b091fa.jpg) +Ms RED [71] + +![](images/72b2078f40acc6a5a726aee131bfa056ea290ebf25979b7bdded3c20e2c0280e.jpg) +DconnNet + +we only compare the best-performing methods. In Fig. 8, DconnNet can accurately segment the lesion even under strong clinical confounders (e.g., the hairs in the first image). Also, DconnNet could learn the topology of skin lesions and make connected predictions in all cases, while others showed topological errors. + +# 5.3. Topological vessel segmentation + +We used this experiment to demonstrate the topology-preserving ability of DconnNet in vessel segmentation, in which anatomical consistency is crucial. Due to the limited sampling size, we did not use SDL in this experiment. + +Comparison of state-of-the-art methods. We compared the results of DconnNet versus up-to-date leading methods, including U-Net [58], Att-UNet [59], GT-DLA [80], CE-Net [60], cclDiceLoss [73], and Graph Cut Loss [72] in Table 3. Our method surpassed other methods on all metrics. The superior performances of DconnNet on cclDice, $\beta_0$ , and $\beta_{1}$ , reflect the topological similarity between predictions and labels. + +Qualitative study on the vessel topology. In Fig. 9, we visually compared different methods. While in part due to limited training data DconnNet could not make perfect predictions across the whole images, it visually outperformed other methods. Our model's predicted vessels are mostly connected and with no significant topological errors. Other models showed more topological issues, e.g., in the form of non-simply connected regions. + +# 5.4. Ablation study + +We conducted ablation studies to compare directional connectivity modeling with the traditional segmentation- + +Table 3. Results on CHASEDB1. The best results are bold. + +
MethodclDiceDSCIOUβ0β1
U-Net [58]74.074.759.31.3902.633
Att-UNet [59]75.375.761.01.3302.531
GT-DLA [80]81.080.667.40.7901.969
CE-Net [60]82.081.068.10.3831.670
clDiceLoss [73]82.981.068.10.3451.656
GraphCutLoss [72]82.681.468.80.4371.692
DconnNet83.381.869.40.3411.630
+ +![](images/24ee4037a0e82fd143a8422b9b551174ce2dcc7c2fd3b278047169fd06e195f4.jpg) +Figure 9. Visualization on CHASEDB1 dataset. + +![](images/3043361a2241bfb4e6934afc2094da1d3f79f4baf660228c9470d62147f914d4.jpg) + +![](images/16336ad29e7892b02336a76afc8be69d5d7eb38384db05b8b5a32ef8667babf6.jpg) + +![](images/960edc1aa50b7d1d3c926e09cad4e994bf4a2777d0d87c95fa21ca797e6a661c.jpg) + +Table 4. Ablation study of the Retouch Dataset. Conn stands for connectivity modeling with $L_{bicon}$ . DS stands for dice loss. + +
ConnModuleLossDSC\( DSC_v \)AVDBACC
SDEIFDDSSDL
1√83.265.00.02587.0
2 √√85.870.30.02487.7
3 √√√86.273.70.02387.9
4 √√√√86.775.20.02388.3
5 √√√√87.778.20.02090.5
+ +based modeling and the naive connectivity modeling [16]. All experiments in this section are on the Retouch Dataset. + +Overall ablation study. The overall ablation study is reported in Table 4. The backbone (Exp. 1), a pretrained ResNet [75] encoder with a regular decoder, is from [62]. Exp. 2 is identical to [16] with a different backbone. Both connectivity modeling (Exp. 2) and directional modeling (Exp. 3 and 4) result in significant performance improvements. Especially, the considerable increases in the $DSC$ terms demonstrate that the model is becoming stable when dealing with the small fluid regions. Finally, by adding SDL (Exp. 5), all metrics got improved showing the impact of the distribution-based weighting scheme. + +Directional prior in SDE. The directional prior in the SDE module was designed to provide an initial prior to disentangle the directional features which will later be utilized across the entire network. Thus, Table 5 compares two experiments: the complete DconnNet and the one without directional prior, i.e., only PAM and CAM in each sub-path of SDE. Even when most of the network structure was kept unchanged, the network performed worse without the guidance of an initial directional embedding prior. + +Sub-path attention vs. single-path attention. In SDE, we applied a sub-path attention unit in each slice to capture the dependency between the contextual-unevenly sliced directional and categorical features. To demonstrate the effectiveness of the sub-path attention, we compared our proposed SDE with the alternative single-path attention units. We first compared it with a regular dual attention unit [10] which is the direct alternative to our SDE since + +Table 5. Ablation study on directional prior. + +
DconnNetDSCDSCvAVDBACC
w/o. prior86.372.30.02389.1
w/. prior87.776.60.02090.5
+ +Table 6. Ablation study on Sub-path attention. Backbone_Conn is the connectivity-based modeling on backbone [16], DA is the dual attention, and NL is the non-local module. + +
Backbone_ConnDSC\( DSC_v \)AVDBACC
+ DA [10]84.769.50.02786.2
+ NL [42]85.170.00.02887.2
+SDE87.776.60.02090.5
+ +we used the same module in each sub-path. We also conducted an experiment with the non-local unit [42]. The results are shown in Table 6, which shows all metrics increase after introducing the sub-path mechanism. + +Disentanglement of directional subspace. To show that the directional subspace is disentangled from the shared latent space with the proposed sub-path slicing method, we conducted two experiments on the DconnNet's latent space. First, we used T-SNE to visualize the learned patchwise feature maps in the latent spaces before and after the SDE module of a trained DconnNet, as shown in Fig. 2. Applying SDE decoupled the latent space and changed the latent features' centered distribution to a polarized distribution. We interpret this as the decoupling process between the directional subspace and categorical subspace. + +Then, to show the well-structured directional subspace between channels, we visualize the learned channel embeddings in the latent spaces before and after the SDE module of a trained DconnNet, as in Fig. 10. After SDE, the channel embeddings naturally grouped into several distinctive parts, demonstrating the effectiveness of the sub-path excitation. + +Comparison of size density loss. Exp. 4 and 5 in Table 4 demonstrated the superiority of the proposed SDL in connectivity modeling. This subsection further analyzes SDL in a pixel-classification-based segmentation setting. + +In Table 7, we compared SDL with alternative loss functions with a similar idea of weighting the region-based Dice loss, including Exponential Logarithmical Loss [81], Focal Dice Loss [82], Dice loss [50], and Generalised Dice [83] based on two networks: U-Net and CPFNet. Our SDL achieves the highest DSC both image- and volume-wise. Moreover, it shows more stability when dealing with a two-level imbalanced medical dataset compared to feedback-based losses (e.g., Focal-like losses) since it is less sensitive to FP prediction on the negative training images. + +Model size. Table 1 compares different model sizes. DconnNet (36.42M parameters) performed far better than the backbone (33.16M) with only $\sim 3\mathrm{M}$ extra parameters. In SDE, due to the channel slicing, we quadratically reduced the size of each sub-path attention (0.196M) from the full-size dual attention [10] (23.35M), resulting in the + +![](images/6e8ee6707013eebd630cb2f4846ee37cd46cd345bc881c212ea4ee9f046a01c5.jpg) +Figure 10. Visualization of latent channel embeddings of DconnNet before and after SDE module using T-SNE. The colors in (b) indicate the unsupervised clustering result. When applied to SDE, the channel embeddings naturally grouped into several distinctive parts. + +Table 7. Ablation study on loss function on Retouch Dataset. + +
LossU-NetCPFNet
DSCDSCvDSCDSCv
Exponential [81]Not Converged
Focal [82]
Dice [50]82.965.683.165.2
Generalised [83]80.154.180.955.5
SDL85.169.285.469.1
+ +Table 8. The components' size of DconnNet. + +
ModuleResNet EncoderSDEIFDFinal DecoderConnect. ModelingTotal
Feature BlockSpace Block
Para. (M)21.801.5711.351.490.180.0336.42
+ +small size of the proposed SDE in Table 8. Also, changing the network to connectivity modeling only takes extra 0.03M parameters. Given the relatively small parameter increase, 3D connectivity modeling is a potential future direction for 3D image segmentation. + +# 6. Conclusion + +This paper proposed a novel directional connectivity modeling network (DconnNet) for medical image segmentation. The core idea is to disentangle the directional subspace from the shared latent space and use the extracted directional features to enhance the overall data representation. We demonstrated the effectiveness of DconnNet in three ways. First, by statistical comparisons to other state-of-the-art methods, we showed the overall better performance of DconnNet. Then, we demonstrated its topology-preserving ability by qualitatively and quantitatively comparing DconnNet to other methods on a topologically sensitive dataset to other methods. Third, by visualizing the latent space of DconnNet, we revealed the disentanglement process of the directional subspace. + +# Acknowledgment + +This research was supported in part by NIH R01 EY030124, U01 EY034687, R01 EY031033, UG1 EY033287, and R01 AG072732. + +# References + +[1] P. L. Bazin, and D. L. Pham, "Topology correction of segmented medical images using a fast-marching algorithm," Comput. Methods Programs Biomed., vol. 88, no. 2, pp. 182-90, 2007. +[2] J. R. Clough, N. Byrne, I. Oksuz, V. A. Zimmer, J. A. Schnabel, and A. P. King, “A topological loss function for deep-learning based image segmentation using persistent homology,” IEEE TPAMI, vol. 44, no. 12, pp. 8766-8778, 2022. +[3] X. Hu, F. Li, D. Samaras, and C. Chen, “Topology-preserving deep image segmentation,” in NIPS, vol. 32, 2019. +[4] T. Y. Kong, and A. Rosenfeld, “Digital topology: Introduction and survey,” Comput. Gr. Image Process., vol. 48, no. 3, pp. 357-393, 1989. +[5] P. K. Saha, R. Strand, and G. 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A promising paradigm for achieving anatomically consistent segmentation via deep networks is incorporating pixel connectivity, a basic concept in digital topology, to model inter-pixel relationships. However, previous works on connectivity modeling have ignored the rich channel-wise directional information in the latent space. In this work, we demonstrate that effective disentanglement of directional sub-space from the shared latent space can significantly enhance the feature representation in the connectivity-based network. To this end, we propose a directional connectivity modeling scheme for segmentation that decouples, tracks, and utilizes the directional information across the network. Experiments on various public medical image segmentation benchmarks show the effectiveness of our model as compared to the state-of-the-art methods. 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As such, by directly modeling the mutual information between pixels or regions, graph-based methods have long been used to correct topological and geometrical errors [6-8]. However, such classic machine vision techniques usually depend on manually defined priors and thus are not easily generalizable for a wide variety of applications." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 69, + 638, + 308, + 708 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 638, + 308, + 708 + ], + "spans": [ + { + "bbox": [ + 69, + 638, + 308, + 708 + ], + "type": "text", + "content": "Alternative to the classic approaches, deep learning-based segmentation methods utilized an encoder-decoder architecture [9] to learn from a group of pixels in a particular receptive field at each layer. More recently, significant progress has been made in capturing the interpixel dependency inside a network's latent space [10-12];" + } + ] + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 354, + 200, + 559, + 323 + ], + "blocks": [ + { + "bbox": [ + 354, + 200, + 559, + 323 + ], + "lines": [ + { + "bbox": [ + 354, + 200, + 559, + 323 + ], + "spans": [ + { + "bbox": [ + 354, + 200, + 559, + 323 + ], + "type": "image", + "image_path": "40ba21137e681264752775952d67769fe75f02d01b5b1fd014bc0a3d0a9278da.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 330, + 323, + 570, + 376 + ], + "lines": [ + { + "bbox": [ + 330, + 323, + 570, + 376 + ], + "spans": [ + { + "bbox": [ + 330, + 323, + 570, + 376 + ], + "type": "text", + "content": "Figure 1. The latent space differences between traditional pixel-classification-based and connectivity-based models. In the former, only categorical features, e.g., boundaries, are highlighted; while in the latter, the feature map also contains directional information (e.g., the horizontal connections between boundary pixels)." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "type": "image", + "bbox": [ + 332, + 379, + 569, + 469 + ], + "blocks": [ + { + "bbox": [ + 332, + 379, + 569, + 469 + ], + "lines": [ + { + "bbox": [ + 332, + 379, + 569, + 469 + ], + "spans": [ + { + "bbox": [ + 332, + 379, + 569, + 469 + ], + "type": "image", + "image_path": "7523ccfec1499837641b23ddc19bf8d9d54e5a792438268750c596d9e8b3f2ab.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 330, + 471, + 569, + 524 + ], + "lines": [ + { + "bbox": [ + 330, + 471, + 569, + 524 + ], + "spans": [ + { + "bbox": [ + 330, + 471, + 569, + 524 + ], + "type": "text", + "content": "Figure 2. The flows of the two groups of latent features (categorical and directional) in the latent space of DconnNet, are visualized by T-SNE [13]. They were first disentangled (Sec 3.2) and then effectively fused in a projected shared manifold (Sec 3.3). The colors are rendered based on the results of clustering." + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + } + ], + "index": 20 + }, + { + "bbox": [ + 329, + 527, + 569, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 527, + 569, + 665 + ], + "spans": [ + { + "bbox": [ + 329, + 527, + 569, + 665 + ], + "type": "text", + "content": "however, very few studies have been conducted on the problem modeling side of the networks. A typical segmentation network models the problem as a pure pixelwise classification task and uses a segmentation mask as the only label. Yet, this pixel-wise modeling scheme is suboptimal as it does not directly exploit inter-pixel relationships and geometrical properties [14, 15]. Thus, these models may result in low spatial coherence (i.e., inconsistent predictions for neighboring pixels that share similar spatial features) in their prediction [16]. Especially, when applied to high noise/artifacts medical data, the lower spatial consistency may lead to topological issues [17]." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 329, + 665, + 569, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 665, + 569, + 712 + ], + "spans": [ + { + "bbox": [ + 329, + 665, + 569, + 712 + ], + "type": "text", + "content": "The concept of pixel connectivity has long been used to ensure the basic topological duality of separation and connectedness in digital images [18]. More recently, in the context of deep learning, the connectivity masks, reviewed" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 15 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 15 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 15 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 198, + 13, + 443, + 25 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 198, + 13, + 443, + 25 + ], + "spans": [ + { + "bbox": [ + 198, + 13, + 443, + 25 + ], + "type": "text", + "content": "Except for this watermark, it is identical to the accepted version;" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 179, + 25, + 462, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 179, + 25, + 462, + 37 + ], + "spans": [ + { + "bbox": [ + 179, + 25, + 462, + 37 + ], + "type": "text", + "content": "the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 294, + 747, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 747, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 747, + 318, + 757 + ], + "type": "text", + "content": "11525" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 73, + 72, + 304, + 170 + ], + "blocks": [ + { + "bbox": [ + 73, + 72, + 304, + 170 + ], + "lines": [ + { + "bbox": [ + 73, + 72, + 304, + 170 + ], + "spans": [ + { + "bbox": [ + 73, + 72, + 304, + 170 + ], + "type": "image", + "image_path": "0099ae811e168b8b62f042f2be4ab122fdb96ef7be584fd0dfabf8a20d4c0979.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 69, + 172, + 308, + 236 + ], + "lines": [ + { + "bbox": [ + 69, + 172, + 308, + 236 + ], + "spans": [ + { + "bbox": [ + 69, + 172, + 308, + 236 + ], + "type": "text", + "content": "Figure 3. Illustration of generating the connectivity mask from the segmentation mask by traversing 8-neighbor pixel connectivity. For each pixel, channel " + }, + { + "bbox": [ + 69, + 172, + 308, + 236 + ], + "type": "inline_equation", + "content": "C_i" + }, + { + "bbox": [ + 69, + 172, + 308, + 236 + ], + "type": "text", + "content": "'s binary value in the converted connectivity vector carries the categorical information (connected or not connected) while " + }, + { + "bbox": [ + 69, + 172, + 308, + 236 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 69, + 172, + 308, + 236 + ], + "type": "text", + "content": " encodes the directional information (direction of connection)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 69, + 239, + 308, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 239, + 308, + 434 + ], + "spans": [ + { + "bbox": [ + 69, + 239, + 308, + 434 + ], + "type": "text", + "content": "in Section 2.1, have been introduced as a topological extension of the segmentation mask [15]. Using connectivity masks as training labels has several advantages over segmentation masks. In terms of problem modeling, using a connectivity mask inherently changes the problem from pixel-wise classification to connectivity prediction, which models and enhances the topological representation between pixels of interest. In terms of label representation, a connectivity mask is more informative in three ways: first, a connectivity mask stores the categorical information among the connections of pixels and it is inter-pixel relation-aware; second, it sparsely represents edge pixels [16]; third, it contains rich directional information channel-wisely. Thus, a network trained with connectivity masks has both categorical (reflected by connectivity) and directional features in its latent space, each of which forms a specific sub-latent space, as shown in Fig. 1." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 69, + 435, + 308, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 435, + 308, + 515 + ], + "spans": [ + { + "bbox": [ + 69, + 435, + 308, + 515 + ], + "type": "text", + "content": "In previous studies [15, 16, 19-22], these two groups of features were learned simultaneously through a shared network path which may result in highly coupled latent space and introduce redundancy [23]. Further, effectively disentangling meaningful subspaces from the shared latent space has been shown effective in accounting for the dependencies/independencies between features [24, 25]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 69, + 515, + 308, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 515, + 308, + 712 + ], + "spans": [ + { + "bbox": [ + 69, + 515, + 308, + 712 + ], + "type": "text", + "content": "Inspired by the idea of latent space disentanglement, in this paper, we propose a novel directional connectivity-based segmentation network (DconnNet) to disentangle the directional subspace from the shared latent space and utilize the extracted directional features to enhance the overall data representation, as in Fig. 2. The disentangling process is conducted by a sub-path slicing-based module called Sub-path Direction Excitation (SDE). The directional-based feature enhancement is applied in a coarse-to-fine manner using an Interactive Feature-space Decoder (IFD) with two top-down interactive decoding flows. Finally, we propose a novel Size Density loss (SDL) that alleviates the common data imbalance problem in medical datasets with a label size distribution-based weighting scheme. With experiments on different public medical image analysis benchmarks, we demonstrate the superiority of DconnNet against other state-of-art methods." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 331, + 72, + 420, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 331, + 72, + 420, + 85 + ], + "spans": [ + { + "bbox": [ + 331, + 72, + 420, + 85 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 331, + 91, + 484, + 104 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 331, + 91, + 484, + 104 + ], + "spans": [ + { + "bbox": [ + 331, + 91, + 484, + 104 + ], + "type": "text", + "content": "2.1. Deep connectivity modeling" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 329, + 109, + 569, + 375 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 109, + 569, + 375 + ], + "spans": [ + { + "bbox": [ + 329, + 109, + 569, + 375 + ], + "type": "text", + "content": "In topology, pixel connectivity describes how neighboring pixels are related to each other [4]. Following broad utilization in characterizing topological properties in classic image processing methods [26, 27], connectivity has found new applications in deep learning-based image segmentation [15, 16, 19-22]. The connectivity-based segmentation networks use the connectivity mask (Fig. 3) as the label, defined as an 8-channel mask with each channel representing if a pixel on the original image belongs to the same class of interest with one of its neighboring pixels at a specific direction. The connectivity mask was first introduced and applied to image segmentation in [15]. This idea was later extended by other works, including [16] which showed the bilateral property of pixel connectivity in saliency detection, and [28] which modeled the cross-modality connectivity for radar-video data fusion. Meanwhile, the effectiveness of connectivity modeling has been demonstrated in different applications such as remote sensing segmentation [19], path planning [20], and medical image segmentation [21, 22, 29]. Although significant progress has been made in this field, we demonstrate that the rich directional information in the connectivity masks has not yet been fully utilized." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 331, + 381, + 492, + 393 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 331, + 381, + 492, + 393 + ], + "spans": [ + { + "bbox": [ + 331, + 381, + 492, + 393 + ], + "type": "text", + "content": "2.2. Interpretation of latent space" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 329, + 398, + 569, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 398, + 569, + 502 + ], + "spans": [ + { + "bbox": [ + 329, + 398, + 569, + 502 + ], + "type": "text", + "content": "Latent space is an embedding of a set of features in a deep network. Interpretation, alignment, and disentanglement of latent spaces are important in different computer vision techniques such as unsupervised learning [30], multi-modal information fusion [24, 31], generative models [32, 33], knowledge distillation [34, 35], and transfer learning [36]. However, the interpretation of latent space is challenging because it usually requires implicit domain knowledge based on human judgment [37]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 329, + 502, + 569, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 502, + 569, + 629 + ], + "spans": [ + { + "bbox": [ + 329, + 502, + 569, + 629 + ], + "type": "text", + "content": "To interpret the latent space, researchers either apply dimension reduction tools such as PCA [38], T-SNE [13], or develop interactive analysis tools [39]. To manipulate latent space, a variation autoencoder (VAE) can be used to map the input to latent space and disentangle/match the different latent spaces [40, 41]. In this work, we utilize the intrinsic property of the connectivity mask and propose a simple yet effective sub-path slicing-based method to disentangle the directional subspace from the shared latent space, followed by a visual demonstration of the effectiveness of our disentanglement process with T-SNE." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 331, + 636, + 474, + 649 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 331, + 636, + 474, + 649 + ], + "spans": [ + { + "bbox": [ + 331, + 636, + 474, + 649 + ], + "type": "text", + "content": "2.3. 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The self-attention mechanism is defined as:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 415, + 696, + 569, + 709 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 415, + 696, + 569, + 709 + ], + "spans": [ + { + "bbox": [ + 415, + 696, + 569, + 709 + ], + "type": "interline_equation", + "content": "\\mathbf {y} = f (\\alpha , g (\\mathbf {x})), \\tag {1}", + "image_path": "ac868fc7e278d06199cf8ce8bca913bb92011fc9292be03e50dc7f5c1f59ecfa.jpg" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 747, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 747, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 747, + 318, + 757 + ], + "type": "text", + "content": "11526" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 75, + 70, + 553, + 228 + ], + "blocks": [ + { + "bbox": [ + 75, + 70, + 553, + 228 + ], + "lines": [ + { + "bbox": [ + 75, + 70, + 553, + 228 + ], + "spans": [ + { + "bbox": [ + 75, + 70, + 553, + 228 + ], + "type": "image", + "image_path": "d1bd85b28bd12db36e57db595a91c999ca99c3d16dec624dcc06735035c33c0b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 69, + 229, + 564, + 251 + ], + "lines": [ + { + "bbox": [ + 69, + 229, + 564, + 251 + ], + "spans": [ + { + "bbox": [ + 69, + 229, + 564, + 251 + ], + "type": "text", + "content": "Figure 4. The overview of the proposed DconnNet. It contains three parts: a pretrained ResNet encoder, a Sub-path Direction Excitation Module, and an Interactive Feature-space Decoder. The term \"up " + }, + { + "bbox": [ + 69, + 229, + 564, + 251 + ], + "type": "inline_equation", + "content": "N \\times" + }, + { + "bbox": [ + 69, + 229, + 564, + 251 + ], + "type": "text", + "content": " \" means upsampling with a stride of " + }, + { + "bbox": [ + 69, + 229, + 564, + 251 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 69, + 229, + 564, + 251 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 69, + 256, + 308, + 414 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 256, + 308, + 414 + ], + "spans": [ + { + "bbox": [ + 69, + 256, + 308, + 414 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 69, + 256, + 308, + 414 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 69, + 256, + 308, + 414 + ], + "type": "text", + "content": " is the input feature map, " + }, + { + "bbox": [ + 69, + 256, + 308, + 414 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 69, + 256, + 308, + 414 + ], + "type": "text", + "content": " is a unary function that computes the embedding of input, and " + }, + { + "bbox": [ + 69, + 256, + 308, + 414 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 69, + 256, + 308, + 414 + ], + "type": "text", + "content": " is usually a matrix multiplication [10, 42] or a simple dot product [11, 43, 44], depending on the definition of " + }, + { + "bbox": [ + 69, + 256, + 308, + 414 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 69, + 256, + 308, + 414 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 69, + 256, + 308, + 414 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 69, + 256, + 308, + 414 + ], + "type": "text", + "content": " is the attention/relation map which can be a mutual relation map by spatial- or channel-wisely computing the similarity between one pixel with other pixels in a feature map, or between two related feature maps from the same feature space [10, 42]; it can be a contextual-spatial relation map generated by similarity estimation between a feature map and a latent vector with abstract contextual meaning [44, 45]. Broadly speaking, " + }, + { + "bbox": [ + 69, + 256, + 308, + 414 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 69, + 256, + 308, + 414 + ], + "type": "text", + "content": " can also be a single map [11] or a vector [43, 46] containing special contextual meaning." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 70, + 426, + 126, + 439 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 426, + 126, + 439 + ], + "spans": [ + { + "bbox": [ + 70, + 426, + 126, + 439 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 69, + 449, + 293, + 462 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 449, + 293, + 462 + ], + "spans": [ + { + "bbox": [ + 69, + 449, + 293, + 462 + ], + "type": "text", + "content": "3.1. Directional space in connectivity modeling" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 69, + 466, + 308, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 466, + 308, + 581 + ], + "spans": [ + { + "bbox": [ + 69, + 466, + 308, + 581 + ], + "type": "text", + "content": "Due to connectivity between different pixel classes and directions, there are two groups of features in the latent space of a connectivity-based network: categorical directional. Each group of features forms its specific subspace in the latent space. In a single-path connectivity network, these two subspaces are highly coupled (Fig. 2), resulting in low-discriminative features. We demonstrate that the efficient disentangling and effective utilization of the direction space can enhance the overall feature representation in the connectivity model." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 69, + 582, + 308, + 708 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 582, + 308, + 708 + ], + "spans": [ + { + "bbox": [ + 69, + 582, + 308, + 708 + ], + "type": "text", + "content": "In a connectivity mask, different channels represent different directions of the pixel connection. Thus, as the network goes deeper, it naturally stores directional information among channels. Based on this property, the directional features can be captured and manipulated through channel-wise operations. Specifically, we propose SDE to disentangle channel-wise directional features from the latent space, followed by IFD to extract the directional embeddings at different layers and use them to enhance the overall feature representation in a self-attention manner. The overall DconnNet structure is shown in Fig. 4." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 330, + 256, + 534, + 269 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 256, + 534, + 269 + ], + "spans": [ + { + "bbox": [ + 330, + 256, + 534, + 269 + ], + "type": "text", + "content": "3.2. Sub-path Direction Excitation Module" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 329, + 273, + 569, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 273, + 569, + 450 + ], + "spans": [ + { + "bbox": [ + 329, + 273, + 569, + 450 + ], + "type": "text", + "content": "Directional prior extraction. Taking advantage of the channel-wise directional information in the connectivity mask, a direct way to get distinctive directional embedding is to coarsely supervise the intermediate features and squeeze the channels of the auxiliary connectivity output. We denote the encoder's outputs as " + }, + { + "bbox": [ + 329, + 273, + 569, + 450 + ], + "type": "inline_equation", + "content": "e_n" + }, + { + "bbox": [ + 329, + 273, + 569, + 450 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 329, + 273, + 569, + 450 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 329, + 273, + 569, + 450 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 329, + 273, + 569, + 450 + ], + "type": "inline_equation", + "content": "n_{th}" + }, + { + "bbox": [ + 329, + 273, + 569, + 450 + ], + "type": "text", + "content": " encoder layer. As shown in Fig. 5, we upsample " + }, + { + "bbox": [ + 329, + 273, + 569, + 450 + ], + "type": "inline_equation", + "content": "e_5" + }, + { + "bbox": [ + 329, + 273, + 569, + 450 + ], + "type": "text", + "content": ", the last encoder output, to the input size and get a preliminary output called " + }, + { + "bbox": [ + 329, + 273, + 569, + 450 + ], + "type": "inline_equation", + "content": "X_{prior}" + }, + { + "bbox": [ + 329, + 273, + 569, + 450 + ], + "type": "text", + "content": ", which will be supervised to learn the connectivity mask in the loss calculation. Therefore, rich, distinctive directional information can be obtained from the channels of " + }, + { + "bbox": [ + 329, + 273, + 569, + 450 + ], + "type": "inline_equation", + "content": "X_{prior}" + }, + { + "bbox": [ + 329, + 273, + 569, + 450 + ], + "type": "text", + "content": ". Then, we squeeze [43] " + }, + { + "bbox": [ + 329, + 273, + 569, + 450 + ], + "type": "inline_equation", + "content": "X_{prior}" + }, + { + "bbox": [ + 329, + 273, + 569, + 450 + ], + "type": "text", + "content": " through a global average pooling (GAP) and map the vector to the same dimension as the latent feature map " + }, + { + "bbox": [ + 329, + 273, + 569, + 450 + ], + "type": "inline_equation", + "content": "e_5 \\in R^{Ce_5 \\times He_5 \\times We_5}" + }, + { + "bbox": [ + 329, + 273, + 569, + 450 + ], + "type": "text", + "content": " with a " + }, + { + "bbox": [ + 329, + 273, + 569, + 450 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 329, + 273, + 569, + 450 + ], + "type": "text", + "content": " convolutional kernel " + }, + { + "bbox": [ + 329, + 273, + 569, + 450 + ], + "type": "inline_equation", + "content": "W_1" + }, + { + "bbox": [ + 329, + 273, + 569, + 450 + ], + "type": "text", + "content": " [44]:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 383, + 452, + 568, + 485 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 383, + 452, + 568, + 485 + ], + "spans": [ + { + "bbox": [ + 383, + 452, + 568, + 485 + ], + "type": "interline_equation", + "content": "G A P (X) = \\frac {1}{H \\times W} \\sum_ {i = 1} ^ {H} \\sum_ {j = 1} ^ {W} X (i, j), \\tag {2}", + "image_path": "dece35baf182642b4d0ae0afede1fceff61b2a81de76023c5bc9bd16dfbe5906.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 384, + 485, + 568, + 504 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 384, + 485, + 568, + 504 + ], + "spans": [ + { + "bbox": [ + 384, + 485, + 568, + 504 + ], + "type": "interline_equation", + "content": "v _ {p r i o r} = \\delta \\left(W _ {1} G A P \\left(X _ {p r i o r}\\right)\\right), \\tag {3}", + "image_path": "9386f4fc0c8c2079222f00c76650a07082f42caeb8fedc8625213f6c06068f87.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 329, + 506, + 569, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 506, + 569, + 594 + ], + "spans": [ + { + "bbox": [ + 329, + 506, + 569, + 594 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 329, + 506, + 569, + 594 + ], + "type": "inline_equation", + "content": "\\mathrm{H}" + }, + { + "bbox": [ + 329, + 506, + 569, + 594 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 329, + 506, + 569, + 594 + ], + "type": "inline_equation", + "content": "\\mathrm{W}" + }, + { + "bbox": [ + 329, + 506, + 569, + 594 + ], + "type": "text", + "content": " are the height and the width of a feature map, " + }, + { + "bbox": [ + 329, + 506, + 569, + 594 + ], + "type": "inline_equation", + "content": "W_{1} \\in R^{C_{e_{5}} \\times C_{k}}" + }, + { + "bbox": [ + 329, + 506, + 569, + 594 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 329, + 506, + 569, + 594 + ], + "type": "inline_equation", + "content": "C_{k}" + }, + { + "bbox": [ + 329, + 506, + 569, + 594 + ], + "type": "text", + "content": " is the channel of " + }, + { + "bbox": [ + 329, + 506, + 569, + 594 + ], + "type": "inline_equation", + "content": "X_{prior}" + }, + { + "bbox": [ + 329, + 506, + 569, + 594 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 329, + 506, + 569, + 594 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 329, + 506, + 569, + 594 + ], + "type": "text", + "content": " is the ReLu activation. The resulting " + }, + { + "bbox": [ + 329, + 506, + 569, + 594 + ], + "type": "inline_equation", + "content": "v_{prior} \\in R^{C_{e_{5}}}" + }, + { + "bbox": [ + 329, + 506, + 569, + 594 + ], + "type": "text", + "content": " has the directional information of a specific direction embedded in each entry. Next, we re-encode " + }, + { + "bbox": [ + 329, + 506, + 569, + 594 + ], + "type": "inline_equation", + "content": "v_{prior}" + }, + { + "bbox": [ + 329, + 506, + 569, + 594 + ], + "type": "text", + "content": " with a " + }, + { + "bbox": [ + 329, + 506, + 569, + 594 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 329, + 506, + 569, + 594 + ], + "type": "text", + "content": " convolution " + }, + { + "bbox": [ + 329, + 506, + 569, + 594 + ], + "type": "inline_equation", + "content": "W_{2} \\in R^{C_{e_{5}} \\times C_{e_{5}}}" + }, + { + "bbox": [ + 329, + 506, + 569, + 594 + ], + "type": "text", + "content": " and apply a sigmoid gating function " + }, + { + "bbox": [ + 329, + 506, + 569, + 594 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 329, + 506, + 569, + 594 + ], + "type": "text", + "content": " to normalize the projected vector:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 399, + 596, + 568, + 610 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 399, + 596, + 568, + 610 + ], + "spans": [ + { + "bbox": [ + 399, + 596, + 568, + 610 + ], + "type": "interline_equation", + "content": "\\alpha_ {p r i o r} = \\sigma \\left(W _ {2} v _ {p r i o r}\\right). \\tag {4}", + "image_path": "d14abb3dcb2fceb2d44276e2512158fd8590aba563134b882ffea190aacc048f.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 329, + 610, + 567, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 610, + 567, + 634 + ], + "spans": [ + { + "bbox": [ + 329, + 610, + 567, + 634 + ], + "type": "text", + "content": "Since " + }, + { + "bbox": [ + 329, + 610, + 567, + 634 + ], + "type": "inline_equation", + "content": "\\alpha_{prior}" + }, + { + "bbox": [ + 329, + 610, + 567, + 634 + ], + "type": "text", + "content": " contains rich element-wise directional information, we call it the directional prior." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 329, + 635, + 569, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 635, + 569, + 696 + ], + "spans": [ + { + "bbox": [ + 329, + 635, + 569, + 696 + ], + "type": "text", + "content": "Channel-wise slicing. To early disentangle the categorical and directional subspaces in the hidden layers, we split the latent features " + }, + { + "bbox": [ + 329, + 635, + 569, + 696 + ], + "type": "inline_equation", + "content": "(e_5)" + }, + { + "bbox": [ + 329, + 635, + 569, + 696 + ], + "type": "text", + "content": " and the directional prior " + }, + { + "bbox": [ + 329, + 635, + 569, + 696 + ], + "type": "inline_equation", + "content": "(\\alpha_{prior})" + }, + { + "bbox": [ + 329, + 635, + 569, + 696 + ], + "type": "text", + "content": " into eight parts by channel-wise slicing. We denote the " + }, + { + "bbox": [ + 329, + 635, + 569, + 696 + ], + "type": "inline_equation", + "content": "i_{th}" + }, + { + "bbox": [ + 329, + 635, + 569, + 696 + ], + "type": "text", + "content": " slices as " + }, + { + "bbox": [ + 329, + 635, + 569, + 696 + ], + "type": "inline_equation", + "content": "e_5^i" + }, + { + "bbox": [ + 329, + 635, + 569, + 696 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 329, + 635, + 569, + 696 + ], + "type": "inline_equation", + "content": "\\alpha_{prior}^{i}" + }, + { + "bbox": [ + 329, + 635, + 569, + 696 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 330, + 697, + 563, + 710 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 697, + 563, + 710 + ], + "spans": [ + { + "bbox": [ + 330, + 697, + 563, + 710 + ], + "type": "text", + "content": "Sub-path excitation (SPE). We construct a sub-path for" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 747, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 747, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 747, + 317, + 757 + ], + "type": "text", + "content": "11527" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 82, + 72, + 566, + 239 + ], + "blocks": [ + { + "bbox": [ + 82, + 72, + 566, + 239 + ], + "lines": [ + { + "bbox": [ + 82, + 72, + 566, + 239 + ], + "spans": [ + { + "bbox": [ + 82, + 72, + 566, + 239 + ], + "type": "image", + "image_path": "4910310916cd4c502f86ac3a626708c63e5b2a590eb1545c877313387b29421e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 93, + 239, + 537, + 251 + ], + "lines": [ + { + "bbox": [ + 93, + 239, + 537, + 251 + ], + "spans": [ + { + "bbox": [ + 93, + 239, + 537, + 251 + ], + "type": "text", + "content": "Figure 5. The SDE module, including three steps: direction prior extraction, channel-wise slicing, and sub-path excitation." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 83, + 264, + 315, + 388 + ], + "blocks": [ + { + "bbox": [ + 83, + 264, + 315, + 388 + ], + "lines": [ + { + "bbox": [ + 83, + 264, + 315, + 388 + ], + "spans": [ + { + "bbox": [ + 83, + 264, + 315, + 388 + ], + "type": "image", + "image_path": "5ceeeb35b134fe49d31d5d85d0ed1572822a3d07f3423d9824b3644887ae9135.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 86, + 389, + 290, + 400 + ], + "lines": [ + { + "bbox": [ + 86, + 389, + 290, + 400 + ], + "spans": [ + { + "bbox": [ + 86, + 389, + 290, + 400 + ], + "type": "text", + "content": "Figure 6. The Interactive Feature-space Decoder (IFD)." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 69, + 403, + 308, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 403, + 308, + 502 + ], + "spans": [ + { + "bbox": [ + 69, + 403, + 308, + 502 + ], + "type": "text", + "content": "each pair of these feature-embedding slices. In each subpath, we pass the feature slice " + }, + { + "bbox": [ + 69, + 403, + 308, + 502 + ], + "type": "inline_equation", + "content": "e_5^i" + }, + { + "bbox": [ + 69, + 403, + 308, + 502 + ], + "type": "text", + "content": " through spatial and channel attention modules [10] to capture the long-range and inter-channel dependencies, resulting in " + }, + { + "bbox": [ + 69, + 403, + 308, + 502 + ], + "type": "inline_equation", + "content": "e_5^{i\\prime}" + }, + { + "bbox": [ + 69, + 403, + 308, + 502 + ], + "type": "text", + "content": ". Next, we channel-wisely multiply the " + }, + { + "bbox": [ + 69, + 403, + 308, + 502 + ], + "type": "inline_equation", + "content": "\\alpha_{prior}^i" + }, + { + "bbox": [ + 69, + 403, + 308, + 502 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 69, + 403, + 308, + 502 + ], + "type": "inline_equation", + "content": "e_5^{i\\prime}" + }, + { + "bbox": [ + 69, + 403, + 308, + 502 + ], + "type": "text", + "content": " to selectivity highlight or suppress features with specific directional information. Then, we recode the output with a " + }, + { + "bbox": [ + 69, + 403, + 308, + 502 + ], + "type": "inline_equation", + "content": "1\\times 1" + }, + { + "bbox": [ + 69, + 403, + 308, + 502 + ], + "type": "text", + "content": " convolution kernel " + }, + { + "bbox": [ + 69, + 403, + 308, + 502 + ], + "type": "inline_equation", + "content": "W_3^i" + }, + { + "bbox": [ + 69, + 403, + 308, + 502 + ], + "type": "text", + "content": " and residually output it as:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 125, + 504, + 307, + 519 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 125, + 504, + 307, + 519 + ], + "spans": [ + { + "bbox": [ + 125, + 504, + 307, + 519 + ], + "type": "interline_equation", + "content": "e _ {S D E} ^ {i} = W _ {3} ^ {i} \\left(\\alpha_ {p r i o r} ^ {i} \\cdot e _ {5} ^ {i ^ {\\prime}}\\right) + e _ {5} ^ {i}. \\tag {5}", + "image_path": "117cd119e7a42b30d01b63bf98601e3115dc80cb7b4ddc6aa2ef50681b95ac43.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 69, + 521, + 308, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 521, + 308, + 545 + ], + "spans": [ + { + "bbox": [ + 69, + 521, + 308, + 545 + ], + "type": "text", + "content": "Finally, we stack all sub-paths outputs " + }, + { + "bbox": [ + 69, + 521, + 308, + 545 + ], + "type": "inline_equation", + "content": "(e_{SDE}^{i})" + }, + { + "bbox": [ + 69, + 521, + 308, + 545 + ], + "type": "text", + "content": " into one and recode it, resulting in a new feature map, " + }, + { + "bbox": [ + 69, + 521, + 308, + 545 + ], + "type": "inline_equation", + "content": "e_{SDE}" + }, + { + "bbox": [ + 69, + 521, + 308, + 545 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 69, + 544, + 308, + 710 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 544, + 308, + 710 + ], + "spans": [ + { + "bbox": [ + 69, + 544, + 308, + 710 + ], + "type": "text", + "content": "Due to the slicing operation, each group of slices will only contain part of the full features. However, the shrink of discriminative contextual information in directional and categorical features differs. Specifically, " + }, + { + "bbox": [ + 69, + 544, + 308, + 710 + ], + "type": "inline_equation", + "content": "\\alpha_{prior}" + }, + { + "bbox": [ + 69, + 544, + 308, + 710 + ], + "type": "text", + "content": " is a highly discriminative directional embedding as it is a low-level linear combination of unique directional features. Thus, channel-wise slicing will cause significant shrinkage of directional information in each slice. However, " + }, + { + "bbox": [ + 69, + 544, + 308, + 710 + ], + "type": "inline_equation", + "content": "e_5" + }, + { + "bbox": [ + 69, + 544, + 308, + 710 + ], + "type": "text", + "content": " contains a group of high-level but less-discriminative categorical features which usually have low variations with others [47]. As a result, high channel-wise categorical correlation and redundancy [48] exist in " + }, + { + "bbox": [ + 69, + 544, + 308, + 710 + ], + "type": "inline_equation", + "content": "e_5" + }, + { + "bbox": [ + 69, + 544, + 308, + 710 + ], + "type": "text", + "content": ". Therefore, a channel-wise slicing will result in less shrinkage [49] of high-discriminative categorical features in " + }, + { + "bbox": [ + 69, + 544, + 308, + 710 + ], + "type": "inline_equation", + "content": "e_5^i" + }, + { + "bbox": [ + 69, + 544, + 308, + 710 + ], + "type": "text", + "content": ". By doing this, we" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 330, + 254, + 569, + 370 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 254, + 569, + 370 + ], + "spans": [ + { + "bbox": [ + 330, + 254, + 569, + 370 + ], + "type": "text", + "content": "contextual-unevernly divide the directional and categorical features in each sub-path and make each sub-path shift its focus to the dominant features. Specifically, inside each sub-path, the network learns how to focus on the dominant class-specific information with less distinctive directional information emphasized in the channels. Between sub-paths, the network learns different distinctive directional information. Then, once we stack the sub-paths back, the direction information will be naturally disentangled from the original latent space and embedded into the channels." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 331, + 377, + 516, + 391 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 331, + 377, + 516, + 391 + ], + "spans": [ + { + "bbox": [ + 331, + 377, + 516, + 391 + ], + "type": "text", + "content": "3.3. Interactive Feature-space Decoder" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 329, + 396, + 569, + 454 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 396, + 569, + 454 + ], + "spans": [ + { + "bbox": [ + 329, + 396, + 569, + 454 + ], + "type": "text", + "content": "To ensure that the direction-dependent information can be effectively fused into feature maps in each layer, we propose an Interactive Feature-space Decoder with two top-down dynamically interactive flows, i.e., space flow and feature flow, as in Fig. 6." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 329, + 457, + 569, + 505 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 457, + 569, + 505 + ], + "spans": [ + { + "bbox": [ + 329, + 457, + 569, + 505 + ], + "type": "text", + "content": "Feature maps. There are two types of feature maps in each layer of IFD: the main feature map " + }, + { + "bbox": [ + 329, + 457, + 569, + 505 + ], + "type": "inline_equation", + "content": "d_{i}" + }, + { + "bbox": [ + 329, + 457, + 569, + 505 + ], + "type": "text", + "content": " and the direction-enhanced map " + }, + { + "bbox": [ + 329, + 457, + 569, + 505 + ], + "type": "inline_equation", + "content": "r_{i}" + }, + { + "bbox": [ + 329, + 457, + 569, + 505 + ], + "type": "text", + "content": ". At the first decoder layer (" + }, + { + "bbox": [ + 329, + 457, + 569, + 505 + ], + "type": "inline_equation", + "content": "i = 5" + }, + { + "bbox": [ + 329, + 457, + 569, + 505 + ], + "type": "text", + "content": "), they are both initialized as the outputs of SDE:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 412, + 506, + 568, + 518 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 412, + 506, + 568, + 518 + ], + "spans": [ + { + "bbox": [ + 412, + 506, + 568, + 518 + ], + "type": "interline_equation", + "content": "r _ {5} = d _ {5} = e _ {S D E}, \\tag {6}", + "image_path": "27c5efe20205a0c3e24bbaf53b946b81a946888ab454eeb7821875274df47a0e.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 329, + 519, + 565, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 519, + 565, + 532 + ], + "spans": [ + { + "bbox": [ + 329, + 519, + 565, + 532 + ], + "type": "text", + "content": "and are updated separately in the space and feature flows." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 329, + 535, + 569, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 535, + 569, + 605 + ], + "spans": [ + { + "bbox": [ + 329, + 535, + 569, + 605 + ], + "type": "text", + "content": "Space flow. In each space flow, a Space Block (S), which contains the embedding squeezing (ES) module and the manifold projection and enhancement (MPE) module, is used to enhance the directional representation. The ES module takes " + }, + { + "bbox": [ + 329, + 535, + 569, + 605 + ], + "type": "inline_equation", + "content": "r_i" + }, + { + "bbox": [ + 329, + 535, + 569, + 605 + ], + "type": "text", + "content": " as the input and outputs a directional embedding " + }, + { + "bbox": [ + 329, + 535, + 569, + 605 + ], + "type": "inline_equation", + "content": "n_i" + }, + { + "bbox": [ + 329, + 535, + 569, + 605 + ], + "type": "text", + "content": ", a high-level directional representation as:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 416, + 606, + 567, + 619 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 416, + 606, + 567, + 619 + ], + "spans": [ + { + "bbox": [ + 416, + 606, + 567, + 619 + ], + "type": "interline_equation", + "content": "n _ {i} = G A P \\left(r _ {i}\\right). \\tag {7}", + "image_path": "c31f28356eb59cc68e423bea46e6865b23ae1227581e79e535a90ed6aa5eba68.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 329, + 620, + 569, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 620, + 569, + 694 + ], + "spans": [ + { + "bbox": [ + 329, + 620, + 569, + 694 + ], + "type": "text", + "content": "Then, we use " + }, + { + "bbox": [ + 329, + 620, + 569, + 694 + ], + "type": "inline_equation", + "content": "n_i" + }, + { + "bbox": [ + 329, + 620, + 569, + 694 + ], + "type": "text", + "content": " as the input of MPE to enhance the directional representation in the main feature map " + }, + { + "bbox": [ + 329, + 620, + 569, + 694 + ], + "type": "inline_equation", + "content": "d_i" + }, + { + "bbox": [ + 329, + 620, + 569, + 694 + ], + "type": "text", + "content": ". In MPE, we first project both the main feature map " + }, + { + "bbox": [ + 329, + 620, + 569, + 694 + ], + "type": "inline_equation", + "content": "d_i \\in R^{C_{d_i} \\times H_{d_i} \\times W_{d_i}}" + }, + { + "bbox": [ + 329, + 620, + 569, + 694 + ], + "type": "text", + "content": " and directional embedding " + }, + { + "bbox": [ + 329, + 620, + 569, + 694 + ], + "type": "inline_equation", + "content": "n_i \\in R^{C_{d_i}/2}" + }, + { + "bbox": [ + 329, + 620, + 569, + 694 + ], + "type": "text", + "content": " onto a shared manifold " + }, + { + "bbox": [ + 329, + 620, + 569, + 694 + ], + "type": "inline_equation", + "content": "R^{C_{d_i}}" + }, + { + "bbox": [ + 329, + 620, + 569, + 694 + ], + "type": "text", + "content": " at the current resolution with two " + }, + { + "bbox": [ + 329, + 620, + 569, + 694 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 329, + 620, + 569, + 694 + ], + "type": "text", + "content": " convolutional projectors:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 398, + 695, + 568, + 709 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 398, + 695, + 568, + 709 + ], + "spans": [ + { + "bbox": [ + 398, + 695, + 568, + 709 + ], + "type": "interline_equation", + "content": "d _ {i} ^ {\\prime} = W _ {d _ {i}} d _ {i}, n _ {i} ^ {\\prime} = W _ {n _ {i}} n _ {i}, \\tag {8}", + "image_path": "ee1e6dfe1dce27b529cee4a9cc44f72cfe03bb1db267feb46b0d95c4bb0d9efa.jpg" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 747, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 747, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 747, + 318, + 757 + ], + "type": "text", + "content": "11528" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 69, + 72, + 309, + 135 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 72, + 309, + 135 + ], + "spans": [ + { + "bbox": [ + 69, + 72, + 309, + 135 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 69, + 72, + 309, + 135 + ], + "type": "inline_equation", + "content": "W_{d_i} \\in R^{C_{d_i} \\times C_{d_i}}" + }, + { + "bbox": [ + 69, + 72, + 309, + 135 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 69, + 72, + 309, + 135 + ], + "type": "inline_equation", + "content": "W_{n_i} \\in R^{C_{d_i} \\times C_{d_i}/2}" + }, + { + "bbox": [ + 69, + 72, + 309, + 135 + ], + "type": "text", + "content": ". Next, we model the category-direction relation by calculating the similarity between the projected directional embedding " + }, + { + "bbox": [ + 69, + 72, + 309, + 135 + ], + "type": "inline_equation", + "content": "n_i'" + }, + { + "bbox": [ + 69, + 72, + 309, + 135 + ], + "type": "text", + "content": " and feature map " + }, + { + "bbox": [ + 69, + 72, + 309, + 135 + ], + "type": "inline_equation", + "content": "d_i'" + }, + { + "bbox": [ + 69, + 72, + 309, + 135 + ], + "type": "text", + "content": " with a channel-wise dot product and a sigmoid activation:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 149, + 137, + 307, + 149 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 149, + 137, + 307, + 149 + ], + "spans": [ + { + "bbox": [ + 149, + 137, + 307, + 149 + ], + "type": "interline_equation", + "content": "\\alpha_ {n d} = \\sigma \\left(d _ {i} ^ {\\prime} \\cdot n _ {i} ^ {\\prime}\\right), \\tag {9}", + "image_path": "ebf610255ecae277be6ea90de7e3ea6b0aa9adfa3f3f45c57b129e876dcf506b.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 69, + 150, + 308, + 220 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 150, + 308, + 220 + ], + "spans": [ + { + "bbox": [ + 69, + 150, + 308, + 220 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 69, + 150, + 308, + 220 + ], + "type": "inline_equation", + "content": "\\alpha_{nd}" + }, + { + "bbox": [ + 69, + 150, + 308, + 220 + ], + "type": "text", + "content": " is the normalized category-direction attention map in which the direction-relevant features are enhanced and the irrelevant features are suppressed across channels. Next, we enhance the directional information in the re-encoded original feature map " + }, + { + "bbox": [ + 69, + 150, + 308, + 220 + ], + "type": "inline_equation", + "content": "d^{\\prime \\prime}_i" + }, + { + "bbox": [ + 69, + 150, + 308, + 220 + ], + "type": "text", + "content": " with the attention map " + }, + { + "bbox": [ + 69, + 150, + 308, + 220 + ], + "type": "inline_equation", + "content": "\\alpha_{nd}" + }, + { + "bbox": [ + 69, + 150, + 308, + 220 + ], + "type": "text", + "content": " using a point-wise inner multiplication:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 149, + 222, + 307, + 235 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 149, + 222, + 307, + 235 + ], + "spans": [ + { + "bbox": [ + 149, + 222, + 307, + 235 + ], + "type": "interline_equation", + "content": "r _ {i - 1} = \\alpha_ {n d} \\cdot d ^ {\\prime \\prime} _ {i}. \\tag {10}", + "image_path": "4a38edd70ce8d07cd8ac741da019a33191fd4b8a6b75f2758c37a8911475214a.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 69, + 236, + 308, + 294 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 236, + 308, + 294 + ], + "spans": [ + { + "bbox": [ + 69, + 236, + 308, + 294 + ], + "type": "text", + "content": "By doing this, we effectively fuse the directional information into the feature map, resulting in a new direction-enhanced map " + }, + { + "bbox": [ + 69, + 236, + 308, + 294 + ], + "type": "inline_equation", + "content": "r_{i-1}" + }, + { + "bbox": [ + 69, + 236, + 308, + 294 + ], + "type": "text", + "content": ", which will be further used as the input of feature flow and to generate the directional embedding " + }, + { + "bbox": [ + 69, + 236, + 308, + 294 + ], + "type": "inline_equation", + "content": "n_{i-1}" + }, + { + "bbox": [ + 69, + 236, + 308, + 294 + ], + "type": "text", + "content": " for the next layer." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 69, + 297, + 308, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 297, + 308, + 344 + ], + "spans": [ + { + "bbox": [ + 69, + 297, + 308, + 344 + ], + "type": "text", + "content": "Feature flow. Each feature flow contains a Feature Block (F), including two convolutional layers and an upsampling layer with a skip connection. It takes " + }, + { + "bbox": [ + 69, + 297, + 308, + 344 + ], + "type": "inline_equation", + "content": "r_i" + }, + { + "bbox": [ + 69, + 297, + 308, + 344 + ], + "type": "text", + "content": " as the input and outputs the upsampled main feature map " + }, + { + "bbox": [ + 69, + 297, + 308, + 344 + ], + "type": "inline_equation", + "content": "d_i" + }, + { + "bbox": [ + 69, + 297, + 308, + 344 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 69, + 344, + 308, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 344, + 308, + 437 + ], + "spans": [ + { + "bbox": [ + 69, + 344, + 308, + 437 + ], + "type": "text", + "content": "This top-down design and dynamic interactions between the two flows are mutually beneficial. Specifically, the embedding " + }, + { + "bbox": [ + 69, + 344, + 308, + 437 + ], + "type": "inline_equation", + "content": "n_i" + }, + { + "bbox": [ + 69, + 344, + 308, + 437 + ], + "type": "text", + "content": " extracted by space flow effectively fuses the directional information into the feature map " + }, + { + "bbox": [ + 69, + 344, + 308, + 437 + ], + "type": "inline_equation", + "content": "d_i" + }, + { + "bbox": [ + 69, + 344, + 308, + 437 + ], + "type": "text", + "content": " from the feature flow. On the other hand, the " + }, + { + "bbox": [ + 69, + 344, + 308, + 437 + ], + "type": "inline_equation", + "content": "d_i" + }, + { + "bbox": [ + 69, + 344, + 308, + 437 + ], + "type": "text", + "content": " generated by feature flow refines the directional representation " + }, + { + "bbox": [ + 69, + 344, + 308, + 437 + ], + "type": "inline_equation", + "content": "n_{i-1}" + }, + { + "bbox": [ + 69, + 344, + 308, + 437 + ], + "type": "text", + "content": " by adding supplementary directional information at a higher resolution to the space flow via MPE and ES." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 69, + 445, + 188, + 458 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 445, + 188, + 458 + ], + "spans": [ + { + "bbox": [ + 69, + 445, + 188, + 458 + ], + "type": "text", + "content": "3.4. Connectivity output" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 69, + 464, + 308, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 464, + 308, + 533 + ], + "spans": [ + { + "bbox": [ + 69, + 464, + 308, + 533 + ], + "type": "text", + "content": "We integrate the main feature maps " + }, + { + "bbox": [ + 69, + 464, + 308, + 533 + ], + "type": "inline_equation", + "content": "d_{1}" + }, + { + "bbox": [ + 69, + 464, + 308, + 533 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 69, + 464, + 308, + 533 + ], + "type": "inline_equation", + "content": "d_{4}" + }, + { + "bbox": [ + 69, + 464, + 308, + 533 + ], + "type": "text", + "content": " to get the final connectivity output " + }, + { + "bbox": [ + 69, + 464, + 308, + 533 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 69, + 464, + 308, + 533 + ], + "type": "text", + "content": ". Every eight channels of " + }, + { + "bbox": [ + 69, + 464, + 308, + 533 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 69, + 464, + 308, + 533 + ], + "type": "text", + "content": " represent the connectivity of one class. In line with [16], we use the Bilateral Voting (BV) module in (11) and the Region-guided Channel Aggregation (RCA) module in (12) to get the final segmentation map." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 101, + 535, + 306, + 578 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 101, + 535, + 306, + 578 + ], + "spans": [ + { + "bbox": [ + 101, + 535, + 306, + 578 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\bar {X} _ {j} (x, y) = \\bar {X} _ {9 - j} (x + a, y + b) \\\\ = X _ {j} (x, y) \\times X _ {9 - j} (x + a, y + b), (11) \\\\ \\tilde {S} (x, y) = \\max \\{\\tilde {X} _ {i} (x, y) \\} _ {i = 1} ^ {8}, (12) \\\\ \\end{array}", + "image_path": "92e14166261518d7c96a92fa04f15b911a9ece66add68ddf9428544ef9b479e7.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 69, + 580, + 308, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 580, + 308, + 616 + ], + "spans": [ + { + "bbox": [ + 69, + 580, + 308, + 616 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 69, + 580, + 308, + 616 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 69, + 580, + 308, + 616 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 69, + 580, + 308, + 616 + ], + "type": "inline_equation", + "content": "j_{th}" + }, + { + "bbox": [ + 69, + 580, + 308, + 616 + ], + "type": "text", + "content": " channel, " + }, + { + "bbox": [ + 69, + 580, + 308, + 616 + ], + "type": "inline_equation", + "content": "a,b\\in \\{0,\\pm 1\\}" + }, + { + "bbox": [ + 69, + 580, + 308, + 616 + ], + "type": "text", + "content": " represent the location of neighboring pixel, " + }, + { + "bbox": [ + 69, + 580, + 308, + 616 + ], + "type": "inline_equation", + "content": "\\tilde{X}" + }, + { + "bbox": [ + 69, + 580, + 308, + 616 + ], + "type": "text", + "content": " is the Bicon map, " + }, + { + "bbox": [ + 69, + 580, + 308, + 616 + ], + "type": "inline_equation", + "content": "\\tilde{S}" + }, + { + "bbox": [ + 69, + 580, + 308, + 616 + ], + "type": "text", + "content": " is the final segmentation prediction [16]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 69, + 622, + 156, + 633 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 622, + 156, + 633 + ], + "spans": [ + { + "bbox": [ + 69, + 622, + 156, + 633 + ], + "type": "text", + "content": "3.5. Loss function" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 80, + 640, + 235, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 640, + 235, + 651 + ], + "spans": [ + { + "bbox": [ + 80, + 640, + 235, + 651 + ], + "type": "text", + "content": "The total loss function of our work is:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 113, + 654, + 306, + 666 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 654, + 306, + 666 + ], + "spans": [ + { + "bbox": [ + 113, + 654, + 306, + 666 + ], + "type": "interline_equation", + "content": "L _ {\\text {t o t a l}} = L (\\text {m a i n}) + 0. 3 * L (\\text {p r i o r}), \\tag {13}", + "image_path": "eb3c729d598e2ed5d9fb348b6ca178fc02f24f6935ab2559ff922f4d2c5e4087.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 69, + 669, + 308, + 704 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 669, + 308, + 704 + ], + "spans": [ + { + "bbox": [ + 69, + 669, + 308, + 704 + ], + "type": "text", + "content": "where main represents the main output and prior represents the auxiliary output from SDE. Each loss " + }, + { + "bbox": [ + 69, + 669, + 308, + 704 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 69, + 669, + 308, + 704 + ], + "type": "text", + "content": " contains two parts, the Size Density Loss " + }, + { + "bbox": [ + 69, + 669, + 308, + 704 + ], + "type": "inline_equation", + "content": "L_{sd}" + }, + { + "bbox": [ + 69, + 669, + 308, + 704 + ], + "type": "text", + "content": " and the" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 331, + 72, + 459, + 85 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 331, + 72, + 459, + 85 + ], + "spans": [ + { + "bbox": [ + 331, + 72, + 459, + 85 + ], + "type": "text", + "content": "original Bicon loss [16] " + }, + { + "bbox": [ + 331, + 72, + 459, + 85 + ], + "type": "inline_equation", + "content": "L_{bicon}" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 408, + 87, + 567, + 100 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 408, + 87, + 567, + 100 + ], + "spans": [ + { + "bbox": [ + 408, + 87, + 567, + 100 + ], + "type": "interline_equation", + "content": "L = L _ {s d} + L _ {b i c o n}. \\tag {14}", + "image_path": "5f2a5eb1eb221ae3dcd1a9029f96eac321f317822b115fb3c2d365d1feec7640.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 329, + 102, + 569, + 148 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 102, + 569, + 148 + ], + "spans": [ + { + "bbox": [ + 329, + 102, + 569, + 148 + ], + "type": "text", + "content": "Size Density Loss. Considering the imbalanced nature of the medical data, we propose a novel imbalanced loss function based on the label size distribution of the classes of interests in the dataset, called Size Density Loss." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 329, + 149, + 569, + 232 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 149, + 569, + 232 + ], + "spans": [ + { + "bbox": [ + 329, + 149, + 569, + 232 + ], + "type": "text", + "content": "Before training, we sample all the training images and calculate the size of the label (total positive pixel number) on each image. Based on the extracted size distribution, for each class " + }, + { + "bbox": [ + 329, + 149, + 569, + 232 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 329, + 149, + 569, + 232 + ], + "type": "text", + "content": ", we calculate the probability density function of label size " + }, + { + "bbox": [ + 329, + 149, + 569, + 232 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 329, + 149, + 569, + 232 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 329, + 149, + 569, + 232 + ], + "type": "inline_equation", + "content": "PDF_{j}(k)" + }, + { + "bbox": [ + 329, + 149, + 569, + 232 + ], + "type": "text", + "content": ". Then, in the training phase, for each training image, we calculate its label size for each class " + }, + { + "bbox": [ + 329, + 149, + 569, + 232 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 329, + 149, + 569, + 232 + ], + "type": "text", + "content": " and get its size density weight " + }, + { + "bbox": [ + 329, + 149, + 569, + 232 + ], + "type": "inline_equation", + "content": "P_{j}(k)" + }, + { + "bbox": [ + 329, + 149, + 569, + 232 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 377, + 233, + 568, + 263 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 377, + 233, + 568, + 263 + ], + "spans": [ + { + "bbox": [ + 377, + 233, + 568, + 263 + ], + "type": "interline_equation", + "content": "P _ {j} (k) = \\left\\{ \\begin{array}{l l} 1, & k = 0, \\\\ - \\log \\left(P D F _ {j} (k)\\right), & k \\neq 0. \\end{array} \\right. \\tag {15}", + "image_path": "36d2cede2aafc5801f750a0f5d290a7374339bbd014b5b610c0851d67d79bf11.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 341, + 265, + 537, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 341, + 265, + 537, + 277 + ], + "spans": [ + { + "bbox": [ + 341, + 265, + 537, + 277 + ], + "type": "text", + "content": "We define the " + }, + { + "bbox": [ + 341, + 265, + 537, + 277 + ], + "type": "inline_equation", + "content": "L_{sd}" + }, + { + "bbox": [ + 341, + 265, + 537, + 277 + ], + "type": "text", + "content": " as a variant of Dice loss [50]:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 354, + 278, + 567, + 311 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 354, + 278, + 567, + 311 + ], + "spans": [ + { + "bbox": [ + 354, + 278, + 567, + 311 + ], + "type": "interline_equation", + "content": "L _ {s d} = \\sum_ {j} ^ {\\text {C l a s s}} P _ {j} (k) \\left(1 - \\frac {2 \\times \\sum \\left(S \\times G _ {s}\\right) + \\varepsilon}{\\sum S + \\sum G _ {s} + \\varepsilon}\\right), \\tag {16}", + "image_path": "295f4a9073413dd25702b84e31d9fcdf795958463ff5dac7b428fbf014d3452a.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 330, + 312, + 569, + 336 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 312, + 569, + 336 + ], + "spans": [ + { + "bbox": [ + 330, + 312, + 569, + 336 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 330, + 312, + 569, + 336 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 330, + 312, + 569, + 336 + ], + "type": "text", + "content": " is the final segmentation prediction, " + }, + { + "bbox": [ + 330, + 312, + 569, + 336 + ], + "type": "inline_equation", + "content": "\\varepsilon" + }, + { + "bbox": [ + 330, + 312, + 569, + 336 + ], + "type": "text", + "content": " is the stabilization term [51] and is usually set as 1." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 330, + 340, + 569, + 363 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 340, + 569, + 363 + ], + "spans": [ + { + "bbox": [ + 330, + 340, + 569, + 363 + ], + "type": "text", + "content": "Bicon Loss term. We use the Bicon Loss " + }, + { + "bbox": [ + 330, + 340, + 569, + 363 + ], + "type": "inline_equation", + "content": "L_{bicon}" + }, + { + "bbox": [ + 330, + 340, + 569, + 363 + ], + "type": "text", + "content": " for connectivity modeling, as originally defined in [16]:" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 383, + 365, + 567, + 377 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 383, + 365, + 567, + 377 + ], + "spans": [ + { + "bbox": [ + 383, + 365, + 567, + 377 + ], + "type": "interline_equation", + "content": "L _ {b i c o n} = L _ {d e c o u p l e} + L _ {c o n \\_ c o n s t}. \\tag {17}", + "image_path": "baed5a5d71e92e1ba2a308bf24893da045a3e614eedc52e56b1c0d12a39352b7.jpg" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 331, + 394, + 411, + 407 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 331, + 394, + 411, + 407 + ], + "spans": [ + { + "bbox": [ + 331, + 394, + 411, + 407 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 330, + 415, + 504, + 426 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 415, + 504, + 426 + ], + "spans": [ + { + "bbox": [ + 330, + 415, + 504, + 426 + ], + "type": "text", + "content": "4.1. Datasets and evaluation metrics" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 329, + 431, + 569, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 431, + 569, + 502 + ], + "spans": [ + { + "bbox": [ + 329, + 431, + 569, + 502 + ], + "type": "text", + "content": "We used three popular and diverse medical benchmark datasets in this paper. Specifically, we used Retouch [52] and ISIC2018 [53] datasets to evaluate the DconnNet performance for large-scale medical segmentation. We used CHASEDB1 [54] dataset to assess the topological performance of the DconnNet." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 329, + 506, + 569, + 704 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 506, + 569, + 704 + ], + "spans": [ + { + "bbox": [ + 329, + 506, + 569, + 704 + ], + "type": "text", + "content": "Retouch is an OCT retinal fluids segmentation benchmark that has been widely used [55, 56] for assessing computer vision methods. It contains three classes of disease biomarkers: intraretinal fluid (IRF), subretinal fluid (SRF), and pigment epithelial detachment (PED). Retouch contains a training set of 70 OCT volumes from three OCT scanners, with frame sizes spanning from " + }, + { + "bbox": [ + 329, + 506, + 569, + 704 + ], + "type": "inline_equation", + "content": "512 \\times 496" + }, + { + "bbox": [ + 329, + 506, + 569, + 704 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 329, + 506, + 569, + 704 + ], + "type": "inline_equation", + "content": "512 \\times 1024" + }, + { + "bbox": [ + 329, + 506, + 569, + 704 + ], + "type": "text", + "content": " pixels. Retouch is a two-level balanced dataset: at the image level, biomarkers do not span the whole volume; at the pixel level, each biomarker has a relatively small size compared to the background. Since the testing labels are unavailable, we implemented the volume-level 3-fold cross-validation (CV) for each scanner on the training data set. Following the official guidelines [52], we used volume-level Dice [65] (" + }, + { + "bbox": [ + 329, + 506, + 569, + 704 + ], + "type": "inline_equation", + "content": "DSC_v" + }, + { + "bbox": [ + 329, + 506, + 569, + 704 + ], + "type": "text", + "content": "), image-level Dice (" + }, + { + "bbox": [ + 329, + 506, + 569, + 704 + ], + "type": "inline_equation", + "content": "DSC" + }, + { + "bbox": [ + 329, + 506, + 569, + 704 + ], + "type": "text", + "content": "), absolute volume difference (" + }, + { + "bbox": [ + 329, + 506, + 569, + 704 + ], + "type": "inline_equation", + "content": "AVD" + }, + { + "bbox": [ + 329, + 506, + 569, + 704 + ], + "type": "text", + "content": "), and volume-wise balanced accuracy [66] (" + }, + { + "bbox": [ + 329, + 506, + 569, + 704 + ], + "type": "inline_equation", + "content": "BACC" + }, + { + "bbox": [ + 329, + 506, + 569, + 704 + ], + "type": "text", + "content": ") to evaluate the results." + } + ] + } + ], + "index": 28 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 747, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 747, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 747, + 318, + 757 + ], + "type": "text", + "content": "11529" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 73, + 76, + 563, + 235 + ], + "blocks": [ + { + "bbox": [ + 73, + 76, + 563, + 235 + ], + "lines": [ + { + "bbox": [ + 73, + 76, + 563, + 235 + ], + "spans": [ + { + "bbox": [ + 73, + 76, + 563, + 235 + ], + "type": "image", + "image_path": "87ec234d67e748f46f4d29a094996dfc527ad655793c98fbe3a3e6d7865c9429.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 70, + 236, + 566, + 256 + ], + "lines": [ + { + "bbox": [ + 70, + 236, + 566, + 256 + ], + "spans": [ + { + "bbox": [ + 70, + 236, + 566, + 256 + ], + "type": "text", + "content": "Figure 7. Visual comparison between the proposed DconnNet and other state-of-the-art methods on Retouch dataset. Different colors of masks represent different biomarker classes. Green: IRF; blue: SRF; red: PED." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 67, + 283, + 311, + 400 + ], + "blocks": [ + { + "bbox": [ + 71, + 261, + 306, + 282 + ], + "lines": [ + { + "bbox": [ + 71, + 261, + 306, + 282 + ], + "spans": [ + { + "bbox": [ + 71, + 261, + 306, + 282 + ], + "type": "text", + "content": "Table 1. Results on Retouch dataset. Model size (M) and testing speed (FPS) are also reported. The best results are bold." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 67, + 283, + 311, + 400 + ], + "lines": [ + { + "bbox": [ + 67, + 283, + 311, + 400 + ], + "spans": [ + { + "bbox": [ + 67, + 283, + 311, + 400 + ], + "type": "table", + "html": "
MethodDSCvDSCAVDBACCSize / Speed
DeepLabv3+ [57]60.282.70.02386.559.3 / 38
U-Net [58]66.184.20.02187.413.4 / 38
Att-UNet [59]65.383.40.02286.634.9 / 36
CE-Net [60]67.384.20.02684.629.0 / 37
nnU-Net [61]67.284.30.02386.430.0 / 20
CPFNet [62]69.085.70.02288.043.3 / 37
Curvature [63]68.284.70.02487.143.3 / 37
MsTGANet [64]68.985.00.02387.111.6 / 37
DconnNet78.287.70.02090.536.4 / 40
", + "image_path": "f6c15b86bfdd100776075bab6135bc11a7a51a82c8e243e3a7aaa9760c60cde2.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 69, + 406, + 307, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 406, + 307, + 464 + ], + "spans": [ + { + "bbox": [ + 69, + 406, + 307, + 464 + ], + "type": "text", + "content": "ISIC 2018 is a popular medical segmentation benchmark [67-70] containing 2594 images of various types of skin lesions at different resolutions. Following [71], we used 5-fold CV and evaluated the results with Dice, IOU, accuracy (ACC), and precision (PREC) metrics." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 69, + 468, + 308, + 561 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 468, + 308, + 561 + ], + "spans": [ + { + "bbox": [ + 69, + 468, + 308, + 561 + ], + "type": "text", + "content": "CHASEDB1 is a vessel segmentation dataset containing 28 fundus images with a resolution of " + }, + { + "bbox": [ + 69, + 468, + 308, + 561 + ], + "type": "inline_equation", + "content": "999 \\times 960" + }, + { + "bbox": [ + 69, + 468, + 308, + 561 + ], + "type": "text", + "content": " pixels and two sets of manual annotations. The first manual annotation is adopted in this work as in [72]. We conducted 5-fold CV and evaluated the results with two volumetric metrics Dice and IOU; and three topology-similarity-based metric clDice, 0- and 1-Betti numbers " + }, + { + "bbox": [ + 69, + 468, + 308, + 561 + ], + "type": "inline_equation", + "content": "(\\beta_0" + }, + { + "bbox": [ + 69, + 468, + 308, + 561 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 69, + 468, + 308, + 561 + ], + "type": "inline_equation", + "content": "\\beta_{1}" + }, + { + "bbox": [ + 69, + 468, + 308, + 561 + ], + "type": "text", + "content": ") [73] to measure the topological similarity." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 70, + 567, + 190, + 578 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 567, + 190, + 578 + ], + "spans": [ + { + "bbox": [ + 70, + 567, + 190, + 578 + ], + "type": "text", + "content": "4.2. Experimental details" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 69, + 584, + 308, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 584, + 308, + 712 + ], + "spans": [ + { + "bbox": [ + 69, + 584, + 308, + 712 + ], + "type": "text", + "content": "We generated the connectivity mask for each image via simple matrix operations [16]. We used the ImageNet [74] pretrained ResNet [75] as our encoder. The hyperparameter setting differed across datasets. For the Retouch dataset, we resized each image to " + }, + { + "bbox": [ + 69, + 584, + 308, + 712 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 69, + 584, + 308, + 712 + ], + "type": "text", + "content": " with no data augmentation and trained DconnNet with a 'poly' learning rate strategy. For ISIC2018, we resized images to " + }, + { + "bbox": [ + 69, + 584, + 308, + 712 + ], + "type": "inline_equation", + "content": "224 \\times 320" + }, + { + "bbox": [ + 69, + 584, + 308, + 712 + ], + "type": "text", + "content": " and used the same data augmentation and the parameter settings in [71]. For CHASEDB1, to fully use the limited data, we resized to " + }, + { + "bbox": [ + 69, + 584, + 308, + 712 + ], + "type": "inline_equation", + "content": "960 \\times 960" + }, + { + "bbox": [ + 69, + 584, + 308, + 712 + ], + "type": "text", + "content": " pixels and applied the same augmentations as in [60]. Since the CHASEDB1 dataset has a limited sample" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 330, + 261, + 569, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 261, + 569, + 319 + ], + "spans": [ + { + "bbox": [ + 330, + 261, + 569, + 319 + ], + "type": "text", + "content": "size, we did not apply SDL loss to this dataset. We did not use any pre-processing for training and no post-processing for evaluation. The framework is built on PyTorch 1.7.0 [76]. All experiments are performed with a GPU NVIDIA GeForce GTX 3090 Ti." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 331, + 330, + 384, + 342 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 331, + 330, + 384, + 342 + ], + "spans": [ + { + "bbox": [ + 331, + 330, + 384, + 342 + ], + "type": "text", + "content": "5. Results" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 331, + 349, + 479, + 361 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 331, + 349, + 479, + 361 + ], + "spans": [ + { + "bbox": [ + 331, + 349, + 479, + 361 + ], + "type": "text", + "content": "5.1. Retinal fluid segmentation" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 329, + 367, + 569, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 367, + 569, + 513 + ], + "spans": [ + { + "bbox": [ + 329, + 367, + 569, + 513 + ], + "type": "text", + "content": "Comparison of state-of-the-art methods. We compared the proposed DconnNet with eight state-of-the-art models for relevant applications, including DeepLab V3+ [57], U-Net [58], Attention UNet [59], CE-Net [60], nnU-Net [61], CPFNet [62], CPFNet-backboned Curvature Loss [63], and MsTGANet [64] in Table 1, which shows the superior performance of the proposed model. Specifically, the improvements on " + }, + { + "bbox": [ + 329, + 367, + 569, + 513 + ], + "type": "inline_equation", + "content": "DSC_{i}" + }, + { + "bbox": [ + 329, + 367, + 569, + 513 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 329, + 367, + 569, + 513 + ], + "type": "inline_equation", + "content": "DSC_{v}" + }, + { + "bbox": [ + 329, + 367, + 569, + 513 + ], + "type": "text", + "content": " demonstrate that our model has a consistent prediction on the small fluid regions, while the improvements on AVD and BACC demonstrate that our model has an overall more accurate prediction on the fluid regions, regardless of the target size." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 329, + 514, + 569, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 514, + 569, + 612 + ], + "spans": [ + { + "bbox": [ + 329, + 514, + 569, + 612 + ], + "type": "text", + "content": "Qualitative study. In Fig. 7, we compared DconnNet with the top-six baselines. In image (a), all competing methods missed the tiny SRF region, while our DconnNet made an accurate prediction. In (b), all methods, except DconnNet, either made false positive (FP) segmentations of IRF or an incomplete segmentation on PED. In (c), only our DconnNet made the topologically connected prediction for PED and accurately segmented the IRF and SRF regions." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 331, + 617, + 470, + 630 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 331, + 617, + 470, + 630 + ], + "spans": [ + { + "bbox": [ + 331, + 617, + 470, + 630 + ], + "type": "text", + "content": "5.2. Skin lesion segmentation" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 329, + 635, + 568, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 635, + 568, + 696 + ], + "spans": [ + { + "bbox": [ + 329, + 635, + 568, + 696 + ], + "type": "text", + "content": "Comparison of state-of-the-art methods. In Table 2, we compared our method with U-Net [58], BCDU-Net [77], CE-Net [60], nnU-Net [61], HiFormer [78], CPFNet [62], FATNet [79], and Ms RED [71]. The proposed DconnNet outperformed all competitive models." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 330, + 699, + 565, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 699, + 565, + 712 + ], + "spans": [ + { + "bbox": [ + 330, + 699, + 565, + 712 + ], + "type": "text", + "content": "Qualitative study. Due to limited space, in Figs. 8 and 9," + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 747, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 747, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 747, + 317, + 757 + ], + "type": "text", + "content": "11530" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 73, + 83, + 304, + 202 + ], + "blocks": [ + { + "bbox": [ + 73, + 72, + 304, + 82 + ], + "lines": [ + { + "bbox": [ + 73, + 72, + 304, + 82 + ], + "spans": [ + { + "bbox": [ + 73, + 72, + 304, + 82 + ], + "type": "text", + "content": "Table 2. Results on ISIC2018 dataset. The best results are bold." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 73, + 83, + 304, + 202 + ], + "lines": [ + { + "bbox": [ + 73, + 83, + 304, + 202 + ], + "spans": [ + { + "bbox": [ + 73, + 83, + 304, + 202 + ], + "type": "table", + "html": "
MethodDSCIOUACCPREC
U-Net [58]88.4181.2395.5390.7
BCDU-Net [77]88.3380.8495.4889.68
CE-Net [60]89.2382.3495.7691.51
nnU-Net [61]89.2482.3595.7991.45
HiFormer [78]88.5481.4595.5991.09
CPFNet [62]89.3482.6495.8991.38
FATNet [79]88.8481.7995.6291.18
Ms RED [71]89.4882.7195.8991.83
DconnNet90.4383.9196.3991.54
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In Fig. 8, DconnNet can accurately segment the lesion even under strong clinical confounders (e.g., the hairs in the first image). Also, DconnNet could learn the topology of skin lesions and make connected predictions in all cases, while others showed topological errors." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 70, + 399, + 242, + 412 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 399, + 242, + 412 + ], + "spans": [ + { + "bbox": [ + 70, + 399, + 242, + 412 + ], + "type": "text", + "content": "5.3. Topological vessel segmentation" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 69, + 417, + 308, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 417, + 308, + 464 + ], + "spans": [ + { + "bbox": [ + 69, + 417, + 308, + 464 + ], + "type": "text", + "content": "We used this experiment to demonstrate the topology-preserving ability of DconnNet in vessel segmentation, in which anatomical consistency is crucial. Due to the limited sampling size, we did not use SDL in this experiment." + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 69, + 467, + 308, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 467, + 308, + 559 + ], + "spans": [ + { + "bbox": [ + 69, + 467, + 308, + 559 + ], + "type": "text", + "content": "Comparison of state-of-the-art methods. We compared the results of DconnNet versus up-to-date leading methods, including U-Net [58], Att-UNet [59], GT-DLA [80], CE-Net [60], cclDiceLoss [73], and Graph Cut Loss [72] in Table 3. Our method surpassed other methods on all metrics. 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While in part due to limited training data DconnNet could not make perfect predictions across the whole images, it visually outperformed other methods. Our model's predicted vessels are mostly connected and with no significant topological errors. Other models showed more topological issues, e.g., in the form of non-simply connected regions." + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 70, + 662, + 162, + 675 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 662, + 162, + 675 + ], + "spans": [ + { + "bbox": [ + 70, + 662, + 162, + 675 + ], + "type": "text", + "content": "5.4. 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MethodclDiceDSCIOUβ0β1
U-Net [58]74.074.759.31.3902.633
Att-UNet [59]75.375.761.01.3302.531
GT-DLA [80]81.080.667.40.7901.969
CE-Net [60]82.081.068.10.3831.670
clDiceLoss [73]82.981.068.10.3451.656
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", + "image_path": "f4d9f060ddbf644e1fbbe3862a79d745729a5e9981faa4e9effb5e30cf3d127f.jpg" + } + ] + } + ], + "index": 43, + "angle": 0, + "type": "table_body" + } + ], + "index": 43 + }, + { + "bbox": [ + 330, + 344, + 567, + 368 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 344, + 567, + 368 + ], + "spans": [ + { + "bbox": [ + 330, + 344, + 567, + 368 + ], + "type": "text", + "content": "based modeling and the naive connectivity modeling [16]. All experiments in this section are on the Retouch Dataset." + } + ] + } + ], + "index": 44 + }, + { + "bbox": [ + 330, + 371, + 569, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 371, + 569, + 499 + ], + "spans": [ + { + "bbox": [ + 330, + 371, + 569, + 499 + ], + "type": "text", + "content": "Overall ablation study. The overall ablation study is reported in Table 4. The backbone (Exp. 1), a pretrained ResNet [75] encoder with a regular decoder, is from [62]. Exp. 2 is identical to [16] with a different backbone. Both connectivity modeling (Exp. 2) and directional modeling (Exp. 3 and 4) result in significant performance improvements. Especially, the considerable increases in the " + }, + { + "bbox": [ + 330, + 371, + 569, + 499 + ], + "type": "inline_equation", + "content": "DSC" + }, + { + "bbox": [ + 330, + 371, + 569, + 499 + ], + "type": "text", + "content": " terms demonstrate that the model is becoming stable when dealing with the small fluid regions. Finally, by adding SDL (Exp. 5), all metrics got improved showing the impact of the distribution-based weighting scheme." + } + ] + } + ], + "index": 45 + }, + { + "bbox": [ + 330, + 502, + 569, + 607 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 502, + 569, + 607 + ], + "spans": [ + { + "bbox": [ + 330, + 502, + 569, + 607 + ], + "type": "text", + "content": "Directional prior in SDE. The directional prior in the SDE module was designed to provide an initial prior to disentangle the directional features which will later be utilized across the entire network. Thus, Table 5 compares two experiments: the complete DconnNet and the one without directional prior, i.e., only PAM and CAM in each sub-path of SDE. Even when most of the network structure was kept unchanged, the network performed worse without the guidance of an initial directional embedding prior." + } + ] + } + ], + "index": 46 + }, + { + "bbox": [ + 330, + 609, + 569, + 703 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 609, + 569, + 703 + ], + "spans": [ + { + "bbox": [ + 330, + 609, + 569, + 703 + ], + "type": "text", + "content": "Sub-path attention vs. single-path attention. In SDE, we applied a sub-path attention unit in each slice to capture the dependency between the contextual-unevenly sliced directional and categorical features. To demonstrate the effectiveness of the sub-path attention, we compared our proposed SDE with the alternative single-path attention units. We first compared it with a regular dual attention unit [10] which is the direct alternative to our SDE since" + } + ] + } + ], + "index": 47 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 747, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 747, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 747, + 317, + 757 + ], + "type": "text", + "content": "11531" + } + ] + } + ], + "index": 48 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 78, + 83, + 300, + 118 + ], + "blocks": [ + { + "bbox": [ + 113, + 72, + 274, + 83 + ], + "lines": [ + { + "bbox": [ + 113, + 72, + 274, + 83 + ], + "spans": [ + { + "bbox": [ + 113, + 72, + 274, + 83 + ], + "type": "text", + "content": "Table 5. Ablation study on directional prior." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 78, + 83, + 300, + 118 + ], + "lines": [ + { + "bbox": [ + 78, + 83, + 300, + 118 + ], + "spans": [ + { + "bbox": [ + 78, + 83, + 300, + 118 + ], + "type": "table", + "html": "
DconnNetDSCDSCvAVDBACC
w/o. prior86.372.30.02389.1
w/. prior87.776.60.02090.5
", + "image_path": "8602d4fba45a068f335b04eeef9ece465d25d1f42ac2c305deb33b72197e02ad.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 70, + 156, + 307, + 205 + ], + "blocks": [ + { + "bbox": [ + 70, + 124, + 307, + 156 + ], + "lines": [ + { + "bbox": [ + 70, + 124, + 307, + 156 + ], + "spans": [ + { + "bbox": [ + 70, + 124, + 307, + 156 + ], + "type": "text", + "content": "Table 6. Ablation study on Sub-path attention. Backbone_Conn is the connectivity-based modeling on backbone [16], DA is the dual attention, and NL is the non-local module." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 70, + 156, + 307, + 205 + ], + "lines": [ + { + "bbox": [ + 70, + 156, + 307, + 205 + ], + "spans": [ + { + "bbox": [ + 70, + 156, + 307, + 205 + ], + "type": "table", + "html": "
Backbone_ConnDSC\\( DSC_v \\)AVDBACC
+ DA [10]84.769.50.02786.2
+ NL [42]85.170.00.02887.2
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", + "image_path": "cf4a251248dd5e3b26e2dd2220a5c69c878c1ffa61ede4f7280aa26b1ac43605.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 69, + 213, + 308, + 259 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 213, + 308, + 259 + ], + "spans": [ + { + "bbox": [ + 69, + 213, + 308, + 259 + ], + "type": "text", + "content": "we used the same module in each sub-path. We also conducted an experiment with the non-local unit [42]. The results are shown in Table 6, which shows all metrics increase after introducing the sub-path mechanism." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 69, + 262, + 308, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 262, + 308, + 389 + ], + "spans": [ + { + "bbox": [ + 69, + 262, + 308, + 389 + ], + "type": "text", + "content": "Disentanglement of directional subspace. To show that the directional subspace is disentangled from the shared latent space with the proposed sub-path slicing method, we conducted two experiments on the DconnNet's latent space. First, we used T-SNE to visualize the learned patchwise feature maps in the latent spaces before and after the SDE module of a trained DconnNet, as shown in Fig. 2. Applying SDE decoupled the latent space and changed the latent features' centered distribution to a polarized distribution. We interpret this as the decoupling process between the directional subspace and categorical subspace." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 69, + 389, + 308, + 470 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 389, + 308, + 470 + ], + "spans": [ + { + "bbox": [ + 69, + 389, + 308, + 470 + ], + "type": "text", + "content": "Then, to show the well-structured directional subspace between channels, we visualize the learned channel embeddings in the latent spaces before and after the SDE module of a trained DconnNet, as in Fig. 10. After SDE, the channel embeddings naturally grouped into several distinctive parts, demonstrating the effectiveness of the sub-path excitation." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 69, + 473, + 308, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 473, + 308, + 520 + ], + "spans": [ + { + "bbox": [ + 69, + 473, + 308, + 520 + ], + "type": "text", + "content": "Comparison of size density loss. Exp. 4 and 5 in Table 4 demonstrated the superiority of the proposed SDL in connectivity modeling. This subsection further analyzes SDL in a pixel-classification-based segmentation setting." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 69, + 520, + 308, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 520, + 308, + 635 + ], + "spans": [ + { + "bbox": [ + 69, + 520, + 308, + 635 + ], + "type": "text", + "content": "In Table 7, we compared SDL with alternative loss functions with a similar idea of weighting the region-based Dice loss, including Exponential Logarithmical Loss [81], Focal Dice Loss [82], Dice loss [50], and Generalised Dice [83] based on two networks: U-Net and CPFNet. Our SDL achieves the highest DSC both image- and volume-wise. Moreover, it shows more stability when dealing with a two-level imbalanced medical dataset compared to feedback-based losses (e.g., Focal-like losses) since it is less sensitive to FP prediction on the negative training images." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 69, + 639, + 308, + 708 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 639, + 308, + 708 + ], + "spans": [ + { + "bbox": [ + 69, + 639, + 308, + 708 + ], + "type": "text", + "content": "Model size. Table 1 compares different model sizes. DconnNet (36.42M parameters) performed far better than the backbone (33.16M) with only " + }, + { + "bbox": [ + 69, + 639, + 308, + 708 + ], + "type": "inline_equation", + "content": "\\sim 3\\mathrm{M}" + }, + { + "bbox": [ + 69, + 639, + 308, + 708 + ], + "type": "text", + "content": " extra parameters. In SDE, due to the channel slicing, we quadratically reduced the size of each sub-path attention (0.196M) from the full-size dual attention [10] (23.35M), resulting in the" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 339, + 75, + 561, + 178 + ], + "blocks": [ + { + "bbox": [ + 339, + 75, + 561, + 178 + ], + "lines": [ + { + "bbox": [ + 339, + 75, + 561, + 178 + ], + "spans": [ + { + "bbox": [ + 339, + 75, + 561, + 178 + ], + "type": "image", + "image_path": "6e8ee6707013eebd630cb2f4846ee37cd46cd345bc881c212ea4ee9f046a01c5.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 330, + 181, + 569, + 234 + ], + "lines": [ + { + "bbox": [ + 330, + 181, + 569, + 234 + ], + "spans": [ + { + "bbox": [ + 330, + 181, + 569, + 234 + ], + "type": "text", + "content": "Figure 10. Visualization of latent channel embeddings of DconnNet before and after SDE module using T-SNE. The colors in (b) indicate the unsupervised clustering result. When applied to SDE, the channel embeddings naturally grouped into several distinctive parts." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 334, + 251, + 566, + 328 + ], + "blocks": [ + { + "bbox": [ + 337, + 239, + 561, + 250 + ], + "lines": [ + { + "bbox": [ + 337, + 239, + 561, + 250 + ], + "spans": [ + { + "bbox": [ + 337, + 239, + 561, + 250 + ], + "type": "text", + "content": "Table 7. Ablation study on loss function on Retouch Dataset." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 334, + 251, + 566, + 328 + ], + "lines": [ + { + "bbox": [ + 334, + 251, + 566, + 328 + ], + "spans": [ + { + "bbox": [ + 334, + 251, + 566, + 328 + ], + "type": "table", + "html": "
LossU-NetCPFNet
DSCDSCvDSCDSCv
Exponential [81]Not Converged
Focal [82]
Dice [50]82.965.683.165.2
Generalised [83]80.154.180.955.5
SDL85.169.285.469.1
", + "image_path": "804e8f54de79bbc099cc616e30899af1b651f9ed40d0faa19cde4e4fe52f609e.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "type": "table", + "bbox": [ + 331, + 346, + 568, + 390 + ], + "blocks": [ + { + "bbox": [ + 367, + 334, + 531, + 344 + ], + "lines": [ + { + "bbox": [ + 367, + 334, + 531, + 344 + ], + "spans": [ + { + "bbox": [ + 367, + 334, + 531, + 344 + ], + "type": "text", + "content": "Table 8. The components' size of DconnNet." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 331, + 346, + 568, + 390 + ], + "lines": [ + { + "bbox": [ + 331, + 346, + 568, + 390 + ], + "spans": [ + { + "bbox": [ + 331, + 346, + 568, + 390 + ], + "type": "table", + "html": "
ModuleResNet EncoderSDEIFDFinal DecoderConnect. ModelingTotal
Feature BlockSpace Block
Para. (M)21.801.5711.351.490.180.0336.42
", + "image_path": "4c6142fa4e12ebcc3f363ace1507e78f76ba989a9c5df25c9890abe40c46f8ad.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_body" + } + ], + "index": 15 + }, + { + "bbox": [ + 330, + 400, + 569, + 459 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 400, + 569, + 459 + ], + "spans": [ + { + "bbox": [ + 330, + 400, + 569, + 459 + ], + "type": "text", + "content": "small size of the proposed SDE in Table 8. Also, changing the network to connectivity modeling only takes extra 0.03M parameters. Given the relatively small parameter increase, 3D connectivity modeling is a potential future direction for 3D image segmentation." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 331, + 469, + 405, + 481 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 331, + 469, + 405, + 481 + ], + "spans": [ + { + "bbox": [ + 331, + 469, + 405, + 481 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 329, + 486, + 569, + 648 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 486, + 569, + 648 + ], + "spans": [ + { + "bbox": [ + 329, + 486, + 569, + 648 + ], + "type": "text", + "content": "This paper proposed a novel directional connectivity modeling network (DconnNet) for medical image segmentation. The core idea is to disentangle the directional subspace from the shared latent space and use the extracted directional features to enhance the overall data representation. We demonstrated the effectiveness of DconnNet in three ways. First, by statistical comparisons to other state-of-the-art methods, we showed the overall better performance of DconnNet. Then, we demonstrated its topology-preserving ability by qualitatively and quantitatively comparing DconnNet to other methods on a topologically sensitive dataset to other methods. Third, by visualizing the latent space of DconnNet, we revealed the disentanglement process of the directional subspace." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 331, + 658, + 424, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 331, + 658, + 424, + 671 + ], + "spans": [ + { + "bbox": [ + 331, + 658, + 424, + 671 + ], + "type": "text", + "content": "Acknowledgment" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 330, + 674, + 568, + 709 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 674, + 568, + 709 + ], + "spans": [ + { + "bbox": [ + 330, + 674, + 568, + 709 + ], + "type": "text", + "content": "This research was supported in part by NIH R01 EY030124, U01 EY034687, R01 EY031033, UG1 EY033287, and R01 AG072732." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 747, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 747, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 747, + 318, + 757 + ], + "type": "text", + "content": "11532" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 70, + 73, + 129, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 73, + 129, + 85 + ], + "spans": [ + { + "bbox": [ + 70, + 73, + 129, + 85 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 71, + 90, + 308, + 712 + ], + "type": "list", + "angle": 0, + "index": 18, + "blocks": [ + { + "bbox": [ + 71, + 90, + 308, + 132 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 71, + 90, + 308, + 132 + ], + "spans": [ + { + "bbox": [ + 71, + 90, + 308, + 132 + ], + "type": "text", + "content": "[1] P. 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Support, pp. 240-248, 2017." + } + ] + } + ], + "index": 12 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 747, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 747, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 747, + 318, + 757 + ], + "type": "text", + "content": "11535" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/DisCo-CLIP_ A Distributed Contrastive Loss for Memory Efficient CLIP Training/e80e2080-33a9-4c63-8bae-91e19a54d7b9_content_list.json b/2023/DisCo-CLIP_ A Distributed Contrastive Loss for Memory Efficient CLIP Training/e80e2080-33a9-4c63-8bae-91e19a54d7b9_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..af5acc99882b72cef4e9dc4516fd739b734b5e52 --- /dev/null +++ b/2023/DisCo-CLIP_ A Distributed Contrastive Loss for Memory Efficient CLIP Training/e80e2080-33a9-4c63-8bae-91e19a54d7b9_content_list.json @@ -0,0 +1,1672 @@ +[ + { + "type": "text", + "text": "DisCo-CLIP: A Distributed Contrastive Loss for Memory Efficient CLIP Training", + "text_level": 1, + "bbox": [ + 258, + 130, + 712, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yihao Chen, Xianbiao Qi, Jianan Wang, Lei Zhang* International Digital Economy Academy (IDEA), Shenzhen, Guangdong, China. {chenyihao, qixianbiao, wangjianan, leizhang}@idea.edu.cn", + "bbox": [ + 147, + 203, + 815, + 258 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 291, + 313, + 306 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We propose DisCo-CLIP, a distributed memory-efficient CLIP training approach, to reduce the memory consumption of contrastive loss when training contrastive learning models. Our approach decomposes the contrastive loss and its gradient computation into two parts, one to calculate the intra-GPU gradients and the other to compute the inter-GPU gradients. According to our decomposition, only the intra-GPU gradients are computed on the current GPU, while the inter-GPU gradients are collected via all-reduce from other GPUs instead of being repeatedly computed on every GPU. In this way, we can reduce the GPU memory consumption of contrastive loss computation from $\\mathcal{O}(B^2)$ to $\\mathcal{O}\\left(\\frac{B^2}{N}\\right)$ , where $B$ and $N$ are the batch size and the number of GPUs used for training. Such a distributed solution is mathematically equivalent to the original non-distributed contrastive loss computation, without sacrificing any computation accuracy. It is particularly efficient for large-batch CLIP training. For instance, DisCo-CLIP can enable contrastive training of a ViT-B/32 model with a batch size of 32K or 196K using 8 or 64 A100 40GB GPUs, compared with the original CLIP solution which requires 128 A100 40GB GPUs to train a ViT-B/32 model with a batch size of 32K.", + "bbox": [ + 75, + 323, + 472, + 672 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 700, + 209, + 715 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Vision-language representation learning from massive image-text pairs has recently attracted tremendous attention for its great potential in many applications such as zero-shot classification and text-image retrieval. Representative works include CLIP [27], ALIGN [17], Florence [47], CoCa [46], and BASIC [26], which all leverage hundreds of millions or even billions of image-text pairs collected from the Web to learn a semantic-rich and language-aligned visual representation [22]. As the web-collected data inevitably contain noises, CLIP [27] for the first time applies", + "bbox": [ + 75, + 726, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "contrastive learning on 400M image-text pairs, which implies a weak but more proper assumption about the data: the relevance between paired image and text is greater than that between unpaired image and text. For its demonstrated performance in CLIP, contrastive learning has been widely adopted in subsequent works. Accordingly, several imagedataset data sets with increasingly larger scales have also been developed and made publicly available, such as Conceptual 12M [3], YFCC 100M [38], WIT 37.6M [37], LAION-400M [35], and LAION-5B [34].", + "bbox": [ + 500, + 292, + 892, + 444 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The goal of contrastive learning in CLIP is to learn an alignment between image and text via two encoders. That is, it encourages paired image and text (called a positive pair) to be similar and meanwhile enforces unpaired image and text (called a negative pair) to be dissimilar. For any positive image-text pair, as there are normally unlimited number (up to the total number of images or texts in a data set) of negative image-text pairs, it is crucial to include a sufficiently large number of negative pairs in a contrastive loss to make the representation learning effective, as validated in all related works such as CLIP [27], Florence [47], OpenCLIP [16], and BASIC [26]. Specifically, BASIC shows that larger batch size, plus larger data set and larger model, theoretically lead to a better generalization performance.", + "bbox": [ + 496, + 445, + 893, + 671 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, a fundamental technical challenge in training a CLIP-like model is how to enlarge its batch size under the constraint of limited GPU memory. For instance, when the batch size is 65,536, the similarity matrix for all imag-text pairs in the batch will cost about 16GB using Float32. As the backbone part also consumes a significant portion of GPU memory, especially for large backbones such as ViT-Large or ViT-Huge [9], scaling up batch size presents a great challenge, usually requiring hundreds of V100 or A100 GPUs [16, 27, 47], which are inaccessible for most research scientists.", + "bbox": [ + 496, + 672, + 893, + 838 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this work, we develop a distributed solution called DisCo-CLIP for constrastive loss computation, which can save a large amount of memory for contrastive loss and make CLIP training more memory-efficient. Our method", + "bbox": [ + 496, + 839, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author.", + "bbox": [ + 94, + 886, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "22648", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "starts from a decomposition of the original contrastive loss. Based on this decomposition, we divide the contrastive loss into two parts, one to calculate the intra-GPU loss and gradients, and the other one to calculate the inter-GPU loss and gradients. For a mini-batch on the $n$ -th GPU (hereinafter called its hosting GPU), its intra-GPU gradients are calculated on its hosting GPU, and its inter-GPU gradients are collected from other GPUs. DisCo is an exact solution, mathematically equivalent to the original non-distributed contrastive loss, but more memory- and computation-efficient. It can decrease the memory cost of contrastive loss from $\\mathcal{O}(B^2)$ to $\\mathcal{O}\\left(\\frac{B^2}{N}\\right)$ , where $B$ and $N$ are the batch size and the number of GPUs. When $N$ equals to 64, it means around $97\\%$ (see Sec. 4.1 for details) of the memory, and similarly the computational cost, in contrastive loss can be saved. Thus, using DisCo in CLIP, we can enable contrastive training with a larger batch size. Using 8 Nvidia A100 40GB GPUs, DisCo-CLIP can enable contrastive training of a ViT-B/32 model with a batch size of 32,768. Using 64 A100 40GB GPUs, DisCo-CLIP can train the same model with a larger batch size of 196K.", + "bbox": [ + 75, + 90, + 472, + 410 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We summarize our contributions in twofold.", + "bbox": [ + 96, + 410, + 388, + 424 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a novel distributed contrastive loss solution called DisCo for memory efficient CLIP training, which can significantly reduce the memory consumption of the contrastive loss computation. Such a solution enables a larger batch size for contrastive training using the same computing resource without sacrificing any computation accuracy.", + "- We further validate that training with a larger batch size can further improve the performance of contrastive learning models." + ], + "bbox": [ + 94, + 436, + 468, + 599 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Background and Related Work", + "text_level": 1, + "bbox": [ + 76, + 613, + 362, + 630 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this section, we will introduce some background information for contrastive language-image pre-training (CLIP) and review some works that reduce memory consumption of the backbone part by trading computation for memory.", + "bbox": [ + 76, + 640, + 468, + 700 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Contrastive Language-Image Pre-training", + "text_level": 1, + "bbox": [ + 76, + 710, + 436, + 727 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The idea behind CLIP [27] is to learn two representations via two encoders, an image encoder [9, 14, 20, 23, 42] and a text encoder [2, 8, 28]. Its target is to encourage positive image-text pairs to have higher similarities, and enforce negative image-text pairs to have lower similarities. The training is supervised by two contrastive losses, an image-to-text loss and a text-to-image loss. Suppose we have $B$ text-image pairs as a batch sending to two encoders and the model is trained using $N$ GPUs, with each GPU assigned $b = \\frac{B}{N}$ pairs. Here, we use $T_A, I_A$ to denote all text and image features obtained from two encoders. Suppose the", + "bbox": [ + 76, + 734, + 470, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "hidden dimension is $D$ , then the shapes of $\\mathrm{T}_A, \\mathrm{I}_A$ are both $B \\times D$ . In this way, our contrastive losses can be written as,", + "bbox": [ + 500, + 90, + 890, + 121 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {1} \\left(\\mathrm {I} _ {A}, \\mathrm {T} _ {A}\\right) + \\mathcal {L} _ {2} \\left(\\mathrm {T} _ {A}, \\mathrm {I} _ {A}\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 136, + 890, + 152 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_1(\\mathrm{I}_A,\\mathrm{T}_A)$ denotes the image-to-text loss, and $\\mathcal{L}_2(\\mathrm{T}_A,\\mathrm{I}_A)$ represents the text-to-image loss. The image-to-text loss means that the loss is to encourage a given image to find its paired text from tens of thousands of texts, and similarly for the text-to-image loss.", + "bbox": [ + 498, + 157, + 890, + 233 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Motivated by the success of CLIP, many new methods have been proposed, such as FILIP [43], LiT [48], ALIGN [17], BASIC [26], BLIP [21], GIT [41], and K-LITE [36]. FILIP attempts to obtain a fine-grained alignment between image patches and text words. In contrast, CLIP only obtains an image-level alignment between an image and a text sentence. FILIP achieves this goal by a modified contrastive loss. Instead of training both image and text models from scratch, LiT [48] shows that employing a pretrained image model and locking it would greatly benefit zero-shot classification. Under the contrastive framework, ALIGN [17] and BASIC [26] investigate how the scaling up of model, data, and batch size benefits contrastive learning. Instead of only leveraging contrastive learning framework, BLIP [21] introduces a mixed contrastive learning and generative learning for vision-language model. Further, GIT [41] employs a pure generative learning framework and demonstrates its superior performance.", + "bbox": [ + 496, + 234, + 892, + 505 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The success of CLIP and the above methods highly depends on large-scale paired image-text data set [3, 17, 34, 35, 37, 38]. Compared with classification data sets, such as ImageNet 1K [7] and ImageNet 21K [33], which require careful human annotation, there are abundant paired image-text data on the Web and can be more easily collected [34].", + "bbox": [ + 496, + 506, + 890, + 595 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Large batch size is a prerequisite for vision-language contrastive learning. Data Parallelism (DP) and Model Parallelism (MP) are two widely used methods in deep learning for distributed training [8,12,28,39,44,45]. There are many related works on this topic, such as DeepSpeed [29-31] and Colossal-AI [1]. We recommend interested readers to refer to these papers for some common distributed learning techniques. In the following, we will describe several methods that trade computation for memory in the backbone part.", + "bbox": [ + 496, + 597, + 890, + 733 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Trade Computation for Memory in Backbone", + "text_level": 1, + "bbox": [ + 500, + 741, + 883, + 758 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Checkpointing [5] is an effective approach to reduce memory consumption, especially for the intermediate results of low-cost operation. It only stores feature maps of some high-cost operations, such as convolution, MLP, and self-attention, but drops feature maps of low-cost operations such as activation (e.g., ReLU, GeLU) and layer normalization in the forward pass. In the backward process, these dropped feature maps can be recomputed quickly at a low cost. By dropping some intermediate feature maps, we can", + "bbox": [ + 496, + 763, + 890, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "22649", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/94733f47f479ccf72c83b72bcba1830dcefdf3e4eff2679a8b399530e87f0eb0.jpg", + "image_caption": [ + "Figure 1. Illustration of the original CLIP training. All image features $\\mathrm{I}_A$ and text features $\\mathrm{T}_A$ are gathered to every GPU via all_gather to calculate the $B\\times B$ similarity matrix for contrastive loss computation. This computation is performed repeatedly on every GPU." + ], + "image_footnote": [], + "bbox": [ + 80, + 89, + 464, + 234 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "save a great amount of memory. Gruslys et al. [13] further extend the idea of Checkpointing to the recursive neural network. Checkpointing is helpful but still not sufficient if we want to further increase the batch size.", + "bbox": [ + 75, + 344, + 468, + 404 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Recently, BASIC [26] introduces a gradient accumulating (GradAccum) method for memory saving in backbone via micro-batching the contrastive loss. This approach is based on the observation that when computing the contrastive loss, we only need the full similarity matrix instead of all intermediate results. Thus, BASIC proposes to trade computation for memory by dropping some intermediate hidden states during the forward process, and then recompute them during back-propagation. This method can effectively reduce the memory consumption in the backbone part but it requires one extra forward computation. A similar gradient cache approach [10] was also introduced for dense passage retriever in natural language processing.", + "bbox": [ + 75, + 405, + 468, + 602 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Reversible model structure [11, 19] is another elegant method for memory saving in backbone. However, it requires block adaption because it needs to reconstruct the input layer according to the output layer in the back propagation process. Reversible structure is particularly suitable for models that do not change activation shape in the whole network. However, reconstructing a layer from its output inevitably takes more backward time.", + "bbox": [ + 75, + 602, + 468, + 722 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "All above three mechanisms mainly focus on reducing memory consumption in the backbone part. However, none of them pays attention to reducing the memory consumption of the contrastive loss, which has been a big bottleneck for large batch size contrastive training. We will explain this problem in the next section.", + "bbox": [ + 75, + 723, + 468, + 813 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Motivation", + "text_level": 1, + "bbox": [ + 76, + 829, + 192, + 844 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Distributed contrastive learning is different from traditional distributed data parallel and model parallel strategies. Data parallel (DP) is particularly effective when activations", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "in the network cost most of the GPU memory. For example, in [12], Goyal et al. succeeded in training an ImageNet classification model in one hour. Each GPU independently performs forward and backward computation. Only after backward computation, the GPUs perform a gradient communication to merge gradients. In contrast, model parallel (MP) is more effective when model parameters (e.g. 10 billions of parameters) consume a large amount of GPU memory. In this way, the model parameters are sliced and assigned to different GPUs. However, different from the DP and MP problems, in contrastive training, besides the backbone and model parameters, the contrastive loss consumes a larger amount of GPU memory especially when a large batch size is used.", + "bbox": [ + 496, + 90, + 890, + 301 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As we have discussed in the introduction section, a large batch size is of crucial importance for contrastive learning. Previous research [26] also proves theoretically that a larger contrastive batch size can lead to a better representation for image-text models. Interested readers can refer to Theorem 1 in [26] and its appendix for the proof.", + "bbox": [ + 496, + 301, + 890, + 393 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "However, a large batch in contrastive loss will consume a large amount of GPU memory, usually of $\\mathcal{O}(B^2)$ , where $B$ is the batch size. Let us take an examination of the memory consumption of contrastive loss. For example, for a batch size of 65,536, it stores a similarity matrix of 4.3 billions parameters which requires 16GB of memory using Float32. Its gradient computation in the back-propagation process will take another 16GB of memory. Considering other memory cost of model parameters and backbone intermediate activations, it cannot be trained using A100 40GB GPUs even with mixed precision computation.", + "bbox": [ + 496, + 393, + 890, + 559 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "After investigating the constrastive loss in depth, we notice that there is much redundant memory consumption and computational waste in the current CLIP training solution. As shown in Fig. 1, in the original CLIP training, to calculate the gradients for the text and image features in the hosting GPU, every GPU in the distributed training environment needs to compute the entire $B \\times B$ similarity matrix, which is not necessary as we will show later.", + "bbox": [ + 496, + 559, + 890, + 679 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our motivation in this paper is to eliminate memory redundancy and remove unnecessary calculation via a loss decomposition, and thus enable large batch training using limited GPU resource.", + "bbox": [ + 496, + 680, + 890, + 739 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. DisCo-CLIP: A Distributed Contrastive Loss for Memory Efficient CLIP Training", + "text_level": 1, + "bbox": [ + 496, + 751, + 890, + 787 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we introduce DisCo, a distributed solution for contrastive loss computation. Using DisCo in CLIP, we accomplish a new memory efficient CLIP training method, called DisCo-CLIP. To this end, we decompose the loss calculation into two parts, one part to compute the intra-GPU loss and gradients and the other part to compute inter-GPU loss and gradients. This section will first intro", + "bbox": [ + 496, + 794, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "22650", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "duce how we decompose this loss calculation. Then, we will describe the algorithm implementation of DisCo-CLIP in detail.", + "bbox": [ + 75, + 90, + 470, + 135 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. DisCo: A Distributed Contrastive Loss", + "text_level": 1, + "bbox": [ + 76, + 146, + 410, + 161 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As shown in Eq. 1, $\\mathrm{I}_A$ and $\\mathrm{T}_A$ denote all image and text features collected from all GPUs. Here, we use $\\mathrm{I}_n$ and $\\mathrm{T}_n$ to denote the image and text features on the $n$ -th GPU, and use $\\mathrm{I}_{\\overline{n}}$ and $\\mathrm{T}_{\\overline{n}}$ to denote the image and text features on all other GPUs. The division is denoted as,", + "bbox": [ + 75, + 170, + 468, + 244 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {I} _ {A} = \\left[ \\begin{array}{l l} \\mathrm {I} _ {n}, & \\mathrm {I} _ {\\overline {{n}}} \\end{array} \\right], \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 220, + 256, + 468, + 280 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {T} _ {A} = \\left[ \\mathrm {T} _ {n}, \\mathrm {T} _ {\\bar {n}} \\right]\n$$\n", + "text_format": "latex", + "bbox": [ + 217, + 275, + 326, + 292 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The shapes of $\\mathrm{I}_A$ and $\\mathrm{T}_A$ are $B\\times D$ , the shapes of $\\mathrm{I}_n$ and $\\mathrm{T}_n$ are $\\frac{B}{N}\\times D$ , and the shapes of $\\mathrm{I}_{\\overline{n}}$ and $\\mathrm{T}_{\\overline{n}}$ are $\\frac{B(N - 1)}{N}\\times D$ .", + "bbox": [ + 76, + 304, + 468, + 337 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "According to the above definition, the contrastive loss can be decomposed and rewritten as,", + "bbox": [ + 76, + 337, + 467, + 364 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {d} = \\mathcal {L} _ {1} \\left(\\mathrm {I} _ {n}, \\mathrm {T} _ {A}\\right) + \\mathcal {L} _ {1} \\left(\\mathrm {I} _ {\\bar {n}}, \\mathrm {T} _ {A}\\right) + \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 378, + 468, + 401 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {2} \\left(\\mathrm {T} _ {n}, \\mathrm {I} _ {A}\\right) + \\mathcal {L} _ {2} \\left(\\mathrm {T} _ {\\bar {n}}, \\mathrm {I} _ {A}\\right),\n$$\n", + "text_format": "latex", + "bbox": [ + 207, + 397, + 385, + 412 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_1(\\mathrm{I}_n,\\mathrm{T}_A)$ denotes the image-to-text contrastive loss between image features $\\mathrm{I}_n$ and text features $\\mathrm{T}_A$ , and $\\mathcal{L}_2(\\mathrm{T}_n,\\mathrm{I}_A)$ denotes the text-to-image loss between $\\mathrm{T}_n$ and $\\mathrm{I}_A$ . Mathematically, the computational result $\\mathcal{L}_d$ in Eq. 3 is the same as the result $\\mathcal{L}$ in Eq. 1. However, by decomposing the loss $\\mathcal{L}_d$ into four parts, the gradient flow in the back-propagation process is more obvious. Meanwhile, we can see that $\\mathcal{L}_1(\\mathrm{I}_{\\overline{n}},\\mathrm{T}_A)$ does not induce gradients with respect to $\\mathrm{I}_n$ and $\\mathcal{L}_2(\\mathrm{T}_{\\overline{n}},\\mathrm{I}_A)$ has no gradients with respect to $\\mathrm{T}_n$ . Actually, these two terms are redundant computation on the $n$ -th GPU in the original contrastive loss, which unnecessarily consume a large amount of memory.", + "bbox": [ + 75, + 426, + 468, + 607 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Thus, according to the decomposition in Eq. 3, we can calculate the gradients $\\frac{\\partial\\mathcal{L}_d}{\\partial\\mathrm{T}_n}$ for image features $\\mathrm{I}_n$ and the gradients $\\frac{\\partial\\mathcal{L}_d}{\\partial\\mathrm{T}_n}$ for text features $\\mathrm{T}_n$ as follows,", + "bbox": [ + 75, + 608, + 468, + 660 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {\\partial \\mathcal {L} _ {d}}{\\partial \\mathrm {I} _ {n}} = \\boxed {\\frac {\\partial \\mathcal {L} _ {1} (\\mathrm {I} _ {n} , \\mathrm {T} _ {A})}{\\partial \\mathrm {I} _ {n}} + \\frac {\\partial \\mathcal {L} _ {2} (\\mathrm {T} _ {n} , \\mathrm {I} _ {A})}{\\partial \\mathrm {I} _ {n}}} + \\boxed {\\frac {\\partial \\mathcal {L} _ {2} (\\mathrm {T} _ {\\bar {n}} , \\mathrm {I} _ {A})}{\\partial \\mathrm {I} _ {n}}}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 665, + 468, + 705 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {\\partial \\mathcal {L} _ {d}}{\\partial \\mathrm {T} _ {n}} = \\boxed {\\frac {\\partial \\mathcal {L} _ {1} (\\mathrm {I} _ {n} , \\mathrm {T} _ {A})}{\\partial \\mathrm {T} _ {n}} + \\frac {\\partial \\mathcal {L} _ {2} (\\mathrm {T} _ {n} , \\mathrm {I} _ {A})}{\\partial \\mathrm {T} _ {n}}} + \\boxed {\\frac {\\partial \\mathcal {L} _ {1} (\\mathrm {I} _ {\\bar {n}} , \\mathrm {T} _ {A})}{\\partial \\mathrm {T} _ {n}}},\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 702, + 464, + 734 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the losses in the red part can be further unfolded in a sum form as,", + "bbox": [ + 76, + 741, + 468, + 768 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {\\partial \\mathcal {L} _ {2} \\left(\\mathrm {T} _ {\\bar {n}} , \\mathrm {I} _ {A}\\right)}{\\partial \\mathrm {I} _ {n}} = \\sum_ {i \\neq n \\& i \\in [ 1, N ]} \\frac {\\partial \\mathcal {L} _ {2} \\left(\\mathrm {T} _ {i} , \\mathrm {I} _ {A}\\right)}{\\partial \\mathrm {I} _ {n}}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 776, + 468, + 814 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {\\partial \\mathcal {L} _ {1} \\left(\\mathrm {I} _ {\\bar {n}} , \\mathrm {T} _ {A}\\right)}{\\partial \\mathrm {T} _ {n}} = \\sum_ {j \\neq n \\& j \\in [ 1, N ]} \\frac {\\partial \\mathcal {L} _ {1} \\left(\\mathrm {I} _ {j} , \\mathrm {T} _ {A}\\right)}{\\partial \\mathrm {T} _ {n}}. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 142, + 811, + 467, + 845 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The gradients of $\\frac{\\partial\\mathcal{L}_d}{\\partial\\mathrm{I}_n}$ and $\\frac{\\partial\\mathcal{L}_d}{\\partial\\mathrm{T}_n}$ both consist of three terms. In both equations, all three terms can be divided into two parts, we mark them with two different colors, blue and", + "bbox": [ + 76, + 854, + 468, + 898 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/5034b66049804954e62df0e061363be9c822e472722edfd920d8fb0ec2981bde.jpg", + "image_caption": [ + "(1) Image-to-Text Contrastive Loss Backward" + ], + "image_footnote": [], + "bbox": [ + 516, + 89, + 883, + 258 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/bfaeffe052037e8c95b6e39f869017153d2f08a946abcbb82d7c283662abcae6.jpg", + "image_caption": [ + "(2) Text-to-Image Contrastive Loss Backward", + "Figure 2. Illustration of the gradient calculation of DisCo on the first GPU. In DisCo, to calculate the gradients on the current GPU, we only need to compute two $\\frac{B}{N} \\times B$ similarity matrices instead of a full $B \\times B$ matrix as shown in Fig. 1." + ], + "image_footnote": [], + "bbox": [ + 511, + 297, + 880, + 470 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "red. The gradients in the blue part are calculated on the $n$ -th (hosting) GPU, and the gradients in the red part are calculated on other GPUs. We call them intra-GPU gradients and inter-GPU gradients, respectively. When computing the red part for $\\frac{\\partial \\mathcal{L}_d}{\\partial \\mathrm{I}_n}$ , the images $\\mathrm{I}_n$ are considered as negative samples. It should be noted that although $\\mathrm{I}_n$ is regarded as negative samples, there still induce gradients for $\\mathrm{I}_n$ .", + "bbox": [ + 496, + 590, + 890, + 695 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "According to this decomposition, to compute $\\frac{\\partial\\mathcal{L}_d}{\\partial\\mathrm{I}_n}$ and $\\frac{\\partial\\mathcal{L}_d}{\\partial\\mathrm{T}_n}$ , the $n$ -th GPU only needs to compute the following four terms,", + "bbox": [ + 500, + 695, + 890, + 743 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left[ \\frac {\\partial \\mathcal {L} _ {1} \\left(\\mathrm {I} _ {n} , \\mathrm {T} _ {A}\\right)}{\\partial \\mathrm {I} _ {n}}, \\frac {\\partial \\mathcal {L} _ {2} \\left(\\mathrm {T} _ {n} , \\mathrm {I} _ {A}\\right)}{\\partial \\mathrm {I} _ {n}}, \\frac {\\partial \\mathcal {L} _ {1} \\left(\\mathrm {I} _ {n} , \\mathrm {T} _ {A}\\right)}{\\partial \\mathrm {T} _ {n}}, \\frac {\\partial \\mathcal {L} _ {2} \\left(\\mathrm {T} _ {n} , \\mathrm {I} _ {A}\\right)}{\\partial \\mathrm {T} _ {n}} \\right]. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 748, + 888, + 792 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "All four terms only need to compute two small similarity matrices of shape $\\frac{B}{N} \\times B$ instead of a full matrix of shape $B \\times B$ which consumes a large amount of memory. In this way, we can reduce memory consumption from $B^2$ to $\\frac{2B^2}{N}$ . For instance, when $N = 16$ , we save $\\frac{7}{8}$ of memory consumption, if $N$ is 64, we save $\\frac{31}{32}$ of memory consumption. Meanwhile, it also saves much computation. The compu", + "bbox": [ + 498, + 792, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "22651", + "bbox": [ + 478, + 945, + 516, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "tational cost for the contrastive similarity matrix decreases from $B^2 D$ to $\\frac{2B^2D}{N}$ .", + "bbox": [ + 76, + 90, + 468, + 121 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For the two red terms in Eq. 4,", + "bbox": [ + 96, + 123, + 302, + 137 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\left[ \\frac {\\partial \\mathcal {L} _ {2} \\left(\\mathrm {T} _ {\\bar {n}} , \\mathrm {I} _ {A}\\right)}{\\partial \\mathrm {I} _ {n}}, \\frac {\\partial \\mathcal {L} _ {1} \\left(\\mathrm {I} _ {\\bar {n}} , \\mathrm {T} _ {A}\\right)}{\\partial \\mathrm {T} _ {n}} \\right], \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 143, + 468, + 176 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "we use the all Reduce operation to perform gradient communication and collect all gradients with respect to $\\mathrm{I}_n$ and $\\mathrm{T}_n$ . Fig. 2 illustrates the gradient calculation of DisCo on the first of $N$ GPUs.", + "bbox": [ + 76, + 181, + 468, + 239 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Let us compare DisCo with the original contrastive loss. In the original implementation, because of the lack of gradient communication in the process of back-propagation among GPUs $^1$ , each GPU must compute the whole similarity matrix between $\\mathrm{I}_A$ and $\\mathrm{T}_A$ to obtain the gradients $\\frac{\\partial\\mathcal{L}_d}{\\partial\\mathrm{I}_n}$ and $\\frac{\\partial\\mathcal{L}_d}{\\partial\\mathrm{T}_n}$ on the $n$ -th GPU. In DisCo, for each GPU, we only need to calculate a subset instead of the whole similarity matrix. We then use an all Reduce operation to conduct gradient communication and collect the gradients. The distributed contrastive loss can also be applied to the contrastive loss computation in self-supervised learning [4, 6].", + "bbox": [ + 75, + 241, + 468, + 411 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Algorithm Implementation of DisCo-CLIP", + "text_level": 1, + "bbox": [ + 76, + 419, + 441, + 435 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Using DisCo in CLIP, we develop a memory efficient CLIP training method, termed as DisCo-CLIP. To make our algorithm clearer, we show the pseudo-code for DisCo-CLIP in Alg. 1. The implementation can be roughly divided into three segments. In the first segment, for each GPU with a global rank number, we extract its image and text features, and then use all_gather to collect image and text features into this GPU. Then in the second segment, we compute the similarity matrix and the two losses: image-to-text and text-to-image, and use the losses to compute the gradients. In this segment, the intra-GPU gradients, $\\left[\\frac{\\partial\\mathcal{L}_1(\\mathrm{I}_n,\\mathrm{T}_A)}{\\partial\\mathrm{I}_n},\\frac{\\partial\\mathcal{L}_2(\\mathrm{T}_n,\\mathrm{I}_A)}{\\partial\\mathrm{I}_n},\\frac{\\partial\\mathcal{L}_1(\\mathrm{I}_n,\\mathrm{T}_A)}{\\partial\\mathrm{T}_n},\\frac{\\partial\\mathcal{L}_2(\\mathrm{T}_n,\\mathrm{I}_A)}{\\partial\\mathrm{T}_n}\\right]$ , as defined in Eq. 6, will be computed on the current GPU. In the last segment, we use all Reduce to finish gradient communication. In this segment, the inter-GPU gradients, $\\left[\\frac{\\partial\\mathcal{L}_2(\\mathrm{T}_{\\overline{n}},\\mathrm{I}_A)}{\\partial\\mathrm{I}_n},\\frac{\\partial\\mathcal{L}_1(\\mathrm{I}_{\\overline{n}},\\mathrm{T}_A)}{\\partial\\mathrm{T}_n}\\right]$ , as defined in Eq. 7, will be collected to the current GPU. The intra-GPU and inter-GPU gradients are averaged to obtain $\\left[\\frac{\\partial\\mathcal{L}_d}{\\partial\\mathrm{I}_n},\\frac{\\partial\\mathcal{L}_d}{\\partial\\mathrm{T}_n}\\right]$ . Finally, we perform backward propagation for the backbone.", + "bbox": [ + 75, + 441, + 468, + 744 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "DisCo-CLIP has two advantages compared with CLIP. First, it decreases the memory consumption for the contrastive loss from $\\mathcal{O}(B^2)$ to $\\mathcal{O}\\left(\\frac{B^2}{N}\\right)$ . Second, it reduces the computational complexity of the contrastive loss from $\\mathcal{O}(B^2D)$ to $\\mathcal{O}\\left(\\frac{B^2}{N}D\\right)$ . Besides these two advantages, DisCo-CLIP is an exact solution for CLIP without sacrificing any computation accuracy.", + "bbox": [ + 75, + 744, + 468, + 854 + ], + "page_idx": 4 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1: Pseudo-code for DisCo-CLIP" + ], + "code_body": "# imageEncoder: ResNet or ViT\n# textEncoder: text Transformer\n# img[b,H,W,C]: minibatch of images\n# text[b,L]: minibatch of texts\n# t: temperature parameter\n# D: feature dimension\n# N: nums of GPU\n# rank: global rank\n# extract feature representations\ni.e = imageEncoder(img) # [b,D]\nt.e = textEncoder(text) # [b,D]\n# gather features from all gpus\nI.E = all_gather(i.e) # [N,b,D]\nT.E = all_gather(t_e) # [N,b,D]\n# scaled dot product similarities\nlogits.i = dot(I_E[rank], T_E)*t # [b,N*b]\nlogits.t = dot(T_E[rank], I_E)*t # [b,N*b]\n# image-to-text and text-to-image losses\nlabels = orange(b) + b * rank\nloss_i = cross_entropy_loss(logits.i, label)\nloss_t = cross_entropy_loss(logits.t, label)\n# loss backward\nloss = (loss.i + loss.t) / 2\nloss.backup()\n# reduce gradients and losses from all gpus\nI.E.grad = all.reduce(I.E.grad, op=AVG)\nT.E.grad = all.reduce(T.E.grad, op=AVG)\nLoss = all.reduce(loss, op=AVG)\n# backbone backward\ni.e.Backward(I.E.grad[rank])\nt.e.Backward(T.E.grad[rank])", + "bbox": [ + 506, + 109, + 890, + 498 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Note that DisCo-CLIP requires an extra all Reduce operator to perform gradient communication, which has the same cost as the all_gather operator. Compared with the full similarity matrix computation, this extra communication cost is quite small and negligible. See Table 4 for a speed comparison.", + "bbox": [ + 496, + 530, + 890, + 619 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For the backbone part, we can also use the GradAccum strategy as proposed in BASIC [26]. BASIC provides a simple yet effective memory-efficient strategy for backbone memory optimization. Combined with GradAccum, DisCo-CLIP can further lead to a more memory-efficient solution.", + "bbox": [ + 496, + 622, + 890, + 698 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/31f226f86503ec6e98ef229da40e87fb4f4a75665657626eb8f3114d11a80231.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsBackboneContra. LossOverall
CLIP [27]O(BNLD)O(B2)O(BNLD) + O(B2)
BASIC [26]O(BN)O(B2)O(BN) + O(B2)
DisCo-CLIPO(BNLD)O(B2/N)O(BNLD) + O(B2/N)
DisCo-CLIP*O(BN)O(B2/N)O(BN) + O(B2/N)
", + "bbox": [ + 509, + 713, + 880, + 801 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 1. Memory consumption comparison of different methods. DisCo-CLIP* denotes the combination of DisCo-CLIP and the GradAccum strategy in BASIC. $B$ denotes the batch size, which is usually very large, e.g. 32K, $N$ is the number of GPUs, $L$ is the number of layers in the backbone, and $D$ is the feature dimension. For simplicity, we use the same $D$ for all layers.", + "bbox": [ + 496, + 813, + 890, + 896 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "Gradient communication here in the process of back-propagation should be distinguished from the gradient collection after model backpropagation which is to collect and average the weight gradients.", + "bbox": [ + 76, + 862, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "22652", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "A detailed comparison of memory consumption for CLIP, BASIC, and DisCo-CLIP is provided in Table 1. With GradAccum, BASIC can reduce the overall memory consumption from $\\mathcal{O}(\\frac{B}{N}LD) + \\mathcal{O}(B^2)$ to $\\mathcal{O}(\\frac{B}{N}D) + \\mathcal{O}(B^2)$ . DisCo-CLIP can reduce the memory consumption to $\\mathcal{O}(\\frac{B}{N}LD) + \\mathcal{O}(\\frac{B^2}{N})$ , DisCo-CLIP* can further reduce the memory consumption to $\\mathcal{O}(\\frac{B}{N}D) + \\mathcal{O}(\\frac{B^2}{N})$ . A practical example is that, in vanilla CLIP [27] based on ViT-B/32, $D = 1024$ , $B = 32768$ , $N = 128$ .", + "bbox": [ + 76, + 90, + 472, + 233 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 76, + 246, + 209, + 263 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we first describe the experimental settings including data sets and pre-training details. Then, we present the experiments regarding memory consumption, training efficiency, batch size, and data scale. Finally, we report zero-shot classification on several data sets.", + "bbox": [ + 76, + 272, + 468, + 348 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Experimental Setting", + "text_level": 1, + "bbox": [ + 76, + 357, + 277, + 375 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Image-Text Data Sets. A large-scale image-text data set is a prerequisite for contrastive image-text pre-training. In the literature, there are many private [17, 37] or public data sets [34, 35, 38]. LAION-400M [35] is a data set with 400 million image-text pairs filtered by CLIP score. We crawl the images according to the provided URLs and finally obtain 360M image-text pairs as some URLs are expired and no longer available. LAION-5B [34] is a larger data set with 5 billion image-text pairs. It contains a subset of 2.32 billion English image-text pairs. We refer to this subset as LAION-2B as in [34]. We also crawl the data set according to the released URLs and finally obtain 2.1 billion image-text pairs. In this paper, for a fair comparison with CLIP [27] and LAION [34] which conduct experiments using 400M data pairs, we create a subset of 400M image-text pairs from our crawled LAION-2B and also make a subset of 100M image-text pairs for ablation study.", + "bbox": [ + 75, + 381, + 468, + 636 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Pre-training Details. The implementation of our DisCo-CLIP is based on OpenCLIP [16], an open source CLIP implementation. We follow the original CLIP [27] and mainly use ViT-B/32 [9] as the vision backbone. Training images are resized to $224 \\times 224$ and fed to the vision backbone. For the text backbone, we use a text Transformer [8, 39], and set the maximum length of text to 76 as in [27]. Due to limited time and GPU resource, we do not train ViT-L/14 because it takes more than four times of training time compared to ViT-B/32. It should also be noted that in all our experiments, we do not use the GradAccum strategy as in BASIC [26]. Checkpointing is enabled in vanilla CLIP and our DisCo-CLIP. We train models using an Adam [18] optimizer and cosine learning rate scheduler with a linear warmup [24]. Weight decay regularization [25]", + "bbox": [ + 75, + 638, + 470, + 864 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "is used on all parameters except bias, layer normalization, and temperature in contrastive loss. Since our training experiments use different batch sizes, according to previous works [12, 28], we change the learning rate for different batch sizes. For our learning rate scheduler, we first define a base learning rate of 5e-4 and a base batch size of 32,768, and then linearly warm it up to the maximum learning rate. The maximum learning rate is determined according to a linear strategy, max_lr = base_lr * batch_size / 32,768. Training stability is a challenging issue in mixed-precision training as NaN might happen in many cases. We obverse that $\\beta_{2}$ in Adam is very important for training stability and find 0.98 works well for our experiments instead of the default value of 0.999. For most of our experiments, we use 64 NVIDIA A100 40GB GPUs for model training, but for some experiments, we only use 8 NVIDIA A100 40GB GPUs to show that our solution is more resource-efficient.", + "bbox": [ + 496, + 90, + 893, + 347 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Evaluation Results", + "text_level": 1, + "bbox": [ + 500, + 357, + 681, + 372 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Equivalence Validation. To empirically validate our theoretical analysis, we conduct experiments to compare CLIP and DisCo-CLIP. We use the same random seed to initiate the network parameters and use the same batch size 32,768 on 64 GPUs, and train ViT-B/32 models with 16 epochs on LAION-100M.", + "bbox": [ + 496, + 380, + 893, + 470 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/f29d8fbb2e66f25a3502cb08017697faa24abb12074d5b17053818f94988b49b.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsMemoryAccuracyTime (Hours)
CLIP27.4GB51.6413.4
DisCo-CLIP16.5GB51.6412.1
", + "bbox": [ + 524, + 481, + 867, + 529 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "From Table 2, we see that DisCo-CLIP has exactly the same accuracy as CLIP, but uses lower memory consumption and less training time. Under the same training settings, DisCo-CLIP and CLIP also have exactly the same training curves. This experiment further validates the numerical equivalence between DisCo-CLIP and CLIP.", + "bbox": [ + 496, + 625, + 890, + 717 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/1d01318a69e53ff382830b6830067abec51d95d7018cc2a1bbf0b6d7b2967dc0.jpg", + "table_caption": [ + "Table 2. CLIP Reproduction. Under the same training settings, DisCo-CLIP has exactly the same accuracy (top-1 zero-shot classification accuracy on ImageNet) as CLIP, but uses lower memory consumption and less training time. Training resource: 64 A100 40GB GPUs." + ], + "table_footnote": [], + "table_body": "
MethodsGPUsBSMemory
CLIP64× A100 40GB32,76827.4GB
CLIP64× A100 40GB65,536OOM
DisCo-CLIP64× A100 40GB32,76816.5GB
DisCo-CLIP64× A100 40GB196,60838.1GB
DisCo-CLIP8× A100 40GB32,76836.9GB
", + "bbox": [ + 517, + 727, + 874, + 816 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 3. Memory consumption of CLIP and DisCo-CLIP under different settings. \"OOM\" means out of memory.", + "bbox": [ + 496, + 825, + 890, + 854 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Memory Consumption. Besides memory consumption of network parameters, backbone and contrastive loss con", + "bbox": [ + 496, + 869, + 890, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "2https://github.com/mlfoundations/open Clip", + "bbox": [ + 91, + 873, + 434, + 886 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "3https://github.com/openai/CLIP", + "bbox": [ + 91, + 886, + 341, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "22653", + "bbox": [ + 478, + 944, + 517, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/d73b17743e1b70af6266910a918d3b2ac8bf39f2d595873485cbe436cd914ae0.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsGPUsBatch sizeBackboneLoss OperatorsLoss TotalBackwardTotal
all_gatherLossall ReduceLoss BPBackbone BP
CLIP6432,768129.46.155.4-61.5414.8605.6
DisCo-CLIP6432,7686.11.64.312.0 (80.5% ↓)2.8337.3481.5 (20.5% ↓)
", + "bbox": [ + 84, + 88, + 885, + 147 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "sumes most memory. We evaluate the memory consumption of the original CLIP and our DisCo-CLIP under different settings. We report the peak memory consumption for different settings, and the results are shown in Table 3.", + "bbox": [ + 75, + 212, + 467, + 272 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We have three observations from Table 3. 1) CLIP with ViT-B/32 can be trained with batch size 32,768 but fails with batch size 65,536. 2) Our DisCo-CLIP can enable training of ViT-B/32 with a much larger batch size, 196,608 with 64 A100 40GB GPU. 3) DisCo-CLIP can enable training of the same model on a cluster with only 8 GPUs.", + "bbox": [ + 75, + 273, + 467, + 363 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Training Speed. One iteration of CLIP consists of extracting features from backbone, gathering features from all GPUs, calculating loss, and executing back-propagation. (We exclude some other factors, including data loading and optimizer update that are not directly related to the model computation or can be ignored.) Instead, DisCo-CLIP decomposes the back-propagation into two BP processes (Loss BP and Backbone BP) and have an additional all Reduce operator. We evaluate the running time of each operator in CLIP and our DisCo-CLIP, and the results are shown in Table 4.", + "bbox": [ + 75, + 364, + 467, + 527 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "From Table 4, we can see that 1) for total loss computation, under the same batch size 32,768, we decrease the computation time from $61.5\\mathrm{ms}$ to $12.0\\mathrm{ms}$ . It is because in DisCo-CLIP, we only need to calculate two subset similarity matrices between multiplying a $\\frac{B}{N} \\times D$ matrix and a $B \\times D$ matrix instead of a full matrix multiplication between two $B \\times D$ matrices. 2) the operators of both all Reduce and all_gather are faster compared to the loss computation. 3) under the same batch size 32,768, DisCo-CLIP improves around $20.5\\%$ total training efficiency.", + "bbox": [ + 75, + 531, + 467, + 681 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Overall, with DisCo-CLIP, we are able to not only train contrastive learning models with a larger batch size, but also improve the training speed considerably. DisCo-CLIP is a free-lunch solution for large-scale contrastive learning.", + "bbox": [ + 75, + 681, + 467, + 743 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/589db2232d045de0036832362af9d8697c38061dccbdcd5bd38166cd7d2076c0.jpg", + "table_caption": [ + "Table 4. Detailed comparisons of training efficiency of CLIP and DisCo-CLIP. All time-related measurements (the last nine columns) are in milliseconds (ms). DisCo-CLIP saves more computational time in loss computation. Training resource: 64 A100 40GB GPUs." + ], + "table_footnote": [], + "table_body": "
Batch SizeStepsEpochsViT-B/32
8,192≈ 200 K1648.76
16,384≈ 100 K1650.95
32,768≈ 50 K1651.64
65,536≈ 25 K1651.91
", + "bbox": [ + 125, + 755, + 423, + 830 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Batch Size. To assess the role of a larger batch size to the final performance, we conduct some controlled experiments for ViT-B/32 on our LAION-100M and LAION-400M subsets. All training hyper-parameters are the same except that we vary the batch size and the number of training steps. To ensure all models \"see\" the same number of training samples, we use fewer training steps when training with a larger batch size. In Table 5, we report the results of all settings.", + "bbox": [ + 496, + 210, + 890, + 332 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "From Table 5, we can see that large batch size generally helps contrastive learning. The performance of using batch size 65,536 improves that of using batch size 32,768 by around $0.3\\%$ . In the evaluation of data scaling, we further observe that the improvement widens when we train the model for more epochs.", + "bbox": [ + 496, + 333, + 890, + 422 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/a849612183492506e2136eaf80a74409e4c6c9f171ffa270ee3b1541371dad92.jpg", + "table_caption": [ + "Table 5. Evaluation of different batch sizes on DisCo-CLIP. All models are trained for 16 epochs on a LAION-100M data set, we show top-1 zero-shot classification accuracy on ImageNet. Training resource: 64 A100 40GB GPUs." + ], + "table_footnote": [], + "table_body": "
Batch Size100M×16400M×4400M×8
16,38450.9554.3658.38
32,76851.6455.5259.69
65,53651.9155.5059.96
", + "bbox": [ + 539, + 436, + 854, + 497 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 6. Evaluation of data scaling on DisCo-CLIP. Three batch sizes are evaluated with two LAION subsets: LAION-100M and LAION-400M. The numbers $\\times 16$ , $\\times 4$ , and $\\times 8$ are the training epochs for each data set. Training resource: 64 A100 40GB GPUs.", + "bbox": [ + 496, + 508, + 890, + 564 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Data Scaling. To investigate the role of data scaling, we also conduct some controlled experiments for ViT-B/32 on the LAION 100M and LAION 400M subsets. For all models, we use three different batch sizes, 16,384, 32,768 and 65,536 for training. Models are trained with three different settings, 100M with 16 epochs, 400M with 4 epochs and 400M with 8 epochs. Table 6 reports the final ImageNet top-1 zero-shot classification accuracy of all models.", + "bbox": [ + 496, + 582, + 890, + 702 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "From Table 6, we observe that, \"seeing\" the same number of training samples (LAION-100M with 16 epochs, LAION-400M with 4 epochs.), the model trained on larger scale of data set can obtain better performance. For example, trained with the same batch size 65,536, the performance improves from $51.91\\%$ to $55.50\\%$ when the data set increases from 100M to 400M. This observation validates the value of data scaling. This observation is also consistent with the combined scaling law in BASIC [26]. We also find that training with more epochs on larger scale of data with larger batch size will bring in larger performance gain. The gap between models (with batch sizes 32,768 and 65,536) trained on 400M with 4 epochs is around $0\\%$ (from", + "bbox": [ + 496, + 704, + 890, + 898 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "22654", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/66624dea6f88f35ab91401025f28b9c238721e8b8bf1f0b05f543212c7d56bac.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelData SetsEpochsStepsBatch SizeINet [7]INet-v2 [32]INet-R [15]INet-S [40]
CLIP [27]CLIP WIT 400M32≈ 400 K32,76863.356.069.442.3
OpenCLIP [16,34]LAION-400M32≈ 400 K32,76862.955.173.449.4
DisCo-CLIPLAION-400M*32≈ 400 K32,76863.255.273.450.6
DisCo-CLIPLAION-400M*32≈ 200 K65,53664.356.273.851.7
", + "bbox": [ + 78, + 87, + 893, + 162 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "55.52% to 55.50%), but it increases to 0.3% (from 59.69% to 59.96%) when the models are trained for 8 epochs. Thus, we can expect that if we use larger scale of data set, we should also use larger batch size to get a better performance.", + "bbox": [ + 75, + 241, + 470, + 303 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.3. Zero-Shot Classification", + "text_level": 1, + "bbox": [ + 76, + 308, + 299, + 324 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Following CLIP [27] and LAION-5B [34], we evaluate zero-shot top-1 classification accuracy of our models on several data sets, including INet [7], INet-v2 [32], INet-R [15] and INet-S [40]. We use exactly the same 80 prompts as CLIP. Some standard prompts are like \"a bad photo of a $\\{\\}$ \", \"a photo of many $\\{\\}$ \", and etc. Following LAION-5B, we extract the embedding for each prompt using the text encoder (text Transformer), and average embeddings of all prompts in each class, and finally get the final class embedding. Given an image, we extract its image embedding via the image encoder (ViT-B/32), and compute its similarities with all class embeddings, and classify it into the class with the highest similarity score.", + "bbox": [ + 75, + 330, + 468, + 527 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We can see from Table 7, that using the same batch size of 32,768 as the OpenCLIP implementation, our DisCo-CLIP obtains a similar performance with OpenCLIP, the result of OpenCLIP is reported by LAION group in [34]. Using a larger batch size of 65,536, DisCo-CLIP achieves a better performance than the OpenCLIP implementation and the original CLIP. Specifically, trained with the same 32 epochs, DisCo-CLIP using a batch size of 65,536 improves the OpenCLIP's result that is based on batch size of 32,768 by $1.4\\%$ . Note that when doubling the batch size, we halve the training steps. This observation further validates that large batch size is important for contrastive learning.", + "bbox": [ + 75, + 527, + 470, + 710 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Discussion", + "text_level": 1, + "bbox": [ + 76, + 720, + 191, + 736 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Recent developments in large-scale contrastive or generative learning, such as CLIP [27], ALIGN [17], FILIP [43], LiT [48], BASIC [26], LAION-5B [34], and GIT [41] have potential for many real-world applications, such as image classification, text-to-image retrieval, recommendation system, and generation models. Besides large-scale data sets, the progress highly depends on powerful GPU or TPU computing resources. As shown in Table 8, all methods use", + "bbox": [ + 75, + 746, + 468, + 868 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "a large amount of computing hardwares. FILIP uses less GPU but also uses smaller batch size.", + "bbox": [ + 500, + 241, + 890, + 270 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/7bfdbe417fb3213e1b5f1d70367b75db2ac0756f3958b4c36ee3d01721f95017.jpg", + "table_caption": [ + "Table 7. Comparison of DisCo-CLIP with vanilla CLIP and re-implemented CLIP by LAION group. We report top-1 zero-shot classification accuracy (\\%) on several data sets. All models are based on ViT-B/32. Our LAION-400M* is a 400M subset of LAION-2B. Training resource: 64 A100 40GB GPUs." + ], + "table_footnote": [], + "table_body": "
MethodsHardware
CLIP [27]256 NVIDIA V100 GPUs
FILIP [43]128 NVIDIA V100 GPUs
LAION-5B [34]128-400 NVIDIA A100 GPUs
LiT [48]128-400 TPUs
BASIC [26]2,048 TPUs v3
", + "bbox": [ + 535, + 282, + 857, + 372 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 8. Several vision-language contrastive learning methods and their used hardwares.", + "bbox": [ + 498, + 382, + 890, + 409 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Unfortunately, only a few big technology companies can afford this task. Large batch contrastive loss consumes a large amount of GPU memory, while large batch size is a prerequisite for contrastive learning. As a result, it is challenging for companies with limited resources or academic research institutes to contribute to research on this topic. Our work provides a simple yet effective solution for reducing memory consumption that can help bridge the gap between academia and industry on this topic.", + "bbox": [ + 496, + 431, + 893, + 569 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 585, + 619, + 602 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we have proposed a simple yet effective distributed contrastive loss solution called DisCo to reduce the memory consumption in contrastive learning. By decomposing the loss computation into intra-GPU computation and inter-GPU computation, we can remove redundant memory consumption and use a all Reduce operator to collect inter-GPU gradients. Using DisCo in CLIP, the introduced DisCo-CLIP can enable a much larger batch contrastive learning compared to CLIP using the same GPU resource. Specifically, we can train DisCo-CLIP models with batch size 32,768 using 8 A100 40GB GPUs, or with batch size 196K using 64 GPUs. We hope DisCo-CLIP will also help and motivate self-supervised learning [4, 6] which also uses contrastive learning.", + "bbox": [ + 496, + 613, + 893, + 825 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "8. Acknowledgement", + "text_level": 1, + "bbox": [ + 500, + 843, + 679, + 859 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was partially supported by OPPO Research Fund.", + "bbox": [ + 500, + 869, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_footnote", + "text": "4https://github.com/openai/CLIP/blob/main/notebooks/Prompt_Engineering_for_ImageNet.ipynb", + "bbox": [ + 76, + 875, + 467, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "22655", + "bbox": [ + 478, + 944, + 517, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Zhengda Bian, Hongxin Liu, Boxiang Wang, Haichen Huang, Yongbin Li, Chuanrui Wang, Fan Cui, and Yang You. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 18123-18133, 2022. 2, 8" + ], + "bbox": [ + 501, + 92, + 890, + 824 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "22657", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/DisCo-CLIP_ A Distributed Contrastive Loss for Memory Efficient CLIP Training/e80e2080-33a9-4c63-8bae-91e19a54d7b9_model.json b/2023/DisCo-CLIP_ A Distributed Contrastive Loss for Memory Efficient CLIP Training/e80e2080-33a9-4c63-8bae-91e19a54d7b9_model.json new file mode 100644 index 0000000000000000000000000000000000000000..90361c71159649f9053f1f247ddabd4a9230f706 --- /dev/null +++ b/2023/DisCo-CLIP_ A Distributed Contrastive Loss for Memory Efficient CLIP Training/e80e2080-33a9-4c63-8bae-91e19a54d7b9_model.json @@ -0,0 +1,2244 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.259, + 0.131, + 0.713, + 0.177 + ], + "angle": 0, + "content": "DisCo-CLIP: A Distributed Contrastive Loss for Memory Efficient CLIP Training" + }, + { + "type": "text", + "bbox": [ + 0.148, + 0.204, + 0.816, + 0.259 + ], + "angle": 0, + "content": "Yihao Chen, Xianbiao Qi, Jianan Wang, Lei Zhang* International Digital Economy Academy (IDEA), Shenzhen, Guangdong, China. {chenyihao, qixianbiao, wangjianan, leizhang}@idea.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.292, + 0.314, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.324, + 0.473, + 0.673 + ], + "angle": 0, + "content": "We propose DisCo-CLIP, a distributed memory-efficient CLIP training approach, to reduce the memory consumption of contrastive loss when training contrastive learning models. Our approach decomposes the contrastive loss and its gradient computation into two parts, one to calculate the intra-GPU gradients and the other to compute the inter-GPU gradients. According to our decomposition, only the intra-GPU gradients are computed on the current GPU, while the inter-GPU gradients are collected via all-reduce from other GPUs instead of being repeatedly computed on every GPU. In this way, we can reduce the GPU memory consumption of contrastive loss computation from \\(\\mathcal{O}(B^2)\\) to \\(\\mathcal{O}\\left(\\frac{B^2}{N}\\right)\\), where \\(B\\) and \\(N\\) are the batch size and the number of GPUs used for training. Such a distributed solution is mathematically equivalent to the original non-distributed contrastive loss computation, without sacrificing any computation accuracy. It is particularly efficient for large-batch CLIP training. For instance, DisCo-CLIP can enable contrastive training of a ViT-B/32 model with a batch size of 32K or 196K using 8 or 64 A100 40GB GPUs, compared with the original CLIP solution which requires 128 A100 40GB GPUs to train a ViT-B/32 model with a batch size of 32K." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.702, + 0.21, + 0.717 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.727, + 0.47, + 0.879 + ], + "angle": 0, + "content": "Vision-language representation learning from massive image-text pairs has recently attracted tremendous attention for its great potential in many applications such as zero-shot classification and text-image retrieval. Representative works include CLIP [27], ALIGN [17], Florence [47], CoCa [46], and BASIC [26], which all leverage hundreds of millions or even billions of image-text pairs collected from the Web to learn a semantic-rich and language-aligned visual representation [22]. As the web-collected data inevitably contain noises, CLIP [27] for the first time applies" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.293, + 0.893, + 0.445 + ], + "angle": 0, + "content": "contrastive learning on 400M image-text pairs, which implies a weak but more proper assumption about the data: the relevance between paired image and text is greater than that between unpaired image and text. For its demonstrated performance in CLIP, contrastive learning has been widely adopted in subsequent works. Accordingly, several imagedataset data sets with increasingly larger scales have also been developed and made publicly available, such as Conceptual 12M [3], YFCC 100M [38], WIT 37.6M [37], LAION-400M [35], and LAION-5B [34]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.446, + 0.895, + 0.672 + ], + "angle": 0, + "content": "The goal of contrastive learning in CLIP is to learn an alignment between image and text via two encoders. That is, it encourages paired image and text (called a positive pair) to be similar and meanwhile enforces unpaired image and text (called a negative pair) to be dissimilar. For any positive image-text pair, as there are normally unlimited number (up to the total number of images or texts in a data set) of negative image-text pairs, it is crucial to include a sufficiently large number of negative pairs in a contrastive loss to make the representation learning effective, as validated in all related works such as CLIP [27], Florence [47], OpenCLIP [16], and BASIC [26]. Specifically, BASIC shows that larger batch size, plus larger data set and larger model, theoretically lead to a better generalization performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.673, + 0.895, + 0.839 + ], + "angle": 0, + "content": "However, a fundamental technical challenge in training a CLIP-like model is how to enlarge its batch size under the constraint of limited GPU memory. For instance, when the batch size is 65,536, the similarity matrix for all imag-text pairs in the batch will cost about 16GB using Float32. As the backbone part also consumes a significant portion of GPU memory, especially for large backbones such as ViT-Large or ViT-Huge [9], scaling up batch size presents a great challenge, usually requiring hundreds of V100 or A100 GPUs [16, 27, 47], which are inaccessible for most research scientists." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.903 + ], + "angle": 0, + "content": "In this work, we develop a distributed solution called DisCo-CLIP for constrastive loss computation, which can save a large amount of memory for contrastive loss and make CLIP training more memory-efficient. Our method" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.222, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "22648" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.411 + ], + "angle": 0, + "content": "starts from a decomposition of the original contrastive loss. Based on this decomposition, we divide the contrastive loss into two parts, one to calculate the intra-GPU loss and gradients, and the other one to calculate the inter-GPU loss and gradients. For a mini-batch on the \\( n \\)-th GPU (hereinafter called its hosting GPU), its intra-GPU gradients are calculated on its hosting GPU, and its inter-GPU gradients are collected from other GPUs. DisCo is an exact solution, mathematically equivalent to the original non-distributed contrastive loss, but more memory- and computation-efficient. It can decrease the memory cost of contrastive loss from \\( \\mathcal{O}(B^2) \\) to \\( \\mathcal{O}\\left(\\frac{B^2}{N}\\right) \\), where \\( B \\) and \\( N \\) are the batch size and the number of GPUs. When \\( N \\) equals to 64, it means around \\( 97\\% \\) (see Sec. 4.1 for details) of the memory, and similarly the computational cost, in contrastive loss can be saved. Thus, using DisCo in CLIP, we can enable contrastive training with a larger batch size. Using 8 Nvidia A100 40GB GPUs, DisCo-CLIP can enable contrastive training of a ViT-B/32 model with a batch size of 32,768. Using 64 A100 40GB GPUs, DisCo-CLIP can train the same model with a larger batch size of 196K." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.411, + 0.39, + 0.425 + ], + "angle": 0, + "content": "We summarize our contributions in twofold." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.437, + 0.47, + 0.543 + ], + "angle": 0, + "content": "- We propose a novel distributed contrastive loss solution called DisCo for memory efficient CLIP training, which can significantly reduce the memory consumption of the contrastive loss computation. Such a solution enables a larger batch size for contrastive training using the same computing resource without sacrificing any computation accuracy." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.555, + 0.469, + 0.6 + ], + "angle": 0, + "content": "- We further validate that training with a larger batch size can further improve the performance of contrastive learning models." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.437, + 0.47, + 0.6 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.614, + 0.364, + 0.631 + ], + "angle": 0, + "content": "2. Background and Related Work" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.641, + 0.47, + 0.702 + ], + "angle": 0, + "content": "In this section, we will introduce some background information for contrastive language-image pre-training (CLIP) and review some works that reduce memory consumption of the backbone part by trading computation for memory." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.711, + 0.437, + 0.728 + ], + "angle": 0, + "content": "2.1. Contrastive Language-Image Pre-training" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.735, + 0.471, + 0.903 + ], + "angle": 0, + "content": "The idea behind CLIP [27] is to learn two representations via two encoders, an image encoder [9, 14, 20, 23, 42] and a text encoder [2, 8, 28]. Its target is to encourage positive image-text pairs to have higher similarities, and enforce negative image-text pairs to have lower similarities. The training is supervised by two contrastive losses, an image-to-text loss and a text-to-image loss. Suppose we have \\( B \\) text-image pairs as a batch sending to two encoders and the model is trained using \\( N \\) GPUs, with each GPU assigned \\( b = \\frac{B}{N} \\) pairs. Here, we use \\( T_A, I_A \\) to denote all text and image features obtained from two encoders. Suppose the" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "hidden dimension is \\(D\\), then the shapes of \\(\\mathrm{T}_A, \\mathrm{I}_A\\) are both \\(B \\times D\\). In this way, our contrastive losses can be written as," + }, + { + "type": "equation", + "bbox": [ + 0.587, + 0.137, + 0.892, + 0.153 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {1} \\left(\\mathrm {I} _ {A}, \\mathrm {T} _ {A}\\right) + \\mathcal {L} _ {2} \\left(\\mathrm {T} _ {A}, \\mathrm {I} _ {A}\\right), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.159, + 0.892, + 0.234 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_1(\\mathrm{I}_A,\\mathrm{T}_A)\\) denotes the image-to-text loss, and \\(\\mathcal{L}_2(\\mathrm{T}_A,\\mathrm{I}_A)\\) represents the text-to-image loss. The image-to-text loss means that the loss is to encourage a given image to find its paired text from tens of thousands of texts, and similarly for the text-to-image loss." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.235, + 0.893, + 0.506 + ], + "angle": 0, + "content": "Motivated by the success of CLIP, many new methods have been proposed, such as FILIP [43], LiT [48], ALIGN [17], BASIC [26], BLIP [21], GIT [41], and K-LITE [36]. FILIP attempts to obtain a fine-grained alignment between image patches and text words. In contrast, CLIP only obtains an image-level alignment between an image and a text sentence. FILIP achieves this goal by a modified contrastive loss. Instead of training both image and text models from scratch, LiT [48] shows that employing a pretrained image model and locking it would greatly benefit zero-shot classification. Under the contrastive framework, ALIGN [17] and BASIC [26] investigate how the scaling up of model, data, and batch size benefits contrastive learning. Instead of only leveraging contrastive learning framework, BLIP [21] introduces a mixed contrastive learning and generative learning for vision-language model. Further, GIT [41] employs a pure generative learning framework and demonstrates its superior performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.507, + 0.892, + 0.597 + ], + "angle": 0, + "content": "The success of CLIP and the above methods highly depends on large-scale paired image-text data set [3, 17, 34, 35, 37, 38]. Compared with classification data sets, such as ImageNet 1K [7] and ImageNet 21K [33], which require careful human annotation, there are abundant paired image-text data on the Web and can be more easily collected [34]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.598, + 0.892, + 0.734 + ], + "angle": 0, + "content": "Large batch size is a prerequisite for vision-language contrastive learning. Data Parallelism (DP) and Model Parallelism (MP) are two widely used methods in deep learning for distributed training [8,12,28,39,44,45]. There are many related works on this topic, such as DeepSpeed [29-31] and Colossal-AI [1]. We recommend interested readers to refer to these papers for some common distributed learning techniques. In the following, we will describe several methods that trade computation for memory in the backbone part." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.742, + 0.885, + 0.759 + ], + "angle": 0, + "content": "2.2. Trade Computation for Memory in Backbone" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Checkpointing [5] is an effective approach to reduce memory consumption, especially for the intermediate results of low-cost operation. It only stores feature maps of some high-cost operations, such as convolution, MLP, and self-attention, but drops feature maps of low-cost operations such as activation (e.g., ReLU, GeLU) and layer normalization in the forward pass. In the backward process, these dropped feature maps can be recomputed quickly at a low cost. By dropping some intermediate feature maps, we can" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "22649" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.09, + 0.465, + 0.236 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.248, + 0.47, + 0.318 + ], + "angle": 0, + "content": "Figure 1. Illustration of the original CLIP training. All image features \\(\\mathrm{I}_A\\) and text features \\(\\mathrm{T}_A\\) are gathered to every GPU via all_gather to calculate the \\(B\\times B\\) similarity matrix for contrastive loss computation. This computation is performed repeatedly on every GPU." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.345, + 0.469, + 0.405 + ], + "angle": 0, + "content": "save a great amount of memory. Gruslys et al. [13] further extend the idea of Checkpointing to the recursive neural network. Checkpointing is helpful but still not sufficient if we want to further increase the batch size." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.406, + 0.469, + 0.603 + ], + "angle": 0, + "content": "Recently, BASIC [26] introduces a gradient accumulating (GradAccum) method for memory saving in backbone via micro-batching the contrastive loss. This approach is based on the observation that when computing the contrastive loss, we only need the full similarity matrix instead of all intermediate results. Thus, BASIC proposes to trade computation for memory by dropping some intermediate hidden states during the forward process, and then recompute them during back-propagation. This method can effectively reduce the memory consumption in the backbone part but it requires one extra forward computation. A similar gradient cache approach [10] was also introduced for dense passage retriever in natural language processing." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.603, + 0.469, + 0.723 + ], + "angle": 0, + "content": "Reversible model structure [11, 19] is another elegant method for memory saving in backbone. However, it requires block adaption because it needs to reconstruct the input layer according to the output layer in the back propagation process. Reversible structure is particularly suitable for models that do not change activation shape in the whole network. However, reconstructing a layer from its output inevitably takes more backward time." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.724, + 0.469, + 0.814 + ], + "angle": 0, + "content": "All above three mechanisms mainly focus on reducing memory consumption in the backbone part. However, none of them pays attention to reducing the memory consumption of the contrastive loss, which has been a big bottleneck for large batch size contrastive training. We will explain this problem in the next section." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.83, + 0.194, + 0.845 + ], + "angle": 0, + "content": "3. Motivation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Distributed contrastive learning is different from traditional distributed data parallel and model parallel strategies. Data parallel (DP) is particularly effective when activations" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.302 + ], + "angle": 0, + "content": "in the network cost most of the GPU memory. For example, in [12], Goyal et al. succeeded in training an ImageNet classification model in one hour. Each GPU independently performs forward and backward computation. Only after backward computation, the GPUs perform a gradient communication to merge gradients. In contrast, model parallel (MP) is more effective when model parameters (e.g. 10 billions of parameters) consume a large amount of GPU memory. In this way, the model parameters are sliced and assigned to different GPUs. However, different from the DP and MP problems, in contrastive training, besides the backbone and model parameters, the contrastive loss consumes a larger amount of GPU memory especially when a large batch size is used." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.303, + 0.892, + 0.394 + ], + "angle": 0, + "content": "As we have discussed in the introduction section, a large batch size is of crucial importance for contrastive learning. Previous research [26] also proves theoretically that a larger contrastive batch size can lead to a better representation for image-text models. Interested readers can refer to Theorem 1 in [26] and its appendix for the proof." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.394, + 0.892, + 0.56 + ], + "angle": 0, + "content": "However, a large batch in contrastive loss will consume a large amount of GPU memory, usually of \\(\\mathcal{O}(B^2)\\), where \\(B\\) is the batch size. Let us take an examination of the memory consumption of contrastive loss. For example, for a batch size of 65,536, it stores a similarity matrix of 4.3 billions parameters which requires 16GB of memory using Float32. Its gradient computation in the back-propagation process will take another 16GB of memory. Considering other memory cost of model parameters and backbone intermediate activations, it cannot be trained using A100 40GB GPUs even with mixed precision computation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.56, + 0.892, + 0.68 + ], + "angle": 0, + "content": "After investigating the constrastive loss in depth, we notice that there is much redundant memory consumption and computational waste in the current CLIP training solution. As shown in Fig. 1, in the original CLIP training, to calculate the gradients for the text and image features in the hosting GPU, every GPU in the distributed training environment needs to compute the entire \\( B \\times B \\) similarity matrix, which is not necessary as we will show later." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.681, + 0.892, + 0.74 + ], + "angle": 0, + "content": "Our motivation in this paper is to eliminate memory redundancy and remove unnecessary calculation via a loss decomposition, and thus enable large batch training using limited GPU resource." + }, + { + "type": "title", + "bbox": [ + 0.498, + 0.752, + 0.892, + 0.788 + ], + "angle": 0, + "content": "4. DisCo-CLIP: A Distributed Contrastive Loss for Memory Efficient CLIP Training" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In this section, we introduce DisCo, a distributed solution for contrastive loss computation. Using DisCo in CLIP, we accomplish a new memory efficient CLIP training method, called DisCo-CLIP. To this end, we decompose the loss calculation into two parts, one part to compute the intra-GPU loss and gradients and the other part to compute inter-GPU loss and gradients. This section will first intro" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "22650" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.136 + ], + "angle": 0, + "content": "duce how we decompose this loss calculation. Then, we will describe the algorithm implementation of DisCo-CLIP in detail." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.147, + 0.411, + 0.162 + ], + "angle": 0, + "content": "4.1. DisCo: A Distributed Contrastive Loss" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.171, + 0.469, + 0.246 + ], + "angle": 0, + "content": "As shown in Eq. 1, \\( \\mathrm{I}_A \\) and \\( \\mathrm{T}_A \\) denote all image and text features collected from all GPUs. Here, we use \\( \\mathrm{I}_n \\) and \\( \\mathrm{T}_n \\) to denote the image and text features on the \\( n \\)-th GPU, and use \\( \\mathrm{I}_{\\overline{n}} \\) and \\( \\mathrm{T}_{\\overline{n}} \\) to denote the image and text features on all other GPUs. The division is denoted as," + }, + { + "type": "equation", + "bbox": [ + 0.221, + 0.257, + 0.469, + 0.281 + ], + "angle": 0, + "content": "\\[\n\\mathrm {I} _ {A} = \\left[ \\begin{array}{l l} \\mathrm {I} _ {n}, & \\mathrm {I} _ {\\overline {{n}}} \\end{array} \\right], \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.218, + 0.276, + 0.328, + 0.293 + ], + "angle": 0, + "content": "\\[\n\\mathrm {T} _ {A} = \\left[ \\mathrm {T} _ {n}, \\mathrm {T} _ {\\bar {n}} \\right]\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.305, + 0.469, + 0.338 + ], + "angle": 0, + "content": "The shapes of \\(\\mathrm{I}_A\\) and \\(\\mathrm{T}_A\\) are \\(B\\times D\\), the shapes of \\(\\mathrm{I}_n\\) and \\(\\mathrm{T}_n\\) are \\(\\frac{B}{N}\\times D\\), and the shapes of \\(\\mathrm{I}_{\\overline{n}}\\) and \\(\\mathrm{T}_{\\overline{n}}\\) are \\(\\frac{B(N - 1)}{N}\\times D\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.338, + 0.468, + 0.366 + ], + "angle": 0, + "content": "According to the above definition, the contrastive loss can be decomposed and rewritten as," + }, + { + "type": "equation", + "bbox": [ + 0.158, + 0.38, + 0.469, + 0.402 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {d} = \\mathcal {L} _ {1} \\left(\\mathrm {I} _ {n}, \\mathrm {T} _ {A}\\right) + \\mathcal {L} _ {1} \\left(\\mathrm {I} _ {\\bar {n}}, \\mathrm {T} _ {A}\\right) + \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.209, + 0.398, + 0.387, + 0.414 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {2} \\left(\\mathrm {T} _ {n}, \\mathrm {I} _ {A}\\right) + \\mathcal {L} _ {2} \\left(\\mathrm {T} _ {\\bar {n}}, \\mathrm {I} _ {A}\\right),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.427, + 0.469, + 0.608 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_1(\\mathrm{I}_n,\\mathrm{T}_A)\\) denotes the image-to-text contrastive loss between image features \\(\\mathrm{I}_n\\) and text features \\(\\mathrm{T}_A\\), and \\(\\mathcal{L}_2(\\mathrm{T}_n,\\mathrm{I}_A)\\) denotes the text-to-image loss between \\(\\mathrm{T}_n\\) and \\(\\mathrm{I}_A\\). Mathematically, the computational result \\(\\mathcal{L}_d\\) in Eq. 3 is the same as the result \\(\\mathcal{L}\\) in Eq. 1. However, by decomposing the loss \\(\\mathcal{L}_d\\) into four parts, the gradient flow in the back-propagation process is more obvious. Meanwhile, we can see that \\(\\mathcal{L}_1(\\mathrm{I}_{\\overline{n}},\\mathrm{T}_A)\\) does not induce gradients with respect to \\(\\mathrm{I}_n\\) and \\(\\mathcal{L}_2(\\mathrm{T}_{\\overline{n}},\\mathrm{I}_A)\\) has no gradients with respect to \\(\\mathrm{T}_n\\). Actually, these two terms are redundant computation on the \\(n\\)-th GPU in the original contrastive loss, which unnecessarily consume a large amount of memory." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.609, + 0.469, + 0.661 + ], + "angle": 0, + "content": "Thus, according to the decomposition in Eq. 3, we can calculate the gradients \\(\\frac{\\partial\\mathcal{L}_d}{\\partial\\mathrm{T}_n}\\) for image features \\(\\mathrm{I}_n\\) and the gradients \\(\\frac{\\partial\\mathcal{L}_d}{\\partial\\mathrm{T}_n}\\) for text features \\(\\mathrm{T}_n\\) as follows," + }, + { + "type": "equation", + "bbox": [ + 0.093, + 0.666, + 0.469, + 0.707 + ], + "angle": 0, + "content": "\\[\n\\frac {\\partial \\mathcal {L} _ {d}}{\\partial \\mathrm {I} _ {n}} = \\boxed {\\frac {\\partial \\mathcal {L} _ {1} (\\mathrm {I} _ {n} , \\mathrm {T} _ {A})}{\\partial \\mathrm {I} _ {n}} + \\frac {\\partial \\mathcal {L} _ {2} (\\mathrm {T} _ {n} , \\mathrm {I} _ {A})}{\\partial \\mathrm {I} _ {n}}} + \\boxed {\\frac {\\partial \\mathcal {L} _ {2} (\\mathrm {T} _ {\\bar {n}} , \\mathrm {I} _ {A})}{\\partial \\mathrm {I} _ {n}}}, \\tag {4}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.093, + 0.703, + 0.465, + 0.736 + ], + "angle": 0, + "content": "\\[\n\\frac {\\partial \\mathcal {L} _ {d}}{\\partial \\mathrm {T} _ {n}} = \\boxed {\\frac {\\partial \\mathcal {L} _ {1} (\\mathrm {I} _ {n} , \\mathrm {T} _ {A})}{\\partial \\mathrm {T} _ {n}} + \\frac {\\partial \\mathcal {L} _ {2} (\\mathrm {T} _ {n} , \\mathrm {I} _ {A})}{\\partial \\mathrm {T} _ {n}}} + \\boxed {\\frac {\\partial \\mathcal {L} _ {1} (\\mathrm {I} _ {\\bar {n}} , \\mathrm {T} _ {A})}{\\partial \\mathrm {T} _ {n}}},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.742, + 0.469, + 0.77 + ], + "angle": 0, + "content": "where the losses in the red part can be further unfolded in a sum form as," + }, + { + "type": "equation", + "bbox": [ + 0.14, + 0.777, + 0.469, + 0.815 + ], + "angle": 0, + "content": "\\[\n\\frac {\\partial \\mathcal {L} _ {2} \\left(\\mathrm {T} _ {\\bar {n}} , \\mathrm {I} _ {A}\\right)}{\\partial \\mathrm {I} _ {n}} = \\sum_ {i \\neq n \\& i \\in [ 1, N ]} \\frac {\\partial \\mathcal {L} _ {2} \\left(\\mathrm {T} _ {i} , \\mathrm {I} _ {A}\\right)}{\\partial \\mathrm {I} _ {n}}, \\tag {5}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.143, + 0.812, + 0.468, + 0.846 + ], + "angle": 0, + "content": "\\[\n\\frac {\\partial \\mathcal {L} _ {1} \\left(\\mathrm {I} _ {\\bar {n}} , \\mathrm {T} _ {A}\\right)}{\\partial \\mathrm {T} _ {n}} = \\sum_ {j \\neq n \\& j \\in [ 1, N ]} \\frac {\\partial \\mathcal {L} _ {1} \\left(\\mathrm {I} _ {j} , \\mathrm {T} _ {A}\\right)}{\\partial \\mathrm {T} _ {n}}. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.855, + 0.469, + 0.9 + ], + "angle": 0, + "content": "The gradients of \\(\\frac{\\partial\\mathcal{L}_d}{\\partial\\mathrm{I}_n}\\) and \\(\\frac{\\partial\\mathcal{L}_d}{\\partial\\mathrm{T}_n}\\) both consist of three terms. In both equations, all three terms can be divided into two parts, we mark them with two different colors, blue and" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.09, + 0.885, + 0.259 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.545, + 0.265, + 0.85, + 0.279 + ], + "angle": 0, + "content": "(1) Image-to-Text Contrastive Loss Backward" + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.299, + 0.882, + 0.471 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.545, + 0.477, + 0.85, + 0.492 + ], + "angle": 0, + "content": "(2) Text-to-Image Contrastive Loss Backward" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.51, + 0.892, + 0.566 + ], + "angle": 0, + "content": "Figure 2. Illustration of the gradient calculation of DisCo on the first GPU. In DisCo, to calculate the gradients on the current GPU, we only need to compute two \\(\\frac{B}{N} \\times B\\) similarity matrices instead of a full \\(B \\times B\\) matrix as shown in Fig. 1." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.591, + 0.891, + 0.696 + ], + "angle": 0, + "content": "red. The gradients in the blue part are calculated on the \\( n \\)-th (hosting) GPU, and the gradients in the red part are calculated on other GPUs. We call them intra-GPU gradients and inter-GPU gradients, respectively. When computing the red part for \\( \\frac{\\partial \\mathcal{L}_d}{\\partial \\mathrm{I}_n} \\), the images \\( \\mathrm{I}_n \\) are considered as negative samples. It should be noted that although \\( \\mathrm{I}_n \\) is regarded as negative samples, there still induce gradients for \\( \\mathrm{I}_n \\)." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.696, + 0.891, + 0.744 + ], + "angle": 0, + "content": "According to this decomposition, to compute \\(\\frac{\\partial\\mathcal{L}_d}{\\partial\\mathrm{I}_n}\\) and \\(\\frac{\\partial\\mathcal{L}_d}{\\partial\\mathrm{T}_n}\\), the \\(n\\)-th GPU only needs to compute the following four terms," + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.749, + 0.89, + 0.793 + ], + "angle": 0, + "content": "\\[\n\\left[ \\frac {\\partial \\mathcal {L} _ {1} \\left(\\mathrm {I} _ {n} , \\mathrm {T} _ {A}\\right)}{\\partial \\mathrm {I} _ {n}}, \\frac {\\partial \\mathcal {L} _ {2} \\left(\\mathrm {T} _ {n} , \\mathrm {I} _ {A}\\right)}{\\partial \\mathrm {I} _ {n}}, \\frac {\\partial \\mathcal {L} _ {1} \\left(\\mathrm {I} _ {n} , \\mathrm {T} _ {A}\\right)}{\\partial \\mathrm {T} _ {n}}, \\frac {\\partial \\mathcal {L} _ {2} \\left(\\mathrm {T} _ {n} , \\mathrm {I} _ {A}\\right)}{\\partial \\mathrm {T} _ {n}} \\right]. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.794, + 0.892, + 0.901 + ], + "angle": 0, + "content": "All four terms only need to compute two small similarity matrices of shape \\(\\frac{B}{N} \\times B\\) instead of a full matrix of shape \\(B \\times B\\) which consumes a large amount of memory. In this way, we can reduce memory consumption from \\(B^2\\) to \\(\\frac{2B^2}{N}\\). For instance, when \\(N = 16\\), we save \\(\\frac{7}{8}\\) of memory consumption, if \\(N\\) is 64, we save \\(\\frac{31}{32}\\) of memory consumption. Meanwhile, it also saves much computation. The compu" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.946, + 0.517, + 0.957 + ], + "angle": 0, + "content": "22651" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.122 + ], + "angle": 0, + "content": "tational cost for the contrastive similarity matrix decreases from \\( B^2 D \\) to \\( \\frac{2B^2D}{N} \\)." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.124, + 0.303, + 0.138 + ], + "angle": 0, + "content": "For the two red terms in Eq. 4," + }, + { + "type": "equation", + "bbox": [ + 0.176, + 0.144, + 0.47, + 0.177 + ], + "angle": 0, + "content": "\\[\n\\left[ \\frac {\\partial \\mathcal {L} _ {2} \\left(\\mathrm {T} _ {\\bar {n}} , \\mathrm {I} _ {A}\\right)}{\\partial \\mathrm {I} _ {n}}, \\frac {\\partial \\mathcal {L} _ {1} \\left(\\mathrm {I} _ {\\bar {n}} , \\mathrm {T} _ {A}\\right)}{\\partial \\mathrm {T} _ {n}} \\right], \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.182, + 0.469, + 0.241 + ], + "angle": 0, + "content": "we use the all Reduce operation to perform gradient communication and collect all gradients with respect to \\(\\mathrm{I}_n\\) and \\(\\mathrm{T}_n\\). Fig. 2 illustrates the gradient calculation of DisCo on the first of \\(N\\) GPUs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.242, + 0.47, + 0.412 + ], + "angle": 0, + "content": "Let us compare DisCo with the original contrastive loss. In the original implementation, because of the lack of gradient communication in the process of back-propagation among GPUs\\(^1\\), each GPU must compute the whole similarity matrix between \\(\\mathrm{I}_A\\) and \\(\\mathrm{T}_A\\) to obtain the gradients \\(\\frac{\\partial\\mathcal{L}_d}{\\partial\\mathrm{I}_n}\\) and \\(\\frac{\\partial\\mathcal{L}_d}{\\partial\\mathrm{T}_n}\\) on the \\(n\\)-th GPU. In DisCo, for each GPU, we only need to calculate a subset instead of the whole similarity matrix. We then use an all Reduce operation to conduct gradient communication and collect the gradients. The distributed contrastive loss can also be applied to the contrastive loss computation in self-supervised learning [4, 6]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.42, + 0.442, + 0.436 + ], + "angle": 0, + "content": "4.2. Algorithm Implementation of DisCo-CLIP" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.443, + 0.47, + 0.746 + ], + "angle": 0, + "content": "Using DisCo in CLIP, we develop a memory efficient CLIP training method, termed as DisCo-CLIP. To make our algorithm clearer, we show the pseudo-code for DisCo-CLIP in Alg. 1. The implementation can be roughly divided into three segments. In the first segment, for each GPU with a global rank number, we extract its image and text features, and then use all_gather to collect image and text features into this GPU. Then in the second segment, we compute the similarity matrix and the two losses: image-to-text and text-to-image, and use the losses to compute the gradients. In this segment, the intra-GPU gradients, \\(\\left[\\frac{\\partial\\mathcal{L}_1(\\mathrm{I}_n,\\mathrm{T}_A)}{\\partial\\mathrm{I}_n},\\frac{\\partial\\mathcal{L}_2(\\mathrm{T}_n,\\mathrm{I}_A)}{\\partial\\mathrm{I}_n},\\frac{\\partial\\mathcal{L}_1(\\mathrm{I}_n,\\mathrm{T}_A)}{\\partial\\mathrm{T}_n},\\frac{\\partial\\mathcal{L}_2(\\mathrm{T}_n,\\mathrm{I}_A)}{\\partial\\mathrm{T}_n}\\right]\\), as defined in Eq. 6, will be computed on the current GPU. In the last segment, we use all Reduce to finish gradient communication. In this segment, the inter-GPU gradients, \\(\\left[\\frac{\\partial\\mathcal{L}_2(\\mathrm{T}_{\\overline{n}},\\mathrm{I}_A)}{\\partial\\mathrm{I}_n},\\frac{\\partial\\mathcal{L}_1(\\mathrm{I}_{\\overline{n}},\\mathrm{T}_A)}{\\partial\\mathrm{T}_n}\\right]\\), as defined in Eq. 7, will be collected to the current GPU. The intra-GPU and inter-GPU gradients are averaged to obtain \\(\\left[\\frac{\\partial\\mathcal{L}_d}{\\partial\\mathrm{I}_n},\\frac{\\partial\\mathcal{L}_d}{\\partial\\mathrm{T}_n}\\right]\\). Finally, we perform backward propagation for the backbone." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.746, + 0.469, + 0.856 + ], + "angle": 0, + "content": "DisCo-CLIP has two advantages compared with CLIP. First, it decreases the memory consumption for the contrastive loss from \\(\\mathcal{O}(B^2)\\) to \\(\\mathcal{O}\\left(\\frac{B^2}{N}\\right)\\). Second, it reduces the computational complexity of the contrastive loss from \\(\\mathcal{O}(B^2D)\\) to \\(\\mathcal{O}\\left(\\frac{B^2}{N}D\\right)\\). Besides these two advantages, DisCo-CLIP is an exact solution for CLIP without sacrificing any computation accuracy." + }, + { + "type": "page_footnote", + "bbox": [ + 0.077, + 0.863, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Gradient communication here in the process of back-propagation should be distinguished from the gradient collection after model backpropagation which is to collect and average the weight gradients." + }, + { + "type": "code_caption", + "bbox": [ + 0.51, + 0.095, + 0.809, + 0.109 + ], + "angle": 0, + "content": "Algorithm 1: Pseudo-code for DisCo-CLIP" + }, + { + "type": "algorithm", + "bbox": [ + 0.508, + 0.111, + 0.892, + 0.499 + ], + "angle": 0, + "content": "# imageEncoder: ResNet or ViT\n# textEncoder: text Transformer\n# img[b,H,W,C]: minibatch of images\n# text[b,L]: minibatch of texts\n# t: temperature parameter\n# D: feature dimension\n# N: nums of GPU\n# rank: global rank\n# extract feature representations\ni.e = imageEncoder(img) # [b,D]\nt.e = textEncoder(text) # [b,D]\n# gather features from all gpus\nI.E = all_gather(i.e) # [N,b,D]\nT.E = all_gather(t_e) # [N,b,D]\n# scaled dot product similarities\nlogits.i = dot(I_E[rank], T_E)*t # [b,N*b]\nlogits.t = dot(T_E[rank], I_E)*t # [b,N*b]\n# image-to-text and text-to-image losses\nlabels = orange(b) + b * rank\nloss_i = cross_entropy_loss(logits.i, label)\nloss_t = cross_entropy_loss(logits.t, label)\n# loss backward\nloss = (loss.i + loss.t) / 2\nloss.backup()\n# reduce gradients and losses from all gpus\nI.E.grad = all.reduce(I.E.grad, op=AVG)\nT.E.grad = all.reduce(T.E.grad, op=AVG)\nLoss = all.reduce(loss, op=AVG)\n# backbone backward\ni.e.Backward(I.E.grad[rank])\nt.e.Backward(T.E.grad[rank])" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.531, + 0.892, + 0.621 + ], + "angle": 0, + "content": "Note that DisCo-CLIP requires an extra all Reduce operator to perform gradient communication, which has the same cost as the all_gather operator. Compared with the full similarity matrix computation, this extra communication cost is quite small and negligible. See Table 4 for a speed comparison." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.623, + 0.892, + 0.699 + ], + "angle": 0, + "content": "For the backbone part, we can also use the GradAccum strategy as proposed in BASIC [26]. BASIC provides a simple yet effective memory-efficient strategy for backbone memory optimization. Combined with GradAccum, DisCo-CLIP can further lead to a more memory-efficient solution." + }, + { + "type": "table", + "bbox": [ + 0.511, + 0.714, + 0.882, + 0.803 + ], + "angle": 0, + "content": "
MethodsBackboneContra. LossOverall
CLIP [27]O(BNLD)O(B2)O(BNLD) + O(B2)
BASIC [26]O(BN)O(B2)O(BN) + O(B2)
DisCo-CLIPO(BNLD)O(B2/N)O(BNLD) + O(B2/N)
DisCo-CLIP*O(BN)O(B2/N)O(BN) + O(B2/N)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.814, + 0.892, + 0.897 + ], + "angle": 0, + "content": "Table 1. Memory consumption comparison of different methods. DisCo-CLIP* denotes the combination of DisCo-CLIP and the GradAccum strategy in BASIC. \\( B \\) denotes the batch size, which is usually very large, e.g. 32K, \\( N \\) is the number of GPUs, \\( L \\) is the number of layers in the backbone, and \\( D \\) is the feature dimension. For simplicity, we use the same \\( D \\) for all layers." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22652" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.234 + ], + "angle": 0, + "content": "A detailed comparison of memory consumption for CLIP, BASIC, and DisCo-CLIP is provided in Table 1. With GradAccum, BASIC can reduce the overall memory consumption from \\(\\mathcal{O}(\\frac{B}{N}LD) + \\mathcal{O}(B^2)\\) to \\(\\mathcal{O}(\\frac{B}{N}D) + \\mathcal{O}(B^2)\\). DisCo-CLIP can reduce the memory consumption to \\(\\mathcal{O}(\\frac{B}{N}LD) + \\mathcal{O}(\\frac{B^2}{N})\\), DisCo-CLIP* can further reduce the memory consumption to \\(\\mathcal{O}(\\frac{B}{N}D) + \\mathcal{O}(\\frac{B^2}{N})\\). A practical example is that, in vanilla CLIP [27] based on ViT-B/32, \\(D = 1024\\), \\(B = 32768\\), \\(N = 128\\)." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.247, + 0.21, + 0.264 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.273, + 0.47, + 0.349 + ], + "angle": 0, + "content": "In this section, we first describe the experimental settings including data sets and pre-training details. Then, we present the experiments regarding memory consumption, training efficiency, batch size, and data scale. Finally, we report zero-shot classification on several data sets." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.358, + 0.279, + 0.375 + ], + "angle": 0, + "content": "5.1. Experimental Setting" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.382, + 0.47, + 0.637 + ], + "angle": 0, + "content": "Image-Text Data Sets. A large-scale image-text data set is a prerequisite for contrastive image-text pre-training. In the literature, there are many private [17, 37] or public data sets [34, 35, 38]. LAION-400M [35] is a data set with 400 million image-text pairs filtered by CLIP score. We crawl the images according to the provided URLs and finally obtain 360M image-text pairs as some URLs are expired and no longer available. LAION-5B [34] is a larger data set with 5 billion image-text pairs. It contains a subset of 2.32 billion English image-text pairs. We refer to this subset as LAION-2B as in [34]. We also crawl the data set according to the released URLs and finally obtain 2.1 billion image-text pairs. In this paper, for a fair comparison with CLIP [27] and LAION [34] which conduct experiments using 400M data pairs, we create a subset of 400M image-text pairs from our crawled LAION-2B and also make a subset of 100M image-text pairs for ablation study." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.639, + 0.471, + 0.866 + ], + "angle": 0, + "content": "Pre-training Details. The implementation of our DisCo-CLIP is based on OpenCLIP [16], an open source CLIP implementation. We follow the original CLIP [27] and mainly use ViT-B/32 [9] as the vision backbone. Training images are resized to \\(224 \\times 224\\) and fed to the vision backbone. For the text backbone, we use a text Transformer [8, 39], and set the maximum length of text to 76 as in [27]. Due to limited time and GPU resource, we do not train ViT-L/14 because it takes more than four times of training time compared to ViT-B/32. It should also be noted that in all our experiments, we do not use the GradAccum strategy as in BASIC [26]. Checkpointing is enabled in vanilla CLIP and our DisCo-CLIP. We train models using an Adam [18] optimizer and cosine learning rate scheduler with a linear warmup [24]. Weight decay regularization [25]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.348 + ], + "angle": 0, + "content": "is used on all parameters except bias, layer normalization, and temperature in contrastive loss. Since our training experiments use different batch sizes, according to previous works [12, 28], we change the learning rate for different batch sizes. For our learning rate scheduler, we first define a base learning rate of 5e-4 and a base batch size of 32,768, and then linearly warm it up to the maximum learning rate. The maximum learning rate is determined according to a linear strategy, max_lr = base_lr * batch_size / 32,768. Training stability is a challenging issue in mixed-precision training as NaN might happen in many cases. We obverse that \\(\\beta_{2}\\) in Adam is very important for training stability and find 0.98 works well for our experiments instead of the default value of 0.999. For most of our experiments, we use 64 NVIDIA A100 40GB GPUs for model training, but for some experiments, we only use 8 NVIDIA A100 40GB GPUs to show that our solution is more resource-efficient." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.358, + 0.682, + 0.373 + ], + "angle": 0, + "content": "5.2. Evaluation Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.381, + 0.894, + 0.472 + ], + "angle": 0, + "content": "Equivalence Validation. To empirically validate our theoretical analysis, we conduct experiments to compare CLIP and DisCo-CLIP. We use the same random seed to initiate the network parameters and use the same batch size 32,768 on 64 GPUs, and train ViT-B/32 models with 16 epochs on LAION-100M." + }, + { + "type": "table", + "bbox": [ + 0.526, + 0.482, + 0.869, + 0.53 + ], + "angle": 0, + "content": "
MethodsMemoryAccuracyTime (Hours)
CLIP27.4GB51.6413.4
DisCo-CLIP16.5GB51.6412.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.54, + 0.894, + 0.609 + ], + "angle": 0, + "content": "Table 2. CLIP Reproduction. Under the same training settings, DisCo-CLIP has exactly the same accuracy (top-1 zero-shot classification accuracy on ImageNet) as CLIP, but uses lower memory consumption and less training time. Training resource: 64 A100 40GB GPUs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.626, + 0.892, + 0.718 + ], + "angle": 0, + "content": "From Table 2, we see that DisCo-CLIP has exactly the same accuracy as CLIP, but uses lower memory consumption and less training time. Under the same training settings, DisCo-CLIP and CLIP also have exactly the same training curves. This experiment further validates the numerical equivalence between DisCo-CLIP and CLIP." + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.728, + 0.875, + 0.817 + ], + "angle": 0, + "content": "
MethodsGPUsBSMemory
CLIP64× A100 40GB32,76827.4GB
CLIP64× A100 40GB65,536OOM
DisCo-CLIP64× A100 40GB32,76816.5GB
DisCo-CLIP64× A100 40GB196,60838.1GB
DisCo-CLIP8× A100 40GB32,76836.9GB
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.856 + ], + "angle": 0, + "content": "Table 3. Memory consumption of CLIP and DisCo-CLIP under different settings. \"OOM\" means out of memory." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Memory Consumption. Besides memory consumption of network parameters, backbone and contrastive loss con" + }, + { + "type": "page_footnote", + "bbox": [ + 0.093, + 0.874, + 0.436, + 0.887 + ], + "angle": 0, + "content": "2https://github.com/mlfoundations/open Clip" + }, + { + "type": "page_footnote", + "bbox": [ + 0.093, + 0.887, + 0.342, + 0.9 + ], + "angle": 0, + "content": "3https://github.com/openai/CLIP" + }, + { + "type": "list", + "bbox": [ + 0.093, + 0.874, + 0.436, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.958 + ], + "angle": 0, + "content": "22653" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.086, + 0.089, + 0.887, + 0.148 + ], + "angle": 0, + "content": "
MethodsGPUsBatch sizeBackboneLoss OperatorsLoss TotalBackwardTotal
all_gatherLossall ReduceLoss BPBackbone BP
CLIP6432,768129.46.155.4-61.5414.8605.6
DisCo-CLIP6432,7686.11.64.312.0 (80.5% ↓)2.8337.3481.5 (20.5% ↓)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.158, + 0.892, + 0.187 + ], + "angle": 0, + "content": "Table 4. Detailed comparisons of training efficiency of CLIP and DisCo-CLIP. All time-related measurements (the last nine columns) are in milliseconds (ms). DisCo-CLIP saves more computational time in loss computation. Training resource: 64 A100 40GB GPUs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.213, + 0.468, + 0.273 + ], + "angle": 0, + "content": "sumes most memory. We evaluate the memory consumption of the original CLIP and our DisCo-CLIP under different settings. We report the peak memory consumption for different settings, and the results are shown in Table 3." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.274, + 0.468, + 0.364 + ], + "angle": 0, + "content": "We have three observations from Table 3. 1) CLIP with ViT-B/32 can be trained with batch size 32,768 but fails with batch size 65,536. 2) Our DisCo-CLIP can enable training of ViT-B/32 with a much larger batch size, 196,608 with 64 A100 40GB GPU. 3) DisCo-CLIP can enable training of the same model on a cluster with only 8 GPUs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.365, + 0.468, + 0.529 + ], + "angle": 0, + "content": "Training Speed. One iteration of CLIP consists of extracting features from backbone, gathering features from all GPUs, calculating loss, and executing back-propagation. (We exclude some other factors, including data loading and optimizer update that are not directly related to the model computation or can be ignored.) Instead, DisCo-CLIP decomposes the back-propagation into two BP processes (Loss BP and Backbone BP) and have an additional all Reduce operator. We evaluate the running time of each operator in CLIP and our DisCo-CLIP, and the results are shown in Table 4." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.532, + 0.468, + 0.682 + ], + "angle": 0, + "content": "From Table 4, we can see that 1) for total loss computation, under the same batch size 32,768, we decrease the computation time from \\(61.5\\mathrm{ms}\\) to \\(12.0\\mathrm{ms}\\). It is because in DisCo-CLIP, we only need to calculate two subset similarity matrices between multiplying a \\(\\frac{B}{N} \\times D\\) matrix and a \\(B \\times D\\) matrix instead of a full matrix multiplication between two \\(B \\times D\\) matrices. 2) the operators of both all Reduce and all_gather are faster compared to the loss computation. 3) under the same batch size 32,768, DisCo-CLIP improves around \\(20.5\\%\\) total training efficiency." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.683, + 0.468, + 0.744 + ], + "angle": 0, + "content": "Overall, with DisCo-CLIP, we are able to not only train contrastive learning models with a larger batch size, but also improve the training speed considerably. DisCo-CLIP is a free-lunch solution for large-scale contrastive learning." + }, + { + "type": "table", + "bbox": [ + 0.126, + 0.756, + 0.424, + 0.831 + ], + "angle": 0, + "content": "
Batch SizeStepsEpochsViT-B/32
8,192≈ 200 K1648.76
16,384≈ 100 K1650.95
32,768≈ 50 K1651.64
65,536≈ 25 K1651.91
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.841, + 0.468, + 0.897 + ], + "angle": 0, + "content": "Table 5. Evaluation of different batch sizes on DisCo-CLIP. All models are trained for 16 epochs on a LAION-100M data set, we show top-1 zero-shot classification accuracy on ImageNet. Training resource: 64 A100 40GB GPUs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.212, + 0.892, + 0.333 + ], + "angle": 0, + "content": "Batch Size. To assess the role of a larger batch size to the final performance, we conduct some controlled experiments for ViT-B/32 on our LAION-100M and LAION-400M subsets. All training hyper-parameters are the same except that we vary the batch size and the number of training steps. To ensure all models \"see\" the same number of training samples, we use fewer training steps when training with a larger batch size. In Table 5, we report the results of all settings." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.334, + 0.892, + 0.424 + ], + "angle": 0, + "content": "From Table 5, we can see that large batch size generally helps contrastive learning. The performance of using batch size 65,536 improves that of using batch size 32,768 by around \\(0.3\\%\\). In the evaluation of data scaling, we further observe that the improvement widens when we train the model for more epochs." + }, + { + "type": "table", + "bbox": [ + 0.54, + 0.438, + 0.855, + 0.498 + ], + "angle": 0, + "content": "
Batch Size100M×16400M×4400M×8
16,38450.9554.3658.38
32,76851.6455.5259.69
65,53651.9155.5059.96
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.509, + 0.892, + 0.565 + ], + "angle": 0, + "content": "Table 6. Evaluation of data scaling on DisCo-CLIP. Three batch sizes are evaluated with two LAION subsets: LAION-100M and LAION-400M. The numbers \\(\\times 16\\), \\(\\times 4\\), and \\(\\times 8\\) are the training epochs for each data set. Training resource: 64 A100 40GB GPUs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.583, + 0.892, + 0.703 + ], + "angle": 0, + "content": "Data Scaling. To investigate the role of data scaling, we also conduct some controlled experiments for ViT-B/32 on the LAION 100M and LAION 400M subsets. For all models, we use three different batch sizes, 16,384, 32,768 and 65,536 for training. Models are trained with three different settings, 100M with 16 epochs, 400M with 4 epochs and 400M with 8 epochs. Table 6 reports the final ImageNet top-1 zero-shot classification accuracy of all models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.892, + 0.9 + ], + "angle": 0, + "content": "From Table 6, we observe that, \"seeing\" the same number of training samples (LAION-100M with 16 epochs, LAION-400M with 4 epochs.), the model trained on larger scale of data set can obtain better performance. For example, trained with the same batch size 65,536, the performance improves from \\(51.91\\%\\) to \\(55.50\\%\\) when the data set increases from 100M to 400M. This observation validates the value of data scaling. This observation is also consistent with the combined scaling law in BASIC [26]. We also find that training with more epochs on larger scale of data with larger batch size will bring in larger performance gain. The gap between models (with batch sizes 32,768 and 65,536) trained on 400M with 4 epochs is around \\(0\\%\\) (from" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22654" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.08, + 0.088, + 0.895, + 0.164 + ], + "angle": 0, + "content": "
ModelData SetsEpochsStepsBatch SizeINet [7]INet-v2 [32]INet-R [15]INet-S [40]
CLIP [27]CLIP WIT 400M32≈ 400 K32,76863.356.069.442.3
OpenCLIP [16,34]LAION-400M32≈ 400 K32,76862.955.173.449.4
DisCo-CLIPLAION-400M*32≈ 400 K32,76863.255.273.450.6
DisCo-CLIPLAION-400M*32≈ 200 K65,53664.356.273.851.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.173, + 0.895, + 0.217 + ], + "angle": 0, + "content": "Table 7. Comparison of DisCo-CLIP with vanilla CLIP and re-implemented CLIP by LAION group. We report top-1 zero-shot classification accuracy (\\%) on several data sets. All models are based on ViT-B/32. Our LAION-400M* is a 400M subset of LAION-2B. Training resource: 64 A100 40GB GPUs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.242, + 0.471, + 0.304 + ], + "angle": 0, + "content": "55.52% to 55.50%), but it increases to 0.3% (from 59.69% to 59.96%) when the models are trained for 8 epochs. Thus, we can expect that if we use larger scale of data set, we should also use larger batch size to get a better performance." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.309, + 0.3, + 0.325 + ], + "angle": 0, + "content": "5.3. Zero-Shot Classification" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.332, + 0.47, + 0.529 + ], + "angle": 0, + "content": "Following CLIP [27] and LAION-5B [34], we evaluate zero-shot top-1 classification accuracy of our models on several data sets, including INet [7], INet-v2 [32], INet-R [15] and INet-S [40]. We use exactly the same 80 prompts as CLIP. Some standard prompts are like \"a bad photo of a \\(\\{\\}\\) \", \"a photo of many \\(\\{\\}\\) \", and etc. Following LAION-5B, we extract the embedding for each prompt using the text encoder (text Transformer), and average embeddings of all prompts in each class, and finally get the final class embedding. Given an image, we extract its image embedding via the image encoder (ViT-B/32), and compute its similarities with all class embeddings, and classify it into the class with the highest similarity score." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.529, + 0.471, + 0.712 + ], + "angle": 0, + "content": "We can see from Table 7, that using the same batch size of 32,768 as the OpenCLIP implementation, our DisCo-CLIP obtains a similar performance with OpenCLIP, the result of OpenCLIP is reported by LAION group in [34]. Using a larger batch size of 65,536, DisCo-CLIP achieves a better performance than the OpenCLIP implementation and the original CLIP. Specifically, trained with the same 32 epochs, DisCo-CLIP using a batch size of 65,536 improves the OpenCLIP's result that is based on batch size of 32,768 by \\(1.4\\%\\). Note that when doubling the batch size, we halve the training steps. This observation further validates that large batch size is important for contrastive learning." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.722, + 0.192, + 0.737 + ], + "angle": 0, + "content": "6. Discussion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.747, + 0.47, + 0.869 + ], + "angle": 0, + "content": "Recent developments in large-scale contrastive or generative learning, such as CLIP [27], ALIGN [17], FILIP [43], LiT [48], BASIC [26], LAION-5B [34], and GIT [41] have potential for many real-world applications, such as image classification, text-to-image retrieval, recommendation system, and generation models. Besides large-scale data sets, the progress highly depends on powerful GPU or TPU computing resources. As shown in Table 8, all methods use" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.242, + 0.892, + 0.271 + ], + "angle": 0, + "content": "a large amount of computing hardwares. FILIP uses less GPU but also uses smaller batch size." + }, + { + "type": "table", + "bbox": [ + 0.537, + 0.284, + 0.858, + 0.373 + ], + "angle": 0, + "content": "
MethodsHardware
CLIP [27]256 NVIDIA V100 GPUs
FILIP [43]128 NVIDIA V100 GPUs
LAION-5B [34]128-400 NVIDIA A100 GPUs
LiT [48]128-400 TPUs
BASIC [26]2,048 TPUs v3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.383, + 0.892, + 0.41 + ], + "angle": 0, + "content": "Table 8. Several vision-language contrastive learning methods and their used hardwares." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.433, + 0.895, + 0.57 + ], + "angle": 0, + "content": "Unfortunately, only a few big technology companies can afford this task. Large batch contrastive loss consumes a large amount of GPU memory, while large batch size is a prerequisite for contrastive learning. As a result, it is challenging for companies with limited resources or academic research institutes to contribute to research on this topic. Our work provides a simple yet effective solution for reducing memory consumption that can help bridge the gap between academia and industry on this topic." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.587, + 0.62, + 0.603 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.894, + 0.827 + ], + "angle": 0, + "content": "In this paper, we have proposed a simple yet effective distributed contrastive loss solution called DisCo to reduce the memory consumption in contrastive learning. By decomposing the loss computation into intra-GPU computation and inter-GPU computation, we can remove redundant memory consumption and use a all Reduce operator to collect inter-GPU gradients. Using DisCo in CLIP, the introduced DisCo-CLIP can enable a much larger batch contrastive learning compared to CLIP using the same GPU resource. Specifically, we can train DisCo-CLIP models with batch size 32,768 using 8 A100 40GB GPUs, or with batch size 196K using 64 GPUs. We hope DisCo-CLIP will also help and motivate self-supervised learning [4, 6] which also uses contrastive learning." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.844, + 0.681, + 0.861 + ], + "angle": 0, + "content": "8. Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.9 + ], + "angle": 0, + "content": "This work was partially supported by OPPO Research Fund." + }, + { + "type": "page_footnote", + "bbox": [ + 0.078, + 0.875, + 0.468, + 0.903 + ], + "angle": 0, + "content": "4https://github.com/openai/CLIP/blob/main/notebooks/Prompt_Engineering_for_ImageNet.ipynb" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.958 + ], + "angle": 0, + "content": "22655" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Zhengda Bian, Hongxin Liu, Boxiang Wang, Haichen Huang, Yongbin Li, Chuanrui Wang, Fan Cui, and Yang You. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 18123-18133, 2022. 2, 8" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.825 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22657" + } + ] +] \ No newline at end of file diff --git a/2023/DisCo-CLIP_ A Distributed Contrastive Loss for Memory Efficient CLIP Training/e80e2080-33a9-4c63-8bae-91e19a54d7b9_origin.pdf b/2023/DisCo-CLIP_ A Distributed Contrastive Loss for Memory Efficient CLIP Training/e80e2080-33a9-4c63-8bae-91e19a54d7b9_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..d4fd784abcf501d9c2b5da17fd7da3718f0d6873 --- /dev/null +++ b/2023/DisCo-CLIP_ A Distributed Contrastive Loss for Memory Efficient CLIP Training/e80e2080-33a9-4c63-8bae-91e19a54d7b9_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:1be3dc3b38a9b336f75a92500afca6e6cc312fc8036a1aa94efd9c08e0770cae +size 1005342 diff --git a/2023/DisCo-CLIP_ A Distributed Contrastive Loss for Memory Efficient CLIP Training/full.md b/2023/DisCo-CLIP_ A Distributed Contrastive Loss for Memory Efficient CLIP Training/full.md new file mode 100644 index 0000000000000000000000000000000000000000..d1bddbf03c119404609b74033b8bf51e3340ba90 --- /dev/null +++ b/2023/DisCo-CLIP_ A Distributed Contrastive Loss for Memory Efficient CLIP Training/full.md @@ -0,0 +1,356 @@ +# DisCo-CLIP: A Distributed Contrastive Loss for Memory Efficient CLIP Training + +Yihao Chen, Xianbiao Qi, Jianan Wang, Lei Zhang* International Digital Economy Academy (IDEA), Shenzhen, Guangdong, China. {chenyihao, qixianbiao, wangjianan, leizhang}@idea.edu.cn + +# Abstract + +We propose DisCo-CLIP, a distributed memory-efficient CLIP training approach, to reduce the memory consumption of contrastive loss when training contrastive learning models. Our approach decomposes the contrastive loss and its gradient computation into two parts, one to calculate the intra-GPU gradients and the other to compute the inter-GPU gradients. According to our decomposition, only the intra-GPU gradients are computed on the current GPU, while the inter-GPU gradients are collected via all-reduce from other GPUs instead of being repeatedly computed on every GPU. In this way, we can reduce the GPU memory consumption of contrastive loss computation from $\mathcal{O}(B^2)$ to $\mathcal{O}\left(\frac{B^2}{N}\right)$ , where $B$ and $N$ are the batch size and the number of GPUs used for training. Such a distributed solution is mathematically equivalent to the original non-distributed contrastive loss computation, without sacrificing any computation accuracy. It is particularly efficient for large-batch CLIP training. For instance, DisCo-CLIP can enable contrastive training of a ViT-B/32 model with a batch size of 32K or 196K using 8 or 64 A100 40GB GPUs, compared with the original CLIP solution which requires 128 A100 40GB GPUs to train a ViT-B/32 model with a batch size of 32K. + +# 1. Introduction + +Vision-language representation learning from massive image-text pairs has recently attracted tremendous attention for its great potential in many applications such as zero-shot classification and text-image retrieval. Representative works include CLIP [27], ALIGN [17], Florence [47], CoCa [46], and BASIC [26], which all leverage hundreds of millions or even billions of image-text pairs collected from the Web to learn a semantic-rich and language-aligned visual representation [22]. As the web-collected data inevitably contain noises, CLIP [27] for the first time applies + +contrastive learning on 400M image-text pairs, which implies a weak but more proper assumption about the data: the relevance between paired image and text is greater than that between unpaired image and text. For its demonstrated performance in CLIP, contrastive learning has been widely adopted in subsequent works. Accordingly, several imagedataset data sets with increasingly larger scales have also been developed and made publicly available, such as Conceptual 12M [3], YFCC 100M [38], WIT 37.6M [37], LAION-400M [35], and LAION-5B [34]. + +The goal of contrastive learning in CLIP is to learn an alignment between image and text via two encoders. That is, it encourages paired image and text (called a positive pair) to be similar and meanwhile enforces unpaired image and text (called a negative pair) to be dissimilar. For any positive image-text pair, as there are normally unlimited number (up to the total number of images or texts in a data set) of negative image-text pairs, it is crucial to include a sufficiently large number of negative pairs in a contrastive loss to make the representation learning effective, as validated in all related works such as CLIP [27], Florence [47], OpenCLIP [16], and BASIC [26]. Specifically, BASIC shows that larger batch size, plus larger data set and larger model, theoretically lead to a better generalization performance. + +However, a fundamental technical challenge in training a CLIP-like model is how to enlarge its batch size under the constraint of limited GPU memory. For instance, when the batch size is 65,536, the similarity matrix for all imag-text pairs in the batch will cost about 16GB using Float32. As the backbone part also consumes a significant portion of GPU memory, especially for large backbones such as ViT-Large or ViT-Huge [9], scaling up batch size presents a great challenge, usually requiring hundreds of V100 or A100 GPUs [16, 27, 47], which are inaccessible for most research scientists. + +In this work, we develop a distributed solution called DisCo-CLIP for constrastive loss computation, which can save a large amount of memory for contrastive loss and make CLIP training more memory-efficient. Our method + +starts from a decomposition of the original contrastive loss. Based on this decomposition, we divide the contrastive loss into two parts, one to calculate the intra-GPU loss and gradients, and the other one to calculate the inter-GPU loss and gradients. For a mini-batch on the $n$ -th GPU (hereinafter called its hosting GPU), its intra-GPU gradients are calculated on its hosting GPU, and its inter-GPU gradients are collected from other GPUs. DisCo is an exact solution, mathematically equivalent to the original non-distributed contrastive loss, but more memory- and computation-efficient. It can decrease the memory cost of contrastive loss from $\mathcal{O}(B^2)$ to $\mathcal{O}\left(\frac{B^2}{N}\right)$ , where $B$ and $N$ are the batch size and the number of GPUs. When $N$ equals to 64, it means around $97\%$ (see Sec. 4.1 for details) of the memory, and similarly the computational cost, in contrastive loss can be saved. Thus, using DisCo in CLIP, we can enable contrastive training with a larger batch size. Using 8 Nvidia A100 40GB GPUs, DisCo-CLIP can enable contrastive training of a ViT-B/32 model with a batch size of 32,768. Using 64 A100 40GB GPUs, DisCo-CLIP can train the same model with a larger batch size of 196K. + +We summarize our contributions in twofold. + +- We propose a novel distributed contrastive loss solution called DisCo for memory efficient CLIP training, which can significantly reduce the memory consumption of the contrastive loss computation. Such a solution enables a larger batch size for contrastive training using the same computing resource without sacrificing any computation accuracy. +- We further validate that training with a larger batch size can further improve the performance of contrastive learning models. + +# 2. Background and Related Work + +In this section, we will introduce some background information for contrastive language-image pre-training (CLIP) and review some works that reduce memory consumption of the backbone part by trading computation for memory. + +# 2.1. Contrastive Language-Image Pre-training + +The idea behind CLIP [27] is to learn two representations via two encoders, an image encoder [9, 14, 20, 23, 42] and a text encoder [2, 8, 28]. Its target is to encourage positive image-text pairs to have higher similarities, and enforce negative image-text pairs to have lower similarities. The training is supervised by two contrastive losses, an image-to-text loss and a text-to-image loss. Suppose we have $B$ text-image pairs as a batch sending to two encoders and the model is trained using $N$ GPUs, with each GPU assigned $b = \frac{B}{N}$ pairs. Here, we use $T_A, I_A$ to denote all text and image features obtained from two encoders. Suppose the + +hidden dimension is $D$ , then the shapes of $\mathrm{T}_A, \mathrm{I}_A$ are both $B \times D$ . In this way, our contrastive losses can be written as, + +$$ +\mathcal {L} = \mathcal {L} _ {1} \left(\mathrm {I} _ {A}, \mathrm {T} _ {A}\right) + \mathcal {L} _ {2} \left(\mathrm {T} _ {A}, \mathrm {I} _ {A}\right), \tag {1} +$$ + +where $\mathcal{L}_1(\mathrm{I}_A,\mathrm{T}_A)$ denotes the image-to-text loss, and $\mathcal{L}_2(\mathrm{T}_A,\mathrm{I}_A)$ represents the text-to-image loss. The image-to-text loss means that the loss is to encourage a given image to find its paired text from tens of thousands of texts, and similarly for the text-to-image loss. + +Motivated by the success of CLIP, many new methods have been proposed, such as FILIP [43], LiT [48], ALIGN [17], BASIC [26], BLIP [21], GIT [41], and K-LITE [36]. FILIP attempts to obtain a fine-grained alignment between image patches and text words. In contrast, CLIP only obtains an image-level alignment between an image and a text sentence. FILIP achieves this goal by a modified contrastive loss. Instead of training both image and text models from scratch, LiT [48] shows that employing a pretrained image model and locking it would greatly benefit zero-shot classification. Under the contrastive framework, ALIGN [17] and BASIC [26] investigate how the scaling up of model, data, and batch size benefits contrastive learning. Instead of only leveraging contrastive learning framework, BLIP [21] introduces a mixed contrastive learning and generative learning for vision-language model. Further, GIT [41] employs a pure generative learning framework and demonstrates its superior performance. + +The success of CLIP and the above methods highly depends on large-scale paired image-text data set [3, 17, 34, 35, 37, 38]. Compared with classification data sets, such as ImageNet 1K [7] and ImageNet 21K [33], which require careful human annotation, there are abundant paired image-text data on the Web and can be more easily collected [34]. + +Large batch size is a prerequisite for vision-language contrastive learning. Data Parallelism (DP) and Model Parallelism (MP) are two widely used methods in deep learning for distributed training [8,12,28,39,44,45]. There are many related works on this topic, such as DeepSpeed [29-31] and Colossal-AI [1]. We recommend interested readers to refer to these papers for some common distributed learning techniques. In the following, we will describe several methods that trade computation for memory in the backbone part. + +# 2.2. Trade Computation for Memory in Backbone + +Checkpointing [5] is an effective approach to reduce memory consumption, especially for the intermediate results of low-cost operation. It only stores feature maps of some high-cost operations, such as convolution, MLP, and self-attention, but drops feature maps of low-cost operations such as activation (e.g., ReLU, GeLU) and layer normalization in the forward pass. In the backward process, these dropped feature maps can be recomputed quickly at a low cost. By dropping some intermediate feature maps, we can + +![](images/94733f47f479ccf72c83b72bcba1830dcefdf3e4eff2679a8b399530e87f0eb0.jpg) +Figure 1. Illustration of the original CLIP training. All image features $\mathrm{I}_A$ and text features $\mathrm{T}_A$ are gathered to every GPU via all_gather to calculate the $B\times B$ similarity matrix for contrastive loss computation. This computation is performed repeatedly on every GPU. + +save a great amount of memory. Gruslys et al. [13] further extend the idea of Checkpointing to the recursive neural network. Checkpointing is helpful but still not sufficient if we want to further increase the batch size. + +Recently, BASIC [26] introduces a gradient accumulating (GradAccum) method for memory saving in backbone via micro-batching the contrastive loss. This approach is based on the observation that when computing the contrastive loss, we only need the full similarity matrix instead of all intermediate results. Thus, BASIC proposes to trade computation for memory by dropping some intermediate hidden states during the forward process, and then recompute them during back-propagation. This method can effectively reduce the memory consumption in the backbone part but it requires one extra forward computation. A similar gradient cache approach [10] was also introduced for dense passage retriever in natural language processing. + +Reversible model structure [11, 19] is another elegant method for memory saving in backbone. However, it requires block adaption because it needs to reconstruct the input layer according to the output layer in the back propagation process. Reversible structure is particularly suitable for models that do not change activation shape in the whole network. However, reconstructing a layer from its output inevitably takes more backward time. + +All above three mechanisms mainly focus on reducing memory consumption in the backbone part. However, none of them pays attention to reducing the memory consumption of the contrastive loss, which has been a big bottleneck for large batch size contrastive training. We will explain this problem in the next section. + +# 3. Motivation + +Distributed contrastive learning is different from traditional distributed data parallel and model parallel strategies. Data parallel (DP) is particularly effective when activations + +in the network cost most of the GPU memory. For example, in [12], Goyal et al. succeeded in training an ImageNet classification model in one hour. Each GPU independently performs forward and backward computation. Only after backward computation, the GPUs perform a gradient communication to merge gradients. In contrast, model parallel (MP) is more effective when model parameters (e.g. 10 billions of parameters) consume a large amount of GPU memory. In this way, the model parameters are sliced and assigned to different GPUs. However, different from the DP and MP problems, in contrastive training, besides the backbone and model parameters, the contrastive loss consumes a larger amount of GPU memory especially when a large batch size is used. + +As we have discussed in the introduction section, a large batch size is of crucial importance for contrastive learning. Previous research [26] also proves theoretically that a larger contrastive batch size can lead to a better representation for image-text models. Interested readers can refer to Theorem 1 in [26] and its appendix for the proof. + +However, a large batch in contrastive loss will consume a large amount of GPU memory, usually of $\mathcal{O}(B^2)$ , where $B$ is the batch size. Let us take an examination of the memory consumption of contrastive loss. For example, for a batch size of 65,536, it stores a similarity matrix of 4.3 billions parameters which requires 16GB of memory using Float32. Its gradient computation in the back-propagation process will take another 16GB of memory. Considering other memory cost of model parameters and backbone intermediate activations, it cannot be trained using A100 40GB GPUs even with mixed precision computation. + +After investigating the constrastive loss in depth, we notice that there is much redundant memory consumption and computational waste in the current CLIP training solution. As shown in Fig. 1, in the original CLIP training, to calculate the gradients for the text and image features in the hosting GPU, every GPU in the distributed training environment needs to compute the entire $B \times B$ similarity matrix, which is not necessary as we will show later. + +Our motivation in this paper is to eliminate memory redundancy and remove unnecessary calculation via a loss decomposition, and thus enable large batch training using limited GPU resource. + +# 4. DisCo-CLIP: A Distributed Contrastive Loss for Memory Efficient CLIP Training + +In this section, we introduce DisCo, a distributed solution for contrastive loss computation. Using DisCo in CLIP, we accomplish a new memory efficient CLIP training method, called DisCo-CLIP. To this end, we decompose the loss calculation into two parts, one part to compute the intra-GPU loss and gradients and the other part to compute inter-GPU loss and gradients. This section will first intro + +duce how we decompose this loss calculation. Then, we will describe the algorithm implementation of DisCo-CLIP in detail. + +# 4.1. DisCo: A Distributed Contrastive Loss + +As shown in Eq. 1, $\mathrm{I}_A$ and $\mathrm{T}_A$ denote all image and text features collected from all GPUs. Here, we use $\mathrm{I}_n$ and $\mathrm{T}_n$ to denote the image and text features on the $n$ -th GPU, and use $\mathrm{I}_{\overline{n}}$ and $\mathrm{T}_{\overline{n}}$ to denote the image and text features on all other GPUs. The division is denoted as, + +$$ +\mathrm {I} _ {A} = \left[ \begin{array}{l l} \mathrm {I} _ {n}, & \mathrm {I} _ {\overline {{n}}} \end{array} \right], \tag {2} +$$ + +$$ +\mathrm {T} _ {A} = \left[ \mathrm {T} _ {n}, \mathrm {T} _ {\bar {n}} \right] +$$ + +The shapes of $\mathrm{I}_A$ and $\mathrm{T}_A$ are $B\times D$ , the shapes of $\mathrm{I}_n$ and $\mathrm{T}_n$ are $\frac{B}{N}\times D$ , and the shapes of $\mathrm{I}_{\overline{n}}$ and $\mathrm{T}_{\overline{n}}$ are $\frac{B(N - 1)}{N}\times D$ . + +According to the above definition, the contrastive loss can be decomposed and rewritten as, + +$$ +\mathcal {L} _ {d} = \mathcal {L} _ {1} \left(\mathrm {I} _ {n}, \mathrm {T} _ {A}\right) + \mathcal {L} _ {1} \left(\mathrm {I} _ {\bar {n}}, \mathrm {T} _ {A}\right) + \tag {3} +$$ + +$$ +\mathcal {L} _ {2} \left(\mathrm {T} _ {n}, \mathrm {I} _ {A}\right) + \mathcal {L} _ {2} \left(\mathrm {T} _ {\bar {n}}, \mathrm {I} _ {A}\right), +$$ + +where $\mathcal{L}_1(\mathrm{I}_n,\mathrm{T}_A)$ denotes the image-to-text contrastive loss between image features $\mathrm{I}_n$ and text features $\mathrm{T}_A$ , and $\mathcal{L}_2(\mathrm{T}_n,\mathrm{I}_A)$ denotes the text-to-image loss between $\mathrm{T}_n$ and $\mathrm{I}_A$ . Mathematically, the computational result $\mathcal{L}_d$ in Eq. 3 is the same as the result $\mathcal{L}$ in Eq. 1. However, by decomposing the loss $\mathcal{L}_d$ into four parts, the gradient flow in the back-propagation process is more obvious. Meanwhile, we can see that $\mathcal{L}_1(\mathrm{I}_{\overline{n}},\mathrm{T}_A)$ does not induce gradients with respect to $\mathrm{I}_n$ and $\mathcal{L}_2(\mathrm{T}_{\overline{n}},\mathrm{I}_A)$ has no gradients with respect to $\mathrm{T}_n$ . Actually, these two terms are redundant computation on the $n$ -th GPU in the original contrastive loss, which unnecessarily consume a large amount of memory. + +Thus, according to the decomposition in Eq. 3, we can calculate the gradients $\frac{\partial\mathcal{L}_d}{\partial\mathrm{T}_n}$ for image features $\mathrm{I}_n$ and the gradients $\frac{\partial\mathcal{L}_d}{\partial\mathrm{T}_n}$ for text features $\mathrm{T}_n$ as follows, + +$$ +\frac {\partial \mathcal {L} _ {d}}{\partial \mathrm {I} _ {n}} = \boxed {\frac {\partial \mathcal {L} _ {1} (\mathrm {I} _ {n} , \mathrm {T} _ {A})}{\partial \mathrm {I} _ {n}} + \frac {\partial \mathcal {L} _ {2} (\mathrm {T} _ {n} , \mathrm {I} _ {A})}{\partial \mathrm {I} _ {n}}} + \boxed {\frac {\partial \mathcal {L} _ {2} (\mathrm {T} _ {\bar {n}} , \mathrm {I} _ {A})}{\partial \mathrm {I} _ {n}}}, \tag {4} +$$ + +$$ +\frac {\partial \mathcal {L} _ {d}}{\partial \mathrm {T} _ {n}} = \boxed {\frac {\partial \mathcal {L} _ {1} (\mathrm {I} _ {n} , \mathrm {T} _ {A})}{\partial \mathrm {T} _ {n}} + \frac {\partial \mathcal {L} _ {2} (\mathrm {T} _ {n} , \mathrm {I} _ {A})}{\partial \mathrm {T} _ {n}}} + \boxed {\frac {\partial \mathcal {L} _ {1} (\mathrm {I} _ {\bar {n}} , \mathrm {T} _ {A})}{\partial \mathrm {T} _ {n}}}, +$$ + +where the losses in the red part can be further unfolded in a sum form as, + +$$ +\frac {\partial \mathcal {L} _ {2} \left(\mathrm {T} _ {\bar {n}} , \mathrm {I} _ {A}\right)}{\partial \mathrm {I} _ {n}} = \sum_ {i \neq n \& i \in [ 1, N ]} \frac {\partial \mathcal {L} _ {2} \left(\mathrm {T} _ {i} , \mathrm {I} _ {A}\right)}{\partial \mathrm {I} _ {n}}, \tag {5} +$$ + +$$ +\frac {\partial \mathcal {L} _ {1} \left(\mathrm {I} _ {\bar {n}} , \mathrm {T} _ {A}\right)}{\partial \mathrm {T} _ {n}} = \sum_ {j \neq n \& j \in [ 1, N ]} \frac {\partial \mathcal {L} _ {1} \left(\mathrm {I} _ {j} , \mathrm {T} _ {A}\right)}{\partial \mathrm {T} _ {n}}. \tag {3} +$$ + +The gradients of $\frac{\partial\mathcal{L}_d}{\partial\mathrm{I}_n}$ and $\frac{\partial\mathcal{L}_d}{\partial\mathrm{T}_n}$ both consist of three terms. In both equations, all three terms can be divided into two parts, we mark them with two different colors, blue and + +![](images/5034b66049804954e62df0e061363be9c822e472722edfd920d8fb0ec2981bde.jpg) +(1) Image-to-Text Contrastive Loss Backward + +![](images/bfaeffe052037e8c95b6e39f869017153d2f08a946abcbb82d7c283662abcae6.jpg) +(2) Text-to-Image Contrastive Loss Backward +Figure 2. Illustration of the gradient calculation of DisCo on the first GPU. In DisCo, to calculate the gradients on the current GPU, we only need to compute two $\frac{B}{N} \times B$ similarity matrices instead of a full $B \times B$ matrix as shown in Fig. 1. + +red. The gradients in the blue part are calculated on the $n$ -th (hosting) GPU, and the gradients in the red part are calculated on other GPUs. We call them intra-GPU gradients and inter-GPU gradients, respectively. When computing the red part for $\frac{\partial \mathcal{L}_d}{\partial \mathrm{I}_n}$ , the images $\mathrm{I}_n$ are considered as negative samples. It should be noted that although $\mathrm{I}_n$ is regarded as negative samples, there still induce gradients for $\mathrm{I}_n$ . + +According to this decomposition, to compute $\frac{\partial\mathcal{L}_d}{\partial\mathrm{I}_n}$ and $\frac{\partial\mathcal{L}_d}{\partial\mathrm{T}_n}$ , the $n$ -th GPU only needs to compute the following four terms, + +$$ +\left[ \frac {\partial \mathcal {L} _ {1} \left(\mathrm {I} _ {n} , \mathrm {T} _ {A}\right)}{\partial \mathrm {I} _ {n}}, \frac {\partial \mathcal {L} _ {2} \left(\mathrm {T} _ {n} , \mathrm {I} _ {A}\right)}{\partial \mathrm {I} _ {n}}, \frac {\partial \mathcal {L} _ {1} \left(\mathrm {I} _ {n} , \mathrm {T} _ {A}\right)}{\partial \mathrm {T} _ {n}}, \frac {\partial \mathcal {L} _ {2} \left(\mathrm {T} _ {n} , \mathrm {I} _ {A}\right)}{\partial \mathrm {T} _ {n}} \right]. \tag {6} +$$ + +All four terms only need to compute two small similarity matrices of shape $\frac{B}{N} \times B$ instead of a full matrix of shape $B \times B$ which consumes a large amount of memory. In this way, we can reduce memory consumption from $B^2$ to $\frac{2B^2}{N}$ . For instance, when $N = 16$ , we save $\frac{7}{8}$ of memory consumption, if $N$ is 64, we save $\frac{31}{32}$ of memory consumption. Meanwhile, it also saves much computation. The compu + +tational cost for the contrastive similarity matrix decreases from $B^2 D$ to $\frac{2B^2D}{N}$ . + +For the two red terms in Eq. 4, + +$$ +\left[ \frac {\partial \mathcal {L} _ {2} \left(\mathrm {T} _ {\bar {n}} , \mathrm {I} _ {A}\right)}{\partial \mathrm {I} _ {n}}, \frac {\partial \mathcal {L} _ {1} \left(\mathrm {I} _ {\bar {n}} , \mathrm {T} _ {A}\right)}{\partial \mathrm {T} _ {n}} \right], \tag {7} +$$ + +we use the all Reduce operation to perform gradient communication and collect all gradients with respect to $\mathrm{I}_n$ and $\mathrm{T}_n$ . Fig. 2 illustrates the gradient calculation of DisCo on the first of $N$ GPUs. + +Let us compare DisCo with the original contrastive loss. In the original implementation, because of the lack of gradient communication in the process of back-propagation among GPUs $^1$ , each GPU must compute the whole similarity matrix between $\mathrm{I}_A$ and $\mathrm{T}_A$ to obtain the gradients $\frac{\partial\mathcal{L}_d}{\partial\mathrm{I}_n}$ and $\frac{\partial\mathcal{L}_d}{\partial\mathrm{T}_n}$ on the $n$ -th GPU. In DisCo, for each GPU, we only need to calculate a subset instead of the whole similarity matrix. We then use an all Reduce operation to conduct gradient communication and collect the gradients. The distributed contrastive loss can also be applied to the contrastive loss computation in self-supervised learning [4, 6]. + +# 4.2. Algorithm Implementation of DisCo-CLIP + +Using DisCo in CLIP, we develop a memory efficient CLIP training method, termed as DisCo-CLIP. To make our algorithm clearer, we show the pseudo-code for DisCo-CLIP in Alg. 1. The implementation can be roughly divided into three segments. In the first segment, for each GPU with a global rank number, we extract its image and text features, and then use all_gather to collect image and text features into this GPU. Then in the second segment, we compute the similarity matrix and the two losses: image-to-text and text-to-image, and use the losses to compute the gradients. In this segment, the intra-GPU gradients, $\left[\frac{\partial\mathcal{L}_1(\mathrm{I}_n,\mathrm{T}_A)}{\partial\mathrm{I}_n},\frac{\partial\mathcal{L}_2(\mathrm{T}_n,\mathrm{I}_A)}{\partial\mathrm{I}_n},\frac{\partial\mathcal{L}_1(\mathrm{I}_n,\mathrm{T}_A)}{\partial\mathrm{T}_n},\frac{\partial\mathcal{L}_2(\mathrm{T}_n,\mathrm{I}_A)}{\partial\mathrm{T}_n}\right]$ , as defined in Eq. 6, will be computed on the current GPU. In the last segment, we use all Reduce to finish gradient communication. In this segment, the inter-GPU gradients, $\left[\frac{\partial\mathcal{L}_2(\mathrm{T}_{\overline{n}},\mathrm{I}_A)}{\partial\mathrm{I}_n},\frac{\partial\mathcal{L}_1(\mathrm{I}_{\overline{n}},\mathrm{T}_A)}{\partial\mathrm{T}_n}\right]$ , as defined in Eq. 7, will be collected to the current GPU. The intra-GPU and inter-GPU gradients are averaged to obtain $\left[\frac{\partial\mathcal{L}_d}{\partial\mathrm{I}_n},\frac{\partial\mathcal{L}_d}{\partial\mathrm{T}_n}\right]$ . Finally, we perform backward propagation for the backbone. + +DisCo-CLIP has two advantages compared with CLIP. First, it decreases the memory consumption for the contrastive loss from $\mathcal{O}(B^2)$ to $\mathcal{O}\left(\frac{B^2}{N}\right)$ . Second, it reduces the computational complexity of the contrastive loss from $\mathcal{O}(B^2D)$ to $\mathcal{O}\left(\frac{B^2}{N}D\right)$ . Besides these two advantages, DisCo-CLIP is an exact solution for CLIP without sacrificing any computation accuracy. + +Algorithm 1: Pseudo-code for DisCo-CLIP +# imageEncoder: ResNet or ViT +# textEncoder: text Transformer +# img[b,H,W,C]: minibatch of images +# text[b,L]: minibatch of texts +# t: temperature parameter +# D: feature dimension +# N: nums of GPU +# rank: global rank +# extract feature representations +i.e = imageEncoder(img) # [b,D] +t.e = textEncoder(text) # [b,D] +# gather features from all gpus +I.E = all_gather(i.e) # [N,b,D] +T.E = all_gather(t_e) # [N,b,D] +# scaled dot product similarities +logits.i = dot(I_E[rank], T_E)*t # [b,N*b] +logits.t = dot(T_E[rank], I_E)*t # [b,N*b] +# image-to-text and text-to-image losses +labels = orange(b) + b * rank +loss_i = cross_entropy_loss(logits.i, label) +loss_t = cross_entropy_loss(logits.t, label) +# loss backward +loss = (loss.i + loss.t) / 2 +loss.backup() +# reduce gradients and losses from all gpus +I.E.grad = all.reduce(I.E.grad, op=AVG) +T.E.grad = all.reduce(T.E.grad, op=AVG) +Loss = all.reduce(loss, op=AVG) +# backbone backward +i.e.Backward(I.E.grad[rank]) +t.e.Backward(T.E.grad[rank]) + +Note that DisCo-CLIP requires an extra all Reduce operator to perform gradient communication, which has the same cost as the all_gather operator. Compared with the full similarity matrix computation, this extra communication cost is quite small and negligible. See Table 4 for a speed comparison. + +For the backbone part, we can also use the GradAccum strategy as proposed in BASIC [26]. BASIC provides a simple yet effective memory-efficient strategy for backbone memory optimization. Combined with GradAccum, DisCo-CLIP can further lead to a more memory-efficient solution. + +
MethodsBackboneContra. LossOverall
CLIP [27]O(BNLD)O(B2)O(BNLD) + O(B2)
BASIC [26]O(BN)O(B2)O(BN) + O(B2)
DisCo-CLIPO(BNLD)O(B2/N)O(BNLD) + O(B2/N)
DisCo-CLIP*O(BN)O(B2/N)O(BN) + O(B2/N)
+ +Table 1. Memory consumption comparison of different methods. DisCo-CLIP* denotes the combination of DisCo-CLIP and the GradAccum strategy in BASIC. $B$ denotes the batch size, which is usually very large, e.g. 32K, $N$ is the number of GPUs, $L$ is the number of layers in the backbone, and $D$ is the feature dimension. For simplicity, we use the same $D$ for all layers. + +A detailed comparison of memory consumption for CLIP, BASIC, and DisCo-CLIP is provided in Table 1. With GradAccum, BASIC can reduce the overall memory consumption from $\mathcal{O}(\frac{B}{N}LD) + \mathcal{O}(B^2)$ to $\mathcal{O}(\frac{B}{N}D) + \mathcal{O}(B^2)$ . DisCo-CLIP can reduce the memory consumption to $\mathcal{O}(\frac{B}{N}LD) + \mathcal{O}(\frac{B^2}{N})$ , DisCo-CLIP* can further reduce the memory consumption to $\mathcal{O}(\frac{B}{N}D) + \mathcal{O}(\frac{B^2}{N})$ . A practical example is that, in vanilla CLIP [27] based on ViT-B/32, $D = 1024$ , $B = 32768$ , $N = 128$ . + +# 5. Experiments + +In this section, we first describe the experimental settings including data sets and pre-training details. Then, we present the experiments regarding memory consumption, training efficiency, batch size, and data scale. Finally, we report zero-shot classification on several data sets. + +# 5.1. Experimental Setting + +Image-Text Data Sets. A large-scale image-text data set is a prerequisite for contrastive image-text pre-training. In the literature, there are many private [17, 37] or public data sets [34, 35, 38]. LAION-400M [35] is a data set with 400 million image-text pairs filtered by CLIP score. We crawl the images according to the provided URLs and finally obtain 360M image-text pairs as some URLs are expired and no longer available. LAION-5B [34] is a larger data set with 5 billion image-text pairs. It contains a subset of 2.32 billion English image-text pairs. We refer to this subset as LAION-2B as in [34]. We also crawl the data set according to the released URLs and finally obtain 2.1 billion image-text pairs. In this paper, for a fair comparison with CLIP [27] and LAION [34] which conduct experiments using 400M data pairs, we create a subset of 400M image-text pairs from our crawled LAION-2B and also make a subset of 100M image-text pairs for ablation study. + +Pre-training Details. The implementation of our DisCo-CLIP is based on OpenCLIP [16], an open source CLIP implementation. We follow the original CLIP [27] and mainly use ViT-B/32 [9] as the vision backbone. Training images are resized to $224 \times 224$ and fed to the vision backbone. For the text backbone, we use a text Transformer [8, 39], and set the maximum length of text to 76 as in [27]. Due to limited time and GPU resource, we do not train ViT-L/14 because it takes more than four times of training time compared to ViT-B/32. It should also be noted that in all our experiments, we do not use the GradAccum strategy as in BASIC [26]. Checkpointing is enabled in vanilla CLIP and our DisCo-CLIP. We train models using an Adam [18] optimizer and cosine learning rate scheduler with a linear warmup [24]. Weight decay regularization [25] + +is used on all parameters except bias, layer normalization, and temperature in contrastive loss. Since our training experiments use different batch sizes, according to previous works [12, 28], we change the learning rate for different batch sizes. For our learning rate scheduler, we first define a base learning rate of 5e-4 and a base batch size of 32,768, and then linearly warm it up to the maximum learning rate. The maximum learning rate is determined according to a linear strategy, max_lr = base_lr * batch_size / 32,768. Training stability is a challenging issue in mixed-precision training as NaN might happen in many cases. We obverse that $\beta_{2}$ in Adam is very important for training stability and find 0.98 works well for our experiments instead of the default value of 0.999. For most of our experiments, we use 64 NVIDIA A100 40GB GPUs for model training, but for some experiments, we only use 8 NVIDIA A100 40GB GPUs to show that our solution is more resource-efficient. + +# 5.2. Evaluation Results + +Equivalence Validation. To empirically validate our theoretical analysis, we conduct experiments to compare CLIP and DisCo-CLIP. We use the same random seed to initiate the network parameters and use the same batch size 32,768 on 64 GPUs, and train ViT-B/32 models with 16 epochs on LAION-100M. + +
MethodsMemoryAccuracyTime (Hours)
CLIP27.4GB51.6413.4
DisCo-CLIP16.5GB51.6412.1
+ +From Table 2, we see that DisCo-CLIP has exactly the same accuracy as CLIP, but uses lower memory consumption and less training time. Under the same training settings, DisCo-CLIP and CLIP also have exactly the same training curves. This experiment further validates the numerical equivalence between DisCo-CLIP and CLIP. + +Table 2. CLIP Reproduction. Under the same training settings, DisCo-CLIP has exactly the same accuracy (top-1 zero-shot classification accuracy on ImageNet) as CLIP, but uses lower memory consumption and less training time. Training resource: 64 A100 40GB GPUs. + +
MethodsGPUsBSMemory
CLIP64× A100 40GB32,76827.4GB
CLIP64× A100 40GB65,536OOM
DisCo-CLIP64× A100 40GB32,76816.5GB
DisCo-CLIP64× A100 40GB196,60838.1GB
DisCo-CLIP8× A100 40GB32,76836.9GB
+ +Table 3. Memory consumption of CLIP and DisCo-CLIP under different settings. "OOM" means out of memory. + +Memory Consumption. Besides memory consumption of network parameters, backbone and contrastive loss con + +
MethodsGPUsBatch sizeBackboneLoss OperatorsLoss TotalBackwardTotal
all_gatherLossall ReduceLoss BPBackbone BP
CLIP6432,768129.46.155.4-61.5414.8605.6
DisCo-CLIP6432,7686.11.64.312.0 (80.5% ↓)2.8337.3481.5 (20.5% ↓)
+ +sumes most memory. We evaluate the memory consumption of the original CLIP and our DisCo-CLIP under different settings. We report the peak memory consumption for different settings, and the results are shown in Table 3. + +We have three observations from Table 3. 1) CLIP with ViT-B/32 can be trained with batch size 32,768 but fails with batch size 65,536. 2) Our DisCo-CLIP can enable training of ViT-B/32 with a much larger batch size, 196,608 with 64 A100 40GB GPU. 3) DisCo-CLIP can enable training of the same model on a cluster with only 8 GPUs. + +Training Speed. One iteration of CLIP consists of extracting features from backbone, gathering features from all GPUs, calculating loss, and executing back-propagation. (We exclude some other factors, including data loading and optimizer update that are not directly related to the model computation or can be ignored.) Instead, DisCo-CLIP decomposes the back-propagation into two BP processes (Loss BP and Backbone BP) and have an additional all Reduce operator. We evaluate the running time of each operator in CLIP and our DisCo-CLIP, and the results are shown in Table 4. + +From Table 4, we can see that 1) for total loss computation, under the same batch size 32,768, we decrease the computation time from $61.5\mathrm{ms}$ to $12.0\mathrm{ms}$ . It is because in DisCo-CLIP, we only need to calculate two subset similarity matrices between multiplying a $\frac{B}{N} \times D$ matrix and a $B \times D$ matrix instead of a full matrix multiplication between two $B \times D$ matrices. 2) the operators of both all Reduce and all_gather are faster compared to the loss computation. 3) under the same batch size 32,768, DisCo-CLIP improves around $20.5\%$ total training efficiency. + +Overall, with DisCo-CLIP, we are able to not only train contrastive learning models with a larger batch size, but also improve the training speed considerably. DisCo-CLIP is a free-lunch solution for large-scale contrastive learning. + +Table 4. Detailed comparisons of training efficiency of CLIP and DisCo-CLIP. All time-related measurements (the last nine columns) are in milliseconds (ms). DisCo-CLIP saves more computational time in loss computation. Training resource: 64 A100 40GB GPUs. + +
Batch SizeStepsEpochsViT-B/32
8,192≈ 200 K1648.76
16,384≈ 100 K1650.95
32,768≈ 50 K1651.64
65,536≈ 25 K1651.91
+ +Batch Size. To assess the role of a larger batch size to the final performance, we conduct some controlled experiments for ViT-B/32 on our LAION-100M and LAION-400M subsets. All training hyper-parameters are the same except that we vary the batch size and the number of training steps. To ensure all models "see" the same number of training samples, we use fewer training steps when training with a larger batch size. In Table 5, we report the results of all settings. + +From Table 5, we can see that large batch size generally helps contrastive learning. The performance of using batch size 65,536 improves that of using batch size 32,768 by around $0.3\%$ . In the evaluation of data scaling, we further observe that the improvement widens when we train the model for more epochs. + +Table 5. Evaluation of different batch sizes on DisCo-CLIP. All models are trained for 16 epochs on a LAION-100M data set, we show top-1 zero-shot classification accuracy on ImageNet. Training resource: 64 A100 40GB GPUs. + +
Batch Size100M×16400M×4400M×8
16,38450.9554.3658.38
32,76851.6455.5259.69
65,53651.9155.5059.96
+ +Table 6. Evaluation of data scaling on DisCo-CLIP. Three batch sizes are evaluated with two LAION subsets: LAION-100M and LAION-400M. The numbers $\times 16$ , $\times 4$ , and $\times 8$ are the training epochs for each data set. Training resource: 64 A100 40GB GPUs. + +Data Scaling. To investigate the role of data scaling, we also conduct some controlled experiments for ViT-B/32 on the LAION 100M and LAION 400M subsets. For all models, we use three different batch sizes, 16,384, 32,768 and 65,536 for training. Models are trained with three different settings, 100M with 16 epochs, 400M with 4 epochs and 400M with 8 epochs. Table 6 reports the final ImageNet top-1 zero-shot classification accuracy of all models. + +From Table 6, we observe that, "seeing" the same number of training samples (LAION-100M with 16 epochs, LAION-400M with 4 epochs.), the model trained on larger scale of data set can obtain better performance. For example, trained with the same batch size 65,536, the performance improves from $51.91\%$ to $55.50\%$ when the data set increases from 100M to 400M. This observation validates the value of data scaling. This observation is also consistent with the combined scaling law in BASIC [26]. We also find that training with more epochs on larger scale of data with larger batch size will bring in larger performance gain. The gap between models (with batch sizes 32,768 and 65,536) trained on 400M with 4 epochs is around $0\%$ (from + +
ModelData SetsEpochsStepsBatch SizeINet [7]INet-v2 [32]INet-R [15]INet-S [40]
CLIP [27]CLIP WIT 400M32≈ 400 K32,76863.356.069.442.3
OpenCLIP [16,34]LAION-400M32≈ 400 K32,76862.955.173.449.4
DisCo-CLIPLAION-400M*32≈ 400 K32,76863.255.273.450.6
DisCo-CLIPLAION-400M*32≈ 200 K65,53664.356.273.851.7
+ +55.52% to 55.50%), but it increases to 0.3% (from 59.69% to 59.96%) when the models are trained for 8 epochs. Thus, we can expect that if we use larger scale of data set, we should also use larger batch size to get a better performance. + +# 5.3. Zero-Shot Classification + +Following CLIP [27] and LAION-5B [34], we evaluate zero-shot top-1 classification accuracy of our models on several data sets, including INet [7], INet-v2 [32], INet-R [15] and INet-S [40]. We use exactly the same 80 prompts as CLIP. Some standard prompts are like "a bad photo of a $\{\}$ ", "a photo of many $\{\}$ ", and etc. Following LAION-5B, we extract the embedding for each prompt using the text encoder (text Transformer), and average embeddings of all prompts in each class, and finally get the final class embedding. Given an image, we extract its image embedding via the image encoder (ViT-B/32), and compute its similarities with all class embeddings, and classify it into the class with the highest similarity score. + +We can see from Table 7, that using the same batch size of 32,768 as the OpenCLIP implementation, our DisCo-CLIP obtains a similar performance with OpenCLIP, the result of OpenCLIP is reported by LAION group in [34]. Using a larger batch size of 65,536, DisCo-CLIP achieves a better performance than the OpenCLIP implementation and the original CLIP. Specifically, trained with the same 32 epochs, DisCo-CLIP using a batch size of 65,536 improves the OpenCLIP's result that is based on batch size of 32,768 by $1.4\%$ . Note that when doubling the batch size, we halve the training steps. This observation further validates that large batch size is important for contrastive learning. + +# 6. Discussion + +Recent developments in large-scale contrastive or generative learning, such as CLIP [27], ALIGN [17], FILIP [43], LiT [48], BASIC [26], LAION-5B [34], and GIT [41] have potential for many real-world applications, such as image classification, text-to-image retrieval, recommendation system, and generation models. Besides large-scale data sets, the progress highly depends on powerful GPU or TPU computing resources. As shown in Table 8, all methods use + +a large amount of computing hardwares. FILIP uses less GPU but also uses smaller batch size. + +Table 7. Comparison of DisCo-CLIP with vanilla CLIP and re-implemented CLIP by LAION group. We report top-1 zero-shot classification accuracy (\%) on several data sets. All models are based on ViT-B/32. Our LAION-400M* is a 400M subset of LAION-2B. Training resource: 64 A100 40GB GPUs. + +
MethodsHardware
CLIP [27]256 NVIDIA V100 GPUs
FILIP [43]128 NVIDIA V100 GPUs
LAION-5B [34]128-400 NVIDIA A100 GPUs
LiT [48]128-400 TPUs
BASIC [26]2,048 TPUs v3
+ +Table 8. Several vision-language contrastive learning methods and their used hardwares. + +Unfortunately, only a few big technology companies can afford this task. Large batch contrastive loss consumes a large amount of GPU memory, while large batch size is a prerequisite for contrastive learning. As a result, it is challenging for companies with limited resources or academic research institutes to contribute to research on this topic. Our work provides a simple yet effective solution for reducing memory consumption that can help bridge the gap between academia and industry on this topic. + +# 7. Conclusion + +In this paper, we have proposed a simple yet effective distributed contrastive loss solution called DisCo to reduce the memory consumption in contrastive learning. By decomposing the loss computation into intra-GPU computation and inter-GPU computation, we can remove redundant memory consumption and use a all Reduce operator to collect inter-GPU gradients. Using DisCo in CLIP, the introduced DisCo-CLIP can enable a much larger batch contrastive learning compared to CLIP using the same GPU resource. Specifically, we can train DisCo-CLIP models with batch size 32,768 using 8 A100 40GB GPUs, or with batch size 196K using 64 GPUs. We hope DisCo-CLIP will also help and motivate self-supervised learning [4, 6] which also uses contrastive learning. + +# 8. Acknowledgement + +This work was partially supported by OPPO Research Fund. + +# References + +[1] Zhengda Bian, Hongxin Liu, Boxiang Wang, Haichen Huang, Yongbin Li, Chuanrui Wang, Fan Cui, and Yang You. Colossal-ai: A unified deep learning system for large-scale parallel training. arXiv preprint arXiv:2110.14883, 2021. 2 +[2] Tom Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared D Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, et al. Language models are few-shot learners. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 18123-18133, 2022. 2, 8 \ No newline at end of file diff --git a/2023/DisCo-CLIP_ A Distributed Contrastive Loss for Memory Efficient CLIP Training/images.zip b/2023/DisCo-CLIP_ A Distributed Contrastive Loss for Memory Efficient CLIP Training/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..1489a2e7729b3480f6e6fce4350b0d62078f2b66 --- /dev/null +++ b/2023/DisCo-CLIP_ A Distributed Contrastive Loss for Memory Efficient CLIP Training/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:3c3afabb0993124b98934b68439df953b783b1ceac3840d7b17652214b645428 +size 314641 diff --git a/2023/DisCo-CLIP_ A Distributed Contrastive Loss for Memory Efficient CLIP Training/layout.json b/2023/DisCo-CLIP_ A Distributed Contrastive Loss for Memory Efficient CLIP Training/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..26ec8583faca704a75717b5cb4d3d46b04e93671 --- /dev/null +++ b/2023/DisCo-CLIP_ A Distributed Contrastive Loss for Memory Efficient CLIP Training/layout.json @@ -0,0 +1,9378 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 158, + 103, + 436, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 158, + 103, + 436, + 140 + ], + "spans": [ + { + "bbox": [ + 158, + 103, + 436, + 140 + ], + "type": "text", + "content": "DisCo-CLIP: A Distributed Contrastive Loss for Memory Efficient CLIP Training" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 90, + 161, + 499, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 90, + 161, + 499, + 205 + ], + "spans": [ + { + "bbox": [ + 90, + 161, + 499, + 205 + ], + "type": "text", + "content": "Yihao Chen, Xianbiao Qi, Jianan Wang, Lei Zhang* International Digital Economy Academy (IDEA), Shenzhen, Guangdong, China. {chenyihao, qixianbiao, wangjianan, leizhang}@idea.edu.cn" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "spans": [ + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 256, + 289, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 256, + 289, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 256, + 289, + 533 + ], + "type": "text", + "content": "We propose DisCo-CLIP, a distributed memory-efficient CLIP training approach, to reduce the memory consumption of contrastive loss when training contrastive learning models. Our approach decomposes the contrastive loss and its gradient computation into two parts, one to calculate the intra-GPU gradients and the other to compute the inter-GPU gradients. According to our decomposition, only the intra-GPU gradients are computed on the current GPU, while the inter-GPU gradients are collected via all-reduce from other GPUs instead of being repeatedly computed on every GPU. 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Such a distributed solution is mathematically equivalent to the original non-distributed contrastive loss computation, without sacrificing any computation accuracy. It is particularly efficient for large-batch CLIP training. For instance, DisCo-CLIP can enable contrastive training of a ViT-B/32 model with a batch size of 32K or 196K using 8 or 64 A100 40GB GPUs, compared with the original CLIP solution which requires 128 A100 40GB GPUs to train a ViT-B/32 model with a batch size of 32K." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 555, + 128, + 567 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 555, + 128, + 567 + ], + "spans": [ + { + "bbox": [ + 47, + 555, + 128, + 567 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 575, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 575, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 575, + 287, + 696 + ], + "type": "text", + "content": "Vision-language representation learning from massive image-text pairs has recently attracted tremendous attention for its great potential in many applications such as zero-shot classification and text-image retrieval. Representative works include CLIP [27], ALIGN [17], Florence [47], CoCa [46], and BASIC [26], which all leverage hundreds of millions or even billions of image-text pairs collected from the Web to learn a semantic-rich and language-aligned visual representation [22]. As the web-collected data inevitably contain noises, CLIP [27] for the first time applies" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 232, + 546, + 352 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 232, + 546, + 352 + ], + "spans": [ + { + "bbox": [ + 306, + 232, + 546, + 352 + ], + "type": "text", + "content": "contrastive learning on 400M image-text pairs, which implies a weak but more proper assumption about the data: the relevance between paired image and text is greater than that between unpaired image and text. For its demonstrated performance in CLIP, contrastive learning has been widely adopted in subsequent works. Accordingly, several imagedataset data sets with increasingly larger scales have also been developed and made publicly available, such as Conceptual 12M [3], YFCC 100M [38], WIT 37.6M [37], LAION-400M [35], and LAION-5B [34]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 353, + 547, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 353, + 547, + 532 + ], + "spans": [ + { + "bbox": [ + 304, + 353, + 547, + 532 + ], + "type": "text", + "content": "The goal of contrastive learning in CLIP is to learn an alignment between image and text via two encoders. That is, it encourages paired image and text (called a positive pair) to be similar and meanwhile enforces unpaired image and text (called a negative pair) to be dissimilar. For any positive image-text pair, as there are normally unlimited number (up to the total number of images or texts in a data set) of negative image-text pairs, it is crucial to include a sufficiently large number of negative pairs in a contrastive loss to make the representation learning effective, as validated in all related works such as CLIP [27], Florence [47], OpenCLIP [16], and BASIC [26]. Specifically, BASIC shows that larger batch size, plus larger data set and larger model, theoretically lead to a better generalization performance." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 533, + 547, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 547, + 664 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 547, + 664 + ], + "type": "text", + "content": "However, a fundamental technical challenge in training a CLIP-like model is how to enlarge its batch size under the constraint of limited GPU memory. For instance, when the batch size is 65,536, the similarity matrix for all imag-text pairs in the batch will cost about 16GB using Float32. As the backbone part also consumes a significant portion of GPU memory, especially for large backbones such as ViT-Large or ViT-Huge [9], scaling up batch size presents a great challenge, usually requiring hundreds of V100 or A100 GPUs [16, 27, 47], which are inaccessible for most research scientists." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": "In this work, we develop a distributed solution called DisCo-CLIP for constrastive loss computation, which can save a large amount of memory for contrastive loss and make CLIP training more memory-efficient. 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Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "type": "text", + "content": "*Corresponding author." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "22648" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 325 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 325 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 325 + ], + "type": "text", + "content": "starts from a decomposition of the original contrastive loss. Based on this decomposition, we divide the contrastive loss into two parts, one to calculate the intra-GPU loss and gradients, and the other one to calculate the inter-GPU loss and gradients. For a mini-batch on the " + }, + { + "bbox": [ + 46, + 72, + 289, + 325 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 72, + 289, + 325 + ], + "type": "text", + "content": "-th GPU (hereinafter called its hosting GPU), its intra-GPU gradients are calculated on its hosting GPU, and its inter-GPU gradients are collected from other GPUs. DisCo is an exact solution, mathematically equivalent to the original non-distributed contrastive loss, but more memory- and computation-efficient. It can decrease the memory cost of contrastive loss from " + }, + { + "bbox": [ + 46, + 72, + 289, + 325 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(B^2)" + }, + { + "bbox": [ + 46, + 72, + 289, + 325 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 72, + 289, + 325 + ], + "type": "inline_equation", + "content": "\\mathcal{O}\\left(\\frac{B^2}{N}\\right)" + }, + { + "bbox": [ + 46, + 72, + 289, + 325 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 72, + 289, + 325 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 46, + 72, + 289, + 325 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 72, + 289, + 325 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 72, + 289, + 325 + ], + "type": "text", + "content": " are the batch size and the number of GPUs. When " + }, + { + "bbox": [ + 46, + 72, + 289, + 325 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 72, + 289, + 325 + ], + "type": "text", + "content": " equals to 64, it means around " + }, + { + "bbox": [ + 46, + 72, + 289, + 325 + ], + "type": "inline_equation", + "content": "97\\%" + }, + { + "bbox": [ + 46, + 72, + 289, + 325 + ], + "type": "text", + "content": " (see Sec. 4.1 for details) of the memory, and similarly the computational cost, in contrastive loss can be saved. Thus, using DisCo in CLIP, we can enable contrastive training with a larger batch size. Using 8 Nvidia A100 40GB GPUs, DisCo-CLIP can enable contrastive training of a ViT-B/32 model with a batch size of 32,768. Using 64 A100 40GB GPUs, DisCo-CLIP can train the same model with a larger batch size of 196K." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 59, + 325, + 238, + 336 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 325, + 238, + 336 + ], + "spans": [ + { + "bbox": [ + 59, + 325, + 238, + 336 + ], + "type": "text", + "content": "We summarize our contributions in twofold." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 346, + 287, + 475 + ], + "type": "list", + "angle": 0, + "index": 4, + "blocks": [ + { + "bbox": [ + 58, + 346, + 287, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 346, + 287, + 430 + ], + "spans": [ + { + "bbox": [ + 58, + 346, + 287, + 430 + ], + "type": "text", + "content": "- We propose a novel distributed contrastive loss solution called DisCo for memory efficient CLIP training, which can significantly reduce the memory consumption of the contrastive loss computation. Such a solution enables a larger batch size for contrastive training using the same computing resource without sacrificing any computation accuracy." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 58, + 439, + 287, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 439, + 287, + 475 + ], + "spans": [ + { + "bbox": [ + 58, + 439, + 287, + 475 + ], + "type": "text", + "content": "- We further validate that training with a larger batch size can further improve the performance of contrastive learning models." + } + ] + } + ], + "index": 3 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 486, + 222, + 499 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 486, + 222, + 499 + ], + "spans": [ + { + "bbox": [ + 47, + 486, + 222, + 499 + ], + "type": "text", + "content": "2. Background and Related Work" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 507, + 287, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 507, + 287, + 555 + ], + "spans": [ + { + "bbox": [ + 47, + 507, + 287, + 555 + ], + "type": "text", + "content": "In this section, we will introduce some background information for contrastive language-image pre-training (CLIP) and review some works that reduce memory consumption of the backbone part by trading computation for memory." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 563, + 267, + 576 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 563, + 267, + 576 + ], + "spans": [ + { + "bbox": [ + 47, + 563, + 267, + 576 + ], + "type": "text", + "content": "2.1. Contrastive Language-Image Pre-training" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 582, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 582, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 582, + 288, + 715 + ], + "type": "text", + "content": "The idea behind CLIP [27] is to learn two representations via two encoders, an image encoder [9, 14, 20, 23, 42] and a text encoder [2, 8, 28]. Its target is to encourage positive image-text pairs to have higher similarities, and enforce negative image-text pairs to have lower similarities. The training is supervised by two contrastive losses, an image-to-text loss and a text-to-image loss. Suppose we have " + }, + { + "bbox": [ + 47, + 582, + 288, + 715 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 47, + 582, + 288, + 715 + ], + "type": "text", + "content": " text-image pairs as a batch sending to two encoders and the model is trained using " + }, + { + "bbox": [ + 47, + 582, + 288, + 715 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 47, + 582, + 288, + 715 + ], + "type": "text", + "content": " GPUs, with each GPU assigned " + }, + { + "bbox": [ + 47, + 582, + 288, + 715 + ], + "type": "inline_equation", + "content": "b = \\frac{B}{N}" + }, + { + "bbox": [ + 47, + 582, + 288, + 715 + ], + "type": "text", + "content": " pairs. Here, we use " + }, + { + "bbox": [ + 47, + 582, + 288, + 715 + ], + "type": "inline_equation", + "content": "T_A, I_A" + }, + { + "bbox": [ + 47, + 582, + 288, + 715 + ], + "type": "text", + "content": " to denote all text and image features obtained from two encoders. Suppose the" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 545, + 96 + ], + "type": "text", + "content": "hidden dimension is " + }, + { + "bbox": [ + 306, + 72, + 545, + 96 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 306, + 72, + 545, + 96 + ], + "type": "text", + "content": ", then the shapes of " + }, + { + "bbox": [ + 306, + 72, + 545, + 96 + ], + "type": "inline_equation", + "content": "\\mathrm{T}_A, \\mathrm{I}_A" + }, + { + "bbox": [ + 306, + 72, + 545, + 96 + ], + "type": "text", + "content": " are both " + }, + { + "bbox": [ + 306, + 72, + 545, + 96 + ], + "type": "inline_equation", + "content": "B \\times D" + }, + { + "bbox": [ + 306, + 72, + 545, + 96 + ], + "type": "text", + "content": ". In this way, our contrastive losses can be written as," + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 359, + 108, + 545, + 121 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 108, + 545, + 121 + ], + "spans": [ + { + "bbox": [ + 359, + 108, + 545, + 121 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {1} \\left(\\mathrm {I} _ {A}, \\mathrm {T} _ {A}\\right) + \\mathcal {L} _ {2} \\left(\\mathrm {T} _ {A}, \\mathrm {I} _ {A}\\right), \\tag {1}", + "image_path": "71ee02371dcdb133080cfffe57d399e293a99ec6bdd3308aad353a5f80fdc1db.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 125, + 545, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 125, + 545, + 185 + ], + "spans": [ + { + "bbox": [ + 305, + 125, + 545, + 185 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 125, + 545, + 185 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_1(\\mathrm{I}_A,\\mathrm{T}_A)" + }, + { + "bbox": [ + 305, + 125, + 545, + 185 + ], + "type": "text", + "content": " denotes the image-to-text loss, and " + }, + { + "bbox": [ + 305, + 125, + 545, + 185 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_2(\\mathrm{T}_A,\\mathrm{I}_A)" + }, + { + "bbox": [ + 305, + 125, + 545, + 185 + ], + "type": "text", + "content": " represents the text-to-image loss. The image-to-text loss means that the loss is to encourage a given image to find its paired text from tens of thousands of texts, and similarly for the text-to-image loss." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 186, + 546, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 186, + 546, + 400 + ], + "spans": [ + { + "bbox": [ + 304, + 186, + 546, + 400 + ], + "type": "text", + "content": "Motivated by the success of CLIP, many new methods have been proposed, such as FILIP [43], LiT [48], ALIGN [17], BASIC [26], BLIP [21], GIT [41], and K-LITE [36]. FILIP attempts to obtain a fine-grained alignment between image patches and text words. In contrast, CLIP only obtains an image-level alignment between an image and a text sentence. FILIP achieves this goal by a modified contrastive loss. Instead of training both image and text models from scratch, LiT [48] shows that employing a pretrained image model and locking it would greatly benefit zero-shot classification. Under the contrastive framework, ALIGN [17] and BASIC [26] investigate how the scaling up of model, data, and batch size benefits contrastive learning. Instead of only leveraging contrastive learning framework, BLIP [21] introduces a mixed contrastive learning and generative learning for vision-language model. Further, GIT [41] employs a pure generative learning framework and demonstrates its superior performance." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 401, + 545, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 401, + 545, + 472 + ], + "spans": [ + { + "bbox": [ + 304, + 401, + 545, + 472 + ], + "type": "text", + "content": "The success of CLIP and the above methods highly depends on large-scale paired image-text data set [3, 17, 34, 35, 37, 38]. Compared with classification data sets, such as ImageNet 1K [7] and ImageNet 21K [33], which require careful human annotation, there are abundant paired image-text data on the Web and can be more easily collected [34]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 473, + 545, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 473, + 545, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 473, + 545, + 581 + ], + "type": "text", + "content": "Large batch size is a prerequisite for vision-language contrastive learning. Data Parallelism (DP) and Model Parallelism (MP) are two widely used methods in deep learning for distributed training [8,12,28,39,44,45]. There are many related works on this topic, such as DeepSpeed [29-31] and Colossal-AI [1]. We recommend interested readers to refer to these papers for some common distributed learning techniques. In the following, we will describe several methods that trade computation for memory in the backbone part." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 587, + 541, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 587, + 541, + 601 + ], + "spans": [ + { + "bbox": [ + 306, + 587, + 541, + 601 + ], + "type": "text", + "content": "2.2. Trade Computation for Memory in Backbone" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 605, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 715 + ], + "type": "text", + "content": "Checkpointing [5] is an effective approach to reduce memory consumption, especially for the intermediate results of low-cost operation. It only stores feature maps of some high-cost operations, such as convolution, MLP, and self-attention, but drops feature maps of low-cost operations such as activation (e.g., ReLU, GeLU) and layer normalization in the forward pass. In the backward process, these dropped feature maps can be recomputed quickly at a low cost. By dropping some intermediate feature maps, we can" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "22649" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 71, + 284, + 186 + ], + "blocks": [ + { + "bbox": [ + 49, + 71, + 284, + 186 + ], + "lines": [ + { + "bbox": [ + 49, + 71, + 284, + 186 + ], + "spans": [ + { + "bbox": [ + 49, + 71, + 284, + 186 + ], + "type": "image", + "image_path": "94733f47f479ccf72c83b72bcba1830dcefdf3e4eff2679a8b399530e87f0eb0.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 196, + 287, + 251 + ], + "lines": [ + { + "bbox": [ + 46, + 196, + 287, + 251 + ], + "spans": [ + { + "bbox": [ + 46, + 196, + 287, + 251 + ], + "type": "text", + "content": "Figure 1. Illustration of the original CLIP training. All image features " + }, + { + "bbox": [ + 46, + 196, + 287, + 251 + ], + "type": "inline_equation", + "content": "\\mathrm{I}_A" + }, + { + "bbox": [ + 46, + 196, + 287, + 251 + ], + "type": "text", + "content": " and text features " + }, + { + "bbox": [ + 46, + 196, + 287, + 251 + ], + "type": "inline_equation", + "content": "\\mathrm{T}_A" + }, + { + "bbox": [ + 46, + 196, + 287, + 251 + ], + "type": "text", + "content": " are gathered to every GPU via all_gather to calculate the " + }, + { + "bbox": [ + 46, + 196, + 287, + 251 + ], + "type": "inline_equation", + "content": "B\\times B" + }, + { + "bbox": [ + 46, + 196, + 287, + 251 + ], + "type": "text", + "content": " similarity matrix for contrastive loss computation. This computation is performed repeatedly on every GPU." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 273, + 287, + 320 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 273, + 287, + 320 + ], + "spans": [ + { + "bbox": [ + 46, + 273, + 287, + 320 + ], + "type": "text", + "content": "save a great amount of memory. Gruslys et al. [13] further extend the idea of Checkpointing to the recursive neural network. Checkpointing is helpful but still not sufficient if we want to further increase the batch size." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 321, + 287, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 321, + 287, + 477 + ], + "spans": [ + { + "bbox": [ + 46, + 321, + 287, + 477 + ], + "type": "text", + "content": "Recently, BASIC [26] introduces a gradient accumulating (GradAccum) method for memory saving in backbone via micro-batching the contrastive loss. This approach is based on the observation that when computing the contrastive loss, we only need the full similarity matrix instead of all intermediate results. Thus, BASIC proposes to trade computation for memory by dropping some intermediate hidden states during the forward process, and then recompute them during back-propagation. This method can effectively reduce the memory consumption in the backbone part but it requires one extra forward computation. A similar gradient cache approach [10] was also introduced for dense passage retriever in natural language processing." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 477, + 287, + 572 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 477, + 287, + 572 + ], + "spans": [ + { + "bbox": [ + 46, + 477, + 287, + 572 + ], + "type": "text", + "content": "Reversible model structure [11, 19] is another elegant method for memory saving in backbone. However, it requires block adaption because it needs to reconstruct the input layer according to the output layer in the back propagation process. Reversible structure is particularly suitable for models that do not change activation shape in the whole network. However, reconstructing a layer from its output inevitably takes more backward time." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 573, + 287, + 644 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 573, + 287, + 644 + ], + "spans": [ + { + "bbox": [ + 46, + 573, + 287, + 644 + ], + "type": "text", + "content": "All above three mechanisms mainly focus on reducing memory consumption in the backbone part. However, none of them pays attention to reducing the memory consumption of the contrastive loss, which has been a big bottleneck for large batch size contrastive training. We will explain this problem in the next section." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 657, + 118, + 669 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 657, + 118, + 669 + ], + "spans": [ + { + "bbox": [ + 47, + 657, + 118, + 669 + ], + "type": "text", + "content": "3. Motivation" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "Distributed contrastive learning is different from traditional distributed data parallel and model parallel strategies. Data parallel (DP) is particularly effective when activations" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "type": "text", + "content": "in the network cost most of the GPU memory. For example, in [12], Goyal et al. succeeded in training an ImageNet classification model in one hour. Each GPU independently performs forward and backward computation. Only after backward computation, the GPUs perform a gradient communication to merge gradients. In contrast, model parallel (MP) is more effective when model parameters (e.g. 10 billions of parameters) consume a large amount of GPU memory. In this way, the model parameters are sliced and assigned to different GPUs. However, different from the DP and MP problems, in contrastive training, besides the backbone and model parameters, the contrastive loss consumes a larger amount of GPU memory especially when a large batch size is used." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 239, + 545, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 239, + 545, + 312 + ], + "spans": [ + { + "bbox": [ + 304, + 239, + 545, + 312 + ], + "type": "text", + "content": "As we have discussed in the introduction section, a large batch size is of crucial importance for contrastive learning. Previous research [26] also proves theoretically that a larger contrastive batch size can lead to a better representation for image-text models. Interested readers can refer to Theorem 1 in [26] and its appendix for the proof." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 312, + 545, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 312, + 545, + 443 + ], + "spans": [ + { + "bbox": [ + 304, + 312, + 545, + 443 + ], + "type": "text", + "content": "However, a large batch in contrastive loss will consume a large amount of GPU memory, usually of " + }, + { + "bbox": [ + 304, + 312, + 545, + 443 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(B^2)" + }, + { + "bbox": [ + 304, + 312, + 545, + 443 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 312, + 545, + 443 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 304, + 312, + 545, + 443 + ], + "type": "text", + "content": " is the batch size. Let us take an examination of the memory consumption of contrastive loss. For example, for a batch size of 65,536, it stores a similarity matrix of 4.3 billions parameters which requires 16GB of memory using Float32. Its gradient computation in the back-propagation process will take another 16GB of memory. Considering other memory cost of model parameters and backbone intermediate activations, it cannot be trained using A100 40GB GPUs even with mixed precision computation." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 443, + 545, + 538 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 443, + 545, + 538 + ], + "spans": [ + { + "bbox": [ + 304, + 443, + 545, + 538 + ], + "type": "text", + "content": "After investigating the constrastive loss in depth, we notice that there is much redundant memory consumption and computational waste in the current CLIP training solution. As shown in Fig. 1, in the original CLIP training, to calculate the gradients for the text and image features in the hosting GPU, every GPU in the distributed training environment needs to compute the entire " + }, + { + "bbox": [ + 304, + 443, + 545, + 538 + ], + "type": "inline_equation", + "content": "B \\times B" + }, + { + "bbox": [ + 304, + 443, + 545, + 538 + ], + "type": "text", + "content": " similarity matrix, which is not necessary as we will show later." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 539, + 545, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 539, + 545, + 586 + ], + "spans": [ + { + "bbox": [ + 304, + 539, + 545, + 586 + ], + "type": "text", + "content": "Our motivation in this paper is to eliminate memory redundancy and remove unnecessary calculation via a loss decomposition, and thus enable large batch training using limited GPU resource." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 595, + 545, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 595, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 595, + 545, + 624 + ], + "type": "text", + "content": "4. DisCo-CLIP: A Distributed Contrastive Loss for Memory Efficient CLIP Training" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": "In this section, we introduce DisCo, a distributed solution for contrastive loss computation. Using DisCo in CLIP, we accomplish a new memory efficient CLIP training method, called DisCo-CLIP. To this end, we decompose the loss calculation into two parts, one part to compute the intra-GPU loss and gradients and the other part to compute inter-GPU loss and gradients. This section will first intro" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "22650" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 107 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 107 + ], + "type": "text", + "content": "duce how we decompose this loss calculation. Then, we will describe the algorithm implementation of DisCo-CLIP in detail." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 116, + 251, + 128 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 116, + 251, + 128 + ], + "spans": [ + { + "bbox": [ + 47, + 116, + 251, + 128 + ], + "type": "text", + "content": "4.1. DisCo: A Distributed Contrastive Loss" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 135, + 287, + 194 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 135, + 287, + 194 + ], + "spans": [ + { + "bbox": [ + 46, + 135, + 287, + 194 + ], + "type": "text", + "content": "As shown in Eq. 1, " + }, + { + "bbox": [ + 46, + 135, + 287, + 194 + ], + "type": "inline_equation", + "content": "\\mathrm{I}_A" + }, + { + "bbox": [ + 46, + 135, + 287, + 194 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 135, + 287, + 194 + ], + "type": "inline_equation", + "content": "\\mathrm{T}_A" + }, + { + "bbox": [ + 46, + 135, + 287, + 194 + ], + "type": "text", + "content": " denote all image and text features collected from all GPUs. Here, we use " + }, + { + "bbox": [ + 46, + 135, + 287, + 194 + ], + "type": "inline_equation", + "content": "\\mathrm{I}_n" + }, + { + "bbox": [ + 46, + 135, + 287, + 194 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 135, + 287, + 194 + ], + "type": "inline_equation", + "content": "\\mathrm{T}_n" + }, + { + "bbox": [ + 46, + 135, + 287, + 194 + ], + "type": "text", + "content": " to denote the image and text features on the " + }, + { + "bbox": [ + 46, + 135, + 287, + 194 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 135, + 287, + 194 + ], + "type": "text", + "content": "-th GPU, and use " + }, + { + "bbox": [ + 46, + 135, + 287, + 194 + ], + "type": "inline_equation", + "content": "\\mathrm{I}_{\\overline{n}}" + }, + { + "bbox": [ + 46, + 135, + 287, + 194 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 135, + 287, + 194 + ], + "type": "inline_equation", + "content": "\\mathrm{T}_{\\overline{n}}" + }, + { + "bbox": [ + 46, + 135, + 287, + 194 + ], + "type": "text", + "content": " to denote the image and text features on all other GPUs. The division is denoted as," + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 135, + 203, + 287, + 222 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 135, + 203, + 287, + 222 + ], + "spans": [ + { + "bbox": [ + 135, + 203, + 287, + 222 + ], + "type": "interline_equation", + "content": "\\mathrm {I} _ {A} = \\left[ \\begin{array}{l l} \\mathrm {I} _ {n}, & \\mathrm {I} _ {\\overline {{n}}} \\end{array} \\right], \\tag {2}", + "image_path": "2697160c7381a4b0fab721a967e970691f50be97083286f615bece6a428e2516.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 133, + 218, + 200, + 232 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 133, + 218, + 200, + 232 + ], + "spans": [ + { + "bbox": [ + 133, + 218, + 200, + 232 + ], + "type": "interline_equation", + "content": "\\mathrm {T} _ {A} = \\left[ \\mathrm {T} _ {n}, \\mathrm {T} _ {\\bar {n}} \\right]", + "image_path": "bfad5df82aac3527e2fac7fb7db47f083dd7423d6e88d2555d5a133ab55b22b4.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 241, + 287, + 267 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 241, + 287, + 267 + ], + "spans": [ + { + "bbox": [ + 47, + 241, + 287, + 267 + ], + "type": "text", + "content": "The shapes of " + }, + { + "bbox": [ + 47, + 241, + 287, + 267 + ], + "type": "inline_equation", + "content": "\\mathrm{I}_A" + }, + { + "bbox": [ + 47, + 241, + 287, + 267 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 241, + 287, + 267 + ], + "type": "inline_equation", + "content": "\\mathrm{T}_A" + }, + { + "bbox": [ + 47, + 241, + 287, + 267 + ], + "type": "text", + "content": " are " + }, + { + "bbox": [ + 47, + 241, + 287, + 267 + ], + "type": "inline_equation", + "content": "B\\times D" + }, + { + "bbox": [ + 47, + 241, + 287, + 267 + ], + "type": "text", + "content": ", the shapes of " + }, + { + "bbox": [ + 47, + 241, + 287, + 267 + ], + "type": "inline_equation", + "content": "\\mathrm{I}_n" + }, + { + "bbox": [ + 47, + 241, + 287, + 267 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 241, + 287, + 267 + ], + "type": "inline_equation", + "content": "\\mathrm{T}_n" + }, + { + "bbox": [ + 47, + 241, + 287, + 267 + ], + "type": "text", + "content": " are " + }, + { + "bbox": [ + 47, + 241, + 287, + 267 + ], + "type": "inline_equation", + "content": "\\frac{B}{N}\\times D" + }, + { + "bbox": [ + 47, + 241, + 287, + 267 + ], + "type": "text", + "content": ", and the shapes of " + }, + { + "bbox": [ + 47, + 241, + 287, + 267 + ], + "type": "inline_equation", + "content": "\\mathrm{I}_{\\overline{n}}" + }, + { + "bbox": [ + 47, + 241, + 287, + 267 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 241, + 287, + 267 + ], + "type": "inline_equation", + "content": "\\mathrm{T}_{\\overline{n}}" + }, + { + "bbox": [ + 47, + 241, + 287, + 267 + ], + "type": "text", + "content": " are " + }, + { + "bbox": [ + 47, + 241, + 287, + 267 + ], + "type": "inline_equation", + "content": "\\frac{B(N - 1)}{N}\\times D" + }, + { + "bbox": [ + 47, + 241, + 287, + 267 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 267, + 286, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 267, + 286, + 289 + ], + "spans": [ + { + "bbox": [ + 47, + 267, + 286, + 289 + ], + "type": "text", + "content": "According to the above definition, the contrastive loss can be decomposed and rewritten as," + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 96, + 300, + 287, + 318 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 300, + 287, + 318 + ], + "spans": [ + { + "bbox": [ + 96, + 300, + 287, + 318 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {d} = \\mathcal {L} _ {1} \\left(\\mathrm {I} _ {n}, \\mathrm {T} _ {A}\\right) + \\mathcal {L} _ {1} \\left(\\mathrm {I} _ {\\bar {n}}, \\mathrm {T} _ {A}\\right) + \\tag {3}", + "image_path": "fea48c252945652b81827ebf28d0e578c766b16ccf4a8342505ca63aa470e501.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 127, + 315, + 236, + 327 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 127, + 315, + 236, + 327 + ], + "spans": [ + { + "bbox": [ + 127, + 315, + 236, + 327 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {2} \\left(\\mathrm {T} _ {n}, \\mathrm {I} _ {A}\\right) + \\mathcal {L} _ {2} \\left(\\mathrm {T} _ {\\bar {n}}, \\mathrm {I} _ {A}\\right),", + "image_path": "d00e2423a23dcb197f84792c24a1dfd0567b7de4129cc026ba7e66516a969377.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 338, + 287, + 481 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 338, + 287, + 481 + ], + "spans": [ + { + "bbox": [ + 46, + 338, + 287, + 481 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 338, + 287, + 481 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_1(\\mathrm{I}_n,\\mathrm{T}_A)" + }, + { + "bbox": [ + 46, + 338, + 287, + 481 + ], + "type": "text", + "content": " denotes the image-to-text contrastive loss between image features " + }, + { + "bbox": [ + 46, + 338, + 287, + 481 + ], + "type": "inline_equation", + "content": "\\mathrm{I}_n" + }, + { + "bbox": [ + 46, + 338, + 287, + 481 + ], + "type": "text", + "content": " and text features " + }, + { + "bbox": [ + 46, + 338, + 287, + 481 + ], + "type": "inline_equation", + "content": "\\mathrm{T}_A" + }, + { + "bbox": [ + 46, + 338, + 287, + 481 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 338, + 287, + 481 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_2(\\mathrm{T}_n,\\mathrm{I}_A)" + }, + { + "bbox": [ + 46, + 338, + 287, + 481 + ], + "type": "text", + "content": " denotes the text-to-image loss between " + }, + { + "bbox": [ + 46, + 338, + 287, + 481 + ], + "type": "inline_equation", + "content": "\\mathrm{T}_n" + }, + { + "bbox": [ + 46, + 338, + 287, + 481 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 338, + 287, + 481 + ], + "type": "inline_equation", + "content": "\\mathrm{I}_A" + }, + { + "bbox": [ + 46, + 338, + 287, + 481 + ], + "type": "text", + "content": ". Mathematically, the computational result " + }, + { + "bbox": [ + 46, + 338, + 287, + 481 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_d" + }, + { + "bbox": [ + 46, + 338, + 287, + 481 + ], + "type": "text", + "content": " in Eq. 3 is the same as the result " + }, + { + "bbox": [ + 46, + 338, + 287, + 481 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 46, + 338, + 287, + 481 + ], + "type": "text", + "content": " in Eq. 1. However, by decomposing the loss " + }, + { + "bbox": [ + 46, + 338, + 287, + 481 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_d" + }, + { + "bbox": [ + 46, + 338, + 287, + 481 + ], + "type": "text", + "content": " into four parts, the gradient flow in the back-propagation process is more obvious. Meanwhile, we can see that " + }, + { + "bbox": [ + 46, + 338, + 287, + 481 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_1(\\mathrm{I}_{\\overline{n}},\\mathrm{T}_A)" + }, + { + "bbox": [ + 46, + 338, + 287, + 481 + ], + "type": "text", + "content": " does not induce gradients with respect to " + }, + { + "bbox": [ + 46, + 338, + 287, + 481 + ], + "type": "inline_equation", + "content": "\\mathrm{I}_n" + }, + { + "bbox": [ + 46, + 338, + 287, + 481 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 338, + 287, + 481 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_2(\\mathrm{T}_{\\overline{n}},\\mathrm{I}_A)" + }, + { + "bbox": [ + 46, + 338, + 287, + 481 + ], + "type": "text", + "content": " has no gradients with respect to " + }, + { + "bbox": [ + 46, + 338, + 287, + 481 + ], + "type": "inline_equation", + "content": "\\mathrm{T}_n" + }, + { + "bbox": [ + 46, + 338, + 287, + 481 + ], + "type": "text", + "content": ". Actually, these two terms are redundant computation on the " + }, + { + "bbox": [ + 46, + 338, + 287, + 481 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 338, + 287, + 481 + ], + "type": "text", + "content": "-th GPU in the original contrastive loss, which unnecessarily consume a large amount of memory." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 482, + 287, + 523 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 482, + 287, + 523 + ], + "spans": [ + { + "bbox": [ + 46, + 482, + 287, + 523 + ], + "type": "text", + "content": "Thus, according to the decomposition in Eq. 3, we can calculate the gradients " + }, + { + "bbox": [ + 46, + 482, + 287, + 523 + ], + "type": "inline_equation", + "content": "\\frac{\\partial\\mathcal{L}_d}{\\partial\\mathrm{T}_n}" + }, + { + "bbox": [ + 46, + 482, + 287, + 523 + ], + "type": "text", + "content": " for image features " + }, + { + "bbox": [ + 46, + 482, + 287, + 523 + ], + "type": "inline_equation", + "content": "\\mathrm{I}_n" + }, + { + "bbox": [ + 46, + 482, + 287, + 523 + ], + "type": "text", + "content": " and the gradients " + }, + { + "bbox": [ + 46, + 482, + 287, + 523 + ], + "type": "inline_equation", + "content": "\\frac{\\partial\\mathcal{L}_d}{\\partial\\mathrm{T}_n}" + }, + { + "bbox": [ + 46, + 482, + 287, + 523 + ], + "type": "text", + "content": " for text features " + }, + { + "bbox": [ + 46, + 482, + 287, + 523 + ], + "type": "inline_equation", + "content": "\\mathrm{T}_n" + }, + { + "bbox": [ + 46, + 482, + 287, + 523 + ], + "type": "text", + "content": " as follows," + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 56, + 527, + 287, + 559 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 527, + 287, + 559 + ], + "spans": [ + { + "bbox": [ + 56, + 527, + 287, + 559 + ], + "type": "interline_equation", + "content": "\\frac {\\partial \\mathcal {L} _ {d}}{\\partial \\mathrm {I} _ {n}} = \\boxed {\\frac {\\partial \\mathcal {L} _ {1} (\\mathrm {I} _ {n} , \\mathrm {T} _ {A})}{\\partial \\mathrm {I} _ {n}} + \\frac {\\partial \\mathcal {L} _ {2} (\\mathrm {T} _ {n} , \\mathrm {I} _ {A})}{\\partial \\mathrm {I} _ {n}}} + \\boxed {\\frac {\\partial \\mathcal {L} _ {2} (\\mathrm {T} _ {\\bar {n}} , \\mathrm {I} _ {A})}{\\partial \\mathrm {I} _ {n}}}, \\tag {4}", + "image_path": "38d12d1c49dc28eda111baa989dab2bdf2173fb5464f6ef6a47786a61be8f849.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 56, + 556, + 284, + 582 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 556, + 284, + 582 + ], + "spans": [ + { + "bbox": [ + 56, + 556, + 284, + 582 + ], + "type": "interline_equation", + "content": "\\frac {\\partial \\mathcal {L} _ {d}}{\\partial \\mathrm {T} _ {n}} = \\boxed {\\frac {\\partial \\mathcal {L} _ {1} (\\mathrm {I} _ {n} , \\mathrm {T} _ {A})}{\\partial \\mathrm {T} _ {n}} + \\frac {\\partial \\mathcal {L} _ {2} (\\mathrm {T} _ {n} , \\mathrm {I} _ {A})}{\\partial \\mathrm {T} _ {n}}} + \\boxed {\\frac {\\partial \\mathcal {L} _ {1} (\\mathrm {I} _ {\\bar {n}} , \\mathrm {T} _ {A})}{\\partial \\mathrm {T} _ {n}}},", + "image_path": "ea9839a02fdd3a2215b64a8f754f7e510819d96d5fa718b698075b4cec763370.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 587, + 287, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 587, + 287, + 609 + ], + "spans": [ + { + "bbox": [ + 47, + 587, + 287, + 609 + ], + "type": "text", + "content": "where the losses in the red part can be further unfolded in a sum form as," + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 85, + 615, + 287, + 645 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 615, + 287, + 645 + ], + "spans": [ + { + "bbox": [ + 85, + 615, + 287, + 645 + ], + "type": "interline_equation", + "content": "\\frac {\\partial \\mathcal {L} _ {2} \\left(\\mathrm {T} _ {\\bar {n}} , \\mathrm {I} _ {A}\\right)}{\\partial \\mathrm {I} _ {n}} = \\sum_ {i \\neq n \\& i \\in [ 1, N ]} \\frac {\\partial \\mathcal {L} _ {2} \\left(\\mathrm {T} _ {i} , \\mathrm {I} _ {A}\\right)}{\\partial \\mathrm {I} _ {n}}, \\tag {5}", + "image_path": "fc4519ccb55f0d359a91e32cae24f6278256e9369f6be1e5a94e8abb9943fa90.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 87, + 643, + 286, + 670 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 643, + 286, + 670 + ], + "spans": [ + { + "bbox": [ + 87, + 643, + 286, + 670 + ], + "type": "interline_equation", + "content": "\\frac {\\partial \\mathcal {L} _ {1} \\left(\\mathrm {I} _ {\\bar {n}} , \\mathrm {T} _ {A}\\right)}{\\partial \\mathrm {T} _ {n}} = \\sum_ {j \\neq n \\& j \\in [ 1, N ]} \\frac {\\partial \\mathcal {L} _ {1} \\left(\\mathrm {I} _ {j} , \\mathrm {T} _ {A}\\right)}{\\partial \\mathrm {T} _ {n}}. \\tag {3}", + "image_path": "e0cc8b772152a8c116642b2a60880e62f6267ad17415c738478f0b758d45ecc2.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 47, + 677, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 712 + ], + "type": "text", + "content": "The gradients of " + }, + { + "bbox": [ + 47, + 677, + 287, + 712 + ], + "type": "inline_equation", + "content": "\\frac{\\partial\\mathcal{L}_d}{\\partial\\mathrm{I}_n}" + }, + { + "bbox": [ + 47, + 677, + 287, + 712 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 677, + 287, + 712 + ], + "type": "inline_equation", + "content": "\\frac{\\partial\\mathcal{L}_d}{\\partial\\mathrm{T}_n}" + }, + { + "bbox": [ + 47, + 677, + 287, + 712 + ], + "type": "text", + "content": " both consist of three terms. In both equations, all three terms can be divided into two parts, we mark them with two different colors, blue and" + } + ] + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 316, + 71, + 541, + 205 + ], + "blocks": [ + { + "bbox": [ + 316, + 71, + 541, + 205 + ], + "lines": [ + { + "bbox": [ + 316, + 71, + 541, + 205 + ], + "spans": [ + { + "bbox": [ + 316, + 71, + 541, + 205 + ], + "type": "image", + "image_path": "5034b66049804954e62df0e061363be9c822e472722edfd920d8fb0ec2981bde.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 333, + 209, + 520, + 220 + ], + "lines": [ + { + "bbox": [ + 333, + 209, + 520, + 220 + ], + "spans": [ + { + "bbox": [ + 333, + 209, + 520, + 220 + ], + "type": "text", + "content": "(1) Image-to-Text Contrastive Loss Backward" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 313, + 236, + 539, + 373 + ], + "blocks": [ + { + "bbox": [ + 313, + 236, + 539, + 373 + ], + "lines": [ + { + "bbox": [ + 313, + 236, + 539, + 373 + ], + "spans": [ + { + "bbox": [ + 313, + 236, + 539, + 373 + ], + "type": "image", + "image_path": "bfaeffe052037e8c95b6e39f869017153d2f08a946abcbb82d7c283662abcae6.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 333, + 377, + 520, + 389 + ], + "lines": [ + { + "bbox": [ + 333, + 377, + 520, + 389 + ], + "spans": [ + { + "bbox": [ + 333, + 377, + 520, + 389 + ], + "type": "text", + "content": "(2) Text-to-Image Contrastive Loss Backward" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 403, + 545, + 448 + ], + "lines": [ + { + "bbox": [ + 305, + 403, + 545, + 448 + ], + "spans": [ + { + "bbox": [ + 305, + 403, + 545, + 448 + ], + "type": "text", + "content": "Figure 2. Illustration of the gradient calculation of DisCo on the first GPU. In DisCo, to calculate the gradients on the current GPU, we only need to compute two " + }, + { + "bbox": [ + 305, + 403, + 545, + 448 + ], + "type": "inline_equation", + "content": "\\frac{B}{N} \\times B" + }, + { + "bbox": [ + 305, + 403, + 545, + 448 + ], + "type": "text", + "content": " similarity matrices instead of a full " + }, + { + "bbox": [ + 305, + 403, + 545, + 448 + ], + "type": "inline_equation", + "content": "B \\times B" + }, + { + "bbox": [ + 305, + 403, + 545, + 448 + ], + "type": "text", + "content": " matrix as shown in Fig. 1." + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 468, + 545, + 551 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 468, + 545, + 551 + ], + "spans": [ + { + "bbox": [ + 304, + 468, + 545, + 551 + ], + "type": "text", + "content": "red. The gradients in the blue part are calculated on the " + }, + { + "bbox": [ + 304, + 468, + 545, + 551 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 468, + 545, + 551 + ], + "type": "text", + "content": "-th (hosting) GPU, and the gradients in the red part are calculated on other GPUs. We call them intra-GPU gradients and inter-GPU gradients, respectively. When computing the red part for " + }, + { + "bbox": [ + 304, + 468, + 545, + 551 + ], + "type": "inline_equation", + "content": "\\frac{\\partial \\mathcal{L}_d}{\\partial \\mathrm{I}_n}" + }, + { + "bbox": [ + 304, + 468, + 545, + 551 + ], + "type": "text", + "content": ", the images " + }, + { + "bbox": [ + 304, + 468, + 545, + 551 + ], + "type": "inline_equation", + "content": "\\mathrm{I}_n" + }, + { + "bbox": [ + 304, + 468, + 545, + 551 + ], + "type": "text", + "content": " are considered as negative samples. It should be noted that although " + }, + { + "bbox": [ + 304, + 468, + 545, + 551 + ], + "type": "inline_equation", + "content": "\\mathrm{I}_n" + }, + { + "bbox": [ + 304, + 468, + 545, + 551 + ], + "type": "text", + "content": " is regarded as negative samples, there still induce gradients for " + }, + { + "bbox": [ + 304, + 468, + 545, + 551 + ], + "type": "inline_equation", + "content": "\\mathrm{I}_n" + }, + { + "bbox": [ + 304, + 468, + 545, + 551 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 551, + 545, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 551, + 545, + 589 + ], + "spans": [ + { + "bbox": [ + 306, + 551, + 545, + 589 + ], + "type": "text", + "content": "According to this decomposition, to compute " + }, + { + "bbox": [ + 306, + 551, + 545, + 589 + ], + "type": "inline_equation", + "content": "\\frac{\\partial\\mathcal{L}_d}{\\partial\\mathrm{I}_n}" + }, + { + "bbox": [ + 306, + 551, + 545, + 589 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 551, + 545, + 589 + ], + "type": "inline_equation", + "content": "\\frac{\\partial\\mathcal{L}_d}{\\partial\\mathrm{T}_n}" + }, + { + "bbox": [ + 306, + 551, + 545, + 589 + ], + "type": "text", + "content": ", the " + }, + { + "bbox": [ + 306, + 551, + 545, + 589 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 306, + 551, + 545, + 589 + ], + "type": "text", + "content": "-th GPU only needs to compute the following four terms," + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 315, + 593, + 544, + 628 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 593, + 544, + 628 + ], + "spans": [ + { + "bbox": [ + 315, + 593, + 544, + 628 + ], + "type": "interline_equation", + "content": "\\left[ \\frac {\\partial \\mathcal {L} _ {1} \\left(\\mathrm {I} _ {n} , \\mathrm {T} _ {A}\\right)}{\\partial \\mathrm {I} _ {n}}, \\frac {\\partial \\mathcal {L} _ {2} \\left(\\mathrm {T} _ {n} , \\mathrm {I} _ {A}\\right)}{\\partial \\mathrm {I} _ {n}}, \\frac {\\partial \\mathcal {L} _ {1} \\left(\\mathrm {I} _ {n} , \\mathrm {T} _ {A}\\right)}{\\partial \\mathrm {T} _ {n}}, \\frac {\\partial \\mathcal {L} _ {2} \\left(\\mathrm {T} _ {n} , \\mathrm {I} _ {A}\\right)}{\\partial \\mathrm {T} _ {n}} \\right]. \\tag {6}", + "image_path": "6933da76584e9f2a324348500ce9b4ae38dcd69cdb8c38d9c99b0b94e420d156.jpg" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 305, + 628, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 628, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 628, + 545, + 713 + ], + "type": "text", + "content": "All four terms only need to compute two small similarity matrices of shape " + }, + { + "bbox": [ + 305, + 628, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\frac{B}{N} \\times B" + }, + { + "bbox": [ + 305, + 628, + 545, + 713 + ], + "type": "text", + "content": " instead of a full matrix of shape " + }, + { + "bbox": [ + 305, + 628, + 545, + 713 + ], + "type": "inline_equation", + "content": "B \\times B" + }, + { + "bbox": [ + 305, + 628, + 545, + 713 + ], + "type": "text", + "content": " which consumes a large amount of memory. In this way, we can reduce memory consumption from " + }, + { + "bbox": [ + 305, + 628, + 545, + 713 + ], + "type": "inline_equation", + "content": "B^2" + }, + { + "bbox": [ + 305, + 628, + 545, + 713 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 305, + 628, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\frac{2B^2}{N}" + }, + { + "bbox": [ + 305, + 628, + 545, + 713 + ], + "type": "text", + "content": ". For instance, when " + }, + { + "bbox": [ + 305, + 628, + 545, + 713 + ], + "type": "inline_equation", + "content": "N = 16" + }, + { + "bbox": [ + 305, + 628, + 545, + 713 + ], + "type": "text", + "content": ", we save " + }, + { + "bbox": [ + 305, + 628, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\frac{7}{8}" + }, + { + "bbox": [ + 305, + 628, + 545, + 713 + ], + "type": "text", + "content": " of memory consumption, if " + }, + { + "bbox": [ + 305, + 628, + 545, + 713 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 305, + 628, + 545, + 713 + ], + "type": "text", + "content": " is 64, we save " + }, + { + "bbox": [ + 305, + 628, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\frac{31}{32}" + }, + { + "bbox": [ + 305, + 628, + 545, + 713 + ], + "type": "text", + "content": " of memory consumption. Meanwhile, it also saves much computation. The compu" + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 316, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 316, + 757 + ], + "type": "text", + "content": "22651" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": "tational cost for the contrastive similarity matrix decreases from " + }, + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "inline_equation", + "content": "B^2 D" + }, + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "inline_equation", + "content": "\\frac{2B^2D}{N}" + }, + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 59, + 98, + 185, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 98, + 185, + 109 + ], + "spans": [ + { + "bbox": [ + 59, + 98, + 185, + 109 + ], + "type": "text", + "content": "For the two red terms in Eq. 4," + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 107, + 114, + 287, + 140 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 114, + 287, + 140 + ], + "spans": [ + { + "bbox": [ + 107, + 114, + 287, + 140 + ], + "type": "interline_equation", + "content": "\\left[ \\frac {\\partial \\mathcal {L} _ {2} \\left(\\mathrm {T} _ {\\bar {n}} , \\mathrm {I} _ {A}\\right)}{\\partial \\mathrm {I} _ {n}}, \\frac {\\partial \\mathcal {L} _ {1} \\left(\\mathrm {I} _ {\\bar {n}} , \\mathrm {T} _ {A}\\right)}{\\partial \\mathrm {T} _ {n}} \\right], \\tag {7}", + "image_path": "4791cc691a142efa497be3ac6dde02b713a115da3a3d6db450915f30f924ab4a.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 144, + 287, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 144, + 287, + 190 + ], + "spans": [ + { + "bbox": [ + 47, + 144, + 287, + 190 + ], + "type": "text", + "content": "we use the all Reduce operation to perform gradient communication and collect all gradients with respect to " + }, + { + "bbox": [ + 47, + 144, + 287, + 190 + ], + "type": "inline_equation", + "content": "\\mathrm{I}_n" + }, + { + "bbox": [ + 47, + 144, + 287, + 190 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 144, + 287, + 190 + ], + "type": "inline_equation", + "content": "\\mathrm{T}_n" + }, + { + "bbox": [ + 47, + 144, + 287, + 190 + ], + "type": "text", + "content": ". Fig. 2 illustrates the gradient calculation of DisCo on the first of " + }, + { + "bbox": [ + 47, + 144, + 287, + 190 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 47, + 144, + 287, + 190 + ], + "type": "text", + "content": " GPUs." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 191, + 287, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 191, + 287, + 326 + ], + "spans": [ + { + "bbox": [ + 46, + 191, + 287, + 326 + ], + "type": "text", + "content": "Let us compare DisCo with the original contrastive loss. In the original implementation, because of the lack of gradient communication in the process of back-propagation among GPUs" + }, + { + "bbox": [ + 46, + 191, + 287, + 326 + ], + "type": "inline_equation", + "content": "^1" + }, + { + "bbox": [ + 46, + 191, + 287, + 326 + ], + "type": "text", + "content": ", each GPU must compute the whole similarity matrix between " + }, + { + "bbox": [ + 46, + 191, + 287, + 326 + ], + "type": "inline_equation", + "content": "\\mathrm{I}_A" + }, + { + "bbox": [ + 46, + 191, + 287, + 326 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 191, + 287, + 326 + ], + "type": "inline_equation", + "content": "\\mathrm{T}_A" + }, + { + "bbox": [ + 46, + 191, + 287, + 326 + ], + "type": "text", + "content": " to obtain the gradients " + }, + { + "bbox": [ + 46, + 191, + 287, + 326 + ], + "type": "inline_equation", + "content": "\\frac{\\partial\\mathcal{L}_d}{\\partial\\mathrm{I}_n}" + }, + { + "bbox": [ + 46, + 191, + 287, + 326 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 191, + 287, + 326 + ], + "type": "inline_equation", + "content": "\\frac{\\partial\\mathcal{L}_d}{\\partial\\mathrm{T}_n}" + }, + { + "bbox": [ + 46, + 191, + 287, + 326 + ], + "type": "text", + "content": " on the " + }, + { + "bbox": [ + 46, + 191, + 287, + 326 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 191, + 287, + 326 + ], + "type": "text", + "content": "-th GPU. In DisCo, for each GPU, we only need to calculate a subset instead of the whole similarity matrix. We then use an all Reduce operation to conduct gradient communication and collect the gradients. The distributed contrastive loss can also be applied to the contrastive loss computation in self-supervised learning [4, 6]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 332, + 270, + 345 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 332, + 270, + 345 + ], + "spans": [ + { + "bbox": [ + 47, + 332, + 270, + 345 + ], + "type": "text", + "content": "4.2. Algorithm Implementation of DisCo-CLIP" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 350, + 287, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 350, + 287, + 590 + ], + "spans": [ + { + "bbox": [ + 46, + 350, + 287, + 590 + ], + "type": "text", + "content": "Using DisCo in CLIP, we develop a memory efficient CLIP training method, termed as DisCo-CLIP. To make our algorithm clearer, we show the pseudo-code for DisCo-CLIP in Alg. 1. The implementation can be roughly divided into three segments. In the first segment, for each GPU with a global rank number, we extract its image and text features, and then use all_gather to collect image and text features into this GPU. Then in the second segment, we compute the similarity matrix and the two losses: image-to-text and text-to-image, and use the losses to compute the gradients. In this segment, the intra-GPU gradients, " + }, + { + "bbox": [ + 46, + 350, + 287, + 590 + ], + "type": "inline_equation", + "content": "\\left[\\frac{\\partial\\mathcal{L}_1(\\mathrm{I}_n,\\mathrm{T}_A)}{\\partial\\mathrm{I}_n},\\frac{\\partial\\mathcal{L}_2(\\mathrm{T}_n,\\mathrm{I}_A)}{\\partial\\mathrm{I}_n},\\frac{\\partial\\mathcal{L}_1(\\mathrm{I}_n,\\mathrm{T}_A)}{\\partial\\mathrm{T}_n},\\frac{\\partial\\mathcal{L}_2(\\mathrm{T}_n,\\mathrm{I}_A)}{\\partial\\mathrm{T}_n}\\right]" + }, + { + "bbox": [ + 46, + 350, + 287, + 590 + ], + "type": "text", + "content": ", as defined in Eq. 6, will be computed on the current GPU. In the last segment, we use all Reduce to finish gradient communication. In this segment, the inter-GPU gradients, " + }, + { + "bbox": [ + 46, + 350, + 287, + 590 + ], + "type": "inline_equation", + "content": "\\left[\\frac{\\partial\\mathcal{L}_2(\\mathrm{T}_{\\overline{n}},\\mathrm{I}_A)}{\\partial\\mathrm{I}_n},\\frac{\\partial\\mathcal{L}_1(\\mathrm{I}_{\\overline{n}},\\mathrm{T}_A)}{\\partial\\mathrm{T}_n}\\right]" + }, + { + "bbox": [ + 46, + 350, + 287, + 590 + ], + "type": "text", + "content": ", as defined in Eq. 7, will be collected to the current GPU. The intra-GPU and inter-GPU gradients are averaged to obtain " + }, + { + "bbox": [ + 46, + 350, + 287, + 590 + ], + "type": "inline_equation", + "content": "\\left[\\frac{\\partial\\mathcal{L}_d}{\\partial\\mathrm{I}_n},\\frac{\\partial\\mathcal{L}_d}{\\partial\\mathrm{T}_n}\\right]" + }, + { + "bbox": [ + 46, + 350, + 287, + 590 + ], + "type": "text", + "content": ". Finally, we perform backward propagation for the backbone." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 590, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 590, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 590, + 287, + 677 + ], + "type": "text", + "content": "DisCo-CLIP has two advantages compared with CLIP. First, it decreases the memory consumption for the contrastive loss from " + }, + { + "bbox": [ + 46, + 590, + 287, + 677 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(B^2)" + }, + { + "bbox": [ + 46, + 590, + 287, + 677 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 590, + 287, + 677 + ], + "type": "inline_equation", + "content": "\\mathcal{O}\\left(\\frac{B^2}{N}\\right)" + }, + { + "bbox": [ + 46, + 590, + 287, + 677 + ], + "type": "text", + "content": ". Second, it reduces the computational complexity of the contrastive loss from " + }, + { + "bbox": [ + 46, + 590, + 287, + 677 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(B^2D)" + }, + { + "bbox": [ + 46, + 590, + 287, + 677 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 590, + 287, + 677 + ], + "type": "inline_equation", + "content": "\\mathcal{O}\\left(\\frac{B^2}{N}D\\right)" + }, + { + "bbox": [ + 46, + 590, + 287, + 677 + ], + "type": "text", + "content": ". Besides these two advantages, DisCo-CLIP is an exact solution for CLIP without sacrificing any computation accuracy." + } + ] + } + ], + "index": 7 + }, + { + "type": "code", + "bbox": [ + 310, + 87, + 545, + 395 + ], + "blocks": [ + { + "bbox": [ + 312, + 75, + 495, + 86 + ], + "lines": [ + { + "bbox": [ + 312, + 75, + 495, + 86 + ], + "spans": [ + { + "bbox": [ + 312, + 75, + 495, + 86 + ], + "type": "text", + "content": "Algorithm 1: Pseudo-code for DisCo-CLIP" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 310, + 87, + 545, + 395 + ], + "lines": [ + { + "bbox": [ + 310, + 87, + 545, + 395 + ], + "spans": [ + { + "bbox": [ + 310, + 87, + 545, + 395 + ], + "type": "text", + "content": "# imageEncoder: ResNet or ViT\n# textEncoder: text Transformer\n# img[b,H,W,C]: minibatch of images\n# text[b,L]: minibatch of texts\n# t: temperature parameter\n# D: feature dimension\n# N: nums of GPU\n# rank: global rank\n# extract feature representations\ni.e = imageEncoder(img) # [b,D]\nt.e = textEncoder(text) # [b,D]\n# gather features from all gpus\nI.E = all_gather(i.e) # [N,b,D]\nT.E = all_gather(t_e) # [N,b,D]\n# scaled dot product similarities\nlogits.i = dot(I_E[rank], T_E)*t # [b,N*b]\nlogits.t = dot(T_E[rank], I_E)*t # [b,N*b]\n# image-to-text and text-to-image losses\nlabels = orange(b) + b * rank\nloss_i = cross_entropy_loss(logits.i, label)\nloss_t = cross_entropy_loss(logits.t, label)\n# loss backward\nloss = (loss.i + loss.t) / 2\nloss.backup()\n# reduce gradients and losses from all gpus\nI.E.grad = all.reduce(I.E.grad, op=AVG)\nT.E.grad = all.reduce(T.E.grad, op=AVG)\nLoss = all.reduce(loss, op=AVG)\n# backbone backward\ni.e.Backward(I.E.grad[rank])\nt.e.Backward(T.E.grad[rank])" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "code_body" + } + ], + "index": 10, + "sub_type": "algorithm" + }, + { + "bbox": [ + 304, + 420, + 545, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 420, + 545, + 491 + ], + "spans": [ + { + "bbox": [ + 304, + 420, + 545, + 491 + ], + "type": "text", + "content": "Note that DisCo-CLIP requires an extra all Reduce operator to perform gradient communication, which has the same cost as the all_gather operator. Compared with the full similarity matrix computation, this extra communication cost is quite small and negligible. See Table 4 for a speed comparison." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 493, + 545, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 493, + 545, + 553 + ], + "spans": [ + { + "bbox": [ + 304, + 493, + 545, + 553 + ], + "type": "text", + "content": "For the backbone part, we can also use the GradAccum strategy as proposed in BASIC [26]. BASIC provides a simple yet effective memory-efficient strategy for backbone memory optimization. Combined with GradAccum, DisCo-CLIP can further lead to a more memory-efficient solution." + } + ] + } + ], + "index": 12 + }, + { + "type": "table", + "bbox": [ + 312, + 565, + 539, + 635 + ], + "blocks": [ + { + "bbox": [ + 312, + 565, + 539, + 635 + ], + "lines": [ + { + "bbox": [ + 312, + 565, + 539, + 635 + ], + "spans": [ + { + "bbox": [ + 312, + 565, + 539, + 635 + ], + "type": "table", + "html": "
MethodsBackboneContra. LossOverall
CLIP [27]O(BNLD)O(B2)O(BNLD) + O(B2)
BASIC [26]O(BN)O(B2)O(BN) + O(B2)
DisCo-CLIPO(BNLD)O(B2/N)O(BNLD) + O(B2/N)
DisCo-CLIP*O(BN)O(B2/N)O(BN) + O(B2/N)
", + "image_path": "31f226f86503ec6e98ef229da40e87fb4f4a75665657626eb8f3114d11a80231.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 644, + 545, + 710 + ], + "lines": [ + { + "bbox": [ + 304, + 644, + 545, + 710 + ], + "spans": [ + { + "bbox": [ + 304, + 644, + 545, + 710 + ], + "type": "text", + "content": "Table 1. Memory consumption comparison of different methods. DisCo-CLIP* denotes the combination of DisCo-CLIP and the GradAccum strategy in BASIC. " + }, + { + "bbox": [ + 304, + 644, + 545, + 710 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 304, + 644, + 545, + 710 + ], + "type": "text", + "content": " denotes the batch size, which is usually very large, e.g. 32K, " + }, + { + "bbox": [ + 304, + 644, + 545, + 710 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 644, + 545, + 710 + ], + "type": "text", + "content": " is the number of GPUs, " + }, + { + "bbox": [ + 304, + 644, + 545, + 710 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 304, + 644, + 545, + 710 + ], + "type": "text", + "content": " is the number of layers in the backbone, and " + }, + { + "bbox": [ + 304, + 644, + 545, + 710 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 644, + 545, + 710 + ], + "type": "text", + "content": " is the feature dimension. For simplicity, we use the same " + }, + { + "bbox": [ + 304, + 644, + 545, + 710 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 644, + 545, + 710 + ], + "type": "text", + "content": " for all layers." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 47, + 683, + 287, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 683, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 683, + 287, + 713 + ], + "type": "text", + "content": "Gradient communication here in the process of back-propagation should be distinguished from the gradient collection after model backpropagation which is to collect and average the weight gradients." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22652" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 185 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 185 + ], + "type": "text", + "content": "A detailed comparison of memory consumption for CLIP, BASIC, and DisCo-CLIP is provided in Table 1. With GradAccum, BASIC can reduce the overall memory consumption from " + }, + { + "bbox": [ + 47, + 72, + 289, + 185 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(\\frac{B}{N}LD) + \\mathcal{O}(B^2)" + }, + { + "bbox": [ + 47, + 72, + 289, + 185 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 47, + 72, + 289, + 185 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(\\frac{B}{N}D) + \\mathcal{O}(B^2)" + }, + { + "bbox": [ + 47, + 72, + 289, + 185 + ], + "type": "text", + "content": ". DisCo-CLIP can reduce the memory consumption to " + }, + { + "bbox": [ + 47, + 72, + 289, + 185 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(\\frac{B}{N}LD) + \\mathcal{O}(\\frac{B^2}{N})" + }, + { + "bbox": [ + 47, + 72, + 289, + 185 + ], + "type": "text", + "content": ", DisCo-CLIP* can further reduce the memory consumption to " + }, + { + "bbox": [ + 47, + 72, + 289, + 185 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(\\frac{B}{N}D) + \\mathcal{O}(\\frac{B^2}{N})" + }, + { + "bbox": [ + 47, + 72, + 289, + 185 + ], + "type": "text", + "content": ". A practical example is that, in vanilla CLIP [27] based on ViT-B/32, " + }, + { + "bbox": [ + 47, + 72, + 289, + 185 + ], + "type": "inline_equation", + "content": "D = 1024" + }, + { + "bbox": [ + 47, + 72, + 289, + 185 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 72, + 289, + 185 + ], + "type": "inline_equation", + "content": "B = 32768" + }, + { + "bbox": [ + 47, + 72, + 289, + 185 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 72, + 289, + 185 + ], + "type": "inline_equation", + "content": "N = 128" + }, + { + "bbox": [ + 47, + 72, + 289, + 185 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 195, + 128, + 209 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 195, + 128, + 209 + ], + "spans": [ + { + "bbox": [ + 47, + 195, + 128, + 209 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 216, + 287, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 216, + 287, + 276 + ], + "spans": [ + { + "bbox": [ + 47, + 216, + 287, + 276 + ], + "type": "text", + "content": "In this section, we first describe the experimental settings including data sets and pre-training details. Then, we present the experiments regarding memory consumption, training efficiency, batch size, and data scale. Finally, we report zero-shot classification on several data sets." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 283, + 170, + 297 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 283, + 170, + 297 + ], + "spans": [ + { + "bbox": [ + 47, + 283, + 170, + 297 + ], + "type": "text", + "content": "5.1. Experimental Setting" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 302, + 287, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 302, + 287, + 504 + ], + "spans": [ + { + "bbox": [ + 46, + 302, + 287, + 504 + ], + "type": "text", + "content": "Image-Text Data Sets. A large-scale image-text data set is a prerequisite for contrastive image-text pre-training. In the literature, there are many private [17, 37] or public data sets [34, 35, 38]. LAION-400M [35] is a data set with 400 million image-text pairs filtered by CLIP score. We crawl the images according to the provided URLs and finally obtain 360M image-text pairs as some URLs are expired and no longer available. LAION-5B [34] is a larger data set with 5 billion image-text pairs. It contains a subset of 2.32 billion English image-text pairs. We refer to this subset as LAION-2B as in [34]. We also crawl the data set according to the released URLs and finally obtain 2.1 billion image-text pairs. In this paper, for a fair comparison with CLIP [27] and LAION [34] which conduct experiments using 400M data pairs, we create a subset of 400M image-text pairs from our crawled LAION-2B and also make a subset of 100M image-text pairs for ablation study." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 506, + 288, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 506, + 288, + 685 + ], + "spans": [ + { + "bbox": [ + 46, + 506, + 288, + 685 + ], + "type": "text", + "content": "Pre-training Details. The implementation of our DisCo-CLIP is based on OpenCLIP [16], an open source CLIP implementation. We follow the original CLIP [27] and mainly use ViT-B/32 [9] as the vision backbone. Training images are resized to " + }, + { + "bbox": [ + 46, + 506, + 288, + 685 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 46, + 506, + 288, + 685 + ], + "type": "text", + "content": " and fed to the vision backbone. For the text backbone, we use a text Transformer [8, 39], and set the maximum length of text to 76 as in [27]. Due to limited time and GPU resource, we do not train ViT-L/14 because it takes more than four times of training time compared to ViT-B/32. It should also be noted that in all our experiments, we do not use the GradAccum strategy as in BASIC [26]. Checkpointing is enabled in vanilla CLIP and our DisCo-CLIP. We train models using an Adam [18] optimizer and cosine learning rate scheduler with a linear warmup [24]. Weight decay regularization [25]" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 547, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 275 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 275 + ], + "type": "text", + "content": "is used on all parameters except bias, layer normalization, and temperature in contrastive loss. Since our training experiments use different batch sizes, according to previous works [12, 28], we change the learning rate for different batch sizes. For our learning rate scheduler, we first define a base learning rate of 5e-4 and a base batch size of 32,768, and then linearly warm it up to the maximum learning rate. The maximum learning rate is determined according to a linear strategy, max_lr = base_lr * batch_size / 32,768. Training stability is a challenging issue in mixed-precision training as NaN might happen in many cases. We obverse that " + }, + { + "bbox": [ + 304, + 72, + 547, + 275 + ], + "type": "inline_equation", + "content": "\\beta_{2}" + }, + { + "bbox": [ + 304, + 72, + 547, + 275 + ], + "type": "text", + "content": " in Adam is very important for training stability and find 0.98 works well for our experiments instead of the default value of 0.999. For most of our experiments, we use 64 NVIDIA A100 40GB GPUs for model training, but for some experiments, we only use 8 NVIDIA A100 40GB GPUs to show that our solution is more resource-efficient." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 283, + 417, + 295 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 283, + 417, + 295 + ], + "spans": [ + { + "bbox": [ + 306, + 283, + 417, + 295 + ], + "type": "text", + "content": "5.2. Evaluation Results" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 301, + 547, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 301, + 547, + 373 + ], + "spans": [ + { + "bbox": [ + 304, + 301, + 547, + 373 + ], + "type": "text", + "content": "Equivalence Validation. To empirically validate our theoretical analysis, we conduct experiments to compare CLIP and DisCo-CLIP. We use the same random seed to initiate the network parameters and use the same batch size 32,768 on 64 GPUs, and train ViT-B/32 models with 16 epochs on LAION-100M." + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 321, + 381, + 531, + 419 + ], + "blocks": [ + { + "bbox": [ + 321, + 381, + 531, + 419 + ], + "lines": [ + { + "bbox": [ + 321, + 381, + 531, + 419 + ], + "spans": [ + { + "bbox": [ + 321, + 381, + 531, + 419 + ], + "type": "table", + "html": "
MethodsMemoryAccuracyTime (Hours)
CLIP27.4GB51.6413.4
DisCo-CLIP16.5GB51.6412.1
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MethodsGPUsBSMemory
CLIP64× A100 40GB32,76827.4GB
CLIP64× A100 40GB65,536OOM
DisCo-CLIP64× A100 40GB32,76816.5GB
DisCo-CLIP64× A100 40GB196,60838.1GB
DisCo-CLIP8× A100 40GB32,76836.9GB
", + "image_path": "1d01318a69e53ff382830b6830067abec51d95d7018cc2a1bbf0b6d7b2967dc0.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 654, + 545, + 677 + ], + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 677 + ], + "type": "text", + "content": "Table 3. Memory consumption of CLIP and DisCo-CLIP under different settings. \"OOM\" means out of memory." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "content": "Memory Consumption. Besides memory consumption of network parameters, backbone and contrastive loss con" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 56, + 692, + 266, + 702 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 692, + 266, + 702 + ], + "spans": [ + { + "bbox": [ + 56, + 692, + 266, + 702 + ], + "type": "text", + "content": "2https://github.com/mlfoundations/open Clip" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 56, + 702, + 209, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 702, + 209, + 712 + ], + "spans": [ + { + "bbox": [ + 56, + 702, + 209, + 712 + ], + "type": "text", + "content": "3https://github.com/openai/CLIP" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "text", + "content": "22653" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 52, + 70, + 542, + 117 + ], + "blocks": [ + { + "bbox": [ + 52, + 70, + 542, + 117 + ], + "lines": [ + { + "bbox": [ + 52, + 70, + 542, + 117 + ], + "spans": [ + { + "bbox": [ + 52, + 70, + 542, + 117 + ], + "type": "table", + "html": "
MethodsGPUsBatch sizeBackboneLoss OperatorsLoss TotalBackwardTotal
all_gatherLossall ReduceLoss BPBackbone BP
CLIP6432,768129.46.155.4-61.5414.8605.6
DisCo-CLIP6432,7686.11.64.312.0 (80.5% ↓)2.8337.3481.5 (20.5% ↓)
", + "image_path": "d73b17743e1b70af6266910a918d3b2ac8bf39f2d595873485cbe436cd914ae0.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 168, + 286, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 168, + 286, + 216 + ], + "spans": [ + { + "bbox": [ + 46, + 168, + 286, + 216 + ], + "type": "text", + "content": "sumes most memory. We evaluate the memory consumption of the original CLIP and our DisCo-CLIP under different settings. We report the peak memory consumption for different settings, and the results are shown in Table 3." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 217, + 286, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 217, + 286, + 288 + ], + "spans": [ + { + "bbox": [ + 46, + 217, + 286, + 288 + ], + "type": "text", + "content": "We have three observations from Table 3. 1) CLIP with ViT-B/32 can be trained with batch size 32,768 but fails with batch size 65,536. 2) Our DisCo-CLIP can enable training of ViT-B/32 with a much larger batch size, 196,608 with 64 A100 40GB GPU. 3) DisCo-CLIP can enable training of the same model on a cluster with only 8 GPUs." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 289, + 286, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 289, + 286, + 418 + ], + "spans": [ + { + "bbox": [ + 46, + 289, + 286, + 418 + ], + "type": "text", + "content": "Training Speed. One iteration of CLIP consists of extracting features from backbone, gathering features from all GPUs, calculating loss, and executing back-propagation. (We exclude some other factors, including data loading and optimizer update that are not directly related to the model computation or can be ignored.) Instead, DisCo-CLIP decomposes the back-propagation into two BP processes (Loss BP and Backbone BP) and have an additional all Reduce operator. We evaluate the running time of each operator in CLIP and our DisCo-CLIP, and the results are shown in Table 4." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 421, + 286, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 421, + 286, + 540 + ], + "spans": [ + { + "bbox": [ + 46, + 421, + 286, + 540 + ], + "type": "text", + "content": "From Table 4, we can see that 1) for total loss computation, under the same batch size 32,768, we decrease the computation time from " + }, + { + "bbox": [ + 46, + 421, + 286, + 540 + ], + "type": "inline_equation", + "content": "61.5\\mathrm{ms}" + }, + { + "bbox": [ + 46, + 421, + 286, + 540 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 421, + 286, + 540 + ], + "type": "inline_equation", + "content": "12.0\\mathrm{ms}" + }, + { + "bbox": [ + 46, + 421, + 286, + 540 + ], + "type": "text", + "content": ". It is because in DisCo-CLIP, we only need to calculate two subset similarity matrices between multiplying a " + }, + { + "bbox": [ + 46, + 421, + 286, + 540 + ], + "type": "inline_equation", + "content": "\\frac{B}{N} \\times D" + }, + { + "bbox": [ + 46, + 421, + 286, + 540 + ], + "type": "text", + "content": " matrix and a " + }, + { + "bbox": [ + 46, + 421, + 286, + 540 + ], + "type": "inline_equation", + "content": "B \\times D" + }, + { + "bbox": [ + 46, + 421, + 286, + 540 + ], + "type": "text", + "content": " matrix instead of a full matrix multiplication between two " + }, + { + "bbox": [ + 46, + 421, + 286, + 540 + ], + "type": "inline_equation", + "content": "B \\times D" + }, + { + "bbox": [ + 46, + 421, + 286, + 540 + ], + "type": "text", + "content": " matrices. 2) the operators of both all Reduce and all_gather are faster compared to the loss computation. 3) under the same batch size 32,768, DisCo-CLIP improves around " + }, + { + "bbox": [ + 46, + 421, + 286, + 540 + ], + "type": "inline_equation", + "content": "20.5\\%" + }, + { + "bbox": [ + 46, + 421, + 286, + 540 + ], + "type": "text", + "content": " total training efficiency." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 540, + 286, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 540, + 286, + 589 + ], + "spans": [ + { + "bbox": [ + 46, + 540, + 286, + 589 + ], + "type": "text", + "content": "Overall, with DisCo-CLIP, we are able to not only train contrastive learning models with a larger batch size, but also improve the training speed considerably. DisCo-CLIP is a free-lunch solution for large-scale contrastive learning." + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 77, + 598, + 259, + 658 + ], + "blocks": [ + { + "bbox": [ + 46, + 125, + 545, + 148 + ], + "lines": [ + { + "bbox": [ + 46, + 125, + 545, + 148 + ], + "spans": [ + { + "bbox": [ + 46, + 125, + 545, + 148 + ], + "type": "text", + "content": "Table 4. Detailed comparisons of training efficiency of CLIP and DisCo-CLIP. All time-related measurements (the last nine columns) are in milliseconds (ms). DisCo-CLIP saves more computational time in loss computation. Training resource: 64 A100 40GB GPUs." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 77, + 598, + 259, + 658 + ], + "lines": [ + { + "bbox": [ + 77, + 598, + 259, + 658 + ], + "spans": [ + { + "bbox": [ + 77, + 598, + 259, + 658 + ], + "type": "table", + "html": "
Batch SizeStepsEpochsViT-B/32
8,192≈ 200 K1648.76
16,384≈ 100 K1650.95
32,768≈ 50 K1651.64
65,536≈ 25 K1651.91
", + "image_path": "589db2232d045de0036832362af9d8697c38061dccbdcd5bd38166cd7d2076c0.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 167, + 545, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 167, + 545, + 263 + ], + "spans": [ + { + "bbox": [ + 304, + 167, + 545, + 263 + ], + "type": "text", + "content": "Batch Size. To assess the role of a larger batch size to the final performance, we conduct some controlled experiments for ViT-B/32 on our LAION-100M and LAION-400M subsets. All training hyper-parameters are the same except that we vary the batch size and the number of training steps. To ensure all models \"see\" the same number of training samples, we use fewer training steps when training with a larger batch size. In Table 5, we report the results of all settings." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 264, + 545, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 264, + 545, + 335 + ], + "spans": [ + { + "bbox": [ + 304, + 264, + 545, + 335 + ], + "type": "text", + "content": "From Table 5, we can see that large batch size generally helps contrastive learning. The performance of using batch size 65,536 improves that of using batch size 32,768 by around " + }, + { + "bbox": [ + 304, + 264, + 545, + 335 + ], + "type": "inline_equation", + "content": "0.3\\%" + }, + { + "bbox": [ + 304, + 264, + 545, + 335 + ], + "type": "text", + "content": ". In the evaluation of data scaling, we further observe that the improvement widens when we train the model for more epochs." + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 330, + 346, + 523, + 394 + ], + "blocks": [ + { + "bbox": [ + 46, + 666, + 286, + 710 + ], + "lines": [ + { + "bbox": [ + 46, + 666, + 286, + 710 + ], + "spans": [ + { + "bbox": [ + 46, + 666, + 286, + 710 + ], + "type": "text", + "content": "Table 5. Evaluation of different batch sizes on DisCo-CLIP. All models are trained for 16 epochs on a LAION-100M data set, we show top-1 zero-shot classification accuracy on ImageNet. Training resource: 64 A100 40GB GPUs." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 330, + 346, + 523, + 394 + ], + "lines": [ + { + "bbox": [ + 330, + 346, + 523, + 394 + ], + "spans": [ + { + "bbox": [ + 330, + 346, + 523, + 394 + ], + "type": "table", + "html": "
Batch Size100M×16400M×4400M×8
16,38450.9554.3658.38
32,76851.6455.5259.69
65,53651.9155.5059.96
", + "image_path": "a849612183492506e2136eaf80a74409e4c6c9f171ffa270ee3b1541371dad92.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 403, + 545, + 447 + ], + "lines": [ + { + "bbox": [ + 304, + 403, + 545, + 447 + ], + "spans": [ + { + "bbox": [ + 304, + 403, + 545, + 447 + ], + "type": "text", + "content": "Table 6. Evaluation of data scaling on DisCo-CLIP. Three batch sizes are evaluated with two LAION subsets: LAION-100M and LAION-400M. The numbers " + }, + { + "bbox": [ + 304, + 403, + 545, + 447 + ], + "type": "inline_equation", + "content": "\\times 16" + }, + { + "bbox": [ + 304, + 403, + 545, + 447 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 403, + 545, + 447 + ], + "type": "inline_equation", + "content": "\\times 4" + }, + { + "bbox": [ + 304, + 403, + 545, + 447 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 403, + 545, + 447 + ], + "type": "inline_equation", + "content": "\\times 8" + }, + { + "bbox": [ + 304, + 403, + 545, + 447 + ], + "type": "text", + "content": " are the training epochs for each data set. Training resource: 64 A100 40GB GPUs." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 461, + 545, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 461, + 545, + 556 + ], + "spans": [ + { + "bbox": [ + 304, + 461, + 545, + 556 + ], + "type": "text", + "content": "Data Scaling. To investigate the role of data scaling, we also conduct some controlled experiments for ViT-B/32 on the LAION 100M and LAION 400M subsets. For all models, we use three different batch sizes, 16,384, 32,768 and 65,536 for training. Models are trained with three different settings, 100M with 16 epochs, 400M with 4 epochs and 400M with 8 epochs. Table 6 reports the final ImageNet top-1 zero-shot classification accuracy of all models." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 558, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 545, + 712 + ], + "type": "text", + "content": "From Table 6, we observe that, \"seeing\" the same number of training samples (LAION-100M with 16 epochs, LAION-400M with 4 epochs.), the model trained on larger scale of data set can obtain better performance. For example, trained with the same batch size 65,536, the performance improves from " + }, + { + "bbox": [ + 304, + 558, + 545, + 712 + ], + "type": "inline_equation", + "content": "51.91\\%" + }, + { + "bbox": [ + 304, + 558, + 545, + 712 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 558, + 545, + 712 + ], + "type": "inline_equation", + "content": "55.50\\%" + }, + { + "bbox": [ + 304, + 558, + 545, + 712 + ], + "type": "text", + "content": " when the data set increases from 100M to 400M. This observation validates the value of data scaling. This observation is also consistent with the combined scaling law in BASIC [26]. We also find that training with more epochs on larger scale of data with larger batch size will bring in larger performance gain. The gap between models (with batch sizes 32,768 and 65,536) trained on 400M with 4 epochs is around " + }, + { + "bbox": [ + 304, + 558, + 545, + 712 + ], + "type": "inline_equation", + "content": "0\\%" + }, + { + "bbox": [ + 304, + 558, + 545, + 712 + ], + "type": "text", + "content": " (from" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22654" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 69, + 547, + 129 + ], + "blocks": [ + { + "bbox": [ + 48, + 69, + 547, + 129 + ], + "lines": [ + { + "bbox": [ + 48, + 69, + 547, + 129 + ], + "spans": [ + { + "bbox": [ + 48, + 69, + 547, + 129 + ], + "type": "table", + "html": "
ModelData SetsEpochsStepsBatch SizeINet [7]INet-v2 [32]INet-R [15]INet-S [40]
CLIP [27]CLIP WIT 400M32≈ 400 K32,76863.356.069.442.3
OpenCLIP [16,34]LAION-400M32≈ 400 K32,76862.955.173.449.4
DisCo-CLIPLAION-400M*32≈ 400 K32,76863.255.273.450.6
DisCo-CLIPLAION-400M*32≈ 200 K65,53664.356.273.851.7
", + "image_path": "66624dea6f88f35ab91401025f28b9c238721e8b8bf1f0b05f543212c7d56bac.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 191, + 288, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 191, + 288, + 240 + ], + "spans": [ + { + "bbox": [ + 46, + 191, + 288, + 240 + ], + "type": "text", + "content": "55.52% to 55.50%), but it increases to 0.3% (from 59.69% to 59.96%) when the models are trained for 8 epochs. Thus, we can expect that if we use larger scale of data set, we should also use larger batch size to get a better performance." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 244, + 183, + 257 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 244, + 183, + 257 + ], + "spans": [ + { + "bbox": [ + 47, + 244, + 183, + 257 + ], + "type": "text", + "content": "5.3. Zero-Shot Classification" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 262, + 287, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 262, + 287, + 418 + ], + "spans": [ + { + "bbox": [ + 46, + 262, + 287, + 418 + ], + "type": "text", + "content": "Following CLIP [27] and LAION-5B [34], we evaluate zero-shot top-1 classification accuracy of our models on several data sets, including INet [7], INet-v2 [32], INet-R [15] and INet-S [40]. We use exactly the same 80 prompts as CLIP. Some standard prompts are like \"a bad photo of a " + }, + { + "bbox": [ + 46, + 262, + 287, + 418 + ], + "type": "inline_equation", + "content": "\\{\\}" + }, + { + "bbox": [ + 46, + 262, + 287, + 418 + ], + "type": "text", + "content": " \", \"a photo of many " + }, + { + "bbox": [ + 46, + 262, + 287, + 418 + ], + "type": "inline_equation", + "content": "\\{\\}" + }, + { + "bbox": [ + 46, + 262, + 287, + 418 + ], + "type": "text", + "content": " \", and etc. Following LAION-5B, we extract the embedding for each prompt using the text encoder (text Transformer), and average embeddings of all prompts in each class, and finally get the final class embedding. Given an image, we extract its image embedding via the image encoder (ViT-B/32), and compute its similarities with all class embeddings, and classify it into the class with the highest similarity score." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 418, + 288, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 418, + 288, + 563 + ], + "spans": [ + { + "bbox": [ + 46, + 418, + 288, + 563 + ], + "type": "text", + "content": "We can see from Table 7, that using the same batch size of 32,768 as the OpenCLIP implementation, our DisCo-CLIP obtains a similar performance with OpenCLIP, the result of OpenCLIP is reported by LAION group in [34]. Using a larger batch size of 65,536, DisCo-CLIP achieves a better performance than the OpenCLIP implementation and the original CLIP. Specifically, trained with the same 32 epochs, DisCo-CLIP using a batch size of 65,536 improves the OpenCLIP's result that is based on batch size of 32,768 by " + }, + { + "bbox": [ + 46, + 418, + 288, + 563 + ], + "type": "inline_equation", + "content": "1.4\\%" + }, + { + "bbox": [ + 46, + 418, + 288, + 563 + ], + "type": "text", + "content": ". Note that when doubling the batch size, we halve the training steps. This observation further validates that large batch size is important for contrastive learning." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 571, + 117, + 583 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 571, + 117, + 583 + ], + "spans": [ + { + "bbox": [ + 47, + 571, + 117, + 583 + ], + "type": "text", + "content": "6. Discussion" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 591, + 287, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 591, + 287, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 591, + 287, + 688 + ], + "type": "text", + "content": "Recent developments in large-scale contrastive or generative learning, such as CLIP [27], ALIGN [17], FILIP [43], LiT [48], BASIC [26], LAION-5B [34], and GIT [41] have potential for many real-world applications, such as image classification, text-to-image retrieval, recommendation system, and generation models. Besides large-scale data sets, the progress highly depends on powerful GPU or TPU computing resources. As shown in Table 8, all methods use" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 191, + 545, + 214 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 191, + 545, + 214 + ], + "spans": [ + { + "bbox": [ + 306, + 191, + 545, + 214 + ], + "type": "text", + "content": "a large amount of computing hardwares. FILIP uses less GPU but also uses smaller batch size." + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 328, + 224, + 525, + 295 + ], + "blocks": [ + { + "bbox": [ + 46, + 137, + 547, + 171 + ], + "lines": [ + { + "bbox": [ + 46, + 137, + 547, + 171 + ], + "spans": [ + { + "bbox": [ + 46, + 137, + 547, + 171 + ], + "type": "text", + "content": "Table 7. Comparison of DisCo-CLIP with vanilla CLIP and re-implemented CLIP by LAION group. We report top-1 zero-shot classification accuracy (\\%) on several data sets. All models are based on ViT-B/32. Our LAION-400M* is a 400M subset of LAION-2B. Training resource: 64 A100 40GB GPUs." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 328, + 224, + 525, + 295 + ], + "lines": [ + { + "bbox": [ + 328, + 224, + 525, + 295 + ], + "spans": [ + { + "bbox": [ + 328, + 224, + 525, + 295 + ], + "type": "table", + "html": "
MethodsHardware
CLIP [27]256 NVIDIA V100 GPUs
FILIP [43]128 NVIDIA V100 GPUs
LAION-5B [34]128-400 NVIDIA A100 GPUs
LiT [48]128-400 TPUs
BASIC [26]2,048 TPUs v3
", + "image_path": "7bfdbe417fb3213e1b5f1d70367b75db2ac0756f3958b4c36ee3d01721f95017.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 303, + 545, + 324 + ], + "lines": [ + { + "bbox": [ + 305, + 303, + 545, + 324 + ], + "spans": [ + { + "bbox": [ + 305, + 303, + 545, + 324 + ], + "type": "text", + "content": "Table 8. Several vision-language contrastive learning methods and their used hardwares." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 342, + 547, + 451 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 342, + 547, + 451 + ], + "spans": [ + { + "bbox": [ + 304, + 342, + 547, + 451 + ], + "type": "text", + "content": "Unfortunately, only a few big technology companies can afford this task. Large batch contrastive loss consumes a large amount of GPU memory, while large batch size is a prerequisite for contrastive learning. As a result, it is challenging for companies with limited resources or academic research institutes to contribute to research on this topic. Our work provides a simple yet effective solution for reducing memory consumption that can help bridge the gap between academia and industry on this topic." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 464, + 379, + 477 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 464, + 379, + 477 + ], + "spans": [ + { + "bbox": [ + 306, + 464, + 379, + 477 + ], + "type": "text", + "content": "7. Conclusion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 486, + 547, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 547, + 654 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 547, + 654 + ], + "type": "text", + "content": "In this paper, we have proposed a simple yet effective distributed contrastive loss solution called DisCo to reduce the memory consumption in contrastive learning. By decomposing the loss computation into intra-GPU computation and inter-GPU computation, we can remove redundant memory consumption and use a all Reduce operator to collect inter-GPU gradients. Using DisCo in CLIP, the introduced DisCo-CLIP can enable a much larger batch contrastive learning compared to CLIP using the same GPU resource. Specifically, we can train DisCo-CLIP models with batch size 32,768 using 8 A100 40GB GPUs, or with batch size 196K using 64 GPUs. We hope DisCo-CLIP will also help and motivate self-supervised learning [4, 6] which also uses contrastive learning." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 668, + 416, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 668, + 416, + 681 + ], + "spans": [ + { + "bbox": [ + 306, + 668, + 416, + 681 + ], + "type": "text", + "content": "8. Acknowledgement" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 689, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 712 + ], + "type": "text", + "content": "This work was partially supported by OPPO Research Fund." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 47, + 693, + 286, + 715 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 286, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 286, + 715 + ], + "type": "text", + "content": "4https://github.com/openai/CLIP/blob/main/notebooks/Prompt_Engineering_for_ImageNet.ipynb" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "text", + "content": "22655" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 91, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "text", + "content": "[1] Zhengda Bian, Hongxin Liu, Boxiang Wang, Haichen Huang, Yongbin Li, Chuanrui Wang, Fan Cui, and Yang You. 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Coca: Contrastive captioners are image-text foundation models. arXiv preprint arXiv:2205.01917, 2022. 1" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 307, + 532, + 545, + 586 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 532, + 545, + 586 + ], + "spans": [ + { + "bbox": [ + 307, + 532, + 545, + 586 + ], + "type": "text", + "content": "[47] Lu Yuan, Dongdong Chen, Yi-Ling Chen, Noel Codella, Xiyang Dai, Jianfeng Gao, Houdong Hu, Xuedong Huang, Boxin Li, Chunyuan Li, et al. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 18123-18133, 2022. 2, 8" + } + ] + } + ], + "index": 24 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "22657" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/DisCoScene_ Spatially Disentangled Generative Radiance Fields for Controllable 3D-Aware Scene Synthesis/bdaa5712-8b26-43d5-9ca1-465a14b26701_content_list.json b/2023/DisCoScene_ Spatially Disentangled Generative Radiance Fields for Controllable 3D-Aware Scene Synthesis/bdaa5712-8b26-43d5-9ca1-465a14b26701_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..2499167ee53ca92f68ead893e96df50526ad5fd6 --- /dev/null +++ b/2023/DisCoScene_ Spatially Disentangled Generative Radiance Fields for Controllable 3D-Aware Scene Synthesis/bdaa5712-8b26-43d5-9ca1-465a14b26701_content_list.json @@ -0,0 +1,1505 @@ +[ + { + "type": "text", + "text": "DisCoScene: Spatially Disentangled Generative Radiance Fields for Controllable 3D-aware Scene Synthesis", + "text_level": 1, + "bbox": [ + 163, + 128, + 807, + 174 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yinghao Xu $^{1,2*}$ Mengei Chai $^{2\\dagger}$ Zifan Shi $^{3}$ Sida Peng $^{4}$ Ivan Skorokhodov $^{5,2*}$ Aliaksandr Siarohin $^{2}$ Ceyuan Yang $^{1}$ Yujun Shen $^{1}$ Hsin-Ying Lee $^{2}$ Bolei Zhou $^{6}$ Sergey Tulyakov $^{2}$ $^{1}\\mathrm{CUHK}$ $^{2}\\mathrm{SnapInc.}$ $^{3}\\mathrm{HKUST}$ $^{4}\\mathrm{ZJU}$ $^{5}\\mathrm{KAUST}$ $^{6}\\mathrm{UCLA}$", + "bbox": [ + 173, + 202, + 795, + 281 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 314, + 313, + 330 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Existing 3D-aware image synthesis approaches mainly focus on generating a single canonical object and show limited capacity in composing a complex scene containing a variety of objects. This work presents DisCoScene: a 3D-aware generative model for high-quality and controllable scene synthesis. The key ingredient of our method is a very abstract object-level representation (i.e., 3D bounding boxes without semantic annotation) as the scene layout prior, which is simple to obtain, general to describe various scene contents, and yet informative to disentangle objects and background. Moreover, it serves as an intuitive user control for scene editing. Based on such a prior, the proposed model spatially disentangles the whole scene into object-centric generative radiance fields by learning on only 2D images with the global-local discrimination. Our model obtains the generation fidelity and editing flexibility of individual objects while being able to efficiently compose objects and the background into a complete scene. We demonstrate state-of-the-art performance on many scene datasets, including the challenging Waymo outdoor dataset. Project page can be found here.", + "bbox": [ + 75, + 345, + 473, + 664 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 691, + 209, + 707 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "3D-consistent image synthesis from single-view 2D data has become a trendy topic in generative modeling. Recent approaches like GRAF [40] and Pi-GAN [5] introduce 3D inductive bias by taking neural radiance fields [1, 28, 29, 36, 38] as the underlying representation, gaining the capability of geometry modeling and explicit camera control. Despite their success in synthesizing individual objects (e.g., faces, cats, cars), they struggle on scene images that contain multiple objects with non-trivial layouts and complex backgrounds. The varying quantity and large", + "bbox": [ + 75, + 715, + 470, + 868 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "diversity of objects, along with the intricate spatial arrangement and mutual occlusions, bring enormous challenges, which exceed the capacity of the object-level generative models [4, 13, 15, 33, 45, 46, 60].", + "bbox": [ + 500, + 316, + 890, + 377 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent efforts have been made towards 3D-aware scene synthesis. Despite the encouraging progress, there are still fundamental drawbacks. For example, Generative Scene Networks (GSN) [8] achieve large-scale scene synthesis by representing the scene as a grid of local radiance fields and training on 2D observations from continuous camera paths. However, object-level editing is not feasible due to spatial entanglement and the lack of explicit object definition. On the contrary, GIRAFFE [32] explicitly composites object-centric radiance fields [16, 34, 56, 63] to support object-level control. Yet, it works poorly on challenging datasets containing multiple objects and complex backgrounds due to the absence of proper spatial priors.", + "bbox": [ + 498, + 381, + 892, + 580 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To achieve high-quality and controllable scene synthesis, the scene representation stands out as one critical design focus. A well-structured scene representation can scale up the generation capability and tackle the aforementioned challenges. Imagine, given an empty apartment and a furniture catalog, what does it take for a person to arrange the space? Would people prefer to walk around and throw things here and there, or instead figure out an overall layout and then attend to each location for the detailed selection? Obviously, a layout describing the arrangement of each furniture in the space substantially eases the scene composition process [17, 26, 58]. From this vantage point, here comes our primary motivation — an abstract object-oriented scene representation, namely a layout prior, could facilitate learning from challenging 2D data as a lightweight supervision signal during training and allow user interaction during inference. More specifically, to make such a prior easy to obtain and generalizable across different scenes, we define it as a set of object bounding boxes without semantic annotation, which describes the spatial composition of objects in the scene and supports intuitive object-level editing.", + "bbox": [ + 496, + 583, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Work partially done during internships at Snap Inc.", + "bbox": [ + 94, + 875, + 372, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding author.", + "bbox": [ + 96, + 887, + 222, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "4402", + "bbox": [ + 482, + 944, + 516, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this work, we present DisCoScene, a novel 3D-aware generative model for complex scenes. Our method allows for high-quality scene synthesis on challenging datasets and flexible user control of both the camera and scene objects. Driven by the aforementioned layout prior, our model spatially disentangles the scene into composable radiance fields which are shared in the same object-centric generative model. To make the best use of the prior as a lightweight supervision during training, we propose global-local discrimination which attends to both the whole scene and individual objects to enforce spatial disentanglement between objects and against the background. Once the model is trained, users can generate and edit a scene by explicitly controlling the camera and the layout of objects' bounding boxes. In addition, we develop an efficient rendering pipeline tailored for the spatially-disentangled radiance fields, which significantly accelerates object rendering and scene composition for both training and inference stages.", + "bbox": [ + 76, + 90, + 472, + 363 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our method is evaluated on diverse datasets, including both indoor and outdoor scenes. Qualitative and quantitative results demonstrate that, compared to existing baselines, our method achieves state-of-the-art performance in terms of both generation quality and editing capability. Tab. 1 compares DisCoScene with relevant works. it is worth noting that, to the best of our knowledge, DisCoScene stands as the first method that achieves high-quality 3D-aware generation on challenging datasets like WAYMO [48], while enabling interactive object manipulation.", + "bbox": [ + 76, + 363, + 472, + 513 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 527, + 218, + 544 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3D-aware Image Synthesis. Generative Adversarial Networks (GANs) have achieved remarkable success in 2D image synthesis [14, 22-25], and have recently been extended to 3D-aware image generation. VON [68] and HoloGAN [30] introduce voxel representations to the generator and use neural rendering to project 3D voxels into 2D space. Then, GRAF [40] and Pi-GAN [5] propose to use implicit functions to learn NeRF from single-view image collections, resulting in better multi-view consistency compared to voxel-based methods. GOF [59], ShadeGAN [35], and GRAM [7] introduce occupancy field, albedo field and radiance surface instead of radiance field to learn better 3D shapes. However, high-resolution image synthesis with direct volumetric rendering is usually expensive. Many works [4, 15, 32, 33, 45, 60, 62] resort to convolutional upsamplers to improve the rendering resolution and quality with lower computation overhead. While some other works [41,46] adopt patch-based sampling and sparse-voxel to speed up training and inference. Note that most of these methods are restricted to well-aligned objects and fail on more complex, multi-object scene imagery. Our work instead naturally handles multi-object scenes with spatial disentangled object-level radiance fields, which can", + "bbox": [ + 76, + 551, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "table", + "img_path": "images/693e807f1f00f79a8d9169112a5ae44e4da3a2df1db9da0bdf84140aa11a2a32.jpg", + "table_caption": [ + "Table 1. Comparison of DisCoScene and relevant works. Multiple Objects: Ability to model multiple objects in a scene. Radiance Field: If radiance fields are used to model scenes. Complex Scene: Ability to handle complex datasets beyond diagnostic scenes. Object Editing: If object-level editing is supported. No Camera Sequence: Not requiring ground truth camera sequences." + ], + "table_footnote": [], + "table_body": "
ModelMultiple ObjectsRadiance FieldComplex SceneObject EditingNo Camera Sequence
GRAF [40]X✓X✓✓
BlockGAN [30]✓XX✓✓
GSN [8]✓✓✓XX
GIRAFFE [32]✓✓X✓✓
DisCoScene✓✓✓✓✓
", + "bbox": [ + 501, + 175, + 893, + 275 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "be scaled to very challenging real-world scene datasets.", + "bbox": [ + 496, + 287, + 864, + 301 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Scene Generation. Scene generation has been a longstanding task. Early works like [52] attempt to model a complex scene by trying to generate it. Recently, with the successes in generative models, scene generation has been advanced significantly. Among them, one popular line is to resort to the setups of image-to-image translation from given conditions, i.e., semantic masks [19,37,49,50,55,67], object-attribute graph [2]. Although able to synthesize photorealistic scene images, they struggle to manipulate the objects in 3D space due to the lack of 3D understanding. Some works [9, 53, 64, 65] reuse the knowledge from 2D GAN models to achieve scene manipulation like the camera pose. But they suffer from poor multi-view consistency due to inadequate geometry modeling. Another active line of work [9, 31, 32, 64] explores adding 3D inductive biases to the scene representation. BlockGAN [31] and GIRAFFE [32] introduce compositional voxels and radiance fields to encode the object structures, but their object control can only be performed at simple diagnostic scenes. DepthGAN [44] introduces depth as a 3D prior but is hard to achieve manipulation and multi-view consistency. GSN [8] proposes to represent a scene with a grid of local radiance fields. However, since this local radiance field does not properly link to the object semantics, individual objects cannot be manipulated with versatile user control. Our work proposes to use an abstract layout prior to spatially disentangle the whole scene into object-centric radiance fields, which enables 3D-aware image synthesis on challenging real-world imagery like WAYMO [48].", + "bbox": [ + 496, + 303, + 890, + 741 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 753, + 591, + 768 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The overall framework is illustrated in Fig. 1. We employ layout as an explicit prior to disentangle objects in our approach (Sec. 3.1). Based on the layout prior, we introduce our spatially disentangled radiance fields (Sec. 3.2) and an efficient rendering pipeline (Sec. 3.3) to achieve controllable 3D-aware scene generation. We also describe our global-local discrimination, which makes training on challenging datasets possible (Sec. 3.4). Finally, we discuss", + "bbox": [ + 496, + 779, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "4403", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/517a558f6f588da66d4f3bcccb751dcde87f157260ea76c97fcee7360fc1a4d9.jpg", + "image_caption": [ + "Figure 1. The overall pipeline of DisCoScene. Conditioned by the layout prior, our spatial disentangle generative radiance fields generate individual objects and the background. Our efficient neural rendering pipeline then composites the scene to a low-resolution feature map with the volume renderer and upsamples to the final high-resolution image with the upsampler. During training, we propose global-local discrimination which applies the scene discriminator to the entire image and the object discriminator to cropped object patches. During inference, users can manipulate the layout to control the generation of a specific scene at the object level." + ], + "image_footnote": [], + "bbox": [ + 130, + 85, + 844, + 272 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "our model's training and inference details on 2D image collections (Sec. 3.5).", + "bbox": [ + 75, + 359, + 470, + 390 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Abstract Layout Prior", + "text_level": 1, + "bbox": [ + 76, + 398, + 285, + 415 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "There exist many representations of a scene, including the popular choice of scene graph [6, 20, 34, 47], where objects and their relations are denoted as nodes and edges. Although graph can describe a scene in rich details, its structure is hard to process and the annotation is laborious to obtain in our case. Therefore, we opt to represent the scene layout in a much-simplified manner - a set of bounding boxes $\\mathcal{B} = \\{\\mathbf{B}_i | i \\in [1, N]\\}$ without category annotation, where $N$ counts objects in the scene. Concretely, each bounding box is defined with 9 parameters, including rotation $a_i$ , translation $t_i$ , and scale $s_i$ .", + "bbox": [ + 75, + 421, + 473, + 589 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {B} _ {i} = \\left[ \\boldsymbol {a} _ {i}, \\boldsymbol {t} _ {i}, \\boldsymbol {s} _ {i} \\right], \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 204, + 599, + 468, + 616 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {a} _ {i} = \\left[ a _ {x}, a _ {y}, a _ {z} \\right], \\boldsymbol {t} _ {i} = \\left[ t _ {x}, t _ {y}, t _ {z} \\right], \\boldsymbol {s} _ {i} = \\left[ s _ {x}, s _ {y}, s _ {z} \\right], \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 94, + 619, + 468, + 637 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{a}_i$ comprises 3 Euler angles, which are easier to convert into rotation matrix $\\mathbf{R}_i$ . Using this notation, the bounding box $\\mathbf{B}_i$ can be transformed from a canonical bounding box $\\mathbf{C}$ , i.e., a unit cube at the coordinate origin:", + "bbox": [ + 75, + 646, + 470, + 708 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {B} _ {i} = \\mathrm {b} _ {i} (\\mathbf {C}) = \\mathbf {R} _ {i} \\cdot \\operatorname {d i a g} \\left(\\boldsymbol {s} _ {i}\\right) \\cdot \\mathbf {C} + \\boldsymbol {t} _ {i}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 143, + 719, + 468, + 736 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{b}_i$ stands for the transformation of $\\mathbf{B}_i$ and $\\mathrm{diag}(\\cdot)$ yields a diagonal matrix with the elements of $s_i$ . Our abstract layout is more friendly to collect and easier to edit, allowing for versatile interactive user control.", + "bbox": [ + 75, + 746, + 468, + 808 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Spatially Disentangled Radiance Fields", + "text_level": 1, + "bbox": [ + 76, + 816, + 413, + 833 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Object Representation. Neural radiance field (NeRF) [29] $\\mathrm{F}(\\pmb{x},\\pmb{v})\\rightarrow (\\pmb{c},\\sigma)$ regresses color $\\pmb {c}\\in \\mathbb{R}^3$ and volume density $\\sigma \\in \\mathbb{R}$ from coordinate $\\pmb {x}\\in \\mathbb{R}^3$ and viewing direction $\\pmb {v}\\in \\mathbb{S}^2$ , parameterized with multi-layer perceptron (MLP)", + "bbox": [ + 76, + 839, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "networks. Recent attempts propose to condition NeRF with a latent code $z$ , resulting in their generative forms [5, 40], $\\mathrm{G}(\\pmb{x},\\pmb{v},\\pmb{z})\\rightarrow (c,\\sigma)$ , to achieve 3D-aware object synthesis.", + "bbox": [ + 498, + 359, + 890, + 404 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Since we use the layout as an internal representation, it naturally disentangles the whole scene into several objects. We can leverage multiple individual generative NeRFs to model different objects, but it can easily lead to an overwhelmingly large number of models and poor training efficiency. To alleviate this issue, we propose to infer generative object radiance field in the canonical space [32, 34], to allow weight sharing among objects:", + "bbox": [ + 496, + 405, + 892, + 526 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\left(\\boldsymbol {c} _ {i}, \\sigma_ {i}\\right) = \\operatorname {G} _ {\\mathrm {o b j}} \\left(\\mathrm {b} _ {i} ^ {- 1} (\\gamma (\\boldsymbol {x})), \\boldsymbol {z} _ {i}\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 539, + 890, + 558 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\gamma (\\cdot)$ is the position encoding function that transforms input into Fourier features. The object generator $\\mathrm{G_{obj}}(\\cdot)$ infers each object independently, resulting in spatially disentangled generative radiance fields. Note that $\\mathrm{G_{obj}}(\\cdot)$ is not conditioned on the viewing direction $\\mathcal{V}$ because the upsampler of our neural renderer can learn the view-dependent effects similar to previous works [4, 15, 60] (Sec. 3.3).", + "bbox": [ + 496, + 569, + 890, + 674 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Spatial Condition. Although object bounding boxes are used as a prior, their latents are still randomly sampled regardless of their spatial configuration, leading to illogical arrangements. To synthesize scene images and infer object radiance fields with proper semantics, we adopt the location and scale of each object as a condition for the generator to encode more consistent intrinsic properties, i.e., shape and category. To this end, we simply modify Eq. (4) by concatenating the latent code with the Fourier features of object location and scale:", + "bbox": [ + 496, + 676, + 892, + 827 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n(\\boldsymbol {c}, \\sigma) = \\operatorname {G} _ {\\mathrm {o b j}} \\left(\\mathrm {b} _ {i} ^ {- 1} (\\gamma (\\boldsymbol {x}))\\right), \\operatorname {c o n c a t} \\left(\\boldsymbol {z} _ {i}, \\gamma \\left(\\boldsymbol {t} _ {i}\\right), \\gamma \\left(\\boldsymbol {s} _ {i}\\right)\\right). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 513, + 839, + 890, + 859 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Therefore, semantic clues are injected into the layout in an unsupervised manner, without explicit category annotation.", + "bbox": [ + 498, + 869, + 890, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "4404", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Background Representation. Unlike objects, the background radiance field is only evaluated in the global space. Considering that the background encodes lots of high-frequency signals, we include the viewing direction $\\pmb{v}$ to help background generator $\\mathrm{G_{bg}}(\\cdot)$ to be able to learn such details. The background generation can be formulated as:", + "bbox": [ + 76, + 90, + 472, + 183 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left(\\boldsymbol {c} _ {\\mathrm {b g}}, \\sigma_ {\\mathrm {b g}}\\right) = \\mathrm {G} _ {\\mathrm {b g}} (\\boldsymbol {x}, \\boldsymbol {v}, \\boldsymbol {z} _ {\\mathrm {b g}}). \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 195, + 468, + 213 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Efficient Rendering Pipeline", + "text_level": 1, + "bbox": [ + 76, + 224, + 331, + 242 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As aforementioned, we use spatial-disentangled radiance fields to represent scenes. However, naive point sampling solutions can lead to prohibitive computational overhead when rendering multiple radiance fields. Considering the independence of objects' radiance fields, we can achieve much more efficient rendering by only focusing on the valid points within the bounding boxes.", + "bbox": [ + 76, + 250, + 468, + 354 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Ray-Box Intersection in Canonical Space. Similar to NeRF [29], we use the pinhole camera model to perform ray casting. For each object, the points on the rays can be sampled at adaptive depths rather than fixed ones since the bounding box provides clues about where the object locates. Specifically, the cast rays $\\mathcal{R} = \\{\\mathbf{r}_j|j\\in [1,\\mathrm{S}^2 ]\\}$ in a resolution S are transformed into the canonical object coordinate system. Then, Ray-AABB [27] (axis-aligned bounding box) intersection algorithm is applied to calculate the adaptive near and far depth $(d_{j,l,n},d_{j,l,f})$ of the intersected segment between the ray $\\mathbf{r}_j$ and the $l$ -th box $\\mathbf{B}_l$ . After that, $\\mathrm{N_d}$ points are sampled equidistantly in the interval $[d_{j,l,n},d_{j,l,f}]$ . It is worth noting that we maintain an intersection matrix $\\mathbf{M}$ of size $\\mathbf{N}\\times \\mathbf{S}^2$ , whose elements indicate if this ray intersects with the box. With $\\mathbf{M}$ , we select only valid points to infer, which can greatly reduce the rendering cost.", + "bbox": [ + 76, + 354, + 468, + 611 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Background Point Sampling. We adopt different background sampling strategies depending on the dataset. In general, we do fixed depth sampling for bounded backgrounds in indoor scenes and inherit the inverse parametrization of $\\mathrm{NeRF}++$ [66] for complex and unbounded outdoor scenes, which uniformly samples background points in an inverse depth range. More details can be founded in the Supplementary Materials.", + "bbox": [ + 76, + 613, + 468, + 733 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Composition and Volume Rendering. In our approach, objects are always assumed to be in front of the background. So objects and background can be rendered independently first and composited thereafter. For a ray $\\mathbf{r}_j$ intersecting with $n_j$ ( $n_j \\geq 1$ ) boxes, its sample points $\\mathcal{X}_j = \\{\\pmb{x}_{j,k} | k \\in [1, n_j \\mathrm{N}_d]\\}$ can be easily obtained from the depth range and the intersection matrix $\\mathbf{M}$ . Since rendering should consider inter-object occlusions, we sort the points $\\mathcal{X}$ by depth, resulting in an ordered point set $\\mathcal{X}_j^s = \\{\\pmb{x}_{j,s_k} | s_k \\in [1, n_j \\mathrm{N}_d], d_{j,s_k} \\leq d_{j,s_{k+1}}\\}$ , where $d_{j,s_k}$ denotes the depth of point $\\pmb{x}_{j,s_k}$ . With color $\\pmb{c}(\\pmb{x}_{j,s_k})$ and density $\\sigma(\\pmb{x}_{j,s_k})$", + "bbox": [ + 76, + 734, + 470, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "of the ordered set inferred with $\\mathrm{G_{obj}}(\\cdot)$ by Eq. (5), the corresponding pixel $\\mathbf{f}(\\mathbf{r}_j)$ is calculated as:", + "bbox": [ + 496, + 90, + 890, + 122 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {f} (\\mathbf {r} _ {j}) = \\sum_ {k = 1} ^ {n _ {j} \\mathrm {N} _ {d}} T _ {j, k} \\alpha_ {j, k} \\boldsymbol {c} \\left(\\boldsymbol {x} _ {j, s _ {k}}\\right), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 578, + 128, + 890, + 172 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nT _ {j, k} = \\exp \\left(- \\sum_ {o = 1} ^ {k - 1} \\sigma \\left(\\boldsymbol {x} _ {j, s _ {k}}\\right) \\delta_ {j, s _ {o}}\\right), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 176, + 890, + 215 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\alpha_ {j, k} = 1 - \\exp (- \\sigma \\left(\\boldsymbol {x} _ {j, s _ {k}}\\right) \\delta_ {j, s _ {k}}). \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 220, + 890, + 237 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For any ray that does not intersect with boxes, its color and density are set to 0 and $-\\infty$ , respectively. So that the foreground object map $\\mathbf{F}$ can be formulated as:", + "bbox": [ + 496, + 244, + 890, + 289 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {F} _ {j} = \\left\\{ \\begin{array}{l l} \\mathbf {f} \\left(\\mathbf {r} _ {j}\\right), & \\text {i f} \\exists m \\in \\mathbf {M} _ {:, j}, m \\text {i s t r u e ,} \\\\ 0, & \\text {e l s e .} \\end{array} \\right. \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 539, + 296, + 890, + 337 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Since the background points are sampled at a fixed depth, we can directly adopt Eq. (6) to evaluate background points in the global space without sorting. And the background map $\\mathbf{N}$ can also be obtained by volume rendering similar to Eq. (7). Finally, $\\mathbf{F}$ and $\\mathbf{N}$ are alpha-blended into the final image $\\mathbf{I}_n$ with alpha extracted from Eq. (9):", + "bbox": [ + 496, + 344, + 890, + 434 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {I} _ {\\mathrm {n}} = \\mathbf {F} + \\prod_ {k = 1} ^ {n _ {j} \\mathrm {N} _ {d}} (1 - \\alpha_ {j, k}) \\odot \\mathbf {N}. \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 589, + 441, + 890, + 484 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Although our rendering pipeline efficiently composites multiple radiance fields, it still suffers from slow performance when rendering high-resolution images. To mitigate this issue, we render a high-dimensional feature map instead of a 3-channel color in a smaller resolution, followed by a StyleGAN2-like architecture that upsamples the feature map to the target resolution.", + "bbox": [ + 496, + 491, + 890, + 598 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Local & Global Discrimination", + "text_level": 1, + "bbox": [ + 500, + 604, + 774, + 619 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Like other GAN-based approaches, discriminators play a crucial role in training. Previous attempts for 3D-aware scene synthesis [8,32] only adopt scene-level discriminators to critique between rendered scenes and real captures. However, such a scene discriminator pays more attention to the global coherence of the whole scene, weakening the supervision for individual objects. Given that each object, especially those far from the camera, occupies a small portion of the rendered frame, the scene discriminator provides weak learning signal to its radiance field, leading to inadequate training and poor object quality. Besides, the scene discriminator shows only minimal capability in disentangling objects and background, allowing the background generator $\\mathrm{G_{bg}}$ to overfit the whole scene easily.", + "bbox": [ + 496, + 628, + 890, + 839 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Similar to [12], we propose to add an extra object discriminator for local discrimination, leading to better object-level supervision. Sepcifically, with the 3D layout $\\mathbf{B}_i$ spatially disentangling different objects, we project them into", + "bbox": [ + 496, + 839, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "4405", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "2D space as $\\mathbf{B}_i^{2D}$ to extract object patches $\\mathcal{P}_{\\mathbf{I}} = \\{\\mathbf{P}_i|\\mathbf{P}_i = \\mathrm{crop}(\\mathbf{I},\\mathbf{B}_i^{2D})\\}$ from synthesized and real scenes images with simple cropping. The object patches are fed into the object discriminator after being scaled to a uniform size. We find that it significantly helps synthesize realistic objects and benefits the disentanglement between objects and the background. More details about our object discrimination are included in the Supplementary Materials.", + "bbox": [ + 75, + 90, + 472, + 212 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Training and Inference", + "text_level": 1, + "bbox": [ + 76, + 220, + 290, + 237 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training Objectives. The whole generation process is formulated as $\\mathbf{I}_f = \\mathrm{G}(\\mathcal{B},\\mathcal{Z},\\xi)$ , where the generator $\\mathrm{G}(\\cdot)$ receives a layout $\\mathcal{B}$ , a latent code set $\\mathcal{Z}$ independently sampled from distribution $\\mathcal{N}(0,1)$ to control objects, and a camera pose $\\xi$ sampled from a prior distribution $p_{\\xi}$ to synthesize the image $\\mathbf{I}_f$ . During training, $\\mathcal{B}$ , $\\mathcal{Z}$ , $\\xi$ are randomly sampled, and the real image $\\mathbf{I}_r$ is sampled from the dataset. Besides the generator, we employ the scene discriminator $\\mathrm{D}_s(\\cdot)$ to guarantee the global coherence of the rendering and the object discriminator $\\mathrm{D}_{\\mathrm{obj}}(\\cdot)$ on individual objects for local discrimination. Generators and discriminators are jointly trained as:", + "bbox": [ + 75, + 244, + 473, + 426 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\min \\mathcal {L} _ {G} = \\mathbb {E} [ f (- \\mathrm {D} _ {s} (\\mathbf {I} _ {f})) ] + \\lambda_ {1} \\mathbb {E} [ f (- \\mathrm {D} _ {\\mathrm {o b j}} (\\mathcal {P} _ {\\mathbf {I} _ {f}})) ], (12) \\\\ \\min \\mathcal {L} _ {D} = \\mathbb {E} [ f (- \\mathrm {D} _ {s} (\\mathbf {I} _ {r})) ] + \\mathbb {E} [ f (\\mathrm {D} _ {s} (\\mathbf {I} _ {f})) ] (13) \\\\ + \\lambda_ {1} (\\mathbb {E} [ f (- \\mathrm {D} _ {\\mathrm {o b j}} (\\mathcal {P} _ {\\mathbf {I} _ {r}}) ]) + \\mathbb {E} [ f (\\mathrm {D} _ {\\mathrm {o b j}} (\\mathcal {P} _ {\\mathbf {I} _ {f}})) ]) \\\\ + \\lambda_ {2} | | \\nabla_ {\\mathbf {I} _ {r}} \\mathrm {D} _ {s} (\\mathbf {I} _ {r}) | | _ {2} ^ {2} + \\lambda_ {3} \\nabla_ {\\mathcal {P} _ {\\mathbf {I} _ {r}}} \\mathrm {D} _ {\\text {o b j}} (\\mathcal {P} _ {\\mathbf {I} _ {r}}) | | _ {2} ^ {2}), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 436, + 467, + 512 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $f(t) = \\log (1 + \\exp (t))$ is the softplus function, and $\\mathcal{P}_{\\mathbf{I}_r}$ and $\\mathcal{P}_{\\mathbf{I}_f}$ are the extracted object patches of synthesized image $\\mathbf{I}_f$ and real image $\\mathbf{I}_r$ , respectively. $\\lambda_{1}$ stands for the loss weight of the object discriminator. The last two terms in Eq. (13) are the gradient penalty regularizers of both discriminators, with $\\lambda_{2}$ and $\\lambda_{3}$ denoting their weights.", + "bbox": [ + 75, + 521, + 468, + 612 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Inference. Besides high-quality scene generation, our method naturally supports object editing by manipulating the layout prior as shown in Fig. 1. Various applications are shown in Sec. 4.3. In particular, ray marching at a small resolution (64) may cause aliasing especially when moving the objects. We adopt supersampling anti-aliasing (SSAA) [43] to perform ray marching at a temporary higher resolution (128) and downsample the feature map to the original resolution before the upsampler. This strategy is used only for object synthesis, and we do not change the background resolution during inference.", + "bbox": [ + 75, + 613, + 468, + 779 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 792, + 207, + 808 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Settings", + "text_level": 1, + "bbox": [ + 76, + 816, + 174, + 832 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. We evaluate DisCoScene on three multi-object scene datasets, including CLEVR [21], 3D-FRONT [10, 11], and WAYMO [48]. CLEVR is a diagnostic multi-object dataset. We use the official script [21] to render scenes", + "bbox": [ + 75, + 839, + 467, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "with 2 and random primitives. Our CLEVR dataset consists of $80K$ samples in $256 \\times 256$ resolution. 3D-FRONT is an indoor scene dataset, containing a collection of $6.8K$ houses with $140K$ rooms. We obtain $4K$ bedrooms after filtering out rooms with uncommon arrangements or unnatural sizes and use BlenderProc to render 20 images per room from random camera positions, resulting in a total of $80K$ images. WAYMO is a large-scale autonomous driving dataset with $1K$ video sequences of outdoor scenes. Six images are provided for each frame, and we only keep the front view. We also apply heuristic rules to filter out small and noisy cars and collect a subset of $70K$ images. Because the width is always larger than height on WAYMO, we adopt the black padding to make images square, similar with StyleGAN2 [25]. More details about data preprocessing and rendering are included in Supplementary Materials.", + "bbox": [ + 496, + 90, + 890, + 332 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Baselines. We compare with both 2D and 3D GANs. For 2D, we compare with StyleGAN2 [25] on image quality. As for 3D, we compare with EpiGRAF [46], VolumeGAN [60], and EG-3D [4] on object generation, and GIRAFFE [32], GSN [8] on scene generation. We use the baseline models either released along with their papers or official implementations to train on our data.", + "bbox": [ + 496, + 334, + 890, + 438 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation Details. We use the same architecture and parameters of the mapping network from StyleGAN2 [25]. For object generator $\\mathrm{G_{obj}(\\cdot)}$ and background generator $\\mathrm{G_{bg}(\\cdot)}$ , we use 8 and 4 Modulated Fully-Connected layers (ModFCs) with 256 and 128 channels, respectively. Ray casting is performed on $64 \\times 64$ and the feature map is rendered to image with neural renderer. The progressive training strategy from PG-GAN [22] is adopted for better image quality and multi-view consistency. Discriminators $\\mathrm{D}_s(\\cdot)$ and $\\mathrm{D_{obj}(\\cdot)}$ both share the similar architecture of StyleGAN2 but with only half channels. Practically, the resolution of $\\mathrm{D_{obj}(\\cdot)}$ is always 1/2 on WAYMO or 1/4 on CLEVR and 3D-FRONT of $\\mathrm{D}_s(\\cdot)$ . All our models are trained on $8 \\times$ V100/A100 GPUs with a batch size of 64. $\\lambda_1$ is set to 1 to balance object and scene discriminators. $\\lambda_2$ and $\\lambda_3$ are set to 1 to maintain training stability. Unless specified, other hyperparameters are same as StyleGAN2. More details about network architecture and training can be found in Supplementary Materials.", + "bbox": [ + 496, + 440, + 890, + 728 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Main Results", + "text_level": 1, + "bbox": [ + 500, + 739, + 637, + 753 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Qualitative Comparison. Fig. 2 presents the synthesized images in a resolution of $256 \\times 256$ of our method and baselines on all the datasets. We compare our method on explicit camera control and object editing with baselines. EG3D, with a single radiance field, can manipulate the global camera of the synthesized images. As for EG3D, although it converges on the datasets, the object fidelity are lower than our method. On CLEVR with a narrow camera distribution, the results of EG3D are inconsistent. In the", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "4406", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/0b529a7430e6a37bcc21c787cdc675d9af41301771039ca179f31c2957d455e3.jpg", + "image_caption": [ + "Figure 2. Qualitative comparison between DisCoScene and baselines. Explicit camera rotation is evaluated on CLEVR and 3D-FRONT. Object rotation (left) and object translation (right) are evaluated on WAYMO. All images are in $256 \\times 256$ resolution." + ], + "image_footnote": [], + "bbox": [ + 119, + 88, + 851, + 349 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/c0d1154b882b168a9c60cd6878d29b0adb2a5569aa254864d5d8b1cdd4eccea4.jpg", + "table_caption": [ + "Table 2. Quantitative comparisons on different datasets. FID, KID $(\\times 10^{3})$ are reported as the evaluation metrics. TR. and INF. denote training and inference costs, evaluated in V100 days and ms/image (single V100 over $1K$ samples), respectively. Note that we highlight the best results among 3D-aware models." + ], + "table_footnote": [], + "table_body": "
ModelCLEVR3D-FRONTWAYMO
FID ↓KID ↓TR. ↓INF. ↓FID ↓KID ↓FID ↓KID ↓
StyleGAN2 [25]4.53.013.34412.54.315.18.3
EpiGRAF [46]10.48.316.0114107.2102.327.026.1
VolumeGAN [60]7.55.115.29052.738.729.918.2
EG3D [4]4.112.725.85519.713.526.045.4
GIRAFFE [32]78.561.55.26256.546.8175.7212.1
GSN [8]----130.787.5--
DisCoScene3.52.118.19513.87.416.08.4
", + "bbox": [ + 133, + 429, + 831, + 606 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "first example, the color of the cylinder changes from gray to green across different views. Meanwhile, our method learns better 3D structure of the objects and achieves better camera control. On the challenging WAYMO dataset, it is difficult to encode huge street scenes within a single generator, thus we train GIRAFFE and our DisCoScene in the camera space to evaluate object editing. GIRAFFE struggles to generate realistic results and, while manipulating objects, their geometry and appearance are not preserved well. Our approach is capable of handling these complicated scenarios with good variations. Wherever the object is placed and regardless of how the rotation is carried out, the synthesized objects are substantially better and more consistent than GIRAFFE. It demonstrates the effectiveness of our spatially disentangle radiance fields built upon the layout prior. More comparisons are included in Supplementary Materials.", + "bbox": [ + 75, + 623, + 470, + 864 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Quantitative Comparison. Tab. 2 reports the quantitative metrics on the quality of results, including FID [18] and", + "bbox": [ + 75, + 869, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "KID [3]. All metrics are calculated between $50K$ generated samples and all real images. DisCoScene consistently outperforms baselines with significant improvement on all datasets. Besides, training cost in V100 days and testing cost in ms/image (on a single V100 over $1K$ samples) are also included to reflect the efficiency of our model. Note that the inference cost of 3D-aware models is evaluated on generating radiance fields rather than images. In such a case, EG3D and EpiGRAF are not fast as excepted due to the heavy computation on tri-planes. With comparable training and testing cost, it even achieves similar level of image quality with state-of-the-art 2D GAN baselines, e.g., StyleGAN2 [25], while allowing for explicit camera control and object editing that are otherwise challenging.", + "bbox": [ + 496, + 623, + 890, + 835 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Controllable Scene Generation", + "text_level": 1, + "bbox": [ + 500, + 845, + 772, + 861 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The layout prior in our model enables versatile user controls of scene objects. In what follows, we evaluate the", + "bbox": [ + 500, + 869, + 892, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "4407", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/3d52a9bce2205b07c0700f0b4500225def531e227d12f8c75c9dc0e9a163ce28.jpg", + "image_caption": [ + "Figure 3. Controllable scene synthesis in $256 \\times 256$ resolution. We perform versatile user control of the global camera and scene objects, such as rearrangement, removal, insertion, and restyling. Editings are performed on the original generations (the left one of each row)." + ], + "image_footnote": [], + "bbox": [ + 76, + 88, + 893, + 262 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "flexibility and effectiveness of our model through various 3D manipulation applications in different datasets. Examples are shown in Fig. 3 and more results can be found in Supplementary Materials.", + "bbox": [ + 75, + 304, + 468, + 364 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Rearranging Objects. We can transform bounding boxes B to rearrange (rotation and translation) the objects in the scenes without affecting their appearance. Transforming shapes in CLEVR, furniture in 3D-FRONT, and cars in WAYMO all show consistent results. In particular, rotating symmetric shapes (i.e., spheres and cylinders) in CLEVR shows little changes, suggesting desired multi-view consistency. Our model can properly handle mutual occlusion. Take the blue cube from CLEVR as example (1-st row of Fig. 3), our model can produce new occlusions between it and the grey cylinder and generate high-quality renderings. Removing and Cloning Objects. Users can update the layout by removing or cloning bounding boxes. Our method seamlessly removes objects with the background inpainted realistically, even without training on any pure background, including the challenging dataset of WAYMO (3-rd row of Fig. 3). Object cloning is also naturally supported, by copying and pasting a box to a new location in the layout.", + "bbox": [ + 75, + 364, + 470, + 638 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Restyling Objects. Although appearance and shape are not explicitly modeled by the latent code, we can reuse the encoded hierarchical knowledge to perform object restyling. Like [15, 42, 61], we arbitrarily sample latent codes and perform style-mixing on different layers to achieve independent control over appearance and shape. Fig. 3 presents the restyling results on certain objects, i.e., the front cylinder in CLEVR, the bed in 3D-FRONT, and the left car in WAYMO. Camera Movement. Explicit camera control is also permitted. Even for CLEVR that is trained on very limited camera ranges, we can rotate the camera up to an extreme side view. Our model also produces consistent results when rotating the camera on 3D-FRONT (2-nd row of Fig. 3).", + "bbox": [ + 75, + 638, + 468, + 835 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 845, + 230, + 863 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We ablate main components of our approach to better understand their individual contributions. In addition to the", + "bbox": [ + 76, + 869, + 470, + 898 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/fcefd9c53c0989fbcab64afae28916bdd5d4ddf914c996e09a21500a7974e835.jpg", + "table_caption": [ + "Table 3. Ablation analysis of object discriminator $\\left( {\\mathrm{D}}_{\\mathrm{{obj}}}\\right)$ ." + ], + "table_footnote": [], + "table_body": "
CLEVR3D-FRONTWAYMO
FIDw/o Dobj5.018.619.5
w/ Dobj3.513.816.0
FIDobjw/o Dobj19.133.795.1
w/ Dobj5.619.516.3
", + "bbox": [ + 509, + 319, + 879, + 411 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/fec9edc1385117231cb6461ceee75dfc8293f59bf6dd45716ed8761cc2347a94.jpg", + "table_caption": [ + "Table 4. Ablation analysis of spatial condition (S-Cond)." + ], + "table_footnote": [], + "table_body": "
FIDFIDobj
w/ S-Condw/o S-Condw/ S-Condw/o S-Cond
3D-FRONT13.815.219.523.2
", + "bbox": [ + 501, + 431, + 888, + 487 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "FID score that measures the quality of the entire image, we also provide another metric $\\mathrm{FID}_{\\mathrm{obj}}$ to measure the quality of individual objects. Specifically, we use the projected 2D boxes to crop objects from the synthesized images and then perform FID evaluation against the ones from real images.", + "bbox": [ + 496, + 503, + 890, + 580 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Object Discriminator. The object discriminator $\\mathrm{D_{obj}}$ plays a crucial role in synthesizing realistic objects, as evaluated in Tab. 3. Obviously, the object fidelity is significantly improved across all datasets with $\\mathrm{D_{obj}}$ . Also, the quality of the whole scene generation is improved as well, contributed by better objects. Fig. 5 visually shows that our method can successfully disentangle objects from the background with the help of object discriminator. Although the baseline model is able to disentangle objects on 3D-FRONT from simple background to certain extent, the background suffers from the entanglement with objects, resulting in obvious artifacts as well as illogical layout. On more challenging datasets like WAYMO, the complex backgrounds make the disentanglement even more difficult, so that the background model easily overfits the whole scene as a single radiance field. Thanks to the object discriminator, our full model benefits from object supervision, leading to better disentanglement, even without seeing a pure background image.", + "bbox": [ + 496, + 580, + 892, + 853 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Spatial Condition. To analyze how spatial condition (S-Cond) affects the quality of generation, we compare results with models trained with and without S-Cond on 3D-", + "bbox": [ + 496, + 854, + 893, + 898 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "4408", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5d9b0718b37ce2aa590226d6da3a38956c846abf247d4a3b66212cbc98151ffe.jpg", + "image_caption": [ + "(a) Spatial condition" + ], + "image_footnote": [], + "bbox": [ + 73, + 89, + 352, + 193 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/51e21fd9bf59849e4e3c6a1308a6ed558d2ef597d9c23b986aee28577f1da04f.jpg", + "image_caption": [ + "(b) Supersampling anti-aliasing" + ], + "image_footnote": [], + "bbox": [ + 352, + 88, + 612, + 193 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/553869722a3b9d548db31c196bb2ba1b349eed7186c88199dee03202a4ebefa5.jpg", + "image_caption": [ + "(c) Upsampler" + ], + "image_footnote": [], + "bbox": [ + 612, + 90, + 887, + 191 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d8b6bdfdbae321f3574a11bcf92de0dfaa74f163d5e6a2c65632179d25fea4c9.jpg", + "image_caption": [ + "Figure 4. Qualitative comparison for ablations on spatial condition (S-Cond), supersampling anti-alising (SSAA), and upsampler (Up.).", + "Figure 5. Ablation on scene disentanglement. We independently infer objects and background to show the quality of scene disentanglement with regard to object discriminator $\\mathrm{D}_{\\mathrm{obj}}$ ." + ], + "image_footnote": [], + "bbox": [ + 76, + 227, + 467, + 313 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "FRONT (Fig. 4a). For example, our full model consistently infers beds at the center of rooms, while the baseline predicts random items like tables or nightstands that rarely appear in the middle of bedrooms. These results demonstrate that spatial condition can assist the generator with appropriate semantics from simple layout priors. Note that this correlation between spatial configurations and object semantics is automatically emerged without any supervision. We also numerically compare the image quality on these two models in Tab. 4, which shows that S-Cond also achieves better image quality at both scene- and object-level, because more proper semantics are more in line with the native distribution of real images.", + "bbox": [ + 75, + 369, + 467, + 566 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Supersampling Anti-Aliasing. We adopt a simple supersampling (SSAA) strategy to reduce edge aliasing by sampling more points during inference (Sec. 3.5). Thanks to our efficient object point sampling, doubling the resolution of foreground points keeps a similar inference speed (105 ms/image), comparable with original speed (95 ms/image). Results with different sampling points are shown in Fig. 4b. Taking the right boundary of the cabinet as an example (see the zoom-in insets for better visualization), when the cabinet is moved, SSAA achieves more consistent boundary compared with the jaggy one in the baseline.", + "bbox": [ + 75, + 566, + 467, + 733 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Neural Renderer for Shadow. We adopt the StyleGAN2-like neural renderer to boost the rendering efficiency (Sec. 3.3). Besides the low computational cost, the added capacity of the neural renderer also brings better implicit modeling of realistic lighting effects such as shadowing. Therefore, without handling the shadowing effect in our rendering pipeline, our model can still synthesize high-quality shaodws on datasets such as CLEVR (Fig. 4c). This is because the large receptive field brought by $3 \\times 3$ convolutions and upsampler blocks make the neural renderer be aware of the object locations and progressively add shadows", + "bbox": [ + 75, + 734, + 467, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8a82525c84b3e0f3b3c0a1a9d9f26bdebdf99b3611927b7a710a80dd46baff5d.jpg", + "image_caption": [ + "Figure 6. Real image inversion and editing." + ], + "image_footnote": [], + "bbox": [ + 501, + 227, + 890, + 344 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "to the low resolution features rendered from radiance fields.", + "bbox": [ + 500, + 376, + 888, + 390 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Discussion and Conclusion", + "text_level": 1, + "bbox": [ + 500, + 404, + 746, + 419 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Real Image Editing. Fig. 6 shows that it is possible to embed a real image into the latent space of our pretrained model using pivotal tuning inversion (PTI) [39]. Besides reconstruction, all object manipulation operations are supported to edit the image. As one of the very first steps towards 3D scene editing from a single image, we believe that our method proves a promising venue and can inspire future research efforts along this direction.", + "bbox": [ + 496, + 430, + 890, + 551 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations and Future Work. Our model requires the abstract layout prior as the input. For in-the-wild datasets, we need monocular 3D object detector [54] to infer pseudo layouts. While existing approaches attempt to learn the layout in an end-to-end manner, they struggle to generalize to complex scenes consisting of multiple objects. So it would be interesting to explore 3D layout estimation for complex scenes and combine with our approach end-to-end. Also, although our work shows significant improvement over existing 3D-aware scene generators, it is still challenging to learn on the street scenes in the global space due to the limited model capacity. Large-scale NeRFs [51, 57] might be one potent solution.", + "bbox": [ + 496, + 556, + 890, + 752 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Conclusion. This work presents DisCoScene, a method for controllable 3D-aware scene synthesis on challenging datasets. By taking spatially disentangled radiance fields as the representation based on a very abstract layout prior, our method is able to generate high-fidelity scene images and allows for versatile object-level editing.", + "bbox": [ + 496, + 756, + 890, + 847 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. We thank Jiatao Gu, Willi Menapace, Jian Ren, Panos Achlioptas, Tai Wang, and Zian Wang for fruitful discussions and comments about this work.", + "bbox": [ + 496, + 854, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "4409", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Jonathan T Barron, Ben Mildenhall, Matthew Tancik, Peter Hedman, Ricardo Martin-Brualla, and Pratul P Srinivasan. Mip-nerf: A multiscale representation for anti-aliasing neural radiance fields. In Int. Conf. Comput. Vis., pages 5855–5864, 2021. 1", + "[2] Daniel Bear, Chaofei Fan, Damian Mrowca, Yunzhu Li, Seth Alter, Aran Nayebi, Jeremy Schwartz, Li F Fei-Fei, Jiajun Wu, Josh Tenenbaum, et al. Learning physical graph representations from visual scenes. Adv. 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Syst., 2018. 2" + ], + "bbox": [ + 78, + 92, + 467, + 657 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "4412", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/DisCoScene_ Spatially Disentangled Generative Radiance Fields for Controllable 3D-Aware Scene Synthesis/bdaa5712-8b26-43d5-9ca1-465a14b26701_model.json b/2023/DisCoScene_ Spatially Disentangled Generative Radiance Fields for Controllable 3D-Aware Scene Synthesis/bdaa5712-8b26-43d5-9ca1-465a14b26701_model.json new file mode 100644 index 0000000000000000000000000000000000000000..16866d3dda5d63beccdc9d3794283625c19a6c7d --- /dev/null +++ b/2023/DisCoScene_ Spatially Disentangled Generative Radiance Fields for Controllable 3D-Aware Scene Synthesis/bdaa5712-8b26-43d5-9ca1-465a14b26701_model.json @@ -0,0 +1,2279 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.165, + 0.13, + 0.808, + 0.175 + ], + "angle": 0, + "content": "DisCoScene: Spatially Disentangled Generative Radiance Fields for Controllable 3D-aware Scene Synthesis" + }, + { + "type": "text", + "bbox": [ + 0.174, + 0.203, + 0.796, + 0.282 + ], + "angle": 0, + "content": "Yinghao Xu\\(^{1,2*}\\) Mengei Chai\\(^{2\\dagger}\\) Zifan Shi\\(^{3}\\) Sida Peng\\(^{4}\\) Ivan Skorokhodov\\(^{5,2*}\\) Aliaksandr Siarohin\\(^{2}\\) Ceyuan Yang\\(^{1}\\) Yujun Shen\\(^{1}\\) Hsin-Ying Lee\\(^{2}\\) Bolei Zhou\\(^{6}\\) Sergey Tulyakov\\(^{2}\\) \\(^{1}\\mathrm{CUHK}\\) \\(^{2}\\mathrm{SnapInc.}\\) \\(^{3}\\mathrm{HKUST}\\) \\(^{4}\\mathrm{ZJU}\\) \\(^{5}\\mathrm{KAUST}\\) \\(^{6}\\mathrm{UCLA}\\)" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.315, + 0.314, + 0.332 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.347, + 0.474, + 0.665 + ], + "angle": 0, + "content": "Existing 3D-aware image synthesis approaches mainly focus on generating a single canonical object and show limited capacity in composing a complex scene containing a variety of objects. This work presents DisCoScene: a 3D-aware generative model for high-quality and controllable scene synthesis. The key ingredient of our method is a very abstract object-level representation (i.e., 3D bounding boxes without semantic annotation) as the scene layout prior, which is simple to obtain, general to describe various scene contents, and yet informative to disentangle objects and background. Moreover, it serves as an intuitive user control for scene editing. Based on such a prior, the proposed model spatially disentangles the whole scene into object-centric generative radiance fields by learning on only 2D images with the global-local discrimination. Our model obtains the generation fidelity and editing flexibility of individual objects while being able to efficiently compose objects and the background into a complete scene. We demonstrate state-of-the-art performance on many scene datasets, including the challenging Waymo outdoor dataset. Project page can be found here." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.692, + 0.21, + 0.708 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.716, + 0.471, + 0.869 + ], + "angle": 0, + "content": "3D-consistent image synthesis from single-view 2D data has become a trendy topic in generative modeling. Recent approaches like GRAF [40] and Pi-GAN [5] introduce 3D inductive bias by taking neural radiance fields [1, 28, 29, 36, 38] as the underlying representation, gaining the capability of geometry modeling and explicit camera control. Despite their success in synthesizing individual objects (e.g., faces, cats, cars), they struggle on scene images that contain multiple objects with non-trivial layouts and complex backgrounds. The varying quantity and large" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.317, + 0.892, + 0.378 + ], + "angle": 0, + "content": "diversity of objects, along with the intricate spatial arrangement and mutual occlusions, bring enormous challenges, which exceed the capacity of the object-level generative models [4, 13, 15, 33, 45, 46, 60]." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.382, + 0.893, + 0.581 + ], + "angle": 0, + "content": "Recent efforts have been made towards 3D-aware scene synthesis. Despite the encouraging progress, there are still fundamental drawbacks. For example, Generative Scene Networks (GSN) [8] achieve large-scale scene synthesis by representing the scene as a grid of local radiance fields and training on 2D observations from continuous camera paths. However, object-level editing is not feasible due to spatial entanglement and the lack of explicit object definition. On the contrary, GIRAFFE [32] explicitly composites object-centric radiance fields [16, 34, 56, 63] to support object-level control. Yet, it works poorly on challenging datasets containing multiple objects and complex backgrounds due to the absence of proper spatial priors." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.895, + 0.903 + ], + "angle": 0, + "content": "To achieve high-quality and controllable scene synthesis, the scene representation stands out as one critical design focus. A well-structured scene representation can scale up the generation capability and tackle the aforementioned challenges. Imagine, given an empty apartment and a furniture catalog, what does it take for a person to arrange the space? Would people prefer to walk around and throw things here and there, or instead figure out an overall layout and then attend to each location for the detailed selection? Obviously, a layout describing the arrangement of each furniture in the space substantially eases the scene composition process [17, 26, 58]. From this vantage point, here comes our primary motivation — an abstract object-oriented scene representation, namely a layout prior, could facilitate learning from challenging 2D data as a lightweight supervision signal during training and allow user interaction during inference. More specifically, to make such a prior easy to obtain and generalizable across different scenes, we define it as a set of object bounding boxes without semantic annotation, which describes the spatial composition of objects in the scene and supports intuitive object-level editing." + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.875, + 0.374, + 0.888 + ], + "angle": 0, + "content": "*Work partially done during internships at Snap Inc." + }, + { + "type": "page_footnote", + "bbox": [ + 0.098, + 0.888, + 0.223, + 0.9 + ], + "angle": 0, + "content": "† Corresponding author." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.875, + 0.374, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.517, + 0.957 + ], + "angle": 0, + "content": "4402" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.364 + ], + "angle": 0, + "content": "In this work, we present DisCoScene, a novel 3D-aware generative model for complex scenes. Our method allows for high-quality scene synthesis on challenging datasets and flexible user control of both the camera and scene objects. Driven by the aforementioned layout prior, our model spatially disentangles the scene into composable radiance fields which are shared in the same object-centric generative model. To make the best use of the prior as a lightweight supervision during training, we propose global-local discrimination which attends to both the whole scene and individual objects to enforce spatial disentanglement between objects and against the background. Once the model is trained, users can generate and edit a scene by explicitly controlling the camera and the layout of objects' bounding boxes. In addition, we develop an efficient rendering pipeline tailored for the spatially-disentangled radiance fields, which significantly accelerates object rendering and scene composition for both training and inference stages." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.364, + 0.473, + 0.515 + ], + "angle": 0, + "content": "Our method is evaluated on diverse datasets, including both indoor and outdoor scenes. Qualitative and quantitative results demonstrate that, compared to existing baselines, our method achieves state-of-the-art performance in terms of both generation quality and editing capability. Tab. 1 compares DisCoScene with relevant works. it is worth noting that, to the best of our knowledge, DisCoScene stands as the first method that achieves high-quality 3D-aware generation on challenging datasets like WAYMO [48], while enabling interactive object manipulation." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.529, + 0.22, + 0.545 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.553, + 0.473, + 0.903 + ], + "angle": 0, + "content": "3D-aware Image Synthesis. Generative Adversarial Networks (GANs) have achieved remarkable success in 2D image synthesis [14, 22-25], and have recently been extended to 3D-aware image generation. VON [68] and HoloGAN [30] introduce voxel representations to the generator and use neural rendering to project 3D voxels into 2D space. Then, GRAF [40] and Pi-GAN [5] propose to use implicit functions to learn NeRF from single-view image collections, resulting in better multi-view consistency compared to voxel-based methods. GOF [59], ShadeGAN [35], and GRAM [7] introduce occupancy field, albedo field and radiance surface instead of radiance field to learn better 3D shapes. However, high-resolution image synthesis with direct volumetric rendering is usually expensive. Many works [4, 15, 32, 33, 45, 60, 62] resort to convolutional upsamplers to improve the rendering resolution and quality with lower computation overhead. While some other works [41,46] adopt patch-based sampling and sparse-voxel to speed up training and inference. Note that most of these methods are restricted to well-aligned objects and fail on more complex, multi-object scene imagery. Our work instead naturally handles multi-object scenes with spatial disentangled object-level radiance fields, which can" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.089, + 0.892, + 0.174 + ], + "angle": 0, + "content": "Table 1. Comparison of DisCoScene and relevant works. Multiple Objects: Ability to model multiple objects in a scene. Radiance Field: If radiance fields are used to model scenes. Complex Scene: Ability to handle complex datasets beyond diagnostic scenes. Object Editing: If object-level editing is supported. No Camera Sequence: Not requiring ground truth camera sequences." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.176, + 0.894, + 0.276 + ], + "angle": 0, + "content": "
ModelMultiple ObjectsRadiance FieldComplex SceneObject EditingNo Camera Sequence
GRAF [40]X✓X✓✓
BlockGAN [30]✓XX✓✓
GSN [8]✓✓✓XX
GIRAFFE [32]✓✓X✓✓
DisCoScene✓✓✓✓✓
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.289, + 0.866, + 0.303 + ], + "angle": 0, + "content": "be scaled to very challenging real-world scene datasets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.304, + 0.892, + 0.742 + ], + "angle": 0, + "content": "Scene Generation. Scene generation has been a longstanding task. Early works like [52] attempt to model a complex scene by trying to generate it. Recently, with the successes in generative models, scene generation has been advanced significantly. Among them, one popular line is to resort to the setups of image-to-image translation from given conditions, i.e., semantic masks [19,37,49,50,55,67], object-attribute graph [2]. Although able to synthesize photorealistic scene images, they struggle to manipulate the objects in 3D space due to the lack of 3D understanding. Some works [9, 53, 64, 65] reuse the knowledge from 2D GAN models to achieve scene manipulation like the camera pose. But they suffer from poor multi-view consistency due to inadequate geometry modeling. Another active line of work [9, 31, 32, 64] explores adding 3D inductive biases to the scene representation. BlockGAN [31] and GIRAFFE [32] introduce compositional voxels and radiance fields to encode the object structures, but their object control can only be performed at simple diagnostic scenes. DepthGAN [44] introduces depth as a 3D prior but is hard to achieve manipulation and multi-view consistency. GSN [8] proposes to represent a scene with a grid of local radiance fields. However, since this local radiance field does not properly link to the object semantics, individual objects cannot be manipulated with versatile user control. Our work proposes to use an abstract layout prior to spatially disentangle the whole scene into object-centric radiance fields, which enables 3D-aware image synthesis on challenging real-world imagery like WAYMO [48]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.755, + 0.593, + 0.77 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.895, + 0.903 + ], + "angle": 0, + "content": "The overall framework is illustrated in Fig. 1. We employ layout as an explicit prior to disentangle objects in our approach (Sec. 3.1). Based on the layout prior, we introduce our spatially disentangled radiance fields (Sec. 3.2) and an efficient rendering pipeline (Sec. 3.3) to achieve controllable 3D-aware scene generation. We also describe our global-local discrimination, which makes training on challenging datasets possible (Sec. 3.4). Finally, we discuss" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4403" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.131, + 0.087, + 0.845, + 0.273 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.277, + 0.895, + 0.348 + ], + "angle": 0, + "content": "Figure 1. The overall pipeline of DisCoScene. Conditioned by the layout prior, our spatial disentangle generative radiance fields generate individual objects and the background. Our efficient neural rendering pipeline then composites the scene to a low-resolution feature map with the volume renderer and upsamples to the final high-resolution image with the upsampler. During training, we propose global-local discrimination which applies the scene discriminator to the entire image and the object discriminator to cropped object patches. During inference, users can manipulate the layout to control the generation of a specific scene at the object level." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.36, + 0.471, + 0.391 + ], + "angle": 0, + "content": "our model's training and inference details on 2D image collections (Sec. 3.5)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.399, + 0.287, + 0.416 + ], + "angle": 0, + "content": "3.1. Abstract Layout Prior" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.422, + 0.474, + 0.59 + ], + "angle": 0, + "content": "There exist many representations of a scene, including the popular choice of scene graph [6, 20, 34, 47], where objects and their relations are denoted as nodes and edges. Although graph can describe a scene in rich details, its structure is hard to process and the annotation is laborious to obtain in our case. Therefore, we opt to represent the scene layout in a much-simplified manner - a set of bounding boxes \\(\\mathcal{B} = \\{\\mathbf{B}_i | i \\in [1, N]\\}\\) without category annotation, where \\(N\\) counts objects in the scene. Concretely, each bounding box is defined with 9 parameters, including rotation \\(a_i\\), translation \\(t_i\\), and scale \\(s_i\\)." + }, + { + "type": "equation", + "bbox": [ + 0.205, + 0.6, + 0.47, + 0.617 + ], + "angle": 0, + "content": "\\[\n\\mathbf {B} _ {i} = \\left[ \\boldsymbol {a} _ {i}, \\boldsymbol {t} _ {i}, \\boldsymbol {s} _ {i} \\right], \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.095, + 0.62, + 0.47, + 0.638 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {a} _ {i} = \\left[ a _ {x}, a _ {y}, a _ {z} \\right], \\boldsymbol {t} _ {i} = \\left[ t _ {x}, t _ {y}, t _ {z} \\right], \\boldsymbol {s} _ {i} = \\left[ s _ {x}, s _ {y}, s _ {z} \\right], \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.647, + 0.471, + 0.709 + ], + "angle": 0, + "content": "where \\(\\mathbf{a}_i\\) comprises 3 Euler angles, which are easier to convert into rotation matrix \\(\\mathbf{R}_i\\). Using this notation, the bounding box \\(\\mathbf{B}_i\\) can be transformed from a canonical bounding box \\(\\mathbf{C}\\), i.e., a unit cube at the coordinate origin:" + }, + { + "type": "equation", + "bbox": [ + 0.144, + 0.72, + 0.47, + 0.737 + ], + "angle": 0, + "content": "\\[\n\\mathbf {B} _ {i} = \\mathrm {b} _ {i} (\\mathbf {C}) = \\mathbf {R} _ {i} \\cdot \\operatorname {d i a g} \\left(\\boldsymbol {s} _ {i}\\right) \\cdot \\mathbf {C} + \\boldsymbol {t} _ {i}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.747, + 0.47, + 0.809 + ], + "angle": 0, + "content": "where \\( \\mathbf{b}_i \\) stands for the transformation of \\( \\mathbf{B}_i \\) and \\( \\mathrm{diag}(\\cdot) \\) yields a diagonal matrix with the elements of \\( s_i \\). Our abstract layout is more friendly to collect and easier to edit, allowing for versatile interactive user control." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.817, + 0.414, + 0.834 + ], + "angle": 0, + "content": "3.2. Spatially Disentangled Radiance Fields" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.84, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Object Representation. Neural radiance field (NeRF) [29] \\(\\mathrm{F}(\\pmb{x},\\pmb{v})\\rightarrow (\\pmb{c},\\sigma)\\) regresses color \\(\\pmb {c}\\in \\mathbb{R}^3\\) and volume density \\(\\sigma \\in \\mathbb{R}\\) from coordinate \\(\\pmb {x}\\in \\mathbb{R}^3\\) and viewing direction \\(\\pmb {v}\\in \\mathbb{S}^2\\), parameterized with multi-layer perceptron (MLP)" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.36, + 0.892, + 0.405 + ], + "angle": 0, + "content": "networks. Recent attempts propose to condition NeRF with a latent code \\(z\\), resulting in their generative forms [5, 40], \\(\\mathrm{G}(\\pmb{x},\\pmb{v},\\pmb{z})\\rightarrow (c,\\sigma)\\), to achieve 3D-aware object synthesis." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.406, + 0.893, + 0.527 + ], + "angle": 0, + "content": "Since we use the layout as an internal representation, it naturally disentangles the whole scene into several objects. We can leverage multiple individual generative NeRFs to model different objects, but it can easily lead to an overwhelmingly large number of models and poor training efficiency. To alleviate this issue, we propose to infer generative object radiance field in the canonical space [32, 34], to allow weight sharing among objects:" + }, + { + "type": "equation", + "bbox": [ + 0.587, + 0.54, + 0.892, + 0.559 + ], + "angle": 0, + "content": "\\[\n\\left(\\boldsymbol {c} _ {i}, \\sigma_ {i}\\right) = \\operatorname {G} _ {\\mathrm {o b j}} \\left(\\mathrm {b} _ {i} ^ {- 1} (\\gamma (\\boldsymbol {x})), \\boldsymbol {z} _ {i}\\right), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.57, + 0.892, + 0.675 + ], + "angle": 0, + "content": "where \\(\\gamma (\\cdot)\\) is the position encoding function that transforms input into Fourier features. The object generator \\(\\mathrm{G_{obj}}(\\cdot)\\) infers each object independently, resulting in spatially disentangled generative radiance fields. Note that \\(\\mathrm{G_{obj}}(\\cdot)\\) is not conditioned on the viewing direction \\(\\mathcal{V}\\) because the upsampler of our neural renderer can learn the view-dependent effects similar to previous works [4, 15, 60] (Sec. 3.3)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.677, + 0.893, + 0.828 + ], + "angle": 0, + "content": "Spatial Condition. Although object bounding boxes are used as a prior, their latents are still randomly sampled regardless of their spatial configuration, leading to illogical arrangements. To synthesize scene images and infer object radiance fields with proper semantics, we adopt the location and scale of each object as a condition for the generator to encode more consistent intrinsic properties, i.e., shape and category. To this end, we simply modify Eq. (4) by concatenating the latent code with the Fourier features of object location and scale:" + }, + { + "type": "equation", + "bbox": [ + 0.514, + 0.84, + 0.892, + 0.86 + ], + "angle": 0, + "content": "\\[\n(\\boldsymbol {c}, \\sigma) = \\operatorname {G} _ {\\mathrm {o b j}} \\left(\\mathrm {b} _ {i} ^ {- 1} (\\gamma (\\boldsymbol {x}))\\right), \\operatorname {c o n c a t} \\left(\\boldsymbol {z} _ {i}, \\gamma \\left(\\boldsymbol {t} _ {i}\\right), \\gamma \\left(\\boldsymbol {s} _ {i}\\right)\\right). \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Therefore, semantic clues are injected into the layout in an unsupervised manner, without explicit category annotation." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4404" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.184 + ], + "angle": 0, + "content": "Background Representation. Unlike objects, the background radiance field is only evaluated in the global space. Considering that the background encodes lots of high-frequency signals, we include the viewing direction \\(\\pmb{v}\\) to help background generator \\(\\mathrm{G_{bg}}(\\cdot)\\) to be able to learn such details. The background generation can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.175, + 0.196, + 0.47, + 0.214 + ], + "angle": 0, + "content": "\\[\n\\left(\\boldsymbol {c} _ {\\mathrm {b g}}, \\sigma_ {\\mathrm {b g}}\\right) = \\mathrm {G} _ {\\mathrm {b g}} (\\boldsymbol {x}, \\boldsymbol {v}, \\boldsymbol {z} _ {\\mathrm {b g}}). \\tag {6}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.226, + 0.332, + 0.243 + ], + "angle": 0, + "content": "3.3. Efficient Rendering Pipeline" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.25, + 0.47, + 0.356 + ], + "angle": 0, + "content": "As aforementioned, we use spatial-disentangled radiance fields to represent scenes. However, naive point sampling solutions can lead to prohibitive computational overhead when rendering multiple radiance fields. Considering the independence of objects' radiance fields, we can achieve much more efficient rendering by only focusing on the valid points within the bounding boxes." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.356, + 0.47, + 0.612 + ], + "angle": 0, + "content": "Ray-Box Intersection in Canonical Space. Similar to NeRF [29], we use the pinhole camera model to perform ray casting. For each object, the points on the rays can be sampled at adaptive depths rather than fixed ones since the bounding box provides clues about where the object locates. Specifically, the cast rays \\(\\mathcal{R} = \\{\\mathbf{r}_j|j\\in [1,\\mathrm{S}^2 ]\\}\\) in a resolution S are transformed into the canonical object coordinate system. Then, Ray-AABB [27] (axis-aligned bounding box) intersection algorithm is applied to calculate the adaptive near and far depth \\((d_{j,l,n},d_{j,l,f})\\) of the intersected segment between the ray \\(\\mathbf{r}_j\\) and the \\(l\\)-th box \\(\\mathbf{B}_l\\). After that, \\(\\mathrm{N_d}\\) points are sampled equidistantly in the interval \\([d_{j,l,n},d_{j,l,f}]\\). It is worth noting that we maintain an intersection matrix \\(\\mathbf{M}\\) of size \\(\\mathbf{N}\\times \\mathbf{S}^2\\), whose elements indicate if this ray intersects with the box. With \\(\\mathbf{M}\\), we select only valid points to infer, which can greatly reduce the rendering cost." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.614, + 0.47, + 0.734 + ], + "angle": 0, + "content": "Background Point Sampling. We adopt different background sampling strategies depending on the dataset. In general, we do fixed depth sampling for bounded backgrounds in indoor scenes and inherit the inverse parametrization of \\(\\mathrm{NeRF}++\\) [66] for complex and unbounded outdoor scenes, which uniformly samples background points in an inverse depth range. More details can be founded in the Supplementary Materials." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.735, + 0.471, + 0.904 + ], + "angle": 0, + "content": "Composition and Volume Rendering. In our approach, objects are always assumed to be in front of the background. So objects and background can be rendered independently first and composited thereafter. For a ray \\(\\mathbf{r}_j\\) intersecting with \\(n_j\\) (\\(n_j \\geq 1\\)) boxes, its sample points \\(\\mathcal{X}_j = \\{\\pmb{x}_{j,k} | k \\in [1, n_j \\mathrm{N}_d]\\}\\) can be easily obtained from the depth range and the intersection matrix \\(\\mathbf{M}\\). Since rendering should consider inter-object occlusions, we sort the points \\(\\mathcal{X}\\) by depth, resulting in an ordered point set \\(\\mathcal{X}_j^s = \\{\\pmb{x}_{j,s_k} | s_k \\in [1, n_j \\mathrm{N}_d], d_{j,s_k} \\leq d_{j,s_{k+1}}\\}\\), where \\(d_{j,s_k}\\) denotes the depth of point \\(\\pmb{x}_{j,s_k}\\). With color \\(\\pmb{c}(\\pmb{x}_{j,s_k})\\) and density \\(\\sigma(\\pmb{x}_{j,s_k})\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.123 + ], + "angle": 0, + "content": "of the ordered set inferred with \\(\\mathrm{G_{obj}}(\\cdot)\\) by Eq. (5), the corresponding pixel \\(\\mathbf{f}(\\mathbf{r}_j)\\) is calculated as:" + }, + { + "type": "equation", + "bbox": [ + 0.579, + 0.13, + 0.892, + 0.173 + ], + "angle": 0, + "content": "\\[\n\\mathbf {f} (\\mathbf {r} _ {j}) = \\sum_ {k = 1} ^ {n _ {j} \\mathrm {N} _ {d}} T _ {j, k} \\alpha_ {j, k} \\boldsymbol {c} \\left(\\boldsymbol {x} _ {j, s _ {k}}\\right), \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.588, + 0.177, + 0.892, + 0.217 + ], + "angle": 0, + "content": "\\[\nT _ {j, k} = \\exp \\left(- \\sum_ {o = 1} ^ {k - 1} \\sigma \\left(\\boldsymbol {x} _ {j, s _ {k}}\\right) \\delta_ {j, s _ {o}}\\right), \\tag {8}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.588, + 0.221, + 0.892, + 0.238 + ], + "angle": 0, + "content": "\\[\n\\alpha_ {j, k} = 1 - \\exp (- \\sigma \\left(\\boldsymbol {x} _ {j, s _ {k}}\\right) \\delta_ {j, s _ {k}}). \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.245, + 0.892, + 0.29 + ], + "angle": 0, + "content": "For any ray that does not intersect with boxes, its color and density are set to 0 and \\(-\\infty\\), respectively. So that the foreground object map \\(\\mathbf{F}\\) can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.54, + 0.297, + 0.892, + 0.338 + ], + "angle": 0, + "content": "\\[\n\\mathbf {F} _ {j} = \\left\\{ \\begin{array}{l l} \\mathbf {f} \\left(\\mathbf {r} _ {j}\\right), & \\text {i f} \\exists m \\in \\mathbf {M} _ {:, j}, m \\text {i s t r u e ,} \\\\ 0, & \\text {e l s e .} \\end{array} \\right. \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.345, + 0.892, + 0.435 + ], + "angle": 0, + "content": "Since the background points are sampled at a fixed depth, we can directly adopt Eq. (6) to evaluate background points in the global space without sorting. And the background map \\(\\mathbf{N}\\) can also be obtained by volume rendering similar to Eq. (7). Finally, \\(\\mathbf{F}\\) and \\(\\mathbf{N}\\) are alpha-blended into the final image \\(\\mathbf{I}_n\\) with alpha extracted from Eq. (9):" + }, + { + "type": "equation", + "bbox": [ + 0.59, + 0.443, + 0.892, + 0.486 + ], + "angle": 0, + "content": "\\[\n\\mathbf {I} _ {\\mathrm {n}} = \\mathbf {F} + \\prod_ {k = 1} ^ {n _ {j} \\mathrm {N} _ {d}} (1 - \\alpha_ {j, k}) \\odot \\mathbf {N}. \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.492, + 0.892, + 0.599 + ], + "angle": 0, + "content": "Although our rendering pipeline efficiently composites multiple radiance fields, it still suffers from slow performance when rendering high-resolution images. To mitigate this issue, we render a high-dimensional feature map instead of a 3-channel color in a smaller resolution, followed by a StyleGAN2-like architecture that upsamples the feature map to the target resolution." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.606, + 0.776, + 0.621 + ], + "angle": 0, + "content": "3.4. Local & Global Discrimination" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.892, + 0.84 + ], + "angle": 0, + "content": "Like other GAN-based approaches, discriminators play a crucial role in training. Previous attempts for 3D-aware scene synthesis [8,32] only adopt scene-level discriminators to critique between rendered scenes and real captures. However, such a scene discriminator pays more attention to the global coherence of the whole scene, weakening the supervision for individual objects. Given that each object, especially those far from the camera, occupies a small portion of the rendered frame, the scene discriminator provides weak learning signal to its radiance field, leading to inadequate training and poor object quality. Besides, the scene discriminator shows only minimal capability in disentangling objects and background, allowing the background generator \\( \\mathrm{G_{bg}} \\) to overfit the whole scene easily." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Similar to [12], we propose to add an extra object discriminator for local discrimination, leading to better object-level supervision. Sepcifically, with the 3D layout \\(\\mathbf{B}_i\\) spatially disentangling different objects, we project them into" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4405" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.473, + 0.213 + ], + "angle": 0, + "content": "2D space as \\(\\mathbf{B}_i^{2D}\\) to extract object patches \\(\\mathcal{P}_{\\mathbf{I}} = \\{\\mathbf{P}_i|\\mathbf{P}_i = \\mathrm{crop}(\\mathbf{I},\\mathbf{B}_i^{2D})\\}\\) from synthesized and real scenes images with simple cropping. The object patches are fed into the object discriminator after being scaled to a uniform size. We find that it significantly helps synthesize realistic objects and benefits the disentanglement between objects and the background. More details about our object discrimination are included in the Supplementary Materials." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.222, + 0.292, + 0.238 + ], + "angle": 0, + "content": "3.5. Training and Inference" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.245, + 0.474, + 0.427 + ], + "angle": 0, + "content": "Training Objectives. The whole generation process is formulated as \\(\\mathbf{I}_f = \\mathrm{G}(\\mathcal{B},\\mathcal{Z},\\xi)\\), where the generator \\(\\mathrm{G}(\\cdot)\\) receives a layout \\(\\mathcal{B}\\), a latent code set \\(\\mathcal{Z}\\) independently sampled from distribution \\(\\mathcal{N}(0,1)\\) to control objects, and a camera pose \\(\\xi\\) sampled from a prior distribution \\(p_{\\xi}\\) to synthesize the image \\(\\mathbf{I}_f\\). During training, \\(\\mathcal{B}\\), \\(\\mathcal{Z}\\), \\(\\xi\\) are randomly sampled, and the real image \\(\\mathbf{I}_r\\) is sampled from the dataset. Besides the generator, we employ the scene discriminator \\(\\mathrm{D}_s(\\cdot)\\) to guarantee the global coherence of the rendering and the object discriminator \\(\\mathrm{D}_{\\mathrm{obj}}(\\cdot)\\) on individual objects for local discrimination. Generators and discriminators are jointly trained as:" + }, + { + "type": "equation", + "bbox": [ + 0.085, + 0.437, + 0.468, + 0.513 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\min \\mathcal {L} _ {G} = \\mathbb {E} [ f (- \\mathrm {D} _ {s} (\\mathbf {I} _ {f})) ] + \\lambda_ {1} \\mathbb {E} [ f (- \\mathrm {D} _ {\\mathrm {o b j}} (\\mathcal {P} _ {\\mathbf {I} _ {f}})) ], (12) \\\\ \\min \\mathcal {L} _ {D} = \\mathbb {E} [ f (- \\mathrm {D} _ {s} (\\mathbf {I} _ {r})) ] + \\mathbb {E} [ f (\\mathrm {D} _ {s} (\\mathbf {I} _ {f})) ] (13) \\\\ + \\lambda_ {1} (\\mathbb {E} [ f (- \\mathrm {D} _ {\\mathrm {o b j}} (\\mathcal {P} _ {\\mathbf {I} _ {r}}) ]) + \\mathbb {E} [ f (\\mathrm {D} _ {\\mathrm {o b j}} (\\mathcal {P} _ {\\mathbf {I} _ {f}})) ]) \\\\ + \\lambda_ {2} | | \\nabla_ {\\mathbf {I} _ {r}} \\mathrm {D} _ {s} (\\mathbf {I} _ {r}) | | _ {2} ^ {2} + \\lambda_ {3} \\nabla_ {\\mathcal {P} _ {\\mathbf {I} _ {r}}} \\mathrm {D} _ {\\text {o b j}} (\\mathcal {P} _ {\\mathbf {I} _ {r}}) | | _ {2} ^ {2}), \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.522, + 0.47, + 0.613 + ], + "angle": 0, + "content": "where \\( f(t) = \\log (1 + \\exp (t)) \\) is the softplus function, and \\( \\mathcal{P}_{\\mathbf{I}_r} \\) and \\( \\mathcal{P}_{\\mathbf{I}_f} \\) are the extracted object patches of synthesized image \\( \\mathbf{I}_f \\) and real image \\( \\mathbf{I}_r \\), respectively. \\( \\lambda_{1} \\) stands for the loss weight of the object discriminator. The last two terms in Eq. (13) are the gradient penalty regularizers of both discriminators, with \\( \\lambda_{2} \\) and \\( \\lambda_{3} \\) denoting their weights." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.614, + 0.47, + 0.78 + ], + "angle": 0, + "content": "Inference. Besides high-quality scene generation, our method naturally supports object editing by manipulating the layout prior as shown in Fig. 1. Various applications are shown in Sec. 4.3. In particular, ray marching at a small resolution (64) may cause aliasing especially when moving the objects. We adopt supersampling anti-aliasing (SSAA) [43] to perform ray marching at a temporary higher resolution (128) and downsample the feature map to the original resolution before the upsampler. This strategy is used only for object synthesis, and we do not change the background resolution during inference." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.793, + 0.209, + 0.809 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.818, + 0.175, + 0.833 + ], + "angle": 0, + "content": "4.1. Settings" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Datasets. We evaluate DisCoScene on three multi-object scene datasets, including CLEVR [21], 3D-FRONT [10, 11], and WAYMO [48]. CLEVR is a diagnostic multi-object dataset. We use the official script [21] to render scenes" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.333 + ], + "angle": 0, + "content": "with 2 and random primitives. Our CLEVR dataset consists of \\(80K\\) samples in \\(256 \\times 256\\) resolution. 3D-FRONT is an indoor scene dataset, containing a collection of \\(6.8K\\) houses with \\(140K\\) rooms. We obtain \\(4K\\) bedrooms after filtering out rooms with uncommon arrangements or unnatural sizes and use BlenderProc to render 20 images per room from random camera positions, resulting in a total of \\(80K\\) images. WAYMO is a large-scale autonomous driving dataset with \\(1K\\) video sequences of outdoor scenes. Six images are provided for each frame, and we only keep the front view. We also apply heuristic rules to filter out small and noisy cars and collect a subset of \\(70K\\) images. Because the width is always larger than height on WAYMO, we adopt the black padding to make images square, similar with StyleGAN2 [25]. More details about data preprocessing and rendering are included in Supplementary Materials." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.335, + 0.892, + 0.439 + ], + "angle": 0, + "content": "Baselines. We compare with both 2D and 3D GANs. For 2D, we compare with StyleGAN2 [25] on image quality. As for 3D, we compare with EpiGRAF [46], VolumeGAN [60], and EG-3D [4] on object generation, and GIRAFFE [32], GSN [8] on scene generation. We use the baseline models either released along with their papers or official implementations to train on our data." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.441, + 0.892, + 0.729 + ], + "angle": 0, + "content": "Implementation Details. We use the same architecture and parameters of the mapping network from StyleGAN2 [25]. For object generator \\( \\mathrm{G_{obj}(\\cdot)} \\) and background generator \\( \\mathrm{G_{bg}(\\cdot)} \\), we use 8 and 4 Modulated Fully-Connected layers (ModFCs) with 256 and 128 channels, respectively. Ray casting is performed on \\( 64 \\times 64 \\) and the feature map is rendered to image with neural renderer. The progressive training strategy from PG-GAN [22] is adopted for better image quality and multi-view consistency. Discriminators \\( \\mathrm{D}_s(\\cdot) \\) and \\( \\mathrm{D_{obj}(\\cdot)} \\) both share the similar architecture of StyleGAN2 but with only half channels. Practically, the resolution of \\( \\mathrm{D_{obj}(\\cdot)} \\) is always 1/2 on WAYMO or 1/4 on CLEVR and 3D-FRONT of \\( \\mathrm{D}_s(\\cdot) \\). All our models are trained on \\( 8 \\times \\) V100/A100 GPUs with a batch size of 64. \\( \\lambda_1 \\) is set to 1 to balance object and scene discriminators. \\( \\lambda_2 \\) and \\( \\lambda_3 \\) are set to 1 to maintain training stability. Unless specified, other hyperparameters are same as StyleGAN2. More details about network architecture and training can be found in Supplementary Materials." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.741, + 0.638, + 0.755 + ], + "angle": 0, + "content": "4.2. Main Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Qualitative Comparison. Fig. 2 presents the synthesized images in a resolution of \\(256 \\times 256\\) of our method and baselines on all the datasets. We compare our method on explicit camera control and object editing with baselines. EG3D, with a single radiance field, can manipulate the global camera of the synthesized images. As for EG3D, although it converges on the datasets, the object fidelity are lower than our method. On CLEVR with a narrow camera distribution, the results of EG3D are inconsistent. In the" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "4406" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.12, + 0.089, + 0.852, + 0.351 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.354, + 0.892, + 0.381 + ], + "angle": 0, + "content": "Figure 2. Qualitative comparison between DisCoScene and baselines. Explicit camera rotation is evaluated on CLEVR and 3D-FRONT. Object rotation (left) and object translation (right) are evaluated on WAYMO. All images are in \\(256 \\times 256\\) resolution." + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.386, + 0.893, + 0.429 + ], + "angle": 0, + "content": "Table 2. Quantitative comparisons on different datasets. FID, KID \\((\\times 10^{3})\\) are reported as the evaluation metrics. TR. and INF. denote training and inference costs, evaluated in V100 days and ms/image (single V100 over \\(1K\\) samples), respectively. Note that we highlight the best results among 3D-aware models." + }, + { + "type": "table", + "bbox": [ + 0.134, + 0.43, + 0.833, + 0.607 + ], + "angle": 0, + "content": "
ModelCLEVR3D-FRONTWAYMO
FID ↓KID ↓TR. ↓INF. ↓FID ↓KID ↓FID ↓KID ↓
StyleGAN2 [25]4.53.013.34412.54.315.18.3
EpiGRAF [46]10.48.316.0114107.2102.327.026.1
VolumeGAN [60]7.55.115.29052.738.729.918.2
EG3D [4]4.112.725.85519.713.526.045.4
GIRAFFE [32]78.561.55.26256.546.8175.7212.1
GSN [8]----130.787.5--
DisCoScene3.52.118.19513.87.416.08.4
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.624, + 0.471, + 0.866 + ], + "angle": 0, + "content": "first example, the color of the cylinder changes from gray to green across different views. Meanwhile, our method learns better 3D structure of the objects and achieves better camera control. On the challenging WAYMO dataset, it is difficult to encode huge street scenes within a single generator, thus we train GIRAFFE and our DisCoScene in the camera space to evaluate object editing. GIRAFFE struggles to generate realistic results and, while manipulating objects, their geometry and appearance are not preserved well. Our approach is capable of handling these complicated scenarios with good variations. Wherever the object is placed and regardless of how the rotation is carried out, the synthesized objects are substantially better and more consistent than GIRAFFE. It demonstrates the effectiveness of our spatially disentangle radiance fields built upon the layout prior. More comparisons are included in Supplementary Materials." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Quantitative Comparison. Tab. 2 reports the quantitative metrics on the quality of results, including FID [18] and" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.624, + 0.892, + 0.837 + ], + "angle": 0, + "content": "KID [3]. All metrics are calculated between \\(50K\\) generated samples and all real images. DisCoScene consistently outperforms baselines with significant improvement on all datasets. Besides, training cost in V100 days and testing cost in ms/image (on a single V100 over \\(1K\\) samples) are also included to reflect the efficiency of our model. Note that the inference cost of 3D-aware models is evaluated on generating radiance fields rather than images. In such a case, EG3D and EpiGRAF are not fast as excepted due to the heavy computation on tri-planes. With comparable training and testing cost, it even achieves similar level of image quality with state-of-the-art 2D GAN baselines, e.g., StyleGAN2 [25], while allowing for explicit camera control and object editing that are otherwise challenging." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.847, + 0.773, + 0.862 + ], + "angle": 0, + "content": "4.3. Controllable Scene Generation" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.893, + 0.901 + ], + "angle": 0, + "content": "The layout prior in our model enables versatile user controls of scene objects. In what follows, we evaluate the" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4407" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.089, + 0.895, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.263, + 0.895, + 0.293 + ], + "angle": 0, + "content": "Figure 3. Controllable scene synthesis in \\(256 \\times 256\\) resolution. We perform versatile user control of the global camera and scene objects, such as rearrangement, removal, insertion, and restyling. Editings are performed on the original generations (the left one of each row)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.305, + 0.47, + 0.366 + ], + "angle": 0, + "content": "flexibility and effectiveness of our model through various 3D manipulation applications in different datasets. Examples are shown in Fig. 3 and more results can be found in Supplementary Materials." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.366, + 0.471, + 0.64 + ], + "angle": 0, + "content": "Rearranging Objects. We can transform bounding boxes B to rearrange (rotation and translation) the objects in the scenes without affecting their appearance. Transforming shapes in CLEVR, furniture in 3D-FRONT, and cars in WAYMO all show consistent results. In particular, rotating symmetric shapes (i.e., spheres and cylinders) in CLEVR shows little changes, suggesting desired multi-view consistency. Our model can properly handle mutual occlusion. Take the blue cube from CLEVR as example (1-st row of Fig. 3), our model can produce new occlusions between it and the grey cylinder and generate high-quality renderings. Removing and Cloning Objects. Users can update the layout by removing or cloning bounding boxes. Our method seamlessly removes objects with the background inpainted realistically, even without training on any pure background, including the challenging dataset of WAYMO (3-rd row of Fig. 3). Object cloning is also naturally supported, by copying and pasting a box to a new location in the layout." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.64, + 0.47, + 0.837 + ], + "angle": 0, + "content": "Restyling Objects. Although appearance and shape are not explicitly modeled by the latent code, we can reuse the encoded hierarchical knowledge to perform object restyling. Like [15, 42, 61], we arbitrarily sample latent codes and perform style-mixing on different layers to achieve independent control over appearance and shape. Fig. 3 presents the restyling results on certain objects, i.e., the front cylinder in CLEVR, the bed in 3D-FRONT, and the left car in WAYMO. Camera Movement. Explicit camera control is also permitted. Even for CLEVR that is trained on very limited camera ranges, we can rotate the camera up to an extreme side view. Our model also produces consistent results when rotating the camera on 3D-FRONT (2-nd row of Fig. 3)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.847, + 0.231, + 0.864 + ], + "angle": 0, + "content": "4.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.471, + 0.9 + ], + "angle": 0, + "content": "We ablate main components of our approach to better understand their individual contributions. In addition to the" + }, + { + "type": "table_caption", + "bbox": [ + 0.522, + 0.304, + 0.871, + 0.318 + ], + "angle": 0, + "content": "Table 3. Ablation analysis of object discriminator \\( \\left( {\\mathrm{D}}_{\\mathrm{{obj}}}\\right) \\) ." + }, + { + "type": "table", + "bbox": [ + 0.511, + 0.32, + 0.88, + 0.412 + ], + "angle": 0, + "content": "
CLEVR3D-FRONTWAYMO
FIDw/o Dobj5.018.619.5
w/ Dobj3.513.816.0
FIDobjw/o Dobj19.133.795.1
w/ Dobj5.619.516.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.524, + 0.416, + 0.868, + 0.43 + ], + "angle": 0, + "content": "Table 4. Ablation analysis of spatial condition (S-Cond)." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.432, + 0.889, + 0.488 + ], + "angle": 0, + "content": "
FIDFIDobj
w/ S-Condw/o S-Condw/ S-Condw/o S-Cond
3D-FRONT13.815.219.523.2
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.505, + 0.892, + 0.581 + ], + "angle": 0, + "content": "FID score that measures the quality of the entire image, we also provide another metric \\(\\mathrm{FID}_{\\mathrm{obj}}\\) to measure the quality of individual objects. Specifically, we use the projected 2D boxes to crop objects from the synthesized images and then perform FID evaluation against the ones from real images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.582, + 0.893, + 0.854 + ], + "angle": 0, + "content": "Object Discriminator. The object discriminator \\( \\mathrm{D_{obj}} \\) plays a crucial role in synthesizing realistic objects, as evaluated in Tab. 3. Obviously, the object fidelity is significantly improved across all datasets with \\( \\mathrm{D_{obj}} \\). Also, the quality of the whole scene generation is improved as well, contributed by better objects. Fig. 5 visually shows that our method can successfully disentangle objects from the background with the help of object discriminator. Although the baseline model is able to disentangle objects on 3D-FRONT from simple background to certain extent, the background suffers from the entanglement with objects, resulting in obvious artifacts as well as illogical layout. On more challenging datasets like WAYMO, the complex backgrounds make the disentanglement even more difficult, so that the background model easily overfits the whole scene as a single radiance field. Thanks to the object discriminator, our full model benefits from object supervision, leading to better disentanglement, even without seeing a pure background image." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.894, + 0.9 + ], + "angle": 0, + "content": "Spatial Condition. To analyze how spatial condition (S-Cond) affects the quality of generation, we compare results with models trained with and without S-Cond on 3D-" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4408" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.075, + 0.09, + 0.353, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.156, + 0.197, + 0.265, + 0.208 + ], + "angle": 0, + "content": "(a) Spatial condition" + }, + { + "type": "image", + "bbox": [ + 0.353, + 0.089, + 0.613, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.395, + 0.197, + 0.562, + 0.208 + ], + "angle": 0, + "content": "(b) Supersampling anti-aliasing" + }, + { + "type": "image", + "bbox": [ + 0.613, + 0.091, + 0.888, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.71, + 0.197, + 0.786, + 0.208 + ], + "angle": 0, + "content": "(c) Upsampler" + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.209, + 0.89, + 0.223 + ], + "angle": 0, + "content": "Figure 4. Qualitative comparison for ablations on spatial condition (S-Cond), supersampling anti-alising (SSAA), and upsampler (Up.)." + }, + { + "type": "image", + "bbox": [ + 0.078, + 0.228, + 0.468, + 0.314 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.319, + 0.468, + 0.361 + ], + "angle": 0, + "content": "Figure 5. Ablation on scene disentanglement. We independently infer objects and background to show the quality of scene disentanglement with regard to object discriminator \\( \\mathrm{D}_{\\mathrm{obj}} \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.371, + 0.468, + 0.567 + ], + "angle": 0, + "content": "FRONT (Fig. 4a). For example, our full model consistently infers beds at the center of rooms, while the baseline predicts random items like tables or nightstands that rarely appear in the middle of bedrooms. These results demonstrate that spatial condition can assist the generator with appropriate semantics from simple layout priors. Note that this correlation between spatial configurations and object semantics is automatically emerged without any supervision. We also numerically compare the image quality on these two models in Tab. 4, which shows that S-Cond also achieves better image quality at both scene- and object-level, because more proper semantics are more in line with the native distribution of real images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.568, + 0.468, + 0.734 + ], + "angle": 0, + "content": "Supersampling Anti-Aliasing. We adopt a simple supersampling (SSAA) strategy to reduce edge aliasing by sampling more points during inference (Sec. 3.5). Thanks to our efficient object point sampling, doubling the resolution of foreground points keeps a similar inference speed (105 ms/image), comparable with original speed (95 ms/image). Results with different sampling points are shown in Fig. 4b. Taking the right boundary of the cabinet as an example (see the zoom-in insets for better visualization), when the cabinet is moved, SSAA achieves more consistent boundary compared with the jaggy one in the baseline." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Neural Renderer for Shadow. We adopt the StyleGAN2-like neural renderer to boost the rendering efficiency (Sec. 3.3). Besides the low computational cost, the added capacity of the neural renderer also brings better implicit modeling of realistic lighting effects such as shadowing. Therefore, without handling the shadowing effect in our rendering pipeline, our model can still synthesize high-quality shaodws on datasets such as CLEVR (Fig. 4c). This is because the large receptive field brought by \\(3 \\times 3\\) convolutions and upsampler blocks make the neural renderer be aware of the object locations and progressively add shadows" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.228, + 0.892, + 0.345 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.56, + 0.352, + 0.831, + 0.366 + ], + "angle": 0, + "content": "Figure 6. Real image inversion and editing." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.377, + 0.89, + 0.391 + ], + "angle": 0, + "content": "to the low resolution features rendered from radiance fields." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.405, + 0.748, + 0.42 + ], + "angle": 0, + "content": "5. Discussion and Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.431, + 0.892, + 0.552 + ], + "angle": 0, + "content": "Real Image Editing. Fig. 6 shows that it is possible to embed a real image into the latent space of our pretrained model using pivotal tuning inversion (PTI) [39]. Besides reconstruction, all object manipulation operations are supported to edit the image. As one of the very first steps towards 3D scene editing from a single image, we believe that our method proves a promising venue and can inspire future research efforts along this direction." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.557, + 0.892, + 0.753 + ], + "angle": 0, + "content": "Limitations and Future Work. Our model requires the abstract layout prior as the input. For in-the-wild datasets, we need monocular 3D object detector [54] to infer pseudo layouts. While existing approaches attempt to learn the layout in an end-to-end manner, they struggle to generalize to complex scenes consisting of multiple objects. So it would be interesting to explore 3D layout estimation for complex scenes and combine with our approach end-to-end. Also, although our work shows significant improvement over existing 3D-aware scene generators, it is still challenging to learn on the street scenes in the global space due to the limited model capacity. Large-scale NeRFs [51, 57] might be one potent solution." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.757, + 0.892, + 0.848 + ], + "angle": 0, + "content": "Conclusion. This work presents DisCoScene, a method for controllable 3D-aware scene synthesis on challenging datasets. By taking spatially disentangled radiance fields as the representation based on a very abstract layout prior, our method is able to generate high-fidelity scene images and allows for versatile object-level editing." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Acknowledgements. We thank Jiatao Gu, Willi Menapace, Jian Ren, Panos Achlioptas, Tai Wang, and Zian Wang for fruitful discussions and comments about this work." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4409" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.184 + ], + "angle": 0, + "content": "[1] Jonathan T Barron, Ben Mildenhall, Matthew Tancik, Peter Hedman, Ricardo Martin-Brualla, and Pratul P Srinivasan. Mip-nerf: A multiscale representation for anti-aliasing neural radiance fields. In Int. Conf. Comput. 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Syst., 2018. 2" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.093, + 0.468, + 0.658 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "4412" + } + ] +] \ No newline at end of file diff --git a/2023/DisCoScene_ Spatially Disentangled Generative Radiance Fields for Controllable 3D-Aware Scene Synthesis/bdaa5712-8b26-43d5-9ca1-465a14b26701_origin.pdf b/2023/DisCoScene_ Spatially Disentangled Generative Radiance Fields for Controllable 3D-Aware Scene Synthesis/bdaa5712-8b26-43d5-9ca1-465a14b26701_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..28cdad3b46bcef0c806cfc7f1a3645f8ffce321a --- /dev/null +++ b/2023/DisCoScene_ Spatially Disentangled Generative Radiance Fields for Controllable 3D-Aware Scene Synthesis/bdaa5712-8b26-43d5-9ca1-465a14b26701_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:c8b3407aa3ae254ed06e2f94dbbd758518fbe9e25ec0859fcb4b0dcd2727e6ab +size 4593788 diff --git a/2023/DisCoScene_ Spatially Disentangled Generative Radiance Fields for Controllable 3D-Aware Scene Synthesis/full.md b/2023/DisCoScene_ Spatially Disentangled Generative Radiance Fields for Controllable 3D-Aware Scene Synthesis/full.md new file mode 100644 index 0000000000000000000000000000000000000000..a37b1158683643070930e848d283e41a529ea565 --- /dev/null +++ b/2023/DisCoScene_ Spatially Disentangled Generative Radiance Fields for Controllable 3D-Aware Scene Synthesis/full.md @@ -0,0 +1,318 @@ +# DisCoScene: Spatially Disentangled Generative Radiance Fields for Controllable 3D-aware Scene Synthesis + +Yinghao Xu $^{1,2*}$ Mengei Chai $^{2\dagger}$ Zifan Shi $^{3}$ Sida Peng $^{4}$ Ivan Skorokhodov $^{5,2*}$ Aliaksandr Siarohin $^{2}$ Ceyuan Yang $^{1}$ Yujun Shen $^{1}$ Hsin-Ying Lee $^{2}$ Bolei Zhou $^{6}$ Sergey Tulyakov $^{2}$ $^{1}\mathrm{CUHK}$ $^{2}\mathrm{SnapInc.}$ $^{3}\mathrm{HKUST}$ $^{4}\mathrm{ZJU}$ $^{5}\mathrm{KAUST}$ $^{6}\mathrm{UCLA}$ + +# Abstract + +Existing 3D-aware image synthesis approaches mainly focus on generating a single canonical object and show limited capacity in composing a complex scene containing a variety of objects. This work presents DisCoScene: a 3D-aware generative model for high-quality and controllable scene synthesis. The key ingredient of our method is a very abstract object-level representation (i.e., 3D bounding boxes without semantic annotation) as the scene layout prior, which is simple to obtain, general to describe various scene contents, and yet informative to disentangle objects and background. Moreover, it serves as an intuitive user control for scene editing. Based on such a prior, the proposed model spatially disentangles the whole scene into object-centric generative radiance fields by learning on only 2D images with the global-local discrimination. Our model obtains the generation fidelity and editing flexibility of individual objects while being able to efficiently compose objects and the background into a complete scene. We demonstrate state-of-the-art performance on many scene datasets, including the challenging Waymo outdoor dataset. Project page can be found here. + +# 1. Introduction + +3D-consistent image synthesis from single-view 2D data has become a trendy topic in generative modeling. Recent approaches like GRAF [40] and Pi-GAN [5] introduce 3D inductive bias by taking neural radiance fields [1, 28, 29, 36, 38] as the underlying representation, gaining the capability of geometry modeling and explicit camera control. Despite their success in synthesizing individual objects (e.g., faces, cats, cars), they struggle on scene images that contain multiple objects with non-trivial layouts and complex backgrounds. The varying quantity and large + +diversity of objects, along with the intricate spatial arrangement and mutual occlusions, bring enormous challenges, which exceed the capacity of the object-level generative models [4, 13, 15, 33, 45, 46, 60]. + +Recent efforts have been made towards 3D-aware scene synthesis. Despite the encouraging progress, there are still fundamental drawbacks. For example, Generative Scene Networks (GSN) [8] achieve large-scale scene synthesis by representing the scene as a grid of local radiance fields and training on 2D observations from continuous camera paths. However, object-level editing is not feasible due to spatial entanglement and the lack of explicit object definition. On the contrary, GIRAFFE [32] explicitly composites object-centric radiance fields [16, 34, 56, 63] to support object-level control. Yet, it works poorly on challenging datasets containing multiple objects and complex backgrounds due to the absence of proper spatial priors. + +To achieve high-quality and controllable scene synthesis, the scene representation stands out as one critical design focus. A well-structured scene representation can scale up the generation capability and tackle the aforementioned challenges. Imagine, given an empty apartment and a furniture catalog, what does it take for a person to arrange the space? Would people prefer to walk around and throw things here and there, or instead figure out an overall layout and then attend to each location for the detailed selection? Obviously, a layout describing the arrangement of each furniture in the space substantially eases the scene composition process [17, 26, 58]. From this vantage point, here comes our primary motivation — an abstract object-oriented scene representation, namely a layout prior, could facilitate learning from challenging 2D data as a lightweight supervision signal during training and allow user interaction during inference. More specifically, to make such a prior easy to obtain and generalizable across different scenes, we define it as a set of object bounding boxes without semantic annotation, which describes the spatial composition of objects in the scene and supports intuitive object-level editing. + +In this work, we present DisCoScene, a novel 3D-aware generative model for complex scenes. Our method allows for high-quality scene synthesis on challenging datasets and flexible user control of both the camera and scene objects. Driven by the aforementioned layout prior, our model spatially disentangles the scene into composable radiance fields which are shared in the same object-centric generative model. To make the best use of the prior as a lightweight supervision during training, we propose global-local discrimination which attends to both the whole scene and individual objects to enforce spatial disentanglement between objects and against the background. Once the model is trained, users can generate and edit a scene by explicitly controlling the camera and the layout of objects' bounding boxes. In addition, we develop an efficient rendering pipeline tailored for the spatially-disentangled radiance fields, which significantly accelerates object rendering and scene composition for both training and inference stages. + +Our method is evaluated on diverse datasets, including both indoor and outdoor scenes. Qualitative and quantitative results demonstrate that, compared to existing baselines, our method achieves state-of-the-art performance in terms of both generation quality and editing capability. Tab. 1 compares DisCoScene with relevant works. it is worth noting that, to the best of our knowledge, DisCoScene stands as the first method that achieves high-quality 3D-aware generation on challenging datasets like WAYMO [48], while enabling interactive object manipulation. + +# 2. Related Work + +3D-aware Image Synthesis. Generative Adversarial Networks (GANs) have achieved remarkable success in 2D image synthesis [14, 22-25], and have recently been extended to 3D-aware image generation. VON [68] and HoloGAN [30] introduce voxel representations to the generator and use neural rendering to project 3D voxels into 2D space. Then, GRAF [40] and Pi-GAN [5] propose to use implicit functions to learn NeRF from single-view image collections, resulting in better multi-view consistency compared to voxel-based methods. GOF [59], ShadeGAN [35], and GRAM [7] introduce occupancy field, albedo field and radiance surface instead of radiance field to learn better 3D shapes. However, high-resolution image synthesis with direct volumetric rendering is usually expensive. Many works [4, 15, 32, 33, 45, 60, 62] resort to convolutional upsamplers to improve the rendering resolution and quality with lower computation overhead. While some other works [41,46] adopt patch-based sampling and sparse-voxel to speed up training and inference. Note that most of these methods are restricted to well-aligned objects and fail on more complex, multi-object scene imagery. Our work instead naturally handles multi-object scenes with spatial disentangled object-level radiance fields, which can + +Table 1. Comparison of DisCoScene and relevant works. Multiple Objects: Ability to model multiple objects in a scene. Radiance Field: If radiance fields are used to model scenes. Complex Scene: Ability to handle complex datasets beyond diagnostic scenes. Object Editing: If object-level editing is supported. No Camera Sequence: Not requiring ground truth camera sequences. + +
ModelMultiple ObjectsRadiance FieldComplex SceneObject EditingNo Camera Sequence
GRAF [40]X✓X✓✓
BlockGAN [30]✓XX✓✓
GSN [8]✓✓✓XX
GIRAFFE [32]✓✓X✓✓
DisCoScene✓✓✓✓✓
+ +be scaled to very challenging real-world scene datasets. + +Scene Generation. Scene generation has been a longstanding task. Early works like [52] attempt to model a complex scene by trying to generate it. Recently, with the successes in generative models, scene generation has been advanced significantly. Among them, one popular line is to resort to the setups of image-to-image translation from given conditions, i.e., semantic masks [19,37,49,50,55,67], object-attribute graph [2]. Although able to synthesize photorealistic scene images, they struggle to manipulate the objects in 3D space due to the lack of 3D understanding. Some works [9, 53, 64, 65] reuse the knowledge from 2D GAN models to achieve scene manipulation like the camera pose. But they suffer from poor multi-view consistency due to inadequate geometry modeling. Another active line of work [9, 31, 32, 64] explores adding 3D inductive biases to the scene representation. BlockGAN [31] and GIRAFFE [32] introduce compositional voxels and radiance fields to encode the object structures, but their object control can only be performed at simple diagnostic scenes. DepthGAN [44] introduces depth as a 3D prior but is hard to achieve manipulation and multi-view consistency. GSN [8] proposes to represent a scene with a grid of local radiance fields. However, since this local radiance field does not properly link to the object semantics, individual objects cannot be manipulated with versatile user control. Our work proposes to use an abstract layout prior to spatially disentangle the whole scene into object-centric radiance fields, which enables 3D-aware image synthesis on challenging real-world imagery like WAYMO [48]. + +# 3. Method + +The overall framework is illustrated in Fig. 1. We employ layout as an explicit prior to disentangle objects in our approach (Sec. 3.1). Based on the layout prior, we introduce our spatially disentangled radiance fields (Sec. 3.2) and an efficient rendering pipeline (Sec. 3.3) to achieve controllable 3D-aware scene generation. We also describe our global-local discrimination, which makes training on challenging datasets possible (Sec. 3.4). Finally, we discuss + +![](images/517a558f6f588da66d4f3bcccb751dcde87f157260ea76c97fcee7360fc1a4d9.jpg) +Figure 1. The overall pipeline of DisCoScene. Conditioned by the layout prior, our spatial disentangle generative radiance fields generate individual objects and the background. Our efficient neural rendering pipeline then composites the scene to a low-resolution feature map with the volume renderer and upsamples to the final high-resolution image with the upsampler. During training, we propose global-local discrimination which applies the scene discriminator to the entire image and the object discriminator to cropped object patches. During inference, users can manipulate the layout to control the generation of a specific scene at the object level. + +our model's training and inference details on 2D image collections (Sec. 3.5). + +# 3.1. Abstract Layout Prior + +There exist many representations of a scene, including the popular choice of scene graph [6, 20, 34, 47], where objects and their relations are denoted as nodes and edges. Although graph can describe a scene in rich details, its structure is hard to process and the annotation is laborious to obtain in our case. Therefore, we opt to represent the scene layout in a much-simplified manner - a set of bounding boxes $\mathcal{B} = \{\mathbf{B}_i | i \in [1, N]\}$ without category annotation, where $N$ counts objects in the scene. Concretely, each bounding box is defined with 9 parameters, including rotation $a_i$ , translation $t_i$ , and scale $s_i$ . + +$$ +\mathbf {B} _ {i} = \left[ \boldsymbol {a} _ {i}, \boldsymbol {t} _ {i}, \boldsymbol {s} _ {i} \right], \tag {1} +$$ + +$$ +\boldsymbol {a} _ {i} = \left[ a _ {x}, a _ {y}, a _ {z} \right], \boldsymbol {t} _ {i} = \left[ t _ {x}, t _ {y}, t _ {z} \right], \boldsymbol {s} _ {i} = \left[ s _ {x}, s _ {y}, s _ {z} \right], \tag {2} +$$ + +where $\mathbf{a}_i$ comprises 3 Euler angles, which are easier to convert into rotation matrix $\mathbf{R}_i$ . Using this notation, the bounding box $\mathbf{B}_i$ can be transformed from a canonical bounding box $\mathbf{C}$ , i.e., a unit cube at the coordinate origin: + +$$ +\mathbf {B} _ {i} = \mathrm {b} _ {i} (\mathbf {C}) = \mathbf {R} _ {i} \cdot \operatorname {d i a g} \left(\boldsymbol {s} _ {i}\right) \cdot \mathbf {C} + \boldsymbol {t} _ {i}, \tag {3} +$$ + +where $\mathbf{b}_i$ stands for the transformation of $\mathbf{B}_i$ and $\mathrm{diag}(\cdot)$ yields a diagonal matrix with the elements of $s_i$ . Our abstract layout is more friendly to collect and easier to edit, allowing for versatile interactive user control. + +# 3.2. Spatially Disentangled Radiance Fields + +Object Representation. Neural radiance field (NeRF) [29] $\mathrm{F}(\pmb{x},\pmb{v})\rightarrow (\pmb{c},\sigma)$ regresses color $\pmb {c}\in \mathbb{R}^3$ and volume density $\sigma \in \mathbb{R}$ from coordinate $\pmb {x}\in \mathbb{R}^3$ and viewing direction $\pmb {v}\in \mathbb{S}^2$ , parameterized with multi-layer perceptron (MLP) + +networks. Recent attempts propose to condition NeRF with a latent code $z$ , resulting in their generative forms [5, 40], $\mathrm{G}(\pmb{x},\pmb{v},\pmb{z})\rightarrow (c,\sigma)$ , to achieve 3D-aware object synthesis. + +Since we use the layout as an internal representation, it naturally disentangles the whole scene into several objects. We can leverage multiple individual generative NeRFs to model different objects, but it can easily lead to an overwhelmingly large number of models and poor training efficiency. To alleviate this issue, we propose to infer generative object radiance field in the canonical space [32, 34], to allow weight sharing among objects: + +$$ +\left(\boldsymbol {c} _ {i}, \sigma_ {i}\right) = \operatorname {G} _ {\mathrm {o b j}} \left(\mathrm {b} _ {i} ^ {- 1} (\gamma (\boldsymbol {x})), \boldsymbol {z} _ {i}\right), \tag {4} +$$ + +where $\gamma (\cdot)$ is the position encoding function that transforms input into Fourier features. The object generator $\mathrm{G_{obj}}(\cdot)$ infers each object independently, resulting in spatially disentangled generative radiance fields. Note that $\mathrm{G_{obj}}(\cdot)$ is not conditioned on the viewing direction $\mathcal{V}$ because the upsampler of our neural renderer can learn the view-dependent effects similar to previous works [4, 15, 60] (Sec. 3.3). + +Spatial Condition. Although object bounding boxes are used as a prior, their latents are still randomly sampled regardless of their spatial configuration, leading to illogical arrangements. To synthesize scene images and infer object radiance fields with proper semantics, we adopt the location and scale of each object as a condition for the generator to encode more consistent intrinsic properties, i.e., shape and category. To this end, we simply modify Eq. (4) by concatenating the latent code with the Fourier features of object location and scale: + +$$ +(\boldsymbol {c}, \sigma) = \operatorname {G} _ {\mathrm {o b j}} \left(\mathrm {b} _ {i} ^ {- 1} (\gamma (\boldsymbol {x}))\right), \operatorname {c o n c a t} \left(\boldsymbol {z} _ {i}, \gamma \left(\boldsymbol {t} _ {i}\right), \gamma \left(\boldsymbol {s} _ {i}\right)\right). \tag {5} +$$ + +Therefore, semantic clues are injected into the layout in an unsupervised manner, without explicit category annotation. + +Background Representation. Unlike objects, the background radiance field is only evaluated in the global space. Considering that the background encodes lots of high-frequency signals, we include the viewing direction $\pmb{v}$ to help background generator $\mathrm{G_{bg}}(\cdot)$ to be able to learn such details. The background generation can be formulated as: + +$$ +\left(\boldsymbol {c} _ {\mathrm {b g}}, \sigma_ {\mathrm {b g}}\right) = \mathrm {G} _ {\mathrm {b g}} (\boldsymbol {x}, \boldsymbol {v}, \boldsymbol {z} _ {\mathrm {b g}}). \tag {6} +$$ + +# 3.3. Efficient Rendering Pipeline + +As aforementioned, we use spatial-disentangled radiance fields to represent scenes. However, naive point sampling solutions can lead to prohibitive computational overhead when rendering multiple radiance fields. Considering the independence of objects' radiance fields, we can achieve much more efficient rendering by only focusing on the valid points within the bounding boxes. + +Ray-Box Intersection in Canonical Space. Similar to NeRF [29], we use the pinhole camera model to perform ray casting. For each object, the points on the rays can be sampled at adaptive depths rather than fixed ones since the bounding box provides clues about where the object locates. Specifically, the cast rays $\mathcal{R} = \{\mathbf{r}_j|j\in [1,\mathrm{S}^2 ]\}$ in a resolution S are transformed into the canonical object coordinate system. Then, Ray-AABB [27] (axis-aligned bounding box) intersection algorithm is applied to calculate the adaptive near and far depth $(d_{j,l,n},d_{j,l,f})$ of the intersected segment between the ray $\mathbf{r}_j$ and the $l$ -th box $\mathbf{B}_l$ . After that, $\mathrm{N_d}$ points are sampled equidistantly in the interval $[d_{j,l,n},d_{j,l,f}]$ . It is worth noting that we maintain an intersection matrix $\mathbf{M}$ of size $\mathbf{N}\times \mathbf{S}^2$ , whose elements indicate if this ray intersects with the box. With $\mathbf{M}$ , we select only valid points to infer, which can greatly reduce the rendering cost. + +Background Point Sampling. We adopt different background sampling strategies depending on the dataset. In general, we do fixed depth sampling for bounded backgrounds in indoor scenes and inherit the inverse parametrization of $\mathrm{NeRF}++$ [66] for complex and unbounded outdoor scenes, which uniformly samples background points in an inverse depth range. More details can be founded in the Supplementary Materials. + +Composition and Volume Rendering. In our approach, objects are always assumed to be in front of the background. So objects and background can be rendered independently first and composited thereafter. For a ray $\mathbf{r}_j$ intersecting with $n_j$ ( $n_j \geq 1$ ) boxes, its sample points $\mathcal{X}_j = \{\pmb{x}_{j,k} | k \in [1, n_j \mathrm{N}_d]\}$ can be easily obtained from the depth range and the intersection matrix $\mathbf{M}$ . Since rendering should consider inter-object occlusions, we sort the points $\mathcal{X}$ by depth, resulting in an ordered point set $\mathcal{X}_j^s = \{\pmb{x}_{j,s_k} | s_k \in [1, n_j \mathrm{N}_d], d_{j,s_k} \leq d_{j,s_{k+1}}\}$ , where $d_{j,s_k}$ denotes the depth of point $\pmb{x}_{j,s_k}$ . With color $\pmb{c}(\pmb{x}_{j,s_k})$ and density $\sigma(\pmb{x}_{j,s_k})$ + +of the ordered set inferred with $\mathrm{G_{obj}}(\cdot)$ by Eq. (5), the corresponding pixel $\mathbf{f}(\mathbf{r}_j)$ is calculated as: + +$$ +\mathbf {f} (\mathbf {r} _ {j}) = \sum_ {k = 1} ^ {n _ {j} \mathrm {N} _ {d}} T _ {j, k} \alpha_ {j, k} \boldsymbol {c} \left(\boldsymbol {x} _ {j, s _ {k}}\right), \tag {7} +$$ + +$$ +T _ {j, k} = \exp \left(- \sum_ {o = 1} ^ {k - 1} \sigma \left(\boldsymbol {x} _ {j, s _ {k}}\right) \delta_ {j, s _ {o}}\right), \tag {8} +$$ + +$$ +\alpha_ {j, k} = 1 - \exp (- \sigma \left(\boldsymbol {x} _ {j, s _ {k}}\right) \delta_ {j, s _ {k}}). \tag {9} +$$ + +For any ray that does not intersect with boxes, its color and density are set to 0 and $-\infty$ , respectively. So that the foreground object map $\mathbf{F}$ can be formulated as: + +$$ +\mathbf {F} _ {j} = \left\{ \begin{array}{l l} \mathbf {f} \left(\mathbf {r} _ {j}\right), & \text {i f} \exists m \in \mathbf {M} _ {:, j}, m \text {i s t r u e ,} \\ 0, & \text {e l s e .} \end{array} \right. \tag {10} +$$ + +Since the background points are sampled at a fixed depth, we can directly adopt Eq. (6) to evaluate background points in the global space without sorting. And the background map $\mathbf{N}$ can also be obtained by volume rendering similar to Eq. (7). Finally, $\mathbf{F}$ and $\mathbf{N}$ are alpha-blended into the final image $\mathbf{I}_n$ with alpha extracted from Eq. (9): + +$$ +\mathbf {I} _ {\mathrm {n}} = \mathbf {F} + \prod_ {k = 1} ^ {n _ {j} \mathrm {N} _ {d}} (1 - \alpha_ {j, k}) \odot \mathbf {N}. \tag {11} +$$ + +Although our rendering pipeline efficiently composites multiple radiance fields, it still suffers from slow performance when rendering high-resolution images. To mitigate this issue, we render a high-dimensional feature map instead of a 3-channel color in a smaller resolution, followed by a StyleGAN2-like architecture that upsamples the feature map to the target resolution. + +# 3.4. Local & Global Discrimination + +Like other GAN-based approaches, discriminators play a crucial role in training. Previous attempts for 3D-aware scene synthesis [8,32] only adopt scene-level discriminators to critique between rendered scenes and real captures. However, such a scene discriminator pays more attention to the global coherence of the whole scene, weakening the supervision for individual objects. Given that each object, especially those far from the camera, occupies a small portion of the rendered frame, the scene discriminator provides weak learning signal to its radiance field, leading to inadequate training and poor object quality. Besides, the scene discriminator shows only minimal capability in disentangling objects and background, allowing the background generator $\mathrm{G_{bg}}$ to overfit the whole scene easily. + +Similar to [12], we propose to add an extra object discriminator for local discrimination, leading to better object-level supervision. Sepcifically, with the 3D layout $\mathbf{B}_i$ spatially disentangling different objects, we project them into + +2D space as $\mathbf{B}_i^{2D}$ to extract object patches $\mathcal{P}_{\mathbf{I}} = \{\mathbf{P}_i|\mathbf{P}_i = \mathrm{crop}(\mathbf{I},\mathbf{B}_i^{2D})\}$ from synthesized and real scenes images with simple cropping. The object patches are fed into the object discriminator after being scaled to a uniform size. We find that it significantly helps synthesize realistic objects and benefits the disentanglement between objects and the background. More details about our object discrimination are included in the Supplementary Materials. + +# 3.5. Training and Inference + +Training Objectives. The whole generation process is formulated as $\mathbf{I}_f = \mathrm{G}(\mathcal{B},\mathcal{Z},\xi)$ , where the generator $\mathrm{G}(\cdot)$ receives a layout $\mathcal{B}$ , a latent code set $\mathcal{Z}$ independently sampled from distribution $\mathcal{N}(0,1)$ to control objects, and a camera pose $\xi$ sampled from a prior distribution $p_{\xi}$ to synthesize the image $\mathbf{I}_f$ . During training, $\mathcal{B}$ , $\mathcal{Z}$ , $\xi$ are randomly sampled, and the real image $\mathbf{I}_r$ is sampled from the dataset. Besides the generator, we employ the scene discriminator $\mathrm{D}_s(\cdot)$ to guarantee the global coherence of the rendering and the object discriminator $\mathrm{D}_{\mathrm{obj}}(\cdot)$ on individual objects for local discrimination. Generators and discriminators are jointly trained as: + +$$ +\begin{array}{l} \min \mathcal {L} _ {G} = \mathbb {E} [ f (- \mathrm {D} _ {s} (\mathbf {I} _ {f})) ] + \lambda_ {1} \mathbb {E} [ f (- \mathrm {D} _ {\mathrm {o b j}} (\mathcal {P} _ {\mathbf {I} _ {f}})) ], (12) \\ \min \mathcal {L} _ {D} = \mathbb {E} [ f (- \mathrm {D} _ {s} (\mathbf {I} _ {r})) ] + \mathbb {E} [ f (\mathrm {D} _ {s} (\mathbf {I} _ {f})) ] (13) \\ + \lambda_ {1} (\mathbb {E} [ f (- \mathrm {D} _ {\mathrm {o b j}} (\mathcal {P} _ {\mathbf {I} _ {r}}) ]) + \mathbb {E} [ f (\mathrm {D} _ {\mathrm {o b j}} (\mathcal {P} _ {\mathbf {I} _ {f}})) ]) \\ + \lambda_ {2} | | \nabla_ {\mathbf {I} _ {r}} \mathrm {D} _ {s} (\mathbf {I} _ {r}) | | _ {2} ^ {2} + \lambda_ {3} \nabla_ {\mathcal {P} _ {\mathbf {I} _ {r}}} \mathrm {D} _ {\text {o b j}} (\mathcal {P} _ {\mathbf {I} _ {r}}) | | _ {2} ^ {2}), \\ \end{array} +$$ + +where $f(t) = \log (1 + \exp (t))$ is the softplus function, and $\mathcal{P}_{\mathbf{I}_r}$ and $\mathcal{P}_{\mathbf{I}_f}$ are the extracted object patches of synthesized image $\mathbf{I}_f$ and real image $\mathbf{I}_r$ , respectively. $\lambda_{1}$ stands for the loss weight of the object discriminator. The last two terms in Eq. (13) are the gradient penalty regularizers of both discriminators, with $\lambda_{2}$ and $\lambda_{3}$ denoting their weights. + +Inference. Besides high-quality scene generation, our method naturally supports object editing by manipulating the layout prior as shown in Fig. 1. Various applications are shown in Sec. 4.3. In particular, ray marching at a small resolution (64) may cause aliasing especially when moving the objects. We adopt supersampling anti-aliasing (SSAA) [43] to perform ray marching at a temporary higher resolution (128) and downsample the feature map to the original resolution before the upsampler. This strategy is used only for object synthesis, and we do not change the background resolution during inference. + +# 4. Experiments + +# 4.1. Settings + +Datasets. We evaluate DisCoScene on three multi-object scene datasets, including CLEVR [21], 3D-FRONT [10, 11], and WAYMO [48]. CLEVR is a diagnostic multi-object dataset. We use the official script [21] to render scenes + +with 2 and random primitives. Our CLEVR dataset consists of $80K$ samples in $256 \times 256$ resolution. 3D-FRONT is an indoor scene dataset, containing a collection of $6.8K$ houses with $140K$ rooms. We obtain $4K$ bedrooms after filtering out rooms with uncommon arrangements or unnatural sizes and use BlenderProc to render 20 images per room from random camera positions, resulting in a total of $80K$ images. WAYMO is a large-scale autonomous driving dataset with $1K$ video sequences of outdoor scenes. Six images are provided for each frame, and we only keep the front view. We also apply heuristic rules to filter out small and noisy cars and collect a subset of $70K$ images. Because the width is always larger than height on WAYMO, we adopt the black padding to make images square, similar with StyleGAN2 [25]. More details about data preprocessing and rendering are included in Supplementary Materials. + +Baselines. We compare with both 2D and 3D GANs. For 2D, we compare with StyleGAN2 [25] on image quality. As for 3D, we compare with EpiGRAF [46], VolumeGAN [60], and EG-3D [4] on object generation, and GIRAFFE [32], GSN [8] on scene generation. We use the baseline models either released along with their papers or official implementations to train on our data. + +Implementation Details. We use the same architecture and parameters of the mapping network from StyleGAN2 [25]. For object generator $\mathrm{G_{obj}(\cdot)}$ and background generator $\mathrm{G_{bg}(\cdot)}$ , we use 8 and 4 Modulated Fully-Connected layers (ModFCs) with 256 and 128 channels, respectively. Ray casting is performed on $64 \times 64$ and the feature map is rendered to image with neural renderer. The progressive training strategy from PG-GAN [22] is adopted for better image quality and multi-view consistency. Discriminators $\mathrm{D}_s(\cdot)$ and $\mathrm{D_{obj}(\cdot)}$ both share the similar architecture of StyleGAN2 but with only half channels. Practically, the resolution of $\mathrm{D_{obj}(\cdot)}$ is always 1/2 on WAYMO or 1/4 on CLEVR and 3D-FRONT of $\mathrm{D}_s(\cdot)$ . All our models are trained on $8 \times$ V100/A100 GPUs with a batch size of 64. $\lambda_1$ is set to 1 to balance object and scene discriminators. $\lambda_2$ and $\lambda_3$ are set to 1 to maintain training stability. Unless specified, other hyperparameters are same as StyleGAN2. More details about network architecture and training can be found in Supplementary Materials. + +# 4.2. Main Results + +Qualitative Comparison. Fig. 2 presents the synthesized images in a resolution of $256 \times 256$ of our method and baselines on all the datasets. We compare our method on explicit camera control and object editing with baselines. EG3D, with a single radiance field, can manipulate the global camera of the synthesized images. As for EG3D, although it converges on the datasets, the object fidelity are lower than our method. On CLEVR with a narrow camera distribution, the results of EG3D are inconsistent. In the + +![](images/0b529a7430e6a37bcc21c787cdc675d9af41301771039ca179f31c2957d455e3.jpg) +Figure 2. Qualitative comparison between DisCoScene and baselines. Explicit camera rotation is evaluated on CLEVR and 3D-FRONT. Object rotation (left) and object translation (right) are evaluated on WAYMO. All images are in $256 \times 256$ resolution. + +Table 2. Quantitative comparisons on different datasets. FID, KID $(\times 10^{3})$ are reported as the evaluation metrics. TR. and INF. denote training and inference costs, evaluated in V100 days and ms/image (single V100 over $1K$ samples), respectively. Note that we highlight the best results among 3D-aware models. + +
ModelCLEVR3D-FRONTWAYMO
FID ↓KID ↓TR. ↓INF. ↓FID ↓KID ↓FID ↓KID ↓
StyleGAN2 [25]4.53.013.34412.54.315.18.3
EpiGRAF [46]10.48.316.0114107.2102.327.026.1
VolumeGAN [60]7.55.115.29052.738.729.918.2
EG3D [4]4.112.725.85519.713.526.045.4
GIRAFFE [32]78.561.55.26256.546.8175.7212.1
GSN [8]----130.787.5--
DisCoScene3.52.118.19513.87.416.08.4
+ +first example, the color of the cylinder changes from gray to green across different views. Meanwhile, our method learns better 3D structure of the objects and achieves better camera control. On the challenging WAYMO dataset, it is difficult to encode huge street scenes within a single generator, thus we train GIRAFFE and our DisCoScene in the camera space to evaluate object editing. GIRAFFE struggles to generate realistic results and, while manipulating objects, their geometry and appearance are not preserved well. Our approach is capable of handling these complicated scenarios with good variations. Wherever the object is placed and regardless of how the rotation is carried out, the synthesized objects are substantially better and more consistent than GIRAFFE. It demonstrates the effectiveness of our spatially disentangle radiance fields built upon the layout prior. More comparisons are included in Supplementary Materials. + +Quantitative Comparison. Tab. 2 reports the quantitative metrics on the quality of results, including FID [18] and + +KID [3]. All metrics are calculated between $50K$ generated samples and all real images. DisCoScene consistently outperforms baselines with significant improvement on all datasets. Besides, training cost in V100 days and testing cost in ms/image (on a single V100 over $1K$ samples) are also included to reflect the efficiency of our model. Note that the inference cost of 3D-aware models is evaluated on generating radiance fields rather than images. In such a case, EG3D and EpiGRAF are not fast as excepted due to the heavy computation on tri-planes. With comparable training and testing cost, it even achieves similar level of image quality with state-of-the-art 2D GAN baselines, e.g., StyleGAN2 [25], while allowing for explicit camera control and object editing that are otherwise challenging. + +# 4.3. Controllable Scene Generation + +The layout prior in our model enables versatile user controls of scene objects. In what follows, we evaluate the + +![](images/3d52a9bce2205b07c0700f0b4500225def531e227d12f8c75c9dc0e9a163ce28.jpg) +Figure 3. Controllable scene synthesis in $256 \times 256$ resolution. We perform versatile user control of the global camera and scene objects, such as rearrangement, removal, insertion, and restyling. Editings are performed on the original generations (the left one of each row). + +flexibility and effectiveness of our model through various 3D manipulation applications in different datasets. Examples are shown in Fig. 3 and more results can be found in Supplementary Materials. + +Rearranging Objects. We can transform bounding boxes B to rearrange (rotation and translation) the objects in the scenes without affecting their appearance. Transforming shapes in CLEVR, furniture in 3D-FRONT, and cars in WAYMO all show consistent results. In particular, rotating symmetric shapes (i.e., spheres and cylinders) in CLEVR shows little changes, suggesting desired multi-view consistency. Our model can properly handle mutual occlusion. Take the blue cube from CLEVR as example (1-st row of Fig. 3), our model can produce new occlusions between it and the grey cylinder and generate high-quality renderings. Removing and Cloning Objects. Users can update the layout by removing or cloning bounding boxes. Our method seamlessly removes objects with the background inpainted realistically, even without training on any pure background, including the challenging dataset of WAYMO (3-rd row of Fig. 3). Object cloning is also naturally supported, by copying and pasting a box to a new location in the layout. + +Restyling Objects. Although appearance and shape are not explicitly modeled by the latent code, we can reuse the encoded hierarchical knowledge to perform object restyling. Like [15, 42, 61], we arbitrarily sample latent codes and perform style-mixing on different layers to achieve independent control over appearance and shape. Fig. 3 presents the restyling results on certain objects, i.e., the front cylinder in CLEVR, the bed in 3D-FRONT, and the left car in WAYMO. Camera Movement. Explicit camera control is also permitted. Even for CLEVR that is trained on very limited camera ranges, we can rotate the camera up to an extreme side view. Our model also produces consistent results when rotating the camera on 3D-FRONT (2-nd row of Fig. 3). + +# 4.4. Ablation Study + +We ablate main components of our approach to better understand their individual contributions. In addition to the + +Table 3. Ablation analysis of object discriminator $\left( {\mathrm{D}}_{\mathrm{{obj}}}\right)$ . + +
CLEVR3D-FRONTWAYMO
FIDw/o Dobj5.018.619.5
w/ Dobj3.513.816.0
FIDobjw/o Dobj19.133.795.1
w/ Dobj5.619.516.3
+ +Table 4. Ablation analysis of spatial condition (S-Cond). + +
FIDFIDobj
w/ S-Condw/o S-Condw/ S-Condw/o S-Cond
3D-FRONT13.815.219.523.2
+ +FID score that measures the quality of the entire image, we also provide another metric $\mathrm{FID}_{\mathrm{obj}}$ to measure the quality of individual objects. Specifically, we use the projected 2D boxes to crop objects from the synthesized images and then perform FID evaluation against the ones from real images. + +Object Discriminator. The object discriminator $\mathrm{D_{obj}}$ plays a crucial role in synthesizing realistic objects, as evaluated in Tab. 3. Obviously, the object fidelity is significantly improved across all datasets with $\mathrm{D_{obj}}$ . Also, the quality of the whole scene generation is improved as well, contributed by better objects. Fig. 5 visually shows that our method can successfully disentangle objects from the background with the help of object discriminator. Although the baseline model is able to disentangle objects on 3D-FRONT from simple background to certain extent, the background suffers from the entanglement with objects, resulting in obvious artifacts as well as illogical layout. On more challenging datasets like WAYMO, the complex backgrounds make the disentanglement even more difficult, so that the background model easily overfits the whole scene as a single radiance field. Thanks to the object discriminator, our full model benefits from object supervision, leading to better disentanglement, even without seeing a pure background image. + +Spatial Condition. To analyze how spatial condition (S-Cond) affects the quality of generation, we compare results with models trained with and without S-Cond on 3D- + +![](images/5d9b0718b37ce2aa590226d6da3a38956c846abf247d4a3b66212cbc98151ffe.jpg) +(a) Spatial condition + +![](images/51e21fd9bf59849e4e3c6a1308a6ed558d2ef597d9c23b986aee28577f1da04f.jpg) +(b) Supersampling anti-aliasing + +![](images/553869722a3b9d548db31c196bb2ba1b349eed7186c88199dee03202a4ebefa5.jpg) +(c) Upsampler + +![](images/d8b6bdfdbae321f3574a11bcf92de0dfaa74f163d5e6a2c65632179d25fea4c9.jpg) +Figure 4. Qualitative comparison for ablations on spatial condition (S-Cond), supersampling anti-alising (SSAA), and upsampler (Up.). +Figure 5. Ablation on scene disentanglement. We independently infer objects and background to show the quality of scene disentanglement with regard to object discriminator $\mathrm{D}_{\mathrm{obj}}$ . + +FRONT (Fig. 4a). For example, our full model consistently infers beds at the center of rooms, while the baseline predicts random items like tables or nightstands that rarely appear in the middle of bedrooms. These results demonstrate that spatial condition can assist the generator with appropriate semantics from simple layout priors. Note that this correlation between spatial configurations and object semantics is automatically emerged without any supervision. We also numerically compare the image quality on these two models in Tab. 4, which shows that S-Cond also achieves better image quality at both scene- and object-level, because more proper semantics are more in line with the native distribution of real images. + +Supersampling Anti-Aliasing. We adopt a simple supersampling (SSAA) strategy to reduce edge aliasing by sampling more points during inference (Sec. 3.5). Thanks to our efficient object point sampling, doubling the resolution of foreground points keeps a similar inference speed (105 ms/image), comparable with original speed (95 ms/image). Results with different sampling points are shown in Fig. 4b. Taking the right boundary of the cabinet as an example (see the zoom-in insets for better visualization), when the cabinet is moved, SSAA achieves more consistent boundary compared with the jaggy one in the baseline. + +Neural Renderer for Shadow. We adopt the StyleGAN2-like neural renderer to boost the rendering efficiency (Sec. 3.3). Besides the low computational cost, the added capacity of the neural renderer also brings better implicit modeling of realistic lighting effects such as shadowing. Therefore, without handling the shadowing effect in our rendering pipeline, our model can still synthesize high-quality shaodws on datasets such as CLEVR (Fig. 4c). This is because the large receptive field brought by $3 \times 3$ convolutions and upsampler blocks make the neural renderer be aware of the object locations and progressively add shadows + +![](images/8a82525c84b3e0f3b3c0a1a9d9f26bdebdf99b3611927b7a710a80dd46baff5d.jpg) +Figure 6. Real image inversion and editing. + +to the low resolution features rendered from radiance fields. + +# 5. Discussion and Conclusion + +Real Image Editing. Fig. 6 shows that it is possible to embed a real image into the latent space of our pretrained model using pivotal tuning inversion (PTI) [39]. Besides reconstruction, all object manipulation operations are supported to edit the image. As one of the very first steps towards 3D scene editing from a single image, we believe that our method proves a promising venue and can inspire future research efforts along this direction. + +Limitations and Future Work. Our model requires the abstract layout prior as the input. For in-the-wild datasets, we need monocular 3D object detector [54] to infer pseudo layouts. While existing approaches attempt to learn the layout in an end-to-end manner, they struggle to generalize to complex scenes consisting of multiple objects. So it would be interesting to explore 3D layout estimation for complex scenes and combine with our approach end-to-end. Also, although our work shows significant improvement over existing 3D-aware scene generators, it is still challenging to learn on the street scenes in the global space due to the limited model capacity. Large-scale NeRFs [51, 57] might be one potent solution. + +Conclusion. This work presents DisCoScene, a method for controllable 3D-aware scene synthesis on challenging datasets. By taking spatially disentangled radiance fields as the representation based on a very abstract layout prior, our method is able to generate high-fidelity scene images and allows for versatile object-level editing. + +Acknowledgements. 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This work presents DisCoScene: a 3D-aware generative model for high-quality and controllable scene synthesis. The key ingredient of our method is a very abstract object-level representation (i.e., 3D bounding boxes without semantic annotation) as the scene layout prior, which is simple to obtain, general to describe various scene contents, and yet informative to disentangle objects and background. Moreover, it serves as an intuitive user control for scene editing. Based on such a prior, the proposed model spatially disentangles the whole scene into object-centric generative radiance fields by learning on only 2D images with the global-local discrimination. Our model obtains the generation fidelity and editing flexibility of individual objects while being able to efficiently compose objects and the background into a complete scene. We demonstrate state-of-the-art performance on many scene datasets, including the challenging Waymo outdoor dataset. Project page can be found here." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 548, + 128, + 560 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 548, + 128, + 560 + ], + "spans": [ + { + "bbox": [ + 47, + 548, + 128, + 560 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 567, + 288, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 567, + 288, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 567, + 288, + 688 + ], + "type": "text", + "content": "3D-consistent image synthesis from single-view 2D data has become a trendy topic in generative modeling. Recent approaches like GRAF [40] and Pi-GAN [5] introduce 3D inductive bias by taking neural radiance fields [1, 28, 29, 36, 38] as the underlying representation, gaining the capability of geometry modeling and explicit camera control. Despite their success in synthesizing individual objects (e.g., faces, cats, cars), they struggle on scene images that contain multiple objects with non-trivial layouts and complex backgrounds. The varying quantity and large" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 251, + 545, + 299 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 251, + 545, + 299 + ], + "spans": [ + { + "bbox": [ + 306, + 251, + 545, + 299 + ], + "type": "text", + "content": "diversity of objects, along with the intricate spatial arrangement and mutual occlusions, bring enormous challenges, which exceed the capacity of the object-level generative models [4, 13, 15, 33, 45, 46, 60]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 302, + 546, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 302, + 546, + 460 + ], + "spans": [ + { + "bbox": [ + 305, + 302, + 546, + 460 + ], + "type": "text", + "content": "Recent efforts have been made towards 3D-aware scene synthesis. Despite the encouraging progress, there are still fundamental drawbacks. For example, Generative Scene Networks (GSN) [8] achieve large-scale scene synthesis by representing the scene as a grid of local radiance fields and training on 2D observations from continuous camera paths. However, object-level editing is not feasible due to spatial entanglement and the lack of explicit object definition. On the contrary, GIRAFFE [32] explicitly composites object-centric radiance fields [16, 34, 56, 63] to support object-level control. Yet, it works poorly on challenging datasets containing multiple objects and complex backgrounds due to the absence of proper spatial priors." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "type": "text", + "content": "To achieve high-quality and controllable scene synthesis, the scene representation stands out as one critical design focus. A well-structured scene representation can scale up the generation capability and tackle the aforementioned challenges. Imagine, given an empty apartment and a furniture catalog, what does it take for a person to arrange the space? Would people prefer to walk around and throw things here and there, or instead figure out an overall layout and then attend to each location for the detailed selection? Obviously, a layout describing the arrangement of each furniture in the space substantially eases the scene composition process [17, 26, 58]. From this vantage point, here comes our primary motivation — an abstract object-oriented scene representation, namely a layout prior, could facilitate learning from challenging 2D data as a lightweight supervision signal during training and allow user interaction during inference. More specifically, to make such a prior easy to obtain and generalizable across different scenes, we define it as a set of object bounding boxes without semantic annotation, which describes the spatial composition of objects in the scene and supports intuitive object-level editing." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 693, + 228, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 693, + 228, + 703 + ], + "spans": [ + { + "bbox": [ + 58, + 693, + 228, + 703 + ], + "type": "text", + "content": "*Work partially done during internships at Snap Inc." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 59, + 703, + 136, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 703, + 136, + 712 + ], + "spans": [ + { + "bbox": [ + 59, + 703, + 136, + 712 + ], + "type": "text", + "content": "† Corresponding author." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "text", + "content": "4402" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 288 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 288 + ], + "type": "text", + "content": "In this work, we present DisCoScene, a novel 3D-aware generative model for complex scenes. Our method allows for high-quality scene synthesis on challenging datasets and flexible user control of both the camera and scene objects. Driven by the aforementioned layout prior, our model spatially disentangles the scene into composable radiance fields which are shared in the same object-centric generative model. To make the best use of the prior as a lightweight supervision during training, we propose global-local discrimination which attends to both the whole scene and individual objects to enforce spatial disentanglement between objects and against the background. Once the model is trained, users can generate and edit a scene by explicitly controlling the camera and the layout of objects' bounding boxes. In addition, we develop an efficient rendering pipeline tailored for the spatially-disentangled radiance fields, which significantly accelerates object rendering and scene composition for both training and inference stages." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 288, + 289, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 288, + 289, + 407 + ], + "spans": [ + { + "bbox": [ + 47, + 288, + 289, + 407 + ], + "type": "text", + "content": "Our method is evaluated on diverse datasets, including both indoor and outdoor scenes. Qualitative and quantitative results demonstrate that, compared to existing baselines, our method achieves state-of-the-art performance in terms of both generation quality and editing capability. Tab. 1 compares DisCoScene with relevant works. it is worth noting that, to the best of our knowledge, DisCoScene stands as the first method that achieves high-quality 3D-aware generation on challenging datasets like WAYMO [48], while enabling interactive object manipulation." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 418, + 134, + 431 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 418, + 134, + 431 + ], + "spans": [ + { + "bbox": [ + 47, + 418, + 134, + 431 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 437, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 437, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 437, + 289, + 715 + ], + "type": "text", + "content": "3D-aware Image Synthesis. Generative Adversarial Networks (GANs) have achieved remarkable success in 2D image synthesis [14, 22-25], and have recently been extended to 3D-aware image generation. VON [68] and HoloGAN [30] introduce voxel representations to the generator and use neural rendering to project 3D voxels into 2D space. Then, GRAF [40] and Pi-GAN [5] propose to use implicit functions to learn NeRF from single-view image collections, resulting in better multi-view consistency compared to voxel-based methods. GOF [59], ShadeGAN [35], and GRAM [7] introduce occupancy field, albedo field and radiance surface instead of radiance field to learn better 3D shapes. However, high-resolution image synthesis with direct volumetric rendering is usually expensive. Many works [4, 15, 32, 33, 45, 60, 62] resort to convolutional upsamplers to improve the rendering resolution and quality with lower computation overhead. While some other works [41,46] adopt patch-based sampling and sparse-voxel to speed up training and inference. Note that most of these methods are restricted to well-aligned objects and fail on more complex, multi-object scene imagery. Our work instead naturally handles multi-object scenes with spatial disentangled object-level radiance fields, which can" + } + ] + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 307, + 139, + 547, + 218 + ], + "blocks": [ + { + "bbox": [ + 304, + 70, + 545, + 137 + ], + "lines": [ + { + "bbox": [ + 304, + 70, + 545, + 137 + ], + "spans": [ + { + "bbox": [ + 304, + 70, + 545, + 137 + ], + "type": "text", + "content": "Table 1. Comparison of DisCoScene and relevant works. Multiple Objects: Ability to model multiple objects in a scene. Radiance Field: If radiance fields are used to model scenes. Complex Scene: Ability to handle complex datasets beyond diagnostic scenes. Object Editing: If object-level editing is supported. No Camera Sequence: Not requiring ground truth camera sequences." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 139, + 547, + 218 + ], + "lines": [ + { + "bbox": [ + 307, + 139, + 547, + 218 + ], + "spans": [ + { + "bbox": [ + 307, + 139, + 547, + 218 + ], + "type": "table", + "html": "
ModelMultiple ObjectsRadiance FieldComplex SceneObject EditingNo Camera Sequence
GRAF [40]X✓X✓✓
BlockGAN [30]✓XX✓✓
GSN [8]✓✓✓XX
GIRAFFE [32]✓✓X✓✓
DisCoScene✓✓✓✓✓
", + "image_path": "693e807f1f00f79a8d9169112a5ae44e4da3a2df1db9da0bdf84140aa11a2a32.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 228, + 529, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 228, + 529, + 239 + ], + "spans": [ + { + "bbox": [ + 304, + 228, + 529, + 239 + ], + "type": "text", + "content": "be scaled to very challenging real-world scene datasets." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 240, + 545, + 587 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 240, + 545, + 587 + ], + "spans": [ + { + "bbox": [ + 304, + 240, + 545, + 587 + ], + "type": "text", + "content": "Scene Generation. Scene generation has been a longstanding task. Early works like [52] attempt to model a complex scene by trying to generate it. Recently, with the successes in generative models, scene generation has been advanced significantly. Among them, one popular line is to resort to the setups of image-to-image translation from given conditions, i.e., semantic masks [19,37,49,50,55,67], object-attribute graph [2]. Although able to synthesize photorealistic scene images, they struggle to manipulate the objects in 3D space due to the lack of 3D understanding. Some works [9, 53, 64, 65] reuse the knowledge from 2D GAN models to achieve scene manipulation like the camera pose. But they suffer from poor multi-view consistency due to inadequate geometry modeling. Another active line of work [9, 31, 32, 64] explores adding 3D inductive biases to the scene representation. BlockGAN [31] and GIRAFFE [32] introduce compositional voxels and radiance fields to encode the object structures, but their object control can only be performed at simple diagnostic scenes. DepthGAN [44] introduces depth as a 3D prior but is hard to achieve manipulation and multi-view consistency. GSN [8] proposes to represent a scene with a grid of local radiance fields. However, since this local radiance field does not properly link to the object semantics, individual objects cannot be manipulated with versatile user control. Our work proposes to use an abstract layout prior to spatially disentangle the whole scene into object-centric radiance fields, which enables 3D-aware image synthesis on challenging real-world imagery like WAYMO [48]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 597, + 362, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 597, + 362, + 609 + ], + "spans": [ + { + "bbox": [ + 306, + 597, + 362, + 609 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "type": "text", + "content": "The overall framework is illustrated in Fig. 1. We employ layout as an explicit prior to disentangle objects in our approach (Sec. 3.1). Based on the layout prior, we introduce our spatially disentangled radiance fields (Sec. 3.2) and an efficient rendering pipeline (Sec. 3.3) to achieve controllable 3D-aware scene generation. We also describe our global-local discrimination, which makes training on challenging datasets possible (Sec. 3.4). Finally, we discuss" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4403" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 80, + 68, + 517, + 216 + ], + "blocks": [ + { + "bbox": [ + 80, + 68, + 517, + 216 + ], + "lines": [ + { + "bbox": [ + 80, + 68, + 517, + 216 + ], + "spans": [ + { + "bbox": [ + 80, + 68, + 517, + 216 + ], + "type": "image", + "image_path": "517a558f6f588da66d4f3bcccb751dcde87f157260ea76c97fcee7360fc1a4d9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 219, + 547, + 275 + ], + "lines": [ + { + "bbox": [ + 46, + 219, + 547, + 275 + ], + "spans": [ + { + "bbox": [ + 46, + 219, + 547, + 275 + ], + "type": "text", + "content": "Figure 1. The overall pipeline of DisCoScene. Conditioned by the layout prior, our spatial disentangle generative radiance fields generate individual objects and the background. Our efficient neural rendering pipeline then composites the scene to a low-resolution feature map with the volume renderer and upsamples to the final high-resolution image with the upsampler. During training, we propose global-local discrimination which applies the scene discriminator to the entire image and the object discriminator to cropped object patches. During inference, users can manipulate the layout to control the generation of a specific scene at the object level." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 285, + 288, + 309 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 285, + 288, + 309 + ], + "spans": [ + { + "bbox": [ + 46, + 285, + 288, + 309 + ], + "type": "text", + "content": "our model's training and inference details on 2D image collections (Sec. 3.5)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 316, + 175, + 329 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 316, + 175, + 329 + ], + "spans": [ + { + "bbox": [ + 47, + 316, + 175, + 329 + ], + "type": "text", + "content": "3.1. Abstract Layout Prior" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 334, + 290, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 334, + 290, + 467 + ], + "spans": [ + { + "bbox": [ + 46, + 334, + 290, + 467 + ], + "type": "text", + "content": "There exist many representations of a scene, including the popular choice of scene graph [6, 20, 34, 47], where objects and their relations are denoted as nodes and edges. Although graph can describe a scene in rich details, its structure is hard to process and the annotation is laborious to obtain in our case. Therefore, we opt to represent the scene layout in a much-simplified manner - a set of bounding boxes " + }, + { + "bbox": [ + 46, + 334, + 290, + 467 + ], + "type": "inline_equation", + "content": "\\mathcal{B} = \\{\\mathbf{B}_i | i \\in [1, N]\\}" + }, + { + "bbox": [ + 46, + 334, + 290, + 467 + ], + "type": "text", + "content": " without category annotation, where " + }, + { + "bbox": [ + 46, + 334, + 290, + 467 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 334, + 290, + 467 + ], + "type": "text", + "content": " counts objects in the scene. Concretely, each bounding box is defined with 9 parameters, including rotation " + }, + { + "bbox": [ + 46, + 334, + 290, + 467 + ], + "type": "inline_equation", + "content": "a_i" + }, + { + "bbox": [ + 46, + 334, + 290, + 467 + ], + "type": "text", + "content": ", translation " + }, + { + "bbox": [ + 46, + 334, + 290, + 467 + ], + "type": "inline_equation", + "content": "t_i" + }, + { + "bbox": [ + 46, + 334, + 290, + 467 + ], + "type": "text", + "content": ", and scale " + }, + { + "bbox": [ + 46, + 334, + 290, + 467 + ], + "type": "inline_equation", + "content": "s_i" + }, + { + "bbox": [ + 46, + 334, + 290, + 467 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 125, + 475, + 287, + 488 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 125, + 475, + 287, + 488 + ], + "spans": [ + { + "bbox": [ + 125, + 475, + 287, + 488 + ], + "type": "interline_equation", + "content": "\\mathbf {B} _ {i} = \\left[ \\boldsymbol {a} _ {i}, \\boldsymbol {t} _ {i}, \\boldsymbol {s} _ {i} \\right], \\tag {1}", + "image_path": "5d8808d9bf1a6a3406828cd54a228329951285db45dc08c8c8180ae0944d673f.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 58, + 491, + 287, + 505 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 491, + 287, + 505 + ], + "spans": [ + { + "bbox": [ + 58, + 491, + 287, + 505 + ], + "type": "interline_equation", + "content": "\\boldsymbol {a} _ {i} = \\left[ a _ {x}, a _ {y}, a _ {z} \\right], \\boldsymbol {t} _ {i} = \\left[ t _ {x}, t _ {y}, t _ {z} \\right], \\boldsymbol {s} _ {i} = \\left[ s _ {x}, s _ {y}, s _ {z} \\right], \\tag {2}", + "image_path": "e9ffb3528f824cc04f6f61ade285cc0d8270f27904fbd7ae90b1e8d3256c119b.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 512, + 288, + 561 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 512, + 288, + 561 + ], + "spans": [ + { + "bbox": [ + 46, + 512, + 288, + 561 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 512, + 288, + 561 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_i" + }, + { + "bbox": [ + 46, + 512, + 288, + 561 + ], + "type": "text", + "content": " comprises 3 Euler angles, which are easier to convert into rotation matrix " + }, + { + "bbox": [ + 46, + 512, + 288, + 561 + ], + "type": "inline_equation", + "content": "\\mathbf{R}_i" + }, + { + "bbox": [ + 46, + 512, + 288, + 561 + ], + "type": "text", + "content": ". Using this notation, the bounding box " + }, + { + "bbox": [ + 46, + 512, + 288, + 561 + ], + "type": "inline_equation", + "content": "\\mathbf{B}_i" + }, + { + "bbox": [ + 46, + 512, + 288, + 561 + ], + "type": "text", + "content": " can be transformed from a canonical bounding box " + }, + { + "bbox": [ + 46, + 512, + 288, + 561 + ], + "type": "inline_equation", + "content": "\\mathbf{C}" + }, + { + "bbox": [ + 46, + 512, + 288, + 561 + ], + "type": "text", + "content": ", i.e., a unit cube at the coordinate origin:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 88, + 570, + 287, + 583 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 570, + 287, + 583 + ], + "spans": [ + { + "bbox": [ + 88, + 570, + 287, + 583 + ], + "type": "interline_equation", + "content": "\\mathbf {B} _ {i} = \\mathrm {b} _ {i} (\\mathbf {C}) = \\mathbf {R} _ {i} \\cdot \\operatorname {d i a g} \\left(\\boldsymbol {s} _ {i}\\right) \\cdot \\mathbf {C} + \\boldsymbol {t} _ {i}, \\tag {3}", + "image_path": "6d790ceab861bd9907755305c7f1d579ae5c086d60e499601c5e23681378acfe.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 591, + 287, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 591, + 287, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 591, + 287, + 640 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 591, + 287, + 640 + ], + "type": "inline_equation", + "content": "\\mathbf{b}_i" + }, + { + "bbox": [ + 46, + 591, + 287, + 640 + ], + "type": "text", + "content": " stands for the transformation of " + }, + { + "bbox": [ + 46, + 591, + 287, + 640 + ], + "type": "inline_equation", + "content": "\\mathbf{B}_i" + }, + { + "bbox": [ + 46, + 591, + 287, + 640 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 591, + 287, + 640 + ], + "type": "inline_equation", + "content": "\\mathrm{diag}(\\cdot)" + }, + { + "bbox": [ + 46, + 591, + 287, + 640 + ], + "type": "text", + "content": " yields a diagonal matrix with the elements of " + }, + { + "bbox": [ + 46, + 591, + 287, + 640 + ], + "type": "inline_equation", + "content": "s_i" + }, + { + "bbox": [ + 46, + 591, + 287, + 640 + ], + "type": "text", + "content": ". Our abstract layout is more friendly to collect and easier to edit, allowing for versatile interactive user control." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 647, + 253, + 660 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 253, + 660 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 253, + 660 + ], + "type": "text", + "content": "3.2. Spatially Disentangled Radiance Fields" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 665, + 288, + 715 + ], + "type": "text", + "content": "Object Representation. Neural radiance field (NeRF) [29] " + }, + { + "bbox": [ + 47, + 665, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathrm{F}(\\pmb{x},\\pmb{v})\\rightarrow (\\pmb{c},\\sigma)" + }, + { + "bbox": [ + 47, + 665, + 288, + 715 + ], + "type": "text", + "content": " regresses color " + }, + { + "bbox": [ + 47, + 665, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\pmb {c}\\in \\mathbb{R}^3" + }, + { + "bbox": [ + 47, + 665, + 288, + 715 + ], + "type": "text", + "content": " and volume density " + }, + { + "bbox": [ + 47, + 665, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\sigma \\in \\mathbb{R}" + }, + { + "bbox": [ + 47, + 665, + 288, + 715 + ], + "type": "text", + "content": " from coordinate " + }, + { + "bbox": [ + 47, + 665, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\pmb {x}\\in \\mathbb{R}^3" + }, + { + "bbox": [ + 47, + 665, + 288, + 715 + ], + "type": "text", + "content": " and viewing direction " + }, + { + "bbox": [ + 47, + 665, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\pmb {v}\\in \\mathbb{S}^2" + }, + { + "bbox": [ + 47, + 665, + 288, + 715 + ], + "type": "text", + "content": ", parameterized with multi-layer perceptron (MLP)" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 285, + 545, + 320 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 285, + 545, + 320 + ], + "spans": [ + { + "bbox": [ + 305, + 285, + 545, + 320 + ], + "type": "text", + "content": "networks. Recent attempts propose to condition NeRF with a latent code " + }, + { + "bbox": [ + 305, + 285, + 545, + 320 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 305, + 285, + 545, + 320 + ], + "type": "text", + "content": ", resulting in their generative forms [5, 40], " + }, + { + "bbox": [ + 305, + 285, + 545, + 320 + ], + "type": "inline_equation", + "content": "\\mathrm{G}(\\pmb{x},\\pmb{v},\\pmb{z})\\rightarrow (c,\\sigma)" + }, + { + "bbox": [ + 305, + 285, + 545, + 320 + ], + "type": "text", + "content": ", to achieve 3D-aware object synthesis." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 321, + 546, + 417 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 321, + 546, + 417 + ], + "spans": [ + { + "bbox": [ + 304, + 321, + 546, + 417 + ], + "type": "text", + "content": "Since we use the layout as an internal representation, it naturally disentangles the whole scene into several objects. We can leverage multiple individual generative NeRFs to model different objects, but it can easily lead to an overwhelmingly large number of models and poor training efficiency. To alleviate this issue, we propose to infer generative object radiance field in the canonical space [32, 34], to allow weight sharing among objects:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 359, + 427, + 545, + 442 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 427, + 545, + 442 + ], + "spans": [ + { + "bbox": [ + 359, + 427, + 545, + 442 + ], + "type": "interline_equation", + "content": "\\left(\\boldsymbol {c} _ {i}, \\sigma_ {i}\\right) = \\operatorname {G} _ {\\mathrm {o b j}} \\left(\\mathrm {b} _ {i} ^ {- 1} (\\gamma (\\boldsymbol {x})), \\boldsymbol {z} _ {i}\\right), \\tag {4}", + "image_path": "1d10f69b73dfa602f87f26e527109fb14cf38e0a7c41fe6a67543232f5a5870a.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 451, + 545, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 451, + 545, + 534 + ], + "spans": [ + { + "bbox": [ + 304, + 451, + 545, + 534 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 451, + 545, + 534 + ], + "type": "inline_equation", + "content": "\\gamma (\\cdot)" + }, + { + "bbox": [ + 304, + 451, + 545, + 534 + ], + "type": "text", + "content": " is the position encoding function that transforms input into Fourier features. The object generator " + }, + { + "bbox": [ + 304, + 451, + 545, + 534 + ], + "type": "inline_equation", + "content": "\\mathrm{G_{obj}}(\\cdot)" + }, + { + "bbox": [ + 304, + 451, + 545, + 534 + ], + "type": "text", + "content": " infers each object independently, resulting in spatially disentangled generative radiance fields. Note that " + }, + { + "bbox": [ + 304, + 451, + 545, + 534 + ], + "type": "inline_equation", + "content": "\\mathrm{G_{obj}}(\\cdot)" + }, + { + "bbox": [ + 304, + 451, + 545, + 534 + ], + "type": "text", + "content": " is not conditioned on the viewing direction " + }, + { + "bbox": [ + 304, + 451, + 545, + 534 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 304, + 451, + 545, + 534 + ], + "type": "text", + "content": " because the upsampler of our neural renderer can learn the view-dependent effects similar to previous works [4, 15, 60] (Sec. 3.3)." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 536, + 546, + 655 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 536, + 546, + 655 + ], + "spans": [ + { + "bbox": [ + 304, + 536, + 546, + 655 + ], + "type": "text", + "content": "Spatial Condition. Although object bounding boxes are used as a prior, their latents are still randomly sampled regardless of their spatial configuration, leading to illogical arrangements. To synthesize scene images and infer object radiance fields with proper semantics, we adopt the location and scale of each object as a condition for the generator to encode more consistent intrinsic properties, i.e., shape and category. To this end, we simply modify Eq. (4) by concatenating the latent code with the Fourier features of object location and scale:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 314, + 665, + 545, + 681 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 665, + 545, + 681 + ], + "spans": [ + { + "bbox": [ + 314, + 665, + 545, + 681 + ], + "type": "interline_equation", + "content": "(\\boldsymbol {c}, \\sigma) = \\operatorname {G} _ {\\mathrm {o b j}} \\left(\\mathrm {b} _ {i} ^ {- 1} (\\gamma (\\boldsymbol {x}))\\right), \\operatorname {c o n c a t} \\left(\\boldsymbol {z} _ {i}, \\gamma \\left(\\boldsymbol {t} _ {i}\\right), \\gamma \\left(\\boldsymbol {s} _ {i}\\right)\\right). \\tag {5}", + "image_path": "2a9ceba875f7ed16b972f44ffbf8a809423cefc517ed68f1b31235cf5437f36d.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": "Therefore, semantic clues are injected into the layout in an unsupervised manner, without explicit category annotation." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4404" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 145 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 145 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 145 + ], + "type": "text", + "content": "Background Representation. Unlike objects, the background radiance field is only evaluated in the global space. Considering that the background encodes lots of high-frequency signals, we include the viewing direction " + }, + { + "bbox": [ + 47, + 72, + 289, + 145 + ], + "type": "inline_equation", + "content": "\\pmb{v}" + }, + { + "bbox": [ + 47, + 72, + 289, + 145 + ], + "type": "text", + "content": " to help background generator " + }, + { + "bbox": [ + 47, + 72, + 289, + 145 + ], + "type": "inline_equation", + "content": "\\mathrm{G_{bg}}(\\cdot)" + }, + { + "bbox": [ + 47, + 72, + 289, + 145 + ], + "type": "text", + "content": " to be able to learn such details. The background generation can be formulated as:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 107, + 155, + 287, + 169 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 155, + 287, + 169 + ], + "spans": [ + { + "bbox": [ + 107, + 155, + 287, + 169 + ], + "type": "interline_equation", + "content": "\\left(\\boldsymbol {c} _ {\\mathrm {b g}}, \\sigma_ {\\mathrm {b g}}\\right) = \\mathrm {G} _ {\\mathrm {b g}} (\\boldsymbol {x}, \\boldsymbol {v}, \\boldsymbol {z} _ {\\mathrm {b g}}). \\tag {6}", + "image_path": "5547b57ca22b6adeab1162250cb339e02587e9f67bfb6acfe72c2497eb28e9fa.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 178, + 203, + 192 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 178, + 203, + 192 + ], + "spans": [ + { + "bbox": [ + 47, + 178, + 203, + 192 + ], + "type": "text", + "content": "3.3. Efficient Rendering Pipeline" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 198, + 287, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 198, + 287, + 281 + ], + "spans": [ + { + "bbox": [ + 47, + 198, + 287, + 281 + ], + "type": "text", + "content": "As aforementioned, we use spatial-disentangled radiance fields to represent scenes. However, naive point sampling solutions can lead to prohibitive computational overhead when rendering multiple radiance fields. Considering the independence of objects' radiance fields, we can achieve much more efficient rendering by only focusing on the valid points within the bounding boxes." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 281, + 287, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 281, + 287, + 484 + ], + "spans": [ + { + "bbox": [ + 47, + 281, + 287, + 484 + ], + "type": "text", + "content": "Ray-Box Intersection in Canonical Space. Similar to NeRF [29], we use the pinhole camera model to perform ray casting. For each object, the points on the rays can be sampled at adaptive depths rather than fixed ones since the bounding box provides clues about where the object locates. Specifically, the cast rays " + }, + { + "bbox": [ + 47, + 281, + 287, + 484 + ], + "type": "inline_equation", + "content": "\\mathcal{R} = \\{\\mathbf{r}_j|j\\in [1,\\mathrm{S}^2 ]\\}" + }, + { + "bbox": [ + 47, + 281, + 287, + 484 + ], + "type": "text", + "content": " in a resolution S are transformed into the canonical object coordinate system. Then, Ray-AABB [27] (axis-aligned bounding box) intersection algorithm is applied to calculate the adaptive near and far depth " + }, + { + "bbox": [ + 47, + 281, + 287, + 484 + ], + "type": "inline_equation", + "content": "(d_{j,l,n},d_{j,l,f})" + }, + { + "bbox": [ + 47, + 281, + 287, + 484 + ], + "type": "text", + "content": " of the intersected segment between the ray " + }, + { + "bbox": [ + 47, + 281, + 287, + 484 + ], + "type": "inline_equation", + "content": "\\mathbf{r}_j" + }, + { + "bbox": [ + 47, + 281, + 287, + 484 + ], + "type": "text", + "content": " and the " + }, + { + "bbox": [ + 47, + 281, + 287, + 484 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 47, + 281, + 287, + 484 + ], + "type": "text", + "content": "-th box " + }, + { + "bbox": [ + 47, + 281, + 287, + 484 + ], + "type": "inline_equation", + "content": "\\mathbf{B}_l" + }, + { + "bbox": [ + 47, + 281, + 287, + 484 + ], + "type": "text", + "content": ". After that, " + }, + { + "bbox": [ + 47, + 281, + 287, + 484 + ], + "type": "inline_equation", + "content": "\\mathrm{N_d}" + }, + { + "bbox": [ + 47, + 281, + 287, + 484 + ], + "type": "text", + "content": " points are sampled equidistantly in the interval " + }, + { + "bbox": [ + 47, + 281, + 287, + 484 + ], + "type": "inline_equation", + "content": "[d_{j,l,n},d_{j,l,f}]" + }, + { + "bbox": [ + 47, + 281, + 287, + 484 + ], + "type": "text", + "content": ". It is worth noting that we maintain an intersection matrix " + }, + { + "bbox": [ + 47, + 281, + 287, + 484 + ], + "type": "inline_equation", + "content": "\\mathbf{M}" + }, + { + "bbox": [ + 47, + 281, + 287, + 484 + ], + "type": "text", + "content": " of size " + }, + { + "bbox": [ + 47, + 281, + 287, + 484 + ], + "type": "inline_equation", + "content": "\\mathbf{N}\\times \\mathbf{S}^2" + }, + { + "bbox": [ + 47, + 281, + 287, + 484 + ], + "type": "text", + "content": ", whose elements indicate if this ray intersects with the box. With " + }, + { + "bbox": [ + 47, + 281, + 287, + 484 + ], + "type": "inline_equation", + "content": "\\mathbf{M}" + }, + { + "bbox": [ + 47, + 281, + 287, + 484 + ], + "type": "text", + "content": ", we select only valid points to infer, which can greatly reduce the rendering cost." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 486, + 287, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 486, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 47, + 486, + 287, + 581 + ], + "type": "text", + "content": "Background Point Sampling. We adopt different background sampling strategies depending on the dataset. In general, we do fixed depth sampling for bounded backgrounds in indoor scenes and inherit the inverse parametrization of " + }, + { + "bbox": [ + 47, + 486, + 287, + 581 + ], + "type": "inline_equation", + "content": "\\mathrm{NeRF}++" + }, + { + "bbox": [ + 47, + 486, + 287, + 581 + ], + "type": "text", + "content": " [66] for complex and unbounded outdoor scenes, which uniformly samples background points in an inverse depth range. More details can be founded in the Supplementary Materials." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 582, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 582, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 582, + 288, + 715 + ], + "type": "text", + "content": "Composition and Volume Rendering. In our approach, objects are always assumed to be in front of the background. So objects and background can be rendered independently first and composited thereafter. For a ray " + }, + { + "bbox": [ + 47, + 582, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{r}_j" + }, + { + "bbox": [ + 47, + 582, + 288, + 715 + ], + "type": "text", + "content": " intersecting with " + }, + { + "bbox": [ + 47, + 582, + 288, + 715 + ], + "type": "inline_equation", + "content": "n_j" + }, + { + "bbox": [ + 47, + 582, + 288, + 715 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 47, + 582, + 288, + 715 + ], + "type": "inline_equation", + "content": "n_j \\geq 1" + }, + { + "bbox": [ + 47, + 582, + 288, + 715 + ], + "type": "text", + "content": ") boxes, its sample points " + }, + { + "bbox": [ + 47, + 582, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{X}_j = \\{\\pmb{x}_{j,k} | k \\in [1, n_j \\mathrm{N}_d]\\}" + }, + { + "bbox": [ + 47, + 582, + 288, + 715 + ], + "type": "text", + "content": " can be easily obtained from the depth range and the intersection matrix " + }, + { + "bbox": [ + 47, + 582, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{M}" + }, + { + "bbox": [ + 47, + 582, + 288, + 715 + ], + "type": "text", + "content": ". Since rendering should consider inter-object occlusions, we sort the points " + }, + { + "bbox": [ + 47, + 582, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 47, + 582, + 288, + 715 + ], + "type": "text", + "content": " by depth, resulting in an ordered point set " + }, + { + "bbox": [ + 47, + 582, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{X}_j^s = \\{\\pmb{x}_{j,s_k} | s_k \\in [1, n_j \\mathrm{N}_d], d_{j,s_k} \\leq d_{j,s_{k+1}}\\}" + }, + { + "bbox": [ + 47, + 582, + 288, + 715 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 582, + 288, + 715 + ], + "type": "inline_equation", + "content": "d_{j,s_k}" + }, + { + "bbox": [ + 47, + 582, + 288, + 715 + ], + "type": "text", + "content": " denotes the depth of point " + }, + { + "bbox": [ + 47, + 582, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\pmb{x}_{j,s_k}" + }, + { + "bbox": [ + 47, + 582, + 288, + 715 + ], + "type": "text", + "content": ". With color " + }, + { + "bbox": [ + 47, + 582, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\pmb{c}(\\pmb{x}_{j,s_k})" + }, + { + "bbox": [ + 47, + 582, + 288, + 715 + ], + "type": "text", + "content": " and density " + }, + { + "bbox": [ + 47, + 582, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\sigma(\\pmb{x}_{j,s_k})" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 545, + 97 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 97 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 97 + ], + "type": "text", + "content": "of the ordered set inferred with " + }, + { + "bbox": [ + 304, + 72, + 545, + 97 + ], + "type": "inline_equation", + "content": "\\mathrm{G_{obj}}(\\cdot)" + }, + { + "bbox": [ + 304, + 72, + 545, + 97 + ], + "type": "text", + "content": " by Eq. (5), the corresponding pixel " + }, + { + "bbox": [ + 304, + 72, + 545, + 97 + ], + "type": "inline_equation", + "content": "\\mathbf{f}(\\mathbf{r}_j)" + }, + { + "bbox": [ + 304, + 72, + 545, + 97 + ], + "type": "text", + "content": " is calculated as:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 354, + 102, + 545, + 137 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 354, + 102, + 545, + 137 + ], + "spans": [ + { + "bbox": [ + 354, + 102, + 545, + 137 + ], + "type": "interline_equation", + "content": "\\mathbf {f} (\\mathbf {r} _ {j}) = \\sum_ {k = 1} ^ {n _ {j} \\mathrm {N} _ {d}} T _ {j, k} \\alpha_ {j, k} \\boldsymbol {c} \\left(\\boldsymbol {x} _ {j, s _ {k}}\\right), \\tag {7}", + "image_path": "59f2108be6bd67259dd90c7e77a450e01af4bd675f3758ff29652c28b68f46c4.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 359, + 140, + 545, + 171 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 140, + 545, + 171 + ], + "spans": [ + { + "bbox": [ + 359, + 140, + 545, + 171 + ], + "type": "interline_equation", + "content": "T _ {j, k} = \\exp \\left(- \\sum_ {o = 1} ^ {k - 1} \\sigma \\left(\\boldsymbol {x} _ {j, s _ {k}}\\right) \\delta_ {j, s _ {o}}\\right), \\tag {8}", + "image_path": "6583ec1bde0413b8c1396277d9f45561ec57ee1b079c4990e66a41d8a55f245d.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 359, + 175, + 545, + 188 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 175, + 545, + 188 + ], + "spans": [ + { + "bbox": [ + 359, + 175, + 545, + 188 + ], + "type": "interline_equation", + "content": "\\alpha_ {j, k} = 1 - \\exp (- \\sigma \\left(\\boldsymbol {x} _ {j, s _ {k}}\\right) \\delta_ {j, s _ {k}}). \\tag {9}", + "image_path": "797a2fd49a914cf08e7005c0bd983866f08608c3f77e924417c5423afd0a584b.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 194, + 545, + 229 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 194, + 545, + 229 + ], + "spans": [ + { + "bbox": [ + 304, + 194, + 545, + 229 + ], + "type": "text", + "content": "For any ray that does not intersect with boxes, its color and density are set to 0 and " + }, + { + "bbox": [ + 304, + 194, + 545, + 229 + ], + "type": "inline_equation", + "content": "-\\infty" + }, + { + "bbox": [ + 304, + 194, + 545, + 229 + ], + "type": "text", + "content": ", respectively. So that the foreground object map " + }, + { + "bbox": [ + 304, + 194, + 545, + 229 + ], + "type": "inline_equation", + "content": "\\mathbf{F}" + }, + { + "bbox": [ + 304, + 194, + 545, + 229 + ], + "type": "text", + "content": " can be formulated as:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 330, + 235, + 545, + 267 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 235, + 545, + 267 + ], + "spans": [ + { + "bbox": [ + 330, + 235, + 545, + 267 + ], + "type": "interline_equation", + "content": "\\mathbf {F} _ {j} = \\left\\{ \\begin{array}{l l} \\mathbf {f} \\left(\\mathbf {r} _ {j}\\right), & \\text {i f} \\exists m \\in \\mathbf {M} _ {:, j}, m \\text {i s t r u e ,} \\\\ 0, & \\text {e l s e .} \\end{array} \\right. \\tag {10}", + "image_path": "7956eca2cf84780cbfe4d888565815a4c34d790a16ec9c0242f651c3bfe8f2f8.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 273, + 545, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 273, + 545, + 344 + ], + "spans": [ + { + "bbox": [ + 304, + 273, + 545, + 344 + ], + "type": "text", + "content": "Since the background points are sampled at a fixed depth, we can directly adopt Eq. (6) to evaluate background points in the global space without sorting. And the background map " + }, + { + "bbox": [ + 304, + 273, + 545, + 344 + ], + "type": "inline_equation", + "content": "\\mathbf{N}" + }, + { + "bbox": [ + 304, + 273, + 545, + 344 + ], + "type": "text", + "content": " can also be obtained by volume rendering similar to Eq. (7). Finally, " + }, + { + "bbox": [ + 304, + 273, + 545, + 344 + ], + "type": "inline_equation", + "content": "\\mathbf{F}" + }, + { + "bbox": [ + 304, + 273, + 545, + 344 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 273, + 545, + 344 + ], + "type": "inline_equation", + "content": "\\mathbf{N}" + }, + { + "bbox": [ + 304, + 273, + 545, + 344 + ], + "type": "text", + "content": " are alpha-blended into the final image " + }, + { + "bbox": [ + 304, + 273, + 545, + 344 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_n" + }, + { + "bbox": [ + 304, + 273, + 545, + 344 + ], + "type": "text", + "content": " with alpha extracted from Eq. (9):" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 361, + 350, + 545, + 384 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 361, + 350, + 545, + 384 + ], + "spans": [ + { + "bbox": [ + 361, + 350, + 545, + 384 + ], + "type": "interline_equation", + "content": "\\mathbf {I} _ {\\mathrm {n}} = \\mathbf {F} + \\prod_ {k = 1} ^ {n _ {j} \\mathrm {N} _ {d}} (1 - \\alpha_ {j, k}) \\odot \\mathbf {N}. \\tag {11}", + "image_path": "ffb42535b40a1c720c03e9ea16fafa82d778566642fd4f9736f8db1c040ed6fb.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 389, + 545, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 389, + 545, + 474 + ], + "spans": [ + { + "bbox": [ + 304, + 389, + 545, + 474 + ], + "type": "text", + "content": "Although our rendering pipeline efficiently composites multiple radiance fields, it still suffers from slow performance when rendering high-resolution images. To mitigate this issue, we render a high-dimensional feature map instead of a 3-channel color in a smaller resolution, followed by a StyleGAN2-like architecture that upsamples the feature map to the target resolution." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 479, + 474, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 479, + 474, + 491 + ], + "spans": [ + { + "bbox": [ + 306, + 479, + 474, + 491 + ], + "type": "text", + "content": "3.4. Local & Global Discrimination" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 498, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 665 + ], + "type": "text", + "content": "Like other GAN-based approaches, discriminators play a crucial role in training. Previous attempts for 3D-aware scene synthesis [8,32] only adopt scene-level discriminators to critique between rendered scenes and real captures. However, such a scene discriminator pays more attention to the global coherence of the whole scene, weakening the supervision for individual objects. Given that each object, especially those far from the camera, occupies a small portion of the rendered frame, the scene discriminator provides weak learning signal to its radiance field, leading to inadequate training and poor object quality. Besides, the scene discriminator shows only minimal capability in disentangling objects and background, allowing the background generator " + }, + { + "bbox": [ + 304, + 498, + 545, + 665 + ], + "type": "inline_equation", + "content": "\\mathrm{G_{bg}}" + }, + { + "bbox": [ + 304, + 498, + 545, + 665 + ], + "type": "text", + "content": " to overfit the whole scene easily." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 665, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 714 + ], + "type": "text", + "content": "Similar to [12], we propose to add an extra object discriminator for local discrimination, leading to better object-level supervision. Sepcifically, with the 3D layout " + }, + { + "bbox": [ + 304, + 665, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{B}_i" + }, + { + "bbox": [ + 304, + 665, + 545, + 714 + ], + "type": "text", + "content": " spatially disentangling different objects, we project them into" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4405" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": "2D space as " + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "inline_equation", + "content": "\\mathbf{B}_i^{2D}" + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": " to extract object patches " + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_{\\mathbf{I}} = \\{\\mathbf{P}_i|\\mathbf{P}_i = \\mathrm{crop}(\\mathbf{I},\\mathbf{B}_i^{2D})\\}" + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": " from synthesized and real scenes images with simple cropping. The object patches are fed into the object discriminator after being scaled to a uniform size. We find that it significantly helps synthesize realistic objects and benefits the disentanglement between objects and the background. More details about our object discrimination are included in the Supplementary Materials." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 175, + 178, + 188 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 175, + 178, + 188 + ], + "spans": [ + { + "bbox": [ + 47, + 175, + 178, + 188 + ], + "type": "text", + "content": "3.5. Training and Inference" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 194, + 290, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 194, + 290, + 338 + ], + "spans": [ + { + "bbox": [ + 46, + 194, + 290, + 338 + ], + "type": "text", + "content": "Training Objectives. The whole generation process is formulated as " + }, + { + "bbox": [ + 46, + 194, + 290, + 338 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_f = \\mathrm{G}(\\mathcal{B},\\mathcal{Z},\\xi)" + }, + { + "bbox": [ + 46, + 194, + 290, + 338 + ], + "type": "text", + "content": ", where the generator " + }, + { + "bbox": [ + 46, + 194, + 290, + 338 + ], + "type": "inline_equation", + "content": "\\mathrm{G}(\\cdot)" + }, + { + "bbox": [ + 46, + 194, + 290, + 338 + ], + "type": "text", + "content": " receives a layout " + }, + { + "bbox": [ + 46, + 194, + 290, + 338 + ], + "type": "inline_equation", + "content": "\\mathcal{B}" + }, + { + "bbox": [ + 46, + 194, + 290, + 338 + ], + "type": "text", + "content": ", a latent code set " + }, + { + "bbox": [ + 46, + 194, + 290, + 338 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}" + }, + { + "bbox": [ + 46, + 194, + 290, + 338 + ], + "type": "text", + "content": " independently sampled from distribution " + }, + { + "bbox": [ + 46, + 194, + 290, + 338 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(0,1)" + }, + { + "bbox": [ + 46, + 194, + 290, + 338 + ], + "type": "text", + "content": " to control objects, and a camera pose " + }, + { + "bbox": [ + 46, + 194, + 290, + 338 + ], + "type": "inline_equation", + "content": "\\xi" + }, + { + "bbox": [ + 46, + 194, + 290, + 338 + ], + "type": "text", + "content": " sampled from a prior distribution " + }, + { + "bbox": [ + 46, + 194, + 290, + 338 + ], + "type": "inline_equation", + "content": "p_{\\xi}" + }, + { + "bbox": [ + 46, + 194, + 290, + 338 + ], + "type": "text", + "content": " to synthesize the image " + }, + { + "bbox": [ + 46, + 194, + 290, + 338 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_f" + }, + { + "bbox": [ + 46, + 194, + 290, + 338 + ], + "type": "text", + "content": ". During training, " + }, + { + "bbox": [ + 46, + 194, + 290, + 338 + ], + "type": "inline_equation", + "content": "\\mathcal{B}" + }, + { + "bbox": [ + 46, + 194, + 290, + 338 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 194, + 290, + 338 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}" + }, + { + "bbox": [ + 46, + 194, + 290, + 338 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 194, + 290, + 338 + ], + "type": "inline_equation", + "content": "\\xi" + }, + { + "bbox": [ + 46, + 194, + 290, + 338 + ], + "type": "text", + "content": " are randomly sampled, and the real image " + }, + { + "bbox": [ + 46, + 194, + 290, + 338 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_r" + }, + { + "bbox": [ + 46, + 194, + 290, + 338 + ], + "type": "text", + "content": " is sampled from the dataset. Besides the generator, we employ the scene discriminator " + }, + { + "bbox": [ + 46, + 194, + 290, + 338 + ], + "type": "inline_equation", + "content": "\\mathrm{D}_s(\\cdot)" + }, + { + "bbox": [ + 46, + 194, + 290, + 338 + ], + "type": "text", + "content": " to guarantee the global coherence of the rendering and the object discriminator " + }, + { + "bbox": [ + 46, + 194, + 290, + 338 + ], + "type": "inline_equation", + "content": "\\mathrm{D}_{\\mathrm{obj}}(\\cdot)" + }, + { + "bbox": [ + 46, + 194, + 290, + 338 + ], + "type": "text", + "content": " on individual objects for local discrimination. Generators and discriminators are jointly trained as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 52, + 346, + 286, + 406 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 346, + 286, + 406 + ], + "spans": [ + { + "bbox": [ + 52, + 346, + 286, + 406 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\min \\mathcal {L} _ {G} = \\mathbb {E} [ f (- \\mathrm {D} _ {s} (\\mathbf {I} _ {f})) ] + \\lambda_ {1} \\mathbb {E} [ f (- \\mathrm {D} _ {\\mathrm {o b j}} (\\mathcal {P} _ {\\mathbf {I} _ {f}})) ], (12) \\\\ \\min \\mathcal {L} _ {D} = \\mathbb {E} [ f (- \\mathrm {D} _ {s} (\\mathbf {I} _ {r})) ] + \\mathbb {E} [ f (\\mathrm {D} _ {s} (\\mathbf {I} _ {f})) ] (13) \\\\ + \\lambda_ {1} (\\mathbb {E} [ f (- \\mathrm {D} _ {\\mathrm {o b j}} (\\mathcal {P} _ {\\mathbf {I} _ {r}}) ]) + \\mathbb {E} [ f (\\mathrm {D} _ {\\mathrm {o b j}} (\\mathcal {P} _ {\\mathbf {I} _ {f}})) ]) \\\\ + \\lambda_ {2} | | \\nabla_ {\\mathbf {I} _ {r}} \\mathrm {D} _ {s} (\\mathbf {I} _ {r}) | | _ {2} ^ {2} + \\lambda_ {3} \\nabla_ {\\mathcal {P} _ {\\mathbf {I} _ {r}}} \\mathrm {D} _ {\\text {o b j}} (\\mathcal {P} _ {\\mathbf {I} _ {r}}) | | _ {2} ^ {2}), \\\\ \\end{array}", + "image_path": "eaa416a8f5c049ee1a5c58e4b8038594d98ac781d09047c05e895c700861b375.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 413, + 287, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 413, + 287, + 485 + ], + "spans": [ + { + "bbox": [ + 46, + 413, + 287, + 485 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 413, + 287, + 485 + ], + "type": "inline_equation", + "content": "f(t) = \\log (1 + \\exp (t))" + }, + { + "bbox": [ + 46, + 413, + 287, + 485 + ], + "type": "text", + "content": " is the softplus function, and " + }, + { + "bbox": [ + 46, + 413, + 287, + 485 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_{\\mathbf{I}_r}" + }, + { + "bbox": [ + 46, + 413, + 287, + 485 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 413, + 287, + 485 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_{\\mathbf{I}_f}" + }, + { + "bbox": [ + 46, + 413, + 287, + 485 + ], + "type": "text", + "content": " are the extracted object patches of synthesized image " + }, + { + "bbox": [ + 46, + 413, + 287, + 485 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_f" + }, + { + "bbox": [ + 46, + 413, + 287, + 485 + ], + "type": "text", + "content": " and real image " + }, + { + "bbox": [ + 46, + 413, + 287, + 485 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_r" + }, + { + "bbox": [ + 46, + 413, + 287, + 485 + ], + "type": "text", + "content": ", respectively. " + }, + { + "bbox": [ + 46, + 413, + 287, + 485 + ], + "type": "inline_equation", + "content": "\\lambda_{1}" + }, + { + "bbox": [ + 46, + 413, + 287, + 485 + ], + "type": "text", + "content": " stands for the loss weight of the object discriminator. The last two terms in Eq. (13) are the gradient penalty regularizers of both discriminators, with " + }, + { + "bbox": [ + 46, + 413, + 287, + 485 + ], + "type": "inline_equation", + "content": "\\lambda_{2}" + }, + { + "bbox": [ + 46, + 413, + 287, + 485 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 413, + 287, + 485 + ], + "type": "inline_equation", + "content": "\\lambda_{3}" + }, + { + "bbox": [ + 46, + 413, + 287, + 485 + ], + "type": "text", + "content": " denoting their weights." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 486, + 287, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 486, + 287, + 617 + ], + "spans": [ + { + "bbox": [ + 46, + 486, + 287, + 617 + ], + "type": "text", + "content": "Inference. Besides high-quality scene generation, our method naturally supports object editing by manipulating the layout prior as shown in Fig. 1. Various applications are shown in Sec. 4.3. In particular, ray marching at a small resolution (64) may cause aliasing especially when moving the objects. We adopt supersampling anti-aliasing (SSAA) [43] to perform ray marching at a temporary higher resolution (128) and downsample the feature map to the original resolution before the upsampler. This strategy is used only for object synthesis, and we do not change the background resolution during inference." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 628, + 127, + 640 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 628, + 127, + 640 + ], + "spans": [ + { + "bbox": [ + 47, + 628, + 127, + 640 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 647, + 107, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 107, + 659 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 107, + 659 + ], + "type": "text", + "content": "4.1. Settings" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 665, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 286, + 713 + ], + "type": "text", + "content": "Datasets. We evaluate DisCoScene on three multi-object scene datasets, including CLEVR [21], 3D-FRONT [10, 11], and WAYMO [48]. CLEVR is a diagnostic multi-object dataset. We use the official script [21] to render scenes" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "type": "text", + "content": "with 2 and random primitives. Our CLEVR dataset consists of " + }, + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "type": "inline_equation", + "content": "80K" + }, + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "type": "text", + "content": " samples in " + }, + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "type": "text", + "content": " resolution. 3D-FRONT is an indoor scene dataset, containing a collection of " + }, + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "type": "inline_equation", + "content": "6.8K" + }, + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "type": "text", + "content": " houses with " + }, + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "type": "inline_equation", + "content": "140K" + }, + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "type": "text", + "content": " rooms. We obtain " + }, + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "type": "inline_equation", + "content": "4K" + }, + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "type": "text", + "content": " bedrooms after filtering out rooms with uncommon arrangements or unnatural sizes and use BlenderProc to render 20 images per room from random camera positions, resulting in a total of " + }, + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "type": "inline_equation", + "content": "80K" + }, + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "type": "text", + "content": " images. WAYMO is a large-scale autonomous driving dataset with " + }, + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "type": "inline_equation", + "content": "1K" + }, + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "type": "text", + "content": " video sequences of outdoor scenes. Six images are provided for each frame, and we only keep the front view. We also apply heuristic rules to filter out small and noisy cars and collect a subset of " + }, + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "type": "inline_equation", + "content": "70K" + }, + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "type": "text", + "content": " images. Because the width is always larger than height on WAYMO, we adopt the black padding to make images square, similar with StyleGAN2 [25]. More details about data preprocessing and rendering are included in Supplementary Materials." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 265, + 545, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 265, + 545, + 347 + ], + "spans": [ + { + "bbox": [ + 304, + 265, + 545, + 347 + ], + "type": "text", + "content": "Baselines. We compare with both 2D and 3D GANs. For 2D, we compare with StyleGAN2 [25] on image quality. As for 3D, we compare with EpiGRAF [46], VolumeGAN [60], and EG-3D [4] on object generation, and GIRAFFE [32], GSN [8] on scene generation. We use the baseline models either released along with their papers or official implementations to train on our data." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 349, + 545, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 349, + 545, + 577 + ], + "spans": [ + { + "bbox": [ + 304, + 349, + 545, + 577 + ], + "type": "text", + "content": "Implementation Details. We use the same architecture and parameters of the mapping network from StyleGAN2 [25]. For object generator " + }, + { + "bbox": [ + 304, + 349, + 545, + 577 + ], + "type": "inline_equation", + "content": "\\mathrm{G_{obj}(\\cdot)}" + }, + { + "bbox": [ + 304, + 349, + 545, + 577 + ], + "type": "text", + "content": " and background generator " + }, + { + "bbox": [ + 304, + 349, + 545, + 577 + ], + "type": "inline_equation", + "content": "\\mathrm{G_{bg}(\\cdot)}" + }, + { + "bbox": [ + 304, + 349, + 545, + 577 + ], + "type": "text", + "content": ", we use 8 and 4 Modulated Fully-Connected layers (ModFCs) with 256 and 128 channels, respectively. Ray casting is performed on " + }, + { + "bbox": [ + 304, + 349, + 545, + 577 + ], + "type": "inline_equation", + "content": "64 \\times 64" + }, + { + "bbox": [ + 304, + 349, + 545, + 577 + ], + "type": "text", + "content": " and the feature map is rendered to image with neural renderer. The progressive training strategy from PG-GAN [22] is adopted for better image quality and multi-view consistency. Discriminators " + }, + { + "bbox": [ + 304, + 349, + 545, + 577 + ], + "type": "inline_equation", + "content": "\\mathrm{D}_s(\\cdot)" + }, + { + "bbox": [ + 304, + 349, + 545, + 577 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 349, + 545, + 577 + ], + "type": "inline_equation", + "content": "\\mathrm{D_{obj}(\\cdot)}" + }, + { + "bbox": [ + 304, + 349, + 545, + 577 + ], + "type": "text", + "content": " both share the similar architecture of StyleGAN2 but with only half channels. Practically, the resolution of " + }, + { + "bbox": [ + 304, + 349, + 545, + 577 + ], + "type": "inline_equation", + "content": "\\mathrm{D_{obj}(\\cdot)}" + }, + { + "bbox": [ + 304, + 349, + 545, + 577 + ], + "type": "text", + "content": " is always 1/2 on WAYMO or 1/4 on CLEVR and 3D-FRONT of " + }, + { + "bbox": [ + 304, + 349, + 545, + 577 + ], + "type": "inline_equation", + "content": "\\mathrm{D}_s(\\cdot)" + }, + { + "bbox": [ + 304, + 349, + 545, + 577 + ], + "type": "text", + "content": ". All our models are trained on " + }, + { + "bbox": [ + 304, + 349, + 545, + 577 + ], + "type": "inline_equation", + "content": "8 \\times" + }, + { + "bbox": [ + 304, + 349, + 545, + 577 + ], + "type": "text", + "content": " V100/A100 GPUs with a batch size of 64. " + }, + { + "bbox": [ + 304, + 349, + 545, + 577 + ], + "type": "inline_equation", + "content": "\\lambda_1" + }, + { + "bbox": [ + 304, + 349, + 545, + 577 + ], + "type": "text", + "content": " is set to 1 to balance object and scene discriminators. " + }, + { + "bbox": [ + 304, + 349, + 545, + 577 + ], + "type": "inline_equation", + "content": "\\lambda_2" + }, + { + "bbox": [ + 304, + 349, + 545, + 577 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 349, + 545, + 577 + ], + "type": "inline_equation", + "content": "\\lambda_3" + }, + { + "bbox": [ + 304, + 349, + 545, + 577 + ], + "type": "text", + "content": " are set to 1 to maintain training stability. Unless specified, other hyperparameters are same as StyleGAN2. More details about network architecture and training can be found in Supplementary Materials." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 586, + 390, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 586, + 390, + 597 + ], + "spans": [ + { + "bbox": [ + 306, + 586, + 390, + 597 + ], + "type": "text", + "content": "4.2. Main Results" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "Qualitative Comparison. Fig. 2 presents the synthesized images in a resolution of " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " of our method and baselines on all the datasets. We compare our method on explicit camera control and object editing with baselines. EG3D, with a single radiance field, can manipulate the global camera of the synthesized images. As for EG3D, although it converges on the datasets, the object fidelity are lower than our method. On CLEVR with a narrow camera distribution, the results of EG3D are inconsistent. In the" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4406" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 73, + 70, + 521, + 277 + ], + "blocks": [ + { + "bbox": [ + 73, + 70, + 521, + 277 + ], + "lines": [ + { + "bbox": [ + 73, + 70, + 521, + 277 + ], + "spans": [ + { + "bbox": [ + 73, + 70, + 521, + 277 + ], + "type": "image", + "image_path": "0b529a7430e6a37bcc21c787cdc675d9af41301771039ca179f31c2957d455e3.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 280, + 545, + 301 + ], + "lines": [ + { + "bbox": [ + 46, + 280, + 545, + 301 + ], + "spans": [ + { + "bbox": [ + 46, + 280, + 545, + 301 + ], + "type": "text", + "content": "Figure 2. Qualitative comparison between DisCoScene and baselines. Explicit camera rotation is evaluated on CLEVR and 3D-FRONT. Object rotation (left) and object translation (right) are evaluated on WAYMO. All images are in " + }, + { + "bbox": [ + 46, + 280, + 545, + 301 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 46, + 280, + 545, + 301 + ], + "type": "text", + "content": " resolution." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 82, + 340, + 509, + 480 + ], + "blocks": [ + { + "bbox": [ + 46, + 305, + 546, + 339 + ], + "lines": [ + { + "bbox": [ + 46, + 305, + 546, + 339 + ], + "spans": [ + { + "bbox": [ + 46, + 305, + 546, + 339 + ], + "type": "text", + "content": "Table 2. Quantitative comparisons on different datasets. FID, KID " + }, + { + "bbox": [ + 46, + 305, + 546, + 339 + ], + "type": "inline_equation", + "content": "(\\times 10^{3})" + }, + { + "bbox": [ + 46, + 305, + 546, + 339 + ], + "type": "text", + "content": " are reported as the evaluation metrics. TR. and INF. denote training and inference costs, evaluated in V100 days and ms/image (single V100 over " + }, + { + "bbox": [ + 46, + 305, + 546, + 339 + ], + "type": "inline_equation", + "content": "1K" + }, + { + "bbox": [ + 46, + 305, + 546, + 339 + ], + "type": "text", + "content": " samples), respectively. Note that we highlight the best results among 3D-aware models." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 82, + 340, + 509, + 480 + ], + "lines": [ + { + "bbox": [ + 82, + 340, + 509, + 480 + ], + "spans": [ + { + "bbox": [ + 82, + 340, + 509, + 480 + ], + "type": "table", + "html": "
ModelCLEVR3D-FRONTWAYMO
FID ↓KID ↓TR. ↓INF. ↓FID ↓KID ↓FID ↓KID ↓
StyleGAN2 [25]4.53.013.34412.54.315.18.3
EpiGRAF [46]10.48.316.0114107.2102.327.026.1
VolumeGAN [60]7.55.115.29052.738.729.918.2
EG3D [4]4.112.725.85519.713.526.045.4
GIRAFFE [32]78.561.55.26256.546.8175.7212.1
GSN [8]----130.787.5--
DisCoScene3.52.118.19513.87.416.08.4
", + "image_path": "c0d1154b882b168a9c60cd6878d29b0adb2a5569aa254864d5d8b1cdd4eccea4.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 494, + 288, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 494, + 288, + 685 + ], + "spans": [ + { + "bbox": [ + 46, + 494, + 288, + 685 + ], + "type": "text", + "content": "first example, the color of the cylinder changes from gray to green across different views. Meanwhile, our method learns better 3D structure of the objects and achieves better camera control. On the challenging WAYMO dataset, it is difficult to encode huge street scenes within a single generator, thus we train GIRAFFE and our DisCoScene in the camera space to evaluate object editing. GIRAFFE struggles to generate realistic results and, while manipulating objects, their geometry and appearance are not preserved well. Our approach is capable of handling these complicated scenarios with good variations. Wherever the object is placed and regardless of how the rotation is carried out, the synthesized objects are substantially better and more consistent than GIRAFFE. It demonstrates the effectiveness of our spatially disentangle radiance fields built upon the layout prior. More comparisons are included in Supplementary Materials." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "text", + "content": "Quantitative Comparison. Tab. 2 reports the quantitative metrics on the quality of results, including FID [18] and" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 494, + 545, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 494, + 545, + 662 + ], + "spans": [ + { + "bbox": [ + 304, + 494, + 545, + 662 + ], + "type": "text", + "content": "KID [3]. All metrics are calculated between " + }, + { + "bbox": [ + 304, + 494, + 545, + 662 + ], + "type": "inline_equation", + "content": "50K" + }, + { + "bbox": [ + 304, + 494, + 545, + 662 + ], + "type": "text", + "content": " generated samples and all real images. DisCoScene consistently outperforms baselines with significant improvement on all datasets. Besides, training cost in V100 days and testing cost in ms/image (on a single V100 over " + }, + { + "bbox": [ + 304, + 494, + 545, + 662 + ], + "type": "inline_equation", + "content": "1K" + }, + { + "bbox": [ + 304, + 494, + 545, + 662 + ], + "type": "text", + "content": " samples) are also included to reflect the efficiency of our model. Note that the inference cost of 3D-aware models is evaluated on generating radiance fields rather than images. In such a case, EG3D and EpiGRAF are not fast as excepted due to the heavy computation on tri-planes. With comparable training and testing cost, it even achieves similar level of image quality with state-of-the-art 2D GAN baselines, e.g., StyleGAN2 [25], while allowing for explicit camera control and object editing that are otherwise challenging." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 670, + 473, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 670, + 473, + 682 + ], + "spans": [ + { + "bbox": [ + 306, + 670, + 473, + 682 + ], + "type": "text", + "content": "4.3. Controllable Scene Generation" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 689, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 546, + 713 + ], + "type": "text", + "content": "The layout prior in our model enables versatile user controls of scene objects. In what follows, we evaluate the" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4407" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 70, + 547, + 208 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 547, + 208 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 547, + 208 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 547, + 208 + ], + "type": "image", + "image_path": "3d52a9bce2205b07c0700f0b4500225def531e227d12f8c75c9dc0e9a163ce28.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 208, + 547, + 232 + ], + "lines": [ + { + "bbox": [ + 46, + 208, + 547, + 232 + ], + "spans": [ + { + "bbox": [ + 46, + 208, + 547, + 232 + ], + "type": "text", + "content": "Figure 3. Controllable scene synthesis in " + }, + { + "bbox": [ + 46, + 208, + 547, + 232 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 46, + 208, + 547, + 232 + ], + "type": "text", + "content": " resolution. We perform versatile user control of the global camera and scene objects, such as rearrangement, removal, insertion, and restyling. Editings are performed on the original generations (the left one of each row)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 241, + 287, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 241, + 287, + 289 + ], + "spans": [ + { + "bbox": [ + 46, + 241, + 287, + 289 + ], + "type": "text", + "content": "flexibility and effectiveness of our model through various 3D manipulation applications in different datasets. Examples are shown in Fig. 3 and more results can be found in Supplementary Materials." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 289, + 288, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 289, + 288, + 506 + ], + "spans": [ + { + "bbox": [ + 46, + 289, + 288, + 506 + ], + "type": "text", + "content": "Rearranging Objects. We can transform bounding boxes B to rearrange (rotation and translation) the objects in the scenes without affecting their appearance. Transforming shapes in CLEVR, furniture in 3D-FRONT, and cars in WAYMO all show consistent results. In particular, rotating symmetric shapes (i.e., spheres and cylinders) in CLEVR shows little changes, suggesting desired multi-view consistency. Our model can properly handle mutual occlusion. Take the blue cube from CLEVR as example (1-st row of Fig. 3), our model can produce new occlusions between it and the grey cylinder and generate high-quality renderings. Removing and Cloning Objects. Users can update the layout by removing or cloning bounding boxes. Our method seamlessly removes objects with the background inpainted realistically, even without training on any pure background, including the challenging dataset of WAYMO (3-rd row of Fig. 3). Object cloning is also naturally supported, by copying and pasting a box to a new location in the layout." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 506, + 287, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 506, + 287, + 662 + ], + "spans": [ + { + "bbox": [ + 46, + 506, + 287, + 662 + ], + "type": "text", + "content": "Restyling Objects. Although appearance and shape are not explicitly modeled by the latent code, we can reuse the encoded hierarchical knowledge to perform object restyling. Like [15, 42, 61], we arbitrarily sample latent codes and perform style-mixing on different layers to achieve independent control over appearance and shape. Fig. 3 presents the restyling results on certain objects, i.e., the front cylinder in CLEVR, the bed in 3D-FRONT, and the left car in WAYMO. Camera Movement. Explicit camera control is also permitted. Even for CLEVR that is trained on very limited camera ranges, we can rotate the camera up to an extreme side view. Our model also produces consistent results when rotating the camera on 3D-FRONT (2-nd row of Fig. 3)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 670, + 141, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 670, + 141, + 684 + ], + "spans": [ + { + "bbox": [ + 47, + 670, + 141, + 684 + ], + "type": "text", + "content": "4.4. Ablation Study" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 689, + 288, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 712 + ], + "type": "text", + "content": "We ablate main components of our approach to better understand their individual contributions. In addition to the" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 312, + 253, + 538, + 326 + ], + "blocks": [ + { + "bbox": [ + 319, + 240, + 533, + 251 + ], + "lines": [ + { + "bbox": [ + 319, + 240, + 533, + 251 + ], + "spans": [ + { + "bbox": [ + 319, + 240, + 533, + 251 + ], + "type": "text", + "content": "Table 3. Ablation analysis of object discriminator " + }, + { + "bbox": [ + 319, + 240, + 533, + 251 + ], + "type": "inline_equation", + "content": "\\left( {\\mathrm{D}}_{\\mathrm{{obj}}}\\right)" + }, + { + "bbox": [ + 319, + 240, + 533, + 251 + ], + "type": "text", + "content": " ." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 312, + 253, + 538, + 326 + ], + "lines": [ + { + "bbox": [ + 312, + 253, + 538, + 326 + ], + "spans": [ + { + "bbox": [ + 312, + 253, + 538, + 326 + ], + "type": "table", + "html": "
CLEVR3D-FRONTWAYMO
FIDw/o Dobj5.018.619.5
w/ Dobj3.513.816.0
FIDobjw/o Dobj19.133.795.1
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", + "image_path": "fcefd9c53c0989fbcab64afae28916bdd5d4ddf914c996e09a21500a7974e835.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 307, + 342, + 544, + 386 + ], + "blocks": [ + { + "bbox": [ + 320, + 329, + 531, + 340 + ], + "lines": [ + { + "bbox": [ + 320, + 329, + 531, + 340 + ], + "spans": [ + { + "bbox": [ + 320, + 329, + 531, + 340 + ], + "type": "text", + "content": "Table 4. Ablation analysis of spatial condition (S-Cond)." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 342, + 544, + 386 + ], + "lines": [ + { + "bbox": [ + 307, + 342, + 544, + 386 + ], + "spans": [ + { + "bbox": [ + 307, + 342, + 544, + 386 + ], + "type": "table", + "html": "
FIDFIDobj
w/ S-Condw/o S-Condw/ S-Condw/o S-Cond
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Specifically, we use the projected 2D boxes to crop objects from the synthesized images and then perform FID evaluation against the ones from real images." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 460, + 546, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 460, + 546, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 460, + 546, + 676 + ], + "type": "text", + "content": "Object Discriminator. The object discriminator " + }, + { + "bbox": [ + 304, + 460, + 546, + 676 + ], + "type": "inline_equation", + "content": "\\mathrm{D_{obj}}" + }, + { + "bbox": [ + 304, + 460, + 546, + 676 + ], + "type": "text", + "content": " plays a crucial role in synthesizing realistic objects, as evaluated in Tab. 3. Obviously, the object fidelity is significantly improved across all datasets with " + }, + { + "bbox": [ + 304, + 460, + 546, + 676 + ], + "type": "inline_equation", + "content": "\\mathrm{D_{obj}}" + }, + { + "bbox": [ + 304, + 460, + 546, + 676 + ], + "type": "text", + "content": ". Also, the quality of the whole scene generation is improved as well, contributed by better objects. Fig. 5 visually shows that our method can successfully disentangle objects from the background with the help of object discriminator. Although the baseline model is able to disentangle objects on 3D-FRONT from simple background to certain extent, the background suffers from the entanglement with objects, resulting in obvious artifacts as well as illogical layout. On more challenging datasets like WAYMO, the complex backgrounds make the disentanglement even more difficult, so that the background model easily overfits the whole scene as a single radiance field. Thanks to the object discriminator, our full model benefits from object supervision, leading to better disentanglement, even without seeing a pure background image." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 677, + 547, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 712 + ], + "type": "text", + "content": "Spatial Condition. To analyze how spatial condition (S-Cond) affects the quality of generation, we compare results with models trained with and without S-Cond on 3D-" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4408" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 45, + 71, + 216, + 153 + ], + "blocks": [ + { + "bbox": [ + 45, + 71, + 216, + 153 + ], + "lines": [ + { + "bbox": [ + 45, + 71, + 216, + 153 + ], + "spans": [ + { + "bbox": [ + 45, + 71, + 216, + 153 + ], + "type": "image", + "image_path": "5d9b0718b37ce2aa590226d6da3a38956c846abf247d4a3b66212cbc98151ffe.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 95, + 156, + 162, + 164 + ], + "lines": [ + { + "bbox": [ + 95, + 156, + 162, + 164 + ], + "spans": [ + { + "bbox": [ + 95, + 156, + 162, + 164 + ], + "type": "text", + "content": "(a) Spatial condition" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 216, + 70, + 375, + 153 + ], + "blocks": [ + { + "bbox": [ + 216, + 70, + 375, + 153 + ], + "lines": [ + { + "bbox": [ + 216, + 70, + 375, + 153 + ], + "spans": [ + { + "bbox": [ + 216, + 70, + 375, + 153 + ], + "type": "image", + "image_path": "51e21fd9bf59849e4e3c6a1308a6ed558d2ef597d9c23b986aee28577f1da04f.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 241, + 156, + 343, + 164 + ], + "lines": [ + { + "bbox": [ + 241, + 156, + 343, + 164 + ], + "spans": [ + { + "bbox": [ + 241, + 156, + 343, + 164 + ], + "type": "text", + "content": "(b) Supersampling anti-aliasing" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 375, + 72, + 543, + 152 + ], + "blocks": [ + { + "bbox": [ + 375, + 72, + 543, + 152 + ], + "lines": [ + { + "bbox": [ + 375, + 72, + 543, + 152 + ], + "spans": [ + { + "bbox": [ + 375, + 72, + 543, + 152 + ], + "type": "image", + "image_path": "553869722a3b9d548db31c196bb2ba1b349eed7186c88199dee03202a4ebefa5.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 434, + 156, + 481, + 164 + ], + "lines": [ + { + "bbox": [ + 434, + 156, + 481, + 164 + ], + "spans": [ + { + "bbox": [ + 434, + 156, + 481, + 164 + ], + "type": "text", + "content": "(c) Upsampler" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 47, + 180, + 286, + 248 + ], + "blocks": [ + { + "bbox": [ + 47, + 165, + 544, + 176 + ], + "lines": [ + { + "bbox": [ + 47, + 165, + 544, + 176 + ], + "spans": [ + { + "bbox": [ + 47, + 165, + 544, + 176 + ], + "type": "text", + "content": "Figure 4. Qualitative comparison for ablations on spatial condition (S-Cond), supersampling anti-alising (SSAA), and upsampler (Up.)." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 47, + 180, + 286, + 248 + ], + "lines": [ + { + "bbox": [ + 47, + 180, + 286, + 248 + ], + "spans": [ + { + "bbox": [ + 47, + 180, + 286, + 248 + ], + "type": "image", + "image_path": "d8b6bdfdbae321f3574a11bcf92de0dfaa74f163d5e6a2c65632179d25fea4c9.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 252, + 286, + 285 + ], + "lines": [ + { + "bbox": [ + 47, + 252, + 286, + 285 + ], + "spans": [ + { + "bbox": [ + 47, + 252, + 286, + 285 + ], + "type": "text", + "content": "Figure 5. Ablation on scene disentanglement. We independently infer objects and background to show the quality of scene disentanglement with regard to object discriminator " + }, + { + "bbox": [ + 47, + 252, + 286, + 285 + ], + "type": "inline_equation", + "content": "\\mathrm{D}_{\\mathrm{obj}}" + }, + { + "bbox": [ + 47, + 252, + 286, + 285 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 293, + 286, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 293, + 286, + 449 + ], + "spans": [ + { + "bbox": [ + 46, + 293, + 286, + 449 + ], + "type": "text", + "content": "FRONT (Fig. 4a). For example, our full model consistently infers beds at the center of rooms, while the baseline predicts random items like tables or nightstands that rarely appear in the middle of bedrooms. These results demonstrate that spatial condition can assist the generator with appropriate semantics from simple layout priors. Note that this correlation between spatial configurations and object semantics is automatically emerged without any supervision. We also numerically compare the image quality on these two models in Tab. 4, which shows that S-Cond also achieves better image quality at both scene- and object-level, because more proper semantics are more in line with the native distribution of real images." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 449, + 286, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 286, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 286, + 581 + ], + "type": "text", + "content": "Supersampling Anti-Aliasing. We adopt a simple supersampling (SSAA) strategy to reduce edge aliasing by sampling more points during inference (Sec. 3.5). Thanks to our efficient object point sampling, doubling the resolution of foreground points keeps a similar inference speed (105 ms/image), comparable with original speed (95 ms/image). Results with different sampling points are shown in Fig. 4b. Taking the right boundary of the cabinet as an example (see the zoom-in insets for better visualization), when the cabinet is moved, SSAA achieves more consistent boundary compared with the jaggy one in the baseline." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "type": "text", + "content": "Neural Renderer for Shadow. We adopt the StyleGAN2-like neural renderer to boost the rendering efficiency (Sec. 3.3). Besides the low computational cost, the added capacity of the neural renderer also brings better implicit modeling of realistic lighting effects such as shadowing. Therefore, without handling the shadowing effect in our rendering pipeline, our model can still synthesize high-quality shaodws on datasets such as CLEVR (Fig. 4c). This is because the large receptive field brought by " + }, + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "type": "text", + "content": " convolutions and upsampler blocks make the neural renderer be aware of the object locations and progressively add shadows" + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 307, + 180, + 545, + 273 + ], + "blocks": [ + { + "bbox": [ + 307, + 180, + 545, + 273 + ], + "lines": [ + { + "bbox": [ + 307, + 180, + 545, + 273 + ], + "spans": [ + { + "bbox": [ + 307, + 180, + 545, + 273 + ], + "type": "image", + "image_path": "8a82525c84b3e0f3b3c0a1a9d9f26bdebdf99b3611927b7a710a80dd46baff5d.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 342, + 278, + 508, + 289 + ], + "lines": [ + { + "bbox": [ + 342, + 278, + 508, + 289 + ], + "spans": [ + { + "bbox": [ + 342, + 278, + 508, + 289 + ], + "type": "text", + "content": "Figure 6. Real image inversion and editing." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 298, + 544, + 309 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 298, + 544, + 309 + ], + "spans": [ + { + "bbox": [ + 306, + 298, + 544, + 309 + ], + "type": "text", + "content": "to the low resolution features rendered from radiance fields." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 320, + 457, + 332 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 320, + 457, + 332 + ], + "spans": [ + { + "bbox": [ + 306, + 320, + 457, + 332 + ], + "type": "text", + "content": "5. Discussion and Conclusion" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 341, + 545, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 341, + 545, + 437 + ], + "spans": [ + { + "bbox": [ + 304, + 341, + 545, + 437 + ], + "type": "text", + "content": "Real Image Editing. Fig. 6 shows that it is possible to embed a real image into the latent space of our pretrained model using pivotal tuning inversion (PTI) [39]. Besides reconstruction, all object manipulation operations are supported to edit the image. As one of the very first steps towards 3D scene editing from a single image, we believe that our method proves a promising venue and can inspire future research efforts along this direction." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 441, + 545, + 596 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 441, + 545, + 596 + ], + "spans": [ + { + "bbox": [ + 304, + 441, + 545, + 596 + ], + "type": "text", + "content": "Limitations and Future Work. Our model requires the abstract layout prior as the input. For in-the-wild datasets, we need monocular 3D object detector [54] to infer pseudo layouts. While existing approaches attempt to learn the layout in an end-to-end manner, they struggle to generalize to complex scenes consisting of multiple objects. So it would be interesting to explore 3D layout estimation for complex scenes and combine with our approach end-to-end. Also, although our work shows significant improvement over existing 3D-aware scene generators, it is still challenging to learn on the street scenes in the global space due to the limited model capacity. Large-scale NeRFs [51, 57] might be one potent solution." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 599, + 545, + 671 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 599, + 545, + 671 + ], + "spans": [ + { + "bbox": [ + 304, + 599, + 545, + 671 + ], + "type": "text", + "content": "Conclusion. This work presents DisCoScene, a method for controllable 3D-aware scene synthesis on challenging datasets. By taking spatially disentangled radiance fields as the representation based on a very abstract layout prior, our method is able to generate high-fidelity scene images and allows for versatile object-level editing." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 677, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 712 + ], + "type": "text", + "content": "Acknowledgements. 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However, the large architecture difference across the teacher-student pairs limits the distillation gains. In contrast to previous adaptive distillation methods to reduce the teacher-student gap, we explore a novel training-free framework to search for the best student architectures for a given teacher. Our work first empirically show that the optimal model under vanilla training cannot be the winner in distillation. Secondly, we find that the similarity of feature semantics and sample relations between random-initialized teacher-student networks have good correlations with final distillation performances. Thus, we efficiently measure similarity matrix conditioned on the semantic activation maps to select the optimal student via an evolutionary algorithm without any training. In this way, our student architecture search for Distillation WithOut Training (DisWOT) significantly improves the performance of the model in the distillation stage with at least $180 \\times$ training acceleration. Additionally, we extend similarity metrics in DisWOT as new distillers and KD-based zero-proxies. Our experiments on CIFAR, ImageNet and NAS-Bench-201 demonstrate that our technique achieves state-of-the-art results on different search spaces. Our project and code are available at https://lilujunai.github.io/DisWOT-CVPR2023/.", + "bbox": [ + 76, + 300, + 473, + 693 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 720, + 209, + 736 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Despite the remarkable achievements of Deep Neural Networks (DNNs) in numerous visual recognition tasks [52, 64-68], they usually lead to heavy costs of memory, computation, and power at model inference due to their large numbers of parameters. To address this issue, Knowledge Distillation (KD) has been proposed as a means of transferring knowledge from a high-capacity teacher model to a low-capacity target student model, providing a more op", + "bbox": [ + 76, + 746, + 470, + 867 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3cc08b42e0202bafabff908c5cc47bb636a1fea8dd8277927ad2d4d26556f539.jpg", + "image_caption": [ + "Figure 1. Left: Ranking correlation of proxies in zero-cost NAS with vanilla and distillation accuracy. Right: Vanilla accuracy, distillation accuracy, prediction scores of DisWOT for ResNet[7,1,3] and ResNet[3,3,3] on search space $S_0$ ." + ], + "image_footnote": [], + "bbox": [ + 501, + 268, + 692, + 378 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/5238b79d9a3d1a33d347906a448e3339f1711cb1fa654d41bcfa8ac33d471d48.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 692, + 268, + 888, + 378 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/79ce25b09d33da7bf08670e1642042532dfcf401cda404f6d2f6706a0dc14a02.jpg", + "image_caption": [ + "Figure 2. Left: KD [22], DisWOT, DisWOT† results for ResNet20 under different teachers. Right: Comparison of distill accuracy & training efficiency with other NAS methods on NAS-Bench-201." + ], + "image_footnote": [], + "bbox": [ + 501, + 458, + 689, + 566 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/50164ccbd478508dc8db20245e777b715c3cfac668e1684a9f171c01ea1f76f5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 692, + 457, + 890, + 566 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "timal accuracy-efficiency trade-off during runtime [4, 7, 76]. The original KD method [22] utilizes the logit outputs of the teacher network as the source of knowledge. Subsequent studies [2, 21, 24, 26, 54, 61, 73] have focused on extracting informative knowledge based on intermediate feature representations. However, as the gap in capacity between students and teachers increases, existing KD methods are unable to improve results, particularly in tasks that depend on large-scale visual models such as VIT and GPT-3 [5, 16]. For example, as shown in Figure 2 (Left), the large teacher (e.g., ResNet110) lead to worse performance for the fixed student than the relatively smaller one (e.g., ResNet56).", + "bbox": [ + 496, + 641, + 893, + 823 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To solve this issue, adaptive KD methods have been proposed in terms of training paradigms (e.g., early stop [10]) and architectural adaptations (e.g., assistant teacher [43] and architecture search [40]), respectively. However, they are ineffective in improving distillation performance or in", + "bbox": [ + 496, + 824, + 895, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author, † equal contribution, PD conducted main experiments, LL proposed ideas and led the project & writing.", + "bbox": [ + 75, + 875, + 470, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "11898", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "volve enormous training costs in the additional model training and search process. In sharp contrast to these methods, we tackle this challenging problem from a new perspective regarding training-free architecture search. To achieve this goal, we construct a search space $S_0$ for ResNet-like models with different depth configurations and obtain vanilla and distill performance for each candidate in $S_0$ by individual training. Then, we evaluate the ranking correlation between predicted scores of training-free search methods and the actual performance of each student model. Surprisingly, as shown in Figure 1 (Left), there are common ranking correlation loss $(10\\% \\downarrow \\sim 20\\% \\downarrow)$ for these methods in predicting distillation accuracy than vanilla accuracy. To clarify this, we carefully analyze the disparities in vanilla and distillation performance for each model: (1) for overall search space, vanilla accuracy only preserves $85\\%$ correlations with actual distillation performance. (2) for a particular instance, as shown in Figure 1 (Right), ResNet20 with 3 res-blocks in each stage (i.e., ResNet[3,3,3]) has more parameters and better standalone performance but is weaker than ResNet[7,1,3] in the distillation process. Considering that ResNet[7,1,3] has more layers than ResNet20, we seek to understand the above phenomenon regarding the vanilla-distillation accuracy gap from the perspective of semantic matching [37]. ResNet[7,1,3] enjoys a larger effective receptive field and more excellent matched knowledge with teacher, resulting in significant distillation gains. Encouraged by this understanding, we strive to design a new zero-proxy regarding the semantic matching of teacher-student. As a result, we find that the similarity scores of feature semantics and sample relations can outperform conventional zero-cost NAS in predicting final distillation accuracy (see the comparison of ranking correlation on search space $S_0$ in Table 8). As shown in Figure 1(Right), similarity scores are also consistent with distillation performance.", + "bbox": [ + 76, + 90, + 472, + 621 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Drawing on the aforementioned observations, we introduce DisWOT, a simple yet effective training-free framework that finds the best student architectures for distilling the given teacher model. For better semantic matching in distillation, DisWOT leverages novel zero-cost metrics regarding the feature semantics and sample relations to select better student model. For the feature semantic similarity metric, we remark that randomly initialized models can localize objects well [6] and generate localization heatmaps via Grad-CAM [56] as reliable semantic information. Then, we measure the channel-wise similarity matrix of localization heatmaps and take the $L_{2}$ distance of the similarity matrix for the teacher-student model as the metric. For input samples, different models have diverse abilities to discriminate their relationships. To improve relational knowledge matching ability, we use the $L_{2}$ distance of sample-relation correlation matrix as a relation similarity metric. Finally, we search for student architectures using an evo", + "bbox": [ + 76, + 628, + 472, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "lutionary algorithm with semantic and relations similarity metrics. Then, the distillation process is implemented between the searched student and the pre-defined teacher. In addition, we leverage these metrics directly as new distillers to enhance the student, as the DisWOT†. Equipped with our train-free search and distillation design, our DisWOT and DisWOT† framework significantly improve the model's accuracy-latency tradeoff in inference with at least $180 \\times$ training acceleration.", + "bbox": [ + 496, + 90, + 893, + 226 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In principle, our DisWOT use higher-order statistics of teacher-student models to optimize the student architecture to fit a given teacher model. Its merits can be highlighted in three aspects: (1) In contrast to training-based student architecture search requires the individual or weight-sharing training, our DisWOT does not require the training of student models in the search phase. In addition, DisWOT is efficient to compute and easy to implement as it uses only the mini-batch data at initialization. (2) DisWOT is a teacher-aware search for distillation, which has better predictive distill accuracy than conventional NAS. (3) DisWOT exploits the distance of higher-order knowledge between the neural networks, bridging knowledge distillation and zero-proxy NAS. We further demonstrate the competitive ranking correlation of DisWOT among 10 knowledge distances in KD as zero-proxy for predicting vanilla accuracy in NAS-Bench-201. We anticipate that our work on KD-based zero-proxy can offer some assistance in furthering research endeavors related to KD and NAS.", + "bbox": [ + 496, + 227, + 895, + 513 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We conduct extensive experiments on CIFAR-100, ImageNet, and the NAS-Bench-201 [14] dataset, demonstrating the superiority of our proposed approach. In contrast to experiments in traditional architectural search, we focus on final distillation accuracy instead of the vanilla accuracy for the student. The results show that our DisWOT can achieve better accuracy than traditional Zero-shot NAS in the same search space. Besides, by switching to a larger space, our DisWOT can obtain new state-of-the-art architectures. For example, in the same ResNet-like search space, we significantly improved $1.62\\%$ Top-1 accuracy over KD for ResNet50-ResNet18 pair under the same training settings. We also conducted comprehensive ablation studies to investigate how our method can use the predictability of zero-cost metrics to boost the distillation performance.", + "bbox": [ + 496, + 513, + 895, + 739 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Main Contributions:", + "text_level": 1, + "bbox": [ + 500, + 739, + 650, + 755 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- By analyzing and exploring the discrepancy between teacher-student capability, we empirically show that their semantic similarities have a stronger correlation with the final distillation accuracy. This motivates us to propose a new student architecture search for the Distillation without Training (DisWOT) framework to reduce the teacher-student capability gap, which, to the best of our knowledge, is not achieved in the area of knowledge distillation.", + "bbox": [ + 517, + 763, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "11899", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- DisWOT proposes novel zero-cost metrics on similarity of feature semantics and sample relations and ensemble these metrics to select the optimal student via an evolutionary algorithm at the initial time. In the distillation stage, DisWOT achieves state-of-the-art performances in multiple datasets and search spaces.", + "- We further expand 10 kinds of knowledge distances including DisWOT as new universal KD-based zero proxies, which enjoy competitive predictive power with actual performance of models. We hope that our contributions in this endeavor may aid to some degree in advancing future research on KD and NAS." + ], + "bbox": [ + 96, + 90, + 470, + 280 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2. Related Work and Background", + "text_level": 1, + "bbox": [ + 76, + 291, + 362, + 309 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we summarize existing knowledge distillation and architecture search methods and clarify their differences to our method.", + "bbox": [ + 76, + 316, + 470, + 361 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.1. General Formulation of Knowledge Distillation", + "text_level": 1, + "bbox": [ + 76, + 369, + 468, + 386 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The fundamental concept underlying Knowledge Distillation (KD) involves utilizing acquired knowledge (e.g., logits [31], feature values [30, 32, 33, 35, 70], and sample relations [45, 59]) from a high-capacity teacher to guide the training of a student model. The training dataset $(X,Y)$ comprises training samples $X = x_{i=1}^{n}$ and their corresponding labels $Y = y_{i=1}^{n}$ . Let $f_{T}$ be the output logits of the fixed teacher $T$ and let $f_{S}$ be the output of student $S$ , respectively. In KD, the student network $f_{S}$ is trained by minimizing:", + "bbox": [ + 75, + 392, + 470, + 542 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {S} = \\mathcal {L} _ {C E} \\left(f _ {S}, Y\\right) + \\mathcal {L} _ {K L} \\left(f _ {S}, f _ {T}\\right) + \\mathcal {D} _ {f} \\left(\\phi_ {S} (x), \\phi_ {T} (x)\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 551, + 468, + 566 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{CE}$ is the regular cross-entropy loss. $\\mathcal{L}_{KL}$ represents Kullback-Leibler (KL) divergence. $\\mathcal{D}_f(\\cdot, \\cdot)$ is the distance function measuring the difference of intermediate feature representations (see Table 1 for particular distillers).", + "bbox": [ + 75, + 573, + 470, + 633 + ], + "page_idx": 2 + }, + { + "type": "table", + "img_path": "images/7537610383b661d4e551c11ed00149b09060387d7f91ff36a9e5ed0b281e2bf3.jpg", + "table_caption": [ + "Table 1. Comparison of recent distillers." + ], + "table_footnote": [], + "table_body": "
MethodKnowledgeDistance Df(·,·)
FitNets [54]Feature representationL2
AT [73]Attention mapsL2
CC [49]Instance relationL2
NST [24]Neuron selectivity patternsLMMD
PKT [46]Similarity probability distributionLKL
", + "bbox": [ + 86, + 652, + 457, + 736 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Comparison with Other Adaptive KDs for Distillation Gap. DisWOT is the first train-free architecture search solution to reduce the teacher-student gap. Unlike training manners [10] and KD-loss designs, DisWOT utilizes the classic KD training configurations and distillers. In addition, DisWOT is free from the assistant teacher in ATKD [43], which involves a complex training routine and budget. AKD [40] searches student via reinforcement learning based on feedback from individual training of lots of models. As a completely alternative technical route to these training-based", + "bbox": [ + 75, + 750, + 470, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Table 2. Formulation of NAS methods. $\\mathcal{A}$ is the search space. A candidate architecture in the search space is denoted as $\\alpha \\in \\mathcal{A}$ , which corresponds to a neural architecture $S(\\alpha, w)$ with weight $w$ . $\\mathcal{W}$ is the weight of the supernet. $\\text{train}$ and $\\text{val}$ are the loss functions on the training and validation sets, respectively.", + "bbox": [ + 496, + 88, + 893, + 159 + ], + "page_idx": 2 + }, + { + "type": "table", + "img_path": "images/021e7aae22f9c4a3ba2de47872621dae87865bb47123563f6bd27631b4eba1f0.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
TypeEvaluationFormula
Training-basedMulti-trial Trainingα* = arg min val(S(α, wα)), s.t. wα = arg min w train(S(α, w))
Weight sharingα* = arg min val(S(α, W_A(α))), s.t. W_A = arg min w train(S(A, W))
Training-freeZero-cost Proxyα* = ZeroProxy(S(α, w)) α∈A
", + "bbox": [ + 511, + 169, + 880, + 353 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "NAS [18], our training-free DisWOT builds on new zero-proxy and achieves $180 \\times 1000 \\times$ training acceleration, which greatly improves its easy-to-use and flexibility.", + "bbox": [ + 496, + 378, + 893, + 425 + ], + "page_idx": 2 + }, + { + "type": "table", + "img_path": "images/06f5dbf7f31b44464c94553a2f7607025a4e82bcd99e04b583d164a41e9b1620.jpg", + "table_caption": [ + "Table 3. Comparison with different training-free NAS." + ], + "table_footnote": [], + "table_body": "
TypeMethodTeacher-awareObjective
Prune-basedSNIP [28], Fisher [1], Synflow [58]✗Vanilla acc.
Activation-basedNWOT [42], Zen-NAS [36]✗Vanilla acc.
KD-basedDisWOT (ours)✓Distill acc.
", + "bbox": [ + 501, + 463, + 890, + 516 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Revisiting Architecture Search Methods", + "text_level": 1, + "bbox": [ + 498, + 542, + 841, + 559 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Neural Architecture Search (NAS) is emerged to reduce human efforts in architecture design and automate the discovery of high-performance networks. As formalized in Tab. 2, Multi-trial NAS methods [40, 79] train a large number of candidates individually, which leads to extensive resource consumption. To alleviate this, many NAS [8,12,23,51] methods adopt a weight-sharing strategy within a single supernet to facilitate the simultaneous training of candidates. The supernet is trained for hundred of epochs by path sampling [11,19] or compound optimization with architecture representations [39,69]. As an orthogonal direction, zero-cost NAS methods [42,71] focus on identifying well-performed architectures with training-free metrics. For example, NWOT [42] calculates the architecture score based on the kernel matrix of binary activations between small batches of samples.", + "bbox": [ + 496, + 566, + 893, + 808 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Comparison with NAS with Teacher. Some training-based NAS [29,50,77] employ a teacher model to supervise supernet training to improve predictive ability in the search stage. However, these methods aim to improve vanilla accuracy, not for distillation, and they do not use the teacher model in the full training stage. In addition, without any", + "bbox": [ + 496, + 810, + 893, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "11900", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/ea0b209d838cdf1732db7233db8049f9f0600bba89416beb8d93117f04f5682b.jpg", + "image_caption": [ + "Figure 3. A schematic overview of our DisWOT, including (a) detailed calculation of the DisWOT scores and (b) evolution of the student architecture via the DisWOT scores. In search phase, DisWOT use semantic similarity metrics and relations similarity metrics to select good student for a given teacher. The semantic similarity metric is measured by $l_{2}$ distance of the channel-wise correlation matrix for Grad-cam activation maps. Similarly, the relation similarity matrix statistics the sample-wise correlation matrix distance of the randomly initialized teacher-student pairs. With the feedback from these metrics, the evolutionary search in DisWOT automatically imitates good student from weak ones. In distillation phase, this searched student is distilled via teacher model and achieves superior gains." + ], + "image_footnote": [], + "bbox": [ + 76, + 85, + 893, + 300 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "training costs, our training-free DisWOT enjoys obvious differences than these methods and advantages in efficiency.", + "bbox": [ + 75, + 409, + 470, + 439 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Compared to Other Training-free NAS. Table 3 clearly summarizes the differences between DisWOT and other zero-cost methods [1, 28, 36, 42, 58]. Moreover, DisWOT outperforms these methods on distillation performance prediction and boosting in our sufficient experiments dealing with diverse datasets and search spaces.", + "bbox": [ + 75, + 440, + 470, + 531 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 76, + 547, + 210, + 565 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Figure 3 provides an overview of the DisWOT framework, which is comprised of two main stages: optimal student network search and distillation with high-order knowledge. In the search stage, we employ the neural architecture search technique to obtain an optimal student network for a pre-defined teacher network. Notably, we propose a training-free proxy called DisWOT to accurately rank enormous student networks and prevent expensive evaluation processes with high efficiency. In the distillation stage, the searched student network is retrained with distillation to imitate high-order knowledge in the teacher network. We give the details of these two designs in the following sections.", + "bbox": [ + 75, + 575, + 470, + 755 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1. Search for Optimal Student Network", + "text_level": 1, + "bbox": [ + 76, + 768, + 397, + 784 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We first present the training-free metrics we designed to score a student architecture, which indicates its final accuracy when distilled with a pre-defined teacher network. Then we depict the details of the evolutionary process to obtain an optimal student candidate.", + "bbox": [ + 75, + 792, + 470, + 868 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Semantic Similarity Metric. The semantic information is meaningful for neural networks to perceive as humans. In", + "bbox": [ + 75, + 869, + 470, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "distillation, the teacher network always has more convolutional operations than the student, resulting in a teacher feature map with a larger receptive field and greater richness of semantic information. In contrast to distiller designs to alleviate semantic gaps, we aim for train-free student architecture to better match the teacher model with computational constraints. We notice that the network with random initial weights also has some semantic localization capability. Thus, we start to analyze the localization performance of the randomly initialized teacher-student model. Specifically, we utilize Grad-CAM maps [78] to localize semantic object regions, which explains the model decisions using gradient information. Given a mini-batch of input images, we define the high-level feature map before the Global Average Pooling (GAP) layer of the teacher network $T$ as $A_{T} \\in \\mathbf{R}^{B \\times C_{T} \\times H_{T} \\times W_{T}}$ , where $B$ represents the batch size, $C_{T}$ denotes the number of output channels, and $H_{T}$ and $W_{T}$ are the spatial dimensions. Additionally, we introduce $A_{T}^{c} \\in \\mathbf{R}^{N \\times H_{T} \\times W_{T}}$ as the c-th spatial map along the channel dimension. For the student network $S_{i}$ , we have feature map $A_{S_{i}}^{c} \\in \\mathbf{R}^{B \\times C_{S} \\times H_{S} \\times W_{S}}$ and spatial map $A_{S_{i}}^{c} \\in \\mathbf{R}^{B \\times H_{S} \\times W_{S}}$ , respectively. To compute the Grad-CAM maps of the $n$ -th class for both the teacher and student networks, we can use the following formulations:", + "bbox": [ + 496, + 409, + 893, + 772 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nG _ {T} = \\sum_ {c = 1} ^ {C _ {T}} w _ {n, c} ^ {T} A _ {T} ^ {c}, \\quad G _ {S _ {i}} = \\sum_ {c = 1} ^ {C _ {S}} w _ {n, c} ^ {S} A _ {S _ {i}} ^ {c}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 560, + 782, + 890, + 819 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $w^{T} \\in \\mathbf{R}^{N \\times C_{T}}$ and $w^{S} \\in \\mathbf{R}^{N \\times C_{S}}$ are weights of the last fully-connected layer in the teacher and student network. $N$ represents the number of classes. $w_{n,c}^{T}$ and $w_{n,c}^{S}$ refer to the element located in the $n$ -th row and $c$ -th column of weight matrices $w^{T}$ and $w^{S}$ , respectively. To quantify", + "bbox": [ + 496, + 823, + 893, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "11901", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the intersection of class-discriminative localization maps, we formulate semantic similarity metric $\\mathcal{M}_s$ as the intercorrelation on the accumulated Grad-CAM maps for both teacher and student networks as follows:", + "bbox": [ + 75, + 90, + 470, + 151 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {G} ^ {T} = \\frac {\\left(G _ {T}\\right) \\cdot \\left(G _ {T}\\right) ^ {\\top}}{\\| \\left(G _ {T}\\right) \\cdot \\left(G _ {T}\\right) ^ {\\top} \\| _ {2}}, \\mathcal {G} ^ {S} = \\frac {\\left(G _ {S}\\right) \\cdot \\left(G _ {S}\\right) ^ {\\top}}{\\| \\left(G _ {S}\\right) \\cdot \\left(G _ {S}\\right) ^ {\\top} \\| _ {2}}, (3)\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 159, + 470, + 196 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {M} _ {s} = \\left\\| \\mathcal {G} ^ {T} - \\mathcal {G} ^ {S _ {i}} \\right\\| _ {2}. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 196, + 210, + 470, + 232 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Relation Similarity Metric. The relationships between input samples are non-trivial for knowledge transfer. To reduce the teacher-student gap and improve the relation-distillation performance, we use the correlation matrix as the sample-wise metric to search for an optimal student network. For the random teacher network $T$ and student network $S_{i}$ with activation maps $A_{T} \\in \\mathbf{R}^{N \\times C_{T} \\times H_{T} \\times W_{T}}$ and $A_{S}^{i} \\in \\mathbf{R}^{N \\times C_{i} \\times H_{i} \\times W_{i}}$ , the correlation matrix of the minibatch samples in the teacher network is formulated as follows:", + "bbox": [ + 75, + 237, + 472, + 387 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {A} ^ {T} = \\frac {(\\tilde {A} _ {T}) \\cdot (\\tilde {A} _ {T}) ^ {\\top}}{\\left\\| (\\tilde {A} _ {T}) \\cdot (\\tilde {A} _ {T} ^ {\\top}) \\right\\| _ {2}}, \\mathcal {A} ^ {S _ {i}} = \\frac {(\\tilde {A} _ {S}) \\cdot (\\tilde {A} _ {S}) ^ {\\top}}{\\left\\| (\\tilde {A} _ {S}) \\cdot (\\tilde {A} _ {S} ^ {\\top}) \\right\\| _ {2}}, (5)\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 396, + 470, + 444 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\tilde{A}_T\\in \\mathbf{R}^{N\\times CHW}$ is a reshaping of $A_{T}$ , and $M_T$ is a $N\\times N$ matrix. Thus, the $(i,j)$ entry in matrix $C_T$ represents the similarity between the $i$ -th and $j$ -th images within the mini-batch. Based on this, the sample similarity metric $\\mathcal{M}_r$ for a potential student model $S_{i}$ is defined as follows:", + "bbox": [ + 76, + 453, + 468, + 531 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {M} _ {r} = \\left\\| \\mathcal {A} ^ {T} - \\mathcal {A} ^ {S _ {i}} \\right\\| _ {2}. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 194, + 541, + 470, + 561 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training-Free Evolutionary Search. Based on the above metric, we conduct a training-free evolutionary search algorithm to efficiently discover the optimal student $\\alpha^{*}$ from search space $\\mathcal{A}$ , as:", + "bbox": [ + 75, + 587, + 468, + 647 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\alpha^ {*} = \\arg \\min _ {\\alpha \\in \\mathcal {A}} \\left(\\mathcal {M} _ {s} + \\mathcal {M} _ {r}\\right). \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 178, + 660, + 468, + 681 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Theoretical Understanding. According to the VC theory [63], the classification error of the vanilla teacher-student network can be decomposed as follows:", + "bbox": [ + 76, + 693, + 468, + 739 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nR \\left(f _ {s}\\right) - R \\left(f _ {r}\\right) \\leq O \\left(\\frac {\\left| \\mathcal {F} _ {s} \\right| _ {C}}{n ^ {\\alpha s r}}\\right) + \\epsilon_ {s r}; R \\left(f _ {t}\\right) - R \\left(f _ {r}\\right) \\leq O \\left(\\frac {\\left| \\mathcal {F} _ {t} \\right| _ {C}}{n ^ {\\alpha t r}}\\right) + \\epsilon_ {t r}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 750, + 468, + 771 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $f_{s}\\in \\mathcal{F}_{s}$ is the student function, $f_{t}\\in \\mathcal{F}_{t}$ is the teacher function, and $f_{r}\\in \\mathcal{F}_{r}$ is the target function. $R$ is the error. $O(\\cdot)$ and $\\epsilon_{sr}$ terms are the estimation and approximation error, respectively. $O(\\cdot)$ is related to the statistical procedure when given the number of data points. In contrast, $\\epsilon_{sr}$ is the approximation error of the student function class $\\mathcal{F}_s$ for $f_{r}\\in \\mathcal{F}_{r}.\\left|\\cdot \\right|_{C}$ is an function class capacity measure, and $n$ is the number of data point. During distillation,", + "bbox": [ + 75, + 779, + 470, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "the student network is supervised purely with the teacher network as follows:", + "bbox": [ + 498, + 90, + 890, + 119 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nR \\left(f _ {s}\\right) - R \\left(f _ {t}\\right) \\leq O \\left(\\frac {\\left| \\mathcal {F} _ {s} \\right| _ {C}}{n ^ {\\alpha_ {s t}}}\\right) + \\epsilon_ {s t}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 570, + 128, + 890, + 162 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\alpha_{st}$ and $\\epsilon_{st}$ are associated to student learning from teacher. By combining Equations 3.1 and 9, we obtain:", + "bbox": [ + 498, + 174, + 890, + 205 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nR \\left(f _ {s}\\right) - R \\left(f _ {r}\\right) \\leq O \\left(\\frac {\\left| \\mathcal {F} _ {t} \\right| _ {C}}{n ^ {\\alpha_ {t r}}}\\right) + \\epsilon_ {t r} + O \\left(\\frac {\\left| \\mathcal {F} _ {s} \\right| _ {C}}{n ^ {\\alpha_ {s t}}}\\right) + \\epsilon_ {s t}. \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 215, + 890, + 239 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "When student obtains gains in KDs, its upper bound of error in distillation is smaller than vanilla training, which satisfies the following inequality:", + "bbox": [ + 498, + 250, + 890, + 296 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nO \\left(\\frac {\\left| \\mathcal {F} _ {t} \\right| _ {C}}{n ^ {\\alpha_ {t r}}} + \\frac {\\left| \\mathcal {F} _ {s} \\right| _ {C}}{n ^ {\\alpha_ {s t}}}\\right) + \\epsilon_ {t r} + \\epsilon_ {s t} \\leq O \\left(\\frac {\\left| \\mathcal {F} _ {s} \\right| _ {C}}{n ^ {\\alpha_ {s r}}}\\right) + \\epsilon_ {s r}. \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 306, + 890, + 333 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Based on the assumption in [22] that $\\epsilon_{tr} + \\epsilon_{st} \\leq \\epsilon_{sr}$ holds consistently, we focus on minimizing $O\\left(\\frac{|\\mathcal{F}_t|_C}{n^{\\alpha_{tr}}} + \\frac{|\\mathcal{F}_s|_C}{n^{\\alpha_{st}}}\\right)$ to improve the distillation performance. As noted in Lopez-Paz et al [41], a better representation allows for a faster learning rate with a fixed amount of data. Hence, when there is a larger gap between the capacities of the student and teacher networks, the value of $\\alpha_{st}$ tends to be lower. Thus we aim to search for an optimal student network that meets the requirement of $\\alpha_{si t} \\leq \\alpha_{so t}$ , where $s_i$ is all candidate student networks, and $s_o$ is our searched student network. In this case, the inequality becomes more effective, and we improve the knowledge distillation by injecting a larger $\\alpha_{so t}$ . Specifically, we present the overall procedure for discovering optimal student in algorithm 1.", + "bbox": [ + 498, + 342, + 893, + 559 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Effects of Search Strategies. We compare the evolution search algorithm and the random search algorithm in search space $S_{2}$ with the same number of iterations, as shown in Figure 4. We find that the evolution search algorithm can consistently find architectures with lower DisWOT, especially when the search space is relatively large, and the evolutionary search can explore better architectures.", + "bbox": [ + 498, + 560, + 893, + 667 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2. Distillation with High-order Knowledge", + "text_level": 1, + "bbox": [ + 500, + 676, + 841, + 694 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In the distillation stage, teacher model $T$ is employed to distill the optimal student network $f_{S}$ . To verify the superiority of our search architecture, we adopt the existing distillers (e.g., KD) as the default distillation setting. In addition, we observe that the metrics we searched for actually serve as minimization optimization goals in the distillation process to transfer the teacher's privileged semantic and sample relational knowledge as the semantic distillation and sample distillation:", + "bbox": [ + 496, + 699, + 893, + 825 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathcal {M} _ {s}} = \\frac {1}{c ^ {2}} \\left\\| \\mathcal {G} ^ {T} - \\mathcal {G} ^ {S} \\right\\| _ {2}, \\mathcal {L} _ {\\mathcal {M} _ {r}} = \\frac {1}{b ^ {2}} \\left\\| \\mathcal {A} ^ {T} - \\mathcal {A} ^ {S} \\right\\| _ {2}, \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 835, + 890, + 861 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finally, we involve these advanced distillers in our framework, called DisWOT†. The total loss for DisWOT and", + "bbox": [ + 500, + 869, + 893, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "11902", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Algorithm 1 Evolution Search for DisWOT", + "text_level": 1, + "bbox": [ + 76, + 90, + 367, + 104 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Input: Search space $S$ , population $\\mathcal{P}$ , architecture constraints $\\mathcal{C}$ , max iteration $\\mathcal{N}$ , sample ratio $r$ , sampled pool $\\mathcal{Q}$ , topk $k$ , teacher network $\\mathcal{T}$ .", + "bbox": [ + 76, + 107, + 468, + 147 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Output: Highest DisWOT score architecture.", + "bbox": [ + 76, + 148, + 348, + 162 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1: $\\mathcal{P}_0\\coloneqq$ Initialize population $(P_{i},\\mathcal{C})$", + "2: sample pool $\\mathcal{Q} := \\emptyset$ ;", + "3: for $i = 1:\\mathcal{N}\\mathbf{d}\\mathbf{o}$", + "4: Clear sample pool $\\mathcal{Q} \\coloneqq \\emptyset$ ;", + "5: Randomly select $r \\times \\mathcal{P}$ subnets $\\hat{P}_i \\in \\mathcal{P}$ to get $\\mathcal{Q}$ ;", + "6: Candidates $\\{A_i\\}_k \\coloneqq \\operatorname{GetTopk}(\\mathcal{Q}, k)$ ;", + "7: Parent $A_{i}\\coloneqq$ RandomSelect $(\\{A_i\\}_k)$", + "8: Mutate $\\hat{P}_i\\coloneqq \\mathrm{MUTATE}(A_i)$", + "9: if $\\hat{P}_i$ do not meet the constraints $\\mathcal{C}$ then", + "10: Do nothing;", + "11: else", + "12: Get DisWOT-Score $z \\coloneqq \\operatorname{DisWOT}(\\hat{P}_i, \\mathcal{T})$ ;", + "13: Append $\\hat{P}_i$ to $\\mathcal{P}$", + "14: end if", + "15: Remove network of smallest DisWOT-score;", + "16: end for" + ], + "bbox": [ + 81, + 179, + 413, + 398 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/35fc33d4661068e9763fa5d56ca3b2d9def20424836406105ca2d91cb9b07dcb.jpg", + "image_caption": [ + "Figure 4. Left: comparison of random search and evolution search. Right: ranking correlation of different distillation methods on NAS-Bench-201." + ], + "image_footnote": [], + "bbox": [ + 78, + 416, + 277, + 525 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e67848fe911182b190df27a081f8fd05620c88d706d2d6548fa66497450225fe.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 279, + 420, + 465, + 525 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/979fe7bf4f4905a901812a06f14e3dae3367121c6ff5aa311136d17e6403aa5d.jpg", + "table_caption": [ + "Table 4. Spearman correlation $\\rho \\left( \\% \\right)$ on NAS-Bench-201." + ], + "table_footnote": [], + "table_body": "
TypeMethodρMethodρ
Zero-costGrad_Norm [1]58.70±0.11Synflow [58]74.61±0.08
SNIP [28]58.17±0.15Jacob [57]73.42±0.03
ProxiesFisher [1]35.91±0.09Zen-NAS [36]41.36±0.06
NWOT [42]64.41±0.08FLOPs [1]63.38±0.06
KD-basedKD [22]54.43±0.09PKT [47]52.65±0.09
FitNets [55]56.18±0.09CC [48]65.90±0.08
ProxiesSP [62]51.24±0.08NST [25]72.35±0.09
RKD [44]25.71±0.17DisWOT72.36±0.02
", + "bbox": [ + 81, + 607, + 465, + 713 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "DisWOT† as:", + "bbox": [ + 76, + 736, + 169, + 751 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {D i s W O T}} = \\mathcal {L} _ {C E} \\left(f _ {S}, Y\\right) + \\mathcal {L} _ {K L} \\left(f _ {S}, f _ {T}\\right), \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 130, + 761, + 468, + 786 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {D i s W O T}} \\dagger = \\mathcal {L} _ {\\text {D i s W O T}} + \\mathcal {L} _ {\\mathcal {M} _ {s}} + \\mathcal {L} _ {\\mathcal {M} _ {r}}.\n$$\n", + "text_format": "latex", + "bbox": [ + 163, + 782, + 411, + 796 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.3. Bridging Distiller and Zero-proxy", + "text_level": 1, + "bbox": [ + 76, + 816, + 372, + 833 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In our DisWOT framework, we use the semantic and relational similarity metrics as a distillation performance predictor and distiller. In addition, DisWOT also enjoys good performance for vanilla performance predictions. Encour", + "bbox": [ + 76, + 839, + 472, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "aged by this intriguing observation, we employ the knowledge function in of different KDs as zero-proxies and evaluate their ranking consistency with vanilla accuracy. As shown in Table 4, these KD-based zero-proxies enjoy competitive rankings with other NAS methods. Detailed results in Figure 4 illustrate that our DisWOT and NST [24] are the winners in the family of KD-based proxies. These attempts reveal the close connections between KD and NAS, and augment $10+$ new universal proxies from the teacher-student learning perspective for training-free NAS research.", + "bbox": [ + 496, + 90, + 893, + 243 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experimental results", + "text_level": 1, + "bbox": [ + 500, + 257, + 697, + 273 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we present the experimental results of our DisWOT on different datasets. First, we describe the four datasets used in our experiments and three search spaces $S_0, S_1, S_2$ in Sec. 4.1. Then, we conduct a comprehensive set of experiments to evaluate the effectiveness of DisWOT.", + "bbox": [ + 496, + 282, + 893, + 359 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 500, + 369, + 689, + 386 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We perform experiments on four datasets, namely CIFAR-10, CIFAR-100, ImageNet-16-120, and ImageNet-1k. In the search process, we only use one batch of training data to get the statistic at nearly no cost. Following previous works, our experiments are conducted on the following three search spaces:", + "bbox": [ + 496, + 393, + 893, + 484 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Search Space $S_0$ : Following CIFar-ResNet [20], the search space consists of three residual blocks and is based on CIFAR-100 datasets. The depth of each residual block is searched in set $\\{1,3,5,7\\}$ .", + "bbox": [ + 496, + 484, + 890, + 545 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Search Space $S_{1}$ : Following NAS-Bench-201 [14], this Darts-like search space is a cell-based search space consisting of stacked directed acyclic graphs. $S_{1}$ is conducted on CIFAR-10, CIFAR-100, and ImageNet-16-120 datasets.", + "bbox": [ + 496, + 546, + 893, + 606 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Search Space $S_{2}$ : Following NDS [53], this search space consists of residual and bottleneck blocks defined in ResNet. $S_{2}$ is based on CIFAR-100 and ImageNet-1k dataset.", + "bbox": [ + 496, + 607, + 893, + 654 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Experiments on CIFAR-100", + "text_level": 1, + "bbox": [ + 500, + 664, + 750, + 680 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details. We compare distillation gains with other zero-nas on search space $S_{1}$ . In the search phase, we configure 48k evolution iters with 512 population sizes. In distillation, All searched student networks are trained via CRD's settings [59] with ResNet56 as the teacher model.", + "bbox": [ + 496, + 688, + 893, + 763 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Distillation Results of Zero-cost Proxies. We conduct detailed experiments on other zero-cost proxies with different knowledge distillation methods. Note that we search the student network under constraints of 1M parameters. The results in Table 5 demonstrated that our proposed DisWOT achieved superior results compared with other zero-cost proxies with different knowledge distillation methods. The DisWOT outperforms its counterparts vanilla networks by around $2\\%$ , while achieving consistent improvements", + "bbox": [ + 496, + 763, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "11903", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/a52e0969f296bc4c1ff5ecd4b5852c49515a34b2a4027af93b98cb40c07357eb.jpg", + "table_caption": [ + "Table 5. Distillation results (\\%) of different zero-cost proxies with knowledge distillation methods under 1M parameters." + ], + "table_footnote": [], + "table_body": "
MethodRandomFLOPsSynflowNWOTDisWOT
Baseline69.5271.3772.8871.8073.12
KD70.4572.1373.7272.5774.73
FitNets70.1272.4073.5572.7274.85
AT70.1672.9773.5272.0874.50
SP70.4672.1473.5072.1674.95
RKD71.1972.2273.6972.6374.62
CRD71.5972.7873.9973.1275.25
", + "bbox": [ + 81, + 128, + 468, + 250 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "among different distillation methods, such as KD [22], Fit-Nets [55], AT [74], SP [62], RKD [44], and CRD [60].", + "bbox": [ + 76, + 276, + 470, + 308 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/e82b3abfca3472b5fe3ef8fdb5e9ea979c29d17f25d43257be2d45737191cbee.jpg", + "table_caption": [ + "Table 6. Distillation results(%) of zero-cost proxies under $\\{0.5,1,2\\}\\mathrm{M}$ parameters." + ], + "table_footnote": [], + "table_body": "
Param.FLOPsNWOTDisWOTDisWOT†
0.5M69.8870.3872.8973.75
1M72.1372.5774.2375.25
2M73.2773.8675.9576.67
", + "bbox": [ + 81, + 359, + 467, + 441 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/35c91b9709e3c85f3cfb911142a5f26d7b71253b087d54d790c569b097fa69d8.jpg", + "table_caption": [ + "Table 7. Distillation results(%) of zero-cost proxies under $\\{50,100\\}$ M FLOPs on space $S_{1}$ ." + ], + "table_footnote": [], + "table_body": "
FLOPsNWOTSynflowDisWOTFLOPsNWOTSynflowDisWOT
50M63.1964.2865.98100M70.3872.1272.89
", + "bbox": [ + 81, + 507, + 467, + 542 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/9646e96821f27d3f9017b163f39315821378989fb73971335f1c943588dbd84a.jpg", + "table_caption": [ + "Table 8. Ranking correlation (\\%) of zero-cost proxies on $S_0$ space on CIFAR-100." + ], + "table_footnote": [], + "table_body": "
MethodKendall's TauSpearmanPearson
FLOPs [1]51.6172.9276.40
Fisher [1]62.8681.3720.90
Grad_Norm [1]63.7582.3539.35
SNIP [28]67.2285.0751.09
NWOT [42]31.8745.6648.99
DisWOT (ours)73.9891.3884.83
", + "bbox": [ + 81, + 609, + 468, + 733 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Analysis on Varying Parameter Constraints. We analyze the performance of student models under different parameter constraints obtained by DisWOT on CIFAR-100. As shown in the Table 7, we compared our method with two zero proxies, a.k.a. FLOPs [1] and NWOT [42], under the parameter constraints of 0.5, 1, and 2M, respectively, and the results demonstrate that our method still achieves excellent results. As shown in Tab. 7, DisWOT also outperforms previous SOTA methods with $0.8\\% \\sim 1.7\\% \\uparrow$ gains under same FLOPs constraints,", + "bbox": [ + 75, + 750, + 472, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ranking Correlation with Distill Accuracy. Based on search space $S_0$ , we perform vanilla training and distillation for each candidate with CRD's settings [59]. Then, we collect these vanilla results as GT and analyze the different zero-proxy's correlation with them. As shown in Table 8, the results illustrate that our DisWOT achieves higher than Fisher, GradNorm, SNIP,FLOPs, and NWOT by a large margin, and achieve results that are on par with the best zero-cost proxy, a.k.a. Zen-NAS and Synflow, on Kendall's Tau, Pearson, and Spearman coefficient.", + "bbox": [ + 496, + 90, + 893, + 243 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Experiments on NAS-Bench-201", + "text_level": 1, + "bbox": [ + 498, + 252, + 784, + 268 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Implementation Details. For search trials, we first adopt ResNet110/56 as the teachers and then Conduct an evolution search with the DisWOT metric and get the best student network. We randomly sampled 50 candidate architectures to evaluate sequencing consistency. The distillation settings are the same as the Sec.4.2", + "bbox": [ + 496, + 275, + 893, + 364 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison results As shown in Table 9, some training-free methods can achieve good results with much faster speedups, such as NWOT and TE-NAS. Our proposed method DisWOT achieves a speedup ratio of $180 \\times$ , where if semantic similarity metric is removed, we can achieve a $300 \\times$ speedup ratio at the expense of some accuracy.", + "bbox": [ + 496, + 364, + 893, + 455 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Experiments on ImageNet", + "text_level": 1, + "bbox": [ + 498, + 465, + 736, + 483 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Implementation Details. We searched the ResNet18 level network regarding the search space in NDS [53]. Specifically, we limit the number of parameters to less than 13M and the depth of the network to up to 20 layers and find the optimal network by evolution algorithm with the DisWOT metric. As shown in Table 10, guided by three different sizes of networks, we used DisWOT to find the optimal student network. We trained the student network obtained by the search using the distillation strategy in DisWOT. Implementation details are available in supplementary materials. Comparison Results. Table 10 reports the performance of DisWOT on ImageNet with ResNet34/50 as teacher network. The results demonstrate that the student architecture of the ResNet18-level obtained by DisWOT under different teacher guidance and using different distillation strategies yielded significantly better results than its counterparts.", + "bbox": [ + 496, + 489, + 893, + 733 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Ablation Studies of DisWOT", + "text_level": 1, + "bbox": [ + 498, + 739, + 756, + 756 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We perform ablation experiments to verify the validity of each component of DisWOT in search space $S_0$ . As shown in Table 11, for semantic knowledge, similarity matrix obtains a more robust ranking improvement than simple Fit-Net [54]. For $\\mathcal{M}_r$ , similarity matrix performs better on relational knowledge than RKD [45]. DisWOT integrates semantic and relational knowledge to obtain an additional ranking improvement than stand-alone scores. The weight initialization scheme plays an important role in zero-proxy.", + "bbox": [ + 496, + 763, + 895, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "11904", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/09b030c721a1fb73ab94aedfadc8899b420cbb6b7ef8a60e345e7bf745027fb7.jpg", + "table_caption": [ + "Table 9. Distillation results on CIFAR-10, CIFAR-100, and ImageNet-16 in NAS-Bench-201 [13]. Dis. Acc. (%) represents the accuracy of the searched architecture after distillation training. Time (s) denotes the time cost (GPU-seconds) during the search phase. The results of NWOT and TE-NAS come from their original papers. Our DisWOT achieves competitive results with the lowest costs." + ], + "table_footnote": [], + "table_body": "
TypeModelCIFAR-10CIFAR-100ImageNet-16-120
Dis. Acc(%)Time (s)Speed-upDis. Acc(%)Time (s)Speed-upDis. Acc(%)Time (s)Speed-up
Multi-trialRS93.63216K1.0×71.28460K1.0×44.881M1.0×
RL [3]92.83216K1.0×71.71460K1.0×44.351M1.0×
BOHB [17]93.49216K1.0×70.84460K1.0×44.331M1.0×
RSPS [34]91.6710K21.6×57.9946K21.6×36.87104K9.6×
Weight-sharingGDAS [15]93.3922K12.0×70.7039K11.7×42.35130K7.7×
DARTS [38]89.2223K9.4×66.2480K5.8×43.18110K9.1×
Training-freeNWOT [42]93.732.2K100×73.314.6K100×45.4310K100×
TE-NAS [9]93.922.2K100×71.244.6K100×44.3810K100×
DisWOTMs & Mr93.551.2K180×74.219.2K180×47.3020K180×
Mr93.490.72K300×73.6218.4K300×45.6340K300×
", + "bbox": [ + 80, + 142, + 890, + 316 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/b12744d5d96c2ec30c2698803874a0d4aca3b102f74822a500c4ea4f1c894ba6.jpg", + "table_caption": [ + "Table 10. The accuracy $(\\%)$ of ResNet18 on ImageNet-1k with various teachers. Results of other KD methods refer to the papers of CRD [60] and ESKD [10]. ATKD $A_{R34}$ [43] denotes ResNet34 used as the assistant teacher. N/A means no available results. Our DisWOT obtains better performance than other methods and improves students' performance positively correlated with that of the teacher." + ], + "table_footnote": [], + "table_body": "
TeacherStudentAcc.TeacherStudentKD [22]ESKD [10]\\( \\mathrm{ATKD}_{A_{R18}} \\) [43]ONE [27]DML [75]CRD [60]DisWOT
ResNet34ResNet18Top-173.4069.7570.6670.8970.7870.5571.0371.1772.08
Top-591.4289.0789.8890.0689.9989.5990.2890.3290.38
TeacherStudentAcc.TeacherStudentKD [22]\\( \\mathrm{ATKD}_{A_{R18}} \\) [43]\\( \\mathrm{ATKD}_{A_{R34}} \\) [43]Seq. ESKD [10]ESKD [10]SRRL [72]DisWOT
ResNet50ResNet18Top-176.1669.7570.6870.6570.8570.6570.9571.2072.30
Top-592.8689.07N/AN/AN/AN/AN/AN/A90.51
", + "bbox": [ + 80, + 382, + 890, + 474 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/1788cadfe112dea57ef2515b1b582ca908c27faa85de8d94e9296f3784acc041.jpg", + "table_caption": [ + "Table 11. Spearman correlation (\"mean±std\") of DisWOT on search space $S_0$ ." + ], + "table_footnote": [], + "table_body": "
KnowledgeMetricSpearman (%)
MsFitNets [54]64.06±6.11
MsSimilarity matrix73.68±5.45
MrRKD [59]13.52±11.51
MrSimilarity matrix72.36±3.42
Ms & MrSimilarity matrix77.51±2.76
", + "bbox": [ + 101, + 537, + 444, + 646 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We verify the effect of the initialization strategy of the network on the ranking consistency. The results in Tab. 12 demonstrate that the Gaussian initialization strategy is detrimental to $\\mathcal{M}_s$ , but beneficial to $\\mathcal{M}_r$ .", + "bbox": [ + 75, + 672, + 470, + 734 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 751, + 196, + 767 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we present DisWOT, a new teacher-aware student architecture search without training framework for distillation. Based on key observations about the difference between vanilla and distillation accuracy, DisWOT measures the new zero-cost proxy conditioned on the similarity of feature semantics and sample relations between random initialized teacher-student network. Then, DisWOT search for the best student architectures for the given teacher us", + "bbox": [ + 75, + 777, + 472, + 902 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/14e7d3d7fda892d73777c45e0ef58f437e1e50192aecc47ef972f462ccf7674a.jpg", + "table_caption": [ + "Table 12. \"mean±std %\" Spearman of proxies via Kaiming and Gaussian initialization on search space $S_0$ and NAS-Bench-201 with various seeds." + ], + "table_footnote": [], + "table_body": "
SpaceInitialFisherGradNormNWOTDisWOT
S0Kaim.81.37±0.0182.35±0.0145.66±0.0584.08±0.03
Gauss.80.99±0.0175.50±0.0145.36±0.0391.38±0.03
NB-201Kaim.54.63±0.1558.70±0.1164.41±0.0865.57±0.02
Gauss.45.91±0.0945.70±0.1162.24±0.0772.36±0.02
", + "bbox": [ + 503, + 550, + 890, + 611 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ing an evolutionary algorithm with these metrics. Thorough evaluations are performed on diverse datasets and search spaces, and DisWOT achieves significant performance gains in various neural networks with at least $180 \\times$ training acceleration. We experimentally and theoretically explained the relationship between similarity difference and distillation performance. In addition, we also extend DisWOT to new distillers and general zero proxy to predict the performance of models. By doing this, we bridge the higher-order knowledge bewteen distillation and network architecture search. This approach represents an elegant and practical solution, which we hope will inspire future research on knowledge distillation and architecture search design.", + "bbox": [ + 496, + 641, + 893, + 837 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations. Following most zero-cost NAS, we evaluate DisWOT in classification tasks. In the future work, we will make efforts to expand the DisWOT for downstream tasks (e.g., object detection and semantic segmentation).", + "bbox": [ + 496, + 839, + 893, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "11905", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Mohamed S Abdelfattah, Abhinav Mehrotra, Lukasz Dudziak, and Nicholas Donald Lane. Zero-cost proxies for lightweight nas. In ICLR, 2020. 3, 4, 6, 7", + "[2] Sungsoo Ahn, Shell Xu Hu, Andreas Damianou, Neil D Lawrence, and Zhenwen Dai. Variational information distillation for knowledge transfer. In CVPR, 2019. 1", + "[3] Bowen Baker, Otkrist Gupta, Nikhil Naik, and Ramesh Raskar. 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In CVPR, 2018. 3" + ], + "bbox": [ + 78, + 90, + 468, + 333 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "11908", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/DisWOT_ Student Architecture Search for Distillation WithOut Training/cc4b4c46-ca23-4c2e-9650-90533edd035d_model.json b/2023/DisWOT_ Student Architecture Search for Distillation WithOut Training/cc4b4c46-ca23-4c2e-9650-90533edd035d_model.json new file mode 100644 index 0000000000000000000000000000000000000000..723b625b127abf01f2e1831c274ce1f224b351a5 --- /dev/null +++ b/2023/DisWOT_ Student Architecture Search for Distillation WithOut Training/cc4b4c46-ca23-4c2e-9650-90533edd035d_model.json @@ -0,0 +1,2763 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.12, + 0.131, + 0.852, + 0.154 + ], + "angle": 0, + "content": "DisWOT: Student Architecture Search for Distillation WithOut Training" + }, + { + "type": "text", + "bbox": [ + 0.176, + 0.18, + 0.793, + 0.234 + ], + "angle": 0, + "content": "Peijie Dong\\(^{1\\dagger}\\) Lujun Li\\(^{2\\dagger*}\\) Zimian Wei\\(^{1\\dagger}\\) \n\\(^{1}\\)National University of Defense Technology, Chinese Academy of Sciences \n\\(^{1}\\{dongpeijie, weizimian16\\} @nudt.edu.cn, ^{2}\\)lilujunai@gmail.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.301, + 0.474, + 0.694 + ], + "angle": 0, + "content": "Knowledge distillation (KD) is an effective training strategy to improve the lightweight student models under the guidance of cumbersome teachers. However, the large architecture difference across the teacher-student pairs limits the distillation gains. In contrast to previous adaptive distillation methods to reduce the teacher-student gap, we explore a novel training-free framework to search for the best student architectures for a given teacher. Our work first empirically show that the optimal model under vanilla training cannot be the winner in distillation. Secondly, we find that the similarity of feature semantics and sample relations between random-initialized teacher-student networks have good correlations with final distillation performances. Thus, we efficiently measure similarity matrix conditioned on the semantic activation maps to select the optimal student via an evolutionary algorithm without any training. In this way, our student architecture search for Distillation WithOut Training (DisWOT) significantly improves the performance of the model in the distillation stage with at least \\(180 \\times\\) training acceleration. Additionally, we extend similarity metrics in DisWOT as new distillers and KD-based zero-proxies. Our experiments on CIFAR, ImageNet and NAS-Bench-201 demonstrate that our technique achieves state-of-the-art results on different search spaces. Our project and code are available at https://lilujunai.github.io/DisWOT-CVPR2023/." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.721, + 0.21, + 0.737 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.747, + 0.472, + 0.868 + ], + "angle": 0, + "content": "Despite the remarkable achievements of Deep Neural Networks (DNNs) in numerous visual recognition tasks [52, 64-68], they usually lead to heavy costs of memory, computation, and power at model inference due to their large numbers of parameters. To address this issue, Knowledge Distillation (KD) has been proposed as a means of transferring knowledge from a high-capacity teacher model to a low-capacity target student model, providing a more op" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.27, + 0.693, + 0.379 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.693, + 0.269, + 0.889, + 0.379 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.383, + 0.895, + 0.44 + ], + "angle": 0, + "content": "Figure 1. Left: Ranking correlation of proxies in zero-cost NAS with vanilla and distillation accuracy. Right: Vanilla accuracy, distillation accuracy, prediction scores of DisWOT for ResNet[7,1,3] and ResNet[3,3,3] on search space \\( S_0 \\)." + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.459, + 0.691, + 0.567 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.693, + 0.458, + 0.891, + 0.567 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.571, + 0.895, + 0.613 + ], + "angle": 0, + "content": "Figure 2. Left: KD [22], DisWOT, DisWOT† results for ResNet20 under different teachers. Right: Comparison of distill accuracy & training efficiency with other NAS methods on NAS-Bench-201." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.642, + 0.895, + 0.824 + ], + "angle": 0, + "content": "timal accuracy-efficiency trade-off during runtime [4, 7, 76]. The original KD method [22] utilizes the logit outputs of the teacher network as the source of knowledge. Subsequent studies [2, 21, 24, 26, 54, 61, 73] have focused on extracting informative knowledge based on intermediate feature representations. However, as the gap in capacity between students and teachers increases, existing KD methods are unable to improve results, particularly in tasks that depend on large-scale visual models such as VIT and GPT-3 [5, 16]. For example, as shown in Figure 2 (Left), the large teacher (e.g., ResNet110) lead to worse performance for the fixed student than the relatively smaller one (e.g., ResNet56)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.897, + 0.901 + ], + "angle": 0, + "content": "To solve this issue, adaptive KD methods have been proposed in terms of training paradigms (e.g., early stop [10]) and architectural adaptations (e.g., assistant teacher [43] and architecture search [40]), respectively. However, they are ineffective in improving distillation performance or in" + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.875, + 0.472, + 0.901 + ], + "angle": 0, + "content": "*Corresponding author, † equal contribution, PD conducted main experiments, LL proposed ideas and led the project & writing." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11898" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.622 + ], + "angle": 0, + "content": "volve enormous training costs in the additional model training and search process. In sharp contrast to these methods, we tackle this challenging problem from a new perspective regarding training-free architecture search. To achieve this goal, we construct a search space \\( S_0 \\) for ResNet-like models with different depth configurations and obtain vanilla and distill performance for each candidate in \\( S_0 \\) by individual training. Then, we evaluate the ranking correlation between predicted scores of training-free search methods and the actual performance of each student model. Surprisingly, as shown in Figure 1 (Left), there are common ranking correlation loss \\( (10\\% \\downarrow \\sim 20\\% \\downarrow) \\) for these methods in predicting distillation accuracy than vanilla accuracy. To clarify this, we carefully analyze the disparities in vanilla and distillation performance for each model: (1) for overall search space, vanilla accuracy only preserves \\( 85\\% \\) correlations with actual distillation performance. (2) for a particular instance, as shown in Figure 1 (Right), ResNet20 with 3 res-blocks in each stage (i.e., ResNet[3,3,3]) has more parameters and better standalone performance but is weaker than ResNet[7,1,3] in the distillation process. Considering that ResNet[7,1,3] has more layers than ResNet20, we seek to understand the above phenomenon regarding the vanilla-distillation accuracy gap from the perspective of semantic matching [37]. ResNet[7,1,3] enjoys a larger effective receptive field and more excellent matched knowledge with teacher, resulting in significant distillation gains. Encouraged by this understanding, we strive to design a new zero-proxy regarding the semantic matching of teacher-student. As a result, we find that the similarity scores of feature semantics and sample relations can outperform conventional zero-cost NAS in predicting final distillation accuracy (see the comparison of ranking correlation on search space \\( S_0 \\) in Table 8). As shown in Figure 1(Right), similarity scores are also consistent with distillation performance." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.629, + 0.473, + 0.902 + ], + "angle": 0, + "content": "Drawing on the aforementioned observations, we introduce DisWOT, a simple yet effective training-free framework that finds the best student architectures for distilling the given teacher model. For better semantic matching in distillation, DisWOT leverages novel zero-cost metrics regarding the feature semantics and sample relations to select better student model. For the feature semantic similarity metric, we remark that randomly initialized models can localize objects well [6] and generate localization heatmaps via Grad-CAM [56] as reliable semantic information. Then, we measure the channel-wise similarity matrix of localization heatmaps and take the \\( L_{2} \\) distance of the similarity matrix for the teacher-student model as the metric. For input samples, different models have diverse abilities to discriminate their relationships. To improve relational knowledge matching ability, we use the \\( L_{2} \\) distance of sample-relation correlation matrix as a relation similarity metric. Finally, we search for student architectures using an evo" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.227 + ], + "angle": 0, + "content": "lutionary algorithm with semantic and relations similarity metrics. Then, the distillation process is implemented between the searched student and the pre-defined teacher. In addition, we leverage these metrics directly as new distillers to enhance the student, as the DisWOT†. Equipped with our train-free search and distillation design, our DisWOT and DisWOT† framework significantly improve the model's accuracy-latency tradeoff in inference with at least \\(180 \\times\\) training acceleration." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.228, + 0.897, + 0.514 + ], + "angle": 0, + "content": "In principle, our DisWOT use higher-order statistics of teacher-student models to optimize the student architecture to fit a given teacher model. Its merits can be highlighted in three aspects: (1) In contrast to training-based student architecture search requires the individual or weight-sharing training, our DisWOT does not require the training of student models in the search phase. In addition, DisWOT is efficient to compute and easy to implement as it uses only the mini-batch data at initialization. (2) DisWOT is a teacher-aware search for distillation, which has better predictive distill accuracy than conventional NAS. (3) DisWOT exploits the distance of higher-order knowledge between the neural networks, bridging knowledge distillation and zero-proxy NAS. We further demonstrate the competitive ranking correlation of DisWOT among 10 knowledge distances in KD as zero-proxy for predicting vanilla accuracy in NAS-Bench-201. We anticipate that our work on KD-based zero-proxy can offer some assistance in furthering research endeavors related to KD and NAS." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.515, + 0.897, + 0.741 + ], + "angle": 0, + "content": "We conduct extensive experiments on CIFAR-100, ImageNet, and the NAS-Bench-201 [14] dataset, demonstrating the superiority of our proposed approach. In contrast to experiments in traditional architectural search, we focus on final distillation accuracy instead of the vanilla accuracy for the student. The results show that our DisWOT can achieve better accuracy than traditional Zero-shot NAS in the same search space. Besides, by switching to a larger space, our DisWOT can obtain new state-of-the-art architectures. For example, in the same ResNet-like search space, we significantly improved \\(1.62\\%\\) Top-1 accuracy over KD for ResNet50-ResNet18 pair under the same training settings. We also conducted comprehensive ablation studies to investigate how our method can use the predictability of zero-cost metrics to boost the distillation performance." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.741, + 0.651, + 0.756 + ], + "angle": 0, + "content": "Main Contributions:" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.765, + 0.895, + 0.903 + ], + "angle": 0, + "content": "- By analyzing and exploring the discrepancy between teacher-student capability, we empirically show that their semantic similarities have a stronger correlation with the final distillation accuracy. This motivates us to propose a new student architecture search for the Distillation without Training (DisWOT) framework to reduce the teacher-student capability gap, which, to the best of our knowledge, is not achieved in the area of knowledge distillation." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "11899" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.097, + 0.092, + 0.471, + 0.182 + ], + "angle": 0, + "content": "- DisWOT proposes novel zero-cost metrics on similarity of feature semantics and sample relations and ensemble these metrics to select the optimal student via an evolutionary algorithm at the initial time. In the distillation stage, DisWOT achieves state-of-the-art performances in multiple datasets and search spaces." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.19, + 0.471, + 0.281 + ], + "angle": 0, + "content": "- We further expand 10 kinds of knowledge distances including DisWOT as new universal KD-based zero proxies, which enjoy competitive predictive power with actual performance of models. We hope that our contributions in this endeavor may aid to some degree in advancing future research on KD and NAS." + }, + { + "type": "list", + "bbox": [ + 0.097, + 0.092, + 0.471, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.292, + 0.364, + 0.31 + ], + "angle": 0, + "content": "2. Related Work and Background" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.318, + 0.471, + 0.362 + ], + "angle": 0, + "content": "In this section, we summarize existing knowledge distillation and architecture search methods and clarify their differences to our method." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.37, + 0.47, + 0.387 + ], + "angle": 0, + "content": "2.1. General Formulation of Knowledge Distillation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.393, + 0.471, + 0.544 + ], + "angle": 0, + "content": "The fundamental concept underlying Knowledge Distillation (KD) involves utilizing acquired knowledge (e.g., logits [31], feature values [30, 32, 33, 35, 70], and sample relations [45, 59]) from a high-capacity teacher to guide the training of a student model. The training dataset \\((X,Y)\\) comprises training samples \\(X = x_{i=1}^{n}\\) and their corresponding labels \\(Y = y_{i=1}^{n}\\). Let \\(f_{T}\\) be the output logits of the fixed teacher \\(T\\) and let \\(f_{S}\\) be the output of student \\(S\\), respectively. In KD, the student network \\(f_{S}\\) is trained by minimizing:" + }, + { + "type": "equation", + "bbox": [ + 0.091, + 0.552, + 0.47, + 0.568 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {S} = \\mathcal {L} _ {C E} \\left(f _ {S}, Y\\right) + \\mathcal {L} _ {K L} \\left(f _ {S}, f _ {T}\\right) + \\mathcal {D} _ {f} \\left(\\phi_ {S} (x), \\phi_ {T} (x)\\right), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.574, + 0.471, + 0.635 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{CE}\\) is the regular cross-entropy loss. \\(\\mathcal{L}_{KL}\\) represents Kullback-Leibler (KL) divergence. \\(\\mathcal{D}_f(\\cdot, \\cdot)\\) is the distance function measuring the difference of intermediate feature representations (see Table 1 for particular distillers)." + }, + { + "type": "table_caption", + "bbox": [ + 0.152, + 0.637, + 0.393, + 0.651 + ], + "angle": 0, + "content": "Table 1. Comparison of recent distillers." + }, + { + "type": "table", + "bbox": [ + 0.088, + 0.653, + 0.458, + 0.737 + ], + "angle": 0, + "content": "
MethodKnowledgeDistance Df(·,·)
FitNets [54]Feature representationL2
AT [73]Attention mapsL2
CC [49]Instance relationL2
NST [24]Neuron selectivity patternsLMMD
PKT [46]Similarity probability distributionLKL
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Comparison with Other Adaptive KDs for Distillation Gap. DisWOT is the first train-free architecture search solution to reduce the teacher-student gap. Unlike training manners [10] and KD-loss designs, DisWOT utilizes the classic KD training configurations and distillers. In addition, DisWOT is free from the assistant teacher in ATKD [43], which involves a complex training routine and budget. AKD [40] searches student via reinforcement learning based on feedback from individual training of lots of models. As a completely alternative technical route to these training-based" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.089, + 0.894, + 0.16 + ], + "angle": 0, + "content": "Table 2. Formulation of NAS methods. \\(\\mathcal{A}\\) is the search space. A candidate architecture in the search space is denoted as \\(\\alpha \\in \\mathcal{A}\\), which corresponds to a neural architecture \\(S(\\alpha, w)\\) with weight \\(w\\). \\(\\mathcal{W}\\) is the weight of the supernet. \\(\\text{train}\\) and \\(\\text{val}\\) are the loss functions on the training and validation sets, respectively." + }, + { + "type": "table", + "bbox": [ + 0.513, + 0.17, + 0.882, + 0.354 + ], + "angle": 0, + "content": "
TypeEvaluationFormula
Training-basedMulti-trial Trainingα* = arg min val(S(α, wα)), s.t. wα = arg min w train(S(α, w))
Weight sharingα* = arg min val(S(α, W_A(α))), s.t. W_A = arg min w train(S(A, W))
Training-freeZero-cost Proxyα* = ZeroProxy(S(α, w)) α∈A
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.379, + 0.894, + 0.426 + ], + "angle": 0, + "content": "NAS [18], our training-free DisWOT builds on new zero-proxy and achieves \\(180 \\times 1000 \\times\\) training acceleration, which greatly improves its easy-to-use and flexibility." + }, + { + "type": "table_caption", + "bbox": [ + 0.533, + 0.44, + 0.858, + 0.454 + ], + "angle": 0, + "content": "Table 3. Comparison with different training-free NAS." + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.464, + 0.892, + 0.517 + ], + "angle": 0, + "content": "
TypeMethodTeacher-awareObjective
Prune-basedSNIP [28], Fisher [1], Synflow [58]✗Vanilla acc.
Activation-basedNWOT [42], Zen-NAS [36]✗Vanilla acc.
KD-basedDisWOT (ours)✓Distill acc.
" + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.544, + 0.843, + 0.56 + ], + "angle": 0, + "content": "2.2. Revisiting Architecture Search Methods" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.568, + 0.894, + 0.809 + ], + "angle": 0, + "content": "Neural Architecture Search (NAS) is emerged to reduce human efforts in architecture design and automate the discovery of high-performance networks. As formalized in Tab. 2, Multi-trial NAS methods [40, 79] train a large number of candidates individually, which leads to extensive resource consumption. To alleviate this, many NAS [8,12,23,51] methods adopt a weight-sharing strategy within a single supernet to facilitate the simultaneous training of candidates. The supernet is trained for hundred of epochs by path sampling [11,19] or compound optimization with architecture representations [39,69]. As an orthogonal direction, zero-cost NAS methods [42,71] focus on identifying well-performed architectures with training-free metrics. For example, NWOT [42] calculates the architecture score based on the kernel matrix of binary activations between small batches of samples." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Comparison with NAS with Teacher. Some training-based NAS [29,50,77] employ a teacher model to supervise supernet training to improve predictive ability in the search stage. However, these methods aim to improve vanilla accuracy, not for distillation, and they do not use the teacher model in the full training stage. In addition, without any" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11900" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.087, + 0.895, + 0.301 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.312, + 0.895, + 0.397 + ], + "angle": 0, + "content": "Figure 3. A schematic overview of our DisWOT, including (a) detailed calculation of the DisWOT scores and (b) evolution of the student architecture via the DisWOT scores. In search phase, DisWOT use semantic similarity metrics and relations similarity metrics to select good student for a given teacher. The semantic similarity metric is measured by \\( l_{2} \\) distance of the channel-wise correlation matrix for Grad-cam activation maps. Similarly, the relation similarity matrix statistics the sample-wise correlation matrix distance of the randomly initialized teacher-student pairs. With the feedback from these metrics, the evolutionary search in DisWOT automatically imitates good student from weak ones. In distillation phase, this searched student is distilled via teacher model and achieves superior gains." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.41, + 0.471, + 0.44 + ], + "angle": 0, + "content": "training costs, our training-free DisWOT enjoys obvious differences than these methods and advantages in efficiency." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.441, + 0.471, + 0.532 + ], + "angle": 0, + "content": "Compared to Other Training-free NAS. Table 3 clearly summarizes the differences between DisWOT and other zero-cost methods [1, 28, 36, 42, 58]. Moreover, DisWOT outperforms these methods on distillation performance prediction and boosting in our sufficient experiments dealing with diverse datasets and search spaces." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.549, + 0.212, + 0.566 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.576, + 0.472, + 0.756 + ], + "angle": 0, + "content": "Figure 3 provides an overview of the DisWOT framework, which is comprised of two main stages: optimal student network search and distillation with high-order knowledge. In the search stage, we employ the neural architecture search technique to obtain an optimal student network for a pre-defined teacher network. Notably, we propose a training-free proxy called DisWOT to accurately rank enormous student networks and prevent expensive evaluation processes with high efficiency. In the distillation stage, the searched student network is retrained with distillation to imitate high-order knowledge in the teacher network. We give the details of these two designs in the following sections." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.77, + 0.398, + 0.785 + ], + "angle": 0, + "content": "3.1. Search for Optimal Student Network" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.794, + 0.471, + 0.869 + ], + "angle": 0, + "content": "We first present the training-free metrics we designed to score a student architecture, which indicates its final accuracy when distilled with a pre-defined teacher network. Then we depict the details of the evolutionary process to obtain an optimal student candidate." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Semantic Similarity Metric. The semantic information is meaningful for neural networks to perceive as humans. In" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.41, + 0.895, + 0.773 + ], + "angle": 0, + "content": "distillation, the teacher network always has more convolutional operations than the student, resulting in a teacher feature map with a larger receptive field and greater richness of semantic information. In contrast to distiller designs to alleviate semantic gaps, we aim for train-free student architecture to better match the teacher model with computational constraints. We notice that the network with random initial weights also has some semantic localization capability. Thus, we start to analyze the localization performance of the randomly initialized teacher-student model. Specifically, we utilize Grad-CAM maps [78] to localize semantic object regions, which explains the model decisions using gradient information. Given a mini-batch of input images, we define the high-level feature map before the Global Average Pooling (GAP) layer of the teacher network \\( T \\) as \\( A_{T} \\in \\mathbf{R}^{B \\times C_{T} \\times H_{T} \\times W_{T}} \\), where \\( B \\) represents the batch size, \\( C_{T} \\) denotes the number of output channels, and \\( H_{T} \\) and \\( W_{T} \\) are the spatial dimensions. Additionally, we introduce \\( A_{T}^{c} \\in \\mathbf{R}^{N \\times H_{T} \\times W_{T}} \\) as the c-th spatial map along the channel dimension. For the student network \\( S_{i} \\), we have feature map \\( A_{S_{i}}^{c} \\in \\mathbf{R}^{B \\times C_{S} \\times H_{S} \\times W_{S}} \\) and spatial map \\( A_{S_{i}}^{c} \\in \\mathbf{R}^{B \\times H_{S} \\times W_{S}} \\), respectively. To compute the Grad-CAM maps of the \\( n \\)-th class for both the teacher and student networks, we can use the following formulations:" + }, + { + "type": "equation", + "bbox": [ + 0.561, + 0.783, + 0.892, + 0.82 + ], + "angle": 0, + "content": "\\[\nG _ {T} = \\sum_ {c = 1} ^ {C _ {T}} w _ {n, c} ^ {T} A _ {T} ^ {c}, \\quad G _ {S _ {i}} = \\sum_ {c = 1} ^ {C _ {S}} w _ {n, c} ^ {S} A _ {S _ {i}} ^ {c}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.824, + 0.895, + 0.901 + ], + "angle": 0, + "content": "where \\( w^{T} \\in \\mathbf{R}^{N \\times C_{T}} \\) and \\( w^{S} \\in \\mathbf{R}^{N \\times C_{S}} \\) are weights of the last fully-connected layer in the teacher and student network. \\( N \\) represents the number of classes. \\( w_{n,c}^{T} \\) and \\( w_{n,c}^{S} \\) refer to the element located in the \\( n \\)-th row and \\( c \\)-th column of weight matrices \\( w^{T} \\) and \\( w^{S} \\), respectively. To quantify" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "11901" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.152 + ], + "angle": 0, + "content": "the intersection of class-discriminative localization maps, we formulate semantic similarity metric \\(\\mathcal{M}_s\\) as the intercorrelation on the accumulated Grad-CAM maps for both teacher and student networks as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.092, + 0.16, + 0.472, + 0.197 + ], + "angle": 0, + "content": "\\[\n\\mathcal {G} ^ {T} = \\frac {\\left(G _ {T}\\right) \\cdot \\left(G _ {T}\\right) ^ {\\top}}{\\| \\left(G _ {T}\\right) \\cdot \\left(G _ {T}\\right) ^ {\\top} \\| _ {2}}, \\mathcal {G} ^ {S} = \\frac {\\left(G _ {S}\\right) \\cdot \\left(G _ {S}\\right) ^ {\\top}}{\\| \\left(G _ {S}\\right) \\cdot \\left(G _ {S}\\right) ^ {\\top} \\| _ {2}}, (3)\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.197, + 0.212, + 0.471, + 0.233 + ], + "angle": 0, + "content": "\\[\n\\mathcal {M} _ {s} = \\left\\| \\mathcal {G} ^ {T} - \\mathcal {G} ^ {S _ {i}} \\right\\| _ {2}. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.238, + 0.473, + 0.388 + ], + "angle": 0, + "content": "Relation Similarity Metric. The relationships between input samples are non-trivial for knowledge transfer. To reduce the teacher-student gap and improve the relation-distillation performance, we use the correlation matrix as the sample-wise metric to search for an optimal student network. For the random teacher network \\(T\\) and student network \\(S_{i}\\) with activation maps \\(A_{T} \\in \\mathbf{R}^{N \\times C_{T} \\times H_{T} \\times W_{T}}\\) and \\(A_{S}^{i} \\in \\mathbf{R}^{N \\times C_{i} \\times H_{i} \\times W_{i}}\\), the correlation matrix of the minibatch samples in the teacher network is formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.092, + 0.397, + 0.472, + 0.445 + ], + "angle": 0, + "content": "\\[\n\\mathcal {A} ^ {T} = \\frac {(\\tilde {A} _ {T}) \\cdot (\\tilde {A} _ {T}) ^ {\\top}}{\\left\\| (\\tilde {A} _ {T}) \\cdot (\\tilde {A} _ {T} ^ {\\top}) \\right\\| _ {2}}, \\mathcal {A} ^ {S _ {i}} = \\frac {(\\tilde {A} _ {S}) \\cdot (\\tilde {A} _ {S}) ^ {\\top}}{\\left\\| (\\tilde {A} _ {S}) \\cdot (\\tilde {A} _ {S} ^ {\\top}) \\right\\| _ {2}}, (5)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.454, + 0.47, + 0.532 + ], + "angle": 0, + "content": "where \\(\\tilde{A}_T\\in \\mathbf{R}^{N\\times CHW}\\) is a reshaping of \\(A_{T}\\), and \\(M_T\\) is a \\(N\\times N\\) matrix. Thus, the \\((i,j)\\) entry in matrix \\(C_T\\) represents the similarity between the \\(i\\)-th and \\(j\\)-th images within the mini-batch. Based on this, the sample similarity metric \\(\\mathcal{M}_r\\) for a potential student model \\(S_{i}\\) is defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.195, + 0.542, + 0.471, + 0.563 + ], + "angle": 0, + "content": "\\[\n\\mathcal {M} _ {r} = \\left\\| \\mathcal {A} ^ {T} - \\mathcal {A} ^ {S _ {i}} \\right\\| _ {2}. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.588, + 0.47, + 0.648 + ], + "angle": 0, + "content": "Training-Free Evolutionary Search. Based on the above metric, we conduct a training-free evolutionary search algorithm to efficiently discover the optimal student \\(\\alpha^{*}\\) from search space \\(\\mathcal{A}\\), as:" + }, + { + "type": "equation", + "bbox": [ + 0.179, + 0.661, + 0.47, + 0.683 + ], + "angle": 0, + "content": "\\[\n\\alpha^ {*} = \\arg \\min _ {\\alpha \\in \\mathcal {A}} \\left(\\mathcal {M} _ {s} + \\mathcal {M} _ {r}\\right). \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.694, + 0.47, + 0.74 + ], + "angle": 0, + "content": "Theoretical Understanding. According to the VC theory [63], the classification error of the vanilla teacher-student network can be decomposed as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.091, + 0.751, + 0.47, + 0.772 + ], + "angle": 0, + "content": "\\[\nR \\left(f _ {s}\\right) - R \\left(f _ {r}\\right) \\leq O \\left(\\frac {\\left| \\mathcal {F} _ {s} \\right| _ {C}}{n ^ {\\alpha s r}}\\right) + \\epsilon_ {s r}; R \\left(f _ {t}\\right) - R \\left(f _ {r}\\right) \\leq O \\left(\\frac {\\left| \\mathcal {F} _ {t} \\right| _ {C}}{n ^ {\\alpha t r}}\\right) + \\epsilon_ {t r}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.472, + 0.902 + ], + "angle": 0, + "content": "where \\(f_{s}\\in \\mathcal{F}_{s}\\) is the student function, \\(f_{t}\\in \\mathcal{F}_{t}\\) is the teacher function, and \\(f_{r}\\in \\mathcal{F}_{r}\\) is the target function. \\(R\\) is the error. \\(O(\\cdot)\\) and \\(\\epsilon_{sr}\\) terms are the estimation and approximation error, respectively. \\(O(\\cdot)\\) is related to the statistical procedure when given the number of data points. In contrast, \\(\\epsilon_{sr}\\) is the approximation error of the student function class \\(\\mathcal{F}_s\\) for \\(f_{r}\\in \\mathcal{F}_{r}.\\left|\\cdot \\right|_{C}\\) is an function class capacity measure, and \\(n\\) is the number of data point. During distillation," + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.121 + ], + "angle": 0, + "content": "the student network is supervised purely with the teacher network as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.571, + 0.13, + 0.892, + 0.164 + ], + "angle": 0, + "content": "\\[\nR \\left(f _ {s}\\right) - R \\left(f _ {t}\\right) \\leq O \\left(\\frac {\\left| \\mathcal {F} _ {s} \\right| _ {C}}{n ^ {\\alpha_ {s t}}}\\right) + \\epsilon_ {s t}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.175, + 0.892, + 0.206 + ], + "angle": 0, + "content": "where \\(\\alpha_{st}\\) and \\(\\epsilon_{st}\\) are associated to student learning from teacher. By combining Equations 3.1 and 9, we obtain:" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.217, + 0.892, + 0.241 + ], + "angle": 0, + "content": "\\[\nR \\left(f _ {s}\\right) - R \\left(f _ {r}\\right) \\leq O \\left(\\frac {\\left| \\mathcal {F} _ {t} \\right| _ {C}}{n ^ {\\alpha_ {t r}}}\\right) + \\epsilon_ {t r} + O \\left(\\frac {\\left| \\mathcal {F} _ {s} \\right| _ {C}}{n ^ {\\alpha_ {s t}}}\\right) + \\epsilon_ {s t}. \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.251, + 0.892, + 0.297 + ], + "angle": 0, + "content": "When student obtains gains in KDs, its upper bound of error in distillation is smaller than vanilla training, which satisfies the following inequality:" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.308, + 0.892, + 0.334 + ], + "angle": 0, + "content": "\\[\nO \\left(\\frac {\\left| \\mathcal {F} _ {t} \\right| _ {C}}{n ^ {\\alpha_ {t r}}} + \\frac {\\left| \\mathcal {F} _ {s} \\right| _ {C}}{n ^ {\\alpha_ {s t}}}\\right) + \\epsilon_ {t r} + \\epsilon_ {s t} \\leq O \\left(\\frac {\\left| \\mathcal {F} _ {s} \\right| _ {C}}{n ^ {\\alpha_ {s r}}}\\right) + \\epsilon_ {s r}. \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.343, + 0.894, + 0.56 + ], + "angle": 0, + "content": "Based on the assumption in [22] that \\(\\epsilon_{tr} + \\epsilon_{st} \\leq \\epsilon_{sr}\\) holds consistently, we focus on minimizing \\(O\\left(\\frac{|\\mathcal{F}_t|_C}{n^{\\alpha_{tr}}} + \\frac{|\\mathcal{F}_s|_C}{n^{\\alpha_{st}}}\\right)\\) to improve the distillation performance. As noted in Lopez-Paz et al [41], a better representation allows for a faster learning rate with a fixed amount of data. Hence, when there is a larger gap between the capacities of the student and teacher networks, the value of \\(\\alpha_{st}\\) tends to be lower. Thus we aim to search for an optimal student network that meets the requirement of \\(\\alpha_{si t} \\leq \\alpha_{so t}\\), where \\(s_i\\) is all candidate student networks, and \\(s_o\\) is our searched student network. In this case, the inequality becomes more effective, and we improve the knowledge distillation by injecting a larger \\(\\alpha_{so t}\\). Specifically, we present the overall procedure for discovering optimal student in algorithm 1." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.561, + 0.894, + 0.668 + ], + "angle": 0, + "content": "Effects of Search Strategies. We compare the evolution search algorithm and the random search algorithm in search space \\( S_{2} \\) with the same number of iterations, as shown in Figure 4. We find that the evolution search algorithm can consistently find architectures with lower DisWOT, especially when the search space is relatively large, and the evolutionary search can explore better architectures." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.678, + 0.842, + 0.695 + ], + "angle": 0, + "content": "3.2. Distillation with High-order Knowledge" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.7, + 0.895, + 0.826 + ], + "angle": 0, + "content": "In the distillation stage, teacher model \\( T \\) is employed to distill the optimal student network \\( f_{S} \\). To verify the superiority of our search architecture, we adopt the existing distillers (e.g., KD) as the default distillation setting. In addition, we observe that the metrics we searched for actually serve as minimization optimization goals in the distillation process to transfer the teacher's privileged semantic and sample relational knowledge as the semantic distillation and sample distillation:" + }, + { + "type": "equation", + "bbox": [ + 0.52, + 0.836, + 0.892, + 0.862 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathcal {M} _ {s}} = \\frac {1}{c ^ {2}} \\left\\| \\mathcal {G} ^ {T} - \\mathcal {G} ^ {S} \\right\\| _ {2}, \\mathcal {L} _ {\\mathcal {M} _ {r}} = \\frac {1}{b ^ {2}} \\left\\| \\mathcal {A} ^ {T} - \\mathcal {A} ^ {S} \\right\\| _ {2}, \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Finally, we involve these advanced distillers in our framework, called DisWOT†. The total loss for DisWOT and" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11902" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.092, + 0.369, + 0.105 + ], + "angle": 0, + "content": "Algorithm 1 Evolution Search for DisWOT" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.108, + 0.47, + 0.148 + ], + "angle": 0, + "content": "Input: Search space \\(S\\), population \\(\\mathcal{P}\\), architecture constraints \\(\\mathcal{C}\\), max iteration \\(\\mathcal{N}\\), sample ratio \\(r\\), sampled pool \\(\\mathcal{Q}\\), topk \\(k\\), teacher network \\(\\mathcal{T}\\)." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.15, + 0.349, + 0.163 + ], + "angle": 0, + "content": "Output: Highest DisWOT score architecture." + }, + { + "type": "text", + "bbox": [ + 0.087, + 0.18, + 0.308, + 0.193 + ], + "angle": 0, + "content": "1: \\(\\mathcal{P}_0\\coloneqq\\) Initialize population \\((P_{i},\\mathcal{C})\\)" + }, + { + "type": "text", + "bbox": [ + 0.087, + 0.194, + 0.225, + 0.207 + ], + "angle": 0, + "content": "2: sample pool \\(\\mathcal{Q} := \\emptyset\\);" + }, + { + "type": "text", + "bbox": [ + 0.087, + 0.208, + 0.208, + 0.22 + ], + "angle": 0, + "content": "3: for \\( i = 1:\\mathcal{N}\\mathbf{d}\\mathbf{o} \\)" + }, + { + "type": "text", + "bbox": [ + 0.087, + 0.222, + 0.278, + 0.235 + ], + "angle": 0, + "content": "4: Clear sample pool \\(\\mathcal{Q} \\coloneqq \\emptyset\\);" + }, + { + "type": "text", + "bbox": [ + 0.087, + 0.235, + 0.415, + 0.248 + ], + "angle": 0, + "content": "5: Randomly select \\(r \\times \\mathcal{P}\\) subnets \\(\\hat{P}_i \\in \\mathcal{P}\\) to get \\(\\mathcal{Q}\\);" + }, + { + "type": "text", + "bbox": [ + 0.087, + 0.249, + 0.343, + 0.262 + ], + "angle": 0, + "content": "6: Candidates \\(\\{A_i\\}_k \\coloneqq \\operatorname{GetTopk}(\\mathcal{Q}, k)\\);" + }, + { + "type": "text", + "bbox": [ + 0.087, + 0.263, + 0.341, + 0.277 + ], + "angle": 0, + "content": "7: Parent \\(A_{i}\\coloneqq\\) RandomSelect \\((\\{A_i\\}_k)\\)" + }, + { + "type": "text", + "bbox": [ + 0.087, + 0.277, + 0.292, + 0.289 + ], + "angle": 0, + "content": "8: Mutate \\(\\hat{P}_i\\coloneqq \\mathrm{MUTATE}(A_i)\\)" + }, + { + "type": "text", + "bbox": [ + 0.087, + 0.29, + 0.356, + 0.303 + ], + "angle": 0, + "content": "9: if \\(\\hat{P}_i\\) do not meet the constraints \\(\\mathcal{C}\\) then" + }, + { + "type": "text", + "bbox": [ + 0.082, + 0.305, + 0.21, + 0.318 + ], + "angle": 0, + "content": "10: Do nothing;" + }, + { + "type": "text", + "bbox": [ + 0.082, + 0.319, + 0.147, + 0.33 + ], + "angle": 0, + "content": "11: else" + }, + { + "type": "text", + "bbox": [ + 0.082, + 0.332, + 0.386, + 0.345 + ], + "angle": 0, + "content": "12: Get DisWOT-Score \\(z \\coloneqq \\operatorname{DisWOT}(\\hat{P}_i, \\mathcal{T})\\);" + }, + { + "type": "text", + "bbox": [ + 0.082, + 0.346, + 0.239, + 0.359 + ], + "angle": 0, + "content": "13: Append \\(\\hat{P}_i\\) to \\(\\mathcal{P}\\)" + }, + { + "type": "text", + "bbox": [ + 0.082, + 0.36, + 0.16, + 0.371 + ], + "angle": 0, + "content": "14: end if" + }, + { + "type": "text", + "bbox": [ + 0.082, + 0.373, + 0.385, + 0.386 + ], + "angle": 0, + "content": "15: Remove network of smallest DisWOT-score;" + }, + { + "type": "text", + "bbox": [ + 0.082, + 0.388, + 0.152, + 0.399 + ], + "angle": 0, + "content": "16: end for" + }, + { + "type": "list", + "bbox": [ + 0.082, + 0.18, + 0.415, + 0.399 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.417, + 0.278, + 0.526 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.28, + 0.421, + 0.467, + 0.526 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.527, + 0.47, + 0.568 + ], + "angle": 0, + "content": "Figure 4. Left: comparison of random search and evolution search. Right: ranking correlation of different distillation methods on NAS-Bench-201." + }, + { + "type": "table_caption", + "bbox": [ + 0.101, + 0.583, + 0.443, + 0.597 + ], + "angle": 0, + "content": "Table 4. Spearman correlation \\( \\rho \\left( \\% \\right) \\) on NAS-Bench-201." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.608, + 0.467, + 0.714 + ], + "angle": 0, + "content": "
TypeMethodρMethodρ
Zero-costGrad_Norm [1]58.70±0.11Synflow [58]74.61±0.08
SNIP [28]58.17±0.15Jacob [57]73.42±0.03
ProxiesFisher [1]35.91±0.09Zen-NAS [36]41.36±0.06
NWOT [42]64.41±0.08FLOPs [1]63.38±0.06
KD-basedKD [22]54.43±0.09PKT [47]52.65±0.09
FitNets [55]56.18±0.09CC [48]65.90±0.08
ProxiesSP [62]51.24±0.08NST [25]72.35±0.09
RKD [44]25.71±0.17DisWOT72.36±0.02
" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.737, + 0.171, + 0.752 + ], + "angle": 0, + "content": "DisWOT† as:" + }, + { + "type": "equation", + "bbox": [ + 0.132, + 0.762, + 0.47, + 0.787 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {D i s W O T}} = \\mathcal {L} _ {C E} \\left(f _ {S}, Y\\right) + \\mathcal {L} _ {K L} \\left(f _ {S}, f _ {T}\\right), \\tag {13}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.165, + 0.784, + 0.412, + 0.797 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {D i s W O T}} \\dagger = \\mathcal {L} _ {\\text {D i s W O T}} + \\mathcal {L} _ {\\mathcal {M} _ {s}} + \\mathcal {L} _ {\\mathcal {M} _ {r}}.\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.817, + 0.373, + 0.834 + ], + "angle": 0, + "content": "3.3. Bridging Distiller and Zero-proxy" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.84, + 0.473, + 0.901 + ], + "angle": 0, + "content": "In our DisWOT framework, we use the semantic and relational similarity metrics as a distillation performance predictor and distiller. In addition, DisWOT also enjoys good performance for vanilla performance predictions. Encour" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.244 + ], + "angle": 0, + "content": "aged by this intriguing observation, we employ the knowledge function in of different KDs as zero-proxies and evaluate their ranking consistency with vanilla accuracy. As shown in Table 4, these KD-based zero-proxies enjoy competitive rankings with other NAS methods. Detailed results in Figure 4 illustrate that our DisWOT and NST [24] are the winners in the family of KD-based proxies. These attempts reveal the close connections between KD and NAS, and augment \\(10+\\) new universal proxies from the teacher-student learning perspective for training-free NAS research." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.258, + 0.699, + 0.275 + ], + "angle": 0, + "content": "4. Experimental results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.284, + 0.894, + 0.36 + ], + "angle": 0, + "content": "In this section, we present the experimental results of our DisWOT on different datasets. First, we describe the four datasets used in our experiments and three search spaces \\( S_0, S_1, S_2 \\) in Sec. 4.1. Then, we conduct a comprehensive set of experiments to evaluate the effectiveness of DisWOT." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.371, + 0.691, + 0.387 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.395, + 0.894, + 0.485 + ], + "angle": 0, + "content": "We perform experiments on four datasets, namely CIFAR-10, CIFAR-100, ImageNet-16-120, and ImageNet-1k. In the search process, we only use one batch of training data to get the statistic at nearly no cost. Following previous works, our experiments are conducted on the following three search spaces:" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.486, + 0.892, + 0.546 + ], + "angle": 0, + "content": "Search Space \\( S_0 \\): Following CIFar-ResNet [20], the search space consists of three residual blocks and is based on CIFAR-100 datasets. The depth of each residual block is searched in set \\( \\{1,3,5,7\\} \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.547, + 0.894, + 0.607 + ], + "angle": 0, + "content": "Search Space \\( S_{1} \\): Following NAS-Bench-201 [14], this Darts-like search space is a cell-based search space consisting of stacked directed acyclic graphs. \\( S_{1} \\) is conducted on CIFAR-10, CIFAR-100, and ImageNet-16-120 datasets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.608, + 0.894, + 0.655 + ], + "angle": 0, + "content": "Search Space \\( S_{2} \\): Following NDS [53], this search space consists of residual and bottleneck blocks defined in ResNet. \\( S_{2} \\) is based on CIFAR-100 and ImageNet-1k dataset." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.665, + 0.75, + 0.681 + ], + "angle": 0, + "content": "4.2. Experiments on CIFAR-100" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.894, + 0.764 + ], + "angle": 0, + "content": "Implementation Details. We compare distillation gains with other zero-nas on search space \\( S_{1} \\). In the search phase, we configure 48k evolution iters with 512 population sizes. In distillation, All searched student networks are trained via CRD's settings [59] with ResNet56 as the teacher model." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Distillation Results of Zero-cost Proxies. We conduct detailed experiments on other zero-cost proxies with different knowledge distillation methods. Note that we search the student network under constraints of 1M parameters. The results in Table 5 demonstrated that our proposed DisWOT achieved superior results compared with other zero-cost proxies with different knowledge distillation methods. The DisWOT outperforms its counterparts vanilla networks by around \\(2\\%\\), while achieving consistent improvements" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11903" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.47, + 0.118 + ], + "angle": 0, + "content": "Table 5. Distillation results (\\%) of different zero-cost proxies with knowledge distillation methods under 1M parameters." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.129, + 0.47, + 0.251 + ], + "angle": 0, + "content": "
MethodRandomFLOPsSynflowNWOTDisWOT
Baseline69.5271.3772.8871.8073.12
KD70.4572.1373.7272.5774.73
FitNets70.1272.4073.5572.7274.85
AT70.1672.9773.5272.0874.50
SP70.4672.1473.5072.1674.95
RKD71.1972.2273.6972.6374.62
CRD71.5972.7873.9973.1275.25
" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.277, + 0.472, + 0.309 + ], + "angle": 0, + "content": "among different distillation methods, such as KD [22], Fit-Nets [55], AT [74], SP [62], RKD [44], and CRD [60]." + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.32, + 0.47, + 0.35 + ], + "angle": 0, + "content": "Table 6. Distillation results(%) of zero-cost proxies under \\(\\{0.5,1,2\\}\\mathrm{M}\\) parameters." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.36, + 0.468, + 0.442 + ], + "angle": 0, + "content": "
Param.FLOPsNWOTDisWOTDisWOT†
0.5M69.8870.3872.8973.75
1M72.1372.5774.2375.25
2M73.2773.8675.9576.67
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.469, + 0.47, + 0.498 + ], + "angle": 0, + "content": "Table 7. Distillation results(%) of zero-cost proxies under \\(\\{50,100\\}\\) M FLOPs on space \\(S_{1}\\)." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.508, + 0.468, + 0.543 + ], + "angle": 0, + "content": "
FLOPsNWOTSynflowDisWOTFLOPsNWOTSynflowDisWOT
50M63.1964.2865.98100M70.3872.1272.89
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.571, + 0.468, + 0.599 + ], + "angle": 0, + "content": "Table 8. Ranking correlation (\\%) of zero-cost proxies on \\( S_0 \\) space on CIFAR-100." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.611, + 0.47, + 0.734 + ], + "angle": 0, + "content": "
MethodKendall's TauSpearmanPearson
FLOPs [1]51.6172.9276.40
Fisher [1]62.8681.3720.90
Grad_Norm [1]63.7582.3539.35
SNIP [28]67.2285.0751.09
NWOT [42]31.8745.6648.99
DisWOT (ours)73.9891.3884.83
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.473, + 0.901 + ], + "angle": 0, + "content": "Analysis on Varying Parameter Constraints. We analyze the performance of student models under different parameter constraints obtained by DisWOT on CIFAR-100. As shown in the Table 7, we compared our method with two zero proxies, a.k.a. FLOPs [1] and NWOT [42], under the parameter constraints of 0.5, 1, and 2M, respectively, and the results demonstrate that our method still achieves excellent results. As shown in Tab. 7, DisWOT also outperforms previous SOTA methods with \\(0.8\\% \\sim 1.7\\% \\uparrow\\) gains under same FLOPs constraints," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.244 + ], + "angle": 0, + "content": "Ranking Correlation with Distill Accuracy. Based on search space \\( S_0 \\), we perform vanilla training and distillation for each candidate with CRD's settings [59]. Then, we collect these vanilla results as GT and analyze the different zero-proxy's correlation with them. As shown in Table 8, the results illustrate that our DisWOT achieves higher than Fisher, GradNorm, SNIP,FLOPs, and NWOT by a large margin, and achieve results that are on par with the best zero-cost proxy, a.k.a. Zen-NAS and Synflow, on Kendall's Tau, Pearson, and Spearman coefficient." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.253, + 0.785, + 0.269 + ], + "angle": 0, + "content": "4.3. Experiments on NAS-Bench-201" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.276, + 0.895, + 0.365 + ], + "angle": 0, + "content": "Implementation Details. For search trials, we first adopt ResNet110/56 as the teachers and then Conduct an evolution search with the DisWOT metric and get the best student network. We randomly sampled 50 candidate architectures to evaluate sequencing consistency. The distillation settings are the same as the Sec.4.2" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.366, + 0.895, + 0.457 + ], + "angle": 0, + "content": "Comparison results As shown in Table 9, some training-free methods can achieve good results with much faster speedups, such as NWOT and TE-NAS. Our proposed method DisWOT achieves a speedup ratio of \\(180 \\times\\), where if semantic similarity metric is removed, we can achieve a \\(300 \\times\\) speedup ratio at the expense of some accuracy." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.467, + 0.738, + 0.484 + ], + "angle": 0, + "content": "4.4. Experiments on ImageNet" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.49, + 0.895, + 0.734 + ], + "angle": 0, + "content": "Implementation Details. We searched the ResNet18 level network regarding the search space in NDS [53]. Specifically, we limit the number of parameters to less than 13M and the depth of the network to up to 20 layers and find the optimal network by evolution algorithm with the DisWOT metric. As shown in Table 10, guided by three different sizes of networks, we used DisWOT to find the optimal student network. We trained the student network obtained by the search using the distillation strategy in DisWOT. Implementation details are available in supplementary materials. Comparison Results. Table 10 reports the performance of DisWOT on ImageNet with ResNet34/50 as teacher network. The results demonstrate that the student architecture of the ResNet18-level obtained by DisWOT under different teacher guidance and using different distillation strategies yielded significantly better results than its counterparts." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.741, + 0.757, + 0.757 + ], + "angle": 0, + "content": "4.5. Ablation Studies of DisWOT" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.897, + 0.903 + ], + "angle": 0, + "content": "We perform ablation experiments to verify the validity of each component of DisWOT in search space \\( S_0 \\). As shown in Table 11, for semantic knowledge, similarity matrix obtains a more robust ranking improvement than simple Fit-Net [54]. For \\( \\mathcal{M}_r \\), similarity matrix performs better on relational knowledge than RKD [45]. DisWOT integrates semantic and relational knowledge to obtain an additional ranking improvement than stand-alone scores. The weight initialization scheme plays an important role in zero-proxy." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "11904" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.133 + ], + "angle": 0, + "content": "Table 9. Distillation results on CIFAR-10, CIFAR-100, and ImageNet-16 in NAS-Bench-201 [13]. Dis. Acc. (%) represents the accuracy of the searched architecture after distillation training. Time (s) denotes the time cost (GPU-seconds) during the search phase. The results of NWOT and TE-NAS come from their original papers. Our DisWOT achieves competitive results with the lowest costs." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.143, + 0.892, + 0.317 + ], + "angle": 0, + "content": "
TypeModelCIFAR-10CIFAR-100ImageNet-16-120
Dis. Acc(%)Time (s)Speed-upDis. Acc(%)Time (s)Speed-upDis. Acc(%)Time (s)Speed-up
Multi-trialRS93.63216K1.0×71.28460K1.0×44.881M1.0×
RL [3]92.83216K1.0×71.71460K1.0×44.351M1.0×
BOHB [17]93.49216K1.0×70.84460K1.0×44.331M1.0×
RSPS [34]91.6710K21.6×57.9946K21.6×36.87104K9.6×
Weight-sharingGDAS [15]93.3922K12.0×70.7039K11.7×42.35130K7.7×
DARTS [38]89.2223K9.4×66.2480K5.8×43.18110K9.1×
Training-freeNWOT [42]93.732.2K100×73.314.6K100×45.4310K100×
TE-NAS [9]93.922.2K100×71.244.6K100×44.3810K100×
DisWOTMs & Mr93.551.2K180×74.219.2K180×47.3020K180×
Mr93.490.72K300×73.6218.4K300×45.6340K300×
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.33, + 0.895, + 0.374 + ], + "angle": 0, + "content": "Table 10. The accuracy \\((\\%)\\) of ResNet18 on ImageNet-1k with various teachers. Results of other KD methods refer to the papers of CRD [60] and ESKD [10]. ATKD \\(A_{R34}\\) [43] denotes ResNet34 used as the assistant teacher. N/A means no available results. Our DisWOT obtains better performance than other methods and improves students' performance positively correlated with that of the teacher." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.383, + 0.892, + 0.476 + ], + "angle": 0, + "content": "
TeacherStudentAcc.TeacherStudentKD [22]ESKD [10]\\( \\mathrm{ATKD}_{A_{R18}} \\) [43]ONE [27]DML [75]CRD [60]DisWOT
ResNet34ResNet18Top-173.4069.7570.6670.8970.7870.5571.0371.1772.08
Top-591.4289.0789.8890.0689.9989.5990.2890.3290.38
TeacherStudentAcc.TeacherStudentKD [22]\\( \\mathrm{ATKD}_{A_{R18}} \\) [43]\\( \\mathrm{ATKD}_{A_{R34}} \\) [43]Seq. ESKD [10]ESKD [10]SRRL [72]DisWOT
ResNet50ResNet18Top-176.1669.7570.6870.6570.8570.6570.9571.2072.30
Top-592.8689.07N/AN/AN/AN/AN/AN/A90.51
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.499, + 0.47, + 0.528 + ], + "angle": 0, + "content": "Table 11. Spearman correlation (\"mean±std\") of DisWOT on search space \\( S_0 \\)." + }, + { + "type": "table", + "bbox": [ + 0.102, + 0.538, + 0.446, + 0.647 + ], + "angle": 0, + "content": "
KnowledgeMetricSpearman (%)
MsFitNets [54]64.06±6.11
MsSimilarity matrix73.68±5.45
MrRKD [59]13.52±11.51
MrSimilarity matrix72.36±3.42
Ms & MrSimilarity matrix77.51±2.76
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.673, + 0.472, + 0.735 + ], + "angle": 0, + "content": "We verify the effect of the initialization strategy of the network on the ranking consistency. The results in Tab. 12 demonstrate that the Gaussian initialization strategy is detrimental to \\(\\mathcal{M}_s\\), but beneficial to \\(\\mathcal{M}_r\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.752, + 0.197, + 0.768 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.779, + 0.473, + 0.903 + ], + "angle": 0, + "content": "In this paper, we present DisWOT, a new teacher-aware student architecture search without training framework for distillation. Based on key observations about the difference between vanilla and distillation accuracy, DisWOT measures the new zero-cost proxy conditioned on the similarity of feature semantics and sample relations between random initialized teacher-student network. Then, DisWOT search for the best student architectures for the given teacher us" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.499, + 0.892, + 0.54 + ], + "angle": 0, + "content": "Table 12. \"mean±std %\" Spearman of proxies via Kaiming and Gaussian initialization on search space \\( S_0 \\) and NAS-Bench-201 with various seeds." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.551, + 0.891, + 0.612 + ], + "angle": 0, + "content": "
SpaceInitialFisherGradNormNWOTDisWOT
S0Kaim.81.37±0.0182.35±0.0145.66±0.0584.08±0.03
Gauss.80.99±0.0175.50±0.0145.36±0.0391.38±0.03
NB-201Kaim.54.63±0.1558.70±0.1164.41±0.0865.57±0.02
Gauss.45.91±0.0945.70±0.1162.24±0.0772.36±0.02
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.642, + 0.895, + 0.838 + ], + "angle": 0, + "content": "ing an evolutionary algorithm with these metrics. Thorough evaluations are performed on diverse datasets and search spaces, and DisWOT achieves significant performance gains in various neural networks with at least \\(180 \\times\\) training acceleration. We experimentally and theoretically explained the relationship between similarity difference and distillation performance. In addition, we also extend DisWOT to new distillers and general zero proxy to predict the performance of models. By doing this, we bridge the higher-order knowledge bewteen distillation and network architecture search. This approach represents an elegant and practical solution, which we hope will inspire future research on knowledge distillation and architecture search design." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.894, + 0.903 + ], + "angle": 0, + "content": "Limitations. Following most zero-cost NAS, we evaluate DisWOT in classification tasks. In the future work, we will make efforts to expand the DisWOT for downstream tasks (e.g., object detection and semantic segmentation)." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "11905" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.156 + ], + "angle": 0, + "content": "[1] Mohamed S Abdelfattah, Abhinav Mehrotra, Lukasz Dudziak, and Nicholas Donald Lane. Zero-cost proxies for lightweight nas. In ICLR, 2020. 3, 4, 6, 7" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.157, + 0.472, + 0.199 + ], + "angle": 0, + "content": "[2] Sungsoo Ahn, Shell Xu Hu, Andreas Damianou, Neil D Lawrence, and Zhenwen Dai. Variational information distillation for knowledge transfer. 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However, the large architecture difference across the teacher-student pairs limits the distillation gains. In contrast to previous adaptive distillation methods to reduce the teacher-student gap, we explore a novel training-free framework to search for the best student architectures for a given teacher. Our work first empirically show that the optimal model under vanilla training cannot be the winner in distillation. Secondly, we find that the similarity of feature semantics and sample relations between random-initialized teacher-student networks have good correlations with final distillation performances. Thus, we efficiently measure similarity matrix conditioned on the semantic activation maps to select the optimal student via an evolutionary algorithm without any training. In this way, our student architecture search for Distillation WithOut Training (DisWOT) significantly improves the performance of the model in the distillation stage with at least $180 \times$ training acceleration. Additionally, we extend similarity metrics in DisWOT as new distillers and KD-based zero-proxies. Our experiments on CIFAR, ImageNet and NAS-Bench-201 demonstrate that our technique achieves state-of-the-art results on different search spaces. Our project and code are available at https://lilujunai.github.io/DisWOT-CVPR2023/. + +# 1. Introduction + +Despite the remarkable achievements of Deep Neural Networks (DNNs) in numerous visual recognition tasks [52, 64-68], they usually lead to heavy costs of memory, computation, and power at model inference due to their large numbers of parameters. To address this issue, Knowledge Distillation (KD) has been proposed as a means of transferring knowledge from a high-capacity teacher model to a low-capacity target student model, providing a more op + +![](images/3cc08b42e0202bafabff908c5cc47bb636a1fea8dd8277927ad2d4d26556f539.jpg) +Figure 1. Left: Ranking correlation of proxies in zero-cost NAS with vanilla and distillation accuracy. Right: Vanilla accuracy, distillation accuracy, prediction scores of DisWOT for ResNet[7,1,3] and ResNet[3,3,3] on search space $S_0$ . + +![](images/5238b79d9a3d1a33d347906a448e3339f1711cb1fa654d41bcfa8ac33d471d48.jpg) + +![](images/79ce25b09d33da7bf08670e1642042532dfcf401cda404f6d2f6706a0dc14a02.jpg) +Figure 2. Left: KD [22], DisWOT, DisWOT† results for ResNet20 under different teachers. Right: Comparison of distill accuracy & training efficiency with other NAS methods on NAS-Bench-201. + +![](images/50164ccbd478508dc8db20245e777b715c3cfac668e1684a9f171c01ea1f76f5.jpg) + +timal accuracy-efficiency trade-off during runtime [4, 7, 76]. The original KD method [22] utilizes the logit outputs of the teacher network as the source of knowledge. Subsequent studies [2, 21, 24, 26, 54, 61, 73] have focused on extracting informative knowledge based on intermediate feature representations. However, as the gap in capacity between students and teachers increases, existing KD methods are unable to improve results, particularly in tasks that depend on large-scale visual models such as VIT and GPT-3 [5, 16]. For example, as shown in Figure 2 (Left), the large teacher (e.g., ResNet110) lead to worse performance for the fixed student than the relatively smaller one (e.g., ResNet56). + +To solve this issue, adaptive KD methods have been proposed in terms of training paradigms (e.g., early stop [10]) and architectural adaptations (e.g., assistant teacher [43] and architecture search [40]), respectively. However, they are ineffective in improving distillation performance or in + +volve enormous training costs in the additional model training and search process. In sharp contrast to these methods, we tackle this challenging problem from a new perspective regarding training-free architecture search. To achieve this goal, we construct a search space $S_0$ for ResNet-like models with different depth configurations and obtain vanilla and distill performance for each candidate in $S_0$ by individual training. Then, we evaluate the ranking correlation between predicted scores of training-free search methods and the actual performance of each student model. Surprisingly, as shown in Figure 1 (Left), there are common ranking correlation loss $(10\% \downarrow \sim 20\% \downarrow)$ for these methods in predicting distillation accuracy than vanilla accuracy. To clarify this, we carefully analyze the disparities in vanilla and distillation performance for each model: (1) for overall search space, vanilla accuracy only preserves $85\%$ correlations with actual distillation performance. (2) for a particular instance, as shown in Figure 1 (Right), ResNet20 with 3 res-blocks in each stage (i.e., ResNet[3,3,3]) has more parameters and better standalone performance but is weaker than ResNet[7,1,3] in the distillation process. Considering that ResNet[7,1,3] has more layers than ResNet20, we seek to understand the above phenomenon regarding the vanilla-distillation accuracy gap from the perspective of semantic matching [37]. ResNet[7,1,3] enjoys a larger effective receptive field and more excellent matched knowledge with teacher, resulting in significant distillation gains. Encouraged by this understanding, we strive to design a new zero-proxy regarding the semantic matching of teacher-student. As a result, we find that the similarity scores of feature semantics and sample relations can outperform conventional zero-cost NAS in predicting final distillation accuracy (see the comparison of ranking correlation on search space $S_0$ in Table 8). As shown in Figure 1(Right), similarity scores are also consistent with distillation performance. + +Drawing on the aforementioned observations, we introduce DisWOT, a simple yet effective training-free framework that finds the best student architectures for distilling the given teacher model. For better semantic matching in distillation, DisWOT leverages novel zero-cost metrics regarding the feature semantics and sample relations to select better student model. For the feature semantic similarity metric, we remark that randomly initialized models can localize objects well [6] and generate localization heatmaps via Grad-CAM [56] as reliable semantic information. Then, we measure the channel-wise similarity matrix of localization heatmaps and take the $L_{2}$ distance of the similarity matrix for the teacher-student model as the metric. For input samples, different models have diverse abilities to discriminate their relationships. To improve relational knowledge matching ability, we use the $L_{2}$ distance of sample-relation correlation matrix as a relation similarity metric. Finally, we search for student architectures using an evo + +lutionary algorithm with semantic and relations similarity metrics. Then, the distillation process is implemented between the searched student and the pre-defined teacher. In addition, we leverage these metrics directly as new distillers to enhance the student, as the DisWOT†. Equipped with our train-free search and distillation design, our DisWOT and DisWOT† framework significantly improve the model's accuracy-latency tradeoff in inference with at least $180 \times$ training acceleration. + +In principle, our DisWOT use higher-order statistics of teacher-student models to optimize the student architecture to fit a given teacher model. Its merits can be highlighted in three aspects: (1) In contrast to training-based student architecture search requires the individual or weight-sharing training, our DisWOT does not require the training of student models in the search phase. In addition, DisWOT is efficient to compute and easy to implement as it uses only the mini-batch data at initialization. (2) DisWOT is a teacher-aware search for distillation, which has better predictive distill accuracy than conventional NAS. (3) DisWOT exploits the distance of higher-order knowledge between the neural networks, bridging knowledge distillation and zero-proxy NAS. We further demonstrate the competitive ranking correlation of DisWOT among 10 knowledge distances in KD as zero-proxy for predicting vanilla accuracy in NAS-Bench-201. We anticipate that our work on KD-based zero-proxy can offer some assistance in furthering research endeavors related to KD and NAS. + +We conduct extensive experiments on CIFAR-100, ImageNet, and the NAS-Bench-201 [14] dataset, demonstrating the superiority of our proposed approach. In contrast to experiments in traditional architectural search, we focus on final distillation accuracy instead of the vanilla accuracy for the student. The results show that our DisWOT can achieve better accuracy than traditional Zero-shot NAS in the same search space. Besides, by switching to a larger space, our DisWOT can obtain new state-of-the-art architectures. For example, in the same ResNet-like search space, we significantly improved $1.62\%$ Top-1 accuracy over KD for ResNet50-ResNet18 pair under the same training settings. We also conducted comprehensive ablation studies to investigate how our method can use the predictability of zero-cost metrics to boost the distillation performance. + +# Main Contributions: + +- By analyzing and exploring the discrepancy between teacher-student capability, we empirically show that their semantic similarities have a stronger correlation with the final distillation accuracy. This motivates us to propose a new student architecture search for the Distillation without Training (DisWOT) framework to reduce the teacher-student capability gap, which, to the best of our knowledge, is not achieved in the area of knowledge distillation. + +- DisWOT proposes novel zero-cost metrics on similarity of feature semantics and sample relations and ensemble these metrics to select the optimal student via an evolutionary algorithm at the initial time. In the distillation stage, DisWOT achieves state-of-the-art performances in multiple datasets and search spaces. +- We further expand 10 kinds of knowledge distances including DisWOT as new universal KD-based zero proxies, which enjoy competitive predictive power with actual performance of models. We hope that our contributions in this endeavor may aid to some degree in advancing future research on KD and NAS. + +# 2. Related Work and Background + +In this section, we summarize existing knowledge distillation and architecture search methods and clarify their differences to our method. + +# 2.1. General Formulation of Knowledge Distillation + +The fundamental concept underlying Knowledge Distillation (KD) involves utilizing acquired knowledge (e.g., logits [31], feature values [30, 32, 33, 35, 70], and sample relations [45, 59]) from a high-capacity teacher to guide the training of a student model. The training dataset $(X,Y)$ comprises training samples $X = x_{i=1}^{n}$ and their corresponding labels $Y = y_{i=1}^{n}$ . Let $f_{T}$ be the output logits of the fixed teacher $T$ and let $f_{S}$ be the output of student $S$ , respectively. In KD, the student network $f_{S}$ is trained by minimizing: + +$$ +\mathcal {L} _ {S} = \mathcal {L} _ {C E} \left(f _ {S}, Y\right) + \mathcal {L} _ {K L} \left(f _ {S}, f _ {T}\right) + \mathcal {D} _ {f} \left(\phi_ {S} (x), \phi_ {T} (x)\right), \tag {1} +$$ + +where $\mathcal{L}_{CE}$ is the regular cross-entropy loss. $\mathcal{L}_{KL}$ represents Kullback-Leibler (KL) divergence. $\mathcal{D}_f(\cdot, \cdot)$ is the distance function measuring the difference of intermediate feature representations (see Table 1 for particular distillers). + +Table 1. Comparison of recent distillers. + +
MethodKnowledgeDistance Df(·,·)
FitNets [54]Feature representationL2
AT [73]Attention mapsL2
CC [49]Instance relationL2
NST [24]Neuron selectivity patternsLMMD
PKT [46]Similarity probability distributionLKL
+ +Comparison with Other Adaptive KDs for Distillation Gap. DisWOT is the first train-free architecture search solution to reduce the teacher-student gap. Unlike training manners [10] and KD-loss designs, DisWOT utilizes the classic KD training configurations and distillers. In addition, DisWOT is free from the assistant teacher in ATKD [43], which involves a complex training routine and budget. AKD [40] searches student via reinforcement learning based on feedback from individual training of lots of models. As a completely alternative technical route to these training-based + +Table 2. Formulation of NAS methods. $\mathcal{A}$ is the search space. A candidate architecture in the search space is denoted as $\alpha \in \mathcal{A}$ , which corresponds to a neural architecture $S(\alpha, w)$ with weight $w$ . $\mathcal{W}$ is the weight of the supernet. $\text{train}$ and $\text{val}$ are the loss functions on the training and validation sets, respectively. + +
TypeEvaluationFormula
Training-basedMulti-trial Trainingα* = arg min val(S(α, wα)), s.t. wα = arg min w train(S(α, w))
Weight sharingα* = arg min val(S(α, W_A(α))), s.t. W_A = arg min w train(S(A, W))
Training-freeZero-cost Proxyα* = ZeroProxy(S(α, w)) α∈A
+ +NAS [18], our training-free DisWOT builds on new zero-proxy and achieves $180 \times 1000 \times$ training acceleration, which greatly improves its easy-to-use and flexibility. + +Table 3. Comparison with different training-free NAS. + +
TypeMethodTeacher-awareObjective
Prune-basedSNIP [28], Fisher [1], Synflow [58]✗Vanilla acc.
Activation-basedNWOT [42], Zen-NAS [36]✗Vanilla acc.
KD-basedDisWOT (ours)✓Distill acc.
+ +# 2.2. Revisiting Architecture Search Methods + +Neural Architecture Search (NAS) is emerged to reduce human efforts in architecture design and automate the discovery of high-performance networks. As formalized in Tab. 2, Multi-trial NAS methods [40, 79] train a large number of candidates individually, which leads to extensive resource consumption. To alleviate this, many NAS [8,12,23,51] methods adopt a weight-sharing strategy within a single supernet to facilitate the simultaneous training of candidates. The supernet is trained for hundred of epochs by path sampling [11,19] or compound optimization with architecture representations [39,69]. As an orthogonal direction, zero-cost NAS methods [42,71] focus on identifying well-performed architectures with training-free metrics. For example, NWOT [42] calculates the architecture score based on the kernel matrix of binary activations between small batches of samples. + +Comparison with NAS with Teacher. Some training-based NAS [29,50,77] employ a teacher model to supervise supernet training to improve predictive ability in the search stage. However, these methods aim to improve vanilla accuracy, not for distillation, and they do not use the teacher model in the full training stage. In addition, without any + +![](images/ea0b209d838cdf1732db7233db8049f9f0600bba89416beb8d93117f04f5682b.jpg) +Figure 3. A schematic overview of our DisWOT, including (a) detailed calculation of the DisWOT scores and (b) evolution of the student architecture via the DisWOT scores. In search phase, DisWOT use semantic similarity metrics and relations similarity metrics to select good student for a given teacher. The semantic similarity metric is measured by $l_{2}$ distance of the channel-wise correlation matrix for Grad-cam activation maps. Similarly, the relation similarity matrix statistics the sample-wise correlation matrix distance of the randomly initialized teacher-student pairs. With the feedback from these metrics, the evolutionary search in DisWOT automatically imitates good student from weak ones. In distillation phase, this searched student is distilled via teacher model and achieves superior gains. + +training costs, our training-free DisWOT enjoys obvious differences than these methods and advantages in efficiency. + +Compared to Other Training-free NAS. Table 3 clearly summarizes the differences between DisWOT and other zero-cost methods [1, 28, 36, 42, 58]. Moreover, DisWOT outperforms these methods on distillation performance prediction and boosting in our sufficient experiments dealing with diverse datasets and search spaces. + +# 3. Methodology + +Figure 3 provides an overview of the DisWOT framework, which is comprised of two main stages: optimal student network search and distillation with high-order knowledge. In the search stage, we employ the neural architecture search technique to obtain an optimal student network for a pre-defined teacher network. Notably, we propose a training-free proxy called DisWOT to accurately rank enormous student networks and prevent expensive evaluation processes with high efficiency. In the distillation stage, the searched student network is retrained with distillation to imitate high-order knowledge in the teacher network. We give the details of these two designs in the following sections. + +# 3.1. Search for Optimal Student Network + +We first present the training-free metrics we designed to score a student architecture, which indicates its final accuracy when distilled with a pre-defined teacher network. Then we depict the details of the evolutionary process to obtain an optimal student candidate. + +Semantic Similarity Metric. The semantic information is meaningful for neural networks to perceive as humans. In + +distillation, the teacher network always has more convolutional operations than the student, resulting in a teacher feature map with a larger receptive field and greater richness of semantic information. In contrast to distiller designs to alleviate semantic gaps, we aim for train-free student architecture to better match the teacher model with computational constraints. We notice that the network with random initial weights also has some semantic localization capability. Thus, we start to analyze the localization performance of the randomly initialized teacher-student model. Specifically, we utilize Grad-CAM maps [78] to localize semantic object regions, which explains the model decisions using gradient information. Given a mini-batch of input images, we define the high-level feature map before the Global Average Pooling (GAP) layer of the teacher network $T$ as $A_{T} \in \mathbf{R}^{B \times C_{T} \times H_{T} \times W_{T}}$ , where $B$ represents the batch size, $C_{T}$ denotes the number of output channels, and $H_{T}$ and $W_{T}$ are the spatial dimensions. Additionally, we introduce $A_{T}^{c} \in \mathbf{R}^{N \times H_{T} \times W_{T}}$ as the c-th spatial map along the channel dimension. For the student network $S_{i}$ , we have feature map $A_{S_{i}}^{c} \in \mathbf{R}^{B \times C_{S} \times H_{S} \times W_{S}}$ and spatial map $A_{S_{i}}^{c} \in \mathbf{R}^{B \times H_{S} \times W_{S}}$ , respectively. To compute the Grad-CAM maps of the $n$ -th class for both the teacher and student networks, we can use the following formulations: + +$$ +G _ {T} = \sum_ {c = 1} ^ {C _ {T}} w _ {n, c} ^ {T} A _ {T} ^ {c}, \quad G _ {S _ {i}} = \sum_ {c = 1} ^ {C _ {S}} w _ {n, c} ^ {S} A _ {S _ {i}} ^ {c}, \tag {2} +$$ + +where $w^{T} \in \mathbf{R}^{N \times C_{T}}$ and $w^{S} \in \mathbf{R}^{N \times C_{S}}$ are weights of the last fully-connected layer in the teacher and student network. $N$ represents the number of classes. $w_{n,c}^{T}$ and $w_{n,c}^{S}$ refer to the element located in the $n$ -th row and $c$ -th column of weight matrices $w^{T}$ and $w^{S}$ , respectively. To quantify + +the intersection of class-discriminative localization maps, we formulate semantic similarity metric $\mathcal{M}_s$ as the intercorrelation on the accumulated Grad-CAM maps for both teacher and student networks as follows: + +$$ +\mathcal {G} ^ {T} = \frac {\left(G _ {T}\right) \cdot \left(G _ {T}\right) ^ {\top}}{\| \left(G _ {T}\right) \cdot \left(G _ {T}\right) ^ {\top} \| _ {2}}, \mathcal {G} ^ {S} = \frac {\left(G _ {S}\right) \cdot \left(G _ {S}\right) ^ {\top}}{\| \left(G _ {S}\right) \cdot \left(G _ {S}\right) ^ {\top} \| _ {2}}, (3) +$$ + +$$ +\mathcal {M} _ {s} = \left\| \mathcal {G} ^ {T} - \mathcal {G} ^ {S _ {i}} \right\| _ {2}. \tag {4} +$$ + +Relation Similarity Metric. The relationships between input samples are non-trivial for knowledge transfer. To reduce the teacher-student gap and improve the relation-distillation performance, we use the correlation matrix as the sample-wise metric to search for an optimal student network. For the random teacher network $T$ and student network $S_{i}$ with activation maps $A_{T} \in \mathbf{R}^{N \times C_{T} \times H_{T} \times W_{T}}$ and $A_{S}^{i} \in \mathbf{R}^{N \times C_{i} \times H_{i} \times W_{i}}$ , the correlation matrix of the minibatch samples in the teacher network is formulated as follows: + +$$ +\mathcal {A} ^ {T} = \frac {(\tilde {A} _ {T}) \cdot (\tilde {A} _ {T}) ^ {\top}}{\left\| (\tilde {A} _ {T}) \cdot (\tilde {A} _ {T} ^ {\top}) \right\| _ {2}}, \mathcal {A} ^ {S _ {i}} = \frac {(\tilde {A} _ {S}) \cdot (\tilde {A} _ {S}) ^ {\top}}{\left\| (\tilde {A} _ {S}) \cdot (\tilde {A} _ {S} ^ {\top}) \right\| _ {2}}, (5) +$$ + +where $\tilde{A}_T\in \mathbf{R}^{N\times CHW}$ is a reshaping of $A_{T}$ , and $M_T$ is a $N\times N$ matrix. Thus, the $(i,j)$ entry in matrix $C_T$ represents the similarity between the $i$ -th and $j$ -th images within the mini-batch. Based on this, the sample similarity metric $\mathcal{M}_r$ for a potential student model $S_{i}$ is defined as follows: + +$$ +\mathcal {M} _ {r} = \left\| \mathcal {A} ^ {T} - \mathcal {A} ^ {S _ {i}} \right\| _ {2}. \tag {6} +$$ + +Training-Free Evolutionary Search. Based on the above metric, we conduct a training-free evolutionary search algorithm to efficiently discover the optimal student $\alpha^{*}$ from search space $\mathcal{A}$ , as: + +$$ +\alpha^ {*} = \arg \min _ {\alpha \in \mathcal {A}} \left(\mathcal {M} _ {s} + \mathcal {M} _ {r}\right). \tag {7} +$$ + +Theoretical Understanding. According to the VC theory [63], the classification error of the vanilla teacher-student network can be decomposed as follows: + +$$ +R \left(f _ {s}\right) - R \left(f _ {r}\right) \leq O \left(\frac {\left| \mathcal {F} _ {s} \right| _ {C}}{n ^ {\alpha s r}}\right) + \epsilon_ {s r}; R \left(f _ {t}\right) - R \left(f _ {r}\right) \leq O \left(\frac {\left| \mathcal {F} _ {t} \right| _ {C}}{n ^ {\alpha t r}}\right) + \epsilon_ {t r}, \tag {8} +$$ + +where $f_{s}\in \mathcal{F}_{s}$ is the student function, $f_{t}\in \mathcal{F}_{t}$ is the teacher function, and $f_{r}\in \mathcal{F}_{r}$ is the target function. $R$ is the error. $O(\cdot)$ and $\epsilon_{sr}$ terms are the estimation and approximation error, respectively. $O(\cdot)$ is related to the statistical procedure when given the number of data points. In contrast, $\epsilon_{sr}$ is the approximation error of the student function class $\mathcal{F}_s$ for $f_{r}\in \mathcal{F}_{r}.\left|\cdot \right|_{C}$ is an function class capacity measure, and $n$ is the number of data point. During distillation, + +the student network is supervised purely with the teacher network as follows: + +$$ +R \left(f _ {s}\right) - R \left(f _ {t}\right) \leq O \left(\frac {\left| \mathcal {F} _ {s} \right| _ {C}}{n ^ {\alpha_ {s t}}}\right) + \epsilon_ {s t}, \tag {9} +$$ + +where $\alpha_{st}$ and $\epsilon_{st}$ are associated to student learning from teacher. By combining Equations 3.1 and 9, we obtain: + +$$ +R \left(f _ {s}\right) - R \left(f _ {r}\right) \leq O \left(\frac {\left| \mathcal {F} _ {t} \right| _ {C}}{n ^ {\alpha_ {t r}}}\right) + \epsilon_ {t r} + O \left(\frac {\left| \mathcal {F} _ {s} \right| _ {C}}{n ^ {\alpha_ {s t}}}\right) + \epsilon_ {s t}. \tag {10} +$$ + +When student obtains gains in KDs, its upper bound of error in distillation is smaller than vanilla training, which satisfies the following inequality: + +$$ +O \left(\frac {\left| \mathcal {F} _ {t} \right| _ {C}}{n ^ {\alpha_ {t r}}} + \frac {\left| \mathcal {F} _ {s} \right| _ {C}}{n ^ {\alpha_ {s t}}}\right) + \epsilon_ {t r} + \epsilon_ {s t} \leq O \left(\frac {\left| \mathcal {F} _ {s} \right| _ {C}}{n ^ {\alpha_ {s r}}}\right) + \epsilon_ {s r}. \tag {11} +$$ + +Based on the assumption in [22] that $\epsilon_{tr} + \epsilon_{st} \leq \epsilon_{sr}$ holds consistently, we focus on minimizing $O\left(\frac{|\mathcal{F}_t|_C}{n^{\alpha_{tr}}} + \frac{|\mathcal{F}_s|_C}{n^{\alpha_{st}}}\right)$ to improve the distillation performance. As noted in Lopez-Paz et al [41], a better representation allows for a faster learning rate with a fixed amount of data. Hence, when there is a larger gap between the capacities of the student and teacher networks, the value of $\alpha_{st}$ tends to be lower. Thus we aim to search for an optimal student network that meets the requirement of $\alpha_{si t} \leq \alpha_{so t}$ , where $s_i$ is all candidate student networks, and $s_o$ is our searched student network. In this case, the inequality becomes more effective, and we improve the knowledge distillation by injecting a larger $\alpha_{so t}$ . Specifically, we present the overall procedure for discovering optimal student in algorithm 1. + +Effects of Search Strategies. We compare the evolution search algorithm and the random search algorithm in search space $S_{2}$ with the same number of iterations, as shown in Figure 4. We find that the evolution search algorithm can consistently find architectures with lower DisWOT, especially when the search space is relatively large, and the evolutionary search can explore better architectures. + +# 3.2. Distillation with High-order Knowledge + +In the distillation stage, teacher model $T$ is employed to distill the optimal student network $f_{S}$ . To verify the superiority of our search architecture, we adopt the existing distillers (e.g., KD) as the default distillation setting. In addition, we observe that the metrics we searched for actually serve as minimization optimization goals in the distillation process to transfer the teacher's privileged semantic and sample relational knowledge as the semantic distillation and sample distillation: + +$$ +\mathcal {L} _ {\mathcal {M} _ {s}} = \frac {1}{c ^ {2}} \left\| \mathcal {G} ^ {T} - \mathcal {G} ^ {S} \right\| _ {2}, \mathcal {L} _ {\mathcal {M} _ {r}} = \frac {1}{b ^ {2}} \left\| \mathcal {A} ^ {T} - \mathcal {A} ^ {S} \right\| _ {2}, \tag {12} +$$ + +Finally, we involve these advanced distillers in our framework, called DisWOT†. The total loss for DisWOT and + +# Algorithm 1 Evolution Search for DisWOT + +Input: Search space $S$ , population $\mathcal{P}$ , architecture constraints $\mathcal{C}$ , max iteration $\mathcal{N}$ , sample ratio $r$ , sampled pool $\mathcal{Q}$ , topk $k$ , teacher network $\mathcal{T}$ . + +Output: Highest DisWOT score architecture. + +1: $\mathcal{P}_0\coloneqq$ Initialize population $(P_{i},\mathcal{C})$ +2: sample pool $\mathcal{Q} := \emptyset$ ; +3: for $i = 1:\mathcal{N}\mathbf{d}\mathbf{o}$ +4: Clear sample pool $\mathcal{Q} \coloneqq \emptyset$ ; +5: Randomly select $r \times \mathcal{P}$ subnets $\hat{P}_i \in \mathcal{P}$ to get $\mathcal{Q}$ ; +6: Candidates $\{A_i\}_k \coloneqq \operatorname{GetTopk}(\mathcal{Q}, k)$ ; +7: Parent $A_{i}\coloneqq$ RandomSelect $(\{A_i\}_k)$ +8: Mutate $\hat{P}_i\coloneqq \mathrm{MUTATE}(A_i)$ +9: if $\hat{P}_i$ do not meet the constraints $\mathcal{C}$ then +10: Do nothing; +11: else +12: Get DisWOT-Score $z \coloneqq \operatorname{DisWOT}(\hat{P}_i, \mathcal{T})$ ; +13: Append $\hat{P}_i$ to $\mathcal{P}$ +14: end if +15: Remove network of smallest DisWOT-score; +16: end for + +![](images/35fc33d4661068e9763fa5d56ca3b2d9def20424836406105ca2d91cb9b07dcb.jpg) +Figure 4. Left: comparison of random search and evolution search. Right: ranking correlation of different distillation methods on NAS-Bench-201. + +![](images/e67848fe911182b190df27a081f8fd05620c88d706d2d6548fa66497450225fe.jpg) + +Table 4. Spearman correlation $\rho \left( \% \right)$ on NAS-Bench-201. + +
TypeMethodρMethodρ
Zero-costGrad_Norm [1]58.70±0.11Synflow [58]74.61±0.08
SNIP [28]58.17±0.15Jacob [57]73.42±0.03
ProxiesFisher [1]35.91±0.09Zen-NAS [36]41.36±0.06
NWOT [42]64.41±0.08FLOPs [1]63.38±0.06
KD-basedKD [22]54.43±0.09PKT [47]52.65±0.09
FitNets [55]56.18±0.09CC [48]65.90±0.08
ProxiesSP [62]51.24±0.08NST [25]72.35±0.09
RKD [44]25.71±0.17DisWOT72.36±0.02
+ +DisWOT† as: + +$$ +\mathcal {L} _ {\text {D i s W O T}} = \mathcal {L} _ {C E} \left(f _ {S}, Y\right) + \mathcal {L} _ {K L} \left(f _ {S}, f _ {T}\right), \tag {13} +$$ + +$$ +\mathcal {L} _ {\text {D i s W O T}} \dagger = \mathcal {L} _ {\text {D i s W O T}} + \mathcal {L} _ {\mathcal {M} _ {s}} + \mathcal {L} _ {\mathcal {M} _ {r}}. +$$ + +# 3.3. Bridging Distiller and Zero-proxy + +In our DisWOT framework, we use the semantic and relational similarity metrics as a distillation performance predictor and distiller. In addition, DisWOT also enjoys good performance for vanilla performance predictions. Encour + +aged by this intriguing observation, we employ the knowledge function in of different KDs as zero-proxies and evaluate their ranking consistency with vanilla accuracy. As shown in Table 4, these KD-based zero-proxies enjoy competitive rankings with other NAS methods. Detailed results in Figure 4 illustrate that our DisWOT and NST [24] are the winners in the family of KD-based proxies. These attempts reveal the close connections between KD and NAS, and augment $10+$ new universal proxies from the teacher-student learning perspective for training-free NAS research. + +# 4. Experimental results + +In this section, we present the experimental results of our DisWOT on different datasets. First, we describe the four datasets used in our experiments and three search spaces $S_0, S_1, S_2$ in Sec. 4.1. Then, we conduct a comprehensive set of experiments to evaluate the effectiveness of DisWOT. + +# 4.1. Experimental Setup + +We perform experiments on four datasets, namely CIFAR-10, CIFAR-100, ImageNet-16-120, and ImageNet-1k. In the search process, we only use one batch of training data to get the statistic at nearly no cost. Following previous works, our experiments are conducted on the following three search spaces: + +Search Space $S_0$ : Following CIFar-ResNet [20], the search space consists of three residual blocks and is based on CIFAR-100 datasets. The depth of each residual block is searched in set $\{1,3,5,7\}$ . + +Search Space $S_{1}$ : Following NAS-Bench-201 [14], this Darts-like search space is a cell-based search space consisting of stacked directed acyclic graphs. $S_{1}$ is conducted on CIFAR-10, CIFAR-100, and ImageNet-16-120 datasets. + +Search Space $S_{2}$ : Following NDS [53], this search space consists of residual and bottleneck blocks defined in ResNet. $S_{2}$ is based on CIFAR-100 and ImageNet-1k dataset. + +# 4.2. Experiments on CIFAR-100 + +Implementation Details. We compare distillation gains with other zero-nas on search space $S_{1}$ . In the search phase, we configure 48k evolution iters with 512 population sizes. In distillation, All searched student networks are trained via CRD's settings [59] with ResNet56 as the teacher model. + +Distillation Results of Zero-cost Proxies. We conduct detailed experiments on other zero-cost proxies with different knowledge distillation methods. Note that we search the student network under constraints of 1M parameters. The results in Table 5 demonstrated that our proposed DisWOT achieved superior results compared with other zero-cost proxies with different knowledge distillation methods. The DisWOT outperforms its counterparts vanilla networks by around $2\%$ , while achieving consistent improvements + +Table 5. Distillation results (\%) of different zero-cost proxies with knowledge distillation methods under 1M parameters. + +
MethodRandomFLOPsSynflowNWOTDisWOT
Baseline69.5271.3772.8871.8073.12
KD70.4572.1373.7272.5774.73
FitNets70.1272.4073.5572.7274.85
AT70.1672.9773.5272.0874.50
SP70.4672.1473.5072.1674.95
RKD71.1972.2273.6972.6374.62
CRD71.5972.7873.9973.1275.25
+ +among different distillation methods, such as KD [22], Fit-Nets [55], AT [74], SP [62], RKD [44], and CRD [60]. + +Table 6. Distillation results(%) of zero-cost proxies under $\{0.5,1,2\}\mathrm{M}$ parameters. + +
Param.FLOPsNWOTDisWOTDisWOT†
0.5M69.8870.3872.8973.75
1M72.1372.5774.2375.25
2M73.2773.8675.9576.67
+ +Table 7. Distillation results(%) of zero-cost proxies under $\{50,100\}$ M FLOPs on space $S_{1}$ . + +
FLOPsNWOTSynflowDisWOTFLOPsNWOTSynflowDisWOT
50M63.1964.2865.98100M70.3872.1272.89
+ +Table 8. Ranking correlation (\%) of zero-cost proxies on $S_0$ space on CIFAR-100. + +
MethodKendall's TauSpearmanPearson
FLOPs [1]51.6172.9276.40
Fisher [1]62.8681.3720.90
Grad_Norm [1]63.7582.3539.35
SNIP [28]67.2285.0751.09
NWOT [42]31.8745.6648.99
DisWOT (ours)73.9891.3884.83
+ +Analysis on Varying Parameter Constraints. We analyze the performance of student models under different parameter constraints obtained by DisWOT on CIFAR-100. As shown in the Table 7, we compared our method with two zero proxies, a.k.a. FLOPs [1] and NWOT [42], under the parameter constraints of 0.5, 1, and 2M, respectively, and the results demonstrate that our method still achieves excellent results. As shown in Tab. 7, DisWOT also outperforms previous SOTA methods with $0.8\% \sim 1.7\% \uparrow$ gains under same FLOPs constraints, + +Ranking Correlation with Distill Accuracy. Based on search space $S_0$ , we perform vanilla training and distillation for each candidate with CRD's settings [59]. Then, we collect these vanilla results as GT and analyze the different zero-proxy's correlation with them. As shown in Table 8, the results illustrate that our DisWOT achieves higher than Fisher, GradNorm, SNIP,FLOPs, and NWOT by a large margin, and achieve results that are on par with the best zero-cost proxy, a.k.a. Zen-NAS and Synflow, on Kendall's Tau, Pearson, and Spearman coefficient. + +# 4.3. Experiments on NAS-Bench-201 + +Implementation Details. For search trials, we first adopt ResNet110/56 as the teachers and then Conduct an evolution search with the DisWOT metric and get the best student network. We randomly sampled 50 candidate architectures to evaluate sequencing consistency. The distillation settings are the same as the Sec.4.2 + +Comparison results As shown in Table 9, some training-free methods can achieve good results with much faster speedups, such as NWOT and TE-NAS. Our proposed method DisWOT achieves a speedup ratio of $180 \times$ , where if semantic similarity metric is removed, we can achieve a $300 \times$ speedup ratio at the expense of some accuracy. + +# 4.4. Experiments on ImageNet + +Implementation Details. We searched the ResNet18 level network regarding the search space in NDS [53]. Specifically, we limit the number of parameters to less than 13M and the depth of the network to up to 20 layers and find the optimal network by evolution algorithm with the DisWOT metric. As shown in Table 10, guided by three different sizes of networks, we used DisWOT to find the optimal student network. We trained the student network obtained by the search using the distillation strategy in DisWOT. Implementation details are available in supplementary materials. Comparison Results. Table 10 reports the performance of DisWOT on ImageNet with ResNet34/50 as teacher network. The results demonstrate that the student architecture of the ResNet18-level obtained by DisWOT under different teacher guidance and using different distillation strategies yielded significantly better results than its counterparts. + +# 4.5. Ablation Studies of DisWOT + +We perform ablation experiments to verify the validity of each component of DisWOT in search space $S_0$ . As shown in Table 11, for semantic knowledge, similarity matrix obtains a more robust ranking improvement than simple Fit-Net [54]. For $\mathcal{M}_r$ , similarity matrix performs better on relational knowledge than RKD [45]. DisWOT integrates semantic and relational knowledge to obtain an additional ranking improvement than stand-alone scores. The weight initialization scheme plays an important role in zero-proxy. + +Table 9. Distillation results on CIFAR-10, CIFAR-100, and ImageNet-16 in NAS-Bench-201 [13]. Dis. Acc. (%) represents the accuracy of the searched architecture after distillation training. Time (s) denotes the time cost (GPU-seconds) during the search phase. The results of NWOT and TE-NAS come from their original papers. Our DisWOT achieves competitive results with the lowest costs. + +
TypeModelCIFAR-10CIFAR-100ImageNet-16-120
Dis. Acc(%)Time (s)Speed-upDis. Acc(%)Time (s)Speed-upDis. Acc(%)Time (s)Speed-up
Multi-trialRS93.63216K1.0×71.28460K1.0×44.881M1.0×
RL [3]92.83216K1.0×71.71460K1.0×44.351M1.0×
BOHB [17]93.49216K1.0×70.84460K1.0×44.331M1.0×
RSPS [34]91.6710K21.6×57.9946K21.6×36.87104K9.6×
Weight-sharingGDAS [15]93.3922K12.0×70.7039K11.7×42.35130K7.7×
DARTS [38]89.2223K9.4×66.2480K5.8×43.18110K9.1×
Training-freeNWOT [42]93.732.2K100×73.314.6K100×45.4310K100×
TE-NAS [9]93.922.2K100×71.244.6K100×44.3810K100×
DisWOTMs & Mr93.551.2K180×74.219.2K180×47.3020K180×
Mr93.490.72K300×73.6218.4K300×45.6340K300×
+ +Table 10. The accuracy $(\%)$ of ResNet18 on ImageNet-1k with various teachers. Results of other KD methods refer to the papers of CRD [60] and ESKD [10]. ATKD $A_{R34}$ [43] denotes ResNet34 used as the assistant teacher. N/A means no available results. Our DisWOT obtains better performance than other methods and improves students' performance positively correlated with that of the teacher. + +
TeacherStudentAcc.TeacherStudentKD [22]ESKD [10]\( \mathrm{ATKD}_{A_{R18}} \) [43]ONE [27]DML [75]CRD [60]DisWOT
ResNet34ResNet18Top-173.4069.7570.6670.8970.7870.5571.0371.1772.08
Top-591.4289.0789.8890.0689.9989.5990.2890.3290.38
TeacherStudentAcc.TeacherStudentKD [22]\( \mathrm{ATKD}_{A_{R18}} \) [43]\( \mathrm{ATKD}_{A_{R34}} \) [43]Seq. ESKD [10]ESKD [10]SRRL [72]DisWOT
ResNet50ResNet18Top-176.1669.7570.6870.6570.8570.6570.9571.2072.30
Top-592.8689.07N/AN/AN/AN/AN/AN/A90.51
+ +Table 11. Spearman correlation ("mean±std") of DisWOT on search space $S_0$ . + +
KnowledgeMetricSpearman (%)
MsFitNets [54]64.06±6.11
MsSimilarity matrix73.68±5.45
MrRKD [59]13.52±11.51
MrSimilarity matrix72.36±3.42
Ms & MrSimilarity matrix77.51±2.76
+ +We verify the effect of the initialization strategy of the network on the ranking consistency. The results in Tab. 12 demonstrate that the Gaussian initialization strategy is detrimental to $\mathcal{M}_s$ , but beneficial to $\mathcal{M}_r$ . + +# 5. Conclusion + +In this paper, we present DisWOT, a new teacher-aware student architecture search without training framework for distillation. Based on key observations about the difference between vanilla and distillation accuracy, DisWOT measures the new zero-cost proxy conditioned on the similarity of feature semantics and sample relations between random initialized teacher-student network. Then, DisWOT search for the best student architectures for the given teacher us + +Table 12. "mean±std %" Spearman of proxies via Kaiming and Gaussian initialization on search space $S_0$ and NAS-Bench-201 with various seeds. + +
SpaceInitialFisherGradNormNWOTDisWOT
S0Kaim.81.37±0.0182.35±0.0145.66±0.0584.08±0.03
Gauss.80.99±0.0175.50±0.0145.36±0.0391.38±0.03
NB-201Kaim.54.63±0.1558.70±0.1164.41±0.0865.57±0.02
Gauss.45.91±0.0945.70±0.1162.24±0.0772.36±0.02
+ +ing an evolutionary algorithm with these metrics. Thorough evaluations are performed on diverse datasets and search spaces, and DisWOT achieves significant performance gains in various neural networks with at least $180 \times$ training acceleration. We experimentally and theoretically explained the relationship between similarity difference and distillation performance. In addition, we also extend DisWOT to new distillers and general zero proxy to predict the performance of models. By doing this, we bridge the higher-order knowledge bewteen distillation and network architecture search. This approach represents an elegant and practical solution, which we hope will inspire future research on knowledge distillation and architecture search design. + +Limitations. Following most zero-cost NAS, we evaluate DisWOT in classification tasks. In the future work, we will make efforts to expand the DisWOT for downstream tasks (e.g., object detection and semantic segmentation). + +# References + +[1] Mohamed S Abdelfattah, Abhinav Mehrotra, Lukasz Dudziak, and Nicholas Donald Lane. Zero-cost proxies for lightweight nas. In ICLR, 2020. 3, 4, 6, 7 +[2] Sungsoo Ahn, Shell Xu Hu, Andreas Damianou, Neil D Lawrence, and Zhenwen Dai. Variational information distillation for knowledge transfer. In CVPR, 2019. 1 +[3] Bowen Baker, Otkrist Gupta, Nikhil Naik, and Ramesh Raskar. Designing neural network architectures using reinforcement learning. In ICLR, 2017. 8 +[4] Lucas Beyer, Xiaohua Zhai, Amélie Royer, Larisa Markeeva, Rohan Anil, and Alexander Kolesnikov. Knowledge distillation: A good teacher is patient and consistent. In CVPR, 2022. 1 +[5] Tom B. 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Learning transferable architectures for scalable image recognition. In CVPR, 2018. 3 \ No newline at end of file diff --git a/2023/DisWOT_ Student Architecture Search for Distillation WithOut Training/images.zip b/2023/DisWOT_ Student Architecture Search for Distillation WithOut Training/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..a2c38c62f5865a6c4a904855af275b7366b9e286 --- /dev/null +++ b/2023/DisWOT_ Student Architecture Search for Distillation WithOut Training/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:53b48710dc9a7551af5ba336796b26ee2b99c27f273ede7d394c49521a1ebcd5 +size 607002 diff --git a/2023/DisWOT_ Student Architecture Search for Distillation WithOut Training/layout.json b/2023/DisWOT_ Student Architecture Search for Distillation WithOut Training/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..222ac0a795c48bb0848cee99e02169325d4aeeac --- /dev/null +++ b/2023/DisWOT_ Student Architecture Search for Distillation WithOut Training/layout.json @@ -0,0 +1,11385 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 73, + 103, + 521, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 73, + 103, + 521, + 121 + ], + "spans": [ + { + "bbox": [ + 73, + 103, + 521, + 121 + ], + "type": "text", + "content": "DisWOT: Student Architecture Search for Distillation WithOut Training" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 107, + 142, + 485, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 142, + 485, + 185 + ], + "spans": [ + { + "bbox": [ + 107, + 142, + 485, + 185 + ], + "type": "text", + "content": "Peijie Dong" + }, + { + "bbox": [ + 107, + 142, + 485, + 185 + ], + "type": "inline_equation", + "content": "^{1\\dagger}" + }, + { + "bbox": [ + 107, + 142, + 485, + 185 + ], + "type": "text", + "content": " Lujun Li" + }, + { + "bbox": [ + 107, + 142, + 485, + 185 + ], + "type": "inline_equation", + "content": "^{2\\dagger*}" + }, + { + "bbox": [ + 107, + 142, + 485, + 185 + ], + "type": "text", + "content": " Zimian Wei" + }, + { + "bbox": [ + 107, + 142, + 485, + 185 + ], + "type": "inline_equation", + "content": "^{1\\dagger}" + }, + { + "bbox": [ + 107, + 142, + 485, + 185 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 107, + 142, + 485, + 185 + ], + "type": "text", + "content": "National University of Defense Technology, Chinese Academy of Sciences \n" + }, + { + "bbox": [ + 107, + 142, + 485, + 185 + ], + "type": "inline_equation", + "content": "^{1}\\{dongpeijie, weizimian16\\} @nudt.edu.cn, ^{2}" + }, + { + "bbox": [ + 107, + 142, + 485, + 185 + ], + "type": "text", + "content": "lilujunai@gmail.com" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "spans": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 238, + 290, + 549 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 238, + 290, + 549 + ], + "spans": [ + { + "bbox": [ + 47, + 238, + 290, + 549 + ], + "type": "text", + "content": "Knowledge distillation (KD) is an effective training strategy to improve the lightweight student models under the guidance of cumbersome teachers. However, the large architecture difference across the teacher-student pairs limits the distillation gains. In contrast to previous adaptive distillation methods to reduce the teacher-student gap, we explore a novel training-free framework to search for the best student architectures for a given teacher. Our work first empirically show that the optimal model under vanilla training cannot be the winner in distillation. Secondly, we find that the similarity of feature semantics and sample relations between random-initialized teacher-student networks have good correlations with final distillation performances. Thus, we efficiently measure similarity matrix conditioned on the semantic activation maps to select the optimal student via an evolutionary algorithm without any training. In this way, our student architecture search for Distillation WithOut Training (DisWOT) significantly improves the performance of the model in the distillation stage with at least " + }, + { + "bbox": [ + 47, + 238, + 290, + 549 + ], + "type": "inline_equation", + "content": "180 \\times" + }, + { + "bbox": [ + 47, + 238, + 290, + 549 + ], + "type": "text", + "content": " training acceleration. Additionally, we extend similarity metrics in DisWOT as new distillers and KD-based zero-proxies. Our experiments on CIFAR, ImageNet and NAS-Bench-201 demonstrate that our technique achieves state-of-the-art results on different search spaces. Our project and code are available at https://lilujunai.github.io/DisWOT-CVPR2023/." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 571, + 128, + 583 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 571, + 128, + 583 + ], + "spans": [ + { + "bbox": [ + 47, + 571, + 128, + 583 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 591, + 288, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 591, + 288, + 687 + ], + "spans": [ + { + "bbox": [ + 47, + 591, + 288, + 687 + ], + "type": "text", + "content": "Despite the remarkable achievements of Deep Neural Networks (DNNs) in numerous visual recognition tasks [52, 64-68], they usually lead to heavy costs of memory, computation, and power at model inference due to their large numbers of parameters. To address this issue, Knowledge Distillation (KD) has been proposed as a means of transferring knowledge from a high-capacity teacher model to a low-capacity target student model, providing a more op" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 307, + 213, + 424, + 300 + ], + "blocks": [ + { + "bbox": [ + 307, + 213, + 424, + 300 + ], + "lines": [ + { + "bbox": [ + 307, + 213, + 424, + 300 + ], + "spans": [ + { + "bbox": [ + 307, + 213, + 424, + 300 + ], + "type": "image", + "image_path": "3cc08b42e0202bafabff908c5cc47bb636a1fea8dd8277927ad2d4d26556f539.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 303, + 547, + 348 + ], + "lines": [ + { + "bbox": [ + 306, + 303, + 547, + 348 + ], + "spans": [ + { + "bbox": [ + 306, + 303, + 547, + 348 + ], + "type": "text", + "content": "Figure 1. Left: Ranking correlation of proxies in zero-cost NAS with vanilla and distillation accuracy. Right: Vanilla accuracy, distillation accuracy, prediction scores of DisWOT for ResNet[7,1,3] and ResNet[3,3,3] on search space " + }, + { + "bbox": [ + 306, + 303, + 547, + 348 + ], + "type": "inline_equation", + "content": "S_0" + }, + { + "bbox": [ + 306, + 303, + 547, + 348 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 424, + 213, + 544, + 300 + ], + "blocks": [ + { + "bbox": [ + 424, + 213, + 544, + 300 + ], + "lines": [ + { + "bbox": [ + 424, + 213, + 544, + 300 + ], + "spans": [ + { + "bbox": [ + 424, + 213, + 544, + 300 + ], + "type": "image", + "image_path": "5238b79d9a3d1a33d347906a448e3339f1711cb1fa654d41bcfa8ac33d471d48.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 307, + 363, + 422, + 449 + ], + "blocks": [ + { + "bbox": [ + 307, + 363, + 422, + 449 + ], + "lines": [ + { + "bbox": [ + 307, + 363, + 422, + 449 + ], + "spans": [ + { + "bbox": [ + 307, + 363, + 422, + 449 + ], + "type": "image", + "image_path": "79ce25b09d33da7bf08670e1642042532dfcf401cda404f6d2f6706a0dc14a02.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 452, + 547, + 485 + ], + "lines": [ + { + "bbox": [ + 306, + 452, + 547, + 485 + ], + "spans": [ + { + "bbox": [ + 306, + 452, + 547, + 485 + ], + "type": "text", + "content": "Figure 2. Left: KD [22], DisWOT, DisWOT† results for ResNet20 under different teachers. Right: Comparison of distill accuracy & training efficiency with other NAS methods on NAS-Bench-201." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 424, + 362, + 545, + 449 + ], + "blocks": [ + { + "bbox": [ + 424, + 362, + 545, + 449 + ], + "lines": [ + { + "bbox": [ + 424, + 362, + 545, + 449 + ], + "spans": [ + { + "bbox": [ + 424, + 362, + 545, + 449 + ], + "type": "image", + "image_path": "50164ccbd478508dc8db20245e777b715c3cfac668e1684a9f171c01ea1f76f5.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 508, + 547, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 508, + 547, + 652 + ], + "spans": [ + { + "bbox": [ + 304, + 508, + 547, + 652 + ], + "type": "text", + "content": "timal accuracy-efficiency trade-off during runtime [4, 7, 76]. The original KD method [22] utilizes the logit outputs of the teacher network as the source of knowledge. Subsequent studies [2, 21, 24, 26, 54, 61, 73] have focused on extracting informative knowledge based on intermediate feature representations. However, as the gap in capacity between students and teachers increases, existing KD methods are unable to improve results, particularly in tasks that depend on large-scale visual models such as VIT and GPT-3 [5, 16]. For example, as shown in Figure 2 (Left), the large teacher (e.g., ResNet110) lead to worse performance for the fixed student than the relatively smaller one (e.g., ResNet56)." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 653, + 548, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 548, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 548, + 713 + ], + "type": "text", + "content": "To solve this issue, adaptive KD methods have been proposed in terms of training paradigms (e.g., early stop [10]) and architectural adaptations (e.g., assistant teacher [43] and architecture search [40]), respectively. However, they are ineffective in improving distillation performance or in" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 693, + 288, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 693, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 693, + 288, + 713 + ], + "type": "text", + "content": "*Corresponding author, † equal contribution, PD conducted main experiments, LL proposed ideas and led the project & writing." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11898" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 492 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 492 + ], + "type": "text", + "content": "volve enormous training costs in the additional model training and search process. In sharp contrast to these methods, we tackle this challenging problem from a new perspective regarding training-free architecture search. To achieve this goal, we construct a search space " + }, + { + "bbox": [ + 47, + 72, + 289, + 492 + ], + "type": "inline_equation", + "content": "S_0" + }, + { + "bbox": [ + 47, + 72, + 289, + 492 + ], + "type": "text", + "content": " for ResNet-like models with different depth configurations and obtain vanilla and distill performance for each candidate in " + }, + { + "bbox": [ + 47, + 72, + 289, + 492 + ], + "type": "inline_equation", + "content": "S_0" + }, + { + "bbox": [ + 47, + 72, + 289, + 492 + ], + "type": "text", + "content": " by individual training. Then, we evaluate the ranking correlation between predicted scores of training-free search methods and the actual performance of each student model. Surprisingly, as shown in Figure 1 (Left), there are common ranking correlation loss " + }, + { + "bbox": [ + 47, + 72, + 289, + 492 + ], + "type": "inline_equation", + "content": "(10\\% \\downarrow \\sim 20\\% \\downarrow)" + }, + { + "bbox": [ + 47, + 72, + 289, + 492 + ], + "type": "text", + "content": " for these methods in predicting distillation accuracy than vanilla accuracy. To clarify this, we carefully analyze the disparities in vanilla and distillation performance for each model: (1) for overall search space, vanilla accuracy only preserves " + }, + { + "bbox": [ + 47, + 72, + 289, + 492 + ], + "type": "inline_equation", + "content": "85\\%" + }, + { + "bbox": [ + 47, + 72, + 289, + 492 + ], + "type": "text", + "content": " correlations with actual distillation performance. (2) for a particular instance, as shown in Figure 1 (Right), ResNet20 with 3 res-blocks in each stage (i.e., ResNet[3,3,3]) has more parameters and better standalone performance but is weaker than ResNet[7,1,3] in the distillation process. Considering that ResNet[7,1,3] has more layers than ResNet20, we seek to understand the above phenomenon regarding the vanilla-distillation accuracy gap from the perspective of semantic matching [37]. ResNet[7,1,3] enjoys a larger effective receptive field and more excellent matched knowledge with teacher, resulting in significant distillation gains. Encouraged by this understanding, we strive to design a new zero-proxy regarding the semantic matching of teacher-student. As a result, we find that the similarity scores of feature semantics and sample relations can outperform conventional zero-cost NAS in predicting final distillation accuracy (see the comparison of ranking correlation on search space " + }, + { + "bbox": [ + 47, + 72, + 289, + 492 + ], + "type": "inline_equation", + "content": "S_0" + }, + { + "bbox": [ + 47, + 72, + 289, + 492 + ], + "type": "text", + "content": " in Table 8). As shown in Figure 1(Right), similarity scores are also consistent with distillation performance." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 498, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 498, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 498, + 289, + 714 + ], + "type": "text", + "content": "Drawing on the aforementioned observations, we introduce DisWOT, a simple yet effective training-free framework that finds the best student architectures for distilling the given teacher model. For better semantic matching in distillation, DisWOT leverages novel zero-cost metrics regarding the feature semantics and sample relations to select better student model. For the feature semantic similarity metric, we remark that randomly initialized models can localize objects well [6] and generate localization heatmaps via Grad-CAM [56] as reliable semantic information. Then, we measure the channel-wise similarity matrix of localization heatmaps and take the " + }, + { + "bbox": [ + 47, + 498, + 289, + 714 + ], + "type": "inline_equation", + "content": "L_{2}" + }, + { + "bbox": [ + 47, + 498, + 289, + 714 + ], + "type": "text", + "content": " distance of the similarity matrix for the teacher-student model as the metric. For input samples, different models have diverse abilities to discriminate their relationships. To improve relational knowledge matching ability, we use the " + }, + { + "bbox": [ + 47, + 498, + 289, + 714 + ], + "type": "inline_equation", + "content": "L_{2}" + }, + { + "bbox": [ + 47, + 498, + 289, + 714 + ], + "type": "text", + "content": " distance of sample-relation correlation matrix as a relation similarity metric. Finally, we search for student architectures using an evo" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 304, + 72, + 547, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 179 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 179 + ], + "type": "text", + "content": "lutionary algorithm with semantic and relations similarity metrics. Then, the distillation process is implemented between the searched student and the pre-defined teacher. In addition, we leverage these metrics directly as new distillers to enhance the student, as the DisWOT†. Equipped with our train-free search and distillation design, our DisWOT and DisWOT† framework significantly improve the model's accuracy-latency tradeoff in inference with at least " + }, + { + "bbox": [ + 304, + 72, + 547, + 179 + ], + "type": "inline_equation", + "content": "180 \\times" + }, + { + "bbox": [ + 304, + 72, + 547, + 179 + ], + "type": "text", + "content": " training acceleration." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 304, + 180, + 548, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 180, + 548, + 407 + ], + "spans": [ + { + "bbox": [ + 304, + 180, + 548, + 407 + ], + "type": "text", + "content": "In principle, our DisWOT use higher-order statistics of teacher-student models to optimize the student architecture to fit a given teacher model. Its merits can be highlighted in three aspects: (1) In contrast to training-based student architecture search requires the individual or weight-sharing training, our DisWOT does not require the training of student models in the search phase. In addition, DisWOT is efficient to compute and easy to implement as it uses only the mini-batch data at initialization. (2) DisWOT is a teacher-aware search for distillation, which has better predictive distill accuracy than conventional NAS. (3) DisWOT exploits the distance of higher-order knowledge between the neural networks, bridging knowledge distillation and zero-proxy NAS. We further demonstrate the competitive ranking correlation of DisWOT among 10 knowledge distances in KD as zero-proxy for predicting vanilla accuracy in NAS-Bench-201. We anticipate that our work on KD-based zero-proxy can offer some assistance in furthering research endeavors related to KD and NAS." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 407, + 548, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 407, + 548, + 586 + ], + "spans": [ + { + "bbox": [ + 304, + 407, + 548, + 586 + ], + "type": "text", + "content": "We conduct extensive experiments on CIFAR-100, ImageNet, and the NAS-Bench-201 [14] dataset, demonstrating the superiority of our proposed approach. In contrast to experiments in traditional architectural search, we focus on final distillation accuracy instead of the vanilla accuracy for the student. The results show that our DisWOT can achieve better accuracy than traditional Zero-shot NAS in the same search space. Besides, by switching to a larger space, our DisWOT can obtain new state-of-the-art architectures. For example, in the same ResNet-like search space, we significantly improved " + }, + { + "bbox": [ + 304, + 407, + 548, + 586 + ], + "type": "inline_equation", + "content": "1.62\\%" + }, + { + "bbox": [ + 304, + 407, + 548, + 586 + ], + "type": "text", + "content": " Top-1 accuracy over KD for ResNet50-ResNet18 pair under the same training settings. We also conducted comprehensive ablation studies to investigate how our method can use the predictability of zero-cost metrics to boost the distillation performance." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 586, + 398, + 598 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 586, + 398, + 598 + ], + "spans": [ + { + "bbox": [ + 306, + 586, + 398, + 598 + ], + "type": "text", + "content": "Main Contributions:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 317, + 605, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 605, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 317, + 605, + 547, + 715 + ], + "type": "text", + "content": "- By analyzing and exploring the discrepancy between teacher-student capability, we empirically show that their semantic similarities have a stronger correlation with the final distillation accuracy. This motivates us to propose a new student architecture search for the Distillation without Training (DisWOT) framework to reduce the teacher-student capability gap, which, to the best of our knowledge, is not achieved in the area of knowledge distillation." + } + ] + } + ], + "index": 6 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "11899" + } + ] + } + ], + "index": 7 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 59, + 72, + 288, + 222 + ], + "type": "list", + "angle": 0, + "index": 2, + "blocks": [ + { + "bbox": [ + 59, + 72, + 288, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 72, + 288, + 144 + ], + "spans": [ + { + "bbox": [ + 59, + 72, + 288, + 144 + ], + "type": "text", + "content": "- DisWOT proposes novel zero-cost metrics on similarity of feature semantics and sample relations and ensemble these metrics to select the optimal student via an evolutionary algorithm at the initial time. In the distillation stage, DisWOT achieves state-of-the-art performances in multiple datasets and search spaces." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 59, + 150, + 288, + 222 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 150, + 288, + 222 + ], + "spans": [ + { + "bbox": [ + 59, + 150, + 288, + 222 + ], + "type": "text", + "content": "- We further expand 10 kinds of knowledge distances including DisWOT as new universal KD-based zero proxies, which enjoy competitive predictive power with actual performance of models. We hope that our contributions in this endeavor may aid to some degree in advancing future research on KD and NAS." + } + ] + } + ], + "index": 1 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 231, + 222, + 245 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 231, + 222, + 245 + ], + "spans": [ + { + "bbox": [ + 47, + 231, + 222, + 245 + ], + "type": "text", + "content": "2. Related Work and Background" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 251, + 288, + 286 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 251, + 288, + 286 + ], + "spans": [ + { + "bbox": [ + 47, + 251, + 288, + 286 + ], + "type": "text", + "content": "In this section, we summarize existing knowledge distillation and architecture search methods and clarify their differences to our method." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 293, + 287, + 306 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 293, + 287, + 306 + ], + "spans": [ + { + "bbox": [ + 47, + 293, + 287, + 306 + ], + "type": "text", + "content": "2.1. General Formulation of Knowledge Distillation" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 311, + 288, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 311, + 288, + 430 + ], + "spans": [ + { + "bbox": [ + 46, + 311, + 288, + 430 + ], + "type": "text", + "content": "The fundamental concept underlying Knowledge Distillation (KD) involves utilizing acquired knowledge (e.g., logits [31], feature values [30, 32, 33, 35, 70], and sample relations [45, 59]) from a high-capacity teacher to guide the training of a student model. The training dataset " + }, + { + "bbox": [ + 46, + 311, + 288, + 430 + ], + "type": "inline_equation", + "content": "(X,Y)" + }, + { + "bbox": [ + 46, + 311, + 288, + 430 + ], + "type": "text", + "content": " comprises training samples " + }, + { + "bbox": [ + 46, + 311, + 288, + 430 + ], + "type": "inline_equation", + "content": "X = x_{i=1}^{n}" + }, + { + "bbox": [ + 46, + 311, + 288, + 430 + ], + "type": "text", + "content": " and their corresponding labels " + }, + { + "bbox": [ + 46, + 311, + 288, + 430 + ], + "type": "inline_equation", + "content": "Y = y_{i=1}^{n}" + }, + { + "bbox": [ + 46, + 311, + 288, + 430 + ], + "type": "text", + "content": ". Let " + }, + { + "bbox": [ + 46, + 311, + 288, + 430 + ], + "type": "inline_equation", + "content": "f_{T}" + }, + { + "bbox": [ + 46, + 311, + 288, + 430 + ], + "type": "text", + "content": " be the output logits of the fixed teacher " + }, + { + "bbox": [ + 46, + 311, + 288, + 430 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 311, + 288, + 430 + ], + "type": "text", + "content": " and let " + }, + { + "bbox": [ + 46, + 311, + 288, + 430 + ], + "type": "inline_equation", + "content": "f_{S}" + }, + { + "bbox": [ + 46, + 311, + 288, + 430 + ], + "type": "text", + "content": " be the output of student " + }, + { + "bbox": [ + 46, + 311, + 288, + 430 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 311, + 288, + 430 + ], + "type": "text", + "content": ", respectively. In KD, the student network " + }, + { + "bbox": [ + 46, + 311, + 288, + 430 + ], + "type": "inline_equation", + "content": "f_{S}" + }, + { + "bbox": [ + 46, + 311, + 288, + 430 + ], + "type": "text", + "content": " is trained by minimizing:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 437, + 287, + 449 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 437, + 287, + 449 + ], + "spans": [ + { + "bbox": [ + 55, + 437, + 287, + 449 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {S} = \\mathcal {L} _ {C E} \\left(f _ {S}, Y\\right) + \\mathcal {L} _ {K L} \\left(f _ {S}, f _ {T}\\right) + \\mathcal {D} _ {f} \\left(\\phi_ {S} (x), \\phi_ {T} (x)\\right), \\tag {1}", + "image_path": "617b88f715b1aaeb72e43306eedcd2e978fffb6d8628266d5eeffc0b62b9a5dc.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 454, + 288, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 454, + 288, + 502 + ], + "spans": [ + { + "bbox": [ + 46, + 454, + 288, + 502 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 454, + 288, + 502 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{CE}" + }, + { + "bbox": [ + 46, + 454, + 288, + 502 + ], + "type": "text", + "content": " is the regular cross-entropy loss. " + }, + { + "bbox": [ + 46, + 454, + 288, + 502 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{KL}" + }, + { + "bbox": [ + 46, + 454, + 288, + 502 + ], + "type": "text", + "content": " represents Kullback-Leibler (KL) divergence. " + }, + { + "bbox": [ + 46, + 454, + 288, + 502 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_f(\\cdot, \\cdot)" + }, + { + "bbox": [ + 46, + 454, + 288, + 502 + ], + "type": "text", + "content": " is the distance function measuring the difference of intermediate feature representations (see Table 1 for particular distillers)." + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 53, + 517, + 280, + 583 + ], + "blocks": [ + { + "bbox": [ + 93, + 504, + 240, + 515 + ], + "lines": [ + { + "bbox": [ + 93, + 504, + 240, + 515 + ], + "spans": [ + { + "bbox": [ + 93, + 504, + 240, + 515 + ], + "type": "text", + "content": "Table 1. Comparison of recent distillers." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 53, + 517, + 280, + 583 + ], + "lines": [ + { + "bbox": [ + 53, + 517, + 280, + 583 + ], + "spans": [ + { + "bbox": [ + 53, + 517, + 280, + 583 + ], + "type": "table", + "html": "
MethodKnowledgeDistance Df(·,·)
FitNets [54]Feature representationL2
AT [73]Attention mapsL2
CC [49]Instance relationL2
NST [24]Neuron selectivity patternsLMMD
PKT [46]Similarity probability distributionLKL
", + "image_path": "7537610383b661d4e551c11ed00149b09060387d7f91ff36a9e5ed0b281e2bf3.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 594, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 713 + ], + "type": "text", + "content": "Comparison with Other Adaptive KDs for Distillation Gap. DisWOT is the first train-free architecture search solution to reduce the teacher-student gap. Unlike training manners [10] and KD-loss designs, DisWOT utilizes the classic KD training configurations and distillers. In addition, DisWOT is free from the assistant teacher in ATKD [43], which involves a complex training routine and budget. AKD [40] searches student via reinforcement learning based on feedback from individual training of lots of models. As a completely alternative technical route to these training-based" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 70, + 547, + 126 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 70, + 547, + 126 + ], + "spans": [ + { + "bbox": [ + 304, + 70, + 547, + 126 + ], + "type": "text", + "content": "Table 2. Formulation of NAS methods. " + }, + { + "bbox": [ + 304, + 70, + 547, + 126 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 304, + 70, + 547, + 126 + ], + "type": "text", + "content": " is the search space. A candidate architecture in the search space is denoted as " + }, + { + "bbox": [ + 304, + 70, + 547, + 126 + ], + "type": "inline_equation", + "content": "\\alpha \\in \\mathcal{A}" + }, + { + "bbox": [ + 304, + 70, + 547, + 126 + ], + "type": "text", + "content": ", which corresponds to a neural architecture " + }, + { + "bbox": [ + 304, + 70, + 547, + 126 + ], + "type": "inline_equation", + "content": "S(\\alpha, w)" + }, + { + "bbox": [ + 304, + 70, + 547, + 126 + ], + "type": "text", + "content": " with weight " + }, + { + "bbox": [ + 304, + 70, + 547, + 126 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 70, + 547, + 126 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 70, + 547, + 126 + ], + "type": "inline_equation", + "content": "\\mathcal{W}" + }, + { + "bbox": [ + 304, + 70, + 547, + 126 + ], + "type": "text", + "content": " is the weight of the supernet. " + }, + { + "bbox": [ + 304, + 70, + 547, + 126 + ], + "type": "inline_equation", + "content": "\\text{train}" + }, + { + "bbox": [ + 304, + 70, + 547, + 126 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 70, + 547, + 126 + ], + "type": "inline_equation", + "content": "\\text{val}" + }, + { + "bbox": [ + 304, + 70, + 547, + 126 + ], + "type": "text", + "content": " are the loss functions on the training and validation sets, respectively." + } + ] + } + ], + "index": 12 + }, + { + "type": "table", + "bbox": [ + 313, + 134, + 539, + 280 + ], + "blocks": [ + { + "bbox": [ + 313, + 134, + 539, + 280 + ], + "lines": [ + { + "bbox": [ + 313, + 134, + 539, + 280 + ], + "spans": [ + { + "bbox": [ + 313, + 134, + 539, + 280 + ], + "type": "table", + "html": "
TypeEvaluationFormula
Training-basedMulti-trial Trainingα* = arg min val(S(α, wα)), s.t. wα = arg min w train(S(α, w))
Weight sharingα* = arg min val(S(α, W_A(α))), s.t. W_A = arg min w train(S(A, W))
Training-freeZero-cost Proxyα* = ZeroProxy(S(α, w)) α∈A
", + "image_path": "021e7aae22f9c4a3ba2de47872621dae87865bb47123563f6bd27631b4eba1f0.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 300, + 547, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 300, + 547, + 337 + ], + "spans": [ + { + "bbox": [ + 304, + 300, + 547, + 337 + ], + "type": "text", + "content": "NAS [18], our training-free DisWOT builds on new zero-proxy and achieves " + }, + { + "bbox": [ + 304, + 300, + 547, + 337 + ], + "type": "inline_equation", + "content": "180 \\times 1000 \\times" + }, + { + "bbox": [ + 304, + 300, + 547, + 337 + ], + "type": "text", + "content": " training acceleration, which greatly improves its easy-to-use and flexibility." + } + ] + } + ], + "index": 14 + }, + { + "type": "table", + "bbox": [ + 307, + 367, + 545, + 409 + ], + "blocks": [ + { + "bbox": [ + 326, + 348, + 525, + 359 + ], + "lines": [ + { + "bbox": [ + 326, + 348, + 525, + 359 + ], + "spans": [ + { + "bbox": [ + 326, + 348, + 525, + 359 + ], + "type": "text", + "content": "Table 3. Comparison with different training-free NAS." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 367, + 545, + 409 + ], + "lines": [ + { + "bbox": [ + 307, + 367, + 545, + 409 + ], + "spans": [ + { + "bbox": [ + 307, + 367, + 545, + 409 + ], + "type": "table", + "html": "
TypeMethodTeacher-awareObjective
Prune-basedSNIP [28], Fisher [1], Synflow [58]✗Vanilla acc.
Activation-basedNWOT [42], Zen-NAS [36]✗Vanilla acc.
KD-basedDisWOT (ours)✓Distill acc.
", + "image_path": "06f5dbf7f31b44464c94553a2f7607025a4e82bcd99e04b583d164a41e9b1620.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "table_body" + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 430, + 515, + 443 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 430, + 515, + 443 + ], + "spans": [ + { + "bbox": [ + 305, + 430, + 515, + 443 + ], + "type": "text", + "content": "2.2. Revisiting Architecture Search Methods" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 449, + 547, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 547, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 547, + 640 + ], + "type": "text", + "content": "Neural Architecture Search (NAS) is emerged to reduce human efforts in architecture design and automate the discovery of high-performance networks. As formalized in Tab. 2, Multi-trial NAS methods [40, 79] train a large number of candidates individually, which leads to extensive resource consumption. To alleviate this, many NAS [8,12,23,51] methods adopt a weight-sharing strategy within a single supernet to facilitate the simultaneous training of candidates. The supernet is trained for hundred of epochs by path sampling [11,19] or compound optimization with architecture representations [39,69]. As an orthogonal direction, zero-cost NAS methods [42,71] focus on identifying well-performed architectures with training-free metrics. For example, NWOT [42] calculates the architecture score based on the kernel matrix of binary activations between small batches of samples." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 642, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 547, + 713 + ], + "type": "text", + "content": "Comparison with NAS with Teacher. Some training-based NAS [29,50,77] employ a teacher model to supervise supernet training to improve predictive ability in the search stage. However, these methods aim to improve vanilla accuracy, not for distillation, and they do not use the teacher model in the full training stage. In addition, without any" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "11900" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 68, + 547, + 238 + ], + "blocks": [ + { + "bbox": [ + 47, + 68, + 547, + 238 + ], + "lines": [ + { + "bbox": [ + 47, + 68, + 547, + 238 + ], + "spans": [ + { + "bbox": [ + 47, + 68, + 547, + 238 + ], + "type": "image", + "image_path": "ea0b209d838cdf1732db7233db8049f9f0600bba89416beb8d93117f04f5682b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "lines": [ + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "spans": [ + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "text", + "content": "Figure 3. A schematic overview of our DisWOT, including (a) detailed calculation of the DisWOT scores and (b) evolution of the student architecture via the DisWOT scores. In search phase, DisWOT use semantic similarity metrics and relations similarity metrics to select good student for a given teacher. The semantic similarity metric is measured by " + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "inline_equation", + "content": "l_{2}" + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "text", + "content": " distance of the channel-wise correlation matrix for Grad-cam activation maps. Similarly, the relation similarity matrix statistics the sample-wise correlation matrix distance of the randomly initialized teacher-student pairs. With the feedback from these metrics, the evolutionary search in DisWOT automatically imitates good student from weak ones. In distillation phase, this searched student is distilled via teacher model and achieves superior gains." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 324, + 288, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 324, + 288, + 348 + ], + "spans": [ + { + "bbox": [ + 46, + 324, + 288, + 348 + ], + "type": "text", + "content": "training costs, our training-free DisWOT enjoys obvious differences than these methods and advantages in efficiency." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 349, + 288, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 349, + 288, + 421 + ], + "spans": [ + { + "bbox": [ + 46, + 349, + 288, + 421 + ], + "type": "text", + "content": "Compared to Other Training-free NAS. Table 3 clearly summarizes the differences between DisWOT and other zero-cost methods [1, 28, 36, 42, 58]. Moreover, DisWOT outperforms these methods on distillation performance prediction and boosting in our sufficient experiments dealing with diverse datasets and search spaces." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 434, + 129, + 448 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 434, + 129, + 448 + ], + "spans": [ + { + "bbox": [ + 47, + 434, + 129, + 448 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 456, + 288, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 456, + 288, + 598 + ], + "spans": [ + { + "bbox": [ + 46, + 456, + 288, + 598 + ], + "type": "text", + "content": "Figure 3 provides an overview of the DisWOT framework, which is comprised of two main stages: optimal student network search and distillation with high-order knowledge. In the search stage, we employ the neural architecture search technique to obtain an optimal student network for a pre-defined teacher network. Notably, we propose a training-free proxy called DisWOT to accurately rank enormous student networks and prevent expensive evaluation processes with high efficiency. In the distillation stage, the searched student network is retrained with distillation to imitate high-order knowledge in the teacher network. We give the details of these two designs in the following sections." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 609, + 243, + 621 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 609, + 243, + 621 + ], + "spans": [ + { + "bbox": [ + 47, + 609, + 243, + 621 + ], + "type": "text", + "content": "3.1. Search for Optimal Student Network" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 628, + 288, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 628, + 288, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 628, + 288, + 688 + ], + "type": "text", + "content": "We first present the training-free metrics we designed to score a student architecture, which indicates its final accuracy when distilled with a pre-defined teacher network. Then we depict the details of the evolutionary process to obtain an optimal student candidate." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 689, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 288, + 713 + ], + "type": "text", + "content": "Semantic Similarity Metric. The semantic information is meaningful for neural networks to perceive as humans. In" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 324, + 547, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 324, + 547, + 612 + ], + "spans": [ + { + "bbox": [ + 304, + 324, + 547, + 612 + ], + "type": "text", + "content": "distillation, the teacher network always has more convolutional operations than the student, resulting in a teacher feature map with a larger receptive field and greater richness of semantic information. In contrast to distiller designs to alleviate semantic gaps, we aim for train-free student architecture to better match the teacher model with computational constraints. We notice that the network with random initial weights also has some semantic localization capability. Thus, we start to analyze the localization performance of the randomly initialized teacher-student model. Specifically, we utilize Grad-CAM maps [78] to localize semantic object regions, which explains the model decisions using gradient information. Given a mini-batch of input images, we define the high-level feature map before the Global Average Pooling (GAP) layer of the teacher network " + }, + { + "bbox": [ + 304, + 324, + 547, + 612 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 324, + 547, + 612 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 304, + 324, + 547, + 612 + ], + "type": "inline_equation", + "content": "A_{T} \\in \\mathbf{R}^{B \\times C_{T} \\times H_{T} \\times W_{T}}" + }, + { + "bbox": [ + 304, + 324, + 547, + 612 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 324, + 547, + 612 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 304, + 324, + 547, + 612 + ], + "type": "text", + "content": " represents the batch size, " + }, + { + "bbox": [ + 304, + 324, + 547, + 612 + ], + "type": "inline_equation", + "content": "C_{T}" + }, + { + "bbox": [ + 304, + 324, + 547, + 612 + ], + "type": "text", + "content": " denotes the number of output channels, and " + }, + { + "bbox": [ + 304, + 324, + 547, + 612 + ], + "type": "inline_equation", + "content": "H_{T}" + }, + { + "bbox": [ + 304, + 324, + 547, + 612 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 324, + 547, + 612 + ], + "type": "inline_equation", + "content": "W_{T}" + }, + { + "bbox": [ + 304, + 324, + 547, + 612 + ], + "type": "text", + "content": " are the spatial dimensions. Additionally, we introduce " + }, + { + "bbox": [ + 304, + 324, + 547, + 612 + ], + "type": "inline_equation", + "content": "A_{T}^{c} \\in \\mathbf{R}^{N \\times H_{T} \\times W_{T}}" + }, + { + "bbox": [ + 304, + 324, + 547, + 612 + ], + "type": "text", + "content": " as the c-th spatial map along the channel dimension. For the student network " + }, + { + "bbox": [ + 304, + 324, + 547, + 612 + ], + "type": "inline_equation", + "content": "S_{i}" + }, + { + "bbox": [ + 304, + 324, + 547, + 612 + ], + "type": "text", + "content": ", we have feature map " + }, + { + "bbox": [ + 304, + 324, + 547, + 612 + ], + "type": "inline_equation", + "content": "A_{S_{i}}^{c} \\in \\mathbf{R}^{B \\times C_{S} \\times H_{S} \\times W_{S}}" + }, + { + "bbox": [ + 304, + 324, + 547, + 612 + ], + "type": "text", + "content": " and spatial map " + }, + { + "bbox": [ + 304, + 324, + 547, + 612 + ], + "type": "inline_equation", + "content": "A_{S_{i}}^{c} \\in \\mathbf{R}^{B \\times H_{S} \\times W_{S}}" + }, + { + "bbox": [ + 304, + 324, + 547, + 612 + ], + "type": "text", + "content": ", respectively. To compute the Grad-CAM maps of the " + }, + { + "bbox": [ + 304, + 324, + 547, + 612 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 324, + 547, + 612 + ], + "type": "text", + "content": "-th class for both the teacher and student networks, we can use the following formulations:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 343, + 620, + 545, + 649 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 343, + 620, + 545, + 649 + ], + "spans": [ + { + "bbox": [ + 343, + 620, + 545, + 649 + ], + "type": "interline_equation", + "content": "G _ {T} = \\sum_ {c = 1} ^ {C _ {T}} w _ {n, c} ^ {T} A _ {T} ^ {c}, \\quad G _ {S _ {i}} = \\sum_ {c = 1} ^ {C _ {S}} w _ {n, c} ^ {S} A _ {S _ {i}} ^ {c}, \\tag {2}", + "image_path": "6024a8905e4fcf2925e31bb5fdf1793f633488f7ce72135daeaba8dc0aec6cf8.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 652, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 652, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 652, + 547, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 652, + 547, + 713 + ], + "type": "inline_equation", + "content": "w^{T} \\in \\mathbf{R}^{N \\times C_{T}}" + }, + { + "bbox": [ + 304, + 652, + 547, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 652, + 547, + 713 + ], + "type": "inline_equation", + "content": "w^{S} \\in \\mathbf{R}^{N \\times C_{S}}" + }, + { + "bbox": [ + 304, + 652, + 547, + 713 + ], + "type": "text", + "content": " are weights of the last fully-connected layer in the teacher and student network. " + }, + { + "bbox": [ + 304, + 652, + 547, + 713 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 652, + 547, + 713 + ], + "type": "text", + "content": " represents the number of classes. " + }, + { + "bbox": [ + 304, + 652, + 547, + 713 + ], + "type": "inline_equation", + "content": "w_{n,c}^{T}" + }, + { + "bbox": [ + 304, + 652, + 547, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 652, + 547, + 713 + ], + "type": "inline_equation", + "content": "w_{n,c}^{S}" + }, + { + "bbox": [ + 304, + 652, + 547, + 713 + ], + "type": "text", + "content": " refer to the element located in the " + }, + { + "bbox": [ + 304, + 652, + 547, + 713 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 652, + 547, + 713 + ], + "type": "text", + "content": "-th row and " + }, + { + "bbox": [ + 304, + 652, + 547, + 713 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 652, + 547, + 713 + ], + "type": "text", + "content": "-th column of weight matrices " + }, + { + "bbox": [ + 304, + 652, + 547, + 713 + ], + "type": "inline_equation", + "content": "w^{T}" + }, + { + "bbox": [ + 304, + 652, + 547, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 652, + 547, + 713 + ], + "type": "inline_equation", + "content": "w^{S}" + }, + { + "bbox": [ + 304, + 652, + 547, + 713 + ], + "type": "text", + "content": ", respectively. To quantify" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "11901" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "type": "text", + "content": "the intersection of class-discriminative localization maps, we formulate semantic similarity metric " + }, + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_s" + }, + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "type": "text", + "content": " as the intercorrelation on the accumulated Grad-CAM maps for both teacher and student networks as follows:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 126, + 288, + 156 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 126, + 288, + 156 + ], + "spans": [ + { + "bbox": [ + 56, + 126, + 288, + 156 + ], + "type": "interline_equation", + "content": "\\mathcal {G} ^ {T} = \\frac {\\left(G _ {T}\\right) \\cdot \\left(G _ {T}\\right) ^ {\\top}}{\\| \\left(G _ {T}\\right) \\cdot \\left(G _ {T}\\right) ^ {\\top} \\| _ {2}}, \\mathcal {G} ^ {S} = \\frac {\\left(G _ {S}\\right) \\cdot \\left(G _ {S}\\right) ^ {\\top}}{\\| \\left(G _ {S}\\right) \\cdot \\left(G _ {S}\\right) ^ {\\top} \\| _ {2}}, (3)", + "image_path": "fa6b36b38f46c89ee9550a855014ac6cb30d0e6761b95e3e4ccf23f29f062fd4.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 120, + 167, + 288, + 184 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 120, + 167, + 288, + 184 + ], + "spans": [ + { + "bbox": [ + 120, + 167, + 288, + 184 + ], + "type": "interline_equation", + "content": "\\mathcal {M} _ {s} = \\left\\| \\mathcal {G} ^ {T} - \\mathcal {G} ^ {S _ {i}} \\right\\| _ {2}. \\tag {4}", + "image_path": "0dee07758546b93b7c86950adc86438137ef253a2c8fd98dd9fcdba3037d2c58.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 188, + 289, + 307 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 188, + 289, + 307 + ], + "spans": [ + { + "bbox": [ + 46, + 188, + 289, + 307 + ], + "type": "text", + "content": "Relation Similarity Metric. The relationships between input samples are non-trivial for knowledge transfer. To reduce the teacher-student gap and improve the relation-distillation performance, we use the correlation matrix as the sample-wise metric to search for an optimal student network. For the random teacher network " + }, + { + "bbox": [ + 46, + 188, + 289, + 307 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 188, + 289, + 307 + ], + "type": "text", + "content": " and student network " + }, + { + "bbox": [ + 46, + 188, + 289, + 307 + ], + "type": "inline_equation", + "content": "S_{i}" + }, + { + "bbox": [ + 46, + 188, + 289, + 307 + ], + "type": "text", + "content": " with activation maps " + }, + { + "bbox": [ + 46, + 188, + 289, + 307 + ], + "type": "inline_equation", + "content": "A_{T} \\in \\mathbf{R}^{N \\times C_{T} \\times H_{T} \\times W_{T}}" + }, + { + "bbox": [ + 46, + 188, + 289, + 307 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 188, + 289, + 307 + ], + "type": "inline_equation", + "content": "A_{S}^{i} \\in \\mathbf{R}^{N \\times C_{i} \\times H_{i} \\times W_{i}}" + }, + { + "bbox": [ + 46, + 188, + 289, + 307 + ], + "type": "text", + "content": ", the correlation matrix of the minibatch samples in the teacher network is formulated as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 56, + 314, + 288, + 352 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 314, + 288, + 352 + ], + "spans": [ + { + "bbox": [ + 56, + 314, + 288, + 352 + ], + "type": "interline_equation", + "content": "\\mathcal {A} ^ {T} = \\frac {(\\tilde {A} _ {T}) \\cdot (\\tilde {A} _ {T}) ^ {\\top}}{\\left\\| (\\tilde {A} _ {T}) \\cdot (\\tilde {A} _ {T} ^ {\\top}) \\right\\| _ {2}}, \\mathcal {A} ^ {S _ {i}} = \\frac {(\\tilde {A} _ {S}) \\cdot (\\tilde {A} _ {S}) ^ {\\top}}{\\left\\| (\\tilde {A} _ {S}) \\cdot (\\tilde {A} _ {S} ^ {\\top}) \\right\\| _ {2}}, (5)", + "image_path": "3f27e86ad6e7c77ebf240fa4f0ea8d2a52a10b9e0baaf8c6abf59cc33d6ed8d7.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 359, + 287, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 359, + 287, + 421 + ], + "spans": [ + { + "bbox": [ + 47, + 359, + 287, + 421 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 359, + 287, + 421 + ], + "type": "inline_equation", + "content": "\\tilde{A}_T\\in \\mathbf{R}^{N\\times CHW}" + }, + { + "bbox": [ + 47, + 359, + 287, + 421 + ], + "type": "text", + "content": " is a reshaping of " + }, + { + "bbox": [ + 47, + 359, + 287, + 421 + ], + "type": "inline_equation", + "content": "A_{T}" + }, + { + "bbox": [ + 47, + 359, + 287, + 421 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 359, + 287, + 421 + ], + "type": "inline_equation", + "content": "M_T" + }, + { + "bbox": [ + 47, + 359, + 287, + 421 + ], + "type": "text", + "content": " is a " + }, + { + "bbox": [ + 47, + 359, + 287, + 421 + ], + "type": "inline_equation", + "content": "N\\times N" + }, + { + "bbox": [ + 47, + 359, + 287, + 421 + ], + "type": "text", + "content": " matrix. Thus, the " + }, + { + "bbox": [ + 47, + 359, + 287, + 421 + ], + "type": "inline_equation", + "content": "(i,j)" + }, + { + "bbox": [ + 47, + 359, + 287, + 421 + ], + "type": "text", + "content": " entry in matrix " + }, + { + "bbox": [ + 47, + 359, + 287, + 421 + ], + "type": "inline_equation", + "content": "C_T" + }, + { + "bbox": [ + 47, + 359, + 287, + 421 + ], + "type": "text", + "content": " represents the similarity between the " + }, + { + "bbox": [ + 47, + 359, + 287, + 421 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 359, + 287, + 421 + ], + "type": "text", + "content": "-th and " + }, + { + "bbox": [ + 47, + 359, + 287, + 421 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 47, + 359, + 287, + 421 + ], + "type": "text", + "content": "-th images within the mini-batch. Based on this, the sample similarity metric " + }, + { + "bbox": [ + 47, + 359, + 287, + 421 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_r" + }, + { + "bbox": [ + 47, + 359, + 287, + 421 + ], + "type": "text", + "content": " for a potential student model " + }, + { + "bbox": [ + 47, + 359, + 287, + 421 + ], + "type": "inline_equation", + "content": "S_{i}" + }, + { + "bbox": [ + 47, + 359, + 287, + 421 + ], + "type": "text", + "content": " is defined as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 119, + 429, + 288, + 445 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 119, + 429, + 288, + 445 + ], + "spans": [ + { + "bbox": [ + 119, + 429, + 288, + 445 + ], + "type": "interline_equation", + "content": "\\mathcal {M} _ {r} = \\left\\| \\mathcal {A} ^ {T} - \\mathcal {A} ^ {S _ {i}} \\right\\| _ {2}. \\tag {6}", + "image_path": "185c0f3485acd3127471b50fe0db037fb37e6ee7496685c734e4528a8601940a.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 465, + 287, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 465, + 287, + 513 + ], + "spans": [ + { + "bbox": [ + 46, + 465, + 287, + 513 + ], + "type": "text", + "content": "Training-Free Evolutionary Search. Based on the above metric, we conduct a training-free evolutionary search algorithm to efficiently discover the optimal student " + }, + { + "bbox": [ + 46, + 465, + 287, + 513 + ], + "type": "inline_equation", + "content": "\\alpha^{*}" + }, + { + "bbox": [ + 46, + 465, + 287, + 513 + ], + "type": "text", + "content": " from search space " + }, + { + "bbox": [ + 46, + 465, + 287, + 513 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 46, + 465, + 287, + 513 + ], + "type": "text", + "content": ", as:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 109, + 523, + 287, + 540 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 109, + 523, + 287, + 540 + ], + "spans": [ + { + "bbox": [ + 109, + 523, + 287, + 540 + ], + "type": "interline_equation", + "content": "\\alpha^ {*} = \\arg \\min _ {\\alpha \\in \\mathcal {A}} \\left(\\mathcal {M} _ {s} + \\mathcal {M} _ {r}\\right). \\tag {7}", + "image_path": "c6a26d1278d6ea5b537d8f2b7d76e25db364c600185fa6bb84601eb6cd647cae.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 549, + 287, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 549, + 287, + 586 + ], + "spans": [ + { + "bbox": [ + 47, + 549, + 287, + 586 + ], + "type": "text", + "content": "Theoretical Understanding. According to the VC theory [63], the classification error of the vanilla teacher-student network can be decomposed as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 594, + 287, + 611 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 594, + 287, + 611 + ], + "spans": [ + { + "bbox": [ + 55, + 594, + 287, + 611 + ], + "type": "interline_equation", + "content": "R \\left(f _ {s}\\right) - R \\left(f _ {r}\\right) \\leq O \\left(\\frac {\\left| \\mathcal {F} _ {s} \\right| _ {C}}{n ^ {\\alpha s r}}\\right) + \\epsilon_ {s r}; R \\left(f _ {t}\\right) - R \\left(f _ {r}\\right) \\leq O \\left(\\frac {\\left| \\mathcal {F} _ {t} \\right| _ {C}}{n ^ {\\alpha t r}}\\right) + \\epsilon_ {t r}, \\tag {8}", + "image_path": "d44dcf84680ff30203b0264bff6d9a7649e05e0d8bfc7f6fa833c6f75e49b488.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "inline_equation", + "content": "f_{s}\\in \\mathcal{F}_{s}" + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "content": " is the student function, " + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "inline_equation", + "content": "f_{t}\\in \\mathcal{F}_{t}" + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "content": " is the teacher function, and " + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "inline_equation", + "content": "f_{r}\\in \\mathcal{F}_{r}" + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "content": " is the target function. " + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "content": " is the error. " + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "inline_equation", + "content": "O(\\cdot)" + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\epsilon_{sr}" + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "content": " terms are the estimation and approximation error, respectively. " + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "inline_equation", + "content": "O(\\cdot)" + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "content": " is related to the statistical procedure when given the number of data points. In contrast, " + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\epsilon_{sr}" + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "content": " is the approximation error of the student function class " + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_s" + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "inline_equation", + "content": "f_{r}\\in \\mathcal{F}_{r}.\\left|\\cdot \\right|_{C}" + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "content": " is an function class capacity measure, and " + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "content": " is the number of data point. During distillation," + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "text", + "content": "the student network is supervised purely with the teacher network as follows:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 349, + 102, + 545, + 129 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 349, + 102, + 545, + 129 + ], + "spans": [ + { + "bbox": [ + 349, + 102, + 545, + 129 + ], + "type": "interline_equation", + "content": "R \\left(f _ {s}\\right) - R \\left(f _ {t}\\right) \\leq O \\left(\\frac {\\left| \\mathcal {F} _ {s} \\right| _ {C}}{n ^ {\\alpha_ {s t}}}\\right) + \\epsilon_ {s t}, \\tag {9}", + "image_path": "f85fc665ba89cbd3a325a7c16336a86dd249815bcaf79de917705d2cbdbf31ad.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 138, + 545, + 163 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 138, + 545, + 163 + ], + "spans": [ + { + "bbox": [ + 305, + 138, + 545, + 163 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 138, + 545, + 163 + ], + "type": "inline_equation", + "content": "\\alpha_{st}" + }, + { + "bbox": [ + 305, + 138, + 545, + 163 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 138, + 545, + 163 + ], + "type": "inline_equation", + "content": "\\epsilon_{st}" + }, + { + "bbox": [ + 305, + 138, + 545, + 163 + ], + "type": "text", + "content": " are associated to student learning from teacher. By combining Equations 3.1 and 9, we obtain:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 315, + 171, + 545, + 190 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 171, + 545, + 190 + ], + "spans": [ + { + "bbox": [ + 315, + 171, + 545, + 190 + ], + "type": "interline_equation", + "content": "R \\left(f _ {s}\\right) - R \\left(f _ {r}\\right) \\leq O \\left(\\frac {\\left| \\mathcal {F} _ {t} \\right| _ {C}}{n ^ {\\alpha_ {t r}}}\\right) + \\epsilon_ {t r} + O \\left(\\frac {\\left| \\mathcal {F} _ {s} \\right| _ {C}}{n ^ {\\alpha_ {s t}}}\\right) + \\epsilon_ {s t}. \\tag {10}", + "image_path": "5238f3eb6bceced5bb8d4c75f327d56a0942c5aeb091b00e0f0ae931db0ab4f1.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 198, + 545, + 235 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 198, + 545, + 235 + ], + "spans": [ + { + "bbox": [ + 305, + 198, + 545, + 235 + ], + "type": "text", + "content": "When student obtains gains in KDs, its upper bound of error in distillation is smaller than vanilla training, which satisfies the following inequality:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 315, + 243, + 545, + 264 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 243, + 545, + 264 + ], + "spans": [ + { + "bbox": [ + 315, + 243, + 545, + 264 + ], + "type": "interline_equation", + "content": "O \\left(\\frac {\\left| \\mathcal {F} _ {t} \\right| _ {C}}{n ^ {\\alpha_ {t r}}} + \\frac {\\left| \\mathcal {F} _ {s} \\right| _ {C}}{n ^ {\\alpha_ {s t}}}\\right) + \\epsilon_ {t r} + \\epsilon_ {s t} \\leq O \\left(\\frac {\\left| \\mathcal {F} _ {s} \\right| _ {C}}{n ^ {\\alpha_ {s r}}}\\right) + \\epsilon_ {s r}. \\tag {11}", + "image_path": "061decf0e0a46454fddf1a6570e91527283b0c52e87df148aa362bcdfd9b72f9.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 271, + 547, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 271, + 547, + 443 + ], + "spans": [ + { + "bbox": [ + 305, + 271, + 547, + 443 + ], + "type": "text", + "content": "Based on the assumption in [22] that " + }, + { + "bbox": [ + 305, + 271, + 547, + 443 + ], + "type": "inline_equation", + "content": "\\epsilon_{tr} + \\epsilon_{st} \\leq \\epsilon_{sr}" + }, + { + "bbox": [ + 305, + 271, + 547, + 443 + ], + "type": "text", + "content": " holds consistently, we focus on minimizing " + }, + { + "bbox": [ + 305, + 271, + 547, + 443 + ], + "type": "inline_equation", + "content": "O\\left(\\frac{|\\mathcal{F}_t|_C}{n^{\\alpha_{tr}}} + \\frac{|\\mathcal{F}_s|_C}{n^{\\alpha_{st}}}\\right)" + }, + { + "bbox": [ + 305, + 271, + 547, + 443 + ], + "type": "text", + "content": " to improve the distillation performance. As noted in Lopez-Paz et al [41], a better representation allows for a faster learning rate with a fixed amount of data. Hence, when there is a larger gap between the capacities of the student and teacher networks, the value of " + }, + { + "bbox": [ + 305, + 271, + 547, + 443 + ], + "type": "inline_equation", + "content": "\\alpha_{st}" + }, + { + "bbox": [ + 305, + 271, + 547, + 443 + ], + "type": "text", + "content": " tends to be lower. Thus we aim to search for an optimal student network that meets the requirement of " + }, + { + "bbox": [ + 305, + 271, + 547, + 443 + ], + "type": "inline_equation", + "content": "\\alpha_{si t} \\leq \\alpha_{so t}" + }, + { + "bbox": [ + 305, + 271, + 547, + 443 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 305, + 271, + 547, + 443 + ], + "type": "inline_equation", + "content": "s_i" + }, + { + "bbox": [ + 305, + 271, + 547, + 443 + ], + "type": "text", + "content": " is all candidate student networks, and " + }, + { + "bbox": [ + 305, + 271, + 547, + 443 + ], + "type": "inline_equation", + "content": "s_o" + }, + { + "bbox": [ + 305, + 271, + 547, + 443 + ], + "type": "text", + "content": " is our searched student network. In this case, the inequality becomes more effective, and we improve the knowledge distillation by injecting a larger " + }, + { + "bbox": [ + 305, + 271, + 547, + 443 + ], + "type": "inline_equation", + "content": "\\alpha_{so t}" + }, + { + "bbox": [ + 305, + 271, + 547, + 443 + ], + "type": "text", + "content": ". Specifically, we present the overall procedure for discovering optimal student in algorithm 1." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 444, + 547, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 444, + 547, + 529 + ], + "spans": [ + { + "bbox": [ + 305, + 444, + 547, + 529 + ], + "type": "text", + "content": "Effects of Search Strategies. We compare the evolution search algorithm and the random search algorithm in search space " + }, + { + "bbox": [ + 305, + 444, + 547, + 529 + ], + "type": "inline_equation", + "content": "S_{2}" + }, + { + "bbox": [ + 305, + 444, + 547, + 529 + ], + "type": "text", + "content": " with the same number of iterations, as shown in Figure 4. We find that the evolution search algorithm can consistently find architectures with lower DisWOT, especially when the search space is relatively large, and the evolutionary search can explore better architectures." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 536, + 515, + 550 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 536, + 515, + 550 + ], + "spans": [ + { + "bbox": [ + 306, + 536, + 515, + 550 + ], + "type": "text", + "content": "3.2. Distillation with High-order Knowledge" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 554, + 547, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 554, + 547, + 654 + ], + "spans": [ + { + "bbox": [ + 304, + 554, + 547, + 654 + ], + "type": "text", + "content": "In the distillation stage, teacher model " + }, + { + "bbox": [ + 304, + 554, + 547, + 654 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 554, + 547, + 654 + ], + "type": "text", + "content": " is employed to distill the optimal student network " + }, + { + "bbox": [ + 304, + 554, + 547, + 654 + ], + "type": "inline_equation", + "content": "f_{S}" + }, + { + "bbox": [ + 304, + 554, + 547, + 654 + ], + "type": "text", + "content": ". To verify the superiority of our search architecture, we adopt the existing distillers (e.g., KD) as the default distillation setting. In addition, we observe that the metrics we searched for actually serve as minimization optimization goals in the distillation process to transfer the teacher's privileged semantic and sample relational knowledge as the semantic distillation and sample distillation:" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 318, + 662, + 545, + 682 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 662, + 545, + 682 + ], + "spans": [ + { + "bbox": [ + 318, + 662, + 545, + 682 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathcal {M} _ {s}} = \\frac {1}{c ^ {2}} \\left\\| \\mathcal {G} ^ {T} - \\mathcal {G} ^ {S} \\right\\| _ {2}, \\mathcal {L} _ {\\mathcal {M} _ {r}} = \\frac {1}{b ^ {2}} \\left\\| \\mathcal {A} ^ {T} - \\mathcal {A} ^ {S} \\right\\| _ {2}, \\tag {12}", + "image_path": "0c90b5290cabc8d5753b41ffa6b53cd2bfa3af9a25e89bddb49bcf3f7680c883.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 689, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 547, + 713 + ], + "type": "text", + "content": "Finally, we involve these advanced distillers in our framework, called DisWOT†. The total loss for DisWOT and" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11902" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 225, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 225, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 225, + 83 + ], + "type": "text", + "content": "Algorithm 1 Evolution Search for DisWOT" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 85, + 287, + 117 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 85, + 287, + 117 + ], + "spans": [ + { + "bbox": [ + 47, + 85, + 287, + 117 + ], + "type": "text", + "content": "Input: 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Left: comparison of random search and evolution search. Right: ranking correlation of different distillation methods on NAS-Bench-201." + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + } + ], + "index": 20 + }, + { + "type": "image", + "bbox": [ + 171, + 333, + 285, + 416 + ], + "blocks": [ + { + "bbox": [ + 171, + 333, + 285, + 416 + ], + "lines": [ + { + "bbox": [ + 171, + 333, + 285, + 416 + ], + "spans": [ + { + "bbox": [ + 171, + 333, + 285, + 416 + ], + "type": "image", + "image_path": "e67848fe911182b190df27a081f8fd05620c88d706d2d6548fa66497450225fe.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + } + ], + "index": 21 + }, + { + "type": "table", + "bbox": [ + 50, + 481, + 285, + 565 + ], + "blocks": [ + { + "bbox": [ + 61, + 461, + 271, + 472 + ], + "lines": [ + { + "bbox": [ + 61, + 461, + 271, + 472 + ], + "spans": [ + { + "bbox": [ + 61, + 461, + 271, + 472 + ], + "type": "text", + "content": "Table 4. Spearman correlation " + }, + { + "bbox": [ + 61, + 461, + 271, + 472 + ], + "type": "inline_equation", + "content": "\\rho \\left( \\% \\right)" + }, + { + "bbox": [ + 61, + 461, + 271, + 472 + ], + "type": "text", + "content": " on NAS-Bench-201." + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 481, + 285, + 565 + ], + "lines": [ + { + "bbox": [ + 50, + 481, + 285, + 565 + ], + "spans": [ + { + "bbox": [ + 50, + 481, + 285, + 565 + ], + "type": "table", + "html": "
TypeMethodρMethodρ
Zero-costGrad_Norm [1]58.70±0.11Synflow [58]74.61±0.08
SNIP [28]58.17±0.15Jacob [57]73.42±0.03
ProxiesFisher [1]35.91±0.09Zen-NAS [36]41.36±0.06
NWOT [42]64.41±0.08FLOPs [1]63.38±0.06
KD-basedKD [22]54.43±0.09PKT [47]52.65±0.09
FitNets [55]56.18±0.09CC [48]65.90±0.08
ProxiesSP [62]51.24±0.08NST [25]72.35±0.09
RKD [44]25.71±0.17DisWOT72.36±0.02
", + "image_path": "979fe7bf4f4905a901812a06f14e3dae3367121c6ff5aa311136d17e6403aa5d.jpg" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "table_body" + } + ], + "index": 24 + }, + { + "bbox": [ + 47, + 583, + 104, + 595 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 583, + 104, + 595 + ], + "spans": [ + { + "bbox": [ + 47, + 583, + 104, + 595 + ], + "type": "text", + "content": "DisWOT† as:" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 80, + 603, + 287, + 623 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 603, + 287, + 623 + ], + "spans": [ + { + "bbox": [ + 80, + 603, + 287, + 623 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {D i s W O T}} = \\mathcal {L} _ {C E} \\left(f _ {S}, Y\\right) + \\mathcal {L} _ {K L} \\left(f _ {S}, f _ {T}\\right), \\tag {13}", + "image_path": "83f344c84d0f830343dc4826f3d7cfe5e190071b34e9abdbf22a249fcdeddc3a.jpg" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 100, + 620, + 252, + 631 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 100, + 620, + 252, + 631 + ], + "spans": [ + { + "bbox": [ + 100, + 620, + 252, + 631 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {D i s W O T}} \\dagger = \\mathcal {L} _ {\\text {D i s W O T}} + \\mathcal {L} _ {\\mathcal {M} _ {s}} + \\mathcal {L} _ {\\mathcal {M} _ {r}}.", + "image_path": "f7ce27a809adfb9c87a95f5906aea30a08e65d54119d5e7e936f6c28fa32bb22.jpg" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 47, + 647, + 228, + 660 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 228, + 660 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 228, + 660 + ], + "type": "text", + "content": "3.3. Bridging Distiller and Zero-proxy" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 47, + 665, + 289, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 665, + 289, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 665, + 289, + 713 + ], + "type": "text", + "content": "In our DisWOT framework, we use the semantic and relational similarity metrics as a distillation performance predictor and distiller. In addition, DisWOT also enjoys good performance for vanilla performance predictions. Encour" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 304, + 72, + 547, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 193 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 193 + ], + "type": "text", + "content": "aged by this intriguing observation, we employ the knowledge function in of different KDs as zero-proxies and evaluate their ranking consistency with vanilla accuracy. As shown in Table 4, these KD-based zero-proxies enjoy competitive rankings with other NAS methods. Detailed results in Figure 4 illustrate that our DisWOT and NST [24] are the winners in the family of KD-based proxies. These attempts reveal the close connections between KD and NAS, and augment " + }, + { + "bbox": [ + 304, + 72, + 547, + 193 + ], + "type": "inline_equation", + "content": "10+" + }, + { + "bbox": [ + 304, + 72, + 547, + 193 + ], + "type": "text", + "content": " new universal proxies from the teacher-student learning perspective for training-free NAS research." + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 306, + 204, + 427, + 217 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 204, + 427, + 217 + ], + "spans": [ + { + "bbox": [ + 306, + 204, + 427, + 217 + ], + "type": "text", + "content": "4. Experimental results" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 304, + 224, + 547, + 285 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 224, + 547, + 285 + ], + "spans": [ + { + "bbox": [ + 304, + 224, + 547, + 285 + ], + "type": "text", + "content": "In this section, we present the experimental results of our DisWOT on different datasets. First, we describe the four datasets used in our experiments and three search spaces " + }, + { + "bbox": [ + 304, + 224, + 547, + 285 + ], + "type": "inline_equation", + "content": "S_0, S_1, S_2" + }, + { + "bbox": [ + 304, + 224, + 547, + 285 + ], + "type": "text", + "content": " in Sec. 4.1. Then, we conduct a comprehensive set of experiments to evaluate the effectiveness of DisWOT." + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 306, + 293, + 422, + 306 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 293, + 422, + 306 + ], + "spans": [ + { + "bbox": [ + 306, + 293, + 422, + 306 + ], + "type": "text", + "content": "4.1. Experimental Setup" + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 304, + 312, + 547, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 312, + 547, + 384 + ], + "spans": [ + { + "bbox": [ + 304, + 312, + 547, + 384 + ], + "type": "text", + "content": "We perform experiments on four datasets, namely CIFAR-10, CIFAR-100, ImageNet-16-120, and ImageNet-1k. In the search process, we only use one batch of training data to get the statistic at nearly no cost. Following previous works, our experiments are conducted on the following three search spaces:" + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 304, + 384, + 545, + 432 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 384, + 545, + 432 + ], + "spans": [ + { + "bbox": [ + 304, + 384, + 545, + 432 + ], + "type": "text", + "content": "Search Space " + }, + { + "bbox": [ + 304, + 384, + 545, + 432 + ], + "type": "inline_equation", + "content": "S_0" + }, + { + "bbox": [ + 304, + 384, + 545, + 432 + ], + "type": "text", + "content": ": Following CIFar-ResNet [20], the search space consists of three residual blocks and is based on CIFAR-100 datasets. The depth of each residual block is searched in set " + }, + { + "bbox": [ + 304, + 384, + 545, + 432 + ], + "type": "inline_equation", + "content": "\\{1,3,5,7\\}" + }, + { + "bbox": [ + 304, + 384, + 545, + 432 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 304, + 433, + 547, + 480 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 433, + 547, + 480 + ], + "spans": [ + { + "bbox": [ + 304, + 433, + 547, + 480 + ], + "type": "text", + "content": "Search Space " + }, + { + "bbox": [ + 304, + 433, + 547, + 480 + ], + "type": "inline_equation", + "content": "S_{1}" + }, + { + "bbox": [ + 304, + 433, + 547, + 480 + ], + "type": "text", + "content": ": Following NAS-Bench-201 [14], this Darts-like search space is a cell-based search space consisting of stacked directed acyclic graphs. " + }, + { + "bbox": [ + 304, + 433, + 547, + 480 + ], + "type": "inline_equation", + "content": "S_{1}" + }, + { + "bbox": [ + 304, + 433, + 547, + 480 + ], + "type": "text", + "content": " is conducted on CIFAR-10, CIFAR-100, and ImageNet-16-120 datasets." + } + ] + } + ], + "index": 36 + }, + { + "bbox": [ + 304, + 481, + 547, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 481, + 547, + 518 + ], + "spans": [ + { + "bbox": [ + 304, + 481, + 547, + 518 + ], + "type": "text", + "content": "Search Space " + }, + { + "bbox": [ + 304, + 481, + 547, + 518 + ], + "type": "inline_equation", + "content": "S_{2}" + }, + { + "bbox": [ + 304, + 481, + 547, + 518 + ], + "type": "text", + "content": ": Following NDS [53], this search space consists of residual and bottleneck blocks defined in ResNet. " + }, + { + "bbox": [ + 304, + 481, + 547, + 518 + ], + "type": "inline_equation", + "content": "S_{2}" + }, + { + "bbox": [ + 304, + 481, + 547, + 518 + ], + "type": "text", + "content": " is based on CIFAR-100 and ImageNet-1k dataset." + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 306, + 526, + 459, + 539 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 526, + 459, + 539 + ], + "spans": [ + { + "bbox": [ + 306, + 526, + 459, + 539 + ], + "type": "text", + "content": "4.2. Experiments on CIFAR-100" + } + ] + } + ], + "index": 38 + }, + { + "bbox": [ + 304, + 545, + 547, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 547, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 547, + 605 + ], + "type": "text", + "content": "Implementation Details. We compare distillation gains with other zero-nas on search space " + }, + { + "bbox": [ + 304, + 545, + 547, + 605 + ], + "type": "inline_equation", + "content": "S_{1}" + }, + { + "bbox": [ + 304, + 545, + 547, + 605 + ], + "type": "text", + "content": ". In the search phase, we configure 48k evolution iters with 512 population sizes. In distillation, All searched student networks are trained via CRD's settings [59] with ResNet56 as the teacher model." + } + ] + } + ], + "index": 39 + }, + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "type": "text", + "content": "Distillation Results of Zero-cost Proxies. We conduct detailed experiments on other zero-cost proxies with different knowledge distillation methods. Note that we search the student network under constraints of 1M parameters. The results in Table 5 demonstrated that our proposed DisWOT achieved superior results compared with other zero-cost proxies with different knowledge distillation methods. The DisWOT outperforms its counterparts vanilla networks by around " + }, + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "type": "inline_equation", + "content": "2\\%" + }, + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "type": "text", + "content": ", while achieving consistent improvements" + } + ] + } + ], + "index": 40 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11903" + } + ] + } + ], + "index": 41 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 102, + 287, + 198 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "type": "text", + "content": "Table 5. Distillation results (\\%) of different zero-cost proxies with knowledge distillation methods under 1M parameters." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 102, + 287, + 198 + ], + "lines": [ + { + "bbox": [ + 50, + 102, + 287, + 198 + ], + "spans": [ + { + "bbox": [ + 50, + 102, + 287, + 198 + ], + "type": "table", + "html": "
MethodRandomFLOPsSynflowNWOTDisWOT
Baseline69.5271.3772.8871.8073.12
KD70.4572.1373.7272.5774.73
FitNets70.1272.4073.5572.7274.85
AT70.1672.9773.5272.0874.50
SP70.4672.1473.5072.1674.95
RKD71.1972.2273.6972.6374.62
CRD71.5972.7873.9973.1275.25
", + "image_path": "a52e0969f296bc4c1ff5ecd4b5852c49515a34b2a4027af93b98cb40c07357eb.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 219, + 288, + 244 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 219, + 288, + 244 + ], + "spans": [ + { + "bbox": [ + 47, + 219, + 288, + 244 + ], + "type": "text", + "content": "among different distillation methods, such as KD [22], Fit-Nets [55], AT [74], SP [62], RKD [44], and CRD [60]." + } + ] + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 50, + 285, + 286, + 350 + ], + "blocks": [ + { + "bbox": [ + 46, + 253, + 287, + 277 + ], + "lines": [ + { + "bbox": [ + 46, + 253, + 287, + 277 + ], + "spans": [ + { + "bbox": [ + 46, + 253, + 287, + 277 + ], + "type": "text", + "content": "Table 6. Distillation results(%) of zero-cost proxies under " + }, + { + "bbox": [ + 46, + 253, + 287, + 277 + ], + "type": "inline_equation", + "content": "\\{0.5,1,2\\}\\mathrm{M}" + }, + { + "bbox": [ + 46, + 253, + 287, + 277 + ], + "type": "text", + "content": " parameters." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 285, + 286, + 350 + ], + "lines": [ + { + "bbox": [ + 50, + 285, + 286, + 350 + ], + "spans": [ + { + "bbox": [ + 50, + 285, + 286, + 350 + ], + "type": "table", + "html": "
Param.FLOPsNWOTDisWOTDisWOT†
0.5M69.8870.3872.8973.75
1M72.1372.5774.2375.25
2M73.2773.8675.9576.67
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FLOPsNWOTSynflowDisWOTFLOPsNWOTSynflowDisWOT
50M63.1964.2865.98100M70.3872.1272.89
", + "image_path": "35c91b9709e3c85f3cfb911142a5f26d7b71253b087d54d790c569b097fa69d8.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 50, + 483, + 287, + 581 + ], + "blocks": [ + { + "bbox": [ + 47, + 452, + 286, + 474 + ], + "lines": [ + { + "bbox": [ + 47, + 452, + 286, + 474 + ], + "spans": [ + { + "bbox": [ + 47, + 452, + 286, + 474 + ], + "type": "text", + "content": "Table 8. Ranking correlation (\\%) of zero-cost proxies on " + }, + { + "bbox": [ + 47, + 452, + 286, + 474 + ], + "type": "inline_equation", + "content": "S_0" + }, + { + "bbox": [ + 47, + 452, + 286, + 474 + ], + "type": "text", + "content": " space on CIFAR-100." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 483, + 287, + 581 + ], + "lines": [ + { + "bbox": [ + 50, + 483, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 50, + 483, + 287, + 581 + ], + "type": "table", + "html": "
MethodKendall's TauSpearmanPearson
FLOPs [1]51.6172.9276.40
Fisher [1]62.8681.3720.90
Grad_Norm [1]63.7582.3539.35
SNIP [28]67.2285.0751.09
NWOT [42]31.8745.6648.99
DisWOT (ours)73.9891.3884.83
", + "image_path": "9646e96821f27d3f9017b163f39315821378989fb73971335f1c943588dbd84a.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 594, + 289, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 289, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 289, + 713 + ], + "type": "text", + "content": "Analysis on Varying Parameter Constraints. We analyze the performance of student models under different parameter constraints obtained by DisWOT on CIFAR-100. As shown in the Table 7, we compared our method with two zero proxies, a.k.a. FLOPs [1] and NWOT [42], under the parameter constraints of 0.5, 1, and 2M, respectively, and the results demonstrate that our method still achieves excellent results. As shown in Tab. 7, DisWOT also outperforms previous SOTA methods with " + }, + { + "bbox": [ + 46, + 594, + 289, + 713 + ], + "type": "inline_equation", + "content": "0.8\\% \\sim 1.7\\% \\uparrow" + }, + { + "bbox": [ + 46, + 594, + 289, + 713 + ], + "type": "text", + "content": " gains under same FLOPs constraints," + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 547, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 193 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 193 + ], + "type": "text", + "content": "Ranking Correlation with Distill Accuracy. Based on search space " + }, + { + "bbox": [ + 304, + 72, + 547, + 193 + ], + "type": "inline_equation", + "content": "S_0" + }, + { + "bbox": [ + 304, + 72, + 547, + 193 + ], + "type": "text", + "content": ", we perform vanilla training and distillation for each candidate with CRD's settings [59]. Then, we collect these vanilla results as GT and analyze the different zero-proxy's correlation with them. As shown in Table 8, the results illustrate that our DisWOT achieves higher than Fisher, GradNorm, SNIP,FLOPs, and NWOT by a large margin, and achieve results that are on par with the best zero-cost proxy, a.k.a. Zen-NAS and Synflow, on Kendall's Tau, Pearson, and Spearman coefficient." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 200, + 480, + 213 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 200, + 480, + 213 + ], + "spans": [ + { + "bbox": [ + 305, + 200, + 480, + 213 + ], + "type": "text", + "content": "4.3. Experiments on NAS-Bench-201" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 218, + 547, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 218, + 547, + 289 + ], + "spans": [ + { + "bbox": [ + 304, + 218, + 547, + 289 + ], + "type": "text", + "content": "Implementation Details. For search trials, we first adopt ResNet110/56 as the teachers and then Conduct an evolution search with the DisWOT metric and get the best student network. We randomly sampled 50 candidate architectures to evaluate sequencing consistency. The distillation settings are the same as the Sec.4.2" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 289, + 547, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 289, + 547, + 361 + ], + "spans": [ + { + "bbox": [ + 304, + 289, + 547, + 361 + ], + "type": "text", + "content": "Comparison results As shown in Table 9, some training-free methods can achieve good results with much faster speedups, such as NWOT and TE-NAS. Our proposed method DisWOT achieves a speedup ratio of " + }, + { + "bbox": [ + 304, + 289, + 547, + 361 + ], + "type": "inline_equation", + "content": "180 \\times" + }, + { + "bbox": [ + 304, + 289, + 547, + 361 + ], + "type": "text", + "content": ", where if semantic similarity metric is removed, we can achieve a " + }, + { + "bbox": [ + 304, + 289, + 547, + 361 + ], + "type": "inline_equation", + "content": "300 \\times" + }, + { + "bbox": [ + 304, + 289, + 547, + 361 + ], + "type": "text", + "content": " speedup ratio at the expense of some accuracy." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 369, + 451, + 383 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 369, + 451, + 383 + ], + "spans": [ + { + "bbox": [ + 305, + 369, + 451, + 383 + ], + "type": "text", + "content": "4.4. Experiments on ImageNet" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 388, + 547, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 388, + 547, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 388, + 547, + 581 + ], + "type": "text", + "content": "Implementation Details. We searched the ResNet18 level network regarding the search space in NDS [53]. Specifically, we limit the number of parameters to less than 13M and the depth of the network to up to 20 layers and find the optimal network by evolution algorithm with the DisWOT metric. As shown in Table 10, guided by three different sizes of networks, we used DisWOT to find the optimal student network. We trained the student network obtained by the search using the distillation strategy in DisWOT. Implementation details are available in supplementary materials. Comparison Results. Table 10 reports the performance of DisWOT on ImageNet with ResNet34/50 as teacher network. The results demonstrate that the student architecture of the ResNet18-level obtained by DisWOT under different teacher guidance and using different distillation strategies yielded significantly better results than its counterparts." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 586, + 463, + 599 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 586, + 463, + 599 + ], + "spans": [ + { + "bbox": [ + 305, + 586, + 463, + 599 + ], + "type": "text", + "content": "4.5. Ablation Studies of DisWOT" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 605, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 548, + 715 + ], + "type": "text", + "content": "We perform ablation experiments to verify the validity of each component of DisWOT in search space " + }, + { + "bbox": [ + 304, + 605, + 548, + 715 + ], + "type": "inline_equation", + "content": "S_0" + }, + { + "bbox": [ + 304, + 605, + 548, + 715 + ], + "type": "text", + "content": ". As shown in Table 11, for semantic knowledge, similarity matrix obtains a more robust ranking improvement than simple Fit-Net [54]. For " + }, + { + "bbox": [ + 304, + 605, + 548, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_r" + }, + { + "bbox": [ + 304, + 605, + 548, + 715 + ], + "type": "text", + "content": ", similarity matrix performs better on relational knowledge than RKD [45]. DisWOT integrates semantic and relational knowledge to obtain an additional ranking improvement than stand-alone scores. The weight initialization scheme plays an important role in zero-proxy." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "11904" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 113, + 545, + 251 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "text", + "content": "Table 9. Distillation results on CIFAR-10, CIFAR-100, and ImageNet-16 in NAS-Bench-201 [13]. Dis. Acc. (%) represents the accuracy of the searched architecture after distillation training. Time (s) denotes the time cost (GPU-seconds) during the search phase. The results of NWOT and TE-NAS come from their original papers. Our DisWOT achieves competitive results with the lowest costs." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 113, + 545, + 251 + ], + "lines": [ + { + "bbox": [ + 49, + 113, + 545, + 251 + ], + "spans": [ + { + "bbox": [ + 49, + 113, + 545, + 251 + ], + "type": "table", + "html": "
TypeModelCIFAR-10CIFAR-100ImageNet-16-120
Dis. Acc(%)Time (s)Speed-upDis. Acc(%)Time (s)Speed-upDis. Acc(%)Time (s)Speed-up
Multi-trialRS93.63216K1.0×71.28460K1.0×44.881M1.0×
RL [3]92.83216K1.0×71.71460K1.0×44.351M1.0×
BOHB [17]93.49216K1.0×70.84460K1.0×44.331M1.0×
RSPS [34]91.6710K21.6×57.9946K21.6×36.87104K9.6×
Weight-sharingGDAS [15]93.3922K12.0×70.7039K11.7×42.35130K7.7×
DARTS [38]89.2223K9.4×66.2480K5.8×43.18110K9.1×
Training-freeNWOT [42]93.732.2K100×73.314.6K100×45.4310K100×
TE-NAS [9]93.922.2K100×71.244.6K100×44.3810K100×
DisWOTMs & Mr93.551.2K180×74.219.2K180×47.3020K180×
Mr93.490.72K300×73.6218.4K300×45.6340K300×
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TeacherStudentAcc.TeacherStudentKD [22]ESKD [10]\\( \\mathrm{ATKD}_{A_{R18}} \\) [43]ONE [27]DML [75]CRD [60]DisWOT
ResNet34ResNet18Top-173.4069.7570.6670.8970.7870.5571.0371.1772.08
Top-591.4289.0789.8890.0689.9989.5990.2890.3290.38
TeacherStudentAcc.TeacherStudentKD [22]\\( \\mathrm{ATKD}_{A_{R18}} \\) [43]\\( \\mathrm{ATKD}_{A_{R34}} \\) [43]Seq. ESKD [10]ESKD [10]SRRL [72]DisWOT
ResNet50ResNet18Top-176.1669.7570.6870.6570.8570.6570.9571.2072.30
Top-592.8689.07N/AN/AN/AN/AN/AN/A90.51
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KnowledgeMetricSpearman (%)
MsFitNets [54]64.06±6.11
MsSimilarity matrix73.68±5.45
MrRKD [59]13.52±11.51
MrSimilarity matrix72.36±3.42
Ms & MrSimilarity matrix77.51±2.76
", + "image_path": "1788cadfe112dea57ef2515b1b582ca908c27faa85de8d94e9296f3784acc041.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 533, + 288, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 288, + 582 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 288, + 582 + ], + "type": "text", + "content": "We verify the effect of the initialization strategy of the network on the ranking consistency. The results in Tab. 12 demonstrate that the Gaussian initialization strategy is detrimental to " + }, + { + "bbox": [ + 46, + 533, + 288, + 582 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_s" + }, + { + "bbox": [ + 46, + 533, + 288, + 582 + ], + "type": "text", + "content": ", but beneficial to " + }, + { + "bbox": [ + 46, + 533, + 288, + 582 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_r" + }, + { + "bbox": [ + 46, + 533, + 288, + 582 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 595, + 120, + 608 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 595, + 120, + 608 + ], + "spans": [ + { + "bbox": [ + 47, + 595, + 120, + 608 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 616, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 616, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 616, + 289, + 715 + ], + "type": "text", + "content": "In this paper, we present DisWOT, a new teacher-aware student architecture search without training framework for distillation. Based on key observations about the difference between vanilla and distillation accuracy, DisWOT measures the new zero-cost proxy conditioned on the similarity of feature semantics and sample relations between random initialized teacher-student network. Then, DisWOT search for the best student architectures for the given teacher us" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 308, + 436, + 545, + 484 + ], + "blocks": [ + { + "bbox": [ + 304, + 395, + 545, + 427 + ], + "lines": [ + { + "bbox": [ + 304, + 395, + 545, + 427 + ], + "spans": [ + { + "bbox": [ + 304, + 395, + 545, + 427 + ], + "type": "text", + "content": "Table 12. \"mean±std %\" Spearman of proxies via Kaiming and Gaussian initialization on search space " + }, + { + "bbox": [ + 304, + 395, + 545, + 427 + ], + "type": "inline_equation", + "content": "S_0" + }, + { + "bbox": [ + 304, + 395, + 545, + 427 + ], + "type": "text", + "content": " and NAS-Bench-201 with various seeds." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 436, + 545, + 484 + ], + "lines": [ + { + "bbox": [ + 308, + 436, + 545, + 484 + ], + "spans": [ + { + "bbox": [ + 308, + 436, + 545, + 484 + ], + "type": "table", + "html": "
SpaceInitialFisherGradNormNWOTDisWOT
S0Kaim.81.37±0.0182.35±0.0145.66±0.0584.08±0.03
Gauss.80.99±0.0175.50±0.0145.36±0.0391.38±0.03
NB-201Kaim.54.63±0.1558.70±0.1164.41±0.0865.57±0.02
Gauss.45.91±0.0945.70±0.1162.24±0.0772.36±0.02
", + "image_path": "14e7d3d7fda892d73777c45e0ef58f437e1e50192aecc47ef972f462ccf7674a.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 508, + 547, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 508, + 547, + 663 + ], + "spans": [ + { + "bbox": [ + 304, + 508, + 547, + 663 + ], + "type": "text", + "content": "ing an evolutionary algorithm with these metrics. Thorough evaluations are performed on diverse datasets and search spaces, and DisWOT achieves significant performance gains in various neural networks with at least " + }, + { + "bbox": [ + 304, + 508, + 547, + 663 + ], + "type": "inline_equation", + "content": "180 \\times" + }, + { + "bbox": [ + 304, + 508, + 547, + 663 + ], + "type": "text", + "content": " training acceleration. We experimentally and theoretically explained the relationship between similarity difference and distillation performance. In addition, we also extend DisWOT to new distillers and general zero proxy to predict the performance of models. By doing this, we bridge the higher-order knowledge bewteen distillation and network architecture search. This approach represents an elegant and practical solution, which we hope will inspire future research on knowledge distillation and architecture search design." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": "Limitations. Following most zero-cost NAS, we evaluate DisWOT in classification tasks. In the future work, we will make efforts to expand the DisWOT for downstream tasks (e.g., object detection and semantic segmentation)." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "11905" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "type": "text", + "content": "[1] Mohamed S Abdelfattah, Abhinav Mehrotra, Lukasz Dudziak, and Nicholas Donald Lane. 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In CVPR, 2018. 3" + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "11908" + } + ] + } + ], + "index": 7 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Discovering the Real Association_ Multimodal Causal Reasoning in Video Question Answering/f46331e4-a9e1-4fa6-843a-36c1e6734399_content_list.json b/2023/Discovering the Real Association_ Multimodal Causal Reasoning in Video Question Answering/f46331e4-a9e1-4fa6-843a-36c1e6734399_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..72868761e4713a2393ace6e3da2b549c19e12816 --- /dev/null +++ b/2023/Discovering the Real Association_ Multimodal Causal Reasoning in Video Question Answering/f46331e4-a9e1-4fa6-843a-36c1e6734399_content_list.json @@ -0,0 +1,1719 @@ +[ + { + "type": "text", + "text": "Discovering the Real Association: Multimodal Causal Reasoning in Video Question Answering", + "text_level": 1, + "bbox": [ + 114, + 128, + 854, + 175 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Chuanqi Zang $^{1}$ , Hanqing Wang $^{1}$ , Mingtao Pei $^{1}$ , Wei Liang $^{1,2*}$", + "bbox": [ + 218, + 184, + 753, + 202 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1School of Computer Science and Technology, Beijing Institute of Technology", + "bbox": [ + 176, + 203, + 792, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ Yangtze Delta Region Academy of Beijing Institute of Technology, Jiaxing", + "bbox": [ + 186, + 220, + 784, + 238 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 287, + 312, + 303 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Video Question Answering (VideoQA) is challenging as it requires capturing accurate correlations between modalities from redundant information. Recent methods focus on the explicit challenges of the task, e.g. multimodal feature extraction, video-text alignment and fusion. Their frameworks reason the answer relying on statistical evidence causes, which ignores potential bias in the multimodal data. In our work, we investigate relational structure from a causal representation perspective on multimodal data and propose a novel inference framework. For visual data, question-irrelevant objects may establish simple matching associations with the answer. For textual data, the model prefers the local phrase semantics which may deviate from the global semantics in long sentences. Therefore, to enhance the generalization of the model, we discover the real association by explicitly capturing visual features that are causally related to the question semantics and weakening the impact of local language semantics on question answering. The experimental results on two large causal VideoQA datasets verify that our proposed framework 1) improves the accuracy of the existing VideoQA backbone, 2) demonstrates robustness on complex scenes and questions. The code will be released at https://github.com/Chuanqi-Zang/Discoverthe-Real-Association.", + "bbox": [ + 73, + 319, + 473, + 696 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 78, + 717, + 209, + 733 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Video Question Answering (VideoQA) aims to understand visual information and describe it in language question-answer format, which is a natural cognitive capability for humans. Computer Vision (CV) and Natural Language Processing (NLP) as the base models for VideoQA have shown significant progress due to the successful application of deep learning, such as action classification [25], object detection [10], instance segmentation [31], and large-scale pre-trained language model [6, 19]. These tremendous", + "bbox": [ + 75, + 743, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/7bfdadcb1c850b12aad0fd02c4d1547594652d91e7a1d7f0663d524c04e2acc2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 501, + 273, + 898, + 309 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Question: What will happen if the power is cut off?", + "bbox": [ + 504, + 311, + 785, + 324 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Answer: TV, indoor $\\rightarrow$ singing karaoke", + "bbox": [ + 506, + 325, + 792, + 349 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "A. [person_1] will stop singing karaoke. Predict", + "bbox": [ + 506, + 351, + 797, + 368 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "B. [person_1] and [person_2] both cannot work. G.T.", + "bbox": [ + 506, + 369, + 797, + 383 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Question: What will happen if the girl sprains?", + "bbox": [ + 506, + 388, + 763, + 402 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Answer: The girl will stop.", + "bbox": [ + 506, + 402, + 655, + 415 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Reason: Someone, help $\\rightarrow$ Reason", + "bbox": [ + 506, + 419, + 751, + 443 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a406292e40734e4feda4624d8a5a72ab15815771e118e3da376f4660bd9ddb13.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 779, + 391, + 848, + 429 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "A.There are a lot people here,and can find someone to help at any time. B.The girl can't exercise because of a sprain and needs to rest.G.T.", + "bbox": [ + 504, + 445, + 893, + 473 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Predict", + "bbox": [ + 841, + 435, + 885, + 448 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Figure 1. Two samples in VideoQA dataset. They exhibit spurious reasoning processes of B2A [26] that rely on statistical patterns, including visually spurious object-relationship associations (top) and textually unilateral semantic representations (bottom).", + "bbox": [ + 500, + 482, + 890, + 537 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "advances in basic applications fuel the confidence in fine-grained multimodal analysis and reasoning, not only feature extraction, but also fine-grained general causality estimation, which is critical for a robust cognitive system.", + "bbox": [ + 496, + 551, + 890, + 612 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent VideoQA methods usually explore multimodal relational knowledge by sophisticated structured architecture, such as memory-augmented model [9], hierarchical model [20], topological model [18], and transformer-based model [37]. Although experiments validate their feature fusion capabilities, we find that these methods concentrate on statistical association based on multimodal data, ignoring the real stable association. They usually use a generally constrained approach with Empirical Risk Minimization (ERM), which tends to over-rely on the co-occurrence bias of repeated objects and words in the collected observational data, and bypasses the impact of complete semantics at the sentence level. This mechanism reduces the robustness of the model on new data, even in the test set which has similar distributions to the training set.", + "bbox": [ + 496, + 613, + 892, + 839 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "For example, as shown in Fig. 1 (top), two people are playing \"cricket\" indoors, and there are other objects in the room, including a TV that is on. If relying on the statistical relationship, the model may be confused by the two im", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Wei Liang is the corresponding author.", + "bbox": [ + 99, + 887, + 313, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "19027", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "important visual factors of \"indoor\" and \"television\", and misjudge the concerned event, that is, \"sing karaoke\". Based on the clues provided by the question, the concerned event is related to the action that is taking place, e.g. \"two men playing cricket\". This requires the model to accurately judge the objects involved in the event and infer the answer. In Fig. 1 (bottom), we show the predicted deviation caused by statistical relationships in the text. When inferring the reasons for answer selection, existing models intensively rely on correlations between local words and video content, e.g. \"someone; help\", ignoring unreasonable inferences from other parts of the sentence, e.g. \"a lot\".", + "bbox": [ + 80, + 90, + 467, + 271 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "From these observations, we summarize two causal challenges for the VideoQA task. 1) Irrelevant objects confounder. The visual information related to the question is usually causally related to finite objects in the video. When other objects or background are considered, they are subject to data bias and become confounders, misleading the model to select the negative candidate. 2) Keywords confounder. The semantics expressed by textual information is represented by the overall sentence. Some long sentences contain partially sensible keywords. When just focusing on local keywords semantics, the model falls into spurious causal inferences, reducing the robustness of the model.", + "bbox": [ + 80, + 276, + 467, + 455 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address the above causal challenges and improve the robustness of the model, we propose a Multimodal Causal Reasoning (MCR) framework for video-text data. In this framework, causal features and confounding features are decoupled separately in visual and textual modes through two training strategies. To explicitly decouple the influence of different objects and scenes, MCR extracts fine-gained object-level appearance features and motion dynamics by spatial Region of Interest (ROI) Align [13] on global visual features. Among them, causally related objects are selected based on the correlation between object features and question semantics. In addition to the visual feature, we also model object coordinate information, category information, and global object interaction information to provide spatio-temporal relation representations for accurate causal attribute classification. For textual confounders, we adopt a strategy to reduce the impact of keywords on causality. MCR relies on the correlation between word encoding and question-visual co-embedding to select keywords which have a crucial impact on the prediction results. These keywords provide negative representations for successive deductive answers. Therefore, we combine these keywords with other candidate answers to generate difficult negative samples to improve the recognition ability of the model. During training, visual intervention and textual intervention are iteratively optimized. Multimodal causal relationships are gradually established which improves the robustness and reusability of the model.", + "bbox": [ + 80, + 460, + 467, + 881 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We summarize our contributions as: (1) We discover two", + "bbox": [ + 99, + 886, + 467, + 898 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "new types of causal challenges for both visual data and textual data. (2) We propose an object-level causal relationship extraction strategy to establish the real association between objects and language semantics, and a keyword broadcasting strategy to cut off the spurious influence of local textual information. (3) We achieve state-of-the-art performance on two latest large causal VideoQA datasets.", + "bbox": [ + 503, + 90, + 888, + 195 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 503, + 210, + 638, + 226 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Video Question Answering (VideoQA). In early works, the long-term dependency features in video and text were extracted by RNN-based modules, and then were fused by element-wise multiplication [42, 43] with attention mechanism [35]. Considering the implicit interaction in multimodal data, Jiang et al. [18] proposed a heterogeneous graph convolution-based network for crossmodal fusion. Park et al. [26] enhanced crossmodal graphs by a bridged visual-to-visual interactions structure. Huang et al. [15] improved graph interaction reasoning at the fine-grained object level. Dang et al. [5] explored the symbol-like manipulable reasoning by a hierarchically nested spatio-temporal graph. Benefited from the pre-trained language-based transformer [6] and video-text-alignment transformer [37, 41], current works [24, 38] can fine-tune the pre-trained model and show remarkable feature extraction ability and cross-model aligning ability. However, these methods ignore the potential bias distribution in the data. While improving the ability of feature extraction and alignment, they introduce confounders that lead to poor generalization.", + "bbox": [ + 503, + 234, + 888, + 536 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Causal learning. Except for representation learning, recent work found that causal reasoning in data is meaningful for VideoQA. In the synthetic dataset [39], inspired by neural-symbolic method [40] for the ImageQA task, some work [4,7,39] explicitly represent the appearance information and physical information of each object in the scene. To investigate the causal modeling ability of models in real life, recent datasets [21, 36, 39] asked questions about behavior causality in addition to descriptive questions. For some common-sense causal knowledge that is not represented in the videos, Chadha et al. [3] proposed a knowledge base as additional guidance. To find clues of causal associations, Xu et al. [36] proposed to dynamically select the frame from the past or future. The same in frame level, Li et al. [22] explored invariant learning [1] to distinguish question-irrelevant scenes.", + "bbox": [ + 503, + 537, + 888, + 777 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In real-life scenes, videos contain redundant object information. Since lacking human annotations, frequently occurring objects are introduced as confounders, which bring more complex spurious guidance for video understanding than rough frame-level background snippets. In addition, in texts involving causal reasoning, some phrases are also prone to become confounders. This paper will unify the analysis of causal inference on multimodal data.", + "bbox": [ + 503, + 780, + 888, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "19028", + "bbox": [ + 482, + 946, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/50d8fbc972427ec226572cbf50648244f80b80e595f46c60aa613396e4ee1d08.jpg", + "image_caption": [ + "Figure 2. Causal formulation of VideoQA. Gray variables are observed data. V is a specific video and S is a specific sentence. D represents the data domain determined by the collected dataset. It causes the co-occurring of objects in video V, various words in sentence S, and answer label Y. The ideal causal inference is that model extracts video event features $E_{v}$ from videos and text event features $E_{s}$ from words. Then it integrates different modal event representations and filters out the event of interest $E$ for answer selection Y. Here, we provide the backdoor adjustment from D to V and from D to S, which produces our MCR architecture." + ], + "image_footnote": [], + "bbox": [ + 178, + 88, + 370, + 196 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 376, + 166, + 390 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Formulation of VideoQA", + "text_level": 1, + "bbox": [ + 76, + 402, + 303, + 417 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Causal Preliminaries. We formalize cross-modal causality for the VideoQA task via a Structure Causal Model [27]. In Fig. 2, we represent the key factors in the VideoQA task as components in the causal graph, and represent the relationships between factors as connecting links that are built by current models [18,23,26,33] as default, including data domain D, video V, sentence S, label Y, visual event features $E_{v}$ , and textual event features $E_{s}$ , alignment events $E$ .", + "bbox": [ + 75, + 426, + 468, + 561 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$V \\rightarrow E_v \\rightarrow E \\leftarrow E_s \\leftarrow S$ denotes feature extraction and alignment of multimodal data. $E_v$ and $E_s$ represent the complete events feature extracted from the video and sentence, respectively. In visual domain, pre-trained feature extraction models extract different objects and interactions as events. In textual domain, pre-trained models represent linguistic concepts in stages as events according to punctuation and connectives. $E_v \\rightarrow E \\leftarrow E_s$ represents multimodal event selection and alignment. The deep model references language events to select video events of interest. Then it aligns event representations and infers a unified event representation $E$ .", + "bbox": [ + 75, + 565, + 468, + 744 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$E \\to Y$ represents the direct causal effect from the unified feature of the concerned event to the label, which is an ideal way that remains invariant in other data D with different data distributions. For example, \"play cricket\" is causally related to cricket bat and swing, and irrelevant to \"indoor\" and \"outdoor\".", + "bbox": [ + 75, + 747, + 468, + 838 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$V \\gets D \\to Y$ denotes that the data domain $D$ as a confounder provides a spurious shortcut from video $V$ to label $Y$ in the visual domain. Specifically, the data domain $D$ represents the statistical relationships contained in the lim", + "bbox": [ + 75, + 839, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ited collected video data to represent the co-occurrence of objects and labels. In the top example in Fig. 1, \"TV\" and \"indoor\" provide the shortcut connection that is identified as \"karaoke\" because of lacking human interaction event.", + "bbox": [ + 496, + 90, + 890, + 151 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$S \\gets D \\to Y$ denotes that the data domain $D$ also establishes spurious associations between sentence $S$ and label $Y$ . This is reflected in the fact that the model is easy to establish the association between labels and local concerned expressions of sentences while ignoring the overall expressions. Especially in multiple-choice questions, the model shows a stronger preference for the local \"key\" representation. For example, in the below example in Fig. 1, the model selects the locally correct answer, \"someone\" and \"help\".", + "bbox": [ + 496, + 151, + 890, + 286 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Causal Intervention. The well-known backdoor adjustment [27] helps in eliminating spurious correlations, resulting in better generalization for the model. We present the true causality from V and S to Y as $P(Y|do(V,S))$ , where $do()$ denotes the interventional operation. $P(Y|do(V,S))$ can cut off the link $D\\to V$ and $D\\rightarrow S$ to block this backdoor path by changing the original training data into new data $\\mathcal{T} = \\{\\tau_1,\\dots,\\tau_h\\}$ . Each of them donates a confounder stratum (total $h$ ), guiding the model to find invariants from the confounder. The backdoor adjustment can be represented as:", + "bbox": [ + 496, + 287, + 890, + 454 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} P \\left(Y \\mid d o (V, S)\\right) = \\sum_ {\\tau \\in \\mathcal {T}} P (Y | V, S, \\tau) P (\\tau) \\\\ = \\sum_ {\\tau_ {v} \\in \\mathcal {T} _ {v}} P (Y | V, \\tau_ {v}) P (\\tau_ {v}) \\tag {1} \\\\ + \\sum_ {\\tau_ {s} \\in \\mathcal {T} _ {s}} P (Y | S, \\tau_ {s}) P (\\tau_ {s}) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 540, + 464, + 890, + 568 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $P(Y|V,S,\\tau)$ denotes the prediction in each new data split $\\tau$ . $P(\\tau)$ denotes confounder selection probability for a specific video and sentence, calculated by $P(\\tau) \\coloneqq \\frac{1}{h}$ . We calculate probability estimates separately by two individual architectures for video and text. In this way, the interaction cuts off the confounder effect in $V \\gets D \\to Y$ and $S \\gets D \\to Y$ as shown in Fig. 2. Take video data as an example, traversing all the confounders for a video is expensive. When the video number in the dataset is $\\mathcal{M}$ , Eq. 1 expands the training data from $\\mathcal{M}$ to $\\mathcal{M}^2$ within one epoch with additional memory consumption. Therefore, to balance the scale of confounder set $\\mathcal{T}_v$ and training speed, we find the confounder by our MCR and combine it with original data V every epoch. After $K$ training epochs, we can approximate the visual part of the adjustment equation, i.e. $\\sum_{\\tau_v \\in \\mathcal{T}_v} P(Y|V, \\tau_v) P(\\tau_v) \\approx \\sum_{k=1}^{K} \\sum_{\\tau_v \\in \\mathcal{T}_v^k} P(Y|V, \\tau_v) P(\\tau_v)$ .", + "bbox": [ + 496, + 579, + 890, + 840 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Preliminary. Given a video $I$ , VideoQA aims to understand acting events by asking questions $q$ and predict the correct answer $\\widetilde{a}$ from a answer candidate set $A = \\{a_{z}\\}_{z=1}^{Z}$ . $Z$ is the candidate number. The process is generally formu", + "bbox": [ + 496, + 840, + 890, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "19029", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/cbf55aa4b01413cbb273709b887b0d1f0da6360e372d3d197559b8b6f81a8cdb.jpg", + "image_caption": [ + "Figure 3. Visual Causal Module. Before the appearance information and motion information are sent to the backbone for question answering, we propose a visual causal module to find object-level causal features and irrelevant features in video data. The image-level visual features are first divided into object-level visual features by the detected bounding box. The category information, location information and interaction relationship of each object are modeled by Interaction Detector. According to the question prompt, the Indicator judges whether the features of different objects are causally related or irrelevant. The uniform representation of causal and irrelevant features are used for further prediction in the VideoQA backbone." + ], + "image_footnote": [], + "bbox": [ + 76, + 87, + 893, + 378 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "lated as follows:", + "bbox": [ + 76, + 500, + 189, + 512 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\widetilde {a} = \\underset {a \\in A} {\\operatorname {a r g m a x}} \\mathcal {F} _ {\\theta} (a | q, I), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 184, + 520, + 468, + 546 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\theta$ represents the set of model parameters of VideoQA function $\\mathcal{F}$ , which maps a pair of video and question into the same feature domain to find the answer. In our work, we do not change the VideoQA function $\\mathcal{F}$ . In a causal view, we intervene video $I$ and answer candidate A.", + "bbox": [ + 76, + 554, + 468, + 628 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Visual Causal Module", + "text_level": 1, + "bbox": [ + 76, + 638, + 282, + 652 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To answer the question with accurate causally related features, we propose a visual causal module that disentangles the confounder and causal factors at the object level. As shown in Fig. 3, the video with shape $W \\times H \\times L$ is encoded by 2D ConvNet, 3D ConvNet into a list of appearance feature and motion feature with shape $\\frac{W}{16} \\times \\frac{H}{16} \\times \\frac{L}{2}$ . They are uniformly represented by frame feature sequence $\\mathcal{V} = \\{v_t\\}_{t=1}^{\\frac{L}{2}}$ , where $t$ means timestamp. The object-level grounding is detected by pre-trained Detection ConvNet and donated as the bounding box $\\mathcal{B} = \\{b_{n,t}\\}_{n=1,t=1}^{N,\\frac{L}{2}}$ , where $N$ is the detected object number. We use Region of Interest (ROI) Align [13] to extract object visual features $\\mathcal{O} = \\{o_{n,t}\\}_{n=1,t=1}^{N,\\frac{L}{2}}$ , expressed as $\\mathcal{O} = ROIAlign(\\mathcal{V}|\\mathcal{B})$ .", + "bbox": [ + 76, + 662, + 468, + 871 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Since the scene in the real video is ever-changing, some objects in the video may suddenly disappear or appear, mak", + "bbox": [ + 76, + 871, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "ing it difficult to obtain accurate instance tracking data. Therefore, we extract unified features for the same category of targets, e.g. human, chairs. When objects of this category do not appear in part of the consecutive frames, we fill the feature with 0 value.", + "bbox": [ + 496, + 500, + 890, + 573 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For each object feature, we employ Multilayer Perceptrons (MLP) and Long short-term memory (LSTM) [12] to encode the temporal embedding for visual feature:", + "bbox": [ + 496, + 574, + 890, + 619 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {O} ^ {g} = L S T M (M L P (\\mathcal {O})), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 602, + 628, + 890, + 646 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{O}^g = \\{o_n^g\\}_{n=1}^N \\in \\mathbb{R}^d$ is the global N object representations, and $d$ is the hidden dimension of LSTM. In addition to the visual encoding, we also model the bounding box position correlations $\\mathcal{B}$ , object category $C$ , and spatiotemporal inter-object and intra-object interactions in an Interaction Detecting stream. They are implemented by Non-local Net [30] with MLP:", + "bbox": [ + 496, + 654, + 890, + 758 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL ^ {g} = \\operatorname {N o n L} \\left(M L P \\left(M L P (\\mathcal {B}); M L P (C)\\right)\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 527, + 768, + 890, + 786 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where; represents channel concatenation. $L^{g} = \\{l_{n}^{g}\\}_{n = 1}^{N}\\in$ $\\mathbb{R}^d$ means detected interaction feature. The outputs of two feature extraction streams are then fused by channel concatenation: $\\mathcal{O}^g = [\\mathcal{O}^g;L^g ]$ . All objects are causal or irrelevant candidates. Their identities are determined by the language semantics of the question. Therefore, given a question sentence, we apply Word Parser and Event Embedding", + "bbox": [ + 496, + 794, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "19030", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "to get the global question representation $q^g$ . The Event Embedding is implemented by LSTM:", + "bbox": [ + 76, + 90, + 468, + 121 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nq ^ {g} = L S T M (P a r s e r (q)), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 133, + 468, + 151 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where Parser uses a pre-trained GloVe model [28] or BERT model [6]. LSTM is implemented by the question embedding model of the VideoQA backbone. With the specific question, causally related objects are usually a small part of object set $\\mathcal{O}^g$ and are interconnected internally. Reasoning about their relationship to unrelated objects is redundant and prone to spurious associations. Therefore, inspired by [22], we use hard segmentation [22] in Indicator to explicitly divide object features into causally related features and irrelevant features, rather than soft GCN inference or attention-based models. Specifically, the question embedding $q^{g}$ and objects feature $\\mathcal{O}^g$ are mapped into the same space by MLP. The Indicator computes a score for each object feature and uses Gumbel-Softmax [17] to classify the causal attribute labels of objects:", + "bbox": [ + 75, + 162, + 468, + 388 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {O} ^ {c} = G S (M L P (q ^ {g}) \\cdot (M L P (\\mathcal {O} ^ {g}) ^ {T})) \\circ \\mathcal {O}, \\\\ \\mathcal {O} ^ {\\bar {c}} = \\mathcal {O} - \\mathcal {O} ^ {c} \\end{array} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 122, + 400, + 468, + 426 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {O} ^ {\\bar {c}} = \\mathcal {O} - \\mathcal {O} ^ {c},\n$$\n", + "text_format": "latex", + "bbox": [ + 127, + 421, + 228, + 436 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where GS means Gumbel-Softmax and $\\cdot$ means matrix multiplication. $\\circ$ means multiply by index. $\\mathcal{O}^c = \\{o_n^c\\}_{n^c = 1}^{N^c},\\mathcal{O}^{\\bar{c}} = \\{o_{n^{\\bar{c}}}^{\\bar{c}}\\}_{n^{\\bar{c}} = 1}^{N^{\\bar{c}}}$ are causal object features set and irrelevant features set, respectively, where the corner mark of length is omitted for clarity. We average the features in these sets to obtain causal visual features and irrelevant visual features, respectively: $\\mathcal{V}^c = \\frac{1}{N^c}\\sum \\mathcal{O}^c,$ $\\mathcal{V}^{\\bar{c}} = \\frac{1}{N^{\\bar{c}}}\\sum \\mathcal{O}^{\\bar{c}}.$", + "bbox": [ + 76, + 449, + 468, + 569 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "According to the deduction of Eq. 1, in the visual part, the video V and the average sampling confounder are combined to predict the label. In model designing, the video V can be present by causal object features $\\nu^{c}$ . The confounder is from the confounder of another example in the same mini-batch, represented by:", + "bbox": [ + 75, + 570, + 468, + 660 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathcal {V}} = \\frac {1}{N ^ {c} + N ^ {\\prime \\bar {c}}} \\sum \\left(O ^ {c} + O ^ {\\prime \\bar {c}}\\right), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 161, + 671, + 468, + 702 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\hat{\\mathcal{V}}$ is the blended features. $O^{\\prime\\bar{c}}$ is the confounder of another example. $N^{\\prime\\bar{c}}$ is the object number of $O^{\\prime\\bar{c}}$ . Both $\\mathcal{V}$ , $\\mathcal{V}^{c}$ , $\\mathcal{V}^{\\bar{c}}$ , and $\\hat{\\mathcal{V}}$ are sent to the VideoQA backbone for training the visual causal module. The visual module can capture causal relationships between object features and labels, providing a stable association for multimodal data.", + "bbox": [ + 76, + 714, + 468, + 806 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Textual Causal Module", + "text_level": 1, + "bbox": [ + 76, + 816, + 290, + 830 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For textual causal inference, prediction is often plagued by correlations between local language semantics and visual features. Therefore, the key to getting rid of text confounders is to enhance the model's ability to recognize", + "bbox": [ + 76, + 839, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/9abda42351a4d760930a942ef6568260b9a7dab9783d0a1e9e699bfc99aa41ee.jpg", + "image_caption": [ + "Figure 4. Textual Causal Module. Keywords are selected as confounders from the prediction results by the indicator. They are sent to the intervenor to generate new candidates." + ], + "image_footnote": [], + "bbox": [ + 501, + 87, + 890, + 205 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "such confusing samples which are implemented by a textual causal module.", + "bbox": [ + 498, + 284, + 890, + 313 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In the VideoQA base model, the visual information and the question have been aligned, containing the events information related to the answer. Therefore, we use the alignment feature $f_{qv} = \\mathcal{F}(\\mathcal{V}^c, q^g)$ to retrieve the keywords in the answer. As shown in Fig. 4, the same with question embedding, we encode the answer by Word Parser and Event Embedding:", + "bbox": [ + 498, + 314, + 890, + 420 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\na ^ {g}, a ^ {l} = L S T M (P a r s e r (a)), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 591, + 429, + 890, + 446 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $a^g$ is the global representation of the answer, and $a^l$ is the local representation of each word. The same with visual Indicator, we select the keyword by the relation score between $a^g$ and $f_{qv}$ :", + "bbox": [ + 498, + 455, + 890, + 518 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\na ^ {\\bar {c}} = G S \\left(M L P \\left(f _ {q v}\\right) \\cdot \\left(M L P \\left(a ^ {g}\\right)\\right) ^ {T}\\right) \\circ a ^ {l}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 547, + 525, + 890, + 542 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $a^{\\bar{c}}$ represents the keywords, which are potential confounders in this question. $a^{c} = a^{l} - a^{\\bar{c}}$ represents other words.", + "bbox": [ + 498, + 551, + 890, + 595 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "According to the textual part of Eq. 1, the label is predicted by the sentence and confounder. Due to the correlation between sentences and videos, we look for confounders of sentences from the same video, especially the predicted answer by VideoQA backbone which contains factors that increase the score. Similar to visual intervention, we pick confounders once per epoch.", + "bbox": [ + 498, + 597, + 890, + 700 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Confounders are used to augment the hard sample of candidates that changes the textual distributions. The model joint original candidates $A = \\{a_{z}\\}_{z=1}^{Z}$ with $a^{\\bar{c}}$ by inserting $a^{\\bar{c}}$ at the beginning or end of a sentence and generate a new candidates set $\\hat{A} = \\{\\hat{a}_{z}\\}_{z=1}^{Z}$ . In the training process, we randomly replace the negative example from the new candidates set $\\hat{A}$ .", + "bbox": [ + 498, + 702, + 890, + 806 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Training", + "text_level": 1, + "bbox": [ + 500, + 816, + 602, + 832 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we introduce our training targets and training pipeline for multimodal data. The algorithm can be found in Supplementary. First of all, to ensure the domain consistency of training sets and test sets, we train", + "bbox": [ + 498, + 840, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "19031", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "the VideoQA backbone with raw data $(\\mathcal{V},\\mathrm{A})$ , which also guarantees that the training process satisfies the pre-defined causal formulation:", + "bbox": [ + 75, + 90, + 468, + 133 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {o} = \\mathrm {X E} \\left(\\mathcal {F} \\left((\\mathcal {V}, \\mathrm {q}), (\\mathcal {V}, \\mathrm {A})\\right), \\mathrm {a}\\right), \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 145, + 468, + 162 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where XE is the cross-entropy loss. $\\mathcal{F}$ calculates the dot-product between question-related visual features and answer-related visual features as the predicted results. At test time, we use the candidate with the highest score as the predicted result as in Eq.2.", + "bbox": [ + 75, + 170, + 468, + 244 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Visual Module Loss. Visual module loss aims to capture causal object features and non-causal object features for further robust prediction. In the training stage, the causal visual features have the same ability for question answering, which is restricted by the cross-entropy loss: $\\mathcal{L}_{\\mathrm{c}}^{\\mathrm{v}}$ . In contrast, non-causal objects are irrelevant to the question and should be unbiased toward answer candidates: $\\mathcal{L}_{\\bar{c}}^{\\mathrm{v}}$ . The blended data $\\hat{\\nu}$ are supposed to obtain the same effect with causal feature: $\\mathcal{L}_o^{\\mathrm{v}}$ . The formulation of visual module loss shows as follows:", + "bbox": [ + 75, + 246, + 468, + 396 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {c}} ^ {\\mathrm {v}} = \\operatorname {X E} \\left(\\mathcal {F} \\left(\\left(\\mathcal {V} ^ {\\mathrm {c}}, \\mathrm {q}\\right), \\left(\\mathcal {V} ^ {\\mathrm {c}}, \\mathrm {A}\\right)\\right), \\mathrm {a}\\right)\n$$\n", + "text_format": "latex", + "bbox": [ + 132, + 402, + 370, + 419 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\bar {c}} ^ {\\mathrm {v}} = \\operatorname {M S E} \\left(\\mathcal {F} \\left(\\left(\\mathcal {V} ^ {\\bar {c}}, \\mathrm {q}\\right), \\left(\\mathcal {V} ^ {\\bar {c}}, \\mathrm {A}\\right)\\right), \\text {a v g}\\right) \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 132, + 421, + 468, + 448 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\hat {\\partial}} ^ {\\mathrm {v}} = \\operatorname {X E} (\\mathcal {F} ((\\hat {\\mathcal {V}}, q), (\\hat {\\mathcal {V}}, A)), a),\n$$\n", + "text_format": "latex", + "bbox": [ + 132, + 445, + 351, + 460 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {v}} = \\mathcal {L} _ {\\mathrm {c}} ^ {\\mathrm {v}} + \\mathcal {L} _ {\\bar {c}} ^ {\\mathrm {v}} + \\mathcal {L} _ {\\hat {o}} ^ {\\mathrm {v}},\n$$\n", + "text_format": "latex", + "bbox": [ + 133, + 464, + 279, + 479 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where avg is the average score of all candidates, avg = $\\mathcal{F}((\\mathcal{V},q),(\\mathcal{V},A))$ . MSE means Mean Square Error for non-causal objects to get a neutral score.", + "bbox": [ + 76, + 488, + 468, + 532 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Textual Module Loss. The text module loss aims to find keywords from the prediction results that directly affect the model selection and reduce the sensitivity of the model to keywords. Intuitively, keywords have the ability for prediction, while other words are difficult to judge the results. We use cross-entropy loss for keywords $\\mathcal{L}_{\\mathrm{c}}^{\\mathrm{s}}$ and MSE for other words $\\mathcal{L}_{\\mathrm{c}}^{\\mathrm{s}}$ . The blended answer is restricted by the cross-entropy loss $\\mathcal{L}_{\\hat{o}}^{\\mathrm{s}}$ . The formulation of textual module loss is:", + "bbox": [ + 75, + 534, + 468, + 654 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\bar {c}} ^ {\\mathrm {s}} = \\mathrm {X E} \\left(\\mathcal {F} \\left((\\mathcal {V}, \\mathrm {q}), (\\mathcal {V}, a ^ {\\bar {c}})\\right), \\mathrm {a}\\right)\n$$\n", + "text_format": "latex", + "bbox": [ + 145, + 664, + 375, + 683 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {c}} ^ {\\mathrm {s}} = \\operatorname {M S E} \\left(\\mathcal {F} \\left(\\left(\\mathcal {V}, \\mathrm {q}\\right), \\left(\\mathcal {V}, a ^ {\\mathrm {c}}\\right)\\right), a v g\\right) \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 684, + 468, + 708 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\hat {\\theta}} ^ {\\mathrm {s}} = \\operatorname {X E} (\\mathcal {F} ((\\mathcal {V}, q), (\\mathcal {V}, \\hat {A})), a)\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 705, + 357, + 722 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {s}} = \\mathcal {L} _ {\\mathrm {c}} ^ {\\mathrm {s}} + \\mathcal {L} _ {\\bar {\\mathrm {c}}} ^ {\\mathrm {s}} + \\mathcal {L} _ {\\delta} ^ {\\mathrm {s}}.\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 724, + 289, + 741 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The overall loss of our model can be expressed as:", + "bbox": [ + 76, + 744, + 408, + 760 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {o} + \\lambda_ {1} \\mathcal {L} _ {\\mathrm {v}} + \\lambda_ {2} \\mathcal {L} _ {\\mathrm {s}}, \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 184, + 768, + 468, + 785 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\lambda_{1}$ and $\\lambda_{2}$ are the hyper-parameters to balance the visual loss and textual loss.", + "bbox": [ + 75, + 795, + 468, + 823 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Intervene Pipeline. We show the Intervene pipeline in Fig. 5. The textual intervention and the visual intervention are accomplished in two steps. Visual causal loss is computed with Eq. 11 and used to obtain causally related object features and irrelevant object features. They are used", + "bbox": [ + 75, + 825, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/59be354d816716dd4f1279a20f12dd18611c9ee409a4f1bf077c85a9b1f0bd4e.jpg", + "image_caption": [ + "Figure 5. Causal intervention pipeline." + ], + "image_footnote": [], + "bbox": [ + 544, + 88, + 851, + 172 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "to generate blended visual data with an intervenor, which is implemented by Eq. 7. Textual causal loss is computed with Eq. 12 and used to obtain keywords. Keywords are sent to textual interveners to generate blended textual data. We execute $K_{2}$ epochs textual interventions after executing $K_{1}$ epochs visual interventions for the visual causal module and the textual causal module.", + "bbox": [ + 498, + 226, + 890, + 330 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiment", + "text_level": 1, + "bbox": [ + 500, + 347, + 622, + 364 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Dataset", + "text_level": 1, + "bbox": [ + 500, + 373, + 593, + 387 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We evaluate our Multimodal Causal Reasoning (MCR) framework on two recent large causal-related VideoQA datasets: Causal-VidQA [21] and NExT-QA [32]. In these datasets, models need to answer not only simple descriptive or statistical questions but also implicit global evidence reasoning. The collected video data is close to the real open scene, including a variety of objects and interactive actions. Answer candidates are sentences with different expression structures and are not limited to a single sentence.", + "bbox": [ + 496, + 396, + 890, + 532 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The Causal-VidQA dataset selects 26,900 video clips from Kinetics-700 [2] and asks 107,600 questions, including description, explanation, prediction, and counterfactual questions. Each question has 5 answers, with 5 more reasons in predictions and counterfactuals. For question-answer accuracies, we adopt the previous causal VideoQA evaluation metrics [21] that report accuracy for each question type, as well as the accuracy of the consistency between answers and reasons.", + "bbox": [ + 496, + 532, + 890, + 667 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "NExT-QA dataset contains 5,440 videos from VidOR [29] and proposes 47,692 questions for the multichoice task, including description, explanation, and temporal reasoning questions. We also report accuracy for each question type.", + "bbox": [ + 496, + 669, + 890, + 744 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Experimental Settings", + "text_level": 1, + "bbox": [ + 500, + 756, + 705, + 772 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We use a unified feature extraction method for both datasets. Each video with varying length is divided into 8 clips, each containing 16 frames. For the object-level motion feature, we uniformly sample from the frame-level appearance features and clip-level motion features by ROI Align [13]. The bounding boxes in each frame are extracted by pre-trained Mask R-CNN [13]. The appearance features and motion features are extracted by ResNet-101 [14] and", + "bbox": [ + 496, + 779, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "19032", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/f93cb09c634f8714b40600f3ef884987617ac8be3b860924934da569a7f7b55a.jpg", + "table_caption": [ + "Table 1. Comparison of accuracy with state-of-the-art methods on Causal-VidQA dataset. D means description question. E means explanation question. P means prediction question. C means counterfactual question. QA means to answer the answer. QR means to answer the reason. QAR means the answer and reason are both accurate." + ], + "table_footnote": [], + "table_body": "
MethodText FeatureAcc-DAcc-EQAAcc-P QRQARQAAcc-C QRQARAcc
HME [8]GloVe47.2543.8041.0242.5323.2535.2934.1915.3432.41
HCRN [20]GloVe58.8953.5343.1445.0726.1743.6943.4722.7540.33
HGA [18]GloVe60.3255.0246.5547.2128.5344.0044.0423.6341.88
B2A [26]GloVe61.2956.4346.8248.1730.0145.1244.9925.2943.26
IGV [22]+B2AGloVe59.2448.4145.7047.3228.2038.9940.9718.8438.67
MCR+B2AGloVe66.7261.2650.4652.1732.1352.1751.5031.9148.01
HME [8]BERT63..3661.4550.2947.5628.9250.38.51.6530.9346.16
HCRN [20]BERT65.3561.6151.7451.2632.5751.5753.4432.6648.05
HGA [18]BERT65.6763.5149.3650.6232.2252.4455.8534.2848.92
B2A [26]BERT66.2162.9248.9650.2231.1553.2756.2735.1649.11
IGV [22]+B2ABERT65.9262.1352.7753.4735.0050.6752.2931.2248.57
MCR+HCRNBERT68.6865.9755.4458.1837.6352.2452.3931.1750.86
MCR+B2ABERT67.4765.5956.4656.4237.8252.3954.0833.3851.06
", + "bbox": [ + 137, + 128, + 838, + 363 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "3D ResNeXt-101 [34] with the pre-trained model, respectively. For textual data, word token representation for questions and answers is provided by GloVe [28] and BERT [6] respectively, which greatly affects the performance of models [21]. MLP is implemented by fully connected layers, followed by Batch Normalization [16] and ReLU [11]. $\\lambda_{1}$ and $\\lambda_{2}$ are both set as 1. $K_{1}$ and $K_{2}$ are set as 1 and 3, respectively. During training, we use Adam optimizer with the initial learning rate of 1e-4 and halve the learning rate in every 5 epochs. The batch size is set as 128 in CausalVidQA dataset and 64 in NExT-QA dataset.", + "bbox": [ + 75, + 388, + 472, + 554 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Comparison with State-of-the-Arts", + "text_level": 1, + "bbox": [ + 76, + 571, + 387, + 588 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results on Causal-QA. Table 1 presents the results of four state-of-the-art baseline methods and one causal method on the Causal-VidQA dataset, including HME [8], HCRN [20], HGA [18], B2A [26], and IGV [22]. Compared to all existing VideoQA methods, MCR achieves the best performance across almost all types of questions. It is worth noting that MCR improves accuracy across all question types when using GloVe as the text model, which has an average performance improvement of $4.75\\%$ over B2A $(48.01\\%$ vs. $43.26\\%)$ . Compared with the IGV, MCR improves by $9.44\\%$ $(48.01\\%$ vs. $38.67\\%)$ . Our result is even comparable to the backbones of using BERT as a language model. When using BERT as the text model and B2A as the VideoQA backbone, MCR achieves an accuracy improvement of $1.85\\%$ on average. In counterfactual questions, it is difficult to answer the content of the associative question with limited knowledge learning from the dataset. Involving additional commonsense knowledge may be helpful. Experimentally, in the absence of commonsense knowledge, VideoQA backbones that rely on data bias can also achieve", + "bbox": [ + 75, + 598, + 472, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/e8b91d2874f7fbbfa8aeaa75cd9bb9d5e27c405fd3aa05964e28878869355570.jpg", + "table_caption": [ + "Table 2. Accuracies on NExT-VidQA of different architectures." + ], + "table_footnote": [], + "table_body": "
ModelsCausalTempDescripAll
HME [8]46.7648.8957.3749.16
HCRN [20]47.0749.2754.0248.82
HGA [18]48.1349.0857.7950.01
B2A [26]47.3749.0158.349.60
IGV [22]48.5651.6759.6451.34
MCR+B2A47.350.2561.2650.42
MCR+HGA49.1951.9862.2952.35
", + "bbox": [ + 540, + 398, + 857, + 526 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "good performance for counterfactual questions.", + "bbox": [ + 498, + 560, + 813, + 575 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Our proposed framework is in parallel with the VideoQA backbone that helps it discover the causal reason. To verify the effectiveness of the parallel strategy, we combine the MCR with different backbones, including HCRN [20] and B2A [26]. We can see that our method has remarkable effects on existing methods. This is due to previous methods being confused by confounders in multimodal data, resulting in poor generalization. Our MCR can effectively alleviate the biased modeling of these methods.", + "bbox": [ + 496, + 579, + 890, + 715 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results on NExT-QA. For further comparison, we evaluate our method on the NExT-QA dataset and report the evaluation results in Table 2. Compared with the baselines, our proposed MCR achieves the top performance in all question types. Specifically, when using B2A as the VideoQA backbone, our MCR is able to improve $0.82\\%$ on average accuracy. When combined with HGA, our MCR surpasses the previous backbone and causal method by clear margins, e.g. $2.34\\%$ and $1.01\\%$ higher than HGA and IGV, respectively. These validate that our multimodal causal reasoning indeed improves the robustness and generalization of baseline on causal reasoning dataset.", + "bbox": [ + 496, + 719, + 893, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "19033", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/91864b7a1c9ab1c39643460dde1383a2d71d959a7575173d7c0511576279e320.jpg", + "image_caption": [ + "Figure 6. Qualitative comparison on Causal dataset validation split. The green bold answer denotes the ground-truth one. The yellow arrows indicate that our method can improve the score of predictions by finding the causal association." + ], + "image_footnote": [], + "bbox": [ + 76, + 85, + 893, + 324 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 377, + 230, + 393 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/780da8eca87e4044bec2affcf6e2713fd231970fdad5f950b18effc38a0701fc.jpg", + "table_caption": [ + "Table 3. Performance comparisons of different variants on CausalQA dataset. \"MCRv\" and \"MCRt\" denote the visual causal module of MCR and the textual module of MCR, respectively." + ], + "table_footnote": [], + "table_body": "
MethodAcc-DAcc-EAcc-PAcc-CAcc
B2A66.2162.9231.1535.1649.11
B2A+MCRv67.7665.3835.5532.9550.41
B2A+MCRt68.5764.3833.7331.6149.57
B2A+MCR68.7265.0136.9233.2150.96
", + "bbox": [ + 89, + 454, + 460, + 537 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We analyze the effectiveness of different modules of MCR in Table 3. When adopting the visual causal module of MCR, we can achieve comparable improvements (1.30% on average), indicating that the visual indicator can change the co-occurrence relationship between irrelevant objects and labels, which improves the robustness of the model to visual data. With only MCR's text module, B2A improves by an average of 0.46%. This is because we eliminate the misleading of local language semantics attention. When adopting both causal modules for multimodal data, B2A+MCR achieves the best performance.", + "bbox": [ + 75, + 542, + 468, + 708 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/dab1ab370eb3b4b25e92d91c10ea1996d883137fa8e4f8e69e02d3aac966b340.jpg", + "table_caption": [ + "Table 4. The influence of hype-parameters of training pipeline on Causal-VideoQA Dataset." + ], + "table_footnote": [], + "table_body": "
k1/k21351/31/5
Acc46.6550.5849.5848.2346.37
", + "bbox": [ + 119, + 747, + 431, + 787 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Hyper-parameters. In this paper, we propose a causal intervention pipeline for multimodal data. Here, we conduct ablation studies on the hyper-parameters setting in Tab. 4. When we interact textual data every 3 epochs and video data every 1 epoch, MCR performs best on average accuracy. More Hyper-parameters about $\\lambda_{1},\\lambda_{2}$ and the ablation study of single loss function are shown in Supplementary.", + "bbox": [ + 75, + 794, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Qualitative Analysis", + "text_level": 1, + "bbox": [ + 498, + 377, + 692, + 395 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Fig. 6 shows the qualitative comparison between our MCR and B2A. Our MCR can reduce the scores of confusing candidates and enhance the confidence for the accurate answer. In the example on the left, B2A chooses the third answer because both the body pose of the human and the environment are related to \"lecture\". Our approach explicitly helps B2A reduce the influence of irrelevant factors and find the causal motion \"smoking\". In the right example, B2A is perturbed by the correlation between \"third\" in the text and the three bottles on the table in the video. According to the causal object selection, MCR effectively arrives at a lower score for it. These examples demonstrate that our model can perform real and generalizable reasoning.", + "bbox": [ + 496, + 401, + 893, + 598 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 603, + 619, + 619 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we revisit causal effects in multimodal data and propose a causal prediction architecture to model the causal association between video and text for the VideoQA task. Compared with previous methods, MCR can modify the distribution of data according to the backdoor adjustment and improve the robustness of the model. Considering limitations, our method intervenes in the textual data by word insertion. Some post-intervention examples express eccentric sentence structures that are easy to distinguish. Intervening the textual data with a reasonable text generator would be a reasonable future work. Besides, MCR cannot be directly adapted to the Video Story QA task in which most videos are human-human interactions rather than human-object interactions. Enhancing interventional operations for human instances may be another future work.", + "bbox": [ + 496, + 628, + 892, + 854 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement This research is supported by the National Natural Science Foundation of China (NSFC) (No. 61972038).", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "19034", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Martin Arjovsky, Léon Bottou, Ishaan Gulrajani, and David Lopez-Paz. Invariant risk minimization. arXiv preprint arXiv:1907.02893, 2019.", + "[2] Joao Carreira, Eric Noland, Chloe Hillier, and Andrew Zisserman. 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Advances" + ], + "bbox": [ + 78, + 90, + 468, + 900 + ], + "page_idx": 9 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "in Neural Information Processing Systems, 34:23634-23651, 2021.", + "[42] Kuo-Hao Zeng, Tseng-Hung Chen, Ching-Yao Chuang, Yuan-Hong Liao, Juan Carlos Niebles, and Min Sun. Leveraging video descriptions to learn video question answering. In Thirty-First AAAI Conference on Artificial Intelligence, 2017.", + "[43] Zhou Zhao, Jinghao Lin, Xinghua Jiang, Deng Cai, Xiaofei He, and Yueting Zhuang. Video question answering via hierarchical dual-level attention network learning. In Proceedings of the 25th ACM international conference on Multimedia, pages 1050-1058, 2017." + ], + "bbox": [ + 501, + 92, + 890, + 260 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "19036", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Discovering the Real Association_ Multimodal Causal Reasoning in Video Question Answering/f46331e4-a9e1-4fa6-843a-36c1e6734399_model.json b/2023/Discovering the Real Association_ Multimodal Causal Reasoning in Video Question Answering/f46331e4-a9e1-4fa6-843a-36c1e6734399_model.json new file mode 100644 index 0000000000000000000000000000000000000000..9fb2598359ab658f19f3f9d8f8cad8ba2dfc218b --- /dev/null +++ b/2023/Discovering the Real Association_ Multimodal Causal Reasoning in Video Question Answering/f46331e4-a9e1-4fa6-843a-36c1e6734399_model.json @@ -0,0 +1,2189 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.115, + 0.13, + 0.856, + 0.176 + ], + "angle": 0, + "content": "Discovering the Real Association: Multimodal Causal Reasoning in Video Question Answering" + }, + { + "type": "text", + "bbox": [ + 0.22, + 0.185, + 0.754, + 0.203 + ], + "angle": 0, + "content": "Chuanqi Zang\\(^{1}\\), Hanqing Wang\\(^{1}\\), Mingtao Pei\\(^{1}\\), Wei Liang\\(^{1,2*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.177, + 0.204, + 0.793, + 0.221 + ], + "angle": 0, + "content": "1School of Computer Science and Technology, Beijing Institute of Technology" + }, + { + "type": "text", + "bbox": [ + 0.187, + 0.222, + 0.785, + 0.239 + ], + "angle": 0, + "content": "\\(^{2}\\)Yangtze Delta Region Academy of Beijing Institute of Technology, Jiaxing" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.288, + 0.313, + 0.304 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.074, + 0.32, + 0.474, + 0.697 + ], + "angle": 0, + "content": "Video Question Answering (VideoQA) is challenging as it requires capturing accurate correlations between modalities from redundant information. Recent methods focus on the explicit challenges of the task, e.g. multimodal feature extraction, video-text alignment and fusion. Their frameworks reason the answer relying on statistical evidence causes, which ignores potential bias in the multimodal data. In our work, we investigate relational structure from a causal representation perspective on multimodal data and propose a novel inference framework. For visual data, question-irrelevant objects may establish simple matching associations with the answer. For textual data, the model prefers the local phrase semantics which may deviate from the global semantics in long sentences. Therefore, to enhance the generalization of the model, we discover the real association by explicitly capturing visual features that are causally related to the question semantics and weakening the impact of local language semantics on question answering. The experimental results on two large causal VideoQA datasets verify that our proposed framework 1) improves the accuracy of the existing VideoQA backbone, 2) demonstrates robustness on complex scenes and questions. The code will be released at https://github.com/Chuanqi-Zang/Discoverthe-Real-Association." + }, + { + "type": "title", + "bbox": [ + 0.079, + 0.718, + 0.21, + 0.734 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.744, + 0.47, + 0.88 + ], + "angle": 0, + "content": "Video Question Answering (VideoQA) aims to understand visual information and describe it in language question-answer format, which is a natural cognitive capability for humans. Computer Vision (CV) and Natural Language Processing (NLP) as the base models for VideoQA have shown significant progress due to the successful application of deep learning, such as action classification [25], object detection [10], instance segmentation [31], and large-scale pre-trained language model [6, 19]. These tremendous" + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.274, + 0.9, + 0.31 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.505, + 0.312, + 0.786, + 0.325 + ], + "angle": 0, + "content": "Question: What will happen if the power is cut off?" + }, + { + "type": "text", + "bbox": [ + 0.508, + 0.327, + 0.793, + 0.35 + ], + "angle": 0, + "content": "Answer: TV, indoor \\(\\rightarrow\\) singing karaoke" + }, + { + "type": "text", + "bbox": [ + 0.508, + 0.352, + 0.798, + 0.369 + ], + "angle": 0, + "content": "A. [person_1] will stop singing karaoke. Predict" + }, + { + "type": "text", + "bbox": [ + 0.508, + 0.37, + 0.798, + 0.384 + ], + "angle": 0, + "content": "B. [person_1] and [person_2] both cannot work. G.T." + }, + { + "type": "text", + "bbox": [ + 0.507, + 0.389, + 0.764, + 0.403 + ], + "angle": 0, + "content": "Question: What will happen if the girl sprains?" + }, + { + "type": "text", + "bbox": [ + 0.507, + 0.404, + 0.656, + 0.416 + ], + "angle": 0, + "content": "Answer: The girl will stop." + }, + { + "type": "text", + "bbox": [ + 0.507, + 0.42, + 0.753, + 0.444 + ], + "angle": 0, + "content": "Reason: Someone, help \\(\\rightarrow\\) Reason" + }, + { + "type": "image", + "bbox": [ + 0.781, + 0.392, + 0.849, + 0.43 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.506, + 0.446, + 0.895, + 0.474 + ], + "angle": 0, + "content": "A.There are a lot people here,and can find someone to help at any time. B.The girl can't exercise because of a sprain and needs to rest.G.T." + }, + { + "type": "text", + "bbox": [ + 0.842, + 0.436, + 0.886, + 0.449 + ], + "angle": 0, + "content": "Predict" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.483, + 0.892, + 0.539 + ], + "angle": 0, + "content": "Figure 1. Two samples in VideoQA dataset. They exhibit spurious reasoning processes of B2A [26] that rely on statistical patterns, including visually spurious object-relationship associations (top) and textually unilateral semantic representations (bottom)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.553, + 0.892, + 0.613 + ], + "angle": 0, + "content": "advances in basic applications fuel the confidence in fine-grained multimodal analysis and reasoning, not only feature extraction, but also fine-grained general causality estimation, which is critical for a robust cognitive system." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.893, + 0.84 + ], + "angle": 0, + "content": "Recent VideoQA methods usually explore multimodal relational knowledge by sophisticated structured architecture, such as memory-augmented model [9], hierarchical model [20], topological model [18], and transformer-based model [37]. Although experiments validate their feature fusion capabilities, we find that these methods concentrate on statistical association based on multimodal data, ignoring the real stable association. They usually use a generally constrained approach with Empirical Risk Minimization (ERM), which tends to over-rely on the co-occurrence bias of repeated objects and words in the collected observational data, and bypasses the impact of complete semantics at the sentence level. This mechanism reduces the robustness of the model on new data, even in the test set which has similar distributions to the training set." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "For example, as shown in Fig. 1 (top), two people are playing \"cricket\" indoors, and there are other objects in the room, including a TV that is on. If relying on the statistical relationship, the model may be confused by the two im" + }, + { + "type": "page_footnote", + "bbox": [ + 0.101, + 0.888, + 0.315, + 0.9 + ], + "angle": 0, + "content": "*Wei Liang is the corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19027" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.081, + 0.092, + 0.468, + 0.272 + ], + "angle": 0, + "content": "important visual factors of \"indoor\" and \"television\", and misjudge the concerned event, that is, \"sing karaoke\". Based on the clues provided by the question, the concerned event is related to the action that is taking place, e.g. \"two men playing cricket\". This requires the model to accurately judge the objects involved in the event and infer the answer. In Fig. 1 (bottom), we show the predicted deviation caused by statistical relationships in the text. When inferring the reasons for answer selection, existing models intensively rely on correlations between local words and video content, e.g. \"someone; help\", ignoring unreasonable inferences from other parts of the sentence, e.g. \"a lot\"." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.277, + 0.468, + 0.456 + ], + "angle": 0, + "content": "From these observations, we summarize two causal challenges for the VideoQA task. 1) Irrelevant objects confounder. The visual information related to the question is usually causally related to finite objects in the video. When other objects or background are considered, they are subject to data bias and become confounders, misleading the model to select the negative candidate. 2) Keywords confounder. The semantics expressed by textual information is represented by the overall sentence. Some long sentences contain partially sensible keywords. When just focusing on local keywords semantics, the model falls into spurious causal inferences, reducing the robustness of the model." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.461, + 0.468, + 0.882 + ], + "angle": 0, + "content": "To address the above causal challenges and improve the robustness of the model, we propose a Multimodal Causal Reasoning (MCR) framework for video-text data. In this framework, causal features and confounding features are decoupled separately in visual and textual modes through two training strategies. To explicitly decouple the influence of different objects and scenes, MCR extracts fine-gained object-level appearance features and motion dynamics by spatial Region of Interest (ROI) Align [13] on global visual features. Among them, causally related objects are selected based on the correlation between object features and question semantics. In addition to the visual feature, we also model object coordinate information, category information, and global object interaction information to provide spatio-temporal relation representations for accurate causal attribute classification. For textual confounders, we adopt a strategy to reduce the impact of keywords on causality. MCR relies on the correlation between word encoding and question-visual co-embedding to select keywords which have a crucial impact on the prediction results. These keywords provide negative representations for successive deductive answers. Therefore, we combine these keywords with other candidate answers to generate difficult negative samples to improve the recognition ability of the model. During training, visual intervention and textual intervention are iteratively optimized. Multimodal causal relationships are gradually established which improves the robustness and reusability of the model." + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.887, + 0.468, + 0.899 + ], + "angle": 0, + "content": "We summarize our contributions as: (1) We discover two" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.092, + 0.89, + 0.196 + ], + "angle": 0, + "content": "new types of causal challenges for both visual data and textual data. (2) We propose an object-level causal relationship extraction strategy to establish the real association between objects and language semantics, and a keyword broadcasting strategy to cut off the spurious influence of local textual information. (3) We achieve state-of-the-art performance on two latest large causal VideoQA datasets." + }, + { + "type": "title", + "bbox": [ + 0.504, + 0.212, + 0.64, + 0.227 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.236, + 0.89, + 0.537 + ], + "angle": 0, + "content": "Video Question Answering (VideoQA). In early works, the long-term dependency features in video and text were extracted by RNN-based modules, and then were fused by element-wise multiplication [42, 43] with attention mechanism [35]. Considering the implicit interaction in multimodal data, Jiang et al. [18] proposed a heterogeneous graph convolution-based network for crossmodal fusion. Park et al. [26] enhanced crossmodal graphs by a bridged visual-to-visual interactions structure. Huang et al. [15] improved graph interaction reasoning at the fine-grained object level. Dang et al. [5] explored the symbol-like manipulable reasoning by a hierarchically nested spatio-temporal graph. Benefited from the pre-trained language-based transformer [6] and video-text-alignment transformer [37, 41], current works [24, 38] can fine-tune the pre-trained model and show remarkable feature extraction ability and cross-model aligning ability. However, these methods ignore the potential bias distribution in the data. While improving the ability of feature extraction and alignment, they introduce confounders that lead to poor generalization." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.539, + 0.89, + 0.779 + ], + "angle": 0, + "content": "Causal learning. Except for representation learning, recent work found that causal reasoning in data is meaningful for VideoQA. In the synthetic dataset [39], inspired by neural-symbolic method [40] for the ImageQA task, some work [4,7,39] explicitly represent the appearance information and physical information of each object in the scene. To investigate the causal modeling ability of models in real life, recent datasets [21, 36, 39] asked questions about behavior causality in addition to descriptive questions. For some common-sense causal knowledge that is not represented in the videos, Chadha et al. [3] proposed a knowledge base as additional guidance. To find clues of causal associations, Xu et al. [36] proposed to dynamically select the frame from the past or future. The same in frame level, Li et al. [22] explored invariant learning [1] to distinguish question-irrelevant scenes." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.781, + 0.89, + 0.9 + ], + "angle": 0, + "content": "In real-life scenes, videos contain redundant object information. Since lacking human annotations, frequently occurring objects are introduced as confounders, which bring more complex spurious guidance for video understanding than rough frame-level background snippets. In addition, in texts involving causal reasoning, some phrases are also prone to become confounders. This paper will unify the analysis of causal inference on multimodal data." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.947, + 0.518, + 0.957 + ], + "angle": 0, + "content": "19028" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.179, + 0.089, + 0.372, + 0.198 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.211, + 0.473, + 0.351 + ], + "angle": 0, + "content": "Figure 2. Causal formulation of VideoQA. Gray variables are observed data. V is a specific video and S is a specific sentence. D represents the data domain determined by the collected dataset. It causes the co-occurring of objects in video V, various words in sentence S, and answer label Y. The ideal causal inference is that model extracts video event features \\( E_{v} \\) from videos and text event features \\( E_{s} \\) from words. Then it integrates different modal event representations and filters out the event of interest \\( E \\) for answer selection Y. Here, we provide the backdoor adjustment from D to V and from D to S, which produces our MCR architecture." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.377, + 0.168, + 0.391 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.403, + 0.305, + 0.419 + ], + "angle": 0, + "content": "3.1. Formulation of VideoQA" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.428, + 0.47, + 0.563 + ], + "angle": 0, + "content": "Causal Preliminaries. We formalize cross-modal causality for the VideoQA task via a Structure Causal Model [27]. In Fig. 2, we represent the key factors in the VideoQA task as components in the causal graph, and represent the relationships between factors as connecting links that are built by current models [18,23,26,33] as default, including data domain D, video V, sentence S, label Y, visual event features \\( E_{v} \\), and textual event features \\( E_{s} \\), alignment events \\( E \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.566, + 0.47, + 0.746 + ], + "angle": 0, + "content": "\\(V \\rightarrow E_v \\rightarrow E \\leftarrow E_s \\leftarrow S\\) denotes feature extraction and alignment of multimodal data. \\(E_v\\) and \\(E_s\\) represent the complete events feature extracted from the video and sentence, respectively. In visual domain, pre-trained feature extraction models extract different objects and interactions as events. In textual domain, pre-trained models represent linguistic concepts in stages as events according to punctuation and connectives. \\(E_v \\rightarrow E \\leftarrow E_s\\) represents multimodal event selection and alignment. The deep model references language events to select video events of interest. Then it aligns event representations and infers a unified event representation \\(E\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.748, + 0.47, + 0.839 + ], + "angle": 0, + "content": "\\(E \\to Y\\) represents the direct causal effect from the unified feature of the concerned event to the label, which is an ideal way that remains invariant in other data D with different data distributions. For example, \"play cricket\" is causally related to cricket bat and swing, and irrelevant to \"indoor\" and \"outdoor\"." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.47, + 0.902 + ], + "angle": 0, + "content": "\\(V \\gets D \\to Y\\) denotes that the data domain \\(D\\) as a confounder provides a spurious shortcut from video \\(V\\) to label \\(Y\\) in the visual domain. Specifically, the data domain \\(D\\) represents the statistical relationships contained in the lim" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.152 + ], + "angle": 0, + "content": "ited collected video data to represent the co-occurrence of objects and labels. In the top example in Fig. 1, \"TV\" and \"indoor\" provide the shortcut connection that is identified as \"karaoke\" because of lacking human interaction event." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.152, + 0.892, + 0.287 + ], + "angle": 0, + "content": "\\(S \\gets D \\to Y\\) denotes that the data domain \\(D\\) also establishes spurious associations between sentence \\(S\\) and label \\(Y\\). This is reflected in the fact that the model is easy to establish the association between labels and local concerned expressions of sentences while ignoring the overall expressions. Especially in multiple-choice questions, the model shows a stronger preference for the local \"key\" representation. For example, in the below example in Fig. 1, the model selects the locally correct answer, \"someone\" and \"help\"." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.288, + 0.892, + 0.455 + ], + "angle": 0, + "content": "Causal Intervention. The well-known backdoor adjustment [27] helps in eliminating spurious correlations, resulting in better generalization for the model. We present the true causality from V and S to Y as \\( P(Y|do(V,S)) \\), where \\( do() \\) denotes the interventional operation. \\( P(Y|do(V,S)) \\) can cut off the link \\( D\\to V \\) and \\( D\\rightarrow S \\) to block this backdoor path by changing the original training data into new data \\( \\mathcal{T} = \\{\\tau_1,\\dots,\\tau_h\\} \\). Each of them donates a confounder stratum (total \\( h \\)), guiding the model to find invariants from the confounder. The backdoor adjustment can be represented as:" + }, + { + "type": "equation", + "bbox": [ + 0.542, + 0.465, + 0.891, + 0.569 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} P \\left(Y \\mid d o (V, S)\\right) = \\sum_ {\\tau \\in \\mathcal {T}} P (Y | V, S, \\tau) P (\\tau) \\\\ = \\sum_ {\\tau_ {v} \\in \\mathcal {T} _ {v}} P (Y | V, \\tau_ {v}) P (\\tau_ {v}) \\tag {1} \\\\ + \\sum_ {\\tau_ {s} \\in \\mathcal {T} _ {s}} P (Y | S, \\tau_ {s}) P (\\tau_ {s}) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.58, + 0.892, + 0.841 + ], + "angle": 0, + "content": "where \\(P(Y|V,S,\\tau)\\) denotes the prediction in each new data split \\(\\tau\\). \\(P(\\tau)\\) denotes confounder selection probability for a specific video and sentence, calculated by \\(P(\\tau) \\coloneqq \\frac{1}{h}\\). We calculate probability estimates separately by two individual architectures for video and text. In this way, the interaction cuts off the confounder effect in \\(V \\gets D \\to Y\\) and \\(S \\gets D \\to Y\\) as shown in Fig. 2. Take video data as an example, traversing all the confounders for a video is expensive. When the video number in the dataset is \\(\\mathcal{M}\\), Eq. 1 expands the training data from \\(\\mathcal{M}\\) to \\(\\mathcal{M}^2\\) within one epoch with additional memory consumption. Therefore, to balance the scale of confounder set \\(\\mathcal{T}_v\\) and training speed, we find the confounder by our MCR and combine it with original data V every epoch. After \\(K\\) training epochs, we can approximate the visual part of the adjustment equation, i.e. \\(\\sum_{\\tau_v \\in \\mathcal{T}_v} P(Y|V, \\tau_v) P(\\tau_v) \\approx \\sum_{k=1}^{K} \\sum_{\\tau_v \\in \\mathcal{T}_v^k} P(Y|V, \\tau_v) P(\\tau_v)\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.841, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Preliminary. Given a video \\( I \\), VideoQA aims to understand acting events by asking questions \\( q \\) and predict the correct answer \\( \\widetilde{a} \\) from a answer candidate set \\( A = \\{a_{z}\\}_{z=1}^{Z} \\). \\( Z \\) is the candidate number. The process is generally formu" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19029" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.088, + 0.895, + 0.379 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.392, + 0.893, + 0.476 + ], + "angle": 0, + "content": "Figure 3. Visual Causal Module. Before the appearance information and motion information are sent to the backbone for question answering, we propose a visual causal module to find object-level causal features and irrelevant features in video data. The image-level visual features are first divided into object-level visual features by the detected bounding box. The category information, location information and interaction relationship of each object are modeled by Interaction Detector. According to the question prompt, the Indicator judges whether the features of different objects are causally related or irrelevant. The uniform representation of causal and irrelevant features are used for further prediction in the VideoQA backbone." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.5, + 0.19, + 0.513 + ], + "angle": 0, + "content": "lated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.186, + 0.521, + 0.469, + 0.547 + ], + "angle": 0, + "content": "\\[\n\\widetilde {a} = \\underset {a \\in A} {\\operatorname {a r g m a x}} \\mathcal {F} _ {\\theta} (a | q, I), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.555, + 0.47, + 0.63 + ], + "angle": 0, + "content": "where \\(\\theta\\) represents the set of model parameters of VideoQA function \\(\\mathcal{F}\\), which maps a pair of video and question into the same feature domain to find the answer. In our work, we do not change the VideoQA function \\(\\mathcal{F}\\). In a causal view, we intervene video \\(I\\) and answer candidate A." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.639, + 0.284, + 0.654 + ], + "angle": 0, + "content": "3.2. Visual Causal Module" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.663, + 0.47, + 0.872 + ], + "angle": 0, + "content": "To answer the question with accurate causally related features, we propose a visual causal module that disentangles the confounder and causal factors at the object level. As shown in Fig. 3, the video with shape \\( W \\times H \\times L \\) is encoded by 2D ConvNet, 3D ConvNet into a list of appearance feature and motion feature with shape \\( \\frac{W}{16} \\times \\frac{H}{16} \\times \\frac{L}{2} \\). They are uniformly represented by frame feature sequence \\( \\mathcal{V} = \\{v_t\\}_{t=1}^{\\frac{L}{2}} \\), where \\( t \\) means timestamp. The object-level grounding is detected by pre-trained Detection ConvNet and donated as the bounding box \\( \\mathcal{B} = \\{b_{n,t}\\}_{n=1,t=1}^{N,\\frac{L}{2}} \\), where \\( N \\) is the detected object number. We use Region of Interest (ROI) Align [13] to extract object visual features \\( \\mathcal{O} = \\{o_{n,t}\\}_{n=1,t=1}^{N,\\frac{L}{2}} \\), expressed as \\( \\mathcal{O} = ROIAlign(\\mathcal{V}|\\mathcal{B}) \\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.872, + 0.469, + 0.902 + ], + "angle": 0, + "content": "Since the scene in the real video is ever-changing, some objects in the video may suddenly disappear or appear, mak" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.5, + 0.892, + 0.574 + ], + "angle": 0, + "content": "ing it difficult to obtain accurate instance tracking data. Therefore, we extract unified features for the same category of targets, e.g. human, chairs. When objects of this category do not appear in part of the consecutive frames, we fill the feature with 0 value." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.575, + 0.892, + 0.621 + ], + "angle": 0, + "content": "For each object feature, we employ Multilayer Perceptrons (MLP) and Long short-term memory (LSTM) [12] to encode the temporal embedding for visual feature:" + }, + { + "type": "equation", + "bbox": [ + 0.604, + 0.63, + 0.891, + 0.647 + ], + "angle": 0, + "content": "\\[\n\\mathcal {O} ^ {g} = L S T M (M L P (\\mathcal {O})), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.655, + 0.892, + 0.76 + ], + "angle": 0, + "content": "where \\(\\mathcal{O}^g = \\{o_n^g\\}_{n=1}^N \\in \\mathbb{R}^d\\) is the global N object representations, and \\(d\\) is the hidden dimension of LSTM. In addition to the visual encoding, we also model the bounding box position correlations \\(\\mathcal{B}\\), object category \\(C\\), and spatiotemporal inter-object and intra-object interactions in an Interaction Detecting stream. They are implemented by Non-local Net [30] with MLP:" + }, + { + "type": "equation", + "bbox": [ + 0.528, + 0.77, + 0.891, + 0.787 + ], + "angle": 0, + "content": "\\[\nL ^ {g} = \\operatorname {N o n L} \\left(M L P \\left(M L P (\\mathcal {B}); M L P (C)\\right)\\right), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.901 + ], + "angle": 0, + "content": "where; represents channel concatenation. \\(L^{g} = \\{l_{n}^{g}\\}_{n = 1}^{N}\\in\\) \\(\\mathbb{R}^d\\) means detected interaction feature. The outputs of two feature extraction streams are then fused by channel concatenation: \\(\\mathcal{O}^g = [\\mathcal{O}^g;L^g ]\\) . All objects are causal or irrelevant candidates. Their identities are determined by the language semantics of the question. Therefore, given a question sentence, we apply Word Parser and Event Embedding" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19030" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.122 + ], + "angle": 0, + "content": "to get the global question representation \\( q^g \\). The Event Embedding is implemented by LSTM:" + }, + { + "type": "equation", + "bbox": [ + 0.181, + 0.135, + 0.469, + 0.152 + ], + "angle": 0, + "content": "\\[\nq ^ {g} = L S T M (P a r s e r (q)), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.163, + 0.47, + 0.39 + ], + "angle": 0, + "content": "where Parser uses a pre-trained GloVe model [28] or BERT model [6]. LSTM is implemented by the question embedding model of the VideoQA backbone. With the specific question, causally related objects are usually a small part of object set \\(\\mathcal{O}^g\\) and are interconnected internally. Reasoning about their relationship to unrelated objects is redundant and prone to spurious associations. Therefore, inspired by [22], we use hard segmentation [22] in Indicator to explicitly divide object features into causally related features and irrelevant features, rather than soft GCN inference or attention-based models. Specifically, the question embedding \\(q^{g}\\) and objects feature \\(\\mathcal{O}^g\\) are mapped into the same space by MLP. The Indicator computes a score for each object feature and uses Gumbel-Softmax [17] to classify the causal attribute labels of objects:" + }, + { + "type": "equation", + "bbox": [ + 0.124, + 0.401, + 0.47, + 0.427 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {O} ^ {c} = G S (M L P (q ^ {g}) \\cdot (M L P (\\mathcal {O} ^ {g}) ^ {T})) \\circ \\mathcal {O}, \\\\ \\mathcal {O} ^ {\\bar {c}} = \\mathcal {O} - \\mathcal {O} ^ {c} \\end{array} \\tag {6}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.128, + 0.422, + 0.23, + 0.437 + ], + "angle": 0, + "content": "\\[\n\\mathcal {O} ^ {\\bar {c}} = \\mathcal {O} - \\mathcal {O} ^ {c},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.45, + 0.469, + 0.57 + ], + "angle": 0, + "content": "where GS means Gumbel-Softmax and \\(\\cdot\\) means matrix multiplication. \\(\\circ\\) means multiply by index. \\(\\mathcal{O}^c = \\{o_n^c\\}_{n^c = 1}^{N^c},\\mathcal{O}^{\\bar{c}} = \\{o_{n^{\\bar{c}}}^{\\bar{c}}\\}_{n^{\\bar{c}} = 1}^{N^{\\bar{c}}}\\) are causal object features set and irrelevant features set, respectively, where the corner mark of length is omitted for clarity. We average the features in these sets to obtain causal visual features and irrelevant visual features, respectively: \\(\\mathcal{V}^c = \\frac{1}{N^c}\\sum \\mathcal{O}^c,\\) \\(\\mathcal{V}^{\\bar{c}} = \\frac{1}{N^{\\bar{c}}}\\sum \\mathcal{O}^{\\bar{c}}.\\)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.571, + 0.469, + 0.661 + ], + "angle": 0, + "content": "According to the deduction of Eq. 1, in the visual part, the video V and the average sampling confounder are combined to predict the label. In model designing, the video V can be present by causal object features \\(\\nu^{c}\\). The confounder is from the confounder of another example in the same mini-batch, represented by:" + }, + { + "type": "equation", + "bbox": [ + 0.163, + 0.672, + 0.469, + 0.703 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathcal {V}} = \\frac {1}{N ^ {c} + N ^ {\\prime \\bar {c}}} \\sum \\left(O ^ {c} + O ^ {\\prime \\bar {c}}\\right), \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.715, + 0.469, + 0.807 + ], + "angle": 0, + "content": "where \\(\\hat{\\mathcal{V}}\\) is the blended features. \\(O^{\\prime\\bar{c}}\\) is the confounder of another example. \\(N^{\\prime\\bar{c}}\\) is the object number of \\(O^{\\prime\\bar{c}}\\). Both \\(\\mathcal{V}\\), \\(\\mathcal{V}^{c}\\), \\(\\mathcal{V}^{\\bar{c}}\\), and \\(\\hat{\\mathcal{V}}\\) are sent to the VideoQA backbone for training the visual causal module. The visual module can capture causal relationships between object features and labels, providing a stable association for multimodal data." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.817, + 0.292, + 0.832 + ], + "angle": 0, + "content": "3.3. Textual Causal Module" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.84, + 0.469, + 0.901 + ], + "angle": 0, + "content": "For textual causal inference, prediction is often plagued by correlations between local language semantics and visual features. Therefore, the key to getting rid of text confounders is to enhance the model's ability to recognize" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.088, + 0.892, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.22, + 0.892, + 0.263 + ], + "angle": 0, + "content": "Figure 4. Textual Causal Module. Keywords are selected as confounders from the prediction results by the indicator. They are sent to the intervenor to generate new candidates." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.285, + 0.891, + 0.314 + ], + "angle": 0, + "content": "such confusing samples which are implemented by a textual causal module." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.315, + 0.892, + 0.421 + ], + "angle": 0, + "content": "In the VideoQA base model, the visual information and the question have been aligned, containing the events information related to the answer. Therefore, we use the alignment feature \\( f_{qv} = \\mathcal{F}(\\mathcal{V}^c, q^g) \\) to retrieve the keywords in the answer. As shown in Fig. 4, the same with question embedding, we encode the answer by Word Parser and Event Embedding:" + }, + { + "type": "equation", + "bbox": [ + 0.592, + 0.43, + 0.891, + 0.447 + ], + "angle": 0, + "content": "\\[\na ^ {g}, a ^ {l} = L S T M (P a r s e r (a)), \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.457, + 0.891, + 0.519 + ], + "angle": 0, + "content": "where \\( a^g \\) is the global representation of the answer, and \\( a^l \\) is the local representation of each word. The same with visual Indicator, we select the keyword by the relation score between \\( a^g \\) and \\( f_{qv} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.548, + 0.526, + 0.891, + 0.544 + ], + "angle": 0, + "content": "\\[\na ^ {\\bar {c}} = G S \\left(M L P \\left(f _ {q v}\\right) \\cdot \\left(M L P \\left(a ^ {g}\\right)\\right) ^ {T}\\right) \\circ a ^ {l}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.552, + 0.891, + 0.596 + ], + "angle": 0, + "content": "where \\( a^{\\bar{c}} \\) represents the keywords, which are potential confounders in this question. \\( a^{c} = a^{l} - a^{\\bar{c}} \\) represents other words." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.598, + 0.891, + 0.702 + ], + "angle": 0, + "content": "According to the textual part of Eq. 1, the label is predicted by the sentence and confounder. Due to the correlation between sentences and videos, we look for confounders of sentences from the same video, especially the predicted answer by VideoQA backbone which contains factors that increase the score. Similar to visual intervention, we pick confounders once per epoch." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.703, + 0.892, + 0.807 + ], + "angle": 0, + "content": "Confounders are used to augment the hard sample of candidates that changes the textual distributions. The model joint original candidates \\( A = \\{a_{z}\\}_{z=1}^{Z} \\) with \\( a^{\\bar{c}} \\) by inserting \\( a^{\\bar{c}} \\) at the beginning or end of a sentence and generate a new candidates set \\( \\hat{A} = \\{\\hat{a}_{z}\\}_{z=1}^{Z} \\). In the training process, we randomly replace the negative example from the new candidates set \\( \\hat{A} \\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.818, + 0.604, + 0.833 + ], + "angle": 0, + "content": "3.4. Training" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.841, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In this section, we introduce our training targets and training pipeline for multimodal data. The algorithm can be found in Supplementary. First of all, to ensure the domain consistency of training sets and test sets, we train" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "19031" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.135 + ], + "angle": 0, + "content": "the VideoQA backbone with raw data \\((\\mathcal{V},\\mathrm{A})\\) , which also guarantees that the training process satisfies the pre-defined causal formulation:" + }, + { + "type": "equation", + "bbox": [ + 0.158, + 0.146, + 0.469, + 0.163 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {o} = \\mathrm {X E} \\left(\\mathcal {F} \\left((\\mathcal {V}, \\mathrm {q}), (\\mathcal {V}, \\mathrm {A})\\right), \\mathrm {a}\\right), \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.171, + 0.469, + 0.246 + ], + "angle": 0, + "content": "where XE is the cross-entropy loss. \\(\\mathcal{F}\\) calculates the dot-product between question-related visual features and answer-related visual features as the predicted results. At test time, we use the candidate with the highest score as the predicted result as in Eq.2." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.247, + 0.469, + 0.397 + ], + "angle": 0, + "content": "Visual Module Loss. Visual module loss aims to capture causal object features and non-causal object features for further robust prediction. In the training stage, the causal visual features have the same ability for question answering, which is restricted by the cross-entropy loss: \\(\\mathcal{L}_{\\mathrm{c}}^{\\mathrm{v}}\\). In contrast, non-causal objects are irrelevant to the question and should be unbiased toward answer candidates: \\(\\mathcal{L}_{\\bar{c}}^{\\mathrm{v}}\\). The blended data \\(\\hat{\\nu}\\) are supposed to obtain the same effect with causal feature: \\(\\mathcal{L}_o^{\\mathrm{v}}\\). The formulation of visual module loss shows as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.133, + 0.403, + 0.372, + 0.42 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {c}} ^ {\\mathrm {v}} = \\operatorname {X E} \\left(\\mathcal {F} \\left(\\left(\\mathcal {V} ^ {\\mathrm {c}}, \\mathrm {q}\\right), \\left(\\mathcal {V} ^ {\\mathrm {c}}, \\mathrm {A}\\right)\\right), \\mathrm {a}\\right)\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.133, + 0.422, + 0.469, + 0.449 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\bar {c}} ^ {\\mathrm {v}} = \\operatorname {M S E} \\left(\\mathcal {F} \\left(\\left(\\mathcal {V} ^ {\\bar {c}}, \\mathrm {q}\\right), \\left(\\mathcal {V} ^ {\\bar {c}}, \\mathrm {A}\\right)\\right), \\text {a v g}\\right) \\tag {11}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.133, + 0.446, + 0.352, + 0.462 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\hat {\\partial}} ^ {\\mathrm {v}} = \\operatorname {X E} (\\mathcal {F} ((\\hat {\\mathcal {V}}, q), (\\hat {\\mathcal {V}}, A)), a),\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.135, + 0.465, + 0.281, + 0.481 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {v}} = \\mathcal {L} _ {\\mathrm {c}} ^ {\\mathrm {v}} + \\mathcal {L} _ {\\bar {c}} ^ {\\mathrm {v}} + \\mathcal {L} _ {\\hat {o}} ^ {\\mathrm {v}},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.489, + 0.469, + 0.533 + ], + "angle": 0, + "content": "where avg is the average score of all candidates, avg = \\(\\mathcal{F}((\\mathcal{V},q),(\\mathcal{V},A))\\) . MSE means Mean Square Error for non-causal objects to get a neutral score." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.535, + 0.469, + 0.655 + ], + "angle": 0, + "content": "Textual Module Loss. The text module loss aims to find keywords from the prediction results that directly affect the model selection and reduce the sensitivity of the model to keywords. Intuitively, keywords have the ability for prediction, while other words are difficult to judge the results. We use cross-entropy loss for keywords \\(\\mathcal{L}_{\\mathrm{c}}^{\\mathrm{s}}\\) and MSE for other words \\(\\mathcal{L}_{\\mathrm{c}}^{\\mathrm{s}}\\). The blended answer is restricted by the cross-entropy loss \\(\\mathcal{L}_{\\hat{o}}^{\\mathrm{s}}\\). The formulation of textual module loss is:" + }, + { + "type": "equation", + "bbox": [ + 0.146, + 0.665, + 0.376, + 0.684 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\bar {c}} ^ {\\mathrm {s}} = \\mathrm {X E} \\left(\\mathcal {F} \\left((\\mathcal {V}, \\mathrm {q}), (\\mathcal {V}, a ^ {\\bar {c}})\\right), \\mathrm {a}\\right)\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.149, + 0.685, + 0.469, + 0.709 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {c}} ^ {\\mathrm {s}} = \\operatorname {M S E} \\left(\\mathcal {F} \\left(\\left(\\mathcal {V}, \\mathrm {q}\\right), \\left(\\mathcal {V}, a ^ {\\mathrm {c}}\\right)\\right), a v g\\right) \\tag {12}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.149, + 0.706, + 0.358, + 0.723 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\hat {\\theta}} ^ {\\mathrm {s}} = \\operatorname {X E} (\\mathcal {F} ((\\mathcal {V}, q), (\\mathcal {V}, \\hat {A})), a)\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.15, + 0.726, + 0.29, + 0.742 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {s}} = \\mathcal {L} _ {\\mathrm {c}} ^ {\\mathrm {s}} + \\mathcal {L} _ {\\bar {\\mathrm {c}}} ^ {\\mathrm {s}} + \\mathcal {L} _ {\\delta} ^ {\\mathrm {s}}.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.746, + 0.41, + 0.761 + ], + "angle": 0, + "content": "The overall loss of our model can be expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.186, + 0.77, + 0.469, + 0.786 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {o} + \\lambda_ {1} \\mathcal {L} _ {\\mathrm {v}} + \\lambda_ {2} \\mathcal {L} _ {\\mathrm {s}}, \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.469, + 0.824 + ], + "angle": 0, + "content": "where \\(\\lambda_{1}\\) and \\(\\lambda_{2}\\) are the hyper-parameters to balance the visual loss and textual loss." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Intervene Pipeline. We show the Intervene pipeline in Fig. 5. The textual intervention and the visual intervention are accomplished in two steps. Visual causal loss is computed with Eq. 11 and used to obtain causally related object features and irrelevant object features. They are used" + }, + { + "type": "image", + "bbox": [ + 0.545, + 0.089, + 0.852, + 0.173 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.58, + 0.187, + 0.81, + 0.202 + ], + "angle": 0, + "content": "Figure 5. Causal intervention pipeline." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.227, + 0.892, + 0.332 + ], + "angle": 0, + "content": "to generate blended visual data with an intervenor, which is implemented by Eq. 7. Textual causal loss is computed with Eq. 12 and used to obtain keywords. Keywords are sent to textual interveners to generate blended textual data. We execute \\( K_{2} \\) epochs textual interventions after executing \\( K_{1} \\) epochs visual interventions for the visual causal module and the textual causal module." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.348, + 0.624, + 0.365 + ], + "angle": 0, + "content": "4. Experiment" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.374, + 0.594, + 0.388 + ], + "angle": 0, + "content": "4.1. Dataset" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.397, + 0.892, + 0.533 + ], + "angle": 0, + "content": "We evaluate our Multimodal Causal Reasoning (MCR) framework on two recent large causal-related VideoQA datasets: Causal-VidQA [21] and NExT-QA [32]. In these datasets, models need to answer not only simple descriptive or statistical questions but also implicit global evidence reasoning. The collected video data is close to the real open scene, including a variety of objects and interactive actions. Answer candidates are sentences with different expression structures and are not limited to a single sentence." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.534, + 0.892, + 0.669 + ], + "angle": 0, + "content": "The Causal-VidQA dataset selects 26,900 video clips from Kinetics-700 [2] and asks 107,600 questions, including description, explanation, prediction, and counterfactual questions. Each question has 5 answers, with 5 more reasons in predictions and counterfactuals. For question-answer accuracies, we adopt the previous causal VideoQA evaluation metrics [21] that report accuracy for each question type, as well as the accuracy of the consistency between answers and reasons." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.67, + 0.892, + 0.746 + ], + "angle": 0, + "content": "NExT-QA dataset contains 5,440 videos from VidOR [29] and proposes 47,692 questions for the multichoice task, including description, explanation, and temporal reasoning questions. We also report accuracy for each question type." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.757, + 0.707, + 0.773 + ], + "angle": 0, + "content": "4.2. Experimental Settings" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We use a unified feature extraction method for both datasets. Each video with varying length is divided into 8 clips, each containing 16 frames. For the object-level motion feature, we uniformly sample from the frame-level appearance features and clip-level motion features by ROI Align [13]. The bounding boxes in each frame are extracted by pre-trained Mask R-CNN [13]. The appearance features and motion features are extracted by ResNet-101 [14] and" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19032" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.087, + 0.895, + 0.129 + ], + "angle": 0, + "content": "Table 1. Comparison of accuracy with state-of-the-art methods on Causal-VidQA dataset. D means description question. E means explanation question. P means prediction question. C means counterfactual question. QA means to answer the answer. QR means to answer the reason. QAR means the answer and reason are both accurate." + }, + { + "type": "table", + "bbox": [ + 0.138, + 0.13, + 0.839, + 0.364 + ], + "angle": 0, + "content": "
MethodText FeatureAcc-DAcc-EQAAcc-P QRQARQAAcc-C QRQARAcc
HME [8]GloVe47.2543.8041.0242.5323.2535.2934.1915.3432.41
HCRN [20]GloVe58.8953.5343.1445.0726.1743.6943.4722.7540.33
HGA [18]GloVe60.3255.0246.5547.2128.5344.0044.0423.6341.88
B2A [26]GloVe61.2956.4346.8248.1730.0145.1244.9925.2943.26
IGV [22]+B2AGloVe59.2448.4145.7047.3228.2038.9940.9718.8438.67
MCR+B2AGloVe66.7261.2650.4652.1732.1352.1751.5031.9148.01
HME [8]BERT63..3661.4550.2947.5628.9250.38.51.6530.9346.16
HCRN [20]BERT65.3561.6151.7451.2632.5751.5753.4432.6648.05
HGA [18]BERT65.6763.5149.3650.6232.2252.4455.8534.2848.92
B2A [26]BERT66.2162.9248.9650.2231.1553.2756.2735.1649.11
IGV [22]+B2ABERT65.9262.1352.7753.4735.0050.6752.2931.2248.57
MCR+HCRNBERT68.6865.9755.4458.1837.6352.2452.3931.1750.86
MCR+B2ABERT67.4765.5956.4656.4237.8252.3954.0833.3851.06
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.389, + 0.473, + 0.555 + ], + "angle": 0, + "content": "3D ResNeXt-101 [34] with the pre-trained model, respectively. For textual data, word token representation for questions and answers is provided by GloVe [28] and BERT [6] respectively, which greatly affects the performance of models [21]. MLP is implemented by fully connected layers, followed by Batch Normalization [16] and ReLU [11]. \\(\\lambda_{1}\\) and \\(\\lambda_{2}\\) are both set as 1. \\(K_{1}\\) and \\(K_{2}\\) are set as 1 and 3, respectively. During training, we use Adam optimizer with the initial learning rate of 1e-4 and halve the learning rate in every 5 epochs. The batch size is set as 128 in CausalVidQA dataset and 64 in NExT-QA dataset." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.573, + 0.388, + 0.589 + ], + "angle": 0, + "content": "4.3. Comparison with State-of-the-Arts" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Results on Causal-QA. Table 1 presents the results of four state-of-the-art baseline methods and one causal method on the Causal-VidQA dataset, including HME [8], HCRN [20], HGA [18], B2A [26], and IGV [22]. Compared to all existing VideoQA methods, MCR achieves the best performance across almost all types of questions. It is worth noting that MCR improves accuracy across all question types when using GloVe as the text model, which has an average performance improvement of \\(4.75\\%\\) over B2A \\((48.01\\%\\) vs. \\(43.26\\%)\\). Compared with the IGV, MCR improves by \\(9.44\\%\\) \\((48.01\\%\\) vs. \\(38.67\\%)\\). Our result is even comparable to the backbones of using BERT as a language model. When using BERT as the text model and B2A as the VideoQA backbone, MCR achieves an accuracy improvement of \\(1.85\\%\\) on average. In counterfactual questions, it is difficult to answer the content of the associative question with limited knowledge learning from the dataset. Involving additional commonsense knowledge may be helpful. Experimentally, in the absence of commonsense knowledge, VideoQA backbones that rely on data bias can also achieve" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.385, + 0.877, + 0.399 + ], + "angle": 0, + "content": "Table 2. Accuracies on NExT-VidQA of different architectures." + }, + { + "type": "table", + "bbox": [ + 0.541, + 0.4, + 0.859, + 0.527 + ], + "angle": 0, + "content": "
ModelsCausalTempDescripAll
HME [8]46.7648.8957.3749.16
HCRN [20]47.0749.2754.0248.82
HGA [18]48.1349.0857.7950.01
B2A [26]47.3749.0158.349.60
IGV [22]48.5651.6759.6451.34
MCR+B2A47.350.2561.2650.42
MCR+HGA49.1951.9862.2952.35
" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.561, + 0.814, + 0.576 + ], + "angle": 0, + "content": "good performance for counterfactual questions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.58, + 0.892, + 0.716 + ], + "angle": 0, + "content": "Our proposed framework is in parallel with the VideoQA backbone that helps it discover the causal reason. To verify the effectiveness of the parallel strategy, we combine the MCR with different backbones, including HCRN [20] and B2A [26]. We can see that our method has remarkable effects on existing methods. This is due to previous methods being confused by confounders in multimodal data, resulting in poor generalization. Our MCR can effectively alleviate the biased modeling of these methods." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Results on NExT-QA. For further comparison, we evaluate our method on the NExT-QA dataset and report the evaluation results in Table 2. Compared with the baselines, our proposed MCR achieves the top performance in all question types. Specifically, when using B2A as the VideoQA backbone, our MCR is able to improve \\(0.82\\%\\) on average accuracy. When combined with HGA, our MCR surpasses the previous backbone and causal method by clear margins, e.g. \\(2.34\\%\\) and \\(1.01\\%\\) higher than HGA and IGV, respectively. These validate that our multimodal causal reasoning indeed improves the robustness and generalization of baseline on causal reasoning dataset." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "19033" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.086, + 0.895, + 0.325 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.334, + 0.893, + 0.364 + ], + "angle": 0, + "content": "Figure 6. Qualitative comparison on Causal dataset validation split. The green bold answer denotes the ground-truth one. The yellow arrows indicate that our method can improve the score of predictions by finding the causal association." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.378, + 0.232, + 0.395 + ], + "angle": 0, + "content": "4.4. Ablation Study" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.413, + 0.47, + 0.455 + ], + "angle": 0, + "content": "Table 3. Performance comparisons of different variants on CausalQA dataset. \"MCRv\" and \"MCRt\" denote the visual causal module of MCR and the textual module of MCR, respectively." + }, + { + "type": "table", + "bbox": [ + 0.091, + 0.455, + 0.462, + 0.539 + ], + "angle": 0, + "content": "
MethodAcc-DAcc-EAcc-PAcc-CAcc
B2A66.2162.9231.1535.1649.11
B2A+MCRv67.7665.3835.5532.9550.41
B2A+MCRt68.5764.3833.7331.6149.57
B2A+MCR68.7265.0136.9233.2150.96
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.543, + 0.47, + 0.709 + ], + "angle": 0, + "content": "We analyze the effectiveness of different modules of MCR in Table 3. When adopting the visual causal module of MCR, we can achieve comparable improvements (1.30% on average), indicating that the visual indicator can change the co-occurrence relationship between irrelevant objects and labels, which improves the robustness of the model to visual data. With only MCR's text module, B2A improves by an average of 0.46%. This is because we eliminate the misleading of local language semantics attention. When adopting both causal modules for multimodal data, B2A+MCR achieves the best performance." + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.721, + 0.47, + 0.747 + ], + "angle": 0, + "content": "Table 4. The influence of hype-parameters of training pipeline on Causal-VideoQA Dataset." + }, + { + "type": "table", + "bbox": [ + 0.12, + 0.748, + 0.432, + 0.789 + ], + "angle": 0, + "content": "
k1/k21351/31/5
Acc46.6550.5849.5848.2346.37
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Hyper-parameters. In this paper, we propose a causal intervention pipeline for multimodal data. Here, we conduct ablation studies on the hyper-parameters setting in Tab. 4. When we interact textual data every 3 epochs and video data every 1 epoch, MCR performs best on average accuracy. More Hyper-parameters about \\(\\lambda_{1},\\lambda_{2}\\) and the ablation study of single loss function are shown in Supplementary." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.378, + 0.693, + 0.396 + ], + "angle": 0, + "content": "4.5. Qualitative Analysis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.402, + 0.895, + 0.599 + ], + "angle": 0, + "content": "Fig. 6 shows the qualitative comparison between our MCR and B2A. Our MCR can reduce the scores of confusing candidates and enhance the confidence for the accurate answer. In the example on the left, B2A chooses the third answer because both the body pose of the human and the environment are related to \"lecture\". Our approach explicitly helps B2A reduce the influence of irrelevant factors and find the causal motion \"smoking\". In the right example, B2A is perturbed by the correlation between \"third\" in the text and the three bottles on the table in the video. According to the causal object selection, MCR effectively arrives at a lower score for it. These examples demonstrate that our model can perform real and generalizable reasoning." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.604, + 0.62, + 0.62 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.893, + 0.856 + ], + "angle": 0, + "content": "In this paper, we revisit causal effects in multimodal data and propose a causal prediction architecture to model the causal association between video and text for the VideoQA task. Compared with previous methods, MCR can modify the distribution of data according to the backdoor adjustment and improve the robustness of the model. Considering limitations, our method intervenes in the textual data by word insertion. Some post-intervention examples express eccentric sentence structures that are easy to distinguish. Intervening the textual data with a reasonable text generator would be a reasonable future work. Besides, MCR cannot be directly adapted to the Video Story QA task in which most videos are human-human interactions rather than human-object interactions. Enhancing interventional operations for human instances may be another future work." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgement This research is supported by the National Natural Science Foundation of China (NSFC) (No. 61972038)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "19034" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.157 + ], + "angle": 0, + "content": "[1] Martin Arjovsky, Léon Bottou, Ishaan Gulrajani, and David Lopez-Paz. Invariant risk minimization. arXiv preprint arXiv:1907.02893, 2019." + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.16, + 0.47, + 0.2 + ], + "angle": 0, + "content": "[2] Joao Carreira, Eric Noland, Chloe Hillier, and Andrew Zisserman. 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In Proceedings of the 25th ACM international conference on Multimedia, pages 1050-1058, 2017." + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.261 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "19036" + } + ] +] \ No newline at end of file diff --git a/2023/Discovering the Real Association_ Multimodal Causal Reasoning in Video Question Answering/f46331e4-a9e1-4fa6-843a-36c1e6734399_origin.pdf b/2023/Discovering the Real Association_ Multimodal Causal Reasoning in Video Question Answering/f46331e4-a9e1-4fa6-843a-36c1e6734399_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..8e3d61ec3a9932bfc2abff0650f5218a602fd978 --- /dev/null +++ b/2023/Discovering the Real Association_ Multimodal Causal Reasoning in Video Question Answering/f46331e4-a9e1-4fa6-843a-36c1e6734399_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:eef819f8239f41e8c526711e9eea23c036182f79d467048da57fd1055a6255ce +size 920196 diff --git a/2023/Discovering the Real Association_ Multimodal Causal Reasoning in Video Question Answering/full.md b/2023/Discovering the Real Association_ Multimodal Causal Reasoning in Video Question Answering/full.md new file mode 100644 index 0000000000000000000000000000000000000000..2e61d35220023c1e354ec9198ae1937f56308a44 --- /dev/null +++ b/2023/Discovering the Real Association_ Multimodal Causal Reasoning in Video Question Answering/full.md @@ -0,0 +1,354 @@ +# Discovering the Real Association: Multimodal Causal Reasoning in Video Question Answering + +Chuanqi Zang $^{1}$ , Hanqing Wang $^{1}$ , Mingtao Pei $^{1}$ , Wei Liang $^{1,2*}$ + +1School of Computer Science and Technology, Beijing Institute of Technology + +$^{2}$ Yangtze Delta Region Academy of Beijing Institute of Technology, Jiaxing + +# Abstract + +Video Question Answering (VideoQA) is challenging as it requires capturing accurate correlations between modalities from redundant information. Recent methods focus on the explicit challenges of the task, e.g. multimodal feature extraction, video-text alignment and fusion. Their frameworks reason the answer relying on statistical evidence causes, which ignores potential bias in the multimodal data. In our work, we investigate relational structure from a causal representation perspective on multimodal data and propose a novel inference framework. For visual data, question-irrelevant objects may establish simple matching associations with the answer. For textual data, the model prefers the local phrase semantics which may deviate from the global semantics in long sentences. Therefore, to enhance the generalization of the model, we discover the real association by explicitly capturing visual features that are causally related to the question semantics and weakening the impact of local language semantics on question answering. The experimental results on two large causal VideoQA datasets verify that our proposed framework 1) improves the accuracy of the existing VideoQA backbone, 2) demonstrates robustness on complex scenes and questions. The code will be released at https://github.com/Chuanqi-Zang/Discoverthe-Real-Association. + +# 1. Introduction + +Video Question Answering (VideoQA) aims to understand visual information and describe it in language question-answer format, which is a natural cognitive capability for humans. Computer Vision (CV) and Natural Language Processing (NLP) as the base models for VideoQA have shown significant progress due to the successful application of deep learning, such as action classification [25], object detection [10], instance segmentation [31], and large-scale pre-trained language model [6, 19]. These tremendous + +![](images/7bfdadcb1c850b12aad0fd02c4d1547594652d91e7a1d7f0663d524c04e2acc2.jpg) + +Question: What will happen if the power is cut off? + +Answer: TV, indoor $\rightarrow$ singing karaoke + +A. [person_1] will stop singing karaoke. Predict + +B. [person_1] and [person_2] both cannot work. G.T. + +Question: What will happen if the girl sprains? + +Answer: The girl will stop. + +Reason: Someone, help $\rightarrow$ Reason + +![](images/a406292e40734e4feda4624d8a5a72ab15815771e118e3da376f4660bd9ddb13.jpg) + +A.There are a lot people here,and can find someone to help at any time. B.The girl can't exercise because of a sprain and needs to rest.G.T. + +Predict + +Figure 1. Two samples in VideoQA dataset. They exhibit spurious reasoning processes of B2A [26] that rely on statistical patterns, including visually spurious object-relationship associations (top) and textually unilateral semantic representations (bottom). + +advances in basic applications fuel the confidence in fine-grained multimodal analysis and reasoning, not only feature extraction, but also fine-grained general causality estimation, which is critical for a robust cognitive system. + +Recent VideoQA methods usually explore multimodal relational knowledge by sophisticated structured architecture, such as memory-augmented model [9], hierarchical model [20], topological model [18], and transformer-based model [37]. Although experiments validate their feature fusion capabilities, we find that these methods concentrate on statistical association based on multimodal data, ignoring the real stable association. They usually use a generally constrained approach with Empirical Risk Minimization (ERM), which tends to over-rely on the co-occurrence bias of repeated objects and words in the collected observational data, and bypasses the impact of complete semantics at the sentence level. This mechanism reduces the robustness of the model on new data, even in the test set which has similar distributions to the training set. + +For example, as shown in Fig. 1 (top), two people are playing "cricket" indoors, and there are other objects in the room, including a TV that is on. If relying on the statistical relationship, the model may be confused by the two im + +important visual factors of "indoor" and "television", and misjudge the concerned event, that is, "sing karaoke". Based on the clues provided by the question, the concerned event is related to the action that is taking place, e.g. "two men playing cricket". This requires the model to accurately judge the objects involved in the event and infer the answer. In Fig. 1 (bottom), we show the predicted deviation caused by statistical relationships in the text. When inferring the reasons for answer selection, existing models intensively rely on correlations between local words and video content, e.g. "someone; help", ignoring unreasonable inferences from other parts of the sentence, e.g. "a lot". + +From these observations, we summarize two causal challenges for the VideoQA task. 1) Irrelevant objects confounder. The visual information related to the question is usually causally related to finite objects in the video. When other objects or background are considered, they are subject to data bias and become confounders, misleading the model to select the negative candidate. 2) Keywords confounder. The semantics expressed by textual information is represented by the overall sentence. Some long sentences contain partially sensible keywords. When just focusing on local keywords semantics, the model falls into spurious causal inferences, reducing the robustness of the model. + +To address the above causal challenges and improve the robustness of the model, we propose a Multimodal Causal Reasoning (MCR) framework for video-text data. In this framework, causal features and confounding features are decoupled separately in visual and textual modes through two training strategies. To explicitly decouple the influence of different objects and scenes, MCR extracts fine-gained object-level appearance features and motion dynamics by spatial Region of Interest (ROI) Align [13] on global visual features. Among them, causally related objects are selected based on the correlation between object features and question semantics. In addition to the visual feature, we also model object coordinate information, category information, and global object interaction information to provide spatio-temporal relation representations for accurate causal attribute classification. For textual confounders, we adopt a strategy to reduce the impact of keywords on causality. MCR relies on the correlation between word encoding and question-visual co-embedding to select keywords which have a crucial impact on the prediction results. These keywords provide negative representations for successive deductive answers. Therefore, we combine these keywords with other candidate answers to generate difficult negative samples to improve the recognition ability of the model. During training, visual intervention and textual intervention are iteratively optimized. Multimodal causal relationships are gradually established which improves the robustness and reusability of the model. + +We summarize our contributions as: (1) We discover two + +new types of causal challenges for both visual data and textual data. (2) We propose an object-level causal relationship extraction strategy to establish the real association between objects and language semantics, and a keyword broadcasting strategy to cut off the spurious influence of local textual information. (3) We achieve state-of-the-art performance on two latest large causal VideoQA datasets. + +# 2. Related Work + +Video Question Answering (VideoQA). In early works, the long-term dependency features in video and text were extracted by RNN-based modules, and then were fused by element-wise multiplication [42, 43] with attention mechanism [35]. Considering the implicit interaction in multimodal data, Jiang et al. [18] proposed a heterogeneous graph convolution-based network for crossmodal fusion. Park et al. [26] enhanced crossmodal graphs by a bridged visual-to-visual interactions structure. Huang et al. [15] improved graph interaction reasoning at the fine-grained object level. Dang et al. [5] explored the symbol-like manipulable reasoning by a hierarchically nested spatio-temporal graph. Benefited from the pre-trained language-based transformer [6] and video-text-alignment transformer [37, 41], current works [24, 38] can fine-tune the pre-trained model and show remarkable feature extraction ability and cross-model aligning ability. However, these methods ignore the potential bias distribution in the data. While improving the ability of feature extraction and alignment, they introduce confounders that lead to poor generalization. + +Causal learning. Except for representation learning, recent work found that causal reasoning in data is meaningful for VideoQA. In the synthetic dataset [39], inspired by neural-symbolic method [40] for the ImageQA task, some work [4,7,39] explicitly represent the appearance information and physical information of each object in the scene. To investigate the causal modeling ability of models in real life, recent datasets [21, 36, 39] asked questions about behavior causality in addition to descriptive questions. For some common-sense causal knowledge that is not represented in the videos, Chadha et al. [3] proposed a knowledge base as additional guidance. To find clues of causal associations, Xu et al. [36] proposed to dynamically select the frame from the past or future. The same in frame level, Li et al. [22] explored invariant learning [1] to distinguish question-irrelevant scenes. + +In real-life scenes, videos contain redundant object information. Since lacking human annotations, frequently occurring objects are introduced as confounders, which bring more complex spurious guidance for video understanding than rough frame-level background snippets. In addition, in texts involving causal reasoning, some phrases are also prone to become confounders. This paper will unify the analysis of causal inference on multimodal data. + +![](images/50d8fbc972427ec226572cbf50648244f80b80e595f46c60aa613396e4ee1d08.jpg) +Figure 2. Causal formulation of VideoQA. Gray variables are observed data. V is a specific video and S is a specific sentence. D represents the data domain determined by the collected dataset. It causes the co-occurring of objects in video V, various words in sentence S, and answer label Y. The ideal causal inference is that model extracts video event features $E_{v}$ from videos and text event features $E_{s}$ from words. Then it integrates different modal event representations and filters out the event of interest $E$ for answer selection Y. Here, we provide the backdoor adjustment from D to V and from D to S, which produces our MCR architecture. + +# 3. Method + +# 3.1. Formulation of VideoQA + +Causal Preliminaries. We formalize cross-modal causality for the VideoQA task via a Structure Causal Model [27]. In Fig. 2, we represent the key factors in the VideoQA task as components in the causal graph, and represent the relationships between factors as connecting links that are built by current models [18,23,26,33] as default, including data domain D, video V, sentence S, label Y, visual event features $E_{v}$ , and textual event features $E_{s}$ , alignment events $E$ . + +$V \rightarrow E_v \rightarrow E \leftarrow E_s \leftarrow S$ denotes feature extraction and alignment of multimodal data. $E_v$ and $E_s$ represent the complete events feature extracted from the video and sentence, respectively. In visual domain, pre-trained feature extraction models extract different objects and interactions as events. In textual domain, pre-trained models represent linguistic concepts in stages as events according to punctuation and connectives. $E_v \rightarrow E \leftarrow E_s$ represents multimodal event selection and alignment. The deep model references language events to select video events of interest. Then it aligns event representations and infers a unified event representation $E$ . + +$E \to Y$ represents the direct causal effect from the unified feature of the concerned event to the label, which is an ideal way that remains invariant in other data D with different data distributions. For example, "play cricket" is causally related to cricket bat and swing, and irrelevant to "indoor" and "outdoor". + +$V \gets D \to Y$ denotes that the data domain $D$ as a confounder provides a spurious shortcut from video $V$ to label $Y$ in the visual domain. Specifically, the data domain $D$ represents the statistical relationships contained in the lim + +ited collected video data to represent the co-occurrence of objects and labels. In the top example in Fig. 1, "TV" and "indoor" provide the shortcut connection that is identified as "karaoke" because of lacking human interaction event. + +$S \gets D \to Y$ denotes that the data domain $D$ also establishes spurious associations between sentence $S$ and label $Y$ . This is reflected in the fact that the model is easy to establish the association between labels and local concerned expressions of sentences while ignoring the overall expressions. Especially in multiple-choice questions, the model shows a stronger preference for the local "key" representation. For example, in the below example in Fig. 1, the model selects the locally correct answer, "someone" and "help". + +Causal Intervention. The well-known backdoor adjustment [27] helps in eliminating spurious correlations, resulting in better generalization for the model. We present the true causality from V and S to Y as $P(Y|do(V,S))$ , where $do()$ denotes the interventional operation. $P(Y|do(V,S))$ can cut off the link $D\to V$ and $D\rightarrow S$ to block this backdoor path by changing the original training data into new data $\mathcal{T} = \{\tau_1,\dots,\tau_h\}$ . Each of them donates a confounder stratum (total $h$ ), guiding the model to find invariants from the confounder. The backdoor adjustment can be represented as: + +$$ +\begin{array}{l} P \left(Y \mid d o (V, S)\right) = \sum_ {\tau \in \mathcal {T}} P (Y | V, S, \tau) P (\tau) \\ = \sum_ {\tau_ {v} \in \mathcal {T} _ {v}} P (Y | V, \tau_ {v}) P (\tau_ {v}) \tag {1} \\ + \sum_ {\tau_ {s} \in \mathcal {T} _ {s}} P (Y | S, \tau_ {s}) P (\tau_ {s}) \\ \end{array} +$$ + +where $P(Y|V,S,\tau)$ denotes the prediction in each new data split $\tau$ . $P(\tau)$ denotes confounder selection probability for a specific video and sentence, calculated by $P(\tau) \coloneqq \frac{1}{h}$ . We calculate probability estimates separately by two individual architectures for video and text. In this way, the interaction cuts off the confounder effect in $V \gets D \to Y$ and $S \gets D \to Y$ as shown in Fig. 2. Take video data as an example, traversing all the confounders for a video is expensive. When the video number in the dataset is $\mathcal{M}$ , Eq. 1 expands the training data from $\mathcal{M}$ to $\mathcal{M}^2$ within one epoch with additional memory consumption. Therefore, to balance the scale of confounder set $\mathcal{T}_v$ and training speed, we find the confounder by our MCR and combine it with original data V every epoch. After $K$ training epochs, we can approximate the visual part of the adjustment equation, i.e. $\sum_{\tau_v \in \mathcal{T}_v} P(Y|V, \tau_v) P(\tau_v) \approx \sum_{k=1}^{K} \sum_{\tau_v \in \mathcal{T}_v^k} P(Y|V, \tau_v) P(\tau_v)$ . + +Preliminary. Given a video $I$ , VideoQA aims to understand acting events by asking questions $q$ and predict the correct answer $\widetilde{a}$ from a answer candidate set $A = \{a_{z}\}_{z=1}^{Z}$ . $Z$ is the candidate number. The process is generally formu + +![](images/cbf55aa4b01413cbb273709b887b0d1f0da6360e372d3d197559b8b6f81a8cdb.jpg) +Figure 3. Visual Causal Module. Before the appearance information and motion information are sent to the backbone for question answering, we propose a visual causal module to find object-level causal features and irrelevant features in video data. The image-level visual features are first divided into object-level visual features by the detected bounding box. The category information, location information and interaction relationship of each object are modeled by Interaction Detector. According to the question prompt, the Indicator judges whether the features of different objects are causally related or irrelevant. The uniform representation of causal and irrelevant features are used for further prediction in the VideoQA backbone. + +lated as follows: + +$$ +\widetilde {a} = \underset {a \in A} {\operatorname {a r g m a x}} \mathcal {F} _ {\theta} (a | q, I), \tag {2} +$$ + +where $\theta$ represents the set of model parameters of VideoQA function $\mathcal{F}$ , which maps a pair of video and question into the same feature domain to find the answer. In our work, we do not change the VideoQA function $\mathcal{F}$ . In a causal view, we intervene video $I$ and answer candidate A. + +# 3.2. Visual Causal Module + +To answer the question with accurate causally related features, we propose a visual causal module that disentangles the confounder and causal factors at the object level. As shown in Fig. 3, the video with shape $W \times H \times L$ is encoded by 2D ConvNet, 3D ConvNet into a list of appearance feature and motion feature with shape $\frac{W}{16} \times \frac{H}{16} \times \frac{L}{2}$ . They are uniformly represented by frame feature sequence $\mathcal{V} = \{v_t\}_{t=1}^{\frac{L}{2}}$ , where $t$ means timestamp. The object-level grounding is detected by pre-trained Detection ConvNet and donated as the bounding box $\mathcal{B} = \{b_{n,t}\}_{n=1,t=1}^{N,\frac{L}{2}}$ , where $N$ is the detected object number. We use Region of Interest (ROI) Align [13] to extract object visual features $\mathcal{O} = \{o_{n,t}\}_{n=1,t=1}^{N,\frac{L}{2}}$ , expressed as $\mathcal{O} = ROIAlign(\mathcal{V}|\mathcal{B})$ . + +Since the scene in the real video is ever-changing, some objects in the video may suddenly disappear or appear, mak + +ing it difficult to obtain accurate instance tracking data. Therefore, we extract unified features for the same category of targets, e.g. human, chairs. When objects of this category do not appear in part of the consecutive frames, we fill the feature with 0 value. + +For each object feature, we employ Multilayer Perceptrons (MLP) and Long short-term memory (LSTM) [12] to encode the temporal embedding for visual feature: + +$$ +\mathcal {O} ^ {g} = L S T M (M L P (\mathcal {O})), \tag {3} +$$ + +where $\mathcal{O}^g = \{o_n^g\}_{n=1}^N \in \mathbb{R}^d$ is the global N object representations, and $d$ is the hidden dimension of LSTM. In addition to the visual encoding, we also model the bounding box position correlations $\mathcal{B}$ , object category $C$ , and spatiotemporal inter-object and intra-object interactions in an Interaction Detecting stream. They are implemented by Non-local Net [30] with MLP: + +$$ +L ^ {g} = \operatorname {N o n L} \left(M L P \left(M L P (\mathcal {B}); M L P (C)\right)\right), \tag {4} +$$ + +where; represents channel concatenation. $L^{g} = \{l_{n}^{g}\}_{n = 1}^{N}\in$ $\mathbb{R}^d$ means detected interaction feature. The outputs of two feature extraction streams are then fused by channel concatenation: $\mathcal{O}^g = [\mathcal{O}^g;L^g ]$ . All objects are causal or irrelevant candidates. Their identities are determined by the language semantics of the question. Therefore, given a question sentence, we apply Word Parser and Event Embedding + +to get the global question representation $q^g$ . The Event Embedding is implemented by LSTM: + +$$ +q ^ {g} = L S T M (P a r s e r (q)), \tag {5} +$$ + +where Parser uses a pre-trained GloVe model [28] or BERT model [6]. LSTM is implemented by the question embedding model of the VideoQA backbone. With the specific question, causally related objects are usually a small part of object set $\mathcal{O}^g$ and are interconnected internally. Reasoning about their relationship to unrelated objects is redundant and prone to spurious associations. Therefore, inspired by [22], we use hard segmentation [22] in Indicator to explicitly divide object features into causally related features and irrelevant features, rather than soft GCN inference or attention-based models. Specifically, the question embedding $q^{g}$ and objects feature $\mathcal{O}^g$ are mapped into the same space by MLP. The Indicator computes a score for each object feature and uses Gumbel-Softmax [17] to classify the causal attribute labels of objects: + +$$ +\begin{array}{l} \mathcal {O} ^ {c} = G S (M L P (q ^ {g}) \cdot (M L P (\mathcal {O} ^ {g}) ^ {T})) \circ \mathcal {O}, \\ \mathcal {O} ^ {\bar {c}} = \mathcal {O} - \mathcal {O} ^ {c} \end{array} \tag {6} +$$ + +$$ +\mathcal {O} ^ {\bar {c}} = \mathcal {O} - \mathcal {O} ^ {c}, +$$ + +where GS means Gumbel-Softmax and $\cdot$ means matrix multiplication. $\circ$ means multiply by index. $\mathcal{O}^c = \{o_n^c\}_{n^c = 1}^{N^c},\mathcal{O}^{\bar{c}} = \{o_{n^{\bar{c}}}^{\bar{c}}\}_{n^{\bar{c}} = 1}^{N^{\bar{c}}}$ are causal object features set and irrelevant features set, respectively, where the corner mark of length is omitted for clarity. We average the features in these sets to obtain causal visual features and irrelevant visual features, respectively: $\mathcal{V}^c = \frac{1}{N^c}\sum \mathcal{O}^c,$ $\mathcal{V}^{\bar{c}} = \frac{1}{N^{\bar{c}}}\sum \mathcal{O}^{\bar{c}}.$ + +According to the deduction of Eq. 1, in the visual part, the video V and the average sampling confounder are combined to predict the label. In model designing, the video V can be present by causal object features $\nu^{c}$ . The confounder is from the confounder of another example in the same mini-batch, represented by: + +$$ +\hat {\mathcal {V}} = \frac {1}{N ^ {c} + N ^ {\prime \bar {c}}} \sum \left(O ^ {c} + O ^ {\prime \bar {c}}\right), \tag {7} +$$ + +where $\hat{\mathcal{V}}$ is the blended features. $O^{\prime\bar{c}}$ is the confounder of another example. $N^{\prime\bar{c}}$ is the object number of $O^{\prime\bar{c}}$ . Both $\mathcal{V}$ , $\mathcal{V}^{c}$ , $\mathcal{V}^{\bar{c}}$ , and $\hat{\mathcal{V}}$ are sent to the VideoQA backbone for training the visual causal module. The visual module can capture causal relationships between object features and labels, providing a stable association for multimodal data. + +# 3.3. Textual Causal Module + +For textual causal inference, prediction is often plagued by correlations between local language semantics and visual features. Therefore, the key to getting rid of text confounders is to enhance the model's ability to recognize + +![](images/9abda42351a4d760930a942ef6568260b9a7dab9783d0a1e9e699bfc99aa41ee.jpg) +Figure 4. Textual Causal Module. Keywords are selected as confounders from the prediction results by the indicator. They are sent to the intervenor to generate new candidates. + +such confusing samples which are implemented by a textual causal module. + +In the VideoQA base model, the visual information and the question have been aligned, containing the events information related to the answer. Therefore, we use the alignment feature $f_{qv} = \mathcal{F}(\mathcal{V}^c, q^g)$ to retrieve the keywords in the answer. As shown in Fig. 4, the same with question embedding, we encode the answer by Word Parser and Event Embedding: + +$$ +a ^ {g}, a ^ {l} = L S T M (P a r s e r (a)), \tag {8} +$$ + +where $a^g$ is the global representation of the answer, and $a^l$ is the local representation of each word. The same with visual Indicator, we select the keyword by the relation score between $a^g$ and $f_{qv}$ : + +$$ +a ^ {\bar {c}} = G S \left(M L P \left(f _ {q v}\right) \cdot \left(M L P \left(a ^ {g}\right)\right) ^ {T}\right) \circ a ^ {l}, \tag {9} +$$ + +where $a^{\bar{c}}$ represents the keywords, which are potential confounders in this question. $a^{c} = a^{l} - a^{\bar{c}}$ represents other words. + +According to the textual part of Eq. 1, the label is predicted by the sentence and confounder. Due to the correlation between sentences and videos, we look for confounders of sentences from the same video, especially the predicted answer by VideoQA backbone which contains factors that increase the score. Similar to visual intervention, we pick confounders once per epoch. + +Confounders are used to augment the hard sample of candidates that changes the textual distributions. The model joint original candidates $A = \{a_{z}\}_{z=1}^{Z}$ with $a^{\bar{c}}$ by inserting $a^{\bar{c}}$ at the beginning or end of a sentence and generate a new candidates set $\hat{A} = \{\hat{a}_{z}\}_{z=1}^{Z}$ . In the training process, we randomly replace the negative example from the new candidates set $\hat{A}$ . + +# 3.4. Training + +In this section, we introduce our training targets and training pipeline for multimodal data. The algorithm can be found in Supplementary. First of all, to ensure the domain consistency of training sets and test sets, we train + +the VideoQA backbone with raw data $(\mathcal{V},\mathrm{A})$ , which also guarantees that the training process satisfies the pre-defined causal formulation: + +$$ +\mathcal {L} _ {o} = \mathrm {X E} \left(\mathcal {F} \left((\mathcal {V}, \mathrm {q}), (\mathcal {V}, \mathrm {A})\right), \mathrm {a}\right), \tag {10} +$$ + +where XE is the cross-entropy loss. $\mathcal{F}$ calculates the dot-product between question-related visual features and answer-related visual features as the predicted results. At test time, we use the candidate with the highest score as the predicted result as in Eq.2. + +Visual Module Loss. Visual module loss aims to capture causal object features and non-causal object features for further robust prediction. In the training stage, the causal visual features have the same ability for question answering, which is restricted by the cross-entropy loss: $\mathcal{L}_{\mathrm{c}}^{\mathrm{v}}$ . In contrast, non-causal objects are irrelevant to the question and should be unbiased toward answer candidates: $\mathcal{L}_{\bar{c}}^{\mathrm{v}}$ . The blended data $\hat{\nu}$ are supposed to obtain the same effect with causal feature: $\mathcal{L}_o^{\mathrm{v}}$ . The formulation of visual module loss shows as follows: + +$$ +\mathcal {L} _ {\mathrm {c}} ^ {\mathrm {v}} = \operatorname {X E} \left(\mathcal {F} \left(\left(\mathcal {V} ^ {\mathrm {c}}, \mathrm {q}\right), \left(\mathcal {V} ^ {\mathrm {c}}, \mathrm {A}\right)\right), \mathrm {a}\right) +$$ + +$$ +\mathcal {L} _ {\bar {c}} ^ {\mathrm {v}} = \operatorname {M S E} \left(\mathcal {F} \left(\left(\mathcal {V} ^ {\bar {c}}, \mathrm {q}\right), \left(\mathcal {V} ^ {\bar {c}}, \mathrm {A}\right)\right), \text {a v g}\right) \tag {11} +$$ + +$$ +\mathcal {L} _ {\hat {\partial}} ^ {\mathrm {v}} = \operatorname {X E} (\mathcal {F} ((\hat {\mathcal {V}}, q), (\hat {\mathcal {V}}, A)), a), +$$ + +$$ +\mathcal {L} _ {\mathrm {v}} = \mathcal {L} _ {\mathrm {c}} ^ {\mathrm {v}} + \mathcal {L} _ {\bar {c}} ^ {\mathrm {v}} + \mathcal {L} _ {\hat {o}} ^ {\mathrm {v}}, +$$ + +where avg is the average score of all candidates, avg = $\mathcal{F}((\mathcal{V},q),(\mathcal{V},A))$ . MSE means Mean Square Error for non-causal objects to get a neutral score. + +Textual Module Loss. The text module loss aims to find keywords from the prediction results that directly affect the model selection and reduce the sensitivity of the model to keywords. Intuitively, keywords have the ability for prediction, while other words are difficult to judge the results. We use cross-entropy loss for keywords $\mathcal{L}_{\mathrm{c}}^{\mathrm{s}}$ and MSE for other words $\mathcal{L}_{\mathrm{c}}^{\mathrm{s}}$ . The blended answer is restricted by the cross-entropy loss $\mathcal{L}_{\hat{o}}^{\mathrm{s}}$ . The formulation of textual module loss is: + +$$ +\mathcal {L} _ {\bar {c}} ^ {\mathrm {s}} = \mathrm {X E} \left(\mathcal {F} \left((\mathcal {V}, \mathrm {q}), (\mathcal {V}, a ^ {\bar {c}})\right), \mathrm {a}\right) +$$ + +$$ +\mathcal {L} _ {\mathrm {c}} ^ {\mathrm {s}} = \operatorname {M S E} \left(\mathcal {F} \left(\left(\mathcal {V}, \mathrm {q}\right), \left(\mathcal {V}, a ^ {\mathrm {c}}\right)\right), a v g\right) \tag {12} +$$ + +$$ +\mathcal {L} _ {\hat {\theta}} ^ {\mathrm {s}} = \operatorname {X E} (\mathcal {F} ((\mathcal {V}, q), (\mathcal {V}, \hat {A})), a) +$$ + +$$ +\mathcal {L} _ {\mathrm {s}} = \mathcal {L} _ {\mathrm {c}} ^ {\mathrm {s}} + \mathcal {L} _ {\bar {\mathrm {c}}} ^ {\mathrm {s}} + \mathcal {L} _ {\delta} ^ {\mathrm {s}}. +$$ + +The overall loss of our model can be expressed as: + +$$ +\mathcal {L} = \mathcal {L} _ {o} + \lambda_ {1} \mathcal {L} _ {\mathrm {v}} + \lambda_ {2} \mathcal {L} _ {\mathrm {s}}, \tag {13} +$$ + +where $\lambda_{1}$ and $\lambda_{2}$ are the hyper-parameters to balance the visual loss and textual loss. + +Intervene Pipeline. We show the Intervene pipeline in Fig. 5. The textual intervention and the visual intervention are accomplished in two steps. Visual causal loss is computed with Eq. 11 and used to obtain causally related object features and irrelevant object features. They are used + +![](images/59be354d816716dd4f1279a20f12dd18611c9ee409a4f1bf077c85a9b1f0bd4e.jpg) +Figure 5. Causal intervention pipeline. + +to generate blended visual data with an intervenor, which is implemented by Eq. 7. Textual causal loss is computed with Eq. 12 and used to obtain keywords. Keywords are sent to textual interveners to generate blended textual data. We execute $K_{2}$ epochs textual interventions after executing $K_{1}$ epochs visual interventions for the visual causal module and the textual causal module. + +# 4. Experiment + +# 4.1. Dataset + +We evaluate our Multimodal Causal Reasoning (MCR) framework on two recent large causal-related VideoQA datasets: Causal-VidQA [21] and NExT-QA [32]. In these datasets, models need to answer not only simple descriptive or statistical questions but also implicit global evidence reasoning. The collected video data is close to the real open scene, including a variety of objects and interactive actions. Answer candidates are sentences with different expression structures and are not limited to a single sentence. + +The Causal-VidQA dataset selects 26,900 video clips from Kinetics-700 [2] and asks 107,600 questions, including description, explanation, prediction, and counterfactual questions. Each question has 5 answers, with 5 more reasons in predictions and counterfactuals. For question-answer accuracies, we adopt the previous causal VideoQA evaluation metrics [21] that report accuracy for each question type, as well as the accuracy of the consistency between answers and reasons. + +NExT-QA dataset contains 5,440 videos from VidOR [29] and proposes 47,692 questions for the multichoice task, including description, explanation, and temporal reasoning questions. We also report accuracy for each question type. + +# 4.2. Experimental Settings + +We use a unified feature extraction method for both datasets. Each video with varying length is divided into 8 clips, each containing 16 frames. For the object-level motion feature, we uniformly sample from the frame-level appearance features and clip-level motion features by ROI Align [13]. The bounding boxes in each frame are extracted by pre-trained Mask R-CNN [13]. The appearance features and motion features are extracted by ResNet-101 [14] and + +Table 1. Comparison of accuracy with state-of-the-art methods on Causal-VidQA dataset. D means description question. E means explanation question. P means prediction question. C means counterfactual question. QA means to answer the answer. QR means to answer the reason. QAR means the answer and reason are both accurate. + +
MethodText FeatureAcc-DAcc-EQAAcc-P QRQARQAAcc-C QRQARAcc
HME [8]GloVe47.2543.8041.0242.5323.2535.2934.1915.3432.41
HCRN [20]GloVe58.8953.5343.1445.0726.1743.6943.4722.7540.33
HGA [18]GloVe60.3255.0246.5547.2128.5344.0044.0423.6341.88
B2A [26]GloVe61.2956.4346.8248.1730.0145.1244.9925.2943.26
IGV [22]+B2AGloVe59.2448.4145.7047.3228.2038.9940.9718.8438.67
MCR+B2AGloVe66.7261.2650.4652.1732.1352.1751.5031.9148.01
HME [8]BERT63..3661.4550.2947.5628.9250.38.51.6530.9346.16
HCRN [20]BERT65.3561.6151.7451.2632.5751.5753.4432.6648.05
HGA [18]BERT65.6763.5149.3650.6232.2252.4455.8534.2848.92
B2A [26]BERT66.2162.9248.9650.2231.1553.2756.2735.1649.11
IGV [22]+B2ABERT65.9262.1352.7753.4735.0050.6752.2931.2248.57
MCR+HCRNBERT68.6865.9755.4458.1837.6352.2452.3931.1750.86
MCR+B2ABERT67.4765.5956.4656.4237.8252.3954.0833.3851.06
+ +3D ResNeXt-101 [34] with the pre-trained model, respectively. For textual data, word token representation for questions and answers is provided by GloVe [28] and BERT [6] respectively, which greatly affects the performance of models [21]. MLP is implemented by fully connected layers, followed by Batch Normalization [16] and ReLU [11]. $\lambda_{1}$ and $\lambda_{2}$ are both set as 1. $K_{1}$ and $K_{2}$ are set as 1 and 3, respectively. During training, we use Adam optimizer with the initial learning rate of 1e-4 and halve the learning rate in every 5 epochs. The batch size is set as 128 in CausalVidQA dataset and 64 in NExT-QA dataset. + +# 4.3. Comparison with State-of-the-Arts + +Results on Causal-QA. Table 1 presents the results of four state-of-the-art baseline methods and one causal method on the Causal-VidQA dataset, including HME [8], HCRN [20], HGA [18], B2A [26], and IGV [22]. Compared to all existing VideoQA methods, MCR achieves the best performance across almost all types of questions. It is worth noting that MCR improves accuracy across all question types when using GloVe as the text model, which has an average performance improvement of $4.75\%$ over B2A $(48.01\%$ vs. $43.26\%)$ . Compared with the IGV, MCR improves by $9.44\%$ $(48.01\%$ vs. $38.67\%)$ . Our result is even comparable to the backbones of using BERT as a language model. When using BERT as the text model and B2A as the VideoQA backbone, MCR achieves an accuracy improvement of $1.85\%$ on average. In counterfactual questions, it is difficult to answer the content of the associative question with limited knowledge learning from the dataset. Involving additional commonsense knowledge may be helpful. Experimentally, in the absence of commonsense knowledge, VideoQA backbones that rely on data bias can also achieve + +Table 2. Accuracies on NExT-VidQA of different architectures. + +
ModelsCausalTempDescripAll
HME [8]46.7648.8957.3749.16
HCRN [20]47.0749.2754.0248.82
HGA [18]48.1349.0857.7950.01
B2A [26]47.3749.0158.349.60
IGV [22]48.5651.6759.6451.34
MCR+B2A47.350.2561.2650.42
MCR+HGA49.1951.9862.2952.35
+ +good performance for counterfactual questions. + +Our proposed framework is in parallel with the VideoQA backbone that helps it discover the causal reason. To verify the effectiveness of the parallel strategy, we combine the MCR with different backbones, including HCRN [20] and B2A [26]. We can see that our method has remarkable effects on existing methods. This is due to previous methods being confused by confounders in multimodal data, resulting in poor generalization. Our MCR can effectively alleviate the biased modeling of these methods. + +Results on NExT-QA. For further comparison, we evaluate our method on the NExT-QA dataset and report the evaluation results in Table 2. Compared with the baselines, our proposed MCR achieves the top performance in all question types. Specifically, when using B2A as the VideoQA backbone, our MCR is able to improve $0.82\%$ on average accuracy. When combined with HGA, our MCR surpasses the previous backbone and causal method by clear margins, e.g. $2.34\%$ and $1.01\%$ higher than HGA and IGV, respectively. These validate that our multimodal causal reasoning indeed improves the robustness and generalization of baseline on causal reasoning dataset. + +![](images/91864b7a1c9ab1c39643460dde1383a2d71d959a7575173d7c0511576279e320.jpg) +Figure 6. Qualitative comparison on Causal dataset validation split. The green bold answer denotes the ground-truth one. The yellow arrows indicate that our method can improve the score of predictions by finding the causal association. + +# 4.4. Ablation Study + +Table 3. Performance comparisons of different variants on CausalQA dataset. "MCRv" and "MCRt" denote the visual causal module of MCR and the textual module of MCR, respectively. + +
MethodAcc-DAcc-EAcc-PAcc-CAcc
B2A66.2162.9231.1535.1649.11
B2A+MCRv67.7665.3835.5532.9550.41
B2A+MCRt68.5764.3833.7331.6149.57
B2A+MCR68.7265.0136.9233.2150.96
+ +We analyze the effectiveness of different modules of MCR in Table 3. When adopting the visual causal module of MCR, we can achieve comparable improvements (1.30% on average), indicating that the visual indicator can change the co-occurrence relationship between irrelevant objects and labels, which improves the robustness of the model to visual data. With only MCR's text module, B2A improves by an average of 0.46%. This is because we eliminate the misleading of local language semantics attention. When adopting both causal modules for multimodal data, B2A+MCR achieves the best performance. + +Table 4. The influence of hype-parameters of training pipeline on Causal-VideoQA Dataset. + +
k1/k21351/31/5
Acc46.6550.5849.5848.2346.37
+ +Hyper-parameters. In this paper, we propose a causal intervention pipeline for multimodal data. Here, we conduct ablation studies on the hyper-parameters setting in Tab. 4. When we interact textual data every 3 epochs and video data every 1 epoch, MCR performs best on average accuracy. More Hyper-parameters about $\lambda_{1},\lambda_{2}$ and the ablation study of single loss function are shown in Supplementary. + +# 4.5. Qualitative Analysis + +Fig. 6 shows the qualitative comparison between our MCR and B2A. Our MCR can reduce the scores of confusing candidates and enhance the confidence for the accurate answer. In the example on the left, B2A chooses the third answer because both the body pose of the human and the environment are related to "lecture". Our approach explicitly helps B2A reduce the influence of irrelevant factors and find the causal motion "smoking". In the right example, B2A is perturbed by the correlation between "third" in the text and the three bottles on the table in the video. According to the causal object selection, MCR effectively arrives at a lower score for it. These examples demonstrate that our model can perform real and generalizable reasoning. + +# 5. Conclusion + +In this paper, we revisit causal effects in multimodal data and propose a causal prediction architecture to model the causal association between video and text for the VideoQA task. Compared with previous methods, MCR can modify the distribution of data according to the backdoor adjustment and improve the robustness of the model. Considering limitations, our method intervenes in the textual data by word insertion. Some post-intervention examples express eccentric sentence structures that are easy to distinguish. Intervening the textual data with a reasonable text generator would be a reasonable future work. Besides, MCR cannot be directly adapted to the Video Story QA task in which most videos are human-human interactions rather than human-object interactions. Enhancing interventional operations for human instances may be another future work. + +Acknowledgement This research is supported by the National Natural Science Foundation of China (NSFC) (No. 61972038). + +# References + +[1] Martin Arjovsky, Léon Bottou, Ishaan Gulrajani, and David Lopez-Paz. Invariant risk minimization. arXiv preprint arXiv:1907.02893, 2019. +[2] Joao Carreira, Eric Noland, Chloe Hillier, and Andrew Zisserman. A short note on the kinetics-700 human action dataset. arXiv preprint arXiv:1907.06987, 2019. +[3] Aman Chadha, Gurneet Arora, and Navpreet Kaloty. iperceive: Applying common-sense reasoning to multi-modal dense video captioning and video question answering. arXiv preprint arXiv:2011.07735, 2020. +[4] Zhenfang Chen, Jiayuan Mao, Jiajun Wu, Kwan-Yee Kenneth Wong, Joshua B Tenenbaum, and Chuang Gan. 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Recent methods focus on the explicit challenges of the task, e.g. multimodal feature extraction, video-text alignment and fusion. Their frameworks reason the answer relying on statistical evidence causes, which ignores potential bias in the multimodal data. In our work, we investigate relational structure from a causal representation perspective on multimodal data and propose a novel inference framework. For visual data, question-irrelevant objects may establish simple matching associations with the answer. For textual data, the model prefers the local phrase semantics which may deviate from the global semantics in long sentences. Therefore, to enhance the generalization of the model, we discover the real association by explicitly capturing visual features that are causally related to the question semantics and weakening the impact of local language semantics on question answering. The experimental results on two large causal VideoQA datasets verify that our proposed framework 1) improves the accuracy of the existing VideoQA backbone, 2) demonstrates robustness on complex scenes and questions. The code will be released at https://github.com/Chuanqi-Zang/Discoverthe-Real-Association." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 48, + 568, + 128, + 581 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 568, + 128, + 581 + ], + "spans": [ + { + "bbox": [ + 48, + 568, + 128, + 581 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 589, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 589, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 589, + 287, + 696 + ], + "type": "text", + "content": "Video Question Answering (VideoQA) aims to understand visual information and describe it in language question-answer format, which is a natural cognitive capability for humans. Computer Vision (CV) and Natural Language Processing (NLP) as the base models for VideoQA have shown significant progress due to the successful application of deep learning, such as action classification [25], object detection [10], instance segmentation [31], and large-scale pre-trained language model [6, 19]. These tremendous" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 307, + 217, + 550, + 245 + ], + "blocks": [ + { + "bbox": [ + 307, + 217, + 550, + 245 + ], + "lines": [ + { + "bbox": [ + 307, + 217, + 550, + 245 + ], + "spans": [ + { + "bbox": [ + 307, + 217, + 550, + 245 + ], + "type": "image", + "image_path": "7bfdadcb1c850b12aad0fd02c4d1547594652d91e7a1d7f0663d524c04e2acc2.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 309, + 247, + 481, + 257 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 247, + 481, + 257 + ], + "spans": [ + { + "bbox": [ + 309, + 247, + 481, + 257 + ], + "type": "text", + "content": "Question: What will happen if the power is cut off?" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 310, + 258, + 485, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 258, + 485, + 277 + ], + "spans": [ + { + "bbox": [ + 310, + 258, + 485, + 277 + ], + "type": "text", + "content": "Answer: TV, indoor " + }, + { + "bbox": [ + 310, + 258, + 485, + 277 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 310, + 258, + 485, + 277 + ], + "type": "text", + "content": " singing karaoke" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 310, + 278, + 488, + 292 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 278, + 488, + 292 + ], + "spans": [ + { + "bbox": [ + 310, + 278, + 488, + 292 + ], + "type": "text", + "content": "A. [person_1] will stop singing karaoke. Predict" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 310, + 293, + 488, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 293, + 488, + 304 + ], + "spans": [ + { + "bbox": [ + 310, + 293, + 488, + 304 + ], + "type": "text", + "content": "B. [person_1] and [person_2] both cannot work. G.T." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 310, + 308, + 467, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 308, + 467, + 319 + ], + "spans": [ + { + "bbox": [ + 310, + 308, + 467, + 319 + ], + "type": "text", + "content": "Question: What will happen if the girl sprains?" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 310, + 319, + 401, + 329 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 319, + 401, + 329 + ], + "spans": [ + { + "bbox": [ + 310, + 319, + 401, + 329 + ], + "type": "text", + "content": "Answer: The girl will stop." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 310, + 332, + 460, + 351 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 332, + 460, + 351 + ], + "spans": [ + { + "bbox": [ + 310, + 332, + 460, + 351 + ], + "type": "text", + "content": "Reason: Someone, help " + }, + { + "bbox": [ + 310, + 332, + 460, + 351 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 310, + 332, + 460, + 351 + ], + "type": "text", + "content": " Reason" + } + ] + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 477, + 310, + 519, + 340 + ], + "blocks": [ + { + "bbox": [ + 477, + 310, + 519, + 340 + ], + "lines": [ + { + "bbox": [ + 477, + 310, + 519, + 340 + ], + "spans": [ + { + "bbox": [ + 477, + 310, + 519, + 340 + ], + "type": "image", + "image_path": "a406292e40734e4feda4624d8a5a72ab15815771e118e3da376f4660bd9ddb13.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + } + ], + "index": 18 + }, + { + "bbox": [ + 309, + 353, + 547, + 375 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 353, + 547, + 375 + ], + "spans": [ + { + "bbox": [ + 309, + 353, + 547, + 375 + ], + "type": "text", + "content": "A.There are a lot people here,and can find someone to help at any time. B.The girl can't exercise because of a sprain and needs to rest.G.T." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 515, + 345, + 542, + 355 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 515, + 345, + 542, + 355 + ], + "spans": [ + { + "bbox": [ + 515, + 345, + 542, + 355 + ], + "type": "text", + "content": "Predict" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 382, + 545, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 382, + 545, + 426 + ], + "spans": [ + { + "bbox": [ + 306, + 382, + 545, + 426 + ], + "type": "text", + "content": "Figure 1. Two samples in VideoQA dataset. They exhibit spurious reasoning processes of B2A [26] that rely on statistical patterns, including visually spurious object-relationship associations (top) and textually unilateral semantic representations (bottom)." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 437, + 545, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 545, + 485 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 545, + 485 + ], + "type": "text", + "content": "advances in basic applications fuel the confidence in fine-grained multimodal analysis and reasoning, not only feature extraction, but also fine-grained general causality estimation, which is critical for a robust cognitive system." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 486, + 546, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 546, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 546, + 665 + ], + "type": "text", + "content": "Recent VideoQA methods usually explore multimodal relational knowledge by sophisticated structured architecture, such as memory-augmented model [9], hierarchical model [20], topological model [18], and transformer-based model [37]. Although experiments validate their feature fusion capabilities, we find that these methods concentrate on statistical association based on multimodal data, ignoring the real stable association. They usually use a generally constrained approach with Empirical Risk Minimization (ERM), which tends to over-rely on the co-occurrence bias of repeated objects and words in the collected observational data, and bypasses the impact of complete semantics at the sentence level. This mechanism reduces the robustness of the model on new data, even in the test set which has similar distributions to the training set." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "For example, as shown in Fig. 1 (top), two people are playing \"cricket\" indoors, and there are other objects in the room, including a TV that is on. If relying on the statistical relationship, the model may be confused by the two im" + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 61, + 703, + 192, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 703, + 192, + 712 + ], + "spans": [ + { + "bbox": [ + 61, + 703, + 192, + 712 + ], + "type": "text", + "content": "*Wei Liang is the corresponding author." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19027" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 49, + 72, + 286, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 72, + 286, + 215 + ], + "spans": [ + { + "bbox": [ + 49, + 72, + 286, + 215 + ], + "type": "text", + "content": "important visual factors of \"indoor\" and \"television\", and misjudge the concerned event, that is, \"sing karaoke\". Based on the clues provided by the question, the concerned event is related to the action that is taking place, e.g. \"two men playing cricket\". This requires the model to accurately judge the objects involved in the event and infer the answer. In Fig. 1 (bottom), we show the predicted deviation caused by statistical relationships in the text. When inferring the reasons for answer selection, existing models intensively rely on correlations between local words and video content, e.g. \"someone; help\", ignoring unreasonable inferences from other parts of the sentence, e.g. \"a lot\"." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 49, + 219, + 286, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 219, + 286, + 361 + ], + "spans": [ + { + "bbox": [ + 49, + 219, + 286, + 361 + ], + "type": "text", + "content": "From these observations, we summarize two causal challenges for the VideoQA task. 1) Irrelevant objects confounder. The visual information related to the question is usually causally related to finite objects in the video. When other objects or background are considered, they are subject to data bias and become confounders, misleading the model to select the negative candidate. 2) Keywords confounder. The semantics expressed by textual information is represented by the overall sentence. Some long sentences contain partially sensible keywords. When just focusing on local keywords semantics, the model falls into spurious causal inferences, reducing the robustness of the model." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 49, + 365, + 286, + 698 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 365, + 286, + 698 + ], + "spans": [ + { + "bbox": [ + 49, + 365, + 286, + 698 + ], + "type": "text", + "content": "To address the above causal challenges and improve the robustness of the model, we propose a Multimodal Causal Reasoning (MCR) framework for video-text data. In this framework, causal features and confounding features are decoupled separately in visual and textual modes through two training strategies. To explicitly decouple the influence of different objects and scenes, MCR extracts fine-gained object-level appearance features and motion dynamics by spatial Region of Interest (ROI) Align [13] on global visual features. Among them, causally related objects are selected based on the correlation between object features and question semantics. In addition to the visual feature, we also model object coordinate information, category information, and global object interaction information to provide spatio-temporal relation representations for accurate causal attribute classification. For textual confounders, we adopt a strategy to reduce the impact of keywords on causality. MCR relies on the correlation between word encoding and question-visual co-embedding to select keywords which have a crucial impact on the prediction results. These keywords provide negative representations for successive deductive answers. Therefore, we combine these keywords with other candidate answers to generate difficult negative samples to improve the recognition ability of the model. During training, visual intervention and textual intervention are iteratively optimized. Multimodal causal relationships are gradually established which improves the robustness and reusability of the model." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 61, + 702, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 702, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 61, + 702, + 286, + 712 + ], + "type": "text", + "content": "We summarize our contributions as: (1) We discover two" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 308, + 72, + 544, + 155 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 72, + 544, + 155 + ], + "spans": [ + { + "bbox": [ + 308, + 72, + 544, + 155 + ], + "type": "text", + "content": "new types of causal challenges for both visual data and textual data. (2) We propose an object-level causal relationship extraction strategy to establish the real association between objects and language semantics, and a keyword broadcasting strategy to cut off the spurious influence of local textual information. (3) We achieve state-of-the-art performance on two latest large causal VideoQA datasets." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 308, + 167, + 391, + 179 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 167, + 391, + 179 + ], + "spans": [ + { + "bbox": [ + 308, + 167, + 391, + 179 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 308, + 186, + 544, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 186, + 544, + 425 + ], + "spans": [ + { + "bbox": [ + 308, + 186, + 544, + 425 + ], + "type": "text", + "content": "Video Question Answering (VideoQA). In early works, the long-term dependency features in video and text were extracted by RNN-based modules, and then were fused by element-wise multiplication [42, 43] with attention mechanism [35]. Considering the implicit interaction in multimodal data, Jiang et al. [18] proposed a heterogeneous graph convolution-based network for crossmodal fusion. Park et al. [26] enhanced crossmodal graphs by a bridged visual-to-visual interactions structure. Huang et al. [15] improved graph interaction reasoning at the fine-grained object level. Dang et al. [5] explored the symbol-like manipulable reasoning by a hierarchically nested spatio-temporal graph. Benefited from the pre-trained language-based transformer [6] and video-text-alignment transformer [37, 41], current works [24, 38] can fine-tune the pre-trained model and show remarkable feature extraction ability and cross-model aligning ability. However, these methods ignore the potential bias distribution in the data. While improving the ability of feature extraction and alignment, they introduce confounders that lead to poor generalization." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 308, + 426, + 544, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 426, + 544, + 616 + ], + "spans": [ + { + "bbox": [ + 308, + 426, + 544, + 616 + ], + "type": "text", + "content": "Causal learning. Except for representation learning, recent work found that causal reasoning in data is meaningful for VideoQA. In the synthetic dataset [39], inspired by neural-symbolic method [40] for the ImageQA task, some work [4,7,39] explicitly represent the appearance information and physical information of each object in the scene. To investigate the causal modeling ability of models in real life, recent datasets [21, 36, 39] asked questions about behavior causality in addition to descriptive questions. For some common-sense causal knowledge that is not represented in the videos, Chadha et al. [3] proposed a knowledge base as additional guidance. To find clues of causal associations, Xu et al. [36] proposed to dynamically select the frame from the past or future. The same in frame level, Li et al. [22] explored invariant learning [1] to distinguish question-irrelevant scenes." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 308, + 618, + 544, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 618, + 544, + 712 + ], + "spans": [ + { + "bbox": [ + 308, + 618, + 544, + 712 + ], + "type": "text", + "content": "In real-life scenes, videos contain redundant object information. Since lacking human annotations, frequently occurring objects are introduced as confounders, which bring more complex spurious guidance for video understanding than rough frame-level background snippets. In addition, in texts involving causal reasoning, some phrases are also prone to become confounders. This paper will unify the analysis of causal inference on multimodal data." + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 750, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 750, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 750, + 317, + 757 + ], + "type": "text", + "content": "19028" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 109, + 70, + 227, + 156 + ], + "blocks": [ + { + "bbox": [ + 109, + 70, + 227, + 156 + ], + "lines": [ + { + "bbox": [ + 109, + 70, + 227, + 156 + ], + "spans": [ + { + "bbox": [ + 109, + 70, + 227, + 156 + ], + "type": "image", + "image_path": "50d8fbc972427ec226572cbf50648244f80b80e595f46c60aa613396e4ee1d08.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 167, + 289, + 277 + ], + "lines": [ + { + "bbox": [ + 46, + 167, + 289, + 277 + ], + "spans": [ + { + "bbox": [ + 46, + 167, + 289, + 277 + ], + "type": "text", + "content": "Figure 2. Causal formulation of VideoQA. Gray variables are observed data. V is a specific video and S is a specific sentence. D represents the data domain determined by the collected dataset. It causes the co-occurring of objects in video V, various words in sentence S, and answer label Y. The ideal causal inference is that model extracts video event features " + }, + { + "bbox": [ + 46, + 167, + 289, + 277 + ], + "type": "inline_equation", + "content": "E_{v}" + }, + { + "bbox": [ + 46, + 167, + 289, + 277 + ], + "type": "text", + "content": " from videos and text event features " + }, + { + "bbox": [ + 46, + 167, + 289, + 277 + ], + "type": "inline_equation", + "content": "E_{s}" + }, + { + "bbox": [ + 46, + 167, + 289, + 277 + ], + "type": "text", + "content": " from words. Then it integrates different modal event representations and filters out the event of interest " + }, + { + "bbox": [ + 46, + 167, + 289, + 277 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 46, + 167, + 289, + 277 + ], + "type": "text", + "content": " for answer selection Y. Here, we provide the backdoor adjustment from D to V and from D to S, which produces our MCR architecture." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 298, + 102, + 309 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 298, + 102, + 309 + ], + "spans": [ + { + "bbox": [ + 47, + 298, + 102, + 309 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 319, + 186, + 331 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 319, + 186, + 331 + ], + "spans": [ + { + "bbox": [ + 47, + 319, + 186, + 331 + ], + "type": "text", + "content": "3.1. Formulation of VideoQA" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 338, + 287, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 338, + 287, + 445 + ], + "spans": [ + { + "bbox": [ + 46, + 338, + 287, + 445 + ], + "type": "text", + "content": "Causal Preliminaries. We formalize cross-modal causality for the VideoQA task via a Structure Causal Model [27]. In Fig. 2, we represent the key factors in the VideoQA task as components in the causal graph, and represent the relationships between factors as connecting links that are built by current models [18,23,26,33] as default, including data domain D, video V, sentence S, label Y, visual event features " + }, + { + "bbox": [ + 46, + 338, + 287, + 445 + ], + "type": "inline_equation", + "content": "E_{v}" + }, + { + "bbox": [ + 46, + 338, + 287, + 445 + ], + "type": "text", + "content": ", and textual event features " + }, + { + "bbox": [ + 46, + 338, + 287, + 445 + ], + "type": "inline_equation", + "content": "E_{s}" + }, + { + "bbox": [ + 46, + 338, + 287, + 445 + ], + "type": "text", + "content": ", alignment events " + }, + { + "bbox": [ + 46, + 338, + 287, + 445 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 46, + 338, + 287, + 445 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 448, + 287, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 448, + 287, + 590 + ], + "spans": [ + { + "bbox": [ + 46, + 448, + 287, + 590 + ], + "type": "inline_equation", + "content": "V \\rightarrow E_v \\rightarrow E \\leftarrow E_s \\leftarrow S" + }, + { + "bbox": [ + 46, + 448, + 287, + 590 + ], + "type": "text", + "content": " denotes feature extraction and alignment of multimodal data. " + }, + { + "bbox": [ + 46, + 448, + 287, + 590 + ], + "type": "inline_equation", + "content": "E_v" + }, + { + "bbox": [ + 46, + 448, + 287, + 590 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 448, + 287, + 590 + ], + "type": "inline_equation", + "content": "E_s" + }, + { + "bbox": [ + 46, + 448, + 287, + 590 + ], + "type": "text", + "content": " represent the complete events feature extracted from the video and sentence, respectively. In visual domain, pre-trained feature extraction models extract different objects and interactions as events. In textual domain, pre-trained models represent linguistic concepts in stages as events according to punctuation and connectives. " + }, + { + "bbox": [ + 46, + 448, + 287, + 590 + ], + "type": "inline_equation", + "content": "E_v \\rightarrow E \\leftarrow E_s" + }, + { + "bbox": [ + 46, + 448, + 287, + 590 + ], + "type": "text", + "content": " represents multimodal event selection and alignment. The deep model references language events to select video events of interest. Then it aligns event representations and infers a unified event representation " + }, + { + "bbox": [ + 46, + 448, + 287, + 590 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 46, + 448, + 287, + 590 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 592, + 287, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 592, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 592, + 287, + 664 + ], + "type": "inline_equation", + "content": "E \\to Y" + }, + { + "bbox": [ + 46, + 592, + 287, + 664 + ], + "type": "text", + "content": " represents the direct causal effect from the unified feature of the concerned event to the label, which is an ideal way that remains invariant in other data D with different data distributions. For example, \"play cricket\" is causally related to cricket bat and swing, and irrelevant to \"indoor\" and \"outdoor\"." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "V \\gets D \\to Y" + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": " denotes that the data domain " + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": " as a confounder provides a spurious shortcut from video " + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": " to label " + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": " in the visual domain. Specifically, the data domain " + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": " represents the statistical relationships contained in the lim" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": "ited collected video data to represent the co-occurrence of objects and labels. In the top example in Fig. 1, \"TV\" and \"indoor\" provide the shortcut connection that is identified as \"karaoke\" because of lacking human interaction event." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 120, + 545, + 227 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 120, + 545, + 227 + ], + "spans": [ + { + "bbox": [ + 304, + 120, + 545, + 227 + ], + "type": "inline_equation", + "content": "S \\gets D \\to Y" + }, + { + "bbox": [ + 304, + 120, + 545, + 227 + ], + "type": "text", + "content": " denotes that the data domain " + }, + { + "bbox": [ + 304, + 120, + 545, + 227 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 120, + 545, + 227 + ], + "type": "text", + "content": " also establishes spurious associations between sentence " + }, + { + "bbox": [ + 304, + 120, + 545, + 227 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 120, + 545, + 227 + ], + "type": "text", + "content": " and label " + }, + { + "bbox": [ + 304, + 120, + 545, + 227 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 304, + 120, + 545, + 227 + ], + "type": "text", + "content": ". This is reflected in the fact that the model is easy to establish the association between labels and local concerned expressions of sentences while ignoring the overall expressions. Especially in multiple-choice questions, the model shows a stronger preference for the local \"key\" representation. For example, in the below example in Fig. 1, the model selects the locally correct answer, \"someone\" and \"help\"." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 228, + 545, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 228, + 545, + 360 + ], + "spans": [ + { + "bbox": [ + 304, + 228, + 545, + 360 + ], + "type": "text", + "content": "Causal Intervention. The well-known backdoor adjustment [27] helps in eliminating spurious correlations, resulting in better generalization for the model. We present the true causality from V and S to Y as " + }, + { + "bbox": [ + 304, + 228, + 545, + 360 + ], + "type": "inline_equation", + "content": "P(Y|do(V,S))" + }, + { + "bbox": [ + 304, + 228, + 545, + 360 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 228, + 545, + 360 + ], + "type": "inline_equation", + "content": "do()" + }, + { + "bbox": [ + 304, + 228, + 545, + 360 + ], + "type": "text", + "content": " denotes the interventional operation. " + }, + { + "bbox": [ + 304, + 228, + 545, + 360 + ], + "type": "inline_equation", + "content": "P(Y|do(V,S))" + }, + { + "bbox": [ + 304, + 228, + 545, + 360 + ], + "type": "text", + "content": " can cut off the link " + }, + { + "bbox": [ + 304, + 228, + 545, + 360 + ], + "type": "inline_equation", + "content": "D\\to V" + }, + { + "bbox": [ + 304, + 228, + 545, + 360 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 228, + 545, + 360 + ], + "type": "inline_equation", + "content": "D\\rightarrow S" + }, + { + "bbox": [ + 304, + 228, + 545, + 360 + ], + "type": "text", + "content": " to block this backdoor path by changing the original training data into new data " + }, + { + "bbox": [ + 304, + 228, + 545, + 360 + ], + "type": "inline_equation", + "content": "\\mathcal{T} = \\{\\tau_1,\\dots,\\tau_h\\}" + }, + { + "bbox": [ + 304, + 228, + 545, + 360 + ], + "type": "text", + "content": ". Each of them donates a confounder stratum (total " + }, + { + "bbox": [ + 304, + 228, + 545, + 360 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 304, + 228, + 545, + 360 + ], + "type": "text", + "content": "), guiding the model to find invariants from the confounder. The backdoor adjustment can be represented as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 331, + 368, + 545, + 450 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 331, + 368, + 545, + 450 + ], + "spans": [ + { + "bbox": [ + 331, + 368, + 545, + 450 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} P \\left(Y \\mid d o (V, S)\\right) = \\sum_ {\\tau \\in \\mathcal {T}} P (Y | V, S, \\tau) P (\\tau) \\\\ = \\sum_ {\\tau_ {v} \\in \\mathcal {T} _ {v}} P (Y | V, \\tau_ {v}) P (\\tau_ {v}) \\tag {1} \\\\ + \\sum_ {\\tau_ {s} \\in \\mathcal {T} _ {s}} P (Y | S, \\tau_ {s}) P (\\tau_ {s}) \\\\ \\end{array}", + "image_path": "8c825e5929e028e047965d045575237be40a0895800ba36f3375f91e1bedbfa0.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 459, + 545, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 459, + 545, + 666 + ], + "spans": [ + { + "bbox": [ + 304, + 459, + 545, + 666 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 459, + 545, + 666 + ], + "type": "inline_equation", + "content": "P(Y|V,S,\\tau)" + }, + { + "bbox": [ + 304, + 459, + 545, + 666 + ], + "type": "text", + "content": " denotes the prediction in each new data split " + }, + { + "bbox": [ + 304, + 459, + 545, + 666 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 459, + 545, + 666 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 459, + 545, + 666 + ], + "type": "inline_equation", + "content": "P(\\tau)" + }, + { + "bbox": [ + 304, + 459, + 545, + 666 + ], + "type": "text", + "content": " denotes confounder selection probability for a specific video and sentence, calculated by " + }, + { + "bbox": [ + 304, + 459, + 545, + 666 + ], + "type": "inline_equation", + "content": "P(\\tau) \\coloneqq \\frac{1}{h}" + }, + { + "bbox": [ + 304, + 459, + 545, + 666 + ], + "type": "text", + "content": ". We calculate probability estimates separately by two individual architectures for video and text. In this way, the interaction cuts off the confounder effect in " + }, + { + "bbox": [ + 304, + 459, + 545, + 666 + ], + "type": "inline_equation", + "content": "V \\gets D \\to Y" + }, + { + "bbox": [ + 304, + 459, + 545, + 666 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 459, + 545, + 666 + ], + "type": "inline_equation", + "content": "S \\gets D \\to Y" + }, + { + "bbox": [ + 304, + 459, + 545, + 666 + ], + "type": "text", + "content": " as shown in Fig. 2. Take video data as an example, traversing all the confounders for a video is expensive. When the video number in the dataset is " + }, + { + "bbox": [ + 304, + 459, + 545, + 666 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 304, + 459, + 545, + 666 + ], + "type": "text", + "content": ", Eq. 1 expands the training data from " + }, + { + "bbox": [ + 304, + 459, + 545, + 666 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 304, + 459, + 545, + 666 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 459, + 545, + 666 + ], + "type": "inline_equation", + "content": "\\mathcal{M}^2" + }, + { + "bbox": [ + 304, + 459, + 545, + 666 + ], + "type": "text", + "content": " within one epoch with additional memory consumption. Therefore, to balance the scale of confounder set " + }, + { + "bbox": [ + 304, + 459, + 545, + 666 + ], + "type": "inline_equation", + "content": "\\mathcal{T}_v" + }, + { + "bbox": [ + 304, + 459, + 545, + 666 + ], + "type": "text", + "content": " and training speed, we find the confounder by our MCR and combine it with original data V every epoch. After " + }, + { + "bbox": [ + 304, + 459, + 545, + 666 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 459, + 545, + 666 + ], + "type": "text", + "content": " training epochs, we can approximate the visual part of the adjustment equation, i.e. " + }, + { + "bbox": [ + 304, + 459, + 545, + 666 + ], + "type": "inline_equation", + "content": "\\sum_{\\tau_v \\in \\mathcal{T}_v} P(Y|V, \\tau_v) P(\\tau_v) \\approx \\sum_{k=1}^{K} \\sum_{\\tau_v \\in \\mathcal{T}_v^k} P(Y|V, \\tau_v) P(\\tau_v)" + }, + { + "bbox": [ + 304, + 459, + 545, + 666 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 666, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 666, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 666, + 545, + 714 + ], + "type": "text", + "content": "Preliminary. Given a video " + }, + { + "bbox": [ + 304, + 666, + 545, + 714 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 666, + 545, + 714 + ], + "type": "text", + "content": ", VideoQA aims to understand acting events by asking questions " + }, + { + "bbox": [ + 304, + 666, + 545, + 714 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 304, + 666, + 545, + 714 + ], + "type": "text", + "content": " and predict the correct answer " + }, + { + "bbox": [ + 304, + 666, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\widetilde{a}" + }, + { + "bbox": [ + 304, + 666, + 545, + 714 + ], + "type": "text", + "content": " from a answer candidate set " + }, + { + "bbox": [ + 304, + 666, + 545, + 714 + ], + "type": "inline_equation", + "content": "A = \\{a_{z}\\}_{z=1}^{Z}" + }, + { + "bbox": [ + 304, + 666, + 545, + 714 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 666, + 545, + 714 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 304, + 666, + 545, + 714 + ], + "type": "text", + "content": " is the candidate number. The process is generally formu" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19029" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 69, + 547, + 300 + ], + "blocks": [ + { + "bbox": [ + 47, + 69, + 547, + 300 + ], + "lines": [ + { + "bbox": [ + 47, + 69, + 547, + 300 + ], + "spans": [ + { + "bbox": [ + 47, + 69, + 547, + 300 + ], + "type": "image", + "image_path": "cbf55aa4b01413cbb273709b887b0d1f0da6360e372d3d197559b8b6f81a8cdb.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 310, + 546, + 376 + ], + "lines": [ + { + "bbox": [ + 46, + 310, + 546, + 376 + ], + "spans": [ + { + "bbox": [ + 46, + 310, + 546, + 376 + ], + "type": "text", + "content": "Figure 3. Visual Causal Module. Before the appearance information and motion information are sent to the backbone for question answering, we propose a visual causal module to find object-level causal features and irrelevant features in video data. The image-level visual features are first divided into object-level visual features by the detected bounding box. The category information, location information and interaction relationship of each object are modeled by Interaction Detector. According to the question prompt, the Indicator judges whether the features of different objects are causally related or irrelevant. The uniform representation of causal and irrelevant features are used for further prediction in the VideoQA backbone." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 396, + 116, + 406 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 396, + 116, + 406 + ], + "spans": [ + { + "bbox": [ + 47, + 396, + 116, + 406 + ], + "type": "text", + "content": "lated as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 113, + 412, + 287, + 433 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 412, + 287, + 433 + ], + "spans": [ + { + "bbox": [ + 113, + 412, + 287, + 433 + ], + "type": "interline_equation", + "content": "\\widetilde {a} = \\underset {a \\in A} {\\operatorname {a r g m a x}} \\mathcal {F} _ {\\theta} (a | q, I), \\tag {2}", + "image_path": "973e48a7fb2c2630450dffc562dddd9e894441c759e51e15ac7b2f890b8cffe1.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 439, + 287, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 439, + 287, + 498 + ], + "spans": [ + { + "bbox": [ + 47, + 439, + 287, + 498 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 439, + 287, + 498 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 47, + 439, + 287, + 498 + ], + "type": "text", + "content": " represents the set of model parameters of VideoQA function " + }, + { + "bbox": [ + 47, + 439, + 287, + 498 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 47, + 439, + 287, + 498 + ], + "type": "text", + "content": ", which maps a pair of video and question into the same feature domain to find the answer. In our work, we do not change the VideoQA function " + }, + { + "bbox": [ + 47, + 439, + 287, + 498 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 47, + 439, + 287, + 498 + ], + "type": "text", + "content": ". In a causal view, we intervene video " + }, + { + "bbox": [ + 47, + 439, + 287, + 498 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 47, + 439, + 287, + 498 + ], + "type": "text", + "content": " and answer candidate A." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 506, + 173, + 517 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 506, + 173, + 517 + ], + "spans": [ + { + "bbox": [ + 47, + 506, + 173, + 517 + ], + "type": "text", + "content": "3.2. Visual Causal Module" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 525, + 287, + 690 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 525, + 287, + 690 + ], + "spans": [ + { + "bbox": [ + 47, + 525, + 287, + 690 + ], + "type": "text", + "content": "To answer the question with accurate causally related features, we propose a visual causal module that disentangles the confounder and causal factors at the object level. As shown in Fig. 3, the video with shape " + }, + { + "bbox": [ + 47, + 525, + 287, + 690 + ], + "type": "inline_equation", + "content": "W \\times H \\times L" + }, + { + "bbox": [ + 47, + 525, + 287, + 690 + ], + "type": "text", + "content": " is encoded by 2D ConvNet, 3D ConvNet into a list of appearance feature and motion feature with shape " + }, + { + "bbox": [ + 47, + 525, + 287, + 690 + ], + "type": "inline_equation", + "content": "\\frac{W}{16} \\times \\frac{H}{16} \\times \\frac{L}{2}" + }, + { + "bbox": [ + 47, + 525, + 287, + 690 + ], + "type": "text", + "content": ". They are uniformly represented by frame feature sequence " + }, + { + "bbox": [ + 47, + 525, + 287, + 690 + ], + "type": "inline_equation", + "content": "\\mathcal{V} = \\{v_t\\}_{t=1}^{\\frac{L}{2}}" + }, + { + "bbox": [ + 47, + 525, + 287, + 690 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 525, + 287, + 690 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 525, + 287, + 690 + ], + "type": "text", + "content": " means timestamp. The object-level grounding is detected by pre-trained Detection ConvNet and donated as the bounding box " + }, + { + "bbox": [ + 47, + 525, + 287, + 690 + ], + "type": "inline_equation", + "content": "\\mathcal{B} = \\{b_{n,t}\\}_{n=1,t=1}^{N,\\frac{L}{2}}" + }, + { + "bbox": [ + 47, + 525, + 287, + 690 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 525, + 287, + 690 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 47, + 525, + 287, + 690 + ], + "type": "text", + "content": " is the detected object number. We use Region of Interest (ROI) Align [13] to extract object visual features " + }, + { + "bbox": [ + 47, + 525, + 287, + 690 + ], + "type": "inline_equation", + "content": "\\mathcal{O} = \\{o_{n,t}\\}_{n=1,t=1}^{N,\\frac{L}{2}}" + }, + { + "bbox": [ + 47, + 525, + 287, + 690 + ], + "type": "text", + "content": ", expressed as " + }, + { + "bbox": [ + 47, + 525, + 287, + 690 + ], + "type": "inline_equation", + "content": "\\mathcal{O} = ROIAlign(\\mathcal{V}|\\mathcal{B})" + }, + { + "bbox": [ + 47, + 525, + 287, + 690 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 690, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 690, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 690, + 287, + 714 + ], + "type": "text", + "content": "Since the scene in the real video is ever-changing, some objects in the video may suddenly disappear or appear, mak" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 396, + 545, + 454 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 396, + 545, + 454 + ], + "spans": [ + { + "bbox": [ + 304, + 396, + 545, + 454 + ], + "type": "text", + "content": "ing it difficult to obtain accurate instance tracking data. Therefore, we extract unified features for the same category of targets, e.g. human, chairs. When objects of this category do not appear in part of the consecutive frames, we fill the feature with 0 value." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 455, + 545, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 455, + 545, + 491 + ], + "spans": [ + { + "bbox": [ + 304, + 455, + 545, + 491 + ], + "type": "text", + "content": "For each object feature, we employ Multilayer Perceptrons (MLP) and Long short-term memory (LSTM) [12] to encode the temporal embedding for visual feature:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 369, + 498, + 545, + 512 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 369, + 498, + 545, + 512 + ], + "spans": [ + { + "bbox": [ + 369, + 498, + 545, + 512 + ], + "type": "interline_equation", + "content": "\\mathcal {O} ^ {g} = L S T M (M L P (\\mathcal {O})), \\tag {3}", + "image_path": "34e74df6a4d414d0074e6e957f2f73d433ff94f7f6b59653a3490dc10c75cccf.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 518, + 545, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 518, + 545, + 601 + ], + "spans": [ + { + "bbox": [ + 304, + 518, + 545, + 601 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 518, + 545, + 601 + ], + "type": "inline_equation", + "content": "\\mathcal{O}^g = \\{o_n^g\\}_{n=1}^N \\in \\mathbb{R}^d" + }, + { + "bbox": [ + 304, + 518, + 545, + 601 + ], + "type": "text", + "content": " is the global N object representations, and " + }, + { + "bbox": [ + 304, + 518, + 545, + 601 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 518, + 545, + 601 + ], + "type": "text", + "content": " is the hidden dimension of LSTM. In addition to the visual encoding, we also model the bounding box position correlations " + }, + { + "bbox": [ + 304, + 518, + 545, + 601 + ], + "type": "inline_equation", + "content": "\\mathcal{B}" + }, + { + "bbox": [ + 304, + 518, + 545, + 601 + ], + "type": "text", + "content": ", object category " + }, + { + "bbox": [ + 304, + 518, + 545, + 601 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 518, + 545, + 601 + ], + "type": "text", + "content": ", and spatiotemporal inter-object and intra-object interactions in an Interaction Detecting stream. They are implemented by Non-local Net [30] with MLP:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 323, + 609, + 545, + 623 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 609, + 545, + 623 + ], + "spans": [ + { + "bbox": [ + 323, + 609, + 545, + 623 + ], + "type": "interline_equation", + "content": "L ^ {g} = \\operatorname {N o n L} \\left(M L P \\left(M L P (\\mathcal {B}); M L P (C)\\right)\\right), \\tag {4}", + "image_path": "281e428ba6e2e4651bbd9b7825e2d22b38e8724dcbc0112beb14f88268196c3b.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": "where; represents channel concatenation. " + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "inline_equation", + "content": "L^{g} = \\{l_{n}^{g}\\}_{n = 1}^{N}\\in" + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^d" + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": " means detected interaction feature. The outputs of two feature extraction streams are then fused by channel concatenation: " + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{O}^g = [\\mathcal{O}^g;L^g ]" + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": " . All objects are causal or irrelevant candidates. Their identities are determined by the language semantics of the question. Therefore, given a question sentence, we apply Word Parser and Event Embedding" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19030" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": "to get the global question representation " + }, + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "inline_equation", + "content": "q^g" + }, + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": ". The Event Embedding is implemented by LSTM:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 110, + 106, + 287, + 120 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 106, + 287, + 120 + ], + "spans": [ + { + "bbox": [ + 110, + 106, + 287, + 120 + ], + "type": "interline_equation", + "content": "q ^ {g} = L S T M (P a r s e r (q)), \\tag {5}", + "image_path": "c75df8e4c77d3aa97bf177300febd81ea59f4a70eb0a250c7e1d0e0899c9aeac.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 129, + 287, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 129, + 287, + 308 + ], + "spans": [ + { + "bbox": [ + 46, + 129, + 287, + 308 + ], + "type": "text", + "content": "where Parser uses a pre-trained GloVe model [28] or BERT model [6]. LSTM is implemented by the question embedding model of the VideoQA backbone. With the specific question, causally related objects are usually a small part of object set " + }, + { + "bbox": [ + 46, + 129, + 287, + 308 + ], + "type": "inline_equation", + "content": "\\mathcal{O}^g" + }, + { + "bbox": [ + 46, + 129, + 287, + 308 + ], + "type": "text", + "content": " and are interconnected internally. Reasoning about their relationship to unrelated objects is redundant and prone to spurious associations. Therefore, inspired by [22], we use hard segmentation [22] in Indicator to explicitly divide object features into causally related features and irrelevant features, rather than soft GCN inference or attention-based models. Specifically, the question embedding " + }, + { + "bbox": [ + 46, + 129, + 287, + 308 + ], + "type": "inline_equation", + "content": "q^{g}" + }, + { + "bbox": [ + 46, + 129, + 287, + 308 + ], + "type": "text", + "content": " and objects feature " + }, + { + "bbox": [ + 46, + 129, + 287, + 308 + ], + "type": "inline_equation", + "content": "\\mathcal{O}^g" + }, + { + "bbox": [ + 46, + 129, + 287, + 308 + ], + "type": "text", + "content": " are mapped into the same space by MLP. The Indicator computes a score for each object feature and uses Gumbel-Softmax [17] to classify the causal attribute labels of objects:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 75, + 317, + 287, + 338 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 75, + 317, + 287, + 338 + ], + "spans": [ + { + "bbox": [ + 75, + 317, + 287, + 338 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {O} ^ {c} = G S (M L P (q ^ {g}) \\cdot (M L P (\\mathcal {O} ^ {g}) ^ {T})) \\circ \\mathcal {O}, \\\\ \\mathcal {O} ^ {\\bar {c}} = \\mathcal {O} - \\mathcal {O} ^ {c} \\end{array} \\tag {6}", + "image_path": "ddafb5c72524c43b5c35b591d2158cc8688bece3d18eb369ec30c86e75c64641.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 78, + 334, + 140, + 346 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 334, + 140, + 346 + ], + "spans": [ + { + "bbox": [ + 78, + 334, + 140, + 346 + ], + "type": "interline_equation", + "content": "\\mathcal {O} ^ {\\bar {c}} = \\mathcal {O} - \\mathcal {O} ^ {c},", + "image_path": "ec2b54c625c5333aa9bb3653abd642426842193c713fe1852998564c5dd1e18b.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 356, + 287, + 451 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 356, + 287, + 451 + ], + "spans": [ + { + "bbox": [ + 47, + 356, + 287, + 451 + ], + "type": "text", + "content": "where GS means Gumbel-Softmax and " + }, + { + "bbox": [ + 47, + 356, + 287, + 451 + ], + "type": "inline_equation", + "content": "\\cdot" + }, + { + "bbox": [ + 47, + 356, + 287, + 451 + ], + "type": "text", + "content": " means matrix multiplication. " + }, + { + "bbox": [ + 47, + 356, + 287, + 451 + ], + "type": "inline_equation", + "content": "\\circ" + }, + { + "bbox": [ + 47, + 356, + 287, + 451 + ], + "type": "text", + "content": " means multiply by index. " + }, + { + "bbox": [ + 47, + 356, + 287, + 451 + ], + "type": "inline_equation", + "content": "\\mathcal{O}^c = \\{o_n^c\\}_{n^c = 1}^{N^c},\\mathcal{O}^{\\bar{c}} = \\{o_{n^{\\bar{c}}}^{\\bar{c}}\\}_{n^{\\bar{c}} = 1}^{N^{\\bar{c}}}" + }, + { + "bbox": [ + 47, + 356, + 287, + 451 + ], + "type": "text", + "content": " are causal object features set and irrelevant features set, respectively, where the corner mark of length is omitted for clarity. We average the features in these sets to obtain causal visual features and irrelevant visual features, respectively: " + }, + { + "bbox": [ + 47, + 356, + 287, + 451 + ], + "type": "inline_equation", + "content": "\\mathcal{V}^c = \\frac{1}{N^c}\\sum \\mathcal{O}^c," + }, + { + "bbox": [ + 47, + 356, + 287, + 451 + ], + "type": "inline_equation", + "content": "\\mathcal{V}^{\\bar{c}} = \\frac{1}{N^{\\bar{c}}}\\sum \\mathcal{O}^{\\bar{c}}." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 452, + 287, + 523 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 452, + 287, + 523 + ], + "spans": [ + { + "bbox": [ + 46, + 452, + 287, + 523 + ], + "type": "text", + "content": "According to the deduction of Eq. 1, in the visual part, the video V and the average sampling confounder are combined to predict the label. In model designing, the video V can be present by causal object features " + }, + { + "bbox": [ + 46, + 452, + 287, + 523 + ], + "type": "inline_equation", + "content": "\\nu^{c}" + }, + { + "bbox": [ + 46, + 452, + 287, + 523 + ], + "type": "text", + "content": ". The confounder is from the confounder of another example in the same mini-batch, represented by:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 99, + 532, + 287, + 556 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 99, + 532, + 287, + 556 + ], + "spans": [ + { + "bbox": [ + 99, + 532, + 287, + 556 + ], + "type": "interline_equation", + "content": "\\hat {\\mathcal {V}} = \\frac {1}{N ^ {c} + N ^ {\\prime \\bar {c}}} \\sum \\left(O ^ {c} + O ^ {\\prime \\bar {c}}\\right), \\tag {7}", + "image_path": "52201db9fcb3d35b3f7c284a7f8ff7074ce651d9d301a1438bb2678bb4ae8cd5.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 566, + 287, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 566, + 287, + 639 + ], + "spans": [ + { + "bbox": [ + 47, + 566, + 287, + 639 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 566, + 287, + 639 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{V}}" + }, + { + "bbox": [ + 47, + 566, + 287, + 639 + ], + "type": "text", + "content": " is the blended features. " + }, + { + "bbox": [ + 47, + 566, + 287, + 639 + ], + "type": "inline_equation", + "content": "O^{\\prime\\bar{c}}" + }, + { + "bbox": [ + 47, + 566, + 287, + 639 + ], + "type": "text", + "content": " is the confounder of another example. " + }, + { + "bbox": [ + 47, + 566, + 287, + 639 + ], + "type": "inline_equation", + "content": "N^{\\prime\\bar{c}}" + }, + { + "bbox": [ + 47, + 566, + 287, + 639 + ], + "type": "text", + "content": " is the object number of " + }, + { + "bbox": [ + 47, + 566, + 287, + 639 + ], + "type": "inline_equation", + "content": "O^{\\prime\\bar{c}}" + }, + { + "bbox": [ + 47, + 566, + 287, + 639 + ], + "type": "text", + "content": ". Both " + }, + { + "bbox": [ + 47, + 566, + 287, + 639 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 47, + 566, + 287, + 639 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 566, + 287, + 639 + ], + "type": "inline_equation", + "content": "\\mathcal{V}^{c}" + }, + { + "bbox": [ + 47, + 566, + 287, + 639 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 566, + 287, + 639 + ], + "type": "inline_equation", + "content": "\\mathcal{V}^{\\bar{c}}" + }, + { + "bbox": [ + 47, + 566, + 287, + 639 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 566, + 287, + 639 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{V}}" + }, + { + "bbox": [ + 47, + 566, + 287, + 639 + ], + "type": "text", + "content": " are sent to the VideoQA backbone for training the visual causal module. The visual module can capture causal relationships between object features and labels, providing a stable association for multimodal data." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 647, + 178, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 178, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 178, + 658 + ], + "type": "text", + "content": "3.3. Textual Causal Module" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 665, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 665, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 665, + 287, + 713 + ], + "type": "text", + "content": "For textual causal inference, prediction is often plagued by correlations between local language semantics and visual features. Therefore, the key to getting rid of text confounders is to enhance the model's ability to recognize" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 307, + 69, + 545, + 163 + ], + "blocks": [ + { + "bbox": [ + 307, + 69, + 545, + 163 + ], + "lines": [ + { + "bbox": [ + 307, + 69, + 545, + 163 + ], + "spans": [ + { + "bbox": [ + 307, + 69, + 545, + 163 + ], + "type": "image", + "image_path": "9abda42351a4d760930a942ef6568260b9a7dab9783d0a1e9e699bfc99aa41ee.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 174, + 545, + 208 + ], + "lines": [ + { + "bbox": [ + 305, + 174, + 545, + 208 + ], + "spans": [ + { + "bbox": [ + 305, + 174, + 545, + 208 + ], + "type": "text", + "content": "Figure 4. Textual Causal Module. Keywords are selected as confounders from the prediction results by the indicator. They are sent to the intervenor to generate new candidates." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 225, + 545, + 248 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 225, + 545, + 248 + ], + "spans": [ + { + "bbox": [ + 305, + 225, + 545, + 248 + ], + "type": "text", + "content": "such confusing samples which are implemented by a textual causal module." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 249, + 545, + 333 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 249, + 545, + 333 + ], + "spans": [ + { + "bbox": [ + 305, + 249, + 545, + 333 + ], + "type": "text", + "content": "In the VideoQA base model, the visual information and the question have been aligned, containing the events information related to the answer. Therefore, we use the alignment feature " + }, + { + "bbox": [ + 305, + 249, + 545, + 333 + ], + "type": "inline_equation", + "content": "f_{qv} = \\mathcal{F}(\\mathcal{V}^c, q^g)" + }, + { + "bbox": [ + 305, + 249, + 545, + 333 + ], + "type": "text", + "content": " to retrieve the keywords in the answer. As shown in Fig. 4, the same with question embedding, we encode the answer by Word Parser and Event Embedding:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 362, + 340, + 545, + 354 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 362, + 340, + 545, + 354 + ], + "spans": [ + { + "bbox": [ + 362, + 340, + 545, + 354 + ], + "type": "interline_equation", + "content": "a ^ {g}, a ^ {l} = L S T M (P a r s e r (a)), \\tag {8}", + "image_path": "74c22ceeae043439465af32ab360841efd2371e7a6c22fad58d56fc86a613d17.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 361, + 545, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 361, + 545, + 411 + ], + "spans": [ + { + "bbox": [ + 305, + 361, + 545, + 411 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 361, + 545, + 411 + ], + "type": "inline_equation", + "content": "a^g" + }, + { + "bbox": [ + 305, + 361, + 545, + 411 + ], + "type": "text", + "content": " is the global representation of the answer, and " + }, + { + "bbox": [ + 305, + 361, + 545, + 411 + ], + "type": "inline_equation", + "content": "a^l" + }, + { + "bbox": [ + 305, + 361, + 545, + 411 + ], + "type": "text", + "content": " is the local representation of each word. The same with visual Indicator, we select the keyword by the relation score between " + }, + { + "bbox": [ + 305, + 361, + 545, + 411 + ], + "type": "inline_equation", + "content": "a^g" + }, + { + "bbox": [ + 305, + 361, + 545, + 411 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 361, + 545, + 411 + ], + "type": "inline_equation", + "content": "f_{qv}" + }, + { + "bbox": [ + 305, + 361, + 545, + 411 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 335, + 416, + 545, + 430 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 335, + 416, + 545, + 430 + ], + "spans": [ + { + "bbox": [ + 335, + 416, + 545, + 430 + ], + "type": "interline_equation", + "content": "a ^ {\\bar {c}} = G S \\left(M L P \\left(f _ {q v}\\right) \\cdot \\left(M L P \\left(a ^ {g}\\right)\\right) ^ {T}\\right) \\circ a ^ {l}, \\tag {9}", + "image_path": "a6f9d9aa52b4210902658ae242f786b278f280e070a1717c8c5593467f13e457.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 437, + 545, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 437, + 545, + 472 + ], + "spans": [ + { + "bbox": [ + 305, + 437, + 545, + 472 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 437, + 545, + 472 + ], + "type": "inline_equation", + "content": "a^{\\bar{c}}" + }, + { + "bbox": [ + 305, + 437, + 545, + 472 + ], + "type": "text", + "content": " represents the keywords, which are potential confounders in this question. " + }, + { + "bbox": [ + 305, + 437, + 545, + 472 + ], + "type": "inline_equation", + "content": "a^{c} = a^{l} - a^{\\bar{c}}" + }, + { + "bbox": [ + 305, + 437, + 545, + 472 + ], + "type": "text", + "content": " represents other words." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 473, + 545, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 473, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 305, + 473, + 545, + 555 + ], + "type": "text", + "content": "According to the textual part of Eq. 1, the label is predicted by the sentence and confounder. Due to the correlation between sentences and videos, we look for confounders of sentences from the same video, especially the predicted answer by VideoQA backbone which contains factors that increase the score. Similar to visual intervention, we pick confounders once per epoch." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 556, + 545, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 556, + 545, + 639 + ], + "spans": [ + { + "bbox": [ + 305, + 556, + 545, + 639 + ], + "type": "text", + "content": "Confounders are used to augment the hard sample of candidates that changes the textual distributions. The model joint original candidates " + }, + { + "bbox": [ + 305, + 556, + 545, + 639 + ], + "type": "inline_equation", + "content": "A = \\{a_{z}\\}_{z=1}^{Z}" + }, + { + "bbox": [ + 305, + 556, + 545, + 639 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 305, + 556, + 545, + 639 + ], + "type": "inline_equation", + "content": "a^{\\bar{c}}" + }, + { + "bbox": [ + 305, + 556, + 545, + 639 + ], + "type": "text", + "content": " by inserting " + }, + { + "bbox": [ + 305, + 556, + 545, + 639 + ], + "type": "inline_equation", + "content": "a^{\\bar{c}}" + }, + { + "bbox": [ + 305, + 556, + 545, + 639 + ], + "type": "text", + "content": " at the beginning or end of a sentence and generate a new candidates set " + }, + { + "bbox": [ + 305, + 556, + 545, + 639 + ], + "type": "inline_equation", + "content": "\\hat{A} = \\{\\hat{a}_{z}\\}_{z=1}^{Z}" + }, + { + "bbox": [ + 305, + 556, + 545, + 639 + ], + "type": "text", + "content": ". In the training process, we randomly replace the negative example from the new candidates set " + }, + { + "bbox": [ + 305, + 556, + 545, + 639 + ], + "type": "inline_equation", + "content": "\\hat{A}" + }, + { + "bbox": [ + 305, + 556, + 545, + 639 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 647, + 369, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 647, + 369, + 659 + ], + "spans": [ + { + "bbox": [ + 306, + 647, + 369, + 659 + ], + "type": "text", + "content": "3.4. Training" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 666, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 666, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 666, + 545, + 713 + ], + "type": "text", + "content": "In this section, we introduce our training targets and training pipeline for multimodal data. The algorithm can be found in Supplementary. First of all, to ensure the domain consistency of training sets and test sets, we train" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19031" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 106 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 106 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 106 + ], + "type": "text", + "content": "the VideoQA backbone with raw data " + }, + { + "bbox": [ + 46, + 72, + 287, + 106 + ], + "type": "inline_equation", + "content": "(\\mathcal{V},\\mathrm{A})" + }, + { + "bbox": [ + 46, + 72, + 287, + 106 + ], + "type": "text", + "content": " , which also guarantees that the training process satisfies the pre-defined causal formulation:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 96, + 115, + 287, + 129 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 115, + 287, + 129 + ], + "spans": [ + { + "bbox": [ + 96, + 115, + 287, + 129 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {o} = \\mathrm {X E} \\left(\\mathcal {F} \\left((\\mathcal {V}, \\mathrm {q}), (\\mathcal {V}, \\mathrm {A})\\right), \\mathrm {a}\\right), \\tag {10}", + "image_path": "bb0e596d6c16eea4b2c27088445df6bf07a6561c8440ea5b60bcb3db79b7fe19.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 135, + 287, + 194 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 135, + 287, + 194 + ], + "spans": [ + { + "bbox": [ + 46, + 135, + 287, + 194 + ], + "type": "text", + "content": "where XE is the cross-entropy loss. " + }, + { + "bbox": [ + 46, + 135, + 287, + 194 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 46, + 135, + 287, + 194 + ], + "type": "text", + "content": " calculates the dot-product between question-related visual features and answer-related visual features as the predicted results. At test time, we use the candidate with the highest score as the predicted result as in Eq.2." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 195, + 287, + 314 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 195, + 287, + 314 + ], + "spans": [ + { + "bbox": [ + 46, + 195, + 287, + 314 + ], + "type": "text", + "content": "Visual Module Loss. Visual module loss aims to capture causal object features and non-causal object features for further robust prediction. In the training stage, the causal visual features have the same ability for question answering, which is restricted by the cross-entropy loss: " + }, + { + "bbox": [ + 46, + 195, + 287, + 314 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{c}}^{\\mathrm{v}}" + }, + { + "bbox": [ + 46, + 195, + 287, + 314 + ], + "type": "text", + "content": ". In contrast, non-causal objects are irrelevant to the question and should be unbiased toward answer candidates: " + }, + { + "bbox": [ + 46, + 195, + 287, + 314 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\bar{c}}^{\\mathrm{v}}" + }, + { + "bbox": [ + 46, + 195, + 287, + 314 + ], + "type": "text", + "content": ". The blended data " + }, + { + "bbox": [ + 46, + 195, + 287, + 314 + ], + "type": "inline_equation", + "content": "\\hat{\\nu}" + }, + { + "bbox": [ + 46, + 195, + 287, + 314 + ], + "type": "text", + "content": " are supposed to obtain the same effect with causal feature: " + }, + { + "bbox": [ + 46, + 195, + 287, + 314 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_o^{\\mathrm{v}}" + }, + { + "bbox": [ + 46, + 195, + 287, + 314 + ], + "type": "text", + "content": ". The formulation of visual module loss shows as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 81, + 319, + 227, + 332 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 81, + 319, + 227, + 332 + ], + "spans": [ + { + "bbox": [ + 81, + 319, + 227, + 332 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {c}} ^ {\\mathrm {v}} = \\operatorname {X E} \\left(\\mathcal {F} \\left(\\left(\\mathcal {V} ^ {\\mathrm {c}}, \\mathrm {q}\\right), \\left(\\mathcal {V} ^ {\\mathrm {c}}, \\mathrm {A}\\right)\\right), \\mathrm {a}\\right)", + "image_path": "5c948f42aa02e78ca100e5b36ef2aff2fa3e292c3fa4d5bec6ef32335691ac08.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 81, + 334, + 287, + 355 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 81, + 334, + 287, + 355 + ], + "spans": [ + { + "bbox": [ + 81, + 334, + 287, + 355 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\bar {c}} ^ {\\mathrm {v}} = \\operatorname {M S E} \\left(\\mathcal {F} \\left(\\left(\\mathcal {V} ^ {\\bar {c}}, \\mathrm {q}\\right), \\left(\\mathcal {V} ^ {\\bar {c}}, \\mathrm {A}\\right)\\right), \\text {a v g}\\right) \\tag {11}", + "image_path": "54d2b7ddcbfd9e891420ec12f4e781697d78d2ae84d2ce7f7965f489f49bdf3a.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 81, + 353, + 215, + 365 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 81, + 353, + 215, + 365 + ], + "spans": [ + { + "bbox": [ + 81, + 353, + 215, + 365 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\hat {\\partial}} ^ {\\mathrm {v}} = \\operatorname {X E} (\\mathcal {F} ((\\hat {\\mathcal {V}}, q), (\\hat {\\mathcal {V}}, A)), a),", + "image_path": "f775ad75d465f940b72f9c0e0ff2ab311536a697e805ec16e37f6ca70dc75752.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 82, + 368, + 171, + 380 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 368, + 171, + 380 + ], + "spans": [ + { + "bbox": [ + 82, + 368, + 171, + 380 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {v}} = \\mathcal {L} _ {\\mathrm {c}} ^ {\\mathrm {v}} + \\mathcal {L} _ {\\bar {c}} ^ {\\mathrm {v}} + \\mathcal {L} _ {\\hat {o}} ^ {\\mathrm {v}},", + "image_path": "28789b04d923715e0132875918473f6eeb0301e66cfff2d7d5226080f57d6788.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 387, + 287, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 387, + 287, + 422 + ], + "spans": [ + { + "bbox": [ + 47, + 387, + 287, + 422 + ], + "type": "text", + "content": "where avg is the average score of all candidates, avg = " + }, + { + "bbox": [ + 47, + 387, + 287, + 422 + ], + "type": "inline_equation", + "content": "\\mathcal{F}((\\mathcal{V},q),(\\mathcal{V},A))" + }, + { + "bbox": [ + 47, + 387, + 287, + 422 + ], + "type": "text", + "content": " . MSE means Mean Square Error for non-causal objects to get a neutral score." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 423, + 287, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 423, + 287, + 518 + ], + "spans": [ + { + "bbox": [ + 46, + 423, + 287, + 518 + ], + "type": "text", + "content": "Textual Module Loss. The text module loss aims to find keywords from the prediction results that directly affect the model selection and reduce the sensitivity of the model to keywords. Intuitively, keywords have the ability for prediction, while other words are difficult to judge the results. We use cross-entropy loss for keywords " + }, + { + "bbox": [ + 46, + 423, + 287, + 518 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{c}}^{\\mathrm{s}}" + }, + { + "bbox": [ + 46, + 423, + 287, + 518 + ], + "type": "text", + "content": " and MSE for other words " + }, + { + "bbox": [ + 46, + 423, + 287, + 518 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{c}}^{\\mathrm{s}}" + }, + { + "bbox": [ + 46, + 423, + 287, + 518 + ], + "type": "text", + "content": ". The blended answer is restricted by the cross-entropy loss " + }, + { + "bbox": [ + 46, + 423, + 287, + 518 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\hat{o}}^{\\mathrm{s}}" + }, + { + "bbox": [ + 46, + 423, + 287, + 518 + ], + "type": "text", + "content": ". The formulation of textual module loss is:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 89, + 526, + 230, + 541 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 89, + 526, + 230, + 541 + ], + "spans": [ + { + "bbox": [ + 89, + 526, + 230, + 541 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\bar {c}} ^ {\\mathrm {s}} = \\mathrm {X E} \\left(\\mathcal {F} \\left((\\mathcal {V}, \\mathrm {q}), (\\mathcal {V}, a ^ {\\bar {c}})\\right), \\mathrm {a}\\right)", + "image_path": "b4456e34951e48c47e140705120e0d171e059ea0f0702c639a7c59e616ad6c85.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 91, + 542, + 287, + 561 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 542, + 287, + 561 + ], + "spans": [ + { + "bbox": [ + 91, + 542, + 287, + 561 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {c}} ^ {\\mathrm {s}} = \\operatorname {M S E} \\left(\\mathcal {F} \\left(\\left(\\mathcal {V}, \\mathrm {q}\\right), \\left(\\mathcal {V}, a ^ {\\mathrm {c}}\\right)\\right), a v g\\right) \\tag {12}", + "image_path": "3b95617559d3a859d7fecd98fcc1824ba5989c172a3a430110d591e04da58bd1.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 91, + 559, + 219, + 572 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 559, + 219, + 572 + ], + "spans": [ + { + "bbox": [ + 91, + 559, + 219, + 572 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\hat {\\theta}} ^ {\\mathrm {s}} = \\operatorname {X E} (\\mathcal {F} ((\\mathcal {V}, q), (\\mathcal {V}, \\hat {A})), a)", + "image_path": "d48516220fd7b8170e9e6fa1a5bdfc68e00d5b653a7207461aebf70d1353fefe.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 91, + 574, + 177, + 587 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 574, + 177, + 587 + ], + "spans": [ + { + "bbox": [ + 91, + 574, + 177, + 587 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {s}} = \\mathcal {L} _ {\\mathrm {c}} ^ {\\mathrm {s}} + \\mathcal {L} _ {\\bar {\\mathrm {c}}} ^ {\\mathrm {s}} + \\mathcal {L} _ {\\delta} ^ {\\mathrm {s}}.", + "image_path": "c486b56e02c994b02f6df4d22c001811ecffc53e6b3860d5919fc80bfa9048e3.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 590, + 250, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 590, + 250, + 602 + ], + "spans": [ + { + "bbox": [ + 47, + 590, + 250, + 602 + ], + "type": "text", + "content": "The overall loss of our model can be expressed as:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 113, + 609, + 287, + 622 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 609, + 287, + 622 + ], + "spans": [ + { + "bbox": [ + 113, + 609, + 287, + 622 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {o} + \\lambda_ {1} \\mathcal {L} _ {\\mathrm {v}} + \\lambda_ {2} \\mathcal {L} _ {\\mathrm {s}}, \\tag {13}", + "image_path": "a1b6684eeee6db3cf6304e505a5ba4f439fb05203b3f1f9d5c044ba5cd9c5b1d.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 630, + 287, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 287, + 652 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 287, + 652 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 630, + 287, + 652 + ], + "type": "inline_equation", + "content": "\\lambda_{1}" + }, + { + "bbox": [ + 46, + 630, + 287, + 652 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 630, + 287, + 652 + ], + "type": "inline_equation", + "content": "\\lambda_{2}" + }, + { + "bbox": [ + 46, + 630, + 287, + 652 + ], + "type": "text", + "content": " are the hyper-parameters to balance the visual loss and textual loss." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "content": "Intervene Pipeline. We show the Intervene pipeline in Fig. 5. The textual intervention and the visual intervention are accomplished in two steps. Visual causal loss is computed with Eq. 11 and used to obtain causally related object features and irrelevant object features. They are used" + } + ] + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 333, + 70, + 521, + 137 + ], + "blocks": [ + { + "bbox": [ + 333, + 70, + 521, + 137 + ], + "lines": [ + { + "bbox": [ + 333, + 70, + 521, + 137 + ], + "spans": [ + { + "bbox": [ + 333, + 70, + 521, + 137 + ], + "type": "image", + "image_path": "59be354d816716dd4f1279a20f12dd18611c9ee409a4f1bf077c85a9b1f0bd4e.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 354, + 148, + 495, + 159 + ], + "lines": [ + { + "bbox": [ + 354, + 148, + 495, + 159 + ], + "spans": [ + { + "bbox": [ + 354, + 148, + 495, + 159 + ], + "type": "text", + "content": "Figure 5. Causal intervention pipeline." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 179, + 545, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 179, + 545, + 262 + ], + "spans": [ + { + "bbox": [ + 305, + 179, + 545, + 262 + ], + "type": "text", + "content": "to generate blended visual data with an intervenor, which is implemented by Eq. 7. Textual causal loss is computed with Eq. 12 and used to obtain keywords. Keywords are sent to textual interveners to generate blended textual data. We execute " + }, + { + "bbox": [ + 305, + 179, + 545, + 262 + ], + "type": "inline_equation", + "content": "K_{2}" + }, + { + "bbox": [ + 305, + 179, + 545, + 262 + ], + "type": "text", + "content": " epochs textual interventions after executing " + }, + { + "bbox": [ + 305, + 179, + 545, + 262 + ], + "type": "inline_equation", + "content": "K_{1}" + }, + { + "bbox": [ + 305, + 179, + 545, + 262 + ], + "type": "text", + "content": " epochs visual interventions for the visual causal module and the textual causal module." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 275, + 381, + 289 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 275, + 381, + 289 + ], + "spans": [ + { + "bbox": [ + 306, + 275, + 381, + 289 + ], + "type": "text", + "content": "4. Experiment" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 296, + 363, + 307 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 296, + 363, + 307 + ], + "spans": [ + { + "bbox": [ + 306, + 296, + 363, + 307 + ], + "type": "text", + "content": "4.1. Dataset" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 314, + 545, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 314, + 545, + 422 + ], + "spans": [ + { + "bbox": [ + 304, + 314, + 545, + 422 + ], + "type": "text", + "content": "We evaluate our Multimodal Causal Reasoning (MCR) framework on two recent large causal-related VideoQA datasets: Causal-VidQA [21] and NExT-QA [32]. In these datasets, models need to answer not only simple descriptive or statistical questions but also implicit global evidence reasoning. The collected video data is close to the real open scene, including a variety of objects and interactive actions. Answer candidates are sentences with different expression structures and are not limited to a single sentence." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 422, + 545, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 422, + 545, + 529 + ], + "spans": [ + { + "bbox": [ + 304, + 422, + 545, + 529 + ], + "type": "text", + "content": "The Causal-VidQA dataset selects 26,900 video clips from Kinetics-700 [2] and asks 107,600 questions, including description, explanation, prediction, and counterfactual questions. Each question has 5 answers, with 5 more reasons in predictions and counterfactuals. For question-answer accuracies, we adopt the previous causal VideoQA evaluation metrics [21] that report accuracy for each question type, as well as the accuracy of the consistency between answers and reasons." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 530, + 545, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 530, + 545, + 590 + ], + "spans": [ + { + "bbox": [ + 304, + 530, + 545, + 590 + ], + "type": "text", + "content": "NExT-QA dataset contains 5,440 videos from VidOR [29] and proposes 47,692 questions for the multichoice task, including description, explanation, and temporal reasoning questions. We also report accuracy for each question type." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 306, + 599, + 432, + 612 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 599, + 432, + 612 + ], + "spans": [ + { + "bbox": [ + 306, + 599, + 432, + 612 + ], + "type": "text", + "content": "4.2. Experimental Settings" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "We use a unified feature extraction method for both datasets. Each video with varying length is divided into 8 clips, each containing 16 frames. For the object-level motion feature, we uniformly sample from the frame-level appearance features and clip-level motion features by ROI Align [13]. The bounding boxes in each frame are extracted by pre-trained Mask R-CNN [13]. The appearance features and motion features are extracted by ResNet-101 [14] and" + } + ] + } + ], + "index": 27 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19032" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 84, + 102, + 513, + 288 + ], + "blocks": [ + { + "bbox": [ + 46, + 68, + 547, + 102 + ], + "lines": [ + { + "bbox": [ + 46, + 68, + 547, + 102 + ], + "spans": [ + { + "bbox": [ + 46, + 68, + 547, + 102 + ], + "type": "text", + "content": "Table 1. Comparison of accuracy with state-of-the-art methods on Causal-VidQA dataset. D means description question. E means explanation question. P means prediction question. C means counterfactual question. QA means to answer the answer. QR means to answer the reason. QAR means the answer and reason are both accurate." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 84, + 102, + 513, + 288 + ], + "lines": [ + { + "bbox": [ + 84, + 102, + 513, + 288 + ], + "spans": [ + { + "bbox": [ + 84, + 102, + 513, + 288 + ], + "type": "table", + "html": "
MethodText FeatureAcc-DAcc-EQAAcc-P QRQARQAAcc-C QRQARAcc
HME [8]GloVe47.2543.8041.0242.5323.2535.2934.1915.3432.41
HCRN [20]GloVe58.8953.5343.1445.0726.1743.6943.4722.7540.33
HGA [18]GloVe60.3255.0246.5547.2128.5344.0044.0423.6341.88
B2A [26]GloVe61.2956.4346.8248.1730.0145.1244.9925.2943.26
IGV [22]+B2AGloVe59.2448.4145.7047.3228.2038.9940.9718.8438.67
MCR+B2AGloVe66.7261.2650.4652.1732.1352.1751.5031.9148.01
HME [8]BERT63..3661.4550.2947.5628.9250.38.51.6530.9346.16
HCRN [20]BERT65.3561.6151.7451.2632.5751.5753.4432.6648.05
HGA [18]BERT65.6763.5149.3650.6232.2252.4455.8534.2848.92
B2A [26]BERT66.2162.9248.9650.2231.1553.2756.2735.1649.11
IGV [22]+B2ABERT65.9262.1352.7753.4735.0050.6752.2931.2248.57
MCR+HCRNBERT68.6865.9755.4458.1837.6352.2452.3931.1750.86
MCR+B2ABERT67.4765.5956.4656.4237.8252.3954.0833.3851.06
", + "image_path": "f93cb09c634f8714b40600f3ef884987617ac8be3b860924934da569a7f7b55a.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 308, + 289, + 439 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 308, + 289, + 439 + ], + "spans": [ + { + "bbox": [ + 46, + 308, + 289, + 439 + ], + "type": "text", + "content": "3D ResNeXt-101 [34] with the pre-trained model, respectively. For textual data, word token representation for questions and answers is provided by GloVe [28] and BERT [6] respectively, which greatly affects the performance of models [21]. MLP is implemented by fully connected layers, followed by Batch Normalization [16] and ReLU [11]. " + }, + { + "bbox": [ + 46, + 308, + 289, + 439 + ], + "type": "inline_equation", + "content": "\\lambda_{1}" + }, + { + "bbox": [ + 46, + 308, + 289, + 439 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 308, + 289, + 439 + ], + "type": "inline_equation", + "content": "\\lambda_{2}" + }, + { + "bbox": [ + 46, + 308, + 289, + 439 + ], + "type": "text", + "content": " are both set as 1. " + }, + { + "bbox": [ + 46, + 308, + 289, + 439 + ], + "type": "inline_equation", + "content": "K_{1}" + }, + { + "bbox": [ + 46, + 308, + 289, + 439 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 308, + 289, + 439 + ], + "type": "inline_equation", + "content": "K_{2}" + }, + { + "bbox": [ + 46, + 308, + 289, + 439 + ], + "type": "text", + "content": " are set as 1 and 3, respectively. During training, we use Adam optimizer with the initial learning rate of 1e-4 and halve the learning rate in every 5 epochs. The batch size is set as 128 in CausalVidQA dataset and 64 in NExT-QA dataset." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 453, + 237, + 466 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 453, + 237, + 466 + ], + "spans": [ + { + "bbox": [ + 47, + 453, + 237, + 466 + ], + "type": "text", + "content": "4.3. Comparison with State-of-the-Arts" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 474, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 289, + 715 + ], + "type": "text", + "content": "Results on Causal-QA. Table 1 presents the results of four state-of-the-art baseline methods and one causal method on the Causal-VidQA dataset, including HME [8], HCRN [20], HGA [18], B2A [26], and IGV [22]. Compared to all existing VideoQA methods, MCR achieves the best performance across almost all types of questions. It is worth noting that MCR improves accuracy across all question types when using GloVe as the text model, which has an average performance improvement of " + }, + { + "bbox": [ + 46, + 474, + 289, + 715 + ], + "type": "inline_equation", + "content": "4.75\\%" + }, + { + "bbox": [ + 46, + 474, + 289, + 715 + ], + "type": "text", + "content": " over B2A " + }, + { + "bbox": [ + 46, + 474, + 289, + 715 + ], + "type": "inline_equation", + "content": "(48.01\\%" + }, + { + "bbox": [ + 46, + 474, + 289, + 715 + ], + "type": "text", + "content": " vs. " + }, + { + "bbox": [ + 46, + 474, + 289, + 715 + ], + "type": "inline_equation", + "content": "43.26\\%)" + }, + { + "bbox": [ + 46, + 474, + 289, + 715 + ], + "type": "text", + "content": ". Compared with the IGV, MCR improves by " + }, + { + "bbox": [ + 46, + 474, + 289, + 715 + ], + "type": "inline_equation", + "content": "9.44\\%" + }, + { + "bbox": [ + 46, + 474, + 289, + 715 + ], + "type": "inline_equation", + "content": "(48.01\\%" + }, + { + "bbox": [ + 46, + 474, + 289, + 715 + ], + "type": "text", + "content": " vs. " + }, + { + "bbox": [ + 46, + 474, + 289, + 715 + ], + "type": "inline_equation", + "content": "38.67\\%)" + }, + { + "bbox": [ + 46, + 474, + 289, + 715 + ], + "type": "text", + "content": ". Our result is even comparable to the backbones of using BERT as a language model. When using BERT as the text model and B2A as the VideoQA backbone, MCR achieves an accuracy improvement of " + }, + { + "bbox": [ + 46, + 474, + 289, + 715 + ], + "type": "inline_equation", + "content": "1.85\\%" + }, + { + "bbox": [ + 46, + 474, + 289, + 715 + ], + "type": "text", + "content": " on average. In counterfactual questions, it is difficult to answer the content of the associative question with limited knowledge learning from the dataset. Involving additional commonsense knowledge may be helpful. Experimentally, in the absence of commonsense knowledge, VideoQA backbones that rely on data bias can also achieve" + } + ] + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 331, + 316, + 525, + 417 + ], + "blocks": [ + { + "bbox": [ + 306, + 304, + 536, + 316 + ], + "lines": [ + { + "bbox": [ + 306, + 304, + 536, + 316 + ], + "spans": [ + { + "bbox": [ + 306, + 304, + 536, + 316 + ], + "type": "text", + "content": "Table 2. Accuracies on NExT-VidQA of different architectures." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 331, + 316, + 525, + 417 + ], + "lines": [ + { + "bbox": [ + 331, + 316, + 525, + 417 + ], + "spans": [ + { + "bbox": [ + 331, + 316, + 525, + 417 + ], + "type": "table", + "html": "
ModelsCausalTempDescripAll
HME [8]46.7648.8957.3749.16
HCRN [20]47.0749.2754.0248.82
HGA [18]48.1349.0857.7950.01
B2A [26]47.3749.0158.349.60
IGV [22]48.5651.6759.6451.34
MCR+B2A47.350.2561.2650.42
MCR+HGA49.1951.9862.2952.35
", + "image_path": "e8b91d2874f7fbbfa8aeaa75cd9bb9d5e27c405fd3aa05964e28878869355570.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 444, + 498, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 444, + 498, + 456 + ], + "spans": [ + { + "bbox": [ + 305, + 444, + 498, + 456 + ], + "type": "text", + "content": "good performance for counterfactual questions." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 459, + 545, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 459, + 545, + 567 + ], + "spans": [ + { + "bbox": [ + 304, + 459, + 545, + 567 + ], + "type": "text", + "content": "Our proposed framework is in parallel with the VideoQA backbone that helps it discover the causal reason. To verify the effectiveness of the parallel strategy, we combine the MCR with different backbones, including HCRN [20] and B2A [26]. We can see that our method has remarkable effects on existing methods. This is due to previous methods being confused by confounders in multimodal data, resulting in poor generalization. Our MCR can effectively alleviate the biased modeling of these methods." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 570, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 714 + ], + "type": "text", + "content": "Results on NExT-QA. For further comparison, we evaluate our method on the NExT-QA dataset and report the evaluation results in Table 2. Compared with the baselines, our proposed MCR achieves the top performance in all question types. Specifically, when using B2A as the VideoQA backbone, our MCR is able to improve " + }, + { + "bbox": [ + 304, + 570, + 547, + 714 + ], + "type": "inline_equation", + "content": "0.82\\%" + }, + { + "bbox": [ + 304, + 570, + 547, + 714 + ], + "type": "text", + "content": " on average accuracy. When combined with HGA, our MCR surpasses the previous backbone and causal method by clear margins, e.g. " + }, + { + "bbox": [ + 304, + 570, + 547, + 714 + ], + "type": "inline_equation", + "content": "2.34\\%" + }, + { + "bbox": [ + 304, + 570, + 547, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 570, + 547, + 714 + ], + "type": "inline_equation", + "content": "1.01\\%" + }, + { + "bbox": [ + 304, + 570, + 547, + 714 + ], + "type": "text", + "content": " higher than HGA and IGV, respectively. These validate that our multimodal causal reasoning indeed improves the robustness and generalization of baseline on causal reasoning dataset." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "19033" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 68, + 547, + 257 + ], + "blocks": [ + { + "bbox": [ + 47, + 68, + 547, + 257 + ], + "lines": [ + { + "bbox": [ + 47, + 68, + 547, + 257 + ], + "spans": [ + { + "bbox": [ + 47, + 68, + 547, + 257 + ], + "type": "image", + "image_path": "91864b7a1c9ab1c39643460dde1383a2d71d959a7575173d7c0511576279e320.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 264, + 546, + 288 + ], + "lines": [ + { + "bbox": [ + 46, + 264, + 546, + 288 + ], + "spans": [ + { + "bbox": [ + 46, + 264, + 546, + 288 + ], + "type": "text", + "content": "Figure 6. Qualitative comparison on Causal dataset validation split. The green bold answer denotes the ground-truth one. The yellow arrows indicate that our method can improve the score of predictions by finding the causal association." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 299, + 141, + 312 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 299, + 141, + 312 + ], + "spans": [ + { + "bbox": [ + 47, + 299, + 141, + 312 + ], + "type": "text", + "content": "4.4. Ablation Study" + } + ] + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 55, + 360, + 282, + 426 + ], + "blocks": [ + { + "bbox": [ + 46, + 327, + 287, + 360 + ], + "lines": [ + { + "bbox": [ + 46, + 327, + 287, + 360 + ], + "spans": [ + { + "bbox": [ + 46, + 327, + 287, + 360 + ], + "type": "text", + "content": "Table 3. Performance comparisons of different variants on CausalQA dataset. \"MCRv\" and \"MCRt\" denote the visual causal module of MCR and the textual module of MCR, respectively." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 55, + 360, + 282, + 426 + ], + "lines": [ + { + "bbox": [ + 55, + 360, + 282, + 426 + ], + "spans": [ + { + "bbox": [ + 55, + 360, + 282, + 426 + ], + "type": "table", + "html": "
MethodAcc-DAcc-EAcc-PAcc-CAcc
B2A66.2162.9231.1535.1649.11
B2A+MCRv67.7665.3835.5532.9550.41
B2A+MCRt68.5764.3833.7331.6149.57
B2A+MCR68.7265.0136.9233.2150.96
", + "image_path": "780da8eca87e4044bec2affcf6e2713fd231970fdad5f950b18effc38a0701fc.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 430, + 287, + 561 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 430, + 287, + 561 + ], + "spans": [ + { + "bbox": [ + 46, + 430, + 287, + 561 + ], + "type": "text", + "content": "We analyze the effectiveness of different modules of MCR in Table 3. When adopting the visual causal module of MCR, we can achieve comparable improvements (1.30% on average), indicating that the visual indicator can change the co-occurrence relationship between irrelevant objects and labels, which improves the robustness of the model to visual data. With only MCR's text module, B2A improves by an average of 0.46%. This is because we eliminate the misleading of local language semantics attention. When adopting both causal modules for multimodal data, B2A+MCR achieves the best performance." + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 73, + 592, + 264, + 624 + ], + "blocks": [ + { + "bbox": [ + 46, + 571, + 287, + 591 + ], + "lines": [ + { + "bbox": [ + 46, + 571, + 287, + 591 + ], + "spans": [ + { + "bbox": [ + 46, + 571, + 287, + 591 + ], + "type": "text", + "content": "Table 4. The influence of hype-parameters of training pipeline on Causal-VideoQA Dataset." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 73, + 592, + 264, + 624 + ], + "lines": [ + { + "bbox": [ + 73, + 592, + 264, + 624 + ], + "spans": [ + { + "bbox": [ + 73, + 592, + 264, + 624 + ], + "type": "table", + "html": "
k1/k21351/31/5
Acc46.6550.5849.5848.2346.37
", + "image_path": "dab1ab370eb3b4b25e92d91c10ea1996d883137fa8e4f8e69e02d3aac966b340.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "content": "Hyper-parameters. In this paper, we propose a causal intervention pipeline for multimodal data. Here, we conduct ablation studies on the hyper-parameters setting in Tab. 4. When we interact textual data every 3 epochs and video data every 1 epoch, MCR performs best on average accuracy. More Hyper-parameters about " + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\lambda_{1},\\lambda_{2}" + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "content": " and the ablation study of single loss function are shown in Supplementary." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 299, + 424, + 313 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 299, + 424, + 313 + ], + "spans": [ + { + "bbox": [ + 305, + 299, + 424, + 313 + ], + "type": "text", + "content": "4.5. Qualitative Analysis" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 318, + 547, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 318, + 547, + 474 + ], + "spans": [ + { + "bbox": [ + 304, + 318, + 547, + 474 + ], + "type": "text", + "content": "Fig. 6 shows the qualitative comparison between our MCR and B2A. Our MCR can reduce the scores of confusing candidates and enhance the confidence for the accurate answer. In the example on the left, B2A chooses the third answer because both the body pose of the human and the environment are related to \"lecture\". Our approach explicitly helps B2A reduce the influence of irrelevant factors and find the causal motion \"smoking\". In the right example, B2A is perturbed by the correlation between \"third\" in the text and the three bottles on the table in the video. According to the causal object selection, MCR effectively arrives at a lower score for it. These examples demonstrate that our model can perform real and generalizable reasoning." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 478, + 379, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 478, + 379, + 491 + ], + "spans": [ + { + "bbox": [ + 306, + 478, + 379, + 491 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 498, + 546, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 546, + 677 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 546, + 677 + ], + "type": "text", + "content": "In this paper, we revisit causal effects in multimodal data and propose a causal prediction architecture to model the causal association between video and text for the VideoQA task. Compared with previous methods, MCR can modify the distribution of data according to the backdoor adjustment and improve the robustness of the model. Considering limitations, our method intervenes in the textual data by word insertion. Some post-intervention examples express eccentric sentence structures that are easy to distinguish. Intervening the textual data with a reasonable text generator would be a reasonable future work. Besides, MCR cannot be directly adapted to the Video Story QA task in which most videos are human-human interactions rather than human-object interactions. Enhancing interventional operations for human instances may be another future work." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgement This research is supported by the National Natural Science Foundation of China (NSFC) (No. 61972038)." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "19034" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "text", + "content": "[1] Martin Arjovsky, Léon Bottou, Ishaan Gulrajani, and David Lopez-Paz. 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In Proceedings of the 25th ACM international conference on Multimedia, pages 1050-1058, 2017." + } + ] + } + ], + "index": 16 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "text", + "content": "19036" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Discrete Point-Wise Attack Is Not Enough_ Generalized Manifold Adversarial Attack for Face Recognition/dc2b0e92-b412-418d-ab5e-fff033c9b7f7_content_list.json b/2023/Discrete Point-Wise Attack Is Not Enough_ Generalized Manifold Adversarial Attack for Face Recognition/dc2b0e92-b412-418d-ab5e-fff033c9b7f7_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..8599041801f95b2647e326e20dff62dcf640b3c0 --- /dev/null +++ b/2023/Discrete Point-Wise Attack Is Not Enough_ Generalized Manifold Adversarial Attack for Face Recognition/dc2b0e92-b412-418d-ab5e-fff033c9b7f7_content_list.json @@ -0,0 +1,1598 @@ +[ + { + "type": "text", + "text": "Discrete Point-wise Attack Is Not Enough: Generalized Manifold Adversarial Attack for Face Recognition", + "text_level": 1, + "bbox": [ + 96, + 128, + 875, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Qian Li, Yuxiao Hu,\\* Ye Liu, Dongxiao Zhang, Xin Jin,\\* Yuntian Chen\\* Eastern Institute for Advanced Study, Ningbo Zhejiang, China", + "bbox": [ + 207, + 203, + 759, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{QianL01205, huyuxiaol205, liuye66a}@gmail.com", + "bbox": [ + 281, + 241, + 687, + 256 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{dzhang, jinxin, ychen}@eias.ac.cn", + "bbox": [ + 328, + 258, + 627, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 308, + 313, + 325 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Classical adversarial attacks for Face Recognition (FR) models typically generate discrete examples for target identity with a single state image. However, such paradigm of point-wise attack exhibits poor generalization against numerous unknown states of identity and can be easily defended. In this paper, by rethinking the inherent relationship between the face of target identity and its variants, we introduce a new pipeline of Generalized Manifold Adversarial Attack (GMAA)1 to achieve a better attack performance by expanding the attack range. Specifically, this expansion lies on two aspects - GMAA not only expands the target to be attacked from one to many to encourage a good generalization ability for the generated adversarial examples, but it also expands the latter from discrete points to manifold by leveraging the domain knowledge that face expression change can be continuous, which enhances the attack effect as a data augmentation mechanism did. Moreover, we further design a dual supervision with local and global constraints as a minor contribution to improve the visual quality of the generated adversarial examples. We demonstrate the effectiveness of our method based on extensive experiments, and reveal that GMAA promises a semantic continuous adversarial space with a higher generalization ability and visual quality.", + "bbox": [ + 75, + 340, + 473, + 705 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 723, + 209, + 739 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Thanks to the rapid development of deep neural networks (DNNs), the face recognition (FR) networks [5, 27] has been applied to identity security identification systems in a variety of crucial applications, such as face unlocking and face payment on smart devices. However, it has been observed that DNNs are easily fooled by adversarial examples and offer incorrect assessments [9, 23], which has risks", + "bbox": [ + 75, + 743, + 468, + 849 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "of unauthorized access to FR systems and stealing personal privacy through poisoned data. These 'well-designed' adversarial examples reveal the aspects of FR models that are vulnerable to be attacked, which makes the adversarial attack a meaningful work to provide reference for improving model robustness.", + "bbox": [ + 500, + 310, + 890, + 400 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Following the point-wise paradigm, previous methods typically tend to attack a single target identity sample with discrete adversarial examples illustrated in Fig. 1. However, these methods are not strong enough both in target domain and adversarial domain. Concretely, for the target domain, attacking a single identity image has a poor generalization on those unseen faces (even if they belong to the same person) in realistic scenarios. For example, Fig. 2 shows these adversarial examples which were used to attack the target (a girl) have a disappointingly lower success rate of attacking the identity with other unseen states. We analyze that's because attacking a single image of target identity overfits the generation of adversarial examples to some fixed factors such as expression, makeup style, etc. In addition to the target domain, we naturally consider the weakness of adversarial domain in the existing methods. Most adversarial attack methods optimize a $L_{p}$ bounded perturbation [24,34] based on the gradient, which limits the problem to searching for discrete adversarial examples in a hypersphere of the clean sample and ignores the continuity of the generated adversarial domain. For example, the recently proposed methods based on makeup style transformation [16,35,37] focus on generating finite adversarial examples that correspond to discrete makeup references. Such methods all overemphasize on mining discrete adversarial examples within a limited scope and ignore the importance of the continuity in adversarial space. The weakness of current adversarial attack tasks motivates us, on the one hand, to explore how to generate adversarial examples that are more general to various target identity's states and, on the other hand, to upgrade adversarial domain from discrete points to continuous manifold for a stronger attack.", + "bbox": [ + 496, + 401, + 893, + 885 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we introduce a new paradigm dubbed Gen", + "bbox": [ + 517, + 885, + 890, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Co-first author", + "bbox": [ + 94, + 862, + 183, + 875 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding author", + "bbox": [ + 96, + 875, + 220, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "1https://github.com/tokaka22/GMAA", + "bbox": [ + 96, + 887, + 356, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "20575", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8946729501018e585a3eefae4ca51cd101d392f6804d35c7fa247541dad75538.jpg", + "image_caption": [ + "Figure 1. The core idea comparison. Discrete point-wise attack methods leverage a single state of the target identity during training and provide discrete adversarial examples. By attacking the target identity's state set and employing domain knowledge, our core idea aims to Generalized Manifold Adversarial Attack (GMAA), which promises a semantic continuous adversarial manifold with a higher generalization ability on the target identity with unknown state." + ], + "image_footnote": [], + "bbox": [ + 89, + 88, + 883, + 338 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/dbf4e9ff7ea4a1bff88ad00f3298a04bcb162914ed92d740905da69e9c423eae.jpg", + "image_caption": [ + "Figure 2. The black-box attack success rate on the Mobileface of attacking target * 1, 2 and 3 during the testing. The three methods are exclusively trained on target *." + ], + "image_footnote": [], + "bbox": [ + 84, + 424, + 447, + 589 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "eralized Manifold Adversarial Attack (GMAA) depicted in Fig. 1, which achieves a higher attack success rate by providing semantic continuous adversarial domains while expanding the target to be attacked from an instance to a group set. Specifically, we train adversarial examples to attack a target identity set rather than a single image, which increases the attack success rate on the target identity with different states. The expansion of target domain naturally prompts us to consider enhancing the adversarial domain. Inspired by the success of some recent data and knowledge dual driven methods [2, 18, 36], we explore a low-dimensional manifold near the sample according to the domain knowledge, which is a simple yet highly-efficient continuous embedding scheme and can be used to augment the data. For such manifold, the data in it share the visual identity same as the original sample and also lie in the decision", + "bbox": [ + 75, + 657, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "boundaries of target identity. More specifically, we employ the Facial Action Coding System (FACS) [10] as prior domain knowledge (a kind of instantiation) to expand adversarial domain from discrete points to manifold. Through using FACS, the expressions can be encoded into a vector space, and by which the adversarial example generator could produce an manifold that is homogeneous with the expression vector space and possesses semantic continuity. In addition, in order to build an adversarial space with high visual quality, we employ four expression editors in GMAA pipeline to supervise the adversarial example generation in terms of global structure and local texture details. A transferability enhancement module is also introduced to drive the model to mine robust and transferable adversarial features. Extensive experiments have shown that these components work well on a wide range of baselines and black-box attack models.", + "bbox": [ + 496, + 426, + 890, + 681 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions are summarized as follows.", + "bbox": [ + 517, + 683, + 818, + 696 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We first pinpoint that the popular adversarial attack methods generally face generalization difficulty caused by the limited point-wise attack mechanism.", + "- To enhance the performance of adversarial attack, a new paradigm of Generalized Manifold Adversarial Attack (GMAA) is proposed with an improved attack success rate and better generalization ability.", + "- GMAA considers the enhancement in terms of both target domain and adversarial domain. For the target domain, it expands the target to be attacked from one to many to encourage a good generalization. For the adversarial domain, the domain knowledge is embedded to strengthen the attack effect from discrete points to continuous manifold." + ], + "bbox": [ + 514, + 696, + 890, + 909 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "20576", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- We instantiate GMAA in the face expression state space for a semantic continuous adversarial manifold and use it to attack a state set of the target identity. As a minor contribution, GMAA supervises the adversarial example generator w.r.t global structure and local details with the pre-trained expression editors for a high visual quality.", + "bbox": [ + 93, + 90, + 468, + 196 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 76, + 205, + 215, + 220 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.1. Adversarial Attacks on Face Recognition", + "text_level": 1, + "bbox": [ + 76, + 223, + 426, + 239 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Adversarial attacks can be divided into white-box attacks and black-box attacks. White-box attacks [11, 24, 32] must entail full information of the target neural networks, however, the parameters and architecture of a real-world face recognition system are typically hard to access. Hence, it is more practical to consider black-box adversarial attacks in face recognition scenarios, which demand high transferability for the unknown FR target models or commercial application programming interfaces (APIs). Query-based adversarial attacks [9, 13], a form of black-box attack, is inappropriate for realistic applications since it optimizes adversarial examples by repeatedly accessing the target model during training. Adding transferable adversarial perturbation is another effective black-box attack form [4, 7, 8, 34]. Unfortunately, the perturbation caused by this method always makes images become unrealistic and unnatural. Besides, limited by the way of pixel-to-pixel similarity computation, the model of this branch could only look for a limited number of discrete adversarial examples around the clean sample. The patch-based adversarial attack [20, 28, 33] severely degrades the visual quality of images, because the adversarial patch does not blend well with the clean background due to the abrupt shift in pixel values around the boundary. Numerous recent works attempt to instantiate adversarial perturbations with different makeup styles [16, 35, 37]. However, such makeup attacks typically result in an unnatural visual appearance due to gender constraints – female images have a higher attack success rate and visual quality than male ones. Regardless of the previous methods (e.g. [26] focuses on a target sample to obtain optimal feature-map interpolation, and [16] generates adversarial examples with various makeup styles to attack the target identity), they all tend to generate discrete adversarial examples for a single target identity sample and ignore the importance of continuity of adversarial space, which might be crucial to the attack performance.", + "bbox": [ + 76, + 241, + 472, + 785 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Facial Expression Editing", + "text_level": 1, + "bbox": [ + 76, + 792, + 310, + 808 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As another challenging task in facial analysis, face expression editing is also related to our study, which aims at modifying facial expressions in a reasonable manner while preserving identity completeness. In recent years, generative adversarial networks (GANs) have achieved surprising advances in facial expression editing: GCGAN [29] uses", + "bbox": [ + 76, + 810, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "the facial geometry as prior knowledge to guide the generation. ExprGAN [6] exploits a controller to adjust the intensity of face expression editing. StarGAN [3] introduces a cycle consistency loss to maintain the identity content invariant. However, these methods are all limited on the discrete expressions generation. GANimation [25] utilizes Action Units [10] to define an expression space and generate continuous-change facial images. EF-GAN [31] achieves progressive facial expression editing with a local-focused cascade GAN structure, and produces fewer artifacts and blurs in large-gap expression transformations. In this paper, we borrow the idea of Action Units as domain prior knowledge (from face expression editing) to re-define the adversarial attack task on a continuous manifold, to finally strengthen attack effect.", + "bbox": [ + 496, + 90, + 890, + 316 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Generalized Manifold Adversarial Attack", + "text_level": 1, + "bbox": [ + 498, + 323, + 870, + 339 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem Definition", + "text_level": 1, + "bbox": [ + 500, + 348, + 681, + 363 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Adversarial face attack tasks can be separated into targeted attacks (i.e. impersonation attacks) and non-targeted attacks (i.e. dodging attacks). Targeted attacks force the generated adversarial examples to have a predetermined output towards the target FR model, while the non-targeted attacks mislead the target FR model to provide incorrect random classification for the adversarial examples. To capture the adversarial examples that can impersonate a specific target identity under face authentication systems, we mainly consider the targeted attack task.", + "bbox": [ + 496, + 371, + 890, + 521 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Current methods always define the targeted attack task as an optimization problem, which can be formalized as", + "bbox": [ + 498, + 522, + 890, + 551 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\min L _ {a d v} = \\min _ {\\boldsymbol {\\theta}} D i s t \\left(\\mathcal {C} \\left(\\boldsymbol {x} ^ {*}\\right), \\mathcal {C} \\left(\\boldsymbol {x} ^ {\\prime}\\right)\\right), \\tag {1} \\\\ \\boldsymbol {x} ^ {\\prime} = G (\\boldsymbol {x}; \\boldsymbol {\\theta}). \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 556, + 890, + 599 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\pmb{x}^*$ is the pre-specified target image belonging to the sample space $\\Omega \\subset \\mathbb{R}^{3 \\times H \\times W}$ , $\\text{Dist}(\\cdot)$ represents a metric of difference, $\\mathcal{C}$ represents the feature extractor of FR neural networks, and $G$ maps the clean sample $\\pmb{x} \\in \\Omega$ to the adversarial version $\\pmb{x}'$ with the parameter $\\pmb{\\theta}$ .", + "bbox": [ + 496, + 604, + 890, + 678 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this paper, we re-define the problem from a broader standpoint. To obtain highly generalized adversarial examples that are more threatening to the target identity with unknown state, the adversarial version $\\pmb{x}^{\\prime}$ attacks the state set $S$ of the target identity during training. In order to capture an adversarial manifold $\\mathcal{M}$ instead of discrete adversarial examples, we aim to construct a distribution on the $\\mathcal{M}$ . The new task can be formalized as Eq. 2.", + "bbox": [ + 496, + 679, + 890, + 800 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\min L _ {a d v} = \\min _ {\\boldsymbol {\\theta}} \\mathbb {E} _ {\\boldsymbol {x} _ {i} ^ {*} \\sim \\mathcal {S}, \\boldsymbol {x} ^ {\\prime} \\sim \\mathcal {M}} D i s t (\\mathcal {C} \\left(\\boldsymbol {x} _ {i} ^ {*}\\right), \\mathcal {C} \\left(\\boldsymbol {x} ^ {\\prime}\\right)), \\tag {2} \\\\ \\mathcal {M} = G (\\boldsymbol {x}; \\boldsymbol {\\theta}). \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 804, + 890, + 845 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In addition to the adversarial attack tasks, we force $G$ to map $\\pmb{x}$ to $\\pmb{x}'$ according to the given expression AU vector. The Facial Action Coding System (FACS) is applied as", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "20577", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/ea51ec7c6f63c20793a24b01ebe052e889ea0cb0b0e31ef53c37db5ff9cc54f3.jpg", + "image_caption": [ + "Figure 3. Overview of GMAA. A face image and a random AU vector are sent to the generative adversarial module as inputs. Meanwhile, the expression supervision module generates supervisory signals based on the AU vector and the input image (or detail patches cropped by the landmarks). In the transferability enhancement module, aiming at white-box FR models, the transformed output attacks the target identity's state set, which is provided by the generalized attack module." + ], + "image_footnote": [], + "bbox": [ + 99, + 89, + 851, + 364 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "prior domain knowledge to establish a continuous expression state space. Specifically, every expression is encoded by an n-element expression vector $\\pmb{\\mu} = (\\mu_{1},\\dots,\\mu_{n})$ which corresponds to $N$ facial action units. Each $\\mu_{n}\\in \\pmb{\\mu}$ represents the magnitude of muscle activity in the n-th region of the face, which indicates that the AU vector is a continuous embedding scheme for different expressions. Thus, for the input image $\\pmb{x}_{\\mu^0}\\in \\mathbb{R}^{3\\times H\\times W}$ with the expression encoded by $\\pmb{\\mu}^0\\in \\mathbb{R}^N$ and the given expression encoded by $\\pmb{\\mu}^i\\in \\mathbb{R}^N$ , $G$ is a binary mapping $G:(\\pmb{x}_{\\mu^0},\\pmb{\\mu}^i)\\to \\pmb{x}_{\\mu^i}^\\prime$ , where $\\pmb{x}_{\\mu^i}^\\prime$ has the same visual label with $\\pmb{x}_{\\mu^0}$ and wearing the expression encoded by $\\pmb{\\mu}^i$ .", + "bbox": [ + 75, + 435, + 472, + 621 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Generalized Manifold Adversarial Attack", + "text_level": 1, + "bbox": [ + 76, + 625, + 431, + 640 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We establish the adversarial examples' distribution on a manifold via WGAN-GP [12]. GMAA comprises a generative adversarial module, an expression supervision module, a transferability enhancement module, and a generalized attack module. In contrast, Manifold Adversarial Attack (MAA) omits the generalized attack module, as it merely extends the adversarial domain from a point to a manifold. The structure of our proposed method is depicted in Fig. 3. Generative adversarial module. The generative adversarial module (red box in Fig. 3) includes a generator $G$ , a discriminator $D_{c}$ and an AU predictor $D_{AU}$ , where $D_{c}$ and $D_{AU}$ both lie in $D$ and share partial parameters.", + "bbox": [ + 75, + 642, + 468, + 824 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As inputs, the generator $G$ receives a clean sample $\\boldsymbol{x}_{\\mu^0}$ and a given expression AU label $\\boldsymbol{\\mu}^i$ , which aims to produce adversarial examples wearing the expression matching to the supplied AU label and maintain the same visual identity with $\\boldsymbol{x}_{\\mu^0}$ . The discriminator $D_{c}$ learns to distinguish real", + "bbox": [ + 75, + 825, + 470, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "images from generated images. Meanwhile, generated images deceive the discriminator $D_{c}$ to force the outputs of the generator $G$ match the real distribution. Our $G$ and $D_{c}$ are trained using WGAN-GP [12], and the critic loss function we employ is", + "bbox": [ + 496, + 435, + 890, + 511 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} L _ {\\text {c r i t i c}} ^ {D} = \\lambda_ {c} \\left(1 - D _ {c} \\left(\\boldsymbol {x} _ {\\boldsymbol {\\mu} ^ {0}}\\right)\\right) ^ {2} + \\lambda_ {c} \\left(D _ {c} \\left(G \\left(\\boldsymbol {x} _ {\\boldsymbol {\\mu} ^ {0}} \\mid \\boldsymbol {\\mu} ^ {i}\\right)\\right) ^ {2} \\right. (3) \\\\ + \\lambda_ {g p} \\left(\\| \\nabla_ {\\widetilde {x}} D _ {c} (\\widetilde {x}) \\| _ {2} - 1\\right) ^ {2}, \\\\ L _ {c r i t i c} ^ {G} = \\lambda_ {c} \\left(1 - D _ {c} \\left(G \\left(\\boldsymbol {x} _ {\\boldsymbol {\\mu} ^ {0}} \\mid \\boldsymbol {\\mu} ^ {i}\\right)\\right)\\right) ^ {2}, (4) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 511, + 516, + 890, + 575 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\widetilde{\\pmb{x}}$ is the random interpolation distribution between the real distribution and the generated images' distribution. To ensure that the generated image matches the provided expression code $\\pmb{\\mu}^i$ , we employ AU regression loss to establish the consistency of the generated expression with $\\pmb{\\mu}^i$ . Specifically, the AU predictor $D_{AU}$ learns the AU coding rules by real images and their AU labels (can be obtained by the open source framework Openface [1]), and the $G$ reduces the AU error between the generated expression and $\\pmb{\\mu}^i$ to satisfy the given expression. The loss function can be formulated as:", + "bbox": [ + 496, + 580, + 890, + 746 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {A U} ^ {D} = \\lambda_ {A U} \\| D _ {A U} \\left(\\boldsymbol {x} _ {\\boldsymbol {\\mu} ^ {0}}\\right) - \\boldsymbol {\\mu} ^ {0} \\| _ {2} ^ {2}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 557, + 751, + 890, + 777 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {A U} ^ {G} = \\lambda_ {A U} \\| D _ {A U} \\left(G \\left(\\boldsymbol {x} _ {\\boldsymbol {\\mu} ^ {0}} \\mid \\boldsymbol {\\mu} ^ {i}\\right)\\right) - \\boldsymbol {\\mu} ^ {i} \\| _ {2} ^ {2}.\n$$\n", + "text_format": "latex", + "bbox": [ + 560, + 772, + 831, + 791 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Expression supervision module. The expression supervision module (blue box in Fig. 3) protects the visual identity of adversarial examples and guides $G$ in expression editing by generating global and local facial supervisory signals. The global branch focuses on structural features of the face, whereas the local branch protects important facial details and reduces artifacts and blurs caused by the global branch.", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "20578", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Specifically, a global editor and three local editors are pre-trained to provide supervisory signals. For the local editors, we crop the eyes, nose, and mouth pixel patches based on face landmarks first. Then the input image and three detail patches are fed into the corresponding generator $G_{global}$ and $G_{j}$ ( $j \\in J = \\{\\text{eyes, nose, mouth}\\}$ ) with the input AU vector $\\mu$ , respectively. Each generator has the network structure similar to [25], which provides the color response $M_{c}^{\\mu}$ and the attention response $M_{a}^{\\mu}$ . $M_{c}^{\\mu}$ and $M_{a}^{\\mu}$ force networks to pay attention to the expression change region and protect the remainder regions from disturbance. The ultimate supervisory signals can be obtained as follows, where $\\otimes$ denotes element-wise multiplication.", + "bbox": [ + 75, + 90, + 472, + 287 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nG _ {j} \\left(\\boldsymbol {x} _ {i n} \\mid \\boldsymbol {\\mu}\\right) = M _ {a} ^ {\\boldsymbol {\\mu}} \\otimes M _ {c} ^ {\\boldsymbol {\\mu}} + \\left(1 - M _ {a} ^ {\\boldsymbol {\\mu}}\\right) \\otimes \\boldsymbol {x} _ {i n}. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 116, + 291, + 468, + 310 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The global editor focuses more on large scale features, such as shape and position of the five senses, and tends to produce artifacts and blurs in the detail region, while the local editors concentrate on significant local features and provide finer details. Therefore, we deploy the global editor to supervise the structural information of adversarial examples and the local editors to supervise local specifics. The loss of expression supervision module can be expressed as", + "bbox": [ + 75, + 316, + 472, + 438 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} L _ {e x p} ^ {G} = \\lambda_ {g} \\mathrm {S S I M} [ G (\\pmb {x} _ {\\pmb {\\mu} ^ {0}} | \\pmb {\\mu} ^ {i}), G _ {g l o b a l} (\\pmb {x} _ {\\pmb {\\mu} ^ {0}} | \\pmb {\\mu} ^ {i}) ] \\\\ + \\lambda_ {l} \\sum_ {j \\in J} \\operatorname {M S E} \\left[ \\operatorname {C r o p} _ {j} \\left(G \\left(\\boldsymbol {x} _ {\\boldsymbol {\\mu} ^ {0}} \\mid \\boldsymbol {\\mu} ^ {i}\\right)\\right), G _ {j} \\left(\\operatorname {C r o p} _ {j} \\left(\\boldsymbol {x} _ {\\boldsymbol {\\mu} ^ {0}}\\right) \\mid \\boldsymbol {\\mu} ^ {i}\\right) \\right], \\tag {7} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 445, + 468, + 513 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathrm{Crop}_j$ denotes the crop operation of local region $j$ according to the face landmarks.", + "bbox": [ + 75, + 513, + 468, + 544 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Transferability enhancement module. To improve the transferability of adversarial examples and the black-box attack success rate, we introduce the transferability enhancement module (yellow box in Fig. 3) from [16]. The generated adversarial examples are transformed with probability $p$ by the function $T_{p}$ (resize with padding or add noise), and then attack $K$ pre-trained high-precision FR models $\\{C_k\\}_{k=1,\\dots,K}$ , which perform as white-box models during the training of $G$ . The adversarial attack loss function is formulated as", + "bbox": [ + 75, + 544, + 468, + 694 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {a d v} ^ {G} = \\frac {\\lambda_ {a d v}}{K} \\sum_ {k = 1} ^ {K} [ 1 - \\cos \\left(\\mathcal {C} _ {k} \\left(\\boldsymbol {x} ^ {*}\\right), \\mathcal {C} _ {k} \\left(T _ {p} \\left(G \\left(\\boldsymbol {x} _ {\\boldsymbol {\\mu} ^ {0}} \\mid \\boldsymbol {\\mu} ^ {i}\\right)\\right)\\right)\\right) ] \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 83, + 696, + 468, + 750 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Generalized attack module. The generalized attack module (green box in Fig. 3) intends to raise the attack success rate on the unseen face belonging to the target identity, which can be introduced into other adversarial attack approaches. The adversarial loss $L_{adv}^{G}$ in GMAA can be further expressed as", + "bbox": [ + 75, + 751, + 468, + 842 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbb {E} _ {\\boldsymbol {x} _ {i} ^ {*}} \\sim_ {\\mathcal {S}} \\frac {\\lambda_ {a d v}}{K} \\sum_ {k = 1} ^ {K} [ 1 - \\cos \\left(\\mathcal {C} _ {k} \\left(\\boldsymbol {x} _ {i} ^ {*}\\right), \\mathcal {C} _ {k} \\left(T _ {p} \\left(G \\left(\\boldsymbol {x} _ {\\boldsymbol {\\mu} ^ {0}} \\mid \\boldsymbol {\\mu} ^ {i}\\right)\\right)\\right)\\right) ], \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 83, + 845, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\boldsymbol{x}_i^*$ and $S$ are defined in 2. However, numerous face recognition datasets and realistic scenarios do not fit this module since an identity only contains a few or single state image. Fortunately, since our method can accomplish both expression editing and adversarial attack, when we remove the loss associated with adversarial attack, we can obtain an expression editor, $G_{exp}$ , by eliminating the adversarial effect $L_{adv}^{G}$ , which can generate the expression state set $S$ by different AU vectors.", + "bbox": [ + 496, + 90, + 890, + 226 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Total loss function. Let $X$ denotes the dataset, and $V$ is the AU vector space. In particular, the given AU vector $\\pmb{\\mu}^i$ is sampled randomly from $V$ to train the generator $G$ to learn the distribution of adversarial expression manifold. For the generator $G$ , we have the loss function as follows,", + "bbox": [ + 496, + 227, + 890, + 303 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL ^ {G} = \\mathbb {E} _ {\\boldsymbol {x} _ {\\mu^ {0}} \\sim \\boldsymbol {X}, \\boldsymbol {\\mu} ^ {i} \\sim V} \\left(L _ {\\text {c r i t i c}} ^ {G} + L _ {A U} ^ {G} + L _ {\\exp} ^ {G} + L _ {a d v} ^ {G}\\right). \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 513, + 306, + 890, + 339 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As for $D$ , the total loss function can be obtained as follows,", + "bbox": [ + 500, + 340, + 885, + 354 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL ^ {D} = \\mathbb {E} _ {\\boldsymbol {x} _ {\\mu^ {0}} \\sim \\boldsymbol {X}, \\boldsymbol {\\mu} ^ {i} \\sim V} \\left(L _ {\\text {c r i t i c}} ^ {D} + L _ {A U} ^ {D}\\right). \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 565, + 359, + 890, + 380 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Continuity of the adversarial space", + "text_level": 1, + "bbox": [ + 498, + 392, + 805, + 407 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this subsection, we illustrate more precisely the continuity of the adversarial space and provide a proof that our method establishes a continuous adversarial manifold.", + "bbox": [ + 496, + 410, + 890, + 454 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Firstly, the definition of continuous adversarial space is shown in Def. 1.", + "bbox": [ + 496, + 455, + 890, + 484 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Definition 1. Let $\\pmb{x}_0 \\in \\mathbb{R}^{3 \\times H \\times W}$ , then $\\mathcal{M}^0 = G(\\pmb{x}_0; \\pmb{\\theta})$ is a continuous adversarial space if and only if (1) $\\mathcal{M}^0$ is a subspace of $\\mathbb{R}^{3 \\times H \\times W}$ .", + "bbox": [ + 496, + 496, + 890, + 542 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "(2) $\\forall \\pmb{x}_i^0\\in \\mathcal{M},\\pmb{x}_i^0$ is an adversarial version of $\\pmb{x}_0$", + "bbox": [ + 500, + 542, + 828, + 559 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Then, we can prove that $\\mathcal{M}^0$ is a continuous manifold.", + "bbox": [ + 500, + 561, + 879, + 577 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Theorem 1. $\\mathcal{M}^0$ generated by $G_0$ is a continuous adversarial manifold, where $G_0: V \\to \\mathcal{M}$ is a map when fixed the input $\\pmb{x}_0$ in $G$ .", + "bbox": [ + 496, + 583, + 890, + 628 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Proof. (1) If $\\mathcal{M}^0$ is homogeneous with the AU vector space $V$ , it is obviously that $\\mathcal{M}^0$ is a subspace of $\\mathbb{R}^{3\\times H\\times W}$ .", + "bbox": [ + 496, + 641, + 890, + 671 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "(1.1) $\\forall \\pmb{\\mu}, \\pmb{\\nu} \\in V$ , if $G_0(\\pmb{\\mu}) = G_0(\\pmb{\\nu})$ , then $D_{AU}(G_0(\\pmb{\\mu})) = D_{AU}(G_0(\\pmb{\\nu}))$ , we have $\\pmb{\\mu} = \\pmb{\\nu}$ and $G_0: V \\to \\mathcal{M}^0$ is a single shot. Besides, $\\forall \\pmb{x}^0 \\in \\mathcal{M}^0$ , $\\exists \\pmb{\\mu} = D_{AU}(\\pmb{x}^0) \\in V$ s.t. $G_0(D_{AU}(\\pmb{x}^0)) = \\pmb{x}^0$ , then $G_0$ is a surjection. Thus, $G_0$ is a bijection.", + "(1.2) $\\forall \\pmb{x}_1^0, \\pmb{x}_2^0 \\in \\mathcal{M}^0$ , we define $d(\\pmb{x}_1^0, \\pmb{x}_2^0) = \\| D_{AU}(\\pmb{x}_1^0) - D_{AU}(\\pmb{x}_2^0)\\|_2$ as the metric between $\\pmb{x}_1^0$ and $\\pmb{x}_2^0$ in $\\mathcal{M}^0$ . Since $(V, \\| \\cdot \\|_2)$ is a metric space, and $D_{AU}(\\pmb{x}_i^0) \\in V$ , $\\forall \\pmb{x}_i^0 \\in \\mathcal{M}^0$ , we prove that $d$ is a metric on $\\mathcal{M}^0$ .", + "(Positivity) $d(\\pmb{x}_1^0, \\pmb{x}_2^0) \\geq 0$ , and if $d(\\pmb{x}_1^0, \\pmb{x}_2^0) = 0$ according to the definition of $d$ we have $D_{AU}(\\pmb{x}_1^0) = D_{AU}(\\pmb{x}_2^0)$ . Since $G_0$ is a bijection, we have $\\pmb{x}_1^0 = G_0(D_{AU}(\\pmb{x}_1^0)) = G_0(D_{AU}(\\pmb{x}_2^0)) = \\pmb{x}_2^0$ .", + "(Symmetry) $d(\\pmb{x}_1^0, \\pmb{x}_2^0) = \\| D_{AU}(\\pmb{x}_1^0) - D_{AU}(\\pmb{x}_2^0)\\|_2 = \\| D_{AU}(\\pmb{x}_2^0) - D_{AU}(\\pmb{x}_1^0)\\|_2 = d(\\pmb{x}_2^0, \\pmb{x}_1^0)$ ." + ], + "bbox": [ + 496, + 672, + 890, + 902 + ], + "page_idx": 4 + }, + { + "type": "footer", + "text": "20579", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/03e15165e49b77229df53f63f8984cea5eaa37e1d7a60d154a5dfe952653fd7e.jpg", + "table_caption": [ + "Table 1. Black-box attack success rate" + ], + "table_footnote": [], + "table_body": "
CelebA-HQLFW
IRSE50IR152FacenetMobilefaceIRSE50IR152FacenetMobileface
Clean3.683.081.318.433.200.060.045.00
PGD [23]24.2013.375.8628.7231.3010.207.4033.50
MI-FGSM [7]38.9020.769.2540.4838.2014.207.6039.40
SemanticAdv [26]26.5310.247.8055.3233.6010.408.8037.40
TIP-IM [34]44.2016.0914.4665.3632.8015.2013.0079.00
AMT-GAN [16]51.0615.6311.6333.2740.7225.2313.8935.67
MAA60.4029.4318.9156.1355.8029.2018.0060.80
", + "bbox": [ + 156, + 104, + 816, + 243 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/2fc4fede75cd2b28134919befe7e5d7aee301f0da081cda19ceda93ee11f554d.jpg", + "table_caption": [ + "Table 2. The unbolded numbers are the black-box ASR of attacking the test target *, 1, 2, 3, and all the models are trained on target *. The bolded numbers are the results of the models that train on the state set. For example, if we train the MAA to attack the state set without target 1, the adversarial examples attack target 1 with an $11.43\\%$ success rate on Facenet during the testing period." + ], + "table_footnote": [], + "table_body": "
Target*Target 1Target 2Target 3
FacenetMobilefaceFacenetMobilefaceFacenetMobilefaceFacenetMobileface
TIP-IM [34] / G-TIP-IM17.6886.334.54 / 7.6258.03 / 70.9310.75 / 20.4234.42 / 49.2011.93 / 19.4122.21 / 42.43
AMT-GAN [16] / G-AMT-GAN16.1255.958.22 / 13.2326.99 / 47.149.78 / 17.1227.67 / 43.9310.91 / 16.1624.69 / 42.37
MAA / GMAA25.2272.6211.43 / 17.8443.44 / 67.5013.30 / 21.7133.08 / 41.2412.64 / 19.1529.56 / 47.21
", + "bbox": [ + 78, + 292, + 893, + 371 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "(Triangle inequality) $\\forall \\pmb{x}_3^0\\in \\mathcal{M}^0$ , we have $d(\\pmb{x}_1^0,\\pmb{x}_3^0) + d(\\pmb{x}_3^0,\\pmb{x}_2^0) = \\| D_{AU}(\\pmb{x}_1^0) - D_{AU}(\\pmb{x}_3^0)\\| _2 + \\| D_{AU}(\\pmb{x}_3^0) -$ $D_{AU}(\\pmb{x}_2^0)\\| _2\\geq \\| D_{AU}(\\pmb{x}_1^0) - D_{AU}(\\pmb{x}_2^0)\\| _2 = d(\\pmb{x}_1^0,\\pmb{x}_2^0).$", + "bbox": [ + 76, + 382, + 468, + 429 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Thus, $(\\mathcal{M}^0,d)$ is a metric space. Then we need to prove that $G_{0}$ is a continuous mapping. $\\forall \\pmb {\\mu},\\pmb {\\nu}\\in V,\\forall \\epsilon >0$ , let $\\delta = \\epsilon$ , when $\\| \\pmb {\\mu} - \\pmb {\\nu}\\| _2 < \\delta$ , we have $d(G_0(\\pmb {\\mu}) - G_0(\\pmb {\\nu})) =$ $\\| D_{AU}(G_0(\\pmb {\\mu})) - D_{AU}(G_0(\\pmb {\\nu}))\\| _2 = \\| \\pmb {\\mu} - \\pmb {\\nu}\\| _2 < \\delta = \\epsilon .$ We get the continuity of $G_{0}$", + "bbox": [ + 76, + 429, + 468, + 503 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "(1.3) It is obviously that $D_{AU}|_{\\mathcal{M}^0} : \\mathcal{M}^0 \\to V$ is the inverse mapping of $G_0$ . $\\forall \\pmb{x}_1^0, \\pmb{x}_2^0 \\in \\mathcal{M}^0, \\epsilon > 0$ , let $\\delta = \\epsilon$ , when $d(\\pmb{x}_1^0, \\pmb{x}_2^0) = \\| D_{AU}(\\pmb{x}_1^0) - D_{AU}(\\pmb{x}_2^0)\\|_2 < \\delta$ , we have $\\| D_{AU}|_{\\mathcal{M}^0}(\\pmb{x}_1^0) - D_{AU}|_{\\mathcal{M}^0}(\\pmb{x}_2^0)\\|_2 = \\| D_{AU}(\\pmb{x}_1^0) - D_{AU}(\\pmb{x}_2^0)\\|_2 < \\delta = \\epsilon$ . We get the continuity of the inverse map of $G_0$ .", + "bbox": [ + 76, + 503, + 468, + 594 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In conclusion, $G_{0}$ is the homeomorphism of $V$ to the manifold $\\mathcal{M}^0$ , i.e. $\\mathcal{M}^0$ homogeneous with the AU vector space $V$ . Since AU vector space is a finite dimensional vector space, $\\mathcal{M}^0$ is a subspace of $\\mathbb{R}^{m\\times n\\times l}$ .", + "bbox": [ + 75, + 594, + 468, + 655 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "(2) By the loss function 8, 7 and the back propagation, $\\pmb{x}_i^0$ is influenced by the 8. It is obviously that $\\pmb{x}_i^0 \\in \\mathcal{M}^0$ is an adversarial example when the model is well-trained.", + "bbox": [ + 75, + 655, + 468, + 700 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Thus, the manifold $\\mathcal{M}^0$ generated by $G_{0}$ is a continuous adversarial manifold.", + "bbox": [ + 75, + 699, + 468, + 729 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Remark 1. Since the $\\mathcal{M}^0$ generated by $G_0$ is a continuous adversarial manifold when fixed the $\\pmb{x}_0$ , then we can assert over the sample space $\\Omega$ , the adversarial examples space generated by $G$ constitutes an adversarial fiber bundle.", + "bbox": [ + 75, + 729, + 468, + 791 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Secondly, the definition of semantic continuous adversarial space is shown in Def. 2.", + "bbox": [ + 75, + 792, + 468, + 821 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Definition 2. $\\mathcal{M}^0$ generated by $\\pmb{x}_0\\in \\mathbb{R}^{3\\times H\\times W}$ is a semantic continuous adversarial space if and only if", + "bbox": [ + 75, + 823, + 468, + 854 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "(1) $\\mathcal{M}^0$ is a continuous adversarial space.", + "(2) $\\forall \\pmb{x}_1^0, \\pmb{x}_2^0 \\in \\mathcal{M}^0$ , if $\\pmb{x}_1^0$ is close to $\\pmb{x}_2^0$ on the $\\mathcal{M}^0$ , then $\\pmb{x}_1^0$ and $\\pmb{x}_2^0$ satisfy the semantic consistency." + ], + "bbox": [ + 76, + 854, + 468, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We can state that $\\mathcal{M}^0$ is a semantic continuous manifold.", + "bbox": [ + 517, + 383, + 890, + 398 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Theorem 2. $\\mathcal{M}^0$ generated by $G_0$ is a semantic continuous adversarial manifold, where $G_0: V \\to \\mathcal{M}$ is a map when fixed the input $\\pmb{x}_0$ in $G$ .", + "bbox": [ + 496, + 405, + 890, + 450 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Proof. Since we have proved that $D_{AD}$ is a continuous mapping, we have $D_{AU}(\\pmb{x}_1^0)$ is close to $D_{AU}(\\pmb{x}_2^0)$ when $\\pmb{x}_1^0$ is close to $\\pmb{x}_2^0$ , which means the AU vectors of $\\pmb{x}_1^0$ and $\\pmb{x}_2^0$ are very close. Thus, the semantic information of $\\pmb{x}_1^0$ and $\\pmb{x}_2^0$ is close.", + "bbox": [ + 496, + 453, + 892, + 529 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 498, + 541, + 633, + 558 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Experimental setting", + "text_level": 1, + "bbox": [ + 498, + 566, + 697, + 582 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation details. We set $\\lambda_{c}$ , $\\lambda_{gp}$ , $\\lambda_{AU}$ , $\\lambda_{g}$ , $\\lambda_{l}$ , $\\lambda_{adv}$ to be 1, 10, 250, 20, 20, 25, respectively. Our method is trained by an Adam optimizer with the learning rate 0.0001 and the exponential decay rates set to be $(\\beta_{1},\\beta_{2}) = (0.5,0.99)$ . We evaluate the black-box attack performance of the models utilizing the attack success rate(ASR) at FAR@0.01 and the confidence scores returned by commercial APIs.", + "bbox": [ + 496, + 583, + 890, + 703 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Dataset. We train the model on two public datasets: 1) CelebA-HQ [19] is a high-quality face dataset, which contains 30,000 face images. 2) LFW [17] is a challenging dataset that collects 13,233 images with complex environmental factors and is a common dataset for face recognition tasks. We remove the images whose AU confidence is below $95\\%$ as extracted by Openface [1], then randomly select $10\\%$ of each dataset as the test set and the remaining images as the training set. Four pairs of images from CelebA [22] with the same identity are used as attack targets for training and testing, respectively, since CelebA [22] contains multiple images of one identity. Besides, the real state set in subsection 4.3 are obtained from the RaFD dataset [21].", + "bbox": [ + 496, + 704, + 892, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "20580", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/f48b047b7b5f0a4c50f9c29dbad0e32ee30d3a0fb79d1865ce84af6d8cf9a4df.jpg", + "table_caption": [ + "Table 3. The effect of the image quantity in state set on improving the generalizability of the adversarial example. The values $n_i$ in $n_1 / n_2 / n_3$ represents each expression state using $i$ images." + ], + "table_footnote": [], + "table_body": "
Target 1Target 2Target 3
FacenetMobilefaceFacenetMobilefaceFacenetMobileface
G-TIP-IM [34]7.6/7.1/7.270.9/70.3/70.120.4/21.5/21.449.2/49.2/49.219.4/19.6/19.439.4/39.6/39.5
G-AMT-GAN [16]13.2/14.4/13.947.1/44.8/45.317.1/16.9/18.943.9/45.4/43.816.2/15.4/15.742.4/44.6/45.4
GMAA17.8/18.2/17.767.5/68.5/69.321.7/21.3/19.641.2/42.6/40.319.2/19.9/21.347.2/45.6/44.7
", + "bbox": [ + 78, + 122, + 890, + 200 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/34c333538aa2679c4cd7ce19f4b2360ce42920bcba81074821636ab4fb7a98de.jpg", + "image_caption": [ + "Figure 4. The confidence scores returned by Face++ and Tencent. The dashed line represents the average confidence level of clean samples." + ], + "image_footnote": [], + "bbox": [ + 81, + 214, + 486, + 383 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ee5dac8c8ac83e63135a5c155b674485abeb05391444afa0c97ddb59985a5ab2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 493, + 213, + 890, + 383 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8456c5e1a748682f82b909cea585b52ba81d25be660f7f1b1ad52c1350c6247b.jpg", + "image_caption": [ + "Figure 5. The left side of the image depicts the five expression states, while the right side of the image depicts the influence of varied AU on the attack performance of Face++ and Tencent." + ], + "image_footnote": [], + "bbox": [ + 76, + 417, + 472, + 553 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/1da490c16cdd3e8e274fc6a938e98762b7705dd5eb0da3ffbf9dd7aeed414e4a.jpg", + "table_caption": [ + "Table 4. This table shows the black-box ASR results of attacking the test target, which is the same person as the train image highlighted by a green square in Fig. 3. The unbolded numbers represent the results of training on the single target image that is shown in Fig. 3, while the bolded numbers are the results of training on the generated state set." + ], + "table_footnote": [], + "table_body": "
FacenetMobileface
TIP-IM [34] / G-TIP-IM5.80 / 9.5017.20 / 23.5
AMT-GAN [16] / G-AMT-GAN4.04 / 8.279.82 / 12.45
MAA / GMAA6.60 / 10.6013.50 / 21.60
", + "bbox": [ + 78, + 704, + 470, + 768 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Competitors. We compare our approach to the baselines PGD [23], MI-FGSM [7], SemanticAdv [26], TIP-IM [34] and AMT-GAN [16]. Since our work belongs to the branch of GAN based unrestricted adversarial attack [30], which is budget-free. Similar to [30], we compare our method MAA/GMAA to both restricted and unrestricted adversarial methods w.r.t attack performance and visual naturalness. All restricted methods are setted to the size of perturbation", + "bbox": [ + 75, + 779, + 470, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "$\\epsilon = 12$ . And all baselines are equipped with the transferability enhancement module for a fair comparison.", + "bbox": [ + 496, + 419, + 890, + 448 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Target models. Following [16], we choose IR152 [14], IRSE50 [15], Facenet [27] and Mobileface [5] as the attacked FR models, with three of them serving as white-box models during training and the remaining as the black-box model for testing.", + "bbox": [ + 496, + 449, + 890, + 525 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Comparison Study", + "text_level": 1, + "bbox": [ + 500, + 530, + 679, + 546 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "This subsection shows the comparison results of the MAA method and competitors in terms of attack performance and visual quality.", + "bbox": [ + 496, + 547, + 890, + 593 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison of attack performance on commercial API. We evaluate the performance of each method against the commercial APIs Face++ $^2$ and Tencent $^3$ . Fig. 4 exhibits the average confidence score of Face++ and Tencent between the adversarial example and the test image of the target identity. Our method MAA achieves the highest score, outperforming all competitors on both datasets, as shown in Fig. 4. Furthermore, in Fig. 5, we display the confidence scores for five typical expressions (happy, angry, sad, surprised, and expressionless) to demonstrate that different AU vectors have little effect on attack performance and are more influenced by the dataset.", + "bbox": [ + 496, + 594, + 890, + 773 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison of black-box attack success rate. Since our model can give us a semantic continuous adversarial manifold and we want to make sure the comparison is fair, we randomly sample the AU vector to get test adversarial examples for calculating the black-box ASR. Tab. 1 shows the", + "bbox": [ + 496, + 775, + 890, + 851 + ], + "page_idx": 6 + }, + { + "type": "page_footnote", + "text": "$^{2}$ https://www(faceplusplus.com/", + "bbox": [ + 514, + 862, + 753, + 875 + ], + "page_idx": 6 + }, + { + "type": "page_footnote", + "text": "3https://cloud.tencent.com/document/product/867/44987", + "bbox": [ + 503, + 876, + 890, + 898 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "20581", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a802c2a541ccf1fea7791d2046e056fb619ac6ff5f6b6d5c6300659ceb97a6ef.jpg", + "image_caption": [ + "Figure 6. The images with green frames are the clean samples, while the images with blue frames are the results of TIP-IM [34]. In the case of the AMT-GAN [16], we chose 8 makeup styles at random, and the visualization results are shown as images with an orange frame. The images highlighted by red frames are the results of MAA, which are generated by a set of AU vectors. Please refer to the supplementary material for more high-definition magnified visualization results." + ], + "image_footnote": [], + "bbox": [ + 78, + 88, + 893, + 189 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "black-box ASR of each method under four FR models and two datasets. Obviously, our method has good performance for black-box attacks, i.e., it has strong transferability.", + "bbox": [ + 75, + 265, + 468, + 311 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Comparison of visual quality. We choose TIP-IM and AMT-GAN, two recent approaches with high black-box ASR, as benchmarks for our assessment of visual quality. Fig. 6 shows the adversarial examples of each method, and the target image is shown in Fig. 3 highlighted by a green square. In particular, to demonstrate that our method can generate semantically continuous adversarial examples, Fig. 6 displays the adversarial examples generated by MAA that continuously transform on four expressions (expressionless, disgusted, happy and surprised in succession). Note that although only 20 adversarial examples are presented in Fig. 6, our method can generate an infinite number of adversarial examples by continuously interpolating between AU vectors since MAA establishes a correspondence with the AU vector space. Moreover, our method has a natural visual quality and is gender-insensitive.", + "bbox": [ + 75, + 311, + 472, + 554 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Attack state set", + "text_level": 1, + "bbox": [ + 76, + 563, + 232, + 577 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Attack real state set. To avoid serendipity, two FR models, three different test targets, and three adversarial attack methods were employed to assess the effectiveness of attacking state set on enhancing the adversarial examples' generalizability. Particularly, one of the FR models is Facenet with high accuracy, and the other is Mobileface with a lightweight network. Targets *, 1, 2 and 3 are shown in Fig. 2. The state set consists of several common expression states (angry, contemptuous, disgusted, fearful, happy, sad and surprised), and each correlates to an image. By comparing the results in Tab. 2, we can summarize that the model trained to attack target * generalizes poorly to test targets 1, 2, 3, whereas adversarial examples generated on the state set generalize better to the test target, even though the test target is not used to train the model.", + "bbox": [ + 75, + 580, + 468, + 808 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We try to add more images in the state set to further improve the performance. Tab. 3 shows the ASR results that the target state set contains each expression state corresponding to $1/2/3$ image(s), respectively. We demonstrate that the generalizability of the adversarial examples can be effectively strengthened as long as the state set contains a", + "bbox": [ + 75, + 810, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "single image of each state, and additional images have minimal impact on the results.", + "bbox": [ + 498, + 265, + 890, + 294 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Attack generated state set. For face image datasets that do not contain rich states, we generate the target state set by the pre-trained generator $G_{exp}$ with AU vectors of common expressions. Tab. 4 shows the comparison results of training on a single target and a generated state set, demonstrating that training the model on the target state set enhances the generalization ability of adversarial examples.", + "bbox": [ + 496, + 295, + 892, + 402 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Future Work", + "text_level": 1, + "bbox": [ + 498, + 412, + 635, + 428 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Considering the ubiquitous applicability of expressions in the facial adversarial attacks, the expression state space was chosen to implement GMAA in this paper. We employ the FACS as the prior domain knowledge to implement GMAA, while the paradigm GMAA can be broadly generalized by integrating other domain information, such as illumination, posture, etc. By selecting different state spaces, our work can be generalized to other adversarial attacks with more general image categories.", + "bbox": [ + 496, + 435, + 890, + 571 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 582, + 619, + 598 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we provide a novel paradigm GMAA that broadens both target domain and adversarial domain to enhance the performance of adversarial attack. For the target domain, GMAA optimizes generalization to the target identity by attacking the state set instead of a single image. Additionally, GMAA leverages the domain knowledge to expand adversarial domain from discrete points to semantic continuous manifold. Numerous comparative experiments have verified that GMAA has a better attack performance and a more natural visual quality than other competitors. Moreover, the generalized attack module can be extended to a wide of applications.", + "bbox": [ + 496, + 604, + 890, + 787 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Acknowledgement", + "text_level": 1, + "bbox": [ + 500, + 797, + 679, + 814 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported and partially funded by the National Natural Science Foundation of China (Grant No. 62106116). This work was also supported in part by ZJNSFC under Grant LQ23F010008. We also would like to thank Han Fang of NUS for the valuable discussion.", + "bbox": [ + 496, + 820, + 890, + 896 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "20582", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Tadas Baltrusaitis, Amir Zadeh, Yao Chong Lim, and Louis-Philippe Morency. Openface 2.0: Facial behavior analysis toolkit. 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IEEE, 2019. 1, 3" + ], + "bbox": [ + 78, + 90, + 468, + 752 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "20584", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Discrete Point-Wise Attack Is Not Enough_ Generalized Manifold Adversarial Attack for Face Recognition/dc2b0e92-b412-418d-ab5e-fff033c9b7f7_model.json b/2023/Discrete Point-Wise Attack Is Not Enough_ Generalized Manifold Adversarial Attack for Face Recognition/dc2b0e92-b412-418d-ab5e-fff033c9b7f7_model.json new file mode 100644 index 0000000000000000000000000000000000000000..2d2a3f318d843a903129f2d0a488652d7f98d928 --- /dev/null +++ b/2023/Discrete Point-Wise Attack Is Not Enough_ Generalized Manifold Adversarial Attack for Face Recognition/dc2b0e92-b412-418d-ab5e-fff033c9b7f7_model.json @@ -0,0 +1,2123 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.098, + 0.13, + 0.877, + 0.177 + ], + "angle": 0, + "content": "Discrete Point-wise Attack Is Not Enough: Generalized Manifold Adversarial Attack for Face Recognition" + }, + { + "type": "text", + "bbox": [ + 0.209, + 0.204, + 0.761, + 0.24 + ], + "angle": 0, + "content": "Qian Li, Yuxiao Hu,\\* Ye Liu, Dongxiao Zhang, Xin Jin,\\* Yuntian Chen\\* Eastern Institute for Advanced Study, Ningbo Zhejiang, China" + }, + { + "type": "text", + "bbox": [ + 0.282, + 0.242, + 0.688, + 0.257 + ], + "angle": 0, + "content": "{QianL01205, huyuxiaol205, liuye66a}@gmail.com" + }, + { + "type": "text", + "bbox": [ + 0.329, + 0.26, + 0.629, + 0.275 + ], + "angle": 0, + "content": "{dzhang, jinxin, ychen}@eias.ac.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.309, + 0.314, + 0.327 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.342, + 0.474, + 0.706 + ], + "angle": 0, + "content": "Classical adversarial attacks for Face Recognition (FR) models typically generate discrete examples for target identity with a single state image. However, such paradigm of point-wise attack exhibits poor generalization against numerous unknown states of identity and can be easily defended. In this paper, by rethinking the inherent relationship between the face of target identity and its variants, we introduce a new pipeline of Generalized Manifold Adversarial Attack (GMAA)1 to achieve a better attack performance by expanding the attack range. Specifically, this expansion lies on two aspects - GMAA not only expands the target to be attacked from one to many to encourage a good generalization ability for the generated adversarial examples, but it also expands the latter from discrete points to manifold by leveraging the domain knowledge that face expression change can be continuous, which enhances the attack effect as a data augmentation mechanism did. Moreover, we further design a dual supervision with local and global constraints as a minor contribution to improve the visual quality of the generated adversarial examples. We demonstrate the effectiveness of our method based on extensive experiments, and reveal that GMAA promises a semantic continuous adversarial space with a higher generalization ability and visual quality." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.724, + 0.21, + 0.74 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.744, + 0.47, + 0.851 + ], + "angle": 0, + "content": "Thanks to the rapid development of deep neural networks (DNNs), the face recognition (FR) networks [5, 27] has been applied to identity security identification systems in a variety of crucial applications, such as face unlocking and face payment on smart devices. However, it has been observed that DNNs are easily fooled by adversarial examples and offer incorrect assessments [9, 23], which has risks" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.311, + 0.892, + 0.401 + ], + "angle": 0, + "content": "of unauthorized access to FR systems and stealing personal privacy through poisoned data. These 'well-designed' adversarial examples reveal the aspects of FR models that are vulnerable to be attacked, which makes the adversarial attack a meaningful work to provide reference for improving model robustness." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.402, + 0.895, + 0.886 + ], + "angle": 0, + "content": "Following the point-wise paradigm, previous methods typically tend to attack a single target identity sample with discrete adversarial examples illustrated in Fig. 1. However, these methods are not strong enough both in target domain and adversarial domain. Concretely, for the target domain, attacking a single identity image has a poor generalization on those unseen faces (even if they belong to the same person) in realistic scenarios. For example, Fig. 2 shows these adversarial examples which were used to attack the target (a girl) have a disappointingly lower success rate of attacking the identity with other unseen states. We analyze that's because attacking a single image of target identity overfits the generation of adversarial examples to some fixed factors such as expression, makeup style, etc. In addition to the target domain, we naturally consider the weakness of adversarial domain in the existing methods. Most adversarial attack methods optimize a \\( L_{p} \\) bounded perturbation [24,34] based on the gradient, which limits the problem to searching for discrete adversarial examples in a hypersphere of the clean sample and ignores the continuity of the generated adversarial domain. For example, the recently proposed methods based on makeup style transformation [16,35,37] focus on generating finite adversarial examples that correspond to discrete makeup references. Such methods all overemphasize on mining discrete adversarial examples within a limited scope and ignore the importance of the continuity in adversarial space. The weakness of current adversarial attack tasks motivates us, on the one hand, to explore how to generate adversarial examples that are more general to various target identity's states and, on the other hand, to upgrade adversarial domain from discrete points to continuous manifold for a stronger attack." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "In this paper, we introduce a new paradigm dubbed Gen" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.863, + 0.184, + 0.875 + ], + "angle": 0, + "content": "*Co-first author" + }, + { + "type": "page_footnote", + "bbox": [ + 0.097, + 0.876, + 0.221, + 0.888 + ], + "angle": 0, + "content": "† Corresponding author" + }, + { + "type": "page_footnote", + "bbox": [ + 0.097, + 0.888, + 0.357, + 0.9 + ], + "angle": 0, + "content": "1https://github.com/tokaka22/GMAA" + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.863, + 0.357, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20575" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.09, + 0.089, + 0.885, + 0.339 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.351, + 0.893, + 0.407 + ], + "angle": 0, + "content": "Figure 1. The core idea comparison. Discrete point-wise attack methods leverage a single state of the target identity during training and provide discrete adversarial examples. By attacking the target identity's state set and employing domain knowledge, our core idea aims to Generalized Manifold Adversarial Attack (GMAA), which promises a semantic continuous adversarial manifold with a higher generalization ability on the target identity with unknown state." + }, + { + "type": "image", + "bbox": [ + 0.086, + 0.425, + 0.449, + 0.59 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.598, + 0.471, + 0.641 + ], + "angle": 0, + "content": "Figure 2. The black-box attack success rate on the Mobileface of attacking target * 1, 2 and 3 during the testing. The three methods are exclusively trained on target *." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.659, + 0.47, + 0.901 + ], + "angle": 0, + "content": "eralized Manifold Adversarial Attack (GMAA) depicted in Fig. 1, which achieves a higher attack success rate by providing semantic continuous adversarial domains while expanding the target to be attacked from an instance to a group set. Specifically, we train adversarial examples to attack a target identity set rather than a single image, which increases the attack success rate on the target identity with different states. The expansion of target domain naturally prompts us to consider enhancing the adversarial domain. Inspired by the success of some recent data and knowledge dual driven methods [2, 18, 36], we explore a low-dimensional manifold near the sample according to the domain knowledge, which is a simple yet highly-efficient continuous embedding scheme and can be used to augment the data. For such manifold, the data in it share the visual identity same as the original sample and also lie in the decision" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.427, + 0.892, + 0.682 + ], + "angle": 0, + "content": "boundaries of target identity. More specifically, we employ the Facial Action Coding System (FACS) [10] as prior domain knowledge (a kind of instantiation) to expand adversarial domain from discrete points to manifold. Through using FACS, the expressions can be encoded into a vector space, and by which the adversarial example generator could produce an manifold that is homogeneous with the expression vector space and possesses semantic continuity. In addition, in order to build an adversarial space with high visual quality, we employ four expression editors in GMAA pipeline to supervise the adversarial example generation in terms of global structure and local texture details. A transferability enhancement module is also introduced to drive the model to mine robust and transferable adversarial features. Extensive experiments have shown that these components work well on a wide range of baselines and black-box attack models." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.684, + 0.82, + 0.697 + ], + "angle": 0, + "content": "Our contributions are summarized as follows." + }, + { + "type": "text", + "bbox": [ + 0.516, + 0.698, + 0.89, + 0.741 + ], + "angle": 0, + "content": "- We first pinpoint that the popular adversarial attack methods generally face generalization difficulty caused by the limited point-wise attack mechanism." + }, + { + "type": "text", + "bbox": [ + 0.516, + 0.744, + 0.89, + 0.803 + ], + "angle": 0, + "content": "- To enhance the performance of adversarial attack, a new paradigm of Generalized Manifold Adversarial Attack (GMAA) is proposed with an improved attack success rate and better generalization ability." + }, + { + "type": "text", + "bbox": [ + 0.516, + 0.806, + 0.891, + 0.91 + ], + "angle": 0, + "content": "- GMAA considers the enhancement in terms of both target domain and adversarial domain. For the target domain, it expands the target to be attacked from one to many to encourage a good generalization. For the adversarial domain, the domain knowledge is embedded to strengthen the attack effect from discrete points to continuous manifold." + }, + { + "type": "list", + "bbox": [ + 0.516, + 0.698, + 0.891, + 0.91 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20576" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.094, + 0.092, + 0.47, + 0.198 + ], + "angle": 0, + "content": "- We instantiate GMAA in the face expression state space for a semantic continuous adversarial manifold and use it to attack a state set of the target identity. As a minor contribution, GMAA supervises the adversarial example generator w.r.t global structure and local details with the pre-trained expression editors for a high visual quality." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.206, + 0.216, + 0.221 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.224, + 0.428, + 0.24 + ], + "angle": 0, + "content": "2.1. Adversarial Attacks on Face Recognition" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.242, + 0.473, + 0.786 + ], + "angle": 0, + "content": "Adversarial attacks can be divided into white-box attacks and black-box attacks. White-box attacks [11, 24, 32] must entail full information of the target neural networks, however, the parameters and architecture of a real-world face recognition system are typically hard to access. Hence, it is more practical to consider black-box adversarial attacks in face recognition scenarios, which demand high transferability for the unknown FR target models or commercial application programming interfaces (APIs). Query-based adversarial attacks [9, 13], a form of black-box attack, is inappropriate for realistic applications since it optimizes adversarial examples by repeatedly accessing the target model during training. Adding transferable adversarial perturbation is another effective black-box attack form [4, 7, 8, 34]. Unfortunately, the perturbation caused by this method always makes images become unrealistic and unnatural. Besides, limited by the way of pixel-to-pixel similarity computation, the model of this branch could only look for a limited number of discrete adversarial examples around the clean sample. The patch-based adversarial attack [20, 28, 33] severely degrades the visual quality of images, because the adversarial patch does not blend well with the clean background due to the abrupt shift in pixel values around the boundary. Numerous recent works attempt to instantiate adversarial perturbations with different makeup styles [16, 35, 37]. However, such makeup attacks typically result in an unnatural visual appearance due to gender constraints – female images have a higher attack success rate and visual quality than male ones. Regardless of the previous methods (e.g. [26] focuses on a target sample to obtain optimal feature-map interpolation, and [16] generates adversarial examples with various makeup styles to attack the target identity), they all tend to generate discrete adversarial examples for a single target identity sample and ignore the importance of continuity of adversarial space, which might be crucial to the attack performance." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.794, + 0.312, + 0.809 + ], + "angle": 0, + "content": "2.2. Facial Expression Editing" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.811, + 0.47, + 0.901 + ], + "angle": 0, + "content": "As another challenging task in facial analysis, face expression editing is also related to our study, which aims at modifying facial expressions in a reasonable manner while preserving identity completeness. In recent years, generative adversarial networks (GANs) have achieved surprising advances in facial expression editing: GCGAN [29] uses" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.318 + ], + "angle": 0, + "content": "the facial geometry as prior knowledge to guide the generation. ExprGAN [6] exploits a controller to adjust the intensity of face expression editing. StarGAN [3] introduces a cycle consistency loss to maintain the identity content invariant. However, these methods are all limited on the discrete expressions generation. GANimation [25] utilizes Action Units [10] to define an expression space and generate continuous-change facial images. EF-GAN [31] achieves progressive facial expression editing with a local-focused cascade GAN structure, and produces fewer artifacts and blurs in large-gap expression transformations. In this paper, we borrow the idea of Action Units as domain prior knowledge (from face expression editing) to re-define the adversarial attack task on a continuous manifold, to finally strengthen attack effect." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.324, + 0.872, + 0.34 + ], + "angle": 0, + "content": "3. Generalized Manifold Adversarial Attack" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.349, + 0.682, + 0.364 + ], + "angle": 0, + "content": "3.1. Problem Definition" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.372, + 0.892, + 0.522 + ], + "angle": 0, + "content": "Adversarial face attack tasks can be separated into targeted attacks (i.e. impersonation attacks) and non-targeted attacks (i.e. dodging attacks). Targeted attacks force the generated adversarial examples to have a predetermined output towards the target FR model, while the non-targeted attacks mislead the target FR model to provide incorrect random classification for the adversarial examples. To capture the adversarial examples that can impersonate a specific target identity under face authentication systems, we mainly consider the targeted attack task." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.523, + 0.892, + 0.553 + ], + "angle": 0, + "content": "Current methods always define the targeted attack task as an optimization problem, which can be formalized as" + }, + { + "type": "equation", + "bbox": [ + 0.568, + 0.558, + 0.892, + 0.6 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\min L _ {a d v} = \\min _ {\\boldsymbol {\\theta}} D i s t \\left(\\mathcal {C} \\left(\\boldsymbol {x} ^ {*}\\right), \\mathcal {C} \\left(\\boldsymbol {x} ^ {\\prime}\\right)\\right), \\tag {1} \\\\ \\boldsymbol {x} ^ {\\prime} = G (\\boldsymbol {x}; \\boldsymbol {\\theta}). \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.605, + 0.892, + 0.679 + ], + "angle": 0, + "content": "where \\( \\pmb{x}^* \\) is the pre-specified target image belonging to the sample space \\( \\Omega \\subset \\mathbb{R}^{3 \\times H \\times W} \\), \\( \\text{Dist}(\\cdot) \\) represents a metric of difference, \\( \\mathcal{C} \\) represents the feature extractor of FR neural networks, and \\( G \\) maps the clean sample \\( \\pmb{x} \\in \\Omega \\) to the adversarial version \\( \\pmb{x}' \\) with the parameter \\( \\pmb{\\theta} \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.68, + 0.892, + 0.801 + ], + "angle": 0, + "content": "In this paper, we re-define the problem from a broader standpoint. To obtain highly generalized adversarial examples that are more threatening to the target identity with unknown state, the adversarial version \\( \\pmb{x}^{\\prime} \\) attacks the state set \\( S \\) of the target identity during training. In order to capture an adversarial manifold \\( \\mathcal{M} \\) instead of discrete adversarial examples, we aim to construct a distribution on the \\( \\mathcal{M} \\). The new task can be formalized as Eq. 2." + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.805, + 0.892, + 0.847 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\min L _ {a d v} = \\min _ {\\boldsymbol {\\theta}} \\mathbb {E} _ {\\boldsymbol {x} _ {i} ^ {*} \\sim \\mathcal {S}, \\boldsymbol {x} ^ {\\prime} \\sim \\mathcal {M}} D i s t (\\mathcal {C} \\left(\\boldsymbol {x} _ {i} ^ {*}\\right), \\mathcal {C} \\left(\\boldsymbol {x} ^ {\\prime}\\right)), \\tag {2} \\\\ \\mathcal {M} = G (\\boldsymbol {x}; \\boldsymbol {\\theta}). \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In addition to the adversarial attack tasks, we force \\( G \\) to map \\( \\pmb{x} \\) to \\( \\pmb{x}' \\) according to the given expression AU vector. The Facial Action Coding System (FACS) is applied as" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20577" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.101, + 0.09, + 0.852, + 0.365 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.372, + 0.895, + 0.43 + ], + "angle": 0, + "content": "Figure 3. Overview of GMAA. A face image and a random AU vector are sent to the generative adversarial module as inputs. Meanwhile, the expression supervision module generates supervisory signals based on the AU vector and the input image (or detail patches cropped by the landmarks). In the transferability enhancement module, aiming at white-box FR models, the transformed output attacks the target identity's state set, which is provided by the generalized attack module." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.436, + 0.473, + 0.622 + ], + "angle": 0, + "content": "prior domain knowledge to establish a continuous expression state space. Specifically, every expression is encoded by an n-element expression vector \\(\\pmb{\\mu} = (\\mu_{1},\\dots,\\mu_{n})\\) which corresponds to \\(N\\) facial action units. Each \\(\\mu_{n}\\in \\pmb{\\mu}\\) represents the magnitude of muscle activity in the n-th region of the face, which indicates that the AU vector is a continuous embedding scheme for different expressions. Thus, for the input image \\(\\pmb{x}_{\\mu^0}\\in \\mathbb{R}^{3\\times H\\times W}\\) with the expression encoded by \\(\\pmb{\\mu}^0\\in \\mathbb{R}^N\\) and the given expression encoded by \\(\\pmb{\\mu}^i\\in \\mathbb{R}^N\\), \\(G\\) is a binary mapping \\(G:(\\pmb{x}_{\\mu^0},\\pmb{\\mu}^i)\\to \\pmb{x}_{\\mu^i}^\\prime\\), where \\(\\pmb{x}_{\\mu^i}^\\prime\\) has the same visual label with \\(\\pmb{x}_{\\mu^0}\\) and wearing the expression encoded by \\(\\pmb{\\mu}^i\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.626, + 0.433, + 0.641 + ], + "angle": 0, + "content": "3.2. Generalized Manifold Adversarial Attack" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.643, + 0.47, + 0.825 + ], + "angle": 0, + "content": "We establish the adversarial examples' distribution on a manifold via WGAN-GP [12]. GMAA comprises a generative adversarial module, an expression supervision module, a transferability enhancement module, and a generalized attack module. In contrast, Manifold Adversarial Attack (MAA) omits the generalized attack module, as it merely extends the adversarial domain from a point to a manifold. The structure of our proposed method is depicted in Fig. 3. Generative adversarial module. The generative adversarial module (red box in Fig. 3) includes a generator \\(G\\), a discriminator \\(D_{c}\\) and an AU predictor \\(D_{AU}\\), where \\(D_{c}\\) and \\(D_{AU}\\) both lie in \\(D\\) and share partial parameters." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.471, + 0.903 + ], + "angle": 0, + "content": "As inputs, the generator \\(G\\) receives a clean sample \\(\\boldsymbol{x}_{\\mu^0}\\) and a given expression AU label \\(\\boldsymbol{\\mu}^i\\), which aims to produce adversarial examples wearing the expression matching to the supplied AU label and maintain the same visual identity with \\(\\boldsymbol{x}_{\\mu^0}\\). The discriminator \\(D_{c}\\) learns to distinguish real" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.436, + 0.892, + 0.512 + ], + "angle": 0, + "content": "images from generated images. Meanwhile, generated images deceive the discriminator \\( D_{c} \\) to force the outputs of the generator \\( G \\) match the real distribution. Our \\( G \\) and \\( D_{c} \\) are trained using WGAN-GP [12], and the critic loss function we employ is" + }, + { + "type": "equation", + "bbox": [ + 0.512, + 0.517, + 0.891, + 0.577 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} L _ {\\text {c r i t i c}} ^ {D} = \\lambda_ {c} \\left(1 - D _ {c} \\left(\\boldsymbol {x} _ {\\boldsymbol {\\mu} ^ {0}}\\right)\\right) ^ {2} + \\lambda_ {c} \\left(D _ {c} \\left(G \\left(\\boldsymbol {x} _ {\\boldsymbol {\\mu} ^ {0}} \\mid \\boldsymbol {\\mu} ^ {i}\\right)\\right) ^ {2} \\right. (3) \\\\ + \\lambda_ {g p} \\left(\\| \\nabla_ {\\widetilde {x}} D _ {c} (\\widetilde {x}) \\| _ {2} - 1\\right) ^ {2}, \\\\ L _ {c r i t i c} ^ {G} = \\lambda_ {c} \\left(1 - D _ {c} \\left(G \\left(\\boldsymbol {x} _ {\\boldsymbol {\\mu} ^ {0}} \\mid \\boldsymbol {\\mu} ^ {i}\\right)\\right)\\right) ^ {2}, (4) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.582, + 0.892, + 0.747 + ], + "angle": 0, + "content": "where \\(\\widetilde{\\pmb{x}}\\) is the random interpolation distribution between the real distribution and the generated images' distribution. To ensure that the generated image matches the provided expression code \\(\\pmb{\\mu}^i\\), we employ AU regression loss to establish the consistency of the generated expression with \\(\\pmb{\\mu}^i\\). Specifically, the AU predictor \\(D_{AU}\\) learns the AU coding rules by real images and their AU labels (can be obtained by the open source framework Openface [1]), and the \\(G\\) reduces the AU error between the generated expression and \\(\\pmb{\\mu}^i\\) to satisfy the given expression. The loss function can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.558, + 0.752, + 0.891, + 0.778 + ], + "angle": 0, + "content": "\\[\nL _ {A U} ^ {D} = \\lambda_ {A U} \\| D _ {A U} \\left(\\boldsymbol {x} _ {\\boldsymbol {\\mu} ^ {0}}\\right) - \\boldsymbol {\\mu} ^ {0} \\| _ {2} ^ {2}, \\tag {5}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.561, + 0.773, + 0.833, + 0.792 + ], + "angle": 0, + "content": "\\[\nL _ {A U} ^ {G} = \\lambda_ {A U} \\| D _ {A U} \\left(G \\left(\\boldsymbol {x} _ {\\boldsymbol {\\mu} ^ {0}} \\mid \\boldsymbol {\\mu} ^ {i}\\right)\\right) - \\boldsymbol {\\mu} ^ {i} \\| _ {2} ^ {2}.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Expression supervision module. The expression supervision module (blue box in Fig. 3) protects the visual identity of adversarial examples and guides \\( G \\) in expression editing by generating global and local facial supervisory signals. The global branch focuses on structural features of the face, whereas the local branch protects important facial details and reduces artifacts and blurs caused by the global branch." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20578" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.288 + ], + "angle": 0, + "content": "Specifically, a global editor and three local editors are pre-trained to provide supervisory signals. For the local editors, we crop the eyes, nose, and mouth pixel patches based on face landmarks first. Then the input image and three detail patches are fed into the corresponding generator \\( G_{global} \\) and \\( G_{j} \\) (\\( j \\in J = \\{\\text{eyes, nose, mouth}\\}\\)) with the input AU vector \\( \\mu \\), respectively. Each generator has the network structure similar to [25], which provides the color response \\( M_{c}^{\\mu} \\) and the attention response \\( M_{a}^{\\mu} \\). \\( M_{c}^{\\mu} \\) and \\( M_{a}^{\\mu} \\) force networks to pay attention to the expression change region and protect the remainder regions from disturbance. The ultimate supervisory signals can be obtained as follows, where \\( \\otimes \\) denotes element-wise multiplication." + }, + { + "type": "equation", + "bbox": [ + 0.117, + 0.292, + 0.47, + 0.311 + ], + "angle": 0, + "content": "\\[\nG _ {j} \\left(\\boldsymbol {x} _ {i n} \\mid \\boldsymbol {\\mu}\\right) = M _ {a} ^ {\\boldsymbol {\\mu}} \\otimes M _ {c} ^ {\\boldsymbol {\\mu}} + \\left(1 - M _ {a} ^ {\\boldsymbol {\\mu}}\\right) \\otimes \\boldsymbol {x} _ {i n}. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.317, + 0.473, + 0.439 + ], + "angle": 0, + "content": "The global editor focuses more on large scale features, such as shape and position of the five senses, and tends to produce artifacts and blurs in the detail region, while the local editors concentrate on significant local features and provide finer details. Therefore, we deploy the global editor to supervise the structural information of adversarial examples and the local editors to supervise local specifics. The loss of expression supervision module can be expressed as" + }, + { + "type": "equation", + "bbox": [ + 0.078, + 0.446, + 0.469, + 0.514 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} L _ {e x p} ^ {G} = \\lambda_ {g} \\mathrm {S S I M} [ G (\\pmb {x} _ {\\pmb {\\mu} ^ {0}} | \\pmb {\\mu} ^ {i}), G _ {g l o b a l} (\\pmb {x} _ {\\pmb {\\mu} ^ {0}} | \\pmb {\\mu} ^ {i}) ] \\\\ + \\lambda_ {l} \\sum_ {j \\in J} \\operatorname {M S E} \\left[ \\operatorname {C r o p} _ {j} \\left(G \\left(\\boldsymbol {x} _ {\\boldsymbol {\\mu} ^ {0}} \\mid \\boldsymbol {\\mu} ^ {i}\\right)\\right), G _ {j} \\left(\\operatorname {C r o p} _ {j} \\left(\\boldsymbol {x} _ {\\boldsymbol {\\mu} ^ {0}}\\right) \\mid \\boldsymbol {\\mu} ^ {i}\\right) \\right], \\tag {7} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.515, + 0.47, + 0.545 + ], + "angle": 0, + "content": "where \\(\\mathrm{Crop}_j\\) denotes the crop operation of local region \\(j\\) according to the face landmarks." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.545, + 0.47, + 0.695 + ], + "angle": 0, + "content": "Transferability enhancement module. To improve the transferability of adversarial examples and the black-box attack success rate, we introduce the transferability enhancement module (yellow box in Fig. 3) from [16]. The generated adversarial examples are transformed with probability \\( p \\) by the function \\( T_{p} \\) (resize with padding or add noise), and then attack \\( K \\) pre-trained high-precision FR models \\( \\{C_k\\}_{k=1,\\dots,K} \\), which perform as white-box models during the training of \\( G \\). The adversarial attack loss function is formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.084, + 0.698, + 0.469, + 0.751 + ], + "angle": 0, + "content": "\\[\nL _ {a d v} ^ {G} = \\frac {\\lambda_ {a d v}}{K} \\sum_ {k = 1} ^ {K} [ 1 - \\cos \\left(\\mathcal {C} _ {k} \\left(\\boldsymbol {x} ^ {*}\\right), \\mathcal {C} _ {k} \\left(T _ {p} \\left(G \\left(\\boldsymbol {x} _ {\\boldsymbol {\\mu} ^ {0}} \\mid \\boldsymbol {\\mu} ^ {i}\\right)\\right)\\right)\\right) ] \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.752, + 0.47, + 0.843 + ], + "angle": 0, + "content": "Generalized attack module. The generalized attack module (green box in Fig. 3) intends to raise the attack success rate on the unseen face belonging to the target identity, which can be introduced into other adversarial attack approaches. The adversarial loss \\( L_{adv}^{G} \\) in GMAA can be further expressed as" + }, + { + "type": "equation", + "bbox": [ + 0.084, + 0.847, + 0.47, + 0.902 + ], + "angle": 0, + "content": "\\[\n\\mathbb {E} _ {\\boldsymbol {x} _ {i} ^ {*}} \\sim_ {\\mathcal {S}} \\frac {\\lambda_ {a d v}}{K} \\sum_ {k = 1} ^ {K} [ 1 - \\cos \\left(\\mathcal {C} _ {k} \\left(\\boldsymbol {x} _ {i} ^ {*}\\right), \\mathcal {C} _ {k} \\left(T _ {p} \\left(G \\left(\\boldsymbol {x} _ {\\boldsymbol {\\mu} ^ {0}} \\mid \\boldsymbol {\\mu} ^ {i}\\right)\\right)\\right)\\right) ], \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.227 + ], + "angle": 0, + "content": "where \\( \\boldsymbol{x}_i^* \\) and \\( S \\) are defined in 2. However, numerous face recognition datasets and realistic scenarios do not fit this module since an identity only contains a few or single state image. Fortunately, since our method can accomplish both expression editing and adversarial attack, when we remove the loss associated with adversarial attack, we can obtain an expression editor, \\( G_{exp} \\), by eliminating the adversarial effect \\( L_{adv}^{G} \\), which can generate the expression state set \\( S \\) by different AU vectors." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.228, + 0.892, + 0.304 + ], + "angle": 0, + "content": "Total loss function. Let \\( X \\) denotes the dataset, and \\( V \\) is the AU vector space. In particular, the given AU vector \\( \\pmb{\\mu}^i \\) is sampled randomly from \\( V \\) to train the generator \\( G \\) to learn the distribution of adversarial expression manifold. For the generator \\( G \\), we have the loss function as follows," + }, + { + "type": "equation", + "bbox": [ + 0.514, + 0.307, + 0.892, + 0.34 + ], + "angle": 0, + "content": "\\[\nL ^ {G} = \\mathbb {E} _ {\\boldsymbol {x} _ {\\mu^ {0}} \\sim \\boldsymbol {X}, \\boldsymbol {\\mu} ^ {i} \\sim V} \\left(L _ {\\text {c r i t i c}} ^ {G} + L _ {A U} ^ {G} + L _ {\\exp} ^ {G} + L _ {a d v} ^ {G}\\right). \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.341, + 0.887, + 0.355 + ], + "angle": 0, + "content": "As for \\(D\\), the total loss function can be obtained as follows," + }, + { + "type": "equation", + "bbox": [ + 0.566, + 0.36, + 0.892, + 0.381 + ], + "angle": 0, + "content": "\\[\nL ^ {D} = \\mathbb {E} _ {\\boldsymbol {x} _ {\\mu^ {0}} \\sim \\boldsymbol {X}, \\boldsymbol {\\mu} ^ {i} \\sim V} \\left(L _ {\\text {c r i t i c}} ^ {D} + L _ {A U} ^ {D}\\right). \\tag {11}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.393, + 0.807, + 0.409 + ], + "angle": 0, + "content": "3.3. Continuity of the adversarial space" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.411, + 0.892, + 0.455 + ], + "angle": 0, + "content": "In this subsection, we illustrate more precisely the continuity of the adversarial space and provide a proof that our method establishes a continuous adversarial manifold." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.456, + 0.892, + 0.485 + ], + "angle": 0, + "content": "Firstly, the definition of continuous adversarial space is shown in Def. 1." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.497, + 0.892, + 0.543 + ], + "angle": 0, + "content": "Definition 1. Let \\( \\pmb{x}_0 \\in \\mathbb{R}^{3 \\times H \\times W} \\), then \\( \\mathcal{M}^0 = G(\\pmb{x}_0; \\pmb{\\theta}) \\) is a continuous adversarial space if and only if (1) \\( \\mathcal{M}^0 \\) is a subspace of \\( \\mathbb{R}^{3 \\times H \\times W} \\)." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.543, + 0.829, + 0.56 + ], + "angle": 0, + "content": "(2) \\(\\forall \\pmb{x}_i^0\\in \\mathcal{M},\\pmb{x}_i^0\\) is an adversarial version of \\(\\pmb{x}_0\\)" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.563, + 0.88, + 0.578 + ], + "angle": 0, + "content": "Then, we can prove that \\(\\mathcal{M}^0\\) is a continuous manifold." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.892, + 0.629 + ], + "angle": 0, + "content": "Theorem 1. \\(\\mathcal{M}^0\\) generated by \\(G_0\\) is a continuous adversarial manifold, where \\(G_0: V \\to \\mathcal{M}\\) is a map when fixed the input \\(\\pmb{x}_0\\) in \\(G\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.642, + 0.892, + 0.672 + ], + "angle": 0, + "content": "Proof. (1) If \\(\\mathcal{M}^0\\) is homogeneous with the AU vector space \\(V\\), it is obviously that \\(\\mathcal{M}^0\\) is a subspace of \\(\\mathbb{R}^{3\\times H\\times W}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.673, + 0.892, + 0.749 + ], + "angle": 0, + "content": "(1.1) \\(\\forall \\pmb{\\mu}, \\pmb{\\nu} \\in V\\), if \\(G_0(\\pmb{\\mu}) = G_0(\\pmb{\\nu})\\), then \\(D_{AU}(G_0(\\pmb{\\mu})) = D_{AU}(G_0(\\pmb{\\nu}))\\), we have \\(\\pmb{\\mu} = \\pmb{\\nu}\\) and \\(G_0: V \\to \\mathcal{M}^0\\) is a single shot. Besides, \\(\\forall \\pmb{x}^0 \\in \\mathcal{M}^0\\), \\(\\exists \\pmb{\\mu} = D_{AU}(\\pmb{x}^0) \\in V\\) s.t. \\(G_0(D_{AU}(\\pmb{x}^0)) = \\pmb{x}^0\\), then \\(G_0\\) is a surjection. Thus, \\(G_0\\) is a bijection." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.748, + 0.892, + 0.81 + ], + "angle": 0, + "content": "(1.2) \\(\\forall \\pmb{x}_1^0, \\pmb{x}_2^0 \\in \\mathcal{M}^0\\), we define \\(d(\\pmb{x}_1^0, \\pmb{x}_2^0) = \\| D_{AU}(\\pmb{x}_1^0) - D_{AU}(\\pmb{x}_2^0)\\|_2\\) as the metric between \\(\\pmb{x}_1^0\\) and \\(\\pmb{x}_2^0\\) in \\(\\mathcal{M}^0\\). Since \\((V, \\| \\cdot \\|_2)\\) is a metric space, and \\(D_{AU}(\\pmb{x}_i^0) \\in V\\), \\(\\forall \\pmb{x}_i^0 \\in \\mathcal{M}^0\\), we prove that \\(d\\) is a metric on \\(\\mathcal{M}^0\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.871 + ], + "angle": 0, + "content": "(Positivity) \\(d(\\pmb{x}_1^0, \\pmb{x}_2^0) \\geq 0\\), and if \\(d(\\pmb{x}_1^0, \\pmb{x}_2^0) = 0\\) according to the definition of \\(d\\) we have \\(D_{AU}(\\pmb{x}_1^0) = D_{AU}(\\pmb{x}_2^0)\\). Since \\(G_0\\) is a bijection, we have \\(\\pmb{x}_1^0 = G_0(D_{AU}(\\pmb{x}_1^0)) = G_0(D_{AU}(\\pmb{x}_2^0)) = \\pmb{x}_2^0\\)." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.903 + ], + "angle": 0, + "content": "(Symmetry) \\(d(\\pmb{x}_1^0, \\pmb{x}_2^0) = \\| D_{AU}(\\pmb{x}_1^0) - D_{AU}(\\pmb{x}_2^0)\\|_2 = \\| D_{AU}(\\pmb{x}_2^0) - D_{AU}(\\pmb{x}_1^0)\\|_2 = d(\\pmb{x}_2^0, \\pmb{x}_1^0)\\)." + }, + { + "type": "list", + "bbox": [ + 0.498, + 0.673, + 0.892, + 0.903 + ], + "angle": 0, + "content": null + }, + { + "type": "footer", + "bbox": [ + 0.479, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "20579" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.37, + 0.09, + 0.6, + 0.103 + ], + "angle": 0, + "content": "Table 1. Black-box attack success rate" + }, + { + "type": "table", + "bbox": [ + 0.158, + 0.105, + 0.817, + 0.244 + ], + "angle": 0, + "content": "
CelebA-HQLFW
IRSE50IR152FacenetMobilefaceIRSE50IR152FacenetMobileface
Clean3.683.081.318.433.200.060.045.00
PGD [23]24.2013.375.8628.7231.3010.207.4033.50
MI-FGSM [7]38.9020.769.2540.4838.2014.207.6039.40
SemanticAdv [26]26.5310.247.8055.3233.6010.408.8037.40
TIP-IM [34]44.2016.0914.4665.3632.8015.2013.0079.00
AMT-GAN [16]51.0615.6311.6333.2740.7225.2313.8935.67
MAA60.4029.4318.9156.1355.8029.2018.0060.80
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.25, + 0.895, + 0.293 + ], + "angle": 0, + "content": "Table 2. The unbolded numbers are the black-box ASR of attacking the test target *, 1, 2, 3, and all the models are trained on target *. The bolded numbers are the results of the models that train on the state set. For example, if we train the MAA to attack the state set without target 1, the adversarial examples attack target 1 with an \\(11.43\\%\\) success rate on Facenet during the testing period." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.293, + 0.895, + 0.372 + ], + "angle": 0, + "content": "
Target*Target 1Target 2Target 3
FacenetMobilefaceFacenetMobilefaceFacenetMobilefaceFacenetMobileface
TIP-IM [34] / G-TIP-IM17.6886.334.54 / 7.6258.03 / 70.9310.75 / 20.4234.42 / 49.2011.93 / 19.4122.21 / 42.43
AMT-GAN [16] / G-AMT-GAN16.1255.958.22 / 13.2326.99 / 47.149.78 / 17.1227.67 / 43.9310.91 / 16.1624.69 / 42.37
MAA / GMAA25.2272.6211.43 / 17.8443.44 / 67.5013.30 / 21.7133.08 / 41.2412.64 / 19.1529.56 / 47.21
" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.383, + 0.469, + 0.43 + ], + "angle": 0, + "content": "(Triangle inequality) \\(\\forall \\pmb{x}_3^0\\in \\mathcal{M}^0\\) , we have \\(d(\\pmb{x}_1^0,\\pmb{x}_3^0) + d(\\pmb{x}_3^0,\\pmb{x}_2^0) = \\| D_{AU}(\\pmb{x}_1^0) - D_{AU}(\\pmb{x}_3^0)\\| _2 + \\| D_{AU}(\\pmb{x}_3^0) -\\) \\(D_{AU}(\\pmb{x}_2^0)\\| _2\\geq \\| D_{AU}(\\pmb{x}_1^0) - D_{AU}(\\pmb{x}_2^0)\\| _2 = d(\\pmb{x}_1^0,\\pmb{x}_2^0).\\)" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.43, + 0.47, + 0.505 + ], + "angle": 0, + "content": "Thus, \\((\\mathcal{M}^0,d)\\) is a metric space. Then we need to prove that \\(G_{0}\\) is a continuous mapping. \\(\\forall \\pmb {\\mu},\\pmb {\\nu}\\in V,\\forall \\epsilon >0\\) , let \\(\\delta = \\epsilon\\) , when \\(\\| \\pmb {\\mu} - \\pmb {\\nu}\\| _2 < \\delta\\) , we have \\(d(G_0(\\pmb {\\mu}) - G_0(\\pmb {\\nu})) =\\) \\(\\| D_{AU}(G_0(\\pmb {\\mu})) - D_{AU}(G_0(\\pmb {\\nu}))\\| _2 = \\| \\pmb {\\mu} - \\pmb {\\nu}\\| _2 < \\delta = \\epsilon .\\) We get the continuity of \\(G_{0}\\)" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.505, + 0.47, + 0.595 + ], + "angle": 0, + "content": "(1.3) It is obviously that \\( D_{AU}|_{\\mathcal{M}^0} : \\mathcal{M}^0 \\to V \\) is the inverse mapping of \\( G_0 \\). \\( \\forall \\pmb{x}_1^0, \\pmb{x}_2^0 \\in \\mathcal{M}^0, \\epsilon > 0 \\), let \\( \\delta = \\epsilon \\), when \\( d(\\pmb{x}_1^0, \\pmb{x}_2^0) = \\| D_{AU}(\\pmb{x}_1^0) - D_{AU}(\\pmb{x}_2^0)\\|_2 < \\delta \\), we have \\( \\| D_{AU}|_{\\mathcal{M}^0}(\\pmb{x}_1^0) - D_{AU}|_{\\mathcal{M}^0}(\\pmb{x}_2^0)\\|_2 = \\| D_{AU}(\\pmb{x}_1^0) - D_{AU}(\\pmb{x}_2^0)\\|_2 < \\delta = \\epsilon \\). We get the continuity of the inverse map of \\( G_0 \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.595, + 0.47, + 0.656 + ], + "angle": 0, + "content": "In conclusion, \\(G_{0}\\) is the homeomorphism of \\(V\\) to the manifold \\(\\mathcal{M}^0\\), i.e. \\(\\mathcal{M}^0\\) homogeneous with the AU vector space \\(V\\). Since AU vector space is a finite dimensional vector space, \\(\\mathcal{M}^0\\) is a subspace of \\(\\mathbb{R}^{m\\times n\\times l}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.656, + 0.469, + 0.701 + ], + "angle": 0, + "content": "(2) By the loss function 8, 7 and the back propagation, \\( \\pmb{x}_i^0 \\) is influenced by the 8. It is obviously that \\( \\pmb{x}_i^0 \\in \\mathcal{M}^0 \\) is an adversarial example when the model is well-trained." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.7, + 0.47, + 0.731 + ], + "angle": 0, + "content": "Thus, the manifold \\(\\mathcal{M}^0\\) generated by \\(G_{0}\\) is a continuous adversarial manifold." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.73, + 0.47, + 0.792 + ], + "angle": 0, + "content": "Remark 1. Since the \\(\\mathcal{M}^0\\) generated by \\(G_0\\) is a continuous adversarial manifold when fixed the \\(\\pmb{x}_0\\), then we can assert over the sample space \\(\\Omega\\), the adversarial examples space generated by \\(G\\) constitutes an adversarial fiber bundle." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.793, + 0.469, + 0.823 + ], + "angle": 0, + "content": "Secondly, the definition of semantic continuous adversarial space is shown in Def. 2." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.824, + 0.469, + 0.856 + ], + "angle": 0, + "content": "Definition 2. \\(\\mathcal{M}^0\\) generated by \\(\\pmb{x}_0\\in \\mathbb{R}^{3\\times H\\times W}\\) is a semantic continuous adversarial space if and only if" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.856, + 0.359, + 0.871 + ], + "angle": 0, + "content": "(1) \\(\\mathcal{M}^0\\) is a continuous adversarial space." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.902 + ], + "angle": 0, + "content": "(2) \\(\\forall \\pmb{x}_1^0, \\pmb{x}_2^0 \\in \\mathcal{M}^0\\), if \\(\\pmb{x}_1^0\\) is close to \\(\\pmb{x}_2^0\\) on the \\(\\mathcal{M}^0\\), then \\(\\pmb{x}_1^0\\) and \\(\\pmb{x}_2^0\\) satisfy the semantic consistency." + }, + { + "type": "list", + "bbox": [ + 0.077, + 0.856, + 0.469, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.384, + 0.892, + 0.399 + ], + "angle": 0, + "content": "We can state that \\(\\mathcal{M}^0\\) is a semantic continuous manifold." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.406, + 0.892, + 0.452 + ], + "angle": 0, + "content": "Theorem 2. \\(\\mathcal{M}^0\\) generated by \\(G_0\\) is a semantic continuous adversarial manifold, where \\(G_0: V \\to \\mathcal{M}\\) is a map when fixed the input \\(\\pmb{x}_0\\) in \\(G\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.454, + 0.893, + 0.53 + ], + "angle": 0, + "content": "Proof. Since we have proved that \\(D_{AD}\\) is a continuous mapping, we have \\(D_{AU}(\\pmb{x}_1^0)\\) is close to \\(D_{AU}(\\pmb{x}_2^0)\\) when \\(\\pmb{x}_1^0\\) is close to \\(\\pmb{x}_2^0\\), which means the AU vectors of \\(\\pmb{x}_1^0\\) and \\(\\pmb{x}_2^0\\) are very close. Thus, the semantic information of \\(\\pmb{x}_1^0\\) and \\(\\pmb{x}_2^0\\) is close." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.542, + 0.634, + 0.559 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.567, + 0.698, + 0.583 + ], + "angle": 0, + "content": "4.1. Experimental setting" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.892, + 0.704 + ], + "angle": 0, + "content": "Implementation details. We set \\(\\lambda_{c}\\), \\(\\lambda_{gp}\\), \\(\\lambda_{AU}\\), \\(\\lambda_{g}\\), \\(\\lambda_{l}\\), \\(\\lambda_{adv}\\) to be 1, 10, 250, 20, 20, 25, respectively. Our method is trained by an Adam optimizer with the learning rate 0.0001 and the exponential decay rates set to be \\((\\beta_{1},\\beta_{2}) = (0.5,0.99)\\). We evaluate the black-box attack performance of the models utilizing the attack success rate(ASR) at FAR@0.01 and the confidence scores returned by commercial APIs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Dataset. We train the model on two public datasets: 1) CelebA-HQ [19] is a high-quality face dataset, which contains 30,000 face images. 2) LFW [17] is a challenging dataset that collects 13,233 images with complex environmental factors and is a common dataset for face recognition tasks. We remove the images whose AU confidence is below \\(95\\%\\) as extracted by Openface [1], then randomly select \\(10\\%\\) of each dataset as the test set and the remaining images as the training set. Four pairs of images from CelebA [22] with the same identity are used as attack targets for training and testing, respectively, since CelebA [22] contains multiple images of one identity. Besides, the real state set in subsection 4.3 are obtained from the RaFD dataset [21]." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20580" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.119 + ], + "angle": 0, + "content": "Table 3. The effect of the image quantity in state set on improving the generalizability of the adversarial example. The values \\( n_i \\) in \\( n_1 / n_2 / n_3 \\) represents each expression state using \\( i \\) images." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.123, + 0.892, + 0.202 + ], + "angle": 0, + "content": "
Target 1Target 2Target 3
FacenetMobilefaceFacenetMobilefaceFacenetMobileface
G-TIP-IM [34]7.6/7.1/7.270.9/70.3/70.120.4/21.5/21.449.2/49.2/49.219.4/19.6/19.439.4/39.6/39.5
G-AMT-GAN [16]13.2/14.4/13.947.1/44.8/45.317.1/16.9/18.943.9/45.4/43.816.2/15.4/15.742.4/44.6/45.4
GMAA17.8/18.2/17.767.5/68.5/69.321.7/21.3/19.641.2/42.6/40.319.2/19.9/21.347.2/45.6/44.7
" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.215, + 0.487, + 0.385 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.494, + 0.214, + 0.891, + 0.384 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.391, + 0.893, + 0.407 + ], + "angle": 0, + "content": "Figure 4. The confidence scores returned by Face++ and Tencent. The dashed line represents the average confidence level of clean samples." + }, + { + "type": "image", + "bbox": [ + 0.078, + 0.419, + 0.473, + 0.554 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.567, + 0.471, + 0.609 + ], + "angle": 0, + "content": "Figure 5. The left side of the image depicts the five expression states, while the right side of the image depicts the influence of varied AU on the attack performance of Face++ and Tencent." + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.622, + 0.47, + 0.704 + ], + "angle": 0, + "content": "Table 4. This table shows the black-box ASR results of attacking the test target, which is the same person as the train image highlighted by a green square in Fig. 3. The unbolded numbers represent the results of training on the single target image that is shown in Fig. 3, while the bolded numbers are the results of training on the generated state set." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.705, + 0.471, + 0.769 + ], + "angle": 0, + "content": "
FacenetMobileface
TIP-IM [34] / G-TIP-IM5.80 / 9.5017.20 / 23.5
AMT-GAN [16] / G-AMT-GAN4.04 / 8.279.82 / 12.45
MAA / GMAA6.60 / 10.6013.50 / 21.60
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Competitors. We compare our approach to the baselines PGD [23], MI-FGSM [7], SemanticAdv [26], TIP-IM [34] and AMT-GAN [16]. Since our work belongs to the branch of GAN based unrestricted adversarial attack [30], which is budget-free. Similar to [30], we compare our method MAA/GMAA to both restricted and unrestricted adversarial methods w.r.t attack performance and visual naturalness. All restricted methods are setted to the size of perturbation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.42, + 0.891, + 0.449 + ], + "angle": 0, + "content": "\\(\\epsilon = 12\\). And all baselines are equipped with the transferability enhancement module for a fair comparison." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.45, + 0.892, + 0.526 + ], + "angle": 0, + "content": "Target models. Following [16], we choose IR152 [14], IRSE50 [15], Facenet [27] and Mobileface [5] as the attacked FR models, with three of them serving as white-box models during training and the remaining as the black-box model for testing." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.531, + 0.681, + 0.547 + ], + "angle": 0, + "content": "4.2. Comparison Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.549, + 0.891, + 0.594 + ], + "angle": 0, + "content": "This subsection shows the comparison results of the MAA method and competitors in terms of attack performance and visual quality." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.595, + 0.892, + 0.775 + ], + "angle": 0, + "content": "Comparison of attack performance on commercial API. We evaluate the performance of each method against the commercial APIs Face++\\(^2\\) and Tencent\\(^3\\). Fig. 4 exhibits the average confidence score of Face++ and Tencent between the adversarial example and the test image of the target identity. Our method MAA achieves the highest score, outperforming all competitors on both datasets, as shown in Fig. 4. Furthermore, in Fig. 5, we display the confidence scores for five typical expressions (happy, angry, sad, surprised, and expressionless) to demonstrate that different AU vectors have little effect on attack performance and are more influenced by the dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.776, + 0.892, + 0.852 + ], + "angle": 0, + "content": "Comparison of black-box attack success rate. Since our model can give us a semantic continuous adversarial manifold and we want to make sure the comparison is fair, we randomly sample the AU vector to get test adversarial examples for calculating the black-box ASR. Tab. 1 shows the" + }, + { + "type": "page_footnote", + "bbox": [ + 0.516, + 0.863, + 0.754, + 0.876 + ], + "angle": 0, + "content": "\\(^{2}\\)https://www(faceplusplus.com/" + }, + { + "type": "page_footnote", + "bbox": [ + 0.504, + 0.877, + 0.892, + 0.899 + ], + "angle": 0, + "content": "3https://cloud.tencent.com/document/product/867/44987" + }, + { + "type": "list", + "bbox": [ + 0.504, + 0.863, + 0.892, + 0.899 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "20581" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.089, + 0.895, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.196, + 0.895, + 0.253 + ], + "angle": 0, + "content": "Figure 6. The images with green frames are the clean samples, while the images with blue frames are the results of TIP-IM [34]. In the case of the AMT-GAN [16], we chose 8 makeup styles at random, and the visualization results are shown as images with an orange frame. The images highlighted by red frames are the results of MAA, which are generated by a set of AU vectors. Please refer to the supplementary material for more high-definition magnified visualization results." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.266, + 0.47, + 0.312 + ], + "angle": 0, + "content": "black-box ASR of each method under four FR models and two datasets. Obviously, our method has good performance for black-box attacks, i.e., it has strong transferability." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.313, + 0.473, + 0.555 + ], + "angle": 0, + "content": "Comparison of visual quality. We choose TIP-IM and AMT-GAN, two recent approaches with high black-box ASR, as benchmarks for our assessment of visual quality. Fig. 6 shows the adversarial examples of each method, and the target image is shown in Fig. 3 highlighted by a green square. In particular, to demonstrate that our method can generate semantically continuous adversarial examples, Fig. 6 displays the adversarial examples generated by MAA that continuously transform on four expressions (expressionless, disgusted, happy and surprised in succession). Note that although only 20 adversarial examples are presented in Fig. 6, our method can generate an infinite number of adversarial examples by continuously interpolating between AU vectors since MAA establishes a correspondence with the AU vector space. Moreover, our method has a natural visual quality and is gender-insensitive." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.564, + 0.233, + 0.578 + ], + "angle": 0, + "content": "4.3. Attack state set" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.582, + 0.47, + 0.809 + ], + "angle": 0, + "content": "Attack real state set. To avoid serendipity, two FR models, three different test targets, and three adversarial attack methods were employed to assess the effectiveness of attacking state set on enhancing the adversarial examples' generalizability. Particularly, one of the FR models is Facenet with high accuracy, and the other is Mobileface with a lightweight network. Targets *, 1, 2 and 3 are shown in Fig. 2. The state set consists of several common expression states (angry, contemptuous, disgusted, fearful, happy, sad and surprised), and each correlates to an image. By comparing the results in Tab. 2, we can summarize that the model trained to attack target * generalizes poorly to test targets 1, 2, 3, whereas adversarial examples generated on the state set generalize better to the test target, even though the test target is not used to train the model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.471, + 0.902 + ], + "angle": 0, + "content": "We try to add more images in the state set to further improve the performance. Tab. 3 shows the ASR results that the target state set contains each expression state corresponding to \\(1/2/3\\) image(s), respectively. We demonstrate that the generalizability of the adversarial examples can be effectively strengthened as long as the state set contains a" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.266, + 0.891, + 0.295 + ], + "angle": 0, + "content": "single image of each state, and additional images have minimal impact on the results." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.296, + 0.893, + 0.403 + ], + "angle": 0, + "content": "Attack generated state set. For face image datasets that do not contain rich states, we generate the target state set by the pre-trained generator \\( G_{exp} \\) with AU vectors of common expressions. Tab. 4 shows the comparison results of training on a single target and a generated state set, demonstrating that training the model on the target state set enhances the generalization ability of adversarial examples." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.413, + 0.637, + 0.429 + ], + "angle": 0, + "content": "5. Future Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.436, + 0.892, + 0.572 + ], + "angle": 0, + "content": "Considering the ubiquitous applicability of expressions in the facial adversarial attacks, the expression state space was chosen to implement GMAA in this paper. We employ the FACS as the prior domain knowledge to implement GMAA, while the paradigm GMAA can be broadly generalized by integrating other domain information, such as illumination, posture, etc. By selecting different state spaces, our work can be generalized to other adversarial attacks with more general image categories." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.583, + 0.62, + 0.599 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.606, + 0.892, + 0.788 + ], + "angle": 0, + "content": "In this paper, we provide a novel paradigm GMAA that broadens both target domain and adversarial domain to enhance the performance of adversarial attack. For the target domain, GMAA optimizes generalization to the target identity by attacking the state set instead of a single image. Additionally, GMAA leverages the domain knowledge to expand adversarial domain from discrete points to semantic continuous manifold. Numerous comparative experiments have verified that GMAA has a better attack performance and a more natural visual quality than other competitors. Moreover, the generalized attack module can be extended to a wide of applications." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.798, + 0.681, + 0.815 + ], + "angle": 0, + "content": "7. Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.821, + 0.892, + 0.897 + ], + "angle": 0, + "content": "This work was supported and partially funded by the National Natural Science Foundation of China (Grant No. 62106116). This work was also supported in part by ZJNSFC under Grant LQ23F010008. We also would like to thank Han Fang of NUS for the valuable discussion." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20582" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.117, + 0.47, + 0.186 + ], + "angle": 0, + "content": "[1] Tadas Baltrusaitis, Amir Zadeh, Yao Chong Lim, and Louis-Philippe Morency. Openface 2.0: Facial behavior analysis toolkit. In 2018 13th IEEE international conference on automatic face & gesture recognition (FG 2018), pages 59–66. IEEE, 2018. 4, 6" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.189, + 0.472, + 0.232 + ], + "angle": 0, + "content": "[2] Yuntian Chen and Dongxiao Zhang. 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However, such paradigm of point-wise attack exhibits poor generalization against numerous unknown states of identity and can be easily defended. In this paper, by rethinking the inherent relationship between the face of target identity and its variants, we introduce a new pipeline of Generalized Manifold Adversarial Attack (GMAA)1 to achieve a better attack performance by expanding the attack range. Specifically, this expansion lies on two aspects - GMAA not only expands the target to be attacked from one to many to encourage a good generalization ability for the generated adversarial examples, but it also expands the latter from discrete points to manifold by leveraging the domain knowledge that face expression change can be continuous, which enhances the attack effect as a data augmentation mechanism did. Moreover, we further design a dual supervision with local and global constraints as a minor contribution to improve the visual quality of the generated adversarial examples. We demonstrate the effectiveness of our method based on extensive experiments, and reveal that GMAA promises a semantic continuous adversarial space with a higher generalization ability and visual quality. + +# 1. Introduction + +Thanks to the rapid development of deep neural networks (DNNs), the face recognition (FR) networks [5, 27] has been applied to identity security identification systems in a variety of crucial applications, such as face unlocking and face payment on smart devices. However, it has been observed that DNNs are easily fooled by adversarial examples and offer incorrect assessments [9, 23], which has risks + +of unauthorized access to FR systems and stealing personal privacy through poisoned data. These 'well-designed' adversarial examples reveal the aspects of FR models that are vulnerable to be attacked, which makes the adversarial attack a meaningful work to provide reference for improving model robustness. + +Following the point-wise paradigm, previous methods typically tend to attack a single target identity sample with discrete adversarial examples illustrated in Fig. 1. However, these methods are not strong enough both in target domain and adversarial domain. Concretely, for the target domain, attacking a single identity image has a poor generalization on those unseen faces (even if they belong to the same person) in realistic scenarios. For example, Fig. 2 shows these adversarial examples which were used to attack the target (a girl) have a disappointingly lower success rate of attacking the identity with other unseen states. We analyze that's because attacking a single image of target identity overfits the generation of adversarial examples to some fixed factors such as expression, makeup style, etc. In addition to the target domain, we naturally consider the weakness of adversarial domain in the existing methods. Most adversarial attack methods optimize a $L_{p}$ bounded perturbation [24,34] based on the gradient, which limits the problem to searching for discrete adversarial examples in a hypersphere of the clean sample and ignores the continuity of the generated adversarial domain. For example, the recently proposed methods based on makeup style transformation [16,35,37] focus on generating finite adversarial examples that correspond to discrete makeup references. Such methods all overemphasize on mining discrete adversarial examples within a limited scope and ignore the importance of the continuity in adversarial space. The weakness of current adversarial attack tasks motivates us, on the one hand, to explore how to generate adversarial examples that are more general to various target identity's states and, on the other hand, to upgrade adversarial domain from discrete points to continuous manifold for a stronger attack. + +In this paper, we introduce a new paradigm dubbed Gen + +![](images/8946729501018e585a3eefae4ca51cd101d392f6804d35c7fa247541dad75538.jpg) +Figure 1. The core idea comparison. Discrete point-wise attack methods leverage a single state of the target identity during training and provide discrete adversarial examples. By attacking the target identity's state set and employing domain knowledge, our core idea aims to Generalized Manifold Adversarial Attack (GMAA), which promises a semantic continuous adversarial manifold with a higher generalization ability on the target identity with unknown state. + +![](images/dbf4e9ff7ea4a1bff88ad00f3298a04bcb162914ed92d740905da69e9c423eae.jpg) +Figure 2. The black-box attack success rate on the Mobileface of attacking target * 1, 2 and 3 during the testing. The three methods are exclusively trained on target *. + +eralized Manifold Adversarial Attack (GMAA) depicted in Fig. 1, which achieves a higher attack success rate by providing semantic continuous adversarial domains while expanding the target to be attacked from an instance to a group set. Specifically, we train adversarial examples to attack a target identity set rather than a single image, which increases the attack success rate on the target identity with different states. The expansion of target domain naturally prompts us to consider enhancing the adversarial domain. Inspired by the success of some recent data and knowledge dual driven methods [2, 18, 36], we explore a low-dimensional manifold near the sample according to the domain knowledge, which is a simple yet highly-efficient continuous embedding scheme and can be used to augment the data. For such manifold, the data in it share the visual identity same as the original sample and also lie in the decision + +boundaries of target identity. More specifically, we employ the Facial Action Coding System (FACS) [10] as prior domain knowledge (a kind of instantiation) to expand adversarial domain from discrete points to manifold. Through using FACS, the expressions can be encoded into a vector space, and by which the adversarial example generator could produce an manifold that is homogeneous with the expression vector space and possesses semantic continuity. In addition, in order to build an adversarial space with high visual quality, we employ four expression editors in GMAA pipeline to supervise the adversarial example generation in terms of global structure and local texture details. A transferability enhancement module is also introduced to drive the model to mine robust and transferable adversarial features. Extensive experiments have shown that these components work well on a wide range of baselines and black-box attack models. + +Our contributions are summarized as follows. + +- We first pinpoint that the popular adversarial attack methods generally face generalization difficulty caused by the limited point-wise attack mechanism. +- To enhance the performance of adversarial attack, a new paradigm of Generalized Manifold Adversarial Attack (GMAA) is proposed with an improved attack success rate and better generalization ability. +- GMAA considers the enhancement in terms of both target domain and adversarial domain. For the target domain, it expands the target to be attacked from one to many to encourage a good generalization. For the adversarial domain, the domain knowledge is embedded to strengthen the attack effect from discrete points to continuous manifold. + +- We instantiate GMAA in the face expression state space for a semantic continuous adversarial manifold and use it to attack a state set of the target identity. As a minor contribution, GMAA supervises the adversarial example generator w.r.t global structure and local details with the pre-trained expression editors for a high visual quality. + +# 2. Related work + +# 2.1. Adversarial Attacks on Face Recognition + +Adversarial attacks can be divided into white-box attacks and black-box attacks. White-box attacks [11, 24, 32] must entail full information of the target neural networks, however, the parameters and architecture of a real-world face recognition system are typically hard to access. Hence, it is more practical to consider black-box adversarial attacks in face recognition scenarios, which demand high transferability for the unknown FR target models or commercial application programming interfaces (APIs). Query-based adversarial attacks [9, 13], a form of black-box attack, is inappropriate for realistic applications since it optimizes adversarial examples by repeatedly accessing the target model during training. Adding transferable adversarial perturbation is another effective black-box attack form [4, 7, 8, 34]. Unfortunately, the perturbation caused by this method always makes images become unrealistic and unnatural. Besides, limited by the way of pixel-to-pixel similarity computation, the model of this branch could only look for a limited number of discrete adversarial examples around the clean sample. The patch-based adversarial attack [20, 28, 33] severely degrades the visual quality of images, because the adversarial patch does not blend well with the clean background due to the abrupt shift in pixel values around the boundary. Numerous recent works attempt to instantiate adversarial perturbations with different makeup styles [16, 35, 37]. However, such makeup attacks typically result in an unnatural visual appearance due to gender constraints – female images have a higher attack success rate and visual quality than male ones. Regardless of the previous methods (e.g. [26] focuses on a target sample to obtain optimal feature-map interpolation, and [16] generates adversarial examples with various makeup styles to attack the target identity), they all tend to generate discrete adversarial examples for a single target identity sample and ignore the importance of continuity of adversarial space, which might be crucial to the attack performance. + +# 2.2. Facial Expression Editing + +As another challenging task in facial analysis, face expression editing is also related to our study, which aims at modifying facial expressions in a reasonable manner while preserving identity completeness. In recent years, generative adversarial networks (GANs) have achieved surprising advances in facial expression editing: GCGAN [29] uses + +the facial geometry as prior knowledge to guide the generation. ExprGAN [6] exploits a controller to adjust the intensity of face expression editing. StarGAN [3] introduces a cycle consistency loss to maintain the identity content invariant. However, these methods are all limited on the discrete expressions generation. GANimation [25] utilizes Action Units [10] to define an expression space and generate continuous-change facial images. EF-GAN [31] achieves progressive facial expression editing with a local-focused cascade GAN structure, and produces fewer artifacts and blurs in large-gap expression transformations. In this paper, we borrow the idea of Action Units as domain prior knowledge (from face expression editing) to re-define the adversarial attack task on a continuous manifold, to finally strengthen attack effect. + +# 3. Generalized Manifold Adversarial Attack + +# 3.1. Problem Definition + +Adversarial face attack tasks can be separated into targeted attacks (i.e. impersonation attacks) and non-targeted attacks (i.e. dodging attacks). Targeted attacks force the generated adversarial examples to have a predetermined output towards the target FR model, while the non-targeted attacks mislead the target FR model to provide incorrect random classification for the adversarial examples. To capture the adversarial examples that can impersonate a specific target identity under face authentication systems, we mainly consider the targeted attack task. + +Current methods always define the targeted attack task as an optimization problem, which can be formalized as + +$$ +\begin{array}{l} \min L _ {a d v} = \min _ {\boldsymbol {\theta}} D i s t \left(\mathcal {C} \left(\boldsymbol {x} ^ {*}\right), \mathcal {C} \left(\boldsymbol {x} ^ {\prime}\right)\right), \tag {1} \\ \boldsymbol {x} ^ {\prime} = G (\boldsymbol {x}; \boldsymbol {\theta}). \\ \end{array} +$$ + +where $\pmb{x}^*$ is the pre-specified target image belonging to the sample space $\Omega \subset \mathbb{R}^{3 \times H \times W}$ , $\text{Dist}(\cdot)$ represents a metric of difference, $\mathcal{C}$ represents the feature extractor of FR neural networks, and $G$ maps the clean sample $\pmb{x} \in \Omega$ to the adversarial version $\pmb{x}'$ with the parameter $\pmb{\theta}$ . + +In this paper, we re-define the problem from a broader standpoint. To obtain highly generalized adversarial examples that are more threatening to the target identity with unknown state, the adversarial version $\pmb{x}^{\prime}$ attacks the state set $S$ of the target identity during training. In order to capture an adversarial manifold $\mathcal{M}$ instead of discrete adversarial examples, we aim to construct a distribution on the $\mathcal{M}$ . The new task can be formalized as Eq. 2. + +$$ +\begin{array}{l} \min L _ {a d v} = \min _ {\boldsymbol {\theta}} \mathbb {E} _ {\boldsymbol {x} _ {i} ^ {*} \sim \mathcal {S}, \boldsymbol {x} ^ {\prime} \sim \mathcal {M}} D i s t (\mathcal {C} \left(\boldsymbol {x} _ {i} ^ {*}\right), \mathcal {C} \left(\boldsymbol {x} ^ {\prime}\right)), \tag {2} \\ \mathcal {M} = G (\boldsymbol {x}; \boldsymbol {\theta}). \\ \end{array} +$$ + +In addition to the adversarial attack tasks, we force $G$ to map $\pmb{x}$ to $\pmb{x}'$ according to the given expression AU vector. The Facial Action Coding System (FACS) is applied as + +![](images/ea51ec7c6f63c20793a24b01ebe052e889ea0cb0b0e31ef53c37db5ff9cc54f3.jpg) +Figure 3. Overview of GMAA. A face image and a random AU vector are sent to the generative adversarial module as inputs. Meanwhile, the expression supervision module generates supervisory signals based on the AU vector and the input image (or detail patches cropped by the landmarks). In the transferability enhancement module, aiming at white-box FR models, the transformed output attacks the target identity's state set, which is provided by the generalized attack module. + +prior domain knowledge to establish a continuous expression state space. Specifically, every expression is encoded by an n-element expression vector $\pmb{\mu} = (\mu_{1},\dots,\mu_{n})$ which corresponds to $N$ facial action units. Each $\mu_{n}\in \pmb{\mu}$ represents the magnitude of muscle activity in the n-th region of the face, which indicates that the AU vector is a continuous embedding scheme for different expressions. Thus, for the input image $\pmb{x}_{\mu^0}\in \mathbb{R}^{3\times H\times W}$ with the expression encoded by $\pmb{\mu}^0\in \mathbb{R}^N$ and the given expression encoded by $\pmb{\mu}^i\in \mathbb{R}^N$ , $G$ is a binary mapping $G:(\pmb{x}_{\mu^0},\pmb{\mu}^i)\to \pmb{x}_{\mu^i}^\prime$ , where $\pmb{x}_{\mu^i}^\prime$ has the same visual label with $\pmb{x}_{\mu^0}$ and wearing the expression encoded by $\pmb{\mu}^i$ . + +# 3.2. Generalized Manifold Adversarial Attack + +We establish the adversarial examples' distribution on a manifold via WGAN-GP [12]. GMAA comprises a generative adversarial module, an expression supervision module, a transferability enhancement module, and a generalized attack module. In contrast, Manifold Adversarial Attack (MAA) omits the generalized attack module, as it merely extends the adversarial domain from a point to a manifold. The structure of our proposed method is depicted in Fig. 3. Generative adversarial module. The generative adversarial module (red box in Fig. 3) includes a generator $G$ , a discriminator $D_{c}$ and an AU predictor $D_{AU}$ , where $D_{c}$ and $D_{AU}$ both lie in $D$ and share partial parameters. + +As inputs, the generator $G$ receives a clean sample $\boldsymbol{x}_{\mu^0}$ and a given expression AU label $\boldsymbol{\mu}^i$ , which aims to produce adversarial examples wearing the expression matching to the supplied AU label and maintain the same visual identity with $\boldsymbol{x}_{\mu^0}$ . The discriminator $D_{c}$ learns to distinguish real + +images from generated images. Meanwhile, generated images deceive the discriminator $D_{c}$ to force the outputs of the generator $G$ match the real distribution. Our $G$ and $D_{c}$ are trained using WGAN-GP [12], and the critic loss function we employ is + +$$ +\begin{array}{l} L _ {\text {c r i t i c}} ^ {D} = \lambda_ {c} \left(1 - D _ {c} \left(\boldsymbol {x} _ {\boldsymbol {\mu} ^ {0}}\right)\right) ^ {2} + \lambda_ {c} \left(D _ {c} \left(G \left(\boldsymbol {x} _ {\boldsymbol {\mu} ^ {0}} \mid \boldsymbol {\mu} ^ {i}\right)\right) ^ {2} \right. (3) \\ + \lambda_ {g p} \left(\| \nabla_ {\widetilde {x}} D _ {c} (\widetilde {x}) \| _ {2} - 1\right) ^ {2}, \\ L _ {c r i t i c} ^ {G} = \lambda_ {c} \left(1 - D _ {c} \left(G \left(\boldsymbol {x} _ {\boldsymbol {\mu} ^ {0}} \mid \boldsymbol {\mu} ^ {i}\right)\right)\right) ^ {2}, (4) \\ \end{array} +$$ + +where $\widetilde{\pmb{x}}$ is the random interpolation distribution between the real distribution and the generated images' distribution. To ensure that the generated image matches the provided expression code $\pmb{\mu}^i$ , we employ AU regression loss to establish the consistency of the generated expression with $\pmb{\mu}^i$ . Specifically, the AU predictor $D_{AU}$ learns the AU coding rules by real images and their AU labels (can be obtained by the open source framework Openface [1]), and the $G$ reduces the AU error between the generated expression and $\pmb{\mu}^i$ to satisfy the given expression. The loss function can be formulated as: + +$$ +L _ {A U} ^ {D} = \lambda_ {A U} \| D _ {A U} \left(\boldsymbol {x} _ {\boldsymbol {\mu} ^ {0}}\right) - \boldsymbol {\mu} ^ {0} \| _ {2} ^ {2}, \tag {5} +$$ + +$$ +L _ {A U} ^ {G} = \lambda_ {A U} \| D _ {A U} \left(G \left(\boldsymbol {x} _ {\boldsymbol {\mu} ^ {0}} \mid \boldsymbol {\mu} ^ {i}\right)\right) - \boldsymbol {\mu} ^ {i} \| _ {2} ^ {2}. +$$ + +Expression supervision module. The expression supervision module (blue box in Fig. 3) protects the visual identity of adversarial examples and guides $G$ in expression editing by generating global and local facial supervisory signals. The global branch focuses on structural features of the face, whereas the local branch protects important facial details and reduces artifacts and blurs caused by the global branch. + +Specifically, a global editor and three local editors are pre-trained to provide supervisory signals. For the local editors, we crop the eyes, nose, and mouth pixel patches based on face landmarks first. Then the input image and three detail patches are fed into the corresponding generator $G_{global}$ and $G_{j}$ ( $j \in J = \{\text{eyes, nose, mouth}\}$ ) with the input AU vector $\mu$ , respectively. Each generator has the network structure similar to [25], which provides the color response $M_{c}^{\mu}$ and the attention response $M_{a}^{\mu}$ . $M_{c}^{\mu}$ and $M_{a}^{\mu}$ force networks to pay attention to the expression change region and protect the remainder regions from disturbance. The ultimate supervisory signals can be obtained as follows, where $\otimes$ denotes element-wise multiplication. + +$$ +G _ {j} \left(\boldsymbol {x} _ {i n} \mid \boldsymbol {\mu}\right) = M _ {a} ^ {\boldsymbol {\mu}} \otimes M _ {c} ^ {\boldsymbol {\mu}} + \left(1 - M _ {a} ^ {\boldsymbol {\mu}}\right) \otimes \boldsymbol {x} _ {i n}. \tag {6} +$$ + +The global editor focuses more on large scale features, such as shape and position of the five senses, and tends to produce artifacts and blurs in the detail region, while the local editors concentrate on significant local features and provide finer details. Therefore, we deploy the global editor to supervise the structural information of adversarial examples and the local editors to supervise local specifics. The loss of expression supervision module can be expressed as + +$$ +\begin{array}{l} L _ {e x p} ^ {G} = \lambda_ {g} \mathrm {S S I M} [ G (\pmb {x} _ {\pmb {\mu} ^ {0}} | \pmb {\mu} ^ {i}), G _ {g l o b a l} (\pmb {x} _ {\pmb {\mu} ^ {0}} | \pmb {\mu} ^ {i}) ] \\ + \lambda_ {l} \sum_ {j \in J} \operatorname {M S E} \left[ \operatorname {C r o p} _ {j} \left(G \left(\boldsymbol {x} _ {\boldsymbol {\mu} ^ {0}} \mid \boldsymbol {\mu} ^ {i}\right)\right), G _ {j} \left(\operatorname {C r o p} _ {j} \left(\boldsymbol {x} _ {\boldsymbol {\mu} ^ {0}}\right) \mid \boldsymbol {\mu} ^ {i}\right) \right], \tag {7} \\ \end{array} +$$ + +where $\mathrm{Crop}_j$ denotes the crop operation of local region $j$ according to the face landmarks. + +Transferability enhancement module. To improve the transferability of adversarial examples and the black-box attack success rate, we introduce the transferability enhancement module (yellow box in Fig. 3) from [16]. The generated adversarial examples are transformed with probability $p$ by the function $T_{p}$ (resize with padding or add noise), and then attack $K$ pre-trained high-precision FR models $\{C_k\}_{k=1,\dots,K}$ , which perform as white-box models during the training of $G$ . The adversarial attack loss function is formulated as + +$$ +L _ {a d v} ^ {G} = \frac {\lambda_ {a d v}}{K} \sum_ {k = 1} ^ {K} [ 1 - \cos \left(\mathcal {C} _ {k} \left(\boldsymbol {x} ^ {*}\right), \mathcal {C} _ {k} \left(T _ {p} \left(G \left(\boldsymbol {x} _ {\boldsymbol {\mu} ^ {0}} \mid \boldsymbol {\mu} ^ {i}\right)\right)\right)\right) ] \tag {8} +$$ + +Generalized attack module. The generalized attack module (green box in Fig. 3) intends to raise the attack success rate on the unseen face belonging to the target identity, which can be introduced into other adversarial attack approaches. The adversarial loss $L_{adv}^{G}$ in GMAA can be further expressed as + +$$ +\mathbb {E} _ {\boldsymbol {x} _ {i} ^ {*}} \sim_ {\mathcal {S}} \frac {\lambda_ {a d v}}{K} \sum_ {k = 1} ^ {K} [ 1 - \cos \left(\mathcal {C} _ {k} \left(\boldsymbol {x} _ {i} ^ {*}\right), \mathcal {C} _ {k} \left(T _ {p} \left(G \left(\boldsymbol {x} _ {\boldsymbol {\mu} ^ {0}} \mid \boldsymbol {\mu} ^ {i}\right)\right)\right)\right) ], \tag {9} +$$ + +where $\boldsymbol{x}_i^*$ and $S$ are defined in 2. However, numerous face recognition datasets and realistic scenarios do not fit this module since an identity only contains a few or single state image. Fortunately, since our method can accomplish both expression editing and adversarial attack, when we remove the loss associated with adversarial attack, we can obtain an expression editor, $G_{exp}$ , by eliminating the adversarial effect $L_{adv}^{G}$ , which can generate the expression state set $S$ by different AU vectors. + +Total loss function. Let $X$ denotes the dataset, and $V$ is the AU vector space. In particular, the given AU vector $\pmb{\mu}^i$ is sampled randomly from $V$ to train the generator $G$ to learn the distribution of adversarial expression manifold. For the generator $G$ , we have the loss function as follows, + +$$ +L ^ {G} = \mathbb {E} _ {\boldsymbol {x} _ {\mu^ {0}} \sim \boldsymbol {X}, \boldsymbol {\mu} ^ {i} \sim V} \left(L _ {\text {c r i t i c}} ^ {G} + L _ {A U} ^ {G} + L _ {\exp} ^ {G} + L _ {a d v} ^ {G}\right). \tag {10} +$$ + +As for $D$ , the total loss function can be obtained as follows, + +$$ +L ^ {D} = \mathbb {E} _ {\boldsymbol {x} _ {\mu^ {0}} \sim \boldsymbol {X}, \boldsymbol {\mu} ^ {i} \sim V} \left(L _ {\text {c r i t i c}} ^ {D} + L _ {A U} ^ {D}\right). \tag {11} +$$ + +# 3.3. Continuity of the adversarial space + +In this subsection, we illustrate more precisely the continuity of the adversarial space and provide a proof that our method establishes a continuous adversarial manifold. + +Firstly, the definition of continuous adversarial space is shown in Def. 1. + +Definition 1. Let $\pmb{x}_0 \in \mathbb{R}^{3 \times H \times W}$ , then $\mathcal{M}^0 = G(\pmb{x}_0; \pmb{\theta})$ is a continuous adversarial space if and only if (1) $\mathcal{M}^0$ is a subspace of $\mathbb{R}^{3 \times H \times W}$ . + +(2) $\forall \pmb{x}_i^0\in \mathcal{M},\pmb{x}_i^0$ is an adversarial version of $\pmb{x}_0$ + +Then, we can prove that $\mathcal{M}^0$ is a continuous manifold. + +Theorem 1. $\mathcal{M}^0$ generated by $G_0$ is a continuous adversarial manifold, where $G_0: V \to \mathcal{M}$ is a map when fixed the input $\pmb{x}_0$ in $G$ . + +Proof. (1) If $\mathcal{M}^0$ is homogeneous with the AU vector space $V$ , it is obviously that $\mathcal{M}^0$ is a subspace of $\mathbb{R}^{3\times H\times W}$ . + +(1.1) $\forall \pmb{\mu}, \pmb{\nu} \in V$ , if $G_0(\pmb{\mu}) = G_0(\pmb{\nu})$ , then $D_{AU}(G_0(\pmb{\mu})) = D_{AU}(G_0(\pmb{\nu}))$ , we have $\pmb{\mu} = \pmb{\nu}$ and $G_0: V \to \mathcal{M}^0$ is a single shot. Besides, $\forall \pmb{x}^0 \in \mathcal{M}^0$ , $\exists \pmb{\mu} = D_{AU}(\pmb{x}^0) \in V$ s.t. $G_0(D_{AU}(\pmb{x}^0)) = \pmb{x}^0$ , then $G_0$ is a surjection. Thus, $G_0$ is a bijection. +(1.2) $\forall \pmb{x}_1^0, \pmb{x}_2^0 \in \mathcal{M}^0$ , we define $d(\pmb{x}_1^0, \pmb{x}_2^0) = \| D_{AU}(\pmb{x}_1^0) - D_{AU}(\pmb{x}_2^0)\|_2$ as the metric between $\pmb{x}_1^0$ and $\pmb{x}_2^0$ in $\mathcal{M}^0$ . Since $(V, \| \cdot \|_2)$ is a metric space, and $D_{AU}(\pmb{x}_i^0) \in V$ , $\forall \pmb{x}_i^0 \in \mathcal{M}^0$ , we prove that $d$ is a metric on $\mathcal{M}^0$ . +(Positivity) $d(\pmb{x}_1^0, \pmb{x}_2^0) \geq 0$ , and if $d(\pmb{x}_1^0, \pmb{x}_2^0) = 0$ according to the definition of $d$ we have $D_{AU}(\pmb{x}_1^0) = D_{AU}(\pmb{x}_2^0)$ . Since $G_0$ is a bijection, we have $\pmb{x}_1^0 = G_0(D_{AU}(\pmb{x}_1^0)) = G_0(D_{AU}(\pmb{x}_2^0)) = \pmb{x}_2^0$ . +(Symmetry) $d(\pmb{x}_1^0, \pmb{x}_2^0) = \| D_{AU}(\pmb{x}_1^0) - D_{AU}(\pmb{x}_2^0)\|_2 = \| D_{AU}(\pmb{x}_2^0) - D_{AU}(\pmb{x}_1^0)\|_2 = d(\pmb{x}_2^0, \pmb{x}_1^0)$ . + +Table 1. Black-box attack success rate + +
CelebA-HQLFW
IRSE50IR152FacenetMobilefaceIRSE50IR152FacenetMobileface
Clean3.683.081.318.433.200.060.045.00
PGD [23]24.2013.375.8628.7231.3010.207.4033.50
MI-FGSM [7]38.9020.769.2540.4838.2014.207.6039.40
SemanticAdv [26]26.5310.247.8055.3233.6010.408.8037.40
TIP-IM [34]44.2016.0914.4665.3632.8015.2013.0079.00
AMT-GAN [16]51.0615.6311.6333.2740.7225.2313.8935.67
MAA60.4029.4318.9156.1355.8029.2018.0060.80
+ +Table 2. The unbolded numbers are the black-box ASR of attacking the test target *, 1, 2, 3, and all the models are trained on target *. The bolded numbers are the results of the models that train on the state set. For example, if we train the MAA to attack the state set without target 1, the adversarial examples attack target 1 with an $11.43\%$ success rate on Facenet during the testing period. + +
Target*Target 1Target 2Target 3
FacenetMobilefaceFacenetMobilefaceFacenetMobilefaceFacenetMobileface
TIP-IM [34] / G-TIP-IM17.6886.334.54 / 7.6258.03 / 70.9310.75 / 20.4234.42 / 49.2011.93 / 19.4122.21 / 42.43
AMT-GAN [16] / G-AMT-GAN16.1255.958.22 / 13.2326.99 / 47.149.78 / 17.1227.67 / 43.9310.91 / 16.1624.69 / 42.37
MAA / GMAA25.2272.6211.43 / 17.8443.44 / 67.5013.30 / 21.7133.08 / 41.2412.64 / 19.1529.56 / 47.21
+ +(Triangle inequality) $\forall \pmb{x}_3^0\in \mathcal{M}^0$ , we have $d(\pmb{x}_1^0,\pmb{x}_3^0) + d(\pmb{x}_3^0,\pmb{x}_2^0) = \| D_{AU}(\pmb{x}_1^0) - D_{AU}(\pmb{x}_3^0)\| _2 + \| D_{AU}(\pmb{x}_3^0) -$ $D_{AU}(\pmb{x}_2^0)\| _2\geq \| D_{AU}(\pmb{x}_1^0) - D_{AU}(\pmb{x}_2^0)\| _2 = d(\pmb{x}_1^0,\pmb{x}_2^0).$ + +Thus, $(\mathcal{M}^0,d)$ is a metric space. Then we need to prove that $G_{0}$ is a continuous mapping. $\forall \pmb {\mu},\pmb {\nu}\in V,\forall \epsilon >0$ , let $\delta = \epsilon$ , when $\| \pmb {\mu} - \pmb {\nu}\| _2 < \delta$ , we have $d(G_0(\pmb {\mu}) - G_0(\pmb {\nu})) =$ $\| D_{AU}(G_0(\pmb {\mu})) - D_{AU}(G_0(\pmb {\nu}))\| _2 = \| \pmb {\mu} - \pmb {\nu}\| _2 < \delta = \epsilon .$ We get the continuity of $G_{0}$ + +(1.3) It is obviously that $D_{AU}|_{\mathcal{M}^0} : \mathcal{M}^0 \to V$ is the inverse mapping of $G_0$ . $\forall \pmb{x}_1^0, \pmb{x}_2^0 \in \mathcal{M}^0, \epsilon > 0$ , let $\delta = \epsilon$ , when $d(\pmb{x}_1^0, \pmb{x}_2^0) = \| D_{AU}(\pmb{x}_1^0) - D_{AU}(\pmb{x}_2^0)\|_2 < \delta$ , we have $\| D_{AU}|_{\mathcal{M}^0}(\pmb{x}_1^0) - D_{AU}|_{\mathcal{M}^0}(\pmb{x}_2^0)\|_2 = \| D_{AU}(\pmb{x}_1^0) - D_{AU}(\pmb{x}_2^0)\|_2 < \delta = \epsilon$ . We get the continuity of the inverse map of $G_0$ . + +In conclusion, $G_{0}$ is the homeomorphism of $V$ to the manifold $\mathcal{M}^0$ , i.e. $\mathcal{M}^0$ homogeneous with the AU vector space $V$ . Since AU vector space is a finite dimensional vector space, $\mathcal{M}^0$ is a subspace of $\mathbb{R}^{m\times n\times l}$ . + +(2) By the loss function 8, 7 and the back propagation, $\pmb{x}_i^0$ is influenced by the 8. It is obviously that $\pmb{x}_i^0 \in \mathcal{M}^0$ is an adversarial example when the model is well-trained. + +Thus, the manifold $\mathcal{M}^0$ generated by $G_{0}$ is a continuous adversarial manifold. + +Remark 1. Since the $\mathcal{M}^0$ generated by $G_0$ is a continuous adversarial manifold when fixed the $\pmb{x}_0$ , then we can assert over the sample space $\Omega$ , the adversarial examples space generated by $G$ constitutes an adversarial fiber bundle. + +Secondly, the definition of semantic continuous adversarial space is shown in Def. 2. + +Definition 2. $\mathcal{M}^0$ generated by $\pmb{x}_0\in \mathbb{R}^{3\times H\times W}$ is a semantic continuous adversarial space if and only if + +(1) $\mathcal{M}^0$ is a continuous adversarial space. +(2) $\forall \pmb{x}_1^0, \pmb{x}_2^0 \in \mathcal{M}^0$ , if $\pmb{x}_1^0$ is close to $\pmb{x}_2^0$ on the $\mathcal{M}^0$ , then $\pmb{x}_1^0$ and $\pmb{x}_2^0$ satisfy the semantic consistency. + +We can state that $\mathcal{M}^0$ is a semantic continuous manifold. + +Theorem 2. $\mathcal{M}^0$ generated by $G_0$ is a semantic continuous adversarial manifold, where $G_0: V \to \mathcal{M}$ is a map when fixed the input $\pmb{x}_0$ in $G$ . + +Proof. Since we have proved that $D_{AD}$ is a continuous mapping, we have $D_{AU}(\pmb{x}_1^0)$ is close to $D_{AU}(\pmb{x}_2^0)$ when $\pmb{x}_1^0$ is close to $\pmb{x}_2^0$ , which means the AU vectors of $\pmb{x}_1^0$ and $\pmb{x}_2^0$ are very close. Thus, the semantic information of $\pmb{x}_1^0$ and $\pmb{x}_2^0$ is close. + +# 4. Experiments + +# 4.1. Experimental setting + +Implementation details. We set $\lambda_{c}$ , $\lambda_{gp}$ , $\lambda_{AU}$ , $\lambda_{g}$ , $\lambda_{l}$ , $\lambda_{adv}$ to be 1, 10, 250, 20, 20, 25, respectively. Our method is trained by an Adam optimizer with the learning rate 0.0001 and the exponential decay rates set to be $(\beta_{1},\beta_{2}) = (0.5,0.99)$ . We evaluate the black-box attack performance of the models utilizing the attack success rate(ASR) at FAR@0.01 and the confidence scores returned by commercial APIs. + +Dataset. We train the model on two public datasets: 1) CelebA-HQ [19] is a high-quality face dataset, which contains 30,000 face images. 2) LFW [17] is a challenging dataset that collects 13,233 images with complex environmental factors and is a common dataset for face recognition tasks. We remove the images whose AU confidence is below $95\%$ as extracted by Openface [1], then randomly select $10\%$ of each dataset as the test set and the remaining images as the training set. Four pairs of images from CelebA [22] with the same identity are used as attack targets for training and testing, respectively, since CelebA [22] contains multiple images of one identity. Besides, the real state set in subsection 4.3 are obtained from the RaFD dataset [21]. + +Table 3. The effect of the image quantity in state set on improving the generalizability of the adversarial example. The values $n_i$ in $n_1 / n_2 / n_3$ represents each expression state using $i$ images. + +
Target 1Target 2Target 3
FacenetMobilefaceFacenetMobilefaceFacenetMobileface
G-TIP-IM [34]7.6/7.1/7.270.9/70.3/70.120.4/21.5/21.449.2/49.2/49.219.4/19.6/19.439.4/39.6/39.5
G-AMT-GAN [16]13.2/14.4/13.947.1/44.8/45.317.1/16.9/18.943.9/45.4/43.816.2/15.4/15.742.4/44.6/45.4
GMAA17.8/18.2/17.767.5/68.5/69.321.7/21.3/19.641.2/42.6/40.319.2/19.9/21.347.2/45.6/44.7
+ +![](images/34c333538aa2679c4cd7ce19f4b2360ce42920bcba81074821636ab4fb7a98de.jpg) +Figure 4. The confidence scores returned by Face++ and Tencent. The dashed line represents the average confidence level of clean samples. + +![](images/ee5dac8c8ac83e63135a5c155b674485abeb05391444afa0c97ddb59985a5ab2.jpg) + +![](images/8456c5e1a748682f82b909cea585b52ba81d25be660f7f1b1ad52c1350c6247b.jpg) +Figure 5. The left side of the image depicts the five expression states, while the right side of the image depicts the influence of varied AU on the attack performance of Face++ and Tencent. + +Table 4. This table shows the black-box ASR results of attacking the test target, which is the same person as the train image highlighted by a green square in Fig. 3. The unbolded numbers represent the results of training on the single target image that is shown in Fig. 3, while the bolded numbers are the results of training on the generated state set. + +
FacenetMobileface
TIP-IM [34] / G-TIP-IM5.80 / 9.5017.20 / 23.5
AMT-GAN [16] / G-AMT-GAN4.04 / 8.279.82 / 12.45
MAA / GMAA6.60 / 10.6013.50 / 21.60
+ +Competitors. We compare our approach to the baselines PGD [23], MI-FGSM [7], SemanticAdv [26], TIP-IM [34] and AMT-GAN [16]. Since our work belongs to the branch of GAN based unrestricted adversarial attack [30], which is budget-free. Similar to [30], we compare our method MAA/GMAA to both restricted and unrestricted adversarial methods w.r.t attack performance and visual naturalness. All restricted methods are setted to the size of perturbation + +$\epsilon = 12$ . And all baselines are equipped with the transferability enhancement module for a fair comparison. + +Target models. Following [16], we choose IR152 [14], IRSE50 [15], Facenet [27] and Mobileface [5] as the attacked FR models, with three of them serving as white-box models during training and the remaining as the black-box model for testing. + +# 4.2. Comparison Study + +This subsection shows the comparison results of the MAA method and competitors in terms of attack performance and visual quality. + +Comparison of attack performance on commercial API. We evaluate the performance of each method against the commercial APIs Face++ $^2$ and Tencent $^3$ . Fig. 4 exhibits the average confidence score of Face++ and Tencent between the adversarial example and the test image of the target identity. Our method MAA achieves the highest score, outperforming all competitors on both datasets, as shown in Fig. 4. Furthermore, in Fig. 5, we display the confidence scores for five typical expressions (happy, angry, sad, surprised, and expressionless) to demonstrate that different AU vectors have little effect on attack performance and are more influenced by the dataset. + +Comparison of black-box attack success rate. Since our model can give us a semantic continuous adversarial manifold and we want to make sure the comparison is fair, we randomly sample the AU vector to get test adversarial examples for calculating the black-box ASR. Tab. 1 shows the + +![](images/a802c2a541ccf1fea7791d2046e056fb619ac6ff5f6b6d5c6300659ceb97a6ef.jpg) +Figure 6. The images with green frames are the clean samples, while the images with blue frames are the results of TIP-IM [34]. In the case of the AMT-GAN [16], we chose 8 makeup styles at random, and the visualization results are shown as images with an orange frame. The images highlighted by red frames are the results of MAA, which are generated by a set of AU vectors. Please refer to the supplementary material for more high-definition magnified visualization results. + +black-box ASR of each method under four FR models and two datasets. Obviously, our method has good performance for black-box attacks, i.e., it has strong transferability. + +Comparison of visual quality. We choose TIP-IM and AMT-GAN, two recent approaches with high black-box ASR, as benchmarks for our assessment of visual quality. Fig. 6 shows the adversarial examples of each method, and the target image is shown in Fig. 3 highlighted by a green square. In particular, to demonstrate that our method can generate semantically continuous adversarial examples, Fig. 6 displays the adversarial examples generated by MAA that continuously transform on four expressions (expressionless, disgusted, happy and surprised in succession). Note that although only 20 adversarial examples are presented in Fig. 6, our method can generate an infinite number of adversarial examples by continuously interpolating between AU vectors since MAA establishes a correspondence with the AU vector space. Moreover, our method has a natural visual quality and is gender-insensitive. + +# 4.3. Attack state set + +Attack real state set. To avoid serendipity, two FR models, three different test targets, and three adversarial attack methods were employed to assess the effectiveness of attacking state set on enhancing the adversarial examples' generalizability. Particularly, one of the FR models is Facenet with high accuracy, and the other is Mobileface with a lightweight network. Targets *, 1, 2 and 3 are shown in Fig. 2. The state set consists of several common expression states (angry, contemptuous, disgusted, fearful, happy, sad and surprised), and each correlates to an image. By comparing the results in Tab. 2, we can summarize that the model trained to attack target * generalizes poorly to test targets 1, 2, 3, whereas adversarial examples generated on the state set generalize better to the test target, even though the test target is not used to train the model. + +We try to add more images in the state set to further improve the performance. Tab. 3 shows the ASR results that the target state set contains each expression state corresponding to $1/2/3$ image(s), respectively. We demonstrate that the generalizability of the adversarial examples can be effectively strengthened as long as the state set contains a + +single image of each state, and additional images have minimal impact on the results. + +Attack generated state set. For face image datasets that do not contain rich states, we generate the target state set by the pre-trained generator $G_{exp}$ with AU vectors of common expressions. Tab. 4 shows the comparison results of training on a single target and a generated state set, demonstrating that training the model on the target state set enhances the generalization ability of adversarial examples. + +# 5. Future Work + +Considering the ubiquitous applicability of expressions in the facial adversarial attacks, the expression state space was chosen to implement GMAA in this paper. We employ the FACS as the prior domain knowledge to implement GMAA, while the paradigm GMAA can be broadly generalized by integrating other domain information, such as illumination, posture, etc. By selecting different state spaces, our work can be generalized to other adversarial attacks with more general image categories. + +# 6. Conclusion + +In this paper, we provide a novel paradigm GMAA that broadens both target domain and adversarial domain to enhance the performance of adversarial attack. For the target domain, GMAA optimizes generalization to the target identity by attacking the state set instead of a single image. Additionally, GMAA leverages the domain knowledge to expand adversarial domain from discrete points to semantic continuous manifold. Numerous comparative experiments have verified that GMAA has a better attack performance and a more natural visual quality than other competitors. Moreover, the generalized attack module can be extended to a wide of applications. + +# 7. Acknowledgement + +This work was supported and partially funded by the National Natural Science Foundation of China (Grant No. 62106116). This work was also supported in part by ZJNSFC under Grant LQ23F010008. We also would like to thank Han Fang of NUS for the valuable discussion. + +# References + +[1] Tadas Baltrusaitis, Amir Zadeh, Yao Chong Lim, and Louis-Philippe Morency. Openface 2.0: Facial behavior analysis toolkit. 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However, such paradigm of point-wise attack exhibits poor generalization against numerous unknown states of identity and can be easily defended. In this paper, by rethinking the inherent relationship between the face of target identity and its variants, we introduce a new pipeline of Generalized Manifold Adversarial Attack (GMAA)1 to achieve a better attack performance by expanding the attack range. Specifically, this expansion lies on two aspects - GMAA not only expands the target to be attacked from one to many to encourage a good generalization ability for the generated adversarial examples, but it also expands the latter from discrete points to manifold by leveraging the domain knowledge that face expression change can be continuous, which enhances the attack effect as a data augmentation mechanism did. Moreover, we further design a dual supervision with local and global constraints as a minor contribution to improve the visual quality of the generated adversarial examples. We demonstrate the effectiveness of our method based on extensive experiments, and reveal that GMAA promises a semantic continuous adversarial space with a higher generalization ability and visual quality." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 573, + 128, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 573, + 128, + 586 + ], + "spans": [ + { + "bbox": [ + 47, + 573, + 128, + 586 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 589, + 287, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 589, + 287, + 673 + ], + "spans": [ + { + "bbox": [ + 46, + 589, + 287, + 673 + ], + "type": "text", + "content": "Thanks to the rapid development of deep neural networks (DNNs), the face recognition (FR) networks [5, 27] has been applied to identity security identification systems in a variety of crucial applications, such as face unlocking and face payment on smart devices. However, it has been observed that DNNs are easily fooled by adversarial examples and offer incorrect assessments [9, 23], which has risks" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 246, + 545, + 317 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 246, + 545, + 317 + ], + "spans": [ + { + "bbox": [ + 306, + 246, + 545, + 317 + ], + "type": "text", + "content": "of unauthorized access to FR systems and stealing personal privacy through poisoned data. These 'well-designed' adversarial examples reveal the aspects of FR models that are vulnerable to be attacked, which makes the adversarial attack a meaningful work to provide reference for improving model robustness." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 318, + 547, + 701 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 318, + 547, + 701 + ], + "spans": [ + { + "bbox": [ + 304, + 318, + 547, + 701 + ], + "type": "text", + "content": "Following the point-wise paradigm, previous methods typically tend to attack a single target identity sample with discrete adversarial examples illustrated in Fig. 1. However, these methods are not strong enough both in target domain and adversarial domain. Concretely, for the target domain, attacking a single identity image has a poor generalization on those unseen faces (even if they belong to the same person) in realistic scenarios. For example, Fig. 2 shows these adversarial examples which were used to attack the target (a girl) have a disappointingly lower success rate of attacking the identity with other unseen states. We analyze that's because attacking a single image of target identity overfits the generation of adversarial examples to some fixed factors such as expression, makeup style, etc. In addition to the target domain, we naturally consider the weakness of adversarial domain in the existing methods. Most adversarial attack methods optimize a " + }, + { + "bbox": [ + 304, + 318, + 547, + 701 + ], + "type": "inline_equation", + "content": "L_{p}" + }, + { + "bbox": [ + 304, + 318, + 547, + 701 + ], + "type": "text", + "content": " bounded perturbation [24,34] based on the gradient, which limits the problem to searching for discrete adversarial examples in a hypersphere of the clean sample and ignores the continuity of the generated adversarial domain. For example, the recently proposed methods based on makeup style transformation [16,35,37] focus on generating finite adversarial examples that correspond to discrete makeup references. Such methods all overemphasize on mining discrete adversarial examples within a limited scope and ignore the importance of the continuity in adversarial space. The weakness of current adversarial attack tasks motivates us, on the one hand, to explore how to generate adversarial examples that are more general to various target identity's states and, on the other hand, to upgrade adversarial domain from discrete points to continuous manifold for a stronger attack." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "text", + "content": "In this paper, we introduce a new paradigm dubbed Gen" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 683, + 112, + 693 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 683, + 112, + 693 + ], + "spans": [ + { + "bbox": [ + 58, + 683, + 112, + 693 + ], + "type": "text", + "content": "*Co-first author" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 59, + 693, + 135, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 693, + 135, + 703 + ], + "spans": [ + { + "bbox": [ + 59, + 693, + 135, + 703 + ], + "type": "text", + "content": "† Corresponding author" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 59, + 703, + 218, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 703, + 218, + 712 + ], + "spans": [ + { + "bbox": [ + 59, + 703, + 218, + 712 + ], + "type": "text", + "content": "1https://github.com/tokaka22/GMAA" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20575" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 55, + 70, + 541, + 268 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 541, + 268 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 541, + 268 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 541, + 268 + ], + "type": "image", + "image_path": "8946729501018e585a3eefae4ca51cd101d392f6804d35c7fa247541dad75538.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 277, + 546, + 322 + ], + "lines": [ + { + "bbox": [ + 46, + 277, + 546, + 322 + ], + "spans": [ + { + "bbox": [ + 46, + 277, + 546, + 322 + ], + "type": "text", + "content": "Figure 1. The core idea comparison. Discrete point-wise attack methods leverage a single state of the target identity during training and provide discrete adversarial examples. By attacking the target identity's state set and employing domain knowledge, our core idea aims to Generalized Manifold Adversarial Attack (GMAA), which promises a semantic continuous adversarial manifold with a higher generalization ability on the target identity with unknown state." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 52, + 336, + 274, + 467 + ], + "blocks": [ + { + "bbox": [ + 52, + 336, + 274, + 467 + ], + "lines": [ + { + "bbox": [ + 52, + 336, + 274, + 467 + ], + "spans": [ + { + "bbox": [ + 52, + 336, + 274, + 467 + ], + "type": "image", + "image_path": "dbf4e9ff7ea4a1bff88ad00f3298a04bcb162914ed92d740905da69e9c423eae.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 473, + 288, + 507 + ], + "lines": [ + { + "bbox": [ + 46, + 473, + 288, + 507 + ], + "spans": [ + { + "bbox": [ + 46, + 473, + 288, + 507 + ], + "type": "text", + "content": "Figure 2. The black-box attack success rate on the Mobileface of attacking target * 1, 2 and 3 during the testing. The three methods are exclusively trained on target *." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 521, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 713 + ], + "type": "text", + "content": "eralized Manifold Adversarial Attack (GMAA) depicted in Fig. 1, which achieves a higher attack success rate by providing semantic continuous adversarial domains while expanding the target to be attacked from an instance to a group set. Specifically, we train adversarial examples to attack a target identity set rather than a single image, which increases the attack success rate on the target identity with different states. The expansion of target domain naturally prompts us to consider enhancing the adversarial domain. Inspired by the success of some recent data and knowledge dual driven methods [2, 18, 36], we explore a low-dimensional manifold near the sample according to the domain knowledge, which is a simple yet highly-efficient continuous embedding scheme and can be used to augment the data. For such manifold, the data in it share the visual identity same as the original sample and also lie in the decision" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 338, + 545, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 338, + 545, + 540 + ], + "spans": [ + { + "bbox": [ + 304, + 338, + 545, + 540 + ], + "type": "text", + "content": "boundaries of target identity. More specifically, we employ the Facial Action Coding System (FACS) [10] as prior domain knowledge (a kind of instantiation) to expand adversarial domain from discrete points to manifold. Through using FACS, the expressions can be encoded into a vector space, and by which the adversarial example generator could produce an manifold that is homogeneous with the expression vector space and possesses semantic continuity. In addition, in order to build an adversarial space with high visual quality, we employ four expression editors in GMAA pipeline to supervise the adversarial example generation in terms of global structure and local texture details. A transferability enhancement module is also introduced to drive the model to mine robust and transferable adversarial features. Extensive experiments have shown that these components work well on a wide range of baselines and black-box attack models." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 317, + 541, + 501, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 541, + 501, + 552 + ], + "spans": [ + { + "bbox": [ + 317, + 541, + 501, + 552 + ], + "type": "text", + "content": "Our contributions are summarized as follows." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 315, + 552, + 545, + 720 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 315, + 552, + 544, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 552, + 544, + 586 + ], + "spans": [ + { + "bbox": [ + 315, + 552, + 544, + 586 + ], + "type": "text", + "content": "- We first pinpoint that the popular adversarial attack methods generally face generalization difficulty caused by the limited point-wise attack mechanism." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 315, + 589, + 544, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 589, + 544, + 635 + ], + "spans": [ + { + "bbox": [ + 315, + 589, + 544, + 635 + ], + "type": "text", + "content": "- To enhance the performance of adversarial attack, a new paradigm of Generalized Manifold Adversarial Attack (GMAA) is proposed with an improved attack success rate and better generalization ability." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 315, + 638, + 545, + 720 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 638, + 545, + 720 + ], + "spans": [ + { + "bbox": [ + 315, + 638, + 545, + 720 + ], + "type": "text", + "content": "- GMAA considers the enhancement in terms of both target domain and adversarial domain. For the target domain, it expands the target to be attacked from one to many to encourage a good generalization. For the adversarial domain, the domain knowledge is embedded to strengthen the attack effect from discrete points to continuous manifold." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20576" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 57, + 72, + 287, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 72, + 287, + 156 + ], + "spans": [ + { + "bbox": [ + 57, + 72, + 287, + 156 + ], + "type": "text", + "content": "- We instantiate GMAA in the face expression state space for a semantic continuous adversarial manifold and use it to attack a state set of the target identity. As a minor contribution, GMAA supervises the adversarial example generator w.r.t global structure and local details with the pre-trained expression editors for a high visual quality." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 163, + 132, + 175 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 163, + 132, + 175 + ], + "spans": [ + { + "bbox": [ + 47, + 163, + 132, + 175 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 177, + 261, + 190 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 177, + 261, + 190 + ], + "spans": [ + { + "bbox": [ + 47, + 177, + 261, + 190 + ], + "type": "text", + "content": "2.1. Adversarial Attacks on Face Recognition" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 191, + 289, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 191, + 289, + 622 + ], + "spans": [ + { + "bbox": [ + 47, + 191, + 289, + 622 + ], + "type": "text", + "content": "Adversarial attacks can be divided into white-box attacks and black-box attacks. White-box attacks [11, 24, 32] must entail full information of the target neural networks, however, the parameters and architecture of a real-world face recognition system are typically hard to access. Hence, it is more practical to consider black-box adversarial attacks in face recognition scenarios, which demand high transferability for the unknown FR target models or commercial application programming interfaces (APIs). Query-based adversarial attacks [9, 13], a form of black-box attack, is inappropriate for realistic applications since it optimizes adversarial examples by repeatedly accessing the target model during training. Adding transferable adversarial perturbation is another effective black-box attack form [4, 7, 8, 34]. Unfortunately, the perturbation caused by this method always makes images become unrealistic and unnatural. Besides, limited by the way of pixel-to-pixel similarity computation, the model of this branch could only look for a limited number of discrete adversarial examples around the clean sample. The patch-based adversarial attack [20, 28, 33] severely degrades the visual quality of images, because the adversarial patch does not blend well with the clean background due to the abrupt shift in pixel values around the boundary. Numerous recent works attempt to instantiate adversarial perturbations with different makeup styles [16, 35, 37]. However, such makeup attacks typically result in an unnatural visual appearance due to gender constraints – female images have a higher attack success rate and visual quality than male ones. Regardless of the previous methods (e.g. [26] focuses on a target sample to obtain optimal feature-map interpolation, and [16] generates adversarial examples with various makeup styles to attack the target identity), they all tend to generate discrete adversarial examples for a single target identity sample and ignore the importance of continuity of adversarial space, which might be crucial to the attack performance." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 628, + 190, + 640 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 628, + 190, + 640 + ], + "spans": [ + { + "bbox": [ + 47, + 628, + 190, + 640 + ], + "type": "text", + "content": "2.2. Facial Expression Editing" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 642, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 642, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 642, + 287, + 713 + ], + "type": "text", + "content": "As another challenging task in facial analysis, face expression editing is also related to our study, which aims at modifying facial expressions in a reasonable manner while preserving identity completeness. In recent years, generative adversarial networks (GANs) have achieved surprising advances in facial expression editing: GCGAN [29] uses" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 545, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 251 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 251 + ], + "type": "text", + "content": "the facial geometry as prior knowledge to guide the generation. ExprGAN [6] exploits a controller to adjust the intensity of face expression editing. StarGAN [3] introduces a cycle consistency loss to maintain the identity content invariant. However, these methods are all limited on the discrete expressions generation. GANimation [25] utilizes Action Units [10] to define an expression space and generate continuous-change facial images. EF-GAN [31] achieves progressive facial expression editing with a local-focused cascade GAN structure, and produces fewer artifacts and blurs in large-gap expression transformations. In this paper, we borrow the idea of Action Units as domain prior knowledge (from face expression editing) to re-define the adversarial attack task on a continuous manifold, to finally strengthen attack effect." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 256, + 533, + 269 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 256, + 533, + 269 + ], + "spans": [ + { + "bbox": [ + 305, + 256, + 533, + 269 + ], + "type": "text", + "content": "3. Generalized Manifold Adversarial Attack" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 276, + 417, + 288 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 276, + 417, + 288 + ], + "spans": [ + { + "bbox": [ + 306, + 276, + 417, + 288 + ], + "type": "text", + "content": "3.1. Problem Definition" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 294, + 545, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 294, + 545, + 413 + ], + "spans": [ + { + "bbox": [ + 304, + 294, + 545, + 413 + ], + "type": "text", + "content": "Adversarial face attack tasks can be separated into targeted attacks (i.e. impersonation attacks) and non-targeted attacks (i.e. dodging attacks). Targeted attacks force the generated adversarial examples to have a predetermined output towards the target FR model, while the non-targeted attacks mislead the target FR model to provide incorrect random classification for the adversarial examples. To capture the adversarial examples that can impersonate a specific target identity under face authentication systems, we mainly consider the targeted attack task." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 414, + 545, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 414, + 545, + 437 + ], + "spans": [ + { + "bbox": [ + 305, + 414, + 545, + 437 + ], + "type": "text", + "content": "Current methods always define the targeted attack task as an optimization problem, which can be formalized as" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 347, + 441, + 545, + 475 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 441, + 545, + 475 + ], + "spans": [ + { + "bbox": [ + 347, + 441, + 545, + 475 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\min L _ {a d v} = \\min _ {\\boldsymbol {\\theta}} D i s t \\left(\\mathcal {C} \\left(\\boldsymbol {x} ^ {*}\\right), \\mathcal {C} \\left(\\boldsymbol {x} ^ {\\prime}\\right)\\right), \\tag {1} \\\\ \\boldsymbol {x} ^ {\\prime} = G (\\boldsymbol {x}; \\boldsymbol {\\theta}). \\\\ \\end{array}", + "image_path": "4b359f7d1214caf0db4ed243793253b76502c1d8c0dffc0c00289aadafb57590.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 479, + 545, + 537 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 479, + 545, + 537 + ], + "spans": [ + { + "bbox": [ + 304, + 479, + 545, + 537 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 479, + 545, + 537 + ], + "type": "inline_equation", + "content": "\\pmb{x}^*" + }, + { + "bbox": [ + 304, + 479, + 545, + 537 + ], + "type": "text", + "content": " is the pre-specified target image belonging to the sample space " + }, + { + "bbox": [ + 304, + 479, + 545, + 537 + ], + "type": "inline_equation", + "content": "\\Omega \\subset \\mathbb{R}^{3 \\times H \\times W}" + }, + { + "bbox": [ + 304, + 479, + 545, + 537 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 479, + 545, + 537 + ], + "type": "inline_equation", + "content": "\\text{Dist}(\\cdot)" + }, + { + "bbox": [ + 304, + 479, + 545, + 537 + ], + "type": "text", + "content": " represents a metric of difference, " + }, + { + "bbox": [ + 304, + 479, + 545, + 537 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 304, + 479, + 545, + 537 + ], + "type": "text", + "content": " represents the feature extractor of FR neural networks, and " + }, + { + "bbox": [ + 304, + 479, + 545, + 537 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 479, + 545, + 537 + ], + "type": "text", + "content": " maps the clean sample " + }, + { + "bbox": [ + 304, + 479, + 545, + 537 + ], + "type": "inline_equation", + "content": "\\pmb{x} \\in \\Omega" + }, + { + "bbox": [ + 304, + 479, + 545, + 537 + ], + "type": "text", + "content": " to the adversarial version " + }, + { + "bbox": [ + 304, + 479, + 545, + 537 + ], + "type": "inline_equation", + "content": "\\pmb{x}'" + }, + { + "bbox": [ + 304, + 479, + 545, + 537 + ], + "type": "text", + "content": " with the parameter " + }, + { + "bbox": [ + 304, + 479, + 545, + 537 + ], + "type": "inline_equation", + "content": "\\pmb{\\theta}" + }, + { + "bbox": [ + 304, + 479, + 545, + 537 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 538, + 545, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 538, + 545, + 634 + ], + "spans": [ + { + "bbox": [ + 304, + 538, + 545, + 634 + ], + "type": "text", + "content": "In this paper, we re-define the problem from a broader standpoint. To obtain highly generalized adversarial examples that are more threatening to the target identity with unknown state, the adversarial version " + }, + { + "bbox": [ + 304, + 538, + 545, + 634 + ], + "type": "inline_equation", + "content": "\\pmb{x}^{\\prime}" + }, + { + "bbox": [ + 304, + 538, + 545, + 634 + ], + "type": "text", + "content": " attacks the state set " + }, + { + "bbox": [ + 304, + 538, + 545, + 634 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 538, + 545, + 634 + ], + "type": "text", + "content": " of the target identity during training. In order to capture an adversarial manifold " + }, + { + "bbox": [ + 304, + 538, + 545, + 634 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 304, + 538, + 545, + 634 + ], + "type": "text", + "content": " instead of discrete adversarial examples, we aim to construct a distribution on the " + }, + { + "bbox": [ + 304, + 538, + 545, + 634 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 304, + 538, + 545, + 634 + ], + "type": "text", + "content": ". The new task can be formalized as Eq. 2." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 315, + 637, + 545, + 670 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 637, + 545, + 670 + ], + "spans": [ + { + "bbox": [ + 315, + 637, + 545, + 670 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\min L _ {a d v} = \\min _ {\\boldsymbol {\\theta}} \\mathbb {E} _ {\\boldsymbol {x} _ {i} ^ {*} \\sim \\mathcal {S}, \\boldsymbol {x} ^ {\\prime} \\sim \\mathcal {M}} D i s t (\\mathcal {C} \\left(\\boldsymbol {x} _ {i} ^ {*}\\right), \\mathcal {C} \\left(\\boldsymbol {x} ^ {\\prime}\\right)), \\tag {2} \\\\ \\mathcal {M} = G (\\boldsymbol {x}; \\boldsymbol {\\theta}). \\\\ \\end{array}", + "image_path": "9710269b8d13bd0dbcdeba1aa280ac923689e8f15e41e035171970b8fdc16bae.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "In addition to the adversarial attack tasks, we force " + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": " to map " + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\pmb{x}'" + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": " according to the given expression AU vector. The Facial Action Coding System (FACS) is applied as" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20577" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 71, + 521, + 289 + ], + "blocks": [ + { + "bbox": [ + 61, + 71, + 521, + 289 + ], + "lines": [ + { + "bbox": [ + 61, + 71, + 521, + 289 + ], + "spans": [ + { + "bbox": [ + 61, + 71, + 521, + 289 + ], + "type": "image", + "image_path": "ea51ec7c6f63c20793a24b01ebe052e889ea0cb0b0e31ef53c37db5ff9cc54f3.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 294, + 547, + 340 + ], + "lines": [ + { + "bbox": [ + 46, + 294, + 547, + 340 + ], + "spans": [ + { + "bbox": [ + 46, + 294, + 547, + 340 + ], + "type": "text", + "content": "Figure 3. Overview of GMAA. A face image and a random AU vector are sent to the generative adversarial module as inputs. Meanwhile, the expression supervision module generates supervisory signals based on the AU vector and the input image (or detail patches cropped by the landmarks). In the transferability enhancement module, aiming at white-box FR models, the transformed output attacks the target identity's state set, which is provided by the generalized attack module." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 345, + 289, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 345, + 289, + 492 + ], + "spans": [ + { + "bbox": [ + 46, + 345, + 289, + 492 + ], + "type": "text", + "content": "prior domain knowledge to establish a continuous expression state space. Specifically, every expression is encoded by an n-element expression vector " + }, + { + "bbox": [ + 46, + 345, + 289, + 492 + ], + "type": "inline_equation", + "content": "\\pmb{\\mu} = (\\mu_{1},\\dots,\\mu_{n})" + }, + { + "bbox": [ + 46, + 345, + 289, + 492 + ], + "type": "text", + "content": " which corresponds to " + }, + { + "bbox": [ + 46, + 345, + 289, + 492 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 345, + 289, + 492 + ], + "type": "text", + "content": " facial action units. Each " + }, + { + "bbox": [ + 46, + 345, + 289, + 492 + ], + "type": "inline_equation", + "content": "\\mu_{n}\\in \\pmb{\\mu}" + }, + { + "bbox": [ + 46, + 345, + 289, + 492 + ], + "type": "text", + "content": " represents the magnitude of muscle activity in the n-th region of the face, which indicates that the AU vector is a continuous embedding scheme for different expressions. Thus, for the input image " + }, + { + "bbox": [ + 46, + 345, + 289, + 492 + ], + "type": "inline_equation", + "content": "\\pmb{x}_{\\mu^0}\\in \\mathbb{R}^{3\\times H\\times W}" + }, + { + "bbox": [ + 46, + 345, + 289, + 492 + ], + "type": "text", + "content": " with the expression encoded by " + }, + { + "bbox": [ + 46, + 345, + 289, + 492 + ], + "type": "inline_equation", + "content": "\\pmb{\\mu}^0\\in \\mathbb{R}^N" + }, + { + "bbox": [ + 46, + 345, + 289, + 492 + ], + "type": "text", + "content": " and the given expression encoded by " + }, + { + "bbox": [ + 46, + 345, + 289, + 492 + ], + "type": "inline_equation", + "content": "\\pmb{\\mu}^i\\in \\mathbb{R}^N" + }, + { + "bbox": [ + 46, + 345, + 289, + 492 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 345, + 289, + 492 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 345, + 289, + 492 + ], + "type": "text", + "content": " is a binary mapping " + }, + { + "bbox": [ + 46, + 345, + 289, + 492 + ], + "type": "inline_equation", + "content": "G:(\\pmb{x}_{\\mu^0},\\pmb{\\mu}^i)\\to \\pmb{x}_{\\mu^i}^\\prime" + }, + { + "bbox": [ + 46, + 345, + 289, + 492 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 345, + 289, + 492 + ], + "type": "inline_equation", + "content": "\\pmb{x}_{\\mu^i}^\\prime" + }, + { + "bbox": [ + 46, + 345, + 289, + 492 + ], + "type": "text", + "content": " has the same visual label with " + }, + { + "bbox": [ + 46, + 345, + 289, + 492 + ], + "type": "inline_equation", + "content": "\\pmb{x}_{\\mu^0}" + }, + { + "bbox": [ + 46, + 345, + 289, + 492 + ], + "type": "text", + "content": " and wearing the expression encoded by " + }, + { + "bbox": [ + 46, + 345, + 289, + 492 + ], + "type": "inline_equation", + "content": "\\pmb{\\mu}^i" + }, + { + "bbox": [ + 46, + 345, + 289, + 492 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 495, + 264, + 507 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 495, + 264, + 507 + ], + "spans": [ + { + "bbox": [ + 47, + 495, + 264, + 507 + ], + "type": "text", + "content": "3.2. Generalized Manifold Adversarial Attack" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 509, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 509, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 509, + 287, + 653 + ], + "type": "text", + "content": "We establish the adversarial examples' distribution on a manifold via WGAN-GP [12]. GMAA comprises a generative adversarial module, an expression supervision module, a transferability enhancement module, and a generalized attack module. In contrast, Manifold Adversarial Attack (MAA) omits the generalized attack module, as it merely extends the adversarial domain from a point to a manifold. The structure of our proposed method is depicted in Fig. 3. Generative adversarial module. The generative adversarial module (red box in Fig. 3) includes a generator " + }, + { + "bbox": [ + 46, + 509, + 287, + 653 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 509, + 287, + 653 + ], + "type": "text", + "content": ", a discriminator " + }, + { + "bbox": [ + 46, + 509, + 287, + 653 + ], + "type": "inline_equation", + "content": "D_{c}" + }, + { + "bbox": [ + 46, + 509, + 287, + 653 + ], + "type": "text", + "content": " and an AU predictor " + }, + { + "bbox": [ + 46, + 509, + 287, + 653 + ], + "type": "inline_equation", + "content": "D_{AU}" + }, + { + "bbox": [ + 46, + 509, + 287, + 653 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 509, + 287, + 653 + ], + "type": "inline_equation", + "content": "D_{c}" + }, + { + "bbox": [ + 46, + 509, + 287, + 653 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 509, + 287, + 653 + ], + "type": "inline_equation", + "content": "D_{AU}" + }, + { + "bbox": [ + 46, + 509, + 287, + 653 + ], + "type": "text", + "content": " both lie in " + }, + { + "bbox": [ + 46, + 509, + 287, + 653 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 509, + 287, + 653 + ], + "type": "text", + "content": " and share partial parameters." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "type": "text", + "content": "As inputs, the generator " + }, + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "type": "text", + "content": " receives a clean sample " + }, + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}_{\\mu^0}" + }, + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "type": "text", + "content": " and a given expression AU label " + }, + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\boldsymbol{\\mu}^i" + }, + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "type": "text", + "content": ", which aims to produce adversarial examples wearing the expression matching to the supplied AU label and maintain the same visual identity with " + }, + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}_{\\mu^0}" + }, + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "type": "text", + "content": ". The discriminator " + }, + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "type": "inline_equation", + "content": "D_{c}" + }, + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "type": "text", + "content": " learns to distinguish real" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 345, + 545, + 405 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 345, + 545, + 405 + ], + "spans": [ + { + "bbox": [ + 304, + 345, + 545, + 405 + ], + "type": "text", + "content": "images from generated images. Meanwhile, generated images deceive the discriminator " + }, + { + "bbox": [ + 304, + 345, + 545, + 405 + ], + "type": "inline_equation", + "content": "D_{c}" + }, + { + "bbox": [ + 304, + 345, + 545, + 405 + ], + "type": "text", + "content": " to force the outputs of the generator " + }, + { + "bbox": [ + 304, + 345, + 545, + 405 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 345, + 545, + 405 + ], + "type": "text", + "content": " match the real distribution. Our " + }, + { + "bbox": [ + 304, + 345, + 545, + 405 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 345, + 545, + 405 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 345, + 545, + 405 + ], + "type": "inline_equation", + "content": "D_{c}" + }, + { + "bbox": [ + 304, + 345, + 545, + 405 + ], + "type": "text", + "content": " are trained using WGAN-GP [12], and the critic loss function we employ is" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 409, + 545, + 456 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 409, + 545, + 456 + ], + "spans": [ + { + "bbox": [ + 313, + 409, + 545, + 456 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} L _ {\\text {c r i t i c}} ^ {D} = \\lambda_ {c} \\left(1 - D _ {c} \\left(\\boldsymbol {x} _ {\\boldsymbol {\\mu} ^ {0}}\\right)\\right) ^ {2} + \\lambda_ {c} \\left(D _ {c} \\left(G \\left(\\boldsymbol {x} _ {\\boldsymbol {\\mu} ^ {0}} \\mid \\boldsymbol {\\mu} ^ {i}\\right)\\right) ^ {2} \\right. (3) \\\\ + \\lambda_ {g p} \\left(\\| \\nabla_ {\\widetilde {x}} D _ {c} (\\widetilde {x}) \\| _ {2} - 1\\right) ^ {2}, \\\\ L _ {c r i t i c} ^ {G} = \\lambda_ {c} \\left(1 - D _ {c} \\left(G \\left(\\boldsymbol {x} _ {\\boldsymbol {\\mu} ^ {0}} \\mid \\boldsymbol {\\mu} ^ {i}\\right)\\right)\\right) ^ {2}, (4) \\\\ \\end{array}", + "image_path": "27352339a0c8f306db40ec3429e7fb142611e1502d4067e2c86ff01352e2fa4d.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 460, + 545, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 460, + 545, + 591 + ], + "spans": [ + { + "bbox": [ + 304, + 460, + 545, + 591 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 460, + 545, + 591 + ], + "type": "inline_equation", + "content": "\\widetilde{\\pmb{x}}" + }, + { + "bbox": [ + 304, + 460, + 545, + 591 + ], + "type": "text", + "content": " is the random interpolation distribution between the real distribution and the generated images' distribution. To ensure that the generated image matches the provided expression code " + }, + { + "bbox": [ + 304, + 460, + 545, + 591 + ], + "type": "inline_equation", + "content": "\\pmb{\\mu}^i" + }, + { + "bbox": [ + 304, + 460, + 545, + 591 + ], + "type": "text", + "content": ", we employ AU regression loss to establish the consistency of the generated expression with " + }, + { + "bbox": [ + 304, + 460, + 545, + 591 + ], + "type": "inline_equation", + "content": "\\pmb{\\mu}^i" + }, + { + "bbox": [ + 304, + 460, + 545, + 591 + ], + "type": "text", + "content": ". Specifically, the AU predictor " + }, + { + "bbox": [ + 304, + 460, + 545, + 591 + ], + "type": "inline_equation", + "content": "D_{AU}" + }, + { + "bbox": [ + 304, + 460, + 545, + 591 + ], + "type": "text", + "content": " learns the AU coding rules by real images and their AU labels (can be obtained by the open source framework Openface [1]), and the " + }, + { + "bbox": [ + 304, + 460, + 545, + 591 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 460, + 545, + 591 + ], + "type": "text", + "content": " reduces the AU error between the generated expression and " + }, + { + "bbox": [ + 304, + 460, + 545, + 591 + ], + "type": "inline_equation", + "content": "\\pmb{\\mu}^i" + }, + { + "bbox": [ + 304, + 460, + 545, + 591 + ], + "type": "text", + "content": " to satisfy the given expression. The loss function can be formulated as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 341, + 595, + 545, + 616 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 341, + 595, + 545, + 616 + ], + "spans": [ + { + "bbox": [ + 341, + 595, + 545, + 616 + ], + "type": "interline_equation", + "content": "L _ {A U} ^ {D} = \\lambda_ {A U} \\| D _ {A U} \\left(\\boldsymbol {x} _ {\\boldsymbol {\\mu} ^ {0}}\\right) - \\boldsymbol {\\mu} ^ {0} \\| _ {2} ^ {2}, \\tag {5}", + "image_path": "36387b8b0936915f458dcd3ec020e6f6d6e3efd92b91cec8e27f04a8ce2c5b3a.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 343, + 612, + 509, + 627 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 343, + 612, + 509, + 627 + ], + "spans": [ + { + "bbox": [ + 343, + 612, + 509, + 627 + ], + "type": "interline_equation", + "content": "L _ {A U} ^ {G} = \\lambda_ {A U} \\| D _ {A U} \\left(G \\left(\\boldsymbol {x} _ {\\boldsymbol {\\mu} ^ {0}} \\mid \\boldsymbol {\\mu} ^ {i}\\right)\\right) - \\boldsymbol {\\mu} ^ {i} \\| _ {2} ^ {2}.", + "image_path": "968831c585a8c4d680c44f4daa9314530a28c4fc58fb24420c53b1c429460b04.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "Expression supervision module. The expression supervision module (blue box in Fig. 3) protects the visual identity of adversarial examples and guides " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": " in expression editing by generating global and local facial supervisory signals. The global branch focuses on structural features of the face, whereas the local branch protects important facial details and reduces artifacts and blurs caused by the global branch." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20578" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": "Specifically, a global editor and three local editors are pre-trained to provide supervisory signals. For the local editors, we crop the eyes, nose, and mouth pixel patches based on face landmarks first. Then the input image and three detail patches are fed into the corresponding generator " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "G_{global}" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "G_{j}" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "j \\in J = \\{\\text{eyes, nose, mouth}\\}" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": ") with the input AU vector " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": ", respectively. Each generator has the network structure similar to [25], which provides the color response " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "M_{c}^{\\mu}" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": " and the attention response " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "M_{a}^{\\mu}" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "M_{c}^{\\mu}" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "M_{a}^{\\mu}" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": " force networks to pay attention to the expression change region and protect the remainder regions from disturbance. The ultimate supervisory signals can be obtained as follows, where " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "\\otimes" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": " denotes element-wise multiplication." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 71, + 231, + 287, + 246 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 71, + 231, + 287, + 246 + ], + "spans": [ + { + "bbox": [ + 71, + 231, + 287, + 246 + ], + "type": "interline_equation", + "content": "G _ {j} \\left(\\boldsymbol {x} _ {i n} \\mid \\boldsymbol {\\mu}\\right) = M _ {a} ^ {\\boldsymbol {\\mu}} \\otimes M _ {c} ^ {\\boldsymbol {\\mu}} + \\left(1 - M _ {a} ^ {\\boldsymbol {\\mu}}\\right) \\otimes \\boldsymbol {x} _ {i n}. \\tag {6}", + "image_path": "8f8861fcb59d9e5acc1eb7f676ac23f36889d76cb1a1b23509763f4e8f64c394.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 251, + 289, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 251, + 289, + 347 + ], + "spans": [ + { + "bbox": [ + 46, + 251, + 289, + 347 + ], + "type": "text", + "content": "The global editor focuses more on large scale features, such as shape and position of the five senses, and tends to produce artifacts and blurs in the detail region, while the local editors concentrate on significant local features and provide finer details. Therefore, we deploy the global editor to supervise the structural information of adversarial examples and the local editors to supervise local specifics. The loss of expression supervision module can be expressed as" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 353, + 287, + 407 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 353, + 287, + 407 + ], + "spans": [ + { + "bbox": [ + 47, + 353, + 287, + 407 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} L _ {e x p} ^ {G} = \\lambda_ {g} \\mathrm {S S I M} [ G (\\pmb {x} _ {\\pmb {\\mu} ^ {0}} | \\pmb {\\mu} ^ {i}), G _ {g l o b a l} (\\pmb {x} _ {\\pmb {\\mu} ^ {0}} | \\pmb {\\mu} ^ {i}) ] \\\\ + \\lambda_ {l} \\sum_ {j \\in J} \\operatorname {M S E} \\left[ \\operatorname {C r o p} _ {j} \\left(G \\left(\\boldsymbol {x} _ {\\boldsymbol {\\mu} ^ {0}} \\mid \\boldsymbol {\\mu} ^ {i}\\right)\\right), G _ {j} \\left(\\operatorname {C r o p} _ {j} \\left(\\boldsymbol {x} _ {\\boldsymbol {\\mu} ^ {0}}\\right) \\mid \\boldsymbol {\\mu} ^ {i}\\right) \\right], \\tag {7} \\\\ \\end{array}", + "image_path": "855b179c006391c9f95b863a7c0f0f4f2de087ff8f26aa6fc6d856bc28bae06a.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 407, + 287, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 407, + 287, + 431 + ], + "spans": [ + { + "bbox": [ + 46, + 407, + 287, + 431 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 407, + 287, + 431 + ], + "type": "inline_equation", + "content": "\\mathrm{Crop}_j" + }, + { + "bbox": [ + 46, + 407, + 287, + 431 + ], + "type": "text", + "content": " denotes the crop operation of local region " + }, + { + "bbox": [ + 46, + 407, + 287, + 431 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 407, + 287, + 431 + ], + "type": "text", + "content": " according to the face landmarks." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 431, + 287, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 431, + 287, + 550 + ], + "spans": [ + { + "bbox": [ + 46, + 431, + 287, + 550 + ], + "type": "text", + "content": "Transferability enhancement module. To improve the transferability of adversarial examples and the black-box attack success rate, we introduce the transferability enhancement module (yellow box in Fig. 3) from [16]. The generated adversarial examples are transformed with probability " + }, + { + "bbox": [ + 46, + 431, + 287, + 550 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 431, + 287, + 550 + ], + "type": "text", + "content": " by the function " + }, + { + "bbox": [ + 46, + 431, + 287, + 550 + ], + "type": "inline_equation", + "content": "T_{p}" + }, + { + "bbox": [ + 46, + 431, + 287, + 550 + ], + "type": "text", + "content": " (resize with padding or add noise), and then attack " + }, + { + "bbox": [ + 46, + 431, + 287, + 550 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 431, + 287, + 550 + ], + "type": "text", + "content": " pre-trained high-precision FR models " + }, + { + "bbox": [ + 46, + 431, + 287, + 550 + ], + "type": "inline_equation", + "content": "\\{C_k\\}_{k=1,\\dots,K}" + }, + { + "bbox": [ + 46, + 431, + 287, + 550 + ], + "type": "text", + "content": ", which perform as white-box models during the training of " + }, + { + "bbox": [ + 46, + 431, + 287, + 550 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 431, + 287, + 550 + ], + "type": "text", + "content": ". The adversarial attack loss function is formulated as" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 51, + 552, + 287, + 594 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 552, + 287, + 594 + ], + "spans": [ + { + "bbox": [ + 51, + 552, + 287, + 594 + ], + "type": "interline_equation", + "content": "L _ {a d v} ^ {G} = \\frac {\\lambda_ {a d v}}{K} \\sum_ {k = 1} ^ {K} [ 1 - \\cos \\left(\\mathcal {C} _ {k} \\left(\\boldsymbol {x} ^ {*}\\right), \\mathcal {C} _ {k} \\left(T _ {p} \\left(G \\left(\\boldsymbol {x} _ {\\boldsymbol {\\mu} ^ {0}} \\mid \\boldsymbol {\\mu} ^ {i}\\right)\\right)\\right)\\right) ] \\tag {8}", + "image_path": "97001124bd3cda4a4d2f7b8d1c498de4e580cd617bb8e5f61575e9a412522624.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 595, + 287, + 667 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 595, + 287, + 667 + ], + "spans": [ + { + "bbox": [ + 46, + 595, + 287, + 667 + ], + "type": "text", + "content": "Generalized attack module. The generalized attack module (green box in Fig. 3) intends to raise the attack success rate on the unseen face belonging to the target identity, which can be introduced into other adversarial attack approaches. The adversarial loss " + }, + { + "bbox": [ + 46, + 595, + 287, + 667 + ], + "type": "inline_equation", + "content": "L_{adv}^{G}" + }, + { + "bbox": [ + 46, + 595, + 287, + 667 + ], + "type": "text", + "content": " in GMAA can be further expressed as" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 51, + 670, + 287, + 714 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 670, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 51, + 670, + 287, + 714 + ], + "type": "interline_equation", + "content": "\\mathbb {E} _ {\\boldsymbol {x} _ {i} ^ {*}} \\sim_ {\\mathcal {S}} \\frac {\\lambda_ {a d v}}{K} \\sum_ {k = 1} ^ {K} [ 1 - \\cos \\left(\\mathcal {C} _ {k} \\left(\\boldsymbol {x} _ {i} ^ {*}\\right), \\mathcal {C} _ {k} \\left(T _ {p} \\left(G \\left(\\boldsymbol {x} _ {\\boldsymbol {\\mu} ^ {0}} \\mid \\boldsymbol {\\mu} ^ {i}\\right)\\right)\\right)\\right) ], \\tag {9}", + "image_path": "f9cdba1b498d30ecbae77139c1388ddde7a590294319ffe43a1a3aa074c4e611.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}_i^*" + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "text", + "content": " are defined in 2. However, numerous face recognition datasets and realistic scenarios do not fit this module since an identity only contains a few or single state image. Fortunately, since our method can accomplish both expression editing and adversarial attack, when we remove the loss associated with adversarial attack, we can obtain an expression editor, " + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "inline_equation", + "content": "G_{exp}" + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "text", + "content": ", by eliminating the adversarial effect " + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "inline_equation", + "content": "L_{adv}^{G}" + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "text", + "content": ", which can generate the expression state set " + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "text", + "content": " by different AU vectors." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 180, + 545, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 180, + 545, + 240 + ], + "spans": [ + { + "bbox": [ + 304, + 180, + 545, + 240 + ], + "type": "text", + "content": "Total loss function. Let " + }, + { + "bbox": [ + 304, + 180, + 545, + 240 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 304, + 180, + 545, + 240 + ], + "type": "text", + "content": " denotes the dataset, and " + }, + { + "bbox": [ + 304, + 180, + 545, + 240 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 304, + 180, + 545, + 240 + ], + "type": "text", + "content": " is the AU vector space. In particular, the given AU vector " + }, + { + "bbox": [ + 304, + 180, + 545, + 240 + ], + "type": "inline_equation", + "content": "\\pmb{\\mu}^i" + }, + { + "bbox": [ + 304, + 180, + 545, + 240 + ], + "type": "text", + "content": " is sampled randomly from " + }, + { + "bbox": [ + 304, + 180, + 545, + 240 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 304, + 180, + 545, + 240 + ], + "type": "text", + "content": " to train the generator " + }, + { + "bbox": [ + 304, + 180, + 545, + 240 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 180, + 545, + 240 + ], + "type": "text", + "content": " to learn the distribution of adversarial expression manifold. For the generator " + }, + { + "bbox": [ + 304, + 180, + 545, + 240 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 180, + 545, + 240 + ], + "type": "text", + "content": ", we have the loss function as follows," + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 314, + 243, + 545, + 269 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 243, + 545, + 269 + ], + "spans": [ + { + "bbox": [ + 314, + 243, + 545, + 269 + ], + "type": "interline_equation", + "content": "L ^ {G} = \\mathbb {E} _ {\\boldsymbol {x} _ {\\mu^ {0}} \\sim \\boldsymbol {X}, \\boldsymbol {\\mu} ^ {i} \\sim V} \\left(L _ {\\text {c r i t i c}} ^ {G} + L _ {A U} ^ {G} + L _ {\\exp} ^ {G} + L _ {a d v} ^ {G}\\right). \\tag {10}", + "image_path": "19d3cf5878acc9618faa9ed487465d7a3f55ff1fe43339815172a3eae2e0a307.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 270, + 542, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 270, + 542, + 281 + ], + "spans": [ + { + "bbox": [ + 306, + 270, + 542, + 281 + ], + "type": "text", + "content": "As for " + }, + { + "bbox": [ + 306, + 270, + 542, + 281 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 306, + 270, + 542, + 281 + ], + "type": "text", + "content": ", the total loss function can be obtained as follows," + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 346, + 285, + 545, + 301 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 346, + 285, + 545, + 301 + ], + "spans": [ + { + "bbox": [ + 346, + 285, + 545, + 301 + ], + "type": "interline_equation", + "content": "L ^ {D} = \\mathbb {E} _ {\\boldsymbol {x} _ {\\mu^ {0}} \\sim \\boldsymbol {X}, \\boldsymbol {\\mu} ^ {i} \\sim V} \\left(L _ {\\text {c r i t i c}} ^ {D} + L _ {A U} ^ {D}\\right). \\tag {11}", + "image_path": "f4488d923d7e25ea4d8680a5c06a9d838ab14d59e57d0c19892680f919e220ac.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 311, + 493, + 323 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 311, + 493, + 323 + ], + "spans": [ + { + "bbox": [ + 305, + 311, + 493, + 323 + ], + "type": "text", + "content": "3.3. Continuity of the adversarial space" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 325, + 545, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 325, + 545, + 360 + ], + "spans": [ + { + "bbox": [ + 304, + 325, + 545, + 360 + ], + "type": "text", + "content": "In this subsection, we illustrate more precisely the continuity of the adversarial space and provide a proof that our method establishes a continuous adversarial manifold." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 361, + 545, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 361, + 545, + 384 + ], + "spans": [ + { + "bbox": [ + 304, + 361, + 545, + 384 + ], + "type": "text", + "content": "Firstly, the definition of continuous adversarial space is shown in Def. 1." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 393, + 545, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 393, + 545, + 430 + ], + "spans": [ + { + "bbox": [ + 304, + 393, + 545, + 430 + ], + "type": "text", + "content": "Definition 1. Let " + }, + { + "bbox": [ + 304, + 393, + 545, + 430 + ], + "type": "inline_equation", + "content": "\\pmb{x}_0 \\in \\mathbb{R}^{3 \\times H \\times W}" + }, + { + "bbox": [ + 304, + 393, + 545, + 430 + ], + "type": "text", + "content": ", then " + }, + { + "bbox": [ + 304, + 393, + 545, + 430 + ], + "type": "inline_equation", + "content": "\\mathcal{M}^0 = G(\\pmb{x}_0; \\pmb{\\theta})" + }, + { + "bbox": [ + 304, + 393, + 545, + 430 + ], + "type": "text", + "content": " is a continuous adversarial space if and only if (1) " + }, + { + "bbox": [ + 304, + 393, + 545, + 430 + ], + "type": "inline_equation", + "content": "\\mathcal{M}^0" + }, + { + "bbox": [ + 304, + 393, + 545, + 430 + ], + "type": "text", + "content": " is a subspace of " + }, + { + "bbox": [ + 304, + 393, + 545, + 430 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{3 \\times H \\times W}" + }, + { + "bbox": [ + 304, + 393, + 545, + 430 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 430, + 507, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 430, + 507, + 443 + ], + "spans": [ + { + "bbox": [ + 306, + 430, + 507, + 443 + ], + "type": "text", + "content": "(2) " + }, + { + "bbox": [ + 306, + 430, + 507, + 443 + ], + "type": "inline_equation", + "content": "\\forall \\pmb{x}_i^0\\in \\mathcal{M},\\pmb{x}_i^0" + }, + { + "bbox": [ + 306, + 430, + 507, + 443 + ], + "type": "text", + "content": " is an adversarial version of " + }, + { + "bbox": [ + 306, + 430, + 507, + 443 + ], + "type": "inline_equation", + "content": "\\pmb{x}_0" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 445, + 538, + 457 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 445, + 538, + 457 + ], + "spans": [ + { + "bbox": [ + 306, + 445, + 538, + 457 + ], + "type": "text", + "content": "Then, we can prove that " + }, + { + "bbox": [ + 306, + 445, + 538, + 457 + ], + "type": "inline_equation", + "content": "\\mathcal{M}^0" + }, + { + "bbox": [ + 306, + 445, + 538, + 457 + ], + "type": "text", + "content": " is a continuous manifold." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 462, + 545, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 545, + 498 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 545, + 498 + ], + "type": "text", + "content": "Theorem 1. " + }, + { + "bbox": [ + 304, + 462, + 545, + 498 + ], + "type": "inline_equation", + "content": "\\mathcal{M}^0" + }, + { + "bbox": [ + 304, + 462, + 545, + 498 + ], + "type": "text", + "content": " generated by " + }, + { + "bbox": [ + 304, + 462, + 545, + 498 + ], + "type": "inline_equation", + "content": "G_0" + }, + { + "bbox": [ + 304, + 462, + 545, + 498 + ], + "type": "text", + "content": " is a continuous adversarial manifold, where " + }, + { + "bbox": [ + 304, + 462, + 545, + 498 + ], + "type": "inline_equation", + "content": "G_0: V \\to \\mathcal{M}" + }, + { + "bbox": [ + 304, + 462, + 545, + 498 + ], + "type": "text", + "content": " is a map when fixed the input " + }, + { + "bbox": [ + 304, + 462, + 545, + 498 + ], + "type": "inline_equation", + "content": "\\pmb{x}_0" + }, + { + "bbox": [ + 304, + 462, + 545, + 498 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 304, + 462, + 545, + 498 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 462, + 545, + 498 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 508, + 545, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 508, + 545, + 532 + ], + "spans": [ + { + "bbox": [ + 304, + 508, + 545, + 532 + ], + "type": "text", + "content": "Proof. (1) If " + }, + { + "bbox": [ + 304, + 508, + 545, + 532 + ], + "type": "inline_equation", + "content": "\\mathcal{M}^0" + }, + { + "bbox": [ + 304, + 508, + 545, + 532 + ], + "type": "text", + "content": " is homogeneous with the AU vector space " + }, + { + "bbox": [ + 304, + 508, + 545, + 532 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 304, + 508, + 545, + 532 + ], + "type": "text", + "content": ", it is obviously that " + }, + { + "bbox": [ + 304, + 508, + 545, + 532 + ], + "type": "inline_equation", + "content": "\\mathcal{M}^0" + }, + { + "bbox": [ + 304, + 508, + 545, + 532 + ], + "type": "text", + "content": " is a subspace of " + }, + { + "bbox": [ + 304, + 508, + 545, + 532 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{3\\times H\\times W}" + }, + { + "bbox": [ + 304, + 508, + 545, + 532 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 533, + 545, + 715 + ], + "type": "list", + "angle": 0, + "index": 26, + "blocks": [ + { + "bbox": [ + 304, + 533, + 545, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 545, + 593 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 545, + 593 + ], + "type": "text", + "content": "(1.1) " + }, + { + "bbox": [ + 304, + 533, + 545, + 593 + ], + "type": "inline_equation", + "content": "\\forall \\pmb{\\mu}, \\pmb{\\nu} \\in V" + }, + { + "bbox": [ + 304, + 533, + 545, + 593 + ], + "type": "text", + "content": ", if " + }, + { + "bbox": [ + 304, + 533, + 545, + 593 + ], + "type": "inline_equation", + "content": "G_0(\\pmb{\\mu}) = G_0(\\pmb{\\nu})" + }, + { + "bbox": [ + 304, + 533, + 545, + 593 + ], + "type": "text", + "content": ", then " + }, + { + "bbox": [ + 304, + 533, + 545, + 593 + ], + "type": "inline_equation", + "content": "D_{AU}(G_0(\\pmb{\\mu})) = D_{AU}(G_0(\\pmb{\\nu}))" + }, + { + "bbox": [ + 304, + 533, + 545, + 593 + ], + "type": "text", + "content": ", we have " + }, + { + "bbox": [ + 304, + 533, + 545, + 593 + ], + "type": "inline_equation", + "content": "\\pmb{\\mu} = \\pmb{\\nu}" + }, + { + "bbox": [ + 304, + 533, + 545, + 593 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 533, + 545, + 593 + ], + "type": "inline_equation", + "content": "G_0: V \\to \\mathcal{M}^0" + }, + { + "bbox": [ + 304, + 533, + 545, + 593 + ], + "type": "text", + "content": " is a single shot. Besides, " + }, + { + "bbox": [ + 304, + 533, + 545, + 593 + ], + "type": "inline_equation", + "content": "\\forall \\pmb{x}^0 \\in \\mathcal{M}^0" + }, + { + "bbox": [ + 304, + 533, + 545, + 593 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 533, + 545, + 593 + ], + "type": "inline_equation", + "content": "\\exists \\pmb{\\mu} = D_{AU}(\\pmb{x}^0) \\in V" + }, + { + "bbox": [ + 304, + 533, + 545, + 593 + ], + "type": "text", + "content": " s.t. " + }, + { + "bbox": [ + 304, + 533, + 545, + 593 + ], + "type": "inline_equation", + "content": "G_0(D_{AU}(\\pmb{x}^0)) = \\pmb{x}^0" + }, + { + "bbox": [ + 304, + 533, + 545, + 593 + ], + "type": "text", + "content": ", then " + }, + { + "bbox": [ + 304, + 533, + 545, + 593 + ], + "type": "inline_equation", + "content": "G_0" + }, + { + "bbox": [ + 304, + 533, + 545, + 593 + ], + "type": "text", + "content": " is a surjection. Thus, " + }, + { + "bbox": [ + 304, + 533, + 545, + 593 + ], + "type": "inline_equation", + "content": "G_0" + }, + { + "bbox": [ + 304, + 533, + 545, + 593 + ], + "type": "text", + "content": " is a bijection." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 592, + 545, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 592, + 545, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 592, + 545, + 641 + ], + "type": "text", + "content": "(1.2) " + }, + { + "bbox": [ + 304, + 592, + 545, + 641 + ], + "type": "inline_equation", + "content": "\\forall \\pmb{x}_1^0, \\pmb{x}_2^0 \\in \\mathcal{M}^0" + }, + { + "bbox": [ + 304, + 592, + 545, + 641 + ], + "type": "text", + "content": ", we define " + }, + { + "bbox": [ + 304, + 592, + 545, + 641 + ], + "type": "inline_equation", + "content": "d(\\pmb{x}_1^0, \\pmb{x}_2^0) = \\| D_{AU}(\\pmb{x}_1^0) - D_{AU}(\\pmb{x}_2^0)\\|_2" + }, + { + "bbox": [ + 304, + 592, + 545, + 641 + ], + "type": "text", + "content": " as the metric between " + }, + { + "bbox": [ + 304, + 592, + 545, + 641 + ], + "type": "inline_equation", + "content": "\\pmb{x}_1^0" + }, + { + "bbox": [ + 304, + 592, + 545, + 641 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 592, + 545, + 641 + ], + "type": "inline_equation", + "content": "\\pmb{x}_2^0" + }, + { + "bbox": [ + 304, + 592, + 545, + 641 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 304, + 592, + 545, + 641 + ], + "type": "inline_equation", + "content": "\\mathcal{M}^0" + }, + { + "bbox": [ + 304, + 592, + 545, + 641 + ], + "type": "text", + "content": ". Since " + }, + { + "bbox": [ + 304, + 592, + 545, + 641 + ], + "type": "inline_equation", + "content": "(V, \\| \\cdot \\|_2)" + }, + { + "bbox": [ + 304, + 592, + 545, + 641 + ], + "type": "text", + "content": " is a metric space, and " + }, + { + "bbox": [ + 304, + 592, + 545, + 641 + ], + "type": "inline_equation", + "content": "D_{AU}(\\pmb{x}_i^0) \\in V" + }, + { + "bbox": [ + 304, + 592, + 545, + 641 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 592, + 545, + 641 + ], + "type": "inline_equation", + "content": "\\forall \\pmb{x}_i^0 \\in \\mathcal{M}^0" + }, + { + "bbox": [ + 304, + 592, + 545, + 641 + ], + "type": "text", + "content": ", we prove that " + }, + { + "bbox": [ + 304, + 592, + 545, + 641 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 592, + 545, + 641 + ], + "type": "text", + "content": " is a metric on " + }, + { + "bbox": [ + 304, + 592, + 545, + 641 + ], + "type": "inline_equation", + "content": "\\mathcal{M}^0" + }, + { + "bbox": [ + 304, + 592, + 545, + 641 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 641, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 689 + ], + "type": "text", + "content": "(Positivity) " + }, + { + "bbox": [ + 304, + 641, + 545, + 689 + ], + "type": "inline_equation", + "content": "d(\\pmb{x}_1^0, \\pmb{x}_2^0) \\geq 0" + }, + { + "bbox": [ + 304, + 641, + 545, + 689 + ], + "type": "text", + "content": ", and if " + }, + { + "bbox": [ + 304, + 641, + 545, + 689 + ], + "type": "inline_equation", + "content": "d(\\pmb{x}_1^0, \\pmb{x}_2^0) = 0" + }, + { + "bbox": [ + 304, + 641, + 545, + 689 + ], + "type": "text", + "content": " according to the definition of " + }, + { + "bbox": [ + 304, + 641, + 545, + 689 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 641, + 545, + 689 + ], + "type": "text", + "content": " we have " + }, + { + "bbox": [ + 304, + 641, + 545, + 689 + ], + "type": "inline_equation", + "content": "D_{AU}(\\pmb{x}_1^0) = D_{AU}(\\pmb{x}_2^0)" + }, + { + "bbox": [ + 304, + 641, + 545, + 689 + ], + "type": "text", + "content": ". Since " + }, + { + "bbox": [ + 304, + 641, + 545, + 689 + ], + "type": "inline_equation", + "content": "G_0" + }, + { + "bbox": [ + 304, + 641, + 545, + 689 + ], + "type": "text", + "content": " is a bijection, we have " + }, + { + "bbox": [ + 304, + 641, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\pmb{x}_1^0 = G_0(D_{AU}(\\pmb{x}_1^0)) = G_0(D_{AU}(\\pmb{x}_2^0)) = \\pmb{x}_2^0" + }, + { + "bbox": [ + 304, + 641, + 545, + 689 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 306, + 689, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 715 + ], + "type": "text", + "content": "(Symmetry) " + }, + { + "bbox": [ + 306, + 689, + 545, + 715 + ], + "type": "inline_equation", + "content": "d(\\pmb{x}_1^0, \\pmb{x}_2^0) = \\| D_{AU}(\\pmb{x}_1^0) - D_{AU}(\\pmb{x}_2^0)\\|_2 = \\| D_{AU}(\\pmb{x}_2^0) - D_{AU}(\\pmb{x}_1^0)\\|_2 = d(\\pmb{x}_2^0, \\pmb{x}_1^0)" + }, + { + "bbox": [ + 306, + 689, + 545, + 715 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 25 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "footer", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "20579" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 96, + 83, + 500, + 193 + ], + "blocks": [ + { + "bbox": [ + 226, + 71, + 367, + 81 + ], + "lines": [ + { + "bbox": [ + 226, + 71, + 367, + 81 + ], + "spans": [ + { + "bbox": [ + 226, + 71, + 367, + 81 + ], + "type": "text", + "content": "Table 1. Black-box attack success rate" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 96, + 83, + 500, + 193 + ], + "lines": [ + { + "bbox": [ + 96, + 83, + 500, + 193 + ], + "spans": [ + { + "bbox": [ + 96, + 83, + 500, + 193 + ], + "type": "table", + "html": "
CelebA-HQLFW
IRSE50IR152FacenetMobilefaceIRSE50IR152FacenetMobileface
Clean3.683.081.318.433.200.060.045.00
PGD [23]24.2013.375.8628.7231.3010.207.4033.50
MI-FGSM [7]38.9020.769.2540.4838.2014.207.6039.40
SemanticAdv [26]26.5310.247.8055.3233.6010.408.8037.40
TIP-IM [34]44.2016.0914.4665.3632.8015.2013.0079.00
AMT-GAN [16]51.0615.6311.6333.2740.7225.2313.8935.67
MAA60.4029.4318.9156.1355.8029.2018.0060.80
", + "image_path": "03e15165e49b77229df53f63f8984cea5eaa37e1d7a60d154a5dfe952653fd7e.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 48, + 232, + 547, + 294 + ], + "blocks": [ + { + "bbox": [ + 46, + 198, + 547, + 232 + ], + "lines": [ + { + "bbox": [ + 46, + 198, + 547, + 232 + ], + "spans": [ + { + "bbox": [ + 46, + 198, + 547, + 232 + ], + "type": "text", + "content": "Table 2. The unbolded numbers are the black-box ASR of attacking the test target *, 1, 2, 3, and all the models are trained on target *. The bolded numbers are the results of the models that train on the state set. For example, if we train the MAA to attack the state set without target 1, the adversarial examples attack target 1 with an " + }, + { + "bbox": [ + 46, + 198, + 547, + 232 + ], + "type": "inline_equation", + "content": "11.43\\%" + }, + { + "bbox": [ + 46, + 198, + 547, + 232 + ], + "type": "text", + "content": " success rate on Facenet during the testing period." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 232, + 547, + 294 + ], + "lines": [ + { + "bbox": [ + 48, + 232, + 547, + 294 + ], + "spans": [ + { + "bbox": [ + 48, + 232, + 547, + 294 + ], + "type": "table", + "html": "
Target*Target 1Target 2Target 3
FacenetMobilefaceFacenetMobilefaceFacenetMobilefaceFacenetMobileface
TIP-IM [34] / G-TIP-IM17.6886.334.54 / 7.6258.03 / 70.9310.75 / 20.4234.42 / 49.2011.93 / 19.4122.21 / 42.43
AMT-GAN [16] / G-AMT-GAN16.1255.958.22 / 13.2326.99 / 47.149.78 / 17.1227.67 / 43.9310.91 / 16.1624.69 / 42.37
MAA / GMAA25.2272.6211.43 / 17.8443.44 / 67.5013.30 / 21.7133.08 / 41.2412.64 / 19.1529.56 / 47.21
", + "image_path": "2fc4fede75cd2b28134919befe7e5d7aee301f0da081cda19ceda93ee11f554d.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 303, + 287, + 340 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 303, + 287, + 340 + ], + "spans": [ + { + "bbox": [ + 47, + 303, + 287, + 340 + ], + "type": "text", + "content": "(Triangle inequality) " + }, + { + "bbox": [ + 47, + 303, + 287, + 340 + ], + "type": "inline_equation", + "content": "\\forall \\pmb{x}_3^0\\in \\mathcal{M}^0" + }, + { + "bbox": [ + 47, + 303, + 287, + 340 + ], + "type": "text", + "content": " , we have " + }, + { + "bbox": [ + 47, + 303, + 287, + 340 + ], + "type": "inline_equation", + "content": "d(\\pmb{x}_1^0,\\pmb{x}_3^0) + d(\\pmb{x}_3^0,\\pmb{x}_2^0) = \\| D_{AU}(\\pmb{x}_1^0) - D_{AU}(\\pmb{x}_3^0)\\| _2 + \\| D_{AU}(\\pmb{x}_3^0) -" + }, + { + "bbox": [ + 47, + 303, + 287, + 340 + ], + "type": "inline_equation", + "content": "D_{AU}(\\pmb{x}_2^0)\\| _2\\geq \\| D_{AU}(\\pmb{x}_1^0) - D_{AU}(\\pmb{x}_2^0)\\| _2 = d(\\pmb{x}_1^0,\\pmb{x}_2^0)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 340, + 287, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 340, + 287, + 399 + ], + "spans": [ + { + "bbox": [ + 47, + 340, + 287, + 399 + ], + "type": "text", + "content": "Thus, " + }, + { + "bbox": [ + 47, + 340, + 287, + 399 + ], + "type": "inline_equation", + "content": "(\\mathcal{M}^0,d)" + }, + { + "bbox": [ + 47, + 340, + 287, + 399 + ], + "type": "text", + "content": " is a metric space. Then we need to prove that " + }, + { + "bbox": [ + 47, + 340, + 287, + 399 + ], + "type": "inline_equation", + "content": "G_{0}" + }, + { + "bbox": [ + 47, + 340, + 287, + 399 + ], + "type": "text", + "content": " is a continuous mapping. " + }, + { + "bbox": [ + 47, + 340, + 287, + 399 + ], + "type": "inline_equation", + "content": "\\forall \\pmb {\\mu},\\pmb {\\nu}\\in V,\\forall \\epsilon >0" + }, + { + "bbox": [ + 47, + 340, + 287, + 399 + ], + "type": "text", + "content": " , let " + }, + { + "bbox": [ + 47, + 340, + 287, + 399 + ], + "type": "inline_equation", + "content": "\\delta = \\epsilon" + }, + { + "bbox": [ + 47, + 340, + 287, + 399 + ], + "type": "text", + "content": " , when " + }, + { + "bbox": [ + 47, + 340, + 287, + 399 + ], + "type": "inline_equation", + "content": "\\| \\pmb {\\mu} - \\pmb {\\nu}\\| _2 < \\delta" + }, + { + "bbox": [ + 47, + 340, + 287, + 399 + ], + "type": "text", + "content": " , we have " + }, + { + "bbox": [ + 47, + 340, + 287, + 399 + ], + "type": "inline_equation", + "content": "d(G_0(\\pmb {\\mu}) - G_0(\\pmb {\\nu})) =" + }, + { + "bbox": [ + 47, + 340, + 287, + 399 + ], + "type": "inline_equation", + "content": "\\| D_{AU}(G_0(\\pmb {\\mu})) - D_{AU}(G_0(\\pmb {\\nu}))\\| _2 = \\| \\pmb {\\mu} - \\pmb {\\nu}\\| _2 < \\delta = \\epsilon ." + }, + { + "bbox": [ + 47, + 340, + 287, + 399 + ], + "type": "text", + "content": " We get the continuity of " + }, + { + "bbox": [ + 47, + 340, + 287, + 399 + ], + "type": "inline_equation", + "content": "G_{0}" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 399, + 287, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 399, + 287, + 471 + ], + "spans": [ + { + "bbox": [ + 47, + 399, + 287, + 471 + ], + "type": "text", + "content": "(1.3) It is obviously that " + }, + { + "bbox": [ + 47, + 399, + 287, + 471 + ], + "type": "inline_equation", + "content": "D_{AU}|_{\\mathcal{M}^0} : \\mathcal{M}^0 \\to V" + }, + { + "bbox": [ + 47, + 399, + 287, + 471 + ], + "type": "text", + "content": " is the inverse mapping of " + }, + { + "bbox": [ + 47, + 399, + 287, + 471 + ], + "type": "inline_equation", + "content": "G_0" + }, + { + "bbox": [ + 47, + 399, + 287, + 471 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 47, + 399, + 287, + 471 + ], + "type": "inline_equation", + "content": "\\forall \\pmb{x}_1^0, \\pmb{x}_2^0 \\in \\mathcal{M}^0, \\epsilon > 0" + }, + { + "bbox": [ + 47, + 399, + 287, + 471 + ], + "type": "text", + "content": ", let " + }, + { + "bbox": [ + 47, + 399, + 287, + 471 + ], + "type": "inline_equation", + "content": "\\delta = \\epsilon" + }, + { + "bbox": [ + 47, + 399, + 287, + 471 + ], + "type": "text", + "content": ", when " + }, + { + "bbox": [ + 47, + 399, + 287, + 471 + ], + "type": "inline_equation", + "content": "d(\\pmb{x}_1^0, \\pmb{x}_2^0) = \\| D_{AU}(\\pmb{x}_1^0) - D_{AU}(\\pmb{x}_2^0)\\|_2 < \\delta" + }, + { + "bbox": [ + 47, + 399, + 287, + 471 + ], + "type": "text", + "content": ", we have " + }, + { + "bbox": [ + 47, + 399, + 287, + 471 + ], + "type": "inline_equation", + "content": "\\| D_{AU}|_{\\mathcal{M}^0}(\\pmb{x}_1^0) - D_{AU}|_{\\mathcal{M}^0}(\\pmb{x}_2^0)\\|_2 = \\| D_{AU}(\\pmb{x}_1^0) - D_{AU}(\\pmb{x}_2^0)\\|_2 < \\delta = \\epsilon" + }, + { + "bbox": [ + 47, + 399, + 287, + 471 + ], + "type": "text", + "content": ". We get the continuity of the inverse map of " + }, + { + "bbox": [ + 47, + 399, + 287, + 471 + ], + "type": "inline_equation", + "content": "G_0" + }, + { + "bbox": [ + 47, + 399, + 287, + 471 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 471, + 287, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 471, + 287, + 519 + ], + "spans": [ + { + "bbox": [ + 46, + 471, + 287, + 519 + ], + "type": "text", + "content": "In conclusion, " + }, + { + "bbox": [ + 46, + 471, + 287, + 519 + ], + "type": "inline_equation", + "content": "G_{0}" + }, + { + "bbox": [ + 46, + 471, + 287, + 519 + ], + "type": "text", + "content": " is the homeomorphism of " + }, + { + "bbox": [ + 46, + 471, + 287, + 519 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 46, + 471, + 287, + 519 + ], + "type": "text", + "content": " to the manifold " + }, + { + "bbox": [ + 46, + 471, + 287, + 519 + ], + "type": "inline_equation", + "content": "\\mathcal{M}^0" + }, + { + "bbox": [ + 46, + 471, + 287, + 519 + ], + "type": "text", + "content": ", i.e. " + }, + { + "bbox": [ + 46, + 471, + 287, + 519 + ], + "type": "inline_equation", + "content": "\\mathcal{M}^0" + }, + { + "bbox": [ + 46, + 471, + 287, + 519 + ], + "type": "text", + "content": " homogeneous with the AU vector space " + }, + { + "bbox": [ + 46, + 471, + 287, + 519 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 46, + 471, + 287, + 519 + ], + "type": "text", + "content": ". Since AU vector space is a finite dimensional vector space, " + }, + { + "bbox": [ + 46, + 471, + 287, + 519 + ], + "type": "inline_equation", + "content": "\\mathcal{M}^0" + }, + { + "bbox": [ + 46, + 471, + 287, + 519 + ], + "type": "text", + "content": " is a subspace of " + }, + { + "bbox": [ + 46, + 471, + 287, + 519 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{m\\times n\\times l}" + }, + { + "bbox": [ + 46, + 471, + 287, + 519 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 519, + 287, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 519, + 287, + 555 + ], + "spans": [ + { + "bbox": [ + 46, + 519, + 287, + 555 + ], + "type": "text", + "content": "(2) By the loss function 8, 7 and the back propagation, " + }, + { + "bbox": [ + 46, + 519, + 287, + 555 + ], + "type": "inline_equation", + "content": "\\pmb{x}_i^0" + }, + { + "bbox": [ + 46, + 519, + 287, + 555 + ], + "type": "text", + "content": " is influenced by the 8. It is obviously that " + }, + { + "bbox": [ + 46, + 519, + 287, + 555 + ], + "type": "inline_equation", + "content": "\\pmb{x}_i^0 \\in \\mathcal{M}^0" + }, + { + "bbox": [ + 46, + 519, + 287, + 555 + ], + "type": "text", + "content": " is an adversarial example when the model is well-trained." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 554, + 287, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 554, + 287, + 578 + ], + "spans": [ + { + "bbox": [ + 46, + 554, + 287, + 578 + ], + "type": "text", + "content": "Thus, the manifold " + }, + { + "bbox": [ + 46, + 554, + 287, + 578 + ], + "type": "inline_equation", + "content": "\\mathcal{M}^0" + }, + { + "bbox": [ + 46, + 554, + 287, + 578 + ], + "type": "text", + "content": " generated by " + }, + { + "bbox": [ + 46, + 554, + 287, + 578 + ], + "type": "inline_equation", + "content": "G_{0}" + }, + { + "bbox": [ + 46, + 554, + 287, + 578 + ], + "type": "text", + "content": " is a continuous adversarial manifold." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 578, + 287, + 627 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 578, + 287, + 627 + ], + "spans": [ + { + "bbox": [ + 46, + 578, + 287, + 627 + ], + "type": "text", + "content": "Remark 1. Since the " + }, + { + "bbox": [ + 46, + 578, + 287, + 627 + ], + "type": "inline_equation", + "content": "\\mathcal{M}^0" + }, + { + "bbox": [ + 46, + 578, + 287, + 627 + ], + "type": "text", + "content": " generated by " + }, + { + "bbox": [ + 46, + 578, + 287, + 627 + ], + "type": "inline_equation", + "content": "G_0" + }, + { + "bbox": [ + 46, + 578, + 287, + 627 + ], + "type": "text", + "content": " is a continuous adversarial manifold when fixed the " + }, + { + "bbox": [ + 46, + 578, + 287, + 627 + ], + "type": "inline_equation", + "content": "\\pmb{x}_0" + }, + { + "bbox": [ + 46, + 578, + 287, + 627 + ], + "type": "text", + "content": ", then we can assert over the sample space " + }, + { + "bbox": [ + 46, + 578, + 287, + 627 + ], + "type": "inline_equation", + "content": "\\Omega" + }, + { + "bbox": [ + 46, + 578, + 287, + 627 + ], + "type": "text", + "content": ", the adversarial examples space generated by " + }, + { + "bbox": [ + 46, + 578, + 287, + 627 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 578, + 287, + 627 + ], + "type": "text", + "content": " constitutes an adversarial fiber bundle." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 628, + 287, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 628, + 287, + 651 + ], + "spans": [ + { + "bbox": [ + 46, + 628, + 287, + 651 + ], + "type": "text", + "content": "Secondly, the definition of semantic continuous adversarial space is shown in Def. 2." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 652, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 652, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 652, + 287, + 677 + ], + "type": "text", + "content": "Definition 2. " + }, + { + "bbox": [ + 46, + 652, + 287, + 677 + ], + "type": "inline_equation", + "content": "\\mathcal{M}^0" + }, + { + "bbox": [ + 46, + 652, + 287, + 677 + ], + "type": "text", + "content": " generated by " + }, + { + "bbox": [ + 46, + 652, + 287, + 677 + ], + "type": "inline_equation", + "content": "\\pmb{x}_0\\in \\mathbb{R}^{3\\times H\\times W}" + }, + { + "bbox": [ + 46, + 652, + 287, + 677 + ], + "type": "text", + "content": " is a semantic continuous adversarial space if and only if" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 47, + 677, + 219, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 219, + 689 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 219, + 689 + ], + "type": "text", + "content": "(1) " + }, + { + "bbox": [ + 47, + 677, + 219, + 689 + ], + "type": "inline_equation", + "content": "\\mathcal{M}^0" + }, + { + "bbox": [ + 47, + 677, + 219, + 689 + ], + "type": "text", + "content": " is a continuous adversarial space." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "(2) " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\forall \\pmb{x}_1^0, \\pmb{x}_2^0 \\in \\mathcal{M}^0" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": ", if " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\pmb{x}_1^0" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": " is close to " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\pmb{x}_2^0" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": " on the " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{M}^0" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": ", then " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\pmb{x}_1^0" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\pmb{x}_2^0" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": " satisfy the semantic consistency." + } + ] + } + ], + "index": 14 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 317, + 304, + 545, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 304, + 545, + 316 + ], + "spans": [ + { + "bbox": [ + 317, + 304, + 545, + 316 + ], + "type": "text", + "content": "We can state that " + }, + { + "bbox": [ + 317, + 304, + 545, + 316 + ], + "type": "inline_equation", + "content": "\\mathcal{M}^0" + }, + { + "bbox": [ + 317, + 304, + 545, + 316 + ], + "type": "text", + "content": " is a semantic continuous manifold." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 321, + 545, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 321, + 545, + 357 + ], + "spans": [ + { + "bbox": [ + 304, + 321, + 545, + 357 + ], + "type": "text", + "content": "Theorem 2. " + }, + { + "bbox": [ + 304, + 321, + 545, + 357 + ], + "type": "inline_equation", + "content": "\\mathcal{M}^0" + }, + { + "bbox": [ + 304, + 321, + 545, + 357 + ], + "type": "text", + "content": " generated by " + }, + { + "bbox": [ + 304, + 321, + 545, + 357 + ], + "type": "inline_equation", + "content": "G_0" + }, + { + "bbox": [ + 304, + 321, + 545, + 357 + ], + "type": "text", + "content": " is a semantic continuous adversarial manifold, where " + }, + { + "bbox": [ + 304, + 321, + 545, + 357 + ], + "type": "inline_equation", + "content": "G_0: V \\to \\mathcal{M}" + }, + { + "bbox": [ + 304, + 321, + 545, + 357 + ], + "type": "text", + "content": " is a map when fixed the input " + }, + { + "bbox": [ + 304, + 321, + 545, + 357 + ], + "type": "inline_equation", + "content": "\\pmb{x}_0" + }, + { + "bbox": [ + 304, + 321, + 545, + 357 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 304, + 321, + 545, + 357 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 321, + 545, + 357 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 359, + 546, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 359, + 546, + 419 + ], + "spans": [ + { + "bbox": [ + 304, + 359, + 546, + 419 + ], + "type": "text", + "content": "Proof. Since we have proved that " + }, + { + "bbox": [ + 304, + 359, + 546, + 419 + ], + "type": "inline_equation", + "content": "D_{AD}" + }, + { + "bbox": [ + 304, + 359, + 546, + 419 + ], + "type": "text", + "content": " is a continuous mapping, we have " + }, + { + "bbox": [ + 304, + 359, + 546, + 419 + ], + "type": "inline_equation", + "content": "D_{AU}(\\pmb{x}_1^0)" + }, + { + "bbox": [ + 304, + 359, + 546, + 419 + ], + "type": "text", + "content": " is close to " + }, + { + "bbox": [ + 304, + 359, + 546, + 419 + ], + "type": "inline_equation", + "content": "D_{AU}(\\pmb{x}_2^0)" + }, + { + "bbox": [ + 304, + 359, + 546, + 419 + ], + "type": "text", + "content": " when " + }, + { + "bbox": [ + 304, + 359, + 546, + 419 + ], + "type": "inline_equation", + "content": "\\pmb{x}_1^0" + }, + { + "bbox": [ + 304, + 359, + 546, + 419 + ], + "type": "text", + "content": " is close to " + }, + { + "bbox": [ + 304, + 359, + 546, + 419 + ], + "type": "inline_equation", + "content": "\\pmb{x}_2^0" + }, + { + "bbox": [ + 304, + 359, + 546, + 419 + ], + "type": "text", + "content": ", which means the AU vectors of " + }, + { + "bbox": [ + 304, + 359, + 546, + 419 + ], + "type": "inline_equation", + "content": "\\pmb{x}_1^0" + }, + { + "bbox": [ + 304, + 359, + 546, + 419 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 359, + 546, + 419 + ], + "type": "inline_equation", + "content": "\\pmb{x}_2^0" + }, + { + "bbox": [ + 304, + 359, + 546, + 419 + ], + "type": "text", + "content": " are very close. Thus, the semantic information of " + }, + { + "bbox": [ + 304, + 359, + 546, + 419 + ], + "type": "inline_equation", + "content": "\\pmb{x}_1^0" + }, + { + "bbox": [ + 304, + 359, + 546, + 419 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 359, + 546, + 419 + ], + "type": "inline_equation", + "content": "\\pmb{x}_2^0" + }, + { + "bbox": [ + 304, + 359, + 546, + 419 + ], + "type": "text", + "content": " is close." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 429, + 388, + 442 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 429, + 388, + 442 + ], + "spans": [ + { + "bbox": [ + 305, + 429, + 388, + 442 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 449, + 427, + 461 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 449, + 427, + 461 + ], + "spans": [ + { + "bbox": [ + 305, + 449, + 427, + 461 + ], + "type": "text", + "content": "4.1. Experimental setting" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 462, + 545, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 545, + 557 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 545, + 557 + ], + "type": "text", + "content": "Implementation details. We set " + }, + { + "bbox": [ + 304, + 462, + 545, + 557 + ], + "type": "inline_equation", + "content": "\\lambda_{c}" + }, + { + "bbox": [ + 304, + 462, + 545, + 557 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 462, + 545, + 557 + ], + "type": "inline_equation", + "content": "\\lambda_{gp}" + }, + { + "bbox": [ + 304, + 462, + 545, + 557 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 462, + 545, + 557 + ], + "type": "inline_equation", + "content": "\\lambda_{AU}" + }, + { + "bbox": [ + 304, + 462, + 545, + 557 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 462, + 545, + 557 + ], + "type": "inline_equation", + "content": "\\lambda_{g}" + }, + { + "bbox": [ + 304, + 462, + 545, + 557 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 462, + 545, + 557 + ], + "type": "inline_equation", + "content": "\\lambda_{l}" + }, + { + "bbox": [ + 304, + 462, + 545, + 557 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 462, + 545, + 557 + ], + "type": "inline_equation", + "content": "\\lambda_{adv}" + }, + { + "bbox": [ + 304, + 462, + 545, + 557 + ], + "type": "text", + "content": " to be 1, 10, 250, 20, 20, 25, respectively. Our method is trained by an Adam optimizer with the learning rate 0.0001 and the exponential decay rates set to be " + }, + { + "bbox": [ + 304, + 462, + 545, + 557 + ], + "type": "inline_equation", + "content": "(\\beta_{1},\\beta_{2}) = (0.5,0.99)" + }, + { + "bbox": [ + 304, + 462, + 545, + 557 + ], + "type": "text", + "content": ". We evaluate the black-box attack performance of the models utilizing the attack success rate(ASR) at FAR@0.01 and the confidence scores returned by commercial APIs." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "text", + "content": "Dataset. We train the model on two public datasets: 1) CelebA-HQ [19] is a high-quality face dataset, which contains 30,000 face images. 2) LFW [17] is a challenging dataset that collects 13,233 images with complex environmental factors and is a common dataset for face recognition tasks. We remove the images whose AU confidence is below " + }, + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "inline_equation", + "content": "95\\%" + }, + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "text", + "content": " as extracted by Openface [1], then randomly select " + }, + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "text", + "content": " of each dataset as the test set and the remaining images as the training set. Four pairs of images from CelebA [22] with the same identity are used as attack targets for training and testing, respectively, since CelebA [22] contains multiple images of one identity. Besides, the real state set in subsection 4.3 are obtained from the RaFD dataset [21]." + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20580" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 97, + 545, + 159 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "type": "text", + "content": "Table 3. The effect of the image quantity in state set on improving the generalizability of the adversarial example. The values " + }, + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "type": "inline_equation", + "content": "n_i" + }, + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "type": "inline_equation", + "content": "n_1 / n_2 / n_3" + }, + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "type": "text", + "content": " represents each expression state using " + }, + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "type": "text", + "content": " images." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 97, + 545, + 159 + ], + "lines": [ + { + "bbox": [ + 48, + 97, + 545, + 159 + ], + "spans": [ + { + "bbox": [ + 48, + 97, + 545, + 159 + ], + "type": "table", + "html": "
Target 1Target 2Target 3
FacenetMobilefaceFacenetMobilefaceFacenetMobileface
G-TIP-IM [34]7.6/7.1/7.270.9/70.3/70.120.4/21.5/21.449.2/49.2/49.219.4/19.6/19.439.4/39.6/39.5
G-AMT-GAN [16]13.2/14.4/13.947.1/44.8/45.317.1/16.9/18.943.9/45.4/43.816.2/15.4/15.742.4/44.6/45.4
GMAA17.8/18.2/17.767.5/68.5/69.321.7/21.3/19.641.2/42.6/40.319.2/19.9/21.347.2/45.6/44.7
", + "image_path": "f48b047b7b5f0a4c50f9c29dbad0e32ee30d3a0fb79d1865ce84af6d8cf9a4df.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 50, + 170, + 298, + 304 + ], + "blocks": [ + { + "bbox": [ + 50, + 170, + 298, + 304 + ], + "lines": [ + { + "bbox": [ + 50, + 170, + 298, + 304 + ], + "spans": [ + { + "bbox": [ + 50, + 170, + 298, + 304 + ], + "type": "image", + "image_path": "34c333538aa2679c4cd7ce19f4b2360ce42920bcba81074821636ab4fb7a98de.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 309, + 546, + 322 + ], + "lines": [ + { + "bbox": [ + 46, + 309, + 546, + 322 + ], + "spans": [ + { + "bbox": [ + 46, + 309, + 546, + 322 + ], + "type": "text", + "content": "Figure 4. The confidence scores returned by Face++ and Tencent. The dashed line represents the average confidence level of clean samples." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 302, + 169, + 545, + 304 + ], + "blocks": [ + { + "bbox": [ + 302, + 169, + 545, + 304 + ], + "lines": [ + { + "bbox": [ + 302, + 169, + 545, + 304 + ], + "spans": [ + { + "bbox": [ + 302, + 169, + 545, + 304 + ], + "type": "image", + "image_path": "ee5dac8c8ac83e63135a5c155b674485abeb05391444afa0c97ddb59985a5ab2.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 47, + 331, + 289, + 438 + ], + "blocks": [ + { + "bbox": [ + 47, + 331, + 289, + 438 + ], + "lines": [ + { + "bbox": [ + 47, + 331, + 289, + 438 + ], + "spans": [ + { + "bbox": [ + 47, + 331, + 289, + 438 + ], + "type": "image", + "image_path": "8456c5e1a748682f82b909cea585b52ba81d25be660f7f1b1ad52c1350c6247b.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 449, + 288, + 482 + ], + "lines": [ + { + "bbox": [ + 46, + 449, + 288, + 482 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 288, + 482 + ], + "type": "text", + "content": "Figure 5. The left side of the image depicts the five expression states, while the right side of the image depicts the influence of varied AU on the attack performance of Face++ and Tencent." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 48, + 558, + 288, + 609 + ], + "blocks": [ + { + "bbox": [ + 46, + 492, + 287, + 557 + ], + "lines": [ + { + "bbox": [ + 46, + 492, + 287, + 557 + ], + "spans": [ + { + "bbox": [ + 46, + 492, + 287, + 557 + ], + "type": "text", + "content": "Table 4. This table shows the black-box ASR results of attacking the test target, which is the same person as the train image highlighted by a green square in Fig. 3. The unbolded numbers represent the results of training on the single target image that is shown in Fig. 3, while the bolded numbers are the results of training on the generated state set." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 558, + 288, + 609 + ], + "lines": [ + { + "bbox": [ + 48, + 558, + 288, + 609 + ], + "spans": [ + { + "bbox": [ + 48, + 558, + 288, + 609 + ], + "type": "table", + "html": "
FacenetMobileface
TIP-IM [34] / G-TIP-IM5.80 / 9.5017.20 / 23.5
AMT-GAN [16] / G-AMT-GAN4.04 / 8.279.82 / 12.45
MAA / GMAA6.60 / 10.6013.50 / 21.60
", + "image_path": "1da490c16cdd3e8e274fc6a938e98762b7705dd5eb0da3ffbf9dd7aeed414e4a.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 617, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 288, + 713 + ], + "type": "text", + "content": "Competitors. We compare our approach to the baselines PGD [23], MI-FGSM [7], SemanticAdv [26], TIP-IM [34] and AMT-GAN [16]. Since our work belongs to the branch of GAN based unrestricted adversarial attack [30], which is budget-free. Similar to [30], we compare our method MAA/GMAA to both restricted and unrestricted adversarial methods w.r.t attack performance and visual naturalness. All restricted methods are setted to the size of perturbation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 332, + 545, + 355 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 332, + 545, + 355 + ], + "spans": [ + { + "bbox": [ + 304, + 332, + 545, + 355 + ], + "type": "inline_equation", + "content": "\\epsilon = 12" + }, + { + "bbox": [ + 304, + 332, + 545, + 355 + ], + "type": "text", + "content": ". And all baselines are equipped with the transferability enhancement module for a fair comparison." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 356, + 545, + 416 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 356, + 545, + 416 + ], + "spans": [ + { + "bbox": [ + 304, + 356, + 545, + 416 + ], + "type": "text", + "content": "Target models. Following [16], we choose IR152 [14], IRSE50 [15], Facenet [27] and Mobileface [5] as the attacked FR models, with three of them serving as white-box models during training and the remaining as the black-box model for testing." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 420, + 416, + 433 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 420, + 416, + 433 + ], + "spans": [ + { + "bbox": [ + 306, + 420, + 416, + 433 + ], + "type": "text", + "content": "4.2. Comparison Study" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 434, + 545, + 470 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 434, + 545, + 470 + ], + "spans": [ + { + "bbox": [ + 304, + 434, + 545, + 470 + ], + "type": "text", + "content": "This subsection shows the comparison results of the MAA method and competitors in terms of attack performance and visual quality." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 471, + 545, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 471, + 545, + 613 + ], + "spans": [ + { + "bbox": [ + 304, + 471, + 545, + 613 + ], + "type": "text", + "content": "Comparison of attack performance on commercial API. We evaluate the performance of each method against the commercial APIs Face++" + }, + { + "bbox": [ + 304, + 471, + 545, + 613 + ], + "type": "inline_equation", + "content": "^2" + }, + { + "bbox": [ + 304, + 471, + 545, + 613 + ], + "type": "text", + "content": " and Tencent" + }, + { + "bbox": [ + 304, + 471, + 545, + 613 + ], + "type": "inline_equation", + "content": "^3" + }, + { + "bbox": [ + 304, + 471, + 545, + 613 + ], + "type": "text", + "content": ". Fig. 4 exhibits the average confidence score of Face++ and Tencent between the adversarial example and the test image of the target identity. Our method MAA achieves the highest score, outperforming all competitors on both datasets, as shown in Fig. 4. Furthermore, in Fig. 5, we display the confidence scores for five typical expressions (happy, angry, sad, surprised, and expressionless) to demonstrate that different AU vectors have little effect on attack performance and are more influenced by the dataset." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 614, + 545, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 614, + 545, + 674 + ], + "spans": [ + { + "bbox": [ + 304, + 614, + 545, + 674 + ], + "type": "text", + "content": "Comparison of black-box attack success rate. Since our model can give us a semantic continuous adversarial manifold and we want to make sure the comparison is fair, we randomly sample the AU vector to get test adversarial examples for calculating the black-box ASR. Tab. 1 shows the" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 315, + 683, + 461, + 693 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 683, + 461, + 693 + ], + "spans": [ + { + "bbox": [ + 315, + 683, + 461, + 693 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 315, + 683, + 461, + 693 + ], + "type": "text", + "content": "https://www(faceplusplus.com/" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 308, + 694, + 545, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 694, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 308, + 694, + 545, + 712 + ], + "type": "text", + "content": "3https://cloud.tencent.com/document/product/867/44987" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20581" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 70, + 547, + 150 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 547, + 150 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 547, + 150 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 547, + 150 + ], + "type": "image", + "image_path": "a802c2a541ccf1fea7791d2046e056fb619ac6ff5f6b6d5c6300659ceb97a6ef.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 155, + 547, + 200 + ], + "lines": [ + { + "bbox": [ + 46, + 155, + 547, + 200 + ], + "spans": [ + { + "bbox": [ + 46, + 155, + 547, + 200 + ], + "type": "text", + "content": "Figure 6. The images with green frames are the clean samples, while the images with blue frames are the results of TIP-IM [34]. In the case of the AMT-GAN [16], we chose 8 makeup styles at random, and the visualization results are shown as images with an orange frame. The images highlighted by red frames are the results of MAA, which are generated by a set of AU vectors. Please refer to the supplementary material for more high-definition magnified visualization results." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 210, + 287, + 247 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 210, + 287, + 247 + ], + "spans": [ + { + "bbox": [ + 46, + 210, + 287, + 247 + ], + "type": "text", + "content": "black-box ASR of each method under four FR models and two datasets. Obviously, our method has good performance for black-box attacks, i.e., it has strong transferability." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 247, + 289, + 439 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 247, + 289, + 439 + ], + "spans": [ + { + "bbox": [ + 46, + 247, + 289, + 439 + ], + "type": "text", + "content": "Comparison of visual quality. We choose TIP-IM and AMT-GAN, two recent approaches with high black-box ASR, as benchmarks for our assessment of visual quality. Fig. 6 shows the adversarial examples of each method, and the target image is shown in Fig. 3 highlighted by a green square. In particular, to demonstrate that our method can generate semantically continuous adversarial examples, Fig. 6 displays the adversarial examples generated by MAA that continuously transform on four expressions (expressionless, disgusted, happy and surprised in succession). Note that although only 20 adversarial examples are presented in Fig. 6, our method can generate an infinite number of adversarial examples by continuously interpolating between AU vectors since MAA establishes a correspondence with the AU vector space. Moreover, our method has a natural visual quality and is gender-insensitive." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 446, + 142, + 457 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 446, + 142, + 457 + ], + "spans": [ + { + "bbox": [ + 47, + 446, + 142, + 457 + ], + "type": "text", + "content": "4.3. Attack state set" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 460, + 287, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 460, + 287, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 460, + 287, + 640 + ], + "type": "text", + "content": "Attack real state set. To avoid serendipity, two FR models, three different test targets, and three adversarial attack methods were employed to assess the effectiveness of attacking state set on enhancing the adversarial examples' generalizability. Particularly, one of the FR models is Facenet with high accuracy, and the other is Mobileface with a lightweight network. Targets *, 1, 2 and 3 are shown in Fig. 2. The state set consists of several common expression states (angry, contemptuous, disgusted, fearful, happy, sad and surprised), and each correlates to an image. By comparing the results in Tab. 2, we can summarize that the model trained to attack target * generalizes poorly to test targets 1, 2, 3, whereas adversarial examples generated on the state set generalize better to the test target, even though the test target is not used to train the model." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": "We try to add more images in the state set to further improve the performance. Tab. 3 shows the ASR results that the target state set contains each expression state corresponding to " + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "inline_equation", + "content": "1/2/3" + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": " image(s), respectively. We demonstrate that the generalizability of the adversarial examples can be effectively strengthened as long as the state set contains a" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 210, + 545, + 233 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 210, + 545, + 233 + ], + "spans": [ + { + "bbox": [ + 305, + 210, + 545, + 233 + ], + "type": "text", + "content": "single image of each state, and additional images have minimal impact on the results." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 234, + 546, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 234, + 546, + 319 + ], + "spans": [ + { + "bbox": [ + 304, + 234, + 546, + 319 + ], + "type": "text", + "content": "Attack generated state set. For face image datasets that do not contain rich states, we generate the target state set by the pre-trained generator " + }, + { + "bbox": [ + 304, + 234, + 546, + 319 + ], + "type": "inline_equation", + "content": "G_{exp}" + }, + { + "bbox": [ + 304, + 234, + 546, + 319 + ], + "type": "text", + "content": " with AU vectors of common expressions. Tab. 4 shows the comparison results of training on a single target and a generated state set, demonstrating that training the model on the target state set enhances the generalization ability of adversarial examples." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 327, + 389, + 339 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 327, + 389, + 339 + ], + "spans": [ + { + "bbox": [ + 305, + 327, + 389, + 339 + ], + "type": "text", + "content": "5. Future Work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 345, + 545, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 345, + 545, + 453 + ], + "spans": [ + { + "bbox": [ + 304, + 345, + 545, + 453 + ], + "type": "text", + "content": "Considering the ubiquitous applicability of expressions in the facial adversarial attacks, the expression state space was chosen to implement GMAA in this paper. We employ the FACS as the prior domain knowledge to implement GMAA, while the paradigm GMAA can be broadly generalized by integrating other domain information, such as illumination, posture, etc. By selecting different state spaces, our work can be generalized to other adversarial attacks with more general image categories." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 461, + 379, + 474 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 461, + 379, + 474 + ], + "spans": [ + { + "bbox": [ + 306, + 461, + 379, + 474 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 479, + 545, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 479, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 479, + 545, + 624 + ], + "type": "text", + "content": "In this paper, we provide a novel paradigm GMAA that broadens both target domain and adversarial domain to enhance the performance of adversarial attack. For the target domain, GMAA optimizes generalization to the target identity by attacking the state set instead of a single image. Additionally, GMAA leverages the domain knowledge to expand adversarial domain from discrete points to semantic continuous manifold. Numerous comparative experiments have verified that GMAA has a better attack performance and a more natural visual quality than other competitors. Moreover, the generalized attack module can be extended to a wide of applications." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 632, + 416, + 645 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 632, + 416, + 645 + ], + "spans": [ + { + "bbox": [ + 306, + 632, + 416, + 645 + ], + "type": "text", + "content": "7. Acknowledgement" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 650, + 545, + 710 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 650, + 545, + 710 + ], + "spans": [ + { + "bbox": [ + 304, + 650, + 545, + 710 + ], + "type": "text", + "content": "This work was supported and partially funded by the National Natural Science Foundation of China (Grant No. 62106116). This work was also supported in part by ZJNSFC under Grant LQ23F010008. We also would like to thank Han Fang of NUS for the valuable discussion." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20582" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 92, + 289, + 713 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 92, + 287, + 147 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 92, + 287, + 147 + ], + "spans": [ + { + "bbox": [ + 53, + 92, + 287, + 147 + ], + "type": "text", + "content": "[1] Tadas Baltrusaitis, Amir Zadeh, Yao Chong Lim, and Louis-Philippe Morency. 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IEEE, 2019. 1, 3" + } + ] + } + ], + "index": 10 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "20584" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Discriminating Known From Unknown Objects via Structure-Enhanced Recurrent Variational AutoEncoder/7f53095f-c4ed-4448-89ff-3db316832dfc_content_list.json b/2023/Discriminating Known From Unknown Objects via Structure-Enhanced Recurrent Variational AutoEncoder/7f53095f-c4ed-4448-89ff-3db316832dfc_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..05fd338e0e48d0d86da65ea03e0a8e241f2943dd --- /dev/null +++ b/2023/Discriminating Known From Unknown Objects via Structure-Enhanced Recurrent Variational AutoEncoder/7f53095f-c4ed-4448-89ff-3db316832dfc_content_list.json @@ -0,0 +1,2079 @@ +[ + { + "type": "text", + "text": "Discriminating Known from Unknown Objects via Structure-Enhanced Recurrent Variational AutoEncoder", + "text_level": 1, + "bbox": [ + 197, + 130, + 772, + 174 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Among Wu, Cheng Deng* \nSchool of Electronic Engineering, Xidian University, Xi'an, China \namwu@xidian.edu.cn, chdeng@mail.xidian.edu.cn", + "bbox": [ + 220, + 204, + 746, + 256 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 291, + 313, + 306 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Discriminating known from unknown objects is an important essential ability for human beings. To simulate this ability, a task of unsupervised out-of-distribution object detection (OOD-OD) is proposed to detect the objects that are never-seen-before during model training, which is beneficial for promoting the safe deployment of object detectors. Due to lacking unknown data for supervision, for this task, the main challenge lies in how to leverage the known in-distribution (ID) data to improve the detector's discrimination ability. In this paper, we first propose a method of Structure-Enhanced Recurrent Variational AutoEncoder (SR-VAE), which mainly consists of two dedicated recurrent VAE branches. Specifically, to boost the performance of object localization, we explore utilizing the classical Laplacian of Gaussian (Log) operator to enhance the structure information in the extracted low-level features. Meanwhile, we design a VAE branch that recurrently generates the augmentation of the classification features to strengthen the discrimination ability of the object classifier. Finally, to alleviate the impact of lacking unknown data, another cycle-consistent conditional VAE branch is proposed to synthesize virtual OOD features that deviate from the distribution of ID features, which improves the capability of distinguishing OOD objects. In the experiments, our method is evaluated on OOD-OD, open-vocabulary detection, and incremental object detection. The significant performance gains over baselines show the superiorities of our method. The code will be released at https://github.com/AmingWu/SR-VAE.", + "bbox": [ + 75, + 323, + 473, + 748 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 775, + 209, + 791 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent years have witnessed the rapid development of deep learning based object detection [5,12,34,36,41], which often follows a close-set assumption that the training and testing processes share the same category space. However, the practical scenario is open and filled with unknown", + "bbox": [ + 75, + 801, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/7d4d371428dcf496326f629095ad3735d7659a23670c12ffbd2d05410cf99fee.jpg", + "image_caption": [ + "Figure 1. Discriminating known from unknown objects (as shown in green boxes) by synthesizing virtual OOD features. For OOD-OD, to alleviate the impact of lacking unknown data, we present an SR-VAE method to constrain the synthesized features (as shown in blue stars) to deviate from the distribution of ID features (as shown in orange). Meanwhile, we consider enhancing the discrimination of the classifier to reduce the risk of misclassifying the ID objects into the OOD category. Through these operations, the ability of distinguishing OOD objects could be improved significantly." + ], + "image_footnote": [], + "bbox": [ + 501, + 290, + 890, + 448 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "objects, e.g., in Fig. 1, an autonomous vehicle may encounter an unseen camel, presenting significant challenges for close-set assumption based detectors. To promote the safe application of detectors, a task of unsupervised out-of-distribution object detection (OOD-OD) [7] is recently proposed, which aims to detect the objects never-seen-before during training without accessing any auxiliary data.", + "bbox": [ + 496, + 582, + 890, + 686 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Towards unsupervised OOD-OD, since there is no auxiliary data available for supervision, leveraging the known in-distribution (ID) data to enhance the detector's discrimination ability becomes the critical challenge. One feasible solution is to synthesize a series of virtual OOD features [7, 35] based on the ID data, which is beneficial for promoting the object detector to learn a clear decision boundary between ID and OOD objects. To this end, the work [7] attempts to synthesize virtual features from the low-likelihood region of the estimated class-conditional distribution. However, this method requires a large number of objects for each category to estimate the distribution, limiting its application to the case of few samples.", + "bbox": [ + 496, + 688, + 892, + 883 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "As shown in Fig. 1, in this paper, we consider improvis", + "bbox": [ + 517, + 885, + 890, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author.", + "bbox": [ + 94, + 887, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "23956", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ing the performance of OOD object detection from two perspectives: One is to strengthen the discrimination capability of the object classifier for the known ID objects, which is conducive to reduce the risk of misclassifying the ID objects into the OOD category. Another is to synthesize the virtual OOD features that significantly deviate from the distribution of the ID features, which is instrumental in boosting the performance of distinguishing OOD objects from ID objects. To attain these two goals, we explore exploiting Variational AutoEncoder (VAE) [15, 20] to separately generate the augmented ID features and virtual OOD features.", + "bbox": [ + 75, + 90, + 472, + 257 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Specifically, an approach of Structure-Enhanced Recurrent Variational AutoEncoder (SR-VAE) is proposed, which mainly consists of two dedicated recurrent VAE branches. In general, an object detector should first localize objects. Then, an object classifier is used to discriminate these objects [12, 36]. To improve the localization performance, enhancing the object-related information in the extracted features is meaningful. To this end, after extracting the low-level features of an input image, we present to utilize the classical Laplacian of Gaussian (LoG) operator [23] to obtain structure-related information, which is used to fuse into the existing features to strengthen the localization ability.", + "bbox": [ + 75, + 258, + 472, + 441 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Next, in order to enhance the discrimination ability, inspired by Invariant Risk Minimization [1], we explore constructing a set of diverse environments to intensify the variance of the input classification features. Concretely, a VAE module [17, 20, 43] is exploited to recurrently output multiple augmented features of the classification features, i.e., the current output is taken as the input of the next iteration. Since the input of each iteration is different, by means of the variation operation, the diversity of the output features could be enlarged. Then, the discrimination ability is improved by minimizing the prediction discrepancy between the augmented features and the classification features.", + "bbox": [ + 75, + 441, + 472, + 625 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Finally, to alleviate the impact of lacking unknown data, we present a cycle-consistent conditional VAE [40] to synthesize virtual OOD features in the absence of paired supervision samples. Concretely, to ameliorate the synthesized features to deviate from the distribution of ID features, we first insert label information in the latent space to force a deterministic constrained representation. Meanwhile, by maximizing the discrepancy between the synthesized features and the input features, the synthesized features could be facilitated to contain plentiful OOD-relevant information, which enhances the ability of distinguishing OOD objects. In the experiments, our method is separately evaluated on three different tasks. Extensive experimental results on multiple datasets demonstrate the superiorities of our method.", + "bbox": [ + 75, + 625, + 472, + 837 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The contributions are summarized as follows:", + "bbox": [ + 96, + 838, + 401, + 852 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "(1) For unsupervised OOD-OD, we observe that using the classical LoG operator could effectively enhance object-related information in the extracted low-level features.", + "bbox": [ + 76, + 854, + 470, + 900 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "(2) To reduce the risk of misclassifying ID objects into the OOD category, we design a dedicated recurrent VAE to generate diverse augmented features of the input classification features, which is beneficial for improving the discrimination ability of the object classifier.", + "(3) To alleviate the impact of lacking unknown data for supervision, we present a cycle-consistent conditional VAE to synthesize virtual OOD features, which is instrumental in distinguishing OOD objects from ID objects.", + "(4) In the experiments, our method is evaluated on OOD-OD [7], open-vocabulary detection [33, 49], and incremental object detection [22, 39]. Particularly, for OpenImages dataset [24], compared with the baseline method [7], our method significantly reduces FPR95 by around $13.73\\%$ ." + ], + "bbox": [ + 496, + 90, + 893, + 303 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 316, + 640, + 330 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "OOD Detection. In order to promote the safe application of models in real scenarios, OOD detection [4, 14, 18] has recently attracted much attention, whose goal is to distinguish OOD data from ID data. Most methods [27, 31, 46, 52] focus on OOD image classification and explore a proper regularization-based method for this task. Particularly, Bendale et al. [2] developed the OpenMax score based on the extreme value theory. Liu et al. [30] proposed to utilize the energy score to discriminate OOD data from ID data. Zhou [52] rethought the commonly used reconstruction autoencoder for OOD detection. Though these methods have been demonstrated to be effective, since object detection involves object localization and classification, these methods could not directly apply to OOD-OD.", + "bbox": [ + 496, + 340, + 893, + 551 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recently, unsupervised OOD-OD [7] is proposed to localize and recognize the objects never-seen-before during training. For this task, Du et al. [7] proposed to use large-scale samples to estimate the distribution of each ID category, which is used to synthesize virtual OOD features. However, calculating accurate distribution estimation may limit its application in real scenarios. Harakeh et al. [11] designed an uncertainty estimation method for the localization branch, which could not well address OOD-OD that involves localization and classification. Besides, the work [6] proposed to use auxiliary video datasets to learn unknown-aware knowledge to effectively improve the performance of distinguishing OOD objects, which could not be used for unsupervised OOD-OD. In this paper, we explore employing the idea of VAE [15, 20] to synthesize virtual OOD features that significantly deviate from the distribution of ID features. And these virtual features are used to strengthen the discrimination ability. Experimental results on three different tasks show the effectiveness of our method.", + "bbox": [ + 496, + 553, + 893, + 839 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Variational AutoEncoder. The goal of VAE [15,20,21, 40] is to map the input data to a multivariate latent distribution, which efficiently addresses the generation problem for high-dimensional data. Most existing methods [15, 17, 44]", + "bbox": [ + 496, + 839, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "23957", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/330d41d90f635edd7312b3476fcd2c33ae0bd7722fbcfd324f4ab2812bee90b7.jpg", + "image_caption": [ + "Figure 2. Structure-Enhanced Recurrent Variational AutoEncoder for Unsupervised OOD-OD. To improve localization performance, we employ the LoG operator to enhance the structure-related information in the features extracted by the backbone network. Meanwhile, we design a VAE module to recurrently generate diverse augmented features of the input classification features, which is beneficial for strengthening the discrimination ability of the object classifier. Finally, to alleviate the impact of lacking unknown data, we propose a cycle-consistent conditional VAE to synthesize virtual OOD features that deviate from the distribution of the ID features significantly, which boosts the performance of distinguishing OOD objects." + ], + "image_footnote": [], + "bbox": [ + 81, + 89, + 890, + 297 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "attempt to adjust the latent representations to generate clear images containing rich content. Particularly, $\\beta$ -VAE [15] is an implementation with a weighted Kullback-Leibler (KL) divergence term to automatically discover disentangled representations without supervision. Conditional VAE [40] inserts label information in the latent space to force a deterministic constrained representation. Different from the above works focusing on pixel-level generation, we explore using VAE to generate virtual OOD features. Experimental results on OOD-OD show the advantages of our method.", + "bbox": [ + 75, + 398, + 472, + 551 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Structure-Enhanced Recurrent VAE", + "text_level": 1, + "bbox": [ + 76, + 564, + 406, + 579 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this paper, we follow the settings introduced in the work [7]. During training, we can only access the ID data. During inference, the object detector should own the capability of distinguishing ID objects from OOD objects.", + "bbox": [ + 75, + 589, + 468, + 650 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Structure Enhancement via LoG Operator", + "text_level": 1, + "bbox": [ + 76, + 659, + 439, + 676 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In general, an object detector should first localize objects accurately and then distinguish them as ID categories or OOD categories. To this end, it is important to enhance object-related information (e.g., object structure information). In the field of image processing, LoG operator [23] is a popular algorithm for edge detection. We explore performing the LoG operation on the extracted low-level features to strengthen the structure-relevant information.", + "bbox": [ + 75, + 681, + 468, + 801 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Concretely, as shown in Fig. 2, we follow the baseline work [7] and adopt the widely used object detector, i.e., Faster R-CNN [12, 36], as the basic detection model. Given an input image, we first employ the backbone network, e.g., ResNet [13], to extract the corresponding feature map $F \\in \\mathbb{R}^{w \\times h \\times c}$ , where $w$ , $h$ , and $c$ separately denote width, height, and channel number. To obtain rich structure", + "bbox": [ + 75, + 801, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "information, a $9 \\times 9$ LoG kernel $\\mathcal{G}$ is defined as follows:", + "bbox": [ + 498, + 398, + 872, + 414 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {G} = \\left[ \\begin{array}{c c c c c c c c c} 0 & 1 & 1 & 2 & 2 & 2 & 1 & 1 & 0 \\\\ 1 & 2 & 4 & 5 & 5 & 5 & 4 & 2 & 1 \\\\ 1 & 4 & 5 & 3 & 0 & 3 & 5 & 4 & 1 \\\\ 2 & 5 & 3 & - 1 2 & - 2 4 & - 1 2 & 3 & 5 & 2 \\\\ 2 & 5 & 0 & - 2 4 & - 4 0 & - 2 4 & 0 & 5 & 2 \\\\ 2 & 5 & 3 & - 1 2 & - 2 4 & - 1 2 & 3 & 5 & 2 \\\\ 1 & 4 & 5 & 3 & 0 & 3 & 5 & 4 & 1 \\\\ 1 & 2 & 4 & 5 & 5 & 5 & 4 & 2 & 1 \\\\ 0 & 1 & 1 & 2 & 2 & 2 & 1 & 1 & 0 \\end{array} \\right]. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 421, + 890, + 549 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Next, $\\mathcal{G}$ is used to perform a convolution operation on $F$ to obtain the structure-enhanced map $E\\in \\mathbb{R}^{w\\times h\\times c}$ . The processes are shown as follows:", + "bbox": [ + 498, + 556, + 892, + 602 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {E} = F * \\mathcal {G}, \\quad E = \\Psi ([ F, \\mathcal {E} ]), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 613, + 890, + 631 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathcal{E} \\in \\mathbb{R}^{w \\times h \\times c}$ is the convolutional result containing plentiful structure-related information. $\\Psi(\\cdot) \\in \\mathbb{R}^{1 \\times 1 \\times 2c \\times c}$ represents one-layer convolution to transform the number of channels. By fusing the structure information into existing features, the object-related information in $F$ could be enhanced effectively, which is instrumental in improving the performance of object localization.", + "bbox": [ + 496, + 641, + 893, + 748 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Recurrent VAE for Improving Discrimination", + "text_level": 1, + "bbox": [ + 498, + 756, + 885, + 772 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To reduce the risk of misclassifying ID objects into the OOD category, we design a VAE module to recurrently generate diverse augmented features of the classification features, which enhances the discrimination ability.", + "bbox": [ + 496, + 779, + 890, + 839 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Specifically, as shown in Fig. 2, the enhanced map $E$ is taken as the input of the RPN module to obtain a set of object proposals $\\mathcal{O}$ . Based on $\\mathcal{O}$ , RoI-Alignment followed by RoI-Feature extraction [12] is performed on $E$ to output", + "bbox": [ + 496, + 839, + 893, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "23958", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/b4216e2c10a4824de61d4ef40a1aa2d8e8f53a45954991067e60cb68cb9f8488.jpg", + "image_caption": [ + "Figure 3. Cycle-consistent conditional VAE for synthesizing virtual OOD features. During the forward process, the OOD features $\\pmb{O}$ are generated based on the ID features $F$ . And during the backward process, the features $\\pmb{F}$ are generated based on $\\pmb{O}$ . By minimizing the cycle-consistency loss between $F$ and $\\pmb{F}$ , the synthesized features $\\pmb{O}$ could be promoted to contain plentiful information that deviates from the distribution of the ID features." + ], + "image_footnote": [], + "bbox": [ + 78, + 88, + 472, + 195 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$P_{\\mathrm{in}} \\in \\mathbb{R}^{m \\times n}$ , where $m$ and $n$ separately denote the number of proposals and channels. Next, we first define two fully-connected networks (i.e., $\\Phi_{\\mu}(\\cdot)$ and $\\Phi_{\\sigma}(\\cdot)$ ) as the encoder to estimate the corresponding means and variances. Then, an encoding operation is performed on the input. Finally, a decoder $\\Theta(\\cdot)$ consisting of three fully-connected layers is leveraged to calculate the output. The overall processes at the $t$ -th iteration are shown as follows:", + "bbox": [ + 75, + 301, + 470, + 421 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mu_ {t} = \\Phi_ {\\mu} \\left(H _ {t - 1}\\right), \\quad \\sigma_ {t} = \\Phi_ {\\sigma} \\left(H _ {t - 1}\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 133, + 430, + 468, + 452 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nh _ {t} = \\mu_ {t} + \\epsilon \\cdot \\exp (\\sigma_ {t}), \\qquad H _ {t} = \\Theta (h _ {t}),\n$$\n", + "text_format": "latex", + "bbox": [ + 135, + 450, + 410, + 465 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $H_{t - 1}\\in \\mathbb{R}^{m\\times n}$ and $H_{t}\\in \\mathbb{R}^{m\\times n}$ respectively indicate the output of the previous iteration and that of the current iteration. And $H_0 = P_{\\mathrm{in}}$ $\\mu_t\\in \\mathbb{R}^{m\\times n}$ and $\\sigma_t\\in \\mathbb{R}^{m\\times n}$ are the estimated means and variances. $\\epsilon$ denotes Gaussian noise sampled from $\\mathcal{N}(0,I)$", + "bbox": [ + 75, + 474, + 468, + 551 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Through $T$ iterations, we can obtain a set of augmented features $H = \\{H_{1},\\dots ,H_{T}\\}$ . Finally, by minimizing the $KL$ -divergence between the prediction probabilities from $H_{t}$ and $P_{\\mathrm{in}}$ , the discrimination ability of the object classifier could be enhanced effectively. During training, $P_{\\mathrm{in}}$ is taken as the input of the object classifier and regressor to calculate the classification and localization losses. The joint training objective is shown as follows:", + "bbox": [ + 75, + 551, + 470, + 674 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {i n}} = \\mathcal {L} _ {\\mathrm {d e t}} + \\alpha \\cdot \\frac {1}{T} \\sum_ {t = 1} ^ {T} \\mathrm {K L} [ p (H _ {t} | H _ {t - 1}), p (P _ {\\mathrm {i n}}) ], \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 681, + 468, + 724 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{\\mathrm{det}}$ is the sum of the classification loss $\\mathcal{L}_{\\mathrm{cls}}$ and the localization loss $\\mathcal{L}_{\\mathrm{loc}}$ , i.e., $\\mathcal{L}_{\\mathrm{det}} = \\mathcal{L}_{\\mathrm{cls}} + \\mathcal{L}_{\\mathrm{loc}}$ . $\\alpha$ is a hyper-parameter. In the experiments, $\\alpha$ is set to 0.001. $p(\\cdot)$ indicates the prediction probability of the object classifier.", + "bbox": [ + 75, + 732, + 468, + 792 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Synthesizing Virtual OOD Features", + "text_level": 1, + "bbox": [ + 76, + 801, + 387, + 816 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Due to lacking unknown data for supervision, it is prone to misclassify OOD objects into ID categories. Hence, synthesizing virtual OOD data is important to distinguish OOD objects. A straightforward idea is to train generative models, e.g., GANs [9], to synthesize images, which is difficult", + "bbox": [ + 75, + 825, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "to optimize [7]. Instead, we propose a cycle-consistent conditional VAE to synthesize virtual OOD features.", + "bbox": [ + 496, + 90, + 890, + 119 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Particularly, as shown in Fig. 3, during the forward process, the extracted features $F$ and corresponding ID label [1, 0] are first concatenated as $\\hat{F} \\in \\mathbb{R}^{w \\times h \\times (c + 2)}$ . Then, two convolutional networks $W_{\\mu}$ and $W_{\\sigma}$ are defined to estimate the corresponding means and variances:", + "bbox": [ + 496, + 121, + 890, + 196 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mu_ {f} = W _ {\\mu} * \\hat {F}, \\quad \\sigma_ {f} = W _ {\\sigma} * \\hat {F}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 202, + 890, + 222 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mu_f \\in \\mathbb{R}^{w \\times h \\times c}$ and $\\sigma_f \\in \\mathbb{R}^{w \\times h \\times c}$ . And an encoding operation is performed to obtain $Z \\in \\mathbb{R}^{w \\times h \\times c}$ , i.e., $Z = \\mu_f + \\epsilon \\cdot \\exp(\\sigma_f)$ . Next, in order to generate virtual OOD features, $Z$ and corresponding OOD label [0, 1] are concatenated as $\\hat{Z} \\in \\mathbb{R}^{w \\times h \\times (c+2)}$ . A decoding network $\\mathcal{D}$ consisting of three convolutional layers is performed on $\\hat{Z}$ to obtain the virtual OOD map $O \\in \\mathbb{R}^{w \\times h \\times c}$ .", + "bbox": [ + 496, + 227, + 890, + 333 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "During the backward process, to alleviate the impact of lacking paired data for supervision, the concatenation result of $\\pmb{O}$ and label [0, 1] is made convolution with $W_{\\mu}$ and $W_{\\sigma}$ . Next, we still take the concatenation of the encoding result and label [1, 0] as the input of the decoder $\\mathcal{D}$ to obtain the output $\\pmb{F} \\in \\mathbb{R}^{w \\times h \\times c}$ . The operations are the same as the forward process. Finally, we introduce a cycle-consistency loss to reduce the discrepancy between $\\pmb{F}$ and $F$ , i.e., $\\mathcal{L}_{\\mathrm{cycle}} = \\frac{1}{wh}\\sum |F - F|$ .", + "bbox": [ + 496, + 334, + 890, + 470 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Moreover, to promote $\\pmb{O}$ to deviate from the distribution of $F$ , as shown in Fig. 2, based on the object proposals $\\mathcal{O}$ , RoI-Alignment followed by RoI-Feature extraction is performed on $\\pmb{O}$ to extract OOD features $P_{\\mathrm{odd}} \\in \\mathbb{R}^{m \\times n}$ . Next, a loss $\\mathcal{L}_{\\mathrm{dis}}$ is defined to maximize the distance between the virtual OOD features and ID features:", + "bbox": [ + 496, + 470, + 890, + 559 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {d i s}} = \\mathrm {K L} [ q (\\boldsymbol {O}), q (F) ] + | p (P _ {\\mathrm {o o d}}) - p (P _ {\\mathrm {i n}}) |, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 540, + 568, + 890, + 585 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $q(\\cdot)$ represents the probability distribution. By maximizing $\\mathcal{L}_{\\mathrm{dis}}$ , the distribution gap between $O$ and $F$ could be enlarged effectively, which promotes the synthesized features $O$ to contain plentiful OOD information. Finally, to achieve the goal of distinguishing OOD objects from ID objects, $P_{\\mathrm{ood}}$ and $P_{\\mathrm{in}}$ are used to calculate an uncertainty loss [7], which regularizes the detector to produce a low OOD score for the ID object features, and a high OOD score for the synthesized OOD features:", + "bbox": [ + 496, + 592, + 890, + 728 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\text {u n c e r t a i n t y}} = \\mathbb {E} _ {u \\sim P _ {\\mathrm {i n}}} [ - \\log \\frac {\\exp^ {- \\mathrm {E} (u)}}{1 + \\exp^ {- \\mathrm {E} (u)}} ] + \\tag {7} \\\\ \\mathbb {E} _ {v \\sim P _ {\\mathrm {o o d}}} [ - \\log \\frac {1}{1 + \\exp^ {- \\mathbf {E} (v)} ], \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 544, + 734, + 890, + 801 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\operatorname{E}(\\cdot)$ is the object-level energy score [7, 30]. During training, the overall objective is shown as follows:", + "bbox": [ + 496, + 808, + 890, + 839 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {\\text {i n}} + \\lambda \\cdot \\left(\\mathcal {L} _ {\\text {c y c l e}} - \\mathcal {L} _ {\\text {d i s}}\\right) + \\tau \\cdot \\mathcal {L} _ {\\text {u n c e r t a i n t y}}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 522, + 845, + 890, + 864 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\lambda$ and $\\tau$ are two hyper-parameters, which are set to 0.001 and 0.1 in the experiments.", + "bbox": [ + 496, + 869, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "23959", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Inference for OOD Object Detection", + "text_level": 1, + "bbox": [ + 76, + 90, + 392, + 107 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "During inference, we only use the LoG operator to perform structure enhancement. And the operations of recurrent VAE and synthesizing virtual OOD features are not utilized in the inference stage. Besides, we only calculate the uncertainty loss for OOD object detection [7]. Specifically, for a predicted bounding box $\\mathbf{b}$ , the processes of distinguishing OOD objects are shown as follows:", + "bbox": [ + 75, + 113, + 468, + 219 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {S} = \\frac {\\exp^ {- \\mathrm {E} (\\mathbf {b})}}{1 + \\exp^ {- \\mathrm {E} (\\mathbf {b})}}, \\quad \\mathcal {C} (\\mathbf {b}) = \\left\\{ \\begin{array}{l l} 0 & \\text {i f} \\mathcal {S} < \\gamma , \\\\ 1 & \\text {i f} \\mathcal {S} \\geq \\gamma . \\end{array} \\right. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 227, + 468, + 263 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For the output of the classifier $\\mathcal{C}(\\cdot)$ , we use the threshold mechanism [7] to distinguish the ID objects (the result is 1) from the OOD objects (the result is 0). The threshold $\\gamma$ is commonly set to 0.95 so that a high fraction of ID data is correctly classified. Finally, Algorithm 1 shows the training and evaluation details of our method.", + "bbox": [ + 75, + 271, + 470, + 361 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 375, + 209, + 393 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In the experiments, for unsupervised OOD-OD, we first evaluate our method on two different OOD object detection benchmarks [7]. Then, to further demonstrate the effectiveness of our method, we verify our method on the task of open-vocabulary detection (OVD) [33,49] that aims to detect new classes defined by an unbounded vocabulary. Finally, we evaluate our method on the task of class-incremental object detection (IOD) [22], i.e., new classes are sequentially introduced into the object detector.", + "bbox": [ + 75, + 400, + 468, + 536 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 76, + 545, + 267, + 561 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation details. We utilize Faster R-CNN [36] with RoI-Alignment layer [12] as the basic detection model. ResNet-50 [13] is taken as the backbone. The weights pretrained on ImageNet [37] are used for initialization. Besides, in Eq. (3), $\\Phi_{\\mu}(\\cdot)$ and $\\Phi_{\\sigma}(\\cdot)$ separately consist of two fully-connected layers. The iteration number $T$ is set to 3. In Eq. (5), $W_{\\mu}$ and $W_{\\sigma}$ contain two convolutional layers, respectively. All the experiments are trained using the standard SGD optimizer with a learning rate of 0.02.", + "bbox": [ + 75, + 568, + 468, + 703 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. For unsupervised OOD-OD, PASCAL VOC [8] and Berkeley DeepDrive (BDD-100k) [48] datasets are taken as the ID training data. Meanwhile, we adopt MSCOCO [29] and OpenImages [24] as the OOD datasets to evaluate the trained model. And the OOD datasets are manually examined the OOD images to ensure they do not contain ID category. For open-vocabulary detection, we follow the work [33] and conduct experiments on COCO [29]. Concretely, COCO-2017 dataset is used for training and validation. Meanwhile, 48 categories are selected as base classes and 17 are selected as new classes. For incremental object detection, we follow the standard evaluation protocol [22] and evaluate our method on PASCAL VOC [8]. We", + "bbox": [ + 75, + 704, + 470, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Algorithm 1 SR-VAE for Unsupervised OOD-OD", + "text_level": 1, + "bbox": [ + 500, + 90, + 834, + 106 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Input: ID data $\\{X,Y\\}$ , randomly initialized detector with parameter $\\theta$ , weight $\\alpha$ for the $KL$ -loss, weight $\\lambda$ for the loss $\\mathcal{L}_{\\mathrm{dis}}$ , weight $\\tau$ for the uncertainty loss $\\mathcal{L}_{\\mathrm{uncertainty}}$ .", + "bbox": [ + 500, + 108, + 890, + 152 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Output: Object detector $\\theta^{*}$ , and OOD classifier $\\mathcal{C}$ .", + "bbox": [ + 500, + 154, + 836, + 167 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "while train do", + "text_level": 1, + "bbox": [ + 500, + 169, + 599, + 181 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Sample images from the ID dataset $\\{X,Y\\}$", + "bbox": [ + 524, + 183, + 816, + 198 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Calculate the structure-enhanced map $E$ and diverse augmented features $H$ using Eq. (2) and (3).", + "bbox": [ + 524, + 198, + 890, + 227 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Synthesize the virtual OOD map $\\pmb{O}$ using Eq. (5).", + "bbox": [ + 524, + 228, + 851, + 243 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Calculate the overall training objective $\\mathcal{L}$ using Eq. (4), (6), (7), and (8).", + "bbox": [ + 524, + 243, + 890, + 272 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Update the parameters $\\theta$ based on Eq. (8).", + "bbox": [ + 524, + 273, + 803, + 289 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "end", + "text_level": 1, + "bbox": [ + 500, + 290, + 529, + 301 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "whileevaldo", + "text_level": 1, + "bbox": [ + 500, + 303, + 593, + 316 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Calculate the OOD uncertainty score using Eq. (9).", + "bbox": [ + 524, + 316, + 862, + 330 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Perform thresholding comparison using Eq. (9).", + "bbox": [ + 524, + 330, + 841, + 345 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "end", + "text_level": 1, + "bbox": [ + 500, + 347, + 529, + 359 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "initially learn 10, 15, or 19 base classes, and then introduce 10, 5, or 1 new classes as the second task.", + "bbox": [ + 500, + 392, + 890, + 422 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Metrics. To evaluate the performance of unsupervised OOD-OD, we report: (1) the false positive rate (FPR95) of OOD objects when the true positive rate of ID objects is at $95\\%$ ; (2) the area under the receiver operating characteristic curve (AUROC); (3) mean average precision (mAP). For open-vocabulary detection and incremental object detection, we only report the mAP performance.", + "bbox": [ + 496, + 424, + 892, + 530 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. OOD-OD Performance Analysis", + "text_level": 1, + "bbox": [ + 500, + 542, + 782, + 559 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 1 shows the performance of unsupervised OOD. We can see that though all methods own similar detection performance, the performance of OOD object detection differs significantly. This shows that existing detection methods are easily affected by OOD objects. Besides, for these two benchmarks, our method significantly outperforms baseline methods. Particularly, taking BDD [48] as the ID training data, based on FPR95 metric, our method separately outperforms VOS [7] by $12.04\\%$ and $13.73\\%$ . Meanwhile, based on AUROC metric, our method is $3.82\\%$ and $5.03\\%$ higher than VOS [7]. These results indicate that our method could indeed reduce the risk of misclassifying ID objects into OOD categories. Meanwhile, the proposed method could effectively synthesize virtual OOD features that deviate from the distribution of ID features, which improves the ability of distinguishing OOD objects.", + "bbox": [ + 496, + 566, + 890, + 808 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In Fig. 4 and 5, we show some OOD detection examples. We can see that compared with the baseline method [7], our method accurately distinguishes OOD objects. Taking the first two columns of Fig. 4 as examples, the baseline method misclassifies OOD objects into ID categories. Our method correctly discriminates these objects as the OOD category.", + "bbox": [ + 496, + 810, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "23960", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/8bffd9721c937ae490d2cf393286c004c543944ad7ce49b4ba00471b95dcfa1c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 94, + 88, + 248, + 167 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/1a98a1fbf3085878d70c2deb0e1ec514fd709528bedf7aec5bce8cb1d4a53153.jpg", + "image_caption": [ + "Figure 4. Detection results on the OOD images from MS-COCO. The first and second rows respectively indicate results based on VOS [7] and our method. The in-distribution dataset is BDD-100k. Blue boxes represent objects detected and classified as one of the ID categories. Green boxes indicate OOD objects. We can see that our method accurately determines OOD objects." + ], + "image_footnote": [], + "bbox": [ + 94, + 169, + 248, + 247 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c21ff860dbb8d3239b199f9e4b7e3b45240132f33f9b30dd686496765a49ef48.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 253, + 88, + 410, + 167 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0541aa68bc109428c17fa672bbd20b0d840def928497fbf5a37380f4c5ad0b4b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 253, + 169, + 410, + 247 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/43efe295148f299fa64d5a1d45eb81325756557f86c495e91cab6762ce3c2f29.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 413, + 88, + 568, + 167 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/bd1232e495747c889475853167fe76226f05144ea618777fc8e62453b173aedd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 413, + 169, + 568, + 247 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/fca7ddfbd0847ef3b86af6ccc153349f953f02fe8bf1d1f01bcb7c351b2efe59.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 571, + 88, + 727, + 167 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/07ded544478ed5eaf2a1307949b6e6a66fcb3c5905a7d6f671c5917c8a6b64e9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 571, + 169, + 727, + 247 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b85929a71880b2468b4e00677573f0e71573d2024165b422865ab12192ee4091.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 730, + 88, + 887, + 167 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/7120febea9414decc042995cb1d67a75ccf498613631982ee7c0a9729cc9b53d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 730, + 169, + 887, + 247 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/164fb8f47bf289eeb64c2b563f9a68722895bf2a8a6490b08033bc332edb09e5.jpg", + "table_caption": [], + "table_footnote": [ + "Table 1. The performance $(\\%)$ of unsupervised OOD-OD. All methods are trained based on ID data and do not use any auxiliary data. $\\uparrow$ denotes larger values are better and $\\downarrow$ denotes smaller values are better. We can see that our method outperforms the comparison methods significantly." + ], + "table_body": "
Method (VOC)FPR95 ↓AUROC ↑mAP (ID)↑
OOD: MS-COCO / OpenImages
MSP [14]70.99 / 73.1383.45 / 81.9148.7
ODIN [28]59.82 / 63.1482.20 / 82.5948.7
Mahalanobis [26]67.73 / 65.4181.45 / 81.4848.7
Gram matrices [38]62.75 / 67.4279.88 / 77.6248.7
Energy score [30]56.89 / 58.6983.69 / 82.9848.7
Generalized ODIN [16]59.57 / 70.2883.12 / 79.2348.1
CSI [42]59.91 / 57.4181.83 / 82.9548.1
GAN-synthesis [25]60.93 / 59.9783.67 / 82.6748.5
VOS (Baseline) [7]47.53 / 51.3388.70 / 85.2348.9
SR-VAE42.17 / 46.2690.28 / 87.8949.4
Method (BDD)FPR95 ↓AUROC ↑mAP (ID)↑
OOD: MS-COCO / OpenImages
MSP [14]80.94 / 79.0475.87 / 77.3831.2
ODIN [28]62.85 / 58.9274.44 / 76.6131.2
Mahalanobis [26]55.74 / 47.6985.71 / 88.0531.2
Gram matrices [38]60.93 / 77.5574.93 / 59.3831.2
Energy score [30]60.06 / 54.9777.48 / 79.6031.2
Generalized ODIN [16]57.27 / 50.1785.22 / 87.1831.8
CSI [42]47.10 / 37.0684.09 / 87.9930.6
GAN-synthesis [25]57.03 / 50.6178.82 / 81.2531.4
VOS (Baseline) [7]44.27 / 35.5486.87 / 88.5231.3
SR-VAE32.23 / 21.8190.69 / 93.5531.5
", + "bbox": [ + 81, + 304, + 468, + 595 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "These results further show that the proposed method could effectively synthesize OOD features and improve the discrimination ability of the object detector.", + "bbox": [ + 75, + 679, + 468, + 724 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Performance Analysis of OVD and IOD", + "text_level": 1, + "bbox": [ + 76, + 738, + 416, + 755 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To demonstrate the superiorities, we further verify our method on OVD [49] and IOD [22]. Table 2 shows the OVD results on COCO. Here, we directly plug our method into the baseline method [33] and do not calculate the uncertainty loss (Eq. (7)). We can see that plugging our method improves OCA's performance by $3.5\\%$ . This shows that our method effectively synthesizes virtual features, which enhances the ability of distinguishing new classes.", + "bbox": [ + 75, + 762, + 468, + 883 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 3 shows the IOD performance on PASCAL VOC.", + "bbox": [ + 96, + 885, + 467, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/a1d777d42c5ec6d24b1c3e09551422c9a4c6eccc39ccd0d03e4ec6e6f19cf32c.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodAPnovelAP
WSDDN [3]19.719.6
Cap2Det [47]20.320.1
OVR-CNN [49]22.839.9
RegionCLIP [50]26.847.5
Detric [51]27.845.0
OCA (Baseline) [33]36.649.4
OCA+Ours40.149.5
", + "bbox": [ + 566, + 304, + 826, + 422 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. OVD results $(\\%)$ on COCO. 'OCA + Ours' indicates that we directly plug our method into OCA [33].", + "bbox": [ + 498, + 425, + 890, + 454 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We still directly plug our method into the baseline method [22] and do not calculate the uncertainty loss. We can see that when the IOU threshold is set to 0.5 and 0.75, plugging our method effectively improves the performance of the baseline method. Particularly, when the IOU threshold is set to 0.75, for the three different settings, our method separately boosts iOD's performance by $2.3\\%$ , $2.9\\%$ , and $4.1\\%$ . These results show that our method could significantly improve the discrimination of the object detector.", + "bbox": [ + 498, + 460, + 890, + 597 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. Ablation and Visualization Analysis", + "text_level": 1, + "bbox": [ + 500, + 604, + 812, + 622 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we utilize BDD-100k as the ID data for training and MS-COCO as the OOD data to perform an ablation analysis of our method.", + "bbox": [ + 498, + 628, + 890, + 672 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Analysis of SR-VAE. In this paper, our method mainly contains the LoG operator used for enhancing object-related information, the VAE module used to generate diverse augmented features of the classification features, and the cycle-consistent conditional VAE module used for synthesizing virtual OOD features. Here, we make an ablation analysis of our method. Table 4 shows the ablation results. We can see that employing the proposed three modules could significantly improve the performance of OOD object detection. Particularly, compared with VOS [7], synthesizing virtual OOD features improves the performance by around $5.21\\%$ based on the FPR95 metric, which shows that the generated virtual OOD features could alleviate the impact of lacking unknown data for supervision and enhance the ability of distinguishing OOD objects. Meanwhile, employing the", + "bbox": [ + 496, + 674, + 892, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "23961", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/bccb2e7e118a079bec784a5bc10912b8985793d5727c5938c06b1af0fb933b05.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
10 + 10 settingaerocyclebirdboatbottlebuscarcatchaircowtabledoghorsebikepersonplantsheepsofatraintvmAP
Faster ILOD (50) [32]72.875.771.260.561.770.483.376.653.172.336.770.966.867.666.124.763.148.157.143.662.2
ORE (50) [19]63.570.958.942.934.176.280.776.334.166.156.170.480.272.381.842.771.668.17767.764.6
OW-DETR (50) [10]61.869.167.845.847.378.378.478.636.271.557.575.376.277.479.540.166.866.375.664.165.7
ROSETTA (50) [45]74.276.264.954.457.476.184.468.852.467.062.963.379.872.878.140.162.361.272.466.866.8
iOD (50) [22]76.074.667.555.957.675.185.477.043.770.860.166.476.072.674.639.764.060.268.560.566.3
iOD + Ours (50)75.975.268.855.355.577.785.679.349.478.261.075.381.474.579.343.872.567.070.265.769.6
iOD (75) [22]39.036.528.419.424.247.256.741.019.148.021.132.143.036.340.014.840.136.537.345.335.3
iOD + Ours (75)43.641.031.324.929.855.460.844.122.446.729.532.335.638.335.715.146.934.637.946.737.6
15 + 5 settingaerocyclebirdboatbottlebuscarcatchaircowtabledoghorsebikepersonplantsheepsofatraintvmAP
Faster ILOD (50) [32]66.578.171.854.661.468.482.682.752.174.363.178.680.578.480.436.761.759.367.959.167.9
ORE (50) [19]75.481.067.151.955.777.285.681.746.176.255.476.786.278.582.132.863.654.777.764.668.5
OW-DETR (50) [10]77.176.569.251.361.379.884.281.049.779.658.179.083.167.885.433.265.162.073.965.069.4
ROSETTA (50) [45]76.577.565.156.060.078.385.578.749.568.267.471.283.975.782.043.060.664.172.867.469.2
iOD (50) [22]78.479.766.954.856.277.784.679.147.775.061.874.781.677.580.237.858.054.673.056.167.8
iOD + Ours (50)78.380.370.551.660.279.485.976.252.579.465.281.883.776.177.941.162.863.872.667.970.4
iOD (75) [22]40.740.928.719.123.861.656.138.823.647.518.740.140.241.539.89.140.632.441.947.636.6
iOD + Ours (75)44.444.536.521.227.655.563.739.824.950.327.241.647.943.941.411.339.138.643.148.539.5
19 + 1 settingaerocyclebirdboatbottlebuscarcatchaircowtabledoghorsebikepersonplantsheepsofatraintvmAP
Faster ILOD (50) [32]64.274.773.255.553.770.882.982.651.679.758.778.881.875.377.443.173.861.769.861.168.6
ORE (50) [19]67.376.860.048.458.881.186.575.841.579.654.672.885.981.782.444.875.868.275.760.168.9
OW-DETR (50) [10]70.577.273.854.055.679.080.880.643.280.453.577.589.582.074.743.371.966.679.462.070.2
ROSETTA (50) [45]75.377.965.356.255.379.684.672.949.273.768.371.078.977.780.744.069.668.576.168.369.6
iOD (50) [22]78.277.569.455.056.078.484.279.246.679.063.278.582.779.179.944.173.266.376.457.670.2
iOD + Ours (50)76.683.574.757.058.077.085.682.551.582.761.481.682.979.877.647.474.768.474.159.071.8
iOD (75) [22]35.944.731.622.426.952.056.538.721.648.421.235.937.930.738.717.238.534.240.746.636.0
iOD + Ours (75)36.445.136.118.028.953.262.238.525.355.127.446.845.942.940.320.950.837.044.447.140.1
", + "bbox": [ + 76, + 93, + 890, + 486 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/1e747a91a4c7ffcfc771597edf7a7437809290c6bdaddb947e92b828c70af73d.jpg", + "table_caption": [ + "Table 3. Performance (%) analysis of class-incremental object detection. 'iOD + Ours' indicates that our method is plugged into iOD [22]. Here, '50' and '75' separately represent that the mAP metric is calculated when the IOU threshold is set to 0.5 and 0.75." + ], + "table_footnote": [ + "Table 4. Ablation analysis of SR-VAE for unsupervised OOD-OD. 'C-VAE' is the proposed cycle-consistent conditional VAE module. 'R-VAE' indicates the VAE module that is used to generate diverse augmented features of the classification features." + ], + "table_body": "
C-VAELoGR-VAEFPR95 ↓AUROC ↑mAP↑
✓39.06%87.83%31.3%
✓✓37.92%88.08%31.2%
✓✓35.13%89.22%31.3%
✓✓✓32.23%90.69%31.5%
", + "bbox": [ + 84, + 527, + 460, + 609 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "LoG operator and R-VAE modules further boosts the performance significantly, which demonstrates that using these two modules is beneficial for enhancing object-related information in the extracted low-level features and improving the discrimination ability of the object detector.", + "bbox": [ + 75, + 671, + 468, + 747 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Analysis of the LoG kernel size. To improve the performance of object localization, we employ the LoG operation (Eq. (1) and (2)) to perform structure enhancement, which is beneficial for strengthening object-related information. Here, we make an ablation analysis of the LoG kernel size. And we only change the kernel size. The other modules are kept unchanged. Table 5 shows the results. We can see that the performance is affected by the kernel size. Small kernel size does not sufficiently capture object structure information, which weakens the performance. For our", + "bbox": [ + 75, + 750, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/42f0c370c01f4239f365b74aa0f5e28dc90a9f52e7558fc35e5e040e9df93600.jpg", + "table_caption": [], + "table_footnote": [ + "Table 5. Ablation analysis of the LoG kernel size." + ], + "table_body": "
LoG Kernel SizeFPR95 ↓AUROC ↑mAP↑
3 × 334.96%87.94%30.9%
5 × 533.85%89.18%31.3%
7 × 733.08%89.76%31.2%
9 × 932.23%90.69%31.5%
11 × 1132.93%90.35%31.6%
", + "bbox": [ + 532, + 529, + 859, + 623 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "method, the performance of using $9 \\times 9$ kernel is the best.", + "bbox": [ + 498, + 642, + 883, + 657 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Analysis of the iteration number. To reduce the risk of misclassifying ID objects into the OOD category, we design a VAE module (Eq. (3)) to generate multiple augmented features of the classification features, which is instrumental in improving the discrimination ability of the object classifier. Here, we make an ablation analysis of the iteration number $T$ . And we only change the iteration number and keep other modules unchanged. Table 6 shows the ablation results. We can see that generating multiple augmented features could improve the detection performance effectively. This shows that enhancing the classification ability of the object classifier is meaningful. Besides, we observe that when the iteration number is larger than a certain threshold, the performance could not be boosted effectively. The reason may be that the object classifier is a linear classifier, which could not sufficiently exploit these augmented fea", + "bbox": [ + 496, + 659, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "23962", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/89f9fa3f2b3c4ee91d39fa6ceee542e2df060c0a96fa6b691b270aa2a318eb8b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 94, + 88, + 263, + 167 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/35812b7634678e8388946905d41b7e063c09f55308a2180fb99c7982698229b4.jpg", + "image_caption": [ + "Figure 5. Detection results on OpenImages. The first and second rows respectively indicate results based on VOS [7] and our method." + ], + "image_footnote": [], + "bbox": [ + 94, + 167, + 263, + 247 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/bd12fc77748a985d8bb3d6e28e09063b395e30d408d7ea6d313a1e93e54a3178.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 263, + 88, + 428, + 167 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1a0f80da737a31486176cd41f90c8effa2ba0b7ef064d18c59c82ff216b0bbd0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 259, + 169, + 428, + 247 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ce54a6a8450f62fbe26910666007291a73c6c36b23d57f6ff1cef06e056a6ae0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 429, + 88, + 553, + 167 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/952c27b9e295be94e01673f3bf1fbd1c8a41229bc87eddb1c19f2a5688ad978a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 429, + 169, + 553, + 247 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ba1d69ea83b6c9090394af24215c0e95dea0e2ffc58933bd933c857dee4848db.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 555, + 88, + 720, + 167 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/fb3c03b8671d8cb98fdb2e60b9d1be9dcdc6fb1b7bb93e71e1375dd98bc0caa0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 555, + 169, + 720, + 247 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/56ab255a820cd51ca4122b810fc156a2aef5e93d1b94a3ccbf110d905a5c0499.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 722, + 88, + 888, + 167 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3bce11c4fedd3e220508e5d102b2d758a98fc9add14a228f66d3781be67e4b02.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 722, + 169, + 888, + 247 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f87167f4f4638cb509a790a55dfc659d9405f1116016ef9f7097fc0d29510751.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 89, + 272, + 222, + 343 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/24c97d69e457679bad55f10337412ade86c7d39a79a20d224d51ce06afeda4ca.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 89, + 343, + 220, + 412 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1f0c47b6ceaa425026c5b1b6d4c1461846a093fa4ff687be6b508baeb9607d66.jpg", + "image_caption": [ + "(a) Input Image" + ], + "image_footnote": [], + "bbox": [ + 89, + 415, + 220, + 483 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ac5149f738ce1b9416fe0c90a7c67e81d282591a9823f4a6e3c03f52677d1a74.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 223, + 272, + 354, + 342 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5a2a6274fbb080542fe601c4f673d6fb49083002714f18842191ffc1ad763c69.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 225, + 343, + 354, + 412 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/41bd8335e03dfe6faecdcf3e9f79942bd18890a5759d113d0a09feded9c2150b.jpg", + "image_caption": [ + "(b) Structure Map" + ], + "image_footnote": [], + "bbox": [ + 225, + 415, + 354, + 483 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/22365964cae6857acd59b6231c7fff42b0b1f34f11fb1b4b97a4d81fb589df97.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 357, + 272, + 490, + 342 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/75d10ba57a81d1052d0e970ec8b5c0bcf4253f50cae637dea9cd2c247d36ceb7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 357, + 343, + 488, + 412 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/568b22420d49cfd2e3628219a99b5b71d6bfe217f44f242199e6d07be7ab1b48.jpg", + "image_caption": [ + "(c) Virtual OOD Map" + ], + "image_footnote": [], + "bbox": [ + 357, + 415, + 488, + 483 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ef925ab32eaf3aee4ede58697db25ae2ec4e1c51372e3c0b29c4392aeb6480c3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 491, + 272, + 624, + 342 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ce7d39d16192018f2dbc35b287b9d623ee875ccdb558d60df1405258d6211895.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 491, + 343, + 622, + 412 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/de4efece6ebf8e033627f5ef8966824b5145c0e73dc38298d6b42e06f82b467b.jpg", + "image_caption": [ + "(d) Input Image", + "Figure 6. Visualization of the Structure-Enhanced map $E$ (Eq. (2)) and Virtual OOD map $\\pmb{O}$ (Eq. (5)) based on the OOD data (MS-COCO). For each feature map, the channels corresponding to the maximum value are selected for visualization." + ], + "image_footnote": [], + "bbox": [ + 491, + 414, + 622, + 483 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8cbd93483275948c8d67b8e2e133475aa5b4df7c6c4e51f7ab85c82e85c15d52.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 627, + 272, + 756, + 342 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/034b8de9b7568051921b25ef07845aae1de6dd6b4e0d56c344cdb78f8cc87d23.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 627, + 343, + 756, + 412 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ebde2aeee30eb042bd0f2747e45b0c458ccbcfee722540513cb4989d08425e99.jpg", + "image_caption": [ + "(e) Structure Map" + ], + "image_footnote": [], + "bbox": [ + 627, + 414, + 756, + 483 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/65784a6220bf019f31080fd3f6583faba573182198bffb4d7c8b1b185a41f427.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 759, + 272, + 890, + 342 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/67e5e180659a3d674758c1558576bc7a28a81c29dd0f3a27151f2e310ae86aaf.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 759, + 343, + 890, + 412 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ebaa659f64db983c2f9a0ee7c7db643d92d36b242ea33e525894c689ba3b9b73.jpg", + "image_caption": [ + "(f) Virtual OOD Map" + ], + "image_footnote": [], + "bbox": [ + 759, + 414, + 890, + 483 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/8a156ea7ccea7169a3bd65e803b44d6a8830fbdcf279354e3c7a039e771adedb.jpg", + "table_caption": [], + "table_footnote": [ + "Table 6. Ablation analysis of the iteration number $T$ ." + ], + "table_body": "
Iteration Number TFPR95 ↓AUROC ↑mAP↑
137.24%88.12%31.2%
332.23%90.69%31.5%
532.46%90.23%31.3%
732.93%90.07%31.2%
", + "bbox": [ + 101, + 542, + 446, + 625 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "tures. For our method, when the iteration number is set to 3, the performance of OOD detection is the best.", + "bbox": [ + 75, + 642, + 468, + 672 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Analysis of cycle-consistent conditional VAE. In order to effectively synthesize virtual OOD features, we propose a cycle-consistency loss $\\mathcal{L}_{\\mathrm{cycle}}$ (Eq. (8)) to reduce the impact of lacking paired samples. Here, we make an ablation analysis of $\\mathcal{L}_{\\mathrm{cycle}}$ . Based on the FPR95 metric, removing $\\mathcal{L}_{\\mathrm{cycle}}$ increases the performance by around $3.8\\%$ . This shows using the cycle-consistency loss $\\mathcal{L}_{\\mathrm{cycle}}$ is beneficial for synthesizing virtual OOD features and improving the ability of distinguishing OOD objects.", + "bbox": [ + 75, + 672, + 468, + 809 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Visualization analysis. Fig. 6 shows some visualization examples. Particularly, we can see that the map $E$ contains plentiful object-related information, which shows that using the LoG operation is indeed helpful for enhancing object-related information. Furthermore, we observe that the synthesized virtual OOD map $O$ involves sufficient informa", + "bbox": [ + 75, + 810, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "tion that is different from object-related features, which indicates that leveraging the synthesized OOD features is instrumental in reducing the impact of lacking unknown data and improving the discrimination ability.", + "bbox": [ + 496, + 546, + 890, + 607 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 618, + 617, + 633 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "For unsupervised OOD-OD, we propose an approach of Structure-Enhanced Recurrent VAE. Particularly, to reduce the risk of misclassifying ID objects into the OOD category, an LoG operator and a dedicated recurrent VAE used to generate diverse augmented features are presented to strengthen the discrimination ability. Meanwhile, to alleviate the impact of lacking unknown data, we design a cycle-consistent conditional VAE to synthesize virtual OOD features, which boosts the performance of distinguishing OOD objects. Extensive experiments on three different tasks and visualization analyses demonstrate the superiorities of our method.", + "bbox": [ + 496, + 643, + 892, + 809 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement. Our work was supported in part by Key Research and Development Program of Shaanxi under Grant 2021ZDLGY01-03, the National Natural Science Foundation of China under Grant 62102293, 62132016, 62171343, and 62071361, and the Fundamental Research Funds for the Central Universities ZDRC2102.", + "bbox": [ + 496, + 810, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "23963", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Martin Arjovsky, Léon Bottou, Ishaan Gulrajani, and David Lopez-Paz. Invariant risk minimization. arXiv preprint arXiv:1907.02893, 2019. 2", + "[2] Abhijit Bendale and Terrance E Boult. Towards open set deep networks. In CVPR, pages 1563-1572, 2016. 2", + "[3] Hakan Bilen and Andrea Vedaldi. 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CVPR, 2022. 2" + ], + "bbox": [ + 501, + 90, + 890, + 246 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "23965", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Discriminating Known From Unknown Objects via Structure-Enhanced Recurrent Variational AutoEncoder/7f53095f-c4ed-4448-89ff-3db316832dfc_model.json b/2023/Discriminating Known From Unknown Objects via Structure-Enhanced Recurrent Variational AutoEncoder/7f53095f-c4ed-4448-89ff-3db316832dfc_model.json new file mode 100644 index 0000000000000000000000000000000000000000..2f08d913891dcf4d24ce7b9fa143102609525ccb --- /dev/null +++ b/2023/Discriminating Known From Unknown Objects via Structure-Enhanced Recurrent Variational AutoEncoder/7f53095f-c4ed-4448-89ff-3db316832dfc_model.json @@ -0,0 +1,2662 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.198, + 0.131, + 0.773, + 0.175 + ], + "angle": 0, + "content": "Discriminating Known from Unknown Objects via Structure-Enhanced Recurrent Variational AutoEncoder" + }, + { + "type": "text", + "bbox": [ + 0.221, + 0.205, + 0.748, + 0.257 + ], + "angle": 0, + "content": "Among Wu, Cheng Deng* \nSchool of Electronic Engineering, Xidian University, Xi'an, China \namwu@xidian.edu.cn, chdeng@mail.xidian.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.292, + 0.314, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.324, + 0.474, + 0.749 + ], + "angle": 0, + "content": "Discriminating known from unknown objects is an important essential ability for human beings. To simulate this ability, a task of unsupervised out-of-distribution object detection (OOD-OD) is proposed to detect the objects that are never-seen-before during model training, which is beneficial for promoting the safe deployment of object detectors. Due to lacking unknown data for supervision, for this task, the main challenge lies in how to leverage the known in-distribution (ID) data to improve the detector's discrimination ability. In this paper, we first propose a method of Structure-Enhanced Recurrent Variational AutoEncoder (SR-VAE), which mainly consists of two dedicated recurrent VAE branches. Specifically, to boost the performance of object localization, we explore utilizing the classical Laplacian of Gaussian (Log) operator to enhance the structure information in the extracted low-level features. Meanwhile, we design a VAE branch that recurrently generates the augmentation of the classification features to strengthen the discrimination ability of the object classifier. Finally, to alleviate the impact of lacking unknown data, another cycle-consistent conditional VAE branch is proposed to synthesize virtual OOD features that deviate from the distribution of ID features, which improves the capability of distinguishing OOD objects. In the experiments, our method is evaluated on OOD-OD, open-vocabulary detection, and incremental object detection. The significant performance gains over baselines show the superiorities of our method. The code will be released at https://github.com/AmingWu/SR-VAE." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.776, + 0.21, + 0.792 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.802, + 0.47, + 0.879 + ], + "angle": 0, + "content": "Recent years have witnessed the rapid development of deep learning based object detection [5,12,34,36,41], which often follows a close-set assumption that the training and testing processes share the same category space. However, the practical scenario is open and filled with unknown" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.291, + 0.891, + 0.449 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.453, + 0.895, + 0.578 + ], + "angle": 0, + "content": "Figure 1. Discriminating known from unknown objects (as shown in green boxes) by synthesizing virtual OOD features. For OOD-OD, to alleviate the impact of lacking unknown data, we present an SR-VAE method to constrain the synthesized features (as shown in blue stars) to deviate from the distribution of ID features (as shown in orange). Meanwhile, we consider enhancing the discrimination of the classifier to reduce the risk of misclassifying the ID objects into the OOD category. Through these operations, the ability of distinguishing OOD objects could be improved significantly." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.583, + 0.892, + 0.688 + ], + "angle": 0, + "content": "objects, e.g., in Fig. 1, an autonomous vehicle may encounter an unseen camel, presenting significant challenges for close-set assumption based detectors. To promote the safe application of detectors, a task of unsupervised out-of-distribution object detection (OOD-OD) [7] is recently proposed, which aims to detect the objects never-seen-before during training without accessing any auxiliary data." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.893, + 0.885 + ], + "angle": 0, + "content": "Towards unsupervised OOD-OD, since there is no auxiliary data available for supervision, leveraging the known in-distribution (ID) data to enhance the detector's discrimination ability becomes the critical challenge. One feasible solution is to synthesize a series of virtual OOD features [7, 35] based on the ID data, which is beneficial for promoting the object detector to learn a clear decision boundary between ID and OOD objects. To this end, the work [7] attempts to synthesize virtual features from the low-likelihood region of the estimated class-conditional distribution. However, this method requires a large number of objects for each category to estimate the distribution, limiting its application to the case of few samples." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "As shown in Fig. 1, in this paper, we consider improvis" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.888, + 0.222, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23956" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.258 + ], + "angle": 0, + "content": "ing the performance of OOD object detection from two perspectives: One is to strengthen the discrimination capability of the object classifier for the known ID objects, which is conducive to reduce the risk of misclassifying the ID objects into the OOD category. Another is to synthesize the virtual OOD features that significantly deviate from the distribution of the ID features, which is instrumental in boosting the performance of distinguishing OOD objects from ID objects. To attain these two goals, we explore exploiting Variational AutoEncoder (VAE) [15, 20] to separately generate the augmented ID features and virtual OOD features." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.26, + 0.473, + 0.442 + ], + "angle": 0, + "content": "Specifically, an approach of Structure-Enhanced Recurrent Variational AutoEncoder (SR-VAE) is proposed, which mainly consists of two dedicated recurrent VAE branches. In general, an object detector should first localize objects. Then, an object classifier is used to discriminate these objects [12, 36]. To improve the localization performance, enhancing the object-related information in the extracted features is meaningful. To this end, after extracting the low-level features of an input image, we present to utilize the classical Laplacian of Gaussian (LoG) operator [23] to obtain structure-related information, which is used to fuse into the existing features to strengthen the localization ability." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.443, + 0.473, + 0.625 + ], + "angle": 0, + "content": "Next, in order to enhance the discrimination ability, inspired by Invariant Risk Minimization [1], we explore constructing a set of diverse environments to intensify the variance of the input classification features. Concretely, a VAE module [17, 20, 43] is exploited to recurrently output multiple augmented features of the classification features, i.e., the current output is taken as the input of the next iteration. Since the input of each iteration is different, by means of the variation operation, the diversity of the output features could be enlarged. Then, the discrimination ability is improved by minimizing the prediction discrepancy between the augmented features and the classification features." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.626, + 0.473, + 0.838 + ], + "angle": 0, + "content": "Finally, to alleviate the impact of lacking unknown data, we present a cycle-consistent conditional VAE [40] to synthesize virtual OOD features in the absence of paired supervision samples. Concretely, to ameliorate the synthesized features to deviate from the distribution of ID features, we first insert label information in the latent space to force a deterministic constrained representation. Meanwhile, by maximizing the discrepancy between the synthesized features and the input features, the synthesized features could be facilitated to contain plentiful OOD-relevant information, which enhances the ability of distinguishing OOD objects. In the experiments, our method is separately evaluated on three different tasks. Extensive experimental results on multiple datasets demonstrate the superiorities of our method." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.839, + 0.402, + 0.853 + ], + "angle": 0, + "content": "The contributions are summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.472, + 0.901 + ], + "angle": 0, + "content": "(1) For unsupervised OOD-OD, we observe that using the classical LoG operator could effectively enhance object-related information in the extracted low-level features." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.167 + ], + "angle": 0, + "content": "(2) To reduce the risk of misclassifying ID objects into the OOD category, we design a dedicated recurrent VAE to generate diverse augmented features of the input classification features, which is beneficial for improving the discrimination ability of the object classifier." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.168, + 0.894, + 0.228 + ], + "angle": 0, + "content": "(3) To alleviate the impact of lacking unknown data for supervision, we present a cycle-consistent conditional VAE to synthesize virtual OOD features, which is instrumental in distinguishing OOD objects from ID objects." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.228, + 0.895, + 0.304 + ], + "angle": 0, + "content": "(4) In the experiments, our method is evaluated on OOD-OD [7], open-vocabulary detection [33, 49], and incremental object detection [22, 39]. Particularly, for OpenImages dataset [24], compared with the baseline method [7], our method significantly reduces FPR95 by around \\(13.73\\%\\)." + }, + { + "type": "list", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.304 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.317, + 0.642, + 0.332 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.342, + 0.895, + 0.553 + ], + "angle": 0, + "content": "OOD Detection. In order to promote the safe application of models in real scenarios, OOD detection [4, 14, 18] has recently attracted much attention, whose goal is to distinguish OOD data from ID data. Most methods [27, 31, 46, 52] focus on OOD image classification and explore a proper regularization-based method for this task. Particularly, Bendale et al. [2] developed the OpenMax score based on the extreme value theory. Liu et al. [30] proposed to utilize the energy score to discriminate OOD data from ID data. Zhou [52] rethought the commonly used reconstruction autoencoder for OOD detection. Though these methods have been demonstrated to be effective, since object detection involves object localization and classification, these methods could not directly apply to OOD-OD." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.554, + 0.895, + 0.84 + ], + "angle": 0, + "content": "Recently, unsupervised OOD-OD [7] is proposed to localize and recognize the objects never-seen-before during training. For this task, Du et al. [7] proposed to use large-scale samples to estimate the distribution of each ID category, which is used to synthesize virtual OOD features. However, calculating accurate distribution estimation may limit its application in real scenarios. Harakeh et al. [11] designed an uncertainty estimation method for the localization branch, which could not well address OOD-OD that involves localization and classification. Besides, the work [6] proposed to use auxiliary video datasets to learn unknown-aware knowledge to effectively improve the performance of distinguishing OOD objects, which could not be used for unsupervised OOD-OD. In this paper, we explore employing the idea of VAE [15, 20] to synthesize virtual OOD features that significantly deviate from the distribution of ID features. And these virtual features are used to strengthen the discrimination ability. Experimental results on three different tasks show the effectiveness of our method." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Variational AutoEncoder. The goal of VAE [15,20,21, 40] is to map the input data to a multivariate latent distribution, which efficiently addresses the generation problem for high-dimensional data. Most existing methods [15, 17, 44]" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23957" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.09, + 0.892, + 0.299 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.303, + 0.894, + 0.388 + ], + "angle": 0, + "content": "Figure 2. Structure-Enhanced Recurrent Variational AutoEncoder for Unsupervised OOD-OD. To improve localization performance, we employ the LoG operator to enhance the structure-related information in the features extracted by the backbone network. Meanwhile, we design a VAE module to recurrently generate diverse augmented features of the input classification features, which is beneficial for strengthening the discrimination ability of the object classifier. Finally, to alleviate the impact of lacking unknown data, we propose a cycle-consistent conditional VAE to synthesize virtual OOD features that deviate from the distribution of the ID features significantly, which boosts the performance of distinguishing OOD objects." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.4, + 0.473, + 0.552 + ], + "angle": 0, + "content": "attempt to adjust the latent representations to generate clear images containing rich content. Particularly, \\(\\beta\\)-VAE [15] is an implementation with a weighted Kullback-Leibler (KL) divergence term to automatically discover disentangled representations without supervision. Conditional VAE [40] inserts label information in the latent space to force a deterministic constrained representation. Different from the above works focusing on pixel-level generation, we explore using VAE to generate virtual OOD features. Experimental results on OOD-OD show the advantages of our method." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.565, + 0.407, + 0.58 + ], + "angle": 0, + "content": "3. Structure-Enhanced Recurrent VAE" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.59, + 0.47, + 0.651 + ], + "angle": 0, + "content": "In this paper, we follow the settings introduced in the work [7]. During training, we can only access the ID data. During inference, the object detector should own the capability of distinguishing ID objects from OOD objects." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.66, + 0.441, + 0.677 + ], + "angle": 0, + "content": "3.1. Structure Enhancement via LoG Operator" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.683, + 0.469, + 0.803 + ], + "angle": 0, + "content": "In general, an object detector should first localize objects accurately and then distinguish them as ID categories or OOD categories. To this end, it is important to enhance object-related information (e.g., object structure information). In the field of image processing, LoG operator [23] is a popular algorithm for edge detection. We explore performing the LoG operation on the extracted low-level features to strengthen the structure-relevant information." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.803, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Concretely, as shown in Fig. 2, we follow the baseline work [7] and adopt the widely used object detector, i.e., Faster R-CNN [12, 36], as the basic detection model. Given an input image, we first employ the backbone network, e.g., ResNet [13], to extract the corresponding feature map \\( F \\in \\mathbb{R}^{w \\times h \\times c} \\), where \\( w \\), \\( h \\), and \\( c \\) separately denote width, height, and channel number. To obtain rich structure" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.4, + 0.874, + 0.415 + ], + "angle": 0, + "content": "information, a \\(9 \\times 9\\) LoG kernel \\(\\mathcal{G}\\) is defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.519, + 0.422, + 0.892, + 0.55 + ], + "angle": 0, + "content": "\\[\n\\mathcal {G} = \\left[ \\begin{array}{c c c c c c c c c} 0 & 1 & 1 & 2 & 2 & 2 & 1 & 1 & 0 \\\\ 1 & 2 & 4 & 5 & 5 & 5 & 4 & 2 & 1 \\\\ 1 & 4 & 5 & 3 & 0 & 3 & 5 & 4 & 1 \\\\ 2 & 5 & 3 & - 1 2 & - 2 4 & - 1 2 & 3 & 5 & 2 \\\\ 2 & 5 & 0 & - 2 4 & - 4 0 & - 2 4 & 0 & 5 & 2 \\\\ 2 & 5 & 3 & - 1 2 & - 2 4 & - 1 2 & 3 & 5 & 2 \\\\ 1 & 4 & 5 & 3 & 0 & 3 & 5 & 4 & 1 \\\\ 1 & 2 & 4 & 5 & 5 & 5 & 4 & 2 & 1 \\\\ 0 & 1 & 1 & 2 & 2 & 2 & 1 & 1 & 0 \\end{array} \\right]. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.558, + 0.893, + 0.603 + ], + "angle": 0, + "content": "Next, \\(\\mathcal{G}\\) is used to perform a convolution operation on \\(F\\) to obtain the structure-enhanced map \\(E\\in \\mathbb{R}^{w\\times h\\times c}\\). The processes are shown as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.585, + 0.614, + 0.892, + 0.632 + ], + "angle": 0, + "content": "\\[\n\\mathcal {E} = F * \\mathcal {G}, \\quad E = \\Psi ([ F, \\mathcal {E} ]), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.642, + 0.894, + 0.749 + ], + "angle": 0, + "content": "where \\(\\mathcal{E} \\in \\mathbb{R}^{w \\times h \\times c}\\) is the convolutional result containing plentiful structure-related information. \\(\\Psi(\\cdot) \\in \\mathbb{R}^{1 \\times 1 \\times 2c \\times c}\\) represents one-layer convolution to transform the number of channels. By fusing the structure information into existing features, the object-related information in \\(F\\) could be enhanced effectively, which is instrumental in improving the performance of object localization." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.757, + 0.886, + 0.773 + ], + "angle": 0, + "content": "3.2. Recurrent VAE for Improving Discrimination" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.84 + ], + "angle": 0, + "content": "To reduce the risk of misclassifying ID objects into the OOD category, we design a VAE module to recurrently generate diverse augmented features of the classification features, which enhances the discrimination ability." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.894, + 0.902 + ], + "angle": 0, + "content": "Specifically, as shown in Fig. 2, the enhanced map \\( E \\) is taken as the input of the RPN module to obtain a set of object proposals \\( \\mathcal{O} \\). Based on \\( \\mathcal{O} \\), RoI-Alignment followed by RoI-Feature extraction [12] is performed on \\( E \\) to output" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23958" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.089, + 0.473, + 0.196 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.198, + 0.47, + 0.295 + ], + "angle": 0, + "content": "Figure 3. Cycle-consistent conditional VAE for synthesizing virtual OOD features. During the forward process, the OOD features \\( \\pmb{O} \\) are generated based on the ID features \\( F \\). And during the backward process, the features \\( \\pmb{F} \\) are generated based on \\( \\pmb{O} \\). By minimizing the cycle-consistency loss between \\( F \\) and \\( \\pmb{F} \\), the synthesized features \\( \\pmb{O} \\) could be promoted to contain plentiful information that deviates from the distribution of the ID features." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.302, + 0.471, + 0.422 + ], + "angle": 0, + "content": "\\(P_{\\mathrm{in}} \\in \\mathbb{R}^{m \\times n}\\), where \\(m\\) and \\(n\\) separately denote the number of proposals and channels. Next, we first define two fully-connected networks (i.e., \\(\\Phi_{\\mu}(\\cdot)\\) and \\(\\Phi_{\\sigma}(\\cdot)\\)) as the encoder to estimate the corresponding means and variances. Then, an encoding operation is performed on the input. Finally, a decoder \\(\\Theta(\\cdot)\\) consisting of three fully-connected layers is leveraged to calculate the output. The overall processes at the \\(t\\)-th iteration are shown as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.134, + 0.431, + 0.47, + 0.453 + ], + "angle": 0, + "content": "\\[\n\\mu_ {t} = \\Phi_ {\\mu} \\left(H _ {t - 1}\\right), \\quad \\sigma_ {t} = \\Phi_ {\\sigma} \\left(H _ {t - 1}\\right), \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.137, + 0.452, + 0.411, + 0.466 + ], + "angle": 0, + "content": "\\[\nh _ {t} = \\mu_ {t} + \\epsilon \\cdot \\exp (\\sigma_ {t}), \\qquad H _ {t} = \\Theta (h _ {t}),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.476, + 0.47, + 0.552 + ], + "angle": 0, + "content": "where \\(H_{t - 1}\\in \\mathbb{R}^{m\\times n}\\) and \\(H_{t}\\in \\mathbb{R}^{m\\times n}\\) respectively indicate the output of the previous iteration and that of the current iteration. And \\(H_0 = P_{\\mathrm{in}}\\) \\(\\mu_t\\in \\mathbb{R}^{m\\times n}\\) and \\(\\sigma_t\\in \\mathbb{R}^{m\\times n}\\) are the estimated means and variances. \\(\\epsilon\\) denotes Gaussian noise sampled from \\(\\mathcal{N}(0,I)\\)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.552, + 0.471, + 0.675 + ], + "angle": 0, + "content": "Through \\( T \\) iterations, we can obtain a set of augmented features \\( H = \\{H_{1},\\dots ,H_{T}\\} \\). Finally, by minimizing the \\( KL \\)-divergence between the prediction probabilities from \\( H_{t} \\) and \\( P_{\\mathrm{in}} \\), the discrimination ability of the object classifier could be enhanced effectively. During training, \\( P_{\\mathrm{in}} \\) is taken as the input of the object classifier and regressor to calculate the classification and localization losses. The joint training objective is shown as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.097, + 0.683, + 0.47, + 0.725 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {i n}} = \\mathcal {L} _ {\\mathrm {d e t}} + \\alpha \\cdot \\frac {1}{T} \\sum_ {t = 1} ^ {T} \\mathrm {K L} [ p (H _ {t} | H _ {t - 1}), p (P _ {\\mathrm {i n}}) ], \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.733, + 0.47, + 0.794 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{\\mathrm{det}}\\) is the sum of the classification loss \\(\\mathcal{L}_{\\mathrm{cls}}\\) and the localization loss \\(\\mathcal{L}_{\\mathrm{loc}}\\), i.e., \\(\\mathcal{L}_{\\mathrm{det}} = \\mathcal{L}_{\\mathrm{cls}} + \\mathcal{L}_{\\mathrm{loc}}\\). \\(\\alpha\\) is a hyper-parameter. In the experiments, \\(\\alpha\\) is set to 0.001. \\(p(\\cdot)\\) indicates the prediction probability of the object classifier." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.802, + 0.388, + 0.818 + ], + "angle": 0, + "content": "3.3. Synthesizing Virtual OOD Features" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Due to lacking unknown data for supervision, it is prone to misclassify OOD objects into ID categories. Hence, synthesizing virtual OOD data is important to distinguish OOD objects. A straightforward idea is to train generative models, e.g., GANs [9], to synthesize images, which is difficult" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.121 + ], + "angle": 0, + "content": "to optimize [7]. Instead, we propose a cycle-consistent conditional VAE to synthesize virtual OOD features." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.122, + 0.892, + 0.198 + ], + "angle": 0, + "content": "Particularly, as shown in Fig. 3, during the forward process, the extracted features \\(F\\) and corresponding ID label [1, 0] are first concatenated as \\(\\hat{F} \\in \\mathbb{R}^{w \\times h \\times (c + 2)}\\). Then, two convolutional networks \\(W_{\\mu}\\) and \\(W_{\\sigma}\\) are defined to estimate the corresponding means and variances:" + }, + { + "type": "equation", + "bbox": [ + 0.578, + 0.203, + 0.892, + 0.223 + ], + "angle": 0, + "content": "\\[\n\\mu_ {f} = W _ {\\mu} * \\hat {F}, \\quad \\sigma_ {f} = W _ {\\sigma} * \\hat {F}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.228, + 0.892, + 0.334 + ], + "angle": 0, + "content": "where \\(\\mu_f \\in \\mathbb{R}^{w \\times h \\times c}\\) and \\(\\sigma_f \\in \\mathbb{R}^{w \\times h \\times c}\\). And an encoding operation is performed to obtain \\(Z \\in \\mathbb{R}^{w \\times h \\times c}\\), i.e., \\(Z = \\mu_f + \\epsilon \\cdot \\exp(\\sigma_f)\\). Next, in order to generate virtual OOD features, \\(Z\\) and corresponding OOD label [0, 1] are concatenated as \\(\\hat{Z} \\in \\mathbb{R}^{w \\times h \\times (c+2)}\\). A decoding network \\(\\mathcal{D}\\) consisting of three convolutional layers is performed on \\(\\hat{Z}\\) to obtain the virtual OOD map \\(O \\in \\mathbb{R}^{w \\times h \\times c}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.335, + 0.892, + 0.472 + ], + "angle": 0, + "content": "During the backward process, to alleviate the impact of lacking paired data for supervision, the concatenation result of \\( \\pmb{O} \\) and label [0, 1] is made convolution with \\( W_{\\mu} \\) and \\( W_{\\sigma} \\). Next, we still take the concatenation of the encoding result and label [1, 0] as the input of the decoder \\( \\mathcal{D} \\) to obtain the output \\( \\pmb{F} \\in \\mathbb{R}^{w \\times h \\times c} \\). The operations are the same as the forward process. Finally, we introduce a cycle-consistency loss to reduce the discrepancy between \\( \\pmb{F} \\) and \\( F \\), i.e., \\( \\mathcal{L}_{\\mathrm{cycle}} = \\frac{1}{wh}\\sum |F - F| \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.471, + 0.892, + 0.56 + ], + "angle": 0, + "content": "Moreover, to promote \\( \\pmb{O} \\) to deviate from the distribution of \\( F \\), as shown in Fig. 2, based on the object proposals \\( \\mathcal{O} \\), RoI-Alignment followed by RoI-Feature extraction is performed on \\( \\pmb{O} \\) to extract OOD features \\( P_{\\mathrm{odd}} \\in \\mathbb{R}^{m \\times n} \\). Next, a loss \\( \\mathcal{L}_{\\mathrm{dis}} \\) is defined to maximize the distance between the virtual OOD features and ID features:" + }, + { + "type": "equation", + "bbox": [ + 0.541, + 0.569, + 0.892, + 0.587 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {d i s}} = \\mathrm {K L} [ q (\\boldsymbol {O}), q (F) ] + | p (P _ {\\mathrm {o o d}}) - p (P _ {\\mathrm {i n}}) |, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.593, + 0.892, + 0.729 + ], + "angle": 0, + "content": "where \\( q(\\cdot) \\) represents the probability distribution. By maximizing \\( \\mathcal{L}_{\\mathrm{dis}} \\), the distribution gap between \\( O \\) and \\( F \\) could be enlarged effectively, which promotes the synthesized features \\( O \\) to contain plentiful OOD information. Finally, to achieve the goal of distinguishing OOD objects from ID objects, \\( P_{\\mathrm{ood}} \\) and \\( P_{\\mathrm{in}} \\) are used to calculate an uncertainty loss [7], which regularizes the detector to produce a low OOD score for the ID object features, and a high OOD score for the synthesized OOD features:" + }, + { + "type": "equation", + "bbox": [ + 0.545, + 0.736, + 0.892, + 0.803 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\text {u n c e r t a i n t y}} = \\mathbb {E} _ {u \\sim P _ {\\mathrm {i n}}} [ - \\log \\frac {\\exp^ {- \\mathrm {E} (u)}}{1 + \\exp^ {- \\mathrm {E} (u)}} ] + \\tag {7} \\\\ \\mathbb {E} _ {v \\sim P _ {\\mathrm {o o d}}} [ - \\log \\frac {1}{1 + \\exp^ {- \\mathbf {E} (v)} ], \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.809, + 0.892, + 0.84 + ], + "angle": 0, + "content": "where \\(\\operatorname{E}(\\cdot)\\) is the object-level energy score [7, 30]. During training, the overall objective is shown as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.524, + 0.847, + 0.892, + 0.865 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {\\text {i n}} + \\lambda \\cdot \\left(\\mathcal {L} _ {\\text {c y c l e}} - \\mathcal {L} _ {\\text {d i s}}\\right) + \\tau \\cdot \\mathcal {L} _ {\\text {u n c e r t a i n t y}}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "where \\(\\lambda\\) and \\(\\tau\\) are two hyper-parameters, which are set to 0.001 and 0.1 in the experiments." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23959" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.091, + 0.393, + 0.108 + ], + "angle": 0, + "content": "3.4. Inference for OOD Object Detection" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.114, + 0.47, + 0.22 + ], + "angle": 0, + "content": "During inference, we only use the LoG operator to perform structure enhancement. And the operations of recurrent VAE and synthesizing virtual OOD features are not utilized in the inference stage. Besides, we only calculate the uncertainty loss for OOD object detection [7]. Specifically, for a predicted bounding box \\(\\mathbf{b}\\), the processes of distinguishing OOD objects are shown as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.097, + 0.228, + 0.47, + 0.264 + ], + "angle": 0, + "content": "\\[\n\\mathcal {S} = \\frac {\\exp^ {- \\mathrm {E} (\\mathbf {b})}}{1 + \\exp^ {- \\mathrm {E} (\\mathbf {b})}}, \\quad \\mathcal {C} (\\mathbf {b}) = \\left\\{ \\begin{array}{l l} 0 & \\text {i f} \\mathcal {S} < \\gamma , \\\\ 1 & \\text {i f} \\mathcal {S} \\geq \\gamma . \\end{array} \\right. \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.272, + 0.471, + 0.362 + ], + "angle": 0, + "content": "For the output of the classifier \\(\\mathcal{C}(\\cdot)\\), we use the threshold mechanism [7] to distinguish the ID objects (the result is 1) from the OOD objects (the result is 0). The threshold \\(\\gamma\\) is commonly set to 0.95 so that a high fraction of ID data is correctly classified. Finally, Algorithm 1 shows the training and evaluation details of our method." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.376, + 0.21, + 0.394 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.401, + 0.47, + 0.537 + ], + "angle": 0, + "content": "In the experiments, for unsupervised OOD-OD, we first evaluate our method on two different OOD object detection benchmarks [7]. Then, to further demonstrate the effectiveness of our method, we verify our method on the task of open-vocabulary detection (OVD) [33,49] that aims to detect new classes defined by an unbounded vocabulary. Finally, we evaluate our method on the task of class-incremental object detection (IOD) [22], i.e., new classes are sequentially introduced into the object detector." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.546, + 0.268, + 0.563 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.569, + 0.47, + 0.704 + ], + "angle": 0, + "content": "Implementation details. We utilize Faster R-CNN [36] with RoI-Alignment layer [12] as the basic detection model. ResNet-50 [13] is taken as the backbone. The weights pretrained on ImageNet [37] are used for initialization. Besides, in Eq. (3), \\(\\Phi_{\\mu}(\\cdot)\\) and \\(\\Phi_{\\sigma}(\\cdot)\\) separately consist of two fully-connected layers. The iteration number \\(T\\) is set to 3. In Eq. (5), \\(W_{\\mu}\\) and \\(W_{\\sigma}\\) contain two convolutional layers, respectively. All the experiments are trained using the standard SGD optimizer with a learning rate of 0.02." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Datasets. For unsupervised OOD-OD, PASCAL VOC [8] and Berkeley DeepDrive (BDD-100k) [48] datasets are taken as the ID training data. Meanwhile, we adopt MSCOCO [29] and OpenImages [24] as the OOD datasets to evaluate the trained model. And the OOD datasets are manually examined the OOD images to ensure they do not contain ID category. For open-vocabulary detection, we follow the work [33] and conduct experiments on COCO [29]. Concretely, COCO-2017 dataset is used for training and validation. Meanwhile, 48 categories are selected as base classes and 17 are selected as new classes. For incremental object detection, we follow the standard evaluation protocol [22] and evaluate our method on PASCAL VOC [8]. We" + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.091, + 0.836, + 0.107 + ], + "angle": 0, + "content": "Algorithm 1 SR-VAE for Unsupervised OOD-OD" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.109, + 0.892, + 0.154 + ], + "angle": 0, + "content": "Input: ID data \\(\\{X,Y\\}\\), randomly initialized detector with parameter \\(\\theta\\), weight \\(\\alpha\\) for the \\(KL\\)-loss, weight \\(\\lambda\\) for the loss \\(\\mathcal{L}_{\\mathrm{dis}}\\), weight \\(\\tau\\) for the uncertainty loss \\(\\mathcal{L}_{\\mathrm{uncertainty}}\\)." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.155, + 0.837, + 0.169 + ], + "angle": 0, + "content": "Output: Object detector \\(\\theta^{*}\\), and OOD classifier \\(\\mathcal{C}\\)." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.17, + 0.6, + 0.183 + ], + "angle": 0, + "content": "while train do" + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.184, + 0.817, + 0.199 + ], + "angle": 0, + "content": "Sample images from the ID dataset \\(\\{X,Y\\}\\)" + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.199, + 0.891, + 0.228 + ], + "angle": 0, + "content": "Calculate the structure-enhanced map \\(E\\) and diverse augmented features \\(H\\) using Eq. (2) and (3)." + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.229, + 0.852, + 0.244 + ], + "angle": 0, + "content": "Synthesize the virtual OOD map \\( \\pmb{O} \\) using Eq. (5)." + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.244, + 0.891, + 0.273 + ], + "angle": 0, + "content": "Calculate the overall training objective \\(\\mathcal{L}\\) using Eq. (4), (6), (7), and (8)." + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.274, + 0.804, + 0.29 + ], + "angle": 0, + "content": "Update the parameters \\(\\theta\\) based on Eq. (8)." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.291, + 0.531, + 0.302 + ], + "angle": 0, + "content": "end" + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.304, + 0.594, + 0.317 + ], + "angle": 0, + "content": "whileevaldo" + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.317, + 0.864, + 0.332 + ], + "angle": 0, + "content": "Calculate the OOD uncertainty score using Eq. (9)." + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.332, + 0.843, + 0.347 + ], + "angle": 0, + "content": "Perform thresholding comparison using Eq. (9)." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.348, + 0.531, + 0.36 + ], + "angle": 0, + "content": "end" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.393, + 0.891, + 0.423 + ], + "angle": 0, + "content": "initially learn 10, 15, or 19 base classes, and then introduce 10, 5, or 1 new classes as the second task." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.425, + 0.893, + 0.531 + ], + "angle": 0, + "content": "Metrics. To evaluate the performance of unsupervised OOD-OD, we report: (1) the false positive rate (FPR95) of OOD objects when the true positive rate of ID objects is at \\(95\\%\\); (2) the area under the receiver operating characteristic curve (AUROC); (3) mean average precision (mAP). For open-vocabulary detection and incremental object detection, we only report the mAP performance." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.543, + 0.783, + 0.56 + ], + "angle": 0, + "content": "4.2. OOD-OD Performance Analysis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.568, + 0.892, + 0.809 + ], + "angle": 0, + "content": "Table 1 shows the performance of unsupervised OOD. We can see that though all methods own similar detection performance, the performance of OOD object detection differs significantly. This shows that existing detection methods are easily affected by OOD objects. Besides, for these two benchmarks, our method significantly outperforms baseline methods. Particularly, taking BDD [48] as the ID training data, based on FPR95 metric, our method separately outperforms VOS [7] by \\(12.04\\%\\) and \\(13.73\\%\\). Meanwhile, based on AUROC metric, our method is \\(3.82\\%\\) and \\(5.03\\%\\) higher than VOS [7]. These results indicate that our method could indeed reduce the risk of misclassifying ID objects into OOD categories. Meanwhile, the proposed method could effectively synthesize virtual OOD features that deviate from the distribution of ID features, which improves the ability of distinguishing OOD objects." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In Fig. 4 and 5, we show some OOD detection examples. We can see that compared with the baseline method [7], our method accurately distinguishes OOD objects. Taking the first two columns of Fig. 4 as examples, the baseline method misclassifies OOD objects into ID categories. Our method correctly discriminates these objects as the OOD category." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "23960" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.095, + 0.089, + 0.249, + 0.169 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.096, + 0.17, + 0.249, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.254, + 0.089, + 0.411, + 0.169 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.254, + 0.17, + 0.411, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.414, + 0.089, + 0.57, + 0.169 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.414, + 0.17, + 0.57, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.572, + 0.089, + 0.728, + 0.169 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.572, + 0.17, + 0.728, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.731, + 0.089, + 0.888, + 0.169 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.731, + 0.17, + 0.888, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.253, + 0.892, + 0.296 + ], + "angle": 0, + "content": "Figure 4. Detection results on the OOD images from MS-COCO. The first and second rows respectively indicate results based on VOS [7] and our method. The in-distribution dataset is BDD-100k. Blue boxes represent objects detected and classified as one of the ID categories. Green boxes indicate OOD objects. We can see that our method accurately determines OOD objects." + }, + { + "type": "table", + "bbox": [ + 0.083, + 0.305, + 0.47, + 0.596 + ], + "angle": 0, + "content": "
Method (VOC)FPR95 ↓AUROC ↑mAP (ID)↑
OOD: MS-COCO / OpenImages
MSP [14]70.99 / 73.1383.45 / 81.9148.7
ODIN [28]59.82 / 63.1482.20 / 82.5948.7
Mahalanobis [26]67.73 / 65.4181.45 / 81.4848.7
Gram matrices [38]62.75 / 67.4279.88 / 77.6248.7
Energy score [30]56.89 / 58.6983.69 / 82.9848.7
Generalized ODIN [16]59.57 / 70.2883.12 / 79.2348.1
CSI [42]59.91 / 57.4181.83 / 82.9548.1
GAN-synthesis [25]60.93 / 59.9783.67 / 82.6748.5
VOS (Baseline) [7]47.53 / 51.3388.70 / 85.2348.9
SR-VAE42.17 / 46.2690.28 / 87.8949.4
Method (BDD)FPR95 ↓AUROC ↑mAP (ID)↑
OOD: MS-COCO / OpenImages
MSP [14]80.94 / 79.0475.87 / 77.3831.2
ODIN [28]62.85 / 58.9274.44 / 76.6131.2
Mahalanobis [26]55.74 / 47.6985.71 / 88.0531.2
Gram matrices [38]60.93 / 77.5574.93 / 59.3831.2
Energy score [30]60.06 / 54.9777.48 / 79.6031.2
Generalized ODIN [16]57.27 / 50.1785.22 / 87.1831.8
CSI [42]47.10 / 37.0684.09 / 87.9930.6
GAN-synthesis [25]57.03 / 50.6178.82 / 81.2531.4
VOS (Baseline) [7]44.27 / 35.5486.87 / 88.5231.3
SR-VAE32.23 / 21.8190.69 / 93.5531.5
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.076, + 0.599, + 0.47, + 0.671 + ], + "angle": 0, + "content": "Table 1. The performance \\((\\%)\\) of unsupervised OOD-OD. All methods are trained based on ID data and do not use any auxiliary data. \\(\\uparrow\\) denotes larger values are better and \\(\\downarrow\\) denotes smaller values are better. We can see that our method outperforms the comparison methods significantly." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.68, + 0.47, + 0.726 + ], + "angle": 0, + "content": "These results further show that the proposed method could effectively synthesize OOD features and improve the discrimination ability of the object detector." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.739, + 0.418, + 0.756 + ], + "angle": 0, + "content": "4.3. Performance Analysis of OVD and IOD" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.763, + 0.47, + 0.884 + ], + "angle": 0, + "content": "To demonstrate the superiorities, we further verify our method on OVD [49] and IOD [22]. Table 2 shows the OVD results on COCO. Here, we directly plug our method into the baseline method [33] and do not calculate the uncertainty loss (Eq. (7)). We can see that plugging our method improves OCA's performance by \\(3.5\\%\\). This shows that our method effectively synthesizes virtual features, which enhances the ability of distinguishing new classes." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Table 3 shows the IOD performance on PASCAL VOC." + }, + { + "type": "table", + "bbox": [ + 0.568, + 0.305, + 0.828, + 0.424 + ], + "angle": 0, + "content": "
MethodAPnovelAP
WSDDN [3]19.719.6
Cap2Det [47]20.320.1
OVR-CNN [49]22.839.9
RegionCLIP [50]26.847.5
Detric [51]27.845.0
OCA (Baseline) [33]36.649.4
OCA+Ours40.149.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.426, + 0.892, + 0.455 + ], + "angle": 0, + "content": "Table 2. OVD results \\((\\%)\\) on COCO. 'OCA + Ours' indicates that we directly plug our method into OCA [33]." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.461, + 0.892, + 0.598 + ], + "angle": 0, + "content": "We still directly plug our method into the baseline method [22] and do not calculate the uncertainty loss. We can see that when the IOU threshold is set to 0.5 and 0.75, plugging our method effectively improves the performance of the baseline method. Particularly, when the IOU threshold is set to 0.75, for the three different settings, our method separately boosts iOD's performance by \\(2.3\\%\\), \\(2.9\\%\\), and \\(4.1\\%\\). These results show that our method could significantly improve the discrimination of the object detector." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.606, + 0.813, + 0.623 + ], + "angle": 0, + "content": "4.4. Ablation and Visualization Analysis" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.629, + 0.892, + 0.674 + ], + "angle": 0, + "content": "In this section, we utilize BDD-100k as the ID data for training and MS-COCO as the OOD data to perform an ablation analysis of our method." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Analysis of SR-VAE. In this paper, our method mainly contains the LoG operator used for enhancing object-related information, the VAE module used to generate diverse augmented features of the classification features, and the cycle-consistent conditional VAE module used for synthesizing virtual OOD features. Here, we make an ablation analysis of our method. Table 4 shows the ablation results. We can see that employing the proposed three modules could significantly improve the performance of OOD object detection. Particularly, compared with VOS [7], synthesizing virtual OOD features improves the performance by around \\(5.21\\%\\) based on the FPR95 metric, which shows that the generated virtual OOD features could alleviate the impact of lacking unknown data for supervision and enhance the ability of distinguishing OOD objects. Meanwhile, employing the" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "23961" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.078, + 0.094, + 0.892, + 0.487 + ], + "angle": 0, + "content": "
10 + 10 settingaerocyclebirdboatbottlebuscarcatchaircowtabledoghorsebikepersonplantsheepsofatraintvmAP
Faster ILOD (50) [32]72.875.771.260.561.770.483.376.653.172.336.770.966.867.666.124.763.148.157.143.662.2
ORE (50) [19]63.570.958.942.934.176.280.776.334.166.156.170.480.272.381.842.771.668.17767.764.6
OW-DETR (50) [10]61.869.167.845.847.378.378.478.636.271.557.575.376.277.479.540.166.866.375.664.165.7
ROSETTA (50) [45]74.276.264.954.457.476.184.468.852.467.062.963.379.872.878.140.162.361.272.466.866.8
iOD (50) [22]76.074.667.555.957.675.185.477.043.770.860.166.476.072.674.639.764.060.268.560.566.3
iOD + Ours (50)75.975.268.855.355.577.785.679.349.478.261.075.381.474.579.343.872.567.070.265.769.6
iOD (75) [22]39.036.528.419.424.247.256.741.019.148.021.132.143.036.340.014.840.136.537.345.335.3
iOD + Ours (75)43.641.031.324.929.855.460.844.122.446.729.532.335.638.335.715.146.934.637.946.737.6
15 + 5 settingaerocyclebirdboatbottlebuscarcatchaircowtabledoghorsebikepersonplantsheepsofatraintvmAP
Faster ILOD (50) [32]66.578.171.854.661.468.482.682.752.174.363.178.680.578.480.436.761.759.367.959.167.9
ORE (50) [19]75.481.067.151.955.777.285.681.746.176.255.476.786.278.582.132.863.654.777.764.668.5
OW-DETR (50) [10]77.176.569.251.361.379.884.281.049.779.658.179.083.167.885.433.265.162.073.965.069.4
ROSETTA (50) [45]76.577.565.156.060.078.385.578.749.568.267.471.283.975.782.043.060.664.172.867.469.2
iOD (50) [22]78.479.766.954.856.277.784.679.147.775.061.874.781.677.580.237.858.054.673.056.167.8
iOD + Ours (50)78.380.370.551.660.279.485.976.252.579.465.281.883.776.177.941.162.863.872.667.970.4
iOD (75) [22]40.740.928.719.123.861.656.138.823.647.518.740.140.241.539.89.140.632.441.947.636.6
iOD + Ours (75)44.444.536.521.227.655.563.739.824.950.327.241.647.943.941.411.339.138.643.148.539.5
19 + 1 settingaerocyclebirdboatbottlebuscarcatchaircowtabledoghorsebikepersonplantsheepsofatraintvmAP
Faster ILOD (50) [32]64.274.773.255.553.770.882.982.651.679.758.778.881.875.377.443.173.861.769.861.168.6
ORE (50) [19]67.376.860.048.458.881.186.575.841.579.654.672.885.981.782.444.875.868.275.760.168.9
OW-DETR (50) [10]70.577.273.854.055.679.080.880.643.280.453.577.589.582.074.743.371.966.679.462.070.2
ROSETTA (50) [45]75.377.965.356.255.379.684.672.949.273.768.371.078.977.780.744.069.668.576.168.369.6
iOD (50) [22]78.277.569.455.056.078.484.279.246.679.063.278.582.779.179.944.173.266.376.457.670.2
iOD + Ours (50)76.683.574.757.058.077.085.682.551.582.761.481.682.979.877.647.474.768.474.159.071.8
iOD (75) [22]35.944.731.622.426.952.056.538.721.648.421.235.937.930.738.717.238.534.240.746.636.0
iOD + Ours (75)36.445.136.118.028.953.262.238.525.355.127.446.845.942.940.320.950.837.044.447.140.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.491, + 0.89, + 0.519 + ], + "angle": 0, + "content": "Table 3. Performance (%) analysis of class-incremental object detection. 'iOD + Ours' indicates that our method is plugged into iOD [22]. Here, '50' and '75' separately represent that the mAP metric is calculated when the IOU threshold is set to 0.5 and 0.75." + }, + { + "type": "table", + "bbox": [ + 0.085, + 0.529, + 0.462, + 0.61 + ], + "angle": 0, + "content": "
C-VAELoGR-VAEFPR95 ↓AUROC ↑mAP↑
✓39.06%87.83%31.3%
✓✓37.92%88.08%31.2%
✓✓35.13%89.22%31.3%
✓✓✓32.23%90.69%31.5%
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.077, + 0.613, + 0.468, + 0.669 + ], + "angle": 0, + "content": "Table 4. Ablation analysis of SR-VAE for unsupervised OOD-OD. 'C-VAE' is the proposed cycle-consistent conditional VAE module. 'R-VAE' indicates the VAE module that is used to generate diverse augmented features of the classification features." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.672, + 0.469, + 0.748 + ], + "angle": 0, + "content": "LoG operator and R-VAE modules further boosts the performance significantly, which demonstrates that using these two modules is beneficial for enhancing object-related information in the extracted low-level features and improving the discrimination ability of the object detector." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Analysis of the LoG kernel size. To improve the performance of object localization, we employ the LoG operation (Eq. (1) and (2)) to perform structure enhancement, which is beneficial for strengthening object-related information. Here, we make an ablation analysis of the LoG kernel size. And we only change the kernel size. The other modules are kept unchanged. Table 5 shows the results. We can see that the performance is affected by the kernel size. Small kernel size does not sufficiently capture object structure information, which weakens the performance. For our" + }, + { + "type": "table", + "bbox": [ + 0.533, + 0.53, + 0.86, + 0.624 + ], + "angle": 0, + "content": "
LoG Kernel SizeFPR95 ↓AUROC ↑mAP↑
3 × 334.96%87.94%30.9%
5 × 533.85%89.18%31.3%
7 × 733.08%89.76%31.2%
9 × 932.23%90.69%31.5%
11 × 1132.93%90.35%31.6%
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.546, + 0.627, + 0.843, + 0.641 + ], + "angle": 0, + "content": "Table 5. Ablation analysis of the LoG kernel size." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.643, + 0.884, + 0.658 + ], + "angle": 0, + "content": "method, the performance of using \\( 9 \\times 9 \\) kernel is the best." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Analysis of the iteration number. To reduce the risk of misclassifying ID objects into the OOD category, we design a VAE module (Eq. (3)) to generate multiple augmented features of the classification features, which is instrumental in improving the discrimination ability of the object classifier. Here, we make an ablation analysis of the iteration number \\( T \\). And we only change the iteration number and keep other modules unchanged. Table 6 shows the ablation results. We can see that generating multiple augmented features could improve the detection performance effectively. This shows that enhancing the classification ability of the object classifier is meaningful. Besides, we observe that when the iteration number is larger than a certain threshold, the performance could not be boosted effectively. The reason may be that the object classifier is a linear classifier, which could not sufficiently exploit these augmented fea" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "23962" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.095, + 0.089, + 0.264, + 0.169 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.096, + 0.169, + 0.264, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.264, + 0.089, + 0.429, + 0.169 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.261, + 0.17, + 0.429, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.43, + 0.089, + 0.555, + 0.169 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.43, + 0.17, + 0.555, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.556, + 0.089, + 0.722, + 0.169 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.556, + 0.17, + 0.722, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.723, + 0.089, + 0.89, + 0.169 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.723, + 0.17, + 0.89, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.253, + 0.88, + 0.268 + ], + "angle": 0, + "content": "Figure 5. Detection results on OpenImages. The first and second rows respectively indicate results based on VOS [7] and our method." + }, + { + "type": "image", + "bbox": [ + 0.09, + 0.273, + 0.223, + 0.344 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.09, + 0.344, + 0.222, + 0.414 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.09, + 0.416, + 0.222, + 0.484 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.104, + 0.486, + 0.197, + 0.499 + ], + "angle": 0, + "content": "(a) Input Image" + }, + { + "type": "image", + "bbox": [ + 0.225, + 0.273, + 0.356, + 0.343 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.226, + 0.344, + 0.355, + 0.414 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.226, + 0.416, + 0.355, + 0.484 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.232, + 0.486, + 0.337, + 0.499 + ], + "angle": 0, + "content": "(b) Structure Map" + }, + { + "type": "image", + "bbox": [ + 0.358, + 0.273, + 0.491, + 0.343 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.359, + 0.344, + 0.49, + 0.414 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.359, + 0.416, + 0.49, + 0.484 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.356, + 0.486, + 0.482, + 0.5 + ], + "angle": 0, + "content": "(c) Virtual OOD Map" + }, + { + "type": "image", + "bbox": [ + 0.493, + 0.273, + 0.625, + 0.343 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.493, + 0.344, + 0.624, + 0.413 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.493, + 0.415, + 0.624, + 0.484 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.507, + 0.486, + 0.598, + 0.5 + ], + "angle": 0, + "content": "(d) Input Image" + }, + { + "type": "image", + "bbox": [ + 0.628, + 0.273, + 0.757, + 0.343 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.629, + 0.344, + 0.757, + 0.413 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.628, + 0.415, + 0.757, + 0.484 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.635, + 0.486, + 0.738, + 0.5 + ], + "angle": 0, + "content": "(e) Structure Map" + }, + { + "type": "image", + "bbox": [ + 0.761, + 0.273, + 0.892, + 0.343 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.761, + 0.344, + 0.892, + 0.413 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.761, + 0.415, + 0.892, + 0.484 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.759, + 0.486, + 0.883, + 0.5 + ], + "angle": 0, + "content": "(f) Virtual OOD Map" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.505, + 0.892, + 0.534 + ], + "angle": 0, + "content": "Figure 6. Visualization of the Structure-Enhanced map \\( E \\) (Eq. (2)) and Virtual OOD map \\( \\pmb{O} \\) (Eq. (5)) based on the OOD data (MS-COCO). For each feature map, the channels corresponding to the maximum value are selected for visualization." + }, + { + "type": "table", + "bbox": [ + 0.102, + 0.544, + 0.447, + 0.626 + ], + "angle": 0, + "content": "
Iteration Number TFPR95 ↓AUROC ↑mAP↑
137.24%88.12%31.2%
332.23%90.69%31.5%
532.46%90.23%31.3%
732.93%90.07%31.2%
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.115, + 0.628, + 0.431, + 0.642 + ], + "angle": 0, + "content": "Table 6. Ablation analysis of the iteration number \\( T \\) ." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.643, + 0.469, + 0.673 + ], + "angle": 0, + "content": "tures. For our method, when the iteration number is set to 3, the performance of OOD detection is the best." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.674, + 0.47, + 0.81 + ], + "angle": 0, + "content": "Analysis of cycle-consistent conditional VAE. In order to effectively synthesize virtual OOD features, we propose a cycle-consistency loss \\(\\mathcal{L}_{\\mathrm{cycle}}\\) (Eq. (8)) to reduce the impact of lacking paired samples. Here, we make an ablation analysis of \\(\\mathcal{L}_{\\mathrm{cycle}}\\). Based on the FPR95 metric, removing \\(\\mathcal{L}_{\\mathrm{cycle}}\\) increases the performance by around \\(3.8\\%\\). This shows using the cycle-consistency loss \\(\\mathcal{L}_{\\mathrm{cycle}}\\) is beneficial for synthesizing virtual OOD features and improving the ability of distinguishing OOD objects." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Visualization analysis. Fig. 6 shows some visualization examples. Particularly, we can see that the map \\( E \\) contains plentiful object-related information, which shows that using the LoG operation is indeed helpful for enhancing object-related information. Furthermore, we observe that the synthesized virtual OOD map \\( O \\) involves sufficient informa" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.547, + 0.892, + 0.608 + ], + "angle": 0, + "content": "tion that is different from object-related features, which indicates that leveraging the synthesized OOD features is instrumental in reducing the impact of lacking unknown data and improving the discrimination ability." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.619, + 0.619, + 0.635 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.893, + 0.81 + ], + "angle": 0, + "content": "For unsupervised OOD-OD, we propose an approach of Structure-Enhanced Recurrent VAE. Particularly, to reduce the risk of misclassifying ID objects into the OOD category, an LoG operator and a dedicated recurrent VAE used to generate diverse augmented features are presented to strengthen the discrimination ability. Meanwhile, to alleviate the impact of lacking unknown data, we design a cycle-consistent conditional VAE to synthesize virtual OOD features, which boosts the performance of distinguishing OOD objects. Extensive experiments on three different tasks and visualization analyses demonstrate the superiorities of our method." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Acknowledgement. Our work was supported in part by Key Research and Development Program of Shaanxi under Grant 2021ZDLGY01-03, the National Natural Science Foundation of China under Grant 62102293, 62132016, 62171343, and 62071361, and the Fundamental Research Funds for the Central Universities ZDRC2102." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23963" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.117, + 0.47, + 0.158 + ], + "angle": 0, + "content": "[1] Martin Arjovsky, Léon Bottou, Ishaan Gulrajani, and David Lopez-Paz. Invariant risk minimization. arXiv preprint arXiv:1907.02893, 2019. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.161, + 0.471, + 0.188 + ], + "angle": 0, + "content": "[2] Abhijit Bendale and Terrance E Boult. Towards open set deep networks. 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To simulate this ability, a task of unsupervised out-of-distribution object detection (OOD-OD) is proposed to detect the objects that are never-seen-before during model training, which is beneficial for promoting the safe deployment of object detectors. Due to lacking unknown data for supervision, for this task, the main challenge lies in how to leverage the known in-distribution (ID) data to improve the detector's discrimination ability. In this paper, we first propose a method of Structure-Enhanced Recurrent Variational AutoEncoder (SR-VAE), which mainly consists of two dedicated recurrent VAE branches. Specifically, to boost the performance of object localization, we explore utilizing the classical Laplacian of Gaussian (Log) operator to enhance the structure information in the extracted low-level features. Meanwhile, we design a VAE branch that recurrently generates the augmentation of the classification features to strengthen the discrimination ability of the object classifier. Finally, to alleviate the impact of lacking unknown data, another cycle-consistent conditional VAE branch is proposed to synthesize virtual OOD features that deviate from the distribution of ID features, which improves the capability of distinguishing OOD objects. In the experiments, our method is evaluated on OOD-OD, open-vocabulary detection, and incremental object detection. The significant performance gains over baselines show the superiorities of our method. The code will be released at https://github.com/AmingWu/SR-VAE. + +# 1. Introduction + +Recent years have witnessed the rapid development of deep learning based object detection [5,12,34,36,41], which often follows a close-set assumption that the training and testing processes share the same category space. However, the practical scenario is open and filled with unknown + +![](images/7d4d371428dcf496326f629095ad3735d7659a23670c12ffbd2d05410cf99fee.jpg) +Figure 1. Discriminating known from unknown objects (as shown in green boxes) by synthesizing virtual OOD features. For OOD-OD, to alleviate the impact of lacking unknown data, we present an SR-VAE method to constrain the synthesized features (as shown in blue stars) to deviate from the distribution of ID features (as shown in orange). Meanwhile, we consider enhancing the discrimination of the classifier to reduce the risk of misclassifying the ID objects into the OOD category. Through these operations, the ability of distinguishing OOD objects could be improved significantly. + +objects, e.g., in Fig. 1, an autonomous vehicle may encounter an unseen camel, presenting significant challenges for close-set assumption based detectors. To promote the safe application of detectors, a task of unsupervised out-of-distribution object detection (OOD-OD) [7] is recently proposed, which aims to detect the objects never-seen-before during training without accessing any auxiliary data. + +Towards unsupervised OOD-OD, since there is no auxiliary data available for supervision, leveraging the known in-distribution (ID) data to enhance the detector's discrimination ability becomes the critical challenge. One feasible solution is to synthesize a series of virtual OOD features [7, 35] based on the ID data, which is beneficial for promoting the object detector to learn a clear decision boundary between ID and OOD objects. To this end, the work [7] attempts to synthesize virtual features from the low-likelihood region of the estimated class-conditional distribution. However, this method requires a large number of objects for each category to estimate the distribution, limiting its application to the case of few samples. + +As shown in Fig. 1, in this paper, we consider improvis + +ing the performance of OOD object detection from two perspectives: One is to strengthen the discrimination capability of the object classifier for the known ID objects, which is conducive to reduce the risk of misclassifying the ID objects into the OOD category. Another is to synthesize the virtual OOD features that significantly deviate from the distribution of the ID features, which is instrumental in boosting the performance of distinguishing OOD objects from ID objects. To attain these two goals, we explore exploiting Variational AutoEncoder (VAE) [15, 20] to separately generate the augmented ID features and virtual OOD features. + +Specifically, an approach of Structure-Enhanced Recurrent Variational AutoEncoder (SR-VAE) is proposed, which mainly consists of two dedicated recurrent VAE branches. In general, an object detector should first localize objects. Then, an object classifier is used to discriminate these objects [12, 36]. To improve the localization performance, enhancing the object-related information in the extracted features is meaningful. To this end, after extracting the low-level features of an input image, we present to utilize the classical Laplacian of Gaussian (LoG) operator [23] to obtain structure-related information, which is used to fuse into the existing features to strengthen the localization ability. + +Next, in order to enhance the discrimination ability, inspired by Invariant Risk Minimization [1], we explore constructing a set of diverse environments to intensify the variance of the input classification features. Concretely, a VAE module [17, 20, 43] is exploited to recurrently output multiple augmented features of the classification features, i.e., the current output is taken as the input of the next iteration. Since the input of each iteration is different, by means of the variation operation, the diversity of the output features could be enlarged. Then, the discrimination ability is improved by minimizing the prediction discrepancy between the augmented features and the classification features. + +Finally, to alleviate the impact of lacking unknown data, we present a cycle-consistent conditional VAE [40] to synthesize virtual OOD features in the absence of paired supervision samples. Concretely, to ameliorate the synthesized features to deviate from the distribution of ID features, we first insert label information in the latent space to force a deterministic constrained representation. Meanwhile, by maximizing the discrepancy between the synthesized features and the input features, the synthesized features could be facilitated to contain plentiful OOD-relevant information, which enhances the ability of distinguishing OOD objects. In the experiments, our method is separately evaluated on three different tasks. Extensive experimental results on multiple datasets demonstrate the superiorities of our method. + +The contributions are summarized as follows: + +(1) For unsupervised OOD-OD, we observe that using the classical LoG operator could effectively enhance object-related information in the extracted low-level features. + +(2) To reduce the risk of misclassifying ID objects into the OOD category, we design a dedicated recurrent VAE to generate diverse augmented features of the input classification features, which is beneficial for improving the discrimination ability of the object classifier. +(3) To alleviate the impact of lacking unknown data for supervision, we present a cycle-consistent conditional VAE to synthesize virtual OOD features, which is instrumental in distinguishing OOD objects from ID objects. +(4) In the experiments, our method is evaluated on OOD-OD [7], open-vocabulary detection [33, 49], and incremental object detection [22, 39]. Particularly, for OpenImages dataset [24], compared with the baseline method [7], our method significantly reduces FPR95 by around $13.73\%$ . + +# 2. Related Work + +OOD Detection. In order to promote the safe application of models in real scenarios, OOD detection [4, 14, 18] has recently attracted much attention, whose goal is to distinguish OOD data from ID data. Most methods [27, 31, 46, 52] focus on OOD image classification and explore a proper regularization-based method for this task. Particularly, Bendale et al. [2] developed the OpenMax score based on the extreme value theory. Liu et al. [30] proposed to utilize the energy score to discriminate OOD data from ID data. Zhou [52] rethought the commonly used reconstruction autoencoder for OOD detection. Though these methods have been demonstrated to be effective, since object detection involves object localization and classification, these methods could not directly apply to OOD-OD. + +Recently, unsupervised OOD-OD [7] is proposed to localize and recognize the objects never-seen-before during training. For this task, Du et al. [7] proposed to use large-scale samples to estimate the distribution of each ID category, which is used to synthesize virtual OOD features. However, calculating accurate distribution estimation may limit its application in real scenarios. Harakeh et al. [11] designed an uncertainty estimation method for the localization branch, which could not well address OOD-OD that involves localization and classification. Besides, the work [6] proposed to use auxiliary video datasets to learn unknown-aware knowledge to effectively improve the performance of distinguishing OOD objects, which could not be used for unsupervised OOD-OD. In this paper, we explore employing the idea of VAE [15, 20] to synthesize virtual OOD features that significantly deviate from the distribution of ID features. And these virtual features are used to strengthen the discrimination ability. Experimental results on three different tasks show the effectiveness of our method. + +Variational AutoEncoder. The goal of VAE [15,20,21, 40] is to map the input data to a multivariate latent distribution, which efficiently addresses the generation problem for high-dimensional data. Most existing methods [15, 17, 44] + +![](images/330d41d90f635edd7312b3476fcd2c33ae0bd7722fbcfd324f4ab2812bee90b7.jpg) +Figure 2. Structure-Enhanced Recurrent Variational AutoEncoder for Unsupervised OOD-OD. To improve localization performance, we employ the LoG operator to enhance the structure-related information in the features extracted by the backbone network. Meanwhile, we design a VAE module to recurrently generate diverse augmented features of the input classification features, which is beneficial for strengthening the discrimination ability of the object classifier. Finally, to alleviate the impact of lacking unknown data, we propose a cycle-consistent conditional VAE to synthesize virtual OOD features that deviate from the distribution of the ID features significantly, which boosts the performance of distinguishing OOD objects. + +attempt to adjust the latent representations to generate clear images containing rich content. Particularly, $\beta$ -VAE [15] is an implementation with a weighted Kullback-Leibler (KL) divergence term to automatically discover disentangled representations without supervision. Conditional VAE [40] inserts label information in the latent space to force a deterministic constrained representation. Different from the above works focusing on pixel-level generation, we explore using VAE to generate virtual OOD features. Experimental results on OOD-OD show the advantages of our method. + +# 3. Structure-Enhanced Recurrent VAE + +In this paper, we follow the settings introduced in the work [7]. During training, we can only access the ID data. During inference, the object detector should own the capability of distinguishing ID objects from OOD objects. + +# 3.1. Structure Enhancement via LoG Operator + +In general, an object detector should first localize objects accurately and then distinguish them as ID categories or OOD categories. To this end, it is important to enhance object-related information (e.g., object structure information). In the field of image processing, LoG operator [23] is a popular algorithm for edge detection. We explore performing the LoG operation on the extracted low-level features to strengthen the structure-relevant information. + +Concretely, as shown in Fig. 2, we follow the baseline work [7] and adopt the widely used object detector, i.e., Faster R-CNN [12, 36], as the basic detection model. Given an input image, we first employ the backbone network, e.g., ResNet [13], to extract the corresponding feature map $F \in \mathbb{R}^{w \times h \times c}$ , where $w$ , $h$ , and $c$ separately denote width, height, and channel number. To obtain rich structure + +information, a $9 \times 9$ LoG kernel $\mathcal{G}$ is defined as follows: + +$$ +\mathcal {G} = \left[ \begin{array}{c c c c c c c c c} 0 & 1 & 1 & 2 & 2 & 2 & 1 & 1 & 0 \\ 1 & 2 & 4 & 5 & 5 & 5 & 4 & 2 & 1 \\ 1 & 4 & 5 & 3 & 0 & 3 & 5 & 4 & 1 \\ 2 & 5 & 3 & - 1 2 & - 2 4 & - 1 2 & 3 & 5 & 2 \\ 2 & 5 & 0 & - 2 4 & - 4 0 & - 2 4 & 0 & 5 & 2 \\ 2 & 5 & 3 & - 1 2 & - 2 4 & - 1 2 & 3 & 5 & 2 \\ 1 & 4 & 5 & 3 & 0 & 3 & 5 & 4 & 1 \\ 1 & 2 & 4 & 5 & 5 & 5 & 4 & 2 & 1 \\ 0 & 1 & 1 & 2 & 2 & 2 & 1 & 1 & 0 \end{array} \right]. \tag {1} +$$ + +Next, $\mathcal{G}$ is used to perform a convolution operation on $F$ to obtain the structure-enhanced map $E\in \mathbb{R}^{w\times h\times c}$ . The processes are shown as follows: + +$$ +\mathcal {E} = F * \mathcal {G}, \quad E = \Psi ([ F, \mathcal {E} ]), \tag {2} +$$ + +where $\mathcal{E} \in \mathbb{R}^{w \times h \times c}$ is the convolutional result containing plentiful structure-related information. $\Psi(\cdot) \in \mathbb{R}^{1 \times 1 \times 2c \times c}$ represents one-layer convolution to transform the number of channels. By fusing the structure information into existing features, the object-related information in $F$ could be enhanced effectively, which is instrumental in improving the performance of object localization. + +# 3.2. Recurrent VAE for Improving Discrimination + +To reduce the risk of misclassifying ID objects into the OOD category, we design a VAE module to recurrently generate diverse augmented features of the classification features, which enhances the discrimination ability. + +Specifically, as shown in Fig. 2, the enhanced map $E$ is taken as the input of the RPN module to obtain a set of object proposals $\mathcal{O}$ . Based on $\mathcal{O}$ , RoI-Alignment followed by RoI-Feature extraction [12] is performed on $E$ to output + +![](images/b4216e2c10a4824de61d4ef40a1aa2d8e8f53a45954991067e60cb68cb9f8488.jpg) +Figure 3. Cycle-consistent conditional VAE for synthesizing virtual OOD features. During the forward process, the OOD features $\pmb{O}$ are generated based on the ID features $F$ . And during the backward process, the features $\pmb{F}$ are generated based on $\pmb{O}$ . By minimizing the cycle-consistency loss between $F$ and $\pmb{F}$ , the synthesized features $\pmb{O}$ could be promoted to contain plentiful information that deviates from the distribution of the ID features. + +$P_{\mathrm{in}} \in \mathbb{R}^{m \times n}$ , where $m$ and $n$ separately denote the number of proposals and channels. Next, we first define two fully-connected networks (i.e., $\Phi_{\mu}(\cdot)$ and $\Phi_{\sigma}(\cdot)$ ) as the encoder to estimate the corresponding means and variances. Then, an encoding operation is performed on the input. Finally, a decoder $\Theta(\cdot)$ consisting of three fully-connected layers is leveraged to calculate the output. The overall processes at the $t$ -th iteration are shown as follows: + +$$ +\mu_ {t} = \Phi_ {\mu} \left(H _ {t - 1}\right), \quad \sigma_ {t} = \Phi_ {\sigma} \left(H _ {t - 1}\right), \tag {3} +$$ + +$$ +h _ {t} = \mu_ {t} + \epsilon \cdot \exp (\sigma_ {t}), \qquad H _ {t} = \Theta (h _ {t}), +$$ + +where $H_{t - 1}\in \mathbb{R}^{m\times n}$ and $H_{t}\in \mathbb{R}^{m\times n}$ respectively indicate the output of the previous iteration and that of the current iteration. And $H_0 = P_{\mathrm{in}}$ $\mu_t\in \mathbb{R}^{m\times n}$ and $\sigma_t\in \mathbb{R}^{m\times n}$ are the estimated means and variances. $\epsilon$ denotes Gaussian noise sampled from $\mathcal{N}(0,I)$ + +Through $T$ iterations, we can obtain a set of augmented features $H = \{H_{1},\dots ,H_{T}\}$ . Finally, by minimizing the $KL$ -divergence between the prediction probabilities from $H_{t}$ and $P_{\mathrm{in}}$ , the discrimination ability of the object classifier could be enhanced effectively. During training, $P_{\mathrm{in}}$ is taken as the input of the object classifier and regressor to calculate the classification and localization losses. The joint training objective is shown as follows: + +$$ +\mathcal {L} _ {\mathrm {i n}} = \mathcal {L} _ {\mathrm {d e t}} + \alpha \cdot \frac {1}{T} \sum_ {t = 1} ^ {T} \mathrm {K L} [ p (H _ {t} | H _ {t - 1}), p (P _ {\mathrm {i n}}) ], \tag {4} +$$ + +where $\mathcal{L}_{\mathrm{det}}$ is the sum of the classification loss $\mathcal{L}_{\mathrm{cls}}$ and the localization loss $\mathcal{L}_{\mathrm{loc}}$ , i.e., $\mathcal{L}_{\mathrm{det}} = \mathcal{L}_{\mathrm{cls}} + \mathcal{L}_{\mathrm{loc}}$ . $\alpha$ is a hyper-parameter. In the experiments, $\alpha$ is set to 0.001. $p(\cdot)$ indicates the prediction probability of the object classifier. + +# 3.3. Synthesizing Virtual OOD Features + +Due to lacking unknown data for supervision, it is prone to misclassify OOD objects into ID categories. Hence, synthesizing virtual OOD data is important to distinguish OOD objects. A straightforward idea is to train generative models, e.g., GANs [9], to synthesize images, which is difficult + +to optimize [7]. Instead, we propose a cycle-consistent conditional VAE to synthesize virtual OOD features. + +Particularly, as shown in Fig. 3, during the forward process, the extracted features $F$ and corresponding ID label [1, 0] are first concatenated as $\hat{F} \in \mathbb{R}^{w \times h \times (c + 2)}$ . Then, two convolutional networks $W_{\mu}$ and $W_{\sigma}$ are defined to estimate the corresponding means and variances: + +$$ +\mu_ {f} = W _ {\mu} * \hat {F}, \quad \sigma_ {f} = W _ {\sigma} * \hat {F}, \tag {5} +$$ + +where $\mu_f \in \mathbb{R}^{w \times h \times c}$ and $\sigma_f \in \mathbb{R}^{w \times h \times c}$ . And an encoding operation is performed to obtain $Z \in \mathbb{R}^{w \times h \times c}$ , i.e., $Z = \mu_f + \epsilon \cdot \exp(\sigma_f)$ . Next, in order to generate virtual OOD features, $Z$ and corresponding OOD label [0, 1] are concatenated as $\hat{Z} \in \mathbb{R}^{w \times h \times (c+2)}$ . A decoding network $\mathcal{D}$ consisting of three convolutional layers is performed on $\hat{Z}$ to obtain the virtual OOD map $O \in \mathbb{R}^{w \times h \times c}$ . + +During the backward process, to alleviate the impact of lacking paired data for supervision, the concatenation result of $\pmb{O}$ and label [0, 1] is made convolution with $W_{\mu}$ and $W_{\sigma}$ . Next, we still take the concatenation of the encoding result and label [1, 0] as the input of the decoder $\mathcal{D}$ to obtain the output $\pmb{F} \in \mathbb{R}^{w \times h \times c}$ . The operations are the same as the forward process. Finally, we introduce a cycle-consistency loss to reduce the discrepancy between $\pmb{F}$ and $F$ , i.e., $\mathcal{L}_{\mathrm{cycle}} = \frac{1}{wh}\sum |F - F|$ . + +Moreover, to promote $\pmb{O}$ to deviate from the distribution of $F$ , as shown in Fig. 2, based on the object proposals $\mathcal{O}$ , RoI-Alignment followed by RoI-Feature extraction is performed on $\pmb{O}$ to extract OOD features $P_{\mathrm{odd}} \in \mathbb{R}^{m \times n}$ . Next, a loss $\mathcal{L}_{\mathrm{dis}}$ is defined to maximize the distance between the virtual OOD features and ID features: + +$$ +\mathcal {L} _ {\mathrm {d i s}} = \mathrm {K L} [ q (\boldsymbol {O}), q (F) ] + | p (P _ {\mathrm {o o d}}) - p (P _ {\mathrm {i n}}) |, \tag {6} +$$ + +where $q(\cdot)$ represents the probability distribution. By maximizing $\mathcal{L}_{\mathrm{dis}}$ , the distribution gap between $O$ and $F$ could be enlarged effectively, which promotes the synthesized features $O$ to contain plentiful OOD information. Finally, to achieve the goal of distinguishing OOD objects from ID objects, $P_{\mathrm{ood}}$ and $P_{\mathrm{in}}$ are used to calculate an uncertainty loss [7], which regularizes the detector to produce a low OOD score for the ID object features, and a high OOD score for the synthesized OOD features: + +$$ +\begin{array}{l} \mathcal {L} _ {\text {u n c e r t a i n t y}} = \mathbb {E} _ {u \sim P _ {\mathrm {i n}}} [ - \log \frac {\exp^ {- \mathrm {E} (u)}}{1 + \exp^ {- \mathrm {E} (u)}} ] + \tag {7} \\ \mathbb {E} _ {v \sim P _ {\mathrm {o o d}}} [ - \log \frac {1}{1 + \exp^ {- \mathbf {E} (v)} ], \\ \end{array} +$$ + +where $\operatorname{E}(\cdot)$ is the object-level energy score [7, 30]. During training, the overall objective is shown as follows: + +$$ +\mathcal {L} = \mathcal {L} _ {\text {i n}} + \lambda \cdot \left(\mathcal {L} _ {\text {c y c l e}} - \mathcal {L} _ {\text {d i s}}\right) + \tau \cdot \mathcal {L} _ {\text {u n c e r t a i n t y}}, \tag {8} +$$ + +where $\lambda$ and $\tau$ are two hyper-parameters, which are set to 0.001 and 0.1 in the experiments. + +# 3.4. Inference for OOD Object Detection + +During inference, we only use the LoG operator to perform structure enhancement. And the operations of recurrent VAE and synthesizing virtual OOD features are not utilized in the inference stage. Besides, we only calculate the uncertainty loss for OOD object detection [7]. Specifically, for a predicted bounding box $\mathbf{b}$ , the processes of distinguishing OOD objects are shown as follows: + +$$ +\mathcal {S} = \frac {\exp^ {- \mathrm {E} (\mathbf {b})}}{1 + \exp^ {- \mathrm {E} (\mathbf {b})}}, \quad \mathcal {C} (\mathbf {b}) = \left\{ \begin{array}{l l} 0 & \text {i f} \mathcal {S} < \gamma , \\ 1 & \text {i f} \mathcal {S} \geq \gamma . \end{array} \right. \tag {9} +$$ + +For the output of the classifier $\mathcal{C}(\cdot)$ , we use the threshold mechanism [7] to distinguish the ID objects (the result is 1) from the OOD objects (the result is 0). The threshold $\gamma$ is commonly set to 0.95 so that a high fraction of ID data is correctly classified. Finally, Algorithm 1 shows the training and evaluation details of our method. + +# 4. Experiments + +In the experiments, for unsupervised OOD-OD, we first evaluate our method on two different OOD object detection benchmarks [7]. Then, to further demonstrate the effectiveness of our method, we verify our method on the task of open-vocabulary detection (OVD) [33,49] that aims to detect new classes defined by an unbounded vocabulary. Finally, we evaluate our method on the task of class-incremental object detection (IOD) [22], i.e., new classes are sequentially introduced into the object detector. + +# 4.1. Experimental Setup + +Implementation details. We utilize Faster R-CNN [36] with RoI-Alignment layer [12] as the basic detection model. ResNet-50 [13] is taken as the backbone. The weights pretrained on ImageNet [37] are used for initialization. Besides, in Eq. (3), $\Phi_{\mu}(\cdot)$ and $\Phi_{\sigma}(\cdot)$ separately consist of two fully-connected layers. The iteration number $T$ is set to 3. In Eq. (5), $W_{\mu}$ and $W_{\sigma}$ contain two convolutional layers, respectively. All the experiments are trained using the standard SGD optimizer with a learning rate of 0.02. + +Datasets. For unsupervised OOD-OD, PASCAL VOC [8] and Berkeley DeepDrive (BDD-100k) [48] datasets are taken as the ID training data. Meanwhile, we adopt MSCOCO [29] and OpenImages [24] as the OOD datasets to evaluate the trained model. And the OOD datasets are manually examined the OOD images to ensure they do not contain ID category. For open-vocabulary detection, we follow the work [33] and conduct experiments on COCO [29]. Concretely, COCO-2017 dataset is used for training and validation. Meanwhile, 48 categories are selected as base classes and 17 are selected as new classes. For incremental object detection, we follow the standard evaluation protocol [22] and evaluate our method on PASCAL VOC [8]. We + +# Algorithm 1 SR-VAE for Unsupervised OOD-OD + +Input: ID data $\{X,Y\}$ , randomly initialized detector with parameter $\theta$ , weight $\alpha$ for the $KL$ -loss, weight $\lambda$ for the loss $\mathcal{L}_{\mathrm{dis}}$ , weight $\tau$ for the uncertainty loss $\mathcal{L}_{\mathrm{uncertainty}}$ . + +Output: Object detector $\theta^{*}$ , and OOD classifier $\mathcal{C}$ . + +# while train do + +Sample images from the ID dataset $\{X,Y\}$ + +Calculate the structure-enhanced map $E$ and diverse augmented features $H$ using Eq. (2) and (3). + +Synthesize the virtual OOD map $\pmb{O}$ using Eq. (5). + +Calculate the overall training objective $\mathcal{L}$ using Eq. (4), (6), (7), and (8). + +Update the parameters $\theta$ based on Eq. (8). + +# end + +# whileevaldo + +Calculate the OOD uncertainty score using Eq. (9). + +Perform thresholding comparison using Eq. (9). + +# end + +initially learn 10, 15, or 19 base classes, and then introduce 10, 5, or 1 new classes as the second task. + +Metrics. To evaluate the performance of unsupervised OOD-OD, we report: (1) the false positive rate (FPR95) of OOD objects when the true positive rate of ID objects is at $95\%$ ; (2) the area under the receiver operating characteristic curve (AUROC); (3) mean average precision (mAP). For open-vocabulary detection and incremental object detection, we only report the mAP performance. + +# 4.2. OOD-OD Performance Analysis + +Table 1 shows the performance of unsupervised OOD. We can see that though all methods own similar detection performance, the performance of OOD object detection differs significantly. This shows that existing detection methods are easily affected by OOD objects. Besides, for these two benchmarks, our method significantly outperforms baseline methods. Particularly, taking BDD [48] as the ID training data, based on FPR95 metric, our method separately outperforms VOS [7] by $12.04\%$ and $13.73\%$ . Meanwhile, based on AUROC metric, our method is $3.82\%$ and $5.03\%$ higher than VOS [7]. These results indicate that our method could indeed reduce the risk of misclassifying ID objects into OOD categories. Meanwhile, the proposed method could effectively synthesize virtual OOD features that deviate from the distribution of ID features, which improves the ability of distinguishing OOD objects. + +In Fig. 4 and 5, we show some OOD detection examples. We can see that compared with the baseline method [7], our method accurately distinguishes OOD objects. Taking the first two columns of Fig. 4 as examples, the baseline method misclassifies OOD objects into ID categories. Our method correctly discriminates these objects as the OOD category. + +![](images/8bffd9721c937ae490d2cf393286c004c543944ad7ce49b4ba00471b95dcfa1c.jpg) + +![](images/1a98a1fbf3085878d70c2deb0e1ec514fd709528bedf7aec5bce8cb1d4a53153.jpg) +Figure 4. Detection results on the OOD images from MS-COCO. The first and second rows respectively indicate results based on VOS [7] and our method. The in-distribution dataset is BDD-100k. Blue boxes represent objects detected and classified as one of the ID categories. Green boxes indicate OOD objects. We can see that our method accurately determines OOD objects. + +![](images/c21ff860dbb8d3239b199f9e4b7e3b45240132f33f9b30dd686496765a49ef48.jpg) + +![](images/0541aa68bc109428c17fa672bbd20b0d840def928497fbf5a37380f4c5ad0b4b.jpg) + +![](images/43efe295148f299fa64d5a1d45eb81325756557f86c495e91cab6762ce3c2f29.jpg) + +![](images/bd1232e495747c889475853167fe76226f05144ea618777fc8e62453b173aedd.jpg) + +![](images/fca7ddfbd0847ef3b86af6ccc153349f953f02fe8bf1d1f01bcb7c351b2efe59.jpg) + +![](images/07ded544478ed5eaf2a1307949b6e6a66fcb3c5905a7d6f671c5917c8a6b64e9.jpg) + +![](images/b85929a71880b2468b4e00677573f0e71573d2024165b422865ab12192ee4091.jpg) + +![](images/7120febea9414decc042995cb1d67a75ccf498613631982ee7c0a9729cc9b53d.jpg) + +
Method (VOC)FPR95 ↓AUROC ↑mAP (ID)↑
OOD: MS-COCO / OpenImages
MSP [14]70.99 / 73.1383.45 / 81.9148.7
ODIN [28]59.82 / 63.1482.20 / 82.5948.7
Mahalanobis [26]67.73 / 65.4181.45 / 81.4848.7
Gram matrices [38]62.75 / 67.4279.88 / 77.6248.7
Energy score [30]56.89 / 58.6983.69 / 82.9848.7
Generalized ODIN [16]59.57 / 70.2883.12 / 79.2348.1
CSI [42]59.91 / 57.4181.83 / 82.9548.1
GAN-synthesis [25]60.93 / 59.9783.67 / 82.6748.5
VOS (Baseline) [7]47.53 / 51.3388.70 / 85.2348.9
SR-VAE42.17 / 46.2690.28 / 87.8949.4
Method (BDD)FPR95 ↓AUROC ↑mAP (ID)↑
OOD: MS-COCO / OpenImages
MSP [14]80.94 / 79.0475.87 / 77.3831.2
ODIN [28]62.85 / 58.9274.44 / 76.6131.2
Mahalanobis [26]55.74 / 47.6985.71 / 88.0531.2
Gram matrices [38]60.93 / 77.5574.93 / 59.3831.2
Energy score [30]60.06 / 54.9777.48 / 79.6031.2
Generalized ODIN [16]57.27 / 50.1785.22 / 87.1831.8
CSI [42]47.10 / 37.0684.09 / 87.9930.6
GAN-synthesis [25]57.03 / 50.6178.82 / 81.2531.4
VOS (Baseline) [7]44.27 / 35.5486.87 / 88.5231.3
SR-VAE32.23 / 21.8190.69 / 93.5531.5
+ +Table 1. The performance $(\%)$ of unsupervised OOD-OD. All methods are trained based on ID data and do not use any auxiliary data. $\uparrow$ denotes larger values are better and $\downarrow$ denotes smaller values are better. We can see that our method outperforms the comparison methods significantly. + +These results further show that the proposed method could effectively synthesize OOD features and improve the discrimination ability of the object detector. + +# 4.3. Performance Analysis of OVD and IOD + +To demonstrate the superiorities, we further verify our method on OVD [49] and IOD [22]. Table 2 shows the OVD results on COCO. Here, we directly plug our method into the baseline method [33] and do not calculate the uncertainty loss (Eq. (7)). We can see that plugging our method improves OCA's performance by $3.5\%$ . This shows that our method effectively synthesizes virtual features, which enhances the ability of distinguishing new classes. + +Table 3 shows the IOD performance on PASCAL VOC. + +
MethodAPnovelAP
WSDDN [3]19.719.6
Cap2Det [47]20.320.1
OVR-CNN [49]22.839.9
RegionCLIP [50]26.847.5
Detric [51]27.845.0
OCA (Baseline) [33]36.649.4
OCA+Ours40.149.5
+ +Table 2. OVD results $(\%)$ on COCO. 'OCA + Ours' indicates that we directly plug our method into OCA [33]. + +We still directly plug our method into the baseline method [22] and do not calculate the uncertainty loss. We can see that when the IOU threshold is set to 0.5 and 0.75, plugging our method effectively improves the performance of the baseline method. Particularly, when the IOU threshold is set to 0.75, for the three different settings, our method separately boosts iOD's performance by $2.3\%$ , $2.9\%$ , and $4.1\%$ . These results show that our method could significantly improve the discrimination of the object detector. + +# 4.4. Ablation and Visualization Analysis + +In this section, we utilize BDD-100k as the ID data for training and MS-COCO as the OOD data to perform an ablation analysis of our method. + +Analysis of SR-VAE. In this paper, our method mainly contains the LoG operator used for enhancing object-related information, the VAE module used to generate diverse augmented features of the classification features, and the cycle-consistent conditional VAE module used for synthesizing virtual OOD features. Here, we make an ablation analysis of our method. Table 4 shows the ablation results. We can see that employing the proposed three modules could significantly improve the performance of OOD object detection. Particularly, compared with VOS [7], synthesizing virtual OOD features improves the performance by around $5.21\%$ based on the FPR95 metric, which shows that the generated virtual OOD features could alleviate the impact of lacking unknown data for supervision and enhance the ability of distinguishing OOD objects. Meanwhile, employing the + +
10 + 10 settingaerocyclebirdboatbottlebuscarcatchaircowtabledoghorsebikepersonplantsheepsofatraintvmAP
Faster ILOD (50) [32]72.875.771.260.561.770.483.376.653.172.336.770.966.867.666.124.763.148.157.143.662.2
ORE (50) [19]63.570.958.942.934.176.280.776.334.166.156.170.480.272.381.842.771.668.17767.764.6
OW-DETR (50) [10]61.869.167.845.847.378.378.478.636.271.557.575.376.277.479.540.166.866.375.664.165.7
ROSETTA (50) [45]74.276.264.954.457.476.184.468.852.467.062.963.379.872.878.140.162.361.272.466.866.8
iOD (50) [22]76.074.667.555.957.675.185.477.043.770.860.166.476.072.674.639.764.060.268.560.566.3
iOD + Ours (50)75.975.268.855.355.577.785.679.349.478.261.075.381.474.579.343.872.567.070.265.769.6
iOD (75) [22]39.036.528.419.424.247.256.741.019.148.021.132.143.036.340.014.840.136.537.345.335.3
iOD + Ours (75)43.641.031.324.929.855.460.844.122.446.729.532.335.638.335.715.146.934.637.946.737.6
15 + 5 settingaerocyclebirdboatbottlebuscarcatchaircowtabledoghorsebikepersonplantsheepsofatraintvmAP
Faster ILOD (50) [32]66.578.171.854.661.468.482.682.752.174.363.178.680.578.480.436.761.759.367.959.167.9
ORE (50) [19]75.481.067.151.955.777.285.681.746.176.255.476.786.278.582.132.863.654.777.764.668.5
OW-DETR (50) [10]77.176.569.251.361.379.884.281.049.779.658.179.083.167.885.433.265.162.073.965.069.4
ROSETTA (50) [45]76.577.565.156.060.078.385.578.749.568.267.471.283.975.782.043.060.664.172.867.469.2
iOD (50) [22]78.479.766.954.856.277.784.679.147.775.061.874.781.677.580.237.858.054.673.056.167.8
iOD + Ours (50)78.380.370.551.660.279.485.976.252.579.465.281.883.776.177.941.162.863.872.667.970.4
iOD (75) [22]40.740.928.719.123.861.656.138.823.647.518.740.140.241.539.89.140.632.441.947.636.6
iOD + Ours (75)44.444.536.521.227.655.563.739.824.950.327.241.647.943.941.411.339.138.643.148.539.5
19 + 1 settingaerocyclebirdboatbottlebuscarcatchaircowtabledoghorsebikepersonplantsheepsofatraintvmAP
Faster ILOD (50) [32]64.274.773.255.553.770.882.982.651.679.758.778.881.875.377.443.173.861.769.861.168.6
ORE (50) [19]67.376.860.048.458.881.186.575.841.579.654.672.885.981.782.444.875.868.275.760.168.9
OW-DETR (50) [10]70.577.273.854.055.679.080.880.643.280.453.577.589.582.074.743.371.966.679.462.070.2
ROSETTA (50) [45]75.377.965.356.255.379.684.672.949.273.768.371.078.977.780.744.069.668.576.168.369.6
iOD (50) [22]78.277.569.455.056.078.484.279.246.679.063.278.582.779.179.944.173.266.376.457.670.2
iOD + Ours (50)76.683.574.757.058.077.085.682.551.582.761.481.682.979.877.647.474.768.474.159.071.8
iOD (75) [22]35.944.731.622.426.952.056.538.721.648.421.235.937.930.738.717.238.534.240.746.636.0
iOD + Ours (75)36.445.136.118.028.953.262.238.525.355.127.446.845.942.940.320.950.837.044.447.140.1
+ +Table 3. Performance (%) analysis of class-incremental object detection. 'iOD + Ours' indicates that our method is plugged into iOD [22]. Here, '50' and '75' separately represent that the mAP metric is calculated when the IOU threshold is set to 0.5 and 0.75. + +
C-VAELoGR-VAEFPR95 ↓AUROC ↑mAP↑
✓39.06%87.83%31.3%
✓✓37.92%88.08%31.2%
✓✓35.13%89.22%31.3%
✓✓✓32.23%90.69%31.5%
+ +Table 4. Ablation analysis of SR-VAE for unsupervised OOD-OD. 'C-VAE' is the proposed cycle-consistent conditional VAE module. 'R-VAE' indicates the VAE module that is used to generate diverse augmented features of the classification features. + +LoG operator and R-VAE modules further boosts the performance significantly, which demonstrates that using these two modules is beneficial for enhancing object-related information in the extracted low-level features and improving the discrimination ability of the object detector. + +Analysis of the LoG kernel size. To improve the performance of object localization, we employ the LoG operation (Eq. (1) and (2)) to perform structure enhancement, which is beneficial for strengthening object-related information. Here, we make an ablation analysis of the LoG kernel size. And we only change the kernel size. The other modules are kept unchanged. Table 5 shows the results. We can see that the performance is affected by the kernel size. Small kernel size does not sufficiently capture object structure information, which weakens the performance. For our + +
LoG Kernel SizeFPR95 ↓AUROC ↑mAP↑
3 × 334.96%87.94%30.9%
5 × 533.85%89.18%31.3%
7 × 733.08%89.76%31.2%
9 × 932.23%90.69%31.5%
11 × 1132.93%90.35%31.6%
+ +Table 5. Ablation analysis of the LoG kernel size. + +method, the performance of using $9 \times 9$ kernel is the best. + +Analysis of the iteration number. To reduce the risk of misclassifying ID objects into the OOD category, we design a VAE module (Eq. (3)) to generate multiple augmented features of the classification features, which is instrumental in improving the discrimination ability of the object classifier. Here, we make an ablation analysis of the iteration number $T$ . And we only change the iteration number and keep other modules unchanged. Table 6 shows the ablation results. We can see that generating multiple augmented features could improve the detection performance effectively. This shows that enhancing the classification ability of the object classifier is meaningful. Besides, we observe that when the iteration number is larger than a certain threshold, the performance could not be boosted effectively. The reason may be that the object classifier is a linear classifier, which could not sufficiently exploit these augmented fea + +![](images/89f9fa3f2b3c4ee91d39fa6ceee542e2df060c0a96fa6b691b270aa2a318eb8b.jpg) + +![](images/35812b7634678e8388946905d41b7e063c09f55308a2180fb99c7982698229b4.jpg) +Figure 5. Detection results on OpenImages. The first and second rows respectively indicate results based on VOS [7] and our method. + +![](images/bd12fc77748a985d8bb3d6e28e09063b395e30d408d7ea6d313a1e93e54a3178.jpg) + +![](images/1a0f80da737a31486176cd41f90c8effa2ba0b7ef064d18c59c82ff216b0bbd0.jpg) + +![](images/ce54a6a8450f62fbe26910666007291a73c6c36b23d57f6ff1cef06e056a6ae0.jpg) + +![](images/952c27b9e295be94e01673f3bf1fbd1c8a41229bc87eddb1c19f2a5688ad978a.jpg) + +![](images/ba1d69ea83b6c9090394af24215c0e95dea0e2ffc58933bd933c857dee4848db.jpg) + +![](images/fb3c03b8671d8cb98fdb2e60b9d1be9dcdc6fb1b7bb93e71e1375dd98bc0caa0.jpg) + +![](images/56ab255a820cd51ca4122b810fc156a2aef5e93d1b94a3ccbf110d905a5c0499.jpg) + +![](images/3bce11c4fedd3e220508e5d102b2d758a98fc9add14a228f66d3781be67e4b02.jpg) + +![](images/f87167f4f4638cb509a790a55dfc659d9405f1116016ef9f7097fc0d29510751.jpg) + +![](images/24c97d69e457679bad55f10337412ade86c7d39a79a20d224d51ce06afeda4ca.jpg) + +![](images/1f0c47b6ceaa425026c5b1b6d4c1461846a093fa4ff687be6b508baeb9607d66.jpg) +(a) Input Image + +![](images/ac5149f738ce1b9416fe0c90a7c67e81d282591a9823f4a6e3c03f52677d1a74.jpg) + +![](images/5a2a6274fbb080542fe601c4f673d6fb49083002714f18842191ffc1ad763c69.jpg) + +![](images/41bd8335e03dfe6faecdcf3e9f79942bd18890a5759d113d0a09feded9c2150b.jpg) +(b) Structure Map + +![](images/22365964cae6857acd59b6231c7fff42b0b1f34f11fb1b4b97a4d81fb589df97.jpg) + +![](images/75d10ba57a81d1052d0e970ec8b5c0bcf4253f50cae637dea9cd2c247d36ceb7.jpg) + +![](images/568b22420d49cfd2e3628219a99b5b71d6bfe217f44f242199e6d07be7ab1b48.jpg) +(c) Virtual OOD Map + +![](images/ef925ab32eaf3aee4ede58697db25ae2ec4e1c51372e3c0b29c4392aeb6480c3.jpg) + +![](images/ce7d39d16192018f2dbc35b287b9d623ee875ccdb558d60df1405258d6211895.jpg) + +![](images/de4efece6ebf8e033627f5ef8966824b5145c0e73dc38298d6b42e06f82b467b.jpg) +(d) Input Image +Figure 6. Visualization of the Structure-Enhanced map $E$ (Eq. (2)) and Virtual OOD map $\pmb{O}$ (Eq. (5)) based on the OOD data (MS-COCO). For each feature map, the channels corresponding to the maximum value are selected for visualization. + +![](images/8cbd93483275948c8d67b8e2e133475aa5b4df7c6c4e51f7ab85c82e85c15d52.jpg) + +![](images/034b8de9b7568051921b25ef07845aae1de6dd6b4e0d56c344cdb78f8cc87d23.jpg) + +![](images/ebde2aeee30eb042bd0f2747e45b0c458ccbcfee722540513cb4989d08425e99.jpg) +(e) Structure Map + +![](images/65784a6220bf019f31080fd3f6583faba573182198bffb4d7c8b1b185a41f427.jpg) + +![](images/67e5e180659a3d674758c1558576bc7a28a81c29dd0f3a27151f2e310ae86aaf.jpg) + +![](images/ebaa659f64db983c2f9a0ee7c7db643d92d36b242ea33e525894c689ba3b9b73.jpg) +(f) Virtual OOD Map + +
Iteration Number TFPR95 ↓AUROC ↑mAP↑
137.24%88.12%31.2%
332.23%90.69%31.5%
532.46%90.23%31.3%
732.93%90.07%31.2%
+ +Table 6. Ablation analysis of the iteration number $T$ . + +tures. For our method, when the iteration number is set to 3, the performance of OOD detection is the best. + +Analysis of cycle-consistent conditional VAE. In order to effectively synthesize virtual OOD features, we propose a cycle-consistency loss $\mathcal{L}_{\mathrm{cycle}}$ (Eq. (8)) to reduce the impact of lacking paired samples. Here, we make an ablation analysis of $\mathcal{L}_{\mathrm{cycle}}$ . Based on the FPR95 metric, removing $\mathcal{L}_{\mathrm{cycle}}$ increases the performance by around $3.8\%$ . This shows using the cycle-consistency loss $\mathcal{L}_{\mathrm{cycle}}$ is beneficial for synthesizing virtual OOD features and improving the ability of distinguishing OOD objects. + +Visualization analysis. Fig. 6 shows some visualization examples. Particularly, we can see that the map $E$ contains plentiful object-related information, which shows that using the LoG operation is indeed helpful for enhancing object-related information. Furthermore, we observe that the synthesized virtual OOD map $O$ involves sufficient informa + +tion that is different from object-related features, which indicates that leveraging the synthesized OOD features is instrumental in reducing the impact of lacking unknown data and improving the discrimination ability. + +# 5. Conclusion + +For unsupervised OOD-OD, we propose an approach of Structure-Enhanced Recurrent VAE. Particularly, to reduce the risk of misclassifying ID objects into the OOD category, an LoG operator and a dedicated recurrent VAE used to generate diverse augmented features are presented to strengthen the discrimination ability. Meanwhile, to alleviate the impact of lacking unknown data, we design a cycle-consistent conditional VAE to synthesize virtual OOD features, which boosts the performance of distinguishing OOD objects. Extensive experiments on three different tasks and visualization analyses demonstrate the superiorities of our method. + +Acknowledgement. Our work was supported in part by Key Research and Development Program of Shaanxi under Grant 2021ZDLGY01-03, the National Natural Science Foundation of China under Grant 62102293, 62132016, 62171343, and 62071361, and the Fundamental Research Funds for the Central Universities ZDRC2102. + +# References + +[1] Martin Arjovsky, Léon Bottou, Ishaan Gulrajani, and David Lopez-Paz. Invariant risk minimization. arXiv preprint arXiv:1907.02893, 2019. 2 +[2] Abhijit Bendale and Terrance E Boult. Towards open set deep networks. In CVPR, pages 1563-1572, 2016. 2 +[3] Hakan Bilen and Andrea Vedaldi. Weakly supervised deep detection networks. 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CVPR, 2022. 2 \ No newline at end of file diff --git a/2023/Discriminating Known From Unknown Objects via Structure-Enhanced Recurrent Variational AutoEncoder/images.zip b/2023/Discriminating Known From Unknown Objects via Structure-Enhanced Recurrent Variational AutoEncoder/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..8d2f7f6121bd1b996489b549a7c4bf57f596220a --- /dev/null +++ b/2023/Discriminating Known From Unknown Objects via Structure-Enhanced Recurrent Variational AutoEncoder/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:7b8d11e3f406579eb8779cddee7d48a88a569f2e2d81072684e405c644e43c04 +size 1067017 diff --git a/2023/Discriminating Known From Unknown Objects via Structure-Enhanced Recurrent Variational AutoEncoder/layout.json b/2023/Discriminating Known From Unknown Objects via Structure-Enhanced Recurrent Variational AutoEncoder/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..f1b0bc02536f0578aead7cdf6d1ebaea238934fc --- /dev/null +++ b/2023/Discriminating Known From Unknown Objects via Structure-Enhanced Recurrent Variational AutoEncoder/layout.json @@ -0,0 +1,11261 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 121, + 103, + 473, + 138 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 121, + 103, + 473, + 138 + ], + "spans": [ + { + "bbox": [ + 121, + 103, + 473, + 138 + ], + "type": "text", + "content": "Discriminating Known from Unknown Objects via Structure-Enhanced Recurrent Variational AutoEncoder" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 135, + 162, + 457, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 135, + 162, + 457, + 203 + ], + "spans": [ + { + "bbox": [ + 135, + 162, + 457, + 203 + ], + "type": "text", + "content": "Among Wu, Cheng Deng* \nSchool of Electronic Engineering, Xidian University, Xi'an, China \namwu@xidian.edu.cn, chdeng@mail.xidian.edu.cn" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "spans": [ + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 256, + 290, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 256, + 290, + 593 + ], + "spans": [ + { + "bbox": [ + 46, + 256, + 290, + 593 + ], + "type": "text", + "content": "Discriminating known from unknown objects is an important essential ability for human beings. To simulate this ability, a task of unsupervised out-of-distribution object detection (OOD-OD) is proposed to detect the objects that are never-seen-before during model training, which is beneficial for promoting the safe deployment of object detectors. Due to lacking unknown data for supervision, for this task, the main challenge lies in how to leverage the known in-distribution (ID) data to improve the detector's discrimination ability. In this paper, we first propose a method of Structure-Enhanced Recurrent Variational AutoEncoder (SR-VAE), which mainly consists of two dedicated recurrent VAE branches. Specifically, to boost the performance of object localization, we explore utilizing the classical Laplacian of Gaussian (Log) operator to enhance the structure information in the extracted low-level features. Meanwhile, we design a VAE branch that recurrently generates the augmentation of the classification features to strengthen the discrimination ability of the object classifier. Finally, to alleviate the impact of lacking unknown data, another cycle-consistent conditional VAE branch is proposed to synthesize virtual OOD features that deviate from the distribution of ID features, which improves the capability of distinguishing OOD objects. In the experiments, our method is evaluated on OOD-OD, open-vocabulary detection, and incremental object detection. The significant performance gains over baselines show the superiorities of our method. The code will be released at https://github.com/AmingWu/SR-VAE." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 614, + 128, + 627 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 614, + 128, + 627 + ], + "spans": [ + { + "bbox": [ + 47, + 614, + 128, + 627 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 635, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 635, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 635, + 287, + 696 + ], + "type": "text", + "content": "Recent years have witnessed the rapid development of deep learning based object detection [5,12,34,36,41], which often follows a close-set assumption that the training and testing processes share the same category space. However, the practical scenario is open and filled with unknown" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 307, + 230, + 545, + 355 + ], + "blocks": [ + { + "bbox": [ + 307, + 230, + 545, + 355 + ], + "lines": [ + { + "bbox": [ + 307, + 230, + 545, + 355 + ], + "spans": [ + { + "bbox": [ + 307, + 230, + 545, + 355 + ], + "type": "image", + "image_path": "7d4d371428dcf496326f629095ad3735d7659a23670c12ffbd2d05410cf99fee.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 358, + 547, + 457 + ], + "lines": [ + { + "bbox": [ + 305, + 358, + 547, + 457 + ], + "spans": [ + { + "bbox": [ + 305, + 358, + 547, + 457 + ], + "type": "text", + "content": "Figure 1. Discriminating known from unknown objects (as shown in green boxes) by synthesizing virtual OOD features. For OOD-OD, to alleviate the impact of lacking unknown data, we present an SR-VAE method to constrain the synthesized features (as shown in blue stars) to deviate from the distribution of ID features (as shown in orange). Meanwhile, we consider enhancing the discrimination of the classifier to reduce the risk of misclassifying the ID objects into the OOD category. Through these operations, the ability of distinguishing OOD objects could be improved significantly." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 461, + 545, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 461, + 545, + 544 + ], + "spans": [ + { + "bbox": [ + 304, + 461, + 545, + 544 + ], + "type": "text", + "content": "objects, e.g., in Fig. 1, an autonomous vehicle may encounter an unseen camel, presenting significant challenges for close-set assumption based detectors. To promote the safe application of detectors, a task of unsupervised out-of-distribution object detection (OOD-OD) [7] is recently proposed, which aims to detect the objects never-seen-before during training without accessing any auxiliary data." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 545, + 546, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 546, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 546, + 700 + ], + "type": "text", + "content": "Towards unsupervised OOD-OD, since there is no auxiliary data available for supervision, leveraging the known in-distribution (ID) data to enhance the detector's discrimination ability becomes the critical challenge. One feasible solution is to synthesize a series of virtual OOD features [7, 35] based on the ID data, which is beneficial for promoting the object detector to learn a clear decision boundary between ID and OOD objects. To this end, the work [7] attempts to synthesize virtual features from the low-likelihood region of the estimated class-conditional distribution. However, this method requires a large number of objects for each category to estimate the distribution, limiting its application to the case of few samples." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "text", + "content": "As shown in Fig. 1, in this paper, we consider improvis" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "type": "text", + "content": "*Corresponding author." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23956" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": "ing the performance of OOD object detection from two perspectives: One is to strengthen the discrimination capability of the object classifier for the known ID objects, which is conducive to reduce the risk of misclassifying the ID objects into the OOD category. Another is to synthesize the virtual OOD features that significantly deviate from the distribution of the ID features, which is instrumental in boosting the performance of distinguishing OOD objects from ID objects. To attain these two goals, we explore exploiting Variational AutoEncoder (VAE) [15, 20] to separately generate the augmented ID features and virtual OOD features." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 205, + 289, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 205, + 289, + 350 + ], + "spans": [ + { + "bbox": [ + 46, + 205, + 289, + 350 + ], + "type": "text", + "content": "Specifically, an approach of Structure-Enhanced Recurrent Variational AutoEncoder (SR-VAE) is proposed, which mainly consists of two dedicated recurrent VAE branches. In general, an object detector should first localize objects. Then, an object classifier is used to discriminate these objects [12, 36]. To improve the localization performance, enhancing the object-related information in the extracted features is meaningful. To this end, after extracting the low-level features of an input image, we present to utilize the classical Laplacian of Gaussian (LoG) operator [23] to obtain structure-related information, which is used to fuse into the existing features to strengthen the localization ability." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 350, + 289, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 350, + 289, + 495 + ], + "spans": [ + { + "bbox": [ + 46, + 350, + 289, + 495 + ], + "type": "text", + "content": "Next, in order to enhance the discrimination ability, inspired by Invariant Risk Minimization [1], we explore constructing a set of diverse environments to intensify the variance of the input classification features. Concretely, a VAE module [17, 20, 43] is exploited to recurrently output multiple augmented features of the classification features, i.e., the current output is taken as the input of the next iteration. Since the input of each iteration is different, by means of the variation operation, the diversity of the output features could be enlarged. Then, the discrimination ability is improved by minimizing the prediction discrepancy between the augmented features and the classification features." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 495, + 289, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 495, + 289, + 663 + ], + "spans": [ + { + "bbox": [ + 46, + 495, + 289, + 663 + ], + "type": "text", + "content": "Finally, to alleviate the impact of lacking unknown data, we present a cycle-consistent conditional VAE [40] to synthesize virtual OOD features in the absence of paired supervision samples. Concretely, to ameliorate the synthesized features to deviate from the distribution of ID features, we first insert label information in the latent space to force a deterministic constrained representation. Meanwhile, by maximizing the discrepancy between the synthesized features and the input features, the synthesized features could be facilitated to contain plentiful OOD-relevant information, which enhances the ability of distinguishing OOD objects. In the experiments, our method is separately evaluated on three different tasks. Extensive experimental results on multiple datasets demonstrate the superiorities of our method." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 59, + 664, + 246, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 664, + 246, + 675 + ], + "spans": [ + { + "bbox": [ + 59, + 664, + 246, + 675 + ], + "type": "text", + "content": "The contributions are summarized as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 677, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 288, + 713 + ], + "type": "text", + "content": "(1) For unsupervised OOD-OD, we observe that using the classical LoG operator could effectively enhance object-related information in the extracted low-level features." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "text", + "content": "(2) To reduce the risk of misclassifying ID objects into the OOD category, we design a dedicated recurrent VAE to generate diverse augmented features of the input classification features, which is beneficial for improving the discrimination ability of the object classifier." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 133, + 547, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 133, + 547, + 180 + ], + "spans": [ + { + "bbox": [ + 304, + 133, + 547, + 180 + ], + "type": "text", + "content": "(3) To alleviate the impact of lacking unknown data for supervision, we present a cycle-consistent conditional VAE to synthesize virtual OOD features, which is instrumental in distinguishing OOD objects from ID objects." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 180, + 547, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 180, + 547, + 240 + ], + "spans": [ + { + "bbox": [ + 304, + 180, + 547, + 240 + ], + "type": "text", + "content": "(4) In the experiments, our method is evaluated on OOD-OD [7], open-vocabulary detection [33, 49], and incremental object detection [22, 39]. Particularly, for OpenImages dataset [24], compared with the baseline method [7], our method significantly reduces FPR95 by around " + }, + { + "bbox": [ + 304, + 180, + 547, + 240 + ], + "type": "inline_equation", + "content": "13.73\\%" + }, + { + "bbox": [ + 304, + 180, + 547, + 240 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 251, + 392, + 262 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 251, + 392, + 262 + ], + "spans": [ + { + "bbox": [ + 306, + 251, + 392, + 262 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 270, + 547, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 270, + 547, + 437 + ], + "spans": [ + { + "bbox": [ + 304, + 270, + 547, + 437 + ], + "type": "text", + "content": "OOD Detection. In order to promote the safe application of models in real scenarios, OOD detection [4, 14, 18] has recently attracted much attention, whose goal is to distinguish OOD data from ID data. Most methods [27, 31, 46, 52] focus on OOD image classification and explore a proper regularization-based method for this task. Particularly, Bendale et al. [2] developed the OpenMax score based on the extreme value theory. Liu et al. [30] proposed to utilize the energy score to discriminate OOD data from ID data. Zhou [52] rethought the commonly used reconstruction autoencoder for OOD detection. Though these methods have been demonstrated to be effective, since object detection involves object localization and classification, these methods could not directly apply to OOD-OD." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 438, + 547, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 438, + 547, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 438, + 547, + 665 + ], + "type": "text", + "content": "Recently, unsupervised OOD-OD [7] is proposed to localize and recognize the objects never-seen-before during training. For this task, Du et al. [7] proposed to use large-scale samples to estimate the distribution of each ID category, which is used to synthesize virtual OOD features. However, calculating accurate distribution estimation may limit its application in real scenarios. Harakeh et al. [11] designed an uncertainty estimation method for the localization branch, which could not well address OOD-OD that involves localization and classification. Besides, the work [6] proposed to use auxiliary video datasets to learn unknown-aware knowledge to effectively improve the performance of distinguishing OOD objects, which could not be used for unsupervised OOD-OD. In this paper, we explore employing the idea of VAE [15, 20] to synthesize virtual OOD features that significantly deviate from the distribution of ID features. And these virtual features are used to strengthen the discrimination ability. Experimental results on three different tasks show the effectiveness of our method." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": "Variational AutoEncoder. The goal of VAE [15,20,21, 40] is to map the input data to a multivariate latent distribution, which efficiently addresses the generation problem for high-dimensional data. Most existing methods [15, 17, 44]" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23957" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 71, + 545, + 236 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 545, + 236 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 545, + 236 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 545, + 236 + ], + "type": "image", + "image_path": "330d41d90f635edd7312b3476fcd2c33ae0bd7722fbcfd324f4ab2812bee90b7.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 239, + 547, + 307 + ], + "lines": [ + { + "bbox": [ + 46, + 239, + 547, + 307 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 547, + 307 + ], + "type": "text", + "content": "Figure 2. Structure-Enhanced Recurrent Variational AutoEncoder for Unsupervised OOD-OD. To improve localization performance, we employ the LoG operator to enhance the structure-related information in the features extracted by the backbone network. Meanwhile, we design a VAE module to recurrently generate diverse augmented features of the input classification features, which is beneficial for strengthening the discrimination ability of the object classifier. Finally, to alleviate the impact of lacking unknown data, we propose a cycle-consistent conditional VAE to synthesize virtual OOD features that deviate from the distribution of the ID features significantly, which boosts the performance of distinguishing OOD objects." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 316, + 289, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 316, + 289, + 437 + ], + "spans": [ + { + "bbox": [ + 46, + 316, + 289, + 437 + ], + "type": "text", + "content": "attempt to adjust the latent representations to generate clear images containing rich content. Particularly, " + }, + { + "bbox": [ + 46, + 316, + 289, + 437 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 316, + 289, + 437 + ], + "type": "text", + "content": "-VAE [15] is an implementation with a weighted Kullback-Leibler (KL) divergence term to automatically discover disentangled representations without supervision. Conditional VAE [40] inserts label information in the latent space to force a deterministic constrained representation. Different from the above works focusing on pixel-level generation, we explore using VAE to generate virtual OOD features. Experimental results on OOD-OD show the advantages of our method." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 447, + 249, + 459 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 447, + 249, + 459 + ], + "spans": [ + { + "bbox": [ + 47, + 447, + 249, + 459 + ], + "type": "text", + "content": "3. Structure-Enhanced Recurrent VAE" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 467, + 287, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 467, + 287, + 515 + ], + "spans": [ + { + "bbox": [ + 46, + 467, + 287, + 515 + ], + "type": "text", + "content": "In this paper, we follow the settings introduced in the work [7]. During training, we can only access the ID data. During inference, the object detector should own the capability of distinguishing ID objects from OOD objects." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 522, + 269, + 536 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 522, + 269, + 536 + ], + "spans": [ + { + "bbox": [ + 47, + 522, + 269, + 536 + ], + "type": "text", + "content": "3.1. Structure Enhancement via LoG Operator" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 540, + 287, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 540, + 287, + 635 + ], + "spans": [ + { + "bbox": [ + 46, + 540, + 287, + 635 + ], + "type": "text", + "content": "In general, an object detector should first localize objects accurately and then distinguish them as ID categories or OOD categories. To this end, it is important to enhance object-related information (e.g., object structure information). In the field of image processing, LoG operator [23] is a popular algorithm for edge detection. We explore performing the LoG operation on the extracted low-level features to strengthen the structure-relevant information." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 635, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 635, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 635, + 287, + 714 + ], + "type": "text", + "content": "Concretely, as shown in Fig. 2, we follow the baseline work [7] and adopt the widely used object detector, i.e., Faster R-CNN [12, 36], as the basic detection model. Given an input image, we first employ the backbone network, e.g., ResNet [13], to extract the corresponding feature map " + }, + { + "bbox": [ + 46, + 635, + 287, + 714 + ], + "type": "inline_equation", + "content": "F \\in \\mathbb{R}^{w \\times h \\times c}" + }, + { + "bbox": [ + 46, + 635, + 287, + 714 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 635, + 287, + 714 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 46, + 635, + 287, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 635, + 287, + 714 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 46, + 635, + 287, + 714 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 635, + 287, + 714 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 635, + 287, + 714 + ], + "type": "text", + "content": " separately denote width, height, and channel number. To obtain rich structure" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 316, + 534, + 328 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 316, + 534, + 328 + ], + "spans": [ + { + "bbox": [ + 305, + 316, + 534, + 328 + ], + "type": "text", + "content": "information, a " + }, + { + "bbox": [ + 305, + 316, + 534, + 328 + ], + "type": "inline_equation", + "content": "9 \\times 9" + }, + { + "bbox": [ + 305, + 316, + 534, + 328 + ], + "type": "text", + "content": " LoG kernel " + }, + { + "bbox": [ + 305, + 316, + 534, + 328 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 305, + 316, + 534, + 328 + ], + "type": "text", + "content": " is defined as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 317, + 334, + 545, + 435 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 334, + 545, + 435 + ], + "spans": [ + { + "bbox": [ + 317, + 334, + 545, + 435 + ], + "type": "interline_equation", + "content": "\\mathcal {G} = \\left[ \\begin{array}{c c c c c c c c c} 0 & 1 & 1 & 2 & 2 & 2 & 1 & 1 & 0 \\\\ 1 & 2 & 4 & 5 & 5 & 5 & 4 & 2 & 1 \\\\ 1 & 4 & 5 & 3 & 0 & 3 & 5 & 4 & 1 \\\\ 2 & 5 & 3 & - 1 2 & - 2 4 & - 1 2 & 3 & 5 & 2 \\\\ 2 & 5 & 0 & - 2 4 & - 4 0 & - 2 4 & 0 & 5 & 2 \\\\ 2 & 5 & 3 & - 1 2 & - 2 4 & - 1 2 & 3 & 5 & 2 \\\\ 1 & 4 & 5 & 3 & 0 & 3 & 5 & 4 & 1 \\\\ 1 & 2 & 4 & 5 & 5 & 5 & 4 & 2 & 1 \\\\ 0 & 1 & 1 & 2 & 2 & 2 & 1 & 1 & 0 \\end{array} \\right]. \\tag {1}", + "image_path": "c63fa01432f7011116ca2169583069e5b755b091692bd1f6d5a40f43a99730bb.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 441, + 546, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 441, + 546, + 477 + ], + "spans": [ + { + "bbox": [ + 305, + 441, + 546, + 477 + ], + "type": "text", + "content": "Next, " + }, + { + "bbox": [ + 305, + 441, + 546, + 477 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 305, + 441, + 546, + 477 + ], + "type": "text", + "content": " is used to perform a convolution operation on " + }, + { + "bbox": [ + 305, + 441, + 546, + 477 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 305, + 441, + 546, + 477 + ], + "type": "text", + "content": " to obtain the structure-enhanced map " + }, + { + "bbox": [ + 305, + 441, + 546, + 477 + ], + "type": "inline_equation", + "content": "E\\in \\mathbb{R}^{w\\times h\\times c}" + }, + { + "bbox": [ + 305, + 441, + 546, + 477 + ], + "type": "text", + "content": ". The processes are shown as follows:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 358, + 486, + 545, + 500 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 486, + 545, + 500 + ], + "spans": [ + { + "bbox": [ + 358, + 486, + 545, + 500 + ], + "type": "interline_equation", + "content": "\\mathcal {E} = F * \\mathcal {G}, \\quad E = \\Psi ([ F, \\mathcal {E} ]), \\tag {2}", + "image_path": "2f71db6ce968ac8c2cf7cf6dede29b8422857f5e0b9a65331caa9af870765f1a.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 508, + 547, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 508, + 547, + 593 + ], + "spans": [ + { + "bbox": [ + 304, + 508, + 547, + 593 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 508, + 547, + 593 + ], + "type": "inline_equation", + "content": "\\mathcal{E} \\in \\mathbb{R}^{w \\times h \\times c}" + }, + { + "bbox": [ + 304, + 508, + 547, + 593 + ], + "type": "text", + "content": " is the convolutional result containing plentiful structure-related information. " + }, + { + "bbox": [ + 304, + 508, + 547, + 593 + ], + "type": "inline_equation", + "content": "\\Psi(\\cdot) \\in \\mathbb{R}^{1 \\times 1 \\times 2c \\times c}" + }, + { + "bbox": [ + 304, + 508, + 547, + 593 + ], + "type": "text", + "content": " represents one-layer convolution to transform the number of channels. By fusing the structure information into existing features, the object-related information in " + }, + { + "bbox": [ + 304, + 508, + 547, + 593 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 304, + 508, + 547, + 593 + ], + "type": "text", + "content": " could be enhanced effectively, which is instrumental in improving the performance of object localization." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 599, + 542, + 612 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 599, + 542, + 612 + ], + "spans": [ + { + "bbox": [ + 305, + 599, + 542, + 612 + ], + "type": "text", + "content": "3.2. Recurrent VAE for Improving Discrimination" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 617, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 665 + ], + "type": "text", + "content": "To reduce the risk of misclassifying ID objects into the OOD category, we design a VAE module to recurrently generate diverse augmented features of the classification features, which enhances the discrimination ability." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "type": "text", + "content": "Specifically, as shown in Fig. 2, the enhanced map " + }, + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "type": "text", + "content": " is taken as the input of the RPN module to obtain a set of object proposals " + }, + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{O}" + }, + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "type": "text", + "content": ". Based on " + }, + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{O}" + }, + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "type": "text", + "content": ", RoI-Alignment followed by RoI-Feature extraction [12] is performed on " + }, + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "type": "text", + "content": " to output" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23958" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 70, + 289, + 155 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 289, + 155 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 289, + 155 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 289, + 155 + ], + "type": "image", + "image_path": "b4216e2c10a4824de61d4ef40a1aa2d8e8f53a45954991067e60cb68cb9f8488.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 156, + 287, + 233 + ], + "lines": [ + { + "bbox": [ + 46, + 156, + 287, + 233 + ], + "spans": [ + { + "bbox": [ + 46, + 156, + 287, + 233 + ], + "type": "text", + "content": "Figure 3. Cycle-consistent conditional VAE for synthesizing virtual OOD features. During the forward process, the OOD features " + }, + { + "bbox": [ + 46, + 156, + 287, + 233 + ], + "type": "inline_equation", + "content": "\\pmb{O}" + }, + { + "bbox": [ + 46, + 156, + 287, + 233 + ], + "type": "text", + "content": " are generated based on the ID features " + }, + { + "bbox": [ + 46, + 156, + 287, + 233 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 46, + 156, + 287, + 233 + ], + "type": "text", + "content": ". And during the backward process, the features " + }, + { + "bbox": [ + 46, + 156, + 287, + 233 + ], + "type": "inline_equation", + "content": "\\pmb{F}" + }, + { + "bbox": [ + 46, + 156, + 287, + 233 + ], + "type": "text", + "content": " are generated based on " + }, + { + "bbox": [ + 46, + 156, + 287, + 233 + ], + "type": "inline_equation", + "content": "\\pmb{O}" + }, + { + "bbox": [ + 46, + 156, + 287, + 233 + ], + "type": "text", + "content": ". By minimizing the cycle-consistency loss between " + }, + { + "bbox": [ + 46, + 156, + 287, + 233 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 46, + 156, + 287, + 233 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 156, + 287, + 233 + ], + "type": "inline_equation", + "content": "\\pmb{F}" + }, + { + "bbox": [ + 46, + 156, + 287, + 233 + ], + "type": "text", + "content": ", the synthesized features " + }, + { + "bbox": [ + 46, + 156, + 287, + 233 + ], + "type": "inline_equation", + "content": "\\pmb{O}" + }, + { + "bbox": [ + 46, + 156, + 287, + 233 + ], + "type": "text", + "content": " could be promoted to contain plentiful information that deviates from the distribution of the ID features." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 239, + 288, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 239, + 288, + 334 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 288, + 334 + ], + "type": "inline_equation", + "content": "P_{\\mathrm{in}} \\in \\mathbb{R}^{m \\times n}" + }, + { + "bbox": [ + 46, + 239, + 288, + 334 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 239, + 288, + 334 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 239, + 288, + 334 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 239, + 288, + 334 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 239, + 288, + 334 + ], + "type": "text", + "content": " separately denote the number of proposals and channels. Next, we first define two fully-connected networks (i.e., " + }, + { + "bbox": [ + 46, + 239, + 288, + 334 + ], + "type": "inline_equation", + "content": "\\Phi_{\\mu}(\\cdot)" + }, + { + "bbox": [ + 46, + 239, + 288, + 334 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 239, + 288, + 334 + ], + "type": "inline_equation", + "content": "\\Phi_{\\sigma}(\\cdot)" + }, + { + "bbox": [ + 46, + 239, + 288, + 334 + ], + "type": "text", + "content": ") as the encoder to estimate the corresponding means and variances. Then, an encoding operation is performed on the input. Finally, a decoder " + }, + { + "bbox": [ + 46, + 239, + 288, + 334 + ], + "type": "inline_equation", + "content": "\\Theta(\\cdot)" + }, + { + "bbox": [ + 46, + 239, + 288, + 334 + ], + "type": "text", + "content": " consisting of three fully-connected layers is leveraged to calculate the output. The overall processes at the " + }, + { + "bbox": [ + 46, + 239, + 288, + 334 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 239, + 288, + 334 + ], + "type": "text", + "content": "-th iteration are shown as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 82, + 341, + 287, + 358 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 341, + 287, + 358 + ], + "spans": [ + { + "bbox": [ + 82, + 341, + 287, + 358 + ], + "type": "interline_equation", + "content": "\\mu_ {t} = \\Phi_ {\\mu} \\left(H _ {t - 1}\\right), \\quad \\sigma_ {t} = \\Phi_ {\\sigma} \\left(H _ {t - 1}\\right), \\tag {3}", + "image_path": "a8c7c1f323a251d714ce297ed2e672c36665859094ed37ef786fa577379386c5.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 83, + 357, + 251, + 369 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 357, + 251, + 369 + ], + "spans": [ + { + "bbox": [ + 83, + 357, + 251, + 369 + ], + "type": "interline_equation", + "content": "h _ {t} = \\mu_ {t} + \\epsilon \\cdot \\exp (\\sigma_ {t}), \\qquad H _ {t} = \\Theta (h _ {t}),", + "image_path": "946c6faf32ef0a1ef421fbd44c5b7833270daa9c4a74a1ec8907fc2e681219de.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 376, + 287, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 376, + 287, + 437 + ], + "spans": [ + { + "bbox": [ + 46, + 376, + 287, + 437 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 376, + 287, + 437 + ], + "type": "inline_equation", + "content": "H_{t - 1}\\in \\mathbb{R}^{m\\times n}" + }, + { + "bbox": [ + 46, + 376, + 287, + 437 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 376, + 287, + 437 + ], + "type": "inline_equation", + "content": "H_{t}\\in \\mathbb{R}^{m\\times n}" + }, + { + "bbox": [ + 46, + 376, + 287, + 437 + ], + "type": "text", + "content": " respectively indicate the output of the previous iteration and that of the current iteration. And " + }, + { + "bbox": [ + 46, + 376, + 287, + 437 + ], + "type": "inline_equation", + "content": "H_0 = P_{\\mathrm{in}}" + }, + { + "bbox": [ + 46, + 376, + 287, + 437 + ], + "type": "inline_equation", + "content": "\\mu_t\\in \\mathbb{R}^{m\\times n}" + }, + { + "bbox": [ + 46, + 376, + 287, + 437 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 376, + 287, + 437 + ], + "type": "inline_equation", + "content": "\\sigma_t\\in \\mathbb{R}^{m\\times n}" + }, + { + "bbox": [ + 46, + 376, + 287, + 437 + ], + "type": "text", + "content": " are the estimated means and variances. " + }, + { + "bbox": [ + 46, + 376, + 287, + 437 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 46, + 376, + 287, + 437 + ], + "type": "text", + "content": " denotes Gaussian noise sampled from " + }, + { + "bbox": [ + 46, + 376, + 287, + 437 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(0,I)" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 437, + 288, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 437, + 288, + 534 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 288, + 534 + ], + "type": "text", + "content": "Through " + }, + { + "bbox": [ + 46, + 437, + 288, + 534 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 437, + 288, + 534 + ], + "type": "text", + "content": " iterations, we can obtain a set of augmented features " + }, + { + "bbox": [ + 46, + 437, + 288, + 534 + ], + "type": "inline_equation", + "content": "H = \\{H_{1},\\dots ,H_{T}\\}" + }, + { + "bbox": [ + 46, + 437, + 288, + 534 + ], + "type": "text", + "content": ". Finally, by minimizing the " + }, + { + "bbox": [ + 46, + 437, + 288, + 534 + ], + "type": "inline_equation", + "content": "KL" + }, + { + "bbox": [ + 46, + 437, + 288, + 534 + ], + "type": "text", + "content": "-divergence between the prediction probabilities from " + }, + { + "bbox": [ + 46, + 437, + 288, + 534 + ], + "type": "inline_equation", + "content": "H_{t}" + }, + { + "bbox": [ + 46, + 437, + 288, + 534 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 437, + 288, + 534 + ], + "type": "inline_equation", + "content": "P_{\\mathrm{in}}" + }, + { + "bbox": [ + 46, + 437, + 288, + 534 + ], + "type": "text", + "content": ", the discrimination ability of the object classifier could be enhanced effectively. During training, " + }, + { + "bbox": [ + 46, + 437, + 288, + 534 + ], + "type": "inline_equation", + "content": "P_{\\mathrm{in}}" + }, + { + "bbox": [ + 46, + 437, + 288, + 534 + ], + "type": "text", + "content": " is taken as the input of the object classifier and regressor to calculate the classification and localization losses. The joint training objective is shown as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 59, + 540, + 287, + 574 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 540, + 287, + 574 + ], + "spans": [ + { + "bbox": [ + 59, + 540, + 287, + 574 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {i n}} = \\mathcal {L} _ {\\mathrm {d e t}} + \\alpha \\cdot \\frac {1}{T} \\sum_ {t = 1} ^ {T} \\mathrm {K L} [ p (H _ {t} | H _ {t - 1}), p (P _ {\\mathrm {i n}}) ], \\tag {4}", + "image_path": "28a82661b566834153972a66175decafed4950d108413d00df2569f8fc94ca2a.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 580, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 580, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 580, + 287, + 628 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 580, + 287, + 628 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{det}}" + }, + { + "bbox": [ + 46, + 580, + 287, + 628 + ], + "type": "text", + "content": " is the sum of the classification loss " + }, + { + "bbox": [ + 46, + 580, + 287, + 628 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{cls}}" + }, + { + "bbox": [ + 46, + 580, + 287, + 628 + ], + "type": "text", + "content": " and the localization loss " + }, + { + "bbox": [ + 46, + 580, + 287, + 628 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{loc}}" + }, + { + "bbox": [ + 46, + 580, + 287, + 628 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 46, + 580, + 287, + 628 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{det}} = \\mathcal{L}_{\\mathrm{cls}} + \\mathcal{L}_{\\mathrm{loc}}" + }, + { + "bbox": [ + 46, + 580, + 287, + 628 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 580, + 287, + 628 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 580, + 287, + 628 + ], + "type": "text", + "content": " is a hyper-parameter. In the experiments, " + }, + { + "bbox": [ + 46, + 580, + 287, + 628 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 580, + 287, + 628 + ], + "type": "text", + "content": " is set to 0.001. " + }, + { + "bbox": [ + 46, + 580, + 287, + 628 + ], + "type": "inline_equation", + "content": "p(\\cdot)" + }, + { + "bbox": [ + 46, + 580, + 287, + 628 + ], + "type": "text", + "content": " indicates the prediction probability of the object classifier." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 635, + 237, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 635, + 237, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 635, + 237, + 647 + ], + "type": "text", + "content": "3.3. Synthesizing Virtual OOD Features" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 654, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 288, + 714 + ], + "type": "text", + "content": "Due to lacking unknown data for supervision, it is prone to misclassify OOD objects into ID categories. Hence, synthesizing virtual OOD data is important to distinguish OOD objects. A straightforward idea is to train generative models, e.g., GANs [9], to synthesize images, which is difficult" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 72, + 545, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 95 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 95 + ], + "type": "text", + "content": "to optimize [7]. Instead, we propose a cycle-consistent conditional VAE to synthesize virtual OOD features." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 96, + 545, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 96, + 545, + 156 + ], + "spans": [ + { + "bbox": [ + 304, + 96, + 545, + 156 + ], + "type": "text", + "content": "Particularly, as shown in Fig. 3, during the forward process, the extracted features " + }, + { + "bbox": [ + 304, + 96, + 545, + 156 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 304, + 96, + 545, + 156 + ], + "type": "text", + "content": " and corresponding ID label [1, 0] are first concatenated as " + }, + { + "bbox": [ + 304, + 96, + 545, + 156 + ], + "type": "inline_equation", + "content": "\\hat{F} \\in \\mathbb{R}^{w \\times h \\times (c + 2)}" + }, + { + "bbox": [ + 304, + 96, + 545, + 156 + ], + "type": "text", + "content": ". Then, two convolutional networks " + }, + { + "bbox": [ + 304, + 96, + 545, + 156 + ], + "type": "inline_equation", + "content": "W_{\\mu}" + }, + { + "bbox": [ + 304, + 96, + 545, + 156 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 96, + 545, + 156 + ], + "type": "inline_equation", + "content": "W_{\\sigma}" + }, + { + "bbox": [ + 304, + 96, + 545, + 156 + ], + "type": "text", + "content": " are defined to estimate the corresponding means and variances:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 353, + 160, + 545, + 176 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 353, + 160, + 545, + 176 + ], + "spans": [ + { + "bbox": [ + 353, + 160, + 545, + 176 + ], + "type": "interline_equation", + "content": "\\mu_ {f} = W _ {\\mu} * \\hat {F}, \\quad \\sigma_ {f} = W _ {\\sigma} * \\hat {F}, \\tag {5}", + "image_path": "3cf85aff2561e4078aaf00afe1e1bdbfddc4033eb420505e75ff0cce5dd37e4c.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 180, + 545, + 264 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 180, + 545, + 264 + ], + "spans": [ + { + "bbox": [ + 304, + 180, + 545, + 264 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 180, + 545, + 264 + ], + "type": "inline_equation", + "content": "\\mu_f \\in \\mathbb{R}^{w \\times h \\times c}" + }, + { + "bbox": [ + 304, + 180, + 545, + 264 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 180, + 545, + 264 + ], + "type": "inline_equation", + "content": "\\sigma_f \\in \\mathbb{R}^{w \\times h \\times c}" + }, + { + "bbox": [ + 304, + 180, + 545, + 264 + ], + "type": "text", + "content": ". And an encoding operation is performed to obtain " + }, + { + "bbox": [ + 304, + 180, + 545, + 264 + ], + "type": "inline_equation", + "content": "Z \\in \\mathbb{R}^{w \\times h \\times c}" + }, + { + "bbox": [ + 304, + 180, + 545, + 264 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 304, + 180, + 545, + 264 + ], + "type": "inline_equation", + "content": "Z = \\mu_f + \\epsilon \\cdot \\exp(\\sigma_f)" + }, + { + "bbox": [ + 304, + 180, + 545, + 264 + ], + "type": "text", + "content": ". Next, in order to generate virtual OOD features, " + }, + { + "bbox": [ + 304, + 180, + 545, + 264 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 304, + 180, + 545, + 264 + ], + "type": "text", + "content": " and corresponding OOD label [0, 1] are concatenated as " + }, + { + "bbox": [ + 304, + 180, + 545, + 264 + ], + "type": "inline_equation", + "content": "\\hat{Z} \\in \\mathbb{R}^{w \\times h \\times (c+2)}" + }, + { + "bbox": [ + 304, + 180, + 545, + 264 + ], + "type": "text", + "content": ". A decoding network " + }, + { + "bbox": [ + 304, + 180, + 545, + 264 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 304, + 180, + 545, + 264 + ], + "type": "text", + "content": " consisting of three convolutional layers is performed on " + }, + { + "bbox": [ + 304, + 180, + 545, + 264 + ], + "type": "inline_equation", + "content": "\\hat{Z}" + }, + { + "bbox": [ + 304, + 180, + 545, + 264 + ], + "type": "text", + "content": " to obtain the virtual OOD map " + }, + { + "bbox": [ + 304, + 180, + 545, + 264 + ], + "type": "inline_equation", + "content": "O \\in \\mathbb{R}^{w \\times h \\times c}" + }, + { + "bbox": [ + 304, + 180, + 545, + 264 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 265, + 545, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 265, + 545, + 373 + ], + "spans": [ + { + "bbox": [ + 304, + 265, + 545, + 373 + ], + "type": "text", + "content": "During the backward process, to alleviate the impact of lacking paired data for supervision, the concatenation result of " + }, + { + "bbox": [ + 304, + 265, + 545, + 373 + ], + "type": "inline_equation", + "content": "\\pmb{O}" + }, + { + "bbox": [ + 304, + 265, + 545, + 373 + ], + "type": "text", + "content": " and label [0, 1] is made convolution with " + }, + { + "bbox": [ + 304, + 265, + 545, + 373 + ], + "type": "inline_equation", + "content": "W_{\\mu}" + }, + { + "bbox": [ + 304, + 265, + 545, + 373 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 265, + 545, + 373 + ], + "type": "inline_equation", + "content": "W_{\\sigma}" + }, + { + "bbox": [ + 304, + 265, + 545, + 373 + ], + "type": "text", + "content": ". Next, we still take the concatenation of the encoding result and label [1, 0] as the input of the decoder " + }, + { + "bbox": [ + 304, + 265, + 545, + 373 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 304, + 265, + 545, + 373 + ], + "type": "text", + "content": " to obtain the output " + }, + { + "bbox": [ + 304, + 265, + 545, + 373 + ], + "type": "inline_equation", + "content": "\\pmb{F} \\in \\mathbb{R}^{w \\times h \\times c}" + }, + { + "bbox": [ + 304, + 265, + 545, + 373 + ], + "type": "text", + "content": ". The operations are the same as the forward process. Finally, we introduce a cycle-consistency loss to reduce the discrepancy between " + }, + { + "bbox": [ + 304, + 265, + 545, + 373 + ], + "type": "inline_equation", + "content": "\\pmb{F}" + }, + { + "bbox": [ + 304, + 265, + 545, + 373 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 265, + 545, + 373 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 304, + 265, + 545, + 373 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 304, + 265, + 545, + 373 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{cycle}} = \\frac{1}{wh}\\sum |F - F|" + }, + { + "bbox": [ + 304, + 265, + 545, + 373 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 373, + 545, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 373, + 545, + 443 + ], + "spans": [ + { + "bbox": [ + 304, + 373, + 545, + 443 + ], + "type": "text", + "content": "Moreover, to promote " + }, + { + "bbox": [ + 304, + 373, + 545, + 443 + ], + "type": "inline_equation", + "content": "\\pmb{O}" + }, + { + "bbox": [ + 304, + 373, + 545, + 443 + ], + "type": "text", + "content": " to deviate from the distribution of " + }, + { + "bbox": [ + 304, + 373, + 545, + 443 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 304, + 373, + 545, + 443 + ], + "type": "text", + "content": ", as shown in Fig. 2, based on the object proposals " + }, + { + "bbox": [ + 304, + 373, + 545, + 443 + ], + "type": "inline_equation", + "content": "\\mathcal{O}" + }, + { + "bbox": [ + 304, + 373, + 545, + 443 + ], + "type": "text", + "content": ", RoI-Alignment followed by RoI-Feature extraction is performed on " + }, + { + "bbox": [ + 304, + 373, + 545, + 443 + ], + "type": "inline_equation", + "content": "\\pmb{O}" + }, + { + "bbox": [ + 304, + 373, + 545, + 443 + ], + "type": "text", + "content": " to extract OOD features " + }, + { + "bbox": [ + 304, + 373, + 545, + 443 + ], + "type": "inline_equation", + "content": "P_{\\mathrm{odd}} \\in \\mathbb{R}^{m \\times n}" + }, + { + "bbox": [ + 304, + 373, + 545, + 443 + ], + "type": "text", + "content": ". Next, a loss " + }, + { + "bbox": [ + 304, + 373, + 545, + 443 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{dis}}" + }, + { + "bbox": [ + 304, + 373, + 545, + 443 + ], + "type": "text", + "content": " is defined to maximize the distance between the virtual OOD features and ID features:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 331, + 450, + 545, + 464 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 331, + 450, + 545, + 464 + ], + "spans": [ + { + "bbox": [ + 331, + 450, + 545, + 464 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {d i s}} = \\mathrm {K L} [ q (\\boldsymbol {O}), q (F) ] + | p (P _ {\\mathrm {o o d}}) - p (P _ {\\mathrm {i n}}) |, \\tag {6}", + "image_path": "348650d10b34489e49a4e49a5c72be22279d63cdb2ad2f19fd8c4575d6f0fe47.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 469, + 545, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 469, + 545, + 577 + ], + "spans": [ + { + "bbox": [ + 304, + 469, + 545, + 577 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 469, + 545, + 577 + ], + "type": "inline_equation", + "content": "q(\\cdot)" + }, + { + "bbox": [ + 304, + 469, + 545, + 577 + ], + "type": "text", + "content": " represents the probability distribution. By maximizing " + }, + { + "bbox": [ + 304, + 469, + 545, + 577 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{dis}}" + }, + { + "bbox": [ + 304, + 469, + 545, + 577 + ], + "type": "text", + "content": ", the distribution gap between " + }, + { + "bbox": [ + 304, + 469, + 545, + 577 + ], + "type": "inline_equation", + "content": "O" + }, + { + "bbox": [ + 304, + 469, + 545, + 577 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 469, + 545, + 577 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 304, + 469, + 545, + 577 + ], + "type": "text", + "content": " could be enlarged effectively, which promotes the synthesized features " + }, + { + "bbox": [ + 304, + 469, + 545, + 577 + ], + "type": "inline_equation", + "content": "O" + }, + { + "bbox": [ + 304, + 469, + 545, + 577 + ], + "type": "text", + "content": " to contain plentiful OOD information. Finally, to achieve the goal of distinguishing OOD objects from ID objects, " + }, + { + "bbox": [ + 304, + 469, + 545, + 577 + ], + "type": "inline_equation", + "content": "P_{\\mathrm{ood}}" + }, + { + "bbox": [ + 304, + 469, + 545, + 577 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 469, + 545, + 577 + ], + "type": "inline_equation", + "content": "P_{\\mathrm{in}}" + }, + { + "bbox": [ + 304, + 469, + 545, + 577 + ], + "type": "text", + "content": " are used to calculate an uncertainty loss [7], which regularizes the detector to produce a low OOD score for the ID object features, and a high OOD score for the synthesized OOD features:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 333, + 582, + 545, + 635 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 333, + 582, + 545, + 635 + ], + "spans": [ + { + "bbox": [ + 333, + 582, + 545, + 635 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\text {u n c e r t a i n t y}} = \\mathbb {E} _ {u \\sim P _ {\\mathrm {i n}}} [ - \\log \\frac {\\exp^ {- \\mathrm {E} (u)}}{1 + \\exp^ {- \\mathrm {E} (u)}} ] + \\tag {7} \\\\ \\mathbb {E} _ {v \\sim P _ {\\mathrm {o o d}}} [ - \\log \\frac {1}{1 + \\exp^ {- \\mathbf {E} (v)} ], \\\\ \\end{array}", + "image_path": "c0ee0d80415ba07a25e62aaebf082139a19ac3715f894833685efb634cab2107.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 640, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 640, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 640, + 545, + 665 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 640, + 545, + 665 + ], + "type": "inline_equation", + "content": "\\operatorname{E}(\\cdot)" + }, + { + "bbox": [ + 304, + 640, + 545, + 665 + ], + "type": "text", + "content": " is the object-level energy score [7, 30]. During training, the overall objective is shown as follows:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 320, + 670, + 545, + 685 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 670, + 545, + 685 + ], + "spans": [ + { + "bbox": [ + 320, + 670, + 545, + 685 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {\\text {i n}} + \\lambda \\cdot \\left(\\mathcal {L} _ {\\text {c y c l e}} - \\mathcal {L} _ {\\text {d i s}}\\right) + \\tau \\cdot \\mathcal {L} _ {\\text {u n c e r t a i n t y}}, \\tag {8}", + "image_path": "40ac7ee8468dfd790b34e866bcf93afac599d8763635fecc6a7742bf50bdfea5.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "content": " are two hyper-parameters, which are set to 0.001 and 0.1 in the experiments." + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23959" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 240, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 240, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 240, + 85 + ], + "type": "text", + "content": "3.4. Inference for OOD Object Detection" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 90, + 287, + 174 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 90, + 287, + 174 + ], + "spans": [ + { + "bbox": [ + 46, + 90, + 287, + 174 + ], + "type": "text", + "content": "During inference, we only use the LoG operator to perform structure enhancement. And the operations of recurrent VAE and synthesizing virtual OOD features are not utilized in the inference stage. Besides, we only calculate the uncertainty loss for OOD object detection [7]. Specifically, for a predicted bounding box " + }, + { + "bbox": [ + 46, + 90, + 287, + 174 + ], + "type": "inline_equation", + "content": "\\mathbf{b}" + }, + { + "bbox": [ + 46, + 90, + 287, + 174 + ], + "type": "text", + "content": ", the processes of distinguishing OOD objects are shown as follows:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 59, + 180, + 287, + 209 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 180, + 287, + 209 + ], + "spans": [ + { + "bbox": [ + 59, + 180, + 287, + 209 + ], + "type": "interline_equation", + "content": "\\mathcal {S} = \\frac {\\exp^ {- \\mathrm {E} (\\mathbf {b})}}{1 + \\exp^ {- \\mathrm {E} (\\mathbf {b})}}, \\quad \\mathcal {C} (\\mathbf {b}) = \\left\\{ \\begin{array}{l l} 0 & \\text {i f} \\mathcal {S} < \\gamma , \\\\ 1 & \\text {i f} \\mathcal {S} \\geq \\gamma . \\end{array} \\right. \\tag {9}", + "image_path": "c9e4ee0cacc2c3344da6c1a81efa5693894816654a79848b28ffd442ab119a37.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 215, + 288, + 286 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 215, + 288, + 286 + ], + "spans": [ + { + "bbox": [ + 46, + 215, + 288, + 286 + ], + "type": "text", + "content": "For the output of the classifier " + }, + { + "bbox": [ + 46, + 215, + 288, + 286 + ], + "type": "inline_equation", + "content": "\\mathcal{C}(\\cdot)" + }, + { + "bbox": [ + 46, + 215, + 288, + 286 + ], + "type": "text", + "content": ", we use the threshold mechanism [7] to distinguish the ID objects (the result is 1) from the OOD objects (the result is 0). The threshold " + }, + { + "bbox": [ + 46, + 215, + 288, + 286 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 46, + 215, + 288, + 286 + ], + "type": "text", + "content": " is commonly set to 0.95 so that a high fraction of ID data is correctly classified. Finally, Algorithm 1 shows the training and evaluation details of our method." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 297, + 128, + 312 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 297, + 128, + 312 + ], + "spans": [ + { + "bbox": [ + 47, + 297, + 128, + 312 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 317, + 287, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 317, + 287, + 425 + ], + "spans": [ + { + "bbox": [ + 46, + 317, + 287, + 425 + ], + "type": "text", + "content": "In the experiments, for unsupervised OOD-OD, we first evaluate our method on two different OOD object detection benchmarks [7]. Then, to further demonstrate the effectiveness of our method, we verify our method on the task of open-vocabulary detection (OVD) [33,49] that aims to detect new classes defined by an unbounded vocabulary. Finally, we evaluate our method on the task of class-incremental object detection (IOD) [22], i.e., new classes are sequentially introduced into the object detector." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 432, + 164, + 445 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 432, + 164, + 445 + ], + "spans": [ + { + "bbox": [ + 47, + 432, + 164, + 445 + ], + "type": "text", + "content": "4.1. Experimental Setup" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 450, + 287, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 450, + 287, + 557 + ], + "spans": [ + { + "bbox": [ + 46, + 450, + 287, + 557 + ], + "type": "text", + "content": "Implementation details. We utilize Faster R-CNN [36] with RoI-Alignment layer [12] as the basic detection model. ResNet-50 [13] is taken as the backbone. The weights pretrained on ImageNet [37] are used for initialization. Besides, in Eq. (3), " + }, + { + "bbox": [ + 46, + 450, + 287, + 557 + ], + "type": "inline_equation", + "content": "\\Phi_{\\mu}(\\cdot)" + }, + { + "bbox": [ + 46, + 450, + 287, + 557 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 450, + 287, + 557 + ], + "type": "inline_equation", + "content": "\\Phi_{\\sigma}(\\cdot)" + }, + { + "bbox": [ + 46, + 450, + 287, + 557 + ], + "type": "text", + "content": " separately consist of two fully-connected layers. The iteration number " + }, + { + "bbox": [ + 46, + 450, + 287, + 557 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 450, + 287, + 557 + ], + "type": "text", + "content": " is set to 3. In Eq. (5), " + }, + { + "bbox": [ + 46, + 450, + 287, + 557 + ], + "type": "inline_equation", + "content": "W_{\\mu}" + }, + { + "bbox": [ + 46, + 450, + 287, + 557 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 450, + 287, + 557 + ], + "type": "inline_equation", + "content": "W_{\\sigma}" + }, + { + "bbox": [ + 46, + 450, + 287, + 557 + ], + "type": "text", + "content": " contain two convolutional layers, respectively. All the experiments are trained using the standard SGD optimizer with a learning rate of 0.02." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "text", + "content": "Datasets. For unsupervised OOD-OD, PASCAL VOC [8] and Berkeley DeepDrive (BDD-100k) [48] datasets are taken as the ID training data. Meanwhile, we adopt MSCOCO [29] and OpenImages [24] as the OOD datasets to evaluate the trained model. And the OOD datasets are manually examined the OOD images to ensure they do not contain ID category. For open-vocabulary detection, we follow the work [33] and conduct experiments on COCO [29]. Concretely, COCO-2017 dataset is used for training and validation. Meanwhile, 48 categories are selected as base classes and 17 are selected as new classes. For incremental object detection, we follow the standard evaluation protocol [22] and evaluate our method on PASCAL VOC [8]. We" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 72, + 511, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 511, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 511, + 84 + ], + "type": "text", + "content": "Algorithm 1 SR-VAE for Unsupervised OOD-OD" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 86, + 545, + 121 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 86, + 545, + 121 + ], + "spans": [ + { + "bbox": [ + 306, + 86, + 545, + 121 + ], + "type": "text", + "content": "Input: ID data " + }, + { + "bbox": [ + 306, + 86, + 545, + 121 + ], + "type": "inline_equation", + "content": "\\{X,Y\\}" + }, + { + "bbox": [ + 306, + 86, + 545, + 121 + ], + "type": "text", + "content": ", randomly initialized detector with parameter " + }, + { + "bbox": [ + 306, + 86, + 545, + 121 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 306, + 86, + 545, + 121 + ], + "type": "text", + "content": ", weight " + }, + { + "bbox": [ + 306, + 86, + 545, + 121 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 306, + 86, + 545, + 121 + ], + "type": "text", + "content": " for the " + }, + { + "bbox": [ + 306, + 86, + 545, + 121 + ], + "type": "inline_equation", + "content": "KL" + }, + { + "bbox": [ + 306, + 86, + 545, + 121 + ], + "type": "text", + "content": "-loss, weight " + }, + { + "bbox": [ + 306, + 86, + 545, + 121 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 306, + 86, + 545, + 121 + ], + "type": "text", + "content": " for the loss " + }, + { + "bbox": [ + 306, + 86, + 545, + 121 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{dis}}" + }, + { + "bbox": [ + 306, + 86, + 545, + 121 + ], + "type": "text", + "content": ", weight " + }, + { + "bbox": [ + 306, + 86, + 545, + 121 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 306, + 86, + 545, + 121 + ], + "type": "text", + "content": " for the uncertainty loss " + }, + { + "bbox": [ + 306, + 86, + 545, + 121 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{uncertainty}}" + }, + { + "bbox": [ + 306, + 86, + 545, + 121 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 122, + 512, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 122, + 512, + 133 + ], + "spans": [ + { + "bbox": [ + 306, + 122, + 512, + 133 + ], + "type": "text", + "content": "Output: Object detector " + }, + { + "bbox": [ + 306, + 122, + 512, + 133 + ], + "type": "inline_equation", + "content": "\\theta^{*}" + }, + { + "bbox": [ + 306, + 122, + 512, + 133 + ], + "type": "text", + "content": ", and OOD classifier " + }, + { + "bbox": [ + 306, + 122, + 512, + 133 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 306, + 122, + 512, + 133 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 134, + 367, + 144 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 134, + 367, + 144 + ], + "spans": [ + { + "bbox": [ + 306, + 134, + 367, + 144 + ], + "type": "text", + "content": "while train do" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 321, + 145, + 500, + 157 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 145, + 500, + 157 + ], + "spans": [ + { + "bbox": [ + 321, + 145, + 500, + 157 + ], + "type": "text", + "content": "Sample images from the ID dataset " + }, + { + "bbox": [ + 321, + 145, + 500, + 157 + ], + "type": "inline_equation", + "content": "\\{X,Y\\}" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 321, + 157, + 545, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 157, + 545, + 180 + ], + "spans": [ + { + "bbox": [ + 321, + 157, + 545, + 180 + ], + "type": "text", + "content": "Calculate the structure-enhanced map " + }, + { + "bbox": [ + 321, + 157, + 545, + 180 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 321, + 157, + 545, + 180 + ], + "type": "text", + "content": " and diverse augmented features " + }, + { + "bbox": [ + 321, + 157, + 545, + 180 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 321, + 157, + 545, + 180 + ], + "type": "text", + "content": " using Eq. 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(8)." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 230, + 324, + 239 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 230, + 324, + 239 + ], + "spans": [ + { + "bbox": [ + 306, + 230, + 324, + 239 + ], + "type": "text", + "content": "end" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 240, + 363, + 251 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 240, + 363, + 251 + ], + "spans": [ + { + "bbox": [ + 306, + 240, + 363, + 251 + ], + "type": "text", + "content": "whileevaldo" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 321, + 251, + 528, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 251, + 528, + 262 + ], + "spans": [ + { + "bbox": [ + 321, + 251, + 528, + 262 + ], + "type": "text", + "content": "Calculate the OOD uncertainty score using Eq. (9)." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 321, + 262, + 515, + 274 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 262, + 515, + 274 + ], + "spans": [ + { + "bbox": [ + 321, + 262, + 515, + 274 + ], + "type": "text", + "content": "Perform thresholding comparison using Eq. (9)." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 275, + 324, + 285 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 275, + 324, + 285 + ], + "spans": [ + { + "bbox": [ + 306, + 275, + 324, + 285 + ], + "type": "text", + "content": "end" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 311, + 545, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 311, + 545, + 335 + ], + "spans": [ + { + "bbox": [ + 306, + 311, + 545, + 335 + ], + "type": "text", + "content": "initially learn 10, 15, or 19 base classes, and then introduce 10, 5, or 1 new classes as the second task." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 336, + 546, + 420 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 336, + 546, + 420 + ], + "spans": [ + { + "bbox": [ + 304, + 336, + 546, + 420 + ], + "type": "text", + "content": "Metrics. To evaluate the performance of unsupervised OOD-OD, we report: (1) the false positive rate (FPR95) of OOD objects when the true positive rate of ID objects is at " + }, + { + "bbox": [ + 304, + 336, + 546, + 420 + ], + "type": "inline_equation", + "content": "95\\%" + }, + { + "bbox": [ + 304, + 336, + 546, + 420 + ], + "type": "text", + "content": "; (2) the area under the receiver operating characteristic curve (AUROC); (3) mean average precision (mAP). For open-vocabulary detection and incremental object detection, we only report the mAP performance." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 306, + 430, + 479, + 443 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 430, + 479, + 443 + ], + "spans": [ + { + "bbox": [ + 306, + 430, + 479, + 443 + ], + "type": "text", + "content": "4.2. OOD-OD Performance Analysis" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 304, + 449, + 545, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 545, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 545, + 640 + ], + "type": "text", + "content": "Table 1 shows the performance of unsupervised OOD. We can see that though all methods own similar detection performance, the performance of OOD object detection differs significantly. This shows that existing detection methods are easily affected by OOD objects. Besides, for these two benchmarks, our method significantly outperforms baseline methods. Particularly, taking BDD [48] as the ID training data, based on FPR95 metric, our method separately outperforms VOS [7] by " + }, + { + "bbox": [ + 304, + 449, + 545, + 640 + ], + "type": "inline_equation", + "content": "12.04\\%" + }, + { + "bbox": [ + 304, + 449, + 545, + 640 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 449, + 545, + 640 + ], + "type": "inline_equation", + "content": "13.73\\%" + }, + { + "bbox": [ + 304, + 449, + 545, + 640 + ], + "type": "text", + "content": ". Meanwhile, based on AUROC metric, our method is " + }, + { + "bbox": [ + 304, + 449, + 545, + 640 + ], + "type": "inline_equation", + "content": "3.82\\%" + }, + { + "bbox": [ + 304, + 449, + 545, + 640 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 449, + 545, + 640 + ], + "type": "inline_equation", + "content": "5.03\\%" + }, + { + "bbox": [ + 304, + 449, + 545, + 640 + ], + "type": "text", + "content": " higher than VOS [7]. These results indicate that our method could indeed reduce the risk of misclassifying ID objects into OOD categories. Meanwhile, the proposed method could effectively synthesize virtual OOD features that deviate from the distribution of ID features, which improves the ability of distinguishing OOD objects." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": "In Fig. 4 and 5, we show some OOD detection examples. We can see that compared with the baseline method [7], our method accurately distinguishes OOD objects. Taking the first two columns of Fig. 4 as examples, the baseline method misclassifies OOD objects into ID categories. Our method correctly discriminates these objects as the OOD category." + } + ] + } + ], + "index": 27 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "23960" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 58, + 70, + 152, + 133 + ], + "blocks": [ + { + "bbox": [ + 58, + 70, + 152, + 133 + ], + "lines": [ + { + "bbox": [ + 58, + 70, + 152, + 133 + ], + "spans": [ + { + "bbox": [ + 58, + 70, + 152, + 133 + ], + "type": "image", + "image_path": "8bffd9721c937ae490d2cf393286c004c543944ad7ce49b4ba00471b95dcfa1c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 58, + 134, + 152, + 196 + ], + "blocks": [ + { + "bbox": [ + 58, + 134, + 152, + 196 + ], + "lines": [ + { + "bbox": [ + 58, + 134, + 152, + 196 + ], + "spans": [ + { + "bbox": [ + 58, + 134, + 152, + 196 + ], + "type": "image", + "image_path": "1a98a1fbf3085878d70c2deb0e1ec514fd709528bedf7aec5bce8cb1d4a53153.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 200, + 545, + 234 + ], + "lines": [ + { + "bbox": [ + 46, + 200, + 545, + 234 + ], + "spans": [ + { + "bbox": [ + 46, + 200, + 545, + 234 + ], + "type": "text", + "content": "Figure 4. Detection results on the OOD images from MS-COCO. The first and second rows respectively indicate results based on VOS [7] and our method. The in-distribution dataset is BDD-100k. Blue boxes represent objects detected and classified as one of the ID categories. Green boxes indicate OOD objects. 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Method (VOC)FPR95 ↓AUROC ↑mAP (ID)↑
OOD: MS-COCO / OpenImages
MSP [14]70.99 / 73.1383.45 / 81.9148.7
ODIN [28]59.82 / 63.1482.20 / 82.5948.7
Mahalanobis [26]67.73 / 65.4181.45 / 81.4848.7
Gram matrices [38]62.75 / 67.4279.88 / 77.6248.7
Energy score [30]56.89 / 58.6983.69 / 82.9848.7
Generalized ODIN [16]59.57 / 70.2883.12 / 79.2348.1
CSI [42]59.91 / 57.4181.83 / 82.9548.1
GAN-synthesis [25]60.93 / 59.9783.67 / 82.6748.5
VOS (Baseline) [7]47.53 / 51.3388.70 / 85.2348.9
SR-VAE42.17 / 46.2690.28 / 87.8949.4
Method (BDD)FPR95 ↓AUROC ↑mAP (ID)↑
OOD: MS-COCO / OpenImages
MSP [14]80.94 / 79.0475.87 / 77.3831.2
ODIN [28]62.85 / 58.9274.44 / 76.6131.2
Mahalanobis [26]55.74 / 47.6985.71 / 88.0531.2
Gram matrices [38]60.93 / 77.5574.93 / 59.3831.2
Energy score [30]60.06 / 54.9777.48 / 79.6031.2
Generalized ODIN [16]57.27 / 50.1785.22 / 87.1831.8
CSI [42]47.10 / 37.0684.09 / 87.9930.6
GAN-synthesis [25]57.03 / 50.6178.82 / 81.2531.4
VOS (Baseline) [7]44.27 / 35.5486.87 / 88.5231.3
SR-VAE32.23 / 21.8190.69 / 93.5531.5
", + "image_path": "164fb8f47bf289eeb64c2b563f9a68722895bf2a8a6490b08033bc332edb09e5.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 46, + 474, + 287, + 531 + ], + "lines": [ + { + "bbox": [ + 46, + 474, + 287, + 531 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 287, + 531 + ], + "type": "text", + "content": "Table 1. The performance " + }, + { + "bbox": [ + 46, + 474, + 287, + 531 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 46, + 474, + 287, + 531 + ], + "type": "text", + "content": " of unsupervised OOD-OD. All methods are trained based on ID data and do not use any auxiliary data. " + }, + { + "bbox": [ + 46, + 474, + 287, + 531 + ], + "type": "inline_equation", + "content": "\\uparrow" + }, + { + "bbox": [ + 46, + 474, + 287, + 531 + ], + "type": "text", + "content": " denotes larger values are better and " + }, + { + "bbox": [ + 46, + 474, + 287, + 531 + ], + "type": "inline_equation", + "content": "\\downarrow" + }, + { + "bbox": [ + 46, + 474, + 287, + 531 + ], + "type": "text", + "content": " denotes smaller values are better. We can see that our method outperforms the comparison methods significantly." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 538, + 287, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 538, + 287, + 574 + ], + "spans": [ + { + "bbox": [ + 46, + 538, + 287, + 574 + ], + "type": "text", + "content": "These results further show that the proposed method could effectively synthesize OOD features and improve the discrimination ability of the object detector." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 585, + 255, + 598 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 585, + 255, + 598 + ], + "spans": [ + { + "bbox": [ + 47, + 585, + 255, + 598 + ], + "type": "text", + "content": "4.3. Performance Analysis of OVD and IOD" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 604, + 287, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 604, + 287, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 604, + 287, + 700 + ], + "type": "text", + "content": "To demonstrate the superiorities, we further verify our method on OVD [49] and IOD [22]. Table 2 shows the OVD results on COCO. Here, we directly plug our method into the baseline method [33] and do not calculate the uncertainty loss (Eq. (7)). We can see that plugging our method improves OCA's performance by " + }, + { + "bbox": [ + 46, + 604, + 287, + 700 + ], + "type": "inline_equation", + "content": "3.5\\%" + }, + { + "bbox": [ + 46, + 604, + 287, + 700 + ], + "type": "text", + "content": ". This shows that our method effectively synthesizes virtual features, which enhances the ability of distinguishing new classes." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 59, + 701, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 286, + 713 + ], + "type": "text", + "content": "Table 3 shows the IOD performance on PASCAL VOC." + } + ] + } + ], + "index": 16 + }, + { + "type": "table", + "bbox": [ + 347, + 241, + 506, + 335 + ], + "blocks": [ + { + "bbox": [ + 347, + 241, + 506, + 335 + ], + "lines": [ + { + "bbox": [ + 347, + 241, + 506, + 335 + ], + "spans": [ + { + "bbox": [ + 347, + 241, + 506, + 335 + ], + "type": "table", + "html": "
MethodAPnovelAP
WSDDN [3]19.719.6
Cap2Det [47]20.320.1
OVR-CNN [49]22.839.9
RegionCLIP [50]26.847.5
Detric [51]27.845.0
OCA (Baseline) [33]36.649.4
OCA+Ours40.149.5
", + "image_path": "a1d777d42c5ec6d24b1c3e09551422c9a4c6eccc39ccd0d03e4ec6e6f19cf32c.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "table_body" + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 337, + 545, + 360 + ], + "lines": [ + { + "bbox": [ + 305, + 337, + 545, + 360 + ], + "spans": [ + { + "bbox": [ + 305, + 337, + 545, + 360 + ], + "type": "text", + "content": "Table 2. OVD results " + }, + { + "bbox": [ + 305, + 337, + 545, + 360 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 305, + 337, + 545, + 360 + ], + "type": "text", + "content": " on COCO. 'OCA + Ours' indicates that we directly plug our method into OCA [33]." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 365, + 545, + 473 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 365, + 545, + 473 + ], + "spans": [ + { + "bbox": [ + 305, + 365, + 545, + 473 + ], + "type": "text", + "content": "We still directly plug our method into the baseline method [22] and do not calculate the uncertainty loss. We can see that when the IOU threshold is set to 0.5 and 0.75, plugging our method effectively improves the performance of the baseline method. Particularly, when the IOU threshold is set to 0.75, for the three different settings, our method separately boosts iOD's performance by " + }, + { + "bbox": [ + 305, + 365, + 545, + 473 + ], + "type": "inline_equation", + "content": "2.3\\%" + }, + { + "bbox": [ + 305, + 365, + 545, + 473 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 365, + 545, + 473 + ], + "type": "inline_equation", + "content": "2.9\\%" + }, + { + "bbox": [ + 305, + 365, + 545, + 473 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 365, + 545, + 473 + ], + "type": "inline_equation", + "content": "4.1\\%" + }, + { + "bbox": [ + 305, + 365, + 545, + 473 + ], + "type": "text", + "content": ". These results show that our method could significantly improve the discrimination of the object detector." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 479, + 497, + 493 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 479, + 497, + 493 + ], + "spans": [ + { + "bbox": [ + 306, + 479, + 497, + 493 + ], + "type": "text", + "content": "4.4. Ablation and Visualization Analysis" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 498, + 545, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 498, + 545, + 533 + ], + "spans": [ + { + "bbox": [ + 305, + 498, + 545, + 533 + ], + "type": "text", + "content": "In this section, we utilize BDD-100k as the ID data for training and MS-COCO as the OOD data to perform an ablation analysis of our method." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "text", + "content": "Analysis of SR-VAE. In this paper, our method mainly contains the LoG operator used for enhancing object-related information, the VAE module used to generate diverse augmented features of the classification features, and the cycle-consistent conditional VAE module used for synthesizing virtual OOD features. Here, we make an ablation analysis of our method. Table 4 shows the ablation results. We can see that employing the proposed three modules could significantly improve the performance of OOD object detection. Particularly, compared with VOS [7], synthesizing virtual OOD features improves the performance by around " + }, + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "inline_equation", + "content": "5.21\\%" + }, + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "text", + "content": " based on the FPR95 metric, which shows that the generated virtual OOD features could alleviate the impact of lacking unknown data for supervision and enhance the ability of distinguishing OOD objects. Meanwhile, employing the" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23961" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 74, + 545, + 385 + ], + "blocks": [ + { + "bbox": [ + 47, + 74, + 545, + 385 + ], + "lines": [ + { + "bbox": [ + 47, + 74, + 545, + 385 + ], + "spans": [ + { + "bbox": [ + 47, + 74, + 545, + 385 + ], + "type": "table", + "html": "
10 + 10 settingaerocyclebirdboatbottlebuscarcatchaircowtabledoghorsebikepersonplantsheepsofatraintvmAP
Faster ILOD (50) [32]72.875.771.260.561.770.483.376.653.172.336.770.966.867.666.124.763.148.157.143.662.2
ORE (50) [19]63.570.958.942.934.176.280.776.334.166.156.170.480.272.381.842.771.668.17767.764.6
OW-DETR (50) [10]61.869.167.845.847.378.378.478.636.271.557.575.376.277.479.540.166.866.375.664.165.7
ROSETTA (50) [45]74.276.264.954.457.476.184.468.852.467.062.963.379.872.878.140.162.361.272.466.866.8
iOD (50) [22]76.074.667.555.957.675.185.477.043.770.860.166.476.072.674.639.764.060.268.560.566.3
iOD + Ours (50)75.975.268.855.355.577.785.679.349.478.261.075.381.474.579.343.872.567.070.265.769.6
iOD (75) [22]39.036.528.419.424.247.256.741.019.148.021.132.143.036.340.014.840.136.537.345.335.3
iOD + Ours (75)43.641.031.324.929.855.460.844.122.446.729.532.335.638.335.715.146.934.637.946.737.6
15 + 5 settingaerocyclebirdboatbottlebuscarcatchaircowtabledoghorsebikepersonplantsheepsofatraintvmAP
Faster ILOD (50) [32]66.578.171.854.661.468.482.682.752.174.363.178.680.578.480.436.761.759.367.959.167.9
ORE (50) [19]75.481.067.151.955.777.285.681.746.176.255.476.786.278.582.132.863.654.777.764.668.5
OW-DETR (50) [10]77.176.569.251.361.379.884.281.049.779.658.179.083.167.885.433.265.162.073.965.069.4
ROSETTA (50) [45]76.577.565.156.060.078.385.578.749.568.267.471.283.975.782.043.060.664.172.867.469.2
iOD (50) [22]78.479.766.954.856.277.784.679.147.775.061.874.781.677.580.237.858.054.673.056.167.8
iOD + Ours (50)78.380.370.551.660.279.485.976.252.579.465.281.883.776.177.941.162.863.872.667.970.4
iOD (75) [22]40.740.928.719.123.861.656.138.823.647.518.740.140.241.539.89.140.632.441.947.636.6
iOD + Ours (75)44.444.536.521.227.655.563.739.824.950.327.241.647.943.941.411.339.138.643.148.539.5
19 + 1 settingaerocyclebirdboatbottlebuscarcatchaircowtabledoghorsebikepersonplantsheepsofatraintvmAP
Faster ILOD (50) [32]64.274.773.255.553.770.882.982.651.679.758.778.881.875.377.443.173.861.769.861.168.6
ORE (50) [19]67.376.860.048.458.881.186.575.841.579.654.672.885.981.782.444.875.868.275.760.168.9
OW-DETR (50) [10]70.577.273.854.055.679.080.880.643.280.453.577.589.582.074.743.371.966.679.462.070.2
ROSETTA (50) [45]75.377.965.356.255.379.684.672.949.273.768.371.078.977.780.744.069.668.576.168.369.6
iOD (50) [22]78.277.569.455.056.078.484.279.246.679.063.278.582.779.179.944.173.266.376.457.670.2
iOD + Ours (50)76.683.574.757.058.077.085.682.551.582.761.481.682.979.877.647.474.768.474.159.071.8
iOD (75) [22]35.944.731.622.426.952.056.538.721.648.421.235.937.930.738.717.238.534.240.746.636.0
iOD + Ours (75)36.445.136.118.028.953.262.238.525.355.127.446.845.942.940.320.950.837.044.447.140.1
", + "image_path": "bccb2e7e118a079bec784a5bc10912b8985793d5727c5938c06b1af0fb933b05.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 52, + 418, + 282, + 483 + ], + "blocks": [ + { + "bbox": [ + 47, + 388, + 544, + 411 + ], + "lines": [ + { + "bbox": [ + 47, + 388, + 544, + 411 + ], + "spans": [ + { + "bbox": [ + 47, + 388, + 544, + 411 + ], + "type": "text", + "content": "Table 3. Performance (%) analysis of class-incremental object detection. 'iOD + Ours' indicates that our method is plugged into iOD [22]. Here, '50' and '75' separately represent that the mAP metric is calculated when the IOU threshold is set to 0.5 and 0.75." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 52, + 418, + 282, + 483 + ], + "lines": [ + { + "bbox": [ + 52, + 418, + 282, + 483 + ], + "spans": [ + { + "bbox": [ + 52, + 418, + 282, + 483 + ], + "type": "table", + "html": "
C-VAELoGR-VAEFPR95 ↓AUROC ↑mAP↑
✓39.06%87.83%31.3%
✓✓37.92%88.08%31.2%
✓✓35.13%89.22%31.3%
✓✓✓32.23%90.69%31.5%
", + "image_path": "1e747a91a4c7ffcfc771597edf7a7437809290c6bdaddb947e92b828c70af73d.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 47, + 485, + 286, + 529 + ], + "lines": [ + { + "bbox": [ + 47, + 485, + 286, + 529 + ], + "spans": [ + { + "bbox": [ + 47, + 485, + 286, + 529 + ], + "type": "text", + "content": "Table 4. Ablation analysis of SR-VAE for unsupervised OOD-OD. 'C-VAE' is the proposed cycle-consistent conditional VAE module. 'R-VAE' indicates the VAE module that is used to generate diverse augmented features of the classification features." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 532, + 287, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 532, + 287, + 592 + ], + "spans": [ + { + "bbox": [ + 46, + 532, + 287, + 592 + ], + "type": "text", + "content": "LoG operator and R-VAE modules further boosts the performance significantly, which demonstrates that using these two modules is beneficial for enhancing object-related information in the extracted low-level features and improving the discrimination ability of the object detector." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "text", + "content": "Analysis of the LoG kernel size. To improve the performance of object localization, we employ the LoG operation (Eq. (1) and (2)) to perform structure enhancement, which is beneficial for strengthening object-related information. Here, we make an ablation analysis of the LoG kernel size. And we only change the kernel size. The other modules are kept unchanged. Table 5 shows the results. We can see that the performance is affected by the kernel size. Small kernel size does not sufficiently capture object structure information, which weakens the performance. For our" + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 326, + 419, + 526, + 494 + ], + "blocks": [ + { + "bbox": [ + 326, + 419, + 526, + 494 + ], + "lines": [ + { + "bbox": [ + 326, + 419, + 526, + 494 + ], + "spans": [ + { + "bbox": [ + 326, + 419, + 526, + 494 + ], + "type": "table", + "html": "
LoG Kernel SizeFPR95 ↓AUROC ↑mAP↑
3 × 334.96%87.94%30.9%
5 × 533.85%89.18%31.3%
7 × 733.08%89.76%31.2%
9 × 932.23%90.69%31.5%
11 × 1132.93%90.35%31.6%
", + "image_path": "42f0c370c01f4239f365b74aa0f5e28dc90a9f52e7558fc35e5e040e9df93600.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 334, + 496, + 515, + 507 + ], + "lines": [ + { + "bbox": [ + 334, + 496, + 515, + 507 + ], + "spans": [ + { + "bbox": [ + 334, + 496, + 515, + 507 + ], + "type": "text", + "content": "Table 5. Ablation analysis of the LoG kernel size." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 509, + 541, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 509, + 541, + 521 + ], + "spans": [ + { + "bbox": [ + 305, + 509, + 541, + 521 + ], + "type": "text", + "content": "method, the performance of using " + }, + { + "bbox": [ + 305, + 509, + 541, + 521 + ], + "type": "inline_equation", + "content": "9 \\times 9" + }, + { + "bbox": [ + 305, + 509, + 541, + 521 + ], + "type": "text", + "content": " kernel is the best." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "content": "Analysis of the iteration number. To reduce the risk of misclassifying ID objects into the OOD category, we design a VAE module (Eq. (3)) to generate multiple augmented features of the classification features, which is instrumental in improving the discrimination ability of the object classifier. Here, we make an ablation analysis of the iteration number " + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "content": ". And we only change the iteration number and keep other modules unchanged. Table 6 shows the ablation results. We can see that generating multiple augmented features could improve the detection performance effectively. This shows that enhancing the classification ability of the object classifier is meaningful. Besides, we observe that when the iteration number is larger than a certain threshold, the performance could not be boosted effectively. The reason may be that the object classifier is a linear classifier, which could not sufficiently exploit these augmented fea" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "23962" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 58, + 70, + 161, + 133 + ], + "blocks": [ + { + "bbox": [ + 58, + 70, + 161, + 133 + ], + "lines": [ + { + "bbox": [ + 58, + 70, + 161, + 133 + ], + "spans": [ + { + "bbox": [ + 58, + 70, + 161, + 133 + ], + "type": "image", + "image_path": "89f9fa3f2b3c4ee91d39fa6ceee542e2df060c0a96fa6b691b270aa2a318eb8b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 58, + 133, + 161, + 196 + ], + "blocks": [ + { + "bbox": [ + 58, + 133, + 161, + 196 + ], + "lines": [ + { + "bbox": [ + 58, + 133, + 161, + 196 + ], + "spans": [ + { + "bbox": [ + 58, + 133, + 161, + 196 + ], + "type": "image", + "image_path": "35812b7634678e8388946905d41b7e063c09f55308a2180fb99c7982698229b4.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 200, + 538, + 212 + ], + "lines": [ + { + "bbox": [ + 55, + 200, + 538, + 212 + ], + "spans": [ + { + "bbox": [ + 55, + 200, + 538, + 212 + ], + "type": "text", + "content": "Figure 5. Detection results on OpenImages. The first and second rows respectively indicate results based on VOS [7] and our method." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 161, + 70, + 262, + 133 + ], + "blocks": [ + { + "bbox": [ + 161, + 70, + 262, + 133 + ], + "lines": [ + { + "bbox": [ + 161, + 70, + 262, + 133 + ], + "spans": [ + { + "bbox": [ + 161, + 70, + 262, + 133 + ], + "type": "image", + "image_path": "bd12fc77748a985d8bb3d6e28e09063b395e30d408d7ea6d313a1e93e54a3178.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 159, + 134, + 262, + 196 + ], + "blocks": [ + { + "bbox": [ + 159, + 134, + 262, + 196 + ], + "lines": [ + { + "bbox": [ + 159, + 134, + 262, + 196 + ], + "spans": [ + { + "bbox": [ + 159, + 134, + 262, + 196 + ], + "type": "image", + "image_path": "1a0f80da737a31486176cd41f90c8effa2ba0b7ef064d18c59c82ff216b0bbd0.jpg" + } + 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Iteration Number TFPR95 ↓AUROC ↑mAP↑
137.24%88.12%31.2%
332.23%90.69%31.5%
532.46%90.23%31.3%
732.93%90.07%31.2%
", + "image_path": "8a156ea7ccea7169a3bd65e803b44d6a8830fbdcf279354e3c7a039e771adedb.jpg" + } + ] + } + ], + "index": 36, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 70, + 497, + 263, + 508 + ], + "lines": [ + { + "bbox": [ + 70, + 497, + 263, + 508 + ], + "spans": [ + { + "bbox": [ + 70, + 497, + 263, + 508 + ], + "type": "text", + "content": "Table 6. Ablation analysis of the iteration number " + }, + { + "bbox": [ + 70, + 497, + 263, + 508 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 70, + 497, + 263, + 508 + ], + "type": "text", + "content": " ." + } + ] + } + ], + "index": 37, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 36 + }, + { + "bbox": [ + 46, + 509, + 287, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 509, + 287, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 509, + 287, + 533 + ], + "type": "text", + "content": "tures. For our method, when the iteration number is set to 3, the performance of OOD detection is the best." + } + ] + } + ], + "index": 38 + }, + { + "bbox": [ + 46, + 533, + 287, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 287, + 641 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 287, + 641 + ], + "type": "text", + "content": "Analysis of cycle-consistent conditional VAE. In order to effectively synthesize virtual OOD features, we propose a cycle-consistency loss " + }, + { + "bbox": [ + 46, + 533, + 287, + 641 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{cycle}}" + }, + { + "bbox": [ + 46, + 533, + 287, + 641 + ], + "type": "text", + "content": " (Eq. (8)) to reduce the impact of lacking paired samples. Here, we make an ablation analysis of " + }, + { + "bbox": [ + 46, + 533, + 287, + 641 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{cycle}}" + }, + { + "bbox": [ + 46, + 533, + 287, + 641 + ], + "type": "text", + "content": ". Based on the FPR95 metric, removing " + }, + { + "bbox": [ + 46, + 533, + 287, + 641 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{cycle}}" + }, + { + "bbox": [ + 46, + 533, + 287, + 641 + ], + "type": "text", + "content": " increases the performance by around " + }, + { + "bbox": [ + 46, + 533, + 287, + 641 + ], + "type": "inline_equation", + "content": "3.8\\%" + }, + { + "bbox": [ + 46, + 533, + 287, + 641 + ], + "type": "text", + "content": ". This shows using the cycle-consistency loss " + }, + { + "bbox": [ + 46, + 533, + 287, + 641 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{cycle}}" + }, + { + "bbox": [ + 46, + 533, + 287, + 641 + ], + "type": "text", + "content": " is beneficial for synthesizing virtual OOD features and improving the ability of distinguishing OOD objects." + } + ] + } + ], + "index": 39 + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": "Visualization analysis. Fig. 6 shows some visualization examples. Particularly, we can see that the map " + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": " contains plentiful object-related information, which shows that using the LoG operation is indeed helpful for enhancing object-related information. Furthermore, we observe that the synthesized virtual OOD map " + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "inline_equation", + "content": "O" + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": " involves sufficient informa" + } + ] + } + ], + "index": 40 + }, + { + "bbox": [ + 304, + 433, + 545, + 481 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 433, + 545, + 481 + ], + "spans": [ + { + "bbox": [ + 304, + 433, + 545, + 481 + ], + "type": "text", + "content": "tion that is different from object-related features, which indicates that leveraging the synthesized OOD features is instrumental in reducing the impact of lacking unknown data and improving the discrimination ability." + } + ] + } + ], + "index": 41 + }, + { + "bbox": [ + 306, + 490, + 378, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 490, + 378, + 502 + ], + "spans": [ + { + "bbox": [ + 306, + 490, + 378, + 502 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 42 + }, + { + "bbox": [ + 304, + 510, + 546, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 546, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 546, + 641 + ], + "type": "text", + "content": "For unsupervised OOD-OD, we propose an approach of Structure-Enhanced Recurrent VAE. Particularly, to reduce the risk of misclassifying ID objects into the OOD category, an LoG operator and a dedicated recurrent VAE used to generate diverse augmented features are presented to strengthen the discrimination ability. Meanwhile, to alleviate the impact of lacking unknown data, we design a cycle-consistent conditional VAE to synthesize virtual OOD features, which boosts the performance of distinguishing OOD objects. Extensive experiments on three different tasks and visualization analyses demonstrate the superiorities of our method." + } + ] + } + ], + "index": 43 + }, + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "type": "text", + "content": "Acknowledgement. Our work was supported in part by Key Research and Development Program of Shaanxi under Grant 2021ZDLGY01-03, the National Natural Science Foundation of China under Grant 62102293, 62132016, 62171343, and 62071361, and the Fundamental Research Funds for the Central Universities ZDRC2102." + } + ] + } + ], + "index": 44 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23963" + } + ] + } + ], + "index": 45 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 92, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 53, + 92, + 287, + 125 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 92, + 287, + 125 + ], + "spans": [ + { + "bbox": [ + 53, + 92, + 287, + 125 + ], + "type": "text", + "content": "[1] Martin Arjovsky, Léon Bottou, Ishaan Gulrajani, and David Lopez-Paz. 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In this paper, we propose a Discriminative co-saliency and background Mining Transformer framework (DMT) based on several economical multi-grained correlation modules to explicitly mine both co-saliency and background information and effectively model their discrimination. Specifically, we first propose a region-to-region correlation module for introducing inter-image relations to pixel-wise segmentation features while maintaining computational efficiency. Then, we use two types of pre-defined tokens to mine co-saliency and background information via our proposed contrast-induced pixel-to-token correlation and co-saliency token-to-token correlation modules. We also design a token-guided feature refinement module to enhance the discriminability of the segmentation features under the guidance of the learned tokens. We perform iterative mutual promotion for the segmentation feature extraction and token construction. Experimental results on three benchmark datasets demonstrate the effectiveness of our proposed method. The source code is available at: https://github.com/dragonlee258079/DMT.", + "bbox": [ + 75, + 340, + 473, + 690 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 718, + 209, + 734 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Unlike standard Salient Object Detection (SOD) [13,21-23, 37, 45], which detects salient objects in a single image, Co-Salient Object Detection (CoSOD) aims to detect common salient objects across a group of relevant images. It often faces the following two challenges: 1) The foreground (FG) in CoSOD refers to co-salient objects, which are inherently hard to detect since they should satisfy both the intra-group commonality and the intra-image saliency. 2) The background (BG) in CoSOD might contain com", + "bbox": [ + 75, + 739, + 468, + 877 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "plex distractions, including extraneous salient objects that are salient but not \"common\", and similar concomitant objects appearing in multiple images (e.g. performers often appear in guitar images). Such difficult distractors can easily seduce CoSOD models to make false positive predictions. Therefore, the effective exploration of both FG and BG and modeling their discrimination to precisely detect co-salient objects while suppressing interference from BG is crucial for CoSOD.", + "bbox": [ + 500, + 310, + 892, + 445 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Although many works have achieved promising performance, most of them [14, 18, 25, 30, 33, 38, 40-42] devoted to the ingenious mining of FG while ignored the explicit exploration of BG. They mainly constructed positive relations between co-salient objects but paid less attention to modeling negative ones between co-saliency regions and BG. [16, 34] followed some SOD methods [4, 43] to incorporate BG features for co-saliency representation learning or contrast learning. However, these methods can be regarded as an univariate FG&BG modeling in which the essential optimization target is limited to FG and there is no explicit BG modeling, thus limiting the discriminative learning capability. To this end, this paper proposes to conduct a bivariate FG&BG modeling paradigm that explicitly models both FG and BG information and effectively facilitates their discriminative modeling.", + "bbox": [ + 496, + 446, + 892, + 688 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "As for co-saliency (FG) information, most previous works [12, 16, 34, 41] detected them by exploring the interimage similarity. Calculating the Pixel-to-Pixel (P2P) correlation between 3D CNN features in a group is widely used in many works [12, 16, 34] and has demonstrated its effectiveness. However, this method introduces heavy computation burdens and hinders sophisticated relation modeling. To alleviate this problem, we introduce economic multi-grained correlations among different images and the co-saliency and BG information, thus enabling modeling sophisticated relations to extract accurate co-saliency as well as BG knowledge.", + "bbox": [ + 496, + 688, + 893, + 869 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Specifically, we construct a Discriminative co-saliency and BG Mining Transformer (DMT) following the", + "bbox": [ + 500, + 869, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "†Corresponding author: liunian228@gmail.com.", + "bbox": [ + 94, + 886, + 354, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "7247", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "paradigm of a semantic segmentation transformer architecture, i.e. MaskFormer [5], which enables explicit co-saliency and BG modeling and the construction of multi-grained correlations. Using this architecture, we decompose the CoSOD modeling into two sub-paths, i.e. generating pixel-wise segmentation feature maps and extracting category information with pre-defined co-saliency and BG detection tokens.", + "bbox": [ + 75, + 90, + 472, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In the first sub-path, to efficiently and thoroughly mine the common cues within the image group, we propose a Region-to-Region correlation (R2R) module to model the inter-image relation and plug it into each decoder layer. In the second sub-path, we transform the pixel-wise features into a co-saliency token and a BG token for each image, abstracting pixel-wise cues into high-level tokens. As such, we achieve sophisticated relation modeling among the tokens and features while largely reducing the computational costs. Concretely, we propose an intra-image Contrast-induced Pixel-to-Token correlation (CtP2T) module to extract the two tokens by considering the contrast relation between co-saliency and BG. Since the co-saliency tokens from CtP2T are separately learned on each image, we further design a Co-saliency Token-to-Token (CoT2T) correlation module to model their common relation.", + "bbox": [ + 75, + 212, + 472, + 450 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "After obtaining the tokens and pixel-wise features, the MaskFormer [5] architecture adopts dot production between them to obtain the final segmentation results. However, such a scheme only achieves unidirectional information propagation, i.e. conveying information from the feature maps to the tokens. We argue that the learned two tokens can also be used to improve the discriminability of the pixel-wise features, thus proposing our Token-Guided Feature Refinement (TGFR) module as a reverse information propagation path. Concretely, we first use the tokens as guidance to distill co-saliency and BG features from the pixel-wise feature maps, and then enhance the discriminability of the segmentation features between the two detection regions. In this way, the refined features become sensitive to both co-saliency and BG, reducing the affect of ambiguous distractors.", + "bbox": [ + 75, + 454, + 472, + 696 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Finally, as shown in Figure 1, our DMT iteratively deploys CtP2T and CoT2T to leverage the segmentation features for updating the tokens, and then adopts TGFR to refine the corresponding decoder feature with the updated tokens. As a result, the learning processes can be effectively promoted, thus obtaining more accurate CoSOD results.", + "bbox": [ + 75, + 696, + 470, + 787 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our major contributions are as follows:", + "bbox": [ + 96, + 787, + 439, + 801 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We model CoSOD from the perspective of explicitly exploring both co-saliency and BG information and effectively modeling their discrimination.", + "- We introduce several computationally economical multi-grained correlation modules, i.e. R2R, CtP2T, CoT2T, for the inter-image and intra-image relations" + ], + "bbox": [ + 94, + 805, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "modeling.", + "bbox": [ + 532, + 92, + 602, + 106 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a novel TGFR module to use the learned tokens as guidance to refine the segmentation features for enhancing their discriminability between co-saliency and BG regions.", + "- Experimental results demonstrate that our DMT model outperforms previous state-of-the-art results on three benchmark datasets." + ], + "bbox": [ + 517, + 108, + 890, + 213 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 228, + 640, + 243 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Co-Salient Object Detection", + "text_level": 1, + "bbox": [ + 500, + 250, + 751, + 265 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recent CoSOD works [12,16,27,34,41,42] have achieve promising performance and can be summarized as a unified paradigm, i.e. first aggregating all image features in the group to form a consensus representation and then distributing it back to each image feature. We refer to these two processes as aggregation and distribution for expression convenience. For example, [42] summed up all features for aggregation and leveraged a gradient feedback mechanism for distribution. [16] formed the consensus cues with a group of enhanced intra-saliency vectors and conducted the distribution via a dense correlation module. [12] generated a consensus attention map with an affinity module and multiplied it back to the individual image features. [41] encoded the consensus information with dynamic kernels and convolved the image features using these kernels as the distribution process. [34] first obtained consensus seeds by processing P2P affinity maps and then propagated the seeds using normalized convolution operations. However, most of them are limited in exploring BG regions, which hinders the discriminability learning. Unlike them, we propose to simultaneously detect the co-saliency and BG regions and sufficiently explore their discriminative modeling. Besides, we utilize tokens under a transformer architecture for aggregation, and then use the learned tokens to conduct the distribution process.", + "bbox": [ + 496, + 268, + 890, + 646 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Transformer", + "text_level": 1, + "bbox": [ + 500, + 654, + 635, + 669 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "After Vaswani et al. [29] first proposed the transformer architecture for machine translation, many successful transformer applications in the computer vision field emerged. Some works [8, 28, 35] directly apply the transformer architecture for feature learning. Some other works mainly focused on using transformers to extract specific semantic concepts, e.g. the category or instance information for object detection [3, 32, 44], semantic segmentation [5, 31], and the saliency and contour information for salient object detection [23]. Concretely, they first use a backbone to extract image feature maps and then adopt transformers to collect semantic concept information and store them in pre-created tokens.", + "bbox": [ + 496, + 674, + 890, + 868 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "This paper follows the second type application to utilize the transformer for simultaneous FG and BG modeling. We", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "7248", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/770164cf23b1cfae99b5f9c5046a5362a0d31320fe4bb87d59076d5287b81928.jpg", + "image_caption": [ + "Figure 1. Overall flowchart of our proposed DMT CoSOD model. Specifically, the framework consists of four components, i.e. R2R for segmentation feature generation, CtP2T and CoT2T for detection token construction, and TGFR for the segmentation feature refinement under the guidance of the tokens." + ], + "image_footnote": [], + "bbox": [ + 81, + 89, + 890, + 311 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "further modify the transformer framework tailored for the CoSOD task by introducing economic multi-grained correlations for modeling sophisticated relations. We also propose to leverage the semantic information encoded in the learned tokens as a guide to refine the features, thus improving its discriminability.", + "bbox": [ + 75, + 367, + 470, + 460 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Proposed Method", + "text_level": 1, + "bbox": [ + 76, + 473, + 250, + 489 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Overview", + "text_level": 1, + "bbox": [ + 76, + 494, + 187, + 508 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Figure 1 illustrates our MaskFormer-style framework for simultaneously detecting co-salient objects and BG regions. It consists of two sub-paths, i.e. pixel-wise segmentation feature generation and detection token construction. We use R2R in the first sub-path to enhance the segmentation features with inter-image consistency. In the second sub-path, CtP2T and CoT2T are designed to effectively construct the co-saliency and BG tokens from segmentation features, capturing the binary detection patterns. Finally, we propose TGFR to use the detection tokens as guidance for refining the segmentation features.", + "bbox": [ + 75, + 515, + 468, + 681 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For ease of understanding, we first briefly describe the vanilla MaskFormer-style framework for simultaneously detecting co-saliency and BG in CoSOD. Then, we progressively introduce the improvements in our proposed DMT, including R2R, CtP2T, CoT2T, and TGFR.", + "bbox": [ + 75, + 681, + 468, + 758 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Vanilla MaskFormer-style Framework", + "text_level": 1, + "bbox": [ + 76, + 768, + 408, + 784 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2.1 Segmentation Feature Generation", + "text_level": 1, + "bbox": [ + 76, + 789, + 366, + 803 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a set of $N$ relevant images $\\{I_i\\}_{i=1}^N$ , we follow the original MaskFormer framework [5] to adopt an FPN [19] for generating pixel-wise segmentation features. Specifically, we use VGG-16 [26] as the encoder and take $\\{I_i\\}_{i=1}^N$ as the input to obtain the highest-level features $\\pmb{F}^e \\in \\mathbb{R}^{N \\times H_0 \\times W_0 \\times C}$ from the last block. Then, based on $\\pmb{F}^e$ , the", + "bbox": [ + 75, + 808, + 470, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "FPN decoder uses five decoder layers to progressively enlarge the feature resolution and obtain five decoder features $\\pmb{F}_{j}^{d}\\in \\mathbb{R}^{N\\times H_{j}\\times W_{j}\\times C},j\\in \\{1\\dots 5\\}$", + "bbox": [ + 498, + 368, + 890, + 415 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2.2 Detection Token Construction", + "text_level": 1, + "bbox": [ + 500, + 421, + 763, + 434 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given the highest-level semantic feature $\\pmb{F}_i^e \\in \\mathbb{R}^{H_0 \\times W_0 \\times C}$ of image $\\pmb{I}_i$ , we extract the detection tokens from it via a vanilla pixel-to-token correlation (P2T) module. First, we define two randomly initialized tokens for $\\pmb{I}_i$ , i.e., a co-saliency token $T_{i,0}^c \\in \\mathbb{R}^{1 \\times C}$ and a BG token $T_{i,0}^b \\in \\mathbb{R}^{1 \\times C}$ and denote their union as $T_{i,0} \\in \\mathbb{R}^{2 \\times C}$ . We also flatten $F_i^e$ along the spatial dimension as $\\hat{F}_i^e \\in \\mathbb{R}^{H_0 W_0 \\times C}$ . Then, we iteratively update the tokens five times. At each iteration $j \\in \\{1, \\dots, 5\\}$ , we obtain $T_{i,j}$ by transforming the information from the feature $\\hat{F}_i^e$ to tokens in (1) and modeling the relationship between the co-saliency and BG tokens in (2), formulated as", + "bbox": [ + 496, + 439, + 890, + 628 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\boldsymbol {T}} _ {i, j} = \\operatorname {T r a n s} \\left(\\boldsymbol {T} _ {i, j - 1}, \\hat {\\boldsymbol {F}} _ {i} ^ {e}\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 599, + 631, + 890, + 650 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {T} _ {i, j} = \\operatorname {T r a n s} \\left(\\hat {\\boldsymbol {T}} _ {i, j}, \\hat {\\boldsymbol {T}} _ {i, j}\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 607, + 654, + 890, + 672 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where Trans is a basic transformer operation following [29]:", + "bbox": [ + 496, + 679, + 890, + 708 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {T r a n s} (\\boldsymbol {X}, \\boldsymbol {Y}) = \\mathrm {r M L P} (\\mathrm {r M H A} (\\boldsymbol {X}, \\boldsymbol {Y})). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 557, + 713, + 890, + 729 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "It can transfer the information from $\\mathbf{Y} \\in \\mathbb{R}^{N_y \\times C}$ to $\\mathbf{X} \\in \\mathbb{R}^{N_x \\times C}$ under the guidance of their relation. rMHA and rMLP denote the residual multi-head attention [29] and residual multi-layer perception, respectively, formulated as", + "bbox": [ + 496, + 741, + 890, + 803 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {r M L P} (\\boldsymbol {X}) = \\boldsymbol {X} + \\operatorname {M L P} (\\operatorname {L N} (\\boldsymbol {X})), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 814, + 890, + 830 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {r M H A} (\\boldsymbol {X}, \\boldsymbol {Y}) = \\boldsymbol {X} + \\operatorname {M H A} (\\ln (\\boldsymbol {X}), \\ln (\\boldsymbol {Y}))), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 840, + 890, + 858 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where LN denotes the layer normalization [2] and MLP is the multi-layer perception consisting of two fully connected", + "bbox": [ + 496, + 869, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "7249", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "layers with a GELU [15] activation function. MHA is the multi-head attention that can be formulated as", + "bbox": [ + 76, + 90, + 468, + 119 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\operatorname {M H A} (\\boldsymbol {X}, \\boldsymbol {Y}) = \\operatorname {C a t} ([ \\operatorname {A t t} _ {m} (\\boldsymbol {X}, \\boldsymbol {Y}) V _ {m} (\\boldsymbol {Y}) ] _ {m = 1} ^ {M}), \\quad (6) \\\\ \\operatorname {A t t} _ {m}, (\\boldsymbol {X}, \\boldsymbol {Y}) = \\operatorname {S o f t m a x} \\left(\\frac {Q _ {m} (\\boldsymbol {X}) K _ {m} (\\boldsymbol {Y}) ^ {\\top}}{\\sqrt {C / M}}\\right), \\tag {7} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 94, + 125, + 468, + 190 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $M$ is the number of used attention heads. The result of each head (with the shape of $N_{x} \\times C / M$ ) is obtained via the matrix multiplication between $\\mathrm{Att}_m(\\mathbf{X}, \\mathbf{Y}) \\in \\mathbb{R}^{N_x \\times N_y}$ and $V_m(\\mathbf{Y}) \\in \\mathbb{R}^{N_y \\times C / M}$ . $\\mathrm{Att}_m(\\mathbf{X}, \\mathbf{Y})$ is the attention matrix calculated in (7). Here $Q_m(\\cdot)$ , $K_m(\\cdot)$ , and $V_m(\\cdot)$ are the query, key, and value embedding functions in the $m$ th head, respectively, and project corresponding tensors from $C$ channels to $C / M$ channels. Finally, $\\mathrm{MHA}(\\mathbf{X}, \\mathbf{Y}) \\in \\mathbb{R}^{N_x \\times C}$ can be obtained by concatenating (Cat) the results of $M$ heads along the channel dimension.", + "bbox": [ + 76, + 199, + 470, + 349 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.3 Prediction", + "text_level": 1, + "bbox": [ + 76, + 354, + 202, + 368 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "After performing the token construction five times on each image, we collect the final tokens of all images, i.e. $T_5^c, T_5^b \\in \\mathbb{R}^{N \\times 1 \\times C}$ . Then, we use the output of the first sub-path, i.e. the segmentation feature $F_5^d$ , to generate the final predictions via the sigmoid matrix multiplication, formulated as", + "bbox": [ + 76, + 375, + 468, + 463 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {P} ^ {c} = \\mathcal {P} \\left(\\boldsymbol {T} _ {5} ^ {c}, \\boldsymbol {F} _ {5} ^ {d}\\right) = \\operatorname {S i g m o i d} \\left(\\boldsymbol {T} _ {5} ^ {c} \\left(\\boldsymbol {F} _ {5} ^ {d}\\right) ^ {\\top}\\right), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 130, + 467, + 468, + 487 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {P} ^ {b} = \\mathcal {P} (\\boldsymbol {T} _ {5} ^ {b}, \\boldsymbol {F} _ {5} ^ {d}) = \\operatorname {S i g m o i d} (\\boldsymbol {T} _ {5} ^ {b} (\\boldsymbol {F} _ {5} ^ {d}) ^ {\\top}), \\qquad (9)\n$$\n", + "text_format": "latex", + "bbox": [ + 133, + 489, + 468, + 508 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $P^c, P^b \\in \\mathbb{R}^{N \\times 1 \\times H \\times W}$ are the segmentation results of co-salient objects and BG regions, respectively.", + "bbox": [ + 76, + 512, + 468, + 544 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Our Improvements for DMT", + "text_level": 1, + "bbox": [ + 76, + 553, + 333, + 569 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3.1 Region-to-Region Correlation", + "text_level": 1, + "bbox": [ + 76, + 577, + 338, + 592 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the first sub-path, the original FPN individually processes each image and lacks the inter-image correlation modeling, which is crucial for CoSOD. However, straightforward P2P correlation is computationally prohibitive for large feature maps and multiple images. To this end, we consider modeling correlations among images in an economical way, thus proposing our R2R module, which uses region-level features instead of pixel-level features to compute correlations.", + "bbox": [ + 75, + 597, + 468, + 715 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Concretely, when given the features $\\pmb{F}_j^d \\in \\mathbb{R}^{N \\times H_j \\times W_j \\times C}$ of $N$ relevant images from the $j$ th decoder layer, we first adopt a transformation $\\mathbb{R}_1$ to divide the $H_j \\times W_j$ feature maps into $K \\times K$ local regions and use max-pooling to pick up the most representative feature for representing each local region. As a result, we can obtain the region-level query with shape $\\mathbb{R}^{N \\times K \\times K \\times C}$ .", + "bbox": [ + 75, + 715, + 468, + 824 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Then, we generate multi-scale region-level key and value via another transformation $\\mathbf{R}_2$ , which consists of three adaptive max-pooling operations with the output spatial sizes of $1 \\times 1$ , $3 \\times 3$ , and $6 \\times 6$ , respectively. The three pooled features are finally flattened and concatenated to generate", + "bbox": [ + 75, + 825, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the key and value with shape $\\mathbb{R}^{N\\times 46\\times C}$ , encoding multiscale robust region information.", + "bbox": [ + 498, + 90, + 888, + 119 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Next, we perform the R2R inter-image correlation among the region-level query, key, and value via the transformer operation (3), thus obtaining the enhanced features with the region-wise correlation.", + "bbox": [ + 498, + 121, + 888, + 181 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Finally, we upsample the enhanced features to the original resolution $H_{j} \\times W_{j}$ via the nearest interpolation, denoted as $\\mathbf{R}_1^{-1}$ . A residual connection is also used to add the original features. Thus, the region correlation results are diffused to the corresponding internal pixels in each local region. The whole process of R2R on $\\pmb{F}_{j}^{d}$ is formulated as", + "bbox": [ + 498, + 181, + 890, + 273 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {F} _ {j} ^ {d r} = \\boldsymbol {F} _ {j} ^ {d} + \\mathrm {R} _ {1} ^ {- 1} (\\operatorname {T r a n s} \\left(\\mathrm {R} _ {1} \\left(\\boldsymbol {F} _ {j} ^ {d}\\right), \\mathrm {R} _ {2} \\left(\\boldsymbol {F} _ {j} ^ {d}\\right)\\right)). \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 527, + 276, + 888, + 296 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3.2 Contrast-induced Pixel-to-Token Correlation", + "text_level": 1, + "bbox": [ + 500, + 301, + 867, + 316 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the second sub-path, the original P2T module uses a transformer operation in (2) to mine relations between the two types of tokens in a data-driven way, while ignoring explicit CoSOD cues, especially the crucial contrast modeling between co-saliency and BG regions. To enhance the discriminability between the tokens, we explicitly model the contrast relation with our proposed CtP2T module, which modifies the transformer layer in (1) and the remaining part keeps the same as P2T.", + "bbox": [ + 496, + 321, + 890, + 455 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Overall, we modify the multi-head attention (denoted as $\\mathrm{MHA}^{\\ast}$ ) and propose a contrast-induced channel attention (CCA) mechanism. The basic idea is to suppress the channels that are not contrastive enough in the generated co-saliency and BG tokens. The contrast is modeled as the opposite of the channel similarity between the two types of tokens, which can be calculated via channel correlation. For brevity's sake, we slightly abuse the notation and use $\\hat{T}, T \\in \\mathbb{R}^{2 \\times C}$ , and $F \\in \\mathbb{R}^{H_0 W_0 \\times C}$ as shorthands for $\\hat{T}_{i,j}$ , $T_{i,j-1}$ , and $\\hat{F}_i^e$ in (1), respectively. Then, (1) can be modified for our CtP2T as below:", + "bbox": [ + 498, + 458, + 890, + 625 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\hat {\\boldsymbol {T}} = \\operatorname {T r a n s} ^ {*} (\\boldsymbol {T}, \\boldsymbol {F}) \\\\ = \\operatorname {r M L P} (\\boldsymbol {T} + \\operatorname {C C A} (\\operatorname {M H A} ^ {*} (\\boldsymbol {T}, \\boldsymbol {F}))). \\tag {11} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 557, + 633, + 888, + 670 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Next, we introduce $\\mathrm{MHA}^*$ and CCA as shown in Figure 2. The LN operations are omitted for expression convenience.", + "bbox": [ + 498, + 681, + 888, + 710 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Modified Multi-Head Attention. To generate co-saliency and BG tokens that can be used for calculating their channel similarity, we make our $\\mathrm{MHA}^*$ able to generate tokens with multiple heads. Concretely, we first replace the original $V_{m}$ in (6) with $V_{m}^{*}$ that embeds $\\pmb{F}$ to the identical channel number $C$ . Thus, the shape of each head's result becomes $2\\times C$ instead of $2\\times C / M$ . Next, we stack the results of $M$ heads to produce the output of $\\mathrm{MHA}^*$ . The whole process can be formulated as", + "bbox": [ + 496, + 719, + 890, + 854 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\boldsymbol {T} _ {M} = \\operatorname {M H A} ^ {*} (\\boldsymbol {T}, \\boldsymbol {F}) \\\\ = \\operatorname {S t a c k} \\left(\\left[ \\operatorname {A t t} _ {m} (\\boldsymbol {T}, \\boldsymbol {F}) V _ {m} ^ {*} (\\boldsymbol {F}) \\right] _ {m = 1} ^ {M}\\right). \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 553, + 864, + 861, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "7250", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/e97107c3e9edef4750840d250fa3ce0f7ac5886cb217c45ede475ace6e732e8c.jpg", + "image_caption": [ + "Modified Multi-Head Attention Contrast-induced Channel Attention", + "Figure 2. Diagram of MHA* and CCA. We first generate multihead tokens $T_{M}^{c}$ and $T_{M}^{b}$ via MHA*. Then, we utilize matrix multiplication of the two tokens to generate the attention weights $W$ for modulating the token channels in CCA." + ], + "image_footnote": [], + "bbox": [ + 80, + 102, + 467, + 304 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$\\pmb{T}_{M} \\in \\mathbb{R}^{2 \\times M \\times C}$ is composed of the co-saliency token and the BG token $\\pmb{T}_{M}^{c}, \\pmb{T}_{M}^{b} \\in \\mathbb{R}^{M \\times C}$ with $M$ heads. Next, we can compute the channel similarity based on them.", + "bbox": [ + 76, + 369, + 468, + 417 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Contrast-induced Channel Attention. Given the multihead tokens $T_{M}^{c}$ and $T_{M}^{b}$ , we generate channel attention $W \\in \\mathbb{R}^{2 \\times 1 \\times C}$ to suppress the token channels with strong mutual similarities since they cannot clearly distinguish between co-saliency and BG.", + "bbox": [ + 76, + 422, + 468, + 498 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "First, we compute a $C \\times C$ channel similarity matrix between $\\pmb{T}_M^c$ and $\\pmb{T}_M^b$ via matrix multiplication. Then, the channel similarity of each token to the other token can be computed as the average along the channel dimension of the other token. The whole process can be denoted as", + "bbox": [ + 76, + 500, + 468, + 573 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {S} ^ {c} = \\operatorname {A v g} \\left(\\boldsymbol {T} _ {M} ^ {c} \\top \\boldsymbol {T} _ {M} ^ {b}\\right), \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 192, + 574, + 467, + 592 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {S} ^ {b} = \\operatorname {A v g} \\left(\\boldsymbol {T} _ {M} ^ {b} ^ {\\top} \\boldsymbol {T} _ {M} ^ {c}\\right), \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 196, + 592, + 467, + 612 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $S^c, S^b \\in \\mathbb{R}^{C \\times 1}$ , representing how similar each channel is to the channels of the other token. Avg means calculating the average along the second dimension.", + "bbox": [ + 76, + 614, + 467, + 660 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Next, we multiply $S^c$ and $S^b$ with $-1$ to turn the similarity measurements into the contrast scores and then compute the channel attention $\\mathbf{W} \\in \\mathbb{R}^{2 \\times 1 \\times C}$ via", + "bbox": [ + 76, + 660, + 467, + 705 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {W} = \\text {S i g m o i d} \\left(\\alpha \\left[ \\begin{array}{c} - \\boldsymbol {S} ^ {c ^ {\\top}} \\\\ - \\boldsymbol {S} ^ {b ^ {\\top}} \\end{array} \\right] + \\beta\\right). \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 147, + 709, + 468, + 751 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Here we use a learnable linear projection with parameters $\\alpha, \\beta$ on each channel of the stacked contrast scores to fit them for the sigmoid activation.", + "bbox": [ + 76, + 757, + 468, + 801 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Once obtained $\\mathbf{W}$ , we adopt the element-wise multiplication between $\\mathbf{T}_M$ and $\\mathbf{W}$ to modulate the token channels based on their contrast and then eliminate the multi-head dimension of the tokens by averaging the head dimension and obtaining the modulated tokens:", + "bbox": [ + 76, + 801, + 468, + 876 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {C C A} \\left(\\boldsymbol {T} _ {M}\\right) = \\operatorname {A v g} \\left(\\boldsymbol {W} \\odot \\boldsymbol {T} _ {M}\\right) \\in \\mathbb {R} ^ {2 \\times C}, \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 133, + 883, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/8549e25ec3bae532cb3bdff0f8cad4caa4fe8915917c41529d837df39883cc24.jpg", + "image_caption": [ + "Figure 3. Diagram of our proposed TGFR module. Specifically, we first distill the co-saliency and BG features under the guidance of the two tokens. Then, we fuse them back to the original segmentation feature for discriminability enhancement." + ], + "image_footnote": [], + "bbox": [ + 503, + 90, + 885, + 234 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\odot$ means element-wise multiplication with broadcasting.", + "bbox": [ + 498, + 305, + 888, + 335 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3.3 Co-saliency Token-to-Token Correlation", + "text_level": 1, + "bbox": [ + 500, + 342, + 833, + 357 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "CtP2T effectively explores the correlation between the two types of tokens within each image, but lacks explicitly modeling the inter-image relation to capture the token-wise group consistency, thus being limited for consensus mining. Therefore, we use co-saliency tokens from all images to model the consensus patterns via our CoT2T module.", + "bbox": [ + 496, + 362, + 890, + 450 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Specifically, we first define a group token $G \\in \\mathbb{R}^{1 \\times C}$ to represent the group-wise consensus information, which is randomly initialized at the first iteration step. At the $j$ th iteration, given the last group token $G_{j-1}$ and the co-saliency tokens $\\tilde{T}_j^c \\in \\mathbb{R}^{N \\times C}$ from the CtP2T module, we aggregate the consensus information from all co-saliency tokens by using $\\tilde{T}_j^c$ to update $G_{j-1}$ , denoted as", + "bbox": [ + 496, + 452, + 890, + 561 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {G} _ {j} = \\operatorname {T r a n s} \\left(\\boldsymbol {G} _ {j - 1}, \\tilde {\\boldsymbol {T}} _ {j} ^ {c}\\right). \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 609, + 566, + 890, + 585 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finally, we distribute the aggregated consensus cues back to $\\tilde{T}_{j}^{c}$ and obtain the final co-saliency tokens $T_{j}^{c}$ :", + "bbox": [ + 498, + 593, + 888, + 625 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {T} _ {j} ^ {c} = \\operatorname {T r a n s} \\left(\\tilde {\\boldsymbol {T}} _ {j} ^ {c}, \\boldsymbol {G} _ {j}\\right). \\tag {18}\n$$\n", + "text_format": "latex", + "bbox": [ + 617, + 628, + 890, + 648 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3.4 Token-guided Feature Refinement", + "text_level": 1, + "bbox": [ + 500, + 659, + 790, + 672 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The vanilla MaskFormer only transforms the information from the segmentation features to the tokens, hindering their complementary learning. To this end, we propose our TGFR module to improve the discriminability of the segmentation features via the detection cues of the tokens. As shown in Figure 3, TGFR consists of two processes, i.e. distillation and refusion. The distillation process is designed to distill the co-saliency and BG features from the segmentation feature under the guidance of the corresponding tokens. The refusion process is to fuse the distilled features back to the segmentation feature to enhance its discriminability.", + "bbox": [ + 496, + 678, + 890, + 845 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Distillation. For image $\\mathbf{I}_i$ at the $j$ th iteration, we have the final co-saliency token $T_{i,j}^{c} \\in \\mathbb{R}^{1 \\times C}$ generated from CoT2T and the final BG token $T_{i,j}^{b} \\in \\mathbb{R}^{1 \\times C}$ outputted by", + "bbox": [ + 498, + 852, + 890, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "7251", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "CtP2T, and the segmentation feature $F_{i,j}^{dr}\\in \\mathbb{R}^{H_j\\times W_j\\times C}$ enhanced by R2R. We first compute two attention maps $A_{i,j}^{c}\\in \\mathbb{R}^{H_{j}\\times W_{j}\\times 1}$ and $A_{i,j}^{b}\\in \\mathbb{R}^{H_{j}\\times W_{j}\\times 1}$ via performing the matrix multiplication between the segmentation feature and the tokens and then adopting a softmax normalization on the spatial dimension, formulated as", + "bbox": [ + 75, + 89, + 472, + 181 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {A} _ {i, j} ^ {c} = \\operatorname {S o f t m a x} \\left(\\boldsymbol {F} _ {i, j} ^ {d r} \\left(\\boldsymbol {T} _ {i, j} ^ {c}\\right) ^ {\\top} / \\sqrt {C}\\right), \\tag {19}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 183, + 468, + 204 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {A} _ {i, j} ^ {b} = \\operatorname {S o f t m a x} \\left(\\boldsymbol {F} _ {i, j} ^ {d r} \\left(\\boldsymbol {T} _ {i, j} ^ {b}\\right) ^ {\\top} / \\sqrt {C}\\right). \\tag {20}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 207, + 468, + 229 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Next, we adopt the computed attention maps to distill the detection features from the segmentation feature via matrix multiplication, denoted as", + "bbox": [ + 75, + 232, + 468, + 277 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {D} _ {i, j} ^ {c} = \\left(\\boldsymbol {A} _ {i, j} ^ {c}\\right) ^ {\\top} \\boldsymbol {F} _ {i, j} ^ {d r}, \\tag {21}\n$$\n", + "text_format": "latex", + "bbox": [ + 199, + 280, + 468, + 300 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {D} _ {i, j} ^ {b} = \\left(\\boldsymbol {A} _ {i, j} ^ {b}\\right) ^ {\\top} \\boldsymbol {F} _ {i, j} ^ {d r}, \\tag {22}\n$$\n", + "text_format": "latex", + "bbox": [ + 200, + 304, + 468, + 325 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $D_{i,j}^{c}, D_{i,j}^{b} \\in \\mathbb{R}^{1 \\times C}$ is the distilled features for co-saliency and BG, respectively.", + "bbox": [ + 75, + 330, + 468, + 362 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Refusion. After producing $D_{i,j}^{c}$ and $D_{i,j}^{b}$ , we conduct the refusion process to fuse them back to $F_{i,j}^{dr}$ sequentially in a cascade way for activating the co-saliency and BG regions in $F_{i,j}^{dr}$ . In this way, we can effectively reduce ambiguous information and enhance feature discriminability. The details can be formulated as", + "bbox": [ + 75, + 368, + 468, + 460 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\boldsymbol {F}} _ {i, j} ^ {d t} = \\operatorname {C o n v} _ {c} \\left(\\operatorname {C a t} \\left(\\left[ \\boldsymbol {F} _ {i, j} ^ {d r}, \\operatorname {E} \\left(\\boldsymbol {D} _ {i, j} ^ {c}\\right) \\right]\\right)\\right), \\tag {23}\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 463, + 468, + 486 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {F} _ {i, j} ^ {d t} = \\operatorname {C o n v} _ {b} \\left(\\operatorname {C a t} \\left(\\left[ \\hat {\\boldsymbol {F}} _ {i, j} ^ {d t}, \\mathrm {E} \\left(\\boldsymbol {D} _ {i, j} ^ {b}\\right) \\right]\\right)\\right), \\tag {24}\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 487, + 468, + 510 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\operatorname{E}(*)$ replicates $D_{i,j}^{c}$ and $D_{i,j}^{b}$ along the spatial dimension to the same size as $F_{i,j}^{dr}$ . Then, we progressively concatenate them with $F_{i,j}^{dr}$ and use a convolution layer to reduce the channel number to $C$ .", + "bbox": [ + 75, + 516, + 468, + 580 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.3.5 Prediction and Loss Function", + "text_level": 1, + "bbox": [ + 76, + 590, + 336, + 604 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In the $j$ th iteration, after obtaining the learned co-saliency and BG tokens, i.e. $\\pmb{T}_j^c,\\pmb{T}_j^b\\in \\mathbb{R}^{N\\times 1\\times C}$ , from CoT2T and CtP2T, respectively, and the improved segmentation features $\\pmb{F}_{j}^{dt}\\in \\mathbb{R}^{N\\times H_{j}\\times W_{j}\\times C}$ from TGFR, we use the prediction function $\\mathcal{P}$ in (8) to generate the co-saliency and the BG predictions, i.e. $\\pmb{P}_{j}^{c}\\pmb{P}_{j}^{b}$ , as follows:", + "bbox": [ + 75, + 609, + 468, + 702 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {P} _ {j} ^ {c} = \\mathcal {P} \\left(\\boldsymbol {T} _ {j} ^ {c}, \\boldsymbol {F} _ {j} ^ {d t}\\right), \\tag {25}\n$$\n", + "text_format": "latex", + "bbox": [ + 207, + 705, + 468, + 726 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {P} _ {j} ^ {b} = \\mathcal {P} \\left(\\boldsymbol {T} _ {j} ^ {b}, \\boldsymbol {F} _ {j} ^ {d t}\\right). \\tag {26}\n$$\n", + "text_format": "latex", + "bbox": [ + 207, + 729, + 468, + 750 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We also supervise the learning of the group token $G_{j} \\in \\mathbb{R}^{1 \\times 1 \\times C}$ in CoT2T and the middle feature $\\hat{\\pmb{F}}_j^{dt} \\in \\mathbb{R}^{N \\times H_j \\times W_j \\times C}$ in TGFR. Two predictions can be obtained from them, respectively:", + "bbox": [ + 75, + 753, + 468, + 821 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {P} _ {j} ^ {g} = \\mathcal {P} (\\text {R e p e a t} (\\boldsymbol {G} _ {j}), \\boldsymbol {F} _ {j} ^ {d t}), \\tag {27}\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 830, + 468, + 859 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {P} _ {j} ^ {d t} = \\mathcal {P} (\\boldsymbol {T} _ {j} ^ {c}, \\hat {\\boldsymbol {F}} _ {j} ^ {d t}),\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 854, + 308, + 876 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where Repeat is to repeat $G_{j}$ $N$ times.", + "bbox": [ + 76, + 885, + 339, + 901 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/57f19a6eaa9972ca6b456c372757c9b373be0d493131adfafea112274c5c8364.jpg", + "table_caption": [ + "Table 1. Quantitative results of different settings of our proposed model. We show the results of progressively adding R2R, CtP2T, CoT2T, and TGFR on the baseline. \"Co\" and \"Bg\" mean explicitly modeling co-saliency and BG, respectively." + ], + "table_footnote": [], + "table_body": "
SettingsCoCA [42]
CoBgR2RCtP2TCoT2TTGFRSm↑Eξ↑maxF↑MAE ↓
✓✓0.67510.76830.54740.1383
✓✓✓0.69450.78240.58150.1234
✓✓✓✓0.70380.78680.59840.1230
✓✓✓✓✓0.71400.78800.60030.1139
✓✓✓✓✓✓0.72460.80010.61900.1084
✓✓✓✓0.70590.79200.59960.1259
", + "bbox": [ + 501, + 148, + 898, + 271 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/1b8d5a0a9a9d5d6819e1fac1c7631adcb00acfa41851a32e264a0e90f2d1506b.jpg", + "image_caption": [ + "Figure 4. Qualitative results of different settings of our proposed model. We show the results of progressively adding the R2R, CtP2T, CoT2T, and TGFR on the baseline." + ], + "image_footnote": [], + "bbox": [ + 501, + 277, + 893, + 383 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our total loss $\\mathcal{L}_{total}$ can be formulated as", + "bbox": [ + 517, + 436, + 795, + 450 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {t o t a l}} = \\sum_ {j = 1} ^ {5} \\left(\\mathcal {L} _ {1} \\left(\\boldsymbol {P} _ {j} ^ {c}, \\boldsymbol {M} _ {j} ^ {c}\\right) + \\mathcal {L} _ {2} \\left(\\boldsymbol {P} _ {j} ^ {c}, \\boldsymbol {M} _ {j} ^ {c}\\right) + \\right. \\tag {28}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 455, + 890, + 500 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\left. \\mathcal {L} _ {2} \\left(\\boldsymbol {P} _ {j} ^ {b}, \\boldsymbol {M} _ {j} ^ {b}\\right) + \\mathcal {L} _ {2} \\left(\\boldsymbol {P} _ {j} ^ {g}, \\boldsymbol {M} _ {j} ^ {c}\\right) + \\mathcal {L} _ {2} \\left(\\boldsymbol {P} _ {j} ^ {d t}, \\boldsymbol {M} _ {j} ^ {c}\\right)\\right),\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 502, + 844, + 527 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_1$ and $\\mathcal{L}_2$ are the IoU [16] and Binary Cross-Entropy (BCE) [7] loss, respectively. $M_j^c$ and $M_j^b$ denote the co-saliency and BG ground truths, respectively, with the spatial shapes aligned to the $j$ th decoder layer.", + "bbox": [ + 498, + 537, + 890, + 599 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 613, + 633, + 630 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Evaluation Datasets and Metrics", + "text_level": 1, + "bbox": [ + 500, + 638, + 785, + 652 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We follow [12, 27, 34] to evaluate our proposed model on three CoSOD benchmark datasets. CoSal2015 [36] and CoSOD3k [11] collect 50 groups with 2015 images and 160 groups with 3316 images, respectively. CoCA [42] is the most challenging dataset and contain 1295 images of 80 groups. We employ four widely-used metrics for quantitative evaluation, i.e. Structure-measure $S_{m}$ [9], Enhanced-alignment measure $E_{\\xi}$ [10], Maximum F-measure (maxF) [1], and Mean Absolute Error (MAE) [6].", + "bbox": [ + 496, + 657, + 890, + 794 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Implementation Details", + "text_level": 1, + "bbox": [ + 500, + 804, + 717, + 820 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We follow [41] to use the COCO-9k [20] (9213 images of 65 groups) and the DUTS class [42] (8250 images of 291 groups) with the synthesis strategy [41] to construct our training set. We follow [22] to perform data augmentation and adopt the Adam optimizer [17] with an initial learning", + "bbox": [ + 496, + 824, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "7252", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b6bb61b7e9fa624d61c4d45e1680900c8432ee0eabf1e0c9f530e717a50c3041.jpg", + "image_caption": [ + "Figure 5. Visual comparison among the channels with different channel attention weights in CtP2T. We visualize some feature maps in $V_{m}^{*}(\\pmb{F})$ for the channels with large and small channel attention (CA) in CtP2T. We visualize two channels for large and small CA, respectively." + ], + "image_footnote": [], + "bbox": [ + 80, + 88, + 191, + 193 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/27e9ff26b9eb13a07b4215eb4e140283f1551bc5b5c159c31ca6b067f3bb2822.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 192, + 88, + 305, + 193 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/1891516425141cf4c3434e24c6138abc0ad24af763d326af727e4aad49cb9e0f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 305, + 88, + 419, + 193 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b2c7ead7ae43c5812f7cb912fff0e2f064fae07518c832472e9cd220a708fff7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 421, + 88, + 478, + 193 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "rate of 0.0001, $\\beta_{1} = 0.9$ , and $\\beta_{2} = 0.99$ to train our model for 80,000 iterations. The learning rate is divided by 10 at the $60000^{\\mathrm{th}}$ iteration. We select at most eight images from each group as a mini-batch to train our network. The training and testing image size is set as $256 \\times 256$ . Our method is implemented using Pytorch [24].", + "bbox": [ + 75, + 275, + 470, + 367 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 378, + 230, + 393 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We conduct ablation studies on the challenging CoCA [42] dataset to verify the effectiveness of our proposed components. As shown in Table 1, we treat the vanilla MaskFormer-style framework as our baseline, shown in the first row, and progressively add our proposed R2R, CtP2T, CoT2T, and TGFR on it for effectiveness analysis.", + "bbox": [ + 75, + 398, + 468, + 489 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of R2R. First, we plug R2R into each decoder layer to enhance the segmentation features. It shows that using R2R largely improves the model performance compared to the baseline, while using vanilla P2P causes the out-of-memory error. The results verify the necessity of using our R2R for inter-image correlation modeling.", + "bbox": [ + 75, + 489, + 468, + 580 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of CtP2T. Next, we consider the contrast relation modeling between the co-saliency and BG tokens, thus replacing the original P2T module to our proposed CtP2T module. By using CtP2T, the model performance can be further improved, indicating that CtP2T is beneficial for enhancing the discriminability between the two types of tokens. We also provide some visual samples in Figure 5. Since the channels of the tokens correspond to those of the values in $\\mathrm{MHA}^*$ , we visualize some feature maps of $V_{m}^{*}(\\pmb {F})$ of the channels with large or small channel attention weights in $\\pmb{W}$ . We can see that the channels with large channel attention (CA) can easily distinguish co-salient objects and distracting objects, while those with small CA usually confuse them. The results demonstrate our generated channel attention is meaningful for accurate co-salient object detection.", + "bbox": [ + 75, + 582, + 470, + 823 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of CoT2T. Furthermore, we supplement CoT2T to explore the inter-image correlations for all co-saliency tokens. CoT2T explicitly promotes consensus information propagation among all co-saliency tokens, thus obtaining obvious improvements.", + "bbox": [ + 75, + 824, + 468, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/980cd91bb7248c643c8a844be5f07f9aa8da856fea1b34de277e54272586718a.jpg", + "table_caption": [ + "Table 2. Quantitative results of different settings in TGFR." + ], + "table_footnote": [], + "table_body": "
SettingsCoCA [42]
Sm↑Eξ↑maxF↑MAE↓
w/o TGFR0.71400.78800.60030.1139
w/o Distillation0.71410.79210.60460.1114
w/ co0.71710.79650.60760.1144
w/ bg0.71550.79350.60640.1112
w/ bg&co0.71970.79070.60920.1069
w/ co&bg0.72460.80010.61900.1084
", + "bbox": [ + 501, + 104, + 897, + 210 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/1ff33136dbbd7d9fd0a3586c037edf9737254f5ad0d072188ed3f93e837d5de2.jpg", + "image_caption": [ + "Image", + "Figure 6. Visualization of some feature maps (Fea.) and predictions (Pred.) of the models with (w/) or without (w/o) using TGFR." + ], + "image_footnote": [], + "bbox": [ + 501, + 215, + 566, + 292 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/584119f4c47ab3b34a780e94aeeebaabf8e807a2d00df350bc17f7374789e3bb.jpg", + "image_caption": [ + "GT" + ], + "image_footnote": [], + "bbox": [ + 566, + 215, + 630, + 292 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/490ab51924231aea23dfa23499631be1ad1e4c2736f94f4749e8b0a1cf4d2c19.jpg", + "image_caption": [ + "Pred. w/o" + ], + "image_footnote": [], + "bbox": [ + 630, + 215, + 694, + 292 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/923c8581e007b126701f1c7fc46748a18619b844abdbc30e3477ee0dbc75735f.jpg", + "image_caption": [ + "Fea. w/o" + ], + "image_footnote": [], + "bbox": [ + 697, + 215, + 756, + 292 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/369179c1a06f2b277927e023d19ed0c7edafaa2ef4461ec4a6773e8ecd34b02a.jpg", + "image_caption": [ + "Pred. w/" + ], + "image_footnote": [], + "bbox": [ + 759, + 215, + 823, + 292 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/1e9a49ff7240403ab36f67f13293ed48d81dcf0fc248dcd522b3a6986111ca18.jpg", + "image_caption": [ + "Fea. w/" + ], + "image_footnote": [], + "bbox": [ + 823, + 215, + 888, + 292 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of TGFR. Finally, we add TGFR to leverage the learned tokens for refining the segmentation features. Table 1 shows that adopting TGFR can bring more performance gains, thus demonstrating its effectiveness. We also visualize some feature maps and predictions of using and without using TGFR in Figure 6. It can be seen that using TGFR obtains more discriminative features for distinguishing co-saliency objects from distractors, thus generating better segmentation results.", + "bbox": [ + 496, + 354, + 890, + 491 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To dive deeper into the effectiveness of TGFR, we report more experimental results in Table 2 for further analysis. First, we directly fuse the tokens and the segmentation features without performing the distillation process (\"w/o Distillation\"). we find this model brings limited improvements compared to the \"w/o TGFR\" model. It is probably because the tokens and features might exist semantic gap, being detrimental for their fusion, hence verifying the necessity of our distillation mechanism. Next, we supplement the distillation process and explore four strategies for the refusion process, i.e. individually refusing the distilled co-saliency (\"w/ co\") or BG features (\"w/ bg\") to the segmentation features, or refusing both with the order of co-saliency feature first (\"w/ co&bg\") or BG feature first (\"w/ bg&co\"). We can find refusing both achieves better performance, thus verifying the necessity of leveraging both features for discrimination enhancement. We also find first refusing the co-saliency feature and then integrating the BG feature obtains the best results. Thus, we adopt this strategy in our final TGFR design.", + "bbox": [ + 496, + 491, + 892, + 792 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of BG Exploration. We remove all BG-related modules in our final model and only explore co-saliency regions, shown in the last row of Table 1. In this setting, CtP2T can not be used while only the co-saliency feature is used in TGFR. We find that the performance significantly drops compared to our final model, thus verifying the necessity of explicit BG modeling.", + "bbox": [ + 496, + 794, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "7253", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/5e7b0d9ca13c5ff1f4d2b5f7a02770758ea0a872e0892af34d0def050bab21da.jpg", + "table_caption": [ + "Table 3. Quantitative comparison of our model with other state-of-the-art methods. We conduct the comparison on three benchmark CoSOD datasets. Red and blue denote the best and the second-best results, respectively." + ], + "table_footnote": [], + "table_body": "
MethodsCoCA [42]CoSal2015 [36]CoSOD3k [11]
Sm↑Eξ↑maxF↑MAE↓Sm↑Eξ↑maxF↑MAE↓Sm↑Eξ↑maxF↑MAE↓
CSMG(CVPR2019) [39]0.62760.73240.49880.12730.77570.84360.78690.13090.72720.82080.72970.1480
GICD(ECCV2020) [42]0.65790.71490.51260.12600.84370.88690.84410.07070.79670.84780.76980.0794
ICNet(NIPS2020) [16]0.65410.70420.51330.14700.85710.90110.85830.05790.79420.84500.76230.0891
GCoNet(CVPR2021) [12]0.67300.75980.54380.10500.84530.88790.84710.06810.80180.86010.77710.0712
CADC(ICCV2021) [41]0.68000.74430.54870.13300.86660.90630.86450.06410.81500.85430.77810.0875
UFO(ArXiv2022) [27]0.69710.78020.56810.09390.85780.90570.86210.06480.81910.86940.79540.0735
DCFM(CVPR2022) [34]0.71010.78260.59810.08450.83800.89290.85590.06720.80940.87420.80450.0674
DMT (Ours)0.72460.80010.61900.10840.89740.93620.90520.04540.85140.89500.83530.0633
", + "bbox": [ + 99, + 118, + 867, + 252 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/01ccf4478dc86201b0e20d2385b32fe3460a31f1bdb4595b0985e4f84302df7b.jpg", + "image_caption": [ + "Figure 7. Qualitative comparisons of our model with other state-of-the-art methods." + ], + "image_footnote": [], + "bbox": [ + 76, + 263, + 897, + 537 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Quantitative Analysis. As shown in Figure 4, we also provide some visual comparison samples for the four key components. We find that the baseline model is easily distracted by complex BG regions, while progressively introducing our four components can gradually exclude these distractors and achieve more and more accurate results.", + "bbox": [ + 75, + 565, + 468, + 655 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Comparison with State-of-the-Art Methods", + "text_level": 1, + "bbox": [ + 76, + 667, + 464, + 684 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We compare our model with other seven state-of-the-art methods, i.e. CSMG [39], GICD [42], ICNet [16], GCoNet [12], CADC [41], UFO [27], and DCFM [34]. We report the quantitative comparison results in Table 3. We can observe that our proposed DMT achieves the best performance on all three benchmark datasets. Especially, on CoSal2015 and CoSOD3k, our DMT model surpasses the second-best model by a large margin, e.g. $3.14\\%$ $S_{m}$ and $4.07\\%$ maxF on CoSal2015 and $3.23\\%$ $S_{m}$ and $3.08\\%$ maxF on CoSOD3k. We also show some visual comparison results in Figure 7. We can find that our method can precisely detect co-salient objects in complex scenarios, e.g. the existence of extraneous salient objects with similar appearances to target objects, and target objects with small", + "bbox": [ + 75, + 689, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "sizes. Nevertheless, other models are heavily distracted in these challenging scenes.", + "bbox": [ + 498, + 565, + 890, + 595 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusions", + "text_level": 1, + "bbox": [ + 500, + 607, + 627, + 622 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose DMT, a transformer-based CoSOD model for explicitly mining both co-saliency and BG information and effectively modeling their discrimination. Specifically, we propose several economic multigrained correlations, i.e. R2R, CtP2T, and CoT2T to model inter-image and intra-image relations. Besides, we propose a TGFR module to leverage the detection information for improving the discriminability of the segmentation features. It is an improvement to the MaskFormer that allows the mutual promotion of two sub-paths. Our model achieves a new state-of-the-art result.", + "bbox": [ + 496, + 630, + 890, + 796 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments: This work was supported in part by Key-Area Research and Development Program of Guangdong Province (No.2021B0101200001), the National Key R&D Program of China under Grant 2021B0101200001, and the National Science Foundation of China under Grant 62036011, U20B2065, 721A0001, 62136004.", + "bbox": [ + 496, + 809, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "7254", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Radhakrishna Achanta, Sheila Hemami, Francisco Estrada, and Sabine Susstrunk. Frequency-tuned salient region detection. 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Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.082, + 0.13, + 0.89, + 0.176 + ], + "angle": 0, + "content": "Discriminative Co-Saliency and Background Mining Transformer for Co-Salient Object Detection" + }, + { + "type": "text", + "bbox": [ + 0.3, + 0.203, + 0.674, + 0.221 + ], + "angle": 0, + "content": "Long Li\\(^{1}\\) Junwei Han\\(^{1}\\) Ni Zhang\\(^{1}\\) Nian Liu\\(^{2\\dagger}\\)" + }, + { + "type": "text", + "bbox": [ + 0.138, + 0.221, + 0.832, + 0.239 + ], + "angle": 0, + "content": "Salman Khan\\(^{2,3}\\) Hisham Cholakkal\\(^{2}\\) Rao Muhammad Anwer\\(^{2}\\) Fahad Shahbaz Khan\\(^{2,4}\\)" + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.239, + 0.878, + 0.257 + ], + "angle": 0, + "content": "1 Northwestern Polytechnical University 2 Mohamed bin Zayed University of Artificial Intelligence" + }, + { + "type": "text", + "bbox": [ + 0.24, + 0.257, + 0.725, + 0.275 + ], + "angle": 0, + "content": "\\(^{3}\\)Australian National University \\(^{4}\\)CVL, Linköping University" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.309, + 0.314, + 0.327 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.342, + 0.474, + 0.691 + ], + "angle": 0, + "content": "Most previous co-salient object detection works mainly focus on extracting co-salient cues via mining the consistency relations across images while ignore explicit exploration of background regions. In this paper, we propose a Discriminative co-saliency and background Mining Transformer framework (DMT) based on several economical multi-grained correlation modules to explicitly mine both co-saliency and background information and effectively model their discrimination. Specifically, we first propose a region-to-region correlation module for introducing inter-image relations to pixel-wise segmentation features while maintaining computational efficiency. Then, we use two types of pre-defined tokens to mine co-saliency and background information via our proposed contrast-induced pixel-to-token correlation and co-saliency token-to-token correlation modules. We also design a token-guided feature refinement module to enhance the discriminability of the segmentation features under the guidance of the learned tokens. We perform iterative mutual promotion for the segmentation feature extraction and token construction. Experimental results on three benchmark datasets demonstrate the effectiveness of our proposed method. The source code is available at: https://github.com/dragonlee258079/DMT." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.719, + 0.21, + 0.735 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.741, + 0.47, + 0.878 + ], + "angle": 0, + "content": "Unlike standard Salient Object Detection (SOD) [13,21-23, 37, 45], which detects salient objects in a single image, Co-Salient Object Detection (CoSOD) aims to detect common salient objects across a group of relevant images. It often faces the following two challenges: 1) The foreground (FG) in CoSOD refers to co-salient objects, which are inherently hard to detect since they should satisfy both the intra-group commonality and the intra-image saliency. 2) The background (BG) in CoSOD might contain com" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.311, + 0.893, + 0.446 + ], + "angle": 0, + "content": "plex distractions, including extraneous salient objects that are salient but not \"common\", and similar concomitant objects appearing in multiple images (e.g. performers often appear in guitar images). Such difficult distractors can easily seduce CoSOD models to make false positive predictions. Therefore, the effective exploration of both FG and BG and modeling their discrimination to precisely detect co-salient objects while suppressing interference from BG is crucial for CoSOD." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.448, + 0.893, + 0.689 + ], + "angle": 0, + "content": "Although many works have achieved promising performance, most of them [14, 18, 25, 30, 33, 38, 40-42] devoted to the ingenious mining of FG while ignored the explicit exploration of BG. They mainly constructed positive relations between co-salient objects but paid less attention to modeling negative ones between co-saliency regions and BG. [16, 34] followed some SOD methods [4, 43] to incorporate BG features for co-saliency representation learning or contrast learning. However, these methods can be regarded as an univariate FG&BG modeling in which the essential optimization target is limited to FG and there is no explicit BG modeling, thus limiting the discriminative learning capability. To this end, this paper proposes to conduct a bivariate FG&BG modeling paradigm that explicitly models both FG and BG information and effectively facilitates their discriminative modeling." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.895, + 0.87 + ], + "angle": 0, + "content": "As for co-saliency (FG) information, most previous works [12, 16, 34, 41] detected them by exploring the interimage similarity. Calculating the Pixel-to-Pixel (P2P) correlation between 3D CNN features in a group is widely used in many works [12, 16, 34] and has demonstrated its effectiveness. However, this method introduces heavy computation burdens and hinders sophisticated relation modeling. To alleviate this problem, we introduce economic multi-grained correlations among different images and the co-saliency and BG information, thus enabling modeling sophisticated relations to extract accurate co-saliency as well as BG knowledge." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.894, + 0.902 + ], + "angle": 0, + "content": "Specifically, we construct a Discriminative co-saliency and BG Mining Transformer (DMT) following the" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.355, + 0.901 + ], + "angle": 0, + "content": "†Corresponding author: liunian228@gmail.com." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7247" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.211 + ], + "angle": 0, + "content": "paradigm of a semantic segmentation transformer architecture, i.e. MaskFormer [5], which enables explicit co-saliency and BG modeling and the construction of multi-grained correlations. Using this architecture, we decompose the CoSOD modeling into two sub-paths, i.e. generating pixel-wise segmentation feature maps and extracting category information with pre-defined co-saliency and BG detection tokens." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.213, + 0.473, + 0.452 + ], + "angle": 0, + "content": "In the first sub-path, to efficiently and thoroughly mine the common cues within the image group, we propose a Region-to-Region correlation (R2R) module to model the inter-image relation and plug it into each decoder layer. In the second sub-path, we transform the pixel-wise features into a co-saliency token and a BG token for each image, abstracting pixel-wise cues into high-level tokens. As such, we achieve sophisticated relation modeling among the tokens and features while largely reducing the computational costs. Concretely, we propose an intra-image Contrast-induced Pixel-to-Token correlation (CtP2T) module to extract the two tokens by considering the contrast relation between co-saliency and BG. Since the co-saliency tokens from CtP2T are separately learned on each image, we further design a Co-saliency Token-to-Token (CoT2T) correlation module to model their common relation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.455, + 0.473, + 0.697 + ], + "angle": 0, + "content": "After obtaining the tokens and pixel-wise features, the MaskFormer [5] architecture adopts dot production between them to obtain the final segmentation results. However, such a scheme only achieves unidirectional information propagation, i.e. conveying information from the feature maps to the tokens. We argue that the learned two tokens can also be used to improve the discriminability of the pixel-wise features, thus proposing our Token-Guided Feature Refinement (TGFR) module as a reverse information propagation path. Concretely, we first use the tokens as guidance to distill co-saliency and BG features from the pixel-wise feature maps, and then enhance the discriminability of the segmentation features between the two detection regions. In this way, the refined features become sensitive to both co-saliency and BG, reducing the affect of ambiguous distractors." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.697, + 0.472, + 0.788 + ], + "angle": 0, + "content": "Finally, as shown in Figure 1, our DMT iteratively deploys CtP2T and CoT2T to leverage the segmentation features for updating the tokens, and then adopts TGFR to refine the corresponding decoder feature with the updated tokens. As a result, the learning processes can be effectively promoted, thus obtaining more accurate CoSOD results." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.788, + 0.441, + 0.802 + ], + "angle": 0, + "content": "In summary, our major contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.806, + 0.468, + 0.851 + ], + "angle": 0, + "content": "- We model CoSOD from the perspective of explicitly exploring both co-saliency and BG information and effectively modeling their discrimination." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.856, + 0.469, + 0.901 + ], + "angle": 0, + "content": "- We introduce several computationally economical multi-grained correlation modules, i.e. R2R, CtP2T, CoT2T, for the inter-image and intra-image relations" + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.806, + 0.469, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.533, + 0.093, + 0.603, + 0.107 + ], + "angle": 0, + "content": "modeling." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.109, + 0.892, + 0.168 + ], + "angle": 0, + "content": "- We propose a novel TGFR module to use the learned tokens as guidance to refine the segmentation features for enhancing their discriminability between co-saliency and BG regions." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.171, + 0.892, + 0.214 + ], + "angle": 0, + "content": "- Experimental results demonstrate that our DMT model outperforms previous state-of-the-art results on three benchmark datasets." + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.109, + 0.892, + 0.214 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.229, + 0.642, + 0.244 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.25, + 0.753, + 0.266 + ], + "angle": 0, + "content": "2.1. Co-Salient Object Detection" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.269, + 0.892, + 0.647 + ], + "angle": 0, + "content": "Recent CoSOD works [12,16,27,34,41,42] have achieve promising performance and can be summarized as a unified paradigm, i.e. first aggregating all image features in the group to form a consensus representation and then distributing it back to each image feature. We refer to these two processes as aggregation and distribution for expression convenience. For example, [42] summed up all features for aggregation and leveraged a gradient feedback mechanism for distribution. [16] formed the consensus cues with a group of enhanced intra-saliency vectors and conducted the distribution via a dense correlation module. [12] generated a consensus attention map with an affinity module and multiplied it back to the individual image features. [41] encoded the consensus information with dynamic kernels and convolved the image features using these kernels as the distribution process. [34] first obtained consensus seeds by processing P2P affinity maps and then propagated the seeds using normalized convolution operations. However, most of them are limited in exploring BG regions, which hinders the discriminability learning. Unlike them, we propose to simultaneously detect the co-saliency and BG regions and sufficiently explore their discriminative modeling. Besides, we utilize tokens under a transformer architecture for aggregation, and then use the learned tokens to conduct the distribution process." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.655, + 0.636, + 0.67 + ], + "angle": 0, + "content": "2.2. Transformer" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.869 + ], + "angle": 0, + "content": "After Vaswani et al. [29] first proposed the transformer architecture for machine translation, many successful transformer applications in the computer vision field emerged. Some works [8, 28, 35] directly apply the transformer architecture for feature learning. Some other works mainly focused on using transformers to extract specific semantic concepts, e.g. the category or instance information for object detection [3, 32, 44], semantic segmentation [5, 31], and the saliency and contour information for salient object detection [23]. Concretely, they first use a backbone to extract image feature maps and then adopt transformers to collect semantic concept information and store them in pre-created tokens." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "This paper follows the second type application to utilize the transformer for simultaneous FG and BG modeling. We" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7248" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.09, + 0.892, + 0.312 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.314, + 0.895, + 0.357 + ], + "angle": 0, + "content": "Figure 1. Overall flowchart of our proposed DMT CoSOD model. Specifically, the framework consists of four components, i.e. R2R for segmentation feature generation, CtP2T and CoT2T for detection token construction, and TGFR for the segmentation feature refinement under the guidance of the tokens." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.368, + 0.471, + 0.461 + ], + "angle": 0, + "content": "further modify the transformer framework tailored for the CoSOD task by introducing economic multi-grained correlations for modeling sophisticated relations. We also propose to leverage the semantic information encoded in the learned tokens as a guide to refine the features, thus improving its discriminability." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.474, + 0.251, + 0.491 + ], + "angle": 0, + "content": "3. Proposed Method" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.496, + 0.188, + 0.51 + ], + "angle": 0, + "content": "3.1. Overview" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.516, + 0.47, + 0.682 + ], + "angle": 0, + "content": "Figure 1 illustrates our MaskFormer-style framework for simultaneously detecting co-salient objects and BG regions. It consists of two sub-paths, i.e. pixel-wise segmentation feature generation and detection token construction. We use R2R in the first sub-path to enhance the segmentation features with inter-image consistency. In the second sub-path, CtP2T and CoT2T are designed to effectively construct the co-saliency and BG tokens from segmentation features, capturing the binary detection patterns. Finally, we propose TGFR to use the detection tokens as guidance for refining the segmentation features." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.683, + 0.47, + 0.759 + ], + "angle": 0, + "content": "For ease of understanding, we first briefly describe the vanilla MaskFormer-style framework for simultaneously detecting co-saliency and BG in CoSOD. Then, we progressively introduce the improvements in our proposed DMT, including R2R, CtP2T, CoT2T, and TGFR." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.769, + 0.409, + 0.785 + ], + "angle": 0, + "content": "3.2. Vanilla MaskFormer-style Framework" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.79, + 0.367, + 0.804 + ], + "angle": 0, + "content": "3.2.1 Segmentation Feature Generation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.809, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Given a set of \\(N\\) relevant images \\(\\{I_i\\}_{i=1}^N\\), we follow the original MaskFormer framework [5] to adopt an FPN [19] for generating pixel-wise segmentation features. Specifically, we use VGG-16 [26] as the encoder and take \\(\\{I_i\\}_{i=1}^N\\) as the input to obtain the highest-level features \\(\\pmb{F}^e \\in \\mathbb{R}^{N \\times H_0 \\times W_0 \\times C}\\) from the last block. Then, based on \\(\\pmb{F}^e\\), the" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.369, + 0.892, + 0.416 + ], + "angle": 0, + "content": "FPN decoder uses five decoder layers to progressively enlarge the feature resolution and obtain five decoder features \\(\\pmb{F}_{j}^{d}\\in \\mathbb{R}^{N\\times H_{j}\\times W_{j}\\times C},j\\in \\{1\\dots 5\\}\\)" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.422, + 0.764, + 0.435 + ], + "angle": 0, + "content": "3.2.2 Detection Token Construction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.44, + 0.892, + 0.629 + ], + "angle": 0, + "content": "Given the highest-level semantic feature \\( \\pmb{F}_i^e \\in \\mathbb{R}^{H_0 \\times W_0 \\times C} \\) of image \\( \\pmb{I}_i \\), we extract the detection tokens from it via a vanilla pixel-to-token correlation (P2T) module. First, we define two randomly initialized tokens for \\( \\pmb{I}_i \\), i.e., a co-saliency token \\( T_{i,0}^c \\in \\mathbb{R}^{1 \\times C} \\) and a BG token \\( T_{i,0}^b \\in \\mathbb{R}^{1 \\times C} \\) and denote their union as \\( T_{i,0} \\in \\mathbb{R}^{2 \\times C} \\). We also flatten \\( F_i^e \\) along the spatial dimension as \\( \\hat{F}_i^e \\in \\mathbb{R}^{H_0 W_0 \\times C} \\). Then, we iteratively update the tokens five times. At each iteration \\( j \\in \\{1, \\dots, 5\\} \\), we obtain \\( T_{i,j} \\) by transforming the information from the feature \\( \\hat{F}_i^e \\) to tokens in (1) and modeling the relationship between the co-saliency and BG tokens in (2), formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.601, + 0.632, + 0.891, + 0.651 + ], + "angle": 0, + "content": "\\[\n\\hat {\\boldsymbol {T}} _ {i, j} = \\operatorname {T r a n s} \\left(\\boldsymbol {T} _ {i, j - 1}, \\hat {\\boldsymbol {F}} _ {i} ^ {e}\\right), \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.608, + 0.655, + 0.891, + 0.673 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {T} _ {i, j} = \\operatorname {T r a n s} \\left(\\hat {\\boldsymbol {T}} _ {i, j}, \\hat {\\boldsymbol {T}} _ {i, j}\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.68, + 0.891, + 0.709 + ], + "angle": 0, + "content": "where Trans is a basic transformer operation following [29]:" + }, + { + "type": "equation", + "bbox": [ + 0.558, + 0.714, + 0.891, + 0.731 + ], + "angle": 0, + "content": "\\[\n\\operatorname {T r a n s} (\\boldsymbol {X}, \\boldsymbol {Y}) = \\mathrm {r M L P} (\\mathrm {r M H A} (\\boldsymbol {X}, \\boldsymbol {Y})). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.742, + 0.892, + 0.804 + ], + "angle": 0, + "content": "It can transfer the information from \\(\\mathbf{Y} \\in \\mathbb{R}^{N_y \\times C}\\) to \\(\\mathbf{X} \\in \\mathbb{R}^{N_x \\times C}\\) under the guidance of their relation. rMHA and rMLP denote the residual multi-head attention [29] and residual multi-layer perception, respectively, formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.575, + 0.815, + 0.891, + 0.832 + ], + "angle": 0, + "content": "\\[\n\\operatorname {r M L P} (\\boldsymbol {X}) = \\boldsymbol {X} + \\operatorname {M L P} (\\operatorname {L N} (\\boldsymbol {X})), \\tag {4}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.52, + 0.842, + 0.891, + 0.859 + ], + "angle": 0, + "content": "\\[\n\\operatorname {r M H A} (\\boldsymbol {X}, \\boldsymbol {Y}) = \\boldsymbol {X} + \\operatorname {M H A} (\\ln (\\boldsymbol {X}), \\ln (\\boldsymbol {Y}))), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "where LN denotes the layer normalization [2] and MLP is the multi-layer perception consisting of two fully connected" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7249" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.091, + 0.47, + 0.121 + ], + "angle": 0, + "content": "layers with a GELU [15] activation function. MHA is the multi-head attention that can be formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.095, + 0.125, + 0.47, + 0.191 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\operatorname {M H A} (\\boldsymbol {X}, \\boldsymbol {Y}) = \\operatorname {C a t} ([ \\operatorname {A t t} _ {m} (\\boldsymbol {X}, \\boldsymbol {Y}) V _ {m} (\\boldsymbol {Y}) ] _ {m = 1} ^ {M}), \\quad (6) \\\\ \\operatorname {A t t} _ {m}, (\\boldsymbol {X}, \\boldsymbol {Y}) = \\operatorname {S o f t m a x} \\left(\\frac {Q _ {m} (\\boldsymbol {X}) K _ {m} (\\boldsymbol {Y}) ^ {\\top}}{\\sqrt {C / M}}\\right), \\tag {7} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.2, + 0.471, + 0.351 + ], + "angle": 0, + "content": "where \\(M\\) is the number of used attention heads. The result of each head (with the shape of \\(N_{x} \\times C / M\\)) is obtained via the matrix multiplication between \\(\\mathrm{Att}_m(\\mathbf{X}, \\mathbf{Y}) \\in \\mathbb{R}^{N_x \\times N_y}\\) and \\(V_m(\\mathbf{Y}) \\in \\mathbb{R}^{N_y \\times C / M}\\). \\(\\mathrm{Att}_m(\\mathbf{X}, \\mathbf{Y})\\) is the attention matrix calculated in (7). Here \\(Q_m(\\cdot)\\), \\(K_m(\\cdot)\\), and \\(V_m(\\cdot)\\) are the query, key, and value embedding functions in the \\(m\\)th head, respectively, and project corresponding tensors from \\(C\\) channels to \\(C / M\\) channels. Finally, \\(\\mathrm{MHA}(\\mathbf{X}, \\mathbf{Y}) \\in \\mathbb{R}^{N_x \\times C}\\) can be obtained by concatenating (Cat) the results of \\(M\\) heads along the channel dimension." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.355, + 0.204, + 0.369 + ], + "angle": 0, + "content": "3.2.3 Prediction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.375, + 0.469, + 0.464 + ], + "angle": 0, + "content": "After performing the token construction five times on each image, we collect the final tokens of all images, i.e. \\( T_5^c, T_5^b \\in \\mathbb{R}^{N \\times 1 \\times C} \\). Then, we use the output of the first sub-path, i.e. the segmentation feature \\( F_5^d \\), to generate the final predictions via the sigmoid matrix multiplication, formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.131, + 0.468, + 0.469, + 0.488 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {P} ^ {c} = \\mathcal {P} \\left(\\boldsymbol {T} _ {5} ^ {c}, \\boldsymbol {F} _ {5} ^ {d}\\right) = \\operatorname {S i g m o i d} \\left(\\boldsymbol {T} _ {5} ^ {c} \\left(\\boldsymbol {F} _ {5} ^ {d}\\right) ^ {\\top}\\right), \\tag {8}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.134, + 0.49, + 0.469, + 0.509 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {P} ^ {b} = \\mathcal {P} (\\boldsymbol {T} _ {5} ^ {b}, \\boldsymbol {F} _ {5} ^ {d}) = \\operatorname {S i g m o i d} (\\boldsymbol {T} _ {5} ^ {b} (\\boldsymbol {F} _ {5} ^ {d}) ^ {\\top}), \\qquad (9)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.513, + 0.469, + 0.545 + ], + "angle": 0, + "content": "where \\(P^c, P^b \\in \\mathbb{R}^{N \\times 1 \\times H \\times W}\\) are the segmentation results of co-salient objects and BG regions, respectively." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.554, + 0.334, + 0.57 + ], + "angle": 0, + "content": "3.3. Our Improvements for DMT" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.578, + 0.339, + 0.593 + ], + "angle": 0, + "content": "3.3.1 Region-to-Region Correlation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.598, + 0.469, + 0.717 + ], + "angle": 0, + "content": "In the first sub-path, the original FPN individually processes each image and lacks the inter-image correlation modeling, which is crucial for CoSOD. However, straightforward P2P correlation is computationally prohibitive for large feature maps and multiple images. To this end, we consider modeling correlations among images in an economical way, thus proposing our R2R module, which uses region-level features instead of pixel-level features to compute correlations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.717, + 0.469, + 0.825 + ], + "angle": 0, + "content": "Concretely, when given the features \\( \\pmb{F}_j^d \\in \\mathbb{R}^{N \\times H_j \\times W_j \\times C} \\) of \\( N \\) relevant images from the \\( j \\)th decoder layer, we first adopt a transformation \\( \\mathbb{R}_1 \\) to divide the \\( H_j \\times W_j \\) feature maps into \\( K \\times K \\) local regions and use max-pooling to pick up the most representative feature for representing each local region. As a result, we can obtain the region-level query with shape \\( \\mathbb{R}^{N \\times K \\times K \\times C} \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Then, we generate multi-scale region-level key and value via another transformation \\(\\mathbf{R}_2\\), which consists of three adaptive max-pooling operations with the output spatial sizes of \\(1 \\times 1\\), \\(3 \\times 3\\), and \\(6 \\times 6\\), respectively. The three pooled features are finally flattened and concatenated to generate" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.091, + 0.89, + 0.121 + ], + "angle": 0, + "content": "the key and value with shape \\(\\mathbb{R}^{N\\times 46\\times C}\\), encoding multiscale robust region information." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.122, + 0.89, + 0.182 + ], + "angle": 0, + "content": "Next, we perform the R2R inter-image correlation among the region-level query, key, and value via the transformer operation (3), thus obtaining the enhanced features with the region-wise correlation." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.183, + 0.891, + 0.274 + ], + "angle": 0, + "content": "Finally, we upsample the enhanced features to the original resolution \\( H_{j} \\times W_{j} \\) via the nearest interpolation, denoted as \\( \\mathbf{R}_1^{-1} \\). A residual connection is also used to add the original features. Thus, the region correlation results are diffused to the corresponding internal pixels in each local region. The whole process of R2R on \\( \\pmb{F}_{j}^{d} \\) is formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.528, + 0.277, + 0.89, + 0.297 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {F} _ {j} ^ {d r} = \\boldsymbol {F} _ {j} ^ {d} + \\mathrm {R} _ {1} ^ {- 1} (\\operatorname {T r a n s} \\left(\\mathrm {R} _ {1} \\left(\\boldsymbol {F} _ {j} ^ {d}\\right), \\mathrm {R} _ {2} \\left(\\boldsymbol {F} _ {j} ^ {d}\\right)\\right)). \\tag {10}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.303, + 0.868, + 0.317 + ], + "angle": 0, + "content": "3.3.2 Contrast-induced Pixel-to-Token Correlation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.323, + 0.892, + 0.457 + ], + "angle": 0, + "content": "In the second sub-path, the original P2T module uses a transformer operation in (2) to mine relations between the two types of tokens in a data-driven way, while ignoring explicit CoSOD cues, especially the crucial contrast modeling between co-saliency and BG regions. To enhance the discriminability between the tokens, we explicitly model the contrast relation with our proposed CtP2T module, which modifies the transformer layer in (1) and the remaining part keeps the same as P2T." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.459, + 0.892, + 0.626 + ], + "angle": 0, + "content": "Overall, we modify the multi-head attention (denoted as \\(\\mathrm{MHA}^{\\ast}\\)) and propose a contrast-induced channel attention (CCA) mechanism. The basic idea is to suppress the channels that are not contrastive enough in the generated co-saliency and BG tokens. The contrast is modeled as the opposite of the channel similarity between the two types of tokens, which can be calculated via channel correlation. For brevity's sake, we slightly abuse the notation and use \\(\\hat{T}, T \\in \\mathbb{R}^{2 \\times C}\\), and \\(F \\in \\mathbb{R}^{H_0 W_0 \\times C}\\) as shorthands for \\(\\hat{T}_{i,j}\\), \\(T_{i,j-1}\\), and \\(\\hat{F}_i^e\\) in (1), respectively. Then, (1) can be modified for our CtP2T as below:" + }, + { + "type": "equation", + "bbox": [ + 0.558, + 0.635, + 0.89, + 0.671 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\hat {\\boldsymbol {T}} = \\operatorname {T r a n s} ^ {*} (\\boldsymbol {T}, \\boldsymbol {F}) \\\\ = \\operatorname {r M L P} (\\boldsymbol {T} + \\operatorname {C C A} (\\operatorname {M H A} ^ {*} (\\boldsymbol {T}, \\boldsymbol {F}))). \\tag {11} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.682, + 0.89, + 0.712 + ], + "angle": 0, + "content": "Next, we introduce \\(\\mathrm{MHA}^*\\) and CCA as shown in Figure 2. The LN operations are omitted for expression convenience." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.855 + ], + "angle": 0, + "content": "Modified Multi-Head Attention. To generate co-saliency and BG tokens that can be used for calculating their channel similarity, we make our \\(\\mathrm{MHA}^*\\) able to generate tokens with multiple heads. Concretely, we first replace the original \\(V_{m}\\) in (6) with \\(V_{m}^{*}\\) that embeds \\(\\pmb{F}\\) to the identical channel number \\(C\\). Thus, the shape of each head's result becomes \\(2\\times C\\) instead of \\(2\\times C / M\\). Next, we stack the results of \\(M\\) heads to produce the output of \\(\\mathrm{MHA}^*\\). The whole process can be formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.555, + 0.865, + 0.862, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\boldsymbol {T} _ {M} = \\operatorname {M H A} ^ {*} (\\boldsymbol {T}, \\boldsymbol {F}) \\\\ = \\operatorname {S t a c k} \\left(\\left[ \\operatorname {A t t} _ {m} (\\boldsymbol {T}, \\boldsymbol {F}) V _ {m} ^ {*} (\\boldsymbol {F}) \\right] _ {m = 1} ^ {M}\\right). \\\\ \\end{array}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7250" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.098, + 0.09, + 0.435, + 0.1 + ], + "angle": 0, + "content": "Modified Multi-Head Attention Contrast-induced Channel Attention" + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.103, + 0.468, + 0.305 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.308, + 0.47, + 0.363 + ], + "angle": 0, + "content": "Figure 2. Diagram of MHA* and CCA. We first generate multihead tokens \\( T_{M}^{c} \\) and \\( T_{M}^{b} \\) via MHA*. Then, we utilize matrix multiplication of the two tokens to generate the attention weights \\( W \\) for modulating the token channels in CCA." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.371, + 0.469, + 0.418 + ], + "angle": 0, + "content": "\\(\\pmb{T}_{M} \\in \\mathbb{R}^{2 \\times M \\times C}\\) is composed of the co-saliency token and the BG token \\(\\pmb{T}_{M}^{c}, \\pmb{T}_{M}^{b} \\in \\mathbb{R}^{M \\times C}\\) with \\(M\\) heads. Next, we can compute the channel similarity based on them." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.424, + 0.469, + 0.499 + ], + "angle": 0, + "content": "Contrast-induced Channel Attention. Given the multihead tokens \\( T_{M}^{c} \\) and \\( T_{M}^{b} \\), we generate channel attention \\( W \\in \\mathbb{R}^{2 \\times 1 \\times C} \\) to suppress the token channels with strong mutual similarities since they cannot clearly distinguish between co-saliency and BG." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.5, + 0.469, + 0.574 + ], + "angle": 0, + "content": "First, we compute a \\(C \\times C\\) channel similarity matrix between \\(\\pmb{T}_M^c\\) and \\(\\pmb{T}_M^b\\) via matrix multiplication. Then, the channel similarity of each token to the other token can be computed as the average along the channel dimension of the other token. The whole process can be denoted as" + }, + { + "type": "equation", + "bbox": [ + 0.194, + 0.575, + 0.468, + 0.593 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {S} ^ {c} = \\operatorname {A v g} \\left(\\boldsymbol {T} _ {M} ^ {c} \\top \\boldsymbol {T} _ {M} ^ {b}\\right), \\tag {13}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.197, + 0.593, + 0.468, + 0.613 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {S} ^ {b} = \\operatorname {A v g} \\left(\\boldsymbol {T} _ {M} ^ {b} ^ {\\top} \\boldsymbol {T} _ {M} ^ {c}\\right), \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.615, + 0.468, + 0.661 + ], + "angle": 0, + "content": "where \\(S^c, S^b \\in \\mathbb{R}^{C \\times 1}\\), representing how similar each channel is to the channels of the other token. Avg means calculating the average along the second dimension." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.661, + 0.468, + 0.706 + ], + "angle": 0, + "content": "Next, we multiply \\(S^c\\) and \\(S^b\\) with \\(-1\\) to turn the similarity measurements into the contrast scores and then compute the channel attention \\(\\mathbf{W} \\in \\mathbb{R}^{2 \\times 1 \\times C}\\) via" + }, + { + "type": "equation", + "bbox": [ + 0.148, + 0.71, + 0.469, + 0.752 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {W} = \\text {S i g m o i d} \\left(\\alpha \\left[ \\begin{array}{c} - \\boldsymbol {S} ^ {c ^ {\\top}} \\\\ - \\boldsymbol {S} ^ {b ^ {\\top}} \\end{array} \\right] + \\beta\\right). \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.758, + 0.469, + 0.802 + ], + "angle": 0, + "content": "Here we use a learnable linear projection with parameters \\(\\alpha, \\beta\\) on each channel of the stacked contrast scores to fit them for the sigmoid activation." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.803, + 0.469, + 0.877 + ], + "angle": 0, + "content": "Once obtained \\( \\mathbf{W} \\), we adopt the element-wise multiplication between \\( \\mathbf{T}_M \\) and \\( \\mathbf{W} \\) to modulate the token channels based on their contrast and then eliminate the multi-head dimension of the tokens by averaging the head dimension and obtaining the modulated tokens:" + }, + { + "type": "equation", + "bbox": [ + 0.135, + 0.884, + 0.469, + 0.902 + ], + "angle": 0, + "content": "\\[\n\\operatorname {C C A} \\left(\\boldsymbol {T} _ {M}\\right) = \\operatorname {A v g} \\left(\\boldsymbol {W} \\odot \\boldsymbol {T} _ {M}\\right) \\in \\mathbb {R} ^ {2 \\times C}, \\tag {16}\n\\]" + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.091, + 0.887, + 0.235 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.238, + 0.892, + 0.293 + ], + "angle": 0, + "content": "Figure 3. Diagram of our proposed TGFR module. Specifically, we first distill the co-saliency and BG features under the guidance of the two tokens. Then, we fuse them back to the original segmentation feature for discriminability enhancement." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.306, + 0.89, + 0.336 + ], + "angle": 0, + "content": "where \\(\\odot\\) means element-wise multiplication with broadcasting." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.343, + 0.834, + 0.358 + ], + "angle": 0, + "content": "3.3.3 Co-saliency Token-to-Token Correlation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.363, + 0.892, + 0.452 + ], + "angle": 0, + "content": "CtP2T effectively explores the correlation between the two types of tokens within each image, but lacks explicitly modeling the inter-image relation to capture the token-wise group consistency, thus being limited for consensus mining. Therefore, we use co-saliency tokens from all images to model the consensus patterns via our CoT2T module." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.453, + 0.892, + 0.563 + ], + "angle": 0, + "content": "Specifically, we first define a group token \\(G \\in \\mathbb{R}^{1 \\times C}\\) to represent the group-wise consensus information, which is randomly initialized at the first iteration step. At the \\(j\\)th iteration, given the last group token \\(G_{j-1}\\) and the co-saliency tokens \\(\\tilde{T}_j^c \\in \\mathbb{R}^{N \\times C}\\) from the CtP2T module, we aggregate the consensus information from all co-saliency tokens by using \\(\\tilde{T}_j^c\\) to update \\(G_{j-1}\\), denoted as" + }, + { + "type": "equation", + "bbox": [ + 0.61, + 0.567, + 0.891, + 0.587 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {G} _ {j} = \\operatorname {T r a n s} \\left(\\boldsymbol {G} _ {j - 1}, \\tilde {\\boldsymbol {T}} _ {j} ^ {c}\\right). \\tag {17}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.594, + 0.89, + 0.626 + ], + "angle": 0, + "content": "Finally, we distribute the aggregated consensus cues back to \\(\\tilde{T}_{j}^{c}\\) and obtain the final co-saliency tokens \\(T_{j}^{c}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.619, + 0.629, + 0.891, + 0.65 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {T} _ {j} ^ {c} = \\operatorname {T r a n s} \\left(\\tilde {\\boldsymbol {T}} _ {j} ^ {c}, \\boldsymbol {G} _ {j}\\right). \\tag {18}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.66, + 0.792, + 0.674 + ], + "angle": 0, + "content": "3.3.4 Token-guided Feature Refinement" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.679, + 0.892, + 0.846 + ], + "angle": 0, + "content": "The vanilla MaskFormer only transforms the information from the segmentation features to the tokens, hindering their complementary learning. To this end, we propose our TGFR module to improve the discriminability of the segmentation features via the detection cues of the tokens. As shown in Figure 3, TGFR consists of two processes, i.e. distillation and refusion. The distillation process is designed to distill the co-saliency and BG features from the segmentation feature under the guidance of the corresponding tokens. The refusion process is to fuse the distilled features back to the segmentation feature to enhance its discriminability." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.853, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Distillation. For image \\( \\mathbf{I}_i \\) at the \\( j \\)th iteration, we have the final co-saliency token \\( T_{i,j}^{c} \\in \\mathbb{R}^{1 \\times C} \\) generated from CoT2T and the final BG token \\( T_{i,j}^{b} \\in \\mathbb{R}^{1 \\times C} \\) outputted by" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "7251" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.09, + 0.473, + 0.182 + ], + "angle": 0, + "content": "CtP2T, and the segmentation feature \\(F_{i,j}^{dr}\\in \\mathbb{R}^{H_j\\times W_j\\times C}\\) enhanced by R2R. We first compute two attention maps \\(A_{i,j}^{c}\\in \\mathbb{R}^{H_{j}\\times W_{j}\\times 1}\\) and \\(A_{i,j}^{b}\\in \\mathbb{R}^{H_{j}\\times W_{j}\\times 1}\\) via performing the matrix multiplication between the segmentation feature and the tokens and then adopting a softmax normalization on the spatial dimension, formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.149, + 0.184, + 0.47, + 0.205 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {A} _ {i, j} ^ {c} = \\operatorname {S o f t m a x} \\left(\\boldsymbol {F} _ {i, j} ^ {d r} \\left(\\boldsymbol {T} _ {i, j} ^ {c}\\right) ^ {\\top} / \\sqrt {C}\\right), \\tag {19}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.15, + 0.208, + 0.469, + 0.23 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {A} _ {i, j} ^ {b} = \\operatorname {S o f t m a x} \\left(\\boldsymbol {F} _ {i, j} ^ {d r} \\left(\\boldsymbol {T} _ {i, j} ^ {b}\\right) ^ {\\top} / \\sqrt {C}\\right). \\tag {20}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.233, + 0.47, + 0.278 + ], + "angle": 0, + "content": "Next, we adopt the computed attention maps to distill the detection features from the segmentation feature via matrix multiplication, denoted as" + }, + { + "type": "equation", + "bbox": [ + 0.2, + 0.281, + 0.469, + 0.301 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {D} _ {i, j} ^ {c} = \\left(\\boldsymbol {A} _ {i, j} ^ {c}\\right) ^ {\\top} \\boldsymbol {F} _ {i, j} ^ {d r}, \\tag {21}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.202, + 0.305, + 0.469, + 0.326 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {D} _ {i, j} ^ {b} = \\left(\\boldsymbol {A} _ {i, j} ^ {b}\\right) ^ {\\top} \\boldsymbol {F} _ {i, j} ^ {d r}, \\tag {22}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.331, + 0.469, + 0.363 + ], + "angle": 0, + "content": "where \\(D_{i,j}^{c}, D_{i,j}^{b} \\in \\mathbb{R}^{1 \\times C}\\) is the distilled features for co-saliency and BG, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.369, + 0.47, + 0.461 + ], + "angle": 0, + "content": "Refusion. After producing \\( D_{i,j}^{c} \\) and \\( D_{i,j}^{b} \\), we conduct the refusion process to fuse them back to \\( F_{i,j}^{dr} \\) sequentially in a cascade way for activating the co-saliency and BG regions in \\( F_{i,j}^{dr} \\). In this way, we can effectively reduce ambiguous information and enhance feature discriminability. The details can be formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.14, + 0.464, + 0.469, + 0.487 + ], + "angle": 0, + "content": "\\[\n\\hat {\\boldsymbol {F}} _ {i, j} ^ {d t} = \\operatorname {C o n v} _ {c} \\left(\\operatorname {C a t} \\left(\\left[ \\boldsymbol {F} _ {i, j} ^ {d r}, \\operatorname {E} \\left(\\boldsymbol {D} _ {i, j} ^ {c}\\right) \\right]\\right)\\right), \\tag {23}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.141, + 0.488, + 0.469, + 0.511 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {F} _ {i, j} ^ {d t} = \\operatorname {C o n v} _ {b} \\left(\\operatorname {C a t} \\left(\\left[ \\hat {\\boldsymbol {F}} _ {i, j} ^ {d t}, \\mathrm {E} \\left(\\boldsymbol {D} _ {i, j} ^ {b}\\right) \\right]\\right)\\right), \\tag {24}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.517, + 0.469, + 0.582 + ], + "angle": 0, + "content": "where \\(\\operatorname{E}(*)\\) replicates \\(D_{i,j}^{c}\\) and \\(D_{i,j}^{b}\\) along the spatial dimension to the same size as \\(F_{i,j}^{dr}\\). Then, we progressively concatenate them with \\(F_{i,j}^{dr}\\) and use a convolution layer to reduce the channel number to \\(C\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.591, + 0.337, + 0.605 + ], + "angle": 0, + "content": "3.3.5 Prediction and Loss Function" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.611, + 0.469, + 0.703 + ], + "angle": 0, + "content": "In the \\(j\\)th iteration, after obtaining the learned co-saliency and BG tokens, i.e. \\(\\pmb{T}_j^c,\\pmb{T}_j^b\\in \\mathbb{R}^{N\\times 1\\times C}\\), from CoT2T and CtP2T, respectively, and the improved segmentation features \\(\\pmb{F}_{j}^{dt}\\in \\mathbb{R}^{N\\times H_{j}\\times W_{j}\\times C}\\) from TGFR, we use the prediction function \\(\\mathcal{P}\\) in (8) to generate the co-saliency and the BG predictions, i.e. \\(\\pmb{P}_{j}^{c}\\pmb{P}_{j}^{b}\\), as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.208, + 0.707, + 0.469, + 0.727 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {P} _ {j} ^ {c} = \\mathcal {P} \\left(\\boldsymbol {T} _ {j} ^ {c}, \\boldsymbol {F} _ {j} ^ {d t}\\right), \\tag {25}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.208, + 0.731, + 0.469, + 0.751 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {P} _ {j} ^ {b} = \\mathcal {P} \\left(\\boldsymbol {T} _ {j} ^ {b}, \\boldsymbol {F} _ {j} ^ {d t}\\right). \\tag {26}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.755, + 0.469, + 0.822 + ], + "angle": 0, + "content": "We also supervise the learning of the group token \\(G_{j} \\in \\mathbb{R}^{1 \\times 1 \\times C}\\) in CoT2T and the middle feature \\(\\hat{\\pmb{F}}_j^{dt} \\in \\mathbb{R}^{N \\times H_j \\times W_j \\times C}\\) in TGFR. Two predictions can be obtained from them, respectively:" + }, + { + "type": "equation", + "bbox": [ + 0.176, + 0.832, + 0.47, + 0.86 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {P} _ {j} ^ {g} = \\mathcal {P} (\\text {R e p e a t} (\\boldsymbol {G} _ {j}), \\boldsymbol {F} _ {j} ^ {d t}), \\tag {27}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.175, + 0.855, + 0.309, + 0.877 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {P} _ {j} ^ {d t} = \\mathcal {P} (\\boldsymbol {T} _ {j} ^ {c}, \\hat {\\boldsymbol {F}} _ {j} ^ {d t}),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.886, + 0.34, + 0.902 + ], + "angle": 0, + "content": "where Repeat is to repeat \\( G_{j} \\) \\( N \\) times." + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.09, + 0.893, + 0.146 + ], + "angle": 0, + "content": "Table 1. Quantitative results of different settings of our proposed model. We show the results of progressively adding R2R, CtP2T, CoT2T, and TGFR on the baseline. \"Co\" and \"Bg\" mean explicitly modeling co-saliency and BG, respectively." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.15, + 0.9, + 0.272 + ], + "angle": 0, + "content": "
SettingsCoCA [42]
CoBgR2RCtP2TCoT2TTGFRSm↑Eξ↑maxF↑MAE ↓
✓✓0.67510.76830.54740.1383
✓✓✓0.69450.78240.58150.1234
✓✓✓✓0.70380.78680.59840.1230
✓✓✓✓✓0.71400.78800.60030.1139
✓✓✓✓✓✓0.72460.80010.61900.1084
✓✓✓✓0.70590.79200.59960.1259
" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.278, + 0.894, + 0.385 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.386, + 0.892, + 0.427 + ], + "angle": 0, + "content": "Figure 4. Qualitative results of different settings of our proposed model. We show the results of progressively adding the R2R, CtP2T, CoT2T, and TGFR on the baseline." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.438, + 0.796, + 0.452 + ], + "angle": 0, + "content": "Our total loss \\(\\mathcal{L}_{total}\\) can be formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.526, + 0.457, + 0.892, + 0.5 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {t o t a l}} = \\sum_ {j = 1} ^ {5} \\left(\\mathcal {L} _ {1} \\left(\\boldsymbol {P} _ {j} ^ {c}, \\boldsymbol {M} _ {j} ^ {c}\\right) + \\mathcal {L} _ {2} \\left(\\boldsymbol {P} _ {j} ^ {c}, \\boldsymbol {M} _ {j} ^ {c}\\right) + \\right. \\tag {28}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.52, + 0.503, + 0.846, + 0.528 + ], + "angle": 0, + "content": "\\[\n\\left. \\mathcal {L} _ {2} \\left(\\boldsymbol {P} _ {j} ^ {b}, \\boldsymbol {M} _ {j} ^ {b}\\right) + \\mathcal {L} _ {2} \\left(\\boldsymbol {P} _ {j} ^ {g}, \\boldsymbol {M} _ {j} ^ {c}\\right) + \\mathcal {L} _ {2} \\left(\\boldsymbol {P} _ {j} ^ {d t}, \\boldsymbol {M} _ {j} ^ {c}\\right)\\right),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.538, + 0.892, + 0.6 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_1\\) and \\(\\mathcal{L}_2\\) are the IoU [16] and Binary Cross-Entropy (BCE) [7] loss, respectively. \\(M_j^c\\) and \\(M_j^b\\) denote the co-saliency and BG ground truths, respectively, with the spatial shapes aligned to the \\(j\\)th decoder layer." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.614, + 0.634, + 0.631 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.639, + 0.787, + 0.654 + ], + "angle": 0, + "content": "4.1. Evaluation Datasets and Metrics" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.892, + 0.795 + ], + "angle": 0, + "content": "We follow [12, 27, 34] to evaluate our proposed model on three CoSOD benchmark datasets. CoSal2015 [36] and CoSOD3k [11] collect 50 groups with 2015 images and 160 groups with 3316 images, respectively. CoCA [42] is the most challenging dataset and contain 1295 images of 80 groups. We employ four widely-used metrics for quantitative evaluation, i.e. Structure-measure \\( S_{m} \\) [9], Enhanced-alignment measure \\( E_{\\xi} \\) [10], Maximum F-measure (maxF) [1], and Mean Absolute Error (MAE) [6]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.805, + 0.718, + 0.821 + ], + "angle": 0, + "content": "4.2. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We follow [41] to use the COCO-9k [20] (9213 images of 65 groups) and the DUTS class [42] (8250 images of 291 groups) with the synthesis strategy [41] to construct our training set. We follow [22] to perform data augmentation and adopt the Adam optimizer [17] with an initial learning" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7252" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.192, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.194, + 0.089, + 0.306, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.307, + 0.089, + 0.42, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.422, + 0.089, + 0.479, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.196, + 0.47, + 0.266 + ], + "angle": 0, + "content": "Figure 5. Visual comparison among the channels with different channel attention weights in CtP2T. We visualize some feature maps in \\( V_{m}^{*}(\\pmb{F}) \\) for the channels with large and small channel attention (CA) in CtP2T. We visualize two channels for large and small CA, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.276, + 0.471, + 0.368 + ], + "angle": 0, + "content": "rate of 0.0001, \\(\\beta_{1} = 0.9\\), and \\(\\beta_{2} = 0.99\\) to train our model for 80,000 iterations. The learning rate is divided by 10 at the \\(60000^{\\mathrm{th}}\\) iteration. We select at most eight images from each group as a mini-batch to train our network. The training and testing image size is set as \\(256 \\times 256\\). Our method is implemented using Pytorch [24]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.379, + 0.231, + 0.395 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.4, + 0.47, + 0.49 + ], + "angle": 0, + "content": "We conduct ablation studies on the challenging CoCA [42] dataset to verify the effectiveness of our proposed components. As shown in Table 1, we treat the vanilla MaskFormer-style framework as our baseline, shown in the first row, and progressively add our proposed R2R, CtP2T, CoT2T, and TGFR on it for effectiveness analysis." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.491, + 0.47, + 0.581 + ], + "angle": 0, + "content": "Effectiveness of R2R. First, we plug R2R into each decoder layer to enhance the segmentation features. It shows that using R2R largely improves the model performance compared to the baseline, while using vanilla P2P causes the out-of-memory error. The results verify the necessity of using our R2R for inter-image correlation modeling." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.583, + 0.471, + 0.824 + ], + "angle": 0, + "content": "Effectiveness of CtP2T. Next, we consider the contrast relation modeling between the co-saliency and BG tokens, thus replacing the original P2T module to our proposed CtP2T module. By using CtP2T, the model performance can be further improved, indicating that CtP2T is beneficial for enhancing the discriminability between the two types of tokens. We also provide some visual samples in Figure 5. Since the channels of the tokens correspond to those of the values in \\(\\mathrm{MHA}^*\\), we visualize some feature maps of \\(V_{m}^{*}(\\pmb {F})\\) of the channels with large or small channel attention weights in \\(\\pmb{W}\\). We can see that the channels with large channel attention (CA) can easily distinguish co-salient objects and distracting objects, while those with small CA usually confuse them. The results demonstrate our generated channel attention is meaningful for accurate co-salient object detection." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Effectiveness of CoT2T. Furthermore, we supplement CoT2T to explore the inter-image correlations for all co-saliency tokens. CoT2T explicitly promotes consensus information propagation among all co-saliency tokens, thus obtaining obvious improvements." + }, + { + "type": "table_caption", + "bbox": [ + 0.51, + 0.089, + 0.88, + 0.103 + ], + "angle": 0, + "content": "Table 2. Quantitative results of different settings in TGFR." + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.105, + 0.898, + 0.212 + ], + "angle": 0, + "content": "
SettingsCoCA [42]
Sm↑Eξ↑maxF↑MAE↓
w/o TGFR0.71400.78800.60030.1139
w/o Distillation0.71410.79210.60460.1114
w/ co0.71710.79650.60760.1144
w/ bg0.71550.79350.60640.1112
w/ bg&co0.71970.79070.60920.1069
w/ co&bg0.72460.80010.61900.1084
" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.216, + 0.568, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.521, + 0.293, + 0.553, + 0.302 + ], + "angle": 0, + "content": "Image" + }, + { + "type": "image", + "bbox": [ + 0.568, + 0.216, + 0.632, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.591, + 0.293, + 0.609, + 0.302 + ], + "angle": 0, + "content": "GT" + }, + { + "type": "image", + "bbox": [ + 0.632, + 0.216, + 0.696, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.641, + 0.293, + 0.69, + 0.302 + ], + "angle": 0, + "content": "Pred. w/o" + }, + { + "type": "image", + "bbox": [ + 0.698, + 0.216, + 0.758, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.708, + 0.293, + 0.749, + 0.301 + ], + "angle": 0, + "content": "Fea. w/o" + }, + { + "type": "image", + "bbox": [ + 0.761, + 0.216, + 0.824, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.771, + 0.293, + 0.815, + 0.302 + ], + "angle": 0, + "content": "Pred. w/" + }, + { + "type": "image", + "bbox": [ + 0.825, + 0.216, + 0.89, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.84, + 0.293, + 0.876, + 0.301 + ], + "angle": 0, + "content": "Fea. w/" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.304, + 0.892, + 0.344 + ], + "angle": 0, + "content": "Figure 6. Visualization of some feature maps (Fea.) and predictions (Pred.) of the models with (w/) or without (w/o) using TGFR." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.355, + 0.892, + 0.492 + ], + "angle": 0, + "content": "Effectiveness of TGFR. Finally, we add TGFR to leverage the learned tokens for refining the segmentation features. Table 1 shows that adopting TGFR can bring more performance gains, thus demonstrating its effectiveness. We also visualize some feature maps and predictions of using and without using TGFR in Figure 6. It can be seen that using TGFR obtains more discriminative features for distinguishing co-saliency objects from distractors, thus generating better segmentation results." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.492, + 0.893, + 0.794 + ], + "angle": 0, + "content": "To dive deeper into the effectiveness of TGFR, we report more experimental results in Table 2 for further analysis. First, we directly fuse the tokens and the segmentation features without performing the distillation process (\"w/o Distillation\"). we find this model brings limited improvements compared to the \"w/o TGFR\" model. It is probably because the tokens and features might exist semantic gap, being detrimental for their fusion, hence verifying the necessity of our distillation mechanism. Next, we supplement the distillation process and explore four strategies for the refusion process, i.e. individually refusing the distilled co-saliency (\"w/ co\") or BG features (\"w/ bg\") to the segmentation features, or refusing both with the order of co-saliency feature first (\"w/ co&bg\") or BG feature first (\"w/ bg&co\"). We can find refusing both achieves better performance, thus verifying the necessity of leveraging both features for discrimination enhancement. We also find first refusing the co-saliency feature and then integrating the BG feature obtains the best results. Thus, we adopt this strategy in our final TGFR design." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Effectiveness of BG Exploration. We remove all BG-related modules in our final model and only explore co-saliency regions, shown in the last row of Table 1. In this setting, CtP2T can not be used while only the co-saliency feature is used in TGFR. We find that the performance significantly drops compared to our final model, thus verifying the necessity of explicit BG modeling." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7253" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.09, + 0.892, + 0.117 + ], + "angle": 0, + "content": "Table 3. Quantitative comparison of our model with other state-of-the-art methods. We conduct the comparison on three benchmark CoSOD datasets. Red and blue denote the best and the second-best results, respectively." + }, + { + "type": "table", + "bbox": [ + 0.1, + 0.119, + 0.868, + 0.253 + ], + "angle": 0, + "content": "
MethodsCoCA [42]CoSal2015 [36]CoSOD3k [11]
Sm↑Eξ↑maxF↑MAE↓Sm↑Eξ↑maxF↑MAE↓Sm↑Eξ↑maxF↑MAE↓
CSMG(CVPR2019) [39]0.62760.73240.49880.12730.77570.84360.78690.13090.72720.82080.72970.1480
GICD(ECCV2020) [42]0.65790.71490.51260.12600.84370.88690.84410.07070.79670.84780.76980.0794
ICNet(NIPS2020) [16]0.65410.70420.51330.14700.85710.90110.85830.05790.79420.84500.76230.0891
GCoNet(CVPR2021) [12]0.67300.75980.54380.10500.84530.88790.84710.06810.80180.86010.77710.0712
CADC(ICCV2021) [41]0.68000.74430.54870.13300.86660.90630.86450.06410.81500.85430.77810.0875
UFO(ArXiv2022) [27]0.69710.78020.56810.09390.85780.90570.86210.06480.81910.86940.79540.0735
DCFM(CVPR2022) [34]0.71010.78260.59810.08450.83800.89290.85590.06720.80940.87420.80450.0674
DMT (Ours)0.72460.80010.61900.10840.89740.93620.90520.04540.85140.89500.83530.0633
" + }, + { + "type": "image", + "bbox": [ + 0.078, + 0.264, + 0.898, + 0.539 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.221, + 0.54, + 0.747, + 0.553 + ], + "angle": 0, + "content": "Figure 7. Qualitative comparisons of our model with other state-of-the-art methods." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.566, + 0.47, + 0.656 + ], + "angle": 0, + "content": "Quantitative Analysis. As shown in Figure 4, we also provide some visual comparison samples for the four key components. We find that the baseline model is easily distracted by complex BG regions, while progressively introducing our four components can gradually exclude these distractors and achieve more and more accurate results." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.668, + 0.465, + 0.685 + ], + "angle": 0, + "content": "5. Comparison with State-of-the-Art Methods" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.69, + 0.47, + 0.901 + ], + "angle": 0, + "content": "We compare our model with other seven state-of-the-art methods, i.e. CSMG [39], GICD [42], ICNet [16], GCoNet [12], CADC [41], UFO [27], and DCFM [34]. We report the quantitative comparison results in Table 3. We can observe that our proposed DMT achieves the best performance on all three benchmark datasets. Especially, on CoSal2015 and CoSOD3k, our DMT model surpasses the second-best model by a large margin, e.g. \\(3.14\\%\\) \\(S_{m}\\) and \\(4.07\\%\\) maxF on CoSal2015 and \\(3.23\\%\\) \\(S_{m}\\) and \\(3.08\\%\\) maxF on CoSOD3k. We also show some visual comparison results in Figure 7. We can find that our method can precisely detect co-salient objects in complex scenarios, e.g. the existence of extraneous salient objects with similar appearances to target objects, and target objects with small" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.566, + 0.892, + 0.597 + ], + "angle": 0, + "content": "sizes. Nevertheless, other models are heavily distracted in these challenging scenes." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.608, + 0.628, + 0.623 + ], + "angle": 0, + "content": "6. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.631, + 0.892, + 0.797 + ], + "angle": 0, + "content": "In this paper, we propose DMT, a transformer-based CoSOD model for explicitly mining both co-saliency and BG information and effectively modeling their discrimination. Specifically, we propose several economic multigrained correlations, i.e. R2R, CtP2T, and CoT2T to model inter-image and intra-image relations. Besides, we propose a TGFR module to leverage the detection information for improving the discriminability of the segmentation features. It is an improvement to the MaskFormer that allows the mutual promotion of two sub-paths. Our model achieves a new state-of-the-art result." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Acknowledgments: This work was supported in part by Key-Area Research and Development Program of Guangdong Province (No.2021B0101200001), the National Key R&D Program of China under Grant 2021B0101200001, and the National Science Foundation of China under Grant 62036011, U20B2065, 721A0001, 62136004." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7254" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Radhakrishna Achanta, Sheila Hemami, Francisco Estrada, and Sabine Susstrunk. Frequency-tuned salient region detection. 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In this paper, we propose a Discriminative co-saliency and background Mining Transformer framework (DMT) based on several economical multi-grained correlation modules to explicitly mine both co-saliency and background information and effectively model their discrimination. Specifically, we first propose a region-to-region correlation module for introducing inter-image relations to pixel-wise segmentation features while maintaining computational efficiency. Then, we use two types of pre-defined tokens to mine co-saliency and background information via our proposed contrast-induced pixel-to-token correlation and co-saliency token-to-token correlation modules. We also design a token-guided feature refinement module to enhance the discriminability of the segmentation features under the guidance of the learned tokens. We perform iterative mutual promotion for the segmentation feature extraction and token construction. Experimental results on three benchmark datasets demonstrate the effectiveness of our proposed method. The source code is available at: https://github.com/dragonlee258079/DMT. + +# 1. Introduction + +Unlike standard Salient Object Detection (SOD) [13,21-23, 37, 45], which detects salient objects in a single image, Co-Salient Object Detection (CoSOD) aims to detect common salient objects across a group of relevant images. It often faces the following two challenges: 1) The foreground (FG) in CoSOD refers to co-salient objects, which are inherently hard to detect since they should satisfy both the intra-group commonality and the intra-image saliency. 2) The background (BG) in CoSOD might contain com + +plex distractions, including extraneous salient objects that are salient but not "common", and similar concomitant objects appearing in multiple images (e.g. performers often appear in guitar images). Such difficult distractors can easily seduce CoSOD models to make false positive predictions. Therefore, the effective exploration of both FG and BG and modeling their discrimination to precisely detect co-salient objects while suppressing interference from BG is crucial for CoSOD. + +Although many works have achieved promising performance, most of them [14, 18, 25, 30, 33, 38, 40-42] devoted to the ingenious mining of FG while ignored the explicit exploration of BG. They mainly constructed positive relations between co-salient objects but paid less attention to modeling negative ones between co-saliency regions and BG. [16, 34] followed some SOD methods [4, 43] to incorporate BG features for co-saliency representation learning or contrast learning. However, these methods can be regarded as an univariate FG&BG modeling in which the essential optimization target is limited to FG and there is no explicit BG modeling, thus limiting the discriminative learning capability. To this end, this paper proposes to conduct a bivariate FG&BG modeling paradigm that explicitly models both FG and BG information and effectively facilitates their discriminative modeling. + +As for co-saliency (FG) information, most previous works [12, 16, 34, 41] detected them by exploring the interimage similarity. Calculating the Pixel-to-Pixel (P2P) correlation between 3D CNN features in a group is widely used in many works [12, 16, 34] and has demonstrated its effectiveness. However, this method introduces heavy computation burdens and hinders sophisticated relation modeling. To alleviate this problem, we introduce economic multi-grained correlations among different images and the co-saliency and BG information, thus enabling modeling sophisticated relations to extract accurate co-saliency as well as BG knowledge. + +Specifically, we construct a Discriminative co-saliency and BG Mining Transformer (DMT) following the + +paradigm of a semantic segmentation transformer architecture, i.e. MaskFormer [5], which enables explicit co-saliency and BG modeling and the construction of multi-grained correlations. Using this architecture, we decompose the CoSOD modeling into two sub-paths, i.e. generating pixel-wise segmentation feature maps and extracting category information with pre-defined co-saliency and BG detection tokens. + +In the first sub-path, to efficiently and thoroughly mine the common cues within the image group, we propose a Region-to-Region correlation (R2R) module to model the inter-image relation and plug it into each decoder layer. In the second sub-path, we transform the pixel-wise features into a co-saliency token and a BG token for each image, abstracting pixel-wise cues into high-level tokens. As such, we achieve sophisticated relation modeling among the tokens and features while largely reducing the computational costs. Concretely, we propose an intra-image Contrast-induced Pixel-to-Token correlation (CtP2T) module to extract the two tokens by considering the contrast relation between co-saliency and BG. Since the co-saliency tokens from CtP2T are separately learned on each image, we further design a Co-saliency Token-to-Token (CoT2T) correlation module to model their common relation. + +After obtaining the tokens and pixel-wise features, the MaskFormer [5] architecture adopts dot production between them to obtain the final segmentation results. However, such a scheme only achieves unidirectional information propagation, i.e. conveying information from the feature maps to the tokens. We argue that the learned two tokens can also be used to improve the discriminability of the pixel-wise features, thus proposing our Token-Guided Feature Refinement (TGFR) module as a reverse information propagation path. Concretely, we first use the tokens as guidance to distill co-saliency and BG features from the pixel-wise feature maps, and then enhance the discriminability of the segmentation features between the two detection regions. In this way, the refined features become sensitive to both co-saliency and BG, reducing the affect of ambiguous distractors. + +Finally, as shown in Figure 1, our DMT iteratively deploys CtP2T and CoT2T to leverage the segmentation features for updating the tokens, and then adopts TGFR to refine the corresponding decoder feature with the updated tokens. As a result, the learning processes can be effectively promoted, thus obtaining more accurate CoSOD results. + +In summary, our major contributions are as follows: + +- We model CoSOD from the perspective of explicitly exploring both co-saliency and BG information and effectively modeling their discrimination. +- We introduce several computationally economical multi-grained correlation modules, i.e. R2R, CtP2T, CoT2T, for the inter-image and intra-image relations + +modeling. + +- We propose a novel TGFR module to use the learned tokens as guidance to refine the segmentation features for enhancing their discriminability between co-saliency and BG regions. +- Experimental results demonstrate that our DMT model outperforms previous state-of-the-art results on three benchmark datasets. + +# 2. Related Work + +# 2.1. Co-Salient Object Detection + +Recent CoSOD works [12,16,27,34,41,42] have achieve promising performance and can be summarized as a unified paradigm, i.e. first aggregating all image features in the group to form a consensus representation and then distributing it back to each image feature. We refer to these two processes as aggregation and distribution for expression convenience. For example, [42] summed up all features for aggregation and leveraged a gradient feedback mechanism for distribution. [16] formed the consensus cues with a group of enhanced intra-saliency vectors and conducted the distribution via a dense correlation module. [12] generated a consensus attention map with an affinity module and multiplied it back to the individual image features. [41] encoded the consensus information with dynamic kernels and convolved the image features using these kernels as the distribution process. [34] first obtained consensus seeds by processing P2P affinity maps and then propagated the seeds using normalized convolution operations. However, most of them are limited in exploring BG regions, which hinders the discriminability learning. Unlike them, we propose to simultaneously detect the co-saliency and BG regions and sufficiently explore their discriminative modeling. Besides, we utilize tokens under a transformer architecture for aggregation, and then use the learned tokens to conduct the distribution process. + +# 2.2. Transformer + +After Vaswani et al. [29] first proposed the transformer architecture for machine translation, many successful transformer applications in the computer vision field emerged. Some works [8, 28, 35] directly apply the transformer architecture for feature learning. Some other works mainly focused on using transformers to extract specific semantic concepts, e.g. the category or instance information for object detection [3, 32, 44], semantic segmentation [5, 31], and the saliency and contour information for salient object detection [23]. Concretely, they first use a backbone to extract image feature maps and then adopt transformers to collect semantic concept information and store them in pre-created tokens. + +This paper follows the second type application to utilize the transformer for simultaneous FG and BG modeling. We + +![](images/770164cf23b1cfae99b5f9c5046a5362a0d31320fe4bb87d59076d5287b81928.jpg) +Figure 1. Overall flowchart of our proposed DMT CoSOD model. Specifically, the framework consists of four components, i.e. R2R for segmentation feature generation, CtP2T and CoT2T for detection token construction, and TGFR for the segmentation feature refinement under the guidance of the tokens. + +further modify the transformer framework tailored for the CoSOD task by introducing economic multi-grained correlations for modeling sophisticated relations. We also propose to leverage the semantic information encoded in the learned tokens as a guide to refine the features, thus improving its discriminability. + +# 3. Proposed Method + +# 3.1. Overview + +Figure 1 illustrates our MaskFormer-style framework for simultaneously detecting co-salient objects and BG regions. It consists of two sub-paths, i.e. pixel-wise segmentation feature generation and detection token construction. We use R2R in the first sub-path to enhance the segmentation features with inter-image consistency. In the second sub-path, CtP2T and CoT2T are designed to effectively construct the co-saliency and BG tokens from segmentation features, capturing the binary detection patterns. Finally, we propose TGFR to use the detection tokens as guidance for refining the segmentation features. + +For ease of understanding, we first briefly describe the vanilla MaskFormer-style framework for simultaneously detecting co-saliency and BG in CoSOD. Then, we progressively introduce the improvements in our proposed DMT, including R2R, CtP2T, CoT2T, and TGFR. + +# 3.2. Vanilla MaskFormer-style Framework + +# 3.2.1 Segmentation Feature Generation + +Given a set of $N$ relevant images $\{I_i\}_{i=1}^N$ , we follow the original MaskFormer framework [5] to adopt an FPN [19] for generating pixel-wise segmentation features. Specifically, we use VGG-16 [26] as the encoder and take $\{I_i\}_{i=1}^N$ as the input to obtain the highest-level features $\pmb{F}^e \in \mathbb{R}^{N \times H_0 \times W_0 \times C}$ from the last block. Then, based on $\pmb{F}^e$ , the + +FPN decoder uses five decoder layers to progressively enlarge the feature resolution and obtain five decoder features $\pmb{F}_{j}^{d}\in \mathbb{R}^{N\times H_{j}\times W_{j}\times C},j\in \{1\dots 5\}$ + +# 3.2.2 Detection Token Construction + +Given the highest-level semantic feature $\pmb{F}_i^e \in \mathbb{R}^{H_0 \times W_0 \times C}$ of image $\pmb{I}_i$ , we extract the detection tokens from it via a vanilla pixel-to-token correlation (P2T) module. First, we define two randomly initialized tokens for $\pmb{I}_i$ , i.e., a co-saliency token $T_{i,0}^c \in \mathbb{R}^{1 \times C}$ and a BG token $T_{i,0}^b \in \mathbb{R}^{1 \times C}$ and denote their union as $T_{i,0} \in \mathbb{R}^{2 \times C}$ . We also flatten $F_i^e$ along the spatial dimension as $\hat{F}_i^e \in \mathbb{R}^{H_0 W_0 \times C}$ . Then, we iteratively update the tokens five times. At each iteration $j \in \{1, \dots, 5\}$ , we obtain $T_{i,j}$ by transforming the information from the feature $\hat{F}_i^e$ to tokens in (1) and modeling the relationship between the co-saliency and BG tokens in (2), formulated as + +$$ +\hat {\boldsymbol {T}} _ {i, j} = \operatorname {T r a n s} \left(\boldsymbol {T} _ {i, j - 1}, \hat {\boldsymbol {F}} _ {i} ^ {e}\right), \tag {1} +$$ + +$$ +\boldsymbol {T} _ {i, j} = \operatorname {T r a n s} \left(\hat {\boldsymbol {T}} _ {i, j}, \hat {\boldsymbol {T}} _ {i, j}\right), \tag {2} +$$ + +where Trans is a basic transformer operation following [29]: + +$$ +\operatorname {T r a n s} (\boldsymbol {X}, \boldsymbol {Y}) = \mathrm {r M L P} (\mathrm {r M H A} (\boldsymbol {X}, \boldsymbol {Y})). \tag {3} +$$ + +It can transfer the information from $\mathbf{Y} \in \mathbb{R}^{N_y \times C}$ to $\mathbf{X} \in \mathbb{R}^{N_x \times C}$ under the guidance of their relation. rMHA and rMLP denote the residual multi-head attention [29] and residual multi-layer perception, respectively, formulated as + +$$ +\operatorname {r M L P} (\boldsymbol {X}) = \boldsymbol {X} + \operatorname {M L P} (\operatorname {L N} (\boldsymbol {X})), \tag {4} +$$ + +$$ +\operatorname {r M H A} (\boldsymbol {X}, \boldsymbol {Y}) = \boldsymbol {X} + \operatorname {M H A} (\ln (\boldsymbol {X}), \ln (\boldsymbol {Y}))), \tag {5} +$$ + +where LN denotes the layer normalization [2] and MLP is the multi-layer perception consisting of two fully connected + +layers with a GELU [15] activation function. MHA is the multi-head attention that can be formulated as + +$$ +\begin{array}{l} \operatorname {M H A} (\boldsymbol {X}, \boldsymbol {Y}) = \operatorname {C a t} ([ \operatorname {A t t} _ {m} (\boldsymbol {X}, \boldsymbol {Y}) V _ {m} (\boldsymbol {Y}) ] _ {m = 1} ^ {M}), \quad (6) \\ \operatorname {A t t} _ {m}, (\boldsymbol {X}, \boldsymbol {Y}) = \operatorname {S o f t m a x} \left(\frac {Q _ {m} (\boldsymbol {X}) K _ {m} (\boldsymbol {Y}) ^ {\top}}{\sqrt {C / M}}\right), \tag {7} \\ \end{array} +$$ + +where $M$ is the number of used attention heads. The result of each head (with the shape of $N_{x} \times C / M$ ) is obtained via the matrix multiplication between $\mathrm{Att}_m(\mathbf{X}, \mathbf{Y}) \in \mathbb{R}^{N_x \times N_y}$ and $V_m(\mathbf{Y}) \in \mathbb{R}^{N_y \times C / M}$ . $\mathrm{Att}_m(\mathbf{X}, \mathbf{Y})$ is the attention matrix calculated in (7). Here $Q_m(\cdot)$ , $K_m(\cdot)$ , and $V_m(\cdot)$ are the query, key, and value embedding functions in the $m$ th head, respectively, and project corresponding tensors from $C$ channels to $C / M$ channels. Finally, $\mathrm{MHA}(\mathbf{X}, \mathbf{Y}) \in \mathbb{R}^{N_x \times C}$ can be obtained by concatenating (Cat) the results of $M$ heads along the channel dimension. + +# 3.2.3 Prediction + +After performing the token construction five times on each image, we collect the final tokens of all images, i.e. $T_5^c, T_5^b \in \mathbb{R}^{N \times 1 \times C}$ . Then, we use the output of the first sub-path, i.e. the segmentation feature $F_5^d$ , to generate the final predictions via the sigmoid matrix multiplication, formulated as + +$$ +\boldsymbol {P} ^ {c} = \mathcal {P} \left(\boldsymbol {T} _ {5} ^ {c}, \boldsymbol {F} _ {5} ^ {d}\right) = \operatorname {S i g m o i d} \left(\boldsymbol {T} _ {5} ^ {c} \left(\boldsymbol {F} _ {5} ^ {d}\right) ^ {\top}\right), \tag {8} +$$ + +$$ +\boldsymbol {P} ^ {b} = \mathcal {P} (\boldsymbol {T} _ {5} ^ {b}, \boldsymbol {F} _ {5} ^ {d}) = \operatorname {S i g m o i d} (\boldsymbol {T} _ {5} ^ {b} (\boldsymbol {F} _ {5} ^ {d}) ^ {\top}), \qquad (9) +$$ + +where $P^c, P^b \in \mathbb{R}^{N \times 1 \times H \times W}$ are the segmentation results of co-salient objects and BG regions, respectively. + +# 3.3. Our Improvements for DMT + +# 3.3.1 Region-to-Region Correlation + +In the first sub-path, the original FPN individually processes each image and lacks the inter-image correlation modeling, which is crucial for CoSOD. However, straightforward P2P correlation is computationally prohibitive for large feature maps and multiple images. To this end, we consider modeling correlations among images in an economical way, thus proposing our R2R module, which uses region-level features instead of pixel-level features to compute correlations. + +Concretely, when given the features $\pmb{F}_j^d \in \mathbb{R}^{N \times H_j \times W_j \times C}$ of $N$ relevant images from the $j$ th decoder layer, we first adopt a transformation $\mathbb{R}_1$ to divide the $H_j \times W_j$ feature maps into $K \times K$ local regions and use max-pooling to pick up the most representative feature for representing each local region. As a result, we can obtain the region-level query with shape $\mathbb{R}^{N \times K \times K \times C}$ . + +Then, we generate multi-scale region-level key and value via another transformation $\mathbf{R}_2$ , which consists of three adaptive max-pooling operations with the output spatial sizes of $1 \times 1$ , $3 \times 3$ , and $6 \times 6$ , respectively. The three pooled features are finally flattened and concatenated to generate + +the key and value with shape $\mathbb{R}^{N\times 46\times C}$ , encoding multiscale robust region information. + +Next, we perform the R2R inter-image correlation among the region-level query, key, and value via the transformer operation (3), thus obtaining the enhanced features with the region-wise correlation. + +Finally, we upsample the enhanced features to the original resolution $H_{j} \times W_{j}$ via the nearest interpolation, denoted as $\mathbf{R}_1^{-1}$ . A residual connection is also used to add the original features. Thus, the region correlation results are diffused to the corresponding internal pixels in each local region. The whole process of R2R on $\pmb{F}_{j}^{d}$ is formulated as + +$$ +\boldsymbol {F} _ {j} ^ {d r} = \boldsymbol {F} _ {j} ^ {d} + \mathrm {R} _ {1} ^ {- 1} (\operatorname {T r a n s} \left(\mathrm {R} _ {1} \left(\boldsymbol {F} _ {j} ^ {d}\right), \mathrm {R} _ {2} \left(\boldsymbol {F} _ {j} ^ {d}\right)\right)). \tag {10} +$$ + +# 3.3.2 Contrast-induced Pixel-to-Token Correlation + +In the second sub-path, the original P2T module uses a transformer operation in (2) to mine relations between the two types of tokens in a data-driven way, while ignoring explicit CoSOD cues, especially the crucial contrast modeling between co-saliency and BG regions. To enhance the discriminability between the tokens, we explicitly model the contrast relation with our proposed CtP2T module, which modifies the transformer layer in (1) and the remaining part keeps the same as P2T. + +Overall, we modify the multi-head attention (denoted as $\mathrm{MHA}^{\ast}$ ) and propose a contrast-induced channel attention (CCA) mechanism. The basic idea is to suppress the channels that are not contrastive enough in the generated co-saliency and BG tokens. The contrast is modeled as the opposite of the channel similarity between the two types of tokens, which can be calculated via channel correlation. For brevity's sake, we slightly abuse the notation and use $\hat{T}, T \in \mathbb{R}^{2 \times C}$ , and $F \in \mathbb{R}^{H_0 W_0 \times C}$ as shorthands for $\hat{T}_{i,j}$ , $T_{i,j-1}$ , and $\hat{F}_i^e$ in (1), respectively. Then, (1) can be modified for our CtP2T as below: + +$$ +\begin{array}{l} \hat {\boldsymbol {T}} = \operatorname {T r a n s} ^ {*} (\boldsymbol {T}, \boldsymbol {F}) \\ = \operatorname {r M L P} (\boldsymbol {T} + \operatorname {C C A} (\operatorname {M H A} ^ {*} (\boldsymbol {T}, \boldsymbol {F}))). \tag {11} \\ \end{array} +$$ + +Next, we introduce $\mathrm{MHA}^*$ and CCA as shown in Figure 2. The LN operations are omitted for expression convenience. + +Modified Multi-Head Attention. To generate co-saliency and BG tokens that can be used for calculating their channel similarity, we make our $\mathrm{MHA}^*$ able to generate tokens with multiple heads. Concretely, we first replace the original $V_{m}$ in (6) with $V_{m}^{*}$ that embeds $\pmb{F}$ to the identical channel number $C$ . Thus, the shape of each head's result becomes $2\times C$ instead of $2\times C / M$ . Next, we stack the results of $M$ heads to produce the output of $\mathrm{MHA}^*$ . The whole process can be formulated as + +$$ +\begin{array}{l} \boldsymbol {T} _ {M} = \operatorname {M H A} ^ {*} (\boldsymbol {T}, \boldsymbol {F}) \\ = \operatorname {S t a c k} \left(\left[ \operatorname {A t t} _ {m} (\boldsymbol {T}, \boldsymbol {F}) V _ {m} ^ {*} (\boldsymbol {F}) \right] _ {m = 1} ^ {M}\right). \\ \end{array} +$$ + +![](images/e97107c3e9edef4750840d250fa3ce0f7ac5886cb217c45ede475ace6e732e8c.jpg) +Modified Multi-Head Attention Contrast-induced Channel Attention +Figure 2. Diagram of MHA* and CCA. We first generate multihead tokens $T_{M}^{c}$ and $T_{M}^{b}$ via MHA*. Then, we utilize matrix multiplication of the two tokens to generate the attention weights $W$ for modulating the token channels in CCA. + +$\pmb{T}_{M} \in \mathbb{R}^{2 \times M \times C}$ is composed of the co-saliency token and the BG token $\pmb{T}_{M}^{c}, \pmb{T}_{M}^{b} \in \mathbb{R}^{M \times C}$ with $M$ heads. Next, we can compute the channel similarity based on them. + +Contrast-induced Channel Attention. Given the multihead tokens $T_{M}^{c}$ and $T_{M}^{b}$ , we generate channel attention $W \in \mathbb{R}^{2 \times 1 \times C}$ to suppress the token channels with strong mutual similarities since they cannot clearly distinguish between co-saliency and BG. + +First, we compute a $C \times C$ channel similarity matrix between $\pmb{T}_M^c$ and $\pmb{T}_M^b$ via matrix multiplication. Then, the channel similarity of each token to the other token can be computed as the average along the channel dimension of the other token. The whole process can be denoted as + +$$ +\boldsymbol {S} ^ {c} = \operatorname {A v g} \left(\boldsymbol {T} _ {M} ^ {c} \top \boldsymbol {T} _ {M} ^ {b}\right), \tag {13} +$$ + +$$ +\boldsymbol {S} ^ {b} = \operatorname {A v g} \left(\boldsymbol {T} _ {M} ^ {b} ^ {\top} \boldsymbol {T} _ {M} ^ {c}\right), \tag {14} +$$ + +where $S^c, S^b \in \mathbb{R}^{C \times 1}$ , representing how similar each channel is to the channels of the other token. Avg means calculating the average along the second dimension. + +Next, we multiply $S^c$ and $S^b$ with $-1$ to turn the similarity measurements into the contrast scores and then compute the channel attention $\mathbf{W} \in \mathbb{R}^{2 \times 1 \times C}$ via + +$$ +\boldsymbol {W} = \text {S i g m o i d} \left(\alpha \left[ \begin{array}{c} - \boldsymbol {S} ^ {c ^ {\top}} \\ - \boldsymbol {S} ^ {b ^ {\top}} \end{array} \right] + \beta\right). \tag {15} +$$ + +Here we use a learnable linear projection with parameters $\alpha, \beta$ on each channel of the stacked contrast scores to fit them for the sigmoid activation. + +Once obtained $\mathbf{W}$ , we adopt the element-wise multiplication between $\mathbf{T}_M$ and $\mathbf{W}$ to modulate the token channels based on their contrast and then eliminate the multi-head dimension of the tokens by averaging the head dimension and obtaining the modulated tokens: + +$$ +\operatorname {C C A} \left(\boldsymbol {T} _ {M}\right) = \operatorname {A v g} \left(\boldsymbol {W} \odot \boldsymbol {T} _ {M}\right) \in \mathbb {R} ^ {2 \times C}, \tag {16} +$$ + +![](images/8549e25ec3bae532cb3bdff0f8cad4caa4fe8915917c41529d837df39883cc24.jpg) +Figure 3. Diagram of our proposed TGFR module. Specifically, we first distill the co-saliency and BG features under the guidance of the two tokens. Then, we fuse them back to the original segmentation feature for discriminability enhancement. + +where $\odot$ means element-wise multiplication with broadcasting. + +# 3.3.3 Co-saliency Token-to-Token Correlation + +CtP2T effectively explores the correlation between the two types of tokens within each image, but lacks explicitly modeling the inter-image relation to capture the token-wise group consistency, thus being limited for consensus mining. Therefore, we use co-saliency tokens from all images to model the consensus patterns via our CoT2T module. + +Specifically, we first define a group token $G \in \mathbb{R}^{1 \times C}$ to represent the group-wise consensus information, which is randomly initialized at the first iteration step. At the $j$ th iteration, given the last group token $G_{j-1}$ and the co-saliency tokens $\tilde{T}_j^c \in \mathbb{R}^{N \times C}$ from the CtP2T module, we aggregate the consensus information from all co-saliency tokens by using $\tilde{T}_j^c$ to update $G_{j-1}$ , denoted as + +$$ +\boldsymbol {G} _ {j} = \operatorname {T r a n s} \left(\boldsymbol {G} _ {j - 1}, \tilde {\boldsymbol {T}} _ {j} ^ {c}\right). \tag {17} +$$ + +Finally, we distribute the aggregated consensus cues back to $\tilde{T}_{j}^{c}$ and obtain the final co-saliency tokens $T_{j}^{c}$ : + +$$ +\boldsymbol {T} _ {j} ^ {c} = \operatorname {T r a n s} \left(\tilde {\boldsymbol {T}} _ {j} ^ {c}, \boldsymbol {G} _ {j}\right). \tag {18} +$$ + +# 3.3.4 Token-guided Feature Refinement + +The vanilla MaskFormer only transforms the information from the segmentation features to the tokens, hindering their complementary learning. To this end, we propose our TGFR module to improve the discriminability of the segmentation features via the detection cues of the tokens. As shown in Figure 3, TGFR consists of two processes, i.e. distillation and refusion. The distillation process is designed to distill the co-saliency and BG features from the segmentation feature under the guidance of the corresponding tokens. The refusion process is to fuse the distilled features back to the segmentation feature to enhance its discriminability. + +Distillation. For image $\mathbf{I}_i$ at the $j$ th iteration, we have the final co-saliency token $T_{i,j}^{c} \in \mathbb{R}^{1 \times C}$ generated from CoT2T and the final BG token $T_{i,j}^{b} \in \mathbb{R}^{1 \times C}$ outputted by + +CtP2T, and the segmentation feature $F_{i,j}^{dr}\in \mathbb{R}^{H_j\times W_j\times C}$ enhanced by R2R. We first compute two attention maps $A_{i,j}^{c}\in \mathbb{R}^{H_{j}\times W_{j}\times 1}$ and $A_{i,j}^{b}\in \mathbb{R}^{H_{j}\times W_{j}\times 1}$ via performing the matrix multiplication between the segmentation feature and the tokens and then adopting a softmax normalization on the spatial dimension, formulated as + +$$ +\boldsymbol {A} _ {i, j} ^ {c} = \operatorname {S o f t m a x} \left(\boldsymbol {F} _ {i, j} ^ {d r} \left(\boldsymbol {T} _ {i, j} ^ {c}\right) ^ {\top} / \sqrt {C}\right), \tag {19} +$$ + +$$ +\boldsymbol {A} _ {i, j} ^ {b} = \operatorname {S o f t m a x} \left(\boldsymbol {F} _ {i, j} ^ {d r} \left(\boldsymbol {T} _ {i, j} ^ {b}\right) ^ {\top} / \sqrt {C}\right). \tag {20} +$$ + +Next, we adopt the computed attention maps to distill the detection features from the segmentation feature via matrix multiplication, denoted as + +$$ +\boldsymbol {D} _ {i, j} ^ {c} = \left(\boldsymbol {A} _ {i, j} ^ {c}\right) ^ {\top} \boldsymbol {F} _ {i, j} ^ {d r}, \tag {21} +$$ + +$$ +\boldsymbol {D} _ {i, j} ^ {b} = \left(\boldsymbol {A} _ {i, j} ^ {b}\right) ^ {\top} \boldsymbol {F} _ {i, j} ^ {d r}, \tag {22} +$$ + +where $D_{i,j}^{c}, D_{i,j}^{b} \in \mathbb{R}^{1 \times C}$ is the distilled features for co-saliency and BG, respectively. + +Refusion. After producing $D_{i,j}^{c}$ and $D_{i,j}^{b}$ , we conduct the refusion process to fuse them back to $F_{i,j}^{dr}$ sequentially in a cascade way for activating the co-saliency and BG regions in $F_{i,j}^{dr}$ . In this way, we can effectively reduce ambiguous information and enhance feature discriminability. The details can be formulated as + +$$ +\hat {\boldsymbol {F}} _ {i, j} ^ {d t} = \operatorname {C o n v} _ {c} \left(\operatorname {C a t} \left(\left[ \boldsymbol {F} _ {i, j} ^ {d r}, \operatorname {E} \left(\boldsymbol {D} _ {i, j} ^ {c}\right) \right]\right)\right), \tag {23} +$$ + +$$ +\boldsymbol {F} _ {i, j} ^ {d t} = \operatorname {C o n v} _ {b} \left(\operatorname {C a t} \left(\left[ \hat {\boldsymbol {F}} _ {i, j} ^ {d t}, \mathrm {E} \left(\boldsymbol {D} _ {i, j} ^ {b}\right) \right]\right)\right), \tag {24} +$$ + +where $\operatorname{E}(*)$ replicates $D_{i,j}^{c}$ and $D_{i,j}^{b}$ along the spatial dimension to the same size as $F_{i,j}^{dr}$ . Then, we progressively concatenate them with $F_{i,j}^{dr}$ and use a convolution layer to reduce the channel number to $C$ . + +# 3.3.5 Prediction and Loss Function + +In the $j$ th iteration, after obtaining the learned co-saliency and BG tokens, i.e. $\pmb{T}_j^c,\pmb{T}_j^b\in \mathbb{R}^{N\times 1\times C}$ , from CoT2T and CtP2T, respectively, and the improved segmentation features $\pmb{F}_{j}^{dt}\in \mathbb{R}^{N\times H_{j}\times W_{j}\times C}$ from TGFR, we use the prediction function $\mathcal{P}$ in (8) to generate the co-saliency and the BG predictions, i.e. $\pmb{P}_{j}^{c}\pmb{P}_{j}^{b}$ , as follows: + +$$ +\boldsymbol {P} _ {j} ^ {c} = \mathcal {P} \left(\boldsymbol {T} _ {j} ^ {c}, \boldsymbol {F} _ {j} ^ {d t}\right), \tag {25} +$$ + +$$ +\boldsymbol {P} _ {j} ^ {b} = \mathcal {P} \left(\boldsymbol {T} _ {j} ^ {b}, \boldsymbol {F} _ {j} ^ {d t}\right). \tag {26} +$$ + +We also supervise the learning of the group token $G_{j} \in \mathbb{R}^{1 \times 1 \times C}$ in CoT2T and the middle feature $\hat{\pmb{F}}_j^{dt} \in \mathbb{R}^{N \times H_j \times W_j \times C}$ in TGFR. Two predictions can be obtained from them, respectively: + +$$ +\boldsymbol {P} _ {j} ^ {g} = \mathcal {P} (\text {R e p e a t} (\boldsymbol {G} _ {j}), \boldsymbol {F} _ {j} ^ {d t}), \tag {27} +$$ + +$$ +\boldsymbol {P} _ {j} ^ {d t} = \mathcal {P} (\boldsymbol {T} _ {j} ^ {c}, \hat {\boldsymbol {F}} _ {j} ^ {d t}), +$$ + +where Repeat is to repeat $G_{j}$ $N$ times. + +Table 1. Quantitative results of different settings of our proposed model. We show the results of progressively adding R2R, CtP2T, CoT2T, and TGFR on the baseline. "Co" and "Bg" mean explicitly modeling co-saliency and BG, respectively. + +
SettingsCoCA [42]
CoBgR2RCtP2TCoT2TTGFRSm↑Eξ↑maxF↑MAE ↓
✓✓0.67510.76830.54740.1383
✓✓✓0.69450.78240.58150.1234
✓✓✓✓0.70380.78680.59840.1230
✓✓✓✓✓0.71400.78800.60030.1139
✓✓✓✓✓✓0.72460.80010.61900.1084
✓✓✓✓0.70590.79200.59960.1259
+ +![](images/1b8d5a0a9a9d5d6819e1fac1c7631adcb00acfa41851a32e264a0e90f2d1506b.jpg) +Figure 4. Qualitative results of different settings of our proposed model. We show the results of progressively adding the R2R, CtP2T, CoT2T, and TGFR on the baseline. + +Our total loss $\mathcal{L}_{total}$ can be formulated as + +$$ +\mathcal {L} _ {\text {t o t a l}} = \sum_ {j = 1} ^ {5} \left(\mathcal {L} _ {1} \left(\boldsymbol {P} _ {j} ^ {c}, \boldsymbol {M} _ {j} ^ {c}\right) + \mathcal {L} _ {2} \left(\boldsymbol {P} _ {j} ^ {c}, \boldsymbol {M} _ {j} ^ {c}\right) + \right. \tag {28} +$$ + +$$ +\left. \mathcal {L} _ {2} \left(\boldsymbol {P} _ {j} ^ {b}, \boldsymbol {M} _ {j} ^ {b}\right) + \mathcal {L} _ {2} \left(\boldsymbol {P} _ {j} ^ {g}, \boldsymbol {M} _ {j} ^ {c}\right) + \mathcal {L} _ {2} \left(\boldsymbol {P} _ {j} ^ {d t}, \boldsymbol {M} _ {j} ^ {c}\right)\right), +$$ + +where $\mathcal{L}_1$ and $\mathcal{L}_2$ are the IoU [16] and Binary Cross-Entropy (BCE) [7] loss, respectively. $M_j^c$ and $M_j^b$ denote the co-saliency and BG ground truths, respectively, with the spatial shapes aligned to the $j$ th decoder layer. + +# 4. Experiments + +# 4.1. Evaluation Datasets and Metrics + +We follow [12, 27, 34] to evaluate our proposed model on three CoSOD benchmark datasets. CoSal2015 [36] and CoSOD3k [11] collect 50 groups with 2015 images and 160 groups with 3316 images, respectively. CoCA [42] is the most challenging dataset and contain 1295 images of 80 groups. We employ four widely-used metrics for quantitative evaluation, i.e. Structure-measure $S_{m}$ [9], Enhanced-alignment measure $E_{\xi}$ [10], Maximum F-measure (maxF) [1], and Mean Absolute Error (MAE) [6]. + +# 4.2. Implementation Details + +We follow [41] to use the COCO-9k [20] (9213 images of 65 groups) and the DUTS class [42] (8250 images of 291 groups) with the synthesis strategy [41] to construct our training set. We follow [22] to perform data augmentation and adopt the Adam optimizer [17] with an initial learning + +![](images/b6bb61b7e9fa624d61c4d45e1680900c8432ee0eabf1e0c9f530e717a50c3041.jpg) +Figure 5. Visual comparison among the channels with different channel attention weights in CtP2T. We visualize some feature maps in $V_{m}^{*}(\pmb{F})$ for the channels with large and small channel attention (CA) in CtP2T. We visualize two channels for large and small CA, respectively. + +![](images/27e9ff26b9eb13a07b4215eb4e140283f1551bc5b5c159c31ca6b067f3bb2822.jpg) + +![](images/1891516425141cf4c3434e24c6138abc0ad24af763d326af727e4aad49cb9e0f.jpg) + +![](images/b2c7ead7ae43c5812f7cb912fff0e2f064fae07518c832472e9cd220a708fff7.jpg) + +rate of 0.0001, $\beta_{1} = 0.9$ , and $\beta_{2} = 0.99$ to train our model for 80,000 iterations. The learning rate is divided by 10 at the $60000^{\mathrm{th}}$ iteration. We select at most eight images from each group as a mini-batch to train our network. The training and testing image size is set as $256 \times 256$ . Our method is implemented using Pytorch [24]. + +# 4.3. Ablation Study + +We conduct ablation studies on the challenging CoCA [42] dataset to verify the effectiveness of our proposed components. As shown in Table 1, we treat the vanilla MaskFormer-style framework as our baseline, shown in the first row, and progressively add our proposed R2R, CtP2T, CoT2T, and TGFR on it for effectiveness analysis. + +Effectiveness of R2R. First, we plug R2R into each decoder layer to enhance the segmentation features. It shows that using R2R largely improves the model performance compared to the baseline, while using vanilla P2P causes the out-of-memory error. The results verify the necessity of using our R2R for inter-image correlation modeling. + +Effectiveness of CtP2T. Next, we consider the contrast relation modeling between the co-saliency and BG tokens, thus replacing the original P2T module to our proposed CtP2T module. By using CtP2T, the model performance can be further improved, indicating that CtP2T is beneficial for enhancing the discriminability between the two types of tokens. We also provide some visual samples in Figure 5. Since the channels of the tokens correspond to those of the values in $\mathrm{MHA}^*$ , we visualize some feature maps of $V_{m}^{*}(\pmb {F})$ of the channels with large or small channel attention weights in $\pmb{W}$ . We can see that the channels with large channel attention (CA) can easily distinguish co-salient objects and distracting objects, while those with small CA usually confuse them. The results demonstrate our generated channel attention is meaningful for accurate co-salient object detection. + +Effectiveness of CoT2T. Furthermore, we supplement CoT2T to explore the inter-image correlations for all co-saliency tokens. CoT2T explicitly promotes consensus information propagation among all co-saliency tokens, thus obtaining obvious improvements. + +Table 2. Quantitative results of different settings in TGFR. + +
SettingsCoCA [42]
Sm↑Eξ↑maxF↑MAE↓
w/o TGFR0.71400.78800.60030.1139
w/o Distillation0.71410.79210.60460.1114
w/ co0.71710.79650.60760.1144
w/ bg0.71550.79350.60640.1112
w/ bg&co0.71970.79070.60920.1069
w/ co&bg0.72460.80010.61900.1084
+ +![](images/1ff33136dbbd7d9fd0a3586c037edf9737254f5ad0d072188ed3f93e837d5de2.jpg) +Image +Figure 6. Visualization of some feature maps (Fea.) and predictions (Pred.) of the models with (w/) or without (w/o) using TGFR. + +![](images/584119f4c47ab3b34a780e94aeeebaabf8e807a2d00df350bc17f7374789e3bb.jpg) +GT + +![](images/490ab51924231aea23dfa23499631be1ad1e4c2736f94f4749e8b0a1cf4d2c19.jpg) +Pred. w/o + +![](images/923c8581e007b126701f1c7fc46748a18619b844abdbc30e3477ee0dbc75735f.jpg) +Fea. w/o + +![](images/369179c1a06f2b277927e023d19ed0c7edafaa2ef4461ec4a6773e8ecd34b02a.jpg) +Pred. w/ + +![](images/1e9a49ff7240403ab36f67f13293ed48d81dcf0fc248dcd522b3a6986111ca18.jpg) +Fea. w/ + +Effectiveness of TGFR. Finally, we add TGFR to leverage the learned tokens for refining the segmentation features. Table 1 shows that adopting TGFR can bring more performance gains, thus demonstrating its effectiveness. We also visualize some feature maps and predictions of using and without using TGFR in Figure 6. It can be seen that using TGFR obtains more discriminative features for distinguishing co-saliency objects from distractors, thus generating better segmentation results. + +To dive deeper into the effectiveness of TGFR, we report more experimental results in Table 2 for further analysis. First, we directly fuse the tokens and the segmentation features without performing the distillation process ("w/o Distillation"). we find this model brings limited improvements compared to the "w/o TGFR" model. It is probably because the tokens and features might exist semantic gap, being detrimental for their fusion, hence verifying the necessity of our distillation mechanism. Next, we supplement the distillation process and explore four strategies for the refusion process, i.e. individually refusing the distilled co-saliency ("w/ co") or BG features ("w/ bg") to the segmentation features, or refusing both with the order of co-saliency feature first ("w/ co&bg") or BG feature first ("w/ bg&co"). We can find refusing both achieves better performance, thus verifying the necessity of leveraging both features for discrimination enhancement. We also find first refusing the co-saliency feature and then integrating the BG feature obtains the best results. Thus, we adopt this strategy in our final TGFR design. + +Effectiveness of BG Exploration. We remove all BG-related modules in our final model and only explore co-saliency regions, shown in the last row of Table 1. In this setting, CtP2T can not be used while only the co-saliency feature is used in TGFR. We find that the performance significantly drops compared to our final model, thus verifying the necessity of explicit BG modeling. + +Table 3. Quantitative comparison of our model with other state-of-the-art methods. We conduct the comparison on three benchmark CoSOD datasets. Red and blue denote the best and the second-best results, respectively. + +
MethodsCoCA [42]CoSal2015 [36]CoSOD3k [11]
Sm↑Eξ↑maxF↑MAE↓Sm↑Eξ↑maxF↑MAE↓Sm↑Eξ↑maxF↑MAE↓
CSMG(CVPR2019) [39]0.62760.73240.49880.12730.77570.84360.78690.13090.72720.82080.72970.1480
GICD(ECCV2020) [42]0.65790.71490.51260.12600.84370.88690.84410.07070.79670.84780.76980.0794
ICNet(NIPS2020) [16]0.65410.70420.51330.14700.85710.90110.85830.05790.79420.84500.76230.0891
GCoNet(CVPR2021) [12]0.67300.75980.54380.10500.84530.88790.84710.06810.80180.86010.77710.0712
CADC(ICCV2021) [41]0.68000.74430.54870.13300.86660.90630.86450.06410.81500.85430.77810.0875
UFO(ArXiv2022) [27]0.69710.78020.56810.09390.85780.90570.86210.06480.81910.86940.79540.0735
DCFM(CVPR2022) [34]0.71010.78260.59810.08450.83800.89290.85590.06720.80940.87420.80450.0674
DMT (Ours)0.72460.80010.61900.10840.89740.93620.90520.04540.85140.89500.83530.0633
+ +![](images/01ccf4478dc86201b0e20d2385b32fe3460a31f1bdb4595b0985e4f84302df7b.jpg) +Figure 7. Qualitative comparisons of our model with other state-of-the-art methods. + +Quantitative Analysis. As shown in Figure 4, we also provide some visual comparison samples for the four key components. We find that the baseline model is easily distracted by complex BG regions, while progressively introducing our four components can gradually exclude these distractors and achieve more and more accurate results. + +# 5. Comparison with State-of-the-Art Methods + +We compare our model with other seven state-of-the-art methods, i.e. CSMG [39], GICD [42], ICNet [16], GCoNet [12], CADC [41], UFO [27], and DCFM [34]. We report the quantitative comparison results in Table 3. We can observe that our proposed DMT achieves the best performance on all three benchmark datasets. Especially, on CoSal2015 and CoSOD3k, our DMT model surpasses the second-best model by a large margin, e.g. $3.14\%$ $S_{m}$ and $4.07\%$ maxF on CoSal2015 and $3.23\%$ $S_{m}$ and $3.08\%$ maxF on CoSOD3k. We also show some visual comparison results in Figure 7. We can find that our method can precisely detect co-salient objects in complex scenarios, e.g. the existence of extraneous salient objects with similar appearances to target objects, and target objects with small + +sizes. Nevertheless, other models are heavily distracted in these challenging scenes. + +# 6. Conclusions + +In this paper, we propose DMT, a transformer-based CoSOD model for explicitly mining both co-saliency and BG information and effectively modeling their discrimination. Specifically, we propose several economic multigrained correlations, i.e. R2R, CtP2T, and CoT2T to model inter-image and intra-image relations. Besides, we propose a TGFR module to leverage the detection information for improving the discriminability of the segmentation features. It is an improvement to the MaskFormer that allows the mutual promotion of two sub-paths. Our model achieves a new state-of-the-art result. + +Acknowledgments: This work was supported in part by Key-Area Research and Development Program of Guangdong Province (No.2021B0101200001), the National Key R&D Program of China under Grant 2021B0101200001, and the National Science Foundation of China under Grant 62036011, U20B2065, 721A0001, 62136004. + +# References + +[1] Radhakrishna Achanta, Sheila Hemami, Francisco Estrada, and Sabine Susstrunk. Frequency-tuned salient region detection. In 2009 IEEE Conference on Computer Vision and Pattern Recognition, pages 1597-1604, 2009. 6 +[2] Jimmy Lei Ba, Jamie Ryan Kiros, and Geoffrey E Hinton. 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In this paper, we propose a Discriminative co-saliency and background Mining Transformer framework (DMT) based on several economical multi-grained correlation modules to explicitly mine both co-saliency and background information and effectively model their discrimination. Specifically, we first propose a region-to-region correlation module for introducing inter-image relations to pixel-wise segmentation features while maintaining computational efficiency. Then, we use two types of pre-defined tokens to mine co-saliency and background information via our proposed contrast-induced pixel-to-token correlation and co-saliency token-to-token correlation modules. We also design a token-guided feature refinement module to enhance the discriminability of the segmentation features under the guidance of the learned tokens. We perform iterative mutual promotion for the segmentation feature extraction and token construction. Experimental results on three benchmark datasets demonstrate the effectiveness of our proposed method. The source code is available at: https://github.com/dragonlee258079/DMT." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 569, + 128, + 582 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 569, + 128, + 582 + ], + "spans": [ + { + "bbox": [ + 47, + 569, + 128, + 582 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 586, + 287, + 695 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 586, + 287, + 695 + ], + "spans": [ + { + "bbox": [ + 46, + 586, + 287, + 695 + ], + "type": "text", + "content": "Unlike standard Salient Object Detection (SOD) [13,21-23, 37, 45], which detects salient objects in a single image, Co-Salient Object Detection (CoSOD) aims to detect common salient objects across a group of relevant images. It often faces the following two challenges: 1) The foreground (FG) in CoSOD refers to co-salient objects, which are inherently hard to detect since they should satisfy both the intra-group commonality and the intra-image saliency. 2) The background (BG) in CoSOD might contain com" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 246, + 546, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 246, + 546, + 353 + ], + "spans": [ + { + "bbox": [ + 306, + 246, + 546, + 353 + ], + "type": "text", + "content": "plex distractions, including extraneous salient objects that are salient but not \"common\", and similar concomitant objects appearing in multiple images (e.g. performers often appear in guitar images). Such difficult distractors can easily seduce CoSOD models to make false positive predictions. Therefore, the effective exploration of both FG and BG and modeling their discrimination to precisely detect co-salient objects while suppressing interference from BG is crucial for CoSOD." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 354, + 546, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 354, + 546, + 545 + ], + "spans": [ + { + "bbox": [ + 304, + 354, + 546, + 545 + ], + "type": "text", + "content": "Although many works have achieved promising performance, most of them [14, 18, 25, 30, 33, 38, 40-42] devoted to the ingenious mining of FG while ignored the explicit exploration of BG. They mainly constructed positive relations between co-salient objects but paid less attention to modeling negative ones between co-saliency regions and BG. [16, 34] followed some SOD methods [4, 43] to incorporate BG features for co-saliency representation learning or contrast learning. However, these methods can be regarded as an univariate FG&BG modeling in which the essential optimization target is limited to FG and there is no explicit BG modeling, thus limiting the discriminative learning capability. To this end, this paper proposes to conduct a bivariate FG&BG modeling paradigm that explicitly models both FG and BG information and effectively facilitates their discriminative modeling." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 545, + 547, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 547, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 547, + 689 + ], + "type": "text", + "content": "As for co-saliency (FG) information, most previous works [12, 16, 34, 41] detected them by exploring the interimage similarity. Calculating the Pixel-to-Pixel (P2P) correlation between 3D CNN features in a group is widely used in many works [12, 16, 34] and has demonstrated its effectiveness. However, this method introduces heavy computation burdens and hinders sophisticated relation modeling. To alleviate this problem, we introduce economic multi-grained correlations among different images and the co-saliency and BG information, thus enabling modeling sophisticated relations to extract accurate co-saliency as well as BG knowledge." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "type": "text", + "content": "Specifically, we construct a Discriminative co-saliency and BG Mining Transformer (DMT) following the" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 217, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 217, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 217, + 713 + ], + "type": "text", + "content": "†Corresponding author: liunian228@gmail.com." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7247" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "content": "paradigm of a semantic segmentation transformer architecture, i.e. MaskFormer [5], which enables explicit co-saliency and BG modeling and the construction of multi-grained correlations. Using this architecture, we decompose the CoSOD modeling into two sub-paths, i.e. generating pixel-wise segmentation feature maps and extracting category information with pre-defined co-saliency and BG detection tokens." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 168, + 289, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 168, + 289, + 357 + ], + "spans": [ + { + "bbox": [ + 46, + 168, + 289, + 357 + ], + "type": "text", + "content": "In the first sub-path, to efficiently and thoroughly mine the common cues within the image group, we propose a Region-to-Region correlation (R2R) module to model the inter-image relation and plug it into each decoder layer. In the second sub-path, we transform the pixel-wise features into a co-saliency token and a BG token for each image, abstracting pixel-wise cues into high-level tokens. As such, we achieve sophisticated relation modeling among the tokens and features while largely reducing the computational costs. Concretely, we propose an intra-image Contrast-induced Pixel-to-Token correlation (CtP2T) module to extract the two tokens by considering the contrast relation between co-saliency and BG. Since the co-saliency tokens from CtP2T are separately learned on each image, we further design a Co-saliency Token-to-Token (CoT2T) correlation module to model their common relation." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 360, + 289, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 360, + 289, + 552 + ], + "spans": [ + { + "bbox": [ + 46, + 360, + 289, + 552 + ], + "type": "text", + "content": "After obtaining the tokens and pixel-wise features, the MaskFormer [5] architecture adopts dot production between them to obtain the final segmentation results. However, such a scheme only achieves unidirectional information propagation, i.e. conveying information from the feature maps to the tokens. We argue that the learned two tokens can also be used to improve the discriminability of the pixel-wise features, thus proposing our Token-Guided Feature Refinement (TGFR) module as a reverse information propagation path. Concretely, we first use the tokens as guidance to distill co-saliency and BG features from the pixel-wise feature maps, and then enhance the discriminability of the segmentation features between the two detection regions. In this way, the refined features become sensitive to both co-saliency and BG, reducing the affect of ambiguous distractors." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 552, + 288, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 552, + 288, + 624 + ], + "spans": [ + { + "bbox": [ + 46, + 552, + 288, + 624 + ], + "type": "text", + "content": "Finally, as shown in Figure 1, our DMT iteratively deploys CtP2T and CoT2T to leverage the segmentation features for updating the tokens, and then adopts TGFR to refine the corresponding decoder feature with the updated tokens. As a result, the learning processes can be effectively promoted, thus obtaining more accurate CoSOD results." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 59, + 624, + 269, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 624, + 269, + 635 + ], + "spans": [ + { + "bbox": [ + 59, + 624, + 269, + 635 + ], + "type": "text", + "content": "In summary, our major contributions are as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 58, + 638, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 58, + 638, + 286, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 638, + 286, + 673 + ], + "spans": [ + { + "bbox": [ + 58, + 638, + 286, + 673 + ], + "type": "text", + "content": "- We model CoSOD from the perspective of explicitly exploring both co-saliency and BG information and effectively modeling their discrimination." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 58, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 677, + 287, + 713 + ], + "type": "text", + "content": "- We introduce several computationally economical multi-grained correlation modules, i.e. R2R, CtP2T, CoT2T, for the inter-image and intra-image relations" + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 326, + 73, + 369, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 73, + 369, + 84 + ], + "spans": [ + { + "bbox": [ + 326, + 73, + 369, + 84 + ], + "type": "text", + "content": "modeling." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 317, + 86, + 545, + 169 + ], + "type": "list", + "angle": 0, + "index": 11, + "blocks": [ + { + "bbox": [ + 317, + 86, + 545, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 86, + 545, + 133 + ], + "spans": [ + { + "bbox": [ + 317, + 86, + 545, + 133 + ], + "type": "text", + "content": "- We propose a novel TGFR module to use the learned tokens as guidance to refine the segmentation features for enhancing their discriminability between co-saliency and BG regions." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 317, + 135, + 545, + 169 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 135, + 545, + 169 + ], + "spans": [ + { + "bbox": [ + 317, + 135, + 545, + 169 + ], + "type": "text", + "content": "- Experimental results demonstrate that our DMT model outperforms previous state-of-the-art results on three benchmark datasets." + } + ] + } + ], + "index": 10 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 181, + 392, + 193 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 181, + 392, + 193 + ], + "spans": [ + { + "bbox": [ + 306, + 181, + 392, + 193 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 198, + 460, + 210 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 198, + 460, + 210 + ], + "spans": [ + { + "bbox": [ + 306, + 198, + 460, + 210 + ], + "type": "text", + "content": "2.1. Co-Salient Object Detection" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 213, + 545, + 512 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 213, + 545, + 512 + ], + "spans": [ + { + "bbox": [ + 304, + 213, + 545, + 512 + ], + "type": "text", + "content": "Recent CoSOD works [12,16,27,34,41,42] have achieve promising performance and can be summarized as a unified paradigm, i.e. first aggregating all image features in the group to form a consensus representation and then distributing it back to each image feature. We refer to these two processes as aggregation and distribution for expression convenience. For example, [42] summed up all features for aggregation and leveraged a gradient feedback mechanism for distribution. [16] formed the consensus cues with a group of enhanced intra-saliency vectors and conducted the distribution via a dense correlation module. [12] generated a consensus attention map with an affinity module and multiplied it back to the individual image features. [41] encoded the consensus information with dynamic kernels and convolved the image features using these kernels as the distribution process. [34] first obtained consensus seeds by processing P2P affinity maps and then propagated the seeds using normalized convolution operations. However, most of them are limited in exploring BG regions, which hinders the discriminability learning. Unlike them, we propose to simultaneously detect the co-saliency and BG regions and sufficiently explore their discriminative modeling. Besides, we utilize tokens under a transformer architecture for aggregation, and then use the learned tokens to conduct the distribution process." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 518, + 389, + 530 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 518, + 389, + 530 + ], + "spans": [ + { + "bbox": [ + 306, + 518, + 389, + 530 + ], + "type": "text", + "content": "2.2. Transformer" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 534, + 545, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 688 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 688 + ], + "type": "text", + "content": "After Vaswani et al. [29] first proposed the transformer architecture for machine translation, many successful transformer applications in the computer vision field emerged. Some works [8, 28, 35] directly apply the transformer architecture for feature learning. Some other works mainly focused on using transformers to extract specific semantic concepts, e.g. the category or instance information for object detection [3, 32, 44], semantic segmentation [5, 31], and the saliency and contour information for salient object detection [23]. Concretely, they first use a backbone to extract image feature maps and then adopt transformers to collect semantic concept information and store them in pre-created tokens." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "This paper follows the second type application to utilize the transformer for simultaneous FG and BG modeling. We" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7248" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 71, + 545, + 247 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 545, + 247 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 545, + 247 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 545, + 247 + ], + "type": "image", + "image_path": "770164cf23b1cfae99b5f9c5046a5362a0d31320fe4bb87d59076d5287b81928.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 248, + 547, + 282 + ], + "lines": [ + { + "bbox": [ + 46, + 248, + 547, + 282 + ], + "spans": [ + { + "bbox": [ + 46, + 248, + 547, + 282 + ], + "type": "text", + "content": "Figure 1. Overall flowchart of our proposed DMT CoSOD model. Specifically, the framework consists of four components, i.e. R2R for segmentation feature generation, CtP2T and CoT2T for detection token construction, and TGFR for the segmentation feature refinement under the guidance of the tokens." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 291, + 288, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 291, + 288, + 365 + ], + "spans": [ + { + "bbox": [ + 46, + 291, + 288, + 365 + ], + "type": "text", + "content": "further modify the transformer framework tailored for the CoSOD task by introducing economic multi-grained correlations for modeling sophisticated relations. We also propose to leverage the semantic information encoded in the learned tokens as a guide to refine the features, thus improving its discriminability." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 375, + 153, + 388 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 375, + 153, + 388 + ], + "spans": [ + { + "bbox": [ + 47, + 375, + 153, + 388 + ], + "type": "text", + "content": "3. Proposed Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 392, + 115, + 403 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 392, + 115, + 403 + ], + "spans": [ + { + "bbox": [ + 47, + 392, + 115, + 403 + ], + "type": "text", + "content": "3.1. Overview" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 408, + 287, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 408, + 287, + 540 + ], + "spans": [ + { + "bbox": [ + 46, + 408, + 287, + 540 + ], + "type": "text", + "content": "Figure 1 illustrates our MaskFormer-style framework for simultaneously detecting co-salient objects and BG regions. It consists of two sub-paths, i.e. pixel-wise segmentation feature generation and detection token construction. We use R2R in the first sub-path to enhance the segmentation features with inter-image consistency. In the second sub-path, CtP2T and CoT2T are designed to effectively construct the co-saliency and BG tokens from segmentation features, capturing the binary detection patterns. Finally, we propose TGFR to use the detection tokens as guidance for refining the segmentation features." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 540, + 287, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 540, + 287, + 601 + ], + "spans": [ + { + "bbox": [ + 46, + 540, + 287, + 601 + ], + "type": "text", + "content": "For ease of understanding, we first briefly describe the vanilla MaskFormer-style framework for simultaneously detecting co-saliency and BG in CoSOD. Then, we progressively introduce the improvements in our proposed DMT, including R2R, CtP2T, CoT2T, and TGFR." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 609, + 250, + 621 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 609, + 250, + 621 + ], + "spans": [ + { + "bbox": [ + 47, + 609, + 250, + 621 + ], + "type": "text", + "content": "3.2. Vanilla MaskFormer-style Framework" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 625, + 224, + 636 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 625, + 224, + 636 + ], + "spans": [ + { + "bbox": [ + 47, + 625, + 224, + 636 + ], + "type": "text", + "content": "3.2.1 Segmentation Feature Generation" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 640, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 640, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 640, + 288, + 713 + ], + "type": "text", + "content": "Given a set of " + }, + { + "bbox": [ + 46, + 640, + 288, + 713 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 640, + 288, + 713 + ], + "type": "text", + "content": " relevant images " + }, + { + "bbox": [ + 46, + 640, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\{I_i\\}_{i=1}^N" + }, + { + "bbox": [ + 46, + 640, + 288, + 713 + ], + "type": "text", + "content": ", we follow the original MaskFormer framework [5] to adopt an FPN [19] for generating pixel-wise segmentation features. Specifically, we use VGG-16 [26] as the encoder and take " + }, + { + "bbox": [ + 46, + 640, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\{I_i\\}_{i=1}^N" + }, + { + "bbox": [ + 46, + 640, + 288, + 713 + ], + "type": "text", + "content": " as the input to obtain the highest-level features " + }, + { + "bbox": [ + 46, + 640, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\pmb{F}^e \\in \\mathbb{R}^{N \\times H_0 \\times W_0 \\times C}" + }, + { + "bbox": [ + 46, + 640, + 288, + 713 + ], + "type": "text", + "content": " from the last block. Then, based on " + }, + { + "bbox": [ + 46, + 640, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\pmb{F}^e" + }, + { + "bbox": [ + 46, + 640, + 288, + 713 + ], + "type": "text", + "content": ", the" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 292, + 545, + 329 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 292, + 545, + 329 + ], + "spans": [ + { + "bbox": [ + 305, + 292, + 545, + 329 + ], + "type": "text", + "content": "FPN decoder uses five decoder layers to progressively enlarge the feature resolution and obtain five decoder features " + }, + { + "bbox": [ + 305, + 292, + 545, + 329 + ], + "type": "inline_equation", + "content": "\\pmb{F}_{j}^{d}\\in \\mathbb{R}^{N\\times H_{j}\\times W_{j}\\times C},j\\in \\{1\\dots 5\\}" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 334, + 467, + 344 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 334, + 467, + 344 + ], + "spans": [ + { + "bbox": [ + 306, + 334, + 467, + 344 + ], + "type": "text", + "content": "3.2.2 Detection Token Construction" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 348, + 545, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 348, + 545, + 498 + ], + "spans": [ + { + "bbox": [ + 304, + 348, + 545, + 498 + ], + "type": "text", + "content": "Given the highest-level semantic feature " + }, + { + "bbox": [ + 304, + 348, + 545, + 498 + ], + "type": "inline_equation", + "content": "\\pmb{F}_i^e \\in \\mathbb{R}^{H_0 \\times W_0 \\times C}" + }, + { + "bbox": [ + 304, + 348, + 545, + 498 + ], + "type": "text", + "content": " of image " + }, + { + "bbox": [ + 304, + 348, + 545, + 498 + ], + "type": "inline_equation", + "content": "\\pmb{I}_i" + }, + { + "bbox": [ + 304, + 348, + 545, + 498 + ], + "type": "text", + "content": ", we extract the detection tokens from it via a vanilla pixel-to-token correlation (P2T) module. First, we define two randomly initialized tokens for " + }, + { + "bbox": [ + 304, + 348, + 545, + 498 + ], + "type": "inline_equation", + "content": "\\pmb{I}_i" + }, + { + "bbox": [ + 304, + 348, + 545, + 498 + ], + "type": "text", + "content": ", i.e., a co-saliency token " + }, + { + "bbox": [ + 304, + 348, + 545, + 498 + ], + "type": "inline_equation", + "content": "T_{i,0}^c \\in \\mathbb{R}^{1 \\times C}" + }, + { + "bbox": [ + 304, + 348, + 545, + 498 + ], + "type": "text", + "content": " and a BG token " + }, + { + "bbox": [ + 304, + 348, + 545, + 498 + ], + "type": "inline_equation", + "content": "T_{i,0}^b \\in \\mathbb{R}^{1 \\times C}" + }, + { + "bbox": [ + 304, + 348, + 545, + 498 + ], + "type": "text", + "content": " and denote their union as " + }, + { + "bbox": [ + 304, + 348, + 545, + 498 + ], + "type": "inline_equation", + "content": "T_{i,0} \\in \\mathbb{R}^{2 \\times C}" + }, + { + "bbox": [ + 304, + 348, + 545, + 498 + ], + "type": "text", + "content": ". We also flatten " + }, + { + "bbox": [ + 304, + 348, + 545, + 498 + ], + "type": "inline_equation", + "content": "F_i^e" + }, + { + "bbox": [ + 304, + 348, + 545, + 498 + ], + "type": "text", + "content": " along the spatial dimension as " + }, + { + "bbox": [ + 304, + 348, + 545, + 498 + ], + "type": "inline_equation", + "content": "\\hat{F}_i^e \\in \\mathbb{R}^{H_0 W_0 \\times C}" + }, + { + "bbox": [ + 304, + 348, + 545, + 498 + ], + "type": "text", + "content": ". Then, we iteratively update the tokens five times. At each iteration " + }, + { + "bbox": [ + 304, + 348, + 545, + 498 + ], + "type": "inline_equation", + "content": "j \\in \\{1, \\dots, 5\\}" + }, + { + "bbox": [ + 304, + 348, + 545, + 498 + ], + "type": "text", + "content": ", we obtain " + }, + { + "bbox": [ + 304, + 348, + 545, + 498 + ], + "type": "inline_equation", + "content": "T_{i,j}" + }, + { + "bbox": [ + 304, + 348, + 545, + 498 + ], + "type": "text", + "content": " by transforming the information from the feature " + }, + { + "bbox": [ + 304, + 348, + 545, + 498 + ], + "type": "inline_equation", + "content": "\\hat{F}_i^e" + }, + { + "bbox": [ + 304, + 348, + 545, + 498 + ], + "type": "text", + "content": " to tokens in (1) and modeling the relationship between the co-saliency and BG tokens in (2), formulated as" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 367, + 500, + 545, + 515 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 367, + 500, + 545, + 515 + ], + "spans": [ + { + "bbox": [ + 367, + 500, + 545, + 515 + ], + "type": "interline_equation", + "content": "\\hat {\\boldsymbol {T}} _ {i, j} = \\operatorname {T r a n s} \\left(\\boldsymbol {T} _ {i, j - 1}, \\hat {\\boldsymbol {F}} _ {i} ^ {e}\\right), \\tag {1}", + "image_path": "cfc76ff2e50a8d5ca27d15e4ff75b44e6da7618c6c1651b9f3bc164543cb10bd.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 372, + 518, + 545, + 533 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 372, + 518, + 545, + 533 + ], + "spans": [ + { + "bbox": [ + 372, + 518, + 545, + 533 + ], + "type": "interline_equation", + "content": "\\boldsymbol {T} _ {i, j} = \\operatorname {T r a n s} \\left(\\hat {\\boldsymbol {T}} _ {i, j}, \\hat {\\boldsymbol {T}} _ {i, j}\\right), \\tag {2}", + "image_path": "73ec929dd26fbd68f9cd5fba80f0dd7e7f6f3faefa80a53701de5f3c97122875.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 538, + 545, + 561 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 538, + 545, + 561 + ], + "spans": [ + { + "bbox": [ + 304, + 538, + 545, + 561 + ], + "type": "text", + "content": "where Trans is a basic transformer operation following [29]:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 341, + 565, + 545, + 578 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 341, + 565, + 545, + 578 + ], + "spans": [ + { + "bbox": [ + 341, + 565, + 545, + 578 + ], + "type": "interline_equation", + "content": "\\operatorname {T r a n s} (\\boldsymbol {X}, \\boldsymbol {Y}) = \\mathrm {r M L P} (\\mathrm {r M H A} (\\boldsymbol {X}, \\boldsymbol {Y})). \\tag {3}", + "image_path": "013d99174d4b1e22c4524b36dd406de6543db087e27d2f54b9593cf805ed55f1.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 587, + 545, + 636 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 587, + 545, + 636 + ], + "spans": [ + { + "bbox": [ + 304, + 587, + 545, + 636 + ], + "type": "text", + "content": "It can transfer the information from " + }, + { + "bbox": [ + 304, + 587, + 545, + 636 + ], + "type": "inline_equation", + "content": "\\mathbf{Y} \\in \\mathbb{R}^{N_y \\times C}" + }, + { + "bbox": [ + 304, + 587, + 545, + 636 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 587, + 545, + 636 + ], + "type": "inline_equation", + "content": "\\mathbf{X} \\in \\mathbb{R}^{N_x \\times C}" + }, + { + "bbox": [ + 304, + 587, + 545, + 636 + ], + "type": "text", + "content": " under the guidance of their relation. rMHA and rMLP denote the residual multi-head attention [29] and residual multi-layer perception, respectively, formulated as" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 351, + 645, + 545, + 658 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 645, + 545, + 658 + ], + "spans": [ + { + "bbox": [ + 351, + 645, + 545, + 658 + ], + "type": "interline_equation", + "content": "\\operatorname {r M L P} (\\boldsymbol {X}) = \\boldsymbol {X} + \\operatorname {M L P} (\\operatorname {L N} (\\boldsymbol {X})), \\tag {4}", + "image_path": "1c3239cd20dd1c1d40335318c50ad1403ded3f21af72cc729c2ee13f5ae2965d.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 318, + 666, + 545, + 680 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 666, + 545, + 680 + ], + "spans": [ + { + "bbox": [ + 318, + 666, + 545, + 680 + ], + "type": "interline_equation", + "content": "\\operatorname {r M H A} (\\boldsymbol {X}, \\boldsymbol {Y}) = \\boldsymbol {X} + \\operatorname {M H A} (\\ln (\\boldsymbol {X}), \\ln (\\boldsymbol {Y}))), \\tag {5}", + "image_path": "b862b657f4b02ecc5bb892a1e056789aead16e4df4bc58aa61d011023028480c.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "content": "where LN denotes the layer normalization [2] and MLP is the multi-layer perception consisting of two fully connected" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7249" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 95 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 95 + ], + "type": "text", + "content": "layers with a GELU [15] activation function. MHA is the multi-head attention that can be formulated as" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 58, + 99, + 287, + 151 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 99, + 287, + 151 + ], + "spans": [ + { + "bbox": [ + 58, + 99, + 287, + 151 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\operatorname {M H A} (\\boldsymbol {X}, \\boldsymbol {Y}) = \\operatorname {C a t} ([ \\operatorname {A t t} _ {m} (\\boldsymbol {X}, \\boldsymbol {Y}) V _ {m} (\\boldsymbol {Y}) ] _ {m = 1} ^ {M}), \\quad (6) \\\\ \\operatorname {A t t} _ {m}, (\\boldsymbol {X}, \\boldsymbol {Y}) = \\operatorname {S o f t m a x} \\left(\\frac {Q _ {m} (\\boldsymbol {X}) K _ {m} (\\boldsymbol {Y}) ^ {\\top}}{\\sqrt {C / M}}\\right), \\tag {7} \\\\ \\end{array}", + "image_path": "ce97289a7d238d1d1a66bcfa791a4c110f8dd87addab072dd90949e895a925ca.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 158, + 288, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 158, + 288, + 277 + ], + "spans": [ + { + "bbox": [ + 47, + 158, + 288, + 277 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 158, + 288, + 277 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 47, + 158, + 288, + 277 + ], + "type": "text", + "content": " is the number of used attention heads. The result of each head (with the shape of " + }, + { + "bbox": [ + 47, + 158, + 288, + 277 + ], + "type": "inline_equation", + "content": "N_{x} \\times C / M" + }, + { + "bbox": [ + 47, + 158, + 288, + 277 + ], + "type": "text", + "content": ") is obtained via the matrix multiplication between " + }, + { + "bbox": [ + 47, + 158, + 288, + 277 + ], + "type": "inline_equation", + "content": "\\mathrm{Att}_m(\\mathbf{X}, \\mathbf{Y}) \\in \\mathbb{R}^{N_x \\times N_y}" + }, + { + "bbox": [ + 47, + 158, + 288, + 277 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 158, + 288, + 277 + ], + "type": "inline_equation", + "content": "V_m(\\mathbf{Y}) \\in \\mathbb{R}^{N_y \\times C / M}" + }, + { + "bbox": [ + 47, + 158, + 288, + 277 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 47, + 158, + 288, + 277 + ], + "type": "inline_equation", + "content": "\\mathrm{Att}_m(\\mathbf{X}, \\mathbf{Y})" + }, + { + "bbox": [ + 47, + 158, + 288, + 277 + ], + "type": "text", + "content": " is the attention matrix calculated in (7). Here " + }, + { + "bbox": [ + 47, + 158, + 288, + 277 + ], + "type": "inline_equation", + "content": "Q_m(\\cdot)" + }, + { + "bbox": [ + 47, + 158, + 288, + 277 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 158, + 288, + 277 + ], + "type": "inline_equation", + "content": "K_m(\\cdot)" + }, + { + "bbox": [ + 47, + 158, + 288, + 277 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 158, + 288, + 277 + ], + "type": "inline_equation", + "content": "V_m(\\cdot)" + }, + { + "bbox": [ + 47, + 158, + 288, + 277 + ], + "type": "text", + "content": " are the query, key, and value embedding functions in the " + }, + { + "bbox": [ + 47, + 158, + 288, + 277 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 47, + 158, + 288, + 277 + ], + "type": "text", + "content": "th head, respectively, and project corresponding tensors from " + }, + { + "bbox": [ + 47, + 158, + 288, + 277 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 47, + 158, + 288, + 277 + ], + "type": "text", + "content": " channels to " + }, + { + "bbox": [ + 47, + 158, + 288, + 277 + ], + "type": "inline_equation", + "content": "C / M" + }, + { + "bbox": [ + 47, + 158, + 288, + 277 + ], + "type": "text", + "content": " channels. Finally, " + }, + { + "bbox": [ + 47, + 158, + 288, + 277 + ], + "type": "inline_equation", + "content": "\\mathrm{MHA}(\\mathbf{X}, \\mathbf{Y}) \\in \\mathbb{R}^{N_x \\times C}" + }, + { + "bbox": [ + 47, + 158, + 288, + 277 + ], + "type": "text", + "content": " can be obtained by concatenating (Cat) the results of " + }, + { + "bbox": [ + 47, + 158, + 288, + 277 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 47, + 158, + 288, + 277 + ], + "type": "text", + "content": " heads along the channel dimension." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 281, + 124, + 292 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 281, + 124, + 292 + ], + "spans": [ + { + "bbox": [ + 47, + 281, + 124, + 292 + ], + "type": "text", + "content": "3.2.3 Prediction" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 297, + 287, + 367 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 297, + 287, + 367 + ], + "spans": [ + { + "bbox": [ + 47, + 297, + 287, + 367 + ], + "type": "text", + "content": "After performing the token construction five times on each image, we collect the final tokens of all images, i.e. " + }, + { + "bbox": [ + 47, + 297, + 287, + 367 + ], + "type": "inline_equation", + "content": "T_5^c, T_5^b \\in \\mathbb{R}^{N \\times 1 \\times C}" + }, + { + "bbox": [ + 47, + 297, + 287, + 367 + ], + "type": "text", + "content": ". Then, we use the output of the first sub-path, i.e. the segmentation feature " + }, + { + "bbox": [ + 47, + 297, + 287, + 367 + ], + "type": "inline_equation", + "content": "F_5^d" + }, + { + "bbox": [ + 47, + 297, + 287, + 367 + ], + "type": "text", + "content": ", to generate the final predictions via the sigmoid matrix multiplication, formulated as" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 80, + 370, + 287, + 386 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 370, + 287, + 386 + ], + "spans": [ + { + "bbox": [ + 80, + 370, + 287, + 386 + ], + "type": "interline_equation", + "content": "\\boldsymbol {P} ^ {c} = \\mathcal {P} \\left(\\boldsymbol {T} _ {5} ^ {c}, \\boldsymbol {F} _ {5} ^ {d}\\right) = \\operatorname {S i g m o i d} \\left(\\boldsymbol {T} _ {5} ^ {c} \\left(\\boldsymbol {F} _ {5} ^ {d}\\right) ^ {\\top}\\right), \\tag {8}", + "image_path": "f79c87e56825ad9a8dda23bd901071ef5bc250f49132ec42c8021b8a232de649.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 82, + 388, + 287, + 403 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 388, + 287, + 403 + ], + "spans": [ + { + "bbox": [ + 82, + 388, + 287, + 403 + ], + "type": "interline_equation", + "content": "\\boldsymbol {P} ^ {b} = \\mathcal {P} (\\boldsymbol {T} _ {5} ^ {b}, \\boldsymbol {F} _ {5} ^ {d}) = \\operatorname {S i g m o i d} (\\boldsymbol {T} _ {5} ^ {b} (\\boldsymbol {F} _ {5} ^ {d}) ^ {\\top}), \\qquad (9)", + "image_path": "8d213cc2f994f82a52933fd0fb8ef889cb72ef10e5a1bfbfe002b5968e377999.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 406, + 287, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 406, + 287, + 431 + ], + "spans": [ + { + "bbox": [ + 47, + 406, + 287, + 431 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 406, + 287, + 431 + ], + "type": "inline_equation", + "content": "P^c, P^b \\in \\mathbb{R}^{N \\times 1 \\times H \\times W}" + }, + { + "bbox": [ + 47, + 406, + 287, + 431 + ], + "type": "text", + "content": " are the segmentation results of co-salient objects and BG regions, respectively." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 438, + 204, + 451 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 438, + 204, + 451 + ], + "spans": [ + { + "bbox": [ + 47, + 438, + 204, + 451 + ], + "type": "text", + "content": "3.3. Our Improvements for DMT" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 457, + 207, + 469 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 457, + 207, + 469 + ], + "spans": [ + { + "bbox": [ + 47, + 457, + 207, + 469 + ], + "type": "text", + "content": "3.3.1 Region-to-Region Correlation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 473, + 287, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 473, + 287, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 473, + 287, + 567 + ], + "type": "text", + "content": "In the first sub-path, the original FPN individually processes each image and lacks the inter-image correlation modeling, which is crucial for CoSOD. However, straightforward P2P correlation is computationally prohibitive for large feature maps and multiple images. To this end, we consider modeling correlations among images in an economical way, thus proposing our R2R module, which uses region-level features instead of pixel-level features to compute correlations." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 567, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 567, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 567, + 287, + 653 + ], + "type": "text", + "content": "Concretely, when given the features " + }, + { + "bbox": [ + 46, + 567, + 287, + 653 + ], + "type": "inline_equation", + "content": "\\pmb{F}_j^d \\in \\mathbb{R}^{N \\times H_j \\times W_j \\times C}" + }, + { + "bbox": [ + 46, + 567, + 287, + 653 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 46, + 567, + 287, + 653 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 567, + 287, + 653 + ], + "type": "text", + "content": " relevant images from the " + }, + { + "bbox": [ + 46, + 567, + 287, + 653 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 567, + 287, + 653 + ], + "type": "text", + "content": "th decoder layer, we first adopt a transformation " + }, + { + "bbox": [ + 46, + 567, + 287, + 653 + ], + "type": "inline_equation", + "content": "\\mathbb{R}_1" + }, + { + "bbox": [ + 46, + 567, + 287, + 653 + ], + "type": "text", + "content": " to divide the " + }, + { + "bbox": [ + 46, + 567, + 287, + 653 + ], + "type": "inline_equation", + "content": "H_j \\times W_j" + }, + { + "bbox": [ + 46, + 567, + 287, + 653 + ], + "type": "text", + "content": " feature maps into " + }, + { + "bbox": [ + 46, + 567, + 287, + 653 + ], + "type": "inline_equation", + "content": "K \\times K" + }, + { + "bbox": [ + 46, + 567, + 287, + 653 + ], + "type": "text", + "content": " local regions and use max-pooling to pick up the most representative feature for representing each local region. As a result, we can obtain the region-level query with shape " + }, + { + "bbox": [ + 46, + 567, + 287, + 653 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{N \\times K \\times K \\times C}" + }, + { + "bbox": [ + 46, + 567, + 287, + 653 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "content": "Then, we generate multi-scale region-level key and value via another transformation " + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{R}_2" + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "content": ", which consists of three adaptive max-pooling operations with the output spatial sizes of " + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "inline_equation", + "content": "6 \\times 6" + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "content": ", respectively. The three pooled features are finally flattened and concatenated to generate" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 72, + 544, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 544, + 95 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 544, + 95 + ], + "type": "text", + "content": "the key and value with shape " + }, + { + "bbox": [ + 305, + 72, + 544, + 95 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{N\\times 46\\times C}" + }, + { + "bbox": [ + 305, + 72, + 544, + 95 + ], + "type": "text", + "content": ", encoding multiscale robust region information." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 96, + 544, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 96, + 544, + 144 + ], + "spans": [ + { + "bbox": [ + 305, + 96, + 544, + 144 + ], + "type": "text", + "content": "Next, we perform the R2R inter-image correlation among the region-level query, key, and value via the transformer operation (3), thus obtaining the enhanced features with the region-wise correlation." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 144, + 545, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 144, + 545, + 217 + ], + "spans": [ + { + "bbox": [ + 305, + 144, + 545, + 217 + ], + "type": "text", + "content": "Finally, we upsample the enhanced features to the original resolution " + }, + { + "bbox": [ + 305, + 144, + 545, + 217 + ], + "type": "inline_equation", + "content": "H_{j} \\times W_{j}" + }, + { + "bbox": [ + 305, + 144, + 545, + 217 + ], + "type": "text", + "content": " via the nearest interpolation, denoted as " + }, + { + "bbox": [ + 305, + 144, + 545, + 217 + ], + "type": "inline_equation", + "content": "\\mathbf{R}_1^{-1}" + }, + { + "bbox": [ + 305, + 144, + 545, + 217 + ], + "type": "text", + "content": ". A residual connection is also used to add the original features. Thus, the region correlation results are diffused to the corresponding internal pixels in each local region. The whole process of R2R on " + }, + { + "bbox": [ + 305, + 144, + 545, + 217 + ], + "type": "inline_equation", + "content": "\\pmb{F}_{j}^{d}" + }, + { + "bbox": [ + 305, + 144, + 545, + 217 + ], + "type": "text", + "content": " is formulated as" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 323, + 219, + 544, + 235 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 219, + 544, + 235 + ], + "spans": [ + { + "bbox": [ + 323, + 219, + 544, + 235 + ], + "type": "interline_equation", + "content": "\\boldsymbol {F} _ {j} ^ {d r} = \\boldsymbol {F} _ {j} ^ {d} + \\mathrm {R} _ {1} ^ {- 1} (\\operatorname {T r a n s} \\left(\\mathrm {R} _ {1} \\left(\\boldsymbol {F} _ {j} ^ {d}\\right), \\mathrm {R} _ {2} \\left(\\boldsymbol {F} _ {j} ^ {d}\\right)\\right)). \\tag {10}", + "image_path": "10b49da93222d66b5e1e6f97359199f7b3207089815d587247f2c6384269fac0.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 239, + 531, + 251 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 239, + 531, + 251 + ], + "spans": [ + { + "bbox": [ + 306, + 239, + 531, + 251 + ], + "type": "text", + "content": "3.3.2 Contrast-induced Pixel-to-Token Correlation" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 255, + 545, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 255, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 304, + 255, + 545, + 361 + ], + "type": "text", + "content": "In the second sub-path, the original P2T module uses a transformer operation in (2) to mine relations between the two types of tokens in a data-driven way, while ignoring explicit CoSOD cues, especially the crucial contrast modeling between co-saliency and BG regions. To enhance the discriminability between the tokens, we explicitly model the contrast relation with our proposed CtP2T module, which modifies the transformer layer in (1) and the remaining part keeps the same as P2T." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 363, + 545, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 363, + 545, + 495 + ], + "spans": [ + { + "bbox": [ + 305, + 363, + 545, + 495 + ], + "type": "text", + "content": "Overall, we modify the multi-head attention (denoted as " + }, + { + "bbox": [ + 305, + 363, + 545, + 495 + ], + "type": "inline_equation", + "content": "\\mathrm{MHA}^{\\ast}" + }, + { + "bbox": [ + 305, + 363, + 545, + 495 + ], + "type": "text", + "content": ") and propose a contrast-induced channel attention (CCA) mechanism. The basic idea is to suppress the channels that are not contrastive enough in the generated co-saliency and BG tokens. The contrast is modeled as the opposite of the channel similarity between the two types of tokens, which can be calculated via channel correlation. For brevity's sake, we slightly abuse the notation and use " + }, + { + "bbox": [ + 305, + 363, + 545, + 495 + ], + "type": "inline_equation", + "content": "\\hat{T}, T \\in \\mathbb{R}^{2 \\times C}" + }, + { + "bbox": [ + 305, + 363, + 545, + 495 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 363, + 545, + 495 + ], + "type": "inline_equation", + "content": "F \\in \\mathbb{R}^{H_0 W_0 \\times C}" + }, + { + "bbox": [ + 305, + 363, + 545, + 495 + ], + "type": "text", + "content": " as shorthands for " + }, + { + "bbox": [ + 305, + 363, + 545, + 495 + ], + "type": "inline_equation", + "content": "\\hat{T}_{i,j}" + }, + { + "bbox": [ + 305, + 363, + 545, + 495 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 363, + 545, + 495 + ], + "type": "inline_equation", + "content": "T_{i,j-1}" + }, + { + "bbox": [ + 305, + 363, + 545, + 495 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 363, + 545, + 495 + ], + "type": "inline_equation", + "content": "\\hat{F}_i^e" + }, + { + "bbox": [ + 305, + 363, + 545, + 495 + ], + "type": "text", + "content": " in (1), respectively. Then, (1) can be modified for our CtP2T as below:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 341, + 502, + 544, + 531 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 341, + 502, + 544, + 531 + ], + "spans": [ + { + "bbox": [ + 341, + 502, + 544, + 531 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\hat {\\boldsymbol {T}} = \\operatorname {T r a n s} ^ {*} (\\boldsymbol {T}, \\boldsymbol {F}) \\\\ = \\operatorname {r M L P} (\\boldsymbol {T} + \\operatorname {C C A} (\\operatorname {M H A} ^ {*} (\\boldsymbol {T}, \\boldsymbol {F}))). \\tag {11} \\\\ \\end{array}", + "image_path": "b04489927f759bd7566f6294e50c6070d13ce15d601572717c295acb2a6d6489.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 540, + 544, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 540, + 544, + 563 + ], + "spans": [ + { + "bbox": [ + 305, + 540, + 544, + 563 + ], + "type": "text", + "content": "Next, we introduce " + }, + { + "bbox": [ + 305, + 540, + 544, + 563 + ], + "type": "inline_equation", + "content": "\\mathrm{MHA}^*" + }, + { + "bbox": [ + 305, + 540, + 544, + 563 + ], + "type": "text", + "content": " and CCA as shown in Figure 2. The LN operations are omitted for expression convenience." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 570, + 545, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 677 + ], + "type": "text", + "content": "Modified Multi-Head Attention. To generate co-saliency and BG tokens that can be used for calculating their channel similarity, we make our " + }, + { + "bbox": [ + 304, + 570, + 545, + 677 + ], + "type": "inline_equation", + "content": "\\mathrm{MHA}^*" + }, + { + "bbox": [ + 304, + 570, + 545, + 677 + ], + "type": "text", + "content": " able to generate tokens with multiple heads. Concretely, we first replace the original " + }, + { + "bbox": [ + 304, + 570, + 545, + 677 + ], + "type": "inline_equation", + "content": "V_{m}" + }, + { + "bbox": [ + 304, + 570, + 545, + 677 + ], + "type": "text", + "content": " in (6) with " + }, + { + "bbox": [ + 304, + 570, + 545, + 677 + ], + "type": "inline_equation", + "content": "V_{m}^{*}" + }, + { + "bbox": [ + 304, + 570, + 545, + 677 + ], + "type": "text", + "content": " that embeds " + }, + { + "bbox": [ + 304, + 570, + 545, + 677 + ], + "type": "inline_equation", + "content": "\\pmb{F}" + }, + { + "bbox": [ + 304, + 570, + 545, + 677 + ], + "type": "text", + "content": " to the identical channel number " + }, + { + "bbox": [ + 304, + 570, + 545, + 677 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 570, + 545, + 677 + ], + "type": "text", + "content": ". Thus, the shape of each head's result becomes " + }, + { + "bbox": [ + 304, + 570, + 545, + 677 + ], + "type": "inline_equation", + "content": "2\\times C" + }, + { + "bbox": [ + 304, + 570, + 545, + 677 + ], + "type": "text", + "content": " instead of " + }, + { + "bbox": [ + 304, + 570, + 545, + 677 + ], + "type": "inline_equation", + "content": "2\\times C / M" + }, + { + "bbox": [ + 304, + 570, + 545, + 677 + ], + "type": "text", + "content": ". Next, we stack the results of " + }, + { + "bbox": [ + 304, + 570, + 545, + 677 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 570, + 545, + 677 + ], + "type": "text", + "content": " heads to produce the output of " + }, + { + "bbox": [ + 304, + 570, + 545, + 677 + ], + "type": "inline_equation", + "content": "\\mathrm{MHA}^*" + }, + { + "bbox": [ + 304, + 570, + 545, + 677 + ], + "type": "text", + "content": ". The whole process can be formulated as" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 339, + 685, + 527, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 339, + 685, + 527, + 715 + ], + "spans": [ + { + "bbox": [ + 339, + 685, + 527, + 715 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\boldsymbol {T} _ {M} = \\operatorname {M H A} ^ {*} (\\boldsymbol {T}, \\boldsymbol {F}) \\\\ = \\operatorname {S t a c k} \\left(\\left[ \\operatorname {A t t} _ {m} (\\boldsymbol {T}, \\boldsymbol {F}) V _ {m} ^ {*} (\\boldsymbol {F}) \\right] _ {m = 1} ^ {M}\\right). \\\\ \\end{array}", + "image_path": "34a78ebc3fb097d2e2ff278030d3049726c485a20249b1ee14c2a6e3db96a6b3.jpg" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7250" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 81, + 286, + 241 + ], + "blocks": [ + { + "bbox": [ + 59, + 71, + 266, + 79 + ], + "lines": [ + { + "bbox": [ + 59, + 71, + 266, + 79 + ], + "spans": [ + { + "bbox": [ + 59, + 71, + 266, + 79 + ], + "type": "text", + "content": "Modified Multi-Head Attention Contrast-induced Channel Attention" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 49, + 81, + 286, + 241 + ], + "lines": [ + { + "bbox": [ + 49, + 81, + 286, + 241 + ], + "spans": [ + { + "bbox": [ + 49, + 81, + 286, + 241 + ], + "type": "image", + "image_path": "e97107c3e9edef4750840d250fa3ce0f7ac5886cb217c45ede475ace6e732e8c.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 243, + 287, + 287 + ], + "lines": [ + { + "bbox": [ + 47, + 243, + 287, + 287 + ], + "spans": [ + { + "bbox": [ + 47, + 243, + 287, + 287 + ], + "type": "text", + "content": "Figure 2. Diagram of MHA* and CCA. We first generate multihead tokens " + }, + { + "bbox": [ + 47, + 243, + 287, + 287 + ], + "type": "inline_equation", + "content": "T_{M}^{c}" + }, + { + "bbox": [ + 47, + 243, + 287, + 287 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 243, + 287, + 287 + ], + "type": "inline_equation", + "content": "T_{M}^{b}" + }, + { + "bbox": [ + 47, + 243, + 287, + 287 + ], + "type": "text", + "content": " via MHA*. Then, we utilize matrix multiplication of the two tokens to generate the attention weights " + }, + { + "bbox": [ + 47, + 243, + 287, + 287 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 47, + 243, + 287, + 287 + ], + "type": "text", + "content": " for modulating the token channels in CCA." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 293, + 287, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 293, + 287, + 331 + ], + "spans": [ + { + "bbox": [ + 47, + 293, + 287, + 331 + ], + "type": "inline_equation", + "content": "\\pmb{T}_{M} \\in \\mathbb{R}^{2 \\times M \\times C}" + }, + { + "bbox": [ + 47, + 293, + 287, + 331 + ], + "type": "text", + "content": " is composed of the co-saliency token and the BG token " + }, + { + "bbox": [ + 47, + 293, + 287, + 331 + ], + "type": "inline_equation", + "content": "\\pmb{T}_{M}^{c}, \\pmb{T}_{M}^{b} \\in \\mathbb{R}^{M \\times C}" + }, + { + "bbox": [ + 47, + 293, + 287, + 331 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 47, + 293, + 287, + 331 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 47, + 293, + 287, + 331 + ], + "type": "text", + "content": " heads. Next, we can compute the channel similarity based on them." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 335, + 287, + 395 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 335, + 287, + 395 + ], + "spans": [ + { + "bbox": [ + 47, + 335, + 287, + 395 + ], + "type": "text", + "content": "Contrast-induced Channel Attention. Given the multihead tokens " + }, + { + "bbox": [ + 47, + 335, + 287, + 395 + ], + "type": "inline_equation", + "content": "T_{M}^{c}" + }, + { + "bbox": [ + 47, + 335, + 287, + 395 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 335, + 287, + 395 + ], + "type": "inline_equation", + "content": "T_{M}^{b}" + }, + { + "bbox": [ + 47, + 335, + 287, + 395 + ], + "type": "text", + "content": ", we generate channel attention " + }, + { + "bbox": [ + 47, + 335, + 287, + 395 + ], + "type": "inline_equation", + "content": "W \\in \\mathbb{R}^{2 \\times 1 \\times C}" + }, + { + "bbox": [ + 47, + 335, + 287, + 395 + ], + "type": "text", + "content": " to suppress the token channels with strong mutual similarities since they cannot clearly distinguish between co-saliency and BG." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 396, + 287, + 454 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 396, + 287, + 454 + ], + "spans": [ + { + "bbox": [ + 47, + 396, + 287, + 454 + ], + "type": "text", + "content": "First, we compute a " + }, + { + "bbox": [ + 47, + 396, + 287, + 454 + ], + "type": "inline_equation", + "content": "C \\times C" + }, + { + "bbox": [ + 47, + 396, + 287, + 454 + ], + "type": "text", + "content": " channel similarity matrix between " + }, + { + "bbox": [ + 47, + 396, + 287, + 454 + ], + "type": "inline_equation", + "content": "\\pmb{T}_M^c" + }, + { + "bbox": [ + 47, + 396, + 287, + 454 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 396, + 287, + 454 + ], + "type": "inline_equation", + "content": "\\pmb{T}_M^b" + }, + { + "bbox": [ + 47, + 396, + 287, + 454 + ], + "type": "text", + "content": " via matrix multiplication. Then, the channel similarity of each token to the other token can be computed as the average along the channel dimension of the other token. The whole process can be denoted as" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 118, + 455, + 286, + 469 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 118, + 455, + 286, + 469 + ], + "spans": [ + { + "bbox": [ + 118, + 455, + 286, + 469 + ], + "type": "interline_equation", + "content": "\\boldsymbol {S} ^ {c} = \\operatorname {A v g} \\left(\\boldsymbol {T} _ {M} ^ {c} \\top \\boldsymbol {T} _ {M} ^ {b}\\right), \\tag {13}", + "image_path": "a444c7f37865abf751e39310814ff5a0936ba23e9c7840dc4497a8c47e9770df.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 120, + 469, + 286, + 485 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 120, + 469, + 286, + 485 + ], + "spans": [ + { + "bbox": [ + 120, + 469, + 286, + 485 + ], + "type": "interline_equation", + "content": "\\boldsymbol {S} ^ {b} = \\operatorname {A v g} \\left(\\boldsymbol {T} _ {M} ^ {b} ^ {\\top} \\boldsymbol {T} _ {M} ^ {c}\\right), \\tag {14}", + "image_path": "f48f5ab1a6055b5019c791792684f124ea6dad4aeff86c4a8db0946ed7c306c3.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 487, + 286, + 523 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 487, + 286, + 523 + ], + "spans": [ + { + "bbox": [ + 47, + 487, + 286, + 523 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 487, + 286, + 523 + ], + "type": "inline_equation", + "content": "S^c, S^b \\in \\mathbb{R}^{C \\times 1}" + }, + { + "bbox": [ + 47, + 487, + 286, + 523 + ], + "type": "text", + "content": ", representing how similar each channel is to the channels of the other token. Avg means calculating the average along the second dimension." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 523, + 286, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 523, + 286, + 559 + ], + "spans": [ + { + "bbox": [ + 47, + 523, + 286, + 559 + ], + "type": "text", + "content": "Next, we multiply " + }, + { + "bbox": [ + 47, + 523, + 286, + 559 + ], + "type": "inline_equation", + "content": "S^c" + }, + { + "bbox": [ + 47, + 523, + 286, + 559 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 523, + 286, + 559 + ], + "type": "inline_equation", + "content": "S^b" + }, + { + "bbox": [ + 47, + 523, + 286, + 559 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 47, + 523, + 286, + 559 + ], + "type": "inline_equation", + "content": "-1" + }, + { + "bbox": [ + 47, + 523, + 286, + 559 + ], + "type": "text", + "content": " to turn the similarity measurements into the contrast scores and then compute the channel attention " + }, + { + "bbox": [ + 47, + 523, + 286, + 559 + ], + "type": "inline_equation", + "content": "\\mathbf{W} \\in \\mathbb{R}^{2 \\times 1 \\times C}" + }, + { + "bbox": [ + 47, + 523, + 286, + 559 + ], + "type": "text", + "content": " via" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 90, + 562, + 287, + 595 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 90, + 562, + 287, + 595 + ], + "spans": [ + { + "bbox": [ + 90, + 562, + 287, + 595 + ], + "type": "interline_equation", + "content": "\\boldsymbol {W} = \\text {S i g m o i d} \\left(\\alpha \\left[ \\begin{array}{c} - \\boldsymbol {S} ^ {c ^ {\\top}} \\\\ - \\boldsymbol {S} ^ {b ^ {\\top}} \\end{array} \\right] + \\beta\\right). \\tag {15}", + "image_path": "4bc41dbe6ab8bfa3c11caaac5439bb7b376d0c6b403bf3502d5a1473ab48563f.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 600, + 287, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 600, + 287, + 635 + ], + "spans": [ + { + "bbox": [ + 47, + 600, + 287, + 635 + ], + "type": "text", + "content": "Here we use a learnable linear projection with parameters " + }, + { + "bbox": [ + 47, + 600, + 287, + 635 + ], + "type": "inline_equation", + "content": "\\alpha, \\beta" + }, + { + "bbox": [ + 47, + 600, + 287, + 635 + ], + "type": "text", + "content": " on each channel of the stacked contrast scores to fit them for the sigmoid activation." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 635, + 287, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 635, + 287, + 694 + ], + "spans": [ + { + "bbox": [ + 47, + 635, + 287, + 694 + ], + "type": "text", + "content": "Once obtained " + }, + { + "bbox": [ + 47, + 635, + 287, + 694 + ], + "type": "inline_equation", + "content": "\\mathbf{W}" + }, + { + "bbox": [ + 47, + 635, + 287, + 694 + ], + "type": "text", + "content": ", we adopt the element-wise multiplication between " + }, + { + "bbox": [ + 47, + 635, + 287, + 694 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_M" + }, + { + "bbox": [ + 47, + 635, + 287, + 694 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 635, + 287, + 694 + ], + "type": "inline_equation", + "content": "\\mathbf{W}" + }, + { + "bbox": [ + 47, + 635, + 287, + 694 + ], + "type": "text", + "content": " to modulate the token channels based on their contrast and then eliminate the multi-head dimension of the tokens by averaging the head dimension and obtaining the modulated tokens:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 82, + 700, + 287, + 714 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 700, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 82, + 700, + 287, + 714 + ], + "type": "interline_equation", + "content": "\\operatorname {C C A} \\left(\\boldsymbol {T} _ {M}\\right) = \\operatorname {A v g} \\left(\\boldsymbol {W} \\odot \\boldsymbol {T} _ {M}\\right) \\in \\mathbb {R} ^ {2 \\times C}, \\tag {16}", + "image_path": "1c448088408455fe0729507cb2e891685208492d8a52768013935cd27dff92f4.jpg" + } + ] + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 308, + 72, + 542, + 186 + ], + "blocks": [ + { + "bbox": [ + 308, + 72, + 542, + 186 + ], + "lines": [ + { + "bbox": [ + 308, + 72, + 542, + 186 + ], + "spans": [ + { + "bbox": [ + 308, + 72, + 542, + 186 + ], + "type": "image", + "image_path": "8549e25ec3bae532cb3bdff0f8cad4caa4fe8915917c41529d837df39883cc24.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 188, + 545, + 232 + ], + "lines": [ + { + "bbox": [ + 305, + 188, + 545, + 232 + ], + "spans": [ + { + "bbox": [ + 305, + 188, + 545, + 232 + ], + "type": "text", + "content": "Figure 3. Diagram of our proposed TGFR module. Specifically, we first distill the co-saliency and BG features under the guidance of the two tokens. Then, we fuse them back to the original segmentation feature for discriminability enhancement." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 242, + 544, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 242, + 544, + 266 + ], + "spans": [ + { + "bbox": [ + 305, + 242, + 544, + 266 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 242, + 544, + 266 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 305, + 242, + 544, + 266 + ], + "type": "text", + "content": " means element-wise multiplication with broadcasting." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 271, + 510, + 283 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 271, + 510, + 283 + ], + "spans": [ + { + "bbox": [ + 306, + 271, + 510, + 283 + ], + "type": "text", + "content": "3.3.3 Co-saliency Token-to-Token Correlation" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 287, + 545, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 287, + 545, + 357 + ], + "spans": [ + { + "bbox": [ + 304, + 287, + 545, + 357 + ], + "type": "text", + "content": "CtP2T effectively explores the correlation between the two types of tokens within each image, but lacks explicitly modeling the inter-image relation to capture the token-wise group consistency, thus being limited for consensus mining. Therefore, we use co-saliency tokens from all images to model the consensus patterns via our CoT2T module." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 358, + 545, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 358, + 545, + 445 + ], + "spans": [ + { + "bbox": [ + 304, + 358, + 545, + 445 + ], + "type": "text", + "content": "Specifically, we first define a group token " + }, + { + "bbox": [ + 304, + 358, + 545, + 445 + ], + "type": "inline_equation", + "content": "G \\in \\mathbb{R}^{1 \\times C}" + }, + { + "bbox": [ + 304, + 358, + 545, + 445 + ], + "type": "text", + "content": " to represent the group-wise consensus information, which is randomly initialized at the first iteration step. At the " + }, + { + "bbox": [ + 304, + 358, + 545, + 445 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 304, + 358, + 545, + 445 + ], + "type": "text", + "content": "th iteration, given the last group token " + }, + { + "bbox": [ + 304, + 358, + 545, + 445 + ], + "type": "inline_equation", + "content": "G_{j-1}" + }, + { + "bbox": [ + 304, + 358, + 545, + 445 + ], + "type": "text", + "content": " and the co-saliency tokens " + }, + { + "bbox": [ + 304, + 358, + 545, + 445 + ], + "type": "inline_equation", + "content": "\\tilde{T}_j^c \\in \\mathbb{R}^{N \\times C}" + }, + { + "bbox": [ + 304, + 358, + 545, + 445 + ], + "type": "text", + "content": " from the CtP2T module, we aggregate the consensus information from all co-saliency tokens by using " + }, + { + "bbox": [ + 304, + 358, + 545, + 445 + ], + "type": "inline_equation", + "content": "\\tilde{T}_j^c" + }, + { + "bbox": [ + 304, + 358, + 545, + 445 + ], + "type": "text", + "content": " to update " + }, + { + "bbox": [ + 304, + 358, + 545, + 445 + ], + "type": "inline_equation", + "content": "G_{j-1}" + }, + { + "bbox": [ + 304, + 358, + 545, + 445 + ], + "type": "text", + "content": ", denoted as" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 373, + 449, + 545, + 464 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 373, + 449, + 545, + 464 + ], + "spans": [ + { + "bbox": [ + 373, + 449, + 545, + 464 + ], + "type": "interline_equation", + "content": "\\boldsymbol {G} _ {j} = \\operatorname {T r a n s} \\left(\\boldsymbol {G} _ {j - 1}, \\tilde {\\boldsymbol {T}} _ {j} ^ {c}\\right). \\tag {17}", + "image_path": "8f0750cdac471e8dd0910d3728799fc294343c5d1ec3c877da46a4f49ae7e223.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 470, + 544, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 470, + 544, + 495 + ], + "spans": [ + { + "bbox": [ + 305, + 470, + 544, + 495 + ], + "type": "text", + "content": "Finally, we distribute the aggregated consensus cues back to " + }, + { + "bbox": [ + 305, + 470, + 544, + 495 + ], + "type": "inline_equation", + "content": "\\tilde{T}_{j}^{c}" + }, + { + "bbox": [ + 305, + 470, + 544, + 495 + ], + "type": "text", + "content": " and obtain the final co-saliency tokens " + }, + { + "bbox": [ + 305, + 470, + 544, + 495 + ], + "type": "inline_equation", + "content": "T_{j}^{c}" + }, + { + "bbox": [ + 305, + 470, + 544, + 495 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 378, + 498, + 545, + 514 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 378, + 498, + 545, + 514 + ], + "spans": [ + { + "bbox": [ + 378, + 498, + 545, + 514 + ], + "type": "interline_equation", + "content": "\\boldsymbol {T} _ {j} ^ {c} = \\operatorname {T r a n s} \\left(\\tilde {\\boldsymbol {T}} _ {j} ^ {c}, \\boldsymbol {G} _ {j}\\right). \\tag {18}", + "image_path": "5cbdb2a5e46b84ad157eeeb8efe7742f635a831f62302b736c22ac12d47af733.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 522, + 484, + 533 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 522, + 484, + 533 + ], + "spans": [ + { + "bbox": [ + 306, + 522, + 484, + 533 + ], + "type": "text", + "content": "3.3.4 Token-guided Feature Refinement" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 537, + 545, + 670 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 537, + 545, + 670 + ], + "spans": [ + { + "bbox": [ + 304, + 537, + 545, + 670 + ], + "type": "text", + "content": "The vanilla MaskFormer only transforms the information from the segmentation features to the tokens, hindering their complementary learning. To this end, we propose our TGFR module to improve the discriminability of the segmentation features via the detection cues of the tokens. As shown in Figure 3, TGFR consists of two processes, i.e. distillation and refusion. The distillation process is designed to distill the co-saliency and BG features from the segmentation feature under the guidance of the corresponding tokens. The refusion process is to fuse the distilled features back to the segmentation feature to enhance its discriminability." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 305, + 675, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 675, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 675, + 545, + 715 + ], + "type": "text", + "content": "Distillation. For image " + }, + { + "bbox": [ + 305, + 675, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_i" + }, + { + "bbox": [ + 305, + 675, + 545, + 715 + ], + "type": "text", + "content": " at the " + }, + { + "bbox": [ + 305, + 675, + 545, + 715 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 305, + 675, + 545, + 715 + ], + "type": "text", + "content": "th iteration, we have the final co-saliency token " + }, + { + "bbox": [ + 305, + 675, + 545, + 715 + ], + "type": "inline_equation", + "content": "T_{i,j}^{c} \\in \\mathbb{R}^{1 \\times C}" + }, + { + "bbox": [ + 305, + 675, + 545, + 715 + ], + "type": "text", + "content": " generated from CoT2T and the final BG token " + }, + { + "bbox": [ + 305, + 675, + 545, + 715 + ], + "type": "inline_equation", + "content": "T_{i,j}^{b} \\in \\mathbb{R}^{1 \\times C}" + }, + { + "bbox": [ + 305, + 675, + 545, + 715 + ], + "type": "text", + "content": " outputted by" + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "7251" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 71, + 289, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 71, + 289, + 144 + ], + "spans": [ + { + "bbox": [ + 46, + 71, + 289, + 144 + ], + "type": "text", + "content": "CtP2T, and the segmentation feature " + }, + { + "bbox": [ + 46, + 71, + 289, + 144 + ], + "type": "inline_equation", + "content": "F_{i,j}^{dr}\\in \\mathbb{R}^{H_j\\times W_j\\times C}" + }, + { + "bbox": [ + 46, + 71, + 289, + 144 + ], + "type": "text", + "content": " enhanced by R2R. We first compute two attention maps " + }, + { + "bbox": [ + 46, + 71, + 289, + 144 + ], + "type": "inline_equation", + "content": "A_{i,j}^{c}\\in \\mathbb{R}^{H_{j}\\times W_{j}\\times 1}" + }, + { + "bbox": [ + 46, + 71, + 289, + 144 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 71, + 289, + 144 + ], + "type": "inline_equation", + "content": "A_{i,j}^{b}\\in \\mathbb{R}^{H_{j}\\times W_{j}\\times 1}" + }, + { + "bbox": [ + 46, + 71, + 289, + 144 + ], + "type": "text", + "content": " via performing the matrix multiplication between the segmentation feature and the tokens and then adopting a softmax normalization on the spatial dimension, formulated as" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 91, + 145, + 287, + 162 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 145, + 287, + 162 + ], + "spans": [ + { + "bbox": [ + 91, + 145, + 287, + 162 + ], + "type": "interline_equation", + "content": "\\boldsymbol {A} _ {i, j} ^ {c} = \\operatorname {S o f t m a x} \\left(\\boldsymbol {F} _ {i, j} ^ {d r} \\left(\\boldsymbol {T} _ {i, j} ^ {c}\\right) ^ {\\top} / \\sqrt {C}\\right), \\tag {19}", + "image_path": "41ed3b687838304299376638b8b55c43fafd62fa0468d36ef2f09f47e46afb6f.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 91, + 164, + 287, + 182 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 164, + 287, + 182 + ], + "spans": [ + { + "bbox": [ + 91, + 164, + 287, + 182 + ], + "type": "interline_equation", + "content": "\\boldsymbol {A} _ {i, j} ^ {b} = \\operatorname {S o f t m a x} \\left(\\boldsymbol {F} _ {i, j} ^ {d r} \\left(\\boldsymbol {T} _ {i, j} ^ {b}\\right) ^ {\\top} / \\sqrt {C}\\right). \\tag {20}", + "image_path": "56a3e8175e69aa15a2c6c7449eb15333d5b2df55fb19f149b454aa9c46766f0e.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 184, + 287, + 220 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 184, + 287, + 220 + ], + "spans": [ + { + "bbox": [ + 46, + 184, + 287, + 220 + ], + "type": "text", + "content": "Next, we adopt the computed attention maps to distill the detection features from the segmentation feature via matrix multiplication, denoted as" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 122, + 222, + 287, + 238 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 122, + 222, + 287, + 238 + ], + "spans": [ + { + "bbox": [ + 122, + 222, + 287, + 238 + ], + "type": "interline_equation", + "content": "\\boldsymbol {D} _ {i, j} ^ {c} = \\left(\\boldsymbol {A} _ {i, j} ^ {c}\\right) ^ {\\top} \\boldsymbol {F} _ {i, j} ^ {d r}, \\tag {21}", + "image_path": "c098317860ee42b26a1e10191b498a9dcdf07c97309830c1c775958a6e047483.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 123, + 241, + 287, + 258 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 241, + 287, + 258 + ], + "spans": [ + { + "bbox": [ + 123, + 241, + 287, + 258 + ], + "type": "interline_equation", + "content": "\\boldsymbol {D} _ {i, j} ^ {b} = \\left(\\boldsymbol {A} _ {i, j} ^ {b}\\right) ^ {\\top} \\boldsymbol {F} _ {i, j} ^ {d r}, \\tag {22}", + "image_path": "db75c7e59a8b97f222671c8344d0f2dc63f22b2cc6716e713d52ae8badfa4709.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 262, + 287, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 262, + 287, + 287 + ], + "spans": [ + { + "bbox": [ + 46, + 262, + 287, + 287 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 262, + 287, + 287 + ], + "type": "inline_equation", + "content": "D_{i,j}^{c}, D_{i,j}^{b} \\in \\mathbb{R}^{1 \\times C}" + }, + { + "bbox": [ + 46, + 262, + 287, + 287 + ], + "type": "text", + "content": " is the distilled features for co-saliency and BG, respectively." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 292, + 287, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 292, + 287, + 365 + ], + "spans": [ + { + "bbox": [ + 46, + 292, + 287, + 365 + ], + "type": "text", + "content": "Refusion. After producing " + }, + { + "bbox": [ + 46, + 292, + 287, + 365 + ], + "type": "inline_equation", + "content": "D_{i,j}^{c}" + }, + { + "bbox": [ + 46, + 292, + 287, + 365 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 292, + 287, + 365 + ], + "type": "inline_equation", + "content": "D_{i,j}^{b}" + }, + { + "bbox": [ + 46, + 292, + 287, + 365 + ], + "type": "text", + "content": ", we conduct the refusion process to fuse them back to " + }, + { + "bbox": [ + 46, + 292, + 287, + 365 + ], + "type": "inline_equation", + "content": "F_{i,j}^{dr}" + }, + { + "bbox": [ + 46, + 292, + 287, + 365 + ], + "type": "text", + "content": " sequentially in a cascade way for activating the co-saliency and BG regions in " + }, + { + "bbox": [ + 46, + 292, + 287, + 365 + ], + "type": "inline_equation", + "content": "F_{i,j}^{dr}" + }, + { + "bbox": [ + 46, + 292, + 287, + 365 + ], + "type": "text", + "content": ". In this way, we can effectively reduce ambiguous information and enhance feature discriminability. The details can be formulated as" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 85, + 367, + 287, + 385 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 367, + 287, + 385 + ], + "spans": [ + { + "bbox": [ + 85, + 367, + 287, + 385 + ], + "type": "interline_equation", + "content": "\\hat {\\boldsymbol {F}} _ {i, j} ^ {d t} = \\operatorname {C o n v} _ {c} \\left(\\operatorname {C a t} \\left(\\left[ \\boldsymbol {F} _ {i, j} ^ {d r}, \\operatorname {E} \\left(\\boldsymbol {D} _ {i, j} ^ {c}\\right) \\right]\\right)\\right), \\tag {23}", + "image_path": "1fc1837b3edb807e14e89beb6de3ef687fd4cb5c27ea88417a85746c1aa6e4b5.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 86, + 386, + 287, + 404 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 386, + 287, + 404 + ], + "spans": [ + { + "bbox": [ + 86, + 386, + 287, + 404 + ], + "type": "interline_equation", + "content": "\\boldsymbol {F} _ {i, j} ^ {d t} = \\operatorname {C o n v} _ {b} \\left(\\operatorname {C a t} \\left(\\left[ \\hat {\\boldsymbol {F}} _ {i, j} ^ {d t}, \\mathrm {E} \\left(\\boldsymbol {D} _ {i, j} ^ {b}\\right) \\right]\\right)\\right), \\tag {24}", + "image_path": "f2c25cdd8542caa3daaff8c11a6f71ae43e2bcd770a350532a04aa75e82beb51.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 409, + 287, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 409, + 287, + 460 + ], + "spans": [ + { + "bbox": [ + 46, + 409, + 287, + 460 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 409, + 287, + 460 + ], + "type": "inline_equation", + "content": "\\operatorname{E}(*)" + }, + { + "bbox": [ + 46, + 409, + 287, + 460 + ], + "type": "text", + "content": " replicates " + }, + { + "bbox": [ + 46, + 409, + 287, + 460 + ], + "type": "inline_equation", + "content": "D_{i,j}^{c}" + }, + { + "bbox": [ + 46, + 409, + 287, + 460 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 409, + 287, + 460 + ], + "type": "inline_equation", + "content": "D_{i,j}^{b}" + }, + { + "bbox": [ + 46, + 409, + 287, + 460 + ], + "type": "text", + "content": " along the spatial dimension to the same size as " + }, + { + "bbox": [ + 46, + 409, + 287, + 460 + ], + "type": "inline_equation", + "content": "F_{i,j}^{dr}" + }, + { + "bbox": [ + 46, + 409, + 287, + 460 + ], + "type": "text", + "content": ". Then, we progressively concatenate them with " + }, + { + "bbox": [ + 46, + 409, + 287, + 460 + ], + "type": "inline_equation", + "content": "F_{i,j}^{dr}" + }, + { + "bbox": [ + 46, + 409, + 287, + 460 + ], + "type": "text", + "content": " and use a convolution layer to reduce the channel number to " + }, + { + "bbox": [ + 46, + 409, + 287, + 460 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 409, + 287, + 460 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 468, + 206, + 479 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 468, + 206, + 479 + ], + "spans": [ + { + "bbox": [ + 47, + 468, + 206, + 479 + ], + "type": "text", + "content": "3.3.5 Prediction and Loss Function" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 483, + 287, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 483, + 287, + 556 + ], + "spans": [ + { + "bbox": [ + 46, + 483, + 287, + 556 + ], + "type": "text", + "content": "In the " + }, + { + "bbox": [ + 46, + 483, + 287, + 556 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 483, + 287, + 556 + ], + "type": "text", + "content": "th iteration, after obtaining the learned co-saliency and BG tokens, i.e. " + }, + { + "bbox": [ + 46, + 483, + 287, + 556 + ], + "type": "inline_equation", + "content": "\\pmb{T}_j^c,\\pmb{T}_j^b\\in \\mathbb{R}^{N\\times 1\\times C}" + }, + { + "bbox": [ + 46, + 483, + 287, + 556 + ], + "type": "text", + "content": ", from CoT2T and CtP2T, respectively, and the improved segmentation features " + }, + { + "bbox": [ + 46, + 483, + 287, + 556 + ], + "type": "inline_equation", + "content": "\\pmb{F}_{j}^{dt}\\in \\mathbb{R}^{N\\times H_{j}\\times W_{j}\\times C}" + }, + { + "bbox": [ + 46, + 483, + 287, + 556 + ], + "type": "text", + "content": " from TGFR, we use the prediction function " + }, + { + "bbox": [ + 46, + 483, + 287, + 556 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 46, + 483, + 287, + 556 + ], + "type": "text", + "content": " in (8) to generate the co-saliency and the BG predictions, i.e. " + }, + { + "bbox": [ + 46, + 483, + 287, + 556 + ], + "type": "inline_equation", + "content": "\\pmb{P}_{j}^{c}\\pmb{P}_{j}^{b}" + }, + { + "bbox": [ + 46, + 483, + 287, + 556 + ], + "type": "text", + "content": ", as follows:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 127, + 559, + 287, + 575 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 127, + 559, + 287, + 575 + ], + "spans": [ + { + "bbox": [ + 127, + 559, + 287, + 575 + ], + "type": "interline_equation", + "content": "\\boldsymbol {P} _ {j} ^ {c} = \\mathcal {P} \\left(\\boldsymbol {T} _ {j} ^ {c}, \\boldsymbol {F} _ {j} ^ {d t}\\right), \\tag {25}", + "image_path": "d79ee17907c0d5411e665a22920f36a63a778a15f5a81f11b70f47f887a26b67.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 127, + 578, + 287, + 594 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 127, + 578, + 287, + 594 + ], + "spans": [ + { + "bbox": [ + 127, + 578, + 287, + 594 + ], + "type": "interline_equation", + "content": "\\boldsymbol {P} _ {j} ^ {b} = \\mathcal {P} \\left(\\boldsymbol {T} _ {j} ^ {b}, \\boldsymbol {F} _ {j} ^ {d t}\\right). \\tag {26}", + "image_path": "95b7a3e3fad8e3498ac57809c27b6dfea0d79ef67abd15e75b9b1377060f2754.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 597, + 287, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 597, + 287, + 651 + ], + "spans": [ + { + "bbox": [ + 46, + 597, + 287, + 651 + ], + "type": "text", + "content": "We also supervise the learning of the group token " + }, + { + "bbox": [ + 46, + 597, + 287, + 651 + ], + "type": "inline_equation", + "content": "G_{j} \\in \\mathbb{R}^{1 \\times 1 \\times C}" + }, + { + "bbox": [ + 46, + 597, + 287, + 651 + ], + "type": "text", + "content": " in CoT2T and the middle feature " + }, + { + "bbox": [ + 46, + 597, + 287, + 651 + ], + "type": "inline_equation", + "content": "\\hat{\\pmb{F}}_j^{dt} \\in \\mathbb{R}^{N \\times H_j \\times W_j \\times C}" + }, + { + "bbox": [ + 46, + 597, + 287, + 651 + ], + "type": "text", + "content": " in TGFR. Two predictions can be obtained from them, respectively:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 107, + 658, + 287, + 681 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 658, + 287, + 681 + ], + "spans": [ + { + "bbox": [ + 107, + 658, + 287, + 681 + ], + "type": "interline_equation", + "content": "\\boldsymbol {P} _ {j} ^ {g} = \\mathcal {P} (\\text {R e p e a t} (\\boldsymbol {G} _ {j}), \\boldsymbol {F} _ {j} ^ {d t}), \\tag {27}", + "image_path": "626fee404be470ab67db560e48d4f9fb754b258db6ed64a440056068dc219cf2.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 107, + 677, + 189, + 694 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 677, + 189, + 694 + ], + "spans": [ + { + "bbox": [ + 107, + 677, + 189, + 694 + ], + "type": "interline_equation", + "content": "\\boldsymbol {P} _ {j} ^ {d t} = \\mathcal {P} (\\boldsymbol {T} _ {j} ^ {c}, \\hat {\\boldsymbol {F}} _ {j} ^ {d t}),", + "image_path": "6ace9be81ec3fbbfff4b15d5206434753f291c8b942e4bb497547f3f0af1233c.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 47, + 701, + 208, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 701, + 208, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 701, + 208, + 714 + ], + "type": "text", + "content": "where Repeat is to repeat " + }, + { + "bbox": [ + 47, + 701, + 208, + 714 + ], + "type": "inline_equation", + "content": "G_{j}" + }, + { + "bbox": [ + 47, + 701, + 208, + 714 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 47, + 701, + 208, + 714 + ], + "type": "text", + "content": " times." + } + ] + } + ], + "index": 18 + }, + { + "type": "table", + "bbox": [ + 307, + 118, + 550, + 215 + ], + "blocks": [ + { + "bbox": [ + 305, + 71, + 546, + 115 + ], + "lines": [ + { + "bbox": [ + 305, + 71, + 546, + 115 + ], + "spans": [ + { + "bbox": [ + 305, + 71, + 546, + 115 + ], + "type": "text", + "content": "Table 1. Quantitative results of different settings of our proposed model. We show the results of progressively adding R2R, CtP2T, CoT2T, and TGFR on the baseline. \"Co\" and \"Bg\" mean explicitly modeling co-saliency and BG, respectively." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 118, + 550, + 215 + ], + "lines": [ + { + "bbox": [ + 307, + 118, + 550, + 215 + ], + "spans": [ + { + "bbox": [ + 307, + 118, + 550, + 215 + ], + "type": "table", + "html": "
SettingsCoCA [42]
CoBgR2RCtP2TCoT2TTGFRSm↑Eξ↑maxF↑MAE ↓
✓✓0.67510.76830.54740.1383
✓✓✓0.69450.78240.58150.1234
✓✓✓✓0.70380.78680.59840.1230
✓✓✓✓✓0.71400.78800.60030.1139
✓✓✓✓✓✓0.72460.80010.61900.1084
✓✓✓✓0.70590.79200.59960.1259
", + "image_path": "57f19a6eaa9972ca6b456c372757c9b373be0d493131adfafea112274c5c8364.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "table_body" + } + ], + "index": 20 + }, + { + "type": "image", + "bbox": [ + 307, + 220, + 547, + 304 + ], + "blocks": [ + { + "bbox": [ + 307, + 220, + 547, + 304 + ], + "lines": [ + { + "bbox": [ + 307, + 220, + 547, + 304 + ], + "spans": [ + { + "bbox": [ + 307, + 220, + 547, + 304 + ], + "type": "image", + "image_path": "1b8d5a0a9a9d5d6819e1fac1c7631adcb00acfa41851a32e264a0e90f2d1506b.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 305, + 545, + 338 + ], + "lines": [ + { + "bbox": [ + 305, + 305, + 545, + 338 + ], + "spans": [ + { + "bbox": [ + 305, + 305, + 545, + 338 + ], + "type": "text", + "content": "Figure 4. Qualitative results of different settings of our proposed model. We show the results of progressively adding the R2R, CtP2T, CoT2T, and TGFR on the baseline." + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + } + ], + "index": 21 + }, + { + "bbox": [ + 317, + 346, + 487, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 346, + 487, + 357 + ], + "spans": [ + { + "bbox": [ + 317, + 346, + 487, + 357 + ], + "type": "text", + "content": "Our total loss " + }, + { + "bbox": [ + 317, + 346, + 487, + 357 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{total}" + }, + { + "bbox": [ + 317, + 346, + 487, + 357 + ], + "type": "text", + "content": " can be formulated as" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 321, + 361, + 545, + 396 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 361, + 545, + 396 + ], + "spans": [ + { + "bbox": [ + 321, + 361, + 545, + 396 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {t o t a l}} = \\sum_ {j = 1} ^ {5} \\left(\\mathcal {L} _ {1} \\left(\\boldsymbol {P} _ {j} ^ {c}, \\boldsymbol {M} _ {j} ^ {c}\\right) + \\mathcal {L} _ {2} \\left(\\boldsymbol {P} _ {j} ^ {c}, \\boldsymbol {M} _ {j} ^ {c}\\right) + \\right. \\tag {28}", + "image_path": "86bcd97c0c696fc576b1581797d11c2f29b8194a1147495b49ed7905d542c2ee.jpg" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 318, + 398, + 517, + 418 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 398, + 517, + 418 + ], + "spans": [ + { + "bbox": [ + 318, + 398, + 517, + 418 + ], + "type": "interline_equation", + "content": "\\left. \\mathcal {L} _ {2} \\left(\\boldsymbol {P} _ {j} ^ {b}, \\boldsymbol {M} _ {j} ^ {b}\\right) + \\mathcal {L} _ {2} \\left(\\boldsymbol {P} _ {j} ^ {g}, \\boldsymbol {M} _ {j} ^ {c}\\right) + \\mathcal {L} _ {2} \\left(\\boldsymbol {P} _ {j} ^ {d t}, \\boldsymbol {M} _ {j} ^ {c}\\right)\\right),", + "image_path": "ca5bf5c6b569807ae36eb0ade56b4cfee5e7301bf0f239b977e657dcb46ab8ff.jpg" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 305, + 426, + 545, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 426, + 545, + 475 + ], + "spans": [ + { + "bbox": [ + 305, + 426, + 545, + 475 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 426, + 545, + 475 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_1" + }, + { + "bbox": [ + 305, + 426, + 545, + 475 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 426, + 545, + 475 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_2" + }, + { + "bbox": [ + 305, + 426, + 545, + 475 + ], + "type": "text", + "content": " are the IoU [16] and Binary Cross-Entropy (BCE) [7] loss, respectively. " + }, + { + "bbox": [ + 305, + 426, + 545, + 475 + ], + "type": "inline_equation", + "content": "M_j^c" + }, + { + "bbox": [ + 305, + 426, + 545, + 475 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 426, + 545, + 475 + ], + "type": "inline_equation", + "content": "M_j^b" + }, + { + "bbox": [ + 305, + 426, + 545, + 475 + ], + "type": "text", + "content": " denote the co-saliency and BG ground truths, respectively, with the spatial shapes aligned to the " + }, + { + "bbox": [ + 305, + 426, + 545, + 475 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 305, + 426, + 545, + 475 + ], + "type": "text", + "content": "th decoder layer." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 306, + 486, + 388, + 499 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 486, + 388, + 499 + ], + "spans": [ + { + "bbox": [ + 306, + 486, + 388, + 499 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 306, + 506, + 481, + 517 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 506, + 481, + 517 + ], + "spans": [ + { + "bbox": [ + 306, + 506, + 481, + 517 + ], + "type": "text", + "content": "4.1. Evaluation Datasets and Metrics" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 304, + 521, + 545, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 545, + 629 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 545, + 629 + ], + "type": "text", + "content": "We follow [12, 27, 34] to evaluate our proposed model on three CoSOD benchmark datasets. CoSal2015 [36] and CoSOD3k [11] collect 50 groups with 2015 images and 160 groups with 3316 images, respectively. CoCA [42] is the most challenging dataset and contain 1295 images of 80 groups. We employ four widely-used metrics for quantitative evaluation, i.e. Structure-measure " + }, + { + "bbox": [ + 304, + 521, + 545, + 629 + ], + "type": "inline_equation", + "content": "S_{m}" + }, + { + "bbox": [ + 304, + 521, + 545, + 629 + ], + "type": "text", + "content": " [9], Enhanced-alignment measure " + }, + { + "bbox": [ + 304, + 521, + 545, + 629 + ], + "type": "inline_equation", + "content": "E_{\\xi}" + }, + { + "bbox": [ + 304, + 521, + 545, + 629 + ], + "type": "text", + "content": " [10], Maximum F-measure (maxF) [1], and Mean Absolute Error (MAE) [6]." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 306, + 637, + 439, + 650 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 637, + 439, + 650 + ], + "spans": [ + { + "bbox": [ + 306, + 637, + 439, + 650 + ], + "type": "text", + "content": "4.2. Implementation Details" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": "We follow [41] to use the COCO-9k [20] (9213 images of 65 groups) and the DUTS class [42] (8250 images of 291 groups) with the synthesis strategy [41] to construct our training set. We follow [22] to perform data augmentation and adopt the Adam optimizer [17] with an initial learning" + } + ] + } + ], + "index": 31 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7252" + } + ] + } + ], + "index": 32 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 117, + 153 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 117, + 153 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 117, + 153 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 117, + 153 + ], + "type": "image", + "image_path": "b6bb61b7e9fa624d61c4d45e1680900c8432ee0eabf1e0c9f530e717a50c3041.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 155, + 287, + 210 + ], + "lines": [ + { + "bbox": [ + 46, + 155, + 287, + 210 + ], + "spans": [ + { + "bbox": [ + 46, + 155, + 287, + 210 + ], + "type": "text", + "content": "Figure 5. Visual comparison among the channels with different channel attention weights in CtP2T. We visualize some feature maps in " + }, + { + "bbox": [ + 46, + 155, + 287, + 210 + ], + "type": "inline_equation", + "content": "V_{m}^{*}(\\pmb{F})" + }, + { + "bbox": [ + 46, + 155, + 287, + 210 + ], + "type": "text", + "content": " for the channels with large and small channel attention (CA) in CtP2T. We visualize two channels for large and small CA, respectively." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 118, + 70, + 187, + 153 + ], + "blocks": [ + { + "bbox": [ + 118, + 70, + 187, + 153 + ], + "lines": [ + { + "bbox": [ + 118, + 70, + 187, + 153 + ], + "spans": [ + { + "bbox": [ + 118, + 70, + 187, + 153 + ], + "type": "image", + "image_path": "27e9ff26b9eb13a07b4215eb4e140283f1551bc5b5c159c31ca6b067f3bb2822.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 187, + 70, + 257, + 153 + ], + "blocks": [ + { + "bbox": [ + 187, + 70, + 257, + 153 + ], + "lines": [ + { + "bbox": [ + 187, + 70, + 257, + 153 + ], + "spans": [ + { + "bbox": [ + 187, + 70, + 257, + 153 + ], + "type": "image", + "image_path": "1891516425141cf4c3434e24c6138abc0ad24af763d326af727e4aad49cb9e0f.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 258, + 70, + 293, + 153 + ], + "blocks": [ + { + "bbox": [ + 258, + 70, + 293, + 153 + ], + "lines": [ + { + "bbox": [ + 258, + 70, + 293, + 153 + ], + "spans": [ + { + "bbox": [ + 258, + 70, + 293, + 153 + ], + "type": "image", + "image_path": "b2c7ead7ae43c5812f7cb912fff0e2f064fae07518c832472e9cd220a708fff7.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 218, + 288, + 291 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 218, + 288, + 291 + ], + "spans": [ + { + "bbox": [ + 46, + 218, + 288, + 291 + ], + "type": "text", + "content": "rate of 0.0001, " + }, + { + "bbox": [ + 46, + 218, + 288, + 291 + ], + "type": "inline_equation", + "content": "\\beta_{1} = 0.9" + }, + { + "bbox": [ + 46, + 218, + 288, + 291 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 218, + 288, + 291 + ], + "type": "inline_equation", + "content": "\\beta_{2} = 0.99" + }, + { + "bbox": [ + 46, + 218, + 288, + 291 + ], + "type": "text", + "content": " to train our model for 80,000 iterations. The learning rate is divided by 10 at the " + }, + { + "bbox": [ + 46, + 218, + 288, + 291 + ], + "type": "inline_equation", + "content": "60000^{\\mathrm{th}}" + }, + { + "bbox": [ + 46, + 218, + 288, + 291 + ], + "type": "text", + "content": " iteration. We select at most eight images from each group as a mini-batch to train our network. The training and testing image size is set as " + }, + { + "bbox": [ + 46, + 218, + 288, + 291 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 46, + 218, + 288, + 291 + ], + "type": "text", + "content": ". Our method is implemented using Pytorch [24]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 300, + 141, + 312 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 300, + 141, + 312 + ], + "spans": [ + { + "bbox": [ + 47, + 300, + 141, + 312 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 316, + 287, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 316, + 287, + 388 + ], + "spans": [ + { + "bbox": [ + 46, + 316, + 287, + 388 + ], + "type": "text", + "content": "We conduct ablation studies on the challenging CoCA [42] dataset to verify the effectiveness of our proposed components. As shown in Table 1, we treat the vanilla MaskFormer-style framework as our baseline, shown in the first row, and progressively add our proposed R2R, CtP2T, CoT2T, and TGFR on it for effectiveness analysis." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 388, + 287, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 388, + 287, + 460 + ], + "spans": [ + { + "bbox": [ + 46, + 388, + 287, + 460 + ], + "type": "text", + "content": "Effectiveness of R2R. First, we plug R2R into each decoder layer to enhance the segmentation features. It shows that using R2R largely improves the model performance compared to the baseline, while using vanilla P2P causes the out-of-memory error. The results verify the necessity of using our R2R for inter-image correlation modeling." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 461, + 288, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 461, + 288, + 652 + ], + "spans": [ + { + "bbox": [ + 46, + 461, + 288, + 652 + ], + "type": "text", + "content": "Effectiveness of CtP2T. Next, we consider the contrast relation modeling between the co-saliency and BG tokens, thus replacing the original P2T module to our proposed CtP2T module. By using CtP2T, the model performance can be further improved, indicating that CtP2T is beneficial for enhancing the discriminability between the two types of tokens. We also provide some visual samples in Figure 5. Since the channels of the tokens correspond to those of the values in " + }, + { + "bbox": [ + 46, + 461, + 288, + 652 + ], + "type": "inline_equation", + "content": "\\mathrm{MHA}^*" + }, + { + "bbox": [ + 46, + 461, + 288, + 652 + ], + "type": "text", + "content": ", we visualize some feature maps of " + }, + { + "bbox": [ + 46, + 461, + 288, + 652 + ], + "type": "inline_equation", + "content": "V_{m}^{*}(\\pmb {F})" + }, + { + "bbox": [ + 46, + 461, + 288, + 652 + ], + "type": "text", + "content": " of the channels with large or small channel attention weights in " + }, + { + "bbox": [ + 46, + 461, + 288, + 652 + ], + "type": "inline_equation", + "content": "\\pmb{W}" + }, + { + "bbox": [ + 46, + 461, + 288, + 652 + ], + "type": "text", + "content": ". We can see that the channels with large channel attention (CA) can easily distinguish co-salient objects and distracting objects, while those with small CA usually confuse them. The results demonstrate our generated channel attention is meaningful for accurate co-salient object detection." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": "Effectiveness of CoT2T. Furthermore, we supplement CoT2T to explore the inter-image correlations for all co-saliency tokens. CoT2T explicitly promotes consensus information propagation among all co-saliency tokens, thus obtaining obvious improvements." + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 307, + 83, + 549, + 167 + ], + "blocks": [ + { + "bbox": [ + 312, + 70, + 538, + 81 + ], + "lines": [ + { + "bbox": [ + 312, + 70, + 538, + 81 + ], + "spans": [ + { + "bbox": [ + 312, + 70, + 538, + 81 + ], + "type": "text", + "content": "Table 2. Quantitative results of different settings in TGFR." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 83, + 549, + 167 + ], + "lines": [ + { + "bbox": [ + 307, + 83, + 549, + 167 + ], + "spans": [ + { + "bbox": [ + 307, + 83, + 549, + 167 + ], + "type": "table", + "html": "
SettingsCoCA [42]
Sm↑Eξ↑maxF↑MAE↓
w/o TGFR0.71400.78800.60030.1139
w/o Distillation0.71410.79210.60460.1114
w/ co0.71710.79650.60760.1144
w/ bg0.71550.79350.60640.1112
w/ bg&co0.71970.79070.60920.1069
w/ co&bg0.72460.80010.61900.1084
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Visualization of some feature maps (Fea.) and predictions (Pred.) of the models with (w/) or without (w/o) using TGFR." + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 347, + 171, + 386, + 232 + ], + "blocks": [ + { + "bbox": [ + 347, + 171, + 386, + 232 + ], + "lines": [ + { + "bbox": [ + 347, + 171, + 386, + 232 + ], + "spans": [ + { + "bbox": [ + 347, + 171, + 386, + 232 + ], + "type": "image", + "image_path": "584119f4c47ab3b34a780e94aeeebaabf8e807a2d00df350bc17f7374789e3bb.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 361, + 232, + 372, + 239 + ], + "lines": [ + { + "bbox": [ + 361, + 232, + 372, + 239 + ], + "spans": [ + { + "bbox": [ + 361, + 232, + 372, + 239 + ], + "type": "text", + "content": "GT" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 386, + 171, + 425, + 232 + ], + "blocks": [ + { + "bbox": [ + 386, + 171, + 425, + 232 + ], + "lines": [ + { + "bbox": [ + 386, + 171, + 425, + 232 + ], + "spans": [ + { + "bbox": [ + 386, + 171, + 425, + 232 + ], + "type": "image", + "image_path": "490ab51924231aea23dfa23499631be1ad1e4c2736f94f4749e8b0a1cf4d2c19.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 392, + 232, + 422, + 239 + ], + "lines": [ + { + "bbox": [ + 392, + 232, + 422, + 239 + ], + "spans": [ + { + "bbox": [ + 392, + 232, + 422, + 239 + ], + "type": "text", + "content": "Pred. w/o" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 427, + 171, + 463, + 232 + ], + "blocks": [ + { + "bbox": [ + 427, + 171, + 463, + 232 + ], + "lines": [ + { + "bbox": [ + 427, + 171, + 463, + 232 + ], + "spans": [ + { + "bbox": [ + 427, + 171, + 463, + 232 + ], + "type": "image", + "image_path": "923c8581e007b126701f1c7fc46748a18619b844abdbc30e3477ee0dbc75735f.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 433, + 232, + 458, + 238 + ], + "lines": [ + { + "bbox": [ + 433, + 232, + 458, + 238 + ], + "spans": [ + { + "bbox": [ + 433, + 232, + 458, + 238 + ], + "type": "text", + "content": "Fea. w/o" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + } + ], + "index": 19 + }, + { + "type": "image", + "bbox": [ + 465, + 171, + 504, + 232 + ], + "blocks": [ + { + "bbox": [ + 465, + 171, + 504, + 232 + ], + "lines": [ + { + "bbox": [ + 465, + 171, + 504, + 232 + ], + "spans": [ + { + "bbox": [ + 465, + 171, + 504, + 232 + ], + "type": "image", + "image_path": "369179c1a06f2b277927e023d19ed0c7edafaa2ef4461ec4a6773e8ecd34b02a.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 471, + 232, + 498, + 239 + ], + "lines": [ + { + "bbox": [ + 471, + 232, + 498, + 239 + ], + "spans": [ + { + "bbox": [ + 471, + 232, + 498, + 239 + ], + "type": "text", + "content": "Pred. w/" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + } + ], + "index": 21 + }, + { + "type": "image", + "bbox": [ + 504, + 171, + 544, + 232 + ], + "blocks": [ + { + "bbox": [ + 504, + 171, + 544, + 232 + ], + "lines": [ + { + "bbox": [ + 504, + 171, + 544, + 232 + ], + "spans": [ + { + "bbox": [ + 504, + 171, + 544, + 232 + ], + "type": "image", + "image_path": "1e9a49ff7240403ab36f67f13293ed48d81dcf0fc248dcd522b3a6986111ca18.jpg" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 514, + 232, + 536, + 238 + ], + "lines": [ + { + "bbox": [ + 514, + 232, + 536, + 238 + ], + "spans": [ + { + "bbox": [ + 514, + 232, + 536, + 238 + ], + "type": "text", + "content": "Fea. w/" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_caption" + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 281, + 545, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 281, + 545, + 389 + ], + "spans": [ + { + "bbox": [ + 304, + 281, + 545, + 389 + ], + "type": "text", + "content": "Effectiveness of TGFR. Finally, we add TGFR to leverage the learned tokens for refining the segmentation features. Table 1 shows that adopting TGFR can bring more performance gains, thus demonstrating its effectiveness. We also visualize some feature maps and predictions of using and without using TGFR in Figure 6. It can be seen that using TGFR obtains more discriminative features for distinguishing co-saliency objects from distractors, thus generating better segmentation results." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 389, + 546, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 389, + 546, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 389, + 546, + 628 + ], + "type": "text", + "content": "To dive deeper into the effectiveness of TGFR, we report more experimental results in Table 2 for further analysis. First, we directly fuse the tokens and the segmentation features without performing the distillation process (\"w/o Distillation\"). we find this model brings limited improvements compared to the \"w/o TGFR\" model. It is probably because the tokens and features might exist semantic gap, being detrimental for their fusion, hence verifying the necessity of our distillation mechanism. Next, we supplement the distillation process and explore four strategies for the refusion process, i.e. individually refusing the distilled co-saliency (\"w/ co\") or BG features (\"w/ bg\") to the segmentation features, or refusing both with the order of co-saliency feature first (\"w/ co&bg\") or BG feature first (\"w/ bg&co\"). We can find refusing both achieves better performance, thus verifying the necessity of leveraging both features for discrimination enhancement. We also find first refusing the co-saliency feature and then integrating the BG feature obtains the best results. Thus, we adopt this strategy in our final TGFR design." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": "Effectiveness of BG Exploration. We remove all BG-related modules in our final model and only explore co-saliency regions, shown in the last row of Table 1. In this setting, CtP2T can not be used while only the co-saliency feature is used in TGFR. We find that the performance significantly drops compared to our final model, thus verifying the necessity of explicit BG modeling." + } + ] + } + ], + "index": 28 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7253" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 61, + 94, + 531, + 200 + ], + "blocks": [ + { + "bbox": [ + 47, + 71, + 545, + 92 + ], + "lines": [ + { + "bbox": [ + 47, + 71, + 545, + 92 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 545, + 92 + ], + "type": "text", + "content": "Table 3. Quantitative comparison of our model with other state-of-the-art methods. We conduct the comparison on three benchmark CoSOD datasets. Red and blue denote the best and the second-best results, respectively." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 61, + 94, + 531, + 200 + ], + "lines": [ + { + "bbox": [ + 61, + 94, + 531, + 200 + ], + "spans": [ + { + "bbox": [ + 61, + 94, + 531, + 200 + ], + "type": "table", + "html": "
MethodsCoCA [42]CoSal2015 [36]CoSOD3k [11]
Sm↑Eξ↑maxF↑MAE↓Sm↑Eξ↑maxF↑MAE↓Sm↑Eξ↑maxF↑MAE↓
CSMG(CVPR2019) [39]0.62760.73240.49880.12730.77570.84360.78690.13090.72720.82080.72970.1480
GICD(ECCV2020) [42]0.65790.71490.51260.12600.84370.88690.84410.07070.79670.84780.76980.0794
ICNet(NIPS2020) [16]0.65410.70420.51330.14700.85710.90110.85830.05790.79420.84500.76230.0891
GCoNet(CVPR2021) [12]0.67300.75980.54380.10500.84530.88790.84710.06810.80180.86010.77710.0712
CADC(ICCV2021) [41]0.68000.74430.54870.13300.86660.90630.86450.06410.81500.85430.77810.0875
UFO(ArXiv2022) [27]0.69710.78020.56810.09390.85780.90570.86210.06480.81910.86940.79540.0735
DCFM(CVPR2022) [34]0.71010.78260.59810.08450.83800.89290.85590.06720.80940.87420.80450.0674
DMT (Ours)0.72460.80010.61900.10840.89740.93620.90520.04540.85140.89500.83530.0633
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Qualitative comparisons of our model with other state-of-the-art methods." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 448, + 287, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 448, + 287, + 519 + ], + "spans": [ + { + "bbox": [ + 46, + 448, + 287, + 519 + ], + "type": "text", + "content": "Quantitative Analysis. As shown in Figure 4, we also provide some visual comparison samples for the four key components. We find that the baseline model is easily distracted by complex BG regions, while progressively introducing our four components can gradually exclude these distractors and achieve more and more accurate results." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 529, + 284, + 542 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 529, + 284, + 542 + ], + "spans": [ + { + "bbox": [ + 47, + 529, + 284, + 542 + ], + "type": "text", + "content": "5. Comparison with State-of-the-Art Methods" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 546, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 546, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 546, + 287, + 713 + ], + "type": "text", + "content": "We compare our model with other seven state-of-the-art methods, i.e. CSMG [39], GICD [42], ICNet [16], GCoNet [12], CADC [41], UFO [27], and DCFM [34]. We report the quantitative comparison results in Table 3. We can observe that our proposed DMT achieves the best performance on all three benchmark datasets. Especially, on CoSal2015 and CoSOD3k, our DMT model surpasses the second-best model by a large margin, e.g. " + }, + { + "bbox": [ + 46, + 546, + 287, + 713 + ], + "type": "inline_equation", + "content": "3.14\\%" + }, + { + "bbox": [ + 46, + 546, + 287, + 713 + ], + "type": "inline_equation", + "content": "S_{m}" + }, + { + "bbox": [ + 46, + 546, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 546, + 287, + 713 + ], + "type": "inline_equation", + "content": "4.07\\%" + }, + { + "bbox": [ + 46, + 546, + 287, + 713 + ], + "type": "text", + "content": " maxF on CoSal2015 and " + }, + { + "bbox": [ + 46, + 546, + 287, + 713 + ], + "type": "inline_equation", + "content": "3.23\\%" + }, + { + "bbox": [ + 46, + 546, + 287, + 713 + ], + "type": "inline_equation", + "content": "S_{m}" + }, + { + "bbox": [ + 46, + 546, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 546, + 287, + 713 + ], + "type": "inline_equation", + "content": "3.08\\%" + }, + { + "bbox": [ + 46, + 546, + 287, + 713 + ], + "type": "text", + "content": " maxF on CoSOD3k. We also show some visual comparison results in Figure 7. We can find that our method can precisely detect co-salient objects in complex scenarios, e.g. the existence of extraneous salient objects with similar appearances to target objects, and target objects with small" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 448, + 545, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 448, + 545, + 472 + ], + "spans": [ + { + "bbox": [ + 305, + 448, + 545, + 472 + ], + "type": "text", + "content": "sizes. Nevertheless, other models are heavily distracted in these challenging scenes." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 481, + 384, + 493 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 481, + 384, + 493 + ], + "spans": [ + { + "bbox": [ + 306, + 481, + 384, + 493 + ], + "type": "text", + "content": "6. Conclusions" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 499, + 545, + 631 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 499, + 545, + 631 + ], + "spans": [ + { + "bbox": [ + 304, + 499, + 545, + 631 + ], + "type": "text", + "content": "In this paper, we propose DMT, a transformer-based CoSOD model for explicitly mining both co-saliency and BG information and effectively modeling their discrimination. Specifically, we propose several economic multigrained correlations, i.e. R2R, CtP2T, and CoT2T to model inter-image and intra-image relations. Besides, we propose a TGFR module to leverage the detection information for improving the discriminability of the segmentation features. It is an improvement to the MaskFormer that allows the mutual promotion of two sub-paths. Our model achieves a new state-of-the-art result." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 641, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 712 + ], + "type": "text", + "content": "Acknowledgments: This work was supported in part by Key-Area Research and Development Program of Guangdong Province (No.2021B0101200001), the National Key R&D Program of China under Grant 2021B0101200001, and the National Science Foundation of China under Grant 62036011, U20B2065, 721A0001, 62136004." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7254" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "text", + "content": "[1] Radhakrishna Achanta, Sheila Hemami, Francisco Estrada, and Sabine Susstrunk. 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Salient object detection" + } + ] + } + ], + "index": 14 + } + ], + "sub_type": "ref_text" + }, + { + "bbox": [ + 326, + 72, + 545, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 72, + 545, + 95 + ], + "spans": [ + { + "bbox": [ + 326, + 72, + 545, + 95 + ], + "type": "text", + "content": "via integrity learning. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2022. 1" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "text", + "content": "7256" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Discriminator-Cooperated Feature Map Distillation for GAN Compression/e9448640-3029-45d7-94ad-42638a17674c_content_list.json b/2023/Discriminator-Cooperated Feature Map Distillation for GAN Compression/e9448640-3029-45d7-94ad-42638a17674c_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..9cf620b1206e865979d8daa9a0b12eed63d5b86e --- /dev/null +++ b/2023/Discriminator-Cooperated Feature Map Distillation for GAN Compression/e9448640-3029-45d7-94ad-42638a17674c_content_list.json @@ -0,0 +1,1352 @@ +[ + { + "type": "text", + "text": "Discriminator-Cooperated Feature Map Distillation for GAN Compression", + "text_level": 1, + "bbox": [ + 107, + 128, + 861, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Tie Hu $^{1}$ , Mingbao Lin $^{3}$ , Lizhou You $^{1}$ , Fei Chao $^{1}$ , Rongrong Ji $^{1,2,4*}$", + "bbox": [ + 223, + 179, + 750, + 198 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ MAC Lab, School of Informatics, Xiamen University", + "bbox": [ + 269, + 198, + 699, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ Institute of Artificial Intelligence, Xiamen University", + "bbox": [ + 269, + 215, + 697, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Tencent Youtu Lab", + "bbox": [ + 405, + 233, + 565, + 250 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "4Shenzhen Research Institute of Xiamen University", + "bbox": [ + 281, + 250, + 689, + 268 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{hutie, lmbxmu, youlizhou}@stu.xmu.edu.cn, {fchao, rrji}@xmu.edu.cn", + "bbox": [ + 187, + 271, + 776, + 287 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 321, + 313, + 338 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Despite excellent performance in image generation, Generative Adversarial Networks (GANs) are notorious for its requirements of enormous storage and intensive computation. As an awesome \"performance maker\", knowledge distillation is demonstrated to be particularly efficacious in exploring low-priced GANs. In this paper, we investigate the irreplaceability of teacher discriminator and present an inventive discriminator-cooperated distillation, abbreviated as DCD, towards refining better feature maps from the generator. In contrast to conventional pixel-to-pixel match methods in feature map distillation, our DCD utilizes teacher discriminator as a transformation to drive intermediate results of the student generator to be perceptually close to corresponding outputs of the teacher generator. Furthermore, in order to mitigate mode collapse in GAN compression, we construct a collaborative adversarial training paradigm where the teacher discriminator is from scratch established to co-train with student generator in company with our DCD. Our DCD shows superior results compared with existing GAN compression methods. For instance, after reducing over $40 \\times$ MACs and $80 \\times$ parameters of CycleGAN, we well decrease FID metric from 61.53 to 48.24 while the current SoTA method merely has 51.92. This work's source code has been made accessible at https://github.com/poopit/DCD-official.", + "bbox": [ + 75, + 353, + 473, + 731 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 760, + 209, + 776 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Image generation transforms random noise or source-domain images to other images in user-required domains. Recent years have witnessed the burgeoning of generative adversarial networks (GANs) that lead to substantial progress in image-to-image translation [8, 9, 18, 49], style transfer [11, 12, 42], image synthesis [3, 22, 23, 32, 46], etc.", + "bbox": [ + 75, + 786, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/97d87c913e3e881e30ce7cedd0aca13e3174e19ffdf57772035167030a60926d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 517, + 330, + 870, + 396 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4f94942d42bad35e0608c293f20a9d1bc64e9e00a36a5bebe81cfaa6a9053de4.jpg", + "image_caption": [ + "Figure 1. (a) Layer-by-layer feature map distillation [34]. (b) Cross-layer feature map distillation [6]. (c) Our discriminator-cooperated feature map distillation." + ], + "image_footnote": [], + "bbox": [ + 545, + 410, + 849, + 484 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Image generation has a wide application in daily entertainment such as TikTok AI image generator, Dream by WOMBO, Google Imagen, and so on. Running platforms performing these applications are typically featured with poor memory storage and limited computational power. However, GANs are also ill-famed for the growing spurt of learnable parameters and multiply-accumulate operations (MACs), raising a huge challenge to the storage requirement and computing ability of deployment infrastructure.", + "bbox": [ + 496, + 551, + 892, + 686 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To address the above dilemma for better usability of GANs in serving human life, methods such as pruning [7, 27, 28, 33], neural network architecture search (NAS) [10, 19, 26] and quantization [39, 40], have been broadly explored to obtain a smaller generator. On the premise of these compression researches, knowledge distillation, in particular to distilling feature maps, has been accepted as a supplementary means to enhance the performance of compressed generators [1, 4, 17, 26, 29, 41]. Originated from image classification, as illustrated in Fig. 1(a), feature map based distillation, which extracts information of intermediate activations and transfers the knowledge from the teacher model to the student one, has been extensively explored and demonstrated to well improve the capability of lightweight mod", + "bbox": [ + 496, + 688, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding Author", + "bbox": [ + 94, + 886, + 223, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "20351", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "els [5, 25, 34, 43, 45]. Distinctive from passing on common feature maps from teacher to student, AT [45] calculates feature attentions as the delivered knowledge; MGD [43] randomly masks feature maps to indirectly guide the student to learn from the teacher; KRD [6] uses a cross-layer distillation method to allow the “new knowledge” of the student to learn from the “old knowledge” in teacher, as shown in Fig. 1(b). Whatever, most methods execute pixel-to-pixel feature maps matching between teacher and student.", + "bbox": [ + 75, + 90, + 470, + 224 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Alike to the implementations on image classification, feature map based distillation is also considered in GAN compression. For example, GCC [28] considers a well pretrained discriminator to absorb high-level information from the teacher-generated image, and fuses it with intermediate activations from the teacher generator, results of which are passed to the corresponding position of the student generator. OMGD [33] utilizes an online multi-granularity strategy to allow a deeper teacher generator and a wider one to simultaneously deliver output image knowledge of different granularities to the student generator. These two methods follow the pipeline of image classification to tune the intermediate outputs of student generator with those of teacher generator in a fashion of per-pixel matching. Although the sustainable progress on multiple benchmark datasets demonstrates the efficacy of intermediate activation outputs, the feature-based distillation, as we reveal in this paper, is not well compatible with the very nature of generating perceptually similar images and adversarial training paradigm.", + "bbox": [ + 75, + 229, + 470, + 517 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Concretely speaking, conversely to image classification that relies on feature vector representations, the essence of image generation is to improve perceptually alike between the real images and generated images. Two important facts cause it is eventually difficult to use per-pixel match to analyze a pair of images: First, two similar images can contain many different pixel values; Second, two dissimilar images can still comprise the same pixel values. Thus, it is not suitable to simply use the per-pixel match. Regarding adversarial training in GANs, a generator learns to synthesize samples that best resemble the dataset, meanwhile a discriminator differentiate samples in the dataset from the generator generated samples. The adversarial results finally lead the generator to creating images of out-of-the-ordinary visual quality, indicating that the discriminator is also empowered with informative capacity and can be exploited to enrich the distillation of feature maps. Therefore, it might be inappropriate to directly extend feature map distillation in image classification to image generation. And GAN compression oriented feature map distillation with discriminator included remains to be well explored.", + "bbox": [ + 75, + 518, + 468, + 837 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In order to achieve this objective, in this paper, we propose a discriminator-cooperated distillation (DCD) method to involve the teacher discriminator in distilling feature maps for student generator. A simple illustration is given in", + "bbox": [ + 76, + 839, + 468, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Fig. 1(c), in contrast to the vanilla pixel-wise distance constraint, our DCD measures the distance at the end of teacher discriminator with the intermediate generator outputs as its inputs. Our DCD is perspicacious in multiple benchmark datasets with a simple implementation. Akin to perceptual loss [20] which employs a pre-trained neural network such as a VGG model [36] to extract features upon which the $\\ell_1$ distance is calculated from activations of hidden layers, the teacher discriminator in DCD also acts as a feature extractor. Due to pooling operations in the hidden layers, feature maps from different sources (student generator and teacher generator) as inputs to the discriminator may lead to identical latent representations, therefore encouraging natural and perceptually pleasing results. In addition, the proposed DCD is used in conjunction with collaborative adversarial training, which is also simple but perspicacious to allow the student generator to fool the discriminator for generating better images. In contrast to discriminator-free paradigm training [28], we find our DCD empowers the compressed student generator with a better capability to compete against teacher discriminator. Thus, we also employ the teacher discriminator to collaboratively determine whether inputs from the student generator are real or not.", + "bbox": [ + 496, + 90, + 890, + 436 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "This work intends to raise the level of feature map distillation to strengthen the compressed student generator to generate high-quality images. The major contributions we have made across the entire paper are listed as follows: (1) An incentive GAN-oriented discriminator-cooperated feature map distillation method to produce images with high fidelity; (2) One novel collaborative adversarial training paradigm to better reach a global equilibrium point in compressing GANs; (3) Remarkable reduction on the generator complexity and significant performance increase.", + "bbox": [ + 496, + 439, + 890, + 590 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 608, + 640, + 625 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. GANs and GAN Compression", + "text_level": 1, + "bbox": [ + 500, + 633, + 764, + 650 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Generative adversarial networks (GANs) [13] have attracted the attention of substantive researchers due to their outstanding performance in image generation tasks [3, 8, 9, 18, 22, 23, 32, 46, 49]. Since the infancy of GAN, many variants have emerged, from DCGAN [32], which embraces convolutional neural networks for the first time, to CycleGAN [49] and Pix2Pix [18] which implement image-to-image translation, to StyleGAN [22] to enable controllable manipulation of various attributes of image synthesis. CycleGAN [49] transfers a source-domain image into a target style in an unpaired configuration, such as a horse image to a zebra pattern or a summer image to a winter style. On the other hand, Pix2Pix [18] is given a ground-truth image and converts a semantic segmentation or contour map into a photo-realistic picture. Albeit the performance, GANs suffer heavy burden on storage and computation.", + "bbox": [ + 496, + 657, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "20352", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Therefore, recent years have witnessed increasing attention on compressing GANs [7, 10, 19, 21, 24, 26, 27, 30, 35, 39, 40, 47]. Co-evolution [35] prunes filters in the generator under the constraint of consistent output distributions. GAN Slimming [39] suggests a compression framework that can integrate pruning, knowledge distillation and quantization. GAN Compression [26] views the teacher output as the pseudo label for student generator and unifies the compression framework for GANs trained on paired data and unpaired data. GCC [28] combines information from discriminator in knowledge distillation, an idea closer to our approach, but the use of discriminator is still under-explored. Although the above approaches have compressed parameters and computation costs, both the generated image quality and the model size are still far from practical applications on mobile devices. OMGD [33] bridges this huge gap in a way by constructing discriminator-free distillation.", + "bbox": [ + 75, + 90, + 472, + 348 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Of the above methods, GCC is the most similar to our approach with major differences in: (1) GCC involves summation of discriminator activations in distilling intermediate layers of student generator. Our DCD calculates distance between teacher and student directly upon feature maps of the discriminator. (2) GCC focuses on a more suitable student discriminator for student generator. Our DCD discards student discriminator by adopting that of teacher. (3) Results show merits of our DCD over GCC in both quantitative and visual quality with a higher compression rate.", + "bbox": [ + 75, + 349, + 472, + 501 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Knowledge Distillation", + "text_level": 1, + "bbox": [ + 76, + 513, + 289, + 529 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Pioneered by FitNet as of 2014 [34], knowledge distillation (KD) [16] has become a regular approach in model compression especially to GAN compression, where a larger model with better performance imparts knowledge to a smaller model. Since then, great efforts have been made to dig out opulent knowledge hints, such as output logits [21, 47, 48], intermediate feature maps [6, 14, 34], instance relation [31, 38] and so on. In this paper, we are mainly inspired by the intermediate feature map based distillation that has been extensively mined to efficiently guide the training of the student network. Compared to other knowledge hints, feature maps often accommodate a richer level of information and provide more detailed guidance for the student network. AT [45] extracts the attention map from the feature maps and trains the student's attention maps to be as close as possible to the one of teacher. MGD [43] transforms direct learning from the teacher into a generative intermediate goal. KRD [6] uses the idea of cross-layer distillation to allow old knowledge from the teacher to guide new knowledge learning from the student network. Nevertheless, conventional methods require per-pixel match between feature maps of teacher and student, which does not fit well in GAN compression because the goal of GANs is to generate perceptually similar images. In", + "bbox": [ + 75, + 537, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "this paper, we dig deeper into the distinctiveness of generative adversarial networks.", + "bbox": [ + 498, + 90, + 890, + 121 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 500, + 137, + 633, + 155 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminaries", + "text_level": 1, + "bbox": [ + 500, + 162, + 640, + 179 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Generative adversarial networks [13], or GANs for short, are an interesting manner to train a generative model by modelling the problem with two sub-models including a generator model $\\mathcal{G}$ and a discriminator model $\\mathcal{D}$ . The two models are trained together in a zero-sum game as:", + "bbox": [ + 498, + 188, + 890, + 263 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\min _ {\\mathcal {G}} \\max _ {\\mathcal {D}} \\mathcal {L} _ {g a n} = \\mathbb {E} _ {y \\sim p _ {r e a l}} \\log \\mathcal {D} (y) \\\\ + \\mathbb {E} _ {x \\sim p (x)} \\left[ \\log \\left(1 - \\mathcal {D} (\\mathcal {G} (x))\\right) \\right]. \\tag {1} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 277, + 890, + 335 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Herein, the generator model $\\mathcal{G}$ is trained to generate new examples, and the discriminator model $\\mathcal{D}$ tries to classify examples as either real (from the domain) or fake (generated). The two models are trained adversarially until the discriminator model is fooled at most times, which indicates that the generator model is producing plausible examples. Then, the generator $\\mathcal{G}$ is deployed online to complete service for reality.", + "bbox": [ + 496, + 348, + 890, + 469 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The serviceability of generator $\\mathcal{G}$ rests with not only the performance, but also the hardware capability that makes a greater demand on generator complexity. Therefore, a lighter student generator, $\\mathcal{G}^S$ , can be developed by various methods. The original generator and discriminator, respectively denoted as $\\mathcal{G}^T$ and $\\mathcal{D}^T$ in this situation to differentiate, play as a teacher to enhance the ability of student generator $\\mathcal{G}^S$ .", + "bbox": [ + 496, + 470, + 890, + 590 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Giving an input variable $x \\sim p(x) \\in \\mathbb{R}^{H \\times W \\times C}$ , we denote the $i$ -th layer output of generator as $\\mathcal{G}_i(x)$ , and $\\mathcal{I}_{\\mathcal{G}}(x)$ as layer index set of extracted intermediate outputs. Thus, the feature maps based distillation is formulated as:", + "bbox": [ + 496, + 592, + 890, + 654 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {f e a - d i s} = \\sum_ {i \\in I _ {\\mathcal {G}}} \\ell \\left(\\mathcal {G} _ {i} ^ {T} (x), f \\left(\\mathcal {G} _ {i} ^ {S} (x)\\right)\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 562, + 666, + 890, + 700 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $f(\\cdot)$ is the affine transformation function to align the channel dimensions between the teacher and student, such as $1 \\times 1$ convolution operators in existing studies [26,28,33]. Also, $\\ell(\\cdot, \\cdot)$ refers to the distance measure function, such as Euclidean distance.", + "bbox": [ + 496, + 714, + 890, + 789 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Additionally, perceptual loss [20], $\\mathcal{L}_{per}$ , is also widely adopted in existing studies to encourage natural and perceptually pleasing restored images. $\\mathcal{L}_{per}$ comprises a feature reconstruction loss $\\mathcal{L}_{fea}$ and a style reconstruction loss $\\mathcal{L}_{sty}$ as:", + "bbox": [ + 496, + 791, + 890, + 868 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {p e r} = \\lambda_ {f e a} \\cdot \\mathcal {L} _ {f e a} + \\lambda_ {s t y} \\cdot \\mathcal {L} _ {s t y}. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 580, + 881, + 890, + 898 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "20353", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/0344f964c1b45b2e4cd2b9dd9e3e59a253c13a00f8ce1d9e4bc1e0c15f9a29a1.jpg", + "image_caption": [ + "Figure 2. Framework of our DCD. Intermediate feature maps from student and teacher are downsampled first to align the dimension, results of which are then fed to the teacher discriminator to minimize distance for a perceptually vivid generated image." + ], + "image_footnote": [], + "bbox": [ + 81, + 90, + 478, + 244 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Herein, $\\mathcal{L}_{fea}$ propels the output representation of the teacher generator to approach to that of the student generator. This is achieved by a pre-trained VGG network $\\Phi (\\cdot)$ [36] and formalized as:", + "bbox": [ + 76, + 345, + 468, + 405 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {f e a} = \\sum_ {j \\in I _ {\\Phi}} \\frac {1}{H _ {j} W _ {j} C _ {j}} \\left\\| \\Phi_ {j} \\left(\\mathcal {G} ^ {T} (x)\\right) - \\Phi_ {j} \\left(\\mathcal {G} ^ {S} (x)\\right) \\right\\| _ {1}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 417, + 468, + 454 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\Phi_j(\\cdot)$ returns the $j$ -th activation output of VGG network and $H_{j}\\times W_{j}\\times C_{j}$ is its shape. Alike to $I_{\\mathcal{G}}$ , $I_{\\Phi}$ contains layer index of extracted intermediate outputs.", + "bbox": [ + 76, + 468, + 468, + 513 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As for $\\mathcal{L}_{sty}$ , it minimizes the difference between Gram matrices of the output and target images in order to preserve style characteristics such as color, textures and common pattern [33]. The $\\mathcal{L}_{sty}$ is calculated as:", + "bbox": [ + 76, + 515, + 468, + 575 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {s t y} = \\sum_ {j \\in I _ {\\Phi}} \\left\\| G \\left(\\Phi_ {j} \\left(\\mathcal {G} ^ {T} (x)\\right)\\right) - G \\left(\\Phi_ {j} \\left(\\mathcal {G} ^ {S} (x)\\right)\\right) \\right\\| _ {1}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 588, + 468, + 625 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $G(\\cdot)$ represents abbreviation of Gram matrices.", + "bbox": [ + 76, + 637, + 433, + 652 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Discriminator-Cooperated Distillation", + "text_level": 1, + "bbox": [ + 76, + 664, + 405, + 681 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Stepping back and reflecting on the feature map based distillation in Eq. (2), we realize that a simple utilization of generator capacity is not intact in earlier methods. The central principle of a GAN is contingent on an \"indirect\" training route through the discriminator updated dynamically to discern how \"realistic\" its input (i.e., generator output) seems. This means that the generator is not trained to minimize the distance from a generated image to a target image, but rather to deceive the discriminator. It is the copetition pattern between the generator and discriminator that even brings about superficially authentic generated images. Thus, the discriminator is also empowered with informative capacity and must be utilized to enrich the distillation of feature maps.", + "bbox": [ + 75, + 688, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As shown in Fig. 2, we rethink Eq. (2) and integrate teacher discriminator to cooperate with the distillation process. Alike to feature reconstruction loss defined in Eq. (4), while taking the generator outputs as its inputs, we accomplish our distillation by aligning the intermediate outputs of the discriminator. We formulate this learning process as:", + "bbox": [ + 496, + 90, + 890, + 181 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {d c d} = \\sum_ {k \\in I _ {\\mathcal {D}}} \\sum_ {i \\in I _ {\\mathcal {G}}} \\ell \\left(\\mathcal {D} _ {k} ^ {T} \\left(f \\left(\\mathcal {G} _ {i} ^ {T} (x)\\right)\\right), \\mathcal {D} _ {k} ^ {T} \\left(f \\left(\\mathcal {G} _ {i} ^ {S} (x)\\right)\\right)\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 501, + 193, + 890, + 244 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{D}_k^T$ stands for the output of its $k$ -th layer. Similar to $I_{\\mathcal{G}}$ , $I_{\\mathcal{D}}$ is a layer index set of the teacher discriminator; herein, $f(\\cdot)$ denotes $1 \\times 1$ convolution operations to down-sample the channel dimensions of both the teacher and student feature maps to those of discriminator input. Usually, the channel number of discriminator input is set to three for an RGB-encoded image. Here, $f(\\cdot)$ for teacher generator becomes constant once initialized while that for student generator continues updating for a better fit with teacher.", + "bbox": [ + 496, + 244, + 890, + 381 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As an analogy to the vanilla feature map based distillation in Eq. (2) that compels the per-pixel match between intermediate outputs of both the teacher generator and student generator, the role of the teacher discriminator resembles the pre-trained VGG in Eq. (4), which acts as a transformed network to enable the intermediate results of student generator to be perceptually alike to these of teacher generator. In contrast, it does not require them to do pixel-by-pixel match, since two images might look similar in perspective, but they often have different pixel values, thus we cannot depend on per-pixel match. Notice that our discriminator-cooperated distillation is complementary to perceptual loss. The former concentrates on object localization while the latter pays attention to style discrepancies. The analysis of this phenomenon is in Sec. 4.4.", + "bbox": [ + 496, + 382, + 892, + 608 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Collaborative Adversarial Training", + "text_level": 1, + "bbox": [ + 500, + 619, + 807, + 635 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "GANs perform an alternating training paradigm for a unique global equilibrium point: 1) Training the discriminator $\\mathcal{D}$ to identify real and generated data while keeping the generator constant; 2) Training the generator $\\mathcal{G}$ to generate vivid data that fools the discriminator while keeping the discriminator constant; 3) Repeating steps 1) and 2) till the discriminator model is fooled at most time. However, the equilibrium is no longer guaranteed when $\\mathcal{D}$ and $\\mathcal{G}$ are empowered with inconsistent abilities, in which case unstable convergence frequently occurs. Generally, the instability stems from two ill-famed issues including vanishing gradient where loss for the generator is zero when the discriminator is perfect, and mode collapse where the stronger generator produces a small set of outputs for any input and the weaker discriminator traps in a local minimum [2].", + "bbox": [ + 496, + 642, + 890, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Especially, the mode collapse issue is even widespread in GAN compression because the compressed student gen", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "20354", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "erator $\\mathcal{G}^S$ is powerless to compete with the original full discriminator [27], in particular a pre-trained one [4, 19, 30]. The community has excavated various approaches to weaken the student discriminator. For example, GCC [28] selectively activates discriminator neurons. Nevertheless, a rule-of-thumb selection has to be carefully designed. Also, training a student discriminator is computationally redundant since it is unwanted in the testing stage. OMGD [33] co-trains teacher generator with the teacher discriminator while the student generator is discriminator-free. The missing adversarial training of student generator somehow barricades the further performance increase.", + "bbox": [ + 75, + 90, + 472, + 271 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this paper, we also reject real student discriminator, and to ensure the teacher's optimization, the teacher discriminator, $\\mathcal{D}^T$ , is online trained from scratch to be well-matched with the teacher generator $\\mathcal{G}^T$ . Comparing to [33], teacher discriminator $\\mathcal{D}^T$ also appears in the form of a collaborative discriminator to determine if the inputs from student generator $\\mathcal{G}^T$ are real or fake. The major concern originates from the actuality that the teacher discriminator is much powerful than the compressed student generator, which causes mode collapse in adversarial training. Luckily, our discriminator-cooperated distillation in Eq. (6) furnishes student generator with increasing capability to battle against teacher discriminator and leads to better performance than [33] as demonstrated in the experiment.", + "bbox": [ + 75, + 272, + 472, + 484 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Based on Eq. (1), our adversarial training is rewritten as:", + "bbox": [ + 96, + 484, + 468, + 500 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\min _ {\\mathcal {G} ^ {T}, \\mathcal {G} ^ {S}} \\max _ {\\mathcal {D} ^ {T}} \\mathcal {L} _ {c o l} = \\mathbb {E} _ {y \\sim p _ {r e a l}} \\log \\mathcal {D} ^ {T} (y) \\\\ + \\mathbb {E} _ {x \\sim p (x)} \\left[ \\log \\left(1 - \\mathcal {D} ^ {T} \\big (\\mathcal {G} ^ {T} (x) \\big)\\right) \\right] \\\\ + \\lambda_ {s t u} \\cdot \\mathbb {E} _ {x \\sim p (x)} \\left[ \\log \\left(1 - \\mathcal {D} ^ {T} \\left(\\mathcal {G} ^ {S} (x)\\right)\\right) \\right], \\tag {7} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 503, + 468, + 614 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\lambda_{stu}$ refers to a trade-off parameter; and $\\lambda_{stu} = 0$ degenerates to discarding student discriminator when constrained with the student generator [33].", + "bbox": [ + 75, + 622, + 468, + 667 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Training Objective", + "text_level": 1, + "bbox": [ + 76, + 674, + 259, + 691 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Looking back to Sec. 3.1, the loss terms in most conventional feature map based distillation methods include $\\mathcal{L}_{gan}$ in Eq. (1), $\\mathcal{L}_{fea - dis}$ in Eq. (2) and $\\mathcal{L}_{per}$ in Eq. (3). In this paper, we improve $\\mathcal{L}_{fea - dis}$ through a discriminator-cooperated feature map distillation loss $\\mathcal{L}_{dcd}$ in Eq. (6), and $\\mathcal{L}_{gan}$ through collaborative adversarial training loss $\\mathcal{L}_{col}$ in Eq. (7). Therefore, the overall training objective in this paper is given in the following:", + "bbox": [ + 75, + 698, + 468, + 819 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\mathcal {G} ^ {T}, \\mathcal {G} ^ {S}} \\max _ {\\mathcal {D} ^ {T}} \\left(\\mathcal {L} _ {g a n} + \\mathcal {L} _ {p e r} + \\lambda_ {d c d} \\cdot \\mathcal {L} _ {d c d}\\right), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 133, + 825, + 468, + 849 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\lambda_{dcd}$ balances the loss term. Four hyper-parameters: $\\lambda_{fea}$ , $\\lambda_{sty}$ , $\\lambda_{stu}$ and $\\lambda_{dcd}$ are used in this paper, influence of each parameter is ablated in the appendix.", + "bbox": [ + 76, + 854, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experimentation", + "text_level": 1, + "bbox": [ + 500, + 89, + 666, + 107 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Setups", + "text_level": 1, + "bbox": [ + 500, + 114, + 588, + 132 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "GAN Models and Benchmarks. We present the performance of compressed CycleGAN [49] and Pix2Pix [18] to follow and compare with existing methods [7, 19, 21, 26, 27, 35, 39, 47]. For a fair comparison with the current SoTA OMGD [33], the compressed generators (students) consist of 1/4 channels of the original full ResNet generators (teachers) [26]. CycleGAN translates images from one domain to another without a one-to-one mapping between the source and target domain. Therefore, we verify the performance upon unpaired image translation benchmarks including horse2zebra [49] and summer2winter [49]. As for Pix2Pix, we perform distillation upon paired edges2shoes [44] because it requires learning a mapping from input images to output images.", + "bbox": [ + 496, + 138, + 890, + 349 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "**Evaluations. Fréchet Inception Distance (FID), or FID for short [15], is particularly developed to evaluate the performance of GANs. It accesses the quality of generated images by an Inception-V3 network [37] to separately embed synthetic and real images to feature space, and then calculate the Wasserstein distance of their distributions. A lower FID score indicate better quality of generated images.**", + "bbox": [ + 496, + 351, + 890, + 455 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementations. We train CycleGAN and Pix2Pix for a total of 100 epochs. The initial learning rate is given as $2 \\times e^{-4}$ and then linearly decayed to 0 as training goes. The batch size is set to 4 on edges2shoes, and 1 on horse2zebra [49] and summer2winter [49]. We have $\\lambda_{dcd} = 1$ , $\\lambda_{fea} = 1 \\times e^{1}$ , $\\lambda_{sty} = 1 \\times e^{4}$ and $\\lambda_{stu} = 1$ across all experiments. In the appendix, specific ablations in regard to these hyper-parameters have been provided.", + "bbox": [ + 496, + 457, + 890, + 579 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Quantitative Comparison", + "text_level": 1, + "bbox": [ + 500, + 589, + 732, + 606 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "GAN Compression. We first compare with existing implementations on GAN compression in Table 1 where the blue number indicates performance drop, while the red number denotes performance increase compared with the original GAN models. We conclude the following observations from Table 1: First, on summer2winter, all methods lead to a performance increase of more or less. On the contrary, most methods cause FID drops on the challenging horse2zebra and edges2shoes while methods such as OMGD [33] and our DCD consistently enhance the performance. Second, our DCD leads to the most complexity reduction w.r.t. MACs and parameters, meanwhile it gains the best performance increase on all the three benchmark datasets. Third, with the same reduction of MACs $(40.3\\times)$ and parameters $(82.5\\times)$ on unpaired CycleGAN, our DCD well outperforms the recent SoTA method, i.e., OMGD. In particular, we drastically increase the performance of 51.92 for OMGD to 48.24, which is also 13.29 increase compared to the original CycleGAN. This increase is very challenging", + "bbox": [ + 496, + 613, + 890, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "20355", + "bbox": [ + 478, + 944, + 517, + 957 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/d520d27125263fe6e0b90232f9aabfbcd3d6286d951d083896b4f444514546a1.jpg", + "table_caption": [ + "Table 1. Performance comparison when compressing CycleGAN on horse2zebra, and Pix2Pix on edges2shoes." + ], + "table_footnote": [], + "table_body": "
ModelDatasetMethodMACs#ParametersFID(↓)
CycleGAN [49]horse2zebra [49]Original [49]56.80G(1.0×)11.30M(1.0×)61.53 (-)
Co-Evolution [35]13.40G(4.2×)-96.15(-34.62)
DMAD [27]2.41G(23.6×)0.28M(40.0×)62.96(-1.43)
Wavelet KD [47]1.68G(33.8×)0.72M(15.81×)77.04(-15.51)
GAN-Compression [26]2.67G(21.3×)0.34M(33.2×)64.95(-3.42)
GCC [28]2.40G(23.6×)-59.31(+2.22)
OMGD [33]1.408G(40.3×)0.137M(82.5×)51.92(+9.61)
DCD (Ours)1.408G(40.3×)0.137M(82.5×)48.24(+13.29)
summer2winter [49]Original [49]56.80G(1.0×)11.30M(1.0×)79.12(-)
Co-Evolution [35]11.10G(5.1×)-78.58(+0.54)
AutoGAN-Distiller [10]4.34G(13.1×)-78.33(+0.79)
DMAD [27]3.18G(17.9×)0.30M(37.7×)78.24(+0.88)
OMGD [33]1.408G(40.3×)0.137M(82.5×)73.79(+5.33)
DCD (Ours)1.408G(40.3×)0.137M(82.5×)73.63(+5.49)
Pix2Pix [18]edges2shoesOriginal [18]18.60G(1.0×)54.40M(1.0×)34.31(-)
DMAD [27]2.99G(6.2×)2.13M(25.5×)46.95(-12.64)
Wavelet KD [47]1.56G(11.92×)13.61M(4.00×)80.13(-45.82)
OMGD [33]1.219G(15.3×)3.404M(16.0×)25.00(+9.41)
DCD (Ours)1.219G(15.3×)3.404M(16.0×)23.43(+10.98)
", + "bbox": [ + 78, + 109, + 897, + 422 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/8d2119266f12d211465b089376d467f8075d65dbc6b6e6298d11377dac0d33bb.jpg", + "table_caption": [ + "Table 2. Comparison between different feature map distillation methods on horse2zebra." + ], + "table_footnote": [], + "table_body": "
DatasetMethodFID(↓)
horse2zebra [49]Baseline65.13
FitNet [34]65.84
MGD [43]67.57
KRD [6]61.53
DCD (Ours)48.24
", + "bbox": [ + 120, + 488, + 423, + 589 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "since 51.92 already is a strong performance. Nevertheless, our increase is very evident. Lastly, similar to CycleGAN, the results on paired Pix2Pix also show the superiority of our DCD over OMGD when compressing $15.3 \\times$ MACs and $16.0 \\times$ parameters. In this case, OMGD leads to 9.41 FID gains while our DCD has a better increase of 10.98.", + "bbox": [ + 75, + 621, + 467, + 712 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Therefore, our discriminator-cooperated feature map distillation has well demonstrated its great capability to boost the performance of a light-weighted generator.", + "bbox": [ + 75, + 715, + 467, + 761 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Feature Map Distillation. As introduced in Sec. 1, current feature map distillation methods such as FitNet [34], MGD [43] and KRD [6] construct pixel-to-pixel matching between the student generator and teacher generator. In contrast, our DCD is constrained to generate perceptually alike images. In Table 2, we replace our DCD with the aforementioned distillation scenarios for performance comparison. All experiments are performed on CycleGAN of $40.3 \\times$ MACs reduction as shown in Table 1. We can", + "bbox": [ + 75, + 763, + 467, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "see that FitNet and MGD incur performance degradation of 0.71 and 2.44 FID. Though KRD allows cross-layer connections and rises the FID by 4.40, the performance increase is very limited if compared with our 13.29 performance gains. To find out the root cause, these methods were initially invented to perform image classification that focuses more on extracting robust image feature vectors. However, GANs often pay great attention to the image contents, which do not call for identical pixel values between two images but urge more for perceptual discrepancies. Therefore, off-the-shelf per-pixel matching studies fail to fit well when directly extended to GAN compression.", + "bbox": [ + 496, + 460, + 890, + 642 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Visualization", + "text_level": 1, + "bbox": [ + 500, + 650, + 635, + 666 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We further present visualization of generated images from original CycleGAN generator as well as its compressed versions in Fig. 3. Evidently, our DCD results in not only more vivid objects (zebras), but also well retains background information. Regarding the objects, our DCD produces sharper and brighter stripes compared to other methods. In particular, existing methods are more or less influenced by the input. For example, the brown fur on horse is retained on the generated zebras (third row) while DCD well overcomes this drawback. As for the background, we find that DCD sometimes presents better visual perception even than the inputs, such as greener meadows and trees (last row). The better visual results are in accordance with better FID in Table 1. More examples of summer2winter and edges2shoes can be referred to the appendix.", + "bbox": [ + 496, + 674, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "20356", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/3d31e3e27ab0b2ab1f58dec89707c57b4b404eb02cffd4573871b0f20166c0d9.jpg", + "image_caption": [ + "Figure 3. Visualization comparison on horse2zebra with CycleGAN." + ], + "image_footnote": [], + "bbox": [ + 133, + 88, + 844, + 547 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/11d5ab460e1e3893305ff5b7c6d1fbea4367ac4b05751baceab8babb9983cc4c.jpg", + "table_caption": [ + "Table 3. Training loss influence to CycleGAN on horse2zebra." + ], + "table_footnote": [], + "table_body": "
LperLcddLganFID(↓)
✓67.20
✓324.27
✓389.77
✓✓55.24
✓✓65.13
✓✓323.63
✓✓✓48.24
", + "bbox": [ + 155, + 603, + 383, + 734 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Analysis", + "text_level": 1, + "bbox": [ + 76, + 741, + 178, + 756 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We continue to conduct ablation studies to analyze influences of different training losses defined in Eq. (8), as well as our downsampling strategies defined in Eq. (6), trying to reveal why our DCD performs well. All experiments are constructed by using CycleGAN on horse2zebra.", + "bbox": [ + 75, + 763, + 468, + 839 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Training Loss. Table 3 manifests the performance of different loss combinations. We observe the significance of the perceptual loss, without which the FID drastically increases to hundreds. Also, both our DCD loss and ad", + "bbox": [ + 75, + 839, + 468, + 898 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "versarial training loss are complementary to perceptual loss where $\\mathcal{L}_{per} + \\mathcal{L}_{dcd}$ increases performance to 55.24 and it is 65.13 for $\\mathcal{L}_{per} + \\mathcal{L}_{gan}$ . Combining all the training losses results in the optimal FID of 48.24.", + "bbox": [ + 500, + 585, + 890, + 646 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Downsampling. In Eq. (6), we adopt $1 \\times 1$ convolution operations to downsample feature maps to a three-channel RGB-encoded image before being fed to the teacher discriminator. We fix downsampling modules for teacher generator while updating those for student generator, which is very crucial to the performance of the student generator. We visualize RGB features from layer 3, 6, 9, and 12 of the teacher and student generators at different training stages, referred to as stage I~IV in order. Results are displayed in Fig.4 where two variants are introduced for comparison including updating both the teacher and student downsampling modules, and updating the teacher downsampling modules while fixing those of student. We can observe that the student generator keeps pace with teacher generator, so that they generate similar feature maps. This indicates the teacher knowledge has been well transferred to learn", + "bbox": [ + 496, + 657, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "20357", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/541d40842f192c53ce2dc98c8c6fcc96a6dc351374e8807492a30218f08bb771.jpg", + "image_caption": [ + "Figure 4. Feature map visualization of teacher and student generators at different training stages." + ], + "image_footnote": [], + "bbox": [ + 96, + 89, + 851, + 518 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "student model. Unfortunately, updating the teacher downsampling modules severely damages the knowledge from the teacher generator where only 61.16 FID is obtained if the student downsampling modules are updated as well and 69.41 otherwise. The poor performance mainly stems from the broken feature maps of teacher, where horse objects become invisible. Therefore, the student generator collapses as well. As for our downsampling strategy where downsampling modules are fixed for teacher generator while updated for student generator, the attention is gradually paid to the target horse objects as network training. Therefore, our discriminator-cooperated feature map distillation benefits more to localizing target objects. This is complementary to the perceptual loss that is engaged in style transferring. Their combination leads the lightweight student generator to finally synthesise vivid images with intricate textures.", + "bbox": [ + 75, + 553, + 472, + 795 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 813, + 194, + 828 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we proposed a novel discriminator-cooperated distillation (DCD) that reshapes the conventional pixel-to-pixel feature map match by skillfully utilizing the teacher discriminator as a transformation to pursue", + "bbox": [ + 75, + 839, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "better visual perception in generated images. Our methods show that the teacher discriminator can also be utilized to co-train with the compressed student generator and accordingly invent a collaborative adversarial training paradigm. Our experimental results demonstrated the significant improvement of DCD in both quantitative and qualitative performance, meanwhile, the complexity of student generator is reduced by a large volume.", + "bbox": [ + 496, + 553, + 890, + 675 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 500, + 704, + 658, + 722 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported by National Key R&D Program of China (No.2022ZD0118201), the National Science Fund for Distinguished Young Scholars (No.62025603), the National Natural Science Foundation of China (No.U21B2037, No.U22B2051, No.62176222, No.62176223, No.62176226, No.62072386, No.62072387, No.62072389, No.62002305 and No.62272401), and the Natural Science Foundation of Fujian Province of China (No.2021J01002, No.2022J06001), Guangdong Basic and Applied Basic Research Foundation (No.2019B1515120049).", + "bbox": [ + 496, + 734, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "20358", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Angeline Aguinaldo, Ping-Yeh Chiang, Alex Gain, Ameya Patil, Kolten Pearson, and Soheil Feizi. 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In Proceedings of the IEEE International Conference on Computer Vision (ICCV), pages 2223-2232, 2017. 1, 2, 5, 6" + ], + "bbox": [ + 501, + 90, + 892, + 768 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "20360", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Discriminator-Cooperated Feature Map Distillation for GAN Compression/e9448640-3029-45d7-94ad-42638a17674c_model.json b/2023/Discriminator-Cooperated Feature Map Distillation for GAN Compression/e9448640-3029-45d7-94ad-42638a17674c_model.json new file mode 100644 index 0000000000000000000000000000000000000000..48e06fef1bae0c51f92d6a4d8e2a7411def9658d --- /dev/null +++ b/2023/Discriminator-Cooperated Feature Map Distillation for GAN Compression/e9448640-3029-45d7-94ad-42638a17674c_model.json @@ -0,0 +1,1881 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.109, + 0.13, + 0.862, + 0.154 + ], + "angle": 0, + "content": "Discriminator-Cooperated Feature Map Distillation for GAN Compression" + }, + { + "type": "text", + "bbox": [ + 0.224, + 0.18, + 0.751, + 0.199 + ], + "angle": 0, + "content": "Tie Hu\\(^{1}\\), Mingbao Lin\\(^{3}\\), Lizhou You\\(^{1}\\), Fei Chao\\(^{1}\\), Rongrong Ji\\(^{1,2,4*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.27, + 0.199, + 0.7, + 0.217 + ], + "angle": 0, + "content": "\\(^{1}\\)MAC Lab, School of Informatics, Xiamen University" + }, + { + "type": "text", + "bbox": [ + 0.27, + 0.217, + 0.699, + 0.234 + ], + "angle": 0, + "content": "\\(^{2}\\)Institute of Artificial Intelligence, Xiamen University" + }, + { + "type": "text", + "bbox": [ + 0.406, + 0.234, + 0.566, + 0.25 + ], + "angle": 0, + "content": "Tencent Youtu Lab" + }, + { + "type": "text", + "bbox": [ + 0.282, + 0.251, + 0.69, + 0.27 + ], + "angle": 0, + "content": "4Shenzhen Research Institute of Xiamen University" + }, + { + "type": "text", + "bbox": [ + 0.189, + 0.272, + 0.777, + 0.288 + ], + "angle": 0, + "content": "{hutie, lmbxmu, youlizhou}@stu.xmu.edu.cn, {fchao, rrji}@xmu.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.322, + 0.314, + 0.339 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.354, + 0.474, + 0.732 + ], + "angle": 0, + "content": "Despite excellent performance in image generation, Generative Adversarial Networks (GANs) are notorious for its requirements of enormous storage and intensive computation. As an awesome \"performance maker\", knowledge distillation is demonstrated to be particularly efficacious in exploring low-priced GANs. In this paper, we investigate the irreplaceability of teacher discriminator and present an inventive discriminator-cooperated distillation, abbreviated as DCD, towards refining better feature maps from the generator. In contrast to conventional pixel-to-pixel match methods in feature map distillation, our DCD utilizes teacher discriminator as a transformation to drive intermediate results of the student generator to be perceptually close to corresponding outputs of the teacher generator. Furthermore, in order to mitigate mode collapse in GAN compression, we construct a collaborative adversarial training paradigm where the teacher discriminator is from scratch established to co-train with student generator in company with our DCD. Our DCD shows superior results compared with existing GAN compression methods. For instance, after reducing over \\(40 \\times\\) MACs and \\(80 \\times\\) parameters of CycleGAN, we well decrease FID metric from 61.53 to 48.24 while the current SoTA method merely has 51.92. This work's source code has been made accessible at https://github.com/poopit/DCD-official." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.761, + 0.21, + 0.777 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.787, + 0.47, + 0.879 + ], + "angle": 0, + "content": "Image generation transforms random noise or source-domain images to other images in user-required domains. Recent years have witnessed the burgeoning of generative adversarial networks (GANs) that lead to substantial progress in image-to-image translation [8, 9, 18, 49], style transfer [11, 12, 42], image synthesis [3, 22, 23, 32, 46], etc." + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.332, + 0.871, + 0.397 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.547, + 0.411, + 0.851, + 0.485 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.499, + 0.893, + 0.542 + ], + "angle": 0, + "content": "Figure 1. (a) Layer-by-layer feature map distillation [34]. (b) Cross-layer feature map distillation [6]. (c) Our discriminator-cooperated feature map distillation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.552, + 0.893, + 0.688 + ], + "angle": 0, + "content": "Image generation has a wide application in daily entertainment such as TikTok AI image generator, Dream by WOMBO, Google Imagen, and so on. Running platforms performing these applications are typically featured with poor memory storage and limited computational power. However, GANs are also ill-famed for the growing spurt of learnable parameters and multiply-accumulate operations (MACs), raising a huge challenge to the storage requirement and computing ability of deployment infrastructure." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.895, + 0.901 + ], + "angle": 0, + "content": "To address the above dilemma for better usability of GANs in serving human life, methods such as pruning [7, 27, 28, 33], neural network architecture search (NAS) [10, 19, 26] and quantization [39, 40], have been broadly explored to obtain a smaller generator. On the premise of these compression researches, knowledge distillation, in particular to distilling feature maps, has been accepted as a supplementary means to enhance the performance of compressed generators [1, 4, 17, 26, 29, 41]. Originated from image classification, as illustrated in Fig. 1(a), feature map based distillation, which extracts information of intermediate activations and transfers the knowledge from the teacher model to the student one, has been extensively explored and demonstrated to well improve the capability of lightweight mod" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.225, + 0.9 + ], + "angle": 0, + "content": "*Corresponding Author" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "20351" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.226 + ], + "angle": 0, + "content": "els [5, 25, 34, 43, 45]. Distinctive from passing on common feature maps from teacher to student, AT [45] calculates feature attentions as the delivered knowledge; MGD [43] randomly masks feature maps to indirectly guide the student to learn from the teacher; KRD [6] uses a cross-layer distillation method to allow the “new knowledge” of the student to learn from the “old knowledge” in teacher, as shown in Fig. 1(b). Whatever, most methods execute pixel-to-pixel feature maps matching between teacher and student." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.23, + 0.471, + 0.518 + ], + "angle": 0, + "content": "Alike to the implementations on image classification, feature map based distillation is also considered in GAN compression. For example, GCC [28] considers a well pretrained discriminator to absorb high-level information from the teacher-generated image, and fuses it with intermediate activations from the teacher generator, results of which are passed to the corresponding position of the student generator. OMGD [33] utilizes an online multi-granularity strategy to allow a deeper teacher generator and a wider one to simultaneously deliver output image knowledge of different granularities to the student generator. These two methods follow the pipeline of image classification to tune the intermediate outputs of student generator with those of teacher generator in a fashion of per-pixel matching. Although the sustainable progress on multiple benchmark datasets demonstrates the efficacy of intermediate activation outputs, the feature-based distillation, as we reveal in this paper, is not well compatible with the very nature of generating perceptually similar images and adversarial training paradigm." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.52, + 0.47, + 0.838 + ], + "angle": 0, + "content": "Concretely speaking, conversely to image classification that relies on feature vector representations, the essence of image generation is to improve perceptually alike between the real images and generated images. Two important facts cause it is eventually difficult to use per-pixel match to analyze a pair of images: First, two similar images can contain many different pixel values; Second, two dissimilar images can still comprise the same pixel values. Thus, it is not suitable to simply use the per-pixel match. Regarding adversarial training in GANs, a generator learns to synthesize samples that best resemble the dataset, meanwhile a discriminator differentiate samples in the dataset from the generator generated samples. The adversarial results finally lead the generator to creating images of out-of-the-ordinary visual quality, indicating that the discriminator is also empowered with informative capacity and can be exploited to enrich the distillation of feature maps. Therefore, it might be inappropriate to directly extend feature map distillation in image classification to image generation. And GAN compression oriented feature map distillation with discriminator included remains to be well explored." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.84, + 0.47, + 0.902 + ], + "angle": 0, + "content": "In order to achieve this objective, in this paper, we propose a discriminator-cooperated distillation (DCD) method to involve the teacher discriminator in distilling feature maps for student generator. A simple illustration is given in" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.438 + ], + "angle": 0, + "content": "Fig. 1(c), in contrast to the vanilla pixel-wise distance constraint, our DCD measures the distance at the end of teacher discriminator with the intermediate generator outputs as its inputs. Our DCD is perspicacious in multiple benchmark datasets with a simple implementation. Akin to perceptual loss [20] which employs a pre-trained neural network such as a VGG model [36] to extract features upon which the \\(\\ell_1\\) distance is calculated from activations of hidden layers, the teacher discriminator in DCD also acts as a feature extractor. Due to pooling operations in the hidden layers, feature maps from different sources (student generator and teacher generator) as inputs to the discriminator may lead to identical latent representations, therefore encouraging natural and perceptually pleasing results. In addition, the proposed DCD is used in conjunction with collaborative adversarial training, which is also simple but perspicacious to allow the student generator to fool the discriminator for generating better images. In contrast to discriminator-free paradigm training [28], we find our DCD empowers the compressed student generator with a better capability to compete against teacher discriminator. Thus, we also employ the teacher discriminator to collaboratively determine whether inputs from the student generator are real or not." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.44, + 0.892, + 0.591 + ], + "angle": 0, + "content": "This work intends to raise the level of feature map distillation to strengthen the compressed student generator to generate high-quality images. The major contributions we have made across the entire paper are listed as follows: (1) An incentive GAN-oriented discriminator-cooperated feature map distillation method to produce images with high fidelity; (2) One novel collaborative adversarial training paradigm to better reach a global equilibrium point in compressing GANs; (3) Remarkable reduction on the generator complexity and significant performance increase." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.609, + 0.642, + 0.625 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.635, + 0.766, + 0.651 + ], + "angle": 0, + "content": "2.1. GANs and GAN Compression" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Generative adversarial networks (GANs) [13] have attracted the attention of substantive researchers due to their outstanding performance in image generation tasks [3, 8, 9, 18, 22, 23, 32, 46, 49]. Since the infancy of GAN, many variants have emerged, from DCGAN [32], which embraces convolutional neural networks for the first time, to CycleGAN [49] and Pix2Pix [18] which implement image-to-image translation, to StyleGAN [22] to enable controllable manipulation of various attributes of image synthesis. CycleGAN [49] transfers a source-domain image into a target style in an unpaired configuration, such as a horse image to a zebra pattern or a summer image to a winter style. On the other hand, Pix2Pix [18] is given a ground-truth image and converts a semantic segmentation or contour map into a photo-realistic picture. Albeit the performance, GANs suffer heavy burden on storage and computation." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20352" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.349 + ], + "angle": 0, + "content": "Therefore, recent years have witnessed increasing attention on compressing GANs [7, 10, 19, 21, 24, 26, 27, 30, 35, 39, 40, 47]. Co-evolution [35] prunes filters in the generator under the constraint of consistent output distributions. GAN Slimming [39] suggests a compression framework that can integrate pruning, knowledge distillation and quantization. GAN Compression [26] views the teacher output as the pseudo label for student generator and unifies the compression framework for GANs trained on paired data and unpaired data. GCC [28] combines information from discriminator in knowledge distillation, an idea closer to our approach, but the use of discriminator is still under-explored. Although the above approaches have compressed parameters and computation costs, both the generated image quality and the model size are still far from practical applications on mobile devices. OMGD [33] bridges this huge gap in a way by constructing discriminator-free distillation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.35, + 0.473, + 0.502 + ], + "angle": 0, + "content": "Of the above methods, GCC is the most similar to our approach with major differences in: (1) GCC involves summation of discriminator activations in distilling intermediate layers of student generator. Our DCD calculates distance between teacher and student directly upon feature maps of the discriminator. (2) GCC focuses on a more suitable student discriminator for student generator. Our DCD discards student discriminator by adopting that of teacher. (3) Results show merits of our DCD over GCC in both quantitative and visual quality with a higher compression rate." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.514, + 0.29, + 0.53 + ], + "angle": 0, + "content": "2.2. Knowledge Distillation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.539, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Pioneered by FitNet as of 2014 [34], knowledge distillation (KD) [16] has become a regular approach in model compression especially to GAN compression, where a larger model with better performance imparts knowledge to a smaller model. Since then, great efforts have been made to dig out opulent knowledge hints, such as output logits [21, 47, 48], intermediate feature maps [6, 14, 34], instance relation [31, 38] and so on. In this paper, we are mainly inspired by the intermediate feature map based distillation that has been extensively mined to efficiently guide the training of the student network. Compared to other knowledge hints, feature maps often accommodate a richer level of information and provide more detailed guidance for the student network. AT [45] extracts the attention map from the feature maps and trains the student's attention maps to be as close as possible to the one of teacher. MGD [43] transforms direct learning from the teacher into a generative intermediate goal. KRD [6] uses the idea of cross-layer distillation to allow old knowledge from the teacher to guide new knowledge learning from the student network. Nevertheless, conventional methods require per-pixel match between feature maps of teacher and student, which does not fit well in GAN compression because the goal of GANs is to generate perceptually similar images. In" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "this paper, we dig deeper into the distinctiveness of generative adversarial networks." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.138, + 0.635, + 0.156 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.164, + 0.642, + 0.18 + ], + "angle": 0, + "content": "3.1. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.189, + 0.892, + 0.265 + ], + "angle": 0, + "content": "Generative adversarial networks [13], or GANs for short, are an interesting manner to train a generative model by modelling the problem with two sub-models including a generator model \\(\\mathcal{G}\\) and a discriminator model \\(\\mathcal{D}\\). The two models are trained together in a zero-sum game as:" + }, + { + "type": "equation", + "bbox": [ + 0.573, + 0.278, + 0.891, + 0.337 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\min _ {\\mathcal {G}} \\max _ {\\mathcal {D}} \\mathcal {L} _ {g a n} = \\mathbb {E} _ {y \\sim p _ {r e a l}} \\log \\mathcal {D} (y) \\\\ + \\mathbb {E} _ {x \\sim p (x)} \\left[ \\log \\left(1 - \\mathcal {D} (\\mathcal {G} (x))\\right) \\right]. \\tag {1} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.349, + 0.892, + 0.47 + ], + "angle": 0, + "content": "Herein, the generator model \\(\\mathcal{G}\\) is trained to generate new examples, and the discriminator model \\(\\mathcal{D}\\) tries to classify examples as either real (from the domain) or fake (generated). The two models are trained adversarially until the discriminator model is fooled at most times, which indicates that the generator model is producing plausible examples. Then, the generator \\(\\mathcal{G}\\) is deployed online to complete service for reality." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.471, + 0.892, + 0.591 + ], + "angle": 0, + "content": "The serviceability of generator \\(\\mathcal{G}\\) rests with not only the performance, but also the hardware capability that makes a greater demand on generator complexity. Therefore, a lighter student generator, \\(\\mathcal{G}^S\\), can be developed by various methods. The original generator and discriminator, respectively denoted as \\(\\mathcal{G}^T\\) and \\(\\mathcal{D}^T\\) in this situation to differentiate, play as a teacher to enhance the ability of student generator \\(\\mathcal{G}^S\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.593, + 0.892, + 0.655 + ], + "angle": 0, + "content": "Giving an input variable \\(x \\sim p(x) \\in \\mathbb{R}^{H \\times W \\times C}\\), we denote the \\(i\\)-th layer output of generator as \\(\\mathcal{G}_i(x)\\), and \\(\\mathcal{I}_{\\mathcal{G}}(x)\\) as layer index set of extracted intermediate outputs. Thus, the feature maps based distillation is formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.563, + 0.667, + 0.892, + 0.702 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {f e a - d i s} = \\sum_ {i \\in I _ {\\mathcal {G}}} \\ell \\left(\\mathcal {G} _ {i} ^ {T} (x), f \\left(\\mathcal {G} _ {i} ^ {S} (x)\\right)\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.715, + 0.892, + 0.79 + ], + "angle": 0, + "content": "where \\( f(\\cdot) \\) is the affine transformation function to align the channel dimensions between the teacher and student, such as \\( 1 \\times 1 \\) convolution operators in existing studies [26,28,33]. Also, \\( \\ell(\\cdot, \\cdot) \\) refers to the distance measure function, such as Euclidean distance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.792, + 0.892, + 0.869 + ], + "angle": 0, + "content": "Additionally, perceptual loss [20], \\(\\mathcal{L}_{per}\\), is also widely adopted in existing studies to encourage natural and perceptually pleasing restored images. \\(\\mathcal{L}_{per}\\) comprises a feature reconstruction loss \\(\\mathcal{L}_{fea}\\) and a style reconstruction loss \\(\\mathcal{L}_{sty}\\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.581, + 0.882, + 0.892, + 0.9 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {p e r} = \\lambda_ {f e a} \\cdot \\mathcal {L} _ {f e a} + \\lambda_ {s t y} \\cdot \\mathcal {L} _ {s t y}. \\tag {3}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20353" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.092, + 0.48, + 0.246 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.261, + 0.471, + 0.318 + ], + "angle": 0, + "content": "Figure 2. Framework of our DCD. Intermediate feature maps from student and teacher are downsampled first to align the dimension, results of which are then fed to the teacher discriminator to minimize distance for a perceptually vivid generated image." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.346, + 0.47, + 0.406 + ], + "angle": 0, + "content": "Herein, \\(\\mathcal{L}_{fea}\\) propels the output representation of the teacher generator to approach to that of the student generator. This is achieved by a pre-trained VGG network \\(\\Phi (\\cdot)\\) [36] and formalized as:" + }, + { + "type": "equation", + "bbox": [ + 0.085, + 0.419, + 0.47, + 0.455 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {f e a} = \\sum_ {j \\in I _ {\\Phi}} \\frac {1}{H _ {j} W _ {j} C _ {j}} \\left\\| \\Phi_ {j} \\left(\\mathcal {G} ^ {T} (x)\\right) - \\Phi_ {j} \\left(\\mathcal {G} ^ {S} (x)\\right) \\right\\| _ {1}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.469, + 0.469, + 0.514 + ], + "angle": 0, + "content": "where \\(\\Phi_j(\\cdot)\\) returns the \\(j\\)-th activation output of VGG network and \\(H_{j}\\times W_{j}\\times C_{j}\\) is its shape. Alike to \\(I_{\\mathcal{G}}\\), \\(I_{\\Phi}\\) contains layer index of extracted intermediate outputs." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.516, + 0.469, + 0.577 + ], + "angle": 0, + "content": "As for \\(\\mathcal{L}_{sty}\\), it minimizes the difference between Gram matrices of the output and target images in order to preserve style characteristics such as color, textures and common pattern [33]. The \\(\\mathcal{L}_{sty}\\) is calculated as:" + }, + { + "type": "equation", + "bbox": [ + 0.085, + 0.589, + 0.47, + 0.625 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {s t y} = \\sum_ {j \\in I _ {\\Phi}} \\left\\| G \\left(\\Phi_ {j} \\left(\\mathcal {G} ^ {T} (x)\\right)\\right) - G \\left(\\Phi_ {j} \\left(\\mathcal {G} ^ {S} (x)\\right)\\right) \\right\\| _ {1}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.638, + 0.434, + 0.654 + ], + "angle": 0, + "content": "where \\(G(\\cdot)\\) represents abbreviation of Gram matrices." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.665, + 0.406, + 0.682 + ], + "angle": 0, + "content": "3.2. Discriminator-Cooperated Distillation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Stepping back and reflecting on the feature map based distillation in Eq. (2), we realize that a simple utilization of generator capacity is not intact in earlier methods. The central principle of a GAN is contingent on an \"indirect\" training route through the discriminator updated dynamically to discern how \"realistic\" its input (i.e., generator output) seems. This means that the generator is not trained to minimize the distance from a generated image to a target image, but rather to deceive the discriminator. It is the copetition pattern between the generator and discriminator that even brings about superficially authentic generated images. Thus, the discriminator is also empowered with informative capacity and must be utilized to enrich the distillation of feature maps." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.183 + ], + "angle": 0, + "content": "As shown in Fig. 2, we rethink Eq. (2) and integrate teacher discriminator to cooperate with the distillation process. Alike to feature reconstruction loss defined in Eq. (4), while taking the generator outputs as its inputs, we accomplish our distillation by aligning the intermediate outputs of the discriminator. We formulate this learning process as:" + }, + { + "type": "equation", + "bbox": [ + 0.503, + 0.194, + 0.892, + 0.245 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {d c d} = \\sum_ {k \\in I _ {\\mathcal {D}}} \\sum_ {i \\in I _ {\\mathcal {G}}} \\ell \\left(\\mathcal {D} _ {k} ^ {T} \\left(f \\left(\\mathcal {G} _ {i} ^ {T} (x)\\right)\\right), \\mathcal {D} _ {k} ^ {T} \\left(f \\left(\\mathcal {G} _ {i} ^ {S} (x)\\right)\\right)\\right), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.246, + 0.892, + 0.382 + ], + "angle": 0, + "content": "where \\(\\mathcal{D}_k^T\\) stands for the output of its \\(k\\)-th layer. Similar to \\(I_{\\mathcal{G}}\\), \\(I_{\\mathcal{D}}\\) is a layer index set of the teacher discriminator; herein, \\(f(\\cdot)\\) denotes \\(1 \\times 1\\) convolution operations to down-sample the channel dimensions of both the teacher and student feature maps to those of discriminator input. Usually, the channel number of discriminator input is set to three for an RGB-encoded image. Here, \\(f(\\cdot)\\) for teacher generator becomes constant once initialized while that for student generator continues updating for a better fit with teacher." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.383, + 0.893, + 0.609 + ], + "angle": 0, + "content": "As an analogy to the vanilla feature map based distillation in Eq. (2) that compels the per-pixel match between intermediate outputs of both the teacher generator and student generator, the role of the teacher discriminator resembles the pre-trained VGG in Eq. (4), which acts as a transformed network to enable the intermediate results of student generator to be perceptually alike to these of teacher generator. In contrast, it does not require them to do pixel-by-pixel match, since two images might look similar in perspective, but they often have different pixel values, thus we cannot depend on per-pixel match. Notice that our discriminator-cooperated distillation is complementary to perceptual loss. The former concentrates on object localization while the latter pays attention to style discrepancies. The analysis of this phenomenon is in Sec. 4.4." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.62, + 0.808, + 0.636 + ], + "angle": 0, + "content": "3.3. Collaborative Adversarial Training" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.643, + 0.892, + 0.87 + ], + "angle": 0, + "content": "GANs perform an alternating training paradigm for a unique global equilibrium point: 1) Training the discriminator \\(\\mathcal{D}\\) to identify real and generated data while keeping the generator constant; 2) Training the generator \\(\\mathcal{G}\\) to generate vivid data that fools the discriminator while keeping the discriminator constant; 3) Repeating steps 1) and 2) till the discriminator model is fooled at most time. However, the equilibrium is no longer guaranteed when \\(\\mathcal{D}\\) and \\(\\mathcal{G}\\) are empowered with inconsistent abilities, in which case unstable convergence frequently occurs. Generally, the instability stems from two ill-famed issues including vanishing gradient where loss for the generator is zero when the discriminator is perfect, and mode collapse where the stronger generator produces a small set of outputs for any input and the weaker discriminator traps in a local minimum [2]." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Especially, the mode collapse issue is even widespread in GAN compression because the compressed student gen" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20354" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.473, + 0.272 + ], + "angle": 0, + "content": "erator \\(\\mathcal{G}^S\\) is powerless to compete with the original full discriminator [27], in particular a pre-trained one [4, 19, 30]. The community has excavated various approaches to weaken the student discriminator. For example, GCC [28] selectively activates discriminator neurons. Nevertheless, a rule-of-thumb selection has to be carefully designed. Also, training a student discriminator is computationally redundant since it is unwanted in the testing stage. OMGD [33] co-trains teacher generator with the teacher discriminator while the student generator is discriminator-free. The missing adversarial training of student generator somehow barricades the further performance increase." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.273, + 0.473, + 0.485 + ], + "angle": 0, + "content": "In this paper, we also reject real student discriminator, and to ensure the teacher's optimization, the teacher discriminator, \\(\\mathcal{D}^T\\), is online trained from scratch to be well-matched with the teacher generator \\(\\mathcal{G}^T\\). Comparing to [33], teacher discriminator \\(\\mathcal{D}^T\\) also appears in the form of a collaborative discriminator to determine if the inputs from student generator \\(\\mathcal{G}^T\\) are real or fake. The major concern originates from the actuality that the teacher discriminator is much powerful than the compressed student generator, which causes mode collapse in adversarial training. Luckily, our discriminator-cooperated distillation in Eq. (6) furnishes student generator with increasing capability to battle against teacher discriminator and leads to better performance than [33] as demonstrated in the experiment." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.485, + 0.47, + 0.5 + ], + "angle": 0, + "content": "Based on Eq. (1), our adversarial training is rewritten as:" + }, + { + "type": "equation", + "bbox": [ + 0.086, + 0.505, + 0.469, + 0.616 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\min _ {\\mathcal {G} ^ {T}, \\mathcal {G} ^ {S}} \\max _ {\\mathcal {D} ^ {T}} \\mathcal {L} _ {c o l} = \\mathbb {E} _ {y \\sim p _ {r e a l}} \\log \\mathcal {D} ^ {T} (y) \\\\ + \\mathbb {E} _ {x \\sim p (x)} \\left[ \\log \\left(1 - \\mathcal {D} ^ {T} \\big (\\mathcal {G} ^ {T} (x) \\big)\\right) \\right] \\\\ + \\lambda_ {s t u} \\cdot \\mathbb {E} _ {x \\sim p (x)} \\left[ \\log \\left(1 - \\mathcal {D} ^ {T} \\left(\\mathcal {G} ^ {S} (x)\\right)\\right) \\right], \\tag {7} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.623, + 0.47, + 0.669 + ], + "angle": 0, + "content": "where \\(\\lambda_{stu}\\) refers to a trade-off parameter; and \\(\\lambda_{stu} = 0\\) degenerates to discarding student discriminator when constrained with the student generator [33]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.675, + 0.26, + 0.692 + ], + "angle": 0, + "content": "3.4. Training Objective" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.699, + 0.47, + 0.82 + ], + "angle": 0, + "content": "Looking back to Sec. 3.1, the loss terms in most conventional feature map based distillation methods include \\(\\mathcal{L}_{gan}\\) in Eq. (1), \\(\\mathcal{L}_{fea - dis}\\) in Eq. (2) and \\(\\mathcal{L}_{per}\\) in Eq. (3). In this paper, we improve \\(\\mathcal{L}_{fea - dis}\\) through a discriminator-cooperated feature map distillation loss \\(\\mathcal{L}_{dcd}\\) in Eq. (6), and \\(\\mathcal{L}_{gan}\\) through collaborative adversarial training loss \\(\\mathcal{L}_{col}\\) in Eq. (7). Therefore, the overall training objective in this paper is given in the following:" + }, + { + "type": "equation", + "bbox": [ + 0.135, + 0.826, + 0.469, + 0.851 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\mathcal {G} ^ {T}, \\mathcal {G} ^ {S}} \\max _ {\\mathcal {D} ^ {T}} \\left(\\mathcal {L} _ {g a n} + \\mathcal {L} _ {p e r} + \\lambda_ {d c d} \\cdot \\mathcal {L} _ {d c d}\\right), \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.47, + 0.902 + ], + "angle": 0, + "content": "where \\(\\lambda_{dcd}\\) balances the loss term. Four hyper-parameters: \\(\\lambda_{fea}\\), \\(\\lambda_{sty}\\), \\(\\lambda_{stu}\\) and \\(\\lambda_{dcd}\\) are used in this paper, influence of each parameter is ablated in the appendix." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.09, + 0.667, + 0.108 + ], + "angle": 0, + "content": "4. Experimentation" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.116, + 0.589, + 0.133 + ], + "angle": 0, + "content": "4.1. Setups" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.139, + 0.892, + 0.351 + ], + "angle": 0, + "content": "GAN Models and Benchmarks. We present the performance of compressed CycleGAN [49] and Pix2Pix [18] to follow and compare with existing methods [7, 19, 21, 26, 27, 35, 39, 47]. For a fair comparison with the current SoTA OMGD [33], the compressed generators (students) consist of 1/4 channels of the original full ResNet generators (teachers) [26]. CycleGAN translates images from one domain to another without a one-to-one mapping between the source and target domain. Therefore, we verify the performance upon unpaired image translation benchmarks including horse2zebra [49] and summer2winter [49]. As for Pix2Pix, we perform distillation upon paired edges2shoes [44] because it requires learning a mapping from input images to output images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.352, + 0.892, + 0.457 + ], + "angle": 0, + "content": "**Evaluations. Fréchet Inception Distance (FID), or FID for short [15], is particularly developed to evaluate the performance of GANs. It accesses the quality of generated images by an Inception-V3 network [37] to separately embed synthetic and real images to feature space, and then calculate the Wasserstein distance of their distributions. A lower FID score indicate better quality of generated images.**" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.458, + 0.892, + 0.58 + ], + "angle": 0, + "content": "Implementations. We train CycleGAN and Pix2Pix for a total of 100 epochs. The initial learning rate is given as \\(2 \\times e^{-4}\\) and then linearly decayed to 0 as training goes. The batch size is set to 4 on edges2shoes, and 1 on horse2zebra [49] and summer2winter [49]. We have \\(\\lambda_{dcd} = 1\\), \\(\\lambda_{fea} = 1 \\times e^{1}\\), \\(\\lambda_{sty} = 1 \\times e^{4}\\) and \\(\\lambda_{stu} = 1\\) across all experiments. In the appendix, specific ablations in regard to these hyper-parameters have been provided." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.59, + 0.733, + 0.607 + ], + "angle": 0, + "content": "4.2. Quantitative Comparison" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.892, + 0.903 + ], + "angle": 0, + "content": "GAN Compression. We first compare with existing implementations on GAN compression in Table 1 where the blue number indicates performance drop, while the red number denotes performance increase compared with the original GAN models. We conclude the following observations from Table 1: First, on summer2winter, all methods lead to a performance increase of more or less. On the contrary, most methods cause FID drops on the challenging horse2zebra and edges2shoes while methods such as OMGD [33] and our DCD consistently enhance the performance. Second, our DCD leads to the most complexity reduction w.r.t. MACs and parameters, meanwhile it gains the best performance increase on all the three benchmark datasets. Third, with the same reduction of MACs \\((40.3\\times)\\) and parameters \\((82.5\\times)\\) on unpaired CycleGAN, our DCD well outperforms the recent SoTA method, i.e., OMGD. In particular, we drastically increase the performance of 51.92 for OMGD to 48.24, which is also 13.29 increase compared to the original CycleGAN. This increase is very challenging" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.958 + ], + "angle": 0, + "content": "20355" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.156, + 0.09, + 0.812, + 0.104 + ], + "angle": 0, + "content": "Table 1. Performance comparison when compressing CycleGAN on horse2zebra, and Pix2Pix on edges2shoes." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.111, + 0.898, + 0.423 + ], + "angle": 0, + "content": "
ModelDatasetMethodMACs#ParametersFID(↓)
CycleGAN [49]horse2zebra [49]Original [49]56.80G(1.0×)11.30M(1.0×)61.53 (-)
Co-Evolution [35]13.40G(4.2×)-96.15(-34.62)
DMAD [27]2.41G(23.6×)0.28M(40.0×)62.96(-1.43)
Wavelet KD [47]1.68G(33.8×)0.72M(15.81×)77.04(-15.51)
GAN-Compression [26]2.67G(21.3×)0.34M(33.2×)64.95(-3.42)
GCC [28]2.40G(23.6×)-59.31(+2.22)
OMGD [33]1.408G(40.3×)0.137M(82.5×)51.92(+9.61)
DCD (Ours)1.408G(40.3×)0.137M(82.5×)48.24(+13.29)
summer2winter [49]Original [49]56.80G(1.0×)11.30M(1.0×)79.12(-)
Co-Evolution [35]11.10G(5.1×)-78.58(+0.54)
AutoGAN-Distiller [10]4.34G(13.1×)-78.33(+0.79)
DMAD [27]3.18G(17.9×)0.30M(37.7×)78.24(+0.88)
OMGD [33]1.408G(40.3×)0.137M(82.5×)73.79(+5.33)
DCD (Ours)1.408G(40.3×)0.137M(82.5×)73.63(+5.49)
Pix2Pix [18]edges2shoesOriginal [18]18.60G(1.0×)54.40M(1.0×)34.31(-)
DMAD [27]2.99G(6.2×)2.13M(25.5×)46.95(-12.64)
Wavelet KD [47]1.56G(11.92×)13.61M(4.00×)80.13(-45.82)
OMGD [33]1.219G(15.3×)3.404M(16.0×)25.00(+9.41)
DCD (Ours)1.219G(15.3×)3.404M(16.0×)23.43(+10.98)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.46, + 0.468, + 0.486 + ], + "angle": 0, + "content": "Table 2. Comparison between different feature map distillation methods on horse2zebra." + }, + { + "type": "table", + "bbox": [ + 0.121, + 0.489, + 0.424, + 0.59 + ], + "angle": 0, + "content": "
DatasetMethodFID(↓)
horse2zebra [49]Baseline65.13
FitNet [34]65.84
MGD [43]67.57
KRD [6]61.53
DCD (Ours)48.24
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.622, + 0.468, + 0.713 + ], + "angle": 0, + "content": "since 51.92 already is a strong performance. Nevertheless, our increase is very evident. Lastly, similar to CycleGAN, the results on paired Pix2Pix also show the superiority of our DCD over OMGD when compressing \\(15.3 \\times\\) MACs and \\(16.0 \\times\\) parameters. In this case, OMGD leads to 9.41 FID gains while our DCD has a better increase of 10.98." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.716, + 0.468, + 0.762 + ], + "angle": 0, + "content": "Therefore, our discriminator-cooperated feature map distillation has well demonstrated its great capability to boost the performance of a light-weighted generator." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Feature Map Distillation. As introduced in Sec. 1, current feature map distillation methods such as FitNet [34], MGD [43] and KRD [6] construct pixel-to-pixel matching between the student generator and teacher generator. In contrast, our DCD is constrained to generate perceptually alike images. In Table 2, we replace our DCD with the aforementioned distillation scenarios for performance comparison. All experiments are performed on CycleGAN of \\(40.3 \\times\\) MACs reduction as shown in Table 1. We can" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.461, + 0.892, + 0.643 + ], + "angle": 0, + "content": "see that FitNet and MGD incur performance degradation of 0.71 and 2.44 FID. Though KRD allows cross-layer connections and rises the FID by 4.40, the performance increase is very limited if compared with our 13.29 performance gains. To find out the root cause, these methods were initially invented to perform image classification that focuses more on extracting robust image feature vectors. However, GANs often pay great attention to the image contents, which do not call for identical pixel values between two images but urge more for perceptual discrepancies. Therefore, off-the-shelf per-pixel matching studies fail to fit well when directly extended to GAN compression." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.651, + 0.637, + 0.667 + ], + "angle": 0, + "content": "4.3. Visualization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We further present visualization of generated images from original CycleGAN generator as well as its compressed versions in Fig. 3. Evidently, our DCD results in not only more vivid objects (zebras), but also well retains background information. Regarding the objects, our DCD produces sharper and brighter stripes compared to other methods. In particular, existing methods are more or less influenced by the input. For example, the brown fur on horse is retained on the generated zebras (third row) while DCD well overcomes this drawback. As for the background, we find that DCD sometimes presents better visual perception even than the inputs, such as greener meadows and trees (last row). The better visual results are in accordance with better FID in Table 1. More examples of summer2winter and edges2shoes can be referred to the appendix." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20356" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.134, + 0.089, + 0.845, + 0.549 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.281, + 0.552, + 0.687, + 0.566 + ], + "angle": 0, + "content": "Figure 3. Visualization comparison on horse2zebra with CycleGAN." + }, + { + "type": "table_caption", + "bbox": [ + 0.087, + 0.584, + 0.457, + 0.598 + ], + "angle": 0, + "content": "Table 3. Training loss influence to CycleGAN on horse2zebra." + }, + { + "type": "table", + "bbox": [ + 0.156, + 0.604, + 0.385, + 0.735 + ], + "angle": 0, + "content": "
LperLcddLganFID(↓)
✓67.20
✓324.27
✓389.77
✓✓55.24
✓✓65.13
✓✓323.63
✓✓✓48.24
" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.742, + 0.179, + 0.757 + ], + "angle": 0, + "content": "4.4. Analysis" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.469, + 0.84 + ], + "angle": 0, + "content": "We continue to conduct ablation studies to analyze influences of different training losses defined in Eq. (8), as well as our downsampling strategies defined in Eq. (6), trying to reveal why our DCD performs well. All experiments are constructed by using CycleGAN on horse2zebra." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.47, + 0.9 + ], + "angle": 0, + "content": "Training Loss. Table 3 manifests the performance of different loss combinations. We observe the significance of the perceptual loss, without which the FID drastically increases to hundreds. Also, both our DCD loss and ad" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.587, + 0.892, + 0.647 + ], + "angle": 0, + "content": "versarial training loss are complementary to perceptual loss where \\(\\mathcal{L}_{per} + \\mathcal{L}_{dcd}\\) increases performance to 55.24 and it is 65.13 for \\(\\mathcal{L}_{per} + \\mathcal{L}_{gan}\\). Combining all the training losses results in the optimal FID of 48.24." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Downsampling. In Eq. (6), we adopt \\(1 \\times 1\\) convolution operations to downsample feature maps to a three-channel RGB-encoded image before being fed to the teacher discriminator. We fix downsampling modules for teacher generator while updating those for student generator, which is very crucial to the performance of the student generator. We visualize RGB features from layer 3, 6, 9, and 12 of the teacher and student generators at different training stages, referred to as stage I~IV in order. Results are displayed in Fig.4 where two variants are introduced for comparison including updating both the teacher and student downsampling modules, and updating the teacher downsampling modules while fixing those of student. We can observe that the student generator keeps pace with teacher generator, so that they generate similar feature maps. This indicates the teacher knowledge has been well transferred to learn" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "20357" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.097, + 0.09, + 0.852, + 0.52 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.198, + 0.525, + 0.771, + 0.54 + ], + "angle": 0, + "content": "Figure 4. Feature map visualization of teacher and student generators at different training stages." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.554, + 0.473, + 0.796 + ], + "angle": 0, + "content": "student model. Unfortunately, updating the teacher downsampling modules severely damages the knowledge from the teacher generator where only 61.16 FID is obtained if the student downsampling modules are updated as well and 69.41 otherwise. The poor performance mainly stems from the broken feature maps of teacher, where horse objects become invisible. Therefore, the student generator collapses as well. As for our downsampling strategy where downsampling modules are fixed for teacher generator while updated for student generator, the attention is gradually paid to the target horse objects as network training. Therefore, our discriminator-cooperated feature map distillation benefits more to localizing target objects. This is complementary to the perceptual loss that is engaged in style transferring. Their combination leads the lightweight student generator to finally synthesise vivid images with intricate textures." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.814, + 0.196, + 0.829 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.903 + ], + "angle": 0, + "content": "In this paper, we proposed a novel discriminator-cooperated distillation (DCD) that reshapes the conventional pixel-to-pixel feature map match by skillfully utilizing the teacher discriminator as a transformation to pursue" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.554, + 0.892, + 0.676 + ], + "angle": 0, + "content": "better visual perception in generated images. Our methods show that the teacher discriminator can also be utilized to co-train with the compressed student generator and accordingly invent a collaborative adversarial training paradigm. Our experimental results demonstrated the significant improvement of DCD in both quantitative and qualitative performance, meanwhile, the complexity of student generator is reduced by a large volume." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.705, + 0.66, + 0.723 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "This work was supported by National Key R&D Program of China (No.2022ZD0118201), the National Science Fund for Distinguished Young Scholars (No.62025603), the National Natural Science Foundation of China (No.U21B2037, No.U22B2051, No.62176222, No.62176223, No.62176226, No.62072386, No.62072387, No.62072389, No.62002305 and No.62272401), and the Natural Science Foundation of Fujian Province of China (No.2021J01002, No.2022J06001), Guangdong Basic and Applied Basic Research Foundation (No.2019B1515120049)." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20358" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.17 + ], + "angle": 0, + "content": "[1] Angeline Aguinaldo, Ping-Yeh Chiang, Alex Gain, Ameya Patil, Kolten Pearson, and Soheil Feizi. 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As an awesome "performance maker", knowledge distillation is demonstrated to be particularly efficacious in exploring low-priced GANs. In this paper, we investigate the irreplaceability of teacher discriminator and present an inventive discriminator-cooperated distillation, abbreviated as DCD, towards refining better feature maps from the generator. In contrast to conventional pixel-to-pixel match methods in feature map distillation, our DCD utilizes teacher discriminator as a transformation to drive intermediate results of the student generator to be perceptually close to corresponding outputs of the teacher generator. Furthermore, in order to mitigate mode collapse in GAN compression, we construct a collaborative adversarial training paradigm where the teacher discriminator is from scratch established to co-train with student generator in company with our DCD. Our DCD shows superior results compared with existing GAN compression methods. For instance, after reducing over $40 \times$ MACs and $80 \times$ parameters of CycleGAN, we well decrease FID metric from 61.53 to 48.24 while the current SoTA method merely has 51.92. This work's source code has been made accessible at https://github.com/poopit/DCD-official. + +# 1. Introduction + +Image generation transforms random noise or source-domain images to other images in user-required domains. Recent years have witnessed the burgeoning of generative adversarial networks (GANs) that lead to substantial progress in image-to-image translation [8, 9, 18, 49], style transfer [11, 12, 42], image synthesis [3, 22, 23, 32, 46], etc. + +![](images/97d87c913e3e881e30ce7cedd0aca13e3174e19ffdf57772035167030a60926d.jpg) + +![](images/4f94942d42bad35e0608c293f20a9d1bc64e9e00a36a5bebe81cfaa6a9053de4.jpg) +Figure 1. (a) Layer-by-layer feature map distillation [34]. (b) Cross-layer feature map distillation [6]. (c) Our discriminator-cooperated feature map distillation. + +Image generation has a wide application in daily entertainment such as TikTok AI image generator, Dream by WOMBO, Google Imagen, and so on. Running platforms performing these applications are typically featured with poor memory storage and limited computational power. However, GANs are also ill-famed for the growing spurt of learnable parameters and multiply-accumulate operations (MACs), raising a huge challenge to the storage requirement and computing ability of deployment infrastructure. + +To address the above dilemma for better usability of GANs in serving human life, methods such as pruning [7, 27, 28, 33], neural network architecture search (NAS) [10, 19, 26] and quantization [39, 40], have been broadly explored to obtain a smaller generator. On the premise of these compression researches, knowledge distillation, in particular to distilling feature maps, has been accepted as a supplementary means to enhance the performance of compressed generators [1, 4, 17, 26, 29, 41]. Originated from image classification, as illustrated in Fig. 1(a), feature map based distillation, which extracts information of intermediate activations and transfers the knowledge from the teacher model to the student one, has been extensively explored and demonstrated to well improve the capability of lightweight mod + +els [5, 25, 34, 43, 45]. Distinctive from passing on common feature maps from teacher to student, AT [45] calculates feature attentions as the delivered knowledge; MGD [43] randomly masks feature maps to indirectly guide the student to learn from the teacher; KRD [6] uses a cross-layer distillation method to allow the “new knowledge” of the student to learn from the “old knowledge” in teacher, as shown in Fig. 1(b). Whatever, most methods execute pixel-to-pixel feature maps matching between teacher and student. + +Alike to the implementations on image classification, feature map based distillation is also considered in GAN compression. For example, GCC [28] considers a well pretrained discriminator to absorb high-level information from the teacher-generated image, and fuses it with intermediate activations from the teacher generator, results of which are passed to the corresponding position of the student generator. OMGD [33] utilizes an online multi-granularity strategy to allow a deeper teacher generator and a wider one to simultaneously deliver output image knowledge of different granularities to the student generator. These two methods follow the pipeline of image classification to tune the intermediate outputs of student generator with those of teacher generator in a fashion of per-pixel matching. Although the sustainable progress on multiple benchmark datasets demonstrates the efficacy of intermediate activation outputs, the feature-based distillation, as we reveal in this paper, is not well compatible with the very nature of generating perceptually similar images and adversarial training paradigm. + +Concretely speaking, conversely to image classification that relies on feature vector representations, the essence of image generation is to improve perceptually alike between the real images and generated images. Two important facts cause it is eventually difficult to use per-pixel match to analyze a pair of images: First, two similar images can contain many different pixel values; Second, two dissimilar images can still comprise the same pixel values. Thus, it is not suitable to simply use the per-pixel match. Regarding adversarial training in GANs, a generator learns to synthesize samples that best resemble the dataset, meanwhile a discriminator differentiate samples in the dataset from the generator generated samples. The adversarial results finally lead the generator to creating images of out-of-the-ordinary visual quality, indicating that the discriminator is also empowered with informative capacity and can be exploited to enrich the distillation of feature maps. Therefore, it might be inappropriate to directly extend feature map distillation in image classification to image generation. And GAN compression oriented feature map distillation with discriminator included remains to be well explored. + +In order to achieve this objective, in this paper, we propose a discriminator-cooperated distillation (DCD) method to involve the teacher discriminator in distilling feature maps for student generator. A simple illustration is given in + +Fig. 1(c), in contrast to the vanilla pixel-wise distance constraint, our DCD measures the distance at the end of teacher discriminator with the intermediate generator outputs as its inputs. Our DCD is perspicacious in multiple benchmark datasets with a simple implementation. Akin to perceptual loss [20] which employs a pre-trained neural network such as a VGG model [36] to extract features upon which the $\ell_1$ distance is calculated from activations of hidden layers, the teacher discriminator in DCD also acts as a feature extractor. Due to pooling operations in the hidden layers, feature maps from different sources (student generator and teacher generator) as inputs to the discriminator may lead to identical latent representations, therefore encouraging natural and perceptually pleasing results. In addition, the proposed DCD is used in conjunction with collaborative adversarial training, which is also simple but perspicacious to allow the student generator to fool the discriminator for generating better images. In contrast to discriminator-free paradigm training [28], we find our DCD empowers the compressed student generator with a better capability to compete against teacher discriminator. Thus, we also employ the teacher discriminator to collaboratively determine whether inputs from the student generator are real or not. + +This work intends to raise the level of feature map distillation to strengthen the compressed student generator to generate high-quality images. The major contributions we have made across the entire paper are listed as follows: (1) An incentive GAN-oriented discriminator-cooperated feature map distillation method to produce images with high fidelity; (2) One novel collaborative adversarial training paradigm to better reach a global equilibrium point in compressing GANs; (3) Remarkable reduction on the generator complexity and significant performance increase. + +# 2. Related Work + +# 2.1. GANs and GAN Compression + +Generative adversarial networks (GANs) [13] have attracted the attention of substantive researchers due to their outstanding performance in image generation tasks [3, 8, 9, 18, 22, 23, 32, 46, 49]. Since the infancy of GAN, many variants have emerged, from DCGAN [32], which embraces convolutional neural networks for the first time, to CycleGAN [49] and Pix2Pix [18] which implement image-to-image translation, to StyleGAN [22] to enable controllable manipulation of various attributes of image synthesis. CycleGAN [49] transfers a source-domain image into a target style in an unpaired configuration, such as a horse image to a zebra pattern or a summer image to a winter style. On the other hand, Pix2Pix [18] is given a ground-truth image and converts a semantic segmentation or contour map into a photo-realistic picture. Albeit the performance, GANs suffer heavy burden on storage and computation. + +Therefore, recent years have witnessed increasing attention on compressing GANs [7, 10, 19, 21, 24, 26, 27, 30, 35, 39, 40, 47]. Co-evolution [35] prunes filters in the generator under the constraint of consistent output distributions. GAN Slimming [39] suggests a compression framework that can integrate pruning, knowledge distillation and quantization. GAN Compression [26] views the teacher output as the pseudo label for student generator and unifies the compression framework for GANs trained on paired data and unpaired data. GCC [28] combines information from discriminator in knowledge distillation, an idea closer to our approach, but the use of discriminator is still under-explored. Although the above approaches have compressed parameters and computation costs, both the generated image quality and the model size are still far from practical applications on mobile devices. OMGD [33] bridges this huge gap in a way by constructing discriminator-free distillation. + +Of the above methods, GCC is the most similar to our approach with major differences in: (1) GCC involves summation of discriminator activations in distilling intermediate layers of student generator. Our DCD calculates distance between teacher and student directly upon feature maps of the discriminator. (2) GCC focuses on a more suitable student discriminator for student generator. Our DCD discards student discriminator by adopting that of teacher. (3) Results show merits of our DCD over GCC in both quantitative and visual quality with a higher compression rate. + +# 2.2. Knowledge Distillation + +Pioneered by FitNet as of 2014 [34], knowledge distillation (KD) [16] has become a regular approach in model compression especially to GAN compression, where a larger model with better performance imparts knowledge to a smaller model. Since then, great efforts have been made to dig out opulent knowledge hints, such as output logits [21, 47, 48], intermediate feature maps [6, 14, 34], instance relation [31, 38] and so on. In this paper, we are mainly inspired by the intermediate feature map based distillation that has been extensively mined to efficiently guide the training of the student network. Compared to other knowledge hints, feature maps often accommodate a richer level of information and provide more detailed guidance for the student network. AT [45] extracts the attention map from the feature maps and trains the student's attention maps to be as close as possible to the one of teacher. MGD [43] transforms direct learning from the teacher into a generative intermediate goal. KRD [6] uses the idea of cross-layer distillation to allow old knowledge from the teacher to guide new knowledge learning from the student network. Nevertheless, conventional methods require per-pixel match between feature maps of teacher and student, which does not fit well in GAN compression because the goal of GANs is to generate perceptually similar images. In + +this paper, we dig deeper into the distinctiveness of generative adversarial networks. + +# 3. Methodology + +# 3.1. Preliminaries + +Generative adversarial networks [13], or GANs for short, are an interesting manner to train a generative model by modelling the problem with two sub-models including a generator model $\mathcal{G}$ and a discriminator model $\mathcal{D}$ . The two models are trained together in a zero-sum game as: + +$$ +\begin{array}{l} \min _ {\mathcal {G}} \max _ {\mathcal {D}} \mathcal {L} _ {g a n} = \mathbb {E} _ {y \sim p _ {r e a l}} \log \mathcal {D} (y) \\ + \mathbb {E} _ {x \sim p (x)} \left[ \log \left(1 - \mathcal {D} (\mathcal {G} (x))\right) \right]. \tag {1} \\ \end{array} +$$ + +Herein, the generator model $\mathcal{G}$ is trained to generate new examples, and the discriminator model $\mathcal{D}$ tries to classify examples as either real (from the domain) or fake (generated). The two models are trained adversarially until the discriminator model is fooled at most times, which indicates that the generator model is producing plausible examples. Then, the generator $\mathcal{G}$ is deployed online to complete service for reality. + +The serviceability of generator $\mathcal{G}$ rests with not only the performance, but also the hardware capability that makes a greater demand on generator complexity. Therefore, a lighter student generator, $\mathcal{G}^S$ , can be developed by various methods. The original generator and discriminator, respectively denoted as $\mathcal{G}^T$ and $\mathcal{D}^T$ in this situation to differentiate, play as a teacher to enhance the ability of student generator $\mathcal{G}^S$ . + +Giving an input variable $x \sim p(x) \in \mathbb{R}^{H \times W \times C}$ , we denote the $i$ -th layer output of generator as $\mathcal{G}_i(x)$ , and $\mathcal{I}_{\mathcal{G}}(x)$ as layer index set of extracted intermediate outputs. Thus, the feature maps based distillation is formulated as: + +$$ +\mathcal {L} _ {f e a - d i s} = \sum_ {i \in I _ {\mathcal {G}}} \ell \left(\mathcal {G} _ {i} ^ {T} (x), f \left(\mathcal {G} _ {i} ^ {S} (x)\right)\right), \tag {2} +$$ + +where $f(\cdot)$ is the affine transformation function to align the channel dimensions between the teacher and student, such as $1 \times 1$ convolution operators in existing studies [26,28,33]. Also, $\ell(\cdot, \cdot)$ refers to the distance measure function, such as Euclidean distance. + +Additionally, perceptual loss [20], $\mathcal{L}_{per}$ , is also widely adopted in existing studies to encourage natural and perceptually pleasing restored images. $\mathcal{L}_{per}$ comprises a feature reconstruction loss $\mathcal{L}_{fea}$ and a style reconstruction loss $\mathcal{L}_{sty}$ as: + +$$ +\mathcal {L} _ {p e r} = \lambda_ {f e a} \cdot \mathcal {L} _ {f e a} + \lambda_ {s t y} \cdot \mathcal {L} _ {s t y}. \tag {3} +$$ + +![](images/0344f964c1b45b2e4cd2b9dd9e3e59a253c13a00f8ce1d9e4bc1e0c15f9a29a1.jpg) +Figure 2. Framework of our DCD. Intermediate feature maps from student and teacher are downsampled first to align the dimension, results of which are then fed to the teacher discriminator to minimize distance for a perceptually vivid generated image. + +Herein, $\mathcal{L}_{fea}$ propels the output representation of the teacher generator to approach to that of the student generator. This is achieved by a pre-trained VGG network $\Phi (\cdot)$ [36] and formalized as: + +$$ +\mathcal {L} _ {f e a} = \sum_ {j \in I _ {\Phi}} \frac {1}{H _ {j} W _ {j} C _ {j}} \left\| \Phi_ {j} \left(\mathcal {G} ^ {T} (x)\right) - \Phi_ {j} \left(\mathcal {G} ^ {S} (x)\right) \right\| _ {1}, \tag {4} +$$ + +where $\Phi_j(\cdot)$ returns the $j$ -th activation output of VGG network and $H_{j}\times W_{j}\times C_{j}$ is its shape. Alike to $I_{\mathcal{G}}$ , $I_{\Phi}$ contains layer index of extracted intermediate outputs. + +As for $\mathcal{L}_{sty}$ , it minimizes the difference between Gram matrices of the output and target images in order to preserve style characteristics such as color, textures and common pattern [33]. The $\mathcal{L}_{sty}$ is calculated as: + +$$ +\mathcal {L} _ {s t y} = \sum_ {j \in I _ {\Phi}} \left\| G \left(\Phi_ {j} \left(\mathcal {G} ^ {T} (x)\right)\right) - G \left(\Phi_ {j} \left(\mathcal {G} ^ {S} (x)\right)\right) \right\| _ {1}, \tag {5} +$$ + +where $G(\cdot)$ represents abbreviation of Gram matrices. + +# 3.2. Discriminator-Cooperated Distillation + +Stepping back and reflecting on the feature map based distillation in Eq. (2), we realize that a simple utilization of generator capacity is not intact in earlier methods. The central principle of a GAN is contingent on an "indirect" training route through the discriminator updated dynamically to discern how "realistic" its input (i.e., generator output) seems. This means that the generator is not trained to minimize the distance from a generated image to a target image, but rather to deceive the discriminator. It is the copetition pattern between the generator and discriminator that even brings about superficially authentic generated images. Thus, the discriminator is also empowered with informative capacity and must be utilized to enrich the distillation of feature maps. + +As shown in Fig. 2, we rethink Eq. (2) and integrate teacher discriminator to cooperate with the distillation process. Alike to feature reconstruction loss defined in Eq. (4), while taking the generator outputs as its inputs, we accomplish our distillation by aligning the intermediate outputs of the discriminator. We formulate this learning process as: + +$$ +\mathcal {L} _ {d c d} = \sum_ {k \in I _ {\mathcal {D}}} \sum_ {i \in I _ {\mathcal {G}}} \ell \left(\mathcal {D} _ {k} ^ {T} \left(f \left(\mathcal {G} _ {i} ^ {T} (x)\right)\right), \mathcal {D} _ {k} ^ {T} \left(f \left(\mathcal {G} _ {i} ^ {S} (x)\right)\right)\right), \tag {6} +$$ + +where $\mathcal{D}_k^T$ stands for the output of its $k$ -th layer. Similar to $I_{\mathcal{G}}$ , $I_{\mathcal{D}}$ is a layer index set of the teacher discriminator; herein, $f(\cdot)$ denotes $1 \times 1$ convolution operations to down-sample the channel dimensions of both the teacher and student feature maps to those of discriminator input. Usually, the channel number of discriminator input is set to three for an RGB-encoded image. Here, $f(\cdot)$ for teacher generator becomes constant once initialized while that for student generator continues updating for a better fit with teacher. + +As an analogy to the vanilla feature map based distillation in Eq. (2) that compels the per-pixel match between intermediate outputs of both the teacher generator and student generator, the role of the teacher discriminator resembles the pre-trained VGG in Eq. (4), which acts as a transformed network to enable the intermediate results of student generator to be perceptually alike to these of teacher generator. In contrast, it does not require them to do pixel-by-pixel match, since two images might look similar in perspective, but they often have different pixel values, thus we cannot depend on per-pixel match. Notice that our discriminator-cooperated distillation is complementary to perceptual loss. The former concentrates on object localization while the latter pays attention to style discrepancies. The analysis of this phenomenon is in Sec. 4.4. + +# 3.3. Collaborative Adversarial Training + +GANs perform an alternating training paradigm for a unique global equilibrium point: 1) Training the discriminator $\mathcal{D}$ to identify real and generated data while keeping the generator constant; 2) Training the generator $\mathcal{G}$ to generate vivid data that fools the discriminator while keeping the discriminator constant; 3) Repeating steps 1) and 2) till the discriminator model is fooled at most time. However, the equilibrium is no longer guaranteed when $\mathcal{D}$ and $\mathcal{G}$ are empowered with inconsistent abilities, in which case unstable convergence frequently occurs. Generally, the instability stems from two ill-famed issues including vanishing gradient where loss for the generator is zero when the discriminator is perfect, and mode collapse where the stronger generator produces a small set of outputs for any input and the weaker discriminator traps in a local minimum [2]. + +Especially, the mode collapse issue is even widespread in GAN compression because the compressed student gen + +erator $\mathcal{G}^S$ is powerless to compete with the original full discriminator [27], in particular a pre-trained one [4, 19, 30]. The community has excavated various approaches to weaken the student discriminator. For example, GCC [28] selectively activates discriminator neurons. Nevertheless, a rule-of-thumb selection has to be carefully designed. Also, training a student discriminator is computationally redundant since it is unwanted in the testing stage. OMGD [33] co-trains teacher generator with the teacher discriminator while the student generator is discriminator-free. The missing adversarial training of student generator somehow barricades the further performance increase. + +In this paper, we also reject real student discriminator, and to ensure the teacher's optimization, the teacher discriminator, $\mathcal{D}^T$ , is online trained from scratch to be well-matched with the teacher generator $\mathcal{G}^T$ . Comparing to [33], teacher discriminator $\mathcal{D}^T$ also appears in the form of a collaborative discriminator to determine if the inputs from student generator $\mathcal{G}^T$ are real or fake. The major concern originates from the actuality that the teacher discriminator is much powerful than the compressed student generator, which causes mode collapse in adversarial training. Luckily, our discriminator-cooperated distillation in Eq. (6) furnishes student generator with increasing capability to battle against teacher discriminator and leads to better performance than [33] as demonstrated in the experiment. + +Based on Eq. (1), our adversarial training is rewritten as: + +$$ +\begin{array}{l} \min _ {\mathcal {G} ^ {T}, \mathcal {G} ^ {S}} \max _ {\mathcal {D} ^ {T}} \mathcal {L} _ {c o l} = \mathbb {E} _ {y \sim p _ {r e a l}} \log \mathcal {D} ^ {T} (y) \\ + \mathbb {E} _ {x \sim p (x)} \left[ \log \left(1 - \mathcal {D} ^ {T} \big (\mathcal {G} ^ {T} (x) \big)\right) \right] \\ + \lambda_ {s t u} \cdot \mathbb {E} _ {x \sim p (x)} \left[ \log \left(1 - \mathcal {D} ^ {T} \left(\mathcal {G} ^ {S} (x)\right)\right) \right], \tag {7} \\ \end{array} +$$ + +where $\lambda_{stu}$ refers to a trade-off parameter; and $\lambda_{stu} = 0$ degenerates to discarding student discriminator when constrained with the student generator [33]. + +# 3.4. Training Objective + +Looking back to Sec. 3.1, the loss terms in most conventional feature map based distillation methods include $\mathcal{L}_{gan}$ in Eq. (1), $\mathcal{L}_{fea - dis}$ in Eq. (2) and $\mathcal{L}_{per}$ in Eq. (3). In this paper, we improve $\mathcal{L}_{fea - dis}$ through a discriminator-cooperated feature map distillation loss $\mathcal{L}_{dcd}$ in Eq. (6), and $\mathcal{L}_{gan}$ through collaborative adversarial training loss $\mathcal{L}_{col}$ in Eq. (7). Therefore, the overall training objective in this paper is given in the following: + +$$ +\min _ {\mathcal {G} ^ {T}, \mathcal {G} ^ {S}} \max _ {\mathcal {D} ^ {T}} \left(\mathcal {L} _ {g a n} + \mathcal {L} _ {p e r} + \lambda_ {d c d} \cdot \mathcal {L} _ {d c d}\right), \tag {8} +$$ + +where $\lambda_{dcd}$ balances the loss term. Four hyper-parameters: $\lambda_{fea}$ , $\lambda_{sty}$ , $\lambda_{stu}$ and $\lambda_{dcd}$ are used in this paper, influence of each parameter is ablated in the appendix. + +# 4. Experimentation + +# 4.1. Setups + +GAN Models and Benchmarks. We present the performance of compressed CycleGAN [49] and Pix2Pix [18] to follow and compare with existing methods [7, 19, 21, 26, 27, 35, 39, 47]. For a fair comparison with the current SoTA OMGD [33], the compressed generators (students) consist of 1/4 channels of the original full ResNet generators (teachers) [26]. CycleGAN translates images from one domain to another without a one-to-one mapping between the source and target domain. Therefore, we verify the performance upon unpaired image translation benchmarks including horse2zebra [49] and summer2winter [49]. As for Pix2Pix, we perform distillation upon paired edges2shoes [44] because it requires learning a mapping from input images to output images. + +**Evaluations. Fréchet Inception Distance (FID), or FID for short [15], is particularly developed to evaluate the performance of GANs. It accesses the quality of generated images by an Inception-V3 network [37] to separately embed synthetic and real images to feature space, and then calculate the Wasserstein distance of their distributions. A lower FID score indicate better quality of generated images.** + +Implementations. We train CycleGAN and Pix2Pix for a total of 100 epochs. The initial learning rate is given as $2 \times e^{-4}$ and then linearly decayed to 0 as training goes. The batch size is set to 4 on edges2shoes, and 1 on horse2zebra [49] and summer2winter [49]. We have $\lambda_{dcd} = 1$ , $\lambda_{fea} = 1 \times e^{1}$ , $\lambda_{sty} = 1 \times e^{4}$ and $\lambda_{stu} = 1$ across all experiments. In the appendix, specific ablations in regard to these hyper-parameters have been provided. + +# 4.2. Quantitative Comparison + +GAN Compression. We first compare with existing implementations on GAN compression in Table 1 where the blue number indicates performance drop, while the red number denotes performance increase compared with the original GAN models. We conclude the following observations from Table 1: First, on summer2winter, all methods lead to a performance increase of more or less. On the contrary, most methods cause FID drops on the challenging horse2zebra and edges2shoes while methods such as OMGD [33] and our DCD consistently enhance the performance. Second, our DCD leads to the most complexity reduction w.r.t. MACs and parameters, meanwhile it gains the best performance increase on all the three benchmark datasets. Third, with the same reduction of MACs $(40.3\times)$ and parameters $(82.5\times)$ on unpaired CycleGAN, our DCD well outperforms the recent SoTA method, i.e., OMGD. In particular, we drastically increase the performance of 51.92 for OMGD to 48.24, which is also 13.29 increase compared to the original CycleGAN. This increase is very challenging + +Table 1. Performance comparison when compressing CycleGAN on horse2zebra, and Pix2Pix on edges2shoes. + +
ModelDatasetMethodMACs#ParametersFID(↓)
CycleGAN [49]horse2zebra [49]Original [49]56.80G(1.0×)11.30M(1.0×)61.53 (-)
Co-Evolution [35]13.40G(4.2×)-96.15(-34.62)
DMAD [27]2.41G(23.6×)0.28M(40.0×)62.96(-1.43)
Wavelet KD [47]1.68G(33.8×)0.72M(15.81×)77.04(-15.51)
GAN-Compression [26]2.67G(21.3×)0.34M(33.2×)64.95(-3.42)
GCC [28]2.40G(23.6×)-59.31(+2.22)
OMGD [33]1.408G(40.3×)0.137M(82.5×)51.92(+9.61)
DCD (Ours)1.408G(40.3×)0.137M(82.5×)48.24(+13.29)
summer2winter [49]Original [49]56.80G(1.0×)11.30M(1.0×)79.12(-)
Co-Evolution [35]11.10G(5.1×)-78.58(+0.54)
AutoGAN-Distiller [10]4.34G(13.1×)-78.33(+0.79)
DMAD [27]3.18G(17.9×)0.30M(37.7×)78.24(+0.88)
OMGD [33]1.408G(40.3×)0.137M(82.5×)73.79(+5.33)
DCD (Ours)1.408G(40.3×)0.137M(82.5×)73.63(+5.49)
Pix2Pix [18]edges2shoesOriginal [18]18.60G(1.0×)54.40M(1.0×)34.31(-)
DMAD [27]2.99G(6.2×)2.13M(25.5×)46.95(-12.64)
Wavelet KD [47]1.56G(11.92×)13.61M(4.00×)80.13(-45.82)
OMGD [33]1.219G(15.3×)3.404M(16.0×)25.00(+9.41)
DCD (Ours)1.219G(15.3×)3.404M(16.0×)23.43(+10.98)
+ +Table 2. Comparison between different feature map distillation methods on horse2zebra. + +
DatasetMethodFID(↓)
horse2zebra [49]Baseline65.13
FitNet [34]65.84
MGD [43]67.57
KRD [6]61.53
DCD (Ours)48.24
+ +since 51.92 already is a strong performance. Nevertheless, our increase is very evident. Lastly, similar to CycleGAN, the results on paired Pix2Pix also show the superiority of our DCD over OMGD when compressing $15.3 \times$ MACs and $16.0 \times$ parameters. In this case, OMGD leads to 9.41 FID gains while our DCD has a better increase of 10.98. + +Therefore, our discriminator-cooperated feature map distillation has well demonstrated its great capability to boost the performance of a light-weighted generator. + +Feature Map Distillation. As introduced in Sec. 1, current feature map distillation methods such as FitNet [34], MGD [43] and KRD [6] construct pixel-to-pixel matching between the student generator and teacher generator. In contrast, our DCD is constrained to generate perceptually alike images. In Table 2, we replace our DCD with the aforementioned distillation scenarios for performance comparison. All experiments are performed on CycleGAN of $40.3 \times$ MACs reduction as shown in Table 1. We can + +see that FitNet and MGD incur performance degradation of 0.71 and 2.44 FID. Though KRD allows cross-layer connections and rises the FID by 4.40, the performance increase is very limited if compared with our 13.29 performance gains. To find out the root cause, these methods were initially invented to perform image classification that focuses more on extracting robust image feature vectors. However, GANs often pay great attention to the image contents, which do not call for identical pixel values between two images but urge more for perceptual discrepancies. Therefore, off-the-shelf per-pixel matching studies fail to fit well when directly extended to GAN compression. + +# 4.3. Visualization + +We further present visualization of generated images from original CycleGAN generator as well as its compressed versions in Fig. 3. Evidently, our DCD results in not only more vivid objects (zebras), but also well retains background information. Regarding the objects, our DCD produces sharper and brighter stripes compared to other methods. In particular, existing methods are more or less influenced by the input. For example, the brown fur on horse is retained on the generated zebras (third row) while DCD well overcomes this drawback. As for the background, we find that DCD sometimes presents better visual perception even than the inputs, such as greener meadows and trees (last row). The better visual results are in accordance with better FID in Table 1. More examples of summer2winter and edges2shoes can be referred to the appendix. + +![](images/3d31e3e27ab0b2ab1f58dec89707c57b4b404eb02cffd4573871b0f20166c0d9.jpg) +Figure 3. Visualization comparison on horse2zebra with CycleGAN. + +Table 3. Training loss influence to CycleGAN on horse2zebra. + +
LperLcddLganFID(↓)
✓67.20
✓324.27
✓389.77
✓✓55.24
✓✓65.13
✓✓323.63
✓✓✓48.24
+ +# 4.4. Analysis + +We continue to conduct ablation studies to analyze influences of different training losses defined in Eq. (8), as well as our downsampling strategies defined in Eq. (6), trying to reveal why our DCD performs well. All experiments are constructed by using CycleGAN on horse2zebra. + +Training Loss. Table 3 manifests the performance of different loss combinations. We observe the significance of the perceptual loss, without which the FID drastically increases to hundreds. Also, both our DCD loss and ad + +versarial training loss are complementary to perceptual loss where $\mathcal{L}_{per} + \mathcal{L}_{dcd}$ increases performance to 55.24 and it is 65.13 for $\mathcal{L}_{per} + \mathcal{L}_{gan}$ . Combining all the training losses results in the optimal FID of 48.24. + +Downsampling. In Eq. (6), we adopt $1 \times 1$ convolution operations to downsample feature maps to a three-channel RGB-encoded image before being fed to the teacher discriminator. We fix downsampling modules for teacher generator while updating those for student generator, which is very crucial to the performance of the student generator. We visualize RGB features from layer 3, 6, 9, and 12 of the teacher and student generators at different training stages, referred to as stage I~IV in order. Results are displayed in Fig.4 where two variants are introduced for comparison including updating both the teacher and student downsampling modules, and updating the teacher downsampling modules while fixing those of student. We can observe that the student generator keeps pace with teacher generator, so that they generate similar feature maps. This indicates the teacher knowledge has been well transferred to learn + +![](images/541d40842f192c53ce2dc98c8c6fcc96a6dc351374e8807492a30218f08bb771.jpg) +Figure 4. Feature map visualization of teacher and student generators at different training stages. + +student model. Unfortunately, updating the teacher downsampling modules severely damages the knowledge from the teacher generator where only 61.16 FID is obtained if the student downsampling modules are updated as well and 69.41 otherwise. The poor performance mainly stems from the broken feature maps of teacher, where horse objects become invisible. Therefore, the student generator collapses as well. As for our downsampling strategy where downsampling modules are fixed for teacher generator while updated for student generator, the attention is gradually paid to the target horse objects as network training. Therefore, our discriminator-cooperated feature map distillation benefits more to localizing target objects. This is complementary to the perceptual loss that is engaged in style transferring. Their combination leads the lightweight student generator to finally synthesise vivid images with intricate textures. + +# 5. Conclusion + +In this paper, we proposed a novel discriminator-cooperated distillation (DCD) that reshapes the conventional pixel-to-pixel feature map match by skillfully utilizing the teacher discriminator as a transformation to pursue + +better visual perception in generated images. Our methods show that the teacher discriminator can also be utilized to co-train with the compressed student generator and accordingly invent a collaborative adversarial training paradigm. Our experimental results demonstrated the significant improvement of DCD in both quantitative and qualitative performance, meanwhile, the complexity of student generator is reduced by a large volume. + +# Acknowledgement + +This work was supported by National Key R&D Program of China (No.2022ZD0118201), the National Science Fund for Distinguished Young Scholars (No.62025603), the National Natural Science Foundation of China (No.U21B2037, No.U22B2051, No.62176222, No.62176223, No.62176226, No.62072386, No.62072387, No.62072389, No.62002305 and No.62272401), and the Natural Science Foundation of Fujian Province of China (No.2021J01002, No.2022J06001), Guangdong Basic and Applied Basic Research Foundation (No.2019B1515120049). + +# References + +[1] Angeline Aguinaldo, Ping-Yeh Chiang, Alex Gain, Ameya Patil, Kolten Pearson, and Soheil Feizi. Compressing gans using knowledge distillation. arXiv preprint arXiv:1902.00159, 2019. 1 +[2] Martin Arjovsky and Léon Bottou. 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In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), June 2016. 5 +[38] Frederick Tung and Greg Mori. Similarity-preserving knowledge distillation. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), pages 1365-1374, 2019. 3 + +[39] Haotao Wang, Shupeng Gui, Haichuan Yang, Ji Liu, and Zhangyang Wang. Gan slimming: All-in-one gan compression by a unified optimization framework. In European Conference on Computer Vision (ECCV), pages 54-73, 2020. 1, 3, 5 +[40] Peiqi Wang, Dongsheng Wang, Yu Ji, Xinfeng Xie, Haoxuan Song, XuXin Liu, Yongqiang Lyu, and Yuan Xie. Qgan: Quantized generative adversarial networks. arXiv preprint arXiv:1901.08263, 2019. 1, 3 +[41] Xiaojie Wang, Rui Zhang, Yu Sun, and Jianzhong Qi. Kdgan: Knowledge distillation with generative adversarial networks. Advances in Neural Information Processing Systems (NeurIPS), 2018. 1 +[42] Wenju Xu, Chengjiang Long, Ruisheng Wang, and Guanghui Wang. 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"Despite excellent performance in image generation, Generative Adversarial Networks (GANs) are notorious for its requirements of enormous storage and intensive computation. As an awesome \"performance maker\", knowledge distillation is demonstrated to be particularly efficacious in exploring low-priced GANs. In this paper, we investigate the irreplaceability of teacher discriminator and present an inventive discriminator-cooperated distillation, abbreviated as DCD, towards refining better feature maps from the generator. In contrast to conventional pixel-to-pixel match methods in feature map distillation, our DCD utilizes teacher discriminator as a transformation to drive intermediate results of the student generator to be perceptually close to corresponding outputs of the teacher generator. Furthermore, in order to mitigate mode collapse in GAN compression, we construct a collaborative adversarial training paradigm where the teacher discriminator is from scratch established to co-train with student generator in company with our DCD. Our DCD shows superior results compared with existing GAN compression methods. For instance, after reducing over " + }, + { + "bbox": [ + 46, + 280, + 290, + 579 + ], + "type": "inline_equation", + "content": "40 \\times" + }, + { + "bbox": [ + 46, + 280, + 290, + 579 + ], + "type": "text", + "content": " MACs and " + }, + { + "bbox": [ + 46, + 280, + 290, + 579 + ], + "type": "inline_equation", + "content": "80 \\times" + }, + { + "bbox": [ + 46, + 280, + 290, + 579 + ], + "type": "text", + "content": " parameters of CycleGAN, we well decrease FID metric from 61.53 to 48.24 while the current SoTA method merely has 51.92. This work's source code has been made accessible at https://github.com/poopit/DCD-official." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 602, + 128, + 615 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 602, + 128, + 615 + ], + "spans": [ + { + "bbox": [ + 47, + 602, + 128, + 615 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 623, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 623, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 623, + 287, + 696 + ], + "type": "text", + "content": "Image generation transforms random noise or source-domain images to other images in user-required domains. Recent years have witnessed the burgeoning of generative adversarial networks (GANs) that lead to substantial progress in image-to-image translation [8, 9, 18, 49], style transfer [11, 12, 42], image synthesis [3, 22, 23, 32, 46], etc." + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 317, + 262, + 533, + 314 + ], + "blocks": [ + { + "bbox": [ + 317, + 262, + 533, + 314 + ], + "lines": [ + { + "bbox": [ + 317, + 262, + 533, + 314 + ], + "spans": [ + { + "bbox": [ + 317, + 262, + 533, + 314 + ], + "type": "image", + "image_path": "97d87c913e3e881e30ce7cedd0aca13e3174e19ffdf57772035167030a60926d.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 334, + 325, + 520, + 384 + ], + "blocks": [ + { + "bbox": [ + 334, + 325, + 520, + 384 + ], + "lines": [ + { + "bbox": [ + 334, + 325, + 520, + 384 + ], + "spans": [ + { + "bbox": [ + 334, + 325, + 520, + 384 + ], + "type": "image", + "image_path": "4f94942d42bad35e0608c293f20a9d1bc64e9e00a36a5bebe81cfaa6a9053de4.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 395, + 546, + 429 + ], + "lines": [ + { + "bbox": [ + 305, + 395, + 546, + 429 + ], + "spans": [ + { + "bbox": [ + 305, + 395, + 546, + 429 + ], + "type": "text", + "content": "Figure 1. (a) Layer-by-layer feature map distillation [34]. (b) Cross-layer feature map distillation [6]. (c) Our discriminator-cooperated feature map distillation." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 437, + 546, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 546, + 544 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 546, + 544 + ], + "type": "text", + "content": "Image generation has a wide application in daily entertainment such as TikTok AI image generator, Dream by WOMBO, Google Imagen, and so on. Running platforms performing these applications are typically featured with poor memory storage and limited computational power. However, GANs are also ill-famed for the growing spurt of learnable parameters and multiply-accumulate operations (MACs), raising a huge challenge to the storage requirement and computing ability of deployment infrastructure." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 545, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 547, + 713 + ], + "type": "text", + "content": "To address the above dilemma for better usability of GANs in serving human life, methods such as pruning [7, 27, 28, 33], neural network architecture search (NAS) [10, 19, 26] and quantization [39, 40], have been broadly explored to obtain a smaller generator. On the premise of these compression researches, knowledge distillation, in particular to distilling feature maps, has been accepted as a supplementary means to enhance the performance of compressed generators [1, 4, 17, 26, 29, 41]. Originated from image classification, as illustrated in Fig. 1(a), feature map based distillation, which extracts information of intermediate activations and transfers the knowledge from the teacher model to the student one, has been extensively explored and demonstrated to well improve the capability of lightweight mod" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 137, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 137, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 137, + 712 + ], + "type": "text", + "content": "*Corresponding Author" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20351" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 178 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 178 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 178 + ], + "type": "text", + "content": "els [5, 25, 34, 43, 45]. Distinctive from passing on common feature maps from teacher to student, AT [45] calculates feature attentions as the delivered knowledge; MGD [43] randomly masks feature maps to indirectly guide the student to learn from the teacher; KRD [6] uses a cross-layer distillation method to allow the “new knowledge” of the student to learn from the “old knowledge” in teacher, as shown in Fig. 1(b). Whatever, most methods execute pixel-to-pixel feature maps matching between teacher and student." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 182, + 288, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 182, + 288, + 410 + ], + "spans": [ + { + "bbox": [ + 46, + 182, + 288, + 410 + ], + "type": "text", + "content": "Alike to the implementations on image classification, feature map based distillation is also considered in GAN compression. For example, GCC [28] considers a well pretrained discriminator to absorb high-level information from the teacher-generated image, and fuses it with intermediate activations from the teacher generator, results of which are passed to the corresponding position of the student generator. OMGD [33] utilizes an online multi-granularity strategy to allow a deeper teacher generator and a wider one to simultaneously deliver output image knowledge of different granularities to the student generator. These two methods follow the pipeline of image classification to tune the intermediate outputs of student generator with those of teacher generator in a fashion of per-pixel matching. Although the sustainable progress on multiple benchmark datasets demonstrates the efficacy of intermediate activation outputs, the feature-based distillation, as we reveal in this paper, is not well compatible with the very nature of generating perceptually similar images and adversarial training paradigm." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 411, + 287, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 411, + 287, + 663 + ], + "spans": [ + { + "bbox": [ + 46, + 411, + 287, + 663 + ], + "type": "text", + "content": "Concretely speaking, conversely to image classification that relies on feature vector representations, the essence of image generation is to improve perceptually alike between the real images and generated images. Two important facts cause it is eventually difficult to use per-pixel match to analyze a pair of images: First, two similar images can contain many different pixel values; Second, two dissimilar images can still comprise the same pixel values. Thus, it is not suitable to simply use the per-pixel match. Regarding adversarial training in GANs, a generator learns to synthesize samples that best resemble the dataset, meanwhile a discriminator differentiate samples in the dataset from the generator generated samples. The adversarial results finally lead the generator to creating images of out-of-the-ordinary visual quality, indicating that the discriminator is also empowered with informative capacity and can be exploited to enrich the distillation of feature maps. Therefore, it might be inappropriate to directly extend feature map distillation in image classification to image generation. And GAN compression oriented feature map distillation with discriminator included remains to be well explored." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "text", + "content": "In order to achieve this objective, in this paper, we propose a discriminator-cooperated distillation (DCD) method to involve the teacher discriminator in distilling feature maps for student generator. A simple illustration is given in" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 545, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 346 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 346 + ], + "type": "text", + "content": "Fig. 1(c), in contrast to the vanilla pixel-wise distance constraint, our DCD measures the distance at the end of teacher discriminator with the intermediate generator outputs as its inputs. Our DCD is perspicacious in multiple benchmark datasets with a simple implementation. Akin to perceptual loss [20] which employs a pre-trained neural network such as a VGG model [36] to extract features upon which the " + }, + { + "bbox": [ + 304, + 72, + 545, + 346 + ], + "type": "inline_equation", + "content": "\\ell_1" + }, + { + "bbox": [ + 304, + 72, + 545, + 346 + ], + "type": "text", + "content": " distance is calculated from activations of hidden layers, the teacher discriminator in DCD also acts as a feature extractor. Due to pooling operations in the hidden layers, feature maps from different sources (student generator and teacher generator) as inputs to the discriminator may lead to identical latent representations, therefore encouraging natural and perceptually pleasing results. In addition, the proposed DCD is used in conjunction with collaborative adversarial training, which is also simple but perspicacious to allow the student generator to fool the discriminator for generating better images. In contrast to discriminator-free paradigm training [28], we find our DCD empowers the compressed student generator with a better capability to compete against teacher discriminator. Thus, we also employ the teacher discriminator to collaboratively determine whether inputs from the student generator are real or not." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 348, + 545, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 348, + 545, + 468 + ], + "spans": [ + { + "bbox": [ + 304, + 348, + 545, + 468 + ], + "type": "text", + "content": "This work intends to raise the level of feature map distillation to strengthen the compressed student generator to generate high-quality images. The major contributions we have made across the entire paper are listed as follows: (1) An incentive GAN-oriented discriminator-cooperated feature map distillation method to produce images with high fidelity; (2) One novel collaborative adversarial training paradigm to better reach a global equilibrium point in compressing GANs; (3) Remarkable reduction on the generator complexity and significant performance increase." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 482, + 392, + 495 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 482, + 392, + 495 + ], + "spans": [ + { + "bbox": [ + 306, + 482, + 392, + 495 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 502, + 468, + 515 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 502, + 468, + 515 + ], + "spans": [ + { + "bbox": [ + 306, + 502, + 468, + 515 + ], + "type": "text", + "content": "2.1. GANs and GAN Compression" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "text", + "content": "Generative adversarial networks (GANs) [13] have attracted the attention of substantive researchers due to their outstanding performance in image generation tasks [3, 8, 9, 18, 22, 23, 32, 46, 49]. Since the infancy of GAN, many variants have emerged, from DCGAN [32], which embraces convolutional neural networks for the first time, to CycleGAN [49] and Pix2Pix [18] which implement image-to-image translation, to StyleGAN [22] to enable controllable manipulation of various attributes of image synthesis. CycleGAN [49] transfers a source-domain image into a target style in an unpaired configuration, such as a horse image to a zebra pattern or a summer image to a winter style. On the other hand, Pix2Pix [18] is given a ground-truth image and converts a semantic segmentation or contour map into a photo-realistic picture. Albeit the performance, GANs suffer heavy burden on storage and computation." + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20352" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 276 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 276 + ], + "type": "text", + "content": "Therefore, recent years have witnessed increasing attention on compressing GANs [7, 10, 19, 21, 24, 26, 27, 30, 35, 39, 40, 47]. Co-evolution [35] prunes filters in the generator under the constraint of consistent output distributions. GAN Slimming [39] suggests a compression framework that can integrate pruning, knowledge distillation and quantization. GAN Compression [26] views the teacher output as the pseudo label for student generator and unifies the compression framework for GANs trained on paired data and unpaired data. GCC [28] combines information from discriminator in knowledge distillation, an idea closer to our approach, but the use of discriminator is still under-explored. Although the above approaches have compressed parameters and computation costs, both the generated image quality and the model size are still far from practical applications on mobile devices. OMGD [33] bridges this huge gap in a way by constructing discriminator-free distillation." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 277, + 289, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 277, + 289, + 397 + ], + "spans": [ + { + "bbox": [ + 46, + 277, + 289, + 397 + ], + "type": "text", + "content": "Of the above methods, GCC is the most similar to our approach with major differences in: (1) GCC involves summation of discriminator activations in distilling intermediate layers of student generator. Our DCD calculates distance between teacher and student directly upon feature maps of the discriminator. (2) GCC focuses on a more suitable student discriminator for student generator. Our DCD discards student discriminator by adopting that of teacher. (3) Results show merits of our DCD over GCC in both quantitative and visual quality with a higher compression rate." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 407, + 177, + 419 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 407, + 177, + 419 + ], + "spans": [ + { + "bbox": [ + 47, + 407, + 177, + 419 + ], + "type": "text", + "content": "2.2. Knowledge Distillation" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 426, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 426, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 289, + 715 + ], + "type": "text", + "content": "Pioneered by FitNet as of 2014 [34], knowledge distillation (KD) [16] has become a regular approach in model compression especially to GAN compression, where a larger model with better performance imparts knowledge to a smaller model. Since then, great efforts have been made to dig out opulent knowledge hints, such as output logits [21, 47, 48], intermediate feature maps [6, 14, 34], instance relation [31, 38] and so on. In this paper, we are mainly inspired by the intermediate feature map based distillation that has been extensively mined to efficiently guide the training of the student network. Compared to other knowledge hints, feature maps often accommodate a richer level of information and provide more detailed guidance for the student network. AT [45] extracts the attention map from the feature maps and trains the student's attention maps to be as close as possible to the one of teacher. MGD [43] transforms direct learning from the teacher into a generative intermediate goal. KRD [6] uses the idea of cross-layer distillation to allow old knowledge from the teacher to guide new knowledge learning from the student network. Nevertheless, conventional methods require per-pixel match between feature maps of teacher and student, which does not fit well in GAN compression because the goal of GANs is to generate perceptually similar images. In" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": "this paper, we dig deeper into the distinctiveness of generative adversarial networks." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 109, + 388, + 123 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 109, + 388, + 123 + ], + "spans": [ + { + "bbox": [ + 306, + 109, + 388, + 123 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 129, + 392, + 142 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 129, + 392, + 142 + ], + "spans": [ + { + "bbox": [ + 306, + 129, + 392, + 142 + ], + "type": "text", + "content": "3.1. Preliminaries" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 149, + 545, + 209 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 149, + 545, + 209 + ], + "spans": [ + { + "bbox": [ + 305, + 149, + 545, + 209 + ], + "type": "text", + "content": "Generative adversarial networks [13], or GANs for short, are an interesting manner to train a generative model by modelling the problem with two sub-models including a generator model " + }, + { + "bbox": [ + 305, + 149, + 545, + 209 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 305, + 149, + 545, + 209 + ], + "type": "text", + "content": " and a discriminator model " + }, + { + "bbox": [ + 305, + 149, + 545, + 209 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 305, + 149, + 545, + 209 + ], + "type": "text", + "content": ". The two models are trained together in a zero-sum game as:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 350, + 220, + 545, + 266 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 350, + 220, + 545, + 266 + ], + "spans": [ + { + "bbox": [ + 350, + 220, + 545, + 266 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\min _ {\\mathcal {G}} \\max _ {\\mathcal {D}} \\mathcal {L} _ {g a n} = \\mathbb {E} _ {y \\sim p _ {r e a l}} \\log \\mathcal {D} (y) \\\\ + \\mathbb {E} _ {x \\sim p (x)} \\left[ \\log \\left(1 - \\mathcal {D} (\\mathcal {G} (x))\\right) \\right]. \\tag {1} \\\\ \\end{array}", + "image_path": "e56bb1e9fe2c2f1ceb27b2e363b6ab6498ff0b841d2914969ad13b5f17bc61a5.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 276, + 545, + 372 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 276, + 545, + 372 + ], + "spans": [ + { + "bbox": [ + 304, + 276, + 545, + 372 + ], + "type": "text", + "content": "Herein, the generator model " + }, + { + "bbox": [ + 304, + 276, + 545, + 372 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 304, + 276, + 545, + 372 + ], + "type": "text", + "content": " is trained to generate new examples, and the discriminator model " + }, + { + "bbox": [ + 304, + 276, + 545, + 372 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 304, + 276, + 545, + 372 + ], + "type": "text", + "content": " tries to classify examples as either real (from the domain) or fake (generated). The two models are trained adversarially until the discriminator model is fooled at most times, which indicates that the generator model is producing plausible examples. Then, the generator " + }, + { + "bbox": [ + 304, + 276, + 545, + 372 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 304, + 276, + 545, + 372 + ], + "type": "text", + "content": " is deployed online to complete service for reality." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 373, + 545, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 373, + 545, + 468 + ], + "spans": [ + { + "bbox": [ + 304, + 373, + 545, + 468 + ], + "type": "text", + "content": "The serviceability of generator " + }, + { + "bbox": [ + 304, + 373, + 545, + 468 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 304, + 373, + 545, + 468 + ], + "type": "text", + "content": " rests with not only the performance, but also the hardware capability that makes a greater demand on generator complexity. Therefore, a lighter student generator, " + }, + { + "bbox": [ + 304, + 373, + 545, + 468 + ], + "type": "inline_equation", + "content": "\\mathcal{G}^S" + }, + { + "bbox": [ + 304, + 373, + 545, + 468 + ], + "type": "text", + "content": ", can be developed by various methods. The original generator and discriminator, respectively denoted as " + }, + { + "bbox": [ + 304, + 373, + 545, + 468 + ], + "type": "inline_equation", + "content": "\\mathcal{G}^T" + }, + { + "bbox": [ + 304, + 373, + 545, + 468 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 373, + 545, + 468 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^T" + }, + { + "bbox": [ + 304, + 373, + 545, + 468 + ], + "type": "text", + "content": " in this situation to differentiate, play as a teacher to enhance the ability of student generator " + }, + { + "bbox": [ + 304, + 373, + 545, + 468 + ], + "type": "inline_equation", + "content": "\\mathcal{G}^S" + }, + { + "bbox": [ + 304, + 373, + 545, + 468 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 469, + 545, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 469, + 545, + 518 + ], + "spans": [ + { + "bbox": [ + 304, + 469, + 545, + 518 + ], + "type": "text", + "content": "Giving an input variable " + }, + { + "bbox": [ + 304, + 469, + 545, + 518 + ], + "type": "inline_equation", + "content": "x \\sim p(x) \\in \\mathbb{R}^{H \\times W \\times C}" + }, + { + "bbox": [ + 304, + 469, + 545, + 518 + ], + "type": "text", + "content": ", we denote the " + }, + { + "bbox": [ + 304, + 469, + 545, + 518 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 469, + 545, + 518 + ], + "type": "text", + "content": "-th layer output of generator as " + }, + { + "bbox": [ + 304, + 469, + 545, + 518 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_i(x)" + }, + { + "bbox": [ + 304, + 469, + 545, + 518 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 469, + 545, + 518 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_{\\mathcal{G}}(x)" + }, + { + "bbox": [ + 304, + 469, + 545, + 518 + ], + "type": "text", + "content": " as layer index set of extracted intermediate outputs. Thus, the feature maps based distillation is formulated as:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 344, + 528, + 545, + 555 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 344, + 528, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 344, + 528, + 545, + 555 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {f e a - d i s} = \\sum_ {i \\in I _ {\\mathcal {G}}} \\ell \\left(\\mathcal {G} _ {i} ^ {T} (x), f \\left(\\mathcal {G} _ {i} ^ {S} (x)\\right)\\right), \\tag {2}", + "image_path": "efc4bce1ecff7b4387cdbc3895eb18ed797bdfb3fa39add8ae6b833da72303f5.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 566, + 545, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 566, + 545, + 625 + ], + "spans": [ + { + "bbox": [ + 304, + 566, + 545, + 625 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 566, + 545, + 625 + ], + "type": "inline_equation", + "content": "f(\\cdot)" + }, + { + "bbox": [ + 304, + 566, + 545, + 625 + ], + "type": "text", + "content": " is the affine transformation function to align the channel dimensions between the teacher and student, such as " + }, + { + "bbox": [ + 304, + 566, + 545, + 625 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 304, + 566, + 545, + 625 + ], + "type": "text", + "content": " convolution operators in existing studies [26,28,33]. Also, " + }, + { + "bbox": [ + 304, + 566, + 545, + 625 + ], + "type": "inline_equation", + "content": "\\ell(\\cdot, \\cdot)" + }, + { + "bbox": [ + 304, + 566, + 545, + 625 + ], + "type": "text", + "content": " refers to the distance measure function, such as Euclidean distance." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 627, + 545, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 627, + 545, + 688 + ], + "spans": [ + { + "bbox": [ + 304, + 627, + 545, + 688 + ], + "type": "text", + "content": "Additionally, perceptual loss [20], " + }, + { + "bbox": [ + 304, + 627, + 545, + 688 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{per}" + }, + { + "bbox": [ + 304, + 627, + 545, + 688 + ], + "type": "text", + "content": ", is also widely adopted in existing studies to encourage natural and perceptually pleasing restored images. " + }, + { + "bbox": [ + 304, + 627, + 545, + 688 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{per}" + }, + { + "bbox": [ + 304, + 627, + 545, + 688 + ], + "type": "text", + "content": " comprises a feature reconstruction loss " + }, + { + "bbox": [ + 304, + 627, + 545, + 688 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{fea}" + }, + { + "bbox": [ + 304, + 627, + 545, + 688 + ], + "type": "text", + "content": " and a style reconstruction loss " + }, + { + "bbox": [ + 304, + 627, + 545, + 688 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{sty}" + }, + { + "bbox": [ + 304, + 627, + 545, + 688 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 355, + 698, + 545, + 712 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 355, + 698, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 355, + 698, + 545, + 712 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {p e r} = \\lambda_ {f e a} \\cdot \\mathcal {L} _ {f e a} + \\lambda_ {s t y} \\cdot \\mathcal {L} _ {s t y}. \\tag {3}", + "image_path": "a58ebacc4cb22a986cb9ac1428c6a69e1a3cffa417713e93725767f3919b41aa.jpg" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20353" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 72, + 293, + 194 + ], + "blocks": [ + { + "bbox": [ + 50, + 72, + 293, + 194 + ], + "lines": [ + { + "bbox": [ + 50, + 72, + 293, + 194 + ], + "spans": [ + { + "bbox": [ + 50, + 72, + 293, + 194 + ], + "type": "image", + "image_path": "0344f964c1b45b2e4cd2b9dd9e3e59a253c13a00f8ce1d9e4bc1e0c15f9a29a1.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 206, + 288, + 251 + ], + "lines": [ + { + "bbox": [ + 46, + 206, + 288, + 251 + ], + "spans": [ + { + "bbox": [ + 46, + 206, + 288, + 251 + ], + "type": "text", + "content": "Figure 2. Framework of our DCD. Intermediate feature maps from student and teacher are downsampled first to align the dimension, results of which are then fed to the teacher discriminator to minimize distance for a perceptually vivid generated image." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 274, + 287, + 321 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 274, + 287, + 321 + ], + "spans": [ + { + "bbox": [ + 47, + 274, + 287, + 321 + ], + "type": "text", + "content": "Herein, " + }, + { + "bbox": [ + 47, + 274, + 287, + 321 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{fea}" + }, + { + "bbox": [ + 47, + 274, + 287, + 321 + ], + "type": "text", + "content": " propels the output representation of the teacher generator to approach to that of the student generator. This is achieved by a pre-trained VGG network " + }, + { + "bbox": [ + 47, + 274, + 287, + 321 + ], + "type": "inline_equation", + "content": "\\Phi (\\cdot)" + }, + { + "bbox": [ + 47, + 274, + 287, + 321 + ], + "type": "text", + "content": " [36] and formalized as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 52, + 331, + 287, + 360 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 331, + 287, + 360 + ], + "spans": [ + { + "bbox": [ + 52, + 331, + 287, + 360 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {f e a} = \\sum_ {j \\in I _ {\\Phi}} \\frac {1}{H _ {j} W _ {j} C _ {j}} \\left\\| \\Phi_ {j} \\left(\\mathcal {G} ^ {T} (x)\\right) - \\Phi_ {j} \\left(\\mathcal {G} ^ {S} (x)\\right) \\right\\| _ {1}, \\tag {4}", + "image_path": "9e58ad54d7ba1328b109ad51ede01259b4c3dcf06abbba862e95e674ff753aef.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 371, + 287, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 371, + 287, + 407 + ], + "spans": [ + { + "bbox": [ + 47, + 371, + 287, + 407 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 371, + 287, + 407 + ], + "type": "inline_equation", + "content": "\\Phi_j(\\cdot)" + }, + { + "bbox": [ + 47, + 371, + 287, + 407 + ], + "type": "text", + "content": " returns the " + }, + { + "bbox": [ + 47, + 371, + 287, + 407 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 47, + 371, + 287, + 407 + ], + "type": "text", + "content": "-th activation output of VGG network and " + }, + { + "bbox": [ + 47, + 371, + 287, + 407 + ], + "type": "inline_equation", + "content": "H_{j}\\times W_{j}\\times C_{j}" + }, + { + "bbox": [ + 47, + 371, + 287, + 407 + ], + "type": "text", + "content": " is its shape. Alike to " + }, + { + "bbox": [ + 47, + 371, + 287, + 407 + ], + "type": "inline_equation", + "content": "I_{\\mathcal{G}}" + }, + { + "bbox": [ + 47, + 371, + 287, + 407 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 371, + 287, + 407 + ], + "type": "inline_equation", + "content": "I_{\\Phi}" + }, + { + "bbox": [ + 47, + 371, + 287, + 407 + ], + "type": "text", + "content": " contains layer index of extracted intermediate outputs." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 408, + 287, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 408, + 287, + 456 + ], + "spans": [ + { + "bbox": [ + 47, + 408, + 287, + 456 + ], + "type": "text", + "content": "As for " + }, + { + "bbox": [ + 47, + 408, + 287, + 456 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{sty}" + }, + { + "bbox": [ + 47, + 408, + 287, + 456 + ], + "type": "text", + "content": ", it minimizes the difference between Gram matrices of the output and target images in order to preserve style characteristics such as color, textures and common pattern [33]. The " + }, + { + "bbox": [ + 47, + 408, + 287, + 456 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{sty}" + }, + { + "bbox": [ + 47, + 408, + 287, + 456 + ], + "type": "text", + "content": " is calculated as:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 52, + 466, + 287, + 495 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 466, + 287, + 495 + ], + "spans": [ + { + "bbox": [ + 52, + 466, + 287, + 495 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {s t y} = \\sum_ {j \\in I _ {\\Phi}} \\left\\| G \\left(\\Phi_ {j} \\left(\\mathcal {G} ^ {T} (x)\\right)\\right) - G \\left(\\Phi_ {j} \\left(\\mathcal {G} ^ {S} (x)\\right)\\right) \\right\\| _ {1}, \\tag {5}", + "image_path": "352ddd6dd6272231135bfab0ff1ddc1767a5a6918275c6971d57390839844ad9.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 505, + 265, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 505, + 265, + 517 + ], + "spans": [ + { + "bbox": [ + 47, + 505, + 265, + 517 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 505, + 265, + 517 + ], + "type": "inline_equation", + "content": "G(\\cdot)" + }, + { + "bbox": [ + 47, + 505, + 265, + 517 + ], + "type": "text", + "content": " represents abbreviation of Gram matrices." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 526, + 248, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 526, + 248, + 540 + ], + "spans": [ + { + "bbox": [ + 47, + 526, + 248, + 540 + ], + "type": "text", + "content": "3.2. Discriminator-Cooperated Distillation" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "text", + "content": "Stepping back and reflecting on the feature map based distillation in Eq. (2), we realize that a simple utilization of generator capacity is not intact in earlier methods. The central principle of a GAN is contingent on an \"indirect\" training route through the discriminator updated dynamically to discern how \"realistic\" its input (i.e., generator output) seems. This means that the generator is not trained to minimize the distance from a generated image to a target image, but rather to deceive the discriminator. It is the copetition pattern between the generator and discriminator that even brings about superficially authentic generated images. Thus, the discriminator is also empowered with informative capacity and must be utilized to enrich the distillation of feature maps." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": "As shown in Fig. 2, we rethink Eq. (2) and integrate teacher discriminator to cooperate with the distillation process. Alike to feature reconstruction loss defined in Eq. (4), while taking the generator outputs as its inputs, we accomplish our distillation by aligning the intermediate outputs of the discriminator. We formulate this learning process as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 307, + 153, + 545, + 194 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 153, + 545, + 194 + ], + "spans": [ + { + "bbox": [ + 307, + 153, + 545, + 194 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {d c d} = \\sum_ {k \\in I _ {\\mathcal {D}}} \\sum_ {i \\in I _ {\\mathcal {G}}} \\ell \\left(\\mathcal {D} _ {k} ^ {T} \\left(f \\left(\\mathcal {G} _ {i} ^ {T} (x)\\right)\\right), \\mathcal {D} _ {k} ^ {T} \\left(f \\left(\\mathcal {G} _ {i} ^ {S} (x)\\right)\\right)\\right), \\tag {6}", + "image_path": "ea546a30e1a089e364ddf66ca13757d8954f3371800669b3cf17afab0ac5eba1.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 194, + 545, + 302 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 194, + 545, + 302 + ], + "spans": [ + { + "bbox": [ + 304, + 194, + 545, + 302 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 194, + 545, + 302 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_k^T" + }, + { + "bbox": [ + 304, + 194, + 545, + 302 + ], + "type": "text", + "content": " stands for the output of its " + }, + { + "bbox": [ + 304, + 194, + 545, + 302 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 194, + 545, + 302 + ], + "type": "text", + "content": "-th layer. Similar to " + }, + { + "bbox": [ + 304, + 194, + 545, + 302 + ], + "type": "inline_equation", + "content": "I_{\\mathcal{G}}" + }, + { + "bbox": [ + 304, + 194, + 545, + 302 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 194, + 545, + 302 + ], + "type": "inline_equation", + "content": "I_{\\mathcal{D}}" + }, + { + "bbox": [ + 304, + 194, + 545, + 302 + ], + "type": "text", + "content": " is a layer index set of the teacher discriminator; herein, " + }, + { + "bbox": [ + 304, + 194, + 545, + 302 + ], + "type": "inline_equation", + "content": "f(\\cdot)" + }, + { + "bbox": [ + 304, + 194, + 545, + 302 + ], + "type": "text", + "content": " denotes " + }, + { + "bbox": [ + 304, + 194, + 545, + 302 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 304, + 194, + 545, + 302 + ], + "type": "text", + "content": " convolution operations to down-sample the channel dimensions of both the teacher and student feature maps to those of discriminator input. Usually, the channel number of discriminator input is set to three for an RGB-encoded image. Here, " + }, + { + "bbox": [ + 304, + 194, + 545, + 302 + ], + "type": "inline_equation", + "content": "f(\\cdot)" + }, + { + "bbox": [ + 304, + 194, + 545, + 302 + ], + "type": "text", + "content": " for teacher generator becomes constant once initialized while that for student generator continues updating for a better fit with teacher." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 303, + 546, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 303, + 546, + 482 + ], + "spans": [ + { + "bbox": [ + 304, + 303, + 546, + 482 + ], + "type": "text", + "content": "As an analogy to the vanilla feature map based distillation in Eq. (2) that compels the per-pixel match between intermediate outputs of both the teacher generator and student generator, the role of the teacher discriminator resembles the pre-trained VGG in Eq. (4), which acts as a transformed network to enable the intermediate results of student generator to be perceptually alike to these of teacher generator. In contrast, it does not require them to do pixel-by-pixel match, since two images might look similar in perspective, but they often have different pixel values, thus we cannot depend on per-pixel match. Notice that our discriminator-cooperated distillation is complementary to perceptual loss. The former concentrates on object localization while the latter pays attention to style discrepancies. The analysis of this phenomenon is in Sec. 4.4." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 491, + 494, + 503 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 491, + 494, + 503 + ], + "spans": [ + { + "bbox": [ + 306, + 491, + 494, + 503 + ], + "type": "text", + "content": "3.3. Collaborative Adversarial Training" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 509, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 509, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 509, + 545, + 689 + ], + "type": "text", + "content": "GANs perform an alternating training paradigm for a unique global equilibrium point: 1) Training the discriminator " + }, + { + "bbox": [ + 304, + 509, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 304, + 509, + 545, + 689 + ], + "type": "text", + "content": " to identify real and generated data while keeping the generator constant; 2) Training the generator " + }, + { + "bbox": [ + 304, + 509, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 304, + 509, + 545, + 689 + ], + "type": "text", + "content": " to generate vivid data that fools the discriminator while keeping the discriminator constant; 3) Repeating steps 1) and 2) till the discriminator model is fooled at most time. However, the equilibrium is no longer guaranteed when " + }, + { + "bbox": [ + 304, + 509, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 304, + 509, + 545, + 689 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 509, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 304, + 509, + 545, + 689 + ], + "type": "text", + "content": " are empowered with inconsistent abilities, in which case unstable convergence frequently occurs. Generally, the instability stems from two ill-famed issues including vanishing gradient where loss for the generator is zero when the discriminator is perfect, and mode collapse where the stronger generator produces a small set of outputs for any input and the weaker discriminator traps in a local minimum [2]." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "Especially, the mode collapse issue is even widespread in GAN compression because the compressed student gen" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20354" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "text", + "content": "erator " + }, + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "inline_equation", + "content": "\\mathcal{G}^S" + }, + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "text", + "content": " is powerless to compete with the original full discriminator [27], in particular a pre-trained one [4, 19, 30]. The community has excavated various approaches to weaken the student discriminator. For example, GCC [28] selectively activates discriminator neurons. Nevertheless, a rule-of-thumb selection has to be carefully designed. Also, training a student discriminator is computationally redundant since it is unwanted in the testing stage. OMGD [33] co-trains teacher generator with the teacher discriminator while the student generator is discriminator-free. The missing adversarial training of student generator somehow barricades the further performance increase." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 216, + 289, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 216, + 289, + 384 + ], + "spans": [ + { + "bbox": [ + 46, + 216, + 289, + 384 + ], + "type": "text", + "content": "In this paper, we also reject real student discriminator, and to ensure the teacher's optimization, the teacher discriminator, " + }, + { + "bbox": [ + 46, + 216, + 289, + 384 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^T" + }, + { + "bbox": [ + 46, + 216, + 289, + 384 + ], + "type": "text", + "content": ", is online trained from scratch to be well-matched with the teacher generator " + }, + { + "bbox": [ + 46, + 216, + 289, + 384 + ], + "type": "inline_equation", + "content": "\\mathcal{G}^T" + }, + { + "bbox": [ + 46, + 216, + 289, + 384 + ], + "type": "text", + "content": ". Comparing to [33], teacher discriminator " + }, + { + "bbox": [ + 46, + 216, + 289, + 384 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^T" + }, + { + "bbox": [ + 46, + 216, + 289, + 384 + ], + "type": "text", + "content": " also appears in the form of a collaborative discriminator to determine if the inputs from student generator " + }, + { + "bbox": [ + 46, + 216, + 289, + 384 + ], + "type": "inline_equation", + "content": "\\mathcal{G}^T" + }, + { + "bbox": [ + 46, + 216, + 289, + 384 + ], + "type": "text", + "content": " are real or fake. The major concern originates from the actuality that the teacher discriminator is much powerful than the compressed student generator, which causes mode collapse in adversarial training. Luckily, our discriminator-cooperated distillation in Eq. (6) furnishes student generator with increasing capability to battle against teacher discriminator and leads to better performance than [33] as demonstrated in the experiment." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 59, + 384, + 287, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 384, + 287, + 396 + ], + "spans": [ + { + "bbox": [ + 59, + 384, + 287, + 396 + ], + "type": "text", + "content": "Based on Eq. (1), our adversarial training is rewritten as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 52, + 399, + 287, + 487 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 399, + 287, + 487 + ], + "spans": [ + { + "bbox": [ + 52, + 399, + 287, + 487 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\min _ {\\mathcal {G} ^ {T}, \\mathcal {G} ^ {S}} \\max _ {\\mathcal {D} ^ {T}} \\mathcal {L} _ {c o l} = \\mathbb {E} _ {y \\sim p _ {r e a l}} \\log \\mathcal {D} ^ {T} (y) \\\\ + \\mathbb {E} _ {x \\sim p (x)} \\left[ \\log \\left(1 - \\mathcal {D} ^ {T} \\big (\\mathcal {G} ^ {T} (x) \\big)\\right) \\right] \\\\ + \\lambda_ {s t u} \\cdot \\mathbb {E} _ {x \\sim p (x)} \\left[ \\log \\left(1 - \\mathcal {D} ^ {T} \\left(\\mathcal {G} ^ {S} (x)\\right)\\right) \\right], \\tag {7} \\\\ \\end{array}", + "image_path": "70038eb29e5112fb86b09ea371d6942b85dc4158ef563078a11a6a333f7b9258.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 493, + 287, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 493, + 287, + 529 + ], + "spans": [ + { + "bbox": [ + 46, + 493, + 287, + 529 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 493, + 287, + 529 + ], + "type": "inline_equation", + "content": "\\lambda_{stu}" + }, + { + "bbox": [ + 46, + 493, + 287, + 529 + ], + "type": "text", + "content": " refers to a trade-off parameter; and " + }, + { + "bbox": [ + 46, + 493, + 287, + 529 + ], + "type": "inline_equation", + "content": "\\lambda_{stu} = 0" + }, + { + "bbox": [ + 46, + 493, + 287, + 529 + ], + "type": "text", + "content": " degenerates to discarding student discriminator when constrained with the student generator [33]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 534, + 159, + 548 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 534, + 159, + 548 + ], + "spans": [ + { + "bbox": [ + 47, + 534, + 159, + 548 + ], + "type": "text", + "content": "3.4. Training Objective" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 553, + 287, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 553, + 287, + 649 + ], + "spans": [ + { + "bbox": [ + 46, + 553, + 287, + 649 + ], + "type": "text", + "content": "Looking back to Sec. 3.1, the loss terms in most conventional feature map based distillation methods include " + }, + { + "bbox": [ + 46, + 553, + 287, + 649 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{gan}" + }, + { + "bbox": [ + 46, + 553, + 287, + 649 + ], + "type": "text", + "content": " in Eq. (1), " + }, + { + "bbox": [ + 46, + 553, + 287, + 649 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{fea - dis}" + }, + { + "bbox": [ + 46, + 553, + 287, + 649 + ], + "type": "text", + "content": " in Eq. (2) and " + }, + { + "bbox": [ + 46, + 553, + 287, + 649 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{per}" + }, + { + "bbox": [ + 46, + 553, + 287, + 649 + ], + "type": "text", + "content": " in Eq. (3). In this paper, we improve " + }, + { + "bbox": [ + 46, + 553, + 287, + 649 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{fea - dis}" + }, + { + "bbox": [ + 46, + 553, + 287, + 649 + ], + "type": "text", + "content": " through a discriminator-cooperated feature map distillation loss " + }, + { + "bbox": [ + 46, + 553, + 287, + 649 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{dcd}" + }, + { + "bbox": [ + 46, + 553, + 287, + 649 + ], + "type": "text", + "content": " in Eq. (6), and " + }, + { + "bbox": [ + 46, + 553, + 287, + 649 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{gan}" + }, + { + "bbox": [ + 46, + 553, + 287, + 649 + ], + "type": "text", + "content": " through collaborative adversarial training loss " + }, + { + "bbox": [ + 46, + 553, + 287, + 649 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{col}" + }, + { + "bbox": [ + 46, + 553, + 287, + 649 + ], + "type": "text", + "content": " in Eq. (7). Therefore, the overall training objective in this paper is given in the following:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 82, + 654, + 287, + 673 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 654, + 287, + 673 + ], + "spans": [ + { + "bbox": [ + 82, + 654, + 287, + 673 + ], + "type": "interline_equation", + "content": "\\min _ {\\mathcal {G} ^ {T}, \\mathcal {G} ^ {S}} \\max _ {\\mathcal {D} ^ {T}} \\left(\\mathcal {L} _ {g a n} + \\mathcal {L} _ {p e r} + \\lambda_ {d c d} \\cdot \\mathcal {L} _ {d c d}\\right), \\tag {8}", + "image_path": "8941cb86e428b7f21044af9476b9e45c80810db7d076cc0b483ecc637d5f145d.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\lambda_{dcd}" + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "text", + "content": " balances the loss term. Four hyper-parameters: " + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\lambda_{fea}" + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\lambda_{sty}" + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\lambda_{stu}" + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\lambda_{dcd}" + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "text", + "content": " are used in this paper, influence of each parameter is ablated in the appendix." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 71, + 408, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 71, + 408, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 408, + 85 + ], + "type": "text", + "content": "4. Experimentation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 91, + 360, + 105 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 91, + 360, + 105 + ], + "spans": [ + { + "bbox": [ + 306, + 91, + 360, + 105 + ], + "type": "text", + "content": "4.1. Setups" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 110, + 545, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 110, + 545, + 277 + ], + "spans": [ + { + "bbox": [ + 304, + 110, + 545, + 277 + ], + "type": "text", + "content": "GAN Models and Benchmarks. We present the performance of compressed CycleGAN [49] and Pix2Pix [18] to follow and compare with existing methods [7, 19, 21, 26, 27, 35, 39, 47]. For a fair comparison with the current SoTA OMGD [33], the compressed generators (students) consist of 1/4 channels of the original full ResNet generators (teachers) [26]. CycleGAN translates images from one domain to another without a one-to-one mapping between the source and target domain. Therefore, we verify the performance upon unpaired image translation benchmarks including horse2zebra [49] and summer2winter [49]. As for Pix2Pix, we perform distillation upon paired edges2shoes [44] because it requires learning a mapping from input images to output images." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 278, + 545, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 278, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 304, + 278, + 545, + 361 + ], + "type": "text", + "content": "**Evaluations. Fréchet Inception Distance (FID), or FID for short [15], is particularly developed to evaluate the performance of GANs. It accesses the quality of generated images by an Inception-V3 network [37] to separately embed synthetic and real images to feature space, and then calculate the Wasserstein distance of their distributions. A lower FID score indicate better quality of generated images.**" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 362, + 545, + 459 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 362, + 545, + 459 + ], + "spans": [ + { + "bbox": [ + 304, + 362, + 545, + 459 + ], + "type": "text", + "content": "Implementations. We train CycleGAN and Pix2Pix for a total of 100 epochs. The initial learning rate is given as " + }, + { + "bbox": [ + 304, + 362, + 545, + 459 + ], + "type": "inline_equation", + "content": "2 \\times e^{-4}" + }, + { + "bbox": [ + 304, + 362, + 545, + 459 + ], + "type": "text", + "content": " and then linearly decayed to 0 as training goes. The batch size is set to 4 on edges2shoes, and 1 on horse2zebra [49] and summer2winter [49]. We have " + }, + { + "bbox": [ + 304, + 362, + 545, + 459 + ], + "type": "inline_equation", + "content": "\\lambda_{dcd} = 1" + }, + { + "bbox": [ + 304, + 362, + 545, + 459 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 362, + 545, + 459 + ], + "type": "inline_equation", + "content": "\\lambda_{fea} = 1 \\times e^{1}" + }, + { + "bbox": [ + 304, + 362, + 545, + 459 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 362, + 545, + 459 + ], + "type": "inline_equation", + "content": "\\lambda_{sty} = 1 \\times e^{4}" + }, + { + "bbox": [ + 304, + 362, + 545, + 459 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 362, + 545, + 459 + ], + "type": "inline_equation", + "content": "\\lambda_{stu} = 1" + }, + { + "bbox": [ + 304, + 362, + 545, + 459 + ], + "type": "text", + "content": " across all experiments. In the appendix, specific ablations in regard to these hyper-parameters have been provided." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 467, + 448, + 480 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 467, + 448, + 480 + ], + "spans": [ + { + "bbox": [ + 306, + 467, + 448, + 480 + ], + "type": "text", + "content": "4.2. Quantitative Comparison" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 486, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 545, + 715 + ], + "type": "text", + "content": "GAN Compression. We first compare with existing implementations on GAN compression in Table 1 where the blue number indicates performance drop, while the red number denotes performance increase compared with the original GAN models. We conclude the following observations from Table 1: First, on summer2winter, all methods lead to a performance increase of more or less. On the contrary, most methods cause FID drops on the challenging horse2zebra and edges2shoes while methods such as OMGD [33] and our DCD consistently enhance the performance. Second, our DCD leads to the most complexity reduction w.r.t. MACs and parameters, meanwhile it gains the best performance increase on all the three benchmark datasets. Third, with the same reduction of MACs " + }, + { + "bbox": [ + 304, + 486, + 545, + 715 + ], + "type": "inline_equation", + "content": "(40.3\\times)" + }, + { + "bbox": [ + 304, + 486, + 545, + 715 + ], + "type": "text", + "content": " and parameters " + }, + { + "bbox": [ + 304, + 486, + 545, + 715 + ], + "type": "inline_equation", + "content": "(82.5\\times)" + }, + { + "bbox": [ + 304, + 486, + 545, + 715 + ], + "type": "text", + "content": " on unpaired CycleGAN, our DCD well outperforms the recent SoTA method, i.e., OMGD. In particular, we drastically increase the performance of 51.92 for OMGD to 48.24, which is also 13.29 increase compared to the original CycleGAN. This increase is very challenging" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "text", + "content": "20355" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 87, + 549, + 335 + ], + "blocks": [ + { + "bbox": [ + 95, + 71, + 496, + 82 + ], + "lines": [ + { + "bbox": [ + 95, + 71, + 496, + 82 + ], + "spans": [ + { + "bbox": [ + 95, + 71, + 496, + 82 + ], + "type": "text", + "content": "Table 1. Performance comparison when compressing CycleGAN on horse2zebra, and Pix2Pix on edges2shoes." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 87, + 549, + 335 + ], + "lines": [ + { + "bbox": [ + 48, + 87, + 549, + 335 + ], + "spans": [ + { + "bbox": [ + 48, + 87, + 549, + 335 + ], + "type": "table", + "html": "
ModelDatasetMethodMACs#ParametersFID(↓)
CycleGAN [49]horse2zebra [49]Original [49]56.80G(1.0×)11.30M(1.0×)61.53 (-)
Co-Evolution [35]13.40G(4.2×)-96.15(-34.62)
DMAD [27]2.41G(23.6×)0.28M(40.0×)62.96(-1.43)
Wavelet KD [47]1.68G(33.8×)0.72M(15.81×)77.04(-15.51)
GAN-Compression [26]2.67G(21.3×)0.34M(33.2×)64.95(-3.42)
GCC [28]2.40G(23.6×)-59.31(+2.22)
OMGD [33]1.408G(40.3×)0.137M(82.5×)51.92(+9.61)
DCD (Ours)1.408G(40.3×)0.137M(82.5×)48.24(+13.29)
summer2winter [49]Original [49]56.80G(1.0×)11.30M(1.0×)79.12(-)
Co-Evolution [35]11.10G(5.1×)-78.58(+0.54)
AutoGAN-Distiller [10]4.34G(13.1×)-78.33(+0.79)
DMAD [27]3.18G(17.9×)0.30M(37.7×)78.24(+0.88)
OMGD [33]1.408G(40.3×)0.137M(82.5×)73.79(+5.33)
DCD (Ours)1.408G(40.3×)0.137M(82.5×)73.63(+5.49)
Pix2Pix [18]edges2shoesOriginal [18]18.60G(1.0×)54.40M(1.0×)34.31(-)
DMAD [27]2.99G(6.2×)2.13M(25.5×)46.95(-12.64)
Wavelet KD [47]1.56G(11.92×)13.61M(4.00×)80.13(-45.82)
OMGD [33]1.219G(15.3×)3.404M(16.0×)25.00(+9.41)
DCD (Ours)1.219G(15.3×)3.404M(16.0×)23.43(+10.98)
", + "image_path": "d520d27125263fe6e0b90232f9aabfbcd3d6286d951d083896b4f444514546a1.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 74, + 387, + 259, + 467 + ], + "blocks": [ + { + "bbox": [ + 47, + 364, + 286, + 384 + ], + "lines": [ + { + "bbox": [ + 47, + 364, + 286, + 384 + ], + "spans": [ + { + "bbox": [ + 47, + 364, + 286, + 384 + ], + "type": "text", + "content": "Table 2. Comparison between different feature map distillation methods on horse2zebra." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 74, + 387, + 259, + 467 + ], + "lines": [ + { + "bbox": [ + 74, + 387, + 259, + 467 + ], + "spans": [ + { + "bbox": [ + 74, + 387, + 259, + 467 + ], + "type": "table", + "html": "
DatasetMethodFID(↓)
horse2zebra [49]Baseline65.13
FitNet [34]65.84
MGD [43]67.57
KRD [6]61.53
DCD (Ours)48.24
", + "image_path": "8d2119266f12d211465b089376d467f8075d65dbc6b6e6298d11377dac0d33bb.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 492, + 286, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 492, + 286, + 564 + ], + "spans": [ + { + "bbox": [ + 46, + 492, + 286, + 564 + ], + "type": "text", + "content": "since 51.92 already is a strong performance. Nevertheless, our increase is very evident. Lastly, similar to CycleGAN, the results on paired Pix2Pix also show the superiority of our DCD over OMGD when compressing " + }, + { + "bbox": [ + 46, + 492, + 286, + 564 + ], + "type": "inline_equation", + "content": "15.3 \\times" + }, + { + "bbox": [ + 46, + 492, + 286, + 564 + ], + "type": "text", + "content": " MACs and " + }, + { + "bbox": [ + 46, + 492, + 286, + 564 + ], + "type": "inline_equation", + "content": "16.0 \\times" + }, + { + "bbox": [ + 46, + 492, + 286, + 564 + ], + "type": "text", + "content": " parameters. In this case, OMGD leads to 9.41 FID gains while our DCD has a better increase of 10.98." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 567, + 286, + 603 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 567, + 286, + 603 + ], + "spans": [ + { + "bbox": [ + 46, + 567, + 286, + 603 + ], + "type": "text", + "content": "Therefore, our discriminator-cooperated feature map distillation has well demonstrated its great capability to boost the performance of a light-weighted generator." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "text", + "content": "Feature Map Distillation. As introduced in Sec. 1, current feature map distillation methods such as FitNet [34], MGD [43] and KRD [6] construct pixel-to-pixel matching between the student generator and teacher generator. In contrast, our DCD is constrained to generate perceptually alike images. In Table 2, we replace our DCD with the aforementioned distillation scenarios for performance comparison. All experiments are performed on CycleGAN of " + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "inline_equation", + "content": "40.3 \\times" + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "text", + "content": " MACs reduction as shown in Table 1. We can" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 365, + 545, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 365, + 545, + 509 + ], + "spans": [ + { + "bbox": [ + 304, + 365, + 545, + 509 + ], + "type": "text", + "content": "see that FitNet and MGD incur performance degradation of 0.71 and 2.44 FID. Though KRD allows cross-layer connections and rises the FID by 4.40, the performance increase is very limited if compared with our 13.29 performance gains. To find out the root cause, these methods were initially invented to perform image classification that focuses more on extracting robust image feature vectors. However, GANs often pay great attention to the image contents, which do not call for identical pixel values between two images but urge more for perceptual discrepancies. Therefore, off-the-shelf per-pixel matching studies fail to fit well when directly extended to GAN compression." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 515, + 389, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 515, + 389, + 528 + ], + "spans": [ + { + "bbox": [ + 306, + 515, + 389, + 528 + ], + "type": "text", + "content": "4.3. Visualization" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": "We further present visualization of generated images from original CycleGAN generator as well as its compressed versions in Fig. 3. Evidently, our DCD results in not only more vivid objects (zebras), but also well retains background information. Regarding the objects, our DCD produces sharper and brighter stripes compared to other methods. In particular, existing methods are more or less influenced by the input. For example, the brown fur on horse is retained on the generated zebras (third row) while DCD well overcomes this drawback. As for the background, we find that DCD sometimes presents better visual perception even than the inputs, such as greener meadows and trees (last row). The better visual results are in accordance with better FID in Table 1. More examples of summer2winter and edges2shoes can be referred to the appendix." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "20356" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 82, + 70, + 517, + 434 + ], + "blocks": [ + { + "bbox": [ + 82, + 70, + 517, + 434 + ], + "lines": [ + { + "bbox": [ + 82, + 70, + 517, + 434 + ], + "spans": [ + { + "bbox": [ + 82, + 70, + 517, + 434 + ], + "type": "image", + "image_path": "3d31e3e27ab0b2ab1f58dec89707c57b4b404eb02cffd4573871b0f20166c0d9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 171, + 437, + 420, + 448 + ], + "lines": [ + { + "bbox": [ + 171, + 437, + 420, + 448 + ], + "spans": [ + { + "bbox": [ + 171, + 437, + 420, + 448 + ], + "type": "text", + "content": "Figure 3. Visualization comparison on horse2zebra with CycleGAN." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 95, + 478, + 235, + 582 + ], + "blocks": [ + { + "bbox": [ + 53, + 462, + 279, + 473 + ], + "lines": [ + { + "bbox": [ + 53, + 462, + 279, + 473 + ], + "spans": [ + { + "bbox": [ + 53, + 462, + 279, + 473 + ], + "type": "text", + "content": "Table 3. Training loss influence to CycleGAN on horse2zebra." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 95, + 478, + 235, + 582 + ], + "lines": [ + { + "bbox": [ + 95, + 478, + 235, + 582 + ], + "spans": [ + { + "bbox": [ + 95, + 478, + 235, + 582 + ], + "type": "table", + "html": "
LperLcddLganFID(↓)
✓67.20
✓324.27
✓389.77
✓✓55.24
✓✓65.13
✓✓323.63
✓✓✓48.24
", + "image_path": "11d5ab460e1e3893305ff5b7c6d1fbea4367ac4b05751baceab8babb9983cc4c.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 587, + 109, + 599 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 587, + 109, + 599 + ], + "spans": [ + { + "bbox": [ + 47, + 587, + 109, + 599 + ], + "type": "text", + "content": "4.4. Analysis" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 605, + 287, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 665 + ], + "type": "text", + "content": "We continue to conduct ablation studies to analyze influences of different training losses defined in Eq. (8), as well as our downsampling strategies defined in Eq. (6), trying to reveal why our DCD performs well. All experiments are constructed by using CycleGAN on horse2zebra." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 665, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 712 + ], + "type": "text", + "content": "Training Loss. Table 3 manifests the performance of different loss combinations. We observe the significance of the perceptual loss, without which the FID drastically increases to hundreds. Also, both our DCD loss and ad" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 464, + 545, + 512 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 464, + 545, + 512 + ], + "spans": [ + { + "bbox": [ + 306, + 464, + 545, + 512 + ], + "type": "text", + "content": "versarial training loss are complementary to perceptual loss where " + }, + { + "bbox": [ + 306, + 464, + 545, + 512 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{per} + \\mathcal{L}_{dcd}" + }, + { + "bbox": [ + 306, + 464, + 545, + 512 + ], + "type": "text", + "content": " increases performance to 55.24 and it is 65.13 for " + }, + { + "bbox": [ + 306, + 464, + 545, + 512 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{per} + \\mathcal{L}_{gan}" + }, + { + "bbox": [ + 306, + 464, + 545, + 512 + ], + "type": "text", + "content": ". Combining all the training losses results in the optimal FID of 48.24." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "text", + "content": "Downsampling. In Eq. (6), we adopt " + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "text", + "content": " convolution operations to downsample feature maps to a three-channel RGB-encoded image before being fed to the teacher discriminator. We fix downsampling modules for teacher generator while updating those for student generator, which is very crucial to the performance of the student generator. We visualize RGB features from layer 3, 6, 9, and 12 of the teacher and student generators at different training stages, referred to as stage I~IV in order. Results are displayed in Fig.4 where two variants are introduced for comparison including updating both the teacher and student downsampling modules, and updating the teacher downsampling modules while fixing those of student. We can observe that the student generator keeps pace with teacher generator, so that they generate similar feature maps. This indicates the teacher knowledge has been well transferred to learn" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20357" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 59, + 71, + 521, + 411 + ], + "blocks": [ + { + "bbox": [ + 59, + 71, + 521, + 411 + ], + "lines": [ + { + "bbox": [ + 59, + 71, + 521, + 411 + ], + "spans": [ + { + "bbox": [ + 59, + 71, + 521, + 411 + ], + "type": "image", + "image_path": "541d40842f192c53ce2dc98c8c6fcc96a6dc351374e8807492a30218f08bb771.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 121, + 415, + 471, + 427 + ], + "lines": [ + { + "bbox": [ + 121, + 415, + 471, + 427 + ], + "spans": [ + { + "bbox": [ + 121, + 415, + 471, + 427 + ], + "type": "text", + "content": "Figure 4. Feature map visualization of teacher and student generators at different training stages." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 438, + 289, + 630 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 438, + 289, + 630 + ], + "spans": [ + { + "bbox": [ + 46, + 438, + 289, + 630 + ], + "type": "text", + "content": "student model. Unfortunately, updating the teacher downsampling modules severely damages the knowledge from the teacher generator where only 61.16 FID is obtained if the student downsampling modules are updated as well and 69.41 otherwise. The poor performance mainly stems from the broken feature maps of teacher, where horse objects become invisible. Therefore, the student generator collapses as well. As for our downsampling strategy where downsampling modules are fixed for teacher generator while updated for student generator, the attention is gradually paid to the target horse objects as network training. Therefore, our discriminator-cooperated feature map distillation benefits more to localizing target objects. This is complementary to the perceptual loss that is engaged in style transferring. Their combination leads the lightweight student generator to finally synthesise vivid images with intricate textures." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 644, + 119, + 656 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 644, + 119, + 656 + ], + "spans": [ + { + "bbox": [ + 47, + 644, + 119, + 656 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": "In this paper, we proposed a novel discriminator-cooperated distillation (DCD) that reshapes the conventional pixel-to-pixel feature map match by skillfully utilizing the teacher discriminator as a transformation to pursue" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 438, + 545, + 535 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 438, + 545, + 535 + ], + "spans": [ + { + "bbox": [ + 304, + 438, + 545, + 535 + ], + "type": "text", + "content": "better visual perception in generated images. Our methods show that the teacher discriminator can also be utilized to co-train with the compressed student generator and accordingly invent a collaborative adversarial training paradigm. Our experimental results demonstrated the significant improvement of DCD in both quantitative and qualitative performance, meanwhile, the complexity of student generator is reduced by a large volume." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 558, + 403, + 572 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 558, + 403, + 572 + ], + "spans": [ + { + "bbox": [ + 306, + 558, + 403, + 572 + ], + "type": "text", + "content": "Acknowledgement" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "This work was supported by National Key R&D Program of China (No.2022ZD0118201), the National Science Fund for Distinguished Young Scholars (No.62025603), the National Natural Science Foundation of China (No.U21B2037, No.U22B2051, No.62176222, No.62176223, No.62176226, No.62072386, No.62072387, No.62072389, No.62002305 and No.62272401), and the Natural Science Foundation of Fujian Province of China (No.2021J01002, No.2022J06001), Guangdong Basic and Applied Basic Research Foundation (No.2019B1515120049)." + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20358" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "text", + "content": "[1] Angeline Aguinaldo, Ping-Yeh Chiang, Alex Gain, Ameya Patil, Kolten Pearson, and Soheil Feizi. 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In Proceedings of the IEEE International Conference on Computer Vision (ICCV), pages 2223-2232, 2017. 1, 2, 5, 6" + } + ] + } + ], + "index": 24 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "20360" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Disentangled Representation Learning for Unsupervised Neural Quantization/06ed76f2-80a7-4ca7-b9b2-5c10f4249fdb_content_list.json b/2023/Disentangled Representation Learning for Unsupervised Neural Quantization/06ed76f2-80a7-4ca7-b9b2-5c10f4249fdb_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..bad588fd905d6c7c1de0052062dee55b18b6dede --- /dev/null +++ b/2023/Disentangled Representation Learning for Unsupervised Neural Quantization/06ed76f2-80a7-4ca7-b9b2-5c10f4249fdb_content_list.json @@ -0,0 +1,1751 @@ +[ + { + "type": "text", + "text": "Disentangled Representation Learning for Unsupervised Neural Quantization", + "text_level": 1, + "bbox": [ + 95, + 161, + 875, + 182 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Haechan Noh1, Sangeek Hyun1, Woojin Jeong1, Hanshin Lim2, Jae-Pil Heo1,* \n1Sungkyunkwan University, 2Electronics and Telecommunications Research Institute {noru0114, hsi1032, us03385, jaepilheo}@skku.edu, hslim@etri.re.kr", + "bbox": [ + 149, + 207, + 821, + 257 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 288, + 312, + 302 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The inverted index is a widely used data structure to avoid the infeasible exhaustive search. It accelerates retrieval significantly by splitting the database into multiple disjoint sets and restricts distance computation to a small fraction of the database. Moreover, it even improves search quality by allowing quantizers to exploit the compact distribution of residual vector space. However, we firstly point out a problem that an existing deep learning-based quantizer hardly benefits from the residual vector space, unlike conventional shallow quantizers. To cope with this problem, we introduce a novel disentangled representation learning for unsupervised neural quantization. Similar to the concept of residual vector space, the proposed method enables more compact latent space by disentangling information of the inverted index from the vectors. Experimental results on large-scale datasets confirm that our method outperforms the state-of-the-art retrieval systems by a large margin.", + "bbox": [ + 75, + 311, + 472, + 547 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 77, + 568, + 208, + 583 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Measuring the distances among feature vectors is a fundamental requirement in various fields of computer vision. One of the tasks most relevant to distance measurement is the nearest neighbor search, which finds the closest data in the database from a query. The task is especially challenging in high-dimensional and large-scale databases due to huge computational costs and memory overhead.", + "bbox": [ + 75, + 592, + 468, + 688 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "By relaxing the complexity, Approximate Nearest Neighbor (ANN) search is popular in practice. Recent approaches for ANN typically learn the compact representation by exploiting Multi-Codebook Quantization (MCQ) [2, 9, 16]. Compared to hashing-based approaches [1, 10, 12], the MCQ provides a more informative asymmetric distance estimator where the query side is not compressed. Moreover, all possible distances between the query and codewords can be stored in a lookup table for efficiency.", + "bbox": [ + 75, + 688, + 468, + 813 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Although the MCQ accelerates the distance computation with the lookup table, exhaustive search on the large-scale", + "bbox": [ + 75, + 814, + 468, + 843 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "dataset is still prohibited. The Inverted File with Asymmetric Distance Computation (IVFADC) [16] is proposed for non-exhaustive ANN search by cooperating with the inverted index [30]. It splits the database into multiple disjoint sets and restricts distance computations to small portions close to the query to accelerate the retrieval speed. Moreover, the compactness of residual vector space between data points and inverted indices substantially enhances the quantization quality.", + "bbox": [ + 499, + 289, + 890, + 414 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Thanks to the rapid advances in deep learning, most areas of computer vision benefit from its great learning capacity compared to shallow methods. However, the state-of-the-art methods of unsupervised quantization remain shallow for a long time because selecting the maximum value (i.e. argmax), which is an essential operation of quantization, is not differentiable. Inspired by a recent generative model with discrete hidden variables [35], the Unsupervised Neural Quantization (UNQ) [23] introduced an encoder-decoder-based architecture for ANN search. The large learning capacity of deep neural architecture significantly improves the retrieval quality compared to conventional shallow methods.", + "bbox": [ + 497, + 419, + 892, + 598 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Despite the outperforming performance of the UNQ, its superiority is validated only on the exhaustive search. To verify its effectiveness on non-exhaustive search, we conduct an experiment of non-exhaustive UNQ with an inverted index. Interestingly, we observe that this deep architecture does not benefit from the residual vector space and it even harms the search quality as reported in Table 1. We hypothesize the reasons for this performance degradation from two perspectives. First, both the residual vector space and latent space of the neural network transform the data into a quantization-friendly distribution, thus deep quantizer has a scant margin to be improved by the residual space. Second, residual space sacrifices the distributional characteristics of each cluster, since the information of cluster center in the original space is removed. For conventional shallow quantizers, the drawback of residual space is obscured by its huge advantage of making a compact distribution. However, deep quantizer only takes the disadvantages (information loss) from residual space without leveraging the effec", + "bbox": [ + 497, + 603, + 894, + 866 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 129, + 49, + 200, + 85 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 252, + 48, + 791, + 87 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author", + "bbox": [ + 95, + 853, + 220, + 866 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "12001", + "bbox": [ + 465, + 887, + 504, + 897 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tiveness such as compactness of residuals.", + "bbox": [ + 77, + 125, + 354, + 138 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we focus on extending the application of deep architectures for non-exhaustive search. To this end, we learn a disentangled representation to harmonize a deep architecture with the inverted index, inspired by recent representation learning techniques for generative models [8,34]. In our disentangled representation learning, both encoder and decoder get information of cluster center as an additional input. Since the information of cluster center is redundant to decoder if latent feature contains information of cluster center, the encoder is trained to remove the information of cluster centers from the latent embedding. The disentangled representation learning is similar to concept of the residual vector space that provides more compact distribution by taking out the information of cluster centers. The experimental results verify that the learning disentangled representation enables the neural quantization to collaborate with inverted index and outperforms the state-of-the-art methods.", + "bbox": [ + 75, + 140, + 468, + 387 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The contributions of our paper include:", + "bbox": [ + 95, + 389, + 356, + 402 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We point out that the residual encoding of the inverted index is incompatible with the neural multi-codebook quantization method.", + "- We propose a novel disentangled representation learning for neural multi-codebook quantization to combine deep quantization and inverted index.", + "- The experimental results show that the proposed method outperforms the state-of-the-art retrieval systems by a large margin." + ], + "bbox": [ + 95, + 404, + 467, + 532 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 77, + 545, + 216, + 558 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Multi-codebook Quantization for ANN", + "text_level": 1, + "bbox": [ + 77, + 568, + 410, + 581 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Vector quantization [11] maps a vector to its nearest codeword within a learned codebook. Specifically, a high-dimensional real-valued vector can be efficiently represented by an integer index of its corresponding cluster. To ensure a high search accuracy, the vector quantization requires a codebook with an extremely large number of codewords. However, enlarging the number of codewords is far from efficiency because the cost of assigning the nearest codeword is proportionally increased with codebook sizes.", + "bbox": [ + 75, + 589, + 467, + 713 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Product Quanztiaton (PQ) [16] decomposes the space into a Cartesian product of lower-dimensional subspaces. By quantizing each subspace separately, multiple codebooks are produced and they enable better search quality with a manageable number of codewords. Optimized Product Quantization (OPQ) [9] and Cartesian K-means [25] introduced to learn transformation to optimize the decomposition step in PQ according to the data distribution.", + "bbox": [ + 75, + 714, + 467, + 823 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "While the PQ encodes a vector into a concatenation of assigned codewords, a number of methods [2, 6, 20, 21, 26, 36] approximated a vector by a sum of assigned codewords.", + "bbox": [ + 75, + 824, + 467, + 866 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "These addition-based methods have a higher degree of freedom than the concatenation-based methods, since the concatenation is a special case of addition where components of addition are mutually orthogonal.", + "bbox": [ + 497, + 125, + 890, + 180 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The state-of-the-art methods of such multi-codebook quantization remain shallow for a long time, while most areas of computer vision benefit from rapid advances in deep learning. The non-differentiability of codeword assignment operation makes the multi-codebook quantization hard to collaborate with deep learning. Vector-Quantized Variational Autoencoder (VQ-VAE) [35] in the area of the generative model proposed a gradient estimation to propagate gradient through discrete variables. Inspired by the VQ-VAE, Unsupervised Neural Quantization (UNQ) [23] introduces a deep neural network for multi-codebook quantization. The much larger learning capacity of UNQ significantly improves the conventional shallow methods.", + "bbox": [ + 497, + 181, + 890, + 361 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Non-exhaustive ANN Search", + "text_level": 1, + "bbox": [ + 499, + 370, + 754, + 384 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "While the quantization techniques accelerate the distance computation, the search is still exhaustive. IVFADC [16] proposed a non-exhaustive approximate nearest neighbor search by cooperating with the inverted index [30]. In addition to the significant acceleration of retrieval speed, the non-exhaustive manner even improves the search quality by allowing more compact residual vector space. The Inverted Multi-Index (IMI) [3] extends the IVFADC by decomposing data space into two sub-spaces and applying the inverted index independently. Similar to the idea of PQ, the decomposed data space of IMI enables much finer partition with a manageable number of indices. Several subsequent non-exhaustive ANN techniques are proposed to improve the data partitioning rather than the quantization [4, 5, 7].", + "bbox": [ + 497, + 391, + 890, + 586 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.3. Disentangled Representation Learning", + "text_level": 1, + "bbox": [ + 499, + 595, + 831, + 610 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In the context of the generative model, disentangled representation is introduced to analyze and utilize the independent effects of latent factors. One straightforward example can be found in conditional generative models [22, 32]. They decompose the conditional information from the others so that they can control the specific conditions of generated images such as spatial layout [8] or class information [22]. For instance, variational U-Net [8] disentangles the shape and appearance representations to synthesize human images of diverse poses with a shared appearance. Similarly, VarSR [13] builds the latent space of high-resolution information disentangled from the low-resolution images. Hence, they can synthesize diverse high-resolution images corresponding to the given low-resolution image.", + "bbox": [ + 497, + 617, + 890, + 809 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The aforementioned examples mainly focus on the controllable generation by disentangling conditional information. However, in this paper, we concentrate on the maximization of the representation capability of the latent space", + "bbox": [ + 497, + 811, + 890, + 866 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "12002", + "bbox": [ + 465, + 887, + 504, + 897 + ], + "page_idx": 1 + }, + { + "type": "table", + "img_path": "images/c81c3d220adcfeb2f1c469a535d66bfec062fa3a6ad3c55861a10571a70ec2e9.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodR@1R@10R@100
PQ0.2280.6530.953
+IVF (w/o residual)0.2280.6530.950
+IVF (with residual)0.2720.7350.969
UNQ0.3460.8280.990
+IVF (w/o residual)0.3310.7980.939
+IVF (with residual)0.2720.7180.867
", + "bbox": [ + 99, + 122, + 443, + 225 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "by disentanglement. Specifically, we build a compact latent space by disentangling the cluster center similar to residual encoding but compatible with the neural multi-codebook quantization method.", + "bbox": [ + 75, + 286, + 468, + 342 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Background", + "text_level": 1, + "bbox": [ + 77, + 353, + 205, + 369 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Let us briefly introduce the ANN task, the MCQ approach, and the residual vector space. With $D$ -dimensional database $X = \\{x_{n}\\}_{n = 1}^{N}, x_{n} \\in \\mathbb{R}^{D}$ and query $y \\in \\mathbb{R}^{D}$ , the nearest neighbor of query $y$ is defined as follows:", + "bbox": [ + 75, + 377, + 468, + 433 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {N N} (y) = \\underset {n \\in \\{1, \\dots , N \\}} {\\arg \\min } \\| y - x _ {n} \\| ^ {2}. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 161, + 441, + 468, + 467 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To alleviate time and memory costs of Eq. 1, the MCQ quantizer $q_{\\mathrm{MCQ}}$ encodes the database $X = \\{x_{n}\\}_{n=1}^{N}$ utilizing $M$ number of multi-codebooks $C^{m} = \\{c_{k}^{m}\\}_{k=1}^{K}, c_{k}^{m} \\in \\mathbb{R}^{D}$ where each codebook has $K$ number of codewords. Then, a vector $x_{n}$ is represented as $M$ number of indices $[i_{n}^{1}, \\dots, i_{n}^{M}]$ and reconstructed by referring the codebooks:", + "bbox": [ + 75, + 476, + 468, + 560 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nx _ {n} \\approx q _ {\\mathrm {M C Q}} \\left(x _ {n}\\right) = \\sum_ {m = 1} ^ {M} c _ {i _ {n} ^ {m}} ^ {m}. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 176, + 568, + 468, + 606 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The goal of this lossy compression process is to learn codebooks that minimize quantization distortion $E$ defined as:", + "bbox": [ + 75, + 615, + 468, + 643 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nE \\left(x _ {n}, C\\right) = \\sum_ {m = 1} ^ {M} \\left| \\left| x _ {n} ^ {m} - c _ {i _ {n} ^ {m}} ^ {m} \\right| \\right| ^ {2}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 164, + 653, + 468, + 691 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $x_{n} = \\sum x_{n}^{m}$ , and $x_{n}^{m}$ is a subvector of $x_{n}$ corresponding to index $i_{n}^{m}$ . The PQ belongs to the MCQ approach where $x_{n}^{m}$ are mutually orthogonal.", + "bbox": [ + 75, + 700, + 468, + 742 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The IVFADC [16] further accelerates ANN search by collaborating with an inverted index. The inverted index $q_{\\mathrm{IVF}}$ splits database $X$ into $K'$ number of disjoint subsets, and the ANN search is then restricted to $w$ number of nearest subsets from query $y$ , where $w$ is much smaller than $K'$ . For a given data point $x_n$ , the inverted index $q_{\\mathrm{IVF}}(\\cdot)$ quantize it to its nearest cluster center $q_{\\mathrm{IVF}}(x_n)$ , and the data points belong to the same cluster are stored adjacently. Moreover, the IVFADC suggested learning codebooks that", + "bbox": [ + 75, + 742, + 468, + 866 + ], + "page_idx": 2 + }, + { + "type": "table", + "img_path": "images/cbdfdb279f8f00468dfe45cc4c42aa4ec66f45e1d0c3b2e122204df08ce2d1f1.jpg", + "table_caption": [ + "Table 1. Comparison of retrieval performances between the PQ and the UNQ on SIFT-1M. The residual vector space improves the performance with the PQ, but does not work with the UNQ." + ], + "table_footnote": [], + "table_body": "
MethodCompression ratioDistortion
PQ128×0.8368
+IVF (with residual)0.7208
PQ64×0.6252
+IVF (with residual)0.5846
PQ32×0.4127
+IVF (with residual)0.4220
PQ16×0.2438
+IVF (with residual)0.2604
PQ4×0.0212
+IVF (with residual)0.0257
", + "bbox": [ + 502, + 123, + 885, + 281 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Table 2. Quantization distortions of the database with varying compression ratios. The residual vector space is profitable with a large compression ratio, but it leads performance drop with a small compression ratio.", + "bbox": [ + 497, + 287, + 890, + 339 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "encode residual vector $r(x_{n}) = x_{n} - q_{\\mathrm{IVF}}(x_{n})$ rather than the original vector as follows:", + "bbox": [ + 497, + 353, + 890, + 380 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nx _ {n} \\approx \\tilde {x} _ {n} = q _ {\\mathrm {M C Q}} \\left(x _ {n} - q _ {\\mathrm {I V F}} \\left(x _ {n}\\right)\\right) + q _ {\\mathrm {I V F}} \\left(x _ {n}\\right). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 539, + 388, + 890, + 403 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Then the distance between query $y$ and target data $x_{n}$ is estimated as follows:", + "bbox": [ + 497, + 409, + 890, + 435 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nd (y, x _ {n}) \\approx d (y - q _ {\\mathrm {I V F}} (x _ {n}), q _ {\\mathrm {M C Q}} (x _ {n} - q _ {\\mathrm {I V F}} (x _ {n}))). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 444, + 890, + 460 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where the $d(\\cdot, \\cdot)$ is the Euclidean distance between two vectors. The IVFADC accelerates the search speed by reducing the number of distance estimations and improves the quantization distortion (Eq. 3) thanks to the compact distribution of the residual vector space.", + "bbox": [ + 497, + 466, + 890, + 535 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Proposed Method", + "text_level": 1, + "bbox": [ + 499, + 546, + 672, + 562 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Motivation", + "text_level": 1, + "bbox": [ + 499, + 568, + 620, + 581 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Recently, the UNQ [23] introduced a deep architecture for MCQ learning and improves conventional shallow MCQ methods by a large margin. However, its effectiveness is only validated by an exhaustive ANN search. To examine the performance of UNQ on non-exhaustive search, we test the retrieval performances of PQ and UNQ with an inverted index on exhaustive and non-exhaustive settings. As reported in Table. 1, the residual encoding (Eq. 4) provides better search quality with the PQ, while it makes the search quality of UNQ even worse.", + "bbox": [ + 497, + 590, + 890, + 726 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To investigate the reasons why residual encoding does not help the UNQ, we need to analyze the mechanism of residual encoding in PQ. To this end, we hypothesize the effect of residual representation in two aspects. First, the advantage of residuals in PQ comes from the transformation of data space into compact and quantization-friendly distribution. Second, the residual encoding is not always beneficial, since they sacrifice the information of the cluster center so that the distributional characteristics of each cluster are suppressed.", + "bbox": [ + 497, + 728, + 890, + 866 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "12003", + "bbox": [ + 465, + 887, + 504, + 897 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/954e5232da019184ff8fc93b45fb605699353c40ac12358c20fd320f136ecc48.jpg", + "image_caption": [ + "Figure 1. By providing additional input of $q_{\\mathrm{IVF}}(x_n)$ to both encoder and decoder, the encoder is not necessary to learn features to reconstruct $q_{\\mathrm{IVF}}(x_n)$ since it is redundant information for the decoder. Thus the information of the cluster center is disentangled from the latent vectors and codebooks. The disentangling enables the quantizer to learn compact representation while preserving the original distribution." + ], + "image_footnote": [], + "bbox": [ + 124, + 130, + 843, + 271 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To validate these hypotheses, we observe the performance variation of PQ with residual encoding by varying compression ratios. The compression ratios are controlled by adjusting the number of codebooks $M$ . As reported in Table. 2, the residual encoding is profitable with large compression ratios, since the sparse original distribution is hard to quantize with the deficient bit-budget. On the other hand, the residual encoding leads to performance drops with small compression ratios, because it is not necessary to represent the data compactly thanks to sufficient numbers of codewords, but the information loss of cluster-wise distributional characteristics still exists.", + "bbox": [ + 75, + 338, + 472, + 503 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Based on these observations, we explain the reasons for UNQ's performance drop with residual encoding. Firstly, UNQ does not benefit from the compact representation of residual encoding. The deep encoder transforms the data into latent space with a reconstruction objective function. That is, the objective of UNQ also encourages to transform the data into compact latent space, so the residual encoding and UNQ affect the model in a similar way. Hence, the residual representation is hardly beneficial to the neural quantizer. Secondly, UNQ takes the disadvantage of residual encoding, the information loss of distributional characteristics of each cluster.", + "bbox": [ + 75, + 504, + 468, + 668 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "These interpretations motivate us to come up with a method that only takes the advantage of residual representation. That is, we aim to make the latent space more compact without the information loss of distributional characteristics of each cluster. To this end, we introduce a disentangled representation learning for unsupervised neural quantization in the following sections.", + "bbox": [ + 75, + 669, + 468, + 767 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Disentangled Neural Quantization", + "text_level": 1, + "bbox": [ + 75, + 775, + 376, + 789 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Inspired by the disentangled representation of conditional generative models [22, 32], we propose disentangled neural quantization. The previous methods exploit the disentanglement for a controllable generation. However, we propose to learn a disentangled representation to reduce", + "bbox": [ + 75, + 796, + 468, + 866 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the quantization distortion. Specifically, a latent feature $(l_{n})$ of UNQ contains information of its input vector $x_{n}$ where $x_{n}$ consists of $q_{\\mathrm{IVF}}(x_n)$ and $x_{n} - q_{\\mathrm{IVF}}(x_{n})$ . However, the $q_{\\mathrm{IVF}}(x_n)$ can be restored without any information loss thanks to the data structure of the inverted index. Thus, encoding the $q_{\\mathrm{IVF}}(x_n)$ is quite wasteful because the MCQ approach has a scarce bit budget in practice. In this paper, we suggest disentangling the $q_{\\mathrm{IVF}}(x_n)$ from $l_{n}$ to provide more compact information.", + "bbox": [ + 497, + 338, + 890, + 461 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To disentangle the $q_{\\mathrm{IVF}}(x_n)$ from $l_{n}$ , we feed additional input of $q_{\\mathrm{IVF}}(x_n)$ to encoder $E(\\cdot)$ and decoder $D(\\cdot)$ . Then the $q_{\\mathrm{IVF}}(x_n)$ is redundant information for $D(\\cdot)$ if $l_{n}$ contains information of $q_{\\mathrm{IVF}}(x_n)$ . Thus, the $E(\\cdot)$ is trained to embed as little information of $q_{\\mathrm{IVF}}(x_n)$ as possible in $l_{n}$ to fully exploit the network capacity. The disentangled representation learning is similar to the concept of the residual encoding of PQ (Eq. 4) in terms of taking out the information of the cluster center. However, there is no information loss because the cluster center $q_{\\mathrm{IVF}}(x_n)$ is provided to $D(\\cdot)$ .", + "bbox": [ + 497, + 461, + 892, + 600 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Figure. 1 describes the proposed disentangled representation learning. The cluster center of input data is provided to the encoder and decoder, and the scarce resource of finite codewords can be fully utilized to quantize the compact latent feature where the information of the cluster center is disentangled. Not only the compact information, but the decoder also preserves the original distribution by reconstructing the original space in an end-to-end manner.", + "bbox": [ + 497, + 600, + 890, + 711 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.3. Network Structure", + "text_level": 1, + "bbox": [ + 499, + 720, + 680, + 733 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We adopt the network structure of [23] except our disentangling module. The network consists of encoder $E(\\cdot)$ , decoder $D(\\cdot)$ , and learnable codebook parameters $[C^1, \\dots, C^M]$ , $C^m = \\{c_k^m\\}_{k=1}^K$ . Both encoder $E(\\cdot)$ and decoder $D(\\cdot)$ are a concatenation of two fully-connected layers with Batch Normalization [14] and ReLU activation function. We feed separate information of cluster center $q_{\\mathrm{IVF}}(x_n)$ to the encoder for the disentanglement. Then the encoder $E(\\cdot)$ embeds the given concatenated inputs", + "bbox": [ + 497, + 741, + 890, + 866 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "12004", + "bbox": [ + 465, + 887, + 505, + 897 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/051611aa86e4bcf5621017286849bfa5071974052234474283c49c92f058987b.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Search mannerMethod64bits encoding128bits encoding
R@1R@10R@100R@1R@10R@100
ExhaustiveOPQ0.2080.6430.9530.4090.8980.999
Catalyst + Lattice0.2890.7580.9790.4910.9411.
LSQ0.2920.7770.9870.5710.9751.
UNQ0.3460.8280.9900.5930.9801.
Non-ExhaustiveIVFADC (210)0.2960.7040.9570.4710.9030.993
IVFADC + QAI (210)0.3110.7300.9650.4960.9280.992
IVFOADC (210)0.2950.7190.9630.4750.9130.995
IVFOADC + QAI (210)0.3210.7560.9720.5000.9310.993
Multi-D-ADC (28 × 28)0.3030.7290.9670.4840.9240.998
Multi-D-ADC + QAI (28 × 28)0.3180.7480.9770.5130.9390.997
UNQ+IVF (210)0.3310.7980.9390.5480.9630.994
Ours (210)0.3980.8770.9710.6000.9740.990
", + "bbox": [ + 105, + 123, + 860, + 321 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 3. Experimental result on the SIFT-1M dataset. All the quantities except Ours and UNQ+IVF are taken from [23, 24]", + "bbox": [ + 119, + 323, + 847, + 337 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$[x_n, q_{\\mathrm{IVF}}(x_n)]$ to $M$ number of latent features as follows:", + "bbox": [ + 77, + 353, + 453, + 370 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nE \\left(\\left[ x _ {n}, q _ {\\mathrm {I V F}} \\left(x _ {n}\\right) \\right]\\right) = \\left[ l _ {n} ^ {1}, \\dots , l _ {n} ^ {M} \\right]. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 164, + 377, + 468, + 394 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The embedded feature $l_{n}^{m}$ is quantized to index $i_n^m$ of the codeword that has the biggest dot-product with $l_{n}^{m}$ as follows:", + "bbox": [ + 75, + 402, + 468, + 441 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\ni _ {n} ^ {m} = \\underset {k \\in \\{1, \\dots , K \\}} {\\arg \\max } l _ {n} ^ {m} \\cdot c _ {k} ^ {m}. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 186, + 442, + 468, + 467 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Because the argmax function is not differentiable, we follow [23] that exploits the Gumbel trick [15]. The Gumbel trick provides a differentiable approximation of Eq. 7 by substituting the argmax with softmax during backpropagation. Then, the sum of assigned codewords $c_{i_n^m}^m$ becomes the input for the decoder $D(\\cdot)$ . Likewise, we concatenate it with the cluster center $q_{\\mathrm{IVF}}(x_n)$ for the disentanglement. The approximated vector $\\tilde{x}_n$ of original vector $x_n$ is obtained as follows:", + "bbox": [ + 75, + 472, + 468, + 597 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {x} _ {n} = D \\left(\\left[ \\sum_ {m = 1} ^ {M} c _ {i _ {n} ^ {m}} ^ {m}, q _ {\\mathrm {I V F}} (x _ {n}) \\right]\\right). \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 144, + 604, + 468, + 643 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The model is trained with two losses. The first one is a reconstruction loss which directly minimizes the quantization distortion as follows:", + "bbox": [ + 75, + 650, + 468, + 690 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {1} = \\sum_ {n = 1} ^ {N} | | x _ {n} - \\tilde {x} _ {n} | | ^ {2}. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 193, + 699, + 468, + 736 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Similar to [23], we adopt the square Coefficient Variation regularizer [29] to encourage the codewords to be evenly selected:", + "bbox": [ + 75, + 744, + 468, + 785 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {2} = \\sum_ {m = 1} ^ {M} \\frac {\\sum_ {n = 1} ^ {N} \\left(p _ {n} ^ {m} - p _ {\\text {a v g}} ^ {m}\\right) ^ {2}}{p _ {\\text {a v g}} ^ {m} {} ^ {2}}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 164, + 792, + 468, + 830 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $p_n^m$ is the softmax probability of $i_n^m$ by the Gumbel approximation in Eq. 7, and $p_{\\mathrm{avg}}^m$ is the average of $p_n^m$ along", + "bbox": [ + 75, + 838, + 468, + 868 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$N$ . The final loss of the model is described as follows:", + "bbox": [ + 500, + 353, + 858, + 368 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL = L _ {1} + \\lambda * L _ {2} \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 636, + 375, + 890, + 389 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The loss ratio $\\lambda$ starts from 1.0 and decreases to 0.05 during the training. For a fair comparison, we adopt other details of [23] including Quasi-Hyperbolic Adam algorithm [19], and One Cycle learning rate schedule [31].", + "bbox": [ + 497, + 394, + 890, + 450 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.4. Retrieval Procedure", + "text_level": 1, + "bbox": [ + 499, + 456, + 690, + 469 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Firstly, each database vector $x_{n}$ is encoded into $M$ number of indices $l_{n} = [i_{n}^{1},\\dots,i_{n}^{M}]$ by Eq. 7. Because the codebooks have $K$ number of codewords, the required bit-budget for the indices $l_{n}$ is $M * \\lceil \\log_2K \\rceil$ . Moreover, the data points that belong to the same inverted index are stored adjacently, and the size of each cluster is stored. Thanks to this data structure of the inverted index, we can identify the $q_{\\mathrm{IVF}(x_n)}$ without any additional costs in the retrieval stage.", + "bbox": [ + 497, + 477, + 890, + 587 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Secondly, a given query $y$ is embedded into latent features $l_{y}$ , and the cluster center of the target is concatenated.", + "bbox": [ + 497, + 587, + 890, + 616 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\left[ l _ {y} ^ {1}, \\dots , l _ {y} ^ {M} \\right] = E \\left(\\left[ y, q _ {\\mathrm {I V F}} \\left(x _ {n}\\right) \\right]\\right). \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 578, + 619, + 890, + 638 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Then the symmetric distance between encoded query $l_{y}$ and encoded target $[i_n^1, \\dots, i_n^M]$ is computed by the cosine similarity as follows:", + "bbox": [ + 497, + 641, + 890, + 682 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nD _ {\\text {s y m}} (y, x _ {n}) = \\sum_ {m = 1} ^ {M} \\frac {l _ {y} ^ {m} \\cdot c _ {i _ {n} ^ {m}} ^ {m}}{| | l _ {y} ^ {m} | | | | c _ {i _ {n} ^ {m}} ^ {m} | |}. \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 581, + 688, + 890, + 726 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Note that, Eq. 13 can be efficiently computed by a lookup table storing precomputed all possible symmetric distances.", + "bbox": [ + 497, + 729, + 890, + 756 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finally, the $R$ top-ranked retrieved data according to the symmetric distance are then re-ranked by the more accurate asymmetric distances between uncompressed query $y$ and $\\tilde{x}_n$ , as follows:", + "bbox": [ + 497, + 757, + 890, + 811 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nD _ {\\text {a s y m}} (y, x _ {n}) = \\left\\| y - \\tilde {x} _ {n} \\right\\| ^ {2}. \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 600, + 817, + 890, + 834 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We set the hyper-parameter $R = 200$ , and we conduct an ablation study of $R$ in Table. 7.", + "bbox": [ + 497, + 838, + 890, + 866 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "12005", + "bbox": [ + 465, + 887, + 504, + 897 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/db259fc8a17473294858dcf2075ad63798e279e978581545d340d4897df694fd.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Search typeMethod64bits encoding128bits encoding
R@1R@10R@100R@1R@10R@100
ExhaustiveOPQ0.1590.5130.8860.3500.8250.991
Catalyst + Lattice0.2460.6830.9610.4480.9080.998
LSQ0.2170.6400.9450.4110.8860.995
UNQ0.2670.7260.9730.4790.9300.998
Non-exhaustiveIVFADC (210)0.2100.6160.9250.4180.8900.995
IVFOADC (210)0.2270.6590.9500.4160.8970.996
Multi-D-ADC (28 × 28)0.2000.6130.9290.3980.8830.995
UNQ+IVF (210)0.2500.6880.9100.4400.9070.996
Ours (210)0.3290.7990.9320.4910.9290.970
", + "bbox": [ + 129, + 122, + 836, + 280 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 4. Experimental results on DEEP-1M dataset. The quantities of Exhaustive methods are taken from [23]", + "bbox": [ + 157, + 285, + 811, + 299 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Evaluation", + "text_level": 1, + "bbox": [ + 77, + 318, + 193, + 332 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Protocol", + "text_level": 1, + "bbox": [ + 77, + 340, + 179, + 355 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We evaluate our method on three datasets:", + "bbox": [ + 95, + 362, + 376, + 375 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- SIFT-1M, SIFT-1B [16]: 128-dimensional SIFT descriptor vectors [18]. The training set includes $\\{500k, 10^8\\}$ vectors for 1M and 1B, respectively. Sets for evaluation have $10^4$ queries and $\\{10^6, 10^9\\}$ number of database for 1M and 1B, respectively.", + "- DEEP-1M [4]: 96-dimensional DNN features extracted from the last fully-connected layer of GoogLeNet [33]. It also includes $500k$ training data, $10^{4}$ queries, and $10^{6}$ database." + ], + "bbox": [ + 95, + 380, + 468, + 510 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The ground truth of a given query is defined as the top-1 nearest neighbor from an uncompressed database. Then, the retrieval performance in compressed space is measured by average $recall@R$ for $R = \\{1, 10, 100\\}$ . The $recall@R$ represents the ratio of queries that contains the ground truth in top- $R$ retrieved vectors.", + "bbox": [ + 75, + 514, + 468, + 596 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Unless specified, we consistently use the following hyper-parameters. We set $K' = 2^{10}$ for inverted index on million-scale datasets, and $K' = 2^{12} \\times 2^{12}$ for inverted multi-index on billion-scale dataset. The bit budget is controlled by the number of codebooks $M$ and the number of codewords $K$ . We fix the $K$ as 256, and control the bit-budgets by changing $M = \\{8,16\\}$ for 64bits and 128bits, respectively. We follow the setting of $w$ from [7, 24] for a fair comparison. For each query, it visits $w$ inverted indices that guarantee at least $\\{50k,10^5\\}$ candidates for million-scale datasets and billion-scale datasets, respectively.", + "bbox": [ + 75, + 597, + 468, + 748 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare the proposed method with two sets of state-of-the-arts that are exhaustive and non-exhaustive methods. In particular, exhaustive methods include the followings:", + "bbox": [ + 75, + 749, + 468, + 790 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- OPQ [9, 25]: Product Quantization [16] with optimized space decomposition.", + "- Catalyst + Lattice [28]: Learning spreaded space that fits with pre-defined lattice.", + "- LSQ [20]: The state-of-the-art of shallow MCQ." + ], + "bbox": [ + 95, + 793, + 467, + 868 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "- UNQ [23]: A deep generalization of MCQ.", + "bbox": [ + 517, + 319, + 818, + 334 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Plus, the non-exhaustive methods include the followings:", + "bbox": [ + 499, + 337, + 875, + 351 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- IVFADC [16]: Product Quantization [16] with the Inverted index [30] and the residual encoding.", + "- IVFOADC [9, 25]: OPQ with the inverted index [30] and the residual encoding.", + "- Multi-D-ADC [3]: The Inverted Multi-Index (IMI).", + "- OMulti-D-OADC [9,25]: The IMI with the OPQ.", + "- QAI [24]: Jointly optimized inverted index and quantizer.", + "- IVFOADC + GP [5]: IVFOADC with grouping and pruning algorithm of [5].", + "- UNQ + IVF: Inverted file system with the UNQ. We omit the residual encoding because it is incompatible with the deep MCQ algorithm (Table. 1).", + "- Ours: Proposed disentangled representation learning. We select a single index for the million-scale datasets and a multi-index for the billion-scale dataset." + ], + "bbox": [ + 517, + 353, + 889, + 600 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Result on Million-Scale Dataset", + "text_level": 1, + "bbox": [ + 499, + 609, + 778, + 623 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table. 3 and Table. 4 report the recall@R scores of exhaustive and non-exhaustive ANN search methods with $\\{64,128\\}$ bits encoding. For all combinations of the dataset and bit budget, the proposed method outperforms the nonexhaustive baselines by a large margin. For example, Ours improves the R@1 score of Multi-D-ADC+QAI about $25\\%$ and $17\\%$ for 64 and 128bits encoding respectively on the SIFT-1M dataset. On the DEEP-1M dataset, the performance gains between Ours and Multi-D-ADC are much larger than the gains on the SIFT-1M, where the gaps are about $65\\%$ and $23\\%$ for 64 and 128bits encoding, respectively.", + "bbox": [ + 497, + 631, + 890, + 796 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Notably, the proposed method even outperforms the exhaustive ANN methods while the proposed method is a nonexhaustive search where only $5\\%$ of the database is considered for the distance computation. For instance, Ours improves the R@1 score of the exhaustive UNQ by about", + "bbox": [ + 497, + 796, + 890, + 866 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "12006", + "bbox": [ + 465, + 887, + 505, + 897 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/ff5415fcfce53aafe72adab6066ece11403939233a7c1123acde719a5b5ad384.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodR@1R@10R@100
Exhaustive Search
Catalyst + Lattice0.3110.7780.983
LSQ0.3800.8560.993
UNQ0.3830.8680.994
Non-Exhaustive Search
IVFADC (220)0.3510.7860.918
Multi-D-ADC (214 × 214)0.3440.8090.960
OMulti-D-OADC (214 × 214)0.3730.8410.973
IVFOADC+GP (220)0.4050.8510.957
Ours (212 × 212)0.4580.8590.903
", + "bbox": [ + 78, + 122, + 490, + 281 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "$15\\%$ on the SIFT-1M and $23\\%$ on the DEEP-1M dataset with 64bits bit budget.", + "bbox": [ + 75, + 338, + 468, + 365 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As our motivation, a naive combination of the UNQ and the inverted index does not improve the performance of the exhaustive UNQ. For example, the UNQ+IVF drops the R@1 score of the exhaustive UNQ about $5\\%$ and $7\\%$ for SIFT-1M and DEEP-1M with 64bits bit budget, respectively. The disentangled representation of Ours improves the R@1 scores of UNQ+IVF about $20\\%$ and $32\\%$ on SIFT-1M and DEEP-1M with 64bits bit budget, respectively.", + "bbox": [ + 75, + 366, + 468, + 477 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Result on Billion-Scale Dataset", + "text_level": 1, + "bbox": [ + 75, + 484, + 349, + 498 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We conduct an experiment on a billion-scale dataset to verify the scalability of the proposed method. Table. 5 reports the experimental results on the SIFT-1B dataset with 128bit budget. The improvement in the R@1 score of Ours over IVFOADC+GP is about $13\\%$ . Moreover, Ours shows $20\\%$ of improvement compared to the UNQ while Ours is a non-exhaustive search and the UNQ is an exhaustive search.", + "bbox": [ + 75, + 505, + 468, + 602 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Notably, the margin of improvement is much larger with the SIFT-1B dataset than the SIFT-1M dataset with 128bits encoding. Because the billion-scale task is a much more challenging task than the million-scale task with an identical bit budget, the billion-scale task has much more room for performance gain.", + "bbox": [ + 75, + 602, + 468, + 685 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Furthermore, we choose a conventional Multi-D-ADC algorithm with $2^{12} \\times 2^{12}$ number of indices for learning the inverted index because our contribution is not about the inverted index. However, the experimental results demonstrate the superiority of Ours compared to methods with much finer inverted index $(2^{14} \\times 2^{14})$ and a sophisticated inverted indexing algorithm (IVFOADC+GP).", + "bbox": [ + 75, + 685, + 468, + 782 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.4. Ablation Study", + "text_level": 1, + "bbox": [ + 75, + 789, + 230, + 804 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We validate our method with ablation study on two hyper-parameters. First, Table. 6 shows ablation study about the number of visited inverted indices $w$ on the SIFT-1M with 64bits encoding. Ours consistently improves", + "bbox": [ + 75, + 809, + 468, + 866 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/e37d6c1b5f89d69cc2de0d540ff24268a89ea109a19878b798e97d9e0edac011.jpg", + "table_caption": [ + "Table 5. Experimental results on the SIFT-1B dataset and 128bits bit-budget. All the quantities except Ours are taken from [5,9,23]." + ], + "table_footnote": [], + "table_body": "
MethodwR@1R@10R@100
UNQ+IVF (w/o residual)10.2160.4120.442
Ours0.2530.4300.442
UNQ+IVF (w/o residual)20.2720.5560.612
Ours0.3170.5880.613
UNQ+IVF (w/o residual)40.3050.6740.763
Ours0.3610.7200.765
UNQ+IVF (w/o residual)80.3220.7530.877
Ours0.3870.8090.880
UNQ+IVF (w/o residual)160.3310.7910.945
Ours0.3970.8570.947
UNQ+IVF (w/o residual)320.3320.8040.977
Ours0.3990.8760.979
UNQ+IVF (w/o residual)640.3320.8060.985
Ours0.3990.8800.987
", + "bbox": [ + 500, + 122, + 915, + 337 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 6. Ablation study about the number of visited inverted indices on the SIFT-1M dataset with 64bits bit budget.", + "bbox": [ + 497, + 346, + 890, + 372 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "UNQ+IVF regardless of the number of $w$ . For example, the performance gain of the R@1 score is about 17% with $w = 1$ and 20% with $w = 64$ . Moreover, these experimental results also highlight that the R@1 score of Ours with only $w = 4$ (out of 1024) is even superior to the exhaustive UNQ in Table.3.", + "bbox": [ + 497, + 399, + 890, + 482 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Second, we verify with various numbers of re-ranking candidates $R = \\{1, 10, 100, 1000\\}$ . It is identical to exclude the re-ranking if $R = 1$ . Table. 7 shows the experimental results on the SIFT-1M and the DEEP-1M datasets with 64bits encoding. For the SIFT-1M dataset, Ours improves the more performance with the fewer number of re-ranking. For example, the performance gains of the R@1 score are about $\\{62\\%, 28\\%, 21\\%, 20\\% \\}$ with $R = \\{1, 10, 100, 1000\\}$ , respectively. On the other hand, Ours improves the more performance with the larger number of re-ranking for the DEEP-1M dataset where the performance gains of the R@1 score are about $\\{17\\%, 29\\%, 32\\%, 32\\% \\}$ .", + "bbox": [ + 497, + 484, + 892, + 650 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.5. Validation of Disentanglement", + "text_level": 1, + "bbox": [ + 499, + 663, + 766, + 678 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We validate disentangled representation of the proposed method by generating new data points. Likewise disentanglement methods for generative models, we generate data points that have desired characteristics by controlling the input of the decoder. In detail, a reconstructed data point $\\tilde{x}_n$ should belong to a specific cluster by substituting the $q_{\\mathrm{IVF}}(x_n)$ by a desired cluster center $T$ . We randomly sample $10^{4}$ data points from the database and generate about $10^{7}$ new data points by concatenating $K^{\\prime} = 1024$ number of cluster centers to each $l_{n}$ . Table. 8 reports the ratio of generated data points that belong to the desired cluster within top-R nearest clusters. The R@1 score of SIFT-1M and DEEP-1M datasets are 0.709 and 0.827, respectively", + "bbox": [ + 497, + 686, + 890, + 866 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "12007", + "bbox": [ + 465, + 887, + 504, + 897 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/28edd2e2ea6916d85e785fed35c4bb5ff6e91c5615601ad97ac04db7d9141fb9.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Method# of re-rankR@1
SIFT-1M 64bits
UNQ+IVF (w/o residual) Oursw/o re-rank0.146 0.236
UNQ+IVF (w/o residual) Ours100.292 0.375
UNQ+IVF (w/o residual) Ours1000.329 0.397
UNQ+IVF (w/o residual) Ours10000.332 0.399
DEEP-1M 64bits
UNQ+IVF (w/o residual) Oursw/o re-rank0.134 0.157
UNQ+IVF (w/o residual) Ours100.228 0.295
UNQ+IVF (w/o residual) Ours1000.248 0.328
UNQ+IVF (w/o residual) Ours10000.249 0.329
", + "bbox": [ + 97, + 122, + 445, + 394 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "while the probability of belonging to the desired cluster of a randomly generated vector is 0.001. The experimental results confirm that the proposed representation is well disentangled as we intended.", + "bbox": [ + 75, + 448, + 468, + 505 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.6. Overhead Analysis", + "text_level": 1, + "bbox": [ + 77, + 513, + 258, + 528 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Finally, we analyze the search time overhead of the proposed method. Table. 9 demonstrates the average search time of Multi-D-ADC and Ours with identical cluster centers of the inverted index. The retrieval procedure of Ours is similar to the Multi-D-ADC except the additional encoding (Eq. 12) and decoding (Eq. 8) steps. In encoding query (Eq. 12), a query $y$ should be concatenated with $w$ number of cluster centers and embedded $w$ times to build the lookup table. To accelerate the encoding query, we propose batch-forwarding $w$ number of lookup tables at once while the Multi-D-ADC build the lookup table in sequence. Similarly, the decoding top-R (Eq. 8) also can be simply accelerated by batch-forwarding. The re-ranking time (Eq. 14) is negligible because the number of re-ranked data $(R = 200)$ is small. The overall search time of Ours is about $12\\%$ slower than the Multi-D-ADC, but we believe it is permissible compared to the performance gain of Ours. Nevertheless, Ours speeds up the search procedure of the UNQ, which requires more than a minute in an exhaustive search. The experimental results are obtained in a single-CPU mode of a $2.2\\mathrm{GHz}$ Intel Xeon processor with Faiss [17], and the encoding and decoding times are measured in a single Nvidia Tesla V100 GPU with Pytorch [27].", + "bbox": [ + 75, + 534, + 468, + 851 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The proposed method requires $\\{21,32\\} \\mathrm{MB}$ for $\\{64,$", + "bbox": [ + 95, + 852, + 467, + 866 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/84297fd9e93a8c1fabd97e42f34aacbe8620dbb00c958f73dd0d8b83387660b0.jpg", + "table_caption": [ + "Table 7. Ablation study about the number of re-ranked candidates on million-scale datasets with 64bits bit budget." + ], + "table_footnote": [], + "table_body": "
DatasetMethodR@1R@3R@5
SIFT-1MD([ln, T])0.7090.9230.968
DEEP-1MD([ln, T])0.8270.9650.987
-Random0.0010.0030.005
", + "bbox": [ + 509, + 123, + 884, + 182 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/5bbbaffda998e4148d342cad54094291f7be0d0f6a46d5940bbf263c5b41413e.jpg", + "table_caption": [ + "Table 8. Experiment to validate disentanglement of proposed method with 64bits bit-budget. The score represents the ratio of generated data points that belong to desired cluster within top-R nearest clusters." + ], + "table_footnote": [], + "table_body": "
MethodTime (ms)
Multi-D-ADC (212 × 212)16.89
Ours (212 × 212)18.88
1. encoding query (Eq. 12)1.27
2. symmetric search (Eq. 13)16.86
3. decoding top-R (Eq. 8)0.70
4. asymmetric re-ranking (Eq. 14)0.04
", + "bbox": [ + 517, + 260, + 873, + 361 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 9. Search time analysis on the SIFT-1B dataset and 128bits bit-budget.", + "bbox": [ + 497, + 370, + 890, + 396 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "128} bits encoding where the UNQ requires $\\{20, 30\\}\\mathrm{MB}$ for the same budget. Note that those additional memory usage is not proportional to the database size, thus it is same for 1M and 1B database.", + "bbox": [ + 499, + 425, + 890, + 480 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 500, + 618, + 515 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose a novel disentangled representation learning for unsupervised neural quantization. We firstly discover the cause of limited application of the deep quantization (UNQ [23]) on non-exhaustive search with the inverted index. Specifically, the deep quantizer is hard to exploit the compact representation of residual vector space and even takes disadvantages such as loss of cluster center information. To address the problem, we disentangle the information of the cluster center and the latent space by feeding the center to both the encoder and decoder to make center information redundant for the decoder. Similar to residual encoding, this disentanglement encourages the latent space compact and quantization-friendly by taking out the center information from latent space, so the quantization distortion is significantly reduced with disentangled representation. Extensive experiments on various datasets from million to billion scales validate the superiority of the proposed method over state-of-the-art retrieval systems.", + "bbox": [ + 497, + 526, + 890, + 775 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. This work was supported in part by ETRI grant funded by the Korean government [23ZH1200, The research of the fundamental media-contents technologies for hyper-realistic media space], and MSIT/IITP [2019-0-00421], MSIT/NRF [NRF-2022R1F1A1076132], and MSIT&KNPA/KIPoT [Police Lab 2.0, 210121M06].", + "bbox": [ + 497, + 783, + 890, + 866 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "12008", + "bbox": [ + 465, + 887, + 504, + 897 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 124, + 173, + 138 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Alexandr Andoni and Piotr Indyk. Near-optimal hashing algorithms for approximate nearest neighbor in high dimensions. Communications of the ACM, 51(1):117-122, 2008. 1", + "[2] Artem Babenko and Victor Lempitsky. Additive quantization for extreme vector compression. 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In International Conference on Machine Learning, pages 838-846. PMLR, 2014. 2" + ], + "bbox": [ + 78, + 125, + 468, + 565 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "12010", + "bbox": [ + 467, + 887, + 504, + 897 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Disentangled Representation Learning for Unsupervised Neural Quantization/06ed76f2-80a7-4ca7-b9b2-5c10f4249fdb_model.json b/2023/Disentangled Representation Learning for Unsupervised Neural Quantization/06ed76f2-80a7-4ca7-b9b2-5c10f4249fdb_model.json new file mode 100644 index 0000000000000000000000000000000000000000..f115872bb78f17fe79df01ed17acaed5bf01cd8a --- /dev/null +++ b/2023/Disentangled Representation Learning for Unsupervised Neural Quantization/06ed76f2-80a7-4ca7-b9b2-5c10f4249fdb_model.json @@ -0,0 +1,2277 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.13, + 0.051, + 0.201, + 0.086 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.253, + 0.049, + 0.793, + 0.088 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.096, + 0.162, + 0.877, + 0.184 + ], + "angle": 0, + "content": "Disentangled Representation Learning for Unsupervised Neural Quantization" + }, + { + "type": "text", + "bbox": [ + 0.151, + 0.208, + 0.823, + 0.258 + ], + "angle": 0, + "content": "Haechan Noh1, Sangeek Hyun1, Woojin Jeong1, Hanshin Lim2, Jae-Pil Heo1,* \n1Sungkyunkwan University, 2Electronics and Telecommunications Research Institute {noru0114, hsi1032, us03385, jaepilheo}@skku.edu, hslim@etri.re.kr" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.289, + 0.314, + 0.304 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.312, + 0.473, + 0.548 + ], + "angle": 0, + "content": "The inverted index is a widely used data structure to avoid the infeasible exhaustive search. It accelerates retrieval significantly by splitting the database into multiple disjoint sets and restricts distance computation to a small fraction of the database. Moreover, it even improves search quality by allowing quantizers to exploit the compact distribution of residual vector space. However, we firstly point out a problem that an existing deep learning-based quantizer hardly benefits from the residual vector space, unlike conventional shallow quantizers. To cope with this problem, we introduce a novel disentangled representation learning for unsupervised neural quantization. Similar to the concept of residual vector space, the proposed method enables more compact latent space by disentangling information of the inverted index from the vectors. Experimental results on large-scale datasets confirm that our method outperforms the state-of-the-art retrieval systems by a large margin." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.569, + 0.21, + 0.584 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.593, + 0.47, + 0.689 + ], + "angle": 0, + "content": "Measuring the distances among feature vectors is a fundamental requirement in various fields of computer vision. One of the tasks most relevant to distance measurement is the nearest neighbor search, which finds the closest data in the database from a query. The task is especially challenging in high-dimensional and large-scale databases due to huge computational costs and memory overhead." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.69, + 0.47, + 0.814 + ], + "angle": 0, + "content": "By relaxing the complexity, Approximate Nearest Neighbor (ANN) search is popular in practice. Recent approaches for ANN typically learn the compact representation by exploiting Multi-Codebook Quantization (MCQ) [2, 9, 16]. Compared to hashing-based approaches [1, 10, 12], the MCQ provides a more informative asymmetric distance estimator where the query side is not compressed. Moreover, all possible distances between the query and codewords can be stored in a lookup table for efficiency." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.815, + 0.47, + 0.844 + ], + "angle": 0, + "content": "Although the MCQ accelerates the distance computation with the lookup table, exhaustive search on the large-scale" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.29, + 0.892, + 0.415 + ], + "angle": 0, + "content": "dataset is still prohibited. The Inverted File with Asymmetric Distance Computation (IVFADC) [16] is proposed for non-exhaustive ANN search by cooperating with the inverted index [30]. It splits the database into multiple disjoint sets and restricts distance computations to small portions close to the query to accelerate the retrieval speed. Moreover, the compactness of residual vector space between data points and inverted indices substantially enhances the quantization quality." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.42, + 0.893, + 0.599 + ], + "angle": 0, + "content": "Thanks to the rapid advances in deep learning, most areas of computer vision benefit from its great learning capacity compared to shallow methods. However, the state-of-the-art methods of unsupervised quantization remain shallow for a long time because selecting the maximum value (i.e. argmax), which is an essential operation of quantization, is not differentiable. Inspired by a recent generative model with discrete hidden variables [35], the Unsupervised Neural Quantization (UNQ) [23] introduced an encoder-decoder-based architecture for ANN search. The large learning capacity of deep neural architecture significantly improves the retrieval quality compared to conventional shallow methods." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.604, + 0.895, + 0.868 + ], + "angle": 0, + "content": "Despite the outperforming performance of the UNQ, its superiority is validated only on the exhaustive search. To verify its effectiveness on non-exhaustive search, we conduct an experiment of non-exhaustive UNQ with an inverted index. Interestingly, we observe that this deep architecture does not benefit from the residual vector space and it even harms the search quality as reported in Table 1. We hypothesize the reasons for this performance degradation from two perspectives. First, both the residual vector space and latent space of the neural network transform the data into a quantization-friendly distribution, thus deep quantizer has a scant margin to be improved by the residual space. Second, residual space sacrifices the distributional characteristics of each cluster, since the information of cluster center in the original space is removed. For conventional shallow quantizers, the drawback of residual space is obscured by its huge advantage of making a compact distribution. However, deep quantizer only takes the disadvantages (information loss) from residual space without leveraging the effec" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.854, + 0.221, + 0.867 + ], + "angle": 0, + "content": "*Corresponding author" + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.888, + 0.505, + 0.899 + ], + "angle": 0, + "content": "12001" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.078, + 0.127, + 0.356, + 0.139 + ], + "angle": 0, + "content": "tiveness such as compactness of residuals." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.141, + 0.47, + 0.388 + ], + "angle": 0, + "content": "In this paper, we focus on extending the application of deep architectures for non-exhaustive search. To this end, we learn a disentangled representation to harmonize a deep architecture with the inverted index, inspired by recent representation learning techniques for generative models [8,34]. In our disentangled representation learning, both encoder and decoder get information of cluster center as an additional input. Since the information of cluster center is redundant to decoder if latent feature contains information of cluster center, the encoder is trained to remove the information of cluster centers from the latent embedding. The disentangled representation learning is similar to concept of the residual vector space that provides more compact distribution by taking out the information of cluster centers. The experimental results verify that the learning disentangled representation enables the neural quantization to collaborate with inverted index and outperforms the state-of-the-art methods." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.39, + 0.357, + 0.403 + ], + "angle": 0, + "content": "The contributions of our paper include:" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.405, + 0.468, + 0.445 + ], + "angle": 0, + "content": "- We point out that the residual encoding of the inverted index is incompatible with the neural multi-codebook quantization method." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.448, + 0.468, + 0.489 + ], + "angle": 0, + "content": "- We propose a novel disentangled representation learning for neural multi-codebook quantization to combine deep quantization and inverted index." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.491, + 0.468, + 0.533 + ], + "angle": 0, + "content": "- The experimental results show that the proposed method outperforms the state-of-the-art retrieval systems by a large margin." + }, + { + "type": "list", + "bbox": [ + 0.097, + 0.405, + 0.468, + 0.533 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.546, + 0.218, + 0.559 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.569, + 0.411, + 0.582 + ], + "angle": 0, + "content": "2.1. Multi-codebook Quantization for ANN" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.59, + 0.468, + 0.714 + ], + "angle": 0, + "content": "Vector quantization [11] maps a vector to its nearest codeword within a learned codebook. Specifically, a high-dimensional real-valued vector can be efficiently represented by an integer index of its corresponding cluster. To ensure a high search accuracy, the vector quantization requires a codebook with an extremely large number of codewords. However, enlarging the number of codewords is far from efficiency because the cost of assigning the nearest codeword is proportionally increased with codebook sizes." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.715, + 0.468, + 0.824 + ], + "angle": 0, + "content": "Product Quanztiaton (PQ) [16] decomposes the space into a Cartesian product of lower-dimensional subspaces. By quantizing each subspace separately, multiple codebooks are produced and they enable better search quality with a manageable number of codewords. Optimized Product Quantization (OPQ) [9] and Cartesian K-means [25] introduced to learn transformation to optimize the decomposition step in PQ according to the data distribution." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.825, + 0.468, + 0.867 + ], + "angle": 0, + "content": "While the PQ encodes a vector into a concatenation of assigned codewords, a number of methods [2, 6, 20, 21, 26, 36] approximated a vector by a sum of assigned codewords." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.127, + 0.891, + 0.181 + ], + "angle": 0, + "content": "These addition-based methods have a higher degree of freedom than the concatenation-based methods, since the concatenation is a special case of addition where components of addition are mutually orthogonal." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.182, + 0.892, + 0.362 + ], + "angle": 0, + "content": "The state-of-the-art methods of such multi-codebook quantization remain shallow for a long time, while most areas of computer vision benefit from rapid advances in deep learning. The non-differentiability of codeword assignment operation makes the multi-codebook quantization hard to collaborate with deep learning. Vector-Quantized Variational Autoencoder (VQ-VAE) [35] in the area of the generative model proposed a gradient estimation to propagate gradient through discrete variables. Inspired by the VQ-VAE, Unsupervised Neural Quantization (UNQ) [23] introduces a deep neural network for multi-codebook quantization. The much larger learning capacity of UNQ significantly improves the conventional shallow methods." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.371, + 0.755, + 0.385 + ], + "angle": 0, + "content": "2.2. Non-exhaustive ANN Search" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.393, + 0.892, + 0.587 + ], + "angle": 0, + "content": "While the quantization techniques accelerate the distance computation, the search is still exhaustive. IVFADC [16] proposed a non-exhaustive approximate nearest neighbor search by cooperating with the inverted index [30]. In addition to the significant acceleration of retrieval speed, the non-exhaustive manner even improves the search quality by allowing more compact residual vector space. The Inverted Multi-Index (IMI) [3] extends the IVFADC by decomposing data space into two sub-spaces and applying the inverted index independently. Similar to the idea of PQ, the decomposed data space of IMI enables much finer partition with a manageable number of indices. Several subsequent non-exhaustive ANN techniques are proposed to improve the data partitioning rather than the quantization [4, 5, 7]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.596, + 0.833, + 0.611 + ], + "angle": 0, + "content": "2.3. Disentangled Representation Learning" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.618, + 0.892, + 0.811 + ], + "angle": 0, + "content": "In the context of the generative model, disentangled representation is introduced to analyze and utilize the independent effects of latent factors. One straightforward example can be found in conditional generative models [22, 32]. They decompose the conditional information from the others so that they can control the specific conditions of generated images such as spatial layout [8] or class information [22]. For instance, variational U-Net [8] disentangles the shape and appearance representations to synthesize human images of diverse poses with a shared appearance. Similarly, VarSR [13] builds the latent space of high-resolution information disentangled from the low-resolution images. Hence, they can synthesize diverse high-resolution images corresponding to the given low-resolution image." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.812, + 0.892, + 0.867 + ], + "angle": 0, + "content": "The aforementioned examples mainly focus on the controllable generation by disentangling conditional information. However, in this paper, we concentrate on the maximization of the representation capability of the latent space" + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.888, + 0.505, + 0.899 + ], + "angle": 0, + "content": "12002" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.1, + 0.123, + 0.445, + 0.226 + ], + "angle": 0, + "content": "
MethodR@1R@10R@100
PQ0.2280.6530.953
+IVF (w/o residual)0.2280.6530.950
+IVF (with residual)0.2720.7350.969
UNQ0.3460.8280.990
+IVF (w/o residual)0.3310.7980.939
+IVF (with residual)0.2720.7180.867
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.231, + 0.47, + 0.271 + ], + "angle": 0, + "content": "Table 1. Comparison of retrieval performances between the PQ and the UNQ on SIFT-1M. The residual vector space improves the performance with the PQ, but does not work with the UNQ." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.287, + 0.469, + 0.343 + ], + "angle": 0, + "content": "by disentanglement. Specifically, we build a compact latent space by disentangling the cluster center similar to residual encoding but compatible with the neural multi-codebook quantization method." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.355, + 0.206, + 0.37 + ], + "angle": 0, + "content": "3. Background" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.378, + 0.469, + 0.434 + ], + "angle": 0, + "content": "Let us briefly introduce the ANN task, the MCQ approach, and the residual vector space. With \\(D\\)-dimensional database \\(X = \\{x_{n}\\}_{n = 1}^{N}, x_{n} \\in \\mathbb{R}^{D}\\) and query \\(y \\in \\mathbb{R}^{D}\\), the nearest neighbor of query \\(y\\) is defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.163, + 0.442, + 0.469, + 0.468 + ], + "angle": 0, + "content": "\\[\n\\operatorname {N N} (y) = \\underset {n \\in \\{1, \\dots , N \\}} {\\arg \\min } \\| y - x _ {n} \\| ^ {2}. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.477, + 0.469, + 0.561 + ], + "angle": 0, + "content": "To alleviate time and memory costs of Eq. 1, the MCQ quantizer \\( q_{\\mathrm{MCQ}} \\) encodes the database \\( X = \\{x_{n}\\}_{n=1}^{N} \\) utilizing \\( M \\) number of multi-codebooks \\( C^{m} = \\{c_{k}^{m}\\}_{k=1}^{K}, c_{k}^{m} \\in \\mathbb{R}^{D} \\) where each codebook has \\( K \\) number of codewords. Then, a vector \\( x_{n} \\) is represented as \\( M \\) number of indices \\( [i_{n}^{1}, \\dots, i_{n}^{M}] \\) and reconstructed by referring the codebooks:" + }, + { + "type": "equation", + "bbox": [ + 0.177, + 0.57, + 0.469, + 0.607 + ], + "angle": 0, + "content": "\\[\nx _ {n} \\approx q _ {\\mathrm {M C Q}} \\left(x _ {n}\\right) = \\sum_ {m = 1} ^ {M} c _ {i _ {n} ^ {m}} ^ {m}. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.616, + 0.469, + 0.644 + ], + "angle": 0, + "content": "The goal of this lossy compression process is to learn codebooks that minimize quantization distortion \\( E \\) defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.165, + 0.654, + 0.469, + 0.692 + ], + "angle": 0, + "content": "\\[\nE \\left(x _ {n}, C\\right) = \\sum_ {m = 1} ^ {M} \\left| \\left| x _ {n} ^ {m} - c _ {i _ {n} ^ {m}} ^ {m} \\right| \\right| ^ {2}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.701, + 0.469, + 0.743 + ], + "angle": 0, + "content": "where \\( x_{n} = \\sum x_{n}^{m} \\), and \\( x_{n}^{m} \\) is a subvector of \\( x_{n} \\) corresponding to index \\( i_{n}^{m} \\). The PQ belongs to the MCQ approach where \\( x_{n}^{m} \\) are mutually orthogonal." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.743, + 0.469, + 0.867 + ], + "angle": 0, + "content": "The IVFADC [16] further accelerates ANN search by collaborating with an inverted index. The inverted index \\( q_{\\mathrm{IVF}} \\) splits database \\( X \\) into \\( K' \\) number of disjoint subsets, and the ANN search is then restricted to \\( w \\) number of nearest subsets from query \\( y \\), where \\( w \\) is much smaller than \\( K' \\). For a given data point \\( x_n \\), the inverted index \\( q_{\\mathrm{IVF}}(\\cdot) \\) quantize it to its nearest cluster center \\( q_{\\mathrm{IVF}}(x_n) \\), and the data points belong to the same cluster are stored adjacently. Moreover, the IVFADC suggested learning codebooks that" + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.124, + 0.886, + 0.282 + ], + "angle": 0, + "content": "
MethodCompression ratioDistortion
PQ128×0.8368
+IVF (with residual)0.7208
PQ64×0.6252
+IVF (with residual)0.5846
PQ32×0.4127
+IVF (with residual)0.4220
PQ16×0.2438
+IVF (with residual)0.2604
PQ4×0.0212
+IVF (with residual)0.0257
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.288, + 0.892, + 0.34 + ], + "angle": 0, + "content": "Table 2. Quantization distortions of the database with varying compression ratios. The residual vector space is profitable with a large compression ratio, but it leads performance drop with a small compression ratio." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.354, + 0.891, + 0.381 + ], + "angle": 0, + "content": "encode residual vector \\(r(x_{n}) = x_{n} - q_{\\mathrm{IVF}}(x_{n})\\) rather than the original vector as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.541, + 0.389, + 0.891, + 0.404 + ], + "angle": 0, + "content": "\\[\nx _ {n} \\approx \\tilde {x} _ {n} = q _ {\\mathrm {M C Q}} \\left(x _ {n} - q _ {\\mathrm {I V F}} \\left(x _ {n}\\right)\\right) + q _ {\\mathrm {I V F}} \\left(x _ {n}\\right). \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.41, + 0.891, + 0.437 + ], + "angle": 0, + "content": "Then the distance between query \\(y\\) and target data \\(x_{n}\\) is estimated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.445, + 0.891, + 0.461 + ], + "angle": 0, + "content": "\\[\nd (y, x _ {n}) \\approx d (y - q _ {\\mathrm {I V F}} (x _ {n}), q _ {\\mathrm {M C Q}} (x _ {n} - q _ {\\mathrm {I V F}} (x _ {n}))). \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.467, + 0.891, + 0.536 + ], + "angle": 0, + "content": "where the \\(d(\\cdot, \\cdot)\\) is the Euclidean distance between two vectors. The IVFADC accelerates the search speed by reducing the number of distance estimations and improves the quantization distortion (Eq. 3) thanks to the compact distribution of the residual vector space." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.547, + 0.673, + 0.563 + ], + "angle": 0, + "content": "4. Proposed Method" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.569, + 0.621, + 0.582 + ], + "angle": 0, + "content": "4.1. Motivation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.591, + 0.892, + 0.728 + ], + "angle": 0, + "content": "Recently, the UNQ [23] introduced a deep architecture for MCQ learning and improves conventional shallow MCQ methods by a large margin. However, its effectiveness is only validated by an exhaustive ANN search. To examine the performance of UNQ on non-exhaustive search, we test the retrieval performances of PQ and UNQ with an inverted index on exhaustive and non-exhaustive settings. As reported in Table. 1, the residual encoding (Eq. 4) provides better search quality with the PQ, while it makes the search quality of UNQ even worse." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.729, + 0.892, + 0.867 + ], + "angle": 0, + "content": "To investigate the reasons why residual encoding does not help the UNQ, we need to analyze the mechanism of residual encoding in PQ. To this end, we hypothesize the effect of residual representation in two aspects. First, the advantage of residuals in PQ comes from the transformation of data space into compact and quantization-friendly distribution. Second, the residual encoding is not always beneficial, since they sacrifice the information of the cluster center so that the distributional characteristics of each cluster are suppressed." + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.888, + 0.505, + 0.899 + ], + "angle": 0, + "content": "12003" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.126, + 0.131, + 0.844, + 0.273 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.282, + 0.893, + 0.322 + ], + "angle": 0, + "content": "Figure 1. By providing additional input of \\( q_{\\mathrm{IVF}}(x_n) \\) to both encoder and decoder, the encoder is not necessary to learn features to reconstruct \\( q_{\\mathrm{IVF}}(x_n) \\) since it is redundant information for the decoder. Thus the information of the cluster center is disentangled from the latent vectors and codebooks. The disentangling enables the quantizer to learn compact representation while preserving the original distribution." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.339, + 0.473, + 0.504 + ], + "angle": 0, + "content": "To validate these hypotheses, we observe the performance variation of PQ with residual encoding by varying compression ratios. The compression ratios are controlled by adjusting the number of codebooks \\( M \\). As reported in Table. 2, the residual encoding is profitable with large compression ratios, since the sparse original distribution is hard to quantize with the deficient bit-budget. On the other hand, the residual encoding leads to performance drops with small compression ratios, because it is not necessary to represent the data compactly thanks to sufficient numbers of codewords, but the information loss of cluster-wise distributional characteristics still exists." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.505, + 0.47, + 0.669 + ], + "angle": 0, + "content": "Based on these observations, we explain the reasons for UNQ's performance drop with residual encoding. Firstly, UNQ does not benefit from the compact representation of residual encoding. The deep encoder transforms the data into latent space with a reconstruction objective function. That is, the objective of UNQ also encourages to transform the data into compact latent space, so the residual encoding and UNQ affect the model in a similar way. Hence, the residual representation is hardly beneficial to the neural quantizer. Secondly, UNQ takes the disadvantage of residual encoding, the information loss of distributional characteristics of each cluster." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.671, + 0.47, + 0.768 + ], + "angle": 0, + "content": "These interpretations motivate us to come up with a method that only takes the advantage of residual representation. That is, we aim to make the latent space more compact without the information loss of distributional characteristics of each cluster. To this end, we introduce a disentangled representation learning for unsupervised neural quantization in the following sections." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.776, + 0.377, + 0.79 + ], + "angle": 0, + "content": "4.2. Disentangled Neural Quantization" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.798, + 0.469, + 0.868 + ], + "angle": 0, + "content": "Inspired by the disentangled representation of conditional generative models [22, 32], we propose disentangled neural quantization. The previous methods exploit the disentanglement for a controllable generation. However, we propose to learn a disentangled representation to reduce" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.339, + 0.892, + 0.463 + ], + "angle": 0, + "content": "the quantization distortion. Specifically, a latent feature \\((l_{n})\\) of UNQ contains information of its input vector \\(x_{n}\\) where \\(x_{n}\\) consists of \\(q_{\\mathrm{IVF}}(x_n)\\) and \\(x_{n} - q_{\\mathrm{IVF}}(x_{n})\\). However, the \\(q_{\\mathrm{IVF}}(x_n)\\) can be restored without any information loss thanks to the data structure of the inverted index. Thus, encoding the \\(q_{\\mathrm{IVF}}(x_n)\\) is quite wasteful because the MCQ approach has a scarce bit budget in practice. In this paper, we suggest disentangling the \\(q_{\\mathrm{IVF}}(x_n)\\) from \\(l_{n}\\) to provide more compact information." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.463, + 0.893, + 0.602 + ], + "angle": 0, + "content": "To disentangle the \\(q_{\\mathrm{IVF}}(x_n)\\) from \\(l_{n}\\), we feed additional input of \\(q_{\\mathrm{IVF}}(x_n)\\) to encoder \\(E(\\cdot)\\) and decoder \\(D(\\cdot)\\). Then the \\(q_{\\mathrm{IVF}}(x_n)\\) is redundant information for \\(D(\\cdot)\\) if \\(l_{n}\\) contains information of \\(q_{\\mathrm{IVF}}(x_n)\\). Thus, the \\(E(\\cdot)\\) is trained to embed as little information of \\(q_{\\mathrm{IVF}}(x_n)\\) as possible in \\(l_{n}\\) to fully exploit the network capacity. The disentangled representation learning is similar to the concept of the residual encoding of PQ (Eq. 4) in terms of taking out the information of the cluster center. However, there is no information loss because the cluster center \\(q_{\\mathrm{IVF}}(x_n)\\) is provided to \\(D(\\cdot)\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.602, + 0.892, + 0.712 + ], + "angle": 0, + "content": "Figure. 1 describes the proposed disentangled representation learning. The cluster center of input data is provided to the encoder and decoder, and the scarce resource of finite codewords can be fully utilized to quantize the compact latent feature where the information of the cluster center is disentangled. Not only the compact information, but the decoder also preserves the original distribution by reconstructing the original space in an end-to-end manner." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.721, + 0.682, + 0.735 + ], + "angle": 0, + "content": "4.3. Network Structure" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.742, + 0.892, + 0.868 + ], + "angle": 0, + "content": "We adopt the network structure of [23] except our disentangling module. The network consists of encoder \\( E(\\cdot) \\), decoder \\( D(\\cdot) \\), and learnable codebook parameters \\( [C^1, \\dots, C^M] \\), \\( C^m = \\{c_k^m\\}_{k=1}^K \\). Both encoder \\( E(\\cdot) \\) and decoder \\( D(\\cdot) \\) are a concatenation of two fully-connected layers with Batch Normalization [14] and ReLU activation function. We feed separate information of cluster center \\( q_{\\mathrm{IVF}}(x_n) \\) to the encoder for the disentanglement. Then the encoder \\( E(\\cdot) \\) embeds the given concatenated inputs" + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.888, + 0.506, + 0.899 + ], + "angle": 0, + "content": "12004" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.107, + 0.124, + 0.861, + 0.322 + ], + "angle": 0, + "content": "
Search mannerMethod64bits encoding128bits encoding
R@1R@10R@100R@1R@10R@100
ExhaustiveOPQ0.2080.6430.9530.4090.8980.999
Catalyst + Lattice0.2890.7580.9790.4910.9411.
LSQ0.2920.7770.9870.5710.9751.
UNQ0.3460.8280.9900.5930.9801.
Non-ExhaustiveIVFADC (210)0.2960.7040.9570.4710.9030.993
IVFADC + QAI (210)0.3110.7300.9650.4960.9280.992
IVFOADC (210)0.2950.7190.9630.4750.9130.995
IVFOADC + QAI (210)0.3210.7560.9720.5000.9310.993
Multi-D-ADC (28 × 28)0.3030.7290.9670.4840.9240.998
Multi-D-ADC + QAI (28 × 28)0.3180.7480.9770.5130.9390.997
UNQ+IVF (210)0.3310.7980.9390.5480.9630.994
Ours (210)0.3980.8770.9710.6000.9740.990
" + }, + { + "type": "table_caption", + "bbox": [ + 0.12, + 0.324, + 0.848, + 0.338 + ], + "angle": 0, + "content": "Table 3. Experimental result on the SIFT-1M dataset. All the quantities except Ours and UNQ+IVF are taken from [23, 24]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.355, + 0.455, + 0.371 + ], + "angle": 0, + "content": "\\([x_n, q_{\\mathrm{IVF}}(x_n)]\\) to \\(M\\) number of latent features as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.165, + 0.378, + 0.469, + 0.395 + ], + "angle": 0, + "content": "\\[\nE \\left(\\left[ x _ {n}, q _ {\\mathrm {I V F}} \\left(x _ {n}\\right) \\right]\\right) = \\left[ l _ {n} ^ {1}, \\dots , l _ {n} ^ {M} \\right]. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.403, + 0.469, + 0.442 + ], + "angle": 0, + "content": "The embedded feature \\(l_{n}^{m}\\) is quantized to index \\(i_n^m\\) of the codeword that has the biggest dot-product with \\(l_{n}^{m}\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.188, + 0.444, + 0.469, + 0.469 + ], + "angle": 0, + "content": "\\[\ni _ {n} ^ {m} = \\underset {k \\in \\{1, \\dots , K \\}} {\\arg \\max } l _ {n} ^ {m} \\cdot c _ {k} ^ {m}. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.473, + 0.469, + 0.598 + ], + "angle": 0, + "content": "Because the argmax function is not differentiable, we follow [23] that exploits the Gumbel trick [15]. The Gumbel trick provides a differentiable approximation of Eq. 7 by substituting the argmax with softmax during backpropagation. Then, the sum of assigned codewords \\( c_{i_n^m}^m \\) becomes the input for the decoder \\( D(\\cdot) \\). Likewise, we concatenate it with the cluster center \\( q_{\\mathrm{IVF}}(x_n) \\) for the disentanglement. The approximated vector \\( \\tilde{x}_n \\) of original vector \\( x_n \\) is obtained as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.146, + 0.605, + 0.469, + 0.644 + ], + "angle": 0, + "content": "\\[\n\\tilde {x} _ {n} = D \\left(\\left[ \\sum_ {m = 1} ^ {M} c _ {i _ {n} ^ {m}} ^ {m}, q _ {\\mathrm {I V F}} (x _ {n}) \\right]\\right). \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.651, + 0.469, + 0.691 + ], + "angle": 0, + "content": "The model is trained with two losses. The first one is a reconstruction loss which directly minimizes the quantization distortion as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.194, + 0.7, + 0.469, + 0.737 + ], + "angle": 0, + "content": "\\[\nL _ {1} = \\sum_ {n = 1} ^ {N} | | x _ {n} - \\tilde {x} _ {n} | | ^ {2}. \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.745, + 0.469, + 0.786 + ], + "angle": 0, + "content": "Similar to [23], we adopt the square Coefficient Variation regularizer [29] to encourage the codewords to be evenly selected:" + }, + { + "type": "equation", + "bbox": [ + 0.165, + 0.793, + 0.469, + 0.831 + ], + "angle": 0, + "content": "\\[\nL _ {2} = \\sum_ {m = 1} ^ {M} \\frac {\\sum_ {n = 1} ^ {N} \\left(p _ {n} ^ {m} - p _ {\\text {a v g}} ^ {m}\\right) ^ {2}}{p _ {\\text {a v g}} ^ {m} {} ^ {2}}, \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.839, + 0.469, + 0.869 + ], + "angle": 0, + "content": "where \\( p_n^m \\) is the softmax probability of \\( i_n^m \\) by the Gumbel approximation in Eq. 7, and \\( p_{\\mathrm{avg}}^m \\) is the average of \\( p_n^m \\) along" + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.355, + 0.859, + 0.369 + ], + "angle": 0, + "content": "\\(N\\). The final loss of the model is described as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.637, + 0.376, + 0.891, + 0.39 + ], + "angle": 0, + "content": "\\[\nL = L _ {1} + \\lambda * L _ {2} \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.395, + 0.892, + 0.451 + ], + "angle": 0, + "content": "The loss ratio \\(\\lambda\\) starts from 1.0 and decreases to 0.05 during the training. For a fair comparison, we adopt other details of [23] including Quasi-Hyperbolic Adam algorithm [19], and One Cycle learning rate schedule [31]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.457, + 0.691, + 0.47 + ], + "angle": 0, + "content": "4.4. Retrieval Procedure" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.478, + 0.892, + 0.589 + ], + "angle": 0, + "content": "Firstly, each database vector \\( x_{n} \\) is encoded into \\( M \\) number of indices \\( l_{n} = [i_{n}^{1},\\dots,i_{n}^{M}] \\) by Eq. 7. Because the codebooks have \\( K \\) number of codewords, the required bit-budget for the indices \\( l_{n} \\) is \\( M * \\lceil \\log_2K \\rceil \\). Moreover, the data points that belong to the same inverted index are stored adjacently, and the size of each cluster is stored. Thanks to this data structure of the inverted index, we can identify the \\( q_{\\mathrm{IVF}(x_n)} \\) without any additional costs in the retrieval stage." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.589, + 0.891, + 0.617 + ], + "angle": 0, + "content": "Secondly, a given query \\(y\\) is embedded into latent features \\(l_{y}\\), and the cluster center of the target is concatenated." + }, + { + "type": "equation", + "bbox": [ + 0.579, + 0.62, + 0.891, + 0.64 + ], + "angle": 0, + "content": "\\[\n\\left[ l _ {y} ^ {1}, \\dots , l _ {y} ^ {M} \\right] = E \\left(\\left[ y, q _ {\\mathrm {I V F}} \\left(x _ {n}\\right) \\right]\\right). \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.642, + 0.891, + 0.683 + ], + "angle": 0, + "content": "Then the symmetric distance between encoded query \\( l_{y} \\) and encoded target \\( [i_n^1, \\dots, i_n^M] \\) is computed by the cosine similarity as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.582, + 0.689, + 0.891, + 0.727 + ], + "angle": 0, + "content": "\\[\nD _ {\\text {s y m}} (y, x _ {n}) = \\sum_ {m = 1} ^ {M} \\frac {l _ {y} ^ {m} \\cdot c _ {i _ {n} ^ {m}} ^ {m}}{| | l _ {y} ^ {m} | | | | c _ {i _ {n} ^ {m}} ^ {m} | |}. \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.73, + 0.891, + 0.757 + ], + "angle": 0, + "content": "Note that, Eq. 13 can be efficiently computed by a lookup table storing precomputed all possible symmetric distances." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.758, + 0.891, + 0.812 + ], + "angle": 0, + "content": "Finally, the \\(R\\) top-ranked retrieved data according to the symmetric distance are then re-ranked by the more accurate asymmetric distances between uncompressed query \\(y\\) and \\(\\tilde{x}_n\\), as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.601, + 0.818, + 0.891, + 0.835 + ], + "angle": 0, + "content": "\\[\nD _ {\\text {a s y m}} (y, x _ {n}) = \\left\\| y - \\tilde {x} _ {n} \\right\\| ^ {2}. \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.839, + 0.891, + 0.867 + ], + "angle": 0, + "content": "We set the hyper-parameter \\( R = 200 \\), and we conduct an ablation study of \\( R \\) in Table. 7." + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.888, + 0.505, + 0.898 + ], + "angle": 0, + "content": "12005" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.131, + 0.123, + 0.837, + 0.281 + ], + "angle": 0, + "content": "
Search typeMethod64bits encoding128bits encoding
R@1R@10R@100R@1R@10R@100
ExhaustiveOPQ0.1590.5130.8860.3500.8250.991
Catalyst + Lattice0.2460.6830.9610.4480.9080.998
LSQ0.2170.6400.9450.4110.8860.995
UNQ0.2670.7260.9730.4790.9300.998
Non-exhaustiveIVFADC (210)0.2100.6160.9250.4180.8900.995
IVFOADC (210)0.2270.6590.9500.4160.8970.996
Multi-D-ADC (28 × 28)0.2000.6130.9290.3980.8830.995
UNQ+IVF (210)0.2500.6880.9100.4400.9070.996
Ours (210)0.3290.7990.9320.4910.9290.970
" + }, + { + "type": "table_caption", + "bbox": [ + 0.158, + 0.286, + 0.812, + 0.3 + ], + "angle": 0, + "content": "Table 4. Experimental results on DEEP-1M dataset. The quantities of Exhaustive methods are taken from [23]" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.319, + 0.194, + 0.333 + ], + "angle": 0, + "content": "5. Evaluation" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.342, + 0.18, + 0.356 + ], + "angle": 0, + "content": "5.1. Protocol" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.363, + 0.377, + 0.376 + ], + "angle": 0, + "content": "We evaluate our method on three datasets:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.381, + 0.469, + 0.451 + ], + "angle": 0, + "content": "- SIFT-1M, SIFT-1B [16]: 128-dimensional SIFT descriptor vectors [18]. The training set includes \\(\\{500k, 10^8\\}\\) vectors for 1M and 1B, respectively. Sets for evaluation have \\(10^4\\) queries and \\(\\{10^6, 10^9\\}\\) number of database for 1M and 1B, respectively." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.456, + 0.47, + 0.511 + ], + "angle": 0, + "content": "- DEEP-1M [4]: 96-dimensional DNN features extracted from the last fully-connected layer of GoogLeNet [33]. It also includes \\(500k\\) training data, \\(10^{4}\\) queries, and \\(10^{6}\\) database." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.381, + 0.47, + 0.511 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.515, + 0.47, + 0.597 + ], + "angle": 0, + "content": "The ground truth of a given query is defined as the top-1 nearest neighbor from an uncompressed database. Then, the retrieval performance in compressed space is measured by average \\( recall@R \\) for \\( R = \\{1, 10, 100\\} \\). The \\( recall@R \\) represents the ratio of queries that contains the ground truth in top- \\( R \\) retrieved vectors." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.598, + 0.469, + 0.749 + ], + "angle": 0, + "content": "Unless specified, we consistently use the following hyper-parameters. We set \\( K' = 2^{10} \\) for inverted index on million-scale datasets, and \\( K' = 2^{12} \\times 2^{12} \\) for inverted multi-index on billion-scale dataset. The bit budget is controlled by the number of codebooks \\( M \\) and the number of codewords \\( K \\). We fix the \\( K \\) as 256, and control the bit-budgets by changing \\( M = \\{8,16\\} \\) for 64bits and 128bits, respectively. We follow the setting of \\( w \\) from [7, 24] for a fair comparison. For each query, it visits \\( w \\) inverted indices that guarantee at least \\( \\{50k,10^5\\} \\) candidates for million-scale datasets and billion-scale datasets, respectively." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.75, + 0.469, + 0.791 + ], + "angle": 0, + "content": "We compare the proposed method with two sets of state-of-the-arts that are exhaustive and non-exhaustive methods. In particular, exhaustive methods include the followings:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.794, + 0.468, + 0.82 + ], + "angle": 0, + "content": "- OPQ [9, 25]: Product Quantization [16] with optimized space decomposition." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.825, + 0.468, + 0.851 + ], + "angle": 0, + "content": "- Catalyst + Lattice [28]: Learning spreaded space that fits with pre-defined lattice." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.856, + 0.431, + 0.869 + ], + "angle": 0, + "content": "- LSQ [20]: The state-of-the-art of shallow MCQ." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.794, + 0.468, + 0.869 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.32, + 0.82, + 0.335 + ], + "angle": 0, + "content": "- UNQ [23]: A deep generalization of MCQ." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.338, + 0.876, + 0.352 + ], + "angle": 0, + "content": "Plus, the non-exhaustive methods include the followings:" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.355, + 0.89, + 0.382 + ], + "angle": 0, + "content": "- IVFADC [16]: Product Quantization [16] with the Inverted index [30] and the residual encoding." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.387, + 0.89, + 0.414 + ], + "angle": 0, + "content": "- IVFOADC [9, 25]: OPQ with the inverted index [30] and the residual encoding." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.418, + 0.876, + 0.431 + ], + "angle": 0, + "content": "- Multi-D-ADC [3]: The Inverted Multi-Index (IMI)." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.435, + 0.865, + 0.449 + ], + "angle": 0, + "content": "- OMulti-D-OADC [9,25]: The IMI with the OPQ." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.453, + 0.89, + 0.479 + ], + "angle": 0, + "content": "- QAI [24]: Jointly optimized inverted index and quantizer." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.484, + 0.89, + 0.512 + ], + "angle": 0, + "content": "- IVFOADC + GP [5]: IVFOADC with grouping and pruning algorithm of [5]." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.516, + 0.89, + 0.557 + ], + "angle": 0, + "content": "- UNQ + IVF: Inverted file system with the UNQ. We omit the residual encoding because it is incompatible with the deep MCQ algorithm (Table. 1)." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.562, + 0.89, + 0.601 + ], + "angle": 0, + "content": "- Ours: Proposed disentangled representation learning. We select a single index for the million-scale datasets and a multi-index for the billion-scale dataset." + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.355, + 0.89, + 0.601 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.61, + 0.779, + 0.624 + ], + "angle": 0, + "content": "5.2. Result on Million-Scale Dataset" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.632, + 0.892, + 0.797 + ], + "angle": 0, + "content": "Table. 3 and Table. 4 report the recall@R scores of exhaustive and non-exhaustive ANN search methods with \\(\\{64,128\\}\\) bits encoding. For all combinations of the dataset and bit budget, the proposed method outperforms the nonexhaustive baselines by a large margin. For example, Ours improves the R@1 score of Multi-D-ADC+QAI about \\(25\\%\\) and \\(17\\%\\) for 64 and 128bits encoding respectively on the SIFT-1M dataset. On the DEEP-1M dataset, the performance gains between Ours and Multi-D-ADC are much larger than the gains on the SIFT-1M, where the gaps are about \\(65\\%\\) and \\(23\\%\\) for 64 and 128bits encoding, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.798, + 0.892, + 0.867 + ], + "angle": 0, + "content": "Notably, the proposed method even outperforms the exhaustive ANN methods while the proposed method is a nonexhaustive search where only \\(5\\%\\) of the database is considered for the distance computation. For instance, Ours improves the R@1 score of the exhaustive UNQ by about" + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.888, + 0.506, + 0.898 + ], + "angle": 0, + "content": "12006" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.079, + 0.123, + 0.491, + 0.282 + ], + "angle": 0, + "content": "
MethodR@1R@10R@100
Exhaustive Search
Catalyst + Lattice0.3110.7780.983
LSQ0.3800.8560.993
UNQ0.3830.8680.994
Non-Exhaustive Search
IVFADC (220)0.3510.7860.918
Multi-D-ADC (214 × 214)0.3440.8090.960
OMulti-D-OADC (214 × 214)0.3730.8410.973
IVFOADC+GP (220)0.4050.8510.957
Ours (212 × 212)0.4580.8590.903
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.29, + 0.47, + 0.318 + ], + "angle": 0, + "content": "Table 5. Experimental results on the SIFT-1B dataset and 128bits bit-budget. All the quantities except Ours are taken from [5,9,23]." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.339, + 0.469, + 0.366 + ], + "angle": 0, + "content": "\\(15\\%\\) on the SIFT-1M and \\(23\\%\\) on the DEEP-1M dataset with 64bits bit budget." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.367, + 0.47, + 0.478 + ], + "angle": 0, + "content": "As our motivation, a naive combination of the UNQ and the inverted index does not improve the performance of the exhaustive UNQ. For example, the UNQ+IVF drops the R@1 score of the exhaustive UNQ about \\(5\\%\\) and \\(7\\%\\) for SIFT-1M and DEEP-1M with 64bits bit budget, respectively. The disentangled representation of Ours improves the R@1 scores of UNQ+IVF about \\(20\\%\\) and \\(32\\%\\) on SIFT-1M and DEEP-1M with 64bits bit budget, respectively." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.485, + 0.35, + 0.499 + ], + "angle": 0, + "content": "5.3. Result on Billion-Scale Dataset" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.506, + 0.469, + 0.603 + ], + "angle": 0, + "content": "We conduct an experiment on a billion-scale dataset to verify the scalability of the proposed method. Table. 5 reports the experimental results on the SIFT-1B dataset with 128bit budget. The improvement in the R@1 score of Ours over IVFOADC+GP is about \\(13\\%\\). Moreover, Ours shows \\(20\\%\\) of improvement compared to the UNQ while Ours is a non-exhaustive search and the UNQ is an exhaustive search." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.603, + 0.469, + 0.686 + ], + "angle": 0, + "content": "Notably, the margin of improvement is much larger with the SIFT-1B dataset than the SIFT-1M dataset with 128bits encoding. Because the billion-scale task is a much more challenging task than the million-scale task with an identical bit budget, the billion-scale task has much more room for performance gain." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.686, + 0.469, + 0.783 + ], + "angle": 0, + "content": "Furthermore, we choose a conventional Multi-D-ADC algorithm with \\(2^{12} \\times 2^{12}\\) number of indices for learning the inverted index because our contribution is not about the inverted index. However, the experimental results demonstrate the superiority of Ours compared to methods with much finer inverted index \\((2^{14} \\times 2^{14})\\) and a sophisticated inverted indexing algorithm (IVFOADC+GP)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.79, + 0.231, + 0.805 + ], + "angle": 0, + "content": "5.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.811, + 0.469, + 0.867 + ], + "angle": 0, + "content": "We validate our method with ablation study on two hyper-parameters. First, Table. 6 shows ablation study about the number of visited inverted indices \\( w \\) on the SIFT-1M with 64bits encoding. Ours consistently improves" + }, + { + "type": "table", + "bbox": [ + 0.501, + 0.123, + 0.916, + 0.338 + ], + "angle": 0, + "content": "
MethodwR@1R@10R@100
UNQ+IVF (w/o residual)10.2160.4120.442
Ours0.2530.4300.442
UNQ+IVF (w/o residual)20.2720.5560.612
Ours0.3170.5880.613
UNQ+IVF (w/o residual)40.3050.6740.763
Ours0.3610.7200.765
UNQ+IVF (w/o residual)80.3220.7530.877
Ours0.3870.8090.880
UNQ+IVF (w/o residual)160.3310.7910.945
Ours0.3970.8570.947
UNQ+IVF (w/o residual)320.3320.8040.977
Ours0.3990.8760.979
UNQ+IVF (w/o residual)640.3320.8060.985
Ours0.3990.8800.987
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.347, + 0.892, + 0.373 + ], + "angle": 0, + "content": "Table 6. Ablation study about the number of visited inverted indices on the SIFT-1M dataset with 64bits bit budget." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.4, + 0.892, + 0.483 + ], + "angle": 0, + "content": "UNQ+IVF regardless of the number of \\( w \\). For example, the performance gain of the R@1 score is about 17% with \\( w = 1 \\) and 20% with \\( w = 64 \\). Moreover, these experimental results also highlight that the R@1 score of Ours with only \\( w = 4 \\) (out of 1024) is even superior to the exhaustive UNQ in Table.3." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.485, + 0.893, + 0.651 + ], + "angle": 0, + "content": "Second, we verify with various numbers of re-ranking candidates \\( R = \\{1, 10, 100, 1000\\} \\). It is identical to exclude the re-ranking if \\( R = 1 \\). Table. 7 shows the experimental results on the SIFT-1M and the DEEP-1M datasets with 64bits encoding. For the SIFT-1M dataset, Ours improves the more performance with the fewer number of re-ranking. For example, the performance gains of the R@1 score are about \\( \\{62\\%, 28\\%, 21\\%, 20\\% \\} \\) with \\( R = \\{1, 10, 100, 1000\\} \\), respectively. On the other hand, Ours improves the more performance with the larger number of re-ranking for the DEEP-1M dataset where the performance gains of the R@1 score are about \\( \\{17\\%, 29\\%, 32\\%, 32\\% \\} \\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.664, + 0.768, + 0.679 + ], + "angle": 0, + "content": "5.5. Validation of Disentanglement" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.687, + 0.892, + 0.867 + ], + "angle": 0, + "content": "We validate disentangled representation of the proposed method by generating new data points. Likewise disentanglement methods for generative models, we generate data points that have desired characteristics by controlling the input of the decoder. In detail, a reconstructed data point \\(\\tilde{x}_n\\) should belong to a specific cluster by substituting the \\(q_{\\mathrm{IVF}}(x_n)\\) by a desired cluster center \\(T\\). We randomly sample \\(10^{4}\\) data points from the database and generate about \\(10^{7}\\) new data points by concatenating \\(K^{\\prime} = 1024\\) number of cluster centers to each \\(l_{n}\\). Table. 8 reports the ratio of generated data points that belong to the desired cluster within top-R nearest clusters. The R@1 score of SIFT-1M and DEEP-1M datasets are 0.709 and 0.827, respectively" + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.888, + 0.505, + 0.899 + ], + "angle": 0, + "content": "12007" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.099, + 0.123, + 0.446, + 0.395 + ], + "angle": 0, + "content": "
Method# of re-rankR@1
SIFT-1M 64bits
UNQ+IVF (w/o residual) Oursw/o re-rank0.146 0.236
UNQ+IVF (w/o residual) Ours100.292 0.375
UNQ+IVF (w/o residual) Ours1000.329 0.397
UNQ+IVF (w/o residual) Ours10000.332 0.399
DEEP-1M 64bits
UNQ+IVF (w/o residual) Oursw/o re-rank0.134 0.157
UNQ+IVF (w/o residual) Ours100.228 0.295
UNQ+IVF (w/o residual) Ours1000.248 0.328
UNQ+IVF (w/o residual) Ours10000.249 0.329
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.401, + 0.47, + 0.426 + ], + "angle": 0, + "content": "Table 7. Ablation study about the number of re-ranked candidates on million-scale datasets with 64bits bit budget." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.45, + 0.47, + 0.506 + ], + "angle": 0, + "content": "while the probability of belonging to the desired cluster of a randomly generated vector is 0.001. The experimental results confirm that the proposed representation is well disentangled as we intended." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.514, + 0.26, + 0.529 + ], + "angle": 0, + "content": "5.6. Overhead Analysis" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.535, + 0.47, + 0.852 + ], + "angle": 0, + "content": "Finally, we analyze the search time overhead of the proposed method. Table. 9 demonstrates the average search time of Multi-D-ADC and Ours with identical cluster centers of the inverted index. The retrieval procedure of Ours is similar to the Multi-D-ADC except the additional encoding (Eq. 12) and decoding (Eq. 8) steps. In encoding query (Eq. 12), a query \\( y \\) should be concatenated with \\( w \\) number of cluster centers and embedded \\( w \\) times to build the lookup table. To accelerate the encoding query, we propose batch-forwarding \\( w \\) number of lookup tables at once while the Multi-D-ADC build the lookup table in sequence. Similarly, the decoding top-R (Eq. 8) also can be simply accelerated by batch-forwarding. The re-ranking time (Eq. 14) is negligible because the number of re-ranked data \\( (R = 200) \\) is small. The overall search time of Ours is about \\( 12\\% \\) slower than the Multi-D-ADC, but we believe it is permissible compared to the performance gain of Ours. Nevertheless, Ours speeds up the search procedure of the UNQ, which requires more than a minute in an exhaustive search. The experimental results are obtained in a single-CPU mode of a \\( 2.2\\mathrm{GHz} \\) Intel Xeon processor with Faiss [17], and the encoding and decoding times are measured in a single Nvidia Tesla V100 GPU with Pytorch [27]." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.853, + 0.468, + 0.867 + ], + "angle": 0, + "content": "The proposed method requires \\(\\{21,32\\} \\mathrm{MB}\\) for \\(\\{64,\\)" + }, + { + "type": "table", + "bbox": [ + 0.51, + 0.124, + 0.885, + 0.184 + ], + "angle": 0, + "content": "
DatasetMethodR@1R@3R@5
SIFT-1MD([ln, T])0.7090.9230.968
DEEP-1MD([ln, T])0.8270.9650.987
-Random0.0010.0030.005
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.192, + 0.893, + 0.243 + ], + "angle": 0, + "content": "Table 8. Experiment to validate disentanglement of proposed method with 64bits bit-budget. The score represents the ratio of generated data points that belong to desired cluster within top-R nearest clusters." + }, + { + "type": "table", + "bbox": [ + 0.519, + 0.261, + 0.875, + 0.362 + ], + "angle": 0, + "content": "
MethodTime (ms)
Multi-D-ADC (212 × 212)16.89
Ours (212 × 212)18.88
1. encoding query (Eq. 12)1.27
2. symmetric search (Eq. 13)16.86
3. decoding top-R (Eq. 8)0.70
4. asymmetric re-ranking (Eq. 14)0.04
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.371, + 0.892, + 0.397 + ], + "angle": 0, + "content": "Table 9. Search time analysis on the SIFT-1B dataset and 128bits bit-budget." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.426, + 0.892, + 0.482 + ], + "angle": 0, + "content": "128} bits encoding where the UNQ requires \\(\\{20, 30\\}\\mathrm{MB}\\) for the same budget. Note that those additional memory usage is not proportional to the database size, thus it is same for 1M and 1B database." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.501, + 0.619, + 0.516 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.527, + 0.892, + 0.776 + ], + "angle": 0, + "content": "In this paper, we propose a novel disentangled representation learning for unsupervised neural quantization. We firstly discover the cause of limited application of the deep quantization (UNQ [23]) on non-exhaustive search with the inverted index. Specifically, the deep quantizer is hard to exploit the compact representation of residual vector space and even takes disadvantages such as loss of cluster center information. To address the problem, we disentangle the information of the cluster center and the latent space by feeding the center to both the encoder and decoder to make center information redundant for the decoder. Similar to residual encoding, this disentanglement encourages the latent space compact and quantization-friendly by taking out the center information from latent space, so the quantization distortion is significantly reduced with disentangled representation. Extensive experiments on various datasets from million to billion scales validate the superiority of the proposed method over state-of-the-art retrieval systems." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.784, + 0.892, + 0.867 + ], + "angle": 0, + "content": "Acknowledgements. This work was supported in part by ETRI grant funded by the Korean government [23ZH1200, The research of the fundamental media-contents technologies for hyper-realistic media space], and MSIT/IITP [2019-0-00421], MSIT/NRF [NRF-2022R1F1A1076132], and MSIT&KNPA/KIPoT [Police Lab 2.0, 210121M06]." + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.888, + 0.505, + 0.899 + ], + "angle": 0, + "content": "12008" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.125, + 0.174, + 0.139 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.148, + 0.47, + 0.197 + ], + "angle": 0, + "content": "[1] Alexandr Andoni and Piotr Indyk. Near-optimal hashing algorithms for approximate nearest neighbor in high dimensions. Communications of the ACM, 51(1):117-122, 2008. 1" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.2, + 0.471, + 0.25 + ], + "angle": 0, + "content": "[2] Artem Babenko and Victor Lempitsky. 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PMLR, 2014. 2" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.127, + 0.47, + 0.566 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.468, + 0.888, + 0.505, + 0.899 + ], + "angle": 0, + "content": "12010" + } + ] +] \ No newline at end of file diff --git a/2023/Disentangled Representation Learning for Unsupervised Neural Quantization/06ed76f2-80a7-4ca7-b9b2-5c10f4249fdb_origin.pdf b/2023/Disentangled Representation Learning for Unsupervised Neural Quantization/06ed76f2-80a7-4ca7-b9b2-5c10f4249fdb_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..ff6e5a038f18c93fef90c4e2b7f94504c891533d --- /dev/null +++ b/2023/Disentangled Representation Learning for Unsupervised Neural Quantization/06ed76f2-80a7-4ca7-b9b2-5c10f4249fdb_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:3a8d5a3e4585cc4996ffcc1c5d529af66969ee313776c76b82f3ed34db7c3a6c +size 215215 diff --git a/2023/Disentangled Representation Learning for Unsupervised Neural Quantization/full.md b/2023/Disentangled Representation Learning for Unsupervised Neural Quantization/full.md new file mode 100644 index 0000000000000000000000000000000000000000..7a88b6a1831a0cde550e676c60edea2bc75755de --- /dev/null +++ b/2023/Disentangled Representation Learning for Unsupervised Neural Quantization/full.md @@ -0,0 +1,350 @@ +# Disentangled Representation Learning for Unsupervised Neural Quantization + +Haechan Noh1, Sangeek Hyun1, Woojin Jeong1, Hanshin Lim2, Jae-Pil Heo1,* +1Sungkyunkwan University, 2Electronics and Telecommunications Research Institute {noru0114, hsi1032, us03385, jaepilheo}@skku.edu, hslim@etri.re.kr + +# Abstract + +The inverted index is a widely used data structure to avoid the infeasible exhaustive search. It accelerates retrieval significantly by splitting the database into multiple disjoint sets and restricts distance computation to a small fraction of the database. Moreover, it even improves search quality by allowing quantizers to exploit the compact distribution of residual vector space. However, we firstly point out a problem that an existing deep learning-based quantizer hardly benefits from the residual vector space, unlike conventional shallow quantizers. To cope with this problem, we introduce a novel disentangled representation learning for unsupervised neural quantization. Similar to the concept of residual vector space, the proposed method enables more compact latent space by disentangling information of the inverted index from the vectors. Experimental results on large-scale datasets confirm that our method outperforms the state-of-the-art retrieval systems by a large margin. + +# 1. Introduction + +Measuring the distances among feature vectors is a fundamental requirement in various fields of computer vision. One of the tasks most relevant to distance measurement is the nearest neighbor search, which finds the closest data in the database from a query. The task is especially challenging in high-dimensional and large-scale databases due to huge computational costs and memory overhead. + +By relaxing the complexity, Approximate Nearest Neighbor (ANN) search is popular in practice. Recent approaches for ANN typically learn the compact representation by exploiting Multi-Codebook Quantization (MCQ) [2, 9, 16]. Compared to hashing-based approaches [1, 10, 12], the MCQ provides a more informative asymmetric distance estimator where the query side is not compressed. Moreover, all possible distances between the query and codewords can be stored in a lookup table for efficiency. + +Although the MCQ accelerates the distance computation with the lookup table, exhaustive search on the large-scale + +dataset is still prohibited. The Inverted File with Asymmetric Distance Computation (IVFADC) [16] is proposed for non-exhaustive ANN search by cooperating with the inverted index [30]. It splits the database into multiple disjoint sets and restricts distance computations to small portions close to the query to accelerate the retrieval speed. Moreover, the compactness of residual vector space between data points and inverted indices substantially enhances the quantization quality. + +Thanks to the rapid advances in deep learning, most areas of computer vision benefit from its great learning capacity compared to shallow methods. However, the state-of-the-art methods of unsupervised quantization remain shallow for a long time because selecting the maximum value (i.e. argmax), which is an essential operation of quantization, is not differentiable. Inspired by a recent generative model with discrete hidden variables [35], the Unsupervised Neural Quantization (UNQ) [23] introduced an encoder-decoder-based architecture for ANN search. The large learning capacity of deep neural architecture significantly improves the retrieval quality compared to conventional shallow methods. + +Despite the outperforming performance of the UNQ, its superiority is validated only on the exhaustive search. To verify its effectiveness on non-exhaustive search, we conduct an experiment of non-exhaustive UNQ with an inverted index. Interestingly, we observe that this deep architecture does not benefit from the residual vector space and it even harms the search quality as reported in Table 1. We hypothesize the reasons for this performance degradation from two perspectives. First, both the residual vector space and latent space of the neural network transform the data into a quantization-friendly distribution, thus deep quantizer has a scant margin to be improved by the residual space. Second, residual space sacrifices the distributional characteristics of each cluster, since the information of cluster center in the original space is removed. For conventional shallow quantizers, the drawback of residual space is obscured by its huge advantage of making a compact distribution. However, deep quantizer only takes the disadvantages (information loss) from residual space without leveraging the effec + +tiveness such as compactness of residuals. + +In this paper, we focus on extending the application of deep architectures for non-exhaustive search. To this end, we learn a disentangled representation to harmonize a deep architecture with the inverted index, inspired by recent representation learning techniques for generative models [8,34]. In our disentangled representation learning, both encoder and decoder get information of cluster center as an additional input. Since the information of cluster center is redundant to decoder if latent feature contains information of cluster center, the encoder is trained to remove the information of cluster centers from the latent embedding. The disentangled representation learning is similar to concept of the residual vector space that provides more compact distribution by taking out the information of cluster centers. The experimental results verify that the learning disentangled representation enables the neural quantization to collaborate with inverted index and outperforms the state-of-the-art methods. + +The contributions of our paper include: + +- We point out that the residual encoding of the inverted index is incompatible with the neural multi-codebook quantization method. +- We propose a novel disentangled representation learning for neural multi-codebook quantization to combine deep quantization and inverted index. +- The experimental results show that the proposed method outperforms the state-of-the-art retrieval systems by a large margin. + +# 2. Related Work + +# 2.1. Multi-codebook Quantization for ANN + +Vector quantization [11] maps a vector to its nearest codeword within a learned codebook. Specifically, a high-dimensional real-valued vector can be efficiently represented by an integer index of its corresponding cluster. To ensure a high search accuracy, the vector quantization requires a codebook with an extremely large number of codewords. However, enlarging the number of codewords is far from efficiency because the cost of assigning the nearest codeword is proportionally increased with codebook sizes. + +Product Quanztiaton (PQ) [16] decomposes the space into a Cartesian product of lower-dimensional subspaces. By quantizing each subspace separately, multiple codebooks are produced and they enable better search quality with a manageable number of codewords. Optimized Product Quantization (OPQ) [9] and Cartesian K-means [25] introduced to learn transformation to optimize the decomposition step in PQ according to the data distribution. + +While the PQ encodes a vector into a concatenation of assigned codewords, a number of methods [2, 6, 20, 21, 26, 36] approximated a vector by a sum of assigned codewords. + +These addition-based methods have a higher degree of freedom than the concatenation-based methods, since the concatenation is a special case of addition where components of addition are mutually orthogonal. + +The state-of-the-art methods of such multi-codebook quantization remain shallow for a long time, while most areas of computer vision benefit from rapid advances in deep learning. The non-differentiability of codeword assignment operation makes the multi-codebook quantization hard to collaborate with deep learning. Vector-Quantized Variational Autoencoder (VQ-VAE) [35] in the area of the generative model proposed a gradient estimation to propagate gradient through discrete variables. Inspired by the VQ-VAE, Unsupervised Neural Quantization (UNQ) [23] introduces a deep neural network for multi-codebook quantization. The much larger learning capacity of UNQ significantly improves the conventional shallow methods. + +# 2.2. Non-exhaustive ANN Search + +While the quantization techniques accelerate the distance computation, the search is still exhaustive. IVFADC [16] proposed a non-exhaustive approximate nearest neighbor search by cooperating with the inverted index [30]. In addition to the significant acceleration of retrieval speed, the non-exhaustive manner even improves the search quality by allowing more compact residual vector space. The Inverted Multi-Index (IMI) [3] extends the IVFADC by decomposing data space into two sub-spaces and applying the inverted index independently. Similar to the idea of PQ, the decomposed data space of IMI enables much finer partition with a manageable number of indices. Several subsequent non-exhaustive ANN techniques are proposed to improve the data partitioning rather than the quantization [4, 5, 7]. + +# 2.3. Disentangled Representation Learning + +In the context of the generative model, disentangled representation is introduced to analyze and utilize the independent effects of latent factors. One straightforward example can be found in conditional generative models [22, 32]. They decompose the conditional information from the others so that they can control the specific conditions of generated images such as spatial layout [8] or class information [22]. For instance, variational U-Net [8] disentangles the shape and appearance representations to synthesize human images of diverse poses with a shared appearance. Similarly, VarSR [13] builds the latent space of high-resolution information disentangled from the low-resolution images. Hence, they can synthesize diverse high-resolution images corresponding to the given low-resolution image. + +The aforementioned examples mainly focus on the controllable generation by disentangling conditional information. However, in this paper, we concentrate on the maximization of the representation capability of the latent space + +
MethodR@1R@10R@100
PQ0.2280.6530.953
+IVF (w/o residual)0.2280.6530.950
+IVF (with residual)0.2720.7350.969
UNQ0.3460.8280.990
+IVF (w/o residual)0.3310.7980.939
+IVF (with residual)0.2720.7180.867
+ +by disentanglement. Specifically, we build a compact latent space by disentangling the cluster center similar to residual encoding but compatible with the neural multi-codebook quantization method. + +# 3. Background + +Let us briefly introduce the ANN task, the MCQ approach, and the residual vector space. With $D$ -dimensional database $X = \{x_{n}\}_{n = 1}^{N}, x_{n} \in \mathbb{R}^{D}$ and query $y \in \mathbb{R}^{D}$ , the nearest neighbor of query $y$ is defined as follows: + +$$ +\operatorname {N N} (y) = \underset {n \in \{1, \dots , N \}} {\arg \min } \| y - x _ {n} \| ^ {2}. \tag {1} +$$ + +To alleviate time and memory costs of Eq. 1, the MCQ quantizer $q_{\mathrm{MCQ}}$ encodes the database $X = \{x_{n}\}_{n=1}^{N}$ utilizing $M$ number of multi-codebooks $C^{m} = \{c_{k}^{m}\}_{k=1}^{K}, c_{k}^{m} \in \mathbb{R}^{D}$ where each codebook has $K$ number of codewords. Then, a vector $x_{n}$ is represented as $M$ number of indices $[i_{n}^{1}, \dots, i_{n}^{M}]$ and reconstructed by referring the codebooks: + +$$ +x _ {n} \approx q _ {\mathrm {M C Q}} \left(x _ {n}\right) = \sum_ {m = 1} ^ {M} c _ {i _ {n} ^ {m}} ^ {m}. \tag {2} +$$ + +The goal of this lossy compression process is to learn codebooks that minimize quantization distortion $E$ defined as: + +$$ +E \left(x _ {n}, C\right) = \sum_ {m = 1} ^ {M} \left| \left| x _ {n} ^ {m} - c _ {i _ {n} ^ {m}} ^ {m} \right| \right| ^ {2}, \tag {3} +$$ + +where $x_{n} = \sum x_{n}^{m}$ , and $x_{n}^{m}$ is a subvector of $x_{n}$ corresponding to index $i_{n}^{m}$ . The PQ belongs to the MCQ approach where $x_{n}^{m}$ are mutually orthogonal. + +The IVFADC [16] further accelerates ANN search by collaborating with an inverted index. The inverted index $q_{\mathrm{IVF}}$ splits database $X$ into $K'$ number of disjoint subsets, and the ANN search is then restricted to $w$ number of nearest subsets from query $y$ , where $w$ is much smaller than $K'$ . For a given data point $x_n$ , the inverted index $q_{\mathrm{IVF}}(\cdot)$ quantize it to its nearest cluster center $q_{\mathrm{IVF}}(x_n)$ , and the data points belong to the same cluster are stored adjacently. Moreover, the IVFADC suggested learning codebooks that + +Table 1. Comparison of retrieval performances between the PQ and the UNQ on SIFT-1M. The residual vector space improves the performance with the PQ, but does not work with the UNQ. + +
MethodCompression ratioDistortion
PQ128×0.8368
+IVF (with residual)0.7208
PQ64×0.6252
+IVF (with residual)0.5846
PQ32×0.4127
+IVF (with residual)0.4220
PQ16×0.2438
+IVF (with residual)0.2604
PQ4×0.0212
+IVF (with residual)0.0257
+ +Table 2. Quantization distortions of the database with varying compression ratios. The residual vector space is profitable with a large compression ratio, but it leads performance drop with a small compression ratio. + +encode residual vector $r(x_{n}) = x_{n} - q_{\mathrm{IVF}}(x_{n})$ rather than the original vector as follows: + +$$ +x _ {n} \approx \tilde {x} _ {n} = q _ {\mathrm {M C Q}} \left(x _ {n} - q _ {\mathrm {I V F}} \left(x _ {n}\right)\right) + q _ {\mathrm {I V F}} \left(x _ {n}\right). \tag {4} +$$ + +Then the distance between query $y$ and target data $x_{n}$ is estimated as follows: + +$$ +d (y, x _ {n}) \approx d (y - q _ {\mathrm {I V F}} (x _ {n}), q _ {\mathrm {M C Q}} (x _ {n} - q _ {\mathrm {I V F}} (x _ {n}))). \tag {5} +$$ + +where the $d(\cdot, \cdot)$ is the Euclidean distance between two vectors. The IVFADC accelerates the search speed by reducing the number of distance estimations and improves the quantization distortion (Eq. 3) thanks to the compact distribution of the residual vector space. + +# 4. Proposed Method + +# 4.1. Motivation + +Recently, the UNQ [23] introduced a deep architecture for MCQ learning and improves conventional shallow MCQ methods by a large margin. However, its effectiveness is only validated by an exhaustive ANN search. To examine the performance of UNQ on non-exhaustive search, we test the retrieval performances of PQ and UNQ with an inverted index on exhaustive and non-exhaustive settings. As reported in Table. 1, the residual encoding (Eq. 4) provides better search quality with the PQ, while it makes the search quality of UNQ even worse. + +To investigate the reasons why residual encoding does not help the UNQ, we need to analyze the mechanism of residual encoding in PQ. To this end, we hypothesize the effect of residual representation in two aspects. First, the advantage of residuals in PQ comes from the transformation of data space into compact and quantization-friendly distribution. Second, the residual encoding is not always beneficial, since they sacrifice the information of the cluster center so that the distributional characteristics of each cluster are suppressed. + +![](images/954e5232da019184ff8fc93b45fb605699353c40ac12358c20fd320f136ecc48.jpg) +Figure 1. By providing additional input of $q_{\mathrm{IVF}}(x_n)$ to both encoder and decoder, the encoder is not necessary to learn features to reconstruct $q_{\mathrm{IVF}}(x_n)$ since it is redundant information for the decoder. Thus the information of the cluster center is disentangled from the latent vectors and codebooks. The disentangling enables the quantizer to learn compact representation while preserving the original distribution. + +To validate these hypotheses, we observe the performance variation of PQ with residual encoding by varying compression ratios. The compression ratios are controlled by adjusting the number of codebooks $M$ . As reported in Table. 2, the residual encoding is profitable with large compression ratios, since the sparse original distribution is hard to quantize with the deficient bit-budget. On the other hand, the residual encoding leads to performance drops with small compression ratios, because it is not necessary to represent the data compactly thanks to sufficient numbers of codewords, but the information loss of cluster-wise distributional characteristics still exists. + +Based on these observations, we explain the reasons for UNQ's performance drop with residual encoding. Firstly, UNQ does not benefit from the compact representation of residual encoding. The deep encoder transforms the data into latent space with a reconstruction objective function. That is, the objective of UNQ also encourages to transform the data into compact latent space, so the residual encoding and UNQ affect the model in a similar way. Hence, the residual representation is hardly beneficial to the neural quantizer. Secondly, UNQ takes the disadvantage of residual encoding, the information loss of distributional characteristics of each cluster. + +These interpretations motivate us to come up with a method that only takes the advantage of residual representation. That is, we aim to make the latent space more compact without the information loss of distributional characteristics of each cluster. To this end, we introduce a disentangled representation learning for unsupervised neural quantization in the following sections. + +# 4.2. Disentangled Neural Quantization + +Inspired by the disentangled representation of conditional generative models [22, 32], we propose disentangled neural quantization. The previous methods exploit the disentanglement for a controllable generation. However, we propose to learn a disentangled representation to reduce + +the quantization distortion. Specifically, a latent feature $(l_{n})$ of UNQ contains information of its input vector $x_{n}$ where $x_{n}$ consists of $q_{\mathrm{IVF}}(x_n)$ and $x_{n} - q_{\mathrm{IVF}}(x_{n})$ . However, the $q_{\mathrm{IVF}}(x_n)$ can be restored without any information loss thanks to the data structure of the inverted index. Thus, encoding the $q_{\mathrm{IVF}}(x_n)$ is quite wasteful because the MCQ approach has a scarce bit budget in practice. In this paper, we suggest disentangling the $q_{\mathrm{IVF}}(x_n)$ from $l_{n}$ to provide more compact information. + +To disentangle the $q_{\mathrm{IVF}}(x_n)$ from $l_{n}$ , we feed additional input of $q_{\mathrm{IVF}}(x_n)$ to encoder $E(\cdot)$ and decoder $D(\cdot)$ . Then the $q_{\mathrm{IVF}}(x_n)$ is redundant information for $D(\cdot)$ if $l_{n}$ contains information of $q_{\mathrm{IVF}}(x_n)$ . Thus, the $E(\cdot)$ is trained to embed as little information of $q_{\mathrm{IVF}}(x_n)$ as possible in $l_{n}$ to fully exploit the network capacity. The disentangled representation learning is similar to the concept of the residual encoding of PQ (Eq. 4) in terms of taking out the information of the cluster center. However, there is no information loss because the cluster center $q_{\mathrm{IVF}}(x_n)$ is provided to $D(\cdot)$ . + +Figure. 1 describes the proposed disentangled representation learning. The cluster center of input data is provided to the encoder and decoder, and the scarce resource of finite codewords can be fully utilized to quantize the compact latent feature where the information of the cluster center is disentangled. Not only the compact information, but the decoder also preserves the original distribution by reconstructing the original space in an end-to-end manner. + +# 4.3. Network Structure + +We adopt the network structure of [23] except our disentangling module. The network consists of encoder $E(\cdot)$ , decoder $D(\cdot)$ , and learnable codebook parameters $[C^1, \dots, C^M]$ , $C^m = \{c_k^m\}_{k=1}^K$ . Both encoder $E(\cdot)$ and decoder $D(\cdot)$ are a concatenation of two fully-connected layers with Batch Normalization [14] and ReLU activation function. We feed separate information of cluster center $q_{\mathrm{IVF}}(x_n)$ to the encoder for the disentanglement. Then the encoder $E(\cdot)$ embeds the given concatenated inputs + +
Search mannerMethod64bits encoding128bits encoding
R@1R@10R@100R@1R@10R@100
ExhaustiveOPQ0.2080.6430.9530.4090.8980.999
Catalyst + Lattice0.2890.7580.9790.4910.9411.
LSQ0.2920.7770.9870.5710.9751.
UNQ0.3460.8280.9900.5930.9801.
Non-ExhaustiveIVFADC (210)0.2960.7040.9570.4710.9030.993
IVFADC + QAI (210)0.3110.7300.9650.4960.9280.992
IVFOADC (210)0.2950.7190.9630.4750.9130.995
IVFOADC + QAI (210)0.3210.7560.9720.5000.9310.993
Multi-D-ADC (28 × 28)0.3030.7290.9670.4840.9240.998
Multi-D-ADC + QAI (28 × 28)0.3180.7480.9770.5130.9390.997
UNQ+IVF (210)0.3310.7980.9390.5480.9630.994
Ours (210)0.3980.8770.9710.6000.9740.990
+ +Table 3. Experimental result on the SIFT-1M dataset. All the quantities except Ours and UNQ+IVF are taken from [23, 24] + +$[x_n, q_{\mathrm{IVF}}(x_n)]$ to $M$ number of latent features as follows: + +$$ +E \left(\left[ x _ {n}, q _ {\mathrm {I V F}} \left(x _ {n}\right) \right]\right) = \left[ l _ {n} ^ {1}, \dots , l _ {n} ^ {M} \right]. \tag {6} +$$ + +The embedded feature $l_{n}^{m}$ is quantized to index $i_n^m$ of the codeword that has the biggest dot-product with $l_{n}^{m}$ as follows: + +$$ +i _ {n} ^ {m} = \underset {k \in \{1, \dots , K \}} {\arg \max } l _ {n} ^ {m} \cdot c _ {k} ^ {m}. \tag {7} +$$ + +Because the argmax function is not differentiable, we follow [23] that exploits the Gumbel trick [15]. The Gumbel trick provides a differentiable approximation of Eq. 7 by substituting the argmax with softmax during backpropagation. Then, the sum of assigned codewords $c_{i_n^m}^m$ becomes the input for the decoder $D(\cdot)$ . Likewise, we concatenate it with the cluster center $q_{\mathrm{IVF}}(x_n)$ for the disentanglement. The approximated vector $\tilde{x}_n$ of original vector $x_n$ is obtained as follows: + +$$ +\tilde {x} _ {n} = D \left(\left[ \sum_ {m = 1} ^ {M} c _ {i _ {n} ^ {m}} ^ {m}, q _ {\mathrm {I V F}} (x _ {n}) \right]\right). \tag {8} +$$ + +The model is trained with two losses. The first one is a reconstruction loss which directly minimizes the quantization distortion as follows: + +$$ +L _ {1} = \sum_ {n = 1} ^ {N} | | x _ {n} - \tilde {x} _ {n} | | ^ {2}. \tag {9} +$$ + +Similar to [23], we adopt the square Coefficient Variation regularizer [29] to encourage the codewords to be evenly selected: + +$$ +L _ {2} = \sum_ {m = 1} ^ {M} \frac {\sum_ {n = 1} ^ {N} \left(p _ {n} ^ {m} - p _ {\text {a v g}} ^ {m}\right) ^ {2}}{p _ {\text {a v g}} ^ {m} {} ^ {2}}, \tag {10} +$$ + +where $p_n^m$ is the softmax probability of $i_n^m$ by the Gumbel approximation in Eq. 7, and $p_{\mathrm{avg}}^m$ is the average of $p_n^m$ along + +$N$ . The final loss of the model is described as follows: + +$$ +L = L _ {1} + \lambda * L _ {2} \tag {11} +$$ + +The loss ratio $\lambda$ starts from 1.0 and decreases to 0.05 during the training. For a fair comparison, we adopt other details of [23] including Quasi-Hyperbolic Adam algorithm [19], and One Cycle learning rate schedule [31]. + +# 4.4. Retrieval Procedure + +Firstly, each database vector $x_{n}$ is encoded into $M$ number of indices $l_{n} = [i_{n}^{1},\dots,i_{n}^{M}]$ by Eq. 7. Because the codebooks have $K$ number of codewords, the required bit-budget for the indices $l_{n}$ is $M * \lceil \log_2K \rceil$ . Moreover, the data points that belong to the same inverted index are stored adjacently, and the size of each cluster is stored. Thanks to this data structure of the inverted index, we can identify the $q_{\mathrm{IVF}(x_n)}$ without any additional costs in the retrieval stage. + +Secondly, a given query $y$ is embedded into latent features $l_{y}$ , and the cluster center of the target is concatenated. + +$$ +\left[ l _ {y} ^ {1}, \dots , l _ {y} ^ {M} \right] = E \left(\left[ y, q _ {\mathrm {I V F}} \left(x _ {n}\right) \right]\right). \tag {12} +$$ + +Then the symmetric distance between encoded query $l_{y}$ and encoded target $[i_n^1, \dots, i_n^M]$ is computed by the cosine similarity as follows: + +$$ +D _ {\text {s y m}} (y, x _ {n}) = \sum_ {m = 1} ^ {M} \frac {l _ {y} ^ {m} \cdot c _ {i _ {n} ^ {m}} ^ {m}}{| | l _ {y} ^ {m} | | | | c _ {i _ {n} ^ {m}} ^ {m} | |}. \tag {13} +$$ + +Note that, Eq. 13 can be efficiently computed by a lookup table storing precomputed all possible symmetric distances. + +Finally, the $R$ top-ranked retrieved data according to the symmetric distance are then re-ranked by the more accurate asymmetric distances between uncompressed query $y$ and $\tilde{x}_n$ , as follows: + +$$ +D _ {\text {a s y m}} (y, x _ {n}) = \left\| y - \tilde {x} _ {n} \right\| ^ {2}. \tag {14} +$$ + +We set the hyper-parameter $R = 200$ , and we conduct an ablation study of $R$ in Table. 7. + +
Search typeMethod64bits encoding128bits encoding
R@1R@10R@100R@1R@10R@100
ExhaustiveOPQ0.1590.5130.8860.3500.8250.991
Catalyst + Lattice0.2460.6830.9610.4480.9080.998
LSQ0.2170.6400.9450.4110.8860.995
UNQ0.2670.7260.9730.4790.9300.998
Non-exhaustiveIVFADC (210)0.2100.6160.9250.4180.8900.995
IVFOADC (210)0.2270.6590.9500.4160.8970.996
Multi-D-ADC (28 × 28)0.2000.6130.9290.3980.8830.995
UNQ+IVF (210)0.2500.6880.9100.4400.9070.996
Ours (210)0.3290.7990.9320.4910.9290.970
+ +Table 4. Experimental results on DEEP-1M dataset. The quantities of Exhaustive methods are taken from [23] + +# 5. Evaluation + +# 5.1. Protocol + +We evaluate our method on three datasets: + +- SIFT-1M, SIFT-1B [16]: 128-dimensional SIFT descriptor vectors [18]. The training set includes $\{500k, 10^8\}$ vectors for 1M and 1B, respectively. Sets for evaluation have $10^4$ queries and $\{10^6, 10^9\}$ number of database for 1M and 1B, respectively. +- DEEP-1M [4]: 96-dimensional DNN features extracted from the last fully-connected layer of GoogLeNet [33]. It also includes $500k$ training data, $10^{4}$ queries, and $10^{6}$ database. + +The ground truth of a given query is defined as the top-1 nearest neighbor from an uncompressed database. Then, the retrieval performance in compressed space is measured by average $recall@R$ for $R = \{1, 10, 100\}$ . The $recall@R$ represents the ratio of queries that contains the ground truth in top- $R$ retrieved vectors. + +Unless specified, we consistently use the following hyper-parameters. We set $K' = 2^{10}$ for inverted index on million-scale datasets, and $K' = 2^{12} \times 2^{12}$ for inverted multi-index on billion-scale dataset. The bit budget is controlled by the number of codebooks $M$ and the number of codewords $K$ . We fix the $K$ as 256, and control the bit-budgets by changing $M = \{8,16\}$ for 64bits and 128bits, respectively. We follow the setting of $w$ from [7, 24] for a fair comparison. For each query, it visits $w$ inverted indices that guarantee at least $\{50k,10^5\}$ candidates for million-scale datasets and billion-scale datasets, respectively. + +We compare the proposed method with two sets of state-of-the-arts that are exhaustive and non-exhaustive methods. In particular, exhaustive methods include the followings: + +- OPQ [9, 25]: Product Quantization [16] with optimized space decomposition. +- Catalyst + Lattice [28]: Learning spreaded space that fits with pre-defined lattice. +- LSQ [20]: The state-of-the-art of shallow MCQ. + +- UNQ [23]: A deep generalization of MCQ. + +Plus, the non-exhaustive methods include the followings: + +- IVFADC [16]: Product Quantization [16] with the Inverted index [30] and the residual encoding. +- IVFOADC [9, 25]: OPQ with the inverted index [30] and the residual encoding. +- Multi-D-ADC [3]: The Inverted Multi-Index (IMI). +- OMulti-D-OADC [9,25]: The IMI with the OPQ. +- QAI [24]: Jointly optimized inverted index and quantizer. +- IVFOADC + GP [5]: IVFOADC with grouping and pruning algorithm of [5]. +- UNQ + IVF: Inverted file system with the UNQ. We omit the residual encoding because it is incompatible with the deep MCQ algorithm (Table. 1). +- Ours: Proposed disentangled representation learning. We select a single index for the million-scale datasets and a multi-index for the billion-scale dataset. + +# 5.2. Result on Million-Scale Dataset + +Table. 3 and Table. 4 report the recall@R scores of exhaustive and non-exhaustive ANN search methods with $\{64,128\}$ bits encoding. For all combinations of the dataset and bit budget, the proposed method outperforms the nonexhaustive baselines by a large margin. For example, Ours improves the R@1 score of Multi-D-ADC+QAI about $25\%$ and $17\%$ for 64 and 128bits encoding respectively on the SIFT-1M dataset. On the DEEP-1M dataset, the performance gains between Ours and Multi-D-ADC are much larger than the gains on the SIFT-1M, where the gaps are about $65\%$ and $23\%$ for 64 and 128bits encoding, respectively. + +Notably, the proposed method even outperforms the exhaustive ANN methods while the proposed method is a nonexhaustive search where only $5\%$ of the database is considered for the distance computation. For instance, Ours improves the R@1 score of the exhaustive UNQ by about + +
MethodR@1R@10R@100
Exhaustive Search
Catalyst + Lattice0.3110.7780.983
LSQ0.3800.8560.993
UNQ0.3830.8680.994
Non-Exhaustive Search
IVFADC (220)0.3510.7860.918
Multi-D-ADC (214 × 214)0.3440.8090.960
OMulti-D-OADC (214 × 214)0.3730.8410.973
IVFOADC+GP (220)0.4050.8510.957
Ours (212 × 212)0.4580.8590.903
+ +$15\%$ on the SIFT-1M and $23\%$ on the DEEP-1M dataset with 64bits bit budget. + +As our motivation, a naive combination of the UNQ and the inverted index does not improve the performance of the exhaustive UNQ. For example, the UNQ+IVF drops the R@1 score of the exhaustive UNQ about $5\%$ and $7\%$ for SIFT-1M and DEEP-1M with 64bits bit budget, respectively. The disentangled representation of Ours improves the R@1 scores of UNQ+IVF about $20\%$ and $32\%$ on SIFT-1M and DEEP-1M with 64bits bit budget, respectively. + +# 5.3. Result on Billion-Scale Dataset + +We conduct an experiment on a billion-scale dataset to verify the scalability of the proposed method. Table. 5 reports the experimental results on the SIFT-1B dataset with 128bit budget. The improvement in the R@1 score of Ours over IVFOADC+GP is about $13\%$ . Moreover, Ours shows $20\%$ of improvement compared to the UNQ while Ours is a non-exhaustive search and the UNQ is an exhaustive search. + +Notably, the margin of improvement is much larger with the SIFT-1B dataset than the SIFT-1M dataset with 128bits encoding. Because the billion-scale task is a much more challenging task than the million-scale task with an identical bit budget, the billion-scale task has much more room for performance gain. + +Furthermore, we choose a conventional Multi-D-ADC algorithm with $2^{12} \times 2^{12}$ number of indices for learning the inverted index because our contribution is not about the inverted index. However, the experimental results demonstrate the superiority of Ours compared to methods with much finer inverted index $(2^{14} \times 2^{14})$ and a sophisticated inverted indexing algorithm (IVFOADC+GP). + +# 5.4. Ablation Study + +We validate our method with ablation study on two hyper-parameters. First, Table. 6 shows ablation study about the number of visited inverted indices $w$ on the SIFT-1M with 64bits encoding. Ours consistently improves + +Table 5. Experimental results on the SIFT-1B dataset and 128bits bit-budget. All the quantities except Ours are taken from [5,9,23]. + +
MethodwR@1R@10R@100
UNQ+IVF (w/o residual)10.2160.4120.442
Ours0.2530.4300.442
UNQ+IVF (w/o residual)20.2720.5560.612
Ours0.3170.5880.613
UNQ+IVF (w/o residual)40.3050.6740.763
Ours0.3610.7200.765
UNQ+IVF (w/o residual)80.3220.7530.877
Ours0.3870.8090.880
UNQ+IVF (w/o residual)160.3310.7910.945
Ours0.3970.8570.947
UNQ+IVF (w/o residual)320.3320.8040.977
Ours0.3990.8760.979
UNQ+IVF (w/o residual)640.3320.8060.985
Ours0.3990.8800.987
+ +Table 6. Ablation study about the number of visited inverted indices on the SIFT-1M dataset with 64bits bit budget. + +UNQ+IVF regardless of the number of $w$ . For example, the performance gain of the R@1 score is about 17% with $w = 1$ and 20% with $w = 64$ . Moreover, these experimental results also highlight that the R@1 score of Ours with only $w = 4$ (out of 1024) is even superior to the exhaustive UNQ in Table.3. + +Second, we verify with various numbers of re-ranking candidates $R = \{1, 10, 100, 1000\}$ . It is identical to exclude the re-ranking if $R = 1$ . Table. 7 shows the experimental results on the SIFT-1M and the DEEP-1M datasets with 64bits encoding. For the SIFT-1M dataset, Ours improves the more performance with the fewer number of re-ranking. For example, the performance gains of the R@1 score are about $\{62\%, 28\%, 21\%, 20\% \}$ with $R = \{1, 10, 100, 1000\}$ , respectively. On the other hand, Ours improves the more performance with the larger number of re-ranking for the DEEP-1M dataset where the performance gains of the R@1 score are about $\{17\%, 29\%, 32\%, 32\% \}$ . + +# 5.5. Validation of Disentanglement + +We validate disentangled representation of the proposed method by generating new data points. Likewise disentanglement methods for generative models, we generate data points that have desired characteristics by controlling the input of the decoder. In detail, a reconstructed data point $\tilde{x}_n$ should belong to a specific cluster by substituting the $q_{\mathrm{IVF}}(x_n)$ by a desired cluster center $T$ . We randomly sample $10^{4}$ data points from the database and generate about $10^{7}$ new data points by concatenating $K^{\prime} = 1024$ number of cluster centers to each $l_{n}$ . Table. 8 reports the ratio of generated data points that belong to the desired cluster within top-R nearest clusters. The R@1 score of SIFT-1M and DEEP-1M datasets are 0.709 and 0.827, respectively + +
Method# of re-rankR@1
SIFT-1M 64bits
UNQ+IVF (w/o residual) Oursw/o re-rank0.146 0.236
UNQ+IVF (w/o residual) Ours100.292 0.375
UNQ+IVF (w/o residual) Ours1000.329 0.397
UNQ+IVF (w/o residual) Ours10000.332 0.399
DEEP-1M 64bits
UNQ+IVF (w/o residual) Oursw/o re-rank0.134 0.157
UNQ+IVF (w/o residual) Ours100.228 0.295
UNQ+IVF (w/o residual) Ours1000.248 0.328
UNQ+IVF (w/o residual) Ours10000.249 0.329
+ +while the probability of belonging to the desired cluster of a randomly generated vector is 0.001. The experimental results confirm that the proposed representation is well disentangled as we intended. + +# 5.6. Overhead Analysis + +Finally, we analyze the search time overhead of the proposed method. Table. 9 demonstrates the average search time of Multi-D-ADC and Ours with identical cluster centers of the inverted index. The retrieval procedure of Ours is similar to the Multi-D-ADC except the additional encoding (Eq. 12) and decoding (Eq. 8) steps. In encoding query (Eq. 12), a query $y$ should be concatenated with $w$ number of cluster centers and embedded $w$ times to build the lookup table. To accelerate the encoding query, we propose batch-forwarding $w$ number of lookup tables at once while the Multi-D-ADC build the lookup table in sequence. Similarly, the decoding top-R (Eq. 8) also can be simply accelerated by batch-forwarding. The re-ranking time (Eq. 14) is negligible because the number of re-ranked data $(R = 200)$ is small. The overall search time of Ours is about $12\%$ slower than the Multi-D-ADC, but we believe it is permissible compared to the performance gain of Ours. Nevertheless, Ours speeds up the search procedure of the UNQ, which requires more than a minute in an exhaustive search. The experimental results are obtained in a single-CPU mode of a $2.2\mathrm{GHz}$ Intel Xeon processor with Faiss [17], and the encoding and decoding times are measured in a single Nvidia Tesla V100 GPU with Pytorch [27]. + +The proposed method requires $\{21,32\} \mathrm{MB}$ for $\{64,$ + +Table 7. Ablation study about the number of re-ranked candidates on million-scale datasets with 64bits bit budget. + +
DatasetMethodR@1R@3R@5
SIFT-1MD([ln, T])0.7090.9230.968
DEEP-1MD([ln, T])0.8270.9650.987
-Random0.0010.0030.005
+ +Table 8. Experiment to validate disentanglement of proposed method with 64bits bit-budget. The score represents the ratio of generated data points that belong to desired cluster within top-R nearest clusters. + +
MethodTime (ms)
Multi-D-ADC (212 × 212)16.89
Ours (212 × 212)18.88
1. encoding query (Eq. 12)1.27
2. symmetric search (Eq. 13)16.86
3. decoding top-R (Eq. 8)0.70
4. asymmetric re-ranking (Eq. 14)0.04
+ +Table 9. Search time analysis on the SIFT-1B dataset and 128bits bit-budget. + +128} bits encoding where the UNQ requires $\{20, 30\}\mathrm{MB}$ for the same budget. Note that those additional memory usage is not proportional to the database size, thus it is same for 1M and 1B database. + +# 6. Conclusion + +In this paper, we propose a novel disentangled representation learning for unsupervised neural quantization. We firstly discover the cause of limited application of the deep quantization (UNQ [23]) on non-exhaustive search with the inverted index. Specifically, the deep quantizer is hard to exploit the compact representation of residual vector space and even takes disadvantages such as loss of cluster center information. To address the problem, we disentangle the information of the cluster center and the latent space by feeding the center to both the encoder and decoder to make center information redundant for the decoder. Similar to residual encoding, this disentanglement encourages the latent space compact and quantization-friendly by taking out the center information from latent space, so the quantization distortion is significantly reduced with disentangled representation. Extensive experiments on various datasets from million to billion scales validate the superiority of the proposed method over state-of-the-art retrieval systems. + +Acknowledgements. This work was supported in part by ETRI grant funded by the Korean government [23ZH1200, The research of the fundamental media-contents technologies for hyper-realistic media space], and MSIT/IITP [2019-0-00421], MSIT/NRF [NRF-2022R1F1A1076132], and MSIT&KNPA/KIPoT [Police Lab 2.0, 210121M06]. + +# References + +[1] Alexandr Andoni and Piotr Indyk. Near-optimal hashing algorithms for approximate nearest neighbor in high dimensions. Communications of the ACM, 51(1):117-122, 2008. 1 +[2] Artem Babenko and Victor Lempitsky. 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IEEE Transactions on Knowledge and Data Engineering, 28(11):2884-2894, 2016. 2 +[27] Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, Alban Desmaison, Andreas Kopf, Edward Yang, Zachary DeVito, Martin Raison, Alykhan Tejani, Sasank Chilamkurthy, Benoit Steiner, Lu Fang, Junjie Bai, and Soumith Chintala. Pytorch: An imperative style, high-performance deep learning library. In Advances in Neural Information Processing Systems 32, pages 8024-8035. Curran Associates, Inc., 2019. 8 +[28] Alexandre Sablayrolles, Matthijs Douze, Cordelia Schmid, and Hervé Jégou. Spreading vectors for similarity search. In ICLR 2019-7th International Conference on Learning Representations, pages 1-13, 2019. 6 +[29] Noam Shazeer, Azalia Mirhoseini, Krzysztof Maziarz, Andy Davis, Quoc V. Le, Geoffrey E. Hinton, and Jeff Dean. + +Outrageously large neural networks: The sparsely-gated mixture-of-experts layer. 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PMLR, 2014. 2 \ No newline at end of file diff --git a/2023/Disentangled Representation Learning for Unsupervised Neural Quantization/images.zip b/2023/Disentangled Representation Learning for Unsupervised Neural Quantization/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..888a22ce1e8a18ab4a71ac23d31f38e4a0d80f9e --- /dev/null +++ b/2023/Disentangled Representation Learning for Unsupervised Neural Quantization/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:2684257be735103b5a17b646c5c2f7c50cf50277b9dc831cc151f565faf61715 +size 516034 diff --git a/2023/Disentangled Representation Learning for Unsupervised Neural Quantization/layout.json b/2023/Disentangled Representation Learning for Unsupervised Neural Quantization/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..fd36b78b9e0f241181315757ac360d0ccb9fffa8 --- /dev/null +++ b/2023/Disentangled Representation Learning for Unsupervised Neural Quantization/layout.json @@ -0,0 +1,10051 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 57, + 136, + 521, + 154 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 136, + 521, + 154 + ], + "spans": [ + { + "bbox": [ + 57, + 136, + 521, + 154 + ], + "type": "text", + "content": "Disentangled Representation Learning for Unsupervised Neural Quantization" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 89, + 175, + 489, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 89, + 175, + 489, + 217 + ], + "spans": [ + { + "bbox": [ + 89, + 175, + 489, + 217 + ], + "type": "text", + "content": "Haechan Noh1, Sangeek Hyun1, Woojin Jeong1, Hanshin Lim2, Jae-Pil Heo1,* \n1Sungkyunkwan University, 2Electronics and Telecommunications Research Institute {noru0114, hsi1032, us03385, jaepilheo}@skku.edu, hslim@etri.re.kr" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 139, + 243, + 186, + 255 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 139, + 243, + 186, + 255 + ], + "spans": [ + { + "bbox": [ + 139, + 243, + 186, + 255 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 262, + 281, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 262, + 281, + 461 + ], + "spans": [ + { + "bbox": [ + 45, + 262, + 281, + 461 + ], + "type": "text", + "content": "The inverted index is a widely used data structure to avoid the infeasible exhaustive search. It accelerates retrieval significantly by splitting the database into multiple disjoint sets and restricts distance computation to a small fraction of the database. Moreover, it even improves search quality by allowing quantizers to exploit the compact distribution of residual vector space. However, we firstly point out a problem that an existing deep learning-based quantizer hardly benefits from the residual vector space, unlike conventional shallow quantizers. To cope with this problem, we introduce a novel disentangled representation learning for unsupervised neural quantization. Similar to the concept of residual vector space, the proposed method enables more compact latent space by disentangling information of the inverted index from the vectors. Experimental results on large-scale datasets confirm that our method outperforms the state-of-the-art retrieval systems by a large margin." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 479, + 124, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 479, + 124, + 491 + ], + "spans": [ + { + "bbox": [ + 46, + 479, + 124, + 491 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 499, + 279, + 580 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 499, + 279, + 580 + ], + "spans": [ + { + "bbox": [ + 45, + 499, + 279, + 580 + ], + "type": "text", + "content": "Measuring the distances among feature vectors is a fundamental requirement in various fields of computer vision. One of the tasks most relevant to distance measurement is the nearest neighbor search, which finds the closest data in the database from a query. The task is especially challenging in high-dimensional and large-scale databases due to huge computational costs and memory overhead." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 580, + 279, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 580, + 279, + 685 + ], + "spans": [ + { + "bbox": [ + 45, + 580, + 279, + 685 + ], + "type": "text", + "content": "By relaxing the complexity, Approximate Nearest Neighbor (ANN) search is popular in practice. Recent approaches for ANN typically learn the compact representation by exploiting Multi-Codebook Quantization (MCQ) [2, 9, 16]. Compared to hashing-based approaches [1, 10, 12], the MCQ provides a more informative asymmetric distance estimator where the query side is not compressed. Moreover, all possible distances between the query and codewords can be stored in a lookup table for efficiency." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 45, + 686, + 279, + 710 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 686, + 279, + 710 + ], + "spans": [ + { + "bbox": [ + 45, + 686, + 279, + 710 + ], + "type": "text", + "content": "Although the MCQ accelerates the distance computation with the lookup table, exhaustive search on the large-scale" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 297, + 244, + 530, + 349 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 244, + 530, + 349 + ], + "spans": [ + { + "bbox": [ + 297, + 244, + 530, + 349 + ], + "type": "text", + "content": "dataset is still prohibited. The Inverted File with Asymmetric Distance Computation (IVFADC) [16] is proposed for non-exhaustive ANN search by cooperating with the inverted index [30]. It splits the database into multiple disjoint sets and restricts distance computations to small portions close to the query to accelerate the retrieval speed. Moreover, the compactness of residual vector space between data points and inverted indices substantially enhances the quantization quality." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 296, + 353, + 531, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 353, + 531, + 504 + ], + "spans": [ + { + "bbox": [ + 296, + 353, + 531, + 504 + ], + "type": "text", + "content": "Thanks to the rapid advances in deep learning, most areas of computer vision benefit from its great learning capacity compared to shallow methods. However, the state-of-the-art methods of unsupervised quantization remain shallow for a long time because selecting the maximum value (i.e. argmax), which is an essential operation of quantization, is not differentiable. Inspired by a recent generative model with discrete hidden variables [35], the Unsupervised Neural Quantization (UNQ) [23] introduced an encoder-decoder-based architecture for ANN search. The large learning capacity of deep neural architecture significantly improves the retrieval quality compared to conventional shallow methods." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 296, + 508, + 532, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 508, + 532, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 508, + 532, + 730 + ], + "type": "text", + "content": "Despite the outperforming performance of the UNQ, its superiority is validated only on the exhaustive search. To verify its effectiveness on non-exhaustive search, we conduct an experiment of non-exhaustive UNQ with an inverted index. Interestingly, we observe that this deep architecture does not benefit from the residual vector space and it even harms the search quality as reported in Table 1. We hypothesize the reasons for this performance degradation from two perspectives. First, both the residual vector space and latent space of the neural network transform the data into a quantization-friendly distribution, thus deep quantizer has a scant margin to be improved by the residual space. Second, residual space sacrifices the distributional characteristics of each cluster, since the information of cluster center in the original space is removed. For conventional shallow quantizers, the drawback of residual space is obscured by its huge advantage of making a compact distribution. However, deep quantizer only takes the disadvantages (information loss) from residual space without leveraging the effec" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 77, + 42, + 119, + 72 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 42, + 119, + 72 + ], + "spans": [ + { + "bbox": [ + 77, + 42, + 119, + 72 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 150, + 41, + 471, + 74 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 150, + 41, + 471, + 74 + ], + "spans": [ + { + "bbox": [ + 150, + 41, + 471, + 74 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 57, + 719, + 131, + 730 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 719, + 131, + 730 + ], + "spans": [ + { + "bbox": [ + 57, + 719, + 131, + 730 + ], + "type": "text", + "content": "*Corresponding author" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 277, + 747, + 300, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 747, + 300, + 756 + ], + "spans": [ + { + "bbox": [ + 277, + 747, + 300, + 756 + ], + "type": "text", + "content": "12001" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 106, + 211, + 117 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 106, + 211, + 117 + ], + "spans": [ + { + "bbox": [ + 46, + 106, + 211, + 117 + ], + "type": "text", + "content": "tiveness such as compactness of residuals." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 118, + 279, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 118, + 279, + 326 + ], + "spans": [ + { + "bbox": [ + 45, + 118, + 279, + 326 + ], + "type": "text", + "content": "In this paper, we focus on extending the application of deep architectures for non-exhaustive search. To this end, we learn a disentangled representation to harmonize a deep architecture with the inverted index, inspired by recent representation learning techniques for generative models [8,34]. In our disentangled representation learning, both encoder and decoder get information of cluster center as an additional input. Since the information of cluster center is redundant to decoder if latent feature contains information of cluster center, the encoder is trained to remove the information of cluster centers from the latent embedding. The disentangled representation learning is similar to concept of the residual vector space that provides more compact distribution by taking out the information of cluster centers. The experimental results verify that the learning disentangled representation enables the neural quantization to collaborate with inverted index and outperforms the state-of-the-art methods." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 57, + 328, + 212, + 339 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 328, + 212, + 339 + ], + "spans": [ + { + "bbox": [ + 57, + 328, + 212, + 339 + ], + "type": "text", + "content": "The contributions of our paper include:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 57, + 341, + 278, + 448 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 57, + 341, + 278, + 374 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 341, + 278, + 374 + ], + "spans": [ + { + "bbox": [ + 57, + 341, + 278, + 374 + ], + "type": "text", + "content": "- We point out that the residual encoding of the inverted index is incompatible with the neural multi-codebook quantization method." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 57, + 377, + 278, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 377, + 278, + 411 + ], + "spans": [ + { + "bbox": [ + 57, + 377, + 278, + 411 + ], + "type": "text", + "content": "- We propose a novel disentangled representation learning for neural multi-codebook quantization to combine deep quantization and inverted index." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 57, + 413, + 278, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 413, + 278, + 448 + ], + "spans": [ + { + "bbox": [ + 57, + 413, + 278, + 448 + ], + "type": "text", + "content": "- The experimental results show that the proposed method outperforms the state-of-the-art retrieval systems by a large margin." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 46, + 459, + 129, + 470 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 459, + 129, + 470 + ], + "spans": [ + { + "bbox": [ + 46, + 459, + 129, + 470 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 479, + 244, + 490 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 479, + 244, + 490 + ], + "spans": [ + { + "bbox": [ + 46, + 479, + 244, + 490 + ], + "type": "text", + "content": "2.1. Multi-codebook Quantization for ANN" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 45, + 496, + 278, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 496, + 278, + 601 + ], + "spans": [ + { + "bbox": [ + 45, + 496, + 278, + 601 + ], + "type": "text", + "content": "Vector quantization [11] maps a vector to its nearest codeword within a learned codebook. Specifically, a high-dimensional real-valued vector can be efficiently represented by an integer index of its corresponding cluster. To ensure a high search accuracy, the vector quantization requires a codebook with an extremely large number of codewords. However, enlarging the number of codewords is far from efficiency because the cost of assigning the nearest codeword is proportionally increased with codebook sizes." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 45, + 602, + 278, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 602, + 278, + 693 + ], + "spans": [ + { + "bbox": [ + 45, + 602, + 278, + 693 + ], + "type": "text", + "content": "Product Quanztiaton (PQ) [16] decomposes the space into a Cartesian product of lower-dimensional subspaces. By quantizing each subspace separately, multiple codebooks are produced and they enable better search quality with a manageable number of codewords. Optimized Product Quantization (OPQ) [9] and Cartesian K-means [25] introduced to learn transformation to optimize the decomposition step in PQ according to the data distribution." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 45, + 694, + 278, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 694, + 278, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 694, + 278, + 730 + ], + "type": "text", + "content": "While the PQ encodes a vector into a concatenation of assigned codewords, a number of methods [2, 6, 20, 21, 26, 36] approximated a vector by a sum of assigned codewords." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 296, + 106, + 530, + 152 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 106, + 530, + 152 + ], + "spans": [ + { + "bbox": [ + 296, + 106, + 530, + 152 + ], + "type": "text", + "content": "These addition-based methods have a higher degree of freedom than the concatenation-based methods, since the concatenation is a special case of addition where components of addition are mutually orthogonal." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 296, + 153, + 530, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 153, + 530, + 304 + ], + "spans": [ + { + "bbox": [ + 296, + 153, + 530, + 304 + ], + "type": "text", + "content": "The state-of-the-art methods of such multi-codebook quantization remain shallow for a long time, while most areas of computer vision benefit from rapid advances in deep learning. The non-differentiability of codeword assignment operation makes the multi-codebook quantization hard to collaborate with deep learning. Vector-Quantized Variational Autoencoder (VQ-VAE) [35] in the area of the generative model proposed a gradient estimation to propagate gradient through discrete variables. Inspired by the VQ-VAE, Unsupervised Neural Quantization (UNQ) [23] introduces a deep neural network for multi-codebook quantization. The much larger learning capacity of UNQ significantly improves the conventional shallow methods." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 297, + 312, + 449, + 324 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 312, + 449, + 324 + ], + "spans": [ + { + "bbox": [ + 297, + 312, + 449, + 324 + ], + "type": "text", + "content": "2.2. Non-exhaustive ANN Search" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 296, + 330, + 530, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 330, + 530, + 494 + ], + "spans": [ + { + "bbox": [ + 296, + 330, + 530, + 494 + ], + "type": "text", + "content": "While the quantization techniques accelerate the distance computation, the search is still exhaustive. IVFADC [16] proposed a non-exhaustive approximate nearest neighbor search by cooperating with the inverted index [30]. In addition to the significant acceleration of retrieval speed, the non-exhaustive manner even improves the search quality by allowing more compact residual vector space. The Inverted Multi-Index (IMI) [3] extends the IVFADC by decomposing data space into two sub-spaces and applying the inverted index independently. Similar to the idea of PQ, the decomposed data space of IMI enables much finer partition with a manageable number of indices. Several subsequent non-exhaustive ANN techniques are proposed to improve the data partitioning rather than the quantization [4, 5, 7]." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 297, + 501, + 495, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 501, + 495, + 514 + ], + "spans": [ + { + "bbox": [ + 297, + 501, + 495, + 514 + ], + "type": "text", + "content": "2.3. Disentangled Representation Learning" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 296, + 520, + 530, + 682 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 520, + 530, + 682 + ], + "spans": [ + { + "bbox": [ + 296, + 520, + 530, + 682 + ], + "type": "text", + "content": "In the context of the generative model, disentangled representation is introduced to analyze and utilize the independent effects of latent factors. One straightforward example can be found in conditional generative models [22, 32]. They decompose the conditional information from the others so that they can control the specific conditions of generated images such as spatial layout [8] or class information [22]. For instance, variational U-Net [8] disentangles the shape and appearance representations to synthesize human images of diverse poses with a shared appearance. Similarly, VarSR [13] builds the latent space of high-resolution information disentangled from the low-resolution images. Hence, they can synthesize diverse high-resolution images corresponding to the given low-resolution image." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 296, + 683, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 683, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 683, + 530, + 730 + ], + "type": "text", + "content": "The aforementioned examples mainly focus on the controllable generation by disentangling conditional information. However, in this paper, we concentrate on the maximization of the representation capability of the latent space" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 277, + 747, + 300, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 747, + 300, + 756 + ], + "spans": [ + { + "bbox": [ + 277, + 747, + 300, + 756 + ], + "type": "text", + "content": "12002" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 59, + 103, + 264, + 190 + ], + "blocks": [ + { + "bbox": [ + 59, + 103, + 264, + 190 + ], + "lines": [ + { + "bbox": [ + 59, + 103, + 264, + 190 + ], + "spans": [ + { + "bbox": [ + 59, + 103, + 264, + 190 + ], + "type": "table", + "html": "
MethodR@1R@10R@100
PQ0.2280.6530.953
+IVF (w/o residual)0.2280.6530.950
+IVF (with residual)0.2720.7350.969
UNQ0.3460.8280.990
+IVF (w/o residual)0.3310.7980.939
+IVF (with residual)0.2720.7180.867
", + "image_path": "c81c3d220adcfeb2f1c469a535d66bfec062fa3a6ad3c55861a10571a70ec2e9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 241, + 279, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 241, + 279, + 288 + ], + "spans": [ + { + "bbox": [ + 45, + 241, + 279, + 288 + ], + "type": "text", + "content": "by disentanglement. Specifically, we build a compact latent space by disentangling the cluster center similar to residual encoding but compatible with the neural multi-codebook quantization method." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 298, + 122, + 311 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 298, + 122, + 311 + ], + "spans": [ + { + "bbox": [ + 46, + 298, + 122, + 311 + ], + "type": "text", + "content": "3. Background" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 318, + 279, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 318, + 279, + 365 + ], + "spans": [ + { + "bbox": [ + 45, + 318, + 279, + 365 + ], + "type": "text", + "content": "Let us briefly introduce the ANN task, the MCQ approach, and the residual vector space. With " + }, + { + "bbox": [ + 45, + 318, + 279, + 365 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 45, + 318, + 279, + 365 + ], + "type": "text", + "content": "-dimensional database " + }, + { + "bbox": [ + 45, + 318, + 279, + 365 + ], + "type": "inline_equation", + "content": "X = \\{x_{n}\\}_{n = 1}^{N}, x_{n} \\in \\mathbb{R}^{D}" + }, + { + "bbox": [ + 45, + 318, + 279, + 365 + ], + "type": "text", + "content": " and query " + }, + { + "bbox": [ + 45, + 318, + 279, + 365 + ], + "type": "inline_equation", + "content": "y \\in \\mathbb{R}^{D}" + }, + { + "bbox": [ + 45, + 318, + 279, + 365 + ], + "type": "text", + "content": ", the nearest neighbor of query " + }, + { + "bbox": [ + 45, + 318, + 279, + 365 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 45, + 318, + 279, + 365 + ], + "type": "text", + "content": " is defined as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 96, + 372, + 279, + 394 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 372, + 279, + 394 + ], + "spans": [ + { + "bbox": [ + 96, + 372, + 279, + 394 + ], + "type": "interline_equation", + "content": "\\operatorname {N N} (y) = \\underset {n \\in \\{1, \\dots , N \\}} {\\arg \\min } \\| y - x _ {n} \\| ^ {2}. \\tag {1}", + "image_path": "900f1a0c2e922016da474b6fc383657b98aa1e6c9ebcdfb0fc6ecbf6320eaecf.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 401, + 279, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 401, + 279, + 472 + ], + "spans": [ + { + "bbox": [ + 45, + 401, + 279, + 472 + ], + "type": "text", + "content": "To alleviate time and memory costs of Eq. 1, the MCQ quantizer " + }, + { + "bbox": [ + 45, + 401, + 279, + 472 + ], + "type": "inline_equation", + "content": "q_{\\mathrm{MCQ}}" + }, + { + "bbox": [ + 45, + 401, + 279, + 472 + ], + "type": "text", + "content": " encodes the database " + }, + { + "bbox": [ + 45, + 401, + 279, + 472 + ], + "type": "inline_equation", + "content": "X = \\{x_{n}\\}_{n=1}^{N}" + }, + { + "bbox": [ + 45, + 401, + 279, + 472 + ], + "type": "text", + "content": " utilizing " + }, + { + "bbox": [ + 45, + 401, + 279, + 472 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 45, + 401, + 279, + 472 + ], + "type": "text", + "content": " number of multi-codebooks " + }, + { + "bbox": [ + 45, + 401, + 279, + 472 + ], + "type": "inline_equation", + "content": "C^{m} = \\{c_{k}^{m}\\}_{k=1}^{K}, c_{k}^{m} \\in \\mathbb{R}^{D}" + }, + { + "bbox": [ + 45, + 401, + 279, + 472 + ], + "type": "text", + "content": " where each codebook has " + }, + { + "bbox": [ + 45, + 401, + 279, + 472 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 45, + 401, + 279, + 472 + ], + "type": "text", + "content": " number of codewords. Then, a vector " + }, + { + "bbox": [ + 45, + 401, + 279, + 472 + ], + "type": "inline_equation", + "content": "x_{n}" + }, + { + "bbox": [ + 45, + 401, + 279, + 472 + ], + "type": "text", + "content": " is represented as " + }, + { + "bbox": [ + 45, + 401, + 279, + 472 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 45, + 401, + 279, + 472 + ], + "type": "text", + "content": " number of indices " + }, + { + "bbox": [ + 45, + 401, + 279, + 472 + ], + "type": "inline_equation", + "content": "[i_{n}^{1}, \\dots, i_{n}^{M}]" + }, + { + "bbox": [ + 45, + 401, + 279, + 472 + ], + "type": "text", + "content": " and reconstructed by referring the codebooks:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 479, + 279, + 511 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 479, + 279, + 511 + ], + "spans": [ + { + "bbox": [ + 105, + 479, + 279, + 511 + ], + "type": "interline_equation", + "content": "x _ {n} \\approx q _ {\\mathrm {M C Q}} \\left(x _ {n}\\right) = \\sum_ {m = 1} ^ {M} c _ {i _ {n} ^ {m}} ^ {m}. \\tag {2}", + "image_path": "85b98e2d3c184fdf30fa27f165a4b4ab0f824b47e2bfdf3b173dd73f90536f77.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 518, + 279, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 518, + 279, + 542 + ], + "spans": [ + { + "bbox": [ + 45, + 518, + 279, + 542 + ], + "type": "text", + "content": "The goal of this lossy compression process is to learn codebooks that minimize quantization distortion " + }, + { + "bbox": [ + 45, + 518, + 279, + 542 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 45, + 518, + 279, + 542 + ], + "type": "text", + "content": " defined as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 98, + 550, + 279, + 582 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 98, + 550, + 279, + 582 + ], + "spans": [ + { + "bbox": [ + 98, + 550, + 279, + 582 + ], + "type": "interline_equation", + "content": "E \\left(x _ {n}, C\\right) = \\sum_ {m = 1} ^ {M} \\left| \\left| x _ {n} ^ {m} - c _ {i _ {n} ^ {m}} ^ {m} \\right| \\right| ^ {2}, \\tag {3}", + "image_path": "25bd03fec879cce5793cfdad9d722ec4c3c2c0e6c5435b60c192826875a73526.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 45, + 590, + 279, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 590, + 279, + 625 + ], + "spans": [ + { + "bbox": [ + 45, + 590, + 279, + 625 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 45, + 590, + 279, + 625 + ], + "type": "inline_equation", + "content": "x_{n} = \\sum x_{n}^{m}" + }, + { + "bbox": [ + 45, + 590, + 279, + 625 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 45, + 590, + 279, + 625 + ], + "type": "inline_equation", + "content": "x_{n}^{m}" + }, + { + "bbox": [ + 45, + 590, + 279, + 625 + ], + "type": "text", + "content": " is a subvector of " + }, + { + "bbox": [ + 45, + 590, + 279, + 625 + ], + "type": "inline_equation", + "content": "x_{n}" + }, + { + "bbox": [ + 45, + 590, + 279, + 625 + ], + "type": "text", + "content": " corresponding to index " + }, + { + "bbox": [ + 45, + 590, + 279, + 625 + ], + "type": "inline_equation", + "content": "i_{n}^{m}" + }, + { + "bbox": [ + 45, + 590, + 279, + 625 + ], + "type": "text", + "content": ". The PQ belongs to the MCQ approach where " + }, + { + "bbox": [ + 45, + 590, + 279, + 625 + ], + "type": "inline_equation", + "content": "x_{n}^{m}" + }, + { + "bbox": [ + 45, + 590, + 279, + 625 + ], + "type": "text", + "content": " are mutually orthogonal." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 45, + 625, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 625, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 625, + 279, + 730 + ], + "type": "text", + "content": "The IVFADC [16] further accelerates ANN search by collaborating with an inverted index. The inverted index " + }, + { + "bbox": [ + 45, + 625, + 279, + 730 + ], + "type": "inline_equation", + "content": "q_{\\mathrm{IVF}}" + }, + { + "bbox": [ + 45, + 625, + 279, + 730 + ], + "type": "text", + "content": " splits database " + }, + { + "bbox": [ + 45, + 625, + 279, + 730 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 45, + 625, + 279, + 730 + ], + "type": "text", + "content": " into " + }, + { + "bbox": [ + 45, + 625, + 279, + 730 + ], + "type": "inline_equation", + "content": "K'" + }, + { + "bbox": [ + 45, + 625, + 279, + 730 + ], + "type": "text", + "content": " number of disjoint subsets, and the ANN search is then restricted to " + }, + { + "bbox": [ + 45, + 625, + 279, + 730 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 45, + 625, + 279, + 730 + ], + "type": "text", + "content": " number of nearest subsets from query " + }, + { + "bbox": [ + 45, + 625, + 279, + 730 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 45, + 625, + 279, + 730 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 45, + 625, + 279, + 730 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 45, + 625, + 279, + 730 + ], + "type": "text", + "content": " is much smaller than " + }, + { + "bbox": [ + 45, + 625, + 279, + 730 + ], + "type": "inline_equation", + "content": "K'" + }, + { + "bbox": [ + 45, + 625, + 279, + 730 + ], + "type": "text", + "content": ". For a given data point " + }, + { + "bbox": [ + 45, + 625, + 279, + 730 + ], + "type": "inline_equation", + "content": "x_n" + }, + { + "bbox": [ + 45, + 625, + 279, + 730 + ], + "type": "text", + "content": ", the inverted index " + }, + { + "bbox": [ + 45, + 625, + 279, + 730 + ], + "type": "inline_equation", + "content": "q_{\\mathrm{IVF}}(\\cdot)" + }, + { + "bbox": [ + 45, + 625, + 279, + 730 + ], + "type": "text", + "content": " quantize it to its nearest cluster center " + }, + { + "bbox": [ + 45, + 625, + 279, + 730 + ], + "type": "inline_equation", + "content": "q_{\\mathrm{IVF}}(x_n)" + }, + { + "bbox": [ + 45, + 625, + 279, + 730 + ], + "type": "text", + "content": ", and the data points belong to the same cluster are stored adjacently. Moreover, the IVFADC suggested learning codebooks that" + } + ] + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 299, + 104, + 527, + 237 + ], + "blocks": [ + { + "bbox": [ + 45, + 194, + 279, + 228 + ], + "lines": [ + { + "bbox": [ + 45, + 194, + 279, + 228 + ], + "spans": [ + { + "bbox": [ + 45, + 194, + 279, + 228 + ], + "type": "text", + "content": "Table 1. Comparison of retrieval performances between the PQ and the UNQ on SIFT-1M. The residual vector space improves the performance with the PQ, but does not work with the UNQ." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 299, + 104, + 527, + 237 + ], + "lines": [ + { + "bbox": [ + 299, + 104, + 527, + 237 + ], + "spans": [ + { + "bbox": [ + 299, + 104, + 527, + 237 + ], + "type": "table", + "html": "
MethodCompression ratioDistortion
PQ128×0.8368
+IVF (with residual)0.7208
PQ64×0.6252
+IVF (with residual)0.5846
PQ32×0.4127
+IVF (with residual)0.4220
PQ16×0.2438
+IVF (with residual)0.2604
PQ4×0.0212
+IVF (with residual)0.0257
", + "image_path": "cbdfdb279f8f00468dfe45cc4c42aa4ec66f45e1d0c3b2e122204df08ce2d1f1.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 296, + 242, + 530, + 286 + ], + "lines": [ + { + "bbox": [ + 296, + 242, + 530, + 286 + ], + "spans": [ + { + "bbox": [ + 296, + 242, + 530, + 286 + ], + "type": "text", + "content": "Table 2. Quantization distortions of the database with varying compression ratios. The residual vector space is profitable with a large compression ratio, but it leads performance drop with a small compression ratio." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 296, + 298, + 530, + 320 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 298, + 530, + 320 + ], + "spans": [ + { + "bbox": [ + 296, + 298, + 530, + 320 + ], + "type": "text", + "content": "encode residual vector " + }, + { + "bbox": [ + 296, + 298, + 530, + 320 + ], + "type": "inline_equation", + "content": "r(x_{n}) = x_{n} - q_{\\mathrm{IVF}}(x_{n})" + }, + { + "bbox": [ + 296, + 298, + 530, + 320 + ], + "type": "text", + "content": " rather than the original vector as follows:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 321, + 327, + 530, + 340 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 327, + 530, + 340 + ], + "spans": [ + { + "bbox": [ + 321, + 327, + 530, + 340 + ], + "type": "interline_equation", + "content": "x _ {n} \\approx \\tilde {x} _ {n} = q _ {\\mathrm {M C Q}} \\left(x _ {n} - q _ {\\mathrm {I V F}} \\left(x _ {n}\\right)\\right) + q _ {\\mathrm {I V F}} \\left(x _ {n}\\right). \\tag {4}", + "image_path": "93717937816875707f22cdbfc9b4a54db93653051e21b5389a6d307d440e6b53.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 296, + 345, + 530, + 367 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 345, + 530, + 367 + ], + "spans": [ + { + "bbox": [ + 296, + 345, + 530, + 367 + ], + "type": "text", + "content": "Then the distance between query " + }, + { + "bbox": [ + 296, + 345, + 530, + 367 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 296, + 345, + 530, + 367 + ], + "type": "text", + "content": " and target data " + }, + { + "bbox": [ + 296, + 345, + 530, + 367 + ], + "type": "inline_equation", + "content": "x_{n}" + }, + { + "bbox": [ + 296, + 345, + 530, + 367 + ], + "type": "text", + "content": " is estimated as follows:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 374, + 530, + 388 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 374, + 530, + 388 + ], + "spans": [ + { + "bbox": [ + 306, + 374, + 530, + 388 + ], + "type": "interline_equation", + "content": "d (y, x _ {n}) \\approx d (y - q _ {\\mathrm {I V F}} (x _ {n}), q _ {\\mathrm {M C Q}} (x _ {n} - q _ {\\mathrm {I V F}} (x _ {n}))). \\tag {5}", + "image_path": "b52dcb4db200e41671df774341f75fb44b8cd25768ed73fcd05f180497a84ebe.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 296, + 393, + 530, + 451 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 393, + 530, + 451 + ], + "spans": [ + { + "bbox": [ + 296, + 393, + 530, + 451 + ], + "type": "text", + "content": "where the " + }, + { + "bbox": [ + 296, + 393, + 530, + 451 + ], + "type": "inline_equation", + "content": "d(\\cdot, \\cdot)" + }, + { + "bbox": [ + 296, + 393, + 530, + 451 + ], + "type": "text", + "content": " is the Euclidean distance between two vectors. The IVFADC accelerates the search speed by reducing the number of distance estimations and improves the quantization distortion (Eq. 3) thanks to the compact distribution of the residual vector space." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 297, + 460, + 400, + 474 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 460, + 400, + 474 + ], + "spans": [ + { + "bbox": [ + 297, + 460, + 400, + 474 + ], + "type": "text", + "content": "4. Proposed Method" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 297, + 479, + 369, + 490 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 479, + 369, + 490 + ], + "spans": [ + { + "bbox": [ + 297, + 479, + 369, + 490 + ], + "type": "text", + "content": "4.1. Motivation" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 296, + 497, + 530, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 497, + 530, + 612 + ], + "spans": [ + { + "bbox": [ + 296, + 497, + 530, + 612 + ], + "type": "text", + "content": "Recently, the UNQ [23] introduced a deep architecture for MCQ learning and improves conventional shallow MCQ methods by a large margin. However, its effectiveness is only validated by an exhaustive ANN search. To examine the performance of UNQ on non-exhaustive search, we test the retrieval performances of PQ and UNQ with an inverted index on exhaustive and non-exhaustive settings. As reported in Table. 1, the residual encoding (Eq. 4) provides better search quality with the PQ, while it makes the search quality of UNQ even worse." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 296, + 613, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 613, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 613, + 530, + 730 + ], + "type": "text", + "content": "To investigate the reasons why residual encoding does not help the UNQ, we need to analyze the mechanism of residual encoding in PQ. To this end, we hypothesize the effect of residual representation in two aspects. First, the advantage of residuals in PQ comes from the transformation of data space into compact and quantization-friendly distribution. Second, the residual encoding is not always beneficial, since they sacrifice the information of the cluster center so that the distributional characteristics of each cluster are suppressed." + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 277, + 747, + 300, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 747, + 300, + 756 + ], + "spans": [ + { + "bbox": [ + 277, + 747, + 300, + 756 + ], + "type": "text", + "content": "12003" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 74, + 110, + 502, + 229 + ], + "blocks": [ + { + "bbox": [ + 74, + 110, + 502, + 229 + ], + "lines": [ + { + "bbox": [ + 74, + 110, + 502, + 229 + ], + "spans": [ + { + "bbox": [ + 74, + 110, + 502, + 229 + ], + "type": "image", + "image_path": "954e5232da019184ff8fc93b45fb605699353c40ac12358c20fd320f136ecc48.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 237, + 531, + 271 + ], + "lines": [ + { + "bbox": [ + 45, + 237, + 531, + 271 + ], + "spans": [ + { + "bbox": [ + 45, + 237, + 531, + 271 + ], + "type": "text", + "content": "Figure 1. By providing additional input of " + }, + { + "bbox": [ + 45, + 237, + 531, + 271 + ], + "type": "inline_equation", + "content": "q_{\\mathrm{IVF}}(x_n)" + }, + { + "bbox": [ + 45, + 237, + 531, + 271 + ], + "type": "text", + "content": " to both encoder and decoder, the encoder is not necessary to learn features to reconstruct " + }, + { + "bbox": [ + 45, + 237, + 531, + 271 + ], + "type": "inline_equation", + "content": "q_{\\mathrm{IVF}}(x_n)" + }, + { + "bbox": [ + 45, + 237, + 531, + 271 + ], + "type": "text", + "content": " since it is redundant information for the decoder. Thus the information of the cluster center is disentangled from the latent vectors and codebooks. The disentangling enables the quantizer to learn compact representation while preserving the original distribution." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 285, + 281, + 424 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 285, + 281, + 424 + ], + "spans": [ + { + "bbox": [ + 45, + 285, + 281, + 424 + ], + "type": "text", + "content": "To validate these hypotheses, we observe the performance variation of PQ with residual encoding by varying compression ratios. The compression ratios are controlled by adjusting the number of codebooks " + }, + { + "bbox": [ + 45, + 285, + 281, + 424 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 45, + 285, + 281, + 424 + ], + "type": "text", + "content": ". As reported in Table. 2, the residual encoding is profitable with large compression ratios, since the sparse original distribution is hard to quantize with the deficient bit-budget. On the other hand, the residual encoding leads to performance drops with small compression ratios, because it is not necessary to represent the data compactly thanks to sufficient numbers of codewords, but the information loss of cluster-wise distributional characteristics still exists." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 425, + 279, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 425, + 279, + 563 + ], + "spans": [ + { + "bbox": [ + 45, + 425, + 279, + 563 + ], + "type": "text", + "content": "Based on these observations, we explain the reasons for UNQ's performance drop with residual encoding. Firstly, UNQ does not benefit from the compact representation of residual encoding. The deep encoder transforms the data into latent space with a reconstruction objective function. That is, the objective of UNQ also encourages to transform the data into compact latent space, so the residual encoding and UNQ affect the model in a similar way. Hence, the residual representation is hardly beneficial to the neural quantizer. Secondly, UNQ takes the disadvantage of residual encoding, the information loss of distributional characteristics of each cluster." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 564, + 279, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 564, + 279, + 646 + ], + "spans": [ + { + "bbox": [ + 45, + 564, + 279, + 646 + ], + "type": "text", + "content": "These interpretations motivate us to come up with a method that only takes the advantage of residual representation. That is, we aim to make the latent space more compact without the information loss of distributional characteristics of each cluster. To this end, we introduce a disentangled representation learning for unsupervised neural quantization in the following sections." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 653, + 224, + 665 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 653, + 224, + 665 + ], + "spans": [ + { + "bbox": [ + 45, + 653, + 224, + 665 + ], + "type": "text", + "content": "4.2. Disentangled Neural Quantization" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 671, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 671, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 671, + 279, + 730 + ], + "type": "text", + "content": "Inspired by the disentangled representation of conditional generative models [22, 32], we propose disentangled neural quantization. The previous methods exploit the disentanglement for a controllable generation. However, we propose to learn a disentangled representation to reduce" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 296, + 285, + 530, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 285, + 530, + 389 + ], + "spans": [ + { + "bbox": [ + 296, + 285, + 530, + 389 + ], + "type": "text", + "content": "the quantization distortion. Specifically, a latent feature " + }, + { + "bbox": [ + 296, + 285, + 530, + 389 + ], + "type": "inline_equation", + "content": "(l_{n})" + }, + { + "bbox": [ + 296, + 285, + 530, + 389 + ], + "type": "text", + "content": " of UNQ contains information of its input vector " + }, + { + "bbox": [ + 296, + 285, + 530, + 389 + ], + "type": "inline_equation", + "content": "x_{n}" + }, + { + "bbox": [ + 296, + 285, + 530, + 389 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 296, + 285, + 530, + 389 + ], + "type": "inline_equation", + "content": "x_{n}" + }, + { + "bbox": [ + 296, + 285, + 530, + 389 + ], + "type": "text", + "content": " consists of " + }, + { + "bbox": [ + 296, + 285, + 530, + 389 + ], + "type": "inline_equation", + "content": "q_{\\mathrm{IVF}}(x_n)" + }, + { + "bbox": [ + 296, + 285, + 530, + 389 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 285, + 530, + 389 + ], + "type": "inline_equation", + "content": "x_{n} - q_{\\mathrm{IVF}}(x_{n})" + }, + { + "bbox": [ + 296, + 285, + 530, + 389 + ], + "type": "text", + "content": ". However, the " + }, + { + "bbox": [ + 296, + 285, + 530, + 389 + ], + "type": "inline_equation", + "content": "q_{\\mathrm{IVF}}(x_n)" + }, + { + "bbox": [ + 296, + 285, + 530, + 389 + ], + "type": "text", + "content": " can be restored without any information loss thanks to the data structure of the inverted index. Thus, encoding the " + }, + { + "bbox": [ + 296, + 285, + 530, + 389 + ], + "type": "inline_equation", + "content": "q_{\\mathrm{IVF}}(x_n)" + }, + { + "bbox": [ + 296, + 285, + 530, + 389 + ], + "type": "text", + "content": " is quite wasteful because the MCQ approach has a scarce bit budget in practice. In this paper, we suggest disentangling the " + }, + { + "bbox": [ + 296, + 285, + 530, + 389 + ], + "type": "inline_equation", + "content": "q_{\\mathrm{IVF}}(x_n)" + }, + { + "bbox": [ + 296, + 285, + 530, + 389 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 296, + 285, + 530, + 389 + ], + "type": "inline_equation", + "content": "l_{n}" + }, + { + "bbox": [ + 296, + 285, + 530, + 389 + ], + "type": "text", + "content": " to provide more compact information." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 296, + 389, + 531, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 389, + 531, + 506 + ], + "spans": [ + { + "bbox": [ + 296, + 389, + 531, + 506 + ], + "type": "text", + "content": "To disentangle the " + }, + { + "bbox": [ + 296, + 389, + 531, + 506 + ], + "type": "inline_equation", + "content": "q_{\\mathrm{IVF}}(x_n)" + }, + { + "bbox": [ + 296, + 389, + 531, + 506 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 296, + 389, + 531, + 506 + ], + "type": "inline_equation", + "content": "l_{n}" + }, + { + "bbox": [ + 296, + 389, + 531, + 506 + ], + "type": "text", + "content": ", we feed additional input of " + }, + { + "bbox": [ + 296, + 389, + 531, + 506 + ], + "type": "inline_equation", + "content": "q_{\\mathrm{IVF}}(x_n)" + }, + { + "bbox": [ + 296, + 389, + 531, + 506 + ], + "type": "text", + "content": " to encoder " + }, + { + "bbox": [ + 296, + 389, + 531, + 506 + ], + "type": "inline_equation", + "content": "E(\\cdot)" + }, + { + "bbox": [ + 296, + 389, + 531, + 506 + ], + "type": "text", + "content": " and decoder " + }, + { + "bbox": [ + 296, + 389, + 531, + 506 + ], + "type": "inline_equation", + "content": "D(\\cdot)" + }, + { + "bbox": [ + 296, + 389, + 531, + 506 + ], + "type": "text", + "content": ". Then the " + }, + { + "bbox": [ + 296, + 389, + 531, + 506 + ], + "type": "inline_equation", + "content": "q_{\\mathrm{IVF}}(x_n)" + }, + { + "bbox": [ + 296, + 389, + 531, + 506 + ], + "type": "text", + "content": " is redundant information for " + }, + { + "bbox": [ + 296, + 389, + 531, + 506 + ], + "type": "inline_equation", + "content": "D(\\cdot)" + }, + { + "bbox": [ + 296, + 389, + 531, + 506 + ], + "type": "text", + "content": " if " + }, + { + "bbox": [ + 296, + 389, + 531, + 506 + ], + "type": "inline_equation", + "content": "l_{n}" + }, + { + "bbox": [ + 296, + 389, + 531, + 506 + ], + "type": "text", + "content": " contains information of " + }, + { + "bbox": [ + 296, + 389, + 531, + 506 + ], + "type": "inline_equation", + "content": "q_{\\mathrm{IVF}}(x_n)" + }, + { + "bbox": [ + 296, + 389, + 531, + 506 + ], + "type": "text", + "content": ". Thus, the " + }, + { + "bbox": [ + 296, + 389, + 531, + 506 + ], + "type": "inline_equation", + "content": "E(\\cdot)" + }, + { + "bbox": [ + 296, + 389, + 531, + 506 + ], + "type": "text", + "content": " is trained to embed as little information of " + }, + { + "bbox": [ + 296, + 389, + 531, + 506 + ], + "type": "inline_equation", + "content": "q_{\\mathrm{IVF}}(x_n)" + }, + { + "bbox": [ + 296, + 389, + 531, + 506 + ], + "type": "text", + "content": " as possible in " + }, + { + "bbox": [ + 296, + 389, + 531, + 506 + ], + "type": "inline_equation", + "content": "l_{n}" + }, + { + "bbox": [ + 296, + 389, + 531, + 506 + ], + "type": "text", + "content": " to fully exploit the network capacity. The disentangled representation learning is similar to the concept of the residual encoding of PQ (Eq. 4) in terms of taking out the information of the cluster center. However, there is no information loss because the cluster center " + }, + { + "bbox": [ + 296, + 389, + 531, + 506 + ], + "type": "inline_equation", + "content": "q_{\\mathrm{IVF}}(x_n)" + }, + { + "bbox": [ + 296, + 389, + 531, + 506 + ], + "type": "text", + "content": " is provided to " + }, + { + "bbox": [ + 296, + 389, + 531, + 506 + ], + "type": "inline_equation", + "content": "D(\\cdot)" + }, + { + "bbox": [ + 296, + 389, + 531, + 506 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 296, + 506, + 530, + 599 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 506, + 530, + 599 + ], + "spans": [ + { + "bbox": [ + 296, + 506, + 530, + 599 + ], + "type": "text", + "content": "Figure. 1 describes the proposed disentangled representation learning. The cluster center of input data is provided to the encoder and decoder, and the scarce resource of finite codewords can be fully utilized to quantize the compact latent feature where the information of the cluster center is disentangled. Not only the compact information, but the decoder also preserves the original distribution by reconstructing the original space in an end-to-end manner." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 297, + 607, + 405, + 618 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 607, + 405, + 618 + ], + "spans": [ + { + "bbox": [ + 297, + 607, + 405, + 618 + ], + "type": "text", + "content": "4.3. Network Structure" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "text", + "content": "We adopt the network structure of [23] except our disentangling module. The network consists of encoder " + }, + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "inline_equation", + "content": "E(\\cdot)" + }, + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "text", + "content": ", decoder " + }, + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "inline_equation", + "content": "D(\\cdot)" + }, + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "text", + "content": ", and learnable codebook parameters " + }, + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "inline_equation", + "content": "[C^1, \\dots, C^M]" + }, + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "inline_equation", + "content": "C^m = \\{c_k^m\\}_{k=1}^K" + }, + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "text", + "content": ". Both encoder " + }, + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "inline_equation", + "content": "E(\\cdot)" + }, + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "text", + "content": " and decoder " + }, + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "inline_equation", + "content": "D(\\cdot)" + }, + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "text", + "content": " are a concatenation of two fully-connected layers with Batch Normalization [14] and ReLU activation function. We feed separate information of cluster center " + }, + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "inline_equation", + "content": "q_{\\mathrm{IVF}}(x_n)" + }, + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "text", + "content": " to the encoder for the disentanglement. Then the encoder " + }, + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "inline_equation", + "content": "E(\\cdot)" + }, + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "text", + "content": " embeds the given concatenated inputs" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 277, + 747, + 301, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 747, + 301, + 756 + ], + "spans": [ + { + "bbox": [ + 277, + 747, + 301, + 756 + ], + "type": "text", + "content": "12004" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 63, + 104, + 512, + 271 + ], + "blocks": [ + { + "bbox": [ + 63, + 104, + 512, + 271 + ], + "lines": [ + { + "bbox": [ + 63, + 104, + 512, + 271 + ], + "spans": [ + { + "bbox": [ + 63, + 104, + 512, + 271 + ], + "type": "table", + "html": "
Search mannerMethod64bits encoding128bits encoding
R@1R@10R@100R@1R@10R@100
ExhaustiveOPQ0.2080.6430.9530.4090.8980.999
Catalyst + Lattice0.2890.7580.9790.4910.9411.
LSQ0.2920.7770.9870.5710.9751.
UNQ0.3460.8280.9900.5930.9801.
Non-ExhaustiveIVFADC (210)0.2960.7040.9570.4710.9030.993
IVFADC + QAI (210)0.3110.7300.9650.4960.9280.992
IVFOADC (210)0.2950.7190.9630.4750.9130.995
IVFOADC + QAI (210)0.3210.7560.9720.5000.9310.993
Multi-D-ADC (28 × 28)0.3030.7290.9670.4840.9240.998
Multi-D-ADC + QAI (28 × 28)0.3180.7480.9770.5130.9390.997
UNQ+IVF (210)0.3310.7980.9390.5480.9630.994
Ours (210)0.3980.8770.9710.6000.9740.990
", + "image_path": "051611aa86e4bcf5621017286849bfa5071974052234474283c49c92f058987b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 71, + 272, + 504, + 284 + ], + "lines": [ + { + "bbox": [ + 71, + 272, + 504, + 284 + ], + "spans": [ + { + "bbox": [ + 71, + 272, + 504, + 284 + ], + "type": "text", + "content": "Table 3. Experimental result on the SIFT-1M dataset. All the quantities except Ours and UNQ+IVF are taken from [23, 24]" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 298, + 270, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 298, + 270, + 312 + ], + "spans": [ + { + "bbox": [ + 46, + 298, + 270, + 312 + ], + "type": "inline_equation", + "content": "[x_n, q_{\\mathrm{IVF}}(x_n)]" + }, + { + "bbox": [ + 46, + 298, + 270, + 312 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 298, + 270, + 312 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 298, + 270, + 312 + ], + "type": "text", + "content": " number of latent features as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 98, + 318, + 279, + 332 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 98, + 318, + 279, + 332 + ], + "spans": [ + { + "bbox": [ + 98, + 318, + 279, + 332 + ], + "type": "interline_equation", + "content": "E \\left(\\left[ x _ {n}, q _ {\\mathrm {I V F}} \\left(x _ {n}\\right) \\right]\\right) = \\left[ l _ {n} ^ {1}, \\dots , l _ {n} ^ {M} \\right]. \\tag {6}", + "image_path": "f0dcd3471cae6cca68117020b4df70704340eb9c873decdf73f1938b700e87a4.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 339, + 279, + 372 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 339, + 279, + 372 + ], + "spans": [ + { + "bbox": [ + 45, + 339, + 279, + 372 + ], + "type": "text", + "content": "The embedded feature " + }, + { + "bbox": [ + 45, + 339, + 279, + 372 + ], + "type": "inline_equation", + "content": "l_{n}^{m}" + }, + { + "bbox": [ + 45, + 339, + 279, + 372 + ], + "type": "text", + "content": " is quantized to index " + }, + { + "bbox": [ + 45, + 339, + 279, + 372 + ], + "type": "inline_equation", + "content": "i_n^m" + }, + { + "bbox": [ + 45, + 339, + 279, + 372 + ], + "type": "text", + "content": " of the codeword that has the biggest dot-product with " + }, + { + "bbox": [ + 45, + 339, + 279, + 372 + ], + "type": "inline_equation", + "content": "l_{n}^{m}" + }, + { + "bbox": [ + 45, + 339, + 279, + 372 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 111, + 373, + 279, + 394 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 373, + 279, + 394 + ], + "spans": [ + { + "bbox": [ + 111, + 373, + 279, + 394 + ], + "type": "interline_equation", + "content": "i _ {n} ^ {m} = \\underset {k \\in \\{1, \\dots , K \\}} {\\arg \\max } l _ {n} ^ {m} \\cdot c _ {k} ^ {m}. \\tag {7}", + "image_path": "4a1b1fc3cef25d431e31e0d779a0db4e9f31ad674e0cea75f8bcb3b286260b19.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 398, + 279, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 398, + 279, + 503 + ], + "spans": [ + { + "bbox": [ + 45, + 398, + 279, + 503 + ], + "type": "text", + "content": "Because the argmax function is not differentiable, we follow [23] that exploits the Gumbel trick [15]. The Gumbel trick provides a differentiable approximation of Eq. 7 by substituting the argmax with softmax during backpropagation. Then, the sum of assigned codewords " + }, + { + "bbox": [ + 45, + 398, + 279, + 503 + ], + "type": "inline_equation", + "content": "c_{i_n^m}^m" + }, + { + "bbox": [ + 45, + 398, + 279, + 503 + ], + "type": "text", + "content": " becomes the input for the decoder " + }, + { + "bbox": [ + 45, + 398, + 279, + 503 + ], + "type": "inline_equation", + "content": "D(\\cdot)" + }, + { + "bbox": [ + 45, + 398, + 279, + 503 + ], + "type": "text", + "content": ". Likewise, we concatenate it with the cluster center " + }, + { + "bbox": [ + 45, + 398, + 279, + 503 + ], + "type": "inline_equation", + "content": "q_{\\mathrm{IVF}}(x_n)" + }, + { + "bbox": [ + 45, + 398, + 279, + 503 + ], + "type": "text", + "content": " for the disentanglement. The approximated vector " + }, + { + "bbox": [ + 45, + 398, + 279, + 503 + ], + "type": "inline_equation", + "content": "\\tilde{x}_n" + }, + { + "bbox": [ + 45, + 398, + 279, + 503 + ], + "type": "text", + "content": " of original vector " + }, + { + "bbox": [ + 45, + 398, + 279, + 503 + ], + "type": "inline_equation", + "content": "x_n" + }, + { + "bbox": [ + 45, + 398, + 279, + 503 + ], + "type": "text", + "content": " is obtained as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 86, + 509, + 279, + 542 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 509, + 279, + 542 + ], + "spans": [ + { + "bbox": [ + 86, + 509, + 279, + 542 + ], + "type": "interline_equation", + "content": "\\tilde {x} _ {n} = D \\left(\\left[ \\sum_ {m = 1} ^ {M} c _ {i _ {n} ^ {m}} ^ {m}, q _ {\\mathrm {I V F}} (x _ {n}) \\right]\\right). \\tag {8}", + "image_path": "033ad7f9a8a0749cb0803dbe3ce33eff12d45ba028e293dbeca296201d096c43.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 548, + 279, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 548, + 279, + 581 + ], + "spans": [ + { + "bbox": [ + 45, + 548, + 279, + 581 + ], + "type": "text", + "content": "The model is trained with two losses. The first one is a reconstruction loss which directly minimizes the quantization distortion as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 115, + 589, + 279, + 620 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 589, + 279, + 620 + ], + "spans": [ + { + "bbox": [ + 115, + 589, + 279, + 620 + ], + "type": "interline_equation", + "content": "L _ {1} = \\sum_ {n = 1} ^ {N} | | x _ {n} - \\tilde {x} _ {n} | | ^ {2}. \\tag {9}", + "image_path": "4ce03c0fc35a905f5ece8aebf4998841c7d7a236f0593eb4a63e60e0ef65d1d8.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 45, + 627, + 279, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 627, + 279, + 661 + ], + "spans": [ + { + "bbox": [ + 45, + 627, + 279, + 661 + ], + "type": "text", + "content": "Similar to [23], we adopt the square Coefficient Variation regularizer [29] to encourage the codewords to be evenly selected:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 98, + 667, + 279, + 699 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 98, + 667, + 279, + 699 + ], + "spans": [ + { + "bbox": [ + 98, + 667, + 279, + 699 + ], + "type": "interline_equation", + "content": "L _ {2} = \\sum_ {m = 1} ^ {M} \\frac {\\sum_ {n = 1} ^ {N} \\left(p _ {n} ^ {m} - p _ {\\text {a v g}} ^ {m}\\right) ^ {2}}{p _ {\\text {a v g}} ^ {m} {} ^ {2}}, \\tag {10}", + "image_path": "bca4f6dd86219b0d42782d26a891e74579a4f2173c861d4aaca183e1dda6ea9b.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 45, + 706, + 279, + 731 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 706, + 279, + 731 + ], + "spans": [ + { + "bbox": [ + 45, + 706, + 279, + 731 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 45, + 706, + 279, + 731 + ], + "type": "inline_equation", + "content": "p_n^m" + }, + { + "bbox": [ + 45, + 706, + 279, + 731 + ], + "type": "text", + "content": " is the softmax probability of " + }, + { + "bbox": [ + 45, + 706, + 279, + 731 + ], + "type": "inline_equation", + "content": "i_n^m" + }, + { + "bbox": [ + 45, + 706, + 279, + 731 + ], + "type": "text", + "content": " by the Gumbel approximation in Eq. 7, and " + }, + { + "bbox": [ + 45, + 706, + 279, + 731 + ], + "type": "inline_equation", + "content": "p_{\\mathrm{avg}}^m" + }, + { + "bbox": [ + 45, + 706, + 279, + 731 + ], + "type": "text", + "content": " is the average of " + }, + { + "bbox": [ + 45, + 706, + 279, + 731 + ], + "type": "inline_equation", + "content": "p_n^m" + }, + { + "bbox": [ + 45, + 706, + 279, + 731 + ], + "type": "text", + "content": " along" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 298, + 298, + 511, + 310 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 298, + 511, + 310 + ], + "spans": [ + { + "bbox": [ + 298, + 298, + 511, + 310 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 298, + 298, + 511, + 310 + ], + "type": "text", + "content": ". The final loss of the model is described as follows:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 379, + 316, + 530, + 328 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 379, + 316, + 530, + 328 + ], + "spans": [ + { + "bbox": [ + 379, + 316, + 530, + 328 + ], + "type": "interline_equation", + "content": "L = L _ {1} + \\lambda * L _ {2} \\tag {11}", + "image_path": "32e7f3ecf2714137c9c8c66897200abcd60a3cab0a1607d10e43d65c08d0948b.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 296, + 332, + 530, + 379 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 332, + 530, + 379 + ], + "spans": [ + { + "bbox": [ + 296, + 332, + 530, + 379 + ], + "type": "text", + "content": "The loss ratio " + }, + { + "bbox": [ + 296, + 332, + 530, + 379 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 296, + 332, + 530, + 379 + ], + "type": "text", + "content": " starts from 1.0 and decreases to 0.05 during the training. For a fair comparison, we adopt other details of [23] including Quasi-Hyperbolic Adam algorithm [19], and One Cycle learning rate schedule [31]." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 297, + 384, + 411, + 395 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 384, + 411, + 395 + ], + "spans": [ + { + "bbox": [ + 297, + 384, + 411, + 395 + ], + "type": "text", + "content": "4.4. Retrieval Procedure" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 296, + 402, + 530, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 402, + 530, + 495 + ], + "spans": [ + { + "bbox": [ + 296, + 402, + 530, + 495 + ], + "type": "text", + "content": "Firstly, each database vector " + }, + { + "bbox": [ + 296, + 402, + 530, + 495 + ], + "type": "inline_equation", + "content": "x_{n}" + }, + { + "bbox": [ + 296, + 402, + 530, + 495 + ], + "type": "text", + "content": " is encoded into " + }, + { + "bbox": [ + 296, + 402, + 530, + 495 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 296, + 402, + 530, + 495 + ], + "type": "text", + "content": " number of indices " + }, + { + "bbox": [ + 296, + 402, + 530, + 495 + ], + "type": "inline_equation", + "content": "l_{n} = [i_{n}^{1},\\dots,i_{n}^{M}]" + }, + { + "bbox": [ + 296, + 402, + 530, + 495 + ], + "type": "text", + "content": " by Eq. 7. Because the codebooks have " + }, + { + "bbox": [ + 296, + 402, + 530, + 495 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 296, + 402, + 530, + 495 + ], + "type": "text", + "content": " number of codewords, the required bit-budget for the indices " + }, + { + "bbox": [ + 296, + 402, + 530, + 495 + ], + "type": "inline_equation", + "content": "l_{n}" + }, + { + "bbox": [ + 296, + 402, + 530, + 495 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 296, + 402, + 530, + 495 + ], + "type": "inline_equation", + "content": "M * \\lceil \\log_2K \\rceil" + }, + { + "bbox": [ + 296, + 402, + 530, + 495 + ], + "type": "text", + "content": ". Moreover, the data points that belong to the same inverted index are stored adjacently, and the size of each cluster is stored. Thanks to this data structure of the inverted index, we can identify the " + }, + { + "bbox": [ + 296, + 402, + 530, + 495 + ], + "type": "inline_equation", + "content": "q_{\\mathrm{IVF}(x_n)}" + }, + { + "bbox": [ + 296, + 402, + 530, + 495 + ], + "type": "text", + "content": " without any additional costs in the retrieval stage." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 296, + 495, + 530, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 495, + 530, + 519 + ], + "spans": [ + { + "bbox": [ + 296, + 495, + 530, + 519 + ], + "type": "text", + "content": "Secondly, a given query " + }, + { + "bbox": [ + 296, + 495, + 530, + 519 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 296, + 495, + 530, + 519 + ], + "type": "text", + "content": " is embedded into latent features " + }, + { + "bbox": [ + 296, + 495, + 530, + 519 + ], + "type": "inline_equation", + "content": "l_{y}" + }, + { + "bbox": [ + 296, + 495, + 530, + 519 + ], + "type": "text", + "content": ", and the cluster center of the target is concatenated." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 344, + 522, + 530, + 538 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 344, + 522, + 530, + 538 + ], + "spans": [ + { + "bbox": [ + 344, + 522, + 530, + 538 + ], + "type": "interline_equation", + "content": "\\left[ l _ {y} ^ {1}, \\dots , l _ {y} ^ {M} \\right] = E \\left(\\left[ y, q _ {\\mathrm {I V F}} \\left(x _ {n}\\right) \\right]\\right). \\tag {12}", + "image_path": "db3d05375f2a492864d9cb8f232b99049f0b8f60059738e5551d444cd21cabff.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 296, + 540, + 530, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 540, + 530, + 575 + ], + "spans": [ + { + "bbox": [ + 296, + 540, + 530, + 575 + ], + "type": "text", + "content": "Then the symmetric distance between encoded query " + }, + { + "bbox": [ + 296, + 540, + 530, + 575 + ], + "type": "inline_equation", + "content": "l_{y}" + }, + { + "bbox": [ + 296, + 540, + 530, + 575 + ], + "type": "text", + "content": " and encoded target " + }, + { + "bbox": [ + 296, + 540, + 530, + 575 + ], + "type": "inline_equation", + "content": "[i_n^1, \\dots, i_n^M]" + }, + { + "bbox": [ + 296, + 540, + 530, + 575 + ], + "type": "text", + "content": " is computed by the cosine similarity as follows:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 346, + 580, + 530, + 612 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 346, + 580, + 530, + 612 + ], + "spans": [ + { + "bbox": [ + 346, + 580, + 530, + 612 + ], + "type": "interline_equation", + "content": "D _ {\\text {s y m}} (y, x _ {n}) = \\sum_ {m = 1} ^ {M} \\frac {l _ {y} ^ {m} \\cdot c _ {i _ {n} ^ {m}} ^ {m}}{| | l _ {y} ^ {m} | | | | c _ {i _ {n} ^ {m}} ^ {m} | |}. \\tag {13}", + "image_path": "5a9d15e2724994d6aec5ff67870bee298e81ad54cdfe531719a4bc8de8271c76.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 296, + 614, + 530, + 637 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 614, + 530, + 637 + ], + "spans": [ + { + "bbox": [ + 296, + 614, + 530, + 637 + ], + "type": "text", + "content": "Note that, Eq. 13 can be efficiently computed by a lookup table storing precomputed all possible symmetric distances." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 296, + 638, + 530, + 683 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 638, + 530, + 683 + ], + "spans": [ + { + "bbox": [ + 296, + 638, + 530, + 683 + ], + "type": "text", + "content": "Finally, the " + }, + { + "bbox": [ + 296, + 638, + 530, + 683 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 296, + 638, + 530, + 683 + ], + "type": "text", + "content": " top-ranked retrieved data according to the symmetric distance are then re-ranked by the more accurate asymmetric distances between uncompressed query " + }, + { + "bbox": [ + 296, + 638, + 530, + 683 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 296, + 638, + 530, + 683 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 638, + 530, + 683 + ], + "type": "inline_equation", + "content": "\\tilde{x}_n" + }, + { + "bbox": [ + 296, + 638, + 530, + 683 + ], + "type": "text", + "content": ", as follows:" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 357, + 688, + 530, + 703 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 357, + 688, + 530, + 703 + ], + "spans": [ + { + "bbox": [ + 357, + 688, + 530, + 703 + ], + "type": "interline_equation", + "content": "D _ {\\text {a s y m}} (y, x _ {n}) = \\left\\| y - \\tilde {x} _ {n} \\right\\| ^ {2}. \\tag {14}", + "image_path": "f1e118a54d61e58a402faafb60100d7e533c84aa9625fd442a1e2585f0a12d86.jpg" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 296, + 706, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 706, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 706, + 530, + 730 + ], + "type": "text", + "content": "We set the hyper-parameter " + }, + { + "bbox": [ + 296, + 706, + 530, + 730 + ], + "type": "inline_equation", + "content": "R = 200" + }, + { + "bbox": [ + 296, + 706, + 530, + 730 + ], + "type": "text", + "content": ", and we conduct an ablation study of " + }, + { + "bbox": [ + 296, + 706, + 530, + 730 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 296, + 706, + 530, + 730 + ], + "type": "text", + "content": " in Table. 7." + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 277, + 747, + 300, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 747, + 300, + 756 + ], + "spans": [ + { + "bbox": [ + 277, + 747, + 300, + 756 + ], + "type": "text", + "content": "12005" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 77, + 103, + 498, + 236 + ], + "blocks": [ + { + "bbox": [ + 77, + 103, + 498, + 236 + ], + "lines": [ + { + "bbox": [ + 77, + 103, + 498, + 236 + ], + "spans": [ + { + "bbox": [ + 77, + 103, + 498, + 236 + ], + "type": "table", + "html": "
Search typeMethod64bits encoding128bits encoding
R@1R@10R@100R@1R@10R@100
ExhaustiveOPQ0.1590.5130.8860.3500.8250.991
Catalyst + Lattice0.2460.6830.9610.4480.9080.998
LSQ0.2170.6400.9450.4110.8860.995
UNQ0.2670.7260.9730.4790.9300.998
Non-exhaustiveIVFADC (210)0.2100.6160.9250.4180.8900.995
IVFOADC (210)0.2270.6590.9500.4160.8970.996
Multi-D-ADC (28 × 28)0.2000.6130.9290.3980.8830.995
UNQ+IVF (210)0.2500.6880.9100.4400.9070.996
Ours (210)0.3290.7990.9320.4910.9290.970
", + "image_path": "db259fc8a17473294858dcf2075ad63798e279e978581545d340d4897df694fd.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 94, + 240, + 483, + 252 + ], + "lines": [ + { + "bbox": [ + 94, + 240, + 483, + 252 + ], + "spans": [ + { + "bbox": [ + 94, + 240, + 483, + 252 + ], + "type": "text", + "content": "Table 4. Experimental results on DEEP-1M dataset. The quantities of Exhaustive methods are taken from [23]" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 268, + 115, + 280 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 268, + 115, + 280 + ], + "spans": [ + { + "bbox": [ + 46, + 268, + 115, + 280 + ], + "type": "text", + "content": "5. Evaluation" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 287, + 107, + 299 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 287, + 107, + 299 + ], + "spans": [ + { + "bbox": [ + 46, + 287, + 107, + 299 + ], + "type": "text", + "content": "5.1. Protocol" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 57, + 305, + 224, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 305, + 224, + 316 + ], + "spans": [ + { + "bbox": [ + 57, + 305, + 224, + 316 + ], + "type": "text", + "content": "We evaluate our method on three datasets:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 57, + 320, + 279, + 430 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 57, + 320, + 279, + 379 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 320, + 279, + 379 + ], + "spans": [ + { + "bbox": [ + 57, + 320, + 279, + 379 + ], + "type": "text", + "content": "- SIFT-1M, SIFT-1B [16]: 128-dimensional SIFT descriptor vectors [18]. The training set includes " + }, + { + "bbox": [ + 57, + 320, + 279, + 379 + ], + "type": "inline_equation", + "content": "\\{500k, 10^8\\}" + }, + { + "bbox": [ + 57, + 320, + 279, + 379 + ], + "type": "text", + "content": " vectors for 1M and 1B, respectively. Sets for evaluation have " + }, + { + "bbox": [ + 57, + 320, + 279, + 379 + ], + "type": "inline_equation", + "content": "10^4" + }, + { + "bbox": [ + 57, + 320, + 279, + 379 + ], + "type": "text", + "content": " queries and " + }, + { + "bbox": [ + 57, + 320, + 279, + 379 + ], + "type": "inline_equation", + "content": "\\{10^6, 10^9\\}" + }, + { + "bbox": [ + 57, + 320, + 279, + 379 + ], + "type": "text", + "content": " number of database for 1M and 1B, respectively." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 57, + 383, + 279, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 383, + 279, + 430 + ], + "spans": [ + { + "bbox": [ + 57, + 383, + 279, + 430 + ], + "type": "text", + "content": "- DEEP-1M [4]: 96-dimensional DNN features extracted from the last fully-connected layer of GoogLeNet [33]. It also includes " + }, + { + "bbox": [ + 57, + 383, + 279, + 430 + ], + "type": "inline_equation", + "content": "500k" + }, + { + "bbox": [ + 57, + 383, + 279, + 430 + ], + "type": "text", + "content": " training data, " + }, + { + "bbox": [ + 57, + 383, + 279, + 430 + ], + "type": "inline_equation", + "content": "10^{4}" + }, + { + "bbox": [ + 57, + 383, + 279, + 430 + ], + "type": "text", + "content": " queries, and " + }, + { + "bbox": [ + 57, + 383, + 279, + 430 + ], + "type": "inline_equation", + "content": "10^{6}" + }, + { + "bbox": [ + 57, + 383, + 279, + 430 + ], + "type": "text", + "content": " database." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 45, + 433, + 279, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 433, + 279, + 502 + ], + "spans": [ + { + "bbox": [ + 45, + 433, + 279, + 502 + ], + "type": "text", + "content": "The ground truth of a given query is defined as the top-1 nearest neighbor from an uncompressed database. Then, the retrieval performance in compressed space is measured by average " + }, + { + "bbox": [ + 45, + 433, + 279, + 502 + ], + "type": "inline_equation", + "content": "recall@R" + }, + { + "bbox": [ + 45, + 433, + 279, + 502 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 45, + 433, + 279, + 502 + ], + "type": "inline_equation", + "content": "R = \\{1, 10, 100\\}" + }, + { + "bbox": [ + 45, + 433, + 279, + 502 + ], + "type": "text", + "content": ". The " + }, + { + "bbox": [ + 45, + 433, + 279, + 502 + ], + "type": "inline_equation", + "content": "recall@R" + }, + { + "bbox": [ + 45, + 433, + 279, + 502 + ], + "type": "text", + "content": " represents the ratio of queries that contains the ground truth in top- " + }, + { + "bbox": [ + 45, + 433, + 279, + 502 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 45, + 433, + 279, + 502 + ], + "type": "text", + "content": " retrieved vectors." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 45, + 503, + 279, + 630 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 503, + 279, + 630 + ], + "spans": [ + { + "bbox": [ + 45, + 503, + 279, + 630 + ], + "type": "text", + "content": "Unless specified, we consistently use the following hyper-parameters. We set " + }, + { + "bbox": [ + 45, + 503, + 279, + 630 + ], + "type": "inline_equation", + "content": "K' = 2^{10}" + }, + { + "bbox": [ + 45, + 503, + 279, + 630 + ], + "type": "text", + "content": " for inverted index on million-scale datasets, and " + }, + { + "bbox": [ + 45, + 503, + 279, + 630 + ], + "type": "inline_equation", + "content": "K' = 2^{12} \\times 2^{12}" + }, + { + "bbox": [ + 45, + 503, + 279, + 630 + ], + "type": "text", + "content": " for inverted multi-index on billion-scale dataset. The bit budget is controlled by the number of codebooks " + }, + { + "bbox": [ + 45, + 503, + 279, + 630 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 45, + 503, + 279, + 630 + ], + "type": "text", + "content": " and the number of codewords " + }, + { + "bbox": [ + 45, + 503, + 279, + 630 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 45, + 503, + 279, + 630 + ], + "type": "text", + "content": ". We fix the " + }, + { + "bbox": [ + 45, + 503, + 279, + 630 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 45, + 503, + 279, + 630 + ], + "type": "text", + "content": " as 256, and control the bit-budgets by changing " + }, + { + "bbox": [ + 45, + 503, + 279, + 630 + ], + "type": "inline_equation", + "content": "M = \\{8,16\\}" + }, + { + "bbox": [ + 45, + 503, + 279, + 630 + ], + "type": "text", + "content": " for 64bits and 128bits, respectively. We follow the setting of " + }, + { + "bbox": [ + 45, + 503, + 279, + 630 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 45, + 503, + 279, + 630 + ], + "type": "text", + "content": " from [7, 24] for a fair comparison. For each query, it visits " + }, + { + "bbox": [ + 45, + 503, + 279, + 630 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 45, + 503, + 279, + 630 + ], + "type": "text", + "content": " inverted indices that guarantee at least " + }, + { + "bbox": [ + 45, + 503, + 279, + 630 + ], + "type": "inline_equation", + "content": "\\{50k,10^5\\}" + }, + { + "bbox": [ + 45, + 503, + 279, + 630 + ], + "type": "text", + "content": " candidates for million-scale datasets and billion-scale datasets, respectively." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 45, + 631, + 279, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 631, + 279, + 666 + ], + "spans": [ + { + "bbox": [ + 45, + 631, + 279, + 666 + ], + "type": "text", + "content": "We compare the proposed method with two sets of state-of-the-arts that are exhaustive and non-exhaustive methods. In particular, exhaustive methods include the followings:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 57, + 668, + 278, + 731 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 57, + 668, + 278, + 690 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 668, + 278, + 690 + ], + "spans": [ + { + "bbox": [ + 57, + 668, + 278, + 690 + ], + "type": "text", + "content": "- OPQ [9, 25]: Product Quantization [16] with optimized space decomposition." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 57, + 694, + 278, + 716 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 694, + 278, + 716 + ], + "spans": [ + { + "bbox": [ + 57, + 694, + 278, + 716 + ], + "type": "text", + "content": "- Catalyst + Lattice [28]: Learning spreaded space that fits with pre-defined lattice." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 57, + 720, + 256, + 731 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 720, + 256, + 731 + ], + "spans": [ + { + "bbox": [ + 57, + 720, + 256, + 731 + ], + "type": "text", + "content": "- LSQ [20]: The state-of-the-art of shallow MCQ." + } + ] + } + ], + "index": 13 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 308, + 269, + 487, + 282 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 269, + 487, + 282 + ], + "spans": [ + { + "bbox": [ + 308, + 269, + 487, + 282 + ], + "type": "text", + "content": "- UNQ [23]: A deep generalization of MCQ." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 297, + 284, + 521, + 296 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 284, + 521, + 296 + ], + "spans": [ + { + "bbox": [ + 297, + 284, + 521, + 296 + ], + "type": "text", + "content": "Plus, the non-exhaustive methods include the followings:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 308, + 298, + 529, + 506 + ], + "type": "list", + "angle": 0, + "index": 25, + "blocks": [ + { + "bbox": [ + 308, + 298, + 529, + 321 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 298, + 529, + 321 + ], + "spans": [ + { + "bbox": [ + 308, + 298, + 529, + 321 + ], + "type": "text", + "content": "- IVFADC [16]: Product Quantization [16] with the Inverted index [30] and the residual encoding." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 308, + 325, + 529, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 325, + 529, + 348 + ], + "spans": [ + { + "bbox": [ + 308, + 325, + 529, + 348 + ], + "type": "text", + "content": "- IVFOADC [9, 25]: OPQ with the inverted index [30] and the residual encoding." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 308, + 351, + 521, + 362 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 351, + 521, + 362 + ], + "spans": [ + { + "bbox": [ + 308, + 351, + 521, + 362 + ], + "type": "text", + "content": "- Multi-D-ADC [3]: The Inverted Multi-Index (IMI)." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 308, + 366, + 514, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 366, + 514, + 378 + ], + "spans": [ + { + "bbox": [ + 308, + 366, + 514, + 378 + ], + "type": "text", + "content": "- OMulti-D-OADC [9,25]: The IMI with the OPQ." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 308, + 381, + 529, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 381, + 529, + 403 + ], + "spans": [ + { + "bbox": [ + 308, + 381, + 529, + 403 + ], + "type": "text", + "content": "- QAI [24]: Jointly optimized inverted index and quantizer." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 308, + 407, + 529, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 407, + 529, + 431 + ], + "spans": [ + { + "bbox": [ + 308, + 407, + 529, + 431 + ], + "type": "text", + "content": "- IVFOADC + GP [5]: IVFOADC with grouping and pruning algorithm of [5]." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 308, + 434, + 529, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 434, + 529, + 468 + ], + "spans": [ + { + "bbox": [ + 308, + 434, + 529, + 468 + ], + "type": "text", + "content": "- UNQ + IVF: Inverted file system with the UNQ. We omit the residual encoding because it is incompatible with the deep MCQ algorithm (Table. 1)." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 308, + 473, + 529, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 473, + 529, + 506 + ], + "spans": [ + { + "bbox": [ + 308, + 473, + 529, + 506 + ], + "type": "text", + "content": "- Ours: Proposed disentangled representation learning. We select a single index for the million-scale datasets and a multi-index for the billion-scale dataset." + } + ] + } + ], + "index": 24 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 297, + 513, + 463, + 525 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 513, + 463, + 525 + ], + "spans": [ + { + "bbox": [ + 297, + 513, + 463, + 525 + ], + "type": "text", + "content": "5.2. Result on Million-Scale Dataset" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 296, + 532, + 530, + 671 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 532, + 530, + 671 + ], + "spans": [ + { + "bbox": [ + 296, + 532, + 530, + 671 + ], + "type": "text", + "content": "Table. 3 and Table. 4 report the recall@R scores of exhaustive and non-exhaustive ANN search methods with " + }, + { + "bbox": [ + 296, + 532, + 530, + 671 + ], + "type": "inline_equation", + "content": "\\{64,128\\}" + }, + { + "bbox": [ + 296, + 532, + 530, + 671 + ], + "type": "text", + "content": " bits encoding. For all combinations of the dataset and bit budget, the proposed method outperforms the nonexhaustive baselines by a large margin. For example, Ours improves the R@1 score of Multi-D-ADC+QAI about " + }, + { + "bbox": [ + 296, + 532, + 530, + 671 + ], + "type": "inline_equation", + "content": "25\\%" + }, + { + "bbox": [ + 296, + 532, + 530, + 671 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 532, + 530, + 671 + ], + "type": "inline_equation", + "content": "17\\%" + }, + { + "bbox": [ + 296, + 532, + 530, + 671 + ], + "type": "text", + "content": " for 64 and 128bits encoding respectively on the SIFT-1M dataset. On the DEEP-1M dataset, the performance gains between Ours and Multi-D-ADC are much larger than the gains on the SIFT-1M, where the gaps are about " + }, + { + "bbox": [ + 296, + 532, + 530, + 671 + ], + "type": "inline_equation", + "content": "65\\%" + }, + { + "bbox": [ + 296, + 532, + 530, + 671 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 532, + 530, + 671 + ], + "type": "inline_equation", + "content": "23\\%" + }, + { + "bbox": [ + 296, + 532, + 530, + 671 + ], + "type": "text", + "content": " for 64 and 128bits encoding, respectively." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 296, + 671, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 671, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 671, + 530, + 730 + ], + "type": "text", + "content": "Notably, the proposed method even outperforms the exhaustive ANN methods while the proposed method is a nonexhaustive search where only " + }, + { + "bbox": [ + 296, + 671, + 530, + 730 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 296, + 671, + 530, + 730 + ], + "type": "text", + "content": " of the database is considered for the distance computation. For instance, Ours improves the R@1 score of the exhaustive UNQ by about" + } + ] + } + ], + "index": 28 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 277, + 747, + 301, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 747, + 301, + 756 + ], + "spans": [ + { + "bbox": [ + 277, + 747, + 301, + 756 + ], + "type": "text", + "content": "12006" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 103, + 292, + 237 + ], + "blocks": [ + { + "bbox": [ + 47, + 103, + 292, + 237 + ], + "lines": [ + { + "bbox": [ + 47, + 103, + 292, + 237 + ], + "spans": [ + { + "bbox": [ + 47, + 103, + 292, + 237 + ], + "type": "table", + "html": "
MethodR@1R@10R@100
Exhaustive Search
Catalyst + Lattice0.3110.7780.983
LSQ0.3800.8560.993
UNQ0.3830.8680.994
Non-Exhaustive Search
IVFADC (220)0.3510.7860.918
Multi-D-ADC (214 × 214)0.3440.8090.960
OMulti-D-OADC (214 × 214)0.3730.8410.973
IVFOADC+GP (220)0.4050.8510.957
Ours (212 × 212)0.4580.8590.903
", + "image_path": "ff5415fcfce53aafe72adab6066ece11403939233a7c1123acde719a5b5ad384.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 285, + 279, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 285, + 279, + 308 + ], + "spans": [ + { + "bbox": [ + 45, + 285, + 279, + 308 + ], + "type": "inline_equation", + "content": "15\\%" + }, + { + "bbox": [ + 45, + 285, + 279, + 308 + ], + "type": "text", + "content": " on the SIFT-1M and " + }, + { + "bbox": [ + 45, + 285, + 279, + 308 + ], + "type": "inline_equation", + "content": "23\\%" + }, + { + "bbox": [ + 45, + 285, + 279, + 308 + ], + "type": "text", + "content": " on the DEEP-1M dataset with 64bits bit budget." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 309, + 279, + 402 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 309, + 279, + 402 + ], + "spans": [ + { + "bbox": [ + 45, + 309, + 279, + 402 + ], + "type": "text", + "content": "As our motivation, a naive combination of the UNQ and the inverted index does not improve the performance of the exhaustive UNQ. For example, the UNQ+IVF drops the R@1 score of the exhaustive UNQ about " + }, + { + "bbox": [ + 45, + 309, + 279, + 402 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 45, + 309, + 279, + 402 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 309, + 279, + 402 + ], + "type": "inline_equation", + "content": "7\\%" + }, + { + "bbox": [ + 45, + 309, + 279, + 402 + ], + "type": "text", + "content": " for SIFT-1M and DEEP-1M with 64bits bit budget, respectively. The disentangled representation of Ours improves the R@1 scores of UNQ+IVF about " + }, + { + "bbox": [ + 45, + 309, + 279, + 402 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 45, + 309, + 279, + 402 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 309, + 279, + 402 + ], + "type": "inline_equation", + "content": "32\\%" + }, + { + "bbox": [ + 45, + 309, + 279, + 402 + ], + "type": "text", + "content": " on SIFT-1M and DEEP-1M with 64bits bit budget, respectively." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 408, + 208, + 420 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 408, + 208, + 420 + ], + "spans": [ + { + "bbox": [ + 45, + 408, + 208, + 420 + ], + "type": "text", + "content": "5.3. Result on Billion-Scale Dataset" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 426, + 279, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 426, + 279, + 507 + ], + "spans": [ + { + "bbox": [ + 45, + 426, + 279, + 507 + ], + "type": "text", + "content": "We conduct an experiment on a billion-scale dataset to verify the scalability of the proposed method. Table. 5 reports the experimental results on the SIFT-1B dataset with 128bit budget. The improvement in the R@1 score of Ours over IVFOADC+GP is about " + }, + { + "bbox": [ + 45, + 426, + 279, + 507 + ], + "type": "inline_equation", + "content": "13\\%" + }, + { + "bbox": [ + 45, + 426, + 279, + 507 + ], + "type": "text", + "content": ". Moreover, Ours shows " + }, + { + "bbox": [ + 45, + 426, + 279, + 507 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 45, + 426, + 279, + 507 + ], + "type": "text", + "content": " of improvement compared to the UNQ while Ours is a non-exhaustive search and the UNQ is an exhaustive search." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 507, + 279, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 507, + 279, + 577 + ], + "spans": [ + { + "bbox": [ + 45, + 507, + 279, + 577 + ], + "type": "text", + "content": "Notably, the margin of improvement is much larger with the SIFT-1B dataset than the SIFT-1M dataset with 128bits encoding. Because the billion-scale task is a much more challenging task than the million-scale task with an identical bit budget, the billion-scale task has much more room for performance gain." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 577, + 279, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 577, + 279, + 659 + ], + "spans": [ + { + "bbox": [ + 45, + 577, + 279, + 659 + ], + "type": "text", + "content": "Furthermore, we choose a conventional Multi-D-ADC algorithm with " + }, + { + "bbox": [ + 45, + 577, + 279, + 659 + ], + "type": "inline_equation", + "content": "2^{12} \\times 2^{12}" + }, + { + "bbox": [ + 45, + 577, + 279, + 659 + ], + "type": "text", + "content": " number of indices for learning the inverted index because our contribution is not about the inverted index. However, the experimental results demonstrate the superiority of Ours compared to methods with much finer inverted index " + }, + { + "bbox": [ + 45, + 577, + 279, + 659 + ], + "type": "inline_equation", + "content": "(2^{14} \\times 2^{14})" + }, + { + "bbox": [ + 45, + 577, + 279, + 659 + ], + "type": "text", + "content": " and a sophisticated inverted indexing algorithm (IVFOADC+GP)." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 665, + 137, + 677 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 665, + 137, + 677 + ], + "spans": [ + { + "bbox": [ + 45, + 665, + 137, + 677 + ], + "type": "text", + "content": "5.4. Ablation Study" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 45, + 682, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 682, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 682, + 279, + 730 + ], + "type": "text", + "content": "We validate our method with ablation study on two hyper-parameters. First, Table. 6 shows ablation study about the number of visited inverted indices " + }, + { + "bbox": [ + 45, + 682, + 279, + 730 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 45, + 682, + 279, + 730 + ], + "type": "text", + "content": " on the SIFT-1M with 64bits encoding. Ours consistently improves" + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 298, + 103, + 545, + 284 + ], + "blocks": [ + { + "bbox": [ + 45, + 244, + 279, + 267 + ], + "lines": [ + { + "bbox": [ + 45, + 244, + 279, + 267 + ], + "spans": [ + { + "bbox": [ + 45, + 244, + 279, + 267 + ], + "type": "text", + "content": "Table 5. Experimental results on the SIFT-1B dataset and 128bits bit-budget. All the quantities except Ours are taken from [5,9,23]." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 298, + 103, + 545, + 284 + ], + "lines": [ + { + "bbox": [ + 298, + 103, + 545, + 284 + ], + "spans": [ + { + "bbox": [ + 298, + 103, + 545, + 284 + ], + "type": "table", + "html": "
MethodwR@1R@10R@100
UNQ+IVF (w/o residual)10.2160.4120.442
Ours0.2530.4300.442
UNQ+IVF (w/o residual)20.2720.5560.612
Ours0.3170.5880.613
UNQ+IVF (w/o residual)40.3050.6740.763
Ours0.3610.7200.765
UNQ+IVF (w/o residual)80.3220.7530.877
Ours0.3870.8090.880
UNQ+IVF (w/o residual)160.3310.7910.945
Ours0.3970.8570.947
UNQ+IVF (w/o residual)320.3320.8040.977
Ours0.3990.8760.979
UNQ+IVF (w/o residual)640.3320.8060.985
Ours0.3990.8800.987
", + "image_path": "e37d6c1b5f89d69cc2de0d540ff24268a89ea109a19878b798e97d9e0edac011.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 296, + 292, + 530, + 314 + ], + "lines": [ + { + "bbox": [ + 296, + 292, + 530, + 314 + ], + "spans": [ + { + "bbox": [ + 296, + 292, + 530, + 314 + ], + "type": "text", + "content": "Table 6. Ablation study about the number of visited inverted indices on the SIFT-1M dataset with 64bits bit budget." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 296, + 336, + 530, + 406 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 336, + 530, + 406 + ], + "spans": [ + { + "bbox": [ + 296, + 336, + 530, + 406 + ], + "type": "text", + "content": "UNQ+IVF regardless of the number of " + }, + { + "bbox": [ + 296, + 336, + 530, + 406 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 296, + 336, + 530, + 406 + ], + "type": "text", + "content": ". For example, the performance gain of the R@1 score is about 17% with " + }, + { + "bbox": [ + 296, + 336, + 530, + 406 + ], + "type": "inline_equation", + "content": "w = 1" + }, + { + "bbox": [ + 296, + 336, + 530, + 406 + ], + "type": "text", + "content": " and 20% with " + }, + { + "bbox": [ + 296, + 336, + 530, + 406 + ], + "type": "inline_equation", + "content": "w = 64" + }, + { + "bbox": [ + 296, + 336, + 530, + 406 + ], + "type": "text", + "content": ". Moreover, these experimental results also highlight that the R@1 score of Ours with only " + }, + { + "bbox": [ + 296, + 336, + 530, + 406 + ], + "type": "inline_equation", + "content": "w = 4" + }, + { + "bbox": [ + 296, + 336, + 530, + 406 + ], + "type": "text", + "content": " (out of 1024) is even superior to the exhaustive UNQ in Table.3." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 296, + 408, + 531, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 408, + 531, + 548 + ], + "spans": [ + { + "bbox": [ + 296, + 408, + 531, + 548 + ], + "type": "text", + "content": "Second, we verify with various numbers of re-ranking candidates " + }, + { + "bbox": [ + 296, + 408, + 531, + 548 + ], + "type": "inline_equation", + "content": "R = \\{1, 10, 100, 1000\\}" + }, + { + "bbox": [ + 296, + 408, + 531, + 548 + ], + "type": "text", + "content": ". It is identical to exclude the re-ranking if " + }, + { + "bbox": [ + 296, + 408, + 531, + 548 + ], + "type": "inline_equation", + "content": "R = 1" + }, + { + "bbox": [ + 296, + 408, + 531, + 548 + ], + "type": "text", + "content": ". Table. 7 shows the experimental results on the SIFT-1M and the DEEP-1M datasets with 64bits encoding. For the SIFT-1M dataset, Ours improves the more performance with the fewer number of re-ranking. For example, the performance gains of the R@1 score are about " + }, + { + "bbox": [ + 296, + 408, + 531, + 548 + ], + "type": "inline_equation", + "content": "\\{62\\%, 28\\%, 21\\%, 20\\% \\}" + }, + { + "bbox": [ + 296, + 408, + 531, + 548 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 296, + 408, + 531, + 548 + ], + "type": "inline_equation", + "content": "R = \\{1, 10, 100, 1000\\}" + }, + { + "bbox": [ + 296, + 408, + 531, + 548 + ], + "type": "text", + "content": ", respectively. On the other hand, Ours improves the more performance with the larger number of re-ranking for the DEEP-1M dataset where the performance gains of the R@1 score are about " + }, + { + "bbox": [ + 296, + 408, + 531, + 548 + ], + "type": "inline_equation", + "content": "\\{17\\%, 29\\%, 32\\%, 32\\% \\}" + }, + { + "bbox": [ + 296, + 408, + 531, + 548 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 297, + 559, + 456, + 571 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 559, + 456, + 571 + ], + "spans": [ + { + "bbox": [ + 297, + 559, + 456, + 571 + ], + "type": "text", + "content": "5.5. Validation of Disentanglement" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 296, + 578, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 578, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 578, + 530, + 730 + ], + "type": "text", + "content": "We validate disentangled representation of the proposed method by generating new data points. Likewise disentanglement methods for generative models, we generate data points that have desired characteristics by controlling the input of the decoder. In detail, a reconstructed data point " + }, + { + "bbox": [ + 296, + 578, + 530, + 730 + ], + "type": "inline_equation", + "content": "\\tilde{x}_n" + }, + { + "bbox": [ + 296, + 578, + 530, + 730 + ], + "type": "text", + "content": " should belong to a specific cluster by substituting the " + }, + { + "bbox": [ + 296, + 578, + 530, + 730 + ], + "type": "inline_equation", + "content": "q_{\\mathrm{IVF}}(x_n)" + }, + { + "bbox": [ + 296, + 578, + 530, + 730 + ], + "type": "text", + "content": " by a desired cluster center " + }, + { + "bbox": [ + 296, + 578, + 530, + 730 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 296, + 578, + 530, + 730 + ], + "type": "text", + "content": ". We randomly sample " + }, + { + "bbox": [ + 296, + 578, + 530, + 730 + ], + "type": "inline_equation", + "content": "10^{4}" + }, + { + "bbox": [ + 296, + 578, + 530, + 730 + ], + "type": "text", + "content": " data points from the database and generate about " + }, + { + "bbox": [ + 296, + 578, + 530, + 730 + ], + "type": "inline_equation", + "content": "10^{7}" + }, + { + "bbox": [ + 296, + 578, + 530, + 730 + ], + "type": "text", + "content": " new data points by concatenating " + }, + { + "bbox": [ + 296, + 578, + 530, + 730 + ], + "type": "inline_equation", + "content": "K^{\\prime} = 1024" + }, + { + "bbox": [ + 296, + 578, + 530, + 730 + ], + "type": "text", + "content": " number of cluster centers to each " + }, + { + "bbox": [ + 296, + 578, + 530, + 730 + ], + "type": "inline_equation", + "content": "l_{n}" + }, + { + "bbox": [ + 296, + 578, + 530, + 730 + ], + "type": "text", + "content": ". Table. 8 reports the ratio of generated data points that belong to the desired cluster within top-R nearest clusters. The R@1 score of SIFT-1M and DEEP-1M datasets are 0.709 and 0.827, respectively" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 277, + 747, + 300, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 747, + 300, + 756 + ], + "spans": [ + { + "bbox": [ + 277, + 747, + 300, + 756 + ], + "type": "text", + "content": "12007" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 58, + 103, + 265, + 332 + ], + "blocks": [ + { + "bbox": [ + 58, + 103, + 265, + 332 + ], + "lines": [ + { + "bbox": [ + 58, + 103, + 265, + 332 + ], + "spans": [ + { + "bbox": [ + 58, + 103, + 265, + 332 + ], + "type": "table", + "html": "
Method# of re-rankR@1
SIFT-1M 64bits
UNQ+IVF (w/o residual) Oursw/o re-rank0.146 0.236
UNQ+IVF (w/o residual) Ours100.292 0.375
UNQ+IVF (w/o residual) Ours1000.329 0.397
UNQ+IVF (w/o residual) Ours10000.332 0.399
DEEP-1M 64bits
UNQ+IVF (w/o residual) Oursw/o re-rank0.134 0.157
UNQ+IVF (w/o residual) Ours100.228 0.295
UNQ+IVF (w/o residual) Ours1000.248 0.328
UNQ+IVF (w/o residual) Ours10000.249 0.329
", + "image_path": "28edd2e2ea6916d85e785fed35c4bb5ff6e91c5615601ad97ac04db7d9141fb9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 378, + 279, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 378, + 279, + 426 + ], + "spans": [ + { + "bbox": [ + 45, + 378, + 279, + 426 + ], + "type": "text", + "content": "while the probability of belonging to the desired cluster of a randomly generated vector is 0.001. The experimental results confirm that the proposed representation is well disentangled as we intended." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 432, + 154, + 445 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 432, + 154, + 445 + ], + "spans": [ + { + "bbox": [ + 46, + 432, + 154, + 445 + ], + "type": "text", + "content": "5.6. Overhead Analysis" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 450, + 279, + 717 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 450, + 279, + 717 + ], + "spans": [ + { + "bbox": [ + 45, + 450, + 279, + 717 + ], + "type": "text", + "content": "Finally, we analyze the search time overhead of the proposed method. Table. 9 demonstrates the average search time of Multi-D-ADC and Ours with identical cluster centers of the inverted index. The retrieval procedure of Ours is similar to the Multi-D-ADC except the additional encoding (Eq. 12) and decoding (Eq. 8) steps. In encoding query (Eq. 12), a query " + }, + { + "bbox": [ + 45, + 450, + 279, + 717 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 45, + 450, + 279, + 717 + ], + "type": "text", + "content": " should be concatenated with " + }, + { + "bbox": [ + 45, + 450, + 279, + 717 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 45, + 450, + 279, + 717 + ], + "type": "text", + "content": " number of cluster centers and embedded " + }, + { + "bbox": [ + 45, + 450, + 279, + 717 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 45, + 450, + 279, + 717 + ], + "type": "text", + "content": " times to build the lookup table. To accelerate the encoding query, we propose batch-forwarding " + }, + { + "bbox": [ + 45, + 450, + 279, + 717 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 45, + 450, + 279, + 717 + ], + "type": "text", + "content": " number of lookup tables at once while the Multi-D-ADC build the lookup table in sequence. Similarly, the decoding top-R (Eq. 8) also can be simply accelerated by batch-forwarding. The re-ranking time (Eq. 14) is negligible because the number of re-ranked data " + }, + { + "bbox": [ + 45, + 450, + 279, + 717 + ], + "type": "inline_equation", + "content": "(R = 200)" + }, + { + "bbox": [ + 45, + 450, + 279, + 717 + ], + "type": "text", + "content": " is small. The overall search time of Ours is about " + }, + { + "bbox": [ + 45, + 450, + 279, + 717 + ], + "type": "inline_equation", + "content": "12\\%" + }, + { + "bbox": [ + 45, + 450, + 279, + 717 + ], + "type": "text", + "content": " slower than the Multi-D-ADC, but we believe it is permissible compared to the performance gain of Ours. Nevertheless, Ours speeds up the search procedure of the UNQ, which requires more than a minute in an exhaustive search. The experimental results are obtained in a single-CPU mode of a " + }, + { + "bbox": [ + 45, + 450, + 279, + 717 + ], + "type": "inline_equation", + "content": "2.2\\mathrm{GHz}" + }, + { + "bbox": [ + 45, + 450, + 279, + 717 + ], + "type": "text", + "content": " Intel Xeon processor with Faiss [17], and the encoding and decoding times are measured in a single Nvidia Tesla V100 GPU with Pytorch [27]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 57, + 718, + 278, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 718, + 278, + 730 + ], + "spans": [ + { + "bbox": [ + 57, + 718, + 278, + 730 + ], + "type": "text", + "content": "The proposed method requires " + }, + { + "bbox": [ + 57, + 718, + 278, + 730 + ], + "type": "inline_equation", + "content": "\\{21,32\\} \\mathrm{MB}" + }, + { + "bbox": [ + 57, + 718, + 278, + 730 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 57, + 718, + 278, + 730 + ], + "type": "inline_equation", + "content": "\\{64," + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 303, + 104, + 526, + 154 + ], + "blocks": [ + { + "bbox": [ + 45, + 337, + 279, + 358 + ], + "lines": [ + { + "bbox": [ + 45, + 337, + 279, + 358 + ], + "spans": [ + { + "bbox": [ + 45, + 337, + 279, + 358 + ], + "type": "text", + "content": "Table 7. Ablation study about the number of re-ranked candidates on million-scale datasets with 64bits bit budget." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 303, + 104, + 526, + 154 + ], + "lines": [ + { + "bbox": [ + 303, + 104, + 526, + 154 + ], + "spans": [ + { + "bbox": [ + 303, + 104, + 526, + 154 + ], + "type": "table", + "html": "
DatasetMethodR@1R@3R@5
SIFT-1MD([ln, T])0.7090.9230.968
DEEP-1MD([ln, T])0.8270.9650.987
-Random0.0010.0030.005
", + "image_path": "84297fd9e93a8c1fabd97e42f34aacbe8620dbb00c958f73dd0d8b83387660b0.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 308, + 219, + 520, + 304 + ], + "blocks": [ + { + "bbox": [ + 296, + 161, + 531, + 204 + ], + "lines": [ + { + "bbox": [ + 296, + 161, + 531, + 204 + ], + "spans": [ + { + "bbox": [ + 296, + 161, + 531, + 204 + ], + "type": "text", + "content": "Table 8. Experiment to validate disentanglement of proposed method with 64bits bit-budget. The score represents the ratio of generated data points that belong to desired cluster within top-R nearest clusters." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 219, + 520, + 304 + ], + "lines": [ + { + "bbox": [ + 308, + 219, + 520, + 304 + ], + "spans": [ + { + "bbox": [ + 308, + 219, + 520, + 304 + ], + "type": "table", + "html": "
MethodTime (ms)
Multi-D-ADC (212 × 212)16.89
Ours (212 × 212)18.88
1. encoding query (Eq. 12)1.27
2. symmetric search (Eq. 13)16.86
3. decoding top-R (Eq. 8)0.70
4. asymmetric re-ranking (Eq. 14)0.04
", + "image_path": "5bbbaffda998e4148d342cad54094291f7be0d0f6a46d5940bbf263c5b41413e.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 296, + 312, + 530, + 334 + ], + "lines": [ + { + "bbox": [ + 296, + 312, + 530, + 334 + ], + "spans": [ + { + "bbox": [ + 296, + 312, + 530, + 334 + ], + "type": "text", + "content": "Table 9. Search time analysis on the SIFT-1B dataset and 128bits bit-budget." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 297, + 358, + 530, + 405 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 358, + 530, + 405 + ], + "spans": [ + { + "bbox": [ + 297, + 358, + 530, + 405 + ], + "type": "text", + "content": "128} bits encoding where the UNQ requires " + }, + { + "bbox": [ + 297, + 358, + 530, + 405 + ], + "type": "inline_equation", + "content": "\\{20, 30\\}\\mathrm{MB}" + }, + { + "bbox": [ + 297, + 358, + 530, + 405 + ], + "type": "text", + "content": " for the same budget. Note that those additional memory usage is not proportional to the database size, thus it is same for 1M and 1B database." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 298, + 421, + 368, + 434 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 421, + 368, + 434 + ], + "spans": [ + { + "bbox": [ + 298, + 421, + 368, + 434 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 296, + 443, + 530, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 443, + 530, + 653 + ], + "spans": [ + { + "bbox": [ + 296, + 443, + 530, + 653 + ], + "type": "text", + "content": "In this paper, we propose a novel disentangled representation learning for unsupervised neural quantization. We firstly discover the cause of limited application of the deep quantization (UNQ [23]) on non-exhaustive search with the inverted index. Specifically, the deep quantizer is hard to exploit the compact representation of residual vector space and even takes disadvantages such as loss of cluster center information. To address the problem, we disentangle the information of the cluster center and the latent space by feeding the center to both the encoder and decoder to make center information redundant for the decoder. Similar to residual encoding, this disentanglement encourages the latent space compact and quantization-friendly by taking out the center information from latent space, so the quantization distortion is significantly reduced with disentangled representation. Extensive experiments on various datasets from million to billion scales validate the superiority of the proposed method over state-of-the-art retrieval systems." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 296, + 660, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 660, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 660, + 530, + 730 + ], + "type": "text", + "content": "Acknowledgements. This work was supported in part by ETRI grant funded by the Korean government [23ZH1200, The research of the fundamental media-contents technologies for hyper-realistic media space], and MSIT/IITP [2019-0-00421], MSIT/NRF [NRF-2022R1F1A1076132], and MSIT&KNPA/KIPoT [Police Lab 2.0, 210121M06]." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 277, + 747, + 300, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 747, + 300, + 756 + ], + "spans": [ + { + "bbox": [ + 277, + 747, + 300, + 756 + ], + "type": "text", + "content": "12008" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 105, + 103, + 117 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 105, + 103, + 117 + ], + "spans": [ + { + "bbox": [ + 47, + 105, + 103, + 117 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 124, + 280, + 730 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 51, + 124, + 279, + 165 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 124, + 279, + 165 + ], + "spans": [ + { + "bbox": [ + 51, + 124, + 279, + 165 + ], + "type": "text", + "content": "[1] Alexandr Andoni and Piotr Indyk. 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PMLR, 2014. 2" + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 278, + 747, + 300, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 278, + 747, + 300, + 756 + ], + "spans": [ + { + "bbox": [ + 278, + 747, + 300, + 756 + ], + "type": "text", + "content": "12010" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Disentangling Orthogonal Planes for Indoor Panoramic Room Layout Estimation With Cross-Scale Distortion Awareness/13fac3e7-4155-4a84-8381-fe68c09139a8_content_list.json b/2023/Disentangling Orthogonal Planes for Indoor Panoramic Room Layout Estimation With Cross-Scale Distortion Awareness/13fac3e7-4155-4a84-8381-fe68c09139a8_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..ea0ee2102c6e0ae357712da21ab7a0c596f9df8d --- /dev/null +++ b/2023/Disentangling Orthogonal Planes for Indoor Panoramic Room Layout Estimation With Cross-Scale Distortion Awareness/13fac3e7-4155-4a84-8381-fe68c09139a8_content_list.json @@ -0,0 +1,1680 @@ +[ + { + "type": "text", + "text": "Disentangling Orthogonal Planes for Indoor Panoramic Room Layout Estimation with Cross-Scale Distortion Awareness", + "text_level": 1, + "bbox": [ + 133, + 130, + 836, + 174 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Zhijie Shen, Zishuo Zheng, Chunyu Lin†, Lang Nie, Kang Liao, Shuai Zheng, and Yao Zhao Institute of Information Science, Beijing Jiaotong University, China Beijing Key Laboratory of Advanced Information Science and Network Technology", + "bbox": [ + 119, + 203, + 848, + 257 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{zhjshen, zszheng, cylin, nielang, kang_liao, zsl997, yzhao}@bjtu.edu.cn", + "bbox": [ + 166, + 258, + 797, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 309, + 313, + 325 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Based on the Manhattan World assumption, most existing indoor layout estimation schemes focus on recovering layouts from vertically compressed 1D sequences. However, the compression procedure confuses the semantics of different planes, yielding inferior performance with ambiguous interpretability.", + "bbox": [ + 76, + 342, + 468, + 433 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To address this issue, we propose to disentangle this 1D representation by pre-segmenting orthogonal (vertical and horizontal) planes from a complex scene, explicitly capturing the geometric cues for indoor layout estimation. Considering the symmetry between the floor boundary and ceiling boundary, we also design a soft-flipping fusion strategy to assist the pre-segmentation. Besides, we present a feature assembling mechanism to effectively integrate shallow and deep features with distortion distribution awareness. To compensate for the potential errors in pre-segmentation, we further leverage triple attention to reconstruct the disentangled sequences for better performance. Experiments on four popular benchmarks demonstrate our superiority over existing SoTA solutions, especially on the 3D IoU metric. The code is available at https://github.com/zhijieshen-bjtu/DOPNet.", + "bbox": [ + 76, + 434, + 472, + 676 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 709, + 209, + 724 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Indoor panoramic layout estimation refers to reconstructing 3D room layouts from omnidirectional images. Since the panoramic vision system captures the whole-room contextual information, we can estimate the complete room layout with a single panoramic image. However, inferring the 3D information from a 2D image is an ill-posed problem. Besides, the $360^{\\circ}$ field-of-view (FoV) of panoramas brings severe distortions that increase along the latitude. Both issues are challenging for indoor layout estimation.", + "bbox": [ + 76, + 734, + 468, + 872 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ee223d0bf847aa88dadd923b2edba5a3d2fddb778db9470cd96f978aa6cff5c2.jpg", + "image_caption": [ + "Figure 1. (a) The commonly used architecture. (b) The proposed one. Compared with the traditional pipeline, ours has two advantages: (1) Disentangling the 1D representation into two separate sequences with different plane semantics. (2) Adaptively integrating shallow and deep features with distortion awareness via a feature assembling mechanism rather than simple concatenation." + ], + "image_footnote": [], + "bbox": [ + 506, + 308, + 895, + 468 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Different from outdoor scenarios, the indoor room has the following properties: (1) The indoor scenes conform to the Manhattan World assumption (The floors and ceilings are all flat planes, and the walls are perpendicular to them). (2) The room layout is always described as the corners or the floor boundary and ceiling boundary. These characteristics could be used as potential priors to guide the design of a reasonable layout estimation method.", + "bbox": [ + 498, + 579, + 892, + 699 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Based on the Manhattan World assumption, previous approaches [19, 20, 8, 14, 21] prefer to estimate the layout from a 1D sequence. They advocate compressing the extracted 2D feature maps in height dimension to obtain a 1D sequence, of which every element in this sequence share the same distortion magnitude (Fig. 1a). We argue that this compressed representation does not eliminate the panoramic distortions because there is no explicit distortion processing when extracting 2D feature maps before compression. Moreover, this strategy roughly mixes the vertical and horizontal planes together, confusing the semantics of different planes that are crucial for layout estimation.", + "bbox": [ + 496, + 700, + 893, + 883 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "On the other hand, some researchers devoted themselves", + "bbox": [ + 517, + 885, + 890, + 898 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "†Corresponding author", + "bbox": [ + 96, + 886, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "17337", + "bbox": [ + 478, + 924, + 517, + 936 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "to adopting different projection formats to boost the performance, e.g., the bird's view of the room [29] and cubemap projection [27]. These projection-based schemes weaken the negative effect of the distortions. Nevertheless, frequent projection operations between different formats raise computational complexity. In addition, there exists an inevitable domain gap between the feature maps from different formats.", + "bbox": [ + 75, + 90, + 472, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address the above problems, we propose a novel architecture (Fig.1b) that disentangles the orthogonal planes in advance to capture an explicit geometric cue. Following [21], our room layout can be recovered from the predicted horizon-depth map and the room height. Therefore, the \"clean\" depth-relevant features and height-relevant features can both help with the layout estimation. To obtain such \"clean\" features free from the disturbance of decorations and furniture, we disentangle the widely used 1D representation into two separate sequences — the horizontal and vertical ones. Specifically, we pre-segment the vertical plane (i.e., walls) and horizontal planes (i.e., floors and ceilings) from the whole-room contextual information. Then these orthogonal planes are compressed into two 1D representations. Especially, based on the symmetry property between the floor boundary and ceiling boundary, we design a soft-flipping fusion strategy to assist this process.", + "bbox": [ + 75, + 212, + 472, + 469 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Moreover, we propose an assembling mechanism to fuse multi-scale features with distortion awareness effectively. To eliminate the negative effect of distortion, we compute the attention among distortion-relevant positions following distortion distribution patterns. Meanwhile, cross-scale interaction is carried out to integrate shallow geometric structures and deep semantic features. Considering the error of pre-segmentation, we further leverage triple attention to reconstruct the two 1D sequences. Particularly, we adopt graph-based attention to generate discriminative channels, self-attention to rebuild long-range dependencies, and cross-attention to provide the missing information for different sequences.", + "bbox": [ + 75, + 469, + 472, + 665 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To demonstrate our effectiveness, we conduct extensive experiments on four popular datasets — MatterportLayout [29], Zind [6], Stanford 2D-3D [1], and PanoContext [26]. The qualitative and quantitative results show that the proposed solution outperforms other SoTA methods. Our contributions can be summarized as follows:", + "bbox": [ + 75, + 666, + 472, + 755 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose to disentangle orthogonal planes to capture an explicit geometric cue for indoor $360^{\\circ}$ room layout estimation, with a soft-flipping fusion strategy to assist this procedure.", + "- We design a cross-scale distortion-aware assembling mechanism to perceive distortion distribution as well as integrate shallow geometric structures and deep semantic features." + ], + "bbox": [ + 96, + 768, + 468, + 898 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- On popular benchmarks, our solution outperforms other SoTA schemes, especially on the metric of intersection over the union of 3D room layouts.", + "bbox": [ + 517, + 90, + 890, + 137 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 176, + 640, + 191 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. $360^{\\circ}$ Room Layout Estimation", + "text_level": 1, + "bbox": [ + 500, + 210, + 767, + 226 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Based on Manhattan World assumption [5] that all walls and floors are aligned with global coordinate system axes and are perpendicular to each other, many approaches utilize convolutional neural networks (CNNs) to extract useful features to improve layout estimation accuracy. Specifically, Zou et al. [28] propose LayoutNet to predict the corner/boundary probability maps directly from the panoramicas and then optimize the layout parameter to generate the final predicted results. Furthermore, they annotate the Stanford 2D-3D dataset [1] with awesome layouts for training and evaluation. Yang et al. [24] propose Dula-Net to predict a 2D floor plane semantic mask from both the equirectangular view and the perspective view of the ceilings. The modified version, LayoutNet v2, and Du la-Net v2, which have better performance than the original version, are presented by Zou et al. [29]. Fernandez et al. [7] present to utilize equirectangular convolutions (EquiConvs) to generate corner/edge probability maps. Sun et al. propose HorizonNet [19] and HoHoNet [20] to simplify the layout estimation processes by representing the room layout with a 1D representation. Besides, they use Bi-LSTM and multi-head self-attention to build long-range dependencies and refine the 1D sequences.", + "bbox": [ + 496, + 242, + 893, + 575 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recently, several approaches have adopted this 1D representation and achieved impressive performance. For example, Rao et al. [15] establish their network based on HorizonNet [19]. They replace standard convolution operation with spherical convolution to reduce distortions and take Bi-GRU to reduce computational complexity. Wang et al. [21] combine the geometric cues across the layout and propose LED2-Net that reformulates the room layout estimation as predicting the depth of walls in the horizontal direction. Not constrained to Manhattan scenes, Pintore et al. [14] introduce AtlantaNet to predict the room layout by combining two projections of the floor and ceiling planes. Driven by the self-attention mechanism, many transformer-based methods [25, 22, 13] proposed to build long-range dependencies. For example, Jiang et al. [8] represent the room layout by horizon depth and room height and introduce a Transformer to enforce the network to learn the geometric relationships. However, the popular 1D representations could confuse the semantics of different planes, thus causing the layout estimation challenging. We disentangle this 1D representation by pre-segmenting orthogonal planes.", + "bbox": [ + 496, + 584, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "17338", + "bbox": [ + 480, + 924, + 519, + 936 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. $360^{\\circ}$ Image Distortion Mitigation", + "text_level": 1, + "bbox": [ + 76, + 90, + 366, + 107 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "When converting spherical data to the equirectangular projection format, severe distortions are introduced. Some recent studies focus on designing spherical customized convolutions to make the network adapt to panoramic distortions and offer superior results compared to standard convolutional networks. Su et al. [18] introduce SphConv to remove distortions by changing the regular planar convolutions kernel size towards each row of the $360^{\\circ}$ images. Cohen et al. [2] propose a spherical CNN that transforms the domain space from Euclidean S2 space to a SO(3) group to reduce the distortion and encodes full rotation invariance in their network. Coors et al. [3] addresses it by defining the convolution kernels on the tangent plane and keeping the convolution domain consistent in each kernel. Therefore, the non-distorted features can be extracted directly on $360^{\\circ}$ images. Rao et al. [15] first applied spherical convolution operation to room layout task and showed significant improvements. Different from the above approaches, Shen et al. [16] propose the first panorama Transformer (PanoFormer) and divide the patches on the tangent plane to remove the negative effect of distortions. But most recent layout estimation works do not treat the distortions seriously because they think that the 1D representations can solve the distortions well. On the contrary, we propose a feature assembling mechanism with cross-scale distortion awareness to deal with distortions. Extensive experimental results demonstrate the necessity of handling distortions before generating 1D representations.", + "bbox": [ + 76, + 121, + 472, + 544 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Approach", + "text_level": 1, + "bbox": [ + 76, + 580, + 184, + 598 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Overview", + "text_level": 1, + "bbox": [ + 76, + 612, + 186, + 628 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As illustrated in Fig. 2, the proposed framework consists of three stages: feature extraction followed by a feature assembling mechanism, orthogonal plane disentanglement, and 1D representation reconstruction. Specifically, we adopt a backbone (basically ResNet) to extract a series of features at 4 different scales from a single panorama. Then a feature assembling mechanism is designed to fuse the multi-scale features and free them from panoramic distortions. In the next stage, we introduce a soft-flipping fusion strategy to explore the symmetry between the floor boundary and the ceiling boundary. After that, we segment the vertical and horizontal planes from the fused features followed by vertical compression, yielding two 1D representations. In the last stage, the disentangled features are reconstructed with triple attention to be more discriminative and informative. Finally, the horizon-depth map and room height are estimated from the reconstructed sequences.", + "bbox": [ + 76, + 643, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Cross-scale Distortion Awareness", + "text_level": 1, + "bbox": [ + 500, + 90, + 790, + 106 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In previous works [19, 20, 21, 8], researchers prefer to follow the architecture of HorizonNet [19] to extract multiscale feature maps of an equirectangular image. These feature maps are merged together via vertical compression and concatenation [12]. However, the popular architecture just concatenates multi-scale features together and neglects the inherent distortion distribution, resulting in an inferior panoramic feature extraction capability. To address the above issues, we propose a novel feature assembling mechanism to deal with distortions, as well as ingeniously integrate shallow and deep features.", + "bbox": [ + 496, + 114, + 890, + 280 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Eliminating Distortions. Motivated by previous works [7, 16], we first polymerize the most relevant features via a virtue tangent plane on the panoramic sphere projection. Based on the projection formula [16, 17, 4] (we discuss it in detail in the supplementary material), we can get the distortion-free sampling coordinates $p \\in \\mathbb{R}^{H \\times W \\times 9 \\times 2}$ (height, width, number of points, number of coordinates) in the 2D feature maps. The learnable offsets $\\Delta p$ are employed to adjust the sampling locations adaptively. Then we obtain gathered features $f_{df} \\in \\mathbb{R}^{C \\times H \\times W \\times 9}$ from the original features $f \\in \\mathbb{R}^{C \\times H \\times W}$ as follows:", + "bbox": [ + 496, + 281, + 890, + 448 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nf _ {d f} = \\sum_ {q = 1} ^ {H \\times W} \\sum_ {k = 1} ^ {9} S a m p l e (f, p _ {q, k} + \\Delta p _ {q, k}), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 534, + 459, + 890, + 494 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $q$ represents the $q^{th}$ point to gather the relevant features; $k$ indexes the $k^{th}$ related features.", + "bbox": [ + 496, + 508, + 890, + 537 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Integrating Shallow and Deep features. We select the $3^{th}$ scale $(\\tilde{s})$ as the reference scale and resize other feature maps to this scale. Specifically, we utilize the learnable sampling coordinates $(p_{q,k} + \\Delta p_{q,k})$ to gather the distortion-free feature maps for every feature with resized scales following Eq.1. Let $f^s \\in \\mathbb{R}^{C \\times H_s \\times W_s}$ be the original feature map at a certain scale $s$ . The gathered multi-scale feature maps $f_{m\\tilde{s}} \\in \\mathbb{R}^{C \\times H_{\\tilde{s}} \\times W_{\\tilde{s}} \\times 9 \\times 4}$ can be represented as:", + "bbox": [ + 496, + 539, + 890, + 661 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nf _ {m \\tilde {s}} = \\sum_ {s = 1} ^ {4} \\sum_ {q = 1} ^ {H _ {\\tilde {s}} \\times W _ {\\tilde {s}}} \\sum_ {k = 1} ^ {9} \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 614, + 674, + 890, + 707 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nS a m p l e (r e s i z e \\left(f ^ {s}, \\tilde {s}\\right), p _ {q, k} ^ {\\tilde {s}} + \\Delta p _ {q, k} ^ {\\tilde {s}}).\n$$\n", + "text_format": "latex", + "bbox": [ + 560, + 707, + 815, + 724 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Then, the designed cross-scale distortion-aware feature assembling mechanism can be applied as:", + "bbox": [ + 500, + 736, + 890, + 767 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nf _ {m \\tilde {s}} ^ {\\prime} = \\operatorname {C S D A} \\left(f _ {m \\tilde {s}}\\right) = \\sum_ {l = 1} ^ {L} A _ {l} \\cdot \\text {r e s h a p e} \\left(f _ {m \\tilde {s}}\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 516, + 779, + 890, + 813 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $L$ indexes the heads of the self-attention; $A_{l}\\in \\mathbb{R}^{L\\times H_{\\tilde{s}}W_{\\tilde{s}}\\times 36}$ is the learnable self-attention weights from $f_{m\\tilde{s}}$ . To complete the calculation, we reshape $f_{m\\tilde{s}}$ into the size of $\\mathbb{R}^{L\\times H_{\\tilde{s}}W_{\\tilde{s}}\\times 36\\times\\frac{C}{L}}$ . The final assembling features are denoted as $f_{m\\tilde{s}}^{\\prime}\\in \\mathbb{R}^{C\\times H_{\\tilde{s}}\\times W_{\\tilde{s}}}$ .", + "bbox": [ + 496, + 824, + 890, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "17339", + "bbox": [ + 478, + 925, + 519, + 936 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/4a0e551cc94c8fab06230e5c69a9f1fdde213b1d541a27545e57992a42382c7a.jpg", + "image_caption": [ + "Figure 2. Overview of the proposed framework. The feature assembling mechanism is designed to deal with distortions as well as integrate shallow and deep features (circled in Blue). Then we disentangle orthogonal planes to produce two 1D representations with distinguished plane semantics (circled in Purple). And triple attention is deployed to reconstruct the 1D representations (circled in Red). Our scheme leverages a single panorama with a resolution of $512 \\times 1024$ as input and predicts the room height and the horizon depth." + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 893, + 422 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/557f50a88eb5bb21a6f2cb2969e62b92233e4552b900a50071a217448a8adc3f.jpg", + "image_caption": [ + "Original version" + ], + "image_footnote": [], + "bbox": [ + 88, + 497, + 209, + 550 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/7e51ae6f7a83c363034e0374e49f403e28790d221c6efa400447c5391f48b3f0.jpg", + "image_caption": [ + "Vertically flipping", + "Figure 3. Illustration of the misaligned case when leveraging the symmetry property." + ], + "image_footnote": [], + "bbox": [ + 212, + 497, + 333, + 550 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/59c1581b4bb66883bc834dce1f51865cf7081ff5dc0fdff4bd9148ff416b4584.jpg", + "image_caption": [ + "Misaligned case" + ], + "image_footnote": [], + "bbox": [ + 334, + 497, + 457, + 550 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Disentangling Orthogonal Planes", + "text_level": 1, + "bbox": [ + 76, + 604, + 367, + 622 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In order to explicitly capture the geometric cues, we propose to disentangle the orthogonal planes. Particularly, we segment the vertical plane and horizontal planes from the whole scenario before compressing the 2D feature maps.", + "bbox": [ + 75, + 628, + 468, + 688 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Symmetry in Manhattan World. It is challenging to learn accurate layout boundaries in a complex scene due to the disturbance of furniture and illumination, e.g., occlusion. To address it, we propose to leverage the symmetry of the Manhattan World assumption (e.g., the floor boundary and ceiling boundary are strictly symmetric in 3D space) to provide complementary information. To exploit this symmetry property, we introduce a soft-flipping fusion strategy.", + "bbox": [ + 75, + 688, + 468, + 809 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We first vertically flip the feature maps to get their symmetrical version. In fact, the floor boundary and ceiling boundary are not strictly symmetric in an image because the shooting position is not in the exact middle of the floor and ceiling. To this end, we adopt a deformable convolution with $3 \\times 3$ kernel size to adaptively adjust the symmetry", + "bbox": [ + 75, + 810, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "cal version. Next, we fuse the original feature and its \"soft\" symmetrical version to provide more informative boundary cues. We denote the fused features as $f_{u} \\in \\mathbb{R}^{C \\times H_{\\bar{s}} \\times W_{\\bar{s}}}$ .", + "bbox": [ + 496, + 500, + 890, + 545 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Segmenting Horizontal/Vertical Planes. To disentangle the 1D representation, we pre-segment the horizon/vertical planes in advance to capture an explicit geometric cue. Specifically, we generate the pseudo labels for the orthogonal planes with layout GT. Then, we use the generated labels to encourage the network to learn a binary mask $S \\in \\mathbb{R}^{H_{\\bar{s}} \\times W_{\\bar{s}}}$ via a simple segmentation head. The two segmented feature maps can be denoted as:", + "bbox": [ + 496, + 546, + 892, + 667 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nf _ {h} ^ {p} = \\left(f _ {u} \\oplus f _ {m \\tilde {s}} ^ {\\prime}\\right) \\otimes \\text {s i g m o i d} (S), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 540, + 675, + 890, + 696 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nf _ {v} ^ {p} = \\left(f _ {u} \\oplus f _ {m \\tilde {s}} ^ {\\prime}\\right) \\otimes (1 - \\text {s i g m o i d} (S))\n$$\n", + "text_format": "latex", + "bbox": [ + 542, + 693, + 813, + 709 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $f_h^p / f_v^p$ represents the horizon/vertical plane features, respectively; $\\oplus$ is the element-wise sum and $\\otimes$ is the element-wise product. Following previous works, we further vertically compress 2D feature maps to two 1D sequences $\\mathbf{Q}_h$ , $\\mathbf{Q}_v \\in \\mathbb{R}^{W_{\\bar{s}} \\times C}$ with differnet plane semantics.", + "bbox": [ + 496, + 717, + 890, + 794 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Reconstructing 1D Representations", + "text_level": 1, + "bbox": [ + 500, + 801, + 807, + 816 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Generating Discriminative Channels. There are generally unconfined dependencies among channels, resulting in confused semantic cues [10]. To this end, we propose a discriminative channels generation mechanism via graph convolution to enforce each channel to concentrate on distin", + "bbox": [ + 496, + 825, + 890, + 898 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "17340", + "bbox": [ + 478, + 924, + 519, + 936 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "guishing features. Different from normal pixel-wise [23] or object-wise [11] graphs, the introduced channel-wise one tends to guide the node to subtract the information from the neighbor nodes rather than aggregation. The formula of the discriminative channels generation mechanism can be represented as:", + "bbox": [ + 75, + 90, + 472, + 181 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nf ^ {\\prime} = \\mathbf {L} f W = (\\mathbf {I} - \\mathbf {A}) f W \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 163, + 195, + 468, + 212 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{L}$ and $\\mathbf{A}$ are the symmetric normalized Laplacian matrix and normalized adjacency matrix of the channelwise graph, and $I$ and $W$ are the identity matrix and learnable weights, respectively. Please refer to the supplementary materials for more details about the channel-wise graph attention. Following Eq. 5, $\\mathbf{Q}_h$ and $\\mathbf{Q}_v$ are first reconstructed to be more discriminative in channels (represented as $\\mathbf{Q}_h^{\\prime},\\mathbf{Q}_v^{\\prime}\\in \\mathbb{R}^{W_{\\bar{s}}\\times C}$ ).", + "bbox": [ + 75, + 224, + 468, + 345 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Rebuilding Long-Range Dependencies. We employ the standard self-attention to reconstruct the intra-sequence long-range dependencies. The attention formula of the horizontal plane sequence can be written as:", + "bbox": [ + 76, + 347, + 468, + 407 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {A t t e n t i o n} \\left(\\mathcal {Q} _ {h} ^ {\\prime}, \\mathcal {K} _ {h} ^ {\\prime}, \\mathcal {V} _ {h} ^ {\\prime}\\right) = \\operatorname {s o f t m a x} \\left(\\frac {\\mathcal {Q} _ {h} ^ {\\prime} \\left(\\mathcal {K} _ {h} ^ {\\prime}\\right) ^ {T}}{\\sqrt {d _ {k}}} \\mathcal {V} _ {h} ^ {\\prime}\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 419, + 468, + 445 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{Q}_h^\\prime ,\\mathcal{K}_h^\\prime ,\\mathcal{V}_h^\\prime$ are all learned from $\\mathbf{Q}_h^\\prime$ via a fully connected layer. Similarly, the calculation for the vertical plane sequence is defined as:", + "bbox": [ + 76, + 455, + 468, + 502 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {A t t e n t i o n} \\left(\\mathcal {Q} _ {v} ^ {\\prime}, \\mathcal {K} _ {v} ^ {\\prime}, \\mathcal {V} _ {v} ^ {\\prime}\\right) = \\operatorname {s o f t m a x} \\left(\\frac {\\mathcal {Q} _ {v} ^ {\\prime} \\left(\\mathcal {K} _ {v} ^ {\\prime}\\right) ^ {T}}{\\sqrt {d _ {k}}} \\mathcal {V} _ {v} ^ {\\prime}\\right). \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 513, + 468, + 539 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "It captures global interactions to adapt to the large FoV of panoramas, contributing to better performance. We denote the two sequences with reconstructed long-range dependencies as $\\mathbf{Q}_h^{\\prime \\prime}$ , $\\mathbf{Q}_v^{\\prime \\prime} \\in \\mathbb{R}^{W_{\\bar{s}} \\times C}$ .", + "bbox": [ + 76, + 550, + 468, + 611 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Providing Missing Residuals. To compensate for inevitable errors in pre-segmentation, we introduce crossattention to provide the missing residuals. For the sequence about the horizontal plane, we extract the potential beneficial residuals as follows:", + "bbox": [ + 76, + 611, + 468, + 686 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {A t t e n t i o n} \\left(\\mathcal {Q} _ {h} ^ {\\prime \\prime}, \\mathcal {K} _ {v} ^ {\\prime \\prime}, \\mathcal {V} _ {v} ^ {\\prime \\prime}\\right) = \\operatorname {s o f t m a x} \\left(\\frac {\\mathcal {Q} _ {h} ^ {\\prime \\prime} \\left(\\mathcal {K} _ {v} ^ {\\prime \\prime}\\right) ^ {T}}{\\sqrt {d _ {k}}} \\mathcal {V} _ {v} ^ {\\prime \\prime}\\right). \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 696, + 472, + 722 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For the other:", + "bbox": [ + 76, + 733, + 169, + 746 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {A t t e n t i o n} \\left(\\mathcal {Q} _ {v} ^ {\\prime \\prime}, \\mathcal {K} _ {h} ^ {\\prime \\prime}, \\mathcal {V} _ {h} ^ {\\prime \\prime}\\right) = \\operatorname {s o f t m a x} \\left(\\frac {\\mathcal {Q} _ {v} ^ {\\prime \\prime} \\left(\\mathcal {K} _ {h} ^ {\\prime \\prime}\\right) ^ {T}}{\\sqrt {d _ {k}}} \\mathcal {V} _ {h} ^ {\\prime \\prime}\\right). \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 757, + 472, + 782 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{Q}_h^{\\prime \\prime},\\mathcal{K}_h^{\\prime \\prime},\\mathcal{V}_h^{\\prime \\prime}$ are all learned from $\\mathbf{Q}_h^{\\prime \\prime}(\\mathcal{Q}_v^{\\prime \\prime},\\mathcal{K}_v^{\\prime \\prime},\\mathcal{V}_v^{\\prime \\prime}$ from $\\mathbf{Q}_v^{\\prime \\prime})$ via a fully connected layer. Then we add the learned residuals with the two 1D sequences to implement the reconstruction. After that, two separate fully connected layers are employed to output the predicted horizon depth from the vertical plane sequence and the room height value from the horizontal plane one, respectively.", + "bbox": [ + 76, + 792, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Objective Function", + "text_level": 1, + "bbox": [ + 500, + 90, + 684, + 107 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our objective function consists of two parts: one for room layout estimation and the other for plane segmentation. For the first part, we strictly follow [8] and it can be denoted as $\\mathcal{L}_{layout}$ . For the segmentation part, we apply binary cross-entropy loss $\\mathcal{L}_{segment}$ as follows:", + "bbox": [ + 496, + 114, + 890, + 190 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {s e g m e n t}} = \\frac {1}{N} \\sum_ {i \\in N} \\left(d _ {i} \\log \\bar {d} _ {i} + \\left(1 D _ {i}\\right) \\log \\left(1 - \\bar {d} _ {i}\\right)\\right) \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 508, + 200, + 890, + 227 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\bar{d}_i$ is the ground truth of generated segmentation label, and $d_i$ is the predicted value. Ultimately, we formulate the objective function as follows:", + "bbox": [ + 496, + 239, + 890, + 285 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\lambda \\mathcal {L} _ {\\text {s e g m e n t}} + \\mathcal {L} _ {\\text {l a y o u t}} \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 589, + 297, + 890, + 315 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\lambda$ is set to 0.75 to balance different constraints.", + "bbox": [ + 498, + 325, + 854, + 340 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 498, + 354, + 633, + 372 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we validate the effectiveness of our solution and compare it with existing SoTA approaches on four popular datasets. Concretely, we conduct experiments on a single GTX 3090 GPU, and the batch size is set to 16 for training. The proposed approach is implemented with PyTorch. We choose Adam [9] as the optimizer and keep the default settings. The initialized learning rate is $1 \\times 10^{-4}$ . As in previous works [19, 8], we adopt standard left-right flipping, panoramic horizontal rotation, luminance change, and pano stretch for data augmentation during training.", + "bbox": [ + 496, + 380, + 890, + 532 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Datasets", + "text_level": 1, + "bbox": [ + 498, + 542, + 601, + 556 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Four datasets are used for our experimental validation: Stanford 2D-3D [1], PanoContext [26], MatterportLayout [29] and ZInd [6].", + "bbox": [ + 496, + 565, + 890, + 609 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "PanoContext [26] and Stanford 2D-3D [1] are two commonly used datasets for indoor panoramic room layout estimation that contain 514 and 552 cuboid room layouts, respectively. Especially, Stanford 2D-3D [1] is labeled by Zou et al. [28] and has a smaller vertical FoV than other datasets. Besides, MatterportLayout [29] is also annotated by Zou et al. [29], which contains 2,295 general room layouts. The final ZInd [6] dataset includes cuboid, general Manhattan, non-Manhattan, and non-flat ceilings layouts, which mimic the real-world data distribution better. The splits of ZInd [6] consists of 24,882 (for training), 3,080 (for validation), and 3,170 (for testing) panoramas. We strictly follow the same training/validation/test splits of the four datasets as in previous works for a fair comparison.", + "bbox": [ + 496, + 611, + 890, + 821 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Evaluation Metrics", + "text_level": 1, + "bbox": [ + 498, + 830, + 684, + 845 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We employ the commonly used standard evaluation metrics for a fair comparison, including corner error (CE), pixel error (PE), intersection over the union of floor shapes", + "bbox": [ + 496, + 854, + 890, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "17341", + "bbox": [ + 480, + 925, + 517, + 936 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/9a21f251ee8ff694003a61ec0bbae634a7340874febbd102fe3ff649cff17671.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Method3D IoU(%)CE(%)PE(%)
Train on PanoContext + Whole Stnfd.2D3D datasets
LayoutNetv2[29]85.020.631.79
Dula-Netv2[29]83.770.812.43
HorizonNet[19]82.630.742.17
LGT-Net[8]85.16--
LGT-Net [w/ Post-proc][8]84.940.692.07
Ours85.46--
Ours [w/ Post-proc]85.000.692.13
Train on Stnfd.2D3D + Whole PanoContext datasets
LayoutNetv2[29]82.660.832.59
Dula-Netv2[29]86.600.672.48
HorizonNet[19]82.720.692.27
AtlantaNet[14]83.940.712.18
LGT-Net[8]85.76--
LGT-Net [w/ Post-proc][8]86.030.632.11
Ours85.47--
Ours [w/ Post-proc]85.580.662.10
", + "bbox": [ + 78, + 89, + 495, + 375 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Quantitative comparison results with the current SoTA solutions evaluated on Stanford 2D-3D and PanoContext[6] dataset.", + "bbox": [ + 75, + 383, + 470, + 412 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "(2D IoU), and 3D room layouts (3D IoU). Among them, 3D IoU yields a better reflection of the accuracy of the layout estimation in 3D space. RMSE and $\\delta_{1.25}$ indicate the performance of depth estimation, e.g. the horizon-depth map,", + "bbox": [ + 75, + 429, + 470, + 491 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Cuboid Room Results", + "text_level": 1, + "bbox": [ + 76, + 500, + 282, + 513 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We follow LGT-Net [8] to use the combined dataset scheme mentioned in Zou et al. [29] to evaluate our network on cuboid datasets. We denote the combined dataset that contains training splits of PanoContext [6] and whole Stanford 2D-3D datasets as \"Train on PanoContext + Whole Stnfd.2D3D datasets\" in Tab. 1. Similarly, \"Train on Stnfd.2D3D + Whole PanoContext\" in Tab. 1 represents that we train our network on the combined dataset that contains training splits of Stanford 2D-3D and the whole PanoContext dataset. The scheme is commonly used in previous works [28, 8]. We also report the results with a post-processing strategy in DuLa-Net [24] that is denoted as \"Ours [w/ Post-proc]\".", + "bbox": [ + 75, + 522, + 468, + 719 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparison results. We exhibit the quantitative comparison results on cuboid room layouts in Tab. 1. From the first group in Tab. 1, we can observe that our approach outperforms all the other SoTA schemes with respect to 3D IoU. But from the second group, Dula-Net v2 [29] offers better 3D IoU than ours. Dula-Net v2 [29] employs a perspective view (i.e., cubemap) that is more effective for panoramas with small vertical FoV. However, once applied to more general room layout datasets, its performance degrades significantly (it is proved with the other two datasets in Sec. 4.4). On the contrary, the proposed approach shows more general performance.", + "bbox": [ + 75, + 719, + 470, + 901 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/3ab09c531d32c950da16db76226b5ba0afc900fa9bca7a45301853871d783739.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Method2D IoU(%)3D IoU(%)RMSEδ1
LayoutNetv2[29]78.7375.820.2580.871
Dula-Netv2[29]78.8275.050.2910.818
HorizonNet[19]81.7179.110.1970.929
AtlantaNet[14]82.0980.02--
HoHoNet[20]82.3279.88--
LED2-Net[21]82.6180.140.2070.947
DMH-Net [27]81.2578.97-0.925
LGT-Net[8]83.5281.110.2040.951
Ours84.1181.700.1970.950
", + "bbox": [ + 500, + 89, + 895, + 251 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/1fbc70ebbecd05cc33eadc74704d2e9ee5f880bb9853125d3471a68d5288ff9e.jpg", + "table_caption": [ + "Table 2. Quantitative comparison results with the current SoTA solutions evaluated on MatterportLayout[29] dataset." + ], + "table_footnote": [], + "table_body": "
Method2D IoU(%)3D IoU(%)RMSEδ1
HorizonNet[19]90.4488.590.1230.957
LED2-Net[21]90.3688.490.1240.955
LGT-Net[8]91.7789.950.1110.960
Ours91.9490.13--
", + "bbox": [ + 501, + 304, + 890, + 391 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 3. Quantitative comparison results with the current SoTA solutions evaluated on ZInD[6] dataset.", + "bbox": [ + 498, + 400, + 890, + 429 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. General Room Results", + "text_level": 1, + "bbox": [ + 500, + 449, + 709, + 464 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "MatterportLayout [29] dataset and ZInD [6] dataset provide more general indoor room layouts, which is much more challenging than the cuboid room layout datasets. Tab. 2/Tab. 3 exhibits the evaluation on MatterportLayout [29]/ZInD [6] datasets. The results of $\\mathsf{LED}^2$ -Net [21] and HorizonNet [19] are from [8] that we strictly followed. Particularly, Jiang et al. utilize their official codeto re-train and re-evaluate with the standard evaluation metrics.", + "bbox": [ + 496, + 474, + 890, + 594 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparison results. We observe that Dula-Net [24] demonstrates much worse performance on the general room layout dataset (MatterportLayout), indicating that these perspective view-based methods are hard to be adapted to the more general indoor scenarios. Moreover, these 1D sequence-based methods are better than those 2D convolution-based schemes. However, they cannot produce accurate 3D layouts from a 1D sequence due to confused plane semantics, even if they introduce more powerful relationship builders (e.g., Bi-LSTM, Transformer). Hence, these methods give worse 3D IoU. Compared with them, our approach offers better performance than all other approaches with respect to 3D IoU because ours captures an explicit 3D geometric cue by disentangling orthogonal planes, which benefits recovering layouts from clear semantics (Fig. 6).", + "bbox": [ + 496, + 595, + 892, + 838 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We show the qualitative comparisons in Fig. 4. From the figure, we can observe that our method offers better 3D results (floor plan). In Fig. 5, our results are much similar to the post-processing version. Both indicate our proposal", + "bbox": [ + 496, + 839, + 893, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "17342", + "bbox": [ + 478, + 925, + 519, + 936 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/6d5cd1be970160438cc7c07ed68f6c5728990f60dd5a90b0eb4fcaa2be200a95.jpg", + "image_caption": [ + "(a) Qualitative comparison on MatterportLayout [29] dataset." + ], + "image_footnote": [], + "bbox": [ + 106, + 85, + 883, + 338 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/92dcbb1e67e745b0c592300ee423c928ccd88a8e9a1127c0ecc4f11fe233bbb0.jpg", + "image_caption": [ + "(b) Qualitative comparison on ZInD [6] dataset.", + "Figure 4. Qualitative comparison results evaluated on general layout datasets, MatterportLayout [29] and ZInD [6]. We compare our method with $\\mathbf{LED}^2$ -Net [21] and LGT-Net [8]. The compared methods are all not employed the post-processing strategy. The boundaries of the room layout on a panorama are shown on the left and the floor plan is on the right. Ground truth is best viewed in Blue lines, and the prediction in Green. The predicted horizon depth, normal, and gradient are visualized below each panorama, and the ground truth is in the first row. We labeled the significant differences with dashed lines." + ], + "image_footnote": [], + "bbox": [ + 106, + 366, + 883, + 618 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "that disentangling orthogonal planes to capture an explicit 3D geometric cue is an effective strategy.", + "bbox": [ + 75, + 726, + 470, + 757 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Ablation study", + "text_level": 1, + "bbox": [ + 75, + 768, + 225, + 786 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We exhibit ablation studies in Tab. 4, where each component of our model is evaluated on MatterportLayout [29]. To demonstrate the effectiveness of the proposed feature assembling mechanism, we first ablate cross-scale interaction in feature assembling (denoted as \"w/o Cross-scale interaction\"). Then, we further remove the distortion elimination (denoted as \"w/o Feature assembling\"). To exhibit the", + "bbox": [ + 75, + 794, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "benefit of orthogonal plane disentanglement, we put off the proposed disentangling orthogonal planes procedure (denoted as \"w/o Disentangling planes\") and soft-flipping fusion, respectively. Finally, we show the effect of each attention mechanism (denoted as \"w/o Discriminative channels\", \"w/o Long-range dependencies\", and \"w/o residuals\", respectively). Specially, we train each model around 500 epochs (not the best ones). Hence, the results of \"Ours [Full]\" are slightly lower than those in Tab. 2.", + "bbox": [ + 496, + 726, + 890, + 862 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Feature assembling mechanism. From Tab. 4, the pipeline without cross-scale interaction shows inferior per", + "bbox": [ + 498, + 869, + 890, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "17343", + "bbox": [ + 478, + 925, + 517, + 936 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f3291e8e1aa7373e28c35f77bea992033e286b40e591c3db59b32c7ea7e4c9d5.jpg", + "image_caption": [ + "(a) Standford 2D-3D [1]" + ], + "image_footnote": [], + "bbox": [ + 91, + 94, + 362, + 181 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f81abe11d6604d59ff83cc79c001e49df74a647fcc0a815c73d29fcc2fa1ca86.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 372, + 93, + 477, + 169 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/eba82dcc16c8f08bd369861fd9afef880d4e9fbfc7f65ef2ad6b66b46d2b37c1.jpg", + "image_caption": [ + "(b) PanoContext [26]" + ], + "image_footnote": [], + "bbox": [ + 486, + 93, + 754, + 181 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6f8a57a3bd529b2c946837e5a020e703356131e2a909d7ab65ae1562d7188fe5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 763, + 103, + 862, + 176 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3992e16df8a36195ad97af317354769f24350bb5bf1aa05121760083d8442572.jpg", + "image_caption": [ + "(c) MatterportLayout [29]" + ], + "image_footnote": [], + "bbox": [ + 91, + 209, + 362, + 297 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/126ef462ca29a1d92575eef83f1464e308ce47eb6efbd699ff9327df123e7d86.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 375, + 218, + 473, + 292 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9c96ae5f51127282c2fb9750b752edb0e3de9e2fde18b59f683adc640534bae8.jpg", + "image_caption": [ + "(d) ZInD [6]" + ], + "image_footnote": [], + "bbox": [ + 486, + 210, + 758, + 297 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/bdd378436c084f72881e3925765687f321d43de8d9132f6777ed717b8d8d9199.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 769, + 220, + 879, + 282 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/340af9f9234af567303c6aa503a22d34143c868e8c6485aec7d703922fc8fac5.jpg", + "image_caption": [ + "Figure 5. The 3D visualization results. We exhibit the predicted boundaries (best viewed in Green lines) and the ones with post-processing of the prediction (best viewed in Red lines) in the pancreas." + ], + "image_footnote": [], + "bbox": [ + 91, + 354, + 349, + 400 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/de6c40e1e0cfa46133bf282375952c8b915ce0a1e6a125125fb6b2c7804604b1.jpg", + "image_caption": [ + "Figure 6. We exhibit the features of the 1D representation. The one without orthogonal plane disentanglement is shown on the left, and ours is on the right. Without disentangling, the left contains redundant and confusing features that are not good for layout estimation. In contrast, our disentangled vertical plane features are more discriminative, showing more attention to the layout corners." + ], + "image_footnote": [], + "bbox": [ + 367, + 354, + 622, + 400 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/fc894017d8b96e2a80379d983bb1c652260bfd69ef3ff325da7834d20d5483a1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 624, + 354, + 877, + 400 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/09dee5727cb4f50b0263cb80209937aca86aa12bff3aac43e30ca3f44842eb26.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Method2D IoU(%)3D IoU(%)
w/o Cross-scale interaction83.2480.71
w/o Feature assembling82.3680.10
w/o Disentangling planes83.2380.60
w/o Flipping fusion83.0180.35
w/o Discriminative channels82.7480.23
w/o Long-range dependencies83.0480.97
w/o Residuals82.8980.45
Ours [Full]83.4681.34
", + "bbox": [ + 78, + 460, + 478, + 609 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4. Ablation study on MatterportLayout [29] dataset.", + "bbox": [ + 99, + 619, + 444, + 633 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "formance to the full model. Further removing the distortion elimination part, the pipeline gives worse results. It is proved that both dealing with distortions and integrating cross-scale features are essential for layout estimation.", + "bbox": [ + 75, + 654, + 468, + 715 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Disentangling orthogonal planes. Since the geometric cues are essential for inferring 3D information from 2D images, we propose to disentangle orthogonal planes. To prove the effectiveness, we remove that stage but preserve the flipping fusion strategy (the effectiveness of this strategy is validated separately). The results in Tab. 4 show that this stage can make the performance more competitive. Besides, the embedding of symmetry property also contributes to the promotion of the predicted results.", + "bbox": [ + 75, + 717, + 468, + 852 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Reconstructing 1D representations. The dependencies of the 1D sequences have changed when disentangling the orthogonal planes. Hence, we propose to reconstruct the 1D", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "representations. We verify the effectiveness of each attention mechanism in turn. From Tab. 4, we can observe that all three reconstruction operations (generating discriminative channels, rebuilding long-range dependencies, and providing the missing residuals) can all benefit the overall performance. Significantly, when removing the channel-wise graph, the pipeline's performance decreases significantly, demonstrating that enforcing the network concentration on discriminative channel information can capture effective information by avoiding redundancy.", + "bbox": [ + 496, + 462, + 890, + 613 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 633, + 617, + 647 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose a novel panoramic indoor room layout estimation approach. Current approaches generate a 1D representation by a vertical compression operation. We argue that this strategy confuses the semantic cues of different planes. To address this issue, we propose to disentangle orthogonal planes to capture geometric cues in 3D space. Specially, we introduce a vertical flip-fusion strategy to leverage the symmetry property of indoor room layout. Besides, our experimental results demonstrate that dealing with distortion, as well as integrating shallow and deep features, can enhance the performance. Experiments demonstrate that our algorithm significantly outperforms current SoTA methods.", + "bbox": [ + 496, + 660, + 890, + 854 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement.", + "text_level": 1, + "bbox": [ + 500, + 858, + 643, + 872 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "by the National", + "bbox": [ + 500, + 872, + 643, + 885 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "of China (Nos.", + "bbox": [ + 500, + 886, + 635, + 898 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported", + "bbox": [ + 665, + 858, + 890, + 872 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Natural Science Foundation", + "bbox": [ + 665, + 872, + 890, + 885 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "62172032, 62120106009).", + "bbox": [ + 692, + 886, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "17344", + "bbox": [ + 480, + 925, + 517, + 936 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 118, + 173, + 133 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Iro Armeni, Sasha Sax, Amir R Zamir, and Silvio Savarese. Joint 2d-3d-semantic data for indoor scene understanding. arXiv:1702.01105, 2017. 2, 5, 8", + "[2] Taco S Cohen, Mario Geiger, Jonas Köhler, and Max Welling. Spherical cnns. arXiv:1801.10130, 2018. 3", + "[3] Benjamin Coors, Alexandru Paul Condurache, and Andreas Geiger. Spherenet: Learning spherical representations for detection and classification in omnidirectional images. In ECCV, 2018. 3", + "[4] Benjamin Coors, Alexandru Paul Condurache, and Andreas Geiger. Spherenet: Learning spherical representations for detection and classification in omnidirectional images. In ECCV, 2018. 3", + "[5] James M Coughlan and Alan L Yuille. Manhattan world: Compass direction from a single image by bayesian inference. In ICCV, 1999. 2", + "[6] Steve Cruz, Will Hutchcroft, Yuguang Li, Naji Khosravan, Ivaylo Boyadzhiev, and Sing Bing Kang. Zillow indoor dataset: Annotated floor plans with 360deg panoramicas and 3d room layouts. 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IJCV, 2021. 2, 5, 6, 7, 8" + ], + "bbox": [ + 501, + 92, + 890, + 756 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "17345", + "bbox": [ + 480, + 926, + 517, + 936 + ], + "page_idx": 8 + } +] \ No newline at end of file diff --git a/2023/Disentangling Orthogonal Planes for Indoor Panoramic Room Layout Estimation With Cross-Scale Distortion Awareness/13fac3e7-4155-4a84-8381-fe68c09139a8_model.json b/2023/Disentangling Orthogonal Planes for Indoor Panoramic Room Layout Estimation With Cross-Scale Distortion Awareness/13fac3e7-4155-4a84-8381-fe68c09139a8_model.json new file mode 100644 index 0000000000000000000000000000000000000000..b02b4220680e918b2340aee7cf83777015b8670b --- /dev/null +++ b/2023/Disentangling Orthogonal Planes for Indoor Panoramic Room Layout Estimation With Cross-Scale Distortion Awareness/13fac3e7-4155-4a84-8381-fe68c09139a8_model.json @@ -0,0 +1,2066 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.134, + 0.131, + 0.838, + 0.175 + ], + "angle": 0, + "content": "Disentangling Orthogonal Planes for Indoor Panoramic Room Layout Estimation with Cross-Scale Distortion Awareness" + }, + { + "type": "text", + "bbox": [ + 0.12, + 0.204, + 0.849, + 0.258 + ], + "angle": 0, + "content": "Zhijie Shen, Zishuo Zheng, Chunyu Lin†, Lang Nie, Kang Liao, Shuai Zheng, and Yao Zhao Institute of Information Science, Beijing Jiaotong University, China Beijing Key Laboratory of Advanced Information Science and Network Technology" + }, + { + "type": "text", + "bbox": [ + 0.167, + 0.26, + 0.798, + 0.275 + ], + "angle": 0, + "content": "{zhjshen, zszheng, cylin, nielang, kang_liao, zsl997, yzhao}@bjtu.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.31, + 0.314, + 0.326 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.343, + 0.47, + 0.434 + ], + "angle": 0, + "content": "Based on the Manhattan World assumption, most existing indoor layout estimation schemes focus on recovering layouts from vertically compressed 1D sequences. However, the compression procedure confuses the semantics of different planes, yielding inferior performance with ambiguous interpretability." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.435, + 0.473, + 0.678 + ], + "angle": 0, + "content": "To address this issue, we propose to disentangle this 1D representation by pre-segmenting orthogonal (vertical and horizontal) planes from a complex scene, explicitly capturing the geometric cues for indoor layout estimation. Considering the symmetry between the floor boundary and ceiling boundary, we also design a soft-flipping fusion strategy to assist the pre-segmentation. Besides, we present a feature assembling mechanism to effectively integrate shallow and deep features with distortion distribution awareness. To compensate for the potential errors in pre-segmentation, we further leverage triple attention to reconstruct the disentangled sequences for better performance. Experiments on four popular benchmarks demonstrate our superiority over existing SoTA solutions, especially on the 3D IoU metric. The code is available at https://github.com/zhijieshen-bjtu/DOPNet." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.71, + 0.21, + 0.725 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.736, + 0.47, + 0.873 + ], + "angle": 0, + "content": "Indoor panoramic layout estimation refers to reconstructing 3D room layouts from omnidirectional images. Since the panoramic vision system captures the whole-room contextual information, we can estimate the complete room layout with a single panoramic image. However, inferring the 3D information from a 2D image is an ill-posed problem. Besides, the \\(360^{\\circ}\\) field-of-view (FoV) of panoramas brings severe distortions that increase along the latitude. Both issues are challenging for indoor layout estimation." + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.309, + 0.897, + 0.469 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.474, + 0.894, + 0.557 + ], + "angle": 0, + "content": "Figure 1. (a) The commonly used architecture. (b) The proposed one. Compared with the traditional pipeline, ours has two advantages: (1) Disentangling the 1D representation into two separate sequences with different plane semantics. (2) Adaptively integrating shallow and deep features with distortion awareness via a feature assembling mechanism rather than simple concatenation." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.58, + 0.893, + 0.7 + ], + "angle": 0, + "content": "Different from outdoor scenarios, the indoor room has the following properties: (1) The indoor scenes conform to the Manhattan World assumption (The floors and ceilings are all flat planes, and the walls are perpendicular to them). (2) The room layout is always described as the corners or the floor boundary and ceiling boundary. These characteristics could be used as potential priors to guide the design of a reasonable layout estimation method." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.702, + 0.895, + 0.884 + ], + "angle": 0, + "content": "Based on the Manhattan World assumption, previous approaches [19, 20, 8, 14, 21] prefer to estimate the layout from a 1D sequence. They advocate compressing the extracted 2D feature maps in height dimension to obtain a 1D sequence, of which every element in this sequence share the same distortion magnitude (Fig. 1a). We argue that this compressed representation does not eliminate the panoramic distortions because there is no explicit distortion processing when extracting 2D feature maps before compression. Moreover, this strategy roughly mixes the vertical and horizontal planes together, confusing the semantics of different planes that are crucial for layout estimation." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.886, + 0.892, + 0.9 + ], + "angle": 0, + "content": "On the other hand, some researchers devoted themselves" + }, + { + "type": "page_footnote", + "bbox": [ + 0.097, + 0.887, + 0.221, + 0.9 + ], + "angle": 0, + "content": "†Corresponding author" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.925, + 0.519, + 0.937 + ], + "angle": 0, + "content": "17337" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.211 + ], + "angle": 0, + "content": "to adopting different projection formats to boost the performance, e.g., the bird's view of the room [29] and cubemap projection [27]. These projection-based schemes weaken the negative effect of the distortions. Nevertheless, frequent projection operations between different formats raise computational complexity. In addition, there exists an inevitable domain gap between the feature maps from different formats." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.213, + 0.473, + 0.47 + ], + "angle": 0, + "content": "To address the above problems, we propose a novel architecture (Fig.1b) that disentangles the orthogonal planes in advance to capture an explicit geometric cue. Following [21], our room layout can be recovered from the predicted horizon-depth map and the room height. Therefore, the \"clean\" depth-relevant features and height-relevant features can both help with the layout estimation. To obtain such \"clean\" features free from the disturbance of decorations and furniture, we disentangle the widely used 1D representation into two separate sequences — the horizontal and vertical ones. Specifically, we pre-segment the vertical plane (i.e., walls) and horizontal planes (i.e., floors and ceilings) from the whole-room contextual information. Then these orthogonal planes are compressed into two 1D representations. Especially, based on the symmetry property between the floor boundary and ceiling boundary, we design a soft-flipping fusion strategy to assist this process." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.47, + 0.473, + 0.666 + ], + "angle": 0, + "content": "Moreover, we propose an assembling mechanism to fuse multi-scale features with distortion awareness effectively. To eliminate the negative effect of distortion, we compute the attention among distortion-relevant positions following distortion distribution patterns. Meanwhile, cross-scale interaction is carried out to integrate shallow geometric structures and deep semantic features. Considering the error of pre-segmentation, we further leverage triple attention to reconstruct the two 1D sequences. Particularly, we adopt graph-based attention to generate discriminative channels, self-attention to rebuild long-range dependencies, and cross-attention to provide the missing information for different sequences." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.667, + 0.473, + 0.756 + ], + "angle": 0, + "content": "To demonstrate our effectiveness, we conduct extensive experiments on four popular datasets — MatterportLayout [29], Zind [6], Stanford 2D-3D [1], and PanoContext [26]. The qualitative and quantitative results show that the proposed solution outperforms other SoTA methods. Our contributions can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.769, + 0.47, + 0.83 + ], + "angle": 0, + "content": "- We propose to disentangle orthogonal planes to capture an explicit geometric cue for indoor \\(360^{\\circ}\\) room layout estimation, with a soft-flipping fusion strategy to assist this procedure." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.84, + 0.47, + 0.9 + ], + "angle": 0, + "content": "- We design a cross-scale distortion-aware assembling mechanism to perceive distortion distribution as well as integrate shallow geometric structures and deep semantic features." + }, + { + "type": "list", + "bbox": [ + 0.097, + 0.769, + 0.47, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.092, + 0.892, + 0.138 + ], + "angle": 0, + "content": "- On popular benchmarks, our solution outperforms other SoTA schemes, especially on the metric of intersection over the union of 3D room layouts." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.177, + 0.642, + 0.193 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.211, + 0.768, + 0.227 + ], + "angle": 0, + "content": "2.1. \\(360^{\\circ}\\) Room Layout Estimation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.243, + 0.895, + 0.577 + ], + "angle": 0, + "content": "Based on Manhattan World assumption [5] that all walls and floors are aligned with global coordinate system axes and are perpendicular to each other, many approaches utilize convolutional neural networks (CNNs) to extract useful features to improve layout estimation accuracy. Specifically, Zou et al. [28] propose LayoutNet to predict the corner/boundary probability maps directly from the panoramicas and then optimize the layout parameter to generate the final predicted results. Furthermore, they annotate the Stanford 2D-3D dataset [1] with awesome layouts for training and evaluation. Yang et al. [24] propose Dula-Net to predict a 2D floor plane semantic mask from both the equirectangular view and the perspective view of the ceilings. The modified version, LayoutNet v2, and Du la-Net v2, which have better performance than the original version, are presented by Zou et al. [29]. Fernandez et al. [7] present to utilize equirectangular convolutions (EquiConvs) to generate corner/edge probability maps. Sun et al. propose HorizonNet [19] and HoHoNet [20] to simplify the layout estimation processes by representing the room layout with a 1D representation. Besides, they use Bi-LSTM and multi-head self-attention to build long-range dependencies and refine the 1D sequences." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.585, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Recently, several approaches have adopted this 1D representation and achieved impressive performance. For example, Rao et al. [15] establish their network based on HorizonNet [19]. They replace standard convolution operation with spherical convolution to reduce distortions and take Bi-GRU to reduce computational complexity. Wang et al. [21] combine the geometric cues across the layout and propose LED2-Net that reformulates the room layout estimation as predicting the depth of walls in the horizontal direction. Not constrained to Manhattan scenes, Pintore et al. [14] introduce AtlantaNet to predict the room layout by combining two projections of the floor and ceiling planes. Driven by the self-attention mechanism, many transformer-based methods [25, 22, 13] proposed to build long-range dependencies. For example, Jiang et al. [8] represent the room layout by horizon depth and room height and introduce a Transformer to enforce the network to learn the geometric relationships. However, the popular 1D representations could confuse the semantics of different planes, thus causing the layout estimation challenging. We disentangle this 1D representation by pre-segmenting orthogonal planes." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.925, + 0.52, + 0.937 + ], + "angle": 0, + "content": "17338" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.091, + 0.367, + 0.108 + ], + "angle": 0, + "content": "2.2. \\(360^{\\circ}\\) Image Distortion Mitigation" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.122, + 0.473, + 0.545 + ], + "angle": 0, + "content": "When converting spherical data to the equirectangular projection format, severe distortions are introduced. Some recent studies focus on designing spherical customized convolutions to make the network adapt to panoramic distortions and offer superior results compared to standard convolutional networks. Su et al. [18] introduce SphConv to remove distortions by changing the regular planar convolutions kernel size towards each row of the \\(360^{\\circ}\\) images. Cohen et al. [2] propose a spherical CNN that transforms the domain space from Euclidean S2 space to a SO(3) group to reduce the distortion and encodes full rotation invariance in their network. Coors et al. [3] addresses it by defining the convolution kernels on the tangent plane and keeping the convolution domain consistent in each kernel. Therefore, the non-distorted features can be extracted directly on \\(360^{\\circ}\\) images. Rao et al. [15] first applied spherical convolution operation to room layout task and showed significant improvements. Different from the above approaches, Shen et al. [16] propose the first panorama Transformer (PanoFormer) and divide the patches on the tangent plane to remove the negative effect of distortions. But most recent layout estimation works do not treat the distortions seriously because they think that the 1D representations can solve the distortions well. On the contrary, we propose a feature assembling mechanism with cross-scale distortion awareness to deal with distortions. Extensive experimental results demonstrate the necessity of handling distortions before generating 1D representations." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.581, + 0.186, + 0.599 + ], + "angle": 0, + "content": "3. Approach" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.613, + 0.187, + 0.629 + ], + "angle": 0, + "content": "3.1. Overview" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.644, + 0.473, + 0.903 + ], + "angle": 0, + "content": "As illustrated in Fig. 2, the proposed framework consists of three stages: feature extraction followed by a feature assembling mechanism, orthogonal plane disentanglement, and 1D representation reconstruction. Specifically, we adopt a backbone (basically ResNet) to extract a series of features at 4 different scales from a single panorama. Then a feature assembling mechanism is designed to fuse the multi-scale features and free them from panoramic distortions. In the next stage, we introduce a soft-flipping fusion strategy to explore the symmetry between the floor boundary and the ceiling boundary. After that, we segment the vertical and horizontal planes from the fused features followed by vertical compression, yielding two 1D representations. In the last stage, the disentangled features are reconstructed with triple attention to be more discriminative and informative. Finally, the horizon-depth map and room height are estimated from the reconstructed sequences." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.792, + 0.107 + ], + "angle": 0, + "content": "3.2. Cross-scale Distortion Awareness" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.115, + 0.892, + 0.281 + ], + "angle": 0, + "content": "In previous works [19, 20, 21, 8], researchers prefer to follow the architecture of HorizonNet [19] to extract multiscale feature maps of an equirectangular image. These feature maps are merged together via vertical compression and concatenation [12]. However, the popular architecture just concatenates multi-scale features together and neglects the inherent distortion distribution, resulting in an inferior panoramic feature extraction capability. To address the above issues, we propose a novel feature assembling mechanism to deal with distortions, as well as ingeniously integrate shallow and deep features." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.282, + 0.892, + 0.449 + ], + "angle": 0, + "content": "Eliminating Distortions. Motivated by previous works [7, 16], we first polymerize the most relevant features via a virtue tangent plane on the panoramic sphere projection. Based on the projection formula [16, 17, 4] (we discuss it in detail in the supplementary material), we can get the distortion-free sampling coordinates \\( p \\in \\mathbb{R}^{H \\times W \\times 9 \\times 2} \\) (height, width, number of points, number of coordinates) in the 2D feature maps. The learnable offsets \\( \\Delta p \\) are employed to adjust the sampling locations adaptively. Then we obtain gathered features \\( f_{df} \\in \\mathbb{R}^{C \\times H \\times W \\times 9} \\) from the original features \\( f \\in \\mathbb{R}^{C \\times H \\times W} \\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.535, + 0.46, + 0.892, + 0.496 + ], + "angle": 0, + "content": "\\[\nf _ {d f} = \\sum_ {q = 1} ^ {H \\times W} \\sum_ {k = 1} ^ {9} S a m p l e (f, p _ {q, k} + \\Delta p _ {q, k}), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.509, + 0.891, + 0.539 + ], + "angle": 0, + "content": "where \\( q \\) represents the \\( q^{th} \\) point to gather the relevant features; \\( k \\) indexes the \\( k^{th} \\) related features." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.54, + 0.892, + 0.662 + ], + "angle": 0, + "content": "Integrating Shallow and Deep features. We select the \\(3^{th}\\) scale \\((\\tilde{s})\\) as the reference scale and resize other feature maps to this scale. Specifically, we utilize the learnable sampling coordinates \\((p_{q,k} + \\Delta p_{q,k})\\) to gather the distortion-free feature maps for every feature with resized scales following Eq.1. Let \\(f^s \\in \\mathbb{R}^{C \\times H_s \\times W_s}\\) be the original feature map at a certain scale \\(s\\). The gathered multi-scale feature maps \\(f_{m\\tilde{s}} \\in \\mathbb{R}^{C \\times H_{\\tilde{s}} \\times W_{\\tilde{s}} \\times 9 \\times 4}\\) can be represented as:" + }, + { + "type": "equation", + "bbox": [ + 0.616, + 0.675, + 0.891, + 0.708 + ], + "angle": 0, + "content": "\\[\nf _ {m \\tilde {s}} = \\sum_ {s = 1} ^ {4} \\sum_ {q = 1} ^ {H _ {\\tilde {s}} \\times W _ {\\tilde {s}}} \\sum_ {k = 1} ^ {9} \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.561, + 0.708, + 0.816, + 0.726 + ], + "angle": 0, + "content": "\\[\nS a m p l e (r e s i z e \\left(f ^ {s}, \\tilde {s}\\right), p _ {q, k} ^ {\\tilde {s}} + \\Delta p _ {q, k} ^ {\\tilde {s}}).\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.737, + 0.891, + 0.768 + ], + "angle": 0, + "content": "Then, the designed cross-scale distortion-aware feature assembling mechanism can be applied as:" + }, + { + "type": "equation", + "bbox": [ + 0.517, + 0.78, + 0.891, + 0.814 + ], + "angle": 0, + "content": "\\[\nf _ {m \\tilde {s}} ^ {\\prime} = \\operatorname {C S D A} \\left(f _ {m \\tilde {s}}\\right) = \\sum_ {l = 1} ^ {L} A _ {l} \\cdot \\text {r e s h a p e} \\left(f _ {m \\tilde {s}}\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.903 + ], + "angle": 0, + "content": "where \\(L\\) indexes the heads of the self-attention; \\(A_{l}\\in \\mathbb{R}^{L\\times H_{\\tilde{s}}W_{\\tilde{s}}\\times 36}\\) is the learnable self-attention weights from \\(f_{m\\tilde{s}}\\). To complete the calculation, we reshape \\(f_{m\\tilde{s}}\\) into the size of \\(\\mathbb{R}^{L\\times H_{\\tilde{s}}W_{\\tilde{s}}\\times 36\\times\\frac{C}{L}}\\). The final assembling features are denoted as \\(f_{m\\tilde{s}}^{\\prime}\\in \\mathbb{R}^{C\\times H_{\\tilde{s}}\\times W_{\\tilde{s}}}\\)." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.926, + 0.52, + 0.938 + ], + "angle": 0, + "content": "17339" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.895, + 0.423 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.427, + 0.895, + 0.486 + ], + "angle": 0, + "content": "Figure 2. Overview of the proposed framework. The feature assembling mechanism is designed to deal with distortions as well as integrate shallow and deep features (circled in Blue). Then we disentangle orthogonal planes to produce two 1D representations with distinguished plane semantics (circled in Purple). And triple attention is deployed to reconstruct the 1D representations (circled in Red). Our scheme leverages a single panorama with a resolution of \\(512 \\times 1024\\) as input and predicts the room height and the horizon depth." + }, + { + "type": "image", + "bbox": [ + 0.089, + 0.498, + 0.21, + 0.551 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.102, + 0.552, + 0.199, + 0.563 + ], + "angle": 0, + "content": "Original version" + }, + { + "type": "image", + "bbox": [ + 0.213, + 0.498, + 0.334, + 0.551 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.221, + 0.552, + 0.328, + 0.564 + ], + "angle": 0, + "content": "Vertically flipping" + }, + { + "type": "image", + "bbox": [ + 0.336, + 0.498, + 0.458, + 0.551 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.35, + 0.552, + 0.442, + 0.563 + ], + "angle": 0, + "content": "Misaligned case" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.567, + 0.47, + 0.595 + ], + "angle": 0, + "content": "Figure 3. Illustration of the misaligned case when leveraging the symmetry property." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.606, + 0.369, + 0.623 + ], + "angle": 0, + "content": "3.3. Disentangling Orthogonal Planes" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.47, + 0.689 + ], + "angle": 0, + "content": "In order to explicitly capture the geometric cues, we propose to disentangle the orthogonal planes. Particularly, we segment the vertical plane and horizontal planes from the whole scenario before compressing the 2D feature maps." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.47, + 0.81 + ], + "angle": 0, + "content": "Symmetry in Manhattan World. It is challenging to learn accurate layout boundaries in a complex scene due to the disturbance of furniture and illumination, e.g., occlusion. To address it, we propose to leverage the symmetry of the Manhattan World assumption (e.g., the floor boundary and ceiling boundary are strictly symmetric in 3D space) to provide complementary information. To exploit this symmetry property, we introduce a soft-flipping fusion strategy." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.471, + 0.902 + ], + "angle": 0, + "content": "We first vertically flip the feature maps to get their symmetrical version. In fact, the floor boundary and ceiling boundary are not strictly symmetric in an image because the shooting position is not in the exact middle of the floor and ceiling. To this end, we adopt a deformable convolution with \\(3 \\times 3\\) kernel size to adaptively adjust the symmetry" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.501, + 0.892, + 0.546 + ], + "angle": 0, + "content": "cal version. Next, we fuse the original feature and its \"soft\" symmetrical version to provide more informative boundary cues. We denote the fused features as \\( f_{u} \\in \\mathbb{R}^{C \\times H_{\\bar{s}} \\times W_{\\bar{s}}} \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.547, + 0.893, + 0.668 + ], + "angle": 0, + "content": "Segmenting Horizontal/Vertical Planes. To disentangle the 1D representation, we pre-segment the horizon/vertical planes in advance to capture an explicit geometric cue. Specifically, we generate the pseudo labels for the orthogonal planes with layout GT. Then, we use the generated labels to encourage the network to learn a binary mask \\( S \\in \\mathbb{R}^{H_{\\bar{s}} \\times W_{\\bar{s}}} \\) via a simple segmentation head. The two segmented feature maps can be denoted as:" + }, + { + "type": "equation", + "bbox": [ + 0.542, + 0.676, + 0.892, + 0.698 + ], + "angle": 0, + "content": "\\[\nf _ {h} ^ {p} = \\left(f _ {u} \\oplus f _ {m \\tilde {s}} ^ {\\prime}\\right) \\otimes \\text {s i g m o i d} (S), \\tag {4}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.544, + 0.694, + 0.815, + 0.71 + ], + "angle": 0, + "content": "\\[\nf _ {v} ^ {p} = \\left(f _ {u} \\oplus f _ {m \\tilde {s}} ^ {\\prime}\\right) \\otimes (1 - \\text {s i g m o i d} (S))\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.718, + 0.892, + 0.795 + ], + "angle": 0, + "content": "where \\(f_h^p / f_v^p\\) represents the horizon/vertical plane features, respectively; \\(\\oplus\\) is the element-wise sum and \\(\\otimes\\) is the element-wise product. Following previous works, we further vertically compress 2D feature maps to two 1D sequences \\(\\mathbf{Q}_h\\), \\(\\mathbf{Q}_v \\in \\mathbb{R}^{W_{\\bar{s}} \\times C}\\) with differnet plane semantics." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.802, + 0.808, + 0.818 + ], + "angle": 0, + "content": "3.4. Reconstructing 1D Representations" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Generating Discriminative Channels. There are generally unconfined dependencies among channels, resulting in confused semantic cues [10]. To this end, we propose a discriminative channels generation mechanism via graph convolution to enforce each channel to concentrate on distin" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.925, + 0.52, + 0.937 + ], + "angle": 0, + "content": "17340" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.182 + ], + "angle": 0, + "content": "guishing features. Different from normal pixel-wise [23] or object-wise [11] graphs, the introduced channel-wise one tends to guide the node to subtract the information from the neighbor nodes rather than aggregation. The formula of the discriminative channels generation mechanism can be represented as:" + }, + { + "type": "equation", + "bbox": [ + 0.165, + 0.196, + 0.47, + 0.213 + ], + "angle": 0, + "content": "\\[\nf ^ {\\prime} = \\mathbf {L} f W = (\\mathbf {I} - \\mathbf {A}) f W \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.226, + 0.469, + 0.346 + ], + "angle": 0, + "content": "where \\(\\mathbf{L}\\) and \\(\\mathbf{A}\\) are the symmetric normalized Laplacian matrix and normalized adjacency matrix of the channelwise graph, and \\(I\\) and \\(W\\) are the identity matrix and learnable weights, respectively. Please refer to the supplementary materials for more details about the channel-wise graph attention. Following Eq. 5, \\(\\mathbf{Q}_h\\) and \\(\\mathbf{Q}_v\\) are first reconstructed to be more discriminative in channels (represented as \\(\\mathbf{Q}_h^{\\prime},\\mathbf{Q}_v^{\\prime}\\in \\mathbb{R}^{W_{\\bar{s}}\\times C}\\))." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.348, + 0.47, + 0.408 + ], + "angle": 0, + "content": "Rebuilding Long-Range Dependencies. We employ the standard self-attention to reconstruct the intra-sequence long-range dependencies. The attention formula of the horizontal plane sequence can be written as:" + }, + { + "type": "equation", + "bbox": [ + 0.086, + 0.42, + 0.47, + 0.446 + ], + "angle": 0, + "content": "\\[\n\\operatorname {A t t e n t i o n} \\left(\\mathcal {Q} _ {h} ^ {\\prime}, \\mathcal {K} _ {h} ^ {\\prime}, \\mathcal {V} _ {h} ^ {\\prime}\\right) = \\operatorname {s o f t m a x} \\left(\\frac {\\mathcal {Q} _ {h} ^ {\\prime} \\left(\\mathcal {K} _ {h} ^ {\\prime}\\right) ^ {T}}{\\sqrt {d _ {k}}} \\mathcal {V} _ {h} ^ {\\prime}\\right), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.457, + 0.469, + 0.503 + ], + "angle": 0, + "content": "where \\(\\mathcal{Q}_h^\\prime ,\\mathcal{K}_h^\\prime ,\\mathcal{V}_h^\\prime\\) are all learned from \\(\\mathbf{Q}_h^\\prime\\) via a fully connected layer. Similarly, the calculation for the vertical plane sequence is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.088, + 0.515, + 0.47, + 0.54 + ], + "angle": 0, + "content": "\\[\n\\operatorname {A t t e n t i o n} \\left(\\mathcal {Q} _ {v} ^ {\\prime}, \\mathcal {K} _ {v} ^ {\\prime}, \\mathcal {V} _ {v} ^ {\\prime}\\right) = \\operatorname {s o f t m a x} \\left(\\frac {\\mathcal {Q} _ {v} ^ {\\prime} \\left(\\mathcal {K} _ {v} ^ {\\prime}\\right) ^ {T}}{\\sqrt {d _ {k}}} \\mathcal {V} _ {v} ^ {\\prime}\\right). \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.551, + 0.47, + 0.612 + ], + "angle": 0, + "content": "It captures global interactions to adapt to the large FoV of panoramas, contributing to better performance. We denote the two sequences with reconstructed long-range dependencies as \\(\\mathbf{Q}_h^{\\prime \\prime}\\), \\(\\mathbf{Q}_v^{\\prime \\prime} \\in \\mathbb{R}^{W_{\\bar{s}} \\times C}\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.612, + 0.47, + 0.687 + ], + "angle": 0, + "content": "Providing Missing Residuals. To compensate for inevitable errors in pre-segmentation, we introduce crossattention to provide the missing residuals. For the sequence about the horizontal plane, we extract the potential beneficial residuals as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.086, + 0.697, + 0.473, + 0.723 + ], + "angle": 0, + "content": "\\[\n\\operatorname {A t t e n t i o n} \\left(\\mathcal {Q} _ {h} ^ {\\prime \\prime}, \\mathcal {K} _ {v} ^ {\\prime \\prime}, \\mathcal {V} _ {v} ^ {\\prime \\prime}\\right) = \\operatorname {s o f t m a x} \\left(\\frac {\\mathcal {Q} _ {h} ^ {\\prime \\prime} \\left(\\mathcal {K} _ {v} ^ {\\prime \\prime}\\right) ^ {T}}{\\sqrt {d _ {k}}} \\mathcal {V} _ {v} ^ {\\prime \\prime}\\right). \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.734, + 0.171, + 0.747 + ], + "angle": 0, + "content": "For the other:" + }, + { + "type": "equation", + "bbox": [ + 0.086, + 0.758, + 0.473, + 0.784 + ], + "angle": 0, + "content": "\\[\n\\operatorname {A t t e n t i o n} \\left(\\mathcal {Q} _ {v} ^ {\\prime \\prime}, \\mathcal {K} _ {h} ^ {\\prime \\prime}, \\mathcal {V} _ {h} ^ {\\prime \\prime}\\right) = \\operatorname {s o f t m a x} \\left(\\frac {\\mathcal {Q} _ {v} ^ {\\prime \\prime} \\left(\\mathcal {K} _ {h} ^ {\\prime \\prime}\\right) ^ {T}}{\\sqrt {d _ {k}}} \\mathcal {V} _ {h} ^ {\\prime \\prime}\\right). \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.794, + 0.47, + 0.901 + ], + "angle": 0, + "content": "where \\(\\mathcal{Q}_h^{\\prime \\prime},\\mathcal{K}_h^{\\prime \\prime},\\mathcal{V}_h^{\\prime \\prime}\\) are all learned from \\(\\mathbf{Q}_h^{\\prime \\prime}(\\mathcal{Q}_v^{\\prime \\prime},\\mathcal{K}_v^{\\prime \\prime},\\mathcal{V}_v^{\\prime \\prime}\\) from \\(\\mathbf{Q}_v^{\\prime \\prime})\\) via a fully connected layer. Then we add the learned residuals with the two 1D sequences to implement the reconstruction. After that, two separate fully connected layers are employed to output the predicted horizon depth from the vertical plane sequence and the room height value from the horizontal plane one, respectively." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.685, + 0.108 + ], + "angle": 0, + "content": "3.5. Objective Function" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.115, + 0.892, + 0.191 + ], + "angle": 0, + "content": "Our objective function consists of two parts: one for room layout estimation and the other for plane segmentation. For the first part, we strictly follow [8] and it can be denoted as \\(\\mathcal{L}_{layout}\\). For the segmentation part, we apply binary cross-entropy loss \\(\\mathcal{L}_{segment}\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.509, + 0.201, + 0.892, + 0.228 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {s e g m e n t}} = \\frac {1}{N} \\sum_ {i \\in N} \\left(d _ {i} \\log \\bar {d} _ {i} + \\left(1 D _ {i}\\right) \\log \\left(1 - \\bar {d} _ {i}\\right)\\right) \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.24, + 0.892, + 0.286 + ], + "angle": 0, + "content": "where \\( \\bar{d}_i \\) is the ground truth of generated segmentation label, and \\( d_i \\) is the predicted value. Ultimately, we formulate the objective function as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.59, + 0.299, + 0.892, + 0.316 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\lambda \\mathcal {L} _ {\\text {s e g m e n t}} + \\mathcal {L} _ {\\text {l a y o u t}} \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.327, + 0.855, + 0.341 + ], + "angle": 0, + "content": "where \\(\\lambda\\) is set to 0.75 to balance different constraints." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.356, + 0.634, + 0.373 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.381, + 0.892, + 0.533 + ], + "angle": 0, + "content": "In this section, we validate the effectiveness of our solution and compare it with existing SoTA approaches on four popular datasets. Concretely, we conduct experiments on a single GTX 3090 GPU, and the batch size is set to 16 for training. The proposed approach is implemented with PyTorch. We choose Adam [9] as the optimizer and keep the default settings. The initialized learning rate is \\(1 \\times 10^{-4}\\). As in previous works [19, 8], we adopt standard left-right flipping, panoramic horizontal rotation, luminance change, and pano stretch for data augmentation during training." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.543, + 0.602, + 0.557 + ], + "angle": 0, + "content": "4.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.566, + 0.892, + 0.611 + ], + "angle": 0, + "content": "Four datasets are used for our experimental validation: Stanford 2D-3D [1], PanoContext [26], MatterportLayout [29] and ZInd [6]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.612, + 0.892, + 0.823 + ], + "angle": 0, + "content": "PanoContext [26] and Stanford 2D-3D [1] are two commonly used datasets for indoor panoramic room layout estimation that contain 514 and 552 cuboid room layouts, respectively. Especially, Stanford 2D-3D [1] is labeled by Zou et al. [28] and has a smaller vertical FoV than other datasets. Besides, MatterportLayout [29] is also annotated by Zou et al. [29], which contains 2,295 general room layouts. The final ZInd [6] dataset includes cuboid, general Manhattan, non-Manhattan, and non-flat ceilings layouts, which mimic the real-world data distribution better. The splits of ZInd [6] consists of 24,882 (for training), 3,080 (for validation), and 3,170 (for testing) panoramas. We strictly follow the same training/validation/test splits of the four datasets as in previous works for a fair comparison." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.832, + 0.685, + 0.847 + ], + "angle": 0, + "content": "4.2. Evaluation Metrics" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.902 + ], + "angle": 0, + "content": "We employ the commonly used standard evaluation metrics for a fair comparison, including corner error (CE), pixel error (PE), intersection over the union of floor shapes" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.926, + 0.518, + 0.938 + ], + "angle": 0, + "content": "17341" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.079, + 0.09, + 0.496, + 0.375 + ], + "angle": 0, + "content": "
Method3D IoU(%)CE(%)PE(%)
Train on PanoContext + Whole Stnfd.2D3D datasets
LayoutNetv2[29]85.020.631.79
Dula-Netv2[29]83.770.812.43
HorizonNet[19]82.630.742.17
LGT-Net[8]85.16--
LGT-Net [w/ Post-proc][8]84.940.692.07
Ours85.46--
Ours [w/ Post-proc]85.000.692.13
Train on Stnfd.2D3D + Whole PanoContext datasets
LayoutNetv2[29]82.660.832.59
Dula-Netv2[29]86.600.672.48
HorizonNet[19]82.720.692.27
AtlantaNet[14]83.940.712.18
LGT-Net[8]85.76--
LGT-Net [w/ Post-proc][8]86.030.632.11
Ours85.47--
Ours [w/ Post-proc]85.580.662.10
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.384, + 0.471, + 0.414 + ], + "angle": 0, + "content": "Table 1. Quantitative comparison results with the current SoTA solutions evaluated on Stanford 2D-3D and PanoContext[6] dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.43, + 0.471, + 0.492 + ], + "angle": 0, + "content": "(2D IoU), and 3D room layouts (3D IoU). Among them, 3D IoU yields a better reflection of the accuracy of the layout estimation in 3D space. RMSE and \\(\\delta_{1.25}\\) indicate the performance of depth estimation, e.g. the horizon-depth map," + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.5, + 0.283, + 0.515 + ], + "angle": 0, + "content": "4.3. Cuboid Room Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.523, + 0.47, + 0.72 + ], + "angle": 0, + "content": "We follow LGT-Net [8] to use the combined dataset scheme mentioned in Zou et al. [29] to evaluate our network on cuboid datasets. We denote the combined dataset that contains training splits of PanoContext [6] and whole Stanford 2D-3D datasets as \"Train on PanoContext + Whole Stnfd.2D3D datasets\" in Tab. 1. Similarly, \"Train on Stnfd.2D3D + Whole PanoContext\" in Tab. 1 represents that we train our network on the combined dataset that contains training splits of Stanford 2D-3D and the whole PanoContext dataset. The scheme is commonly used in previous works [28, 8]. We also report the results with a post-processing strategy in DuLa-Net [24] that is denoted as \"Ours [w/ Post-proc]\"." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Comparison results. We exhibit the quantitative comparison results on cuboid room layouts in Tab. 1. From the first group in Tab. 1, we can observe that our approach outperforms all the other SoTA schemes with respect to 3D IoU. But from the second group, Dula-Net v2 [29] offers better 3D IoU than ours. Dula-Net v2 [29] employs a perspective view (i.e., cubemap) that is more effective for panoramas with small vertical FoV. However, once applied to more general room layout datasets, its performance degrades significantly (it is proved with the other two datasets in Sec. 4.4). On the contrary, the proposed approach shows more general performance." + }, + { + "type": "table", + "bbox": [ + 0.501, + 0.09, + 0.896, + 0.252 + ], + "angle": 0, + "content": "
Method2D IoU(%)3D IoU(%)RMSEδ1
LayoutNetv2[29]78.7375.820.2580.871
Dula-Netv2[29]78.8275.050.2910.818
HorizonNet[19]81.7179.110.1970.929
AtlantaNet[14]82.0980.02--
HoHoNet[20]82.3279.88--
LED2-Net[21]82.6180.140.2070.947
DMH-Net [27]81.2578.97-0.925
LGT-Net[8]83.5281.110.2040.951
Ours84.1181.700.1970.950
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.261, + 0.892, + 0.292 + ], + "angle": 0, + "content": "Table 2. Quantitative comparison results with the current SoTA solutions evaluated on MatterportLayout[29] dataset." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.305, + 0.892, + 0.392 + ], + "angle": 0, + "content": "
Method2D IoU(%)3D IoU(%)RMSEδ1
HorizonNet[19]90.4488.590.1230.957
LED2-Net[21]90.3688.490.1240.955
LGT-Net[8]91.7789.950.1110.960
Ours91.9490.13--
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.401, + 0.892, + 0.43 + ], + "angle": 0, + "content": "Table 3. Quantitative comparison results with the current SoTA solutions evaluated on ZInD[6] dataset." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.45, + 0.71, + 0.465 + ], + "angle": 0, + "content": "4.4. General Room Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.475, + 0.892, + 0.595 + ], + "angle": 0, + "content": "MatterportLayout [29] dataset and ZInD [6] dataset provide more general indoor room layouts, which is much more challenging than the cuboid room layout datasets. Tab. 2/Tab. 3 exhibits the evaluation on MatterportLayout [29]/ZInD [6] datasets. The results of \\(\\mathsf{LED}^2\\)-Net [21] and HorizonNet [19] are from [8] that we strictly followed. Particularly, Jiang et al. utilize their official codeto re-train and re-evaluate with the standard evaluation metrics." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.597, + 0.893, + 0.839 + ], + "angle": 0, + "content": "Comparison results. We observe that Dula-Net [24] demonstrates much worse performance on the general room layout dataset (MatterportLayout), indicating that these perspective view-based methods are hard to be adapted to the more general indoor scenarios. Moreover, these 1D sequence-based methods are better than those 2D convolution-based schemes. However, they cannot produce accurate 3D layouts from a 1D sequence due to confused plane semantics, even if they introduce more powerful relationship builders (e.g., Bi-LSTM, Transformer). Hence, these methods give worse 3D IoU. Compared with them, our approach offers better performance than all other approaches with respect to 3D IoU because ours captures an explicit 3D geometric cue by disentangling orthogonal planes, which benefits recovering layouts from clear semantics (Fig. 6)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.894, + 0.902 + ], + "angle": 0, + "content": "We show the qualitative comparisons in Fig. 4. From the figure, we can observe that our method offers better 3D results (floor plan). In Fig. 5, our results are much similar to the post-processing version. Both indicate our proposal" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.926, + 0.521, + 0.938 + ], + "angle": 0, + "content": "17342" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.107, + 0.087, + 0.885, + 0.339 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.328, + 0.344, + 0.651, + 0.357 + ], + "angle": 0, + "content": "(a) Qualitative comparison on MatterportLayout [29] dataset." + }, + { + "type": "image", + "bbox": [ + 0.107, + 0.367, + 0.885, + 0.619 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.361, + 0.623, + 0.616, + 0.636 + ], + "angle": 0, + "content": "(b) Qualitative comparison on ZInD [6] dataset." + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.639, + 0.892, + 0.709 + ], + "angle": 0, + "content": "Figure 4. Qualitative comparison results evaluated on general layout datasets, MatterportLayout [29] and ZInD [6]. We compare our method with \\(\\mathbf{LED}^2\\)-Net [21] and LGT-Net [8]. The compared methods are all not employed the post-processing strategy. The boundaries of the room layout on a panorama are shown on the left and the floor plan is on the right. Ground truth is best viewed in Blue lines, and the prediction in Green. The predicted horizon depth, normal, and gradient are visualized below each panorama, and the ground truth is in the first row. We labeled the significant differences with dashed lines." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.727, + 0.471, + 0.758 + ], + "angle": 0, + "content": "that disentangling orthogonal planes to capture an explicit 3D geometric cue is an effective strategy." + }, + { + "type": "title", + "bbox": [ + 0.076, + 0.77, + 0.227, + 0.787 + ], + "angle": 0, + "content": "4.5. Ablation study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.47, + 0.901 + ], + "angle": 0, + "content": "We exhibit ablation studies in Tab. 4, where each component of our model is evaluated on MatterportLayout [29]. To demonstrate the effectiveness of the proposed feature assembling mechanism, we first ablate cross-scale interaction in feature assembling (denoted as \"w/o Cross-scale interaction\"). Then, we further remove the distortion elimination (denoted as \"w/o Feature assembling\"). To exhibit the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.727, + 0.892, + 0.863 + ], + "angle": 0, + "content": "benefit of orthogonal plane disentanglement, we put off the proposed disentangling orthogonal planes procedure (denoted as \"w/o Disentangling planes\") and soft-flipping fusion, respectively. Finally, we show the effect of each attention mechanism (denoted as \"w/o Discriminative channels\", \"w/o Long-range dependencies\", and \"w/o residuals\", respectively). Specially, we train each model around 500 epochs (not the best ones). Hence, the results of \"Ours [Full]\" are slightly lower than those in Tab. 2." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Feature assembling mechanism. From Tab. 4, the pipeline without cross-scale interaction shows inferior per" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.926, + 0.519, + 0.938 + ], + "angle": 0, + "content": "17343" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.092, + 0.095, + 0.363, + 0.182 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.221, + 0.186, + 0.355, + 0.2 + ], + "angle": 0, + "content": "(a) Standford 2D-3D [1]" + }, + { + "type": "image", + "bbox": [ + 0.374, + 0.094, + 0.478, + 0.17 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.487, + 0.094, + 0.755, + 0.182 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.626, + 0.186, + 0.741, + 0.199 + ], + "angle": 0, + "content": "(b) PanoContext [26]" + }, + { + "type": "image", + "bbox": [ + 0.764, + 0.104, + 0.864, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.092, + 0.21, + 0.363, + 0.298 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.217, + 0.302, + 0.358, + 0.314 + ], + "angle": 0, + "content": "(c) MatterportLayout [29]" + }, + { + "type": "image", + "bbox": [ + 0.377, + 0.219, + 0.474, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.487, + 0.211, + 0.759, + 0.298 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.648, + 0.302, + 0.719, + 0.314 + ], + "angle": 0, + "content": "(d) ZInD [6]" + }, + { + "type": "image", + "bbox": [ + 0.77, + 0.221, + 0.88, + 0.283 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.318, + 0.893, + 0.347 + ], + "angle": 0, + "content": "Figure 5. The 3D visualization results. We exhibit the predicted boundaries (best viewed in Green lines) and the ones with post-processing of the prediction (best viewed in Red lines) in the pancreas." + }, + { + "type": "image", + "bbox": [ + 0.092, + 0.355, + 0.351, + 0.401 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.368, + 0.355, + 0.624, + 0.401 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.625, + 0.355, + 0.879, + 0.401 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.403, + 0.893, + 0.445 + ], + "angle": 0, + "content": "Figure 6. We exhibit the features of the 1D representation. The one without orthogonal plane disentanglement is shown on the left, and ours is on the right. Without disentangling, the left contains redundant and confusing features that are not good for layout estimation. In contrast, our disentangled vertical plane features are more discriminative, showing more attention to the layout corners." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.462, + 0.479, + 0.61 + ], + "angle": 0, + "content": "
Method2D IoU(%)3D IoU(%)
w/o Cross-scale interaction83.2480.71
w/o Feature assembling82.3680.10
w/o Disentangling planes83.2380.60
w/o Flipping fusion83.0180.35
w/o Discriminative channels82.7480.23
w/o Long-range dependencies83.0480.97
w/o Residuals82.8980.45
Ours [Full]83.4681.34
" + }, + { + "type": "table_caption", + "bbox": [ + 0.101, + 0.62, + 0.445, + 0.634 + ], + "angle": 0, + "content": "Table 4. Ablation study on MatterportLayout [29] dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.655, + 0.47, + 0.716 + ], + "angle": 0, + "content": "formance to the full model. Further removing the distortion elimination part, the pipeline gives worse results. It is proved that both dealing with distortions and integrating cross-scale features are essential for layout estimation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.718, + 0.469, + 0.853 + ], + "angle": 0, + "content": "Disentangling orthogonal planes. Since the geometric cues are essential for inferring 3D information from 2D images, we propose to disentangle orthogonal planes. To prove the effectiveness, we remove that stage but preserve the flipping fusion strategy (the effectiveness of this strategy is validated separately). The results in Tab. 4 show that this stage can make the performance more competitive. Besides, the embedding of symmetry property also contributes to the promotion of the predicted results." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Reconstructing 1D representations. The dependencies of the 1D sequences have changed when disentangling the orthogonal planes. Hence, we propose to reconstruct the 1D" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.463, + 0.892, + 0.614 + ], + "angle": 0, + "content": "representations. We verify the effectiveness of each attention mechanism in turn. From Tab. 4, we can observe that all three reconstruction operations (generating discriminative channels, rebuilding long-range dependencies, and providing the missing residuals) can all benefit the overall performance. Significantly, when removing the channel-wise graph, the pipeline's performance decreases significantly, demonstrating that enforcing the network concentration on discriminative channel information can capture effective information by avoiding redundancy." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.634, + 0.619, + 0.648 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.661, + 0.892, + 0.856 + ], + "angle": 0, + "content": "In this paper, we propose a novel panoramic indoor room layout estimation approach. Current approaches generate a 1D representation by a vertical compression operation. We argue that this strategy confuses the semantic cues of different planes. To address this issue, we propose to disentangle orthogonal planes to capture geometric cues in 3D space. Specially, we introduce a vertical flip-fusion strategy to leverage the symmetry property of indoor room layout. Besides, our experimental results demonstrate that dealing with distortion, as well as integrating shallow and deep features, can enhance the performance. Experiments demonstrate that our algorithm significantly outperforms current SoTA methods." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.859, + 0.645, + 0.873 + ], + "angle": 0, + "content": "Acknowledgement." + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.873, + 0.645, + 0.886 + ], + "angle": 0, + "content": "by the National" + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.887, + 0.637, + 0.9 + ], + "angle": 0, + "content": "of China (Nos." + }, + { + "type": "text", + "bbox": [ + 0.666, + 0.859, + 0.892, + 0.873 + ], + "angle": 0, + "content": "This work was supported" + }, + { + "type": "text", + "bbox": [ + 0.666, + 0.873, + 0.892, + 0.886 + ], + "angle": 0, + "content": "Natural Science Foundation" + }, + { + "type": "text", + "bbox": [ + 0.694, + 0.887, + 0.892, + 0.9 + ], + "angle": 0, + "content": "62172032, 62120106009)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.926, + 0.519, + 0.938 + ], + "angle": 0, + "content": "17344" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.119, + 0.174, + 0.134 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.144, + 0.468, + 0.185 + ], + "angle": 0, + "content": "[1] Iro Armeni, Sasha Sax, Amir R Zamir, and Silvio Savarese. 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However, the compression procedure confuses the semantics of different planes, yielding inferior performance with ambiguous interpretability. + +To address this issue, we propose to disentangle this 1D representation by pre-segmenting orthogonal (vertical and horizontal) planes from a complex scene, explicitly capturing the geometric cues for indoor layout estimation. Considering the symmetry between the floor boundary and ceiling boundary, we also design a soft-flipping fusion strategy to assist the pre-segmentation. Besides, we present a feature assembling mechanism to effectively integrate shallow and deep features with distortion distribution awareness. To compensate for the potential errors in pre-segmentation, we further leverage triple attention to reconstruct the disentangled sequences for better performance. Experiments on four popular benchmarks demonstrate our superiority over existing SoTA solutions, especially on the 3D IoU metric. The code is available at https://github.com/zhijieshen-bjtu/DOPNet. + +# 1. Introduction + +Indoor panoramic layout estimation refers to reconstructing 3D room layouts from omnidirectional images. Since the panoramic vision system captures the whole-room contextual information, we can estimate the complete room layout with a single panoramic image. However, inferring the 3D information from a 2D image is an ill-posed problem. Besides, the $360^{\circ}$ field-of-view (FoV) of panoramas brings severe distortions that increase along the latitude. Both issues are challenging for indoor layout estimation. + +![](images/ee223d0bf847aa88dadd923b2edba5a3d2fddb778db9470cd96f978aa6cff5c2.jpg) +Figure 1. (a) The commonly used architecture. (b) The proposed one. Compared with the traditional pipeline, ours has two advantages: (1) Disentangling the 1D representation into two separate sequences with different plane semantics. (2) Adaptively integrating shallow and deep features with distortion awareness via a feature assembling mechanism rather than simple concatenation. + +Different from outdoor scenarios, the indoor room has the following properties: (1) The indoor scenes conform to the Manhattan World assumption (The floors and ceilings are all flat planes, and the walls are perpendicular to them). (2) The room layout is always described as the corners or the floor boundary and ceiling boundary. These characteristics could be used as potential priors to guide the design of a reasonable layout estimation method. + +Based on the Manhattan World assumption, previous approaches [19, 20, 8, 14, 21] prefer to estimate the layout from a 1D sequence. They advocate compressing the extracted 2D feature maps in height dimension to obtain a 1D sequence, of which every element in this sequence share the same distortion magnitude (Fig. 1a). We argue that this compressed representation does not eliminate the panoramic distortions because there is no explicit distortion processing when extracting 2D feature maps before compression. Moreover, this strategy roughly mixes the vertical and horizontal planes together, confusing the semantics of different planes that are crucial for layout estimation. + +On the other hand, some researchers devoted themselves + +to adopting different projection formats to boost the performance, e.g., the bird's view of the room [29] and cubemap projection [27]. These projection-based schemes weaken the negative effect of the distortions. Nevertheless, frequent projection operations between different formats raise computational complexity. In addition, there exists an inevitable domain gap between the feature maps from different formats. + +To address the above problems, we propose a novel architecture (Fig.1b) that disentangles the orthogonal planes in advance to capture an explicit geometric cue. Following [21], our room layout can be recovered from the predicted horizon-depth map and the room height. Therefore, the "clean" depth-relevant features and height-relevant features can both help with the layout estimation. To obtain such "clean" features free from the disturbance of decorations and furniture, we disentangle the widely used 1D representation into two separate sequences — the horizontal and vertical ones. Specifically, we pre-segment the vertical plane (i.e., walls) and horizontal planes (i.e., floors and ceilings) from the whole-room contextual information. Then these orthogonal planes are compressed into two 1D representations. Especially, based on the symmetry property between the floor boundary and ceiling boundary, we design a soft-flipping fusion strategy to assist this process. + +Moreover, we propose an assembling mechanism to fuse multi-scale features with distortion awareness effectively. To eliminate the negative effect of distortion, we compute the attention among distortion-relevant positions following distortion distribution patterns. Meanwhile, cross-scale interaction is carried out to integrate shallow geometric structures and deep semantic features. Considering the error of pre-segmentation, we further leverage triple attention to reconstruct the two 1D sequences. Particularly, we adopt graph-based attention to generate discriminative channels, self-attention to rebuild long-range dependencies, and cross-attention to provide the missing information for different sequences. + +To demonstrate our effectiveness, we conduct extensive experiments on four popular datasets — MatterportLayout [29], Zind [6], Stanford 2D-3D [1], and PanoContext [26]. The qualitative and quantitative results show that the proposed solution outperforms other SoTA methods. Our contributions can be summarized as follows: + +- We propose to disentangle orthogonal planes to capture an explicit geometric cue for indoor $360^{\circ}$ room layout estimation, with a soft-flipping fusion strategy to assist this procedure. +- We design a cross-scale distortion-aware assembling mechanism to perceive distortion distribution as well as integrate shallow geometric structures and deep semantic features. + +- On popular benchmarks, our solution outperforms other SoTA schemes, especially on the metric of intersection over the union of 3D room layouts. + +# 2. Related Work + +# 2.1. $360^{\circ}$ Room Layout Estimation + +Based on Manhattan World assumption [5] that all walls and floors are aligned with global coordinate system axes and are perpendicular to each other, many approaches utilize convolutional neural networks (CNNs) to extract useful features to improve layout estimation accuracy. Specifically, Zou et al. [28] propose LayoutNet to predict the corner/boundary probability maps directly from the panoramicas and then optimize the layout parameter to generate the final predicted results. Furthermore, they annotate the Stanford 2D-3D dataset [1] with awesome layouts for training and evaluation. Yang et al. [24] propose Dula-Net to predict a 2D floor plane semantic mask from both the equirectangular view and the perspective view of the ceilings. The modified version, LayoutNet v2, and Du la-Net v2, which have better performance than the original version, are presented by Zou et al. [29]. Fernandez et al. [7] present to utilize equirectangular convolutions (EquiConvs) to generate corner/edge probability maps. Sun et al. propose HorizonNet [19] and HoHoNet [20] to simplify the layout estimation processes by representing the room layout with a 1D representation. Besides, they use Bi-LSTM and multi-head self-attention to build long-range dependencies and refine the 1D sequences. + +Recently, several approaches have adopted this 1D representation and achieved impressive performance. For example, Rao et al. [15] establish their network based on HorizonNet [19]. They replace standard convolution operation with spherical convolution to reduce distortions and take Bi-GRU to reduce computational complexity. Wang et al. [21] combine the geometric cues across the layout and propose LED2-Net that reformulates the room layout estimation as predicting the depth of walls in the horizontal direction. Not constrained to Manhattan scenes, Pintore et al. [14] introduce AtlantaNet to predict the room layout by combining two projections of the floor and ceiling planes. Driven by the self-attention mechanism, many transformer-based methods [25, 22, 13] proposed to build long-range dependencies. For example, Jiang et al. [8] represent the room layout by horizon depth and room height and introduce a Transformer to enforce the network to learn the geometric relationships. However, the popular 1D representations could confuse the semantics of different planes, thus causing the layout estimation challenging. We disentangle this 1D representation by pre-segmenting orthogonal planes. + +# 2.2. $360^{\circ}$ Image Distortion Mitigation + +When converting spherical data to the equirectangular projection format, severe distortions are introduced. Some recent studies focus on designing spherical customized convolutions to make the network adapt to panoramic distortions and offer superior results compared to standard convolutional networks. Su et al. [18] introduce SphConv to remove distortions by changing the regular planar convolutions kernel size towards each row of the $360^{\circ}$ images. Cohen et al. [2] propose a spherical CNN that transforms the domain space from Euclidean S2 space to a SO(3) group to reduce the distortion and encodes full rotation invariance in their network. Coors et al. [3] addresses it by defining the convolution kernels on the tangent plane and keeping the convolution domain consistent in each kernel. Therefore, the non-distorted features can be extracted directly on $360^{\circ}$ images. Rao et al. [15] first applied spherical convolution operation to room layout task and showed significant improvements. Different from the above approaches, Shen et al. [16] propose the first panorama Transformer (PanoFormer) and divide the patches on the tangent plane to remove the negative effect of distortions. But most recent layout estimation works do not treat the distortions seriously because they think that the 1D representations can solve the distortions well. On the contrary, we propose a feature assembling mechanism with cross-scale distortion awareness to deal with distortions. Extensive experimental results demonstrate the necessity of handling distortions before generating 1D representations. + +# 3. Approach + +# 3.1. Overview + +As illustrated in Fig. 2, the proposed framework consists of three stages: feature extraction followed by a feature assembling mechanism, orthogonal plane disentanglement, and 1D representation reconstruction. Specifically, we adopt a backbone (basically ResNet) to extract a series of features at 4 different scales from a single panorama. Then a feature assembling mechanism is designed to fuse the multi-scale features and free them from panoramic distortions. In the next stage, we introduce a soft-flipping fusion strategy to explore the symmetry between the floor boundary and the ceiling boundary. After that, we segment the vertical and horizontal planes from the fused features followed by vertical compression, yielding two 1D representations. In the last stage, the disentangled features are reconstructed with triple attention to be more discriminative and informative. Finally, the horizon-depth map and room height are estimated from the reconstructed sequences. + +# 3.2. Cross-scale Distortion Awareness + +In previous works [19, 20, 21, 8], researchers prefer to follow the architecture of HorizonNet [19] to extract multiscale feature maps of an equirectangular image. These feature maps are merged together via vertical compression and concatenation [12]. However, the popular architecture just concatenates multi-scale features together and neglects the inherent distortion distribution, resulting in an inferior panoramic feature extraction capability. To address the above issues, we propose a novel feature assembling mechanism to deal with distortions, as well as ingeniously integrate shallow and deep features. + +Eliminating Distortions. Motivated by previous works [7, 16], we first polymerize the most relevant features via a virtue tangent plane on the panoramic sphere projection. Based on the projection formula [16, 17, 4] (we discuss it in detail in the supplementary material), we can get the distortion-free sampling coordinates $p \in \mathbb{R}^{H \times W \times 9 \times 2}$ (height, width, number of points, number of coordinates) in the 2D feature maps. The learnable offsets $\Delta p$ are employed to adjust the sampling locations adaptively. Then we obtain gathered features $f_{df} \in \mathbb{R}^{C \times H \times W \times 9}$ from the original features $f \in \mathbb{R}^{C \times H \times W}$ as follows: + +$$ +f _ {d f} = \sum_ {q = 1} ^ {H \times W} \sum_ {k = 1} ^ {9} S a m p l e (f, p _ {q, k} + \Delta p _ {q, k}), \tag {1} +$$ + +where $q$ represents the $q^{th}$ point to gather the relevant features; $k$ indexes the $k^{th}$ related features. + +Integrating Shallow and Deep features. We select the $3^{th}$ scale $(\tilde{s})$ as the reference scale and resize other feature maps to this scale. Specifically, we utilize the learnable sampling coordinates $(p_{q,k} + \Delta p_{q,k})$ to gather the distortion-free feature maps for every feature with resized scales following Eq.1. Let $f^s \in \mathbb{R}^{C \times H_s \times W_s}$ be the original feature map at a certain scale $s$ . The gathered multi-scale feature maps $f_{m\tilde{s}} \in \mathbb{R}^{C \times H_{\tilde{s}} \times W_{\tilde{s}} \times 9 \times 4}$ can be represented as: + +$$ +f _ {m \tilde {s}} = \sum_ {s = 1} ^ {4} \sum_ {q = 1} ^ {H _ {\tilde {s}} \times W _ {\tilde {s}}} \sum_ {k = 1} ^ {9} \tag {2} +$$ + +$$ +S a m p l e (r e s i z e \left(f ^ {s}, \tilde {s}\right), p _ {q, k} ^ {\tilde {s}} + \Delta p _ {q, k} ^ {\tilde {s}}). +$$ + +Then, the designed cross-scale distortion-aware feature assembling mechanism can be applied as: + +$$ +f _ {m \tilde {s}} ^ {\prime} = \operatorname {C S D A} \left(f _ {m \tilde {s}}\right) = \sum_ {l = 1} ^ {L} A _ {l} \cdot \text {r e s h a p e} \left(f _ {m \tilde {s}}\right), \tag {3} +$$ + +where $L$ indexes the heads of the self-attention; $A_{l}\in \mathbb{R}^{L\times H_{\tilde{s}}W_{\tilde{s}}\times 36}$ is the learnable self-attention weights from $f_{m\tilde{s}}$ . To complete the calculation, we reshape $f_{m\tilde{s}}$ into the size of $\mathbb{R}^{L\times H_{\tilde{s}}W_{\tilde{s}}\times 36\times\frac{C}{L}}$ . The final assembling features are denoted as $f_{m\tilde{s}}^{\prime}\in \mathbb{R}^{C\times H_{\tilde{s}}\times W_{\tilde{s}}}$ . + +![](images/4a0e551cc94c8fab06230e5c69a9f1fdde213b1d541a27545e57992a42382c7a.jpg) +Figure 2. Overview of the proposed framework. The feature assembling mechanism is designed to deal with distortions as well as integrate shallow and deep features (circled in Blue). Then we disentangle orthogonal planes to produce two 1D representations with distinguished plane semantics (circled in Purple). And triple attention is deployed to reconstruct the 1D representations (circled in Red). Our scheme leverages a single panorama with a resolution of $512 \times 1024$ as input and predicts the room height and the horizon depth. + +![](images/557f50a88eb5bb21a6f2cb2969e62b92233e4552b900a50071a217448a8adc3f.jpg) +Original version + +![](images/7e51ae6f7a83c363034e0374e49f403e28790d221c6efa400447c5391f48b3f0.jpg) +Vertically flipping +Figure 3. Illustration of the misaligned case when leveraging the symmetry property. + +![](images/59c1581b4bb66883bc834dce1f51865cf7081ff5dc0fdff4bd9148ff416b4584.jpg) +Misaligned case + +# 3.3. Disentangling Orthogonal Planes + +In order to explicitly capture the geometric cues, we propose to disentangle the orthogonal planes. Particularly, we segment the vertical plane and horizontal planes from the whole scenario before compressing the 2D feature maps. + +Symmetry in Manhattan World. It is challenging to learn accurate layout boundaries in a complex scene due to the disturbance of furniture and illumination, e.g., occlusion. To address it, we propose to leverage the symmetry of the Manhattan World assumption (e.g., the floor boundary and ceiling boundary are strictly symmetric in 3D space) to provide complementary information. To exploit this symmetry property, we introduce a soft-flipping fusion strategy. + +We first vertically flip the feature maps to get their symmetrical version. In fact, the floor boundary and ceiling boundary are not strictly symmetric in an image because the shooting position is not in the exact middle of the floor and ceiling. To this end, we adopt a deformable convolution with $3 \times 3$ kernel size to adaptively adjust the symmetry + +cal version. Next, we fuse the original feature and its "soft" symmetrical version to provide more informative boundary cues. We denote the fused features as $f_{u} \in \mathbb{R}^{C \times H_{\bar{s}} \times W_{\bar{s}}}$ . + +Segmenting Horizontal/Vertical Planes. To disentangle the 1D representation, we pre-segment the horizon/vertical planes in advance to capture an explicit geometric cue. Specifically, we generate the pseudo labels for the orthogonal planes with layout GT. Then, we use the generated labels to encourage the network to learn a binary mask $S \in \mathbb{R}^{H_{\bar{s}} \times W_{\bar{s}}}$ via a simple segmentation head. The two segmented feature maps can be denoted as: + +$$ +f _ {h} ^ {p} = \left(f _ {u} \oplus f _ {m \tilde {s}} ^ {\prime}\right) \otimes \text {s i g m o i d} (S), \tag {4} +$$ + +$$ +f _ {v} ^ {p} = \left(f _ {u} \oplus f _ {m \tilde {s}} ^ {\prime}\right) \otimes (1 - \text {s i g m o i d} (S)) +$$ + +where $f_h^p / f_v^p$ represents the horizon/vertical plane features, respectively; $\oplus$ is the element-wise sum and $\otimes$ is the element-wise product. Following previous works, we further vertically compress 2D feature maps to two 1D sequences $\mathbf{Q}_h$ , $\mathbf{Q}_v \in \mathbb{R}^{W_{\bar{s}} \times C}$ with differnet plane semantics. + +# 3.4. Reconstructing 1D Representations + +Generating Discriminative Channels. There are generally unconfined dependencies among channels, resulting in confused semantic cues [10]. To this end, we propose a discriminative channels generation mechanism via graph convolution to enforce each channel to concentrate on distin + +guishing features. Different from normal pixel-wise [23] or object-wise [11] graphs, the introduced channel-wise one tends to guide the node to subtract the information from the neighbor nodes rather than aggregation. The formula of the discriminative channels generation mechanism can be represented as: + +$$ +f ^ {\prime} = \mathbf {L} f W = (\mathbf {I} - \mathbf {A}) f W \tag {5} +$$ + +where $\mathbf{L}$ and $\mathbf{A}$ are the symmetric normalized Laplacian matrix and normalized adjacency matrix of the channelwise graph, and $I$ and $W$ are the identity matrix and learnable weights, respectively. Please refer to the supplementary materials for more details about the channel-wise graph attention. Following Eq. 5, $\mathbf{Q}_h$ and $\mathbf{Q}_v$ are first reconstructed to be more discriminative in channels (represented as $\mathbf{Q}_h^{\prime},\mathbf{Q}_v^{\prime}\in \mathbb{R}^{W_{\bar{s}}\times C}$ ). + +Rebuilding Long-Range Dependencies. We employ the standard self-attention to reconstruct the intra-sequence long-range dependencies. The attention formula of the horizontal plane sequence can be written as: + +$$ +\operatorname {A t t e n t i o n} \left(\mathcal {Q} _ {h} ^ {\prime}, \mathcal {K} _ {h} ^ {\prime}, \mathcal {V} _ {h} ^ {\prime}\right) = \operatorname {s o f t m a x} \left(\frac {\mathcal {Q} _ {h} ^ {\prime} \left(\mathcal {K} _ {h} ^ {\prime}\right) ^ {T}}{\sqrt {d _ {k}}} \mathcal {V} _ {h} ^ {\prime}\right), \tag {6} +$$ + +where $\mathcal{Q}_h^\prime ,\mathcal{K}_h^\prime ,\mathcal{V}_h^\prime$ are all learned from $\mathbf{Q}_h^\prime$ via a fully connected layer. Similarly, the calculation for the vertical plane sequence is defined as: + +$$ +\operatorname {A t t e n t i o n} \left(\mathcal {Q} _ {v} ^ {\prime}, \mathcal {K} _ {v} ^ {\prime}, \mathcal {V} _ {v} ^ {\prime}\right) = \operatorname {s o f t m a x} \left(\frac {\mathcal {Q} _ {v} ^ {\prime} \left(\mathcal {K} _ {v} ^ {\prime}\right) ^ {T}}{\sqrt {d _ {k}}} \mathcal {V} _ {v} ^ {\prime}\right). \tag {7} +$$ + +It captures global interactions to adapt to the large FoV of panoramas, contributing to better performance. We denote the two sequences with reconstructed long-range dependencies as $\mathbf{Q}_h^{\prime \prime}$ , $\mathbf{Q}_v^{\prime \prime} \in \mathbb{R}^{W_{\bar{s}} \times C}$ . + +Providing Missing Residuals. To compensate for inevitable errors in pre-segmentation, we introduce crossattention to provide the missing residuals. For the sequence about the horizontal plane, we extract the potential beneficial residuals as follows: + +$$ +\operatorname {A t t e n t i o n} \left(\mathcal {Q} _ {h} ^ {\prime \prime}, \mathcal {K} _ {v} ^ {\prime \prime}, \mathcal {V} _ {v} ^ {\prime \prime}\right) = \operatorname {s o f t m a x} \left(\frac {\mathcal {Q} _ {h} ^ {\prime \prime} \left(\mathcal {K} _ {v} ^ {\prime \prime}\right) ^ {T}}{\sqrt {d _ {k}}} \mathcal {V} _ {v} ^ {\prime \prime}\right). \tag {8} +$$ + +For the other: + +$$ +\operatorname {A t t e n t i o n} \left(\mathcal {Q} _ {v} ^ {\prime \prime}, \mathcal {K} _ {h} ^ {\prime \prime}, \mathcal {V} _ {h} ^ {\prime \prime}\right) = \operatorname {s o f t m a x} \left(\frac {\mathcal {Q} _ {v} ^ {\prime \prime} \left(\mathcal {K} _ {h} ^ {\prime \prime}\right) ^ {T}}{\sqrt {d _ {k}}} \mathcal {V} _ {h} ^ {\prime \prime}\right). \tag {9} +$$ + +where $\mathcal{Q}_h^{\prime \prime},\mathcal{K}_h^{\prime \prime},\mathcal{V}_h^{\prime \prime}$ are all learned from $\mathbf{Q}_h^{\prime \prime}(\mathcal{Q}_v^{\prime \prime},\mathcal{K}_v^{\prime \prime},\mathcal{V}_v^{\prime \prime}$ from $\mathbf{Q}_v^{\prime \prime})$ via a fully connected layer. Then we add the learned residuals with the two 1D sequences to implement the reconstruction. After that, two separate fully connected layers are employed to output the predicted horizon depth from the vertical plane sequence and the room height value from the horizontal plane one, respectively. + +# 3.5. Objective Function + +Our objective function consists of two parts: one for room layout estimation and the other for plane segmentation. For the first part, we strictly follow [8] and it can be denoted as $\mathcal{L}_{layout}$ . For the segmentation part, we apply binary cross-entropy loss $\mathcal{L}_{segment}$ as follows: + +$$ +\mathcal {L} _ {\text {s e g m e n t}} = \frac {1}{N} \sum_ {i \in N} \left(d _ {i} \log \bar {d} _ {i} + \left(1 D _ {i}\right) \log \left(1 - \bar {d} _ {i}\right)\right) \tag {10} +$$ + +where $\bar{d}_i$ is the ground truth of generated segmentation label, and $d_i$ is the predicted value. Ultimately, we formulate the objective function as follows: + +$$ +\mathcal {L} = \lambda \mathcal {L} _ {\text {s e g m e n t}} + \mathcal {L} _ {\text {l a y o u t}} \tag {11} +$$ + +where $\lambda$ is set to 0.75 to balance different constraints. + +# 4. Experiments + +In this section, we validate the effectiveness of our solution and compare it with existing SoTA approaches on four popular datasets. Concretely, we conduct experiments on a single GTX 3090 GPU, and the batch size is set to 16 for training. The proposed approach is implemented with PyTorch. We choose Adam [9] as the optimizer and keep the default settings. The initialized learning rate is $1 \times 10^{-4}$ . As in previous works [19, 8], we adopt standard left-right flipping, panoramic horizontal rotation, luminance change, and pano stretch for data augmentation during training. + +# 4.1. Datasets + +Four datasets are used for our experimental validation: Stanford 2D-3D [1], PanoContext [26], MatterportLayout [29] and ZInd [6]. + +PanoContext [26] and Stanford 2D-3D [1] are two commonly used datasets for indoor panoramic room layout estimation that contain 514 and 552 cuboid room layouts, respectively. Especially, Stanford 2D-3D [1] is labeled by Zou et al. [28] and has a smaller vertical FoV than other datasets. Besides, MatterportLayout [29] is also annotated by Zou et al. [29], which contains 2,295 general room layouts. The final ZInd [6] dataset includes cuboid, general Manhattan, non-Manhattan, and non-flat ceilings layouts, which mimic the real-world data distribution better. The splits of ZInd [6] consists of 24,882 (for training), 3,080 (for validation), and 3,170 (for testing) panoramas. We strictly follow the same training/validation/test splits of the four datasets as in previous works for a fair comparison. + +# 4.2. Evaluation Metrics + +We employ the commonly used standard evaluation metrics for a fair comparison, including corner error (CE), pixel error (PE), intersection over the union of floor shapes + +
Method3D IoU(%)CE(%)PE(%)
Train on PanoContext + Whole Stnfd.2D3D datasets
LayoutNetv2[29]85.020.631.79
Dula-Netv2[29]83.770.812.43
HorizonNet[19]82.630.742.17
LGT-Net[8]85.16--
LGT-Net [w/ Post-proc][8]84.940.692.07
Ours85.46--
Ours [w/ Post-proc]85.000.692.13
Train on Stnfd.2D3D + Whole PanoContext datasets
LayoutNetv2[29]82.660.832.59
Dula-Netv2[29]86.600.672.48
HorizonNet[19]82.720.692.27
AtlantaNet[14]83.940.712.18
LGT-Net[8]85.76--
LGT-Net [w/ Post-proc][8]86.030.632.11
Ours85.47--
Ours [w/ Post-proc]85.580.662.10
+ +Table 1. Quantitative comparison results with the current SoTA solutions evaluated on Stanford 2D-3D and PanoContext[6] dataset. + +(2D IoU), and 3D room layouts (3D IoU). Among them, 3D IoU yields a better reflection of the accuracy of the layout estimation in 3D space. RMSE and $\delta_{1.25}$ indicate the performance of depth estimation, e.g. the horizon-depth map, + +# 4.3. Cuboid Room Results + +We follow LGT-Net [8] to use the combined dataset scheme mentioned in Zou et al. [29] to evaluate our network on cuboid datasets. We denote the combined dataset that contains training splits of PanoContext [6] and whole Stanford 2D-3D datasets as "Train on PanoContext + Whole Stnfd.2D3D datasets" in Tab. 1. Similarly, "Train on Stnfd.2D3D + Whole PanoContext" in Tab. 1 represents that we train our network on the combined dataset that contains training splits of Stanford 2D-3D and the whole PanoContext dataset. The scheme is commonly used in previous works [28, 8]. We also report the results with a post-processing strategy in DuLa-Net [24] that is denoted as "Ours [w/ Post-proc]". + +Comparison results. We exhibit the quantitative comparison results on cuboid room layouts in Tab. 1. From the first group in Tab. 1, we can observe that our approach outperforms all the other SoTA schemes with respect to 3D IoU. But from the second group, Dula-Net v2 [29] offers better 3D IoU than ours. Dula-Net v2 [29] employs a perspective view (i.e., cubemap) that is more effective for panoramas with small vertical FoV. However, once applied to more general room layout datasets, its performance degrades significantly (it is proved with the other two datasets in Sec. 4.4). On the contrary, the proposed approach shows more general performance. + +
Method2D IoU(%)3D IoU(%)RMSEδ1
LayoutNetv2[29]78.7375.820.2580.871
Dula-Netv2[29]78.8275.050.2910.818
HorizonNet[19]81.7179.110.1970.929
AtlantaNet[14]82.0980.02--
HoHoNet[20]82.3279.88--
LED2-Net[21]82.6180.140.2070.947
DMH-Net [27]81.2578.97-0.925
LGT-Net[8]83.5281.110.2040.951
Ours84.1181.700.1970.950
+ +Table 2. Quantitative comparison results with the current SoTA solutions evaluated on MatterportLayout[29] dataset. + +
Method2D IoU(%)3D IoU(%)RMSEδ1
HorizonNet[19]90.4488.590.1230.957
LED2-Net[21]90.3688.490.1240.955
LGT-Net[8]91.7789.950.1110.960
Ours91.9490.13--
+ +Table 3. Quantitative comparison results with the current SoTA solutions evaluated on ZInD[6] dataset. + +# 4.4. General Room Results + +MatterportLayout [29] dataset and ZInD [6] dataset provide more general indoor room layouts, which is much more challenging than the cuboid room layout datasets. Tab. 2/Tab. 3 exhibits the evaluation on MatterportLayout [29]/ZInD [6] datasets. The results of $\mathsf{LED}^2$ -Net [21] and HorizonNet [19] are from [8] that we strictly followed. Particularly, Jiang et al. utilize their official codeto re-train and re-evaluate with the standard evaluation metrics. + +Comparison results. We observe that Dula-Net [24] demonstrates much worse performance on the general room layout dataset (MatterportLayout), indicating that these perspective view-based methods are hard to be adapted to the more general indoor scenarios. Moreover, these 1D sequence-based methods are better than those 2D convolution-based schemes. However, they cannot produce accurate 3D layouts from a 1D sequence due to confused plane semantics, even if they introduce more powerful relationship builders (e.g., Bi-LSTM, Transformer). Hence, these methods give worse 3D IoU. Compared with them, our approach offers better performance than all other approaches with respect to 3D IoU because ours captures an explicit 3D geometric cue by disentangling orthogonal planes, which benefits recovering layouts from clear semantics (Fig. 6). + +We show the qualitative comparisons in Fig. 4. From the figure, we can observe that our method offers better 3D results (floor plan). In Fig. 5, our results are much similar to the post-processing version. Both indicate our proposal + +![](images/6d5cd1be970160438cc7c07ed68f6c5728990f60dd5a90b0eb4fcaa2be200a95.jpg) +(a) Qualitative comparison on MatterportLayout [29] dataset. + +![](images/92dcbb1e67e745b0c592300ee423c928ccd88a8e9a1127c0ecc4f11fe233bbb0.jpg) +(b) Qualitative comparison on ZInD [6] dataset. +Figure 4. Qualitative comparison results evaluated on general layout datasets, MatterportLayout [29] and ZInD [6]. We compare our method with $\mathbf{LED}^2$ -Net [21] and LGT-Net [8]. The compared methods are all not employed the post-processing strategy. The boundaries of the room layout on a panorama are shown on the left and the floor plan is on the right. Ground truth is best viewed in Blue lines, and the prediction in Green. The predicted horizon depth, normal, and gradient are visualized below each panorama, and the ground truth is in the first row. We labeled the significant differences with dashed lines. + +that disentangling orthogonal planes to capture an explicit 3D geometric cue is an effective strategy. + +# 4.5. Ablation study + +We exhibit ablation studies in Tab. 4, where each component of our model is evaluated on MatterportLayout [29]. To demonstrate the effectiveness of the proposed feature assembling mechanism, we first ablate cross-scale interaction in feature assembling (denoted as "w/o Cross-scale interaction"). Then, we further remove the distortion elimination (denoted as "w/o Feature assembling"). To exhibit the + +benefit of orthogonal plane disentanglement, we put off the proposed disentangling orthogonal planes procedure (denoted as "w/o Disentangling planes") and soft-flipping fusion, respectively. Finally, we show the effect of each attention mechanism (denoted as "w/o Discriminative channels", "w/o Long-range dependencies", and "w/o residuals", respectively). Specially, we train each model around 500 epochs (not the best ones). Hence, the results of "Ours [Full]" are slightly lower than those in Tab. 2. + +Feature assembling mechanism. From Tab. 4, the pipeline without cross-scale interaction shows inferior per + +![](images/f3291e8e1aa7373e28c35f77bea992033e286b40e591c3db59b32c7ea7e4c9d5.jpg) +(a) Standford 2D-3D [1] + +![](images/f81abe11d6604d59ff83cc79c001e49df74a647fcc0a815c73d29fcc2fa1ca86.jpg) + +![](images/eba82dcc16c8f08bd369861fd9afef880d4e9fbfc7f65ef2ad6b66b46d2b37c1.jpg) +(b) PanoContext [26] + +![](images/6f8a57a3bd529b2c946837e5a020e703356131e2a909d7ab65ae1562d7188fe5.jpg) + +![](images/3992e16df8a36195ad97af317354769f24350bb5bf1aa05121760083d8442572.jpg) +(c) MatterportLayout [29] + +![](images/126ef462ca29a1d92575eef83f1464e308ce47eb6efbd699ff9327df123e7d86.jpg) + +![](images/9c96ae5f51127282c2fb9750b752edb0e3de9e2fde18b59f683adc640534bae8.jpg) +(d) ZInD [6] + +![](images/bdd378436c084f72881e3925765687f321d43de8d9132f6777ed717b8d8d9199.jpg) + +![](images/340af9f9234af567303c6aa503a22d34143c868e8c6485aec7d703922fc8fac5.jpg) +Figure 5. The 3D visualization results. We exhibit the predicted boundaries (best viewed in Green lines) and the ones with post-processing of the prediction (best viewed in Red lines) in the pancreas. + +![](images/de6c40e1e0cfa46133bf282375952c8b915ce0a1e6a125125fb6b2c7804604b1.jpg) +Figure 6. We exhibit the features of the 1D representation. The one without orthogonal plane disentanglement is shown on the left, and ours is on the right. Without disentangling, the left contains redundant and confusing features that are not good for layout estimation. In contrast, our disentangled vertical plane features are more discriminative, showing more attention to the layout corners. + +![](images/fc894017d8b96e2a80379d983bb1c652260bfd69ef3ff325da7834d20d5483a1.jpg) + +
Method2D IoU(%)3D IoU(%)
w/o Cross-scale interaction83.2480.71
w/o Feature assembling82.3680.10
w/o Disentangling planes83.2380.60
w/o Flipping fusion83.0180.35
w/o Discriminative channels82.7480.23
w/o Long-range dependencies83.0480.97
w/o Residuals82.8980.45
Ours [Full]83.4681.34
+ +Table 4. Ablation study on MatterportLayout [29] dataset. + +formance to the full model. Further removing the distortion elimination part, the pipeline gives worse results. It is proved that both dealing with distortions and integrating cross-scale features are essential for layout estimation. + +Disentangling orthogonal planes. Since the geometric cues are essential for inferring 3D information from 2D images, we propose to disentangle orthogonal planes. To prove the effectiveness, we remove that stage but preserve the flipping fusion strategy (the effectiveness of this strategy is validated separately). The results in Tab. 4 show that this stage can make the performance more competitive. Besides, the embedding of symmetry property also contributes to the promotion of the predicted results. + +Reconstructing 1D representations. The dependencies of the 1D sequences have changed when disentangling the orthogonal planes. Hence, we propose to reconstruct the 1D + +representations. We verify the effectiveness of each attention mechanism in turn. From Tab. 4, we can observe that all three reconstruction operations (generating discriminative channels, rebuilding long-range dependencies, and providing the missing residuals) can all benefit the overall performance. Significantly, when removing the channel-wise graph, the pipeline's performance decreases significantly, demonstrating that enforcing the network concentration on discriminative channel information can capture effective information by avoiding redundancy. + +# 5. Conclusion + +In this paper, we propose a novel panoramic indoor room layout estimation approach. Current approaches generate a 1D representation by a vertical compression operation. We argue that this strategy confuses the semantic cues of different planes. To address this issue, we propose to disentangle orthogonal planes to capture geometric cues in 3D space. Specially, we introduce a vertical flip-fusion strategy to leverage the symmetry property of indoor room layout. Besides, our experimental results demonstrate that dealing with distortion, as well as integrating shallow and deep features, can enhance the performance. Experiments demonstrate that our algorithm significantly outperforms current SoTA methods. + +# Acknowledgement. + +by the National + +of China (Nos. + +This work was supported + +Natural Science Foundation + +62172032, 62120106009). + +# References + +[1] Iro Armeni, Sasha Sax, Amir R Zamir, and Silvio Savarese. Joint 2d-3d-semantic data for indoor scene understanding. arXiv:1702.01105, 2017. 2, 5, 8 +[2] Taco S Cohen, Mario Geiger, Jonas Köhler, and Max Welling. Spherical cnns. arXiv:1801.10130, 2018. 3 +[3] Benjamin Coors, Alexandru Paul Condurache, and Andreas Geiger. Spherenet: Learning spherical representations for detection and classification in omnidirectional images. In ECCV, 2018. 3 +[4] Benjamin Coors, Alexandru Paul Condurache, and Andreas Geiger. Spherenet: Learning spherical representations for detection and classification in omnidirectional images. In ECCV, 2018. 3 +[5] James M Coughlan and Alan L Yuille. Manhattan world: Compass direction from a single image by bayesian inference. In ICCV, 1999. 2 +[6] Steve Cruz, Will Hutchcroft, Yuguang Li, Naji Khosravan, Ivaylo Boyadzhiev, and Sing Bing Kang. Zillow indoor dataset: Annotated floor plans with 360deg panoramicas and 3d room layouts. In CVPR, 2021. 2, 5, 6, 7, 8 +[7] Clara Fernandez-Labrador, Jose M Facil, Alejandro Perez-Yus, Cédric Demonceaux, Javier Civera, and Jose J Guerrero. Corners for layout: End-to-end layout recovery from 360 images. IEEE Robotics and Automation Letters, 2020. 2, 3 +[8] Zhigang Jiang, Zhongzheng Xiang, Jinhua Xu, and Ming Zhao. Lgt-net: Indoor panoramic room layout estimation with geometry-aware transformer network. In CVPR, 2022. 1, 2, 3, 5, 6, 7 +[9] Diederik P Kingma and Jimmy Ba. Adam: A method for stochastic optimization. In ICLR, 2015. 5 +[10] Yin Li and Abhinav Gupta. Beyond grids: Learning graph representations for visual recognition. Advances in Neural Information Processing Systems, 2018. 4 +[11] Chen Lin, Shuai Zheng, Zhizhe Liu, Youru Li, Zhenfeng Zhu, and Yao Zhao. Sgt: Scene graph-guided transformer for surgical report generation. In MICCAI, 2022. 5 +[12] Tsung-Yi Lin, Piotr Dólar, Ross Girshick, Kaiming He, Bharath Hariharan, and Serge Belongie. Feature pyramid networks for object detection. In CVPR, 2017. 3 +[13] Ze Liu, Yutong Lin, Yue Cao, Han Hu, Yixuan Wei, Zheng Zhang, Stephen Lin, and Baining Guo. Swin transformer: Hierarchical vision transformer using shifted windows. In ICCV, 2021. 2 +[14] Giovanni Pintore, Marco Agus, and Enrico Gobbetti. Atlantanet: Inferring the 3d indoor layout from a single 360 image beyond the Manhattan world assumption. In ECCV, 2020. 1, 2, 6 +[15] Shivansh Rao, Vikas Kumar, Daniel Kifer, C Lee Giles, and Ankur Mali. Omnilayout: Room layout reconstruction from indoor spherical panoramas. In CVPR, 2021. 2, 3 +[16] Zhijie Shen, Chunyu Lin, Kang Liao, Lang Nie, Zishuo Zheng, and Yao Zhao. Panofformer: Panorama transformer for indoor $360^{\circ}$ depth estimation. In ECCV, 2022. 3 + +[17] Zhijie Shen, Chunyu Lin, Lang Nie, Kang Liao, and Yao Zhao. Distortion-tolerant monocular depth estimation on omnidirectional images using dual-cubemap. In ICME, 2021. 3 +[18] Yu-Chuan Su and Kristen Grauman. Learning spherical convolution for fast features from 360 imagery. Advances in Neural Information Processing Systems, 2017. 3 +[19] Cheng Sun, Chi-Wei Hsiao, Min Sun, and Hwann-Tzong Chen. Horizonnet: Learning room layout with 1d representation and pano stretch data augmentation. In CVPR, 2019, 1, 2, 3, 5, 6 +[20] Cheng Sun, Min Sun, and Hwann-Tzong Chen. Hohonet: 360 indoor holistic understanding with latent horizontal features. In CVPR, 2021. 1, 2, 3, 6 +[21] Fu-En Wang, Yu-Hsuan Yeh, Min Sun, Wei-Chen Chiu, and Yi-Hsuan Tsai. Led 2-net: Monocular $360^{\circ}$ layout estimation via differentiable depth rendering. In CVPR, 2021. 1, 2, 3, 6, 7 +[22] Wenhai Wang, Enze Xie, Xiang Li, Deng-Ping Fan, Kaitao Song, Ding Liang, Tong Lu, Ping Luo, and Ling Shao. Pyramid vision transformer: A versatile backbone for dense prediction without convolutions. In ICCV, 2021. 2 +[23] Xiang Wang, Sifei Liu, Huimin Ma, and Ming-Hsuan Yang. Weakly-supervised semantic segmentation by iterative affinity learning. IJCV, 128(6):1736-1749, 2020. 5 +[24] Shang-Ta Yang, Fu-En Wang, Chi-Han Peng, Peter Wonka, Min Sun, and Hung-Kuo Chu. Dula-net: A dual-projection network for estimating room layouts from a single rgb panorama. In CVPR, 2019. 2, 6 +[25] Li Yuan, Yunpeng Chen, Tao Wang, Weihao Yu, Yujun Shi, Zi-Hang Jiang, Francis EH Tay, Jiashi Feng, and Shuicheng Yan. Tokens-to-token vit: Training vision transformers from scratch onImagenet. In ICCV, 2021. 2 +[26] Yinda Zhang, Shuran Song, Ping Tan, and Jianxiong Xiao. Panocontext: A whole-room 3d context model for panoramic scene understanding. In ECCV, 2014. 2, 5, 8 +[27] Yining Zhao, Chao Wen, Zhou Xue, and Yue Gao. 3d room layout estimation from a cubemap of panorama image via deep Manhattan hough transform. In ECCV, 2022. 2, 6 +[28] Chuhang Zou, Alex Colburn, Qi Shan, and Derek Hoiem. Layoutnet: Reconstructing the 3d room layout from a single rgb image. In CVPR, 2018. 2, 5, 6 +[29] Chuhang Zou, Jheng-Wei Su, Chi-Han Peng, Alex Colburn, Qi Shan, Peter Wonka, Hung-Kuo Chu, and Derek Hoiem. Manhattan room layout reconstruction from a single $360^{\circ}$ image: A comparative study of state-of-the-art methods. IJCV, 2021. 2, 5, 6, 7, 8 \ No newline at end of file diff --git a/2023/Disentangling Orthogonal Planes for Indoor Panoramic Room Layout Estimation With Cross-Scale Distortion Awareness/images.zip b/2023/Disentangling Orthogonal Planes for Indoor Panoramic Room Layout Estimation With Cross-Scale Distortion Awareness/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..235ce8673b84341bdeccef30d7cc88d26d9e9b68 --- /dev/null +++ b/2023/Disentangling Orthogonal Planes for Indoor Panoramic Room Layout Estimation With Cross-Scale Distortion Awareness/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:7139c5918a1b5926d3664fc74aae5e8b4eb47f253d7c3d56bb73578e3bc9c1c0 +size 717858 diff --git a/2023/Disentangling Orthogonal Planes for Indoor Panoramic Room Layout Estimation With Cross-Scale Distortion Awareness/layout.json b/2023/Disentangling Orthogonal Planes for Indoor Panoramic Room Layout Estimation With Cross-Scale Distortion Awareness/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..41d84830aa32ff384773d43d8fbc30dae6abf4d1 --- /dev/null +++ b/2023/Disentangling Orthogonal Planes for Indoor Panoramic Room Layout Estimation With Cross-Scale Distortion Awareness/layout.json @@ -0,0 +1,7687 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 82, + 103, + 512, + 138 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 103, + 512, + 138 + ], + "spans": [ + { + "bbox": [ + 82, + 103, + 512, + 138 + ], + "type": "text", + "content": "Disentangling Orthogonal Planes for Indoor Panoramic Room Layout Estimation with Cross-Scale Distortion Awareness" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 73, + 161, + 519, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 73, + 161, + 519, + 204 + ], + "spans": [ + { + "bbox": [ + 73, + 161, + 519, + 204 + ], + "type": "text", + "content": "Zhijie Shen, Zishuo Zheng, Chunyu Lin†, Lang Nie, Kang Liao, Shuai Zheng, and Yao Zhao Institute of Information Science, Beijing Jiaotong University, China Beijing Key Laboratory of Advanced Information Science and Network Technology" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 102, + 205, + 488, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 205, + 488, + 217 + ], + "spans": [ + { + "bbox": [ + 102, + 205, + 488, + 217 + ], + "type": "text", + "content": "{zhjshen, zszheng, cylin, nielang, kang_liao, zsl997, yzhao}@bjtu.edu.cn" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 245, + 192, + 258 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 245, + 192, + 258 + ], + "spans": [ + { + "bbox": [ + 143, + 245, + 192, + 258 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 271, + 287, + 343 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 271, + 287, + 343 + ], + "spans": [ + { + "bbox": [ + 47, + 271, + 287, + 343 + ], + "type": "text", + "content": "Based on the Manhattan World assumption, most existing indoor layout estimation schemes focus on recovering layouts from vertically compressed 1D sequences. However, the compression procedure confuses the semantics of different planes, yielding inferior performance with ambiguous interpretability." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 344, + 289, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 344, + 289, + 536 + ], + "spans": [ + { + "bbox": [ + 47, + 344, + 289, + 536 + ], + "type": "text", + "content": "To address this issue, we propose to disentangle this 1D representation by pre-segmenting orthogonal (vertical and horizontal) planes from a complex scene, explicitly capturing the geometric cues for indoor layout estimation. Considering the symmetry between the floor boundary and ceiling boundary, we also design a soft-flipping fusion strategy to assist the pre-segmentation. Besides, we present a feature assembling mechanism to effectively integrate shallow and deep features with distortion distribution awareness. 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Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 582, + 287, + 691 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 582, + 287, + 691 + ], + "spans": [ + { + "bbox": [ + 47, + 582, + 287, + 691 + ], + "type": "text", + "content": "Indoor panoramic layout estimation refers to reconstructing 3D room layouts from omnidirectional images. Since the panoramic vision system captures the whole-room contextual information, we can estimate the complete room layout with a single panoramic image. However, inferring the 3D information from a 2D image is an ill-posed problem. Besides, the " + }, + { + "bbox": [ + 47, + 582, + 287, + 691 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 47, + 582, + 287, + 691 + ], + "type": "text", + "content": " field-of-view (FoV) of panoramas brings severe distortions that increase along the latitude. Both issues are challenging for indoor layout estimation." + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 310, + 244, + 548, + 371 + ], + "blocks": [ + { + "bbox": [ + 310, + 244, + 548, + 371 + ], + "lines": [ + { + "bbox": [ + 310, + 244, + 548, + 371 + ], + "spans": [ + { + "bbox": [ + 310, + 244, + 548, + 371 + ], + "type": "image", + "image_path": "ee223d0bf847aa88dadd923b2edba5a3d2fddb778db9470cd96f978aa6cff5c2.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 375, + 547, + 441 + ], + "lines": [ + { + "bbox": [ + 305, + 375, + 547, + 441 + ], + "spans": [ + { + "bbox": [ + 305, + 375, + 547, + 441 + ], + "type": "text", + "content": "Figure 1. (a) The commonly used architecture. (b) The proposed one. Compared with the traditional pipeline, ours has two advantages: (1) Disentangling the 1D representation into two separate sequences with different plane semantics. (2) Adaptively integrating shallow and deep features with distortion awareness via a feature assembling mechanism rather than simple concatenation." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 459, + 546, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 459, + 546, + 554 + ], + "spans": [ + { + "bbox": [ + 305, + 459, + 546, + 554 + ], + "type": "text", + "content": "Different from outdoor scenarios, the indoor room has the following properties: (1) The indoor scenes conform to the Manhattan World assumption (The floors and ceilings are all flat planes, and the walls are perpendicular to them). (2) The room layout is always described as the corners or the floor boundary and ceiling boundary. These characteristics could be used as potential priors to guide the design of a reasonable layout estimation method." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 555, + 547, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 555, + 547, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 555, + 547, + 700 + ], + "type": "text", + "content": "Based on the Manhattan World assumption, previous approaches [19, 20, 8, 14, 21] prefer to estimate the layout from a 1D sequence. They advocate compressing the extracted 2D feature maps in height dimension to obtain a 1D sequence, of which every element in this sequence share the same distortion magnitude (Fig. 1a). We argue that this compressed representation does not eliminate the panoramic distortions because there is no explicit distortion processing when extracting 2D feature maps before compression. Moreover, this strategy roughly mixes the vertical and horizontal planes together, confusing the semantics of different planes that are crucial for layout estimation." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 317, + 701, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 701, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 317, + 701, + 545, + 712 + ], + "type": "text", + "content": "On the other hand, some researchers devoted themselves" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 59, + 702, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 702, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 59, + 702, + 135, + 712 + ], + "type": "text", + "content": "†Corresponding author" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "type": "text", + "content": "17337" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "content": "to adopting different projection formats to boost the performance, e.g., the bird's view of the room [29] and cubemap projection [27]. These projection-based schemes weaken the negative effect of the distortions. Nevertheless, frequent projection operations between different formats raise computational complexity. In addition, there exists an inevitable domain gap between the feature maps from different formats." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 168, + 289, + 372 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 168, + 289, + 372 + ], + "spans": [ + { + "bbox": [ + 46, + 168, + 289, + 372 + ], + "type": "text", + "content": "To address the above problems, we propose a novel architecture (Fig.1b) that disentangles the orthogonal planes in advance to capture an explicit geometric cue. Following [21], our room layout can be recovered from the predicted horizon-depth map and the room height. Therefore, the \"clean\" depth-relevant features and height-relevant features can both help with the layout estimation. To obtain such \"clean\" features free from the disturbance of decorations and furniture, we disentangle the widely used 1D representation into two separate sequences — the horizontal and vertical ones. Specifically, we pre-segment the vertical plane (i.e., walls) and horizontal planes (i.e., floors and ceilings) from the whole-room contextual information. Then these orthogonal planes are compressed into two 1D representations. Especially, based on the symmetry property between the floor boundary and ceiling boundary, we design a soft-flipping fusion strategy to assist this process." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 372, + 289, + 527 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 372, + 289, + 527 + ], + "spans": [ + { + "bbox": [ + 46, + 372, + 289, + 527 + ], + "type": "text", + "content": "Moreover, we propose an assembling mechanism to fuse multi-scale features with distortion awareness effectively. To eliminate the negative effect of distortion, we compute the attention among distortion-relevant positions following distortion distribution patterns. Meanwhile, cross-scale interaction is carried out to integrate shallow geometric structures and deep semantic features. Considering the error of pre-segmentation, we further leverage triple attention to reconstruct the two 1D sequences. Particularly, we adopt graph-based attention to generate discriminative channels, self-attention to rebuild long-range dependencies, and cross-attention to provide the missing information for different sequences." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 528, + 289, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 528, + 289, + 598 + ], + "spans": [ + { + "bbox": [ + 46, + 528, + 289, + 598 + ], + "type": "text", + "content": "To demonstrate our effectiveness, we conduct extensive experiments on four popular datasets — MatterportLayout [29], Zind [6], Stanford 2D-3D [1], and PanoContext [26]. The qualitative and quantitative results show that the proposed solution outperforms other SoTA methods. Our contributions can be summarized as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 59, + 609, + 287, + 712 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 59, + 609, + 287, + 657 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 609, + 287, + 657 + ], + "spans": [ + { + "bbox": [ + 59, + 609, + 287, + 657 + ], + "type": "text", + "content": "- We propose to disentangle orthogonal planes to capture an explicit geometric cue for indoor " + }, + { + "bbox": [ + 59, + 609, + 287, + 657 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 59, + 609, + 287, + 657 + ], + "type": "text", + "content": " room layout estimation, with a soft-flipping fusion strategy to assist this procedure." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 59, + 665, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 665, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 59, + 665, + 287, + 712 + ], + "type": "text", + "content": "- We design a cross-scale distortion-aware assembling mechanism to perceive distortion distribution as well as integrate shallow geometric structures and deep semantic features." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 317, + 72, + 545, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 72, + 545, + 109 + ], + "spans": [ + { + "bbox": [ + 317, + 72, + 545, + 109 + ], + "type": "text", + "content": "- On popular benchmarks, our solution outperforms other SoTA schemes, especially on the metric of intersection over the union of 3D room layouts." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 140, + 392, + 152 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 140, + 392, + 152 + ], + "spans": [ + { + "bbox": [ + 306, + 140, + 392, + 152 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 167, + 470, + 179 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 167, + 470, + 179 + ], + "spans": [ + { + "bbox": [ + 306, + 167, + 470, + 179 + ], + "type": "text", + "content": "2.1. " + }, + { + "bbox": [ + 306, + 167, + 470, + 179 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 306, + 167, + 470, + 179 + ], + "type": "text", + "content": " Room Layout Estimation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 192, + 547, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 192, + 547, + 456 + ], + "spans": [ + { + "bbox": [ + 304, + 192, + 547, + 456 + ], + "type": "text", + "content": "Based on Manhattan World assumption [5] that all walls and floors are aligned with global coordinate system axes and are perpendicular to each other, many approaches utilize convolutional neural networks (CNNs) to extract useful features to improve layout estimation accuracy. Specifically, Zou et al. [28] propose LayoutNet to predict the corner/boundary probability maps directly from the panoramicas and then optimize the layout parameter to generate the final predicted results. Furthermore, they annotate the Stanford 2D-3D dataset [1] with awesome layouts for training and evaluation. Yang et al. [24] propose Dula-Net to predict a 2D floor plane semantic mask from both the equirectangular view and the perspective view of the ceilings. The modified version, LayoutNet v2, and Du la-Net v2, which have better performance than the original version, are presented by Zou et al. [29]. Fernandez et al. [7] present to utilize equirectangular convolutions (EquiConvs) to generate corner/edge probability maps. Sun et al. propose HorizonNet [19] and HoHoNet [20] to simplify the layout estimation processes by representing the room layout with a 1D representation. Besides, they use Bi-LSTM and multi-head self-attention to build long-range dependencies and refine the 1D sequences." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 463, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 463, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 463, + 547, + 715 + ], + "type": "text", + "content": "Recently, several approaches have adopted this 1D representation and achieved impressive performance. For example, Rao et al. [15] establish their network based on HorizonNet [19]. They replace standard convolution operation with spherical convolution to reduce distortions and take Bi-GRU to reduce computational complexity. Wang et al. [21] combine the geometric cues across the layout and propose LED2-Net that reformulates the room layout estimation as predicting the depth of walls in the horizontal direction. Not constrained to Manhattan scenes, Pintore et al. [14] introduce AtlantaNet to predict the room layout by combining two projections of the floor and ceiling planes. Driven by the self-attention mechanism, many transformer-based methods [25, 22, 13] proposed to build long-range dependencies. For example, Jiang et al. [8] represent the room layout by horizon depth and room height and introduce a Transformer to enforce the network to learn the geometric relationships. However, the popular 1D representations could confuse the semantics of different planes, thus causing the layout estimation challenging. We disentangle this 1D representation by pre-segmenting orthogonal planes." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 732, + 318, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 732, + 318, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 732, + 318, + 742 + ], + "type": "text", + "content": "17338" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 224, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 224, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 224, + 85 + ], + "type": "text", + "content": "2.2. " + }, + { + "bbox": [ + 47, + 72, + 224, + 85 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 47, + 72, + 224, + 85 + ], + "type": "text", + "content": " Image Distortion Mitigation" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 96, + 289, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 96, + 289, + 431 + ], + "spans": [ + { + "bbox": [ + 47, + 96, + 289, + 431 + ], + "type": "text", + "content": "When converting spherical data to the equirectangular projection format, severe distortions are introduced. Some recent studies focus on designing spherical customized convolutions to make the network adapt to panoramic distortions and offer superior results compared to standard convolutional networks. Su et al. [18] introduce SphConv to remove distortions by changing the regular planar convolutions kernel size towards each row of the " + }, + { + "bbox": [ + 47, + 96, + 289, + 431 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 47, + 96, + 289, + 431 + ], + "type": "text", + "content": " images. Cohen et al. [2] propose a spherical CNN that transforms the domain space from Euclidean S2 space to a SO(3) group to reduce the distortion and encodes full rotation invariance in their network. Coors et al. [3] addresses it by defining the convolution kernels on the tangent plane and keeping the convolution domain consistent in each kernel. Therefore, the non-distorted features can be extracted directly on " + }, + { + "bbox": [ + 47, + 96, + 289, + 431 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 47, + 96, + 289, + 431 + ], + "type": "text", + "content": " images. Rao et al. [15] first applied spherical convolution operation to room layout task and showed significant improvements. Different from the above approaches, Shen et al. [16] propose the first panorama Transformer (PanoFormer) and divide the patches on the tangent plane to remove the negative effect of distortions. But most recent layout estimation works do not treat the distortions seriously because they think that the 1D representations can solve the distortions well. On the contrary, we propose a feature assembling mechanism with cross-scale distortion awareness to deal with distortions. Extensive experimental results demonstrate the necessity of handling distortions before generating 1D representations." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 460, + 113, + 474 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 460, + 113, + 474 + ], + "spans": [ + { + "bbox": [ + 47, + 460, + 113, + 474 + ], + "type": "text", + "content": "3. Approach" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 485, + 114, + 498 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 485, + 114, + 498 + ], + "spans": [ + { + "bbox": [ + 47, + 485, + 114, + 498 + ], + "type": "text", + "content": "3.1. Overview" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 510, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 510, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 510, + 289, + 715 + ], + "type": "text", + "content": "As illustrated in Fig. 2, the proposed framework consists of three stages: feature extraction followed by a feature assembling mechanism, orthogonal plane disentanglement, and 1D representation reconstruction. Specifically, we adopt a backbone (basically ResNet) to extract a series of features at 4 different scales from a single panorama. Then a feature assembling mechanism is designed to fuse the multi-scale features and free them from panoramic distortions. In the next stage, we introduce a soft-flipping fusion strategy to explore the symmetry between the floor boundary and the ceiling boundary. After that, we segment the vertical and horizontal planes from the fused features followed by vertical compression, yielding two 1D representations. In the last stage, the disentangled features are reconstructed with triple attention to be more discriminative and informative. Finally, the horizon-depth map and room height are estimated from the reconstructed sequences." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 72, + 484, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 484, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 484, + 84 + ], + "type": "text", + "content": "3.2. Cross-scale Distortion Awareness" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 91, + 545, + 222 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 91, + 545, + 222 + ], + "spans": [ + { + "bbox": [ + 304, + 91, + 545, + 222 + ], + "type": "text", + "content": "In previous works [19, 20, 21, 8], researchers prefer to follow the architecture of HorizonNet [19] to extract multiscale feature maps of an equirectangular image. These feature maps are merged together via vertical compression and concatenation [12]. However, the popular architecture just concatenates multi-scale features together and neglects the inherent distortion distribution, resulting in an inferior panoramic feature extraction capability. To address the above issues, we propose a novel feature assembling mechanism to deal with distortions, as well as ingeniously integrate shallow and deep features." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 223, + 545, + 355 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 223, + 545, + 355 + ], + "spans": [ + { + "bbox": [ + 304, + 223, + 545, + 355 + ], + "type": "text", + "content": "Eliminating Distortions. Motivated by previous works [7, 16], we first polymerize the most relevant features via a virtue tangent plane on the panoramic sphere projection. Based on the projection formula [16, 17, 4] (we discuss it in detail in the supplementary material), we can get the distortion-free sampling coordinates " + }, + { + "bbox": [ + 304, + 223, + 545, + 355 + ], + "type": "inline_equation", + "content": "p \\in \\mathbb{R}^{H \\times W \\times 9 \\times 2}" + }, + { + "bbox": [ + 304, + 223, + 545, + 355 + ], + "type": "text", + "content": " (height, width, number of points, number of coordinates) in the 2D feature maps. The learnable offsets " + }, + { + "bbox": [ + 304, + 223, + 545, + 355 + ], + "type": "inline_equation", + "content": "\\Delta p" + }, + { + "bbox": [ + 304, + 223, + 545, + 355 + ], + "type": "text", + "content": " are employed to adjust the sampling locations adaptively. Then we obtain gathered features " + }, + { + "bbox": [ + 304, + 223, + 545, + 355 + ], + "type": "inline_equation", + "content": "f_{df} \\in \\mathbb{R}^{C \\times H \\times W \\times 9}" + }, + { + "bbox": [ + 304, + 223, + 545, + 355 + ], + "type": "text", + "content": " from the original features " + }, + { + "bbox": [ + 304, + 223, + 545, + 355 + ], + "type": "inline_equation", + "content": "f \\in \\mathbb{R}^{C \\times H \\times W}" + }, + { + "bbox": [ + 304, + 223, + 545, + 355 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 327, + 364, + 545, + 392 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 327, + 364, + 545, + 392 + ], + "spans": [ + { + "bbox": [ + 327, + 364, + 545, + 392 + ], + "type": "interline_equation", + "content": "f _ {d f} = \\sum_ {q = 1} ^ {H \\times W} \\sum_ {k = 1} ^ {9} S a m p l e (f, p _ {q, k} + \\Delta p _ {q, k}), \\tag {1}", + "image_path": "275ef8bb9ec59c64fb42326539b8e1dbf7efe7ebe30c0d1d4430e1687bedad73.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 403, + 545, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 403, + 545, + 426 + ], + "spans": [ + { + "bbox": [ + 304, + 403, + 545, + 426 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 403, + 545, + 426 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 304, + 403, + 545, + 426 + ], + "type": "text", + "content": " represents the " + }, + { + "bbox": [ + 304, + 403, + 545, + 426 + ], + "type": "inline_equation", + "content": "q^{th}" + }, + { + "bbox": [ + 304, + 403, + 545, + 426 + ], + "type": "text", + "content": " point to gather the relevant features; " + }, + { + "bbox": [ + 304, + 403, + 545, + 426 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 403, + 545, + 426 + ], + "type": "text", + "content": " indexes the " + }, + { + "bbox": [ + 304, + 403, + 545, + 426 + ], + "type": "inline_equation", + "content": "k^{th}" + }, + { + "bbox": [ + 304, + 403, + 545, + 426 + ], + "type": "text", + "content": " related features." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 427, + 545, + 524 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 427, + 545, + 524 + ], + "spans": [ + { + "bbox": [ + 304, + 427, + 545, + 524 + ], + "type": "text", + "content": "Integrating Shallow and Deep features. We select the " + }, + { + "bbox": [ + 304, + 427, + 545, + 524 + ], + "type": "inline_equation", + "content": "3^{th}" + }, + { + "bbox": [ + 304, + 427, + 545, + 524 + ], + "type": "text", + "content": " scale " + }, + { + "bbox": [ + 304, + 427, + 545, + 524 + ], + "type": "inline_equation", + "content": "(\\tilde{s})" + }, + { + "bbox": [ + 304, + 427, + 545, + 524 + ], + "type": "text", + "content": " as the reference scale and resize other feature maps to this scale. Specifically, we utilize the learnable sampling coordinates " + }, + { + "bbox": [ + 304, + 427, + 545, + 524 + ], + "type": "inline_equation", + "content": "(p_{q,k} + \\Delta p_{q,k})" + }, + { + "bbox": [ + 304, + 427, + 545, + 524 + ], + "type": "text", + "content": " to gather the distortion-free feature maps for every feature with resized scales following Eq.1. Let " + }, + { + "bbox": [ + 304, + 427, + 545, + 524 + ], + "type": "inline_equation", + "content": "f^s \\in \\mathbb{R}^{C \\times H_s \\times W_s}" + }, + { + "bbox": [ + 304, + 427, + 545, + 524 + ], + "type": "text", + "content": " be the original feature map at a certain scale " + }, + { + "bbox": [ + 304, + 427, + 545, + 524 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 427, + 545, + 524 + ], + "type": "text", + "content": ". The gathered multi-scale feature maps " + }, + { + "bbox": [ + 304, + 427, + 545, + 524 + ], + "type": "inline_equation", + "content": "f_{m\\tilde{s}} \\in \\mathbb{R}^{C \\times H_{\\tilde{s}} \\times W_{\\tilde{s}} \\times 9 \\times 4}" + }, + { + "bbox": [ + 304, + 427, + 545, + 524 + ], + "type": "text", + "content": " can be represented as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 376, + 534, + 545, + 560 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 376, + 534, + 545, + 560 + ], + "spans": [ + { + "bbox": [ + 376, + 534, + 545, + 560 + ], + "type": "interline_equation", + "content": "f _ {m \\tilde {s}} = \\sum_ {s = 1} ^ {4} \\sum_ {q = 1} ^ {H _ {\\tilde {s}} \\times W _ {\\tilde {s}}} \\sum_ {k = 1} ^ {9} \\tag {2}", + "image_path": "78b592c8b62b8728e9f92fd281b5a52ccc08f61e2e0cf00aaf8da568a6f09248.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 343, + 560, + 499, + 574 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 343, + 560, + 499, + 574 + ], + "spans": [ + { + "bbox": [ + 343, + 560, + 499, + 574 + ], + "type": "interline_equation", + "content": "S a m p l e (r e s i z e \\left(f ^ {s}, \\tilde {s}\\right), p _ {q, k} ^ {\\tilde {s}} + \\Delta p _ {q, k} ^ {\\tilde {s}}).", + "image_path": "97da5132c22d5e6a68f75aac648ea8ce7c81e8e784684e24bb704f31e3f0591f.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 583, + 545, + 608 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 583, + 545, + 608 + ], + "spans": [ + { + "bbox": [ + 306, + 583, + 545, + 608 + ], + "type": "text", + "content": "Then, the designed cross-scale distortion-aware feature assembling mechanism can be applied as:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 316, + 617, + 545, + 644 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 617, + 545, + 644 + ], + "spans": [ + { + "bbox": [ + 316, + 617, + 545, + 644 + ], + "type": "interline_equation", + "content": "f _ {m \\tilde {s}} ^ {\\prime} = \\operatorname {C S D A} \\left(f _ {m \\tilde {s}}\\right) = \\sum_ {l = 1} ^ {L} A _ {l} \\cdot \\text {r e s h a p e} \\left(f _ {m \\tilde {s}}\\right), \\tag {3}", + "image_path": "f63e164268dace1a16137ed4bb8380411e324fcf3def3868add368e9882af9e1.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 653, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 653, + 545, + 715 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 304, + 653, + 545, + 715 + ], + "type": "text", + "content": " indexes the heads of the self-attention; " + }, + { + "bbox": [ + 304, + 653, + 545, + 715 + ], + "type": "inline_equation", + "content": "A_{l}\\in \\mathbb{R}^{L\\times H_{\\tilde{s}}W_{\\tilde{s}}\\times 36}" + }, + { + "bbox": [ + 304, + 653, + 545, + 715 + ], + "type": "text", + "content": " is the learnable self-attention weights from " + }, + { + "bbox": [ + 304, + 653, + 545, + 715 + ], + "type": "inline_equation", + "content": "f_{m\\tilde{s}}" + }, + { + "bbox": [ + 304, + 653, + 545, + 715 + ], + "type": "text", + "content": ". To complete the calculation, we reshape " + }, + { + "bbox": [ + 304, + 653, + 545, + 715 + ], + "type": "inline_equation", + "content": "f_{m\\tilde{s}}" + }, + { + "bbox": [ + 304, + 653, + 545, + 715 + ], + "type": "text", + "content": " into the size of " + }, + { + "bbox": [ + 304, + 653, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{L\\times H_{\\tilde{s}}W_{\\tilde{s}}\\times 36\\times\\frac{C}{L}}" + }, + { + "bbox": [ + 304, + 653, + 545, + 715 + ], + "type": "text", + "content": ". The final assembling features are denoted as " + }, + { + "bbox": [ + 304, + 653, + 545, + 715 + ], + "type": "inline_equation", + "content": "f_{m\\tilde{s}}^{\\prime}\\in \\mathbb{R}^{C\\times H_{\\tilde{s}}\\times W_{\\tilde{s}}}" + }, + { + "bbox": [ + 304, + 653, + 545, + 715 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 733, + 318, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 733, + 318, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 733, + 318, + 742 + ], + "type": "text", + "content": "17339" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 70, + 547, + 335 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 547, + 335 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 547, + 335 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 547, + 335 + ], + "type": "image", + "image_path": "4a0e551cc94c8fab06230e5c69a9f1fdde213b1d541a27545e57992a42382c7a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 338, + 547, + 384 + ], + "lines": [ + { + "bbox": [ + 46, + 338, + 547, + 384 + ], + "spans": [ + { + "bbox": [ + 46, + 338, + 547, + 384 + ], + "type": "text", + "content": "Figure 2. Overview of the proposed framework. The feature assembling mechanism is designed to deal with distortions as well as integrate shallow and deep features (circled in Blue). Then we disentangle orthogonal planes to produce two 1D representations with distinguished plane semantics (circled in Purple). And triple attention is deployed to reconstruct the 1D representations (circled in Red). Our scheme leverages a single panorama with a resolution of " + }, + { + "bbox": [ + 46, + 338, + 547, + 384 + ], + "type": "inline_equation", + "content": "512 \\times 1024" + }, + { + "bbox": [ + 46, + 338, + 547, + 384 + ], + "type": "text", + "content": " as input and predicts the room height and the horizon depth." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 54, + 394, + 128, + 436 + ], + "blocks": [ + { + "bbox": [ + 54, + 394, + 128, + 436 + ], + "lines": [ + { + "bbox": [ + 54, + 394, + 128, + 436 + ], + "spans": [ + { + "bbox": [ + 54, + 394, + 128, + 436 + ], + "type": "image", + "image_path": "557f50a88eb5bb21a6f2cb2969e62b92233e4552b900a50071a217448a8adc3f.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 62, + 437, + 121, + 445 + ], + "lines": [ + { + "bbox": [ + 62, + 437, + 121, + 445 + ], + "spans": [ + { + "bbox": [ + 62, + 437, + 121, + 445 + ], + "type": "text", + "content": "Original version" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 130, + 394, + 204, + 436 + ], + "blocks": [ + { + "bbox": [ + 130, + 394, + 204, + 436 + ], + "lines": [ + { + "bbox": [ + 130, + 394, + 204, + 436 + ], + "spans": [ + { + "bbox": [ + 130, + 394, + 204, + 436 + ], + "type": "image", + "image_path": "7e51ae6f7a83c363034e0374e49f403e28790d221c6efa400447c5391f48b3f0.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 135, + 437, + 200, + 446 + ], + "lines": [ + { + "bbox": [ + 135, + 437, + 200, + 446 + ], + "spans": [ + { + "bbox": [ + 135, + 437, + 200, + 446 + ], + "type": "text", + "content": "Vertically flipping" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 449, + 287, + 471 + ], + "lines": [ + { + "bbox": [ + 46, + 449, + 287, + 471 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 287, + 471 + ], + "type": "text", + "content": "Figure 3. Illustration of the misaligned case when leveraging the symmetry property." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 205, + 394, + 280, + 436 + ], + "blocks": [ + { + "bbox": [ + 205, + 394, + 280, + 436 + ], + "lines": [ + { + "bbox": [ + 205, + 394, + 280, + 436 + ], + "spans": [ + { + "bbox": [ + 205, + 394, + 280, + 436 + ], + "type": "image", + "image_path": "59c1581b4bb66883bc834dce1f51865cf7081ff5dc0fdff4bd9148ff416b4584.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 214, + 437, + 270, + 445 + ], + "lines": [ + { + "bbox": [ + 214, + 437, + 270, + 445 + ], + "spans": [ + { + "bbox": [ + 214, + 437, + 270, + 445 + ], + "type": "text", + "content": "Misaligned case" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 479, + 225, + 493 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 479, + 225, + 493 + ], + "spans": [ + { + "bbox": [ + 47, + 479, + 225, + 493 + ], + "type": "text", + "content": "3.3. Disentangling Orthogonal Planes" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 498, + 287, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 287, + 545 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 287, + 545 + ], + "type": "text", + "content": "In order to explicitly capture the geometric cues, we propose to disentangle the orthogonal planes. Particularly, we segment the vertical plane and horizontal planes from the whole scenario before compressing the 2D feature maps." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 545, + 287, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 287, + 641 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 287, + 641 + ], + "type": "text", + "content": "Symmetry in Manhattan World. It is challenging to learn accurate layout boundaries in a complex scene due to the disturbance of furniture and illumination, e.g., occlusion. To address it, we propose to leverage the symmetry of the Manhattan World assumption (e.g., the floor boundary and ceiling boundary are strictly symmetric in 3D space) to provide complementary information. To exploit this symmetry property, we introduce a soft-flipping fusion strategy." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": "We first vertically flip the feature maps to get their symmetrical version. In fact, the floor boundary and ceiling boundary are not strictly symmetric in an image because the shooting position is not in the exact middle of the floor and ceiling. To this end, we adopt a deformable convolution with " + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": " kernel size to adaptively adjust the symmetry" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 396, + 545, + 432 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 396, + 545, + 432 + ], + "spans": [ + { + "bbox": [ + 304, + 396, + 545, + 432 + ], + "type": "text", + "content": "cal version. Next, we fuse the original feature and its \"soft\" symmetrical version to provide more informative boundary cues. We denote the fused features as " + }, + { + "bbox": [ + 304, + 396, + 545, + 432 + ], + "type": "inline_equation", + "content": "f_{u} \\in \\mathbb{R}^{C \\times H_{\\bar{s}} \\times W_{\\bar{s}}}" + }, + { + "bbox": [ + 304, + 396, + 545, + 432 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 433, + 546, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 433, + 546, + 529 + ], + "spans": [ + { + "bbox": [ + 304, + 433, + 546, + 529 + ], + "type": "text", + "content": "Segmenting Horizontal/Vertical Planes. To disentangle the 1D representation, we pre-segment the horizon/vertical planes in advance to capture an explicit geometric cue. Specifically, we generate the pseudo labels for the orthogonal planes with layout GT. Then, we use the generated labels to encourage the network to learn a binary mask " + }, + { + "bbox": [ + 304, + 433, + 546, + 529 + ], + "type": "inline_equation", + "content": "S \\in \\mathbb{R}^{H_{\\bar{s}} \\times W_{\\bar{s}}}" + }, + { + "bbox": [ + 304, + 433, + 546, + 529 + ], + "type": "text", + "content": " via a simple segmentation head. The two segmented feature maps can be denoted as:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 331, + 535, + 545, + 552 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 331, + 535, + 545, + 552 + ], + "spans": [ + { + "bbox": [ + 331, + 535, + 545, + 552 + ], + "type": "interline_equation", + "content": "f _ {h} ^ {p} = \\left(f _ {u} \\oplus f _ {m \\tilde {s}} ^ {\\prime}\\right) \\otimes \\text {s i g m o i d} (S), \\tag {4}", + "image_path": "4ba0dfd7a0436245ea2a457cc237840f4c2b9b78461c591baa3171d5693020ba.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 332, + 549, + 498, + 562 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 332, + 549, + 498, + 562 + ], + "spans": [ + { + "bbox": [ + 332, + 549, + 498, + 562 + ], + "type": "interline_equation", + "content": "f _ {v} ^ {p} = \\left(f _ {u} \\oplus f _ {m \\tilde {s}} ^ {\\prime}\\right) \\otimes (1 - \\text {s i g m o i d} (S))", + "image_path": "134117aa3c17ef5dad0f6225cf5d3df8776f1301d46345162185859148335320.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 568, + 545, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 568, + 545, + 629 + ], + "spans": [ + { + "bbox": [ + 304, + 568, + 545, + 629 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 568, + 545, + 629 + ], + "type": "inline_equation", + "content": "f_h^p / f_v^p" + }, + { + "bbox": [ + 304, + 568, + 545, + 629 + ], + "type": "text", + "content": " represents the horizon/vertical plane features, respectively; " + }, + { + "bbox": [ + 304, + 568, + 545, + 629 + ], + "type": "inline_equation", + "content": "\\oplus" + }, + { + "bbox": [ + 304, + 568, + 545, + 629 + ], + "type": "text", + "content": " is the element-wise sum and " + }, + { + "bbox": [ + 304, + 568, + 545, + 629 + ], + "type": "inline_equation", + "content": "\\otimes" + }, + { + "bbox": [ + 304, + 568, + 545, + 629 + ], + "type": "text", + "content": " is the element-wise product. Following previous works, we further vertically compress 2D feature maps to two 1D sequences " + }, + { + "bbox": [ + 304, + 568, + 545, + 629 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_h" + }, + { + "bbox": [ + 304, + 568, + 545, + 629 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 568, + 545, + 629 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_v \\in \\mathbb{R}^{W_{\\bar{s}} \\times C}" + }, + { + "bbox": [ + 304, + 568, + 545, + 629 + ], + "type": "text", + "content": " with differnet plane semantics." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 635, + 494, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 635, + 494, + 647 + ], + "spans": [ + { + "bbox": [ + 306, + 635, + 494, + 647 + ], + "type": "text", + "content": "3.4. Reconstructing 1D Representations" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 654, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 712 + ], + "type": "text", + "content": "Generating Discriminative Channels. There are generally unconfined dependencies among channels, resulting in confused semantic cues [10]. To this end, we propose a discriminative channels generation mechanism via graph convolution to enforce each channel to concentrate on distin" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 732, + 318, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 732, + 318, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 732, + 318, + 742 + ], + "type": "text", + "content": "17340" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 144 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 144 + ], + "type": "text", + "content": "guishing features. Different from normal pixel-wise [23] or object-wise [11] graphs, the introduced channel-wise one tends to guide the node to subtract the information from the neighbor nodes rather than aggregation. The formula of the discriminative channels generation mechanism can be represented as:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 100, + 155, + 287, + 168 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 100, + 155, + 287, + 168 + ], + "spans": [ + { + "bbox": [ + 100, + 155, + 287, + 168 + ], + "type": "interline_equation", + "content": "f ^ {\\prime} = \\mathbf {L} f W = (\\mathbf {I} - \\mathbf {A}) f W \\tag {5}", + "image_path": "e8d4aed50f3ff73eff6bac8640e5ee97b0c11ed767e05cb260b661e9bcbd0ce5.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 178, + 287, + 274 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 178, + 287, + 274 + ], + "spans": [ + { + "bbox": [ + 46, + 178, + 287, + 274 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 178, + 287, + 274 + ], + "type": "inline_equation", + "content": "\\mathbf{L}" + }, + { + "bbox": [ + 46, + 178, + 287, + 274 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 178, + 287, + 274 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 46, + 178, + 287, + 274 + ], + "type": "text", + "content": " are the symmetric normalized Laplacian matrix and normalized adjacency matrix of the channelwise graph, and " + }, + { + "bbox": [ + 46, + 178, + 287, + 274 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 178, + 287, + 274 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 178, + 287, + 274 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 46, + 178, + 287, + 274 + ], + "type": "text", + "content": " are the identity matrix and learnable weights, respectively. Please refer to the supplementary materials for more details about the channel-wise graph attention. Following Eq. 5, " + }, + { + "bbox": [ + 46, + 178, + 287, + 274 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_h" + }, + { + "bbox": [ + 46, + 178, + 287, + 274 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 178, + 287, + 274 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_v" + }, + { + "bbox": [ + 46, + 178, + 287, + 274 + ], + "type": "text", + "content": " are first reconstructed to be more discriminative in channels (represented as " + }, + { + "bbox": [ + 46, + 178, + 287, + 274 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_h^{\\prime},\\mathbf{Q}_v^{\\prime}\\in \\mathbb{R}^{W_{\\bar{s}}\\times C}" + }, + { + "bbox": [ + 46, + 178, + 287, + 274 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 275, + 287, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 275, + 287, + 323 + ], + "spans": [ + { + "bbox": [ + 47, + 275, + 287, + 323 + ], + "type": "text", + "content": "Rebuilding Long-Range Dependencies. We employ the standard self-attention to reconstruct the intra-sequence long-range dependencies. The attention formula of the horizontal plane sequence can be written as:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 52, + 332, + 287, + 353 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 332, + 287, + 353 + ], + "spans": [ + { + "bbox": [ + 52, + 332, + 287, + 353 + ], + "type": "interline_equation", + "content": "\\operatorname {A t t e n t i o n} \\left(\\mathcal {Q} _ {h} ^ {\\prime}, \\mathcal {K} _ {h} ^ {\\prime}, \\mathcal {V} _ {h} ^ {\\prime}\\right) = \\operatorname {s o f t m a x} \\left(\\frac {\\mathcal {Q} _ {h} ^ {\\prime} \\left(\\mathcal {K} _ {h} ^ {\\prime}\\right) ^ {T}}{\\sqrt {d _ {k}}} \\mathcal {V} _ {h} ^ {\\prime}\\right), \\tag {6}", + "image_path": "7b4ed90be1993b8d8c5f4dc589d87a9eca3042ac189fa6fba9a2e67dd284493d.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 361, + 287, + 398 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 361, + 287, + 398 + ], + "spans": [ + { + "bbox": [ + 47, + 361, + 287, + 398 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 361, + 287, + 398 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}_h^\\prime ,\\mathcal{K}_h^\\prime ,\\mathcal{V}_h^\\prime" + }, + { + "bbox": [ + 47, + 361, + 287, + 398 + ], + "type": "text", + "content": " are all learned from " + }, + { + "bbox": [ + 47, + 361, + 287, + 398 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_h^\\prime" + }, + { + "bbox": [ + 47, + 361, + 287, + 398 + ], + "type": "text", + "content": " via a fully connected layer. Similarly, the calculation for the vertical plane sequence is defined as:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 53, + 407, + 287, + 427 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 407, + 287, + 427 + ], + "spans": [ + { + "bbox": [ + 53, + 407, + 287, + 427 + ], + "type": "interline_equation", + "content": "\\operatorname {A t t e n t i o n} \\left(\\mathcal {Q} _ {v} ^ {\\prime}, \\mathcal {K} _ {v} ^ {\\prime}, \\mathcal {V} _ {v} ^ {\\prime}\\right) = \\operatorname {s o f t m a x} \\left(\\frac {\\mathcal {Q} _ {v} ^ {\\prime} \\left(\\mathcal {K} _ {v} ^ {\\prime}\\right) ^ {T}}{\\sqrt {d _ {k}}} \\mathcal {V} _ {v} ^ {\\prime}\\right). \\tag {7}", + "image_path": "afeca713e40c65fdc6bd5c38bf776ae0de697e500e910416261903dd37244b51.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 436, + 287, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 436, + 287, + 484 + ], + "spans": [ + { + "bbox": [ + 47, + 436, + 287, + 484 + ], + "type": "text", + "content": "It captures global interactions to adapt to the large FoV of panoramas, contributing to better performance. We denote the two sequences with reconstructed long-range dependencies as " + }, + { + "bbox": [ + 47, + 436, + 287, + 484 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_h^{\\prime \\prime}" + }, + { + "bbox": [ + 47, + 436, + 287, + 484 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 436, + 287, + 484 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_v^{\\prime \\prime} \\in \\mathbb{R}^{W_{\\bar{s}} \\times C}" + }, + { + "bbox": [ + 47, + 436, + 287, + 484 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 484, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 484, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 47, + 484, + 287, + 544 + ], + "type": "text", + "content": "Providing Missing Residuals. To compensate for inevitable errors in pre-segmentation, we introduce crossattention to provide the missing residuals. For the sequence about the horizontal plane, we extract the potential beneficial residuals as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 52, + 552, + 289, + 572 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 552, + 289, + 572 + ], + "spans": [ + { + "bbox": [ + 52, + 552, + 289, + 572 + ], + "type": "interline_equation", + "content": "\\operatorname {A t t e n t i o n} \\left(\\mathcal {Q} _ {h} ^ {\\prime \\prime}, \\mathcal {K} _ {v} ^ {\\prime \\prime}, \\mathcal {V} _ {v} ^ {\\prime \\prime}\\right) = \\operatorname {s o f t m a x} \\left(\\frac {\\mathcal {Q} _ {h} ^ {\\prime \\prime} \\left(\\mathcal {K} _ {v} ^ {\\prime \\prime}\\right) ^ {T}}{\\sqrt {d _ {k}}} \\mathcal {V} _ {v} ^ {\\prime \\prime}\\right). \\tag {8}", + "image_path": "22781ec771cfedc45c601b99ce77da49130a42d1e1a3dc11f7c07cf05ec24fb3.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 581, + 104, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 581, + 104, + 591 + ], + "spans": [ + { + "bbox": [ + 47, + 581, + 104, + 591 + ], + "type": "text", + "content": "For the other:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 52, + 600, + 289, + 620 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 600, + 289, + 620 + ], + "spans": [ + { + "bbox": [ + 52, + 600, + 289, + 620 + ], + "type": "interline_equation", + "content": "\\operatorname {A t t e n t i o n} \\left(\\mathcal {Q} _ {v} ^ {\\prime \\prime}, \\mathcal {K} _ {h} ^ {\\prime \\prime}, \\mathcal {V} _ {h} ^ {\\prime \\prime}\\right) = \\operatorname {s o f t m a x} \\left(\\frac {\\mathcal {Q} _ {v} ^ {\\prime \\prime} \\left(\\mathcal {K} _ {h} ^ {\\prime \\prime}\\right) ^ {T}}{\\sqrt {d _ {k}}} \\mathcal {V} _ {h} ^ {\\prime \\prime}\\right). \\tag {9}", + "image_path": "36be97fe7f7c1668ceaafce2e5d7bba0af808f25f8eb18d642ff21f55388883a.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 628, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 628, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 628, + 287, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 628, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}_h^{\\prime \\prime},\\mathcal{K}_h^{\\prime \\prime},\\mathcal{V}_h^{\\prime \\prime}" + }, + { + "bbox": [ + 47, + 628, + 287, + 713 + ], + "type": "text", + "content": " are all learned from " + }, + { + "bbox": [ + 47, + 628, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_h^{\\prime \\prime}(\\mathcal{Q}_v^{\\prime \\prime},\\mathcal{K}_v^{\\prime \\prime},\\mathcal{V}_v^{\\prime \\prime}" + }, + { + "bbox": [ + 47, + 628, + 287, + 713 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 47, + 628, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_v^{\\prime \\prime})" + }, + { + "bbox": [ + 47, + 628, + 287, + 713 + ], + "type": "text", + "content": " via a fully connected layer. Then we add the learned residuals with the two 1D sequences to implement the reconstruction. After that, two separate fully connected layers are employed to output the predicted horizon depth from the vertical plane sequence and the room height value from the horizontal plane one, respectively." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 72, + 419, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 419, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 419, + 85 + ], + "type": "text", + "content": "3.5. Objective Function" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 91, + 545, + 151 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 91, + 545, + 151 + ], + "spans": [ + { + "bbox": [ + 304, + 91, + 545, + 151 + ], + "type": "text", + "content": "Our objective function consists of two parts: one for room layout estimation and the other for plane segmentation. For the first part, we strictly follow [8] and it can be denoted as " + }, + { + "bbox": [ + 304, + 91, + 545, + 151 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{layout}" + }, + { + "bbox": [ + 304, + 91, + 545, + 151 + ], + "type": "text", + "content": ". For the segmentation part, we apply binary cross-entropy loss " + }, + { + "bbox": [ + 304, + 91, + 545, + 151 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{segment}" + }, + { + "bbox": [ + 304, + 91, + 545, + 151 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 311, + 159, + 545, + 180 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 159, + 545, + 180 + ], + "spans": [ + { + "bbox": [ + 311, + 159, + 545, + 180 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {s e g m e n t}} = \\frac {1}{N} \\sum_ {i \\in N} \\left(d _ {i} \\log \\bar {d} _ {i} + \\left(1 D _ {i}\\right) \\log \\left(1 - \\bar {d} _ {i}\\right)\\right) \\tag {10}", + "image_path": "dd2ea68adaeb29c93a6907b5c58990ebb7570806de51e00158185c6fc6b9f784.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 190, + 545, + 226 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 190, + 545, + 226 + ], + "spans": [ + { + "bbox": [ + 304, + 190, + 545, + 226 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 190, + 545, + 226 + ], + "type": "inline_equation", + "content": "\\bar{d}_i" + }, + { + "bbox": [ + 304, + 190, + 545, + 226 + ], + "type": "text", + "content": " is the ground truth of generated segmentation label, and " + }, + { + "bbox": [ + 304, + 190, + 545, + 226 + ], + "type": "inline_equation", + "content": "d_i" + }, + { + "bbox": [ + 304, + 190, + 545, + 226 + ], + "type": "text", + "content": " is the predicted value. Ultimately, we formulate the objective function as follows:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 361, + 236, + 545, + 250 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 361, + 236, + 545, + 250 + ], + "spans": [ + { + "bbox": [ + 361, + 236, + 545, + 250 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\lambda \\mathcal {L} _ {\\text {s e g m e n t}} + \\mathcal {L} _ {\\text {l a y o u t}} \\tag {11}", + "image_path": "f1a88d54aff672eb7462ea7631cd9c8fe464550a2e907e48e8aff90b17e0722e.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 258, + 523, + 270 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 258, + 523, + 270 + ], + "spans": [ + { + "bbox": [ + 305, + 258, + 523, + 270 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 258, + 523, + 270 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 305, + 258, + 523, + 270 + ], + "type": "text", + "content": " is set to 0.75 to balance different constraints." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 281, + 388, + 295 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 281, + 388, + 295 + ], + "spans": [ + { + "bbox": [ + 305, + 281, + 388, + 295 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 301, + 545, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 301, + 545, + 422 + ], + "spans": [ + { + "bbox": [ + 304, + 301, + 545, + 422 + ], + "type": "text", + "content": "In this section, we validate the effectiveness of our solution and compare it with existing SoTA approaches on four popular datasets. Concretely, we conduct experiments on a single GTX 3090 GPU, and the batch size is set to 16 for training. The proposed approach is implemented with PyTorch. We choose Adam [9] as the optimizer and keep the default settings. The initialized learning rate is " + }, + { + "bbox": [ + 304, + 301, + 545, + 422 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-4}" + }, + { + "bbox": [ + 304, + 301, + 545, + 422 + ], + "type": "text", + "content": ". As in previous works [19, 8], we adopt standard left-right flipping, panoramic horizontal rotation, luminance change, and pano stretch for data augmentation during training." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 430, + 368, + 441 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 430, + 368, + 441 + ], + "spans": [ + { + "bbox": [ + 305, + 430, + 368, + 441 + ], + "type": "text", + "content": "4.1. Datasets" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 448, + 545, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 448, + 545, + 483 + ], + "spans": [ + { + "bbox": [ + 304, + 448, + 545, + 483 + ], + "type": "text", + "content": "Four datasets are used for our experimental validation: Stanford 2D-3D [1], PanoContext [26], MatterportLayout [29] and ZInd [6]." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 484, + 545, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 484, + 545, + 651 + ], + "spans": [ + { + "bbox": [ + 304, + 484, + 545, + 651 + ], + "type": "text", + "content": "PanoContext [26] and Stanford 2D-3D [1] are two commonly used datasets for indoor panoramic room layout estimation that contain 514 and 552 cuboid room layouts, respectively. Especially, Stanford 2D-3D [1] is labeled by Zou et al. [28] and has a smaller vertical FoV than other datasets. Besides, MatterportLayout [29] is also annotated by Zou et al. [29], which contains 2,295 general room layouts. The final ZInd [6] dataset includes cuboid, general Manhattan, non-Manhattan, and non-flat ceilings layouts, which mimic the real-world data distribution better. The splits of ZInd [6] consists of 24,882 (for training), 3,080 (for validation), and 3,170 (for testing) panoramas. We strictly follow the same training/validation/test splits of the four datasets as in previous works for a fair comparison." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 305, + 658, + 419, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 658, + 419, + 670 + ], + "spans": [ + { + "bbox": [ + 305, + 658, + 419, + 670 + ], + "type": "text", + "content": "4.2. Evaluation Metrics" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "type": "text", + "content": "We employ the commonly used standard evaluation metrics for a fair comparison, including corner error (CE), pixel error (PE), intersection over the union of floor shapes" + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 733, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 733, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 733, + 317, + 742 + ], + "type": "text", + "content": "17341" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 71, + 303, + 297 + ], + "blocks": [ + { + "bbox": [ + 48, + 71, + 303, + 297 + ], + "lines": [ + { + "bbox": [ + 48, + 71, + 303, + 297 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 303, + 297 + ], + "type": "table", + "html": "
Method3D IoU(%)CE(%)PE(%)
Train on PanoContext + Whole Stnfd.2D3D datasets
LayoutNetv2[29]85.020.631.79
Dula-Netv2[29]83.770.812.43
HorizonNet[19]82.630.742.17
LGT-Net[8]85.16--
LGT-Net [w/ Post-proc][8]84.940.692.07
Ours85.46--
Ours [w/ Post-proc]85.000.692.13
Train on Stnfd.2D3D + Whole PanoContext datasets
LayoutNetv2[29]82.660.832.59
Dula-Netv2[29]86.600.672.48
HorizonNet[19]82.720.692.27
AtlantaNet[14]83.940.712.18
LGT-Net[8]85.76--
LGT-Net [w/ Post-proc][8]86.030.632.11
Ours85.47--
Ours [w/ Post-proc]85.580.662.10
", + "image_path": "9a21f251ee8ff694003a61ec0bbae634a7340874febbd102fe3ff649cff17671.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 304, + 288, + 327 + ], + "lines": [ + { + "bbox": [ + 46, + 304, + 288, + 327 + ], + "spans": [ + { + "bbox": [ + 46, + 304, + 288, + 327 + ], + "type": "text", + "content": "Table 1. Quantitative comparison results with the current SoTA solutions evaluated on Stanford 2D-3D and PanoContext[6] dataset." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 340, + 288, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 340, + 288, + 389 + ], + "spans": [ + { + "bbox": [ + 46, + 340, + 288, + 389 + ], + "type": "text", + "content": "(2D IoU), and 3D room layouts (3D IoU). Among them, 3D IoU yields a better reflection of the accuracy of the layout estimation in 3D space. RMSE and " + }, + { + "bbox": [ + 46, + 340, + 288, + 389 + ], + "type": "inline_equation", + "content": "\\delta_{1.25}" + }, + { + "bbox": [ + 46, + 340, + 288, + 389 + ], + "type": "text", + "content": " indicate the performance of depth estimation, e.g. the horizon-depth map," + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 396, + 173, + 407 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 396, + 173, + 407 + ], + "spans": [ + { + "bbox": [ + 47, + 396, + 173, + 407 + ], + "type": "text", + "content": "4.3. Cuboid Room Results" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 414, + 287, + 570 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 414, + 287, + 570 + ], + "spans": [ + { + "bbox": [ + 46, + 414, + 287, + 570 + ], + "type": "text", + "content": "We follow LGT-Net [8] to use the combined dataset scheme mentioned in Zou et al. [29] to evaluate our network on cuboid datasets. We denote the combined dataset that contains training splits of PanoContext [6] and whole Stanford 2D-3D datasets as \"Train on PanoContext + Whole Stnfd.2D3D datasets\" in Tab. 1. Similarly, \"Train on Stnfd.2D3D + Whole PanoContext\" in Tab. 1 represents that we train our network on the combined dataset that contains training splits of Stanford 2D-3D and the whole PanoContext dataset. The scheme is commonly used in previous works [28, 8]. We also report the results with a post-processing strategy in DuLa-Net [24] that is denoted as \"Ours [w/ Post-proc]\"." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": "Comparison results. We exhibit the quantitative comparison results on cuboid room layouts in Tab. 1. From the first group in Tab. 1, we can observe that our approach outperforms all the other SoTA schemes with respect to 3D IoU. But from the second group, Dula-Net v2 [29] offers better 3D IoU than ours. Dula-Net v2 [29] employs a perspective view (i.e., cubemap) that is more effective for panoramas with small vertical FoV. However, once applied to more general room layout datasets, its performance degrades significantly (it is proved with the other two datasets in Sec. 4.4). On the contrary, the proposed approach shows more general performance." + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 306, + 71, + 548, + 199 + ], + "blocks": [ + { + "bbox": [ + 306, + 71, + 548, + 199 + ], + "lines": [ + { + "bbox": [ + 306, + 71, + 548, + 199 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 548, + 199 + ], + "type": "table", + "html": "
Method2D IoU(%)3D IoU(%)RMSEδ1
LayoutNetv2[29]78.7375.820.2580.871
Dula-Netv2[29]78.8275.050.2910.818
HorizonNet[19]81.7179.110.1970.929
AtlantaNet[14]82.0980.02--
HoHoNet[20]82.3279.88--
LED2-Net[21]82.6180.140.2070.947
DMH-Net [27]81.2578.97-0.925
LGT-Net[8]83.5281.110.2040.951
Ours84.1181.700.1970.950
", + "image_path": "3ab09c531d32c950da16db76226b5ba0afc900fa9bca7a45301853871d783739.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 307, + 241, + 545, + 310 + ], + "blocks": [ + { + "bbox": [ + 306, + 206, + 545, + 231 + ], + "lines": [ + { + "bbox": [ + 306, + 206, + 545, + 231 + ], + "spans": [ + { + "bbox": [ + 306, + 206, + 545, + 231 + ], + "type": "text", + "content": "Table 2. Quantitative comparison results with the current SoTA solutions evaluated on MatterportLayout[29] dataset." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 241, + 545, + 310 + ], + "lines": [ + { + "bbox": [ + 307, + 241, + 545, + 310 + ], + "spans": [ + { + "bbox": [ + 307, + 241, + 545, + 310 + ], + "type": "table", + "html": "
Method2D IoU(%)3D IoU(%)RMSEδ1
HorizonNet[19]90.4488.590.1230.957
LED2-Net[21]90.3688.490.1240.955
LGT-Net[8]91.7789.950.1110.960
Ours91.9490.13--
", + "image_path": "1fbc70ebbecd05cc33eadc74704d2e9ee5f880bb9853125d3471a68d5288ff9e.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 317, + 545, + 340 + ], + "lines": [ + { + "bbox": [ + 305, + 317, + 545, + 340 + ], + "spans": [ + { + "bbox": [ + 305, + 317, + 545, + 340 + ], + "type": "text", + "content": "Table 3. Quantitative comparison results with the current SoTA solutions evaluated on ZInD[6] dataset." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 356, + 434, + 368 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 356, + 434, + 368 + ], + "spans": [ + { + "bbox": [ + 306, + 356, + 434, + 368 + ], + "type": "text", + "content": "4.4. General Room Results" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 376, + 545, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 376, + 545, + 471 + ], + "spans": [ + { + "bbox": [ + 304, + 376, + 545, + 471 + ], + "type": "text", + "content": "MatterportLayout [29] dataset and ZInD [6] dataset provide more general indoor room layouts, which is much more challenging than the cuboid room layout datasets. Tab. 2/Tab. 3 exhibits the evaluation on MatterportLayout [29]/ZInD [6] datasets. The results of " + }, + { + "bbox": [ + 304, + 376, + 545, + 471 + ], + "type": "inline_equation", + "content": "\\mathsf{LED}^2" + }, + { + "bbox": [ + 304, + 376, + 545, + 471 + ], + "type": "text", + "content": "-Net [21] and HorizonNet [19] are from [8] that we strictly followed. Particularly, Jiang et al. utilize their official codeto re-train and re-evaluate with the standard evaluation metrics." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 472, + 546, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 472, + 546, + 664 + ], + "spans": [ + { + "bbox": [ + 304, + 472, + 546, + 664 + ], + "type": "text", + "content": "Comparison results. We observe that Dula-Net [24] demonstrates much worse performance on the general room layout dataset (MatterportLayout), indicating that these perspective view-based methods are hard to be adapted to the more general indoor scenarios. Moreover, these 1D sequence-based methods are better than those 2D convolution-based schemes. However, they cannot produce accurate 3D layouts from a 1D sequence due to confused plane semantics, even if they introduce more powerful relationship builders (e.g., Bi-LSTM, Transformer). Hence, these methods give worse 3D IoU. Compared with them, our approach offers better performance than all other approaches with respect to 3D IoU because ours captures an explicit 3D geometric cue by disentangling orthogonal planes, which benefits recovering layouts from clear semantics (Fig. 6)." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "type": "text", + "content": "We show the qualitative comparisons in Fig. 4. From the figure, we can observe that our method offers better 3D results (floor plan). In Fig. 5, our results are much similar to the post-processing version. Both indicate our proposal" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 733, + 318, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 733, + 318, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 733, + 318, + 742 + ], + "type": "text", + "content": "17342" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 65, + 68, + 541, + 268 + ], + "blocks": [ + { + "bbox": [ + 65, + 68, + 541, + 268 + ], + "lines": [ + { + "bbox": [ + 65, + 68, + 541, + 268 + ], + "spans": [ + { + "bbox": [ + 65, + 68, + 541, + 268 + ], + "type": "image", + "image_path": "6d5cd1be970160438cc7c07ed68f6c5728990f60dd5a90b0eb4fcaa2be200a95.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 200, + 272, + 398, + 282 + ], + "lines": [ + { + "bbox": [ + 200, + 272, + 398, + 282 + ], + "spans": [ + { + "bbox": [ + 200, + 272, + 398, + 282 + ], + "type": "text", + "content": "(a) Qualitative comparison on MatterportLayout [29] dataset." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 65, + 290, + 541, + 490 + ], + "blocks": [ + { + "bbox": [ + 65, + 290, + 541, + 490 + ], + "lines": [ + { + "bbox": [ + 65, + 290, + 541, + 490 + ], + "spans": [ + { + "bbox": [ + 65, + 290, + 541, + 490 + ], + "type": "image", + "image_path": "92dcbb1e67e745b0c592300ee423c928ccd88a8e9a1127c0ecc4f11fe233bbb0.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 220, + 493, + 376, + 503 + ], + "lines": [ + { + "bbox": [ + 220, + 493, + 376, + 503 + ], + "spans": [ + { + "bbox": [ + 220, + 493, + 376, + 503 + ], + "type": "text", + "content": "(b) Qualitative comparison on ZInD [6] dataset." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 45, + 506, + 545, + 561 + ], + "lines": [ + { + "bbox": [ + 45, + 506, + 545, + 561 + ], + "spans": [ + { + "bbox": [ + 45, + 506, + 545, + 561 + ], + "type": "text", + "content": "Figure 4. Qualitative comparison results evaluated on general layout datasets, MatterportLayout [29] and ZInD [6]. We compare our method with " + }, + { + "bbox": [ + 45, + 506, + 545, + 561 + ], + "type": "inline_equation", + "content": "\\mathbf{LED}^2" + }, + { + "bbox": [ + 45, + 506, + 545, + 561 + ], + "type": "text", + "content": "-Net [21] and LGT-Net [8]. The compared methods are all not employed the post-processing strategy. The boundaries of the room layout on a panorama are shown on the left and the floor plan is on the right. Ground truth is best viewed in Blue lines, and the prediction in Green. The predicted horizon depth, normal, and gradient are visualized below each panorama, and the ground truth is in the first row. We labeled the significant differences with dashed lines." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 575, + 288, + 600 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 575, + 288, + 600 + ], + "spans": [ + { + "bbox": [ + 46, + 575, + 288, + 600 + ], + "type": "text", + "content": "that disentangling orthogonal planes to capture an explicit 3D geometric cue is an effective strategy." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 609, + 138, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 609, + 138, + 623 + ], + "spans": [ + { + "bbox": [ + 46, + 609, + 138, + 623 + ], + "type": "text", + "content": "4.5. Ablation study" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": "We exhibit ablation studies in Tab. 4, where each component of our model is evaluated on MatterportLayout [29]. To demonstrate the effectiveness of the proposed feature assembling mechanism, we first ablate cross-scale interaction in feature assembling (denoted as \"w/o Cross-scale interaction\"). Then, we further remove the distortion elimination (denoted as \"w/o Feature assembling\"). To exhibit the" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 575, + 545, + 683 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 575, + 545, + 683 + ], + "spans": [ + { + "bbox": [ + 304, + 575, + 545, + 683 + ], + "type": "text", + "content": "benefit of orthogonal plane disentanglement, we put off the proposed disentangling orthogonal planes procedure (denoted as \"w/o Disentangling planes\") and soft-flipping fusion, respectively. Finally, we show the effect of each attention mechanism (denoted as \"w/o Discriminative channels\", \"w/o Long-range dependencies\", and \"w/o residuals\", respectively). Specially, we train each model around 500 epochs (not the best ones). Hence, the results of \"Ours [Full]\" are slightly lower than those in Tab. 2." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": "Feature assembling mechanism. From Tab. 4, the pipeline without cross-scale interaction shows inferior per" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 733, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 733, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 733, + 317, + 742 + ], + "type": "text", + "content": "17343" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 75, + 222, + 144 + ], + "blocks": [ + { + "bbox": [ + 56, + 75, + 222, + 144 + ], + "lines": [ + { + "bbox": [ + 56, + 75, + 222, + 144 + ], + "spans": [ + { + "bbox": [ + 56, + 75, + 222, + 144 + ], + "type": "image", + "image_path": "f3291e8e1aa7373e28c35f77bea992033e286b40e591c3db59b32c7ea7e4c9d5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 135, + 147, + 217, + 158 + ], + "lines": [ + { + 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The 3D visualization results. We exhibit the predicted boundaries (best viewed in Green lines) and the ones with post-processing of the prediction (best viewed in Red lines) in the pancreas." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 56, + 281, + 214, + 317 + ], + "lines": [ + { + "bbox": [ + 56, + 281, + 214, + 317 + ], + "spans": [ + { + "bbox": [ + 56, + 281, + 214, + 317 + ], + "type": "image", + "image_path": "340af9f9234af567303c6aa503a22d34143c868e8c6485aec7d703922fc8fac5.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 225, + 281, + 381, + 317 + ], + "blocks": [ + { + "bbox": [ + 225, + 281, + 381, + 317 + ], + "lines": [ + { + "bbox": [ + 225, + 281, + 381, + 317 + ], + "spans": [ + { + "bbox": [ + 225, + 281, + 381, + 317 + ], + "type": "image", + "image_path": "de6c40e1e0cfa46133bf282375952c8b915ce0a1e6a125125fb6b2c7804604b1.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 319, + 546, + 352 + ], + "lines": [ + { + "bbox": [ + 46, + 319, + 546, + 352 + ], + "spans": [ + { + "bbox": [ + 46, + 319, + 546, + 352 + ], + "type": "text", + "content": "Figure 6. We exhibit the features of the 1D representation. The one without orthogonal plane disentanglement is shown on the left, and ours is on the right. Without disentangling, the left contains redundant and confusing features that are not good for layout estimation. In contrast, our disentangled vertical plane features are more discriminative, showing more attention to the layout corners." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 382, + 281, + 537, + 317 + ], + "blocks": [ + { + "bbox": [ + 382, + 281, + 537, + 317 + ], + "lines": [ + { + "bbox": [ + 382, + 281, + 537, + 317 + ], + "spans": [ + { + "bbox": [ + 382, + 281, + 537, + 317 + ], + "type": "image", + "image_path": "fc894017d8b96e2a80379d983bb1c652260bfd69ef3ff325da7834d20d5483a1.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "type": "table", + "bbox": [ + 48, + 365, + 293, + 483 + ], + "blocks": [ + { + "bbox": [ + 48, + 365, + 293, + 483 + ], + "lines": [ + { + "bbox": [ + 48, + 365, + 293, + 483 + ], + "spans": [ + { + "bbox": [ + 48, + 365, + 293, + 483 + ], + "type": "table", + "html": "
Method2D IoU(%)3D IoU(%)
w/o Cross-scale interaction83.2480.71
w/o Feature assembling82.3680.10
w/o Disentangling planes83.2380.60
w/o Flipping fusion83.0180.35
w/o Discriminative channels82.7480.23
w/o Long-range dependencies83.0480.97
w/o Residuals82.8980.45
Ours [Full]83.4681.34
", + "image_path": "09dee5727cb4f50b0263cb80209937aca86aa12bff3aac43e30ca3f44842eb26.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "table_body" + } + ], + "index": 17 + }, + { + "bbox": [ + 61, + 491, + 272, + 502 + ], + "lines": [ + { + "bbox": [ + 61, + 491, + 272, + 502 + ], + "spans": [ + { + "bbox": [ + 61, + 491, + 272, + 502 + ], + "type": "text", + "content": "Table 4. Ablation study on MatterportLayout [29] dataset." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 518, + 287, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 518, + 287, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 518, + 287, + 567 + ], + "type": "text", + "content": "formance to the full model. Further removing the distortion elimination part, the pipeline gives worse results. It is proved that both dealing with distortions and integrating cross-scale features are essential for layout estimation." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 46, + 568, + 287, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 568, + 287, + 675 + ], + "spans": [ + { + "bbox": [ + 46, + 568, + 287, + 675 + ], + "type": "text", + "content": "Disentangling orthogonal planes. Since the geometric cues are essential for inferring 3D information from 2D images, we propose to disentangle orthogonal planes. To prove the effectiveness, we remove that stage but preserve the flipping fusion strategy (the effectiveness of this strategy is validated separately). The results in Tab. 4 show that this stage can make the performance more competitive. Besides, the embedding of symmetry property also contributes to the promotion of the predicted results." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "Reconstructing 1D representations. The dependencies of the 1D sequences have changed when disentangling the orthogonal planes. Hence, we propose to reconstruct the 1D" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 366, + 545, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 366, + 545, + 486 + ], + "spans": [ + { + "bbox": [ + 304, + 366, + 545, + 486 + ], + "type": "text", + "content": "representations. We verify the effectiveness of each attention mechanism in turn. From Tab. 4, we can observe that all three reconstruction operations (generating discriminative channels, rebuilding long-range dependencies, and providing the missing residuals) can all benefit the overall performance. Significantly, when removing the channel-wise graph, the pipeline's performance decreases significantly, demonstrating that enforcing the network concentration on discriminative channel information can capture effective information by avoiding redundancy." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 502, + 378, + 513 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 502, + 378, + 513 + ], + "spans": [ + { + "bbox": [ + 306, + 502, + 378, + 513 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 523, + 545, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 523, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 304, + 523, + 545, + 677 + ], + "type": "text", + "content": "In this paper, we propose a novel panoramic indoor room layout estimation approach. Current approaches generate a 1D representation by a vertical compression operation. We argue that this strategy confuses the semantic cues of different planes. To address this issue, we propose to disentangle orthogonal planes to capture geometric cues in 3D space. Specially, we introduce a vertical flip-fusion strategy to leverage the symmetry property of indoor room layout. Besides, our experimental results demonstrate that dealing with distortion, as well as integrating shallow and deep features, can enhance the performance. Experiments demonstrate that our algorithm significantly outperforms current SoTA methods." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 306, + 680, + 394, + 691 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 680, + 394, + 691 + ], + "spans": [ + { + "bbox": [ + 306, + 680, + 394, + 691 + ], + "type": "text", + "content": "Acknowledgement." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 306, + 691, + 394, + 701 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 691, + 394, + 701 + ], + "spans": [ + { + "bbox": [ + 306, + 691, + 394, + 701 + ], + "type": "text", + "content": "by the National" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 306, + 702, + 389, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 702, + 389, + 712 + ], + "spans": [ + { + "bbox": [ + 306, + 702, + 389, + 712 + ], + "type": "text", + "content": "of China (Nos." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 407, + 680, + 545, + 691 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 407, + 680, + 545, + 691 + ], + "spans": [ + { + "bbox": [ + 407, + 680, + 545, + 691 + ], + "type": "text", + "content": "This work was supported" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 407, + 691, + 545, + 701 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 407, + 691, + 545, + 701 + ], + "spans": [ + { + "bbox": [ + 407, + 691, + 545, + 701 + ], + "type": "text", + "content": "Natural Science Foundation" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 424, + 702, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 424, + 702, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 424, + 702, + 545, + 712 + ], + "type": "text", + "content": "62172032, 62120106009)." + } + ] + } + ], + "index": 30 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 733, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 733, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 733, + 317, + 742 + ], + "type": "text", + "content": "17344" + } + ] + } + ], + "index": 31 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 94, + 106, + 106 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 94, + 106, + 106 + ], + "spans": [ + { + "bbox": [ + 48, + 94, + 106, + 106 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 114, + 286, + 712 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 53, + 114, + 286, + 146 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 114, + 286, + 146 + ], + "spans": [ + { + "bbox": [ + 53, + 114, + 286, + 146 + ], + "type": "text", + "content": "[1] Iro Armeni, Sasha Sax, Amir R Zamir, and Silvio Savarese. 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Manhattan room layout reconstruction from a single " + }, + { + "bbox": [ + 307, + 545, + 545, + 599 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 307, + 545, + 545, + 599 + ], + "type": "text", + "content": " image: A comparative study of state-of-the-art methods. 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Recently, RNN-based methods have been proposed to generate stylized online Chinese characters. However, these methods mainly focus on capturing a person's overall writing style, neglecting subtle style inconsistencies between characters written by the same person. For example, while a person's handwriting typically exhibits general uniformity (e.g., glyph slant and aspect ratios), there are still small style variations in finer details (e.g., stroke length and curvature) of characters. In light of this, we propose to disentangle the style representations at both writer and character levels from individual handwritings to synthesize realistic stylized online handwritten characters. Specifically, we present the style-disentangled Transformer (SDT), which employs two complementary contrastive objectives to extract the style commonalities of reference samples and capture the detailed style patterns of each sample, respectively. Extensive experiments on various language scripts demonstrate the effectiveness of SDT. Notably, our empirical findings reveal that the two learned style representations provide information at different frequency magnitudes, underscoring the importance of separate style extraction. Our source code is public at: https://github.com/dailenson/SDT.", + "bbox": [ + 76, + 335, + 473, + 698 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 718, + 209, + 734 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "As the oldest writing system, Chinese characters are widely used across Asian countries. When compared with Latin scripts, Chinese characters encompass an exceptionally vast lexicon (87,887 characters in GB18030-2022字符) and have intricate structures composed of multiple strokes. Recently, the intriguing task of generating Chinese characters has garnered significant attention [10, 23, 32]. A promising approach to synthesising realistic handwritings is", + "bbox": [ + 76, + 744, + 468, + 864 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b410e9e460dc5e8b28f818a563869721c0f36b5f797ec109e37bbb191ca71af6.jpg", + "image_caption": [ + "Figure 1. Illustration of two online handwritten Chinese characters, with each color representing a stroke. The increasing numbers indicate the writing order from the start to the end." + ], + "image_footnote": [], + "bbox": [ + 532, + 301, + 859, + 452 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "to progressively generate online characters (i.e., the handwriting trajectory in a sequential format) [40]. As shown in Figure 1, online characters convey richer information (e.g., the order of writing) and thus pave the way for various applications, including writing robots [39].", + "bbox": [ + 496, + 516, + 892, + 592 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Our goal is to automatically generate online Chinese handwritings that not only correspond to specific textual content, but also emulate the calligraphic style of a given exemplar writer (e.g., glyph slant, shape, stroke length, and curvature). This task thus holds potential for a wide range of applications, such as font design and calligraphy education. A popular solution [18] is to extract style information from the provided stylized samples and merge it with the content reference. DeepImitator [44] concatenates the style vector obtained from a CNN encoder with a character embedding, which is then fed into the RNN decoder to generate stylized online characters. WriteLikeYou [30] adopts the largemargin softmax loss [36] to promote discriminative learning of style features. However, these methods mainly focus on the overall writing style, thus overlooking the detailed style inconsistencies (e.g., the highlighted regions in Figure 2) between characters produced by the same writer.", + "bbox": [ + 496, + 595, + 893, + 851 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The observations mentioned above inspire us to disentangle style representations at the writer and character levels from the stylized handwritings. However, accurately cap", + "bbox": [ + 498, + 854, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Authors contributed equally.", + "bbox": [ + 94, + 875, + 253, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding author", + "bbox": [ + 96, + 887, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "5977", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e5a987f2d1b7791c1120526224645047f85461aabb433a8b1808a6e1d353369b.jpg", + "image_caption": [ + "Left Slant" + ], + "image_footnote": [], + "bbox": [ + 197, + 80, + 433, + 135 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/22ef2d35f403b00cb44419f5ae3b169d672020c028323223a8c5b5b0d1e3a278.jpg", + "image_caption": [ + "No Slant" + ], + "image_footnote": [], + "bbox": [ + 197, + 140, + 429, + 194 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/70078260ca8255ee1d9594637c31db63e71dc85cbe90f414cfb7e20a96423c6b.jpg", + "image_caption": [ + "Right Slant", + "Figure 2. Handwritten character samples from three unique writers, with each row containing characters by the same person. Despite sharing similar overall handwriting styles (e.g., glyph slant), subtle style differences (e.g., stroke length, location, and curvature) can still be observed among them." + ], + "image_footnote": [], + "bbox": [ + 197, + 200, + 429, + 256 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "turing these two styles is a challenging task. To address this, we propose a style-disentangled Transformer (SDT) equipped with a dual-head style encoder. Specifically, we employ the contrastive learning framework [13] to guide each head in concentrating on writer-wise and character-wise styles, respectively. For the overall writer-wise style, we treat characters from the same writer as positive instances, and characters from different writers as negatives. This enables the encoder to learn the style commonalities among characters written by the same writer. Regarding the detailed character-wise style, we independently sample positive pairs within a character, and sample negative samples from other characters, as illustrated in Figure 3. Aggregating positive views of a character encourages the encoder to focus on the intricate character style patterns.", + "bbox": [ + 75, + 347, + 468, + 571 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In addition, we introduce a content encoder for SDT to learn a textual feature with a global context. The two style representations, along with the textual feature, are then fed into a decoder that progressively generates online characters. Given that the output characters are in sequential form, we employ Transformer [35], a powerful sequence modeling architecture, as our backbone.", + "bbox": [ + 75, + 573, + 468, + 678 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To extend SDT for generating offline Chinese handwritings (i.e., character images with stroke-width, e.g., Figures 3-7 in Appendix), we further propose an offline-to-offline generation framework. We first use SDT to generate online characters with significant shape changes, and then decorate them with stroke width, ink-blot effects, etc. This enables us to generate authentic offline handwritings. For more details, please refer to Appendix A.4.", + "bbox": [ + 75, + 679, + 468, + 799 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We summarize our contributions in three key aspects:", + "bbox": [ + 96, + 800, + 449, + 815 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- We are the first to disentangle two style representations (i.e., writer-wise and character-wise) for enhancing Chinese handwriting generation. Our findings show that the former focuses more on low-frequency information, while the latter captures higher frequencies.", + "bbox": [ + 94, + 824, + 468, + 901 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/e600574515ad03777cfc07f480446a60b464ef0060c00014b85fc318a6148345.jpg", + "image_caption": [ + "Figure 3. In this two-character example, we independently sample the positive pair, i.e., $o$ and $o^{+}$ , within the first character, while the negative $o^{-}$ is sampled from another character. Our sampling strategy randomly selects a small subset of patches, following a uniform distribution." + ], + "image_footnote": [], + "bbox": [ + 542, + 80, + 849, + 257 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We introduce a novel online character generation method, i.e., SDT. Extensive experiments on handwriting datasets in Chinese, English, Japanese, and Indic scripts demonstrate its effectiveness and superiority.", + "- Building on the SDT, we further develop an offline-to-offline framework that can produce more plausible offline handwritten Chinese characters, as evidenced in Appendix A.4." + ], + "bbox": [ + 517, + 345, + 890, + 476 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 497, + 640, + 512 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Handwriting generation. Various style-content disentangling methods [1, 8, 18, 21, 24] have been proposed to generate handwritings with arbitrary styles. These methods assume that reference samples can be decomposed into style and content spaces. They disentangle calligraphic styles from reference samples and recombine them with specific textual content for controllable style synthesis. For instance, DeepWriting [1] adopts RNNs to extract the style vectors from online handwritings, and then combines them with character embeddings for synthesizing stylized online handwritings. However, it typically over-smooths the styles of distinct letters and loses key details, since its extracted style vectors are letter-independent [21].", + "bbox": [ + 496, + 523, + 890, + 718 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "DSD [21] addresses the over-smooth problem by segmenting online handwritten words into isolated letters and encoding them into global and letter-specific style vectors, improving synthetic handwriting quality. Compared with it, our method can explicitly capture more fine-grained details (e.g., stroke length, location and curvature), which are more difficult to obtain. Besides, these methods [1, 21, 34] rely on extra fine annotations to segment input cursive scripts, while our SDT need not. Recently, HWT [3] uses a vanilla Transformer encoder for style pattern extraction. However, these methods [1, 3, 8, 18, 21] rely on complex content references, such as recurrent embeddings and letter-wise fil", + "bbox": [ + 496, + 719, + 892, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "5978", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ter maps. SLOGAN [24] addresses this issue by extracting textual contents from easily obtainable printed images, but it struggles with generalizing to unseen handwriting styles due to the fixed writer ID. In contrast, our SDT effectively obtains content and style information, and thus can synthesize characters with arbitrary styles well.", + "bbox": [ + 75, + 90, + 467, + 181 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Regarding handwritten Chinese characters, several attempts [4, 16, 20] use GANs to generate Chinese handwriting images, but always result in characteristic artifacts. Drawing [40] and FontRNN [31] adopt RNNs, but they cannot flexibly control the handwriting styles. In addition, DeepImitator [44] and WriteLikeYou [30] propose style-controlled generation using style representations from offline images [44] or online trajectories [30]. Unlike these methods [30,44] that only extract an overall writer style, our SDT captures both writer and character-level styles, significantly improving the performance of handwriting imitation.", + "bbox": [ + 75, + 181, + 467, + 348 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Contrastive learning. Contrastive learning [13, 41] has been widely used in various fields [9, 28, 29, 33, 42, 43]. Some image translation studies [14, 27] use contrastive learning to enhance natural image generation quality, encouraging content preservation during transfer. Unlike these methods [14, 27], our SDT aligns independently sampled patches from the same input, aiming to improve style representations of handwritings.", + "bbox": [ + 75, + 362, + 467, + 483 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 496, + 166, + 511 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Problem statement. We aim to synthesize stylized online handwritings with conditional content and style. Given a content image $I$ and a set of style images $X_{s} = \\{x_{s}^{i}\\}_{i = 1}^{K}$ , randomly sampled from a writer $w_{s}$ , we aim to generate an online handwritten Chinese character $\\hat{Y}_s$ that reflects the calligraphic style of $w_{s}$ and retains the textual content of $I$ . The key challenge lies in obtaining discriminative style representations from a limited number of stylized samples.", + "bbox": [ + 75, + 521, + 467, + 641 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To address this task, inspired by our observations (cf. Figure 2) of the overall uniformity (i.e., writer-wise style) and inconsistent details (i.e., character-wise style), we propose to disentangle the style of exemplar writers into overall and detailed styles for enhancing handwriting imitation performance. To achieve this, we introduce a new style-disentangled Transformer (SDT) approach to decouple the two styles from individual handwritings. The overall scheme of SDT is presented below.", + "bbox": [ + 75, + 642, + 467, + 777 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Overall Scheme", + "text_level": 1, + "bbox": [ + 76, + 786, + 233, + 800 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As shown in Figure 4, SDT consists of a dual-head style encoder, a content encoder, and a Transformer decoder. The style encoder (cf. Section 3.2) is designed to learn the writer-wise and character-wise styles. It firstly extracts rich calligraphic style patterns from reference style examples $X_{s}$ via a sequential combination of a CNN and a Transformer", + "bbox": [ + 75, + 809, + 467, + 898 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "encoder, followed by the writer and glyph heads to disentangle the writer-wise and character-wise styles from the extracted style patterns. To this end, we propose two contrastive objectives, WriterNCE $\\mathcal{L}_{wri}$ and GlyphNCE $\\mathcal{L}_{gly}$ , to encourage the encoder to learn the two styles, respectively. Specifically, $\\mathcal{L}_{wri}$ maximizes the mutual information between character instances belonging to the same writer, while $\\mathcal{L}_{gly}$ associates the positive pair independently sampled from the same character. Guided by $\\mathcal{L}_{wri}$ and $\\mathcal{L}_{gly}$ , the writer and glyph heads can acquire discriminative writerwise and character-wise style features, respectively.", + "bbox": [ + 496, + 90, + 890, + 257 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The content encoder uses a standard Resnet18 [15] as the CNN backbone to learn the compact feature map $q_{\\text{map}} \\in \\mathbb{R}^{h \\times w \\times c}$ from a content reference $I$ , and feeds the flattened feature patches into a Transformer encoder to extract the textual content representation $q \\in \\mathbb{R}^{d \\times c}$ , where $d = h \\times w$ and $c$ is the channel dimension. Benefiting from the strong capability of Transformer to capture long-range dependencies between feature patches, the content encoder expects an informative content feature $q$ with a global context.", + "bbox": [ + 496, + 260, + 890, + 397 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "After the two encoders, a multi-layer Transformer decoder (cf. Section 3.3) is used to synthesize $\\hat{Y}_s$ in an autoregressive fashion, conditioned on the two style representations and the content feature. This decoder is supervised by the pen moving prediction loss $\\mathcal{L}_{pre}$ and pen state classification loss $\\mathcal{L}_{cls}$ .", + "bbox": [ + 496, + 400, + 890, + 491 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To summarize, the overall training objective of SDT combines all four loss functions:", + "bbox": [ + 498, + 494, + 890, + 523 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {w r i} + \\mathcal {L} _ {g l y} + \\mathcal {L} _ {p r e} + \\lambda \\mathcal {L} _ {c l s}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 545, + 890, + 561 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\lambda$ serves as a trade-off factor. Each component of our SDT is detailed in the following Section 3.2 and Section 3.3.", + "bbox": [ + 498, + 580, + 890, + 609 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Dual-head Style Encoder", + "text_level": 1, + "bbox": [ + 500, + 632, + 725, + 647 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As illustrated in Figure 2, there are two distinct styles in a person's handwriting: writer-wise and character-wise styles. We propose a dual-head style encoder to obtain the two style representations. As shown in Figure 4, the input $X = \\{x^{i}\\}_{i=1}^{K}$ is firstly encoded by ResNet18 to obtain a sequence of feature maps $F_{m} = \\{f_{m}^{i}\\}_{i=1}^{K} \\in \\mathbb{R}^{K \\times h \\times w \\times c}$ . Next, we flatten the spatial dimension of each feature map to obtain feature sequences $F = \\{f^{i}\\}_{i=1}^{K} \\in \\mathbb{R}^{K \\times d \\times c}$ . These feature sequences are then fed into a Transformer encoder to extract more informative feature sequences $Z = \\{z^{i}\\}_{i=1}^{K} \\in \\mathbb{R}^{K \\times d \\times c}$ . Finally, we use the two heads, built on self-attention [35], to further disentangle $Z$ into the writer-wise style representations $E = \\{e^{i}\\}_{i=1}^{K} \\in \\mathbb{R}^{K \\times d \\times c}$ via $\\mathcal{L}_{wri}$ and the character-wise counterparts $G = \\{g^{i}\\}_{i=1}^{K} \\in \\mathbb{R}^{K \\times d \\times c}$ via $\\mathcal{L}_{gly}$ , respectively. We next detail the two contrastive learning objectives as follows.", + "bbox": [ + 496, + 659, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "5979", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/6f49830c6fef29eed3ff51233ef994e4ad983229aff59af86864af7a0df03cf2.jpg", + "image_caption": [ + "Figure 4. Overview of the proposed method. Our SDT consists of a dual-head style encoder, a content encoder and a Transformer decoder. The writer-wise and character-wise style representations extracted by style encoder and the learned content feature are fed into the Transformer decoder to progressively generate online handwritings. We utilize the WriterNCE $\\mathcal{L}_{wri}$ and GlyphNCE $\\mathcal{L}_{gly}$ to guide the two heads for learning the corresponding styles. $\\mathcal{L}_{pre}$ and $\\mathcal{L}_{cls}$ denote the pen moving prediction and state classification loss, respectively." + ], + "image_footnote": [], + "bbox": [ + 181, + 79, + 795, + 300 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.1 Writer-wise Contrastive Learning", + "text_level": 1, + "bbox": [ + 75, + 383, + 369, + 398 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To explicitly encourage the writer head to learn the witer-wise style, we propose to learn a feature space where the style features from the same writer are closer than those from different writers. The intuition is that one person's handwritings consistently exhibit similar style information, which can serve as a crucial clue for distinguishing writers. To this end, we take characters written by the same person as positive pairs and those from different writers as negative samples, and develop a new WriterNCE loss for writer-wise style learning.", + "bbox": [ + 75, + 407, + 470, + 556 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Specifically, let $j \\in M = \\{1, \\dots, N\\}$ be the index of an element within a mini-batch and let $A(j) = M \\setminus \\{j\\}$ be other indices distinct from $j$ , where $N$ is the batch size. Given a writer-wise style feature $e_j$ belonging to writer $w_j$ as the anchor, we denote its in-batch positive sample set as $P(j) = \\{p \\in A(j) : w_p = w_j\\}$ and its negative set as $A(j) \\setminus P(j)$ . The WriterNCE loss is formulated as follows:", + "bbox": [ + 75, + 558, + 470, + 666 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {w r i} = \\frac {- 1}{N} \\sum_ {j \\in M} \\frac {1}{| P (j) |} \\sum_ {p \\in P (j)} \\log \\frac {\\exp \\left(\\sin \\left(e _ {j} , e _ {p}\\right) / \\tau\\right)}{\\sum_ {a \\in A (j)} \\exp \\left(\\sin \\left(e _ {j} , e _ {a}\\right) / \\tau\\right)}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 686, + 478, + 733 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\operatorname{sim}(e_j, e_p) = f_1(e_j)^\\top f_1(e_p)$ , $\\tau$ is a temperature parameter and $f_1(\\cdot)$ is a multi-layer perceptron (MLP) that projects features to a $\\ell_2$ -normalized feature space where $\\mathcal{L}_{wri}$ is applied.", + "bbox": [ + 76, + 733, + 468, + 796 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.2 Character-wise Contrastive Learning", + "text_level": 1, + "bbox": [ + 76, + 816, + 393, + 830 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Compared with the overall writer-wise style, character-wise style differences often exist in the fine details of distinct characters, e.g., stroke length and curvature (cf. Figure 3). Inspired by this, we aim to maximize the mutual informa", + "bbox": [ + 75, + 839, + 470, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "tion between diverse views of a character, thereby enforcing the glyph head to learn the character-wise style. As strokes are distributed across arbitrary spatial locations in character images, we propose to capture stroke details via contrastive learning, by randomly selecting a small subset of patches following a uniform distribution. Specifically, we conduct sampling over the sequential patch tokens obtained from the glyph head.", + "bbox": [ + 496, + 383, + 890, + 503 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given character-wise style features $\\{g_j\\}_{j=1}^B \\in \\mathbb{R}^{B \\times d \\times c}$ extracted from $B$ characters, we sample a positive patch pair (i.e., $o \\in \\mathbb{R}^{n \\times c}$ and $o^+ \\in \\mathbb{R}^{n \\times c}$ ) from the same randomly selected $g$ , and $B-1$ negative patches $\\{o_j^-\\}_{j=1}^{B-1}$ from the remaining $B-1$ style features. Here, the number of sampled patch tokens is $n = d \\cdot \\alpha$ , where $\\alpha$ is the sampling ratio. The GlyphNCE loss is formulated as:", + "bbox": [ + 496, + 503, + 892, + 609 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {g l y} = - \\log \\frac {\\exp (\\sin (o , o ^ {+}) / \\tau)}{\\exp (\\sin (o , o ^ {+}) / \\tau) + \\sum_ {j = 1} ^ {B - 1} \\exp (\\sin (o , o _ {j} ^ {-}) / \\tau)}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 621, + 893, + 667 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\operatorname{sim}(o, o^+) = f_2(o)^\\top f_2(o^+)$ , and $f_2(\\cdot)$ is an MLP with the same structure as $f_1(\\cdot)$ .", + "bbox": [ + 500, + 667, + 890, + 699 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Transformer Decoder for Handwriting", + "text_level": 1, + "bbox": [ + 500, + 710, + 831, + 726 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The goal of the Transformer decoder is to progressively generate realistic online characters, denoted as $\\hat{Y}$ , based on the global content feature $q$ and the obtained style representations (i.e., $E = \\{e^i\\}_{i=1}^K$ and $G = \\{g^i\\}_{i=1}^K$ ). As each online character consists of numerous points (i.e., $\\hat{Y} = \\{\\hat{y}_j\\}_{j=1}^L$ , with $L$ being the total number of points; see more details in Appendix A.10), the decoder faces the challenge of effectively integrating content and style features to accurately depict all points of the character. To address this challenge, we propose to fuse $q$ , $E$ and $H$ within the multi-head attention layers of our Transformer decoder. As shown", + "bbox": [ + 496, + 734, + 893, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "5980", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/298e9fcdfd835c546dbcaf600c60363e2126917371505ff5e7a4c23d829b9d61.jpg", + "image_caption": [ + "Figure 5. Illustration of the fusion of the style information in our Transformer decoder. At each time step, the query vector is first encoded from the content feature $q$ and previous points $\\{y_j\\}_{j=1}^{t-1}$ . Then, it successively attends to the writer-wise and character-wise style features (i.e., $E$ and $G$ ) for adaptively aggregating style information, which is finally decoded into the current-step output." + ], + "image_footnote": [], + "bbox": [ + 140, + 87, + 405, + 270 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "in Figure 5, $E$ and $H$ serve as the key/value vectors, while $Q$ serves as the query vector that successively attends to $E$ and $G$ to aggregate style information.", + "bbox": [ + 75, + 383, + 468, + 428 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "During training, at any decoding step $t$ , we take $q$ as the initial point. As shown in Figure 5, we apply self-attention to the point sequence, i.e. the content context $[q, y_1, \\dots, y_{t-1}]$ , to obtain the query vector $Q_t \\in \\mathbb{R}^c$ . Here, the ground-truth points $\\{y_j\\}_{j=1}^{t-1}$ are used to accelerate model convergence in training [30, 37]. Subsequently, $Q_t$ attends to $E$ and $G$ over the subsequent decoding layers to adaptively aggregate style information, ultimately generating the output $O_t \\in \\mathbb{R}^{6R+3}$ . The output with $6R + 3$ logits is then used to generate the pen moving $(\\Delta \\hat{u}_t, \\Delta \\hat{v}_t)$ and the pen state $(\\hat{m}_t^1, \\hat{m}_t^2, \\hat{m}_t^3)$ . Specifically, we use a Gaussian mixture model (GMM) [11] with $R$ bivariate normal distributions to predict the pen moving, with each normal distribution containing 6 parameters. Moreover, we use the other 3 logits to generate the pen state. The training loss for supervising the decoder comprises two parts: the pen movement prediction loss $\\mathcal{L}_{pre}(\\Delta \\hat{u}_t, \\Delta \\hat{v}_t)$ , and the pen state classification loss $\\mathcal{L}_{cls}(\\hat{m}_t^1, \\hat{m}_t^2, \\hat{m}_t^3)$ . Please refer to Appendix A.11 for more details of these losses.", + "bbox": [ + 75, + 429, + 468, + 715 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The inference phase is different from the training phase, where the ground truth $y$ is not available at test time. Instead, we take the generated points $\\{\\hat{y}_j\\}_{j=1}^{t-1}$ as the input of the step $t$ , and combine them with $q, E$ , and $G$ to predict the next point $\\hat{y}_t$ . Such a process repeats until a pen-end state $(\\hat{m}_{t-1}^3 = 1)$ is received.", + "bbox": [ + 75, + 715, + 468, + 808 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 821, + 209, + 838 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Chinese handwriting generation", + "text_level": 1, + "bbox": [ + 76, + 845, + 359, + 863 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Dataset. To evaluate SDT in generating Chinese handwritings, we use CASIA-OLHWDB (1.0-1.2) [22] for model", + "bbox": [ + 75, + 869, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "training and ICDAR-2013 competition database [38] for testing. The training set consists of about 3.7 million online Chinese handwritten characters produced by 1,020 writers, while the test set contains 60 writers, with each contributing 3,755 most frequently used characters set of GB2312-80. Following [12], we use the Ramer-Douglas-Peucker algorithm [7] with a parameter of $\\epsilon = 2$ to remove redundant points of characters, leading to an average sequence length of 50. Following [44], we render offline style references using coordinate points of online characters, and each style sample is randomly sampled from the target-writer hand-writings during inference, as shown in Figure 4. For content images, we use the popular average Chinese font [17].", + "bbox": [ + 496, + 90, + 890, + 287 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation metrics. We use Dynamic Time Warping (DTW) [2,5], an elastic matching technique for aligning the given two sequences, to calculate the distance between the generated and real characters. Moreover, we use Content Score [44] to measure the structure correctness of generated characters, and adopt Style Score [30] to quantify the style similarity between the generated and real handwritings. We also conduct user preference studies to quantify the subjective quality of the output characters. More details are provided in Appendix A.1.1.", + "bbox": [ + 496, + 289, + 892, + 441 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation details. We set the number of the style reference to $K = 15$ , and resize the reference style and content images to $64 \\times 64$ . Moreover, each Transformer encoder contains 2 self-attention layers, while the Transformer decoder has 4 layers for obtaining style representations (2 for writer-wise and 2 for character-wise). Following the original Transformer [35], each Transformer layer contains the multi-head attention with $c = 512$ dimensional states and 8 attention heads. Contrary to HWT [3], where $F$ is concatenated before the Transformer encoder, we process each feature sequence $f \\in F$ individually. Moreover, we apply sinusoidal positional encoding [35] to input tokens before feeding them to the Transformer encoder and decoder. For training, we first pre-train the content encoder with 138k iterations (batch size of 256) for character classification on training samples and then train the whole model with 148k iterations (batch size of 128), on a single RTX3090 GPU. The optimizer is Adam [19], with a learning rate of 0.0002 and gradient clipping of 5.0. The sampling ratio $\\alpha$ is determined through a search over 0.25, 0.5, 0.75, 1.00, and 0.25 is chosen. Following [30], we set $\\lambda = 2$ . Further implementation details are provided in Appendix A.1.2.", + "bbox": [ + 496, + 444, + 892, + 777 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Compared methods. We compare our proposed SDT with state-of-the-art online Chinese character generation methods, i.e. Drawing [40], FontRNN [31], DeepImitator [44], and WriteLikeYou [30]. To ensure a fair comparison, we re-implement Drawing and FontRNN by adding the style branch of DeepImitator [44], enabling them to achieve arbitrary stylized character generation. To adapt Write-LikeYou [30] to handle images, we update its encoder to", + "bbox": [ + 496, + 779, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "5981", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/2f29eed1b588d43801107048fc85393801f9541ccecf22d7f3a6a6c0f90c98f7.jpg", + "image_caption": [ + "Figure 6. Comparisons with the state-of-the-art methods for online Chinese handwriting generation. The red and blue boxes highlight failures of style imitation and structure preservation, respectively. WriteLi. indicates the WriteLikeYou-v2. The green boxes highlight comparisons between the fine details of targets and generated characters." + ], + "image_footnote": [], + "bbox": [ + 151, + 89, + 821, + 335 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/338570295d02018b4580cadfff9cf26d94095395912b45f184c6c1503180bb75.jpg", + "table_caption": [ + "Table 1. Comparisons with state-of-the-art methods on Chinese dataset. See more results of WriteLikeYou [30] in Appendix A.6." + ], + "table_footnote": [], + "table_body": "
MethodStyle Score ↑Content Score ↑DTW ↓User Prefer. (%) ↑
Drawing [40]35.8378.151.18133.53
FontRNN [31]46.1492.181.04487.07
DeepImitator [44]50.6790.921.06227.99
WriteLikeYou-v1 [30]71.0993.890.983211.67
WriteLikeYou-v2 [30]72.3796.440.928913.07
SDT(Ours)94.5097.040.878956.67
", + "bbox": [ + 81, + 431, + 470, + 545 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "create two new variants: WriteLikeYou-v1 (i.e., CNN encoder [44]) and WriteLikeYou-v2 (i.e., the same CNN-Transformer encoder as our SDT), based on the released official code1. More details are available in Appendix A.1.3.", + "bbox": [ + 75, + 573, + 468, + 633 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Quantitative comparison. Quantitative results are in Table 1, revealing that SDT outperforms other methods across all evaluation metrics. Notably, SDT surpasses the second-best method by a significant $22.13\\%$ margin in Style Score, demonstrating the proposed method's exceptional style imitation performance.", + "bbox": [ + 75, + 633, + 468, + 724 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Qualitative comparison. We visualize the generated samples of each method in Figure 6, which intuitively explains the significant superiority of SDT in the user preference study. In Figure 6, Drawing [40] generates the least satisfactory results, often producing unreadable characters. FontRNN [31] and DeepImitator [44] occasionally synthesize unpleasant stroke paddings, and WriteLikeYou [30] struggles with generating complex characters regarding style mimicry. In contrast, our method yields higher-quality results, particularly in recovering fine character details.", + "bbox": [ + 75, + 724, + 470, + 876 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/8c9da4d907bbd59adeb136cdcae1a731520edc8ed91854ac785cb04a8f2ebfd2.jpg", + "table_caption": [ + "Table 2. Ablation study. Here, we further use FID to measure the distance between generated and real samples for each writer separately, and finally average them." + ], + "table_footnote": [], + "table_body": "
writer-wisecharacter-wiseGenerated SamplesStyle Score↑FID↓DTW↓
倾朝朝85.5227.750.8941
✓倾朝朝91.3826.380.8841
✓倾朝朝90.3126.890.8803
✓✓倾朝朝94.5025.460.8789
Ground Truth倾朝朝
", + "bbox": [ + 506, + 450, + 890, + 588 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Analysis", + "text_level": 1, + "bbox": [ + 500, + 604, + 602, + 619 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we assess the impact of the two learned style features and that of the style inputs. We also analyze the effect of the sampling ratio $\\alpha$ , and discuss the combination strategies in the Transformer decoder in Appendix A.5. Besides, we discuss failure cases in Appendix A.7.", + "bbox": [ + 496, + 627, + 892, + 702 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Quantitative evaluation of two style representations. We ablate the effects of the two extracted style representations in Table 2. The findings include: (1) Both style representations enhance the quality of generated outcomes in all evaluation metrics, particularly in terms of Style Score, improving by $4.79\\%$ and $5.86\\%$ , respectively. (2) Combining the two style features further boosts model performance across all evaluation metrics, suggesting that the extracted styles are complementary. Moreover, the order in which the two style features are input into the Transformer decoder has no significant impact on Style Score $(93.72\\%)$ vs. $94.50\\%$ .", + "bbox": [ + 496, + 703, + 893, + 869 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Qualitative comparison between two style representations. To further analyze the differences between the", + "bbox": [ + 498, + 869, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "", + "bbox": [ + 94, + 886, + 434, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "5982", + "bbox": [ + 482, + 944, + 516, + 957 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a065116e58a3f204a1e13d80137c1343ffec24e4715c9902c660629daf2d3eab.jpg", + "image_caption": [ + "Figure 7. Spectrum analysis of two style representations. We provide frequency magnitude visualizations belonging to 7 writers, where the top row shows the writer-wise style while the bottom represents the character-wise one. Each spectrum map is averaged over 100 character samples written by the same person. The brighter the color, the larger the magnitude. A pixel farther from the center means a higher frequency [26]. We find that the writer-wise style representations capture more low-frequency information, while character-wise style representations capture more high-frequency information." + ], + "image_footnote": [], + "bbox": [ + 117, + 89, + 846, + 238 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/acb6a5a538a7bc801c1165fcbd4619548dfba3873c38c08a9a016e7829269fe2.jpg", + "image_caption": [ + "Figure 8. The heat map of the DTW matrix. The dark diagonal indicates that the generated characters still own a higher similarity even using different $X_{s}$ belonging to the same writer." + ], + "image_footnote": [], + "bbox": [ + 114, + 330, + 429, + 534 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "two styles, we resize the output patch tokens representing the two styles to feature maps, respectively, and visualize their frequency magnitudes in Figure 7. We find that character-wise style features capture more high-frequency information, whereas writer-wise features mainly focus on low-frequency information. According to [6], the high-frequency information in an image usually captures fine details while the low frequencies contain the overall part of objects. This finding supports our motivation that the writer head helps to imitate the overall style (e.g., glyph slant), while the glyph head captures the detailed style (e.g., stroke curvature), as shown in Table 2.", + "bbox": [ + 75, + 598, + 468, + 777 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effect of using different style inputs. As mentioned in [30], given different style inputs $X_{s}$ belonging to the same writer $w_{s}$ , the imitation model may generate inconsistent characters. To evaluate the effect of different style inputs, we conduct two independent experiments using different $X_{s}$ based on the same model. Following [30], we use the model to generate 200 characters for each writer in the test set. We then calculate the DTW distance between corre", + "bbox": [ + 75, + 779, + 470, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/9a3e3056066074ec4dba06a2d29ac42e4eee59dec07d4a69f0fd4807232161ab.jpg", + "table_caption": [ + "Table 3. Quantitative evaluations of our SDT and competitors on Japanese, Indic, and English datasets." + ], + "table_footnote": [], + "table_body": "
DatasetsMethodsContent Score↑DTW ↓
JapaneseDrawing [40]50.741.4657
DeepImitator [44]53.201.2564
WriteLikeYou-v2 [30]85.611.2066
SDT(Ours)91.311.1289
IndicDrawing [40]2.349.8230
DeepImitator [44]4.136.7421
WriteLikeYou-v2 [30]13.194.5130
SDT(Ours)97.220.7075
EnglishDrawing [40]79.141.8519
DeepImitator [44]76.531.6460
WriteLikeYou-v2 [30]84.411.6215
SDT(Ours)85.521.6048
", + "bbox": [ + 511, + 371, + 883, + 565 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "sponding characters individually and average them according to the writer index (see Appendix A.1.4 for more details) to get a DTW square matrix. The resulting DTW square matrix is visualized in Figure 8. The dark diagonal in Figure 8 suggests that the generated characters maintain a high degree of similarity even when using different $X_{s}$ belonging to the same writer, demonstrating that our SDT can generate consistent results from various style inputs.", + "bbox": [ + 496, + 594, + 890, + 715 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Applications to Other Languages", + "text_level": 1, + "bbox": [ + 498, + 724, + 790, + 742 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Japanese handwriting generation. For the Japanese handwriting generation task, we conduct experiments on TUAT HANDS [25] database (see more details in Appendix A.1.5) to evaluate the effectiveness of our method. Figure 9 (a) and Table 3 verify the effectiveness of SDT for Japanese handwriting generation. Specifically, from Table 3, we observe that our SDT outperforms all compared methods in terms of two quantitative metrics, indicating that SDT performs well in multiple languages. Furthermore, we provide additional evaluation metrics in Appendix A.8.", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "5983", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a18b439f0cb77c25fe69aa0049f3d76c09a737798a8d7572f754227ade8d1505.jpg", + "image_caption": [ + "Figure 9. Comparisons with the competitors for online handwriting generation on various scripts. WriteLi. indicates WriteLikeYou-v2." + ], + "image_footnote": [], + "bbox": [ + 122, + 89, + 851, + 333 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Indic handwriting generation. We evaluate our method on the Indic handwriting generation task based on the $\\mathrm{Tamil}^2$ dataset. It is worth noting that Indic handwriting generation presents a more significant challenge, as Indic characters contain more trajectory points than Chinese, Japanese, and English scripts (i.e., 88 vs. 68, 50, 30 on average; see Appendix A.1.5 for more dataset information). We compare our method with other approaches on the official test set in terms of Content Score and Dynamic Time Warping (DTW). As shown in Table 3, we find that our SDT significantly outperforms the second-best method in terms of the two quantitative metrics, achieving an $84.03\\%$ higher Content Score and a 3.8055 lower DTW. This indicates that our SDT can handle handwritten characters with a large number of points (averaging 88) and ensure the quality of synthetic samples, as illustrated in Figure 9 (b). The potential advantages of our SDT are: (1) The improved style representations extracted by our SDT prevent the collapse of generated characters. (2) Our Transformer decoder facilitates long-distance dependence between trajectory points. We provide more experimental analysis in Appendix A.9.", + "bbox": [ + 76, + 381, + 472, + 700 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "English handwriting generation. To evaluate our method in generating English handwritings, we collect all of the English samples from the symbol part of CASIA-OLHWDB(1.0-1.2) [22] and ICDAR-2013 competition database [38] (see more details in Appendix A.1.5). Similarly, we use Content Score and DTW as evaluation metrics. As shown in Figure 9 (c), we find that all methods achieve sound and comparable performance. One reason for this is that the English script contains fewer character classes and a smaller number of trajectory points (averaging 30), making", + "bbox": [ + 76, + 713, + 470, + 867 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "their imitation easier compared to other scripts. Nevertheless, our SDT still outperforms other methods by a small margin in terms of both Content Score and DTW, as shown in Table 3. Moreover, we observe that corresponding uppercase and lowercase letters sometimes exhibit subtle inter-class differences (e.g., O vs. o), which leads our SDT to achieve a relatively low Content Score.", + "bbox": [ + 496, + 381, + 893, + 488 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 498, + 500, + 619, + 516 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we have proposed a novel method, named style-disentangled Transformer (SDT), to synthesize realistic and diverse online handwritings. SDT enhances imitation performance by disentangling the writer-wise and character-wise style representations from individual handwriting samples. For the writer-wise style, we group characters from the same writer and separate those from different writers, promoting SDT's ability to learn uniformity in individual handwritings. For the character-wise style, we maximize the mutual information between the distinct views of a character. Moreover, we extend SDT and introduce an offline-to-offline framework for improving the generation quality of offline Chinese handwritings. Promising results on various language scripts verify the effectiveness of our SDT. Although primarily designed for handwriting generation, SDT still holds the potential for extension to other generative tasks, such as font generation.", + "bbox": [ + 496, + 525, + 893, + 785 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments This research is partially supported by NSFC (Grant No.62176093, 61673182), Key Realm R&D Program of Guangzhou (No.202206030001), Guangdong Basic and Applied Basic Research Foundation (No.2021A1515012282) and Guangdong Provincial Key Laboratory of Human Digital Twin (2022B1212010004).", + "bbox": [ + 496, + 800, + 893, + 893 + ], + "page_idx": 7 + }, + { + "type": "page_footnote", + "text": "$^{2}$ http : // lipitk . sourceforge . net / datasets / familialchdata.htm", + "bbox": [ + 76, + 875, + 470, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "5984", + "bbox": [ + 482, + 944, + 514, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Emre Aksan, Fabrizio Pece, and Otmar Hilliges. 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Pattern Recognition, 104:107080, 2020. 1, 3, 5, 6, 7" + ], + "bbox": [ + 501, + 92, + 890, + 556 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "5986", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Disentangling Writer and Character Styles for Handwriting Generation/39ec325e-e585-4646-a631-108d72fa1121_model.json b/2023/Disentangling Writer and Character Styles for Handwriting Generation/39ec325e-e585-4646-a631-108d72fa1121_model.json new file mode 100644 index 0000000000000000000000000000000000000000..80f1bbb73cc229a12344eacf122f6b81938a9b42 --- /dev/null +++ b/2023/Disentangling Writer and Character Styles for Handwriting Generation/39ec325e-e585-4646-a631-108d72fa1121_model.json @@ -0,0 +1,1958 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.123, + 0.131, + 0.848, + 0.154 + ], + "angle": 0, + "content": "Disentangling Writer and Character Styles for Handwriting Generation" + }, + { + "type": "text", + "bbox": [ + 0.205, + 0.18, + 0.764, + 0.217 + ], + "angle": 0, + "content": "Gang Dai\\(^{1*}\\), Yifan Zhang\\(^{2*}\\), Qingfeng Wang\\(^{1}\\), Qing Du\\(^{1}\\), Zhuliang Yu\\(^{1}\\), Zhuoman Liu\\(^{3}\\), Shuangping Huang\\(^{1,4\\dagger}\\)" + }, + { + "type": "text", + "bbox": [ + 0.189, + 0.217, + 0.782, + 0.234 + ], + "angle": 0, + "content": "\\(^{1}\\)South China University of Technology, \\(^{2}\\)National University of Singapore," + }, + { + "type": "text", + "bbox": [ + 0.242, + 0.234, + 0.729, + 0.253 + ], + "angle": 0, + "content": "3The Hong Kong Polytechnic University, 4Pazhou Laboratory" + }, + { + "type": "text", + "bbox": [ + 0.189, + 0.255, + 0.775, + 0.269 + ], + "angle": 0, + "content": "eedaigang@mail.scut.edu.cn, yifan.zhang@u.nus.edu, eehsp@scut.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.305, + 0.314, + 0.32 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.337, + 0.474, + 0.699 + ], + "angle": 0, + "content": "Training machines to synthesize diverse handwritings is an intriguing task. Recently, RNN-based methods have been proposed to generate stylized online Chinese characters. However, these methods mainly focus on capturing a person's overall writing style, neglecting subtle style inconsistencies between characters written by the same person. For example, while a person's handwriting typically exhibits general uniformity (e.g., glyph slant and aspect ratios), there are still small style variations in finer details (e.g., stroke length and curvature) of characters. In light of this, we propose to disentangle the style representations at both writer and character levels from individual handwritings to synthesize realistic stylized online handwritten characters. Specifically, we present the style-disentangled Transformer (SDT), which employs two complementary contrastive objectives to extract the style commonalities of reference samples and capture the detailed style patterns of each sample, respectively. Extensive experiments on various language scripts demonstrate the effectiveness of SDT. Notably, our empirical findings reveal that the two learned style representations provide information at different frequency magnitudes, underscoring the importance of separate style extraction. Our source code is public at: https://github.com/dailenson/SDT." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.719, + 0.21, + 0.735 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.745, + 0.47, + 0.866 + ], + "angle": 0, + "content": "As the oldest writing system, Chinese characters are widely used across Asian countries. When compared with Latin scripts, Chinese characters encompass an exceptionally vast lexicon (87,887 characters in GB18030-2022字符) and have intricate structures composed of multiple strokes. Recently, the intriguing task of generating Chinese characters has garnered significant attention [10, 23, 32]. A promising approach to synthesising realistic handwritings is" + }, + { + "type": "image", + "bbox": [ + 0.533, + 0.303, + 0.86, + 0.453 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.46, + 0.893, + 0.502 + ], + "angle": 0, + "content": "Figure 1. Illustration of two online handwritten Chinese characters, with each color representing a stroke. The increasing numbers indicate the writing order from the start to the end." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.517, + 0.893, + 0.593 + ], + "angle": 0, + "content": "to progressively generate online characters (i.e., the handwriting trajectory in a sequential format) [40]. As shown in Figure 1, online characters convey richer information (e.g., the order of writing) and thus pave the way for various applications, including writing robots [39]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.596, + 0.895, + 0.852 + ], + "angle": 0, + "content": "Our goal is to automatically generate online Chinese handwritings that not only correspond to specific textual content, but also emulate the calligraphic style of a given exemplar writer (e.g., glyph slant, shape, stroke length, and curvature). This task thus holds potential for a wide range of applications, such as font design and calligraphy education. A popular solution [18] is to extract style information from the provided stylized samples and merge it with the content reference. DeepImitator [44] concatenates the style vector obtained from a CNN encoder with a character embedding, which is then fed into the RNN decoder to generate stylized online characters. WriteLikeYou [30] adopts the largemargin softmax loss [36] to promote discriminative learning of style features. However, these methods mainly focus on the overall writing style, thus overlooking the detailed style inconsistencies (e.g., the highlighted regions in Figure 2) between characters produced by the same writer." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.894, + 0.901 + ], + "angle": 0, + "content": "The observations mentioned above inspire us to disentangle style representations at the writer and character levels from the stylized handwritings. However, accurately cap" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.875, + 0.254, + 0.888 + ], + "angle": 0, + "content": "*Authors contributed equally." + }, + { + "type": "page_footnote", + "bbox": [ + 0.098, + 0.888, + 0.221, + 0.9 + ], + "angle": 0, + "content": "† Corresponding author" + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.875, + 0.254, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5977" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.11, + 0.1, + 0.178, + 0.113 + ], + "angle": 0, + "content": "Left Slant" + }, + { + "type": "image", + "bbox": [ + 0.199, + 0.082, + 0.434, + 0.136 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.11, + 0.158, + 0.171, + 0.171 + ], + "angle": 0, + "content": "No Slant" + }, + { + "type": "image", + "bbox": [ + 0.199, + 0.141, + 0.43, + 0.195 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.11, + 0.218, + 0.187, + 0.232 + ], + "angle": 0, + "content": "Right Slant" + }, + { + "type": "image", + "bbox": [ + 0.198, + 0.202, + 0.43, + 0.257 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.26, + 0.47, + 0.331 + ], + "angle": 0, + "content": "Figure 2. Handwritten character samples from three unique writers, with each row containing characters by the same person. Despite sharing similar overall handwriting styles (e.g., glyph slant), subtle style differences (e.g., stroke length, location, and curvature) can still be observed among them." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.348, + 0.47, + 0.573 + ], + "angle": 0, + "content": "turing these two styles is a challenging task. To address this, we propose a style-disentangled Transformer (SDT) equipped with a dual-head style encoder. Specifically, we employ the contrastive learning framework [13] to guide each head in concentrating on writer-wise and character-wise styles, respectively. For the overall writer-wise style, we treat characters from the same writer as positive instances, and characters from different writers as negatives. This enables the encoder to learn the style commonalities among characters written by the same writer. Regarding the detailed character-wise style, we independently sample positive pairs within a character, and sample negative samples from other characters, as illustrated in Figure 3. Aggregating positive views of a character encourages the encoder to focus on the intricate character style patterns." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.574, + 0.47, + 0.679 + ], + "angle": 0, + "content": "In addition, we introduce a content encoder for SDT to learn a textual feature with a global context. The two style representations, along with the textual feature, are then fed into a decoder that progressively generates online characters. Given that the output characters are in sequential form, we employ Transformer [35], a powerful sequence modeling architecture, as our backbone." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.68, + 0.469, + 0.8 + ], + "angle": 0, + "content": "To extend SDT for generating offline Chinese handwritings (i.e., character images with stroke-width, e.g., Figures 3-7 in Appendix), we further propose an offline-to-offline generation framework. We first use SDT to generate online characters with significant shape changes, and then decorate them with stroke width, ink-blot effects, etc. This enables us to generate authentic offline handwritings. For more details, please refer to Appendix A.4." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.801, + 0.45, + 0.816 + ], + "angle": 0, + "content": "We summarize our contributions in three key aspects:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.825, + 0.47, + 0.902 + ], + "angle": 0, + "content": "- We are the first to disentangle two style representations (i.e., writer-wise and character-wise) for enhancing Chinese handwriting generation. Our findings show that the former focuses more on low-frequency information, while the latter captures higher frequencies." + }, + { + "type": "image", + "bbox": [ + 0.543, + 0.081, + 0.85, + 0.258 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.261, + 0.892, + 0.331 + ], + "angle": 0, + "content": "Figure 3. In this two-character example, we independently sample the positive pair, i.e., \\( o \\) and \\( o^{+} \\), within the first character, while the negative \\( o^{-} \\) is sampled from another character. Our sampling strategy randomly selects a small subset of patches, following a uniform distribution." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.347, + 0.892, + 0.409 + ], + "angle": 0, + "content": "- We introduce a novel online character generation method, i.e., SDT. Extensive experiments on handwriting datasets in Chinese, English, Japanese, and Indic scripts demonstrate its effectiveness and superiority." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.417, + 0.892, + 0.477 + ], + "angle": 0, + "content": "- Building on the SDT, we further develop an offline-to-offline framework that can produce more plausible offline handwritten Chinese characters, as evidenced in Appendix A.4." + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.347, + 0.892, + 0.477 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.498, + 0.642, + 0.513 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.524, + 0.892, + 0.719 + ], + "angle": 0, + "content": "Handwriting generation. Various style-content disentangling methods [1, 8, 18, 21, 24] have been proposed to generate handwritings with arbitrary styles. These methods assume that reference samples can be decomposed into style and content spaces. They disentangle calligraphic styles from reference samples and recombine them with specific textual content for controllable style synthesis. For instance, DeepWriting [1] adopts RNNs to extract the style vectors from online handwritings, and then combines them with character embeddings for synthesizing stylized online handwritings. However, it typically over-smooths the styles of distinct letters and loses key details, since its extracted style vectors are letter-independent [21]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.893, + 0.901 + ], + "angle": 0, + "content": "DSD [21] addresses the over-smooth problem by segmenting online handwritten words into isolated letters and encoding them into global and letter-specific style vectors, improving synthetic handwriting quality. Compared with it, our method can explicitly capture more fine-grained details (e.g., stroke length, location and curvature), which are more difficult to obtain. Besides, these methods [1, 21, 34] rely on extra fine annotations to segment input cursive scripts, while our SDT need not. Recently, HWT [3] uses a vanilla Transformer encoder for style pattern extraction. However, these methods [1, 3, 8, 18, 21] rely on complex content references, such as recurrent embeddings and letter-wise fil" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5978" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.468, + 0.182 + ], + "angle": 0, + "content": "ter maps. SLOGAN [24] addresses this issue by extracting textual contents from easily obtainable printed images, but it struggles with generalizing to unseen handwriting styles due to the fixed writer ID. In contrast, our SDT effectively obtains content and style information, and thus can synthesize characters with arbitrary styles well." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.183, + 0.468, + 0.349 + ], + "angle": 0, + "content": "Regarding handwritten Chinese characters, several attempts [4, 16, 20] use GANs to generate Chinese handwriting images, but always result in characteristic artifacts. Drawing [40] and FontRNN [31] adopt RNNs, but they cannot flexibly control the handwriting styles. In addition, DeepImitator [44] and WriteLikeYou [30] propose style-controlled generation using style representations from offline images [44] or online trajectories [30]. Unlike these methods [30,44] that only extract an overall writer style, our SDT captures both writer and character-level styles, significantly improving the performance of handwriting imitation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.363, + 0.468, + 0.484 + ], + "angle": 0, + "content": "Contrastive learning. Contrastive learning [13, 41] has been widely used in various fields [9, 28, 29, 33, 42, 43]. Some image translation studies [14, 27] use contrastive learning to enhance natural image generation quality, encouraging content preservation during transfer. Unlike these methods [14, 27], our SDT aligns independently sampled patches from the same input, aiming to improve style representations of handwritings." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.497, + 0.168, + 0.512 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.522, + 0.468, + 0.642 + ], + "angle": 0, + "content": "Problem statement. We aim to synthesize stylized online handwritings with conditional content and style. Given a content image \\( I \\) and a set of style images \\( X_{s} = \\{x_{s}^{i}\\}_{i = 1}^{K} \\), randomly sampled from a writer \\( w_{s} \\), we aim to generate an online handwritten Chinese character \\( \\hat{Y}_s \\) that reflects the calligraphic style of \\( w_{s} \\) and retains the textual content of \\( I \\). The key challenge lies in obtaining discriminative style representations from a limited number of stylized samples." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.643, + 0.468, + 0.779 + ], + "angle": 0, + "content": "To address this task, inspired by our observations (cf. Figure 2) of the overall uniformity (i.e., writer-wise style) and inconsistent details (i.e., character-wise style), we propose to disentangle the style of exemplar writers into overall and detailed styles for enhancing handwriting imitation performance. To achieve this, we introduce a new style-disentangled Transformer (SDT) approach to decouple the two styles from individual handwritings. The overall scheme of SDT is presented below." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.787, + 0.235, + 0.801 + ], + "angle": 0, + "content": "3.1. Overall Scheme" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.468, + 0.9 + ], + "angle": 0, + "content": "As shown in Figure 4, SDT consists of a dual-head style encoder, a content encoder, and a Transformer decoder. The style encoder (cf. Section 3.2) is designed to learn the writer-wise and character-wise styles. It firstly extracts rich calligraphic style patterns from reference style examples \\( X_{s} \\) via a sequential combination of a CNN and a Transformer" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.258 + ], + "angle": 0, + "content": "encoder, followed by the writer and glyph heads to disentangle the writer-wise and character-wise styles from the extracted style patterns. To this end, we propose two contrastive objectives, WriterNCE \\(\\mathcal{L}_{wri}\\) and GlyphNCE \\(\\mathcal{L}_{gly}\\), to encourage the encoder to learn the two styles, respectively. Specifically, \\(\\mathcal{L}_{wri}\\) maximizes the mutual information between character instances belonging to the same writer, while \\(\\mathcal{L}_{gly}\\) associates the positive pair independently sampled from the same character. Guided by \\(\\mathcal{L}_{wri}\\) and \\(\\mathcal{L}_{gly}\\), the writer and glyph heads can acquire discriminative writerwise and character-wise style features, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.261, + 0.892, + 0.398 + ], + "angle": 0, + "content": "The content encoder uses a standard Resnet18 [15] as the CNN backbone to learn the compact feature map \\( q_{\\text{map}} \\in \\mathbb{R}^{h \\times w \\times c} \\) from a content reference \\( I \\), and feeds the flattened feature patches into a Transformer encoder to extract the textual content representation \\( q \\in \\mathbb{R}^{d \\times c} \\), where \\( d = h \\times w \\) and \\( c \\) is the channel dimension. Benefiting from the strong capability of Transformer to capture long-range dependencies between feature patches, the content encoder expects an informative content feature \\( q \\) with a global context." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.401, + 0.891, + 0.492 + ], + "angle": 0, + "content": "After the two encoders, a multi-layer Transformer decoder (cf. Section 3.3) is used to synthesize \\(\\hat{Y}_s\\) in an autoregressive fashion, conditioned on the two style representations and the content feature. This decoder is supervised by the pen moving prediction loss \\(\\mathcal{L}_{pre}\\) and pen state classification loss \\(\\mathcal{L}_{cls}\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.495, + 0.891, + 0.525 + ], + "angle": 0, + "content": "To summarize, the overall training objective of SDT combines all four loss functions:" + }, + { + "type": "equation", + "bbox": [ + 0.578, + 0.546, + 0.891, + 0.562 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {w r i} + \\mathcal {L} _ {g l y} + \\mathcal {L} _ {p r e} + \\lambda \\mathcal {L} _ {c l s}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.581, + 0.891, + 0.611 + ], + "angle": 0, + "content": "where \\(\\lambda\\) serves as a trade-off factor. Each component of our SDT is detailed in the following Section 3.2 and Section 3.3." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.633, + 0.727, + 0.648 + ], + "angle": 0, + "content": "3.2. Dual-head Style Encoder" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.892, + 0.901 + ], + "angle": 0, + "content": "As illustrated in Figure 2, there are two distinct styles in a person's handwriting: writer-wise and character-wise styles. We propose a dual-head style encoder to obtain the two style representations. As shown in Figure 4, the input \\( X = \\{x^{i}\\}_{i=1}^{K} \\) is firstly encoded by ResNet18 to obtain a sequence of feature maps \\( F_{m} = \\{f_{m}^{i}\\}_{i=1}^{K} \\in \\mathbb{R}^{K \\times h \\times w \\times c} \\). Next, we flatten the spatial dimension of each feature map to obtain feature sequences \\( F = \\{f^{i}\\}_{i=1}^{K} \\in \\mathbb{R}^{K \\times d \\times c} \\). These feature sequences are then fed into a Transformer encoder to extract more informative feature sequences \\( Z = \\{z^{i}\\}_{i=1}^{K} \\in \\mathbb{R}^{K \\times d \\times c} \\). Finally, we use the two heads, built on self-attention [35], to further disentangle \\( Z \\) into the writer-wise style representations \\( E = \\{e^{i}\\}_{i=1}^{K} \\in \\mathbb{R}^{K \\times d \\times c} \\) via \\( \\mathcal{L}_{wri} \\) and the character-wise counterparts \\( G = \\{g^{i}\\}_{i=1}^{K} \\in \\mathbb{R}^{K \\times d \\times c} \\) via \\( \\mathcal{L}_{gly} \\), respectively. We next detail the two contrastive learning objectives as follows." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5979" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.182, + 0.08, + 0.796, + 0.301 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.309, + 0.895, + 0.368 + ], + "angle": 0, + "content": "Figure 4. Overview of the proposed method. Our SDT consists of a dual-head style encoder, a content encoder and a Transformer decoder. The writer-wise and character-wise style representations extracted by style encoder and the learned content feature are fed into the Transformer decoder to progressively generate online handwritings. We utilize the WriterNCE \\(\\mathcal{L}_{wri}\\) and GlyphNCE \\(\\mathcal{L}_{gly}\\) to guide the two heads for learning the corresponding styles. \\(\\mathcal{L}_{pre}\\) and \\(\\mathcal{L}_{cls}\\) denote the pen moving prediction and state classification loss, respectively." + }, + { + "type": "title", + "bbox": [ + 0.076, + 0.384, + 0.37, + 0.399 + ], + "angle": 0, + "content": "3.2.1 Writer-wise Contrastive Learning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.408, + 0.471, + 0.558 + ], + "angle": 0, + "content": "To explicitly encourage the writer head to learn the witer-wise style, we propose to learn a feature space where the style features from the same writer are closer than those from different writers. The intuition is that one person's handwritings consistently exhibit similar style information, which can serve as a crucial clue for distinguishing writers. To this end, we take characters written by the same person as positive pairs and those from different writers as negative samples, and develop a new WriterNCE loss for writer-wise style learning." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.559, + 0.472, + 0.667 + ], + "angle": 0, + "content": "Specifically, let \\( j \\in M = \\{1, \\dots, N\\} \\) be the index of an element within a mini-batch and let \\( A(j) = M \\setminus \\{j\\} \\) be other indices distinct from \\( j \\), where \\( N \\) is the batch size. Given a writer-wise style feature \\( e_j \\) belonging to writer \\( w_j \\) as the anchor, we denote its in-batch positive sample set as \\( P(j) = \\{p \\in A(j) : w_p = w_j\\} \\) and its negative set as \\( A(j) \\setminus P(j) \\). The WriterNCE loss is formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.077, + 0.687, + 0.48, + 0.734 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {w r i} = \\frac {- 1}{N} \\sum_ {j \\in M} \\frac {1}{| P (j) |} \\sum_ {p \\in P (j)} \\log \\frac {\\exp \\left(\\sin \\left(e _ {j} , e _ {p}\\right) / \\tau\\right)}{\\sum_ {a \\in A (j)} \\exp \\left(\\sin \\left(e _ {j} , e _ {a}\\right) / \\tau\\right)}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.734, + 0.47, + 0.797 + ], + "angle": 0, + "content": "where \\(\\operatorname{sim}(e_j, e_p) = f_1(e_j)^\\top f_1(e_p)\\), \\(\\tau\\) is a temperature parameter and \\(f_1(\\cdot)\\) is a multi-layer perceptron (MLP) that projects features to a \\(\\ell_2\\)-normalized feature space where \\(\\mathcal{L}_{wri}\\) is applied." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.817, + 0.394, + 0.832 + ], + "angle": 0, + "content": "3.2.2 Character-wise Contrastive Learning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Compared with the overall writer-wise style, character-wise style differences often exist in the fine details of distinct characters, e.g., stroke length and curvature (cf. Figure 3). Inspired by this, we aim to maximize the mutual informa" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.384, + 0.892, + 0.504 + ], + "angle": 0, + "content": "tion between diverse views of a character, thereby enforcing the glyph head to learn the character-wise style. As strokes are distributed across arbitrary spatial locations in character images, we propose to capture stroke details via contrastive learning, by randomly selecting a small subset of patches following a uniform distribution. Specifically, we conduct sampling over the sequential patch tokens obtained from the glyph head." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.504, + 0.893, + 0.611 + ], + "angle": 0, + "content": "Given character-wise style features \\(\\{g_j\\}_{j=1}^B \\in \\mathbb{R}^{B \\times d \\times c}\\) extracted from \\(B\\) characters, we sample a positive patch pair (i.e., \\(o \\in \\mathbb{R}^{n \\times c}\\) and \\(o^+ \\in \\mathbb{R}^{n \\times c}\\)) from the same randomly selected \\(g\\), and \\(B-1\\) negative patches \\(\\{o_j^-\\}_{j=1}^{B-1}\\) from the remaining \\(B-1\\) style features. Here, the number of sampled patch tokens is \\(n = d \\cdot \\alpha\\), where \\(\\alpha\\) is the sampling ratio. The GlyphNCE loss is formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.622, + 0.894, + 0.668 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {g l y} = - \\log \\frac {\\exp (\\sin (o , o ^ {+}) / \\tau)}{\\exp (\\sin (o , o ^ {+}) / \\tau) + \\sum_ {j = 1} ^ {B - 1} \\exp (\\sin (o , o _ {j} ^ {-}) / \\tau)}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.668, + 0.892, + 0.7 + ], + "angle": 0, + "content": "where \\(\\operatorname{sim}(o, o^+) = f_2(o)^\\top f_2(o^+)\\), and \\(f_2(\\cdot)\\) is an MLP with the same structure as \\(f_1(\\cdot)\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.711, + 0.833, + 0.727 + ], + "angle": 0, + "content": "3.3. Transformer Decoder for Handwriting" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.895, + 0.901 + ], + "angle": 0, + "content": "The goal of the Transformer decoder is to progressively generate realistic online characters, denoted as \\(\\hat{Y}\\), based on the global content feature \\(q\\) and the obtained style representations (i.e., \\(E = \\{e^i\\}_{i=1}^K\\) and \\(G = \\{g^i\\}_{i=1}^K\\)). As each online character consists of numerous points (i.e., \\(\\hat{Y} = \\{\\hat{y}_j\\}_{j=1}^L\\), with \\(L\\) being the total number of points; see more details in Appendix A.10), the decoder faces the challenge of effectively integrating content and style features to accurately depict all points of the character. To address this challenge, we propose to fuse \\(q\\), \\(E\\) and \\(H\\) within the multi-head attention layers of our Transformer decoder. As shown" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5980" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.141, + 0.088, + 0.406, + 0.271 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.282, + 0.473, + 0.368 + ], + "angle": 0, + "content": "Figure 5. Illustration of the fusion of the style information in our Transformer decoder. At each time step, the query vector is first encoded from the content feature \\( q \\) and previous points \\( \\{y_j\\}_{j=1}^{t-1} \\). Then, it successively attends to the writer-wise and character-wise style features (i.e., \\( E \\) and \\( G \\)) for adaptively aggregating style information, which is finally decoded into the current-step output." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.384, + 0.47, + 0.429 + ], + "angle": 0, + "content": "in Figure 5, \\( E \\) and \\( H \\) serve as the key/value vectors, while \\( Q \\) serves as the query vector that successively attends to \\( E \\) and \\( G \\) to aggregate style information." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.43, + 0.47, + 0.716 + ], + "angle": 0, + "content": "During training, at any decoding step \\( t \\), we take \\( q \\) as the initial point. As shown in Figure 5, we apply self-attention to the point sequence, i.e. the content context \\( [q, y_1, \\dots, y_{t-1}] \\), to obtain the query vector \\( Q_t \\in \\mathbb{R}^c \\). Here, the ground-truth points \\( \\{y_j\\}_{j=1}^{t-1} \\) are used to accelerate model convergence in training [30, 37]. Subsequently, \\( Q_t \\) attends to \\( E \\) and \\( G \\) over the subsequent decoding layers to adaptively aggregate style information, ultimately generating the output \\( O_t \\in \\mathbb{R}^{6R+3} \\). The output with \\( 6R + 3 \\) logits is then used to generate the pen moving \\( (\\Delta \\hat{u}_t, \\Delta \\hat{v}_t) \\) and the pen state \\( (\\hat{m}_t^1, \\hat{m}_t^2, \\hat{m}_t^3) \\). Specifically, we use a Gaussian mixture model (GMM) [11] with \\( R \\) bivariate normal distributions to predict the pen moving, with each normal distribution containing 6 parameters. Moreover, we use the other 3 logits to generate the pen state. The training loss for supervising the decoder comprises two parts: the pen movement prediction loss \\( \\mathcal{L}_{pre}(\\Delta \\hat{u}_t, \\Delta \\hat{v}_t) \\), and the pen state classification loss \\( \\mathcal{L}_{cls}(\\hat{m}_t^1, \\hat{m}_t^2, \\hat{m}_t^3) \\). Please refer to Appendix A.11 for more details of these losses." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.717, + 0.47, + 0.809 + ], + "angle": 0, + "content": "The inference phase is different from the training phase, where the ground truth \\(y\\) is not available at test time. Instead, we take the generated points \\(\\{\\hat{y}_j\\}_{j=1}^{t-1}\\) as the input of the step \\(t\\), and combine them with \\(q, E\\), and \\(G\\) to predict the next point \\(\\hat{y}_t\\). Such a process repeats until a pen-end state \\((\\hat{m}_{t-1}^3 = 1)\\) is received." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.822, + 0.21, + 0.839 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.847, + 0.36, + 0.864 + ], + "angle": 0, + "content": "4.1. Chinese handwriting generation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Dataset. To evaluate SDT in generating Chinese handwritings, we use CASIA-OLHWDB (1.0-1.2) [22] for model" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.288 + ], + "angle": 0, + "content": "training and ICDAR-2013 competition database [38] for testing. The training set consists of about 3.7 million online Chinese handwritten characters produced by 1,020 writers, while the test set contains 60 writers, with each contributing 3,755 most frequently used characters set of GB2312-80. Following [12], we use the Ramer-Douglas-Peucker algorithm [7] with a parameter of \\(\\epsilon = 2\\) to remove redundant points of characters, leading to an average sequence length of 50. Following [44], we render offline style references using coordinate points of online characters, and each style sample is randomly sampled from the target-writer hand-writings during inference, as shown in Figure 4. For content images, we use the popular average Chinese font [17]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.29, + 0.893, + 0.442 + ], + "angle": 0, + "content": "Evaluation metrics. We use Dynamic Time Warping (DTW) [2,5], an elastic matching technique for aligning the given two sequences, to calculate the distance between the generated and real characters. Moreover, we use Content Score [44] to measure the structure correctness of generated characters, and adopt Style Score [30] to quantify the style similarity between the generated and real handwritings. We also conduct user preference studies to quantify the subjective quality of the output characters. More details are provided in Appendix A.1.1." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.445, + 0.893, + 0.779 + ], + "angle": 0, + "content": "Implementation details. We set the number of the style reference to \\( K = 15 \\), and resize the reference style and content images to \\( 64 \\times 64 \\). Moreover, each Transformer encoder contains 2 self-attention layers, while the Transformer decoder has 4 layers for obtaining style representations (2 for writer-wise and 2 for character-wise). Following the original Transformer [35], each Transformer layer contains the multi-head attention with \\( c = 512 \\) dimensional states and 8 attention heads. Contrary to HWT [3], where \\( F \\) is concatenated before the Transformer encoder, we process each feature sequence \\( f \\in F \\) individually. Moreover, we apply sinusoidal positional encoding [35] to input tokens before feeding them to the Transformer encoder and decoder. For training, we first pre-train the content encoder with 138k iterations (batch size of 256) for character classification on training samples and then train the whole model with 148k iterations (batch size of 128), on a single RTX3090 GPU. The optimizer is Adam [19], with a learning rate of 0.0002 and gradient clipping of 5.0. The sampling ratio \\( \\alpha \\) is determined through a search over 0.25, 0.5, 0.75, 1.00, and 0.25 is chosen. Following [30], we set \\( \\lambda = 2 \\). Further implementation details are provided in Appendix A.1.2." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Compared methods. We compare our proposed SDT with state-of-the-art online Chinese character generation methods, i.e. Drawing [40], FontRNN [31], DeepImitator [44], and WriteLikeYou [30]. To ensure a fair comparison, we re-implement Drawing and FontRNN by adding the style branch of DeepImitator [44], enabling them to achieve arbitrary stylized character generation. To adapt Write-LikeYou [30] to handle images, we update its encoder to" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "5981" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.153, + 0.09, + 0.822, + 0.337 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.34, + 0.895, + 0.385 + ], + "angle": 0, + "content": "Figure 6. Comparisons with the state-of-the-art methods for online Chinese handwriting generation. The red and blue boxes highlight failures of style imitation and structure preservation, respectively. WriteLi. indicates the WriteLikeYou-v2. The green boxes highlight comparisons between the fine details of targets and generated characters." + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.398, + 0.473, + 0.428 + ], + "angle": 0, + "content": "Table 1. Comparisons with state-of-the-art methods on Chinese dataset. See more results of WriteLikeYou [30] in Appendix A.6." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.433, + 0.472, + 0.546 + ], + "angle": 0, + "content": "
MethodStyle Score ↑Content Score ↑DTW ↓User Prefer. (%) ↑
Drawing [40]35.8378.151.18133.53
FontRNN [31]46.1492.181.04487.07
DeepImitator [44]50.6790.921.06227.99
WriteLikeYou-v1 [30]71.0993.890.983211.67
WriteLikeYou-v2 [30]72.3796.440.928913.07
SDT(Ours)94.5097.040.878956.67
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.574, + 0.47, + 0.634 + ], + "angle": 0, + "content": "create two new variants: WriteLikeYou-v1 (i.e., CNN encoder [44]) and WriteLikeYou-v2 (i.e., the same CNN-Transformer encoder as our SDT), based on the released official code1. More details are available in Appendix A.1.3." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.634, + 0.47, + 0.725 + ], + "angle": 0, + "content": "Quantitative comparison. Quantitative results are in Table 1, revealing that SDT outperforms other methods across all evaluation metrics. Notably, SDT surpasses the second-best method by a significant \\(22.13\\%\\) margin in Style Score, demonstrating the proposed method's exceptional style imitation performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.726, + 0.471, + 0.877 + ], + "angle": 0, + "content": "Qualitative comparison. We visualize the generated samples of each method in Figure 6, which intuitively explains the significant superiority of SDT in the user preference study. In Figure 6, Drawing [40] generates the least satisfactory results, often producing unreadable characters. FontRNN [31] and DeepImitator [44] occasionally synthesize unpleasant stroke paddings, and WriteLikeYou [30] struggles with generating complex characters regarding style mimicry. In contrast, our method yields higher-quality results, particularly in recovering fine character details." + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.398, + 0.893, + 0.441 + ], + "angle": 0, + "content": "Table 2. Ablation study. Here, we further use FID to measure the distance between generated and real samples for each writer separately, and finally average them." + }, + { + "type": "table", + "bbox": [ + 0.507, + 0.451, + 0.891, + 0.589 + ], + "angle": 0, + "content": "
writer-wisecharacter-wiseGenerated SamplesStyle Score↑FID↓DTW↓
倾朝朝85.5227.750.8941
✓倾朝朝91.3826.380.8841
✓倾朝朝90.3126.890.8803
✓✓倾朝朝94.5025.460.8789
Ground Truth倾朝朝
" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.605, + 0.604, + 0.621 + ], + "angle": 0, + "content": "4.2. Analysis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.628, + 0.893, + 0.703 + ], + "angle": 0, + "content": "In this section, we assess the impact of the two learned style features and that of the style inputs. We also analyze the effect of the sampling ratio \\(\\alpha\\), and discuss the combination strategies in the Transformer decoder in Appendix A.5. Besides, we discuss failure cases in Appendix A.7." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.895, + 0.87 + ], + "angle": 0, + "content": "Quantitative evaluation of two style representations. We ablate the effects of the two extracted style representations in Table 2. The findings include: (1) Both style representations enhance the quality of generated outcomes in all evaluation metrics, particularly in terms of Style Score, improving by \\(4.79\\%\\) and \\(5.86\\%\\), respectively. (2) Combining the two style features further boosts model performance across all evaluation metrics, suggesting that the extracted styles are complementary. Moreover, the order in which the two style features are input into the Transformer decoder has no significant impact on Style Score \\((93.72\\%)\\) vs. \\(94.50\\%\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Qualitative comparison between two style representations. To further analyze the differences between the" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.435, + 0.902 + ], + "angle": 0, + "content": "" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.517, + 0.958 + ], + "angle": 0, + "content": "5982" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.118, + 0.09, + 0.847, + 0.239 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.244, + 0.895, + 0.314 + ], + "angle": 0, + "content": "Figure 7. Spectrum analysis of two style representations. We provide frequency magnitude visualizations belonging to 7 writers, where the top row shows the writer-wise style while the bottom represents the character-wise one. Each spectrum map is averaged over 100 character samples written by the same person. The brighter the color, the larger the magnitude. A pixel farther from the center means a higher frequency [26]. We find that the writer-wise style representations capture more low-frequency information, while character-wise style representations capture more high-frequency information." + }, + { + "type": "image", + "bbox": [ + 0.115, + 0.332, + 0.43, + 0.535 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.538, + 0.471, + 0.581 + ], + "angle": 0, + "content": "Figure 8. The heat map of the DTW matrix. The dark diagonal indicates that the generated characters still own a higher similarity even using different \\( X_{s} \\) belonging to the same writer." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.47, + 0.779 + ], + "angle": 0, + "content": "two styles, we resize the output patch tokens representing the two styles to feature maps, respectively, and visualize their frequency magnitudes in Figure 7. We find that character-wise style features capture more high-frequency information, whereas writer-wise features mainly focus on low-frequency information. According to [6], the high-frequency information in an image usually captures fine details while the low frequencies contain the overall part of objects. This finding supports our motivation that the writer head helps to imitate the overall style (e.g., glyph slant), while the glyph head captures the detailed style (e.g., stroke curvature), as shown in Table 2." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Effect of using different style inputs. As mentioned in [30], given different style inputs \\( X_{s} \\) belonging to the same writer \\( w_{s} \\), the imitation model may generate inconsistent characters. To evaluate the effect of different style inputs, we conduct two independent experiments using different \\( X_{s} \\) based on the same model. Following [30], we use the model to generate 200 characters for each writer in the test set. We then calculate the DTW distance between corre" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.329, + 0.892, + 0.357 + ], + "angle": 0, + "content": "Table 3. Quantitative evaluations of our SDT and competitors on Japanese, Indic, and English datasets." + }, + { + "type": "table", + "bbox": [ + 0.513, + 0.372, + 0.885, + 0.566 + ], + "angle": 0, + "content": "
DatasetsMethodsContent Score↑DTW ↓
JapaneseDrawing [40]50.741.4657
DeepImitator [44]53.201.2564
WriteLikeYou-v2 [30]85.611.2066
SDT(Ours)91.311.1289
IndicDrawing [40]2.349.8230
DeepImitator [44]4.136.7421
WriteLikeYou-v2 [30]13.194.5130
SDT(Ours)97.220.7075
EnglishDrawing [40]79.141.8519
DeepImitator [44]76.531.6460
WriteLikeYou-v2 [30]84.411.6215
SDT(Ours)85.521.6048
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.595, + 0.892, + 0.716 + ], + "angle": 0, + "content": "sponding characters individually and average them according to the writer index (see Appendix A.1.4 for more details) to get a DTW square matrix. The resulting DTW square matrix is visualized in Figure 8. The dark diagonal in Figure 8 suggests that the generated characters maintain a high degree of similarity even when using different \\( X_{s} \\) belonging to the same writer, demonstrating that our SDT can generate consistent results from various style inputs." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.726, + 0.791, + 0.743 + ], + "angle": 0, + "content": "4.3. Applications to Other Languages" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Japanese handwriting generation. For the Japanese handwriting generation task, we conduct experiments on TUAT HANDS [25] database (see more details in Appendix A.1.5) to evaluate the effectiveness of our method. Figure 9 (a) and Table 3 verify the effectiveness of SDT for Japanese handwriting generation. Specifically, from Table 3, we observe that our SDT outperforms all compared methods in terms of two quantitative metrics, indicating that SDT performs well in multiple languages. Furthermore, we provide additional evaluation metrics in Appendix A.8." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5983" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.123, + 0.09, + 0.852, + 0.334 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.084, + 0.34, + 0.885, + 0.357 + ], + "angle": 0, + "content": "Figure 9. Comparisons with the competitors for online handwriting generation on various scripts. WriteLi. indicates WriteLikeYou-v2." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.382, + 0.473, + 0.701 + ], + "angle": 0, + "content": "Indic handwriting generation. We evaluate our method on the Indic handwriting generation task based on the \\(\\mathrm{Tamil}^2\\) dataset. It is worth noting that Indic handwriting generation presents a more significant challenge, as Indic characters contain more trajectory points than Chinese, Japanese, and English scripts (i.e., 88 vs. 68, 50, 30 on average; see Appendix A.1.5 for more dataset information). We compare our method with other approaches on the official test set in terms of Content Score and Dynamic Time Warping (DTW). As shown in Table 3, we find that our SDT significantly outperforms the second-best method in terms of the two quantitative metrics, achieving an \\(84.03\\%\\) higher Content Score and a 3.8055 lower DTW. This indicates that our SDT can handle handwritten characters with a large number of points (averaging 88) and ensure the quality of synthetic samples, as illustrated in Figure 9 (b). The potential advantages of our SDT are: (1) The improved style representations extracted by our SDT prevent the collapse of generated characters. (2) Our Transformer decoder facilitates long-distance dependence between trajectory points. We provide more experimental analysis in Appendix A.9." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.714, + 0.472, + 0.868 + ], + "angle": 0, + "content": "English handwriting generation. To evaluate our method in generating English handwritings, we collect all of the English samples from the symbol part of CASIA-OLHWDB(1.0-1.2) [22] and ICDAR-2013 competition database [38] (see more details in Appendix A.1.5). Similarly, we use Content Score and DTW as evaluation metrics. As shown in Figure 9 (c), we find that all methods achieve sound and comparable performance. One reason for this is that the English script contains fewer character classes and a smaller number of trajectory points (averaging 30), making" + }, + { + "type": "page_footnote", + "bbox": [ + 0.078, + 0.875, + 0.471, + 0.901 + ], + "angle": 0, + "content": "\\(^{2}\\)http : // lipitk . sourceforge . net / datasets / familialchdata.htm" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.382, + 0.895, + 0.489 + ], + "angle": 0, + "content": "their imitation easier compared to other scripts. Nevertheless, our SDT still outperforms other methods by a small margin in terms of both Content Score and DTW, as shown in Table 3. Moreover, we observe that corresponding uppercase and lowercase letters sometimes exhibit subtle inter-class differences (e.g., O vs. o), which leads our SDT to achieve a relatively low Content Score." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.501, + 0.62, + 0.517 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.526, + 0.895, + 0.786 + ], + "angle": 0, + "content": "In this paper, we have proposed a novel method, named style-disentangled Transformer (SDT), to synthesize realistic and diverse online handwritings. SDT enhances imitation performance by disentangling the writer-wise and character-wise style representations from individual handwriting samples. For the writer-wise style, we group characters from the same writer and separate those from different writers, promoting SDT's ability to learn uniformity in individual handwritings. For the character-wise style, we maximize the mutual information between the distinct views of a character. Moreover, we extend SDT and introduce an offline-to-offline framework for improving the generation quality of offline Chinese handwritings. Promising results on various language scripts verify the effectiveness of our SDT. Although primarily designed for handwriting generation, SDT still holds the potential for extension to other generative tasks, such as font generation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.801, + 0.895, + 0.894 + ], + "angle": 0, + "content": "Acknowledgments This research is partially supported by NSFC (Grant No.62176093, 61673182), Key Realm R&D Program of Guangzhou (No.202206030001), Guangdong Basic and Applied Basic Research Foundation (No.2021A1515012282) and Guangdong Provincial Key Laboratory of Human Digital Twin (2022B1212010004)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.958 + ], + "angle": 0, + "content": "5984" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Emre Aksan, Fabrizio Pece, and Otmar Hilliges. 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Recently, RNN-based methods have been proposed to generate stylized online Chinese characters. However, these methods mainly focus on capturing a person's overall writing style, neglecting subtle style inconsistencies between characters written by the same person. For example, while a person's handwriting typically exhibits general uniformity (e.g., glyph slant and aspect ratios), there are still small style variations in finer details (e.g., stroke length and curvature) of characters. In light of this, we propose to disentangle the style representations at both writer and character levels from individual handwritings to synthesize realistic stylized online handwritten characters. Specifically, we present the style-disentangled Transformer (SDT), which employs two complementary contrastive objectives to extract the style commonalities of reference samples and capture the detailed style patterns of each sample, respectively. Extensive experiments on various language scripts demonstrate the effectiveness of SDT. Notably, our empirical findings reveal that the two learned style representations provide information at different frequency magnitudes, underscoring the importance of separate style extraction. Our source code is public at: https://github.com/dailenson/SDT. + +# 1. Introduction + +As the oldest writing system, Chinese characters are widely used across Asian countries. When compared with Latin scripts, Chinese characters encompass an exceptionally vast lexicon (87,887 characters in GB18030-2022字符) and have intricate structures composed of multiple strokes. Recently, the intriguing task of generating Chinese characters has garnered significant attention [10, 23, 32]. A promising approach to synthesising realistic handwritings is + +![](images/b410e9e460dc5e8b28f818a563869721c0f36b5f797ec109e37bbb191ca71af6.jpg) +Figure 1. Illustration of two online handwritten Chinese characters, with each color representing a stroke. The increasing numbers indicate the writing order from the start to the end. + +to progressively generate online characters (i.e., the handwriting trajectory in a sequential format) [40]. As shown in Figure 1, online characters convey richer information (e.g., the order of writing) and thus pave the way for various applications, including writing robots [39]. + +Our goal is to automatically generate online Chinese handwritings that not only correspond to specific textual content, but also emulate the calligraphic style of a given exemplar writer (e.g., glyph slant, shape, stroke length, and curvature). This task thus holds potential for a wide range of applications, such as font design and calligraphy education. A popular solution [18] is to extract style information from the provided stylized samples and merge it with the content reference. DeepImitator [44] concatenates the style vector obtained from a CNN encoder with a character embedding, which is then fed into the RNN decoder to generate stylized online characters. WriteLikeYou [30] adopts the largemargin softmax loss [36] to promote discriminative learning of style features. However, these methods mainly focus on the overall writing style, thus overlooking the detailed style inconsistencies (e.g., the highlighted regions in Figure 2) between characters produced by the same writer. + +The observations mentioned above inspire us to disentangle style representations at the writer and character levels from the stylized handwritings. However, accurately cap + +![](images/e5a987f2d1b7791c1120526224645047f85461aabb433a8b1808a6e1d353369b.jpg) +Left Slant + +![](images/22ef2d35f403b00cb44419f5ae3b169d672020c028323223a8c5b5b0d1e3a278.jpg) +No Slant + +![](images/70078260ca8255ee1d9594637c31db63e71dc85cbe90f414cfb7e20a96423c6b.jpg) +Right Slant +Figure 2. Handwritten character samples from three unique writers, with each row containing characters by the same person. Despite sharing similar overall handwriting styles (e.g., glyph slant), subtle style differences (e.g., stroke length, location, and curvature) can still be observed among them. + +turing these two styles is a challenging task. To address this, we propose a style-disentangled Transformer (SDT) equipped with a dual-head style encoder. Specifically, we employ the contrastive learning framework [13] to guide each head in concentrating on writer-wise and character-wise styles, respectively. For the overall writer-wise style, we treat characters from the same writer as positive instances, and characters from different writers as negatives. This enables the encoder to learn the style commonalities among characters written by the same writer. Regarding the detailed character-wise style, we independently sample positive pairs within a character, and sample negative samples from other characters, as illustrated in Figure 3. Aggregating positive views of a character encourages the encoder to focus on the intricate character style patterns. + +In addition, we introduce a content encoder for SDT to learn a textual feature with a global context. The two style representations, along with the textual feature, are then fed into a decoder that progressively generates online characters. Given that the output characters are in sequential form, we employ Transformer [35], a powerful sequence modeling architecture, as our backbone. + +To extend SDT for generating offline Chinese handwritings (i.e., character images with stroke-width, e.g., Figures 3-7 in Appendix), we further propose an offline-to-offline generation framework. We first use SDT to generate online characters with significant shape changes, and then decorate them with stroke width, ink-blot effects, etc. This enables us to generate authentic offline handwritings. For more details, please refer to Appendix A.4. + +We summarize our contributions in three key aspects: + +- We are the first to disentangle two style representations (i.e., writer-wise and character-wise) for enhancing Chinese handwriting generation. Our findings show that the former focuses more on low-frequency information, while the latter captures higher frequencies. + +![](images/e600574515ad03777cfc07f480446a60b464ef0060c00014b85fc318a6148345.jpg) +Figure 3. In this two-character example, we independently sample the positive pair, i.e., $o$ and $o^{+}$ , within the first character, while the negative $o^{-}$ is sampled from another character. Our sampling strategy randomly selects a small subset of patches, following a uniform distribution. + +- We introduce a novel online character generation method, i.e., SDT. Extensive experiments on handwriting datasets in Chinese, English, Japanese, and Indic scripts demonstrate its effectiveness and superiority. +- Building on the SDT, we further develop an offline-to-offline framework that can produce more plausible offline handwritten Chinese characters, as evidenced in Appendix A.4. + +# 2. Related Work + +Handwriting generation. Various style-content disentangling methods [1, 8, 18, 21, 24] have been proposed to generate handwritings with arbitrary styles. These methods assume that reference samples can be decomposed into style and content spaces. They disentangle calligraphic styles from reference samples and recombine them with specific textual content for controllable style synthesis. For instance, DeepWriting [1] adopts RNNs to extract the style vectors from online handwritings, and then combines them with character embeddings for synthesizing stylized online handwritings. However, it typically over-smooths the styles of distinct letters and loses key details, since its extracted style vectors are letter-independent [21]. + +DSD [21] addresses the over-smooth problem by segmenting online handwritten words into isolated letters and encoding them into global and letter-specific style vectors, improving synthetic handwriting quality. Compared with it, our method can explicitly capture more fine-grained details (e.g., stroke length, location and curvature), which are more difficult to obtain. Besides, these methods [1, 21, 34] rely on extra fine annotations to segment input cursive scripts, while our SDT need not. Recently, HWT [3] uses a vanilla Transformer encoder for style pattern extraction. However, these methods [1, 3, 8, 18, 21] rely on complex content references, such as recurrent embeddings and letter-wise fil + +ter maps. SLOGAN [24] addresses this issue by extracting textual contents from easily obtainable printed images, but it struggles with generalizing to unseen handwriting styles due to the fixed writer ID. In contrast, our SDT effectively obtains content and style information, and thus can synthesize characters with arbitrary styles well. + +Regarding handwritten Chinese characters, several attempts [4, 16, 20] use GANs to generate Chinese handwriting images, but always result in characteristic artifacts. Drawing [40] and FontRNN [31] adopt RNNs, but they cannot flexibly control the handwriting styles. In addition, DeepImitator [44] and WriteLikeYou [30] propose style-controlled generation using style representations from offline images [44] or online trajectories [30]. Unlike these methods [30,44] that only extract an overall writer style, our SDT captures both writer and character-level styles, significantly improving the performance of handwriting imitation. + +Contrastive learning. Contrastive learning [13, 41] has been widely used in various fields [9, 28, 29, 33, 42, 43]. Some image translation studies [14, 27] use contrastive learning to enhance natural image generation quality, encouraging content preservation during transfer. Unlike these methods [14, 27], our SDT aligns independently sampled patches from the same input, aiming to improve style representations of handwritings. + +# 3. Method + +Problem statement. We aim to synthesize stylized online handwritings with conditional content and style. Given a content image $I$ and a set of style images $X_{s} = \{x_{s}^{i}\}_{i = 1}^{K}$ , randomly sampled from a writer $w_{s}$ , we aim to generate an online handwritten Chinese character $\hat{Y}_s$ that reflects the calligraphic style of $w_{s}$ and retains the textual content of $I$ . The key challenge lies in obtaining discriminative style representations from a limited number of stylized samples. + +To address this task, inspired by our observations (cf. Figure 2) of the overall uniformity (i.e., writer-wise style) and inconsistent details (i.e., character-wise style), we propose to disentangle the style of exemplar writers into overall and detailed styles for enhancing handwriting imitation performance. To achieve this, we introduce a new style-disentangled Transformer (SDT) approach to decouple the two styles from individual handwritings. The overall scheme of SDT is presented below. + +# 3.1. Overall Scheme + +As shown in Figure 4, SDT consists of a dual-head style encoder, a content encoder, and a Transformer decoder. The style encoder (cf. Section 3.2) is designed to learn the writer-wise and character-wise styles. It firstly extracts rich calligraphic style patterns from reference style examples $X_{s}$ via a sequential combination of a CNN and a Transformer + +encoder, followed by the writer and glyph heads to disentangle the writer-wise and character-wise styles from the extracted style patterns. To this end, we propose two contrastive objectives, WriterNCE $\mathcal{L}_{wri}$ and GlyphNCE $\mathcal{L}_{gly}$ , to encourage the encoder to learn the two styles, respectively. Specifically, $\mathcal{L}_{wri}$ maximizes the mutual information between character instances belonging to the same writer, while $\mathcal{L}_{gly}$ associates the positive pair independently sampled from the same character. Guided by $\mathcal{L}_{wri}$ and $\mathcal{L}_{gly}$ , the writer and glyph heads can acquire discriminative writerwise and character-wise style features, respectively. + +The content encoder uses a standard Resnet18 [15] as the CNN backbone to learn the compact feature map $q_{\text{map}} \in \mathbb{R}^{h \times w \times c}$ from a content reference $I$ , and feeds the flattened feature patches into a Transformer encoder to extract the textual content representation $q \in \mathbb{R}^{d \times c}$ , where $d = h \times w$ and $c$ is the channel dimension. Benefiting from the strong capability of Transformer to capture long-range dependencies between feature patches, the content encoder expects an informative content feature $q$ with a global context. + +After the two encoders, a multi-layer Transformer decoder (cf. Section 3.3) is used to synthesize $\hat{Y}_s$ in an autoregressive fashion, conditioned on the two style representations and the content feature. This decoder is supervised by the pen moving prediction loss $\mathcal{L}_{pre}$ and pen state classification loss $\mathcal{L}_{cls}$ . + +To summarize, the overall training objective of SDT combines all four loss functions: + +$$ +\mathcal {L} = \mathcal {L} _ {w r i} + \mathcal {L} _ {g l y} + \mathcal {L} _ {p r e} + \lambda \mathcal {L} _ {c l s}, \tag {1} +$$ + +where $\lambda$ serves as a trade-off factor. Each component of our SDT is detailed in the following Section 3.2 and Section 3.3. + +# 3.2. Dual-head Style Encoder + +As illustrated in Figure 2, there are two distinct styles in a person's handwriting: writer-wise and character-wise styles. We propose a dual-head style encoder to obtain the two style representations. As shown in Figure 4, the input $X = \{x^{i}\}_{i=1}^{K}$ is firstly encoded by ResNet18 to obtain a sequence of feature maps $F_{m} = \{f_{m}^{i}\}_{i=1}^{K} \in \mathbb{R}^{K \times h \times w \times c}$ . Next, we flatten the spatial dimension of each feature map to obtain feature sequences $F = \{f^{i}\}_{i=1}^{K} \in \mathbb{R}^{K \times d \times c}$ . These feature sequences are then fed into a Transformer encoder to extract more informative feature sequences $Z = \{z^{i}\}_{i=1}^{K} \in \mathbb{R}^{K \times d \times c}$ . Finally, we use the two heads, built on self-attention [35], to further disentangle $Z$ into the writer-wise style representations $E = \{e^{i}\}_{i=1}^{K} \in \mathbb{R}^{K \times d \times c}$ via $\mathcal{L}_{wri}$ and the character-wise counterparts $G = \{g^{i}\}_{i=1}^{K} \in \mathbb{R}^{K \times d \times c}$ via $\mathcal{L}_{gly}$ , respectively. We next detail the two contrastive learning objectives as follows. + +![](images/6f49830c6fef29eed3ff51233ef994e4ad983229aff59af86864af7a0df03cf2.jpg) +Figure 4. Overview of the proposed method. Our SDT consists of a dual-head style encoder, a content encoder and a Transformer decoder. The writer-wise and character-wise style representations extracted by style encoder and the learned content feature are fed into the Transformer decoder to progressively generate online handwritings. We utilize the WriterNCE $\mathcal{L}_{wri}$ and GlyphNCE $\mathcal{L}_{gly}$ to guide the two heads for learning the corresponding styles. $\mathcal{L}_{pre}$ and $\mathcal{L}_{cls}$ denote the pen moving prediction and state classification loss, respectively. + +# 3.2.1 Writer-wise Contrastive Learning + +To explicitly encourage the writer head to learn the witer-wise style, we propose to learn a feature space where the style features from the same writer are closer than those from different writers. The intuition is that one person's handwritings consistently exhibit similar style information, which can serve as a crucial clue for distinguishing writers. To this end, we take characters written by the same person as positive pairs and those from different writers as negative samples, and develop a new WriterNCE loss for writer-wise style learning. + +Specifically, let $j \in M = \{1, \dots, N\}$ be the index of an element within a mini-batch and let $A(j) = M \setminus \{j\}$ be other indices distinct from $j$ , where $N$ is the batch size. Given a writer-wise style feature $e_j$ belonging to writer $w_j$ as the anchor, we denote its in-batch positive sample set as $P(j) = \{p \in A(j) : w_p = w_j\}$ and its negative set as $A(j) \setminus P(j)$ . The WriterNCE loss is formulated as follows: + +$$ +\mathcal {L} _ {w r i} = \frac {- 1}{N} \sum_ {j \in M} \frac {1}{| P (j) |} \sum_ {p \in P (j)} \log \frac {\exp \left(\sin \left(e _ {j} , e _ {p}\right) / \tau\right)}{\sum_ {a \in A (j)} \exp \left(\sin \left(e _ {j} , e _ {a}\right) / \tau\right)}, \tag {2} +$$ + +where $\operatorname{sim}(e_j, e_p) = f_1(e_j)^\top f_1(e_p)$ , $\tau$ is a temperature parameter and $f_1(\cdot)$ is a multi-layer perceptron (MLP) that projects features to a $\ell_2$ -normalized feature space where $\mathcal{L}_{wri}$ is applied. + +# 3.2.2 Character-wise Contrastive Learning + +Compared with the overall writer-wise style, character-wise style differences often exist in the fine details of distinct characters, e.g., stroke length and curvature (cf. Figure 3). Inspired by this, we aim to maximize the mutual informa + +tion between diverse views of a character, thereby enforcing the glyph head to learn the character-wise style. As strokes are distributed across arbitrary spatial locations in character images, we propose to capture stroke details via contrastive learning, by randomly selecting a small subset of patches following a uniform distribution. Specifically, we conduct sampling over the sequential patch tokens obtained from the glyph head. + +Given character-wise style features $\{g_j\}_{j=1}^B \in \mathbb{R}^{B \times d \times c}$ extracted from $B$ characters, we sample a positive patch pair (i.e., $o \in \mathbb{R}^{n \times c}$ and $o^+ \in \mathbb{R}^{n \times c}$ ) from the same randomly selected $g$ , and $B-1$ negative patches $\{o_j^-\}_{j=1}^{B-1}$ from the remaining $B-1$ style features. Here, the number of sampled patch tokens is $n = d \cdot \alpha$ , where $\alpha$ is the sampling ratio. The GlyphNCE loss is formulated as: + +$$ +\mathcal {L} _ {g l y} = - \log \frac {\exp (\sin (o , o ^ {+}) / \tau)}{\exp (\sin (o , o ^ {+}) / \tau) + \sum_ {j = 1} ^ {B - 1} \exp (\sin (o , o _ {j} ^ {-}) / \tau)}, \tag {3} +$$ + +where $\operatorname{sim}(o, o^+) = f_2(o)^\top f_2(o^+)$ , and $f_2(\cdot)$ is an MLP with the same structure as $f_1(\cdot)$ . + +# 3.3. Transformer Decoder for Handwriting + +The goal of the Transformer decoder is to progressively generate realistic online characters, denoted as $\hat{Y}$ , based on the global content feature $q$ and the obtained style representations (i.e., $E = \{e^i\}_{i=1}^K$ and $G = \{g^i\}_{i=1}^K$ ). As each online character consists of numerous points (i.e., $\hat{Y} = \{\hat{y}_j\}_{j=1}^L$ , with $L$ being the total number of points; see more details in Appendix A.10), the decoder faces the challenge of effectively integrating content and style features to accurately depict all points of the character. To address this challenge, we propose to fuse $q$ , $E$ and $H$ within the multi-head attention layers of our Transformer decoder. As shown + +![](images/298e9fcdfd835c546dbcaf600c60363e2126917371505ff5e7a4c23d829b9d61.jpg) +Figure 5. Illustration of the fusion of the style information in our Transformer decoder. At each time step, the query vector is first encoded from the content feature $q$ and previous points $\{y_j\}_{j=1}^{t-1}$ . Then, it successively attends to the writer-wise and character-wise style features (i.e., $E$ and $G$ ) for adaptively aggregating style information, which is finally decoded into the current-step output. + +in Figure 5, $E$ and $H$ serve as the key/value vectors, while $Q$ serves as the query vector that successively attends to $E$ and $G$ to aggregate style information. + +During training, at any decoding step $t$ , we take $q$ as the initial point. As shown in Figure 5, we apply self-attention to the point sequence, i.e. the content context $[q, y_1, \dots, y_{t-1}]$ , to obtain the query vector $Q_t \in \mathbb{R}^c$ . Here, the ground-truth points $\{y_j\}_{j=1}^{t-1}$ are used to accelerate model convergence in training [30, 37]. Subsequently, $Q_t$ attends to $E$ and $G$ over the subsequent decoding layers to adaptively aggregate style information, ultimately generating the output $O_t \in \mathbb{R}^{6R+3}$ . The output with $6R + 3$ logits is then used to generate the pen moving $(\Delta \hat{u}_t, \Delta \hat{v}_t)$ and the pen state $(\hat{m}_t^1, \hat{m}_t^2, \hat{m}_t^3)$ . Specifically, we use a Gaussian mixture model (GMM) [11] with $R$ bivariate normal distributions to predict the pen moving, with each normal distribution containing 6 parameters. Moreover, we use the other 3 logits to generate the pen state. The training loss for supervising the decoder comprises two parts: the pen movement prediction loss $\mathcal{L}_{pre}(\Delta \hat{u}_t, \Delta \hat{v}_t)$ , and the pen state classification loss $\mathcal{L}_{cls}(\hat{m}_t^1, \hat{m}_t^2, \hat{m}_t^3)$ . Please refer to Appendix A.11 for more details of these losses. + +The inference phase is different from the training phase, where the ground truth $y$ is not available at test time. Instead, we take the generated points $\{\hat{y}_j\}_{j=1}^{t-1}$ as the input of the step $t$ , and combine them with $q, E$ , and $G$ to predict the next point $\hat{y}_t$ . Such a process repeats until a pen-end state $(\hat{m}_{t-1}^3 = 1)$ is received. + +# 4. Experiments + +# 4.1. Chinese handwriting generation + +Dataset. To evaluate SDT in generating Chinese handwritings, we use CASIA-OLHWDB (1.0-1.2) [22] for model + +training and ICDAR-2013 competition database [38] for testing. The training set consists of about 3.7 million online Chinese handwritten characters produced by 1,020 writers, while the test set contains 60 writers, with each contributing 3,755 most frequently used characters set of GB2312-80. Following [12], we use the Ramer-Douglas-Peucker algorithm [7] with a parameter of $\epsilon = 2$ to remove redundant points of characters, leading to an average sequence length of 50. Following [44], we render offline style references using coordinate points of online characters, and each style sample is randomly sampled from the target-writer hand-writings during inference, as shown in Figure 4. For content images, we use the popular average Chinese font [17]. + +Evaluation metrics. We use Dynamic Time Warping (DTW) [2,5], an elastic matching technique for aligning the given two sequences, to calculate the distance between the generated and real characters. Moreover, we use Content Score [44] to measure the structure correctness of generated characters, and adopt Style Score [30] to quantify the style similarity between the generated and real handwritings. We also conduct user preference studies to quantify the subjective quality of the output characters. More details are provided in Appendix A.1.1. + +Implementation details. We set the number of the style reference to $K = 15$ , and resize the reference style and content images to $64 \times 64$ . Moreover, each Transformer encoder contains 2 self-attention layers, while the Transformer decoder has 4 layers for obtaining style representations (2 for writer-wise and 2 for character-wise). Following the original Transformer [35], each Transformer layer contains the multi-head attention with $c = 512$ dimensional states and 8 attention heads. Contrary to HWT [3], where $F$ is concatenated before the Transformer encoder, we process each feature sequence $f \in F$ individually. Moreover, we apply sinusoidal positional encoding [35] to input tokens before feeding them to the Transformer encoder and decoder. For training, we first pre-train the content encoder with 138k iterations (batch size of 256) for character classification on training samples and then train the whole model with 148k iterations (batch size of 128), on a single RTX3090 GPU. The optimizer is Adam [19], with a learning rate of 0.0002 and gradient clipping of 5.0. The sampling ratio $\alpha$ is determined through a search over 0.25, 0.5, 0.75, 1.00, and 0.25 is chosen. Following [30], we set $\lambda = 2$ . Further implementation details are provided in Appendix A.1.2. + +Compared methods. We compare our proposed SDT with state-of-the-art online Chinese character generation methods, i.e. Drawing [40], FontRNN [31], DeepImitator [44], and WriteLikeYou [30]. To ensure a fair comparison, we re-implement Drawing and FontRNN by adding the style branch of DeepImitator [44], enabling them to achieve arbitrary stylized character generation. To adapt Write-LikeYou [30] to handle images, we update its encoder to + +![](images/2f29eed1b588d43801107048fc85393801f9541ccecf22d7f3a6a6c0f90c98f7.jpg) +Figure 6. Comparisons with the state-of-the-art methods for online Chinese handwriting generation. The red and blue boxes highlight failures of style imitation and structure preservation, respectively. WriteLi. indicates the WriteLikeYou-v2. The green boxes highlight comparisons between the fine details of targets and generated characters. + +Table 1. Comparisons with state-of-the-art methods on Chinese dataset. See more results of WriteLikeYou [30] in Appendix A.6. + +
MethodStyle Score ↑Content Score ↑DTW ↓User Prefer. (%) ↑
Drawing [40]35.8378.151.18133.53
FontRNN [31]46.1492.181.04487.07
DeepImitator [44]50.6790.921.06227.99
WriteLikeYou-v1 [30]71.0993.890.983211.67
WriteLikeYou-v2 [30]72.3796.440.928913.07
SDT(Ours)94.5097.040.878956.67
+ +create two new variants: WriteLikeYou-v1 (i.e., CNN encoder [44]) and WriteLikeYou-v2 (i.e., the same CNN-Transformer encoder as our SDT), based on the released official code1. More details are available in Appendix A.1.3. + +Quantitative comparison. Quantitative results are in Table 1, revealing that SDT outperforms other methods across all evaluation metrics. Notably, SDT surpasses the second-best method by a significant $22.13\%$ margin in Style Score, demonstrating the proposed method's exceptional style imitation performance. + +Qualitative comparison. We visualize the generated samples of each method in Figure 6, which intuitively explains the significant superiority of SDT in the user preference study. In Figure 6, Drawing [40] generates the least satisfactory results, often producing unreadable characters. FontRNN [31] and DeepImitator [44] occasionally synthesize unpleasant stroke paddings, and WriteLikeYou [30] struggles with generating complex characters regarding style mimicry. In contrast, our method yields higher-quality results, particularly in recovering fine character details. + +Table 2. Ablation study. Here, we further use FID to measure the distance between generated and real samples for each writer separately, and finally average them. + +
writer-wisecharacter-wiseGenerated SamplesStyle Score↑FID↓DTW↓
倾朝朝85.5227.750.8941
✓倾朝朝91.3826.380.8841
✓倾朝朝90.3126.890.8803
✓✓倾朝朝94.5025.460.8789
Ground Truth倾朝朝
+ +# 4.2. Analysis + +In this section, we assess the impact of the two learned style features and that of the style inputs. We also analyze the effect of the sampling ratio $\alpha$ , and discuss the combination strategies in the Transformer decoder in Appendix A.5. Besides, we discuss failure cases in Appendix A.7. + +Quantitative evaluation of two style representations. We ablate the effects of the two extracted style representations in Table 2. The findings include: (1) Both style representations enhance the quality of generated outcomes in all evaluation metrics, particularly in terms of Style Score, improving by $4.79\%$ and $5.86\%$ , respectively. (2) Combining the two style features further boosts model performance across all evaluation metrics, suggesting that the extracted styles are complementary. Moreover, the order in which the two style features are input into the Transformer decoder has no significant impact on Style Score $(93.72\%)$ vs. $94.50\%$ . + +Qualitative comparison between two style representations. To further analyze the differences between the + +![](images/a065116e58a3f204a1e13d80137c1343ffec24e4715c9902c660629daf2d3eab.jpg) +Figure 7. Spectrum analysis of two style representations. We provide frequency magnitude visualizations belonging to 7 writers, where the top row shows the writer-wise style while the bottom represents the character-wise one. Each spectrum map is averaged over 100 character samples written by the same person. The brighter the color, the larger the magnitude. A pixel farther from the center means a higher frequency [26]. We find that the writer-wise style representations capture more low-frequency information, while character-wise style representations capture more high-frequency information. + +![](images/acb6a5a538a7bc801c1165fcbd4619548dfba3873c38c08a9a016e7829269fe2.jpg) +Figure 8. The heat map of the DTW matrix. The dark diagonal indicates that the generated characters still own a higher similarity even using different $X_{s}$ belonging to the same writer. + +two styles, we resize the output patch tokens representing the two styles to feature maps, respectively, and visualize their frequency magnitudes in Figure 7. We find that character-wise style features capture more high-frequency information, whereas writer-wise features mainly focus on low-frequency information. According to [6], the high-frequency information in an image usually captures fine details while the low frequencies contain the overall part of objects. This finding supports our motivation that the writer head helps to imitate the overall style (e.g., glyph slant), while the glyph head captures the detailed style (e.g., stroke curvature), as shown in Table 2. + +Effect of using different style inputs. As mentioned in [30], given different style inputs $X_{s}$ belonging to the same writer $w_{s}$ , the imitation model may generate inconsistent characters. To evaluate the effect of different style inputs, we conduct two independent experiments using different $X_{s}$ based on the same model. Following [30], we use the model to generate 200 characters for each writer in the test set. We then calculate the DTW distance between corre + +Table 3. Quantitative evaluations of our SDT and competitors on Japanese, Indic, and English datasets. + +
DatasetsMethodsContent Score↑DTW ↓
JapaneseDrawing [40]50.741.4657
DeepImitator [44]53.201.2564
WriteLikeYou-v2 [30]85.611.2066
SDT(Ours)91.311.1289
IndicDrawing [40]2.349.8230
DeepImitator [44]4.136.7421
WriteLikeYou-v2 [30]13.194.5130
SDT(Ours)97.220.7075
EnglishDrawing [40]79.141.8519
DeepImitator [44]76.531.6460
WriteLikeYou-v2 [30]84.411.6215
SDT(Ours)85.521.6048
+ +sponding characters individually and average them according to the writer index (see Appendix A.1.4 for more details) to get a DTW square matrix. The resulting DTW square matrix is visualized in Figure 8. The dark diagonal in Figure 8 suggests that the generated characters maintain a high degree of similarity even when using different $X_{s}$ belonging to the same writer, demonstrating that our SDT can generate consistent results from various style inputs. + +# 4.3. Applications to Other Languages + +Japanese handwriting generation. For the Japanese handwriting generation task, we conduct experiments on TUAT HANDS [25] database (see more details in Appendix A.1.5) to evaluate the effectiveness of our method. Figure 9 (a) and Table 3 verify the effectiveness of SDT for Japanese handwriting generation. Specifically, from Table 3, we observe that our SDT outperforms all compared methods in terms of two quantitative metrics, indicating that SDT performs well in multiple languages. Furthermore, we provide additional evaluation metrics in Appendix A.8. + +![](images/a18b439f0cb77c25fe69aa0049f3d76c09a737798a8d7572f754227ade8d1505.jpg) +Figure 9. Comparisons with the competitors for online handwriting generation on various scripts. WriteLi. indicates WriteLikeYou-v2. + +Indic handwriting generation. We evaluate our method on the Indic handwriting generation task based on the $\mathrm{Tamil}^2$ dataset. It is worth noting that Indic handwriting generation presents a more significant challenge, as Indic characters contain more trajectory points than Chinese, Japanese, and English scripts (i.e., 88 vs. 68, 50, 30 on average; see Appendix A.1.5 for more dataset information). We compare our method with other approaches on the official test set in terms of Content Score and Dynamic Time Warping (DTW). As shown in Table 3, we find that our SDT significantly outperforms the second-best method in terms of the two quantitative metrics, achieving an $84.03\%$ higher Content Score and a 3.8055 lower DTW. This indicates that our SDT can handle handwritten characters with a large number of points (averaging 88) and ensure the quality of synthetic samples, as illustrated in Figure 9 (b). The potential advantages of our SDT are: (1) The improved style representations extracted by our SDT prevent the collapse of generated characters. (2) Our Transformer decoder facilitates long-distance dependence between trajectory points. We provide more experimental analysis in Appendix A.9. + +English handwriting generation. To evaluate our method in generating English handwritings, we collect all of the English samples from the symbol part of CASIA-OLHWDB(1.0-1.2) [22] and ICDAR-2013 competition database [38] (see more details in Appendix A.1.5). Similarly, we use Content Score and DTW as evaluation metrics. As shown in Figure 9 (c), we find that all methods achieve sound and comparable performance. One reason for this is that the English script contains fewer character classes and a smaller number of trajectory points (averaging 30), making + +their imitation easier compared to other scripts. Nevertheless, our SDT still outperforms other methods by a small margin in terms of both Content Score and DTW, as shown in Table 3. Moreover, we observe that corresponding uppercase and lowercase letters sometimes exhibit subtle inter-class differences (e.g., O vs. o), which leads our SDT to achieve a relatively low Content Score. + +# 5. Conclusion + +In this paper, we have proposed a novel method, named style-disentangled Transformer (SDT), to synthesize realistic and diverse online handwritings. SDT enhances imitation performance by disentangling the writer-wise and character-wise style representations from individual handwriting samples. For the writer-wise style, we group characters from the same writer and separate those from different writers, promoting SDT's ability to learn uniformity in individual handwritings. For the character-wise style, we maximize the mutual information between the distinct views of a character. Moreover, we extend SDT and introduce an offline-to-offline framework for improving the generation quality of offline Chinese handwritings. Promising results on various language scripts verify the effectiveness of our SDT. Although primarily designed for handwriting generation, SDT still holds the potential for extension to other generative tasks, such as font generation. + +Acknowledgments This research is partially supported by NSFC (Grant No.62176093, 61673182), Key Realm R&D Program of Guangzhou (No.202206030001), Guangdong Basic and Applied Basic Research Foundation (No.2021A1515012282) and Guangdong Provincial Key Laboratory of Human Digital Twin (2022B1212010004). + +# References + +[1] Emre Aksan, Fabrizio Pece, and Otmar Hilliges. Deepwriting: Making digital ink editable via deep generative modeling. In Proceedings of the 2018 CHI Conference on Human Factors in Computing Systems, pages 1-14, 2018. 2 +[2] Donald J Berndt and James Clifford. Using dynamic time warping to find patterns in time series. 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Recently, RNN-based methods have been proposed to generate stylized online Chinese characters. However, these methods mainly focus on capturing a person's overall writing style, neglecting subtle style inconsistencies between characters written by the same person. For example, while a person's handwriting typically exhibits general uniformity (e.g., glyph slant and aspect ratios), there are still small style variations in finer details (e.g., stroke length and curvature) of characters. In light of this, we propose to disentangle the style representations at both writer and character levels from individual handwritings to synthesize realistic stylized online handwritten characters. Specifically, we present the style-disentangled Transformer (SDT), which employs two complementary contrastive objectives to extract the style commonalities of reference samples and capture the detailed style patterns of each sample, respectively. 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When compared with Latin scripts, Chinese characters encompass an exceptionally vast lexicon (87,887 characters in GB18030-2022字符) and have intricate structures composed of multiple strokes. Recently, the intriguing task of generating Chinese characters has garnered significant attention [10, 23, 32]. 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The increasing numbers indicate the writing order from the start to the end." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 409, + 546, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 409, + 546, + 469 + ], + "spans": [ + { + "bbox": [ + 304, + 409, + 546, + 469 + ], + "type": "text", + "content": "to progressively generate online characters (i.e., the handwriting trajectory in a sequential format) [40]. As shown in Figure 1, online characters convey richer information (e.g., the order of writing) and thus pave the way for various applications, including writing robots [39]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 472, + 547, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 472, + 547, + 674 + ], + "spans": [ + { + "bbox": [ + 304, + 472, + 547, + 674 + ], + "type": "text", + "content": "Our goal is to automatically generate online Chinese handwritings that not only correspond to specific textual content, but also emulate the calligraphic style of a given exemplar writer (e.g., glyph slant, shape, stroke length, and curvature). This task thus holds potential for a wide range of applications, such as font design and calligraphy education. A popular solution [18] is to extract style information from the provided stylized samples and merge it with the content reference. DeepImitator [44] concatenates the style vector obtained from a CNN encoder with a character embedding, which is then fed into the RNN decoder to generate stylized online characters. WriteLikeYou [30] adopts the largemargin softmax loss [36] to promote discriminative learning of style features. However, these methods mainly focus on the overall writing style, thus overlooking the detailed style inconsistencies (e.g., the highlighted regions in Figure 2) between characters produced by the same writer." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "text", + "content": "The observations mentioned above inspire us to disentangle style representations at the writer and character levels from the stylized handwritings. However, accurately cap" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 693, + 155, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 693, + 155, + 703 + ], + "spans": [ + { + "bbox": [ + 58, + 693, + 155, + 703 + ], + "type": "text", + "content": "*Authors contributed equally." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 59, + 703, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 703, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 59, + 703, + 135, + 712 + ], + "type": "text", + "content": "† Corresponding author" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5977" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 121, + 64, + 265, + 107 + ], + "blocks": [ + { + "bbox": [ + 67, + 79, + 108, + 89 + ], + "lines": [ + { + "bbox": [ + 67, + 79, + 108, + 89 + ], + "spans": [ + { + "bbox": [ + 67, + 79, + 108, + 89 + ], + "type": "text", + "content": "Left Slant" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 121, + 64, + 265, + 107 + ], + "lines": [ + { + "bbox": [ + 121, + 64, + 265, + 107 + ], + "spans": [ + { + "bbox": [ + 121, + 64, + 265, + 107 + ], + "type": "image", + "image_path": "e5a987f2d1b7791c1120526224645047f85461aabb433a8b1808a6e1d353369b.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 121, + 111, + 263, + 154 + ], + "blocks": [ + { + "bbox": [ + 67, + 125, + 104, + 135 + ], + "lines": [ + { + "bbox": [ + 67, + 125, + 104, + 135 + ], + "spans": [ + { + "bbox": [ + 67, + 125, + 104, + 135 + ], + "type": "text", + "content": "No Slant" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 121, + 111, + 263, + 154 + ], + "lines": [ + { + "bbox": [ + 121, + 111, + 263, + 154 + ], + "spans": [ + { + "bbox": [ + 121, + 111, + 263, + 154 + ], + "type": "image", + "image_path": "22ef2d35f403b00cb44419f5ae3b169d672020c028323223a8c5b5b0d1e3a278.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 121, + 159, + 263, + 203 + ], + "blocks": [ + { + "bbox": [ + 67, + 172, + 114, + 183 + ], + "lines": [ + { + "bbox": [ + 67, + 172, + 114, + 183 + ], + "spans": [ + { + "bbox": [ + 67, + 172, + 114, + 183 + ], + "type": "text", + "content": "Right Slant" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 121, + 159, + 263, + 203 + ], + "lines": [ + { + "bbox": [ + 121, + 159, + 263, + 203 + ], + "spans": [ + { + "bbox": [ + 121, + 159, + 263, + 203 + ], + "type": "image", + "image_path": "70078260ca8255ee1d9594637c31db63e71dc85cbe90f414cfb7e20a96423c6b.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 205, + 287, + 262 + ], + "lines": [ + { + "bbox": [ + 46, + 205, + 287, + 262 + ], + "spans": [ + { + "bbox": [ + 46, + 205, + 287, + 262 + ], + "type": "text", + "content": "Figure 2. Handwritten character samples from three unique writers, with each row containing characters by the same person. Despite sharing similar overall handwriting styles (e.g., glyph slant), subtle style differences (e.g., stroke length, location, and curvature) can still be observed among them." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 275, + 287, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 275, + 287, + 453 + ], + "spans": [ + { + "bbox": [ + 46, + 275, + 287, + 453 + ], + "type": "text", + "content": "turing these two styles is a challenging task. To address this, we propose a style-disentangled Transformer (SDT) equipped with a dual-head style encoder. Specifically, we employ the contrastive learning framework [13] to guide each head in concentrating on writer-wise and character-wise styles, respectively. For the overall writer-wise style, we treat characters from the same writer as positive instances, and characters from different writers as negatives. This enables the encoder to learn the style commonalities among characters written by the same writer. Regarding the detailed character-wise style, we independently sample positive pairs within a character, and sample negative samples from other characters, as illustrated in Figure 3. Aggregating positive views of a character encourages the encoder to focus on the intricate character style patterns." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 454, + 287, + 537 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 454, + 287, + 537 + ], + "spans": [ + { + "bbox": [ + 46, + 454, + 287, + 537 + ], + "type": "text", + "content": "In addition, we introduce a content encoder for SDT to learn a textual feature with a global context. The two style representations, along with the textual feature, are then fed into a decoder that progressively generates online characters. Given that the output characters are in sequential form, we employ Transformer [35], a powerful sequence modeling architecture, as our backbone." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 538, + 287, + 633 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 538, + 287, + 633 + ], + "spans": [ + { + "bbox": [ + 46, + 538, + 287, + 633 + ], + "type": "text", + "content": "To extend SDT for generating offline Chinese handwritings (i.e., character images with stroke-width, e.g., Figures 3-7 in Appendix), we further propose an offline-to-offline generation framework. We first use SDT to generate online characters with significant shape changes, and then decorate them with stroke width, ink-blot effects, etc. This enables us to generate authentic offline handwritings. For more details, please refer to Appendix A.4." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 59, + 634, + 275, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 634, + 275, + 646 + ], + "spans": [ + { + "bbox": [ + 59, + 634, + 275, + 646 + ], + "type": "text", + "content": "We summarize our contributions in three key aspects:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 58, + 653, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 653, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 58, + 653, + 287, + 714 + ], + "type": "text", + "content": "- We are the first to disentangle two style representations (i.e., writer-wise and character-wise) for enhancing Chinese handwriting generation. Our findings show that the former focuses more on low-frequency information, while the latter captures higher frequencies." + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 332, + 64, + 520, + 204 + ], + "blocks": [ + { + "bbox": [ + 332, + 64, + 520, + 204 + ], + "lines": [ + { + "bbox": [ + 332, + 64, + 520, + 204 + ], + "spans": [ + { + "bbox": [ + 332, + 64, + 520, + 204 + ], + "type": "image", + "image_path": "e600574515ad03777cfc07f480446a60b464ef0060c00014b85fc318a6148345.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 206, + 545, + 262 + ], + "lines": [ + { + "bbox": [ + 304, + 206, + 545, + 262 + ], + "spans": [ + { + "bbox": [ + 304, + 206, + 545, + 262 + ], + "type": "text", + "content": "Figure 3. In this two-character example, we independently sample the positive pair, i.e., " + }, + { + "bbox": [ + 304, + 206, + 545, + 262 + ], + "type": "inline_equation", + "content": "o" + }, + { + "bbox": [ + 304, + 206, + 545, + 262 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 206, + 545, + 262 + ], + "type": "inline_equation", + "content": "o^{+}" + }, + { + "bbox": [ + 304, + 206, + 545, + 262 + ], + "type": "text", + "content": ", within the first character, while the negative " + }, + { + "bbox": [ + 304, + 206, + 545, + 262 + ], + "type": "inline_equation", + "content": "o^{-}" + }, + { + "bbox": [ + 304, + 206, + 545, + 262 + ], + "type": "text", + "content": " is sampled from another character. Our sampling strategy randomly selects a small subset of patches, following a uniform distribution." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 317, + 274, + 545, + 377 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 317, + 274, + 545, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 274, + 545, + 323 + ], + "spans": [ + { + "bbox": [ + 317, + 274, + 545, + 323 + ], + "type": "text", + "content": "- We introduce a novel online character generation method, i.e., SDT. Extensive experiments on handwriting datasets in Chinese, English, Japanese, and Indic scripts demonstrate its effectiveness and superiority." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 317, + 330, + 545, + 377 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 330, + 545, + 377 + ], + "spans": [ + { + "bbox": [ + 317, + 330, + 545, + 377 + ], + "type": "text", + "content": "- Building on the SDT, we further develop an offline-to-offline framework that can produce more plausible offline handwritten Chinese characters, as evidenced in Appendix A.4." + } + ] + } + ], + "index": 15 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 394, + 392, + 406 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 394, + 392, + 406 + ], + "spans": [ + { + "bbox": [ + 306, + 394, + 392, + 406 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 415, + 545, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 415, + 545, + 569 + ], + "spans": [ + { + "bbox": [ + 304, + 415, + 545, + 569 + ], + "type": "text", + "content": "Handwriting generation. Various style-content disentangling methods [1, 8, 18, 21, 24] have been proposed to generate handwritings with arbitrary styles. These methods assume that reference samples can be decomposed into style and content spaces. They disentangle calligraphic styles from reference samples and recombine them with specific textual content for controllable style synthesis. For instance, DeepWriting [1] adopts RNNs to extract the style vectors from online handwritings, and then combines them with character embeddings for synthesizing stylized online handwritings. However, it typically over-smooths the styles of distinct letters and loses key details, since its extracted style vectors are letter-independent [21]." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "content": "DSD [21] addresses the over-smooth problem by segmenting online handwritten words into isolated letters and encoding them into global and letter-specific style vectors, improving synthetic handwriting quality. Compared with it, our method can explicitly capture more fine-grained details (e.g., stroke length, location and curvature), which are more difficult to obtain. Besides, these methods [1, 21, 34] rely on extra fine annotations to segment input cursive scripts, while our SDT need not. Recently, HWT [3] uses a vanilla Transformer encoder for style pattern extraction. However, these methods [1, 3, 8, 18, 21] rely on complex content references, such as recurrent embeddings and letter-wise fil" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5978" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 286, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 286, + 144 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 286, + 144 + ], + "type": "text", + "content": "ter maps. SLOGAN [24] addresses this issue by extracting textual contents from easily obtainable printed images, but it struggles with generalizing to unseen handwriting styles due to the fixed writer ID. In contrast, our SDT effectively obtains content and style information, and thus can synthesize characters with arbitrary styles well." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 144, + 286, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 144, + 286, + 276 + ], + "spans": [ + { + "bbox": [ + 46, + 144, + 286, + 276 + ], + "type": "text", + "content": "Regarding handwritten Chinese characters, several attempts [4, 16, 20] use GANs to generate Chinese handwriting images, but always result in characteristic artifacts. Drawing [40] and FontRNN [31] adopt RNNs, but they cannot flexibly control the handwriting styles. In addition, DeepImitator [44] and WriteLikeYou [30] propose style-controlled generation using style representations from offline images [44] or online trajectories [30]. Unlike these methods [30,44] that only extract an overall writer style, our SDT captures both writer and character-level styles, significantly improving the performance of handwriting imitation." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 287, + 286, + 383 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 287, + 286, + 383 + ], + "spans": [ + { + "bbox": [ + 46, + 287, + 286, + 383 + ], + "type": "text", + "content": "Contrastive learning. Contrastive learning [13, 41] has been widely used in various fields [9, 28, 29, 33, 42, 43]. Some image translation studies [14, 27] use contrastive learning to enhance natural image generation quality, encouraging content preservation during transfer. Unlike these methods [14, 27], our SDT aligns independently sampled patches from the same input, aiming to improve style representations of handwritings." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 393, + 102, + 405 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 393, + 102, + 405 + ], + "spans": [ + { + "bbox": [ + 47, + 393, + 102, + 405 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 413, + 286, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 413, + 286, + 508 + ], + "spans": [ + { + "bbox": [ + 46, + 413, + 286, + 508 + ], + "type": "text", + "content": "Problem statement. We aim to synthesize stylized online handwritings with conditional content and style. Given a content image " + }, + { + "bbox": [ + 46, + 413, + 286, + 508 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 413, + 286, + 508 + ], + "type": "text", + "content": " and a set of style images " + }, + { + "bbox": [ + 46, + 413, + 286, + 508 + ], + "type": "inline_equation", + "content": "X_{s} = \\{x_{s}^{i}\\}_{i = 1}^{K}" + }, + { + "bbox": [ + 46, + 413, + 286, + 508 + ], + "type": "text", + "content": ", randomly sampled from a writer " + }, + { + "bbox": [ + 46, + 413, + 286, + 508 + ], + "type": "inline_equation", + "content": "w_{s}" + }, + { + "bbox": [ + 46, + 413, + 286, + 508 + ], + "type": "text", + "content": ", we aim to generate an online handwritten Chinese character " + }, + { + "bbox": [ + 46, + 413, + 286, + 508 + ], + "type": "inline_equation", + "content": "\\hat{Y}_s" + }, + { + "bbox": [ + 46, + 413, + 286, + 508 + ], + "type": "text", + "content": " that reflects the calligraphic style of " + }, + { + "bbox": [ + 46, + 413, + 286, + 508 + ], + "type": "inline_equation", + "content": "w_{s}" + }, + { + "bbox": [ + 46, + 413, + 286, + 508 + ], + "type": "text", + "content": " and retains the textual content of " + }, + { + "bbox": [ + 46, + 413, + 286, + 508 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 413, + 286, + 508 + ], + "type": "text", + "content": ". The key challenge lies in obtaining discriminative style representations from a limited number of stylized samples." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 509, + 286, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 509, + 286, + 616 + ], + "spans": [ + { + "bbox": [ + 46, + 509, + 286, + 616 + ], + "type": "text", + "content": "To address this task, inspired by our observations (cf. Figure 2) of the overall uniformity (i.e., writer-wise style) and inconsistent details (i.e., character-wise style), we propose to disentangle the style of exemplar writers into overall and detailed styles for enhancing handwriting imitation performance. To achieve this, we introduce a new style-disentangled Transformer (SDT) approach to decouple the two styles from individual handwritings. The overall scheme of SDT is presented below." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 623, + 143, + 634 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 623, + 143, + 634 + ], + "spans": [ + { + "bbox": [ + 47, + 623, + 143, + 634 + ], + "type": "text", + "content": "3.1. Overall Scheme" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 641, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 286, + 712 + ], + "type": "text", + "content": "As shown in Figure 4, SDT consists of a dual-head style encoder, a content encoder, and a Transformer decoder. The style encoder (cf. Section 3.2) is designed to learn the writer-wise and character-wise styles. It firstly extracts rich calligraphic style patterns from reference style examples " + }, + { + "bbox": [ + 46, + 641, + 286, + 712 + ], + "type": "inline_equation", + "content": "X_{s}" + }, + { + "bbox": [ + 46, + 641, + 286, + 712 + ], + "type": "text", + "content": " via a sequential combination of a CNN and a Transformer" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "content": "encoder, followed by the writer and glyph heads to disentangle the writer-wise and character-wise styles from the extracted style patterns. To this end, we propose two contrastive objectives, WriterNCE " + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{wri}" + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "content": " and GlyphNCE " + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{gly}" + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "content": ", to encourage the encoder to learn the two styles, respectively. Specifically, " + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{wri}" + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "content": " maximizes the mutual information between character instances belonging to the same writer, while " + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{gly}" + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "content": " associates the positive pair independently sampled from the same character. Guided by " + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{wri}" + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{gly}" + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "content": ", the writer and glyph heads can acquire discriminative writerwise and character-wise style features, respectively." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 206, + 545, + 315 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 206, + 545, + 315 + ], + "spans": [ + { + "bbox": [ + 304, + 206, + 545, + 315 + ], + "type": "text", + "content": "The content encoder uses a standard Resnet18 [15] as the CNN backbone to learn the compact feature map " + }, + { + "bbox": [ + 304, + 206, + 545, + 315 + ], + "type": "inline_equation", + "content": "q_{\\text{map}} \\in \\mathbb{R}^{h \\times w \\times c}" + }, + { + "bbox": [ + 304, + 206, + 545, + 315 + ], + "type": "text", + "content": " from a content reference " + }, + { + "bbox": [ + 304, + 206, + 545, + 315 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 206, + 545, + 315 + ], + "type": "text", + "content": ", and feeds the flattened feature patches into a Transformer encoder to extract the textual content representation " + }, + { + "bbox": [ + 304, + 206, + 545, + 315 + ], + "type": "inline_equation", + "content": "q \\in \\mathbb{R}^{d \\times c}" + }, + { + "bbox": [ + 304, + 206, + 545, + 315 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 206, + 545, + 315 + ], + "type": "inline_equation", + "content": "d = h \\times w" + }, + { + "bbox": [ + 304, + 206, + 545, + 315 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 206, + 545, + 315 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 206, + 545, + 315 + ], + "type": "text", + "content": " is the channel dimension. Benefiting from the strong capability of Transformer to capture long-range dependencies between feature patches, the content encoder expects an informative content feature " + }, + { + "bbox": [ + 304, + 206, + 545, + 315 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 304, + 206, + 545, + 315 + ], + "type": "text", + "content": " with a global context." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 317, + 545, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 317, + 545, + 389 + ], + "spans": [ + { + "bbox": [ + 304, + 317, + 545, + 389 + ], + "type": "text", + "content": "After the two encoders, a multi-layer Transformer decoder (cf. Section 3.3) is used to synthesize " + }, + { + "bbox": [ + 304, + 317, + 545, + 389 + ], + "type": "inline_equation", + "content": "\\hat{Y}_s" + }, + { + "bbox": [ + 304, + 317, + 545, + 389 + ], + "type": "text", + "content": " in an autoregressive fashion, conditioned on the two style representations and the content feature. This decoder is supervised by the pen moving prediction loss " + }, + { + "bbox": [ + 304, + 317, + 545, + 389 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{pre}" + }, + { + "bbox": [ + 304, + 317, + 545, + 389 + ], + "type": "text", + "content": " and pen state classification loss " + }, + { + "bbox": [ + 304, + 317, + 545, + 389 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cls}" + }, + { + "bbox": [ + 304, + 317, + 545, + 389 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 392, + 545, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 392, + 545, + 415 + ], + "spans": [ + { + "bbox": [ + 305, + 392, + 545, + 415 + ], + "type": "text", + "content": "To summarize, the overall training objective of SDT combines all four loss functions:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 353, + 432, + 545, + 445 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 353, + 432, + 545, + 445 + ], + "spans": [ + { + "bbox": [ + 353, + 432, + 545, + 445 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {w r i} + \\mathcal {L} _ {g l y} + \\mathcal {L} _ {p r e} + \\lambda \\mathcal {L} _ {c l s}, \\tag {1}", + "image_path": "955da69617380085e9989b53023a0358ebfaed660672d2ce156d3d6c771c40e5.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 460, + 545, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 460, + 545, + 483 + ], + "spans": [ + { + "bbox": [ + 305, + 460, + 545, + 483 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 460, + 545, + 483 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 305, + 460, + 545, + 483 + ], + "type": "text", + "content": " serves as a trade-off factor. Each component of our SDT is detailed in the following Section 3.2 and Section 3.3." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 501, + 444, + 513 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 501, + 444, + 513 + ], + "spans": [ + { + "bbox": [ + 306, + 501, + 444, + 513 + ], + "type": "text", + "content": "3.2. Dual-head Style Encoder" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "content": "As illustrated in Figure 2, there are two distinct styles in a person's handwriting: writer-wise and character-wise styles. We propose a dual-head style encoder to obtain the two style representations. As shown in Figure 4, the input " + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "X = \\{x^{i}\\}_{i=1}^{K}" + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "content": " is firstly encoded by ResNet18 to obtain a sequence of feature maps " + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "F_{m} = \\{f_{m}^{i}\\}_{i=1}^{K} \\in \\mathbb{R}^{K \\times h \\times w \\times c}" + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "content": ". Next, we flatten the spatial dimension of each feature map to obtain feature sequences " + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "F = \\{f^{i}\\}_{i=1}^{K} \\in \\mathbb{R}^{K \\times d \\times c}" + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "content": ". These feature sequences are then fed into a Transformer encoder to extract more informative feature sequences " + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "Z = \\{z^{i}\\}_{i=1}^{K} \\in \\mathbb{R}^{K \\times d \\times c}" + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "content": ". Finally, we use the two heads, built on self-attention [35], to further disentangle " + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "content": " into the writer-wise style representations " + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "E = \\{e^{i}\\}_{i=1}^{K} \\in \\mathbb{R}^{K \\times d \\times c}" + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "content": " via " + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{wri}" + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "content": " and the character-wise counterparts " + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "G = \\{g^{i}\\}_{i=1}^{K} \\in \\mathbb{R}^{K \\times d \\times c}" + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "content": " via " + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{gly}" + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "content": ", respectively. We next detail the two contrastive learning objectives as follows." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5979" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 111, + 63, + 487, + 238 + ], + "blocks": [ + { + "bbox": [ + 111, + 63, + 487, + 238 + ], + "lines": [ + { + "bbox": [ + 111, + 63, + 487, + 238 + ], + "spans": [ + { + "bbox": [ + 111, + 63, + 487, + 238 + ], + "type": "image", + "image_path": "6f49830c6fef29eed3ff51233ef994e4ad983229aff59af86864af7a0df03cf2.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 244, + 547, + 291 + ], + "lines": [ + { + "bbox": [ + 45, + 244, + 547, + 291 + ], + "spans": [ + { + "bbox": [ + 45, + 244, + 547, + 291 + ], + "type": "text", + "content": "Figure 4. Overview of the proposed method. Our SDT consists of a dual-head style encoder, a content encoder and a Transformer decoder. The writer-wise and character-wise style representations extracted by style encoder and the learned content feature are fed into the Transformer decoder to progressively generate online handwritings. We utilize the WriterNCE " + }, + { + "bbox": [ + 45, + 244, + 547, + 291 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{wri}" + }, + { + "bbox": [ + 45, + 244, + 547, + 291 + ], + "type": "text", + "content": " and GlyphNCE " + }, + { + "bbox": [ + 45, + 244, + 547, + 291 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{gly}" + }, + { + "bbox": [ + 45, + 244, + 547, + 291 + ], + "type": "text", + "content": " to guide the two heads for learning the corresponding styles. " + }, + { + "bbox": [ + 45, + 244, + 547, + 291 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{pre}" + }, + { + "bbox": [ + 45, + 244, + 547, + 291 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 244, + 547, + 291 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cls}" + }, + { + "bbox": [ + 45, + 244, + 547, + 291 + ], + "type": "text", + "content": " denote the pen moving prediction and state classification loss, respectively." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 304, + 226, + 316 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 304, + 226, + 316 + ], + "spans": [ + { + "bbox": [ + 46, + 304, + 226, + 316 + ], + "type": "text", + "content": "3.2.1 Writer-wise Contrastive Learning" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 323, + 288, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 323, + 288, + 441 + ], + "spans": [ + { + "bbox": [ + 46, + 323, + 288, + 441 + ], + "type": "text", + "content": "To explicitly encourage the writer head to learn the witer-wise style, we propose to learn a feature space where the style features from the same writer are closer than those from different writers. The intuition is that one person's handwritings consistently exhibit similar style information, which can serve as a crucial clue for distinguishing writers. To this end, we take characters written by the same person as positive pairs and those from different writers as negative samples, and develop a new WriterNCE loss for writer-wise style learning." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 442, + 288, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 442, + 288, + 528 + ], + "spans": [ + { + "bbox": [ + 46, + 442, + 288, + 528 + ], + "type": "text", + "content": "Specifically, let " + }, + { + "bbox": [ + 46, + 442, + 288, + 528 + ], + "type": "inline_equation", + "content": "j \\in M = \\{1, \\dots, N\\}" + }, + { + "bbox": [ + 46, + 442, + 288, + 528 + ], + "type": "text", + "content": " be the index of an element within a mini-batch and let " + }, + { + "bbox": [ + 46, + 442, + 288, + 528 + ], + "type": "inline_equation", + "content": "A(j) = M \\setminus \\{j\\}" + }, + { + "bbox": [ + 46, + 442, + 288, + 528 + ], + "type": "text", + "content": " be other indices distinct from " + }, + { + "bbox": [ + 46, + 442, + 288, + 528 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 442, + 288, + 528 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 442, + 288, + 528 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 442, + 288, + 528 + ], + "type": "text", + "content": " is the batch size. Given a writer-wise style feature " + }, + { + "bbox": [ + 46, + 442, + 288, + 528 + ], + "type": "inline_equation", + "content": "e_j" + }, + { + "bbox": [ + 46, + 442, + 288, + 528 + ], + "type": "text", + "content": " belonging to writer " + }, + { + "bbox": [ + 46, + 442, + 288, + 528 + ], + "type": "inline_equation", + "content": "w_j" + }, + { + "bbox": [ + 46, + 442, + 288, + 528 + ], + "type": "text", + "content": " as the anchor, we denote its in-batch positive sample set as " + }, + { + "bbox": [ + 46, + 442, + 288, + 528 + ], + "type": "inline_equation", + "content": "P(j) = \\{p \\in A(j) : w_p = w_j\\}" + }, + { + "bbox": [ + 46, + 442, + 288, + 528 + ], + "type": "text", + "content": " and its negative set as " + }, + { + "bbox": [ + 46, + 442, + 288, + 528 + ], + "type": "inline_equation", + "content": "A(j) \\setminus P(j)" + }, + { + "bbox": [ + 46, + 442, + 288, + 528 + ], + "type": "text", + "content": ". The WriterNCE loss is formulated as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 544, + 293, + 581 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 544, + 293, + 581 + ], + "spans": [ + { + "bbox": [ + 47, + 544, + 293, + 581 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {w r i} = \\frac {- 1}{N} \\sum_ {j \\in M} \\frac {1}{| P (j) |} \\sum_ {p \\in P (j)} \\log \\frac {\\exp \\left(\\sin \\left(e _ {j} , e _ {p}\\right) / \\tau\\right)}{\\sum_ {a \\in A (j)} \\exp \\left(\\sin \\left(e _ {j} , e _ {a}\\right) / \\tau\\right)}, \\tag {2}", + "image_path": "0a6729b8ad750e673c3596e14c8c7326ca8c67d98ce23b76b6e01d5d32e58058.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 581, + 287, + 631 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 581, + 287, + 631 + ], + "spans": [ + { + "bbox": [ + 47, + 581, + 287, + 631 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 581, + 287, + 631 + ], + "type": "inline_equation", + "content": "\\operatorname{sim}(e_j, e_p) = f_1(e_j)^\\top f_1(e_p)" + }, + { + "bbox": [ + 47, + 581, + 287, + 631 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 581, + 287, + 631 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 47, + 581, + 287, + 631 + ], + "type": "text", + "content": " is a temperature parameter and " + }, + { + "bbox": [ + 47, + 581, + 287, + 631 + ], + "type": "inline_equation", + "content": "f_1(\\cdot)" + }, + { + "bbox": [ + 47, + 581, + 287, + 631 + ], + "type": "text", + "content": " is a multi-layer perceptron (MLP) that projects features to a " + }, + { + "bbox": [ + 47, + 581, + 287, + 631 + ], + "type": "inline_equation", + "content": "\\ell_2" + }, + { + "bbox": [ + 47, + 581, + 287, + 631 + ], + "type": "text", + "content": "-normalized feature space where " + }, + { + "bbox": [ + 47, + 581, + 287, + 631 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{wri}" + }, + { + "bbox": [ + 47, + 581, + 287, + 631 + ], + "type": "text", + "content": " is applied." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 647, + 241, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 241, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 241, + 658 + ], + "type": "text", + "content": "3.2.2 Character-wise Contrastive Learning" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 665, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 713 + ], + "type": "text", + "content": "Compared with the overall writer-wise style, character-wise style differences often exist in the fine details of distinct characters, e.g., stroke length and curvature (cf. Figure 3). Inspired by this, we aim to maximize the mutual informa" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 304, + 545, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 304, + 545, + 399 + ], + "spans": [ + { + "bbox": [ + 304, + 304, + 545, + 399 + ], + "type": "text", + "content": "tion between diverse views of a character, thereby enforcing the glyph head to learn the character-wise style. As strokes are distributed across arbitrary spatial locations in character images, we propose to capture stroke details via contrastive learning, by randomly selecting a small subset of patches following a uniform distribution. Specifically, we conduct sampling over the sequential patch tokens obtained from the glyph head." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 399, + 546, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 399, + 546, + 483 + ], + "spans": [ + { + "bbox": [ + 304, + 399, + 546, + 483 + ], + "type": "text", + "content": "Given character-wise style features " + }, + { + "bbox": [ + 304, + 399, + 546, + 483 + ], + "type": "inline_equation", + "content": "\\{g_j\\}_{j=1}^B \\in \\mathbb{R}^{B \\times d \\times c}" + }, + { + "bbox": [ + 304, + 399, + 546, + 483 + ], + "type": "text", + "content": " extracted from " + }, + { + "bbox": [ + 304, + 399, + 546, + 483 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 304, + 399, + 546, + 483 + ], + "type": "text", + "content": " characters, we sample a positive patch pair (i.e., " + }, + { + "bbox": [ + 304, + 399, + 546, + 483 + ], + "type": "inline_equation", + "content": "o \\in \\mathbb{R}^{n \\times c}" + }, + { + "bbox": [ + 304, + 399, + 546, + 483 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 399, + 546, + 483 + ], + "type": "inline_equation", + "content": "o^+ \\in \\mathbb{R}^{n \\times c}" + }, + { + "bbox": [ + 304, + 399, + 546, + 483 + ], + "type": "text", + "content": ") from the same randomly selected " + }, + { + "bbox": [ + 304, + 399, + 546, + 483 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 304, + 399, + 546, + 483 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 399, + 546, + 483 + ], + "type": "inline_equation", + "content": "B-1" + }, + { + "bbox": [ + 304, + 399, + 546, + 483 + ], + "type": "text", + "content": " negative patches " + }, + { + "bbox": [ + 304, + 399, + 546, + 483 + ], + "type": "inline_equation", + "content": "\\{o_j^-\\}_{j=1}^{B-1}" + }, + { + "bbox": [ + 304, + 399, + 546, + 483 + ], + "type": "text", + "content": " from the remaining " + }, + { + "bbox": [ + 304, + 399, + 546, + 483 + ], + "type": "inline_equation", + "content": "B-1" + }, + { + "bbox": [ + 304, + 399, + 546, + 483 + ], + "type": "text", + "content": " style features. Here, the number of sampled patch tokens is " + }, + { + "bbox": [ + 304, + 399, + 546, + 483 + ], + "type": "inline_equation", + "content": "n = d \\cdot \\alpha" + }, + { + "bbox": [ + 304, + 399, + 546, + 483 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 399, + 546, + 483 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 399, + 546, + 483 + ], + "type": "text", + "content": " is the sampling ratio. The GlyphNCE loss is formulated as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 492, + 547, + 529 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 492, + 547, + 529 + ], + "spans": [ + { + "bbox": [ + 306, + 492, + 547, + 529 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {g l y} = - \\log \\frac {\\exp (\\sin (o , o ^ {+}) / \\tau)}{\\exp (\\sin (o , o ^ {+}) / \\tau) + \\sum_ {j = 1} ^ {B - 1} \\exp (\\sin (o , o _ {j} ^ {-}) / \\tau)}, \\tag {3}", + "image_path": "1e3f5df2a1527d997c704a12906d9d275123660eec3a53b19784e9cae357c0ac.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 529, + 545, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 529, + 545, + 554 + ], + "spans": [ + { + "bbox": [ + 306, + 529, + 545, + 554 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 529, + 545, + 554 + ], + "type": "inline_equation", + "content": "\\operatorname{sim}(o, o^+) = f_2(o)^\\top f_2(o^+)" + }, + { + "bbox": [ + 306, + 529, + 545, + 554 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 306, + 529, + 545, + 554 + ], + "type": "inline_equation", + "content": "f_2(\\cdot)" + }, + { + "bbox": [ + 306, + 529, + 545, + 554 + ], + "type": "text", + "content": " is an MLP with the same structure as " + }, + { + "bbox": [ + 306, + 529, + 545, + 554 + ], + "type": "inline_equation", + "content": "f_1(\\cdot)" + }, + { + "bbox": [ + 306, + 529, + 545, + 554 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 563, + 509, + 575 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 563, + 509, + 575 + ], + "spans": [ + { + "bbox": [ + 306, + 563, + 509, + 575 + ], + "type": "text", + "content": "3.3. Transformer Decoder for Handwriting" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "text", + "content": "The goal of the Transformer decoder is to progressively generate realistic online characters, denoted as " + }, + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\hat{Y}" + }, + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "text", + "content": ", based on the global content feature " + }, + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "text", + "content": " and the obtained style representations (i.e., " + }, + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "inline_equation", + "content": "E = \\{e^i\\}_{i=1}^K" + }, + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "inline_equation", + "content": "G = \\{g^i\\}_{i=1}^K" + }, + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "text", + "content": "). As each online character consists of numerous points (i.e., " + }, + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\hat{Y} = \\{\\hat{y}_j\\}_{j=1}^L" + }, + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "text", + "content": " being the total number of points; see more details in Appendix A.10), the decoder faces the challenge of effectively integrating content and style features to accurately depict all points of the character. To address this challenge, we propose to fuse " + }, + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "text", + "content": " within the multi-head attention layers of our Transformer decoder. As shown" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5980" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 86, + 69, + 248, + 214 + ], + "blocks": [ + { + "bbox": [ + 86, + 69, + 248, + 214 + ], + "lines": [ + { + "bbox": [ + 86, + 69, + 248, + 214 + ], + "spans": [ + { + "bbox": [ + 86, + 69, + 248, + 214 + ], + "type": "image", + "image_path": "298e9fcdfd835c546dbcaf600c60363e2126917371505ff5e7a4c23d829b9d61.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 223, + 289, + 291 + ], + "lines": [ + { + "bbox": [ + 46, + 223, + 289, + 291 + ], + "spans": [ + { + "bbox": [ + 46, + 223, + 289, + 291 + ], + "type": "text", + "content": "Figure 5. Illustration of the fusion of the style information in our Transformer decoder. At each time step, the query vector is first encoded from the content feature " + }, + { + "bbox": [ + 46, + 223, + 289, + 291 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 46, + 223, + 289, + 291 + ], + "type": "text", + "content": " and previous points " + }, + { + "bbox": [ + 46, + 223, + 289, + 291 + ], + "type": "inline_equation", + "content": "\\{y_j\\}_{j=1}^{t-1}" + }, + { + "bbox": [ + 46, + 223, + 289, + 291 + ], + "type": "text", + "content": ". Then, it successively attends to the writer-wise and character-wise style features (i.e., " + }, + { + "bbox": [ + 46, + 223, + 289, + 291 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 46, + 223, + 289, + 291 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 223, + 289, + 291 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 223, + 289, + 291 + ], + "type": "text", + "content": ") for adaptively aggregating style information, which is finally decoded into the current-step output." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 304, + 287, + 339 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 304, + 287, + 339 + ], + "spans": [ + { + "bbox": [ + 46, + 304, + 287, + 339 + ], + "type": "text", + "content": "in Figure 5, " + }, + { + "bbox": [ + 46, + 304, + 287, + 339 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 46, + 304, + 287, + 339 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 304, + 287, + 339 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 46, + 304, + 287, + 339 + ], + "type": "text", + "content": " serve as the key/value vectors, while " + }, + { + "bbox": [ + 46, + 304, + 287, + 339 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 46, + 304, + 287, + 339 + ], + "type": "text", + "content": " serves as the query vector that successively attends to " + }, + { + "bbox": [ + 46, + 304, + 287, + 339 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 46, + 304, + 287, + 339 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 304, + 287, + 339 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 304, + 287, + 339 + ], + "type": "text", + "content": " to aggregate style information." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 340, + 287, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 340, + 287, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 340, + 287, + 567 + ], + "type": "text", + "content": "During training, at any decoding step " + }, + { + "bbox": [ + 46, + 340, + 287, + 567 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 340, + 287, + 567 + ], + "type": "text", + "content": ", we take " + }, + { + "bbox": [ + 46, + 340, + 287, + 567 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 46, + 340, + 287, + 567 + ], + "type": "text", + "content": " as the initial point. As shown in Figure 5, we apply self-attention to the point sequence, i.e. the content context " + }, + { + "bbox": [ + 46, + 340, + 287, + 567 + ], + "type": "inline_equation", + "content": "[q, y_1, \\dots, y_{t-1}]" + }, + { + "bbox": [ + 46, + 340, + 287, + 567 + ], + "type": "text", + "content": ", to obtain the query vector " + }, + { + "bbox": [ + 46, + 340, + 287, + 567 + ], + "type": "inline_equation", + "content": "Q_t \\in \\mathbb{R}^c" + }, + { + "bbox": [ + 46, + 340, + 287, + 567 + ], + "type": "text", + "content": ". Here, the ground-truth points " + }, + { + "bbox": [ + 46, + 340, + 287, + 567 + ], + "type": "inline_equation", + "content": "\\{y_j\\}_{j=1}^{t-1}" + }, + { + "bbox": [ + 46, + 340, + 287, + 567 + ], + "type": "text", + "content": " are used to accelerate model convergence in training [30, 37]. Subsequently, " + }, + { + "bbox": [ + 46, + 340, + 287, + 567 + ], + "type": "inline_equation", + "content": "Q_t" + }, + { + "bbox": [ + 46, + 340, + 287, + 567 + ], + "type": "text", + "content": " attends to " + }, + { + "bbox": [ + 46, + 340, + 287, + 567 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 46, + 340, + 287, + 567 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 340, + 287, + 567 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 340, + 287, + 567 + ], + "type": "text", + "content": " over the subsequent decoding layers to adaptively aggregate style information, ultimately generating the output " + }, + { + "bbox": [ + 46, + 340, + 287, + 567 + ], + "type": "inline_equation", + "content": "O_t \\in \\mathbb{R}^{6R+3}" + }, + { + "bbox": [ + 46, + 340, + 287, + 567 + ], + "type": "text", + "content": ". The output with " + }, + { + "bbox": [ + 46, + 340, + 287, + 567 + ], + "type": "inline_equation", + "content": "6R + 3" + }, + { + "bbox": [ + 46, + 340, + 287, + 567 + ], + "type": "text", + "content": " logits is then used to generate the pen moving " + }, + { + "bbox": [ + 46, + 340, + 287, + 567 + ], + "type": "inline_equation", + "content": "(\\Delta \\hat{u}_t, \\Delta \\hat{v}_t)" + }, + { + "bbox": [ + 46, + 340, + 287, + 567 + ], + "type": "text", + "content": " and the pen state " + }, + { + "bbox": [ + 46, + 340, + 287, + 567 + ], + "type": "inline_equation", + "content": "(\\hat{m}_t^1, \\hat{m}_t^2, \\hat{m}_t^3)" + }, + { + "bbox": [ + 46, + 340, + 287, + 567 + ], + "type": "text", + "content": ". Specifically, we use a Gaussian mixture model (GMM) [11] with " + }, + { + "bbox": [ + 46, + 340, + 287, + 567 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 46, + 340, + 287, + 567 + ], + "type": "text", + "content": " bivariate normal distributions to predict the pen moving, with each normal distribution containing 6 parameters. Moreover, we use the other 3 logits to generate the pen state. The training loss for supervising the decoder comprises two parts: the pen movement prediction loss " + }, + { + "bbox": [ + 46, + 340, + 287, + 567 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{pre}(\\Delta \\hat{u}_t, \\Delta \\hat{v}_t)" + }, + { + "bbox": [ + 46, + 340, + 287, + 567 + ], + "type": "text", + "content": ", and the pen state classification loss " + }, + { + "bbox": [ + 46, + 340, + 287, + 567 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cls}(\\hat{m}_t^1, \\hat{m}_t^2, \\hat{m}_t^3)" + }, + { + "bbox": [ + 46, + 340, + 287, + 567 + ], + "type": "text", + "content": ". Please refer to Appendix A.11 for more details of these losses." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 567, + 287, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 567, + 287, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 567, + 287, + 640 + ], + "type": "text", + "content": "The inference phase is different from the training phase, where the ground truth " + }, + { + "bbox": [ + 46, + 567, + 287, + 640 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 567, + 287, + 640 + ], + "type": "text", + "content": " is not available at test time. Instead, we take the generated points " + }, + { + "bbox": [ + 46, + 567, + 287, + 640 + ], + "type": "inline_equation", + "content": "\\{\\hat{y}_j\\}_{j=1}^{t-1}" + }, + { + "bbox": [ + 46, + 567, + 287, + 640 + ], + "type": "text", + "content": " as the input of the step " + }, + { + "bbox": [ + 46, + 567, + 287, + 640 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 567, + 287, + 640 + ], + "type": "text", + "content": ", and combine them with " + }, + { + "bbox": [ + 46, + 567, + 287, + 640 + ], + "type": "inline_equation", + "content": "q, E" + }, + { + "bbox": [ + 46, + 567, + 287, + 640 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 567, + 287, + 640 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 567, + 287, + 640 + ], + "type": "text", + "content": " to predict the next point " + }, + { + "bbox": [ + 46, + 567, + 287, + 640 + ], + "type": "inline_equation", + "content": "\\hat{y}_t" + }, + { + "bbox": [ + 46, + 567, + 287, + 640 + ], + "type": "text", + "content": ". Such a process repeats until a pen-end state " + }, + { + "bbox": [ + 46, + 567, + 287, + 640 + ], + "type": "inline_equation", + "content": "(\\hat{m}_{t-1}^3 = 1)" + }, + { + "bbox": [ + 46, + 567, + 287, + 640 + ], + "type": "text", + "content": " is received." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 651, + 128, + 664 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 651, + 128, + 664 + ], + "spans": [ + { + "bbox": [ + 47, + 651, + 128, + 664 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 670, + 220, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 670, + 220, + 684 + ], + "spans": [ + { + "bbox": [ + 47, + 670, + 220, + 684 + ], + "type": "text", + "content": "4.1. Chinese handwriting generation" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "content": "Dataset. To evaluate SDT in generating Chinese handwritings, we use CASIA-OLHWDB (1.0-1.2) [22] for model" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "content": "training and ICDAR-2013 competition database [38] for testing. The training set consists of about 3.7 million online Chinese handwritten characters produced by 1,020 writers, while the test set contains 60 writers, with each contributing 3,755 most frequently used characters set of GB2312-80. Following [12], we use the Ramer-Douglas-Peucker algorithm [7] with a parameter of " + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "inline_equation", + "content": "\\epsilon = 2" + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "content": " to remove redundant points of characters, leading to an average sequence length of 50. Following [44], we render offline style references using coordinate points of online characters, and each style sample is randomly sampled from the target-writer hand-writings during inference, as shown in Figure 4. For content images, we use the popular average Chinese font [17]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 229, + 546, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 229, + 546, + 350 + ], + "spans": [ + { + "bbox": [ + 304, + 229, + 546, + 350 + ], + "type": "text", + "content": "Evaluation metrics. We use Dynamic Time Warping (DTW) [2,5], an elastic matching technique for aligning the given two sequences, to calculate the distance between the generated and real characters. Moreover, we use Content Score [44] to measure the structure correctness of generated characters, and adopt Style Score [30] to quantify the style similarity between the generated and real handwritings. We also conduct user preference studies to quantify the subjective quality of the output characters. More details are provided in Appendix A.1.1." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 352, + 546, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 352, + 546, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 352, + 546, + 616 + ], + "type": "text", + "content": "Implementation details. We set the number of the style reference to " + }, + { + "bbox": [ + 304, + 352, + 546, + 616 + ], + "type": "inline_equation", + "content": "K = 15" + }, + { + "bbox": [ + 304, + 352, + 546, + 616 + ], + "type": "text", + "content": ", and resize the reference style and content images to " + }, + { + "bbox": [ + 304, + 352, + 546, + 616 + ], + "type": "inline_equation", + "content": "64 \\times 64" + }, + { + "bbox": [ + 304, + 352, + 546, + 616 + ], + "type": "text", + "content": ". Moreover, each Transformer encoder contains 2 self-attention layers, while the Transformer decoder has 4 layers for obtaining style representations (2 for writer-wise and 2 for character-wise). Following the original Transformer [35], each Transformer layer contains the multi-head attention with " + }, + { + "bbox": [ + 304, + 352, + 546, + 616 + ], + "type": "inline_equation", + "content": "c = 512" + }, + { + "bbox": [ + 304, + 352, + 546, + 616 + ], + "type": "text", + "content": " dimensional states and 8 attention heads. Contrary to HWT [3], where " + }, + { + "bbox": [ + 304, + 352, + 546, + 616 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 304, + 352, + 546, + 616 + ], + "type": "text", + "content": " is concatenated before the Transformer encoder, we process each feature sequence " + }, + { + "bbox": [ + 304, + 352, + 546, + 616 + ], + "type": "inline_equation", + "content": "f \\in F" + }, + { + "bbox": [ + 304, + 352, + 546, + 616 + ], + "type": "text", + "content": " individually. Moreover, we apply sinusoidal positional encoding [35] to input tokens before feeding them to the Transformer encoder and decoder. For training, we first pre-train the content encoder with 138k iterations (batch size of 256) for character classification on training samples and then train the whole model with 148k iterations (batch size of 128), on a single RTX3090 GPU. The optimizer is Adam [19], with a learning rate of 0.0002 and gradient clipping of 5.0. The sampling ratio " + }, + { + "bbox": [ + 304, + 352, + 546, + 616 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 352, + 546, + 616 + ], + "type": "text", + "content": " is determined through a search over 0.25, 0.5, 0.75, 1.00, and 0.25 is chosen. Following [30], we set " + }, + { + "bbox": [ + 304, + 352, + 546, + 616 + ], + "type": "inline_equation", + "content": "\\lambda = 2" + }, + { + "bbox": [ + 304, + 352, + 546, + 616 + ], + "type": "text", + "content": ". Further implementation details are provided in Appendix A.1.2." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "Compared methods. We compare our proposed SDT with state-of-the-art online Chinese character generation methods, i.e. Drawing [40], FontRNN [31], DeepImitator [44], and WriteLikeYou [30]. To ensure a fair comparison, we re-implement Drawing and FontRNN by adding the style branch of DeepImitator [44], enabling them to achieve arbitrary stylized character generation. To adapt Write-LikeYou [30] to handle images, we update its encoder to" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "5981" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 93, + 71, + 503, + 266 + ], + "blocks": [ + { + "bbox": [ + 93, + 71, + 503, + 266 + ], + "lines": [ + { + "bbox": [ + 93, + 71, + 503, + 266 + ], + "spans": [ + { + "bbox": [ + 93, + 71, + 503, + 266 + ], + "type": "image", + "image_path": "2f29eed1b588d43801107048fc85393801f9541ccecf22d7f3a6a6c0f90c98f7.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 269, + 547, + 304 + ], + "lines": [ + { + "bbox": [ + 46, + 269, + 547, + 304 + ], + "spans": [ + { + "bbox": [ + 46, + 269, + 547, + 304 + ], + "type": "text", + "content": "Figure 6. Comparisons with the state-of-the-art methods for online Chinese handwriting generation. The red and blue boxes highlight failures of style imitation and structure preservation, respectively. WriteLi. indicates the WriteLikeYou-v2. The green boxes highlight comparisons between the fine details of targets and generated characters." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 50, + 342, + 288, + 432 + ], + "blocks": [ + { + "bbox": [ + 47, + 315, + 289, + 338 + ], + "lines": [ + { + "bbox": [ + 47, + 315, + 289, + 338 + ], + "spans": [ + { + "bbox": [ + 47, + 315, + 289, + 338 + ], + "type": "text", + "content": "Table 1. Comparisons with state-of-the-art methods on Chinese dataset. See more results of WriteLikeYou [30] in Appendix A.6." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 342, + 288, + 432 + ], + "lines": [ + { + "bbox": [ + 50, + 342, + 288, + 432 + ], + "spans": [ + { + "bbox": [ + 50, + 342, + 288, + 432 + ], + "type": "table", + "html": "
MethodStyle Score ↑Content Score ↑DTW ↓User Prefer. (%) ↑
Drawing [40]35.8378.151.18133.53
FontRNN [31]46.1492.181.04487.07
DeepImitator [44]50.6790.921.06227.99
WriteLikeYou-v1 [30]71.0993.890.983211.67
WriteLikeYou-v2 [30]72.3796.440.928913.07
SDT(Ours)94.5097.040.878956.67
", + "image_path": "338570295d02018b4580cadfff9cf26d94095395912b45f184c6c1503180bb75.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 454, + 287, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 454, + 287, + 502 + ], + "spans": [ + { + "bbox": [ + 46, + 454, + 287, + 502 + ], + "type": "text", + "content": "create two new variants: WriteLikeYou-v1 (i.e., CNN encoder [44]) and WriteLikeYou-v2 (i.e., the same CNN-Transformer encoder as our SDT), based on the released official code1. More details are available in Appendix A.1.3." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 502, + 287, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 502, + 287, + 574 + ], + "spans": [ + { + "bbox": [ + 46, + 502, + 287, + 574 + ], + "type": "text", + "content": "Quantitative comparison. Quantitative results are in Table 1, revealing that SDT outperforms other methods across all evaluation metrics. Notably, SDT surpasses the second-best method by a significant " + }, + { + "bbox": [ + 46, + 502, + 287, + 574 + ], + "type": "inline_equation", + "content": "22.13\\%" + }, + { + "bbox": [ + 46, + 502, + 287, + 574 + ], + "type": "text", + "content": " margin in Style Score, demonstrating the proposed method's exceptional style imitation performance." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 574, + 288, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 574, + 288, + 694 + ], + "spans": [ + { + "bbox": [ + 46, + 574, + 288, + 694 + ], + "type": "text", + "content": "Qualitative comparison. We visualize the generated samples of each method in Figure 6, which intuitively explains the significant superiority of SDT in the user preference study. In Figure 6, Drawing [40] generates the least satisfactory results, often producing unreadable characters. FontRNN [31] and DeepImitator [44] occasionally synthesize unpleasant stroke paddings, and WriteLikeYou [30] struggles with generating complex characters regarding style mimicry. In contrast, our method yields higher-quality results, particularly in recovering fine character details." + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 310, + 357, + 545, + 466 + ], + "blocks": [ + { + "bbox": [ + 306, + 315, + 546, + 349 + ], + "lines": [ + { + "bbox": [ + 306, + 315, + 546, + 349 + ], + "spans": [ + { + "bbox": [ + 306, + 315, + 546, + 349 + ], + "type": "text", + "content": "Table 2. Ablation study. Here, we further use FID to measure the distance between generated and real samples for each writer separately, and finally average them." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 310, + 357, + 545, + 466 + ], + "lines": [ + { + "bbox": [ + 310, + 357, + 545, + 466 + ], + "spans": [ + { + "bbox": [ + 310, + 357, + 545, + 466 + ], + "type": "table", + "html": "
writer-wisecharacter-wiseGenerated SamplesStyle Score↑FID↓DTW↓
倾朝朝85.5227.750.8941
✓倾朝朝91.3826.380.8841
✓倾朝朝90.3126.890.8803
✓✓倾朝朝94.5025.460.8789
Ground Truth倾朝朝
", + "image_path": "8c9da4d907bbd59adeb136cdcae1a731520edc8ed91854ac785cb04a8f2ebfd2.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 479, + 369, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 479, + 369, + 491 + ], + "spans": [ + { + "bbox": [ + 306, + 479, + 369, + 491 + ], + "type": "text", + "content": "4.2. Analysis" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 497, + 546, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 497, + 546, + 556 + ], + "spans": [ + { + "bbox": [ + 304, + 497, + 546, + 556 + ], + "type": "text", + "content": "In this section, we assess the impact of the two learned style features and that of the style inputs. We also analyze the effect of the sampling ratio " + }, + { + "bbox": [ + 304, + 497, + 546, + 556 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 497, + 546, + 556 + ], + "type": "text", + "content": ", and discuss the combination strategies in the Transformer decoder in Appendix A.5. Besides, we discuss failure cases in Appendix A.7." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 557, + 547, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 547, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 547, + 689 + ], + "type": "text", + "content": "Quantitative evaluation of two style representations. We ablate the effects of the two extracted style representations in Table 2. The findings include: (1) Both style representations enhance the quality of generated outcomes in all evaluation metrics, particularly in terms of Style Score, improving by " + }, + { + "bbox": [ + 304, + 557, + 547, + 689 + ], + "type": "inline_equation", + "content": "4.79\\%" + }, + { + "bbox": [ + 304, + 557, + 547, + 689 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 557, + 547, + 689 + ], + "type": "inline_equation", + "content": "5.86\\%" + }, + { + "bbox": [ + 304, + 557, + 547, + 689 + ], + "type": "text", + "content": ", respectively. (2) Combining the two style features further boosts model performance across all evaluation metrics, suggesting that the extracted styles are complementary. Moreover, the order in which the two style features are input into the Transformer decoder has no significant impact on Style Score " + }, + { + "bbox": [ + 304, + 557, + 547, + 689 + ], + "type": "inline_equation", + "content": "(93.72\\%)" + }, + { + "bbox": [ + 304, + 557, + 547, + 689 + ], + "type": "text", + "content": " vs. " + }, + { + "bbox": [ + 304, + 557, + 547, + 689 + ], + "type": "inline_equation", + "content": "94.50\\%" + }, + { + "bbox": [ + 304, + 557, + 547, + 689 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 689, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 547, + 715 + ], + "type": "text", + "content": "Qualitative comparison between two style representations. To further analyze the differences between the" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 58, + 702, + 266, + 714 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 266, + 714 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 266, + 714 + ], + "type": "text", + "content": "" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 295, + 748, + 316, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 316, + 758 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 316, + 758 + ], + "type": "text", + "content": "5982" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 72, + 71, + 518, + 189 + ], + "blocks": [ + { + "bbox": [ + 72, + 71, + 518, + 189 + ], + "lines": [ + { + "bbox": [ + 72, + 71, + 518, + 189 + ], + "spans": [ + { + "bbox": [ + 72, + 71, + 518, + 189 + ], + "type": "image", + "image_path": "a065116e58a3f204a1e13d80137c1343ffec24e4715c9902c660629daf2d3eab.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 193, + 547, + 248 + ], + "lines": [ + { + "bbox": [ + 46, + 193, + 547, + 248 + ], + "spans": [ + { + "bbox": [ + 46, + 193, + 547, + 248 + ], + "type": "text", + "content": "Figure 7. Spectrum analysis of two style representations. We provide frequency magnitude visualizations belonging to 7 writers, where the top row shows the writer-wise style while the bottom represents the character-wise one. Each spectrum map is averaged over 100 character samples written by the same person. The brighter the color, the larger the magnitude. A pixel farther from the center means a higher frequency [26]. We find that the writer-wise style representations capture more low-frequency information, while character-wise style representations capture more high-frequency information." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 70, + 262, + 263, + 423 + ], + "blocks": [ + { + "bbox": [ + 70, + 262, + 263, + 423 + ], + "lines": [ + { + "bbox": [ + 70, + 262, + 263, + 423 + ], + "spans": [ + { + "bbox": [ + 70, + 262, + 263, + 423 + ], + "type": "image", + "image_path": "acb6a5a538a7bc801c1165fcbd4619548dfba3873c38c08a9a016e7829269fe2.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 426, + 288, + 460 + ], + "lines": [ + { + "bbox": [ + 46, + 426, + 288, + 460 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 288, + 460 + ], + "type": "text", + "content": "Figure 8. The heat map of the DTW matrix. The dark diagonal indicates that the generated characters still own a higher similarity even using different " + }, + { + "bbox": [ + 46, + 426, + 288, + 460 + ], + "type": "inline_equation", + "content": "X_{s}" + }, + { + "bbox": [ + 46, + 426, + 288, + 460 + ], + "type": "text", + "content": " belonging to the same writer." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 474, + 287, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 287, + 616 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 287, + 616 + ], + "type": "text", + "content": "two styles, we resize the output patch tokens representing the two styles to feature maps, respectively, and visualize their frequency magnitudes in Figure 7. We find that character-wise style features capture more high-frequency information, whereas writer-wise features mainly focus on low-frequency information. According to [6], the high-frequency information in an image usually captures fine details while the low frequencies contain the overall part of objects. This finding supports our motivation that the writer head helps to imitate the overall style (e.g., glyph slant), while the glyph head captures the detailed style (e.g., stroke curvature), as shown in Table 2." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 617, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 288, + 713 + ], + "type": "text", + "content": "Effect of using different style inputs. As mentioned in [30], given different style inputs " + }, + { + "bbox": [ + 46, + 617, + 288, + 713 + ], + "type": "inline_equation", + "content": "X_{s}" + }, + { + "bbox": [ + 46, + 617, + 288, + 713 + ], + "type": "text", + "content": " belonging to the same writer " + }, + { + "bbox": [ + 46, + 617, + 288, + 713 + ], + "type": "inline_equation", + "content": "w_{s}" + }, + { + "bbox": [ + 46, + 617, + 288, + 713 + ], + "type": "text", + "content": ", the imitation model may generate inconsistent characters. To evaluate the effect of different style inputs, we conduct two independent experiments using different " + }, + { + "bbox": [ + 46, + 617, + 288, + 713 + ], + "type": "inline_equation", + "content": "X_{s}" + }, + { + "bbox": [ + 46, + 617, + 288, + 713 + ], + "type": "text", + "content": " based on the same model. Following [30], we use the model to generate 200 characters for each writer in the test set. We then calculate the DTW distance between corre" + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 313, + 294, + 541, + 448 + ], + "blocks": [ + { + "bbox": [ + 305, + 260, + 545, + 282 + ], + "lines": [ + { + "bbox": [ + 305, + 260, + 545, + 282 + ], + "spans": [ + { + "bbox": [ + 305, + 260, + 545, + 282 + ], + "type": "text", + "content": "Table 3. Quantitative evaluations of our SDT and competitors on Japanese, Indic, and English datasets." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 313, + 294, + 541, + 448 + ], + "lines": [ + { + "bbox": [ + 313, + 294, + 541, + 448 + ], + "spans": [ + { + "bbox": [ + 313, + 294, + 541, + 448 + ], + "type": "table", + "html": "
DatasetsMethodsContent Score↑DTW ↓
JapaneseDrawing [40]50.741.4657
DeepImitator [44]53.201.2564
WriteLikeYou-v2 [30]85.611.2066
SDT(Ours)91.311.1289
IndicDrawing [40]2.349.8230
DeepImitator [44]4.136.7421
WriteLikeYou-v2 [30]13.194.5130
SDT(Ours)97.220.7075
EnglishDrawing [40]79.141.8519
DeepImitator [44]76.531.6460
WriteLikeYou-v2 [30]84.411.6215
SDT(Ours)85.521.6048
", + "image_path": "9a3e3056066074ec4dba06a2d29ac42e4eee59dec07d4a69f0fd4807232161ab.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 471, + 545, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 471, + 545, + 567 + ], + "spans": [ + { + "bbox": [ + 304, + 471, + 545, + 567 + ], + "type": "text", + "content": "sponding characters individually and average them according to the writer index (see Appendix A.1.4 for more details) to get a DTW square matrix. The resulting DTW square matrix is visualized in Figure 8. The dark diagonal in Figure 8 suggests that the generated characters maintain a high degree of similarity even when using different " + }, + { + "bbox": [ + 304, + 471, + 545, + 567 + ], + "type": "inline_equation", + "content": "X_{s}" + }, + { + "bbox": [ + 304, + 471, + 545, + 567 + ], + "type": "text", + "content": " belonging to the same writer, demonstrating that our SDT can generate consistent results from various style inputs." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 574, + 484, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 574, + 484, + 588 + ], + "spans": [ + { + "bbox": [ + 305, + 574, + 484, + 588 + ], + "type": "text", + "content": "4.3. Applications to Other Languages" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "Japanese handwriting generation. For the Japanese handwriting generation task, we conduct experiments on TUAT HANDS [25] database (see more details in Appendix A.1.5) to evaluate the effectiveness of our method. Figure 9 (a) and Table 3 verify the effectiveness of SDT for Japanese handwriting generation. Specifically, from Table 3, we observe that our SDT outperforms all compared methods in terms of two quantitative metrics, indicating that SDT performs well in multiple languages. Furthermore, we provide additional evaluation metrics in Appendix A.8." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5983" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 75, + 71, + 521, + 264 + ], + "blocks": [ + { + "bbox": [ + 75, + 71, + 521, + 264 + ], + "lines": [ + { + "bbox": [ + 75, + 71, + 521, + 264 + ], + "spans": [ + { + "bbox": [ + 75, + 71, + 521, + 264 + ], + "type": "image", + "image_path": "a18b439f0cb77c25fe69aa0049f3d76c09a737798a8d7572f754227ade8d1505.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 51, + 269, + 541, + 282 + ], + "lines": [ + { + "bbox": [ + 51, + 269, + 541, + 282 + ], + "spans": [ + { + "bbox": [ + 51, + 269, + 541, + 282 + ], + "type": "text", + "content": "Figure 9. Comparisons with the competitors for online handwriting generation on various scripts. WriteLi. indicates WriteLikeYou-v2." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 302, + 289, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 302, + 289, + 555 + ], + "spans": [ + { + "bbox": [ + 47, + 302, + 289, + 555 + ], + "type": "text", + "content": "Indic handwriting generation. We evaluate our method on the Indic handwriting generation task based on the " + }, + { + "bbox": [ + 47, + 302, + 289, + 555 + ], + "type": "inline_equation", + "content": "\\mathrm{Tamil}^2" + }, + { + "bbox": [ + 47, + 302, + 289, + 555 + ], + "type": "text", + "content": " dataset. It is worth noting that Indic handwriting generation presents a more significant challenge, as Indic characters contain more trajectory points than Chinese, Japanese, and English scripts (i.e., 88 vs. 68, 50, 30 on average; see Appendix A.1.5 for more dataset information). We compare our method with other approaches on the official test set in terms of Content Score and Dynamic Time Warping (DTW). As shown in Table 3, we find that our SDT significantly outperforms the second-best method in terms of the two quantitative metrics, achieving an " + }, + { + "bbox": [ + 47, + 302, + 289, + 555 + ], + "type": "inline_equation", + "content": "84.03\\%" + }, + { + "bbox": [ + 47, + 302, + 289, + 555 + ], + "type": "text", + "content": " higher Content Score and a 3.8055 lower DTW. This indicates that our SDT can handle handwritten characters with a large number of points (averaging 88) and ensure the quality of synthetic samples, as illustrated in Figure 9 (b). The potential advantages of our SDT are: (1) The improved style representations extracted by our SDT prevent the collapse of generated characters. (2) Our Transformer decoder facilitates long-distance dependence between trajectory points. We provide more experimental analysis in Appendix A.9." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 565, + 288, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 565, + 288, + 687 + ], + "spans": [ + { + "bbox": [ + 47, + 565, + 288, + 687 + ], + "type": "text", + "content": "English handwriting generation. To evaluate our method in generating English handwritings, we collect all of the English samples from the symbol part of CASIA-OLHWDB(1.0-1.2) [22] and ICDAR-2013 competition database [38] (see more details in Appendix A.1.5). Similarly, we use Content Score and DTW as evaluation metrics. As shown in Figure 9 (c), we find that all methods achieve sound and comparable performance. One reason for this is that the English script contains fewer character classes and a smaller number of trajectory points (averaging 30), making" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 302, + 547, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 302, + 547, + 387 + ], + "spans": [ + { + "bbox": [ + 304, + 302, + 547, + 387 + ], + "type": "text", + "content": "their imitation easier compared to other scripts. Nevertheless, our SDT still outperforms other methods by a small margin in terms of both Content Score and DTW, as shown in Table 3. Moreover, we observe that corresponding uppercase and lowercase letters sometimes exhibit subtle inter-class differences (e.g., O vs. o), which leads our SDT to achieve a relatively low Content Score." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 396, + 379, + 409 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 396, + 379, + 409 + ], + "spans": [ + { + "bbox": [ + 305, + 396, + 379, + 409 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 416, + 547, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 416, + 547, + 622 + ], + "spans": [ + { + "bbox": [ + 304, + 416, + 547, + 622 + ], + "type": "text", + "content": "In this paper, we have proposed a novel method, named style-disentangled Transformer (SDT), to synthesize realistic and diverse online handwritings. SDT enhances imitation performance by disentangling the writer-wise and character-wise style representations from individual handwriting samples. For the writer-wise style, we group characters from the same writer and separate those from different writers, promoting SDT's ability to learn uniformity in individual handwritings. For the character-wise style, we maximize the mutual information between the distinct views of a character. Moreover, we extend SDT and introduce an offline-to-offline framework for improving the generation quality of offline Chinese handwritings. Promising results on various language scripts verify the effectiveness of our SDT. Although primarily designed for handwriting generation, SDT still holds the potential for extension to other generative tasks, such as font generation." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 634, + 547, + 708 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 634, + 547, + 708 + ], + "spans": [ + { + "bbox": [ + 304, + 634, + 547, + 708 + ], + "type": "text", + "content": "Acknowledgments This research is partially supported by NSFC (Grant No.62176093, 61673182), Key Realm R&D Program of Guangzhou (No.202206030001), Guangdong Basic and Applied Basic Research Foundation (No.2021A1515012282) and Guangdong Provincial Key Laboratory of Human Digital Twin (2022B1212010004)." + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 47, + 693, + 288, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 288, + 713 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 47, + 693, + 288, + 713 + ], + "type": "text", + "content": "http : // lipitk . sourceforge . net / datasets / familialchdata.htm" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "type": "text", + "content": "5984" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 708 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "text", + "content": "[1] Emre Aksan, Fabrizio Pece, and Otmar Hilliges. 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Pattern Recognition, 104:107080, 2020. 1, 3, 5, 6, 7" + } + ] + } + ], + "index": 16 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "5986" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/DistilPose_ Tokenized Pose Regression With Heatmap Distillation/3fcfeb96-13c3-4c6a-a012-9770732b455e_content_list.json b/2023/DistilPose_ Tokenized Pose Regression With Heatmap Distillation/3fcfeb96-13c3-4c6a-a012-9770732b455e_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..5b28ce596a964b5fe110c8b33fc5739c03979512 --- /dev/null +++ b/2023/DistilPose_ Tokenized Pose Regression With Heatmap Distillation/3fcfeb96-13c3-4c6a-a012-9770732b455e_content_list.json @@ -0,0 +1,1611 @@ +[ + { + "type": "text", + "text": "DistilPose: Tokenized Pose Regression with Heatmap Distillation", + "text_level": 1, + "bbox": [ + 157, + 161, + 811, + 182 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Suhang Ye $^{1*}$ Yingyi Zhang $^{2*}$ Jie Hu $^{1*}$ Liujuan Cao $^{1}$", + "bbox": [ + 231, + 206, + 761, + 224 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Shengchuan Zhang $^{1\\dagger}$ Lei Shen $^{2}$ Jun Wang $^{3}$ Shouhong Ding $^{2}$ Rongrong Ji $^{1}$", + "bbox": [ + 127, + 224, + 867, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1Key Laboratory of Multimedia Trusted Perception and Efficient Computing,", + "bbox": [ + 193, + 239, + 801, + 256 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Ministry of Education of China, Xiamen University, 2Tencent Youtu Lab, 3Tencent WeChat Pay Lab33", + "bbox": [ + 85, + 256, + 894, + 274 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 304, + 312, + 319 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In the field of human pose estimation, regression-based methods have been dominated in terms of speed, while heatmap-based methods are far ahead in terms of performance. How to take advantage of both schemes remains a challenging problem. In this paper, we propose a novel human pose estimation framework termed DistilPose, which bridges the gaps between heatmap-based and regression-based methods. Specifically, DistilPose maximizes the transfer of knowledge from the teacher model (heatmap-based) to the student model (regression-based) through Token-distilling Encoder (TDE) and Simulated Heatmaps. TDE aligns the feature spaces of heatmap-based and regression-based models by introducing tokenization, while Simulated Heatmaps transfer explicit guidance (distribution and confidence) from teacher heatmaps into student models. Extensive experiments show that the proposed DistilPose can significantly improve the performance of the regression-based models while maintaining efficiency. Specifically, on the MSCOCO validation dataset, DistilPose-S obtains $71.6\\%$ mAP with 5.36M parameters, 2.38 GFLOPs, and 40.2 FPS, which saves $12.95\\times$ , $7.16\\times$ computational cost and is $4.9\\times$ faster than its teacher model with only 0.9 points performance drop. Furthermore, DistilPose-L obtains $74.4\\%$ mAP on MSCOCO validation dataset, achieving a new state-of-the-art among predominant regression-based models. Code will be available at https://github.com/yshMars/DistilPose.", + "bbox": [ + 75, + 333, + 473, + 707 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 78, + 731, + 208, + 745 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "2D Human Pose Estimation (HPE) aims to detect the anatomical joints of a human in a given image to estimate the poses. HPE is typically used as a preprocessing module that participates in many downstream tasks, such as activity recognition [28, 31], human motion analysis [1], mo", + "bbox": [ + 75, + 754, + 468, + 825 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/1670b087b179fc64322c5faf3fb075b718ec6939689ef00f59fc689933cf3007.jpg", + "image_caption": [ + "Figure 1. Comparisons between the SOTA methods and the proposed DistilPose on MSCOCO val dataset. Red circles at the upper left corner denote DistilPose. DistilPose outperforms SOTA models in terms of accuracy (AP), Parameter and computational cost (GFLOPs)." + ], + "image_footnote": [], + "bbox": [ + 504, + 302, + 890, + 484 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tion capture [16], etc. Previous studies on 2D HPE can be mainly divided into two mainstreams: heatmap-based and regression-based methods. Regression-based methods have significant advantages in speed and are well-suited for mobile devices. However, the insufficient accuracy of regression models will affect the performance of downstream tasks. In contrast, heatmap-based methods can explicitly learn spatial information by estimating likelihood heatmaps, resulting in high accuracy on HPE tasks. But the estimation of likelihood heatmaps requires exceptionally high computational cost, which leads to slow preprocessing operations. Thus, how to take advantages of both heatmap-based and regression-based methods remains a challenging problem.", + "bbox": [ + 497, + 562, + 892, + 741 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "One possible way to solve the above problem is to transfer the knowledge from heatmap-based to regression-based models [8,23]. However, due to the different output spaces of regression models and heatmap models (the former is a vector, and the latter is a heatmap), transferring knowledge between heatmaps and vectors faces the following two problems: (1) The regression head usually vectorizes the feature map output by the backbone. And much spatial information will be lost through Global Average Pooling", + "bbox": [ + 497, + 742, + 892, + 866 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 127, + 49, + 200, + 85 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 252, + 48, + 791, + 87 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* Equal contribution. This work was done when Suhang Ye was an intern at Tencent Youtu Lab.", + "bbox": [ + 75, + 831, + 468, + 853 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding author: zsc_2016@xmu.edu.cn", + "bbox": [ + 102, + 853, + 383, + 865 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "2163", + "bbox": [ + 468, + 885, + 500, + 897 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "(GAP) or Flatten operation. Thus, previous work failed to transfer heatmap knowledge to regression models fully. (2) Compared to the coordinate regression, heatmaps naturally contain shape, position, and gradient information [3]. Due to the lack of explicit guidance for such information, regression-based methods are more difficult to learn the implicit relationship between features and keypoints than heatmap-based methods.", + "bbox": [ + 75, + 125, + 467, + 235 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we propose a novel human pose estimation framework, DistilPose, which learns to transfer the heatmap-based knowledge from a teacher model to a regression-based student model. DistilPose mainly includes the following two components:", + "bbox": [ + 75, + 236, + 467, + 305 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "(1) A knowledge-transferring module called Token-distilling Encoder (TDE) is designed to align the feature spaces of heatmap-based and regression-based models by introducing tokenization, which consists of a series of transformer encoders. TDE can capture the relationship between keypoints and feature maps/other keypoints [10,32]. (2) We propose to simulate heatmaps to obtain the heatmap information for regression-based students explicitly. The resulting Simulated Heatmaps provide two explicit guidelines, including each keypoint's 2D distribution and confidence. Note that the proposed Simulated Heatmaps can be inserted between any heatmap-based and regression-based methods to transfer heatmap knowledge to regression models.", + "bbox": [ + 75, + 305, + 467, + 484 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "DistilPose achieves comparable performance to heatmap-based models with less computational cost and surpasses the state-of-the-art (SOTA) regression-based methods. Specifically, on the MSCOCO validation dataset, DistilPose-S achieves $71.6\\%$ mAP with 5.36M parameters, 2.38 GFLOPs and 40.3 FPS. DistilPose-L achieves $74.4\\%$ mAP with 21.27M parameters and 10.33 GFLOPs, which outperforms its heatmap-based teacher model in performance, parameters and computational cost. In summary, DistilPose significantly reduces the computation while achieving competitive accuracy, bringing advantages from both heatmap-based and regression-based schemes. As shown in Figure 1, DistilPose outperforms previous SOTA regression-based methods, such as RLE [8] and PRTR [9] with fewer parameters and GFLOPs.", + "bbox": [ + 75, + 485, + 467, + 691 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions are summarized as follows:", + "bbox": [ + 95, + 692, + 396, + 704 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a novel human pose estimation framework, DistilPose, which is the first work to transfer knowledge between heatmap-based and regression-based models losslessly.", + "- We introduce a novel Token-distilling Encoder (TDE) to take advantage of both heatmap-based and regression-based models. With the proposed TDE, the gap between the output space of heatmaps and coordinate vectors can be facilitated in a tokenized manner.", + "- We propose Simulated Heatmaps to model explicit" + ], + "bbox": [ + 95, + 712, + 467, + 866 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "heatmap information, including 2D keypoint distributions and keypoint confidences. With the aid of Simulated Heatmaps, we can transform the regression-based HPE task into a more straightforward learning task that fully exploits local information. Simulated Heatmaps can be applied to any heatmap-based and regression-based models for transferring heatmap knowledge to regression models.", + "bbox": [ + 529, + 125, + 890, + 236 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 499, + 254, + 640, + 269 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Heatmap-based & Regression-based HPE", + "text_level": 1, + "bbox": [ + 499, + 277, + 853, + 292 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Heatmap-based pose estimation [10, 17, 21, 22, 25, 29, 30, 32] dominated the area of human pose estimation in terms of performance. Some studies [10, 17, 21, 29, 32] constructed novel networks to extract better features. While others [5, 20, 24, 33] built upon an optimization perspective trying to mitigate quantization errors. In summary, heatmap-based methods made full use of the spatial information of the feature map and obtain a preferable performance. However, efficiency is still a certain drawback of heatmap-based methods.", + "bbox": [ + 497, + 298, + 890, + 435 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "For regression-based methods, Deeppose [26] is firstly proposed to regress the joint coordinates directly. CenterNet [36] and DirectPose [23] are proposed to accomplish multi-person human pose estimation in a one-stage object detection framework, which directly regresses the joint coordinates instead of the bounding box. SPM [18] introduced the root joints to indicate different person instances and hierarchical rooted human body joints representations to better predict long-range displacements for some joints. Recently, RLE [8] introduced a flow model to capture the underlying output distribution and gets a satisfying performance. Although these methods have made great efforts to find the implicit relationship of keypoints, their performance improvement is still insufficient due to the lack of explicit guidance of heatmaps.", + "bbox": [ + 497, + 437, + 890, + 643 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Transformer in HPE", + "text_level": 1, + "bbox": [ + 499, + 650, + 694, + 665 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Transformer is proposed in [27] and achieves great success in Natural Language Processing (NLP). Recent studies in vision tasks used Transformer as an alternative backbone to CNN for its ability to capture global dependencies. In the area of 2D human pose estimation, many efforts [9, 10, 14, 15, 19, 30, 32] have been done to incorporate the Transformers. TFPose [14] first introduced Transformer to the pose estimation framework in a regression-based manner. PRTR [9] proposed a two-stage and end-to-end regression-based framework using cascade Transformers and achieves SOTA performance in regression-based methods. TransPose [32] and TokenPose [10] introduced Transformer for heatmap-based human pose estimation achieving comparable performance while being more", + "bbox": [ + 497, + 672, + 890, + 866 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "2164", + "bbox": [ + 468, + 885, + 500, + 897 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/8d8f430e799836bec0244613079a2b97917681064844cb4e7bacaf0917925b8e.jpg", + "image_caption": [ + "Figure 2. Overall architecture of DistilPose. During training, a well-trained and fixed heatmap-based teacher provides its knowledge to help the training of regression-based student with TDE and Simulated Heatmaps." + ], + "image_footnote": [], + "bbox": [ + 85, + 127, + 892, + 324 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "lightweight. In our work, we introduce the transformer module to assist in finding potential relationships between keypoints.", + "bbox": [ + 75, + 369, + 468, + 410 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Distillation in HPE", + "text_level": 1, + "bbox": [ + 77, + 419, + 258, + 432 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Knowledge Distillation (KD) is formally proposed in [4], which aims to transfer the teacher's learned knowledge to the student model. In 2D human pose estimation, FPD [34] first used knowledge distillation classically based on the Hourglass network. OKDHP [11] introduced an online pose distillation approach that distills the pose structure knowledge in a one-stage manner. ViTpose [30] also implemented a large-to-small model knowledge distillation to prove its knowledge transferability. However, all previous distillation works on human pose estimation ignore the knowledge transferring between heatmap-based and regression-based methods. In this work, for the first time, we propose a heatmap-to-regression distillation framework to take benefits from both schemes.", + "bbox": [ + 75, + 441, + 468, + 633 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 77, + 646, + 166, + 659 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we propose a distillation-based human pose estimation framework DistilPose, the overall framework of which is shown in Fig. 2. In our proposed DistilPose, the teacher is a heatmap-based model, and the student is a regression-based model. We transfer the heatmap knowledge of the teacher model to the student model during training and only use the faster student model in the inference stage. DistilPose mainly consists of two modules: Token-distilling Encoder and Simulated Heatmaps.", + "bbox": [ + 75, + 669, + 468, + 794 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Token-distilling Encoder", + "text_level": 1, + "bbox": [ + 77, + 802, + 302, + 817 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Previous works have tried to introduce the advantages of heatmap models in regression-based methods, such as heatmap pre-training [8], auxiliary heatmap loss [23], etc.", + "bbox": [ + 75, + 824, + 468, + 866 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "However, the predict-heads cannot be aligned due to the misalignment of the output space. That's why these works can only perform knowledge transfer on the backbone, which brings models limited performance improvement. According to Fig. 3(a), the heatmap-auxiliary model pays too much attention to regions other than the human body. Hence, we propose a Token-distilling Encoder (TDE) to align the output space of teacher and student by introducing tokenization. By introducing aligned tokenized features, the heatmap knowledge is transferred to the student model losslessly. Thus, the student model learns information that is more focused on the human body itself, as shown in Fig. 3(a).", + "bbox": [ + 497, + 369, + 890, + 549 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Specifically, for an input image $I$ , we divide it into several patches according to the size of $pw \\times ph$ to form a visual-token. Next, we add $K$ empty nodes as keypoints-stoken, which are concatenated with visual-token and sent to several transformer encoder layers of TDE. Inspired by LVViT [6], we align the visual-tokens and keypoints-tokens between the student and teacher models to obtain the teacher model's refined attention matrix. As shown in Fig. 3(b), the attention matrix in TDE can learn the relationship between the keypoints-tokens and the visual-tokens of the corresponding position. As for performance improvement, TDE enables our student model to achieve much higher performance than the heatmap-auxiliary training (7.8% ↑ in Fig. 3(a)).", + "bbox": [ + 497, + 551, + 892, + 745 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Simulated Heatmaps", + "text_level": 1, + "bbox": [ + 499, + 758, + 695, + 774 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Basic Distribution Simulation After the head of the student model obtained the aligned knowledge with TDE, we began to think about whether there were other ways to transfer other knowledge of the teacher model further. Existing object detection distillation pipelines give us inspiration [35]: in addition to feature distillation, the output of", + "bbox": [ + 497, + 783, + 890, + 866 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "2165", + "bbox": [ + 468, + 885, + 500, + 897 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/931cee34a98f8554135ad547f0fed27f223f5eb6e19d4de3f20d4f674080975d.jpg", + "image_caption": [ + "(a) Backbone Feature Map" + ], + "image_footnote": [], + "bbox": [ + 80, + 124, + 497, + 320 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/f2f716e9e3ac01ebf778a99a56cdf8c0d1746dcf1ef7d1343c4566b8e10de79c.jpg", + "image_caption": [ + "Input image $I$" + ], + "image_footnote": [], + "bbox": [ + 500, + 131, + 640, + 286 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/f33b37c4428aae1bcc41be5a43008df31c2557d5e83b0abe9df247a72d73b068.jpg", + "image_caption": [ + "DistilPose-S (teacher TokenPose-L)" + ], + "image_footnote": [], + "bbox": [ + 640, + 131, + 884, + 214 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/eca8448f8d4700539272a622b0034b4362f11565ed67c7eb730d1c70f093b6fa.jpg", + "image_caption": [ + "Layer1", + "Layer2", + "Layer3", + "(b) Attention Matrix" + ], + "image_footnote": [], + "bbox": [ + 645, + 229, + 880, + 298 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/3d7e2f870dfe38a0e118ea3750ce8ca80537b5971e9764e8a73f4bfdf94d49a7.jpg", + "image_caption": [ + "Figure 3. Visualization of backbone feature maps and attention matrix. (a) The first row represent backbone feature maps of direct training, heatmap-auxiliary training, and our proposed distillation training (distill TDE only and distill both TDE and Simulated Heatmaps), respectively. While the second row represent backbone feature maps of the heatmap-based method TokenPose with different backbones. It can be seen here that the full structure of DistilPose is more focused on the human body than the model distill TDE only (the former the feature map background is darker). (b) These are attention matrix between the keypoint-token of \"right-ankle\" (red dot) and visual-tokens.", + "Figure 4. Visualization of Basis distribution simulation of $k^{th}$ keypoint in Simulated Heatmaps." + ], + "image_footnote": [], + "bbox": [ + 154, + 426, + 381, + 576 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the teacher model can also be used as a soft label to further distill knowledge to the student model. Compared with the coordinate vector, the distribution with a well-defined shape and good gradient contained in the heatmap is explicit guide information, which can prompt the model to pay attention to the local information around the keypoints. Not only that, but teacher heatmaps may be closer to reality. It is because there may be erroneous annotations in ground-truth, and the teacher model can filter out these faulty parts by summarizing the knowledge during training. However, heatmaps and coordinate vectors are in different output spaces. How to introduce the distribution information on the heatmap into the space of the coordinate vector has become an urgent problem to be solved.", + "bbox": [ + 75, + 616, + 467, + 808 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For this purpose, we do the opposite and propose the concept of Simulated Heatmaps to introduce coordinate vectors into the heatmap space. We let the student model predict both the keypoint coordinates and the correspond", + "bbox": [ + 75, + 811, + 467, + 866 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "ing $\\sigma$ values, using a Gaussian distribution to build a virtual heatmap (as shown in Fig. 4). Since the heatmap of the teacher model is not necessarily a regular distribution, we predict $\\sigma_{x}$ and $\\sigma_{y}$ from the horizontal/vertical directions, respectively, to construct a heatmap closer to the actual one. The Gaussian distribution is calculated as follows:", + "bbox": [ + 497, + 423, + 890, + 505 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nf (x, y) = \\frac {1}{2 \\pi \\sigma_ {x} \\sigma_ {y}} e ^ {- \\frac {1}{2} \\left(\\frac {(x - \\mu_ {x}) ^ {2}}{\\sigma_ {x} ^ {2}} + \\frac {(y - \\mu_ {y}) ^ {2}}{\\sigma_ {y} ^ {2}}\\right)}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 554, + 516, + 890, + 549 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To align with the ground-truth of the teacher model, we ignore the constant coefficient $\\frac{1}{2\\pi\\sigma_x\\sigma_y}$ multiplied by the Gaussian distribution, and the final formula for simulating a heatmap for $k_{th}$ keypoint can be summarized as:", + "bbox": [ + 497, + 551, + 890, + 608 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nH _ {k} (x, y) = e ^ {- \\frac {1}{2} \\left(\\frac {(x - \\mu_ {x k}) ^ {2}}{\\sigma_ {x k} ^ {2}} + \\frac {(y - \\mu_ {y k}) ^ {2}}{\\sigma_ {y k} ^ {2}}\\right)}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 569, + 612, + 890, + 640 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $0 < x \\leq hW$ , $0 < y \\leq hH$ and $0 < k \\leq K$ . $hW$ and $hH$ are the width and height of the heatmap, $K$ is the total number of keypoints, and $H_{k}$ refers to the $k^{th}$ simulated heatmap. $(\\mu_{xk}, \\mu_{yk})$ is the predicted keypoints coordinate, and $(\\sigma_{xk}, \\sigma_{yk})$ is the corresponding deviation pair. In the end, we get $K$ heatmap as shown in Fig. 5.", + "bbox": [ + 497, + 644, + 890, + 726 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Confidence Distillation. In addition to distribution information, heatmaps also provide keypoint confidence, which helps filter out incorrect model predictions and is critical in industrial applications. However, our simulated heatmap defaults to 1 at the peak, which cannot be included in the calculation as a valid confidence.", + "bbox": [ + 497, + 726, + 890, + 809 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To this end, we prompt the student model to predict the confidence of keypoints $s_k$ directly. Each keypoint confidence $s_k$ corresponds to the keypoint coordinate and is constrained by the corresponding value of the coordinate on the", + "bbox": [ + 497, + 811, + 890, + 866 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "2166", + "bbox": [ + 468, + 885, + 500, + 897 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/fc1645d711a204ec86adbc71e2a077ff2095aa1e926a16d3ce456bcf75aeb427.jpg", + "image_caption": [ + "Figure 5. Visualization of Simulated Heatmaps and teacher heatmaps." + ], + "image_footnote": [], + "bbox": [ + 87, + 124, + 890, + 283 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "teacher's heatmap. The keypoint confidence $s_k$ will be accumulated in the human instance score, which is calculated as follows:", + "bbox": [ + 75, + 307, + 470, + 349 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\ns ^ {h u m a n} = s ^ {b b o x} * \\frac {\\sum_ {i = 1} ^ {K} s _ {k}}{K}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 176, + 356, + 468, + 387 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $s^{human}$ is the prediction score of the human instance, and $s^{bbox}$ refers to the confidence score given by the human detector.", + "bbox": [ + 75, + 395, + 468, + 437 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Loss Function", + "text_level": 1, + "bbox": [ + 77, + 446, + 221, + 459 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For TDE, we perform distillation for visual-tokens and keypoint-tokens, respectively, and the corresponding loss functions are:", + "bbox": [ + 75, + 467, + 468, + 508 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {K T} = M S E \\left(\\boldsymbol {K T} _ {h}, \\boldsymbol {K T} _ {r}\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 516, + 468, + 536 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {V T} = M S E \\left(\\boldsymbol {V} \\boldsymbol {T} _ {h}, \\boldsymbol {V} \\boldsymbol {T} _ {r}\\right),\n$$\n", + "text_format": "latex", + "bbox": [ + 184, + 534, + 364, + 549 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $KT \\in \\mathbb{R}^{K \\times D}$ and $VT \\in \\mathbb{R}^{P \\times D}$ refer to keypoint-tokens and visual-tokens. $P$ is the number of patches, and $D$ refers to the dimension of tokens. The subscript $h$ and $r$ refer to the heatmap-based and regression-based model accordingly. $MSE$ refers to the Mean Squared Error Loss used to measure the difference between teacher and student", + "bbox": [ + 75, + 559, + 468, + 642 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For the Simulated Heatmaps, we try to align the simulated ones to the teacher heatmaps, and the corresponding loss function is:", + "bbox": [ + 75, + 643, + 468, + 682 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {S H} = \\sum_ {i = 1} ^ {K} M S E \\left(H _ {k}, H _ {T k}\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 169, + 691, + 468, + 729 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $H_{Tk}$ indicates the $k^{th}$ teacher heatmap.", + "bbox": [ + 75, + 739, + 383, + 752 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For the peak constraint of the Simulated Heatmaps, we design the following loss function:", + "bbox": [ + 75, + 754, + 468, + 781 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {C S} = \\sum_ {i = 1} ^ {K} \\left| H _ {T k} \\left(\\left[ x _ {k} \\right], \\left[ y _ {k} \\right]\\right) - s _ {k} \\right|, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 154, + 790, + 468, + 828 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $(x_{k},y_{k}),k\\in [1,K]$ refers to student coordinate predictions. $[\\cdot ]$ indicates the round-off operation.", + "bbox": [ + 75, + 838, + 468, + 866 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In summary, we train regression-based student models simultaneously under task supervision and knowledge distillation. The overall loss function of our distillation framework is as follows:", + "bbox": [ + 497, + 307, + 890, + 362 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL = L _ {r e g} + \\alpha_ {1} L _ {K T} + \\alpha_ {2} L _ {V T} + \\alpha_ {3} L _ {S H} + \\alpha_ {4} L _ {C S}. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 509, + 372, + 890, + 388 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $L_{reg}$ is the regression task loss for human pose estimation. We use Smooth L1 Loss as $L_{reg}$ to compute the distance between predicted joints and ground-truth coordinates. Invisible keypoints will be filtered, including ground-truth coordinates or predicted coordinates outside the image. In other words, we did not use these invisible keypoints for loss calculation.", + "bbox": [ + 497, + 396, + 890, + 492 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 499, + 505, + 631, + 520 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we evaluate the proposed distillation framework on the MSCOCO dataset. What's more, we carry out a series of ablation studies to prove the effectiveness and validity of DistilPose. The implementation of our method is based on MMPose [2].", + "bbox": [ + 497, + 528, + 890, + 598 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Implementation Details", + "text_level": 1, + "bbox": [ + 499, + 605, + 715, + 619 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1.1 Datasets", + "text_level": 1, + "bbox": [ + 499, + 627, + 611, + 638 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We mainly conduct our experiments on the MSCOCO dataset [13]. The MSCOCO dataset contains over 200k images and 250k human instances. Each human instance is labeled with $K = 17$ keypoints representing a human pose. Our models are trained on MSCOCO train2017 with 57k images and evaluated on both MSCOCO val2017 and testdev2017, which contain 5k and 20k images, respectively. Furthermore, the ablation experiments are conducted on the MSCOCO val dataset. We mainly report the commonly used standard evaluation metric Average Precision(AP) as previous works done on the MSCOCO dataset.", + "bbox": [ + 497, + 648, + 890, + 800 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1.2 Training", + "text_level": 1, + "bbox": [ + 499, + 815, + 615, + 831 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We follow the top-down human pose estimation paradigm. All input images are resized into $256 \\times 192$ resolution. We", + "bbox": [ + 499, + 838, + 890, + 866 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "2167", + "bbox": [ + 468, + 885, + 500, + 897 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/e66a08a35d92ebcbf06cedc10fa9084c73f451e2fbeaa908715fad7580d3c856.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsBackboneInput SizeParam.(M)GFLOPsmAP(%)
Heatmap-based Methods
SimpleBaselines [29]ResNet-50256×19234.08.9070.4
SimpleBaselines [29]ResNet-101256×19253.012.4071.4
SimpleBaselines [29]ResNet-152256×19268.615.7072.0
HRNet [21]HRNet-W32256×19228.57.1074.4
HRNet [21]HRNet-W48256×19263.614.6075.1
TokenPose [10]stemnet256×1926.62.4072.5
TokenPose [10]HRNet-W48-stage3256×19227.511.6075.8
TransPose [32]ResNet-small256×1925.05.4071.5
TransPose [32]HRNet-Small-W48256×19217.521.8075.8
Distillation-based Methods
OKDHP [12]2-Stack HG256×19213.025.5072.8
OKDHP [12]4-Stack HG256×19224.047.0074.8
Regression-based Methods
PRTR* [9]ResNet-50256×19241.55.4563.7
PRTR [9]ResNet-50384×28841.511.0068.2
PRTR [9]ResNet-50512×38441.518.8071.0
PRTR* [9]HRNet-W32256×19257.210.2372.9
PRTR [9]HRNet-W32384×28857.221.6073.1
PRTR [9]HRNet-W32512×38457.237.8073.3
RLE [8]ResNet-50256×19223.64.0470.5
RLE* [8]HRNet-W48256×19275.615.7674.2
Poseur [15]MobileNetV2256×19211.360.571.9
Poseur [15]ResNet-50256×19233.264.675.4
DistilPose-S (Ours)stemnet256×1925.42.3871.6
DistilPose-L (Ours)HRNet-W48-stage3256×19221.310.3374.4
", + "bbox": [ + 200, + 123, + 766, + 453 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/e3d6fc10239489120ad650aa67aeee2f7d4acdc9ddfda9b21e1e20fc95d85ed9.jpg", + "table_caption": [ + "Table 1. Comparison on MSCOCO val dataset. Flip test is used on all methods. * indicates that we re-train and evaluate the models." + ], + "table_footnote": [], + "table_body": "
MethodsBackboneInput SizeAP(%)\\( AP_{50}( \\)% )\\( AP_{75}( \\)% )\\( AP_M( \\)% )\\( AP_L( \\)% )
PRTR [9]ResNet-101384×28868.889.976.964.775.8
PRTR [9]ResNet-101512×38470.690.378.566.277.7
RLE* [8]ResNet-50256×19269.890.177.567.274.3
DistilPose-S (Ours)stemnet256×19271.091.078.967.576.8
PRTR [9]HRNet-W32384×28871.790.679.667.678.4
PRTR [9]HRNet-W32512×38472.190.479.668.179.0
RLE* [8]HRNet-W48256×19273.791.481.471.178.6
DistilPose-L (Ours)HRNet-W48-stage3256×19273.791.681.170.279.6
", + "bbox": [ + 144, + 472, + 823, + 589 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Comparison on MSCOCO test-dev dataset. * indicates that we re-train and evaluate the models.", + "bbox": [ + 174, + 598, + 791, + 611 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "adopt a commonly used person detector provided by SimpleBaselines [29] with $56.4\\%$ AP for the MSCOCO val dataset and $60.9\\%$ AP for the MSCOCO test-dev dataset. All the models are trained with a batch size of 64 images per GPU, using 8 Tesla V100 GPUs. We adopt Adam as our optimizer and train the models for 300 epochs. The base learning rate is set to 1e-3, and decays to 1e-4 and 1e-5 at the $200^{th}$ and $260^{th}$ epoch, respectively. We follow the data augmentation setting in HRNet [21]. We empirically set the hyper-parameters to $\\alpha_{1} = \\alpha_{2} = 5e - 4, \\alpha_{3} = 1, \\alpha_{4} = 1e - 2$ .", + "bbox": [ + 75, + 619, + 470, + 771 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1.3 Model Setting", + "text_level": 1, + "bbox": [ + 75, + 788, + 228, + 802 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "If not specified, the teacher model we use is a heatmap-based model with a performance of $72.5\\%$ ( $75.2\\%$ if extra-post-processing [33] is used during inference) at the cost of 69.41M parameters and 17.03 GFLOPs, which adopts", + "bbox": [ + 75, + 809, + 468, + 866 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "HRNet-W48 as its backbone.", + "bbox": [ + 499, + 619, + 694, + 631 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "DistilPose-S adopts a lightweight backbone named stemnet from TokenPose [10], which is widely used to down-sample the feature map into $1/4$ input resolution quickly. Stemnet is a very shallow convolutional structure and is trained from scratch. Besides, DistilPose-L uses feature map output by HRNet-W48 [21] at the $3^{rd}$ stage, following the same setting as TokenPose-L [10].", + "bbox": [ + 497, + 633, + 890, + 730 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For the architecture configurations of TDE of DistilPose, the num of transformer layers is 12, embedding dim is 192, the num of heads is 8, and patch size $p_w \\times p_h$ is $4 \\times 3$ .", + "bbox": [ + 497, + 730, + 890, + 771 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Main Results", + "text_level": 1, + "bbox": [ + 499, + 780, + 638, + 794 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2.1 Comparison with SOTA Regression Methods", + "text_level": 1, + "bbox": [ + 499, + 802, + 865, + 815 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare the proposed DistilPose with the SOTA regression-based methods on MSCOCO val and test-dev dataset, and the experimental results are shown in Table 1.", + "bbox": [ + 497, + 824, + 890, + 866 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "2168", + "bbox": [ + 468, + 885, + 500, + 897 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/783a0df305f541d80aec9b724c55e4ecb32def5d8496c4835200fa9b672d3c11.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelRoleBackboneMethodsEx-post.AP(%)Param(M)GFLOPsFPS
TokenPose*TeacherHRNet-W48heatmapY75.269.4117.037.8
TokenPose*TeacherHRNet-W48heatmapN72.569.4117.038.2
DistilPose-SStudentstemnetregression-71.6 (0.9↓)5.36 (12.95× ↓)2.38 (7.16× ↓)40.2 (4.90× ↑)
DistilPose-LStudentHRNet-W48-s3regression-74.4 (1.9↑)21.27 (3.26× ↓)10.33 (1.65× ↓)13.7 (1.72× ↑)
", + "bbox": [ + 92, + 122, + 877, + 188 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "and Table 2, respectively. Also, a line chart is drawn for more visual comparison in Figure 1. We mainly compare our methods with PRTR [9] and RLE [8]. Since PRTR is also Transformer-based methods that achieved SOTA performance among regression-based methods, RLE still dominates regression-based methods. We further compare DistilPose with the latest regression-based SOTA method Poseur [15] in our supplementary materials.", + "bbox": [ + 75, + 244, + 468, + 355 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Specifically, DistilPose-S achieves $71.6\\%$ with 5.36M and 2.38 GFLOPs, which outperforms PRTR-Res50 by $7.9\\%$ at the same input resolution $256\\times 192$ while reducing 36.14M $(87.1\\% \\downarrow)$ parameters and 3.07 GFLOPs $(56.3\\% \\downarrow)$ . Even if PRTR adopts larger input resolutions $(384\\times 288, 512\\times 384)$ , DistilPose still performs better using $256\\times 192$ input resolution.", + "bbox": [ + 75, + 355, + 468, + 451 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Compared to non-Transformer SOTA algorithms, DistilPose exceeds RLE in performance, parameter, and computation simultaneously on MSCOCO val dataset. As shown in Table 2, we can see that DistilPose performs much better than RLE on large human instances. Since RLE is the first regression-based work with superior performance to contemporary heatmap-based methods and DistilPose outperforms RLE, we also claim that DistilPose achieves comparable performance on par with heatmap-based methods, as shown in Table 1.", + "bbox": [ + 75, + 452, + 470, + 590 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2.2 Comparison with Teacher Model", + "text_level": 1, + "bbox": [ + 75, + 609, + 361, + 623 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We conduct experiments to compare the performance of the student and teacher models in the dimension of AP, Parameter, GFLOPs, and FPS on the MSCOCO val dataset. Extra post-processing [5, 33] is always used in the heatmap-based model for the heatmap-to-coordinate transformation during inference to eliminate quantization error, significantly improving performance, but is also followed by extra test-time overhead. In this part, we remove the extra post-processing [33] for more fairly exploring the advantages and disadvantages of heatmap-based and regression-based methods. We report the results between student and teacher without extra post-processing. As shown in Table 3, DistilPose-S sacrifices $0.9\\%$ precision but dramatically improves in the reduction of parameter, computation, and test-time overhead. DistilPose-L comprehensively outperformed the heatmap-based teacher. That's because DistilPose is not only immune to quantization error", + "bbox": [ + 75, + 631, + 468, + 866 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/0f90666eb354a1e07035cf1c4111d5446681160d8543b9e4fa9820d49383e262.jpg", + "table_caption": [ + "Table 3. Comparison with Teacher Model. Ex-post. = extra post-processing, which means extra post-processing used to refine the heatmap-to-coordinate transformation during inference. We compute the multiples in comparison with non extra post-processing heatmap-based method. * indicates that we re-train and evaluate the models. And HRNet-W48-s3 is short for HRNet-W48-stage3." + ], + "table_footnote": [], + "table_body": "
DistillationSimulated HeatmapsTDEAPImprov.
LCSLSHLKTLVT
No----56.0%-
Yes✓63.2%+7.2%
✓56.4%+0.4%
✓✓64.1%+8.1%
✓67.1%+11.1%
✓61.7%+5.7%
✓✓67.5%+11.5%
✓✓✓✓71.6%+15.6%
", + "bbox": [ + 504, + 242, + 887, + 377 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4. Ablation studies for different types of knowledge distillation. All types of proposed knowledge transferring benefit the regression-based model, and the combination of all proposed knowledge transferring brings the best performance. Improv. = Improvement.", + "bbox": [ + 497, + 387, + 892, + 451 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "of heatmaps, but also maintains the structural advantages of the regression model [7]. Even if compared to the heatmap-based teacher with extra post-processing, DistilPose-L still achieves comparable performance with much less resource consumption. The experiments above demonstrate that DistilPose can aggregate heatmap and coordinate information and benefit from both schemes.", + "bbox": [ + 497, + 461, + 890, + 557 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 499, + 584, + 653, + 600 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3.1 Performance Gain from Different Parts", + "text_level": 1, + "bbox": [ + 499, + 611, + 828, + 625 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this subsection, we conduct several ablation experiments to show how each type of knowledge transfer helps the training of the regression-based student. As shown in Table 4, all types of proposed knowledge transfer benefit the regression-based model. From the perspective of knowledge levels, TDE and Simulated Heatmaps each bring an improvement of $11.5\\%$ and $8.1\\%$ , respectively. In the simulation heatmap module, the Gaussian simulation heatmaps combined with the confidence prediction can improve the contribution of the two by $0.5\\%$ . This proves that confidence predictions and Simulated Heatmaps have mutually reinforcing effects within the model. The combination of all proposed knowledge transfers brings the best performance, which significantly improves the performance by $15.6\\%$ comparing to the non-distillation regression-based student model.", + "bbox": [ + 497, + 644, + 890, + 866 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "2169", + "bbox": [ + 468, + 885, + 500, + 897 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/421d80885a67e288979d9e74eda981c6cb1e447e3f4a715392c927a72e0dac8a.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Teacher\nStudentNonestemnetHRNet-W48
stemnet56.0%63.6%71.6%
HRNet-W48-stage363.0%66.8%74.4%
", + "bbox": [ + 102, + 123, + 442, + 175 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/8cbedc326ecfeeb02c9efad8a97078ceaba7fabe804ad0d72bebaf9fb71d5b02.jpg", + "table_caption": [ + "Table 5. Ablation studies on different volumes of student and teacher, which demonstrates that regression-based student model performs better with a stronger teacher." + ], + "table_footnote": [], + "table_body": "
ModelSimulated HeatmapsRolemAPImprov.
SimpleBaseline-Teacher70.4%-
Deeppose×-52.6%-
Deeppose✓Student59.7%+ 6.9%
", + "bbox": [ + 82, + 218, + 462, + 283 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 6. Generalization on CNN-based Model. We only implement Simulated Heatmaps to transfer heatmap-level knowledge on CNN-based models and get a significant performance improvement. Improv. = Improvement.", + "bbox": [ + 75, + 287, + 468, + 338 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3.2 Better Teacher, Better Performance", + "text_level": 1, + "bbox": [ + 75, + 347, + 378, + 359 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We conduct experiments to study the performance gain between different students and teachers. As shown in Table 5, we demonstrate that the student models will perform better if they are guided by stronger teacher models. This suggests that the performance of DistilPose we report is not the upper-bound accuracy of our distillation framework but an example to illustrate validity. In practice, we could get help from previous algorithms to train a more potent teacher, which can be further used to enhance the performance of the student model. Or we can simply expand the teacher model's capacity, finding a trade-off between performance and training memory limitation to maximize the utilization of training resources and not introduce any test-time overhead during inference.", + "bbox": [ + 75, + 368, + 468, + 562 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3.3 Generalization on CNN-based Model", + "text_level": 1, + "bbox": [ + 75, + 579, + 388, + 591 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We also conduct an ablation study on a CNN-based model to show its generalizability. We adopt Deeppose [26] as the student and SimpleBaselines [29] as the teacher. Both are the most concise algorithms in regression-based and heatmap-based models, respectively. We introduce Simulated Heatmaps to transfer heatmap-level knowledge as we do in DistilPose, and ignore TDE for the CNN-based model. Both student and teacher adopt ResNet-50 as the backbone, and the experimental results in Table 6 show that Simulated Heatmaps adapted from DistilPose improve the regression-based student's performance significantly with no extra test-time overhead.", + "bbox": [ + 75, + 600, + 468, + 764 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Visualization of Confidence Scoring", + "text_level": 1, + "bbox": [ + 75, + 775, + 386, + 789 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We show that the confidence score predicted by DistilPose for each coordinate is plausible. As the examples shown in Figure 6, most of the joint predictions are in the right position, and the confidence score predictions of these joints are relatively high. However, there are also some poor", + "bbox": [ + 75, + 796, + 468, + 866 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/994c38075a8748bf2dbb980a543e7057a9876af47f32dde7359dfcb167895998.jpg", + "image_caption": [ + "Figure 6. Visualization of confidence scoring. There are 2 rows in each box, representing the type of joint and the confidence score prediction value, respectively. The box border color represents whether the predicted joint is in the correct position (green is correct while red is wrong)." + ], + "image_footnote": [], + "bbox": [ + 507, + 122, + 880, + 280 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "predictions(e.g., the predictions denoted by red box in Figure 6). Fortunately, DistilPose can predict a low confidence score for most poor predictions while keeping high confidence in the correct predictions. Thus we could filter these poor predictions simply by setting a threshold. A plausible confidence score not only enhances the performance of the pose estimator, but is significant in practical applications and downstream tasks for pose estimation.", + "bbox": [ + 497, + 353, + 890, + 465 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 499, + 477, + 616, + 491 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we proposed a novel human pose estimation framework, termed DistilPose, which includes Token-distilling Module (TDE) and Simulated Heatmaps to perform heatmap-to-regression knowledge distillation. In this way, the student regression model acquired refined heatmap knowledge at both feature and label levels, achieving a big leap in performance while maintaining efficiency. Extensive experiments were conducted on the MSCOCO dataset to demonstrate the effectiveness of our proposed DistilPose. In short, DistilPose achieved state-of-the-art performance among regression-based methods with a much lower computational cost.", + "bbox": [ + 497, + 501, + 890, + 667 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 499, + 679, + 658, + 694 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported by National Key R&D Program of China (No.2022ZD0118202), the National Science Fund for Distinguished Young Scholars (No.62025603), the National Natural Science Foundation of China (No.U21B2037, No.U22B2051, No.62176222, No.62176223, No.62176226, No.62072386, No.62072387, No.62072389, No.62002305 and No.62272401) and the Natural Science Foundation of Fujian Province of China (No.2021J01002, No.2022J06001). We thank Peng-Tao Jiang from Nankai University for the inspiration during our research.", + "bbox": [ + 497, + 701, + 890, + 853 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "2170", + "bbox": [ + 468, + 885, + 500, + 897 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 124, + 171, + 138 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Lulu Chen, Hong Wei, and James Ferryman. A survey of human motion analysis using depth imagery. Pattern Recognition Letters, 34(15):1995-2006, 2013. 1", + "[2] MMPose Contributors. Openmmlab pose estimation toolbox and benchmark. https://github.com/open-mmlab/mmpose, 2020.5", + "[3] Kerui Gu, Linlin Yang, and Angela Yao. Dive deeper into integral pose regression. In International Conference on Learning Representations, 2021. 2", + "[4] Geoffrey Hinton, Oriol Vinyals, Jeff Dean, et al. 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Objects as points. arXiv preprint arXiv:1904.07850, 2019. 2" + ], + "bbox": [ + 78, + 125, + 468, + 592 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "2172", + "bbox": [ + 468, + 885, + 500, + 897 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/DistilPose_ Tokenized Pose Regression With Heatmap Distillation/3fcfeb96-13c3-4c6a-a012-9770732b455e_model.json b/2023/DistilPose_ Tokenized Pose Regression With Heatmap Distillation/3fcfeb96-13c3-4c6a-a012-9770732b455e_model.json new file mode 100644 index 0000000000000000000000000000000000000000..d4c503b2e34f6b8325cb0429f8619c10eb21e1f0 --- /dev/null +++ b/2023/DistilPose_ Tokenized Pose Regression With Heatmap Distillation/3fcfeb96-13c3-4c6a-a012-9770732b455e_model.json @@ -0,0 +1,2101 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.129, + 0.051, + 0.201, + 0.086 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.253, + 0.049, + 0.792, + 0.088 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.159, + 0.162, + 0.812, + 0.184 + ], + "angle": 0, + "content": "DistilPose: Tokenized Pose Regression with Heatmap Distillation" + }, + { + "type": "text", + "bbox": [ + 0.233, + 0.207, + 0.762, + 0.225 + ], + "angle": 0, + "content": "Suhang Ye\\(^{1*}\\) Yingyi Zhang\\(^{2*}\\) Jie Hu\\(^{1*}\\) Liujuan Cao\\(^{1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.129, + 0.225, + 0.868, + 0.241 + ], + "angle": 0, + "content": "Shengchuan Zhang\\(^{1\\dagger}\\) Lei Shen\\(^{2}\\) Jun Wang\\(^{3}\\) Shouhong Ding\\(^{2}\\) Rongrong Ji\\(^{1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.194, + 0.241, + 0.803, + 0.257 + ], + "angle": 0, + "content": "1Key Laboratory of Multimedia Trusted Perception and Efficient Computing," + }, + { + "type": "text", + "bbox": [ + 0.087, + 0.257, + 0.895, + 0.275 + ], + "angle": 0, + "content": "Ministry of Education of China, Xiamen University, 2Tencent Youtu Lab, 3Tencent WeChat Pay Lab33" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.305, + 0.314, + 0.32 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.334, + 0.474, + 0.709 + ], + "angle": 0, + "content": "In the field of human pose estimation, regression-based methods have been dominated in terms of speed, while heatmap-based methods are far ahead in terms of performance. How to take advantage of both schemes remains a challenging problem. In this paper, we propose a novel human pose estimation framework termed DistilPose, which bridges the gaps between heatmap-based and regression-based methods. Specifically, DistilPose maximizes the transfer of knowledge from the teacher model (heatmap-based) to the student model (regression-based) through Token-distilling Encoder (TDE) and Simulated Heatmaps. TDE aligns the feature spaces of heatmap-based and regression-based models by introducing tokenization, while Simulated Heatmaps transfer explicit guidance (distribution and confidence) from teacher heatmaps into student models. Extensive experiments show that the proposed DistilPose can significantly improve the performance of the regression-based models while maintaining efficiency. Specifically, on the MSCOCO validation dataset, DistilPose-S obtains \\(71.6\\%\\) mAP with 5.36M parameters, 2.38 GFLOPs, and 40.2 FPS, which saves \\(12.95\\times\\), \\(7.16\\times\\) computational cost and is \\(4.9\\times\\) faster than its teacher model with only 0.9 points performance drop. Furthermore, DistilPose-L obtains \\(74.4\\%\\) mAP on MSCOCO validation dataset, achieving a new state-of-the-art among predominant regression-based models. Code will be available at https://github.com/yshMars/DistilPose." + }, + { + "type": "title", + "bbox": [ + 0.079, + 0.732, + 0.21, + 0.746 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.755, + 0.47, + 0.826 + ], + "angle": 0, + "content": "2D Human Pose Estimation (HPE) aims to detect the anatomical joints of a human in a given image to estimate the poses. HPE is typically used as a preprocessing module that participates in many downstream tasks, such as activity recognition [28, 31], human motion analysis [1], mo" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.304, + 0.891, + 0.485 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.494, + 0.893, + 0.558 + ], + "angle": 0, + "content": "Figure 1. Comparisons between the SOTA methods and the proposed DistilPose on MSCOCO val dataset. Red circles at the upper left corner denote DistilPose. DistilPose outperforms SOTA models in terms of accuracy (AP), Parameter and computational cost (GFLOPs)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.563, + 0.893, + 0.742 + ], + "angle": 0, + "content": "tion capture [16], etc. Previous studies on 2D HPE can be mainly divided into two mainstreams: heatmap-based and regression-based methods. Regression-based methods have significant advantages in speed and are well-suited for mobile devices. However, the insufficient accuracy of regression models will affect the performance of downstream tasks. In contrast, heatmap-based methods can explicitly learn spatial information by estimating likelihood heatmaps, resulting in high accuracy on HPE tasks. But the estimation of likelihood heatmaps requires exceptionally high computational cost, which leads to slow preprocessing operations. Thus, how to take advantages of both heatmap-based and regression-based methods remains a challenging problem." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.743, + 0.894, + 0.868 + ], + "angle": 0, + "content": "One possible way to solve the above problem is to transfer the knowledge from heatmap-based to regression-based models [8,23]. However, due to the different output spaces of regression models and heatmap models (the former is a vector, and the latter is a heatmap), transferring knowledge between heatmaps and vectors faces the following two problems: (1) The regression head usually vectorizes the feature map output by the backbone. And much spatial information will be lost through Global Average Pooling" + }, + { + "type": "page_footnote", + "bbox": [ + 0.077, + 0.832, + 0.47, + 0.854 + ], + "angle": 0, + "content": "* Equal contribution. This work was done when Suhang Ye was an intern at Tencent Youtu Lab." + }, + { + "type": "page_footnote", + "bbox": [ + 0.103, + 0.855, + 0.384, + 0.866 + ], + "angle": 0, + "content": "† Corresponding author: zsc_2016@xmu.edu.cn" + }, + { + "type": "list", + "bbox": [ + 0.077, + 0.832, + 0.47, + 0.866 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.887, + 0.502, + 0.898 + ], + "angle": 0, + "content": "2163" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.126, + 0.468, + 0.236 + ], + "angle": 0, + "content": "(GAP) or Flatten operation. Thus, previous work failed to transfer heatmap knowledge to regression models fully. (2) Compared to the coordinate regression, heatmaps naturally contain shape, position, and gradient information [3]. Due to the lack of explicit guidance for such information, regression-based methods are more difficult to learn the implicit relationship between features and keypoints than heatmap-based methods." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.237, + 0.468, + 0.306 + ], + "angle": 0, + "content": "In this paper, we propose a novel human pose estimation framework, DistilPose, which learns to transfer the heatmap-based knowledge from a teacher model to a regression-based student model. DistilPose mainly includes the following two components:" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.306, + 0.468, + 0.485 + ], + "angle": 0, + "content": "(1) A knowledge-transferring module called Token-distilling Encoder (TDE) is designed to align the feature spaces of heatmap-based and regression-based models by introducing tokenization, which consists of a series of transformer encoders. TDE can capture the relationship between keypoints and feature maps/other keypoints [10,32]. (2) We propose to simulate heatmaps to obtain the heatmap information for regression-based students explicitly. The resulting Simulated Heatmaps provide two explicit guidelines, including each keypoint's 2D distribution and confidence. Note that the proposed Simulated Heatmaps can be inserted between any heatmap-based and regression-based methods to transfer heatmap knowledge to regression models." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.486, + 0.468, + 0.692 + ], + "angle": 0, + "content": "DistilPose achieves comparable performance to heatmap-based models with less computational cost and surpasses the state-of-the-art (SOTA) regression-based methods. Specifically, on the MSCOCO validation dataset, DistilPose-S achieves \\(71.6\\%\\) mAP with 5.36M parameters, 2.38 GFLOPs and 40.3 FPS. DistilPose-L achieves \\(74.4\\%\\) mAP with 21.27M parameters and 10.33 GFLOPs, which outperforms its heatmap-based teacher model in performance, parameters and computational cost. In summary, DistilPose significantly reduces the computation while achieving competitive accuracy, bringing advantages from both heatmap-based and regression-based schemes. As shown in Figure 1, DistilPose outperforms previous SOTA regression-based methods, such as RLE [8] and PRTR [9] with fewer parameters and GFLOPs." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.693, + 0.398, + 0.705 + ], + "angle": 0, + "content": "Our contributions are summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.713, + 0.468, + 0.768 + ], + "angle": 0, + "content": "- We propose a novel human pose estimation framework, DistilPose, which is the first work to transfer knowledge between heatmap-based and regression-based models losslessly." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.776, + 0.468, + 0.844 + ], + "angle": 0, + "content": "- We introduce a novel Token-distilling Encoder (TDE) to take advantage of both heatmap-based and regression-based models. With the proposed TDE, the gap between the output space of heatmaps and coordinate vectors can be facilitated in a tokenized manner." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.853, + 0.468, + 0.867 + ], + "angle": 0, + "content": "- We propose Simulated Heatmaps to model explicit" + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.713, + 0.468, + 0.867 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.531, + 0.127, + 0.892, + 0.237 + ], + "angle": 0, + "content": "heatmap information, including 2D keypoint distributions and keypoint confidences. With the aid of Simulated Heatmaps, we can transform the regression-based HPE task into a more straightforward learning task that fully exploits local information. Simulated Heatmaps can be applied to any heatmap-based and regression-based models for transferring heatmap knowledge to regression models." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.255, + 0.642, + 0.27 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.278, + 0.855, + 0.293 + ], + "angle": 0, + "content": "2.1. Heatmap-based & Regression-based HPE" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.299, + 0.892, + 0.436 + ], + "angle": 0, + "content": "Heatmap-based pose estimation [10, 17, 21, 22, 25, 29, 30, 32] dominated the area of human pose estimation in terms of performance. Some studies [10, 17, 21, 29, 32] constructed novel networks to extract better features. While others [5, 20, 24, 33] built upon an optimization perspective trying to mitigate quantization errors. In summary, heatmap-based methods made full use of the spatial information of the feature map and obtain a preferable performance. However, efficiency is still a certain drawback of heatmap-based methods." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.438, + 0.892, + 0.644 + ], + "angle": 0, + "content": "For regression-based methods, Deeppose [26] is firstly proposed to regress the joint coordinates directly. CenterNet [36] and DirectPose [23] are proposed to accomplish multi-person human pose estimation in a one-stage object detection framework, which directly regresses the joint coordinates instead of the bounding box. SPM [18] introduced the root joints to indicate different person instances and hierarchical rooted human body joints representations to better predict long-range displacements for some joints. Recently, RLE [8] introduced a flow model to capture the underlying output distribution and gets a satisfying performance. Although these methods have made great efforts to find the implicit relationship of keypoints, their performance improvement is still insufficient due to the lack of explicit guidance of heatmaps." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.652, + 0.695, + 0.666 + ], + "angle": 0, + "content": "2.2. Transformer in HPE" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.673, + 0.892, + 0.867 + ], + "angle": 0, + "content": "Transformer is proposed in [27] and achieves great success in Natural Language Processing (NLP). Recent studies in vision tasks used Transformer as an alternative backbone to CNN for its ability to capture global dependencies. In the area of 2D human pose estimation, many efforts [9, 10, 14, 15, 19, 30, 32] have been done to incorporate the Transformers. TFPose [14] first introduced Transformer to the pose estimation framework in a regression-based manner. PRTR [9] proposed a two-stage and end-to-end regression-based framework using cascade Transformers and achieves SOTA performance in regression-based methods. TransPose [32] and TokenPose [10] introduced Transformer for heatmap-based human pose estimation achieving comparable performance while being more" + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.887, + 0.501, + 0.898 + ], + "angle": 0, + "content": "2164" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.128, + 0.894, + 0.325 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.336, + 0.893, + 0.363 + ], + "angle": 0, + "content": "Figure 2. Overall architecture of DistilPose. During training, a well-trained and fixed heatmap-based teacher provides its knowledge to help the training of regression-based student with TDE and Simulated Heatmaps." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.37, + 0.47, + 0.412 + ], + "angle": 0, + "content": "lightweight. In our work, we introduce the transformer module to assist in finding potential relationships between keypoints." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.42, + 0.26, + 0.433 + ], + "angle": 0, + "content": "2.3. Distillation in HPE" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.442, + 0.47, + 0.634 + ], + "angle": 0, + "content": "Knowledge Distillation (KD) is formally proposed in [4], which aims to transfer the teacher's learned knowledge to the student model. In 2D human pose estimation, FPD [34] first used knowledge distillation classically based on the Hourglass network. OKDHP [11] introduced an online pose distillation approach that distills the pose structure knowledge in a one-stage manner. ViTpose [30] also implemented a large-to-small model knowledge distillation to prove its knowledge transferability. However, all previous distillation works on human pose estimation ignore the knowledge transferring between heatmap-based and regression-based methods. In this work, for the first time, we propose a heatmap-to-regression distillation framework to take benefits from both schemes." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.647, + 0.168, + 0.66 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.671, + 0.469, + 0.795 + ], + "angle": 0, + "content": "In this section, we propose a distillation-based human pose estimation framework DistilPose, the overall framework of which is shown in Fig. 2. In our proposed DistilPose, the teacher is a heatmap-based model, and the student is a regression-based model. We transfer the heatmap knowledge of the teacher model to the student model during training and only use the faster student model in the inference stage. DistilPose mainly consists of two modules: Token-distilling Encoder and Simulated Heatmaps." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.804, + 0.304, + 0.818 + ], + "angle": 0, + "content": "3.1. Token-distilling Encoder" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.469, + 0.867 + ], + "angle": 0, + "content": "Previous works have tried to introduce the advantages of heatmap models in regression-based methods, such as heatmap pre-training [8], auxiliary heatmap loss [23], etc." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.37, + 0.892, + 0.55 + ], + "angle": 0, + "content": "However, the predict-heads cannot be aligned due to the misalignment of the output space. That's why these works can only perform knowledge transfer on the backbone, which brings models limited performance improvement. According to Fig. 3(a), the heatmap-auxiliary model pays too much attention to regions other than the human body. Hence, we propose a Token-distilling Encoder (TDE) to align the output space of teacher and student by introducing tokenization. By introducing aligned tokenized features, the heatmap knowledge is transferred to the student model losslessly. Thus, the student model learns information that is more focused on the human body itself, as shown in Fig. 3(a)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.552, + 0.893, + 0.746 + ], + "angle": 0, + "content": "Specifically, for an input image \\( I \\), we divide it into several patches according to the size of \\( pw \\times ph \\) to form a visual-token. Next, we add \\( K \\) empty nodes as keypoints-stoken, which are concatenated with visual-token and sent to several transformer encoder layers of TDE. Inspired by LVViT [6], we align the visual-tokens and keypoints-tokens between the student and teacher models to obtain the teacher model's refined attention matrix. As shown in Fig. 3(b), the attention matrix in TDE can learn the relationship between the keypoints-tokens and the visual-tokens of the corresponding position. As for performance improvement, TDE enables our student model to achieve much higher performance than the heatmap-auxiliary training (7.8% ↑ in Fig. 3(a))." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.76, + 0.696, + 0.775 + ], + "angle": 0, + "content": "3.2. Simulated Heatmaps" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.784, + 0.892, + 0.867 + ], + "angle": 0, + "content": "Basic Distribution Simulation After the head of the student model obtained the aligned knowledge with TDE, we began to think about whether there were other ways to transfer other knowledge of the teacher model further. Existing object detection distillation pipelines give us inspiration [35]: in addition to feature distillation, the output of" + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.887, + 0.501, + 0.898 + ], + "angle": 0, + "content": "2165" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.125, + 0.498, + 0.321 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.191, + 0.329, + 0.368, + 0.344 + ], + "angle": 0, + "content": "(a) Backbone Feature Map" + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.133, + 0.641, + 0.287 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.538, + 0.291, + 0.604, + 0.301 + ], + "angle": 0, + "content": "Input image \\(I\\)" + }, + { + "type": "image", + "bbox": [ + 0.641, + 0.133, + 0.885, + 0.215 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.691, + 0.219, + 0.838, + 0.228 + ], + "angle": 0, + "content": "DistilPose-S (teacher TokenPose-L)" + }, + { + "type": "image", + "bbox": [ + 0.646, + 0.23, + 0.882, + 0.299 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.678, + 0.3, + 0.703, + 0.309 + ], + "angle": 0, + "content": "Layer1" + }, + { + "type": "image_caption", + "bbox": [ + 0.754, + 0.3, + 0.78, + 0.308 + ], + "angle": 0, + "content": "Layer2" + }, + { + "type": "image_caption", + "bbox": [ + 0.832, + 0.3, + 0.858, + 0.308 + ], + "angle": 0, + "content": "Layer3" + }, + { + "type": "image_caption", + "bbox": [ + 0.634, + 0.329, + 0.771, + 0.343 + ], + "angle": 0, + "content": "(b) Attention Matrix" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.353, + 0.892, + 0.417 + ], + "angle": 0, + "content": "Figure 3. Visualization of backbone feature maps and attention matrix. (a) The first row represent backbone feature maps of direct training, heatmap-auxiliary training, and our proposed distillation training (distill TDE only and distill both TDE and Simulated Heatmaps), respectively. While the second row represent backbone feature maps of the heatmap-based method TokenPose with different backbones. It can be seen here that the full structure of DistilPose is more focused on the human body than the model distill TDE only (the former the feature map background is darker). (b) These are attention matrix between the keypoint-token of \"right-ankle\" (red dot) and visual-tokens." + }, + { + "type": "image", + "bbox": [ + 0.156, + 0.427, + 0.383, + 0.577 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.581, + 0.468, + 0.608 + ], + "angle": 0, + "content": "Figure 4. Visualization of Basis distribution simulation of \\( k^{th} \\) keypoint in Simulated Heatmaps." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.617, + 0.468, + 0.809 + ], + "angle": 0, + "content": "the teacher model can also be used as a soft label to further distill knowledge to the student model. Compared with the coordinate vector, the distribution with a well-defined shape and good gradient contained in the heatmap is explicit guide information, which can prompt the model to pay attention to the local information around the keypoints. Not only that, but teacher heatmaps may be closer to reality. It is because there may be erroneous annotations in ground-truth, and the teacher model can filter out these faulty parts by summarizing the knowledge during training. However, heatmaps and coordinate vectors are in different output spaces. How to introduce the distribution information on the heatmap into the space of the coordinate vector has become an urgent problem to be solved." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.812, + 0.468, + 0.867 + ], + "angle": 0, + "content": "For this purpose, we do the opposite and propose the concept of Simulated Heatmaps to introduce coordinate vectors into the heatmap space. We let the student model predict both the keypoint coordinates and the correspond" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.425, + 0.892, + 0.507 + ], + "angle": 0, + "content": "ing \\(\\sigma\\) values, using a Gaussian distribution to build a virtual heatmap (as shown in Fig. 4). Since the heatmap of the teacher model is not necessarily a regular distribution, we predict \\(\\sigma_{x}\\) and \\(\\sigma_{y}\\) from the horizontal/vertical directions, respectively, to construct a heatmap closer to the actual one. The Gaussian distribution is calculated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.555, + 0.517, + 0.891, + 0.551 + ], + "angle": 0, + "content": "\\[\nf (x, y) = \\frac {1}{2 \\pi \\sigma_ {x} \\sigma_ {y}} e ^ {- \\frac {1}{2} \\left(\\frac {(x - \\mu_ {x}) ^ {2}}{\\sigma_ {x} ^ {2}} + \\frac {(y - \\mu_ {y}) ^ {2}}{\\sigma_ {y} ^ {2}}\\right)}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.552, + 0.892, + 0.609 + ], + "angle": 0, + "content": "To align with the ground-truth of the teacher model, we ignore the constant coefficient \\(\\frac{1}{2\\pi\\sigma_x\\sigma_y}\\) multiplied by the Gaussian distribution, and the final formula for simulating a heatmap for \\(k_{th}\\) keypoint can be summarized as:" + }, + { + "type": "equation", + "bbox": [ + 0.571, + 0.613, + 0.891, + 0.641 + ], + "angle": 0, + "content": "\\[\nH _ {k} (x, y) = e ^ {- \\frac {1}{2} \\left(\\frac {(x - \\mu_ {x k}) ^ {2}}{\\sigma_ {x k} ^ {2}} + \\frac {(y - \\mu_ {y k}) ^ {2}}{\\sigma_ {y k} ^ {2}}\\right)}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.645, + 0.892, + 0.728 + ], + "angle": 0, + "content": "where \\(0 < x \\leq hW\\), \\(0 < y \\leq hH\\) and \\(0 < k \\leq K\\). \\(hW\\) and \\(hH\\) are the width and height of the heatmap, \\(K\\) is the total number of keypoints, and \\(H_{k}\\) refers to the \\(k^{th}\\) simulated heatmap. \\((\\mu_{xk}, \\mu_{yk})\\) is the predicted keypoints coordinate, and \\((\\sigma_{xk}, \\sigma_{yk})\\) is the corresponding deviation pair. In the end, we get \\(K\\) heatmap as shown in Fig. 5." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.728, + 0.892, + 0.81 + ], + "angle": 0, + "content": "Confidence Distillation. In addition to distribution information, heatmaps also provide keypoint confidence, which helps filter out incorrect model predictions and is critical in industrial applications. However, our simulated heatmap defaults to 1 at the peak, which cannot be included in the calculation as a valid confidence." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.812, + 0.892, + 0.867 + ], + "angle": 0, + "content": "To this end, we prompt the student model to predict the confidence of keypoints \\( s_k \\) directly. Each keypoint confidence \\( s_k \\) corresponds to the keypoint coordinate and is constrained by the corresponding value of the coordinate on the" + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.887, + 0.502, + 0.898 + ], + "angle": 0, + "content": "2166" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.125, + 0.891, + 0.284 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.276, + 0.288, + 0.692, + 0.301 + ], + "angle": 0, + "content": "Figure 5. Visualization of Simulated Heatmaps and teacher heatmaps." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.308, + 0.471, + 0.35 + ], + "angle": 0, + "content": "teacher's heatmap. The keypoint confidence \\( s_k \\) will be accumulated in the human instance score, which is calculated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.177, + 0.357, + 0.469, + 0.388 + ], + "angle": 0, + "content": "\\[\ns ^ {h u m a n} = s ^ {b b o x} * \\frac {\\sum_ {i = 1} ^ {K} s _ {k}}{K}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.396, + 0.47, + 0.438 + ], + "angle": 0, + "content": "where \\( s^{human} \\) is the prediction score of the human instance, and \\( s^{bbox} \\) refers to the confidence score given by the human detector." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.447, + 0.223, + 0.46 + ], + "angle": 0, + "content": "3.3. Loss Function" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.468, + 0.47, + 0.509 + ], + "angle": 0, + "content": "For TDE, we perform distillation for visual-tokens and keypoint-tokens, respectively, and the corresponding loss functions are:" + }, + { + "type": "equation", + "bbox": [ + 0.18, + 0.517, + 0.47, + 0.538 + ], + "angle": 0, + "content": "\\[\nL _ {K T} = M S E \\left(\\boldsymbol {K T} _ {h}, \\boldsymbol {K T} _ {r}\\right), \\tag {4}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.185, + 0.535, + 0.366, + 0.55 + ], + "angle": 0, + "content": "\\[\nL _ {V T} = M S E \\left(\\boldsymbol {V} \\boldsymbol {T} _ {h}, \\boldsymbol {V} \\boldsymbol {T} _ {r}\\right),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.56, + 0.47, + 0.643 + ], + "angle": 0, + "content": "where \\(KT \\in \\mathbb{R}^{K \\times D}\\) and \\(VT \\in \\mathbb{R}^{P \\times D}\\) refer to keypoint-tokens and visual-tokens. \\(P\\) is the number of patches, and \\(D\\) refers to the dimension of tokens. The subscript \\(h\\) and \\(r\\) refer to the heatmap-based and regression-based model accordingly. \\(MSE\\) refers to the Mean Squared Error Loss used to measure the difference between teacher and student" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.644, + 0.469, + 0.684 + ], + "angle": 0, + "content": "For the Simulated Heatmaps, we try to align the simulated ones to the teacher heatmaps, and the corresponding loss function is:" + }, + { + "type": "equation", + "bbox": [ + 0.171, + 0.692, + 0.469, + 0.73 + ], + "angle": 0, + "content": "\\[\nL _ {S H} = \\sum_ {i = 1} ^ {K} M S E \\left(H _ {k}, H _ {T k}\\right), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.74, + 0.384, + 0.754 + ], + "angle": 0, + "content": "where \\(H_{Tk}\\) indicates the \\(k^{th}\\) teacher heatmap." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.755, + 0.469, + 0.782 + ], + "angle": 0, + "content": "For the peak constraint of the Simulated Heatmaps, we design the following loss function:" + }, + { + "type": "equation", + "bbox": [ + 0.155, + 0.792, + 0.469, + 0.83 + ], + "angle": 0, + "content": "\\[\nL _ {C S} = \\sum_ {i = 1} ^ {K} \\left| H _ {T k} \\left(\\left[ x _ {k} \\right], \\left[ y _ {k} \\right]\\right) - s _ {k} \\right|, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.839, + 0.469, + 0.868 + ], + "angle": 0, + "content": "where \\((x_{k},y_{k}),k\\in [1,K]\\) refers to student coordinate predictions. \\([\\cdot ]\\) indicates the round-off operation." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.308, + 0.892, + 0.363 + ], + "angle": 0, + "content": "In summary, we train regression-based student models simultaneously under task supervision and knowledge distillation. The overall loss function of our distillation framework is as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.51, + 0.373, + 0.892, + 0.389 + ], + "angle": 0, + "content": "\\[\nL = L _ {r e g} + \\alpha_ {1} L _ {K T} + \\alpha_ {2} L _ {V T} + \\alpha_ {3} L _ {S H} + \\alpha_ {4} L _ {C S}. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.397, + 0.892, + 0.493 + ], + "angle": 0, + "content": "where \\( L_{reg} \\) is the regression task loss for human pose estimation. We use Smooth L1 Loss as \\( L_{reg} \\) to compute the distance between predicted joints and ground-truth coordinates. Invisible keypoints will be filtered, including ground-truth coordinates or predicted coordinates outside the image. In other words, we did not use these invisible keypoints for loss calculation." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.506, + 0.633, + 0.521 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.529, + 0.892, + 0.599 + ], + "angle": 0, + "content": "In this section, we evaluate the proposed distillation framework on the MSCOCO dataset. What's more, we carry out a series of ablation studies to prove the effectiveness and validity of DistilPose. The implementation of our method is based on MMPose [2]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.606, + 0.717, + 0.621 + ], + "angle": 0, + "content": "4.1. Implementation Details" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.628, + 0.613, + 0.64 + ], + "angle": 0, + "content": "4.1.1 Datasets" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.649, + 0.892, + 0.801 + ], + "angle": 0, + "content": "We mainly conduct our experiments on the MSCOCO dataset [13]. The MSCOCO dataset contains over 200k images and 250k human instances. Each human instance is labeled with \\( K = 17 \\) keypoints representing a human pose. Our models are trained on MSCOCO train2017 with 57k images and evaluated on both MSCOCO val2017 and testdev2017, which contain 5k and 20k images, respectively. Furthermore, the ablation experiments are conducted on the MSCOCO val dataset. We mainly report the commonly used standard evaluation metric Average Precision(AP) as previous works done on the MSCOCO dataset." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.817, + 0.616, + 0.832 + ], + "angle": 0, + "content": "4.1.2 Training" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.839, + 0.892, + 0.867 + ], + "angle": 0, + "content": "We follow the top-down human pose estimation paradigm. All input images are resized into \\(256 \\times 192\\) resolution. We" + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.887, + 0.502, + 0.898 + ], + "angle": 0, + "content": "2167" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.201, + 0.124, + 0.768, + 0.454 + ], + "angle": 0, + "content": "
MethodsBackboneInput SizeParam.(M)GFLOPsmAP(%)
Heatmap-based Methods
SimpleBaselines [29]ResNet-50256×19234.08.9070.4
SimpleBaselines [29]ResNet-101256×19253.012.4071.4
SimpleBaselines [29]ResNet-152256×19268.615.7072.0
HRNet [21]HRNet-W32256×19228.57.1074.4
HRNet [21]HRNet-W48256×19263.614.6075.1
TokenPose [10]stemnet256×1926.62.4072.5
TokenPose [10]HRNet-W48-stage3256×19227.511.6075.8
TransPose [32]ResNet-small256×1925.05.4071.5
TransPose [32]HRNet-Small-W48256×19217.521.8075.8
Distillation-based Methods
OKDHP [12]2-Stack HG256×19213.025.5072.8
OKDHP [12]4-Stack HG256×19224.047.0074.8
Regression-based Methods
PRTR* [9]ResNet-50256×19241.55.4563.7
PRTR [9]ResNet-50384×28841.511.0068.2
PRTR [9]ResNet-50512×38441.518.8071.0
PRTR* [9]HRNet-W32256×19257.210.2372.9
PRTR [9]HRNet-W32384×28857.221.6073.1
PRTR [9]HRNet-W32512×38457.237.8073.3
RLE [8]ResNet-50256×19223.64.0470.5
RLE* [8]HRNet-W48256×19275.615.7674.2
Poseur [15]MobileNetV2256×19211.360.571.9
Poseur [15]ResNet-50256×19233.264.675.4
DistilPose-S (Ours)stemnet256×1925.42.3871.6
DistilPose-L (Ours)HRNet-W48-stage3256×19221.310.3374.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.095, + 0.457, + 0.873, + 0.47 + ], + "angle": 0, + "content": "Table 1. Comparison on MSCOCO val dataset. Flip test is used on all methods. * indicates that we re-train and evaluate the models." + }, + { + "type": "table", + "bbox": [ + 0.145, + 0.473, + 0.825, + 0.59 + ], + "angle": 0, + "content": "
MethodsBackboneInput SizeAP(%)\\( AP_{50}( \\)% )\\( AP_{75}( \\)% )\\( AP_M( \\)% )\\( AP_L( \\)% )
PRTR [9]ResNet-101384×28868.889.976.964.775.8
PRTR [9]ResNet-101512×38470.690.378.566.277.7
RLE* [8]ResNet-50256×19269.890.177.567.274.3
DistilPose-S (Ours)stemnet256×19271.091.078.967.576.8
PRTR [9]HRNet-W32384×28871.790.679.667.678.4
PRTR [9]HRNet-W32512×38472.190.479.668.179.0
RLE* [8]HRNet-W48256×19273.791.481.471.178.6
DistilPose-L (Ours)HRNet-W48-stage3256×19273.791.681.170.279.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.175, + 0.599, + 0.793, + 0.612 + ], + "angle": 0, + "content": "Table 2. Comparison on MSCOCO test-dev dataset. * indicates that we re-train and evaluate the models." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.62, + 0.471, + 0.772 + ], + "angle": 0, + "content": "adopt a commonly used person detector provided by SimpleBaselines [29] with \\(56.4\\%\\) AP for the MSCOCO val dataset and \\(60.9\\%\\) AP for the MSCOCO test-dev dataset. All the models are trained with a batch size of 64 images per GPU, using 8 Tesla V100 GPUs. We adopt Adam as our optimizer and train the models for 300 epochs. The base learning rate is set to 1e-3, and decays to 1e-4 and 1e-5 at the \\(200^{th}\\) and \\(260^{th}\\) epoch, respectively. We follow the data augmentation setting in HRNet [21]. We empirically set the hyper-parameters to \\(\\alpha_{1} = \\alpha_{2} = 5e - 4, \\alpha_{3} = 1, \\alpha_{4} = 1e - 2\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.789, + 0.229, + 0.804 + ], + "angle": 0, + "content": "4.1.3 Model Setting" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.47, + 0.868 + ], + "angle": 0, + "content": "If not specified, the teacher model we use is a heatmap-based model with a performance of \\(72.5\\%\\) (\\(75.2\\%\\) if extra-post-processing [33] is used during inference) at the cost of 69.41M parameters and 17.03 GFLOPs, which adopts" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.62, + 0.695, + 0.632 + ], + "angle": 0, + "content": "HRNet-W48 as its backbone." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.634, + 0.892, + 0.731 + ], + "angle": 0, + "content": "DistilPose-S adopts a lightweight backbone named stemnet from TokenPose [10], which is widely used to down-sample the feature map into \\(1/4\\) input resolution quickly. Stemnet is a very shallow convolutional structure and is trained from scratch. Besides, DistilPose-L uses feature map output by HRNet-W48 [21] at the \\(3^{rd}\\) stage, following the same setting as TokenPose-L [10]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.731, + 0.892, + 0.773 + ], + "angle": 0, + "content": "For the architecture configurations of TDE of DistilPose, the num of transformer layers is 12, embedding dim is 192, the num of heads is 8, and patch size \\( p_w \\times p_h \\) is \\( 4 \\times 3 \\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.781, + 0.64, + 0.795 + ], + "angle": 0, + "content": "4.2. Main Results" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.803, + 0.866, + 0.817 + ], + "angle": 0, + "content": "4.2.1 Comparison with SOTA Regression Methods" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.867 + ], + "angle": 0, + "content": "We compare the proposed DistilPose with the SOTA regression-based methods on MSCOCO val and test-dev dataset, and the experimental results are shown in Table 1." + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.887, + 0.502, + 0.898 + ], + "angle": 0, + "content": "2168" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.093, + 0.123, + 0.878, + 0.19 + ], + "angle": 0, + "content": "
ModelRoleBackboneMethodsEx-post.AP(%)Param(M)GFLOPsFPS
TokenPose*TeacherHRNet-W48heatmapY75.269.4117.037.8
TokenPose*TeacherHRNet-W48heatmapN72.569.4117.038.2
DistilPose-SStudentstemnetregression-71.6 (0.9↓)5.36 (12.95× ↓)2.38 (7.16× ↓)40.2 (4.90× ↑)
DistilPose-LStudentHRNet-W48-s3regression-74.4 (1.9↑)21.27 (3.26× ↓)10.33 (1.65× ↓)13.7 (1.72× ↑)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.199, + 0.893, + 0.239 + ], + "angle": 0, + "content": "Table 3. Comparison with Teacher Model. Ex-post. = extra post-processing, which means extra post-processing used to refine the heatmap-to-coordinate transformation during inference. We compute the multiples in comparison with non extra post-processing heatmap-based method. * indicates that we re-train and evaluate the models. And HRNet-W48-s3 is short for HRNet-W48-stage3." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.245, + 0.47, + 0.356 + ], + "angle": 0, + "content": "and Table 2, respectively. Also, a line chart is drawn for more visual comparison in Figure 1. We mainly compare our methods with PRTR [9] and RLE [8]. Since PRTR is also Transformer-based methods that achieved SOTA performance among regression-based methods, RLE still dominates regression-based methods. We further compare DistilPose with the latest regression-based SOTA method Poseur [15] in our supplementary materials." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.356, + 0.47, + 0.452 + ], + "angle": 0, + "content": "Specifically, DistilPose-S achieves \\(71.6\\%\\) with 5.36M and 2.38 GFLOPs, which outperforms PRTR-Res50 by \\(7.9\\%\\) at the same input resolution \\(256\\times 192\\) while reducing 36.14M \\((87.1\\% \\downarrow)\\) parameters and 3.07 GFLOPs \\((56.3\\% \\downarrow)\\). Even if PRTR adopts larger input resolutions \\((384\\times 288, 512\\times 384)\\), DistilPose still performs better using \\(256\\times 192\\) input resolution." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.453, + 0.471, + 0.591 + ], + "angle": 0, + "content": "Compared to non-Transformer SOTA algorithms, DistilPose exceeds RLE in performance, parameter, and computation simultaneously on MSCOCO val dataset. As shown in Table 2, we can see that DistilPose performs much better than RLE on large human instances. Since RLE is the first regression-based work with superior performance to contemporary heatmap-based methods and DistilPose outperforms RLE, we also claim that DistilPose achieves comparable performance on par with heatmap-based methods, as shown in Table 1." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.61, + 0.362, + 0.624 + ], + "angle": 0, + "content": "4.2.2 Comparison with Teacher Model" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.632, + 0.47, + 0.867 + ], + "angle": 0, + "content": "We conduct experiments to compare the performance of the student and teacher models in the dimension of AP, Parameter, GFLOPs, and FPS on the MSCOCO val dataset. Extra post-processing [5, 33] is always used in the heatmap-based model for the heatmap-to-coordinate transformation during inference to eliminate quantization error, significantly improving performance, but is also followed by extra test-time overhead. In this part, we remove the extra post-processing [33] for more fairly exploring the advantages and disadvantages of heatmap-based and regression-based methods. We report the results between student and teacher without extra post-processing. As shown in Table 3, DistilPose-S sacrifices \\(0.9\\%\\) precision but dramatically improves in the reduction of parameter, computation, and test-time overhead. DistilPose-L comprehensively outperformed the heatmap-based teacher. That's because DistilPose is not only immune to quantization error" + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.243, + 0.889, + 0.378 + ], + "angle": 0, + "content": "
DistillationSimulated HeatmapsTDEAPImprov.
LCSLSHLKTLVT
No----56.0%-
Yes✓63.2%+7.2%
✓56.4%+0.4%
✓✓64.1%+8.1%
✓67.1%+11.1%
✓61.7%+5.7%
✓✓67.5%+11.5%
✓✓✓✓71.6%+15.6%
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.388, + 0.893, + 0.452 + ], + "angle": 0, + "content": "Table 4. Ablation studies for different types of knowledge distillation. All types of proposed knowledge transferring benefit the regression-based model, and the combination of all proposed knowledge transferring brings the best performance. Improv. = Improvement." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.462, + 0.892, + 0.558 + ], + "angle": 0, + "content": "of heatmaps, but also maintains the structural advantages of the regression model [7]. Even if compared to the heatmap-based teacher with extra post-processing, DistilPose-L still achieves comparable performance with much less resource consumption. The experiments above demonstrate that DistilPose can aggregate heatmap and coordinate information and benefit from both schemes." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.585, + 0.654, + 0.601 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.612, + 0.83, + 0.626 + ], + "angle": 0, + "content": "4.3.1 Performance Gain from Different Parts" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.645, + 0.892, + 0.867 + ], + "angle": 0, + "content": "In this subsection, we conduct several ablation experiments to show how each type of knowledge transfer helps the training of the regression-based student. As shown in Table 4, all types of proposed knowledge transfer benefit the regression-based model. From the perspective of knowledge levels, TDE and Simulated Heatmaps each bring an improvement of \\(11.5\\%\\) and \\(8.1\\%\\), respectively. In the simulation heatmap module, the Gaussian simulation heatmaps combined with the confidence prediction can improve the contribution of the two by \\(0.5\\%\\). This proves that confidence predictions and Simulated Heatmaps have mutually reinforcing effects within the model. The combination of all proposed knowledge transfers brings the best performance, which significantly improves the performance by \\(15.6\\%\\) comparing to the non-distillation regression-based student model." + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.887, + 0.502, + 0.898 + ], + "angle": 0, + "content": "2169" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.103, + 0.124, + 0.443, + 0.176 + ], + "angle": 0, + "content": "
Teacher\nStudentNonestemnetHRNet-W48
stemnet56.0%63.6%71.6%
HRNet-W48-stage363.0%66.8%74.4%
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.18, + 0.47, + 0.218 + ], + "angle": 0, + "content": "Table 5. Ablation studies on different volumes of student and teacher, which demonstrates that regression-based student model performs better with a stronger teacher." + }, + { + "type": "table", + "bbox": [ + 0.084, + 0.219, + 0.463, + 0.284 + ], + "angle": 0, + "content": "
ModelSimulated HeatmapsRolemAPImprov.
SimpleBaseline-Teacher70.4%-
Deeppose×-52.6%-
Deeppose✓Student59.7%+ 6.9%
" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.288, + 0.469, + 0.339 + ], + "angle": 0, + "content": "Table 6. Generalization on CNN-based Model. We only implement Simulated Heatmaps to transfer heatmap-level knowledge on CNN-based models and get a significant performance improvement. Improv. = Improvement." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.348, + 0.379, + 0.361 + ], + "angle": 0, + "content": "4.3.2 Better Teacher, Better Performance" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.369, + 0.47, + 0.563 + ], + "angle": 0, + "content": "We conduct experiments to study the performance gain between different students and teachers. As shown in Table 5, we demonstrate that the student models will perform better if they are guided by stronger teacher models. This suggests that the performance of DistilPose we report is not the upper-bound accuracy of our distillation framework but an example to illustrate validity. In practice, we could get help from previous algorithms to train a more potent teacher, which can be further used to enhance the performance of the student model. Or we can simply expand the teacher model's capacity, finding a trade-off between performance and training memory limitation to maximize the utilization of training resources and not introduce any test-time overhead during inference." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.58, + 0.389, + 0.592 + ], + "angle": 0, + "content": "4.3.3 Generalization on CNN-based Model" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.601, + 0.469, + 0.766 + ], + "angle": 0, + "content": "We also conduct an ablation study on a CNN-based model to show its generalizability. We adopt Deeppose [26] as the student and SimpleBaselines [29] as the teacher. Both are the most concise algorithms in regression-based and heatmap-based models, respectively. We introduce Simulated Heatmaps to transfer heatmap-level knowledge as we do in DistilPose, and ignore TDE for the CNN-based model. Both student and teacher adopt ResNet-50 as the backbone, and the experimental results in Table 6 show that Simulated Heatmaps adapted from DistilPose improve the regression-based student's performance significantly with no extra test-time overhead." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.776, + 0.387, + 0.79 + ], + "angle": 0, + "content": "4.4. Visualization of Confidence Scoring" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.798, + 0.469, + 0.867 + ], + "angle": 0, + "content": "We show that the confidence score predicted by DistilPose for each coordinate is plausible. As the examples shown in Figure 6, most of the joint predictions are in the right position, and the confidence score predictions of these joints are relatively high. However, there are also some poor" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.123, + 0.882, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.283, + 0.892, + 0.348 + ], + "angle": 0, + "content": "Figure 6. Visualization of confidence scoring. There are 2 rows in each box, representing the type of joint and the confidence score prediction value, respectively. The box border color represents whether the predicted joint is in the correct position (green is correct while red is wrong)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.355, + 0.892, + 0.466 + ], + "angle": 0, + "content": "predictions(e.g., the predictions denoted by red box in Figure 6). Fortunately, DistilPose can predict a low confidence score for most poor predictions while keeping high confidence in the correct predictions. Thus we could filter these poor predictions simply by setting a threshold. A plausible confidence score not only enhances the performance of the pose estimator, but is significant in practical applications and downstream tasks for pose estimation." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.478, + 0.618, + 0.492 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.502, + 0.892, + 0.668 + ], + "angle": 0, + "content": "In this work, we proposed a novel human pose estimation framework, termed DistilPose, which includes Token-distilling Module (TDE) and Simulated Heatmaps to perform heatmap-to-regression knowledge distillation. In this way, the student regression model acquired refined heatmap knowledge at both feature and label levels, achieving a big leap in performance while maintaining efficiency. Extensive experiments were conducted on the MSCOCO dataset to demonstrate the effectiveness of our proposed DistilPose. In short, DistilPose achieved state-of-the-art performance among regression-based methods with a much lower computational cost." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.68, + 0.659, + 0.695 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.703, + 0.892, + 0.854 + ], + "angle": 0, + "content": "This work was supported by National Key R&D Program of China (No.2022ZD0118202), the National Science Fund for Distinguished Young Scholars (No.62025603), the National Natural Science Foundation of China (No.U21B2037, No.U22B2051, No.62176222, No.62176223, No.62176226, No.62072386, No.62072387, No.62072389, No.62002305 and No.62272401) and the Natural Science Foundation of Fujian Province of China (No.2021J01002, No.2022J06001). 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Objects as points. arXiv preprint arXiv:1904.07850, 2019. 2" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.127, + 0.47, + 0.593 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.887, + 0.501, + 0.898 + ], + "angle": 0, + "content": "2172" + } + ] +] \ No newline at end of file diff --git a/2023/DistilPose_ Tokenized Pose Regression With Heatmap Distillation/3fcfeb96-13c3-4c6a-a012-9770732b455e_origin.pdf b/2023/DistilPose_ Tokenized Pose Regression With Heatmap Distillation/3fcfeb96-13c3-4c6a-a012-9770732b455e_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..13d5770082361525de4791619fc82569a4d92948 --- /dev/null +++ b/2023/DistilPose_ Tokenized Pose Regression With Heatmap Distillation/3fcfeb96-13c3-4c6a-a012-9770732b455e_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:bef9830c187f7d4fa6f5a340763c63f57ac3ff4a0cc7fc9289acfeb10e341f34 +size 344796 diff --git a/2023/DistilPose_ Tokenized Pose Regression With Heatmap Distillation/full.md b/2023/DistilPose_ Tokenized Pose Regression With Heatmap Distillation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..67a9de6a80281a12a8f0dea033957431da04f32c --- /dev/null +++ b/2023/DistilPose_ Tokenized Pose Regression With Heatmap Distillation/full.md @@ -0,0 +1,308 @@ +# DistilPose: Tokenized Pose Regression with Heatmap Distillation + +Suhang Ye $^{1*}$ Yingyi Zhang $^{2*}$ Jie Hu $^{1*}$ Liujuan Cao $^{1}$ + +Shengchuan Zhang $^{1\dagger}$ Lei Shen $^{2}$ Jun Wang $^{3}$ Shouhong Ding $^{2}$ Rongrong Ji $^{1}$ + +1Key Laboratory of Multimedia Trusted Perception and Efficient Computing, + +Ministry of Education of China, Xiamen University, 2Tencent Youtu Lab, 3Tencent WeChat Pay Lab33 + +# Abstract + +In the field of human pose estimation, regression-based methods have been dominated in terms of speed, while heatmap-based methods are far ahead in terms of performance. How to take advantage of both schemes remains a challenging problem. In this paper, we propose a novel human pose estimation framework termed DistilPose, which bridges the gaps between heatmap-based and regression-based methods. Specifically, DistilPose maximizes the transfer of knowledge from the teacher model (heatmap-based) to the student model (regression-based) through Token-distilling Encoder (TDE) and Simulated Heatmaps. TDE aligns the feature spaces of heatmap-based and regression-based models by introducing tokenization, while Simulated Heatmaps transfer explicit guidance (distribution and confidence) from teacher heatmaps into student models. Extensive experiments show that the proposed DistilPose can significantly improve the performance of the regression-based models while maintaining efficiency. Specifically, on the MSCOCO validation dataset, DistilPose-S obtains $71.6\%$ mAP with 5.36M parameters, 2.38 GFLOPs, and 40.2 FPS, which saves $12.95\times$ , $7.16\times$ computational cost and is $4.9\times$ faster than its teacher model with only 0.9 points performance drop. Furthermore, DistilPose-L obtains $74.4\%$ mAP on MSCOCO validation dataset, achieving a new state-of-the-art among predominant regression-based models. Code will be available at https://github.com/yshMars/DistilPose. + +# 1. Introduction + +2D Human Pose Estimation (HPE) aims to detect the anatomical joints of a human in a given image to estimate the poses. HPE is typically used as a preprocessing module that participates in many downstream tasks, such as activity recognition [28, 31], human motion analysis [1], mo + +![](images/1670b087b179fc64322c5faf3fb075b718ec6939689ef00f59fc689933cf3007.jpg) +Figure 1. Comparisons between the SOTA methods and the proposed DistilPose on MSCOCO val dataset. Red circles at the upper left corner denote DistilPose. DistilPose outperforms SOTA models in terms of accuracy (AP), Parameter and computational cost (GFLOPs). + +tion capture [16], etc. Previous studies on 2D HPE can be mainly divided into two mainstreams: heatmap-based and regression-based methods. Regression-based methods have significant advantages in speed and are well-suited for mobile devices. However, the insufficient accuracy of regression models will affect the performance of downstream tasks. In contrast, heatmap-based methods can explicitly learn spatial information by estimating likelihood heatmaps, resulting in high accuracy on HPE tasks. But the estimation of likelihood heatmaps requires exceptionally high computational cost, which leads to slow preprocessing operations. Thus, how to take advantages of both heatmap-based and regression-based methods remains a challenging problem. + +One possible way to solve the above problem is to transfer the knowledge from heatmap-based to regression-based models [8,23]. However, due to the different output spaces of regression models and heatmap models (the former is a vector, and the latter is a heatmap), transferring knowledge between heatmaps and vectors faces the following two problems: (1) The regression head usually vectorizes the feature map output by the backbone. And much spatial information will be lost through Global Average Pooling + +(GAP) or Flatten operation. Thus, previous work failed to transfer heatmap knowledge to regression models fully. (2) Compared to the coordinate regression, heatmaps naturally contain shape, position, and gradient information [3]. Due to the lack of explicit guidance for such information, regression-based methods are more difficult to learn the implicit relationship between features and keypoints than heatmap-based methods. + +In this paper, we propose a novel human pose estimation framework, DistilPose, which learns to transfer the heatmap-based knowledge from a teacher model to a regression-based student model. DistilPose mainly includes the following two components: + +(1) A knowledge-transferring module called Token-distilling Encoder (TDE) is designed to align the feature spaces of heatmap-based and regression-based models by introducing tokenization, which consists of a series of transformer encoders. TDE can capture the relationship between keypoints and feature maps/other keypoints [10,32]. (2) We propose to simulate heatmaps to obtain the heatmap information for regression-based students explicitly. The resulting Simulated Heatmaps provide two explicit guidelines, including each keypoint's 2D distribution and confidence. Note that the proposed Simulated Heatmaps can be inserted between any heatmap-based and regression-based methods to transfer heatmap knowledge to regression models. + +DistilPose achieves comparable performance to heatmap-based models with less computational cost and surpasses the state-of-the-art (SOTA) regression-based methods. Specifically, on the MSCOCO validation dataset, DistilPose-S achieves $71.6\%$ mAP with 5.36M parameters, 2.38 GFLOPs and 40.3 FPS. DistilPose-L achieves $74.4\%$ mAP with 21.27M parameters and 10.33 GFLOPs, which outperforms its heatmap-based teacher model in performance, parameters and computational cost. In summary, DistilPose significantly reduces the computation while achieving competitive accuracy, bringing advantages from both heatmap-based and regression-based schemes. As shown in Figure 1, DistilPose outperforms previous SOTA regression-based methods, such as RLE [8] and PRTR [9] with fewer parameters and GFLOPs. + +Our contributions are summarized as follows: + +- We propose a novel human pose estimation framework, DistilPose, which is the first work to transfer knowledge between heatmap-based and regression-based models losslessly. +- We introduce a novel Token-distilling Encoder (TDE) to take advantage of both heatmap-based and regression-based models. With the proposed TDE, the gap between the output space of heatmaps and coordinate vectors can be facilitated in a tokenized manner. +- We propose Simulated Heatmaps to model explicit + +heatmap information, including 2D keypoint distributions and keypoint confidences. With the aid of Simulated Heatmaps, we can transform the regression-based HPE task into a more straightforward learning task that fully exploits local information. Simulated Heatmaps can be applied to any heatmap-based and regression-based models for transferring heatmap knowledge to regression models. + +# 2. Related Work + +# 2.1. Heatmap-based & Regression-based HPE + +Heatmap-based pose estimation [10, 17, 21, 22, 25, 29, 30, 32] dominated the area of human pose estimation in terms of performance. Some studies [10, 17, 21, 29, 32] constructed novel networks to extract better features. While others [5, 20, 24, 33] built upon an optimization perspective trying to mitigate quantization errors. In summary, heatmap-based methods made full use of the spatial information of the feature map and obtain a preferable performance. However, efficiency is still a certain drawback of heatmap-based methods. + +For regression-based methods, Deeppose [26] is firstly proposed to regress the joint coordinates directly. CenterNet [36] and DirectPose [23] are proposed to accomplish multi-person human pose estimation in a one-stage object detection framework, which directly regresses the joint coordinates instead of the bounding box. SPM [18] introduced the root joints to indicate different person instances and hierarchical rooted human body joints representations to better predict long-range displacements for some joints. Recently, RLE [8] introduced a flow model to capture the underlying output distribution and gets a satisfying performance. Although these methods have made great efforts to find the implicit relationship of keypoints, their performance improvement is still insufficient due to the lack of explicit guidance of heatmaps. + +# 2.2. Transformer in HPE + +Transformer is proposed in [27] and achieves great success in Natural Language Processing (NLP). Recent studies in vision tasks used Transformer as an alternative backbone to CNN for its ability to capture global dependencies. In the area of 2D human pose estimation, many efforts [9, 10, 14, 15, 19, 30, 32] have been done to incorporate the Transformers. TFPose [14] first introduced Transformer to the pose estimation framework in a regression-based manner. PRTR [9] proposed a two-stage and end-to-end regression-based framework using cascade Transformers and achieves SOTA performance in regression-based methods. TransPose [32] and TokenPose [10] introduced Transformer for heatmap-based human pose estimation achieving comparable performance while being more + +![](images/8d8f430e799836bec0244613079a2b97917681064844cb4e7bacaf0917925b8e.jpg) +Figure 2. Overall architecture of DistilPose. During training, a well-trained and fixed heatmap-based teacher provides its knowledge to help the training of regression-based student with TDE and Simulated Heatmaps. + +lightweight. In our work, we introduce the transformer module to assist in finding potential relationships between keypoints. + +# 2.3. Distillation in HPE + +Knowledge Distillation (KD) is formally proposed in [4], which aims to transfer the teacher's learned knowledge to the student model. In 2D human pose estimation, FPD [34] first used knowledge distillation classically based on the Hourglass network. OKDHP [11] introduced an online pose distillation approach that distills the pose structure knowledge in a one-stage manner. ViTpose [30] also implemented a large-to-small model knowledge distillation to prove its knowledge transferability. However, all previous distillation works on human pose estimation ignore the knowledge transferring between heatmap-based and regression-based methods. In this work, for the first time, we propose a heatmap-to-regression distillation framework to take benefits from both schemes. + +# 3. Method + +In this section, we propose a distillation-based human pose estimation framework DistilPose, the overall framework of which is shown in Fig. 2. In our proposed DistilPose, the teacher is a heatmap-based model, and the student is a regression-based model. We transfer the heatmap knowledge of the teacher model to the student model during training and only use the faster student model in the inference stage. DistilPose mainly consists of two modules: Token-distilling Encoder and Simulated Heatmaps. + +# 3.1. Token-distilling Encoder + +Previous works have tried to introduce the advantages of heatmap models in regression-based methods, such as heatmap pre-training [8], auxiliary heatmap loss [23], etc. + +However, the predict-heads cannot be aligned due to the misalignment of the output space. That's why these works can only perform knowledge transfer on the backbone, which brings models limited performance improvement. According to Fig. 3(a), the heatmap-auxiliary model pays too much attention to regions other than the human body. Hence, we propose a Token-distilling Encoder (TDE) to align the output space of teacher and student by introducing tokenization. By introducing aligned tokenized features, the heatmap knowledge is transferred to the student model losslessly. Thus, the student model learns information that is more focused on the human body itself, as shown in Fig. 3(a). + +Specifically, for an input image $I$ , we divide it into several patches according to the size of $pw \times ph$ to form a visual-token. Next, we add $K$ empty nodes as keypoints-stoken, which are concatenated with visual-token and sent to several transformer encoder layers of TDE. Inspired by LVViT [6], we align the visual-tokens and keypoints-tokens between the student and teacher models to obtain the teacher model's refined attention matrix. As shown in Fig. 3(b), the attention matrix in TDE can learn the relationship between the keypoints-tokens and the visual-tokens of the corresponding position. As for performance improvement, TDE enables our student model to achieve much higher performance than the heatmap-auxiliary training (7.8% ↑ in Fig. 3(a)). + +# 3.2. Simulated Heatmaps + +Basic Distribution Simulation After the head of the student model obtained the aligned knowledge with TDE, we began to think about whether there were other ways to transfer other knowledge of the teacher model further. Existing object detection distillation pipelines give us inspiration [35]: in addition to feature distillation, the output of + +![](images/931cee34a98f8554135ad547f0fed27f223f5eb6e19d4de3f20d4f674080975d.jpg) +(a) Backbone Feature Map + +![](images/f2f716e9e3ac01ebf778a99a56cdf8c0d1746dcf1ef7d1343c4566b8e10de79c.jpg) +Input image $I$ + +![](images/f33b37c4428aae1bcc41be5a43008df31c2557d5e83b0abe9df247a72d73b068.jpg) +DistilPose-S (teacher TokenPose-L) + +![](images/eca8448f8d4700539272a622b0034b4362f11565ed67c7eb730d1c70f093b6fa.jpg) +Layer1 +Layer2 +Layer3 +(b) Attention Matrix + +![](images/3d7e2f870dfe38a0e118ea3750ce8ca80537b5971e9764e8a73f4bfdf94d49a7.jpg) +Figure 3. Visualization of backbone feature maps and attention matrix. (a) The first row represent backbone feature maps of direct training, heatmap-auxiliary training, and our proposed distillation training (distill TDE only and distill both TDE and Simulated Heatmaps), respectively. While the second row represent backbone feature maps of the heatmap-based method TokenPose with different backbones. It can be seen here that the full structure of DistilPose is more focused on the human body than the model distill TDE only (the former the feature map background is darker). (b) These are attention matrix between the keypoint-token of "right-ankle" (red dot) and visual-tokens. +Figure 4. Visualization of Basis distribution simulation of $k^{th}$ keypoint in Simulated Heatmaps. + +the teacher model can also be used as a soft label to further distill knowledge to the student model. Compared with the coordinate vector, the distribution with a well-defined shape and good gradient contained in the heatmap is explicit guide information, which can prompt the model to pay attention to the local information around the keypoints. Not only that, but teacher heatmaps may be closer to reality. It is because there may be erroneous annotations in ground-truth, and the teacher model can filter out these faulty parts by summarizing the knowledge during training. However, heatmaps and coordinate vectors are in different output spaces. How to introduce the distribution information on the heatmap into the space of the coordinate vector has become an urgent problem to be solved. + +For this purpose, we do the opposite and propose the concept of Simulated Heatmaps to introduce coordinate vectors into the heatmap space. We let the student model predict both the keypoint coordinates and the correspond + +ing $\sigma$ values, using a Gaussian distribution to build a virtual heatmap (as shown in Fig. 4). Since the heatmap of the teacher model is not necessarily a regular distribution, we predict $\sigma_{x}$ and $\sigma_{y}$ from the horizontal/vertical directions, respectively, to construct a heatmap closer to the actual one. The Gaussian distribution is calculated as follows: + +$$ +f (x, y) = \frac {1}{2 \pi \sigma_ {x} \sigma_ {y}} e ^ {- \frac {1}{2} \left(\frac {(x - \mu_ {x}) ^ {2}}{\sigma_ {x} ^ {2}} + \frac {(y - \mu_ {y}) ^ {2}}{\sigma_ {y} ^ {2}}\right)}, \tag {1} +$$ + +To align with the ground-truth of the teacher model, we ignore the constant coefficient $\frac{1}{2\pi\sigma_x\sigma_y}$ multiplied by the Gaussian distribution, and the final formula for simulating a heatmap for $k_{th}$ keypoint can be summarized as: + +$$ +H _ {k} (x, y) = e ^ {- \frac {1}{2} \left(\frac {(x - \mu_ {x k}) ^ {2}}{\sigma_ {x k} ^ {2}} + \frac {(y - \mu_ {y k}) ^ {2}}{\sigma_ {y k} ^ {2}}\right)}, \tag {2} +$$ + +where $0 < x \leq hW$ , $0 < y \leq hH$ and $0 < k \leq K$ . $hW$ and $hH$ are the width and height of the heatmap, $K$ is the total number of keypoints, and $H_{k}$ refers to the $k^{th}$ simulated heatmap. $(\mu_{xk}, \mu_{yk})$ is the predicted keypoints coordinate, and $(\sigma_{xk}, \sigma_{yk})$ is the corresponding deviation pair. In the end, we get $K$ heatmap as shown in Fig. 5. + +Confidence Distillation. In addition to distribution information, heatmaps also provide keypoint confidence, which helps filter out incorrect model predictions and is critical in industrial applications. However, our simulated heatmap defaults to 1 at the peak, which cannot be included in the calculation as a valid confidence. + +To this end, we prompt the student model to predict the confidence of keypoints $s_k$ directly. Each keypoint confidence $s_k$ corresponds to the keypoint coordinate and is constrained by the corresponding value of the coordinate on the + +![](images/fc1645d711a204ec86adbc71e2a077ff2095aa1e926a16d3ce456bcf75aeb427.jpg) +Figure 5. Visualization of Simulated Heatmaps and teacher heatmaps. + +teacher's heatmap. The keypoint confidence $s_k$ will be accumulated in the human instance score, which is calculated as follows: + +$$ +s ^ {h u m a n} = s ^ {b b o x} * \frac {\sum_ {i = 1} ^ {K} s _ {k}}{K}, \tag {3} +$$ + +where $s^{human}$ is the prediction score of the human instance, and $s^{bbox}$ refers to the confidence score given by the human detector. + +# 3.3. Loss Function + +For TDE, we perform distillation for visual-tokens and keypoint-tokens, respectively, and the corresponding loss functions are: + +$$ +L _ {K T} = M S E \left(\boldsymbol {K T} _ {h}, \boldsymbol {K T} _ {r}\right), \tag {4} +$$ + +$$ +L _ {V T} = M S E \left(\boldsymbol {V} \boldsymbol {T} _ {h}, \boldsymbol {V} \boldsymbol {T} _ {r}\right), +$$ + +where $KT \in \mathbb{R}^{K \times D}$ and $VT \in \mathbb{R}^{P \times D}$ refer to keypoint-tokens and visual-tokens. $P$ is the number of patches, and $D$ refers to the dimension of tokens. The subscript $h$ and $r$ refer to the heatmap-based and regression-based model accordingly. $MSE$ refers to the Mean Squared Error Loss used to measure the difference between teacher and student + +For the Simulated Heatmaps, we try to align the simulated ones to the teacher heatmaps, and the corresponding loss function is: + +$$ +L _ {S H} = \sum_ {i = 1} ^ {K} M S E \left(H _ {k}, H _ {T k}\right), \tag {5} +$$ + +where $H_{Tk}$ indicates the $k^{th}$ teacher heatmap. + +For the peak constraint of the Simulated Heatmaps, we design the following loss function: + +$$ +L _ {C S} = \sum_ {i = 1} ^ {K} \left| H _ {T k} \left(\left[ x _ {k} \right], \left[ y _ {k} \right]\right) - s _ {k} \right|, \tag {6} +$$ + +where $(x_{k},y_{k}),k\in [1,K]$ refers to student coordinate predictions. $[\cdot ]$ indicates the round-off operation. + +In summary, we train regression-based student models simultaneously under task supervision and knowledge distillation. The overall loss function of our distillation framework is as follows: + +$$ +L = L _ {r e g} + \alpha_ {1} L _ {K T} + \alpha_ {2} L _ {V T} + \alpha_ {3} L _ {S H} + \alpha_ {4} L _ {C S}. \tag {7} +$$ + +where $L_{reg}$ is the regression task loss for human pose estimation. We use Smooth L1 Loss as $L_{reg}$ to compute the distance between predicted joints and ground-truth coordinates. Invisible keypoints will be filtered, including ground-truth coordinates or predicted coordinates outside the image. In other words, we did not use these invisible keypoints for loss calculation. + +# 4. Experiments + +In this section, we evaluate the proposed distillation framework on the MSCOCO dataset. What's more, we carry out a series of ablation studies to prove the effectiveness and validity of DistilPose. The implementation of our method is based on MMPose [2]. + +# 4.1. Implementation Details + +# 4.1.1 Datasets + +We mainly conduct our experiments on the MSCOCO dataset [13]. The MSCOCO dataset contains over 200k images and 250k human instances. Each human instance is labeled with $K = 17$ keypoints representing a human pose. Our models are trained on MSCOCO train2017 with 57k images and evaluated on both MSCOCO val2017 and testdev2017, which contain 5k and 20k images, respectively. Furthermore, the ablation experiments are conducted on the MSCOCO val dataset. We mainly report the commonly used standard evaluation metric Average Precision(AP) as previous works done on the MSCOCO dataset. + +# 4.1.2 Training + +We follow the top-down human pose estimation paradigm. All input images are resized into $256 \times 192$ resolution. We + +
MethodsBackboneInput SizeParam.(M)GFLOPsmAP(%)
Heatmap-based Methods
SimpleBaselines [29]ResNet-50256×19234.08.9070.4
SimpleBaselines [29]ResNet-101256×19253.012.4071.4
SimpleBaselines [29]ResNet-152256×19268.615.7072.0
HRNet [21]HRNet-W32256×19228.57.1074.4
HRNet [21]HRNet-W48256×19263.614.6075.1
TokenPose [10]stemnet256×1926.62.4072.5
TokenPose [10]HRNet-W48-stage3256×19227.511.6075.8
TransPose [32]ResNet-small256×1925.05.4071.5
TransPose [32]HRNet-Small-W48256×19217.521.8075.8
Distillation-based Methods
OKDHP [12]2-Stack HG256×19213.025.5072.8
OKDHP [12]4-Stack HG256×19224.047.0074.8
Regression-based Methods
PRTR* [9]ResNet-50256×19241.55.4563.7
PRTR [9]ResNet-50384×28841.511.0068.2
PRTR [9]ResNet-50512×38441.518.8071.0
PRTR* [9]HRNet-W32256×19257.210.2372.9
PRTR [9]HRNet-W32384×28857.221.6073.1
PRTR [9]HRNet-W32512×38457.237.8073.3
RLE [8]ResNet-50256×19223.64.0470.5
RLE* [8]HRNet-W48256×19275.615.7674.2
Poseur [15]MobileNetV2256×19211.360.571.9
Poseur [15]ResNet-50256×19233.264.675.4
DistilPose-S (Ours)stemnet256×1925.42.3871.6
DistilPose-L (Ours)HRNet-W48-stage3256×19221.310.3374.4
+ +Table 1. Comparison on MSCOCO val dataset. Flip test is used on all methods. * indicates that we re-train and evaluate the models. + +
MethodsBackboneInput SizeAP(%)\( AP_{50}( \)% )\( AP_{75}( \)% )\( AP_M( \)% )\( AP_L( \)% )
PRTR [9]ResNet-101384×28868.889.976.964.775.8
PRTR [9]ResNet-101512×38470.690.378.566.277.7
RLE* [8]ResNet-50256×19269.890.177.567.274.3
DistilPose-S (Ours)stemnet256×19271.091.078.967.576.8
PRTR [9]HRNet-W32384×28871.790.679.667.678.4
PRTR [9]HRNet-W32512×38472.190.479.668.179.0
RLE* [8]HRNet-W48256×19273.791.481.471.178.6
DistilPose-L (Ours)HRNet-W48-stage3256×19273.791.681.170.279.6
+ +Table 2. Comparison on MSCOCO test-dev dataset. * indicates that we re-train and evaluate the models. + +adopt a commonly used person detector provided by SimpleBaselines [29] with $56.4\%$ AP for the MSCOCO val dataset and $60.9\%$ AP for the MSCOCO test-dev dataset. All the models are trained with a batch size of 64 images per GPU, using 8 Tesla V100 GPUs. We adopt Adam as our optimizer and train the models for 300 epochs. The base learning rate is set to 1e-3, and decays to 1e-4 and 1e-5 at the $200^{th}$ and $260^{th}$ epoch, respectively. We follow the data augmentation setting in HRNet [21]. We empirically set the hyper-parameters to $\alpha_{1} = \alpha_{2} = 5e - 4, \alpha_{3} = 1, \alpha_{4} = 1e - 2$ . + +# 4.1.3 Model Setting + +If not specified, the teacher model we use is a heatmap-based model with a performance of $72.5\%$ ( $75.2\%$ if extra-post-processing [33] is used during inference) at the cost of 69.41M parameters and 17.03 GFLOPs, which adopts + +HRNet-W48 as its backbone. + +DistilPose-S adopts a lightweight backbone named stemnet from TokenPose [10], which is widely used to down-sample the feature map into $1/4$ input resolution quickly. Stemnet is a very shallow convolutional structure and is trained from scratch. Besides, DistilPose-L uses feature map output by HRNet-W48 [21] at the $3^{rd}$ stage, following the same setting as TokenPose-L [10]. + +For the architecture configurations of TDE of DistilPose, the num of transformer layers is 12, embedding dim is 192, the num of heads is 8, and patch size $p_w \times p_h$ is $4 \times 3$ . + +# 4.2. Main Results + +# 4.2.1 Comparison with SOTA Regression Methods + +We compare the proposed DistilPose with the SOTA regression-based methods on MSCOCO val and test-dev dataset, and the experimental results are shown in Table 1. + +
ModelRoleBackboneMethodsEx-post.AP(%)Param(M)GFLOPsFPS
TokenPose*TeacherHRNet-W48heatmapY75.269.4117.037.8
TokenPose*TeacherHRNet-W48heatmapN72.569.4117.038.2
DistilPose-SStudentstemnetregression-71.6 (0.9↓)5.36 (12.95× ↓)2.38 (7.16× ↓)40.2 (4.90× ↑)
DistilPose-LStudentHRNet-W48-s3regression-74.4 (1.9↑)21.27 (3.26× ↓)10.33 (1.65× ↓)13.7 (1.72× ↑)
+ +and Table 2, respectively. Also, a line chart is drawn for more visual comparison in Figure 1. We mainly compare our methods with PRTR [9] and RLE [8]. Since PRTR is also Transformer-based methods that achieved SOTA performance among regression-based methods, RLE still dominates regression-based methods. We further compare DistilPose with the latest regression-based SOTA method Poseur [15] in our supplementary materials. + +Specifically, DistilPose-S achieves $71.6\%$ with 5.36M and 2.38 GFLOPs, which outperforms PRTR-Res50 by $7.9\%$ at the same input resolution $256\times 192$ while reducing 36.14M $(87.1\% \downarrow)$ parameters and 3.07 GFLOPs $(56.3\% \downarrow)$ . Even if PRTR adopts larger input resolutions $(384\times 288, 512\times 384)$ , DistilPose still performs better using $256\times 192$ input resolution. + +Compared to non-Transformer SOTA algorithms, DistilPose exceeds RLE in performance, parameter, and computation simultaneously on MSCOCO val dataset. As shown in Table 2, we can see that DistilPose performs much better than RLE on large human instances. Since RLE is the first regression-based work with superior performance to contemporary heatmap-based methods and DistilPose outperforms RLE, we also claim that DistilPose achieves comparable performance on par with heatmap-based methods, as shown in Table 1. + +# 4.2.2 Comparison with Teacher Model + +We conduct experiments to compare the performance of the student and teacher models in the dimension of AP, Parameter, GFLOPs, and FPS on the MSCOCO val dataset. Extra post-processing [5, 33] is always used in the heatmap-based model for the heatmap-to-coordinate transformation during inference to eliminate quantization error, significantly improving performance, but is also followed by extra test-time overhead. In this part, we remove the extra post-processing [33] for more fairly exploring the advantages and disadvantages of heatmap-based and regression-based methods. We report the results between student and teacher without extra post-processing. As shown in Table 3, DistilPose-S sacrifices $0.9\%$ precision but dramatically improves in the reduction of parameter, computation, and test-time overhead. DistilPose-L comprehensively outperformed the heatmap-based teacher. That's because DistilPose is not only immune to quantization error + +Table 3. Comparison with Teacher Model. Ex-post. = extra post-processing, which means extra post-processing used to refine the heatmap-to-coordinate transformation during inference. We compute the multiples in comparison with non extra post-processing heatmap-based method. * indicates that we re-train and evaluate the models. And HRNet-W48-s3 is short for HRNet-W48-stage3. + +
DistillationSimulated HeatmapsTDEAPImprov.
LCSLSHLKTLVT
No----56.0%-
Yes✓63.2%+7.2%
✓56.4%+0.4%
✓✓64.1%+8.1%
✓67.1%+11.1%
✓61.7%+5.7%
✓✓67.5%+11.5%
✓✓✓✓71.6%+15.6%
+ +Table 4. Ablation studies for different types of knowledge distillation. All types of proposed knowledge transferring benefit the regression-based model, and the combination of all proposed knowledge transferring brings the best performance. Improv. = Improvement. + +of heatmaps, but also maintains the structural advantages of the regression model [7]. Even if compared to the heatmap-based teacher with extra post-processing, DistilPose-L still achieves comparable performance with much less resource consumption. The experiments above demonstrate that DistilPose can aggregate heatmap and coordinate information and benefit from both schemes. + +# 4.3. Ablation Study + +# 4.3.1 Performance Gain from Different Parts + +In this subsection, we conduct several ablation experiments to show how each type of knowledge transfer helps the training of the regression-based student. As shown in Table 4, all types of proposed knowledge transfer benefit the regression-based model. From the perspective of knowledge levels, TDE and Simulated Heatmaps each bring an improvement of $11.5\%$ and $8.1\%$ , respectively. In the simulation heatmap module, the Gaussian simulation heatmaps combined with the confidence prediction can improve the contribution of the two by $0.5\%$ . This proves that confidence predictions and Simulated Heatmaps have mutually reinforcing effects within the model. The combination of all proposed knowledge transfers brings the best performance, which significantly improves the performance by $15.6\%$ comparing to the non-distillation regression-based student model. + +
Teacher +StudentNonestemnetHRNet-W48
stemnet56.0%63.6%71.6%
HRNet-W48-stage363.0%66.8%74.4%
+ +Table 5. Ablation studies on different volumes of student and teacher, which demonstrates that regression-based student model performs better with a stronger teacher. + +
ModelSimulated HeatmapsRolemAPImprov.
SimpleBaseline-Teacher70.4%-
Deeppose×-52.6%-
Deeppose✓Student59.7%+ 6.9%
+ +Table 6. Generalization on CNN-based Model. We only implement Simulated Heatmaps to transfer heatmap-level knowledge on CNN-based models and get a significant performance improvement. Improv. = Improvement. + +# 4.3.2 Better Teacher, Better Performance + +We conduct experiments to study the performance gain between different students and teachers. As shown in Table 5, we demonstrate that the student models will perform better if they are guided by stronger teacher models. This suggests that the performance of DistilPose we report is not the upper-bound accuracy of our distillation framework but an example to illustrate validity. In practice, we could get help from previous algorithms to train a more potent teacher, which can be further used to enhance the performance of the student model. Or we can simply expand the teacher model's capacity, finding a trade-off between performance and training memory limitation to maximize the utilization of training resources and not introduce any test-time overhead during inference. + +# 4.3.3 Generalization on CNN-based Model + +We also conduct an ablation study on a CNN-based model to show its generalizability. We adopt Deeppose [26] as the student and SimpleBaselines [29] as the teacher. Both are the most concise algorithms in regression-based and heatmap-based models, respectively. We introduce Simulated Heatmaps to transfer heatmap-level knowledge as we do in DistilPose, and ignore TDE for the CNN-based model. Both student and teacher adopt ResNet-50 as the backbone, and the experimental results in Table 6 show that Simulated Heatmaps adapted from DistilPose improve the regression-based student's performance significantly with no extra test-time overhead. + +# 4.4. Visualization of Confidence Scoring + +We show that the confidence score predicted by DistilPose for each coordinate is plausible. As the examples shown in Figure 6, most of the joint predictions are in the right position, and the confidence score predictions of these joints are relatively high. However, there are also some poor + +![](images/994c38075a8748bf2dbb980a543e7057a9876af47f32dde7359dfcb167895998.jpg) +Figure 6. Visualization of confidence scoring. There are 2 rows in each box, representing the type of joint and the confidence score prediction value, respectively. The box border color represents whether the predicted joint is in the correct position (green is correct while red is wrong). + +predictions(e.g., the predictions denoted by red box in Figure 6). Fortunately, DistilPose can predict a low confidence score for most poor predictions while keeping high confidence in the correct predictions. Thus we could filter these poor predictions simply by setting a threshold. A plausible confidence score not only enhances the performance of the pose estimator, but is significant in practical applications and downstream tasks for pose estimation. + +# 5. Conclusion + +In this work, we proposed a novel human pose estimation framework, termed DistilPose, which includes Token-distilling Module (TDE) and Simulated Heatmaps to perform heatmap-to-regression knowledge distillation. In this way, the student regression model acquired refined heatmap knowledge at both feature and label levels, achieving a big leap in performance while maintaining efficiency. Extensive experiments were conducted on the MSCOCO dataset to demonstrate the effectiveness of our proposed DistilPose. In short, DistilPose achieved state-of-the-art performance among regression-based methods with a much lower computational cost. + +# Acknowledgement + +This work was supported by National Key R&D Program of China (No.2022ZD0118202), the National Science Fund for Distinguished Young Scholars (No.62025603), the National Natural Science Foundation of China (No.U21B2037, No.U22B2051, No.62176222, No.62176223, No.62176226, No.62072386, No.62072387, No.62072389, No.62002305 and No.62272401) and the Natural Science Foundation of Fujian Province of China (No.2021J01002, No.2022J06001). We thank Peng-Tao Jiang from Nankai University for the inspiration during our research. + +# References + +[1] Lulu Chen, Hong Wei, and James Ferryman. A survey of human motion analysis using depth imagery. Pattern Recognition Letters, 34(15):1995-2006, 2013. 1 +[2] MMPose Contributors. 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Efficient object localization using convolutional networks. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 648-656, 2015. 2 +[25] Jonathan J. Tompson, Arjun Jain, Yann LeCun, and Christoph Bregler. Joint training of a convolutional network and a graphical model for human pose estimation. Advances in neural information processing systems, 27, 2014. 2 +[26] Alexander Toshev and Christian Szegedy. Deeppose: Human pose estimation via deep neural networks. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 1653-1660, 2014. 2, 8 +[27] Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Lukasz Kaiser, and Illia Polosukhin. Attention is all you need. Advances in neural information processing systems, 30, 2017. 2 + +[28] Arpita Vats and David C. Anastasiu. Key point-based driver activity recognition. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, pages 3274-3281, June 2022. 1 +[29] Bin Xiao, Haiping Wu, and Yichen Wei. Simple baselines for human pose estimation and tracking. In Proceedings of the European Conference on Computer Vision (ECCV), September 2018. 2, 6, 8 +[30] Yufei Xu, Jing Zhang, Qiming Zhang, and Dacheng Tao. Vitpose: Simple vision transformer baselines for human pose estimation. arXiv preprint arXiv:2204.12484, 2022. 2, 3 +[31] Santosh Kumar Yadav, Achleshwar Luthra, Kamlesh Tiwari, Hari Mohan Pandey, and Shaik Ali Akbar. Arfdnet: An efficient activity recognition & fall detection system using latent feature pooling. Knowledge-Based Systems, 239:107948, 2022. 1 +[32] Sen Yang, Zhibin Quan, Mu Nie, and Wankou Yang. Transpose: Keypoint localization via transformer. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 11802-11812, 2021. 2, 6 +[33] Feng Zhang, Xiatian Zhu, Hanbin Dai, Mao Ye, and Ce Zhu. Distribution-aware coordinate representation for human pose estimation. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 7093-7102, 2020. 2, 6, 7 +[34] Feng Zhang, Xiatian Zhu, and Mao Ye. Fast human pose estimation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 3517-3526, 2019. 3 +[35] Zhaohui Zheng, Rongguang Ye, Ping Wang, Dongwei Ren, Wangmeng Zuo, Qibin Hou, and Ming-Ming Cheng. Localization distillation for dense object detection. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 9407-9416, 2022. 3 +[36] Xingyi Zhou, Dequan Wang, and Philipp Krahenbuhl. Objects as points. arXiv preprint arXiv:1904.07850, 2019. 2 \ No newline at end of file diff --git a/2023/DistilPose_ Tokenized Pose Regression With Heatmap Distillation/images.zip b/2023/DistilPose_ Tokenized Pose Regression With Heatmap Distillation/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..d1da07b8d6c049d5f4185e916aa96be6a6e5235a --- /dev/null +++ b/2023/DistilPose_ Tokenized Pose Regression With Heatmap Distillation/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:28eecf1b38a00b9df1310a676764c9ed18f4c0a482675814e2a40a9846d7bb44 +size 552972 diff --git a/2023/DistilPose_ Tokenized Pose Regression With Heatmap Distillation/layout.json b/2023/DistilPose_ Tokenized Pose Regression With Heatmap Distillation/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..570171e8a09444287738e5996b3c74d405d78309 --- /dev/null +++ b/2023/DistilPose_ Tokenized Pose Regression With Heatmap Distillation/layout.json @@ -0,0 +1,8008 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 94, + 136, + 483, + 154 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 136, + 483, + 154 + ], + "spans": [ + { + "bbox": [ + 94, + 136, + 483, + 154 + ], + "type": "text", + "content": "DistilPose: Tokenized Pose Regression with Heatmap Distillation" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 138, + 174, + 453, + 189 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 138, + 174, + 453, + 189 + ], + "spans": [ + { + "bbox": [ + 138, + 174, + 453, + 189 + ], + "type": "text", + "content": "Suhang Ye" + }, + { + "bbox": [ + 138, + 174, + 453, + 189 + ], + "type": "inline_equation", + "content": "^{1*}" + }, + { + "bbox": [ + 138, + 174, + 453, + 189 + ], + "type": "text", + "content": " Yingyi Zhang" + }, + { + "bbox": [ + 138, + 174, + 453, + 189 + ], + "type": "inline_equation", + "content": "^{2*}" + }, + { + "bbox": [ + 138, + 174, + 453, + 189 + ], + "type": "text", + "content": " Jie Hu" + }, + { + "bbox": [ + 138, + 174, + 453, + 189 + ], + "type": "inline_equation", + "content": "^{1*}" + }, + { + "bbox": [ + 138, + 174, + 453, + 189 + ], + "type": "text", + "content": " Liujuan Cao" + }, + { + "bbox": [ + 138, + 174, + 453, + 189 + ], + "type": "inline_equation", + "content": "^{1}" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 76, + 189, + 516, + 202 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 76, + 189, + 516, + 202 + ], + "spans": [ + { + "bbox": [ + 76, + 189, + 516, + 202 + ], + "type": "text", + "content": "Shengchuan Zhang" + }, + { + "bbox": [ + 76, + 189, + 516, + 202 + ], + "type": "inline_equation", + "content": "^{1\\dagger}" + }, + { + "bbox": [ + 76, + 189, + 516, + 202 + ], + "type": "text", + "content": " Lei Shen" + }, + { + "bbox": [ + 76, + 189, + 516, + 202 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 76, + 189, + 516, + 202 + ], + "type": "text", + "content": " Jun Wang" + }, + { + "bbox": [ + 76, + 189, + 516, + 202 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 76, + 189, + 516, + 202 + ], + "type": "text", + "content": " Shouhong Ding" + }, + { + "bbox": [ + 76, + 189, + 516, + 202 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 76, + 189, + 516, + 202 + ], + "type": "text", + "content": " Rongrong Ji" + }, + { + "bbox": [ + 76, + 189, + 516, + 202 + ], + "type": "inline_equation", + "content": "^{1}" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 115, + 202, + 477, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 202, + 477, + 216 + ], + "spans": [ + { + "bbox": [ + 115, + 202, + 477, + 216 + ], + "type": "text", + "content": "1Key Laboratory of Multimedia Trusted Perception and Efficient Computing," + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 51, + 216, + 532, + 231 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 216, + 532, + 231 + ], + "spans": [ + { + "bbox": [ + 51, + 216, + 532, + 231 + ], + "type": "text", + "content": "Ministry of Education of China, Xiamen University, 2Tencent Youtu Lab, 3Tencent WeChat Pay Lab33" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 139, + 256, + 186, + 269 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 139, + 256, + 186, + 269 + ], + "spans": [ + { + "bbox": [ + 139, + 256, + 186, + 269 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 281, + 282, + 596 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 281, + 282, + 596 + ], + "spans": [ + { + "bbox": [ + 45, + 281, + 282, + 596 + ], + "type": "text", + "content": "In the field of human pose estimation, regression-based methods have been dominated in terms of speed, while heatmap-based methods are far ahead in terms of performance. How to take advantage of both schemes remains a challenging problem. In this paper, we propose a novel human pose estimation framework termed DistilPose, which bridges the gaps between heatmap-based and regression-based methods. Specifically, DistilPose maximizes the transfer of knowledge from the teacher model (heatmap-based) to the student model (regression-based) through Token-distilling Encoder (TDE) and Simulated Heatmaps. TDE aligns the feature spaces of heatmap-based and regression-based models by introducing tokenization, while Simulated Heatmaps transfer explicit guidance (distribution and confidence) from teacher heatmaps into student models. Extensive experiments show that the proposed DistilPose can significantly improve the performance of the regression-based models while maintaining efficiency. Specifically, on the MSCOCO validation dataset, DistilPose-S obtains " + }, + { + "bbox": [ + 45, + 281, + 282, + 596 + ], + "type": "inline_equation", + "content": "71.6\\%" + }, + { + "bbox": [ + 45, + 281, + 282, + 596 + ], + "type": "text", + "content": " mAP with 5.36M parameters, 2.38 GFLOPs, and 40.2 FPS, which saves " + }, + { + "bbox": [ + 45, + 281, + 282, + 596 + ], + "type": "inline_equation", + "content": "12.95\\times" + }, + { + "bbox": [ + 45, + 281, + 282, + 596 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 45, + 281, + 282, + 596 + ], + "type": "inline_equation", + "content": "7.16\\times" + }, + { + "bbox": [ + 45, + 281, + 282, + 596 + ], + "type": "text", + "content": " computational cost and is " + }, + { + "bbox": [ + 45, + 281, + 282, + 596 + ], + "type": "inline_equation", + "content": "4.9\\times" + }, + { + "bbox": [ + 45, + 281, + 282, + 596 + ], + "type": "text", + "content": " faster than its teacher model with only 0.9 points performance drop. Furthermore, DistilPose-L obtains " + }, + { + "bbox": [ + 45, + 281, + 282, + 596 + ], + "type": "inline_equation", + "content": "74.4\\%" + }, + { + "bbox": [ + 45, + 281, + 282, + 596 + ], + "type": "text", + "content": " mAP on MSCOCO validation dataset, achieving a new state-of-the-art among predominant regression-based models. Code will be available at https://github.com/yshMars/DistilPose." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 616, + 124, + 628 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 616, + 124, + 628 + ], + "spans": [ + { + "bbox": [ + 47, + 616, + 124, + 628 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 45, + 635, + 279, + 695 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 635, + 279, + 695 + ], + "spans": [ + { + "bbox": [ + 45, + 635, + 279, + 695 + ], + "type": "text", + "content": "2D Human Pose Estimation (HPE) aims to detect the anatomical joints of a human in a given image to estimate the poses. HPE is typically used as a preprocessing module that participates in many downstream tasks, such as activity recognition [28, 31], human motion analysis [1], mo" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 300, + 255, + 530, + 408 + ], + "blocks": [ + { + "bbox": [ + 300, + 255, + 530, + 408 + ], + "lines": [ + { + "bbox": [ + 300, + 255, + 530, + 408 + ], + "spans": [ + { + "bbox": [ + 300, + 255, + 530, + 408 + ], + "type": "image", + "image_path": "1670b087b179fc64322c5faf3fb075b718ec6939689ef00f59fc689933cf3007.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 296, + 415, + 531, + 469 + ], + "lines": [ + { + "bbox": [ + 296, + 415, + 531, + 469 + ], + "spans": [ + { + "bbox": [ + 296, + 415, + 531, + 469 + ], + "type": "text", + "content": "Figure 1. Comparisons between the SOTA methods and the proposed DistilPose on MSCOCO val dataset. Red circles at the upper left corner denote DistilPose. DistilPose outperforms SOTA models in terms of accuracy (AP), Parameter and computational cost (GFLOPs)." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 296, + 474, + 531, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 474, + 531, + 624 + ], + "spans": [ + { + "bbox": [ + 296, + 474, + 531, + 624 + ], + "type": "text", + "content": "tion capture [16], etc. Previous studies on 2D HPE can be mainly divided into two mainstreams: heatmap-based and regression-based methods. Regression-based methods have significant advantages in speed and are well-suited for mobile devices. However, the insufficient accuracy of regression models will affect the performance of downstream tasks. In contrast, heatmap-based methods can explicitly learn spatial information by estimating likelihood heatmaps, resulting in high accuracy on HPE tasks. But the estimation of likelihood heatmaps requires exceptionally high computational cost, which leads to slow preprocessing operations. Thus, how to take advantages of both heatmap-based and regression-based methods remains a challenging problem." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 296, + 625, + 531, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 625, + 531, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 625, + 531, + 730 + ], + "type": "text", + "content": "One possible way to solve the above problem is to transfer the knowledge from heatmap-based to regression-based models [8,23]. However, due to the different output spaces of regression models and heatmap models (the former is a vector, and the latter is a heatmap), transferring knowledge between heatmaps and vectors faces the following two problems: (1) The regression head usually vectorizes the feature map output by the backbone. And much spatial information will be lost through Global Average Pooling" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 76, + 42, + 119, + 72 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 76, + 42, + 119, + 72 + ], + "spans": [ + { + "bbox": [ + 76, + 42, + 119, + 72 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 150, + 41, + 471, + 74 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 150, + 41, + 471, + 74 + ], + "spans": [ + { + "bbox": [ + 150, + 41, + 471, + 74 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 700, + 279, + 719 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 700, + 279, + 719 + ], + "spans": [ + { + "bbox": [ + 45, + 700, + 279, + 719 + ], + "type": "text", + "content": "* Equal contribution. This work was done when Suhang Ye was an intern at Tencent Youtu Lab." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 61, + 719, + 228, + 729 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 719, + 228, + 729 + ], + "spans": [ + { + "bbox": [ + 61, + 719, + 228, + 729 + ], + "type": "text", + "content": "† Corresponding author: zsc_2016@xmu.edu.cn" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "text", + "content": "2163" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 45, + 106, + 278, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 106, + 278, + 198 + ], + "spans": [ + { + "bbox": [ + 45, + 106, + 278, + 198 + ], + "type": "text", + "content": "(GAP) or Flatten operation. Thus, previous work failed to transfer heatmap knowledge to regression models fully. (2) Compared to the coordinate regression, heatmaps naturally contain shape, position, and gradient information [3]. Due to the lack of explicit guidance for such information, regression-based methods are more difficult to learn the implicit relationship between features and keypoints than heatmap-based methods." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 199, + 278, + 257 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 199, + 278, + 257 + ], + "spans": [ + { + "bbox": [ + 45, + 199, + 278, + 257 + ], + "type": "text", + "content": "In this paper, we propose a novel human pose estimation framework, DistilPose, which learns to transfer the heatmap-based knowledge from a teacher model to a regression-based student model. DistilPose mainly includes the following two components:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 257, + 278, + 408 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 257, + 278, + 408 + ], + "spans": [ + { + "bbox": [ + 45, + 257, + 278, + 408 + ], + "type": "text", + "content": "(1) A knowledge-transferring module called Token-distilling Encoder (TDE) is designed to align the feature spaces of heatmap-based and regression-based models by introducing tokenization, which consists of a series of transformer encoders. TDE can capture the relationship between keypoints and feature maps/other keypoints [10,32]. (2) We propose to simulate heatmaps to obtain the heatmap information for regression-based students explicitly. The resulting Simulated Heatmaps provide two explicit guidelines, including each keypoint's 2D distribution and confidence. Note that the proposed Simulated Heatmaps can be inserted between any heatmap-based and regression-based methods to transfer heatmap knowledge to regression models." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 409, + 278, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 409, + 278, + 582 + ], + "spans": [ + { + "bbox": [ + 45, + 409, + 278, + 582 + ], + "type": "text", + "content": "DistilPose achieves comparable performance to heatmap-based models with less computational cost and surpasses the state-of-the-art (SOTA) regression-based methods. Specifically, on the MSCOCO validation dataset, DistilPose-S achieves " + }, + { + "bbox": [ + 45, + 409, + 278, + 582 + ], + "type": "inline_equation", + "content": "71.6\\%" + }, + { + "bbox": [ + 45, + 409, + 278, + 582 + ], + "type": "text", + "content": " mAP with 5.36M parameters, 2.38 GFLOPs and 40.3 FPS. DistilPose-L achieves " + }, + { + "bbox": [ + 45, + 409, + 278, + 582 + ], + "type": "inline_equation", + "content": "74.4\\%" + }, + { + "bbox": [ + 45, + 409, + 278, + 582 + ], + "type": "text", + "content": " mAP with 21.27M parameters and 10.33 GFLOPs, which outperforms its heatmap-based teacher model in performance, parameters and computational cost. In summary, DistilPose significantly reduces the computation while achieving competitive accuracy, bringing advantages from both heatmap-based and regression-based schemes. As shown in Figure 1, DistilPose outperforms previous SOTA regression-based methods, such as RLE [8] and PRTR [9] with fewer parameters and GFLOPs." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 57, + 583, + 236, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 583, + 236, + 593 + ], + "spans": [ + { + "bbox": [ + 57, + 583, + 236, + 593 + ], + "type": "text", + "content": "Our contributions are summarized as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 57, + 600, + 278, + 730 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 57, + 600, + 278, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 600, + 278, + 646 + ], + "spans": [ + { + "bbox": [ + 57, + 600, + 278, + 646 + ], + "type": "text", + "content": "- We propose a novel human pose estimation framework, DistilPose, which is the first work to transfer knowledge between heatmap-based and regression-based models losslessly." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 57, + 653, + 278, + 710 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 653, + 278, + 710 + ], + "spans": [ + { + "bbox": [ + 57, + 653, + 278, + 710 + ], + "type": "text", + "content": "- We introduce a novel Token-distilling Encoder (TDE) to take advantage of both heatmap-based and regression-based models. With the proposed TDE, the gap between the output space of heatmaps and coordinate vectors can be facilitated in a tokenized manner." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 57, + 718, + 278, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 718, + 278, + 730 + ], + "spans": [ + { + "bbox": [ + 57, + 718, + 278, + 730 + ], + "type": "text", + "content": "- We propose Simulated Heatmaps to model explicit" + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 315, + 106, + 530, + 199 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 106, + 530, + 199 + ], + "spans": [ + { + "bbox": [ + 315, + 106, + 530, + 199 + ], + "type": "text", + "content": "heatmap information, including 2D keypoint distributions and keypoint confidences. With the aid of Simulated Heatmaps, we can transform the regression-based HPE task into a more straightforward learning task that fully exploits local information. Simulated Heatmaps can be applied to any heatmap-based and regression-based models for transferring heatmap knowledge to regression models." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 297, + 214, + 381, + 227 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 214, + 381, + 227 + ], + "spans": [ + { + "bbox": [ + 297, + 214, + 381, + 227 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 297, + 234, + 508, + 246 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 234, + 508, + 246 + ], + "spans": [ + { + "bbox": [ + 297, + 234, + 508, + 246 + ], + "type": "text", + "content": "2.1. Heatmap-based & Regression-based HPE" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 296, + 251, + 530, + 367 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 251, + 530, + 367 + ], + "spans": [ + { + "bbox": [ + 296, + 251, + 530, + 367 + ], + "type": "text", + "content": "Heatmap-based pose estimation [10, 17, 21, 22, 25, 29, 30, 32] dominated the area of human pose estimation in terms of performance. Some studies [10, 17, 21, 29, 32] constructed novel networks to extract better features. While others [5, 20, 24, 33] built upon an optimization perspective trying to mitigate quantization errors. In summary, heatmap-based methods made full use of the spatial information of the feature map and obtain a preferable performance. However, efficiency is still a certain drawback of heatmap-based methods." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 296, + 368, + 530, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 368, + 530, + 542 + ], + "spans": [ + { + "bbox": [ + 296, + 368, + 530, + 542 + ], + "type": "text", + "content": "For regression-based methods, Deeppose [26] is firstly proposed to regress the joint coordinates directly. CenterNet [36] and DirectPose [23] are proposed to accomplish multi-person human pose estimation in a one-stage object detection framework, which directly regresses the joint coordinates instead of the bounding box. SPM [18] introduced the root joints to indicate different person instances and hierarchical rooted human body joints representations to better predict long-range displacements for some joints. Recently, RLE [8] introduced a flow model to capture the underlying output distribution and gets a satisfying performance. Although these methods have made great efforts to find the implicit relationship of keypoints, their performance improvement is still insufficient due to the lack of explicit guidance of heatmaps." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 297, + 548, + 413, + 560 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 548, + 413, + 560 + ], + "spans": [ + { + "bbox": [ + 297, + 548, + 413, + 560 + ], + "type": "text", + "content": "2.2. Transformer in HPE" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 296, + 566, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 566, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 566, + 530, + 730 + ], + "type": "text", + "content": "Transformer is proposed in [27] and achieves great success in Natural Language Processing (NLP). Recent studies in vision tasks used Transformer as an alternative backbone to CNN for its ability to capture global dependencies. In the area of 2D human pose estimation, many efforts [9, 10, 14, 15, 19, 30, 32] have been done to incorporate the Transformers. TFPose [14] first introduced Transformer to the pose estimation framework in a regression-based manner. PRTR [9] proposed a two-stage and end-to-end regression-based framework using cascade Transformers and achieves SOTA performance in regression-based methods. TransPose [32] and TokenPose [10] introduced Transformer for heatmap-based human pose estimation achieving comparable performance while being more" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "text", + "content": "2164" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 107, + 531, + 273 + ], + "blocks": [ + { + "bbox": [ + 51, + 107, + 531, + 273 + ], + "lines": [ + { + "bbox": [ + 51, + 107, + 531, + 273 + ], + "spans": [ + { + "bbox": [ + 51, + 107, + 531, + 273 + ], + "type": "image", + "image_path": "8d8f430e799836bec0244613079a2b97917681064844cb4e7bacaf0917925b8e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 282, + 531, + 305 + ], + "lines": [ + { + "bbox": [ + 45, + 282, + 531, + 305 + ], + "spans": [ + { + "bbox": [ + 45, + 282, + 531, + 305 + ], + "type": "text", + "content": "Figure 2. Overall architecture of DistilPose. During training, a well-trained and fixed heatmap-based teacher provides its knowledge to help the training of regression-based student with TDE and Simulated Heatmaps." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 311, + 279, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 311, + 279, + 346 + ], + "spans": [ + { + "bbox": [ + 45, + 311, + 279, + 346 + ], + "type": "text", + "content": "lightweight. In our work, we introduce the transformer module to assist in finding potential relationships between keypoints." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 353, + 154, + 364 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 353, + 154, + 364 + ], + "spans": [ + { + "bbox": [ + 46, + 353, + 154, + 364 + ], + "type": "text", + "content": "2.3. Distillation in HPE" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 372, + 279, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 372, + 279, + 533 + ], + "spans": [ + { + "bbox": [ + 45, + 372, + 279, + 533 + ], + "type": "text", + "content": "Knowledge Distillation (KD) is formally proposed in [4], which aims to transfer the teacher's learned knowledge to the student model. In 2D human pose estimation, FPD [34] first used knowledge distillation classically based on the Hourglass network. OKDHP [11] introduced an online pose distillation approach that distills the pose structure knowledge in a one-stage manner. ViTpose [30] also implemented a large-to-small model knowledge distillation to prove its knowledge transferability. However, all previous distillation works on human pose estimation ignore the knowledge transferring between heatmap-based and regression-based methods. In this work, for the first time, we propose a heatmap-to-regression distillation framework to take benefits from both schemes." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 544, + 99, + 555 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 544, + 99, + 555 + ], + "spans": [ + { + "bbox": [ + 46, + 544, + 99, + 555 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 564, + 279, + 669 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 564, + 279, + 669 + ], + "spans": [ + { + "bbox": [ + 45, + 564, + 279, + 669 + ], + "type": "text", + "content": "In this section, we propose a distillation-based human pose estimation framework DistilPose, the overall framework of which is shown in Fig. 2. In our proposed DistilPose, the teacher is a heatmap-based model, and the student is a regression-based model. We transfer the heatmap knowledge of the teacher model to the student model during training and only use the faster student model in the inference stage. DistilPose mainly consists of two modules: Token-distilling Encoder and Simulated Heatmaps." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 676, + 180, + 688 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 676, + 180, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 676, + 180, + 688 + ], + "type": "text", + "content": "3.1. Token-distilling Encoder" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 694, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 694, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 694, + 279, + 730 + ], + "type": "text", + "content": "Previous works have tried to introduce the advantages of heatmap models in regression-based methods, such as heatmap pre-training [8], auxiliary heatmap loss [23], etc." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 296, + 311, + 530, + 463 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 311, + 530, + 463 + ], + "spans": [ + { + "bbox": [ + 296, + 311, + 530, + 463 + ], + "type": "text", + "content": "However, the predict-heads cannot be aligned due to the misalignment of the output space. That's why these works can only perform knowledge transfer on the backbone, which brings models limited performance improvement. According to Fig. 3(a), the heatmap-auxiliary model pays too much attention to regions other than the human body. Hence, we propose a Token-distilling Encoder (TDE) to align the output space of teacher and student by introducing tokenization. By introducing aligned tokenized features, the heatmap knowledge is transferred to the student model losslessly. Thus, the student model learns information that is more focused on the human body itself, as shown in Fig. 3(a)." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 296, + 464, + 531, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 464, + 531, + 628 + ], + "spans": [ + { + "bbox": [ + 296, + 464, + 531, + 628 + ], + "type": "text", + "content": "Specifically, for an input image " + }, + { + "bbox": [ + 296, + 464, + 531, + 628 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 296, + 464, + 531, + 628 + ], + "type": "text", + "content": ", we divide it into several patches according to the size of " + }, + { + "bbox": [ + 296, + 464, + 531, + 628 + ], + "type": "inline_equation", + "content": "pw \\times ph" + }, + { + "bbox": [ + 296, + 464, + 531, + 628 + ], + "type": "text", + "content": " to form a visual-token. Next, we add " + }, + { + "bbox": [ + 296, + 464, + 531, + 628 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 296, + 464, + 531, + 628 + ], + "type": "text", + "content": " empty nodes as keypoints-stoken, which are concatenated with visual-token and sent to several transformer encoder layers of TDE. Inspired by LVViT [6], we align the visual-tokens and keypoints-tokens between the student and teacher models to obtain the teacher model's refined attention matrix. As shown in Fig. 3(b), the attention matrix in TDE can learn the relationship between the keypoints-tokens and the visual-tokens of the corresponding position. As for performance improvement, TDE enables our student model to achieve much higher performance than the heatmap-auxiliary training (7.8% ↑ in Fig. 3(a))." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 297, + 639, + 414, + 652 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 639, + 414, + 652 + ], + "spans": [ + { + "bbox": [ + 297, + 639, + 414, + 652 + ], + "type": "text", + "content": "3.2. Simulated Heatmaps" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 296, + 660, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 660, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 660, + 530, + 730 + ], + "type": "text", + "content": "Basic Distribution Simulation After the head of the student model obtained the aligned knowledge with TDE, we began to think about whether there were other ways to transfer other knowledge of the teacher model further. Existing object detection distillation pipelines give us inspiration [35]: in addition to feature distillation, the output of" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "text", + "content": "2165" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 105, + 296, + 270 + ], + "blocks": [ + { + "bbox": [ + 48, + 105, + 296, + 270 + ], + "lines": [ + { + "bbox": [ + 48, + 105, + 296, + 270 + ], + "spans": [ + { + "bbox": [ + 48, + 105, + 296, + 270 + ], + "type": "image", + "image_path": "931cee34a98f8554135ad547f0fed27f223f5eb6e19d4de3f20d4f674080975d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 113, + 277, + 218, + 289 + ], + "lines": [ + { + "bbox": [ + 113, + 277, + 218, + 289 + ], + "spans": [ + { + "bbox": [ + 113, + 277, + 218, + 289 + ], + "type": "text", + "content": "(a) Backbone Feature Map" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 298, + 111, + 381, + 241 + ], + "blocks": [ + { + "bbox": [ + 298, + 111, + 381, + 241 + ], + "lines": [ + { + "bbox": [ + 298, + 111, + 381, + 241 + ], + "spans": [ + { + "bbox": [ + 298, + 111, + 381, + 241 + ], + "type": "image", + "image_path": "f2f716e9e3ac01ebf778a99a56cdf8c0d1746dcf1ef7d1343c4566b8e10de79c.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 320, + 245, + 359, + 253 + ], + "lines": [ + { + "bbox": [ + 320, + 245, + 359, + 253 + ], + "spans": [ + { + "bbox": [ + 320, + 245, + 359, + 253 + ], + "type": "text", + "content": "Input image " + }, + { + "bbox": [ + 320, + 245, + 359, + 253 + ], + "type": "inline_equation", + "content": "I" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 381, + 111, + 526, + 181 + ], + "blocks": [ + { + "bbox": [ + 381, + 111, + 526, + 181 + ], + "lines": [ + { + "bbox": [ + 381, + 111, + 526, + 181 + ], + "spans": [ + { + "bbox": [ + 381, + 111, + 526, + 181 + ], + "type": "image", + "image_path": "f33b37c4428aae1bcc41be5a43008df31c2557d5e83b0abe9df247a72d73b068.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 411, + 184, + 498, + 191 + ], + "lines": [ + { + "bbox": [ + 411, + 184, + 498, + 191 + ], + "spans": [ + { + "bbox": [ + 411, + 184, + 498, + 191 + ], + "type": "text", + "content": "DistilPose-S (teacher TokenPose-L)" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 384, + 193, + 524, + 251 + ], + "blocks": [ + { + "bbox": [ + 384, + 193, + 524, + 251 + ], + "lines": [ + { + "bbox": [ + 384, + 193, + 524, + 251 + ], + "spans": [ + { + "bbox": [ + 384, + 193, + 524, + 251 + ], + "type": "image", + "image_path": "eca8448f8d4700539272a622b0034b4362f11565ed67c7eb730d1c70f093b6fa.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 403, + 252, + 418, + 260 + ], + "lines": [ + { + "bbox": [ + 403, + 252, + 418, + 260 + ], + "spans": [ + { + "bbox": [ + 403, + 252, + 418, + 260 + ], + "type": "text", + "content": "Layer1" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 448, + 252, + 464, + 259 + ], + "lines": [ + { + "bbox": [ + 448, + 252, + 464, + 259 + ], + "spans": [ + { + "bbox": [ + 448, + 252, + 464, + 259 + ], + "type": "text", + "content": "Layer2" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 495, + 252, + 510, + 259 + ], + "lines": [ + { + "bbox": [ + 495, + 252, + 510, + 259 + ], + "spans": [ + { + "bbox": [ + 495, + 252, + 510, + 259 + ], + "type": "text", + "content": "Layer3" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 377, + 277, + 458, + 288 + ], + "lines": [ + { + "bbox": [ + 377, + 277, + 458, + 288 + ], + "spans": [ + { + "bbox": [ + 377, + 277, + 458, + 288 + ], + "type": "text", + "content": "(b) Attention Matrix" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 92, + 359, + 227, + 485 + ], + "blocks": [ + { + "bbox": [ + 45, + 297, + 530, + 351 + ], + "lines": [ + { + "bbox": [ + 45, + 297, + 530, + 351 + ], + "spans": [ + { + "bbox": [ + 45, + 297, + 530, + 351 + ], + "type": "text", + "content": "Figure 3. Visualization of backbone feature maps and attention matrix. (a) The first row represent backbone feature maps of direct training, heatmap-auxiliary training, and our proposed distillation training (distill TDE only and distill both TDE and Simulated Heatmaps), respectively. While the second row represent backbone feature maps of the heatmap-based method TokenPose with different backbones. It can be seen here that the full structure of DistilPose is more focused on the human body than the model distill TDE only (the former the feature map background is darker). (b) These are attention matrix between the keypoint-token of \"right-ankle\" (red dot) and visual-tokens." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 92, + 359, + 227, + 485 + ], + "lines": [ + { + "bbox": [ + 92, + 359, + 227, + 485 + ], + "spans": [ + { + "bbox": [ + 92, + 359, + 227, + 485 + ], + "type": "image", + "image_path": "3d7e2f870dfe38a0e118ea3750ce8ca80537b5971e9764e8a73f4bfdf94d49a7.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 489, + 278, + 511 + ], + "lines": [ + { + "bbox": [ + 45, + 489, + 278, + 511 + ], + "spans": [ + { + "bbox": [ + 45, + 489, + 278, + 511 + ], + "type": "text", + "content": "Figure 4. Visualization of Basis distribution simulation of " + }, + { + "bbox": [ + 45, + 489, + 278, + 511 + ], + "type": "inline_equation", + "content": "k^{th}" + }, + { + "bbox": [ + 45, + 489, + 278, + 511 + ], + "type": "text", + "content": " keypoint in Simulated Heatmaps." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 45, + 519, + 278, + 681 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 519, + 278, + 681 + ], + "spans": [ + { + "bbox": [ + 45, + 519, + 278, + 681 + ], + "type": "text", + "content": "the teacher model can also be used as a soft label to further distill knowledge to the student model. Compared with the coordinate vector, the distribution with a well-defined shape and good gradient contained in the heatmap is explicit guide information, which can prompt the model to pay attention to the local information around the keypoints. Not only that, but teacher heatmaps may be closer to reality. It is because there may be erroneous annotations in ground-truth, and the teacher model can filter out these faulty parts by summarizing the knowledge during training. However, heatmaps and coordinate vectors are in different output spaces. How to introduce the distribution information on the heatmap into the space of the coordinate vector has become an urgent problem to be solved." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 45, + 683, + 278, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 683, + 278, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 683, + 278, + 730 + ], + "type": "text", + "content": "For this purpose, we do the opposite and propose the concept of Simulated Heatmaps to introduce coordinate vectors into the heatmap space. We let the student model predict both the keypoint coordinates and the correspond" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 296, + 357, + 530, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 357, + 530, + 426 + ], + "spans": [ + { + "bbox": [ + 296, + 357, + 530, + 426 + ], + "type": "text", + "content": "ing " + }, + { + "bbox": [ + 296, + 357, + 530, + 426 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 296, + 357, + 530, + 426 + ], + "type": "text", + "content": " values, using a Gaussian distribution to build a virtual heatmap (as shown in Fig. 4). Since the heatmap of the teacher model is not necessarily a regular distribution, we predict " + }, + { + "bbox": [ + 296, + 357, + 530, + 426 + ], + "type": "inline_equation", + "content": "\\sigma_{x}" + }, + { + "bbox": [ + 296, + 357, + 530, + 426 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 357, + 530, + 426 + ], + "type": "inline_equation", + "content": "\\sigma_{y}" + }, + { + "bbox": [ + 296, + 357, + 530, + 426 + ], + "type": "text", + "content": " from the horizontal/vertical directions, respectively, to construct a heatmap closer to the actual one. The Gaussian distribution is calculated as follows:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 330, + 435, + 530, + 463 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 435, + 530, + 463 + ], + "spans": [ + { + "bbox": [ + 330, + 435, + 530, + 463 + ], + "type": "interline_equation", + "content": "f (x, y) = \\frac {1}{2 \\pi \\sigma_ {x} \\sigma_ {y}} e ^ {- \\frac {1}{2} \\left(\\frac {(x - \\mu_ {x}) ^ {2}}{\\sigma_ {x} ^ {2}} + \\frac {(y - \\mu_ {y}) ^ {2}}{\\sigma_ {y} ^ {2}}\\right)}, \\tag {1}", + "image_path": "6f426b702a6f71cb44f3c19ceb2c136bcc80274b0632b2d0fb662e2111e86e81.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 296, + 464, + 530, + 512 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 464, + 530, + 512 + ], + "spans": [ + { + "bbox": [ + 296, + 464, + 530, + 512 + ], + "type": "text", + "content": "To align with the ground-truth of the teacher model, we ignore the constant coefficient " + }, + { + "bbox": [ + 296, + 464, + 530, + 512 + ], + "type": "inline_equation", + "content": "\\frac{1}{2\\pi\\sigma_x\\sigma_y}" + }, + { + "bbox": [ + 296, + 464, + 530, + 512 + ], + "type": "text", + "content": " multiplied by the Gaussian distribution, and the final formula for simulating a heatmap for " + }, + { + "bbox": [ + 296, + 464, + 530, + 512 + ], + "type": "inline_equation", + "content": "k_{th}" + }, + { + "bbox": [ + 296, + 464, + 530, + 512 + ], + "type": "text", + "content": " keypoint can be summarized as:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 339, + 516, + 530, + 539 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 339, + 516, + 530, + 539 + ], + "spans": [ + { + "bbox": [ + 339, + 516, + 530, + 539 + ], + "type": "interline_equation", + "content": "H _ {k} (x, y) = e ^ {- \\frac {1}{2} \\left(\\frac {(x - \\mu_ {x k}) ^ {2}}{\\sigma_ {x k} ^ {2}} + \\frac {(y - \\mu_ {y k}) ^ {2}}{\\sigma_ {y k} ^ {2}}\\right)}, \\tag {2}", + "image_path": "c912e3472d8d78f54f58269498f1f7e258cdeb059bc3f594a1a8fc70af799bfc.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 296, + 543, + 530, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 543, + 530, + 612 + ], + "spans": [ + { + "bbox": [ + 296, + 543, + 530, + 612 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 296, + 543, + 530, + 612 + ], + "type": "inline_equation", + "content": "0 < x \\leq hW" + }, + { + "bbox": [ + 296, + 543, + 530, + 612 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 296, + 543, + 530, + 612 + ], + "type": "inline_equation", + "content": "0 < y \\leq hH" + }, + { + "bbox": [ + 296, + 543, + 530, + 612 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 543, + 530, + 612 + ], + "type": "inline_equation", + "content": "0 < k \\leq K" + }, + { + "bbox": [ + 296, + 543, + 530, + 612 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 296, + 543, + 530, + 612 + ], + "type": "inline_equation", + "content": "hW" + }, + { + "bbox": [ + 296, + 543, + 530, + 612 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 543, + 530, + 612 + ], + "type": "inline_equation", + "content": "hH" + }, + { + "bbox": [ + 296, + 543, + 530, + 612 + ], + "type": "text", + "content": " are the width and height of the heatmap, " + }, + { + "bbox": [ + 296, + 543, + 530, + 612 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 296, + 543, + 530, + 612 + ], + "type": "text", + "content": " is the total number of keypoints, and " + }, + { + "bbox": [ + 296, + 543, + 530, + 612 + ], + "type": "inline_equation", + "content": "H_{k}" + }, + { + "bbox": [ + 296, + 543, + 530, + 612 + ], + "type": "text", + "content": " refers to the " + }, + { + "bbox": [ + 296, + 543, + 530, + 612 + ], + "type": "inline_equation", + "content": "k^{th}" + }, + { + "bbox": [ + 296, + 543, + 530, + 612 + ], + "type": "text", + "content": " simulated heatmap. " + }, + { + "bbox": [ + 296, + 543, + 530, + 612 + ], + "type": "inline_equation", + "content": "(\\mu_{xk}, \\mu_{yk})" + }, + { + "bbox": [ + 296, + 543, + 530, + 612 + ], + "type": "text", + "content": " is the predicted keypoints coordinate, and " + }, + { + "bbox": [ + 296, + 543, + 530, + 612 + ], + "type": "inline_equation", + "content": "(\\sigma_{xk}, \\sigma_{yk})" + }, + { + "bbox": [ + 296, + 543, + 530, + 612 + ], + "type": "text", + "content": " is the corresponding deviation pair. In the end, we get " + }, + { + "bbox": [ + 296, + 543, + 530, + 612 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 296, + 543, + 530, + 612 + ], + "type": "text", + "content": " heatmap as shown in Fig. 5." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 296, + 612, + 530, + 682 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 612, + 530, + 682 + ], + "spans": [ + { + "bbox": [ + 296, + 612, + 530, + 682 + ], + "type": "text", + "content": "Confidence Distillation. In addition to distribution information, heatmaps also provide keypoint confidence, which helps filter out incorrect model predictions and is critical in industrial applications. However, our simulated heatmap defaults to 1 at the peak, which cannot be included in the calculation as a valid confidence." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 296, + 683, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 683, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 683, + 530, + 730 + ], + "type": "text", + "content": "To this end, we prompt the student model to predict the confidence of keypoints " + }, + { + "bbox": [ + 296, + 683, + 530, + 730 + ], + "type": "inline_equation", + "content": "s_k" + }, + { + "bbox": [ + 296, + 683, + 530, + 730 + ], + "type": "text", + "content": " directly. Each keypoint confidence " + }, + { + "bbox": [ + 296, + 683, + 530, + 730 + ], + "type": "inline_equation", + "content": "s_k" + }, + { + "bbox": [ + 296, + 683, + 530, + 730 + ], + "type": "text", + "content": " corresponds to the keypoint coordinate and is constrained by the corresponding value of the coordinate on the" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "text", + "content": "2166" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 105, + 530, + 239 + ], + "blocks": [ + { + "bbox": [ + 52, + 105, + 530, + 239 + ], + "lines": [ + { + "bbox": [ + 52, + 105, + 530, + 239 + ], + "spans": [ + { + "bbox": [ + 52, + 105, + 530, + 239 + ], + "type": "image", + "image_path": "fc1645d711a204ec86adbc71e2a077ff2095aa1e926a16d3ce456bcf75aeb427.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 164, + 242, + 411, + 253 + ], + "lines": [ + { + "bbox": [ + 164, + 242, + 411, + 253 + ], + "spans": [ + { + "bbox": [ + 164, + 242, + 411, + 253 + ], + "type": "text", + "content": "Figure 5. Visualization of Simulated Heatmaps and teacher heatmaps." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 259, + 280, + 294 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 259, + 280, + 294 + ], + "spans": [ + { + "bbox": [ + 45, + 259, + 280, + 294 + ], + "type": "text", + "content": "teacher's heatmap. The keypoint confidence " + }, + { + "bbox": [ + 45, + 259, + 280, + 294 + ], + "type": "inline_equation", + "content": "s_k" + }, + { + "bbox": [ + 45, + 259, + 280, + 294 + ], + "type": "text", + "content": " will be accumulated in the human instance score, which is calculated as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 300, + 279, + 326 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 300, + 279, + 326 + ], + "spans": [ + { + "bbox": [ + 105, + 300, + 279, + 326 + ], + "type": "interline_equation", + "content": "s ^ {h u m a n} = s ^ {b b o x} * \\frac {\\sum_ {i = 1} ^ {K} s _ {k}}{K}, \\tag {3}", + "image_path": "d4f03e412e2ed49112868ad62f91ae626ad4e73e2f27a587ad8d1f4bd827e90e.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 333, + 279, + 368 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 333, + 279, + 368 + ], + "spans": [ + { + "bbox": [ + 45, + 333, + 279, + 368 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 45, + 333, + 279, + 368 + ], + "type": "inline_equation", + "content": "s^{human}" + }, + { + "bbox": [ + 45, + 333, + 279, + 368 + ], + "type": "text", + "content": " is the prediction score of the human instance, and " + }, + { + "bbox": [ + 45, + 333, + 279, + 368 + ], + "type": "inline_equation", + "content": "s^{bbox}" + }, + { + "bbox": [ + 45, + 333, + 279, + 368 + ], + "type": "text", + "content": " refers to the confidence score given by the human detector." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 376, + 132, + 387 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 376, + 132, + 387 + ], + "spans": [ + { + "bbox": [ + 46, + 376, + 132, + 387 + ], + "type": "text", + "content": "3.3. Loss Function" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 394, + 279, + 428 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 394, + 279, + 428 + ], + "spans": [ + { + "bbox": [ + 45, + 394, + 279, + 428 + ], + "type": "text", + "content": "For TDE, we perform distillation for visual-tokens and keypoint-tokens, respectively, and the corresponding loss functions are:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 107, + 435, + 279, + 452 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 435, + 279, + 452 + ], + "spans": [ + { + "bbox": [ + 107, + 435, + 279, + 452 + ], + "type": "interline_equation", + "content": "L _ {K T} = M S E \\left(\\boldsymbol {K T} _ {h}, \\boldsymbol {K T} _ {r}\\right), \\tag {4}", + "image_path": "e18e81f665e5ed8957f6e0b895b271b1e8dc90b8cee19fac98f0fd0883d02f0a.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 110, + 450, + 217, + 463 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 450, + 217, + 463 + ], + "spans": [ + { + "bbox": [ + 110, + 450, + 217, + 463 + ], + "type": "interline_equation", + "content": "L _ {V T} = M S E \\left(\\boldsymbol {V} \\boldsymbol {T} _ {h}, \\boldsymbol {V} \\boldsymbol {T} _ {r}\\right),", + "image_path": "b4d99654d716e5f80c492275eaa69cf48874389b6732de3e7a1e9bbab49330b1.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 45, + 471, + 279, + 541 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 471, + 279, + 541 + ], + "spans": [ + { + "bbox": [ + 45, + 471, + 279, + 541 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 45, + 471, + 279, + 541 + ], + "type": "inline_equation", + "content": "KT \\in \\mathbb{R}^{K \\times D}" + }, + { + "bbox": [ + 45, + 471, + 279, + 541 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 471, + 279, + 541 + ], + "type": "inline_equation", + "content": "VT \\in \\mathbb{R}^{P \\times D}" + }, + { + "bbox": [ + 45, + 471, + 279, + 541 + ], + "type": "text", + "content": " refer to keypoint-tokens and visual-tokens. " + }, + { + "bbox": [ + 45, + 471, + 279, + 541 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 45, + 471, + 279, + 541 + ], + "type": "text", + "content": " is the number of patches, and " + }, + { + "bbox": [ + 45, + 471, + 279, + 541 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 45, + 471, + 279, + 541 + ], + "type": "text", + "content": " refers to the dimension of tokens. The subscript " + }, + { + "bbox": [ + 45, + 471, + 279, + 541 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 45, + 471, + 279, + 541 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 471, + 279, + 541 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 45, + 471, + 279, + 541 + ], + "type": "text", + "content": " refer to the heatmap-based and regression-based model accordingly. " + }, + { + "bbox": [ + 45, + 471, + 279, + 541 + ], + "type": "inline_equation", + "content": "MSE" + }, + { + "bbox": [ + 45, + 471, + 279, + 541 + ], + "type": "text", + "content": " refers to the Mean Squared Error Loss used to measure the difference between teacher and student" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 45, + 542, + 279, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 542, + 279, + 575 + ], + "spans": [ + { + "bbox": [ + 45, + 542, + 279, + 575 + ], + "type": "text", + "content": "For the Simulated Heatmaps, we try to align the simulated ones to the teacher heatmaps, and the corresponding loss function is:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 101, + 582, + 279, + 614 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 101, + 582, + 279, + 614 + ], + "spans": [ + { + "bbox": [ + 101, + 582, + 279, + 614 + ], + "type": "interline_equation", + "content": "L _ {S H} = \\sum_ {i = 1} ^ {K} M S E \\left(H _ {k}, H _ {T k}\\right), \\tag {5}", + "image_path": "1f08caa5a0f3ac02c2442350e9895035aec28419a95c5c07deb4a42c013cb090.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 45, + 623, + 228, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 623, + 228, + 634 + ], + "spans": [ + { + "bbox": [ + 45, + 623, + 228, + 634 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 45, + 623, + 228, + 634 + ], + "type": "inline_equation", + "content": "H_{Tk}" + }, + { + "bbox": [ + 45, + 623, + 228, + 634 + ], + "type": "text", + "content": " indicates the " + }, + { + "bbox": [ + 45, + 623, + 228, + 634 + ], + "type": "inline_equation", + "content": "k^{th}" + }, + { + "bbox": [ + 45, + 623, + 228, + 634 + ], + "type": "text", + "content": " teacher heatmap." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 45, + 635, + 279, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 635, + 279, + 658 + ], + "spans": [ + { + "bbox": [ + 45, + 635, + 279, + 658 + ], + "type": "text", + "content": "For the peak constraint of the Simulated Heatmaps, we design the following loss function:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 92, + 666, + 279, + 698 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 92, + 666, + 279, + 698 + ], + "spans": [ + { + "bbox": [ + 92, + 666, + 279, + 698 + ], + "type": "interline_equation", + "content": "L _ {C S} = \\sum_ {i = 1} ^ {K} \\left| H _ {T k} \\left(\\left[ x _ {k} \\right], \\left[ y _ {k} \\right]\\right) - s _ {k} \\right|, \\tag {6}", + "image_path": "80c4aebe81022103742f8d21662c8c8d7b682a1d9089effe381bb8d761dcf31a.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 45, + 706, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 706, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 706, + 279, + 730 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 45, + 706, + 279, + 730 + ], + "type": "inline_equation", + "content": "(x_{k},y_{k}),k\\in [1,K]" + }, + { + "bbox": [ + 45, + 706, + 279, + 730 + ], + "type": "text", + "content": " refers to student coordinate predictions. " + }, + { + "bbox": [ + 45, + 706, + 279, + 730 + ], + "type": "inline_equation", + "content": "[\\cdot ]" + }, + { + "bbox": [ + 45, + 706, + 279, + 730 + ], + "type": "text", + "content": " indicates the round-off operation." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 296, + 259, + 530, + 305 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 259, + 530, + 305 + ], + "spans": [ + { + "bbox": [ + 296, + 259, + 530, + 305 + ], + "type": "text", + "content": "In summary, we train regression-based student models simultaneously under task supervision and knowledge distillation. The overall loss function of our distillation framework is as follows:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 303, + 314, + 530, + 327 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 303, + 314, + 530, + 327 + ], + "spans": [ + { + "bbox": [ + 303, + 314, + 530, + 327 + ], + "type": "interline_equation", + "content": "L = L _ {r e g} + \\alpha_ {1} L _ {K T} + \\alpha_ {2} L _ {V T} + \\alpha_ {3} L _ {S H} + \\alpha_ {4} L _ {C S}. \\tag {7}", + "image_path": "90b3a63bac44d8cdd98e4e4446ce1d901c4e4068717c70da4d06ec62c482bf4c.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 296, + 334, + 530, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 334, + 530, + 415 + ], + "spans": [ + { + "bbox": [ + 296, + 334, + 530, + 415 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 296, + 334, + 530, + 415 + ], + "type": "inline_equation", + "content": "L_{reg}" + }, + { + "bbox": [ + 296, + 334, + 530, + 415 + ], + "type": "text", + "content": " is the regression task loss for human pose estimation. We use Smooth L1 Loss as " + }, + { + "bbox": [ + 296, + 334, + 530, + 415 + ], + "type": "inline_equation", + "content": "L_{reg}" + }, + { + "bbox": [ + 296, + 334, + 530, + 415 + ], + "type": "text", + "content": " to compute the distance between predicted joints and ground-truth coordinates. Invisible keypoints will be filtered, including ground-truth coordinates or predicted coordinates outside the image. In other words, we did not use these invisible keypoints for loss calculation." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 297, + 426, + 376, + 438 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 426, + 376, + 438 + ], + "spans": [ + { + "bbox": [ + 297, + 426, + 376, + 438 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 296, + 445, + 530, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 445, + 530, + 504 + ], + "spans": [ + { + "bbox": [ + 296, + 445, + 530, + 504 + ], + "type": "text", + "content": "In this section, we evaluate the proposed distillation framework on the MSCOCO dataset. What's more, we carry out a series of ablation studies to prove the effectiveness and validity of DistilPose. The implementation of our method is based on MMPose [2]." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 297, + 510, + 426, + 522 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 510, + 426, + 522 + ], + "spans": [ + { + "bbox": [ + 297, + 510, + 426, + 522 + ], + "type": "text", + "content": "4.1. Implementation Details" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 297, + 528, + 364, + 538 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 528, + 364, + 538 + ], + "spans": [ + { + "bbox": [ + 297, + 528, + 364, + 538 + ], + "type": "text", + "content": "4.1.1 Datasets" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 296, + 546, + 530, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 546, + 530, + 674 + ], + "spans": [ + { + "bbox": [ + 296, + 546, + 530, + 674 + ], + "type": "text", + "content": "We mainly conduct our experiments on the MSCOCO dataset [13]. The MSCOCO dataset contains over 200k images and 250k human instances. Each human instance is labeled with " + }, + { + "bbox": [ + 296, + 546, + 530, + 674 + ], + "type": "inline_equation", + "content": "K = 17" + }, + { + "bbox": [ + 296, + 546, + 530, + 674 + ], + "type": "text", + "content": " keypoints representing a human pose. Our models are trained on MSCOCO train2017 with 57k images and evaluated on both MSCOCO val2017 and testdev2017, which contain 5k and 20k images, respectively. Furthermore, the ablation experiments are conducted on the MSCOCO val dataset. We mainly report the commonly used standard evaluation metric Average Precision(AP) as previous works done on the MSCOCO dataset." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 297, + 687, + 366, + 700 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 687, + 366, + 700 + ], + "spans": [ + { + "bbox": [ + 297, + 687, + 366, + 700 + ], + "type": "text", + "content": "4.1.2 Training" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 297, + 706, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 706, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 297, + 706, + 530, + 730 + ], + "type": "text", + "content": "We follow the top-down human pose estimation paradigm. All input images are resized into " + }, + { + "bbox": [ + 297, + 706, + 530, + 730 + ], + "type": "inline_equation", + "content": "256 \\times 192" + }, + { + "bbox": [ + 297, + 706, + 530, + 730 + ], + "type": "text", + "content": " resolution. We" + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "text", + "content": "2167" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 119, + 104, + 456, + 382 + ], + "blocks": [ + { + "bbox": [ + 119, + 104, + 456, + 382 + ], + "lines": [ + { + "bbox": [ + 119, + 104, + 456, + 382 + ], + "spans": [ + { + "bbox": [ + 119, + 104, + 456, + 382 + ], + "type": "table", + "html": "
MethodsBackboneInput SizeParam.(M)GFLOPsmAP(%)
Heatmap-based Methods
SimpleBaselines [29]ResNet-50256×19234.08.9070.4
SimpleBaselines [29]ResNet-101256×19253.012.4071.4
SimpleBaselines [29]ResNet-152256×19268.615.7072.0
HRNet [21]HRNet-W32256×19228.57.1074.4
HRNet [21]HRNet-W48256×19263.614.6075.1
TokenPose [10]stemnet256×1926.62.4072.5
TokenPose [10]HRNet-W48-stage3256×19227.511.6075.8
TransPose [32]ResNet-small256×1925.05.4071.5
TransPose [32]HRNet-Small-W48256×19217.521.8075.8
Distillation-based Methods
OKDHP [12]2-Stack HG256×19213.025.5072.8
OKDHP [12]4-Stack HG256×19224.047.0074.8
Regression-based Methods
PRTR* [9]ResNet-50256×19241.55.4563.7
PRTR [9]ResNet-50384×28841.511.0068.2
PRTR [9]ResNet-50512×38441.518.8071.0
PRTR* [9]HRNet-W32256×19257.210.2372.9
PRTR [9]HRNet-W32384×28857.221.6073.1
PRTR [9]HRNet-W32512×38457.237.8073.3
RLE [8]ResNet-50256×19223.64.0470.5
RLE* [8]HRNet-W48256×19275.615.7674.2
Poseur [15]MobileNetV2256×19211.360.571.9
Poseur [15]ResNet-50256×19233.264.675.4
DistilPose-S (Ours)stemnet256×1925.42.3871.6
DistilPose-L (Ours)HRNet-W48-stage3256×19221.310.3374.4
", + "image_path": "e66a08a35d92ebcbf06cedc10fa9084c73f451e2fbeaa908715fad7580d3c856.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 86, + 398, + 490, + 496 + ], + "blocks": [ + { + "bbox": [ + 56, + 384, + 519, + 395 + ], + "lines": [ + { + "bbox": [ + 56, + 384, + 519, + 395 + ], + "spans": [ + { + "bbox": [ + 56, + 384, + 519, + 395 + ], + "type": "text", + "content": "Table 1. Comparison on MSCOCO val dataset. Flip test is used on all methods. * indicates that we re-train and evaluate the models." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 86, + 398, + 490, + 496 + ], + "lines": [ + { + "bbox": [ + 86, + 398, + 490, + 496 + ], + "spans": [ + { + "bbox": [ + 86, + 398, + 490, + 496 + ], + "type": "table", + "html": "
MethodsBackboneInput SizeAP(%)\\( AP_{50}( \\)% )\\( AP_{75}( \\)% )\\( AP_M( \\)% )\\( AP_L( \\)% )
PRTR [9]ResNet-101384×28868.889.976.964.775.8
PRTR [9]ResNet-101512×38470.690.378.566.277.7
RLE* [8]ResNet-50256×19269.890.177.567.274.3
DistilPose-S (Ours)stemnet256×19271.091.078.967.576.8
PRTR [9]HRNet-W32384×28871.790.679.667.678.4
PRTR [9]HRNet-W32512×38472.190.479.668.179.0
RLE* [8]HRNet-W48256×19273.791.481.471.178.6
DistilPose-L (Ours)HRNet-W48-stage3256×19273.791.681.170.279.6
", + "image_path": "e3d6fc10239489120ad650aa67aeee2f7d4acdc9ddfda9b21e1e20fc95d85ed9.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 104, + 504, + 471, + 515 + ], + "lines": [ + { + "bbox": [ + 104, + 504, + 471, + 515 + ], + "spans": [ + { + "bbox": [ + 104, + 504, + 471, + 515 + ], + "type": "text", + "content": "Table 2. Comparison on MSCOCO test-dev dataset. * indicates that we re-train and evaluate the models." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 45, + 522, + 280, + 650 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 522, + 280, + 650 + ], + "spans": [ + { + "bbox": [ + 45, + 522, + 280, + 650 + ], + "type": "text", + "content": "adopt a commonly used person detector provided by SimpleBaselines [29] with " + }, + { + "bbox": [ + 45, + 522, + 280, + 650 + ], + "type": "inline_equation", + "content": "56.4\\%" + }, + { + "bbox": [ + 45, + 522, + 280, + 650 + ], + "type": "text", + "content": " AP for the MSCOCO val dataset and " + }, + { + "bbox": [ + 45, + 522, + 280, + 650 + ], + "type": "inline_equation", + "content": "60.9\\%" + }, + { + "bbox": [ + 45, + 522, + 280, + 650 + ], + "type": "text", + "content": " AP for the MSCOCO test-dev dataset. All the models are trained with a batch size of 64 images per GPU, using 8 Tesla V100 GPUs. We adopt Adam as our optimizer and train the models for 300 epochs. The base learning rate is set to 1e-3, and decays to 1e-4 and 1e-5 at the " + }, + { + "bbox": [ + 45, + 522, + 280, + 650 + ], + "type": "inline_equation", + "content": "200^{th}" + }, + { + "bbox": [ + 45, + 522, + 280, + 650 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 522, + 280, + 650 + ], + "type": "inline_equation", + "content": "260^{th}" + }, + { + "bbox": [ + 45, + 522, + 280, + 650 + ], + "type": "text", + "content": " epoch, respectively. We follow the data augmentation setting in HRNet [21]. We empirically set the hyper-parameters to " + }, + { + "bbox": [ + 45, + 522, + 280, + 650 + ], + "type": "inline_equation", + "content": "\\alpha_{1} = \\alpha_{2} = 5e - 4, \\alpha_{3} = 1, \\alpha_{4} = 1e - 2" + }, + { + "bbox": [ + 45, + 522, + 280, + 650 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 664, + 136, + 676 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 664, + 136, + 676 + ], + "spans": [ + { + "bbox": [ + 45, + 664, + 136, + 676 + ], + "type": "text", + "content": "4.1.3 Model Setting" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 682, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 682, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 682, + 279, + 730 + ], + "type": "text", + "content": "If not specified, the teacher model we use is a heatmap-based model with a performance of " + }, + { + "bbox": [ + 45, + 682, + 279, + 730 + ], + "type": "inline_equation", + "content": "72.5\\%" + }, + { + "bbox": [ + 45, + 682, + 279, + 730 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 45, + 682, + 279, + 730 + ], + "type": "inline_equation", + "content": "75.2\\%" + }, + { + "bbox": [ + 45, + 682, + 279, + 730 + ], + "type": "text", + "content": " if extra-post-processing [33] is used during inference) at the cost of 69.41M parameters and 17.03 GFLOPs, which adopts" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 297, + 522, + 413, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 522, + 413, + 532 + ], + "spans": [ + { + "bbox": [ + 297, + 522, + 413, + 532 + ], + "type": "text", + "content": "HRNet-W48 as its backbone." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 296, + 533, + 530, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 533, + 530, + 615 + ], + "spans": [ + { + "bbox": [ + 296, + 533, + 530, + 615 + ], + "type": "text", + "content": "DistilPose-S adopts a lightweight backbone named stemnet from TokenPose [10], which is widely used to down-sample the feature map into " + }, + { + "bbox": [ + 296, + 533, + 530, + 615 + ], + "type": "inline_equation", + "content": "1/4" + }, + { + "bbox": [ + 296, + 533, + 530, + 615 + ], + "type": "text", + "content": " input resolution quickly. Stemnet is a very shallow convolutional structure and is trained from scratch. Besides, DistilPose-L uses feature map output by HRNet-W48 [21] at the " + }, + { + "bbox": [ + 296, + 533, + 530, + 615 + ], + "type": "inline_equation", + "content": "3^{rd}" + }, + { + "bbox": [ + 296, + 533, + 530, + 615 + ], + "type": "text", + "content": " stage, following the same setting as TokenPose-L [10]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 296, + 615, + 530, + 650 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 615, + 530, + 650 + ], + "spans": [ + { + "bbox": [ + 296, + 615, + 530, + 650 + ], + "type": "text", + "content": "For the architecture configurations of TDE of DistilPose, the num of transformer layers is 12, embedding dim is 192, the num of heads is 8, and patch size " + }, + { + "bbox": [ + 296, + 615, + 530, + 650 + ], + "type": "inline_equation", + "content": "p_w \\times p_h" + }, + { + "bbox": [ + 296, + 615, + 530, + 650 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 296, + 615, + 530, + 650 + ], + "type": "inline_equation", + "content": "4 \\times 3" + }, + { + "bbox": [ + 296, + 615, + 530, + 650 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 297, + 657, + 380, + 669 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 657, + 380, + 669 + ], + "spans": [ + { + "bbox": [ + 297, + 657, + 380, + 669 + ], + "type": "text", + "content": "4.2. Main Results" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 297, + 676, + 515, + 687 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 676, + 515, + 687 + ], + "spans": [ + { + "bbox": [ + 297, + 676, + 515, + 687 + ], + "type": "text", + "content": "4.2.1 Comparison with SOTA Regression Methods" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 296, + 694, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 694, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 694, + 530, + 730 + ], + "type": "text", + "content": "We compare the proposed DistilPose with the SOTA regression-based methods on MSCOCO val and test-dev dataset, and the experimental results are shown in Table 1." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "text", + "content": "2168" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 55, + 103, + 522, + 159 + ], + "blocks": [ + { + "bbox": [ + 55, + 103, + 522, + 159 + ], + "lines": [ + { + "bbox": [ + 55, + 103, + 522, + 159 + ], + "spans": [ + { + "bbox": [ + 55, + 103, + 522, + 159 + ], + "type": "table", + "html": "
ModelRoleBackboneMethodsEx-post.AP(%)Param(M)GFLOPsFPS
TokenPose*TeacherHRNet-W48heatmapY75.269.4117.037.8
TokenPose*TeacherHRNet-W48heatmapN72.569.4117.038.2
DistilPose-SStudentstemnetregression-71.6 (0.9↓)5.36 (12.95× ↓)2.38 (7.16× ↓)40.2 (4.90× ↑)
DistilPose-LStudentHRNet-W48-s3regression-74.4 (1.9↑)21.27 (3.26× ↓)10.33 (1.65× ↓)13.7 (1.72× ↑)
", + "image_path": "783a0df305f541d80aec9b724c55e4ecb32def5d8496c4835200fa9b672d3c11.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 206, + 279, + 299 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 206, + 279, + 299 + ], + "spans": [ + { + "bbox": [ + 45, + 206, + 279, + 299 + ], + "type": "text", + "content": "and Table 2, respectively. Also, a line chart is drawn for more visual comparison in Figure 1. We mainly compare our methods with PRTR [9] and RLE [8]. Since PRTR is also Transformer-based methods that achieved SOTA performance among regression-based methods, RLE still dominates regression-based methods. We further compare DistilPose with the latest regression-based SOTA method Poseur [15] in our supplementary materials." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 299, + 279, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 299, + 279, + 380 + ], + "spans": [ + { + "bbox": [ + 45, + 299, + 279, + 380 + ], + "type": "text", + "content": "Specifically, DistilPose-S achieves " + }, + { + "bbox": [ + 45, + 299, + 279, + 380 + ], + "type": "inline_equation", + "content": "71.6\\%" + }, + { + "bbox": [ + 45, + 299, + 279, + 380 + ], + "type": "text", + "content": " with 5.36M and 2.38 GFLOPs, which outperforms PRTR-Res50 by " + }, + { + "bbox": [ + 45, + 299, + 279, + 380 + ], + "type": "inline_equation", + "content": "7.9\\%" + }, + { + "bbox": [ + 45, + 299, + 279, + 380 + ], + "type": "text", + "content": " at the same input resolution " + }, + { + "bbox": [ + 45, + 299, + 279, + 380 + ], + "type": "inline_equation", + "content": "256\\times 192" + }, + { + "bbox": [ + 45, + 299, + 279, + 380 + ], + "type": "text", + "content": " while reducing 36.14M " + }, + { + "bbox": [ + 45, + 299, + 279, + 380 + ], + "type": "inline_equation", + "content": "(87.1\\% \\downarrow)" + }, + { + "bbox": [ + 45, + 299, + 279, + 380 + ], + "type": "text", + "content": " parameters and 3.07 GFLOPs " + }, + { + "bbox": [ + 45, + 299, + 279, + 380 + ], + "type": "inline_equation", + "content": "(56.3\\% \\downarrow)" + }, + { + "bbox": [ + 45, + 299, + 279, + 380 + ], + "type": "text", + "content": ". Even if PRTR adopts larger input resolutions " + }, + { + "bbox": [ + 45, + 299, + 279, + 380 + ], + "type": "inline_equation", + "content": "(384\\times 288, 512\\times 384)" + }, + { + "bbox": [ + 45, + 299, + 279, + 380 + ], + "type": "text", + "content": ", DistilPose still performs better using " + }, + { + "bbox": [ + 45, + 299, + 279, + 380 + ], + "type": "inline_equation", + "content": "256\\times 192" + }, + { + "bbox": [ + 45, + 299, + 279, + 380 + ], + "type": "text", + "content": " input resolution." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 381, + 280, + 497 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 381, + 280, + 497 + ], + "spans": [ + { + "bbox": [ + 45, + 381, + 280, + 497 + ], + "type": "text", + "content": "Compared to non-Transformer SOTA algorithms, DistilPose exceeds RLE in performance, parameter, and computation simultaneously on MSCOCO val dataset. As shown in Table 2, we can see that DistilPose performs much better than RLE on large human instances. Since RLE is the first regression-based work with superior performance to contemporary heatmap-based methods and DistilPose outperforms RLE, we also claim that DistilPose achieves comparable performance on par with heatmap-based methods, as shown in Table 1." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 513, + 215, + 525 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 513, + 215, + 525 + ], + "spans": [ + { + "bbox": [ + 45, + 513, + 215, + 525 + ], + "type": "text", + "content": "4.2.2 Comparison with Teacher Model" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 532, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 532, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 532, + 279, + 730 + ], + "type": "text", + "content": "We conduct experiments to compare the performance of the student and teacher models in the dimension of AP, Parameter, GFLOPs, and FPS on the MSCOCO val dataset. Extra post-processing [5, 33] is always used in the heatmap-based model for the heatmap-to-coordinate transformation during inference to eliminate quantization error, significantly improving performance, but is also followed by extra test-time overhead. In this part, we remove the extra post-processing [33] for more fairly exploring the advantages and disadvantages of heatmap-based and regression-based methods. We report the results between student and teacher without extra post-processing. As shown in Table 3, DistilPose-S sacrifices " + }, + { + "bbox": [ + 45, + 532, + 279, + 730 + ], + "type": "inline_equation", + "content": "0.9\\%" + }, + { + "bbox": [ + 45, + 532, + 279, + 730 + ], + "type": "text", + "content": " precision but dramatically improves in the reduction of parameter, computation, and test-time overhead. DistilPose-L comprehensively outperformed the heatmap-based teacher. That's because DistilPose is not only immune to quantization error" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 300, + 204, + 528, + 318 + ], + "blocks": [ + { + "bbox": [ + 45, + 167, + 531, + 201 + ], + "lines": [ + { + "bbox": [ + 45, + 167, + 531, + 201 + ], + "spans": [ + { + "bbox": [ + 45, + 167, + 531, + 201 + ], + "type": "text", + "content": "Table 3. Comparison with Teacher Model. Ex-post. = extra post-processing, which means extra post-processing used to refine the heatmap-to-coordinate transformation during inference. We compute the multiples in comparison with non extra post-processing heatmap-based method. * indicates that we re-train and evaluate the models. And HRNet-W48-s3 is short for HRNet-W48-stage3." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 300, + 204, + 528, + 318 + ], + "lines": [ + { + "bbox": [ + 300, + 204, + 528, + 318 + ], + "spans": [ + { + "bbox": [ + 300, + 204, + 528, + 318 + ], + "type": "table", + "html": "
DistillationSimulated HeatmapsTDEAPImprov.
LCSLSHLKTLVT
No----56.0%-
Yes✓63.2%+7.2%
✓56.4%+0.4%
✓✓64.1%+8.1%
✓67.1%+11.1%
✓61.7%+5.7%
✓✓67.5%+11.5%
✓✓✓✓71.6%+15.6%
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Teacher\nStudentNonestemnetHRNet-W48
stemnet56.0%63.6%71.6%
HRNet-W48-stage363.0%66.8%74.4%
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ModelSimulated HeatmapsRolemAPImprov.
SimpleBaseline-Teacher70.4%-
Deeppose×-52.6%-
Deeppose✓Student59.7%+ 6.9%
", + "image_path": "8cbedc326ecfeeb02c9efad8a97078ceaba7fabe804ad0d72bebaf9fb71d5b02.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 242, + 279, + 285 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 242, + 279, + 285 + ], + "spans": [ + { + "bbox": [ + 45, + 242, + 279, + 285 + ], + "type": "text", + "content": "Table 6. Generalization on CNN-based Model. We only implement Simulated Heatmaps to transfer heatmap-level knowledge on CNN-based models and get a significant performance improvement. Improv. = Improvement." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 293, + 225, + 303 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 293, + 225, + 303 + ], + "spans": [ + { + "bbox": [ + 45, + 293, + 225, + 303 + ], + "type": "text", + "content": "4.3.2 Better Teacher, Better Performance" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 310, + 279, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 310, + 279, + 474 + ], + "spans": [ + { + "bbox": [ + 45, + 310, + 279, + 474 + ], + "type": "text", + "content": "We conduct experiments to study the performance gain between different students and teachers. As shown in Table 5, we demonstrate that the student models will perform better if they are guided by stronger teacher models. This suggests that the performance of DistilPose we report is not the upper-bound accuracy of our distillation framework but an example to illustrate validity. In practice, we could get help from previous algorithms to train a more potent teacher, which can be further used to enhance the performance of the student model. Or we can simply expand the teacher model's capacity, finding a trade-off between performance and training memory limitation to maximize the utilization of training resources and not introduce any test-time overhead during inference." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 488, + 231, + 498 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 488, + 231, + 498 + ], + "spans": [ + { + "bbox": [ + 45, + 488, + 231, + 498 + ], + "type": "text", + "content": "4.3.3 Generalization on CNN-based Model" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 506, + 279, + 644 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 506, + 279, + 644 + ], + "spans": [ + { + "bbox": [ + 45, + 506, + 279, + 644 + ], + "type": "text", + "content": "We also conduct an ablation study on a CNN-based model to show its generalizability. We adopt Deeppose [26] as the student and SimpleBaselines [29] as the teacher. Both are the most concise algorithms in regression-based and heatmap-based models, respectively. We introduce Simulated Heatmaps to transfer heatmap-level knowledge as we do in DistilPose, and ignore TDE for the CNN-based model. Both student and teacher adopt ResNet-50 as the backbone, and the experimental results in Table 6 show that Simulated Heatmaps adapted from DistilPose improve the regression-based student's performance significantly with no extra test-time overhead." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 653, + 230, + 665 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 653, + 230, + 665 + ], + "spans": [ + { + "bbox": [ + 45, + 653, + 230, + 665 + ], + "type": "text", + "content": "4.4. Visualization of Confidence Scoring" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 45, + 671, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 671, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 671, + 279, + 730 + ], + "type": "text", + "content": "We show that the confidence score predicted by DistilPose for each coordinate is plausible. As the examples shown in Figure 6, most of the joint predictions are in the right position, and the confidence score predictions of these joints are relatively high. However, there are also some poor" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 302, + 103, + 524, + 236 + ], + "blocks": [ + { + "bbox": [ + 302, + 103, + 524, + 236 + ], + "lines": [ + { + "bbox": [ + 302, + 103, + 524, + 236 + ], + "spans": [ + { + "bbox": [ + 302, + 103, + 524, + 236 + ], + "type": "image", + "image_path": "994c38075a8748bf2dbb980a543e7057a9876af47f32dde7359dfcb167895998.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 296, + 238, + 530, + 293 + ], + "lines": [ + { + "bbox": [ + 296, + 238, + 530, + 293 + ], + "spans": [ + { + "bbox": [ + 296, + 238, + 530, + 293 + ], + "type": "text", + "content": "Figure 6. Visualization of confidence scoring. There are 2 rows in each box, representing the type of joint and the confidence score prediction value, respectively. The box border color represents whether the predicted joint is in the correct position (green is correct while red is wrong)." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 296, + 298, + 530, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 298, + 530, + 392 + ], + "spans": [ + { + "bbox": [ + 296, + 298, + 530, + 392 + ], + "type": "text", + "content": "predictions(e.g., the predictions denoted by red box in Figure 6). Fortunately, DistilPose can predict a low confidence score for most poor predictions while keeping high confidence in the correct predictions. Thus we could filter these poor predictions simply by setting a threshold. A plausible confidence score not only enhances the performance of the pose estimator, but is significant in practical applications and downstream tasks for pose estimation." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 297, + 402, + 367, + 414 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 402, + 367, + 414 + ], + "spans": [ + { + "bbox": [ + 297, + 402, + 367, + 414 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 296, + 422, + 530, + 562 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 422, + 530, + 562 + ], + "spans": [ + { + "bbox": [ + 296, + 422, + 530, + 562 + ], + "type": "text", + "content": "In this work, we proposed a novel human pose estimation framework, termed DistilPose, which includes Token-distilling Module (TDE) and Simulated Heatmaps to perform heatmap-to-regression knowledge distillation. In this way, the student regression model acquired refined heatmap knowledge at both feature and label levels, achieving a big leap in performance while maintaining efficiency. Extensive experiments were conducted on the MSCOCO dataset to demonstrate the effectiveness of our proposed DistilPose. In short, DistilPose achieved state-of-the-art performance among regression-based methods with a much lower computational cost." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 297, + 572, + 392, + 585 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 572, + 392, + 585 + ], + "spans": [ + { + "bbox": [ + 297, + 572, + 392, + 585 + ], + "type": "text", + "content": "Acknowledgement" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 296, + 591, + 530, + 719 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 591, + 530, + 719 + ], + "spans": [ + { + "bbox": [ + 296, + 591, + 530, + 719 + ], + "type": "text", + "content": "This work was supported by National Key R&D Program of China (No.2022ZD0118202), the National Science Fund for Distinguished Young Scholars (No.62025603), the National Natural Science Foundation of China (No.U21B2037, No.U22B2051, No.62176222, No.62176223, No.62176226, No.62072386, No.62072387, No.62072389, No.62002305 and No.62272401) and the Natural Science Foundation of Fujian Province of China (No.2021J01002, No.2022J06001). 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State-of-the-art methods typically have two modules, a spatial perception module and a temporal aggregation module, which are jointly learned end-to-end. Existing results in [9, 20, 25, 36] have indicated that, as the frontal component of the overall model, the spatial perception module used for spatial feature extraction tends to be insufficiently trained. In this paper, we first conduct empirical studies and show that a shallow temporal aggregation module allows more thorough training of the spatial perception module. However, a shallow temporal aggregation module cannot well capture both local and global temporal context information in sign language. To address this dilemma, we propose a cross-temporal context aggregation (CTCA) model. Specifically, we build a dual-path network that contains two branches for perceptions of local temporal context and global temporal context. We further design a cross-context knowledge distillation learning objective to aggregate the two types of context and the linguistic prior. The knowledge distillation enables the resultant one-branch temporal aggregation module to perceive local-global temporal and semantic context. This shallow temporal perception module structure facilitates spatial perception module learning. Extensive experiments on challenging CSLR benchmarks demonstrate that our method outperforms all state-of-the-art methods.", + "bbox": [ + 75, + 354, + 473, + 748 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 777, + 209, + 792 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Sign language is a visual language for deaf and hearing-impaired people for ease of communication. Because sign language has a different grammatical structure and expression from natural spoken language, deaf and hearing-", + "bbox": [ + 75, + 803, + 468, + 864 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/367a6f0353a843c5ecf0bb1464de13b6a6e4cdf73588157f747f04644d50b683.jpg", + "image_caption": [ + "Figure 1. (a) is the common CSLR framework. (b) presents the generalization capability (i.e., information stored in weights (IIW) [31]) of TAMs and SPMs of baseline, state-of-the-art methods and the proposed method. (c) is the performance of the state-of-the-art methods including word error rate, test time, and model size." + ], + "image_footnote": [], + "bbox": [ + 501, + 318, + 671, + 566 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/9facce7d33b7c8c9cd4b94d6b62a2c6253ee22ba4b33022eb65bc751476e050d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 674, + 318, + 893, + 569 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "impaired people hardly communicate normally with hearing people in daily life. To eliminate this communication gap, continuous sign language recognition (CSLR) enforces to recognition of various glosses from a sign language video. Due to the data collection and annotation being labor-intensive, CSLR benchmarks adopt a sentence-annotation manner for all sign language videos [1, 15, 33].", + "bbox": [ + 496, + 657, + 893, + 763 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In recent years, there is a consensus among state-of-the-art methods on a baseline framework (See Fig. 1 (a)). It is made up of a spatial perception module (SPM), and a temporal aggregation module (TAM) including two components for local and global temporal perception module, and the connectionist temporal classification (CTC) loss [8] for training. At present, these methods [9,20,25,36] have perceived one limitation of this framework that the temporal aggregation module can lead to insufficiently trained spatial", + "bbox": [ + 496, + 763, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Wanli Xue and Qing Guo are corresponding authors (xue-wanli@email.tjut.edu.cn and tsingqguo@ieee.org).", + "bbox": [ + 76, + 875, + 468, + 901 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "10771", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "perception module and affect the final accuracy. We use a recent interpretation method (i.e., the compression of information stored in weights (IIW) [31]) to measure the generalization capability of different neural modules. Fig. 1 (b) shows the IIWs of TAMs and SPMs of baseline and state-of-the-art works and infers their positive relation, i.e., low-generalization TAM (i.e., high IIW) usually leads to low-generalization SPM. We provide more studies in Sec. 3.", + "bbox": [ + 75, + 90, + 468, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Y. Min et al. [20] measure the difference of correctly and incorrectly recognized results between auxiliary and primary classifiers to evaluate model overfitting, and A. Hao et al. [9] visualized heatmaps of TAM's self-similarity matrices to show what the local and global temporal perception learning. However, there are no straightforward quantitative studies to discuss the effects of TAM on SPM, and we do not know how significant the effects could be and have no idea about the desired temporal aggregation. In this paper, we extensively study the limitation and desirable properties of the temporal aggregation module in the CSLR framework via constructing a baseline framework and extensive empirical studies. We insight that a desired temporal aggregation module should be a shallow architecture to allow more effective training of spatial perception module but also should be a deep one for a high temporal aggregation capability. Whereas, it is quite challenging for the temporal aggregation module to achieve these properties simultaneously.", + "bbox": [ + 75, + 212, + 470, + 483 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To overcome this challenge, we propose the cross-temporal context aggregation (CTCA) that a shallow temporal aggregation module has capable of incorporating local-global temporal contexts and the linguistic prior. Specifically, we construct a dual-path network, which decouples the local and global perception modules and imposes a linguistic module in parallel. This architecture ensures the local context perception, global context perception, and linguistic prior extraction. Furthermore, we propose a cross-context knowledge distillation loss function to transfer the local temporal context and the linguistic prior to the global perception module. Notice that the spatial perception module can facilitate itself by receiving cross-context knowledge as supervision during distillation. Fig. 1(b) shows that both SPM and TAM in CTCA achieve higher generalization than the ones of baselines. Consequently, Fig. 1(c) delivers CTCA's superiority and it outperforms the state-of-the-art methods on WER, test time, and model size.", + "bbox": [ + 75, + 484, + 468, + 755 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 768, + 218, + 786 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Continuous sign language recognition. To learn stronger representation under the sentence-annotated benchmarks, current deep learning-based approaches exploit the Connectionist Temporal Classification (CTC) [8], which provides a many-to-one mapping between frames and glosses. To mitigate the insufficient training problem [9,20,25,36], a time-consuming iterative fine-tuning strategy [6, 25] is utilized", + "bbox": [ + 75, + 794, + 468, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "to boost the model generalization. In contrast, the end-to-end methods proposed, such as VAC [20] and SMKD [9] proposed an end-to-end alignment constraint to make the learning of local and global temporal context to be consistent. $\\mathrm{C}^2\\mathrm{SLR}$ [36] designed two constraints for building spatial consistency and temporal perception consistency to enhance the representation power of the model. Y. Min et al. [21] proposed an optimized CTC loss, which can constrain features on a hypersphere and control the peak behavior of CTC loss to enhance the feature generalization. In this paper, we achieve a shallower temporal perception module that not only promotes more thorough training of spatial perception model but also aggregates local-global temporal context via a cross-temporal context distillation.", + "bbox": [ + 496, + 90, + 890, + 301 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Knowledge distillation. Knowledge distillation (KD) is a model compression technique that facilitates student models to achieve strong performance by excavating knowledge from large teacher models [11] or itself [16]. To eliminates huge training cost needs the ONE [16] proposes a multibranch network to conduct an ensemble on-the-fly. VAC [20] conducts its local and global temporal context module as an implicit teacher to promote each one to gain advanced generalization. Wang et al. [30] propose that consistent knowledge of multi-modal contains in each channel, and can achieve multi-modal fusion by exchanging their channels. POS-SCAN [35], LGD [32], and ELG [27] assume the linguistic information shares similar semantics with the visual. They transfer the image-text alignment from teacher to student. In this paper, we distill the local-global temporal information and linguistic context to a single one-branch temporal aggregation module.", + "bbox": [ + 496, + 303, + 892, + 560 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Preliminaries and Analysis", + "text_level": 1, + "bbox": [ + 500, + 577, + 750, + 594 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3.1. General CSLR Framework", + "text_level": 1, + "bbox": [ + 500, + 603, + 746, + 618 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Given a sign language video $\\mathcal{X} = \\{\\mathbf{X}_t\\}_{t=1}^T$ having $T$ frames, a continuous sign language recognition method (CSLR) denoted as $\\phi(\\cdot)$ contributes to predicting $L$ glosses (i.e., $\\mathcal{Y} = \\{y_i\\}_{i=1}^L$ ) contained in the video where $y_i$ is the $i$ -th gloss, and we have $\\mathcal{Y} = \\phi(\\mathcal{X})$ . As shown in Fig. 1(a), we show three clips in the input video, which are highlighted with pink, blue, and green colors. A CSLR method is desired to predict the corresponding three glosses, i.e., 'JETZT', 'WETTER', and 'APRIL'. The existing training dataset only provides sentence annotation (See the annotation in Fig. 1) instead of the ground truth of each frame and we even do not know the exact number of glosses in the input video. Hence, the task is a weakly-supervised learning problem and significantly challenging.", + "bbox": [ + 496, + 626, + 890, + 839 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The dominant CSLR framework [9, 20, 36] mainly involves three modules: spatial perception module (SPM) to extract feature representation of each frame independently, temporal aggregation module (TAM) to sequentially con", + "bbox": [ + 496, + 839, + 890, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "10772", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/7a903fbb9c557e3cf636b0bed5c0deeed83d969a5551d7de5ef0bf2cdab96eef.jpg", + "image_caption": [ + "Figure 2. Experiments about chain depth variants of TAM in the general CSLR framework. The IIW [31] is exploited to measure the generalization gap (the larger gap, the larger the IIW) of SPM and TAM. The WER value is utilized to estimate the performance." + ], + "image_footnote": [], + "bbox": [ + 98, + 82, + 450, + 333 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "duct local and global aggregation across frames' features, and the classification module for the final prediction. We denote the three modules as $\\phi_{\\mathrm{spm}}(\\cdot),\\phi_{\\mathrm{tam}}(\\cdot)$ ,and $\\phi_{\\mathrm{cls}}(\\cdot)$ , respectively, and can reformulate the whole process as $\\mathcal{V} =$ $\\phi (\\mathcal{X}) = \\phi_{\\mathrm{cls}}(\\phi_{\\mathrm{tam}}(\\phi_{\\mathrm{spm}}(\\mathcal{X}))$ (See Fig. 1(a)). Specifically, $\\phi_{\\mathrm{spm}}(\\cdot)$ first extracts features of all frames via a convolution neural network like ResNet18 [10], which are denoted as $\\mathcal{V} = \\{\\mathbf{V}_t\\}_{t = 1}^T$ . Then, $\\phi_{\\mathrm{tam}}(\\cdot)$ uses a local temporal context perception component like temporal convolution network (i.e., 1D-TCN) [5, 9, 20, 36] to capture the correlation across adjacent frames and map the representations $\\nu$ to a new one, i.e., $\\mathcal{V}^{\\mathrm{loc}} = \\{\\mathbf{V}_t^{\\mathrm{loc}}\\}_{t = 1}^T$ $\\phi_{\\mathrm{tam}}(\\cdot)$ further feeds the locally-aggregated representations to the global perception component like a two-layer BLSTM [9, 20, 34, 36] to capture the global temporal patterns across all frames and get $\\mathcal{V}^{\\mathrm{glo}} = \\{\\mathbf{V}_t^{\\mathrm{glo}}\\}_{t = 1}^T$ . Then, the $\\mathcal{V}^{\\mathrm{glo}}$ is further passed to $\\phi_{\\mathrm{cls}}$ , which is a fully-connected layer to predict logits $\\mathcal{Z}^{\\mathrm{glo}} = \\{\\mathbf{Z}_t^{\\mathrm{glo}}\\}_{t = 1}^T$ . Finally, the $\\mathcal{Z}^{\\mathrm{glo}}$ is fed into the CTC to align the prediction and ground truth and calculate the loss.", + "bbox": [ + 75, + 405, + 472, + 694 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Empirical Studies", + "text_level": 1, + "bbox": [ + 76, + 703, + 250, + 719 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Following the fact about chain rules of backpropagation, we study the effects of the chain depth of the temporal aggregation module to the spatial perception module. Intuitively, the temporal aggregation module with fewer layers (i.e., a shallow TAM) has fewer effects on the back-propagation of gradients, and a shallower TAM could lead to a more powerful SPM. To conduct a solid analysis, we have the following setups:", + "bbox": [ + 75, + 727, + 468, + 849 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "- Baseline CSLR. We follow the general CSLR framework in Sec. 3.1 and construct a CSLR method including a cascaded ResNet18 as the SPM, $K$ -layer 1D", + "bbox": [ + 94, + 854, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "TCNs and a two-layer BLSTM as the TAM, and the classifier and the CTC as the classification module. The $K$ -layer 1D-TCNs and BLSTM are used for local and global temporal contexts perception, respectively.", + "bbox": [ + 529, + 90, + 890, + 151 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "- TAM with different chain depths. We set five variants of TAM by stacking $K$ 1D-TCNs where we set $K \\in \\{0,1,3,9,22\\}^*$ . We do not tune the depth of the BLSTM since the BLSTM is prone to over-fitting [9, 20], we contribute to exploring the influence of the depth between SPM and BLSTM.", + "bbox": [ + 517, + 152, + 893, + 242 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "- Evaluation of SPM and CSLR. Following existing works, we use the word error rate (WER) to evaluate the performance of the whole CSLR method. In contrast, for TAM and SPM, we choose another metric, i.e., the compression of information stored in weights (IIW) [31], which is designed to understand the behavior of neural networks and can be an indicator of generalization gap (i.e., the accuracy difference on the test and training datasets) of neural networks [31]. Intuitively, with the same training dataset, a lower IIW of a module means that the module contributes more to the accuracy of the test dataset.", + "bbox": [ + 517, + 243, + 893, + 425 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "With the above setups, we get five CSLR variants with five TAMs having different chain depths. Then, we train and test all variants on the RWTH-2014 dataset [15]. Specifically, we can calculate the word error rate (WER) of the five variants for the prediction accuracy evaluation. We further count the information stored in weights (IIW) of the SPMs and TAMs of the five variants, respectively. As the results are shown in Fig. 2, we have the following observations: ① When we consider the chain depth (i.e., $K$ ) from 1 to 22, the IIW of SPM gradually increases and reaches the maximum at $K = 22$ while the IIW of TAM gradually decreases, which means the effects of chain depth to the capability of SPM and TAM have completely opposite trends. A powerful SPM desires a shallow TAM while the TAM itself requires a deeper architecture. ② Considering the changes of WER of the CSLR along different chain depths, we see that the trend of WER is consistent with the IIW's variation trend, which means the SPM has higher effects than the TAM on the final prediction accuracy.", + "bbox": [ + 496, + 430, + 893, + 719 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Motivations", + "text_level": 1, + "bbox": [ + 500, + 726, + 629, + 739 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "According to the above studies, a desired temporal aggregation module should be a shallow architecture to allow more effective training of the spatial perception module but also should be a deep one for a high temporal aggregation capability. Such a contradiction makes the designing of a suitable TAM challenging. Because SPM is directly related to the final accuracy, we tend to select a shallow TAM.", + "bbox": [ + 496, + 750, + 893, + 854 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "*0 illustrates the TAM drop the 1D-TCN. We adjust channels of 1D-TCN to make sure different variants have the same model size. Such as 1,3,9,22 denote their channels are 1024,512,256 and 128, respectively.", + "bbox": [ + 500, + 862, + 893, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "10773", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/df13b1bb0ef0506ceab92c0d269f3859ad75f10ace36414d1e810c909bf0c08b.jpg", + "image_caption": [ + "Figure 3. Pipeline of the CTCA. In particular, the steps with black borders or black arrows belong to the CTCA test process." + ], + "image_footnote": [], + "bbox": [ + 80, + 89, + 467, + 303 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Then, the key problem becomes how to make TAM shallower and contribute more to the final prediction accuracy.", + "bbox": [ + 75, + 352, + 468, + 383 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Existing works have noticed that both local and global temporal perception are critical to prediction accuracy. We also conduct a simple study and observe that removing any temporal perception components leads to a significant accuracy drop (See the supplementary material). All the above observations motivate us to develop a shallower but more powerful temporal aggregation module that has the capability of perceiving local and global context perception.", + "bbox": [ + 75, + 383, + 468, + 505 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Cross-Temporal Context Aggregation", + "text_level": 1, + "bbox": [ + 76, + 521, + 415, + 539 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "An intuitive idea is to utilize knowledge distillation to integrate local and global contexts into a shallow architecture. As a result, the two opposite requirements for TAM in Sec. 3.3 could be handled simultaneously. To this end, we first provide a vanilla distillation solution in Sec. 4.1, which has several inherent limitations. Then, we impose a more advanced distillation method, i.e., cross-temporal context aggregation (CTCA), in Sec. 4.2 and Sec. 4.3.", + "bbox": [ + 75, + 547, + 468, + 667 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. A Vanilla Distillation Solution", + "text_level": 1, + "bbox": [ + 76, + 680, + 341, + 695 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We follow the baseline CSLR in Sec. 3.2 and construct two independent CSLRs that have the same spatial perception module (SPM) and classification module but a different temporal aggregation module (TAM). The first one retains the global perception component (i.e., a BLSTM) and removes the local component (i.e., 1D-TCN). Such a CSLR has the shallowest TAM (i.e., $K = 0$ in Sec. 3.2) and we denote it as CSLR-GloTAM. The second one only contains the local perception component and the BLSTM layer is removed and we denote it as CSLR-LocTAM. The main goal is to train a CSLR-GloTAM to let its TAM have the local temporal contexts. To this end, we use the CSLR-LocTAM to teach the CSLR-GloTAM for acquiring local information", + "bbox": [ + 75, + 703, + 470, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "and only use the CSLR-GloTAM for inference. The teaching manner follows the vanilla distillation [11].", + "bbox": [ + 498, + 90, + 890, + 121 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "However, such a vanilla distillation approach has some limitations: 1) In terms of CSLR-GloTAM, when BLSTM over-fits the training data, the loss can be hardly propagated to the SPM. The distillation based on two separated CSLRs cannot address this issue properly. 2) By adapting existing distillation methods directly, we need to design two exclusive optimization schemes for the two independent CSLRs, respectively, which inevitably leads to high time and computing costs. 3) The vanilla distillation leverages a fully-supervised distillation loss, which cannot be adapted to the weakly-supervised optimization like CSLR directly.", + "bbox": [ + 496, + 122, + 890, + 287 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. SPM-Shared Dual-Path Network", + "text_level": 1, + "bbox": [ + 498, + 300, + 787, + 315 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Enforcing to resolve the first and second limitations in Sec. 4.1, we propose the SPM-Shared Dual-Path Network (SDPN). Inspired by [16], we adopt a multi-branch architecture with a shared SPM to merge the training processes of teacher and student, which distills from each other in a peer-teaching manner. As a result, this structure avoids the requirement of two optimization schemes trade-offs. It is easy to train with only one optimization scheme. As such, different from the vanilla distillation approach has two separate networks, the SDPN is composed of a shared SPM and followed a dual-path (See Fig. 3): local temporal perception branch (i.e., 1D-TCN branch), global temporal perception branch (i.e., BLSTM branch). Specifically, each branch itself of SDPN stands for the specific knowledge concurrently, which conducts a native ensemble model on-the-fly. With the above architecture, even if the BLSTM branch is over-fitted, other branches like the 1D-TCN branch can still back-propagate the loss to the shared SPM straightforwardly. More importantly, the SDPN is easy to adopt distillation losses (See Sec. 4.3) to distill the local temporal context and the linguistic prior to reinforcing BLSTM. The two branches of SDPN have different objectives and architectures as done in [9, 17, 20]. In particular, we only use the BLSTM branch during inference, rather than both branches. We detail the architectural designs in the following:", + "bbox": [ + 496, + 325, + 890, + 700 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Shared spatial perception module. We use the ResNet18 for the spatial perception module (See Sec. 3.1) where the fully-connection layer is removed, which takes the video clips as inputs and outputs the spatial representation $\\nu$ .", + "bbox": [ + 496, + 703, + 890, + 763 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Local & global temporal perception branches. The local branch consists of a 1D-TCN and a local classifier $\\mathcal{F}^{\\mathrm{loc}}$ . The 1D-TCN is able to provide local temporal representations $\\mathcal{V}^{\\mathrm{loc}}$ maintained sign-wise information. And the local classifier outputs the local prediction $\\mathcal{Z}^{\\mathrm{loc}}$ . The global branch contains a two-layer BLSTM and a global classifier $\\mathcal{F}^{\\mathrm{glo}}$ . The BLSTM outputs global temporal representations $\\mathcal{V}^{\\mathrm{glo}}$ , which contains the order and correlation of co-occurring signs. The global classifier outputs the global prediction", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "10774", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\mathcal{Z}^{\\mathrm{glo}}$ . Note that, both $\\mathcal{Z}^{\\mathrm{glo}}$ and $\\mathcal{Z}^{\\mathrm{loc}}$ are optimized by CTC loss to achieve a knowledge complementary to the spatial perception module reinforcement, and the 1D-TCN is removed during inference.", + "bbox": [ + 76, + 90, + 468, + 151 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Cross-Context Knowledge Distillation Loss", + "text_level": 1, + "bbox": [ + 76, + 162, + 442, + 178 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To make the shallow BLSTM branch learn both local & global perceptions and achieve the desired property against the third limitation in Sec. 4.1, we propose the Cross-Context Knowledge Distillation Loss (CCKD). CCKD composes a cross-temporal knowledge distillation (CTD) and a cross-modality knowledge distillation (CMD). The CTD builds a mutual temporal context distillation that enables the BLSTM and 1D-TCN branches to incorporate complementary knowledge to refine themselves and the SPM. The CMD distills linguistic prior i.e., inter-gloss semantic correlation from glosses sequence to BLSTM branch to reinforce its temporal aggregation. In contrast to the vanilla distillation that enhances the student's ability to achieve consistent prediction scores with the teacher, the CCKD focuses on distilling channel-wise knowledge from intermediate feature hints [28]. By doing so, CCKD facilitates students to learn how to learn, rather than how to get prediction scores, which is more applicable to CSLR.", + "bbox": [ + 75, + 185, + 468, + 455 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Cross-temporal knowledge distillation. ① Local temporal context guidance loss $(\\mathcal{L}_{l2g})$ . Given the local and global temporal representation $\\mathcal{V}^{\\mathrm{loc}}$ and $\\mathcal{V}^{\\mathrm{glo}}$ , the $\\mathcal{L}_{l2g}$ encourages the $\\mathcal{V}^{\\mathrm{glo}}$ to learn sign-wise context maintained in $\\mathcal{V}^{\\mathrm{loc}}$ to remain local-global temporal contexts. Due to the knowledge of sign-wise context being distinct from the global context, knowledge confusion may occur during the $\\mathcal{L}_{l2g}$ procedure. To relieve the confusion, we weight the $\\mathcal{V}^{\\mathrm{loc}}$ by the intersection information $I(\\mathcal{V}^{\\mathrm{loc}}, \\mathcal{V}^{\\mathrm{glo}})$ among $\\mathcal{V}^{\\mathrm{loc}}$ and $\\mathcal{V}^{\\mathrm{glo}}$ to suppress signs information of $\\mathcal{V}^{\\mathrm{loc}}$ who differs with $\\mathcal{V}^{\\mathrm{glo}}$ .", + "bbox": [ + 75, + 458, + 467, + 609 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {l 2 g} \\left(\\mathcal {V} ^ {\\mathrm {g l o}}, \\mathcal {V} ^ {\\mathrm {l o c}}\\right) = \\varphi \\left(\\mathcal {V} ^ {\\mathrm {g l o}}, \\mathcal {V} ^ {\\mathrm {l o c}} \\cdot I \\left(\\mathcal {V} ^ {\\mathrm {l o c}}, \\mathcal {V} ^ {\\mathrm {g l o}}\\right)\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 116, + 616, + 468, + 636 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\varphi \\left(\\mathcal {V} ^ {\\text {g l o}}, \\mathcal {V} ^ {\\text {l o c}}\\right) = \\frac {\\tau^ {2}}{C} \\sum_ {c = 1} ^ {C} \\sum_ {i = 1} ^ {T} K L \\left(\\left(\\mathbf {V} _ {c, i} ^ {\\text {g l o}}\\right), \\left(\\mathbf {V} _ {c, i} ^ {\\text {l o c}}\\right)\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 116, + 647, + 468, + 688 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nI \\left(\\mathcal {V} ^ {\\text {l o c}}, \\mathcal {V} ^ {\\text {g l o}}\\right) = \\frac {1}{\\frac {\\sigma \\left(\\mathbf {V} _ {c , i} ^ {\\text {l o c}}\\right)}{\\sigma \\left(\\mathbf {V} _ {c , i} ^ {\\text {g l o}}\\right)} + 1}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 178, + 699, + 468, + 742 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where if $\\frac{\\sigma(\\mathbf{V}_{c,i}^{\\mathrm{loc}})}{\\sigma(\\mathbf{V}_{c,i}^{\\mathrm{glo}})}$ is large and thus $I(\\mathcal{V}^{\\mathrm{loc}},\\mathcal{V}^{\\mathrm{glo}})$ is small, meaning the large different between $\\nu^{\\mathrm{loc}}$ and $\\nu^{\\mathrm{glo}}$ . The $KL$ denotes the KL divergence, $\\tau$ is the temperature factor for smooth, $\\sigma$ indicates the softmax function and $C$ corresponds to the feature channels. As indicated in [28], the KL divergence can be used between intermediate feature hints. 2 Global temporal context guidance loss $(\\mathcal{L}_{g2l})$ . In addition, the $\\mathcal{L}_{g2l}$ loss evolves distilling global contexts i.e., signs order and correlation among co-occurring signs", + "bbox": [ + 75, + 750, + 467, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "to the 1D-TCN branch. As a result, remaining the local-global context, the 1D-TCN is applicable to learning signwise contexts by taking into account global contexts. The $\\mathcal{L}_{g2l}$ loss is also formulated as a similarly form with $\\mathcal{L}_{l2g}$ :", + "bbox": [ + 498, + 90, + 890, + 152 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {g 2 l} \\left(\\mathcal {V} ^ {\\text {l o c}}, \\mathcal {V} ^ {\\text {g l o}}\\right) = \\varphi \\left(\\mathcal {V} ^ {\\text {l o c}}, \\mathcal {V} ^ {\\text {g l o}}\\right). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 160, + 890, + 178 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$\\Theta$ Reconstruction loss $(\\mathcal{L}_{rc})$ . The intuition behind this loss is that the distillation between 1D-TCN and BLSTM should be further enhanced when the local representation is welllearned. Therefore, we impose the $\\mathcal{L}_{rc}$ as the reconstruction function for the local temporal representation $\\mathcal{V}^{\\mathrm{loc}}$ to reinforce cross-temporal context distillation. Notably, we experimentally follow the entropy principle [13, 18] to measure knowledge uncertainty by $w(\\mathbf{V}_i^{\\mathrm{loc}})$ . If the estimated $\\mathcal{V}^{\\mathrm{loc}}$ is well-trained and has a high certainty, $H(\\mathbf{V}_i^{\\mathrm{loc}})$ becomes small, leading to a large weight $(1 + w(\\mathbf{V}_i^{\\mathrm{loc}}))$ . Then, the consistency between local & global representations is further enhanced via the $\\mathcal{L}_{rc}$ . We also adopt a residual connection for stable weighting.", + "bbox": [ + 496, + 186, + 890, + 383 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {r c} = \\sqrt {\\sum_ {i = 1} ^ {T} \\left(\\mathbf {V} _ {i} ^ {\\mathrm {g l o}} - \\mathbf {V} _ {i} ^ {\\mathrm {l o c}}\\right) ^ {2}} \\cdot \\sum_ {i = 1} ^ {T} (1 + w (\\mathbf {V} _ {i} ^ {\\mathrm {l o c}})), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 393, + 890, + 441 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nw \\left(\\mathbf {V} _ {i} ^ {\\text {l o c}}\\right) = \\exp^ {- H \\left(\\mathbf {V} _ {i} ^ {\\text {l o c}}\\right)}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 614, + 452, + 890, + 470 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As mentioned above, the CTD loss is formulated as:", + "bbox": [ + 500, + 477, + 844, + 491 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {c t d} = \\alpha_ {1} \\mathcal {L} _ {l 2 g} + \\alpha_ {2} \\mathcal {L} _ {g 2 l} + \\alpha_ {3} \\mathcal {L} _ {r c}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 502, + 890, + 518 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Where the $\\alpha_{1}$ , $\\alpha_{2}$ , $\\alpha_{3}$ achieve trade-offs among losses in the CTD loss. Furthermore, the CTD loss ensures the spatial perception module to be propagated the local-global information during the whole training time, which avoids the propagation effect of BSLTM overfitting and enhances SPM generalization ability, implicitly.", + "bbox": [ + 496, + 527, + 890, + 618 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Cross-modality knowledge distillation. The CTD loss only restricts the cross-temporal context statistics yet has weak semantic context supervision i.e., the linguistic prior. Motivated by CLIP [26] and ELG [27], the cross-modality knowledge distillation (CMD) is proposed to distill inter-gloss semantic correlation from glosses sequence to BLSTM branch. In practice, given the gloss sequence $\\mathcal{V} = \\{y_i\\}_{i=1}^L$ corresponding to $\\mathcal{X}$ with $L$ glosses, it will be embedded by pre-trained BERT to generate high-dimensional semantic features $\\mathcal{G}^{\\mathrm{gls}} = \\{\\mathbf{G}_i^{\\mathrm{gls}}\\}_{i=1}^L \\in \\mathbb{R}^{Y \\times L}$ . Further, the $\\mathcal{G}^{\\mathrm{gls}}$ and global temporal representation $\\mathcal{V}^{\\mathrm{glo}}$ will be computed by cross-attention [29] to generate the linguistic-visual relation $\\mathcal{G}^{\\widehat{t}} \\in \\mathbb{R}^{Y \\times L}$ .", + "bbox": [ + 496, + 619, + 890, + 816 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {G} ^ {\\widehat {t}} = \\operatorname {s o f t m a x} \\left(\\frac {f _ {\\mathcal {Q}} \\left(\\mathcal {G} ^ {\\mathrm {g l s}}\\right) f _ {\\mathcal {K}} \\left(\\mathcal {V} ^ {\\mathrm {g l o}}\\right) ^ {\\mathrm {T}}}{\\sqrt {C}}\\right) f _ {\\mathcal {V}} \\left(\\mathcal {V} ^ {\\mathrm {g l o}}\\right), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 539, + 824, + 890, + 859 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Moreover, the self-correlation matrix $\\underline{cor}^{\\hat{t}}$ will be obtained by the matrix product of $\\mathcal{G}^{\\hat{t}}$ and $(\\mathcal{G}^{\\hat{t}})^{\\mathrm{T}}$ . The $cor^t$ is a", + "bbox": [ + 496, + 869, + 890, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "10775", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "self-correlation matrix of gloss features $\\mathcal{G}^{\\mathrm{gls}}$ , i.e., $cor^{t} = \\left\\| \\mathcal{G}^{\\mathrm{gls}}\\right\\|_{2}\\left(\\left\\| \\mathcal{G}^{\\mathrm{gls}}\\right\\|_{2}\\right)^{\\mathrm{T}}$ . Finally, we distill the inter-gloss discrimination from the $cor^{t}$ to the $cor^{\\hat{t}}$ via the cross-modality distillation loss $\\mathcal{L}_{cmd}$ . The $t$ and $\\hat{t}$ represent the gloss modality and visual modality, respectively.", + "bbox": [ + 76, + 90, + 472, + 174 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {c m d} = \\frac {1}{L} \\sum_ {i = 1} ^ {L} \\sigma \\left(\\operatorname {c o r} _ {i} ^ {\\hat {t}}\\right) \\cdot \\log \\left[ \\frac {\\sigma \\left(\\operatorname {c o r} _ {i} ^ {\\hat {t}}\\right)}{\\sigma \\left(\\operatorname {c o r} _ {i} ^ {t}\\right)} \\right], \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 133, + 183, + 468, + 226 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\sigma$ indicates the softmax function. We involve $cor^t$ to have the same knowledge with $cor^t$ to enhance the linguistic-visual relation, which encourages $\\nu^{\\mathrm{glo}}$ to have the inter-gloss discrimination indirectly.", + "bbox": [ + 76, + 233, + 468, + 295 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Combining all loss functions, the CCKD is denoted as:", + "bbox": [ + 94, + 296, + 460, + 311 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathcal {C C K D}} = \\alpha \\mathcal {L} _ {c t d} + \\beta \\mathcal {L} _ {c m d} + \\gamma \\mathcal {L} _ {c t c}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 150, + 323, + 468, + 340 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where the $\\alpha, \\beta$ , and $\\gamma$ control the trade-off among losses.", + "bbox": [ + 76, + 351, + 455, + 367 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. Implementation Details", + "text_level": 1, + "bbox": [ + 76, + 376, + 294, + 393 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Network details. We set $K = 3$ and kernel size is 3 for 1D-TCN, each layer equips with a 1D Batch Norm layer and a ReLU activation. The output channel of each temporal layer in 1D-TCN is set to 1024 and BLSTM is set to 2048.", + "bbox": [ + 76, + 398, + 468, + 459 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Hyperparameters setting. The $\\tau$ in Eq. (2) is set to 4, the $\\alpha_{1},\\alpha_{2},\\alpha_{3}$ in Eq. (7) are set to 0.2, 1, 1 respectively. And $\\alpha ,\\beta ,$ and $\\gamma$ in Eq. (10) are set to 3, 130, 1 respectively. We find that the $\\alpha_{1}$ is chosen in [0.1, 1) and the $\\beta$ needs to be set to among [50, 150] to obtain good performance.", + "bbox": [ + 76, + 460, + 468, + 536 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Training and test strategy. During both the training and test stages for all benchmarks, we randomly discard half of video frames as inputs following SFL [22]. We then resize the frame size to $256 \\times 256$ and perform randomly cropping frames to $224 \\times 224$ , as well as random horizontal flip (50%) in the training stage (only center crop frames to $224 \\times 224$ in the test stage). The BERT in the CMD loss is frozen and only employed in the training stage. In the test, only the spatial perception module and the global temporal perception branch are exploited to generate predictions. The CTCA is implemented in PyTorch with one A100 GPU.", + "bbox": [ + 75, + 536, + 470, + 703 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 76, + 715, + 209, + 733 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Dataset and Evaluation", + "text_level": 1, + "bbox": [ + 76, + 739, + 294, + 756 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "RWTH-2014 [15] is a German sign language dataset, it consists of a total of 6,841 sentences with a vocabulary of 1,295 glosses, signed by 9 different singers.", + "bbox": [ + 76, + 763, + 468, + 809 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "RWTH-2014T [1] can be used for both CSLR and sign language translation tasks [1]. It involves a vocabulary of 1,085 glosses, split into 7,096, 519, and 642 samples in the train set, dev set, and test set, respectively.", + "bbox": [ + 76, + 810, + 468, + 869 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "CSL-Daily [33] is a large Chinese sign language dataset about people's daily life. It can be employed in both CSLR", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/3b07462cf73c8d46ddc25a34ae1145475770369798da5cbeba39321f04799915.jpg", + "table_caption": [ + "Table 1. Comparison with state-of-the-art methods on the RWTH2014 dataset. (WER(%) the lower is the better)." + ], + "table_footnote": [], + "table_body": "
MethodsDevTest
del/insWERdel/insWER
DNF [6]7.8/3.523.87.8/3.424.4
FCN [5]-23.7-23.9
VAC [20]7.9/2.521.28.4/2.622.3
CMA [23]7.3/2.721.37.3/2.421.9
SMKD [9]6.8/2.520.86.3/2.321.0
C²SLR [36]-20.5-20.4
TLP [17]6.3/2.819.76.1/2.920.8
RadialCTC [21]6.5/2.719.46.1/2.620.2
CTCA(Ours)6.2/2.919.56.1/2.620.1
", + "bbox": [ + 516, + 116, + 874, + 287 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/1c3ba0d85f8446ccd00ea83bdeffd3eeecad6d7e276a8a00652f31ac8b0a57be.jpg", + "table_caption": [ + "Table 2. Comparison with state-of-the-art methods on the RWTH-2014T dataset. (WER(%) the lower is the better)." + ], + "table_footnote": [], + "table_body": "
MethodsWER
DevTest
SLT [2]24.624.5
CNN+LSTM+HMM [14]22.124.1
BN-TIN+Transf [33]22.723.9
V-L Mapper [4]21.922.5
SMKD [9]20.822.4
C2SLR [36]20.220.4
TLP [9]19.421.2
CTCA(Ours)19.320.3
", + "bbox": [ + 557, + 325, + 831, + 481 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "and sign language translation. There are 18,401, 1,077, and 1,176 videos for the training set, dev set, and test set, respectively. It has a vocabulary of 2,000 glosses for CSLR.", + "bbox": [ + 498, + 506, + 890, + 551 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation metric. In this paper, we adopt the word error rate (WER) metrics for CSLR methods evaluation. It measures the minimum number of substitutions, deletions, and insertions that need to convert one predicted glosses sequence to a given reference sequence [15].", + "bbox": [ + 498, + 551, + 890, + 626 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Comparison with State-of-the-arts", + "text_level": 1, + "bbox": [ + 500, + 636, + 802, + 651 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation on RWTH-2014. The objective of the VAC and SMKD is to enhance the discriminative capacity of the visual module (i.e., SPM+1D-TCN). Meanwhile, our CTCA focuses on investigating and designing the desired TAM for CSLR. As demonstrated in Tab. 1, the proposed CTCA solely utilizes the RGB information of sign language videos, yet it achieves competitive performance in terms of the WER (19.5% and 20.1%). Notably, it surpasses other RGB cue-based approaches, i.e., SMKD, C2SLR, and TLP, thereby validating the effectiveness of CTCA.", + "bbox": [ + 498, + 657, + 890, + 809 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation on RWTH-2014T. In Tab. 2, it is evident that the CTCA gains the best performance (19.3% and 20.3%) compared with other state-of-the-art approaches.", + "bbox": [ + 498, + 810, + 890, + 854 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation on CSL-Daily. To further assess the CTCA's generalization capacity, we evaluate it on the CSL-Daily benchmark. As presented in Tab. 3, the CTCA outperforms", + "bbox": [ + 498, + 854, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "10776", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/592d638d2535413afae9da396a50f09c0e33eab4ee3c450d5990e46d2da3573a.jpg", + "table_caption": [ + "Table 3. Comparison with state-of-the-art methods on the CSL-Daily. (WER(%) the lower is the better)." + ], + "table_footnote": [], + "table_body": "
MethodsDevTest
del/insWERdel/insWER
LS-HAN [12]14.6/5.739.014.8/5.039.4
SLT(Gloss+Text) [2]10.3/4.433.19.6/4.132.0
FCN [5]12.8/4.033.212.6/3.732.5
BN-TIN+Transf [33]13.9/3.433.613.5/3.033.1
TIN-Iterative [6]12.8/3.332.812.5/2.732.4
CTCA(Ours)9.2/2.531.38.1/2.329.4
", + "bbox": [ + 76, + 116, + 467, + 242 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/62533a2fc38869d1977c6d567674d3b4eab71341104b22e522d631a4cb944296.jpg", + "table_caption": [ + "Table 4. Effect of the SDPN architecture on the RWTH-2014." + ], + "table_footnote": [], + "table_body": "
MethodsIIWDevTest
del/insWERdel/insWER
Baseline6.7E-57.0/3.021.86.7/2.722.1
Baseline+SDPN5.6E-57.3/3.121.77.4/2.421.8
VAC(VE) [20]5.4E-5-23.3-23.8
VAC(VE)+SDPN4.2E-57.6/3.122.07.6/3.022.6
", + "bbox": [ + 84, + 270, + 457, + 364 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "all other methods and achieves a $3\\%$ WER advantage over the second-best performer, the TIN-Iterative.", + "bbox": [ + 75, + 392, + 468, + 422 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 435, + 230, + 452 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Benefits of SPM-Shared Dual-Path Network. Tab. 4 illustrates that when both baseline and VAC are constructed to SDPN architecture, achieving lower generalization gap (lower IIW) and improved performance (lower WER). It is noteworthy that during the testing, only the spatial perception module and the BLSTM branch of SDPN are utilized. These results suggest that the SDPN architecture can facilitate thorough training for the spatial perception module, leading to improved performance.", + "bbox": [ + 75, + 459, + 468, + 595 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Benefits of components of Cross-Context Knowledge Distillation loss. $\\bullet$ Effect of vanilla distillation solution. We compare the vanilla distillation approach, as discussed in Sec. 4.1 with the baseline. As presented in Tab. 5, the vanilla distillation yields an improvement over the baseline, yet it is still inferior to each component of the CCKD.", + "bbox": [ + 75, + 597, + 468, + 686 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "$\\Theta$ Effect of $\\mathcal{L}_{l2g}$ loss and $\\mathcal{L}_{g2l}$ loss. We introduced two distillation methods, SDPN A and SDPN B based on the SDPN model. SDPN A is the 1D-TCN distilling sign-wise knowledge to the BLSTM via the $\\mathcal{L}_{l2g}$ . This method improves performance on the test set by $1.0\\%$ compared to the baseline. We also removes the intersection information weighted term $I(:,)$ from SDPN A, which results in a $0.4\\%$ drop in performance on the test set, implying its effectiveness. SDPN B, on the other hand, is an SDPN model optimized by the $\\mathcal{L}_{g2l}$ , which yields a $1.4\\%$ WER improvement over the baseline on the test set. It is noteworthy that SDPN A's performance is inferior to SDPN B. This can be explained that BLSTM tends to overfit on the sequential order of signs, which is easy to learn and leads to fast convergence", + "bbox": [ + 75, + 688, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/41beb5459570f617d5578fb530cf16e0f7af421e04f0933310c68f53f2707e31.jpg", + "table_caption": [ + "Table 5. Ablation study on cross-context knowledge distillation loss on the RWTH-2014." + ], + "table_footnote": [], + "table_body": "
MethodLctdLcmdDevTest
Ll2gLg2lLrc
Baseline----21.822.1
Vanilla----21.721.9
SDPN A✓---21.021.1
SDPN A-I(;;)✓---21.321.5
SDPN B-✓--20.820.7
SDPN C✓✓--20.420.6
SDPN D✓✓✓-20.020.4
SDPN D-w(;;)✓✓✓-20.220.6
SDPN E---✓21.321.0
CTCA✓✓✓✓19.520.1
", + "bbox": [ + 506, + 116, + 883, + 301 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/bfc50f8f463bdbbc67b0160ce8b51a67796244ce948aec7b738f0a1aa8d49845.jpg", + "table_caption": [ + "Table 6. Comparison of different knowledge fusion schemes on the RWTH-2014. \"Wasserstein\" is the Wasserstein distance." + ], + "table_footnote": [], + "table_body": "
MethodKnowledge fusionDevTest
SDPN-21.721.8
Vanilla distillation [11]21.621.6
Wasserstein [3]21.621.5
JMMD [19]21.321.3
CKD [28]21.321.5
CTCA(ℓl2g)21.021.1
concatenation22.723.6
point-wise addition21.222.3
attention22.222.6
", + "bbox": [ + 542, + 354, + 846, + 511 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "optimized by CTC [9, 25]. Although the BSLTM in SDPN A receives local context knowledge, it still propagates limited local-global information to SPM, resulting in limited gain for SPM when it is overfitting. Furthermore, the 1D-TCN is less prone to overfitting [5] and in SDPN B facilitated by the $\\mathcal{L}_{g2l}$ the 1D-TCN can learn sign-wise context by taking into account global contexts. Then it can provide richer sign-wise supervision to the SPM for locating signs, which can eliminate the limited back-propagation. As a result, more robust features SPM can generate, and they are fed into BLSTM, which outperforms SDPN A. This finding is consistent with the observation $\\pmb{\\Theta}$ in Sec. 3.2 that the SPM has a high effect on the final prediction performance. The results of SDPN C show that the mutual distillation approach gains $20.6\\%$ on the test set. This technique can enhance both the $\\mathcal{L}_{l2g}$ and $\\mathcal{L}_{g2l}$ , resulting in improved 1D-TCN and BLSTM. This success is also verified by [9].", + "bbox": [ + 496, + 537, + 890, + 792 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effect of $\\mathcal{L}_{rc}$ loss and $\\mathcal{L}_{cmd}$ loss. Seen from Tab. 5, based on the SDPN C model the SDPN D combines the $\\mathcal{L}_{rc}$ , which is effective in enhancing performance. Specifically, when SDPN D drops the $w(:,)$ , it gives a worse result, it shows the effect of entropy measurement. Moreover, SDPN E, achieves relatively better performance, which validates the need for linguistic prior supervision.", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "10777", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/52a8357e1a2b67ec85bd596609d98f0a78c41c9e5300f3a998595da18bffe8d2.jpg", + "table_caption": [ + "Table 7. Performance comparison of local temporal perception module with distinct temporal window widths on the RWTH-2014. $Ft$ and $Ft(d)$ correspond to the 1D temporal convolution layer with kernel of $t$ and dilation of $d$ , respectively." + ], + "table_footnote": [], + "table_body": "
MethodvariantswindowsDevTest
1D-TCNF3-F3-F37*219.520.1
F3(1)-F3(2)7*219.820.3
F5-F59*220.620.6
F5-F5-F513*219.920.6
F7-F713*220.120.3
", + "bbox": [ + 112, + 156, + 433, + 250 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/3eb9ed19e119590fee17fe606c7028f6e24fde4834636de38adf2ee7ab22241a.jpg", + "table_caption": [ + "Table 8. Comparison of CTCA with distinct global temporal perception modules (GTPM) on the RWTH-2014." + ], + "table_footnote": [], + "table_body": "
MethodvariantsDevTest
GTPM-branchBLSTM19.520.1
Dilated blocks22.222.6
Transformer28.728.9
Transformer+BLSTM24.424.1
", + "bbox": [ + 86, + 303, + 455, + 383 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.4. Module Analysis", + "text_level": 1, + "bbox": [ + 76, + 409, + 241, + 425 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Other choices of knowledge fusion schemes. In Tab. 6, we compare distinct knowledge fusion schemes based on our SDPN, including the knowledge distillation strategies (upper part of Tab. 6) and feature fusion strategies (bottom of Tab. 6). Specifically, all schemes use only SPM and BLSTM in testing and all knowledge distillation schemes distill knowledge from 1D-TCN to BLSTM. We observe that feature fusion strategies have limited promotion and even worse results than the SDPN, while all knowledge distillation schemes gained an improvement by the SDPN. This validates the effectiveness of knowledge distillation and shows that simply concatenating or summing features lacks the constraint for 1D-TCN and BLSTM to guide them to possess context knowledge of the other. And the attention mechanism only learns the correlation between 1D-TCN and BLSTM, neglecting context knowledge transferring.", + "bbox": [ + 75, + 431, + 468, + 674 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Impact of different distillation objects. The Tab. 6 also shows the performance of using intermediate feature hints versus prediction scores as distillation objects. The Wasserstein distance [3, 7] and JMMD [19] enforce to align the intermediate feature distributions. And the CKD [28] distills significant activation values in each channel of intermediate feature hints. Further, based on the CKD our $\\mathcal{L}_{l2g}$ weights the distillation by the intersection information of intermediate feature hints. On the other hand, the vanilla distillation [11] is designed for aligning glosses prediction scores, gives the worst performance. Overall, results suggest that adopting intermediate feature hints as distillation objects is more effective than employing prediction scores to teach how to generate the desired output.", + "bbox": [ + 75, + 674, + 468, + 885 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Impact of different temporal window widths of 1D-", + "bbox": [ + 76, + 885, + 468, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "TCN. Tab. 7 delivers that the window width designed to approximate the average length of isolated sign [6] performs the best. (Since half of the frames are selected for training, i.e., SFL [22], the actual window width needs to be multiplied by 2). Whereas, variants of 1D-TCN with substantially different window widths (ranging from 14 to 26) do not show a significant performance gap. We explain that variants of 1D-TCN can learn sign-wise knowledge through global context guidance optimized by the $\\mathcal{L}_{g2l}$ , which relieves the effect of receptive field discrepancy.", + "bbox": [ + 496, + 90, + 890, + 241 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Other choices of global temporal perception modules. Tab. 8 ablates the performance of distinct global temporal perception modules, such as BLSTM, Dilated blocks [24], Transformer [2, 22], and Transformer+BLSTM. The BLSTM achieves the best performance. The plausible reason is that sign language videos have a semantic sequence with grammatical rules, which means both forward and backward frames should be taken into consideration [25], which BLSTM achieves natively. However, Transformer is unable to do it to learn the semantic sequence well.", + "bbox": [ + 496, + 242, + 890, + 393 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 407, + 617, + 422 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we have extensively studied the limitation and desired properties of the temporal aggregation module (TAM) in the continuous sign language recognition framework. In particular, with an advanced analysis tool (i.e., information stored in weights [31]), we showed that the desired TAM should be a shallow architecture to allow more effective training of spatial perception module but also should be a deep one for a high temporal aggregation capability. To achieve this property, we proposed cross-temporal context aggregation (CTCA) with a dual-path network. Moreover, we proposed a cross-context knowledge distillation loss function to transfer the local temporal context and the linguistic prior to the global perception module. Extensive experimental results demonstrated that our CTCA effectively enhances the generalization of the spatial perception module while achieving the leading accuracy with fewer parameters and higher efficiency.", + "bbox": [ + 496, + 431, + 890, + 688 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations. In the redesign of the temporal aggregation module, the improvement of global temporal context perception still follows the current scheme, which still tends to cause overfitting. Therefore finding a more suitable global temporal context perception for the weakly supervised CSLR task is a challenge to be solved. Meanwhile, the CTCA is not tested on real-world with complex scenes, which deserves further study.", + "bbox": [ + 496, + 688, + 890, + 809 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments. This work was supported by the National Natural Science Foundation of China (61906135, 62020106004, 92048301, 62276141), and the Tianjin Research Innovation Project for Postgraduate Students (2021YJSB244). It was also supported by A\\*STAR Centre for Frontier AI Research.", + "bbox": [ + 496, + 810, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "10778", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Necati Cihan Camgoz, Simon Hadfield, Oscar Koller, Hermann Ney, and Richard Bowden. Neural sign language translation. In CVPR, 2018. 1, 6", + "[2] Necati Cihan Camgoz, Oscar Koller, Simon Hadfield, and Richard Bowden. Sign language transformers: Joint end-to-end sign language recognition and translation. 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In CVPR, 2022. 1, 2, 3, 6" + ], + "bbox": [ + 78, + 90, + 468, + 176 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "10780", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Distilling Cross-Temporal Contexts for Continuous Sign Language Recognition/67f2d609-710a-4aac-8b1f-1eb63e00c70c_model.json b/2023/Distilling Cross-Temporal Contexts for Continuous Sign Language Recognition/67f2d609-710a-4aac-8b1f-1eb63e00c70c_model.json new file mode 100644 index 0000000000000000000000000000000000000000..0049ee9296355024e10b4abecdb11223105516ec --- /dev/null +++ b/2023/Distilling Cross-Temporal Contexts for Continuous Sign Language Recognition/67f2d609-710a-4aac-8b1f-1eb63e00c70c_model.json @@ -0,0 +1,1991 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.087, + 0.131, + 0.885, + 0.154 + ], + "angle": 0, + "content": "Distilling Cross-Temporal Contexts for Continuous Sign Language Recognition" + }, + { + "type": "text", + "bbox": [ + 0.24, + 0.18, + 0.812, + 0.217 + ], + "angle": 0, + "content": "Leming Guo\\(^{1}\\) Wanli Xue\\(^{1*}\\) Qing Guo\\(^{2*}\\) Bo Liu\\(^{3}\\) Kaihua Zhang\\(^{4}\\) \nTiantian Yuan\\(^{5}\\) Shengyong Chen\\(^{1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.199, + 0.217, + 0.848, + 0.235 + ], + "angle": 0, + "content": "1 School of Computer Science and Engineering, Tianjin University of Technology," + }, + { + "type": "text", + "bbox": [ + 0.087, + 0.234, + 0.964, + 0.252 + ], + "angle": 0, + "content": "2 Centre for Frontier AI Research (CFAR), A*STAR, Singapore, 3 Walmart Global Tech, Sunnyvale, CA, USA," + }, + { + "type": "text", + "bbox": [ + 0.144, + 0.252, + 0.904, + 0.27 + ], + "angle": 0, + "content": "\\(^{4}\\) School of Computer and Software, Nanjing University of Information Science and Technology," + }, + { + "type": "text", + "bbox": [ + 0.259, + 0.27, + 0.787, + 0.288 + ], + "angle": 0, + "content": "5 Technical College for the Deaf, Tianjin University of Technology" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.322, + 0.314, + 0.339 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.355, + 0.474, + 0.749 + ], + "angle": 0, + "content": "Continuous sign language recognition (CSLR) aims to recognize glosses in a sign language video. State-of-the-art methods typically have two modules, a spatial perception module and a temporal aggregation module, which are jointly learned end-to-end. Existing results in [9, 20, 25, 36] have indicated that, as the frontal component of the overall model, the spatial perception module used for spatial feature extraction tends to be insufficiently trained. In this paper, we first conduct empirical studies and show that a shallow temporal aggregation module allows more thorough training of the spatial perception module. However, a shallow temporal aggregation module cannot well capture both local and global temporal context information in sign language. To address this dilemma, we propose a cross-temporal context aggregation (CTCA) model. Specifically, we build a dual-path network that contains two branches for perceptions of local temporal context and global temporal context. We further design a cross-context knowledge distillation learning objective to aggregate the two types of context and the linguistic prior. The knowledge distillation enables the resultant one-branch temporal aggregation module to perceive local-global temporal and semantic context. This shallow temporal perception module structure facilitates spatial perception module learning. Extensive experiments on challenging CSLR benchmarks demonstrate that our method outperforms all state-of-the-art methods." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.778, + 0.21, + 0.793 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.804, + 0.47, + 0.866 + ], + "angle": 0, + "content": "Sign language is a visual language for deaf and hearing-impaired people for ease of communication. Because sign language has a different grammatical structure and expression from natural spoken language, deaf and hearing-" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.319, + 0.673, + 0.567 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.675, + 0.319, + 0.895, + 0.57 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.579, + 0.895, + 0.651 + ], + "angle": 0, + "content": "Figure 1. (a) is the common CSLR framework. (b) presents the generalization capability (i.e., information stored in weights (IIW) [31]) of TAMs and SPMs of baseline, state-of-the-art methods and the proposed method. (c) is the performance of the state-of-the-art methods including word error rate, test time, and model size." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.894, + 0.765 + ], + "angle": 0, + "content": "impaired people hardly communicate normally with hearing people in daily life. To eliminate this communication gap, continuous sign language recognition (CSLR) enforces to recognition of various glosses from a sign language video. Due to the data collection and annotation being labor-intensive, CSLR benchmarks adopt a sentence-annotation manner for all sign language videos [1, 15, 33]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.895, + 0.903 + ], + "angle": 0, + "content": "In recent years, there is a consensus among state-of-the-art methods on a baseline framework (See Fig. 1 (a)). It is made up of a spatial perception module (SPM), and a temporal aggregation module (TAM) including two components for local and global temporal perception module, and the connectionist temporal classification (CTC) loss [8] for training. At present, these methods [9,20,25,36] have perceived one limitation of this framework that the temporal aggregation module can lead to insufficiently trained spatial" + }, + { + "type": "page_footnote", + "bbox": [ + 0.078, + 0.875, + 0.47, + 0.902 + ], + "angle": 0, + "content": "*Wanli Xue and Qing Guo are corresponding authors (xue-wanli@email.tjut.edu.cn and tsingqguo@ieee.org)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "10771" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.212 + ], + "angle": 0, + "content": "perception module and affect the final accuracy. We use a recent interpretation method (i.e., the compression of information stored in weights (IIW) [31]) to measure the generalization capability of different neural modules. Fig. 1 (b) shows the IIWs of TAMs and SPMs of baseline and state-of-the-art works and infers their positive relation, i.e., low-generalization TAM (i.e., high IIW) usually leads to low-generalization SPM. We provide more studies in Sec. 3." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.213, + 0.471, + 0.484 + ], + "angle": 0, + "content": "Y. Min et al. [20] measure the difference of correctly and incorrectly recognized results between auxiliary and primary classifiers to evaluate model overfitting, and A. Hao et al. [9] visualized heatmaps of TAM's self-similarity matrices to show what the local and global temporal perception learning. However, there are no straightforward quantitative studies to discuss the effects of TAM on SPM, and we do not know how significant the effects could be and have no idea about the desired temporal aggregation. In this paper, we extensively study the limitation and desirable properties of the temporal aggregation module in the CSLR framework via constructing a baseline framework and extensive empirical studies. We insight that a desired temporal aggregation module should be a shallow architecture to allow more effective training of spatial perception module but also should be a deep one for a high temporal aggregation capability. Whereas, it is quite challenging for the temporal aggregation module to achieve these properties simultaneously." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.485, + 0.47, + 0.756 + ], + "angle": 0, + "content": "To overcome this challenge, we propose the cross-temporal context aggregation (CTCA) that a shallow temporal aggregation module has capable of incorporating local-global temporal contexts and the linguistic prior. Specifically, we construct a dual-path network, which decouples the local and global perception modules and imposes a linguistic module in parallel. This architecture ensures the local context perception, global context perception, and linguistic prior extraction. Furthermore, we propose a cross-context knowledge distillation loss function to transfer the local temporal context and the linguistic prior to the global perception module. Notice that the spatial perception module can facilitate itself by receiving cross-context knowledge as supervision during distillation. Fig. 1(b) shows that both SPM and TAM in CTCA achieve higher generalization than the ones of baselines. Consequently, Fig. 1(c) delivers CTCA's superiority and it outperforms the state-of-the-art methods on WER, test time, and model size." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.77, + 0.22, + 0.787 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Continuous sign language recognition. To learn stronger representation under the sentence-annotated benchmarks, current deep learning-based approaches exploit the Connectionist Temporal Classification (CTC) [8], which provides a many-to-one mapping between frames and glosses. To mitigate the insufficient training problem [9,20,25,36], a time-consuming iterative fine-tuning strategy [6, 25] is utilized" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.303 + ], + "angle": 0, + "content": "to boost the model generalization. In contrast, the end-to-end methods proposed, such as VAC [20] and SMKD [9] proposed an end-to-end alignment constraint to make the learning of local and global temporal context to be consistent. \\(\\mathrm{C}^2\\mathrm{SLR}\\) [36] designed two constraints for building spatial consistency and temporal perception consistency to enhance the representation power of the model. Y. Min et al. [21] proposed an optimized CTC loss, which can constrain features on a hypersphere and control the peak behavior of CTC loss to enhance the feature generalization. In this paper, we achieve a shallower temporal perception module that not only promotes more thorough training of spatial perception model but also aggregates local-global temporal context via a cross-temporal context distillation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.304, + 0.893, + 0.561 + ], + "angle": 0, + "content": "Knowledge distillation. Knowledge distillation (KD) is a model compression technique that facilitates student models to achieve strong performance by excavating knowledge from large teacher models [11] or itself [16]. To eliminates huge training cost needs the ONE [16] proposes a multibranch network to conduct an ensemble on-the-fly. VAC [20] conducts its local and global temporal context module as an implicit teacher to promote each one to gain advanced generalization. Wang et al. [30] propose that consistent knowledge of multi-modal contains in each channel, and can achieve multi-modal fusion by exchanging their channels. POS-SCAN [35], LGD [32], and ELG [27] assume the linguistic information shares similar semantics with the visual. They transfer the image-text alignment from teacher to student. In this paper, we distill the local-global temporal information and linguistic context to a single one-branch temporal aggregation module." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.578, + 0.75, + 0.595 + ], + "angle": 0, + "content": "3. Preliminaries and Analysis" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.604, + 0.747, + 0.619 + ], + "angle": 0, + "content": "3.1. General CSLR Framework" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.627, + 0.892, + 0.84 + ], + "angle": 0, + "content": "Given a sign language video \\(\\mathcal{X} = \\{\\mathbf{X}_t\\}_{t=1}^T\\) having \\(T\\) frames, a continuous sign language recognition method (CSLR) denoted as \\(\\phi(\\cdot)\\) contributes to predicting \\(L\\) glosses (i.e., \\(\\mathcal{Y} = \\{y_i\\}_{i=1}^L\\)) contained in the video where \\(y_i\\) is the \\(i\\)-th gloss, and we have \\(\\mathcal{Y} = \\phi(\\mathcal{X})\\). As shown in Fig. 1(a), we show three clips in the input video, which are highlighted with pink, blue, and green colors. A CSLR method is desired to predict the corresponding three glosses, i.e., 'JETZT', 'WETTER', and 'APRIL'. The existing training dataset only provides sentence annotation (See the annotation in Fig. 1) instead of the ground truth of each frame and we even do not know the exact number of glosses in the input video. Hence, the task is a weakly-supervised learning problem and significantly challenging." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.902 + ], + "angle": 0, + "content": "The dominant CSLR framework [9, 20, 36] mainly involves three modules: spatial perception module (SPM) to extract feature representation of each frame independently, temporal aggregation module (TAM) to sequentially con" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "10772" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.099, + 0.083, + 0.451, + 0.334 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.342, + 0.473, + 0.399 + ], + "angle": 0, + "content": "Figure 2. Experiments about chain depth variants of TAM in the general CSLR framework. The IIW [31] is exploited to measure the generalization gap (the larger gap, the larger the IIW) of SPM and TAM. The WER value is utilized to estimate the performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.406, + 0.473, + 0.695 + ], + "angle": 0, + "content": "duct local and global aggregation across frames' features, and the classification module for the final prediction. We denote the three modules as \\(\\phi_{\\mathrm{spm}}(\\cdot),\\phi_{\\mathrm{tam}}(\\cdot)\\) ,and \\(\\phi_{\\mathrm{cls}}(\\cdot)\\) , respectively, and can reformulate the whole process as \\(\\mathcal{V} =\\) \\(\\phi (\\mathcal{X}) = \\phi_{\\mathrm{cls}}(\\phi_{\\mathrm{tam}}(\\phi_{\\mathrm{spm}}(\\mathcal{X}))\\) (See Fig. 1(a)). Specifically, \\(\\phi_{\\mathrm{spm}}(\\cdot)\\) first extracts features of all frames via a convolution neural network like ResNet18 [10], which are denoted as \\(\\mathcal{V} = \\{\\mathbf{V}_t\\}_{t = 1}^T\\) . Then, \\(\\phi_{\\mathrm{tam}}(\\cdot)\\) uses a local temporal context perception component like temporal convolution network (i.e., 1D-TCN) [5, 9, 20, 36] to capture the correlation across adjacent frames and map the representations \\(\\nu\\) to a new one, i.e., \\(\\mathcal{V}^{\\mathrm{loc}} = \\{\\mathbf{V}_t^{\\mathrm{loc}}\\}_{t = 1}^T\\) \\(\\phi_{\\mathrm{tam}}(\\cdot)\\) further feeds the locally-aggregated representations to the global perception component like a two-layer BLSTM [9, 20, 34, 36] to capture the global temporal patterns across all frames and get \\(\\mathcal{V}^{\\mathrm{glo}} = \\{\\mathbf{V}_t^{\\mathrm{glo}}\\}_{t = 1}^T\\) . Then, the \\(\\mathcal{V}^{\\mathrm{glo}}\\) is further passed to \\(\\phi_{\\mathrm{cls}}\\) , which is a fully-connected layer to predict logits \\(\\mathcal{Z}^{\\mathrm{glo}} = \\{\\mathbf{Z}_t^{\\mathrm{glo}}\\}_{t = 1}^T\\) . Finally, the \\(\\mathcal{Z}^{\\mathrm{glo}}\\) is fed into the CTC to align the prediction and ground truth and calculate the loss." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.704, + 0.251, + 0.72 + ], + "angle": 0, + "content": "3.2. Empirical Studies" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.728, + 0.47, + 0.85 + ], + "angle": 0, + "content": "Following the fact about chain rules of backpropagation, we study the effects of the chain depth of the temporal aggregation module to the spatial perception module. Intuitively, the temporal aggregation module with fewer layers (i.e., a shallow TAM) has fewer effects on the back-propagation of gradients, and a shallower TAM could lead to a more powerful SPM. To conduct a solid analysis, we have the following setups:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.856, + 0.471, + 0.903 + ], + "angle": 0, + "content": "- Baseline CSLR. We follow the general CSLR framework in Sec. 3.1 and construct a CSLR method including a cascaded ResNet18 as the SPM, \\(K\\)-layer 1D" + }, + { + "type": "text", + "bbox": [ + 0.53, + 0.092, + 0.892, + 0.152 + ], + "angle": 0, + "content": "TCNs and a two-layer BLSTM as the TAM, and the classifier and the CTC as the classification module. The \\(K\\)-layer 1D-TCNs and BLSTM are used for local and global temporal contexts perception, respectively." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.153, + 0.894, + 0.243 + ], + "angle": 0, + "content": "- TAM with different chain depths. We set five variants of TAM by stacking \\( K \\) 1D-TCNs where we set \\( K \\in \\{0,1,3,9,22\\}^* \\). We do not tune the depth of the BLSTM since the BLSTM is prone to over-fitting [9, 20], we contribute to exploring the influence of the depth between SPM and BLSTM." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.244, + 0.895, + 0.426 + ], + "angle": 0, + "content": "- Evaluation of SPM and CSLR. Following existing works, we use the word error rate (WER) to evaluate the performance of the whole CSLR method. In contrast, for TAM and SPM, we choose another metric, i.e., the compression of information stored in weights (IIW) [31], which is designed to understand the behavior of neural networks and can be an indicator of generalization gap (i.e., the accuracy difference on the test and training datasets) of neural networks [31]. Intuitively, with the same training dataset, a lower IIW of a module means that the module contributes more to the accuracy of the test dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.431, + 0.895, + 0.72 + ], + "angle": 0, + "content": "With the above setups, we get five CSLR variants with five TAMs having different chain depths. Then, we train and test all variants on the RWTH-2014 dataset [15]. Specifically, we can calculate the word error rate (WER) of the five variants for the prediction accuracy evaluation. We further count the information stored in weights (IIW) of the SPMs and TAMs of the five variants, respectively. As the results are shown in Fig. 2, we have the following observations: ① When we consider the chain depth (i.e., \\( K \\)) from 1 to 22, the IIW of SPM gradually increases and reaches the maximum at \\( K = 22 \\) while the IIW of TAM gradually decreases, which means the effects of chain depth to the capability of SPM and TAM have completely opposite trends. A powerful SPM desires a shallow TAM while the TAM itself requires a deeper architecture. ② Considering the changes of WER of the CSLR along different chain depths, we see that the trend of WER is consistent with the IIW's variation trend, which means the SPM has higher effects than the TAM on the final prediction accuracy." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.727, + 0.63, + 0.741 + ], + "angle": 0, + "content": "3.3. Motivations" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.894, + 0.856 + ], + "angle": 0, + "content": "According to the above studies, a desired temporal aggregation module should be a shallow architecture to allow more effective training of the spatial perception module but also should be a deep one for a high temporal aggregation capability. Such a contradiction makes the designing of a suitable TAM challenging. Because SPM is directly related to the final accuracy, we tend to select a shallow TAM." + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.863, + 0.894, + 0.901 + ], + "angle": 0, + "content": "*0 illustrates the TAM drop the 1D-TCN. We adjust channels of 1D-TCN to make sure different variants have the same model size. Such as 1,3,9,22 denote their channels are 1024,512,256 and 128, respectively." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10773" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.09, + 0.468, + 0.304 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.316, + 0.47, + 0.345 + ], + "angle": 0, + "content": "Figure 3. Pipeline of the CTCA. In particular, the steps with black borders or black arrows belong to the CTCA test process." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.353, + 0.469, + 0.384 + ], + "angle": 0, + "content": "Then, the key problem becomes how to make TAM shallower and contribute more to the final prediction accuracy." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.385, + 0.469, + 0.506 + ], + "angle": 0, + "content": "Existing works have noticed that both local and global temporal perception are critical to prediction accuracy. We also conduct a simple study and observe that removing any temporal perception components leads to a significant accuracy drop (See the supplementary material). All the above observations motivate us to develop a shallower but more powerful temporal aggregation module that has the capability of perceiving local and global context perception." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.522, + 0.416, + 0.54 + ], + "angle": 0, + "content": "4. Cross-Temporal Context Aggregation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.548, + 0.47, + 0.669 + ], + "angle": 0, + "content": "An intuitive idea is to utilize knowledge distillation to integrate local and global contexts into a shallow architecture. As a result, the two opposite requirements for TAM in Sec. 3.3 could be handled simultaneously. To this end, we first provide a vanilla distillation solution in Sec. 4.1, which has several inherent limitations. Then, we impose a more advanced distillation method, i.e., cross-temporal context aggregation (CTCA), in Sec. 4.2 and Sec. 4.3." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.681, + 0.343, + 0.696 + ], + "angle": 0, + "content": "4.1. A Vanilla Distillation Solution" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.471, + 0.901 + ], + "angle": 0, + "content": "We follow the baseline CSLR in Sec. 3.2 and construct two independent CSLRs that have the same spatial perception module (SPM) and classification module but a different temporal aggregation module (TAM). The first one retains the global perception component (i.e., a BLSTM) and removes the local component (i.e., 1D-TCN). Such a CSLR has the shallowest TAM (i.e., \\( K = 0 \\) in Sec. 3.2) and we denote it as CSLR-GloTAM. The second one only contains the local perception component and the BLSTM layer is removed and we denote it as CSLR-LocTAM. The main goal is to train a CSLR-GloTAM to let its TAM have the local temporal contexts. To this end, we use the CSLR-LocTAM to teach the CSLR-GloTAM for acquiring local information" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.891, + 0.122 + ], + "angle": 0, + "content": "and only use the CSLR-GloTAM for inference. The teaching manner follows the vanilla distillation [11]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.123, + 0.892, + 0.289 + ], + "angle": 0, + "content": "However, such a vanilla distillation approach has some limitations: 1) In terms of CSLR-GloTAM, when BLSTM over-fits the training data, the loss can be hardly propagated to the SPM. The distillation based on two separated CSLRs cannot address this issue properly. 2) By adapting existing distillation methods directly, we need to design two exclusive optimization schemes for the two independent CSLRs, respectively, which inevitably leads to high time and computing costs. 3) The vanilla distillation leverages a fully-supervised distillation loss, which cannot be adapted to the weakly-supervised optimization like CSLR directly." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.301, + 0.788, + 0.316 + ], + "angle": 0, + "content": "4.2. SPM-Shared Dual-Path Network" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.326, + 0.892, + 0.702 + ], + "angle": 0, + "content": "Enforcing to resolve the first and second limitations in Sec. 4.1, we propose the SPM-Shared Dual-Path Network (SDPN). Inspired by [16], we adopt a multi-branch architecture with a shared SPM to merge the training processes of teacher and student, which distills from each other in a peer-teaching manner. As a result, this structure avoids the requirement of two optimization schemes trade-offs. It is easy to train with only one optimization scheme. As such, different from the vanilla distillation approach has two separate networks, the SDPN is composed of a shared SPM and followed a dual-path (See Fig. 3): local temporal perception branch (i.e., 1D-TCN branch), global temporal perception branch (i.e., BLSTM branch). Specifically, each branch itself of SDPN stands for the specific knowledge concurrently, which conducts a native ensemble model on-the-fly. With the above architecture, even if the BLSTM branch is over-fitted, other branches like the 1D-TCN branch can still back-propagate the loss to the shared SPM straightforwardly. More importantly, the SDPN is easy to adopt distillation losses (See Sec. 4.3) to distill the local temporal context and the linguistic prior to reinforcing BLSTM. The two branches of SDPN have different objectives and architectures as done in [9, 17, 20]. In particular, we only use the BLSTM branch during inference, rather than both branches. We detail the architectural designs in the following:" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.892, + 0.764 + ], + "angle": 0, + "content": "Shared spatial perception module. We use the ResNet18 for the spatial perception module (See Sec. 3.1) where the fully-connection layer is removed, which takes the video clips as inputs and outputs the spatial representation \\(\\nu\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Local & global temporal perception branches. The local branch consists of a 1D-TCN and a local classifier \\(\\mathcal{F}^{\\mathrm{loc}}\\). The 1D-TCN is able to provide local temporal representations \\(\\mathcal{V}^{\\mathrm{loc}}\\) maintained sign-wise information. And the local classifier outputs the local prediction \\(\\mathcal{Z}^{\\mathrm{loc}}\\). The global branch contains a two-layer BLSTM and a global classifier \\(\\mathcal{F}^{\\mathrm{glo}}\\). The BLSTM outputs global temporal representations \\(\\mathcal{V}^{\\mathrm{glo}}\\), which contains the order and correlation of co-occurring signs. The global classifier outputs the global prediction" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10774" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.091, + 0.47, + 0.152 + ], + "angle": 0, + "content": "\\(\\mathcal{Z}^{\\mathrm{glo}}\\). Note that, both \\(\\mathcal{Z}^{\\mathrm{glo}}\\) and \\(\\mathcal{Z}^{\\mathrm{loc}}\\) are optimized by CTC loss to achieve a knowledge complementary to the spatial perception module reinforcement, and the 1D-TCN is removed during inference." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.163, + 0.443, + 0.179 + ], + "angle": 0, + "content": "4.3. Cross-Context Knowledge Distillation Loss" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.186, + 0.47, + 0.457 + ], + "angle": 0, + "content": "To make the shallow BLSTM branch learn both local & global perceptions and achieve the desired property against the third limitation in Sec. 4.1, we propose the Cross-Context Knowledge Distillation Loss (CCKD). CCKD composes a cross-temporal knowledge distillation (CTD) and a cross-modality knowledge distillation (CMD). The CTD builds a mutual temporal context distillation that enables the BLSTM and 1D-TCN branches to incorporate complementary knowledge to refine themselves and the SPM. The CMD distills linguistic prior i.e., inter-gloss semantic correlation from glosses sequence to BLSTM branch to reinforce its temporal aggregation. In contrast to the vanilla distillation that enhances the student's ability to achieve consistent prediction scores with the teacher, the CCKD focuses on distilling channel-wise knowledge from intermediate feature hints [28]. By doing so, CCKD facilitates students to learn how to learn, rather than how to get prediction scores, which is more applicable to CSLR." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.459, + 0.468, + 0.61 + ], + "angle": 0, + "content": "Cross-temporal knowledge distillation. ① Local temporal context guidance loss \\((\\mathcal{L}_{l2g})\\). Given the local and global temporal representation \\(\\mathcal{V}^{\\mathrm{loc}}\\) and \\(\\mathcal{V}^{\\mathrm{glo}}\\), the \\(\\mathcal{L}_{l2g}\\) encourages the \\(\\mathcal{V}^{\\mathrm{glo}}\\) to learn sign-wise context maintained in \\(\\mathcal{V}^{\\mathrm{loc}}\\) to remain local-global temporal contexts. Due to the knowledge of sign-wise context being distinct from the global context, knowledge confusion may occur during the \\(\\mathcal{L}_{l2g}\\) procedure. To relieve the confusion, we weight the \\(\\mathcal{V}^{\\mathrm{loc}}\\) by the intersection information \\(I(\\mathcal{V}^{\\mathrm{loc}}, \\mathcal{V}^{\\mathrm{glo}})\\) among \\(\\mathcal{V}^{\\mathrm{loc}}\\) and \\(\\mathcal{V}^{\\mathrm{glo}}\\) to suppress signs information of \\(\\mathcal{V}^{\\mathrm{loc}}\\) who differs with \\(\\mathcal{V}^{\\mathrm{glo}}\\)." + }, + { + "type": "equation", + "bbox": [ + 0.117, + 0.617, + 0.469, + 0.637 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {l 2 g} \\left(\\mathcal {V} ^ {\\mathrm {g l o}}, \\mathcal {V} ^ {\\mathrm {l o c}}\\right) = \\varphi \\left(\\mathcal {V} ^ {\\mathrm {g l o}}, \\mathcal {V} ^ {\\mathrm {l o c}} \\cdot I \\left(\\mathcal {V} ^ {\\mathrm {l o c}}, \\mathcal {V} ^ {\\mathrm {g l o}}\\right)\\right), \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.117, + 0.648, + 0.469, + 0.689 + ], + "angle": 0, + "content": "\\[\n\\varphi \\left(\\mathcal {V} ^ {\\text {g l o}}, \\mathcal {V} ^ {\\text {l o c}}\\right) = \\frac {\\tau^ {2}}{C} \\sum_ {c = 1} ^ {C} \\sum_ {i = 1} ^ {T} K L \\left(\\left(\\mathbf {V} _ {c, i} ^ {\\text {g l o}}\\right), \\left(\\mathbf {V} _ {c, i} ^ {\\text {l o c}}\\right)\\right), \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.179, + 0.7, + 0.469, + 0.743 + ], + "angle": 0, + "content": "\\[\nI \\left(\\mathcal {V} ^ {\\text {l o c}}, \\mathcal {V} ^ {\\text {g l o}}\\right) = \\frac {1}{\\frac {\\sigma \\left(\\mathbf {V} _ {c , i} ^ {\\text {l o c}}\\right)}{\\sigma \\left(\\mathbf {V} _ {c , i} ^ {\\text {g l o}}\\right)} + 1}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.751, + 0.468, + 0.902 + ], + "angle": 0, + "content": "where if \\(\\frac{\\sigma(\\mathbf{V}_{c,i}^{\\mathrm{loc}})}{\\sigma(\\mathbf{V}_{c,i}^{\\mathrm{glo}})}\\) is large and thus \\(I(\\mathcal{V}^{\\mathrm{loc}},\\mathcal{V}^{\\mathrm{glo}})\\) is small, meaning the large different between \\(\\nu^{\\mathrm{loc}}\\) and \\(\\nu^{\\mathrm{glo}}\\). The \\(KL\\) denotes the KL divergence, \\(\\tau\\) is the temperature factor for smooth, \\(\\sigma\\) indicates the softmax function and \\(C\\) corresponds to the feature channels. As indicated in [28], the KL divergence can be used between intermediate feature hints. 2 Global temporal context guidance loss \\((\\mathcal{L}_{g2l})\\). In addition, the \\(\\mathcal{L}_{g2l}\\) loss evolves distilling global contexts i.e., signs order and correlation among co-occurring signs" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.153 + ], + "angle": 0, + "content": "to the 1D-TCN branch. As a result, remaining the local-global context, the 1D-TCN is applicable to learning signwise contexts by taking into account global contexts. The \\(\\mathcal{L}_{g2l}\\) loss is also formulated as a similarly form with \\(\\mathcal{L}_{l2g}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.587, + 0.161, + 0.892, + 0.179 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {g 2 l} \\left(\\mathcal {V} ^ {\\text {l o c}}, \\mathcal {V} ^ {\\text {g l o}}\\right) = \\varphi \\left(\\mathcal {V} ^ {\\text {l o c}}, \\mathcal {V} ^ {\\text {g l o}}\\right). \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.187, + 0.892, + 0.385 + ], + "angle": 0, + "content": "\\(\\Theta\\) Reconstruction loss \\((\\mathcal{L}_{rc})\\). The intuition behind this loss is that the distillation between 1D-TCN and BLSTM should be further enhanced when the local representation is welllearned. Therefore, we impose the \\(\\mathcal{L}_{rc}\\) as the reconstruction function for the local temporal representation \\(\\mathcal{V}^{\\mathrm{loc}}\\) to reinforce cross-temporal context distillation. Notably, we experimentally follow the entropy principle [13, 18] to measure knowledge uncertainty by \\(w(\\mathbf{V}_i^{\\mathrm{loc}})\\). If the estimated \\(\\mathcal{V}^{\\mathrm{loc}}\\) is well-trained and has a high certainty, \\(H(\\mathbf{V}_i^{\\mathrm{loc}})\\) becomes small, leading to a large weight \\((1 + w(\\mathbf{V}_i^{\\mathrm{loc}}))\\). Then, the consistency between local & global representations is further enhanced via the \\(\\mathcal{L}_{rc}\\). We also adopt a residual connection for stable weighting." + }, + { + "type": "equation", + "bbox": [ + 0.525, + 0.394, + 0.892, + 0.442 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {r c} = \\sqrt {\\sum_ {i = 1} ^ {T} \\left(\\mathbf {V} _ {i} ^ {\\mathrm {g l o}} - \\mathbf {V} _ {i} ^ {\\mathrm {l o c}}\\right) ^ {2}} \\cdot \\sum_ {i = 1} ^ {T} (1 + w (\\mathbf {V} _ {i} ^ {\\mathrm {l o c}})), \\tag {5}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.616, + 0.453, + 0.891, + 0.472 + ], + "angle": 0, + "content": "\\[\nw \\left(\\mathbf {V} _ {i} ^ {\\text {l o c}}\\right) = \\exp^ {- H \\left(\\mathbf {V} _ {i} ^ {\\text {l o c}}\\right)}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.478, + 0.845, + 0.492 + ], + "angle": 0, + "content": "As mentioned above, the CTD loss is formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.577, + 0.503, + 0.891, + 0.519 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {c t d} = \\alpha_ {1} \\mathcal {L} _ {l 2 g} + \\alpha_ {2} \\mathcal {L} _ {g 2 l} + \\alpha_ {3} \\mathcal {L} _ {r c}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.528, + 0.892, + 0.619 + ], + "angle": 0, + "content": "Where the \\(\\alpha_{1}\\), \\(\\alpha_{2}\\), \\(\\alpha_{3}\\) achieve trade-offs among losses in the CTD loss. Furthermore, the CTD loss ensures the spatial perception module to be propagated the local-global information during the whole training time, which avoids the propagation effect of BSLTM overfitting and enhances SPM generalization ability, implicitly." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.62, + 0.892, + 0.817 + ], + "angle": 0, + "content": "Cross-modality knowledge distillation. The CTD loss only restricts the cross-temporal context statistics yet has weak semantic context supervision i.e., the linguistic prior. Motivated by CLIP [26] and ELG [27], the cross-modality knowledge distillation (CMD) is proposed to distill inter-gloss semantic correlation from glosses sequence to BLSTM branch. In practice, given the gloss sequence \\(\\mathcal{V} = \\{y_i\\}_{i=1}^L\\) corresponding to \\(\\mathcal{X}\\) with \\(L\\) glosses, it will be embedded by pre-trained BERT to generate high-dimensional semantic features \\(\\mathcal{G}^{\\mathrm{gls}} = \\{\\mathbf{G}_i^{\\mathrm{gls}}\\}_{i=1}^L \\in \\mathbb{R}^{Y \\times L}\\). Further, the \\(\\mathcal{G}^{\\mathrm{gls}}\\) and global temporal representation \\(\\mathcal{V}^{\\mathrm{glo}}\\) will be computed by cross-attention [29] to generate the linguistic-visual relation \\(\\mathcal{G}^{\\widehat{t}} \\in \\mathbb{R}^{Y \\times L}\\)." + }, + { + "type": "equation", + "bbox": [ + 0.54, + 0.825, + 0.892, + 0.86 + ], + "angle": 0, + "content": "\\[\n\\mathcal {G} ^ {\\widehat {t}} = \\operatorname {s o f t m a x} \\left(\\frac {f _ {\\mathcal {Q}} \\left(\\mathcal {G} ^ {\\mathrm {g l s}}\\right) f _ {\\mathcal {K}} \\left(\\mathcal {V} ^ {\\mathrm {g l o}}\\right) ^ {\\mathrm {T}}}{\\sqrt {C}}\\right) f _ {\\mathcal {V}} \\left(\\mathcal {V} ^ {\\mathrm {g l o}}\\right), \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.87, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Moreover, the self-correlation matrix \\( \\underline{cor}^{\\hat{t}} \\) will be obtained by the matrix product of \\( \\mathcal{G}^{\\hat{t}} \\) and \\( (\\mathcal{G}^{\\hat{t}})^{\\mathrm{T}} \\). The \\( cor^t \\) is a" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10775" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.091, + 0.473, + 0.175 + ], + "angle": 0, + "content": "self-correlation matrix of gloss features \\(\\mathcal{G}^{\\mathrm{gls}}\\), i.e., \\(cor^{t} = \\left\\| \\mathcal{G}^{\\mathrm{gls}}\\right\\|_{2}\\left(\\left\\| \\mathcal{G}^{\\mathrm{gls}}\\right\\|_{2}\\right)^{\\mathrm{T}}\\). Finally, we distill the inter-gloss discrimination from the \\(cor^{t}\\) to the \\(cor^{\\hat{t}}\\) via the cross-modality distillation loss \\(\\mathcal{L}_{cmd}\\). The \\(t\\) and \\(\\hat{t}\\) represent the gloss modality and visual modality, respectively." + }, + { + "type": "equation", + "bbox": [ + 0.135, + 0.184, + 0.47, + 0.227 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {c m d} = \\frac {1}{L} \\sum_ {i = 1} ^ {L} \\sigma \\left(\\operatorname {c o r} _ {i} ^ {\\hat {t}}\\right) \\cdot \\log \\left[ \\frac {\\sigma \\left(\\operatorname {c o r} _ {i} ^ {\\hat {t}}\\right)}{\\sigma \\left(\\operatorname {c o r} _ {i} ^ {t}\\right)} \\right], \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.234, + 0.47, + 0.296 + ], + "angle": 0, + "content": "where \\(\\sigma\\) indicates the softmax function. We involve \\(cor^t\\) to have the same knowledge with \\(cor^t\\) to enhance the linguistic-visual relation, which encourages \\(\\nu^{\\mathrm{glo}}\\) to have the inter-gloss discrimination indirectly." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.297, + 0.462, + 0.312 + ], + "angle": 0, + "content": "Combining all loss functions, the CCKD is denoted as:" + }, + { + "type": "equation", + "bbox": [ + 0.151, + 0.324, + 0.469, + 0.341 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathcal {C C K D}} = \\alpha \\mathcal {L} _ {c t d} + \\beta \\mathcal {L} _ {c m d} + \\gamma \\mathcal {L} _ {c t c}, \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.352, + 0.456, + 0.368 + ], + "angle": 0, + "content": "where the \\(\\alpha, \\beta\\), and \\(\\gamma\\) control the trade-off among losses." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.377, + 0.295, + 0.394 + ], + "angle": 0, + "content": "4.4. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.4, + 0.47, + 0.46 + ], + "angle": 0, + "content": "Network details. We set \\( K = 3 \\) and kernel size is 3 for 1D-TCN, each layer equips with a 1D Batch Norm layer and a ReLU activation. The output channel of each temporal layer in 1D-TCN is set to 1024 and BLSTM is set to 2048." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.461, + 0.47, + 0.537 + ], + "angle": 0, + "content": "Hyperparameters setting. The \\(\\tau\\) in Eq. (2) is set to 4, the \\(\\alpha_{1},\\alpha_{2},\\alpha_{3}\\) in Eq. (7) are set to 0.2, 1, 1 respectively. And \\(\\alpha ,\\beta ,\\) and \\(\\gamma\\) in Eq. (10) are set to 3, 130, 1 respectively. We find that the \\(\\alpha_{1}\\) is chosen in [0.1, 1) and the \\(\\beta\\) needs to be set to among [50, 150] to obtain good performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.537, + 0.471, + 0.704 + ], + "angle": 0, + "content": "Training and test strategy. During both the training and test stages for all benchmarks, we randomly discard half of video frames as inputs following SFL [22]. We then resize the frame size to \\(256 \\times 256\\) and perform randomly cropping frames to \\(224 \\times 224\\), as well as random horizontal flip (50%) in the training stage (only center crop frames to \\(224 \\times 224\\) in the test stage). The BERT in the CMD loss is frozen and only employed in the training stage. In the test, only the spatial perception module and the global temporal perception branch are exploited to generate predictions. The CTCA is implemented in PyTorch with one A100 GPU." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.717, + 0.21, + 0.734 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.741, + 0.295, + 0.757 + ], + "angle": 0, + "content": "5.1. Dataset and Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.765, + 0.47, + 0.81 + ], + "angle": 0, + "content": "RWTH-2014 [15] is a German sign language dataset, it consists of a total of 6,841 sentences with a vocabulary of 1,295 glosses, signed by 9 different singers." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.811, + 0.469, + 0.87 + ], + "angle": 0, + "content": "RWTH-2014T [1] can be used for both CSLR and sign language translation tasks [1]. It involves a vocabulary of 1,085 glosses, split into 7,096, 519, and 642 samples in the train set, dev set, and test set, respectively." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "CSL-Daily [33] is a large Chinese sign language dataset about people's daily life. It can be employed in both CSLR" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.09, + 0.892, + 0.116 + ], + "angle": 0, + "content": "Table 1. Comparison with state-of-the-art methods on the RWTH2014 dataset. (WER(%) the lower is the better)." + }, + { + "type": "table", + "bbox": [ + 0.517, + 0.117, + 0.875, + 0.288 + ], + "angle": 0, + "content": "
MethodsDevTest
del/insWERdel/insWER
DNF [6]7.8/3.523.87.8/3.424.4
FCN [5]-23.7-23.9
VAC [20]7.9/2.521.28.4/2.622.3
CMA [23]7.3/2.721.37.3/2.421.9
SMKD [9]6.8/2.520.86.3/2.321.0
C²SLR [36]-20.5-20.4
TLP [17]6.3/2.819.76.1/2.920.8
RadialCTC [21]6.5/2.719.46.1/2.620.2
CTCA(Ours)6.2/2.919.56.1/2.620.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.299, + 0.892, + 0.327 + ], + "angle": 0, + "content": "Table 2. Comparison with state-of-the-art methods on the RWTH-2014T dataset. (WER(%) the lower is the better)." + }, + { + "type": "table", + "bbox": [ + 0.558, + 0.327, + 0.832, + 0.482 + ], + "angle": 0, + "content": "
MethodsWER
DevTest
SLT [2]24.624.5
CNN+LSTM+HMM [14]22.124.1
BN-TIN+Transf [33]22.723.9
V-L Mapper [4]21.922.5
SMKD [9]20.822.4
C2SLR [36]20.220.4
TLP [9]19.421.2
CTCA(Ours)19.320.3
" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.507, + 0.892, + 0.552 + ], + "angle": 0, + "content": "and sign language translation. There are 18,401, 1,077, and 1,176 videos for the training set, dev set, and test set, respectively. It has a vocabulary of 2,000 glosses for CSLR." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.553, + 0.892, + 0.627 + ], + "angle": 0, + "content": "Evaluation metric. In this paper, we adopt the word error rate (WER) metrics for CSLR methods evaluation. It measures the minimum number of substitutions, deletions, and insertions that need to convert one predicted glosses sequence to a given reference sequence [15]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.637, + 0.803, + 0.652 + ], + "angle": 0, + "content": "5.2. Comparison with State-of-the-arts" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.659, + 0.892, + 0.81 + ], + "angle": 0, + "content": "Evaluation on RWTH-2014. The objective of the VAC and SMKD is to enhance the discriminative capacity of the visual module (i.e., SPM+1D-TCN). Meanwhile, our CTCA focuses on investigating and designing the desired TAM for CSLR. As demonstrated in Tab. 1, the proposed CTCA solely utilizes the RGB information of sign language videos, yet it achieves competitive performance in terms of the WER (19.5% and 20.1%). Notably, it surpasses other RGB cue-based approaches, i.e., SMKD, C2SLR, and TLP, thereby validating the effectiveness of CTCA." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.811, + 0.892, + 0.856 + ], + "angle": 0, + "content": "Evaluation on RWTH-2014T. In Tab. 2, it is evident that the CTCA gains the best performance (19.3% and 20.3%) compared with other state-of-the-art approaches." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Evaluation on CSL-Daily. To further assess the CTCA's generalization capacity, we evaluate it on the CSL-Daily benchmark. As presented in Tab. 3, the CTCA outperforms" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "10776" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.47, + 0.117 + ], + "angle": 0, + "content": "Table 3. Comparison with state-of-the-art methods on the CSL-Daily. (WER(%) the lower is the better)." + }, + { + "type": "table", + "bbox": [ + 0.078, + 0.117, + 0.468, + 0.243 + ], + "angle": 0, + "content": "
MethodsDevTest
del/insWERdel/insWER
LS-HAN [12]14.6/5.739.014.8/5.039.4
SLT(Gloss+Text) [2]10.3/4.433.19.6/4.132.0
FCN [5]12.8/4.033.212.6/3.732.5
BN-TIN+Transf [33]13.9/3.433.613.5/3.033.1
TIN-Iterative [6]12.8/3.332.812.5/2.732.4
CTCA(Ours)9.2/2.531.38.1/2.329.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.257, + 0.456, + 0.27 + ], + "angle": 0, + "content": "Table 4. Effect of the SDPN architecture on the RWTH-2014." + }, + { + "type": "table", + "bbox": [ + 0.086, + 0.271, + 0.458, + 0.366 + ], + "angle": 0, + "content": "
MethodsIIWDevTest
del/insWERdel/insWER
Baseline6.7E-57.0/3.021.86.7/2.722.1
Baseline+SDPN5.6E-57.3/3.121.77.4/2.421.8
VAC(VE) [20]5.4E-5-23.3-23.8
VAC(VE)+SDPN4.2E-57.6/3.122.07.6/3.022.6
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.393, + 0.47, + 0.424 + ], + "angle": 0, + "content": "all other methods and achieves a \\(3\\%\\) WER advantage over the second-best performer, the TIN-Iterative." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.436, + 0.231, + 0.453 + ], + "angle": 0, + "content": "5.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.46, + 0.47, + 0.597 + ], + "angle": 0, + "content": "Benefits of SPM-Shared Dual-Path Network. Tab. 4 illustrates that when both baseline and VAC are constructed to SDPN architecture, achieving lower generalization gap (lower IIW) and improved performance (lower WER). It is noteworthy that during the testing, only the spatial perception module and the BLSTM branch of SDPN are utilized. These results suggest that the SDPN architecture can facilitate thorough training for the spatial perception module, leading to improved performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.598, + 0.47, + 0.688 + ], + "angle": 0, + "content": "Benefits of components of Cross-Context Knowledge Distillation loss. \\(\\bullet\\) Effect of vanilla distillation solution. We compare the vanilla distillation approach, as discussed in Sec. 4.1 with the baseline. As presented in Tab. 5, the vanilla distillation yields an improvement over the baseline, yet it is still inferior to each component of the CCKD." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.471, + 0.902 + ], + "angle": 0, + "content": "\\(\\Theta\\) Effect of \\(\\mathcal{L}_{l2g}\\) loss and \\(\\mathcal{L}_{g2l}\\) loss. We introduced two distillation methods, SDPN A and SDPN B based on the SDPN model. SDPN A is the 1D-TCN distilling sign-wise knowledge to the BLSTM via the \\(\\mathcal{L}_{l2g}\\). This method improves performance on the test set by \\(1.0\\%\\) compared to the baseline. We also removes the intersection information weighted term \\(I(:,)\\) from SDPN A, which results in a \\(0.4\\%\\) drop in performance on the test set, implying its effectiveness. SDPN B, on the other hand, is an SDPN model optimized by the \\(\\mathcal{L}_{g2l}\\), which yields a \\(1.4\\%\\) WER improvement over the baseline on the test set. It is noteworthy that SDPN A's performance is inferior to SDPN B. This can be explained that BLSTM tends to overfit on the sequential order of signs, which is easy to learn and leads to fast convergence" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.089, + 0.892, + 0.116 + ], + "angle": 0, + "content": "Table 5. Ablation study on cross-context knowledge distillation loss on the RWTH-2014." + }, + { + "type": "table", + "bbox": [ + 0.507, + 0.117, + 0.885, + 0.303 + ], + "angle": 0, + "content": "
MethodLctdLcmdDevTest
Ll2gLg2lLrc
Baseline----21.822.1
Vanilla----21.721.9
SDPN A✓---21.021.1
SDPN A-I(;;)✓---21.321.5
SDPN B-✓--20.820.7
SDPN C✓✓--20.420.6
SDPN D✓✓✓-20.020.4
SDPN D-w(;;)✓✓✓-20.220.6
SDPN E---✓21.321.0
CTCA✓✓✓✓19.520.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.317, + 0.892, + 0.345 + ], + "angle": 0, + "content": "Table 6. Comparison of different knowledge fusion schemes on the RWTH-2014. \"Wasserstein\" is the Wasserstein distance." + }, + { + "type": "table", + "bbox": [ + 0.544, + 0.356, + 0.847, + 0.512 + ], + "angle": 0, + "content": "
MethodKnowledge fusionDevTest
SDPN-21.721.8
Vanilla distillation [11]21.621.6
Wasserstein [3]21.621.5
JMMD [19]21.321.3
CKD [28]21.321.5
CTCA(ℓl2g)21.021.1
concatenation22.723.6
point-wise addition21.222.3
attention22.222.6
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.538, + 0.892, + 0.794 + ], + "angle": 0, + "content": "optimized by CTC [9, 25]. Although the BSLTM in SDPN A receives local context knowledge, it still propagates limited local-global information to SPM, resulting in limited gain for SPM when it is overfitting. Furthermore, the 1D-TCN is less prone to overfitting [5] and in SDPN B facilitated by the \\(\\mathcal{L}_{g2l}\\) the 1D-TCN can learn sign-wise context by taking into account global contexts. Then it can provide richer sign-wise supervision to the SPM for locating signs, which can eliminate the limited back-propagation. As a result, more robust features SPM can generate, and they are fed into BLSTM, which outperforms SDPN A. This finding is consistent with the observation \\(\\pmb{\\Theta}\\) in Sec. 3.2 that the SPM has a high effect on the final prediction performance. The results of SDPN C show that the mutual distillation approach gains \\(20.6\\%\\) on the test set. This technique can enhance both the \\(\\mathcal{L}_{l2g}\\) and \\(\\mathcal{L}_{g2l}\\), resulting in improved 1D-TCN and BLSTM. This success is also verified by [9]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Effect of \\(\\mathcal{L}_{rc}\\) loss and \\(\\mathcal{L}_{cmd}\\) loss. Seen from Tab. 5, based on the SDPN C model the SDPN D combines the \\(\\mathcal{L}_{rc}\\), which is effective in enhancing performance. Specifically, when SDPN D drops the \\(w(:,)\\), it gives a worse result, it shows the effect of entropy measurement. Moreover, SDPN E, achieves relatively better performance, which validates the need for linguistic prior supervision." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10777" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.472, + 0.146 + ], + "angle": 0, + "content": "Table 7. Performance comparison of local temporal perception module with distinct temporal window widths on the RWTH-2014. \\( Ft \\) and \\( Ft(d) \\) correspond to the 1D temporal convolution layer with kernel of \\( t \\) and dilation of \\( d \\), respectively." + }, + { + "type": "table", + "bbox": [ + 0.113, + 0.157, + 0.434, + 0.251 + ], + "angle": 0, + "content": "
MethodvariantswindowsDevTest
1D-TCNF3-F3-F37*219.520.1
F3(1)-F3(2)7*219.820.3
F5-F59*220.620.6
F5-F5-F513*219.920.6
F7-F713*220.120.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.265, + 0.47, + 0.294 + ], + "angle": 0, + "content": "Table 8. Comparison of CTCA with distinct global temporal perception modules (GTPM) on the RWTH-2014." + }, + { + "type": "table", + "bbox": [ + 0.088, + 0.304, + 0.457, + 0.384 + ], + "angle": 0, + "content": "
MethodvariantsDevTest
GTPM-branchBLSTM19.520.1
Dilated blocks22.222.6
Transformer28.728.9
Transformer+BLSTM24.424.1
" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.41, + 0.242, + 0.426 + ], + "angle": 0, + "content": "5.4. Module Analysis" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.433, + 0.47, + 0.675 + ], + "angle": 0, + "content": "Other choices of knowledge fusion schemes. In Tab. 6, we compare distinct knowledge fusion schemes based on our SDPN, including the knowledge distillation strategies (upper part of Tab. 6) and feature fusion strategies (bottom of Tab. 6). Specifically, all schemes use only SPM and BLSTM in testing and all knowledge distillation schemes distill knowledge from 1D-TCN to BLSTM. We observe that feature fusion strategies have limited promotion and even worse results than the SDPN, while all knowledge distillation schemes gained an improvement by the SDPN. This validates the effectiveness of knowledge distillation and shows that simply concatenating or summing features lacks the constraint for 1D-TCN and BLSTM to guide them to possess context knowledge of the other. And the attention mechanism only learns the correlation between 1D-TCN and BLSTM, neglecting context knowledge transferring." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.675, + 0.47, + 0.886 + ], + "angle": 0, + "content": "Impact of different distillation objects. The Tab. 6 also shows the performance of using intermediate feature hints versus prediction scores as distillation objects. The Wasserstein distance [3, 7] and JMMD [19] enforce to align the intermediate feature distributions. And the CKD [28] distills significant activation values in each channel of intermediate feature hints. Further, based on the CKD our \\(\\mathcal{L}_{l2g}\\) weights the distillation by the intersection information of intermediate feature hints. On the other hand, the vanilla distillation [11] is designed for aligning glosses prediction scores, gives the worst performance. Overall, results suggest that adopting intermediate feature hints as distillation objects is more effective than employing prediction scores to teach how to generate the desired output." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.886, + 0.469, + 0.902 + ], + "angle": 0, + "content": "Impact of different temporal window widths of 1D-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.242 + ], + "angle": 0, + "content": "TCN. Tab. 7 delivers that the window width designed to approximate the average length of isolated sign [6] performs the best. (Since half of the frames are selected for training, i.e., SFL [22], the actual window width needs to be multiplied by 2). Whereas, variants of 1D-TCN with substantially different window widths (ranging from 14 to 26) do not show a significant performance gap. We explain that variants of 1D-TCN can learn sign-wise knowledge through global context guidance optimized by the \\(\\mathcal{L}_{g2l}\\), which relieves the effect of receptive field discrepancy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.243, + 0.892, + 0.394 + ], + "angle": 0, + "content": "Other choices of global temporal perception modules. Tab. 8 ablates the performance of distinct global temporal perception modules, such as BLSTM, Dilated blocks [24], Transformer [2, 22], and Transformer+BLSTM. The BLSTM achieves the best performance. The plausible reason is that sign language videos have a semantic sequence with grammatical rules, which means both forward and backward frames should be taken into consideration [25], which BLSTM achieves natively. However, Transformer is unable to do it to learn the semantic sequence well." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.408, + 0.619, + 0.423 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.433, + 0.892, + 0.689 + ], + "angle": 0, + "content": "In this work, we have extensively studied the limitation and desired properties of the temporal aggregation module (TAM) in the continuous sign language recognition framework. In particular, with an advanced analysis tool (i.e., information stored in weights [31]), we showed that the desired TAM should be a shallow architecture to allow more effective training of spatial perception module but also should be a deep one for a high temporal aggregation capability. To achieve this property, we proposed cross-temporal context aggregation (CTCA) with a dual-path network. Moreover, we proposed a cross-context knowledge distillation loss function to transfer the local temporal context and the linguistic prior to the global perception module. Extensive experimental results demonstrated that our CTCA effectively enhances the generalization of the spatial perception module while achieving the leading accuracy with fewer parameters and higher efficiency." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.892, + 0.81 + ], + "angle": 0, + "content": "Limitations. In the redesign of the temporal aggregation module, the improvement of global temporal context perception still follows the current scheme, which still tends to cause overfitting. Therefore finding a more suitable global temporal context perception for the weakly supervised CSLR task is a challenge to be solved. Meanwhile, the CTCA is not tested on real-world with complex scenes, which deserves further study." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Acknowledgments. This work was supported by the National Natural Science Foundation of China (61906135, 62020106004, 92048301, 62276141), and the Tianjin Research Innovation Project for Postgraduate Students (2021YJSB244). It was also supported by A\\*STAR Centre for Frontier AI Research." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10778" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.117, + 0.47, + 0.158 + ], + "angle": 0, + "content": "[1] Necati Cihan Camgoz, Simon Hadfield, Oscar Koller, Hermann Ney, and Richard Bowden. Neural sign language translation. In CVPR, 2018. 1, 6" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.16, + 0.472, + 0.215 + ], + "angle": 0, + "content": "[2] Necati Cihan Camgoz, Oscar Koller, Simon Hadfield, and Richard Bowden. 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State-of-the-art methods typically have two modules, a spatial perception module and a temporal aggregation module, which are jointly learned end-to-end. Existing results in [9, 20, 25, 36] have indicated that, as the frontal component of the overall model, the spatial perception module used for spatial feature extraction tends to be insufficiently trained. In this paper, we first conduct empirical studies and show that a shallow temporal aggregation module allows more thorough training of the spatial perception module. However, a shallow temporal aggregation module cannot well capture both local and global temporal context information in sign language. To address this dilemma, we propose a cross-temporal context aggregation (CTCA) model. Specifically, we build a dual-path network that contains two branches for perceptions of local temporal context and global temporal context. We further design a cross-context knowledge distillation learning objective to aggregate the two types of context and the linguistic prior. The knowledge distillation enables the resultant one-branch temporal aggregation module to perceive local-global temporal and semantic context. This shallow temporal perception module structure facilitates spatial perception module learning. Extensive experiments on challenging CSLR benchmarks demonstrate that our method outperforms all state-of-the-art methods. + +# 1. Introduction + +Sign language is a visual language for deaf and hearing-impaired people for ease of communication. Because sign language has a different grammatical structure and expression from natural spoken language, deaf and hearing- + +![](images/367a6f0353a843c5ecf0bb1464de13b6a6e4cdf73588157f747f04644d50b683.jpg) +Figure 1. (a) is the common CSLR framework. (b) presents the generalization capability (i.e., information stored in weights (IIW) [31]) of TAMs and SPMs of baseline, state-of-the-art methods and the proposed method. (c) is the performance of the state-of-the-art methods including word error rate, test time, and model size. + +![](images/9facce7d33b7c8c9cd4b94d6b62a2c6253ee22ba4b33022eb65bc751476e050d.jpg) + +impaired people hardly communicate normally with hearing people in daily life. To eliminate this communication gap, continuous sign language recognition (CSLR) enforces to recognition of various glosses from a sign language video. Due to the data collection and annotation being labor-intensive, CSLR benchmarks adopt a sentence-annotation manner for all sign language videos [1, 15, 33]. + +In recent years, there is a consensus among state-of-the-art methods on a baseline framework (See Fig. 1 (a)). It is made up of a spatial perception module (SPM), and a temporal aggregation module (TAM) including two components for local and global temporal perception module, and the connectionist temporal classification (CTC) loss [8] for training. At present, these methods [9,20,25,36] have perceived one limitation of this framework that the temporal aggregation module can lead to insufficiently trained spatial + +perception module and affect the final accuracy. We use a recent interpretation method (i.e., the compression of information stored in weights (IIW) [31]) to measure the generalization capability of different neural modules. Fig. 1 (b) shows the IIWs of TAMs and SPMs of baseline and state-of-the-art works and infers their positive relation, i.e., low-generalization TAM (i.e., high IIW) usually leads to low-generalization SPM. We provide more studies in Sec. 3. + +Y. Min et al. [20] measure the difference of correctly and incorrectly recognized results between auxiliary and primary classifiers to evaluate model overfitting, and A. Hao et al. [9] visualized heatmaps of TAM's self-similarity matrices to show what the local and global temporal perception learning. However, there are no straightforward quantitative studies to discuss the effects of TAM on SPM, and we do not know how significant the effects could be and have no idea about the desired temporal aggregation. In this paper, we extensively study the limitation and desirable properties of the temporal aggregation module in the CSLR framework via constructing a baseline framework and extensive empirical studies. We insight that a desired temporal aggregation module should be a shallow architecture to allow more effective training of spatial perception module but also should be a deep one for a high temporal aggregation capability. Whereas, it is quite challenging for the temporal aggregation module to achieve these properties simultaneously. + +To overcome this challenge, we propose the cross-temporal context aggregation (CTCA) that a shallow temporal aggregation module has capable of incorporating local-global temporal contexts and the linguistic prior. Specifically, we construct a dual-path network, which decouples the local and global perception modules and imposes a linguistic module in parallel. This architecture ensures the local context perception, global context perception, and linguistic prior extraction. Furthermore, we propose a cross-context knowledge distillation loss function to transfer the local temporal context and the linguistic prior to the global perception module. Notice that the spatial perception module can facilitate itself by receiving cross-context knowledge as supervision during distillation. Fig. 1(b) shows that both SPM and TAM in CTCA achieve higher generalization than the ones of baselines. Consequently, Fig. 1(c) delivers CTCA's superiority and it outperforms the state-of-the-art methods on WER, test time, and model size. + +# 2. Related Work + +Continuous sign language recognition. To learn stronger representation under the sentence-annotated benchmarks, current deep learning-based approaches exploit the Connectionist Temporal Classification (CTC) [8], which provides a many-to-one mapping between frames and glosses. To mitigate the insufficient training problem [9,20,25,36], a time-consuming iterative fine-tuning strategy [6, 25] is utilized + +to boost the model generalization. In contrast, the end-to-end methods proposed, such as VAC [20] and SMKD [9] proposed an end-to-end alignment constraint to make the learning of local and global temporal context to be consistent. $\mathrm{C}^2\mathrm{SLR}$ [36] designed two constraints for building spatial consistency and temporal perception consistency to enhance the representation power of the model. Y. Min et al. [21] proposed an optimized CTC loss, which can constrain features on a hypersphere and control the peak behavior of CTC loss to enhance the feature generalization. In this paper, we achieve a shallower temporal perception module that not only promotes more thorough training of spatial perception model but also aggregates local-global temporal context via a cross-temporal context distillation. + +Knowledge distillation. Knowledge distillation (KD) is a model compression technique that facilitates student models to achieve strong performance by excavating knowledge from large teacher models [11] or itself [16]. To eliminates huge training cost needs the ONE [16] proposes a multibranch network to conduct an ensemble on-the-fly. VAC [20] conducts its local and global temporal context module as an implicit teacher to promote each one to gain advanced generalization. Wang et al. [30] propose that consistent knowledge of multi-modal contains in each channel, and can achieve multi-modal fusion by exchanging their channels. POS-SCAN [35], LGD [32], and ELG [27] assume the linguistic information shares similar semantics with the visual. They transfer the image-text alignment from teacher to student. In this paper, we distill the local-global temporal information and linguistic context to a single one-branch temporal aggregation module. + +# 3. Preliminaries and Analysis + +# 3.1. General CSLR Framework + +Given a sign language video $\mathcal{X} = \{\mathbf{X}_t\}_{t=1}^T$ having $T$ frames, a continuous sign language recognition method (CSLR) denoted as $\phi(\cdot)$ contributes to predicting $L$ glosses (i.e., $\mathcal{Y} = \{y_i\}_{i=1}^L$ ) contained in the video where $y_i$ is the $i$ -th gloss, and we have $\mathcal{Y} = \phi(\mathcal{X})$ . As shown in Fig. 1(a), we show three clips in the input video, which are highlighted with pink, blue, and green colors. A CSLR method is desired to predict the corresponding three glosses, i.e., 'JETZT', 'WETTER', and 'APRIL'. The existing training dataset only provides sentence annotation (See the annotation in Fig. 1) instead of the ground truth of each frame and we even do not know the exact number of glosses in the input video. Hence, the task is a weakly-supervised learning problem and significantly challenging. + +The dominant CSLR framework [9, 20, 36] mainly involves three modules: spatial perception module (SPM) to extract feature representation of each frame independently, temporal aggregation module (TAM) to sequentially con + +![](images/7a903fbb9c557e3cf636b0bed5c0deeed83d969a5551d7de5ef0bf2cdab96eef.jpg) +Figure 2. Experiments about chain depth variants of TAM in the general CSLR framework. The IIW [31] is exploited to measure the generalization gap (the larger gap, the larger the IIW) of SPM and TAM. The WER value is utilized to estimate the performance. + +duct local and global aggregation across frames' features, and the classification module for the final prediction. We denote the three modules as $\phi_{\mathrm{spm}}(\cdot),\phi_{\mathrm{tam}}(\cdot)$ ,and $\phi_{\mathrm{cls}}(\cdot)$ , respectively, and can reformulate the whole process as $\mathcal{V} =$ $\phi (\mathcal{X}) = \phi_{\mathrm{cls}}(\phi_{\mathrm{tam}}(\phi_{\mathrm{spm}}(\mathcal{X}))$ (See Fig. 1(a)). Specifically, $\phi_{\mathrm{spm}}(\cdot)$ first extracts features of all frames via a convolution neural network like ResNet18 [10], which are denoted as $\mathcal{V} = \{\mathbf{V}_t\}_{t = 1}^T$ . Then, $\phi_{\mathrm{tam}}(\cdot)$ uses a local temporal context perception component like temporal convolution network (i.e., 1D-TCN) [5, 9, 20, 36] to capture the correlation across adjacent frames and map the representations $\nu$ to a new one, i.e., $\mathcal{V}^{\mathrm{loc}} = \{\mathbf{V}_t^{\mathrm{loc}}\}_{t = 1}^T$ $\phi_{\mathrm{tam}}(\cdot)$ further feeds the locally-aggregated representations to the global perception component like a two-layer BLSTM [9, 20, 34, 36] to capture the global temporal patterns across all frames and get $\mathcal{V}^{\mathrm{glo}} = \{\mathbf{V}_t^{\mathrm{glo}}\}_{t = 1}^T$ . Then, the $\mathcal{V}^{\mathrm{glo}}$ is further passed to $\phi_{\mathrm{cls}}$ , which is a fully-connected layer to predict logits $\mathcal{Z}^{\mathrm{glo}} = \{\mathbf{Z}_t^{\mathrm{glo}}\}_{t = 1}^T$ . Finally, the $\mathcal{Z}^{\mathrm{glo}}$ is fed into the CTC to align the prediction and ground truth and calculate the loss. + +# 3.2. Empirical Studies + +Following the fact about chain rules of backpropagation, we study the effects of the chain depth of the temporal aggregation module to the spatial perception module. Intuitively, the temporal aggregation module with fewer layers (i.e., a shallow TAM) has fewer effects on the back-propagation of gradients, and a shallower TAM could lead to a more powerful SPM. To conduct a solid analysis, we have the following setups: + +- Baseline CSLR. We follow the general CSLR framework in Sec. 3.1 and construct a CSLR method including a cascaded ResNet18 as the SPM, $K$ -layer 1D + +TCNs and a two-layer BLSTM as the TAM, and the classifier and the CTC as the classification module. The $K$ -layer 1D-TCNs and BLSTM are used for local and global temporal contexts perception, respectively. + +- TAM with different chain depths. We set five variants of TAM by stacking $K$ 1D-TCNs where we set $K \in \{0,1,3,9,22\}^*$ . We do not tune the depth of the BLSTM since the BLSTM is prone to over-fitting [9, 20], we contribute to exploring the influence of the depth between SPM and BLSTM. + +- Evaluation of SPM and CSLR. Following existing works, we use the word error rate (WER) to evaluate the performance of the whole CSLR method. In contrast, for TAM and SPM, we choose another metric, i.e., the compression of information stored in weights (IIW) [31], which is designed to understand the behavior of neural networks and can be an indicator of generalization gap (i.e., the accuracy difference on the test and training datasets) of neural networks [31]. Intuitively, with the same training dataset, a lower IIW of a module means that the module contributes more to the accuracy of the test dataset. + +With the above setups, we get five CSLR variants with five TAMs having different chain depths. Then, we train and test all variants on the RWTH-2014 dataset [15]. Specifically, we can calculate the word error rate (WER) of the five variants for the prediction accuracy evaluation. We further count the information stored in weights (IIW) of the SPMs and TAMs of the five variants, respectively. As the results are shown in Fig. 2, we have the following observations: ① When we consider the chain depth (i.e., $K$ ) from 1 to 22, the IIW of SPM gradually increases and reaches the maximum at $K = 22$ while the IIW of TAM gradually decreases, which means the effects of chain depth to the capability of SPM and TAM have completely opposite trends. A powerful SPM desires a shallow TAM while the TAM itself requires a deeper architecture. ② Considering the changes of WER of the CSLR along different chain depths, we see that the trend of WER is consistent with the IIW's variation trend, which means the SPM has higher effects than the TAM on the final prediction accuracy. + +# 3.3. Motivations + +According to the above studies, a desired temporal aggregation module should be a shallow architecture to allow more effective training of the spatial perception module but also should be a deep one for a high temporal aggregation capability. Such a contradiction makes the designing of a suitable TAM challenging. Because SPM is directly related to the final accuracy, we tend to select a shallow TAM. + +![](images/df13b1bb0ef0506ceab92c0d269f3859ad75f10ace36414d1e810c909bf0c08b.jpg) +Figure 3. Pipeline of the CTCA. In particular, the steps with black borders or black arrows belong to the CTCA test process. + +Then, the key problem becomes how to make TAM shallower and contribute more to the final prediction accuracy. + +Existing works have noticed that both local and global temporal perception are critical to prediction accuracy. We also conduct a simple study and observe that removing any temporal perception components leads to a significant accuracy drop (See the supplementary material). All the above observations motivate us to develop a shallower but more powerful temporal aggregation module that has the capability of perceiving local and global context perception. + +# 4. Cross-Temporal Context Aggregation + +An intuitive idea is to utilize knowledge distillation to integrate local and global contexts into a shallow architecture. As a result, the two opposite requirements for TAM in Sec. 3.3 could be handled simultaneously. To this end, we first provide a vanilla distillation solution in Sec. 4.1, which has several inherent limitations. Then, we impose a more advanced distillation method, i.e., cross-temporal context aggregation (CTCA), in Sec. 4.2 and Sec. 4.3. + +# 4.1. A Vanilla Distillation Solution + +We follow the baseline CSLR in Sec. 3.2 and construct two independent CSLRs that have the same spatial perception module (SPM) and classification module but a different temporal aggregation module (TAM). The first one retains the global perception component (i.e., a BLSTM) and removes the local component (i.e., 1D-TCN). Such a CSLR has the shallowest TAM (i.e., $K = 0$ in Sec. 3.2) and we denote it as CSLR-GloTAM. The second one only contains the local perception component and the BLSTM layer is removed and we denote it as CSLR-LocTAM. The main goal is to train a CSLR-GloTAM to let its TAM have the local temporal contexts. To this end, we use the CSLR-LocTAM to teach the CSLR-GloTAM for acquiring local information + +and only use the CSLR-GloTAM for inference. The teaching manner follows the vanilla distillation [11]. + +However, such a vanilla distillation approach has some limitations: 1) In terms of CSLR-GloTAM, when BLSTM over-fits the training data, the loss can be hardly propagated to the SPM. The distillation based on two separated CSLRs cannot address this issue properly. 2) By adapting existing distillation methods directly, we need to design two exclusive optimization schemes for the two independent CSLRs, respectively, which inevitably leads to high time and computing costs. 3) The vanilla distillation leverages a fully-supervised distillation loss, which cannot be adapted to the weakly-supervised optimization like CSLR directly. + +# 4.2. SPM-Shared Dual-Path Network + +Enforcing to resolve the first and second limitations in Sec. 4.1, we propose the SPM-Shared Dual-Path Network (SDPN). Inspired by [16], we adopt a multi-branch architecture with a shared SPM to merge the training processes of teacher and student, which distills from each other in a peer-teaching manner. As a result, this structure avoids the requirement of two optimization schemes trade-offs. It is easy to train with only one optimization scheme. As such, different from the vanilla distillation approach has two separate networks, the SDPN is composed of a shared SPM and followed a dual-path (See Fig. 3): local temporal perception branch (i.e., 1D-TCN branch), global temporal perception branch (i.e., BLSTM branch). Specifically, each branch itself of SDPN stands for the specific knowledge concurrently, which conducts a native ensemble model on-the-fly. With the above architecture, even if the BLSTM branch is over-fitted, other branches like the 1D-TCN branch can still back-propagate the loss to the shared SPM straightforwardly. More importantly, the SDPN is easy to adopt distillation losses (See Sec. 4.3) to distill the local temporal context and the linguistic prior to reinforcing BLSTM. The two branches of SDPN have different objectives and architectures as done in [9, 17, 20]. In particular, we only use the BLSTM branch during inference, rather than both branches. We detail the architectural designs in the following: + +Shared spatial perception module. We use the ResNet18 for the spatial perception module (See Sec. 3.1) where the fully-connection layer is removed, which takes the video clips as inputs and outputs the spatial representation $\nu$ . + +Local & global temporal perception branches. The local branch consists of a 1D-TCN and a local classifier $\mathcal{F}^{\mathrm{loc}}$ . The 1D-TCN is able to provide local temporal representations $\mathcal{V}^{\mathrm{loc}}$ maintained sign-wise information. And the local classifier outputs the local prediction $\mathcal{Z}^{\mathrm{loc}}$ . The global branch contains a two-layer BLSTM and a global classifier $\mathcal{F}^{\mathrm{glo}}$ . The BLSTM outputs global temporal representations $\mathcal{V}^{\mathrm{glo}}$ , which contains the order and correlation of co-occurring signs. The global classifier outputs the global prediction + +$\mathcal{Z}^{\mathrm{glo}}$ . Note that, both $\mathcal{Z}^{\mathrm{glo}}$ and $\mathcal{Z}^{\mathrm{loc}}$ are optimized by CTC loss to achieve a knowledge complementary to the spatial perception module reinforcement, and the 1D-TCN is removed during inference. + +# 4.3. Cross-Context Knowledge Distillation Loss + +To make the shallow BLSTM branch learn both local & global perceptions and achieve the desired property against the third limitation in Sec. 4.1, we propose the Cross-Context Knowledge Distillation Loss (CCKD). CCKD composes a cross-temporal knowledge distillation (CTD) and a cross-modality knowledge distillation (CMD). The CTD builds a mutual temporal context distillation that enables the BLSTM and 1D-TCN branches to incorporate complementary knowledge to refine themselves and the SPM. The CMD distills linguistic prior i.e., inter-gloss semantic correlation from glosses sequence to BLSTM branch to reinforce its temporal aggregation. In contrast to the vanilla distillation that enhances the student's ability to achieve consistent prediction scores with the teacher, the CCKD focuses on distilling channel-wise knowledge from intermediate feature hints [28]. By doing so, CCKD facilitates students to learn how to learn, rather than how to get prediction scores, which is more applicable to CSLR. + +Cross-temporal knowledge distillation. ① Local temporal context guidance loss $(\mathcal{L}_{l2g})$ . Given the local and global temporal representation $\mathcal{V}^{\mathrm{loc}}$ and $\mathcal{V}^{\mathrm{glo}}$ , the $\mathcal{L}_{l2g}$ encourages the $\mathcal{V}^{\mathrm{glo}}$ to learn sign-wise context maintained in $\mathcal{V}^{\mathrm{loc}}$ to remain local-global temporal contexts. Due to the knowledge of sign-wise context being distinct from the global context, knowledge confusion may occur during the $\mathcal{L}_{l2g}$ procedure. To relieve the confusion, we weight the $\mathcal{V}^{\mathrm{loc}}$ by the intersection information $I(\mathcal{V}^{\mathrm{loc}}, \mathcal{V}^{\mathrm{glo}})$ among $\mathcal{V}^{\mathrm{loc}}$ and $\mathcal{V}^{\mathrm{glo}}$ to suppress signs information of $\mathcal{V}^{\mathrm{loc}}$ who differs with $\mathcal{V}^{\mathrm{glo}}$ . + +$$ +\mathcal {L} _ {l 2 g} \left(\mathcal {V} ^ {\mathrm {g l o}}, \mathcal {V} ^ {\mathrm {l o c}}\right) = \varphi \left(\mathcal {V} ^ {\mathrm {g l o}}, \mathcal {V} ^ {\mathrm {l o c}} \cdot I \left(\mathcal {V} ^ {\mathrm {l o c}}, \mathcal {V} ^ {\mathrm {g l o}}\right)\right), \tag {1} +$$ + +$$ +\varphi \left(\mathcal {V} ^ {\text {g l o}}, \mathcal {V} ^ {\text {l o c}}\right) = \frac {\tau^ {2}}{C} \sum_ {c = 1} ^ {C} \sum_ {i = 1} ^ {T} K L \left(\left(\mathbf {V} _ {c, i} ^ {\text {g l o}}\right), \left(\mathbf {V} _ {c, i} ^ {\text {l o c}}\right)\right), \tag {2} +$$ + +$$ +I \left(\mathcal {V} ^ {\text {l o c}}, \mathcal {V} ^ {\text {g l o}}\right) = \frac {1}{\frac {\sigma \left(\mathbf {V} _ {c , i} ^ {\text {l o c}}\right)}{\sigma \left(\mathbf {V} _ {c , i} ^ {\text {g l o}}\right)} + 1}, \tag {3} +$$ + +where if $\frac{\sigma(\mathbf{V}_{c,i}^{\mathrm{loc}})}{\sigma(\mathbf{V}_{c,i}^{\mathrm{glo}})}$ is large and thus $I(\mathcal{V}^{\mathrm{loc}},\mathcal{V}^{\mathrm{glo}})$ is small, meaning the large different between $\nu^{\mathrm{loc}}$ and $\nu^{\mathrm{glo}}$ . The $KL$ denotes the KL divergence, $\tau$ is the temperature factor for smooth, $\sigma$ indicates the softmax function and $C$ corresponds to the feature channels. As indicated in [28], the KL divergence can be used between intermediate feature hints. 2 Global temporal context guidance loss $(\mathcal{L}_{g2l})$ . In addition, the $\mathcal{L}_{g2l}$ loss evolves distilling global contexts i.e., signs order and correlation among co-occurring signs + +to the 1D-TCN branch. As a result, remaining the local-global context, the 1D-TCN is applicable to learning signwise contexts by taking into account global contexts. The $\mathcal{L}_{g2l}$ loss is also formulated as a similarly form with $\mathcal{L}_{l2g}$ : + +$$ +\mathcal {L} _ {g 2 l} \left(\mathcal {V} ^ {\text {l o c}}, \mathcal {V} ^ {\text {g l o}}\right) = \varphi \left(\mathcal {V} ^ {\text {l o c}}, \mathcal {V} ^ {\text {g l o}}\right). \tag {4} +$$ + +$\Theta$ Reconstruction loss $(\mathcal{L}_{rc})$ . The intuition behind this loss is that the distillation between 1D-TCN and BLSTM should be further enhanced when the local representation is welllearned. Therefore, we impose the $\mathcal{L}_{rc}$ as the reconstruction function for the local temporal representation $\mathcal{V}^{\mathrm{loc}}$ to reinforce cross-temporal context distillation. Notably, we experimentally follow the entropy principle [13, 18] to measure knowledge uncertainty by $w(\mathbf{V}_i^{\mathrm{loc}})$ . If the estimated $\mathcal{V}^{\mathrm{loc}}$ is well-trained and has a high certainty, $H(\mathbf{V}_i^{\mathrm{loc}})$ becomes small, leading to a large weight $(1 + w(\mathbf{V}_i^{\mathrm{loc}}))$ . Then, the consistency between local & global representations is further enhanced via the $\mathcal{L}_{rc}$ . We also adopt a residual connection for stable weighting. + +$$ +\mathcal {L} _ {r c} = \sqrt {\sum_ {i = 1} ^ {T} \left(\mathbf {V} _ {i} ^ {\mathrm {g l o}} - \mathbf {V} _ {i} ^ {\mathrm {l o c}}\right) ^ {2}} \cdot \sum_ {i = 1} ^ {T} (1 + w (\mathbf {V} _ {i} ^ {\mathrm {l o c}})), \tag {5} +$$ + +$$ +w \left(\mathbf {V} _ {i} ^ {\text {l o c}}\right) = \exp^ {- H \left(\mathbf {V} _ {i} ^ {\text {l o c}}\right)}, \tag {6} +$$ + +As mentioned above, the CTD loss is formulated as: + +$$ +\mathcal {L} _ {c t d} = \alpha_ {1} \mathcal {L} _ {l 2 g} + \alpha_ {2} \mathcal {L} _ {g 2 l} + \alpha_ {3} \mathcal {L} _ {r c}, \tag {7} +$$ + +Where the $\alpha_{1}$ , $\alpha_{2}$ , $\alpha_{3}$ achieve trade-offs among losses in the CTD loss. Furthermore, the CTD loss ensures the spatial perception module to be propagated the local-global information during the whole training time, which avoids the propagation effect of BSLTM overfitting and enhances SPM generalization ability, implicitly. + +Cross-modality knowledge distillation. The CTD loss only restricts the cross-temporal context statistics yet has weak semantic context supervision i.e., the linguistic prior. Motivated by CLIP [26] and ELG [27], the cross-modality knowledge distillation (CMD) is proposed to distill inter-gloss semantic correlation from glosses sequence to BLSTM branch. In practice, given the gloss sequence $\mathcal{V} = \{y_i\}_{i=1}^L$ corresponding to $\mathcal{X}$ with $L$ glosses, it will be embedded by pre-trained BERT to generate high-dimensional semantic features $\mathcal{G}^{\mathrm{gls}} = \{\mathbf{G}_i^{\mathrm{gls}}\}_{i=1}^L \in \mathbb{R}^{Y \times L}$ . Further, the $\mathcal{G}^{\mathrm{gls}}$ and global temporal representation $\mathcal{V}^{\mathrm{glo}}$ will be computed by cross-attention [29] to generate the linguistic-visual relation $\mathcal{G}^{\widehat{t}} \in \mathbb{R}^{Y \times L}$ . + +$$ +\mathcal {G} ^ {\widehat {t}} = \operatorname {s o f t m a x} \left(\frac {f _ {\mathcal {Q}} \left(\mathcal {G} ^ {\mathrm {g l s}}\right) f _ {\mathcal {K}} \left(\mathcal {V} ^ {\mathrm {g l o}}\right) ^ {\mathrm {T}}}{\sqrt {C}}\right) f _ {\mathcal {V}} \left(\mathcal {V} ^ {\mathrm {g l o}}\right), \tag {8} +$$ + +Moreover, the self-correlation matrix $\underline{cor}^{\hat{t}}$ will be obtained by the matrix product of $\mathcal{G}^{\hat{t}}$ and $(\mathcal{G}^{\hat{t}})^{\mathrm{T}}$ . The $cor^t$ is a + +self-correlation matrix of gloss features $\mathcal{G}^{\mathrm{gls}}$ , i.e., $cor^{t} = \left\| \mathcal{G}^{\mathrm{gls}}\right\|_{2}\left(\left\| \mathcal{G}^{\mathrm{gls}}\right\|_{2}\right)^{\mathrm{T}}$ . Finally, we distill the inter-gloss discrimination from the $cor^{t}$ to the $cor^{\hat{t}}$ via the cross-modality distillation loss $\mathcal{L}_{cmd}$ . The $t$ and $\hat{t}$ represent the gloss modality and visual modality, respectively. + +$$ +\mathcal {L} _ {c m d} = \frac {1}{L} \sum_ {i = 1} ^ {L} \sigma \left(\operatorname {c o r} _ {i} ^ {\hat {t}}\right) \cdot \log \left[ \frac {\sigma \left(\operatorname {c o r} _ {i} ^ {\hat {t}}\right)}{\sigma \left(\operatorname {c o r} _ {i} ^ {t}\right)} \right], \tag {9} +$$ + +where $\sigma$ indicates the softmax function. We involve $cor^t$ to have the same knowledge with $cor^t$ to enhance the linguistic-visual relation, which encourages $\nu^{\mathrm{glo}}$ to have the inter-gloss discrimination indirectly. + +Combining all loss functions, the CCKD is denoted as: + +$$ +\mathcal {L} _ {\mathcal {C C K D}} = \alpha \mathcal {L} _ {c t d} + \beta \mathcal {L} _ {c m d} + \gamma \mathcal {L} _ {c t c}, \tag {10} +$$ + +where the $\alpha, \beta$ , and $\gamma$ control the trade-off among losses. + +# 4.4. Implementation Details + +Network details. We set $K = 3$ and kernel size is 3 for 1D-TCN, each layer equips with a 1D Batch Norm layer and a ReLU activation. The output channel of each temporal layer in 1D-TCN is set to 1024 and BLSTM is set to 2048. + +Hyperparameters setting. The $\tau$ in Eq. (2) is set to 4, the $\alpha_{1},\alpha_{2},\alpha_{3}$ in Eq. (7) are set to 0.2, 1, 1 respectively. And $\alpha ,\beta ,$ and $\gamma$ in Eq. (10) are set to 3, 130, 1 respectively. We find that the $\alpha_{1}$ is chosen in [0.1, 1) and the $\beta$ needs to be set to among [50, 150] to obtain good performance. + +Training and test strategy. During both the training and test stages for all benchmarks, we randomly discard half of video frames as inputs following SFL [22]. We then resize the frame size to $256 \times 256$ and perform randomly cropping frames to $224 \times 224$ , as well as random horizontal flip (50%) in the training stage (only center crop frames to $224 \times 224$ in the test stage). The BERT in the CMD loss is frozen and only employed in the training stage. In the test, only the spatial perception module and the global temporal perception branch are exploited to generate predictions. The CTCA is implemented in PyTorch with one A100 GPU. + +# 5. Experiments + +# 5.1. Dataset and Evaluation + +RWTH-2014 [15] is a German sign language dataset, it consists of a total of 6,841 sentences with a vocabulary of 1,295 glosses, signed by 9 different singers. + +RWTH-2014T [1] can be used for both CSLR and sign language translation tasks [1]. It involves a vocabulary of 1,085 glosses, split into 7,096, 519, and 642 samples in the train set, dev set, and test set, respectively. + +CSL-Daily [33] is a large Chinese sign language dataset about people's daily life. It can be employed in both CSLR + +Table 1. Comparison with state-of-the-art methods on the RWTH2014 dataset. (WER(%) the lower is the better). + +
MethodsDevTest
del/insWERdel/insWER
DNF [6]7.8/3.523.87.8/3.424.4
FCN [5]-23.7-23.9
VAC [20]7.9/2.521.28.4/2.622.3
CMA [23]7.3/2.721.37.3/2.421.9
SMKD [9]6.8/2.520.86.3/2.321.0
C²SLR [36]-20.5-20.4
TLP [17]6.3/2.819.76.1/2.920.8
RadialCTC [21]6.5/2.719.46.1/2.620.2
CTCA(Ours)6.2/2.919.56.1/2.620.1
+ +Table 2. Comparison with state-of-the-art methods on the RWTH-2014T dataset. (WER(%) the lower is the better). + +
MethodsWER
DevTest
SLT [2]24.624.5
CNN+LSTM+HMM [14]22.124.1
BN-TIN+Transf [33]22.723.9
V-L Mapper [4]21.922.5
SMKD [9]20.822.4
C2SLR [36]20.220.4
TLP [9]19.421.2
CTCA(Ours)19.320.3
+ +and sign language translation. There are 18,401, 1,077, and 1,176 videos for the training set, dev set, and test set, respectively. It has a vocabulary of 2,000 glosses for CSLR. + +Evaluation metric. In this paper, we adopt the word error rate (WER) metrics for CSLR methods evaluation. It measures the minimum number of substitutions, deletions, and insertions that need to convert one predicted glosses sequence to a given reference sequence [15]. + +# 5.2. Comparison with State-of-the-arts + +Evaluation on RWTH-2014. The objective of the VAC and SMKD is to enhance the discriminative capacity of the visual module (i.e., SPM+1D-TCN). Meanwhile, our CTCA focuses on investigating and designing the desired TAM for CSLR. As demonstrated in Tab. 1, the proposed CTCA solely utilizes the RGB information of sign language videos, yet it achieves competitive performance in terms of the WER (19.5% and 20.1%). Notably, it surpasses other RGB cue-based approaches, i.e., SMKD, C2SLR, and TLP, thereby validating the effectiveness of CTCA. + +Evaluation on RWTH-2014T. In Tab. 2, it is evident that the CTCA gains the best performance (19.3% and 20.3%) compared with other state-of-the-art approaches. + +Evaluation on CSL-Daily. To further assess the CTCA's generalization capacity, we evaluate it on the CSL-Daily benchmark. As presented in Tab. 3, the CTCA outperforms + +Table 3. Comparison with state-of-the-art methods on the CSL-Daily. (WER(%) the lower is the better). + +
MethodsDevTest
del/insWERdel/insWER
LS-HAN [12]14.6/5.739.014.8/5.039.4
SLT(Gloss+Text) [2]10.3/4.433.19.6/4.132.0
FCN [5]12.8/4.033.212.6/3.732.5
BN-TIN+Transf [33]13.9/3.433.613.5/3.033.1
TIN-Iterative [6]12.8/3.332.812.5/2.732.4
CTCA(Ours)9.2/2.531.38.1/2.329.4
+ +Table 4. Effect of the SDPN architecture on the RWTH-2014. + +
MethodsIIWDevTest
del/insWERdel/insWER
Baseline6.7E-57.0/3.021.86.7/2.722.1
Baseline+SDPN5.6E-57.3/3.121.77.4/2.421.8
VAC(VE) [20]5.4E-5-23.3-23.8
VAC(VE)+SDPN4.2E-57.6/3.122.07.6/3.022.6
+ +all other methods and achieves a $3\%$ WER advantage over the second-best performer, the TIN-Iterative. + +# 5.3. Ablation Study + +Benefits of SPM-Shared Dual-Path Network. Tab. 4 illustrates that when both baseline and VAC are constructed to SDPN architecture, achieving lower generalization gap (lower IIW) and improved performance (lower WER). It is noteworthy that during the testing, only the spatial perception module and the BLSTM branch of SDPN are utilized. These results suggest that the SDPN architecture can facilitate thorough training for the spatial perception module, leading to improved performance. + +Benefits of components of Cross-Context Knowledge Distillation loss. $\bullet$ Effect of vanilla distillation solution. We compare the vanilla distillation approach, as discussed in Sec. 4.1 with the baseline. As presented in Tab. 5, the vanilla distillation yields an improvement over the baseline, yet it is still inferior to each component of the CCKD. + +$\Theta$ Effect of $\mathcal{L}_{l2g}$ loss and $\mathcal{L}_{g2l}$ loss. We introduced two distillation methods, SDPN A and SDPN B based on the SDPN model. SDPN A is the 1D-TCN distilling sign-wise knowledge to the BLSTM via the $\mathcal{L}_{l2g}$ . This method improves performance on the test set by $1.0\%$ compared to the baseline. We also removes the intersection information weighted term $I(:,)$ from SDPN A, which results in a $0.4\%$ drop in performance on the test set, implying its effectiveness. SDPN B, on the other hand, is an SDPN model optimized by the $\mathcal{L}_{g2l}$ , which yields a $1.4\%$ WER improvement over the baseline on the test set. It is noteworthy that SDPN A's performance is inferior to SDPN B. This can be explained that BLSTM tends to overfit on the sequential order of signs, which is easy to learn and leads to fast convergence + +Table 5. Ablation study on cross-context knowledge distillation loss on the RWTH-2014. + +
MethodLctdLcmdDevTest
Ll2gLg2lLrc
Baseline----21.822.1
Vanilla----21.721.9
SDPN A✓---21.021.1
SDPN A-I(;;)✓---21.321.5
SDPN B-✓--20.820.7
SDPN C✓✓--20.420.6
SDPN D✓✓✓-20.020.4
SDPN D-w(;;)✓✓✓-20.220.6
SDPN E---✓21.321.0
CTCA✓✓✓✓19.520.1
+ +Table 6. Comparison of different knowledge fusion schemes on the RWTH-2014. "Wasserstein" is the Wasserstein distance. + +
MethodKnowledge fusionDevTest
SDPN-21.721.8
Vanilla distillation [11]21.621.6
Wasserstein [3]21.621.5
JMMD [19]21.321.3
CKD [28]21.321.5
CTCA(ℓl2g)21.021.1
concatenation22.723.6
point-wise addition21.222.3
attention22.222.6
+ +optimized by CTC [9, 25]. Although the BSLTM in SDPN A receives local context knowledge, it still propagates limited local-global information to SPM, resulting in limited gain for SPM when it is overfitting. Furthermore, the 1D-TCN is less prone to overfitting [5] and in SDPN B facilitated by the $\mathcal{L}_{g2l}$ the 1D-TCN can learn sign-wise context by taking into account global contexts. Then it can provide richer sign-wise supervision to the SPM for locating signs, which can eliminate the limited back-propagation. As a result, more robust features SPM can generate, and they are fed into BLSTM, which outperforms SDPN A. This finding is consistent with the observation $\pmb{\Theta}$ in Sec. 3.2 that the SPM has a high effect on the final prediction performance. The results of SDPN C show that the mutual distillation approach gains $20.6\%$ on the test set. This technique can enhance both the $\mathcal{L}_{l2g}$ and $\mathcal{L}_{g2l}$ , resulting in improved 1D-TCN and BLSTM. This success is also verified by [9]. + +Effect of $\mathcal{L}_{rc}$ loss and $\mathcal{L}_{cmd}$ loss. Seen from Tab. 5, based on the SDPN C model the SDPN D combines the $\mathcal{L}_{rc}$ , which is effective in enhancing performance. Specifically, when SDPN D drops the $w(:,)$ , it gives a worse result, it shows the effect of entropy measurement. Moreover, SDPN E, achieves relatively better performance, which validates the need for linguistic prior supervision. + +Table 7. Performance comparison of local temporal perception module with distinct temporal window widths on the RWTH-2014. $Ft$ and $Ft(d)$ correspond to the 1D temporal convolution layer with kernel of $t$ and dilation of $d$ , respectively. + +
MethodvariantswindowsDevTest
1D-TCNF3-F3-F37*219.520.1
F3(1)-F3(2)7*219.820.3
F5-F59*220.620.6
F5-F5-F513*219.920.6
F7-F713*220.120.3
+ +Table 8. Comparison of CTCA with distinct global temporal perception modules (GTPM) on the RWTH-2014. + +
MethodvariantsDevTest
GTPM-branchBLSTM19.520.1
Dilated blocks22.222.6
Transformer28.728.9
Transformer+BLSTM24.424.1
+ +# 5.4. Module Analysis + +Other choices of knowledge fusion schemes. In Tab. 6, we compare distinct knowledge fusion schemes based on our SDPN, including the knowledge distillation strategies (upper part of Tab. 6) and feature fusion strategies (bottom of Tab. 6). Specifically, all schemes use only SPM and BLSTM in testing and all knowledge distillation schemes distill knowledge from 1D-TCN to BLSTM. We observe that feature fusion strategies have limited promotion and even worse results than the SDPN, while all knowledge distillation schemes gained an improvement by the SDPN. This validates the effectiveness of knowledge distillation and shows that simply concatenating or summing features lacks the constraint for 1D-TCN and BLSTM to guide them to possess context knowledge of the other. And the attention mechanism only learns the correlation between 1D-TCN and BLSTM, neglecting context knowledge transferring. + +Impact of different distillation objects. The Tab. 6 also shows the performance of using intermediate feature hints versus prediction scores as distillation objects. The Wasserstein distance [3, 7] and JMMD [19] enforce to align the intermediate feature distributions. And the CKD [28] distills significant activation values in each channel of intermediate feature hints. Further, based on the CKD our $\mathcal{L}_{l2g}$ weights the distillation by the intersection information of intermediate feature hints. On the other hand, the vanilla distillation [11] is designed for aligning glosses prediction scores, gives the worst performance. Overall, results suggest that adopting intermediate feature hints as distillation objects is more effective than employing prediction scores to teach how to generate the desired output. + +Impact of different temporal window widths of 1D- + +TCN. Tab. 7 delivers that the window width designed to approximate the average length of isolated sign [6] performs the best. (Since half of the frames are selected for training, i.e., SFL [22], the actual window width needs to be multiplied by 2). Whereas, variants of 1D-TCN with substantially different window widths (ranging from 14 to 26) do not show a significant performance gap. We explain that variants of 1D-TCN can learn sign-wise knowledge through global context guidance optimized by the $\mathcal{L}_{g2l}$ , which relieves the effect of receptive field discrepancy. + +Other choices of global temporal perception modules. Tab. 8 ablates the performance of distinct global temporal perception modules, such as BLSTM, Dilated blocks [24], Transformer [2, 22], and Transformer+BLSTM. The BLSTM achieves the best performance. The plausible reason is that sign language videos have a semantic sequence with grammatical rules, which means both forward and backward frames should be taken into consideration [25], which BLSTM achieves natively. However, Transformer is unable to do it to learn the semantic sequence well. + +# 6. Conclusion + +In this work, we have extensively studied the limitation and desired properties of the temporal aggregation module (TAM) in the continuous sign language recognition framework. In particular, with an advanced analysis tool (i.e., information stored in weights [31]), we showed that the desired TAM should be a shallow architecture to allow more effective training of spatial perception module but also should be a deep one for a high temporal aggregation capability. To achieve this property, we proposed cross-temporal context aggregation (CTCA) with a dual-path network. Moreover, we proposed a cross-context knowledge distillation loss function to transfer the local temporal context and the linguistic prior to the global perception module. Extensive experimental results demonstrated that our CTCA effectively enhances the generalization of the spatial perception module while achieving the leading accuracy with fewer parameters and higher efficiency. + +Limitations. In the redesign of the temporal aggregation module, the improvement of global temporal context perception still follows the current scheme, which still tends to cause overfitting. Therefore finding a more suitable global temporal context perception for the weakly supervised CSLR task is a challenge to be solved. Meanwhile, the CTCA is not tested on real-world with complex scenes, which deserves further study. + +Acknowledgments. This work was supported by the National Natural Science Foundation of China (61906135, 62020106004, 92048301, 62276141), and the Tianjin Research Innovation Project for Postgraduate Students (2021YJSB244). 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State-of-the-art methods typically have two modules, a spatial perception module and a temporal aggregation module, which are jointly learned end-to-end. Existing results in [9, 20, 25, 36] have indicated that, as the frontal component of the overall model, the spatial perception module used for spatial feature extraction tends to be insufficiently trained. In this paper, we first conduct empirical studies and show that a shallow temporal aggregation module allows more thorough training of the spatial perception module. However, a shallow temporal aggregation module cannot well capture both local and global temporal context information in sign language. To address this dilemma, we propose a cross-temporal context aggregation (CTCA) model. Specifically, we build a dual-path network that contains two branches for perceptions of local temporal context and global temporal context. We further design a cross-context knowledge distillation learning objective to aggregate the two types of context and the linguistic prior. The knowledge distillation enables the resultant one-branch temporal aggregation module to perceive local-global temporal and semantic context. This shallow temporal perception module structure facilitates spatial perception module learning. Extensive experiments on challenging CSLR benchmarks demonstrate that our method outperforms all state-of-the-art methods." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 616, + 128, + 628 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 616, + 128, + 628 + ], + "spans": [ + { + "bbox": [ + 47, + 616, + 128, + 628 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 636, + 287, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 636, + 287, + 685 + ], + "spans": [ + { + "bbox": [ + 46, + 636, + 287, + 685 + ], + "type": "text", + "content": "Sign language is a visual language for deaf and hearing-impaired people for ease of communication. Because sign language has a different grammatical structure and expression from natural spoken language, deaf and hearing-" + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 307, + 252, + 411, + 449 + ], + "blocks": [ + { + "bbox": [ + 307, + 252, + 411, + 449 + ], + "lines": [ + { + "bbox": [ + 307, + 252, + 411, + 449 + ], + "spans": [ + { + "bbox": [ + 307, + 252, + 411, + 449 + ], + "type": "image", + "image_path": "367a6f0353a843c5ecf0bb1464de13b6a6e4cdf73588157f747f04644d50b683.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 458, + 547, + 515 + ], + "lines": [ + { + "bbox": [ + 305, + 458, + 547, + 515 + ], + "spans": [ + { + "bbox": [ + 305, + 458, + 547, + 515 + ], + "type": "text", + "content": "Figure 1. (a) is the common CSLR framework. (b) presents the generalization capability (i.e., information stored in weights (IIW) [31]) of TAMs and SPMs of baseline, state-of-the-art methods and the proposed method. (c) is the performance of the state-of-the-art methods including word error rate, test time, and model size." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 413, + 252, + 547, + 451 + ], + "blocks": [ + { + "bbox": [ + 413, + 252, + 547, + 451 + ], + "lines": [ + { + "bbox": [ + 413, + 252, + 547, + 451 + ], + "spans": [ + { + "bbox": [ + 413, + 252, + 547, + 451 + ], + "type": "image", + "image_path": "9facce7d33b7c8c9cd4b94d6b62a2c6253ee22ba4b33022eb65bc751476e050d.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 521, + 547, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 547, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 547, + 605 + ], + "type": "text", + "content": "impaired people hardly communicate normally with hearing people in daily life. To eliminate this communication gap, continuous sign language recognition (CSLR) enforces to recognition of various glosses from a sign language video. Due to the data collection and annotation being labor-intensive, CSLR benchmarks adopt a sentence-annotation manner for all sign language videos [1, 15, 33]." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": "In recent years, there is a consensus among state-of-the-art methods on a baseline framework (See Fig. 1 (a)). It is made up of a spatial perception module (SPM), and a temporal aggregation module (TAM) including two components for local and global temporal perception module, and the connectionist temporal classification (CTC) loss [8] for training. At present, these methods [9,20,25,36] have perceived one limitation of this framework that the temporal aggregation module can lead to insufficiently trained spatial" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 693, + 287, + 714 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 287, + 714 + ], + "type": "text", + "content": "*Wanli Xue and Qing Guo are corresponding authors (xue-wanli@email.tjut.edu.cn and tsingqguo@ieee.org)." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10771" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "type": "text", + "content": "perception module and affect the final accuracy. We use a recent interpretation method (i.e., the compression of information stored in weights (IIW) [31]) to measure the generalization capability of different neural modules. Fig. 1 (b) shows the IIWs of TAMs and SPMs of baseline and state-of-the-art works and infers their positive relation, i.e., low-generalization TAM (i.e., high IIW) usually leads to low-generalization SPM. We provide more studies in Sec. 3." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 168, + 288, + 383 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 168, + 288, + 383 + ], + "spans": [ + { + "bbox": [ + 46, + 168, + 288, + 383 + ], + "type": "text", + "content": "Y. Min et al. [20] measure the difference of correctly and incorrectly recognized results between auxiliary and primary classifiers to evaluate model overfitting, and A. Hao et al. [9] visualized heatmaps of TAM's self-similarity matrices to show what the local and global temporal perception learning. However, there are no straightforward quantitative studies to discuss the effects of TAM on SPM, and we do not know how significant the effects could be and have no idea about the desired temporal aggregation. In this paper, we extensively study the limitation and desirable properties of the temporal aggregation module in the CSLR framework via constructing a baseline framework and extensive empirical studies. We insight that a desired temporal aggregation module should be a shallow architecture to allow more effective training of spatial perception module but also should be a deep one for a high temporal aggregation capability. Whereas, it is quite challenging for the temporal aggregation module to achieve these properties simultaneously." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 384, + 287, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 384, + 287, + 598 + ], + "spans": [ + { + "bbox": [ + 46, + 384, + 287, + 598 + ], + "type": "text", + "content": "To overcome this challenge, we propose the cross-temporal context aggregation (CTCA) that a shallow temporal aggregation module has capable of incorporating local-global temporal contexts and the linguistic prior. Specifically, we construct a dual-path network, which decouples the local and global perception modules and imposes a linguistic module in parallel. This architecture ensures the local context perception, global context perception, and linguistic prior extraction. Furthermore, we propose a cross-context knowledge distillation loss function to transfer the local temporal context and the linguistic prior to the global perception module. Notice that the spatial perception module can facilitate itself by receiving cross-context knowledge as supervision during distillation. Fig. 1(b) shows that both SPM and TAM in CTCA achieve higher generalization than the ones of baselines. Consequently, Fig. 1(c) delivers CTCA's superiority and it outperforms the state-of-the-art methods on WER, test time, and model size." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 609, + 134, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 609, + 134, + 623 + ], + "spans": [ + { + "bbox": [ + 47, + 609, + 134, + 623 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": "Continuous sign language recognition. To learn stronger representation under the sentence-annotated benchmarks, current deep learning-based approaches exploit the Connectionist Temporal Classification (CTC) [8], which provides a many-to-one mapping between frames and glosses. To mitigate the insufficient training problem [9,20,25,36], a time-consuming iterative fine-tuning strategy [6, 25] is utilized" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "type": "text", + "content": "to boost the model generalization. In contrast, the end-to-end methods proposed, such as VAC [20] and SMKD [9] proposed an end-to-end alignment constraint to make the learning of local and global temporal context to be consistent. " + }, + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "type": "inline_equation", + "content": "\\mathrm{C}^2\\mathrm{SLR}" + }, + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "type": "text", + "content": " [36] designed two constraints for building spatial consistency and temporal perception consistency to enhance the representation power of the model. Y. Min et al. [21] proposed an optimized CTC loss, which can constrain features on a hypersphere and control the peak behavior of CTC loss to enhance the feature generalization. In this paper, we achieve a shallower temporal perception module that not only promotes more thorough training of spatial perception model but also aggregates local-global temporal context via a cross-temporal context distillation." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 240, + 546, + 444 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 240, + 546, + 444 + ], + "spans": [ + { + "bbox": [ + 304, + 240, + 546, + 444 + ], + "type": "text", + "content": "Knowledge distillation. Knowledge distillation (KD) is a model compression technique that facilitates student models to achieve strong performance by excavating knowledge from large teacher models [11] or itself [16]. To eliminates huge training cost needs the ONE [16] proposes a multibranch network to conduct an ensemble on-the-fly. VAC [20] conducts its local and global temporal context module as an implicit teacher to promote each one to gain advanced generalization. Wang et al. [30] propose that consistent knowledge of multi-modal contains in each channel, and can achieve multi-modal fusion by exchanging their channels. POS-SCAN [35], LGD [32], and ELG [27] assume the linguistic information shares similar semantics with the visual. They transfer the image-text alignment from teacher to student. In this paper, we distill the local-global temporal information and linguistic context to a single one-branch temporal aggregation module." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 457, + 459, + 471 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 457, + 459, + 471 + ], + "spans": [ + { + "bbox": [ + 306, + 457, + 459, + 471 + ], + "type": "text", + "content": "3. Preliminaries and Analysis" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 478, + 457, + 490 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 478, + 457, + 490 + ], + "spans": [ + { + "bbox": [ + 306, + 478, + 457, + 490 + ], + "type": "text", + "content": "3.1. General CSLR Framework" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 496, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 496, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 496, + 545, + 665 + ], + "type": "text", + "content": "Given a sign language video " + }, + { + "bbox": [ + 304, + 496, + 545, + 665 + ], + "type": "inline_equation", + "content": "\\mathcal{X} = \\{\\mathbf{X}_t\\}_{t=1}^T" + }, + { + "bbox": [ + 304, + 496, + 545, + 665 + ], + "type": "text", + "content": " having " + }, + { + "bbox": [ + 304, + 496, + 545, + 665 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 496, + 545, + 665 + ], + "type": "text", + "content": " frames, a continuous sign language recognition method (CSLR) denoted as " + }, + { + "bbox": [ + 304, + 496, + 545, + 665 + ], + "type": "inline_equation", + "content": "\\phi(\\cdot)" + }, + { + "bbox": [ + 304, + 496, + 545, + 665 + ], + "type": "text", + "content": " contributes to predicting " + }, + { + "bbox": [ + 304, + 496, + 545, + 665 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 304, + 496, + 545, + 665 + ], + "type": "text", + "content": " glosses (i.e., " + }, + { + "bbox": [ + 304, + 496, + 545, + 665 + ], + "type": "inline_equation", + "content": "\\mathcal{Y} = \\{y_i\\}_{i=1}^L" + }, + { + "bbox": [ + 304, + 496, + 545, + 665 + ], + "type": "text", + "content": ") contained in the video where " + }, + { + "bbox": [ + 304, + 496, + 545, + 665 + ], + "type": "inline_equation", + "content": "y_i" + }, + { + "bbox": [ + 304, + 496, + 545, + 665 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 304, + 496, + 545, + 665 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 496, + 545, + 665 + ], + "type": "text", + "content": "-th gloss, and we have " + }, + { + "bbox": [ + 304, + 496, + 545, + 665 + ], + "type": "inline_equation", + "content": "\\mathcal{Y} = \\phi(\\mathcal{X})" + }, + { + "bbox": [ + 304, + 496, + 545, + 665 + ], + "type": "text", + "content": ". As shown in Fig. 1(a), we show three clips in the input video, which are highlighted with pink, blue, and green colors. A CSLR method is desired to predict the corresponding three glosses, i.e., 'JETZT', 'WETTER', and 'APRIL'. The existing training dataset only provides sentence annotation (See the annotation in Fig. 1) instead of the ground truth of each frame and we even do not know the exact number of glosses in the input video. Hence, the task is a weakly-supervised learning problem and significantly challenging." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 665, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 714 + ], + "type": "text", + "content": "The dominant CSLR framework [9, 20, 36] mainly involves three modules: spatial perception module (SPM) to extract feature representation of each frame independently, temporal aggregation module (TAM) to sequentially con" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "10772" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 60, + 65, + 276, + 264 + ], + "blocks": [ + { + "bbox": [ + 60, + 65, + 276, + 264 + ], + "lines": [ + { + "bbox": [ + 60, + 65, + 276, + 264 + ], + "spans": [ + { + "bbox": [ + 60, + 65, + 276, + 264 + ], + "type": "image", + "image_path": "7a903fbb9c557e3cf636b0bed5c0deeed83d969a5551d7de5ef0bf2cdab96eef.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 270, + 289, + 316 + ], + "lines": [ + { + "bbox": [ + 46, + 270, + 289, + 316 + ], + "spans": [ + { + "bbox": [ + 46, + 270, + 289, + 316 + ], + "type": "text", + "content": "Figure 2. Experiments about chain depth variants of TAM in the general CSLR framework. The IIW [31] is exploited to measure the generalization gap (the larger gap, the larger the IIW) of SPM and TAM. The WER value is utilized to estimate the performance." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 321, + 289, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 321, + 289, + 550 + ], + "spans": [ + { + "bbox": [ + 46, + 321, + 289, + 550 + ], + "type": "text", + "content": "duct local and global aggregation across frames' features, and the classification module for the final prediction. We denote the three modules as " + }, + { + "bbox": [ + 46, + 321, + 289, + 550 + ], + "type": "inline_equation", + "content": "\\phi_{\\mathrm{spm}}(\\cdot),\\phi_{\\mathrm{tam}}(\\cdot)" + }, + { + "bbox": [ + 46, + 321, + 289, + 550 + ], + "type": "text", + "content": " ,and " + }, + { + "bbox": [ + 46, + 321, + 289, + 550 + ], + "type": "inline_equation", + "content": "\\phi_{\\mathrm{cls}}(\\cdot)" + }, + { + "bbox": [ + 46, + 321, + 289, + 550 + ], + "type": "text", + "content": " , respectively, and can reformulate the whole process as " + }, + { + "bbox": [ + 46, + 321, + 289, + 550 + ], + "type": "inline_equation", + "content": "\\mathcal{V} =" + }, + { + "bbox": [ + 46, + 321, + 289, + 550 + ], + "type": "inline_equation", + "content": "\\phi (\\mathcal{X}) = \\phi_{\\mathrm{cls}}(\\phi_{\\mathrm{tam}}(\\phi_{\\mathrm{spm}}(\\mathcal{X}))" + }, + { + "bbox": [ + 46, + 321, + 289, + 550 + ], + "type": "text", + "content": " (See Fig. 1(a)). Specifically, " + }, + { + "bbox": [ + 46, + 321, + 289, + 550 + ], + "type": "inline_equation", + "content": "\\phi_{\\mathrm{spm}}(\\cdot)" + }, + { + "bbox": [ + 46, + 321, + 289, + 550 + ], + "type": "text", + "content": " first extracts features of all frames via a convolution neural network like ResNet18 [10], which are denoted as " + }, + { + "bbox": [ + 46, + 321, + 289, + 550 + ], + "type": "inline_equation", + "content": "\\mathcal{V} = \\{\\mathbf{V}_t\\}_{t = 1}^T" + }, + { + "bbox": [ + 46, + 321, + 289, + 550 + ], + "type": "text", + "content": " . Then, " + }, + { + "bbox": [ + 46, + 321, + 289, + 550 + ], + "type": "inline_equation", + "content": "\\phi_{\\mathrm{tam}}(\\cdot)" + }, + { + "bbox": [ + 46, + 321, + 289, + 550 + ], + "type": "text", + "content": " uses a local temporal context perception component like temporal convolution network (i.e., 1D-TCN) [5, 9, 20, 36] to capture the correlation across adjacent frames and map the representations " + }, + { + "bbox": [ + 46, + 321, + 289, + 550 + ], + "type": "inline_equation", + "content": "\\nu" + }, + { + "bbox": [ + 46, + 321, + 289, + 550 + ], + "type": "text", + "content": " to a new one, i.e., " + }, + { + "bbox": [ + 46, + 321, + 289, + 550 + ], + "type": "inline_equation", + "content": "\\mathcal{V}^{\\mathrm{loc}} = \\{\\mathbf{V}_t^{\\mathrm{loc}}\\}_{t = 1}^T" + }, + { + "bbox": [ + 46, + 321, + 289, + 550 + ], + "type": "inline_equation", + "content": "\\phi_{\\mathrm{tam}}(\\cdot)" + }, + { + "bbox": [ + 46, + 321, + 289, + 550 + ], + "type": "text", + "content": " further feeds the locally-aggregated representations to the global perception component like a two-layer BLSTM [9, 20, 34, 36] to capture the global temporal patterns across all frames and get " + }, + { + "bbox": [ + 46, + 321, + 289, + 550 + ], + "type": "inline_equation", + "content": "\\mathcal{V}^{\\mathrm{glo}} = \\{\\mathbf{V}_t^{\\mathrm{glo}}\\}_{t = 1}^T" + }, + { + "bbox": [ + 46, + 321, + 289, + 550 + ], + "type": "text", + "content": " . Then, the " + }, + { + "bbox": [ + 46, + 321, + 289, + 550 + ], + "type": "inline_equation", + "content": "\\mathcal{V}^{\\mathrm{glo}}" + }, + { + "bbox": [ + 46, + 321, + 289, + 550 + ], + "type": "text", + "content": " is further passed to " + }, + { + "bbox": [ + 46, + 321, + 289, + 550 + ], + "type": "inline_equation", + "content": "\\phi_{\\mathrm{cls}}" + }, + { + "bbox": [ + 46, + 321, + 289, + 550 + ], + "type": "text", + "content": " , which is a fully-connected layer to predict logits " + }, + { + "bbox": [ + 46, + 321, + 289, + 550 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}^{\\mathrm{glo}} = \\{\\mathbf{Z}_t^{\\mathrm{glo}}\\}_{t = 1}^T" + }, + { + "bbox": [ + 46, + 321, + 289, + 550 + ], + "type": "text", + "content": " . Finally, the " + }, + { + "bbox": [ + 46, + 321, + 289, + 550 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}^{\\mathrm{glo}}" + }, + { + "bbox": [ + 46, + 321, + 289, + 550 + ], + "type": "text", + "content": " is fed into the CTC to align the prediction and ground truth and calculate the loss." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 557, + 153, + 570 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 557, + 153, + 570 + ], + "spans": [ + { + "bbox": [ + 47, + 557, + 153, + 570 + ], + "type": "text", + "content": "3.2. Empirical Studies" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 576, + 287, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 576, + 287, + 673 + ], + "spans": [ + { + "bbox": [ + 46, + 576, + 287, + 673 + ], + "type": "text", + "content": "Following the fact about chain rules of backpropagation, we study the effects of the chain depth of the temporal aggregation module to the spatial perception module. Intuitively, the temporal aggregation module with fewer layers (i.e., a shallow TAM) has fewer effects on the back-propagation of gradients, and a shallower TAM could lead to a more powerful SPM. To conduct a solid analysis, we have the following setups:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 58, + 677, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 677, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 58, + 677, + 288, + 715 + ], + "type": "text", + "content": "- Baseline CSLR. We follow the general CSLR framework in Sec. 3.1 and construct a CSLR method including a cascaded ResNet18 as the SPM, " + }, + { + "bbox": [ + 58, + 677, + 288, + 715 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 58, + 677, + 288, + 715 + ], + "type": "text", + "content": "-layer 1D" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 324, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 324, + 72, + 545, + 120 + ], + "type": "text", + "content": "TCNs and a two-layer BLSTM as the TAM, and the classifier and the CTC as the classification module. The " + }, + { + "bbox": [ + 324, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 324, + 72, + 545, + 120 + ], + "type": "text", + "content": "-layer 1D-TCNs and BLSTM are used for local and global temporal contexts perception, respectively." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 121, + 547, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 121, + 547, + 192 + ], + "spans": [ + { + "bbox": [ + 317, + 121, + 547, + 192 + ], + "type": "text", + "content": "- TAM with different chain depths. We set five variants of TAM by stacking " + }, + { + "bbox": [ + 317, + 121, + 547, + 192 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 317, + 121, + 547, + 192 + ], + "type": "text", + "content": " 1D-TCNs where we set " + }, + { + "bbox": [ + 317, + 121, + 547, + 192 + ], + "type": "inline_equation", + "content": "K \\in \\{0,1,3,9,22\\}^*" + }, + { + "bbox": [ + 317, + 121, + 547, + 192 + ], + "type": "text", + "content": ". We do not tune the depth of the BLSTM since the BLSTM is prone to over-fitting [9, 20], we contribute to exploring the influence of the depth between SPM and BLSTM." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 317, + 193, + 547, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 193, + 547, + 337 + ], + "spans": [ + { + "bbox": [ + 317, + 193, + 547, + 337 + ], + "type": "text", + "content": "- Evaluation of SPM and CSLR. Following existing works, we use the word error rate (WER) to evaluate the performance of the whole CSLR method. In contrast, for TAM and SPM, we choose another metric, i.e., the compression of information stored in weights (IIW) [31], which is designed to understand the behavior of neural networks and can be an indicator of generalization gap (i.e., the accuracy difference on the test and training datasets) of neural networks [31]. Intuitively, with the same training dataset, a lower IIW of a module means that the module contributes more to the accuracy of the test dataset." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 341, + 547, + 570 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 341, + 547, + 570 + ], + "spans": [ + { + "bbox": [ + 304, + 341, + 547, + 570 + ], + "type": "text", + "content": "With the above setups, we get five CSLR variants with five TAMs having different chain depths. Then, we train and test all variants on the RWTH-2014 dataset [15]. Specifically, we can calculate the word error rate (WER) of the five variants for the prediction accuracy evaluation. We further count the information stored in weights (IIW) of the SPMs and TAMs of the five variants, respectively. As the results are shown in Fig. 2, we have the following observations: ① When we consider the chain depth (i.e., " + }, + { + "bbox": [ + 304, + 341, + 547, + 570 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 341, + 547, + 570 + ], + "type": "text", + "content": ") from 1 to 22, the IIW of SPM gradually increases and reaches the maximum at " + }, + { + "bbox": [ + 304, + 341, + 547, + 570 + ], + "type": "inline_equation", + "content": "K = 22" + }, + { + "bbox": [ + 304, + 341, + 547, + 570 + ], + "type": "text", + "content": " while the IIW of TAM gradually decreases, which means the effects of chain depth to the capability of SPM and TAM have completely opposite trends. A powerful SPM desires a shallow TAM while the TAM itself requires a deeper architecture. ② Considering the changes of WER of the CSLR along different chain depths, we see that the trend of WER is consistent with the IIW's variation trend, which means the SPM has higher effects than the TAM on the final prediction accuracy." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 575, + 385, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 575, + 385, + 586 + ], + "spans": [ + { + "bbox": [ + 306, + 575, + 385, + 586 + ], + "type": "text", + "content": "3.3. Motivations" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 594, + 547, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 677 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 677 + ], + "type": "text", + "content": "According to the above studies, a desired temporal aggregation module should be a shallow architecture to allow more effective training of the spatial perception module but also should be a deep one for a high temporal aggregation capability. Such a contradiction makes the designing of a suitable TAM challenging. Because SPM is directly related to the final accuracy, we tend to select a shallow TAM." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 683, + 547, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 683, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 683, + 547, + 713 + ], + "type": "text", + "content": "*0 illustrates the TAM drop the 1D-TCN. We adjust channels of 1D-TCN to make sure different variants have the same model size. Such as 1,3,9,22 denote their channels are 1024,512,256 and 128, respectively." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10773" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 71, + 286, + 240 + ], + "blocks": [ + { + "bbox": [ + 49, + 71, + 286, + 240 + ], + "lines": [ + { + "bbox": [ + 49, + 71, + 286, + 240 + ], + "spans": [ + { + "bbox": [ + 49, + 71, + 286, + 240 + ], + "type": "image", + "image_path": "df13b1bb0ef0506ceab92c0d269f3859ad75f10ace36414d1e810c909bf0c08b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 250, + 287, + 273 + ], + "lines": [ + { + "bbox": [ + 46, + 250, + 287, + 273 + ], + "spans": [ + { + "bbox": [ + 46, + 250, + 287, + 273 + ], + "type": "text", + "content": "Figure 3. Pipeline of the CTCA. In particular, the steps with black borders or black arrows belong to the CTCA test process." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 279, + 287, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 279, + 287, + 304 + ], + "spans": [ + { + "bbox": [ + 46, + 279, + 287, + 304 + ], + "type": "text", + "content": "Then, the key problem becomes how to make TAM shallower and contribute more to the final prediction accuracy." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 304, + 287, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 304, + 287, + 400 + ], + "spans": [ + { + "bbox": [ + 46, + 304, + 287, + 400 + ], + "type": "text", + "content": "Existing works have noticed that both local and global temporal perception are critical to prediction accuracy. We also conduct a simple study and observe that removing any temporal perception components leads to a significant accuracy drop (See the supplementary material). All the above observations motivate us to develop a shallower but more powerful temporal aggregation module that has the capability of perceiving local and global context perception." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 413, + 254, + 427 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 413, + 254, + 427 + ], + "spans": [ + { + "bbox": [ + 47, + 413, + 254, + 427 + ], + "type": "text", + "content": "4. Cross-Temporal Context Aggregation" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 434, + 287, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 434, + 287, + 529 + ], + "spans": [ + { + "bbox": [ + 46, + 434, + 287, + 529 + ], + "type": "text", + "content": "An intuitive idea is to utilize knowledge distillation to integrate local and global contexts into a shallow architecture. As a result, the two opposite requirements for TAM in Sec. 3.3 could be handled simultaneously. To this end, we first provide a vanilla distillation solution in Sec. 4.1, which has several inherent limitations. Then, we impose a more advanced distillation method, i.e., cross-temporal context aggregation (CTCA), in Sec. 4.2 and Sec. 4.3." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 539, + 209, + 551 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 539, + 209, + 551 + ], + "spans": [ + { + "bbox": [ + 47, + 539, + 209, + 551 + ], + "type": "text", + "content": "4.1. A Vanilla Distillation Solution" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 557, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 288, + 713 + ], + "type": "text", + "content": "We follow the baseline CSLR in Sec. 3.2 and construct two independent CSLRs that have the same spatial perception module (SPM) and classification module but a different temporal aggregation module (TAM). The first one retains the global perception component (i.e., a BLSTM) and removes the local component (i.e., 1D-TCN). Such a CSLR has the shallowest TAM (i.e., " + }, + { + "bbox": [ + 46, + 557, + 288, + 713 + ], + "type": "inline_equation", + "content": "K = 0" + }, + { + "bbox": [ + 46, + 557, + 288, + 713 + ], + "type": "text", + "content": " in Sec. 3.2) and we denote it as CSLR-GloTAM. The second one only contains the local perception component and the BLSTM layer is removed and we denote it as CSLR-LocTAM. The main goal is to train a CSLR-GloTAM to let its TAM have the local temporal contexts. To this end, we use the CSLR-LocTAM to teach the CSLR-GloTAM for acquiring local information" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": "and only use the CSLR-GloTAM for inference. The teaching manner follows the vanilla distillation [11]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 97, + 545, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 97, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 304, + 97, + 545, + 228 + ], + "type": "text", + "content": "However, such a vanilla distillation approach has some limitations: 1) In terms of CSLR-GloTAM, when BLSTM over-fits the training data, the loss can be hardly propagated to the SPM. The distillation based on two separated CSLRs cannot address this issue properly. 2) By adapting existing distillation methods directly, we need to design two exclusive optimization schemes for the two independent CSLRs, respectively, which inevitably leads to high time and computing costs. 3) The vanilla distillation leverages a fully-supervised distillation loss, which cannot be adapted to the weakly-supervised optimization like CSLR directly." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 238, + 482, + 250 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 238, + 482, + 250 + ], + "spans": [ + { + "bbox": [ + 305, + 238, + 482, + 250 + ], + "type": "text", + "content": "4.2. SPM-Shared Dual-Path Network" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 258, + 545, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 258, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 258, + 545, + 555 + ], + "type": "text", + "content": "Enforcing to resolve the first and second limitations in Sec. 4.1, we propose the SPM-Shared Dual-Path Network (SDPN). Inspired by [16], we adopt a multi-branch architecture with a shared SPM to merge the training processes of teacher and student, which distills from each other in a peer-teaching manner. As a result, this structure avoids the requirement of two optimization schemes trade-offs. It is easy to train with only one optimization scheme. As such, different from the vanilla distillation approach has two separate networks, the SDPN is composed of a shared SPM and followed a dual-path (See Fig. 3): local temporal perception branch (i.e., 1D-TCN branch), global temporal perception branch (i.e., BLSTM branch). Specifically, each branch itself of SDPN stands for the specific knowledge concurrently, which conducts a native ensemble model on-the-fly. With the above architecture, even if the BLSTM branch is over-fitted, other branches like the 1D-TCN branch can still back-propagate the loss to the shared SPM straightforwardly. More importantly, the SDPN is easy to adopt distillation losses (See Sec. 4.3) to distill the local temporal context and the linguistic prior to reinforcing BLSTM. The two branches of SDPN have different objectives and architectures as done in [9, 17, 20]. In particular, we only use the BLSTM branch during inference, rather than both branches. We detail the architectural designs in the following:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 557, + 545, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 545, + 605 + ], + "type": "text", + "content": "Shared spatial perception module. We use the ResNet18 for the spatial perception module (See Sec. 3.1) where the fully-connection layer is removed, which takes the video clips as inputs and outputs the spatial representation " + }, + { + "bbox": [ + 304, + 557, + 545, + 605 + ], + "type": "inline_equation", + "content": "\\nu" + }, + { + "bbox": [ + 304, + 557, + 545, + 605 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "Local & global temporal perception branches. The local branch consists of a 1D-TCN and a local classifier " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{F}^{\\mathrm{loc}}" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": ". The 1D-TCN is able to provide local temporal representations " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{V}^{\\mathrm{loc}}" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " maintained sign-wise information. And the local classifier outputs the local prediction " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}^{\\mathrm{loc}}" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": ". The global branch contains a two-layer BLSTM and a global classifier " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{F}^{\\mathrm{glo}}" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": ". The BLSTM outputs global temporal representations " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{V}^{\\mathrm{glo}}" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": ", which contains the order and correlation of co-occurring signs. The global classifier outputs the global prediction" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10774" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}^{\\mathrm{glo}}" + }, + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "text", + "content": ". Note that, both " + }, + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}^{\\mathrm{glo}}" + }, + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}^{\\mathrm{loc}}" + }, + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "text", + "content": " are optimized by CTC loss to achieve a knowledge complementary to the spatial perception module reinforcement, and the 1D-TCN is removed during inference." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 129, + 271, + 141 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 129, + 271, + 141 + ], + "spans": [ + { + "bbox": [ + 47, + 129, + 271, + 141 + ], + "type": "text", + "content": "4.3. Cross-Context Knowledge Distillation Loss" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 147, + 287, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 147, + 287, + 361 + ], + "spans": [ + { + "bbox": [ + 46, + 147, + 287, + 361 + ], + "type": "text", + "content": "To make the shallow BLSTM branch learn both local & global perceptions and achieve the desired property against the third limitation in Sec. 4.1, we propose the Cross-Context Knowledge Distillation Loss (CCKD). CCKD composes a cross-temporal knowledge distillation (CTD) and a cross-modality knowledge distillation (CMD). The CTD builds a mutual temporal context distillation that enables the BLSTM and 1D-TCN branches to incorporate complementary knowledge to refine themselves and the SPM. The CMD distills linguistic prior i.e., inter-gloss semantic correlation from glosses sequence to BLSTM branch to reinforce its temporal aggregation. In contrast to the vanilla distillation that enhances the student's ability to achieve consistent prediction scores with the teacher, the CCKD focuses on distilling channel-wise knowledge from intermediate feature hints [28]. By doing so, CCKD facilitates students to learn how to learn, rather than how to get prediction scores, which is more applicable to CSLR." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 363, + 286, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 363, + 286, + 483 + ], + "spans": [ + { + "bbox": [ + 46, + 363, + 286, + 483 + ], + "type": "text", + "content": "Cross-temporal knowledge distillation. ① Local temporal context guidance loss " + }, + { + "bbox": [ + 46, + 363, + 286, + 483 + ], + "type": "inline_equation", + "content": "(\\mathcal{L}_{l2g})" + }, + { + "bbox": [ + 46, + 363, + 286, + 483 + ], + "type": "text", + "content": ". Given the local and global temporal representation " + }, + { + "bbox": [ + 46, + 363, + 286, + 483 + ], + "type": "inline_equation", + "content": "\\mathcal{V}^{\\mathrm{loc}}" + }, + { + "bbox": [ + 46, + 363, + 286, + 483 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 363, + 286, + 483 + ], + "type": "inline_equation", + "content": "\\mathcal{V}^{\\mathrm{glo}}" + }, + { + "bbox": [ + 46, + 363, + 286, + 483 + ], + "type": "text", + "content": ", the " + }, + { + "bbox": [ + 46, + 363, + 286, + 483 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{l2g}" + }, + { + "bbox": [ + 46, + 363, + 286, + 483 + ], + "type": "text", + "content": " encourages the " + }, + { + "bbox": [ + 46, + 363, + 286, + 483 + ], + "type": "inline_equation", + "content": "\\mathcal{V}^{\\mathrm{glo}}" + }, + { + "bbox": [ + 46, + 363, + 286, + 483 + ], + "type": "text", + "content": " to learn sign-wise context maintained in " + }, + { + "bbox": [ + 46, + 363, + 286, + 483 + ], + "type": "inline_equation", + "content": "\\mathcal{V}^{\\mathrm{loc}}" + }, + { + "bbox": [ + 46, + 363, + 286, + 483 + ], + "type": "text", + "content": " to remain local-global temporal contexts. Due to the knowledge of sign-wise context being distinct from the global context, knowledge confusion may occur during the " + }, + { + "bbox": [ + 46, + 363, + 286, + 483 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{l2g}" + }, + { + "bbox": [ + 46, + 363, + 286, + 483 + ], + "type": "text", + "content": " procedure. To relieve the confusion, we weight the " + }, + { + "bbox": [ + 46, + 363, + 286, + 483 + ], + "type": "inline_equation", + "content": "\\mathcal{V}^{\\mathrm{loc}}" + }, + { + "bbox": [ + 46, + 363, + 286, + 483 + ], + "type": "text", + "content": " by the intersection information " + }, + { + "bbox": [ + 46, + 363, + 286, + 483 + ], + "type": "inline_equation", + "content": "I(\\mathcal{V}^{\\mathrm{loc}}, \\mathcal{V}^{\\mathrm{glo}})" + }, + { + "bbox": [ + 46, + 363, + 286, + 483 + ], + "type": "text", + "content": " among " + }, + { + "bbox": [ + 46, + 363, + 286, + 483 + ], + "type": "inline_equation", + "content": "\\mathcal{V}^{\\mathrm{loc}}" + }, + { + "bbox": [ + 46, + 363, + 286, + 483 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 363, + 286, + 483 + ], + "type": "inline_equation", + "content": "\\mathcal{V}^{\\mathrm{glo}}" + }, + { + "bbox": [ + 46, + 363, + 286, + 483 + ], + "type": "text", + "content": " to suppress signs information of " + }, + { + "bbox": [ + 46, + 363, + 286, + 483 + ], + "type": "inline_equation", + "content": "\\mathcal{V}^{\\mathrm{loc}}" + }, + { + "bbox": [ + 46, + 363, + 286, + 483 + ], + "type": "text", + "content": " who differs with " + }, + { + "bbox": [ + 46, + 363, + 286, + 483 + ], + "type": "inline_equation", + "content": "\\mathcal{V}^{\\mathrm{glo}}" + }, + { + "bbox": [ + 46, + 363, + 286, + 483 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 71, + 488, + 287, + 504 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 71, + 488, + 287, + 504 + ], + "spans": [ + { + "bbox": [ + 71, + 488, + 287, + 504 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {l 2 g} \\left(\\mathcal {V} ^ {\\mathrm {g l o}}, \\mathcal {V} ^ {\\mathrm {l o c}}\\right) = \\varphi \\left(\\mathcal {V} ^ {\\mathrm {g l o}}, \\mathcal {V} ^ {\\mathrm {l o c}} \\cdot I \\left(\\mathcal {V} ^ {\\mathrm {l o c}}, \\mathcal {V} ^ {\\mathrm {g l o}}\\right)\\right), \\tag {1}", + "image_path": "205b541c9c6b45ff952bfff3ecc21c6ab82041716c2cdaffac0a4f34f330572b.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 71, + 513, + 287, + 545 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 71, + 513, + 287, + 545 + ], + "spans": [ + { + "bbox": [ + 71, + 513, + 287, + 545 + ], + "type": "interline_equation", + "content": "\\varphi \\left(\\mathcal {V} ^ {\\text {g l o}}, \\mathcal {V} ^ {\\text {l o c}}\\right) = \\frac {\\tau^ {2}}{C} \\sum_ {c = 1} ^ {C} \\sum_ {i = 1} ^ {T} K L \\left(\\left(\\mathbf {V} _ {c, i} ^ {\\text {g l o}}\\right), \\left(\\mathbf {V} _ {c, i} ^ {\\text {l o c}}\\right)\\right), \\tag {2}", + "image_path": "0ab2c17c91f94711e9003367317a9875c53b44361927a720282851e404154f18.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 109, + 554, + 287, + 588 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 109, + 554, + 287, + 588 + ], + "spans": [ + { + "bbox": [ + 109, + 554, + 287, + 588 + ], + "type": "interline_equation", + "content": "I \\left(\\mathcal {V} ^ {\\text {l o c}}, \\mathcal {V} ^ {\\text {g l o}}\\right) = \\frac {1}{\\frac {\\sigma \\left(\\mathbf {V} _ {c , i} ^ {\\text {l o c}}\\right)}{\\sigma \\left(\\mathbf {V} _ {c , i} ^ {\\text {g l o}}\\right)} + 1}, \\tag {3}", + "image_path": "a7240701c56d6c92f282bf701628dc36c0a6c3058685ba097d0b0e96de36fcbd.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 594, + 286, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 286, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 286, + 714 + ], + "type": "text", + "content": "where if " + }, + { + "bbox": [ + 46, + 594, + 286, + 714 + ], + "type": "inline_equation", + "content": "\\frac{\\sigma(\\mathbf{V}_{c,i}^{\\mathrm{loc}})}{\\sigma(\\mathbf{V}_{c,i}^{\\mathrm{glo}})}" + }, + { + "bbox": [ + 46, + 594, + 286, + 714 + ], + "type": "text", + "content": " is large and thus " + }, + { + "bbox": [ + 46, + 594, + 286, + 714 + ], + "type": "inline_equation", + "content": "I(\\mathcal{V}^{\\mathrm{loc}},\\mathcal{V}^{\\mathrm{glo}})" + }, + { + "bbox": [ + 46, + 594, + 286, + 714 + ], + "type": "text", + "content": " is small, meaning the large different between " + }, + { + "bbox": [ + 46, + 594, + 286, + 714 + ], + "type": "inline_equation", + "content": "\\nu^{\\mathrm{loc}}" + }, + { + "bbox": [ + 46, + 594, + 286, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 594, + 286, + 714 + ], + "type": "inline_equation", + "content": "\\nu^{\\mathrm{glo}}" + }, + { + "bbox": [ + 46, + 594, + 286, + 714 + ], + "type": "text", + "content": ". The " + }, + { + "bbox": [ + 46, + 594, + 286, + 714 + ], + "type": "inline_equation", + "content": "KL" + }, + { + "bbox": [ + 46, + 594, + 286, + 714 + ], + "type": "text", + "content": " denotes the KL divergence, " + }, + { + "bbox": [ + 46, + 594, + 286, + 714 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 594, + 286, + 714 + ], + "type": "text", + "content": " is the temperature factor for smooth, " + }, + { + "bbox": [ + 46, + 594, + 286, + 714 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 594, + 286, + 714 + ], + "type": "text", + "content": " indicates the softmax function and " + }, + { + "bbox": [ + 46, + 594, + 286, + 714 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 594, + 286, + 714 + ], + "type": "text", + "content": " corresponds to the feature channels. As indicated in [28], the KL divergence can be used between intermediate feature hints. 2 Global temporal context guidance loss " + }, + { + "bbox": [ + 46, + 594, + 286, + 714 + ], + "type": "inline_equation", + "content": "(\\mathcal{L}_{g2l})" + }, + { + "bbox": [ + 46, + 594, + 286, + 714 + ], + "type": "text", + "content": ". In addition, the " + }, + { + "bbox": [ + 46, + 594, + 286, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{g2l}" + }, + { + "bbox": [ + 46, + 594, + 286, + 714 + ], + "type": "text", + "content": " loss evolves distilling global contexts i.e., signs order and correlation among co-occurring signs" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 72, + 545, + 121 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 121 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 121 + ], + "type": "text", + "content": "to the 1D-TCN branch. As a result, remaining the local-global context, the 1D-TCN is applicable to learning signwise contexts by taking into account global contexts. The " + }, + { + "bbox": [ + 305, + 72, + 545, + 121 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{g2l}" + }, + { + "bbox": [ + 305, + 72, + 545, + 121 + ], + "type": "text", + "content": " loss is also formulated as a similarly form with " + }, + { + "bbox": [ + 305, + 72, + 545, + 121 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{l2g}" + }, + { + "bbox": [ + 305, + 72, + 545, + 121 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 359, + 127, + 545, + 141 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 127, + 545, + 141 + ], + "spans": [ + { + "bbox": [ + 359, + 127, + 545, + 141 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {g 2 l} \\left(\\mathcal {V} ^ {\\text {l o c}}, \\mathcal {V} ^ {\\text {g l o}}\\right) = \\varphi \\left(\\mathcal {V} ^ {\\text {l o c}}, \\mathcal {V} ^ {\\text {g l o}}\\right). \\tag {4}", + "image_path": "4ccab3355ebf1f44b52cdbc8899779c56e9d8b61d6a21267613962ed284d239d.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 148, + 545, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 148, + 545, + 304 + ], + "spans": [ + { + "bbox": [ + 304, + 148, + 545, + 304 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 304, + 148, + 545, + 304 + ], + "type": "text", + "content": " Reconstruction loss " + }, + { + "bbox": [ + 304, + 148, + 545, + 304 + ], + "type": "inline_equation", + "content": "(\\mathcal{L}_{rc})" + }, + { + "bbox": [ + 304, + 148, + 545, + 304 + ], + "type": "text", + "content": ". The intuition behind this loss is that the distillation between 1D-TCN and BLSTM should be further enhanced when the local representation is welllearned. Therefore, we impose the " + }, + { + "bbox": [ + 304, + 148, + 545, + 304 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rc}" + }, + { + "bbox": [ + 304, + 148, + 545, + 304 + ], + "type": "text", + "content": " as the reconstruction function for the local temporal representation " + }, + { + "bbox": [ + 304, + 148, + 545, + 304 + ], + "type": "inline_equation", + "content": "\\mathcal{V}^{\\mathrm{loc}}" + }, + { + "bbox": [ + 304, + 148, + 545, + 304 + ], + "type": "text", + "content": " to reinforce cross-temporal context distillation. Notably, we experimentally follow the entropy principle [13, 18] to measure knowledge uncertainty by " + }, + { + "bbox": [ + 304, + 148, + 545, + 304 + ], + "type": "inline_equation", + "content": "w(\\mathbf{V}_i^{\\mathrm{loc}})" + }, + { + "bbox": [ + 304, + 148, + 545, + 304 + ], + "type": "text", + "content": ". If the estimated " + }, + { + "bbox": [ + 304, + 148, + 545, + 304 + ], + "type": "inline_equation", + "content": "\\mathcal{V}^{\\mathrm{loc}}" + }, + { + "bbox": [ + 304, + 148, + 545, + 304 + ], + "type": "text", + "content": " is well-trained and has a high certainty, " + }, + { + "bbox": [ + 304, + 148, + 545, + 304 + ], + "type": "inline_equation", + "content": "H(\\mathbf{V}_i^{\\mathrm{loc}})" + }, + { + "bbox": [ + 304, + 148, + 545, + 304 + ], + "type": "text", + "content": " becomes small, leading to a large weight " + }, + { + "bbox": [ + 304, + 148, + 545, + 304 + ], + "type": "inline_equation", + "content": "(1 + w(\\mathbf{V}_i^{\\mathrm{loc}}))" + }, + { + "bbox": [ + 304, + 148, + 545, + 304 + ], + "type": "text", + "content": ". Then, the consistency between local & global representations is further enhanced via the " + }, + { + "bbox": [ + 304, + 148, + 545, + 304 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rc}" + }, + { + "bbox": [ + 304, + 148, + 545, + 304 + ], + "type": "text", + "content": ". We also adopt a residual connection for stable weighting." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 321, + 312, + 545, + 350 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 312, + 545, + 350 + ], + "spans": [ + { + "bbox": [ + 321, + 312, + 545, + 350 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {r c} = \\sqrt {\\sum_ {i = 1} ^ {T} \\left(\\mathbf {V} _ {i} ^ {\\mathrm {g l o}} - \\mathbf {V} _ {i} ^ {\\mathrm {l o c}}\\right) ^ {2}} \\cdot \\sum_ {i = 1} ^ {T} (1 + w (\\mathbf {V} _ {i} ^ {\\mathrm {l o c}})), \\tag {5}", + "image_path": "873ce902bb111b3327a01da4a450d5649133c63d90d98d05265af6bb97a3589b.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 376, + 358, + 545, + 373 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 376, + 358, + 545, + 373 + ], + "spans": [ + { + "bbox": [ + 376, + 358, + 545, + 373 + ], + "type": "interline_equation", + "content": "w \\left(\\mathbf {V} _ {i} ^ {\\text {l o c}}\\right) = \\exp^ {- H \\left(\\mathbf {V} _ {i} ^ {\\text {l o c}}\\right)}, \\tag {6}", + "image_path": "b8c731ae2109789eb8281d8ea6f8404179665d80d7b4e5c7c64b7ef9feb57c95.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 378, + 517, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 378, + 517, + 389 + ], + "spans": [ + { + "bbox": [ + 306, + 378, + 517, + 389 + ], + "type": "text", + "content": "As mentioned above, the CTD loss is formulated as:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 353, + 398, + 545, + 411 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 353, + 398, + 545, + 411 + ], + "spans": [ + { + "bbox": [ + 353, + 398, + 545, + 411 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {c t d} = \\alpha_ {1} \\mathcal {L} _ {l 2 g} + \\alpha_ {2} \\mathcal {L} _ {g 2 l} + \\alpha_ {3} \\mathcal {L} _ {r c}, \\tag {7}", + "image_path": "8f9edf8bd056d053206c9b5e168a1ea339bea983452632728f25646c429601af.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 418, + 545, + 490 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 418, + 545, + 490 + ], + "spans": [ + { + "bbox": [ + 304, + 418, + 545, + 490 + ], + "type": "text", + "content": "Where the " + }, + { + "bbox": [ + 304, + 418, + 545, + 490 + ], + "type": "inline_equation", + "content": "\\alpha_{1}" + }, + { + "bbox": [ + 304, + 418, + 545, + 490 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 418, + 545, + 490 + ], + "type": "inline_equation", + "content": "\\alpha_{2}" + }, + { + "bbox": [ + 304, + 418, + 545, + 490 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 418, + 545, + 490 + ], + "type": "inline_equation", + "content": "\\alpha_{3}" + }, + { + "bbox": [ + 304, + 418, + 545, + 490 + ], + "type": "text", + "content": " achieve trade-offs among losses in the CTD loss. Furthermore, the CTD loss ensures the spatial perception module to be propagated the local-global information during the whole training time, which avoids the propagation effect of BSLTM overfitting and enhances SPM generalization ability, implicitly." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 491, + 545, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 491, + 545, + 647 + ], + "spans": [ + { + "bbox": [ + 304, + 491, + 545, + 647 + ], + "type": "text", + "content": "Cross-modality knowledge distillation. The CTD loss only restricts the cross-temporal context statistics yet has weak semantic context supervision i.e., the linguistic prior. Motivated by CLIP [26] and ELG [27], the cross-modality knowledge distillation (CMD) is proposed to distill inter-gloss semantic correlation from glosses sequence to BLSTM branch. In practice, given the gloss sequence " + }, + { + "bbox": [ + 304, + 491, + 545, + 647 + ], + "type": "inline_equation", + "content": "\\mathcal{V} = \\{y_i\\}_{i=1}^L" + }, + { + "bbox": [ + 304, + 491, + 545, + 647 + ], + "type": "text", + "content": " corresponding to " + }, + { + "bbox": [ + 304, + 491, + 545, + 647 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 304, + 491, + 545, + 647 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 491, + 545, + 647 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 304, + 491, + 545, + 647 + ], + "type": "text", + "content": " glosses, it will be embedded by pre-trained BERT to generate high-dimensional semantic features " + }, + { + "bbox": [ + 304, + 491, + 545, + 647 + ], + "type": "inline_equation", + "content": "\\mathcal{G}^{\\mathrm{gls}} = \\{\\mathbf{G}_i^{\\mathrm{gls}}\\}_{i=1}^L \\in \\mathbb{R}^{Y \\times L}" + }, + { + "bbox": [ + 304, + 491, + 545, + 647 + ], + "type": "text", + "content": ". Further, the " + }, + { + "bbox": [ + 304, + 491, + 545, + 647 + ], + "type": "inline_equation", + "content": "\\mathcal{G}^{\\mathrm{gls}}" + }, + { + "bbox": [ + 304, + 491, + 545, + 647 + ], + "type": "text", + "content": " and global temporal representation " + }, + { + "bbox": [ + 304, + 491, + 545, + 647 + ], + "type": "inline_equation", + "content": "\\mathcal{V}^{\\mathrm{glo}}" + }, + { + "bbox": [ + 304, + 491, + 545, + 647 + ], + "type": "text", + "content": " will be computed by cross-attention [29] to generate the linguistic-visual relation " + }, + { + "bbox": [ + 304, + 491, + 545, + 647 + ], + "type": "inline_equation", + "content": "\\mathcal{G}^{\\widehat{t}} \\in \\mathbb{R}^{Y \\times L}" + }, + { + "bbox": [ + 304, + 491, + 545, + 647 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 330, + 653, + 545, + 681 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 653, + 545, + 681 + ], + "spans": [ + { + "bbox": [ + 330, + 653, + 545, + 681 + ], + "type": "interline_equation", + "content": "\\mathcal {G} ^ {\\widehat {t}} = \\operatorname {s o f t m a x} \\left(\\frac {f _ {\\mathcal {Q}} \\left(\\mathcal {G} ^ {\\mathrm {g l s}}\\right) f _ {\\mathcal {K}} \\left(\\mathcal {V} ^ {\\mathrm {g l o}}\\right) ^ {\\mathrm {T}}}{\\sqrt {C}}\\right) f _ {\\mathcal {V}} \\left(\\mathcal {V} ^ {\\mathrm {g l o}}\\right), \\tag {8}", + "image_path": "4f3d54971015a48ec754e580eac2cfe1630cd0ba949d90ed96b20d4eb9335639.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "content": "Moreover, the self-correlation matrix " + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\underline{cor}^{\\hat{t}}" + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "content": " will be obtained by the matrix product of " + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{G}^{\\hat{t}}" + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "(\\mathcal{G}^{\\hat{t}})^{\\mathrm{T}}" + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "content": ". The " + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "cor^t" + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "content": " is a" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10775" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 138 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 138 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 138 + ], + "type": "text", + "content": "self-correlation matrix of gloss features " + }, + { + "bbox": [ + 47, + 72, + 289, + 138 + ], + "type": "inline_equation", + "content": "\\mathcal{G}^{\\mathrm{gls}}" + }, + { + "bbox": [ + 47, + 72, + 289, + 138 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 47, + 72, + 289, + 138 + ], + "type": "inline_equation", + "content": "cor^{t} = \\left\\| \\mathcal{G}^{\\mathrm{gls}}\\right\\|_{2}\\left(\\left\\| \\mathcal{G}^{\\mathrm{gls}}\\right\\|_{2}\\right)^{\\mathrm{T}}" + }, + { + "bbox": [ + 47, + 72, + 289, + 138 + ], + "type": "text", + "content": ". Finally, we distill the inter-gloss discrimination from the " + }, + { + "bbox": [ + 47, + 72, + 289, + 138 + ], + "type": "inline_equation", + "content": "cor^{t}" + }, + { + "bbox": [ + 47, + 72, + 289, + 138 + ], + "type": "text", + "content": " to the " + }, + { + "bbox": [ + 47, + 72, + 289, + 138 + ], + "type": "inline_equation", + "content": "cor^{\\hat{t}}" + }, + { + "bbox": [ + 47, + 72, + 289, + 138 + ], + "type": "text", + "content": " via the cross-modality distillation loss " + }, + { + "bbox": [ + 47, + 72, + 289, + 138 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cmd}" + }, + { + "bbox": [ + 47, + 72, + 289, + 138 + ], + "type": "text", + "content": ". The " + }, + { + "bbox": [ + 47, + 72, + 289, + 138 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 72, + 289, + 138 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 72, + 289, + 138 + ], + "type": "inline_equation", + "content": "\\hat{t}" + }, + { + "bbox": [ + 47, + 72, + 289, + 138 + ], + "type": "text", + "content": " represent the gloss modality and visual modality, respectively." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 82, + 145, + 287, + 179 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 145, + 287, + 179 + ], + "spans": [ + { + "bbox": [ + 82, + 145, + 287, + 179 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {c m d} = \\frac {1}{L} \\sum_ {i = 1} ^ {L} \\sigma \\left(\\operatorname {c o r} _ {i} ^ {\\hat {t}}\\right) \\cdot \\log \\left[ \\frac {\\sigma \\left(\\operatorname {c o r} _ {i} ^ {\\hat {t}}\\right)}{\\sigma \\left(\\operatorname {c o r} _ {i} ^ {t}\\right)} \\right], \\tag {9}", + "image_path": "258f255187799fbb992923e34ca6c89506f352838ab4cee5e0f80b02eda9b31b.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 185, + 287, + 234 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 185, + 287, + 234 + ], + "spans": [ + { + "bbox": [ + 47, + 185, + 287, + 234 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 185, + 287, + 234 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 47, + 185, + 287, + 234 + ], + "type": "text", + "content": " indicates the softmax function. We involve " + }, + { + "bbox": [ + 47, + 185, + 287, + 234 + ], + "type": "inline_equation", + "content": "cor^t" + }, + { + "bbox": [ + 47, + 185, + 287, + 234 + ], + "type": "text", + "content": " to have the same knowledge with " + }, + { + "bbox": [ + 47, + 185, + 287, + 234 + ], + "type": "inline_equation", + "content": "cor^t" + }, + { + "bbox": [ + 47, + 185, + 287, + 234 + ], + "type": "text", + "content": " to enhance the linguistic-visual relation, which encourages " + }, + { + "bbox": [ + 47, + 185, + 287, + 234 + ], + "type": "inline_equation", + "content": "\\nu^{\\mathrm{glo}}" + }, + { + "bbox": [ + 47, + 185, + 287, + 234 + ], + "type": "text", + "content": " to have the inter-gloss discrimination indirectly." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 58, + 235, + 282, + 247 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 235, + 282, + 247 + ], + "spans": [ + { + "bbox": [ + 58, + 235, + 282, + 247 + ], + "type": "text", + "content": "Combining all loss functions, the CCKD is denoted as:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 92, + 256, + 287, + 270 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 92, + 256, + 287, + 270 + ], + "spans": [ + { + "bbox": [ + 92, + 256, + 287, + 270 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathcal {C C K D}} = \\alpha \\mathcal {L} _ {c t d} + \\beta \\mathcal {L} _ {c m d} + \\gamma \\mathcal {L} _ {c t c}, \\tag {10}", + "image_path": "42da389bc8d5240bbb72d404f5c0ffd95099ff440208503b30586b5638dc418d.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 278, + 279, + 291 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 278, + 279, + 291 + ], + "spans": [ + { + "bbox": [ + 47, + 278, + 279, + 291 + ], + "type": "text", + "content": "where the " + }, + { + "bbox": [ + 47, + 278, + 279, + 291 + ], + "type": "inline_equation", + "content": "\\alpha, \\beta" + }, + { + "bbox": [ + 47, + 278, + 279, + 291 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 278, + 279, + 291 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 47, + 278, + 279, + 291 + ], + "type": "text", + "content": " control the trade-off among losses." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 298, + 180, + 312 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 298, + 180, + 312 + ], + "spans": [ + { + "bbox": [ + 47, + 298, + 180, + 312 + ], + "type": "text", + "content": "4.4. Implementation Details" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 316, + 287, + 364 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 316, + 287, + 364 + ], + "spans": [ + { + "bbox": [ + 47, + 316, + 287, + 364 + ], + "type": "text", + "content": "Network details. We set " + }, + { + "bbox": [ + 47, + 316, + 287, + 364 + ], + "type": "inline_equation", + "content": "K = 3" + }, + { + "bbox": [ + 47, + 316, + 287, + 364 + ], + "type": "text", + "content": " and kernel size is 3 for 1D-TCN, each layer equips with a 1D Batch Norm layer and a ReLU activation. The output channel of each temporal layer in 1D-TCN is set to 1024 and BLSTM is set to 2048." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 365, + 287, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 365, + 287, + 425 + ], + "spans": [ + { + "bbox": [ + 47, + 365, + 287, + 425 + ], + "type": "text", + "content": "Hyperparameters setting. The " + }, + { + "bbox": [ + 47, + 365, + 287, + 425 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 47, + 365, + 287, + 425 + ], + "type": "text", + "content": " in Eq. (2) is set to 4, the " + }, + { + "bbox": [ + 47, + 365, + 287, + 425 + ], + "type": "inline_equation", + "content": "\\alpha_{1},\\alpha_{2},\\alpha_{3}" + }, + { + "bbox": [ + 47, + 365, + 287, + 425 + ], + "type": "text", + "content": " in Eq. (7) are set to 0.2, 1, 1 respectively. And " + }, + { + "bbox": [ + 47, + 365, + 287, + 425 + ], + "type": "inline_equation", + "content": "\\alpha ,\\beta ," + }, + { + "bbox": [ + 47, + 365, + 287, + 425 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 365, + 287, + 425 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 47, + 365, + 287, + 425 + ], + "type": "text", + "content": " in Eq. (10) are set to 3, 130, 1 respectively. We find that the " + }, + { + "bbox": [ + 47, + 365, + 287, + 425 + ], + "type": "inline_equation", + "content": "\\alpha_{1}" + }, + { + "bbox": [ + 47, + 365, + 287, + 425 + ], + "type": "text", + "content": " is chosen in [0.1, 1) and the " + }, + { + "bbox": [ + 47, + 365, + 287, + 425 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 47, + 365, + 287, + 425 + ], + "type": "text", + "content": " needs to be set to among [50, 150] to obtain good performance." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 425, + 288, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 425, + 288, + 557 + ], + "spans": [ + { + "bbox": [ + 46, + 425, + 288, + 557 + ], + "type": "text", + "content": "Training and test strategy. During both the training and test stages for all benchmarks, we randomly discard half of video frames as inputs following SFL [22]. We then resize the frame size to " + }, + { + "bbox": [ + 46, + 425, + 288, + 557 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 46, + 425, + 288, + 557 + ], + "type": "text", + "content": " and perform randomly cropping frames to " + }, + { + "bbox": [ + 46, + 425, + 288, + 557 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 46, + 425, + 288, + 557 + ], + "type": "text", + "content": ", as well as random horizontal flip (50%) in the training stage (only center crop frames to " + }, + { + "bbox": [ + 46, + 425, + 288, + 557 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 46, + 425, + 288, + 557 + ], + "type": "text", + "content": " in the test stage). The BERT in the CMD loss is frozen and only employed in the training stage. In the test, only the spatial perception module and the global temporal perception branch are exploited to generate predictions. The CTCA is implemented in PyTorch with one A100 GPU." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 567, + 128, + 581 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 567, + 128, + 581 + ], + "spans": [ + { + "bbox": [ + 47, + 567, + 128, + 581 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 586, + 180, + 599 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 586, + 180, + 599 + ], + "spans": [ + { + "bbox": [ + 47, + 586, + 180, + 599 + ], + "type": "text", + "content": "5.1. Dataset and Evaluation" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 605, + 287, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 605, + 287, + 641 + ], + "spans": [ + { + "bbox": [ + 47, + 605, + 287, + 641 + ], + "type": "text", + "content": "RWTH-2014 [15] is a German sign language dataset, it consists of a total of 6,841 sentences with a vocabulary of 1,295 glosses, signed by 9 different singers." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 642, + 287, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 642, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 47, + 642, + 287, + 689 + ], + "type": "text", + "content": "RWTH-2014T [1] can be used for both CSLR and sign language translation tasks [1]. It involves a vocabulary of 1,085 glosses, split into 7,096, 519, and 642 samples in the train set, dev set, and test set, respectively." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "CSL-Daily [33] is a large Chinese sign language dataset about people's daily life. It can be employed in both CSLR" + } + ] + } + ], + "index": 14 + }, + { + "type": "table", + "bbox": [ + 316, + 92, + 535, + 228 + ], + "blocks": [ + { + "bbox": [ + 305, + 71, + 545, + 91 + ], + "lines": [ + { + "bbox": [ + 305, + 71, + 545, + 91 + ], + "spans": [ + { + "bbox": [ + 305, + 71, + 545, + 91 + ], + "type": "text", + "content": "Table 1. Comparison with state-of-the-art methods on the RWTH2014 dataset. (WER(%) the lower is the better)." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 316, + 92, + 535, + 228 + ], + "lines": [ + { + "bbox": [ + 316, + 92, + 535, + 228 + ], + "spans": [ + { + "bbox": [ + 316, + 92, + 535, + 228 + ], + "type": "table", + "html": "
MethodsDevTest
del/insWERdel/insWER
DNF [6]7.8/3.523.87.8/3.424.4
FCN [5]-23.7-23.9
VAC [20]7.9/2.521.28.4/2.622.3
CMA [23]7.3/2.721.37.3/2.421.9
SMKD [9]6.8/2.520.86.3/2.321.0
C²SLR [36]-20.5-20.4
TLP [17]6.3/2.819.76.1/2.920.8
RadialCTC [21]6.5/2.719.46.1/2.620.2
CTCA(Ours)6.2/2.919.56.1/2.620.1
", + "image_path": "3b07462cf73c8d46ddc25a34ae1145475770369798da5cbeba39321f04799915.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "table_body" + } + ], + "index": 16 + }, + { + "type": "table", + "bbox": [ + 341, + 258, + 509, + 381 + ], + "blocks": [ + { + "bbox": [ + 305, + 236, + 545, + 258 + ], + "lines": [ + { + "bbox": [ + 305, + 236, + 545, + 258 + ], + "spans": [ + { + "bbox": [ + 305, + 236, + 545, + 258 + ], + "type": "text", + "content": "Table 2. Comparison with state-of-the-art methods on the RWTH-2014T dataset. (WER(%) the lower is the better)." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 341, + 258, + 509, + 381 + ], + "lines": [ + { + "bbox": [ + 341, + 258, + 509, + 381 + ], + "spans": [ + { + "bbox": [ + 341, + 258, + 509, + 381 + ], + "type": "table", + "html": "
MethodsWER
DevTest
SLT [2]24.624.5
CNN+LSTM+HMM [14]22.124.1
BN-TIN+Transf [33]22.723.9
V-L Mapper [4]21.922.5
SMKD [9]20.822.4
C2SLR [36]20.220.4
TLP [9]19.421.2
CTCA(Ours)19.320.3
", + "image_path": "1c3ba0d85f8446ccd00ea83bdeffd3eeecad6d7e276a8a00652f31ac8b0a57be.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "table_body" + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 401, + 545, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 401, + 545, + 437 + ], + "spans": [ + { + "bbox": [ + 305, + 401, + 545, + 437 + ], + "type": "text", + "content": "and sign language translation. There are 18,401, 1,077, and 1,176 videos for the training set, dev set, and test set, respectively. It has a vocabulary of 2,000 glosses for CSLR." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 437, + 545, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 437, + 545, + 496 + ], + "spans": [ + { + "bbox": [ + 305, + 437, + 545, + 496 + ], + "type": "text", + "content": "Evaluation metric. In this paper, we adopt the word error rate (WER) metrics for CSLR methods evaluation. It measures the minimum number of substitutions, deletions, and insertions that need to convert one predicted glosses sequence to a given reference sequence [15]." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 504, + 491, + 516 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 504, + 491, + 516 + ], + "spans": [ + { + "bbox": [ + 306, + 504, + 491, + 516 + ], + "type": "text", + "content": "5.2. Comparison with State-of-the-arts" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 521, + 545, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 521, + 545, + 641 + ], + "spans": [ + { + "bbox": [ + 305, + 521, + 545, + 641 + ], + "type": "text", + "content": "Evaluation on RWTH-2014. The objective of the VAC and SMKD is to enhance the discriminative capacity of the visual module (i.e., SPM+1D-TCN). Meanwhile, our CTCA focuses on investigating and designing the desired TAM for CSLR. As demonstrated in Tab. 1, the proposed CTCA solely utilizes the RGB information of sign language videos, yet it achieves competitive performance in terms of the WER (19.5% and 20.1%). Notably, it surpasses other RGB cue-based approaches, i.e., SMKD, C2SLR, and TLP, thereby validating the effectiveness of CTCA." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 305, + 642, + 545, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 642, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 305, + 642, + 545, + 677 + ], + "type": "text", + "content": "Evaluation on RWTH-2014T. In Tab. 2, it is evident that the CTCA gains the best performance (19.3% and 20.3%) compared with other state-of-the-art approaches." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": "Evaluation on CSL-Daily. To further assess the CTCA's generalization capacity, we evaluate it on the CSL-Daily benchmark. As presented in Tab. 3, the CTCA outperforms" + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "10776" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 92, + 286, + 192 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 287, + 92 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 287, + 92 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 287, + 92 + ], + "type": "text", + "content": "Table 3. Comparison with state-of-the-art methods on the CSL-Daily. (WER(%) the lower is the better)." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 47, + 92, + 286, + 192 + ], + "lines": [ + { + "bbox": [ + 47, + 92, + 286, + 192 + ], + "spans": [ + { + "bbox": [ + 47, + 92, + 286, + 192 + ], + "type": "table", + "html": "
MethodsDevTest
del/insWERdel/insWER
LS-HAN [12]14.6/5.739.014.8/5.039.4
SLT(Gloss+Text) [2]10.3/4.433.19.6/4.132.0
FCN [5]12.8/4.033.212.6/3.732.5
BN-TIN+Transf [33]13.9/3.433.613.5/3.033.1
TIN-Iterative [6]12.8/3.332.812.5/2.732.4
CTCA(Ours)9.2/2.531.38.1/2.329.4
", + "image_path": "592d638d2535413afae9da396a50f09c0e33eab4ee3c450d5990e46d2da3573a.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 52, + 214, + 280, + 289 + ], + "blocks": [ + { + "bbox": [ + 55, + 203, + 279, + 213 + ], + "lines": [ + { + "bbox": [ + 55, + 203, + 279, + 213 + ], + "spans": [ + { + "bbox": [ + 55, + 203, + 279, + 213 + ], + "type": "text", + "content": "Table 4. Effect of the SDPN architecture on the RWTH-2014." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 52, + 214, + 280, + 289 + ], + "lines": [ + { + "bbox": [ + 52, + 214, + 280, + 289 + ], + "spans": [ + { + "bbox": [ + 52, + 214, + 280, + 289 + ], + "type": "table", + "html": "
MethodsIIWDevTest
del/insWERdel/insWER
Baseline6.7E-57.0/3.021.86.7/2.722.1
Baseline+SDPN5.6E-57.3/3.121.77.4/2.421.8
VAC(VE) [20]5.4E-5-23.3-23.8
VAC(VE)+SDPN4.2E-57.6/3.122.07.6/3.022.6
", + "image_path": "62533a2fc38869d1977c6d567674d3b4eab71341104b22e522d631a4cb944296.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 311, + 287, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 311, + 287, + 335 + ], + "spans": [ + { + "bbox": [ + 46, + 311, + 287, + 335 + ], + "type": "text", + "content": "all other methods and achieves a " + }, + { + "bbox": [ + 46, + 311, + 287, + 335 + ], + "type": "inline_equation", + "content": "3\\%" + }, + { + "bbox": [ + 46, + 311, + 287, + 335 + ], + "type": "text", + "content": " WER advantage over the second-best performer, the TIN-Iterative." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 345, + 141, + 358 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 345, + 141, + 358 + ], + "spans": [ + { + "bbox": [ + 47, + 345, + 141, + 358 + ], + "type": "text", + "content": "5.3. Ablation Study" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 364, + 287, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 364, + 287, + 472 + ], + "spans": [ + { + "bbox": [ + 46, + 364, + 287, + 472 + ], + "type": "text", + "content": "Benefits of SPM-Shared Dual-Path Network. Tab. 4 illustrates that when both baseline and VAC are constructed to SDPN architecture, achieving lower generalization gap (lower IIW) and improved performance (lower WER). It is noteworthy that during the testing, only the spatial perception module and the BLSTM branch of SDPN are utilized. These results suggest that the SDPN architecture can facilitate thorough training for the spatial perception module, leading to improved performance." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 473, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 473, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 473, + 287, + 544 + ], + "type": "text", + "content": "Benefits of components of Cross-Context Knowledge Distillation loss. " + }, + { + "bbox": [ + 46, + 473, + 287, + 544 + ], + "type": "inline_equation", + "content": "\\bullet" + }, + { + "bbox": [ + 46, + 473, + 287, + 544 + ], + "type": "text", + "content": " Effect of vanilla distillation solution. We compare the vanilla distillation approach, as discussed in Sec. 4.1 with the baseline. As presented in Tab. 5, the vanilla distillation yields an improvement over the baseline, yet it is still inferior to each component of the CCKD." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "content": " Effect of " + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{l2g}" + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "content": " loss and " + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{g2l}" + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "content": " loss. We introduced two distillation methods, SDPN A and SDPN B based on the SDPN model. SDPN A is the 1D-TCN distilling sign-wise knowledge to the BLSTM via the " + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{l2g}" + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "content": ". This method improves performance on the test set by " + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "inline_equation", + "content": "1.0\\%" + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "content": " compared to the baseline. We also removes the intersection information weighted term " + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "inline_equation", + "content": "I(:,)" + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "content": " from SDPN A, which results in a " + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "inline_equation", + "content": "0.4\\%" + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "content": " drop in performance on the test set, implying its effectiveness. SDPN B, on the other hand, is an SDPN model optimized by the " + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{g2l}" + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "content": ", which yields a " + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "inline_equation", + "content": "1.4\\%" + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "content": " WER improvement over the baseline on the test set. It is noteworthy that SDPN A's performance is inferior to SDPN B. This can be explained that BLSTM tends to overfit on the sequential order of signs, which is easy to learn and leads to fast convergence" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 310, + 92, + 541, + 239 + ], + "blocks": [ + { + "bbox": [ + 305, + 70, + 545, + 91 + ], + "lines": [ + { + "bbox": [ + 305, + 70, + 545, + 91 + ], + "spans": [ + { + "bbox": [ + 305, + 70, + 545, + 91 + ], + "type": "text", + "content": "Table 5. Ablation study on cross-context knowledge distillation loss on the RWTH-2014." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 310, + 92, + 541, + 239 + ], + "lines": [ + { + "bbox": [ + 310, + 92, + 541, + 239 + ], + "spans": [ + { + "bbox": [ + 310, + 92, + 541, + 239 + ], + "type": "table", + "html": "
MethodLctdLcmdDevTest
Ll2gLg2lLrc
Baseline----21.822.1
Vanilla----21.721.9
SDPN A✓---21.021.1
SDPN A-I(;;)✓---21.321.5
SDPN B-✓--20.820.7
SDPN C✓✓--20.420.6
SDPN D✓✓✓-20.020.4
SDPN D-w(;;)✓✓✓-20.220.6
SDPN E---✓21.321.0
CTCA✓✓✓✓19.520.1
", + "image_path": "41beb5459570f617d5578fb530cf16e0f7af421e04f0933310c68f53f2707e31.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 332, + 281, + 518, + 405 + ], + "blocks": [ + { + "bbox": [ + 305, + 251, + 545, + 273 + ], + "lines": [ + { + "bbox": [ + 305, + 251, + 545, + 273 + ], + "spans": [ + { + "bbox": [ + 305, + 251, + 545, + 273 + ], + "type": "text", + "content": "Table 6. Comparison of different knowledge fusion schemes on the RWTH-2014. \"Wasserstein\" is the Wasserstein distance." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 332, + 281, + 518, + 405 + ], + "lines": [ + { + "bbox": [ + 332, + 281, + 518, + 405 + ], + "spans": [ + { + "bbox": [ + 332, + 281, + 518, + 405 + ], + "type": "table", + "html": "
MethodKnowledge fusionDevTest
SDPN-21.721.8
Vanilla distillation [11]21.621.6
Wasserstein [3]21.621.5
JMMD [19]21.321.3
CKD [28]21.321.5
CTCA(ℓl2g)21.021.1
concatenation22.723.6
point-wise addition21.222.3
attention22.222.6
", + "image_path": "bfc50f8f463bdbbc67b0160ce8b51a67796244ce948aec7b738f0a1aa8d49845.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 426, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 545, + 628 + ], + "type": "text", + "content": "optimized by CTC [9, 25]. Although the BSLTM in SDPN A receives local context knowledge, it still propagates limited local-global information to SPM, resulting in limited gain for SPM when it is overfitting. Furthermore, the 1D-TCN is less prone to overfitting [5] and in SDPN B facilitated by the " + }, + { + "bbox": [ + 304, + 426, + 545, + 628 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{g2l}" + }, + { + "bbox": [ + 304, + 426, + 545, + 628 + ], + "type": "text", + "content": " the 1D-TCN can learn sign-wise context by taking into account global contexts. Then it can provide richer sign-wise supervision to the SPM for locating signs, which can eliminate the limited back-propagation. As a result, more robust features SPM can generate, and they are fed into BLSTM, which outperforms SDPN A. This finding is consistent with the observation " + }, + { + "bbox": [ + 304, + 426, + 545, + 628 + ], + "type": "inline_equation", + "content": "\\pmb{\\Theta}" + }, + { + "bbox": [ + 304, + 426, + 545, + 628 + ], + "type": "text", + "content": " in Sec. 3.2 that the SPM has a high effect on the final prediction performance. The results of SDPN C show that the mutual distillation approach gains " + }, + { + "bbox": [ + 304, + 426, + 545, + 628 + ], + "type": "inline_equation", + "content": "20.6\\%" + }, + { + "bbox": [ + 304, + 426, + 545, + 628 + ], + "type": "text", + "content": " on the test set. This technique can enhance both the " + }, + { + "bbox": [ + 304, + 426, + 545, + 628 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{l2g}" + }, + { + "bbox": [ + 304, + 426, + 545, + 628 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 426, + 545, + 628 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{g2l}" + }, + { + "bbox": [ + 304, + 426, + 545, + 628 + ], + "type": "text", + "content": ", resulting in improved 1D-TCN and BLSTM. This success is also verified by [9]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "Effect of " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rc}" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": " loss and " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cmd}" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": " loss. Seen from Tab. 5, based on the SDPN C model the SDPN D combines the " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rc}" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": ", which is effective in enhancing performance. Specifically, when SDPN D drops the " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "w(:,)" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": ", it gives a worse result, it shows the effect of entropy measurement. Moreover, SDPN E, achieves relatively better performance, which validates the need for linguistic prior supervision." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10777" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 69, + 124, + 265, + 198 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 288, + 115 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 288, + 115 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 288, + 115 + ], + "type": "text", + "content": "Table 7. Performance comparison of local temporal perception module with distinct temporal window widths on the RWTH-2014. " + }, + { + "bbox": [ + 47, + 70, + 288, + 115 + ], + "type": "inline_equation", + "content": "Ft" + }, + { + "bbox": [ + 47, + 70, + 288, + 115 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 70, + 288, + 115 + ], + "type": "inline_equation", + "content": "Ft(d)" + }, + { + "bbox": [ + 47, + 70, + 288, + 115 + ], + "type": "text", + "content": " correspond to the 1D temporal convolution layer with kernel of " + }, + { + "bbox": [ + 47, + 70, + 288, + 115 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 70, + 288, + 115 + ], + "type": "text", + "content": " and dilation of " + }, + { + "bbox": [ + 47, + 70, + 288, + 115 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 47, + 70, + 288, + 115 + ], + "type": "text", + "content": ", respectively." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 69, + 124, + 265, + 198 + ], + "lines": [ + { + "bbox": [ + 69, + 124, + 265, + 198 + ], + "spans": [ + { + "bbox": [ + 69, + 124, + 265, + 198 + ], + "type": "table", + "html": "
MethodvariantswindowsDevTest
1D-TCNF3-F3-F37*219.520.1
F3(1)-F3(2)7*219.820.3
F5-F59*220.620.6
F5-F5-F513*219.920.6
F7-F713*220.120.3
", + "image_path": "52a8357e1a2b67ec85bd596609d98f0a78c41c9e5300f3a998595da18bffe8d2.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 53, + 240, + 279, + 304 + ], + "blocks": [ + { + "bbox": [ + 47, + 209, + 287, + 232 + ], + "lines": [ + { + "bbox": [ + 47, + 209, + 287, + 232 + ], + "spans": [ + { + "bbox": [ + 47, + 209, + 287, + 232 + ], + "type": "text", + "content": "Table 8. Comparison of CTCA with distinct global temporal perception modules (GTPM) on the RWTH-2014." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 53, + 240, + 279, + 304 + ], + "lines": [ + { + "bbox": [ + 53, + 240, + 279, + 304 + ], + "spans": [ + { + "bbox": [ + 53, + 240, + 279, + 304 + ], + "type": "table", + "html": "
MethodvariantsDevTest
GTPM-branchBLSTM19.520.1
Dilated blocks22.222.6
Transformer28.728.9
Transformer+BLSTM24.424.1
", + "image_path": "3eb9ed19e119590fee17fe606c7028f6e24fde4834636de38adf2ee7ab22241a.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 324, + 148, + 337 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 324, + 148, + 337 + ], + "spans": [ + { + "bbox": [ + 47, + 324, + 148, + 337 + ], + "type": "text", + "content": "5.4. Module Analysis" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 342, + 287, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 342, + 287, + 534 + ], + "spans": [ + { + "bbox": [ + 46, + 342, + 287, + 534 + ], + "type": "text", + "content": "Other choices of knowledge fusion schemes. In Tab. 6, we compare distinct knowledge fusion schemes based on our SDPN, including the knowledge distillation strategies (upper part of Tab. 6) and feature fusion strategies (bottom of Tab. 6). Specifically, all schemes use only SPM and BLSTM in testing and all knowledge distillation schemes distill knowledge from 1D-TCN to BLSTM. We observe that feature fusion strategies have limited promotion and even worse results than the SDPN, while all knowledge distillation schemes gained an improvement by the SDPN. This validates the effectiveness of knowledge distillation and shows that simply concatenating or summing features lacks the constraint for 1D-TCN and BLSTM to guide them to possess context knowledge of the other. And the attention mechanism only learns the correlation between 1D-TCN and BLSTM, neglecting context knowledge transferring." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 534, + 287, + 701 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 534, + 287, + 701 + ], + "spans": [ + { + "bbox": [ + 46, + 534, + 287, + 701 + ], + "type": "text", + "content": "Impact of different distillation objects. The Tab. 6 also shows the performance of using intermediate feature hints versus prediction scores as distillation objects. The Wasserstein distance [3, 7] and JMMD [19] enforce to align the intermediate feature distributions. And the CKD [28] distills significant activation values in each channel of intermediate feature hints. Further, based on the CKD our " + }, + { + "bbox": [ + 46, + 534, + 287, + 701 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{l2g}" + }, + { + "bbox": [ + 46, + 534, + 287, + 701 + ], + "type": "text", + "content": " weights the distillation by the intersection information of intermediate feature hints. On the other hand, the vanilla distillation [11] is designed for aligning glosses prediction scores, gives the worst performance. Overall, results suggest that adopting intermediate feature hints as distillation objects is more effective than employing prediction scores to teach how to generate the desired output." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 701, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 701, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 701, + 287, + 714 + ], + "type": "text", + "content": "Impact of different temporal window widths of 1D-" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "text", + "content": "TCN. Tab. 7 delivers that the window width designed to approximate the average length of isolated sign [6] performs the best. (Since half of the frames are selected for training, i.e., SFL [22], the actual window width needs to be multiplied by 2). Whereas, variants of 1D-TCN with substantially different window widths (ranging from 14 to 26) do not show a significant performance gap. We explain that variants of 1D-TCN can learn sign-wise knowledge through global context guidance optimized by the " + }, + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{g2l}" + }, + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "text", + "content": ", which relieves the effect of receptive field discrepancy." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 192, + 545, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 192, + 545, + 312 + ], + "spans": [ + { + "bbox": [ + 304, + 192, + 545, + 312 + ], + "type": "text", + "content": "Other choices of global temporal perception modules. Tab. 8 ablates the performance of distinct global temporal perception modules, such as BLSTM, Dilated blocks [24], Transformer [2, 22], and Transformer+BLSTM. The BLSTM achieves the best performance. The plausible reason is that sign language videos have a semantic sequence with grammatical rules, which means both forward and backward frames should be taken into consideration [25], which BLSTM achieves natively. However, Transformer is unable to do it to learn the semantic sequence well." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 323, + 378, + 335 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 323, + 378, + 335 + ], + "spans": [ + { + "bbox": [ + 306, + 323, + 378, + 335 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 342, + 545, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 342, + 545, + 545 + ], + "spans": [ + { + "bbox": [ + 304, + 342, + 545, + 545 + ], + "type": "text", + "content": "In this work, we have extensively studied the limitation and desired properties of the temporal aggregation module (TAM) in the continuous sign language recognition framework. In particular, with an advanced analysis tool (i.e., information stored in weights [31]), we showed that the desired TAM should be a shallow architecture to allow more effective training of spatial perception module but also should be a deep one for a high temporal aggregation capability. To achieve this property, we proposed cross-temporal context aggregation (CTCA) with a dual-path network. Moreover, we proposed a cross-context knowledge distillation loss function to transfer the local temporal context and the linguistic prior to the global perception module. Extensive experimental results demonstrated that our CTCA effectively enhances the generalization of the spatial perception module while achieving the leading accuracy with fewer parameters and higher efficiency." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 545, + 545, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 545, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 545, + 641 + ], + "type": "text", + "content": "Limitations. In the redesign of the temporal aggregation module, the improvement of global temporal context perception still follows the current scheme, which still tends to cause overfitting. Therefore finding a more suitable global temporal context perception for the weakly supervised CSLR task is a challenge to be solved. Meanwhile, the CTCA is not tested on real-world with complex scenes, which deserves further study." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "type": "text", + "content": "Acknowledgments. This work was supported by the National Natural Science Foundation of China (61906135, 62020106004, 92048301, 62276141), and the Tianjin Research Innovation Project for Postgraduate Students (2021YJSB244). It was also supported by A\\*STAR Centre for Frontier AI Research." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10778" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 92, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 53, + 92, + 287, + 125 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 92, + 287, + 125 + ], + "spans": [ + { + "bbox": [ + 53, + 92, + 287, + 125 + ], + "type": "text", + "content": "[1] Necati Cihan Camgoz, Simon Hadfield, Oscar Koller, Hermann Ney, and Richard Bowden. 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In CVPR, 2022. 1, 2, 3, 6" + } + ] + } + ], + "index": 1 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "10780" + } + ] + } + ], + "index": 3 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Distilling Focal Knowledge From Imperfect Expert for 3D Object Detection/26d504d2-cd24-4e73-99c4-214e67e817bc_content_list.json b/2023/Distilling Focal Knowledge From Imperfect Expert for 3D Object Detection/26d504d2-cd24-4e73-99c4-214e67e817bc_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..e7c82ea3ddfe138a9143581cf55207532464eca4 --- /dev/null +++ b/2023/Distilling Focal Knowledge From Imperfect Expert for 3D Object Detection/26d504d2-cd24-4e73-99c4-214e67e817bc_content_list.json @@ -0,0 +1,1618 @@ +[ + { + "type": "text", + "text": "Distilling Focal Knowledge from Imperfect Expert for 3D Object Detection", + "text_level": 1, + "bbox": [ + 169, + 159, + 800, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Jia Zeng $^{1,2}$ Li Chen $^{1}$ Hanming Deng $^{3}$ Lewei Lu $^{3}$", + "bbox": [ + 265, + 201, + 702, + 219 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Junchi Yan $^{2,1}$ Yu Qiao $^{1}$ Hongyang Li $^{1,2*}$", + "bbox": [ + 322, + 220, + 672, + 236 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1OpenDriveLab, Shanghai AI Lab 2Shanghai Jiao Tong University 3SenseTime Research", + "bbox": [ + 115, + 236, + 853, + 252 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{zengjia,lichen,qiaoyu,lihongyang}@pjlab.org.cn", + "bbox": [ + 277, + 254, + 690, + 268 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{denghanming,luotto}@sensetime.com yanjunchi@sjtu.edu.cn", + "bbox": [ + 228, + 270, + 734, + 283 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 315, + 312, + 330 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Multi-camera 3D object detection blossoms in recent years and most of state-of-the-art methods are built up on the bird's-eye-view (BEV) representations. Albeit remarkable performance, these works suffer from low efficiency. Typically, knowledge distillation can be used for model compression. However, due to unclear 3D geometry reasoning, expert features usually contain some noisy and confusing areas. In this work, we investigate on how to distill the knowledge from an imperfect expert. We propose FD3D, a Focal Distiller for 3D object detection. Specifically, a set of queries are leveraged to locate the instance-level areas for masked feature generation, to intensify feature representation ability in these areas. Moreover, these queries search out the representative fine-grained positions for refined distillation. We verify the effectiveness of our method by applying it to two popular detection models, BEVFormer and DETR3D. The results demonstrate that our method achieves improvements of 4.07 and 3.17 points respectively in terms of NDS metric on nuScenes benchmark. Code is hosted at https://github.com/OpenPerceptionX/BEVPerception-Survey-Recipe.", + "bbox": [ + 75, + 345, + 473, + 636 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 78, + 665, + 208, + 679 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Accurate 3D object detection is a vital component in autonomous driving. To achieve this, most methods [14, 37] resort to LiDAR sensors and dominate the public benchmarks [1, 27]. Despite the performance gap, pure vision approaches are still worthy of in-depth inquiry, since cameras can provide rich semantic information and are low-cost and easy-to-deploy. Among these, bird's-eye-view (BEV) detection has drawn extensive attention from both industry and academia, and shown great potential to narrow down the performance gap [15, 21]. However, such models tend to be computationally consuming.", + "bbox": [ + 75, + 688, + 468, + 843 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ffa8ebad8e6f0ad3b53d396adb21c9762af885b642080874d3afe5f63698f632.jpg", + "image_caption": [ + "(a) Global distillation" + ], + "image_footnote": [], + "bbox": [ + 542, + 324, + 658, + 404 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/1a6f8b20b938679291d0300b50afa69bb824933b635f1e3a8eb0f25aa7fc12e2.jpg", + "image_caption": [ + "Expert Abstraction" + ], + "image_footnote": [], + "bbox": [ + 764, + 315, + 880, + 403 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/de867f18a7cbd2b933b6a4bba0e5259fee6f692c28c53545c569c16b59b62db9.jpg", + "image_caption": [ + "(c) Generative distillation with random mask", + "Apprentice Representation", + "Figure 1. Illustration of the proposed generative and focal distillation method. Compared with others, the proposed manner in 1 (d) leverages queries to generate instance masks for masked generative distillation, rather than random masks in 1 (c). Moreover, the queries meanwhile search for the representative position to perform refined distillation, where the distillation region selection is more fine-grained and flexible than 1 (b)." + ], + "image_footnote": [], + "bbox": [ + 537, + 426, + 653, + 539 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/1b040ca24c7bb6988a96e4e3afe8ef39dab5a708b52b89641a4622c12faf50ba.jpg", + "image_caption": [ + "(b) Attentive distillation", + "Query offset", + "(d) Generative and focal distillation (ours)" + ], + "image_footnote": [], + "bbox": [ + 768, + 426, + 882, + 539 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In common practice, knowledge distillation can compress the model and is usually applied to alleviate computation overhead. One possible solution is to utilize the LiDAR-based model as the expert [4, 17], but this requires complex spatial-temporal calibrations and also needs to handle heterogeneous problems from different modalities. An intuitive question is, can we distill these models solely based on camera sensors? In this work, we intend to address this problem and focus on the camera-only distillation setting. To the best of our knowledge, our work is the first solution tailored for this setting.", + "bbox": [ + 497, + 695, + 890, + 849 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Distillation methods in 2D object detection have derived", + "bbox": [ + 519, + 852, + 890, + 866 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 129, + 49, + 200, + 84 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 252, + 48, + 791, + 87 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author at lihongyang@pjlab.org.cn", + "bbox": [ + 95, + 853, + 415, + 866 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "992", + "bbox": [ + 472, + 887, + 497, + 897 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c8d177b72138eeb9d6c9f0b6cbe2105139a4a55e5e84c9b72bb761a425a6de63.jpg", + "image_caption": [ + "Figure 2. Visualization of the predicted bounding boxes and bird's eye view feature of BEVFormer [19]. At the center is the autonomous vehicle. In the left subfigure, green and blue boxes denote the ground truth and predictions respectively. In the right subfigure, the BEV feature is ray-shaped and contains a lot of noise. Areas with incorrect high activation appear behind objects due to occlusion, which easily introduces false positives, e.g., the region circled by the ellipse." + ], + "image_footnote": [], + "bbox": [ + 112, + 122, + 228, + 242 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/4dae3c92ea8eb911f23e4a5f69ab73260e8d360576e78141f2f0afd7ca6228b7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 265, + 122, + 436, + 242 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "various types as depicted in Fig. 1 (a)-(c), but their effectiveness is not verified in 3D object detection. The main challenge in camera-to-camera distillation for 3D object detection comes from the imperfect expert features. Due to the lack of accurate 3D information, expert features drawn from 2D images usually contain some noisy and confusing areas. To better illustrate this point, we visualize the BEV features from BEVFormer [19] in Fig. 2. The unclear occlusion reasoning makes the BEV features suffer from the ray-shape artifacts. The imperfect BEV features result in many false positives. Directly mimicking these features from experts such as Fig. 1 (a) may exacerbate the drawback. Some 2D detection distillation methods [29] propose to focus on foreground-orient regions, as shown in Fig. 1 (b). However, background regions are also important as proved in [7, 35, 13]. We categorize these methods as attentive distillation. Compared with 2D object detection, the imbalance between foreground and background in 3D areas is much more severe. Balancing these weights is not a general solution. The latest study MGD [36] demonstrates the effectiveness of masked image modeling (MIM) distillation as depicted in Fig. 1 (c). However, the global random mask cannot greatly enhance 3D object detection, which is validated in Tab. 4a.", + "bbox": [ + 75, + 381, + 468, + 712 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To this end, we propose a Focal Distiller for 3D object detection, shortened as FD3D. The schematic diagram of FD3D is shown in Fig. 1 (d). Specifically, A set of queries are leveraged to locate the instance-level focal regions, masked generative distillation is performed within the regions. Moreover, these queries dynamically search fine-grained representative positions for focal distillation. Two complementary modules guide the apprentice network to generate enhanced feature representation on focal regions. In summary, our work makes three-fold contributions:", + "bbox": [ + 75, + 713, + 468, + 865 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. To the best of our knowledge, this is the first work to explore knowledge distillation on the camera-only 3D object detection. We reveal the challenge relies on how to distill focal knowledge from an imperfect 3D object detector expert.", + "2. We propose FD3D, which utilizes a set of queries to distill focal knowledge. With these queries, coarse-grained focal regions are selected for masked generation, and fine-grained focal regions are searched out for instance-oriented refinement distillation.", + "3. FD3D serves as a plug-and-play module. It can be easily extended to various detectors. The improvements with 4.07 and 3.17 NDS can be obtained with FD3D assembled in BEVFormer and DETR3D, respectively." + ], + "bbox": [ + 510, + 125, + 890, + 342 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 499, + 368, + 640, + 383 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Knowledge distillation on 2D object detection. Knowledge distillation is originally proposed by Hinton et al. [9]. It regards teachers' output logits as knowledge and is employed as a model compression approach in the classification task. FitNet [26] extends the knowledge to intermediate features. Recently, many works successfully apply knowledge distillation on object detection [3]. Knowledge distillation on object detection encounters extreme imbalance between positive and negative instances. Global feature imitation [29] such as Fig. 1 (a) brings marginal improvement, and even exacerbates the performance. It is almost a consensus that distillation should not treat all regions equally. Revisiting from the latest works, where to perform distillation is of great concern in distilling object detectors, and they invariably resort to attentive distillation as depicted in Fig. 1 (b). Mimic [16] performs distillation on ROI regions sampled by an RPN network, but this framework can only be applied to a two-stage detector. FIFG [29] claims the distillation should be performed on near-object regions. However, the near-object regions are defined by hand-crafted rules and require manual refinement. GID [6] focuses on regions where there is a significant difference between the student and the teacher outputs. DeFeat [7] separates foreground and background by ground truth and performs distillation independently. GID [6] and DeFeat [7] prove that the informative cues in the background also benefit the student network. FGD [35] designs a more elaborate structure to focus on critical pixels and channels. Albeit the effectiveness of the aforementioned studies, they require manual hyper-parameter tuning to adjust the concentration of distillation. ICD [13] encodes the instance annotations as queries, and attention maps are generated to guide the distillation region concentration. We deem such a query-based approach is more flexible. MGD [36] proposes a simple but", + "bbox": [ + 497, + 396, + 890, + 866 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "993", + "bbox": [ + 472, + 887, + 497, + 897 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/d8847ca9288b269f61b06441109b027614043478c1bcc8a5d9cddfef15385139.jpg", + "image_caption": [ + "Figure 3. We present FD3D, a Focal Distiller for 3D object detection. The framework aims to transfer the dark knowledge of the focal region from the expert network to the compact apprentice network, where the feature distillation is performed on both perspective view (PV) and bird's-eye-view (BEV). We employ aligned BEV queries. With these queries, the instance masks in PV and BEV are generated, and masked generative distillation is performed within the mask region to enhance the feature representation. Moreover, these queries meanwhile leverage deformable attention mechanism to search out the representative features on focal BEV regions. The representative features are utilized for refined distillation." + ], + "image_footnote": [], + "bbox": [ + 154, + 125, + 811, + 355 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "effective distillation paradigm as shown in Fig. 1 (c): the student features are randomly masked and then recovered to mimic teacher features.", + "bbox": [ + 75, + 459, + 470, + 501 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Multi-camera 3D Object Detection. Early studies [22, 30] independently process monocular images from multiple views, and aggregate the results across cameras for postprocessing. FCOS3D [30] extends the popular anchor-free detector FCOS [28] by directly predicting 3D bounding boxes from 2D image features. Recent studies tend to predict object location in 3D space. One branch of researchers converts 2D image features to 3D space through depth estimation. The typical approach is to convert the estimated depth map into pseudo-LiDAR [31]. Lift-Splat-Shoot (LSS) [23] estimates the depth distribution of each image pixel and uses voxel pooling to generate BEV features. Its follow-up studies BEVDet [11], BEVDet4D [10], BEVDepth [18] further explore data augmentation, accelerating voxel pooling module and improving depth estimation accuracy. Another branch of studies indexes 2D image feature to 3D space through the camera extrinsic and intrinsic. Following DETR [2], DETR3D [32] defines a set of 3D object queries and samples 2D image features on the queries' projection points to predict 3D bounding boxes. BEVFormer [19] explicitly defines queries in BEV space, and performs 2D-to-3D transformation with deformable attention to generate the BEV feature for downstream tasks. PolarFormer [12] adopts polar coordinate system for more accurate BEV feature construction. These state-of-the-art models suffer from high computation overhead. It is natu", + "bbox": [ + 75, + 507, + 472, + 866 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ral to consider applying knowledge distillation to compress the model. However, regardless of the view transform approaches, the 2D-to-3D transformation is ill-posed, so the vision-based 3D object detector experts cannot provide a reliable feature for imitation.", + "bbox": [ + 497, + 459, + 890, + 528 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "LiDAR-based knowledge distillation. In 3D object detection, there are existing studies covering knowledge distillation under LiDAR [33, 34] and extending to LiDAR-camera cross-modality knowledge transfer. Monodistill [4] projects the LiDAR points to the image plane, aligning two modalities for knowledge transfer. UVTR [17] represents the image and LiDAR in a unified voxel space, and the feature distillation is performed on the query projection points. To exclude the heterogeneous problems from different modalities and focus on the exploration of distillation from an imperfect expect, the extent of this study is set at camera-only distillation.", + "bbox": [ + 497, + 533, + 892, + 699 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 499, + 713, + 636, + 730 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Fig. 3 illustrates the pipeline of our distillation approach. The overall structure of FD3D is presented in Sec. 3.1. The two proposed distillation modules are elaborated in Sec. 3.2 and Sec. 3.3.", + "bbox": [ + 497, + 736, + 890, + 792 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Overall Structure", + "text_level": 1, + "bbox": [ + 499, + 802, + 672, + 817 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The state-of-the-art multi-camera 3D object detection networks suffer from high computation overhead. This shortcoming mainly originates from the heavy network ar", + "bbox": [ + 497, + 824, + 890, + 866 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "994", + "bbox": [ + 472, + 887, + 497, + 897 + ], + "page_idx": 2 + }, + { + "type": "table", + "img_path": "images/c9c829379fe5df1335c9d9ebd5716140b9759ed4af740c8449b8ecabe17a8d42.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodBackboneImage ResolutionBEV ResolutionEncoder Layer
BEVFormer -Base* (E)R101900×1600200×2006
BEVFormer -Tiny (A)R50450×800100×1003
BEVFormer -Base (E)R101-DCN†900×1600200×2006
BEVFormer -Small (A)R101-DCN†450×800100×1003
DETR3D -R101 (E)R101-DCN†900×1600--
DETR3D -R50 (A)R50900×1600--
", + "bbox": [ + 78, + 123, + 468, + 302 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Table 1. The setting of expert- apprentice pairs. The symbol \"E\" and \"A\" denote \"expert\" and \"apprentice\" respectively. By setting different network depth, input resolution or BEV resolution, we obtain expert- apprentice pairs. * represents this version of BEVFormer-Base apply ResNet101 as backbone rather than ResNet101-DCN, which is different from the original version [19]. † indicates using nuScene pretrained weight with FCOS3D [30]. Unless otherwise specified, the backbone is pretrained on ImageNet only.", + "bbox": [ + 75, + 312, + 468, + 428 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "chitecture and high input resolution. By compressing the network depth or input resolution, we obtain more compact networks. However, the lightweight networks inevitably suffer from accuracy attenuation. Therefore, we employ the heavy state-of-the-art model as the expert, adopt the lightweight counterpart as the apprentice, and perform knowledge transfer between them. We freeze the expert network, and leverage the intermediate features of the expert network as auxiliary supervision for the apprentice network. The setting of adopted expert- apprentice pairs is depicted in Tab. 1. Their GLOPS and FPS are presented at Tab. 2.", + "bbox": [ + 75, + 448, + 468, + 600 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As depicted in Fig. 3, a distillation framework between the expert network and the apprentice network is constructed. For the BEV perception model, the distillation is performed on both the perspective view (PV) and BEV features. We set up an extra distillation head and employ a set of aligned BEV queries $Q$ for distillation. The structure of the distillation head is similar to the head of Deformable DETR [39]. Based on the deformable attention mechanism, $N$ queries sample key features from BEV features and generate 3D bounding boxes. The generated 3D bounding boxes are projected into PV and BEV. The projection areas are used for masked generative distillation, and the sampled BEV features in the deformable attention process are adopted for refined distillation. In order to urge the projection areas locate at the foreground area and the sampled BEV features come from the object region, the distillation head is also optimized with auxiliary detection losses.", + "bbox": [ + 75, + 600, + 468, + 836 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The distillation head is built upon the expert BEV features. The distillation queries go through a self-attention", + "bbox": [ + 75, + 838, + 468, + 866 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "layer, and then sample expert BEV feature $F^{E}$ to generate $y^{E}$ through a deformable attention (DEFORMATTN) layer and a feed-forward network $(\\mathcal{FFN})$ . The latter process is formulated as:", + "bbox": [ + 497, + 125, + 890, + 179 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ny ^ {E} = \\mathcal {F F N} (\\text {D E F O R M A T T N} (Q, F ^ {E})), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 561, + 192, + 890, + 209 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $y^{E} = \\{[c_{1}^{E},b_{1}^{E}],[c_{2}^{E},b_{2}^{E}],\\ldots ,[c_{N}^{E},b_{N}^{E}]\\}$ , and $c_{i}^{E},b_{i}^{E}$ represent classification score and regression bounding box corresponding to $i$ -th distillation query. Based on bipartite matching approach in [2], we search for the optimal permutations $\\hat{\\sigma}$ and optimize the distillation head by $\\mathcal{L}_{dh}$ as follows:", + "bbox": [ + 497, + 211, + 890, + 294 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{ \\begin{array}{l} \\hat {\\sigma} = \\underset {\\sigma \\in \\mathfrak {S} _ {N}} {\\arg \\min } \\sum_ {i} ^ {N} \\alpha \\mathcal {L} _ {c l s} \\left(c _ {\\sigma (i)} ^ {E}, c _ {i} ^ {g t}\\right) + \\beta \\mathcal {L} _ {b b o x} \\left(b _ {\\sigma (i)} ^ {E}, b _ {i} ^ {g t}\\right), \\\\ \\mathcal {L} _ {d h} = \\sum_ {i} ^ {N} \\alpha \\mathcal {L} _ {c l s} \\left(c _ {\\hat {\\sigma} (i)} ^ {E}, c _ {i} ^ {g t}\\right) + \\beta \\mathcal {L} _ {b b o x} \\left(b _ {\\hat {\\sigma} (i)} ^ {E}, b _ {i} ^ {g t}\\right), \\end{array} \\right. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 299, + 890, + 353 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{cls}$ and $\\mathcal{L}_{bbox}$ take the same form as FocalLoss [20] and L1 loss respectively, $b^{gt}$ and $c^{gt}$ represent ground truth boxes coordinates and classes, and $\\alpha$ as well as $\\beta$ balance the loss weight.", + "bbox": [ + 497, + 355, + 890, + 409 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "During the optimization process of the distillation head, the queries with a confidence higher than $\\rho_{c}$ and GIOU greater than $\\rho_{b}$ are filtered out as focal queries, termed as $Q^{f}$ . The number of $Q^{f}$ is denoted as $N_{f}$ . Finally, the generated 3D boxes and sampled BEV features corresponding to the focal queries $Q^{f}$ are selected to perform masked generative distillation and refined distillation.", + "bbox": [ + 497, + 409, + 890, + 505 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Selective Masked Generative Distillation", + "text_level": 1, + "bbox": [ + 499, + 513, + 843, + 527 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The generated 3D boxes by focal queries $Q_{f}$ are projected to PV and BEV. The 3D boxes are projected to PV according to the camera extrinsics and intrinsics, and simply flattened to BEV from the top-down view. The masking process described below is the same for both PV and BEV, so we describe the process without distinction between PV and BEV.", + "bbox": [ + 497, + 534, + 890, + 630 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "An instance mask $I_{i}^{fg}$ is generated with the projection area corresponding to one focal query $Q_{i}^{f}$ . The dimension of the instance mask is identical to that of the apprentice feature. If a pixel is inside the bounding box $b_{i}^{E}$ , the value is set to be 0, otherwise its value is set to be 1. The formulation of $I_{i}^{fg}$ is described as follows:", + "bbox": [ + 497, + 630, + 890, + 716 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nI _ {i, u v} ^ {f g} = \\left\\{ \\begin{array}{l l} 0, & \\text {i f} (u, v) \\text {i n} b _ {i} ^ {E} \\\\ 1, & \\text {O t h e r w i s e} \\end{array} . \\right. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 722, + 890, + 758 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "All instance masks are merged together to form the final mask $I^{fg}$ . The process of mask stacking is formulated as follows:", + "bbox": [ + 497, + 764, + 890, + 802 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nI ^ {f g} = I _ {0} ^ {f g} \\wedge I _ {1} ^ {f g} \\wedge \\dots \\wedge I _ {N - 1} ^ {f g}. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 589, + 804, + 890, + 821 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The masked region indicates where the objects reside in, and the masked generation is performed within the masked region.", + "bbox": [ + 497, + 824, + 890, + 866 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "995", + "bbox": [ + 472, + 887, + 497, + 897 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The selective mask indicates that the pixels of apprentice feature within $I^{fg}$ are masked by ratio $r$ . A random mask $I^r$ with the same size of $I^{fg}$ is generated:", + "bbox": [ + 77, + 125, + 468, + 167 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nI _ {u v} ^ {r} = \\left\\{ \\begin{array}{l l} 0, & \\text {i f} R _ {u, v} < r \\\\ 1, & \\text {O t h e r w i s e} \\end{array} , \\right. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 174, + 468, + 212 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $R_{u,v}$ is a uniformly random number between 0 and 1. The process of the selective mask is expressed as an OR operation between $I^{fg}$ and $I^r$ :", + "bbox": [ + 77, + 219, + 468, + 260 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nI ^ {m} = I ^ {f g} \\vee I ^ {r}. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 216, + 268, + 468, + 283 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Then the apprentice feature $F^A$ is masked with $I^m$ . The masked apprentice feature is forced to recover with a generator $\\mathcal{G}$ :", + "bbox": [ + 75, + 292, + 468, + 332 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {F} ^ {A} = \\mathcal {G} \\left(F ^ {A} \\cdot I ^ {m}\\right). \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 206, + 332, + 468, + 347 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The generator $\\mathcal{G}$ here includes two convolutional layers, the first one of which switches to a deconvolutional layer if the dimensions of the apprentice feature and expert feature are not identical. After generating $\\hat{F}^A$ , the channel-wise distribution [25] is calculated as follows:", + "bbox": [ + 75, + 353, + 468, + 421 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {S M G D} = \\frac {\\tau^ {2}}{C} \\sum_ {c = 1} ^ {C} \\sum_ {i = 1} ^ {H \\times W} \\varphi \\left(F _ {c, i} ^ {E}\\right) \\log \\frac {\\varphi \\left(F _ {c , i} ^ {E}\\right)}{\\varphi \\left(\\hat {F} _ {c , i} ^ {A}\\right)}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 119, + 429, + 468, + 467 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\varphi \\left(F _ {c, i}\\right) = \\frac {\\exp \\left(\\frac {F _ {c , i}}{\\tau}\\right)}{\\sum_ {i = 1} ^ {H \\times W} \\exp \\left(\\frac {F _ {c , i}}{\\tau}\\right)}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 169, + 475, + 468, + 511 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\tau$ is the temperature factor of the SoftMax layer, $C$ means the feature channels, and $H$ , $W$ represent feature height and width respectively.", + "bbox": [ + 75, + 515, + 468, + 555 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Query-based Focal Distillation", + "text_level": 1, + "bbox": [ + 77, + 564, + 346, + 578 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Focal distillation denotes the refined distillation focusing on the local feature pattern of focal positions. We aim to leverage a set of queries to automatically search out the representative positions of objects, and perform distillation on the identical positions between expert features and apprentice features. We resort to the deformable attention module to achieve the goal. The deformable attention module generates a set of offsets around a reference point. Based on the offsets to the reference point, the features on the crucial sampling points are sampled for object detection. We exploit this mechanism to conduct a refined distillation on such representative features as illustrated in Fig. 4.", + "bbox": [ + 75, + 585, + 468, + 750 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "A set of focal queries $Q^{f}$ are filtered out as described in Sec. 3.1. For each focal query $q \\in Q^{f}$ , the reference point $p_{q}$ is generated by the query feature $z_{q}$ with a linear projection $\\mathcal{M}\\mathcal{LP}$ :", + "bbox": [ + 75, + 751, + 468, + 806 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\np _ {q} = \\mathcal {M L P} \\left(z _ {q}\\right). \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 211, + 815, + 468, + 831 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The reference point $p_q$ represents the projection center of the estimated bounding box on the sampling feature plane.", + "bbox": [ + 75, + 838, + 468, + 866 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/ad8a436a6a171b799e9c7952fe4fabedfaa2b3f4cef7fc17fe2a58e60ce4b0fe.jpg", + "image_caption": [ + "Figure 4. Process of query-based offset generation, feature sampling and query parameter update. Leveraging the deformable attention mechanism, the local expert feature and apprentice feature are sampled at the same position, based on the offset generated by the query. In addition, the query parameter is updated with the collected expert feature." + ], + "image_footnote": [], + "bbox": [ + 544, + 125, + 843, + 264 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For each focal query $q$ , $M$ attention heads are attached on $z_{q}$ . Each attention head generates $K$ sampling offsets by another linear projection $\\mathcal{MLP}'$ . The offset is computed by the following:", + "bbox": [ + 497, + 357, + 890, + 412 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\Delta p _ {m q k} = \\mathcal {M L P} ^ {\\prime} \\left(z _ {q}, m, k\\right), \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 598, + 425, + 890, + 441 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $m$ indexes the attention head, and $k$ represents the sampling point.", + "bbox": [ + 497, + 452, + 889, + 480 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The positions searched by the generated offsets are viewed as key representative positions. The query-based focal distillation is conducted on such key representative positions. Let $F_{mqk}^{E}, F_{mqk}^{A}$ represent the sampled features from the identical key positions for expert and apprentice, respectively. They are calculated as follows:", + "bbox": [ + 497, + 480, + 890, + 564 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nF _ {m q k} ^ {E} = F ^ {E} \\left(p _ {q} + \\Delta p _ {m q k}\\right), \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 601, + 574, + 890, + 592 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nF _ {m q k} ^ {A} = F ^ {A} \\left(p _ {q} + \\Delta p _ {m q k}\\right). \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 601, + 606, + 890, + 624 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The sampled expert feature and apprentice feature are normalized to $\\widetilde{F}_{mqk}^{T}$ and $\\widetilde{F}_{mqk}^{S}$ according to their maximum and minimum. Finally, the L2 loss is computed between the normalized key sampled features:", + "bbox": [ + 497, + 631, + 890, + 686 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {Q F D} = \\frac {1}{N _ {f}} \\sum_ {q \\in Q _ {f}} \\sum_ {m = 1} ^ {M} \\sum_ {k = 1} ^ {K} L _ {2} \\left(\\widetilde {F} _ {m q k} ^ {A}, \\widetilde {F} _ {m q k} ^ {E}\\right). \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 527, + 698, + 890, + 738 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Through the loss for the fine-grained local region, the refined distillation on these representative positions is conducted. Query-based focal distillation aims to optimize the local patterns on the instances' representative positions.", + "bbox": [ + 497, + 750, + 890, + 806 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Overall Distillation Loss", + "text_level": 1, + "bbox": [ + 499, + 815, + 721, + 828 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Besides being supervised by ground truth, the intermediate feature of the apprentice detector is also supervised by", + "bbox": [ + 499, + 838, + 890, + 866 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "996", + "bbox": [ + 472, + 887, + 497, + 897 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "the masked generative distillation loss $\\mathcal{L}_{SMGD}$ and query-based focal distillation loss $\\mathcal{L}_{QFD}$ . The total knowledge distillation loss is defined as follows:", + "bbox": [ + 75, + 125, + 468, + 167 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {K D} = \\lambda \\mathcal {L} _ {S M G D} + \\eta \\mathcal {L} _ {Q F D}. \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 171, + 176, + 468, + 191 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "$\\mathcal{L}_{SMGD}$ is used to optimize the global feature distribution, indicating where should be with high activation. $\\mathcal{L}_{QFD}$ is leveraged for optimizing the local feature pattern on searched focal positions. The hyper-parameters $\\lambda$ and $\\eta$ control the loss weight.", + "bbox": [ + 75, + 200, + 468, + 270 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Note that only the gradients w.r.t. the vanilla detection loss and the distillation loss $\\mathcal{L}_{KD}$ back-propagate to the apprentice network. $\\mathcal{L}_{dh}$ only optimizes the parameters of the distillation head.", + "bbox": [ + 75, + 270, + 468, + 325 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 75, + 337, + 208, + 353 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Dataset and metrics", + "text_level": 1, + "bbox": [ + 75, + 359, + 265, + 372 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We conduct experiments on nuScenes dataset [1], a large-scale autonomous driving dataset. This dataset contains 700, 150, 150 scenes for training, validation and testing, respectively. Each scene has roughly 20 seconds of duration. The key frame is annotated at $2\\mathrm{Hz}$ .", + "bbox": [ + 75, + 380, + 468, + 448 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The two dominant metrics of the nuScenes detection task are nuScenes Detection Score (NDS) and mean Average Precision (mAP). The mAP of nuScenes is computed by the center distance between predictions and annotations on the ground plane. In addition, the nuScenes dataset defines five true positive metrics mATE, mASE, mAOE, mAVE, mAAE for measuring translation, scale, orientation, velocity and attribute, respectively. NDS of nuScenes is a weighted sum of mAP and the five true positive metrics, defined as $NDS = \\frac{1}{10} [5mAP + \\sum_{mTP}(1 - \\min(1, mTP))]$ .", + "bbox": [ + 75, + 450, + 468, + 589 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Implementation Details", + "text_level": 1, + "bbox": [ + 75, + 596, + 294, + 611 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We conduct experiments on BEVFormer [19] and DETR3D [32]. Settings of expert- apprentice pairs are illustrated in Tab. 1. We obtain three groups of expert- apprentice combinations by changing the backbone, input image resolution and BEV grip resolution. ResNet [8] with or without deformable convolution [38] are used for all backbones. When applied to BEV perception model BEVFormer, the selective masked generation is performed on both the PV feature and BEV feature, and query-based focal distillation is performed on the BEV feature, while both selective masked generative distillation and query-based focal distillation are performed on PV feature when it comes to the BEV-free perception model DETR3D. We also conduct the experiment on BEVDepth in supplementary materials.", + "bbox": [ + 75, + 617, + 468, + 809 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The codebase is developed upon MMDetection3D [5]. All models are trained on 8 NVIDIA A100 GPUs. For BEVFormer and DETR3D, the models are trained for 24 epochs with an initial learning rate of 2e-4 and per-GPU", + "bbox": [ + 75, + 809, + 468, + 866 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "batch size of 1. No data augmentation is introduced when training BEVFormer and DETR3D. Feature pyramid position shift [24] is adopted for PV feature alignment between low-resolution apprentice and high-resolution expert. The hyperparameters $r$ , $\\tau$ , $\\alpha$ , $\\beta$ , $\\lambda$ , $\\eta$ are set to be 0.5, 2.0, 2.0, 0.25, 0.25 and 0.001, respectively.", + "bbox": [ + 497, + 125, + 890, + 209 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Comparison to State-of-the-arts", + "text_level": 1, + "bbox": [ + 497, + 219, + 779, + 233 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As depicted in Tab. 2, the proposed distillation method brings significant improvement on BEVFormer-Tiny, BEVFormer-Small and DETR3D by 4.07, 2.47 and 3.17 NDS, respectively. The gain comes mainly from the improved mAP and velocity estimation accuracy. The devised method brings 4.13 points to BEVFormer-Tiny and 3.08 points to BEVFormer-Small in terms of mAP, which demonstrates the enhancement of localization and classification. The proposed approach also achieves improvements of 4.97 points to BEVFormer-Tiny and 8.21 points to DETR3D-R50 in terms of mAVE. In regard to the classic distillation methods on the 2D field, regardless of BEVFormer-Tiny or DETR3D-R50, FitNet obtains marginal improvement, yet CWD achieves larger gains. MGD with the global random mask cannot outperform CWD, indicating that random masked generative distillation in 3D detection scenes is not as powerful as that in 2D scenes. The proposed FD3D outperforms all classic distillation methods on the 2D field by an obvious margin. The comparison reveals that the devised fine-grained distillation on focal regions truly improves the distillation quality. In the supplementary materials, we conduct further experiments to validate the efficacy of FD3D on another BEV perception model BEVDepth. It can be observed that FD3D leads to improved performance on BEVDepth. These findings demonstrate the generalizability of the proposed distillation method across various 3D object detectors. Moreover, we also present the gains achieved by FD3D on the nuScenes test set, which are consistent with the effects observed on the nuScenes val set.", + "bbox": [ + 497, + 239, + 890, + 654 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. Ablative Study", + "text_level": 1, + "bbox": [ + 497, + 663, + 650, + 679 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Contribution of each module. For a better understanding of the contribution of each proposed module to the distillation performance, we test each component independently on group BEVFormer Base-Tiny and report the corresponding accuracy in Tab. 3. The channel-wise distribution (CWD) is adopted as a baseline distillation method and obtains 41.80 NDS. When compared to this baseline, the selective masked generation can achieve an additional 1.07 NDS improvement, revealing that such technique can enhance feature learning on focal regions. Query-based focal distillation yields an extra 0.95 NDS gain over the baseline, thereby highlighting the significance of the refined distillation on the fine-grained position. With the two proposed", + "bbox": [ + 497, + 686, + 890, + 866 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "997", + "bbox": [ + 472, + 887, + 497, + 897 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/82283d487007dda4620ce2c56d2df851408938dbb921931372280e728a170b0a.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodNDS↑mAP↑mATE↓mASE↓mAOE↓mAVE↓mAAE↓GFLOPs↓FPS↑
BEVFormer-Base* (E)47.3736.4473.5128.1444.9842.3819.501845.362.0
BEVFormer-Tiny (A)39.0226.8783.4329.4859.7350.0321.49
+ FitNet [26]40.5728.2681.5228.9652.9651.3220.84
+ CWD [25]41.8029.7980.8128.5550.6349.8721.21381.957.3
+ MGD [36]41.3329.0880.1928.8352.8350.0020.19
+ FD3D (Ours)43.09 (↑4.07)31.00 (↑4.13)79.3128.0050.7745.0620.97
BEVFormer-Base (E)51.7441.6467.2627.3437.0439.4119.741323.411.8
BEVFormer-Small (A)46.2634.5674.2728.0044.5343.9819.41416.465.9
+ FD3D (Ours)48.73 (↑2.47)37.64 (↑3.08)71.9427.5040.8939.4121.16
DETR3D-R101 (E)42.534.677.326.838.384.221.61016.832.5
DETR3D-R50 (A)35.7828.8585.3927.9054.0995.1523.95
+ FitNet [26]36.1929.7683.9028.0056.1894.5324.33
+ CWD [25]37.2230.1382.7427.6549.4094.6523.98876.944.0
+ MGD [36]37.0329.8983.3527.7953.2892.7421.98
+ FD3D (Ours)38.95 (↑3.17)31.33 (↑2.48)82.3227.6548.4086.9421.87
", + "bbox": [ + 80, + 123, + 890, + 347 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/edd1a64fb2ef7431409ae4cad69e998ec94328e8ebc9035afda34bd4fc0e45aa.jpg", + "table_caption": [ + "Table 2. 3D object detection improvement on nuScenes val set. The results demonstrate that the proposed distillation method benefits various 3D object detectors and surpasses the classic 2D distillation methods. We also show their efficiency metrics with GFLOPs and FPS. The FPS is measured on RTX 2080TI." + ], + "table_footnote": [], + "table_body": "
ComponentNDSmAP
CWDSMGDQFD
BEVFormer Base-Tiny✓39.0226.87
41.8029.79
✓42.8730.59
✓42.7530.47
✓✓43.0931.00
", + "bbox": [ + 92, + 408, + 450, + 515 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Contribution by each component. SMGD and QFD are the proposed two novel modules. SMGD represents selective masked generative distillation, and QFD indicates query-based focal distillation. Channel-wise distribution (CWD) is applied as the baseline distillation method for comparison.", + "bbox": [ + 75, + 520, + 468, + 586 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "modules applied in conjunction, there is an observed increase in performance of 1.29 NDS, providing evidence of their efficacy and compatibility.", + "bbox": [ + 75, + 600, + 468, + 641 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Mask region selection. As shown in Tab. 4a, variation in the impact of masked generative distillation across different regions is substantial. Global random mask leads to worsened results. Mask on foreground regions defined by the ground truth yields significant gains. Furthermore, applying masks to the predicted focal regions, as defined by focal queries, results in further improvement. This is probably attributed to the selection of focal queries, which effectively filter out regions with high confidence while excluding challenging-to-discriminate regions.", + "bbox": [ + 75, + 643, + 468, + 781 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Distillation region. The terms \"global distribution\" and \"local pattern\" refer to two distillation mode focusing on the global overall activation and the local feature representation, respectively. And their performances are evaluated in Tab. 4b. The results demonstrate that distilling with global distribution alone already yields improvement, and when", + "bbox": [ + 75, + 783, + 468, + 866 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "focusing on the local pattern of focal regions, a slightly higher gain is observed. The best performance is achieved through the combined optimization of them.", + "bbox": [ + 497, + 409, + 890, + 450 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Distillation stage. The view transform module takes PV features as input and generates BEV features. PV features and BEV features are from different stages of the network. We explore the difference when global distillation (Fig. 1 (a)) is performed at different stages. The channel-wise distribution (CWD) is adopted in this ablation study. As shown in Tab. 4c, separate distillation on PV features obtains an improvement while separate distillation on BEV features leads to a deterioration in performance. This is due to the BEV feature containing a lot of shadow-like artifacts due to the unclear occlusion. This result demonstrates the necessity of selective distillation under BEV feature.", + "bbox": [ + 497, + 451, + 890, + 617 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Feature alignment approach. When the BEV resolution differs between expert and apprentice, the BEV feature alignment is needed. There are two choices for alignment: upsampling the apprentice feature through a deconvolutional layer or directly downsampling the expert feature. We compare the two alignment approaches in Tab. 4d. Downsampling expert feature provokes inferior results than upsampling apprentice feature. This is potentially caused by the fatal information loss of the expert feature.", + "bbox": [ + 497, + 617, + 890, + 742 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Visualization", + "text_level": 1, + "bbox": [ + 499, + 748, + 636, + 762 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The feature representation and prediction of the apprentice network BEVFormer-tiny with or without our proposed method are presented in Fig. 5. For PV, the feature activations from the first FPN layer in front left view, front right view and back left are displayed. The activation of many background regions is high without distillation, making the foreground and background indistinguishable. With", + "bbox": [ + 497, + 769, + 890, + 866 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "998", + "bbox": [ + 472, + 887, + 497, + 897 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/9bb7368866e775ca8b719763425f83736605e6d2fce87e4a9bb856688b6c5e33.jpg", + "table_caption": [], + "table_footnote": [ + "(a) Mask region selection. Global random masked generation exacerbates the performance, while the selective masked generation on focal regions brings a remarkable improvement." + ], + "table_body": "
GroupDistillation RegionNDSmAP
BEVFormer Base-Tinydirectly imitation41.8029.79
global random mask41.1428.49
mask on GT42.4129.85
selective focal mask42.8730.59
DETR3D R101-R50directly imitation37.2230.13
global random mask37.1930.03
mask on GT37.5830.11
selective focal mask37.9129.87
", + "bbox": [ + 126, + 119, + 438, + 243 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/9e4fe3490c3a7237df2716270416a2d0a1ecfe334d63b7894f8065b6df0212d0.jpg", + "table_caption": [], + "table_footnote": [ + "(c) Distillation stage. Effect of global channel-wise distribution distillation (Fig. 1 (a)) on PV or BEV. The result indicates that combined distillation on PV and BEV achieves the highest improvement. Note that separate global distillation on BEV feature leads to a deterioration in performance." + ], + "table_body": "
GroupDistillation StageNDSmAP
PVBEV
BEVFormer✓46.2634.56
Base-Small✓47.0635.52
45.2433.56
✓✓47.6035.97
", + "bbox": [ + 109, + 293, + 455, + 383 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/f3482b5810a0f076cc31ea1dcb1b02253a668078f0e18720e977b062e4fe7d85.jpg", + "table_caption": [], + "table_footnote": [ + "(b) Distillation region. Global distribution means the channel-wise distribution of feature activation, and local pattern represents the feature values on the fine-grained focal regions. Distillation on both global distribution and local patterns achieves the best performance." + ], + "table_body": "
GroupDistillation RegionNDSmAP
BEVFormer Base-Tinyglobal distribution41.8029.79
local pattern41.9129.89
global distribution + local pattern42.6830.30
DETR3D R101-R50global distribution37.4330.41
local pattern38.0030.21
global distribution + local pattern38.7230.57
", + "bbox": [ + 534, + 123, + 848, + 243 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/99c8af04893014907e61e0683e1d5b792cb54ac91585935d70167495dbd925e7.jpg", + "table_caption": [], + "table_footnote": [ + "(d) Feature alignment. Downsampling expert feature gets significantly worse results than upsampling apprentice feature through a deconvolutional layer." + ], + "table_body": "
GroupFeature AlignmentNDSmAP
BEVFormerdownsample47.4736.66
Base-Smalldeconvolution48.7337.50
", + "bbox": [ + 521, + 299, + 860, + 382 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4. FD3D ablations on nuScenes val set. We show nuScenes detection score (NDS) and mean average precision (mAP) metrics (%). Default settings are marked in gray.", + "bbox": [ + 75, + 448, + 890, + 473 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6b1c2f6c51205dd3296107cb34e84c6ed62017585c8ec741b5d896116e629d41.jpg", + "image_caption": [ + "Figure 5. Visualization of feature activation and the predicted results before and after knowledge distillation. In comparison with the feature activation on PV, the foreground and background become clearly distinguishable with distillation. The predictions are illustrated on BEV, where green and blue boxes denote the ground truth and predictions respectively. With the devised method, the prediction accuracy of detection boxes is significantly improved." + ], + "image_footnote": [], + "bbox": [ + 152, + 484, + 388, + 707 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "the proposed approach, they become clearly distinguishable. The PV feature visualization confirms that the distillation makes the backbone of the apprentice network well", + "bbox": [ + 75, + 824, + 468, + 866 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "optimized. High-quality 2D image feature extraction is the basis for BEV feature production and subsequent detection. In addition, we give a comparison of predicted bounding boxes in BEV. Through the comparison of the area within the red dashed box, our approach significantly reduces the translation error. Though the accuracy of the bounding boxes is obviously improved, the false positive issues are still serious after distillation due to the inherent detects in the 3D object detection model.", + "bbox": [ + 497, + 482, + 890, + 606 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion and Future Work", + "text_level": 1, + "bbox": [ + 499, + 618, + 769, + 633 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we apply knowledge distillation to camera-only 3D object detection, and we reveal that the challenge lies in how to distill focal knowledge when confronted with an imperfect expert. We devise FD3D, a flexible query-based approach that automatically searches the representative regions and highlights these regions for distillation. It serves as a plug-and-play module and successfully applies to various 3D object detectors.", + "bbox": [ + 497, + 641, + 890, + 751 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitation and future work. The challenge of distilling knowledge from imperfect experts exists in not only the 3D object detection domain, but also in other fields. The proposed approach is needed to be extended to address more general scenarios.", + "bbox": [ + 497, + 752, + 890, + 821 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. This work is partially supported by NSFC (62206172, 62222607), and the Shanghai Committee of Science and Technology (21DZ1100100).", + "bbox": [ + 497, + 824, + 890, + 866 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "999", + "bbox": [ + 472, + 887, + 497, + 897 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 124, + 171, + 138 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Holger Caesar, Varun Bankiti, Alex H Lang, Sourabh Vora, Venice Erin Liong, Qiang Xu, Anush Krishnan, Yu Pan, Giancarlo Baldan, and Oscar Beijbom. nuscenes: A multimodal dataset for autonomous driving. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 11621-11631, 2020. 1, 6", + "[2] Nicolas Carion, Francisco Massa, Gabriel Synnaeve, Nicolas Usunier, Alexander Kirillov, and Sergey Zagoruyko. End-to-end object detection with transformers. 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Deformable detr: Deformable transformers for end-to-end object detection. arXiv preprint arXiv:2010.04159, 2020. 4" + ], + "bbox": [ + 78, + 125, + 468, + 809 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "1001", + "bbox": [ + 468, + 887, + 499, + 897 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Distilling Focal Knowledge From Imperfect Expert for 3D Object Detection/26d504d2-cd24-4e73-99c4-214e67e817bc_model.json b/2023/Distilling Focal Knowledge From Imperfect Expert for 3D Object Detection/26d504d2-cd24-4e73-99c4-214e67e817bc_model.json new file mode 100644 index 0000000000000000000000000000000000000000..d80a7718074769e57a6def42ecbcdafa77657faa --- /dev/null +++ b/2023/Distilling Focal Knowledge From Imperfect Expert for 3D Object Detection/26d504d2-cd24-4e73-99c4-214e67e817bc_model.json @@ -0,0 +1,2156 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.13, + 0.051, + 0.201, + 0.085 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.253, + 0.049, + 0.792, + 0.088 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.17, + 0.16, + 0.8, + 0.178 + ], + "angle": 0, + "content": "Distilling Focal Knowledge from Imperfect Expert for 3D Object Detection" + }, + { + "type": "text", + "bbox": [ + 0.266, + 0.203, + 0.704, + 0.22 + ], + "angle": 0, + "content": "Jia Zeng\\(^{1,2}\\) Li Chen\\(^{1}\\) Hanming Deng\\(^{3}\\) Lewei Lu\\(^{3}\\)" + }, + { + "type": "text", + "bbox": [ + 0.323, + 0.221, + 0.673, + 0.237 + ], + "angle": 0, + "content": "Junchi Yan\\(^{2,1}\\) Yu Qiao\\(^{1}\\) Hongyang Li\\(^{1,2*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.117, + 0.237, + 0.855, + 0.253 + ], + "angle": 0, + "content": "1OpenDriveLab, Shanghai AI Lab 2Shanghai Jiao Tong University 3SenseTime Research" + }, + { + "type": "text", + "bbox": [ + 0.278, + 0.255, + 0.692, + 0.269 + ], + "angle": 0, + "content": "{zengjia,lichen,qiaoyu,lihongyang}@pjlab.org.cn" + }, + { + "type": "text", + "bbox": [ + 0.23, + 0.271, + 0.736, + 0.285 + ], + "angle": 0, + "content": "{denghanming,luotto}@sensetime.com yanjunchi@sjtu.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.316, + 0.313, + 0.331 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.346, + 0.474, + 0.637 + ], + "angle": 0, + "content": "Multi-camera 3D object detection blossoms in recent years and most of state-of-the-art methods are built up on the bird's-eye-view (BEV) representations. Albeit remarkable performance, these works suffer from low efficiency. Typically, knowledge distillation can be used for model compression. However, due to unclear 3D geometry reasoning, expert features usually contain some noisy and confusing areas. In this work, we investigate on how to distill the knowledge from an imperfect expert. We propose FD3D, a Focal Distiller for 3D object detection. Specifically, a set of queries are leveraged to locate the instance-level areas for masked feature generation, to intensify feature representation ability in these areas. Moreover, these queries search out the representative fine-grained positions for refined distillation. We verify the effectiveness of our method by applying it to two popular detection models, BEVFormer and DETR3D. The results demonstrate that our method achieves improvements of 4.07 and 3.17 points respectively in terms of NDS metric on nuScenes benchmark. Code is hosted at https://github.com/OpenPerceptionX/BEVPerception-Survey-Recipe." + }, + { + "type": "title", + "bbox": [ + 0.079, + 0.666, + 0.21, + 0.68 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.69, + 0.47, + 0.844 + ], + "angle": 0, + "content": "Accurate 3D object detection is a vital component in autonomous driving. To achieve this, most methods [14, 37] resort to LiDAR sensors and dominate the public benchmarks [1, 27]. Despite the performance gap, pure vision approaches are still worthy of in-depth inquiry, since cameras can provide rich semantic information and are low-cost and easy-to-deploy. Among these, bird's-eye-view (BEV) detection has drawn extensive attention from both industry and academia, and shown great potential to narrow down the performance gap [15, 21]. However, such models tend to be computationally consuming." + }, + { + "type": "image", + "bbox": [ + 0.543, + 0.325, + 0.66, + 0.405 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.515, + 0.41, + 0.645, + 0.422 + ], + "angle": 0, + "content": "(a) Global distillation" + }, + { + "type": "image_caption", + "bbox": [ + 0.679, + 0.381, + 0.735, + 0.403 + ], + "angle": 0, + "content": "Expert Abstraction" + }, + { + "type": "image", + "bbox": [ + 0.765, + 0.316, + 0.882, + 0.404 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.744, + 0.41, + 0.888, + 0.422 + ], + "angle": 0, + "content": "(b) Attentive distillation" + }, + { + "type": "image", + "bbox": [ + 0.539, + 0.427, + 0.654, + 0.54 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.552, + 0.667, + 0.576 + ], + "angle": 0, + "content": "(c) Generative distillation with random mask" + }, + { + "type": "image_caption", + "bbox": [ + 0.668, + 0.441, + 0.74, + 0.462 + ], + "angle": 0, + "content": "Apprentice Representation" + }, + { + "type": "image", + "bbox": [ + 0.769, + 0.427, + 0.884, + 0.54 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.795, + 0.54, + 0.855, + 0.55 + ], + "angle": 0, + "content": "Query offset" + }, + { + "type": "image_caption", + "bbox": [ + 0.75, + 0.552, + 0.899, + 0.577 + ], + "angle": 0, + "content": "(d) Generative and focal distillation (ours)" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.589, + 0.893, + 0.679 + ], + "angle": 0, + "content": "Figure 1. Illustration of the proposed generative and focal distillation method. Compared with others, the proposed manner in 1 (d) leverages queries to generate instance masks for masked generative distillation, rather than random masks in 1 (c). Moreover, the queries meanwhile search for the representative position to perform refined distillation, where the distillation region selection is more fine-grained and flexible than 1 (b)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.697, + 0.892, + 0.85 + ], + "angle": 0, + "content": "In common practice, knowledge distillation can compress the model and is usually applied to alleviate computation overhead. One possible solution is to utilize the LiDAR-based model as the expert [4, 17], but this requires complex spatial-temporal calibrations and also needs to handle heterogeneous problems from different modalities. An intuitive question is, can we distill these models solely based on camera sensors? In this work, we intend to address this problem and focus on the camera-only distillation setting. To the best of our knowledge, our work is the first solution tailored for this setting." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.853, + 0.892, + 0.867 + ], + "angle": 0, + "content": "Distillation methods in 2D object detection have derived" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.854, + 0.416, + 0.867 + ], + "angle": 0, + "content": "*Corresponding author at lihongyang@pjlab.org.cn" + }, + { + "type": "page_number", + "bbox": [ + 0.473, + 0.888, + 0.498, + 0.898 + ], + "angle": 0, + "content": "992" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.113, + 0.123, + 0.23, + 0.243 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.267, + 0.123, + 0.437, + 0.243 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.251, + 0.473, + 0.354 + ], + "angle": 0, + "content": "Figure 2. Visualization of the predicted bounding boxes and bird's eye view feature of BEVFormer [19]. At the center is the autonomous vehicle. In the left subfigure, green and blue boxes denote the ground truth and predictions respectively. In the right subfigure, the BEV feature is ray-shaped and contains a lot of noise. Areas with incorrect high activation appear behind objects due to occlusion, which easily introduces false positives, e.g., the region circled by the ellipse." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.382, + 0.47, + 0.713 + ], + "angle": 0, + "content": "various types as depicted in Fig. 1 (a)-(c), but their effectiveness is not verified in 3D object detection. The main challenge in camera-to-camera distillation for 3D object detection comes from the imperfect expert features. Due to the lack of accurate 3D information, expert features drawn from 2D images usually contain some noisy and confusing areas. To better illustrate this point, we visualize the BEV features from BEVFormer [19] in Fig. 2. The unclear occlusion reasoning makes the BEV features suffer from the ray-shape artifacts. The imperfect BEV features result in many false positives. Directly mimicking these features from experts such as Fig. 1 (a) may exacerbate the drawback. Some 2D detection distillation methods [29] propose to focus on foreground-orient regions, as shown in Fig. 1 (b). However, background regions are also important as proved in [7, 35, 13]. We categorize these methods as attentive distillation. Compared with 2D object detection, the imbalance between foreground and background in 3D areas is much more severe. Balancing these weights is not a general solution. The latest study MGD [36] demonstrates the effectiveness of masked image modeling (MIM) distillation as depicted in Fig. 1 (c). However, the global random mask cannot greatly enhance 3D object detection, which is validated in Tab. 4a." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.714, + 0.47, + 0.866 + ], + "angle": 0, + "content": "To this end, we propose a Focal Distiller for 3D object detection, shortened as FD3D. The schematic diagram of FD3D is shown in Fig. 1 (d). Specifically, A set of queries are leveraged to locate the instance-level focal regions, masked generative distillation is performed within the regions. Moreover, these queries dynamically search fine-grained representative positions for focal distillation. Two complementary modules guide the apprentice network to generate enhanced feature representation on focal regions. In summary, our work makes three-fold contributions:" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.127, + 0.892, + 0.196 + ], + "angle": 0, + "content": "1. To the best of our knowledge, this is the first work to explore knowledge distillation on the camera-only 3D object detection. We reveal the challenge relies on how to distill focal knowledge from an imperfect 3D object detector expert." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.207, + 0.892, + 0.275 + ], + "angle": 0, + "content": "2. We propose FD3D, which utilizes a set of queries to distill focal knowledge. With these queries, coarse-grained focal regions are selected for masked generation, and fine-grained focal regions are searched out for instance-oriented refinement distillation." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.287, + 0.892, + 0.343 + ], + "angle": 0, + "content": "3. FD3D serves as a plug-and-play module. It can be easily extended to various detectors. The improvements with 4.07 and 3.17 NDS can be obtained with FD3D assembled in BEVFormer and DETR3D, respectively." + }, + { + "type": "list", + "bbox": [ + 0.512, + 0.127, + 0.892, + 0.343 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.369, + 0.642, + 0.384 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.397, + 0.892, + 0.868 + ], + "angle": 0, + "content": "Knowledge distillation on 2D object detection. Knowledge distillation is originally proposed by Hinton et al. [9]. It regards teachers' output logits as knowledge and is employed as a model compression approach in the classification task. FitNet [26] extends the knowledge to intermediate features. Recently, many works successfully apply knowledge distillation on object detection [3]. Knowledge distillation on object detection encounters extreme imbalance between positive and negative instances. Global feature imitation [29] such as Fig. 1 (a) brings marginal improvement, and even exacerbates the performance. It is almost a consensus that distillation should not treat all regions equally. Revisiting from the latest works, where to perform distillation is of great concern in distilling object detectors, and they invariably resort to attentive distillation as depicted in Fig. 1 (b). Mimic [16] performs distillation on ROI regions sampled by an RPN network, but this framework can only be applied to a two-stage detector. FIFG [29] claims the distillation should be performed on near-object regions. However, the near-object regions are defined by hand-crafted rules and require manual refinement. GID [6] focuses on regions where there is a significant difference between the student and the teacher outputs. DeFeat [7] separates foreground and background by ground truth and performs distillation independently. GID [6] and DeFeat [7] prove that the informative cues in the background also benefit the student network. FGD [35] designs a more elaborate structure to focus on critical pixels and channels. Albeit the effectiveness of the aforementioned studies, they require manual hyper-parameter tuning to adjust the concentration of distillation. ICD [13] encodes the instance annotations as queries, and attention maps are generated to guide the distillation region concentration. We deem such a query-based approach is more flexible. MGD [36] proposes a simple but" + }, + { + "type": "page_number", + "bbox": [ + 0.473, + 0.888, + 0.498, + 0.898 + ], + "angle": 0, + "content": "993" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.156, + 0.127, + 0.812, + 0.356 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.36, + 0.895, + 0.437 + ], + "angle": 0, + "content": "Figure 3. We present FD3D, a Focal Distiller for 3D object detection. The framework aims to transfer the dark knowledge of the focal region from the expert network to the compact apprentice network, where the feature distillation is performed on both perspective view (PV) and bird's-eye-view (BEV). We employ aligned BEV queries. With these queries, the instance masks in PV and BEV are generated, and masked generative distillation is performed within the mask region to enhance the feature representation. Moreover, these queries meanwhile leverage deformable attention mechanism to search out the representative features on focal BEV regions. The representative features are utilized for refined distillation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.46, + 0.471, + 0.502 + ], + "angle": 0, + "content": "effective distillation paradigm as shown in Fig. 1 (c): the student features are randomly masked and then recovered to mimic teacher features." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.508, + 0.473, + 0.868 + ], + "angle": 0, + "content": "Multi-camera 3D Object Detection. Early studies [22, 30] independently process monocular images from multiple views, and aggregate the results across cameras for postprocessing. FCOS3D [30] extends the popular anchor-free detector FCOS [28] by directly predicting 3D bounding boxes from 2D image features. Recent studies tend to predict object location in 3D space. One branch of researchers converts 2D image features to 3D space through depth estimation. The typical approach is to convert the estimated depth map into pseudo-LiDAR [31]. Lift-Splat-Shoot (LSS) [23] estimates the depth distribution of each image pixel and uses voxel pooling to generate BEV features. Its follow-up studies BEVDet [11], BEVDet4D [10], BEVDepth [18] further explore data augmentation, accelerating voxel pooling module and improving depth estimation accuracy. Another branch of studies indexes 2D image feature to 3D space through the camera extrinsic and intrinsic. Following DETR [2], DETR3D [32] defines a set of 3D object queries and samples 2D image features on the queries' projection points to predict 3D bounding boxes. BEVFormer [19] explicitly defines queries in BEV space, and performs 2D-to-3D transformation with deformable attention to generate the BEV feature for downstream tasks. PolarFormer [12] adopts polar coordinate system for more accurate BEV feature construction. These state-of-the-art models suffer from high computation overhead. It is natu" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.46, + 0.892, + 0.529 + ], + "angle": 0, + "content": "ral to consider applying knowledge distillation to compress the model. However, regardless of the view transform approaches, the 2D-to-3D transformation is ill-posed, so the vision-based 3D object detector experts cannot provide a reliable feature for imitation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.534, + 0.893, + 0.7 + ], + "angle": 0, + "content": "LiDAR-based knowledge distillation. In 3D object detection, there are existing studies covering knowledge distillation under LiDAR [33, 34] and extending to LiDAR-camera cross-modality knowledge transfer. Monodistill [4] projects the LiDAR points to the image plane, aligning two modalities for knowledge transfer. UVTR [17] represents the image and LiDAR in a unified voxel space, and the feature distillation is performed on the query projection points. To exclude the heterogeneous problems from different modalities and focus on the exploration of distillation from an imperfect expect, the extent of this study is set at camera-only distillation." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.714, + 0.637, + 0.731 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.737, + 0.892, + 0.793 + ], + "angle": 0, + "content": "Fig. 3 illustrates the pipeline of our distillation approach. The overall structure of FD3D is presented in Sec. 3.1. The two proposed distillation modules are elaborated in Sec. 3.2 and Sec. 3.3." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.804, + 0.673, + 0.818 + ], + "angle": 0, + "content": "3.1. Overall Structure" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.868 + ], + "angle": 0, + "content": "The state-of-the-art multi-camera 3D object detection networks suffer from high computation overhead. This shortcoming mainly originates from the heavy network ar" + }, + { + "type": "page_number", + "bbox": [ + 0.473, + 0.888, + 0.498, + 0.898 + ], + "angle": 0, + "content": "994" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.08, + 0.124, + 0.47, + 0.304 + ], + "angle": 0, + "content": "
MethodBackboneImage ResolutionBEV ResolutionEncoder Layer
BEVFormer -Base* (E)R101900×1600200×2006
BEVFormer -Tiny (A)R50450×800100×1003
BEVFormer -Base (E)R101-DCN†900×1600200×2006
BEVFormer -Small (A)R101-DCN†450×800100×1003
DETR3D -R101 (E)R101-DCN†900×1600--
DETR3D -R50 (A)R50900×1600--
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.313, + 0.47, + 0.429 + ], + "angle": 0, + "content": "Table 1. The setting of expert- apprentice pairs. The symbol \"E\" and \"A\" denote \"expert\" and \"apprentice\" respectively. By setting different network depth, input resolution or BEV resolution, we obtain expert- apprentice pairs. * represents this version of BEVFormer-Base apply ResNet101 as backbone rather than ResNet101-DCN, which is different from the original version [19]. † indicates using nuScene pretrained weight with FCOS3D [30]. Unless otherwise specified, the backbone is pretrained on ImageNet only." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.449, + 0.469, + 0.601 + ], + "angle": 0, + "content": "chitecture and high input resolution. By compressing the network depth or input resolution, we obtain more compact networks. However, the lightweight networks inevitably suffer from accuracy attenuation. Therefore, we employ the heavy state-of-the-art model as the expert, adopt the lightweight counterpart as the apprentice, and perform knowledge transfer between them. We freeze the expert network, and leverage the intermediate features of the expert network as auxiliary supervision for the apprentice network. The setting of adopted expert- apprentice pairs is depicted in Tab. 1. Their GLOPS and FPS are presented at Tab. 2." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.602, + 0.469, + 0.837 + ], + "angle": 0, + "content": "As depicted in Fig. 3, a distillation framework between the expert network and the apprentice network is constructed. For the BEV perception model, the distillation is performed on both the perspective view (PV) and BEV features. We set up an extra distillation head and employ a set of aligned BEV queries \\( Q \\) for distillation. The structure of the distillation head is similar to the head of Deformable DETR [39]. Based on the deformable attention mechanism, \\( N \\) queries sample key features from BEV features and generate 3D bounding boxes. The generated 3D bounding boxes are projected into PV and BEV. The projection areas are used for masked generative distillation, and the sampled BEV features in the deformable attention process are adopted for refined distillation. In order to urge the projection areas locate at the foreground area and the sampled BEV features come from the object region, the distillation head is also optimized with auxiliary detection losses." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.839, + 0.469, + 0.867 + ], + "angle": 0, + "content": "The distillation head is built upon the expert BEV features. The distillation queries go through a self-attention" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.126, + 0.892, + 0.18 + ], + "angle": 0, + "content": "layer, and then sample expert BEV feature \\(F^{E}\\) to generate \\(y^{E}\\) through a deformable attention (DEFORMATTN) layer and a feed-forward network \\((\\mathcal{FFN})\\). The latter process is formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.563, + 0.193, + 0.891, + 0.21 + ], + "angle": 0, + "content": "\\[\ny ^ {E} = \\mathcal {F F N} (\\text {D E F O R M A T T N} (Q, F ^ {E})), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.212, + 0.892, + 0.295 + ], + "angle": 0, + "content": "where \\(y^{E} = \\{[c_{1}^{E},b_{1}^{E}],[c_{2}^{E},b_{2}^{E}],\\ldots ,[c_{N}^{E},b_{N}^{E}]\\}\\), and \\(c_{i}^{E},b_{i}^{E}\\) represent classification score and regression bounding box corresponding to \\(i\\)-th distillation query. Based on bipartite matching approach in [2], we search for the optimal permutations \\(\\hat{\\sigma}\\) and optimize the distillation head by \\(\\mathcal{L}_{dh}\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.502, + 0.3, + 0.891, + 0.354 + ], + "angle": 0, + "content": "\\[\n\\left\\{ \\begin{array}{l} \\hat {\\sigma} = \\underset {\\sigma \\in \\mathfrak {S} _ {N}} {\\arg \\min } \\sum_ {i} ^ {N} \\alpha \\mathcal {L} _ {c l s} \\left(c _ {\\sigma (i)} ^ {E}, c _ {i} ^ {g t}\\right) + \\beta \\mathcal {L} _ {b b o x} \\left(b _ {\\sigma (i)} ^ {E}, b _ {i} ^ {g t}\\right), \\\\ \\mathcal {L} _ {d h} = \\sum_ {i} ^ {N} \\alpha \\mathcal {L} _ {c l s} \\left(c _ {\\hat {\\sigma} (i)} ^ {E}, c _ {i} ^ {g t}\\right) + \\beta \\mathcal {L} _ {b b o x} \\left(b _ {\\hat {\\sigma} (i)} ^ {E}, b _ {i} ^ {g t}\\right), \\end{array} \\right. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.356, + 0.892, + 0.41 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{cls}\\) and \\(\\mathcal{L}_{bbox}\\) take the same form as FocalLoss [20] and L1 loss respectively, \\(b^{gt}\\) and \\(c^{gt}\\) represent ground truth boxes coordinates and classes, and \\(\\alpha\\) as well as \\(\\beta\\) balance the loss weight." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.41, + 0.892, + 0.507 + ], + "angle": 0, + "content": "During the optimization process of the distillation head, the queries with a confidence higher than \\(\\rho_{c}\\) and GIOU greater than \\(\\rho_{b}\\) are filtered out as focal queries, termed as \\(Q^{f}\\). The number of \\(Q^{f}\\) is denoted as \\(N_{f}\\). Finally, the generated 3D boxes and sampled BEV features corresponding to the focal queries \\(Q^{f}\\) are selected to perform masked generative distillation and refined distillation." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.514, + 0.845, + 0.528 + ], + "angle": 0, + "content": "3.2. Selective Masked Generative Distillation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.535, + 0.891, + 0.631 + ], + "angle": 0, + "content": "The generated 3D boxes by focal queries \\( Q_{f} \\) are projected to PV and BEV. The 3D boxes are projected to PV according to the camera extrinsics and intrinsics, and simply flattened to BEV from the top-down view. The masking process described below is the same for both PV and BEV, so we describe the process without distinction between PV and BEV." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.631, + 0.892, + 0.717 + ], + "angle": 0, + "content": "An instance mask \\( I_{i}^{fg} \\) is generated with the projection area corresponding to one focal query \\( Q_{i}^{f} \\). The dimension of the instance mask is identical to that of the apprentice feature. If a pixel is inside the bounding box \\( b_{i}^{E} \\), the value is set to be 0, otherwise its value is set to be 1. The formulation of \\( I_{i}^{fg} \\) is described as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.596, + 0.723, + 0.891, + 0.76 + ], + "angle": 0, + "content": "\\[\nI _ {i, u v} ^ {f g} = \\left\\{ \\begin{array}{l l} 0, & \\text {i f} (u, v) \\text {i n} b _ {i} ^ {E} \\\\ 1, & \\text {O t h e r w i s e} \\end{array} . \\right. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.766, + 0.891, + 0.804 + ], + "angle": 0, + "content": "All instance masks are merged together to form the final mask \\( I^{fg} \\). The process of mask stacking is formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.59, + 0.805, + 0.891, + 0.823 + ], + "angle": 0, + "content": "\\[\nI ^ {f g} = I _ {0} ^ {f g} \\wedge I _ {1} ^ {f g} \\wedge \\dots \\wedge I _ {N - 1} ^ {f g}. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.891, + 0.867 + ], + "angle": 0, + "content": "The masked region indicates where the objects reside in, and the masked generation is performed within the masked region." + }, + { + "type": "page_number", + "bbox": [ + 0.473, + 0.888, + 0.498, + 0.898 + ], + "angle": 0, + "content": "995" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.078, + 0.126, + 0.47, + 0.168 + ], + "angle": 0, + "content": "The selective mask indicates that the pixels of apprentice feature within \\( I^{fg} \\) are masked by ratio \\( r \\). A random mask \\( I^r \\) with the same size of \\( I^{fg} \\) is generated:" + }, + { + "type": "equation", + "bbox": [ + 0.183, + 0.175, + 0.469, + 0.213 + ], + "angle": 0, + "content": "\\[\nI _ {u v} ^ {r} = \\left\\{ \\begin{array}{l l} 0, & \\text {i f} R _ {u, v} < r \\\\ 1, & \\text {O t h e r w i s e} \\end{array} , \\right. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.22, + 0.469, + 0.261 + ], + "angle": 0, + "content": "where \\( R_{u,v} \\) is a uniformly random number between 0 and 1. The process of the selective mask is expressed as an OR operation between \\( I^{fg} \\) and \\( I^r \\):" + }, + { + "type": "equation", + "bbox": [ + 0.218, + 0.269, + 0.469, + 0.284 + ], + "angle": 0, + "content": "\\[\nI ^ {m} = I ^ {f g} \\vee I ^ {r}. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.293, + 0.469, + 0.333 + ], + "angle": 0, + "content": "Then the apprentice feature \\( F^A \\) is masked with \\( I^m \\). The masked apprentice feature is forced to recover with a generator \\( \\mathcal{G} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.207, + 0.333, + 0.469, + 0.349 + ], + "angle": 0, + "content": "\\[\n\\hat {F} ^ {A} = \\mathcal {G} \\left(F ^ {A} \\cdot I ^ {m}\\right). \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.354, + 0.469, + 0.422 + ], + "angle": 0, + "content": "The generator \\(\\mathcal{G}\\) here includes two convolutional layers, the first one of which switches to a deconvolutional layer if the dimensions of the apprentice feature and expert feature are not identical. After generating \\(\\hat{F}^A\\), the channel-wise distribution [25] is calculated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.121, + 0.43, + 0.469, + 0.468 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {S M G D} = \\frac {\\tau^ {2}}{C} \\sum_ {c = 1} ^ {C} \\sum_ {i = 1} ^ {H \\times W} \\varphi \\left(F _ {c, i} ^ {E}\\right) \\log \\frac {\\varphi \\left(F _ {c , i} ^ {E}\\right)}{\\varphi \\left(\\hat {F} _ {c , i} ^ {A}\\right)}, \\tag {8}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.17, + 0.476, + 0.469, + 0.513 + ], + "angle": 0, + "content": "\\[\n\\varphi \\left(F _ {c, i}\\right) = \\frac {\\exp \\left(\\frac {F _ {c , i}}{\\tau}\\right)}{\\sum_ {i = 1} ^ {H \\times W} \\exp \\left(\\frac {F _ {c , i}}{\\tau}\\right)}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.516, + 0.469, + 0.557 + ], + "angle": 0, + "content": "where \\(\\tau\\) is the temperature factor of the SoftMax layer, \\(C\\) means the feature channels, and \\(H\\), \\(W\\) represent feature height and width respectively." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.565, + 0.347, + 0.579 + ], + "angle": 0, + "content": "3.3. Query-based Focal Distillation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.586, + 0.469, + 0.751 + ], + "angle": 0, + "content": "Focal distillation denotes the refined distillation focusing on the local feature pattern of focal positions. We aim to leverage a set of queries to automatically search out the representative positions of objects, and perform distillation on the identical positions between expert features and apprentice features. We resort to the deformable attention module to achieve the goal. The deformable attention module generates a set of offsets around a reference point. Based on the offsets to the reference point, the features on the crucial sampling points are sampled for object detection. We exploit this mechanism to conduct a refined distillation on such representative features as illustrated in Fig. 4." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.752, + 0.469, + 0.807 + ], + "angle": 0, + "content": "A set of focal queries \\( Q^{f} \\) are filtered out as described in Sec. 3.1. For each focal query \\( q \\in Q^{f} \\), the reference point \\( p_{q} \\) is generated by the query feature \\( z_{q} \\) with a linear projection \\( \\mathcal{M}\\mathcal{LP} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.213, + 0.816, + 0.469, + 0.832 + ], + "angle": 0, + "content": "\\[\np _ {q} = \\mathcal {M L P} \\left(z _ {q}\\right). \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.839, + 0.469, + 0.867 + ], + "angle": 0, + "content": "The reference point \\( p_q \\) represents the projection center of the estimated bounding box on the sampling feature plane." + }, + { + "type": "image", + "bbox": [ + 0.545, + 0.127, + 0.845, + 0.265 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.268, + 0.892, + 0.343 + ], + "angle": 0, + "content": "Figure 4. Process of query-based offset generation, feature sampling and query parameter update. Leveraging the deformable attention mechanism, the local expert feature and apprentice feature are sampled at the same position, based on the offset generated by the query. In addition, the query parameter is updated with the collected expert feature." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.358, + 0.891, + 0.413 + ], + "angle": 0, + "content": "For each focal query \\(q\\), \\(M\\) attention heads are attached on \\(z_{q}\\). Each attention head generates \\(K\\) sampling offsets by another linear projection \\(\\mathcal{MLP}'\\). The offset is computed by the following:" + }, + { + "type": "equation", + "bbox": [ + 0.599, + 0.426, + 0.891, + 0.442 + ], + "angle": 0, + "content": "\\[\n\\Delta p _ {m q k} = \\mathcal {M L P} ^ {\\prime} \\left(z _ {q}, m, k\\right), \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.453, + 0.89, + 0.481 + ], + "angle": 0, + "content": "where \\(m\\) indexes the attention head, and \\(k\\) represents the sampling point." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.482, + 0.891, + 0.565 + ], + "angle": 0, + "content": "The positions searched by the generated offsets are viewed as key representative positions. The query-based focal distillation is conducted on such key representative positions. Let \\( F_{mqk}^{E}, F_{mqk}^{A} \\) represent the sampled features from the identical key positions for expert and apprentice, respectively. They are calculated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.602, + 0.575, + 0.891, + 0.593 + ], + "angle": 0, + "content": "\\[\nF _ {m q k} ^ {E} = F ^ {E} \\left(p _ {q} + \\Delta p _ {m q k}\\right), \\tag {12}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.603, + 0.607, + 0.891, + 0.625 + ], + "angle": 0, + "content": "\\[\nF _ {m q k} ^ {A} = F ^ {A} \\left(p _ {q} + \\Delta p _ {m q k}\\right). \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.632, + 0.891, + 0.687 + ], + "angle": 0, + "content": "The sampled expert feature and apprentice feature are normalized to \\(\\widetilde{F}_{mqk}^{T}\\) and \\(\\widetilde{F}_{mqk}^{S}\\) according to their maximum and minimum. Finally, the L2 loss is computed between the normalized key sampled features:" + }, + { + "type": "equation", + "bbox": [ + 0.528, + 0.699, + 0.891, + 0.739 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {Q F D} = \\frac {1}{N _ {f}} \\sum_ {q \\in Q _ {f}} \\sum_ {m = 1} ^ {M} \\sum_ {k = 1} ^ {K} L _ {2} \\left(\\widetilde {F} _ {m q k} ^ {A}, \\widetilde {F} _ {m q k} ^ {E}\\right). \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.751, + 0.891, + 0.807 + ], + "angle": 0, + "content": "Through the loss for the fine-grained local region, the refined distillation on these representative positions is conducted. Query-based focal distillation aims to optimize the local patterns on the instances' representative positions." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.817, + 0.722, + 0.83 + ], + "angle": 0, + "content": "3.4. Overall Distillation Loss" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.839, + 0.891, + 0.867 + ], + "angle": 0, + "content": "Besides being supervised by ground truth, the intermediate feature of the apprentice detector is also supervised by" + }, + { + "type": "page_number", + "bbox": [ + 0.473, + 0.888, + 0.498, + 0.898 + ], + "angle": 0, + "content": "996" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.127, + 0.47, + 0.168 + ], + "angle": 0, + "content": "the masked generative distillation loss \\(\\mathcal{L}_{SMGD}\\) and query-based focal distillation loss \\(\\mathcal{L}_{QFD}\\). The total knowledge distillation loss is defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.172, + 0.178, + 0.469, + 0.192 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {K D} = \\lambda \\mathcal {L} _ {S M G D} + \\eta \\mathcal {L} _ {Q F D}. \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.201, + 0.469, + 0.271 + ], + "angle": 0, + "content": "\\(\\mathcal{L}_{SMGD}\\) is used to optimize the global feature distribution, indicating where should be with high activation. \\(\\mathcal{L}_{QFD}\\) is leveraged for optimizing the local feature pattern on searched focal positions. The hyper-parameters \\(\\lambda\\) and \\(\\eta\\) control the loss weight." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.271, + 0.469, + 0.326 + ], + "angle": 0, + "content": "Note that only the gradients w.r.t. the vanilla detection loss and the distillation loss \\(\\mathcal{L}_{KD}\\) back-propagate to the apprentice network. \\(\\mathcal{L}_{dh}\\) only optimizes the parameters of the distillation head." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.338, + 0.21, + 0.354 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.36, + 0.267, + 0.374 + ], + "angle": 0, + "content": "4.1. Dataset and metrics" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.381, + 0.47, + 0.45 + ], + "angle": 0, + "content": "We conduct experiments on nuScenes dataset [1], a large-scale autonomous driving dataset. This dataset contains 700, 150, 150 scenes for training, validation and testing, respectively. Each scene has roughly 20 seconds of duration. The key frame is annotated at \\(2\\mathrm{Hz}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.451, + 0.469, + 0.59 + ], + "angle": 0, + "content": "The two dominant metrics of the nuScenes detection task are nuScenes Detection Score (NDS) and mean Average Precision (mAP). The mAP of nuScenes is computed by the center distance between predictions and annotations on the ground plane. In addition, the nuScenes dataset defines five true positive metrics mATE, mASE, mAOE, mAVE, mAAE for measuring translation, scale, orientation, velocity and attribute, respectively. NDS of nuScenes is a weighted sum of mAP and the five true positive metrics, defined as \\( NDS = \\frac{1}{10} [5mAP + \\sum_{mTP}(1 - \\min(1, mTP))] \\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.597, + 0.295, + 0.612 + ], + "angle": 0, + "content": "4.2. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.618, + 0.469, + 0.811 + ], + "angle": 0, + "content": "We conduct experiments on BEVFormer [19] and DETR3D [32]. Settings of expert- apprentice pairs are illustrated in Tab. 1. We obtain three groups of expert- apprentice combinations by changing the backbone, input image resolution and BEV grip resolution. ResNet [8] with or without deformable convolution [38] are used for all backbones. When applied to BEV perception model BEVFormer, the selective masked generation is performed on both the PV feature and BEV feature, and query-based focal distillation is performed on the BEV feature, while both selective masked generative distillation and query-based focal distillation are performed on PV feature when it comes to the BEV-free perception model DETR3D. We also conduct the experiment on BEVDepth in supplementary materials." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.469, + 0.867 + ], + "angle": 0, + "content": "The codebase is developed upon MMDetection3D [5]. All models are trained on 8 NVIDIA A100 GPUs. For BEVFormer and DETR3D, the models are trained for 24 epochs with an initial learning rate of 2e-4 and per-GPU" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.127, + 0.892, + 0.21 + ], + "angle": 0, + "content": "batch size of 1. No data augmentation is introduced when training BEVFormer and DETR3D. Feature pyramid position shift [24] is adopted for PV feature alignment between low-resolution apprentice and high-resolution expert. The hyperparameters \\(r\\), \\(\\tau\\), \\(\\alpha\\), \\(\\beta\\), \\(\\lambda\\), \\(\\eta\\) are set to be 0.5, 2.0, 2.0, 0.25, 0.25 and 0.001, respectively." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.22, + 0.78, + 0.234 + ], + "angle": 0, + "content": "4.3. Comparison to State-of-the-arts" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.241, + 0.892, + 0.655 + ], + "angle": 0, + "content": "As depicted in Tab. 2, the proposed distillation method brings significant improvement on BEVFormer-Tiny, BEVFormer-Small and DETR3D by 4.07, 2.47 and 3.17 NDS, respectively. The gain comes mainly from the improved mAP and velocity estimation accuracy. The devised method brings 4.13 points to BEVFormer-Tiny and 3.08 points to BEVFormer-Small in terms of mAP, which demonstrates the enhancement of localization and classification. The proposed approach also achieves improvements of 4.97 points to BEVFormer-Tiny and 8.21 points to DETR3D-R50 in terms of mAVE. In regard to the classic distillation methods on the 2D field, regardless of BEVFormer-Tiny or DETR3D-R50, FitNet obtains marginal improvement, yet CWD achieves larger gains. MGD with the global random mask cannot outperform CWD, indicating that random masked generative distillation in 3D detection scenes is not as powerful as that in 2D scenes. The proposed FD3D outperforms all classic distillation methods on the 2D field by an obvious margin. The comparison reveals that the devised fine-grained distillation on focal regions truly improves the distillation quality. In the supplementary materials, we conduct further experiments to validate the efficacy of FD3D on another BEV perception model BEVDepth. It can be observed that FD3D leads to improved performance on BEVDepth. These findings demonstrate the generalizability of the proposed distillation method across various 3D object detectors. Moreover, we also present the gains achieved by FD3D on the nuScenes test set, which are consistent with the effects observed on the nuScenes val set." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.665, + 0.651, + 0.68 + ], + "angle": 0, + "content": "4.4. Ablative Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.687, + 0.892, + 0.867 + ], + "angle": 0, + "content": "Contribution of each module. For a better understanding of the contribution of each proposed module to the distillation performance, we test each component independently on group BEVFormer Base-Tiny and report the corresponding accuracy in Tab. 3. The channel-wise distribution (CWD) is adopted as a baseline distillation method and obtains 41.80 NDS. When compared to this baseline, the selective masked generation can achieve an additional 1.07 NDS improvement, revealing that such technique can enhance feature learning on focal regions. Query-based focal distillation yields an extra 0.95 NDS gain over the baseline, thereby highlighting the significance of the refined distillation on the fine-grained position. With the two proposed" + }, + { + "type": "page_number", + "bbox": [ + 0.473, + 0.888, + 0.498, + 0.898 + ], + "angle": 0, + "content": "997" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.124, + 0.891, + 0.348 + ], + "angle": 0, + "content": "
MethodNDS↑mAP↑mATE↓mASE↓mAOE↓mAVE↓mAAE↓GFLOPs↓FPS↑
BEVFormer-Base* (E)47.3736.4473.5128.1444.9842.3819.501845.362.0
BEVFormer-Tiny (A)39.0226.8783.4329.4859.7350.0321.49
+ FitNet [26]40.5728.2681.5228.9652.9651.3220.84
+ CWD [25]41.8029.7980.8128.5550.6349.8721.21381.957.3
+ MGD [36]41.3329.0880.1928.8352.8350.0020.19
+ FD3D (Ours)43.09 (↑4.07)31.00 (↑4.13)79.3128.0050.7745.0620.97
BEVFormer-Base (E)51.7441.6467.2627.3437.0439.4119.741323.411.8
BEVFormer-Small (A)46.2634.5674.2728.0044.5343.9819.41416.465.9
+ FD3D (Ours)48.73 (↑2.47)37.64 (↑3.08)71.9427.5040.8939.4121.16
DETR3D-R101 (E)42.534.677.326.838.384.221.61016.832.5
DETR3D-R50 (A)35.7828.8585.3927.9054.0995.1523.95
+ FitNet [26]36.1929.7683.9028.0056.1894.5324.33
+ CWD [25]37.2230.1382.7427.6549.4094.6523.98876.944.0
+ MGD [36]37.0329.8983.3527.7953.2892.7421.98
+ FD3D (Ours)38.95 (↑3.17)31.33 (↑2.48)82.3227.6548.4086.9421.87
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.353, + 0.893, + 0.392 + ], + "angle": 0, + "content": "Table 2. 3D object detection improvement on nuScenes val set. The results demonstrate that the proposed distillation method benefits various 3D object detectors and surpasses the classic 2D distillation methods. We also show their efficiency metrics with GFLOPs and FPS. The FPS is measured on RTX 2080TI." + }, + { + "type": "table", + "bbox": [ + 0.093, + 0.409, + 0.451, + 0.516 + ], + "angle": 0, + "content": "
ComponentNDSmAP
CWDSMGDQFD
BEVFormer Base-Tiny✓39.0226.87
41.8029.79
✓42.8730.59
✓42.7530.47
✓✓43.0931.00
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.521, + 0.47, + 0.587 + ], + "angle": 0, + "content": "Table 3. Contribution by each component. SMGD and QFD are the proposed two novel modules. SMGD represents selective masked generative distillation, and QFD indicates query-based focal distillation. Channel-wise distribution (CWD) is applied as the baseline distillation method for comparison." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.601, + 0.47, + 0.642 + ], + "angle": 0, + "content": "modules applied in conjunction, there is an observed increase in performance of 1.29 NDS, providing evidence of their efficacy and compatibility." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.644, + 0.469, + 0.782 + ], + "angle": 0, + "content": "Mask region selection. As shown in Tab. 4a, variation in the impact of masked generative distillation across different regions is substantial. Global random mask leads to worsened results. Mask on foreground regions defined by the ground truth yields significant gains. Furthermore, applying masks to the predicted focal regions, as defined by focal queries, results in further improvement. This is probably attributed to the selection of focal queries, which effectively filter out regions with high confidence while excluding challenging-to-discriminate regions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.784, + 0.47, + 0.868 + ], + "angle": 0, + "content": "Distillation region. The terms \"global distribution\" and \"local pattern\" refer to two distillation mode focusing on the global overall activation and the local feature representation, respectively. And their performances are evaluated in Tab. 4b. The results demonstrate that distilling with global distribution alone already yields improvement, and when" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.41, + 0.892, + 0.451 + ], + "angle": 0, + "content": "focusing on the local pattern of focal regions, a slightly higher gain is observed. The best performance is achieved through the combined optimization of them." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.452, + 0.892, + 0.618 + ], + "angle": 0, + "content": "Distillation stage. The view transform module takes PV features as input and generates BEV features. PV features and BEV features are from different stages of the network. We explore the difference when global distillation (Fig. 1 (a)) is performed at different stages. The channel-wise distribution (CWD) is adopted in this ablation study. As shown in Tab. 4c, separate distillation on PV features obtains an improvement while separate distillation on BEV features leads to a deterioration in performance. This is due to the BEV feature containing a lot of shadow-like artifacts due to the unclear occlusion. This result demonstrates the necessity of selective distillation under BEV feature." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.618, + 0.892, + 0.743 + ], + "angle": 0, + "content": "Feature alignment approach. When the BEV resolution differs between expert and apprentice, the BEV feature alignment is needed. There are two choices for alignment: upsampling the apprentice feature through a deconvolutional layer or directly downsampling the expert feature. We compare the two alignment approaches in Tab. 4d. Downsampling expert feature provokes inferior results than upsampling apprentice feature. This is potentially caused by the fatal information loss of the expert feature." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.749, + 0.637, + 0.763 + ], + "angle": 0, + "content": "4.5. Visualization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.77, + 0.892, + 0.868 + ], + "angle": 0, + "content": "The feature representation and prediction of the apprentice network BEVFormer-tiny with or without our proposed method are presented in Fig. 5. For PV, the feature activations from the first FPN layer in front left view, front right view and back left are displayed. The activation of many background regions is high without distillation, making the foreground and background indistinguishable. With" + }, + { + "type": "page_number", + "bbox": [ + 0.473, + 0.888, + 0.498, + 0.898 + ], + "angle": 0, + "content": "998" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.127, + 0.121, + 0.44, + 0.244 + ], + "angle": 0, + "content": "
GroupDistillation RegionNDSmAP
BEVFormer Base-Tinydirectly imitation41.8029.79
global random mask41.1428.49
mask on GT42.4129.85
selective focal mask42.8730.59
DETR3D R101-R50directly imitation37.2230.13
global random mask37.1930.03
mask on GT37.5830.11
selective focal mask37.9129.87
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.091, + 0.247, + 0.47, + 0.281 + ], + "angle": 0, + "content": "(a) Mask region selection. Global random masked generation exacerbates the performance, while the selective masked generation on focal regions brings a remarkable improvement." + }, + { + "type": "table", + "bbox": [ + 0.11, + 0.294, + 0.457, + 0.384 + ], + "angle": 0, + "content": "
GroupDistillation StageNDSmAP
PVBEV
BEVFormer✓46.2634.56
Base-Small✓47.0635.52
45.2433.56
✓✓47.6035.97
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.091, + 0.385, + 0.47, + 0.441 + ], + "angle": 0, + "content": "(c) Distillation stage. Effect of global channel-wise distribution distillation (Fig. 1 (a)) on PV or BEV. The result indicates that combined distillation on PV and BEV achieves the highest improvement. Note that separate global distillation on BEV feature leads to a deterioration in performance." + }, + { + "type": "table", + "bbox": [ + 0.536, + 0.124, + 0.849, + 0.244 + ], + "angle": 0, + "content": "
GroupDistillation RegionNDSmAP
BEVFormer Base-Tinyglobal distribution41.8029.79
local pattern41.9129.89
global distribution + local pattern42.6830.30
DETR3D R101-R50global distribution37.4330.41
local pattern38.0030.21
global distribution + local pattern38.7230.57
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.5, + 0.247, + 0.878, + 0.291 + ], + "angle": 0, + "content": "(b) Distillation region. Global distribution means the channel-wise distribution of feature activation, and local pattern represents the feature values on the fine-grained focal regions. Distillation on both global distribution and local patterns achieves the best performance." + }, + { + "type": "table", + "bbox": [ + 0.522, + 0.3, + 0.862, + 0.383 + ], + "angle": 0, + "content": "
GroupFeature AlignmentNDSmAP
BEVFormerdownsample47.4736.66
Base-Smalldeconvolution48.7337.50
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.5, + 0.385, + 0.878, + 0.419 + ], + "angle": 0, + "content": "(d) Feature alignment. Downsampling expert feature gets significantly worse results than upsampling apprentice feature through a deconvolutional layer." + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.449, + 0.892, + 0.475 + ], + "angle": 0, + "content": "Table 4. FD3D ablations on nuScenes val set. We show nuScenes detection score (NDS) and mean average precision (mAP) metrics (%). Default settings are marked in gray." + }, + { + "type": "image", + "bbox": [ + 0.153, + 0.485, + 0.389, + 0.708 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.717, + 0.47, + 0.807 + ], + "angle": 0, + "content": "Figure 5. Visualization of feature activation and the predicted results before and after knowledge distillation. In comparison with the feature activation on PV, the foreground and background become clearly distinguishable with distillation. The predictions are illustrated on BEV, where green and blue boxes denote the ground truth and predictions respectively. With the devised method, the prediction accuracy of detection boxes is significantly improved." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.867 + ], + "angle": 0, + "content": "the proposed approach, they become clearly distinguishable. The PV feature visualization confirms that the distillation makes the backbone of the apprentice network well" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.483, + 0.892, + 0.608 + ], + "angle": 0, + "content": "optimized. High-quality 2D image feature extraction is the basis for BEV feature production and subsequent detection. In addition, we give a comparison of predicted bounding boxes in BEV. Through the comparison of the area within the red dashed box, our approach significantly reduces the translation error. Though the accuracy of the bounding boxes is obviously improved, the false positive issues are still serious after distillation due to the inherent detects in the 3D object detection model." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.619, + 0.771, + 0.634 + ], + "angle": 0, + "content": "5. Conclusion and Future Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.642, + 0.892, + 0.752 + ], + "angle": 0, + "content": "In this work, we apply knowledge distillation to camera-only 3D object detection, and we reveal that the challenge lies in how to distill focal knowledge when confronted with an imperfect expert. We devise FD3D, a flexible query-based approach that automatically searches the representative regions and highlights these regions for distillation. It serves as a plug-and-play module and successfully applies to various 3D object detectors." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.753, + 0.892, + 0.822 + ], + "angle": 0, + "content": "Limitation and future work. The challenge of distilling knowledge from imperfect experts exists in not only the 3D object detection domain, but also in other fields. The proposed approach is needed to be extended to address more general scenarios." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.867 + ], + "angle": 0, + "content": "Acknowledgements. This work is partially supported by NSFC (62206172, 62222607), and the Shanghai Committee of Science and Technology (21DZ1100100)." + }, + { + "type": "page_number", + "bbox": [ + 0.473, + 0.888, + 0.498, + 0.898 + ], + "angle": 0, + "content": "999" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.125, + 0.173, + 0.139 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.148, + 0.47, + 0.224 + ], + "angle": 0, + "content": "[1] Holger Caesar, Varun Bankiti, Alex H Lang, Sourabh Vora, Venice Erin Liong, Qiang Xu, Anush Krishnan, Yu Pan, Giancarlo Baldan, and Oscar Beijbom. nuscenes: A multimodal dataset for autonomous driving. 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Albeit remarkable performance, these works suffer from low efficiency. Typically, knowledge distillation can be used for model compression. However, due to unclear 3D geometry reasoning, expert features usually contain some noisy and confusing areas. In this work, we investigate on how to distill the knowledge from an imperfect expert. We propose FD3D, a Focal Distiller for 3D object detection. Specifically, a set of queries are leveraged to locate the instance-level areas for masked feature generation, to intensify feature representation ability in these areas. Moreover, these queries search out the representative fine-grained positions for refined distillation. We verify the effectiveness of our method by applying it to two popular detection models, BEVFormer and DETR3D. The results demonstrate that our method achieves improvements of 4.07 and 3.17 points respectively in terms of NDS metric on nuScenes benchmark. Code is hosted at https://github.com/OpenPerceptionX/BEVPerception-Survey-Recipe. + +# 1. Introduction + +Accurate 3D object detection is a vital component in autonomous driving. To achieve this, most methods [14, 37] resort to LiDAR sensors and dominate the public benchmarks [1, 27]. Despite the performance gap, pure vision approaches are still worthy of in-depth inquiry, since cameras can provide rich semantic information and are low-cost and easy-to-deploy. Among these, bird's-eye-view (BEV) detection has drawn extensive attention from both industry and academia, and shown great potential to narrow down the performance gap [15, 21]. However, such models tend to be computationally consuming. + +![](images/ffa8ebad8e6f0ad3b53d396adb21c9762af885b642080874d3afe5f63698f632.jpg) +(a) Global distillation + +![](images/1a6f8b20b938679291d0300b50afa69bb824933b635f1e3a8eb0f25aa7fc12e2.jpg) +Expert Abstraction + +![](images/de867f18a7cbd2b933b6a4bba0e5259fee6f692c28c53545c569c16b59b62db9.jpg) +(c) Generative distillation with random mask +Apprentice Representation +Figure 1. Illustration of the proposed generative and focal distillation method. Compared with others, the proposed manner in 1 (d) leverages queries to generate instance masks for masked generative distillation, rather than random masks in 1 (c). Moreover, the queries meanwhile search for the representative position to perform refined distillation, where the distillation region selection is more fine-grained and flexible than 1 (b). + +![](images/1b040ca24c7bb6988a96e4e3afe8ef39dab5a708b52b89641a4622c12faf50ba.jpg) +(b) Attentive distillation +Query offset +(d) Generative and focal distillation (ours) + +In common practice, knowledge distillation can compress the model and is usually applied to alleviate computation overhead. One possible solution is to utilize the LiDAR-based model as the expert [4, 17], but this requires complex spatial-temporal calibrations and also needs to handle heterogeneous problems from different modalities. An intuitive question is, can we distill these models solely based on camera sensors? In this work, we intend to address this problem and focus on the camera-only distillation setting. To the best of our knowledge, our work is the first solution tailored for this setting. + +Distillation methods in 2D object detection have derived + +![](images/c8d177b72138eeb9d6c9f0b6cbe2105139a4a55e5e84c9b72bb761a425a6de63.jpg) +Figure 2. Visualization of the predicted bounding boxes and bird's eye view feature of BEVFormer [19]. At the center is the autonomous vehicle. In the left subfigure, green and blue boxes denote the ground truth and predictions respectively. In the right subfigure, the BEV feature is ray-shaped and contains a lot of noise. Areas with incorrect high activation appear behind objects due to occlusion, which easily introduces false positives, e.g., the region circled by the ellipse. + +![](images/4dae3c92ea8eb911f23e4a5f69ab73260e8d360576e78141f2f0afd7ca6228b7.jpg) + +various types as depicted in Fig. 1 (a)-(c), but their effectiveness is not verified in 3D object detection. The main challenge in camera-to-camera distillation for 3D object detection comes from the imperfect expert features. Due to the lack of accurate 3D information, expert features drawn from 2D images usually contain some noisy and confusing areas. To better illustrate this point, we visualize the BEV features from BEVFormer [19] in Fig. 2. The unclear occlusion reasoning makes the BEV features suffer from the ray-shape artifacts. The imperfect BEV features result in many false positives. Directly mimicking these features from experts such as Fig. 1 (a) may exacerbate the drawback. Some 2D detection distillation methods [29] propose to focus on foreground-orient regions, as shown in Fig. 1 (b). However, background regions are also important as proved in [7, 35, 13]. We categorize these methods as attentive distillation. Compared with 2D object detection, the imbalance between foreground and background in 3D areas is much more severe. Balancing these weights is not a general solution. The latest study MGD [36] demonstrates the effectiveness of masked image modeling (MIM) distillation as depicted in Fig. 1 (c). However, the global random mask cannot greatly enhance 3D object detection, which is validated in Tab. 4a. + +To this end, we propose a Focal Distiller for 3D object detection, shortened as FD3D. The schematic diagram of FD3D is shown in Fig. 1 (d). Specifically, A set of queries are leveraged to locate the instance-level focal regions, masked generative distillation is performed within the regions. Moreover, these queries dynamically search fine-grained representative positions for focal distillation. Two complementary modules guide the apprentice network to generate enhanced feature representation on focal regions. In summary, our work makes three-fold contributions: + +1. To the best of our knowledge, this is the first work to explore knowledge distillation on the camera-only 3D object detection. We reveal the challenge relies on how to distill focal knowledge from an imperfect 3D object detector expert. +2. We propose FD3D, which utilizes a set of queries to distill focal knowledge. With these queries, coarse-grained focal regions are selected for masked generation, and fine-grained focal regions are searched out for instance-oriented refinement distillation. +3. FD3D serves as a plug-and-play module. It can be easily extended to various detectors. The improvements with 4.07 and 3.17 NDS can be obtained with FD3D assembled in BEVFormer and DETR3D, respectively. + +# 2. Related Work + +Knowledge distillation on 2D object detection. Knowledge distillation is originally proposed by Hinton et al. [9]. It regards teachers' output logits as knowledge and is employed as a model compression approach in the classification task. FitNet [26] extends the knowledge to intermediate features. Recently, many works successfully apply knowledge distillation on object detection [3]. Knowledge distillation on object detection encounters extreme imbalance between positive and negative instances. Global feature imitation [29] such as Fig. 1 (a) brings marginal improvement, and even exacerbates the performance. It is almost a consensus that distillation should not treat all regions equally. Revisiting from the latest works, where to perform distillation is of great concern in distilling object detectors, and they invariably resort to attentive distillation as depicted in Fig. 1 (b). Mimic [16] performs distillation on ROI regions sampled by an RPN network, but this framework can only be applied to a two-stage detector. FIFG [29] claims the distillation should be performed on near-object regions. However, the near-object regions are defined by hand-crafted rules and require manual refinement. GID [6] focuses on regions where there is a significant difference between the student and the teacher outputs. DeFeat [7] separates foreground and background by ground truth and performs distillation independently. GID [6] and DeFeat [7] prove that the informative cues in the background also benefit the student network. FGD [35] designs a more elaborate structure to focus on critical pixels and channels. Albeit the effectiveness of the aforementioned studies, they require manual hyper-parameter tuning to adjust the concentration of distillation. ICD [13] encodes the instance annotations as queries, and attention maps are generated to guide the distillation region concentration. We deem such a query-based approach is more flexible. MGD [36] proposes a simple but + +![](images/d8847ca9288b269f61b06441109b027614043478c1bcc8a5d9cddfef15385139.jpg) +Figure 3. We present FD3D, a Focal Distiller for 3D object detection. The framework aims to transfer the dark knowledge of the focal region from the expert network to the compact apprentice network, where the feature distillation is performed on both perspective view (PV) and bird's-eye-view (BEV). We employ aligned BEV queries. With these queries, the instance masks in PV and BEV are generated, and masked generative distillation is performed within the mask region to enhance the feature representation. Moreover, these queries meanwhile leverage deformable attention mechanism to search out the representative features on focal BEV regions. The representative features are utilized for refined distillation. + +effective distillation paradigm as shown in Fig. 1 (c): the student features are randomly masked and then recovered to mimic teacher features. + +Multi-camera 3D Object Detection. Early studies [22, 30] independently process monocular images from multiple views, and aggregate the results across cameras for postprocessing. FCOS3D [30] extends the popular anchor-free detector FCOS [28] by directly predicting 3D bounding boxes from 2D image features. Recent studies tend to predict object location in 3D space. One branch of researchers converts 2D image features to 3D space through depth estimation. The typical approach is to convert the estimated depth map into pseudo-LiDAR [31]. Lift-Splat-Shoot (LSS) [23] estimates the depth distribution of each image pixel and uses voxel pooling to generate BEV features. Its follow-up studies BEVDet [11], BEVDet4D [10], BEVDepth [18] further explore data augmentation, accelerating voxel pooling module and improving depth estimation accuracy. Another branch of studies indexes 2D image feature to 3D space through the camera extrinsic and intrinsic. Following DETR [2], DETR3D [32] defines a set of 3D object queries and samples 2D image features on the queries' projection points to predict 3D bounding boxes. BEVFormer [19] explicitly defines queries in BEV space, and performs 2D-to-3D transformation with deformable attention to generate the BEV feature for downstream tasks. PolarFormer [12] adopts polar coordinate system for more accurate BEV feature construction. These state-of-the-art models suffer from high computation overhead. It is natu + +ral to consider applying knowledge distillation to compress the model. However, regardless of the view transform approaches, the 2D-to-3D transformation is ill-posed, so the vision-based 3D object detector experts cannot provide a reliable feature for imitation. + +LiDAR-based knowledge distillation. In 3D object detection, there are existing studies covering knowledge distillation under LiDAR [33, 34] and extending to LiDAR-camera cross-modality knowledge transfer. Monodistill [4] projects the LiDAR points to the image plane, aligning two modalities for knowledge transfer. UVTR [17] represents the image and LiDAR in a unified voxel space, and the feature distillation is performed on the query projection points. To exclude the heterogeneous problems from different modalities and focus on the exploration of distillation from an imperfect expect, the extent of this study is set at camera-only distillation. + +# 3. Methodology + +Fig. 3 illustrates the pipeline of our distillation approach. The overall structure of FD3D is presented in Sec. 3.1. The two proposed distillation modules are elaborated in Sec. 3.2 and Sec. 3.3. + +# 3.1. Overall Structure + +The state-of-the-art multi-camera 3D object detection networks suffer from high computation overhead. This shortcoming mainly originates from the heavy network ar + +
MethodBackboneImage ResolutionBEV ResolutionEncoder Layer
BEVFormer -Base* (E)R101900×1600200×2006
BEVFormer -Tiny (A)R50450×800100×1003
BEVFormer -Base (E)R101-DCN†900×1600200×2006
BEVFormer -Small (A)R101-DCN†450×800100×1003
DETR3D -R101 (E)R101-DCN†900×1600--
DETR3D -R50 (A)R50900×1600--
+ +Table 1. The setting of expert- apprentice pairs. The symbol "E" and "A" denote "expert" and "apprentice" respectively. By setting different network depth, input resolution or BEV resolution, we obtain expert- apprentice pairs. * represents this version of BEVFormer-Base apply ResNet101 as backbone rather than ResNet101-DCN, which is different from the original version [19]. † indicates using nuScene pretrained weight with FCOS3D [30]. Unless otherwise specified, the backbone is pretrained on ImageNet only. + +chitecture and high input resolution. By compressing the network depth or input resolution, we obtain more compact networks. However, the lightweight networks inevitably suffer from accuracy attenuation. Therefore, we employ the heavy state-of-the-art model as the expert, adopt the lightweight counterpart as the apprentice, and perform knowledge transfer between them. We freeze the expert network, and leverage the intermediate features of the expert network as auxiliary supervision for the apprentice network. The setting of adopted expert- apprentice pairs is depicted in Tab. 1. Their GLOPS and FPS are presented at Tab. 2. + +As depicted in Fig. 3, a distillation framework between the expert network and the apprentice network is constructed. For the BEV perception model, the distillation is performed on both the perspective view (PV) and BEV features. We set up an extra distillation head and employ a set of aligned BEV queries $Q$ for distillation. The structure of the distillation head is similar to the head of Deformable DETR [39]. Based on the deformable attention mechanism, $N$ queries sample key features from BEV features and generate 3D bounding boxes. The generated 3D bounding boxes are projected into PV and BEV. The projection areas are used for masked generative distillation, and the sampled BEV features in the deformable attention process are adopted for refined distillation. In order to urge the projection areas locate at the foreground area and the sampled BEV features come from the object region, the distillation head is also optimized with auxiliary detection losses. + +The distillation head is built upon the expert BEV features. The distillation queries go through a self-attention + +layer, and then sample expert BEV feature $F^{E}$ to generate $y^{E}$ through a deformable attention (DEFORMATTN) layer and a feed-forward network $(\mathcal{FFN})$ . The latter process is formulated as: + +$$ +y ^ {E} = \mathcal {F F N} (\text {D E F O R M A T T N} (Q, F ^ {E})), \tag {1} +$$ + +where $y^{E} = \{[c_{1}^{E},b_{1}^{E}],[c_{2}^{E},b_{2}^{E}],\ldots ,[c_{N}^{E},b_{N}^{E}]\}$ , and $c_{i}^{E},b_{i}^{E}$ represent classification score and regression bounding box corresponding to $i$ -th distillation query. Based on bipartite matching approach in [2], we search for the optimal permutations $\hat{\sigma}$ and optimize the distillation head by $\mathcal{L}_{dh}$ as follows: + +$$ +\left\{ \begin{array}{l} \hat {\sigma} = \underset {\sigma \in \mathfrak {S} _ {N}} {\arg \min } \sum_ {i} ^ {N} \alpha \mathcal {L} _ {c l s} \left(c _ {\sigma (i)} ^ {E}, c _ {i} ^ {g t}\right) + \beta \mathcal {L} _ {b b o x} \left(b _ {\sigma (i)} ^ {E}, b _ {i} ^ {g t}\right), \\ \mathcal {L} _ {d h} = \sum_ {i} ^ {N} \alpha \mathcal {L} _ {c l s} \left(c _ {\hat {\sigma} (i)} ^ {E}, c _ {i} ^ {g t}\right) + \beta \mathcal {L} _ {b b o x} \left(b _ {\hat {\sigma} (i)} ^ {E}, b _ {i} ^ {g t}\right), \end{array} \right. \tag {2} +$$ + +where $\mathcal{L}_{cls}$ and $\mathcal{L}_{bbox}$ take the same form as FocalLoss [20] and L1 loss respectively, $b^{gt}$ and $c^{gt}$ represent ground truth boxes coordinates and classes, and $\alpha$ as well as $\beta$ balance the loss weight. + +During the optimization process of the distillation head, the queries with a confidence higher than $\rho_{c}$ and GIOU greater than $\rho_{b}$ are filtered out as focal queries, termed as $Q^{f}$ . The number of $Q^{f}$ is denoted as $N_{f}$ . Finally, the generated 3D boxes and sampled BEV features corresponding to the focal queries $Q^{f}$ are selected to perform masked generative distillation and refined distillation. + +# 3.2. Selective Masked Generative Distillation + +The generated 3D boxes by focal queries $Q_{f}$ are projected to PV and BEV. The 3D boxes are projected to PV according to the camera extrinsics and intrinsics, and simply flattened to BEV from the top-down view. The masking process described below is the same for both PV and BEV, so we describe the process without distinction between PV and BEV. + +An instance mask $I_{i}^{fg}$ is generated with the projection area corresponding to one focal query $Q_{i}^{f}$ . The dimension of the instance mask is identical to that of the apprentice feature. If a pixel is inside the bounding box $b_{i}^{E}$ , the value is set to be 0, otherwise its value is set to be 1. The formulation of $I_{i}^{fg}$ is described as follows: + +$$ +I _ {i, u v} ^ {f g} = \left\{ \begin{array}{l l} 0, & \text {i f} (u, v) \text {i n} b _ {i} ^ {E} \\ 1, & \text {O t h e r w i s e} \end{array} . \right. \tag {3} +$$ + +All instance masks are merged together to form the final mask $I^{fg}$ . The process of mask stacking is formulated as follows: + +$$ +I ^ {f g} = I _ {0} ^ {f g} \wedge I _ {1} ^ {f g} \wedge \dots \wedge I _ {N - 1} ^ {f g}. \tag {4} +$$ + +The masked region indicates where the objects reside in, and the masked generation is performed within the masked region. + +The selective mask indicates that the pixels of apprentice feature within $I^{fg}$ are masked by ratio $r$ . A random mask $I^r$ with the same size of $I^{fg}$ is generated: + +$$ +I _ {u v} ^ {r} = \left\{ \begin{array}{l l} 0, & \text {i f} R _ {u, v} < r \\ 1, & \text {O t h e r w i s e} \end{array} , \right. \tag {5} +$$ + +where $R_{u,v}$ is a uniformly random number between 0 and 1. The process of the selective mask is expressed as an OR operation between $I^{fg}$ and $I^r$ : + +$$ +I ^ {m} = I ^ {f g} \vee I ^ {r}. \tag {6} +$$ + +Then the apprentice feature $F^A$ is masked with $I^m$ . The masked apprentice feature is forced to recover with a generator $\mathcal{G}$ : + +$$ +\hat {F} ^ {A} = \mathcal {G} \left(F ^ {A} \cdot I ^ {m}\right). \tag {7} +$$ + +The generator $\mathcal{G}$ here includes two convolutional layers, the first one of which switches to a deconvolutional layer if the dimensions of the apprentice feature and expert feature are not identical. After generating $\hat{F}^A$ , the channel-wise distribution [25] is calculated as follows: + +$$ +\mathcal {L} _ {S M G D} = \frac {\tau^ {2}}{C} \sum_ {c = 1} ^ {C} \sum_ {i = 1} ^ {H \times W} \varphi \left(F _ {c, i} ^ {E}\right) \log \frac {\varphi \left(F _ {c , i} ^ {E}\right)}{\varphi \left(\hat {F} _ {c , i} ^ {A}\right)}, \tag {8} +$$ + +$$ +\varphi \left(F _ {c, i}\right) = \frac {\exp \left(\frac {F _ {c , i}}{\tau}\right)}{\sum_ {i = 1} ^ {H \times W} \exp \left(\frac {F _ {c , i}}{\tau}\right)}, \tag {9} +$$ + +where $\tau$ is the temperature factor of the SoftMax layer, $C$ means the feature channels, and $H$ , $W$ represent feature height and width respectively. + +# 3.3. Query-based Focal Distillation + +Focal distillation denotes the refined distillation focusing on the local feature pattern of focal positions. We aim to leverage a set of queries to automatically search out the representative positions of objects, and perform distillation on the identical positions between expert features and apprentice features. We resort to the deformable attention module to achieve the goal. The deformable attention module generates a set of offsets around a reference point. Based on the offsets to the reference point, the features on the crucial sampling points are sampled for object detection. We exploit this mechanism to conduct a refined distillation on such representative features as illustrated in Fig. 4. + +A set of focal queries $Q^{f}$ are filtered out as described in Sec. 3.1. For each focal query $q \in Q^{f}$ , the reference point $p_{q}$ is generated by the query feature $z_{q}$ with a linear projection $\mathcal{M}\mathcal{LP}$ : + +$$ +p _ {q} = \mathcal {M L P} \left(z _ {q}\right). \tag {10} +$$ + +The reference point $p_q$ represents the projection center of the estimated bounding box on the sampling feature plane. + +![](images/ad8a436a6a171b799e9c7952fe4fabedfaa2b3f4cef7fc17fe2a58e60ce4b0fe.jpg) +Figure 4. Process of query-based offset generation, feature sampling and query parameter update. Leveraging the deformable attention mechanism, the local expert feature and apprentice feature are sampled at the same position, based on the offset generated by the query. In addition, the query parameter is updated with the collected expert feature. + +For each focal query $q$ , $M$ attention heads are attached on $z_{q}$ . Each attention head generates $K$ sampling offsets by another linear projection $\mathcal{MLP}'$ . The offset is computed by the following: + +$$ +\Delta p _ {m q k} = \mathcal {M L P} ^ {\prime} \left(z _ {q}, m, k\right), \tag {11} +$$ + +where $m$ indexes the attention head, and $k$ represents the sampling point. + +The positions searched by the generated offsets are viewed as key representative positions. The query-based focal distillation is conducted on such key representative positions. Let $F_{mqk}^{E}, F_{mqk}^{A}$ represent the sampled features from the identical key positions for expert and apprentice, respectively. They are calculated as follows: + +$$ +F _ {m q k} ^ {E} = F ^ {E} \left(p _ {q} + \Delta p _ {m q k}\right), \tag {12} +$$ + +$$ +F _ {m q k} ^ {A} = F ^ {A} \left(p _ {q} + \Delta p _ {m q k}\right). \tag {13} +$$ + +The sampled expert feature and apprentice feature are normalized to $\widetilde{F}_{mqk}^{T}$ and $\widetilde{F}_{mqk}^{S}$ according to their maximum and minimum. Finally, the L2 loss is computed between the normalized key sampled features: + +$$ +\mathcal {L} _ {Q F D} = \frac {1}{N _ {f}} \sum_ {q \in Q _ {f}} \sum_ {m = 1} ^ {M} \sum_ {k = 1} ^ {K} L _ {2} \left(\widetilde {F} _ {m q k} ^ {A}, \widetilde {F} _ {m q k} ^ {E}\right). \tag {14} +$$ + +Through the loss for the fine-grained local region, the refined distillation on these representative positions is conducted. Query-based focal distillation aims to optimize the local patterns on the instances' representative positions. + +# 3.4. Overall Distillation Loss + +Besides being supervised by ground truth, the intermediate feature of the apprentice detector is also supervised by + +the masked generative distillation loss $\mathcal{L}_{SMGD}$ and query-based focal distillation loss $\mathcal{L}_{QFD}$ . The total knowledge distillation loss is defined as follows: + +$$ +\mathcal {L} _ {K D} = \lambda \mathcal {L} _ {S M G D} + \eta \mathcal {L} _ {Q F D}. \tag {15} +$$ + +$\mathcal{L}_{SMGD}$ is used to optimize the global feature distribution, indicating where should be with high activation. $\mathcal{L}_{QFD}$ is leveraged for optimizing the local feature pattern on searched focal positions. The hyper-parameters $\lambda$ and $\eta$ control the loss weight. + +Note that only the gradients w.r.t. the vanilla detection loss and the distillation loss $\mathcal{L}_{KD}$ back-propagate to the apprentice network. $\mathcal{L}_{dh}$ only optimizes the parameters of the distillation head. + +# 4. Experiments + +# 4.1. Dataset and metrics + +We conduct experiments on nuScenes dataset [1], a large-scale autonomous driving dataset. This dataset contains 700, 150, 150 scenes for training, validation and testing, respectively. Each scene has roughly 20 seconds of duration. The key frame is annotated at $2\mathrm{Hz}$ . + +The two dominant metrics of the nuScenes detection task are nuScenes Detection Score (NDS) and mean Average Precision (mAP). The mAP of nuScenes is computed by the center distance between predictions and annotations on the ground plane. In addition, the nuScenes dataset defines five true positive metrics mATE, mASE, mAOE, mAVE, mAAE for measuring translation, scale, orientation, velocity and attribute, respectively. NDS of nuScenes is a weighted sum of mAP and the five true positive metrics, defined as $NDS = \frac{1}{10} [5mAP + \sum_{mTP}(1 - \min(1, mTP))]$ . + +# 4.2. Implementation Details + +We conduct experiments on BEVFormer [19] and DETR3D [32]. Settings of expert- apprentice pairs are illustrated in Tab. 1. We obtain three groups of expert- apprentice combinations by changing the backbone, input image resolution and BEV grip resolution. ResNet [8] with or without deformable convolution [38] are used for all backbones. When applied to BEV perception model BEVFormer, the selective masked generation is performed on both the PV feature and BEV feature, and query-based focal distillation is performed on the BEV feature, while both selective masked generative distillation and query-based focal distillation are performed on PV feature when it comes to the BEV-free perception model DETR3D. We also conduct the experiment on BEVDepth in supplementary materials. + +The codebase is developed upon MMDetection3D [5]. All models are trained on 8 NVIDIA A100 GPUs. For BEVFormer and DETR3D, the models are trained for 24 epochs with an initial learning rate of 2e-4 and per-GPU + +batch size of 1. No data augmentation is introduced when training BEVFormer and DETR3D. Feature pyramid position shift [24] is adopted for PV feature alignment between low-resolution apprentice and high-resolution expert. The hyperparameters $r$ , $\tau$ , $\alpha$ , $\beta$ , $\lambda$ , $\eta$ are set to be 0.5, 2.0, 2.0, 0.25, 0.25 and 0.001, respectively. + +# 4.3. Comparison to State-of-the-arts + +As depicted in Tab. 2, the proposed distillation method brings significant improvement on BEVFormer-Tiny, BEVFormer-Small and DETR3D by 4.07, 2.47 and 3.17 NDS, respectively. The gain comes mainly from the improved mAP and velocity estimation accuracy. The devised method brings 4.13 points to BEVFormer-Tiny and 3.08 points to BEVFormer-Small in terms of mAP, which demonstrates the enhancement of localization and classification. The proposed approach also achieves improvements of 4.97 points to BEVFormer-Tiny and 8.21 points to DETR3D-R50 in terms of mAVE. In regard to the classic distillation methods on the 2D field, regardless of BEVFormer-Tiny or DETR3D-R50, FitNet obtains marginal improvement, yet CWD achieves larger gains. MGD with the global random mask cannot outperform CWD, indicating that random masked generative distillation in 3D detection scenes is not as powerful as that in 2D scenes. The proposed FD3D outperforms all classic distillation methods on the 2D field by an obvious margin. The comparison reveals that the devised fine-grained distillation on focal regions truly improves the distillation quality. In the supplementary materials, we conduct further experiments to validate the efficacy of FD3D on another BEV perception model BEVDepth. It can be observed that FD3D leads to improved performance on BEVDepth. These findings demonstrate the generalizability of the proposed distillation method across various 3D object detectors. Moreover, we also present the gains achieved by FD3D on the nuScenes test set, which are consistent with the effects observed on the nuScenes val set. + +# 4.4. Ablative Study + +Contribution of each module. For a better understanding of the contribution of each proposed module to the distillation performance, we test each component independently on group BEVFormer Base-Tiny and report the corresponding accuracy in Tab. 3. The channel-wise distribution (CWD) is adopted as a baseline distillation method and obtains 41.80 NDS. When compared to this baseline, the selective masked generation can achieve an additional 1.07 NDS improvement, revealing that such technique can enhance feature learning on focal regions. Query-based focal distillation yields an extra 0.95 NDS gain over the baseline, thereby highlighting the significance of the refined distillation on the fine-grained position. With the two proposed + +
MethodNDS↑mAP↑mATE↓mASE↓mAOE↓mAVE↓mAAE↓GFLOPs↓FPS↑
BEVFormer-Base* (E)47.3736.4473.5128.1444.9842.3819.501845.362.0
BEVFormer-Tiny (A)39.0226.8783.4329.4859.7350.0321.49
+ FitNet [26]40.5728.2681.5228.9652.9651.3220.84
+ CWD [25]41.8029.7980.8128.5550.6349.8721.21381.957.3
+ MGD [36]41.3329.0880.1928.8352.8350.0020.19
+ FD3D (Ours)43.09 (↑4.07)31.00 (↑4.13)79.3128.0050.7745.0620.97
BEVFormer-Base (E)51.7441.6467.2627.3437.0439.4119.741323.411.8
BEVFormer-Small (A)46.2634.5674.2728.0044.5343.9819.41416.465.9
+ FD3D (Ours)48.73 (↑2.47)37.64 (↑3.08)71.9427.5040.8939.4121.16
DETR3D-R101 (E)42.534.677.326.838.384.221.61016.832.5
DETR3D-R50 (A)35.7828.8585.3927.9054.0995.1523.95
+ FitNet [26]36.1929.7683.9028.0056.1894.5324.33
+ CWD [25]37.2230.1382.7427.6549.4094.6523.98876.944.0
+ MGD [36]37.0329.8983.3527.7953.2892.7421.98
+ FD3D (Ours)38.95 (↑3.17)31.33 (↑2.48)82.3227.6548.4086.9421.87
+ +Table 2. 3D object detection improvement on nuScenes val set. The results demonstrate that the proposed distillation method benefits various 3D object detectors and surpasses the classic 2D distillation methods. We also show their efficiency metrics with GFLOPs and FPS. The FPS is measured on RTX 2080TI. + +
ComponentNDSmAP
CWDSMGDQFD
BEVFormer Base-Tiny✓39.0226.87
41.8029.79
✓42.8730.59
✓42.7530.47
✓✓43.0931.00
+ +Table 3. Contribution by each component. SMGD and QFD are the proposed two novel modules. SMGD represents selective masked generative distillation, and QFD indicates query-based focal distillation. Channel-wise distribution (CWD) is applied as the baseline distillation method for comparison. + +modules applied in conjunction, there is an observed increase in performance of 1.29 NDS, providing evidence of their efficacy and compatibility. + +Mask region selection. As shown in Tab. 4a, variation in the impact of masked generative distillation across different regions is substantial. Global random mask leads to worsened results. Mask on foreground regions defined by the ground truth yields significant gains. Furthermore, applying masks to the predicted focal regions, as defined by focal queries, results in further improvement. This is probably attributed to the selection of focal queries, which effectively filter out regions with high confidence while excluding challenging-to-discriminate regions. + +Distillation region. The terms "global distribution" and "local pattern" refer to two distillation mode focusing on the global overall activation and the local feature representation, respectively. And their performances are evaluated in Tab. 4b. The results demonstrate that distilling with global distribution alone already yields improvement, and when + +focusing on the local pattern of focal regions, a slightly higher gain is observed. The best performance is achieved through the combined optimization of them. + +Distillation stage. The view transform module takes PV features as input and generates BEV features. PV features and BEV features are from different stages of the network. We explore the difference when global distillation (Fig. 1 (a)) is performed at different stages. The channel-wise distribution (CWD) is adopted in this ablation study. As shown in Tab. 4c, separate distillation on PV features obtains an improvement while separate distillation on BEV features leads to a deterioration in performance. This is due to the BEV feature containing a lot of shadow-like artifacts due to the unclear occlusion. This result demonstrates the necessity of selective distillation under BEV feature. + +Feature alignment approach. When the BEV resolution differs between expert and apprentice, the BEV feature alignment is needed. There are two choices for alignment: upsampling the apprentice feature through a deconvolutional layer or directly downsampling the expert feature. We compare the two alignment approaches in Tab. 4d. Downsampling expert feature provokes inferior results than upsampling apprentice feature. This is potentially caused by the fatal information loss of the expert feature. + +# 4.5. Visualization + +The feature representation and prediction of the apprentice network BEVFormer-tiny with or without our proposed method are presented in Fig. 5. For PV, the feature activations from the first FPN layer in front left view, front right view and back left are displayed. The activation of many background regions is high without distillation, making the foreground and background indistinguishable. With + +
GroupDistillation RegionNDSmAP
BEVFormer Base-Tinydirectly imitation41.8029.79
global random mask41.1428.49
mask on GT42.4129.85
selective focal mask42.8730.59
DETR3D R101-R50directly imitation37.2230.13
global random mask37.1930.03
mask on GT37.5830.11
selective focal mask37.9129.87
+ +(a) Mask region selection. Global random masked generation exacerbates the performance, while the selective masked generation on focal regions brings a remarkable improvement. + +
GroupDistillation StageNDSmAP
PVBEV
BEVFormer✓46.2634.56
Base-Small✓47.0635.52
45.2433.56
✓✓47.6035.97
+ +(c) Distillation stage. Effect of global channel-wise distribution distillation (Fig. 1 (a)) on PV or BEV. The result indicates that combined distillation on PV and BEV achieves the highest improvement. Note that separate global distillation on BEV feature leads to a deterioration in performance. + +
GroupDistillation RegionNDSmAP
BEVFormer Base-Tinyglobal distribution41.8029.79
local pattern41.9129.89
global distribution + local pattern42.6830.30
DETR3D R101-R50global distribution37.4330.41
local pattern38.0030.21
global distribution + local pattern38.7230.57
+ +(b) Distillation region. Global distribution means the channel-wise distribution of feature activation, and local pattern represents the feature values on the fine-grained focal regions. Distillation on both global distribution and local patterns achieves the best performance. + +
GroupFeature AlignmentNDSmAP
BEVFormerdownsample47.4736.66
Base-Smalldeconvolution48.7337.50
+ +(d) Feature alignment. Downsampling expert feature gets significantly worse results than upsampling apprentice feature through a deconvolutional layer. + +Table 4. FD3D ablations on nuScenes val set. We show nuScenes detection score (NDS) and mean average precision (mAP) metrics (%). Default settings are marked in gray. + +![](images/6b1c2f6c51205dd3296107cb34e84c6ed62017585c8ec741b5d896116e629d41.jpg) +Figure 5. Visualization of feature activation and the predicted results before and after knowledge distillation. In comparison with the feature activation on PV, the foreground and background become clearly distinguishable with distillation. The predictions are illustrated on BEV, where green and blue boxes denote the ground truth and predictions respectively. With the devised method, the prediction accuracy of detection boxes is significantly improved. + +the proposed approach, they become clearly distinguishable. The PV feature visualization confirms that the distillation makes the backbone of the apprentice network well + +optimized. High-quality 2D image feature extraction is the basis for BEV feature production and subsequent detection. In addition, we give a comparison of predicted bounding boxes in BEV. Through the comparison of the area within the red dashed box, our approach significantly reduces the translation error. Though the accuracy of the bounding boxes is obviously improved, the false positive issues are still serious after distillation due to the inherent detects in the 3D object detection model. + +# 5. Conclusion and Future Work + +In this work, we apply knowledge distillation to camera-only 3D object detection, and we reveal that the challenge lies in how to distill focal knowledge when confronted with an imperfect expert. We devise FD3D, a flexible query-based approach that automatically searches the representative regions and highlights these regions for distillation. It serves as a plug-and-play module and successfully applies to various 3D object detectors. + +Limitation and future work. The challenge of distilling knowledge from imperfect experts exists in not only the 3D object detection domain, but also in other fields. The proposed approach is needed to be extended to address more general scenarios. + +Acknowledgements. This work is partially supported by NSFC (62206172, 62222607), and the Shanghai Committee of Science and Technology (21DZ1100100). + +# References + +[1] Holger Caesar, Varun Bankiti, Alex H Lang, Sourabh Vora, Venice Erin Liong, Qiang Xu, Anush Krishnan, Yu Pan, Giancarlo Baldan, and Oscar Beijbom. nuscenes: A multimodal dataset for autonomous driving. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 11621-11631, 2020. 1, 6 +[2] Nicolas Carion, Francisco Massa, Gabriel Synnaeve, Nicolas Usunier, Alexander Kirillov, and Sergey Zagoruyko. End-to-end object detection with transformers. 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Albeit remarkable performance, these works suffer from low efficiency. Typically, knowledge distillation can be used for model compression. However, due to unclear 3D geometry reasoning, expert features usually contain some noisy and confusing areas. In this work, we investigate on how to distill the knowledge from an imperfect expert. We propose FD3D, a Focal Distiller for 3D object detection. Specifically, a set of queries are leveraged to locate the instance-level areas for masked feature generation, to intensify feature representation ability in these areas. Moreover, these queries search out the representative fine-grained positions for refined distillation. We verify the effectiveness of our method by applying it to two popular detection models, BEVFormer and DETR3D. The results demonstrate that our method achieves improvements of 4.07 and 3.17 points respectively in terms of NDS metric on nuScenes benchmark. Code is hosted at https://github.com/OpenPerceptionX/BEVPerception-Survey-Recipe." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 560, + 124, + 572 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 560, + 124, + 572 + ], + "spans": [ + { + "bbox": [ + 47, + 560, + 124, + 572 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 45, + 580, + 279, + 710 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 580, + 279, + 710 + ], + "spans": [ + { + "bbox": [ + 45, + 580, + 279, + 710 + ], + "type": "text", + "content": "Accurate 3D object detection is a vital component in autonomous driving. To achieve this, most methods [14, 37] resort to LiDAR sensors and dominate the public benchmarks [1, 27]. Despite the performance gap, pure vision approaches are still worthy of in-depth inquiry, since cameras can provide rich semantic information and are low-cost and easy-to-deploy. Among these, bird's-eye-view (BEV) detection has drawn extensive attention from both industry and academia, and shown great potential to narrow down the performance gap [15, 21]. However, such models tend to be computationally consuming." + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 323, + 273, + 392, + 341 + ], + "blocks": [ + { + "bbox": [ + 323, + 273, + 392, + 341 + ], + "lines": [ + { + "bbox": [ + 323, + 273, + 392, + 341 + ], + "spans": [ + { + "bbox": [ + 323, + 273, + 392, + 341 + ], + "type": "image", + "image_path": "ffa8ebad8e6f0ad3b53d396adb21c9762af885b642080874d3afe5f63698f632.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 345, + 383, + 355 + ], + "lines": [ + { + "bbox": [ + 306, + 345, + 383, + 355 + ], + "spans": [ + { + "bbox": [ + 306, + 345, + 383, + 355 + ], + "type": "text", + "content": "(a) Global distillation" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 455, + 266, + 524, + 340 + ], + "blocks": [ + { + "bbox": [ + 404, + 320, + 437, + 339 + ], + "lines": [ + { + "bbox": [ + 404, + 320, + 437, + 339 + ], + "spans": [ + { + "bbox": [ + 404, + 320, + 437, + 339 + ], + "type": "text", + "content": "Expert Abstraction" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 455, + 266, + 524, + 340 + ], + "lines": [ + { + "bbox": [ + 455, + 266, + 524, + 340 + ], + "spans": [ + { + "bbox": [ + 455, + 266, + 524, + 340 + ], + "type": "image", + "image_path": "1a6f8b20b938679291d0300b50afa69bb824933b635f1e3a8eb0f25aa7fc12e2.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 320, + 359, + 389, + 454 + ], + "blocks": [ + { + "bbox": [ + 320, + 359, + 389, + 454 + ], + "lines": [ + { + "bbox": [ + 320, + 359, + 389, + 454 + ], + "spans": [ + { + "bbox": [ + 320, + 359, + 389, + 454 + ], + "type": "image", + "image_path": "de867f18a7cbd2b933b6a4bba0e5259fee6f692c28c53545c569c16b59b62db9.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 464, + 396, + 484 + ], + "lines": [ + { + "bbox": [ + 305, + 464, + 396, + 484 + ], + "spans": [ + { + "bbox": [ + 305, + 464, + 396, + 484 + ], + "type": "text", + "content": "(c) Generative distillation with random mask" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 397, + 371, + 440, + 389 + ], + "lines": [ + { + "bbox": [ + 397, + 371, + 440, + 389 + ], + "spans": [ + { + "bbox": [ + 397, + 371, + 440, + 389 + ], + "type": "text", + "content": "Apprentice Representation" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 296, + 495, + 531, + 571 + ], + "lines": [ + { + "bbox": [ + 296, + 495, + 531, + 571 + ], + "spans": [ + { + "bbox": [ + 296, + 495, + 531, + 571 + ], + "type": "text", + "content": "Figure 1. Illustration of the proposed generative and focal distillation method. Compared with others, the proposed manner in 1 (d) leverages queries to generate instance masks for masked generative distillation, rather than random masks in 1 (c). Moreover, the queries meanwhile search for the representative position to perform refined distillation, where the distillation region selection is more fine-grained and flexible than 1 (b)." + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 457, + 359, + 525, + 454 + ], + "blocks": [ + { + "bbox": [ + 442, + 345, + 528, + 355 + ], + "lines": [ + { + "bbox": [ + 442, + 345, + 528, + 355 + ], + "spans": [ + { + "bbox": [ + 442, + 345, + 528, + 355 + ], + "type": "text", + "content": "(b) Attentive distillation" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 457, + 359, + 525, + 454 + ], + "lines": [ + { + "bbox": [ + 457, + 359, + 525, + 454 + ], + "spans": [ + { + "bbox": [ + 457, + 359, + 525, + 454 + ], + "type": "image", + "image_path": "1b040ca24c7bb6988a96e4e3afe8ef39dab5a708b52b89641a4622c12faf50ba.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 473, + 454, + 508, + 463 + ], + "lines": [ + { + "bbox": [ + 473, + 454, + 508, + 463 + ], + "spans": [ + { + "bbox": [ + 473, + 454, + 508, + 463 + ], + "type": "text", + "content": "Query offset" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 446, + 464, + 534, + 485 + ], + "lines": [ + { + "bbox": [ + 446, + 464, + 534, + 485 + ], + "spans": [ + { + "bbox": [ + 446, + 464, + 534, + 485 + ], + "type": "text", + "content": "(d) Generative and focal distillation (ours)" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + } + ], + "index": 20 + }, + { + "bbox": [ + 296, + 586, + 530, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 586, + 530, + 715 + ], + "spans": [ + { + "bbox": [ + 296, + 586, + 530, + 715 + ], + "type": "text", + "content": "In common practice, knowledge distillation can compress the model and is usually applied to alleviate computation overhead. One possible solution is to utilize the LiDAR-based model as the expert [4, 17], but this requires complex spatial-temporal calibrations and also needs to handle heterogeneous problems from different modalities. An intuitive question is, can we distill these models solely based on camera sensors? In this work, we intend to address this problem and focus on the camera-only distillation setting. To the best of our knowledge, our work is the first solution tailored for this setting." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 309, + 718, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 718, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 309, + 718, + 530, + 730 + ], + "type": "text", + "content": "Distillation methods in 2D object detection have derived" + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 77, + 42, + 119, + 71 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 42, + 119, + 71 + ], + "spans": [ + { + "bbox": [ + 77, + 42, + 119, + 71 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 150, + 41, + 471, + 74 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 150, + 41, + 471, + 74 + ], + "spans": [ + { + "bbox": [ + 150, + 41, + 471, + 74 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 57, + 719, + 247, + 730 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 719, + 247, + 730 + ], + "spans": [ + { + "bbox": [ + 57, + 719, + 247, + 730 + ], + "type": "text", + "content": "*Corresponding author at lihongyang@pjlab.org.cn" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 281, + 747, + 296, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 281, + 747, + 296, + 756 + ], + "spans": [ + { + "bbox": [ + 281, + 747, + 296, + 756 + ], + "type": "text", + "content": "992" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 67, + 103, + 136, + 204 + ], + "blocks": [ + { + "bbox": [ + 67, + 103, + 136, + 204 + ], + "lines": [ + { + "bbox": [ + 67, + 103, + 136, + 204 + ], + "spans": [ + { + "bbox": [ + 67, + 103, + 136, + 204 + ], + "type": "image", + "image_path": "c8d177b72138eeb9d6c9f0b6cbe2105139a4a55e5e84c9b72bb761a425a6de63.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 211, + 281, + 298 + ], + "lines": [ + { + "bbox": [ + 45, + 211, + 281, + 298 + ], + "spans": [ + { + "bbox": [ + 45, + 211, + 281, + 298 + ], + "type": "text", + "content": "Figure 2. Visualization of the predicted bounding boxes and bird's eye view feature of BEVFormer [19]. At the center is the autonomous vehicle. In the left subfigure, green and blue boxes denote the ground truth and predictions respectively. In the right subfigure, the BEV feature is ray-shaped and contains a lot of noise. Areas with incorrect high activation appear behind objects due to occlusion, which easily introduces false positives, e.g., the region circled by the ellipse." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 158, + 103, + 260, + 204 + ], + "blocks": [ + { + "bbox": [ + 158, + 103, + 260, + 204 + ], + "lines": [ + { + "bbox": [ + 158, + 103, + 260, + 204 + ], + "spans": [ + { + "bbox": [ + 158, + 103, + 260, + 204 + ], + "type": "image", + "image_path": "4dae3c92ea8eb911f23e4a5f69ab73260e8d360576e78141f2f0afd7ca6228b7.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 321, + 279, + 600 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 321, + 279, + 600 + ], + "spans": [ + { + "bbox": [ + 45, + 321, + 279, + 600 + ], + "type": "text", + "content": "various types as depicted in Fig. 1 (a)-(c), but their effectiveness is not verified in 3D object detection. The main challenge in camera-to-camera distillation for 3D object detection comes from the imperfect expert features. Due to the lack of accurate 3D information, expert features drawn from 2D images usually contain some noisy and confusing areas. To better illustrate this point, we visualize the BEV features from BEVFormer [19] in Fig. 2. The unclear occlusion reasoning makes the BEV features suffer from the ray-shape artifacts. The imperfect BEV features result in many false positives. Directly mimicking these features from experts such as Fig. 1 (a) may exacerbate the drawback. Some 2D detection distillation methods [29] propose to focus on foreground-orient regions, as shown in Fig. 1 (b). However, background regions are also important as proved in [7, 35, 13]. We categorize these methods as attentive distillation. Compared with 2D object detection, the imbalance between foreground and background in 3D areas is much more severe. Balancing these weights is not a general solution. The latest study MGD [36] demonstrates the effectiveness of masked image modeling (MIM) distillation as depicted in Fig. 1 (c). However, the global random mask cannot greatly enhance 3D object detection, which is validated in Tab. 4a." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 601, + 279, + 729 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 601, + 279, + 729 + ], + "spans": [ + { + "bbox": [ + 45, + 601, + 279, + 729 + ], + "type": "text", + "content": "To this end, we propose a Focal Distiller for 3D object detection, shortened as FD3D. The schematic diagram of FD3D is shown in Fig. 1 (d). Specifically, A set of queries are leveraged to locate the instance-level focal regions, masked generative distillation is performed within the regions. Moreover, these queries dynamically search fine-grained representative positions for focal distillation. Two complementary modules guide the apprentice network to generate enhanced feature representation on focal regions. In summary, our work makes three-fold contributions:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 106, + 530, + 288 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 305, + 106, + 530, + 165 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 106, + 530, + 165 + ], + "spans": [ + { + "bbox": [ + 305, + 106, + 530, + 165 + ], + "type": "text", + "content": "1. To the best of our knowledge, this is the first work to explore knowledge distillation on the camera-only 3D object detection. We reveal the challenge relies on how to distill focal knowledge from an imperfect 3D object detector expert." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 174, + 530, + 231 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 174, + 530, + 231 + ], + "spans": [ + { + "bbox": [ + 304, + 174, + 530, + 231 + ], + "type": "text", + "content": "2. We propose FD3D, which utilizes a set of queries to distill focal knowledge. With these queries, coarse-grained focal regions are selected for masked generation, and fine-grained focal regions are searched out for instance-oriented refinement distillation." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 241, + 530, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 241, + 530, + 288 + ], + "spans": [ + { + "bbox": [ + 304, + 241, + 530, + 288 + ], + "type": "text", + "content": "3. FD3D serves as a plug-and-play module. It can be easily extended to various detectors. The improvements with 4.07 and 3.17 NDS can be obtained with FD3D assembled in BEVFormer and DETR3D, respectively." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 297, + 310, + 381, + 323 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 310, + 381, + 323 + ], + "spans": [ + { + "bbox": [ + 297, + 310, + 381, + 323 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 296, + 334, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 334, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 334, + 530, + 730 + ], + "type": "text", + "content": "Knowledge distillation on 2D object detection. Knowledge distillation is originally proposed by Hinton et al. [9]. It regards teachers' output logits as knowledge and is employed as a model compression approach in the classification task. FitNet [26] extends the knowledge to intermediate features. Recently, many works successfully apply knowledge distillation on object detection [3]. Knowledge distillation on object detection encounters extreme imbalance between positive and negative instances. Global feature imitation [29] such as Fig. 1 (a) brings marginal improvement, and even exacerbates the performance. It is almost a consensus that distillation should not treat all regions equally. Revisiting from the latest works, where to perform distillation is of great concern in distilling object detectors, and they invariably resort to attentive distillation as depicted in Fig. 1 (b). Mimic [16] performs distillation on ROI regions sampled by an RPN network, but this framework can only be applied to a two-stage detector. FIFG [29] claims the distillation should be performed on near-object regions. However, the near-object regions are defined by hand-crafted rules and require manual refinement. GID [6] focuses on regions where there is a significant difference between the student and the teacher outputs. DeFeat [7] separates foreground and background by ground truth and performs distillation independently. GID [6] and DeFeat [7] prove that the informative cues in the background also benefit the student network. FGD [35] designs a more elaborate structure to focus on critical pixels and channels. Albeit the effectiveness of the aforementioned studies, they require manual hyper-parameter tuning to adjust the concentration of distillation. ICD [13] encodes the instance annotations as queries, and attention maps are generated to guide the distillation region concentration. We deem such a query-based approach is more flexible. MGD [36] proposes a simple but" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 281, + 747, + 296, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 281, + 747, + 296, + 756 + ], + "spans": [ + { + "bbox": [ + 281, + 747, + 296, + 756 + ], + "type": "text", + "content": "993" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 92, + 106, + 483, + 299 + ], + "blocks": [ + { + "bbox": [ + 92, + 106, + 483, + 299 + ], + "lines": [ + { + "bbox": [ + 92, + 106, + 483, + 299 + ], + "spans": [ + { + "bbox": [ + 92, + 106, + 483, + 299 + ], + "type": "image", + "image_path": "d8847ca9288b269f61b06441109b027614043478c1bcc8a5d9cddfef15385139.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 303, + 532, + 367 + ], + "lines": [ + { + "bbox": [ + 45, + 303, + 532, + 367 + ], + "spans": [ + { + "bbox": [ + 45, + 303, + 532, + 367 + ], + "type": "text", + "content": "Figure 3. We present FD3D, a Focal Distiller for 3D object detection. The framework aims to transfer the dark knowledge of the focal region from the expert network to the compact apprentice network, where the feature distillation is performed on both perspective view (PV) and bird's-eye-view (BEV). We employ aligned BEV queries. With these queries, the instance masks in PV and BEV are generated, and masked generative distillation is performed within the mask region to enhance the feature representation. Moreover, these queries meanwhile leverage deformable attention mechanism to search out the representative features on focal BEV regions. The representative features are utilized for refined distillation." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 387, + 280, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 387, + 280, + 422 + ], + "spans": [ + { + "bbox": [ + 45, + 387, + 280, + 422 + ], + "type": "text", + "content": "effective distillation paradigm as shown in Fig. 1 (c): the student features are randomly masked and then recovered to mimic teacher features." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 427, + 281, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 427, + 281, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 427, + 281, + 730 + ], + "type": "text", + "content": "Multi-camera 3D Object Detection. Early studies [22, 30] independently process monocular images from multiple views, and aggregate the results across cameras for postprocessing. FCOS3D [30] extends the popular anchor-free detector FCOS [28] by directly predicting 3D bounding boxes from 2D image features. Recent studies tend to predict object location in 3D space. One branch of researchers converts 2D image features to 3D space through depth estimation. The typical approach is to convert the estimated depth map into pseudo-LiDAR [31]. Lift-Splat-Shoot (LSS) [23] estimates the depth distribution of each image pixel and uses voxel pooling to generate BEV features. Its follow-up studies BEVDet [11], BEVDet4D [10], BEVDepth [18] further explore data augmentation, accelerating voxel pooling module and improving depth estimation accuracy. Another branch of studies indexes 2D image feature to 3D space through the camera extrinsic and intrinsic. Following DETR [2], DETR3D [32] defines a set of 3D object queries and samples 2D image features on the queries' projection points to predict 3D bounding boxes. BEVFormer [19] explicitly defines queries in BEV space, and performs 2D-to-3D transformation with deformable attention to generate the BEV feature for downstream tasks. PolarFormer [12] adopts polar coordinate system for more accurate BEV feature construction. These state-of-the-art models suffer from high computation overhead. It is natu" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 296, + 387, + 530, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 387, + 530, + 445 + ], + "spans": [ + { + "bbox": [ + 296, + 387, + 530, + 445 + ], + "type": "text", + "content": "ral to consider applying knowledge distillation to compress the model. However, regardless of the view transform approaches, the 2D-to-3D transformation is ill-posed, so the vision-based 3D object detector experts cannot provide a reliable feature for imitation." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 296, + 449, + 531, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 449, + 531, + 589 + ], + "spans": [ + { + "bbox": [ + 296, + 449, + 531, + 589 + ], + "type": "text", + "content": "LiDAR-based knowledge distillation. In 3D object detection, there are existing studies covering knowledge distillation under LiDAR [33, 34] and extending to LiDAR-camera cross-modality knowledge transfer. Monodistill [4] projects the LiDAR points to the image plane, aligning two modalities for knowledge transfer. UVTR [17] represents the image and LiDAR in a unified voxel space, and the feature distillation is performed on the query projection points. To exclude the heterogeneous problems from different modalities and focus on the exploration of distillation from an imperfect expect, the extent of this study is set at camera-only distillation." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 297, + 601, + 379, + 615 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 601, + 379, + 615 + ], + "spans": [ + { + "bbox": [ + 297, + 601, + 379, + 615 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 296, + 620, + 530, + 667 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 620, + 530, + 667 + ], + "spans": [ + { + "bbox": [ + 296, + 620, + 530, + 667 + ], + "type": "text", + "content": "Fig. 3 illustrates the pipeline of our distillation approach. The overall structure of FD3D is presented in Sec. 3.1. The two proposed distillation modules are elaborated in Sec. 3.2 and Sec. 3.3." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 297, + 676, + 400, + 688 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 676, + 400, + 688 + ], + "spans": [ + { + "bbox": [ + 297, + 676, + 400, + 688 + ], + "type": "text", + "content": "3.1. Overall Structure" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 296, + 694, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 694, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 694, + 530, + 730 + ], + "type": "text", + "content": "The state-of-the-art multi-camera 3D object detection networks suffer from high computation overhead. This shortcoming mainly originates from the heavy network ar" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 281, + 747, + 296, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 281, + 747, + 296, + 756 + ], + "spans": [ + { + "bbox": [ + 281, + 747, + 296, + 756 + ], + "type": "text", + "content": "994" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 104, + 279, + 255 + ], + "blocks": [ + { + "bbox": [ + 47, + 104, + 279, + 255 + ], + "lines": [ + { + "bbox": [ + 47, + 104, + 279, + 255 + ], + "spans": [ + { + "bbox": [ + 47, + 104, + 279, + 255 + ], + "type": "table", + "html": "
MethodBackboneImage ResolutionBEV ResolutionEncoder Layer
BEVFormer -Base* (E)R101900×1600200×2006
BEVFormer -Tiny (A)R50450×800100×1003
BEVFormer -Base (E)R101-DCN†900×1600200×2006
BEVFormer -Small (A)R101-DCN†450×800100×1003
DETR3D -R101 (E)R101-DCN†900×1600--
DETR3D -R50 (A)R50900×1600--
", + "image_path": "c9c829379fe5df1335c9d9ebd5716140b9759ed4af740c8449b8ecabe17a8d42.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 263, + 279, + 361 + ], + "lines": [ + { + "bbox": [ + 45, + 263, + 279, + 361 + ], + "spans": [ + { + "bbox": [ + 45, + 263, + 279, + 361 + ], + "type": "text", + "content": "Table 1. The setting of expert- apprentice pairs. The symbol \"E\" and \"A\" denote \"expert\" and \"apprentice\" respectively. By setting different network depth, input resolution or BEV resolution, we obtain expert- apprentice pairs. * represents this version of BEVFormer-Base apply ResNet101 as backbone rather than ResNet101-DCN, which is different from the original version [19]. † indicates using nuScene pretrained weight with FCOS3D [30]. Unless otherwise specified, the backbone is pretrained on ImageNet only." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 45, + 378, + 279, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 378, + 279, + 506 + ], + "spans": [ + { + "bbox": [ + 45, + 378, + 279, + 506 + ], + "type": "text", + "content": "chitecture and high input resolution. By compressing the network depth or input resolution, we obtain more compact networks. However, the lightweight networks inevitably suffer from accuracy attenuation. Therefore, we employ the heavy state-of-the-art model as the expert, adopt the lightweight counterpart as the apprentice, and perform knowledge transfer between them. We freeze the expert network, and leverage the intermediate features of the expert network as auxiliary supervision for the apprentice network. The setting of adopted expert- apprentice pairs is depicted in Tab. 1. Their GLOPS and FPS are presented at Tab. 2." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 506, + 279, + 704 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 506, + 279, + 704 + ], + "spans": [ + { + "bbox": [ + 45, + 506, + 279, + 704 + ], + "type": "text", + "content": "As depicted in Fig. 3, a distillation framework between the expert network and the apprentice network is constructed. For the BEV perception model, the distillation is performed on both the perspective view (PV) and BEV features. We set up an extra distillation head and employ a set of aligned BEV queries " + }, + { + "bbox": [ + 45, + 506, + 279, + 704 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 45, + 506, + 279, + 704 + ], + "type": "text", + "content": " for distillation. The structure of the distillation head is similar to the head of Deformable DETR [39]. Based on the deformable attention mechanism, " + }, + { + "bbox": [ + 45, + 506, + 279, + 704 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 45, + 506, + 279, + 704 + ], + "type": "text", + "content": " queries sample key features from BEV features and generate 3D bounding boxes. The generated 3D bounding boxes are projected into PV and BEV. The projection areas are used for masked generative distillation, and the sampled BEV features in the deformable attention process are adopted for refined distillation. In order to urge the projection areas locate at the foreground area and the sampled BEV features come from the object region, the distillation head is also optimized with auxiliary detection losses." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 706, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 706, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 706, + 279, + 730 + ], + "type": "text", + "content": "The distillation head is built upon the expert BEV features. The distillation queries go through a self-attention" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 296, + 106, + 530, + 151 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 106, + 530, + 151 + ], + "spans": [ + { + "bbox": [ + 296, + 106, + 530, + 151 + ], + "type": "text", + "content": "layer, and then sample expert BEV feature " + }, + { + "bbox": [ + 296, + 106, + 530, + 151 + ], + "type": "inline_equation", + "content": "F^{E}" + }, + { + "bbox": [ + 296, + 106, + 530, + 151 + ], + "type": "text", + "content": " to generate " + }, + { + "bbox": [ + 296, + 106, + 530, + 151 + ], + "type": "inline_equation", + "content": "y^{E}" + }, + { + "bbox": [ + 296, + 106, + 530, + 151 + ], + "type": "text", + "content": " through a deformable attention (DEFORMATTN) layer and a feed-forward network " + }, + { + "bbox": [ + 296, + 106, + 530, + 151 + ], + "type": "inline_equation", + "content": "(\\mathcal{FFN})" + }, + { + "bbox": [ + 296, + 106, + 530, + 151 + ], + "type": "text", + "content": ". The latter process is formulated as:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 334, + 162, + 530, + 176 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 334, + 162, + 530, + 176 + ], + "spans": [ + { + "bbox": [ + 334, + 162, + 530, + 176 + ], + "type": "interline_equation", + "content": "y ^ {E} = \\mathcal {F F N} (\\text {D E F O R M A T T N} (Q, F ^ {E})), \\tag {1}", + "image_path": "86546edc195b6181ce8181f675c42213ea1b5706a903eddf85447be7c8956104.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 296, + 178, + 530, + 248 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 178, + 530, + 248 + ], + "spans": [ + { + "bbox": [ + 296, + 178, + 530, + 248 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 296, + 178, + 530, + 248 + ], + "type": "inline_equation", + "content": "y^{E} = \\{[c_{1}^{E},b_{1}^{E}],[c_{2}^{E},b_{2}^{E}],\\ldots ,[c_{N}^{E},b_{N}^{E}]\\}" + }, + { + "bbox": [ + 296, + 178, + 530, + 248 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 296, + 178, + 530, + 248 + ], + "type": "inline_equation", + "content": "c_{i}^{E},b_{i}^{E}" + }, + { + "bbox": [ + 296, + 178, + 530, + 248 + ], + "type": "text", + "content": " represent classification score and regression bounding box corresponding to " + }, + { + "bbox": [ + 296, + 178, + 530, + 248 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 296, + 178, + 530, + 248 + ], + "type": "text", + "content": "-th distillation query. Based on bipartite matching approach in [2], we search for the optimal permutations " + }, + { + "bbox": [ + 296, + 178, + 530, + 248 + ], + "type": "inline_equation", + "content": "\\hat{\\sigma}" + }, + { + "bbox": [ + 296, + 178, + 530, + 248 + ], + "type": "text", + "content": " and optimize the distillation head by " + }, + { + "bbox": [ + 296, + 178, + 530, + 248 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{dh}" + }, + { + "bbox": [ + 296, + 178, + 530, + 248 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 298, + 252, + 530, + 298 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 252, + 530, + 298 + ], + "spans": [ + { + "bbox": [ + 298, + 252, + 530, + 298 + ], + "type": "interline_equation", + "content": "\\left\\{ \\begin{array}{l} \\hat {\\sigma} = \\underset {\\sigma \\in \\mathfrak {S} _ {N}} {\\arg \\min } \\sum_ {i} ^ {N} \\alpha \\mathcal {L} _ {c l s} \\left(c _ {\\sigma (i)} ^ {E}, c _ {i} ^ {g t}\\right) + \\beta \\mathcal {L} _ {b b o x} \\left(b _ {\\sigma (i)} ^ {E}, b _ {i} ^ {g t}\\right), \\\\ \\mathcal {L} _ {d h} = \\sum_ {i} ^ {N} \\alpha \\mathcal {L} _ {c l s} \\left(c _ {\\hat {\\sigma} (i)} ^ {E}, c _ {i} ^ {g t}\\right) + \\beta \\mathcal {L} _ {b b o x} \\left(b _ {\\hat {\\sigma} (i)} ^ {E}, b _ {i} ^ {g t}\\right), \\end{array} \\right. \\tag {2}", + "image_path": "2281178fecfcb9eb17c9d7b3b95b8cbb0079b3405a5bafb33b5ad9187182bc71.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 296, + 299, + 530, + 345 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 299, + 530, + 345 + ], + "spans": [ + { + "bbox": [ + 296, + 299, + 530, + 345 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 296, + 299, + 530, + 345 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cls}" + }, + { + "bbox": [ + 296, + 299, + 530, + 345 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 299, + 530, + 345 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{bbox}" + }, + { + "bbox": [ + 296, + 299, + 530, + 345 + ], + "type": "text", + "content": " take the same form as FocalLoss [20] and L1 loss respectively, " + }, + { + "bbox": [ + 296, + 299, + 530, + 345 + ], + "type": "inline_equation", + "content": "b^{gt}" + }, + { + "bbox": [ + 296, + 299, + 530, + 345 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 299, + 530, + 345 + ], + "type": "inline_equation", + "content": "c^{gt}" + }, + { + "bbox": [ + 296, + 299, + 530, + 345 + ], + "type": "text", + "content": " represent ground truth boxes coordinates and classes, and " + }, + { + "bbox": [ + 296, + 299, + 530, + 345 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 296, + 299, + 530, + 345 + ], + "type": "text", + "content": " as well as " + }, + { + "bbox": [ + 296, + 299, + 530, + 345 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 296, + 299, + 530, + 345 + ], + "type": "text", + "content": " balance the loss weight." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 296, + 345, + 530, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 345, + 530, + 426 + ], + "spans": [ + { + "bbox": [ + 296, + 345, + 530, + 426 + ], + "type": "text", + "content": "During the optimization process of the distillation head, the queries with a confidence higher than " + }, + { + "bbox": [ + 296, + 345, + 530, + 426 + ], + "type": "inline_equation", + "content": "\\rho_{c}" + }, + { + "bbox": [ + 296, + 345, + 530, + 426 + ], + "type": "text", + "content": " and GIOU greater than " + }, + { + "bbox": [ + 296, + 345, + 530, + 426 + ], + "type": "inline_equation", + "content": "\\rho_{b}" + }, + { + "bbox": [ + 296, + 345, + 530, + 426 + ], + "type": "text", + "content": " are filtered out as focal queries, termed as " + }, + { + "bbox": [ + 296, + 345, + 530, + 426 + ], + "type": "inline_equation", + "content": "Q^{f}" + }, + { + "bbox": [ + 296, + 345, + 530, + 426 + ], + "type": "text", + "content": ". The number of " + }, + { + "bbox": [ + 296, + 345, + 530, + 426 + ], + "type": "inline_equation", + "content": "Q^{f}" + }, + { + "bbox": [ + 296, + 345, + 530, + 426 + ], + "type": "text", + "content": " is denoted as " + }, + { + "bbox": [ + 296, + 345, + 530, + 426 + ], + "type": "inline_equation", + "content": "N_{f}" + }, + { + "bbox": [ + 296, + 345, + 530, + 426 + ], + "type": "text", + "content": ". Finally, the generated 3D boxes and sampled BEV features corresponding to the focal queries " + }, + { + "bbox": [ + 296, + 345, + 530, + 426 + ], + "type": "inline_equation", + "content": "Q^{f}" + }, + { + "bbox": [ + 296, + 345, + 530, + 426 + ], + "type": "text", + "content": " are selected to perform masked generative distillation and refined distillation." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 297, + 432, + 502, + 444 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 432, + 502, + 444 + ], + "spans": [ + { + "bbox": [ + 297, + 432, + 502, + 444 + ], + "type": "text", + "content": "3.2. Selective Masked Generative Distillation" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 296, + 450, + 530, + 531 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 450, + 530, + 531 + ], + "spans": [ + { + "bbox": [ + 296, + 450, + 530, + 531 + ], + "type": "text", + "content": "The generated 3D boxes by focal queries " + }, + { + "bbox": [ + 296, + 450, + 530, + 531 + ], + "type": "inline_equation", + "content": "Q_{f}" + }, + { + "bbox": [ + 296, + 450, + 530, + 531 + ], + "type": "text", + "content": " are projected to PV and BEV. The 3D boxes are projected to PV according to the camera extrinsics and intrinsics, and simply flattened to BEV from the top-down view. The masking process described below is the same for both PV and BEV, so we describe the process without distinction between PV and BEV." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 296, + 531, + 530, + 603 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 531, + 530, + 603 + ], + "spans": [ + { + "bbox": [ + 296, + 531, + 530, + 603 + ], + "type": "text", + "content": "An instance mask " + }, + { + "bbox": [ + 296, + 531, + 530, + 603 + ], + "type": "inline_equation", + "content": "I_{i}^{fg}" + }, + { + "bbox": [ + 296, + 531, + 530, + 603 + ], + "type": "text", + "content": " is generated with the projection area corresponding to one focal query " + }, + { + "bbox": [ + 296, + 531, + 530, + 603 + ], + "type": "inline_equation", + "content": "Q_{i}^{f}" + }, + { + "bbox": [ + 296, + 531, + 530, + 603 + ], + "type": "text", + "content": ". The dimension of the instance mask is identical to that of the apprentice feature. If a pixel is inside the bounding box " + }, + { + "bbox": [ + 296, + 531, + 530, + 603 + ], + "type": "inline_equation", + "content": "b_{i}^{E}" + }, + { + "bbox": [ + 296, + 531, + 530, + 603 + ], + "type": "text", + "content": ", the value is set to be 0, otherwise its value is set to be 1. The formulation of " + }, + { + "bbox": [ + 296, + 531, + 530, + 603 + ], + "type": "inline_equation", + "content": "I_{i}^{fg}" + }, + { + "bbox": [ + 296, + 531, + 530, + 603 + ], + "type": "text", + "content": " is described as follows:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 354, + 608, + 530, + 639 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 354, + 608, + 530, + 639 + ], + "spans": [ + { + "bbox": [ + 354, + 608, + 530, + 639 + ], + "type": "interline_equation", + "content": "I _ {i, u v} ^ {f g} = \\left\\{ \\begin{array}{l l} 0, & \\text {i f} (u, v) \\text {i n} b _ {i} ^ {E} \\\\ 1, & \\text {O t h e r w i s e} \\end{array} . \\right. \\tag {3}", + "image_path": "f241f129a3dc095279a090c9a02bd3ae611a5b133f52c50702707eb61eb8e051.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 296, + 644, + 530, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 644, + 530, + 676 + ], + "spans": [ + { + "bbox": [ + 296, + 644, + 530, + 676 + ], + "type": "text", + "content": "All instance masks are merged together to form the final mask " + }, + { + "bbox": [ + 296, + 644, + 530, + 676 + ], + "type": "inline_equation", + "content": "I^{fg}" + }, + { + "bbox": [ + 296, + 644, + 530, + 676 + ], + "type": "text", + "content": ". The process of mask stacking is formulated as follows:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 351, + 677, + 530, + 692 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 677, + 530, + 692 + ], + "spans": [ + { + "bbox": [ + 351, + 677, + 530, + 692 + ], + "type": "interline_equation", + "content": "I ^ {f g} = I _ {0} ^ {f g} \\wedge I _ {1} ^ {f g} \\wedge \\dots \\wedge I _ {N - 1} ^ {f g}. \\tag {4}", + "image_path": "f50531ccd32d3870c5c9816a6fd9d45171ac060530a078ac731adfb25dc784e1.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 296, + 694, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 694, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 694, + 530, + 730 + ], + "type": "text", + "content": "The masked region indicates where the objects reside in, and the masked generation is performed within the masked region." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 281, + 747, + 296, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 281, + 747, + 296, + 756 + ], + "spans": [ + { + "bbox": [ + 281, + 747, + 296, + 756 + ], + "type": "text", + "content": "995" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 106, + 279, + 141 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 106, + 279, + 141 + ], + "spans": [ + { + "bbox": [ + 46, + 106, + 279, + 141 + ], + "type": "text", + "content": "The selective mask indicates that the pixels of apprentice feature within " + }, + { + "bbox": [ + 46, + 106, + 279, + 141 + ], + "type": "inline_equation", + "content": "I^{fg}" + }, + { + "bbox": [ + 46, + 106, + 279, + 141 + ], + "type": "text", + "content": " are masked by ratio " + }, + { + "bbox": [ + 46, + 106, + 279, + 141 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 106, + 279, + 141 + ], + "type": "text", + "content": ". A random mask " + }, + { + "bbox": [ + 46, + 106, + 279, + 141 + ], + "type": "inline_equation", + "content": "I^r" + }, + { + "bbox": [ + 46, + 106, + 279, + 141 + ], + "type": "text", + "content": " with the same size of " + }, + { + "bbox": [ + 46, + 106, + 279, + 141 + ], + "type": "inline_equation", + "content": "I^{fg}" + }, + { + "bbox": [ + 46, + 106, + 279, + 141 + ], + "type": "text", + "content": " is generated:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 108, + 147, + 279, + 179 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 147, + 279, + 179 + ], + "spans": [ + { + "bbox": [ + 108, + 147, + 279, + 179 + ], + "type": "interline_equation", + "content": "I _ {u v} ^ {r} = \\left\\{ \\begin{array}{l l} 0, & \\text {i f} R _ {u, v} < r \\\\ 1, & \\text {O t h e r w i s e} \\end{array} , \\right. \\tag {5}", + "image_path": "4c78ed1d4f8bc12672dc5e257f9c2515ebf98a0f27ff3d1e7ecfdee7db5e6895.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 185, + 279, + 219 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 185, + 279, + 219 + ], + "spans": [ + { + "bbox": [ + 46, + 185, + 279, + 219 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 185, + 279, + 219 + ], + "type": "inline_equation", + "content": "R_{u,v}" + }, + { + "bbox": [ + 46, + 185, + 279, + 219 + ], + "type": "text", + "content": " is a uniformly random number between 0 and 1. The process of the selective mask is expressed as an OR operation between " + }, + { + "bbox": [ + 46, + 185, + 279, + 219 + ], + "type": "inline_equation", + "content": "I^{fg}" + }, + { + "bbox": [ + 46, + 185, + 279, + 219 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 185, + 279, + 219 + ], + "type": "inline_equation", + "content": "I^r" + }, + { + "bbox": [ + 46, + 185, + 279, + 219 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 129, + 226, + 279, + 239 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 129, + 226, + 279, + 239 + ], + "spans": [ + { + "bbox": [ + 129, + 226, + 279, + 239 + ], + "type": "interline_equation", + "content": "I ^ {m} = I ^ {f g} \\vee I ^ {r}. \\tag {6}", + "image_path": "a283bd9a54cac588118507ac7ea796e8a81d0f5c3fd783aaa7e33c315f4ef66f.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 246, + 279, + 280 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 246, + 279, + 280 + ], + "spans": [ + { + "bbox": [ + 45, + 246, + 279, + 280 + ], + "type": "text", + "content": "Then the apprentice feature " + }, + { + "bbox": [ + 45, + 246, + 279, + 280 + ], + "type": "inline_equation", + "content": "F^A" + }, + { + "bbox": [ + 45, + 246, + 279, + 280 + ], + "type": "text", + "content": " is masked with " + }, + { + "bbox": [ + 45, + 246, + 279, + 280 + ], + "type": "inline_equation", + "content": "I^m" + }, + { + "bbox": [ + 45, + 246, + 279, + 280 + ], + "type": "text", + "content": ". The masked apprentice feature is forced to recover with a generator " + }, + { + "bbox": [ + 45, + 246, + 279, + 280 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 45, + 246, + 279, + 280 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 123, + 280, + 279, + 293 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 280, + 279, + 293 + ], + "spans": [ + { + "bbox": [ + 123, + 280, + 279, + 293 + ], + "type": "interline_equation", + "content": "\\hat {F} ^ {A} = \\mathcal {G} \\left(F ^ {A} \\cdot I ^ {m}\\right). \\tag {7}", + "image_path": "2aafd352591c96e47e6d93359c018645f220a10f11d634fb58a89608d07377e6.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 298, + 279, + 355 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 298, + 279, + 355 + ], + "spans": [ + { + "bbox": [ + 45, + 298, + 279, + 355 + ], + "type": "text", + "content": "The generator " + }, + { + "bbox": [ + 45, + 298, + 279, + 355 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 45, + 298, + 279, + 355 + ], + "type": "text", + "content": " here includes two convolutional layers, the first one of which switches to a deconvolutional layer if the dimensions of the apprentice feature and expert feature are not identical. After generating " + }, + { + "bbox": [ + 45, + 298, + 279, + 355 + ], + "type": "inline_equation", + "content": "\\hat{F}^A" + }, + { + "bbox": [ + 45, + 298, + 279, + 355 + ], + "type": "text", + "content": ", the channel-wise distribution [25] is calculated as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 71, + 362, + 279, + 394 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 71, + 362, + 279, + 394 + ], + "spans": [ + { + "bbox": [ + 71, + 362, + 279, + 394 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {S M G D} = \\frac {\\tau^ {2}}{C} \\sum_ {c = 1} ^ {C} \\sum_ {i = 1} ^ {H \\times W} \\varphi \\left(F _ {c, i} ^ {E}\\right) \\log \\frac {\\varphi \\left(F _ {c , i} ^ {E}\\right)}{\\varphi \\left(\\hat {F} _ {c , i} ^ {A}\\right)}, \\tag {8}", + "image_path": "a24c2cb8fcd61569fd57e3aaaf39413c50201d22290025e7baaaf5127a250b29.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 101, + 400, + 279, + 431 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 101, + 400, + 279, + 431 + ], + "spans": [ + { + "bbox": [ + 101, + 400, + 279, + 431 + ], + "type": "interline_equation", + "content": "\\varphi \\left(F _ {c, i}\\right) = \\frac {\\exp \\left(\\frac {F _ {c , i}}{\\tau}\\right)}{\\sum_ {i = 1} ^ {H \\times W} \\exp \\left(\\frac {F _ {c , i}}{\\tau}\\right)}, \\tag {9}", + "image_path": "6d79f0bb29953337a58cb7f11062cbb48a9ef64915de02cb3b0f31d0c406d01d.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 45, + 434, + 279, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 434, + 279, + 468 + ], + "spans": [ + { + "bbox": [ + 45, + 434, + 279, + 468 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 45, + 434, + 279, + 468 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 45, + 434, + 279, + 468 + ], + "type": "text", + "content": " is the temperature factor of the SoftMax layer, " + }, + { + "bbox": [ + 45, + 434, + 279, + 468 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 45, + 434, + 279, + 468 + ], + "type": "text", + "content": " means the feature channels, and " + }, + { + "bbox": [ + 45, + 434, + 279, + 468 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 45, + 434, + 279, + 468 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 45, + 434, + 279, + 468 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 45, + 434, + 279, + 468 + ], + "type": "text", + "content": " represent feature height and width respectively." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 475, + 206, + 487 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 475, + 206, + 487 + ], + "spans": [ + { + "bbox": [ + 46, + 475, + 206, + 487 + ], + "type": "text", + "content": "3.3. Query-based Focal Distillation" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 45, + 493, + 279, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 493, + 279, + 632 + ], + "spans": [ + { + "bbox": [ + 45, + 493, + 279, + 632 + ], + "type": "text", + "content": "Focal distillation denotes the refined distillation focusing on the local feature pattern of focal positions. We aim to leverage a set of queries to automatically search out the representative positions of objects, and perform distillation on the identical positions between expert features and apprentice features. We resort to the deformable attention module to achieve the goal. The deformable attention module generates a set of offsets around a reference point. Based on the offsets to the reference point, the features on the crucial sampling points are sampled for object detection. We exploit this mechanism to conduct a refined distillation on such representative features as illustrated in Fig. 4." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 45, + 633, + 279, + 679 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 633, + 279, + 679 + ], + "spans": [ + { + "bbox": [ + 45, + 633, + 279, + 679 + ], + "type": "text", + "content": "A set of focal queries " + }, + { + "bbox": [ + 45, + 633, + 279, + 679 + ], + "type": "inline_equation", + "content": "Q^{f}" + }, + { + "bbox": [ + 45, + 633, + 279, + 679 + ], + "type": "text", + "content": " are filtered out as described in Sec. 3.1. For each focal query " + }, + { + "bbox": [ + 45, + 633, + 279, + 679 + ], + "type": "inline_equation", + "content": "q \\in Q^{f}" + }, + { + "bbox": [ + 45, + 633, + 279, + 679 + ], + "type": "text", + "content": ", the reference point " + }, + { + "bbox": [ + 45, + 633, + 279, + 679 + ], + "type": "inline_equation", + "content": "p_{q}" + }, + { + "bbox": [ + 45, + 633, + 279, + 679 + ], + "type": "text", + "content": " is generated by the query feature " + }, + { + "bbox": [ + 45, + 633, + 279, + 679 + ], + "type": "inline_equation", + "content": "z_{q}" + }, + { + "bbox": [ + 45, + 633, + 279, + 679 + ], + "type": "text", + "content": " with a linear projection " + }, + { + "bbox": [ + 45, + 633, + 279, + 679 + ], + "type": "inline_equation", + "content": "\\mathcal{M}\\mathcal{LP}" + }, + { + "bbox": [ + 45, + 633, + 279, + 679 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 126, + 687, + 279, + 700 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 126, + 687, + 279, + 700 + ], + "spans": [ + { + "bbox": [ + 126, + 687, + 279, + 700 + ], + "type": "interline_equation", + "content": "p _ {q} = \\mathcal {M L P} \\left(z _ {q}\\right). \\tag {10}", + "image_path": "e276f807f928dec529b875e607a604c615672a4ebbe6367866ea7d43996ac031.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 45, + 706, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 706, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 706, + 279, + 730 + ], + "type": "text", + "content": "The reference point " + }, + { + "bbox": [ + 45, + 706, + 279, + 730 + ], + "type": "inline_equation", + "content": "p_q" + }, + { + "bbox": [ + 45, + 706, + 279, + 730 + ], + "type": "text", + "content": " represents the projection center of the estimated bounding box on the sampling feature plane." + } + ] + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 324, + 106, + 502, + 223 + ], + "blocks": [ + { + "bbox": [ + 324, + 106, + 502, + 223 + ], + "lines": [ + { + "bbox": [ + 324, + 106, + 502, + 223 + ], + "spans": [ + { + "bbox": [ + 324, + 106, + 502, + 223 + ], + "type": "image", + "image_path": "ad8a436a6a171b799e9c7952fe4fabedfaa2b3f4cef7fc17fe2a58e60ce4b0fe.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 296, + 225, + 530, + 288 + ], + "lines": [ + { + "bbox": [ + 296, + 225, + 530, + 288 + ], + "spans": [ + { + "bbox": [ + 296, + 225, + 530, + 288 + ], + "type": "text", + "content": "Figure 4. Process of query-based offset generation, feature sampling and query parameter update. Leveraging the deformable attention mechanism, the local expert feature and apprentice feature are sampled at the same position, based on the offset generated by the query. In addition, the query parameter is updated with the collected expert feature." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "bbox": [ + 296, + 301, + 530, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 301, + 530, + 347 + ], + "spans": [ + { + "bbox": [ + 296, + 301, + 530, + 347 + ], + "type": "text", + "content": "For each focal query " + }, + { + "bbox": [ + 296, + 301, + 530, + 347 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 296, + 301, + 530, + 347 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 296, + 301, + 530, + 347 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 296, + 301, + 530, + 347 + ], + "type": "text", + "content": " attention heads are attached on " + }, + { + "bbox": [ + 296, + 301, + 530, + 347 + ], + "type": "inline_equation", + "content": "z_{q}" + }, + { + "bbox": [ + 296, + 301, + 530, + 347 + ], + "type": "text", + "content": ". Each attention head generates " + }, + { + "bbox": [ + 296, + 301, + 530, + 347 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 296, + 301, + 530, + 347 + ], + "type": "text", + "content": " sampling offsets by another linear projection " + }, + { + "bbox": [ + 296, + 301, + 530, + 347 + ], + "type": "inline_equation", + "content": "\\mathcal{MLP}'" + }, + { + "bbox": [ + 296, + 301, + 530, + 347 + ], + "type": "text", + "content": ". The offset is computed by the following:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 356, + 358, + 530, + 372 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 356, + 358, + 530, + 372 + ], + "spans": [ + { + "bbox": [ + 356, + 358, + 530, + 372 + ], + "type": "interline_equation", + "content": "\\Delta p _ {m q k} = \\mathcal {M L P} ^ {\\prime} \\left(z _ {q}, m, k\\right), \\tag {11}", + "image_path": "20b91dadc34cda6769428fcd000831ea21b53df084cd58e3f452467a3257463b.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 296, + 381, + 529, + 405 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 381, + 529, + 405 + ], + "spans": [ + { + "bbox": [ + 296, + 381, + 529, + 405 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 296, + 381, + 529, + 405 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 296, + 381, + 529, + 405 + ], + "type": "text", + "content": " indexes the attention head, and " + }, + { + "bbox": [ + 296, + 381, + 529, + 405 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 296, + 381, + 529, + 405 + ], + "type": "text", + "content": " represents the sampling point." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 296, + 405, + 530, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 405, + 530, + 475 + ], + "spans": [ + { + "bbox": [ + 296, + 405, + 530, + 475 + ], + "type": "text", + "content": "The positions searched by the generated offsets are viewed as key representative positions. The query-based focal distillation is conducted on such key representative positions. Let " + }, + { + "bbox": [ + 296, + 405, + 530, + 475 + ], + "type": "inline_equation", + "content": "F_{mqk}^{E}, F_{mqk}^{A}" + }, + { + "bbox": [ + 296, + 405, + 530, + 475 + ], + "type": "text", + "content": " represent the sampled features from the identical key positions for expert and apprentice, respectively. They are calculated as follows:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 358, + 484, + 530, + 499 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 484, + 530, + 499 + ], + "spans": [ + { + "bbox": [ + 358, + 484, + 530, + 499 + ], + "type": "interline_equation", + "content": "F _ {m q k} ^ {E} = F ^ {E} \\left(p _ {q} + \\Delta p _ {m q k}\\right), \\tag {12}", + "image_path": "bfd5e447c63ce2d0148753515699a6d9e93f42aba92539df08afce7a65c4dd3c.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 358, + 511, + 530, + 526 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 511, + 530, + 526 + ], + "spans": [ + { + "bbox": [ + 358, + 511, + 530, + 526 + ], + "type": "interline_equation", + "content": "F _ {m q k} ^ {A} = F ^ {A} \\left(p _ {q} + \\Delta p _ {m q k}\\right). \\tag {13}", + "image_path": "e27c77f3fe6352ea5458257cb0435c2f8fe398ae319bdd122a0e20bb773a8e76.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 296, + 532, + 530, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 532, + 530, + 578 + ], + "spans": [ + { + "bbox": [ + 296, + 532, + 530, + 578 + ], + "type": "text", + "content": "The sampled expert feature and apprentice feature are normalized to " + }, + { + "bbox": [ + 296, + 532, + 530, + 578 + ], + "type": "inline_equation", + "content": "\\widetilde{F}_{mqk}^{T}" + }, + { + "bbox": [ + 296, + 532, + 530, + 578 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 532, + 530, + 578 + ], + "type": "inline_equation", + "content": "\\widetilde{F}_{mqk}^{S}" + }, + { + "bbox": [ + 296, + 532, + 530, + 578 + ], + "type": "text", + "content": " according to their maximum and minimum. Finally, the L2 loss is computed between the normalized key sampled features:" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 314, + 588, + 530, + 622 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 588, + 530, + 622 + ], + "spans": [ + { + "bbox": [ + 314, + 588, + 530, + 622 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {Q F D} = \\frac {1}{N _ {f}} \\sum_ {q \\in Q _ {f}} \\sum_ {m = 1} ^ {M} \\sum_ {k = 1} ^ {K} L _ {2} \\left(\\widetilde {F} _ {m q k} ^ {A}, \\widetilde {F} _ {m q k} ^ {E}\\right). \\tag {14}", + "image_path": "13edcef250a3eff32b8983a9e59585c37b040297d967421a2fd527b0e0189200.jpg" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 296, + 632, + 530, + 679 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 632, + 530, + 679 + ], + "spans": [ + { + "bbox": [ + 296, + 632, + 530, + 679 + ], + "type": "text", + "content": "Through the loss for the fine-grained local region, the refined distillation on these representative positions is conducted. Query-based focal distillation aims to optimize the local patterns on the instances' representative positions." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 297, + 687, + 429, + 698 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 687, + 429, + 698 + ], + "spans": [ + { + "bbox": [ + 297, + 687, + 429, + 698 + ], + "type": "text", + "content": "3.4. Overall Distillation Loss" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 297, + 706, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 706, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 297, + 706, + 530, + 730 + ], + "type": "text", + "content": "Besides being supervised by ground truth, the intermediate feature of the apprentice detector is also supervised by" + } + ] + } + ], + "index": 27 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 281, + 747, + 296, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 281, + 747, + 296, + 756 + ], + "spans": [ + { + "bbox": [ + 281, + 747, + 296, + 756 + ], + "type": "text", + "content": "996" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 45, + 106, + 279, + 141 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 106, + 279, + 141 + ], + "spans": [ + { + "bbox": [ + 45, + 106, + 279, + 141 + ], + "type": "text", + "content": "the masked generative distillation loss " + }, + { + "bbox": [ + 45, + 106, + 279, + 141 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{SMGD}" + }, + { + "bbox": [ + 45, + 106, + 279, + 141 + ], + "type": "text", + "content": " and query-based focal distillation loss " + }, + { + "bbox": [ + 45, + 106, + 279, + 141 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{QFD}" + }, + { + "bbox": [ + 45, + 106, + 279, + 141 + ], + "type": "text", + "content": ". The total knowledge distillation loss is defined as follows:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 102, + 149, + 279, + 161 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 149, + 279, + 161 + ], + "spans": [ + { + "bbox": [ + 102, + 149, + 279, + 161 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {K D} = \\lambda \\mathcal {L} _ {S M G D} + \\eta \\mathcal {L} _ {Q F D}. \\tag {15}", + "image_path": "9712cf2b0e6c8fb5f3af758c758b4bab1865bed09e92f86ad83f7ca78197f6b3.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 169, + 279, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 169, + 279, + 228 + ], + "spans": [ + { + "bbox": [ + 45, + 169, + 279, + 228 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{SMGD}" + }, + { + "bbox": [ + 45, + 169, + 279, + 228 + ], + "type": "text", + "content": " is used to optimize the global feature distribution, indicating where should be with high activation. " + }, + { + "bbox": [ + 45, + 169, + 279, + 228 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{QFD}" + }, + { + "bbox": [ + 45, + 169, + 279, + 228 + ], + "type": "text", + "content": " is leveraged for optimizing the local feature pattern on searched focal positions. The hyper-parameters " + }, + { + "bbox": [ + 45, + 169, + 279, + 228 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 45, + 169, + 279, + 228 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 169, + 279, + 228 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 45, + 169, + 279, + 228 + ], + "type": "text", + "content": " control the loss weight." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 228, + 279, + 274 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 228, + 279, + 274 + ], + "spans": [ + { + "bbox": [ + 45, + 228, + 279, + 274 + ], + "type": "text", + "content": "Note that only the gradients w.r.t. the vanilla detection loss and the distillation loss " + }, + { + "bbox": [ + 45, + 228, + 279, + 274 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{KD}" + }, + { + "bbox": [ + 45, + 228, + 279, + 274 + ], + "type": "text", + "content": " back-propagate to the apprentice network. " + }, + { + "bbox": [ + 45, + 228, + 279, + 274 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{dh}" + }, + { + "bbox": [ + 45, + 228, + 279, + 274 + ], + "type": "text", + "content": " only optimizes the parameters of the distillation head." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 284, + 124, + 298 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 284, + 124, + 298 + ], + "spans": [ + { + "bbox": [ + 45, + 284, + 124, + 298 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 303, + 158, + 314 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 303, + 158, + 314 + ], + "spans": [ + { + "bbox": [ + 45, + 303, + 158, + 314 + ], + "type": "text", + "content": "4.1. Dataset and metrics" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 320, + 279, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 320, + 279, + 378 + ], + "spans": [ + { + "bbox": [ + 45, + 320, + 279, + 378 + ], + "type": "text", + "content": "We conduct experiments on nuScenes dataset [1], a large-scale autonomous driving dataset. This dataset contains 700, 150, 150 scenes for training, validation and testing, respectively. Each scene has roughly 20 seconds of duration. The key frame is annotated at " + }, + { + "bbox": [ + 45, + 320, + 279, + 378 + ], + "type": "inline_equation", + "content": "2\\mathrm{Hz}" + }, + { + "bbox": [ + 45, + 320, + 279, + 378 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 379, + 279, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 379, + 279, + 496 + ], + "spans": [ + { + "bbox": [ + 45, + 379, + 279, + 496 + ], + "type": "text", + "content": "The two dominant metrics of the nuScenes detection task are nuScenes Detection Score (NDS) and mean Average Precision (mAP). The mAP of nuScenes is computed by the center distance between predictions and annotations on the ground plane. In addition, the nuScenes dataset defines five true positive metrics mATE, mASE, mAOE, mAVE, mAAE for measuring translation, scale, orientation, velocity and attribute, respectively. NDS of nuScenes is a weighted sum of mAP and the five true positive metrics, defined as " + }, + { + "bbox": [ + 45, + 379, + 279, + 496 + ], + "type": "inline_equation", + "content": "NDS = \\frac{1}{10} [5mAP + \\sum_{mTP}(1 - \\min(1, mTP))]" + }, + { + "bbox": [ + 45, + 379, + 279, + 496 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 502, + 175, + 515 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 502, + 175, + 515 + ], + "spans": [ + { + "bbox": [ + 45, + 502, + 175, + 515 + ], + "type": "text", + "content": "4.2. Implementation Details" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 45, + 520, + 279, + 682 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 520, + 279, + 682 + ], + "spans": [ + { + "bbox": [ + 45, + 520, + 279, + 682 + ], + "type": "text", + "content": "We conduct experiments on BEVFormer [19] and DETR3D [32]. Settings of expert- apprentice pairs are illustrated in Tab. 1. We obtain three groups of expert- apprentice combinations by changing the backbone, input image resolution and BEV grip resolution. ResNet [8] with or without deformable convolution [38] are used for all backbones. When applied to BEV perception model BEVFormer, the selective masked generation is performed on both the PV feature and BEV feature, and query-based focal distillation is performed on the BEV feature, while both selective masked generative distillation and query-based focal distillation are performed on PV feature when it comes to the BEV-free perception model DETR3D. We also conduct the experiment on BEVDepth in supplementary materials." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 45, + 682, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 682, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 682, + 279, + 730 + ], + "type": "text", + "content": "The codebase is developed upon MMDetection3D [5]. All models are trained on 8 NVIDIA A100 GPUs. For BEVFormer and DETR3D, the models are trained for 24 epochs with an initial learning rate of 2e-4 and per-GPU" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 296, + 106, + 530, + 176 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 106, + 530, + 176 + ], + "spans": [ + { + "bbox": [ + 296, + 106, + 530, + 176 + ], + "type": "text", + "content": "batch size of 1. No data augmentation is introduced when training BEVFormer and DETR3D. Feature pyramid position shift [24] is adopted for PV feature alignment between low-resolution apprentice and high-resolution expert. The hyperparameters " + }, + { + "bbox": [ + 296, + 106, + 530, + 176 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 296, + 106, + 530, + 176 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 296, + 106, + 530, + 176 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 296, + 106, + 530, + 176 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 296, + 106, + 530, + 176 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 296, + 106, + 530, + 176 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 296, + 106, + 530, + 176 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 296, + 106, + 530, + 176 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 296, + 106, + 530, + 176 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 296, + 106, + 530, + 176 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 296, + 106, + 530, + 176 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 296, + 106, + 530, + 176 + ], + "type": "text", + "content": " are set to be 0.5, 2.0, 2.0, 0.25, 0.25 and 0.001, respectively." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 296, + 185, + 464, + 197 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 185, + 464, + 197 + ], + "spans": [ + { + "bbox": [ + 296, + 185, + 464, + 197 + ], + "type": "text", + "content": "4.3. Comparison to State-of-the-arts" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 296, + 202, + 530, + 551 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 202, + 530, + 551 + ], + "spans": [ + { + "bbox": [ + 296, + 202, + 530, + 551 + ], + "type": "text", + "content": "As depicted in Tab. 2, the proposed distillation method brings significant improvement on BEVFormer-Tiny, BEVFormer-Small and DETR3D by 4.07, 2.47 and 3.17 NDS, respectively. The gain comes mainly from the improved mAP and velocity estimation accuracy. The devised method brings 4.13 points to BEVFormer-Tiny and 3.08 points to BEVFormer-Small in terms of mAP, which demonstrates the enhancement of localization and classification. The proposed approach also achieves improvements of 4.97 points to BEVFormer-Tiny and 8.21 points to DETR3D-R50 in terms of mAVE. In regard to the classic distillation methods on the 2D field, regardless of BEVFormer-Tiny or DETR3D-R50, FitNet obtains marginal improvement, yet CWD achieves larger gains. MGD with the global random mask cannot outperform CWD, indicating that random masked generative distillation in 3D detection scenes is not as powerful as that in 2D scenes. The proposed FD3D outperforms all classic distillation methods on the 2D field by an obvious margin. The comparison reveals that the devised fine-grained distillation on focal regions truly improves the distillation quality. In the supplementary materials, we conduct further experiments to validate the efficacy of FD3D on another BEV perception model BEVDepth. It can be observed that FD3D leads to improved performance on BEVDepth. These findings demonstrate the generalizability of the proposed distillation method across various 3D object detectors. Moreover, we also present the gains achieved by FD3D on the nuScenes test set, which are consistent with the effects observed on the nuScenes val set." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 296, + 559, + 387, + 572 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 559, + 387, + 572 + ], + "spans": [ + { + "bbox": [ + 296, + 559, + 387, + 572 + ], + "type": "text", + "content": "4.4. Ablative Study" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 296, + 578, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 578, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 578, + 530, + 730 + ], + "type": "text", + "content": "Contribution of each module. For a better understanding of the contribution of each proposed module to the distillation performance, we test each component independently on group BEVFormer Base-Tiny and report the corresponding accuracy in Tab. 3. The channel-wise distribution (CWD) is adopted as a baseline distillation method and obtains 41.80 NDS. When compared to this baseline, the selective masked generation can achieve an additional 1.07 NDS improvement, revealing that such technique can enhance feature learning on focal regions. Query-based focal distillation yields an extra 0.95 NDS gain over the baseline, thereby highlighting the significance of the refined distillation on the fine-grained position. With the two proposed" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 281, + 747, + 296, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 281, + 747, + 296, + 756 + ], + "spans": [ + { + "bbox": [ + 281, + 747, + 296, + 756 + ], + "type": "text", + "content": "997" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 104, + 530, + 293 + ], + "blocks": [ + { + "bbox": [ + 48, + 104, + 530, + 293 + ], + "lines": [ + { + "bbox": [ + 48, + 104, + 530, + 293 + ], + "spans": [ + { + "bbox": [ + 48, + 104, + 530, + 293 + ], + "type": "table", + "html": "
MethodNDS↑mAP↑mATE↓mASE↓mAOE↓mAVE↓mAAE↓GFLOPs↓FPS↑
BEVFormer-Base* (E)47.3736.4473.5128.1444.9842.3819.501845.362.0
BEVFormer-Tiny (A)39.0226.8783.4329.4859.7350.0321.49
+ FitNet [26]40.5728.2681.5228.9652.9651.3220.84
+ CWD [25]41.8029.7980.8128.5550.6349.8721.21381.957.3
+ MGD [36]41.3329.0880.1928.8352.8350.0020.19
+ FD3D (Ours)43.09 (↑4.07)31.00 (↑4.13)79.3128.0050.7745.0620.97
BEVFormer-Base (E)51.7441.6467.2627.3437.0439.4119.741323.411.8
BEVFormer-Small (A)46.2634.5674.2728.0044.5343.9819.41416.465.9
+ FD3D (Ours)48.73 (↑2.47)37.64 (↑3.08)71.9427.5040.8939.4121.16
DETR3D-R101 (E)42.534.677.326.838.384.221.61016.832.5
DETR3D-R50 (A)35.7828.8585.3927.9054.0995.1523.95
+ FitNet [26]36.1929.7683.9028.0056.1894.5324.33
+ CWD [25]37.2230.1382.7427.6549.4094.6523.98876.944.0
+ MGD [36]37.0329.8983.3527.7953.2892.7421.98
+ FD3D (Ours)38.95 (↑3.17)31.33 (↑2.48)82.3227.6548.4086.9421.87
", + "image_path": "82283d487007dda4620ce2c56d2df851408938dbb921931372280e728a170b0a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 55, + 344, + 268, + 434 + ], + "blocks": [ + { + "bbox": [ + 45, + 297, + 531, + 330 + ], + "lines": [ + { + "bbox": [ + 45, + 297, + 531, + 330 + ], + "spans": [ + { + "bbox": [ + 45, + 297, + 531, + 330 + ], + "type": "text", + "content": "Table 2. 3D object detection improvement on nuScenes val set. The results demonstrate that the proposed distillation method benefits various 3D object detectors and surpasses the classic 2D distillation methods. We also show their efficiency metrics with GFLOPs and FPS. The FPS is measured on RTX 2080TI." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 55, + 344, + 268, + 434 + ], + "lines": [ + { + "bbox": [ + 55, + 344, + 268, + 434 + ], + "spans": [ + { + "bbox": [ + 55, + 344, + 268, + 434 + ], + "type": "table", + "html": "
ComponentNDSmAP
CWDSMGDQFD
BEVFormer Base-Tiny✓39.0226.87
41.8029.79
✓42.8730.59
✓42.7530.47
✓✓43.0931.00
", + "image_path": "edd1a64fb2ef7431409ae4cad69e998ec94328e8ebc9035afda34bd4fc0e45aa.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 438, + 279, + 494 + ], + "lines": [ + { + "bbox": [ + 45, + 438, + 279, + 494 + ], + "spans": [ + { + "bbox": [ + 45, + 438, + 279, + 494 + ], + "type": "text", + "content": "Table 3. Contribution by each component. SMGD and QFD are the proposed two novel modules. SMGD represents selective masked generative distillation, and QFD indicates query-based focal distillation. Channel-wise distribution (CWD) is applied as the baseline distillation method for comparison." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 45, + 506, + 279, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 506, + 279, + 540 + ], + "spans": [ + { + "bbox": [ + 45, + 506, + 279, + 540 + ], + "type": "text", + "content": "modules applied in conjunction, there is an observed increase in performance of 1.29 NDS, providing evidence of their efficacy and compatibility." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 542, + 279, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 542, + 279, + 658 + ], + "spans": [ + { + "bbox": [ + 45, + 542, + 279, + 658 + ], + "type": "text", + "content": "Mask region selection. As shown in Tab. 4a, variation in the impact of masked generative distillation across different regions is substantial. Global random mask leads to worsened results. Mask on foreground regions defined by the ground truth yields significant gains. Furthermore, applying masks to the predicted focal regions, as defined by focal queries, results in further improvement. This is probably attributed to the selection of focal queries, which effectively filter out regions with high confidence while excluding challenging-to-discriminate regions." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 660, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 660, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 660, + 279, + 730 + ], + "type": "text", + "content": "Distillation region. The terms \"global distribution\" and \"local pattern\" refer to two distillation mode focusing on the global overall activation and the local feature representation, respectively. And their performances are evaluated in Tab. 4b. The results demonstrate that distilling with global distribution alone already yields improvement, and when" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 296, + 345, + 530, + 379 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 345, + 530, + 379 + ], + "spans": [ + { + "bbox": [ + 296, + 345, + 530, + 379 + ], + "type": "text", + "content": "focusing on the local pattern of focal regions, a slightly higher gain is observed. The best performance is achieved through the combined optimization of them." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 296, + 380, + 530, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 380, + 530, + 520 + ], + "spans": [ + { + "bbox": [ + 296, + 380, + 530, + 520 + ], + "type": "text", + "content": "Distillation stage. The view transform module takes PV features as input and generates BEV features. PV features and BEV features are from different stages of the network. We explore the difference when global distillation (Fig. 1 (a)) is performed at different stages. The channel-wise distribution (CWD) is adopted in this ablation study. As shown in Tab. 4c, separate distillation on PV features obtains an improvement while separate distillation on BEV features leads to a deterioration in performance. This is due to the BEV feature containing a lot of shadow-like artifacts due to the unclear occlusion. This result demonstrates the necessity of selective distillation under BEV feature." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 296, + 520, + 530, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 520, + 530, + 625 + ], + "spans": [ + { + "bbox": [ + 296, + 520, + 530, + 625 + ], + "type": "text", + "content": "Feature alignment approach. When the BEV resolution differs between expert and apprentice, the BEV feature alignment is needed. There are two choices for alignment: upsampling the apprentice feature through a deconvolutional layer or directly downsampling the expert feature. We compare the two alignment approaches in Tab. 4d. Downsampling expert feature provokes inferior results than upsampling apprentice feature. This is potentially caused by the fatal information loss of the expert feature." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 297, + 630, + 379, + 642 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 630, + 379, + 642 + ], + "spans": [ + { + "bbox": [ + 297, + 630, + 379, + 642 + ], + "type": "text", + "content": "4.5. Visualization" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 296, + 648, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 648, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 648, + 530, + 730 + ], + "type": "text", + "content": "The feature representation and prediction of the apprentice network BEVFormer-tiny with or without our proposed method are presented in Fig. 5. For PV, the feature activations from the first FPN layer in front left view, front right view and back left are displayed. The activation of many background regions is high without distillation, making the foreground and background indistinguishable. With" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 281, + 747, + 296, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 281, + 747, + 296, + 756 + ], + "spans": [ + { + "bbox": [ + 281, + 747, + 296, + 756 + ], + "type": "text", + "content": "998" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 75, + 101, + 261, + 205 + ], + "blocks": [ + { + "bbox": [ + 75, + 101, + 261, + 205 + ], + "lines": [ + { + "bbox": [ + 75, + 101, + 261, + 205 + ], + "spans": [ + { + "bbox": [ + 75, + 101, + 261, + 205 + ], + "type": "table", + "html": "
GroupDistillation RegionNDSmAP
BEVFormer Base-Tinydirectly imitation41.8029.79
global random mask41.1428.49
mask on GT42.4129.85
selective focal mask42.8730.59
DETR3D R101-R50directly imitation37.2230.13
global random mask37.1930.03
mask on GT37.5830.11
selective focal mask37.9129.87
", + "image_path": "9bb7368866e775ca8b719763425f83736605e6d2fce87e4a9bb856688b6c5e33.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 54, + 207, + 279, + 236 + ], + "lines": [ + { + "bbox": [ + 54, + 207, + 279, + 236 + ], + "spans": [ + { + "bbox": [ + 54, + 207, + 279, + 236 + ], + "type": "text", + "content": "(a) Mask region selection. Global random masked generation exacerbates the performance, while the selective masked generation on focal regions brings a remarkable improvement." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 65, + 247, + 271, + 323 + ], + "blocks": [ + { + "bbox": [ + 65, + 247, + 271, + 323 + ], + "lines": [ + { + "bbox": [ + 65, + 247, + 271, + 323 + ], + "spans": [ + { + "bbox": [ + 65, + 247, + 271, + 323 + ], + "type": "table", + "html": "
GroupDistillation StageNDSmAP
PVBEV
BEVFormer✓46.2634.56
Base-Small✓47.0635.52
45.2433.56
✓✓47.6035.97
", + "image_path": "9e4fe3490c3a7237df2716270416a2d0a1ecfe334d63b7894f8065b6df0212d0.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 54, + 324, + 279, + 371 + ], + "lines": [ + { + "bbox": [ + 54, + 324, + 279, + 371 + ], + "spans": [ + { + "bbox": [ + 54, + 324, + 279, + 371 + ], + "type": "text", + "content": "(c) Distillation stage. Effect of global channel-wise distribution distillation (Fig. 1 (a)) on PV or BEV. The result indicates that combined distillation on PV and BEV achieves the highest improvement. Note that separate global distillation on BEV feature leads to a deterioration in performance." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 318, + 104, + 505, + 205 + ], + "blocks": [ + { + "bbox": [ + 318, + 104, + 505, + 205 + ], + "lines": [ + { + "bbox": [ + 318, + 104, + 505, + 205 + ], + "spans": [ + { + "bbox": [ + 318, + 104, + 505, + 205 + ], + "type": "table", + "html": "
GroupDistillation RegionNDSmAP
BEVFormer Base-Tinyglobal distribution41.8029.79
local pattern41.9129.89
global distribution + local pattern42.6830.30
DETR3D R101-R50global distribution37.4330.41
local pattern38.0030.21
global distribution + local pattern38.7230.57
", + "image_path": "f3482b5810a0f076cc31ea1dcb1b02253a668078f0e18720e977b062e4fe7d85.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 297, + 207, + 522, + 245 + ], + "lines": [ + { + "bbox": [ + 297, + 207, + 522, + 245 + ], + "spans": [ + { + "bbox": [ + 297, + 207, + 522, + 245 + ], + "type": "text", + "content": "(b) Distillation region. Global distribution means the channel-wise distribution of feature activation, and local pattern represents the feature values on the fine-grained focal regions. Distillation on both global distribution and local patterns achieves the best performance." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 310, + 252, + 512, + 322 + ], + "blocks": [ + { + "bbox": [ + 310, + 252, + 512, + 322 + ], + "lines": [ + { + "bbox": [ + 310, + 252, + 512, + 322 + ], + "spans": [ + { + "bbox": [ + 310, + 252, + 512, + 322 + ], + "type": "table", + "html": "
GroupFeature AlignmentNDSmAP
BEVFormerdownsample47.4736.66
Base-Smalldeconvolution48.7337.50
", + "image_path": "99c8af04893014907e61e0683e1d5b792cb54ac91585935d70167495dbd925e7.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 297, + 324, + 522, + 352 + ], + "lines": [ + { + "bbox": [ + 297, + 324, + 522, + 352 + ], + "spans": [ + { + "bbox": [ + 297, + 324, + 522, + 352 + ], + "type": "text", + "content": "(d) Feature alignment. Downsampling expert feature gets significantly worse results than upsampling apprentice feature through a deconvolutional layer." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 378, + 530, + 399 + ], + "lines": [ + { + "bbox": [ + 45, + 378, + 530, + 399 + ], + "spans": [ + { + "bbox": [ + 45, + 378, + 530, + 399 + ], + "type": "text", + "content": "Table 4. FD3D ablations on nuScenes val set. We show nuScenes detection score (NDS) and mean average precision (mAP) metrics (%). Default settings are marked in gray." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 91, + 408, + 231, + 596 + ], + "blocks": [ + { + "bbox": [ + 91, + 408, + 231, + 596 + ], + "lines": [ + { + "bbox": [ + 91, + 408, + 231, + 596 + ], + "spans": [ + { + "bbox": [ + 91, + 408, + 231, + 596 + ], + "type": "image", + "image_path": "6b1c2f6c51205dd3296107cb34e84c6ed62017585c8ec741b5d896116e629d41.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 603, + 279, + 679 + ], + "lines": [ + { + "bbox": [ + 45, + 603, + 279, + 679 + ], + "spans": [ + { + "bbox": [ + 45, + 603, + 279, + 679 + ], + "type": "text", + "content": "Figure 5. Visualization of feature activation and the predicted results before and after knowledge distillation. In comparison with the feature activation on PV, the foreground and background become clearly distinguishable with distillation. The predictions are illustrated on BEV, where green and blue boxes denote the ground truth and predictions respectively. With the devised method, the prediction accuracy of detection boxes is significantly improved." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 45, + 694, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 694, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 694, + 279, + 730 + ], + "type": "text", + "content": "the proposed approach, they become clearly distinguishable. The PV feature visualization confirms that the distillation makes the backbone of the apprentice network well" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 296, + 406, + 530, + 511 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 406, + 530, + 511 + ], + "spans": [ + { + "bbox": [ + 296, + 406, + 530, + 511 + ], + "type": "text", + "content": "optimized. High-quality 2D image feature extraction is the basis for BEV feature production and subsequent detection. In addition, we give a comparison of predicted bounding boxes in BEV. Through the comparison of the area within the red dashed box, our approach significantly reduces the translation error. Though the accuracy of the bounding boxes is obviously improved, the false positive issues are still serious after distillation due to the inherent detects in the 3D object detection model." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 297, + 521, + 458, + 533 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 521, + 458, + 533 + ], + "spans": [ + { + "bbox": [ + 297, + 521, + 458, + 533 + ], + "type": "text", + "content": "5. Conclusion and Future Work" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 296, + 540, + 530, + 633 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 540, + 530, + 633 + ], + "spans": [ + { + "bbox": [ + 296, + 540, + 530, + 633 + ], + "type": "text", + "content": "In this work, we apply knowledge distillation to camera-only 3D object detection, and we reveal that the challenge lies in how to distill focal knowledge when confronted with an imperfect expert. We devise FD3D, a flexible query-based approach that automatically searches the representative regions and highlights these regions for distillation. It serves as a plug-and-play module and successfully applies to various 3D object detectors." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 296, + 634, + 530, + 692 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 634, + 530, + 692 + ], + "spans": [ + { + "bbox": [ + 296, + 634, + 530, + 692 + ], + "type": "text", + "content": "Limitation and future work. The challenge of distilling knowledge from imperfect experts exists in not only the 3D object detection domain, but also in other fields. The proposed approach is needed to be extended to address more general scenarios." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 296, + 694, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 694, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 694, + 530, + 730 + ], + "type": "text", + "content": "Acknowledgements. This work is partially supported by NSFC (62206172, 62222607), and the Shanghai Committee of Science and Technology (21DZ1100100)." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 281, + 747, + 296, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 281, + 747, + 296, + 756 + ], + "spans": [ + { + "bbox": [ + 281, + 747, + 296, + 756 + ], + "type": "text", + "content": "999" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 105, + 102, + 117 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 105, + 102, + 117 + ], + "spans": [ + { + "bbox": [ + 47, + 105, + 102, + 117 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 124, + 280, + 730 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 51, + 124, + 279, + 188 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 124, + 279, + 188 + ], + "spans": [ + { + "bbox": [ + 51, + 124, + 279, + 188 + ], + "type": "text", + "content": "[1] Holger Caesar, Varun Bankiti, Alex H Lang, Sourabh Vora, Venice Erin Liong, Qiang Xu, Anush Krishnan, Yu Pan, Giancarlo Baldan, and Oscar Beijbom. nuscenes: A multimodal dataset for autonomous driving. 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Deformable detr: Deformable transformers for end-to-end object detection. arXiv preprint arXiv:2010.04159, 2020. 4" + } + ] + } + ], + "index": 12 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 747, + 297, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 747, + 297, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 747, + 297, + 756 + ], + "type": "text", + "content": "1001" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Distilling Neural Fields for Real-Time Articulated Shape Reconstruction/b3e477ee-24cc-4767-adae-b678b4d54a08_content_list.json b/2023/Distilling Neural Fields for Real-Time Articulated Shape Reconstruction/b3e477ee-24cc-4767-adae-b678b4d54a08_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..9ed123d7fffa91900f6b7936a92fd1f0fd5426ee --- /dev/null +++ b/2023/Distilling Neural Fields for Real-Time Articulated Shape Reconstruction/b3e477ee-24cc-4767-adae-b678b4d54a08_content_list.json @@ -0,0 +1,1556 @@ +[ + { + "type": "text", + "text": "Distilling Neural Fields for Real-Time Articulated Shape Reconstruction", + "text_level": 1, + "bbox": [ + 120, + 130, + 849, + 152 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/bdb7dd45e9767fab14f12396d4578e42862557549a6e0760024adcb1aec80dcb.jpg", + "image_caption": [ + "Figure 1. By distilling knowledge from dynamic NeRFs fitted to offline video data at scale [16, 44], we present a method to train category-specific real-time video shape predictors, which output temporally-consistent viewpoint, articulation, and appearance given casual input videos. Our method replaces expensive test-time optimization with a single forward pass, allowing real-time inference on a RTX-3090 GPU. Compared to existing model-based methods for reconstructing humans and animals in motion [13, 18, 31], our method does not require pre-defined 3D templates or ground-truth 3D data to train. (Project page: https://jefftan969.github.io/dasr)." + ], + "image_footnote": [], + "bbox": [ + 145, + 180, + 826, + 444 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 531, + 313, + 546 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We present a method for reconstructing articulated 3D models from videos in real-time, without test-time optimization or manual 3D supervision at training time. Prior work often relies on pre-built deformable models (e.g. SMAL/SMPL), or slow per-scene optimization through differentiable rendering (e.g. dynamic NeRFs). Such methods fail to support arbitrary object categories, or are unsuitable for real-time applications. To address the challenge of collecting large-scale 3D training data for arbitrary deformable object categories, our key insight is to use off-the-shelf video-based dynamic NeRFs as 3D supervision to train a fast feed-forward network, turning 3D shape and motion prediction into a supervised distillation task. Our temporal-aware network uses articulated bones and blend skinning to represent arbitrary deformations, and is self-supervised on video datasets without requiring 3D shapes or viewpoints as input. Through distillation, our network learns to 3D-reconstruct unseen articulated objects at interactive frame rates. Our method yields higher-fidelity 3D reconstructions than prior real-time methods for animals, with the ability to render realistic images at novel viewpoints and poses.", + "bbox": [ + 73, + 564, + 472, + 898 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 501, + 531, + 630, + 546 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We are interested in building high-quality animatable models of articulated 3D objects from videos in real time. One promising application is virtual and augmented reality, where the goal is to create high-fidelity 3D experiences from images and videos captured live by users. For rigid scenes, structure from motion (SfM) and neural rendering can be used to build accurate 3D cities and landmarks from Internet image collections [1, 20, 33]. For articulated objects such as friends and pets, many works parameterize the range of motions using category-specific templates such as SMPL [18] for humans and SMAL [4] for quadruped animals. Although these methods can be trained on large-scale video datasets, they rely on parametric body template models built from extensive real-world 3D scans: these body models are not easy to generate for diverse categories in the wild such as clothed humans or pets with distinct morphologies, which are often the focus of user content.", + "bbox": [ + 496, + 561, + 890, + 819 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Inspired by the breakthrough success of neural radiance fields [21], many works reconstruct arbitrary articulated objects in an analysis-by-synthesis framework [16, 27, 28, 30, 36, 44] by defining time-dependent 3D warping fields and establishing long-range correspondences on top of canon-", + "bbox": [ + 496, + 825, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "4692", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ical shape and appearance models. These methods output high-quality reconstructions of arbitrary objects without 3D data or pre-defined templates, but the output representations are scene-specific and often require hours to compute from scratch on unseen videos - an unacceptable cost for real-time VR/AR tasks. We are thus interested in dynamic 3D reconstruction algorithms that achieve the best of both worlds: the speed of template-based models and the quality and generalization ability of dynamic NeRFs. To achieve this, our key insight is remarkably simple: we train category-specific feed-forward 3D predictors at scale by self-supervising them with dynamic NeRF \"teachers\" fitted to offline video data.", + "bbox": [ + 75, + 90, + 472, + 287 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "By leveraging scene-fitted dynamic NeRFs for 3D supervision at scale, our method learns a feed-forward predictor for appearance, 3D shape, and articulations of non-rigid objects from videos. Our learned 3D models use linear blend skinning to express articulations, allowing it to be animated by manipulating bone transformations. We address three key challenges in our work: (1) how to supervise feed-forward models with internal representations of dynamic NeRFs, (2) how to produce temporally consistent predictions of pose, articulation, and appearance, and (3) how to build efficient systems for real-time reconstruction.", + "bbox": [ + 75, + 287, + 472, + 454 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 467, + 218, + 483 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Template-Based Dynamic Reconstruction A large body of work uses parametric body models [18, 48, 49] to recover 3D shapes and motions for human and animal reconstruction, given a single image as input [2, 3, 13, 32]. These models are built from registered 3D scans of real humans or toy animals, and achieve great success in reconstructing categories for which large volumes of ground-truth 3D data are available (especially human reconstruction). However, it is challenging to apply these methods to arbitrary categories with diverse morphologies, especially where 3D data is limited. Our work aims to generalize these approaches to arbitrary articulated object categories without requiring ground-truth 3D data or pre-registered 3D scans during training.", + "bbox": [ + 75, + 492, + 468, + 688 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Template-Free Dynamic Reconstruction Several methods build deformable 3D models without templates by recovering shapes and poses from internet-scale 2D image collections, using weak supervision such as keypoints and object silhouettes from off-the-shelf models or human annotators [6, 10, 14, 34]. As it is inherently ambiguous to reconstruct 3D outputs from the sparse and limited 2D observations available in images, these methods must leverage strong data priors and apply heavily regularization to ensure reasonable outputs, often resulting in blurry or oversmoothed shapes and textures. Leveraging the temporal context available in videos can help these methods learn temporally consistent results [38], however the output quality is still low perhaps due to over-regularization.", + "bbox": [ + 75, + 688, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Neural Radiance Fields Neural fields are a powerful method for 3D reconstruction using 2D image supervision, achieving state-of-the-art quality on both static and dynamic scenes. Although historically limited to rigid scenes with known cameras [20, 21, 36], recent works extend NeRF to dynamic scenes by deforming view-space points to a canonical space over time, using time-dependent 3D warping fields and dense correspondences [5, 16, 17, 27, 30]. Dynamic NeRFs are able to learn high-fidelity animatable 3D models from several casual videos capturing the same object instance [42-44], by leveraging the temporal context available in videos. Unfortunately, dynamic NeRFs are slow and require optimization from scratch on unseen videos at test-time. Although architectures exist to speed up static NeRFs using explicit voxel grids [46] or hash-table caching [22], more work is required to speed up dynamic NeRFs by similar factors due to the additional overheads of time-dependent warping and correspondence matching. Our aim is to leverage the high-quality outputs of dynamic NeRFs to supervise a fast and lightweight architecture for articulated 3D reconstruction.", + "bbox": [ + 496, + 90, + 893, + 409 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 428, + 591, + 443 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In order to train category-specific feed-forward 3D predictors from dynamic NeRF teacher models, we combine a single-frame image encoder that regresses viewpoint, shape, and appearance from images, and a temporal encoder that reasons about these predictions over time. In this section, we describe the problem setup, scene representation, network architecture, training procedure, and losses.", + "bbox": [ + 496, + 455, + 893, + 561 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3.1. Problem Setup", + "text_level": 1, + "bbox": [ + 500, + 577, + 651, + 593 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Given an input video centered on an articulated object, we train a feed-forward network to predict the viewpoint, articulations, and appearance, which are used to render a posed and textured object model. Our network is supervised on the pseudo-ground-truth outputs of a dynamic NeRF teacher, which builds animatable 3D models from casually collected videos including shape, appearance, and time-varying articulations. Our particular implementation uses BANMo [44] as the teacher, as it has public code and yields good results on humans and quadrupeds. Similar to the teacher, our method requires no pre-defined shape templates, registered cameras, or 3D ground truths.", + "bbox": [ + 496, + 595, + 893, + 777 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Fig. 2 summarizes our approach and how it differs from the teacher model. Sec. 3.2 and Sec. 3.3 introduce our object and motion representation, while Sec. 3.4 discusses the underlying feed-forward neural architecture. Finally, Sec. 3.5 describes the training losses used to supervise our models. In contrast to our teacher [44] which uses volume rendering (which can be slow), we render textured meshes to enable efficient rasterization.", + "bbox": [ + 496, + 779, + 893, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "4693", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/c5928dc0e6d942bffa1eb30629d2c668ff53ad26e551253143272f4f57eaefd5.jpg", + "image_caption": [ + "Figure 2. Architecture details. We train a feed-forward network (shown in blue) to predict articulations and textures from videos, supervised by the pseudo-ground-truth outputs of an offline dynamic NeRF teacher [44] (including 3D shapes, articulations, and textures). To simplify the learning task, our feed-forward network outputs in a high-dimensional latent space: the dynamic NeRF's frozen decoder networks (shown in purple) are used to convert articulation codes into joint angles and texture codes into 3D surface textures. Spatial per-vertex $\\mathcal{L}_2$ losses are used to supervise the articulated 3D outputs against the articulated pseudo-ground-truths (shown in green)." + ], + "image_footnote": [], + "bbox": [ + 119, + 64, + 843, + 338 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Object Representation", + "text_level": 1, + "bbox": [ + 76, + 422, + 285, + 439 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Category-level shape. We model articulated objects as a canonical rest shape that is transformed by time-dependent poses and articulations. The rest shape is a category-specific triangular mesh $M = (V, F)$ that represents the mean shape of instances in the category: the faces $F$ define the vertex connectivity and we assume it remains fixed. To initialize the rest mesh, we run marching cubes on a $128^3$ grid to find the zero level set of the neural field that serves as the teacher NeRF's implicit rest shape. Although explicit mesh representations are less expressive than implicit neural fields, we find that a feed-forward predictor benefits from the speed of rasterization and the simplicity of regressing vertex colors.", + "bbox": [ + 75, + 446, + 468, + 628 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Per-instance pose and articulation. At each frame $t$ , we model the object's viewpoint and articulation similar to the dynamic NeRF literature. The viewpoint is a root body transformation $\\mathbf{G}^t \\in SE(3)$ , and we use neural blend skinning [9, 39] to express object articulations. For each frame, the bone configurations for neural blend skinning are parameterized by a joint angle vector $\\mathbf{B}^t \\in SO(3)^b$ , which is predicted by our feed-forward network from input video frames. See Sec. 3.3 for more details.", + "bbox": [ + 75, + 628, + 468, + 763 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Appearance. As our mesh topology is fixed, we can simply model the object's appearance as an array of per-vertex colors $\\mathbf{C}^t\\in \\mathbb{R}^{|V|\\times 3}$ at each frame $t$ . Following the standard rasterization pipeline, barycentric coordinates are used to interpolate the vertex colors per triangle during rendering.", + "bbox": [ + 75, + 763, + 468, + 840 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Rendering. We assume a weak-perspective camera projection defined by a fixed camera at the origin pointed along the negative- $z$ axis. To render the object in video frame $t$ , we apply the predicted viewpoint $\\mathbf{G}^t \\in SE(3)$ at time", + "bbox": [ + 75, + 840, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$t$ , followed by the blend skinning deformation specified by predicted bone configuration $\\mathbf{B}^t \\in SO(3)^b$ using forward kinematics and dual-quaternion blend skinning.", + "bbox": [ + 498, + 424, + 890, + 470 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Time-Varying Articulation via Blend Skinning", + "text_level": 1, + "bbox": [ + 498, + 478, + 890, + 494 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To represent articulated body motion, we use a neural blend skinning model to define a 3D warping field $\\mathcal{W}^t$ on top of a category-level kinematic skeleton. After computing the skeleton's forward kinematics, each point is deformed by a weighted combination of per-bone transformations.", + "bbox": [ + 496, + 501, + 890, + 575 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Category-level skeleton. Unlike color and 3D shape which are directly observable from imagery, an object's bone structure is much harder to infer. Automatic skeletal rigging methods [15,26] rely heavily on shape priors, or are sensitive to input data. Fortunately, bone structures are largely fixed within categories up to slight variations in bone length and body part scale. Thus, we can use readily available generic skeletons of humans, quadrupeds, and other categories to specify the bone structure of each category. Skeletons are defined by a tree structure with $B + 1$ variable-length bones and $B$ ball joints, where $B = 19$ for humans and $B = 26$ for quadrupeds.", + "bbox": [ + 496, + 577, + 890, + 758 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Forward kinematics. Each bone $b$ has a link transformation $\\mathbf{L}_b\\in SE(3)$ specifying the bone length and a joint transformation $\\mathbf{J}_b^t\\in SE(3)$ specified by the joint angle $\\mathbf{B}_b^t\\in SO(3)$ . The result for each link $b$ is a sequence of alternating transformations from the skeleton's base to the link's end, where $b_{1},b_{2},\\ldots ,b$ are the parent links up to $b$ :", + "bbox": [ + 496, + 758, + 890, + 849 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {T} _ {b} ^ {t} = \\mathbf {J} _ {b} ^ {t} \\mathbf {L} _ {b} \\dots \\mathbf {J} _ {b _ {2}} ^ {t} \\mathbf {L} _ {b _ {2}} \\dots \\mathbf {J} _ {b _ {1}} ^ {t} \\mathbf {L} _ {b _ {1}}\n$$\n", + "text_format": "latex", + "bbox": [ + 583, + 858, + 803, + 876 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Blend skinning. From per-bone kinematic transformations", + "bbox": [ + 500, + 885, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "4694", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$\\mathbf{T}_b^t$ and root body pose $\\mathbf{G}^t$ , we use dual-quaternion blend skinning to compute a 3D warping field $\\mathcal{W}(\\mathbf{X})$ :", + "bbox": [ + 76, + 90, + 470, + 121 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {W} (\\mathbf {X}) ^ {t} = \\left(\\sum_ {b} \\mathbf {W} (\\mathbf {X}) _ {b} ^ {t} \\cdot \\mathbf {T} _ {b} ^ {t}\\right) \\cdot \\mathbf {G} ^ {t}\n$$\n", + "text_format": "latex", + "bbox": [ + 155, + 133, + 388, + 152 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Skinning weights $\\mathbf{W}(X)_b^t$ are specified by the softmax'ed distances between rest mesh vertices $\\mathbf{X}$ and bone centers.", + "bbox": [ + 76, + 164, + 468, + 194 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Network Architecture", + "text_level": 1, + "bbox": [ + 76, + 207, + 282, + 222 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Single-frame image encoder. Given a video of length $T$ , we use off-the-shelf PointRend [12] to compute segmentations and DensePose [7, 23, 24] to compute per-pixel CSE features. Each RGB image is concatenated with features, then masked and cropped to $1.2\\mathrm{x}$ the tight bounding box of the object. We find that using dense pretrained features improves convergence speed over RGB inputs alone. We pass the preprocessed frames into a convolutional stacked hourglass network [25], which uses repeated pooling and upsampling to process features across multiple scales and spatial locations. The stacked intermediate outputs of each hourglass module are passed into a ResNet18 [8] network which predicts latent vectors $z_{\\mathrm{view}}$ and $z_{\\mathrm{art}}$ : $z_{\\mathrm{view}}$ is decoded into the viewpoint $\\mathbf{G}^t \\in SE(3)$ and $z_{\\mathrm{art}}$ is decoded into articulated joint angles $\\mathbf{B}^t \\in SO(3)^B$ . We use 6D rotations to represent angles during training [47].", + "bbox": [ + 75, + 229, + 468, + 472 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Viewpoint branch. As the space of possible viewpoints is discontinuous and multi-modal, it is difficult to approach the optimum through iterative gradient descent. Following [6], we use a viewpoint decoder network $\\mathbf{MLP}_{\\mathrm{view}}$ to decode $z_{\\mathrm{pose}}$ into a set of $M$ viewpoints hypotheses $\\mathbf{G}_{\\{1,\\dots,M\\}}^t$ weighted by $w_{\\mathbf{G}}^{t}\\in \\mathbb{R}^{M}$ . Fig. 3 shows the variation over viewpoint hypotheses at an early stage of training.", + "bbox": [ + 75, + 473, + 468, + 582 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Articulation branch. Estimating 3D articulations from monocular images can be difficult due to depth ambiguities and occlusions. To resolve this, recent work on human pose estimation [37] uses a normalizing flow articulation prior represented as an invertible neural network, trained on large-scale human motion capture datasets. Without access to such datasets for other categories, we achieve a similar effect by leveraging the teacher's articulation priors, using the teacher's frozen articulation decoder $\\mathbf{MLP}_{\\mathrm{art}}$ to decode $z_{\\mathrm{art}}$ . Fig. 4 visualizes the principal components of $z_{\\mathrm{art}}$ 's latent space: we find that perturbing $z_{\\mathrm{art}}$ along its principal components causes the resulting articulated shape to perform natural motions, such as curling up in a ball.", + "bbox": [ + 75, + 583, + 468, + 779 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Appearance branch. As the object in the video is only partially observable at any given time, we must use data priors or look at nearby frames to output complete appearance predictions $\\mathbf{C}^t\\in \\mathbb{R}^{|V|\\times 3}$ , represented as per-vertex colors of the articulated mesh at each frame. Our teacher [44] models global object appearances as a category-level neural field modulated by a texture code $z_{\\mathrm{color}}\\in \\mathbb{R}^{64}$ . We leverage these appearance priors by predicting an environment code per", + "bbox": [ + 75, + 780, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/7ffad52c18e195531c6012e8ec728d1138596e61f14a22d4e045bf4e89582f1b.jpg", + "image_caption": [ + "Figure 3. Viewpoint multiplexing during training. To overcome the discontinuous and multi-modal nature of pose optimization, we train our feed-forward predictor to output a set of $M$ viewpoint hypotheses rather than a single viewpoint. Blending multiple viewpoint hypotheses yields a more accurate prediction (here $M = 5$ ). Top row: Input frames. Second row (white): Blended viewpoint prediction. Bottom rows (light blue): $M$ viewpoint hypotheses" + ], + "image_footnote": [], + "bbox": [ + 500, + 88, + 890, + 292 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/5319b1470e805c243ad8a66e80a4dc413ca4f3da4773d989e4bb08f5bc213e6d.jpg", + "image_caption": [ + "Figure 4. Visualizing articulation code. Rather than training our feed-forward predictor to output high-dimensional (75) skeletal articulations, we leverage the teacher's pre-trained articulation space by predicting a low-dimensional (16) code. We visualize the first four principal components of the articulation code learned from the training dataset and find that variations along each axis correspond to interpretable motions: (1) whether the left or right paw is in front, (2) whether the hind paws are retracted or extended, (3) whether the front paws are retracted or extended, and (4) whether the cat has a straightened or curled-up posture." + ], + "image_footnote": [], + "bbox": [ + 508, + 391, + 879, + 606 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "frame, modulating the teacher's frozen category-level neural field, and querying it at the rest mesh's vertex locations.", + "bbox": [ + 496, + 777, + 890, + 808 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Temporal encoder. Predicting pose and shape from single images can be highly ambiguous due to motion blur, occlusions, and depth ambiguities. To output temporally consistent results over long videos, we define a temporal encoder that updates $z_{\\mathrm{view}}$ , $z_{\\mathrm{art}}$ , and $z_{\\mathrm{color}}$ across many frames. We treat the viewpoint multiplex $z_{\\mathrm{view}}$ as a single vector by con", + "bbox": [ + 496, + 810, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "4695", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "catenating all $M$ hypotheses. Following prior work [11], our temporal encoder has several 1D convolutional layers acting on a temporal window centered at time $t$ .", + "bbox": [ + 75, + 90, + 468, + 137 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Losses and Supervision", + "text_level": 1, + "bbox": [ + 76, + 143, + 292, + 159 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Optimization objective. Treating the teacher's outputs as pseudo-ground truths, our model can be trained in a standard supervised manner. We would like to use the teacher's inferred low-dimensional latent codes as supervisory targets for the student. But rather than defining $\\mathcal{L}_2$ losses in the latent embedding space, where each dimension of $z_{\\mathrm{view}}$ , $z_{\\mathrm{art}}$ , and $z_{\\mathrm{color}}$ has varying importance, we instead render these codes and compute 3D losses. As all articulated meshes have the same topology, we can define geometry and color losses as per-vertex $\\mathcal{L}_2$ error:", + "bbox": [ + 75, + 160, + 468, + 311 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\mathrm {g e o m}} = \\left\\| \\mathbf {X} ^ {t} - \\widehat {\\mathbf {X}} ^ {t} \\right\\| _ {2} \\quad L _ {\\mathrm {c o l o r}} = \\left\\| \\mathbf {C} ^ {t} - \\widehat {\\mathbf {C}} ^ {t} \\right\\| _ {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 109, + 316, + 437, + 344 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To improve articulation learning and account for multiple possible inverse kinematics solutions while solving for joint articulations, we add a joint loss defined as geodesic distance between predicted and actual joint angles at each joint. We find that this improves deformation quality.", + "bbox": [ + 75, + 348, + 468, + 422 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In summary, we train the image encoder and temporal encoder with the following objective:", + "bbox": [ + 75, + 424, + 468, + 454 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL = L _ {\\text {g e o m}} + L _ {\\text {j o i n t}} + L _ {\\text {c o l o r}}\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 460, + 364, + 478 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 489, + 209, + 506 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Although we could have distilled a student using any dynamic NeRF as the teacher, our implementation uses BANMo [44] because it has public code, accepts unannotated monocular videos as input, and produces good results on humans and quadropeds. We modified BANMo to replace the bag-of-bones deformation model with a skeleton. Hyperparameters. Our method is implemented in PyTorch. We use the AdamW optimizer and train the model for 16k iterations, taking around 4 hours on a single RTX-3090 GPU. We use $224 \\times 224$ images with batch size 56. We use 8 stacked hourglass blocks in the image encoder and a window size of 13 frames in the temporal encoder. All losses are weighted to have similar initial magnitudes.", + "bbox": [ + 75, + 508, + 468, + 703 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Staged training. We adopt a two-stage training strategy at every epoch to reduce the computational costs of evaluating an image encoder at every frame, when only a single frame per time window will receive a gradient update. In the first stage, we send frames through the image encoder and compute per-frame losses without using the temporal encoder, storing per-frame values of $z_{\\mathrm{pose}}$ , $z_{\\mathrm{art}}$ , and $z_{\\mathrm{color}}$ . In the second stage, we send time windows of cached features through the temporal encoder without using the image encoder. Two-staged training reduces redundant image encoder evaluations and ensures that the temporal encoder can be safely removed if we only have access to single images rather than time windows of frames at test time.", + "bbox": [ + 75, + 704, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/6db580876c0f859ef1b9004ed2581be599ad47cce0f1227ddfa339e5cdf01107.jpg", + "table_caption": [ + "Table 1. Datasets. All videos are treated as casually collected monocular RGB videos, except when additional groundtruth meshes or depth maps are needed for evaluation. Processing time includes computing segmentations and per-pixel features with off-the-shelf networks, as well as computing pseudo-ground truth 3D outputs with the teacher." + ], + "table_footnote": [], + "table_body": "
Total VideosTotal InstancesTotal FramesTest InstancesTest FramesProcessing Time (hr)
Humans48286.4k101.6k22.0
Cats775611.7k132.7k23.2
Dogs88789.7k171.7k23.8
", + "bbox": [ + 501, + 183, + 898, + 260 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Datasets", + "text_level": 1, + "bbox": [ + 500, + 273, + 602, + 287 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We collect datasets for three categories: humans, cats, and dogs. For humans, we combine datasets from AMA [35], MonoPerfCap [41], DAVIS [29], and BANMo [44] to obtain 48 human videos. We evaluate on AMA and MonoPerfCap as they have ground-truth meshes. For cats and dogs, we collect 77 cat videos and 88 dog videos from the Pixels stock video website as well as BANMo released data. We also used an iPad Pro to capture two RGB-D videos to evaluate depth accuracy on cats and dogs. Video frames are extracted at 10fps. Datasets are summarized in Tab. 1.", + "bbox": [ + 496, + 292, + 890, + 443 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To compute BANMo pseudo-ground-truths per category without optimizing dozens of independent BANMo models, we optimize a single BANMo model per category, using articulation and texture codes to model shape and appearance differences across instances. As a result, the total dataset processing time is about 24 hours per category on 8 RTX-3090 GPUs. We find that BANMo generalizes quite well from the instance-level to the category-level setting [45], and that the articulation and texture latent spaces cover the range of motions and textures across all instances.", + "bbox": [ + 496, + 445, + 890, + 595 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Reconstructing Humans", + "text_level": 1, + "bbox": [ + 498, + 609, + 723, + 625 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Dataset. Following BANMo, we evaluate human reconstruction on the AMA [35] dataset, containing 10 real-world mesh sequences depicting 3 different humans. The subjects wear loose clothing and perform challenging actions such as dancing and performing a handstand. Although the AMA videos were captured in an 8-camera studio to enable ground-truth mesh extraction, we treat them as casually collected monocular videos and do not use the camera intrinsics, camera extrinsic, or time synchronization.", + "bbox": [ + 496, + 627, + 890, + 763 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Comparisons. We compare against template-free BANMo [44], as well as model-based methods HuMoR [31] and ICON [40]. BANMo fits an animatable 3D model to multiple monocular videos of an object instance by performing differentiable rendering optimization. We train BANMo on the same dataset as our model. HuMoR is a human-specific temporal pose and shape predictor that performs test-time optimization on video sequences, leveraging OpenPose keypoint detection and motion priors learned", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "4696", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/de319ab15924845971c13213ed9b50646c686ac4d93baa317a78a7b021e3870b.jpg", + "image_caption": [ + "Figure 5. Qualitative results on humans (left), cats (middle), and dogs (right) in the test set. From left to right for each category, we show the input images, articulated shape and texture predictions overlaid on the input images, and three different viewpoints of the predicted geometry. Our method operates on casual monocular videos and predicts plausible shape, articulations, and textures in real-time. Our predictions align well with the image evidence on challenging inputs." + ], + "image_footnote": [], + "bbox": [ + 98, + 80, + 205, + 363 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b0da028f4f2b813d0d4307bbb025b5736903f67f0a918d3d721a27b3d996d142.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 207, + 80, + 352, + 354 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b066a9c299a639213fda32706134dfac55bcc65fabc911d9e3ec9e5ffc156336.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 354, + 80, + 462, + 362 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/5e9549b31b812e668cc1790c3b3d3e8bf43301c5e36dc4100b4baae707b5ba43.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 464, + 80, + 609, + 354 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/075ad9ae709ba73c836a44a22668e7ac2cf4ece0643164784dc8d07df26d0703.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 609, + 80, + 717, + 362 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/17e0ce9abcf93e46b3a00ea95828ab481ae7bbdf035cf6d2b1f79053e729e5d6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 715, + 80, + 870, + 354 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "from large-scale human motion capture datasets. ICON is the current SOTA for single-view human reconstruction, and it combines implicit functions with the SMPL human body model, using test-time optimization to fit surface normal predictions and improve pose accuracy and reconstruction quality. All our baselines require far more processing time than our model, which runs in real-time.", + "bbox": [ + 75, + 449, + 470, + 555 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Metrics. We report 3D chamfer distance and F-scores on three held-out test sequences in Tab. 2, averaged across all frames. Chamfer distance is the average distance between the ground-truth and predicted mesh vertices using nearest neighbor matches. As this can be sensitive to outliers, we also evaluate F-score at distance thresholds $d \\in \\{1\\%, 2\\%, 5\\% \\}$ to better quantify reconstruction error at different granularities. We scale predicted meshes by their view-space bounding box height to account for unknown scale compared to registered ground-truths. Our model approaches the performance of BANMo and baselines, while requiring nearly 1000x less compute at test time.", + "bbox": [ + 75, + 561, + 468, + 743 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Qualitative Results. We show qualitative comparisons for upright and inverted humans in Fig. 7. HuMoR outputs a deformed SMPL model, while ICON and BANMo optimize for both shape and articulation. Although our method outputs reasonable articulations for the upright pose, the woman lacks fine-grained geometry details and the viewpoint on the handstand video is inaccurate. We hypothesize that these failures occur due to the entanglement between articulations and per-instance morphologies, and the lack of handstand examples in the training set.", + "bbox": [ + 75, + 750, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Reconstructing Cats and Dogs", + "text_level": 1, + "bbox": [ + 498, + 449, + 767, + 465 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Dataset. We evaluate cat and dog reconstruction on two RGB-D pet videos, as well as a held-out test set of pet videos from BANMo's dataset. These videos contain challenging motions such as rapid turns and jumping off chairs. Comparisons. We compare against BANMo [44] and BARC [32], a model-based approach and the current SOTA for dog shape and pose estimation from images. BARC trains a feed-forward network using images with keypoint labels and synthetic SMAL dog models [4], leveraging breed losses as additional supervision. As BARC is image-based, we run it separately on each video frame.", + "bbox": [ + 496, + 465, + 890, + 632 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Metrics We report the root mean square depth error and depth accuracy for all foreground pixels in Tab. 3, averaged across all frames. We render a synthetic depth map per frame, and following [19], we account for the unknown global scale factor between depth maps by aligning the median rendered and ground-truth depths at each frame:", + "bbox": [ + 496, + 632, + 890, + 723 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\ns _ {i} = \\operatorname * {m e d i a n} _ {x} \\left\\{D _ {i} ^ {p r e d} (x) / D ^ {g t} (x) \\right\\}\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 729, + 813, + 758 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Depth accuracy is computed as the proportion of foreground pixels whose synthetic depth is within a given threshold.", + "bbox": [ + 496, + 763, + 890, + 795 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Qualitative Results We show qualitative results comparing to BARC in Fig. 6. BARC performs well at predicting coarse shape and deformations, and more faithfully captures the fine motion and geometry details of the dog when it is positioned well in frame. However, as BARC entangles shape and breed, we find that BARC may predict biased shapes for certain breeds. For example, in the bottom left", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "4697", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f66c1c22a0ffce9145eab82ecbc4cdb1d9944bf2d41ec6ddadbdbfb9c0b641a0.jpg", + "image_caption": [ + "t-1" + ], + "image_footnote": [], + "bbox": [ + 158, + 75, + 362, + 204 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8a16d35e61ccd2191701ad3d0424660029aeb78dba736f7d4f371cc69a3e5ac4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 383, + 75, + 558, + 204 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/915c363f5da0168e8e933cb46c63cdfb30ad866e907efd922c4e7b63b543f8a3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 575, + 83, + 602, + 111 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/bd315a81fc1abb43bb89f8347d127c261adf40ec95c86278307fe15294f0dba1.jpg", + "image_caption": [ + "M", + "#", + "#" + ], + "image_footnote": [], + "bbox": [ + 611, + 77, + 781, + 204 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c5dbdc849075302d3603f201f72593edcfa70a5d60eab93d961d93dd530832a7.jpg", + "image_caption": [ + "$t - 1$", + "t", + "t+1", + "Figure 6. Qualitative comparisons on pet sequences. From left to right in each column, we show (left) the input image, (middle-left) BARC's prediction, (middle-right) our articulated shape and texture predictions, and (right) our geometry predictions. Our method operates on videos and predicts plausible shape, articulations, and texture in real time. BARC operates on each video frame independently, resulting in jittery predictions when the pet is small or not clearly visible (top row). While BARC's geometry and motion predictions are largely accurate, they can be biased for certain breeds (bottom left), predicting an arched back for a flat-backed dog." + ], + "image_footnote": [], + "bbox": [ + 158, + 215, + 380, + 351 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e72a24506d3f772cb787ba7d1ff73214baa04b6dbd34e5dff8bb38e91e7f81ff.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 383, + 215, + 584, + 351 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3b74cc276034cd958caad99e1635a72ffb2ecee4214eac45af94b9d39dd5d54f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 609, + 215, + 782, + 349 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/449ac868039cad4f91f9469b0b311781137e64ab80ce4a50ae64ece466280321.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 795, + 228, + 818, + 349 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/dc9f3863d9773d1d4bdeffb321188d92bcbfe2a22c74991dfcaba1c478d781cb.jpg", + "table_caption": [ + "Table 2. Quantitative results on AMA sequences. 3D chamfer distance (cm, ↓) and F-score (%, ↑) for articulated meshes, averaged over all frames. T_samba is a held-out video of a person that was seen during training, while the D_bouncing and D_handstand sequences contain a previously unseen person. Our model approaches the performance of BANMo and baselines while requiring nearly three orders of magnitude less compute at test time. Notably, our method performs better on T_samba, as it has fewer challenging poses and contains a person previously seen during training. Other baselines are trained on 3D human data, rely on the SMPL body model, or use expensive test-time optimization to improve results. We also report the inference time (ms) per frame. Results marked by * are different runs with the same hyperparameters. The best results are in bold. Please refer to Sec. 4.4 for discussions on the ablation results." + ], + "table_footnote": [], + "table_body": "
MethodTimeT_sambaD_bouncingD_handstand
CDF@1%F@2%F@5%CDF@1%F@2%F@5%CDF@1%F@2%F@5%
HuMoR420009.823.347.483.611.421.146.183.221.913.528.858.5
ICON6300010.118.939.985.29.727.853.586.414.123.545.275.6
BANMo4300010.325.348.883.611.626.750.881.514.222.544.174.7
Ours*2210.625.849.684.112.023.446.179.917.317.935.967.2
No temporal encoder2012.223.144.778.912.922.745.077.516.917.935.868.2
Conv1D encoder*2210.826.049.282.712.123.846.779.915.024.945.473.1
Transformer encoder2710.626.350.083.213.222.344.076.516.818.737.168.2
w/o frozen decoders2111.024.648.081.611.525.649.881.417.922.341.870.4
\\( 64^3 \\) template grid1012.021.042.279.112.722.945.278.015.622.543.671.8
\\( 128^3 \\) template grid*2210.525.649.884.412.423.646.078.713.724.346.575.6
\\( 256^3 \\) template grid2810.427.150.783.912.523.646.478.715.719.238.571.1
5 train videos2211.222.444.381.013.720.841.675.317.117.535.367.1
16 train videos2210.524.346.983.613.321.743.076.615.821.640.770.6
26 train videos2210.228.051.684.313.222.043.676.817.717.835.667.2
35 train videos*2210.824.047.483.612.323.346.379.016.819.038.069.2
", + "bbox": [ + 84, + 551, + 883, + 837 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "of Fig. 6, BARC predicts a rounded back but the back is flat in reality. For the inputs on the top row, BARC's single-frame architecture makes jittery predictions from frame to", + "bbox": [ + 75, + 849, + 470, + 895 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "frame, while our temporal architecture enforces consistency and prevents large discontinuities in pose and deformation. In the middle top image, which is particularly challeng-", + "bbox": [ + 498, + 849, + 890, + 895 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "4698", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/4e0d4202433daa09bd9a0e7409d4579d085557921e47963d2b287719ddae0693.jpg", + "table_caption": [ + "Table 3. Quantitative results on RGB-D pet sequences. Root mean square depth error (↓) and depth accuracy (%, ↑) for all foreground pixels in the depth map, averaged over all frames. We also report the total processing time per frame (ms) on a RTX-3090 GPU. Although BANMo consistently does better, our method approaches its quality while being nearly 1000x faster at test time. Best results are in bold." + ], + "table_footnote": [], + "table_body": "
MethodTimedogcat
RMSEAcc-1%Acc-2%Acc-5%RMSEAcc-1%Acc-2%Acc-5%
BANMo54s0.041128.645.372.70.075727.747.476.5
Ours100ms0.056917.731.656.60.129819.133.861.4
", + "bbox": [ + 153, + 141, + 815, + 220 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3ace91fa95b8627fd71ad0b2f21d9df0fa15c9f7729196a81769808aca48dd1e.jpg", + "image_caption": [ + "Image" + ], + "image_footnote": [], + "bbox": [ + 119, + 233, + 176, + 304 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ebbe64bcd4acd62ad47b9cb866c5eb73220a8fff0fb2dc7c8fdc9744deddb46e.jpg", + "image_caption": [ + "HuMoR" + ], + "image_footnote": [], + "bbox": [ + 183, + 234, + 238, + 303 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f9db9c96f939688020a2e040b8d2d2becfd4dfe4e0d944e1de47095b10f96fbd.jpg", + "image_caption": [ + "ICON" + ], + "image_footnote": [], + "bbox": [ + 243, + 234, + 297, + 303 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/32ff58cefc9413694008eb202528aefcf01cbbd2eb5f4d47dae70a099023539d.jpg", + "image_caption": [ + "BANMo" + ], + "image_footnote": [], + "bbox": [ + 307, + 234, + 362, + 303 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/72c5582a3f2231176b51f7477733e011da2ccc579d440070fc4f1325d3b1ca8b.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 367, + 234, + 429, + 304 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/bdeb9da3c3cf2798aff024d917977a8405c7e2daad8a3bff751a16b4ea721914.jpg", + "image_caption": [ + "Image" + ], + "image_footnote": [], + "bbox": [ + 119, + 319, + 176, + 388 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/fbf57c117253423b9292eef4238c1ad9bc8f1388d566f13ca274e20bb4ab39fc.jpg", + "image_caption": [ + "HuMoR" + ], + "image_footnote": [], + "bbox": [ + 183, + 325, + 228, + 385 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1a42072221b057dd91089041a733f44125f9d21701f4ca45d50e581a8ccd0f5b.jpg", + "image_caption": [ + "ICON" + ], + "image_footnote": [], + "bbox": [ + 256, + 327, + 287, + 383 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3b0bcea5b5f938ffde2346af42f8007470e0f25bbf64b0bca013a8e31dbd211d.jpg", + "image_caption": [ + "BANMo", + "Figure 7. Qualitative comparisons on human sequences. From left to right, we show the output of HuMoR [31], ICON [40], BANMo [44], and our method on dancing (top) and handstand (bottom) sequences. Our method outputs plausible articulations for the dancing sequence, although the shape lacks fine details. In comparison, HuMoR outputs the SMPL template human shape, while ICON and BANMo output more detailed shapes. All methods perform poorly on the highly challenging handstand pose: HuMoR outputs unrealistic and self-intersecting articulations, ICON's prediction appears bumpy and twisted in an unnatural way, BANMo's prediction is also twisted and misses the head, and our method outputs incorrect viewpoint and arm articulations." + ], + "image_footnote": [], + "bbox": [ + 313, + 327, + 349, + 383 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/44cc8c17ac2d7a543adbeda0a46f8a42905146400271e4e04f7f86df307440de.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 374, + 323, + 421, + 383 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ing because the dog is standing on its hind legs, both our method and BARC fail to show that the dog is lifting its front paws. As our method does not disentangle articulation and morphology variation between breeds, incorporating breed and/or instance information would likely improve our ability to represent fine motion and geometry details.", + "bbox": [ + 75, + 587, + 468, + 679 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Ablations", + "text_level": 1, + "bbox": [ + 76, + 686, + 187, + 700 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We performed an ablation study on several architectural details including the choice of temporal encoder, the use of frozen decoders from the teacher, the template grid resolution, and the number of training videos. Most notably, we find that increasing the density of mesh points by running marching cubes at a finer resolution (from $64^{3}$ to $128^{3}$ improves the F@1% and F@2% accuracy of our student, as well as using a temporal encoder. Changing the marching cubes resolution involves no change to the student, but simply a more faithful post-processing of the teacher's output.", + "bbox": [ + 75, + 704, + 468, + 854 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of temporal encoder. The student model performs better with a temporal encoder across all sequences, perhaps by providing additional temporal context to help smooth the", + "bbox": [ + 75, + 854, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "predictions. In general, the Conv1D encoder seems to outperform the transformer encoder in both speed and accuracy, although this could be caused by the increased difficulty of training a transformer encoder.", + "bbox": [ + 496, + 234, + 890, + 294 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of frozen decoders. We find that the student model's performance generally drops without using the teacher's frozen articulation decoder to regularize pose predictions.", + "bbox": [ + 496, + 294, + 890, + 339 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of template shape resolution. When extracting the template shape with a $64^{3}$ grid, our model's F@1%, F@2%, and F@5% accuracy all seem to drop. Qualitatively, the $64^{3}$ template shape is less detailed and appears fuzzy compared to $128^{3}$ or $256^{3}$ , though the predicted articulations are similar. There seems to be little difference between $128^{3}$ and $256^{3}$ , and the observed results could be up to noise. As more points need to be warped to the deformed space, more detailed templates have slower inference speed.", + "bbox": [ + 496, + 340, + 890, + 474 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of dataset size. We find that performance generally deteriorates with less data, although the trend is not as clear. Here, each smaller set of training videos is a subset of the immediately larger video set: as all videos containing the T_samba identity are within the set of 26 videos, increasing the dataset size from 26 to 35 involved adding videos of unrelated identities which seemed to hurt performance.", + "bbox": [ + 496, + 476, + 890, + 580 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Discussion", + "text_level": 1, + "bbox": [ + 500, + 594, + 612, + 609 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We present a method to train category-specific feedforward video shape predictors by distilling knowledge from dynamic NeRF teachers fitted to offline video data at scale. Our temporal architecture predicts consistent viewpoint, articulation, and appearance, producing real-time video reconstruction results on humans, cats, and dogs with the ability to support other categories as well. We qualitatively outperform existing feed-forward predictors for dog shape and pose, and approach the quality of test-time fitting methods while using nearly 1000x less computation.", + "bbox": [ + 496, + 613, + 890, + 763 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations: As our method is trained on the pseudoground truth outputs of a teacher model, we are upper-bounded by the teacher's performance and reconstruction fidelity. We expect the performance of our method to improve given larger-scale, more diverse, and higher-quality video data. Compared with optimization-based methods, our method is hundreds of times faster but produces results less faithful to the inputs: we leave incorporating optimization into the feed-forward architecture as future work.", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "4699", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 106 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Sameer Agarwal, Yasutaka Furukawa, Noah Snavely, Ian Simon, Brian Curless, Steven M. Seitz, and Richard Szeliski. Building rome in a day. ICCV, 2009. 1", + "[2] Marc Bager, Yufu Wang, Adarsh Modh, Ammon Perkes, Nikos Kolotouros, Bernd Pfrommer, Marc Schmidt, and Kostas Daniilidis. 3d bird reconstruction: A dataset, model, and shape recovery from a single view. 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CVPR, 2017. 2" + ], + "bbox": [ + 78, + 90, + 467, + 829 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "4701", + "bbox": [ + 482, + 945, + 513, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Distilling Neural Fields for Real-Time Articulated Shape Reconstruction/b3e477ee-24cc-4767-adae-b678b4d54a08_model.json b/2023/Distilling Neural Fields for Real-Time Articulated Shape Reconstruction/b3e477ee-24cc-4767-adae-b678b4d54a08_model.json new file mode 100644 index 0000000000000000000000000000000000000000..27380e3d4d6c1a5e354b8c72761357da940dd999 --- /dev/null +++ b/2023/Distilling Neural Fields for Real-Time Articulated Shape Reconstruction/b3e477ee-24cc-4767-adae-b678b4d54a08_model.json @@ -0,0 +1,2222 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.121, + 0.131, + 0.85, + 0.154 + ], + "angle": 0, + "content": "Distilling Neural Fields for Real-Time Articulated Shape Reconstruction" + }, + { + "type": "image", + "bbox": [ + 0.147, + 0.181, + 0.827, + 0.445 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.449, + 0.895, + 0.52 + ], + "angle": 0, + "content": "Figure 1. By distilling knowledge from dynamic NeRFs fitted to offline video data at scale [16, 44], we present a method to train category-specific real-time video shape predictors, which output temporally-consistent viewpoint, articulation, and appearance given casual input videos. Our method replaces expensive test-time optimization with a single forward pass, allowing real-time inference on a RTX-3090 GPU. Compared to existing model-based methods for reconstructing humans and animals in motion [13, 18, 31], our method does not require pre-defined 3D templates or ground-truth 3D data to train. (Project page: https://jefftan969.github.io/dasr)." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.532, + 0.314, + 0.547 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.565, + 0.473, + 0.899 + ], + "angle": 0, + "content": "We present a method for reconstructing articulated 3D models from videos in real-time, without test-time optimization or manual 3D supervision at training time. Prior work often relies on pre-built deformable models (e.g. SMAL/SMPL), or slow per-scene optimization through differentiable rendering (e.g. dynamic NeRFs). Such methods fail to support arbitrary object categories, or are unsuitable for real-time applications. To address the challenge of collecting large-scale 3D training data for arbitrary deformable object categories, our key insight is to use off-the-shelf video-based dynamic NeRFs as 3D supervision to train a fast feed-forward network, turning 3D shape and motion prediction into a supervised distillation task. Our temporal-aware network uses articulated bones and blend skinning to represent arbitrary deformations, and is self-supervised on video datasets without requiring 3D shapes or viewpoints as input. Through distillation, our network learns to 3D-reconstruct unseen articulated objects at interactive frame rates. Our method yields higher-fidelity 3D reconstructions than prior real-time methods for animals, with the ability to render realistic images at novel viewpoints and poses." + }, + { + "type": "title", + "bbox": [ + 0.502, + 0.532, + 0.631, + 0.547 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.563, + 0.892, + 0.82 + ], + "angle": 0, + "content": "We are interested in building high-quality animatable models of articulated 3D objects from videos in real time. One promising application is virtual and augmented reality, where the goal is to create high-fidelity 3D experiences from images and videos captured live by users. For rigid scenes, structure from motion (SfM) and neural rendering can be used to build accurate 3D cities and landmarks from Internet image collections [1, 20, 33]. For articulated objects such as friends and pets, many works parameterize the range of motions using category-specific templates such as SMPL [18] for humans and SMAL [4] for quadruped animals. Although these methods can be trained on large-scale video datasets, they rely on parametric body template models built from extensive real-world 3D scans: these body models are not easy to generate for diverse categories in the wild such as clothed humans or pets with distinct morphologies, which are often the focus of user content." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.827, + 0.894, + 0.903 + ], + "angle": 0, + "content": "Inspired by the breakthrough success of neural radiance fields [21], many works reconstruct arbitrary articulated objects in an analysis-by-synthesis framework [16, 27, 28, 30, 36, 44] by defining time-dependent 3D warping fields and establishing long-range correspondences on top of canon-" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4692" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.288 + ], + "angle": 0, + "content": "ical shape and appearance models. These methods output high-quality reconstructions of arbitrary objects without 3D data or pre-defined templates, but the output representations are scene-specific and often require hours to compute from scratch on unseen videos - an unacceptable cost for real-time VR/AR tasks. We are thus interested in dynamic 3D reconstruction algorithms that achieve the best of both worlds: the speed of template-based models and the quality and generalization ability of dynamic NeRFs. To achieve this, our key insight is remarkably simple: we train category-specific feed-forward 3D predictors at scale by self-supervising them with dynamic NeRF \"teachers\" fitted to offline video data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.288, + 0.473, + 0.455 + ], + "angle": 0, + "content": "By leveraging scene-fitted dynamic NeRFs for 3D supervision at scale, our method learns a feed-forward predictor for appearance, 3D shape, and articulations of non-rigid objects from videos. Our learned 3D models use linear blend skinning to express articulations, allowing it to be animated by manipulating bone transformations. We address three key challenges in our work: (1) how to supervise feed-forward models with internal representations of dynamic NeRFs, (2) how to produce temporally consistent predictions of pose, articulation, and appearance, and (3) how to build efficient systems for real-time reconstruction." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.468, + 0.22, + 0.484 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.493, + 0.47, + 0.689 + ], + "angle": 0, + "content": "Template-Based Dynamic Reconstruction A large body of work uses parametric body models [18, 48, 49] to recover 3D shapes and motions for human and animal reconstruction, given a single image as input [2, 3, 13, 32]. These models are built from registered 3D scans of real humans or toy animals, and achieve great success in reconstructing categories for which large volumes of ground-truth 3D data are available (especially human reconstruction). However, it is challenging to apply these methods to arbitrary categories with diverse morphologies, especially where 3D data is limited. Our work aims to generalize these approaches to arbitrary articulated object categories without requiring ground-truth 3D data or pre-registered 3D scans during training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Template-Free Dynamic Reconstruction Several methods build deformable 3D models without templates by recovering shapes and poses from internet-scale 2D image collections, using weak supervision such as keypoints and object silhouettes from off-the-shelf models or human annotators [6, 10, 14, 34]. As it is inherently ambiguous to reconstruct 3D outputs from the sparse and limited 2D observations available in images, these methods must leverage strong data priors and apply heavily regularization to ensure reasonable outputs, often resulting in blurry or oversmoothed shapes and textures. Leveraging the temporal context available in videos can help these methods learn temporally consistent results [38], however the output quality is still low perhaps due to over-regularization." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.41 + ], + "angle": 0, + "content": "Neural Radiance Fields Neural fields are a powerful method for 3D reconstruction using 2D image supervision, achieving state-of-the-art quality on both static and dynamic scenes. Although historically limited to rigid scenes with known cameras [20, 21, 36], recent works extend NeRF to dynamic scenes by deforming view-space points to a canonical space over time, using time-dependent 3D warping fields and dense correspondences [5, 16, 17, 27, 30]. Dynamic NeRFs are able to learn high-fidelity animatable 3D models from several casual videos capturing the same object instance [42-44], by leveraging the temporal context available in videos. Unfortunately, dynamic NeRFs are slow and require optimization from scratch on unseen videos at test-time. Although architectures exist to speed up static NeRFs using explicit voxel grids [46] or hash-table caching [22], more work is required to speed up dynamic NeRFs by similar factors due to the additional overheads of time-dependent warping and correspondence matching. Our aim is to leverage the high-quality outputs of dynamic NeRFs to supervise a fast and lightweight architecture for articulated 3D reconstruction." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.429, + 0.593, + 0.444 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.457, + 0.894, + 0.563 + ], + "angle": 0, + "content": "In order to train category-specific feed-forward 3D predictors from dynamic NeRF teacher models, we combine a single-frame image encoder that regresses viewpoint, shape, and appearance from images, and a temporal encoder that reasons about these predictions over time. In this section, we describe the problem setup, scene representation, network architecture, training procedure, and losses." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.578, + 0.652, + 0.594 + ], + "angle": 0, + "content": "3.1. Problem Setup" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.597, + 0.895, + 0.779 + ], + "angle": 0, + "content": "Given an input video centered on an articulated object, we train a feed-forward network to predict the viewpoint, articulations, and appearance, which are used to render a posed and textured object model. Our network is supervised on the pseudo-ground-truth outputs of a dynamic NeRF teacher, which builds animatable 3D models from casually collected videos including shape, appearance, and time-varying articulations. Our particular implementation uses BANMo [44] as the teacher, as it has public code and yields good results on humans and quadrupeds. Similar to the teacher, our method requires no pre-defined shape templates, registered cameras, or 3D ground truths." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Fig. 2 summarizes our approach and how it differs from the teacher model. Sec. 3.2 and Sec. 3.3 introduce our object and motion representation, while Sec. 3.4 discusses the underlying feed-forward neural architecture. Finally, Sec. 3.5 describes the training losses used to supervise our models. In contrast to our teacher [44] which uses volume rendering (which can be slow), we render textured meshes to enable efficient rasterization." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4693" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.12, + 0.065, + 0.844, + 0.339 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.341, + 0.892, + 0.412 + ], + "angle": 0, + "content": "Figure 2. Architecture details. We train a feed-forward network (shown in blue) to predict articulations and textures from videos, supervised by the pseudo-ground-truth outputs of an offline dynamic NeRF teacher [44] (including 3D shapes, articulations, and textures). To simplify the learning task, our feed-forward network outputs in a high-dimensional latent space: the dynamic NeRF's frozen decoder networks (shown in purple) are used to convert articulation codes into joint angles and texture codes into 3D surface textures. Spatial per-vertex \\(\\mathcal{L}_2\\) losses are used to supervise the articulated 3D outputs against the articulated pseudo-ground-truths (shown in green)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.424, + 0.286, + 0.44 + ], + "angle": 0, + "content": "3.2. Object Representation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.448, + 0.47, + 0.629 + ], + "angle": 0, + "content": "Category-level shape. We model articulated objects as a canonical rest shape that is transformed by time-dependent poses and articulations. The rest shape is a category-specific triangular mesh \\( M = (V, F) \\) that represents the mean shape of instances in the category: the faces \\( F \\) define the vertex connectivity and we assume it remains fixed. To initialize the rest mesh, we run marching cubes on a \\( 128^3 \\) grid to find the zero level set of the neural field that serves as the teacher NeRF's implicit rest shape. Although explicit mesh representations are less expressive than implicit neural fields, we find that a feed-forward predictor benefits from the speed of rasterization and the simplicity of regressing vertex colors." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.63, + 0.47, + 0.764 + ], + "angle": 0, + "content": "Per-instance pose and articulation. At each frame \\( t \\), we model the object's viewpoint and articulation similar to the dynamic NeRF literature. The viewpoint is a root body transformation \\( \\mathbf{G}^t \\in SE(3) \\), and we use neural blend skinning [9, 39] to express object articulations. For each frame, the bone configurations for neural blend skinning are parameterized by a joint angle vector \\( \\mathbf{B}^t \\in SO(3)^b \\), which is predicted by our feed-forward network from input video frames. See Sec. 3.3 for more details." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.469, + 0.841 + ], + "angle": 0, + "content": "Appearance. As our mesh topology is fixed, we can simply model the object's appearance as an array of per-vertex colors \\(\\mathbf{C}^t\\in \\mathbb{R}^{|V|\\times 3}\\) at each frame \\(t\\). Following the standard rasterization pipeline, barycentric coordinates are used to interpolate the vertex colors per triangle during rendering." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.841, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Rendering. We assume a weak-perspective camera projection defined by a fixed camera at the origin pointed along the negative- \\(z\\) axis. To render the object in video frame \\(t\\), we apply the predicted viewpoint \\(\\mathbf{G}^t \\in SE(3)\\) at time" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.425, + 0.892, + 0.471 + ], + "angle": 0, + "content": "\\(t\\), followed by the blend skinning deformation specified by predicted bone configuration \\(\\mathbf{B}^t \\in SO(3)^b\\) using forward kinematics and dual-quaternion blend skinning." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.479, + 0.891, + 0.495 + ], + "angle": 0, + "content": "3.3. Time-Varying Articulation via Blend Skinning" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.502, + 0.892, + 0.577 + ], + "angle": 0, + "content": "To represent articulated body motion, we use a neural blend skinning model to define a 3D warping field \\(\\mathcal{W}^t\\) on top of a category-level kinematic skeleton. After computing the skeleton's forward kinematics, each point is deformed by a weighted combination of per-bone transformations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.578, + 0.892, + 0.759 + ], + "angle": 0, + "content": "Category-level skeleton. Unlike color and 3D shape which are directly observable from imagery, an object's bone structure is much harder to infer. Automatic skeletal rigging methods [15,26] rely heavily on shape priors, or are sensitive to input data. Fortunately, bone structures are largely fixed within categories up to slight variations in bone length and body part scale. Thus, we can use readily available generic skeletons of humans, quadrupeds, and other categories to specify the bone structure of each category. Skeletons are defined by a tree structure with \\( B + 1 \\) variable-length bones and \\( B \\) ball joints, where \\( B = 19 \\) for humans and \\( B = 26 \\) for quadrupeds." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.759, + 0.892, + 0.85 + ], + "angle": 0, + "content": "Forward kinematics. Each bone \\(b\\) has a link transformation \\(\\mathbf{L}_b\\in SE(3)\\) specifying the bone length and a joint transformation \\(\\mathbf{J}_b^t\\in SE(3)\\) specified by the joint angle \\(\\mathbf{B}_b^t\\in SO(3)\\). The result for each link \\(b\\) is a sequence of alternating transformations from the skeleton's base to the link's end, where \\(b_{1},b_{2},\\ldots ,b\\) are the parent links up to \\(b\\):" + }, + { + "type": "equation", + "bbox": [ + 0.584, + 0.859, + 0.805, + 0.877 + ], + "angle": 0, + "content": "\\[\n\\mathbf {T} _ {b} ^ {t} = \\mathbf {J} _ {b} ^ {t} \\mathbf {L} _ {b} \\dots \\mathbf {J} _ {b _ {2}} ^ {t} \\mathbf {L} _ {b _ {2}} \\dots \\mathbf {J} _ {b _ {1}} ^ {t} \\mathbf {L} _ {b _ {1}}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.886, + 0.891, + 0.901 + ], + "angle": 0, + "content": "Blend skinning. From per-bone kinematic transformations" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4694" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.091, + 0.471, + 0.122 + ], + "angle": 0, + "content": "\\(\\mathbf{T}_b^t\\) and root body pose \\(\\mathbf{G}^t\\), we use dual-quaternion blend skinning to compute a 3D warping field \\(\\mathcal{W}(\\mathbf{X})\\):" + }, + { + "type": "equation", + "bbox": [ + 0.156, + 0.135, + 0.39, + 0.153 + ], + "angle": 0, + "content": "\\[\n\\mathcal {W} (\\mathbf {X}) ^ {t} = \\left(\\sum_ {b} \\mathbf {W} (\\mathbf {X}) _ {b} ^ {t} \\cdot \\mathbf {T} _ {b} ^ {t}\\right) \\cdot \\mathbf {G} ^ {t}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.165, + 0.47, + 0.195 + ], + "angle": 0, + "content": "Skinning weights \\(\\mathbf{W}(X)_b^t\\) are specified by the softmax'ed distances between rest mesh vertices \\(\\mathbf{X}\\) and bone centers." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.208, + 0.283, + 0.223 + ], + "angle": 0, + "content": "3.4. Network Architecture" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.231, + 0.47, + 0.473 + ], + "angle": 0, + "content": "Single-frame image encoder. Given a video of length \\( T \\), we use off-the-shelf PointRend [12] to compute segmentations and DensePose [7, 23, 24] to compute per-pixel CSE features. Each RGB image is concatenated with features, then masked and cropped to \\( 1.2\\mathrm{x} \\) the tight bounding box of the object. We find that using dense pretrained features improves convergence speed over RGB inputs alone. We pass the preprocessed frames into a convolutional stacked hourglass network [25], which uses repeated pooling and upsampling to process features across multiple scales and spatial locations. The stacked intermediate outputs of each hourglass module are passed into a ResNet18 [8] network which predicts latent vectors \\( z_{\\mathrm{view}} \\) and \\( z_{\\mathrm{art}} \\): \\( z_{\\mathrm{view}} \\) is decoded into the viewpoint \\( \\mathbf{G}^t \\in SE(3) \\) and \\( z_{\\mathrm{art}} \\) is decoded into articulated joint angles \\( \\mathbf{B}^t \\in SO(3)^B \\). We use 6D rotations to represent angles during training [47]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.474, + 0.47, + 0.583 + ], + "angle": 0, + "content": "Viewpoint branch. As the space of possible viewpoints is discontinuous and multi-modal, it is difficult to approach the optimum through iterative gradient descent. Following [6], we use a viewpoint decoder network \\(\\mathbf{MLP}_{\\mathrm{view}}\\) to decode \\(z_{\\mathrm{pose}}\\) into a set of \\(M\\) viewpoints hypotheses \\(\\mathbf{G}_{\\{1,\\dots,M\\}}^t\\) weighted by \\(w_{\\mathbf{G}}^{t}\\in \\mathbb{R}^{M}\\). Fig. 3 shows the variation over viewpoint hypotheses at an early stage of training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.584, + 0.469, + 0.78 + ], + "angle": 0, + "content": "Articulation branch. Estimating 3D articulations from monocular images can be difficult due to depth ambiguities and occlusions. To resolve this, recent work on human pose estimation [37] uses a normalizing flow articulation prior represented as an invertible neural network, trained on large-scale human motion capture datasets. Without access to such datasets for other categories, we achieve a similar effect by leveraging the teacher's articulation priors, using the teacher's frozen articulation decoder \\(\\mathbf{MLP}_{\\mathrm{art}}\\) to decode \\(z_{\\mathrm{art}}\\). Fig. 4 visualizes the principal components of \\(z_{\\mathrm{art}}\\) 's latent space: we find that perturbing \\(z_{\\mathrm{art}}\\) along its principal components causes the resulting articulated shape to perform natural motions, such as curling up in a ball." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Appearance branch. As the object in the video is only partially observable at any given time, we must use data priors or look at nearby frames to output complete appearance predictions \\(\\mathbf{C}^t\\in \\mathbb{R}^{|V|\\times 3}\\), represented as per-vertex colors of the articulated mesh at each frame. Our teacher [44] models global object appearances as a category-level neural field modulated by a texture code \\(z_{\\mathrm{color}}\\in \\mathbb{R}^{64}\\). We leverage these appearance priors by predicting an environment code per" + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.089, + 0.891, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.293, + 0.893, + 0.391 + ], + "angle": 0, + "content": "Figure 3. Viewpoint multiplexing during training. To overcome the discontinuous and multi-modal nature of pose optimization, we train our feed-forward predictor to output a set of \\( M \\) viewpoint hypotheses rather than a single viewpoint. Blending multiple viewpoint hypotheses yields a more accurate prediction (here \\( M = 5 \\)). Top row: Input frames. Second row (white): Blended viewpoint prediction. Bottom rows (light blue): \\( M \\) viewpoint hypotheses" + }, + { + "type": "image", + "bbox": [ + 0.509, + 0.392, + 0.88, + 0.607 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.626, + 0.892, + 0.765 + ], + "angle": 0, + "content": "Figure 4. Visualizing articulation code. Rather than training our feed-forward predictor to output high-dimensional (75) skeletal articulations, we leverage the teacher's pre-trained articulation space by predicting a low-dimensional (16) code. We visualize the first four principal components of the articulation code learned from the training dataset and find that variations along each axis correspond to interpretable motions: (1) whether the left or right paw is in front, (2) whether the hind paws are retracted or extended, (3) whether the front paws are retracted or extended, and (4) whether the cat has a straightened or curled-up posture." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.778, + 0.892, + 0.809 + ], + "angle": 0, + "content": "frame, modulating the teacher's frozen category-level neural field, and querying it at the rest mesh's vertex locations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Temporal encoder. Predicting pose and shape from single images can be highly ambiguous due to motion blur, occlusions, and depth ambiguities. To output temporally consistent results over long videos, we define a temporal encoder that updates \\( z_{\\mathrm{view}} \\), \\( z_{\\mathrm{art}} \\), and \\( z_{\\mathrm{color}} \\) across many frames. We treat the viewpoint multiplex \\( z_{\\mathrm{view}} \\) as a single vector by con" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4695" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.47, + 0.138 + ], + "angle": 0, + "content": "catenating all \\(M\\) hypotheses. Following prior work [11], our temporal encoder has several 1D convolutional layers acting on a temporal window centered at time \\(t\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.144, + 0.294, + 0.16 + ], + "angle": 0, + "content": "3.5. Losses and Supervision" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.161, + 0.47, + 0.312 + ], + "angle": 0, + "content": "Optimization objective. Treating the teacher's outputs as pseudo-ground truths, our model can be trained in a standard supervised manner. We would like to use the teacher's inferred low-dimensional latent codes as supervisory targets for the student. But rather than defining \\(\\mathcal{L}_2\\) losses in the latent embedding space, where each dimension of \\(z_{\\mathrm{view}}\\), \\(z_{\\mathrm{art}}\\), and \\(z_{\\mathrm{color}}\\) has varying importance, we instead render these codes and compute 3D losses. As all articulated meshes have the same topology, we can define geometry and color losses as per-vertex \\(\\mathcal{L}_2\\) error:" + }, + { + "type": "equation", + "bbox": [ + 0.11, + 0.317, + 0.438, + 0.345 + ], + "angle": 0, + "content": "\\[\nL _ {\\mathrm {g e o m}} = \\left\\| \\mathbf {X} ^ {t} - \\widehat {\\mathbf {X}} ^ {t} \\right\\| _ {2} \\quad L _ {\\mathrm {c o l o r}} = \\left\\| \\mathbf {C} ^ {t} - \\widehat {\\mathbf {C}} ^ {t} \\right\\| _ {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.349, + 0.47, + 0.424 + ], + "angle": 0, + "content": "To improve articulation learning and account for multiple possible inverse kinematics solutions while solving for joint articulations, we add a joint loss defined as geodesic distance between predicted and actual joint angles at each joint. We find that this improves deformation quality." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.425, + 0.469, + 0.455 + ], + "angle": 0, + "content": "In summary, we train the image encoder and temporal encoder with the following objective:" + }, + { + "type": "equation", + "bbox": [ + 0.181, + 0.462, + 0.366, + 0.479 + ], + "angle": 0, + "content": "\\[\nL = L _ {\\text {g e o m}} + L _ {\\text {j o i n t}} + L _ {\\text {c o l o r}}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.49, + 0.21, + 0.507 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.509, + 0.469, + 0.704 + ], + "angle": 0, + "content": "Although we could have distilled a student using any dynamic NeRF as the teacher, our implementation uses BANMo [44] because it has public code, accepts unannotated monocular videos as input, and produces good results on humans and quadropeds. We modified BANMo to replace the bag-of-bones deformation model with a skeleton. Hyperparameters. Our method is implemented in PyTorch. We use the AdamW optimizer and train the model for 16k iterations, taking around 4 hours on a single RTX-3090 GPU. We use \\(224 \\times 224\\) images with batch size 56. We use 8 stacked hourglass blocks in the image encoder and a window size of 13 frames in the temporal encoder. All losses are weighted to have similar initial magnitudes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Staged training. We adopt a two-stage training strategy at every epoch to reduce the computational costs of evaluating an image encoder at every frame, when only a single frame per time window will receive a gradient update. In the first stage, we send frames through the image encoder and compute per-frame losses without using the temporal encoder, storing per-frame values of \\( z_{\\mathrm{pose}} \\), \\( z_{\\mathrm{art}} \\), and \\( z_{\\mathrm{color}} \\). In the second stage, we send time windows of cached features through the temporal encoder without using the image encoder. Two-staged training reduces redundant image encoder evaluations and ensures that the temporal encoder can be safely removed if we only have access to single images rather than time windows of frames at test time." + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.089, + 0.892, + 0.173 + ], + "angle": 0, + "content": "Table 1. Datasets. All videos are treated as casually collected monocular RGB videos, except when additional groundtruth meshes or depth maps are needed for evaluation. Processing time includes computing segmentations and per-pixel features with off-the-shelf networks, as well as computing pseudo-ground truth 3D outputs with the teacher." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.184, + 0.9, + 0.261 + ], + "angle": 0, + "content": "
Total VideosTotal InstancesTotal FramesTest InstancesTest FramesProcessing Time (hr)
Humans48286.4k101.6k22.0
Cats775611.7k132.7k23.2
Dogs88789.7k171.7k23.8
" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.275, + 0.603, + 0.289 + ], + "angle": 0, + "content": "4.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.293, + 0.892, + 0.444 + ], + "angle": 0, + "content": "We collect datasets for three categories: humans, cats, and dogs. For humans, we combine datasets from AMA [35], MonoPerfCap [41], DAVIS [29], and BANMo [44] to obtain 48 human videos. We evaluate on AMA and MonoPerfCap as they have ground-truth meshes. For cats and dogs, we collect 77 cat videos and 88 dog videos from the Pixels stock video website as well as BANMo released data. We also used an iPad Pro to capture two RGB-D videos to evaluate depth accuracy on cats and dogs. Video frames are extracted at 10fps. Datasets are summarized in Tab. 1." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.446, + 0.892, + 0.596 + ], + "angle": 0, + "content": "To compute BANMo pseudo-ground-truths per category without optimizing dozens of independent BANMo models, we optimize a single BANMo model per category, using articulation and texture codes to model shape and appearance differences across instances. As a result, the total dataset processing time is about 24 hours per category on 8 RTX-3090 GPUs. We find that BANMo generalizes quite well from the instance-level to the category-level setting [45], and that the articulation and texture latent spaces cover the range of motions and textures across all instances." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.61, + 0.724, + 0.626 + ], + "angle": 0, + "content": "4.2. Reconstructing Humans" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.628, + 0.892, + 0.764 + ], + "angle": 0, + "content": "Dataset. Following BANMo, we evaluate human reconstruction on the AMA [35] dataset, containing 10 real-world mesh sequences depicting 3 different humans. The subjects wear loose clothing and perform challenging actions such as dancing and performing a handstand. Although the AMA videos were captured in an 8-camera studio to enable ground-truth mesh extraction, we treat them as casually collected monocular videos and do not use the camera intrinsics, camera extrinsic, or time synchronization." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Comparisons. We compare against template-free BANMo [44], as well as model-based methods HuMoR [31] and ICON [40]. BANMo fits an animatable 3D model to multiple monocular videos of an object instance by performing differentiable rendering optimization. We train BANMo on the same dataset as our model. HuMoR is a human-specific temporal pose and shape predictor that performs test-time optimization on video sequences, leveraging OpenPose keypoint detection and motion priors learned" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4696" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.099, + 0.081, + 0.207, + 0.364 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.209, + 0.081, + 0.354, + 0.356 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.356, + 0.081, + 0.464, + 0.363 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.465, + 0.081, + 0.61, + 0.356 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.61, + 0.081, + 0.718, + 0.363 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.716, + 0.081, + 0.872, + 0.356 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.38, + 0.895, + 0.437 + ], + "angle": 0, + "content": "Figure 5. Qualitative results on humans (left), cats (middle), and dogs (right) in the test set. From left to right for each category, we show the input images, articulated shape and texture predictions overlaid on the input images, and three different viewpoints of the predicted geometry. Our method operates on casual monocular videos and predicts plausible shape, articulations, and textures in real-time. Our predictions align well with the image evidence on challenging inputs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.45, + 0.471, + 0.556 + ], + "angle": 0, + "content": "from large-scale human motion capture datasets. ICON is the current SOTA for single-view human reconstruction, and it combines implicit functions with the SMPL human body model, using test-time optimization to fit surface normal predictions and improve pose accuracy and reconstruction quality. All our baselines require far more processing time than our model, which runs in real-time." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.563, + 0.47, + 0.744 + ], + "angle": 0, + "content": "Metrics. We report 3D chamfer distance and F-scores on three held-out test sequences in Tab. 2, averaged across all frames. Chamfer distance is the average distance between the ground-truth and predicted mesh vertices using nearest neighbor matches. As this can be sensitive to outliers, we also evaluate F-score at distance thresholds \\( d \\in \\{1\\%, 2\\%, 5\\% \\} \\) to better quantify reconstruction error at different granularities. We scale predicted meshes by their view-space bounding box height to account for unknown scale compared to registered ground-truths. Our model approaches the performance of BANMo and baselines, while requiring nearly 1000x less compute at test time." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Qualitative Results. We show qualitative comparisons for upright and inverted humans in Fig. 7. HuMoR outputs a deformed SMPL model, while ICON and BANMo optimize for both shape and articulation. Although our method outputs reasonable articulations for the upright pose, the woman lacks fine-grained geometry details and the viewpoint on the handstand video is inaccurate. We hypothesize that these failures occur due to the entanglement between articulations and per-instance morphologies, and the lack of handstand examples in the training set." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.45, + 0.769, + 0.466 + ], + "angle": 0, + "content": "4.3. Reconstructing Cats and Dogs" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.467, + 0.892, + 0.633 + ], + "angle": 0, + "content": "Dataset. We evaluate cat and dog reconstruction on two RGB-D pet videos, as well as a held-out test set of pet videos from BANMo's dataset. These videos contain challenging motions such as rapid turns and jumping off chairs. Comparisons. We compare against BANMo [44] and BARC [32], a model-based approach and the current SOTA for dog shape and pose estimation from images. BARC trains a feed-forward network using images with keypoint labels and synthetic SMAL dog models [4], leveraging breed losses as additional supervision. As BARC is image-based, we run it separately on each video frame." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.633, + 0.892, + 0.724 + ], + "angle": 0, + "content": "Metrics We report the root mean square depth error and depth accuracy for all foreground pixels in Tab. 3, averaged across all frames. We render a synthetic depth map per frame, and following [19], we account for the unknown global scale factor between depth maps by aligning the median rendered and ground-truth depths at each frame:" + }, + { + "type": "equation", + "bbox": [ + 0.577, + 0.731, + 0.814, + 0.759 + ], + "angle": 0, + "content": "\\[\ns _ {i} = \\operatorname * {m e d i a n} _ {x} \\left\\{D _ {i} ^ {p r e d} (x) / D ^ {g t} (x) \\right\\}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.796 + ], + "angle": 0, + "content": "Depth accuracy is computed as the proportion of foreground pixels whose synthetic depth is within a given threshold." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Qualitative Results We show qualitative results comparing to BARC in Fig. 6. BARC performs well at predicting coarse shape and deformations, and more faithfully captures the fine motion and geometry details of the dog when it is positioned well in frame. However, as BARC entangles shape and breed, we find that BARC may predict biased shapes for certain breeds. For example, in the bottom left" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4697" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.123, + 0.086, + 0.149, + 0.101 + ], + "angle": 0, + "content": "t-1" + }, + { + "type": "image", + "bbox": [ + 0.159, + 0.077, + 0.364, + 0.205 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.384, + 0.077, + 0.559, + 0.205 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.576, + 0.084, + 0.604, + 0.112 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.612, + 0.078, + 0.782, + 0.205 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.795, + 0.093, + 0.812, + 0.108 + ], + "angle": 0, + "content": "M" + }, + { + "type": "image_caption", + "bbox": [ + 0.795, + 0.136, + 0.812, + 0.15 + ], + "angle": 0, + "content": "#" + }, + { + "type": "image_caption", + "bbox": [ + 0.795, + 0.179, + 0.812, + 0.193 + ], + "angle": 0, + "content": "#" + }, + { + "type": "image_caption", + "bbox": [ + 0.125, + 0.235, + 0.149, + 0.249 + ], + "angle": 0, + "content": "\\(t - 1\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.133, + 0.278, + 0.144, + 0.291 + ], + "angle": 0, + "content": "t" + }, + { + "type": "image_caption", + "bbox": [ + 0.129, + 0.322, + 0.151, + 0.334 + ], + "angle": 0, + "content": "t+1" + }, + { + "type": "image", + "bbox": [ + 0.16, + 0.216, + 0.382, + 0.352 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.385, + 0.216, + 0.585, + 0.352 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.61, + 0.216, + 0.783, + 0.351 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.797, + 0.229, + 0.82, + 0.351 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.36, + 0.895, + 0.432 + ], + "angle": 0, + "content": "Figure 6. Qualitative comparisons on pet sequences. From left to right in each column, we show (left) the input image, (middle-left) BARC's prediction, (middle-right) our articulated shape and texture predictions, and (right) our geometry predictions. Our method operates on videos and predicts plausible shape, articulations, and texture in real time. BARC operates on each video frame independently, resulting in jittery predictions when the pet is small or not clearly visible (top row). While BARC's geometry and motion predictions are largely accurate, they can be biased for certain breeds (bottom left), predicting an arched back for a flat-backed dog." + }, + { + "type": "table_caption", + "bbox": [ + 0.075, + 0.445, + 0.892, + 0.542 + ], + "angle": 0, + "content": "Table 2. Quantitative results on AMA sequences. 3D chamfer distance (cm, ↓) and F-score (%, ↑) for articulated meshes, averaged over all frames. T_samba is a held-out video of a person that was seen during training, while the D_bouncing and D_handstand sequences contain a previously unseen person. Our model approaches the performance of BANMo and baselines while requiring nearly three orders of magnitude less compute at test time. Notably, our method performs better on T_samba, as it has fewer challenging poses and contains a person previously seen during training. Other baselines are trained on 3D human data, rely on the SMPL body model, or use expensive test-time optimization to improve results. We also report the inference time (ms) per frame. Results marked by * are different runs with the same hyperparameters. The best results are in bold. Please refer to Sec. 4.4 for discussions on the ablation results." + }, + { + "type": "table", + "bbox": [ + 0.085, + 0.553, + 0.884, + 0.838 + ], + "angle": 0, + "content": "
MethodTimeT_sambaD_bouncingD_handstand
CDF@1%F@2%F@5%CDF@1%F@2%F@5%CDF@1%F@2%F@5%
HuMoR420009.823.347.483.611.421.146.183.221.913.528.858.5
ICON6300010.118.939.985.29.727.853.586.414.123.545.275.6
BANMo4300010.325.348.883.611.626.750.881.514.222.544.174.7
Ours*2210.625.849.684.112.023.446.179.917.317.935.967.2
No temporal encoder2012.223.144.778.912.922.745.077.516.917.935.868.2
Conv1D encoder*2210.826.049.282.712.123.846.779.915.024.945.473.1
Transformer encoder2710.626.350.083.213.222.344.076.516.818.737.168.2
w/o frozen decoders2111.024.648.081.611.525.649.881.417.922.341.870.4
\\( 64^3 \\) template grid1012.021.042.279.112.722.945.278.015.622.543.671.8
\\( 128^3 \\) template grid*2210.525.649.884.412.423.646.078.713.724.346.575.6
\\( 256^3 \\) template grid2810.427.150.783.912.523.646.478.715.719.238.571.1
5 train videos2211.222.444.381.013.720.841.675.317.117.535.367.1
16 train videos2210.524.346.983.613.321.743.076.615.821.640.770.6
26 train videos2210.228.051.684.313.222.043.676.817.717.835.667.2
35 train videos*2210.824.047.483.612.323.346.379.016.819.038.069.2
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.85, + 0.471, + 0.896 + ], + "angle": 0, + "content": "of Fig. 6, BARC predicts a rounded back but the back is flat in reality. For the inputs on the top row, BARC's single-frame architecture makes jittery predictions from frame to" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.85, + 0.892, + 0.896 + ], + "angle": 0, + "content": "frame, while our temporal architecture enforces consistency and prevents large discontinuities in pose and deformation. In the middle top image, which is particularly challeng-" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4698" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.132 + ], + "angle": 0, + "content": "Table 3. Quantitative results on RGB-D pet sequences. Root mean square depth error (↓) and depth accuracy (%, ↑) for all foreground pixels in the depth map, averaged over all frames. We also report the total processing time per frame (ms) on a RTX-3090 GPU. Although BANMo consistently does better, our method approaches its quality while being nearly 1000x faster at test time. Best results are in bold." + }, + { + "type": "table", + "bbox": [ + 0.154, + 0.142, + 0.816, + 0.222 + ], + "angle": 0, + "content": "
MethodTimedogcat
RMSEAcc-1%Acc-2%Acc-5%RMSEAcc-1%Acc-2%Acc-5%
BANMo54s0.041128.645.372.70.075727.747.476.5
Ours100ms0.056917.731.656.60.129819.133.861.4
" + }, + { + "type": "image", + "bbox": [ + 0.12, + 0.234, + 0.177, + 0.305 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.134, + 0.306, + 0.162, + 0.315 + ], + "angle": 0, + "content": "Image" + }, + { + "type": "image", + "bbox": [ + 0.184, + 0.236, + 0.239, + 0.304 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.192, + 0.306, + 0.23, + 0.314 + ], + "angle": 0, + "content": "HuMoR" + }, + { + "type": "image", + "bbox": [ + 0.245, + 0.236, + 0.298, + 0.304 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.255, + 0.306, + 0.284, + 0.314 + ], + "angle": 0, + "content": "ICON" + }, + { + "type": "image", + "bbox": [ + 0.308, + 0.235, + 0.363, + 0.304 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.315, + 0.306, + 0.353, + 0.314 + ], + "angle": 0, + "content": "BANMo" + }, + { + "type": "image", + "bbox": [ + 0.368, + 0.235, + 0.43, + 0.305 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.386, + 0.306, + 0.409, + 0.314 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.12, + 0.32, + 0.177, + 0.389 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.134, + 0.393, + 0.162, + 0.403 + ], + "angle": 0, + "content": "Image" + }, + { + "type": "image", + "bbox": [ + 0.184, + 0.327, + 0.23, + 0.386 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.193, + 0.393, + 0.23, + 0.402 + ], + "angle": 0, + "content": "HuMoR" + }, + { + "type": "image", + "bbox": [ + 0.258, + 0.328, + 0.288, + 0.385 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.256, + 0.393, + 0.284, + 0.402 + ], + "angle": 0, + "content": "ICON" + }, + { + "type": "image", + "bbox": [ + 0.315, + 0.328, + 0.35, + 0.384 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.314, + 0.393, + 0.353, + 0.402 + ], + "angle": 0, + "content": "BANMo" + }, + { + "type": "image", + "bbox": [ + 0.375, + 0.324, + 0.423, + 0.384 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.386, + 0.393, + 0.409, + 0.403 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.414, + 0.473, + 0.581 + ], + "angle": 0, + "content": "Figure 7. Qualitative comparisons on human sequences. From left to right, we show the output of HuMoR [31], ICON [40], BANMo [44], and our method on dancing (top) and handstand (bottom) sequences. Our method outputs plausible articulations for the dancing sequence, although the shape lacks fine details. In comparison, HuMoR outputs the SMPL template human shape, while ICON and BANMo output more detailed shapes. All methods perform poorly on the highly challenging handstand pose: HuMoR outputs unrealistic and self-intersecting articulations, ICON's prediction appears bumpy and twisted in an unnatural way, BANMo's prediction is also twisted and misses the head, and our method outputs incorrect viewpoint and arm articulations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.588, + 0.47, + 0.68 + ], + "angle": 0, + "content": "ing because the dog is standing on its hind legs, both our method and BARC fail to show that the dog is lifting its front paws. As our method does not disentangle articulation and morphology variation between breeds, incorporating breed and/or instance information would likely improve our ability to represent fine motion and geometry details." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.688, + 0.189, + 0.702 + ], + "angle": 0, + "content": "4.4. Ablations" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.47, + 0.856 + ], + "angle": 0, + "content": "We performed an ablation study on several architectural details including the choice of temporal encoder, the use of frozen decoders from the teacher, the template grid resolution, and the number of training videos. Most notably, we find that increasing the density of mesh points by running marching cubes at a finer resolution (from \\(64^{3}\\) to \\(128^{3}\\) improves the F@1% and F@2% accuracy of our student, as well as using a temporal encoder. Changing the marching cubes resolution involves no change to the student, but simply a more faithful post-processing of the teacher's output." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Effect of temporal encoder. The student model performs better with a temporal encoder across all sequences, perhaps by providing additional temporal context to help smooth the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.235, + 0.892, + 0.295 + ], + "angle": 0, + "content": "predictions. In general, the Conv1D encoder seems to outperform the transformer encoder in both speed and accuracy, although this could be caused by the increased difficulty of training a transformer encoder." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.295, + 0.892, + 0.34 + ], + "angle": 0, + "content": "Effect of frozen decoders. We find that the student model's performance generally drops without using the teacher's frozen articulation decoder to regularize pose predictions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.341, + 0.892, + 0.476 + ], + "angle": 0, + "content": "Effect of template shape resolution. When extracting the template shape with a \\(64^{3}\\) grid, our model's F@1%, F@2%, and F@5% accuracy all seem to drop. Qualitatively, the \\(64^{3}\\) template shape is less detailed and appears fuzzy compared to \\(128^{3}\\) or \\(256^{3}\\), though the predicted articulations are similar. There seems to be little difference between \\(128^{3}\\) and \\(256^{3}\\), and the observed results could be up to noise. As more points need to be warped to the deformed space, more detailed templates have slower inference speed." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.477, + 0.892, + 0.582 + ], + "angle": 0, + "content": "Effect of dataset size. We find that performance generally deteriorates with less data, although the trend is not as clear. Here, each smaller set of training videos is a subset of the immediately larger video set: as all videos containing the T_samba identity are within the set of 26 videos, increasing the dataset size from 26 to 35 involved adding videos of unrelated identities which seemed to hurt performance." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.595, + 0.614, + 0.61 + ], + "angle": 0, + "content": "5. Discussion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.892, + 0.765 + ], + "angle": 0, + "content": "We present a method to train category-specific feedforward video shape predictors by distilling knowledge from dynamic NeRF teachers fitted to offline video data at scale. Our temporal architecture predicts consistent viewpoint, articulation, and appearance, producing real-time video reconstruction results on humans, cats, and dogs with the ability to support other categories as well. We qualitatively outperform existing feed-forward predictors for dog shape and pose, and approach the quality of test-time fitting methods while using nearly 1000x less computation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Limitations: As our method is trained on the pseudoground truth outputs of a teacher model, we are upper-bounded by the teacher's performance and reconstruction fidelity. We expect the performance of our method to improve given larger-scale, more diverse, and higher-quality video data. Compared with optimization-based methods, our method is hundreds of times faster but produces results less faithful to the inputs: we leave incorporating optimization into the feed-forward architecture as future work." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4699" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.107 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.468, + 0.157 + ], + "angle": 0, + "content": "[1] Sameer Agarwal, Yasutaka Furukawa, Noah Snavely, Ian Simon, Brian Curless, Steven M. Seitz, and Richard Szeliski. Building rome in a day. 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By distilling knowledge from dynamic NeRFs fitted to offline video data at scale [16, 44], we present a method to train category-specific real-time video shape predictors, which output temporally-consistent viewpoint, articulation, and appearance given casual input videos. Our method replaces expensive test-time optimization with a single forward pass, allowing real-time inference on a RTX-3090 GPU. Compared to existing model-based methods for reconstructing humans and animals in motion [13, 18, 31], our method does not require pre-defined 3D templates or ground-truth 3D data to train. (Project page: https://jefftan969.github.io/dasr). + +# Abstract + +We present a method for reconstructing articulated 3D models from videos in real-time, without test-time optimization or manual 3D supervision at training time. Prior work often relies on pre-built deformable models (e.g. SMAL/SMPL), or slow per-scene optimization through differentiable rendering (e.g. dynamic NeRFs). Such methods fail to support arbitrary object categories, or are unsuitable for real-time applications. To address the challenge of collecting large-scale 3D training data for arbitrary deformable object categories, our key insight is to use off-the-shelf video-based dynamic NeRFs as 3D supervision to train a fast feed-forward network, turning 3D shape and motion prediction into a supervised distillation task. Our temporal-aware network uses articulated bones and blend skinning to represent arbitrary deformations, and is self-supervised on video datasets without requiring 3D shapes or viewpoints as input. Through distillation, our network learns to 3D-reconstruct unseen articulated objects at interactive frame rates. Our method yields higher-fidelity 3D reconstructions than prior real-time methods for animals, with the ability to render realistic images at novel viewpoints and poses. + +# 1. Introduction + +We are interested in building high-quality animatable models of articulated 3D objects from videos in real time. One promising application is virtual and augmented reality, where the goal is to create high-fidelity 3D experiences from images and videos captured live by users. For rigid scenes, structure from motion (SfM) and neural rendering can be used to build accurate 3D cities and landmarks from Internet image collections [1, 20, 33]. For articulated objects such as friends and pets, many works parameterize the range of motions using category-specific templates such as SMPL [18] for humans and SMAL [4] for quadruped animals. Although these methods can be trained on large-scale video datasets, they rely on parametric body template models built from extensive real-world 3D scans: these body models are not easy to generate for diverse categories in the wild such as clothed humans or pets with distinct morphologies, which are often the focus of user content. + +Inspired by the breakthrough success of neural radiance fields [21], many works reconstruct arbitrary articulated objects in an analysis-by-synthesis framework [16, 27, 28, 30, 36, 44] by defining time-dependent 3D warping fields and establishing long-range correspondences on top of canon- + +ical shape and appearance models. These methods output high-quality reconstructions of arbitrary objects without 3D data or pre-defined templates, but the output representations are scene-specific and often require hours to compute from scratch on unseen videos - an unacceptable cost for real-time VR/AR tasks. We are thus interested in dynamic 3D reconstruction algorithms that achieve the best of both worlds: the speed of template-based models and the quality and generalization ability of dynamic NeRFs. To achieve this, our key insight is remarkably simple: we train category-specific feed-forward 3D predictors at scale by self-supervising them with dynamic NeRF "teachers" fitted to offline video data. + +By leveraging scene-fitted dynamic NeRFs for 3D supervision at scale, our method learns a feed-forward predictor for appearance, 3D shape, and articulations of non-rigid objects from videos. Our learned 3D models use linear blend skinning to express articulations, allowing it to be animated by manipulating bone transformations. We address three key challenges in our work: (1) how to supervise feed-forward models with internal representations of dynamic NeRFs, (2) how to produce temporally consistent predictions of pose, articulation, and appearance, and (3) how to build efficient systems for real-time reconstruction. + +# 2. Related Work + +Template-Based Dynamic Reconstruction A large body of work uses parametric body models [18, 48, 49] to recover 3D shapes and motions for human and animal reconstruction, given a single image as input [2, 3, 13, 32]. These models are built from registered 3D scans of real humans or toy animals, and achieve great success in reconstructing categories for which large volumes of ground-truth 3D data are available (especially human reconstruction). However, it is challenging to apply these methods to arbitrary categories with diverse morphologies, especially where 3D data is limited. Our work aims to generalize these approaches to arbitrary articulated object categories without requiring ground-truth 3D data or pre-registered 3D scans during training. + +Template-Free Dynamic Reconstruction Several methods build deformable 3D models without templates by recovering shapes and poses from internet-scale 2D image collections, using weak supervision such as keypoints and object silhouettes from off-the-shelf models or human annotators [6, 10, 14, 34]. As it is inherently ambiguous to reconstruct 3D outputs from the sparse and limited 2D observations available in images, these methods must leverage strong data priors and apply heavily regularization to ensure reasonable outputs, often resulting in blurry or oversmoothed shapes and textures. Leveraging the temporal context available in videos can help these methods learn temporally consistent results [38], however the output quality is still low perhaps due to over-regularization. + +Neural Radiance Fields Neural fields are a powerful method for 3D reconstruction using 2D image supervision, achieving state-of-the-art quality on both static and dynamic scenes. Although historically limited to rigid scenes with known cameras [20, 21, 36], recent works extend NeRF to dynamic scenes by deforming view-space points to a canonical space over time, using time-dependent 3D warping fields and dense correspondences [5, 16, 17, 27, 30]. Dynamic NeRFs are able to learn high-fidelity animatable 3D models from several casual videos capturing the same object instance [42-44], by leveraging the temporal context available in videos. Unfortunately, dynamic NeRFs are slow and require optimization from scratch on unseen videos at test-time. Although architectures exist to speed up static NeRFs using explicit voxel grids [46] or hash-table caching [22], more work is required to speed up dynamic NeRFs by similar factors due to the additional overheads of time-dependent warping and correspondence matching. Our aim is to leverage the high-quality outputs of dynamic NeRFs to supervise a fast and lightweight architecture for articulated 3D reconstruction. + +# 3. Method + +In order to train category-specific feed-forward 3D predictors from dynamic NeRF teacher models, we combine a single-frame image encoder that regresses viewpoint, shape, and appearance from images, and a temporal encoder that reasons about these predictions over time. In this section, we describe the problem setup, scene representation, network architecture, training procedure, and losses. + +# 3.1. Problem Setup + +Given an input video centered on an articulated object, we train a feed-forward network to predict the viewpoint, articulations, and appearance, which are used to render a posed and textured object model. Our network is supervised on the pseudo-ground-truth outputs of a dynamic NeRF teacher, which builds animatable 3D models from casually collected videos including shape, appearance, and time-varying articulations. Our particular implementation uses BANMo [44] as the teacher, as it has public code and yields good results on humans and quadrupeds. Similar to the teacher, our method requires no pre-defined shape templates, registered cameras, or 3D ground truths. + +Fig. 2 summarizes our approach and how it differs from the teacher model. Sec. 3.2 and Sec. 3.3 introduce our object and motion representation, while Sec. 3.4 discusses the underlying feed-forward neural architecture. Finally, Sec. 3.5 describes the training losses used to supervise our models. In contrast to our teacher [44] which uses volume rendering (which can be slow), we render textured meshes to enable efficient rasterization. + +![](images/c5928dc0e6d942bffa1eb30629d2c668ff53ad26e551253143272f4f57eaefd5.jpg) +Figure 2. Architecture details. We train a feed-forward network (shown in blue) to predict articulations and textures from videos, supervised by the pseudo-ground-truth outputs of an offline dynamic NeRF teacher [44] (including 3D shapes, articulations, and textures). To simplify the learning task, our feed-forward network outputs in a high-dimensional latent space: the dynamic NeRF's frozen decoder networks (shown in purple) are used to convert articulation codes into joint angles and texture codes into 3D surface textures. Spatial per-vertex $\mathcal{L}_2$ losses are used to supervise the articulated 3D outputs against the articulated pseudo-ground-truths (shown in green). + +# 3.2. Object Representation + +Category-level shape. We model articulated objects as a canonical rest shape that is transformed by time-dependent poses and articulations. The rest shape is a category-specific triangular mesh $M = (V, F)$ that represents the mean shape of instances in the category: the faces $F$ define the vertex connectivity and we assume it remains fixed. To initialize the rest mesh, we run marching cubes on a $128^3$ grid to find the zero level set of the neural field that serves as the teacher NeRF's implicit rest shape. Although explicit mesh representations are less expressive than implicit neural fields, we find that a feed-forward predictor benefits from the speed of rasterization and the simplicity of regressing vertex colors. + +Per-instance pose and articulation. At each frame $t$ , we model the object's viewpoint and articulation similar to the dynamic NeRF literature. The viewpoint is a root body transformation $\mathbf{G}^t \in SE(3)$ , and we use neural blend skinning [9, 39] to express object articulations. For each frame, the bone configurations for neural blend skinning are parameterized by a joint angle vector $\mathbf{B}^t \in SO(3)^b$ , which is predicted by our feed-forward network from input video frames. See Sec. 3.3 for more details. + +Appearance. As our mesh topology is fixed, we can simply model the object's appearance as an array of per-vertex colors $\mathbf{C}^t\in \mathbb{R}^{|V|\times 3}$ at each frame $t$ . Following the standard rasterization pipeline, barycentric coordinates are used to interpolate the vertex colors per triangle during rendering. + +Rendering. We assume a weak-perspective camera projection defined by a fixed camera at the origin pointed along the negative- $z$ axis. To render the object in video frame $t$ , we apply the predicted viewpoint $\mathbf{G}^t \in SE(3)$ at time + +$t$ , followed by the blend skinning deformation specified by predicted bone configuration $\mathbf{B}^t \in SO(3)^b$ using forward kinematics and dual-quaternion blend skinning. + +# 3.3. Time-Varying Articulation via Blend Skinning + +To represent articulated body motion, we use a neural blend skinning model to define a 3D warping field $\mathcal{W}^t$ on top of a category-level kinematic skeleton. After computing the skeleton's forward kinematics, each point is deformed by a weighted combination of per-bone transformations. + +Category-level skeleton. Unlike color and 3D shape which are directly observable from imagery, an object's bone structure is much harder to infer. Automatic skeletal rigging methods [15,26] rely heavily on shape priors, or are sensitive to input data. Fortunately, bone structures are largely fixed within categories up to slight variations in bone length and body part scale. Thus, we can use readily available generic skeletons of humans, quadrupeds, and other categories to specify the bone structure of each category. Skeletons are defined by a tree structure with $B + 1$ variable-length bones and $B$ ball joints, where $B = 19$ for humans and $B = 26$ for quadrupeds. + +Forward kinematics. Each bone $b$ has a link transformation $\mathbf{L}_b\in SE(3)$ specifying the bone length and a joint transformation $\mathbf{J}_b^t\in SE(3)$ specified by the joint angle $\mathbf{B}_b^t\in SO(3)$ . The result for each link $b$ is a sequence of alternating transformations from the skeleton's base to the link's end, where $b_{1},b_{2},\ldots ,b$ are the parent links up to $b$ : + +$$ +\mathbf {T} _ {b} ^ {t} = \mathbf {J} _ {b} ^ {t} \mathbf {L} _ {b} \dots \mathbf {J} _ {b _ {2}} ^ {t} \mathbf {L} _ {b _ {2}} \dots \mathbf {J} _ {b _ {1}} ^ {t} \mathbf {L} _ {b _ {1}} +$$ + +Blend skinning. From per-bone kinematic transformations + +$\mathbf{T}_b^t$ and root body pose $\mathbf{G}^t$ , we use dual-quaternion blend skinning to compute a 3D warping field $\mathcal{W}(\mathbf{X})$ : + +$$ +\mathcal {W} (\mathbf {X}) ^ {t} = \left(\sum_ {b} \mathbf {W} (\mathbf {X}) _ {b} ^ {t} \cdot \mathbf {T} _ {b} ^ {t}\right) \cdot \mathbf {G} ^ {t} +$$ + +Skinning weights $\mathbf{W}(X)_b^t$ are specified by the softmax'ed distances between rest mesh vertices $\mathbf{X}$ and bone centers. + +# 3.4. Network Architecture + +Single-frame image encoder. Given a video of length $T$ , we use off-the-shelf PointRend [12] to compute segmentations and DensePose [7, 23, 24] to compute per-pixel CSE features. Each RGB image is concatenated with features, then masked and cropped to $1.2\mathrm{x}$ the tight bounding box of the object. We find that using dense pretrained features improves convergence speed over RGB inputs alone. We pass the preprocessed frames into a convolutional stacked hourglass network [25], which uses repeated pooling and upsampling to process features across multiple scales and spatial locations. The stacked intermediate outputs of each hourglass module are passed into a ResNet18 [8] network which predicts latent vectors $z_{\mathrm{view}}$ and $z_{\mathrm{art}}$ : $z_{\mathrm{view}}$ is decoded into the viewpoint $\mathbf{G}^t \in SE(3)$ and $z_{\mathrm{art}}$ is decoded into articulated joint angles $\mathbf{B}^t \in SO(3)^B$ . We use 6D rotations to represent angles during training [47]. + +Viewpoint branch. As the space of possible viewpoints is discontinuous and multi-modal, it is difficult to approach the optimum through iterative gradient descent. Following [6], we use a viewpoint decoder network $\mathbf{MLP}_{\mathrm{view}}$ to decode $z_{\mathrm{pose}}$ into a set of $M$ viewpoints hypotheses $\mathbf{G}_{\{1,\dots,M\}}^t$ weighted by $w_{\mathbf{G}}^{t}\in \mathbb{R}^{M}$ . Fig. 3 shows the variation over viewpoint hypotheses at an early stage of training. + +Articulation branch. Estimating 3D articulations from monocular images can be difficult due to depth ambiguities and occlusions. To resolve this, recent work on human pose estimation [37] uses a normalizing flow articulation prior represented as an invertible neural network, trained on large-scale human motion capture datasets. Without access to such datasets for other categories, we achieve a similar effect by leveraging the teacher's articulation priors, using the teacher's frozen articulation decoder $\mathbf{MLP}_{\mathrm{art}}$ to decode $z_{\mathrm{art}}$ . Fig. 4 visualizes the principal components of $z_{\mathrm{art}}$ 's latent space: we find that perturbing $z_{\mathrm{art}}$ along its principal components causes the resulting articulated shape to perform natural motions, such as curling up in a ball. + +Appearance branch. As the object in the video is only partially observable at any given time, we must use data priors or look at nearby frames to output complete appearance predictions $\mathbf{C}^t\in \mathbb{R}^{|V|\times 3}$ , represented as per-vertex colors of the articulated mesh at each frame. Our teacher [44] models global object appearances as a category-level neural field modulated by a texture code $z_{\mathrm{color}}\in \mathbb{R}^{64}$ . We leverage these appearance priors by predicting an environment code per + +![](images/7ffad52c18e195531c6012e8ec728d1138596e61f14a22d4e045bf4e89582f1b.jpg) +Figure 3. Viewpoint multiplexing during training. To overcome the discontinuous and multi-modal nature of pose optimization, we train our feed-forward predictor to output a set of $M$ viewpoint hypotheses rather than a single viewpoint. Blending multiple viewpoint hypotheses yields a more accurate prediction (here $M = 5$ ). Top row: Input frames. Second row (white): Blended viewpoint prediction. Bottom rows (light blue): $M$ viewpoint hypotheses + +![](images/5319b1470e805c243ad8a66e80a4dc413ca4f3da4773d989e4bb08f5bc213e6d.jpg) +Figure 4. Visualizing articulation code. Rather than training our feed-forward predictor to output high-dimensional (75) skeletal articulations, we leverage the teacher's pre-trained articulation space by predicting a low-dimensional (16) code. We visualize the first four principal components of the articulation code learned from the training dataset and find that variations along each axis correspond to interpretable motions: (1) whether the left or right paw is in front, (2) whether the hind paws are retracted or extended, (3) whether the front paws are retracted or extended, and (4) whether the cat has a straightened or curled-up posture. + +frame, modulating the teacher's frozen category-level neural field, and querying it at the rest mesh's vertex locations. + +Temporal encoder. Predicting pose and shape from single images can be highly ambiguous due to motion blur, occlusions, and depth ambiguities. To output temporally consistent results over long videos, we define a temporal encoder that updates $z_{\mathrm{view}}$ , $z_{\mathrm{art}}$ , and $z_{\mathrm{color}}$ across many frames. We treat the viewpoint multiplex $z_{\mathrm{view}}$ as a single vector by con + +catenating all $M$ hypotheses. Following prior work [11], our temporal encoder has several 1D convolutional layers acting on a temporal window centered at time $t$ . + +# 3.5. Losses and Supervision + +Optimization objective. Treating the teacher's outputs as pseudo-ground truths, our model can be trained in a standard supervised manner. We would like to use the teacher's inferred low-dimensional latent codes as supervisory targets for the student. But rather than defining $\mathcal{L}_2$ losses in the latent embedding space, where each dimension of $z_{\mathrm{view}}$ , $z_{\mathrm{art}}$ , and $z_{\mathrm{color}}$ has varying importance, we instead render these codes and compute 3D losses. As all articulated meshes have the same topology, we can define geometry and color losses as per-vertex $\mathcal{L}_2$ error: + +$$ +L _ {\mathrm {g e o m}} = \left\| \mathbf {X} ^ {t} - \widehat {\mathbf {X}} ^ {t} \right\| _ {2} \quad L _ {\mathrm {c o l o r}} = \left\| \mathbf {C} ^ {t} - \widehat {\mathbf {C}} ^ {t} \right\| _ {2} +$$ + +To improve articulation learning and account for multiple possible inverse kinematics solutions while solving for joint articulations, we add a joint loss defined as geodesic distance between predicted and actual joint angles at each joint. We find that this improves deformation quality. + +In summary, we train the image encoder and temporal encoder with the following objective: + +$$ +L = L _ {\text {g e o m}} + L _ {\text {j o i n t}} + L _ {\text {c o l o r}} +$$ + +# 4. Experiments + +Although we could have distilled a student using any dynamic NeRF as the teacher, our implementation uses BANMo [44] because it has public code, accepts unannotated monocular videos as input, and produces good results on humans and quadropeds. We modified BANMo to replace the bag-of-bones deformation model with a skeleton. Hyperparameters. Our method is implemented in PyTorch. We use the AdamW optimizer and train the model for 16k iterations, taking around 4 hours on a single RTX-3090 GPU. We use $224 \times 224$ images with batch size 56. We use 8 stacked hourglass blocks in the image encoder and a window size of 13 frames in the temporal encoder. All losses are weighted to have similar initial magnitudes. + +Staged training. We adopt a two-stage training strategy at every epoch to reduce the computational costs of evaluating an image encoder at every frame, when only a single frame per time window will receive a gradient update. In the first stage, we send frames through the image encoder and compute per-frame losses without using the temporal encoder, storing per-frame values of $z_{\mathrm{pose}}$ , $z_{\mathrm{art}}$ , and $z_{\mathrm{color}}$ . In the second stage, we send time windows of cached features through the temporal encoder without using the image encoder. Two-staged training reduces redundant image encoder evaluations and ensures that the temporal encoder can be safely removed if we only have access to single images rather than time windows of frames at test time. + +Table 1. Datasets. All videos are treated as casually collected monocular RGB videos, except when additional groundtruth meshes or depth maps are needed for evaluation. Processing time includes computing segmentations and per-pixel features with off-the-shelf networks, as well as computing pseudo-ground truth 3D outputs with the teacher. + +
Total VideosTotal InstancesTotal FramesTest InstancesTest FramesProcessing Time (hr)
Humans48286.4k101.6k22.0
Cats775611.7k132.7k23.2
Dogs88789.7k171.7k23.8
+ +# 4.1. Datasets + +We collect datasets for three categories: humans, cats, and dogs. For humans, we combine datasets from AMA [35], MonoPerfCap [41], DAVIS [29], and BANMo [44] to obtain 48 human videos. We evaluate on AMA and MonoPerfCap as they have ground-truth meshes. For cats and dogs, we collect 77 cat videos and 88 dog videos from the Pixels stock video website as well as BANMo released data. We also used an iPad Pro to capture two RGB-D videos to evaluate depth accuracy on cats and dogs. Video frames are extracted at 10fps. Datasets are summarized in Tab. 1. + +To compute BANMo pseudo-ground-truths per category without optimizing dozens of independent BANMo models, we optimize a single BANMo model per category, using articulation and texture codes to model shape and appearance differences across instances. As a result, the total dataset processing time is about 24 hours per category on 8 RTX-3090 GPUs. We find that BANMo generalizes quite well from the instance-level to the category-level setting [45], and that the articulation and texture latent spaces cover the range of motions and textures across all instances. + +# 4.2. Reconstructing Humans + +Dataset. Following BANMo, we evaluate human reconstruction on the AMA [35] dataset, containing 10 real-world mesh sequences depicting 3 different humans. The subjects wear loose clothing and perform challenging actions such as dancing and performing a handstand. Although the AMA videos were captured in an 8-camera studio to enable ground-truth mesh extraction, we treat them as casually collected monocular videos and do not use the camera intrinsics, camera extrinsic, or time synchronization. + +Comparisons. We compare against template-free BANMo [44], as well as model-based methods HuMoR [31] and ICON [40]. BANMo fits an animatable 3D model to multiple monocular videos of an object instance by performing differentiable rendering optimization. We train BANMo on the same dataset as our model. HuMoR is a human-specific temporal pose and shape predictor that performs test-time optimization on video sequences, leveraging OpenPose keypoint detection and motion priors learned + +![](images/de319ab15924845971c13213ed9b50646c686ac4d93baa317a78a7b021e3870b.jpg) +Figure 5. Qualitative results on humans (left), cats (middle), and dogs (right) in the test set. From left to right for each category, we show the input images, articulated shape and texture predictions overlaid on the input images, and three different viewpoints of the predicted geometry. Our method operates on casual monocular videos and predicts plausible shape, articulations, and textures in real-time. Our predictions align well with the image evidence on challenging inputs. + +![](images/b0da028f4f2b813d0d4307bbb025b5736903f67f0a918d3d721a27b3d996d142.jpg) + +![](images/b066a9c299a639213fda32706134dfac55bcc65fabc911d9e3ec9e5ffc156336.jpg) + +![](images/5e9549b31b812e668cc1790c3b3d3e8bf43301c5e36dc4100b4baae707b5ba43.jpg) + +![](images/075ad9ae709ba73c836a44a22668e7ac2cf4ece0643164784dc8d07df26d0703.jpg) + +![](images/17e0ce9abcf93e46b3a00ea95828ab481ae7bbdf035cf6d2b1f79053e729e5d6.jpg) + +from large-scale human motion capture datasets. ICON is the current SOTA for single-view human reconstruction, and it combines implicit functions with the SMPL human body model, using test-time optimization to fit surface normal predictions and improve pose accuracy and reconstruction quality. All our baselines require far more processing time than our model, which runs in real-time. + +Metrics. We report 3D chamfer distance and F-scores on three held-out test sequences in Tab. 2, averaged across all frames. Chamfer distance is the average distance between the ground-truth and predicted mesh vertices using nearest neighbor matches. As this can be sensitive to outliers, we also evaluate F-score at distance thresholds $d \in \{1\%, 2\%, 5\% \}$ to better quantify reconstruction error at different granularities. We scale predicted meshes by their view-space bounding box height to account for unknown scale compared to registered ground-truths. Our model approaches the performance of BANMo and baselines, while requiring nearly 1000x less compute at test time. + +Qualitative Results. We show qualitative comparisons for upright and inverted humans in Fig. 7. HuMoR outputs a deformed SMPL model, while ICON and BANMo optimize for both shape and articulation. Although our method outputs reasonable articulations for the upright pose, the woman lacks fine-grained geometry details and the viewpoint on the handstand video is inaccurate. We hypothesize that these failures occur due to the entanglement between articulations and per-instance morphologies, and the lack of handstand examples in the training set. + +# 4.3. Reconstructing Cats and Dogs + +Dataset. We evaluate cat and dog reconstruction on two RGB-D pet videos, as well as a held-out test set of pet videos from BANMo's dataset. These videos contain challenging motions such as rapid turns and jumping off chairs. Comparisons. We compare against BANMo [44] and BARC [32], a model-based approach and the current SOTA for dog shape and pose estimation from images. BARC trains a feed-forward network using images with keypoint labels and synthetic SMAL dog models [4], leveraging breed losses as additional supervision. As BARC is image-based, we run it separately on each video frame. + +Metrics We report the root mean square depth error and depth accuracy for all foreground pixels in Tab. 3, averaged across all frames. We render a synthetic depth map per frame, and following [19], we account for the unknown global scale factor between depth maps by aligning the median rendered and ground-truth depths at each frame: + +$$ +s _ {i} = \operatorname * {m e d i a n} _ {x} \left\{D _ {i} ^ {p r e d} (x) / D ^ {g t} (x) \right\} +$$ + +Depth accuracy is computed as the proportion of foreground pixels whose synthetic depth is within a given threshold. + +Qualitative Results We show qualitative results comparing to BARC in Fig. 6. BARC performs well at predicting coarse shape and deformations, and more faithfully captures the fine motion and geometry details of the dog when it is positioned well in frame. However, as BARC entangles shape and breed, we find that BARC may predict biased shapes for certain breeds. For example, in the bottom left + +![](images/f66c1c22a0ffce9145eab82ecbc4cdb1d9944bf2d41ec6ddadbdbfb9c0b641a0.jpg) +t-1 + +![](images/8a16d35e61ccd2191701ad3d0424660029aeb78dba736f7d4f371cc69a3e5ac4.jpg) + +![](images/915c363f5da0168e8e933cb46c63cdfb30ad866e907efd922c4e7b63b543f8a3.jpg) + +![](images/bd315a81fc1abb43bb89f8347d127c261adf40ec95c86278307fe15294f0dba1.jpg) +M +# +# + +![](images/c5dbdc849075302d3603f201f72593edcfa70a5d60eab93d961d93dd530832a7.jpg) +$t - 1$ +t +t+1 +Figure 6. Qualitative comparisons on pet sequences. From left to right in each column, we show (left) the input image, (middle-left) BARC's prediction, (middle-right) our articulated shape and texture predictions, and (right) our geometry predictions. Our method operates on videos and predicts plausible shape, articulations, and texture in real time. BARC operates on each video frame independently, resulting in jittery predictions when the pet is small or not clearly visible (top row). While BARC's geometry and motion predictions are largely accurate, they can be biased for certain breeds (bottom left), predicting an arched back for a flat-backed dog. + +![](images/e72a24506d3f772cb787ba7d1ff73214baa04b6dbd34e5dff8bb38e91e7f81ff.jpg) + +![](images/3b74cc276034cd958caad99e1635a72ffb2ecee4214eac45af94b9d39dd5d54f.jpg) + +![](images/449ac868039cad4f91f9469b0b311781137e64ab80ce4a50ae64ece466280321.jpg) + +Table 2. Quantitative results on AMA sequences. 3D chamfer distance (cm, ↓) and F-score (%, ↑) for articulated meshes, averaged over all frames. T_samba is a held-out video of a person that was seen during training, while the D_bouncing and D_handstand sequences contain a previously unseen person. Our model approaches the performance of BANMo and baselines while requiring nearly three orders of magnitude less compute at test time. Notably, our method performs better on T_samba, as it has fewer challenging poses and contains a person previously seen during training. Other baselines are trained on 3D human data, rely on the SMPL body model, or use expensive test-time optimization to improve results. We also report the inference time (ms) per frame. Results marked by * are different runs with the same hyperparameters. The best results are in bold. Please refer to Sec. 4.4 for discussions on the ablation results. + +
MethodTimeT_sambaD_bouncingD_handstand
CDF@1%F@2%F@5%CDF@1%F@2%F@5%CDF@1%F@2%F@5%
HuMoR420009.823.347.483.611.421.146.183.221.913.528.858.5
ICON6300010.118.939.985.29.727.853.586.414.123.545.275.6
BANMo4300010.325.348.883.611.626.750.881.514.222.544.174.7
Ours*2210.625.849.684.112.023.446.179.917.317.935.967.2
No temporal encoder2012.223.144.778.912.922.745.077.516.917.935.868.2
Conv1D encoder*2210.826.049.282.712.123.846.779.915.024.945.473.1
Transformer encoder2710.626.350.083.213.222.344.076.516.818.737.168.2
w/o frozen decoders2111.024.648.081.611.525.649.881.417.922.341.870.4
\( 64^3 \) template grid1012.021.042.279.112.722.945.278.015.622.543.671.8
\( 128^3 \) template grid*2210.525.649.884.412.423.646.078.713.724.346.575.6
\( 256^3 \) template grid2810.427.150.783.912.523.646.478.715.719.238.571.1
5 train videos2211.222.444.381.013.720.841.675.317.117.535.367.1
16 train videos2210.524.346.983.613.321.743.076.615.821.640.770.6
26 train videos2210.228.051.684.313.222.043.676.817.717.835.667.2
35 train videos*2210.824.047.483.612.323.346.379.016.819.038.069.2
+ +of Fig. 6, BARC predicts a rounded back but the back is flat in reality. For the inputs on the top row, BARC's single-frame architecture makes jittery predictions from frame to + +frame, while our temporal architecture enforces consistency and prevents large discontinuities in pose and deformation. In the middle top image, which is particularly challeng- + +Table 3. Quantitative results on RGB-D pet sequences. Root mean square depth error (↓) and depth accuracy (%, ↑) for all foreground pixels in the depth map, averaged over all frames. We also report the total processing time per frame (ms) on a RTX-3090 GPU. Although BANMo consistently does better, our method approaches its quality while being nearly 1000x faster at test time. Best results are in bold. + +
MethodTimedogcat
RMSEAcc-1%Acc-2%Acc-5%RMSEAcc-1%Acc-2%Acc-5%
BANMo54s0.041128.645.372.70.075727.747.476.5
Ours100ms0.056917.731.656.60.129819.133.861.4
+ +![](images/3ace91fa95b8627fd71ad0b2f21d9df0fa15c9f7729196a81769808aca48dd1e.jpg) +Image + +![](images/ebbe64bcd4acd62ad47b9cb866c5eb73220a8fff0fb2dc7c8fdc9744deddb46e.jpg) +HuMoR + +![](images/f9db9c96f939688020a2e040b8d2d2becfd4dfe4e0d944e1de47095b10f96fbd.jpg) +ICON + +![](images/32ff58cefc9413694008eb202528aefcf01cbbd2eb5f4d47dae70a099023539d.jpg) +BANMo + +![](images/72c5582a3f2231176b51f7477733e011da2ccc579d440070fc4f1325d3b1ca8b.jpg) +Ours + +![](images/bdeb9da3c3cf2798aff024d917977a8405c7e2daad8a3bff751a16b4ea721914.jpg) +Image + +![](images/fbf57c117253423b9292eef4238c1ad9bc8f1388d566f13ca274e20bb4ab39fc.jpg) +HuMoR + +![](images/1a42072221b057dd91089041a733f44125f9d21701f4ca45d50e581a8ccd0f5b.jpg) +ICON + +![](images/3b0bcea5b5f938ffde2346af42f8007470e0f25bbf64b0bca013a8e31dbd211d.jpg) +BANMo +Figure 7. Qualitative comparisons on human sequences. From left to right, we show the output of HuMoR [31], ICON [40], BANMo [44], and our method on dancing (top) and handstand (bottom) sequences. Our method outputs plausible articulations for the dancing sequence, although the shape lacks fine details. In comparison, HuMoR outputs the SMPL template human shape, while ICON and BANMo output more detailed shapes. All methods perform poorly on the highly challenging handstand pose: HuMoR outputs unrealistic and self-intersecting articulations, ICON's prediction appears bumpy and twisted in an unnatural way, BANMo's prediction is also twisted and misses the head, and our method outputs incorrect viewpoint and arm articulations. + +![](images/44cc8c17ac2d7a543adbeda0a46f8a42905146400271e4e04f7f86df307440de.jpg) +Ours + +ing because the dog is standing on its hind legs, both our method and BARC fail to show that the dog is lifting its front paws. As our method does not disentangle articulation and morphology variation between breeds, incorporating breed and/or instance information would likely improve our ability to represent fine motion and geometry details. + +# 4.4. Ablations + +We performed an ablation study on several architectural details including the choice of temporal encoder, the use of frozen decoders from the teacher, the template grid resolution, and the number of training videos. Most notably, we find that increasing the density of mesh points by running marching cubes at a finer resolution (from $64^{3}$ to $128^{3}$ improves the F@1% and F@2% accuracy of our student, as well as using a temporal encoder. Changing the marching cubes resolution involves no change to the student, but simply a more faithful post-processing of the teacher's output. + +Effect of temporal encoder. The student model performs better with a temporal encoder across all sequences, perhaps by providing additional temporal context to help smooth the + +predictions. In general, the Conv1D encoder seems to outperform the transformer encoder in both speed and accuracy, although this could be caused by the increased difficulty of training a transformer encoder. + +Effect of frozen decoders. We find that the student model's performance generally drops without using the teacher's frozen articulation decoder to regularize pose predictions. + +Effect of template shape resolution. When extracting the template shape with a $64^{3}$ grid, our model's F@1%, F@2%, and F@5% accuracy all seem to drop. Qualitatively, the $64^{3}$ template shape is less detailed and appears fuzzy compared to $128^{3}$ or $256^{3}$ , though the predicted articulations are similar. There seems to be little difference between $128^{3}$ and $256^{3}$ , and the observed results could be up to noise. As more points need to be warped to the deformed space, more detailed templates have slower inference speed. + +Effect of dataset size. We find that performance generally deteriorates with less data, although the trend is not as clear. Here, each smaller set of training videos is a subset of the immediately larger video set: as all videos containing the T_samba identity are within the set of 26 videos, increasing the dataset size from 26 to 35 involved adding videos of unrelated identities which seemed to hurt performance. + +# 5. Discussion + +We present a method to train category-specific feedforward video shape predictors by distilling knowledge from dynamic NeRF teachers fitted to offline video data at scale. Our temporal architecture predicts consistent viewpoint, articulation, and appearance, producing real-time video reconstruction results on humans, cats, and dogs with the ability to support other categories as well. We qualitatively outperform existing feed-forward predictors for dog shape and pose, and approach the quality of test-time fitting methods while using nearly 1000x less computation. + +Limitations: As our method is trained on the pseudoground truth outputs of a teacher model, we are upper-bounded by the teacher's performance and reconstruction fidelity. We expect the performance of our method to improve given larger-scale, more diverse, and higher-quality video data. Compared with optimization-based methods, our method is hundreds of times faster but produces results less faithful to the inputs: we leave incorporating optimization into the feed-forward architecture as future work. + +# References + +[1] Sameer Agarwal, Yasutaka Furukawa, Noah Snavely, Ian Simon, Brian Curless, Steven M. Seitz, and Richard Szeliski. Building rome in a day. 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CVPR, 2020. 1, 2 +[31] Davis Rempe, Tolga Birdal, Aaron Hertzmann, Jimei Yang, Srinath Sridhar, and Leonidas J. Guibas. HuMoR: 3D Human Motion Model for Robust Pose Estimation. ICCV, 2021. 1, 5, 8 +[32] Nadine Rueegg, Silvia Zuffi, Konrad Schindler, and Michael J. Black. BARC: Learning to Regress 3D Dog Shape from Images by Exploiting Breed Information. CVPR, 2022. 2, 6 +[33] Noah Snavely, Steven M. Seitz, and Richard Szeliski. Photo Tourism: Exploring Photo Collections in 3D. SIGGRAPH, 2006. 1 + +[34] Shubham Tulsiani, Nilesh Kulkarni, and Abhinav Gupta. Implicit Mesh Reconstruction From Unannotated Image Collections. arXiv, 2020. 2 +[35] Daniel Vlasic, Ilya Baran, Wojciech Matusik, and Jovan Popovic. Articulated Mesh Animation from Multi-View Silhouettes. ACM TOG, 2008. 5 +[36] Zirui Wang, Shangzhe Wu, Weidi Xie, Min Chen, and Victor Adrian Prisacariu. Nerf-: Neural Radiance Fields Without Known Camera Parameters. arXiv, 2021. 1, 2 +[37] Tom Wehrbein, Marco Rudolph, Bodo Rosenhahn, and Bastian Wandt. Probabilistic Monocular 3D Human Pose Estimation with Normalizing Flows. ICCV, 2021. 4 +[38] Shangzhe Wu, Tomas Jakab, Christian Rupprecht, and Andrea Vedaldi. DOVE: Learning Deformable 3D Objects by Watching Videos. arXiv, 2022. 2 +[39] Yuefan Wu, Zeyuan Chen, Shaowei Liu, Zhongzheng Ren, and Shenlong Wang. CASA: Category-Agnostic Skeletal Animal Reconstruction. CVPR, 2019. 3 +[40] Yuliang Xiu, Jinlong Yang, Dimitrios Tzionas, and Michael J. Black. ICON: Implicit Clothed Humans Obtained from Normals. CVPR, 2022. 5, 8 +[41] Weipeng Xu, Avishek Chatterjee, Michael Zollhoefer, Helge Rhodin, Dushyant Mehta, Hans-Peter Seidel, and Christian Theobalt. MonoPerfCap: Human Performance Capture from Monocular Video. ACM TOG, 2018. 5 +[42] Gengshan Yang, Deqing Sun, Varun Jampani, Daniel Vlasic, Forrester Cole, Huiwen Chang, Deva Ramanan, William T. Freeman, and Ce Liu. LASR: Learning Articulated Shape Reconstruction from a Monocular Video. CVPR, 2021. 2 +[43] Gengshan Yang, Deqing Sun, Varun Jampani, Daniel Vlasic, Forrester Cole, Ce Liu, and Deva Ramanan. ViSER: Video-Specific Surface Embeddings for Articulated 3D Shape Reconstruction. NeurIPS, 2021. 2 +[44] Gengshan Yang, Minh Vo, Natalia Neverova, Deva Ramanan, Andrea Vedaldi, and Hanbyul Joo. BANMo: Building Animatable 3D Neural Models from Many Casual Videos. CVPR, 2022. 1, 2, 3, 4, 5, 6, 8 +[45] Gengshan Yang, Chaoyang Wang, N Dinesh Reddy, and Deva Ramanan. RAC: Reconstructing Animatable Categories from Videos. CVPR, 2023. 5 +[46] Alex Yu, Sara Fridovich-Keil, Matthew Tancik, Qinhong Chen, Benjamin Recht, and Angjoo Kanazawa. Plenoxels: Radiance Fields Without Neural Networks. CVPR, 2022. 2 +[47] Yi Zhou, Connelly Barnes, Jingwan Lu, Jimei Yang, and Hao Li. On the Continuity of Rotation Representations in Neural Networks. CVPR, 2019. 4 +[48] Silvia Zuffi, Angjoo Kanazawa, and Michael J. Black. Lions and Tigers and Bears: Capturing Non-Rigid, 3D, Articulated Shape From Images. CVPR, 2018. 2 +[49] Silvia Zuffi, Angjoo Kanazawa, David Jacobs, and Michael J. Black. 3D Menagerie: Modeling the 3D Shape and Pose of Animals. 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By distilling knowledge from dynamic NeRFs fitted to offline video data at scale [16, 44], we present a method to train category-specific real-time video shape predictors, which output temporally-consistent viewpoint, articulation, and appearance given casual input videos. Our method replaces expensive test-time optimization with a single forward pass, allowing real-time inference on a RTX-3090 GPU. Compared to existing model-based methods for reconstructing humans and animals in motion [13, 18, 31], our method does not require pre-defined 3D templates or ground-truth 3D data to train. (Project page: https://jefftan969.github.io/dasr)." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 421, + 192, + 433 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 421, + 192, + 433 + ], + "spans": [ + { + "bbox": [ + 143, + 421, + 192, + 433 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 447, + 289, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 447, + 289, + 712 + ], + "spans": [ + { + "bbox": [ + 45, + 447, + 289, + 712 + ], + "type": "text", + "content": "We present a method for reconstructing articulated 3D models from videos in real-time, without test-time optimization or manual 3D supervision at training time. Prior work often relies on pre-built deformable models (e.g. SMAL/SMPL), or slow per-scene optimization through differentiable rendering (e.g. dynamic NeRFs). Such methods fail to support arbitrary object categories, or are unsuitable for real-time applications. To address the challenge of collecting large-scale 3D training data for arbitrary deformable object categories, our key insight is to use off-the-shelf video-based dynamic NeRFs as 3D supervision to train a fast feed-forward network, turning 3D shape and motion prediction into a supervised distillation task. Our temporal-aware network uses articulated bones and blend skinning to represent arbitrary deformations, and is self-supervised on video datasets without requiring 3D shapes or viewpoints as input. Through distillation, our network learns to 3D-reconstruct unseen articulated objects at interactive frame rates. Our method yields higher-fidelity 3D reconstructions than prior real-time methods for animals, with the ability to render realistic images at novel viewpoints and poses." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 307, + 421, + 386, + 433 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 421, + 386, + 433 + ], + "spans": [ + { + "bbox": [ + 307, + 421, + 386, + 433 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 445, + 545, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 445, + 545, + 649 + ], + "spans": [ + { + "bbox": [ + 304, + 445, + 545, + 649 + ], + "type": "text", + "content": "We are interested in building high-quality animatable models of articulated 3D objects from videos in real time. One promising application is virtual and augmented reality, where the goal is to create high-fidelity 3D experiences from images and videos captured live by users. For rigid scenes, structure from motion (SfM) and neural rendering can be used to build accurate 3D cities and landmarks from Internet image collections [1, 20, 33]. For articulated objects such as friends and pets, many works parameterize the range of motions using category-specific templates such as SMPL [18] for humans and SMAL [4] for quadruped animals. Although these methods can be trained on large-scale video datasets, they rely on parametric body template models built from extensive real-world 3D scans: these body models are not easy to generate for diverse categories in the wild such as clothed humans or pets with distinct morphologies, which are often the focus of user content." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "content": "Inspired by the breakthrough success of neural radiance fields [21], many works reconstruct arbitrary articulated objects in an analysis-by-synthesis framework [16, 27, 28, 30, 36, 44] by defining time-dependent 3D warping fields and establishing long-range correspondences on top of canon-" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4692" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": "ical shape and appearance models. These methods output high-quality reconstructions of arbitrary objects without 3D data or pre-defined templates, but the output representations are scene-specific and often require hours to compute from scratch on unseen videos - an unacceptable cost for real-time VR/AR tasks. We are thus interested in dynamic 3D reconstruction algorithms that achieve the best of both worlds: the speed of template-based models and the quality and generalization ability of dynamic NeRFs. To achieve this, our key insight is remarkably simple: we train category-specific feed-forward 3D predictors at scale by self-supervising them with dynamic NeRF \"teachers\" fitted to offline video data." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 228, + 289, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 228, + 289, + 360 + ], + "spans": [ + { + "bbox": [ + 46, + 228, + 289, + 360 + ], + "type": "text", + "content": "By leveraging scene-fitted dynamic NeRFs for 3D supervision at scale, our method learns a feed-forward predictor for appearance, 3D shape, and articulations of non-rigid objects from videos. Our learned 3D models use linear blend skinning to express articulations, allowing it to be animated by manipulating bone transformations. We address three key challenges in our work: (1) how to supervise feed-forward models with internal representations of dynamic NeRFs, (2) how to produce temporally consistent predictions of pose, articulation, and appearance, and (3) how to build efficient systems for real-time reconstruction." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 370, + 134, + 383 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 370, + 134, + 383 + ], + "spans": [ + { + "bbox": [ + 47, + 370, + 134, + 383 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 390, + 287, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 390, + 287, + 545 + ], + "spans": [ + { + "bbox": [ + 46, + 390, + 287, + 545 + ], + "type": "text", + "content": "Template-Based Dynamic Reconstruction A large body of work uses parametric body models [18, 48, 49] to recover 3D shapes and motions for human and animal reconstruction, given a single image as input [2, 3, 13, 32]. These models are built from registered 3D scans of real humans or toy animals, and achieve great success in reconstructing categories for which large volumes of ground-truth 3D data are available (especially human reconstruction). However, it is challenging to apply these methods to arbitrary categories with diverse morphologies, especially where 3D data is limited. Our work aims to generalize these approaches to arbitrary articulated object categories without requiring ground-truth 3D data or pre-registered 3D scans during training." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "content": "Template-Free Dynamic Reconstruction Several methods build deformable 3D models without templates by recovering shapes and poses from internet-scale 2D image collections, using weak supervision such as keypoints and object silhouettes from off-the-shelf models or human annotators [6, 10, 14, 34]. As it is inherently ambiguous to reconstruct 3D outputs from the sparse and limited 2D observations available in images, these methods must leverage strong data priors and apply heavily regularization to ensure reasonable outputs, often resulting in blurry or oversmoothed shapes and textures. Leveraging the temporal context available in videos can help these methods learn temporally consistent results [38], however the output quality is still low perhaps due to over-regularization." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "text", + "content": "Neural Radiance Fields Neural fields are a powerful method for 3D reconstruction using 2D image supervision, achieving state-of-the-art quality on both static and dynamic scenes. Although historically limited to rigid scenes with known cameras [20, 21, 36], recent works extend NeRF to dynamic scenes by deforming view-space points to a canonical space over time, using time-dependent 3D warping fields and dense correspondences [5, 16, 17, 27, 30]. Dynamic NeRFs are able to learn high-fidelity animatable 3D models from several casual videos capturing the same object instance [42-44], by leveraging the temporal context available in videos. Unfortunately, dynamic NeRFs are slow and require optimization from scratch on unseen videos at test-time. Although architectures exist to speed up static NeRFs using explicit voxel grids [46] or hash-table caching [22], more work is required to speed up dynamic NeRFs by similar factors due to the additional overheads of time-dependent warping and correspondence matching. Our aim is to leverage the high-quality outputs of dynamic NeRFs to supervise a fast and lightweight architecture for articulated 3D reconstruction." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 339, + 362, + 351 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 339, + 362, + 351 + ], + "spans": [ + { + "bbox": [ + 306, + 339, + 362, + 351 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 361, + 547, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 361, + 547, + 445 + ], + "spans": [ + { + "bbox": [ + 304, + 361, + 547, + 445 + ], + "type": "text", + "content": "In order to train category-specific feed-forward 3D predictors from dynamic NeRF teacher models, we combine a single-frame image encoder that regresses viewpoint, shape, and appearance from images, and a temporal encoder that reasons about these predictions over time. In this section, we describe the problem setup, scene representation, network architecture, training procedure, and losses." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 457, + 399, + 470 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 457, + 399, + 470 + ], + "spans": [ + { + "bbox": [ + 306, + 457, + 399, + 470 + ], + "type": "text", + "content": "3.1. Problem Setup" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 472, + 547, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 472, + 547, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 472, + 547, + 616 + ], + "type": "text", + "content": "Given an input video centered on an articulated object, we train a feed-forward network to predict the viewpoint, articulations, and appearance, which are used to render a posed and textured object model. Our network is supervised on the pseudo-ground-truth outputs of a dynamic NeRF teacher, which builds animatable 3D models from casually collected videos including shape, appearance, and time-varying articulations. Our particular implementation uses BANMo [44] as the teacher, as it has public code and yields good results on humans and quadrupeds. Similar to the teacher, our method requires no pre-defined shape templates, registered cameras, or 3D ground truths." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "text", + "content": "Fig. 2 summarizes our approach and how it differs from the teacher model. Sec. 3.2 and Sec. 3.3 introduce our object and motion representation, while Sec. 3.4 discusses the underlying feed-forward neural architecture. Finally, Sec. 3.5 describes the training losses used to supervise our models. In contrast to our teacher [44] which uses volume rendering (which can be slow), we render textured meshes to enable efficient rasterization." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4693" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 73, + 51, + 516, + 268 + ], + "blocks": [ + { + "bbox": [ + 73, + 51, + 516, + 268 + ], + "lines": [ + { + "bbox": [ + 73, + 51, + 516, + 268 + ], + "spans": [ + { + "bbox": [ + 73, + 51, + 516, + 268 + ], + "type": "image", + "image_path": "c5928dc0e6d942bffa1eb30629d2c668ff53ad26e551253143272f4f57eaefd5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 270, + 545, + 326 + ], + "lines": [ + { + "bbox": [ + 46, + 270, + 545, + 326 + ], + "spans": [ + { + "bbox": [ + 46, + 270, + 545, + 326 + ], + "type": "text", + "content": "Figure 2. Architecture details. We train a feed-forward network (shown in blue) to predict articulations and textures from videos, supervised by the pseudo-ground-truth outputs of an offline dynamic NeRF teacher [44] (including 3D shapes, articulations, and textures). To simplify the learning task, our feed-forward network outputs in a high-dimensional latent space: the dynamic NeRF's frozen decoder networks (shown in purple) are used to convert articulation codes into joint angles and texture codes into 3D surface textures. Spatial per-vertex " + }, + { + "bbox": [ + 46, + 270, + 545, + 326 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_2" + }, + { + "bbox": [ + 46, + 270, + 545, + 326 + ], + "type": "text", + "content": " losses are used to supervise the articulated 3D outputs against the articulated pseudo-ground-truths (shown in green)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 335, + 175, + 348 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 335, + 175, + 348 + ], + "spans": [ + { + "bbox": [ + 47, + 335, + 175, + 348 + ], + "type": "text", + "content": "3.2. Object Representation" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 354, + 287, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 354, + 287, + 498 + ], + "spans": [ + { + "bbox": [ + 46, + 354, + 287, + 498 + ], + "type": "text", + "content": "Category-level shape. We model articulated objects as a canonical rest shape that is transformed by time-dependent poses and articulations. The rest shape is a category-specific triangular mesh " + }, + { + "bbox": [ + 46, + 354, + 287, + 498 + ], + "type": "inline_equation", + "content": "M = (V, F)" + }, + { + "bbox": [ + 46, + 354, + 287, + 498 + ], + "type": "text", + "content": " that represents the mean shape of instances in the category: the faces " + }, + { + "bbox": [ + 46, + 354, + 287, + 498 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 46, + 354, + 287, + 498 + ], + "type": "text", + "content": " define the vertex connectivity and we assume it remains fixed. To initialize the rest mesh, we run marching cubes on a " + }, + { + "bbox": [ + 46, + 354, + 287, + 498 + ], + "type": "inline_equation", + "content": "128^3" + }, + { + "bbox": [ + 46, + 354, + 287, + 498 + ], + "type": "text", + "content": " grid to find the zero level set of the neural field that serves as the teacher NeRF's implicit rest shape. Although explicit mesh representations are less expressive than implicit neural fields, we find that a feed-forward predictor benefits from the speed of rasterization and the simplicity of regressing vertex colors." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 498, + 287, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 287, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 287, + 605 + ], + "type": "text", + "content": "Per-instance pose and articulation. At each frame " + }, + { + "bbox": [ + 46, + 498, + 287, + 605 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 498, + 287, + 605 + ], + "type": "text", + "content": ", we model the object's viewpoint and articulation similar to the dynamic NeRF literature. The viewpoint is a root body transformation " + }, + { + "bbox": [ + 46, + 498, + 287, + 605 + ], + "type": "inline_equation", + "content": "\\mathbf{G}^t \\in SE(3)" + }, + { + "bbox": [ + 46, + 498, + 287, + 605 + ], + "type": "text", + "content": ", and we use neural blend skinning [9, 39] to express object articulations. For each frame, the bone configurations for neural blend skinning are parameterized by a joint angle vector " + }, + { + "bbox": [ + 46, + 498, + 287, + 605 + ], + "type": "inline_equation", + "content": "\\mathbf{B}^t \\in SO(3)^b" + }, + { + "bbox": [ + 46, + 498, + 287, + 605 + ], + "type": "text", + "content": ", which is predicted by our feed-forward network from input video frames. See Sec. 3.3 for more details." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 605, + 287, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 666 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 666 + ], + "type": "text", + "content": "Appearance. As our mesh topology is fixed, we can simply model the object's appearance as an array of per-vertex colors " + }, + { + "bbox": [ + 46, + 605, + 287, + 666 + ], + "type": "inline_equation", + "content": "\\mathbf{C}^t\\in \\mathbb{R}^{|V|\\times 3}" + }, + { + "bbox": [ + 46, + 605, + 287, + 666 + ], + "type": "text", + "content": " at each frame " + }, + { + "bbox": [ + 46, + 605, + 287, + 666 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 605, + 287, + 666 + ], + "type": "text", + "content": ". Following the standard rasterization pipeline, barycentric coordinates are used to interpolate the vertex colors per triangle during rendering." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 666, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 666, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 666, + 287, + 713 + ], + "type": "text", + "content": "Rendering. We assume a weak-perspective camera projection defined by a fixed camera at the origin pointed along the negative- " + }, + { + "bbox": [ + 46, + 666, + 287, + 713 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 666, + 287, + 713 + ], + "type": "text", + "content": " axis. To render the object in video frame " + }, + { + "bbox": [ + 46, + 666, + 287, + 713 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 666, + 287, + 713 + ], + "type": "text", + "content": ", we apply the predicted viewpoint " + }, + { + "bbox": [ + 46, + 666, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{G}^t \\in SE(3)" + }, + { + "bbox": [ + 46, + 666, + 287, + 713 + ], + "type": "text", + "content": " at time" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 336, + 545, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 336, + 545, + 373 + ], + "spans": [ + { + "bbox": [ + 305, + 336, + 545, + 373 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 305, + 336, + 545, + 373 + ], + "type": "text", + "content": ", followed by the blend skinning deformation specified by predicted bone configuration " + }, + { + "bbox": [ + 305, + 336, + 545, + 373 + ], + "type": "inline_equation", + "content": "\\mathbf{B}^t \\in SO(3)^b" + }, + { + "bbox": [ + 305, + 336, + 545, + 373 + ], + "type": "text", + "content": " using forward kinematics and dual-quaternion blend skinning." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 379, + 545, + 392 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 379, + 545, + 392 + ], + "spans": [ + { + "bbox": [ + 305, + 379, + 545, + 392 + ], + "type": "text", + "content": "3.3. Time-Varying Articulation via Blend Skinning" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 397, + 545, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 397, + 545, + 456 + ], + "spans": [ + { + "bbox": [ + 304, + 397, + 545, + 456 + ], + "type": "text", + "content": "To represent articulated body motion, we use a neural blend skinning model to define a 3D warping field " + }, + { + "bbox": [ + 304, + 397, + 545, + 456 + ], + "type": "inline_equation", + "content": "\\mathcal{W}^t" + }, + { + "bbox": [ + 304, + 397, + 545, + 456 + ], + "type": "text", + "content": " on top of a category-level kinematic skeleton. After computing the skeleton's forward kinematics, each point is deformed by a weighted combination of per-bone transformations." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 457, + 545, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 457, + 545, + 601 + ], + "spans": [ + { + "bbox": [ + 304, + 457, + 545, + 601 + ], + "type": "text", + "content": "Category-level skeleton. Unlike color and 3D shape which are directly observable from imagery, an object's bone structure is much harder to infer. Automatic skeletal rigging methods [15,26] rely heavily on shape priors, or are sensitive to input data. Fortunately, bone structures are largely fixed within categories up to slight variations in bone length and body part scale. Thus, we can use readily available generic skeletons of humans, quadrupeds, and other categories to specify the bone structure of each category. Skeletons are defined by a tree structure with " + }, + { + "bbox": [ + 304, + 457, + 545, + 601 + ], + "type": "inline_equation", + "content": "B + 1" + }, + { + "bbox": [ + 304, + 457, + 545, + 601 + ], + "type": "text", + "content": " variable-length bones and " + }, + { + "bbox": [ + 304, + 457, + 545, + 601 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 304, + 457, + 545, + 601 + ], + "type": "text", + "content": " ball joints, where " + }, + { + "bbox": [ + 304, + 457, + 545, + 601 + ], + "type": "inline_equation", + "content": "B = 19" + }, + { + "bbox": [ + 304, + 457, + 545, + 601 + ], + "type": "text", + "content": " for humans and " + }, + { + "bbox": [ + 304, + 457, + 545, + 601 + ], + "type": "inline_equation", + "content": "B = 26" + }, + { + "bbox": [ + 304, + 457, + 545, + 601 + ], + "type": "text", + "content": " for quadrupeds." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 601, + 545, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 601, + 545, + 673 + ], + "spans": [ + { + "bbox": [ + 304, + 601, + 545, + 673 + ], + "type": "text", + "content": "Forward kinematics. Each bone " + }, + { + "bbox": [ + 304, + 601, + 545, + 673 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 304, + 601, + 545, + 673 + ], + "type": "text", + "content": " has a link transformation " + }, + { + "bbox": [ + 304, + 601, + 545, + 673 + ], + "type": "inline_equation", + "content": "\\mathbf{L}_b\\in SE(3)" + }, + { + "bbox": [ + 304, + 601, + 545, + 673 + ], + "type": "text", + "content": " specifying the bone length and a joint transformation " + }, + { + "bbox": [ + 304, + 601, + 545, + 673 + ], + "type": "inline_equation", + "content": "\\mathbf{J}_b^t\\in SE(3)" + }, + { + "bbox": [ + 304, + 601, + 545, + 673 + ], + "type": "text", + "content": " specified by the joint angle " + }, + { + "bbox": [ + 304, + 601, + 545, + 673 + ], + "type": "inline_equation", + "content": "\\mathbf{B}_b^t\\in SO(3)" + }, + { + "bbox": [ + 304, + 601, + 545, + 673 + ], + "type": "text", + "content": ". The result for each link " + }, + { + "bbox": [ + 304, + 601, + 545, + 673 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 304, + 601, + 545, + 673 + ], + "type": "text", + "content": " is a sequence of alternating transformations from the skeleton's base to the link's end, where " + }, + { + "bbox": [ + 304, + 601, + 545, + 673 + ], + "type": "inline_equation", + "content": "b_{1},b_{2},\\ldots ,b" + }, + { + "bbox": [ + 304, + 601, + 545, + 673 + ], + "type": "text", + "content": " are the parent links up to " + }, + { + "bbox": [ + 304, + 601, + 545, + 673 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 304, + 601, + 545, + 673 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 357, + 680, + 492, + 694 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 357, + 680, + 492, + 694 + ], + "spans": [ + { + "bbox": [ + 357, + 680, + 492, + 694 + ], + "type": "interline_equation", + "content": "\\mathbf {T} _ {b} ^ {t} = \\mathbf {J} _ {b} ^ {t} \\mathbf {L} _ {b} \\dots \\mathbf {J} _ {b _ {2}} ^ {t} \\mathbf {L} _ {b _ {2}} \\dots \\mathbf {J} _ {b _ {1}} ^ {t} \\mathbf {L} _ {b _ {1}}", + "image_path": "9f41daa298c3008bdba9ae094ba6bc00189b447534521745f821c188cf5220b5.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 701, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 701, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 701, + 545, + 713 + ], + "type": "text", + "content": "Blend skinning. From per-bone kinematic transformations" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "4694" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 288, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 288, + 96 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 288, + 96 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_b^t" + }, + { + "bbox": [ + 47, + 72, + 288, + 96 + ], + "type": "text", + "content": " and root body pose " + }, + { + "bbox": [ + 47, + 72, + 288, + 96 + ], + "type": "inline_equation", + "content": "\\mathbf{G}^t" + }, + { + "bbox": [ + 47, + 72, + 288, + 96 + ], + "type": "text", + "content": ", we use dual-quaternion blend skinning to compute a 3D warping field " + }, + { + "bbox": [ + 47, + 72, + 288, + 96 + ], + "type": "inline_equation", + "content": "\\mathcal{W}(\\mathbf{X})" + }, + { + "bbox": [ + 47, + 72, + 288, + 96 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 95, + 106, + 238, + 121 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 95, + 106, + 238, + 121 + ], + "spans": [ + { + "bbox": [ + 95, + 106, + 238, + 121 + ], + "type": "interline_equation", + "content": "\\mathcal {W} (\\mathbf {X}) ^ {t} = \\left(\\sum_ {b} \\mathbf {W} (\\mathbf {X}) _ {b} ^ {t} \\cdot \\mathbf {T} _ {b} ^ {t}\\right) \\cdot \\mathbf {G} ^ {t}", + "image_path": "32621a97bebaa409ed64ef42036cbec67c371be57f23f1d6ac1a9ba78546c620.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 130, + 287, + 154 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 130, + 287, + 154 + ], + "spans": [ + { + "bbox": [ + 47, + 130, + 287, + 154 + ], + "type": "text", + "content": "Skinning weights " + }, + { + "bbox": [ + 47, + 130, + 287, + 154 + ], + "type": "inline_equation", + "content": "\\mathbf{W}(X)_b^t" + }, + { + "bbox": [ + 47, + 130, + 287, + 154 + ], + "type": "text", + "content": " are specified by the softmax'ed distances between rest mesh vertices " + }, + { + "bbox": [ + 47, + 130, + 287, + 154 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 47, + 130, + 287, + 154 + ], + "type": "text", + "content": " and bone centers." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 164, + 173, + 176 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 164, + 173, + 176 + ], + "spans": [ + { + "bbox": [ + 47, + 164, + 173, + 176 + ], + "type": "text", + "content": "3.4. Network Architecture" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 182, + 287, + 374 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 182, + 287, + 374 + ], + "spans": [ + { + "bbox": [ + 46, + 182, + 287, + 374 + ], + "type": "text", + "content": "Single-frame image encoder. Given a video of length " + }, + { + "bbox": [ + 46, + 182, + 287, + 374 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 182, + 287, + 374 + ], + "type": "text", + "content": ", we use off-the-shelf PointRend [12] to compute segmentations and DensePose [7, 23, 24] to compute per-pixel CSE features. Each RGB image is concatenated with features, then masked and cropped to " + }, + { + "bbox": [ + 46, + 182, + 287, + 374 + ], + "type": "inline_equation", + "content": "1.2\\mathrm{x}" + }, + { + "bbox": [ + 46, + 182, + 287, + 374 + ], + "type": "text", + "content": " the tight bounding box of the object. We find that using dense pretrained features improves convergence speed over RGB inputs alone. We pass the preprocessed frames into a convolutional stacked hourglass network [25], which uses repeated pooling and upsampling to process features across multiple scales and spatial locations. The stacked intermediate outputs of each hourglass module are passed into a ResNet18 [8] network which predicts latent vectors " + }, + { + "bbox": [ + 46, + 182, + 287, + 374 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{view}}" + }, + { + "bbox": [ + 46, + 182, + 287, + 374 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 182, + 287, + 374 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{art}}" + }, + { + "bbox": [ + 46, + 182, + 287, + 374 + ], + "type": "text", + "content": ": " + }, + { + "bbox": [ + 46, + 182, + 287, + 374 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{view}}" + }, + { + "bbox": [ + 46, + 182, + 287, + 374 + ], + "type": "text", + "content": " is decoded into the viewpoint " + }, + { + "bbox": [ + 46, + 182, + 287, + 374 + ], + "type": "inline_equation", + "content": "\\mathbf{G}^t \\in SE(3)" + }, + { + "bbox": [ + 46, + 182, + 287, + 374 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 182, + 287, + 374 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{art}}" + }, + { + "bbox": [ + 46, + 182, + 287, + 374 + ], + "type": "text", + "content": " is decoded into articulated joint angles " + }, + { + "bbox": [ + 46, + 182, + 287, + 374 + ], + "type": "inline_equation", + "content": "\\mathbf{B}^t \\in SO(3)^B" + }, + { + "bbox": [ + 46, + 182, + 287, + 374 + ], + "type": "text", + "content": ". We use 6D rotations to represent angles during training [47]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 375, + 287, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 375, + 287, + 461 + ], + "spans": [ + { + "bbox": [ + 46, + 375, + 287, + 461 + ], + "type": "text", + "content": "Viewpoint branch. As the space of possible viewpoints is discontinuous and multi-modal, it is difficult to approach the optimum through iterative gradient descent. Following [6], we use a viewpoint decoder network " + }, + { + "bbox": [ + 46, + 375, + 287, + 461 + ], + "type": "inline_equation", + "content": "\\mathbf{MLP}_{\\mathrm{view}}" + }, + { + "bbox": [ + 46, + 375, + 287, + 461 + ], + "type": "text", + "content": " to decode " + }, + { + "bbox": [ + 46, + 375, + 287, + 461 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{pose}}" + }, + { + "bbox": [ + 46, + 375, + 287, + 461 + ], + "type": "text", + "content": " into a set of " + }, + { + "bbox": [ + 46, + 375, + 287, + 461 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 375, + 287, + 461 + ], + "type": "text", + "content": " viewpoints hypotheses " + }, + { + "bbox": [ + 46, + 375, + 287, + 461 + ], + "type": "inline_equation", + "content": "\\mathbf{G}_{\\{1,\\dots,M\\}}^t" + }, + { + "bbox": [ + 46, + 375, + 287, + 461 + ], + "type": "text", + "content": " weighted by " + }, + { + "bbox": [ + 46, + 375, + 287, + 461 + ], + "type": "inline_equation", + "content": "w_{\\mathbf{G}}^{t}\\in \\mathbb{R}^{M}" + }, + { + "bbox": [ + 46, + 375, + 287, + 461 + ], + "type": "text", + "content": ". Fig. 3 shows the variation over viewpoint hypotheses at an early stage of training." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 462, + 287, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 462, + 287, + 617 + ], + "spans": [ + { + "bbox": [ + 46, + 462, + 287, + 617 + ], + "type": "text", + "content": "Articulation branch. Estimating 3D articulations from monocular images can be difficult due to depth ambiguities and occlusions. To resolve this, recent work on human pose estimation [37] uses a normalizing flow articulation prior represented as an invertible neural network, trained on large-scale human motion capture datasets. Without access to such datasets for other categories, we achieve a similar effect by leveraging the teacher's articulation priors, using the teacher's frozen articulation decoder " + }, + { + "bbox": [ + 46, + 462, + 287, + 617 + ], + "type": "inline_equation", + "content": "\\mathbf{MLP}_{\\mathrm{art}}" + }, + { + "bbox": [ + 46, + 462, + 287, + 617 + ], + "type": "text", + "content": " to decode " + }, + { + "bbox": [ + 46, + 462, + 287, + 617 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{art}}" + }, + { + "bbox": [ + 46, + 462, + 287, + 617 + ], + "type": "text", + "content": ". Fig. 4 visualizes the principal components of " + }, + { + "bbox": [ + 46, + 462, + 287, + 617 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{art}}" + }, + { + "bbox": [ + 46, + 462, + 287, + 617 + ], + "type": "text", + "content": " 's latent space: we find that perturbing " + }, + { + "bbox": [ + 46, + 462, + 287, + 617 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{art}}" + }, + { + "bbox": [ + 46, + 462, + 287, + 617 + ], + "type": "text", + "content": " along its principal components causes the resulting articulated shape to perform natural motions, such as curling up in a ball." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "text", + "content": "Appearance branch. As the object in the video is only partially observable at any given time, we must use data priors or look at nearby frames to output complete appearance predictions " + }, + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{C}^t\\in \\mathbb{R}^{|V|\\times 3}" + }, + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "text", + "content": ", represented as per-vertex colors of the articulated mesh at each frame. Our teacher [44] models global object appearances as a category-level neural field modulated by a texture code " + }, + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{color}}\\in \\mathbb{R}^{64}" + }, + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "text", + "content": ". We leverage these appearance priors by predicting an environment code per" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 306, + 70, + 545, + 232 + ], + "blocks": [ + { + "bbox": [ + 306, + 70, + 545, + 232 + ], + "lines": [ + { + "bbox": [ + 306, + 70, + 545, + 232 + ], + "spans": [ + { + "bbox": [ + 306, + 70, + 545, + 232 + ], + "type": "image", + "image_path": "7ffad52c18e195531c6012e8ec728d1138596e61f14a22d4e045bf4e89582f1b.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 232, + 546, + 309 + ], + "lines": [ + { + "bbox": [ + 305, + 232, + 546, + 309 + ], + "spans": [ + { + "bbox": [ + 305, + 232, + 546, + 309 + ], + "type": "text", + "content": "Figure 3. Viewpoint multiplexing during training. To overcome the discontinuous and multi-modal nature of pose optimization, we train our feed-forward predictor to output a set of " + }, + { + "bbox": [ + 305, + 232, + 546, + 309 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 305, + 232, + 546, + 309 + ], + "type": "text", + "content": " viewpoint hypotheses rather than a single viewpoint. Blending multiple viewpoint hypotheses yields a more accurate prediction (here " + }, + { + "bbox": [ + 305, + 232, + 546, + 309 + ], + "type": "inline_equation", + "content": "M = 5" + }, + { + "bbox": [ + 305, + 232, + 546, + 309 + ], + "type": "text", + "content": "). Top row: Input frames. Second row (white): Blended viewpoint prediction. Bottom rows (light blue): " + }, + { + "bbox": [ + 305, + 232, + 546, + 309 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 305, + 232, + 546, + 309 + ], + "type": "text", + "content": " viewpoint hypotheses" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 311, + 310, + 538, + 480 + ], + "blocks": [ + { + "bbox": [ + 311, + 310, + 538, + 480 + ], + "lines": [ + { + "bbox": [ + 311, + 310, + 538, + 480 + ], + "spans": [ + { + "bbox": [ + 311, + 310, + 538, + 480 + ], + "type": "image", + "image_path": "5319b1470e805c243ad8a66e80a4dc413ca4f3da4773d989e4bb08f5bc213e6d.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 495, + 545, + 605 + ], + "lines": [ + { + "bbox": [ + 304, + 495, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 495, + 545, + 605 + ], + "type": "text", + "content": "Figure 4. Visualizing articulation code. Rather than training our feed-forward predictor to output high-dimensional (75) skeletal articulations, we leverage the teacher's pre-trained articulation space by predicting a low-dimensional (16) code. We visualize the first four principal components of the articulation code learned from the training dataset and find that variations along each axis correspond to interpretable motions: (1) whether the left or right paw is in front, (2) whether the hind paws are retracted or extended, (3) whether the front paws are retracted or extended, and (4) whether the cat has a straightened or curled-up posture." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 616, + 545, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 616, + 545, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 616, + 545, + 640 + ], + "type": "text", + "content": "frame, modulating the teacher's frozen category-level neural field, and querying it at the rest mesh's vertex locations." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": "Temporal encoder. Predicting pose and shape from single images can be highly ambiguous due to motion blur, occlusions, and depth ambiguities. To output temporally consistent results over long videos, we define a temporal encoder that updates " + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{view}}" + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{art}}" + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{color}}" + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": " across many frames. We treat the viewpoint multiplex " + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{view}}" + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": " as a single vector by con" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4695" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "text", + "content": "catenating all " + }, + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "text", + "content": " hypotheses. Following prior work [11], our temporal encoder has several 1D convolutional layers acting on a temporal window centered at time " + }, + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 114, + 179, + 126 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 114, + 179, + 126 + ], + "spans": [ + { + "bbox": [ + 47, + 114, + 179, + 126 + ], + "type": "text", + "content": "3.5. Losses and Supervision" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 127, + 287, + 247 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 127, + 287, + 247 + ], + "spans": [ + { + "bbox": [ + 46, + 127, + 287, + 247 + ], + "type": "text", + "content": "Optimization objective. Treating the teacher's outputs as pseudo-ground truths, our model can be trained in a standard supervised manner. We would like to use the teacher's inferred low-dimensional latent codes as supervisory targets for the student. But rather than defining " + }, + { + "bbox": [ + 46, + 127, + 287, + 247 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_2" + }, + { + "bbox": [ + 46, + 127, + 287, + 247 + ], + "type": "text", + "content": " losses in the latent embedding space, where each dimension of " + }, + { + "bbox": [ + 46, + 127, + 287, + 247 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{view}}" + }, + { + "bbox": [ + 46, + 127, + 287, + 247 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 127, + 287, + 247 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{art}}" + }, + { + "bbox": [ + 46, + 127, + 287, + 247 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 127, + 287, + 247 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{color}}" + }, + { + "bbox": [ + 46, + 127, + 287, + 247 + ], + "type": "text", + "content": " has varying importance, we instead render these codes and compute 3D losses. As all articulated meshes have the same topology, we can define geometry and color losses as per-vertex " + }, + { + "bbox": [ + 46, + 127, + 287, + 247 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_2" + }, + { + "bbox": [ + 46, + 127, + 287, + 247 + ], + "type": "text", + "content": " error:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 67, + 251, + 268, + 273 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 251, + 268, + 273 + ], + "spans": [ + { + "bbox": [ + 67, + 251, + 268, + 273 + ], + "type": "interline_equation", + "content": "L _ {\\mathrm {g e o m}} = \\left\\| \\mathbf {X} ^ {t} - \\widehat {\\mathbf {X}} ^ {t} \\right\\| _ {2} \\quad L _ {\\mathrm {c o l o r}} = \\left\\| \\mathbf {C} ^ {t} - \\widehat {\\mathbf {C}} ^ {t} \\right\\| _ {2}", + "image_path": "770ab174d7cde0f6eaf2d734d8e50f645d4af203ed30ca39bc1abc323d1af83e.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 276, + 287, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 276, + 287, + 335 + ], + "spans": [ + { + "bbox": [ + 46, + 276, + 287, + 335 + ], + "type": "text", + "content": "To improve articulation learning and account for multiple possible inverse kinematics solutions while solving for joint articulations, we add a joint loss defined as geodesic distance between predicted and actual joint angles at each joint. We find that this improves deformation quality." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 336, + 287, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 336, + 287, + 360 + ], + "spans": [ + { + "bbox": [ + 46, + 336, + 287, + 360 + ], + "type": "text", + "content": "In summary, we train the image encoder and temporal encoder with the following objective:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 110, + 365, + 223, + 379 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 365, + 223, + 379 + ], + "spans": [ + { + "bbox": [ + 110, + 365, + 223, + 379 + ], + "type": "interline_equation", + "content": "L = L _ {\\text {g e o m}} + L _ {\\text {j o i n t}} + L _ {\\text {c o l o r}}", + "image_path": "951f4d8358fa3f4b30391648c81011e47e362347de107778d70d3658a9fd70ee.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 388, + 128, + 401 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 388, + 128, + 401 + ], + "spans": [ + { + "bbox": [ + 47, + 388, + 128, + 401 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 403, + 287, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 403, + 287, + 557 + ], + "spans": [ + { + "bbox": [ + 46, + 403, + 287, + 557 + ], + "type": "text", + "content": "Although we could have distilled a student using any dynamic NeRF as the teacher, our implementation uses BANMo [44] because it has public code, accepts unannotated monocular videos as input, and produces good results on humans and quadropeds. We modified BANMo to replace the bag-of-bones deformation model with a skeleton. Hyperparameters. Our method is implemented in PyTorch. We use the AdamW optimizer and train the model for 16k iterations, taking around 4 hours on a single RTX-3090 GPU. We use " + }, + { + "bbox": [ + 46, + 403, + 287, + 557 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 46, + 403, + 287, + 557 + ], + "type": "text", + "content": " images with batch size 56. We use 8 stacked hourglass blocks in the image encoder and a window size of 13 frames in the temporal encoder. All losses are weighted to have similar initial magnitudes." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "type": "text", + "content": "Staged training. We adopt a two-stage training strategy at every epoch to reduce the computational costs of evaluating an image encoder at every frame, when only a single frame per time window will receive a gradient update. In the first stage, we send frames through the image encoder and compute per-frame losses without using the temporal encoder, storing per-frame values of " + }, + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{pose}}" + }, + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{art}}" + }, + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{color}}" + }, + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "type": "text", + "content": ". In the second stage, we send time windows of cached features through the temporal encoder without using the image encoder. Two-staged training reduces redundant image encoder evaluations and ensures that the temporal encoder can be safely removed if we only have access to single images rather than time windows of frames at test time." + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 307, + 145, + 550, + 206 + ], + "blocks": [ + { + "bbox": [ + 304, + 70, + 545, + 137 + ], + "lines": [ + { + "bbox": [ + 304, + 70, + 545, + 137 + ], + "spans": [ + { + "bbox": [ + 304, + 70, + 545, + 137 + ], + "type": "text", + "content": "Table 1. Datasets. All videos are treated as casually collected monocular RGB videos, except when additional groundtruth meshes or depth maps are needed for evaluation. Processing time includes computing segmentations and per-pixel features with off-the-shelf networks, as well as computing pseudo-ground truth 3D outputs with the teacher." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 145, + 550, + 206 + ], + "lines": [ + { + "bbox": [ + 307, + 145, + 550, + 206 + ], + "spans": [ + { + "bbox": [ + 307, + 145, + 550, + 206 + ], + "type": "table", + "html": "
Total VideosTotal InstancesTotal FramesTest InstancesTest FramesProcessing Time (hr)
Humans48286.4k101.6k22.0
Cats775611.7k132.7k23.2
Dogs88789.7k171.7k23.8
", + "image_path": "6db580876c0f859ef1b9004ed2581be599ad47cce0f1227ddfa339e5cdf01107.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 217, + 369, + 228 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 217, + 369, + 228 + ], + "spans": [ + { + "bbox": [ + 306, + 217, + 369, + 228 + ], + "type": "text", + "content": "4.1. Datasets" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 232, + 545, + 351 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 232, + 545, + 351 + ], + "spans": [ + { + "bbox": [ + 304, + 232, + 545, + 351 + ], + "type": "text", + "content": "We collect datasets for three categories: humans, cats, and dogs. For humans, we combine datasets from AMA [35], MonoPerfCap [41], DAVIS [29], and BANMo [44] to obtain 48 human videos. We evaluate on AMA and MonoPerfCap as they have ground-truth meshes. For cats and dogs, we collect 77 cat videos and 88 dog videos from the Pixels stock video website as well as BANMo released data. We also used an iPad Pro to capture two RGB-D videos to evaluate depth accuracy on cats and dogs. Video frames are extracted at 10fps. Datasets are summarized in Tab. 1." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 353, + 545, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 353, + 545, + 472 + ], + "spans": [ + { + "bbox": [ + 304, + 353, + 545, + 472 + ], + "type": "text", + "content": "To compute BANMo pseudo-ground-truths per category without optimizing dozens of independent BANMo models, we optimize a single BANMo model per category, using articulation and texture codes to model shape and appearance differences across instances. As a result, the total dataset processing time is about 24 hours per category on 8 RTX-3090 GPUs. We find that BANMo generalizes quite well from the instance-level to the category-level setting [45], and that the articulation and texture latent spaces cover the range of motions and textures across all instances." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 483, + 443, + 495 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 483, + 443, + 495 + ], + "spans": [ + { + "bbox": [ + 305, + 483, + 443, + 495 + ], + "type": "text", + "content": "4.2. Reconstructing Humans" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 497, + 545, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 497, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 497, + 545, + 605 + ], + "type": "text", + "content": "Dataset. Following BANMo, we evaluate human reconstruction on the AMA [35] dataset, containing 10 real-world mesh sequences depicting 3 different humans. The subjects wear loose clothing and perform challenging actions such as dancing and performing a handstand. Although the AMA videos were captured in an 8-camera studio to enable ground-truth mesh extraction, we treat them as casually collected monocular videos and do not use the camera intrinsics, camera extrinsic, or time synchronization." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "Comparisons. We compare against template-free BANMo [44], as well as model-based methods HuMoR [31] and ICON [40]. BANMo fits an animatable 3D model to multiple monocular videos of an object instance by performing differentiable rendering optimization. We train BANMo on the same dataset as our model. HuMoR is a human-specific temporal pose and shape predictor that performs test-time optimization on video sequences, leveraging OpenPose keypoint detection and motion priors learned" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "4696" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 60, + 64, + 126, + 288 + ], + "blocks": [ + { + "bbox": [ + 60, + 64, + 126, + 288 + ], + "lines": [ + { + "bbox": [ + 60, + 64, + 126, + 288 + ], + "spans": [ + { + "bbox": [ + 60, + 64, + 126, + 288 + ], + "type": "image", + "image_path": "de319ab15924845971c13213ed9b50646c686ac4d93baa317a78a7b021e3870b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 300, + 547, + 346 + ], + "lines": [ + { + "bbox": [ + 46, + 300, + 547, + 346 + ], + "spans": [ + { + "bbox": [ + 46, + 300, + 547, + 346 + ], + "type": "text", + "content": "Figure 5. Qualitative results on humans (left), cats (middle), and dogs (right) in the test set. From left to right for each category, we show the input images, articulated shape and texture predictions overlaid on the input images, and three different viewpoints of the predicted geometry. Our method operates on casual monocular videos and predicts plausible shape, articulations, and textures in real-time. Our predictions align well with the image evidence on challenging inputs." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 127, + 64, + 216, + 281 + ], + "blocks": [ + { + "bbox": [ + 127, + 64, + 216, + 281 + ], + "lines": [ + { + "bbox": [ + 127, + 64, + 216, + 281 + ], + "spans": [ + { + "bbox": [ + 127, + 64, + 216, + 281 + ], + "type": "image", + "image_path": "b0da028f4f2b813d0d4307bbb025b5736903f67f0a918d3d721a27b3d996d142.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 217, + 64, + 283, + 287 + ], + "blocks": [ + { + "bbox": [ + 217, + 64, + 283, + 287 + ], + "lines": [ + { + "bbox": [ + 217, + 64, + 283, + 287 + ], + "spans": [ + { + "bbox": [ + 217, + 64, + 283, + 287 + ], + "type": "image", + "image_path": "b066a9c299a639213fda32706134dfac55bcc65fabc911d9e3ec9e5ffc156336.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 284, + 64, + 373, + 281 + ], + "blocks": [ + { + "bbox": [ + 284, + 64, + 373, + 281 + ], + "lines": [ + { + "bbox": [ + 284, + 64, + 373, + 281 + ], + "spans": [ + { + "bbox": [ + 284, + 64, + 373, + 281 + ], + "type": "image", + "image_path": "5e9549b31b812e668cc1790c3b3d3e8bf43301c5e36dc4100b4baae707b5ba43.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 373, + 64, + 439, + 287 + ], + "blocks": [ + { + "bbox": [ + 373, + 64, + 439, + 287 + ], + "lines": [ + { + "bbox": [ + 373, + 64, + 439, + 287 + ], + "spans": [ + { + "bbox": [ + 373, + 64, + 439, + 287 + ], + "type": "image", + "image_path": "075ad9ae709ba73c836a44a22668e7ac2cf4ece0643164784dc8d07df26d0703.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 438, + 64, + 533, + 281 + ], + "blocks": [ + { + "bbox": [ + 438, + 64, + 533, + 281 + ], + "lines": [ + { + "bbox": [ + 438, + 64, + 533, + 281 + ], + "spans": [ + { + "bbox": [ + 438, + 64, + 533, + 281 + ], + "type": "image", + "image_path": "17e0ce9abcf93e46b3a00ea95828ab481ae7bbdf035cf6d2b1f79053e729e5d6.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 356, + 288, + 440 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 356, + 288, + 440 + ], + "spans": [ + { + "bbox": [ + 46, + 356, + 288, + 440 + ], + "type": "text", + "content": "from large-scale human motion capture datasets. ICON is the current SOTA for single-view human reconstruction, and it combines implicit functions with the SMPL human body model, using test-time optimization to fit surface normal predictions and improve pose accuracy and reconstruction quality. All our baselines require far more processing time than our model, which runs in real-time." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 445, + 287, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 445, + 287, + 589 + ], + "spans": [ + { + "bbox": [ + 46, + 445, + 287, + 589 + ], + "type": "text", + "content": "Metrics. We report 3D chamfer distance and F-scores on three held-out test sequences in Tab. 2, averaged across all frames. Chamfer distance is the average distance between the ground-truth and predicted mesh vertices using nearest neighbor matches. As this can be sensitive to outliers, we also evaluate F-score at distance thresholds " + }, + { + "bbox": [ + 46, + 445, + 287, + 589 + ], + "type": "inline_equation", + "content": "d \\in \\{1\\%, 2\\%, 5\\% \\}" + }, + { + "bbox": [ + 46, + 445, + 287, + 589 + ], + "type": "text", + "content": " to better quantify reconstruction error at different granularities. We scale predicted meshes by their view-space bounding box height to account for unknown scale compared to registered ground-truths. Our model approaches the performance of BANMo and baselines, while requiring nearly 1000x less compute at test time." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "content": "Qualitative Results. We show qualitative comparisons for upright and inverted humans in Fig. 7. HuMoR outputs a deformed SMPL model, while ICON and BANMo optimize for both shape and articulation. Although our method outputs reasonable articulations for the upright pose, the woman lacks fine-grained geometry details and the viewpoint on the handstand video is inaccurate. We hypothesize that these failures occur due to the entanglement between articulations and per-instance morphologies, and the lack of handstand examples in the training set." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 356, + 470, + 369 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 356, + 470, + 369 + ], + "spans": [ + { + "bbox": [ + 305, + 356, + 470, + 369 + ], + "type": "text", + "content": "4.3. Reconstructing Cats and Dogs" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 369, + 545, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 369, + 545, + 501 + ], + "spans": [ + { + "bbox": [ + 304, + 369, + 545, + 501 + ], + "type": "text", + "content": "Dataset. We evaluate cat and dog reconstruction on two RGB-D pet videos, as well as a held-out test set of pet videos from BANMo's dataset. These videos contain challenging motions such as rapid turns and jumping off chairs. Comparisons. We compare against BANMo [44] and BARC [32], a model-based approach and the current SOTA for dog shape and pose estimation from images. BARC trains a feed-forward network using images with keypoint labels and synthetic SMAL dog models [4], leveraging breed losses as additional supervision. As BARC is image-based, we run it separately on each video frame." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 501, + 545, + 573 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 501, + 545, + 573 + ], + "spans": [ + { + "bbox": [ + 304, + 501, + 545, + 573 + ], + "type": "text", + "content": "Metrics We report the root mean square depth error and depth accuracy for all foreground pixels in Tab. 3, averaged across all frames. We render a synthetic depth map per frame, and following [19], we account for the unknown global scale factor between depth maps by aligning the median rendered and ground-truth depths at each frame:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 353, + 578, + 498, + 601 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 353, + 578, + 498, + 601 + ], + "spans": [ + { + "bbox": [ + 353, + 578, + 498, + 601 + ], + "type": "interline_equation", + "content": "s _ {i} = \\operatorname * {m e d i a n} _ {x} \\left\\{D _ {i} ^ {p r e d} (x) / D ^ {g t} (x) \\right\\}", + "image_path": "91520d8c10f8e728f62d948feaf14ce7a10f2a2967c6d29b17db2f3a63ebb337.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 605, + 545, + 630 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 630 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 630 + ], + "type": "text", + "content": "Depth accuracy is computed as the proportion of foreground pixels whose synthetic depth is within a given threshold." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "Qualitative Results We show qualitative results comparing to BARC in Fig. 6. BARC performs well at predicting coarse shape and deformations, and more faithfully captures the fine motion and geometry details of the dog when it is positioned well in frame. However, as BARC entangles shape and breed, we find that BARC may predict biased shapes for certain breeds. 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Qualitative comparisons on pet sequences. From left to right in each column, we show (left) the input image, (middle-left) BARC's prediction, (middle-right) our articulated shape and texture predictions, and (right) our geometry predictions. Our method operates on videos and predicts plausible shape, articulations, and texture in real time. BARC operates on each video frame independently, resulting in jittery predictions when the pet is small or not clearly visible (top row). While BARC's geometry and motion predictions are largely accurate, they can be biased for certain breeds (bottom left), predicting an arched back for a flat-backed dog." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 235, + 171, + 358, + 278 + ], + "blocks": [ + { + "bbox": [ + 235, + 171, + 358, + 278 + ], + "lines": [ + { + "bbox": [ + 235, + 171, + 358, + 278 + ], + "spans": [ + { + "bbox": [ + 235, + 171, + 358, + 278 + ], + "type": "image", + "image_path": "e72a24506d3f772cb787ba7d1ff73214baa04b6dbd34e5dff8bb38e91e7f81ff.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 373, + 171, + 479, + 277 + ], + "blocks": [ + { + "bbox": [ + 373, + 171, + 479, + 277 + ], + "lines": [ + { + "bbox": [ + 373, + 171, + 479, + 277 + ], + "spans": [ + { + "bbox": [ + 373, + 171, + 479, + 277 + ], + "type": "image", + "image_path": "3b74cc276034cd958caad99e1635a72ffb2ecee4214eac45af94b9d39dd5d54f.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 487, + 181, + 501, + 277 + ], + "blocks": [ + { + "bbox": [ + 487, + 181, + 501, + 277 + ], + "lines": [ + { + "bbox": [ + 487, + 181, + 501, + 277 + ], + "spans": [ + { + "bbox": [ + 487, + 181, + 501, + 277 + ], + "type": "image", + "image_path": "449ac868039cad4f91f9469b0b311781137e64ab80ce4a50ae64ece466280321.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "type": "table", + "bbox": [ + 52, + 437, + 541, + 663 + ], + "blocks": [ + { + "bbox": [ + 45, + 352, + 545, + 429 + ], + "lines": [ + { + "bbox": [ + 45, + 352, + 545, + 429 + ], + "spans": [ + { + "bbox": [ + 45, + 352, + 545, + 429 + ], + "type": "text", + "content": "Table 2. Quantitative results on AMA sequences. 3D chamfer distance (cm, ↓) and F-score (%, ↑) for articulated meshes, averaged over all frames. T_samba is a held-out video of a person that was seen during training, while the D_bouncing and D_handstand sequences contain a previously unseen person. Our model approaches the performance of BANMo and baselines while requiring nearly three orders of magnitude less compute at test time. Notably, our method performs better on T_samba, as it has fewer challenging poses and contains a person previously seen during training. Other baselines are trained on 3D human data, rely on the SMPL body model, or use expensive test-time optimization to improve results. We also report the inference time (ms) per frame. Results marked by * are different runs with the same hyperparameters. The best results are in bold. Please refer to Sec. 4.4 for discussions on the ablation results." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 52, + 437, + 541, + 663 + ], + "lines": [ + { + "bbox": [ + 52, + 437, + 541, + 663 + ], + "spans": [ + { + "bbox": [ + 52, + 437, + 541, + 663 + ], + "type": "table", + "html": "
MethodTimeT_sambaD_bouncingD_handstand
CDF@1%F@2%F@5%CDF@1%F@2%F@5%CDF@1%F@2%F@5%
HuMoR420009.823.347.483.611.421.146.183.221.913.528.858.5
ICON6300010.118.939.985.29.727.853.586.414.123.545.275.6
BANMo4300010.325.348.883.611.626.750.881.514.222.544.174.7
Ours*2210.625.849.684.112.023.446.179.917.317.935.967.2
No temporal encoder2012.223.144.778.912.922.745.077.516.917.935.868.2
Conv1D encoder*2210.826.049.282.712.123.846.779.915.024.945.473.1
Transformer encoder2710.626.350.083.213.222.344.076.516.818.737.168.2
w/o frozen decoders2111.024.648.081.611.525.649.881.417.922.341.870.4
\\( 64^3 \\) template grid1012.021.042.279.112.722.945.278.015.622.543.671.8
\\( 128^3 \\) template grid*2210.525.649.884.412.423.646.078.713.724.346.575.6
\\( 256^3 \\) template grid2810.427.150.783.912.523.646.478.715.719.238.571.1
5 train videos2211.222.444.381.013.720.841.675.317.117.535.367.1
16 train videos2210.524.346.983.613.321.743.076.615.821.640.770.6
26 train videos2210.228.051.684.313.222.043.676.817.717.835.667.2
35 train videos*2210.824.047.483.612.323.346.379.016.819.038.069.2
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BANMo54s0.041128.645.372.70.075727.747.476.5
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Qualitative comparisons on human sequences. From left to right, we show the output of HuMoR [31], ICON [40], BANMo [44], and our method on dancing (top) and handstand (bottom) sequences. Our method outputs plausible articulations for the dancing sequence, although the shape lacks fine details. In comparison, HuMoR outputs the SMPL template human shape, while ICON and BANMo output more detailed shapes. All methods perform poorly on the highly challenging handstand pose: HuMoR outputs unrealistic and self-intersecting articulations, ICON's prediction appears bumpy and twisted in an unnatural way, BANMo's prediction is also twisted and misses the head, and our method outputs incorrect viewpoint and arm articulations." + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "type": "image", + "bbox": [ + 229, + 256, + 258, + 304 + ], + "blocks": [ + { + "bbox": [ + 229, + 256, + 258, + 304 + ], + "lines": [ + { + "bbox": [ + 229, + 256, + 258, + 304 + ], + "spans": [ + { + "bbox": [ + 229, + 256, + 258, + 304 + ], + "type": "image", + "image_path": "44cc8c17ac2d7a543adbeda0a46f8a42905146400271e4e04f7f86df307440de.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 236, + 311, + 250, + 319 + ], + "lines": [ + { + "bbox": [ + 236, + 311, + 250, + 319 + ], + "spans": [ + { + "bbox": [ + 236, + 311, + 250, + 319 + ], + "type": "text", + "content": "Ours" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + } + ], + "index": 20 + }, + { + "bbox": [ + 46, + 465, + 287, + 538 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 465, + 287, + 538 + ], + "spans": [ + { + "bbox": [ + 46, + 465, + 287, + 538 + ], + "type": "text", + "content": "ing because the dog is standing on its hind legs, both our method and BARC fail to show that the dog is lifting its front paws. As our method does not disentangle articulation and morphology variation between breeds, incorporating breed and/or instance information would likely improve our ability to represent fine motion and geometry details." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 47, + 544, + 115, + 555 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 544, + 115, + 555 + ], + "spans": [ + { + "bbox": [ + 47, + 544, + 115, + 555 + ], + "type": "text", + "content": "4.4. Ablations" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 46, + 558, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 287, + 677 + ], + "type": "text", + "content": "We performed an ablation study on several architectural details including the choice of temporal encoder, the use of frozen decoders from the teacher, the template grid resolution, and the number of training videos. Most notably, we find that increasing the density of mesh points by running marching cubes at a finer resolution (from " + }, + { + "bbox": [ + 46, + 558, + 287, + 677 + ], + "type": "inline_equation", + "content": "64^{3}" + }, + { + "bbox": [ + 46, + 558, + 287, + 677 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 558, + 287, + 677 + ], + "type": "inline_equation", + "content": "128^{3}" + }, + { + "bbox": [ + 46, + 558, + 287, + 677 + ], + "type": "text", + "content": " improves the F@1% and F@2% accuracy of our student, as well as using a temporal encoder. Changing the marching cubes resolution involves no change to the student, but simply a more faithful post-processing of the teacher's output." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 46, + 677, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 714 + ], + "type": "text", + "content": "Effect of temporal encoder. The student model performs better with a temporal encoder across all sequences, perhaps by providing additional temporal context to help smooth the" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 186, + 545, + 233 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 186, + 545, + 233 + ], + "spans": [ + { + "bbox": [ + 304, + 186, + 545, + 233 + ], + "type": "text", + "content": "predictions. In general, the Conv1D encoder seems to outperform the transformer encoder in both speed and accuracy, although this could be caused by the increased difficulty of training a transformer encoder." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 304, + 233, + 545, + 269 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 233, + 545, + 269 + ], + "spans": [ + { + "bbox": [ + 304, + 233, + 545, + 269 + ], + "type": "text", + "content": "Effect of frozen decoders. We find that the student model's performance generally drops without using the teacher's frozen articulation decoder to regularize pose predictions." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 304, + 270, + 545, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 270, + 545, + 376 + ], + "spans": [ + { + "bbox": [ + 304, + 270, + 545, + 376 + ], + "type": "text", + "content": "Effect of template shape resolution. When extracting the template shape with a " + }, + { + "bbox": [ + 304, + 270, + 545, + 376 + ], + "type": "inline_equation", + "content": "64^{3}" + }, + { + "bbox": [ + 304, + 270, + 545, + 376 + ], + "type": "text", + "content": " grid, our model's F@1%, F@2%, and F@5% accuracy all seem to drop. Qualitatively, the " + }, + { + "bbox": [ + 304, + 270, + 545, + 376 + ], + "type": "inline_equation", + "content": "64^{3}" + }, + { + "bbox": [ + 304, + 270, + 545, + 376 + ], + "type": "text", + "content": " template shape is less detailed and appears fuzzy compared to " + }, + { + "bbox": [ + 304, + 270, + 545, + 376 + ], + "type": "inline_equation", + "content": "128^{3}" + }, + { + "bbox": [ + 304, + 270, + 545, + 376 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 304, + 270, + 545, + 376 + ], + "type": "inline_equation", + "content": "256^{3}" + }, + { + "bbox": [ + 304, + 270, + 545, + 376 + ], + "type": "text", + "content": ", though the predicted articulations are similar. There seems to be little difference between " + }, + { + "bbox": [ + 304, + 270, + 545, + 376 + ], + "type": "inline_equation", + "content": "128^{3}" + }, + { + "bbox": [ + 304, + 270, + 545, + 376 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 270, + 545, + 376 + ], + "type": "inline_equation", + "content": "256^{3}" + }, + { + "bbox": [ + 304, + 270, + 545, + 376 + ], + "type": "text", + "content": ", and the observed results could be up to noise. As more points need to be warped to the deformed space, more detailed templates have slower inference speed." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 304, + 377, + 545, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 377, + 545, + 460 + ], + "spans": [ + { + "bbox": [ + 304, + 377, + 545, + 460 + ], + "type": "text", + "content": "Effect of dataset size. We find that performance generally deteriorates with less data, although the trend is not as clear. Here, each smaller set of training videos is a subset of the immediately larger video set: as all videos containing the T_samba identity are within the set of 26 videos, increasing the dataset size from 26 to 35 involved adding videos of unrelated identities which seemed to hurt performance." + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 306, + 471, + 375, + 483 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 471, + 375, + 483 + ], + "spans": [ + { + "bbox": [ + 306, + 471, + 375, + 483 + ], + "type": "text", + "content": "5. Discussion" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 304, + 486, + 545, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 545, + 605 + ], + "type": "text", + "content": "We present a method to train category-specific feedforward video shape predictors by distilling knowledge from dynamic NeRF teachers fitted to offline video data at scale. Our temporal architecture predicts consistent viewpoint, articulation, and appearance, producing real-time video reconstruction results on humans, cats, and dogs with the ability to support other categories as well. We qualitatively outperform existing feed-forward predictors for dog shape and pose, and approach the quality of test-time fitting methods while using nearly 1000x less computation." + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "Limitations: As our method is trained on the pseudoground truth outputs of a teacher model, we are upper-bounded by the teacher's performance and reconstruction fidelity. We expect the performance of our method to improve given larger-scale, more diverse, and higher-quality video data. Compared with optimization-based methods, our method is hundreds of times faster but produces results less faithful to the inputs: we leave incorporating optimization into the feed-forward architecture as future work." + } + ] + } + ], + "index": 33 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4699" + } + ] + } + ], + "index": 34 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 286, + 712 + ], + "type": "list", + "angle": 0, + "index": 18, + "blocks": [ + { + "bbox": [ + 53, + 91, + 286, + 124 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 286, + 124 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 286, + 124 + ], + "type": "text", + "content": "[1] Sameer Agarwal, Yasutaka Furukawa, Noah Snavely, Ian Simon, Brian Curless, Steven M. 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CVPR, 2017. 2" + } + ] + } + ], + "index": 15 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 314, + 757 + ], + "type": "text", + "content": "4701" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Distilling Self-Supervised Vision Transformers for Weakly-Supervised Few-Shot Classification & Segmentation/e6a6b9de-f70e-4a6b-bd84-70683a76add4_content_list.json b/2023/Distilling Self-Supervised Vision Transformers for Weakly-Supervised Few-Shot Classification & Segmentation/e6a6b9de-f70e-4a6b-bd84-70683a76add4_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..167346cb5173ee5a6ead9166cd60c5c91065dc10 --- /dev/null +++ b/2023/Distilling Self-Supervised Vision Transformers for Weakly-Supervised Few-Shot Classification & Segmentation/e6a6b9de-f70e-4a6b-bd84-70683a76add4_content_list.json @@ -0,0 +1,1583 @@ +[ + { + "type": "text", + "text": "Distilling Self-Supervised Vision Transformers for Weakly-Supervised Few-Shot Classification & Segmentation", + "text_level": 1, + "bbox": [ + 161, + 130, + 805, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Dahyun Kang $^{1,2*}$ Piotr Koniusz $^{3,4}$ Minsu Cho $^{2}$ Naila Murray $^{1}$ $^{1}$ Meta AI $^{2}$ POSTECH $^{3}$ Data61♥CSIRO $^{4}$ Australian National University", + "bbox": [ + 173, + 202, + 795, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 273, + 312, + 289 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We address the task of weakly-supervised few-shot image classification and segmentation, by leveraging a Vision Transformer (ViT) pretrained with self-supervision. Our proposed method takes token representations from the self-supervised ViT and leverages their correlations, via self-attention, to produce classification and segmentation predictions through separate task heads. Our model is able to effectively learn to perform classification and segmentation in the absence of pixel-level labels during training, using only image-level labels. To do this it uses attention maps, created from tokens generated by the self-supervised ViT backbone, as pixel-level pseudo-labels. We also explore a practical setup with \"mixed\" supervision, where a small number of training images contains ground-truth pixel-level labels and the remaining images have only image-level labels. For this mixed setup, we propose to improve the pseudo-labels using a pseudo-label enhancer that was trained using the available ground-truth pixel-level labels. Experiments on Pascal-5 $^i$ and COCO-20 $^i$ demonstrate significant performance gains in a variety of supervision settings, and in particular when little-to-no pixel-level labels are available.", + "bbox": [ + 75, + 305, + 473, + 638 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 667, + 207, + 684 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Few-shot learning [22, 23, 77] is the problem of learning to perform a prediction task using only a small number of examples (i.e. supports) of the completed task, typically in the range of 1-10 examples. This problem setting is appealing for applications where large amounts of annotated data are expensive or impractical to collect. In computer vision, few-shot learning has been actively studied for image classification [24, 36, 46, 66, 70, 85] and semantic segmentation [17, 58, 61, 88, 89]. In this work, we focus on the combined task of few-shot classification and segmentation (FS-CS) [33], which aims to jointly predict (i) the presence of each support class, i.e., multi-label classification, and (ii)", + "bbox": [ + 75, + 694, + 468, + 876 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/bb27f4b8af88c0dce2e78ee4f1ca87b9d4d4a73f8ea0197be7c202e00db80057.jpg", + "image_caption": [ + "Figure 1. Weakly-supervised few-shot classification and segmentation. In this paper, we explore training few-shot models using little-to-no ground-truth segmentation masks." + ], + "image_footnote": [], + "bbox": [ + 504, + 272, + 890, + 484 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "its pixel-level semantic segmentation.", + "bbox": [ + 500, + 547, + 750, + 563 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Few-shot learners are typically trained either by meta-learning [24, 56, 63, 71] or by transfer learning with fine-tuning [11, 12, 16]. Both these paradigms commonly assume the availability of a large-scale and fully-annotated training dataset. For FS-CS, we need Ground-Truth (GT) segmentation masks for query and support images during training. We also need these GT masks for support images during testing. A natural alternative to collecting such expensive segmentation masks would be to instead employ a weaker supervision, e.g. image-level [52, 59] or box-level labels [13, 30], for learning, i.e., to adopt a weakly-supervised learning approach [5, 41, 43, 51]. Compared to conventional weakly-supervised learning however, weakly-supervised few-shot learning has rarely been explored in the literature and is significantly more challenging. This is because in few-shot learning, object classes are completely disjoint between training and testing, resulting in models which are susceptible to severe over-fitting to the classes seen during training.", + "bbox": [ + 496, + 565, + 892, + 852 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this work we tackle this challenging scenario, addressing weakly-supervised FS-CS where only image-level labels, i.e. class labels, are available (cf. Fig. 1). Inspired by", + "bbox": [ + 498, + 854, + 890, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Work done during an internship at FAIR.", + "bbox": [ + 94, + 886, + 318, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "19627", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "recent work by Caron et al. [9], which showed that pixel-level semantic attention emerges from self-supervised vision transformers (ViTs) [18], we leverage attention maps from a frozen self-supervised ViT to generate pseudo-GT segmentation masks. We train an FS-CS learner on top of the frozen ViT using the generated pseudo-GT masks as pixel-level supervision. The FS-CS learner is a small transformer network that takes features from the ViT as input and is trained to predict the pseudo-GT masks. Our complete model thus learns to segment using its own intermediate byproduct, with no segmentation labeling cost, in a form of distillation [2, 28, 91, 94] between layers within a model.", + "bbox": [ + 75, + 90, + 472, + 272 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We also explore a practical training setting where a limited number of training images have both image-level and pixel-level annotations, while the remaining images have only image-level labels. For this mixed-supervised setting, we propose to train an auxiliary mask enhancer that refines attention maps into pseudo-GT masks. The enhancer is supervised using the small number of available GT masks and is used to generate the final pseudo-GT masks for the training images that do not have GT masks.", + "bbox": [ + 75, + 273, + 472, + 411 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Lastly, to effectively address this weakly-supervised FS-CS task, we propose a Classification-Segmentation Transformer (CST) architecture. CST takes as input ViT tokens for query and support images, computes correlations between them, and then predicts classification and segmentation outputs through separate task heads; the classification head is trained with class labels while the segmentation head is trained with either GT masks or pseudo-GT masks, depending on availability. Unlike prior work using ViTs that generate prediction for a single task using either the class token [18, 74] or image tokens [50, 65], CST uses each of them for each task prediction, which proves advantageous for both tasks. CST achieves moderate-to-large performance gains for FS-CS on all three supervision levels (image-level-, mixed-level, and pixel-level), when compared to prior state-of-the-art methods.", + "bbox": [ + 75, + 411, + 472, + 654 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions are the following:", + "bbox": [ + 96, + 655, + 336, + 670 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "i. We introduce a powerful baseline for few-shot classification and segmentation (FS-CS) using only image-level supervision, which leverages localized semantic information encoded in self-supervised ViTs [9].", + "ii. We propose a learning setup for FS-CS with mixed supervision, and present an auxiliary mask enhancer to improve performance compared to image-level supervision only.", + "iii. We design Classification-Segmentation Transformer, and a multi-task learning objective of classification and segmentation, which is beneficial for both tasks, and allows for flexibly tuning the degree of supervision." + ], + "bbox": [ + 78, + 685, + 468, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 500, + 89, + 637, + 106 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Few-shot classification and segmentation. This paper tackles the recently proposed task of few-shot classification and segmentation (FS-CS) [33], which generalizes and combines the conventional few-shot classification (FS-C) [11, 24, 34, 63, 70] and few-shot segmentation (FS-S) [58, 71, 89] tasks. FS-C assumes that a query contains only one of the support classes, while FS-S assumes that the query always contains all of them. In contrast, FS-CS breaks the assumption that a query image contains one class (or all classes) from the support set. As a result, FS-CS models must predict i) the presence or absence of each support class in the query; and ii) pixel-level segmentation masks. Our work explores a more challenging weakly-supervised version of FS-CS with image-level annotations but few or no pixel-level annotations. Prior work on weakly-supervised FS-S used supervision such as language [40, 60] or bounding boxes [55]. Our work does not adopt any extra modalities and uses weaker (image-level) supervision than bounding boxes. Other applications of few-shot learning include few-shot object detection [92, 93], action recognition [72, 73], and metric learning [32].", + "bbox": [ + 496, + 116, + 893, + 435 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Weakly-supervised segmentation. A common paradigm for weakly-supervised semantic segmentation uses class labels [1,39] to generate pseudo-GT masks from class activation maps (CAM) [57, 95], followed by pseudo-supervised training [37, 96, 99]. CAM requires a classification backbone pre-trained from many examples on seen classes whereas, in our few-shot setting, we devise a pseudo-GT mask generation method that requires only a small number of examples, and can handle unseen classes. We also investigate the extent to which a pseudo-mask enhancement module, trained using a small amount of GT masks, can generate better pseudo-GT masks. While such \"mixed-supervision\" learning has been called semi-weakly-supervised segmentation [4, 38, 42, 75] and studied in the standard seen-class many-shot learning paradigm, our work is the first to propose mixed-supervision learning for few-shot semantic segmentation, to the best of our knowledge.", + "bbox": [ + 496, + 440, + 893, + 698 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Self-supervised learning. Self-supervised learning [31] has proven highly effective for learning powerful representations for downstream tasks [7-10, 80, 97]. One popular approach [9, 25] trains a model to map an image and its augmented views to nearby coordinates in a representation space. This class-agnostic objective trains the model to capture view-invariant semantics that transcend designated image categories. In addition, DINO-trained ViTs [9] capture localized semantics in the learned token representations. In this work, we leverage these representations to create attention map-based pseudo-GT masks for weakly-supervised FS-CS, using a novel and efficient self-distillation approach. The representations have also ben", + "bbox": [ + 496, + 703, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "19628", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/5240162eddae44e78dff6e8d41d2a3b9fba4959e3c7407fc9ca2492daba83c9d.jpg", + "image_caption": [ + "Figure 2. Classification-Segmentation Transformer. A query and a support image pass through a frozen DINO ViT to extract class and images tokens, which are cross-correlated to form correlation tokens. The correlation tokens are then fed to a correlation transformer and transform to task tokens. At the end, each classification and segmentation head takes each task token map and predicts each task." + ], + "image_footnote": [], + "bbox": [ + 78, + 90, + 893, + 345 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "efited several other dense prediction tasks, including unsupervised object discovery [62, 76] and unsupervised image/video segmentation [9, 86, 87, 98].", + "bbox": [ + 75, + 410, + 470, + 455 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Weakly-supervised few-shot classification and segmentation", + "text_level": 1, + "bbox": [ + 76, + 472, + 468, + 506 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this paper we tackle few-shot classification and segmentation (FS-CS) [33]. Given a small number $K$ of labeled support images for each of $N$ classes, an FS-CS model is trained to i) identify the presence of each class in a query image and ii) segment the associated pixels. This setting is conventionally called an $N$ -way $K$ -shot episode [53, 70]. We adopt a meta-learning approach [29, 63, 70] to train our model, where an annotated training dataset (with a class set disjoint from the test set classes) is used to generate a sequence of $N$ -way $K$ -shot episodes. In our setting, annotations consist of class labels and segmentation masks. When ground-truth segmentation masks are available for all support and query images during training, we refer to this as pixel-level supervision. When only class labels are available we refer to this as image-level supervision. When ground-truth segmentation masks are available for only a small percentage of training images, we refer to this as mixed supervision.", + "bbox": [ + 75, + 516, + 468, + 787 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the remainder of this section, we first introduce our base model architecture, which we call Classification-Segmentation Transformer (CST), and then describe training paradigms for the different levels of supervision mentioned above.", + "bbox": [ + 75, + 789, + 468, + 863 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Classification-Segmentation transformer", + "text_level": 1, + "bbox": [ + 500, + 409, + 846, + 425 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our Classification-Segmentation Transformer (CST) architecture first computes the cross-correlation of DINO ViT [9,18] tokens between support and query image pairs. It then generates two new sets of tokens which serve as input to the classification and segmentation prediction heads respectively. The objective function then combines the losses from each task head. The details of CST's architecture are shown in Fig. 2 and described in the following paragraphs.", + "bbox": [ + 496, + 433, + 890, + 555 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Correlation tokens. We use a frozen ViT architecture pretrained with DINO as a backbone, which takes as input an image and produces $T = HW$ image (patch) tokens $\\mathbf{F} \\in \\mathbb{R}^{C \\times T}$ and one class token $\\mathbf{h} \\in \\mathbb{R}^C$ , where $C$ denotes the token feature dimensionality. The terms \"image\" and \"class\" tokens are used in analogous fashion to previous work [9, 15, 18, 68]. The backbone first transforms a query image $q$ and a support image $s$ into two sets of tokens, $\\{\\mathbf{F_q}, \\mathbf{h_q}\\}$ and $\\{\\mathbf{F_s}, \\mathbf{h_s}\\}$ . The query image tokens $\\mathbf{F_q}$ are cross-correlated, by cosine similarity, with the support class token $\\mathbf{h_s}$ and the support image tokens $\\mathbf{F_s}$ , to generate a set of correlation tokens $\\mathbf{c}_{\\mathrm{cls}} \\in \\mathbb{R}^{T_{\\mathrm{q}}}$ and $\\mathbf{C}_{\\mathrm{img}} \\in \\mathbb{R}^{T_{\\mathrm{q}} \\times T_{\\mathrm{s}}}$ respectively:", + "bbox": [ + 496, + 559, + 892, + 755 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {c} _ {\\mathrm {c l s}} = \\overline {{\\mathbf {F}}} _ {\\mathrm {q}} ^ {\\top} \\overline {{\\mathbf {h}}} _ {\\mathrm {s}}, \\quad \\mathbf {C} _ {\\mathrm {i m g}} = \\overline {{\\mathbf {F}}} _ {\\mathrm {q}} ^ {\\top} \\overline {{\\mathbf {F}}} _ {\\mathrm {s}}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 602, + 756, + 890, + 777 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\overline{\\mathbf{F}}$ and $\\overline{\\mathbf{h}}$ denote l2-normalized tokens. We retain the semantic diversity of the $M$ heads of the ViT backbone by computing $M$ separate correlation tokens. In addition, prior work [26, 44] has demonstrated the value of incorporating multi-layer semantics. Similarly, we compute correlation", + "bbox": [ + 496, + 786, + 890, + 863 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "1Note that the terms, meta-training and meta-testing, are used interchangeably with training and testing in this paper.", + "bbox": [ + 76, + 875, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "2The cosine similarity between two vectors is the uncentered Pearson correlation coefficient.", + "bbox": [ + 500, + 875, + 890, + 898 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "19629", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "tokens for each of the $L$ transformer layers of the ViT. In all, we compute $ML$ different sets of correlation tokens and concatenate them along a new dimension to generate:", + "bbox": [ + 75, + 90, + 468, + 136 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {c} _ {\\mathrm {c l s}} ^ {\\prime} \\in \\mathbb {R} ^ {T _ {\\mathrm {q}} \\times M L}, \\quad \\mathbf {C} _ {\\mathrm {i m g}} ^ {\\prime} \\in \\mathbb {R} ^ {T _ {\\mathrm {q}} \\times T _ {\\mathrm {s}} \\times M L}. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 158, + 141, + 468, + 162 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Correlation transformer. We first concatenate $\\mathbf{c}_{\\mathrm{cls},i}^{\\prime}\\in \\mathbb{R}^{ML}$ and $\\mathbf{C}_{\\mathrm{img},i}^{\\prime}\\in \\mathbb{R}^{T_{\\mathrm{s}}\\times ML}$ , where $i\\in [1,\\dots ,T_{\\mathrm{q}}]$ is an index over the query image tokens, to produce $\\mathbf{Z}_{0,i}\\in \\mathbb{R}^{(1 + T_{\\mathrm{s}})\\times ML}$ . Our correlation transformer is a 2-layer transformer [69] that takes $\\mathbf{Z}_{0,i}$ and a segmentation mask label for the support image $(\\mathbf{M}_{\\mathrm{gt}}\\in \\{0,1\\}^{T_{\\mathrm{s}}})$ as input, and returns two tokens - a classification task token and a segmentation task token - for query image token $i$ . Each layer has the following form:", + "bbox": [ + 75, + 167, + 468, + 294 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {Z} _ {j, i} ^ {\\prime} = \\operatorname {N o r m} _ {j} ^ {\\prime} \\left(\\mathrm {M S A} _ {j} \\left(\\mathbf {Z} _ {j, i}, \\mathbf {M} _ {\\mathrm {g t}}\\right) + \\mathbf {Z} _ {j, i}\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 315, + 468, + 333 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {Z} _ {j + 1, i} = \\operatorname {N o r m} _ {j} \\left(\\mathrm {M L P} _ {j} \\left(\\mathbf {Z} _ {j, i} ^ {\\prime}\\right) + \\mathbf {Z} _ {j, i} ^ {\\prime}\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 335, + 468, + 354 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where MSA, Norm, and MLP correspond to a multi-head self-attention, a group normalization [78], and a linear layer, respectively, and $j$ denotes the transformer layer index. Additionally, in each MSA layer, the generated query embeddings $\\mathbf{Q}$ are spatially pooled (using a $4\\times 4$ and $3\\times 3$ kernel in layers 1 and 2 respectively) by reshaping $\\mathbf{Q}$ to recover its $H_{\\mathrm{s}},W_{\\mathrm{s}}$ dimensions, applying spatial pooling, and flattening the output. This progressively reduces the number of image tokens, collapsing the input spatial size from $T_{\\mathrm{s}} = 12\\times 12$ to 1. This spatial pooling, illustrated in Fig. 2, reduces memory consumption, similarly to [14]. The output of the correlation transformer is then $\\mathbf{Z}_{2,i}\\in \\mathbb{R}^{2\\times C'}$ , where $C^\\prime$ denotes the new token dimensionality after MLP projection. This process is broadcast over the correlation tokens $\\mathbf{C}_{\\mathrm{img},i}^{\\prime}$ for each query image token $i$ , resulting in $\\mathbf{Z}_2\\in \\mathbb{R}^{T_{\\mathrm{q}}\\times 2\\times C'}$ . We then split this tensor, along the second dimension, into classification and segmentation tokens $\\mathbf{C}_{\\mathrm{clf}},\\mathbf{C}_{\\mathrm{seg}}\\in \\mathbb{R}^{T_{\\mathrm{q}}\\times C'}$ . Lastly, $\\mathbf{C}_{\\mathrm{clf}}$ and $\\mathbf{C}_{\\mathrm{seg}}$ are reshaped into spatial dimensions as $\\mathbf{C}_{\\mathrm{clf}},\\mathbf{C}_{\\mathrm{seg}}\\in \\mathbb{R}^{H_{\\mathrm{q}}\\times W_{\\mathrm{q}}\\times C'}$ and then fed to their respective task heads, described next.", + "bbox": [ + 75, + 359, + 468, + 662 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Classification and segmentation heads. The classification head consists of two $1 \\times 1$ convolutions followed by global average pooling, and estimates the class presence probability $\\mathbf{y}_{\\mathrm{clf}}$ of the query image corresponding to the support image class. The segmentation head consists of two $3 \\times 3$ convolutions followed by bilinear interpolation to the original query image size and predicts a segmentation map $\\mathbf{Y}_{\\mathrm{seg}}$ .", + "bbox": [ + 75, + 666, + 468, + 772 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Learning objective. Given predictions from the task heads, the classification and segmentation losses are computed as the cross-entropy between the prediction and the ground-truth for each task:", + "bbox": [ + 75, + 775, + 468, + 834 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {c l f}} = - \\mathbf {y} _ {\\mathrm {g t}} \\log \\mathbf {y} _ {\\mathrm {c l f}}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 843, + 468, + 859 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {s e g}} = - \\frac {1}{H W} \\sum_ {\\mathbf {x} \\in [ H ] \\times [ W ]} \\mathbf {Y} _ {\\mathrm {g t}} (\\mathbf {x}) \\log \\mathbf {Y} _ {\\mathrm {s e g}} (\\mathbf {x}), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 145, + 861, + 468, + 896 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/d319c42048644019db331b1a53c2cd7b43df03da8f39f751d1a37f0223293ec2.jpg", + "image_caption": [ + "Figure 3. a) Image-level-supervision learners generate pseudo-GT masks by averaging multi-head cross-(self-) attention followed by thresholding (Sec. 3.2). b) Mixed-supervision learners first pre-train a mask enhancer with a few GT masks during training to enhance the pseudo-GT mask quality (Sec. 3.3)." + ], + "image_footnote": [], + "bbox": [ + 501, + 90, + 890, + 207 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{y}_{\\mathrm{gt}} \\in \\{0,1\\}$ is the image-level ground-truth label and $\\mathbf{Y}_{\\mathrm{gt}}(\\mathbf{x}) \\in \\{0,1\\}$ is the ground-truth label for each pixel $\\mathbf{x}$ . The final learning loss combines the two losses so that the model learns both tasks jointly:", + "bbox": [ + 498, + 297, + 890, + 358 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\lambda \\mathcal {L} _ {\\mathrm {c l f}} + \\mathcal {L} _ {\\mathrm {s e g}}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 635, + 371, + 890, + 386 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\lambda$ is a balancing hyperparameter.", + "bbox": [ + 500, + 398, + 759, + 414 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Inference. For $N$ -way $K$ -shot inference, $K$ class logits and segmentation masks are generated using $K$ support images, for each of $N$ classes. These are then averaged, resulting in one estimate per class $n$ , $\\hat{\\mathbf{y}}_{\\mathrm{clf}}^{(n)}$ and $\\hat{\\mathbf{Y}}_{\\mathrm{seg}}^{(n)}$ . Multi-label classification $\\hat{\\mathbf{y}}_{\\mathrm{clf}}^{(n)}$ is then obtained by thresholding each class response $\\hat{\\mathbf{y}}_{\\mathrm{clf}}^{(n)}$ with an arbitrarily chosen threshold of $\\delta = 0.5$ .", + "bbox": [ + 496, + 417, + 890, + 513 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For segmentation, a pixel $\\mathbf{x}$ is labeled as the class with the highest response, or as background (i.e. the $N + 1$ -th class) if none of the $N$ class responses exceeds $\\delta$ . Formally:", + "bbox": [ + 498, + 513, + 890, + 558 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {\\mathbf {Y}} _ {\\text {s e g}} (\\mathbf {x}) = \\left\\{ \\begin{array}{l} N + 1 \\quad \\text {i f} \\forall \\{\\hat {\\mathbf {Y}} _ {\\text {s e g}} ^ {(n)} (\\mathbf {x}) \\} _ {n = 1} ^ {N} \\leq \\delta , \\\\ \\arg \\max _ {n \\in [ 1, \\dots , N ]} \\{\\hat {\\mathbf {Y}} _ {\\text {s e g}} ^ {(n)} (\\mathbf {x}) \\} _ {n = 1} ^ {N}. \\end{array} \\right. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 545, + 582, + 890, + 622 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Learning with image-level supervision", + "text_level": 1, + "bbox": [ + 500, + 632, + 826, + 648 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The previously-described learning objective assumes access to GT support and query segmentation mask labels, $\\mathbf{M}_{\\mathrm{gt}}$ and $\\mathbf{Y}_{\\mathrm{gt}}$ . To remove the dependence on such expensive annotations, in this section we propose a learning framework for FS-CS that relies only on image-level annotations, i.e., ground-truth class labels. Using the same model architecture, we adopt a method akin to self-distillation [91, 94], that generates pseudo-GT masks, $\\mathbf{M}_{\\mathrm{ps}}$ and $\\mathbf{Y}_{\\mathrm{ps}}$ , and uses them in place of GT mask labels in equations 3 and 6.", + "bbox": [ + 496, + 655, + 890, + 790 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Pseudo-GT mask generation. As empirically investigated in previous studies [3, 9], query-key attention maps can capture semantically salient foreground objects. Inspired by this, we generate pseudo-GT masks for query and support images on the fly by computing the cross- and self-attention from the last DINO ViT layer. We intercept the key and query embeddings $\\mathbf{K}_{\\mathrm{s}}^{m}, \\mathbf{Q}_{\\mathrm{s}}^{m} \\in \\mathbb{R}^{(1 + T_{\\mathrm{s}}) \\times C}$ and", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "19630", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\mathbf{K}_{\\mathrm{q}}^{m}, \\mathbf{Q}_{\\mathrm{q}}^{m} \\in \\mathbb{R}^{(1 + T_{\\mathrm{q}}) \\times C}$ for the support and query images respectively, for the $m$ -th head from the last ViT layer. The support and query image pseudo-GT mask values $\\mathbf{M}_{\\mathrm{ps}, i_{\\mathrm{s}}}$ and $\\mathbf{Y}_{\\mathrm{ps}, i_{\\mathrm{q}}}$ (where $i_{\\mathrm{s}}$ and $i_{\\mathrm{q}}$ index the support and query image tokens respectively) are then computed as:", + "bbox": [ + 76, + 90, + 468, + 167 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {P} _ {\\mathrm {s}} \\in \\mathbb {R} ^ {M \\times T _ {\\mathrm {s}}}; \\quad \\mathbf {P} _ {\\mathrm {s}, i _ {\\mathrm {s}}} ^ {m} = \\overline {{\\mathbf {K}}} _ {\\mathrm {s}, i _ {\\mathrm {s}}} ^ {m} \\text {T} \\overline {{\\mathbf {Q}}} _ {\\mathrm {s}, c _ {\\mathrm {s}}} ^ {m},\n$$\n", + "text_format": "latex", + "bbox": [ + 161, + 175, + 380, + 196 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {P} _ {\\mathrm {q}} \\in \\mathbb {R} ^ {M \\times T _ {\\mathrm {q}}}; \\quad \\mathbf {P} _ {\\mathrm {q}, i _ {\\mathrm {q}}} ^ {m} = \\overline {{\\mathbf {K}}} _ {\\mathrm {q}, i _ {\\mathrm {q}}} ^ {m} \\text {T} \\overline {{\\mathbf {Q}}} _ {\\mathrm {s}, c _ {\\mathrm {s}}} ^ {m}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 161, + 199, + 468, + 223 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {M} _ {\\mathrm {p s}, i _ {\\mathrm {s}}} ^ {\\prime} = \\frac {1}{M} \\sum_ {m = 1} ^ {M} \\mathbf {P} _ {\\mathrm {s}, i _ {\\mathrm {s}}} ^ {m}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 234, + 468, + 282 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {Y} _ {\\mathrm {p s}, i _ {\\mathrm {q}}} ^ {\\prime} = \\left\\{ \\begin{array}{l l} \\mathbf {0} & \\text {i f} \\quad \\mathbf {y} _ {\\mathrm {c l f}} = \\mathbf {0} \\\\ \\frac {1}{M} \\sum_ {m = 1} ^ {M} \\mathbf {P} _ {\\mathrm {q}, i _ {\\mathrm {q}}} ^ {m}, \\end{array} \\right.\n$$\n", + "text_format": "latex", + "bbox": [ + 183, + 280, + 348, + 319 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {M} _ {\\mathrm {p s}} = \\Pi (\\xi (\\mathbf {M} _ {\\mathrm {p s}} ^ {\\prime}), \\alpha); \\mathbf {Y} _ {\\mathrm {p s}} = \\Pi (\\xi (\\mathbf {Y} _ {\\mathrm {p s}} ^ {\\prime}), \\alpha), \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 109, + 330, + 468, + 352 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "with $c_{s}$ denoting the index of the class token for the support image, $\\xi(\\cdot)$ performing spatial reshaping and bilinear interpolation to the input image size, and $\\Pi(\\cdot, \\alpha)$ applying an element-wise binary threshold $\\alpha = -0.1$ (set via hyperparameter search). The semantics captured in the support class token are matched with the localized semantics of the (query or support) image tokens, using (cross- or self-) attention. This localized semantic matching is then captured in the resulting pseudo-GT masks. Our pseudo-mask generation process brings negligible extra computation by leveraging internal byproducts from the ViT backbone.", + "bbox": [ + 75, + 354, + 468, + 521 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This learning framework also relates to self-knowledge distillation [91, 94], in the sense that our model is supervised using its own (intermediate) features. We can think of the backbone as the teacher and the full CST model as the student. However, a key difference is that in our approach the student model learns additional parameters. In contrast, in strictly self-knowledge distillation approaches the student and teacher model architectures are identical.", + "bbox": [ + 75, + 521, + 468, + 642 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Extension to mixed-supervision learning", + "text_level": 1, + "bbox": [ + 76, + 650, + 421, + 667 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As shown in Sec. 4, our pseudo-masks provide effective supervision for segmentation. However, there is unsurprisingly still a quality gap between these masks and the GT segmentation masks, which degrades segmentation performance. In this section, we propose a practical learning setting for FS-CS with mixed supervision, which reduces this degradation in segmentation performance, by using a small number of GT segmentation masks during training. Mixed-supervised FS-CS assumes that all training images contain image-level labels, and a small subset of them also contains pixel-level labels, which are relatively inexpensive compared to full supervision.", + "bbox": [ + 75, + 674, + 468, + 854 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To obtain higher-quality pseudo-GT masks, we use the small number of images with GT masks to train a mask enhancer. We reshape $\\mathbf{P}_{\\mathrm{s}}$ and $\\mathbf{P}_{\\mathrm{q}}$ in Eq. (9) into spatial tensors", + "bbox": [ + 75, + 854, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/aa5ed93456dd3aad5847e1409704491bd092f40652607deaf586947dd6c19f83.jpg", + "image_caption": [ + "support image", + "To query pseudo-GT mask enhanced pseudo-GT mask,", + "query GT mask", + "Figure 4. Examples of pseudo-GT & enhanced pseudo-GT masks." + ], + "image_footnote": [], + "bbox": [ + 501, + 104, + 890, + 253 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "and use them as inputs to the enhancer, which returns binary masks. During training the enhancer is supervised with the available GT masks. The mask enhancer is a network of three $3 \\times 3$ convolutional layers followed by a Sigmoid. For mixed-supervision learning, we pre-train this mask enhancer and all pseudo-masks are obtained via the enhancer before being used as supervision during meta-training and meta-testing. Figure 3 compares the two proposed pseudoGT mask generation processes under the image-level- and mixed-supervision learning settings.", + "bbox": [ + 496, + 289, + 890, + 441 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 455, + 630, + 472 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section we provide implementation details for our approach, and present quantitative and qualitative results to experimentally evaluate its performance. The attached supplementary material contains more analyses and details.", + "bbox": [ + 496, + 482, + 890, + 542 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Architecture and training. To compare with prior work based on ResNet50 [33,48,67,71], we use a ViT-small backbone [18] with 21M parameters that was pre-trained via self-supervision with DINO [9] on ImageNet 1K [54]. The size and training data are comparable with ResNet50 [27], which has 23M parameters and was also trained on ImageNet 1K, but using class labels as supervision. ViT-small consists of $L = 12$ transformer layers of $M = 6$ attention heads, with $C = 64$ -dimensional query-key-value embeddings. The backbone is frozen, as in previous work [67,90], and the additional layers are trained using Adam [35] with a learning rate of $10^{-3}$ . Consistent with [33], CST is trained with 1-way 1-shot episodes and is used for any $N$ -way $K$ -shot inference. We set the task token dimensionality $C' = 128$ , and the loss balancing hyperparameter $\\lambda = 0.1$ .", + "bbox": [ + 496, + 547, + 890, + 775 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. We report results on two standard FS-CS benchmarks [33], Pascal- $5^{i}$ [20,58] and COCO- $20^{i}$ [45,49]. Both datasets use 4-fold validation, where the folds $i \\in \\{0,1,2,3\\}$ are created by splitting the 20 (resp. 80) classes into 4 mutually disjoint class sets, with 10K (resp. 100K) images per fold. For training and validation, support and query image pairs are sampled on the fly, as done in [33]. For each training episode, $N$ support classes are chosen randomly from", + "bbox": [ + 496, + 779, + 890, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "19631", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/71657a57f087c3434f33ed338ee1499654890f520f5a6e56253c4d81fd729064.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
methodps-mask1-way 1-shot2-way 1-shotlearn.
classification 0/1 exact ratio (%)segmentation mIoU (%)classification 0/1 exact ratio (%)segmentation mIoU (%)params.
50515253avg.50515253avg.50515253avg.50515253avg.
HSNet [48]X84.584.860.885.378.920.023.516.216.619.170.867.036.570.161.111.023.415.417.017.72.6M
ASNet [33]X80.284.066.282.778.311.721.113.416.215.667.670.244.569.362.910.320.712.615.914.91.3M
CST (image)X83.980.765.982.778.311.920.715.016.316.072.665.343.269.562.611.920.515.016.615.70.4M
DINO [9]◇-----20.023.416.216.619.1-----12.812.910.09.911.40
CST✓84.082.270.882.679.935.838.928.929.233.274.367.249.067.864.635.736.026.829.131.90.4M
", + "bbox": [ + 81, + 88, + 885, + 193 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/2143eba9194240ed344585948785cd11790a456d8665d1831a8c721ea0f8b1a0.jpg", + "table_caption": [ + "Table 1. Comparing model performance on FS-CS when trained with image-level supervision on Pascal-5 $^i$ [58]. \"ps-mask\" refers to using pseudo-GT masks during training. Our CST model compares favourably to prior works on classification, and outperforms them on segmentation. Results for DINO [9] were generated without any training on Pascal-5 $^i$ (denoted by $\\diamond$ ). See section 4.1 for details." + ], + "table_footnote": [], + "table_body": "
methodps-mask1-way 1-shot2-way 1-shot
cls. ERseg. mIoUclf. ERseg. mIoU
CST✘74.510.362.39.8
DINO [9]◇-12.1-7.4
CST✓78.219.662.418.3
", + "bbox": [ + 86, + 255, + 455, + 340 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "the split and $K$ images are chosen randomly from each of the $N$ target classes to construct an $N$ -way $K$ -shot support set. When a support image contains multiple classes, only one of them is set as its image class and the rest are set as background. While this introduces noise into support sets containing multi-class images, we find that it performs well in practice. A query image is also chosen randomly and may contain between 0 to $N$ of the target classes. The image-level label for the query is then constructed as an $N$ -dimensional binary vector containing 1 if the query contains the $n$ -th class, and 0 otherwise. Similarly, its pixel-level label is defined as an $(N + 1)$ -way segmentation mask, including background. For mixed-supervision learning, we sort the images in a training split by their image names and use pixel-level labels for the first e.g. $5\\%$ of images, and only image-level labels for the remainder. This effectively randomizes the subset of images with full-supervision.", + "bbox": [ + 75, + 404, + 468, + 661 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation and metrics. We follow the established evaluation protocol for each FS-CS benchmark [33, 49, 58]. To evaluate multi-label classification, we use the $0/1$ exact match ratio [19], where an image is considered to be correctly classified if the binary label for each of the $N$ classes is correct. For semantic segmentation, we use mean IoU, $\\mathrm{mIoU} = \\frac{1}{R}\\sum_{R}\\mathrm{IoU}_{r}$ [58, 71], where $\\mathrm{IoU}_r$ is the IoU of all images labeled with the $r_{\\mathrm{th}}$ -class. The best model is chosen based on the highest validation mIoU averaged with 1000 random validation episodes.", + "bbox": [ + 75, + 667, + 468, + 819 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Results with image-level supervision", + "text_level": 1, + "bbox": [ + 76, + 830, + 393, + 847 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Tables 1 and 2 compare the performance of our image-level-supervised CST with baseline methods. The only prior work that addresses this setting [33] generates a seg", + "bbox": [ + 76, + 854, + 468, + 902 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/0582b02ad7f06654252eb6532894023e6564d97212f53fdfe9680f820943a6cc.jpg", + "table_caption": [ + "Table 2. Comparing model performance on FS-CS when trained with image-level supervision on COCO- $20^{i}$ [49], averaged over 4 folds. See section 4.1 for details." + ], + "table_footnote": [], + "table_body": "
% GT training set masks →0%2.5%5%10%100%
(a): pseudo-mask baseline33.241.443.544.5-
(b): (a) + mask enhancer-43.244.145.2-
(c): (b) + GT test set S masks-47.548.450.155.5
", + "bbox": [ + 503, + 255, + 901, + 321 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 3. Comparing segmentation mIoU of CST on FS-CS with mixed supervision on Pascal-5 $^i$ , for different $\\%$ of training set ground-truth masks, averaged over 4 folds. In (c), ground-truth masks were used for all support $(S)$ images during testing.", + "bbox": [ + 498, + 321, + 893, + 378 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "mentation mask that is then globally average-pooled. The cross-entropy between the average-pooled prediction and the ground-truth image label is used as the objective function. We adopt this approach for [48], which did not address this setting, to construct another baseline, and we also evaluate CST in this setting, which we denote with $\\mathbf{x}$ . The result for DINO is computed by evaluating segmentation masks that were generated as in [9] (denoted by $\\diamond$ ), without using any training data from the target datasets. Our CST model, trained with pseudo-masks via self-distillation (denoted by $\\checkmark$ ), performs comparably to prior work on classification and, because of the superior supervision provided by our pseudo-masks during training, outperforms these models on segmentation. In particular, CST achieves an over 100% improvement over ASNet [33] in both the 1-way 1-shot and 2-way 1-shot settings. We also note that training CST with pseudo-GT masks $(\\checkmark)$ also improves classification performance by 1.6% (1-way 1-shot) and 2% (2-way 1-shot) on Pascal-5 when compared to training without $(\\mathbf{x})$ .", + "bbox": [ + 496, + 393, + 893, + 681 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Results with mixed supervision", + "text_level": 1, + "bbox": [ + 500, + 694, + 774, + 710 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To validate the effectiveness of the mixed-supervision setting, we vary the percentage of pixel-level annotated images used in training and present the results in Table 3. We observe that using just $5\\%$ of GT masks is remarkably effective at improving performance, when compared to using $0\\%$ (43.5% vs. 33.2%). The mask enhancer brings much improvement with fewer ground-truth segmentation masks. The effect of the mask enhancer is visually demonstrated in Fig. 4. We observe that the mask enhancer reduces foreground noise and often filters out objects irrelevant to a support image. Note that mixed-supervision learning assumes access to pixel-level annotations only during training. Dur", + "bbox": [ + 496, + 719, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "19632", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/4d1a67bc1b7605f9ed2b5530507a3d4efe12ed4b960b7e8d3f44c7b2aefa41d8.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
method1-way 1-shot2-way 1-shotlearn. \nparams.
classification 0/1 exact ratio (%)segmentation mIoU (%)classification 0/1 exact ratio (%)segmentation mIoU (%)
50515253avg.50515253avg.50515253avg.50515253avg.
PANet [71]69.967.768.869.469.032.845.831.035.136.256.247.544.655.450.933.346.031.238.437.2
PFENet [67]69.882.468.177.974.638.354.735.143.843.022.561.740.339.541.031.147.330.832.235.3
HSNet [48]86.684.876.986.383.749.159.741.049.049.768.073.257.070.967.342.453.734.043.943.5
ASNet [33]84.989.679.086.284.951.761.543.352.852.368.576.258.670.068.348.558.336.348.347.8
CST86.988.081.586.585.755.661.647.756.955.570.374.962.074.470.456.961.048.057.055.7
", + "bbox": [ + 81, + 88, + 883, + 200 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/054e972b97e33bf5a06bcf3b084acc0f798659ea2c395007c35ec341e872951f.jpg", + "table_caption": [ + "Table 4. Comparing FS-CS models trained with pixel-level supervision on Pascal-5 ${}^{i}$ ." + ], + "table_footnote": [], + "table_body": "
method1-way 1-shot2-way 1-shot
clf. ERseg. mIoUclf. ERseg. mIoU
PANet [71]66.725.248.523.6
PFENet [67]71.431.936.522.6
HSNet [48]77.034.362.529.5
ASNet [33]78.635.863.131.6
CST80.838.364.036.2
", + "bbox": [ + 96, + 227, + 447, + 335 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ed773aa75609e23194fbf51cbb6d27401ff8f26b8508e5f35a48c51beafc5169.jpg", + "image_caption": [ + "Figure 5. Comparing performance on FS-CS with pixel-level supervision on $N$ -way 1-shot Pascal-5 $^i$ ." + ], + "image_footnote": [], + "bbox": [ + 78, + 387, + 464, + 494 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ing testing, support images use pseudo-masks without (Table 3 (a)) or with (Table 3 (b)) mask enhancement. In (c), we use one-shot support GT mask during testing, but still use reduced amounts of GT masks in training. In this setting, the performance is only $5.4\\% -8.0\\%$ lower than the fully-supervised model, indicating that our approach allows for significant pixel-level annotation efficiency during training.", + "bbox": [ + 75, + 539, + 468, + 645 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Results with full, i.e. pixel-level, supervision", + "text_level": 1, + "bbox": [ + 76, + 662, + 446, + 680 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Tables 4 and 5, as well as Fig. 5, compare our model's performance on FS-CS with state-of-the-art methods whose results, included here, were initially reported in [33]. CST achieves significant improvements over previous work, which we attribute to (i) our correlation tokens that leverage the localized semantics encoded in our self-supervised ViT backbone model; and (ii) the two task heads of our transformer (see ablations in Sec. 4.4). Figure 6 visually demonstrates qualitative examples of final segmentation predictions with increasing levels of supervision, from image-level to pixel-level. Image-level supervised predictions roughly segment out objects that correspond with the support classes, and the predictions become less noisy as more pixel-level supervision is used.", + "bbox": [ + 75, + 688, + 470, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/f824585f391a783e77dc913d7fbfa5314847b1ccf495777034ff8f39dbf39675.jpg", + "table_caption": [ + "Table 5. Comparing performance on FS-CS with pixel-level supervision on COCO-20i." + ], + "table_footnote": [], + "table_body": "
labels → archi. →class-sup. ViT [18]self-sup. CNN [27]self-sup. ViT [9]*self-sup. ViT [9]
seg. mIoU (%)6.920.715.633.2
", + "bbox": [ + 509, + 227, + 883, + 282 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/e24b8aedbc359af4f4d5dd6fb0138aae76dfbaf0bd4582fdb85b10c0c57bd130.jpg", + "table_caption": [ + "Table 6. FS-CS model comparison trained with image-level labels on 1-way 1-shot Pascal- $5^{j}$ by varying pseudo-mask generation models. Different columns denote model architectures for pseudolabeling and their pre-training supervision levels. The method * uses the final layer tokens from [9] for generating pseudo-labels." + ], + "table_footnote": [], + "table_body": "
clf. & seg.\nprediction headssuperv.\nlevel1-way 1-shot2-way 1-shot
clf.\nERseg.\nmIoUclf.\nERseg.\nmIoU
coupledimage78.532.959.531.9
decoupled (CST)image79.933.264.531.9
coupledpixel84.354.267.053.0
decoupled (CST)pixel85.755.570.555.7
", + "bbox": [ + 504, + 381, + 887, + 500 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 7. Ablation study of coupling or decoupling classification and segmentation prediction heads for FS-CS on Pascal-5 $^i$ .", + "bbox": [ + 500, + 510, + 890, + 539 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Ablation study", + "text_level": 1, + "bbox": [ + 500, + 551, + 648, + 568 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Pseudo-labeling with different models. We explore other learning-free pseudo-labeling methods by using alternative pre-trained feature extractors to generate pseudo-GT masks. Rather than self-distillation, where we train CST with pseudo-GT masks generated from its own self-supervised DINO ViT backbone, in these experiments we train CST with pseudo-GT masks generated from class-supervised ViT [18], self-supervised DINO ResNet50 [27], or the output layer tokens from the self-supervised DINO ViT [9]. As ResNets do not have class tokens, we apply global-average pooling on the support feature map from the last ResNet layer and use the pooled feature as a class token for generating the pseudo-GT masks. As seen in Table 6, pseudo-GT masks generated from alternative feature extractors do not perform as well as the intermediate attention maps from DINO. We qualitatively observed that the alternatives' less accurate pseudo-masks lead to lower segmentation accuracy when used in pseudo-supervised learning: the self-supervised ResNet50 produces pseudo-masks with indistinct object boundaries, while the class-supervised ViT produces noisy patches throughout the pseudo-mask (as was", + "bbox": [ + 496, + 583, + 890, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "19633", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/205ac74edb80f691925641215594c10f4ca84473c366f4c9c9f2e263dff94c83.jpg", + "image_caption": [ + "Figure 6. 2-way 1-shot segmentation examples from CST trained with image-level, mixed, and pixel-level supervision. Note that image-level-supervised and mixed-supervised models do not have access to ground-truth support masks. In both cases, the model is still effective." + ], + "image_footnote": [], + "bbox": [ + 88, + 88, + 880, + 258 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a1cd7409b8a459b70104bc613f0272ecee8c1f8ac89fff887cd65aff0d85056f.jpg", + "image_caption": [ + "Figure 7. An example of channel-averaged $\\mathbf{C}_{\\mathrm{clf}}$ , $\\mathbf{C}_{\\mathrm{seg}}$ . Each task token tends to capture different aspects, e.g., clearer edges of $\\mathbf{C}_{\\mathrm{seg}}$ ." + ], + "image_footnote": [], + "bbox": [ + 96, + 301, + 447, + 402 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/5e409ce9c356ab352bddf5ada61c8279302fb1961a3d89c16b00ca0fa35a6539.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
method1-way 1-shot1-way 5-shot# learn. \nparams.
mIoUFBIoUmIoUFBIoU
RPMM [83]30.6-35.5-38.6M
RePRI [6]34.0-42.1--
SSP [21]37.4-44.1-8.7M
MMNet [79]37.5-38.2-10.4M
MLC [84]33.9-40.6-8.7M
NTRENet [47]39.368.540.369.2-
CMN [81]39.361.743.163.3-
HSNet [48]39.268.246.970.72.6M
DACM [82]40.668.948.171.6-
ASNet [33]42.268.847.971.61.3M
CST44.070.348.773.70.4M
", + "bbox": [ + 94, + 440, + 450, + 614 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 8. Comparing FS-S models trained with pixel-level supervision on COCO-20i.", + "bbox": [ + 76, + 618, + 468, + 647 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "similarly observed in [9]).", + "bbox": [ + 76, + 655, + 251, + 671 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of decoupled task heads. Table 7 compares the impact of coupling and decoupling the classification and segmentation task heads. The coupled architecture has a single segmentation task head, and the image is classified with the foreground class if any pixels are predicted as foreground, and is otherwise classified as the background class. Having separate heads for each task benefits both tasks in both the image-level and pixel-level supervision settings. A similar observation was made for object detection [64] when decoupling localization from classification. Figure 7 visualizes an example of channel-averaged $\\mathbf{C}_{\\mathrm{clf}}$ and $\\mathbf{C}_{\\mathrm{seg}}$ tensors. We observe that these two intermediate representations tend to highlight different areas; $\\mathbf{C}_{\\mathrm{clf}}$ has large responses in highly-localized class-specific image regions, while $\\mathbf{C}_{\\mathrm{seg}}$ better distinguishes the overall object support and boundaries.", + "bbox": [ + 75, + 672, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Comparison on FS-S. In Table 8, CST is also evaluated in the conventional FS-S setting [58, 71], i.e., binary segmentation using mask supervision, and compared with previous works that use different ResNet50-based architectures. FS-S is equivalent to FS-CS with the precondition that a query and a support always share a class label; classification is not required. We train CST on this setting and find that it achieves state-of-the-art segmentation performance. It is also worth noting that it achieves this with fewer learned parameters than others, which is also the case for the comparisons in Table 1 and Table 4. Our small number of learned parameters may help to avoid overfitting.", + "bbox": [ + 496, + 301, + 893, + 486 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 526, + 619, + 542 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we propose an approach to generating effective pseudo-GT masks for few-shot classification and segmentation (FS-CS) using the localized semantics encoded in the tokens of self-supervised vision transformers. We show that using these pseudo-GT masks, sometimes combined with a small number of GT masks, we can train effective FS-CS models. Our work is the first to explore this practical weakly-supervised FS-CS setting, which drastically reduces the amount of expensive pixel-level annotations needed for training and deployment. Extensive experiments show that our approach achieves significant performance gains when compared to state-of-the-art methods in a variety of supervision settings, on two FS-CS benchmarks.", + "bbox": [ + 496, + 560, + 893, + 758 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. This work was partly supported by the IITP grants (2022-0-00959: Few-Shot Learning of Causal Inference in Vision and Language, 2022-0-00113: Sustainable Collaborative Multi-modal Lifelong Learning) funded by Ministry of Science and ICT, Korea. 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International Conference on Learning Representations (ICLR), 2021. 2" + ], + "bbox": [ + 501, + 92, + 890, + 247 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "19638", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 11 + } +] \ No newline at end of file diff --git a/2023/Distilling Self-Supervised Vision Transformers for Weakly-Supervised Few-Shot Classification & Segmentation/e6a6b9de-f70e-4a6b-bd84-70683a76add4_model.json b/2023/Distilling Self-Supervised Vision Transformers for Weakly-Supervised Few-Shot Classification & Segmentation/e6a6b9de-f70e-4a6b-bd84-70683a76add4_model.json new file mode 100644 index 0000000000000000000000000000000000000000..87b27976738646d16d49099ef4483e842b7cf71e --- /dev/null +++ b/2023/Distilling Self-Supervised Vision Transformers for Weakly-Supervised Few-Shot Classification & Segmentation/e6a6b9de-f70e-4a6b-bd84-70683a76add4_model.json @@ -0,0 +1,2721 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.163, + 0.131, + 0.807, + 0.177 + ], + "angle": 0, + "content": "Distilling Self-Supervised Vision Transformers for Weakly-Supervised Few-Shot Classification & Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.174, + 0.203, + 0.796, + 0.24 + ], + "angle": 0, + "content": "Dahyun Kang\\(^{1,2*}\\) Piotr Koniusz\\(^{3,4}\\) Minsu Cho\\(^{2}\\) Naila Murray\\(^{1}\\) \n\\(^{1}\\)Meta AI \\(^{2}\\)POSTECH \\(^{3}\\)Data61♥CSIRO \\(^{4}\\)Australian National University" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.274, + 0.313, + 0.29 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.306, + 0.474, + 0.64 + ], + "angle": 0, + "content": "We address the task of weakly-supervised few-shot image classification and segmentation, by leveraging a Vision Transformer (ViT) pretrained with self-supervision. Our proposed method takes token representations from the self-supervised ViT and leverages their correlations, via self-attention, to produce classification and segmentation predictions through separate task heads. Our model is able to effectively learn to perform classification and segmentation in the absence of pixel-level labels during training, using only image-level labels. To do this it uses attention maps, created from tokens generated by the self-supervised ViT backbone, as pixel-level pseudo-labels. We also explore a practical setup with \"mixed\" supervision, where a small number of training images contains ground-truth pixel-level labels and the remaining images have only image-level labels. For this mixed setup, we propose to improve the pseudo-labels using a pseudo-label enhancer that was trained using the available ground-truth pixel-level labels. Experiments on Pascal-5\\(^i\\) and COCO-20\\(^i\\) demonstrate significant performance gains in a variety of supervision settings, and in particular when little-to-no pixel-level labels are available." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.669, + 0.208, + 0.685 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.695, + 0.47, + 0.877 + ], + "angle": 0, + "content": "Few-shot learning [22, 23, 77] is the problem of learning to perform a prediction task using only a small number of examples (i.e. supports) of the completed task, typically in the range of 1-10 examples. This problem setting is appealing for applications where large amounts of annotated data are expensive or impractical to collect. In computer vision, few-shot learning has been actively studied for image classification [24, 36, 46, 66, 70, 85] and semantic segmentation [17, 58, 61, 88, 89]. In this work, we focus on the combined task of few-shot classification and segmentation (FS-CS) [33], which aims to jointly predict (i) the presence of each support class, i.e., multi-label classification, and (ii)" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.273, + 0.891, + 0.486 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.496, + 0.893, + 0.539 + ], + "angle": 0, + "content": "Figure 1. Weakly-supervised few-shot classification and segmentation. In this paper, we explore training few-shot models using little-to-no ground-truth segmentation masks." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.549, + 0.75, + 0.564 + ], + "angle": 0, + "content": "its pixel-level semantic segmentation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.566, + 0.893, + 0.853 + ], + "angle": 0, + "content": "Few-shot learners are typically trained either by meta-learning [24, 56, 63, 71] or by transfer learning with fine-tuning [11, 12, 16]. Both these paradigms commonly assume the availability of a large-scale and fully-annotated training dataset. For FS-CS, we need Ground-Truth (GT) segmentation masks for query and support images during training. We also need these GT masks for support images during testing. A natural alternative to collecting such expensive segmentation masks would be to instead employ a weaker supervision, e.g. image-level [52, 59] or box-level labels [13, 30], for learning, i.e., to adopt a weakly-supervised learning approach [5, 41, 43, 51]. Compared to conventional weakly-supervised learning however, weakly-supervised few-shot learning has rarely been explored in the literature and is significantly more challenging. This is because in few-shot learning, object classes are completely disjoint between training and testing, resulting in models which are susceptible to severe over-fitting to the classes seen during training." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.903 + ], + "angle": 0, + "content": "In this work we tackle this challenging scenario, addressing weakly-supervised FS-CS where only image-level labels, i.e. class labels, are available (cf. Fig. 1). Inspired by" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.32, + 0.9 + ], + "angle": 0, + "content": "*Work done during an internship at FAIR." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19627" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.273 + ], + "angle": 0, + "content": "recent work by Caron et al. [9], which showed that pixel-level semantic attention emerges from self-supervised vision transformers (ViTs) [18], we leverage attention maps from a frozen self-supervised ViT to generate pseudo-GT segmentation masks. We train an FS-CS learner on top of the frozen ViT using the generated pseudo-GT masks as pixel-level supervision. The FS-CS learner is a small transformer network that takes features from the ViT as input and is trained to predict the pseudo-GT masks. Our complete model thus learns to segment using its own intermediate byproduct, with no segmentation labeling cost, in a form of distillation [2, 28, 91, 94] between layers within a model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.274, + 0.473, + 0.412 + ], + "angle": 0, + "content": "We also explore a practical training setting where a limited number of training images have both image-level and pixel-level annotations, while the remaining images have only image-level labels. For this mixed-supervised setting, we propose to train an auxiliary mask enhancer that refines attention maps into pseudo-GT masks. The enhancer is supervised using the small number of available GT masks and is used to generate the final pseudo-GT masks for the training images that do not have GT masks." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.412, + 0.473, + 0.655 + ], + "angle": 0, + "content": "Lastly, to effectively address this weakly-supervised FS-CS task, we propose a Classification-Segmentation Transformer (CST) architecture. CST takes as input ViT tokens for query and support images, computes correlations between them, and then predicts classification and segmentation outputs through separate task heads; the classification head is trained with class labels while the segmentation head is trained with either GT masks or pseudo-GT masks, depending on availability. Unlike prior work using ViTs that generate prediction for a single task using either the class token [18, 74] or image tokens [50, 65], CST uses each of them for each task prediction, which proves advantageous for both tasks. CST achieves moderate-to-large performance gains for FS-CS on all three supervision levels (image-level-, mixed-level, and pixel-level), when compared to prior state-of-the-art methods." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.656, + 0.338, + 0.671 + ], + "angle": 0, + "content": "Our contributions are the following:" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.686, + 0.47, + 0.747 + ], + "angle": 0, + "content": "i. We introduce a powerful baseline for few-shot classification and segmentation (FS-CS) using only image-level supervision, which leverages localized semantic information encoded in self-supervised ViTs [9]." + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.763, + 0.47, + 0.825 + ], + "angle": 0, + "content": "ii. We propose a learning setup for FS-CS with mixed supervision, and present an auxiliary mask enhancer to improve performance compared to image-level supervision only." + }, + { + "type": "text", + "bbox": [ + 0.08, + 0.84, + 0.47, + 0.902 + ], + "angle": 0, + "content": "iii. We design Classification-Segmentation Transformer, and a multi-task learning objective of classification and segmentation, which is beneficial for both tasks, and allows for flexibly tuning the degree of supervision." + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.686, + 0.47, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.09, + 0.638, + 0.107 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.117, + 0.895, + 0.436 + ], + "angle": 0, + "content": "Few-shot classification and segmentation. This paper tackles the recently proposed task of few-shot classification and segmentation (FS-CS) [33], which generalizes and combines the conventional few-shot classification (FS-C) [11, 24, 34, 63, 70] and few-shot segmentation (FS-S) [58, 71, 89] tasks. FS-C assumes that a query contains only one of the support classes, while FS-S assumes that the query always contains all of them. In contrast, FS-CS breaks the assumption that a query image contains one class (or all classes) from the support set. As a result, FS-CS models must predict i) the presence or absence of each support class in the query; and ii) pixel-level segmentation masks. Our work explores a more challenging weakly-supervised version of FS-CS with image-level annotations but few or no pixel-level annotations. Prior work on weakly-supervised FS-S used supervision such as language [40, 60] or bounding boxes [55]. Our work does not adopt any extra modalities and uses weaker (image-level) supervision than bounding boxes. Other applications of few-shot learning include few-shot object detection [92, 93], action recognition [72, 73], and metric learning [32]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.441, + 0.895, + 0.699 + ], + "angle": 0, + "content": "Weakly-supervised segmentation. A common paradigm for weakly-supervised semantic segmentation uses class labels [1,39] to generate pseudo-GT masks from class activation maps (CAM) [57, 95], followed by pseudo-supervised training [37, 96, 99]. CAM requires a classification backbone pre-trained from many examples on seen classes whereas, in our few-shot setting, we devise a pseudo-GT mask generation method that requires only a small number of examples, and can handle unseen classes. We also investigate the extent to which a pseudo-mask enhancement module, trained using a small amount of GT masks, can generate better pseudo-GT masks. While such \"mixed-supervision\" learning has been called semi-weakly-supervised segmentation [4, 38, 42, 75] and studied in the standard seen-class many-shot learning paradigm, our work is the first to propose mixed-supervision learning for few-shot semantic segmentation, to the best of our knowledge." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Self-supervised learning. Self-supervised learning [31] has proven highly effective for learning powerful representations for downstream tasks [7-10, 80, 97]. One popular approach [9, 25] trains a model to map an image and its augmented views to nearby coordinates in a representation space. This class-agnostic objective trains the model to capture view-invariant semantics that transcend designated image categories. In addition, DINO-trained ViTs [9] capture localized semantics in the learned token representations. In this work, we leverage these representations to create attention map-based pseudo-GT masks for weakly-supervised FS-CS, using a novel and efficient self-distillation approach. The representations have also ben" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "19628" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.092, + 0.895, + 0.346 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.357, + 0.895, + 0.4 + ], + "angle": 0, + "content": "Figure 2. Classification-Segmentation Transformer. A query and a support image pass through a frozen DINO ViT to extract class and images tokens, which are cross-correlated to form correlation tokens. The correlation tokens are then fed to a correlation transformer and transform to task tokens. At the end, each classification and segmentation head takes each task token map and predicts each task." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.411, + 0.471, + 0.456 + ], + "angle": 0, + "content": "efited several other dense prediction tasks, including unsupervised object discovery [62, 76] and unsupervised image/video segmentation [9, 86, 87, 98]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.473, + 0.47, + 0.507 + ], + "angle": 0, + "content": "3. Weakly-supervised few-shot classification and segmentation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.517, + 0.47, + 0.789 + ], + "angle": 0, + "content": "In this paper we tackle few-shot classification and segmentation (FS-CS) [33]. Given a small number \\( K \\) of labeled support images for each of \\( N \\) classes, an FS-CS model is trained to i) identify the presence of each class in a query image and ii) segment the associated pixels. This setting is conventionally called an \\( N \\)-way \\( K \\)-shot episode [53, 70]. We adopt a meta-learning approach [29, 63, 70] to train our model, where an annotated training dataset (with a class set disjoint from the test set classes) is used to generate a sequence of \\( N \\)-way \\( K \\)-shot episodes. In our setting, annotations consist of class labels and segmentation masks. When ground-truth segmentation masks are available for all support and query images during training, we refer to this as pixel-level supervision. When only class labels are available we refer to this as image-level supervision. When ground-truth segmentation masks are available for only a small percentage of training images, we refer to this as mixed supervision." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.79, + 0.469, + 0.864 + ], + "angle": 0, + "content": "In the remainder of this section, we first introduce our base model architecture, which we call Classification-Segmentation Transformer (CST), and then describe training paradigms for the different levels of supervision mentioned above." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.41, + 0.848, + 0.426 + ], + "angle": 0, + "content": "3.1. Classification-Segmentation transformer" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.434, + 0.892, + 0.556 + ], + "angle": 0, + "content": "Our Classification-Segmentation Transformer (CST) architecture first computes the cross-correlation of DINO ViT [9,18] tokens between support and query image pairs. It then generates two new sets of tokens which serve as input to the classification and segmentation prediction heads respectively. The objective function then combines the losses from each task head. The details of CST's architecture are shown in Fig. 2 and described in the following paragraphs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.56, + 0.893, + 0.756 + ], + "angle": 0, + "content": "Correlation tokens. We use a frozen ViT architecture pretrained with DINO as a backbone, which takes as input an image and produces \\( T = HW \\) image (patch) tokens \\( \\mathbf{F} \\in \\mathbb{R}^{C \\times T} \\) and one class token \\( \\mathbf{h} \\in \\mathbb{R}^C \\), where \\( C \\) denotes the token feature dimensionality. The terms \"image\" and \"class\" tokens are used in analogous fashion to previous work [9, 15, 18, 68]. The backbone first transforms a query image \\( q \\) and a support image \\( s \\) into two sets of tokens, \\( \\{\\mathbf{F_q}, \\mathbf{h_q}\\} \\) and \\( \\{\\mathbf{F_s}, \\mathbf{h_s}\\} \\). The query image tokens \\( \\mathbf{F_q} \\) are cross-correlated, by cosine similarity, with the support class token \\( \\mathbf{h_s} \\) and the support image tokens \\( \\mathbf{F_s} \\), to generate a set of correlation tokens \\( \\mathbf{c}_{\\mathrm{cls}} \\in \\mathbb{R}^{T_{\\mathrm{q}}} \\) and \\( \\mathbf{C}_{\\mathrm{img}} \\in \\mathbb{R}^{T_{\\mathrm{q}} \\times T_{\\mathrm{s}}} \\) respectively:" + }, + { + "type": "equation", + "bbox": [ + 0.604, + 0.757, + 0.891, + 0.779 + ], + "angle": 0, + "content": "\\[\n\\mathbf {c} _ {\\mathrm {c l s}} = \\overline {{\\mathbf {F}}} _ {\\mathrm {q}} ^ {\\top} \\overline {{\\mathbf {h}}} _ {\\mathrm {s}}, \\quad \\mathbf {C} _ {\\mathrm {i m g}} = \\overline {{\\mathbf {F}}} _ {\\mathrm {q}} ^ {\\top} \\overline {{\\mathbf {F}}} _ {\\mathrm {s}}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.787, + 0.892, + 0.864 + ], + "angle": 0, + "content": "where \\(\\overline{\\mathbf{F}}\\) and \\(\\overline{\\mathbf{h}}\\) denote l2-normalized tokens. We retain the semantic diversity of the \\(M\\) heads of the ViT backbone by computing \\(M\\) separate correlation tokens. In addition, prior work [26, 44] has demonstrated the value of incorporating multi-layer semantics. Similarly, we compute correlation" + }, + { + "type": "page_footnote", + "bbox": [ + 0.077, + 0.875, + 0.469, + 0.901 + ], + "angle": 0, + "content": "1Note that the terms, meta-training and meta-testing, are used interchangeably with training and testing in this paper." + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.875, + 0.892, + 0.899 + ], + "angle": 0, + "content": "2The cosine similarity between two vectors is the uncentered Pearson correlation coefficient." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19629" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.137 + ], + "angle": 0, + "content": "tokens for each of the \\(L\\) transformer layers of the ViT. In all, we compute \\(ML\\) different sets of correlation tokens and concatenate them along a new dimension to generate:" + }, + { + "type": "equation", + "bbox": [ + 0.16, + 0.142, + 0.469, + 0.163 + ], + "angle": 0, + "content": "\\[\n\\mathbf {c} _ {\\mathrm {c l s}} ^ {\\prime} \\in \\mathbb {R} ^ {T _ {\\mathrm {q}} \\times M L}, \\quad \\mathbf {C} _ {\\mathrm {i m g}} ^ {\\prime} \\in \\mathbb {R} ^ {T _ {\\mathrm {q}} \\times T _ {\\mathrm {s}} \\times M L}. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.168, + 0.47, + 0.295 + ], + "angle": 0, + "content": "Correlation transformer. We first concatenate \\(\\mathbf{c}_{\\mathrm{cls},i}^{\\prime}\\in \\mathbb{R}^{ML}\\) and \\(\\mathbf{C}_{\\mathrm{img},i}^{\\prime}\\in \\mathbb{R}^{T_{\\mathrm{s}}\\times ML}\\), where \\(i\\in [1,\\dots ,T_{\\mathrm{q}}]\\) is an index over the query image tokens, to produce \\(\\mathbf{Z}_{0,i}\\in \\mathbb{R}^{(1 + T_{\\mathrm{s}})\\times ML}\\). Our correlation transformer is a 2-layer transformer [69] that takes \\(\\mathbf{Z}_{0,i}\\) and a segmentation mask label for the support image \\((\\mathbf{M}_{\\mathrm{gt}}\\in \\{0,1\\}^{T_{\\mathrm{s}}})\\) as input, and returns two tokens - a classification task token and a segmentation task token - for query image token \\(i\\). Each layer has the following form:" + }, + { + "type": "equation", + "bbox": [ + 0.154, + 0.316, + 0.469, + 0.334 + ], + "angle": 0, + "content": "\\[\n\\mathbf {Z} _ {j, i} ^ {\\prime} = \\operatorname {N o r m} _ {j} ^ {\\prime} \\left(\\mathrm {M S A} _ {j} \\left(\\mathbf {Z} _ {j, i}, \\mathbf {M} _ {\\mathrm {g t}}\\right) + \\mathbf {Z} _ {j, i}\\right), \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.141, + 0.337, + 0.469, + 0.355 + ], + "angle": 0, + "content": "\\[\n\\mathbf {Z} _ {j + 1, i} = \\operatorname {N o r m} _ {j} \\left(\\mathrm {M L P} _ {j} \\left(\\mathbf {Z} _ {j, i} ^ {\\prime}\\right) + \\mathbf {Z} _ {j, i} ^ {\\prime}\\right), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.36, + 0.47, + 0.664 + ], + "angle": 0, + "content": "where MSA, Norm, and MLP correspond to a multi-head self-attention, a group normalization [78], and a linear layer, respectively, and \\(j\\) denotes the transformer layer index. Additionally, in each MSA layer, the generated query embeddings \\(\\mathbf{Q}\\) are spatially pooled (using a \\(4\\times 4\\) and \\(3\\times 3\\) kernel in layers 1 and 2 respectively) by reshaping \\(\\mathbf{Q}\\) to recover its \\(H_{\\mathrm{s}},W_{\\mathrm{s}}\\) dimensions, applying spatial pooling, and flattening the output. This progressively reduces the number of image tokens, collapsing the input spatial size from \\(T_{\\mathrm{s}} = 12\\times 12\\) to 1. This spatial pooling, illustrated in Fig. 2, reduces memory consumption, similarly to [14]. The output of the correlation transformer is then \\(\\mathbf{Z}_{2,i}\\in \\mathbb{R}^{2\\times C'}\\), where \\(C^\\prime\\) denotes the new token dimensionality after MLP projection. This process is broadcast over the correlation tokens \\(\\mathbf{C}_{\\mathrm{img},i}^{\\prime}\\) for each query image token \\(i\\), resulting in \\(\\mathbf{Z}_2\\in \\mathbb{R}^{T_{\\mathrm{q}}\\times 2\\times C'}\\). We then split this tensor, along the second dimension, into classification and segmentation tokens \\(\\mathbf{C}_{\\mathrm{clf}},\\mathbf{C}_{\\mathrm{seg}}\\in \\mathbb{R}^{T_{\\mathrm{q}}\\times C'}\\). Lastly, \\(\\mathbf{C}_{\\mathrm{clf}}\\) and \\(\\mathbf{C}_{\\mathrm{seg}}\\) are reshaped into spatial dimensions as \\(\\mathbf{C}_{\\mathrm{clf}},\\mathbf{C}_{\\mathrm{seg}}\\in \\mathbb{R}^{H_{\\mathrm{q}}\\times W_{\\mathrm{q}}\\times C'}\\) and then fed to their respective task heads, described next." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.667, + 0.469, + 0.773 + ], + "angle": 0, + "content": "Classification and segmentation heads. The classification head consists of two \\(1 \\times 1\\) convolutions followed by global average pooling, and estimates the class presence probability \\(\\mathbf{y}_{\\mathrm{clf}}\\) of the query image corresponding to the support image class. The segmentation head consists of two \\(3 \\times 3\\) convolutions followed by bilinear interpolation to the original query image size and predicts a segmentation map \\(\\mathbf{Y}_{\\mathrm{seg}}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.776, + 0.469, + 0.835 + ], + "angle": 0, + "content": "Learning objective. Given predictions from the task heads, the classification and segmentation losses are computed as the cross-entropy between the prediction and the ground-truth for each task:" + }, + { + "type": "equation", + "bbox": [ + 0.149, + 0.844, + 0.469, + 0.86 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {c l f}} = - \\mathbf {y} _ {\\mathrm {g t}} \\log \\mathbf {y} _ {\\mathrm {c l f}}, \\tag {5}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.147, + 0.862, + 0.469, + 0.897 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {s e g}} = - \\frac {1}{H W} \\sum_ {\\mathbf {x} \\in [ H ] \\times [ W ]} \\mathbf {Y} _ {\\mathrm {g t}} (\\mathbf {x}) \\log \\mathbf {Y} _ {\\mathrm {s e g}} (\\mathbf {x}), \\tag {6}\n\\]" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.092, + 0.891, + 0.208 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.22, + 0.892, + 0.29 + ], + "angle": 0, + "content": "Figure 3. a) Image-level-supervision learners generate pseudo-GT masks by averaging multi-head cross-(self-) attention followed by thresholding (Sec. 3.2). b) Mixed-supervision learners first pre-train a mask enhancer with a few GT masks during training to enhance the pseudo-GT mask quality (Sec. 3.3)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.298, + 0.892, + 0.359 + ], + "angle": 0, + "content": "where \\(\\mathbf{y}_{\\mathrm{gt}} \\in \\{0,1\\}\\) is the image-level ground-truth label and \\(\\mathbf{Y}_{\\mathrm{gt}}(\\mathbf{x}) \\in \\{0,1\\}\\) is the ground-truth label for each pixel \\(\\mathbf{x}\\). The final learning loss combines the two losses so that the model learns both tasks jointly:" + }, + { + "type": "equation", + "bbox": [ + 0.637, + 0.372, + 0.891, + 0.387 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\lambda \\mathcal {L} _ {\\mathrm {c l f}} + \\mathcal {L} _ {\\mathrm {s e g}}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.4, + 0.76, + 0.415 + ], + "angle": 0, + "content": "where \\(\\lambda\\) is a balancing hyperparameter." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.418, + 0.892, + 0.514 + ], + "angle": 0, + "content": "Inference. For \\(N\\)-way \\(K\\)-shot inference, \\(K\\) class logits and segmentation masks are generated using \\(K\\) support images, for each of \\(N\\) classes. These are then averaged, resulting in one estimate per class \\(n\\), \\(\\hat{\\mathbf{y}}_{\\mathrm{clf}}^{(n)}\\) and \\(\\hat{\\mathbf{Y}}_{\\mathrm{seg}}^{(n)}\\). Multi-label classification \\(\\hat{\\mathbf{y}}_{\\mathrm{clf}}^{(n)}\\) is then obtained by thresholding each class response \\(\\hat{\\mathbf{y}}_{\\mathrm{clf}}^{(n)}\\) with an arbitrarily chosen threshold of \\(\\delta = 0.5\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.515, + 0.892, + 0.559 + ], + "angle": 0, + "content": "For segmentation, a pixel \\(\\mathbf{x}\\) is labeled as the class with the highest response, or as background (i.e. the \\(N + 1\\)-th class) if none of the \\(N\\) class responses exceeds \\(\\delta\\). Formally:" + }, + { + "type": "equation", + "bbox": [ + 0.547, + 0.583, + 0.891, + 0.623 + ], + "angle": 0, + "content": "\\[\n\\tilde {\\mathbf {Y}} _ {\\text {s e g}} (\\mathbf {x}) = \\left\\{ \\begin{array}{l} N + 1 \\quad \\text {i f} \\forall \\{\\hat {\\mathbf {Y}} _ {\\text {s e g}} ^ {(n)} (\\mathbf {x}) \\} _ {n = 1} ^ {N} \\leq \\delta , \\\\ \\arg \\max _ {n \\in [ 1, \\dots , N ]} \\{\\hat {\\mathbf {Y}} _ {\\text {s e g}} ^ {(n)} (\\mathbf {x}) \\} _ {n = 1} ^ {N}. \\end{array} \\right. \\tag {8}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.633, + 0.828, + 0.649 + ], + "angle": 0, + "content": "3.2. Learning with image-level supervision" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.656, + 0.892, + 0.791 + ], + "angle": 0, + "content": "The previously-described learning objective assumes access to GT support and query segmentation mask labels, \\(\\mathbf{M}_{\\mathrm{gt}}\\) and \\(\\mathbf{Y}_{\\mathrm{gt}}\\). To remove the dependence on such expensive annotations, in this section we propose a learning framework for FS-CS that relies only on image-level annotations, i.e., ground-truth class labels. Using the same model architecture, we adopt a method akin to self-distillation [91, 94], that generates pseudo-GT masks, \\(\\mathbf{M}_{\\mathrm{ps}}\\) and \\(\\mathbf{Y}_{\\mathrm{ps}}\\), and uses them in place of GT mask labels in equations 3 and 6." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Pseudo-GT mask generation. As empirically investigated in previous studies [3, 9], query-key attention maps can capture semantically salient foreground objects. Inspired by this, we generate pseudo-GT masks for query and support images on the fly by computing the cross- and self-attention from the last DINO ViT layer. We intercept the key and query embeddings \\(\\mathbf{K}_{\\mathrm{s}}^{m}, \\mathbf{Q}_{\\mathrm{s}}^{m} \\in \\mathbb{R}^{(1 + T_{\\mathrm{s}}) \\times C}\\) and" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19630" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.091, + 0.47, + 0.168 + ], + "angle": 0, + "content": "\\(\\mathbf{K}_{\\mathrm{q}}^{m}, \\mathbf{Q}_{\\mathrm{q}}^{m} \\in \\mathbb{R}^{(1 + T_{\\mathrm{q}}) \\times C}\\) for the support and query images respectively, for the \\(m\\)-th head from the last ViT layer. The support and query image pseudo-GT mask values \\(\\mathbf{M}_{\\mathrm{ps}, i_{\\mathrm{s}}}\\) and \\(\\mathbf{Y}_{\\mathrm{ps}, i_{\\mathrm{q}}}\\) (where \\(i_{\\mathrm{s}}\\) and \\(i_{\\mathrm{q}}\\) index the support and query image tokens respectively) are then computed as:" + }, + { + "type": "equation", + "bbox": [ + 0.162, + 0.176, + 0.382, + 0.198 + ], + "angle": 0, + "content": "\\[\n\\mathbf {P} _ {\\mathrm {s}} \\in \\mathbb {R} ^ {M \\times T _ {\\mathrm {s}}}; \\quad \\mathbf {P} _ {\\mathrm {s}, i _ {\\mathrm {s}}} ^ {m} = \\overline {{\\mathbf {K}}} _ {\\mathrm {s}, i _ {\\mathrm {s}}} ^ {m} \\text {T} \\overline {{\\mathbf {Q}}} _ {\\mathrm {s}, c _ {\\mathrm {s}}} ^ {m},\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.162, + 0.2, + 0.469, + 0.224 + ], + "angle": 0, + "content": "\\[\n\\mathbf {P} _ {\\mathrm {q}} \\in \\mathbb {R} ^ {M \\times T _ {\\mathrm {q}}}; \\quad \\mathbf {P} _ {\\mathrm {q}, i _ {\\mathrm {q}}} ^ {m} = \\overline {{\\mathbf {K}}} _ {\\mathrm {q}, i _ {\\mathrm {q}}} ^ {m} \\text {T} \\overline {{\\mathbf {Q}}} _ {\\mathrm {s}, c _ {\\mathrm {s}}} ^ {m}, \\tag {9}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.18, + 0.236, + 0.469, + 0.284 + ], + "angle": 0, + "content": "\\[\n\\mathbf {M} _ {\\mathrm {p s}, i _ {\\mathrm {s}}} ^ {\\prime} = \\frac {1}{M} \\sum_ {m = 1} ^ {M} \\mathbf {P} _ {\\mathrm {s}, i _ {\\mathrm {s}}} ^ {m}, \\tag {10}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.184, + 0.281, + 0.349, + 0.32 + ], + "angle": 0, + "content": "\\[\n\\mathbf {Y} _ {\\mathrm {p s}, i _ {\\mathrm {q}}} ^ {\\prime} = \\left\\{ \\begin{array}{l l} \\mathbf {0} & \\text {i f} \\quad \\mathbf {y} _ {\\mathrm {c l f}} = \\mathbf {0} \\\\ \\frac {1}{M} \\sum_ {m = 1} ^ {M} \\mathbf {P} _ {\\mathrm {q}, i _ {\\mathrm {q}}} ^ {m}, \\end{array} \\right.\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.11, + 0.331, + 0.469, + 0.353 + ], + "angle": 0, + "content": "\\[\n\\mathbf {M} _ {\\mathrm {p s}} = \\Pi (\\xi (\\mathbf {M} _ {\\mathrm {p s}} ^ {\\prime}), \\alpha); \\mathbf {Y} _ {\\mathrm {p s}} = \\Pi (\\xi (\\mathbf {Y} _ {\\mathrm {p s}} ^ {\\prime}), \\alpha), \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.356, + 0.469, + 0.522 + ], + "angle": 0, + "content": "with \\( c_{s} \\) denoting the index of the class token for the support image, \\( \\xi(\\cdot) \\) performing spatial reshaping and bilinear interpolation to the input image size, and \\( \\Pi(\\cdot, \\alpha) \\) applying an element-wise binary threshold \\( \\alpha = -0.1 \\) (set via hyperparameter search). The semantics captured in the support class token are matched with the localized semantics of the (query or support) image tokens, using (cross- or self-) attention. This localized semantic matching is then captured in the resulting pseudo-GT masks. Our pseudo-mask generation process brings negligible extra computation by leveraging internal byproducts from the ViT backbone." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.522, + 0.469, + 0.643 + ], + "angle": 0, + "content": "This learning framework also relates to self-knowledge distillation [91, 94], in the sense that our model is supervised using its own (intermediate) features. We can think of the backbone as the teacher and the full CST model as the student. However, a key difference is that in our approach the student model learns additional parameters. In contrast, in strictly self-knowledge distillation approaches the student and teacher model architectures are identical." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.651, + 0.422, + 0.668 + ], + "angle": 0, + "content": "3.3. Extension to mixed-supervision learning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.675, + 0.469, + 0.856 + ], + "angle": 0, + "content": "As shown in Sec. 4, our pseudo-masks provide effective supervision for segmentation. However, there is unsurprisingly still a quality gap between these masks and the GT segmentation masks, which degrades segmentation performance. In this section, we propose a practical learning setting for FS-CS with mixed supervision, which reduces this degradation in segmentation performance, by using a small number of GT segmentation masks during training. Mixed-supervised FS-CS assumes that all training images contain image-level labels, and a small subset of them also contains pixel-level labels, which are relatively inexpensive compared to full supervision." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.469, + 0.902 + ], + "angle": 0, + "content": "To obtain higher-quality pseudo-GT masks, we use the small number of images with GT masks to train a mask enhancer. We reshape \\(\\mathbf{P}_{\\mathrm{s}}\\) and \\(\\mathbf{P}_{\\mathrm{q}}\\) in Eq. (9) into spatial tensors" + }, + { + "type": "image_caption", + "bbox": [ + 0.524, + 0.095, + 0.58, + 0.104 + ], + "angle": 0, + "content": "support image" + }, + { + "type": "image_caption", + "bbox": [ + 0.604, + 0.095, + 0.794, + 0.103 + ], + "angle": 0, + "content": "To query pseudo-GT mask enhanced pseudo-GT mask," + }, + { + "type": "image_caption", + "bbox": [ + 0.813, + 0.095, + 0.871, + 0.103 + ], + "angle": 0, + "content": "query GT mask" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.105, + 0.892, + 0.255 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.259, + 0.89, + 0.273 + ], + "angle": 0, + "content": "Figure 4. Examples of pseudo-GT & enhanced pseudo-GT masks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.29, + 0.892, + 0.442 + ], + "angle": 0, + "content": "and use them as inputs to the enhancer, which returns binary masks. During training the enhancer is supervised with the available GT masks. The mask enhancer is a network of three \\(3 \\times 3\\) convolutional layers followed by a Sigmoid. For mixed-supervision learning, we pre-train this mask enhancer and all pseudo-masks are obtained via the enhancer before being used as supervision during meta-training and meta-testing. Figure 3 compares the two proposed pseudoGT mask generation processes under the image-level- and mixed-supervision learning settings." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.457, + 0.632, + 0.473 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.483, + 0.892, + 0.544 + ], + "angle": 0, + "content": "In this section we provide implementation details for our approach, and present quantitative and qualitative results to experimentally evaluate its performance. The attached supplementary material contains more analyses and details." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.549, + 0.892, + 0.776 + ], + "angle": 0, + "content": "Architecture and training. To compare with prior work based on ResNet50 [33,48,67,71], we use a ViT-small backbone [18] with 21M parameters that was pre-trained via self-supervision with DINO [9] on ImageNet 1K [54]. The size and training data are comparable with ResNet50 [27], which has 23M parameters and was also trained on ImageNet 1K, but using class labels as supervision. ViT-small consists of \\( L = 12 \\) transformer layers of \\( M = 6 \\) attention heads, with \\( C = 64 \\)-dimensional query-key-value embeddings. The backbone is frozen, as in previous work [67,90], and the additional layers are trained using Adam [35] with a learning rate of \\( 10^{-3} \\). Consistent with [33], CST is trained with 1-way 1-shot episodes and is used for any \\( N \\)-way \\( K \\)-shot inference. We set the task token dimensionality \\( C' = 128 \\), and the loss balancing hyperparameter \\( \\lambda = 0.1 \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Datasets. We report results on two standard FS-CS benchmarks [33], Pascal- \\(5^{i}\\) [20,58] and COCO- \\(20^{i}\\) [45,49]. Both datasets use 4-fold validation, where the folds \\(i \\in \\{0,1,2,3\\}\\) are created by splitting the 20 (resp. 80) classes into 4 mutually disjoint class sets, with 10K (resp. 100K) images per fold. For training and validation, support and query image pairs are sampled on the fly, as done in [33]. For each training episode, \\(N\\) support classes are chosen randomly from" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.518, + 0.957 + ], + "angle": 0, + "content": "19631" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.887, + 0.194 + ], + "angle": 0, + "content": "
methodps-mask1-way 1-shot2-way 1-shotlearn.
classification 0/1 exact ratio (%)segmentation mIoU (%)classification 0/1 exact ratio (%)segmentation mIoU (%)params.
50515253avg.50515253avg.50515253avg.50515253avg.
HSNet [48]X84.584.860.885.378.920.023.516.216.619.170.867.036.570.161.111.023.415.417.017.72.6M
ASNet [33]X80.284.066.282.778.311.721.113.416.215.667.670.244.569.362.910.320.712.615.914.91.3M
CST (image)X83.980.765.982.778.311.920.715.016.316.072.665.343.269.562.611.920.515.016.615.70.4M
DINO [9]◇-----20.023.416.216.619.1-----12.812.910.09.911.40
CST✓84.082.270.882.679.935.838.928.929.233.274.367.249.067.864.635.736.026.829.131.90.4M
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.197, + 0.895, + 0.242 + ], + "angle": 0, + "content": "Table 1. Comparing model performance on FS-CS when trained with image-level supervision on Pascal-5\\(^i\\) [58]. \"ps-mask\" refers to using pseudo-GT masks during training. Our CST model compares favourably to prior works on classification, and outperforms them on segmentation. Results for DINO [9] were generated without any training on Pascal-5\\(^i\\) (denoted by \\(\\diamond\\)). See section 4.1 for details." + }, + { + "type": "table", + "bbox": [ + 0.088, + 0.256, + 0.457, + 0.341 + ], + "angle": 0, + "content": "
methodps-mask1-way 1-shot2-way 1-shot
cls. ERseg. mIoUclf. ERseg. mIoU
CST✘74.510.362.39.8
DINO [9]◇-12.1-7.4
CST✓78.219.662.418.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.351, + 0.472, + 0.394 + ], + "angle": 0, + "content": "Table 2. Comparing model performance on FS-CS when trained with image-level supervision on COCO- \\(20^{i}\\) [49], averaged over 4 folds. See section 4.1 for details." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.405, + 0.47, + 0.662 + ], + "angle": 0, + "content": "the split and \\( K \\) images are chosen randomly from each of the \\( N \\) target classes to construct an \\( N \\)-way \\( K \\)-shot support set. When a support image contains multiple classes, only one of them is set as its image class and the rest are set as background. While this introduces noise into support sets containing multi-class images, we find that it performs well in practice. A query image is also chosen randomly and may contain between 0 to \\( N \\) of the target classes. The image-level label for the query is then constructed as an \\( N \\)-dimensional binary vector containing 1 if the query contains the \\( n \\)-th class, and 0 otherwise. Similarly, its pixel-level label is defined as an \\( (N + 1) \\)-way segmentation mask, including background. For mixed-supervision learning, we sort the images in a training split by their image names and use pixel-level labels for the first e.g. \\( 5\\% \\) of images, and only image-level labels for the remainder. This effectively randomizes the subset of images with full-supervision." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.668, + 0.47, + 0.82 + ], + "angle": 0, + "content": "Evaluation and metrics. We follow the established evaluation protocol for each FS-CS benchmark [33, 49, 58]. To evaluate multi-label classification, we use the \\(0/1\\) exact match ratio [19], where an image is considered to be correctly classified if the binary label for each of the \\(N\\) classes is correct. For semantic segmentation, we use mean IoU, \\(\\mathrm{mIoU} = \\frac{1}{R}\\sum_{R}\\mathrm{IoU}_{r}\\) [58, 71], where \\(\\mathrm{IoU}_r\\) is the IoU of all images labeled with the \\(r_{\\mathrm{th}}\\)-class. The best model is chosen based on the highest validation mIoU averaged with 1000 random validation episodes." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.831, + 0.394, + 0.848 + ], + "angle": 0, + "content": "4.1. Results with image-level supervision" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Tables 1 and 2 compare the performance of our image-level-supervised CST with baseline methods. The only prior work that addresses this setting [33] generates a seg" + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.256, + 0.902, + 0.322 + ], + "angle": 0, + "content": "
% GT training set masks →0%2.5%5%10%100%
(a): pseudo-mask baseline33.241.443.544.5-
(b): (a) + mask enhancer-43.244.145.2-
(c): (b) + GT test set S masks-47.548.450.155.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.323, + 0.895, + 0.38 + ], + "angle": 0, + "content": "Table 3. Comparing segmentation mIoU of CST on FS-CS with mixed supervision on Pascal-5\\(^i\\), for different \\(\\%\\) of training set ground-truth masks, averaged over 4 folds. In (c), ground-truth masks were used for all support \\((S)\\) images during testing." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.394, + 0.895, + 0.683 + ], + "angle": 0, + "content": "mentation mask that is then globally average-pooled. The cross-entropy between the average-pooled prediction and the ground-truth image label is used as the objective function. We adopt this approach for [48], which did not address this setting, to construct another baseline, and we also evaluate CST in this setting, which we denote with \\( \\mathbf{x} \\). The result for DINO is computed by evaluating segmentation masks that were generated as in [9] (denoted by \\( \\diamond \\)), without using any training data from the target datasets. Our CST model, trained with pseudo-masks via self-distillation (denoted by \\( \\checkmark \\)), performs comparably to prior work on classification and, because of the superior supervision provided by our pseudo-masks during training, outperforms these models on segmentation. In particular, CST achieves an over 100% improvement over ASNet [33] in both the 1-way 1-shot and 2-way 1-shot settings. We also note that training CST with pseudo-GT masks \\( (\\checkmark) \\) also improves classification performance by 1.6% (1-way 1-shot) and 2% (2-way 1-shot) on Pascal-5 when compared to training without \\( (\\mathbf{x}) \\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.695, + 0.776, + 0.712 + ], + "angle": 0, + "content": "4.2. Results with mixed supervision" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.894, + 0.903 + ], + "angle": 0, + "content": "To validate the effectiveness of the mixed-supervision setting, we vary the percentage of pixel-level annotated images used in training and present the results in Table 3. We observe that using just \\(5\\%\\) of GT masks is remarkably effective at improving performance, when compared to using \\(0\\%\\) (43.5% vs. 33.2%). The mask enhancer brings much improvement with fewer ground-truth segmentation masks. The effect of the mask enhancer is visually demonstrated in Fig. 4. We observe that the mask enhancer reduces foreground noise and often filters out objects irrelevant to a support image. Note that mixed-supervision learning assumes access to pixel-level annotations only during training. Dur" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "19632" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.885, + 0.201 + ], + "angle": 0, + "content": "
method1-way 1-shot2-way 1-shotlearn. \nparams.
classification 0/1 exact ratio (%)segmentation mIoU (%)classification 0/1 exact ratio (%)segmentation mIoU (%)
50515253avg.50515253avg.50515253avg.50515253avg.
PANet [71]69.967.768.869.469.032.845.831.035.136.256.247.544.655.450.933.346.031.238.437.2
PFENet [67]69.882.468.177.974.638.354.735.143.843.022.561.740.339.541.031.147.330.832.235.3
HSNet [48]86.684.876.986.383.749.159.741.049.049.768.073.257.070.967.342.453.734.043.943.5
ASNet [33]84.989.679.086.284.951.761.543.352.852.368.576.258.670.068.348.558.336.348.347.8
CST86.988.081.586.585.755.661.647.756.955.570.374.962.074.470.456.961.048.057.055.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.233, + 0.205, + 0.735, + 0.219 + ], + "angle": 0, + "content": "Table 4. Comparing FS-CS models trained with pixel-level supervision on Pascal-5 \\( {}^{i} \\) ." + }, + { + "type": "table", + "bbox": [ + 0.097, + 0.228, + 0.449, + 0.336 + ], + "angle": 0, + "content": "
method1-way 1-shot2-way 1-shot
clf. ERseg. mIoUclf. ERseg. mIoU
PANet [71]66.725.248.523.6
PFENet [67]71.431.936.522.6
HSNet [48]77.034.362.529.5
ASNet [33]78.635.863.131.6
CST80.838.364.036.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.347, + 0.47, + 0.375 + ], + "angle": 0, + "content": "Table 5. Comparing performance on FS-CS with pixel-level supervision on COCO-20i." + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.388, + 0.465, + 0.496 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.497, + 0.469, + 0.525 + ], + "angle": 0, + "content": "Figure 5. Comparing performance on FS-CS with pixel-level supervision on \\(N\\)-way 1-shot Pascal-5\\(^i\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.54, + 0.47, + 0.646 + ], + "angle": 0, + "content": "ing testing, support images use pseudo-masks without (Table 3 (a)) or with (Table 3 (b)) mask enhancement. In (c), we use one-shot support GT mask during testing, but still use reduced amounts of GT masks in training. In this setting, the performance is only \\(5.4\\% -8.0\\%\\) lower than the fully-supervised model, indicating that our approach allows for significant pixel-level annotation efficiency during training." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.663, + 0.447, + 0.681 + ], + "angle": 0, + "content": "4.3. Results with full, i.e. pixel-level, supervision" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Tables 4 and 5, as well as Fig. 5, compare our model's performance on FS-CS with state-of-the-art methods whose results, included here, were initially reported in [33]. CST achieves significant improvements over previous work, which we attribute to (i) our correlation tokens that leverage the localized semantics encoded in our self-supervised ViT backbone model; and (ii) the two task heads of our transformer (see ablations in Sec. 4.4). Figure 6 visually demonstrates qualitative examples of final segmentation predictions with increasing levels of supervision, from image-level to pixel-level. Image-level supervised predictions roughly segment out objects that correspond with the support classes, and the predictions become less noisy as more pixel-level supervision is used." + }, + { + "type": "table", + "bbox": [ + 0.511, + 0.228, + 0.885, + 0.284 + ], + "angle": 0, + "content": "
labels → archi. →class-sup. ViT [18]self-sup. CNN [27]self-sup. ViT [9]*self-sup. ViT [9]
seg. mIoU (%)6.920.715.633.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.294, + 0.892, + 0.365 + ], + "angle": 0, + "content": "Table 6. FS-CS model comparison trained with image-level labels on 1-way 1-shot Pascal- \\(5^{j}\\) by varying pseudo-mask generation models. Different columns denote model architectures for pseudolabeling and their pre-training supervision levels. The method * uses the final layer tokens from [9] for generating pseudo-labels." + }, + { + "type": "table", + "bbox": [ + 0.506, + 0.382, + 0.888, + 0.501 + ], + "angle": 0, + "content": "
clf. & seg.\nprediction headssuperv.\nlevel1-way 1-shot2-way 1-shot
clf.\nERseg.\nmIoUclf.\nERseg.\nmIoU
coupledimage78.532.959.531.9
decoupled (CST)image79.933.264.531.9
coupledpixel84.354.267.053.0
decoupled (CST)pixel85.755.570.555.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.511, + 0.892, + 0.54 + ], + "angle": 0, + "content": "Table 7. Ablation study of coupling or decoupling classification and segmentation prediction heads for FS-CS on Pascal-5\\(^i\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.552, + 0.65, + 0.569 + ], + "angle": 0, + "content": "4.4. Ablation study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Pseudo-labeling with different models. We explore other learning-free pseudo-labeling methods by using alternative pre-trained feature extractors to generate pseudo-GT masks. Rather than self-distillation, where we train CST with pseudo-GT masks generated from its own self-supervised DINO ViT backbone, in these experiments we train CST with pseudo-GT masks generated from class-supervised ViT [18], self-supervised DINO ResNet50 [27], or the output layer tokens from the self-supervised DINO ViT [9]. As ResNets do not have class tokens, we apply global-average pooling on the support feature map from the last ResNet layer and use the pooled feature as a class token for generating the pseudo-GT masks. As seen in Table 6, pseudo-GT masks generated from alternative feature extractors do not perform as well as the intermediate attention maps from DINO. We qualitatively observed that the alternatives' less accurate pseudo-masks lead to lower segmentation accuracy when used in pseudo-supervised learning: the self-supervised ResNet50 produces pseudo-masks with indistinct object boundaries, while the class-supervised ViT produces noisy patches throughout the pseudo-mask (as was" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19633" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.089, + 0.089, + 0.881, + 0.26 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.262, + 0.895, + 0.293 + ], + "angle": 0, + "content": "Figure 6. 2-way 1-shot segmentation examples from CST trained with image-level, mixed, and pixel-level supervision. Note that image-level-supervised and mixed-supervised models do not have access to ground-truth support masks. In both cases, the model is still effective." + }, + { + "type": "image", + "bbox": [ + 0.097, + 0.302, + 0.449, + 0.404 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.406, + 0.471, + 0.437 + ], + "angle": 0, + "content": "Figure 7. An example of channel-averaged \\(\\mathbf{C}_{\\mathrm{clf}}\\), \\(\\mathbf{C}_{\\mathrm{seg}}\\). Each task token tends to capture different aspects, e.g., clearer edges of \\(\\mathbf{C}_{\\mathrm{seg}}\\)." + }, + { + "type": "table", + "bbox": [ + 0.096, + 0.441, + 0.451, + 0.616 + ], + "angle": 0, + "content": "
method1-way 1-shot1-way 5-shot# learn. \nparams.
mIoUFBIoUmIoUFBIoU
RPMM [83]30.6-35.5-38.6M
RePRI [6]34.0-42.1--
SSP [21]37.4-44.1-8.7M
MMNet [79]37.5-38.2-10.4M
MLC [84]33.9-40.6-8.7M
NTRENet [47]39.368.540.369.2-
CMN [81]39.361.743.163.3-
HSNet [48]39.268.246.970.72.6M
DACM [82]40.668.948.171.6-
ASNet [33]42.268.847.971.61.3M
CST44.070.348.773.70.4M
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.619, + 0.47, + 0.648 + ], + "angle": 0, + "content": "Table 8. Comparing FS-S models trained with pixel-level supervision on COCO-20i." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.656, + 0.253, + 0.672 + ], + "angle": 0, + "content": "similarly observed in [9])." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.674, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Effect of decoupled task heads. Table 7 compares the impact of coupling and decoupling the classification and segmentation task heads. The coupled architecture has a single segmentation task head, and the image is classified with the foreground class if any pixels are predicted as foreground, and is otherwise classified as the background class. Having separate heads for each task benefits both tasks in both the image-level and pixel-level supervision settings. A similar observation was made for object detection [64] when decoupling localization from classification. Figure 7 visualizes an example of channel-averaged \\(\\mathbf{C}_{\\mathrm{clf}}\\) and \\(\\mathbf{C}_{\\mathrm{seg}}\\) tensors. We observe that these two intermediate representations tend to highlight different areas; \\(\\mathbf{C}_{\\mathrm{clf}}\\) has large responses in highly-localized class-specific image regions, while \\(\\mathbf{C}_{\\mathrm{seg}}\\) better distinguishes the overall object support and boundaries." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.303, + 0.895, + 0.487 + ], + "angle": 0, + "content": "Comparison on FS-S. In Table 8, CST is also evaluated in the conventional FS-S setting [58, 71], i.e., binary segmentation using mask supervision, and compared with previous works that use different ResNet50-based architectures. FS-S is equivalent to FS-CS with the precondition that a query and a support always share a class label; classification is not required. We train CST on this setting and find that it achieves state-of-the-art segmentation performance. It is also worth noting that it achieves this with fewer learned parameters than others, which is also the case for the comparisons in Table 1 and Table 4. Our small number of learned parameters may help to avoid overfitting." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.527, + 0.62, + 0.543 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.561, + 0.895, + 0.759 + ], + "angle": 0, + "content": "In this work, we propose an approach to generating effective pseudo-GT masks for few-shot classification and segmentation (FS-CS) using the localized semantics encoded in the tokens of self-supervised vision transformers. We show that using these pseudo-GT masks, sometimes combined with a small number of GT masks, we can train effective FS-CS models. Our work is the first to explore this practical weakly-supervised FS-CS setting, which drastically reduces the amount of expensive pixel-level annotations needed for training and deployment. Extensive experiments show that our approach achieves significant performance gains when compared to state-of-the-art methods in a variety of supervision settings, on two FS-CS benchmarks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Acknowledgements. This work was partly supported by the IITP grants (2022-0-00959: Few-Shot Learning of Causal Inference in Vision and Language, 2022-0-00113: Sustainable Collaborative Multi-modal Lifelong Learning) funded by Ministry of Science and ICT, Korea. 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Our proposed method takes token representations from the self-supervised ViT and leverages their correlations, via self-attention, to produce classification and segmentation predictions through separate task heads. Our model is able to effectively learn to perform classification and segmentation in the absence of pixel-level labels during training, using only image-level labels. To do this it uses attention maps, created from tokens generated by the self-supervised ViT backbone, as pixel-level pseudo-labels. We also explore a practical setup with "mixed" supervision, where a small number of training images contains ground-truth pixel-level labels and the remaining images have only image-level labels. For this mixed setup, we propose to improve the pseudo-labels using a pseudo-label enhancer that was trained using the available ground-truth pixel-level labels. Experiments on Pascal-5 $^i$ and COCO-20 $^i$ demonstrate significant performance gains in a variety of supervision settings, and in particular when little-to-no pixel-level labels are available. + +# 1. Introduction + +Few-shot learning [22, 23, 77] is the problem of learning to perform a prediction task using only a small number of examples (i.e. supports) of the completed task, typically in the range of 1-10 examples. This problem setting is appealing for applications where large amounts of annotated data are expensive or impractical to collect. In computer vision, few-shot learning has been actively studied for image classification [24, 36, 46, 66, 70, 85] and semantic segmentation [17, 58, 61, 88, 89]. In this work, we focus on the combined task of few-shot classification and segmentation (FS-CS) [33], which aims to jointly predict (i) the presence of each support class, i.e., multi-label classification, and (ii) + +![](images/bb27f4b8af88c0dce2e78ee4f1ca87b9d4d4a73f8ea0197be7c202e00db80057.jpg) +Figure 1. Weakly-supervised few-shot classification and segmentation. In this paper, we explore training few-shot models using little-to-no ground-truth segmentation masks. + +its pixel-level semantic segmentation. + +Few-shot learners are typically trained either by meta-learning [24, 56, 63, 71] or by transfer learning with fine-tuning [11, 12, 16]. Both these paradigms commonly assume the availability of a large-scale and fully-annotated training dataset. For FS-CS, we need Ground-Truth (GT) segmentation masks for query and support images during training. We also need these GT masks for support images during testing. A natural alternative to collecting such expensive segmentation masks would be to instead employ a weaker supervision, e.g. image-level [52, 59] or box-level labels [13, 30], for learning, i.e., to adopt a weakly-supervised learning approach [5, 41, 43, 51]. Compared to conventional weakly-supervised learning however, weakly-supervised few-shot learning has rarely been explored in the literature and is significantly more challenging. This is because in few-shot learning, object classes are completely disjoint between training and testing, resulting in models which are susceptible to severe over-fitting to the classes seen during training. + +In this work we tackle this challenging scenario, addressing weakly-supervised FS-CS where only image-level labels, i.e. class labels, are available (cf. Fig. 1). Inspired by + +recent work by Caron et al. [9], which showed that pixel-level semantic attention emerges from self-supervised vision transformers (ViTs) [18], we leverage attention maps from a frozen self-supervised ViT to generate pseudo-GT segmentation masks. We train an FS-CS learner on top of the frozen ViT using the generated pseudo-GT masks as pixel-level supervision. The FS-CS learner is a small transformer network that takes features from the ViT as input and is trained to predict the pseudo-GT masks. Our complete model thus learns to segment using its own intermediate byproduct, with no segmentation labeling cost, in a form of distillation [2, 28, 91, 94] between layers within a model. + +We also explore a practical training setting where a limited number of training images have both image-level and pixel-level annotations, while the remaining images have only image-level labels. For this mixed-supervised setting, we propose to train an auxiliary mask enhancer that refines attention maps into pseudo-GT masks. The enhancer is supervised using the small number of available GT masks and is used to generate the final pseudo-GT masks for the training images that do not have GT masks. + +Lastly, to effectively address this weakly-supervised FS-CS task, we propose a Classification-Segmentation Transformer (CST) architecture. CST takes as input ViT tokens for query and support images, computes correlations between them, and then predicts classification and segmentation outputs through separate task heads; the classification head is trained with class labels while the segmentation head is trained with either GT masks or pseudo-GT masks, depending on availability. Unlike prior work using ViTs that generate prediction for a single task using either the class token [18, 74] or image tokens [50, 65], CST uses each of them for each task prediction, which proves advantageous for both tasks. CST achieves moderate-to-large performance gains for FS-CS on all three supervision levels (image-level-, mixed-level, and pixel-level), when compared to prior state-of-the-art methods. + +Our contributions are the following: + +i. We introduce a powerful baseline for few-shot classification and segmentation (FS-CS) using only image-level supervision, which leverages localized semantic information encoded in self-supervised ViTs [9]. +ii. We propose a learning setup for FS-CS with mixed supervision, and present an auxiliary mask enhancer to improve performance compared to image-level supervision only. +iii. We design Classification-Segmentation Transformer, and a multi-task learning objective of classification and segmentation, which is beneficial for both tasks, and allows for flexibly tuning the degree of supervision. + +# 2. Related work + +Few-shot classification and segmentation. This paper tackles the recently proposed task of few-shot classification and segmentation (FS-CS) [33], which generalizes and combines the conventional few-shot classification (FS-C) [11, 24, 34, 63, 70] and few-shot segmentation (FS-S) [58, 71, 89] tasks. FS-C assumes that a query contains only one of the support classes, while FS-S assumes that the query always contains all of them. In contrast, FS-CS breaks the assumption that a query image contains one class (or all classes) from the support set. As a result, FS-CS models must predict i) the presence or absence of each support class in the query; and ii) pixel-level segmentation masks. Our work explores a more challenging weakly-supervised version of FS-CS with image-level annotations but few or no pixel-level annotations. Prior work on weakly-supervised FS-S used supervision such as language [40, 60] or bounding boxes [55]. Our work does not adopt any extra modalities and uses weaker (image-level) supervision than bounding boxes. Other applications of few-shot learning include few-shot object detection [92, 93], action recognition [72, 73], and metric learning [32]. + +Weakly-supervised segmentation. A common paradigm for weakly-supervised semantic segmentation uses class labels [1,39] to generate pseudo-GT masks from class activation maps (CAM) [57, 95], followed by pseudo-supervised training [37, 96, 99]. CAM requires a classification backbone pre-trained from many examples on seen classes whereas, in our few-shot setting, we devise a pseudo-GT mask generation method that requires only a small number of examples, and can handle unseen classes. We also investigate the extent to which a pseudo-mask enhancement module, trained using a small amount of GT masks, can generate better pseudo-GT masks. While such "mixed-supervision" learning has been called semi-weakly-supervised segmentation [4, 38, 42, 75] and studied in the standard seen-class many-shot learning paradigm, our work is the first to propose mixed-supervision learning for few-shot semantic segmentation, to the best of our knowledge. + +Self-supervised learning. Self-supervised learning [31] has proven highly effective for learning powerful representations for downstream tasks [7-10, 80, 97]. One popular approach [9, 25] trains a model to map an image and its augmented views to nearby coordinates in a representation space. This class-agnostic objective trains the model to capture view-invariant semantics that transcend designated image categories. In addition, DINO-trained ViTs [9] capture localized semantics in the learned token representations. In this work, we leverage these representations to create attention map-based pseudo-GT masks for weakly-supervised FS-CS, using a novel and efficient self-distillation approach. The representations have also ben + +![](images/5240162eddae44e78dff6e8d41d2a3b9fba4959e3c7407fc9ca2492daba83c9d.jpg) +Figure 2. Classification-Segmentation Transformer. A query and a support image pass through a frozen DINO ViT to extract class and images tokens, which are cross-correlated to form correlation tokens. The correlation tokens are then fed to a correlation transformer and transform to task tokens. At the end, each classification and segmentation head takes each task token map and predicts each task. + +efited several other dense prediction tasks, including unsupervised object discovery [62, 76] and unsupervised image/video segmentation [9, 86, 87, 98]. + +# 3. Weakly-supervised few-shot classification and segmentation + +In this paper we tackle few-shot classification and segmentation (FS-CS) [33]. Given a small number $K$ of labeled support images for each of $N$ classes, an FS-CS model is trained to i) identify the presence of each class in a query image and ii) segment the associated pixels. This setting is conventionally called an $N$ -way $K$ -shot episode [53, 70]. We adopt a meta-learning approach [29, 63, 70] to train our model, where an annotated training dataset (with a class set disjoint from the test set classes) is used to generate a sequence of $N$ -way $K$ -shot episodes. In our setting, annotations consist of class labels and segmentation masks. When ground-truth segmentation masks are available for all support and query images during training, we refer to this as pixel-level supervision. When only class labels are available we refer to this as image-level supervision. When ground-truth segmentation masks are available for only a small percentage of training images, we refer to this as mixed supervision. + +In the remainder of this section, we first introduce our base model architecture, which we call Classification-Segmentation Transformer (CST), and then describe training paradigms for the different levels of supervision mentioned above. + +# 3.1. Classification-Segmentation transformer + +Our Classification-Segmentation Transformer (CST) architecture first computes the cross-correlation of DINO ViT [9,18] tokens between support and query image pairs. It then generates two new sets of tokens which serve as input to the classification and segmentation prediction heads respectively. The objective function then combines the losses from each task head. The details of CST's architecture are shown in Fig. 2 and described in the following paragraphs. + +Correlation tokens. We use a frozen ViT architecture pretrained with DINO as a backbone, which takes as input an image and produces $T = HW$ image (patch) tokens $\mathbf{F} \in \mathbb{R}^{C \times T}$ and one class token $\mathbf{h} \in \mathbb{R}^C$ , where $C$ denotes the token feature dimensionality. The terms "image" and "class" tokens are used in analogous fashion to previous work [9, 15, 18, 68]. The backbone first transforms a query image $q$ and a support image $s$ into two sets of tokens, $\{\mathbf{F_q}, \mathbf{h_q}\}$ and $\{\mathbf{F_s}, \mathbf{h_s}\}$ . The query image tokens $\mathbf{F_q}$ are cross-correlated, by cosine similarity, with the support class token $\mathbf{h_s}$ and the support image tokens $\mathbf{F_s}$ , to generate a set of correlation tokens $\mathbf{c}_{\mathrm{cls}} \in \mathbb{R}^{T_{\mathrm{q}}}$ and $\mathbf{C}_{\mathrm{img}} \in \mathbb{R}^{T_{\mathrm{q}} \times T_{\mathrm{s}}}$ respectively: + +$$ +\mathbf {c} _ {\mathrm {c l s}} = \overline {{\mathbf {F}}} _ {\mathrm {q}} ^ {\top} \overline {{\mathbf {h}}} _ {\mathrm {s}}, \quad \mathbf {C} _ {\mathrm {i m g}} = \overline {{\mathbf {F}}} _ {\mathrm {q}} ^ {\top} \overline {{\mathbf {F}}} _ {\mathrm {s}}, \tag {1} +$$ + +where $\overline{\mathbf{F}}$ and $\overline{\mathbf{h}}$ denote l2-normalized tokens. We retain the semantic diversity of the $M$ heads of the ViT backbone by computing $M$ separate correlation tokens. In addition, prior work [26, 44] has demonstrated the value of incorporating multi-layer semantics. Similarly, we compute correlation + +tokens for each of the $L$ transformer layers of the ViT. In all, we compute $ML$ different sets of correlation tokens and concatenate them along a new dimension to generate: + +$$ +\mathbf {c} _ {\mathrm {c l s}} ^ {\prime} \in \mathbb {R} ^ {T _ {\mathrm {q}} \times M L}, \quad \mathbf {C} _ {\mathrm {i m g}} ^ {\prime} \in \mathbb {R} ^ {T _ {\mathrm {q}} \times T _ {\mathrm {s}} \times M L}. \tag {2} +$$ + +Correlation transformer. We first concatenate $\mathbf{c}_{\mathrm{cls},i}^{\prime}\in \mathbb{R}^{ML}$ and $\mathbf{C}_{\mathrm{img},i}^{\prime}\in \mathbb{R}^{T_{\mathrm{s}}\times ML}$ , where $i\in [1,\dots ,T_{\mathrm{q}}]$ is an index over the query image tokens, to produce $\mathbf{Z}_{0,i}\in \mathbb{R}^{(1 + T_{\mathrm{s}})\times ML}$ . Our correlation transformer is a 2-layer transformer [69] that takes $\mathbf{Z}_{0,i}$ and a segmentation mask label for the support image $(\mathbf{M}_{\mathrm{gt}}\in \{0,1\}^{T_{\mathrm{s}}})$ as input, and returns two tokens - a classification task token and a segmentation task token - for query image token $i$ . Each layer has the following form: + +$$ +\mathbf {Z} _ {j, i} ^ {\prime} = \operatorname {N o r m} _ {j} ^ {\prime} \left(\mathrm {M S A} _ {j} \left(\mathbf {Z} _ {j, i}, \mathbf {M} _ {\mathrm {g t}}\right) + \mathbf {Z} _ {j, i}\right), \tag {3} +$$ + +$$ +\mathbf {Z} _ {j + 1, i} = \operatorname {N o r m} _ {j} \left(\mathrm {M L P} _ {j} \left(\mathbf {Z} _ {j, i} ^ {\prime}\right) + \mathbf {Z} _ {j, i} ^ {\prime}\right), \tag {4} +$$ + +where MSA, Norm, and MLP correspond to a multi-head self-attention, a group normalization [78], and a linear layer, respectively, and $j$ denotes the transformer layer index. Additionally, in each MSA layer, the generated query embeddings $\mathbf{Q}$ are spatially pooled (using a $4\times 4$ and $3\times 3$ kernel in layers 1 and 2 respectively) by reshaping $\mathbf{Q}$ to recover its $H_{\mathrm{s}},W_{\mathrm{s}}$ dimensions, applying spatial pooling, and flattening the output. This progressively reduces the number of image tokens, collapsing the input spatial size from $T_{\mathrm{s}} = 12\times 12$ to 1. This spatial pooling, illustrated in Fig. 2, reduces memory consumption, similarly to [14]. The output of the correlation transformer is then $\mathbf{Z}_{2,i}\in \mathbb{R}^{2\times C'}$ , where $C^\prime$ denotes the new token dimensionality after MLP projection. This process is broadcast over the correlation tokens $\mathbf{C}_{\mathrm{img},i}^{\prime}$ for each query image token $i$ , resulting in $\mathbf{Z}_2\in \mathbb{R}^{T_{\mathrm{q}}\times 2\times C'}$ . We then split this tensor, along the second dimension, into classification and segmentation tokens $\mathbf{C}_{\mathrm{clf}},\mathbf{C}_{\mathrm{seg}}\in \mathbb{R}^{T_{\mathrm{q}}\times C'}$ . Lastly, $\mathbf{C}_{\mathrm{clf}}$ and $\mathbf{C}_{\mathrm{seg}}$ are reshaped into spatial dimensions as $\mathbf{C}_{\mathrm{clf}},\mathbf{C}_{\mathrm{seg}}\in \mathbb{R}^{H_{\mathrm{q}}\times W_{\mathrm{q}}\times C'}$ and then fed to their respective task heads, described next. + +Classification and segmentation heads. The classification head consists of two $1 \times 1$ convolutions followed by global average pooling, and estimates the class presence probability $\mathbf{y}_{\mathrm{clf}}$ of the query image corresponding to the support image class. The segmentation head consists of two $3 \times 3$ convolutions followed by bilinear interpolation to the original query image size and predicts a segmentation map $\mathbf{Y}_{\mathrm{seg}}$ . + +Learning objective. Given predictions from the task heads, the classification and segmentation losses are computed as the cross-entropy between the prediction and the ground-truth for each task: + +$$ +\mathcal {L} _ {\mathrm {c l f}} = - \mathbf {y} _ {\mathrm {g t}} \log \mathbf {y} _ {\mathrm {c l f}}, \tag {5} +$$ + +$$ +\mathcal {L} _ {\mathrm {s e g}} = - \frac {1}{H W} \sum_ {\mathbf {x} \in [ H ] \times [ W ]} \mathbf {Y} _ {\mathrm {g t}} (\mathbf {x}) \log \mathbf {Y} _ {\mathrm {s e g}} (\mathbf {x}), \tag {6} +$$ + +![](images/d319c42048644019db331b1a53c2cd7b43df03da8f39f751d1a37f0223293ec2.jpg) +Figure 3. a) Image-level-supervision learners generate pseudo-GT masks by averaging multi-head cross-(self-) attention followed by thresholding (Sec. 3.2). b) Mixed-supervision learners first pre-train a mask enhancer with a few GT masks during training to enhance the pseudo-GT mask quality (Sec. 3.3). + +where $\mathbf{y}_{\mathrm{gt}} \in \{0,1\}$ is the image-level ground-truth label and $\mathbf{Y}_{\mathrm{gt}}(\mathbf{x}) \in \{0,1\}$ is the ground-truth label for each pixel $\mathbf{x}$ . The final learning loss combines the two losses so that the model learns both tasks jointly: + +$$ +\mathcal {L} = \lambda \mathcal {L} _ {\mathrm {c l f}} + \mathcal {L} _ {\mathrm {s e g}}, \tag {7} +$$ + +where $\lambda$ is a balancing hyperparameter. + +Inference. For $N$ -way $K$ -shot inference, $K$ class logits and segmentation masks are generated using $K$ support images, for each of $N$ classes. These are then averaged, resulting in one estimate per class $n$ , $\hat{\mathbf{y}}_{\mathrm{clf}}^{(n)}$ and $\hat{\mathbf{Y}}_{\mathrm{seg}}^{(n)}$ . Multi-label classification $\hat{\mathbf{y}}_{\mathrm{clf}}^{(n)}$ is then obtained by thresholding each class response $\hat{\mathbf{y}}_{\mathrm{clf}}^{(n)}$ with an arbitrarily chosen threshold of $\delta = 0.5$ . + +For segmentation, a pixel $\mathbf{x}$ is labeled as the class with the highest response, or as background (i.e. the $N + 1$ -th class) if none of the $N$ class responses exceeds $\delta$ . Formally: + +$$ +\tilde {\mathbf {Y}} _ {\text {s e g}} (\mathbf {x}) = \left\{ \begin{array}{l} N + 1 \quad \text {i f} \forall \{\hat {\mathbf {Y}} _ {\text {s e g}} ^ {(n)} (\mathbf {x}) \} _ {n = 1} ^ {N} \leq \delta , \\ \arg \max _ {n \in [ 1, \dots , N ]} \{\hat {\mathbf {Y}} _ {\text {s e g}} ^ {(n)} (\mathbf {x}) \} _ {n = 1} ^ {N}. \end{array} \right. \tag {8} +$$ + +# 3.2. Learning with image-level supervision + +The previously-described learning objective assumes access to GT support and query segmentation mask labels, $\mathbf{M}_{\mathrm{gt}}$ and $\mathbf{Y}_{\mathrm{gt}}$ . To remove the dependence on such expensive annotations, in this section we propose a learning framework for FS-CS that relies only on image-level annotations, i.e., ground-truth class labels. Using the same model architecture, we adopt a method akin to self-distillation [91, 94], that generates pseudo-GT masks, $\mathbf{M}_{\mathrm{ps}}$ and $\mathbf{Y}_{\mathrm{ps}}$ , and uses them in place of GT mask labels in equations 3 and 6. + +Pseudo-GT mask generation. As empirically investigated in previous studies [3, 9], query-key attention maps can capture semantically salient foreground objects. Inspired by this, we generate pseudo-GT masks for query and support images on the fly by computing the cross- and self-attention from the last DINO ViT layer. We intercept the key and query embeddings $\mathbf{K}_{\mathrm{s}}^{m}, \mathbf{Q}_{\mathrm{s}}^{m} \in \mathbb{R}^{(1 + T_{\mathrm{s}}) \times C}$ and + +$\mathbf{K}_{\mathrm{q}}^{m}, \mathbf{Q}_{\mathrm{q}}^{m} \in \mathbb{R}^{(1 + T_{\mathrm{q}}) \times C}$ for the support and query images respectively, for the $m$ -th head from the last ViT layer. The support and query image pseudo-GT mask values $\mathbf{M}_{\mathrm{ps}, i_{\mathrm{s}}}$ and $\mathbf{Y}_{\mathrm{ps}, i_{\mathrm{q}}}$ (where $i_{\mathrm{s}}$ and $i_{\mathrm{q}}$ index the support and query image tokens respectively) are then computed as: + +$$ +\mathbf {P} _ {\mathrm {s}} \in \mathbb {R} ^ {M \times T _ {\mathrm {s}}}; \quad \mathbf {P} _ {\mathrm {s}, i _ {\mathrm {s}}} ^ {m} = \overline {{\mathbf {K}}} _ {\mathrm {s}, i _ {\mathrm {s}}} ^ {m} \text {T} \overline {{\mathbf {Q}}} _ {\mathrm {s}, c _ {\mathrm {s}}} ^ {m}, +$$ + +$$ +\mathbf {P} _ {\mathrm {q}} \in \mathbb {R} ^ {M \times T _ {\mathrm {q}}}; \quad \mathbf {P} _ {\mathrm {q}, i _ {\mathrm {q}}} ^ {m} = \overline {{\mathbf {K}}} _ {\mathrm {q}, i _ {\mathrm {q}}} ^ {m} \text {T} \overline {{\mathbf {Q}}} _ {\mathrm {s}, c _ {\mathrm {s}}} ^ {m}, \tag {9} +$$ + +$$ +\mathbf {M} _ {\mathrm {p s}, i _ {\mathrm {s}}} ^ {\prime} = \frac {1}{M} \sum_ {m = 1} ^ {M} \mathbf {P} _ {\mathrm {s}, i _ {\mathrm {s}}} ^ {m}, \tag {10} +$$ + +$$ +\mathbf {Y} _ {\mathrm {p s}, i _ {\mathrm {q}}} ^ {\prime} = \left\{ \begin{array}{l l} \mathbf {0} & \text {i f} \quad \mathbf {y} _ {\mathrm {c l f}} = \mathbf {0} \\ \frac {1}{M} \sum_ {m = 1} ^ {M} \mathbf {P} _ {\mathrm {q}, i _ {\mathrm {q}}} ^ {m}, \end{array} \right. +$$ + +$$ +\mathbf {M} _ {\mathrm {p s}} = \Pi (\xi (\mathbf {M} _ {\mathrm {p s}} ^ {\prime}), \alpha); \mathbf {Y} _ {\mathrm {p s}} = \Pi (\xi (\mathbf {Y} _ {\mathrm {p s}} ^ {\prime}), \alpha), \tag {11} +$$ + +with $c_{s}$ denoting the index of the class token for the support image, $\xi(\cdot)$ performing spatial reshaping and bilinear interpolation to the input image size, and $\Pi(\cdot, \alpha)$ applying an element-wise binary threshold $\alpha = -0.1$ (set via hyperparameter search). The semantics captured in the support class token are matched with the localized semantics of the (query or support) image tokens, using (cross- or self-) attention. This localized semantic matching is then captured in the resulting pseudo-GT masks. Our pseudo-mask generation process brings negligible extra computation by leveraging internal byproducts from the ViT backbone. + +This learning framework also relates to self-knowledge distillation [91, 94], in the sense that our model is supervised using its own (intermediate) features. We can think of the backbone as the teacher and the full CST model as the student. However, a key difference is that in our approach the student model learns additional parameters. In contrast, in strictly self-knowledge distillation approaches the student and teacher model architectures are identical. + +# 3.3. Extension to mixed-supervision learning + +As shown in Sec. 4, our pseudo-masks provide effective supervision for segmentation. However, there is unsurprisingly still a quality gap between these masks and the GT segmentation masks, which degrades segmentation performance. In this section, we propose a practical learning setting for FS-CS with mixed supervision, which reduces this degradation in segmentation performance, by using a small number of GT segmentation masks during training. Mixed-supervised FS-CS assumes that all training images contain image-level labels, and a small subset of them also contains pixel-level labels, which are relatively inexpensive compared to full supervision. + +To obtain higher-quality pseudo-GT masks, we use the small number of images with GT masks to train a mask enhancer. We reshape $\mathbf{P}_{\mathrm{s}}$ and $\mathbf{P}_{\mathrm{q}}$ in Eq. (9) into spatial tensors + +![](images/aa5ed93456dd3aad5847e1409704491bd092f40652607deaf586947dd6c19f83.jpg) +support image +To query pseudo-GT mask enhanced pseudo-GT mask, +query GT mask +Figure 4. Examples of pseudo-GT & enhanced pseudo-GT masks. + +and use them as inputs to the enhancer, which returns binary masks. During training the enhancer is supervised with the available GT masks. The mask enhancer is a network of three $3 \times 3$ convolutional layers followed by a Sigmoid. For mixed-supervision learning, we pre-train this mask enhancer and all pseudo-masks are obtained via the enhancer before being used as supervision during meta-training and meta-testing. Figure 3 compares the two proposed pseudoGT mask generation processes under the image-level- and mixed-supervision learning settings. + +# 4. Experiments + +In this section we provide implementation details for our approach, and present quantitative and qualitative results to experimentally evaluate its performance. The attached supplementary material contains more analyses and details. + +Architecture and training. To compare with prior work based on ResNet50 [33,48,67,71], we use a ViT-small backbone [18] with 21M parameters that was pre-trained via self-supervision with DINO [9] on ImageNet 1K [54]. The size and training data are comparable with ResNet50 [27], which has 23M parameters and was also trained on ImageNet 1K, but using class labels as supervision. ViT-small consists of $L = 12$ transformer layers of $M = 6$ attention heads, with $C = 64$ -dimensional query-key-value embeddings. The backbone is frozen, as in previous work [67,90], and the additional layers are trained using Adam [35] with a learning rate of $10^{-3}$ . Consistent with [33], CST is trained with 1-way 1-shot episodes and is used for any $N$ -way $K$ -shot inference. We set the task token dimensionality $C' = 128$ , and the loss balancing hyperparameter $\lambda = 0.1$ . + +Datasets. We report results on two standard FS-CS benchmarks [33], Pascal- $5^{i}$ [20,58] and COCO- $20^{i}$ [45,49]. Both datasets use 4-fold validation, where the folds $i \in \{0,1,2,3\}$ are created by splitting the 20 (resp. 80) classes into 4 mutually disjoint class sets, with 10K (resp. 100K) images per fold. For training and validation, support and query image pairs are sampled on the fly, as done in [33]. For each training episode, $N$ support classes are chosen randomly from + +
methodps-mask1-way 1-shot2-way 1-shotlearn.
classification 0/1 exact ratio (%)segmentation mIoU (%)classification 0/1 exact ratio (%)segmentation mIoU (%)params.
50515253avg.50515253avg.50515253avg.50515253avg.
HSNet [48]X84.584.860.885.378.920.023.516.216.619.170.867.036.570.161.111.023.415.417.017.72.6M
ASNet [33]X80.284.066.282.778.311.721.113.416.215.667.670.244.569.362.910.320.712.615.914.91.3M
CST (image)X83.980.765.982.778.311.920.715.016.316.072.665.343.269.562.611.920.515.016.615.70.4M
DINO [9]◇-----20.023.416.216.619.1-----12.812.910.09.911.40
CST✓84.082.270.882.679.935.838.928.929.233.274.367.249.067.864.635.736.026.829.131.90.4M
+ +Table 1. Comparing model performance on FS-CS when trained with image-level supervision on Pascal-5 $^i$ [58]. "ps-mask" refers to using pseudo-GT masks during training. Our CST model compares favourably to prior works on classification, and outperforms them on segmentation. Results for DINO [9] were generated without any training on Pascal-5 $^i$ (denoted by $\diamond$ ). See section 4.1 for details. + +
methodps-mask1-way 1-shot2-way 1-shot
cls. ERseg. mIoUclf. ERseg. mIoU
CST✘74.510.362.39.8
DINO [9]◇-12.1-7.4
CST✓78.219.662.418.3
+ +the split and $K$ images are chosen randomly from each of the $N$ target classes to construct an $N$ -way $K$ -shot support set. When a support image contains multiple classes, only one of them is set as its image class and the rest are set as background. While this introduces noise into support sets containing multi-class images, we find that it performs well in practice. A query image is also chosen randomly and may contain between 0 to $N$ of the target classes. The image-level label for the query is then constructed as an $N$ -dimensional binary vector containing 1 if the query contains the $n$ -th class, and 0 otherwise. Similarly, its pixel-level label is defined as an $(N + 1)$ -way segmentation mask, including background. For mixed-supervision learning, we sort the images in a training split by their image names and use pixel-level labels for the first e.g. $5\%$ of images, and only image-level labels for the remainder. This effectively randomizes the subset of images with full-supervision. + +Evaluation and metrics. We follow the established evaluation protocol for each FS-CS benchmark [33, 49, 58]. To evaluate multi-label classification, we use the $0/1$ exact match ratio [19], where an image is considered to be correctly classified if the binary label for each of the $N$ classes is correct. For semantic segmentation, we use mean IoU, $\mathrm{mIoU} = \frac{1}{R}\sum_{R}\mathrm{IoU}_{r}$ [58, 71], where $\mathrm{IoU}_r$ is the IoU of all images labeled with the $r_{\mathrm{th}}$ -class. The best model is chosen based on the highest validation mIoU averaged with 1000 random validation episodes. + +# 4.1. Results with image-level supervision + +Tables 1 and 2 compare the performance of our image-level-supervised CST with baseline methods. The only prior work that addresses this setting [33] generates a seg + +Table 2. Comparing model performance on FS-CS when trained with image-level supervision on COCO- $20^{i}$ [49], averaged over 4 folds. See section 4.1 for details. + +
% GT training set masks →0%2.5%5%10%100%
(a): pseudo-mask baseline33.241.443.544.5-
(b): (a) + mask enhancer-43.244.145.2-
(c): (b) + GT test set S masks-47.548.450.155.5
+ +Table 3. Comparing segmentation mIoU of CST on FS-CS with mixed supervision on Pascal-5 $^i$ , for different $\%$ of training set ground-truth masks, averaged over 4 folds. In (c), ground-truth masks were used for all support $(S)$ images during testing. + +mentation mask that is then globally average-pooled. The cross-entropy between the average-pooled prediction and the ground-truth image label is used as the objective function. We adopt this approach for [48], which did not address this setting, to construct another baseline, and we also evaluate CST in this setting, which we denote with $\mathbf{x}$ . The result for DINO is computed by evaluating segmentation masks that were generated as in [9] (denoted by $\diamond$ ), without using any training data from the target datasets. Our CST model, trained with pseudo-masks via self-distillation (denoted by $\checkmark$ ), performs comparably to prior work on classification and, because of the superior supervision provided by our pseudo-masks during training, outperforms these models on segmentation. In particular, CST achieves an over 100% improvement over ASNet [33] in both the 1-way 1-shot and 2-way 1-shot settings. We also note that training CST with pseudo-GT masks $(\checkmark)$ also improves classification performance by 1.6% (1-way 1-shot) and 2% (2-way 1-shot) on Pascal-5 when compared to training without $(\mathbf{x})$ . + +# 4.2. Results with mixed supervision + +To validate the effectiveness of the mixed-supervision setting, we vary the percentage of pixel-level annotated images used in training and present the results in Table 3. We observe that using just $5\%$ of GT masks is remarkably effective at improving performance, when compared to using $0\%$ (43.5% vs. 33.2%). The mask enhancer brings much improvement with fewer ground-truth segmentation masks. The effect of the mask enhancer is visually demonstrated in Fig. 4. We observe that the mask enhancer reduces foreground noise and often filters out objects irrelevant to a support image. Note that mixed-supervision learning assumes access to pixel-level annotations only during training. Dur + +
method1-way 1-shot2-way 1-shotlearn. +params.
classification 0/1 exact ratio (%)segmentation mIoU (%)classification 0/1 exact ratio (%)segmentation mIoU (%)
50515253avg.50515253avg.50515253avg.50515253avg.
PANet [71]69.967.768.869.469.032.845.831.035.136.256.247.544.655.450.933.346.031.238.437.2
PFENet [67]69.882.468.177.974.638.354.735.143.843.022.561.740.339.541.031.147.330.832.235.3
HSNet [48]86.684.876.986.383.749.159.741.049.049.768.073.257.070.967.342.453.734.043.943.5
ASNet [33]84.989.679.086.284.951.761.543.352.852.368.576.258.670.068.348.558.336.348.347.8
CST86.988.081.586.585.755.661.647.756.955.570.374.962.074.470.456.961.048.057.055.7
+ +Table 4. Comparing FS-CS models trained with pixel-level supervision on Pascal-5 ${}^{i}$ . + +
method1-way 1-shot2-way 1-shot
clf. ERseg. mIoUclf. ERseg. mIoU
PANet [71]66.725.248.523.6
PFENet [67]71.431.936.522.6
HSNet [48]77.034.362.529.5
ASNet [33]78.635.863.131.6
CST80.838.364.036.2
+ +![](images/ed773aa75609e23194fbf51cbb6d27401ff8f26b8508e5f35a48c51beafc5169.jpg) +Figure 5. Comparing performance on FS-CS with pixel-level supervision on $N$ -way 1-shot Pascal-5 $^i$ . + +ing testing, support images use pseudo-masks without (Table 3 (a)) or with (Table 3 (b)) mask enhancement. In (c), we use one-shot support GT mask during testing, but still use reduced amounts of GT masks in training. In this setting, the performance is only $5.4\% -8.0\%$ lower than the fully-supervised model, indicating that our approach allows for significant pixel-level annotation efficiency during training. + +# 4.3. Results with full, i.e. pixel-level, supervision + +Tables 4 and 5, as well as Fig. 5, compare our model's performance on FS-CS with state-of-the-art methods whose results, included here, were initially reported in [33]. CST achieves significant improvements over previous work, which we attribute to (i) our correlation tokens that leverage the localized semantics encoded in our self-supervised ViT backbone model; and (ii) the two task heads of our transformer (see ablations in Sec. 4.4). Figure 6 visually demonstrates qualitative examples of final segmentation predictions with increasing levels of supervision, from image-level to pixel-level. Image-level supervised predictions roughly segment out objects that correspond with the support classes, and the predictions become less noisy as more pixel-level supervision is used. + +Table 5. Comparing performance on FS-CS with pixel-level supervision on COCO-20i. + +
labels → archi. →class-sup. ViT [18]self-sup. CNN [27]self-sup. ViT [9]*self-sup. ViT [9]
seg. mIoU (%)6.920.715.633.2
+ +Table 6. FS-CS model comparison trained with image-level labels on 1-way 1-shot Pascal- $5^{j}$ by varying pseudo-mask generation models. Different columns denote model architectures for pseudolabeling and their pre-training supervision levels. The method * uses the final layer tokens from [9] for generating pseudo-labels. + +
clf. & seg. +prediction headssuperv. +level1-way 1-shot2-way 1-shot
clf. +ERseg. +mIoUclf. +ERseg. +mIoU
coupledimage78.532.959.531.9
decoupled (CST)image79.933.264.531.9
coupledpixel84.354.267.053.0
decoupled (CST)pixel85.755.570.555.7
+ +Table 7. Ablation study of coupling or decoupling classification and segmentation prediction heads for FS-CS on Pascal-5 $^i$ . + +# 4.4. Ablation study + +Pseudo-labeling with different models. We explore other learning-free pseudo-labeling methods by using alternative pre-trained feature extractors to generate pseudo-GT masks. Rather than self-distillation, where we train CST with pseudo-GT masks generated from its own self-supervised DINO ViT backbone, in these experiments we train CST with pseudo-GT masks generated from class-supervised ViT [18], self-supervised DINO ResNet50 [27], or the output layer tokens from the self-supervised DINO ViT [9]. As ResNets do not have class tokens, we apply global-average pooling on the support feature map from the last ResNet layer and use the pooled feature as a class token for generating the pseudo-GT masks. As seen in Table 6, pseudo-GT masks generated from alternative feature extractors do not perform as well as the intermediate attention maps from DINO. We qualitatively observed that the alternatives' less accurate pseudo-masks lead to lower segmentation accuracy when used in pseudo-supervised learning: the self-supervised ResNet50 produces pseudo-masks with indistinct object boundaries, while the class-supervised ViT produces noisy patches throughout the pseudo-mask (as was + +![](images/205ac74edb80f691925641215594c10f4ca84473c366f4c9c9f2e263dff94c83.jpg) +Figure 6. 2-way 1-shot segmentation examples from CST trained with image-level, mixed, and pixel-level supervision. Note that image-level-supervised and mixed-supervised models do not have access to ground-truth support masks. In both cases, the model is still effective. + +![](images/a1cd7409b8a459b70104bc613f0272ecee8c1f8ac89fff887cd65aff0d85056f.jpg) +Figure 7. An example of channel-averaged $\mathbf{C}_{\mathrm{clf}}$ , $\mathbf{C}_{\mathrm{seg}}$ . Each task token tends to capture different aspects, e.g., clearer edges of $\mathbf{C}_{\mathrm{seg}}$ . + +
method1-way 1-shot1-way 5-shot# learn. +params.
mIoUFBIoUmIoUFBIoU
RPMM [83]30.6-35.5-38.6M
RePRI [6]34.0-42.1--
SSP [21]37.4-44.1-8.7M
MMNet [79]37.5-38.2-10.4M
MLC [84]33.9-40.6-8.7M
NTRENet [47]39.368.540.369.2-
CMN [81]39.361.743.163.3-
HSNet [48]39.268.246.970.72.6M
DACM [82]40.668.948.171.6-
ASNet [33]42.268.847.971.61.3M
CST44.070.348.773.70.4M
+ +Table 8. Comparing FS-S models trained with pixel-level supervision on COCO-20i. + +similarly observed in [9]). + +Effect of decoupled task heads. Table 7 compares the impact of coupling and decoupling the classification and segmentation task heads. The coupled architecture has a single segmentation task head, and the image is classified with the foreground class if any pixels are predicted as foreground, and is otherwise classified as the background class. Having separate heads for each task benefits both tasks in both the image-level and pixel-level supervision settings. A similar observation was made for object detection [64] when decoupling localization from classification. Figure 7 visualizes an example of channel-averaged $\mathbf{C}_{\mathrm{clf}}$ and $\mathbf{C}_{\mathrm{seg}}$ tensors. We observe that these two intermediate representations tend to highlight different areas; $\mathbf{C}_{\mathrm{clf}}$ has large responses in highly-localized class-specific image regions, while $\mathbf{C}_{\mathrm{seg}}$ better distinguishes the overall object support and boundaries. + +Comparison on FS-S. In Table 8, CST is also evaluated in the conventional FS-S setting [58, 71], i.e., binary segmentation using mask supervision, and compared with previous works that use different ResNet50-based architectures. FS-S is equivalent to FS-CS with the precondition that a query and a support always share a class label; classification is not required. We train CST on this setting and find that it achieves state-of-the-art segmentation performance. It is also worth noting that it achieves this with fewer learned parameters than others, which is also the case for the comparisons in Table 1 and Table 4. Our small number of learned parameters may help to avoid overfitting. + +# 5. Conclusion + +In this work, we propose an approach to generating effective pseudo-GT masks for few-shot classification and segmentation (FS-CS) using the localized semantics encoded in the tokens of self-supervised vision transformers. We show that using these pseudo-GT masks, sometimes combined with a small number of GT masks, we can train effective FS-CS models. Our work is the first to explore this practical weakly-supervised FS-CS setting, which drastically reduces the amount of expensive pixel-level annotations needed for training and deployment. Extensive experiments show that our approach achieves significant performance gains when compared to state-of-the-art methods in a variety of supervision settings, on two FS-CS benchmarks. + +Acknowledgements. 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Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 550, + 287, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 550, + 287, + 694 + ], + "spans": [ + { + "bbox": [ + 46, + 550, + 287, + 694 + ], + "type": "text", + "content": "Few-shot learning [22, 23, 77] is the problem of learning to perform a prediction task using only a small number of examples (i.e. supports) of the completed task, typically in the range of 1-10 examples. This problem setting is appealing for applications where large amounts of annotated data are expensive or impractical to collect. In computer vision, few-shot learning has been actively studied for image classification [24, 36, 46, 66, 70, 85] and semantic segmentation [17, 58, 61, 88, 89]. In this work, we focus on the combined task of few-shot classification and segmentation (FS-CS) [33], which aims to jointly predict (i) the presence of each support class, i.e., multi-label classification, and (ii)" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 309, + 216, + 545, + 384 + ], + "blocks": [ + { + "bbox": [ + 309, + 216, + 545, + 384 + ], + "lines": [ + { + "bbox": [ + 309, + 216, + 545, + 384 + ], + "spans": [ + { + "bbox": [ + 309, + 216, + 545, + 384 + ], + "type": "image", + "image_path": "bb27f4b8af88c0dce2e78ee4f1ca87b9d4d4a73f8ea0197be7c202e00db80057.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 392, + 546, + 426 + ], + "lines": [ + { + "bbox": [ + 305, + 392, + 546, + 426 + ], + "spans": [ + { + "bbox": [ + 305, + 392, + 546, + 426 + ], + "type": "text", + "content": "Figure 1. Weakly-supervised few-shot classification and segmentation. In this paper, we explore training few-shot models using little-to-no ground-truth segmentation masks." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 434, + 459, + 446 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 434, + 459, + 446 + ], + "spans": [ + { + "bbox": [ + 306, + 434, + 459, + 446 + ], + "type": "text", + "content": "its pixel-level semantic segmentation." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 448, + 546, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 448, + 546, + 675 + ], + "spans": [ + { + "bbox": [ + 304, + 448, + 546, + 675 + ], + "type": "text", + "content": "Few-shot learners are typically trained either by meta-learning [24, 56, 63, 71] or by transfer learning with fine-tuning [11, 12, 16]. Both these paradigms commonly assume the availability of a large-scale and fully-annotated training dataset. For FS-CS, we need Ground-Truth (GT) segmentation masks for query and support images during training. We also need these GT masks for support images during testing. A natural alternative to collecting such expensive segmentation masks would be to instead employ a weaker supervision, e.g. image-level [52, 59] or box-level labels [13, 30], for learning, i.e., to adopt a weakly-supervised learning approach [5, 41, 43, 51]. Compared to conventional weakly-supervised learning however, weakly-supervised few-shot learning has rarely been explored in the literature and is significantly more challenging. This is because in few-shot learning, object classes are completely disjoint between training and testing, resulting in models which are susceptible to severe over-fitting to the classes seen during training." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 677, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 715 + ], + "type": "text", + "content": "In this work we tackle this challenging scenario, addressing weakly-supervised FS-CS where only image-level labels, i.e. class labels, are available (cf. Fig. 1). Inspired by" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 195, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 195, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 195, + 712 + ], + "type": "text", + "content": "*Work done during an internship at FAIR." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19627" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "content": "recent work by Caron et al. [9], which showed that pixel-level semantic attention emerges from self-supervised vision transformers (ViTs) [18], we leverage attention maps from a frozen self-supervised ViT to generate pseudo-GT segmentation masks. We train an FS-CS learner on top of the frozen ViT using the generated pseudo-GT masks as pixel-level supervision. The FS-CS learner is a small transformer network that takes features from the ViT as input and is trained to predict the pseudo-GT masks. Our complete model thus learns to segment using its own intermediate byproduct, with no segmentation labeling cost, in a form of distillation [2, 28, 91, 94] between layers within a model." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 217, + 289, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 217, + 289, + 326 + ], + "spans": [ + { + "bbox": [ + 46, + 217, + 289, + 326 + ], + "type": "text", + "content": "We also explore a practical training setting where a limited number of training images have both image-level and pixel-level annotations, while the remaining images have only image-level labels. For this mixed-supervised setting, we propose to train an auxiliary mask enhancer that refines attention maps into pseudo-GT masks. The enhancer is supervised using the small number of available GT masks and is used to generate the final pseudo-GT masks for the training images that do not have GT masks." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 326, + 289, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 326, + 289, + 518 + ], + "spans": [ + { + "bbox": [ + 46, + 326, + 289, + 518 + ], + "type": "text", + "content": "Lastly, to effectively address this weakly-supervised FS-CS task, we propose a Classification-Segmentation Transformer (CST) architecture. CST takes as input ViT tokens for query and support images, computes correlations between them, and then predicts classification and segmentation outputs through separate task heads; the classification head is trained with class labels while the segmentation head is trained with either GT masks or pseudo-GT masks, depending on availability. Unlike prior work using ViTs that generate prediction for a single task using either the class token [18, 74] or image tokens [50, 65], CST uses each of them for each task prediction, which proves advantageous for both tasks. CST achieves moderate-to-large performance gains for FS-CS on all three supervision levels (image-level-, mixed-level, and pixel-level), when compared to prior state-of-the-art methods." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 519, + 206, + 531 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 519, + 206, + 531 + ], + "spans": [ + { + "bbox": [ + 59, + 519, + 206, + 531 + ], + "type": "text", + "content": "Our contributions are the following:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 48, + 543, + 287, + 714 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 53, + 543, + 287, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 543, + 287, + 591 + ], + "spans": [ + { + "bbox": [ + 53, + 543, + 287, + 591 + ], + "type": "text", + "content": "i. We introduce a powerful baseline for few-shot classification and segmentation (FS-CS) using only image-level supervision, which leverages localized semantic information encoded in self-supervised ViTs [9]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 51, + 604, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 604, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 51, + 604, + 287, + 653 + ], + "type": "text", + "content": "ii. We propose a learning setup for FS-CS with mixed supervision, and present an auxiliary mask enhancer to improve performance compared to image-level supervision only." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 48, + 665, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 665, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 48, + 665, + 287, + 714 + ], + "type": "text", + "content": "iii. We design Classification-Segmentation Transformer, and a multi-task learning objective of classification and segmentation, which is beneficial for both tasks, and allows for flexibly tuning the degree of supervision." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 71, + 390, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 71, + 390, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 390, + 84 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 92, + 547, + 345 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 92, + 547, + 345 + ], + "spans": [ + { + "bbox": [ + 304, + 92, + 547, + 345 + ], + "type": "text", + "content": "Few-shot classification and segmentation. This paper tackles the recently proposed task of few-shot classification and segmentation (FS-CS) [33], which generalizes and combines the conventional few-shot classification (FS-C) [11, 24, 34, 63, 70] and few-shot segmentation (FS-S) [58, 71, 89] tasks. FS-C assumes that a query contains only one of the support classes, while FS-S assumes that the query always contains all of them. In contrast, FS-CS breaks the assumption that a query image contains one class (or all classes) from the support set. As a result, FS-CS models must predict i) the presence or absence of each support class in the query; and ii) pixel-level segmentation masks. Our work explores a more challenging weakly-supervised version of FS-CS with image-level annotations but few or no pixel-level annotations. Prior work on weakly-supervised FS-S used supervision such as language [40, 60] or bounding boxes [55]. Our work does not adopt any extra modalities and uses weaker (image-level) supervision than bounding boxes. Other applications of few-shot learning include few-shot object detection [92, 93], action recognition [72, 73], and metric learning [32]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 349, + 547, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 349, + 547, + 553 + ], + "spans": [ + { + "bbox": [ + 304, + 349, + 547, + 553 + ], + "type": "text", + "content": "Weakly-supervised segmentation. A common paradigm for weakly-supervised semantic segmentation uses class labels [1,39] to generate pseudo-GT masks from class activation maps (CAM) [57, 95], followed by pseudo-supervised training [37, 96, 99]. CAM requires a classification backbone pre-trained from many examples on seen classes whereas, in our few-shot setting, we devise a pseudo-GT mask generation method that requires only a small number of examples, and can handle unseen classes. We also investigate the extent to which a pseudo-mask enhancement module, trained using a small amount of GT masks, can generate better pseudo-GT masks. While such \"mixed-supervision\" learning has been called semi-weakly-supervised segmentation [4, 38, 42, 75] and studied in the standard seen-class many-shot learning paradigm, our work is the first to propose mixed-supervision learning for few-shot semantic segmentation, to the best of our knowledge." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 557, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 547, + 715 + ], + "type": "text", + "content": "Self-supervised learning. Self-supervised learning [31] has proven highly effective for learning powerful representations for downstream tasks [7-10, 80, 97]. One popular approach [9, 25] trains a model to map an image and its augmented views to nearby coordinates in a representation space. This class-agnostic objective trains the model to capture view-invariant semantics that transcend designated image categories. In addition, DINO-trained ViTs [9] capture localized semantics in the learned token representations. In this work, we leverage these representations to create attention map-based pseudo-GT masks for weakly-supervised FS-CS, using a novel and efficient self-distillation approach. The representations have also ben" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "19628" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 72, + 547, + 274 + ], + "blocks": [ + { + "bbox": [ + 48, + 72, + 547, + 274 + ], + "lines": [ + { + "bbox": [ + 48, + 72, + 547, + 274 + ], + "spans": [ + { + "bbox": [ + 48, + 72, + 547, + 274 + ], + "type": "image", + "image_path": "5240162eddae44e78dff6e8d41d2a3b9fba4959e3c7407fc9ca2492daba83c9d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 282, + 547, + 316 + ], + "lines": [ + { + "bbox": [ + 46, + 282, + 547, + 316 + ], + "spans": [ + { + "bbox": [ + 46, + 282, + 547, + 316 + ], + "type": "text", + "content": "Figure 2. Classification-Segmentation Transformer. A query and a support image pass through a frozen DINO ViT to extract class and images tokens, which are cross-correlated to form correlation tokens. The correlation tokens are then fed to a correlation transformer and transform to task tokens. At the end, each classification and segmentation head takes each task token map and predicts each task." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 325, + 288, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 325, + 288, + 361 + ], + "spans": [ + { + "bbox": [ + 46, + 325, + 288, + 361 + ], + "type": "text", + "content": "efited several other dense prediction tasks, including unsupervised object discovery [62, 76] and unsupervised image/video segmentation [9, 86, 87, 98]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 374, + 287, + 401 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 374, + 287, + 401 + ], + "spans": [ + { + "bbox": [ + 47, + 374, + 287, + 401 + ], + "type": "text", + "content": "3. Weakly-supervised few-shot classification and segmentation" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 409, + 287, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 409, + 287, + 624 + ], + "spans": [ + { + "bbox": [ + 46, + 409, + 287, + 624 + ], + "type": "text", + "content": "In this paper we tackle few-shot classification and segmentation (FS-CS) [33]. Given a small number " + }, + { + "bbox": [ + 46, + 409, + 287, + 624 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 409, + 287, + 624 + ], + "type": "text", + "content": " of labeled support images for each of " + }, + { + "bbox": [ + 46, + 409, + 287, + 624 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 409, + 287, + 624 + ], + "type": "text", + "content": " classes, an FS-CS model is trained to i) identify the presence of each class in a query image and ii) segment the associated pixels. This setting is conventionally called an " + }, + { + "bbox": [ + 46, + 409, + 287, + 624 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 409, + 287, + 624 + ], + "type": "text", + "content": "-way " + }, + { + "bbox": [ + 46, + 409, + 287, + 624 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 409, + 287, + 624 + ], + "type": "text", + "content": "-shot episode [53, 70]. We adopt a meta-learning approach [29, 63, 70] to train our model, where an annotated training dataset (with a class set disjoint from the test set classes) is used to generate a sequence of " + }, + { + "bbox": [ + 46, + 409, + 287, + 624 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 409, + 287, + 624 + ], + "type": "text", + "content": "-way " + }, + { + "bbox": [ + 46, + 409, + 287, + 624 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 409, + 287, + 624 + ], + "type": "text", + "content": "-shot episodes. In our setting, annotations consist of class labels and segmentation masks. When ground-truth segmentation masks are available for all support and query images during training, we refer to this as pixel-level supervision. When only class labels are available we refer to this as image-level supervision. When ground-truth segmentation masks are available for only a small percentage of training images, we refer to this as mixed supervision." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 625, + 287, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 625, + 287, + 684 + ], + "spans": [ + { + "bbox": [ + 46, + 625, + 287, + 684 + ], + "type": "text", + "content": "In the remainder of this section, we first introduce our base model architecture, which we call Classification-Segmentation Transformer (CST), and then describe training paradigms for the different levels of supervision mentioned above." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 324, + 518, + 337 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 324, + 518, + 337 + ], + "spans": [ + { + "bbox": [ + 306, + 324, + 518, + 337 + ], + "type": "text", + "content": "3.1. Classification-Segmentation transformer" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 343, + 545, + 440 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 343, + 545, + 440 + ], + "spans": [ + { + "bbox": [ + 304, + 343, + 545, + 440 + ], + "type": "text", + "content": "Our Classification-Segmentation Transformer (CST) architecture first computes the cross-correlation of DINO ViT [9,18] tokens between support and query image pairs. It then generates two new sets of tokens which serve as input to the classification and segmentation prediction heads respectively. The objective function then combines the losses from each task head. The details of CST's architecture are shown in Fig. 2 and described in the following paragraphs." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 443, + 546, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 443, + 546, + 598 + ], + "spans": [ + { + "bbox": [ + 304, + 443, + 546, + 598 + ], + "type": "text", + "content": "Correlation tokens. We use a frozen ViT architecture pretrained with DINO as a backbone, which takes as input an image and produces " + }, + { + "bbox": [ + 304, + 443, + 546, + 598 + ], + "type": "inline_equation", + "content": "T = HW" + }, + { + "bbox": [ + 304, + 443, + 546, + 598 + ], + "type": "text", + "content": " image (patch) tokens " + }, + { + "bbox": [ + 304, + 443, + 546, + 598 + ], + "type": "inline_equation", + "content": "\\mathbf{F} \\in \\mathbb{R}^{C \\times T}" + }, + { + "bbox": [ + 304, + 443, + 546, + 598 + ], + "type": "text", + "content": " and one class token " + }, + { + "bbox": [ + 304, + 443, + 546, + 598 + ], + "type": "inline_equation", + "content": "\\mathbf{h} \\in \\mathbb{R}^C" + }, + { + "bbox": [ + 304, + 443, + 546, + 598 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 443, + 546, + 598 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 443, + 546, + 598 + ], + "type": "text", + "content": " denotes the token feature dimensionality. The terms \"image\" and \"class\" tokens are used in analogous fashion to previous work [9, 15, 18, 68]. The backbone first transforms a query image " + }, + { + "bbox": [ + 304, + 443, + 546, + 598 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 304, + 443, + 546, + 598 + ], + "type": "text", + "content": " and a support image " + }, + { + "bbox": [ + 304, + 443, + 546, + 598 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 443, + 546, + 598 + ], + "type": "text", + "content": " into two sets of tokens, " + }, + { + "bbox": [ + 304, + 443, + 546, + 598 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{F_q}, \\mathbf{h_q}\\}" + }, + { + "bbox": [ + 304, + 443, + 546, + 598 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 443, + 546, + 598 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{F_s}, \\mathbf{h_s}\\}" + }, + { + "bbox": [ + 304, + 443, + 546, + 598 + ], + "type": "text", + "content": ". The query image tokens " + }, + { + "bbox": [ + 304, + 443, + 546, + 598 + ], + "type": "inline_equation", + "content": "\\mathbf{F_q}" + }, + { + "bbox": [ + 304, + 443, + 546, + 598 + ], + "type": "text", + "content": " are cross-correlated, by cosine similarity, with the support class token " + }, + { + "bbox": [ + 304, + 443, + 546, + 598 + ], + "type": "inline_equation", + "content": "\\mathbf{h_s}" + }, + { + "bbox": [ + 304, + 443, + 546, + 598 + ], + "type": "text", + "content": " and the support image tokens " + }, + { + "bbox": [ + 304, + 443, + 546, + 598 + ], + "type": "inline_equation", + "content": "\\mathbf{F_s}" + }, + { + "bbox": [ + 304, + 443, + 546, + 598 + ], + "type": "text", + "content": ", to generate a set of correlation tokens " + }, + { + "bbox": [ + 304, + 443, + 546, + 598 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_{\\mathrm{cls}} \\in \\mathbb{R}^{T_{\\mathrm{q}}}" + }, + { + "bbox": [ + 304, + 443, + 546, + 598 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 443, + 546, + 598 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_{\\mathrm{img}} \\in \\mathbb{R}^{T_{\\mathrm{q}} \\times T_{\\mathrm{s}}}" + }, + { + "bbox": [ + 304, + 443, + 546, + 598 + ], + "type": "text", + "content": " respectively:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 369, + 599, + 545, + 616 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 369, + 599, + 545, + 616 + ], + "spans": [ + { + "bbox": [ + 369, + 599, + 545, + 616 + ], + "type": "interline_equation", + "content": "\\mathbf {c} _ {\\mathrm {c l s}} = \\overline {{\\mathbf {F}}} _ {\\mathrm {q}} ^ {\\top} \\overline {{\\mathbf {h}}} _ {\\mathrm {s}}, \\quad \\mathbf {C} _ {\\mathrm {i m g}} = \\overline {{\\mathbf {F}}} _ {\\mathrm {q}} ^ {\\top} \\overline {{\\mathbf {F}}} _ {\\mathrm {s}}, \\tag {1}", + "image_path": "96ee98fc0f8e8d87e95f0b14aa5bfe69c12739d7437dd1c2a551c8dd46bb51d7.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 623, + 545, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 623, + 545, + 684 + ], + "spans": [ + { + "bbox": [ + 304, + 623, + 545, + 684 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 623, + 545, + 684 + ], + "type": "inline_equation", + "content": "\\overline{\\mathbf{F}}" + }, + { + "bbox": [ + 304, + 623, + 545, + 684 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 623, + 545, + 684 + ], + "type": "inline_equation", + "content": "\\overline{\\mathbf{h}}" + }, + { + "bbox": [ + 304, + 623, + 545, + 684 + ], + "type": "text", + "content": " denote l2-normalized tokens. We retain the semantic diversity of the " + }, + { + "bbox": [ + 304, + 623, + 545, + 684 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 623, + 545, + 684 + ], + "type": "text", + "content": " heads of the ViT backbone by computing " + }, + { + "bbox": [ + 304, + 623, + 545, + 684 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 623, + 545, + 684 + ], + "type": "text", + "content": " separate correlation tokens. In addition, prior work [26, 44] has demonstrated the value of incorporating multi-layer semantics. Similarly, we compute correlation" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 47, + 693, + 287, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 287, + 713 + ], + "type": "text", + "content": "1Note that the terms, meta-training and meta-testing, are used interchangeably with training and testing in this paper." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 693, + 545, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 545, + 712 + ], + "type": "text", + "content": "2The cosine similarity between two vectors is the uncentered Pearson correlation coefficient." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19629" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": "tokens for each of the " + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": " transformer layers of the ViT. In all, we compute " + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "inline_equation", + "content": "ML" + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": " different sets of correlation tokens and concatenate them along a new dimension to generate:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 97, + 112, + 287, + 129 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 112, + 287, + 129 + ], + "spans": [ + { + "bbox": [ + 97, + 112, + 287, + 129 + ], + "type": "interline_equation", + "content": "\\mathbf {c} _ {\\mathrm {c l s}} ^ {\\prime} \\in \\mathbb {R} ^ {T _ {\\mathrm {q}} \\times M L}, \\quad \\mathbf {C} _ {\\mathrm {i m g}} ^ {\\prime} \\in \\mathbb {R} ^ {T _ {\\mathrm {q}} \\times T _ {\\mathrm {s}} \\times M L}. \\tag {2}", + "image_path": "ec0275aae8af12d1ebca94130914e3b4b6035c11bed0964c0fc4eaf89d1407f9.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 133, + 287, + 233 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 133, + 287, + 233 + ], + "spans": [ + { + "bbox": [ + 46, + 133, + 287, + 233 + ], + "type": "text", + "content": "Correlation transformer. We first concatenate " + }, + { + "bbox": [ + 46, + 133, + 287, + 233 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_{\\mathrm{cls},i}^{\\prime}\\in \\mathbb{R}^{ML}" + }, + { + "bbox": [ + 46, + 133, + 287, + 233 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 133, + 287, + 233 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_{\\mathrm{img},i}^{\\prime}\\in \\mathbb{R}^{T_{\\mathrm{s}}\\times ML}" + }, + { + "bbox": [ + 46, + 133, + 287, + 233 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 133, + 287, + 233 + ], + "type": "inline_equation", + "content": "i\\in [1,\\dots ,T_{\\mathrm{q}}]" + }, + { + "bbox": [ + 46, + 133, + 287, + 233 + ], + "type": "text", + "content": " is an index over the query image tokens, to produce " + }, + { + "bbox": [ + 46, + 133, + 287, + 233 + ], + "type": "inline_equation", + "content": "\\mathbf{Z}_{0,i}\\in \\mathbb{R}^{(1 + T_{\\mathrm{s}})\\times ML}" + }, + { + "bbox": [ + 46, + 133, + 287, + 233 + ], + "type": "text", + "content": ". Our correlation transformer is a 2-layer transformer [69] that takes " + }, + { + "bbox": [ + 46, + 133, + 287, + 233 + ], + "type": "inline_equation", + "content": "\\mathbf{Z}_{0,i}" + }, + { + "bbox": [ + 46, + 133, + 287, + 233 + ], + "type": "text", + "content": " and a segmentation mask label for the support image " + }, + { + "bbox": [ + 46, + 133, + 287, + 233 + ], + "type": "inline_equation", + "content": "(\\mathbf{M}_{\\mathrm{gt}}\\in \\{0,1\\}^{T_{\\mathrm{s}}})" + }, + { + "bbox": [ + 46, + 133, + 287, + 233 + ], + "type": "text", + "content": " as input, and returns two tokens - a classification task token and a segmentation task token - for query image token " + }, + { + "bbox": [ + 46, + 133, + 287, + 233 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 133, + 287, + 233 + ], + "type": "text", + "content": ". Each layer has the following form:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 94, + 250, + 287, + 264 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 250, + 287, + 264 + ], + "spans": [ + { + "bbox": [ + 94, + 250, + 287, + 264 + ], + "type": "interline_equation", + "content": "\\mathbf {Z} _ {j, i} ^ {\\prime} = \\operatorname {N o r m} _ {j} ^ {\\prime} \\left(\\mathrm {M S A} _ {j} \\left(\\mathbf {Z} _ {j, i}, \\mathbf {M} _ {\\mathrm {g t}}\\right) + \\mathbf {Z} _ {j, i}\\right), \\tag {3}", + "image_path": "b8e1cb2b9974ca7cf96817b1adfdfea9e3f70d76ffad03a475a3da3344a51c48.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 86, + 266, + 287, + 281 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 266, + 287, + 281 + ], + "spans": [ + { + "bbox": [ + 86, + 266, + 287, + 281 + ], + "type": "interline_equation", + "content": "\\mathbf {Z} _ {j + 1, i} = \\operatorname {N o r m} _ {j} \\left(\\mathrm {M L P} _ {j} \\left(\\mathbf {Z} _ {j, i} ^ {\\prime}\\right) + \\mathbf {Z} _ {j, i} ^ {\\prime}\\right), \\tag {4}", + "image_path": "064597f5dba0388b99c7569b48f8b03caafd70e446221dfad65171a44f49c925.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 285, + 287, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 285, + 287, + 525 + ], + "spans": [ + { + "bbox": [ + 46, + 285, + 287, + 525 + ], + "type": "text", + "content": "where MSA, Norm, and MLP correspond to a multi-head self-attention, a group normalization [78], and a linear layer, respectively, and " + }, + { + "bbox": [ + 46, + 285, + 287, + 525 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 285, + 287, + 525 + ], + "type": "text", + "content": " denotes the transformer layer index. Additionally, in each MSA layer, the generated query embeddings " + }, + { + "bbox": [ + 46, + 285, + 287, + 525 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}" + }, + { + "bbox": [ + 46, + 285, + 287, + 525 + ], + "type": "text", + "content": " are spatially pooled (using a " + }, + { + "bbox": [ + 46, + 285, + 287, + 525 + ], + "type": "inline_equation", + "content": "4\\times 4" + }, + { + "bbox": [ + 46, + 285, + 287, + 525 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 285, + 287, + 525 + ], + "type": "inline_equation", + "content": "3\\times 3" + }, + { + "bbox": [ + 46, + 285, + 287, + 525 + ], + "type": "text", + "content": " kernel in layers 1 and 2 respectively) by reshaping " + }, + { + "bbox": [ + 46, + 285, + 287, + 525 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}" + }, + { + "bbox": [ + 46, + 285, + 287, + 525 + ], + "type": "text", + "content": " to recover its " + }, + { + "bbox": [ + 46, + 285, + 287, + 525 + ], + "type": "inline_equation", + "content": "H_{\\mathrm{s}},W_{\\mathrm{s}}" + }, + { + "bbox": [ + 46, + 285, + 287, + 525 + ], + "type": "text", + "content": " dimensions, applying spatial pooling, and flattening the output. This progressively reduces the number of image tokens, collapsing the input spatial size from " + }, + { + "bbox": [ + 46, + 285, + 287, + 525 + ], + "type": "inline_equation", + "content": "T_{\\mathrm{s}} = 12\\times 12" + }, + { + "bbox": [ + 46, + 285, + 287, + 525 + ], + "type": "text", + "content": " to 1. This spatial pooling, illustrated in Fig. 2, reduces memory consumption, similarly to [14]. The output of the correlation transformer is then " + }, + { + "bbox": [ + 46, + 285, + 287, + 525 + ], + "type": "inline_equation", + "content": "\\mathbf{Z}_{2,i}\\in \\mathbb{R}^{2\\times C'}" + }, + { + "bbox": [ + 46, + 285, + 287, + 525 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 285, + 287, + 525 + ], + "type": "inline_equation", + "content": "C^\\prime" + }, + { + "bbox": [ + 46, + 285, + 287, + 525 + ], + "type": "text", + "content": " denotes the new token dimensionality after MLP projection. This process is broadcast over the correlation tokens " + }, + { + "bbox": [ + 46, + 285, + 287, + 525 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_{\\mathrm{img},i}^{\\prime}" + }, + { + "bbox": [ + 46, + 285, + 287, + 525 + ], + "type": "text", + "content": " for each query image token " + }, + { + "bbox": [ + 46, + 285, + 287, + 525 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 285, + 287, + 525 + ], + "type": "text", + "content": ", resulting in " + }, + { + "bbox": [ + 46, + 285, + 287, + 525 + ], + "type": "inline_equation", + "content": "\\mathbf{Z}_2\\in \\mathbb{R}^{T_{\\mathrm{q}}\\times 2\\times C'}" + }, + { + "bbox": [ + 46, + 285, + 287, + 525 + ], + "type": "text", + "content": ". We then split this tensor, along the second dimension, into classification and segmentation tokens " + }, + { + "bbox": [ + 46, + 285, + 287, + 525 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_{\\mathrm{clf}},\\mathbf{C}_{\\mathrm{seg}}\\in \\mathbb{R}^{T_{\\mathrm{q}}\\times C'}" + }, + { + "bbox": [ + 46, + 285, + 287, + 525 + ], + "type": "text", + "content": ". Lastly, " + }, + { + "bbox": [ + 46, + 285, + 287, + 525 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_{\\mathrm{clf}}" + }, + { + "bbox": [ + 46, + 285, + 287, + 525 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 285, + 287, + 525 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_{\\mathrm{seg}}" + }, + { + "bbox": [ + 46, + 285, + 287, + 525 + ], + "type": "text", + "content": " are reshaped into spatial dimensions as " + }, + { + "bbox": [ + 46, + 285, + 287, + 525 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_{\\mathrm{clf}},\\mathbf{C}_{\\mathrm{seg}}\\in \\mathbb{R}^{H_{\\mathrm{q}}\\times W_{\\mathrm{q}}\\times C'}" + }, + { + "bbox": [ + 46, + 285, + 287, + 525 + ], + "type": "text", + "content": " and then fed to their respective task heads, described next." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 528, + 287, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 528, + 287, + 612 + ], + "spans": [ + { + "bbox": [ + 46, + 528, + 287, + 612 + ], + "type": "text", + "content": "Classification and segmentation heads. The classification head consists of two " + }, + { + "bbox": [ + 46, + 528, + 287, + 612 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 46, + 528, + 287, + 612 + ], + "type": "text", + "content": " convolutions followed by global average pooling, and estimates the class presence probability " + }, + { + "bbox": [ + 46, + 528, + 287, + 612 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_{\\mathrm{clf}}" + }, + { + "bbox": [ + 46, + 528, + 287, + 612 + ], + "type": "text", + "content": " of the query image corresponding to the support image class. The segmentation head consists of two " + }, + { + "bbox": [ + 46, + 528, + 287, + 612 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 46, + 528, + 287, + 612 + ], + "type": "text", + "content": " convolutions followed by bilinear interpolation to the original query image size and predicts a segmentation map " + }, + { + "bbox": [ + 46, + 528, + 287, + 612 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}_{\\mathrm{seg}}" + }, + { + "bbox": [ + 46, + 528, + 287, + 612 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 614, + 287, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 614, + 287, + 661 + ], + "spans": [ + { + "bbox": [ + 46, + 614, + 287, + 661 + ], + "type": "text", + "content": "Learning objective. Given predictions from the task heads, the classification and segmentation losses are computed as the cross-entropy between the prediction and the ground-truth for each task:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 91, + 668, + 287, + 681 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 668, + 287, + 681 + ], + "spans": [ + { + "bbox": [ + 91, + 668, + 287, + 681 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {c l f}} = - \\mathbf {y} _ {\\mathrm {g t}} \\log \\mathbf {y} _ {\\mathrm {c l f}}, \\tag {5}", + "image_path": "d88e32324d147313e5722bc0bc30475c87218f2a2c04a85eb5bdd3976c0647df.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 89, + 682, + 287, + 710 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 89, + 682, + 287, + 710 + ], + "spans": [ + { + "bbox": [ + 89, + 682, + 287, + 710 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {s e g}} = - \\frac {1}{H W} \\sum_ {\\mathbf {x} \\in [ H ] \\times [ W ]} \\mathbf {Y} _ {\\mathrm {g t}} (\\mathbf {x}) \\log \\mathbf {Y} _ {\\mathrm {s e g}} (\\mathbf {x}), \\tag {6}", + "image_path": "c7b5e18c83765b1532d8ed995b4473d74eba6362f5f0f0d5dcd124ea2604e3f2.jpg" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 307, + 72, + 545, + 164 + ], + "blocks": [ + { + "bbox": [ + 307, + 72, + 545, + 164 + ], + "lines": [ + { + "bbox": [ + 307, + 72, + 545, + 164 + ], + "spans": [ + { + "bbox": [ + 307, + 72, + 545, + 164 + ], + "type": "image", + "image_path": "d319c42048644019db331b1a53c2cd7b43df03da8f39f751d1a37f0223293ec2.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 174, + 545, + 229 + ], + "lines": [ + { + "bbox": [ + 304, + 174, + 545, + 229 + ], + "spans": [ + { + "bbox": [ + 304, + 174, + 545, + 229 + ], + "type": "text", + "content": "Figure 3. a) Image-level-supervision learners generate pseudo-GT masks by averaging multi-head cross-(self-) attention followed by thresholding (Sec. 3.2). b) Mixed-supervision learners first pre-train a mask enhancer with a few GT masks during training to enhance the pseudo-GT mask quality (Sec. 3.3)." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 236, + 545, + 284 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 236, + 545, + 284 + ], + "spans": [ + { + "bbox": [ + 305, + 236, + 545, + 284 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 236, + 545, + 284 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_{\\mathrm{gt}} \\in \\{0,1\\}" + }, + { + "bbox": [ + 305, + 236, + 545, + 284 + ], + "type": "text", + "content": " is the image-level ground-truth label and " + }, + { + "bbox": [ + 305, + 236, + 545, + 284 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}_{\\mathrm{gt}}(\\mathbf{x}) \\in \\{0,1\\}" + }, + { + "bbox": [ + 305, + 236, + 545, + 284 + ], + "type": "text", + "content": " is the ground-truth label for each pixel " + }, + { + "bbox": [ + 305, + 236, + 545, + 284 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 305, + 236, + 545, + 284 + ], + "type": "text", + "content": ". The final learning loss combines the two losses so that the model learns both tasks jointly:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 389, + 294, + 545, + 306 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 389, + 294, + 545, + 306 + ], + "spans": [ + { + "bbox": [ + 389, + 294, + 545, + 306 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\lambda \\mathcal {L} _ {\\mathrm {c l f}} + \\mathcal {L} _ {\\mathrm {s e g}}, \\tag {7}", + "image_path": "6bdb62d6fac11d30721b9650b53e5c6ba87d29ed767dc742fc3b03b2b40696da.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 316, + 465, + 328 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 316, + 465, + 328 + ], + "spans": [ + { + "bbox": [ + 306, + 316, + 465, + 328 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 316, + 465, + 328 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 306, + 316, + 465, + 328 + ], + "type": "text", + "content": " is a balancing hyperparameter." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 331, + 545, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 331, + 545, + 407 + ], + "spans": [ + { + "bbox": [ + 304, + 331, + 545, + 407 + ], + "type": "text", + "content": "Inference. For " + }, + { + "bbox": [ + 304, + 331, + 545, + 407 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 331, + 545, + 407 + ], + "type": "text", + "content": "-way " + }, + { + "bbox": [ + 304, + 331, + 545, + 407 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 331, + 545, + 407 + ], + "type": "text", + "content": "-shot inference, " + }, + { + "bbox": [ + 304, + 331, + 545, + 407 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 331, + 545, + 407 + ], + "type": "text", + "content": " class logits and segmentation masks are generated using " + }, + { + "bbox": [ + 304, + 331, + 545, + 407 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 331, + 545, + 407 + ], + "type": "text", + "content": " support images, for each of " + }, + { + "bbox": [ + 304, + 331, + 545, + 407 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 331, + 545, + 407 + ], + "type": "text", + "content": " classes. These are then averaged, resulting in one estimate per class " + }, + { + "bbox": [ + 304, + 331, + 545, + 407 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 331, + 545, + 407 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 331, + 545, + 407 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{y}}_{\\mathrm{clf}}^{(n)}" + }, + { + "bbox": [ + 304, + 331, + 545, + 407 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 331, + 545, + 407 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{Y}}_{\\mathrm{seg}}^{(n)}" + }, + { + "bbox": [ + 304, + 331, + 545, + 407 + ], + "type": "text", + "content": ". Multi-label classification " + }, + { + "bbox": [ + 304, + 331, + 545, + 407 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{y}}_{\\mathrm{clf}}^{(n)}" + }, + { + "bbox": [ + 304, + 331, + 545, + 407 + ], + "type": "text", + "content": " is then obtained by thresholding each class response " + }, + { + "bbox": [ + 304, + 331, + 545, + 407 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{y}}_{\\mathrm{clf}}^{(n)}" + }, + { + "bbox": [ + 304, + 331, + 545, + 407 + ], + "type": "text", + "content": " with an arbitrarily chosen threshold of " + }, + { + "bbox": [ + 304, + 331, + 545, + 407 + ], + "type": "inline_equation", + "content": "\\delta = 0.5" + }, + { + "bbox": [ + 304, + 331, + 545, + 407 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 407, + 545, + 442 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 407, + 545, + 442 + ], + "spans": [ + { + "bbox": [ + 305, + 407, + 545, + 442 + ], + "type": "text", + "content": "For segmentation, a pixel " + }, + { + "bbox": [ + 305, + 407, + 545, + 442 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 305, + 407, + 545, + 442 + ], + "type": "text", + "content": " is labeled as the class with the highest response, or as background (i.e. the " + }, + { + "bbox": [ + 305, + 407, + 545, + 442 + ], + "type": "inline_equation", + "content": "N + 1" + }, + { + "bbox": [ + 305, + 407, + 545, + 442 + ], + "type": "text", + "content": "-th class) if none of the " + }, + { + "bbox": [ + 305, + 407, + 545, + 442 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 305, + 407, + 545, + 442 + ], + "type": "text", + "content": " class responses exceeds " + }, + { + "bbox": [ + 305, + 407, + 545, + 442 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 305, + 407, + 545, + 442 + ], + "type": "text", + "content": ". Formally:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 334, + 461, + 545, + 493 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 334, + 461, + 545, + 493 + ], + "spans": [ + { + "bbox": [ + 334, + 461, + 545, + 493 + ], + "type": "interline_equation", + "content": "\\tilde {\\mathbf {Y}} _ {\\text {s e g}} (\\mathbf {x}) = \\left\\{ \\begin{array}{l} N + 1 \\quad \\text {i f} \\forall \\{\\hat {\\mathbf {Y}} _ {\\text {s e g}} ^ {(n)} (\\mathbf {x}) \\} _ {n = 1} ^ {N} \\leq \\delta , \\\\ \\arg \\max _ {n \\in [ 1, \\dots , N ]} \\{\\hat {\\mathbf {Y}} _ {\\text {s e g}} ^ {(n)} (\\mathbf {x}) \\} _ {n = 1} ^ {N}. \\end{array} \\right. \\tag {8}", + "image_path": "6a6954ac09d85cc058a059c7e8db034bb97d06a21f703f56381f063b34eafc3b.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 501, + 506, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 501, + 506, + 514 + ], + "spans": [ + { + "bbox": [ + 306, + 501, + 506, + 514 + ], + "type": "text", + "content": "3.2. Learning with image-level supervision" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 519, + 545, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 519, + 545, + 626 + ], + "spans": [ + { + "bbox": [ + 304, + 519, + 545, + 626 + ], + "type": "text", + "content": "The previously-described learning objective assumes access to GT support and query segmentation mask labels, " + }, + { + "bbox": [ + 304, + 519, + 545, + 626 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_{\\mathrm{gt}}" + }, + { + "bbox": [ + 304, + 519, + 545, + 626 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 519, + 545, + 626 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}_{\\mathrm{gt}}" + }, + { + "bbox": [ + 304, + 519, + 545, + 626 + ], + "type": "text", + "content": ". To remove the dependence on such expensive annotations, in this section we propose a learning framework for FS-CS that relies only on image-level annotations, i.e., ground-truth class labels. Using the same model architecture, we adopt a method akin to self-distillation [91, 94], that generates pseudo-GT masks, " + }, + { + "bbox": [ + 304, + 519, + 545, + 626 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_{\\mathrm{ps}}" + }, + { + "bbox": [ + 304, + 519, + 545, + 626 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 519, + 545, + 626 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}_{\\mathrm{ps}}" + }, + { + "bbox": [ + 304, + 519, + 545, + 626 + ], + "type": "text", + "content": ", and uses them in place of GT mask labels in equations 3 and 6." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "Pseudo-GT mask generation. As empirically investigated in previous studies [3, 9], query-key attention maps can capture semantically salient foreground objects. Inspired by this, we generate pseudo-GT masks for query and support images on the fly by computing the cross- and self-attention from the last DINO ViT layer. We intercept the key and query embeddings " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{K}_{\\mathrm{s}}^{m}, \\mathbf{Q}_{\\mathrm{s}}^{m} \\in \\mathbb{R}^{(1 + T_{\\mathrm{s}}) \\times C}" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": " and" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19630" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "inline_equation", + "content": "\\mathbf{K}_{\\mathrm{q}}^{m}, \\mathbf{Q}_{\\mathrm{q}}^{m} \\in \\mathbb{R}^{(1 + T_{\\mathrm{q}}) \\times C}" + }, + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "text", + "content": " for the support and query images respectively, for the " + }, + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "text", + "content": "-th head from the last ViT layer. The support and query image pseudo-GT mask values " + }, + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_{\\mathrm{ps}, i_{\\mathrm{s}}}" + }, + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}_{\\mathrm{ps}, i_{\\mathrm{q}}}" + }, + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "text", + "content": " (where " + }, + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "inline_equation", + "content": "i_{\\mathrm{s}}" + }, + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "inline_equation", + "content": "i_{\\mathrm{q}}" + }, + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "text", + "content": " index the support and query image tokens respectively) are then computed as:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 99, + 139, + 233, + 156 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 99, + 139, + 233, + 156 + ], + "spans": [ + { + "bbox": [ + 99, + 139, + 233, + 156 + ], + "type": "interline_equation", + "content": "\\mathbf {P} _ {\\mathrm {s}} \\in \\mathbb {R} ^ {M \\times T _ {\\mathrm {s}}}; \\quad \\mathbf {P} _ {\\mathrm {s}, i _ {\\mathrm {s}}} ^ {m} = \\overline {{\\mathbf {K}}} _ {\\mathrm {s}, i _ {\\mathrm {s}}} ^ {m} \\text {T} \\overline {{\\mathbf {Q}}} _ {\\mathrm {s}, c _ {\\mathrm {s}}} ^ {m},", + "image_path": "4de3cf468e18efb5549c9bb0f9d16bed1057ee564ad90f7f2bd90020f6260eaa.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 99, + 158, + 287, + 177 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 99, + 158, + 287, + 177 + ], + "spans": [ + { + "bbox": [ + 99, + 158, + 287, + 177 + ], + "type": "interline_equation", + "content": "\\mathbf {P} _ {\\mathrm {q}} \\in \\mathbb {R} ^ {M \\times T _ {\\mathrm {q}}}; \\quad \\mathbf {P} _ {\\mathrm {q}, i _ {\\mathrm {q}}} ^ {m} = \\overline {{\\mathbf {K}}} _ {\\mathrm {q}, i _ {\\mathrm {q}}} ^ {m} \\text {T} \\overline {{\\mathbf {Q}}} _ {\\mathrm {s}, c _ {\\mathrm {s}}} ^ {m}, \\tag {9}", + "image_path": "8997546e9e54ad9f66aa90fa4e54360c9ee357c0727d33e939d4913e10c8ba06.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 110, + 186, + 287, + 224 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 186, + 287, + 224 + ], + "spans": [ + { + "bbox": [ + 110, + 186, + 287, + 224 + ], + "type": "interline_equation", + "content": "\\mathbf {M} _ {\\mathrm {p s}, i _ {\\mathrm {s}}} ^ {\\prime} = \\frac {1}{M} \\sum_ {m = 1} ^ {M} \\mathbf {P} _ {\\mathrm {s}, i _ {\\mathrm {s}}} ^ {m}, \\tag {10}", + "image_path": "6d2fcc8d3dd152037bdb8e8e71724a60979cb8500b1bdb928edc3cca443f7113.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 112, + 222, + 213, + 253 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 112, + 222, + 213, + 253 + ], + "spans": [ + { + "bbox": [ + 112, + 222, + 213, + 253 + ], + "type": "interline_equation", + "content": "\\mathbf {Y} _ {\\mathrm {p s}, i _ {\\mathrm {q}}} ^ {\\prime} = \\left\\{ \\begin{array}{l l} \\mathbf {0} & \\text {i f} \\quad \\mathbf {y} _ {\\mathrm {c l f}} = \\mathbf {0} \\\\ \\frac {1}{M} \\sum_ {m = 1} ^ {M} \\mathbf {P} _ {\\mathrm {q}, i _ {\\mathrm {q}}} ^ {m}, \\end{array} \\right.", + "image_path": "f625349da100864855507788baca122d1559f9b340cda62b1d42e7b13a377135.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 67, + 262, + 287, + 279 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 262, + 287, + 279 + ], + "spans": [ + { + "bbox": [ + 67, + 262, + 287, + 279 + ], + "type": "interline_equation", + "content": "\\mathbf {M} _ {\\mathrm {p s}} = \\Pi (\\xi (\\mathbf {M} _ {\\mathrm {p s}} ^ {\\prime}), \\alpha); \\mathbf {Y} _ {\\mathrm {p s}} = \\Pi (\\xi (\\mathbf {Y} _ {\\mathrm {p s}} ^ {\\prime}), \\alpha), \\tag {11}", + "image_path": "66008fe89b5f7c8bb9c16422c5b0c74655d9603f93ee4c5d3c94f70bec404ea9.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 281, + 287, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 281, + 287, + 413 + ], + "spans": [ + { + "bbox": [ + 46, + 281, + 287, + 413 + ], + "type": "text", + "content": "with " + }, + { + "bbox": [ + 46, + 281, + 287, + 413 + ], + "type": "inline_equation", + "content": "c_{s}" + }, + { + "bbox": [ + 46, + 281, + 287, + 413 + ], + "type": "text", + "content": " denoting the index of the class token for the support image, " + }, + { + "bbox": [ + 46, + 281, + 287, + 413 + ], + "type": "inline_equation", + "content": "\\xi(\\cdot)" + }, + { + "bbox": [ + 46, + 281, + 287, + 413 + ], + "type": "text", + "content": " performing spatial reshaping and bilinear interpolation to the input image size, and " + }, + { + "bbox": [ + 46, + 281, + 287, + 413 + ], + "type": "inline_equation", + "content": "\\Pi(\\cdot, \\alpha)" + }, + { + "bbox": [ + 46, + 281, + 287, + 413 + ], + "type": "text", + "content": " applying an element-wise binary threshold " + }, + { + "bbox": [ + 46, + 281, + 287, + 413 + ], + "type": "inline_equation", + "content": "\\alpha = -0.1" + }, + { + "bbox": [ + 46, + 281, + 287, + 413 + ], + "type": "text", + "content": " (set via hyperparameter search). The semantics captured in the support class token are matched with the localized semantics of the (query or support) image tokens, using (cross- or self-) attention. This localized semantic matching is then captured in the resulting pseudo-GT masks. Our pseudo-mask generation process brings negligible extra computation by leveraging internal byproducts from the ViT backbone." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 413, + 287, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 413, + 287, + 509 + ], + "spans": [ + { + "bbox": [ + 46, + 413, + 287, + 509 + ], + "type": "text", + "content": "This learning framework also relates to self-knowledge distillation [91, 94], in the sense that our model is supervised using its own (intermediate) features. We can think of the backbone as the teacher and the full CST model as the student. However, a key difference is that in our approach the student model learns additional parameters. In contrast, in strictly self-knowledge distillation approaches the student and teacher model architectures are identical." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 515, + 258, + 529 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 515, + 258, + 529 + ], + "spans": [ + { + "bbox": [ + 47, + 515, + 258, + 529 + ], + "type": "text", + "content": "3.3. Extension to mixed-supervision learning" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 534, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 534, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 534, + 287, + 677 + ], + "type": "text", + "content": "As shown in Sec. 4, our pseudo-masks provide effective supervision for segmentation. However, there is unsurprisingly still a quality gap between these masks and the GT segmentation masks, which degrades segmentation performance. In this section, we propose a practical learning setting for FS-CS with mixed supervision, which reduces this degradation in segmentation performance, by using a small number of GT segmentation masks during training. Mixed-supervised FS-CS assumes that all training images contain image-level labels, and a small subset of them also contains pixel-level labels, which are relatively inexpensive compared to full supervision." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "content": "To obtain higher-quality pseudo-GT masks, we use the small number of images with GT masks to train a mask enhancer. We reshape " + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_{\\mathrm{s}}" + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_{\\mathrm{q}}" + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "content": " in Eq. (9) into spatial tensors" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 307, + 83, + 545, + 201 + ], + "blocks": [ + { + "bbox": [ + 320, + 75, + 354, + 82 + ], + "lines": [ + { + "bbox": [ + 320, + 75, + 354, + 82 + ], + "spans": [ + { + "bbox": [ + 320, + 75, + 354, + 82 + ], + "type": "text", + "content": "support image" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 369, + 75, + 485, + 81 + ], + "lines": [ + { + "bbox": [ + 369, + 75, + 485, + 81 + ], + "spans": [ + { + "bbox": [ + 369, + 75, + 485, + 81 + ], + "type": "text", + "content": "To query pseudo-GT mask enhanced pseudo-GT mask," + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 497, + 75, + 533, + 81 + ], + "lines": [ + { + "bbox": [ + 497, + 75, + 533, + 81 + ], + "spans": [ + { + "bbox": [ + 497, + 75, + 533, + 81 + ], + "type": "text", + "content": "query GT mask" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 307, + 83, + 545, + 201 + ], + "lines": [ + { + "bbox": [ + 307, + 83, + 545, + 201 + ], + "spans": [ + { + "bbox": [ + 307, + 83, + 545, + 201 + ], + "type": "image", + "image_path": "aa5ed93456dd3aad5847e1409704491bd092f40652607deaf586947dd6c19f83.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 205, + 544, + 216 + ], + "lines": [ + { + "bbox": [ + 306, + 205, + 544, + 216 + ], + "spans": [ + { + "bbox": [ + 306, + 205, + 544, + 216 + ], + "type": "text", + "content": "Figure 4. Examples of pseudo-GT & enhanced pseudo-GT masks." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 229, + 545, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 229, + 545, + 350 + ], + "spans": [ + { + "bbox": [ + 304, + 229, + 545, + 350 + ], + "type": "text", + "content": "and use them as inputs to the enhancer, which returns binary masks. During training the enhancer is supervised with the available GT masks. The mask enhancer is a network of three " + }, + { + "bbox": [ + 304, + 229, + 545, + 350 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 304, + 229, + 545, + 350 + ], + "type": "text", + "content": " convolutional layers followed by a Sigmoid. For mixed-supervision learning, we pre-train this mask enhancer and all pseudo-masks are obtained via the enhancer before being used as supervision during meta-training and meta-testing. Figure 3 compares the two proposed pseudoGT mask generation processes under the image-level- and mixed-supervision learning settings." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 361, + 386, + 374 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 361, + 386, + 374 + ], + "spans": [ + { + "bbox": [ + 306, + 361, + 386, + 374 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 382, + 545, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 382, + 545, + 430 + ], + "spans": [ + { + "bbox": [ + 304, + 382, + 545, + 430 + ], + "type": "text", + "content": "In this section we provide implementation details for our approach, and present quantitative and qualitative results to experimentally evaluate its performance. The attached supplementary material contains more analyses and details." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 434, + 545, + 614 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 434, + 545, + 614 + ], + "spans": [ + { + "bbox": [ + 304, + 434, + 545, + 614 + ], + "type": "text", + "content": "Architecture and training. To compare with prior work based on ResNet50 [33,48,67,71], we use a ViT-small backbone [18] with 21M parameters that was pre-trained via self-supervision with DINO [9] on ImageNet 1K [54]. The size and training data are comparable with ResNet50 [27], which has 23M parameters and was also trained on ImageNet 1K, but using class labels as supervision. ViT-small consists of " + }, + { + "bbox": [ + 304, + 434, + 545, + 614 + ], + "type": "inline_equation", + "content": "L = 12" + }, + { + "bbox": [ + 304, + 434, + 545, + 614 + ], + "type": "text", + "content": " transformer layers of " + }, + { + "bbox": [ + 304, + 434, + 545, + 614 + ], + "type": "inline_equation", + "content": "M = 6" + }, + { + "bbox": [ + 304, + 434, + 545, + 614 + ], + "type": "text", + "content": " attention heads, with " + }, + { + "bbox": [ + 304, + 434, + 545, + 614 + ], + "type": "inline_equation", + "content": "C = 64" + }, + { + "bbox": [ + 304, + 434, + 545, + 614 + ], + "type": "text", + "content": "-dimensional query-key-value embeddings. The backbone is frozen, as in previous work [67,90], and the additional layers are trained using Adam [35] with a learning rate of " + }, + { + "bbox": [ + 304, + 434, + 545, + 614 + ], + "type": "inline_equation", + "content": "10^{-3}" + }, + { + "bbox": [ + 304, + 434, + 545, + 614 + ], + "type": "text", + "content": ". Consistent with [33], CST is trained with 1-way 1-shot episodes and is used for any " + }, + { + "bbox": [ + 304, + 434, + 545, + 614 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 434, + 545, + 614 + ], + "type": "text", + "content": "-way " + }, + { + "bbox": [ + 304, + 434, + 545, + 614 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 434, + 545, + 614 + ], + "type": "text", + "content": "-shot inference. We set the task token dimensionality " + }, + { + "bbox": [ + 304, + 434, + 545, + 614 + ], + "type": "inline_equation", + "content": "C' = 128" + }, + { + "bbox": [ + 304, + 434, + 545, + 614 + ], + "type": "text", + "content": ", and the loss balancing hyperparameter " + }, + { + "bbox": [ + 304, + 434, + 545, + 614 + ], + "type": "inline_equation", + "content": "\\lambda = 0.1" + }, + { + "bbox": [ + 304, + 434, + 545, + 614 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 617, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 714 + ], + "type": "text", + "content": "Datasets. We report results on two standard FS-CS benchmarks [33], Pascal- " + }, + { + "bbox": [ + 304, + 617, + 545, + 714 + ], + "type": "inline_equation", + "content": "5^{i}" + }, + { + "bbox": [ + 304, + 617, + 545, + 714 + ], + "type": "text", + "content": " [20,58] and COCO- " + }, + { + "bbox": [ + 304, + 617, + 545, + 714 + ], + "type": "inline_equation", + "content": "20^{i}" + }, + { + "bbox": [ + 304, + 617, + 545, + 714 + ], + "type": "text", + "content": " [45,49]. Both datasets use 4-fold validation, where the folds " + }, + { + "bbox": [ + 304, + 617, + 545, + 714 + ], + "type": "inline_equation", + "content": "i \\in \\{0,1,2,3\\}" + }, + { + "bbox": [ + 304, + 617, + 545, + 714 + ], + "type": "text", + "content": " are created by splitting the 20 (resp. 80) classes into 4 mutually disjoint class sets, with 10K (resp. 100K) images per fold. For training and validation, support and query image pairs are sampled on the fly, as done in [33]. 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methodps-mask1-way 1-shot2-way 1-shotlearn.
classification 0/1 exact ratio (%)segmentation mIoU (%)classification 0/1 exact ratio (%)segmentation mIoU (%)params.
50515253avg.50515253avg.50515253avg.50515253avg.
HSNet [48]X84.584.860.885.378.920.023.516.216.619.170.867.036.570.161.111.023.415.417.017.72.6M
ASNet [33]X80.284.066.282.778.311.721.113.416.215.667.670.244.569.362.910.320.712.615.914.91.3M
CST (image)X83.980.765.982.778.311.920.715.016.316.072.665.343.269.562.611.920.515.016.615.70.4M
DINO [9]◇-----20.023.416.216.619.1-----12.812.910.09.911.40
CST✓84.082.270.882.679.935.838.928.929.233.274.367.249.067.864.635.736.026.829.131.90.4M
", + "image_path": "71657a57f087c3434f33ed338ee1499654890f520f5a6e56253c4d81fd729064.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 53, + 202, + 279, + 270 + ], + "blocks": [ + { + "bbox": [ + 47, + 156, + 547, + 191 + ], + "lines": [ + { + "bbox": [ + 47, + 156, + 547, + 191 + ], + "spans": [ + { + "bbox": [ + 47, + 156, + 547, + 191 + ], + "type": "text", + "content": "Table 1. Comparing model performance on FS-CS when trained with image-level supervision on Pascal-5" + }, + { + "bbox": [ + 47, + 156, + 547, + 191 + ], + "type": "inline_equation", + "content": "^i" + }, + { + "bbox": [ + 47, + 156, + 547, + 191 + ], + "type": "text", + "content": " [58]. \"ps-mask\" refers to using pseudo-GT masks during training. Our CST model compares favourably to prior works on classification, and outperforms them on segmentation. Results for DINO [9] were generated without any training on Pascal-5" + }, + { + "bbox": [ + 47, + 156, + 547, + 191 + ], + "type": "inline_equation", + "content": "^i" + }, + { + "bbox": [ + 47, + 156, + 547, + 191 + ], + "type": "text", + "content": " (denoted by " + }, + { + "bbox": [ + 47, + 156, + 547, + 191 + ], + "type": "inline_equation", + "content": "\\diamond" + }, + { + "bbox": [ + 47, + 156, + 547, + 191 + ], + "type": "text", + "content": "). See section 4.1 for details." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 53, + 202, + 279, + 270 + ], + "lines": [ + { + "bbox": [ + 53, + 202, + 279, + 270 + ], + "spans": [ + { + "bbox": [ + 53, + 202, + 279, + 270 + ], + "type": "table", + "html": "
methodps-mask1-way 1-shot2-way 1-shot
cls. ERseg. mIoUclf. ERseg. mIoU
CST✘74.510.362.39.8
DINO [9]◇-12.1-7.4
CST✓78.219.662.418.3
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When a support image contains multiple classes, only one of them is set as its image class and the rest are set as background. While this introduces noise into support sets containing multi-class images, we find that it performs well in practice. A query image is also chosen randomly and may contain between 0 to " + }, + { + "bbox": [ + 46, + 320, + 287, + 524 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 320, + 287, + 524 + ], + "type": "text", + "content": " of the target classes. The image-level label for the query is then constructed as an " + }, + { + "bbox": [ + 46, + 320, + 287, + 524 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 320, + 287, + 524 + ], + "type": "text", + "content": "-dimensional binary vector containing 1 if the query contains the " + }, + { + "bbox": [ + 46, + 320, + 287, + 524 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 320, + 287, + 524 + ], + "type": "text", + "content": "-th class, and 0 otherwise. Similarly, its pixel-level label is defined as an " + }, + { + "bbox": [ + 46, + 320, + 287, + 524 + ], + "type": "inline_equation", + "content": "(N + 1)" + }, + { + "bbox": [ + 46, + 320, + 287, + 524 + ], + "type": "text", + "content": "-way segmentation mask, including background. For mixed-supervision learning, we sort the images in a training split by their image names and use pixel-level labels for the first e.g. " + }, + { + "bbox": [ + 46, + 320, + 287, + 524 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 46, + 320, + 287, + 524 + ], + "type": "text", + "content": " of images, and only image-level labels for the remainder. This effectively randomizes the subset of images with full-supervision." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 529, + 287, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 529, + 287, + 649 + ], + "spans": [ + { + "bbox": [ + 46, + 529, + 287, + 649 + ], + "type": "text", + "content": "Evaluation and metrics. We follow the established evaluation protocol for each FS-CS benchmark [33, 49, 58]. To evaluate multi-label classification, we use the " + }, + { + "bbox": [ + 46, + 529, + 287, + 649 + ], + "type": "inline_equation", + "content": "0/1" + }, + { + "bbox": [ + 46, + 529, + 287, + 649 + ], + "type": "text", + "content": " exact match ratio [19], where an image is considered to be correctly classified if the binary label for each of the " + }, + { + "bbox": [ + 46, + 529, + 287, + 649 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 529, + 287, + 649 + ], + "type": "text", + "content": " classes is correct. For semantic segmentation, we use mean IoU, " + }, + { + "bbox": [ + 46, + 529, + 287, + 649 + ], + "type": "inline_equation", + "content": "\\mathrm{mIoU} = \\frac{1}{R}\\sum_{R}\\mathrm{IoU}_{r}" + }, + { + "bbox": [ + 46, + 529, + 287, + 649 + ], + "type": "text", + "content": " [58, 71], where " + }, + { + "bbox": [ + 46, + 529, + 287, + 649 + ], + "type": "inline_equation", + "content": "\\mathrm{IoU}_r" + }, + { + "bbox": [ + 46, + 529, + 287, + 649 + ], + "type": "text", + "content": " is the IoU of all images labeled with the " + }, + { + "bbox": [ + 46, + 529, + 287, + 649 + ], + "type": "inline_equation", + "content": "r_{\\mathrm{th}}" + }, + { + "bbox": [ + 46, + 529, + 287, + 649 + ], + "type": "text", + "content": "-class. The best model is chosen based on the highest validation mIoU averaged with 1000 random validation episodes." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 658, + 241, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 241, + 671 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 241, + 671 + ], + "type": "text", + "content": "4.1. Results with image-level supervision" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "content": "Tables 1 and 2 compare the performance of our image-level-supervised CST with baseline methods. The only prior work that addresses this setting [33] generates a seg" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 308, + 202, + 552, + 255 + ], + "blocks": [ + { + "bbox": [ + 47, + 277, + 288, + 312 + ], + "lines": [ + { + "bbox": [ + 47, + 277, + 288, + 312 + ], + "spans": [ + { + "bbox": [ + 47, + 277, + 288, + 312 + ], + "type": "text", + "content": "Table 2. Comparing model performance on FS-CS when trained with image-level supervision on COCO- " + }, + { + "bbox": [ + 47, + 277, + 288, + 312 + ], + "type": "inline_equation", + "content": "20^{i}" + }, + { + "bbox": [ + 47, + 277, + 288, + 312 + ], + "type": "text", + "content": " [49], averaged over 4 folds. See section 4.1 for details." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 202, + 552, + 255 + ], + "lines": [ + { + "bbox": [ + 308, + 202, + 552, + 255 + ], + "spans": [ + { + "bbox": [ + 308, + 202, + 552, + 255 + ], + "type": "table", + "html": "
% GT training set masks →0%2.5%5%10%100%
(a): pseudo-mask baseline33.241.443.544.5-
(b): (a) + mask enhancer-43.244.145.2-
(c): (b) + GT test set S masks-47.548.450.155.5
", + "image_path": "0582b02ad7f06654252eb6532894023e6564d97212f53fdfe9680f820943a6cc.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 255, + 547, + 300 + ], + "lines": [ + { + "bbox": [ + 305, + 255, + 547, + 300 + ], + "spans": [ + { + "bbox": [ + 305, + 255, + 547, + 300 + ], + "type": "text", + "content": "Table 3. Comparing segmentation mIoU of CST on FS-CS with mixed supervision on Pascal-5" + }, + { + "bbox": [ + 305, + 255, + 547, + 300 + ], + "type": "inline_equation", + "content": "^i" + }, + { + "bbox": [ + 305, + 255, + 547, + 300 + ], + "type": "text", + "content": ", for different " + }, + { + "bbox": [ + 305, + 255, + 547, + 300 + ], + "type": "inline_equation", + "content": "\\%" + }, + { + "bbox": [ + 305, + 255, + 547, + 300 + ], + "type": "text", + "content": " of training set ground-truth masks, averaged over 4 folds. In (c), ground-truth masks were used for all support " + }, + { + "bbox": [ + 305, + 255, + 547, + 300 + ], + "type": "inline_equation", + "content": "(S)" + }, + { + "bbox": [ + 305, + 255, + 547, + 300 + ], + "type": "text", + "content": " images during testing." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 312, + 547, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 312, + 547, + 540 + ], + "spans": [ + { + "bbox": [ + 304, + 312, + 547, + 540 + ], + "type": "text", + "content": "mentation mask that is then globally average-pooled. The cross-entropy between the average-pooled prediction and the ground-truth image label is used as the objective function. We adopt this approach for [48], which did not address this setting, to construct another baseline, and we also evaluate CST in this setting, which we denote with " + }, + { + "bbox": [ + 304, + 312, + 547, + 540 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 312, + 547, + 540 + ], + "type": "text", + "content": ". The result for DINO is computed by evaluating segmentation masks that were generated as in [9] (denoted by " + }, + { + "bbox": [ + 304, + 312, + 547, + 540 + ], + "type": "inline_equation", + "content": "\\diamond" + }, + { + "bbox": [ + 304, + 312, + 547, + 540 + ], + "type": "text", + "content": "), without using any training data from the target datasets. Our CST model, trained with pseudo-masks via self-distillation (denoted by " + }, + { + "bbox": [ + 304, + 312, + 547, + 540 + ], + "type": "inline_equation", + "content": "\\checkmark" + }, + { + "bbox": [ + 304, + 312, + 547, + 540 + ], + "type": "text", + "content": "), performs comparably to prior work on classification and, because of the superior supervision provided by our pseudo-masks during training, outperforms these models on segmentation. In particular, CST achieves an over 100% improvement over ASNet [33] in both the 1-way 1-shot and 2-way 1-shot settings. We also note that training CST with pseudo-GT masks " + }, + { + "bbox": [ + 304, + 312, + 547, + 540 + ], + "type": "inline_equation", + "content": "(\\checkmark)" + }, + { + "bbox": [ + 304, + 312, + 547, + 540 + ], + "type": "text", + "content": " also improves classification performance by 1.6% (1-way 1-shot) and 2% (2-way 1-shot) on Pascal-5 when compared to training without " + }, + { + "bbox": [ + 304, + 312, + 547, + 540 + ], + "type": "inline_equation", + "content": "(\\mathbf{x})" + }, + { + "bbox": [ + 304, + 312, + 547, + 540 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 550, + 474, + 563 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 550, + 474, + 563 + ], + "spans": [ + { + "bbox": [ + 306, + 550, + 474, + 563 + ], + "type": "text", + "content": "4.2. Results with mixed supervision" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": "To validate the effectiveness of the mixed-supervision setting, we vary the percentage of pixel-level annotated images used in training and present the results in Table 3. We observe that using just " + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": " of GT masks is remarkably effective at improving performance, when compared to using " + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "inline_equation", + "content": "0\\%" + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": " (43.5% vs. 33.2%). The mask enhancer brings much improvement with fewer ground-truth segmentation masks. The effect of the mask enhancer is visually demonstrated in Fig. 4. We observe that the mask enhancer reduces foreground noise and often filters out objects irrelevant to a support image. Note that mixed-supervision learning assumes access to pixel-level annotations only during training. Dur" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "19632" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 541, + 159 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 541, + 159 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 541, + 159 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 541, + 159 + ], + "type": "table", + "html": "
method1-way 1-shot2-way 1-shotlearn. \nparams.
classification 0/1 exact ratio (%)segmentation mIoU (%)classification 0/1 exact ratio (%)segmentation mIoU (%)
50515253avg.50515253avg.50515253avg.50515253avg.
PANet [71]69.967.768.869.469.032.845.831.035.136.256.247.544.655.450.933.346.031.238.437.2
PFENet [67]69.882.468.177.974.638.354.735.143.843.022.561.740.339.541.031.147.330.832.235.3
HSNet [48]86.684.876.986.383.749.159.741.049.049.768.073.257.070.967.342.453.734.043.943.5
ASNet [33]84.989.679.086.284.951.761.543.352.852.368.576.258.670.068.348.558.336.348.347.8
CST86.988.081.586.585.755.661.647.756.955.570.374.962.074.470.456.961.048.057.055.7
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method1-way 1-shot2-way 1-shot
clf. ERseg. mIoUclf. ERseg. mIoU
PANet [71]66.725.248.523.6
PFENet [67]71.431.936.522.6
HSNet [48]77.034.362.529.5
ASNet [33]78.635.863.131.6
CST80.838.364.036.2
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labels → archi. →class-sup. ViT [18]self-sup. CNN [27]self-sup. ViT [9]*self-sup. ViT [9]
seg. mIoU (%)6.920.715.633.2
", + "image_path": "f824585f391a783e77dc913d7fbfa5314847b1ccf495777034ff8f39dbf39675.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 309, + 302, + 543, + 396 + ], + "blocks": [ + { + "bbox": [ + 305, + 232, + 545, + 289 + ], + "lines": [ + { + "bbox": [ + 305, + 232, + 545, + 289 + ], + "spans": [ + { + "bbox": [ + 305, + 232, + 545, + 289 + ], + "type": "text", + "content": "Table 6. FS-CS model comparison trained with image-level labels on 1-way 1-shot Pascal- " + }, + { + "bbox": [ + 305, + 232, + 545, + 289 + ], + "type": "inline_equation", + "content": "5^{j}" + }, + { + "bbox": [ + 305, + 232, + 545, + 289 + ], + "type": "text", + "content": " by varying pseudo-mask generation models. Different columns denote model architectures for pseudolabeling and their pre-training supervision levels. The method * uses the final layer tokens from [9] for generating pseudo-labels." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 302, + 543, + 396 + ], + "lines": [ + { + "bbox": [ + 309, + 302, + 543, + 396 + ], + "spans": [ + { + "bbox": [ + 309, + 302, + 543, + 396 + ], + "type": "table", + "html": "
clf. & seg.\nprediction headssuperv.\nlevel1-way 1-shot2-way 1-shot
clf.\nERseg.\nmIoUclf.\nERseg.\nmIoU
coupledimage78.532.959.531.9
decoupled (CST)image79.933.264.531.9
coupledpixel84.354.267.053.0
decoupled (CST)pixel85.755.570.555.7
", + "image_path": "e24b8aedbc359af4f4d5dd6fb0138aae76dfbaf0bd4582fdb85b10c0c57bd130.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 404, + 545, + 427 + ], + "lines": [ + { + "bbox": [ + 306, + 404, + 545, + 427 + ], + "spans": [ + { + "bbox": [ + 306, + 404, + 545, + 427 + ], + "type": "text", + "content": "Table 7. Ablation study of coupling or decoupling classification and segmentation prediction heads for FS-CS on Pascal-5" + }, + { + "bbox": [ + 306, + 404, + 545, + 427 + ], + "type": "inline_equation", + "content": "^i" + }, + { + "bbox": [ + 306, + 404, + 545, + 427 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 437, + 397, + 450 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 437, + 397, + 450 + ], + "spans": [ + { + "bbox": [ + 306, + 437, + 397, + 450 + ], + "type": "text", + "content": "4.4. Ablation study" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 462, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 545, + 715 + ], + "type": "text", + "content": "Pseudo-labeling with different models. We explore other learning-free pseudo-labeling methods by using alternative pre-trained feature extractors to generate pseudo-GT masks. Rather than self-distillation, where we train CST with pseudo-GT masks generated from its own self-supervised DINO ViT backbone, in these experiments we train CST with pseudo-GT masks generated from class-supervised ViT [18], self-supervised DINO ResNet50 [27], or the output layer tokens from the self-supervised DINO ViT [9]. As ResNets do not have class tokens, we apply global-average pooling on the support feature map from the last ResNet layer and use the pooled feature as a class token for generating the pseudo-GT masks. As seen in Table 6, pseudo-GT masks generated from alternative feature extractors do not perform as well as the intermediate attention maps from DINO. We qualitatively observed that the alternatives' less accurate pseudo-masks lead to lower segmentation accuracy when used in pseudo-supervised learning: the self-supervised ResNet50 produces pseudo-masks with indistinct object boundaries, while the class-supervised ViT produces noisy patches throughout the pseudo-mask (as was" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19633" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 54, + 70, + 539, + 205 + ], + "blocks": [ + { + "bbox": [ + 54, + 70, + 539, + 205 + ], + "lines": [ + { + "bbox": [ + 54, + 70, + 539, + 205 + ], + "spans": [ + { + "bbox": [ + 54, + 70, + 539, + 205 + ], + "type": "image", + "image_path": "205ac74edb80f691925641215594c10f4ca84473c366f4c9c9f2e263dff94c83.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 207, + 547, + 232 + ], + "lines": [ + { + "bbox": [ + 46, + 207, + 547, + 232 + ], + "spans": [ + { + "bbox": [ + 46, + 207, + 547, + 232 + ], + "type": "text", + "content": "Figure 6. 2-way 1-shot segmentation examples from CST trained with image-level, mixed, and pixel-level supervision. Note that image-level-supervised and mixed-supervised models do not have access to ground-truth support masks. In both cases, the model is still effective." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 59, + 239, + 274, + 319 + ], + "blocks": [ + { + "bbox": [ + 59, + 239, + 274, + 319 + ], + "lines": [ + { + "bbox": [ + 59, + 239, + 274, + 319 + ], + "spans": [ + { + "bbox": [ + 59, + 239, + 274, + 319 + ], + "type": "image", + "image_path": "a1cd7409b8a459b70104bc613f0272ecee8c1f8ac89fff887cd65aff0d85056f.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 321, + 288, + 346 + ], + "lines": [ + { + "bbox": [ + 47, + 321, + 288, + 346 + ], + "spans": [ + { + "bbox": [ + 47, + 321, + 288, + 346 + ], + "type": "text", + "content": "Figure 7. An example of channel-averaged " + }, + { + "bbox": [ + 47, + 321, + 288, + 346 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_{\\mathrm{clf}}" + }, + { + "bbox": [ + 47, + 321, + 288, + 346 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 321, + 288, + 346 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_{\\mathrm{seg}}" + }, + { + "bbox": [ + 47, + 321, + 288, + 346 + ], + "type": "text", + "content": ". Each task token tends to capture different aspects, e.g., clearer edges of " + }, + { + "bbox": [ + 47, + 321, + 288, + 346 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_{\\mathrm{seg}}" + }, + { + "bbox": [ + 47, + 321, + 288, + 346 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 58, + 349, + 276, + 487 + ], + "blocks": [ + { + "bbox": [ + 58, + 349, + 276, + 487 + ], + "lines": [ + { + "bbox": [ + 58, + 349, + 276, + 487 + ], + "spans": [ + { + "bbox": [ + 58, + 349, + 276, + 487 + ], + "type": "table", + "html": "
method1-way 1-shot1-way 5-shot# learn. \nparams.
mIoUFBIoUmIoUFBIoU
RPMM [83]30.6-35.5-38.6M
RePRI [6]34.0-42.1--
SSP [21]37.4-44.1-8.7M
MMNet [79]37.5-38.2-10.4M
MLC [84]33.9-40.6-8.7M
NTRENet [47]39.368.540.369.2-
CMN [81]39.361.743.163.3-
HSNet [48]39.268.246.970.72.6M
DACM [82]40.668.948.171.6-
ASNet [33]42.268.847.971.61.3M
CST44.070.348.773.70.4M
", + "image_path": "5e409ce9c356ab352bddf5ada61c8279302fb1961a3d89c16b00ca0fa35a6539.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 490, + 287, + 513 + ], + "lines": [ + { + "bbox": [ + 47, + 490, + 287, + 513 + ], + "spans": [ + { + "bbox": [ + 47, + 490, + 287, + 513 + ], + "type": "text", + "content": "Table 8. Comparing FS-S models trained with pixel-level supervision on COCO-20i." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 519, + 154, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 519, + 154, + 532 + ], + "spans": [ + { + "bbox": [ + 47, + 519, + 154, + 532 + ], + "type": "text", + "content": "similarly observed in [9])." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 533, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 288, + 715 + ], + "type": "text", + "content": "Effect of decoupled task heads. Table 7 compares the impact of coupling and decoupling the classification and segmentation task heads. The coupled architecture has a single segmentation task head, and the image is classified with the foreground class if any pixels are predicted as foreground, and is otherwise classified as the background class. Having separate heads for each task benefits both tasks in both the image-level and pixel-level supervision settings. A similar observation was made for object detection [64] when decoupling localization from classification. Figure 7 visualizes an example of channel-averaged " + }, + { + "bbox": [ + 46, + 533, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_{\\mathrm{clf}}" + }, + { + "bbox": [ + 46, + 533, + 288, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 533, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_{\\mathrm{seg}}" + }, + { + "bbox": [ + 46, + 533, + 288, + 715 + ], + "type": "text", + "content": " tensors. We observe that these two intermediate representations tend to highlight different areas; " + }, + { + "bbox": [ + 46, + 533, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_{\\mathrm{clf}}" + }, + { + "bbox": [ + 46, + 533, + 288, + 715 + ], + "type": "text", + "content": " has large responses in highly-localized class-specific image regions, while " + }, + { + "bbox": [ + 46, + 533, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_{\\mathrm{seg}}" + }, + { + "bbox": [ + 46, + 533, + 288, + 715 + ], + "type": "text", + "content": " better distinguishes the overall object support and boundaries." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 239, + 547, + 385 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 239, + 547, + 385 + ], + "spans": [ + { + "bbox": [ + 304, + 239, + 547, + 385 + ], + "type": "text", + "content": "Comparison on FS-S. In Table 8, CST is also evaluated in the conventional FS-S setting [58, 71], i.e., binary segmentation using mask supervision, and compared with previous works that use different ResNet50-based architectures. FS-S is equivalent to FS-CS with the precondition that a query and a support always share a class label; classification is not required. We train CST on this setting and find that it achieves state-of-the-art segmentation performance. It is also worth noting that it achieves this with fewer learned parameters than others, which is also the case for the comparisons in Table 1 and Table 4. Our small number of learned parameters may help to avoid overfitting." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 417, + 379, + 430 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 417, + 379, + 430 + ], + "spans": [ + { + "bbox": [ + 306, + 417, + 379, + 430 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 444, + 547, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 444, + 547, + 601 + ], + "spans": [ + { + "bbox": [ + 304, + 444, + 547, + 601 + ], + "type": "text", + "content": "In this work, we propose an approach to generating effective pseudo-GT masks for few-shot classification and segmentation (FS-CS) using the localized semantics encoded in the tokens of self-supervised vision transformers. We show that using these pseudo-GT masks, sometimes combined with a small number of GT masks, we can train effective FS-CS models. Our work is the first to explore this practical weakly-supervised FS-CS setting, which drastically reduces the amount of expensive pixel-level annotations needed for training and deployment. Extensive experiments show that our approach achieves significant performance gains when compared to state-of-the-art methods in a variety of supervision settings, on two FS-CS benchmarks." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "type": "text", + "content": "Acknowledgements. This work was partly supported by the IITP grants (2022-0-00959: Few-Shot Learning of Causal Inference in Vision and Language, 2022-0-00113: Sustainable Collaborative Multi-modal Lifelong Learning) funded by Ministry of Science and ICT, Korea. 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Most methods widely adopt the off-the-shelf Classification-Based Pre-training (CBP) to generate video features for action localization. However, the different optimization objectives between classification and localization, make temporally localized results suffer from the serious incomplete issue. To tackle this issue without additional annotations, this paper considers to distill free action knowledge from Vision-Language Pre-training (VLP), as we surprisingly observe that the localization results of vanilla VLP have an over-complete issue, which is just complementary to the CBP results. To fuse such complementarity, we propose a novel distillation-collaboration framework with two branches acting as CBP and VLP respectively. The framework is optimized through a dual-branch alternate training strategy. Specifically, during the $B$ step, we distill the confident background pseudo-labels from the CBP branch; while during the $F$ step, the confident foreground pseudo-labels are distilled from the VLP branch. As a result, the dual-branch complementarity is effectively fused to promote one strong alliance. Extensive experiments and ablation studies on THUMOS14 and ActivityNet1.2 reveal that our method significantly outperforms state-of-the-art methods.", + "bbox": [ + 75, + 349, + 473, + 713 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 736, + 209, + 752 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Temporal action localization (TAL), which aims to localize and classify action instances from untrimmed long videos, has been recognized as an indispensable component of video understanding [13, 72, 92]. To avoid laborious temporal boundary annotations, the weakly-supervised setting (WTAL) [31, 62, 64, 78], i.e. only video-level category labels are available, has gained increasing attentions.", + "bbox": [ + 75, + 763, + 468, + 868 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To date in the literature, almost all WTAL methods rely on Classification-Based Pre-training (CBP) for video fea", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b2486122ea2d1bfac110d59bfa81db123542096d43ce83fad90a5f78cb0481c2.jpg", + "image_caption": [ + "Figure 1. (A) Complementarity. Most works use Classification-Based Pre-training (CBP) for localization, bringing high TN yet serious FN. Vanilla Vision-Language Pre-training (VLP) confuses action and background, bringing high TP yet serious FP. (B) Our distillation-collaboration framework distills foreground from the VLP branch while background from the CBP branch, and promotes mutual collaboration, bringing satisfactory results." + ], + "image_footnote": [], + "bbox": [ + 498, + 311, + 893, + 483 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ture extraction [5, 73]. A popular pipeline is to train an action classifier with CBP features, then threshold the frame-level classification probabilities for final localization results. As demonstrated in Figure 1(A), these CBP methods suffer from the serious incompleteness issue, i.e. only detecting sparse discriminative action frames and incurring high false negatives. The main reason is that the optimization objective of classification pre-training, is to find several discriminative frames for action recognition, which is far from the objective of complete localization. As a result, features from CBP are inevitably biased towards partial discriminative frames. To solve the incompleteness issue, many efforts [33, 43, 56, 96] have been attempted, but most of them are trapped in a 'performance-cost dilemma', namely, solely digging from barren category labels to keep costs low. Lacking location labels fundamentally limits the performance, leaving a huge gap from strong supervision.", + "bbox": [ + 496, + 612, + 892, + 868 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To jump out of the dilemma, this paper raises one novel question: is there free action knowledge available, to help", + "bbox": [ + 498, + 869, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "14751", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "complete detection results while maintain cheap annotation overhead at the same time? We naturally turn our sights to the prevalent Vision-Language Pre-training (VLP) [22, 66]. VLP has demonstrated great success to learn joint visual-textual representations from large-scale web data. As language covers rich information about objects, human-object interactions, and object-object relationships, these learned representations could provide powerful human-object co-occurrence priors: valuable gifts for action localization.", + "bbox": [ + 75, + 90, + 472, + 227 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We here take one step towards positively answering the question, i.e. fill the research gap of distilling action priors from VLP, namely CLIP [66], to solve the incomplete issue for WTAL. As illustrated in Figure 1 (A), we first naively evaluate the temporal localization performance of VLP by frame-wise classification. But the results are far from satisfactory, suffering from the serious over-complete issue, i.e. confusing multiple action instances into a whole, causing high false positives. We conjecture the main reasons are: (1) due to data and computational burden, almost all VLPs are trained using image-text pairs. Hence, VLP lacks sufficient temporal knowledge and relies more on human-object co-occurrence for localization, making it struggle to distinguish the actions with visually similar background contexts; (2) some background contexts have similar (confusing) textual semantics to actions, such as run-up vs. running.", + "bbox": [ + 75, + 229, + 472, + 470 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Although simply steering VLP for WTAL is infeasible, we fortunately observe the complementary property between CBP and VLP paradigms: the former localizes high true negatives but serious false negatives, while the latter has high true positives but serious false positives. To leverage the complementarity, as shown in Figure 1 (B), we design a novel distillation-collaboration framework that uses two branches to play the roles of CBP and VLP, respectively. The design rationale is to distill background knowledge from the CBP branch, while foreground knowledge from the VLP branch, for strong alliances. Specifically, we first warm up the CBP branch using only category supervision to initialize confident background frames, and then optimize the framework via an alternating strategy. During $B$ step, we distill background pseudo-labels for the VLP branch to solve the over-complete issue, hence obtaining high-quality foreground pseudo-labels. During $F$ step, we leverage high-quality pseudo-labels for the CBP branch to tackle the incomplete issue. Besides, in each step, we introduce both confident knowledge distillation and representation contrastive learning for pseudo-label denoising, effectively fusing complementarity for better results.", + "bbox": [ + 75, + 473, + 472, + 806 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "On two standard benchmarks: THUMOS14 and ActivityNet1.2, our method improves the average performance by $3.5\\%$ and $2.7\\%$ over state-of-the-art methods. We also conduct extensive ablation studies to reveal the effectiveness of each component, both quantitatively and qualitatively.", + "bbox": [ + 75, + 806, + 470, + 883 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To sum up, our contributions lie in three folds:", + "bbox": [ + 96, + 885, + 405, + 900 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We pioneer the first exploration in distilling free action knowledge from off-the-shelf VLP to facilitate WTAL;", + "- We design a novel distillation-collaboration framework that encourages the CBP branch and VLP branch to complement each other, by an alternating optimization strategy;", + "- We conduct extensive experiments and ablation studies to reveal the significance of distilling VLP and our superior performance on two public benchmarks." + ], + "bbox": [ + 496, + 90, + 893, + 217 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 233, + 640, + 250 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Vision-Language Pre-training (VLP) aims to learn cross-modal representations [10, 25, 57, 82] from large-scale web data. Compared to video, image usually needs fewer costs for annotation and computation, hence almost all VLPs are image-based, e.g. [1, 22, 66, 80, 91, 93]. Recently, several studies adopted VLP to provide free visual-semantic knowledge for downstream image tasks, such as detection [16,94], segmentation [44,54,67,103], human-object interaction [29, 36], synthesis [47], and generation [9, 76, 77]. In terms of the video domain, [42, 51, 79] equipped VLP with temporal transformers for action recognition. [23, 24, 59] introduced prompt learning for efficient retrieval or detection. However, these studies focus more on open-vocabulary scenarios or short video understanding. On the contrary, this paper makes the first exploration to steer VLP for long video temporal localization, under the weakly-supervised setting.", + "bbox": [ + 496, + 257, + 893, + 501 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Strongly-supervised Temporal Action Localization has achieved great progress [38,46,65,95], given precise action boundaries and categories. There are two popular pipelines: the top-down framework [6,14,40,69,71,75,81,83,85,104] pre-defines massive anchors based on the action distribution prior, and uses fixed-length sliding windows to generate initial proposals, then regresses to refine boundaries; the bottom-up framework [3,8,37,39,41,58,74,85,87,100,101] trains frame-wise boundary detectors for extreme frames (start, end, center), then groups extreme frames or estimates action lengths to produce proposals. In addition, some papers [11, 49, 88] proposed various fusion strategies to complement these frameworks. Several studies [45, 95] are devoted to better post-processing. Nevertheless, all the above methods demand precise boundary annotations, which are time-consuming and expensive in reality.", + "bbox": [ + 496, + 503, + 893, + 746 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Weakly-supervised Temporal Action Localization significantly alleviates annotation costs, training with only category labels. The pivotal component is CAS [21, 62, 64, 78] obtained from Classification-Based Pre-training (CBP). But due to the gap of classification and localization, CBP suffers from one serious incomplete issue: only localize discriminative action fragments or even background. To solve this issue, [27, 56, 102] introduced the erasing strategy. [43, 52, 60] produced multiple CAS in parallel for complementarity. [32, 33, 63, 68] proposed background modeling", + "bbox": [ + 496, + 750, + 895, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "14752", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/59453d5eecfd774c0444e957b5333195085e5613625f50124ad901ed40b5c086.jpg", + "image_caption": [ + "Figure 2. Distillation-Collaboration Framework. It covers two parallel branches, named CBP and VLP, and is optimized by an alternating strategy. We warm up the CBP branch in advance. In B step, we freeze both CLIP encoders, and distill confident background pseudo-labels from the CBP branch, to train prompt vectors and temporal Transformer in the VLP branch. In F step, confident foreground pseudo-labels are distilled for the CBP branch. We utilize both knowledge distillation loss and contrastive loss during dual-branch collaboration." + ], + "image_footnote": [], + "bbox": [ + 84, + 89, + 885, + 368 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "and context separation. [12, 17, 19, 97] enhanced features by intra- and inter-video modeling. To iteratively refine results, some papers [53, 89, 96] introduced the self-training strategy, [50, 70] adopted outer-inner contrastive learning. While encouraging, most of them are trapped in the 'performance-cost dilemma', i.e. solely digging from barren category labels to keep costs low. But the lack of annotations leads to a huge performance gap between strong and weak supervisions. To this end, [26, 28, 30, 55, 61, 86] explored to add instance-number or single-frame annotations for further improvements. Some papers [2, 4, 84, 99] tried long-video pretraining for TAL. As a fresh departure from existing work, to pursue better performance without additional annotation costs, this paper intends to distill free action knowledge from off-the-shelf VLPs, to assist WTAL.", + "bbox": [ + 75, + 458, + 472, + 684 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 698, + 169, + 713 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Notations and Preliminaries", + "text_level": 1, + "bbox": [ + 76, + 722, + 328, + 736 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Task Formulation. Given $N$ untrimmed videos $\\{v_{i}\\}_{i = 1}^{N}$ and their video-level category labels $\\{\\mathbf{y}_i\\in \\mathbb{R}^C\\}_{i = 1}^N$ , where $C$ means the total number of action categories, WTAL intends to detect and classify all action instances, in terms of a set of quadruples $\\{(s,e,c,p)\\}$ , where $s,e,c,p$ represent the start time, the end time, the action category and detection score of the action proposal, respectively. Note that each video may contain multiple action instances.", + "bbox": [ + 75, + 744, + 468, + 866 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Motivation. There exists significant complementarity between the localization results of Classification-Based Pre", + "bbox": [ + 75, + 869, + 470, + 898 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "training and Vision-Language Pre-training, as concluded in Table 3. The former suffers from incomplete results (serious false negatives), but has good true negatives; the latter suffers from over-complete results (serious false positives), but has good true positives. Such investigations motivate us to collaborate the complementary results for strong alliances, through a distillation-collaboration framework.", + "bbox": [ + 496, + 458, + 892, + 564 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Framework Overview. As demonstrated in Figure 2, the distillation-collaboration framework consists of two parallel branches, named CBP branch and VLP branch respectively, and is optimized by an alternating strategy. The CBP branch is first warmed-up to produce rich background information with only classification supervision. During B step, we distill confident background pseudo-labels from CBP branch, for VLP branch to tackle the over-complete issue, and thus localize high-quality foreground and background information. During F step, we distill superior pseudo-labels from the well-trained VLP branch, for CBP branch to tackle the incomplete issue. Through such dual-branch collaboration, we effectively fuse the complementary results.", + "bbox": [ + 496, + 568, + 893, + 765 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Distillation of Foreground and Background", + "text_level": 1, + "bbox": [ + 500, + 784, + 867, + 800 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The CBP Branch is utilized to identify a large number of background frames as well as several discriminative action frames, by exploiting Classification-Based Pre-training.", + "bbox": [ + 496, + 809, + 892, + 854 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Following literature [33, 43], we adopt CB pre-training, i.e. the I3D architecture pre-trained on Kinetics [5], to extract RGB and Flow features, and then concatenate them", + "bbox": [ + 496, + 854, + 892, + 898 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "14753", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "to form the two-stream features $\\mathbf{F}_{\\mathrm{i3d}} \\in \\mathbb{R}^{T \\times 2D}$ , where $T$ and $D$ refer to the temporal length and feature dimension. Next, feeding with $\\mathbf{F}_{\\mathrm{i3d}}$ , the CBP branch uses the backbone network for feature fine-tuning and localization, and finally outputs the frame-level action probabilities $\\mathbf{P}^{\\mathrm{cb}} \\in \\mathbb{R}^{T \\times C}$ .", + "bbox": [ + 75, + 89, + 467, + 166 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To achieve action classification, we adopt multiple instance learning, i.e. for the output $\\mathbf{P}^{\\mathrm{cb}}$ from the backbone network, we aggregate (pool) the top- $k$ frames' scores as video-level category scores $\\widehat{\\mathbf{y}}\\in \\mathbb{R}^{C}$ , then supervise it via the binary cross-entropy loss, which is formulated as:", + "bbox": [ + 75, + 167, + 467, + 242 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {c l s}} = \\sum_ {c = 1} ^ {C} - y _ {c} \\log \\widehat {y} _ {c}, \\quad \\widehat {y} _ {c} = \\sigma \\left(\\frac {1}{k} \\sum \\mathcal {K} \\left(\\mathbf {P} ^ {\\mathrm {c b}}\\right)\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 251, + 467, + 292 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{K}$ denotes the top- $k$ score set in the temporal domain, and $\\sigma$ refers to the softmax function.", + "bbox": [ + 76, + 301, + 467, + 330 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Remark. Under CB Pre-training and category-only supervision, $\\mathbf{P}^{\\mathrm{cb}}$ is well known for focusing on sparse discriminative action frames, i.e. high true negatives but serious false negatives, thus can provide rich background information.", + "bbox": [ + 75, + 337, + 467, + 397 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The VLP Branch is designed to mine free action knowledge from VL Pre-training, e.g. CLIP [66]. Since imagetext pre-training lacks sufficient temporal priors, its vanilla localization results have a serious over-complete issue, i.e. high false positives. To tackle this issue, we propose to finetune CLIP using extensive background samples.", + "bbox": [ + 75, + 404, + 467, + 494 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Instead of linear probing, we use efficient prompt learning [23, 34] for fine-tuning: we freeze the CLIP backbone, only optimize several prompt vectors and temporal layers.", + "bbox": [ + 75, + 494, + 467, + 539 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Concretely, for the visual stream, we first split the video into consecutive frames, and then utilize the CLIP image encoder to extract frame-level features $\\mathbf{F}_{\\mathrm{vis}} \\in \\mathbb{R}^{T \\times D}$ . For temporal relationship construction, we strengthen $\\mathbf{F}_{\\mathrm{vis}}$ into $\\mathbf{F}_{\\mathrm{vid}} \\in \\mathbb{R}^{T \\times D}$ through simple temporal transformer layers $\\Phi_{\\mathrm{temp}}(\\cdot)$ . While for the textual stream, we first prepend and append several learnable prompt vectors $\\Phi_{\\mathrm{prmp}}(\\cdot)$ to category names, then feed them into the CLIP text encoder, to obtain textual features $\\mathbf{F}_{\\mathrm{txt}} \\in \\mathbb{R}^{C \\times D}$ . Formally,", + "bbox": [ + 75, + 541, + 467, + 676 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {F} _ {\\mathrm {v i d}} = \\Phi_ {\\text {t e m p}} (\\mathbf {F} _ {\\text {v i s}}), \\quad \\mathbf {F} _ {\\mathrm {t x t}} = \\Phi_ {\\mathrm {t x t}} \\left(\\Phi_ {\\text {p r m p}} \\left(\\mathrm {C} _ {\\text {n a m e}}\\right)\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 686, + 467, + 704 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $C_{\\text{name}}$ refers to action category names, and $\\Phi_{\\text{txt}}(\\cdot)$ is the CLIP textual encoder. Thereafter, the frame-level localization results $\\mathbf{P}^{\\text{vl}}$ for this branch can be calculated as:", + "bbox": [ + 75, + 712, + 467, + 758 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {P} ^ {\\mathrm {v l}} = \\sigma \\left(\\mathbf {F} _ {\\mathrm {v i d}} \\cdot \\mathbf {F} _ {\\mathrm {t x t}} ^ {\\top}\\right) \\in \\mathbb {R} ^ {T \\times C}. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 165, + 770, + 467, + 789 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Remark. For the VLP branch, we only optimize lightweight model parameters for false-positive suppression, naturally bringing two main benefits: (1) the frozen CLIP backbone preserves the action prior knowledge in pre-training, thus maintaining high true-positive results; (2) it matches the demand for less supervision data under weakly-supervised settings, and also saves the memory footprint.", + "bbox": [ + 75, + 795, + 467, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Confident Pseudo-labels. Since both $\\mathbf{P}^{\\mathrm{vl}}$ and $\\mathbf{P}^{\\mathrm{cb}}$ contain somewhat noise, to make reliable use of complementary information, we distill confident location pseudo-labels of foreground and background respectively. That is, for the CBP branch, we distill extensive background pseudo-labels from the output $\\mathbf{P}^{\\mathrm{cb}}$ ; while for the VLP branch, we distill sufficient foreground pseudo-labels from the output $\\mathbf{P}^{\\mathrm{vl}}$ .", + "bbox": [ + 496, + 90, + 890, + 196 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For both branches, we leverage double thresholds $\\delta_h$ and $\\delta_l$ ( $\\delta_h > \\delta_l$ ), to convert localization results $\\mathbf{P}$ into ternary pseudo-labels $\\mathbf{H} \\in \\mathbb{R}^{T \\times C}$ , which are formally written as:", + "bbox": [ + 496, + 196, + 890, + 242 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nh _ {t, c} = \\left\\{ \\begin{array}{c} 1 \\text {i f} p _ {t} > \\delta_ {h} \\text {a n d} p _ {c} = y _ {c} \\\\ 0 \\text {i f} p _ {t} < \\delta_ {l} \\text {o r} p _ {c} \\neq y _ {c} \\\\ - 1 \\quad \\text {o t h e r w i s e} \\end{array} \\right. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 562, + 252, + 890, + 306 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the subscripts $c$ and $t$ refer to the indices of category and frame. More specifically, for either branch, we regard frames with scores more than $\\delta_h$ and the correct action category as the foreground; while frames with scores less than $\\delta_l$ or with the wrong action category are treated as the background; the remaining frames are considered uncertain. As a result, the pseudo-labels $\\mathbf{H}^{\\mathrm{cb}}$ cover vast confident background frames, as well as trivial foreground frames; while the pseudo-labels $\\mathbf{H}^{\\mathrm{vl}}$ contain dense confident foreground frames, and partial background frames. Note that, for both branches, we generate positive and negative frames to avoid trivial solutions, and facilitate contrastive feature learning.", + "bbox": [ + 496, + 316, + 890, + 500 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Collaboration of Dual-Branch Optimization", + "text_level": 1, + "bbox": [ + 498, + 513, + 870, + 530 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section, we encourage two branches to collaborate with each other, such that forming a strong alliance of their complementary localization results. To reduce serious noises in pseudo-labels, we introduce an alternate training strategy for dual-branch collaborative optimization.", + "bbox": [ + 496, + 537, + 890, + 613 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The design rationale is to distill Background knowledge from the CBP branch for B step, while distill Foreground knowledge from the VLP branch in F step. To be specific, we warm up the CBP branch in advance, using only category supervision, to initialize reliable background frames. During B Step, we freeze the well-trained CBP branch, and then generate confident background pseudo-labels $\\mathbf{H}^{\\mathrm{cb}}$ to supervise the VLP branch. As a result, these false-positive confusions from vanilla CLIP pre-training are greatly tackled, and the resultant pseudo-labels contain a large number of confident foreground frames and background frames. During F Step, the high-quality pseudo-labels $\\mathbf{H}^{\\mathrm{vl}}$ are distilled from the frozen VLP branch, to guide the CBP branch for the false-negative suppression. Under such an alternating strategy, these two branches not only complement each other, but also correct each other, thus jointly contributing to more precise and complete action localization.", + "bbox": [ + 496, + 614, + 890, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "During each step, to supervise either branch, we adopt both the knowledge distillation loss $\\mathcal{L}_{\\mathrm{kd}}$ and foreground", + "bbox": [ + 496, + 869, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "14754", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "background contrastive loss $\\mathcal{L}_{\\mathrm{fb}}$ . The total optimization loss can be written with a balancing ratio $\\lambda$ , as follows:", + "bbox": [ + 76, + 90, + 468, + 121 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {a l l}} = \\mathcal {L} _ {\\mathrm {k d}} \\left(\\mathbf {H} ^ {\\prime}, \\mathbf {P}\\right) + \\lambda \\mathcal {L} _ {\\mathrm {f b}} \\left(\\Psi^ {+}, \\Psi^ {-}\\right). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 128, + 468, + 147 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Here, $\\mathcal{L}_{\\mathrm{kd}}$ regularizes one branch to output similar detection results with pseudo-labels from the other branch. Given that there exist some noises in pseudo-labels, i.e. uncertain frames, we only make supervision on confident frames.", + "bbox": [ + 76, + 155, + 468, + 215 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {k d}} \\left(\\mathbf {H} ^ {\\prime}, \\mathbf {P}\\right) = \\frac {1}{O} \\sum_ {c = 1} ^ {C} \\sum_ {t = 1} ^ {O} D _ {\\mathrm {K L}} \\left(h _ {t, c} ^ {\\prime} \\mid \\mid p _ {t, c}\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 127, + 223, + 468, + 263 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $D_{\\mathrm{KL}}(p(x) || q(x))$ refers to the Kullback-Leibler divergence of distribution $p(x)$ from distribution $q(x)$ , $O$ is the total number of confident frames, and $\\mathbf{H}'$ denotes the pseudo-labels from the other branch. Note that, the pseudolabels contain two types of confident frames: foreground and background, which could help to avoid falling into the trivial solutions under one single type of labels.", + "bbox": [ + 76, + 272, + 468, + 378 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Moreover, in untrimmed long videos, some background contexts could appear visually similar with the action (foreground). We further introduce contrastive learning to pull foreground features and push background features. Specifically, we treat confident foreground frames from the same action category as the positive set $\\Psi^{+}$ , while all confident background frames as the negative set $\\Psi^{-}$ , then foreground-background contrastive loss is formulated as:", + "bbox": [ + 75, + 378, + 468, + 500 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {f b}} \\left(\\Psi_ {i} ^ {+}, \\Psi_ {i} ^ {-}\\right) = \\sum_ {i} - \\log \\frac {\\sum_ {m \\in \\Psi_ {i} ^ {+}} \\exp \\left(\\mathbf {f} _ {i} \\cdot \\mathbf {f} _ {m} / \\tau\\right)}{\\sum_ {j \\in *} \\exp \\left(\\mathbf {f} _ {i} \\cdot \\mathbf {f} _ {j} / \\tau\\right)}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 506, + 468, + 546 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{f} \\in \\mathbb{R}^D$ refers to the frame feature, $\\tau$ means the temperature hyper-parameter for scaling, and $*$ means the union of $\\Psi_i^+$ and $\\Psi_i^-$ . Take the VLP branch as an example, sufficient background pseudo-labels contain considerable hard negative samples, to help distinguish features of foreground and contexts. In addition, the enhanced features of uncertain frames also become more discriminative, further facilitating more complete temporal action localization.", + "bbox": [ + 76, + 555, + 468, + 676 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Discussion. Comparing to various fusion strategies, our alternating strategy produces more precise and complete results (see Table 4 for details). This strategy plays a similar role as the multi-view co-training, where CBP and VLP branches can be deemed as two distinctive views, thus being quite robust to pseudo-label noises. For B step, we prompt the VLP branch for high-quality pseudo-labels, where some frames with conflicting predictions are still treated as uncertain. In F step, we use feature contrastive loss to make their results more discriminative, i.e. further denoising.", + "bbox": [ + 75, + 680, + 468, + 832 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Inference", + "text_level": 1, + "bbox": [ + 76, + 847, + 186, + 861 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "At testing time, we leverage the results from the CBP branch for post-processing, as vision-language pre-training", + "bbox": [ + 76, + 869, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "cannot handle Optical Flow, which is essential for WTAL. Given an input video, we first obtain video-level category probabilities and frame-level localization scores. For action classification, we select the classes with probability greater than $\\theta_{cls}$ ; and for localization, we threshold detection scores with $\\theta_{loc}$ , concatenate consecutive snippets as action proposals, and eliminate redundant proposals with soft nonmaximum suppression (NMS). Each proposal is scored with the detection maximum in the proposal interval.", + "bbox": [ + 496, + 90, + 890, + 227 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 498, + 241, + 633, + 258 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Implementation", + "text_level": 1, + "bbox": [ + 500, + 267, + 660, + 282 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. THUMOS14 owns 413 untrimmed videos from 20 categories, and each video contains an average of 15 instances. As conventions, we train on 200 validation videos, and evaluate on 213 testing videos. Despite its small scale, this dataset is challenging, since video lengths vary widely and actions occur frequently. ActivityNet1.2 covers 9682 videos belonging to 100 categories. Almost all the videos are single-category, and action regions take up more than half of the video duration. We train on 4619 training videos and evaluate on 2383 validation videos.", + "bbox": [ + 496, + 289, + 890, + 440 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Metrics. To evaluate localization performance, we follow the standard protocol to use mean Average Precision (mAP) at different intersections over union (IoU) thresholds. Note that a proposal is regarded as positive only if both the category prediction is correct and IoU exceeds the set threshold. To clearly evaluate the quality of pseudo-labels, we also report mean Intersection over Union (mIoU) averaged over the foreground categories and the background category.", + "bbox": [ + 496, + 445, + 890, + 566 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Details. To handle the large variety in video durations, we randomly sample $T$ consecutive snippets for each video. $T$ is set to 1000 on THUMOS14, and 400 on ActivityNet1.2. We utilize the TV-L1 algorithm to extract optical flow from RGB data. For the CBP branch, we use Transformer architectures (multi-head self-attention, layer norm, and MLPs) as the backbone network. For the VLP branch, we use a 2-layer temporal Transformer, preprocess and append 16 prompt vectors to textual inputs, both are initialized by $\\mathcal{N}(0,0.01)$ . Both CLIP image encoder and text encoder are adopted from ViT-B/16. The framework is optimized by Adam with the learning rate of $10^{-4}$ . All hyper-parameters are set by grid search: pseudo-label thresholds $\\delta_h = 0.3$ , $\\delta_l = 0.1$ , inference thresholds $\\theta_{cls} = 0.85$ , $\\theta_{loc} = 0.45$ , the balancing ratio $\\lambda = 0.05$ , the temperature $\\tau = 0.07$ .", + "bbox": [ + 496, + 569, + 890, + 796 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Comparison with State-of-the-art Methods", + "text_level": 1, + "bbox": [ + 500, + 813, + 864, + 829 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Here, we make comprehensive comparisons with current state-of-the-art methods across multiple IoU thresholds.", + "bbox": [ + 500, + 838, + 890, + 867 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Performance. The comparisons on THUMOS14 are provided in Table 1. Here, we separate two levels of supervi", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "14755", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/e12804a0a7a62f6b8e8868349f9f4f96227538f3b34e344b6d21c282dd7903fd.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
SupervisionMethodFeaturemAP@IoUAVG(0.1-0.5)AVG(0.3-0.7)
0.10.20.30.40.50.60.7
StrongDBS [15]I3D56.754.750.643.134.324.414.747.933.4
BUMR [100]--53.950.745.438.028.5-43.3
GCM [95]72.570.966.560.851.9--64.5-
RCL [81]--70.162.352.942.730.7-51.7
ActionFormer [98]--82.177.871.059.443.9-66.8
WeakHAM-Net [21]I3D65.459.050.341.131.020.711.449.430.9
UM [33]63.056.649.040.930.421.010.448.030.3
TS-PCA [48]67.661.153.443.434.324.713.752.033.9
FTCL [12]69.663.455.245.235.623.712.253.834.4
ACGNet [90]68.162.653.144.634.722.612.052.633.4
DCC [35]69.063.855.945.935.724.313.754.135.1
ASM-Loc [17]71.265.557.146.836.625.213.455.435.8
CO2-Net [18]70.163.654.545.738.326.413.454.435.7
RSKP [20]71.365.355.847.538.225.412.555.635.9
DELU [7]71.566.256.547.740.527.215.356.537.4
CO2-Net†I3D67.460.651.943.135.023.312.151.633.0
CO2-Net‡68.862.152.643.936.124.112.052.733.7
DELU†+CLIP68.660.852.243.435.623.313.352.133.6
DELU‡70.363.955.445.939.026.014.354.936.0
Ours73.568.861.553.842.029.416.860.040.8
", + "bbox": [ + 89, + 88, + 877, + 407 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/741e68137424c80db7842807e9a73768124b44644aed192274858e2416455228.jpg", + "table_caption": [ + "Table 1. Comparison with state-of-the-art methods on THUMOS14. For fair comparisons, we reproduce the results of SOTA methods: CO2-Net [18] and DELU [7], by inputting both I3D [5] and CLIP [66] features. † and ‡ refer to averaging or concatenating these two features. AVG(0.1-0.5) and AVG(0.3-0.7) are the average mAP from IoU 0.1 to 0.5 and from IoU 0.3 to 0.7. Our framework significantly surpasses all weakly-supervised competitors using identical features, and is even comparable to early strongly-supervised methods." + ], + "table_footnote": [], + "table_body": "
MethodFeaturemAP@IoUAVG
0.50.750.95
CleanNet [50]I3D37.120.35.021.6
CMCS [43]36.822.05.622.4
TSCN [96]37.623.75.723.6
BasNet [31]38.524.25.624.3
DGAM [68]41.023.55.324.4
UM [33]41.225.66.025.9
ACGNet [90]41.826.05.926.1
D2-Net [60]42.325.55.826.0
CO2-Net [18]43.326.35.226.4
DELU [7]44.226.75.426.9
CO2-Net†I3D44.826.95.527.1
CO2-Net‡45.227.15.827.6
DELU†+45.427.35.727.5
DELU‡CLIP46.027.85.928.0
Ours48.329.36.129.6
", + "bbox": [ + 78, + 503, + 464, + 750 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Comparison with state-of-the-art methods on ActivityNet1.2. For fair comparisons, we reproduce CO2-Net [18] and DELU [7], by inputting I3D [5] and CLIP [66] features. $\\dagger$ and $\\ddagger$ refer to averaging or concatenating these features. AVG is the average mAP at the thresholds 0.5:0.05:0.95. Our method significantly surpasses all competitors, especially at loose IoU thresholds.", + "bbox": [ + 75, + 758, + 470, + 845 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "sion: strong and weak, for better quantification. Generally speaking, our framework achieves new state-of-the-art on", + "bbox": [ + 75, + 869, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "all IoU regimes. Comparing with recent methods, the gain of the average mAP (0.3-0.7) even reaches $4 - 5\\%$ , further narrowing the performance gap between weak and strong supervisions. Moreover, our method achieves considerable gains on strict and loose evaluations. For example, when comparing to DELU [7], the gains are $3.5\\%$ average mAP (0.1-0.5) and $3.4\\%$ average mAP (0.3-0.7), indicating that our results are complete and precise. Furthermore, despite being weakly-supervised settings, at several low IoU thresholds, our framework even performs comparably with some earlier strongly-supervised methods [14, 15, 101].", + "bbox": [ + 496, + 498, + 890, + 666 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2 shows the comparison results on ActivityNet1.2. On all IoU thresholds, our designed framework surpasses existing methods by a large margin. In terms of the average mAP, the performance improvement can reach $2.7\\%$ , taking the state-of-the-art to a new level. However, due to the lack of precise location annotations, the gain decreases as the IoU threshold becomes stricter, e.g. $4.1\\%$ @IoU 0.5 vs. $0.7\\%$ @IoU 0.95, when comparing to DELU [7].", + "bbox": [ + 496, + 667, + 890, + 792 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Source of Gain. Comparing to existing methods, we leverage Vision-Language Pre-training for free knowledge. To make fair comparisons, we also input both I3D and CLIP features into two SOTA methods [7, 18], by one early fusion mode (average or concatenate these features). In general, simply adding CLIP features gives only slight or even negative gains on both datasets, which is due to the bad over", + "bbox": [ + 496, + 794, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "14756", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/7f8284725b92921436f811a10695b3af65f60edc4b48049a933fbfeb8ddab968.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
SettingTHUMOSActivityNet
ForeBackForeBack
CB Pre-training56.088.754.788.3
VL Pre-training75.634.172.145.0
Ours72.480.069.571.7
", + "bbox": [ + 78, + 88, + 464, + 170 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/cc66964deecab33d7f270b1bfea1a9548c32eda7334a5e2d3bbefc45c6d43956.jpg", + "table_caption": [ + "Table 3. Complementarity of pre-training. CB Pre-training has good background mIoU but inferior foreground mIoU. VL Pretraining has good foreground mIoU but inferior background mIoU. Our method achieves both high foreground and background mIoU." + ], + "table_footnote": [], + "table_body": "
Fusion StrategymAP@IoUAVG(0.3-0.7)
0.30.50.7
Only F step (AVG)40.016.13.319.1
Only F step (Weight)52.825.56.127.7
Only B step (AVG)56.733.611.334.1
Only B step (Weight)58.538.814.837.8
Alternating61.542.016.840.8
", + "bbox": [ + 78, + 260, + 464, + 371 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "complete issue of CLIP (detailed in Table 3). For THUMOS with complex and frequent actions, over-complete worsens results. While in ActivityNet, most videos only contain one action that takes up half of the video duration, thus benefiting a bit from over-complete. Nevertheless, with identical features, our method significantly outperforms existing competitors, proving the effectiveness of our framework.", + "bbox": [ + 75, + 476, + 468, + 583 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Study and Comparison", + "text_level": 1, + "bbox": [ + 76, + 599, + 362, + 614 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Here, we evaluate the contributions of each component and framework designs, to further dissect our framework.", + "bbox": [ + 76, + 622, + 468, + 652 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Complementarity of pre-trainings. As the detection performance is mainly determined by pseudo-labels, here we show the quality of pseudo-labels, in terms of foreground mIoU and background mIoU. Table 3 provides the comprehensive results for various settings on both benchmarks.", + "bbox": [ + 76, + 657, + 468, + 733 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For common Classification-Based Pre-training, its localization results suffer from the incomplete issue. In detail, the background mIoU is impressive, i.e. high true negatives, while the foreground mIoU is poor, i.e. serious false negatives. The main reason is that features pre-trained on action classification datasets only highlight sparse discriminative frames. While the results of Vision-Language Pre-training are just the opposite: suffering from the over-complete issue. The foreground mIoU is considerable, i.e. high true positives, but the background mIoU is terrible, i.e. serious false positives. The main reason is that VLP using image", + "bbox": [ + 75, + 734, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/613f74baabd367ca9a2986b24563413e0fdaa39cba2be291e6a75d1c305cdc04.jpg", + "table_caption": [ + "Table 4. Comparison of optimization strategies. \"Only F step\": extract pseudo-labels from vanilla VLP to train the CBP branch. \"Only B step\": get pseudo-labels from the warm-up CBP branch to train the VLP branch. We combine two branches by averaging and weighting. Our alternating strategy shows clear superiority." + ], + "table_footnote": [], + "table_body": "
ModelLkdLf bmAP@IoUAVG(0.3-0.7)
0.30.50.7
A1✓57.137.012.636.0
A2✓51.731.29.430.9
A3✓✓61.542.016.840.8
", + "bbox": [ + 501, + 89, + 887, + 170 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/7d4e804e79d21efbc8307781ce3a06ad139974140217afa83332ee836e827b0e.jpg", + "table_caption": [ + "Table 5. Contribution of optimization losses on THUMOS14. The single knowledge distillation loss $\\mathcal{L}_{\\mathrm{kd}}$ has brought gratifying localization results, and the additional foreground-background contrastive loss $\\mathcal{L}_{\\mathrm{fb}}$ further boosts the performance to the best." + ], + "table_footnote": [], + "table_body": "
MethodmAP@IoUAVG (0.3-0.7)
0.30.50.7
UM [33]49.030.410.430.3
UM + Ours53.934.713.634.3
CO2-Net [18]54.538.313.435.7
CO2-Net + Ours56.239.715.937.5
", + "bbox": [ + 503, + 255, + 885, + 351 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 6. Framework generalization on THUMOS14. Our proposed framework is generalized, i.e. existing methods can serve as our CBP branch, to achieve further improvements.", + "bbox": [ + 498, + 358, + 890, + 401 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "text pairs lacks temporal priors. The above results strongly prove the complementarity between these two pre-training.", + "bbox": [ + 498, + 428, + 890, + 458 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Moreover, on both datasets, our method achieves high foreground and background mIoU, that is, more precise and complete localization. This mainly benefits from extensive background supervision provided by the CBP branch, and extensive foreground supervision distilled from the VLP branch. Besides, comparing to VL Pre-training, our results achieve immediate gains on the background mIoU, while only slight drops on the foreground mIoU. This reveals that the lightweight trainable parameters, i.e. prompts + Transformer, indeed retain the action prior knowledge in VLP, and also significantly suppress false-positive results.", + "bbox": [ + 496, + 458, + 890, + 625 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison of optimization strategies. To evaluate the alternating efficacy, Table 4 compares with another two solutions. (1) 'Only F step': extract foreground pseudo-labels from the vanilla VLP, then provide them to the CBP branch for auxiliary training; (2) 'Only B step': distill background pseudo-labels from the warm-up CBP branch to train the VLP branch. And for each solution, we combine the dual-branch results by averaging and weighting, respectively.", + "bbox": [ + 496, + 628, + 890, + 750 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "'Only F step' performs the worst, mainly suffering from heavy noise in vanilla VLP pseudo-labels (over-complete). By fine-tuning vanilla VLP with many background frames, 'Only B step' gets great improvements, but still lacks full fusion of complementarity. Moreover, the weighted operation could suppress noise somewhat, and thus causes better results than the average operation. By comparison, our alternating strategy shows great advantages over competitors, proving the non-trivial nature of fusing complementary information, and robust denoising to pseudo-labels.", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "14757", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/1f8532f9bdd1800484187c111544bc22987b84b98185af21a2f9ffb3039dabf5.jpg", + "image_caption": [ + "Figure 3. Qualitative comparisons. The first two rows are videos and ground-truth action intervals. The last six rows are frame-level action probabilities, and localization results of Classification-Based Pre-training (CBP), Vision-Language Pre-training (VLP), and our framework, respectively. CBP suffers from the incomplete issue, while VLP has the over-complete issue. Our framework distills foreground knowledge from VLP and background from CBP, for the strong collaborative alliance, thus bringing more complete and precise results." + ], + "image_footnote": [], + "bbox": [ + 106, + 84, + 867, + 318 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Contribution of various losses. To train our method, both knowledge distillation loss $\\mathcal{L}_{\\mathrm{kd}}$ and foreground-background contrastive loss $\\mathcal{L}_{\\mathrm{fb}}$ are leveraged. In Table 5, we analyze the effectiveness of optimization losses on THUMOS14. The single $\\mathcal{L}_{\\mathrm{kd}}$ (model A1) already brings gratifying performance. This reveals that the confident pseudo-labels of foreground and background distilled from two branches, are well fused by the alternate optimization. On the other hand, with only $\\mathcal{L}_{\\mathrm{fb}}$ , model A2 also performs barely satisfactory results. This is because $\\mathcal{L}_{\\mathrm{fb}}$ differentiates foreground features and background features, thus eliminating extensive uncertain frames, and also making the localization task easier. Overall, these two losses jointly contribute to the best performance, indicating that both are essential.", + "bbox": [ + 75, + 405, + 472, + 618 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Framework generalization. Our distillation-collaboration framework is generalized, which means that existing WTAL methods can be employed as the CBP branch. Table 6 takes two typical methods: CO2-Net [18] and UM [33], as examples. Our framework further improves their performance by up to $2 - 4\\%$ average mAP, showing a good generalization to other methods and other backbone designs.", + "bbox": [ + 75, + 621, + 470, + 728 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Qualitative Results", + "text_level": 1, + "bbox": [ + 76, + 741, + 261, + 758 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To intuitively demonstrate the superiority, Figure 3 visualizes results from various types of videos. Classification-Based Pre-training highlights only some discriminative action frames (the incomplete issue), which is more prominent for videos containing low-frequency actions. On the contrary, Vision-Language Pre-training tends to over-activate action foreground to background (the over-complete issue), which is especially evident in videos with high-frequency actions. We design the distillation-collaboration framework", + "bbox": [ + 75, + 763, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "to fuse the complementarity from these two pre-trainings. In B step, extensive confident background is distilled from the well-trained CBP branch, to supervise the VLP branch for false-positive suppression. While in F step, sufficient confident foreground information is distilled from the VLP branch, to guide the CBP branch for false-negative elimination. Hence, our method establishes the strong alliance by collaborative optimization, bringing precise and complete detection results, regardless of dense or sparse actions.", + "bbox": [ + 496, + 405, + 893, + 542 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 556, + 619, + 571 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work proposes the novel distillation-collaboration framework to distill free knowledge from Vision-Language Pre-training, for weakly-supervised temporal action localization. Our core insight is that existing VLP often localizes over-complete actions, which is just complementary to the incomplete results of conventional Classification-Based Pre-training. And to form strong alliances, we optimize the framework containing complementary dual branches by an alternating strategy: distill confident background pseudolabels from the CBP branch, and the confident foreground pseudo-labels from the VLP branch, for collaborative training. Extensive experiments show the significance of distilling VLP and our superior performance. Thorough ablations are studied both quantitatively and qualitatively.", + "bbox": [ + 496, + 579, + 893, + 792 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements", + "text_level": 1, + "bbox": [ + 500, + 803, + 668, + 819 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This research is supported by the National Key R&D Program of China (No. 2022ZD0160702), STCSM (No. 22511106101, No. 18DZ2270700, No. 21DZ1100100), 111 plan (No. BP0719010), and State Key Laboratory of UHD Video and Audio Production and Presentation.", + "bbox": [ + 496, + 825, + 893, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "14758", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 106 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Jean-Baptiste Alayrac, Jeff Donahue, Pauline Luc, Antoine Miech, Iain Barr, Yana Hasson, Karel Lenc, Arthur Mensch, Katie Millican, Malcolm Reynolds, et al. 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Vis., 2021. 2" + ], + "bbox": [ + 501, + 90, + 890, + 415 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "14762", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 11 + } +] \ No newline at end of file diff --git a/2023/Distilling Vision-Language Pre-Training To Collaborate With Weakly-Supervised Temporal Action Localization/01d592ea-9922-4de7-a537-4d96044a494d_model.json b/2023/Distilling Vision-Language Pre-Training To Collaborate With Weakly-Supervised Temporal Action Localization/01d592ea-9922-4de7-a537-4d96044a494d_model.json new file mode 100644 index 0000000000000000000000000000000000000000..62bdb5a65afcd3f92358445fcb58732cea12d380 --- /dev/null +++ b/2023/Distilling Vision-Language Pre-Training To Collaborate With Weakly-Supervised Temporal Action Localization/01d592ea-9922-4de7-a537-4d96044a494d_model.json @@ -0,0 +1,2688 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.185, + 0.131, + 0.787, + 0.177 + ], + "angle": 0, + "content": "Distilling Vision-Language Pre-training to Collaborate with Weakly-Supervised Temporal Action Localization" + }, + { + "type": "text", + "bbox": [ + 0.184, + 0.203, + 0.784, + 0.24 + ], + "angle": 0, + "content": "Chen Ju\\(^{1*}\\), Kunhao Zheng\\(^{1*}\\), Jinxiang Liu\\(^{1}\\), Peisen Zhao\\(^{3}\\), Ya Zhang\\(^{1,2}\\), Jianlong Chang\\(^{3}\\), Qi Tian\\(^{3}\\), Yanfeng Wang\\(^{1,2\\boxtimes}\\)" + }, + { + "type": "text", + "bbox": [ + 0.155, + 0.246, + 0.816, + 0.265 + ], + "angle": 0, + "content": "\\(^{1}\\)CMIC, Shanghai Jiao Tong University \\(^{2}\\)Shanghai AI Laboratory \\(^{3}\\)Huawei Cloud" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.268, + 0.878, + 0.283 + ], + "angle": 0, + "content": "{ju_chen, dyekuu, jinxliu, ya_zhang, wangyanfeng}@sjtu.edu.cn, {pszhao93, jianlong.chang, tian.qi1}@huawei.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.317, + 0.314, + 0.334 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.35, + 0.474, + 0.714 + ], + "angle": 0, + "content": "Weakly-supervised temporal action localization (WTAL) learns to detect and classify action instances with only category labels. Most methods widely adopt the off-the-shelf Classification-Based Pre-training (CBP) to generate video features for action localization. However, the different optimization objectives between classification and localization, make temporally localized results suffer from the serious incomplete issue. To tackle this issue without additional annotations, this paper considers to distill free action knowledge from Vision-Language Pre-training (VLP), as we surprisingly observe that the localization results of vanilla VLP have an over-complete issue, which is just complementary to the CBP results. To fuse such complementarity, we propose a novel distillation-collaboration framework with two branches acting as CBP and VLP respectively. The framework is optimized through a dual-branch alternate training strategy. Specifically, during the \\(B\\) step, we distill the confident background pseudo-labels from the CBP branch; while during the \\(F\\) step, the confident foreground pseudo-labels are distilled from the VLP branch. As a result, the dual-branch complementarity is effectively fused to promote one strong alliance. Extensive experiments and ablation studies on THUMOS14 and ActivityNet1.2 reveal that our method significantly outperforms state-of-the-art methods." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.737, + 0.21, + 0.753 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.764, + 0.47, + 0.869 + ], + "angle": 0, + "content": "Temporal action localization (TAL), which aims to localize and classify action instances from untrimmed long videos, has been recognized as an indispensable component of video understanding [13, 72, 92]. To avoid laborious temporal boundary annotations, the weakly-supervised setting (WTAL) [31, 62, 64, 78], i.e. only video-level category labels are available, has gained increasing attentions." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.901 + ], + "angle": 0, + "content": "To date in the literature, almost all WTAL methods rely on Classification-Based Pre-training (CBP) for video fea" + }, + { + "type": "image", + "bbox": [ + 0.499, + 0.312, + 0.895, + 0.484 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.489, + 0.895, + 0.587 + ], + "angle": 0, + "content": "Figure 1. (A) Complementarity. Most works use Classification-Based Pre-training (CBP) for localization, bringing high TN yet serious FN. Vanilla Vision-Language Pre-training (VLP) confuses action and background, bringing high TP yet serious FP. (B) Our distillation-collaboration framework distills foreground from the VLP branch while background from the CBP branch, and promotes mutual collaboration, bringing satisfactory results." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.613, + 0.893, + 0.869 + ], + "angle": 0, + "content": "ture extraction [5, 73]. A popular pipeline is to train an action classifier with CBP features, then threshold the frame-level classification probabilities for final localization results. As demonstrated in Figure 1(A), these CBP methods suffer from the serious incompleteness issue, i.e. only detecting sparse discriminative action frames and incurring high false negatives. The main reason is that the optimization objective of classification pre-training, is to find several discriminative frames for action recognition, which is far from the objective of complete localization. As a result, features from CBP are inevitably biased towards partial discriminative frames. To solve the incompleteness issue, many efforts [33, 43, 56, 96] have been attempted, but most of them are trapped in a 'performance-cost dilemma', namely, solely digging from barren category labels to keep costs low. Lacking location labels fundamentally limits the performance, leaving a huge gap from strong supervision." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.894, + 0.901 + ], + "angle": 0, + "content": "To jump out of the dilemma, this paper raises one novel question: is there free action knowledge available, to help" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "14751" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.228 + ], + "angle": 0, + "content": "complete detection results while maintain cheap annotation overhead at the same time? We naturally turn our sights to the prevalent Vision-Language Pre-training (VLP) [22, 66]. VLP has demonstrated great success to learn joint visual-textual representations from large-scale web data. As language covers rich information about objects, human-object interactions, and object-object relationships, these learned representations could provide powerful human-object co-occurrence priors: valuable gifts for action localization." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.23, + 0.473, + 0.472 + ], + "angle": 0, + "content": "We here take one step towards positively answering the question, i.e. fill the research gap of distilling action priors from VLP, namely CLIP [66], to solve the incomplete issue for WTAL. As illustrated in Figure 1 (A), we first naively evaluate the temporal localization performance of VLP by frame-wise classification. But the results are far from satisfactory, suffering from the serious over-complete issue, i.e. confusing multiple action instances into a whole, causing high false positives. We conjecture the main reasons are: (1) due to data and computational burden, almost all VLPs are trained using image-text pairs. Hence, VLP lacks sufficient temporal knowledge and relies more on human-object co-occurrence for localization, making it struggle to distinguish the actions with visually similar background contexts; (2) some background contexts have similar (confusing) textual semantics to actions, such as run-up vs. running." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.474, + 0.473, + 0.807 + ], + "angle": 0, + "content": "Although simply steering VLP for WTAL is infeasible, we fortunately observe the complementary property between CBP and VLP paradigms: the former localizes high true negatives but serious false negatives, while the latter has high true positives but serious false positives. To leverage the complementarity, as shown in Figure 1 (B), we design a novel distillation-collaboration framework that uses two branches to play the roles of CBP and VLP, respectively. The design rationale is to distill background knowledge from the CBP branch, while foreground knowledge from the VLP branch, for strong alliances. Specifically, we first warm up the CBP branch using only category supervision to initialize confident background frames, and then optimize the framework via an alternating strategy. During \\( B \\) step, we distill background pseudo-labels for the VLP branch to solve the over-complete issue, hence obtaining high-quality foreground pseudo-labels. During \\( F \\) step, we leverage high-quality pseudo-labels for the CBP branch to tackle the incomplete issue. Besides, in each step, we introduce both confident knowledge distillation and representation contrastive learning for pseudo-label denoising, effectively fusing complementarity for better results." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.808, + 0.472, + 0.884 + ], + "angle": 0, + "content": "On two standard benchmarks: THUMOS14 and ActivityNet1.2, our method improves the average performance by \\(3.5\\%\\) and \\(2.7\\%\\) over state-of-the-art methods. We also conduct extensive ablation studies to reveal the effectiveness of each component, both quantitatively and qualitatively." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.406, + 0.901 + ], + "angle": 0, + "content": "To sum up, our contributions lie in three folds:" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "- We pioneer the first exploration in distilling free action knowledge from off-the-shelf VLP to facilitate WTAL;" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.124, + 0.894, + 0.17 + ], + "angle": 0, + "content": "- We design a novel distillation-collaboration framework that encourages the CBP branch and VLP branch to complement each other, by an alternating optimization strategy;" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.172, + 0.894, + 0.218 + ], + "angle": 0, + "content": "- We conduct extensive experiments and ablation studies to reveal the significance of distilling VLP and our superior performance on two public benchmarks." + }, + { + "type": "list", + "bbox": [ + 0.498, + 0.092, + 0.894, + 0.218 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.234, + 0.642, + 0.25 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.258, + 0.895, + 0.502 + ], + "angle": 0, + "content": "Vision-Language Pre-training (VLP) aims to learn cross-modal representations [10, 25, 57, 82] from large-scale web data. Compared to video, image usually needs fewer costs for annotation and computation, hence almost all VLPs are image-based, e.g. [1, 22, 66, 80, 91, 93]. Recently, several studies adopted VLP to provide free visual-semantic knowledge for downstream image tasks, such as detection [16,94], segmentation [44,54,67,103], human-object interaction [29, 36], synthesis [47], and generation [9, 76, 77]. In terms of the video domain, [42, 51, 79] equipped VLP with temporal transformers for action recognition. [23, 24, 59] introduced prompt learning for efficient retrieval or detection. However, these studies focus more on open-vocabulary scenarios or short video understanding. On the contrary, this paper makes the first exploration to steer VLP for long video temporal localization, under the weakly-supervised setting." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.505, + 0.895, + 0.747 + ], + "angle": 0, + "content": "Strongly-supervised Temporal Action Localization has achieved great progress [38,46,65,95], given precise action boundaries and categories. There are two popular pipelines: the top-down framework [6,14,40,69,71,75,81,83,85,104] pre-defines massive anchors based on the action distribution prior, and uses fixed-length sliding windows to generate initial proposals, then regresses to refine boundaries; the bottom-up framework [3,8,37,39,41,58,74,85,87,100,101] trains frame-wise boundary detectors for extreme frames (start, end, center), then groups extreme frames or estimates action lengths to produce proposals. In addition, some papers [11, 49, 88] proposed various fusion strategies to complement these frameworks. Several studies [45, 95] are devoted to better post-processing. Nevertheless, all the above methods demand precise boundary annotations, which are time-consuming and expensive in reality." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.897, + 0.903 + ], + "angle": 0, + "content": "Weakly-supervised Temporal Action Localization significantly alleviates annotation costs, training with only category labels. The pivotal component is CAS [21, 62, 64, 78] obtained from Classification-Based Pre-training (CBP). But due to the gap of classification and localization, CBP suffers from one serious incomplete issue: only localize discriminative action fragments or even background. To solve this issue, [27, 56, 102] introduced the erasing strategy. [43, 52, 60] produced multiple CAS in parallel for complementarity. [32, 33, 63, 68] proposed background modeling" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "14752" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.09, + 0.887, + 0.369 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.376, + 0.893, + 0.435 + ], + "angle": 0, + "content": "Figure 2. Distillation-Collaboration Framework. It covers two parallel branches, named CBP and VLP, and is optimized by an alternating strategy. We warm up the CBP branch in advance. In B step, we freeze both CLIP encoders, and distill confident background pseudo-labels from the CBP branch, to train prompt vectors and temporal Transformer in the VLP branch. In F step, confident foreground pseudo-labels are distilled for the CBP branch. We utilize both knowledge distillation loss and contrastive loss during dual-branch collaboration." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.459, + 0.473, + 0.685 + ], + "angle": 0, + "content": "and context separation. [12, 17, 19, 97] enhanced features by intra- and inter-video modeling. To iteratively refine results, some papers [53, 89, 96] introduced the self-training strategy, [50, 70] adopted outer-inner contrastive learning. While encouraging, most of them are trapped in the 'performance-cost dilemma', i.e. solely digging from barren category labels to keep costs low. But the lack of annotations leads to a huge performance gap between strong and weak supervisions. To this end, [26, 28, 30, 55, 61, 86] explored to add instance-number or single-frame annotations for further improvements. Some papers [2, 4, 84, 99] tried long-video pretraining for TAL. As a fresh departure from existing work, to pursue better performance without additional annotation costs, this paper intends to distill free action knowledge from off-the-shelf VLPs, to assist WTAL." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.699, + 0.17, + 0.714 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.723, + 0.33, + 0.737 + ], + "angle": 0, + "content": "3.1. Notations and Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.746, + 0.47, + 0.867 + ], + "angle": 0, + "content": "Task Formulation. Given \\(N\\) untrimmed videos \\(\\{v_{i}\\}_{i = 1}^{N}\\) and their video-level category labels \\(\\{\\mathbf{y}_i\\in \\mathbb{R}^C\\}_{i = 1}^N\\) , where \\(C\\) means the total number of action categories, WTAL intends to detect and classify all action instances, in terms of a set of quadruples \\(\\{(s,e,c,p)\\}\\) , where \\(s,e,c,p\\) represent the start time, the end time, the action category and detection score of the action proposal, respectively. Note that each video may contain multiple action instances." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.471, + 0.9 + ], + "angle": 0, + "content": "Motivation. There exists significant complementarity between the localization results of Classification-Based Pre" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.459, + 0.893, + 0.565 + ], + "angle": 0, + "content": "training and Vision-Language Pre-training, as concluded in Table 3. The former suffers from incomplete results (serious false negatives), but has good true negatives; the latter suffers from over-complete results (serious false positives), but has good true positives. Such investigations motivate us to collaborate the complementary results for strong alliances, through a distillation-collaboration framework." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.569, + 0.895, + 0.766 + ], + "angle": 0, + "content": "Framework Overview. As demonstrated in Figure 2, the distillation-collaboration framework consists of two parallel branches, named CBP branch and VLP branch respectively, and is optimized by an alternating strategy. The CBP branch is first warmed-up to produce rich background information with only classification supervision. During B step, we distill confident background pseudo-labels from CBP branch, for VLP branch to tackle the over-complete issue, and thus localize high-quality foreground and background information. During F step, we distill superior pseudo-labels from the well-trained VLP branch, for CBP branch to tackle the incomplete issue. Through such dual-branch collaboration, we effectively fuse the complementary results." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.785, + 0.869, + 0.801 + ], + "angle": 0, + "content": "3.2. Distillation of Foreground and Background" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.893, + 0.855 + ], + "angle": 0, + "content": "The CBP Branch is utilized to identify a large number of background frames as well as several discriminative action frames, by exploiting Classification-Based Pre-training." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.893, + 0.9 + ], + "angle": 0, + "content": "Following literature [33, 43], we adopt CB pre-training, i.e. the I3D architecture pre-trained on Kinetics [5], to extract RGB and Flow features, and then concatenate them" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14753" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.09, + 0.468, + 0.167 + ], + "angle": 0, + "content": "to form the two-stream features \\(\\mathbf{F}_{\\mathrm{i3d}} \\in \\mathbb{R}^{T \\times 2D}\\), where \\(T\\) and \\(D\\) refer to the temporal length and feature dimension. Next, feeding with \\(\\mathbf{F}_{\\mathrm{i3d}}\\), the CBP branch uses the backbone network for feature fine-tuning and localization, and finally outputs the frame-level action probabilities \\(\\mathbf{P}^{\\mathrm{cb}} \\in \\mathbb{R}^{T \\times C}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.168, + 0.468, + 0.243 + ], + "angle": 0, + "content": "To achieve action classification, we adopt multiple instance learning, i.e. for the output \\(\\mathbf{P}^{\\mathrm{cb}}\\) from the backbone network, we aggregate (pool) the top- \\(k\\) frames' scores as video-level category scores \\(\\widehat{\\mathbf{y}}\\in \\mathbb{R}^{C}\\), then supervise it via the binary cross-entropy loss, which is formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.097, + 0.252, + 0.468, + 0.294 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {c l s}} = \\sum_ {c = 1} ^ {C} - y _ {c} \\log \\widehat {y} _ {c}, \\quad \\widehat {y} _ {c} = \\sigma \\left(\\frac {1}{k} \\sum \\mathcal {K} \\left(\\mathbf {P} ^ {\\mathrm {c b}}\\right)\\right), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.302, + 0.468, + 0.332 + ], + "angle": 0, + "content": "where \\(\\mathcal{K}\\) denotes the top-\\(k\\) score set in the temporal domain, and \\(\\sigma\\) refers to the softmax function." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.338, + 0.468, + 0.398 + ], + "angle": 0, + "content": "Remark. Under CB Pre-training and category-only supervision, \\(\\mathbf{P}^{\\mathrm{cb}}\\) is well known for focusing on sparse discriminative action frames, i.e. high true negatives but serious false negatives, thus can provide rich background information." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.405, + 0.468, + 0.495 + ], + "angle": 0, + "content": "The VLP Branch is designed to mine free action knowledge from VL Pre-training, e.g. CLIP [66]. Since imagetext pre-training lacks sufficient temporal priors, its vanilla localization results have a serious over-complete issue, i.e. high false positives. To tackle this issue, we propose to finetune CLIP using extensive background samples." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.496, + 0.468, + 0.54 + ], + "angle": 0, + "content": "Instead of linear probing, we use efficient prompt learning [23, 34] for fine-tuning: we freeze the CLIP backbone, only optimize several prompt vectors and temporal layers." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.542, + 0.468, + 0.678 + ], + "angle": 0, + "content": "Concretely, for the visual stream, we first split the video into consecutive frames, and then utilize the CLIP image encoder to extract frame-level features \\(\\mathbf{F}_{\\mathrm{vis}} \\in \\mathbb{R}^{T \\times D}\\). For temporal relationship construction, we strengthen \\(\\mathbf{F}_{\\mathrm{vis}}\\) into \\(\\mathbf{F}_{\\mathrm{vid}} \\in \\mathbb{R}^{T \\times D}\\) through simple temporal transformer layers \\(\\Phi_{\\mathrm{temp}}(\\cdot)\\). While for the textual stream, we first prepend and append several learnable prompt vectors \\(\\Phi_{\\mathrm{prmp}}(\\cdot)\\) to category names, then feed them into the CLIP text encoder, to obtain textual features \\(\\mathbf{F}_{\\mathrm{txt}} \\in \\mathbb{R}^{C \\times D}\\). Formally," + }, + { + "type": "equation", + "bbox": [ + 0.087, + 0.687, + 0.468, + 0.705 + ], + "angle": 0, + "content": "\\[\n\\mathbf {F} _ {\\mathrm {v i d}} = \\Phi_ {\\text {t e m p}} (\\mathbf {F} _ {\\text {v i s}}), \\quad \\mathbf {F} _ {\\mathrm {t x t}} = \\Phi_ {\\mathrm {t x t}} \\left(\\Phi_ {\\text {p r m p}} \\left(\\mathrm {C} _ {\\text {n a m e}}\\right)\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.713, + 0.468, + 0.759 + ], + "angle": 0, + "content": "where \\( C_{\\text{name}} \\) refers to action category names, and \\( \\Phi_{\\text{txt}}(\\cdot) \\) is the CLIP textual encoder. Thereafter, the frame-level localization results \\( \\mathbf{P}^{\\text{vl}} \\) for this branch can be calculated as:" + }, + { + "type": "equation", + "bbox": [ + 0.166, + 0.771, + 0.468, + 0.79 + ], + "angle": 0, + "content": "\\[\n\\mathbf {P} ^ {\\mathrm {v l}} = \\sigma \\left(\\mathbf {F} _ {\\mathrm {v i d}} \\cdot \\mathbf {F} _ {\\mathrm {t x t}} ^ {\\top}\\right) \\in \\mathbb {R} ^ {T \\times C}. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Remark. For the VLP branch, we only optimize lightweight model parameters for false-positive suppression, naturally bringing two main benefits: (1) the frozen CLIP backbone preserves the action prior knowledge in pre-training, thus maintaining high true-positive results; (2) it matches the demand for less supervision data under weakly-supervised settings, and also saves the memory footprint." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.091, + 0.892, + 0.197 + ], + "angle": 0, + "content": "Confident Pseudo-labels. Since both \\(\\mathbf{P}^{\\mathrm{vl}}\\) and \\(\\mathbf{P}^{\\mathrm{cb}}\\) contain somewhat noise, to make reliable use of complementary information, we distill confident location pseudo-labels of foreground and background respectively. That is, for the CBP branch, we distill extensive background pseudo-labels from the output \\(\\mathbf{P}^{\\mathrm{cb}}\\); while for the VLP branch, we distill sufficient foreground pseudo-labels from the output \\(\\mathbf{P}^{\\mathrm{vl}}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.198, + 0.892, + 0.243 + ], + "angle": 0, + "content": "For both branches, we leverage double thresholds \\(\\delta_h\\) and \\(\\delta_l\\) (\\(\\delta_h > \\delta_l\\)), to convert localization results \\(\\mathbf{P}\\) into ternary pseudo-labels \\(\\mathbf{H} \\in \\mathbb{R}^{T \\times C}\\), which are formally written as:" + }, + { + "type": "equation", + "bbox": [ + 0.563, + 0.253, + 0.892, + 0.308 + ], + "angle": 0, + "content": "\\[\nh _ {t, c} = \\left\\{ \\begin{array}{c} 1 \\text {i f} p _ {t} > \\delta_ {h} \\text {a n d} p _ {c} = y _ {c} \\\\ 0 \\text {i f} p _ {t} < \\delta_ {l} \\text {o r} p _ {c} \\neq y _ {c} \\\\ - 1 \\quad \\text {o t h e r w i s e} \\end{array} \\right. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.318, + 0.892, + 0.5 + ], + "angle": 0, + "content": "where the subscripts \\(c\\) and \\(t\\) refer to the indices of category and frame. More specifically, for either branch, we regard frames with scores more than \\(\\delta_h\\) and the correct action category as the foreground; while frames with scores less than \\(\\delta_l\\) or with the wrong action category are treated as the background; the remaining frames are considered uncertain. As a result, the pseudo-labels \\(\\mathbf{H}^{\\mathrm{cb}}\\) cover vast confident background frames, as well as trivial foreground frames; while the pseudo-labels \\(\\mathbf{H}^{\\mathrm{vl}}\\) contain dense confident foreground frames, and partial background frames. Note that, for both branches, we generate positive and negative frames to avoid trivial solutions, and facilitate contrastive feature learning." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.515, + 0.872, + 0.531 + ], + "angle": 0, + "content": "3.3. Collaboration of Dual-Branch Optimization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.539, + 0.892, + 0.614 + ], + "angle": 0, + "content": "In this section, we encourage two branches to collaborate with each other, such that forming a strong alliance of their complementary localization results. To reduce serious noises in pseudo-labels, we introduce an alternate training strategy for dual-branch collaborative optimization." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.615, + 0.892, + 0.87 + ], + "angle": 0, + "content": "The design rationale is to distill Background knowledge from the CBP branch for B step, while distill Foreground knowledge from the VLP branch in F step. To be specific, we warm up the CBP branch in advance, using only category supervision, to initialize reliable background frames. During B Step, we freeze the well-trained CBP branch, and then generate confident background pseudo-labels \\(\\mathbf{H}^{\\mathrm{cb}}\\) to supervise the VLP branch. As a result, these false-positive confusions from vanilla CLIP pre-training are greatly tackled, and the resultant pseudo-labels contain a large number of confident foreground frames and background frames. During F Step, the high-quality pseudo-labels \\(\\mathbf{H}^{\\mathrm{vl}}\\) are distilled from the frozen VLP branch, to guide the CBP branch for the false-negative suppression. Under such an alternating strategy, these two branches not only complement each other, but also correct each other, thus jointly contributing to more precise and complete action localization." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "During each step, to supervise either branch, we adopt both the knowledge distillation loss \\(\\mathcal{L}_{\\mathrm{kd}}\\) and foreground" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14754" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.122 + ], + "angle": 0, + "content": "background contrastive loss \\(\\mathcal{L}_{\\mathrm{fb}}\\). The total optimization loss can be written with a balancing ratio \\(\\lambda\\), as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.14, + 0.13, + 0.469, + 0.148 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {a l l}} = \\mathcal {L} _ {\\mathrm {k d}} \\left(\\mathbf {H} ^ {\\prime}, \\mathbf {P}\\right) + \\lambda \\mathcal {L} _ {\\mathrm {f b}} \\left(\\Psi^ {+}, \\Psi^ {-}\\right). \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.156, + 0.469, + 0.216 + ], + "angle": 0, + "content": "Here, \\(\\mathcal{L}_{\\mathrm{kd}}\\) regularizes one branch to output similar detection results with pseudo-labels from the other branch. Given that there exist some noises in pseudo-labels, i.e. uncertain frames, we only make supervision on confident frames." + }, + { + "type": "equation", + "bbox": [ + 0.129, + 0.224, + 0.469, + 0.265 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {k d}} \\left(\\mathbf {H} ^ {\\prime}, \\mathbf {P}\\right) = \\frac {1}{O} \\sum_ {c = 1} ^ {C} \\sum_ {t = 1} ^ {O} D _ {\\mathrm {K L}} \\left(h _ {t, c} ^ {\\prime} \\mid \\mid p _ {t, c}\\right), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.273, + 0.469, + 0.379 + ], + "angle": 0, + "content": "where \\( D_{\\mathrm{KL}}(p(x) || q(x)) \\) refers to the Kullback-Leibler divergence of distribution \\( p(x) \\) from distribution \\( q(x) \\), \\( O \\) is the total number of confident frames, and \\( \\mathbf{H}' \\) denotes the pseudo-labels from the other branch. Note that, the pseudolabels contain two types of confident frames: foreground and background, which could help to avoid falling into the trivial solutions under one single type of labels." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.379, + 0.469, + 0.501 + ], + "angle": 0, + "content": "Moreover, in untrimmed long videos, some background contexts could appear visually similar with the action (foreground). We further introduce contrastive learning to pull foreground features and push background features. Specifically, we treat confident foreground frames from the same action category as the positive set \\(\\Psi^{+}\\), while all confident background frames as the negative set \\(\\Psi^{-}\\), then foreground-background contrastive loss is formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.091, + 0.507, + 0.469, + 0.547 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {f b}} \\left(\\Psi_ {i} ^ {+}, \\Psi_ {i} ^ {-}\\right) = \\sum_ {i} - \\log \\frac {\\sum_ {m \\in \\Psi_ {i} ^ {+}} \\exp \\left(\\mathbf {f} _ {i} \\cdot \\mathbf {f} _ {m} / \\tau\\right)}{\\sum_ {j \\in *} \\exp \\left(\\mathbf {f} _ {i} \\cdot \\mathbf {f} _ {j} / \\tau\\right)}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.556, + 0.469, + 0.678 + ], + "angle": 0, + "content": "where \\(\\mathbf{f} \\in \\mathbb{R}^D\\) refers to the frame feature, \\(\\tau\\) means the temperature hyper-parameter for scaling, and \\(*\\) means the union of \\(\\Psi_i^+\\) and \\(\\Psi_i^-\\). Take the VLP branch as an example, sufficient background pseudo-labels contain considerable hard negative samples, to help distinguish features of foreground and contexts. In addition, the enhanced features of uncertain frames also become more discriminative, further facilitating more complete temporal action localization." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.681, + 0.469, + 0.833 + ], + "angle": 0, + "content": "Discussion. Comparing to various fusion strategies, our alternating strategy produces more precise and complete results (see Table 4 for details). This strategy plays a similar role as the multi-view co-training, where CBP and VLP branches can be deemed as two distinctive views, thus being quite robust to pseudo-label noises. For B step, we prompt the VLP branch for high-quality pseudo-labels, where some frames with conflicting predictions are still treated as uncertain. In F step, we use feature contrastive loss to make their results more discriminative, i.e. further denoising." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.848, + 0.187, + 0.862 + ], + "angle": 0, + "content": "3.4. Inference" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.902 + ], + "angle": 0, + "content": "At testing time, we leverage the results from the CBP branch for post-processing, as vision-language pre-training" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.228 + ], + "angle": 0, + "content": "cannot handle Optical Flow, which is essential for WTAL. Given an input video, we first obtain video-level category probabilities and frame-level localization scores. For action classification, we select the classes with probability greater than \\(\\theta_{cls}\\); and for localization, we threshold detection scores with \\(\\theta_{loc}\\), concatenate consecutive snippets as action proposals, and eliminate redundant proposals with soft nonmaximum suppression (NMS). Each proposal is scored with the detection maximum in the proposal interval." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.242, + 0.634, + 0.259 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.268, + 0.661, + 0.284 + ], + "angle": 0, + "content": "4.1. Implementation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.29, + 0.892, + 0.441 + ], + "angle": 0, + "content": "Datasets. THUMOS14 owns 413 untrimmed videos from 20 categories, and each video contains an average of 15 instances. As conventions, we train on 200 validation videos, and evaluate on 213 testing videos. Despite its small scale, this dataset is challenging, since video lengths vary widely and actions occur frequently. ActivityNet1.2 covers 9682 videos belonging to 100 categories. Almost all the videos are single-category, and action regions take up more than half of the video duration. We train on 4619 training videos and evaluate on 2383 validation videos." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.446, + 0.892, + 0.568 + ], + "angle": 0, + "content": "Metrics. To evaluate localization performance, we follow the standard protocol to use mean Average Precision (mAP) at different intersections over union (IoU) thresholds. Note that a proposal is regarded as positive only if both the category prediction is correct and IoU exceeds the set threshold. To clearly evaluate the quality of pseudo-labels, we also report mean Intersection over Union (mIoU) averaged over the foreground categories and the background category." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.57, + 0.892, + 0.797 + ], + "angle": 0, + "content": "Details. To handle the large variety in video durations, we randomly sample \\( T \\) consecutive snippets for each video. \\( T \\) is set to 1000 on THUMOS14, and 400 on ActivityNet1.2. We utilize the TV-L1 algorithm to extract optical flow from RGB data. For the CBP branch, we use Transformer architectures (multi-head self-attention, layer norm, and MLPs) as the backbone network. For the VLP branch, we use a 2-layer temporal Transformer, preprocess and append 16 prompt vectors to textual inputs, both are initialized by \\( \\mathcal{N}(0,0.01) \\). Both CLIP image encoder and text encoder are adopted from ViT-B/16. The framework is optimized by Adam with the learning rate of \\( 10^{-4} \\). All hyper-parameters are set by grid search: pseudo-label thresholds \\( \\delta_h = 0.3 \\), \\( \\delta_l = 0.1 \\), inference thresholds \\( \\theta_{cls} = 0.85 \\), \\( \\theta_{loc} = 0.45 \\), the balancing ratio \\( \\lambda = 0.05 \\), the temperature \\( \\tau = 0.07 \\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.814, + 0.866, + 0.83 + ], + "angle": 0, + "content": "4.2. Comparison with State-of-the-art Methods" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.839, + 0.892, + 0.868 + ], + "angle": 0, + "content": "Here, we make comprehensive comparisons with current state-of-the-art methods across multiple IoU thresholds." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Performance. The comparisons on THUMOS14 are provided in Table 1. Here, we separate two levels of supervi" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14755" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.091, + 0.089, + 0.878, + 0.409 + ], + "angle": 0, + "content": "
SupervisionMethodFeaturemAP@IoUAVG(0.1-0.5)AVG(0.3-0.7)
0.10.20.30.40.50.60.7
StrongDBS [15]I3D56.754.750.643.134.324.414.747.933.4
BUMR [100]--53.950.745.438.028.5-43.3
GCM [95]72.570.966.560.851.9--64.5-
RCL [81]--70.162.352.942.730.7-51.7
ActionFormer [98]--82.177.871.059.443.9-66.8
WeakHAM-Net [21]I3D65.459.050.341.131.020.711.449.430.9
UM [33]63.056.649.040.930.421.010.448.030.3
TS-PCA [48]67.661.153.443.434.324.713.752.033.9
FTCL [12]69.663.455.245.235.623.712.253.834.4
ACGNet [90]68.162.653.144.634.722.612.052.633.4
DCC [35]69.063.855.945.935.724.313.754.135.1
ASM-Loc [17]71.265.557.146.836.625.213.455.435.8
CO2-Net [18]70.163.654.545.738.326.413.454.435.7
RSKP [20]71.365.355.847.538.225.412.555.635.9
DELU [7]71.566.256.547.740.527.215.356.537.4
CO2-Net†I3D67.460.651.943.135.023.312.151.633.0
CO2-Net‡68.862.152.643.936.124.112.052.733.7
DELU†+CLIP68.660.852.243.435.623.313.352.133.6
DELU‡70.363.955.445.939.026.014.354.936.0
Ours73.568.861.553.842.029.416.860.040.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.416, + 0.894, + 0.477 + ], + "angle": 0, + "content": "Table 1. Comparison with state-of-the-art methods on THUMOS14. For fair comparisons, we reproduce the results of SOTA methods: CO2-Net [18] and DELU [7], by inputting both I3D [5] and CLIP [66] features. † and ‡ refer to averaging or concatenating these two features. AVG(0.1-0.5) and AVG(0.3-0.7) are the average mAP from IoU 0.1 to 0.5 and from IoU 0.3 to 0.7. Our framework significantly surpasses all weakly-supervised competitors using identical features, and is even comparable to early strongly-supervised methods." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.504, + 0.465, + 0.751 + ], + "angle": 0, + "content": "
MethodFeaturemAP@IoUAVG
0.50.750.95
CleanNet [50]I3D37.120.35.021.6
CMCS [43]36.822.05.622.4
TSCN [96]37.623.75.723.6
BasNet [31]38.524.25.624.3
DGAM [68]41.023.55.324.4
UM [33]41.225.66.025.9
ACGNet [90]41.826.05.926.1
D2-Net [60]42.325.55.826.0
CO2-Net [18]43.326.35.226.4
DELU [7]44.226.75.426.9
CO2-Net†I3D44.826.95.527.1
CO2-Net‡45.227.15.827.6
DELU†+45.427.35.727.5
DELU‡CLIP46.027.85.928.0
Ours48.329.36.129.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.76, + 0.472, + 0.847 + ], + "angle": 0, + "content": "Table 2. Comparison with state-of-the-art methods on ActivityNet1.2. For fair comparisons, we reproduce CO2-Net [18] and DELU [7], by inputting I3D [5] and CLIP [66] features. \\(\\dagger\\) and \\(\\ddagger\\) refer to averaging or concatenating these features. AVG is the average mAP at the thresholds 0.5:0.05:0.95. Our method significantly surpasses all competitors, especially at loose IoU thresholds." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.472, + 0.903 + ], + "angle": 0, + "content": "sion: strong and weak, for better quantification. Generally speaking, our framework achieves new state-of-the-art on" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.499, + 0.892, + 0.667 + ], + "angle": 0, + "content": "all IoU regimes. Comparing with recent methods, the gain of the average mAP (0.3-0.7) even reaches \\(4 - 5\\%\\), further narrowing the performance gap between weak and strong supervisions. Moreover, our method achieves considerable gains on strict and loose evaluations. For example, when comparing to DELU [7], the gains are \\(3.5\\%\\) average mAP (0.1-0.5) and \\(3.4\\%\\) average mAP (0.3-0.7), indicating that our results are complete and precise. Furthermore, despite being weakly-supervised settings, at several low IoU thresholds, our framework even performs comparably with some earlier strongly-supervised methods [14, 15, 101]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.669, + 0.892, + 0.793 + ], + "angle": 0, + "content": "Table 2 shows the comparison results on ActivityNet1.2. On all IoU thresholds, our designed framework surpasses existing methods by a large margin. In terms of the average mAP, the performance improvement can reach \\(2.7\\%\\), taking the state-of-the-art to a new level. However, due to the lack of precise location annotations, the gain decreases as the IoU threshold becomes stricter, e.g. \\(4.1\\%\\) @IoU 0.5 vs. \\(0.7\\%\\) @IoU 0.95, when comparing to DELU [7]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Source of Gain. Comparing to existing methods, we leverage Vision-Language Pre-training for free knowledge. To make fair comparisons, we also input both I3D and CLIP features into two SOTA methods [7, 18], by one early fusion mode (average or concatenate these features). In general, simply adding CLIP features gives only slight or even negative gains on both datasets, which is due to the bad over" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "14756" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.08, + 0.089, + 0.465, + 0.171 + ], + "angle": 0, + "content": "
SettingTHUMOSActivityNet
ForeBackForeBack
CB Pre-training56.088.754.788.3
VL Pre-training75.634.172.145.0
Ours72.480.069.571.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.179, + 0.47, + 0.234 + ], + "angle": 0, + "content": "Table 3. Complementarity of pre-training. CB Pre-training has good background mIoU but inferior foreground mIoU. VL Pretraining has good foreground mIoU but inferior background mIoU. Our method achieves both high foreground and background mIoU." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.261, + 0.465, + 0.372 + ], + "angle": 0, + "content": "
Fusion StrategymAP@IoUAVG(0.3-0.7)
0.30.50.7
Only F step (AVG)40.016.13.319.1
Only F step (Weight)52.825.56.127.7
Only B step (AVG)56.733.611.334.1
Only B step (Weight)58.538.814.837.8
Alternating61.542.016.840.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.379, + 0.468, + 0.449 + ], + "angle": 0, + "content": "Table 4. Comparison of optimization strategies. \"Only F step\": extract pseudo-labels from vanilla VLP to train the CBP branch. \"Only B step\": get pseudo-labels from the warm-up CBP branch to train the VLP branch. We combine two branches by averaging and weighting. Our alternating strategy shows clear superiority." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.477, + 0.469, + 0.584 + ], + "angle": 0, + "content": "complete issue of CLIP (detailed in Table 3). For THUMOS with complex and frequent actions, over-complete worsens results. While in ActivityNet, most videos only contain one action that takes up half of the video duration, thus benefiting a bit from over-complete. Nevertheless, with identical features, our method significantly outperforms existing competitors, proving the effectiveness of our framework." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.6, + 0.363, + 0.616 + ], + "angle": 0, + "content": "4.3. Ablation Study and Comparison" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.623, + 0.469, + 0.654 + ], + "angle": 0, + "content": "Here, we evaluate the contributions of each component and framework designs, to further dissect our framework." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.659, + 0.469, + 0.734 + ], + "angle": 0, + "content": "Complementarity of pre-trainings. As the detection performance is mainly determined by pseudo-labels, here we show the quality of pseudo-labels, in terms of foreground mIoU and background mIoU. Table 3 provides the comprehensive results for various settings on both benchmarks." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.469, + 0.901 + ], + "angle": 0, + "content": "For common Classification-Based Pre-training, its localization results suffer from the incomplete issue. In detail, the background mIoU is impressive, i.e. high true negatives, while the foreground mIoU is poor, i.e. serious false negatives. The main reason is that features pre-trained on action classification datasets only highlight sparse discriminative frames. While the results of Vision-Language Pre-training are just the opposite: suffering from the over-complete issue. The foreground mIoU is considerable, i.e. high true positives, but the background mIoU is terrible, i.e. serious false positives. The main reason is that VLP using image" + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.09, + 0.888, + 0.171 + ], + "angle": 0, + "content": "
ModelLkdLf bmAP@IoUAVG(0.3-0.7)
0.30.50.7
A1✓57.137.012.636.0
A2✓51.731.29.430.9
A3✓✓61.542.016.840.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.179, + 0.892, + 0.234 + ], + "angle": 0, + "content": "Table 5. Contribution of optimization losses on THUMOS14. The single knowledge distillation loss \\(\\mathcal{L}_{\\mathrm{kd}}\\) has brought gratifying localization results, and the additional foreground-background contrastive loss \\(\\mathcal{L}_{\\mathrm{fb}}\\) further boosts the performance to the best." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.256, + 0.887, + 0.352 + ], + "angle": 0, + "content": "
MethodmAP@IoUAVG (0.3-0.7)
0.30.50.7
UM [33]49.030.410.430.3
UM + Ours53.934.713.634.3
CO2-Net [18]54.538.313.435.7
CO2-Net + Ours56.239.715.937.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.359, + 0.892, + 0.402 + ], + "angle": 0, + "content": "Table 6. Framework generalization on THUMOS14. Our proposed framework is generalized, i.e. existing methods can serve as our CBP branch, to achieve further improvements." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.429, + 0.891, + 0.459 + ], + "angle": 0, + "content": "text pairs lacks temporal priors. The above results strongly prove the complementarity between these two pre-training." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.459, + 0.892, + 0.626 + ], + "angle": 0, + "content": "Moreover, on both datasets, our method achieves high foreground and background mIoU, that is, more precise and complete localization. This mainly benefits from extensive background supervision provided by the CBP branch, and extensive foreground supervision distilled from the VLP branch. Besides, comparing to VL Pre-training, our results achieve immediate gains on the background mIoU, while only slight drops on the foreground mIoU. This reveals that the lightweight trainable parameters, i.e. prompts + Transformer, indeed retain the action prior knowledge in VLP, and also significantly suppress false-positive results." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.892, + 0.75 + ], + "angle": 0, + "content": "Comparison of optimization strategies. To evaluate the alternating efficacy, Table 4 compares with another two solutions. (1) 'Only F step': extract foreground pseudo-labels from the vanilla VLP, then provide them to the CBP branch for auxiliary training; (2) 'Only B step': distill background pseudo-labels from the warm-up CBP branch to train the VLP branch. And for each solution, we combine the dual-branch results by averaging and weighting, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "'Only F step' performs the worst, mainly suffering from heavy noise in vanilla VLP pseudo-labels (over-complete). By fine-tuning vanilla VLP with many background frames, 'Only B step' gets great improvements, but still lacks full fusion of complementarity. Moreover, the weighted operation could suppress noise somewhat, and thus causes better results than the average operation. By comparison, our alternating strategy shows great advantages over competitors, proving the non-trivial nature of fusing complementary information, and robust denoising to pseudo-labels." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14757" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.107, + 0.085, + 0.868, + 0.319 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.324, + 0.896, + 0.381 + ], + "angle": 0, + "content": "Figure 3. Qualitative comparisons. The first two rows are videos and ground-truth action intervals. The last six rows are frame-level action probabilities, and localization results of Classification-Based Pre-training (CBP), Vision-Language Pre-training (VLP), and our framework, respectively. CBP suffers from the incomplete issue, while VLP has the over-complete issue. Our framework distills foreground knowledge from VLP and background from CBP, for the strong collaborative alliance, thus bringing more complete and precise results." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.406, + 0.473, + 0.619 + ], + "angle": 0, + "content": "Contribution of various losses. To train our method, both knowledge distillation loss \\(\\mathcal{L}_{\\mathrm{kd}}\\) and foreground-background contrastive loss \\(\\mathcal{L}_{\\mathrm{fb}}\\) are leveraged. In Table 5, we analyze the effectiveness of optimization losses on THUMOS14. The single \\(\\mathcal{L}_{\\mathrm{kd}}\\) (model A1) already brings gratifying performance. This reveals that the confident pseudo-labels of foreground and background distilled from two branches, are well fused by the alternate optimization. On the other hand, with only \\(\\mathcal{L}_{\\mathrm{fb}}\\), model A2 also performs barely satisfactory results. This is because \\(\\mathcal{L}_{\\mathrm{fb}}\\) differentiates foreground features and background features, thus eliminating extensive uncertain frames, and also making the localization task easier. Overall, these two losses jointly contribute to the best performance, indicating that both are essential." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.622, + 0.471, + 0.729 + ], + "angle": 0, + "content": "Framework generalization. Our distillation-collaboration framework is generalized, which means that existing WTAL methods can be employed as the CBP branch. Table 6 takes two typical methods: CO2-Net [18] and UM [33], as examples. Our framework further improves their performance by up to \\(2 - 4\\%\\) average mAP, showing a good generalization to other methods and other backbone designs." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.742, + 0.262, + 0.759 + ], + "angle": 0, + "content": "4.4. Qualitative Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.471, + 0.903 + ], + "angle": 0, + "content": "To intuitively demonstrate the superiority, Figure 3 visualizes results from various types of videos. Classification-Based Pre-training highlights only some discriminative action frames (the incomplete issue), which is more prominent for videos containing low-frequency actions. On the contrary, Vision-Language Pre-training tends to over-activate action foreground to background (the over-complete issue), which is especially evident in videos with high-frequency actions. We design the distillation-collaboration framework" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.406, + 0.895, + 0.543 + ], + "angle": 0, + "content": "to fuse the complementarity from these two pre-trainings. In B step, extensive confident background is distilled from the well-trained CBP branch, to supervise the VLP branch for false-positive suppression. While in F step, sufficient confident foreground information is distilled from the VLP branch, to guide the CBP branch for false-negative elimination. Hence, our method establishes the strong alliance by collaborative optimization, bringing precise and complete detection results, regardless of dense or sparse actions." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.557, + 0.62, + 0.573 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.58, + 0.895, + 0.793 + ], + "angle": 0, + "content": "This work proposes the novel distillation-collaboration framework to distill free knowledge from Vision-Language Pre-training, for weakly-supervised temporal action localization. Our core insight is that existing VLP often localizes over-complete actions, which is just complementary to the incomplete results of conventional Classification-Based Pre-training. And to form strong alliances, we optimize the framework containing complementary dual branches by an alternating strategy: distill confident background pseudolabels from the CBP branch, and the confident foreground pseudo-labels from the VLP branch, for collaborative training. Extensive experiments show the significance of distilling VLP and our superior performance. Thorough ablations are studied both quantitatively and qualitatively." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.804, + 0.669, + 0.82 + ], + "angle": 0, + "content": "Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.895, + 0.901 + ], + "angle": 0, + "content": "This research is supported by the National Key R&D Program of China (No. 2022ZD0160702), STCSM (No. 22511106101, No. 18DZ2270700, No. 21DZ1100100), 111 plan (No. BP0719010), and State Key Laboratory of UHD Video and Audio Production and Presentation." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "14758" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.09, + 0.176, + 0.107 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.093, + 0.115, + 0.47, + 0.184 + ], + "angle": 0, + "content": "[1] Jean-Baptiste Alayrac, Jeff Donahue, Pauline Luc, Antoine Miech, Iain Barr, Yana Hasson, Karel Lenc, Arthur Mensch, Katie Millican, Malcolm Reynolds, et al. 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Most methods widely adopt the off-the-shelf Classification-Based Pre-training (CBP) to generate video features for action localization. However, the different optimization objectives between classification and localization, make temporally localized results suffer from the serious incomplete issue. To tackle this issue without additional annotations, this paper considers to distill free action knowledge from Vision-Language Pre-training (VLP), as we surprisingly observe that the localization results of vanilla VLP have an over-complete issue, which is just complementary to the CBP results. To fuse such complementarity, we propose a novel distillation-collaboration framework with two branches acting as CBP and VLP respectively. The framework is optimized through a dual-branch alternate training strategy. Specifically, during the $B$ step, we distill the confident background pseudo-labels from the CBP branch; while during the $F$ step, the confident foreground pseudo-labels are distilled from the VLP branch. As a result, the dual-branch complementarity is effectively fused to promote one strong alliance. Extensive experiments and ablation studies on THUMOS14 and ActivityNet1.2 reveal that our method significantly outperforms state-of-the-art methods. + +# 1. Introduction + +Temporal action localization (TAL), which aims to localize and classify action instances from untrimmed long videos, has been recognized as an indispensable component of video understanding [13, 72, 92]. To avoid laborious temporal boundary annotations, the weakly-supervised setting (WTAL) [31, 62, 64, 78], i.e. only video-level category labels are available, has gained increasing attentions. + +To date in the literature, almost all WTAL methods rely on Classification-Based Pre-training (CBP) for video fea + +![](images/b2486122ea2d1bfac110d59bfa81db123542096d43ce83fad90a5f78cb0481c2.jpg) +Figure 1. (A) Complementarity. Most works use Classification-Based Pre-training (CBP) for localization, bringing high TN yet serious FN. Vanilla Vision-Language Pre-training (VLP) confuses action and background, bringing high TP yet serious FP. (B) Our distillation-collaboration framework distills foreground from the VLP branch while background from the CBP branch, and promotes mutual collaboration, bringing satisfactory results. + +ture extraction [5, 73]. A popular pipeline is to train an action classifier with CBP features, then threshold the frame-level classification probabilities for final localization results. As demonstrated in Figure 1(A), these CBP methods suffer from the serious incompleteness issue, i.e. only detecting sparse discriminative action frames and incurring high false negatives. The main reason is that the optimization objective of classification pre-training, is to find several discriminative frames for action recognition, which is far from the objective of complete localization. As a result, features from CBP are inevitably biased towards partial discriminative frames. To solve the incompleteness issue, many efforts [33, 43, 56, 96] have been attempted, but most of them are trapped in a 'performance-cost dilemma', namely, solely digging from barren category labels to keep costs low. Lacking location labels fundamentally limits the performance, leaving a huge gap from strong supervision. + +To jump out of the dilemma, this paper raises one novel question: is there free action knowledge available, to help + +complete detection results while maintain cheap annotation overhead at the same time? We naturally turn our sights to the prevalent Vision-Language Pre-training (VLP) [22, 66]. VLP has demonstrated great success to learn joint visual-textual representations from large-scale web data. As language covers rich information about objects, human-object interactions, and object-object relationships, these learned representations could provide powerful human-object co-occurrence priors: valuable gifts for action localization. + +We here take one step towards positively answering the question, i.e. fill the research gap of distilling action priors from VLP, namely CLIP [66], to solve the incomplete issue for WTAL. As illustrated in Figure 1 (A), we first naively evaluate the temporal localization performance of VLP by frame-wise classification. But the results are far from satisfactory, suffering from the serious over-complete issue, i.e. confusing multiple action instances into a whole, causing high false positives. We conjecture the main reasons are: (1) due to data and computational burden, almost all VLPs are trained using image-text pairs. Hence, VLP lacks sufficient temporal knowledge and relies more on human-object co-occurrence for localization, making it struggle to distinguish the actions with visually similar background contexts; (2) some background contexts have similar (confusing) textual semantics to actions, such as run-up vs. running. + +Although simply steering VLP for WTAL is infeasible, we fortunately observe the complementary property between CBP and VLP paradigms: the former localizes high true negatives but serious false negatives, while the latter has high true positives but serious false positives. To leverage the complementarity, as shown in Figure 1 (B), we design a novel distillation-collaboration framework that uses two branches to play the roles of CBP and VLP, respectively. The design rationale is to distill background knowledge from the CBP branch, while foreground knowledge from the VLP branch, for strong alliances. Specifically, we first warm up the CBP branch using only category supervision to initialize confident background frames, and then optimize the framework via an alternating strategy. During $B$ step, we distill background pseudo-labels for the VLP branch to solve the over-complete issue, hence obtaining high-quality foreground pseudo-labels. During $F$ step, we leverage high-quality pseudo-labels for the CBP branch to tackle the incomplete issue. Besides, in each step, we introduce both confident knowledge distillation and representation contrastive learning for pseudo-label denoising, effectively fusing complementarity for better results. + +On two standard benchmarks: THUMOS14 and ActivityNet1.2, our method improves the average performance by $3.5\%$ and $2.7\%$ over state-of-the-art methods. We also conduct extensive ablation studies to reveal the effectiveness of each component, both quantitatively and qualitatively. + +To sum up, our contributions lie in three folds: + +- We pioneer the first exploration in distilling free action knowledge from off-the-shelf VLP to facilitate WTAL; +- We design a novel distillation-collaboration framework that encourages the CBP branch and VLP branch to complement each other, by an alternating optimization strategy; +- We conduct extensive experiments and ablation studies to reveal the significance of distilling VLP and our superior performance on two public benchmarks. + +# 2. Related Work + +Vision-Language Pre-training (VLP) aims to learn cross-modal representations [10, 25, 57, 82] from large-scale web data. Compared to video, image usually needs fewer costs for annotation and computation, hence almost all VLPs are image-based, e.g. [1, 22, 66, 80, 91, 93]. Recently, several studies adopted VLP to provide free visual-semantic knowledge for downstream image tasks, such as detection [16,94], segmentation [44,54,67,103], human-object interaction [29, 36], synthesis [47], and generation [9, 76, 77]. In terms of the video domain, [42, 51, 79] equipped VLP with temporal transformers for action recognition. [23, 24, 59] introduced prompt learning for efficient retrieval or detection. However, these studies focus more on open-vocabulary scenarios or short video understanding. On the contrary, this paper makes the first exploration to steer VLP for long video temporal localization, under the weakly-supervised setting. + +Strongly-supervised Temporal Action Localization has achieved great progress [38,46,65,95], given precise action boundaries and categories. There are two popular pipelines: the top-down framework [6,14,40,69,71,75,81,83,85,104] pre-defines massive anchors based on the action distribution prior, and uses fixed-length sliding windows to generate initial proposals, then regresses to refine boundaries; the bottom-up framework [3,8,37,39,41,58,74,85,87,100,101] trains frame-wise boundary detectors for extreme frames (start, end, center), then groups extreme frames or estimates action lengths to produce proposals. In addition, some papers [11, 49, 88] proposed various fusion strategies to complement these frameworks. Several studies [45, 95] are devoted to better post-processing. Nevertheless, all the above methods demand precise boundary annotations, which are time-consuming and expensive in reality. + +Weakly-supervised Temporal Action Localization significantly alleviates annotation costs, training with only category labels. The pivotal component is CAS [21, 62, 64, 78] obtained from Classification-Based Pre-training (CBP). But due to the gap of classification and localization, CBP suffers from one serious incomplete issue: only localize discriminative action fragments or even background. To solve this issue, [27, 56, 102] introduced the erasing strategy. [43, 52, 60] produced multiple CAS in parallel for complementarity. [32, 33, 63, 68] proposed background modeling + +![](images/59453d5eecfd774c0444e957b5333195085e5613625f50124ad901ed40b5c086.jpg) +Figure 2. Distillation-Collaboration Framework. It covers two parallel branches, named CBP and VLP, and is optimized by an alternating strategy. We warm up the CBP branch in advance. In B step, we freeze both CLIP encoders, and distill confident background pseudo-labels from the CBP branch, to train prompt vectors and temporal Transformer in the VLP branch. In F step, confident foreground pseudo-labels are distilled for the CBP branch. We utilize both knowledge distillation loss and contrastive loss during dual-branch collaboration. + +and context separation. [12, 17, 19, 97] enhanced features by intra- and inter-video modeling. To iteratively refine results, some papers [53, 89, 96] introduced the self-training strategy, [50, 70] adopted outer-inner contrastive learning. While encouraging, most of them are trapped in the 'performance-cost dilemma', i.e. solely digging from barren category labels to keep costs low. But the lack of annotations leads to a huge performance gap between strong and weak supervisions. To this end, [26, 28, 30, 55, 61, 86] explored to add instance-number or single-frame annotations for further improvements. Some papers [2, 4, 84, 99] tried long-video pretraining for TAL. As a fresh departure from existing work, to pursue better performance without additional annotation costs, this paper intends to distill free action knowledge from off-the-shelf VLPs, to assist WTAL. + +# 3. Method + +# 3.1. Notations and Preliminaries + +Task Formulation. Given $N$ untrimmed videos $\{v_{i}\}_{i = 1}^{N}$ and their video-level category labels $\{\mathbf{y}_i\in \mathbb{R}^C\}_{i = 1}^N$ , where $C$ means the total number of action categories, WTAL intends to detect and classify all action instances, in terms of a set of quadruples $\{(s,e,c,p)\}$ , where $s,e,c,p$ represent the start time, the end time, the action category and detection score of the action proposal, respectively. Note that each video may contain multiple action instances. + +Motivation. There exists significant complementarity between the localization results of Classification-Based Pre + +training and Vision-Language Pre-training, as concluded in Table 3. The former suffers from incomplete results (serious false negatives), but has good true negatives; the latter suffers from over-complete results (serious false positives), but has good true positives. Such investigations motivate us to collaborate the complementary results for strong alliances, through a distillation-collaboration framework. + +Framework Overview. As demonstrated in Figure 2, the distillation-collaboration framework consists of two parallel branches, named CBP branch and VLP branch respectively, and is optimized by an alternating strategy. The CBP branch is first warmed-up to produce rich background information with only classification supervision. During B step, we distill confident background pseudo-labels from CBP branch, for VLP branch to tackle the over-complete issue, and thus localize high-quality foreground and background information. During F step, we distill superior pseudo-labels from the well-trained VLP branch, for CBP branch to tackle the incomplete issue. Through such dual-branch collaboration, we effectively fuse the complementary results. + +# 3.2. Distillation of Foreground and Background + +The CBP Branch is utilized to identify a large number of background frames as well as several discriminative action frames, by exploiting Classification-Based Pre-training. + +Following literature [33, 43], we adopt CB pre-training, i.e. the I3D architecture pre-trained on Kinetics [5], to extract RGB and Flow features, and then concatenate them + +to form the two-stream features $\mathbf{F}_{\mathrm{i3d}} \in \mathbb{R}^{T \times 2D}$ , where $T$ and $D$ refer to the temporal length and feature dimension. Next, feeding with $\mathbf{F}_{\mathrm{i3d}}$ , the CBP branch uses the backbone network for feature fine-tuning and localization, and finally outputs the frame-level action probabilities $\mathbf{P}^{\mathrm{cb}} \in \mathbb{R}^{T \times C}$ . + +To achieve action classification, we adopt multiple instance learning, i.e. for the output $\mathbf{P}^{\mathrm{cb}}$ from the backbone network, we aggregate (pool) the top- $k$ frames' scores as video-level category scores $\widehat{\mathbf{y}}\in \mathbb{R}^{C}$ , then supervise it via the binary cross-entropy loss, which is formulated as: + +$$ +\mathcal {L} _ {\mathrm {c l s}} = \sum_ {c = 1} ^ {C} - y _ {c} \log \widehat {y} _ {c}, \quad \widehat {y} _ {c} = \sigma \left(\frac {1}{k} \sum \mathcal {K} \left(\mathbf {P} ^ {\mathrm {c b}}\right)\right), \tag {1} +$$ + +where $\mathcal{K}$ denotes the top- $k$ score set in the temporal domain, and $\sigma$ refers to the softmax function. + +Remark. Under CB Pre-training and category-only supervision, $\mathbf{P}^{\mathrm{cb}}$ is well known for focusing on sparse discriminative action frames, i.e. high true negatives but serious false negatives, thus can provide rich background information. + +The VLP Branch is designed to mine free action knowledge from VL Pre-training, e.g. CLIP [66]. Since imagetext pre-training lacks sufficient temporal priors, its vanilla localization results have a serious over-complete issue, i.e. high false positives. To tackle this issue, we propose to finetune CLIP using extensive background samples. + +Instead of linear probing, we use efficient prompt learning [23, 34] for fine-tuning: we freeze the CLIP backbone, only optimize several prompt vectors and temporal layers. + +Concretely, for the visual stream, we first split the video into consecutive frames, and then utilize the CLIP image encoder to extract frame-level features $\mathbf{F}_{\mathrm{vis}} \in \mathbb{R}^{T \times D}$ . For temporal relationship construction, we strengthen $\mathbf{F}_{\mathrm{vis}}$ into $\mathbf{F}_{\mathrm{vid}} \in \mathbb{R}^{T \times D}$ through simple temporal transformer layers $\Phi_{\mathrm{temp}}(\cdot)$ . While for the textual stream, we first prepend and append several learnable prompt vectors $\Phi_{\mathrm{prmp}}(\cdot)$ to category names, then feed them into the CLIP text encoder, to obtain textual features $\mathbf{F}_{\mathrm{txt}} \in \mathbb{R}^{C \times D}$ . Formally, + +$$ +\mathbf {F} _ {\mathrm {v i d}} = \Phi_ {\text {t e m p}} (\mathbf {F} _ {\text {v i s}}), \quad \mathbf {F} _ {\mathrm {t x t}} = \Phi_ {\mathrm {t x t}} \left(\Phi_ {\text {p r m p}} \left(\mathrm {C} _ {\text {n a m e}}\right)\right), \tag {2} +$$ + +where $C_{\text{name}}$ refers to action category names, and $\Phi_{\text{txt}}(\cdot)$ is the CLIP textual encoder. Thereafter, the frame-level localization results $\mathbf{P}^{\text{vl}}$ for this branch can be calculated as: + +$$ +\mathbf {P} ^ {\mathrm {v l}} = \sigma \left(\mathbf {F} _ {\mathrm {v i d}} \cdot \mathbf {F} _ {\mathrm {t x t}} ^ {\top}\right) \in \mathbb {R} ^ {T \times C}. \tag {3} +$$ + +Remark. For the VLP branch, we only optimize lightweight model parameters for false-positive suppression, naturally bringing two main benefits: (1) the frozen CLIP backbone preserves the action prior knowledge in pre-training, thus maintaining high true-positive results; (2) it matches the demand for less supervision data under weakly-supervised settings, and also saves the memory footprint. + +Confident Pseudo-labels. Since both $\mathbf{P}^{\mathrm{vl}}$ and $\mathbf{P}^{\mathrm{cb}}$ contain somewhat noise, to make reliable use of complementary information, we distill confident location pseudo-labels of foreground and background respectively. That is, for the CBP branch, we distill extensive background pseudo-labels from the output $\mathbf{P}^{\mathrm{cb}}$ ; while for the VLP branch, we distill sufficient foreground pseudo-labels from the output $\mathbf{P}^{\mathrm{vl}}$ . + +For both branches, we leverage double thresholds $\delta_h$ and $\delta_l$ ( $\delta_h > \delta_l$ ), to convert localization results $\mathbf{P}$ into ternary pseudo-labels $\mathbf{H} \in \mathbb{R}^{T \times C}$ , which are formally written as: + +$$ +h _ {t, c} = \left\{ \begin{array}{c} 1 \text {i f} p _ {t} > \delta_ {h} \text {a n d} p _ {c} = y _ {c} \\ 0 \text {i f} p _ {t} < \delta_ {l} \text {o r} p _ {c} \neq y _ {c} \\ - 1 \quad \text {o t h e r w i s e} \end{array} \right. \tag {4} +$$ + +where the subscripts $c$ and $t$ refer to the indices of category and frame. More specifically, for either branch, we regard frames with scores more than $\delta_h$ and the correct action category as the foreground; while frames with scores less than $\delta_l$ or with the wrong action category are treated as the background; the remaining frames are considered uncertain. As a result, the pseudo-labels $\mathbf{H}^{\mathrm{cb}}$ cover vast confident background frames, as well as trivial foreground frames; while the pseudo-labels $\mathbf{H}^{\mathrm{vl}}$ contain dense confident foreground frames, and partial background frames. Note that, for both branches, we generate positive and negative frames to avoid trivial solutions, and facilitate contrastive feature learning. + +# 3.3. Collaboration of Dual-Branch Optimization + +In this section, we encourage two branches to collaborate with each other, such that forming a strong alliance of their complementary localization results. To reduce serious noises in pseudo-labels, we introduce an alternate training strategy for dual-branch collaborative optimization. + +The design rationale is to distill Background knowledge from the CBP branch for B step, while distill Foreground knowledge from the VLP branch in F step. To be specific, we warm up the CBP branch in advance, using only category supervision, to initialize reliable background frames. During B Step, we freeze the well-trained CBP branch, and then generate confident background pseudo-labels $\mathbf{H}^{\mathrm{cb}}$ to supervise the VLP branch. As a result, these false-positive confusions from vanilla CLIP pre-training are greatly tackled, and the resultant pseudo-labels contain a large number of confident foreground frames and background frames. During F Step, the high-quality pseudo-labels $\mathbf{H}^{\mathrm{vl}}$ are distilled from the frozen VLP branch, to guide the CBP branch for the false-negative suppression. Under such an alternating strategy, these two branches not only complement each other, but also correct each other, thus jointly contributing to more precise and complete action localization. + +During each step, to supervise either branch, we adopt both the knowledge distillation loss $\mathcal{L}_{\mathrm{kd}}$ and foreground + +background contrastive loss $\mathcal{L}_{\mathrm{fb}}$ . The total optimization loss can be written with a balancing ratio $\lambda$ , as follows: + +$$ +\mathcal {L} _ {\mathrm {a l l}} = \mathcal {L} _ {\mathrm {k d}} \left(\mathbf {H} ^ {\prime}, \mathbf {P}\right) + \lambda \mathcal {L} _ {\mathrm {f b}} \left(\Psi^ {+}, \Psi^ {-}\right). \tag {5} +$$ + +Here, $\mathcal{L}_{\mathrm{kd}}$ regularizes one branch to output similar detection results with pseudo-labels from the other branch. Given that there exist some noises in pseudo-labels, i.e. uncertain frames, we only make supervision on confident frames. + +$$ +\mathcal {L} _ {\mathrm {k d}} \left(\mathbf {H} ^ {\prime}, \mathbf {P}\right) = \frac {1}{O} \sum_ {c = 1} ^ {C} \sum_ {t = 1} ^ {O} D _ {\mathrm {K L}} \left(h _ {t, c} ^ {\prime} \mid \mid p _ {t, c}\right), \tag {6} +$$ + +where $D_{\mathrm{KL}}(p(x) || q(x))$ refers to the Kullback-Leibler divergence of distribution $p(x)$ from distribution $q(x)$ , $O$ is the total number of confident frames, and $\mathbf{H}'$ denotes the pseudo-labels from the other branch. Note that, the pseudolabels contain two types of confident frames: foreground and background, which could help to avoid falling into the trivial solutions under one single type of labels. + +Moreover, in untrimmed long videos, some background contexts could appear visually similar with the action (foreground). We further introduce contrastive learning to pull foreground features and push background features. Specifically, we treat confident foreground frames from the same action category as the positive set $\Psi^{+}$ , while all confident background frames as the negative set $\Psi^{-}$ , then foreground-background contrastive loss is formulated as: + +$$ +\mathcal {L} _ {\mathrm {f b}} \left(\Psi_ {i} ^ {+}, \Psi_ {i} ^ {-}\right) = \sum_ {i} - \log \frac {\sum_ {m \in \Psi_ {i} ^ {+}} \exp \left(\mathbf {f} _ {i} \cdot \mathbf {f} _ {m} / \tau\right)}{\sum_ {j \in *} \exp \left(\mathbf {f} _ {i} \cdot \mathbf {f} _ {j} / \tau\right)}, \tag {7} +$$ + +where $\mathbf{f} \in \mathbb{R}^D$ refers to the frame feature, $\tau$ means the temperature hyper-parameter for scaling, and $*$ means the union of $\Psi_i^+$ and $\Psi_i^-$ . Take the VLP branch as an example, sufficient background pseudo-labels contain considerable hard negative samples, to help distinguish features of foreground and contexts. In addition, the enhanced features of uncertain frames also become more discriminative, further facilitating more complete temporal action localization. + +Discussion. Comparing to various fusion strategies, our alternating strategy produces more precise and complete results (see Table 4 for details). This strategy plays a similar role as the multi-view co-training, where CBP and VLP branches can be deemed as two distinctive views, thus being quite robust to pseudo-label noises. For B step, we prompt the VLP branch for high-quality pseudo-labels, where some frames with conflicting predictions are still treated as uncertain. In F step, we use feature contrastive loss to make their results more discriminative, i.e. further denoising. + +# 3.4. Inference + +At testing time, we leverage the results from the CBP branch for post-processing, as vision-language pre-training + +cannot handle Optical Flow, which is essential for WTAL. Given an input video, we first obtain video-level category probabilities and frame-level localization scores. For action classification, we select the classes with probability greater than $\theta_{cls}$ ; and for localization, we threshold detection scores with $\theta_{loc}$ , concatenate consecutive snippets as action proposals, and eliminate redundant proposals with soft nonmaximum suppression (NMS). Each proposal is scored with the detection maximum in the proposal interval. + +# 4. Experiments + +# 4.1. Implementation + +Datasets. THUMOS14 owns 413 untrimmed videos from 20 categories, and each video contains an average of 15 instances. As conventions, we train on 200 validation videos, and evaluate on 213 testing videos. Despite its small scale, this dataset is challenging, since video lengths vary widely and actions occur frequently. ActivityNet1.2 covers 9682 videos belonging to 100 categories. Almost all the videos are single-category, and action regions take up more than half of the video duration. We train on 4619 training videos and evaluate on 2383 validation videos. + +Metrics. To evaluate localization performance, we follow the standard protocol to use mean Average Precision (mAP) at different intersections over union (IoU) thresholds. Note that a proposal is regarded as positive only if both the category prediction is correct and IoU exceeds the set threshold. To clearly evaluate the quality of pseudo-labels, we also report mean Intersection over Union (mIoU) averaged over the foreground categories and the background category. + +Details. To handle the large variety in video durations, we randomly sample $T$ consecutive snippets for each video. $T$ is set to 1000 on THUMOS14, and 400 on ActivityNet1.2. We utilize the TV-L1 algorithm to extract optical flow from RGB data. For the CBP branch, we use Transformer architectures (multi-head self-attention, layer norm, and MLPs) as the backbone network. For the VLP branch, we use a 2-layer temporal Transformer, preprocess and append 16 prompt vectors to textual inputs, both are initialized by $\mathcal{N}(0,0.01)$ . Both CLIP image encoder and text encoder are adopted from ViT-B/16. The framework is optimized by Adam with the learning rate of $10^{-4}$ . All hyper-parameters are set by grid search: pseudo-label thresholds $\delta_h = 0.3$ , $\delta_l = 0.1$ , inference thresholds $\theta_{cls} = 0.85$ , $\theta_{loc} = 0.45$ , the balancing ratio $\lambda = 0.05$ , the temperature $\tau = 0.07$ . + +# 4.2. Comparison with State-of-the-art Methods + +Here, we make comprehensive comparisons with current state-of-the-art methods across multiple IoU thresholds. + +Performance. The comparisons on THUMOS14 are provided in Table 1. Here, we separate two levels of supervi + +
SupervisionMethodFeaturemAP@IoUAVG(0.1-0.5)AVG(0.3-0.7)
0.10.20.30.40.50.60.7
StrongDBS [15]I3D56.754.750.643.134.324.414.747.933.4
BUMR [100]--53.950.745.438.028.5-43.3
GCM [95]72.570.966.560.851.9--64.5-
RCL [81]--70.162.352.942.730.7-51.7
ActionFormer [98]--82.177.871.059.443.9-66.8
WeakHAM-Net [21]I3D65.459.050.341.131.020.711.449.430.9
UM [33]63.056.649.040.930.421.010.448.030.3
TS-PCA [48]67.661.153.443.434.324.713.752.033.9
FTCL [12]69.663.455.245.235.623.712.253.834.4
ACGNet [90]68.162.653.144.634.722.612.052.633.4
DCC [35]69.063.855.945.935.724.313.754.135.1
ASM-Loc [17]71.265.557.146.836.625.213.455.435.8
CO2-Net [18]70.163.654.545.738.326.413.454.435.7
RSKP [20]71.365.355.847.538.225.412.555.635.9
DELU [7]71.566.256.547.740.527.215.356.537.4
CO2-Net†I3D67.460.651.943.135.023.312.151.633.0
CO2-Net‡68.862.152.643.936.124.112.052.733.7
DELU†+CLIP68.660.852.243.435.623.313.352.133.6
DELU‡70.363.955.445.939.026.014.354.936.0
Ours73.568.861.553.842.029.416.860.040.8
+ +Table 1. Comparison with state-of-the-art methods on THUMOS14. For fair comparisons, we reproduce the results of SOTA methods: CO2-Net [18] and DELU [7], by inputting both I3D [5] and CLIP [66] features. † and ‡ refer to averaging or concatenating these two features. AVG(0.1-0.5) and AVG(0.3-0.7) are the average mAP from IoU 0.1 to 0.5 and from IoU 0.3 to 0.7. Our framework significantly surpasses all weakly-supervised competitors using identical features, and is even comparable to early strongly-supervised methods. + +
MethodFeaturemAP@IoUAVG
0.50.750.95
CleanNet [50]I3D37.120.35.021.6
CMCS [43]36.822.05.622.4
TSCN [96]37.623.75.723.6
BasNet [31]38.524.25.624.3
DGAM [68]41.023.55.324.4
UM [33]41.225.66.025.9
ACGNet [90]41.826.05.926.1
D2-Net [60]42.325.55.826.0
CO2-Net [18]43.326.35.226.4
DELU [7]44.226.75.426.9
CO2-Net†I3D44.826.95.527.1
CO2-Net‡45.227.15.827.6
DELU†+45.427.35.727.5
DELU‡CLIP46.027.85.928.0
Ours48.329.36.129.6
+ +Table 2. Comparison with state-of-the-art methods on ActivityNet1.2. For fair comparisons, we reproduce CO2-Net [18] and DELU [7], by inputting I3D [5] and CLIP [66] features. $\dagger$ and $\ddagger$ refer to averaging or concatenating these features. AVG is the average mAP at the thresholds 0.5:0.05:0.95. Our method significantly surpasses all competitors, especially at loose IoU thresholds. + +sion: strong and weak, for better quantification. Generally speaking, our framework achieves new state-of-the-art on + +all IoU regimes. Comparing with recent methods, the gain of the average mAP (0.3-0.7) even reaches $4 - 5\%$ , further narrowing the performance gap between weak and strong supervisions. Moreover, our method achieves considerable gains on strict and loose evaluations. For example, when comparing to DELU [7], the gains are $3.5\%$ average mAP (0.1-0.5) and $3.4\%$ average mAP (0.3-0.7), indicating that our results are complete and precise. Furthermore, despite being weakly-supervised settings, at several low IoU thresholds, our framework even performs comparably with some earlier strongly-supervised methods [14, 15, 101]. + +Table 2 shows the comparison results on ActivityNet1.2. On all IoU thresholds, our designed framework surpasses existing methods by a large margin. In terms of the average mAP, the performance improvement can reach $2.7\%$ , taking the state-of-the-art to a new level. However, due to the lack of precise location annotations, the gain decreases as the IoU threshold becomes stricter, e.g. $4.1\%$ @IoU 0.5 vs. $0.7\%$ @IoU 0.95, when comparing to DELU [7]. + +Source of Gain. Comparing to existing methods, we leverage Vision-Language Pre-training for free knowledge. To make fair comparisons, we also input both I3D and CLIP features into two SOTA methods [7, 18], by one early fusion mode (average or concatenate these features). In general, simply adding CLIP features gives only slight or even negative gains on both datasets, which is due to the bad over + +
SettingTHUMOSActivityNet
ForeBackForeBack
CB Pre-training56.088.754.788.3
VL Pre-training75.634.172.145.0
Ours72.480.069.571.7
+ +Table 3. Complementarity of pre-training. CB Pre-training has good background mIoU but inferior foreground mIoU. VL Pretraining has good foreground mIoU but inferior background mIoU. Our method achieves both high foreground and background mIoU. + +
Fusion StrategymAP@IoUAVG(0.3-0.7)
0.30.50.7
Only F step (AVG)40.016.13.319.1
Only F step (Weight)52.825.56.127.7
Only B step (AVG)56.733.611.334.1
Only B step (Weight)58.538.814.837.8
Alternating61.542.016.840.8
+ +complete issue of CLIP (detailed in Table 3). For THUMOS with complex and frequent actions, over-complete worsens results. While in ActivityNet, most videos only contain one action that takes up half of the video duration, thus benefiting a bit from over-complete. Nevertheless, with identical features, our method significantly outperforms existing competitors, proving the effectiveness of our framework. + +# 4.3. Ablation Study and Comparison + +Here, we evaluate the contributions of each component and framework designs, to further dissect our framework. + +Complementarity of pre-trainings. As the detection performance is mainly determined by pseudo-labels, here we show the quality of pseudo-labels, in terms of foreground mIoU and background mIoU. Table 3 provides the comprehensive results for various settings on both benchmarks. + +For common Classification-Based Pre-training, its localization results suffer from the incomplete issue. In detail, the background mIoU is impressive, i.e. high true negatives, while the foreground mIoU is poor, i.e. serious false negatives. The main reason is that features pre-trained on action classification datasets only highlight sparse discriminative frames. While the results of Vision-Language Pre-training are just the opposite: suffering from the over-complete issue. The foreground mIoU is considerable, i.e. high true positives, but the background mIoU is terrible, i.e. serious false positives. The main reason is that VLP using image + +Table 4. Comparison of optimization strategies. "Only F step": extract pseudo-labels from vanilla VLP to train the CBP branch. "Only B step": get pseudo-labels from the warm-up CBP branch to train the VLP branch. We combine two branches by averaging and weighting. Our alternating strategy shows clear superiority. + +
ModelLkdLf bmAP@IoUAVG(0.3-0.7)
0.30.50.7
A1✓57.137.012.636.0
A2✓51.731.29.430.9
A3✓✓61.542.016.840.8
+ +Table 5. Contribution of optimization losses on THUMOS14. The single knowledge distillation loss $\mathcal{L}_{\mathrm{kd}}$ has brought gratifying localization results, and the additional foreground-background contrastive loss $\mathcal{L}_{\mathrm{fb}}$ further boosts the performance to the best. + +
MethodmAP@IoUAVG (0.3-0.7)
0.30.50.7
UM [33]49.030.410.430.3
UM + Ours53.934.713.634.3
CO2-Net [18]54.538.313.435.7
CO2-Net + Ours56.239.715.937.5
+ +Table 6. Framework generalization on THUMOS14. Our proposed framework is generalized, i.e. existing methods can serve as our CBP branch, to achieve further improvements. + +text pairs lacks temporal priors. The above results strongly prove the complementarity between these two pre-training. + +Moreover, on both datasets, our method achieves high foreground and background mIoU, that is, more precise and complete localization. This mainly benefits from extensive background supervision provided by the CBP branch, and extensive foreground supervision distilled from the VLP branch. Besides, comparing to VL Pre-training, our results achieve immediate gains on the background mIoU, while only slight drops on the foreground mIoU. This reveals that the lightweight trainable parameters, i.e. prompts + Transformer, indeed retain the action prior knowledge in VLP, and also significantly suppress false-positive results. + +Comparison of optimization strategies. To evaluate the alternating efficacy, Table 4 compares with another two solutions. (1) 'Only F step': extract foreground pseudo-labels from the vanilla VLP, then provide them to the CBP branch for auxiliary training; (2) 'Only B step': distill background pseudo-labels from the warm-up CBP branch to train the VLP branch. And for each solution, we combine the dual-branch results by averaging and weighting, respectively. + +'Only F step' performs the worst, mainly suffering from heavy noise in vanilla VLP pseudo-labels (over-complete). By fine-tuning vanilla VLP with many background frames, 'Only B step' gets great improvements, but still lacks full fusion of complementarity. Moreover, the weighted operation could suppress noise somewhat, and thus causes better results than the average operation. By comparison, our alternating strategy shows great advantages over competitors, proving the non-trivial nature of fusing complementary information, and robust denoising to pseudo-labels. + +![](images/1f8532f9bdd1800484187c111544bc22987b84b98185af21a2f9ffb3039dabf5.jpg) +Figure 3. Qualitative comparisons. The first two rows are videos and ground-truth action intervals. The last six rows are frame-level action probabilities, and localization results of Classification-Based Pre-training (CBP), Vision-Language Pre-training (VLP), and our framework, respectively. CBP suffers from the incomplete issue, while VLP has the over-complete issue. Our framework distills foreground knowledge from VLP and background from CBP, for the strong collaborative alliance, thus bringing more complete and precise results. + +Contribution of various losses. To train our method, both knowledge distillation loss $\mathcal{L}_{\mathrm{kd}}$ and foreground-background contrastive loss $\mathcal{L}_{\mathrm{fb}}$ are leveraged. In Table 5, we analyze the effectiveness of optimization losses on THUMOS14. The single $\mathcal{L}_{\mathrm{kd}}$ (model A1) already brings gratifying performance. This reveals that the confident pseudo-labels of foreground and background distilled from two branches, are well fused by the alternate optimization. On the other hand, with only $\mathcal{L}_{\mathrm{fb}}$ , model A2 also performs barely satisfactory results. This is because $\mathcal{L}_{\mathrm{fb}}$ differentiates foreground features and background features, thus eliminating extensive uncertain frames, and also making the localization task easier. Overall, these two losses jointly contribute to the best performance, indicating that both are essential. + +Framework generalization. Our distillation-collaboration framework is generalized, which means that existing WTAL methods can be employed as the CBP branch. Table 6 takes two typical methods: CO2-Net [18] and UM [33], as examples. Our framework further improves their performance by up to $2 - 4\%$ average mAP, showing a good generalization to other methods and other backbone designs. + +# 4.4. Qualitative Results + +To intuitively demonstrate the superiority, Figure 3 visualizes results from various types of videos. Classification-Based Pre-training highlights only some discriminative action frames (the incomplete issue), which is more prominent for videos containing low-frequency actions. On the contrary, Vision-Language Pre-training tends to over-activate action foreground to background (the over-complete issue), which is especially evident in videos with high-frequency actions. We design the distillation-collaboration framework + +to fuse the complementarity from these two pre-trainings. In B step, extensive confident background is distilled from the well-trained CBP branch, to supervise the VLP branch for false-positive suppression. While in F step, sufficient confident foreground information is distilled from the VLP branch, to guide the CBP branch for false-negative elimination. Hence, our method establishes the strong alliance by collaborative optimization, bringing precise and complete detection results, regardless of dense or sparse actions. + +# 5. Conclusion + +This work proposes the novel distillation-collaboration framework to distill free knowledge from Vision-Language Pre-training, for weakly-supervised temporal action localization. Our core insight is that existing VLP often localizes over-complete actions, which is just complementary to the incomplete results of conventional Classification-Based Pre-training. And to form strong alliances, we optimize the framework containing complementary dual branches by an alternating strategy: distill confident background pseudolabels from the CBP branch, and the confident foreground pseudo-labels from the VLP branch, for collaborative training. Extensive experiments show the significance of distilling VLP and our superior performance. Thorough ablations are studied both quantitatively and qualitatively. + +# Acknowledgements + +This research is supported by the National Key R&D Program of China (No. 2022ZD0160702), STCSM (No. 22511106101, No. 18DZ2270700, No. 21DZ1100100), 111 plan (No. BP0719010), and State Key Laboratory of UHD Video and Audio Production and Presentation. + +# References + +[1] Jean-Baptiste Alayrac, Jeff Donahue, Pauline Luc, Antoine Miech, Iain Barr, Yana Hasson, Karel Lenc, Arthur Mensch, Katie Millican, Malcolm Reynolds, et al. Flamingo: a visual language model for few-shot learning. In Adv. Neural Inform. Process. 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209 + ], + "type": "text", + "content": "Shanghai AI Laboratory " + }, + { + "bbox": [ + 94, + 194, + 499, + 209 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 94, + 194, + 499, + 209 + ], + "type": "text", + "content": "Huawei Cloud" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 212, + 537, + 224 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 212, + 537, + 224 + ], + "spans": [ + { + "bbox": [ + 54, + 212, + 537, + 224 + ], + "type": "text", + "content": "{ju_chen, dyekuu, jinxliu, ya_zhang, wangyanfeng}@sjtu.edu.cn, {pszhao93, jianlong.chang, tian.qi1}@huawei.com" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 143, + 251, + 192, + 264 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 251, + 192, + 264 + ], + "spans": [ + { + "bbox": [ + 143, + 251, + 192, + 264 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 277, + 290, + 565 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 277, + 290, + 565 + ], + "spans": [ + { + "bbox": [ + 46, + 277, + 290, + 565 + ], + "type": "text", + "content": "Weakly-supervised temporal action localization (WTAL) learns to detect and classify action instances with only category labels. Most methods widely adopt the off-the-shelf Classification-Based Pre-training (CBP) to generate video features for action localization. However, the different optimization objectives between classification and localization, make temporally localized results suffer from the serious incomplete issue. To tackle this issue without additional annotations, this paper considers to distill free action knowledge from Vision-Language Pre-training (VLP), as we surprisingly observe that the localization results of vanilla VLP have an over-complete issue, which is just complementary to the CBP results. To fuse such complementarity, we propose a novel distillation-collaboration framework with two branches acting as CBP and VLP respectively. The framework is optimized through a dual-branch alternate training strategy. Specifically, during the " + }, + { + "bbox": [ + 46, + 277, + 290, + 565 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 46, + 277, + 290, + 565 + ], + "type": "text", + "content": " step, we distill the confident background pseudo-labels from the CBP branch; while during the " + }, + { + "bbox": [ + 46, + 277, + 290, + 565 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 46, + 277, + 290, + 565 + ], + "type": "text", + "content": " step, the confident foreground pseudo-labels are distilled from the VLP branch. As a result, the dual-branch complementarity is effectively fused to promote one strong alliance. Extensive experiments and ablation studies on THUMOS14 and ActivityNet1.2 reveal that our method significantly outperforms state-of-the-art methods." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 583, + 128, + 596 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 583, + 128, + 596 + ], + "spans": [ + { + "bbox": [ + 47, + 583, + 128, + 596 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 605, + 287, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 688 + ], + "type": "text", + "content": "Temporal action localization (TAL), which aims to localize and classify action instances from untrimmed long videos, has been recognized as an indispensable component of video understanding [13, 72, 92]. To avoid laborious temporal boundary annotations, the weakly-supervised setting (WTAL) [31, 62, 64, 78], i.e. only video-level category labels are available, has gained increasing attentions." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "To date in the literature, almost all WTAL methods rely on Classification-Based Pre-training (CBP) for video fea" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 305, + 247, + 547, + 383 + ], + "blocks": [ + { + "bbox": [ + 305, + 247, + 547, + 383 + ], + "lines": [ + { + "bbox": [ + 305, + 247, + 547, + 383 + ], + "spans": [ + { + "bbox": [ + 305, + 247, + 547, + 383 + ], + "type": "image", + "image_path": "b2486122ea2d1bfac110d59bfa81db123542096d43ce83fad90a5f78cb0481c2.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 387, + 547, + 464 + ], + "lines": [ + { + "bbox": [ + 304, + 387, + 547, + 464 + ], + "spans": [ + { + "bbox": [ + 304, + 387, + 547, + 464 + ], + "type": "text", + "content": "Figure 1. (A) Complementarity. Most works use Classification-Based Pre-training (CBP) for localization, bringing high TN yet serious FN. Vanilla Vision-Language Pre-training (VLP) confuses action and background, bringing high TP yet serious FP. (B) Our distillation-collaboration framework distills foreground from the VLP branch while background from the CBP branch, and promotes mutual collaboration, bringing satisfactory results." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 485, + 546, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 485, + 546, + 688 + ], + "spans": [ + { + "bbox": [ + 304, + 485, + 546, + 688 + ], + "type": "text", + "content": "ture extraction [5, 73]. A popular pipeline is to train an action classifier with CBP features, then threshold the frame-level classification probabilities for final localization results. As demonstrated in Figure 1(A), these CBP methods suffer from the serious incompleteness issue, i.e. only detecting sparse discriminative action frames and incurring high false negatives. The main reason is that the optimization objective of classification pre-training, is to find several discriminative frames for action recognition, which is far from the objective of complete localization. As a result, features from CBP are inevitably biased towards partial discriminative frames. To solve the incompleteness issue, many efforts [33, 43, 56, 96] have been attempted, but most of them are trapped in a 'performance-cost dilemma', namely, solely digging from barren category labels to keep costs low. Lacking location labels fundamentally limits the performance, leaving a huge gap from strong supervision." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 689, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 547, + 713 + ], + "type": "text", + "content": "To jump out of the dilemma, this paper raises one novel question: is there free action knowledge available, to help" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14751" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "type": "text", + "content": "complete detection results while maintain cheap annotation overhead at the same time? We naturally turn our sights to the prevalent Vision-Language Pre-training (VLP) [22, 66]. VLP has demonstrated great success to learn joint visual-textual representations from large-scale web data. As language covers rich information about objects, human-object interactions, and object-object relationships, these learned representations could provide powerful human-object co-occurrence priors: valuable gifts for action localization." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 182, + 289, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 182, + 289, + 373 + ], + "spans": [ + { + "bbox": [ + 46, + 182, + 289, + 373 + ], + "type": "text", + "content": "We here take one step towards positively answering the question, i.e. fill the research gap of distilling action priors from VLP, namely CLIP [66], to solve the incomplete issue for WTAL. As illustrated in Figure 1 (A), we first naively evaluate the temporal localization performance of VLP by frame-wise classification. But the results are far from satisfactory, suffering from the serious over-complete issue, i.e. confusing multiple action instances into a whole, causing high false positives. We conjecture the main reasons are: (1) due to data and computational burden, almost all VLPs are trained using image-text pairs. Hence, VLP lacks sufficient temporal knowledge and relies more on human-object co-occurrence for localization, making it struggle to distinguish the actions with visually similar background contexts; (2) some background contexts have similar (confusing) textual semantics to actions, such as run-up vs. running." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 375, + 289, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 375, + 289, + 639 + ], + "spans": [ + { + "bbox": [ + 46, + 375, + 289, + 639 + ], + "type": "text", + "content": "Although simply steering VLP for WTAL is infeasible, we fortunately observe the complementary property between CBP and VLP paradigms: the former localizes high true negatives but serious false negatives, while the latter has high true positives but serious false positives. To leverage the complementarity, as shown in Figure 1 (B), we design a novel distillation-collaboration framework that uses two branches to play the roles of CBP and VLP, respectively. The design rationale is to distill background knowledge from the CBP branch, while foreground knowledge from the VLP branch, for strong alliances. Specifically, we first warm up the CBP branch using only category supervision to initialize confident background frames, and then optimize the framework via an alternating strategy. During " + }, + { + "bbox": [ + 46, + 375, + 289, + 639 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 46, + 375, + 289, + 639 + ], + "type": "text", + "content": " step, we distill background pseudo-labels for the VLP branch to solve the over-complete issue, hence obtaining high-quality foreground pseudo-labels. During " + }, + { + "bbox": [ + 46, + 375, + 289, + 639 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 46, + 375, + 289, + 639 + ], + "type": "text", + "content": " step, we leverage high-quality pseudo-labels for the CBP branch to tackle the incomplete issue. Besides, in each step, we introduce both confident knowledge distillation and representation contrastive learning for pseudo-label denoising, effectively fusing complementarity for better results." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 639, + 288, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 639, + 288, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 639, + 288, + 700 + ], + "type": "text", + "content": "On two standard benchmarks: THUMOS14 and ActivityNet1.2, our method improves the average performance by " + }, + { + "bbox": [ + 46, + 639, + 288, + 700 + ], + "type": "inline_equation", + "content": "3.5\\%" + }, + { + "bbox": [ + 46, + 639, + 288, + 700 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 639, + 288, + 700 + ], + "type": "inline_equation", + "content": "2.7\\%" + }, + { + "bbox": [ + 46, + 639, + 288, + 700 + ], + "type": "text", + "content": " over state-of-the-art methods. We also conduct extensive ablation studies to reveal the effectiveness of each component, both quantitatively and qualitatively." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 59, + 701, + 248, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 248, + 713 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 248, + 713 + ], + "type": "text", + "content": "To sum up, our contributions lie in three folds:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 547, + 172 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 304, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 96 + ], + "type": "text", + "content": "- We pioneer the first exploration in distilling free action knowledge from off-the-shelf VLP to facilitate WTAL;" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 98, + 547, + 134 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 98, + 547, + 134 + ], + "spans": [ + { + "bbox": [ + 304, + 98, + 547, + 134 + ], + "type": "text", + "content": "- We design a novel distillation-collaboration framework that encourages the CBP branch and VLP branch to complement each other, by an alternating optimization strategy;" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 136, + 547, + 172 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 136, + 547, + 172 + ], + "spans": [ + { + "bbox": [ + 304, + 136, + 547, + 172 + ], + "type": "text", + "content": "- We conduct extensive experiments and ablation studies to reveal the significance of distilling VLP and our superior performance on two public benchmarks." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 185, + 392, + 198 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 185, + 392, + 198 + ], + "spans": [ + { + "bbox": [ + 306, + 185, + 392, + 198 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 204, + 547, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 204, + 547, + 397 + ], + "spans": [ + { + "bbox": [ + 304, + 204, + 547, + 397 + ], + "type": "text", + "content": "Vision-Language Pre-training (VLP) aims to learn cross-modal representations [10, 25, 57, 82] from large-scale web data. Compared to video, image usually needs fewer costs for annotation and computation, hence almost all VLPs are image-based, e.g. [1, 22, 66, 80, 91, 93]. Recently, several studies adopted VLP to provide free visual-semantic knowledge for downstream image tasks, such as detection [16,94], segmentation [44,54,67,103], human-object interaction [29, 36], synthesis [47], and generation [9, 76, 77]. In terms of the video domain, [42, 51, 79] equipped VLP with temporal transformers for action recognition. [23, 24, 59] introduced prompt learning for efficient retrieval or detection. However, these studies focus more on open-vocabulary scenarios or short video understanding. On the contrary, this paper makes the first exploration to steer VLP for long video temporal localization, under the weakly-supervised setting." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 399, + 547, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 399, + 547, + 591 + ], + "spans": [ + { + "bbox": [ + 304, + 399, + 547, + 591 + ], + "type": "text", + "content": "Strongly-supervised Temporal Action Localization has achieved great progress [38,46,65,95], given precise action boundaries and categories. There are two popular pipelines: the top-down framework [6,14,40,69,71,75,81,83,85,104] pre-defines massive anchors based on the action distribution prior, and uses fixed-length sliding windows to generate initial proposals, then regresses to refine boundaries; the bottom-up framework [3,8,37,39,41,58,74,85,87,100,101] trains frame-wise boundary detectors for extreme frames (start, end, center), then groups extreme frames or estimates action lengths to produce proposals. In addition, some papers [11, 49, 88] proposed various fusion strategies to complement these frameworks. Several studies [45, 95] are devoted to better post-processing. Nevertheless, all the above methods demand precise boundary annotations, which are time-consuming and expensive in reality." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 594, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 548, + 715 + ], + "type": "text", + "content": "Weakly-supervised Temporal Action Localization significantly alleviates annotation costs, training with only category labels. The pivotal component is CAS [21, 62, 64, 78] obtained from Classification-Based Pre-training (CBP). But due to the gap of classification and localization, CBP suffers from one serious incomplete issue: only localize discriminative action fragments or even background. To solve this issue, [27, 56, 102] introduced the erasing strategy. [43, 52, 60] produced multiple CAS in parallel for complementarity. [32, 33, 63, 68] proposed background modeling" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "14752" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 71, + 542, + 292 + ], + "blocks": [ + { + "bbox": [ + 52, + 71, + 542, + 292 + ], + "lines": [ + { + "bbox": [ + 52, + 71, + 542, + 292 + ], + "spans": [ + { + "bbox": [ + 52, + 71, + 542, + 292 + ], + "type": "image", + "image_path": "59453d5eecfd774c0444e957b5333195085e5613625f50124ad901ed40b5c086.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 297, + 546, + 344 + ], + "lines": [ + { + "bbox": [ + 46, + 297, + 546, + 344 + ], + "spans": [ + { + "bbox": [ + 46, + 297, + 546, + 344 + ], + "type": "text", + "content": "Figure 2. Distillation-Collaboration Framework. It covers two parallel branches, named CBP and VLP, and is optimized by an alternating strategy. We warm up the CBP branch in advance. In B step, we freeze both CLIP encoders, and distill confident background pseudo-labels from the CBP branch, to train prompt vectors and temporal Transformer in the VLP branch. In F step, confident foreground pseudo-labels are distilled for the CBP branch. We utilize both knowledge distillation loss and contrastive loss during dual-branch collaboration." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 363, + 289, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 363, + 289, + 542 + ], + "spans": [ + { + "bbox": [ + 46, + 363, + 289, + 542 + ], + "type": "text", + "content": "and context separation. [12, 17, 19, 97] enhanced features by intra- and inter-video modeling. To iteratively refine results, some papers [53, 89, 96] introduced the self-training strategy, [50, 70] adopted outer-inner contrastive learning. While encouraging, most of them are trapped in the 'performance-cost dilemma', i.e. solely digging from barren category labels to keep costs low. But the lack of annotations leads to a huge performance gap between strong and weak supervisions. To this end, [26, 28, 30, 55, 61, 86] explored to add instance-number or single-frame annotations for further improvements. Some papers [2, 4, 84, 99] tried long-video pretraining for TAL. As a fresh departure from existing work, to pursue better performance without additional annotation costs, this paper intends to distill free action knowledge from off-the-shelf VLPs, to assist WTAL." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 553, + 104, + 565 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 553, + 104, + 565 + ], + "spans": [ + { + "bbox": [ + 47, + 553, + 104, + 565 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 572, + 201, + 583 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 572, + 201, + 583 + ], + "spans": [ + { + "bbox": [ + 47, + 572, + 201, + 583 + ], + "type": "text", + "content": "3.1. Notations and Preliminaries" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 590, + 287, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 590, + 287, + 686 + ], + "spans": [ + { + "bbox": [ + 46, + 590, + 287, + 686 + ], + "type": "text", + "content": "Task Formulation. Given " + }, + { + "bbox": [ + 46, + 590, + 287, + 686 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 590, + 287, + 686 + ], + "type": "text", + "content": " untrimmed videos " + }, + { + "bbox": [ + 46, + 590, + 287, + 686 + ], + "type": "inline_equation", + "content": "\\{v_{i}\\}_{i = 1}^{N}" + }, + { + "bbox": [ + 46, + 590, + 287, + 686 + ], + "type": "text", + "content": " and their video-level category labels " + }, + { + "bbox": [ + 46, + 590, + 287, + 686 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{y}_i\\in \\mathbb{R}^C\\}_{i = 1}^N" + }, + { + "bbox": [ + 46, + 590, + 287, + 686 + ], + "type": "text", + "content": " , where " + }, + { + "bbox": [ + 46, + 590, + 287, + 686 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 590, + 287, + 686 + ], + "type": "text", + "content": " means the total number of action categories, WTAL intends to detect and classify all action instances, in terms of a set of quadruples " + }, + { + "bbox": [ + 46, + 590, + 287, + 686 + ], + "type": "inline_equation", + "content": "\\{(s,e,c,p)\\}" + }, + { + "bbox": [ + 46, + 590, + 287, + 686 + ], + "type": "text", + "content": " , where " + }, + { + "bbox": [ + 46, + 590, + 287, + 686 + ], + "type": "inline_equation", + "content": "s,e,c,p" + }, + { + "bbox": [ + 46, + 590, + 287, + 686 + ], + "type": "text", + "content": " represent the start time, the end time, the action category and detection score of the action proposal, respectively. Note that each video may contain multiple action instances." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 689, + 288, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 288, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 288, + 712 + ], + "type": "text", + "content": "Motivation. There exists significant complementarity between the localization results of Classification-Based Pre" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 363, + 546, + 447 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 363, + 546, + 447 + ], + "spans": [ + { + "bbox": [ + 304, + 363, + 546, + 447 + ], + "type": "text", + "content": "training and Vision-Language Pre-training, as concluded in Table 3. The former suffers from incomplete results (serious false negatives), but has good true negatives; the latter suffers from over-complete results (serious false positives), but has good true positives. Such investigations motivate us to collaborate the complementary results for strong alliances, through a distillation-collaboration framework." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 450, + 547, + 606 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 450, + 547, + 606 + ], + "spans": [ + { + "bbox": [ + 304, + 450, + 547, + 606 + ], + "type": "text", + "content": "Framework Overview. As demonstrated in Figure 2, the distillation-collaboration framework consists of two parallel branches, named CBP branch and VLP branch respectively, and is optimized by an alternating strategy. The CBP branch is first warmed-up to produce rich background information with only classification supervision. During B step, we distill confident background pseudo-labels from CBP branch, for VLP branch to tackle the over-complete issue, and thus localize high-quality foreground and background information. During F step, we distill superior pseudo-labels from the well-trained VLP branch, for CBP branch to tackle the incomplete issue. Through such dual-branch collaboration, we effectively fuse the complementary results." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 621, + 531, + 634 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 621, + 531, + 634 + ], + "spans": [ + { + "bbox": [ + 306, + 621, + 531, + 634 + ], + "type": "text", + "content": "3.2. Distillation of Foreground and Background" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 641, + 546, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 546, + 677 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 546, + 677 + ], + "type": "text", + "content": "The CBP Branch is utilized to identify a large number of background frames as well as several discriminative action frames, by exploiting Classification-Based Pre-training." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 677, + 546, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 546, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 546, + 712 + ], + "type": "text", + "content": "Following literature [33, 43], we adopt CB pre-training, i.e. the I3D architecture pre-trained on Kinetics [5], to extract RGB and Flow features, and then concatenate them" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14753" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 71, + 286, + 132 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 71, + 286, + 132 + ], + "spans": [ + { + "bbox": [ + 46, + 71, + 286, + 132 + ], + "type": "text", + "content": "to form the two-stream features " + }, + { + "bbox": [ + 46, + 71, + 286, + 132 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathrm{i3d}} \\in \\mathbb{R}^{T \\times 2D}" + }, + { + "bbox": [ + 46, + 71, + 286, + 132 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 71, + 286, + 132 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 71, + 286, + 132 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 71, + 286, + 132 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 71, + 286, + 132 + ], + "type": "text", + "content": " refer to the temporal length and feature dimension. Next, feeding with " + }, + { + "bbox": [ + 46, + 71, + 286, + 132 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathrm{i3d}}" + }, + { + "bbox": [ + 46, + 71, + 286, + 132 + ], + "type": "text", + "content": ", the CBP branch uses the backbone network for feature fine-tuning and localization, and finally outputs the frame-level action probabilities " + }, + { + "bbox": [ + 46, + 71, + 286, + 132 + ], + "type": "inline_equation", + "content": "\\mathbf{P}^{\\mathrm{cb}} \\in \\mathbb{R}^{T \\times C}" + }, + { + "bbox": [ + 46, + 71, + 286, + 132 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 133, + 286, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 133, + 286, + 192 + ], + "spans": [ + { + "bbox": [ + 46, + 133, + 286, + 192 + ], + "type": "text", + "content": "To achieve action classification, we adopt multiple instance learning, i.e. for the output " + }, + { + "bbox": [ + 46, + 133, + 286, + 192 + ], + "type": "inline_equation", + "content": "\\mathbf{P}^{\\mathrm{cb}}" + }, + { + "bbox": [ + 46, + 133, + 286, + 192 + ], + "type": "text", + "content": " from the backbone network, we aggregate (pool) the top- " + }, + { + "bbox": [ + 46, + 133, + 286, + 192 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 133, + 286, + 192 + ], + "type": "text", + "content": " frames' scores as video-level category scores " + }, + { + "bbox": [ + 46, + 133, + 286, + 192 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathbf{y}}\\in \\mathbb{R}^{C}" + }, + { + "bbox": [ + 46, + 133, + 286, + 192 + ], + "type": "text", + "content": ", then supervise it via the binary cross-entropy loss, which is formulated as:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 59, + 199, + 286, + 232 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 199, + 286, + 232 + ], + "spans": [ + { + "bbox": [ + 59, + 199, + 286, + 232 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {c l s}} = \\sum_ {c = 1} ^ {C} - y _ {c} \\log \\widehat {y} _ {c}, \\quad \\widehat {y} _ {c} = \\sigma \\left(\\frac {1}{k} \\sum \\mathcal {K} \\left(\\mathbf {P} ^ {\\mathrm {c b}}\\right)\\right), \\tag {1}", + "image_path": "0dc69b4dc9690ffb072cb570a6c794024e77ea862355af94359590b6dadd06ac.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 239, + 286, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 239, + 286, + 262 + ], + "spans": [ + { + "bbox": [ + 47, + 239, + 286, + 262 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 239, + 286, + 262 + ], + "type": "inline_equation", + "content": "\\mathcal{K}" + }, + { + "bbox": [ + 47, + 239, + 286, + 262 + ], + "type": "text", + "content": " denotes the top-" + }, + { + "bbox": [ + 47, + 239, + 286, + 262 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 239, + 286, + 262 + ], + "type": "text", + "content": " score set in the temporal domain, and " + }, + { + "bbox": [ + 47, + 239, + 286, + 262 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 47, + 239, + 286, + 262 + ], + "type": "text", + "content": " refers to the softmax function." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 267, + 286, + 315 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 267, + 286, + 315 + ], + "spans": [ + { + "bbox": [ + 46, + 267, + 286, + 315 + ], + "type": "text", + "content": "Remark. Under CB Pre-training and category-only supervision, " + }, + { + "bbox": [ + 46, + 267, + 286, + 315 + ], + "type": "inline_equation", + "content": "\\mathbf{P}^{\\mathrm{cb}}" + }, + { + "bbox": [ + 46, + 267, + 286, + 315 + ], + "type": "text", + "content": " is well known for focusing on sparse discriminative action frames, i.e. high true negatives but serious false negatives, thus can provide rich background information." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 320, + 286, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 320, + 286, + 392 + ], + "spans": [ + { + "bbox": [ + 46, + 320, + 286, + 392 + ], + "type": "text", + "content": "The VLP Branch is designed to mine free action knowledge from VL Pre-training, e.g. CLIP [66]. Since imagetext pre-training lacks sufficient temporal priors, its vanilla localization results have a serious over-complete issue, i.e. high false positives. To tackle this issue, we propose to finetune CLIP using extensive background samples." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 392, + 286, + 427 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 392, + 286, + 427 + ], + "spans": [ + { + "bbox": [ + 46, + 392, + 286, + 427 + ], + "type": "text", + "content": "Instead of linear probing, we use efficient prompt learning [23, 34] for fine-tuning: we freeze the CLIP backbone, only optimize several prompt vectors and temporal layers." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 429, + 286, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 429, + 286, + 536 + ], + "spans": [ + { + "bbox": [ + 46, + 429, + 286, + 536 + ], + "type": "text", + "content": "Concretely, for the visual stream, we first split the video into consecutive frames, and then utilize the CLIP image encoder to extract frame-level features " + }, + { + "bbox": [ + 46, + 429, + 286, + 536 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathrm{vis}} \\in \\mathbb{R}^{T \\times D}" + }, + { + "bbox": [ + 46, + 429, + 286, + 536 + ], + "type": "text", + "content": ". For temporal relationship construction, we strengthen " + }, + { + "bbox": [ + 46, + 429, + 286, + 536 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathrm{vis}}" + }, + { + "bbox": [ + 46, + 429, + 286, + 536 + ], + "type": "text", + "content": " into " + }, + { + "bbox": [ + 46, + 429, + 286, + 536 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathrm{vid}} \\in \\mathbb{R}^{T \\times D}" + }, + { + "bbox": [ + 46, + 429, + 286, + 536 + ], + "type": "text", + "content": " through simple temporal transformer layers " + }, + { + "bbox": [ + 46, + 429, + 286, + 536 + ], + "type": "inline_equation", + "content": "\\Phi_{\\mathrm{temp}}(\\cdot)" + }, + { + "bbox": [ + 46, + 429, + 286, + 536 + ], + "type": "text", + "content": ". While for the textual stream, we first prepend and append several learnable prompt vectors " + }, + { + "bbox": [ + 46, + 429, + 286, + 536 + ], + "type": "inline_equation", + "content": "\\Phi_{\\mathrm{prmp}}(\\cdot)" + }, + { + "bbox": [ + 46, + 429, + 286, + 536 + ], + "type": "text", + "content": " to category names, then feed them into the CLIP text encoder, to obtain textual features " + }, + { + "bbox": [ + 46, + 429, + 286, + 536 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathrm{txt}} \\in \\mathbb{R}^{C \\times D}" + }, + { + "bbox": [ + 46, + 429, + 286, + 536 + ], + "type": "text", + "content": ". Formally," + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 53, + 544, + 286, + 558 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 544, + 286, + 558 + ], + "spans": [ + { + "bbox": [ + 53, + 544, + 286, + 558 + ], + "type": "interline_equation", + "content": "\\mathbf {F} _ {\\mathrm {v i d}} = \\Phi_ {\\text {t e m p}} (\\mathbf {F} _ {\\text {v i s}}), \\quad \\mathbf {F} _ {\\mathrm {t x t}} = \\Phi_ {\\mathrm {t x t}} \\left(\\Phi_ {\\text {p r m p}} \\left(\\mathrm {C} _ {\\text {n a m e}}\\right)\\right), \\tag {2}", + "image_path": "c80ff4360dc62d5c9a9736936d4ad1b3077b780185d2ceb3f0a7828fd6b7b7ad.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 564, + 286, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 564, + 286, + 601 + ], + "spans": [ + { + "bbox": [ + 46, + 564, + 286, + 601 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 564, + 286, + 601 + ], + "type": "inline_equation", + "content": "C_{\\text{name}}" + }, + { + "bbox": [ + 46, + 564, + 286, + 601 + ], + "type": "text", + "content": " refers to action category names, and " + }, + { + "bbox": [ + 46, + 564, + 286, + 601 + ], + "type": "inline_equation", + "content": "\\Phi_{\\text{txt}}(\\cdot)" + }, + { + "bbox": [ + 46, + 564, + 286, + 601 + ], + "type": "text", + "content": " is the CLIP textual encoder. Thereafter, the frame-level localization results " + }, + { + "bbox": [ + 46, + 564, + 286, + 601 + ], + "type": "inline_equation", + "content": "\\mathbf{P}^{\\text{vl}}" + }, + { + "bbox": [ + 46, + 564, + 286, + 601 + ], + "type": "text", + "content": " for this branch can be calculated as:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 101, + 610, + 286, + 625 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 101, + 610, + 286, + 625 + ], + "spans": [ + { + "bbox": [ + 101, + 610, + 286, + 625 + ], + "type": "interline_equation", + "content": "\\mathbf {P} ^ {\\mathrm {v l}} = \\sigma \\left(\\mathbf {F} _ {\\mathrm {v i d}} \\cdot \\mathbf {F} _ {\\mathrm {t x t}} ^ {\\top}\\right) \\in \\mathbb {R} ^ {T \\times C}. \\tag {3}", + "image_path": "88d8f5f512ec6fc2cab8d5460f24aa7bab1c010c8cd26dae001b43443c90e4a6.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "type": "text", + "content": "Remark. For the VLP branch, we only optimize lightweight model parameters for false-positive suppression, naturally bringing two main benefits: (1) the frozen CLIP backbone preserves the action prior knowledge in pre-training, thus maintaining high true-positive results; (2) it matches the demand for less supervision data under weakly-supervised settings, and also saves the memory footprint." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": "Confident Pseudo-labels. Since both " + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "\\mathbf{P}^{\\mathrm{vl}}" + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "\\mathbf{P}^{\\mathrm{cb}}" + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": " contain somewhat noise, to make reliable use of complementary information, we distill confident location pseudo-labels of foreground and background respectively. That is, for the CBP branch, we distill extensive background pseudo-labels from the output " + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "\\mathbf{P}^{\\mathrm{cb}}" + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": "; while for the VLP branch, we distill sufficient foreground pseudo-labels from the output " + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "\\mathbf{P}^{\\mathrm{vl}}" + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 156, + 545, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 156, + 545, + 192 + ], + "spans": [ + { + "bbox": [ + 304, + 156, + 545, + 192 + ], + "type": "text", + "content": "For both branches, we leverage double thresholds " + }, + { + "bbox": [ + 304, + 156, + 545, + 192 + ], + "type": "inline_equation", + "content": "\\delta_h" + }, + { + "bbox": [ + 304, + 156, + 545, + 192 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 156, + 545, + 192 + ], + "type": "inline_equation", + "content": "\\delta_l" + }, + { + "bbox": [ + 304, + 156, + 545, + 192 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 304, + 156, + 545, + 192 + ], + "type": "inline_equation", + "content": "\\delta_h > \\delta_l" + }, + { + "bbox": [ + 304, + 156, + 545, + 192 + ], + "type": "text", + "content": "), to convert localization results " + }, + { + "bbox": [ + 304, + 156, + 545, + 192 + ], + "type": "inline_equation", + "content": "\\mathbf{P}" + }, + { + "bbox": [ + 304, + 156, + 545, + 192 + ], + "type": "text", + "content": " into ternary pseudo-labels " + }, + { + "bbox": [ + 304, + 156, + 545, + 192 + ], + "type": "inline_equation", + "content": "\\mathbf{H} \\in \\mathbb{R}^{T \\times C}" + }, + { + "bbox": [ + 304, + 156, + 545, + 192 + ], + "type": "text", + "content": ", which are formally written as:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 344, + 200, + 545, + 243 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 344, + 200, + 545, + 243 + ], + "spans": [ + { + "bbox": [ + 344, + 200, + 545, + 243 + ], + "type": "interline_equation", + "content": "h _ {t, c} = \\left\\{ \\begin{array}{c} 1 \\text {i f} p _ {t} > \\delta_ {h} \\text {a n d} p _ {c} = y _ {c} \\\\ 0 \\text {i f} p _ {t} < \\delta_ {l} \\text {o r} p _ {c} \\neq y _ {c} \\\\ - 1 \\quad \\text {o t h e r w i s e} \\end{array} \\right. \\tag {4}", + "image_path": "014054bdd61809576f6e276c7aaf48a5de0e9ab5c71548fad0b003192685ea4b.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 251, + 545, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 251, + 545, + 396 + ], + "spans": [ + { + "bbox": [ + 304, + 251, + 545, + 396 + ], + "type": "text", + "content": "where the subscripts " + }, + { + "bbox": [ + 304, + 251, + 545, + 396 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 251, + 545, + 396 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 251, + 545, + 396 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 251, + 545, + 396 + ], + "type": "text", + "content": " refer to the indices of category and frame. More specifically, for either branch, we regard frames with scores more than " + }, + { + "bbox": [ + 304, + 251, + 545, + 396 + ], + "type": "inline_equation", + "content": "\\delta_h" + }, + { + "bbox": [ + 304, + 251, + 545, + 396 + ], + "type": "text", + "content": " and the correct action category as the foreground; while frames with scores less than " + }, + { + "bbox": [ + 304, + 251, + 545, + 396 + ], + "type": "inline_equation", + "content": "\\delta_l" + }, + { + "bbox": [ + 304, + 251, + 545, + 396 + ], + "type": "text", + "content": " or with the wrong action category are treated as the background; the remaining frames are considered uncertain. As a result, the pseudo-labels " + }, + { + "bbox": [ + 304, + 251, + 545, + 396 + ], + "type": "inline_equation", + "content": "\\mathbf{H}^{\\mathrm{cb}}" + }, + { + "bbox": [ + 304, + 251, + 545, + 396 + ], + "type": "text", + "content": " cover vast confident background frames, as well as trivial foreground frames; while the pseudo-labels " + }, + { + "bbox": [ + 304, + 251, + 545, + 396 + ], + "type": "inline_equation", + "content": "\\mathbf{H}^{\\mathrm{vl}}" + }, + { + "bbox": [ + 304, + 251, + 545, + 396 + ], + "type": "text", + "content": " contain dense confident foreground frames, and partial background frames. Note that, for both branches, we generate positive and negative frames to avoid trivial solutions, and facilitate contrastive feature learning." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 407, + 533, + 420 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 407, + 533, + 420 + ], + "spans": [ + { + "bbox": [ + 305, + 407, + 533, + 420 + ], + "type": "text", + "content": "3.3. Collaboration of Dual-Branch Optimization" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 426, + 545, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 545, + 486 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 545, + 486 + ], + "type": "text", + "content": "In this section, we encourage two branches to collaborate with each other, such that forming a strong alliance of their complementary localization results. To reduce serious noises in pseudo-labels, we introduce an alternate training strategy for dual-branch collaborative optimization." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 487, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 487, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 487, + 545, + 689 + ], + "type": "text", + "content": "The design rationale is to distill Background knowledge from the CBP branch for B step, while distill Foreground knowledge from the VLP branch in F step. To be specific, we warm up the CBP branch in advance, using only category supervision, to initialize reliable background frames. During B Step, we freeze the well-trained CBP branch, and then generate confident background pseudo-labels " + }, + { + "bbox": [ + 304, + 487, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\mathbf{H}^{\\mathrm{cb}}" + }, + { + "bbox": [ + 304, + 487, + 545, + 689 + ], + "type": "text", + "content": " to supervise the VLP branch. As a result, these false-positive confusions from vanilla CLIP pre-training are greatly tackled, and the resultant pseudo-labels contain a large number of confident foreground frames and background frames. During F Step, the high-quality pseudo-labels " + }, + { + "bbox": [ + 304, + 487, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\mathbf{H}^{\\mathrm{vl}}" + }, + { + "bbox": [ + 304, + 487, + 545, + 689 + ], + "type": "text", + "content": " are distilled from the frozen VLP branch, to guide the CBP branch for the false-negative suppression. Under such an alternating strategy, these two branches not only complement each other, but also correct each other, thus jointly contributing to more precise and complete action localization." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "content": "During each step, to supervise either branch, we adopt both the knowledge distillation loss " + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{kd}}" + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "content": " and foreground" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14754" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": "background contrastive loss " + }, + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{fb}}" + }, + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": ". The total optimization loss can be written with a balancing ratio " + }, + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": ", as follows:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 85, + 102, + 287, + 117 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 102, + 287, + 117 + ], + "spans": [ + { + "bbox": [ + 85, + 102, + 287, + 117 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {a l l}} = \\mathcal {L} _ {\\mathrm {k d}} \\left(\\mathbf {H} ^ {\\prime}, \\mathbf {P}\\right) + \\lambda \\mathcal {L} _ {\\mathrm {f b}} \\left(\\Psi^ {+}, \\Psi^ {-}\\right). \\tag {5}", + "image_path": "c446d3bd7bcf354194e129cc1d72ed38cba7a190c22c2fbb85fadf093b8a1fb0.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 123, + 287, + 171 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 123, + 287, + 171 + ], + "spans": [ + { + "bbox": [ + 47, + 123, + 287, + 171 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 47, + 123, + 287, + 171 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{kd}}" + }, + { + "bbox": [ + 47, + 123, + 287, + 171 + ], + "type": "text", + "content": " regularizes one branch to output similar detection results with pseudo-labels from the other branch. Given that there exist some noises in pseudo-labels, i.e. uncertain frames, we only make supervision on confident frames." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 78, + 177, + 287, + 209 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 177, + 287, + 209 + ], + "spans": [ + { + "bbox": [ + 78, + 177, + 287, + 209 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {k d}} \\left(\\mathbf {H} ^ {\\prime}, \\mathbf {P}\\right) = \\frac {1}{O} \\sum_ {c = 1} ^ {C} \\sum_ {t = 1} ^ {O} D _ {\\mathrm {K L}} \\left(h _ {t, c} ^ {\\prime} \\mid \\mid p _ {t, c}\\right), \\tag {6}", + "image_path": "57e4fa38ca6ebb341678c57c09570da5d99a73f387e6612f150cc186596e4634.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 216, + 287, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 216, + 287, + 300 + ], + "spans": [ + { + "bbox": [ + 47, + 216, + 287, + 300 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 216, + 287, + 300 + ], + "type": "inline_equation", + "content": "D_{\\mathrm{KL}}(p(x) || q(x))" + }, + { + "bbox": [ + 47, + 216, + 287, + 300 + ], + "type": "text", + "content": " refers to the Kullback-Leibler divergence of distribution " + }, + { + "bbox": [ + 47, + 216, + 287, + 300 + ], + "type": "inline_equation", + "content": "p(x)" + }, + { + "bbox": [ + 47, + 216, + 287, + 300 + ], + "type": "text", + "content": " from distribution " + }, + { + "bbox": [ + 47, + 216, + 287, + 300 + ], + "type": "inline_equation", + "content": "q(x)" + }, + { + "bbox": [ + 47, + 216, + 287, + 300 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 216, + 287, + 300 + ], + "type": "inline_equation", + "content": "O" + }, + { + "bbox": [ + 47, + 216, + 287, + 300 + ], + "type": "text", + "content": " is the total number of confident frames, and " + }, + { + "bbox": [ + 47, + 216, + 287, + 300 + ], + "type": "inline_equation", + "content": "\\mathbf{H}'" + }, + { + "bbox": [ + 47, + 216, + 287, + 300 + ], + "type": "text", + "content": " denotes the pseudo-labels from the other branch. Note that, the pseudolabels contain two types of confident frames: foreground and background, which could help to avoid falling into the trivial solutions under one single type of labels." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 300, + 287, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 300, + 287, + 396 + ], + "spans": [ + { + "bbox": [ + 46, + 300, + 287, + 396 + ], + "type": "text", + "content": "Moreover, in untrimmed long videos, some background contexts could appear visually similar with the action (foreground). We further introduce contrastive learning to pull foreground features and push background features. Specifically, we treat confident foreground frames from the same action category as the positive set " + }, + { + "bbox": [ + 46, + 300, + 287, + 396 + ], + "type": "inline_equation", + "content": "\\Psi^{+}" + }, + { + "bbox": [ + 46, + 300, + 287, + 396 + ], + "type": "text", + "content": ", while all confident background frames as the negative set " + }, + { + "bbox": [ + 46, + 300, + 287, + 396 + ], + "type": "inline_equation", + "content": "\\Psi^{-}" + }, + { + "bbox": [ + 46, + 300, + 287, + 396 + ], + "type": "text", + "content": ", then foreground-background contrastive loss is formulated as:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 401, + 287, + 433 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 401, + 287, + 433 + ], + "spans": [ + { + "bbox": [ + 55, + 401, + 287, + 433 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {f b}} \\left(\\Psi_ {i} ^ {+}, \\Psi_ {i} ^ {-}\\right) = \\sum_ {i} - \\log \\frac {\\sum_ {m \\in \\Psi_ {i} ^ {+}} \\exp \\left(\\mathbf {f} _ {i} \\cdot \\mathbf {f} _ {m} / \\tau\\right)}{\\sum_ {j \\in *} \\exp \\left(\\mathbf {f} _ {i} \\cdot \\mathbf {f} _ {j} / \\tau\\right)}, \\tag {7}", + "image_path": "2356001d404724d1d856c6d7f63b4eeb2ec89cfe11079bd8b9701995b7775648.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 440, + 287, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 440, + 287, + 536 + ], + "spans": [ + { + "bbox": [ + 47, + 440, + 287, + 536 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 440, + 287, + 536 + ], + "type": "inline_equation", + "content": "\\mathbf{f} \\in \\mathbb{R}^D" + }, + { + "bbox": [ + 47, + 440, + 287, + 536 + ], + "type": "text", + "content": " refers to the frame feature, " + }, + { + "bbox": [ + 47, + 440, + 287, + 536 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 47, + 440, + 287, + 536 + ], + "type": "text", + "content": " means the temperature hyper-parameter for scaling, and " + }, + { + "bbox": [ + 47, + 440, + 287, + 536 + ], + "type": "inline_equation", + "content": "*" + }, + { + "bbox": [ + 47, + 440, + 287, + 536 + ], + "type": "text", + "content": " means the union of " + }, + { + "bbox": [ + 47, + 440, + 287, + 536 + ], + "type": "inline_equation", + "content": "\\Psi_i^+" + }, + { + "bbox": [ + 47, + 440, + 287, + 536 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 440, + 287, + 536 + ], + "type": "inline_equation", + "content": "\\Psi_i^-" + }, + { + "bbox": [ + 47, + 440, + 287, + 536 + ], + "type": "text", + "content": ". Take the VLP branch as an example, sufficient background pseudo-labels contain considerable hard negative samples, to help distinguish features of foreground and contexts. In addition, the enhanced features of uncertain frames also become more discriminative, further facilitating more complete temporal action localization." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 539, + 287, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 539, + 287, + 659 + ], + "spans": [ + { + "bbox": [ + 46, + 539, + 287, + 659 + ], + "type": "text", + "content": "Discussion. Comparing to various fusion strategies, our alternating strategy produces more precise and complete results (see Table 4 for details). This strategy plays a similar role as the multi-view co-training, where CBP and VLP branches can be deemed as two distinctive views, thus being quite robust to pseudo-label noises. For B step, we prompt the VLP branch for high-quality pseudo-labels, where some frames with conflicting predictions are still treated as uncertain. In F step, we use feature contrastive loss to make their results more discriminative, i.e. further denoising." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 671, + 114, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 114, + 682 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 114, + 682 + ], + "type": "text", + "content": "3.4. Inference" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "At testing time, we leverage the results from the CBP branch for post-processing, as vision-language pre-training" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "content": "cannot handle Optical Flow, which is essential for WTAL. Given an input video, we first obtain video-level category probabilities and frame-level localization scores. For action classification, we select the classes with probability greater than " + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "inline_equation", + "content": "\\theta_{cls}" + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "content": "; and for localization, we threshold detection scores with " + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "inline_equation", + "content": "\\theta_{loc}" + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "content": ", concatenate consecutive snippets as action proposals, and eliminate redundant proposals with soft nonmaximum suppression (NMS). Each proposal is scored with the detection maximum in the proposal interval." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 191, + 388, + 205 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 191, + 388, + 205 + ], + "spans": [ + { + "bbox": [ + 305, + 191, + 388, + 205 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 212, + 404, + 224 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 212, + 404, + 224 + ], + "spans": [ + { + "bbox": [ + 306, + 212, + 404, + 224 + ], + "type": "text", + "content": "4.1. Implementation" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 229, + 545, + 349 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 229, + 545, + 349 + ], + "spans": [ + { + "bbox": [ + 304, + 229, + 545, + 349 + ], + "type": "text", + "content": "Datasets. THUMOS14 owns 413 untrimmed videos from 20 categories, and each video contains an average of 15 instances. As conventions, we train on 200 validation videos, and evaluate on 213 testing videos. Despite its small scale, this dataset is challenging, since video lengths vary widely and actions occur frequently. ActivityNet1.2 covers 9682 videos belonging to 100 categories. Almost all the videos are single-category, and action regions take up more than half of the video duration. We train on 4619 training videos and evaluate on 2383 validation videos." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 353, + 545, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 353, + 545, + 449 + ], + "spans": [ + { + "bbox": [ + 304, + 353, + 545, + 449 + ], + "type": "text", + "content": "Metrics. To evaluate localization performance, we follow the standard protocol to use mean Average Precision (mAP) at different intersections over union (IoU) thresholds. Note that a proposal is regarded as positive only if both the category prediction is correct and IoU exceeds the set threshold. To clearly evaluate the quality of pseudo-labels, we also report mean Intersection over Union (mIoU) averaged over the foreground categories and the background category." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 451, + 545, + 631 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 451, + 545, + 631 + ], + "spans": [ + { + "bbox": [ + 304, + 451, + 545, + 631 + ], + "type": "text", + "content": "Details. To handle the large variety in video durations, we randomly sample " + }, + { + "bbox": [ + 304, + 451, + 545, + 631 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 451, + 545, + 631 + ], + "type": "text", + "content": " consecutive snippets for each video. " + }, + { + "bbox": [ + 304, + 451, + 545, + 631 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 451, + 545, + 631 + ], + "type": "text", + "content": " is set to 1000 on THUMOS14, and 400 on ActivityNet1.2. We utilize the TV-L1 algorithm to extract optical flow from RGB data. For the CBP branch, we use Transformer architectures (multi-head self-attention, layer norm, and MLPs) as the backbone network. For the VLP branch, we use a 2-layer temporal Transformer, preprocess and append 16 prompt vectors to textual inputs, both are initialized by " + }, + { + "bbox": [ + 304, + 451, + 545, + 631 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(0,0.01)" + }, + { + "bbox": [ + 304, + 451, + 545, + 631 + ], + "type": "text", + "content": ". Both CLIP image encoder and text encoder are adopted from ViT-B/16. The framework is optimized by Adam with the learning rate of " + }, + { + "bbox": [ + 304, + 451, + 545, + 631 + ], + "type": "inline_equation", + "content": "10^{-4}" + }, + { + "bbox": [ + 304, + 451, + 545, + 631 + ], + "type": "text", + "content": ". All hyper-parameters are set by grid search: pseudo-label thresholds " + }, + { + "bbox": [ + 304, + 451, + 545, + 631 + ], + "type": "inline_equation", + "content": "\\delta_h = 0.3" + }, + { + "bbox": [ + 304, + 451, + 545, + 631 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 451, + 545, + 631 + ], + "type": "inline_equation", + "content": "\\delta_l = 0.1" + }, + { + "bbox": [ + 304, + 451, + 545, + 631 + ], + "type": "text", + "content": ", inference thresholds " + }, + { + "bbox": [ + 304, + 451, + 545, + 631 + ], + "type": "inline_equation", + "content": "\\theta_{cls} = 0.85" + }, + { + "bbox": [ + 304, + 451, + 545, + 631 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 451, + 545, + 631 + ], + "type": "inline_equation", + "content": "\\theta_{loc} = 0.45" + }, + { + "bbox": [ + 304, + 451, + 545, + 631 + ], + "type": "text", + "content": ", the balancing ratio " + }, + { + "bbox": [ + 304, + 451, + 545, + 631 + ], + "type": "inline_equation", + "content": "\\lambda = 0.05" + }, + { + "bbox": [ + 304, + 451, + 545, + 631 + ], + "type": "text", + "content": ", the temperature " + }, + { + "bbox": [ + 304, + 451, + 545, + 631 + ], + "type": "inline_equation", + "content": "\\tau = 0.07" + }, + { + "bbox": [ + 304, + 451, + 545, + 631 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 644, + 529, + 657 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 644, + 529, + 657 + ], + "spans": [ + { + "bbox": [ + 306, + 644, + 529, + 657 + ], + "type": "text", + "content": "4.2. Comparison with State-of-the-art Methods" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 664, + 545, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 664, + 545, + 687 + ], + "spans": [ + { + "bbox": [ + 306, + 664, + 545, + 687 + ], + "type": "text", + "content": "Here, we make comprehensive comparisons with current state-of-the-art methods across multiple IoU thresholds." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "Performance. The comparisons on THUMOS14 are provided in Table 1. Here, we separate two levels of supervi" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14755" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 55, + 70, + 537, + 323 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 537, + 323 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 537, + 323 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 537, + 323 + ], + "type": "table", + "html": "
SupervisionMethodFeaturemAP@IoUAVG(0.1-0.5)AVG(0.3-0.7)
0.10.20.30.40.50.60.7
StrongDBS [15]I3D56.754.750.643.134.324.414.747.933.4
BUMR [100]--53.950.745.438.028.5-43.3
GCM [95]72.570.966.560.851.9--64.5-
RCL [81]--70.162.352.942.730.7-51.7
ActionFormer [98]--82.177.871.059.443.9-66.8
WeakHAM-Net [21]I3D65.459.050.341.131.020.711.449.430.9
UM [33]63.056.649.040.930.421.010.448.030.3
TS-PCA [48]67.661.153.443.434.324.713.752.033.9
FTCL [12]69.663.455.245.235.623.712.253.834.4
ACGNet [90]68.162.653.144.634.722.612.052.633.4
DCC [35]69.063.855.945.935.724.313.754.135.1
ASM-Loc [17]71.265.557.146.836.625.213.455.435.8
CO2-Net [18]70.163.654.545.738.326.413.454.435.7
RSKP [20]71.365.355.847.538.225.412.555.635.9
DELU [7]71.566.256.547.740.527.215.356.537.4
CO2-Net†I3D67.460.651.943.135.023.312.151.633.0
CO2-Net‡68.862.152.643.936.124.112.052.733.7
DELU†+CLIP68.660.852.243.435.623.313.352.133.6
DELU‡70.363.955.445.939.026.014.354.936.0
Ours73.568.861.553.842.029.416.860.040.8
", + "image_path": "e12804a0a7a62f6b8e8868349f9f4f96227538f3b34e344b6d21c282dd7903fd.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 48, + 399, + 284, + 594 + ], + "blocks": [ + { + "bbox": [ + 46, + 329, + 547, + 377 + ], + "lines": [ + { + "bbox": [ + 46, + 329, + 547, + 377 + ], + "spans": [ + { + "bbox": [ + 46, + 329, + 547, + 377 + ], + "type": "text", + "content": "Table 1. Comparison with state-of-the-art methods on THUMOS14. For fair comparisons, we reproduce the results of SOTA methods: CO2-Net [18] and DELU [7], by inputting both I3D [5] and CLIP [66] features. † and ‡ refer to averaging or concatenating these two features. AVG(0.1-0.5) and AVG(0.3-0.7) are the average mAP from IoU 0.1 to 0.5 and from IoU 0.3 to 0.7. Our framework significantly surpasses all weakly-supervised competitors using identical features, and is even comparable to early strongly-supervised methods." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 399, + 284, + 594 + ], + "lines": [ + { + "bbox": [ + 48, + 399, + 284, + 594 + ], + "spans": [ + { + "bbox": [ + 48, + 399, + 284, + 594 + ], + "type": "table", + "html": "
MethodFeaturemAP@IoUAVG
0.50.750.95
CleanNet [50]I3D37.120.35.021.6
CMCS [43]36.822.05.622.4
TSCN [96]37.623.75.723.6
BasNet [31]38.524.25.624.3
DGAM [68]41.023.55.324.4
UM [33]41.225.66.025.9
ACGNet [90]41.826.05.926.1
D2-Net [60]42.325.55.826.0
CO2-Net [18]43.326.35.226.4
DELU [7]44.226.75.426.9
CO2-Net†I3D44.826.95.527.1
CO2-Net‡45.227.15.827.6
DELU†+45.427.35.727.5
DELU‡CLIP46.027.85.928.0
Ours48.329.36.129.6
", + "image_path": "741e68137424c80db7842807e9a73768124b44644aed192274858e2416455228.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 601, + 288, + 670 + ], + "lines": [ + { + "bbox": [ + 46, + 601, + 288, + 670 + ], + "spans": [ + { + "bbox": [ + 46, + 601, + 288, + 670 + ], + "type": "text", + "content": "Table 2. Comparison with state-of-the-art methods on ActivityNet1.2. For fair comparisons, we reproduce CO2-Net [18] and DELU [7], by inputting I3D [5] and CLIP [66] features. " + }, + { + "bbox": [ + 46, + 601, + 288, + 670 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 46, + 601, + 288, + 670 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 601, + 288, + 670 + ], + "type": "inline_equation", + "content": "\\ddagger" + }, + { + "bbox": [ + 46, + 601, + 288, + 670 + ], + "type": "text", + "content": " refer to averaging or concatenating these features. AVG is the average mAP at the thresholds 0.5:0.05:0.95. Our method significantly surpasses all competitors, especially at loose IoU thresholds." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "text", + "content": "sion: strong and weak, for better quantification. Generally speaking, our framework achieves new state-of-the-art on" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 395, + 545, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 395, + 545, + 528 + ], + "spans": [ + { + "bbox": [ + 304, + 395, + 545, + 528 + ], + "type": "text", + "content": "all IoU regimes. Comparing with recent methods, the gain of the average mAP (0.3-0.7) even reaches " + }, + { + "bbox": [ + 304, + 395, + 545, + 528 + ], + "type": "inline_equation", + "content": "4 - 5\\%" + }, + { + "bbox": [ + 304, + 395, + 545, + 528 + ], + "type": "text", + "content": ", further narrowing the performance gap between weak and strong supervisions. Moreover, our method achieves considerable gains on strict and loose evaluations. For example, when comparing to DELU [7], the gains are " + }, + { + "bbox": [ + 304, + 395, + 545, + 528 + ], + "type": "inline_equation", + "content": "3.5\\%" + }, + { + "bbox": [ + 304, + 395, + 545, + 528 + ], + "type": "text", + "content": " average mAP (0.1-0.5) and " + }, + { + "bbox": [ + 304, + 395, + 545, + 528 + ], + "type": "inline_equation", + "content": "3.4\\%" + }, + { + "bbox": [ + 304, + 395, + 545, + 528 + ], + "type": "text", + "content": " average mAP (0.3-0.7), indicating that our results are complete and precise. Furthermore, despite being weakly-supervised settings, at several low IoU thresholds, our framework even performs comparably with some earlier strongly-supervised methods [14, 15, 101]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 529, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 529, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 529, + 545, + 628 + ], + "type": "text", + "content": "Table 2 shows the comparison results on ActivityNet1.2. On all IoU thresholds, our designed framework surpasses existing methods by a large margin. In terms of the average mAP, the performance improvement can reach " + }, + { + "bbox": [ + 304, + 529, + 545, + 628 + ], + "type": "inline_equation", + "content": "2.7\\%" + }, + { + "bbox": [ + 304, + 529, + 545, + 628 + ], + "type": "text", + "content": ", taking the state-of-the-art to a new level. However, due to the lack of precise location annotations, the gain decreases as the IoU threshold becomes stricter, e.g. " + }, + { + "bbox": [ + 304, + 529, + 545, + 628 + ], + "type": "inline_equation", + "content": "4.1\\%" + }, + { + "bbox": [ + 304, + 529, + 545, + 628 + ], + "type": "text", + "content": " @IoU 0.5 vs. " + }, + { + "bbox": [ + 304, + 529, + 545, + 628 + ], + "type": "inline_equation", + "content": "0.7\\%" + }, + { + "bbox": [ + 304, + 529, + 545, + 628 + ], + "type": "text", + "content": " @IoU 0.95, when comparing to DELU [7]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "text", + "content": "Source of Gain. Comparing to existing methods, we leverage Vision-Language Pre-training for free knowledge. To make fair comparisons, we also input both I3D and CLIP features into two SOTA methods [7, 18], by one early fusion mode (average or concatenate these features). In general, simply adding CLIP features gives only slight or even negative gains on both datasets, which is due to the bad over" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "14756" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 70, + 284, + 135 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 284, + 135 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 284, + 135 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 284, + 135 + ], + "type": "table", + "html": "
SettingTHUMOSActivityNet
ForeBackForeBack
CB Pre-training56.088.754.788.3
VL Pre-training75.634.172.145.0
Ours72.480.069.571.7
", + "image_path": "7f8284725b92921436f811a10695b3af65f60edc4b48049a933fbfeb8ddab968.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 48, + 206, + 284, + 294 + ], + "blocks": [ + { + "bbox": [ + 47, + 141, + 287, + 185 + ], + "lines": [ + { + "bbox": [ + 47, + 141, + 287, + 185 + ], + "spans": [ + { + "bbox": [ + 47, + 141, + 287, + 185 + ], + "type": "text", + "content": "Table 3. Complementarity of pre-training. CB Pre-training has good background mIoU but inferior foreground mIoU. VL Pretraining has good foreground mIoU but inferior background mIoU. Our method achieves both high foreground and background mIoU." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 206, + 284, + 294 + ], + "lines": [ + { + "bbox": [ + 48, + 206, + 284, + 294 + ], + "spans": [ + { + "bbox": [ + 48, + 206, + 284, + 294 + ], + "type": "table", + "html": "
Fusion StrategymAP@IoUAVG(0.3-0.7)
0.30.50.7
Only F step (AVG)40.016.13.319.1
Only F step (Weight)52.825.56.127.7
Only B step (AVG)56.733.611.334.1
Only B step (Weight)58.538.814.837.8
Alternating61.542.016.840.8
", + "image_path": "cc66964deecab33d7f270b1bfea1a9548c32eda7334a5e2d3bbefc45c6d43956.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 377, + 287, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 377, + 287, + 462 + ], + "spans": [ + { + "bbox": [ + 46, + 377, + 287, + 462 + ], + "type": "text", + "content": "complete issue of CLIP (detailed in Table 3). For THUMOS with complex and frequent actions, over-complete worsens results. While in ActivityNet, most videos only contain one action that takes up half of the video duration, thus benefiting a bit from over-complete. Nevertheless, with identical features, our method significantly outperforms existing competitors, proving the effectiveness of our framework." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 475, + 222, + 487 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 475, + 222, + 487 + ], + "spans": [ + { + "bbox": [ + 47, + 475, + 222, + 487 + ], + "type": "text", + "content": "4.3. Ablation Study and Comparison" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 493, + 287, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 493, + 287, + 517 + ], + "spans": [ + { + "bbox": [ + 47, + 493, + 287, + 517 + ], + "type": "text", + "content": "Here, we evaluate the contributions of each component and framework designs, to further dissect our framework." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 521, + 287, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 521, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 47, + 521, + 287, + 581 + ], + "type": "text", + "content": "Complementarity of pre-trainings. As the detection performance is mainly determined by pseudo-labels, here we show the quality of pseudo-labels, in terms of foreground mIoU and background mIoU. Table 3 provides the comprehensive results for various settings on both benchmarks." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "content": "For common Classification-Based Pre-training, its localization results suffer from the incomplete issue. In detail, the background mIoU is impressive, i.e. high true negatives, while the foreground mIoU is poor, i.e. serious false negatives. The main reason is that features pre-trained on action classification datasets only highlight sparse discriminative frames. While the results of Vision-Language Pre-training are just the opposite: suffering from the over-complete issue. The foreground mIoU is considerable, i.e. high true positives, but the background mIoU is terrible, i.e. serious false positives. The main reason is that VLP using image" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 307, + 71, + 543, + 135 + ], + "blocks": [ + { + "bbox": [ + 47, + 300, + 286, + 355 + ], + "lines": [ + { + "bbox": [ + 47, + 300, + 286, + 355 + ], + "spans": [ + { + "bbox": [ + 47, + 300, + 286, + 355 + ], + "type": "text", + "content": "Table 4. Comparison of optimization strategies. \"Only F step\": extract pseudo-labels from vanilla VLP to train the CBP branch. \"Only B step\": get pseudo-labels from the warm-up CBP branch to train the VLP branch. We combine two branches by averaging and weighting. Our alternating strategy shows clear superiority." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 71, + 543, + 135 + ], + "lines": [ + { + "bbox": [ + 307, + 71, + 543, + 135 + ], + "spans": [ + { + "bbox": [ + 307, + 71, + 543, + 135 + ], + "type": "table", + "html": "
ModelLkdLf bmAP@IoUAVG(0.3-0.7)
0.30.50.7
A1✓57.137.012.636.0
A2✓51.731.29.430.9
A3✓✓61.542.016.840.8
", + "image_path": "613f74baabd367ca9a2986b24563413e0fdaa39cba2be291e6a75d1c305cdc04.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 308, + 202, + 542, + 278 + ], + "blocks": [ + { + "bbox": [ + 305, + 141, + 545, + 185 + ], + "lines": [ + { + "bbox": [ + 305, + 141, + 545, + 185 + ], + "spans": [ + { + "bbox": [ + 305, + 141, + 545, + 185 + ], + "type": "text", + "content": "Table 5. Contribution of optimization losses on THUMOS14. The single knowledge distillation loss " + }, + { + "bbox": [ + 305, + 141, + 545, + 185 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{kd}}" + }, + { + "bbox": [ + 305, + 141, + 545, + 185 + ], + "type": "text", + "content": " has brought gratifying localization results, and the additional foreground-background contrastive loss " + }, + { + "bbox": [ + 305, + 141, + 545, + 185 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{fb}}" + }, + { + "bbox": [ + 305, + 141, + 545, + 185 + ], + "type": "text", + "content": " further boosts the performance to the best." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 202, + 542, + 278 + ], + "lines": [ + { + "bbox": [ + 308, + 202, + 542, + 278 + ], + "spans": [ + { + "bbox": [ + 308, + 202, + 542, + 278 + ], + "type": "table", + "html": "
MethodmAP@IoUAVG (0.3-0.7)
0.30.50.7
UM [33]49.030.410.430.3
UM + Ours53.934.713.634.3
CO2-Net [18]54.538.313.435.7
CO2-Net + Ours56.239.715.937.5
", + "image_path": "7d4e804e79d21efbc8307781ce3a06ad139974140217afa83332ee836e827b0e.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 284, + 545, + 318 + ], + "lines": [ + { + "bbox": [ + 305, + 284, + 545, + 318 + ], + "spans": [ + { + "bbox": [ + 305, + 284, + 545, + 318 + ], + "type": "text", + "content": "Table 6. Framework generalization on THUMOS14. Our proposed framework is generalized, i.e. existing methods can serve as our CBP branch, to achieve further improvements." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 339, + 545, + 363 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 339, + 545, + 363 + ], + "spans": [ + { + "bbox": [ + 305, + 339, + 545, + 363 + ], + "type": "text", + "content": "text pairs lacks temporal priors. The above results strongly prove the complementarity between these two pre-training." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 363, + 545, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 363, + 545, + 495 + ], + "spans": [ + { + "bbox": [ + 304, + 363, + 545, + 495 + ], + "type": "text", + "content": "Moreover, on both datasets, our method achieves high foreground and background mIoU, that is, more precise and complete localization. This mainly benefits from extensive background supervision provided by the CBP branch, and extensive foreground supervision distilled from the VLP branch. Besides, comparing to VL Pre-training, our results achieve immediate gains on the background mIoU, while only slight drops on the foreground mIoU. This reveals that the lightweight trainable parameters, i.e. prompts + Transformer, indeed retain the action prior knowledge in VLP, and also significantly suppress false-positive results." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 498, + 545, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 594 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 594 + ], + "type": "text", + "content": "Comparison of optimization strategies. To evaluate the alternating efficacy, Table 4 compares with another two solutions. (1) 'Only F step': extract foreground pseudo-labels from the vanilla VLP, then provide them to the CBP branch for auxiliary training; (2) 'Only B step': distill background pseudo-labels from the warm-up CBP branch to train the VLP branch. And for each solution, we combine the dual-branch results by averaging and weighting, respectively." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "'Only F step' performs the worst, mainly suffering from heavy noise in vanilla VLP pseudo-labels (over-complete). By fine-tuning vanilla VLP with many background frames, 'Only B step' gets great improvements, but still lacks full fusion of complementarity. Moreover, the weighted operation could suppress noise somewhat, and thus causes better results than the average operation. By comparison, our alternating strategy shows great advantages over competitors, proving the non-trivial nature of fusing complementary information, and robust denoising to pseudo-labels." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14757" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 65, + 67, + 531, + 252 + ], + "blocks": [ + { + "bbox": [ + 65, + 67, + 531, + 252 + ], + "lines": [ + { + "bbox": [ + 65, + 67, + 531, + 252 + ], + "spans": [ + { + "bbox": [ + 65, + 67, + 531, + 252 + ], + "type": "image", + "image_path": "1f8532f9bdd1800484187c111544bc22987b84b98185af21a2f9ffb3039dabf5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 256, + 548, + 301 + ], + "lines": [ + { + "bbox": [ + 46, + 256, + 548, + 301 + ], + "spans": [ + { + "bbox": [ + 46, + 256, + 548, + 301 + ], + "type": "text", + "content": "Figure 3. Qualitative comparisons. The first two rows are videos and ground-truth action intervals. The last six rows are frame-level action probabilities, and localization results of Classification-Based Pre-training (CBP), Vision-Language Pre-training (VLP), and our framework, respectively. CBP suffers from the incomplete issue, while VLP has the over-complete issue. Our framework distills foreground knowledge from VLP and background from CBP, for the strong collaborative alliance, thus bringing more complete and precise results." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 321, + 289, + 490 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 321, + 289, + 490 + ], + "spans": [ + { + "bbox": [ + 46, + 321, + 289, + 490 + ], + "type": "text", + "content": "Contribution of various losses. To train our method, both knowledge distillation loss " + }, + { + "bbox": [ + 46, + 321, + 289, + 490 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{kd}}" + }, + { + "bbox": [ + 46, + 321, + 289, + 490 + ], + "type": "text", + "content": " and foreground-background contrastive loss " + }, + { + "bbox": [ + 46, + 321, + 289, + 490 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{fb}}" + }, + { + "bbox": [ + 46, + 321, + 289, + 490 + ], + "type": "text", + "content": " are leveraged. In Table 5, we analyze the effectiveness of optimization losses on THUMOS14. The single " + }, + { + "bbox": [ + 46, + 321, + 289, + 490 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{kd}}" + }, + { + "bbox": [ + 46, + 321, + 289, + 490 + ], + "type": "text", + "content": " (model A1) already brings gratifying performance. This reveals that the confident pseudo-labels of foreground and background distilled from two branches, are well fused by the alternate optimization. On the other hand, with only " + }, + { + "bbox": [ + 46, + 321, + 289, + 490 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{fb}}" + }, + { + "bbox": [ + 46, + 321, + 289, + 490 + ], + "type": "text", + "content": ", model A2 also performs barely satisfactory results. This is because " + }, + { + "bbox": [ + 46, + 321, + 289, + 490 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{fb}}" + }, + { + "bbox": [ + 46, + 321, + 289, + 490 + ], + "type": "text", + "content": " differentiates foreground features and background features, thus eliminating extensive uncertain frames, and also making the localization task easier. Overall, these two losses jointly contribute to the best performance, indicating that both are essential." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 492, + 288, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 492, + 288, + 577 + ], + "spans": [ + { + "bbox": [ + 46, + 492, + 288, + 577 + ], + "type": "text", + "content": "Framework generalization. Our distillation-collaboration framework is generalized, which means that existing WTAL methods can be employed as the CBP branch. Table 6 takes two typical methods: CO2-Net [18] and UM [33], as examples. Our framework further improves their performance by up to " + }, + { + "bbox": [ + 46, + 492, + 288, + 577 + ], + "type": "inline_equation", + "content": "2 - 4\\%" + }, + { + "bbox": [ + 46, + 492, + 288, + 577 + ], + "type": "text", + "content": " average mAP, showing a good generalization to other methods and other backbone designs." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 587, + 160, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 587, + 160, + 601 + ], + "spans": [ + { + "bbox": [ + 47, + 587, + 160, + 601 + ], + "type": "text", + "content": "4.4. Qualitative Results" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": "To intuitively demonstrate the superiority, Figure 3 visualizes results from various types of videos. Classification-Based Pre-training highlights only some discriminative action frames (the incomplete issue), which is more prominent for videos containing low-frequency actions. On the contrary, Vision-Language Pre-training tends to over-activate action foreground to background (the over-complete issue), which is especially evident in videos with high-frequency actions. We design the distillation-collaboration framework" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 321, + 547, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 321, + 547, + 430 + ], + "spans": [ + { + "bbox": [ + 304, + 321, + 547, + 430 + ], + "type": "text", + "content": "to fuse the complementarity from these two pre-trainings. In B step, extensive confident background is distilled from the well-trained CBP branch, to supervise the VLP branch for false-positive suppression. While in F step, sufficient confident foreground information is distilled from the VLP branch, to guide the CBP branch for false-negative elimination. Hence, our method establishes the strong alliance by collaborative optimization, bringing precise and complete detection results, regardless of dense or sparse actions." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 441, + 379, + 453 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 441, + 379, + 453 + ], + "spans": [ + { + "bbox": [ + 306, + 441, + 379, + 453 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "text", + "content": "This work proposes the novel distillation-collaboration framework to distill free knowledge from Vision-Language Pre-training, for weakly-supervised temporal action localization. Our core insight is that existing VLP often localizes over-complete actions, which is just complementary to the incomplete results of conventional Classification-Based Pre-training. And to form strong alliances, we optimize the framework containing complementary dual branches by an alternating strategy: distill confident background pseudolabels from the CBP branch, and the confident foreground pseudo-labels from the VLP branch, for collaborative training. Extensive experiments show the significance of distilling VLP and our superior performance. Thorough ablations are studied both quantitatively and qualitatively." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 636, + 409, + 649 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 636, + 409, + 649 + ], + "spans": [ + { + "bbox": [ + 306, + 636, + 409, + 649 + ], + "type": "text", + "content": "Acknowledgements" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "type": "text", + "content": "This research is supported by the National Key R&D Program of China (No. 2022ZD0160702), STCSM (No. 22511106101, No. 18DZ2270700, No. 21DZ1100100), 111 plan (No. BP0719010), and State Key Laboratory of UHD Video and Audio Production and Presentation." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "14758" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 53, + 91, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 56, + 91, + 287, + 145 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 91, + 287, + 145 + ], + "spans": [ + { + "bbox": [ + 56, + 91, + 287, + 145 + ], + "type": "text", + "content": "[1] Jean-Baptiste Alayrac, Jeff Donahue, Pauline Luc, Antoine Miech, Iain Barr, Yana Hasson, Karel Lenc, Arthur Mensch, Katie Millican, Malcolm Reynolds, et al. 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Vis., 2021. 2" + } + ] + } + ], + "index": 20 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "14762" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 11 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/DistractFlow_ Improving Optical Flow Estimation via Realistic Distractions and Pseudo-Labeling/71dcd135-f623-44d3-88eb-6335db05d14d_content_list.json b/2023/DistractFlow_ Improving Optical Flow Estimation via Realistic Distractions and Pseudo-Labeling/71dcd135-f623-44d3-88eb-6335db05d14d_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..2d1d046fff34160ca45bc7e7c3b9c9b3f97c2c12 --- /dev/null +++ b/2023/DistractFlow_ Improving Optical Flow Estimation via Realistic Distractions and Pseudo-Labeling/71dcd135-f623-44d3-88eb-6335db05d14d_content_list.json @@ -0,0 +1,1874 @@ +[ + { + "type": "text", + "text": "DistractFlow: Improving Optical Flow Estimation via Realistic Distractions and Pseudo-Labeling", + "text_level": 1, + "bbox": [ + 214, + 108, + 756, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Jisoo Jeong Hong Cai Risheek Garrepalli Fatih Porikli Qualcomm AI Research†", + "bbox": [ + 235, + 181, + 712, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{jisojeon, hongcai, rgarrepα, fporikli}@qti.qualcomm.com", + "bbox": [ + 233, + 223, + 728, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 265, + 313, + 280 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We propose a novel data augmentation approach, DistractFlow, for training optical flow estimation models by introducing realistic distractions to the input frames. Based on a mixing ratio, we combine one of the frames in the pair with a distractor image depicting a similar domain, which allows for inducing visual perturbations congruent with natural objects and scenes. We refer to such pairs as distracted pairs. Our intuition is that using semantically meaningful distractors enables the model to learn related variations and attain robustness against challenging deviations, compared to conventional augmentation schemes focusing only on low-level aspects and modifications. More specifically, in addition to the supervised loss computed between the estimated flow for the original pair and its ground-truth flow, we include a second supervised loss defined between the distracted pair's flow and the original pair's ground-truth flow, weighted with the same mixing ratio. Furthermore, when unlabeled data is available, we extend our augmentation approach to self-supervised settings through pseudo-labeling and cross-consistency regularization. Given an original pair and its distracted version, we enforce the estimated flow on the distracted pair to agree with the flow of the original pair. Our approach allows increasing the number of available training pairs significantly without requiring additional annotations. It is agnostic to the model architecture and can be applied to training any optical flow estimation models. Our extensive evaluations on multiple benchmarks, including Sintel, KITTI, and SlowFlow, show that DistractFlow improves existing models consistently, outperforming the latest state of the art.", + "bbox": [ + 75, + 297, + 473, + 750 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 779, + 209, + 794 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent years have seen significant progress in optical flow estimation thanks to the development of deep learning, e.g., [4,7,8,23]. Among the latest works, many focus on developing novel neural network architectures, such as PwC-Net [29], RAFT [30], and FlowFormer [6]. Other stud", + "bbox": [ + 75, + 801, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/84022b53e58956380e01a8e8baf182bac0eb32dc4a7eba004d634350475ab945.jpg", + "image_caption": [ + "Figure 1. Existing augmentation schemes apply low-level visual modifications, such as color jittering, block-wise random occlusion, and flipping, to augment the training data (top), while DistractFlow introduces high-level semantic perturbations to the frames (bottom). DistractFlow can further leverage unlabeled data to generate a self-supervised regularization. Our training leads to more accurate and robust optical flow estimation models, especially in challenging real-world settings." + ], + "image_footnote": [], + "bbox": [ + 503, + 263, + 883, + 513 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ies investigate how to improve different aspects of supervised training [27], e.g., gradient clipping, learning rate, and training compute load. More related to our paper are those incorporating data augmentation during training (e.g., [30]), including color jittering, random occlusion, cropping, and flipping. While these image manipulations can effectively expand the training data and enhance the robustness of the neural models, they fixate on the low-level aspects of the images.", + "bbox": [ + 496, + 642, + 892, + 777 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Since obtaining ground truth optical flow on real data is very challenging, another line of work investigates how to leverage unlabeled data. To this end, semi-supervised methods [9, 12] that utilize frame pairs with ground-truth flow annotations in conjunction with unlabeled data in training have been proposed. For instance, FlowSupervisor [9] adopts a teacher-student distillation approach to exploit unlabeled data. This method, however, does not consider lo", + "bbox": [ + 496, + 779, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Qualcomm AI Research is an initiative of Qualcomm Technologies, Inc.", + "bbox": [ + 76, + 886, + 467, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "13691", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "calized uncertainty but computes the loss for the entire image between the teacher and student network.", + "bbox": [ + 75, + 90, + 468, + 119 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we present a novel approach, DistractFlow, which performs semantically meaningful data augmentations by introducing images of real objects and natural scenes as distractors or perturbations to training frame pairs. More specifically, given a pair of consecutive frames, we combine the second frame with a random image depicting similar scenarios based on a mixing ratio. In this way, related objects and scenes are overlaid on top of the original second frame; see Figure 1 for an example. As a result, we obtain challenging yet appropriate distractions for the optical flow estimation model that seeks dense correspondences from the first frame to the second frame (and in reverse too). The original first frame and the composite second frame constitute a distracted pair of frames, which we use as an additional data sample in both supervised and self-supervised training settings. Unlike our approach, existing data augmentation schemes for optical flow training apply only low-level variations such as contrast changes, geometric manipulations, random blocks, haze, motion blur, and simple noise and shapes insertions [28, 30]. While such augmentations can still lead to performance improvements, they are disconnected from natural variations, scene context, and semantics. As we shall see in our experimental validation, the use of realistic distractions in training can provide a bigger boost to performance.", + "bbox": [ + 75, + 121, + 472, + 498 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Figure 1 provides a high-level outline of DistractFlow. We apply DistractFlow in supervised learning settings using the ground-truth flow of the original pair. Distracted pairs contribute to the backpropagated loss proportional to the mixing ratios used in their construction. Additionally, when unlabeled frame pairs are available, DistractFlow allows us to impose a self-supervised regularization by further leveraging pseudo-labeling. Given an unlabeled pair of frames, we create a distracted version. Then, we enforce the estimated flow on the distracted pair to match that on the original pair. In other words, the prediction of the original pair is treated as a pseudo ground truth flow for the distracted pair. Since the estimation on the original pair can be erroneous, we further derive and impose a confidence map to employ only highly confident pixel-wise flow estimations as the pseudo ground truth. This prevents the model from reinforcing incorrect predictions, leading to a more stable training process.", + "bbox": [ + 75, + 500, + 472, + 770 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our main contributions are as follows:", + "bbox": [ + 96, + 771, + 434, + 785 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We introduce DistractFlow, a novel data augmentation approach that improves optical flow estimation by utilizing distractions from natural images. Our method provides augmentations with realistic semantic contents compared to existing augmentation schemes.", + "- We present a semi-supervised learning scheme for optical flow estimation that adopts the proposed dis" + ], + "bbox": [ + 94, + 787, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "tracted pairs to leverage unlabeled data. We compute a confidence map to generate uncertainty-aware pseudo labels and to enhance training stability and overall performance.", + "bbox": [ + 529, + 90, + 890, + 150 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- We demonstrate the effectiveness of DistractFlow in supervised [6, 14, 30] and semi-supervised settings, showing that DistractFlow outperforms the very recent FlowSupervisor [9] that require additional in-domain unlabeled data.", + "bbox": [ + 517, + 157, + 893, + 232 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 244, + 640, + 260 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Optical Flow Estimation: Several deep architectures have been proposed for optical flow [4, 8, 23, 29, 30, 38]. Among these, Recurrent All Pairs Field Transforms (RAFT) [30] have shown significant performance improvement over previous methods, inspiring many subsequent works [6, 14, 26, 27, 35]. Following the structure of RAFT architecture, complementary studies [12, 14, 33, 35, 39] proposed advancements on feature extraction, 4D correlation volume, recurrent update blocks, and more recently, transformer extensions [6,39]. In DistractFlow, we introduce a new model-agnostic training method that can help any model.", + "bbox": [ + 496, + 266, + 890, + 431 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Data Augmentation: Data augmentation is a widely used technique to better train deep learning models. Common augmentations include color and contrast jittering, flipping, geometric manipulation, and random noise. While they can improve the robustness of the model, these operations mainly focus on the low-level visual aspects and do not account for variations in the semantic contents.", + "bbox": [ + 496, + 431, + 890, + 537 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recently, several data augmentation schemes, such as adversarial perturbation and regularization methods, have been proposed for classification tasks. Adversarial perturbation [32] is one of the well-known augmentation methods for classification tasks, but recent work [24] shows that it does not work well for optical flow estimation. Interpolation-based Regularization (IR) [34, 36], which mixes a couple of images and trains the model with mixed label, improves the performance in classification tasks and is employed in other fields such as object detection [13, 37] and segmentation [10]. In a regression problem, however, mixed ground truth does not correspond with mixed input. Fixmatch [25] as a data augmentation scheme has demonstrated state-of-the-art performance in classification tasks. It combines pseudo-labeling and consistency regularization by applying two different augmentations (weak, strong) to the same image and generates pseudo-labels with weak augmentation output. For classification tasks, it is possible to create pseudo-labels since the output and ground-truth annotations represent class probabilities. However, there are no such class probabilities for optical flow. Thus, these methods cannot be readily applicable.", + "bbox": [ + 496, + 537, + 892, + 869 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "AutoFlow [28] proposed a new dataset for optical flow, taking a versatile approach to data rendering, where motion,", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "13692", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/0dccf075568d9755a27092a17f3d575aef08e7802466301106fc6914d568bd63.jpg", + "image_caption": [ + "Figure 2. Left: Introducing realistic distractions in the supervised learning setting. Right: Semi-supervised learning leveraging distractions and pseudo-labeling." + ], + "image_footnote": [], + "bbox": [ + 99, + 88, + 478, + 334 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/a113308527ae124dfbdda65784cc8399bf1736bdb6ea3bd12b821b9c192b03ac.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 483, + 88, + 867, + 334 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "shape, and appearance are controlled via learnable hyperparameters. Though its performance gain is notable, AutoFlow employs synthetic augmentations. The work in [27] utilizes AutoFlow and argues that it is important to disentangle architecture and training pipeline. [27] also points out that some of the performance improvements of the recent methods are due to hyperparameters, dataset extensions, and training optimizations. Our work focuses on more capable augmentations for model agnostic training, not architecture novelties.", + "bbox": [ + 75, + 378, + 468, + 529 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Semi-Supervised Learning: Semi-supervised optical flow learning methods [12, 17] aim to make the best use of unlabeled data as there is only a limited amount of optical flow ground truth data for real and natural scenes. And even in those datasets, the optical flow ground truths are computed. RAFT-OCTC [12] proposed transformation consistency for semi-supervised learning, which applies spatial transformations to image pairs and enforces flow equivariance between the original and transformed pairs. FlowSupervisor [9] introduced a teacher network for stable semisupervised fine-tuning. Its student model is trained for all pixels using teacher network output. In DistractFlow, we propose uncertainty-aware pseudo-labeling, which uses two different image pairs instead of different networks. We further employ forward-backward consistency to derive dense confidence scores, which steer the training process to impose loss only within high-consistency image regions to prevent feedback from incorrect flow estimates.", + "bbox": [ + 75, + 534, + 470, + 805 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Since acquiring optical flow ground truth for real videos is problematic (not possible for most cases), unsupervised training methods [15,21,26] seek out training models without ground truth flows. Even though they report promising results comparable to the earlier deep learning approaches, unsupervised training methods still entail limitations.", + "bbox": [ + 75, + 809, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. DistractFlow", + "text_level": 1, + "bbox": [ + 498, + 377, + 633, + 393 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our approach incorporates augmentation and supervision techniques to enhance the training of optical flow estimation models. In Section 3.1, we describe how we construct realistic distractions for optical flow training and how we employ them in supervised settings. Next, in Section 3.2, we extend our approach to semi-supervised learning with additional unlabeled data. We derive a self-supervised regularization objective by utilizing the distracted samples and pseudo-labeling.", + "bbox": [ + 496, + 400, + 890, + 536 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Realistic Distractions as Augmentation", + "text_level": 1, + "bbox": [ + 498, + 547, + 831, + 563 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Consider a pair of video frames during training: $(I_{t}, I_{t+1})$ . The distracted version of them is denoted as $(I_{t}, D_{\\lambda}(I_{t+1}, \\tilde{I}_{d})$ , where $D_{\\lambda}(I_{t+1}, \\tilde{I}_{d})$ is the perturbed second frame obtained by combing with another image $\\tilde{I}_{d}$ based on a mixing ratio of $\\lambda \\in (0, 1)$ . Specifically, $D_{\\lambda}(I_{t+1}, \\tilde{I}_{d})$ is calculated as $\\lambda \\cdot I_{t+1} + (1 - \\lambda) \\cdot \\tilde{I}_{d}$ , where $\\lambda$ is sampled from a Beta $(\\alpha, \\alpha)$ distribution, same as defined in [34, 36].", + "bbox": [ + 496, + 568, + 890, + 686 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Figure 2 shows an example of a distracted pair of video frames. It can be seen that the actual objects and the real scene from one image are overlaid onto the second one. Such perturbations can reflect challenging real-world scenarios, e.g., foreground/background objects that only start to appear in the second frame, drastic motion blur, out-of-focus artifacts, reflections on specular surfaces, partial occlusions, etc. Furthermore, since the distractions are from the same dataset, the visual context of the original pair and distractor image are similar. For instance, the original pair and distractor depict similar classes (road, car, building, etc.). The spatial arrangement of the class and object regions in those images are similar, e.g., roads are within the lower part of the images, and so do the sky, buildings, and", + "bbox": [ + 496, + 689, + 892, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "13693", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/720c22f228b4ca3b05e64d8b9321e62e3bdff2144209713c2ad79e8b6930ccc9.jpg", + "image_caption": [ + "Figure 3. Semi-supervised learning that leverages distractions and confidence-aware pseudo-labeling." + ], + "image_footnote": [], + "bbox": [ + 84, + 87, + 459, + 327 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "vehicles. While one may attempt to render such scenarios synthetically, our DistractFlow provides a convenient and automatic way that can still capture such natural and semantically related variations. Compared to conventional augmentation methods that use noise or simple shapes, our method allows the model to be more robust to perturbations caused by real-world image contents.", + "bbox": [ + 75, + 369, + 468, + 476 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Additionally, we note that applying realistic distractions to the first or both frames is possible. As we shall see in the experiments, all of these options will result in improved accuracy.", + "bbox": [ + 75, + 477, + 468, + 537 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To provide supervision on the distracted pair of frames, we use the ground-truth flow of the original pair. The loss is computed as follows:", + "bbox": [ + 75, + 537, + 468, + 580 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {d i s t}} = \\left\\| V _ {\\left(I _ {t}, I _ {t + 1}\\right)} ^ {f} - f \\left(I _ {t}, D _ {\\lambda} \\left(I _ {t + 1}, \\tilde {I} _ {d}\\right)\\right) \\right\\| _ {1}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 124, + 585, + 468, + 609 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $V_{(I_t, I_{t+1})}^f$ is the ground-truth forward flow for the original pair $(I_t, I_{t+1})$ and $f(\\cdot, \\cdot)$ denotes the predicted flow based on model $f$ .", + "bbox": [ + 75, + 614, + 468, + 662 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the supervised learning setting, where all training samples are labeled, the total training loss is then given as follows:", + "bbox": [ + 75, + 662, + 468, + 705 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\sup } = \\mathcal {L} _ {\\text {b a s e}} + w _ {\\text {d i s t}} \\mathcal {L} _ {\\text {d i s t}}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 703, + 468, + 720 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $L_{base}$ is the conventional supervised loss and $w_{\\mathrm{dist}} > 0$ weights $\\mathcal{L}_{\\mathrm{dist}}$ . For iterative models like RAFT, we compute and apply this loss at each recurrent iteration.", + "bbox": [ + 75, + 720, + 468, + 767 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Semi-Supervised Learning via Realistic Distraction and Pseudo-Labeling", + "text_level": 1, + "bbox": [ + 76, + 773, + 468, + 806 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "During training, when unlabeled frame pairs are available, we can further leverage our distracted pairs of frames to derive additional self-supervised regularization. More specifically, given a distracted pair of frames, $(I_{t},D_{\\lambda}(I_{t + 1},\\tilde{I}_{d}))$ , and the original pair, $(I_{t},I_{t + 1})$ , we enforce the model's prediction on the distracted pair to match", + "bbox": [ + 76, + 810, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "that on the original pair. In other words, the prediction on the original pair, $f(I_{t}, I_{t+1})$ , is treated as the pseudo label. By doing this, the model learns to produce optical flow estimation on the distracted pair that is consistent with that of the original pair, despite the distractions. Such regularization promotes the model's robustness when processing real-world data, as we show in our experiments.", + "bbox": [ + 496, + 90, + 890, + 196 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We note that, however, using all of $f(I_{t}, I_{t+1})$ as the training target for the distracted pair is problematic. This is because the model's prediction can be erroneous and noisy during the training process, even on the original frame pairs. The low-quality pseudo labels can be detrimental to the overall training, even leading to instability.", + "bbox": [ + 496, + 196, + 890, + 287 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To address this issue, we adopt uncertainty-aware pseudo labels by calculating a confidence map based on forward backward consistency, and only using highly confident pixels' predictions as pseudo ground truth, as shown in Figure 3. On a frame pair $(I_t, I_{t+1})$ , let $\\widehat{V}^f(x)$ and $\\widehat{V}^b(x)$ denote the predicted forward and backward flows at the pixel location $x$ . When they satisfy the following constraint [21], we can assume that the prediction is accurate.", + "bbox": [ + 496, + 287, + 890, + 407 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\left| \\widehat {V} ^ {f} (x) + \\widehat {V} ^ {b} \\left(x + \\widehat {V} ^ {f} (x)\\right) \\right| ^ {2} \\\\ < \\gamma_ {1} \\Big (| \\widehat {V} ^ {f} | ^ {2} + | \\widehat {V} ^ {b} (x + \\widehat {V} ^ {f} (x)) | ^ {2} \\Big) + \\gamma_ {2}, \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 542, + 415, + 890, + 465 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\gamma_{1} = 0.01$ and $\\gamma_{2} = 0.5$ from [21].", + "bbox": [ + 500, + 472, + 767, + 487 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As such, we derive the confidence map as follows:", + "bbox": [ + 517, + 488, + 852, + 503 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nM _ {\\text {c o n f}} = \\exp \\left(- \\frac {\\left| \\widehat {V} ^ {f} (x) + \\widehat {V} ^ {b} \\left(x + \\widehat {V} ^ {f} (x)\\right) \\right| ^ {2}}{\\gamma_ {1} \\left(\\left| \\widehat {V} ^ {f} \\right| ^ {2} + \\left| \\widehat {V} ^ {b} \\left(x + \\widehat {V} ^ {f} (x)\\right) \\right| ^ {2}\\right) + \\gamma_ {2}}\\right). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 511, + 890, + 570 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our confidence map provides a measure of reliability of the predicted optical flow. Specifically, in Eq. 4, if the numerator and the denominator are equal, the confidence value is then approximately $0.37(e^{-1})$ . In this paper, we use a very high threshold and it could provide a more accurate optical flow pseudo ground truth.", + "bbox": [ + 496, + 570, + 890, + 660 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "By incorporating the confidence map, our self-supervised regularization is then given as follows:", + "bbox": [ + 496, + 660, + 890, + 691 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {s e l f}} = \\left\\| \\left[ M _ {\\text {c o n f}} \\geq \\tau \\right] \\left(f \\left(I _ {t}, I _ {t + 1}\\right) - f \\left(I _ {t}, D _ {\\lambda} \\left(I _ {t + 1}, \\tilde {I} _ {d}\\right)\\right)\\right) \\right\\| _ {1}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 699, + 893, + 731 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $[\\cdot ]$ is the Iverson bracket and $\\tau$ is the confidence threshold.", + "bbox": [ + 496, + 732, + 890, + 760 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In summary, in the semi-supervised learning setting, where labeled and unlabeled data are both used in training, the total loss is as follows:", + "bbox": [ + 496, + 762, + 890, + 806 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {\\sup } + w _ {\\text {s e l f}} \\mathcal {L} _ {\\text {s e l f}}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 611, + 814, + 890, + 830 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{\\mathrm{sup}}$ is the supervised loss of Eq. 2, $\\mathcal{L}_{\\mathrm{self}}$ is the self-supervised loss of Eq. 5, and $w_{\\mathrm{self}} > 0$ weights $\\mathcal{L}_{\\mathrm{self}}$ .", + "bbox": [ + 496, + 835, + 890, + 867 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "1By $[M_{\\mathrm{conf}} \\geq \\tau]$ , we note that the Iverson bracket is applied pixel-wise to produce a binary confidence map.", + "bbox": [ + 500, + 875, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "13694", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/1fe9fa90221a3eaebf976d55e60358224bc1bd6f8e148c12242e96bb992eeefd.jpg", + "table_caption": [ + "Table 1. Optical flow estimation results on SlowFlow, Sintel (train), and KITTI (train) datasets. We train the models on FlyingChairs (C) and FlyingThings (T) in the supervised setting. In the semi-supervised setting, we finetune the model on FlyingThings (T) as labeled data and Sintel (test) and KITTI (test) (S/K) as unlabeled data. * indicates test results of existing models generated by us." + ], + "table_footnote": [], + "table_body": "
MethodModelLabeled dataUnlabeled dataSlowFlow (100px)Sintel (train)KITTI (train)
1357(Final-epe)(Fl-epe)(Fl-all)
SupervisedSupervised DistractFlow (Our)RAFT [30]C+T3.737.986.729.962.73*4.94*16.9*
3.373.936.218.182.614.5716.4
Supervise DistractFlow (Our)GMA [14]2.494.995.959.152.85*4.88*17.1*
2.533.495.438.242.664.7616.9
Supervised DistractFlow (Our)FlowFormer [6]2.723.735.246.782.39*4.10*14.7*
2.512.774.396.302.314.0013.9
Semi-SupervisedSupervised RAFT-A [28]RAFT [30]C + TT (subsampled)3.737.986.729.962.73*4.94*16.9*
AutoFlow [28]----2.574.23-
RAFT-OCTC [12]----2.674.7216.3
Fixed Teacher [9]C + TS/K----2.584.9115.9
FlowSupervisor [9]S/K----2.463.3511.1
DistractFlow (Our)S/K2.463.605.156.952.353.0111.7
Supervised DistractFlow (Our)GMA [14]S/K2.494.995.959.152.85*4.88*17.1*
2.442.794.386.572.313.2111.0
Supervised DistractFlow (Our)FlowFormer [6]S/K2.723.735.246.782.39*4.29*15.4*
2.482.694.316.292.333.0311.8
", + "bbox": [ + 99, + 132, + 867, + 349 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 361, + 209, + 378 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section (and in the supplementary), we present a comprehensive evaluation of DistractFlow on several benchmark datasets, compare it with baselines and the latest state-of-the-art (SOTA) methods, and conduct extensive ablation studies. We focus our evaluations on realistic or real-world data, including SlowFlow, Sintel (final), and KITTI; we provide results on Sintel (clean) in the Supplementary.", + "bbox": [ + 75, + 383, + 470, + 491 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 76, + 500, + 267, + 517 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation Settings: We consider two settings for running the experiments. In the first setting, we consider a supervised learning setting where the network is trained on fully labeled data. The second setting considers semi-supervised learning, where unlabeled data can be used during training, in addition to labeled training data.", + "bbox": [ + 75, + 521, + 468, + 611 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation Metrics: We use the common evaluation metrics for optical flow estimation, including End-Point Error (EPE) and Fl-all, which is the percentage of optical flow with EPE larger than 3 pixels or over $5\\%$ of the ground truth. The goal is to lower both of these metrics.", + "bbox": [ + 75, + 612, + 468, + 686 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets: Following commonly adopted evaluation protocols in the literature [6, 14, 30, 35], we train our model on FlyingChairs (C) [4] and FlyingThings3D (T) [20] for supervised training when evaluating on SlowFlow [11] (100px flow magnitude) dataset and the training splits of Sintel (S) [2] and KITTI (K) [5, 22]. In particular, on SlowFlow, we use 4 blur durations with a larger duration having larger motion blurs. When we evaluate on Sintel test set, we use FlyingThings3D, Sintel training set, KITTI training set, and HD1K (H) [16] for supervised training. And, we finetune on KITTI training dataset for evaluation on KITTI test set.", + "bbox": [ + 75, + 688, + 468, + 853 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For the additional unlabeled data used during training, we followed the same setting from [9]. We use FlyingThings as labeled dataset and Sintel test set as unlabeled", + "bbox": [ + 75, + 854, + 470, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "dataset for evaluating on Sintel and SlowFlow, and the video frames from KITTI test raw sequences for evaluating on KITTI training dataset. When we evaluate on Sintel and KITTI test sets, we use the labeled dataset from supervised training settings, and use additional KITTI train raw sequences, Sintel training data (only using every other frame), Monkaa (M) [20], and Driving (D) [20] as the unlabeled datasets. Note that we do not use Sintel and KITTI test sets as unlabeled datasets for Sintel and KITTI test evaluation. We further experiment with utilizing unlabeled open-source Blender videos as additional unsupervised training data, such as Sintel and Big Buck Bunny.", + "bbox": [ + 496, + 362, + 890, + 544 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Networks and Training: We use RAFT [30], GMA [14], FlowFormer [6] as our baselines, and utilize their official codes. For objectiveness, we train all the baselines in the same framework and reported the results we obtained. We set $(w_{dist}, w_{self})$ and $\\tau$ to $(\\lambda$ (mixing ratio), 1) and 0.95, respectively. For supervised training, we follow RAFT and GMA learning parameters such as optimizer, number of GRU iterations, training iterations, and so on. For semi-supervised training, we use labeled and unlabeled data with a 1:1 ratio. For FlowFormer, we reduce the total batch size and only finetune it due to GPU memory overflow. All settings and training details are provided in the Supplementary.", + "bbox": [ + 496, + 545, + 892, + 727 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Evaluations on SlowFlow, Sintel (train), and KITTI (train)", + "text_level": 1, + "bbox": [ + 498, + 738, + 890, + 770 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Supervised Setting: Table 1 shows the performance evaluation of the supervised and semi-supervised training results on SlowFlow, Sintel (train), and KITTI (train). In the top section of Table 1, we provide results of existing supervised models and our models trained using DistractFlow", + "bbox": [ + 496, + 773, + 890, + 851 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "2RAFT: https://github.com/princeton-vl/RAFT, GMA: https://github.com/zacjiang/GMA, FlowFormer: https://github.com/drinkingcoder/FlowFormer-Official", + "bbox": [ + 500, + 862, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "13695", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/0bcde9c31ef863a352cc11939084b39980291941d0d09cb73a88046ffb293fd4.jpg", + "table_caption": [ + "Table 2. Optical flow estimation results on Sintel (test) and KITTI (test) datasets. We train the models on FlyingChairs (C), FlyingThings (T), Sintel (S), KITTI (K), and HD1K (H) in the supervised setting. When using the semi-supervised setting/using additional data for training, RAFT-A trains on $\\mathrm{A + S + K + H + T}$ datasets where A stands for AutoFlow, FlowSupervisor trains on $\\mathrm{C + T + S + K + H}$ (labeled) and uses Sintel, KITTI, and Spring as unlabeled datasets. In our case, we use $\\mathrm{C + T + S + K + H}$ as labeled data and Sintel, KITTI, and Sceneflow (Monkaa, Driving) as unlabeled data. * indicates results obtained using warm-start [30]." + ], + "table_footnote": [], + "table_body": "
MethodModelSintel (test)KITTI (test)
(Final-epe)(Fl-all)
Supervised
SupervisedRAFT [30]2.86*5.10
DistractFlow (Our)2.77*4.82
Semi-Supervised / Additional dataset
SupervisedRAFT-A [28]2.86*5.10
3.144.78
RAFT-OCTC [12]RAFT [30]3.094.72
FlowSupervisor [9]2.79*4.85
DistractFlow (Our)2.71*4.71
", + "bbox": [ + 89, + 229, + 452, + 373 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "supervised augmentation. Our supervised models trained on FlyingChairs and FlyingThings3D show significant improvements across the test datasets for all the architectures. For SlowFlow with a 3-frame blur duration, the existing RAFT model shows very large errors (over 100 EPE) on a few samples. DistractFlow, on the other hand, leads to more robust results and a much smaller EPE.", + "bbox": [ + 75, + 385, + 468, + 489 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Semi-Supervised Setting: In this part, we evaluate our proposed approach when additional unlabeled data becomes available. In the bottom section of Table 1, we show results of the previous semi-supervised learning methods and our proposed method. Following FlowSupervisor, we finetune each model on FlyingThings (labeled) and Sintel test (unlabeled), and evaluate on the SlowFlow and Sintel train dataset. For evaluation on KITTI train dataset, we finetune the pre-trained models (from Sintel unlabeled) on FlyingThings (labeled) and raw KITTI test (unlabeled). We can see that DistractFlow (RAFT) shows better performance as compared to RAFT-OCTC, RAFT-A, FixTeacher, and FlowSupervisor. Furthermore, we apply our semi-supervised approach to GMA and FlowFormer, and DistractFlow improves their performance.", + "bbox": [ + 75, + 491, + 470, + 717 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Evaluations on Sintel (test) and KITTI (test)", + "text_level": 1, + "bbox": [ + 76, + 728, + 452, + 744 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Supervised Setting: The top section of Table 2 summarizes the supervised and semi-supervised training results on Sintel (test) and KITTI (test) datasets. From the first part of Table 2, we can see that our proposed DistractFlow permits significant improvements over the baseline RAFT model. It is noteworthy that without using additional unlabeled data, our model trained under the supervised setting already outperforms the semi-supervised FlowSupervisor, which leverages additional data.", + "bbox": [ + 75, + 750, + 468, + 883 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Semi-Supervised Setting: In the second part of Ta-", + "bbox": [ + 96, + 885, + 468, + 901 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/bdafcb452fce168f421bc8dc2742b721caad7176fe80537a15ebbd86b2c9e79f.jpg", + "table_caption": [ + "Table 3. Effects of different types of perturbations applied to the frames, as data augmentation during training." + ], + "table_footnote": [], + "table_body": "
MethodPerturbationSintel (train)KITTI (train)
(Final-epe)(Fl-epe)(Fl-all)
RAFT [30]2.734.9416.9
OurGaussian noise2.684.8617.6
Random shapes2.664.8216.8
Realistic Distractions2.614.5716.4
", + "bbox": [ + 504, + 117, + 890, + 193 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/41e90da4c62cb49bee45a2bae752a59ceb5bf6866264cc147382100934574aac.jpg", + "table_caption": [ + "Table 4. Distracting $I_{t}$ and/or $I_{t+1}$ on Sintel (train) and KITTI (train) datasets. We train RAFT with distractions to $I_{1}$ or $I_{2}$ or both. $\\alpha$ is the coefficient in the Beta distribution for sampling $\\lambda$ . $\\alpha_{1}$ and $\\alpha_{2}$ are for applying distractions to $I_{1}$ and $I_{2}$ , respectively." + ], + "table_footnote": [], + "table_body": "
MethodDistractionα1α2Sintel (train)KITTI (train)
(Final-epe)(Fl-epe)(Fl-all)
RAFT [30]2.734.9416.9
DistractFlowOn It0.12.694.8116.4
12.645.2517.6
102.555.3217.8
On It+10.12.654.6616.3
12.614.5716.4
102.704.8217.2
On It & It+1 (same)0.112.705.3318.3
On It & It+1 (diff)0.112.644.9216.7
", + "bbox": [ + 504, + 260, + 890, + 375 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ble 2, we provide results for semi-supervised methods or methods that train with additional datasets. RAFT-A is trained with an additional AutoFlow dataset but still underperforms the RAFT trained with our DistractFlow approach. RAFT-OCTC applies a semi-supervised method as well as changes the architecture for occlusion prediction. Although RAFT-OCTC uses a slightly more complex architecture, our DistractFlow-trained RAFT still shows better performance. In addition, our method also considerably outperforms FlowSupervisor.", + "bbox": [ + 496, + 391, + 890, + 542 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. Ablation Studies", + "text_level": 1, + "bbox": [ + 500, + 558, + 663, + 571 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We conduct extensive ablation studies on various aspects of our method, by using RAFT as the base model. In the supervised setting, we train on FlyingChairs (C) and FlyingThings3D (T). In the semi-supervised setting, we take the RAFT model pretrained from the supervised setting and then finetune it using FlyingThings3D (labeled) and Sintel (test)/KITTI (test) (unlabeled). The evaluation is done on Sintel (train) and KITTI (train).", + "bbox": [ + 496, + 579, + 890, + 699 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Type of Perturbations: When applying visual perturbations, we compare using realistic distractions in Distract-Flow with using synthetic noise such as Gaussian noise and random shapes. For generating random shapes, we make random background colors and add 5 to 10 shapes (e.g., circles, triangles, and rectangles) of random colors and sizes. As shown in Table 3, while introducing perturbations with Gaussian noise or random shapes can result in performance gains, the improvements are not as significant as compared to the case of using our proposed augmentation strategy.", + "bbox": [ + 496, + 702, + 890, + 853 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Distracting $I_{t}$ or $I_{t + 1}$ or both: We compare applying distractions to $I_{t}$ or $I_{t + 1}$ or both in Table. 4. At the top of Table. 4, we generate distracted $I_{t}$ using the $\\alpha_{1}$ values", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "13696", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a13bab61264d376d0eeb18a09ef6f6cad0126d9aa7e0222c3534e1e4b2805524.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 83, + 103, + 281, + 170 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ebb12d9a7e9db81e5fe857fc6c54282709be305f32eb84d51fd6f6de7c7cc8f0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 282, + 103, + 480, + 170 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3ae220b74642227b081487fc3d6e92ed9f5824e408986d0d2fdd3beed5b7d741.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 482, + 103, + 679, + 170 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d080916d5ab9b8907c0a5fa62847d5b932aa5e51df5bafed9fdb0b2b22f093f9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 681, + 103, + 880, + 170 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/90e44e917b6e990fc73c4cbce6d693f4134df61818f59953861a6fd5a534be7e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 83, + 172, + 279, + 239 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/bcd25c3229c1d0cf9ce09c42680e19393eed88184d722921357850ecda7fe846.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 282, + 172, + 480, + 239 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/722efd892c916d9dedacb3f9bfd6c4393fb83b73de410f657adbe546a576ce36.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 482, + 172, + 679, + 239 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/fa1f860293e819e47154ae27abbcb5d4011cb27d82e17736000c27eeebc199ae.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 681, + 172, + 880, + 239 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6ea365cf806f719081548f24504870cd25a6e74da0f319fb53ef7abee4e10aac.jpg", + "image_caption": [ + "Figure 4. Qualitative results on Sintel (train) using RAFT, FlowFormer, DistractFlow-RAFT, and DistractFlow-FlowFormer (the last two are empowered with our proposed method). All models are trained on FlyingChairs and FlyingThings3D. It can be seen that DistractFlow can generate more accurate predictions, with better spatial consistency and finer details, as highlighted by circles." + ], + "image_footnote": [], + "bbox": [ + 83, + 242, + 279, + 308 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3fce0f9c6325fa65aab0afb0055923c06b73492a3de0971264f16b7866646435.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 282, + 242, + 480, + 308 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/df414442ad6ba68d546d238116d82d7d693a1d2fcf838dd16cbd0f32068a7b65.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 482, + 242, + 679, + 308 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f4e35eee6aa17a8b4a531718657e2c6bd698c1c5152bf2ad498b741f27dcef25.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 681, + 242, + 880, + 308 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/a9c4d970ef45f97915b6d3569e594bac828f652ed153fef39d3b6f2c517ec2c5.jpg", + "table_caption": [ + "Table 5. Effectiveness of ${L}_{dist}$" + ], + "table_footnote": [], + "table_body": "
Method\\( \\mathcal{L}_{base} \\)\\( \\mathcal{L}_{dist} \\)Sintel (train)KITTI (train)
(Final-epe)(Fl-epe)(Fl-all)
RAFT [30]✓2.734.9416.9
DistractFlow✓2.825.4319.0
✓✓2.614.5716.4
", + "bbox": [ + 91, + 380, + 454, + 445 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "for sampling $\\lambda$ and train the model accordingly. $^3$ All three variants show improvements on Sintel. However, when $\\alpha_{1}$ s are 1 or 10, the performance drops on KITTI compared to RAFT. We suspect that the Sintel (final) dataset has a heavy visual effect even in $I_{t}$ , and using strongly distracted $I_{t}$ could help the training. $^4$ On the other hand, since KITTI has relatively cleaner images, strongly distracted $I_{t}$ does not improve the performance.", + "bbox": [ + 75, + 458, + 468, + 578 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In the middle of Table 4, we distract $I_{t+1}$ according to the different $\\alpha_2$ values and train the model. In most of these cases DistractFlow improves upon the baseline RAFT, and it shows the best performance at $\\alpha_2 = 1$ . This result shows that various mixing of the images is helpful.", + "bbox": [ + 75, + 580, + 468, + 655 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "At the bottom of Table 4, we distract $I_{t}$ and $I_{t+1}$ simultaneously. When we apply the same distraction to both frames, two consecutive videos, it degrades the performance. This is because applying the same distraction to both frame introduces new correspondences which are not part of the ground truth. On the other hand, when we apply distractions from two different images to $I_{t}$ and $I_{t+1}$ , the trained model shows better performance compared to baseline RAF. Overall, distracting $I_{t+1}$ shows the best performance and we carry out experiments with this setting.", + "bbox": [ + 75, + 656, + 468, + 806 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of $\\mathcal{L}_{\\mathrm{dist}}$ : Table 5 shows the effectiveness of $\\mathcal{L}_{\\mathrm{dist}}$ . Without the supervised loss on the original pairs,", + "bbox": [ + 76, + 808, + 468, + 839 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 6. Effectiveness of confidence map and $\\lambda$ weight for $\\mathcal{L}_{\\mathrm{self}}$ in semi-supervised setting. $\\tau$ is the confidence threshold in Eq. 5 and in $w_{\\mathrm{self}}$ is the weight for the self-supervised loss. Note that 0.37 corresponds to having equal nominator and denominator in Eq. 3.", + "bbox": [ + 500, + 364, + 890, + 421 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/6720db44a496fc351fa25d15e62d5276e41d2d9086dacb628efc78ca10247d2e.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodτSintel (train)KITTI (train)
(Final-epe)(Fl-epe)(Fl-all)
RAFT [30]2.734.9416.9
DistractFlowdiverged
✓(0.37)2.353.3712.42
✓(0.95)2.353.0111.71
", + "bbox": [ + 527, + 422, + 864, + 500 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/53f6743eb53dcc53e64d013a13ee014faf2ee59636c4992ce2085e839cdbaacf.jpg", + "table_caption": [ + "Table 7. Effects of using different unlabeled datasets in the semi-supervised training. Our DistractFlow enables consistent performance improvements when using any of the unlabeled datasets." + ], + "table_footnote": [], + "table_body": "
MethodUnlabeled data (# of pairs)Sintel (train)
(Final-epe)
RAFT [30]2.73
DistractFlowSintel-test (1.1k)2.35
Monkaa (17k) & Driving (9k)2.42
Big Buck Bunny (14k)2.58
", + "bbox": [ + 522, + 549, + 869, + 628 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "a model trained only with $\\mathcal{L}_{\\mathrm{dist}}$ still provides reasonable estimation performance, but shows worse accuracy as compared to the original model. Combining $\\mathcal{L}_{\\mathrm{base}}$ with $\\mathcal{L}_{\\mathrm{dist}}$ shows a significant improvement.", + "bbox": [ + 496, + 642, + 890, + 702 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of Confidence Map: Table 6 shows our study on the impacts of confidence-based thresholding in the semi-supervised training. When training the model without any confidence maps, erroneous predictions are used for backpropagation and training the network, causing the training to diverge. On the other hand, our confidence map allows the network to only train on highly accurate predictions and enables stability when training the model.", + "bbox": [ + 496, + 703, + 890, + 823 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "When we set $\\tau = 0.37$ (a common choice for forward-backward consistency), we can stably train the model and it shows improvement. Higher $\\tau$ (e.g., 0.95) shows further accuracy improvement on KITTI. This may be due to the larger displacements in KITTI, which can make the model", + "bbox": [ + 496, + 824, + 890, + 898 + ], + "page_idx": 6 + }, + { + "type": "page_footnote", + "text": "3When $\\alpha < 1$ , sampled $\\lambda$ is close to 0 or 1. When $\\alpha > 1$ , sampled $\\lambda$ is close to 0.5. When $\\alpha = 1$ , $\\lambda$ is sampled from a uniform distribution.", + "bbox": [ + 75, + 849, + 467, + 875 + ], + "page_idx": 6 + }, + { + "type": "page_footnote", + "text": "4Since we set $w_{dist} = \\lambda$ , when $\\lambda$ is close to zero, the distracted pair only impacts the training minimally.", + "bbox": [ + 76, + 875, + 467, + 898 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "13697", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a5355a7d1d000a813e6d36df5dcada7a2336ac793e85676dccad840f34a200ee.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 86, + 88, + 272, + 203 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/dd5bb6f7b1b6f7cbc7b6cf791f9fadfdd43f3f5fb5f2ee79a8f8c5a5921d33f2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 274, + 88, + 457, + 203 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c4ba3c407c61e6ef5edca432eb2ccf6e58c84e559b6be88dd0c12524b48336e9.jpg", + "image_caption": [ + "Figure 5. Qualitative results on SlowFlow using the original RAFT and DistractFlow-trained RAFT models in supervised and semi-supervised model settings. We see that DistractFlow training enables the network to produce more accurate results, despite the severe motion blur." + ], + "image_footnote": [], + "bbox": [ + 86, + 205, + 272, + 319 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3b0d90fee5bacea388005847be093f2ef3703be8a50607d7b308f08b936c55a0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 274, + 205, + 457, + 319 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "more prone to in accurate predictions. As such, creating pseudo labels with a higher confidence threshold is beneficial in this case.", + "bbox": [ + 75, + 407, + 468, + 450 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Qualitative Results", + "text_level": 1, + "bbox": [ + 76, + 463, + 259, + 479 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Figure 4 shows qualitative results on the Sintel (train, final) using the original RAFT and FlowFormer, as well as our DistractFlow-trained RAFT and FlowFormer. These models are trained on FlyingChairs and FlyingThings3D. Because Sintel (final) contains visual effects such as fog and blur, the original models generate erroneous estimations. On the other hand, our DistractFlow-trained models show more accurate and robust flow estimation results. Especially, it shows accurate predictions at the object boundary without any edge- or segmentation-aware training [1,3].", + "bbox": [ + 75, + 484, + 468, + 635 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Figure 5 shows qualitative results on SlowFlow using the original RAFT, as well as DistractFlow-trained RAFT models (supervised and semi-supervised). Our supervised training allows the model to generate more accurate and robust flows compared to the baseline RAFT. With our semi-supervised setting, our model shows further improvements.", + "bbox": [ + 75, + 636, + 468, + 726 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Discussion", + "text_level": 1, + "bbox": [ + 76, + 741, + 191, + 757 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Unlabeled Dataset: Table 7 shows the results on Sintel (train) when using different unlabeled data in semi-supervised training. Sintel (test) shows significant improvement compared to supervised training since it is in the same domain as Sintel (train). Although Monkaa & Driving or Bunny dataset have more unlabeled pairs and can still improve upon the original RAFT, they exhibit worse performance than using Sintel (test) pairs. This indicates that for semi-supervised setting, it is important to use unlabeled", + "bbox": [ + 75, + 763, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/01983531e01bcce3e7c2d066d245b4cff02ff51db7471f6564dafb5950859403.jpg", + "image_caption": [ + "Images" + ], + "image_footnote": [], + "bbox": [ + 506, + 103, + 629, + 145 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6789cc4651c1d1a13c603a3424f202ac8fd5c29be47c8a93f7fea43b4ba26f89.jpg", + "image_caption": [ + "RAFT" + ], + "image_footnote": [], + "bbox": [ + 630, + 103, + 754, + 145 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d6956111d7a855409e37c2ec2ee4f1f5986d3d8d3b8452ec35e5a99a7a1b5ce9.jpg", + "image_caption": [ + "DistractFlow" + ], + "image_footnote": [], + "bbox": [ + 756, + 103, + 880, + 145 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1967203d9f1dab1049045f9a76a1de2bed59a1f4e092713671ddd23aef0b308e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 148, + 629, + 191 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b90a459f1a8578dcffa67ee201e97116594645090b437fd70359cc6bd939a87e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 630, + 148, + 754, + 191 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/cc542818c60d97c3863afc9ff1eebb5436a8131dac27fa0bb0c5c41f089011ac.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 756, + 148, + 880, + 191 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f611be49b5acbff220b02c7e92d9ab2b8ab263aced96c59587698a74fac9b2ee.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 195, + 629, + 239 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/25237df28bfb13a6eb2d3b12582988fe265ad90e2508743e21f9304f45ae9adf.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 630, + 195, + 754, + 239 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0b0306458e7643e7246f4eba948ae8a282e55a52c137dceb11cba40fde778faf.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 756, + 195, + 880, + 239 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/afb48d245691bda2a6678a5da57ae5045e5b444aab1c6ca0141b325a5e2ab2ea.jpg", + "image_caption": [ + "Figure 6. Predictions on distracted video frame pairs. In the first column, the first row shows the overlaid original pair and the second to fourth rows show the distracted pairs. The mixing weight for the distractor increases from top to bottom. The RAFT model trained with DistractFlow performs robustly, while the original RAFT model completely fails when the distraction becomes large." + ], + "image_footnote": [], + "bbox": [ + 506, + 241, + 629, + 284 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a3e688ccac00fe140df449962fb87011a1cc67c49eb5a09bb1d79a4b2077f441.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 630, + 241, + 754, + 284 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9dd03f817fa7c9552f7f8661d250ec1dfcbf6d7670fcb7de107a7fdfae33413e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 756, + 241, + 880, + 284 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "data with scenes and distributions resembling the target use case. We leave data distribution robustness (e.g., addressing out-of-distribution samples [18, 19, 31] as part of future work. Nevertheless, our semi-supervised method improves the performance when using any of the unlabeled datasets.", + "bbox": [ + 496, + 391, + 890, + 465 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Robust Prediction: Figure 6 shows the predictions of RAFT and DistractFlow-RAFT (trained with FlyingChairs and FlyingThings3D) on distracted frames pairs, using mixing ratios of 1, 0.75, 0.5, and 0.25. When the original $I_{t+1}$ has a small portion of a distracted image, the original RAFT has degraded performance. It completely fails to find the correspondence for the red car when $\\lambda = 0.25$ . In contrast, the model trained using DistractFlow still robustly finds the correspondence in the distracted image.", + "bbox": [ + 496, + 467, + 890, + 603 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 616, + 617, + 632 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We proposed a novel method, DistractFlow, to augment optical flow training. We introduced realistic distractions to the video frame pairs which provided consistent improvements to optical flow estimation models. When unlabeled data was available, based on the original and distracted pairs, we devised a semi-supervised learning scheme using pseudo labels. We also incorporated forward-backward consistency through confidence maps that provided training stability and enhanced the performance further. Through extensive experiments on several optical flow estimation benchmarks: SlowFlow, Sintel, and KITTI, we showed that our method achieved significant improvements over the previous state of the art without inducing additional complexity during inference. In particular, models trained using our DistractFlow strategy are more robust in practical, challenging scenarios (e.g., consistent error reductions on SlowFlow despite strong motion blurs).", + "bbox": [ + 496, + 638, + 890, + 895 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "13698", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Shubhankar Borse, Ying Wang, Yizhe Zhang, and Fatih Porikli. Inverseform: A loss function for structured boundary-aware segmentation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 5901-5911, 2021. 8", + "[2] Daniel J Butler, Jonas Wulff, Garrett B Stanley, and Michael J Black. A naturalistic open source movie for optical flow evaluation. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 17592-17601, 2022. 2" + ], + "bbox": [ + 501, + 92, + 893, + 318 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "13700", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/DistractFlow_ Improving Optical Flow Estimation via Realistic Distractions and Pseudo-Labeling/71dcd135-f623-44d3-88eb-6335db05d14d_model.json b/2023/DistractFlow_ Improving Optical Flow Estimation via Realistic Distractions and Pseudo-Labeling/71dcd135-f623-44d3-88eb-6335db05d14d_model.json new file mode 100644 index 0000000000000000000000000000000000000000..52aa48434b2b1373e435d1693605735751e0995b --- /dev/null +++ b/2023/DistractFlow_ Improving Optical Flow Estimation via Realistic Distractions and Pseudo-Labeling/71dcd135-f623-44d3-88eb-6335db05d14d_model.json @@ -0,0 +1,2343 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.215, + 0.109, + 0.757, + 0.154 + ], + "angle": 0, + "content": "DistractFlow: Improving Optical Flow Estimation via Realistic Distractions and Pseudo-Labeling" + }, + { + "type": "text", + "bbox": [ + 0.236, + 0.182, + 0.713, + 0.221 + ], + "angle": 0, + "content": "Jisoo Jeong Hong Cai Risheek Garrepalli Fatih Porikli Qualcomm AI Research†" + }, + { + "type": "text", + "bbox": [ + 0.235, + 0.224, + 0.73, + 0.24 + ], + "angle": 0, + "content": "{jisojeon, hongcai, rgarrepα, fporikli}@qti.qualcomm.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.266, + 0.314, + 0.281 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.298, + 0.474, + 0.751 + ], + "angle": 0, + "content": "We propose a novel data augmentation approach, DistractFlow, for training optical flow estimation models by introducing realistic distractions to the input frames. Based on a mixing ratio, we combine one of the frames in the pair with a distractor image depicting a similar domain, which allows for inducing visual perturbations congruent with natural objects and scenes. We refer to such pairs as distracted pairs. Our intuition is that using semantically meaningful distractors enables the model to learn related variations and attain robustness against challenging deviations, compared to conventional augmentation schemes focusing only on low-level aspects and modifications. More specifically, in addition to the supervised loss computed between the estimated flow for the original pair and its ground-truth flow, we include a second supervised loss defined between the distracted pair's flow and the original pair's ground-truth flow, weighted with the same mixing ratio. Furthermore, when unlabeled data is available, we extend our augmentation approach to self-supervised settings through pseudo-labeling and cross-consistency regularization. Given an original pair and its distracted version, we enforce the estimated flow on the distracted pair to agree with the flow of the original pair. Our approach allows increasing the number of available training pairs significantly without requiring additional annotations. It is agnostic to the model architecture and can be applied to training any optical flow estimation models. Our extensive evaluations on multiple benchmarks, including Sintel, KITTI, and SlowFlow, show that DistractFlow improves existing models consistently, outperforming the latest state of the art." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.78, + 0.21, + 0.795 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.802, + 0.47, + 0.879 + ], + "angle": 0, + "content": "Recent years have seen significant progress in optical flow estimation thanks to the development of deep learning, e.g., [4,7,8,23]. Among the latest works, many focus on developing novel neural network architectures, such as PwC-Net [29], RAFT [30], and FlowFormer [6]. Other stud" + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.265, + 0.885, + 0.514 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.518, + 0.892, + 0.63 + ], + "angle": 0, + "content": "Figure 1. Existing augmentation schemes apply low-level visual modifications, such as color jittering, block-wise random occlusion, and flipping, to augment the training data (top), while DistractFlow introduces high-level semantic perturbations to the frames (bottom). DistractFlow can further leverage unlabeled data to generate a self-supervised regularization. Our training leads to more accurate and robust optical flow estimation models, especially in challenging real-world settings." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.643, + 0.893, + 0.779 + ], + "angle": 0, + "content": "ies investigate how to improve different aspects of supervised training [27], e.g., gradient clipping, learning rate, and training compute load. More related to our paper are those incorporating data augmentation during training (e.g., [30]), including color jittering, random occlusion, cropping, and flipping. While these image manipulations can effectively expand the training data and enhance the robustness of the neural models, they fixate on the low-level aspects of the images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Since obtaining ground truth optical flow on real data is very challenging, another line of work investigates how to leverage unlabeled data. To this end, semi-supervised methods [9, 12] that utilize frame pairs with ground-truth flow annotations in conjunction with unlabeled data in training have been proposed. For instance, FlowSupervisor [9] adopts a teacher-student distillation approach to exploit unlabeled data. This method, however, does not consider lo" + }, + { + "type": "page_footnote", + "bbox": [ + 0.078, + 0.887, + 0.468, + 0.901 + ], + "angle": 0, + "content": "† Qualcomm AI Research is an initiative of Qualcomm Technologies, Inc." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "13691" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.121 + ], + "angle": 0, + "content": "calized uncertainty but computes the loss for the entire image between the teacher and student network." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.122, + 0.473, + 0.499 + ], + "angle": 0, + "content": "In this paper, we present a novel approach, DistractFlow, which performs semantically meaningful data augmentations by introducing images of real objects and natural scenes as distractors or perturbations to training frame pairs. More specifically, given a pair of consecutive frames, we combine the second frame with a random image depicting similar scenarios based on a mixing ratio. In this way, related objects and scenes are overlaid on top of the original second frame; see Figure 1 for an example. As a result, we obtain challenging yet appropriate distractions for the optical flow estimation model that seeks dense correspondences from the first frame to the second frame (and in reverse too). The original first frame and the composite second frame constitute a distracted pair of frames, which we use as an additional data sample in both supervised and self-supervised training settings. Unlike our approach, existing data augmentation schemes for optical flow training apply only low-level variations such as contrast changes, geometric manipulations, random blocks, haze, motion blur, and simple noise and shapes insertions [28, 30]. While such augmentations can still lead to performance improvements, they are disconnected from natural variations, scene context, and semantics. As we shall see in our experimental validation, the use of realistic distractions in training can provide a bigger boost to performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.5, + 0.473, + 0.771 + ], + "angle": 0, + "content": "Figure 1 provides a high-level outline of DistractFlow. We apply DistractFlow in supervised learning settings using the ground-truth flow of the original pair. Distracted pairs contribute to the backpropagated loss proportional to the mixing ratios used in their construction. Additionally, when unlabeled frame pairs are available, DistractFlow allows us to impose a self-supervised regularization by further leveraging pseudo-labeling. Given an unlabeled pair of frames, we create a distracted version. Then, we enforce the estimated flow on the distracted pair to match that on the original pair. In other words, the prediction of the original pair is treated as a pseudo ground truth flow for the distracted pair. Since the estimation on the original pair can be erroneous, we further derive and impose a confidence map to employ only highly confident pixel-wise flow estimations as the pseudo ground truth. This prevents the model from reinforcing incorrect predictions, leading to a more stable training process." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.772, + 0.435, + 0.786 + ], + "angle": 0, + "content": "In summary, our main contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.789, + 0.47, + 0.865 + ], + "angle": 0, + "content": "- We introduce DistractFlow, a novel data augmentation approach that improves optical flow estimation by utilizing distractions from natural images. Our method provides augmentations with realistic semantic contents compared to existing augmentation schemes." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.871, + 0.471, + 0.902 + ], + "angle": 0, + "content": "- We present a semi-supervised learning scheme for optical flow estimation that adopts the proposed dis" + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.789, + 0.471, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.531, + 0.092, + 0.892, + 0.151 + ], + "angle": 0, + "content": "tracted pairs to leverage unlabeled data. We compute a confidence map to generate uncertainty-aware pseudo labels and to enhance training stability and overall performance." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.158, + 0.894, + 0.233 + ], + "angle": 0, + "content": "- We demonstrate the effectiveness of DistractFlow in supervised [6, 14, 30] and semi-supervised settings, showing that DistractFlow outperforms the very recent FlowSupervisor [9] that require additional in-domain unlabeled data." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.245, + 0.642, + 0.261 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.267, + 0.892, + 0.433 + ], + "angle": 0, + "content": "Optical Flow Estimation: Several deep architectures have been proposed for optical flow [4, 8, 23, 29, 30, 38]. Among these, Recurrent All Pairs Field Transforms (RAFT) [30] have shown significant performance improvement over previous methods, inspiring many subsequent works [6, 14, 26, 27, 35]. Following the structure of RAFT architecture, complementary studies [12, 14, 33, 35, 39] proposed advancements on feature extraction, 4D correlation volume, recurrent update blocks, and more recently, transformer extensions [6,39]. In DistractFlow, we introduce a new model-agnostic training method that can help any model." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.433, + 0.892, + 0.538 + ], + "angle": 0, + "content": "Data Augmentation: Data augmentation is a widely used technique to better train deep learning models. Common augmentations include color and contrast jittering, flipping, geometric manipulation, and random noise. While they can improve the robustness of the model, these operations mainly focus on the low-level visual aspects and do not account for variations in the semantic contents." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.539, + 0.893, + 0.871 + ], + "angle": 0, + "content": "Recently, several data augmentation schemes, such as adversarial perturbation and regularization methods, have been proposed for classification tasks. Adversarial perturbation [32] is one of the well-known augmentation methods for classification tasks, but recent work [24] shows that it does not work well for optical flow estimation. Interpolation-based Regularization (IR) [34, 36], which mixes a couple of images and trains the model with mixed label, improves the performance in classification tasks and is employed in other fields such as object detection [13, 37] and segmentation [10]. In a regression problem, however, mixed ground truth does not correspond with mixed input. Fixmatch [25] as a data augmentation scheme has demonstrated state-of-the-art performance in classification tasks. It combines pseudo-labeling and consistency regularization by applying two different augmentations (weak, strong) to the same image and generates pseudo-labels with weak augmentation output. For classification tasks, it is possible to create pseudo-labels since the output and ground-truth annotations represent class probabilities. However, there are no such class probabilities for optical flow. Thus, these methods cannot be readily applicable." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "AutoFlow [28] proposed a new dataset for optical flow, taking a versatile approach to data rendering, where motion," + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "13692" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.101, + 0.089, + 0.48, + 0.335 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.484, + 0.089, + 0.868, + 0.335 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.337, + 0.894, + 0.366 + ], + "angle": 0, + "content": "Figure 2. Left: Introducing realistic distractions in the supervised learning setting. Right: Semi-supervised learning leveraging distractions and pseudo-labeling." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.38, + 0.47, + 0.53 + ], + "angle": 0, + "content": "shape, and appearance are controlled via learnable hyperparameters. Though its performance gain is notable, AutoFlow employs synthetic augmentations. The work in [27] utilizes AutoFlow and argues that it is important to disentangle architecture and training pipeline. [27] also points out that some of the performance improvements of the recent methods are due to hyperparameters, dataset extensions, and training optimizations. Our work focuses on more capable augmentations for model agnostic training, not architecture novelties." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.535, + 0.471, + 0.806 + ], + "angle": 0, + "content": "Semi-Supervised Learning: Semi-supervised optical flow learning methods [12, 17] aim to make the best use of unlabeled data as there is only a limited amount of optical flow ground truth data for real and natural scenes. And even in those datasets, the optical flow ground truths are computed. RAFT-OCTC [12] proposed transformation consistency for semi-supervised learning, which applies spatial transformations to image pairs and enforces flow equivariance between the original and transformed pairs. FlowSupervisor [9] introduced a teacher network for stable semisupervised fine-tuning. Its student model is trained for all pixels using teacher network output. In DistractFlow, we propose uncertainty-aware pseudo-labeling, which uses two different image pairs instead of different networks. We further employ forward-backward consistency to derive dense confidence scores, which steer the training process to impose loss only within high-consistency image regions to prevent feedback from incorrect flow estimates." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Since acquiring optical flow ground truth for real videos is problematic (not possible for most cases), unsupervised training methods [15,21,26] seek out training models without ground truth flows. Even though they report promising results comparable to the earlier deep learning approaches, unsupervised training methods still entail limitations." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.378, + 0.634, + 0.394 + ], + "angle": 0, + "content": "3. DistractFlow" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.401, + 0.892, + 0.537 + ], + "angle": 0, + "content": "Our approach incorporates augmentation and supervision techniques to enhance the training of optical flow estimation models. In Section 3.1, we describe how we construct realistic distractions for optical flow training and how we employ them in supervised settings. Next, in Section 3.2, we extend our approach to semi-supervised learning with additional unlabeled data. We derive a self-supervised regularization objective by utilizing the distracted samples and pseudo-labeling." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.548, + 0.833, + 0.564 + ], + "angle": 0, + "content": "3.1. Realistic Distractions as Augmentation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.569, + 0.892, + 0.688 + ], + "angle": 0, + "content": "Consider a pair of video frames during training: \\((I_{t}, I_{t+1})\\). The distracted version of them is denoted as \\((I_{t}, D_{\\lambda}(I_{t+1}, \\tilde{I}_{d})\\), where \\(D_{\\lambda}(I_{t+1}, \\tilde{I}_{d})\\) is the perturbed second frame obtained by combing with another image \\(\\tilde{I}_{d}\\) based on a mixing ratio of \\(\\lambda \\in (0, 1)\\). Specifically, \\(D_{\\lambda}(I_{t+1}, \\tilde{I}_{d})\\) is calculated as \\(\\lambda \\cdot I_{t+1} + (1 - \\lambda) \\cdot \\tilde{I}_{d}\\), where \\(\\lambda\\) is sampled from a Beta \\((\\alpha, \\alpha)\\) distribution, same as defined in [34, 36]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.69, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Figure 2 shows an example of a distracted pair of video frames. It can be seen that the actual objects and the real scene from one image are overlaid onto the second one. Such perturbations can reflect challenging real-world scenarios, e.g., foreground/background objects that only start to appear in the second frame, drastic motion blur, out-of-focus artifacts, reflections on specular surfaces, partial occlusions, etc. Furthermore, since the distractions are from the same dataset, the visual context of the original pair and distractor image are similar. For instance, the original pair and distractor depict similar classes (road, car, building, etc.). The spatial arrangement of the class and object regions in those images are similar, e.g., roads are within the lower part of the images, and so do the sky, buildings, and" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13693" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.088, + 0.46, + 0.328 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.331, + 0.47, + 0.36 + ], + "angle": 0, + "content": "Figure 3. Semi-supervised learning that leverages distractions and confidence-aware pseudo-labeling." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.371, + 0.47, + 0.477 + ], + "angle": 0, + "content": "vehicles. While one may attempt to render such scenarios synthetically, our DistractFlow provides a convenient and automatic way that can still capture such natural and semantically related variations. Compared to conventional augmentation methods that use noise or simple shapes, our method allows the model to be more robust to perturbations caused by real-world image contents." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.478, + 0.47, + 0.538 + ], + "angle": 0, + "content": "Additionally, we note that applying realistic distractions to the first or both frames is possible. As we shall see in the experiments, all of these options will result in improved accuracy." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.538, + 0.47, + 0.582 + ], + "angle": 0, + "content": "To provide supervision on the distracted pair of frames, we use the ground-truth flow of the original pair. The loss is computed as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.125, + 0.587, + 0.47, + 0.61 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {d i s t}} = \\left\\| V _ {\\left(I _ {t}, I _ {t + 1}\\right)} ^ {f} - f \\left(I _ {t}, D _ {\\lambda} \\left(I _ {t + 1}, \\tilde {I} _ {d}\\right)\\right) \\right\\| _ {1}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.616, + 0.47, + 0.664 + ], + "angle": 0, + "content": "where \\( V_{(I_t, I_{t+1})}^f \\) is the ground-truth forward flow for the original pair \\( (I_t, I_{t+1}) \\) and \\( f(\\cdot, \\cdot) \\) denotes the predicted flow based on model \\( f \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.664, + 0.47, + 0.707 + ], + "angle": 0, + "content": "In the supervised learning setting, where all training samples are labeled, the total training loss is then given as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.19, + 0.704, + 0.469, + 0.721 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\sup } = \\mathcal {L} _ {\\text {b a s e}} + w _ {\\text {d i s t}} \\mathcal {L} _ {\\text {d i s t}}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.722, + 0.469, + 0.768 + ], + "angle": 0, + "content": "where \\( L_{base} \\) is the conventional supervised loss and \\( w_{\\mathrm{dist}} > 0 \\) weights \\( \\mathcal{L}_{\\mathrm{dist}} \\). For iterative models like RAFT, we compute and apply this loss at each recurrent iteration." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.775, + 0.469, + 0.807 + ], + "angle": 0, + "content": "3.2. Semi-Supervised Learning via Realistic Distraction and Pseudo-Labeling" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.811, + 0.47, + 0.902 + ], + "angle": 0, + "content": "During training, when unlabeled frame pairs are available, we can further leverage our distracted pairs of frames to derive additional self-supervised regularization. More specifically, given a distracted pair of frames, \\((I_{t},D_{\\lambda}(I_{t + 1},\\tilde{I}_{d}))\\), and the original pair, \\((I_{t},I_{t + 1})\\), we enforce the model's prediction on the distracted pair to match" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.197 + ], + "angle": 0, + "content": "that on the original pair. In other words, the prediction on the original pair, \\( f(I_{t}, I_{t+1}) \\), is treated as the pseudo label. By doing this, the model learns to produce optical flow estimation on the distracted pair that is consistent with that of the original pair, despite the distractions. Such regularization promotes the model's robustness when processing real-world data, as we show in our experiments." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.198, + 0.892, + 0.288 + ], + "angle": 0, + "content": "We note that, however, using all of \\( f(I_{t}, I_{t+1}) \\) as the training target for the distracted pair is problematic. This is because the model's prediction can be erroneous and noisy during the training process, even on the original frame pairs. The low-quality pseudo labels can be detrimental to the overall training, even leading to instability." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.288, + 0.892, + 0.409 + ], + "angle": 0, + "content": "To address this issue, we adopt uncertainty-aware pseudo labels by calculating a confidence map based on forward backward consistency, and only using highly confident pixels' predictions as pseudo ground truth, as shown in Figure 3. On a frame pair \\((I_t, I_{t+1})\\), let \\(\\widehat{V}^f(x)\\) and \\(\\widehat{V}^b(x)\\) denote the predicted forward and backward flows at the pixel location \\(x\\). When they satisfy the following constraint [21], we can assume that the prediction is accurate." + }, + { + "type": "equation", + "bbox": [ + 0.544, + 0.416, + 0.892, + 0.466 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\left| \\widehat {V} ^ {f} (x) + \\widehat {V} ^ {b} \\left(x + \\widehat {V} ^ {f} (x)\\right) \\right| ^ {2} \\\\ < \\gamma_ {1} \\Big (| \\widehat {V} ^ {f} | ^ {2} + | \\widehat {V} ^ {b} (x + \\widehat {V} ^ {f} (x)) | ^ {2} \\Big) + \\gamma_ {2}, \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.473, + 0.768, + 0.488 + ], + "angle": 0, + "content": "where \\(\\gamma_{1} = 0.01\\) and \\(\\gamma_{2} = 0.5\\) from [21]." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.489, + 0.853, + 0.504 + ], + "angle": 0, + "content": "As such, we derive the confidence map as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.512, + 0.891, + 0.571 + ], + "angle": 0, + "content": "\\[\nM _ {\\text {c o n f}} = \\exp \\left(- \\frac {\\left| \\widehat {V} ^ {f} (x) + \\widehat {V} ^ {b} \\left(x + \\widehat {V} ^ {f} (x)\\right) \\right| ^ {2}}{\\gamma_ {1} \\left(\\left| \\widehat {V} ^ {f} \\right| ^ {2} + \\left| \\widehat {V} ^ {b} \\left(x + \\widehat {V} ^ {f} (x)\\right) \\right| ^ {2}\\right) + \\gamma_ {2}}\\right). \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.571, + 0.892, + 0.661 + ], + "angle": 0, + "content": "Our confidence map provides a measure of reliability of the predicted optical flow. Specifically, in Eq. 4, if the numerator and the denominator are equal, the confidence value is then approximately \\(0.37(e^{-1})\\). In this paper, we use a very high threshold and it could provide a more accurate optical flow pseudo ground truth." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.661, + 0.892, + 0.692 + ], + "angle": 0, + "content": "By incorporating the confidence map, our self-supervised regularization is then given as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.7, + 0.894, + 0.732 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {s e l f}} = \\left\\| \\left[ M _ {\\text {c o n f}} \\geq \\tau \\right] \\left(f \\left(I _ {t}, I _ {t + 1}\\right) - f \\left(I _ {t}, D _ {\\lambda} \\left(I _ {t + 1}, \\tilde {I} _ {d}\\right)\\right)\\right) \\right\\| _ {1}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.733, + 0.892, + 0.761 + ], + "angle": 0, + "content": "where \\([\\cdot ]\\) is the Iverson bracket and \\(\\tau\\) is the confidence threshold." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.763, + 0.892, + 0.807 + ], + "angle": 0, + "content": "In summary, in the semi-supervised learning setting, where labeled and unlabeled data are both used in training, the total loss is as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.612, + 0.815, + 0.892, + 0.832 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {\\sup } + w _ {\\text {s e l f}} \\mathcal {L} _ {\\text {s e l f}}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.837, + 0.892, + 0.868 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{\\mathrm{sup}}\\) is the supervised loss of Eq. 2, \\(\\mathcal{L}_{\\mathrm{self}}\\) is the self-supervised loss of Eq. 5, and \\(w_{\\mathrm{self}} > 0\\) weights \\(\\mathcal{L}_{\\mathrm{self}}\\)." + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.875, + 0.892, + 0.901 + ], + "angle": 0, + "content": "1By \\([M_{\\mathrm{conf}} \\geq \\tau]\\), we note that the Iverson bracket is applied pixel-wise to produce a binary confidence map." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13694" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.131 + ], + "angle": 0, + "content": "Table 1. Optical flow estimation results on SlowFlow, Sintel (train), and KITTI (train) datasets. We train the models on FlyingChairs (C) and FlyingThings (T) in the supervised setting. In the semi-supervised setting, we finetune the model on FlyingThings (T) as labeled data and Sintel (test) and KITTI (test) (S/K) as unlabeled data. * indicates test results of existing models generated by us." + }, + { + "type": "table", + "bbox": [ + 0.1, + 0.133, + 0.868, + 0.351 + ], + "angle": 0, + "content": "
MethodModelLabeled dataUnlabeled dataSlowFlow (100px)Sintel (train)KITTI (train)
1357(Final-epe)(Fl-epe)(Fl-all)
SupervisedSupervised DistractFlow (Our)RAFT [30]C+T3.737.986.729.962.73*4.94*16.9*
3.373.936.218.182.614.5716.4
Supervise DistractFlow (Our)GMA [14]2.494.995.959.152.85*4.88*17.1*
2.533.495.438.242.664.7616.9
Supervised DistractFlow (Our)FlowFormer [6]2.723.735.246.782.39*4.10*14.7*
2.512.774.396.302.314.0013.9
Semi-SupervisedSupervised RAFT-A [28]RAFT [30]C + TT (subsampled)3.737.986.729.962.73*4.94*16.9*
AutoFlow [28]----2.574.23-
RAFT-OCTC [12]----2.674.7216.3
Fixed Teacher [9]C + TS/K----2.584.9115.9
FlowSupervisor [9]S/K----2.463.3511.1
DistractFlow (Our)S/K2.463.605.156.952.353.0111.7
Supervised DistractFlow (Our)GMA [14]S/K2.494.995.959.152.85*4.88*17.1*
2.442.794.386.572.313.2111.0
Supervised DistractFlow (Our)FlowFormer [6]S/K2.723.735.246.782.39*4.29*15.4*
2.482.694.316.292.333.0311.8
" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.362, + 0.21, + 0.379 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.385, + 0.471, + 0.492 + ], + "angle": 0, + "content": "In this section (and in the supplementary), we present a comprehensive evaluation of DistractFlow on several benchmark datasets, compare it with baselines and the latest state-of-the-art (SOTA) methods, and conduct extensive ablation studies. We focus our evaluations on realistic or real-world data, including SlowFlow, Sintel (final), and KITTI; we provide results on Sintel (clean) in the Supplementary." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.501, + 0.268, + 0.518 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.522, + 0.47, + 0.612 + ], + "angle": 0, + "content": "Evaluation Settings: We consider two settings for running the experiments. In the first setting, we consider a supervised learning setting where the network is trained on fully labeled data. The second setting considers semi-supervised learning, where unlabeled data can be used during training, in addition to labeled training data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.613, + 0.47, + 0.688 + ], + "angle": 0, + "content": "Evaluation Metrics: We use the common evaluation metrics for optical flow estimation, including End-Point Error (EPE) and Fl-all, which is the percentage of optical flow with EPE larger than 3 pixels or over \\(5\\%\\) of the ground truth. The goal is to lower both of these metrics." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.47, + 0.854 + ], + "angle": 0, + "content": "Datasets: Following commonly adopted evaluation protocols in the literature [6, 14, 30, 35], we train our model on FlyingChairs (C) [4] and FlyingThings3D (T) [20] for supervised training when evaluating on SlowFlow [11] (100px flow magnitude) dataset and the training splits of Sintel (S) [2] and KITTI (K) [5, 22]. In particular, on SlowFlow, we use 4 blur durations with a larger duration having larger motion blurs. When we evaluate on Sintel test set, we use FlyingThings3D, Sintel training set, KITTI training set, and HD1K (H) [16] for supervised training. And, we finetune on KITTI training dataset for evaluation on KITTI test set." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.471, + 0.901 + ], + "angle": 0, + "content": "For the additional unlabeled data used during training, we followed the same setting from [9]. We use FlyingThings as labeled dataset and Sintel test set as unlabeled" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.363, + 0.892, + 0.545 + ], + "angle": 0, + "content": "dataset for evaluating on Sintel and SlowFlow, and the video frames from KITTI test raw sequences for evaluating on KITTI training dataset. When we evaluate on Sintel and KITTI test sets, we use the labeled dataset from supervised training settings, and use additional KITTI train raw sequences, Sintel training data (only using every other frame), Monkaa (M) [20], and Driving (D) [20] as the unlabeled datasets. Note that we do not use Sintel and KITTI test sets as unlabeled datasets for Sintel and KITTI test evaluation. We further experiment with utilizing unlabeled open-source Blender videos as additional unsupervised training data, such as Sintel and Big Buck Bunny." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.546, + 0.893, + 0.728 + ], + "angle": 0, + "content": "Networks and Training: We use RAFT [30], GMA [14], FlowFormer [6] as our baselines, and utilize their official codes. For objectiveness, we train all the baselines in the same framework and reported the results we obtained. We set \\((w_{dist}, w_{self})\\) and \\(\\tau\\) to \\((\\lambda\\) (mixing ratio), 1) and 0.95, respectively. For supervised training, we follow RAFT and GMA learning parameters such as optimizer, number of GRU iterations, training iterations, and so on. For semi-supervised training, we use labeled and unlabeled data with a 1:1 ratio. For FlowFormer, we reduce the total batch size and only finetune it due to GPU memory overflow. All settings and training details are provided in the Supplementary." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.739, + 0.892, + 0.771 + ], + "angle": 0, + "content": "4.2. Evaluations on SlowFlow, Sintel (train), and KITTI (train)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.775, + 0.892, + 0.852 + ], + "angle": 0, + "content": "Supervised Setting: Table 1 shows the performance evaluation of the supervised and semi-supervised training results on SlowFlow, Sintel (train), and KITTI (train). In the top section of Table 1, we provide results of existing supervised models and our models trained using DistractFlow" + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.863, + 0.892, + 0.901 + ], + "angle": 0, + "content": "2RAFT: https://github.com/princeton-vl/RAFT, GMA: https://github.com/zacjiang/GMA, FlowFormer: https://github.com/drinkingcoder/FlowFormer-Official" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13695" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.473, + 0.228 + ], + "angle": 0, + "content": "Table 2. Optical flow estimation results on Sintel (test) and KITTI (test) datasets. We train the models on FlyingChairs (C), FlyingThings (T), Sintel (S), KITTI (K), and HD1K (H) in the supervised setting. When using the semi-supervised setting/using additional data for training, RAFT-A trains on \\(\\mathrm{A + S + K + H + T}\\) datasets where A stands for AutoFlow, FlowSupervisor trains on \\(\\mathrm{C + T + S + K + H}\\) (labeled) and uses Sintel, KITTI, and Spring as unlabeled datasets. In our case, we use \\(\\mathrm{C + T + S + K + H}\\) as labeled data and Sintel, KITTI, and Sceneflow (Monkaa, Driving) as unlabeled data. * indicates results obtained using warm-start [30]." + }, + { + "type": "table", + "bbox": [ + 0.091, + 0.23, + 0.454, + 0.374 + ], + "angle": 0, + "content": "
MethodModelSintel (test)KITTI (test)
(Final-epe)(Fl-all)
Supervised
SupervisedRAFT [30]2.86*5.10
DistractFlow (Our)2.77*4.82
Semi-Supervised / Additional dataset
SupervisedRAFT-A [28]2.86*5.10
3.144.78
RAFT-OCTC [12]RAFT [30]3.094.72
FlowSupervisor [9]2.79*4.85
DistractFlow (Our)2.71*4.71
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.386, + 0.47, + 0.491 + ], + "angle": 0, + "content": "supervised augmentation. Our supervised models trained on FlyingChairs and FlyingThings3D show significant improvements across the test datasets for all the architectures. For SlowFlow with a 3-frame blur duration, the existing RAFT model shows very large errors (over 100 EPE) on a few samples. DistractFlow, on the other hand, leads to more robust results and a much smaller EPE." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.492, + 0.471, + 0.718 + ], + "angle": 0, + "content": "Semi-Supervised Setting: In this part, we evaluate our proposed approach when additional unlabeled data becomes available. In the bottom section of Table 1, we show results of the previous semi-supervised learning methods and our proposed method. Following FlowSupervisor, we finetune each model on FlyingThings (labeled) and Sintel test (unlabeled), and evaluate on the SlowFlow and Sintel train dataset. For evaluation on KITTI train dataset, we finetune the pre-trained models (from Sintel unlabeled) on FlyingThings (labeled) and raw KITTI test (unlabeled). We can see that DistractFlow (RAFT) shows better performance as compared to RAFT-OCTC, RAFT-A, FixTeacher, and FlowSupervisor. Furthermore, we apply our semi-supervised approach to GMA and FlowFormer, and DistractFlow improves their performance." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.729, + 0.454, + 0.745 + ], + "angle": 0, + "content": "4.3. Evaluations on Sintel (test) and KITTI (test)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.47, + 0.884 + ], + "angle": 0, + "content": "Supervised Setting: The top section of Table 2 summarizes the supervised and semi-supervised training results on Sintel (test) and KITTI (test) datasets. From the first part of Table 2, we can see that our proposed DistractFlow permits significant improvements over the baseline RAFT model. It is noteworthy that without using additional unlabeled data, our model trained under the supervised setting already outperforms the semi-supervised FlowSupervisor, which leverages additional data." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Semi-Supervised Setting: In the second part of Ta-" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.089, + 0.892, + 0.117 + ], + "angle": 0, + "content": "Table 3. Effects of different types of perturbations applied to the frames, as data augmentation during training." + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.118, + 0.892, + 0.194 + ], + "angle": 0, + "content": "
MethodPerturbationSintel (train)KITTI (train)
(Final-epe)(Fl-epe)(Fl-all)
RAFT [30]2.734.9416.9
OurGaussian noise2.684.8617.6
Random shapes2.664.8216.8
Realistic Distractions2.614.5716.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.203, + 0.892, + 0.258 + ], + "angle": 0, + "content": "Table 4. Distracting \\( I_{t} \\) and/or \\( I_{t+1} \\) on Sintel (train) and KITTI (train) datasets. We train RAFT with distractions to \\( I_{1} \\) or \\( I_{2} \\) or both. \\( \\alpha \\) is the coefficient in the Beta distribution for sampling \\( \\lambda \\). \\( \\alpha_{1} \\) and \\( \\alpha_{2} \\) are for applying distractions to \\( I_{1} \\) and \\( I_{2} \\), respectively." + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.261, + 0.892, + 0.375 + ], + "angle": 0, + "content": "
MethodDistractionα1α2Sintel (train)KITTI (train)
(Final-epe)(Fl-epe)(Fl-all)
RAFT [30]2.734.9416.9
DistractFlowOn It0.12.694.8116.4
12.645.2517.6
102.555.3217.8
On It+10.12.654.6616.3
12.614.5716.4
102.704.8217.2
On It & It+1 (same)0.112.705.3318.3
On It & It+1 (diff)0.112.644.9216.7
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.392, + 0.892, + 0.543 + ], + "angle": 0, + "content": "ble 2, we provide results for semi-supervised methods or methods that train with additional datasets. RAFT-A is trained with an additional AutoFlow dataset but still underperforms the RAFT trained with our DistractFlow approach. RAFT-OCTC applies a semi-supervised method as well as changes the architecture for occlusion prediction. Although RAFT-OCTC uses a slightly more complex architecture, our DistractFlow-trained RAFT still shows better performance. In addition, our method also considerably outperforms FlowSupervisor." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.559, + 0.665, + 0.573 + ], + "angle": 0, + "content": "4.4. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.58, + 0.892, + 0.7 + ], + "angle": 0, + "content": "We conduct extensive ablation studies on various aspects of our method, by using RAFT as the base model. In the supervised setting, we train on FlyingChairs (C) and FlyingThings3D (T). In the semi-supervised setting, we take the RAFT model pretrained from the supervised setting and then finetune it using FlyingThings3D (labeled) and Sintel (test)/KITTI (test) (unlabeled). The evaluation is done on Sintel (train) and KITTI (train)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.703, + 0.892, + 0.854 + ], + "angle": 0, + "content": "Type of Perturbations: When applying visual perturbations, we compare using realistic distractions in Distract-Flow with using synthetic noise such as Gaussian noise and random shapes. For generating random shapes, we make random background colors and add 5 to 10 shapes (e.g., circles, triangles, and rectangles) of random colors and sizes. As shown in Table 3, while introducing perturbations with Gaussian noise or random shapes can result in performance gains, the improvements are not as significant as compared to the case of using our proposed augmentation strategy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Distracting \\( I_{t} \\) or \\( I_{t + 1} \\) or both: We compare applying distractions to \\( I_{t} \\) or \\( I_{t + 1} \\) or both in Table. 4. At the top of Table. 4, we generate distracted \\( I_{t} \\) using the \\( \\alpha_{1} \\) values" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "13696" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.104, + 0.282, + 0.171 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.284, + 0.104, + 0.481, + 0.171 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.483, + 0.104, + 0.681, + 0.171 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.683, + 0.104, + 0.882, + 0.171 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.174, + 0.28, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.284, + 0.174, + 0.481, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.483, + 0.174, + 0.681, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.683, + 0.174, + 0.882, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.243, + 0.28, + 0.309 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.284, + 0.243, + 0.481, + 0.309 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.483, + 0.243, + 0.681, + 0.309 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.683, + 0.243, + 0.882, + 0.309 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.312, + 0.894, + 0.355 + ], + "angle": 0, + "content": "Figure 4. Qualitative results on Sintel (train) using RAFT, FlowFormer, DistractFlow-RAFT, and DistractFlow-FlowFormer (the last two are empowered with our proposed method). All models are trained on FlyingChairs and FlyingThings3D. It can be seen that DistractFlow can generate more accurate predictions, with better spatial consistency and finer details, as highlighted by circles." + }, + { + "type": "table_caption", + "bbox": [ + 0.18, + 0.366, + 0.366, + 0.379 + ], + "angle": 0, + "content": "Table 5. Effectiveness of \\( {L}_{dist} \\)" + }, + { + "type": "table", + "bbox": [ + 0.093, + 0.381, + 0.455, + 0.446 + ], + "angle": 0, + "content": "
Method\\( \\mathcal{L}_{base} \\)\\( \\mathcal{L}_{dist} \\)Sintel (train)KITTI (train)
(Final-epe)(Fl-epe)(Fl-all)
RAFT [30]✓2.734.9416.9
DistractFlow✓2.825.4319.0
✓✓2.614.5716.4
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.459, + 0.47, + 0.579 + ], + "angle": 0, + "content": "for sampling \\(\\lambda\\) and train the model accordingly.\\(^3\\) All three variants show improvements on Sintel. However, when \\(\\alpha_{1}\\)s are 1 or 10, the performance drops on KITTI compared to RAFT. We suspect that the Sintel (final) dataset has a heavy visual effect even in \\(I_{t}\\), and using strongly distracted \\(I_{t}\\) could help the training.\\(^4\\) On the other hand, since KITTI has relatively cleaner images, strongly distracted \\(I_{t}\\) does not improve the performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.581, + 0.47, + 0.656 + ], + "angle": 0, + "content": "In the middle of Table 4, we distract \\( I_{t+1} \\) according to the different \\( \\alpha_2 \\) values and train the model. In most of these cases DistractFlow improves upon the baseline RAFT, and it shows the best performance at \\( \\alpha_2 = 1 \\). This result shows that various mixing of the images is helpful." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.657, + 0.47, + 0.808 + ], + "angle": 0, + "content": "At the bottom of Table 4, we distract \\( I_{t} \\) and \\( I_{t+1} \\) simultaneously. When we apply the same distraction to both frames, two consecutive videos, it degrades the performance. This is because applying the same distraction to both frame introduces new correspondences which are not part of the ground truth. On the other hand, when we apply distractions from two different images to \\( I_{t} \\) and \\( I_{t+1} \\), the trained model shows better performance compared to baseline RAF. Overall, distracting \\( I_{t+1} \\) shows the best performance and we carry out experiments with this setting." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.809, + 0.47, + 0.84 + ], + "angle": 0, + "content": "Effectiveness of \\(\\mathcal{L}_{\\mathrm{dist}}\\): Table 5 shows the effectiveness of \\(\\mathcal{L}_{\\mathrm{dist}}\\). Without the supervised loss on the original pairs," + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.366, + 0.892, + 0.422 + ], + "angle": 0, + "content": "Table 6. Effectiveness of confidence map and \\(\\lambda\\) weight for \\(\\mathcal{L}_{\\mathrm{self}}\\) in semi-supervised setting. \\(\\tau\\) is the confidence threshold in Eq. 5 and in \\(w_{\\mathrm{self}}\\) is the weight for the self-supervised loss. Note that 0.37 corresponds to having equal nominator and denominator in Eq. 3." + }, + { + "type": "table", + "bbox": [ + 0.528, + 0.423, + 0.866, + 0.5 + ], + "angle": 0, + "content": "
MethodτSintel (train)KITTI (train)
(Final-epe)(Fl-epe)(Fl-all)
RAFT [30]2.734.9416.9
DistractFlowdiverged
✓(0.37)2.353.3712.42
✓(0.95)2.353.0111.71
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.507, + 0.892, + 0.548 + ], + "angle": 0, + "content": "Table 7. Effects of using different unlabeled datasets in the semi-supervised training. Our DistractFlow enables consistent performance improvements when using any of the unlabeled datasets." + }, + { + "type": "table", + "bbox": [ + 0.524, + 0.55, + 0.87, + 0.629 + ], + "angle": 0, + "content": "
MethodUnlabeled data (# of pairs)Sintel (train)
(Final-epe)
RAFT [30]2.73
DistractFlowSintel-test (1.1k)2.35
Monkaa (17k) & Driving (9k)2.42
Big Buck Bunny (14k)2.58
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.643, + 0.892, + 0.703 + ], + "angle": 0, + "content": "a model trained only with \\(\\mathcal{L}_{\\mathrm{dist}}\\) still provides reasonable estimation performance, but shows worse accuracy as compared to the original model. Combining \\(\\mathcal{L}_{\\mathrm{base}}\\) with \\(\\mathcal{L}_{\\mathrm{dist}}\\) shows a significant improvement." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.892, + 0.824 + ], + "angle": 0, + "content": "Effectiveness of Confidence Map: Table 6 shows our study on the impacts of confidence-based thresholding in the semi-supervised training. When training the model without any confidence maps, erroneous predictions are used for backpropagation and training the network, causing the training to diverge. On the other hand, our confidence map allows the network to only train on highly accurate predictions and enables stability when training the model." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.9 + ], + "angle": 0, + "content": "When we set \\(\\tau = 0.37\\) (a common choice for forward-backward consistency), we can stably train the model and it shows improvement. Higher \\(\\tau\\) (e.g., 0.95) shows further accuracy improvement on KITTI. This may be due to the larger displacements in KITTI, which can make the model" + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.85, + 0.468, + 0.875 + ], + "angle": 0, + "content": "3When \\(\\alpha < 1\\), sampled \\(\\lambda\\) is close to 0 or 1. When \\(\\alpha > 1\\), sampled \\(\\lambda\\) is close to 0.5. When \\(\\alpha = 1\\), \\(\\lambda\\) is sampled from a uniform distribution." + }, + { + "type": "page_footnote", + "bbox": [ + 0.077, + 0.876, + 0.468, + 0.9 + ], + "angle": 0, + "content": "4Since we set \\( w_{dist} = \\lambda \\), when \\( \\lambda \\) is close to zero, the distracted pair only impacts the training minimally." + }, + { + "type": "list", + "bbox": [ + 0.076, + 0.85, + 0.468, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13697" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.089, + 0.273, + 0.204 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.276, + 0.089, + 0.459, + 0.204 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.206, + 0.273, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.275, + 0.206, + 0.459, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.322, + 0.47, + 0.391 + ], + "angle": 0, + "content": "Figure 5. Qualitative results on SlowFlow using the original RAFT and DistractFlow-trained RAFT models in supervised and semi-supervised model settings. We see that DistractFlow training enables the network to produce more accurate results, despite the severe motion blur." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.408, + 0.47, + 0.452 + ], + "angle": 0, + "content": "more prone to in accurate predictions. As such, creating pseudo labels with a higher confidence threshold is beneficial in this case." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.464, + 0.26, + 0.48 + ], + "angle": 0, + "content": "4.5. Qualitative Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.485, + 0.469, + 0.636 + ], + "angle": 0, + "content": "Figure 4 shows qualitative results on the Sintel (train, final) using the original RAFT and FlowFormer, as well as our DistractFlow-trained RAFT and FlowFormer. These models are trained on FlyingChairs and FlyingThings3D. Because Sintel (final) contains visual effects such as fog and blur, the original models generate erroneous estimations. On the other hand, our DistractFlow-trained models show more accurate and robust flow estimation results. Especially, it shows accurate predictions at the object boundary without any edge- or segmentation-aware training [1,3]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.637, + 0.469, + 0.727 + ], + "angle": 0, + "content": "Figure 5 shows qualitative results on SlowFlow using the original RAFT, as well as DistractFlow-trained RAFT models (supervised and semi-supervised). Our supervised training allows the model to generate more accurate and robust flows compared to the baseline RAFT. With our semi-supervised setting, our model shows further improvements." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.742, + 0.192, + 0.758 + ], + "angle": 0, + "content": "5. Discussion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Unlabeled Dataset: Table 7 shows the results on Sintel (train) when using different unlabeled data in semi-supervised training. Sintel (test) shows significant improvement compared to supervised training since it is in the same domain as Sintel (train). Although Monkaa & Driving or Bunny dataset have more unlabeled pairs and can still improve upon the original RAFT, they exhibit worse performance than using Sintel (test) pairs. This indicates that for semi-supervised setting, it is important to use unlabeled" + }, + { + "type": "image_caption", + "bbox": [ + 0.549, + 0.09, + 0.593, + 0.103 + ], + "angle": 0, + "content": "Images" + }, + { + "type": "image_caption", + "bbox": [ + 0.682, + 0.09, + 0.721, + 0.102 + ], + "angle": 0, + "content": "RAFT" + }, + { + "type": "image_caption", + "bbox": [ + 0.79, + 0.09, + 0.868, + 0.101 + ], + "angle": 0, + "content": "DistractFlow" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.104, + 0.63, + 0.146 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.632, + 0.104, + 0.755, + 0.146 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.758, + 0.104, + 0.881, + 0.146 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.149, + 0.63, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.632, + 0.149, + 0.755, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.758, + 0.149, + 0.881, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.196, + 0.63, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.632, + 0.196, + 0.755, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.758, + 0.196, + 0.881, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.242, + 0.63, + 0.285 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.632, + 0.242, + 0.755, + 0.285 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.758, + 0.242, + 0.881, + 0.285 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.289, + 0.892, + 0.373 + ], + "angle": 0, + "content": "Figure 6. Predictions on distracted video frame pairs. In the first column, the first row shows the overlaid original pair and the second to fourth rows show the distracted pairs. The mixing weight for the distractor increases from top to bottom. The RAFT model trained with DistractFlow performs robustly, while the original RAFT model completely fails when the distraction becomes large." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.392, + 0.892, + 0.467 + ], + "angle": 0, + "content": "data with scenes and distributions resembling the target use case. We leave data distribution robustness (e.g., addressing out-of-distribution samples [18, 19, 31] as part of future work. Nevertheless, our semi-supervised method improves the performance when using any of the unlabeled datasets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.468, + 0.892, + 0.604 + ], + "angle": 0, + "content": "Robust Prediction: Figure 6 shows the predictions of RAFT and DistractFlow-RAFT (trained with FlyingChairs and FlyingThings3D) on distracted frames pairs, using mixing ratios of 1, 0.75, 0.5, and 0.25. When the original \\( I_{t+1} \\) has a small portion of a distracted image, the original RAFT has degraded performance. It completely fails to find the correspondence for the red car when \\( \\lambda = 0.25 \\). In contrast, the model trained using DistractFlow still robustly finds the correspondence in the distracted image." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.617, + 0.619, + 0.633 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.639, + 0.892, + 0.896 + ], + "angle": 0, + "content": "We proposed a novel method, DistractFlow, to augment optical flow training. We introduced realistic distractions to the video frame pairs which provided consistent improvements to optical flow estimation models. When unlabeled data was available, based on the original and distracted pairs, we devised a semi-supervised learning scheme using pseudo labels. We also incorporated forward-backward consistency through confidence maps that provided training stability and enhanced the performance further. Through extensive experiments on several optical flow estimation benchmarks: SlowFlow, Sintel, and KITTI, we showed that our method achieved significant improvements over the previous state of the art without inducing additional complexity during inference. In particular, models trained using our DistractFlow strategy are more robust in practical, challenging scenarios (e.g., consistent error reductions on SlowFlow despite strong motion blurs)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13698" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.184 + ], + "angle": 0, + "content": "[1] Shubhankar Borse, Ying Wang, Yizhe Zhang, and Fatih Porikli. Inverseform: A loss function for structured boundary-aware segmentation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 5901-5911, 2021. 8" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.186, + 0.472, + 0.242 + ], + "angle": 0, + "content": "[2] Daniel J Butler, Jonas Wulff, Garrett B Stanley, and Michael J Black. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 17592-17601, 2022. 2" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.894, + 0.319 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "13700" + } + ] +] \ No newline at end of file diff --git a/2023/DistractFlow_ Improving Optical Flow Estimation via Realistic Distractions and Pseudo-Labeling/71dcd135-f623-44d3-88eb-6335db05d14d_origin.pdf b/2023/DistractFlow_ Improving Optical Flow Estimation via Realistic Distractions and Pseudo-Labeling/71dcd135-f623-44d3-88eb-6335db05d14d_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..cb69cb4fb7d46ef4e784c55a5674f6c01b477cf1 --- /dev/null +++ b/2023/DistractFlow_ Improving Optical Flow Estimation via Realistic Distractions and Pseudo-Labeling/71dcd135-f623-44d3-88eb-6335db05d14d_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:50670065a04b7669b0c9a1165e6d914fdc668b706003efa557458dcef3cc9dac +size 5729107 diff --git a/2023/DistractFlow_ Improving Optical Flow Estimation via Realistic Distractions and Pseudo-Labeling/full.md b/2023/DistractFlow_ Improving Optical Flow Estimation via Realistic Distractions and Pseudo-Labeling/full.md new file mode 100644 index 0000000000000000000000000000000000000000..3575460baba2821c14aefe4f39ad115ad790ecde --- /dev/null +++ b/2023/DistractFlow_ Improving Optical Flow Estimation via Realistic Distractions and Pseudo-Labeling/full.md @@ -0,0 +1,341 @@ +# DistractFlow: Improving Optical Flow Estimation via Realistic Distractions and Pseudo-Labeling + +Jisoo Jeong Hong Cai Risheek Garrepalli Fatih Porikli Qualcomm AI Research† + +{jisojeon, hongcai, rgarrepα, fporikli}@qti.qualcomm.com + +# Abstract + +We propose a novel data augmentation approach, DistractFlow, for training optical flow estimation models by introducing realistic distractions to the input frames. Based on a mixing ratio, we combine one of the frames in the pair with a distractor image depicting a similar domain, which allows for inducing visual perturbations congruent with natural objects and scenes. We refer to such pairs as distracted pairs. Our intuition is that using semantically meaningful distractors enables the model to learn related variations and attain robustness against challenging deviations, compared to conventional augmentation schemes focusing only on low-level aspects and modifications. More specifically, in addition to the supervised loss computed between the estimated flow for the original pair and its ground-truth flow, we include a second supervised loss defined between the distracted pair's flow and the original pair's ground-truth flow, weighted with the same mixing ratio. Furthermore, when unlabeled data is available, we extend our augmentation approach to self-supervised settings through pseudo-labeling and cross-consistency regularization. Given an original pair and its distracted version, we enforce the estimated flow on the distracted pair to agree with the flow of the original pair. Our approach allows increasing the number of available training pairs significantly without requiring additional annotations. It is agnostic to the model architecture and can be applied to training any optical flow estimation models. Our extensive evaluations on multiple benchmarks, including Sintel, KITTI, and SlowFlow, show that DistractFlow improves existing models consistently, outperforming the latest state of the art. + +# 1. Introduction + +Recent years have seen significant progress in optical flow estimation thanks to the development of deep learning, e.g., [4,7,8,23]. Among the latest works, many focus on developing novel neural network architectures, such as PwC-Net [29], RAFT [30], and FlowFormer [6]. Other stud + +![](images/84022b53e58956380e01a8e8baf182bac0eb32dc4a7eba004d634350475ab945.jpg) +Figure 1. Existing augmentation schemes apply low-level visual modifications, such as color jittering, block-wise random occlusion, and flipping, to augment the training data (top), while DistractFlow introduces high-level semantic perturbations to the frames (bottom). DistractFlow can further leverage unlabeled data to generate a self-supervised regularization. Our training leads to more accurate and robust optical flow estimation models, especially in challenging real-world settings. + +ies investigate how to improve different aspects of supervised training [27], e.g., gradient clipping, learning rate, and training compute load. More related to our paper are those incorporating data augmentation during training (e.g., [30]), including color jittering, random occlusion, cropping, and flipping. While these image manipulations can effectively expand the training data and enhance the robustness of the neural models, they fixate on the low-level aspects of the images. + +Since obtaining ground truth optical flow on real data is very challenging, another line of work investigates how to leverage unlabeled data. To this end, semi-supervised methods [9, 12] that utilize frame pairs with ground-truth flow annotations in conjunction with unlabeled data in training have been proposed. For instance, FlowSupervisor [9] adopts a teacher-student distillation approach to exploit unlabeled data. This method, however, does not consider lo + +calized uncertainty but computes the loss for the entire image between the teacher and student network. + +In this paper, we present a novel approach, DistractFlow, which performs semantically meaningful data augmentations by introducing images of real objects and natural scenes as distractors or perturbations to training frame pairs. More specifically, given a pair of consecutive frames, we combine the second frame with a random image depicting similar scenarios based on a mixing ratio. In this way, related objects and scenes are overlaid on top of the original second frame; see Figure 1 for an example. As a result, we obtain challenging yet appropriate distractions for the optical flow estimation model that seeks dense correspondences from the first frame to the second frame (and in reverse too). The original first frame and the composite second frame constitute a distracted pair of frames, which we use as an additional data sample in both supervised and self-supervised training settings. Unlike our approach, existing data augmentation schemes for optical flow training apply only low-level variations such as contrast changes, geometric manipulations, random blocks, haze, motion blur, and simple noise and shapes insertions [28, 30]. While such augmentations can still lead to performance improvements, they are disconnected from natural variations, scene context, and semantics. As we shall see in our experimental validation, the use of realistic distractions in training can provide a bigger boost to performance. + +Figure 1 provides a high-level outline of DistractFlow. We apply DistractFlow in supervised learning settings using the ground-truth flow of the original pair. Distracted pairs contribute to the backpropagated loss proportional to the mixing ratios used in their construction. Additionally, when unlabeled frame pairs are available, DistractFlow allows us to impose a self-supervised regularization by further leveraging pseudo-labeling. Given an unlabeled pair of frames, we create a distracted version. Then, we enforce the estimated flow on the distracted pair to match that on the original pair. In other words, the prediction of the original pair is treated as a pseudo ground truth flow for the distracted pair. Since the estimation on the original pair can be erroneous, we further derive and impose a confidence map to employ only highly confident pixel-wise flow estimations as the pseudo ground truth. This prevents the model from reinforcing incorrect predictions, leading to a more stable training process. + +In summary, our main contributions are as follows: + +- We introduce DistractFlow, a novel data augmentation approach that improves optical flow estimation by utilizing distractions from natural images. Our method provides augmentations with realistic semantic contents compared to existing augmentation schemes. +- We present a semi-supervised learning scheme for optical flow estimation that adopts the proposed dis + +tracted pairs to leverage unlabeled data. We compute a confidence map to generate uncertainty-aware pseudo labels and to enhance training stability and overall performance. + +- We demonstrate the effectiveness of DistractFlow in supervised [6, 14, 30] and semi-supervised settings, showing that DistractFlow outperforms the very recent FlowSupervisor [9] that require additional in-domain unlabeled data. + +# 2. Related Work + +Optical Flow Estimation: Several deep architectures have been proposed for optical flow [4, 8, 23, 29, 30, 38]. Among these, Recurrent All Pairs Field Transforms (RAFT) [30] have shown significant performance improvement over previous methods, inspiring many subsequent works [6, 14, 26, 27, 35]. Following the structure of RAFT architecture, complementary studies [12, 14, 33, 35, 39] proposed advancements on feature extraction, 4D correlation volume, recurrent update blocks, and more recently, transformer extensions [6,39]. In DistractFlow, we introduce a new model-agnostic training method that can help any model. + +Data Augmentation: Data augmentation is a widely used technique to better train deep learning models. Common augmentations include color and contrast jittering, flipping, geometric manipulation, and random noise. While they can improve the robustness of the model, these operations mainly focus on the low-level visual aspects and do not account for variations in the semantic contents. + +Recently, several data augmentation schemes, such as adversarial perturbation and regularization methods, have been proposed for classification tasks. Adversarial perturbation [32] is one of the well-known augmentation methods for classification tasks, but recent work [24] shows that it does not work well for optical flow estimation. Interpolation-based Regularization (IR) [34, 36], which mixes a couple of images and trains the model with mixed label, improves the performance in classification tasks and is employed in other fields such as object detection [13, 37] and segmentation [10]. In a regression problem, however, mixed ground truth does not correspond with mixed input. Fixmatch [25] as a data augmentation scheme has demonstrated state-of-the-art performance in classification tasks. It combines pseudo-labeling and consistency regularization by applying two different augmentations (weak, strong) to the same image and generates pseudo-labels with weak augmentation output. For classification tasks, it is possible to create pseudo-labels since the output and ground-truth annotations represent class probabilities. However, there are no such class probabilities for optical flow. Thus, these methods cannot be readily applicable. + +AutoFlow [28] proposed a new dataset for optical flow, taking a versatile approach to data rendering, where motion, + +![](images/0dccf075568d9755a27092a17f3d575aef08e7802466301106fc6914d568bd63.jpg) +Figure 2. Left: Introducing realistic distractions in the supervised learning setting. Right: Semi-supervised learning leveraging distractions and pseudo-labeling. + +![](images/a113308527ae124dfbdda65784cc8399bf1736bdb6ea3bd12b821b9c192b03ac.jpg) + +shape, and appearance are controlled via learnable hyperparameters. Though its performance gain is notable, AutoFlow employs synthetic augmentations. The work in [27] utilizes AutoFlow and argues that it is important to disentangle architecture and training pipeline. [27] also points out that some of the performance improvements of the recent methods are due to hyperparameters, dataset extensions, and training optimizations. Our work focuses on more capable augmentations for model agnostic training, not architecture novelties. + +Semi-Supervised Learning: Semi-supervised optical flow learning methods [12, 17] aim to make the best use of unlabeled data as there is only a limited amount of optical flow ground truth data for real and natural scenes. And even in those datasets, the optical flow ground truths are computed. RAFT-OCTC [12] proposed transformation consistency for semi-supervised learning, which applies spatial transformations to image pairs and enforces flow equivariance between the original and transformed pairs. FlowSupervisor [9] introduced a teacher network for stable semisupervised fine-tuning. Its student model is trained for all pixels using teacher network output. In DistractFlow, we propose uncertainty-aware pseudo-labeling, which uses two different image pairs instead of different networks. We further employ forward-backward consistency to derive dense confidence scores, which steer the training process to impose loss only within high-consistency image regions to prevent feedback from incorrect flow estimates. + +Since acquiring optical flow ground truth for real videos is problematic (not possible for most cases), unsupervised training methods [15,21,26] seek out training models without ground truth flows. Even though they report promising results comparable to the earlier deep learning approaches, unsupervised training methods still entail limitations. + +# 3. DistractFlow + +Our approach incorporates augmentation and supervision techniques to enhance the training of optical flow estimation models. In Section 3.1, we describe how we construct realistic distractions for optical flow training and how we employ them in supervised settings. Next, in Section 3.2, we extend our approach to semi-supervised learning with additional unlabeled data. We derive a self-supervised regularization objective by utilizing the distracted samples and pseudo-labeling. + +# 3.1. Realistic Distractions as Augmentation + +Consider a pair of video frames during training: $(I_{t}, I_{t+1})$ . The distracted version of them is denoted as $(I_{t}, D_{\lambda}(I_{t+1}, \tilde{I}_{d})$ , where $D_{\lambda}(I_{t+1}, \tilde{I}_{d})$ is the perturbed second frame obtained by combing with another image $\tilde{I}_{d}$ based on a mixing ratio of $\lambda \in (0, 1)$ . Specifically, $D_{\lambda}(I_{t+1}, \tilde{I}_{d})$ is calculated as $\lambda \cdot I_{t+1} + (1 - \lambda) \cdot \tilde{I}_{d}$ , where $\lambda$ is sampled from a Beta $(\alpha, \alpha)$ distribution, same as defined in [34, 36]. + +Figure 2 shows an example of a distracted pair of video frames. It can be seen that the actual objects and the real scene from one image are overlaid onto the second one. Such perturbations can reflect challenging real-world scenarios, e.g., foreground/background objects that only start to appear in the second frame, drastic motion blur, out-of-focus artifacts, reflections on specular surfaces, partial occlusions, etc. Furthermore, since the distractions are from the same dataset, the visual context of the original pair and distractor image are similar. For instance, the original pair and distractor depict similar classes (road, car, building, etc.). The spatial arrangement of the class and object regions in those images are similar, e.g., roads are within the lower part of the images, and so do the sky, buildings, and + +![](images/720c22f228b4ca3b05e64d8b9321e62e3bdff2144209713c2ad79e8b6930ccc9.jpg) +Figure 3. Semi-supervised learning that leverages distractions and confidence-aware pseudo-labeling. + +vehicles. While one may attempt to render such scenarios synthetically, our DistractFlow provides a convenient and automatic way that can still capture such natural and semantically related variations. Compared to conventional augmentation methods that use noise or simple shapes, our method allows the model to be more robust to perturbations caused by real-world image contents. + +Additionally, we note that applying realistic distractions to the first or both frames is possible. As we shall see in the experiments, all of these options will result in improved accuracy. + +To provide supervision on the distracted pair of frames, we use the ground-truth flow of the original pair. The loss is computed as follows: + +$$ +\mathcal {L} _ {\text {d i s t}} = \left\| V _ {\left(I _ {t}, I _ {t + 1}\right)} ^ {f} - f \left(I _ {t}, D _ {\lambda} \left(I _ {t + 1}, \tilde {I} _ {d}\right)\right) \right\| _ {1}, \tag {1} +$$ + +where $V_{(I_t, I_{t+1})}^f$ is the ground-truth forward flow for the original pair $(I_t, I_{t+1})$ and $f(\cdot, \cdot)$ denotes the predicted flow based on model $f$ . + +In the supervised learning setting, where all training samples are labeled, the total training loss is then given as follows: + +$$ +\mathcal {L} _ {\sup } = \mathcal {L} _ {\text {b a s e}} + w _ {\text {d i s t}} \mathcal {L} _ {\text {d i s t}}, \tag {2} +$$ + +where $L_{base}$ is the conventional supervised loss and $w_{\mathrm{dist}} > 0$ weights $\mathcal{L}_{\mathrm{dist}}$ . For iterative models like RAFT, we compute and apply this loss at each recurrent iteration. + +# 3.2. Semi-Supervised Learning via Realistic Distraction and Pseudo-Labeling + +During training, when unlabeled frame pairs are available, we can further leverage our distracted pairs of frames to derive additional self-supervised regularization. More specifically, given a distracted pair of frames, $(I_{t},D_{\lambda}(I_{t + 1},\tilde{I}_{d}))$ , and the original pair, $(I_{t},I_{t + 1})$ , we enforce the model's prediction on the distracted pair to match + +that on the original pair. In other words, the prediction on the original pair, $f(I_{t}, I_{t+1})$ , is treated as the pseudo label. By doing this, the model learns to produce optical flow estimation on the distracted pair that is consistent with that of the original pair, despite the distractions. Such regularization promotes the model's robustness when processing real-world data, as we show in our experiments. + +We note that, however, using all of $f(I_{t}, I_{t+1})$ as the training target for the distracted pair is problematic. This is because the model's prediction can be erroneous and noisy during the training process, even on the original frame pairs. The low-quality pseudo labels can be detrimental to the overall training, even leading to instability. + +To address this issue, we adopt uncertainty-aware pseudo labels by calculating a confidence map based on forward backward consistency, and only using highly confident pixels' predictions as pseudo ground truth, as shown in Figure 3. On a frame pair $(I_t, I_{t+1})$ , let $\widehat{V}^f(x)$ and $\widehat{V}^b(x)$ denote the predicted forward and backward flows at the pixel location $x$ . When they satisfy the following constraint [21], we can assume that the prediction is accurate. + +$$ +\begin{array}{l} \left| \widehat {V} ^ {f} (x) + \widehat {V} ^ {b} \left(x + \widehat {V} ^ {f} (x)\right) \right| ^ {2} \\ < \gamma_ {1} \Big (| \widehat {V} ^ {f} | ^ {2} + | \widehat {V} ^ {b} (x + \widehat {V} ^ {f} (x)) | ^ {2} \Big) + \gamma_ {2}, \\ \end{array} +$$ + +where $\gamma_{1} = 0.01$ and $\gamma_{2} = 0.5$ from [21]. + +As such, we derive the confidence map as follows: + +$$ +M _ {\text {c o n f}} = \exp \left(- \frac {\left| \widehat {V} ^ {f} (x) + \widehat {V} ^ {b} \left(x + \widehat {V} ^ {f} (x)\right) \right| ^ {2}}{\gamma_ {1} \left(\left| \widehat {V} ^ {f} \right| ^ {2} + \left| \widehat {V} ^ {b} \left(x + \widehat {V} ^ {f} (x)\right) \right| ^ {2}\right) + \gamma_ {2}}\right). \tag {4} +$$ + +Our confidence map provides a measure of reliability of the predicted optical flow. Specifically, in Eq. 4, if the numerator and the denominator are equal, the confidence value is then approximately $0.37(e^{-1})$ . In this paper, we use a very high threshold and it could provide a more accurate optical flow pseudo ground truth. + +By incorporating the confidence map, our self-supervised regularization is then given as follows: + +$$ +\mathcal {L} _ {\text {s e l f}} = \left\| \left[ M _ {\text {c o n f}} \geq \tau \right] \left(f \left(I _ {t}, I _ {t + 1}\right) - f \left(I _ {t}, D _ {\lambda} \left(I _ {t + 1}, \tilde {I} _ {d}\right)\right)\right) \right\| _ {1}, \tag {5} +$$ + +where $[\cdot ]$ is the Iverson bracket and $\tau$ is the confidence threshold. + +In summary, in the semi-supervised learning setting, where labeled and unlabeled data are both used in training, the total loss is as follows: + +$$ +\mathcal {L} _ {\text {t o t a l}} = \mathcal {L} _ {\sup } + w _ {\text {s e l f}} \mathcal {L} _ {\text {s e l f}}, \tag {6} +$$ + +where $\mathcal{L}_{\mathrm{sup}}$ is the supervised loss of Eq. 2, $\mathcal{L}_{\mathrm{self}}$ is the self-supervised loss of Eq. 5, and $w_{\mathrm{self}} > 0$ weights $\mathcal{L}_{\mathrm{self}}$ . + +Table 1. Optical flow estimation results on SlowFlow, Sintel (train), and KITTI (train) datasets. We train the models on FlyingChairs (C) and FlyingThings (T) in the supervised setting. In the semi-supervised setting, we finetune the model on FlyingThings (T) as labeled data and Sintel (test) and KITTI (test) (S/K) as unlabeled data. * indicates test results of existing models generated by us. + +
MethodModelLabeled dataUnlabeled dataSlowFlow (100px)Sintel (train)KITTI (train)
1357(Final-epe)(Fl-epe)(Fl-all)
SupervisedSupervised DistractFlow (Our)RAFT [30]C+T3.737.986.729.962.73*4.94*16.9*
3.373.936.218.182.614.5716.4
Supervise DistractFlow (Our)GMA [14]2.494.995.959.152.85*4.88*17.1*
2.533.495.438.242.664.7616.9
Supervised DistractFlow (Our)FlowFormer [6]2.723.735.246.782.39*4.10*14.7*
2.512.774.396.302.314.0013.9
Semi-SupervisedSupervised RAFT-A [28]RAFT [30]C + TT (subsampled)3.737.986.729.962.73*4.94*16.9*
AutoFlow [28]----2.574.23-
RAFT-OCTC [12]----2.674.7216.3
Fixed Teacher [9]C + TS/K----2.584.9115.9
FlowSupervisor [9]S/K----2.463.3511.1
DistractFlow (Our)S/K2.463.605.156.952.353.0111.7
Supervised DistractFlow (Our)GMA [14]S/K2.494.995.959.152.85*4.88*17.1*
2.442.794.386.572.313.2111.0
Supervised DistractFlow (Our)FlowFormer [6]S/K2.723.735.246.782.39*4.29*15.4*
2.482.694.316.292.333.0311.8
+ +# 4. Experiments + +In this section (and in the supplementary), we present a comprehensive evaluation of DistractFlow on several benchmark datasets, compare it with baselines and the latest state-of-the-art (SOTA) methods, and conduct extensive ablation studies. We focus our evaluations on realistic or real-world data, including SlowFlow, Sintel (final), and KITTI; we provide results on Sintel (clean) in the Supplementary. + +# 4.1. Experimental Setup + +Evaluation Settings: We consider two settings for running the experiments. In the first setting, we consider a supervised learning setting where the network is trained on fully labeled data. The second setting considers semi-supervised learning, where unlabeled data can be used during training, in addition to labeled training data. + +Evaluation Metrics: We use the common evaluation metrics for optical flow estimation, including End-Point Error (EPE) and Fl-all, which is the percentage of optical flow with EPE larger than 3 pixels or over $5\%$ of the ground truth. The goal is to lower both of these metrics. + +Datasets: Following commonly adopted evaluation protocols in the literature [6, 14, 30, 35], we train our model on FlyingChairs (C) [4] and FlyingThings3D (T) [20] for supervised training when evaluating on SlowFlow [11] (100px flow magnitude) dataset and the training splits of Sintel (S) [2] and KITTI (K) [5, 22]. In particular, on SlowFlow, we use 4 blur durations with a larger duration having larger motion blurs. When we evaluate on Sintel test set, we use FlyingThings3D, Sintel training set, KITTI training set, and HD1K (H) [16] for supervised training. And, we finetune on KITTI training dataset for evaluation on KITTI test set. + +For the additional unlabeled data used during training, we followed the same setting from [9]. We use FlyingThings as labeled dataset and Sintel test set as unlabeled + +dataset for evaluating on Sintel and SlowFlow, and the video frames from KITTI test raw sequences for evaluating on KITTI training dataset. When we evaluate on Sintel and KITTI test sets, we use the labeled dataset from supervised training settings, and use additional KITTI train raw sequences, Sintel training data (only using every other frame), Monkaa (M) [20], and Driving (D) [20] as the unlabeled datasets. Note that we do not use Sintel and KITTI test sets as unlabeled datasets for Sintel and KITTI test evaluation. We further experiment with utilizing unlabeled open-source Blender videos as additional unsupervised training data, such as Sintel and Big Buck Bunny. + +Networks and Training: We use RAFT [30], GMA [14], FlowFormer [6] as our baselines, and utilize their official codes. For objectiveness, we train all the baselines in the same framework and reported the results we obtained. We set $(w_{dist}, w_{self})$ and $\tau$ to $(\lambda$ (mixing ratio), 1) and 0.95, respectively. For supervised training, we follow RAFT and GMA learning parameters such as optimizer, number of GRU iterations, training iterations, and so on. For semi-supervised training, we use labeled and unlabeled data with a 1:1 ratio. For FlowFormer, we reduce the total batch size and only finetune it due to GPU memory overflow. All settings and training details are provided in the Supplementary. + +# 4.2. Evaluations on SlowFlow, Sintel (train), and KITTI (train) + +Supervised Setting: Table 1 shows the performance evaluation of the supervised and semi-supervised training results on SlowFlow, Sintel (train), and KITTI (train). In the top section of Table 1, we provide results of existing supervised models and our models trained using DistractFlow + +Table 2. Optical flow estimation results on Sintel (test) and KITTI (test) datasets. We train the models on FlyingChairs (C), FlyingThings (T), Sintel (S), KITTI (K), and HD1K (H) in the supervised setting. When using the semi-supervised setting/using additional data for training, RAFT-A trains on $\mathrm{A + S + K + H + T}$ datasets where A stands for AutoFlow, FlowSupervisor trains on $\mathrm{C + T + S + K + H}$ (labeled) and uses Sintel, KITTI, and Spring as unlabeled datasets. In our case, we use $\mathrm{C + T + S + K + H}$ as labeled data and Sintel, KITTI, and Sceneflow (Monkaa, Driving) as unlabeled data. * indicates results obtained using warm-start [30]. + +
MethodModelSintel (test)KITTI (test)
(Final-epe)(Fl-all)
Supervised
SupervisedRAFT [30]2.86*5.10
DistractFlow (Our)2.77*4.82
Semi-Supervised / Additional dataset
SupervisedRAFT-A [28]2.86*5.10
3.144.78
RAFT-OCTC [12]RAFT [30]3.094.72
FlowSupervisor [9]2.79*4.85
DistractFlow (Our)2.71*4.71
+ +supervised augmentation. Our supervised models trained on FlyingChairs and FlyingThings3D show significant improvements across the test datasets for all the architectures. For SlowFlow with a 3-frame blur duration, the existing RAFT model shows very large errors (over 100 EPE) on a few samples. DistractFlow, on the other hand, leads to more robust results and a much smaller EPE. + +Semi-Supervised Setting: In this part, we evaluate our proposed approach when additional unlabeled data becomes available. In the bottom section of Table 1, we show results of the previous semi-supervised learning methods and our proposed method. Following FlowSupervisor, we finetune each model on FlyingThings (labeled) and Sintel test (unlabeled), and evaluate on the SlowFlow and Sintel train dataset. For evaluation on KITTI train dataset, we finetune the pre-trained models (from Sintel unlabeled) on FlyingThings (labeled) and raw KITTI test (unlabeled). We can see that DistractFlow (RAFT) shows better performance as compared to RAFT-OCTC, RAFT-A, FixTeacher, and FlowSupervisor. Furthermore, we apply our semi-supervised approach to GMA and FlowFormer, and DistractFlow improves their performance. + +# 4.3. Evaluations on Sintel (test) and KITTI (test) + +Supervised Setting: The top section of Table 2 summarizes the supervised and semi-supervised training results on Sintel (test) and KITTI (test) datasets. From the first part of Table 2, we can see that our proposed DistractFlow permits significant improvements over the baseline RAFT model. It is noteworthy that without using additional unlabeled data, our model trained under the supervised setting already outperforms the semi-supervised FlowSupervisor, which leverages additional data. + +Semi-Supervised Setting: In the second part of Ta- + +Table 3. Effects of different types of perturbations applied to the frames, as data augmentation during training. + +
MethodPerturbationSintel (train)KITTI (train)
(Final-epe)(Fl-epe)(Fl-all)
RAFT [30]2.734.9416.9
OurGaussian noise2.684.8617.6
Random shapes2.664.8216.8
Realistic Distractions2.614.5716.4
+ +Table 4. Distracting $I_{t}$ and/or $I_{t+1}$ on Sintel (train) and KITTI (train) datasets. We train RAFT with distractions to $I_{1}$ or $I_{2}$ or both. $\alpha$ is the coefficient in the Beta distribution for sampling $\lambda$ . $\alpha_{1}$ and $\alpha_{2}$ are for applying distractions to $I_{1}$ and $I_{2}$ , respectively. + +
MethodDistractionα1α2Sintel (train)KITTI (train)
(Final-epe)(Fl-epe)(Fl-all)
RAFT [30]2.734.9416.9
DistractFlowOn It0.12.694.8116.4
12.645.2517.6
102.555.3217.8
On It+10.12.654.6616.3
12.614.5716.4
102.704.8217.2
On It & It+1 (same)0.112.705.3318.3
On It & It+1 (diff)0.112.644.9216.7
+ +ble 2, we provide results for semi-supervised methods or methods that train with additional datasets. RAFT-A is trained with an additional AutoFlow dataset but still underperforms the RAFT trained with our DistractFlow approach. RAFT-OCTC applies a semi-supervised method as well as changes the architecture for occlusion prediction. Although RAFT-OCTC uses a slightly more complex architecture, our DistractFlow-trained RAFT still shows better performance. In addition, our method also considerably outperforms FlowSupervisor. + +# 4.4. Ablation Studies + +We conduct extensive ablation studies on various aspects of our method, by using RAFT as the base model. In the supervised setting, we train on FlyingChairs (C) and FlyingThings3D (T). In the semi-supervised setting, we take the RAFT model pretrained from the supervised setting and then finetune it using FlyingThings3D (labeled) and Sintel (test)/KITTI (test) (unlabeled). The evaluation is done on Sintel (train) and KITTI (train). + +Type of Perturbations: When applying visual perturbations, we compare using realistic distractions in Distract-Flow with using synthetic noise such as Gaussian noise and random shapes. For generating random shapes, we make random background colors and add 5 to 10 shapes (e.g., circles, triangles, and rectangles) of random colors and sizes. As shown in Table 3, while introducing perturbations with Gaussian noise or random shapes can result in performance gains, the improvements are not as significant as compared to the case of using our proposed augmentation strategy. + +Distracting $I_{t}$ or $I_{t + 1}$ or both: We compare applying distractions to $I_{t}$ or $I_{t + 1}$ or both in Table. 4. At the top of Table. 4, we generate distracted $I_{t}$ using the $\alpha_{1}$ values + +![](images/a13bab61264d376d0eeb18a09ef6f6cad0126d9aa7e0222c3534e1e4b2805524.jpg) + +![](images/ebb12d9a7e9db81e5fe857fc6c54282709be305f32eb84d51fd6f6de7c7cc8f0.jpg) + +![](images/3ae220b74642227b081487fc3d6e92ed9f5824e408986d0d2fdd3beed5b7d741.jpg) + +![](images/d080916d5ab9b8907c0a5fa62847d5b932aa5e51df5bafed9fdb0b2b22f093f9.jpg) + +![](images/90e44e917b6e990fc73c4cbce6d693f4134df61818f59953861a6fd5a534be7e.jpg) + +![](images/bcd25c3229c1d0cf9ce09c42680e19393eed88184d722921357850ecda7fe846.jpg) + +![](images/722efd892c916d9dedacb3f9bfd6c4393fb83b73de410f657adbe546a576ce36.jpg) + +![](images/fa1f860293e819e47154ae27abbcb5d4011cb27d82e17736000c27eeebc199ae.jpg) + +![](images/6ea365cf806f719081548f24504870cd25a6e74da0f319fb53ef7abee4e10aac.jpg) +Figure 4. Qualitative results on Sintel (train) using RAFT, FlowFormer, DistractFlow-RAFT, and DistractFlow-FlowFormer (the last two are empowered with our proposed method). All models are trained on FlyingChairs and FlyingThings3D. It can be seen that DistractFlow can generate more accurate predictions, with better spatial consistency and finer details, as highlighted by circles. + +![](images/3fce0f9c6325fa65aab0afb0055923c06b73492a3de0971264f16b7866646435.jpg) + +![](images/df414442ad6ba68d546d238116d82d7d693a1d2fcf838dd16cbd0f32068a7b65.jpg) + +![](images/f4e35eee6aa17a8b4a531718657e2c6bd698c1c5152bf2ad498b741f27dcef25.jpg) + +Table 5. Effectiveness of ${L}_{dist}$ + +
Method\( \mathcal{L}_{base} \)\( \mathcal{L}_{dist} \)Sintel (train)KITTI (train)
(Final-epe)(Fl-epe)(Fl-all)
RAFT [30]✓2.734.9416.9
DistractFlow✓2.825.4319.0
✓✓2.614.5716.4
+ +for sampling $\lambda$ and train the model accordingly. $^3$ All three variants show improvements on Sintel. However, when $\alpha_{1}$ s are 1 or 10, the performance drops on KITTI compared to RAFT. We suspect that the Sintel (final) dataset has a heavy visual effect even in $I_{t}$ , and using strongly distracted $I_{t}$ could help the training. $^4$ On the other hand, since KITTI has relatively cleaner images, strongly distracted $I_{t}$ does not improve the performance. + +In the middle of Table 4, we distract $I_{t+1}$ according to the different $\alpha_2$ values and train the model. In most of these cases DistractFlow improves upon the baseline RAFT, and it shows the best performance at $\alpha_2 = 1$ . This result shows that various mixing of the images is helpful. + +At the bottom of Table 4, we distract $I_{t}$ and $I_{t+1}$ simultaneously. When we apply the same distraction to both frames, two consecutive videos, it degrades the performance. This is because applying the same distraction to both frame introduces new correspondences which are not part of the ground truth. On the other hand, when we apply distractions from two different images to $I_{t}$ and $I_{t+1}$ , the trained model shows better performance compared to baseline RAF. Overall, distracting $I_{t+1}$ shows the best performance and we carry out experiments with this setting. + +Effectiveness of $\mathcal{L}_{\mathrm{dist}}$ : Table 5 shows the effectiveness of $\mathcal{L}_{\mathrm{dist}}$ . Without the supervised loss on the original pairs, + +Table 6. Effectiveness of confidence map and $\lambda$ weight for $\mathcal{L}_{\mathrm{self}}$ in semi-supervised setting. $\tau$ is the confidence threshold in Eq. 5 and in $w_{\mathrm{self}}$ is the weight for the self-supervised loss. Note that 0.37 corresponds to having equal nominator and denominator in Eq. 3. + +
MethodτSintel (train)KITTI (train)
(Final-epe)(Fl-epe)(Fl-all)
RAFT [30]2.734.9416.9
DistractFlowdiverged
✓(0.37)2.353.3712.42
✓(0.95)2.353.0111.71
+ +Table 7. Effects of using different unlabeled datasets in the semi-supervised training. Our DistractFlow enables consistent performance improvements when using any of the unlabeled datasets. + +
MethodUnlabeled data (# of pairs)Sintel (train)
(Final-epe)
RAFT [30]2.73
DistractFlowSintel-test (1.1k)2.35
Monkaa (17k) & Driving (9k)2.42
Big Buck Bunny (14k)2.58
+ +a model trained only with $\mathcal{L}_{\mathrm{dist}}$ still provides reasonable estimation performance, but shows worse accuracy as compared to the original model. Combining $\mathcal{L}_{\mathrm{base}}$ with $\mathcal{L}_{\mathrm{dist}}$ shows a significant improvement. + +Effectiveness of Confidence Map: Table 6 shows our study on the impacts of confidence-based thresholding in the semi-supervised training. When training the model without any confidence maps, erroneous predictions are used for backpropagation and training the network, causing the training to diverge. On the other hand, our confidence map allows the network to only train on highly accurate predictions and enables stability when training the model. + +When we set $\tau = 0.37$ (a common choice for forward-backward consistency), we can stably train the model and it shows improvement. Higher $\tau$ (e.g., 0.95) shows further accuracy improvement on KITTI. This may be due to the larger displacements in KITTI, which can make the model + +![](images/a5355a7d1d000a813e6d36df5dcada7a2336ac793e85676dccad840f34a200ee.jpg) + +![](images/dd5bb6f7b1b6f7cbc7b6cf791f9fadfdd43f3f5fb5f2ee79a8f8c5a5921d33f2.jpg) + +![](images/c4ba3c407c61e6ef5edca432eb2ccf6e58c84e559b6be88dd0c12524b48336e9.jpg) +Figure 5. Qualitative results on SlowFlow using the original RAFT and DistractFlow-trained RAFT models in supervised and semi-supervised model settings. We see that DistractFlow training enables the network to produce more accurate results, despite the severe motion blur. + +![](images/3b0d90fee5bacea388005847be093f2ef3703be8a50607d7b308f08b936c55a0.jpg) + +more prone to in accurate predictions. As such, creating pseudo labels with a higher confidence threshold is beneficial in this case. + +# 4.5. Qualitative Results + +Figure 4 shows qualitative results on the Sintel (train, final) using the original RAFT and FlowFormer, as well as our DistractFlow-trained RAFT and FlowFormer. These models are trained on FlyingChairs and FlyingThings3D. Because Sintel (final) contains visual effects such as fog and blur, the original models generate erroneous estimations. On the other hand, our DistractFlow-trained models show more accurate and robust flow estimation results. Especially, it shows accurate predictions at the object boundary without any edge- or segmentation-aware training [1,3]. + +Figure 5 shows qualitative results on SlowFlow using the original RAFT, as well as DistractFlow-trained RAFT models (supervised and semi-supervised). Our supervised training allows the model to generate more accurate and robust flows compared to the baseline RAFT. With our semi-supervised setting, our model shows further improvements. + +# 5. Discussion + +Unlabeled Dataset: Table 7 shows the results on Sintel (train) when using different unlabeled data in semi-supervised training. Sintel (test) shows significant improvement compared to supervised training since it is in the same domain as Sintel (train). Although Monkaa & Driving or Bunny dataset have more unlabeled pairs and can still improve upon the original RAFT, they exhibit worse performance than using Sintel (test) pairs. This indicates that for semi-supervised setting, it is important to use unlabeled + +![](images/01983531e01bcce3e7c2d066d245b4cff02ff51db7471f6564dafb5950859403.jpg) +Images + +![](images/6789cc4651c1d1a13c603a3424f202ac8fd5c29be47c8a93f7fea43b4ba26f89.jpg) +RAFT + +![](images/d6956111d7a855409e37c2ec2ee4f1f5986d3d8d3b8452ec35e5a99a7a1b5ce9.jpg) +DistractFlow + +![](images/1967203d9f1dab1049045f9a76a1de2bed59a1f4e092713671ddd23aef0b308e.jpg) + +![](images/b90a459f1a8578dcffa67ee201e97116594645090b437fd70359cc6bd939a87e.jpg) + +![](images/cc542818c60d97c3863afc9ff1eebb5436a8131dac27fa0bb0c5c41f089011ac.jpg) + +![](images/f611be49b5acbff220b02c7e92d9ab2b8ab263aced96c59587698a74fac9b2ee.jpg) + +![](images/25237df28bfb13a6eb2d3b12582988fe265ad90e2508743e21f9304f45ae9adf.jpg) + +![](images/0b0306458e7643e7246f4eba948ae8a282e55a52c137dceb11cba40fde778faf.jpg) + +![](images/afb48d245691bda2a6678a5da57ae5045e5b444aab1c6ca0141b325a5e2ab2ea.jpg) +Figure 6. Predictions on distracted video frame pairs. In the first column, the first row shows the overlaid original pair and the second to fourth rows show the distracted pairs. The mixing weight for the distractor increases from top to bottom. The RAFT model trained with DistractFlow performs robustly, while the original RAFT model completely fails when the distraction becomes large. + +![](images/a3e688ccac00fe140df449962fb87011a1cc67c49eb5a09bb1d79a4b2077f441.jpg) + +![](images/9dd03f817fa7c9552f7f8661d250ec1dfcbf6d7670fcb7de107a7fdfae33413e.jpg) + +data with scenes and distributions resembling the target use case. We leave data distribution robustness (e.g., addressing out-of-distribution samples [18, 19, 31] as part of future work. Nevertheless, our semi-supervised method improves the performance when using any of the unlabeled datasets. + +Robust Prediction: Figure 6 shows the predictions of RAFT and DistractFlow-RAFT (trained with FlyingChairs and FlyingThings3D) on distracted frames pairs, using mixing ratios of 1, 0.75, 0.5, and 0.25. When the original $I_{t+1}$ has a small portion of a distracted image, the original RAFT has degraded performance. It completely fails to find the correspondence for the red car when $\lambda = 0.25$ . In contrast, the model trained using DistractFlow still robustly finds the correspondence in the distracted image. + +# 6. Conclusion + +We proposed a novel method, DistractFlow, to augment optical flow training. We introduced realistic distractions to the video frame pairs which provided consistent improvements to optical flow estimation models. When unlabeled data was available, based on the original and distracted pairs, we devised a semi-supervised learning scheme using pseudo labels. We also incorporated forward-backward consistency through confidence maps that provided training stability and enhanced the performance further. Through extensive experiments on several optical flow estimation benchmarks: SlowFlow, Sintel, and KITTI, we showed that our method achieved significant improvements over the previous state of the art without inducing additional complexity during inference. In particular, models trained using our DistractFlow strategy are more robust in practical, challenging scenarios (e.g., consistent error reductions on SlowFlow despite strong motion blurs). + +# References + +[1] Shubhankar Borse, Ying Wang, Yizhe Zhang, and Fatih Porikli. Inverseform: A loss function for structured boundary-aware segmentation. 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In International Conference on Learning Representations, 2022. 8 +[32] Cihang Xie, Mingxing Tan, Boqing Gong, Jiang Wang, Alan L Yuille, and Quoc V Le. Adversarial examples improve image recognition. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 819-828, 2020. 2 +[33] Haofei Xu, Jiaolong Yang, Jianfei Cai, Juyong Zhang, and Xin Tong. High-resolution optical flow from 1d attention and correlation. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 10498-10507, 2021. 2 +[34] Sangdoo Yun, Dongyoon Han, Seong Joon Oh, Sanghyuk Chun, Junsuk Choe, and Youngjoon Yoo. Cutmix: Regularization strategy to train strong classifiers with localizable features. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 6023-6032, 2019. 2, 3 +[35] Feihu Zhang, Oliver J Woodford, Victor Adrian Prisacariu, and Philip HS Torr. Separable flow: Learning motion cost volumes for optical flow estimation. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 10807-10817, 2021. 2, 5 +[36] Hongyi Zhang, Moustapha Cisse, Yann N. Dauphin, and David Lopez-Paz. mixup: Beyond empirical risk minimiza + +tion. In International Conference on Learning Representations, 2018. 2, 3 +[37] Zhi Zhang, Tong He, Hang Zhang, Zhongyue Zhang, Jun-yuan Xie, and Mu Li. Bag of freebies for training object detection neural networks. arXiv preprint arXiv:1902.04103, 2019. 2 +[38] Shengyu Zhao, Yilun Sheng, Yue Dong, Eric I Chang, Yan Xu, et al. Maskflownet: Asymmetric feature matching with learnable occlusion mask. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 6278-6287, 2020. 2 +[39] Shiyu Zhao, Long Zhao, Zhixing Zhang, Enyu Zhou, and Dimitris Metaxas. Global matching with overlapping attention for optical flow estimation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 17592-17601, 2022. 2 \ No newline at end of file diff --git a/2023/DistractFlow_ Improving Optical Flow Estimation via Realistic Distractions and Pseudo-Labeling/images.zip b/2023/DistractFlow_ Improving Optical Flow Estimation via Realistic Distractions and Pseudo-Labeling/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..d1b8fd9b56582a58d0ccf61ec360f421592b9ca1 --- /dev/null +++ b/2023/DistractFlow_ Improving Optical Flow Estimation via Realistic Distractions and Pseudo-Labeling/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:cd00e0382af3c0fd90af438d437fc7902e77271e9d4a3cab4deb3c36fa231791 +size 647571 diff --git a/2023/DistractFlow_ Improving Optical Flow Estimation via Realistic Distractions and Pseudo-Labeling/layout.json b/2023/DistractFlow_ Improving Optical Flow Estimation via Realistic Distractions and Pseudo-Labeling/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..d6e49158280b0e2040f433dd2e871d3df8760bbd --- /dev/null +++ b/2023/DistractFlow_ Improving Optical Flow Estimation via Realistic Distractions and Pseudo-Labeling/layout.json @@ -0,0 +1,9302 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 131, + 86, + 463, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 131, + 86, + 463, + 121 + ], + "spans": [ + { + "bbox": [ + 131, + 86, + 463, + 121 + ], + "type": "text", + "content": "DistractFlow: Improving Optical Flow Estimation via Realistic Distractions and Pseudo-Labeling" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 144, + 144, + 436, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 144, + 144, + 436, + 175 + ], + "spans": [ + { + "bbox": [ + 144, + 144, + 436, + 175 + ], + "type": "text", + "content": "Jisoo Jeong Hong Cai Risheek Garrepalli Fatih Porikli Qualcomm AI Research†" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 177, + 446, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 177, + 446, + 190 + ], + "spans": [ + { + "bbox": [ + 143, + 177, + 446, + 190 + ], + "type": "text", + "content": "{jisojeon, hongcai, rgarrepα, fporikli}@qti.qualcomm.com" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 210, + 192, + 222 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 210, + 192, + 222 + ], + "spans": [ + { + "bbox": [ + 143, + 210, + 192, + 222 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 236, + 290, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 236, + 290, + 594 + ], + "spans": [ + { + "bbox": [ + 46, + 236, + 290, + 594 + ], + "type": "text", + "content": "We propose a novel data augmentation approach, DistractFlow, for training optical flow estimation models by introducing realistic distractions to the input frames. Based on a mixing ratio, we combine one of the frames in the pair with a distractor image depicting a similar domain, which allows for inducing visual perturbations congruent with natural objects and scenes. We refer to such pairs as distracted pairs. Our intuition is that using semantically meaningful distractors enables the model to learn related variations and attain robustness against challenging deviations, compared to conventional augmentation schemes focusing only on low-level aspects and modifications. More specifically, in addition to the supervised loss computed between the estimated flow for the original pair and its ground-truth flow, we include a second supervised loss defined between the distracted pair's flow and the original pair's ground-truth flow, weighted with the same mixing ratio. Furthermore, when unlabeled data is available, we extend our augmentation approach to self-supervised settings through pseudo-labeling and cross-consistency regularization. Given an original pair and its distracted version, we enforce the estimated flow on the distracted pair to agree with the flow of the original pair. Our approach allows increasing the number of available training pairs significantly without requiring additional annotations. It is agnostic to the model architecture and can be applied to training any optical flow estimation models. Our extensive evaluations on multiple benchmarks, including Sintel, KITTI, and SlowFlow, show that DistractFlow improves existing models consistently, outperforming the latest state of the art." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 617, + 128, + 629 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 617, + 128, + 629 + ], + "spans": [ + { + "bbox": [ + 47, + 617, + 128, + 629 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 635, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 635, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 635, + 287, + 696 + ], + "type": "text", + "content": "Recent years have seen significant progress in optical flow estimation thanks to the development of deep learning, e.g., [4,7,8,23]. Among the latest works, many focus on developing novel neural network architectures, such as PwC-Net [29], RAFT [30], and FlowFormer [6]. Other stud" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 308, + 209, + 541, + 407 + ], + "blocks": [ + { + "bbox": [ + 308, + 209, + 541, + 407 + ], + "lines": [ + { + "bbox": [ + 308, + 209, + 541, + 407 + ], + "spans": [ + { + "bbox": [ + 308, + 209, + 541, + 407 + ], + "type": "image", + "image_path": "84022b53e58956380e01a8e8baf182bac0eb32dc4a7eba004d634350475ab945.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 410, + 545, + 498 + ], + "lines": [ + { + "bbox": [ + 305, + 410, + 545, + 498 + ], + "spans": [ + { + "bbox": [ + 305, + 410, + 545, + 498 + ], + "type": "text", + "content": "Figure 1. Existing augmentation schemes apply low-level visual modifications, such as color jittering, block-wise random occlusion, and flipping, to augment the training data (top), while DistractFlow introduces high-level semantic perturbations to the frames (bottom). DistractFlow can further leverage unlabeled data to generate a self-supervised regularization. Our training leads to more accurate and robust optical flow estimation models, especially in challenging real-world settings." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 509, + 546, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 509, + 546, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 509, + 546, + 616 + ], + "type": "text", + "content": "ies investigate how to improve different aspects of supervised training [27], e.g., gradient clipping, learning rate, and training compute load. More related to our paper are those incorporating data augmentation during training (e.g., [30]), including color jittering, random occlusion, cropping, and flipping. While these image manipulations can effectively expand the training data and enhance the robustness of the neural models, they fixate on the low-level aspects of the images." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "text", + "content": "Since obtaining ground truth optical flow on real data is very challenging, another line of work investigates how to leverage unlabeled data. To this end, semi-supervised methods [9, 12] that utilize frame pairs with ground-truth flow annotations in conjunction with unlabeled data in training have been proposed. For instance, FlowSupervisor [9] adopts a teacher-student distillation approach to exploit unlabeled data. This method, however, does not consider lo" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 702, + 286, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 702, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 702, + 286, + 713 + ], + "type": "text", + "content": "† Qualcomm AI Research is an initiative of Qualcomm Technologies, Inc." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13691" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": "calized uncertainty but computes the loss for the entire image between the teacher and student network." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 96, + 289, + 395 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 96, + 289, + 395 + ], + "spans": [ + { + "bbox": [ + 46, + 96, + 289, + 395 + ], + "type": "text", + "content": "In this paper, we present a novel approach, DistractFlow, which performs semantically meaningful data augmentations by introducing images of real objects and natural scenes as distractors or perturbations to training frame pairs. More specifically, given a pair of consecutive frames, we combine the second frame with a random image depicting similar scenarios based on a mixing ratio. In this way, related objects and scenes are overlaid on top of the original second frame; see Figure 1 for an example. As a result, we obtain challenging yet appropriate distractions for the optical flow estimation model that seeks dense correspondences from the first frame to the second frame (and in reverse too). The original first frame and the composite second frame constitute a distracted pair of frames, which we use as an additional data sample in both supervised and self-supervised training settings. Unlike our approach, existing data augmentation schemes for optical flow training apply only low-level variations such as contrast changes, geometric manipulations, random blocks, haze, motion blur, and simple noise and shapes insertions [28, 30]. While such augmentations can still lead to performance improvements, they are disconnected from natural variations, scene context, and semantics. As we shall see in our experimental validation, the use of realistic distractions in training can provide a bigger boost to performance." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 396, + 289, + 610 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 396, + 289, + 610 + ], + "spans": [ + { + "bbox": [ + 46, + 396, + 289, + 610 + ], + "type": "text", + "content": "Figure 1 provides a high-level outline of DistractFlow. We apply DistractFlow in supervised learning settings using the ground-truth flow of the original pair. Distracted pairs contribute to the backpropagated loss proportional to the mixing ratios used in their construction. Additionally, when unlabeled frame pairs are available, DistractFlow allows us to impose a self-supervised regularization by further leveraging pseudo-labeling. Given an unlabeled pair of frames, we create a distracted version. Then, we enforce the estimated flow on the distracted pair to match that on the original pair. In other words, the prediction of the original pair is treated as a pseudo ground truth flow for the distracted pair. Since the estimation on the original pair can be erroneous, we further derive and impose a confidence map to employ only highly confident pixel-wise flow estimations as the pseudo ground truth. This prevents the model from reinforcing incorrect predictions, leading to a more stable training process." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 611, + 266, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 611, + 266, + 622 + ], + "spans": [ + { + "bbox": [ + 59, + 611, + 266, + 622 + ], + "type": "text", + "content": "In summary, our main contributions are as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 624, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 58, + 624, + 287, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 624, + 287, + 685 + ], + "spans": [ + { + "bbox": [ + 58, + 624, + 287, + 685 + ], + "type": "text", + "content": "- We introduce DistractFlow, a novel data augmentation approach that improves optical flow estimation by utilizing distractions from natural images. Our method provides augmentations with realistic semantic contents compared to existing augmentation schemes." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 58, + 689, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 689, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 58, + 689, + 288, + 714 + ], + "type": "text", + "content": "- We present a semi-supervised learning scheme for optical flow estimation that adopts the proposed dis" + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 324, + 72, + 545, + 119 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 72, + 545, + 119 + ], + "spans": [ + { + "bbox": [ + 324, + 72, + 545, + 119 + ], + "type": "text", + "content": "tracted pairs to leverage unlabeled data. We compute a confidence map to generate uncertainty-aware pseudo labels and to enhance training stability and overall performance." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 317, + 125, + 547, + 184 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 125, + 547, + 184 + ], + "spans": [ + { + "bbox": [ + 317, + 125, + 547, + 184 + ], + "type": "text", + "content": "- We demonstrate the effectiveness of DistractFlow in supervised [6, 14, 30] and semi-supervised settings, showing that DistractFlow outperforms the very recent FlowSupervisor [9] that require additional in-domain unlabeled data." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 194, + 392, + 206 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 194, + 392, + 206 + ], + "spans": [ + { + "bbox": [ + 306, + 194, + 392, + 206 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 211, + 545, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 211, + 545, + 342 + ], + "spans": [ + { + "bbox": [ + 304, + 211, + 545, + 342 + ], + "type": "text", + "content": "Optical Flow Estimation: Several deep architectures have been proposed for optical flow [4, 8, 23, 29, 30, 38]. Among these, Recurrent All Pairs Field Transforms (RAFT) [30] have shown significant performance improvement over previous methods, inspiring many subsequent works [6, 14, 26, 27, 35]. Following the structure of RAFT architecture, complementary studies [12, 14, 33, 35, 39] proposed advancements on feature extraction, 4D correlation volume, recurrent update blocks, and more recently, transformer extensions [6,39]. In DistractFlow, we introduce a new model-agnostic training method that can help any model." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 342, + 545, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 342, + 545, + 426 + ], + "spans": [ + { + "bbox": [ + 304, + 342, + 545, + 426 + ], + "type": "text", + "content": "Data Augmentation: Data augmentation is a widely used technique to better train deep learning models. Common augmentations include color and contrast jittering, flipping, geometric manipulation, and random noise. While they can improve the robustness of the model, these operations mainly focus on the low-level visual aspects and do not account for variations in the semantic contents." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 426, + 546, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 546, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 546, + 689 + ], + "type": "text", + "content": "Recently, several data augmentation schemes, such as adversarial perturbation and regularization methods, have been proposed for classification tasks. Adversarial perturbation [32] is one of the well-known augmentation methods for classification tasks, but recent work [24] shows that it does not work well for optical flow estimation. Interpolation-based Regularization (IR) [34, 36], which mixes a couple of images and trains the model with mixed label, improves the performance in classification tasks and is employed in other fields such as object detection [13, 37] and segmentation [10]. In a regression problem, however, mixed ground truth does not correspond with mixed input. Fixmatch [25] as a data augmentation scheme has demonstrated state-of-the-art performance in classification tasks. It combines pseudo-labeling and consistency regularization by applying two different augmentations (weak, strong) to the same image and generates pseudo-labels with weak augmentation output. For classification tasks, it is possible to create pseudo-labels since the output and ground-truth annotations represent class probabilities. However, there are no such class probabilities for optical flow. Thus, these methods cannot be readily applicable." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "AutoFlow [28] proposed a new dataset for optical flow, taking a versatile approach to data rendering, where motion," + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "13692" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 70, + 293, + 265 + ], + "blocks": [ + { + "bbox": [ + 61, + 70, + 293, + 265 + ], + "lines": [ + { + "bbox": [ + 61, + 70, + 293, + 265 + ], + "spans": [ + { + "bbox": [ + 61, + 70, + 293, + 265 + ], + "type": "image", + "image_path": "0dccf075568d9755a27092a17f3d575aef08e7802466301106fc6914d568bd63.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 266, + 547, + 289 + ], + "lines": [ + { + "bbox": [ + 46, + 266, + 547, + 289 + ], + "spans": [ + { + "bbox": [ + 46, + 266, + 547, + 289 + ], + "type": "text", + "content": "Figure 2. Left: Introducing realistic distractions in the supervised learning setting. Right: Semi-supervised learning leveraging distractions and pseudo-labeling." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 296, + 70, + 531, + 265 + ], + "blocks": [ + { + "bbox": [ + 296, + 70, + 531, + 265 + ], + "lines": [ + { + "bbox": [ + 296, + 70, + 531, + 265 + ], + "spans": [ + { + "bbox": [ + 296, + 70, + 531, + 265 + ], + "type": "image", + "image_path": "a113308527ae124dfbdda65784cc8399bf1736bdb6ea3bd12b821b9c192b03ac.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 300, + 287, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 300, + 287, + 419 + ], + "spans": [ + { + "bbox": [ + 46, + 300, + 287, + 419 + ], + "type": "text", + "content": "shape, and appearance are controlled via learnable hyperparameters. Though its performance gain is notable, AutoFlow employs synthetic augmentations. The work in [27] utilizes AutoFlow and argues that it is important to disentangle architecture and training pipeline. [27] also points out that some of the performance improvements of the recent methods are due to hyperparameters, dataset extensions, and training optimizations. Our work focuses on more capable augmentations for model agnostic training, not architecture novelties." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 423, + 288, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 423, + 288, + 638 + ], + "spans": [ + { + "bbox": [ + 46, + 423, + 288, + 638 + ], + "type": "text", + "content": "Semi-Supervised Learning: Semi-supervised optical flow learning methods [12, 17] aim to make the best use of unlabeled data as there is only a limited amount of optical flow ground truth data for real and natural scenes. And even in those datasets, the optical flow ground truths are computed. RAFT-OCTC [12] proposed transformation consistency for semi-supervised learning, which applies spatial transformations to image pairs and enforces flow equivariance between the original and transformed pairs. FlowSupervisor [9] introduced a teacher network for stable semisupervised fine-tuning. Its student model is trained for all pixels using teacher network output. In DistractFlow, we propose uncertainty-aware pseudo-labeling, which uses two different image pairs instead of different networks. We further employ forward-backward consistency to derive dense confidence scores, which steer the training process to impose loss only within high-consistency image regions to prevent feedback from incorrect flow estimates." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "type": "text", + "content": "Since acquiring optical flow ground truth for real videos is problematic (not possible for most cases), unsupervised training methods [15,21,26] seek out training models without ground truth flows. Even though they report promising results comparable to the earlier deep learning approaches, unsupervised training methods still entail limitations." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 299, + 388, + 312 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 299, + 388, + 312 + ], + "spans": [ + { + "bbox": [ + 305, + 299, + 388, + 312 + ], + "type": "text", + "content": "3. DistractFlow" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 317, + 545, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 317, + 545, + 425 + ], + "spans": [ + { + "bbox": [ + 304, + 317, + 545, + 425 + ], + "type": "text", + "content": "Our approach incorporates augmentation and supervision techniques to enhance the training of optical flow estimation models. In Section 3.1, we describe how we construct realistic distractions for optical flow training and how we employ them in supervised settings. Next, in Section 3.2, we extend our approach to semi-supervised learning with additional unlabeled data. We derive a self-supervised regularization objective by utilizing the distracted samples and pseudo-labeling." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 434, + 509, + 446 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 434, + 509, + 446 + ], + "spans": [ + { + "bbox": [ + 305, + 434, + 509, + 446 + ], + "type": "text", + "content": "3.1. Realistic Distractions as Augmentation" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 450, + 545, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 450, + 545, + 544 + ], + "spans": [ + { + "bbox": [ + 304, + 450, + 545, + 544 + ], + "type": "text", + "content": "Consider a pair of video frames during training: " + }, + { + "bbox": [ + 304, + 450, + 545, + 544 + ], + "type": "inline_equation", + "content": "(I_{t}, I_{t+1})" + }, + { + "bbox": [ + 304, + 450, + 545, + 544 + ], + "type": "text", + "content": ". The distracted version of them is denoted as " + }, + { + "bbox": [ + 304, + 450, + 545, + 544 + ], + "type": "inline_equation", + "content": "(I_{t}, D_{\\lambda}(I_{t+1}, \\tilde{I}_{d})" + }, + { + "bbox": [ + 304, + 450, + 545, + 544 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 450, + 545, + 544 + ], + "type": "inline_equation", + "content": "D_{\\lambda}(I_{t+1}, \\tilde{I}_{d})" + }, + { + "bbox": [ + 304, + 450, + 545, + 544 + ], + "type": "text", + "content": " is the perturbed second frame obtained by combing with another image " + }, + { + "bbox": [ + 304, + 450, + 545, + 544 + ], + "type": "inline_equation", + "content": "\\tilde{I}_{d}" + }, + { + "bbox": [ + 304, + 450, + 545, + 544 + ], + "type": "text", + "content": " based on a mixing ratio of " + }, + { + "bbox": [ + 304, + 450, + 545, + 544 + ], + "type": "inline_equation", + "content": "\\lambda \\in (0, 1)" + }, + { + "bbox": [ + 304, + 450, + 545, + 544 + ], + "type": "text", + "content": ". Specifically, " + }, + { + "bbox": [ + 304, + 450, + 545, + 544 + ], + "type": "inline_equation", + "content": "D_{\\lambda}(I_{t+1}, \\tilde{I}_{d})" + }, + { + "bbox": [ + 304, + 450, + 545, + 544 + ], + "type": "text", + "content": " is calculated as " + }, + { + "bbox": [ + 304, + 450, + 545, + 544 + ], + "type": "inline_equation", + "content": "\\lambda \\cdot I_{t+1} + (1 - \\lambda) \\cdot \\tilde{I}_{d}" + }, + { + "bbox": [ + 304, + 450, + 545, + 544 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 450, + 545, + 544 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 450, + 545, + 544 + ], + "type": "text", + "content": " is sampled from a Beta " + }, + { + "bbox": [ + 304, + 450, + 545, + 544 + ], + "type": "inline_equation", + "content": "(\\alpha, \\alpha)" + }, + { + "bbox": [ + 304, + 450, + 545, + 544 + ], + "type": "text", + "content": " distribution, same as defined in [34, 36]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "text", + "content": "Figure 2 shows an example of a distracted pair of video frames. It can be seen that the actual objects and the real scene from one image are overlaid onto the second one. Such perturbations can reflect challenging real-world scenarios, e.g., foreground/background objects that only start to appear in the second frame, drastic motion blur, out-of-focus artifacts, reflections on specular surfaces, partial occlusions, etc. Furthermore, since the distractions are from the same dataset, the visual context of the original pair and distractor image are similar. For instance, the original pair and distractor depict similar classes (road, car, building, etc.). The spatial arrangement of the class and object regions in those images are similar, e.g., roads are within the lower part of the images, and so do the sky, buildings, and" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13693" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 69, + 281, + 259 + ], + "blocks": [ + { + "bbox": [ + 52, + 69, + 281, + 259 + ], + "lines": [ + { + "bbox": [ + 52, + 69, + 281, + 259 + ], + "spans": [ + { + "bbox": [ + 52, + 69, + 281, + 259 + ], + "type": "image", + "image_path": "720c22f228b4ca3b05e64d8b9321e62e3bdff2144209713c2ad79e8b6930ccc9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 262, + 287, + 285 + ], + "lines": [ + { + "bbox": [ + 47, + 262, + 287, + 285 + ], + "spans": [ + { + "bbox": [ + 47, + 262, + 287, + 285 + ], + "type": "text", + "content": "Figure 3. Semi-supervised learning that leverages distractions and confidence-aware pseudo-labeling." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 293, + 287, + 377 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 293, + 287, + 377 + ], + "spans": [ + { + "bbox": [ + 46, + 293, + 287, + 377 + ], + "type": "text", + "content": "vehicles. While one may attempt to render such scenarios synthetically, our DistractFlow provides a convenient and automatic way that can still capture such natural and semantically related variations. Compared to conventional augmentation methods that use noise or simple shapes, our method allows the model to be more robust to perturbations caused by real-world image contents." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 378, + 287, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 378, + 287, + 426 + ], + "spans": [ + { + "bbox": [ + 46, + 378, + 287, + 426 + ], + "type": "text", + "content": "Additionally, we note that applying realistic distractions to the first or both frames is possible. As we shall see in the experiments, all of these options will result in improved accuracy." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 426, + 287, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 426, + 287, + 460 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 287, + 460 + ], + "type": "text", + "content": "To provide supervision on the distracted pair of frames, we use the ground-truth flow of the original pair. The loss is computed as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 76, + 464, + 287, + 483 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 76, + 464, + 287, + 483 + ], + "spans": [ + { + "bbox": [ + 76, + 464, + 287, + 483 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {d i s t}} = \\left\\| V _ {\\left(I _ {t}, I _ {t + 1}\\right)} ^ {f} - f \\left(I _ {t}, D _ {\\lambda} \\left(I _ {t + 1}, \\tilde {I} _ {d}\\right)\\right) \\right\\| _ {1}, \\tag {1}", + "image_path": "7de1abd8a66e23a46c9d80466ec4656220aded47cd474c35569f340d6a58526c.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 487, + 287, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 487, + 287, + 525 + ], + "spans": [ + { + "bbox": [ + 46, + 487, + 287, + 525 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 487, + 287, + 525 + ], + "type": "inline_equation", + "content": "V_{(I_t, I_{t+1})}^f" + }, + { + "bbox": [ + 46, + 487, + 287, + 525 + ], + "type": "text", + "content": " is the ground-truth forward flow for the original pair " + }, + { + "bbox": [ + 46, + 487, + 287, + 525 + ], + "type": "inline_equation", + "content": "(I_t, I_{t+1})" + }, + { + "bbox": [ + 46, + 487, + 287, + 525 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 487, + 287, + 525 + ], + "type": "inline_equation", + "content": "f(\\cdot, \\cdot)" + }, + { + "bbox": [ + 46, + 487, + 287, + 525 + ], + "type": "text", + "content": " denotes the predicted flow based on model " + }, + { + "bbox": [ + 46, + 487, + 287, + 525 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 487, + 287, + 525 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 525, + 287, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 525, + 287, + 559 + ], + "spans": [ + { + "bbox": [ + 46, + 525, + 287, + 559 + ], + "type": "text", + "content": "In the supervised learning setting, where all training samples are labeled, the total training loss is then given as follows:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 116, + 557, + 287, + 571 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 557, + 287, + 571 + ], + "spans": [ + { + "bbox": [ + 116, + 557, + 287, + 571 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\sup } = \\mathcal {L} _ {\\text {b a s e}} + w _ {\\text {d i s t}} \\mathcal {L} _ {\\text {d i s t}}, \\tag {2}", + "image_path": "508e12ca50ad292cd2133b3622c6c29b47adb9a0d7d268b3c3db7ab2712dc736.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 571, + 287, + 608 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 571, + 287, + 608 + ], + "spans": [ + { + "bbox": [ + 46, + 571, + 287, + 608 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 571, + 287, + 608 + ], + "type": "inline_equation", + "content": "L_{base}" + }, + { + "bbox": [ + 46, + 571, + 287, + 608 + ], + "type": "text", + "content": " is the conventional supervised loss and " + }, + { + "bbox": [ + 46, + 571, + 287, + 608 + ], + "type": "inline_equation", + "content": "w_{\\mathrm{dist}} > 0" + }, + { + "bbox": [ + 46, + 571, + 287, + 608 + ], + "type": "text", + "content": " weights " + }, + { + "bbox": [ + 46, + 571, + 287, + 608 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{dist}}" + }, + { + "bbox": [ + 46, + 571, + 287, + 608 + ], + "type": "text", + "content": ". For iterative models like RAFT, we compute and apply this loss at each recurrent iteration." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 613, + 287, + 639 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 613, + 287, + 639 + ], + "spans": [ + { + "bbox": [ + 47, + 613, + 287, + 639 + ], + "type": "text", + "content": "3.2. Semi-Supervised Learning via Realistic Distraction and Pseudo-Labeling" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 642, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 642, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 642, + 287, + 714 + ], + "type": "text", + "content": "During training, when unlabeled frame pairs are available, we can further leverage our distracted pairs of frames to derive additional self-supervised regularization. More specifically, given a distracted pair of frames, " + }, + { + "bbox": [ + 47, + 642, + 287, + 714 + ], + "type": "inline_equation", + "content": "(I_{t},D_{\\lambda}(I_{t + 1},\\tilde{I}_{d}))" + }, + { + "bbox": [ + 47, + 642, + 287, + 714 + ], + "type": "text", + "content": ", and the original pair, " + }, + { + "bbox": [ + 47, + 642, + 287, + 714 + ], + "type": "inline_equation", + "content": "(I_{t},I_{t + 1})" + }, + { + "bbox": [ + 47, + 642, + 287, + 714 + ], + "type": "text", + "content": ", we enforce the model's prediction on the distracted pair to match" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": "that on the original pair. In other words, the prediction on the original pair, " + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "f(I_{t}, I_{t+1})" + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": ", is treated as the pseudo label. By doing this, the model learns to produce optical flow estimation on the distracted pair that is consistent with that of the original pair, despite the distractions. Such regularization promotes the model's robustness when processing real-world data, as we show in our experiments." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 156, + 545, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 156, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 304, + 156, + 545, + 228 + ], + "type": "text", + "content": "We note that, however, using all of " + }, + { + "bbox": [ + 304, + 156, + 545, + 228 + ], + "type": "inline_equation", + "content": "f(I_{t}, I_{t+1})" + }, + { + "bbox": [ + 304, + 156, + 545, + 228 + ], + "type": "text", + "content": " as the training target for the distracted pair is problematic. This is because the model's prediction can be erroneous and noisy during the training process, even on the original frame pairs. The low-quality pseudo labels can be detrimental to the overall training, even leading to instability." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 228, + 545, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 228, + 545, + 323 + ], + "spans": [ + { + "bbox": [ + 304, + 228, + 545, + 323 + ], + "type": "text", + "content": "To address this issue, we adopt uncertainty-aware pseudo labels by calculating a confidence map based on forward backward consistency, and only using highly confident pixels' predictions as pseudo ground truth, as shown in Figure 3. On a frame pair " + }, + { + "bbox": [ + 304, + 228, + 545, + 323 + ], + "type": "inline_equation", + "content": "(I_t, I_{t+1})" + }, + { + "bbox": [ + 304, + 228, + 545, + 323 + ], + "type": "text", + "content": ", let " + }, + { + "bbox": [ + 304, + 228, + 545, + 323 + ], + "type": "inline_equation", + "content": "\\widehat{V}^f(x)" + }, + { + "bbox": [ + 304, + 228, + 545, + 323 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 228, + 545, + 323 + ], + "type": "inline_equation", + "content": "\\widehat{V}^b(x)" + }, + { + "bbox": [ + 304, + 228, + 545, + 323 + ], + "type": "text", + "content": " denote the predicted forward and backward flows at the pixel location " + }, + { + "bbox": [ + 304, + 228, + 545, + 323 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 228, + 545, + 323 + ], + "type": "text", + "content": ". When they satisfy the following constraint [21], we can assume that the prediction is accurate." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 332, + 329, + 545, + 369 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 332, + 329, + 545, + 369 + ], + "spans": [ + { + "bbox": [ + 332, + 329, + 545, + 369 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\left| \\widehat {V} ^ {f} (x) + \\widehat {V} ^ {b} \\left(x + \\widehat {V} ^ {f} (x)\\right) \\right| ^ {2} \\\\ < \\gamma_ {1} \\Big (| \\widehat {V} ^ {f} | ^ {2} + | \\widehat {V} ^ {b} (x + \\widehat {V} ^ {f} (x)) | ^ {2} \\Big) + \\gamma_ {2}, \\\\ \\end{array}", + "image_path": "efaf237841c2bd04b6fc186083410429b1dbeb9b245d47e91e41224734d4b761.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 374, + 470, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 374, + 470, + 386 + ], + "spans": [ + { + "bbox": [ + 306, + 374, + 470, + 386 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 374, + 470, + 386 + ], + "type": "inline_equation", + "content": "\\gamma_{1} = 0.01" + }, + { + "bbox": [ + 306, + 374, + 470, + 386 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 374, + 470, + 386 + ], + "type": "inline_equation", + "content": "\\gamma_{2} = 0.5" + }, + { + "bbox": [ + 306, + 374, + 470, + 386 + ], + "type": "text", + "content": " from [21]." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 317, + 387, + 522, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 387, + 522, + 399 + ], + "spans": [ + { + "bbox": [ + 317, + 387, + 522, + 399 + ], + "type": "text", + "content": "As such, we derive the confidence map as follows:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 405, + 545, + 452 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 405, + 545, + 452 + ], + "spans": [ + { + "bbox": [ + 306, + 405, + 545, + 452 + ], + "type": "interline_equation", + "content": "M _ {\\text {c o n f}} = \\exp \\left(- \\frac {\\left| \\widehat {V} ^ {f} (x) + \\widehat {V} ^ {b} \\left(x + \\widehat {V} ^ {f} (x)\\right) \\right| ^ {2}}{\\gamma_ {1} \\left(\\left| \\widehat {V} ^ {f} \\right| ^ {2} + \\left| \\widehat {V} ^ {b} \\left(x + \\widehat {V} ^ {f} (x)\\right) \\right| ^ {2}\\right) + \\gamma_ {2}}\\right). \\tag {4}", + "image_path": "6c8242663f2bc725924743e98d3a09871cc6523b5f9b7052ced4527ef8418f4a.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 452, + 545, + 523 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 452, + 545, + 523 + ], + "spans": [ + { + "bbox": [ + 304, + 452, + 545, + 523 + ], + "type": "text", + "content": "Our confidence map provides a measure of reliability of the predicted optical flow. Specifically, in Eq. 4, if the numerator and the denominator are equal, the confidence value is then approximately " + }, + { + "bbox": [ + 304, + 452, + 545, + 523 + ], + "type": "inline_equation", + "content": "0.37(e^{-1})" + }, + { + "bbox": [ + 304, + 452, + 545, + 523 + ], + "type": "text", + "content": ". In this paper, we use a very high threshold and it could provide a more accurate optical flow pseudo ground truth." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 523, + 545, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 523, + 545, + 548 + ], + "spans": [ + { + "bbox": [ + 304, + 523, + 545, + 548 + ], + "type": "text", + "content": "By incorporating the confidence map, our self-supervised regularization is then given as follows:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 554, + 547, + 579 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 554, + 547, + 579 + ], + "spans": [ + { + "bbox": [ + 306, + 554, + 547, + 579 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {s e l f}} = \\left\\| \\left[ M _ {\\text {c o n f}} \\geq \\tau \\right] \\left(f \\left(I _ {t}, I _ {t + 1}\\right) - f \\left(I _ {t}, D _ {\\lambda} \\left(I _ {t + 1}, \\tilde {I} _ {d}\\right)\\right)\\right) \\right\\| _ {1}, \\tag {5}", + "image_path": "3df4ba43eb6271debe982fd70528a8134e36fd5e4ef4f9f03190adcec2bf89d2.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 580, + 545, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 580, + 545, + 602 + ], + "spans": [ + { + "bbox": [ + 304, + 580, + 545, + 602 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 580, + 545, + 602 + ], + "type": "inline_equation", + "content": "[\\cdot ]" + }, + { + "bbox": [ + 304, + 580, + 545, + 602 + ], + "type": "text", + "content": " is the Iverson bracket and " + }, + { + "bbox": [ + 304, + 580, + 545, + 602 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 580, + 545, + 602 + ], + "type": "text", + "content": " is the confidence threshold." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 604, + 545, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 604, + 545, + 639 + ], + "spans": [ + { + "bbox": [ + 304, + 604, + 545, + 639 + ], + "type": "text", + "content": "In summary, in the semi-supervised learning setting, where labeled and unlabeled data are both used in training, the total loss is as follows:" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 374, + 645, + 545, + 658 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 374, + 645, + 545, + 658 + ], + "spans": [ + { + "bbox": [ + 374, + 645, + 545, + 658 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {\\sup } + w _ {\\text {s e l f}} \\mathcal {L} _ {\\text {s e l f}}, \\tag {6}", + "image_path": "02811c6c9ec050c17b7d19f15c2bf27a9b26963d91e219c3fffefcd343f185f8.jpg" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 662, + 545, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 662, + 545, + 687 + ], + "spans": [ + { + 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+ "content": "." + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "text", + "content": "1By " + }, + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "inline_equation", + "content": "[M_{\\mathrm{conf}} \\geq \\tau]" + }, + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "text", + "content": ", we note that the Iverson bracket is applied pixel-wise to produce a binary confidence map." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13694" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 61, + 105, + 531, + 277 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 103 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 103 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 103 + ], + "type": "text", + "content": "Table 1. Optical flow estimation results on SlowFlow, Sintel (train), and KITTI (train) datasets. We train the models on FlyingChairs (C) and FlyingThings (T) in the supervised setting. In the semi-supervised setting, we finetune the model on FlyingThings (T) as labeled data and Sintel (test) and KITTI (test) (S/K) as unlabeled data. * indicates test results of existing models generated by us." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 61, + 105, + 531, + 277 + ], + "lines": [ + { + "bbox": [ + 61, + 105, + 531, + 277 + ], + "spans": [ + { + "bbox": [ + 61, + 105, + 531, + 277 + ], + "type": "table", + "html": "
MethodModelLabeled dataUnlabeled dataSlowFlow (100px)Sintel (train)KITTI (train)
1357(Final-epe)(Fl-epe)(Fl-all)
SupervisedSupervised DistractFlow (Our)RAFT [30]C+T3.737.986.729.962.73*4.94*16.9*
3.373.936.218.182.614.5716.4
Supervise DistractFlow (Our)GMA [14]2.494.995.959.152.85*4.88*17.1*
2.533.495.438.242.664.7616.9
Supervised DistractFlow (Our)FlowFormer [6]2.723.735.246.782.39*4.10*14.7*
2.512.774.396.302.314.0013.9
Semi-SupervisedSupervised RAFT-A [28]RAFT [30]C + TT (subsampled)3.737.986.729.962.73*4.94*16.9*
AutoFlow [28]----2.574.23-
RAFT-OCTC [12]----2.674.7216.3
Fixed Teacher [9]C + TS/K----2.584.9115.9
FlowSupervisor [9]S/K----2.463.3511.1
DistractFlow (Our)S/K2.463.605.156.952.353.0111.7
Supervised DistractFlow (Our)GMA [14]S/K2.494.995.959.152.85*4.88*17.1*
2.442.794.386.572.313.2111.0
Supervised DistractFlow (Our)FlowFormer [6]S/K2.723.735.246.782.39*4.29*15.4*
2.482.694.316.292.333.0311.8
", + "image_path": "1fe9fa90221a3eaebf976d55e60358224bc1bd6f8e148c12242e96bb992eeefd.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 286, + 128, + 300 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 286, + 128, + 300 + ], + "spans": [ + { + "bbox": [ + 47, + 286, + 128, + 300 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 304, + 288, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 304, + 288, + 389 + ], + "spans": [ + { + "bbox": [ + 46, + 304, + 288, + 389 + ], + "type": "text", + "content": "In this section (and in the supplementary), we present a comprehensive evaluation of DistractFlow on several benchmark datasets, compare it with baselines and the latest state-of-the-art (SOTA) methods, and conduct extensive ablation studies. We focus our evaluations on realistic or real-world data, including SlowFlow, Sintel (final), and KITTI; we provide results on Sintel (clean) in the Supplementary." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 396, + 164, + 410 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 396, + 164, + 410 + ], + "spans": [ + { + "bbox": [ + 47, + 396, + 164, + 410 + ], + "type": "text", + "content": "4.1. Experimental Setup" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 413, + 287, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 413, + 287, + 484 + ], + "spans": [ + { + "bbox": [ + 46, + 413, + 287, + 484 + ], + "type": "text", + "content": "Evaluation Settings: We consider two settings for running the experiments. In the first setting, we consider a supervised learning setting where the network is trained on fully labeled data. The second setting considers semi-supervised learning, where unlabeled data can be used during training, in addition to labeled training data." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 485, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 485, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 485, + 287, + 544 + ], + "type": "text", + "content": "Evaluation Metrics: We use the common evaluation metrics for optical flow estimation, including End-Point Error (EPE) and Fl-all, which is the percentage of optical flow with EPE larger than 3 pixels or over " + }, + { + "bbox": [ + 46, + 485, + 287, + 544 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 46, + 485, + 287, + 544 + ], + "type": "text", + "content": " of the ground truth. The goal is to lower both of these metrics." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 545, + 287, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 287, + 676 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 287, + 676 + ], + "type": "text", + "content": "Datasets: Following commonly adopted evaluation protocols in the literature [6, 14, 30, 35], we train our model on FlyingChairs (C) [4] and FlyingThings3D (T) [20] for supervised training when evaluating on SlowFlow [11] (100px flow magnitude) dataset and the training splits of Sintel (S) [2] and KITTI (K) [5, 22]. In particular, on SlowFlow, we use 4 blur durations with a larger duration having larger motion blurs. When we evaluate on Sintel test set, we use FlyingThings3D, Sintel training set, KITTI training set, and HD1K (H) [16] for supervised training. And, we finetune on KITTI training dataset for evaluation on KITTI test set." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "type": "text", + "content": "For the additional unlabeled data used during training, we followed the same setting from [9]. We use FlyingThings as labeled dataset and Sintel test set as unlabeled" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 287, + 545, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 287, + 545, + 431 + ], + "spans": [ + { + "bbox": [ + 304, + 287, + 545, + 431 + ], + "type": "text", + "content": "dataset for evaluating on Sintel and SlowFlow, and the video frames from KITTI test raw sequences for evaluating on KITTI training dataset. When we evaluate on Sintel and KITTI test sets, we use the labeled dataset from supervised training settings, and use additional KITTI train raw sequences, Sintel training data (only using every other frame), Monkaa (M) [20], and Driving (D) [20] as the unlabeled datasets. Note that we do not use Sintel and KITTI test sets as unlabeled datasets for Sintel and KITTI test evaluation. We further experiment with utilizing unlabeled open-source Blender videos as additional unsupervised training data, such as Sintel and Big Buck Bunny." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 432, + 546, + 576 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 432, + 546, + 576 + ], + "spans": [ + { + "bbox": [ + 304, + 432, + 546, + 576 + ], + "type": "text", + "content": "Networks and Training: We use RAFT [30], GMA [14], FlowFormer [6] as our baselines, and utilize their official codes. For objectiveness, we train all the baselines in the same framework and reported the results we obtained. We set " + }, + { + "bbox": [ + 304, + 432, + 546, + 576 + ], + "type": "inline_equation", + "content": "(w_{dist}, w_{self})" + }, + { + "bbox": [ + 304, + 432, + 546, + 576 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 432, + 546, + 576 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 432, + 546, + 576 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 432, + 546, + 576 + ], + "type": "inline_equation", + "content": "(\\lambda" + }, + { + "bbox": [ + 304, + 432, + 546, + 576 + ], + "type": "text", + "content": " (mixing ratio), 1) and 0.95, respectively. For supervised training, we follow RAFT and GMA learning parameters such as optimizer, number of GRU iterations, training iterations, and so on. For semi-supervised training, we use labeled and unlabeled data with a 1:1 ratio. For FlowFormer, we reduce the total batch size and only finetune it due to GPU memory overflow. All settings and training details are provided in the Supplementary." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 585, + 545, + 610 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 585, + 545, + 610 + ], + "spans": [ + { + "bbox": [ + 305, + 585, + 545, + 610 + ], + "type": "text", + "content": "4.2. Evaluations on SlowFlow, Sintel (train), and KITTI (train)" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 613, + 545, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 613, + 545, + 674 + ], + "spans": [ + { + "bbox": [ + 304, + 613, + 545, + 674 + ], + "type": "text", + "content": "Supervised Setting: Table 1 shows the performance evaluation of the supervised and semi-supervised training results on SlowFlow, Sintel (train), and KITTI (train). In the top section of Table 1, we provide results of existing supervised models and our models trained using DistractFlow" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 683, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 683, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 683, + 545, + 713 + ], + "type": "text", + "content": "2RAFT: https://github.com/princeton-vl/RAFT, GMA: https://github.com/zacjiang/GMA, FlowFormer: https://github.com/drinkingcoder/FlowFormer-Official" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13695" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 55, + 182, + 277, + 296 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 289, + 180 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 289, + 180 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 289, + 180 + ], + "type": "text", + "content": "Table 2. Optical flow estimation results on Sintel (test) and KITTI (test) datasets. We train the models on FlyingChairs (C), FlyingThings (T), Sintel (S), KITTI (K), and HD1K (H) in the supervised setting. When using the semi-supervised setting/using additional data for training, RAFT-A trains on " + }, + { + "bbox": [ + 46, + 70, + 289, + 180 + ], + "type": "inline_equation", + "content": "\\mathrm{A + S + K + H + T}" + }, + { + "bbox": [ + 46, + 70, + 289, + 180 + ], + "type": "text", + "content": " datasets where A stands for AutoFlow, FlowSupervisor trains on " + }, + { + "bbox": [ + 46, + 70, + 289, + 180 + ], + "type": "inline_equation", + "content": "\\mathrm{C + T + S + K + H}" + }, + { + "bbox": [ + 46, + 70, + 289, + 180 + ], + "type": "text", + "content": " (labeled) and uses Sintel, KITTI, and Spring as unlabeled datasets. In our case, we use " + }, + { + "bbox": [ + 46, + 70, + 289, + 180 + ], + "type": "inline_equation", + "content": "\\mathrm{C + T + S + K + H}" + }, + { + "bbox": [ + 46, + 70, + 289, + 180 + ], + "type": "text", + "content": " as labeled data and Sintel, KITTI, and Sceneflow (Monkaa, Driving) as unlabeled data. * indicates results obtained using warm-start [30]." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 55, + 182, + 277, + 296 + ], + "lines": [ + { + "bbox": [ + 55, + 182, + 277, + 296 + ], + "spans": [ + { + "bbox": [ + 55, + 182, + 277, + 296 + ], + "type": "table", + "html": "
MethodModelSintel (test)KITTI (test)
(Final-epe)(Fl-all)
Supervised
SupervisedRAFT [30]2.86*5.10
DistractFlow (Our)2.77*4.82
Semi-Supervised / Additional dataset
SupervisedRAFT-A [28]2.86*5.10
3.144.78
RAFT-OCTC [12]RAFT [30]3.094.72
FlowSupervisor [9]2.79*4.85
DistractFlow (Our)2.71*4.71
", + "image_path": "0bcde9c31ef863a352cc11939084b39980291941d0d09cb73a88046ffb293fd4.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 305, + 287, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 305, + 287, + 388 + ], + "spans": [ + { + "bbox": [ + 46, + 305, + 287, + 388 + ], + "type": "text", + "content": "supervised augmentation. Our supervised models trained on FlyingChairs and FlyingThings3D show significant improvements across the test datasets for all the architectures. For SlowFlow with a 3-frame blur duration, the existing RAFT model shows very large errors (over 100 EPE) on a few samples. DistractFlow, on the other hand, leads to more robust results and a much smaller EPE." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 389, + 288, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 389, + 288, + 568 + ], + "spans": [ + { + "bbox": [ + 46, + 389, + 288, + 568 + ], + "type": "text", + "content": "Semi-Supervised Setting: In this part, we evaluate our proposed approach when additional unlabeled data becomes available. In the bottom section of Table 1, we show results of the previous semi-supervised learning methods and our proposed method. Following FlowSupervisor, we finetune each model on FlyingThings (labeled) and Sintel test (unlabeled), and evaluate on the SlowFlow and Sintel train dataset. For evaluation on KITTI train dataset, we finetune the pre-trained models (from Sintel unlabeled) on FlyingThings (labeled) and raw KITTI test (unlabeled). We can see that DistractFlow (RAFT) shows better performance as compared to RAFT-OCTC, RAFT-A, FixTeacher, and FlowSupervisor. Furthermore, we apply our semi-supervised approach to GMA and FlowFormer, and DistractFlow improves their performance." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 577, + 277, + 590 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 577, + 277, + 590 + ], + "spans": [ + { + "bbox": [ + 47, + 577, + 277, + 590 + ], + "type": "text", + "content": "4.3. Evaluations on Sintel (test) and KITTI (test)" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 594, + 287, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 700 + ], + "type": "text", + "content": "Supervised Setting: The top section of Table 2 summarizes the supervised and semi-supervised training results on Sintel (test) and KITTI (test) datasets. From the first part of Table 2, we can see that our proposed DistractFlow permits significant improvements over the baseline RAFT model. It is noteworthy that without using additional unlabeled data, our model trained under the supervised setting already outperforms the semi-supervised FlowSupervisor, which leverages additional data." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 59, + 701, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 287, + 714 + ], + "type": "text", + "content": "Semi-Supervised Setting: In the second part of Ta-" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 309, + 93, + 545, + 153 + ], + "blocks": [ + { + "bbox": [ + 305, + 70, + 545, + 92 + ], + "lines": [ + { + "bbox": [ + 305, + 70, + 545, + 92 + ], + "spans": [ + { + "bbox": [ + 305, + 70, + 545, + 92 + ], + "type": "text", + "content": "Table 3. Effects of different types of perturbations applied to the frames, as data augmentation during training." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 93, + 545, + 153 + ], + "lines": [ + { + "bbox": [ + 309, + 93, + 545, + 153 + ], + "spans": [ + { + "bbox": [ + 309, + 93, + 545, + 153 + ], + "type": "table", + "html": "
MethodPerturbationSintel (train)KITTI (train)
(Final-epe)(Fl-epe)(Fl-all)
RAFT [30]2.734.9416.9
OurGaussian noise2.684.8617.6
Random shapes2.664.8216.8
Realistic Distractions2.614.5716.4
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MethodDistractionα1α2Sintel (train)KITTI (train)
(Final-epe)(Fl-epe)(Fl-all)
RAFT [30]2.734.9416.9
DistractFlowOn It0.12.694.8116.4
12.645.2517.6
102.555.3217.8
On It+10.12.654.6616.3
12.614.5716.4
102.704.8217.2
On It & It+1 (same)0.112.705.3318.3
On It & It+1 (diff)0.112.644.9216.7
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In addition, our method also considerably outperforms FlowSupervisor." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 442, + 406, + 453 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 442, + 406, + 453 + ], + "spans": [ + { + "bbox": [ + 306, + 442, + 406, + 453 + ], + "type": "text", + "content": "4.4. Ablation Studies" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 459, + 545, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 459, + 545, + 554 + ], + "spans": [ + { + "bbox": [ + 304, + 459, + 545, + 554 + ], + "type": "text", + "content": "We conduct extensive ablation studies on various aspects of our method, by using RAFT as the base model. In the supervised setting, we train on FlyingChairs (C) and FlyingThings3D (T). In the semi-supervised setting, we take the RAFT model pretrained from the supervised setting and then finetune it using FlyingThings3D (labeled) and Sintel (test)/KITTI (test) (unlabeled). The evaluation is done on Sintel (train) and KITTI (train)." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 556, + 545, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 556, + 545, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 556, + 545, + 676 + ], + "type": "text", + "content": "Type of Perturbations: When applying visual perturbations, we compare using realistic distractions in Distract-Flow with using synthetic noise such as Gaussian noise and random shapes. For generating random shapes, we make random background colors and add 5 to 10 shapes (e.g., circles, triangles, and rectangles) of random colors and sizes. 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Qualitative results on Sintel (train) using RAFT, FlowFormer, DistractFlow-RAFT, and DistractFlow-FlowFormer (the last two are empowered with our proposed method). All models are trained on FlyingChairs and FlyingThings3D. It can be seen that DistractFlow can generate more accurate predictions, with better spatial consistency and finer details, as highlighted by circles." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 173, + 192, + 294, + 244 + ], + "blocks": [ + { + "bbox": [ + 173, + 192, + 294, + 244 + ], + "lines": [ + { + "bbox": [ + 173, + 192, + 294, + 244 + ], + "spans": [ + { + "bbox": [ + 173, + 192, + 294, + 244 + ], + "type": "image", + "image_path": "3fce0f9c6325fa65aab0afb0055923c06b73492a3de0971264f16b7866646435.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 295, + 192, + 416, + 244 + ], + "blocks": [ + { + "bbox": [ + 295, + 192, + 416, + 244 + ], + "lines": [ + { + "bbox": [ + 295, + 192, + 416, + 244 + ], + "spans": [ + { + "bbox": [ + 295, + 192, + 416, + 244 + ], + "type": "image", + "image_path": "df414442ad6ba68d546d238116d82d7d693a1d2fcf838dd16cbd0f32068a7b65.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 417, + 192, + 539, + 244 + ], + "blocks": [ + { + "bbox": [ + 417, + 192, + 539, + 244 + ], + "lines": [ + { + "bbox": [ + 417, + 192, + 539, + 244 + ], + "spans": [ + { + "bbox": [ + 417, + 192, + 539, + 244 + ], + "type": "image", + "image_path": "f4e35eee6aa17a8b4a531718657e2c6bd698c1c5152bf2ad498b741f27dcef25.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 56, + 301, + 278, + 353 + ], + "blocks": [ + { + "bbox": [ + 110, + 289, + 223, + 300 + ], + "lines": [ + { + "bbox": [ + 110, + 289, + 223, + 300 + ], + "spans": [ + { + "bbox": [ + 110, + 289, + 223, + 300 + ], + "type": "text", + "content": "Table 5. Effectiveness of " + }, + { + "bbox": [ + 110, + 289, + 223, + 300 + ], + "type": "inline_equation", + "content": "{L}_{dist}" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 301, + 278, + 353 + ], + "lines": [ + { + "bbox": [ + 56, + 301, + 278, + 353 + ], + "spans": [ + { + "bbox": [ + 56, + 301, + 278, + 353 + ], + "type": "table", + "html": "
Method\\( \\mathcal{L}_{base} \\)\\( \\mathcal{L}_{dist} \\)Sintel (train)KITTI (train)
(Final-epe)(Fl-epe)(Fl-all)
RAFT [30]✓2.734.9416.9
DistractFlow✓2.825.4319.0
✓✓2.614.5716.4
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However, when " + }, + { + "bbox": [ + 46, + 363, + 287, + 458 + ], + "type": "inline_equation", + "content": "\\alpha_{1}" + }, + { + "bbox": [ + 46, + 363, + 287, + 458 + ], + "type": "text", + "content": "s are 1 or 10, the performance drops on KITTI compared to RAFT. We suspect that the Sintel (final) dataset has a heavy visual effect even in " + }, + { + "bbox": [ + 46, + 363, + 287, + 458 + ], + "type": "inline_equation", + "content": "I_{t}" + }, + { + "bbox": [ + 46, + 363, + 287, + 458 + ], + "type": "text", + "content": ", and using strongly distracted " + }, + { + "bbox": [ + 46, + 363, + 287, + 458 + ], + "type": "inline_equation", + "content": "I_{t}" + }, + { + "bbox": [ + 46, + 363, + 287, + 458 + ], + "type": "text", + "content": " could help the training." + }, + { + "bbox": [ + 46, + 363, + 287, + 458 + ], + "type": "inline_equation", + "content": "^4" + }, + { + "bbox": [ + 46, + 363, + 287, + 458 + ], + "type": "text", + "content": " On the other hand, since KITTI has relatively cleaner images, strongly distracted " + }, + { + "bbox": [ + 46, + 363, + 287, + 458 + ], + "type": "inline_equation", + "content": "I_{t}" + }, + { + "bbox": [ + 46, + 363, + 287, + 458 + ], + "type": "text", + "content": " does not improve the performance." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 460, + 287, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 460, + 287, + 519 + ], + "spans": [ + { + "bbox": [ + 46, + 460, + 287, + 519 + ], + "type": "text", + "content": "In the middle of Table 4, we distract " + }, + { + "bbox": [ + 46, + 460, + 287, + 519 + ], + "type": "inline_equation", + "content": "I_{t+1}" + }, + { + "bbox": [ + 46, + 460, + 287, + 519 + ], + "type": "text", + "content": " according to the different " + }, + { + "bbox": [ + 46, + 460, + 287, + 519 + ], + "type": "inline_equation", + "content": "\\alpha_2" + }, + { + "bbox": [ + 46, + 460, + 287, + 519 + ], + "type": "text", + "content": " values and train the model. In most of these cases DistractFlow improves upon the baseline RAFT, and it shows the best performance at " + }, + { + "bbox": [ + 46, + 460, + 287, + 519 + ], + "type": "inline_equation", + "content": "\\alpha_2 = 1" + }, + { + "bbox": [ + 46, + 460, + 287, + 519 + ], + "type": "text", + "content": ". This result shows that various mixing of the images is helpful." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 46, + 520, + 287, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 520, + 287, + 639 + ], + "spans": [ + { + "bbox": [ + 46, + 520, + 287, + 639 + ], + "type": "text", + "content": "At the bottom of Table 4, we distract " + }, + { + "bbox": [ + 46, + 520, + 287, + 639 + ], + "type": "inline_equation", + "content": "I_{t}" + }, + { + "bbox": [ + 46, + 520, + 287, + 639 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 520, + 287, + 639 + ], + "type": "inline_equation", + "content": "I_{t+1}" + }, + { + "bbox": [ + 46, + 520, + 287, + 639 + ], + "type": "text", + "content": " simultaneously. When we apply the same distraction to both frames, two consecutive videos, it degrades the performance. This is because applying the same distraction to both frame introduces new correspondences which are not part of the ground truth. On the other hand, when we apply distractions from two different images to " + }, + { + "bbox": [ + 46, + 520, + 287, + 639 + ], + "type": "inline_equation", + "content": "I_{t}" + }, + { + "bbox": [ + 46, + 520, + 287, + 639 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 520, + 287, + 639 + ], + "type": "inline_equation", + "content": "I_{t+1}" + }, + { + "bbox": [ + 46, + 520, + 287, + 639 + ], + "type": "text", + "content": ", the trained model shows better performance compared to baseline RAF. Overall, distracting " + }, + { + "bbox": [ + 46, + 520, + 287, + 639 + ], + "type": "inline_equation", + "content": "I_{t+1}" + }, + { + "bbox": [ + 46, + 520, + 287, + 639 + ], + "type": "text", + "content": " shows the best performance and we carry out experiments with this setting." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 47, + 640, + 287, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 640, + 287, + 665 + ], + "spans": [ + { + "bbox": [ + 47, + 640, + 287, + 665 + ], + "type": "text", + "content": "Effectiveness of " + }, + { + "bbox": [ + 47, + 640, + 287, + 665 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{dist}}" + }, + { + "bbox": [ + 47, + 640, + 287, + 665 + ], + "type": "text", + "content": ": Table 5 shows the effectiveness of " + }, + { + "bbox": [ + 47, + 640, + 287, + 665 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{dist}}" + }, + { + "bbox": [ + 47, + 640, + 287, + 665 + ], + "type": "text", + "content": ". Without the supervised loss on the original pairs," + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 289, + 545, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 289, + 545, + 334 + ], + "spans": [ + { + "bbox": [ + 306, + 289, + 545, + 334 + ], + "type": "text", + "content": "Table 6. Effectiveness of confidence map and " + }, + { + "bbox": [ + 306, + 289, + 545, + 334 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 306, + 289, + 545, + 334 + ], + "type": "text", + "content": " weight for " + }, + { + "bbox": [ + 306, + 289, + 545, + 334 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{self}}" + }, + { + "bbox": [ + 306, + 289, + 545, + 334 + ], + "type": "text", + "content": " in semi-supervised setting. " + }, + { + "bbox": [ + 306, + 289, + 545, + 334 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 306, + 289, + 545, + 334 + ], + "type": "text", + "content": " is the confidence threshold in Eq. 5 and in " + }, + { + "bbox": [ + 306, + 289, + 545, + 334 + ], + "type": "inline_equation", + "content": "w_{\\mathrm{self}}" + }, + { + "bbox": [ + 306, + 289, + 545, + 334 + ], + "type": "text", + "content": " is the weight for the self-supervised loss. Note that 0.37 corresponds to having equal nominator and denominator in Eq. 3." + } + ] + } + ], + "index": 19 + }, + { + "type": "table", + "bbox": [ + 323, + 335, + 529, + 396 + ], + "blocks": [ + { + "bbox": [ + 323, + 335, + 529, + 396 + ], + "lines": [ + { + "bbox": [ + 323, + 335, + 529, + 396 + ], + "spans": [ + { + "bbox": [ + 323, + 335, + 529, + 396 + ], + "type": "table", + "html": "
MethodτSintel (train)KITTI (train)
(Final-epe)(Fl-epe)(Fl-all)
RAFT [30]2.734.9416.9
DistractFlowdiverged
✓(0.37)2.353.3712.42
✓(0.95)2.353.0111.71
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MethodUnlabeled data (# of pairs)Sintel (train)
(Final-epe)
RAFT [30]2.73
DistractFlowSintel-test (1.1k)2.35
Monkaa (17k) & Driving (9k)2.42
Big Buck Bunny (14k)2.58
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Combining " + }, + { + "bbox": [ + 304, + 509, + 545, + 556 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{base}}" + }, + { + "bbox": [ + 304, + 509, + 545, + 556 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 509, + 545, + 556 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{dist}}" + }, + { + "bbox": [ + 304, + 509, + 545, + 556 + ], + "type": "text", + "content": " shows a significant improvement." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 557, + 545, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 545, + 652 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 545, + 652 + ], + "type": "text", + "content": "Effectiveness of Confidence Map: Table 6 shows our study on the impacts of confidence-based thresholding in the semi-supervised training. When training the model without any confidence maps, erroneous predictions are used for backpropagation and training the network, causing the training to diverge. On the other hand, our confidence map allows the network to only train on highly accurate predictions and enables stability when training the model." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 653, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 712 + ], + "type": "text", + "content": "When we set " + }, + { + "bbox": [ + 304, + 653, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\tau = 0.37" + }, + { + "bbox": [ + 304, + 653, + 545, + 712 + ], + "type": "text", + "content": " (a common choice for forward-backward consistency), we can stably train the model and it shows improvement. Higher " + }, + { + "bbox": [ + 304, + 653, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 653, + 545, + 712 + ], + "type": "text", + "content": " (e.g., 0.95) shows further accuracy improvement on KITTI. This may be due to the larger displacements in KITTI, which can make the model" + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 46, + 673, + 286, + 693 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 673, + 286, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 673, + 286, + 693 + ], + "type": "text", + "content": "3When " + }, + { + "bbox": [ + 46, + 673, + 286, + 693 + ], + "type": "inline_equation", + "content": "\\alpha < 1" + }, + { + "bbox": [ + 46, + 673, + 286, + 693 + ], + "type": "text", + "content": ", sampled " + }, + { + "bbox": [ + 46, + 673, + 286, + 693 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 673, + 286, + 693 + ], + "type": "text", + "content": " is close to 0 or 1. When " + }, + { + "bbox": [ + 46, + 673, + 286, + 693 + ], + "type": "inline_equation", + "content": "\\alpha > 1" + }, + { + "bbox": [ + 46, + 673, + 286, + 693 + ], + "type": "text", + "content": ", sampled " + }, + { + "bbox": [ + 46, + 673, + 286, + 693 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 673, + 286, + 693 + ], + "type": "text", + "content": " is close to 0.5. When " + }, + { + "bbox": [ + 46, + 673, + 286, + 693 + ], + "type": "inline_equation", + "content": "\\alpha = 1" + }, + { + "bbox": [ + 46, + 673, + 286, + 693 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 673, + 286, + 693 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 673, + 286, + 693 + ], + "type": "text", + "content": " is sampled from a uniform distribution." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 47, + 693, + 286, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 286, + 712 + ], + "type": "text", + "content": "4Since we set " + }, + { + "bbox": [ + 47, + 693, + 286, + 712 + ], + "type": "inline_equation", + "content": "w_{dist} = \\lambda" + }, + { + "bbox": [ + 47, + 693, + 286, + 712 + ], + "type": "text", + "content": ", when " + }, + { + "bbox": [ + 47, + 693, + 286, + 712 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 47, + 693, + 286, + 712 + ], + "type": "text", + "content": " is close to zero, the distracted pair only impacts the training minimally." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13697" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 70, + 167, + 161 + ], + "blocks": [ + { + "bbox": [ + 53, + 70, + 167, + 161 + ], + "lines": [ + { + "bbox": [ + 53, + 70, + 167, + 161 + ], + "spans": [ + { + "bbox": [ + 53, + 70, + 167, + 161 + ], + "type": "image", + "image_path": "a5355a7d1d000a813e6d36df5dcada7a2336ac793e85676dccad840f34a200ee.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 168, + 70, + 280, + 161 + ], + "blocks": [ + { + "bbox": [ + 168, + 70, + 280, + 161 + ], + "lines": [ + { + "bbox": [ + 168, + 70, + 280, + 161 + ], + "spans": [ + { + "bbox": [ + 168, + 70, + 280, + 161 + ], + "type": "image", + "image_path": "dd5bb6f7b1b6f7cbc7b6cf791f9fadfdd43f3f5fb5f2ee79a8f8c5a5921d33f2.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 53, + 163, + 167, + 253 + ], + "blocks": [ + { + "bbox": [ + 53, + 163, + 167, + 253 + ], + "lines": [ + { + "bbox": [ + 53, + 163, + 167, + 253 + ], + "spans": [ + { + "bbox": [ + 53, + 163, + 167, + 253 + ], + "type": "image", + "image_path": "c4ba3c407c61e6ef5edca432eb2ccf6e58c84e559b6be88dd0c12524b48336e9.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 255, + 287, + 309 + ], + "lines": [ + { + "bbox": [ + 46, + 255, + 287, + 309 + ], + "spans": [ + { + "bbox": [ + 46, + 255, + 287, + 309 + ], + "type": "text", + "content": "Figure 5. Qualitative results on SlowFlow using the original RAFT and DistractFlow-trained RAFT models in supervised and semi-supervised model settings. We see that DistractFlow training enables the network to produce more accurate results, despite the severe motion blur." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 168, + 163, + 280, + 253 + ], + "blocks": [ + { + "bbox": [ + 168, + 163, + 280, + 253 + ], + "lines": [ + { + "bbox": [ + 168, + 163, + 280, + 253 + ], + "spans": [ + { + "bbox": [ + 168, + 163, + 280, + 253 + ], + "type": "image", + "image_path": "3b0d90fee5bacea388005847be093f2ef3703be8a50607d7b308f08b936c55a0.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 323, + 287, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 323, + 287, + 357 + ], + "spans": [ + { + "bbox": [ + 46, + 323, + 287, + 357 + ], + "type": "text", + "content": "more prone to in accurate predictions. As such, creating pseudo labels with a higher confidence threshold is beneficial in this case." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 367, + 159, + 380 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 367, + 159, + 380 + ], + "spans": [ + { + "bbox": [ + 47, + 367, + 159, + 380 + ], + "type": "text", + "content": "4.5. Qualitative Results" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 384, + 287, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 384, + 287, + 503 + ], + "spans": [ + { + "bbox": [ + 46, + 384, + 287, + 503 + ], + "type": "text", + "content": "Figure 4 shows qualitative results on the Sintel (train, final) using the original RAFT and FlowFormer, as well as our DistractFlow-trained RAFT and FlowFormer. These models are trained on FlyingChairs and FlyingThings3D. Because Sintel (final) contains visual effects such as fog and blur, the original models generate erroneous estimations. On the other hand, our DistractFlow-trained models show more accurate and robust flow estimation results. Especially, it shows accurate predictions at the object boundary without any edge- or segmentation-aware training [1,3]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 504, + 287, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 504, + 287, + 575 + ], + "spans": [ + { + "bbox": [ + 46, + 504, + 287, + 575 + ], + "type": "text", + "content": "Figure 5 shows qualitative results on SlowFlow using the original RAFT, as well as DistractFlow-trained RAFT models (supervised and semi-supervised). Our supervised training allows the model to generate more accurate and robust flows compared to the baseline RAFT. With our semi-supervised setting, our model shows further improvements." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 587, + 117, + 600 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 587, + 117, + 600 + ], + "spans": [ + { + "bbox": [ + 47, + 587, + 117, + 600 + ], + "type": "text", + "content": "5. Discussion" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": "Unlabeled Dataset: Table 7 shows the results on Sintel (train) when using different unlabeled data in semi-supervised training. Sintel (test) shows significant improvement compared to supervised training since it is in the same domain as Sintel (train). Although Monkaa & Driving or Bunny dataset have more unlabeled pairs and can still improve upon the original RAFT, they exhibit worse performance than using Sintel (test) pairs. This indicates that for semi-supervised setting, it is important to use unlabeled" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 310, + 82, + 385, + 115 + ], + "blocks": [ + { + "bbox": [ + 335, + 71, + 362, + 81 + ], + "lines": [ + { + "bbox": [ + 335, + 71, + 362, + 81 + ], + "spans": [ + { + "bbox": [ + 335, + 71, + 362, + 81 + ], + "type": "text", + "content": "Images" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 310, + 82, + 385, + 115 + ], + "lines": [ + { + "bbox": [ + 310, + 82, + 385, + 115 + ], + "spans": [ + { + "bbox": [ + 310, + 82, + 385, + 115 + ], + "type": "image", + "image_path": "01983531e01bcce3e7c2d066d245b4cff02ff51db7471f6564dafb5950859403.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 386, + 82, + 462, + 115 + ], + "blocks": [ + { + "bbox": [ + 417, + 71, + 441, + 80 + ], + "lines": [ + { + 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"index": 22, + "angle": 0, + "type": "image_body" + } + ], + "index": 22 + }, + { + "type": "image", + "bbox": [ + 310, + 191, + 385, + 225 + ], + "blocks": [ + { + "bbox": [ + 310, + 191, + 385, + 225 + ], + "lines": [ + { + "bbox": [ + 310, + 191, + 385, + 225 + ], + "spans": [ + { + "bbox": [ + 310, + 191, + 385, + 225 + ], + "type": "image", + "image_path": "afb48d245691bda2a6678a5da57ae5045e5b444aab1c6ca0141b325a5e2ab2ea.jpg" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 228, + 545, + 295 + ], + "lines": [ + { + "bbox": [ + 305, + 228, + 545, + 295 + ], + "spans": [ + { + "bbox": [ + 305, + 228, + 545, + 295 + ], + "type": "text", + "content": "Figure 6. Predictions on distracted video frame pairs. In the first column, the first row shows the overlaid original pair and the second to fourth rows show the distracted pairs. The mixing weight for the distractor increases from top to bottom. The RAFT model trained with DistractFlow performs robustly, while the original RAFT model completely fails when the distraction becomes large." + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "image_caption" + } + ], + "index": 23 + }, + { + "type": "image", + "bbox": [ + 386, + 191, + 462, + 225 + ], + "blocks": [ + { + "bbox": [ + 386, + 191, + 462, + 225 + ], + "lines": [ + { + "bbox": [ + 386, + 191, + 462, + 225 + ], + "spans": [ + { + "bbox": [ + 386, + 191, + 462, + 225 + ], + "type": "image", + "image_path": "a3e688ccac00fe140df449962fb87011a1cc67c49eb5a09bb1d79a4b2077f441.jpg" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_body" + } + ], + "index": 24 + }, + { + "type": "image", + "bbox": [ + 463, + 191, + 539, + 225 + ], + "blocks": [ + { + "bbox": [ + 463, + 191, + 539, + 225 + ], + "lines": [ + { + "bbox": [ + 463, + 191, + 539, + 225 + ], + "spans": [ + { + "bbox": [ + 463, + 191, + 539, + 225 + ], + "type": "image", + "image_path": "9dd03f817fa7c9552f7f8661d250ec1dfcbf6d7670fcb7de107a7fdfae33413e.jpg" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_body" + } + ], + "index": 25 + }, + { + "bbox": [ + 304, + 310, + 545, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 310, + 545, + 369 + ], + "spans": [ + { + "bbox": [ + 304, + 310, + 545, + 369 + ], + "type": "text", + "content": "data with scenes and distributions resembling the target use case. We leave data distribution robustness (e.g., addressing out-of-distribution samples [18, 19, 31] as part of future work. Nevertheless, our semi-supervised method improves the performance when using any of the unlabeled datasets." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 304, + 370, + 545, + 478 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 370, + 545, + 478 + ], + "spans": [ + { + "bbox": [ + 304, + 370, + 545, + 478 + ], + "type": "text", + "content": "Robust Prediction: Figure 6 shows the predictions of RAFT and DistractFlow-RAFT (trained with FlyingChairs and FlyingThings3D) on distracted frames pairs, using mixing ratios of 1, 0.75, 0.5, and 0.25. When the original " + }, + { + "bbox": [ + 304, + 370, + 545, + 478 + ], + "type": "inline_equation", + "content": "I_{t+1}" + }, + { + "bbox": [ + 304, + 370, + 545, + 478 + ], + "type": "text", + "content": " has a small portion of a distracted image, the original RAFT has degraded performance. It completely fails to find the correspondence for the red car when " + }, + { + "bbox": [ + 304, + 370, + 545, + 478 + ], + "type": "inline_equation", + "content": "\\lambda = 0.25" + }, + { + "bbox": [ + 304, + 370, + 545, + 478 + ], + "type": "text", + "content": ". In contrast, the model trained using DistractFlow still robustly finds the correspondence in the distracted image." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 306, + 488, + 378, + 501 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 488, + 378, + 501 + ], + "spans": [ + { + "bbox": [ + 306, + 488, + 378, + 501 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 304, + 506, + 545, + 709 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 506, + 545, + 709 + ], + "spans": [ + { + "bbox": [ + 304, + 506, + 545, + 709 + ], + "type": "text", + "content": "We proposed a novel method, DistractFlow, to augment optical flow training. We introduced realistic distractions to the video frame pairs which provided consistent improvements to optical flow estimation models. When unlabeled data was available, based on the original and distracted pairs, we devised a semi-supervised learning scheme using pseudo labels. We also incorporated forward-backward consistency through confidence maps that provided training stability and enhanced the performance further. Through extensive experiments on several optical flow estimation benchmarks: SlowFlow, Sintel, and KITTI, we showed that our method achieved significant improvements over the previous state of the art without inducing additional complexity during inference. In particular, models trained using our DistractFlow strategy are more robust in practical, challenging scenarios (e.g., consistent error reductions on SlowFlow despite strong motion blurs)." + } + ] + } + ], + "index": 30 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13698" + } + ] + } + ], + "index": 31 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "text", + "content": "[1] Shubhankar Borse, Ying Wang, Yizhe Zhang, and Fatih Porikli. 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Transformed OoD samples from PACS dataset. Odd rows show the original OoD images, and even rows show their transformation results to the source distribution, obtained by the proposed DSI. Please zoom in for better visualization." + ], + "image_footnote": [], + "bbox": [ + 91, + 243, + 877, + 348 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 398, + 313, + 415 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Machine learning society has witnessed the emergence of a myriad of Out-of-Distribution (OoD) algorithms, which address the distribution shift between the training and the testing distribution by searching for a unified predictor or invariant feature representation. However, the task of directly mitigating the distribution shift in the unseen testing set is rarely investigated, due to the unavailability of the testing distribution during the training phase and thus the impossibility of training a distribution translator mapping between the training and testing distribution. In this paper, we explore how to bypass the requirement of testing distribution for distribution translator training and make the distribution translation useful for OoD prediction. We propose a portable Distribution Shift Inversion (DSI) algorithm, in which, before being fed into the prediction model, the OoD testing samples are first linearly combined with additional Gaussian noise and then transferred back towards the training distribution using a diffusion model trained only on the source distribution. Theoretical analysis reveals the feasibility of our method. Experimental results, on both multiple-domain generalization datasets and single-domain generalization datasets, show that our method provides a general performance gain when plugged into a wide range of commonly used OoD algorithms. Our code is available at https://github.com/yu-rp/Distribution-Shift-Iverson.", + "bbox": [ + 75, + 419, + 473, + 797 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 824, + 209, + 839 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The ubiquity of the distribution shift between the training and testing data in the real-world application of machine", + "bbox": [ + 76, + 848, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "learning systems induces the study of Out-of-Distribution (OoD) generalization (or domain generalization). [18, 64, 71, 79] Within the scope of OoD generalization, machine learning algorithms are required to generalize from the seen training domain to the unseen testing domain without the independent and identically distributed assumption. The bulk of the OoD algorithms in previous literature focuses on promoting the generalization capability of the machine learning models themselves by utilizing the domain invariant feature [2, 13, 36], context-based data augmentation [47, 74], distributionally robust optimization [59], subnetwork searching [81], neural network calibration [70], etc.", + "bbox": [ + 500, + 401, + 893, + 582 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this work, orthogonal to enhancing the generalization capability of the model, we consider a novel pathway to OoD prediction. On the way, the testing(target) distribution is explicitly transformed towards the training.source) distribution to straightforwardly mitigate the distribution shift between the testing and the training distribution. Therein, the OoD prediction can be regarded as a two-step procedure, (1) transferring testing samples back towards training distribution, and (2) drawing prediction. The second step can be implemented by any OoD prediction algorithm. In this paper, we concentrate on the exploration of the first step, the distribution transformation.", + "bbox": [ + 496, + 583, + 895, + 763 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Unlike previous works on distribution translation and domain transformation, in which certain target distribution is accessible during the training phase, here the target distribution is arbitrary and unavailable during the training. We term this new task as Unseen Distribution Transformation (UDT), in which a domain translator is trained on the source distribution and works to transform unseen target distribution towards the source distribution. The uniqueness, as well as the superiority, of UDT is listed as followings.", + "bbox": [ + 496, + 763, + 895, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 1, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding author.", + "bbox": [ + 94, + 886, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "3592", + "bbox": [ + 482, + 944, + 514, + 957 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d3b3409097f1042a2e129adde8fa4f1fc40f31f3937c1441e9f7dc59bd6ef724.jpg", + "image_caption": [ + "Figure 2. Using a Diffusion Model to solve the one-dimensional UDT. OoD samples are transformed to the source distribution with limited failure of label preservation." + ], + "image_footnote": [], + "bbox": [ + 78, + 88, + 467, + 246 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- UDT puts no requirements on the data from both source and testing distribution like previous works do. This is practically valuable, because the real-world testing distributions are uncountable and dynamically changing.", + "- UDT is able to transform various distributions using only one model. However, the previous distribution translator works for the translation between certain source and target distributions. With a different source-target pair, a new translator is required.", + "- Considering the application of UDT in OoD prediction, it is free from the extra assumptions commonly used by the OoD generalization algorithms, such as the multi-training domain assumption and the various forms of the domain invariant assumption." + ], + "bbox": [ + 96, + 305, + 468, + 521 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Despite the advantages, the unavailability of the testing distribution poses new difficulty. Releasing this constraint, the idea of distribution alignment is well established in domain adaptation (DA). Wherein, a distribution translator is trained with the (pixel, feature, and semantic level) cycle consistency loss [23, 38, 82]. However, the training of such distribution transfer modules necessitates the testing distribution, which is unsuitable under the setting of OoD prediction and makes the transplant of the methods in DA to OoD even impossible.", + "bbox": [ + 75, + 522, + 468, + 672 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To circumvent the requirement of testing distribution during training time, we propose a novel method, named Distribution Shift Inversion (DSI). Instead of using a model transferring from testing distribution to training distribution, an unconditional generative model, trained only on the source distribution, is used, which transfers data from a reference noise distribution to the source distribution. The method operates in two successive parts. First, the OoD target distribution is transferred to the neighborhood of the noise distribution and aligned with the input of the generative model, thereafter we refer to this process as the forward transformation. The crux of this step is designing to what degree the target distribution is aligned to the noise distribution. In our implementation, the forward transformation is conducted by linearly combining the OoD samples and random noise with", + "bbox": [ + 75, + 674, + 470, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "the weights controlling the alignment. Then, in the second step, the outcome of the first step is transferred towards the source distribution by a generative model, thereafter we refer to this process as the backward transformation. In this paper, the generative model is chosen to be the diffusion model [21]. The superiority of the diffusion model is that its input is the linear combination of the source sample and the noise with varying magnitude, which is in accord with our design of the forward transformation and naturally allows strength control. Comparatively, VAE [28] and GAN [16] have a fixed level of noise in their input, which makes the forward transformation strength control indirect. Our theoretical analyses of the diffusion model also show the feasibility of using the diffusion model for UDT.", + "bbox": [ + 496, + 90, + 893, + 301 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Illustrative Example. A one-dimensional example is shown in Fig. 2. The example considers a binary classification problem, in which, given label, the conditional distributions of the samples are Gaussian in both the source and the testing domain. The testing distribution is constructed to be OoD and located in the region where the source distribution has a low density. The diffusion model is trained only on the source distribution. Passing through the noise space alignment and diffusion model transformation, the OoD samples are transformed to the source distribution with limited failure of label preservation.", + "bbox": [ + 496, + 305, + 893, + 470 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Transformed Images. Fig. 1 shows some transformation results of OoD images towards the source distribution. The observation is twofold. (1) The distribution (here is the style) of the images is successfully transformed. All of the transferred images can be correctly classified by the ERM model trained on the source domain. (2) The transformed images are correlated to the original images. Some structural and color characteristics are mutually shared between them. This indicates that the diffusion model has extracted some low-level information and is capable to preserve it during the transformation. We would like to highlight again that, during the training, the diffusion model is isolated from the testing domain.", + "bbox": [ + 496, + 474, + 893, + 672 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions are therefore summarized as:", + "bbox": [ + 517, + 675, + 831, + 689 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We put forward the unseen distribution transformation (UDT) and study its application to OoD prediction.", + "- We offer theoretical analyses of the feasibility of UDT.", + "- we propose DSI, a sample adaptive distribution transformation algorithm for efficient distribution adaptation and semantic information preservation.", + "- We perform extensive experiments to demonstrate that our method is suitable for various OoD algorithms to achieve performance gain on diversified OoD benchmarks. On average, adding in our method produces $2.26\\%$ accuracy gain on multi-training domain generalization datasets and $2.28\\%$ on single-training domain generalization datasets." + ], + "bbox": [ + 517, + 694, + 893, + 897 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "3593", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 80, + 89, + 217, + 104 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.1. Out-of-Distribution Generalization", + "text_level": 1, + "bbox": [ + 80, + 114, + 379, + 130 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To achieve OoD generalization, diverse methods have been proposed.", + "bbox": [ + 80, + 138, + 467, + 169 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Causal inference methods extract the invariant feature among training domains and build up a unified predictor for all domains. For example, CNBB [19] down-weights the samples which introduce big changes to the feature space by evaluating the causal effect of each sample; ICP [51] find the subset of features satisfying the property that the conditional probability of the target given this set of features is invariant among the domains; IRM [2] regularizes the ERM loss with the norm of the gradient of loss corresponding to the latent features; IB-IRM [1] extends the IRM to the case, where the invariant features are only partially informative, by adding an extra entropy loss term of the latent feature.", + "bbox": [ + 80, + 171, + 467, + 351 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Context-based data augmentation methods enrich the training feature space by linear interpolation between the features of inter-domain and intra-domain samples [74]; or combining the normalized feature of one sample with the mean and variance of the feature of another sample [47].", + "bbox": [ + 80, + 353, + 467, + 428 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Distributional Robust Optimization method, like Group-DRO [59], theoretically formulates the OoD generalization as a min-max optimization and practically up-weights the domains with large losses in an online learning style to guarantee the model fit on all domains.", + "bbox": [ + 80, + 429, + 467, + 503 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Feature alignment methods learn a unified feature representation among all training domains with the assumption that this representation is shared by the testing domain data. For example, DANN [13] and CDANN [36] align the marginal and conditional feature distribution by domain adversarial training, respectively; CORAL [67] matches the covariance of the features in every training domain; MASF [11] proposes model-agnostic episodic learning to regularize the semantic structure of the feature space; using the contrastive learning as the regularization term, SelfReg [27] minimizes the distance between the features of the samples within the sample class; CAD and ConCAD [58] minimize the mutual information between the feature and domain variable as well as the negative mutual information between the feature of original samples and the feature of augmented samples.", + "bbox": [ + 80, + 506, + 467, + 732 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Context feature separation methods recognize the context feature by an extra context discriminator and disentangle them from the category feature by orthogonality penalty [4].", + "bbox": [ + 80, + 734, + 467, + 777 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Gradient manipulation methods are designed based on the intuitions that (1) to train a unified predictor, only the gradient common across all domains should be used; or the intuition that (2) the spurious correlation, which leads to larger gradients, is easier to be fitted to and prevent the algorithm from learning other features. For example, IGA [30] and SD [52] penalize the variance of the gradients and the $l_{2}$ norm of the logits, respectively; RSC [25] only takes", + "bbox": [ + 80, + 780, + 467, + 898 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "the samples whose gradients are small into consideration; MLDG [34] updates the parameters only when there are performance gains in two separated parts of the training dataset; ANDMask [50] and its ReLU-smoothed version SANDMask [63] only update the parameter whose gradients in most of the domains have the same sign.", + "bbox": [ + 503, + 90, + 890, + 181 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Different from the previous works, DSI tackles the OoD generalization problem by test time sample adaption. Instead of increasing the OoD generalization ability of the model, DSI aims to mitigate the distribution shift of the testing samples by shifting them back towards the source distribution. Though input enhancing is investigated in dataset distillation [39] and domain adaptation [23, 38, 82], we are the first to test this idea in OoD generalization. Besides its novelty, DSI is orthogonal to the previous algorithms, which allows it to be portably used as a common technique for OoD tasks.", + "bbox": [ + 503, + 181, + 890, + 332 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Diffusion Model", + "text_level": 1, + "bbox": [ + 503, + 343, + 658, + 358 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Neural network reuse has drawn recent interest [75-78]. In this work, we consider reusing pre-trained diffusion models. With promising performance and theoretical explanation, the diffusion model has been intensively investigated in the field of time series generalization/imputation/prediction [29, 32, 56, 68], image generalization/editing/inpainting [3, 6-8, 41, 44, 54, 61], text generalization/modeling [35, 80], text2image generalization [17, 48, 55, 60], text2speech generalization [53], video generalization [22], graph generalization [24, 73], 3D point cloud generalization [42, 43, 83]. Besides, these generation tasks, diffusion model conduces to the downstream tasks such as image segmenting [5], testing time sample adaptation for corrupted images [14], and adversarial attack defense [49]. In DSI, we explore a new application of the diffusion model in which it enhances the OoD prediction by transferring the OoD samples towards the source distribution.", + "bbox": [ + 503, + 367, + 890, + 622 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Prediction Confidence Estimation", + "text_level": 1, + "bbox": [ + 503, + 633, + 790, + 648 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In DSI, the prediction confidence score is used for selecting poorly predicted samples and achieving an adaptive distribution shift inversion at the sample level. By satisfying the partial order relationship of uncertainty, commonly used loss functions, such as softmax cross entropy, are suitable confidence metrics. [31] Other softmax-based scores, such as the maximum class probability [15, 20], true class probability [10] and the KL-divergence between the softmax distribution and the uniform distribution [20] are also widely used. Based on the Bayesian method, Monte Carlo dropout [12], use the standard uncertainty criteria (e.g., variance, entropy) of the stochastic network predictions as the confidence score. Taking a modified nearest-neighbor classifier as the reference, trust score [26] uses a minimal distance ratio as the confidence score. We note that measurements in the field of OoD detection [37,40,46,57,62] and sample", + "bbox": [ + 503, + 659, + 890, + 898 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "3594", + "bbox": [ + 483, + 946, + 513, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "difficulty estimation may also serve as proper filtering metrics for DSI. But, in this paper, we prefer to establish a new OoD prediction framework and leave the discovery of the potential filtering metrics as future work.", + "bbox": [ + 75, + 90, + 470, + 151 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3. Preliminary", + "text_level": 1, + "bbox": [ + 76, + 165, + 202, + 181 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The task of sampling an instance $\\pmb{x}$ of a random variable $\\pmb{X} \\in \\mathcal{R}^d$ with distribution $p(\\pmb{x})$ is generally intractable due to the fact that $p(\\pmb{x})$ is complex or unknown. Diffusion model, such as ScoreFlow [66] and DDPM [21], first samples from an simple distribution $\\rho(\\pmb{x})$ and then iteratively transforms sample $\\pmb{x}$ to make its distribution consistent with $p(\\pmb{x})$ .", + "bbox": [ + 75, + 190, + 468, + 295 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Under the continuous time setting, diffusion model formulates the forward transformation from $p(\\pmb{x})$ to $\\rho(\\pmb{x})$ as a stochastic process $\\{x_t\\}_{t=0}^T$ following the Stochastic Differential Equation (SDE)", + "bbox": [ + 75, + 296, + 470, + 356 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nd \\boldsymbol {x} = f (\\boldsymbol {x}, t) d t + g (t) d \\boldsymbol {w}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 368, + 468, + 383 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $f(\\cdot, t): \\mathcal{R}^d \\to \\mathcal{R}^d$ is named drift coefficient, $g(t) \\in \\mathcal{R}$ is named diffusion coefficient, and $\\pmb{w}$ is the Wiener process whose derivative $d\\pmb{w}$ is characterized by a standard Gaussian random variable (white Gaussian noise). The corresponding marginal distribution $p_t(\\pmb{x})$ at time $t$ satisfies $p_0(\\pmb{x}) = p(\\pmb{x})$ and $p_T(\\pmb{x}) \\approx \\rho(\\pmb{x})$ . To sample from $p(\\pmb{x})$ , the diffusion model first samples from $\\rho(\\pmb{x})$ and then transforms $\\pmb{x}$ backward according to the inverse SDE associated with Eq. (1)", + "bbox": [ + 75, + 396, + 470, + 532 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nd \\boldsymbol {x} = [ f (\\boldsymbol {x}, t) - g ^ {2} (t) \\nabla_ {\\boldsymbol {x}} \\log p _ {t} (\\boldsymbol {x}) ] d t + g (t) d \\bar {\\boldsymbol {w}}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 542, + 468, + 560 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $dt$ is the negative time flow, evolving from $t = T$ to $t = 0$ , and $\\bar{w}$ is the Wiener process in the inverse time direction whose derivative $d\\bar{w}$ is again a standard Gaussian random variable because of the Gaussian increment characterization of Wiener process. In Eq. (2), $\\nabla_{\\pmb{x}}\\log p_t(\\pmb {x})$ is the unknown score function of $\\pmb{x}$ at time $t$ , which is estimated by a neural network $s_{\\theta}(\\pmb {x},t)$ with the weighted score matching loss", + "bbox": [ + 75, + 571, + 468, + 691 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {J} _ {S M} (\\boldsymbol {\\theta}; \\lambda (\\cdot)) \\\\ = \\frac {1}{2} \\int_ {0} ^ {T} \\mathbb {E} _ {p _ {t} (\\boldsymbol {x})} [ \\lambda (t) | | \\nabla_ {\\boldsymbol {x}} \\log p _ {t} (\\boldsymbol {x}) - s _ {\\boldsymbol {\\theta}} (\\boldsymbol {x}, t) | | _ {2} ^ {2} ] d t. \\tag {3} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 88, + 704, + 468, + 772 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Unseen Distribution Transformation", + "text_level": 1, + "bbox": [ + 76, + 784, + 405, + 800 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "First, we motivate our method by analyzing why the diffusion model helps promote the OoD generalization.", + "bbox": [ + 76, + 809, + 470, + 840 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here, we proof that, by feeding a linear combination of the OoD samples and the standard Gaussian noise to a diffusion model, the OoD samples can be transformed to the ID samples.", + "bbox": [ + 75, + 840, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Theorem 1. Given a diffusion model trained on the source distribution $p(x)$ , let $p_t$ denote the distribution at time $t$ in the forward transformation, let $\\bar{p}(x)$ denote the output distribution when the input of the backward process is standard Gaussian noise $\\epsilon$ whose distribution is denoted by $\\rho(x)$ , let $\\omega(x)$ denote the output distribution when the input of backward process is a convex combination $(1 - \\alpha)X' + \\alpha\\epsilon$ , where random variable $X'$ is sampled following the target distribution $q(x)$ and $\\alpha \\in (0,1)$ . Under some regularity conditions detailed in Appendix, we have", + "bbox": [ + 496, + 90, + 893, + 242 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nK L (p \\mid \\mid \\omega) \\leqslant \\mathcal {J} _ {S M} + K L (p _ {T} \\mid \\mid \\rho) + \\mathcal {F} (\\alpha) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 555, + 252, + 890, + 268 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Theorem 1 proves that the testing distribution can be transformed to the source distribution and the convergence is controlled by $\\alpha$ . The first terms in the inequality are introduced by the pretrained diffusion model. The loss term $\\mathcal{I}_{SM}$ is small after sufficient training and can be reduced if the training procedure is further optimized. The KL-divergence term $KL(p_{T}||\\rho)$ indicates the distance between the real distribution achieved by the forward transformation and the manually chosen standard Gaussian distribution, which is monotonically decreasing as the $T$ goes larger and converges to 0 as the $T$ is sufficient large. The third term (detailed in Appendix) is introduced by the distribution of the OOD testing samples, which is controlled by $\\alpha$ and converges to 0 as $\\alpha$ goes to 1.", + "bbox": [ + 496, + 279, + 893, + 491 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Implementation", + "text_level": 1, + "bbox": [ + 500, + 500, + 658, + 515 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this part, we describe DSI to realize the idea of shifting testing image towards the training distribution to boost the OoD generalization. The entire workflow is illustrated in Fig. 3.", + "bbox": [ + 496, + 523, + 890, + 582 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the previous analysis, by constructing a linear combination of the OoD input and the noise, the alignment between the testing and the training distributions is converted to an alignment problem in the noise space. To be consistent with the diffusion model literature, we rewrite the linear combination as $\\hat{x} = \\beta x + \\alpha \\epsilon$ . By adjusting the coefficients $\\alpha$ , $\\beta$ and the starting time $s$ , the distance between the distribution of $\\hat{x}$ (i.e., $w(\\hat{x})$ ) and the input distribution of the diffusion model (during the training time) at time $s$ (i.e., $p_s(x)$ ) is controlled. To better match $w(\\hat{x})$ to $p_s(x)$ , utilizing the common practice [21, 65] that $x_s$ is designed to be a linear combination of $x$ and Gaussian noise, we keep $s$ as a hyperparameter and calculate $\\alpha$ and $\\beta$ from $s$ . Conditioned on the diffusion model, the maps from $s$ to $\\alpha$ and $\\beta$ vary. Taking DDPM as an example, the calculations can be written as $\\alpha = \\sqrt{1 - \\prod_{l=1}^{s}(1 - \\sigma_l)}$ and $\\beta = \\sqrt{\\prod_{l=1}^{s}(1 - \\sigma_l)}$ , where $\\sigma_l$ is the standard deviation of the noise in the forward process at time $l$ .", + "bbox": [ + 496, + 584, + 893, + 853 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Next, we look into the schedule of starting time $s$ . Two factors are taken into consideration. First is the time efficiency. The generation of the diffusion model requires an", + "bbox": [ + 496, + 854, + 893, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "3595", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/99eacc1478574a02f4741191d676d3bb9ade6871d4b7b5895ede64ac63678d9e.jpg", + "image_caption": [ + "Figure 3. Illustrative example of DSI finished in two iterations. In the first iteration, insufficient transformation leads to wrong prediction with low confidence. Our algorithm rejects the prediction and continues the second iteration. In the second iteration, with proper transformation, the correct prediction is drawn and accepted. Then, the algorithm finished." + ], + "image_footnote": [], + "bbox": [ + 83, + 98, + 877, + 327 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "iterative sampling in which the total sampling steps (thus the sampling time) are controlled by the starting time $s$ . Though providing more sufficient distribution transformation, using a large $s$ is time-consuming and inappropriate for the online testing environment. [9, 72] Second is the sample differences. As discovered in image editing [45] using the diffusion model, the starting time controls the faithfulness and reality of the generated images. Analogically, in using the diffusion model to transfer the OoD data, $s$ is a controller of the degree of distribution transformation and the preservation of semantic information, which are both crucial to OoD prediction. In practice, the distance from different samples to the training distribution is different and the difficulty of the semantic label preservation varies among the samples, which makes a uniform starting time schedule improper.", + "bbox": [ + 75, + 420, + 473, + 648 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Thus, in DSI, a sample adaptive schedule of the starting time index is used, in which $s$ increases gradually. Specifically, given a predefined starting time sequence $\\{s_l\\}_{l=0}^L$ , where $s_0 < s_1 < \\dots < s_L$ , for each OoD sample $x$ , DSI begins with the smallest $s_0$ , uses the diffusion model to transfer the combination $\\hat{x}$ , and lets the predictor output the prediction result $h$ together with the confidence score $c$ of the prediction. If the $c$ is greater than a predefined threshold $k$ , the prediction is accepted. Otherwise, DSI rejects the prediction, move to the next time index, and repeats the above procedure (transfer, prediction, and then using confidence score to make a judgment). If the prediction confidence score still does not meet the threshold at time index $s_L$ , the last prediction is accepted. By doing so, DSI allocates a small starting time index to the samples close to the source distribution and a larger one to the samples far from the", + "bbox": [ + 75, + 657, + 472, + 901 + ], + "page_idx": 4 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1 Distribution Shift Inversion" + ], + "code_body": "Input: Predictor: $f$ , Diffusion Models: $\\{g_m\\}_{m=1}^M$ , Function for calculating $\\alpha$ and $\\beta$ : $\\phi$ , Ensemble function: $\\xi$ , Confidence score function: $\\psi$ \nInput: Starting time series: $\\{s_l\\}_{l=0}^L$ , Threshold: $k$ \nInput: OoD sample: $x$ \n1: $h_0 \\gets f(x)$ $\\triangleright$ Draw prediction from original sample \n2: for $l$ in $1, \\dots, L$ do \n3: $\\alpha, \\beta \\gets \\phi(t_l)$ \n4: $\\hat{x} \\gets \\beta x + \\alpha \\epsilon$ \n5: for $m$ in $1, \\dots, M$ do \n6: $\\tilde{x} \\gets g_m(\\hat{x})$ $\\triangleright$ Transfer \n7: $h_m \\gets f(\\tilde{x})$ \n8: end for \n9: $h \\gets \\xi(h_0, \\dots, h_M)$ $\\triangleright$ Ensemble \n10: if $\\psi(h) > k$ then $\\triangleright$ Confidence Filtering \n11: break \n12: end if \n13: end for \n14: output prediction $h$ $\\triangleright$ Accept the last prediction", + "bbox": [ + 500, + 436, + 893, + 734 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "source distribution. Thus, this adaptation procedure avoids the use of a uniformly small time step which causes some samples to not be fully transferred, or a uniformly large time steps to cause the diffusion model to take too long to proceed. In our experiments, we use the maximum class probability as the confidence score and set the confidence threshold as hyperparameter.", + "bbox": [ + 496, + 762, + 893, + 868 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Usually, under the setting of OoD prediction, multiple training domains are available. The majority of the OoD", + "bbox": [ + 498, + 869, + 893, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "3596", + "bbox": [ + 482, + 944, + 516, + 957 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/c6116856a12d7cc6bdc95890b5540962b4e5024decc5fcddc5fc35c20e3786ff.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DatasetPACSOfficeHome
Testing DomainACPSAverageACPRAverage
ERM76.24±0.4467.90±0.6494.47±0.4460.32±0.8574.73±0.5960.81±0.5154.17±0.1774.80±0.3576.11±0.4066.47±0.36
ERM*78.52±0.8170.90±0.7695.80±0.1667.97±0.6878.30±0.6061.15±0.5655.96±0.7675.55±0.2376.56±0.2967.31±0.46
ANDMask [50]67.35±0.5163.22±2.2393.98±0.2660.35±1.0571.23±1.0160.84±0.6055.73±0.6073.80±0.4475.88±0.0866.56±0.43
ANDMask*69.43±0.4068.23±2.2994.99±0.2469.63±0.5775.57±0.8861.18±0.6556.80±0.4174.35±0.4076.40±0.5467.18±0.50
CAD [58]75.42±0.5168.20±0.6495.02±0.5559.77±2.1474.60±0.9660.71±0.6453.39±0.1874.41±0.2975.36±0.3965.97±0.38
CAD*76.11±0.8171.81±0.5996.09±0.1669.56±1.6978.39±0.8161.04±0.6355.08±0.4475.20±0.2976.14±0.2866.87±0.41
CondCAD [58]75.55±0.3867.77±0.5095.57±0.1259.99±1.9074.72±0.7360.74±0.3755.27±0.8374.64±0.2675.42±0.2066.52±0.42
CondCAD*77.12±0.3671.61±0.3796.03±0.0969.79±1.9678.64±0.7061.15±0.2856.09±0.5875.52±0.4176.43±0.1767.30±0.36
GroupDRO [59]69.56±1.0163.77±3.7493.16±0.7764.16±1.7872.66±1.8360.32±0.2653.12±0.6471.61±0.6675.68±0.2165.18±0.44
GroupDRO*71.61±0.8167.45±2.7593.78±0.4071.88±1.0276.18±1.2560.73±0.2655.83±0.7973.01±0.9276.14±0.1866.43±0.54
IB_ERM [1]77.18±0.2069.76±0.2494.82±0.8061.26±0.5875.76±0.4658.30±0.7854.39±0.1070.36±0.0572.02±0.4463.77±0.34
IB_ERM*79.07±0.2071.88±0.4495.83±0.3069.95±0.8879.18±0.4658.66±0.8155.66±0.3971.29±0.0172.90±0.3464.63±0.39
IB_IRM [1]75.26±1.0967.77±0.9794.76±0.4560.25±2.4074.51±1.2358.01±0.4452.60±1.0072.75±0.6074.90±0.6564.57±0.67
IB_IRM*77.31±1.0870.70±0.6395.96±0.1268.03±1.6778.00±0.8858.37±0.3953.68±0.4472.95±0.8475.55±0.7965.14±0.62
Mixup [74]71.29±0.4966.11±2.3294.08±0.4764.81±2.8874.07±1.5461.46±0.2055.83±0.6574.06±0.4476.73±0.4167.02±0.43
Mixup*73.18±0.1769.63±2.3594.56±0.4071.45±2.7477.21±1.4262.25±0.3157.85±0.8575.10±0.4077.21±0.2668.10±0.46
SANDMask [63]67.35±0.5162.50±3.8594.17±0.6264.58±0.5872.15±1.3961.78±0.3655.24±0.1273.34±0.4075.68±0.3766.51±0.31
SANDMask*69.43±0.4067.42±2.9694.73±0.4272.66±0.6376.06±1.1062.14±0.3556.58±0.2873.50±0.2376.27±0.2967.12±0.29
SelfReg [27]76.86±0.0868.62±0.7496.09±0.1461.39±0.8175.74±0.4462.50±0.7656.09±0.2375.52±0.3875.75±0.2467.47±0.40
SelfReg*78.61±0.4171.55±0.7496.39±0.2171.19±0.2179.44±0.3962.90±0.8257.52±0.1476.37±0.3776.79±0.2068.40±0.38
Average Gain1.83±0.433.55±0.850.80±0.348.52±1.063.68±0.670.41±0.131.52±0.520.75±0.350.69±0.210.84±0.30
", + "bbox": [ + 76, + 88, + 890, + 347 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. The average accuracy $\\pm$ the standard deviation of base algorithms w/o our method on PACS and OfficeHome datasets. The performance is generally boosted when our method is plugged in, whichever base algorithm is used.", + "bbox": [ + 75, + 359, + 890, + 388 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "prediction algorithms are based on this multiple-training domain assumption to extract stable features and establish a uniform predictor. Consistent with this common setting, for the multiple training domain problem, we use a unified predictor $f$ trained on all available training domains. However, a mixture of multiple distributions increases the difficulty of training for the diffusion model, which leads to a slower convergence and domain collapse (only generating samples from easy domains). Given consideration to these undesired phenomena, for the multiple training domain problem, we train individual diffusion model $g_{m}$ , where $m = 1,\\dots ,M$ is the training domain index, on each training domain, use every $g_{m}$ to transfer the OoD sample, and then obtain the prediction $h_m$ from every transferred sample using $f$ . Finally, we ensemble the predictions $\\{h_m\\}_{m = 1}^M$ together to get the overall prediction. In our experiments, the ensemble is conducted by averaging the logits (the inputs of the softmax layer) in the predictor neural network.", + "bbox": [ + 73, + 405, + 472, + 676 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The overall framework of DSI is shown in Algorithm 1.", + "bbox": [ + 96, + 678, + 465, + 693 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 76, + 708, + 209, + 724 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. In the main text, experiments on the following datasets are reported. More experiments can be found in supplementary materials. (1) PACS [33] contains 999,1 colored images from 7 classes and 4 domains (art painting, cartoon, photo, and sketch); (2) Office-Home [69] contains around 15,500 images from 65 different classes and 4 domains (artistic, clip art, product, and real-world).", + "bbox": [ + 75, + 733, + 470, + 839 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Base Methods. Based on the taxonomy in Sec. 2, we select one (or two) up-to-date or representative algorithm(s) from each category as the base methods in the experiments with multiple training domains. For experiments with a", + "bbox": [ + 75, + 839, + 470, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "single training domain, we adjust the list of base methods by only choosing the algorithms without multi-domain assumption. For each experimental configuration (dataset and training-testing split), the hyperparameters of each algorithm are optimized based on the performance metric on the testing set over 10 random searches. The searching regions are reported in supplementary materials. Fixing the optimal hyperparameters, we repeat the experimental pipeline three times and report the average results together with the standard deviations to alleviate the influence of the lucky weight initialization and dataset split.", + "bbox": [ + 496, + 405, + 893, + 571 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In Tabs. 1 and 2, we use [algorithm]* to indicate the use of DSI, the green cells to indicate our method improves the base method, and the green cells with text in bold to indicate our method improves the base method with non-overlapped confidence interval.", + "bbox": [ + 496, + 573, + 893, + 650 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Multi-training Domain Generalization", + "text_level": 1, + "bbox": [ + 498, + 662, + 831, + 680 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The experiments for multi-training domain generalization are conducted on PACS and OfficeHome. For each dataset, one domain is left as the testing domain and the other three are used for training. The performance comparison of base methods with and without our method are listed in Tab. 1. Our method generally enhances the OoD prediction of all types of base methods by $3.68\\%$ on PACS and $0.84\\%$ on OfficeHome, which indicates DSI successfully closes the distance between the OoD samples and the training distribution. The significance of the improvements varies among different leave-one-out settings, because the accuracy of the base methods varies. When the accuracy of the base method is low (e.g., the average accuracy of the base methods is $61.88\\%$ for S of PACS), more $(8.22\\%)$ improvement is achieved. When", + "bbox": [ + 496, + 688, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "3597", + "bbox": [ + 482, + 944, + 514, + 957 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/70088e06ce5bf277c1e9cb102615e93aa6f2ef442e63e07be6d4936309a0faa6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 86, + 88, + 285, + 210 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/655137bc8068ff47a55d854fd950e24ba04e80dde50938442b83f2fd92d34cba.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 285, + 88, + 483, + 210 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ec1a14765d5a5e4627dc90d065d471d22c7053f7c4ad9aae4722adfd064de1b9.jpg", + "image_caption": [ + "(a) Testing Domain: Art", + "(e) Testing Domain: Art" + ], + "image_footnote": [], + "bbox": [ + 86, + 228, + 284, + 353 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4a75f29c16c22d22f66cf3b066dd758daa510d4fee43b7ef9a3a1d8624c65100.jpg", + "image_caption": [ + "(b) Testing Domain: Cartoon", + "(f) Testing Domain: Cartoon" + ], + "image_footnote": [], + "bbox": [ + 285, + 228, + 480, + 353 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ba9abe231334927a55c18704cedc53f602271c98cb6a17115186d39f284ccadc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 483, + 88, + 681, + 210 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5366802d15f708ad4b32f8ebf6d893ab6651f25c813f7d05eb0df6a371d933a5.jpg", + "image_caption": [ + "(c) Testing Domain: Photo", + "(g) Testing Domain: Photo" + ], + "image_footnote": [], + "bbox": [ + 483, + 228, + 679, + 353 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5795729edff7d571812b33f38bbcbcf1ab1f459f32accdcdc072889caf16a18a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 684, + 88, + 882, + 210 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a9f0285724b3b97b9e69f011f7e5bd121a7e295921ecf14f7fc5fc671f1a31fe.jpg", + "image_caption": [ + "(d) Testing Domain: Sketch", + "(h) Testing Domain: Sketch" + ], + "image_footnote": [], + "bbox": [ + 683, + 228, + 879, + 353 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "the accuracy of the base method is high (e.g., the average accuracy of the base methods is $94.61\\%$ for P of PACS), the absolute value of the improvement is less $(0.89\\%)$ . We also notice that the rise in performance on OfficeHome dataset is less than the PACS, which can be attributed to that the larger number of classes in OfficeHome increases the hardness of the semantic label preservation of our method.", + "bbox": [ + 75, + 426, + 470, + 531 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We further analyze whether the performance gain depends on a certain class or domain. We count, for each class in each testing domain, (1) the number of samples correctly predicted by both the base methods and the base methods with DSI(# Both Correct), (2) the number of samples correctly predicted by the base methods with DSI but wrongly predicted by base methods (# Only Ours Correct), (3) the number of samples correctly predicted by the base methods (# Base Correct), and (4) the number of samples wrongly predicted by the base methods (# Base Wrong). Fig. 4 shows the preservation ratio calculated by $\\frac{\\# \\text{Both Correct}}{\\# \\text{Base Correct}}$ and the correction ratio calculated by $\\frac{\\# \\text{Only Ours Correct}}{\\# \\text{Base Wrong}}$ . The preservation ratio indicates the percentage of the correct predictions that are still correct when our method is used. The correction ratio indicates the percentage of the wrong predictions that are corrected when our method is used. Averaging over testing domains and classes, $94.52\\%$ of the correct predictions are still correct when our method is used. The highest preservation ratio is $95.95\\%$ appearing when photo is the testing domain. Among the testing domains and the classes, our method can at least correct $8.57\\%$ wrong predictions and averagely $28.17\\%$ . These results prove the general effectiveness of our methods across different domains and classes.", + "bbox": [ + 75, + 534, + 472, + 900 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/636c714e2f68cde0e10dc7ad9767c1d1e0412c3a61a996b9782761dd4212ee2f.jpg", + "image_caption": [ + "Figure 4. The percentage of correct prediction when using our method among the samples which are correctly predicted by the base method (in Fig. 4a to Fig. 4d), or wrongly predicted by the base method (in Fig. 4e to Fig. 4h). The plot is separately drawn for each leave-one-out setting and each class.", + "Figure 5. Accuracy v.s. Starting Time $s$ on PACS dataset with the testing domain of \"Cartoon\"." + ], + "image_footnote": [], + "bbox": [ + 504, + 426, + 888, + 570 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Single-training Domain Generalization", + "text_level": 1, + "bbox": [ + 500, + 614, + 834, + 631 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To cover the harder single training domain generalization, we do experiments on PACS datasets in which we use each domain as the training domain and test on the other three. The performance comparison of base methods with and without our method on the dataset with single training domains are listed in Tab. 2. With our method, irrelevant to the training and testing domain, general performance gains are achieved and the average performance gain is $2.42\\%$ .", + "bbox": [ + 496, + 638, + 893, + 758 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Discussion on the starting time $s$", + "text_level": 1, + "bbox": [ + 500, + 770, + 782, + 787 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Transforming the distribution closer to the source distribution increases the confidence of the prediction based on the transformed image. On the other hand, the well-preserved label information guarantees the prediction of the generated image has the same label as its origin. However, increasing $s$ to get further distribution transformation will destroy the label information, contrarily, decreasing $s$ to preserve the", + "bbox": [ + 496, + 794, + 893, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "3598", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/62d3367c0df0bd15d57d30aa3c76c0aa495486cb425141d67b4e99f04e099f7d.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DatasetPACS
Training DomainACPS
Testing DomainCPSAPSACSACP
ERM55.37±0.3297.92±0.0542.84±1.6855.63±0.2683.43±0.3257.42±2.2764.84±1.0228.26±3.8623.24±4.8815.82±1.3314.26±0.7012.66±0.49
ERM*57.58±0.2697.90±0.0348.54±1.1257.03±0.4483.98±0.5663.74±2.0065.92±0.3732.75±3.7825.68±4.7816.41±1.5116.80±0.7612.92±0.20
CORAL56.35±2.6396.68±0.6342.32±2.6055.47±0.5284.15±0.7057.81±1.6562.04±0.7432.16±5.8426.33±8.4615.27±0.6815.76±1.1611.65±0.81
CORAL*58.76±2.9696.84±0.5347.56±1.1656.87±0.0984.38±0.8364.65±2.0163.90±1.0135.97±4.8029.23±7.9915.98±0.6616.50±1.0412.27±0.92
RSC55.21±0.2898.18±0.1744.66±1.6954.36±1.0683.79±0.6259.41±2.3363.05±0.9631.61±6.7524.90±5.1216.57±0.5916.37±0.2613.77±1.92
RSC*57.39±0.4598.24±0.1550.39±1.2555.70±0.7483.95±0.5665.98±1.6064.13±1.6435.29±5.7728.22±4.8717.68±0.6817.45±0.6914.49±1.88
SagNet56.41±0.4797.95±0.0846.81±3.3358.82±1.1886.95±0.7957.91±2.6267.32±0.9941.76±2.3535.77±2.4815.76±0.9114.23±2.4516.76±1.51
SagNet*58.85±0.5197.96±0.0853.48±3.3059.51±1.4087.14±0.9764.71±3.5067.74±0.7544.34±2.0038.64±1.8418.03±0.6715.95±2.1718.26±1.90
Average Gain2.31±0.120.05±0.075.83±0.521.20±0.300.28±0.166.63±0.211.11±0.513.64±0.692.88±0.311.17±0.671.52±0.680.77±0.45
", + "bbox": [ + 76, + 89, + 890, + 244 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 2. The average accuracy $\\pm$ the standard deviation of base algorithms w/o our method on PACS datasets with single training domain setting. The performance is generally boosted when our method is plugged in, whichever base algorithm used.", + "bbox": [ + 75, + 255, + 892, + 285 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/08087e127fd3fd318a5f1c871cde0e1c7ba016d49781fe1f41669647276ef705.jpg", + "image_caption": [ + "(a) Accuracy v.s. Ensemble Set" + ], + "image_footnote": [], + "bbox": [ + 83, + 292, + 464, + 416 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6c2990f47ab1d9bd4de9f486c5dfd3e816ad567ae6725d7893eaef02a3f2f784.jpg", + "image_caption": [ + "(b) Accuracy v.s. Threshold", + "Figure 6. Discussion about the influence of hyperparameters: Ensemble set (Fig. 6a) and Threshold (Fig. 6b) on the PACS dataset with the testing domain of \"Cartoon\". The y-axis label of Fig. 6a indicates the components of the ensemble set with the corresponding accuracy's show on the right. The row of \"C\" corresponds to the setting using the original testing images alone. The areas below(above) correspond to the ensembles with(without) the original testing images." + ], + "image_footnote": [], + "bbox": [ + 91, + 435, + 449, + 540 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "label information will limit the distribution transformation. Thus, an optimal $s$ exists for each algorithm. (see Fig. 5)", + "bbox": [ + 75, + 684, + 468, + 715 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.4. Discussions on hyperparameters", + "text_level": 1, + "bbox": [ + 76, + 726, + 362, + 742 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "**Ensemble.** We analyze whether only transforming the testing domain data to a subset of the training domains influences the performance gain or not. Fig. 6a shows the accuracy with different ensemble sets on PACS with the multi-training domain setting and Cartoon is the testing domain. Each row corresponds to one kind of ensemble. For example, row \"C\" shows the accuracy when the prediction is only based on the original testing image, which is the accuracy of the base methods; row \"C,A\" shows the accuracy when the prediction based on the original testing image and", + "bbox": [ + 75, + 750, + 470, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "prediction based on the image transformed towards the domain Art are considered together. As shown from the figure, including more components in the ensemble set increases the average performance and reduces its variance; ensembles without the original prediction can perform comparably with the base method; the ensembles with the original prediction and any (one, two, or all) of the predictions based on the transformed image is statistically better than the base methods.", + "bbox": [ + 496, + 292, + 893, + 426 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "**Confidence Threshold.** We analyze the influence of the confidence threshold $k$ , and the performance with varying $k$ are shown in 6b. Base methods are special cases when $k = 0$ , their performances are shown along the red vertical line. Though tuning $k$ enlarges the performance gain, when $k > 0$ , our method is activated and there are always performance improvements.", + "bbox": [ + 496, + 428, + 893, + 532 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 541, + 617, + 556 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we investigate a novel task, termed unseen distribution transformation, which aims at transforming the unseen distribution towards the seen distribution. We frame the first solution to unseen distribution transformation, in which the unseen distribution is first linearly combined with the Gaussian noise and then transformed by a diffusion model trained on the seen domain. By solving this task, we provide a new perspective for addressing the OoD prediction task by first closing the distance between the testing domain and the training domain and then drawing prediction. We propose the portable DSI, which conducts sample adaptive unseen distribution transformation to enhance the OoD prediction algorithms. Experimental results show that our method results in general performance gains when inserted into various types of base methods under multi-training and single-training domain generalization problems.", + "bbox": [ + 496, + 560, + 893, + 801 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Acknowledgment", + "text_level": 1, + "bbox": [ + 500, + 815, + 669, + 832 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This project is supported by the Singapore Ministry of Education Academic Research Fund Tier 1 (Grantor's Reference Number: 23-0306-A0001), a project titled \"Towards Robust Single Domain Generalization in Deep Learning\".", + "bbox": [ + 496, + 839, + 893, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "3599", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Kartik Ahuja, Ethan Caballero, Dinghuai Zhang, Yoshua Bengio, Ioannis Mitliagkas, and Irina Rish. 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In ICCV, 2021. 3" + ], + "bbox": [ + 78, + 90, + 470, + 703 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "3602", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Distribution Shift Inversion for Out-of-Distribution Prediction/2bfae0da-d459-4405-8157-11be349e6b0f_model.json b/2023/Distribution Shift Inversion for Out-of-Distribution Prediction/2bfae0da-d459-4405-8157-11be349e6b0f_model.json new file mode 100644 index 0000000000000000000000000000000000000000..2d0d39fbdd632ddd9d35b916b1f2d83f2d9b51a2 --- /dev/null +++ b/2023/Distribution Shift Inversion for Out-of-Distribution Prediction/2bfae0da-d459-4405-8157-11be349e6b0f_model.json @@ -0,0 +1,2510 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.002, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.171, + 0.131, + 0.8, + 0.151 + ], + "angle": 0, + "content": "Distribution Shift Inversion for Out-of-Distribution Prediction" + }, + { + "type": "title", + "bbox": [ + 0.223, + 0.18, + 0.744, + 0.218 + ], + "angle": 0, + "content": "Runpeng Yu Songhua Liu Xingyi Yang Xinchao Wang† National University of Singapore" + }, + { + "type": "text", + "bbox": [ + 0.241, + 0.22, + 0.725, + 0.235 + ], + "angle": 0, + "content": "{r.yu, songhua.liu, xyang}@u.nus.edu xinchao@nus.edu.sg" + }, + { + "type": "image", + "bbox": [ + 0.092, + 0.244, + 0.878, + 0.349 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.359, + 0.893, + 0.388 + ], + "angle": 0, + "content": "Figure 1. Transformed OoD samples from PACS dataset. Odd rows show the original OoD images, and even rows show their transformation results to the source distribution, obtained by the proposed DSI. Please zoom in for better visualization." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.4, + 0.314, + 0.416 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.42, + 0.474, + 0.798 + ], + "angle": 0, + "content": "Machine learning society has witnessed the emergence of a myriad of Out-of-Distribution (OoD) algorithms, which address the distribution shift between the training and the testing distribution by searching for a unified predictor or invariant feature representation. However, the task of directly mitigating the distribution shift in the unseen testing set is rarely investigated, due to the unavailability of the testing distribution during the training phase and thus the impossibility of training a distribution translator mapping between the training and testing distribution. In this paper, we explore how to bypass the requirement of testing distribution for distribution translator training and make the distribution translation useful for OoD prediction. We propose a portable Distribution Shift Inversion (DSI) algorithm, in which, before being fed into the prediction model, the OoD testing samples are first linearly combined with additional Gaussian noise and then transferred back towards the training distribution using a diffusion model trained only on the source distribution. Theoretical analysis reveals the feasibility of our method. Experimental results, on both multiple-domain generalization datasets and single-domain generalization datasets, show that our method provides a general performance gain when plugged into a wide range of commonly used OoD algorithms. Our code is available at https://github.com/yu-rp/Distribution-Shift-Iverson." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.825, + 0.21, + 0.84 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.849, + 0.47, + 0.88 + ], + "angle": 0, + "content": "The ubiquity of the distribution shift between the training and testing data in the real-world application of machine" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.402, + 0.895, + 0.583 + ], + "angle": 0, + "content": "learning systems induces the study of Out-of-Distribution (OoD) generalization (or domain generalization). [18, 64, 71, 79] Within the scope of OoD generalization, machine learning algorithms are required to generalize from the seen training domain to the unseen testing domain without the independent and identically distributed assumption. The bulk of the OoD algorithms in previous literature focuses on promoting the generalization capability of the machine learning models themselves by utilizing the domain invariant feature [2, 13, 36], context-based data augmentation [47, 74], distributionally robust optimization [59], subnetwork searching [81], neural network calibration [70], etc." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.896, + 0.764 + ], + "angle": 0, + "content": "In this work, orthogonal to enhancing the generalization capability of the model, we consider a novel pathway to OoD prediction. On the way, the testing(target) distribution is explicitly transformed towards the training.source) distribution to straightforwardly mitigate the distribution shift between the testing and the training distribution. Therein, the OoD prediction can be regarded as a two-step procedure, (1) transferring testing samples back towards training distribution, and (2) drawing prediction. The second step can be implemented by any OoD prediction algorithm. In this paper, we concentrate on the exploration of the first step, the distribution transformation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.897, + 0.902 + ], + "angle": 0, + "content": "Unlike previous works on distribution translation and domain transformation, in which certain target distribution is accessible during the training phase, here the target distribution is arbitrary and unavailable during the training. We term this new task as Unseen Distribution Transformation (UDT), in which a domain translator is trained on the source distribution and works to transform unseen target distribution towards the source distribution. The uniqueness, as well as the superiority, of UDT is listed as followings." + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.222, + 0.9 + ], + "angle": 0, + "content": "† Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.958 + ], + "angle": 0, + "content": "3592" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.089, + 0.468, + 0.247 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.26, + 0.47, + 0.302 + ], + "angle": 0, + "content": "Figure 2. Using a Diffusion Model to solve the one-dimensional UDT. OoD samples are transformed to the source distribution with limited failure of label preservation." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.306, + 0.47, + 0.367 + ], + "angle": 0, + "content": "- UDT puts no requirements on the data from both source and testing distribution like previous works do. This is practically valuable, because the real-world testing distributions are uncountable and dynamically changing." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.368, + 0.47, + 0.444 + ], + "angle": 0, + "content": "- UDT is able to transform various distributions using only one model. However, the previous distribution translator works for the translation between certain source and target distributions. With a different source-target pair, a new translator is required." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.447, + 0.47, + 0.522 + ], + "angle": 0, + "content": "- Considering the application of UDT in OoD prediction, it is free from the extra assumptions commonly used by the OoD generalization algorithms, such as the multi-training domain assumption and the various forms of the domain invariant assumption." + }, + { + "type": "list", + "bbox": [ + 0.097, + 0.306, + 0.47, + 0.522 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.523, + 0.47, + 0.674 + ], + "angle": 0, + "content": "Despite the advantages, the unavailability of the testing distribution poses new difficulty. Releasing this constraint, the idea of distribution alignment is well established in domain adaptation (DA). Wherein, a distribution translator is trained with the (pixel, feature, and semantic level) cycle consistency loss [23, 38, 82]. However, the training of such distribution transfer modules necessitates the testing distribution, which is unsuitable under the setting of OoD prediction and makes the transplant of the methods in DA to OoD even impossible." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.675, + 0.471, + 0.901 + ], + "angle": 0, + "content": "To circumvent the requirement of testing distribution during training time, we propose a novel method, named Distribution Shift Inversion (DSI). Instead of using a model transferring from testing distribution to training distribution, an unconditional generative model, trained only on the source distribution, is used, which transfers data from a reference noise distribution to the source distribution. The method operates in two successive parts. First, the OoD target distribution is transferred to the neighborhood of the noise distribution and aligned with the input of the generative model, thereafter we refer to this process as the forward transformation. The crux of this step is designing to what degree the target distribution is aligned to the noise distribution. In our implementation, the forward transformation is conducted by linearly combining the OoD samples and random noise with" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.302 + ], + "angle": 0, + "content": "the weights controlling the alignment. Then, in the second step, the outcome of the first step is transferred towards the source distribution by a generative model, thereafter we refer to this process as the backward transformation. In this paper, the generative model is chosen to be the diffusion model [21]. The superiority of the diffusion model is that its input is the linear combination of the source sample and the noise with varying magnitude, which is in accord with our design of the forward transformation and naturally allows strength control. Comparatively, VAE [28] and GAN [16] have a fixed level of noise in their input, which makes the forward transformation strength control indirect. Our theoretical analyses of the diffusion model also show the feasibility of using the diffusion model for UDT." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.306, + 0.895, + 0.472 + ], + "angle": 0, + "content": "Illustrative Example. A one-dimensional example is shown in Fig. 2. The example considers a binary classification problem, in which, given label, the conditional distributions of the samples are Gaussian in both the source and the testing domain. The testing distribution is constructed to be OoD and located in the region where the source distribution has a low density. The diffusion model is trained only on the source distribution. Passing through the noise space alignment and diffusion model transformation, the OoD samples are transformed to the source distribution with limited failure of label preservation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.476, + 0.895, + 0.673 + ], + "angle": 0, + "content": "Transformed Images. Fig. 1 shows some transformation results of OoD images towards the source distribution. The observation is twofold. (1) The distribution (here is the style) of the images is successfully transformed. All of the transferred images can be correctly classified by the ERM model trained on the source domain. (2) The transformed images are correlated to the original images. Some structural and color characteristics are mutually shared between them. This indicates that the diffusion model has extracted some low-level information and is capable to preserve it during the transformation. We would like to highlight again that, during the training, the diffusion model is isolated from the testing domain." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.676, + 0.833, + 0.69 + ], + "angle": 0, + "content": "Our contributions are therefore summarized as:" + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.695, + 0.892, + 0.725 + ], + "angle": 0, + "content": "- We put forward the unseen distribution transformation (UDT) and study its application to OoD prediction." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.727, + 0.894, + 0.743 + ], + "angle": 0, + "content": "- We offer theoretical analyses of the feasibility of UDT." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.746, + 0.894, + 0.79 + ], + "angle": 0, + "content": "- we propose DSI, a sample adaptive distribution transformation algorithm for efficient distribution adaptation and semantic information preservation." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.793, + 0.895, + 0.898 + ], + "angle": 0, + "content": "- We perform extensive experiments to demonstrate that our method is suitable for various OoD algorithms to achieve performance gain on diversified OoD benchmarks. On average, adding in our method produces \\(2.26\\%\\) accuracy gain on multi-training domain generalization datasets and \\(2.28\\%\\) on single-training domain generalization datasets." + }, + { + "type": "list", + "bbox": [ + 0.519, + 0.695, + 0.895, + 0.898 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3593" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.081, + 0.09, + 0.218, + 0.106 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.081, + 0.115, + 0.38, + 0.131 + ], + "angle": 0, + "content": "2.1. Out-of-Distribution Generalization" + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.14, + 0.468, + 0.17 + ], + "angle": 0, + "content": "To achieve OoD generalization, diverse methods have been proposed." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.172, + 0.468, + 0.352 + ], + "angle": 0, + "content": "Causal inference methods extract the invariant feature among training domains and build up a unified predictor for all domains. For example, CNBB [19] down-weights the samples which introduce big changes to the feature space by evaluating the causal effect of each sample; ICP [51] find the subset of features satisfying the property that the conditional probability of the target given this set of features is invariant among the domains; IRM [2] regularizes the ERM loss with the norm of the gradient of loss corresponding to the latent features; IB-IRM [1] extends the IRM to the case, where the invariant features are only partially informative, by adding an extra entropy loss term of the latent feature." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.354, + 0.468, + 0.429 + ], + "angle": 0, + "content": "Context-based data augmentation methods enrich the training feature space by linear interpolation between the features of inter-domain and intra-domain samples [74]; or combining the normalized feature of one sample with the mean and variance of the feature of another sample [47]." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.43, + 0.468, + 0.504 + ], + "angle": 0, + "content": "Distributional Robust Optimization method, like Group-DRO [59], theoretically formulates the OoD generalization as a min-max optimization and practically up-weights the domains with large losses in an online learning style to guarantee the model fit on all domains." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.507, + 0.468, + 0.733 + ], + "angle": 0, + "content": "Feature alignment methods learn a unified feature representation among all training domains with the assumption that this representation is shared by the testing domain data. For example, DANN [13] and CDANN [36] align the marginal and conditional feature distribution by domain adversarial training, respectively; CORAL [67] matches the covariance of the features in every training domain; MASF [11] proposes model-agnostic episodic learning to regularize the semantic structure of the feature space; using the contrastive learning as the regularization term, SelfReg [27] minimizes the distance between the features of the samples within the sample class; CAD and ConCAD [58] minimize the mutual information between the feature and domain variable as well as the negative mutual information between the feature of original samples and the feature of augmented samples." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.735, + 0.468, + 0.779 + ], + "angle": 0, + "content": "Context feature separation methods recognize the context feature by an extra context discriminator and disentangle them from the category feature by orthogonality penalty [4]." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.781, + 0.468, + 0.9 + ], + "angle": 0, + "content": "Gradient manipulation methods are designed based on the intuitions that (1) to train a unified predictor, only the gradient common across all domains should be used; or the intuition that (2) the spurious correlation, which leads to larger gradients, is easier to be fitted to and prevent the algorithm from learning other features. For example, IGA [30] and SD [52] penalize the variance of the gradients and the \\(l_{2}\\) norm of the logits, respectively; RSC [25] only takes" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.092, + 0.891, + 0.182 + ], + "angle": 0, + "content": "the samples whose gradients are small into consideration; MLDG [34] updates the parameters only when there are performance gains in two separated parts of the training dataset; ANDMask [50] and its ReLU-smoothed version SANDMask [63] only update the parameter whose gradients in most of the domains have the same sign." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.183, + 0.892, + 0.333 + ], + "angle": 0, + "content": "Different from the previous works, DSI tackles the OoD generalization problem by test time sample adaption. Instead of increasing the OoD generalization ability of the model, DSI aims to mitigate the distribution shift of the testing samples by shifting them back towards the source distribution. Though input enhancing is investigated in dataset distillation [39] and domain adaptation [23, 38, 82], we are the first to test this idea in OoD generalization. Besides its novelty, DSI is orthogonal to the previous algorithms, which allows it to be portably used as a common technique for OoD tasks." + }, + { + "type": "title", + "bbox": [ + 0.504, + 0.344, + 0.659, + 0.359 + ], + "angle": 0, + "content": "2.2. Diffusion Model" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.368, + 0.892, + 0.623 + ], + "angle": 0, + "content": "Neural network reuse has drawn recent interest [75-78]. In this work, we consider reusing pre-trained diffusion models. With promising performance and theoretical explanation, the diffusion model has been intensively investigated in the field of time series generalization/imputation/prediction [29, 32, 56, 68], image generalization/editing/inpainting [3, 6-8, 41, 44, 54, 61], text generalization/modeling [35, 80], text2image generalization [17, 48, 55, 60], text2speech generalization [53], video generalization [22], graph generalization [24, 73], 3D point cloud generalization [42, 43, 83]. Besides, these generation tasks, diffusion model conduces to the downstream tasks such as image segmenting [5], testing time sample adaptation for corrupted images [14], and adversarial attack defense [49]. In DSI, we explore a new application of the diffusion model in which it enhances the OoD prediction by transferring the OoD samples towards the source distribution." + }, + { + "type": "title", + "bbox": [ + 0.504, + 0.635, + 0.792, + 0.65 + ], + "angle": 0, + "content": "2.3. Prediction Confidence Estimation" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.66, + 0.892, + 0.9 + ], + "angle": 0, + "content": "In DSI, the prediction confidence score is used for selecting poorly predicted samples and achieving an adaptive distribution shift inversion at the sample level. By satisfying the partial order relationship of uncertainty, commonly used loss functions, such as softmax cross entropy, are suitable confidence metrics. [31] Other softmax-based scores, such as the maximum class probability [15, 20], true class probability [10] and the KL-divergence between the softmax distribution and the uniform distribution [20] are also widely used. Based on the Bayesian method, Monte Carlo dropout [12], use the standard uncertainty criteria (e.g., variance, entropy) of the stochastic network predictions as the confidence score. Taking a modified nearest-neighbor classifier as the reference, trust score [26] uses a minimal distance ratio as the confidence score. We note that measurements in the field of OoD detection [37,40,46,57,62] and sample" + }, + { + "type": "page_number", + "bbox": [ + 0.485, + 0.947, + 0.514, + 0.957 + ], + "angle": 0, + "content": "3594" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.152 + ], + "angle": 0, + "content": "difficulty estimation may also serve as proper filtering metrics for DSI. But, in this paper, we prefer to establish a new OoD prediction framework and leave the discovery of the potential filtering metrics as future work." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.166, + 0.204, + 0.183 + ], + "angle": 0, + "content": "3. Preliminary" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.191, + 0.47, + 0.296 + ], + "angle": 0, + "content": "The task of sampling an instance \\( \\pmb{x} \\) of a random variable \\( \\pmb{X} \\in \\mathcal{R}^d \\) with distribution \\( p(\\pmb{x}) \\) is generally intractable due to the fact that \\( p(\\pmb{x}) \\) is complex or unknown. Diffusion model, such as ScoreFlow [66] and DDPM [21], first samples from an simple distribution \\( \\rho(\\pmb{x}) \\) and then iteratively transforms sample \\( \\pmb{x} \\) to make its distribution consistent with \\( p(\\pmb{x}) \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.297, + 0.471, + 0.357 + ], + "angle": 0, + "content": "Under the continuous time setting, diffusion model formulates the forward transformation from \\( p(\\pmb{x}) \\) to \\( \\rho(\\pmb{x}) \\) as a stochastic process \\( \\{x_t\\}_{t=0}^T \\) following the Stochastic Differential Equation (SDE)" + }, + { + "type": "equation", + "bbox": [ + 0.182, + 0.369, + 0.47, + 0.385 + ], + "angle": 0, + "content": "\\[\nd \\boldsymbol {x} = f (\\boldsymbol {x}, t) d t + g (t) d \\boldsymbol {w}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.397, + 0.471, + 0.533 + ], + "angle": 0, + "content": "where \\( f(\\cdot, t): \\mathcal{R}^d \\to \\mathcal{R}^d \\) is named drift coefficient, \\( g(t) \\in \\mathcal{R} \\) is named diffusion coefficient, and \\( \\pmb{w} \\) is the Wiener process whose derivative \\( d\\pmb{w} \\) is characterized by a standard Gaussian random variable (white Gaussian noise). The corresponding marginal distribution \\( p_t(\\pmb{x}) \\) at time \\( t \\) satisfies \\( p_0(\\pmb{x}) = p(\\pmb{x}) \\) and \\( p_T(\\pmb{x}) \\approx \\rho(\\pmb{x}) \\). To sample from \\( p(\\pmb{x}) \\), the diffusion model first samples from \\( \\rho(\\pmb{x}) \\) and then transforms \\( \\pmb{x} \\) backward according to the inverse SDE associated with Eq. (1)" + }, + { + "type": "equation", + "bbox": [ + 0.098, + 0.544, + 0.47, + 0.561 + ], + "angle": 0, + "content": "\\[\nd \\boldsymbol {x} = [ f (\\boldsymbol {x}, t) - g ^ {2} (t) \\nabla_ {\\boldsymbol {x}} \\log p _ {t} (\\boldsymbol {x}) ] d t + g (t) d \\bar {\\boldsymbol {w}}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.573, + 0.47, + 0.692 + ], + "angle": 0, + "content": "where \\( dt \\) is the negative time flow, evolving from \\( t = T \\) to \\( t = 0 \\), and \\( \\bar{w} \\) is the Wiener process in the inverse time direction whose derivative \\( d\\bar{w} \\) is again a standard Gaussian random variable because of the Gaussian increment characterization of Wiener process. In Eq. (2), \\( \\nabla_{\\pmb{x}}\\log p_t(\\pmb {x}) \\) is the unknown score function of \\( \\pmb{x} \\) at time \\( t \\), which is estimated by a neural network \\( s_{\\theta}(\\pmb {x},t) \\) with the weighted score matching loss" + }, + { + "type": "equation", + "bbox": [ + 0.089, + 0.705, + 0.47, + 0.773 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {J} _ {S M} (\\boldsymbol {\\theta}; \\lambda (\\cdot)) \\\\ = \\frac {1}{2} \\int_ {0} ^ {T} \\mathbb {E} _ {p _ {t} (\\boldsymbol {x})} [ \\lambda (t) | | \\nabla_ {\\boldsymbol {x}} \\log p _ {t} (\\boldsymbol {x}) - s _ {\\boldsymbol {\\theta}} (\\boldsymbol {x}, t) | | _ {2} ^ {2} ] d t. \\tag {3} \\\\ \\end{array}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.785, + 0.406, + 0.801 + ], + "angle": 0, + "content": "4. Unseen Distribution Transformation" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.81, + 0.471, + 0.841 + ], + "angle": 0, + "content": "First, we motivate our method by analyzing why the diffusion model helps promote the OoD generalization." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.841, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Here, we proof that, by feeding a linear combination of the OoD samples and the standard Gaussian noise to a diffusion model, the OoD samples can be transformed to the ID samples." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.243 + ], + "angle": 0, + "content": "Theorem 1. Given a diffusion model trained on the source distribution \\( p(x) \\), let \\( p_t \\) denote the distribution at time \\( t \\) in the forward transformation, let \\( \\bar{p}(x) \\) denote the output distribution when the input of the backward process is standard Gaussian noise \\( \\epsilon \\) whose distribution is denoted by \\( \\rho(x) \\), let \\( \\omega(x) \\) denote the output distribution when the input of backward process is a convex combination \\( (1 - \\alpha)X' + \\alpha\\epsilon \\), where random variable \\( X' \\) is sampled following the target distribution \\( q(x) \\) and \\( \\alpha \\in (0,1) \\). Under some regularity conditions detailed in Appendix, we have" + }, + { + "type": "equation", + "bbox": [ + 0.557, + 0.253, + 0.892, + 0.27 + ], + "angle": 0, + "content": "\\[\nK L (p \\mid \\mid \\omega) \\leqslant \\mathcal {J} _ {S M} + K L (p _ {T} \\mid \\mid \\rho) + \\mathcal {F} (\\alpha) \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.28, + 0.895, + 0.492 + ], + "angle": 0, + "content": "Theorem 1 proves that the testing distribution can be transformed to the source distribution and the convergence is controlled by \\(\\alpha\\). The first terms in the inequality are introduced by the pretrained diffusion model. The loss term \\(\\mathcal{I}_{SM}\\) is small after sufficient training and can be reduced if the training procedure is further optimized. The KL-divergence term \\(KL(p_{T}||\\rho)\\) indicates the distance between the real distribution achieved by the forward transformation and the manually chosen standard Gaussian distribution, which is monotonically decreasing as the \\(T\\) goes larger and converges to 0 as the \\(T\\) is sufficient large. The third term (detailed in Appendix) is introduced by the distribution of the OOD testing samples, which is controlled by \\(\\alpha\\) and converges to 0 as \\(\\alpha\\) goes to 1." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.5, + 0.66, + 0.516 + ], + "angle": 0, + "content": "4.1. Implementation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.524, + 0.892, + 0.583 + ], + "angle": 0, + "content": "In this part, we describe DSI to realize the idea of shifting testing image towards the training distribution to boost the OoD generalization. The entire workflow is illustrated in Fig. 3." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.585, + 0.895, + 0.854 + ], + "angle": 0, + "content": "In the previous analysis, by constructing a linear combination of the OoD input and the noise, the alignment between the testing and the training distributions is converted to an alignment problem in the noise space. To be consistent with the diffusion model literature, we rewrite the linear combination as \\(\\hat{x} = \\beta x + \\alpha \\epsilon\\). By adjusting the coefficients \\(\\alpha\\), \\(\\beta\\) and the starting time \\(s\\), the distance between the distribution of \\(\\hat{x}\\) (i.e., \\(w(\\hat{x})\\)) and the input distribution of the diffusion model (during the training time) at time \\(s\\) (i.e., \\(p_s(x)\\)) is controlled. To better match \\(w(\\hat{x})\\) to \\(p_s(x)\\), utilizing the common practice [21, 65] that \\(x_s\\) is designed to be a linear combination of \\(x\\) and Gaussian noise, we keep \\(s\\) as a hyperparameter and calculate \\(\\alpha\\) and \\(\\beta\\) from \\(s\\). Conditioned on the diffusion model, the maps from \\(s\\) to \\(\\alpha\\) and \\(\\beta\\) vary. Taking DDPM as an example, the calculations can be written as \\(\\alpha = \\sqrt{1 - \\prod_{l=1}^{s}(1 - \\sigma_l)}\\) and \\(\\beta = \\sqrt{\\prod_{l=1}^{s}(1 - \\sigma_l)}\\), where \\(\\sigma_l\\) is the standard deviation of the noise in the forward process at time \\(l\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Next, we look into the schedule of starting time \\( s \\). Two factors are taken into consideration. First is the time efficiency. The generation of the diffusion model requires an" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3595" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.099, + 0.878, + 0.328 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.352, + 0.895, + 0.396 + ], + "angle": 0, + "content": "Figure 3. Illustrative example of DSI finished in two iterations. In the first iteration, insufficient transformation leads to wrong prediction with low confidence. Our algorithm rejects the prediction and continues the second iteration. In the second iteration, with proper transformation, the correct prediction is drawn and accepted. Then, the algorithm finished." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.421, + 0.474, + 0.649 + ], + "angle": 0, + "content": "iterative sampling in which the total sampling steps (thus the sampling time) are controlled by the starting time \\( s \\). Though providing more sufficient distribution transformation, using a large \\( s \\) is time-consuming and inappropriate for the online testing environment. [9, 72] Second is the sample differences. As discovered in image editing [45] using the diffusion model, the starting time controls the faithfulness and reality of the generated images. Analogically, in using the diffusion model to transfer the OoD data, \\( s \\) is a controller of the degree of distribution transformation and the preservation of semantic information, which are both crucial to OoD prediction. In practice, the distance from different samples to the training distribution is different and the difficulty of the semantic label preservation varies among the samples, which makes a uniform starting time schedule improper." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.659, + 0.473, + 0.902 + ], + "angle": 0, + "content": "Thus, in DSI, a sample adaptive schedule of the starting time index is used, in which \\( s \\) increases gradually. Specifically, given a predefined starting time sequence \\( \\{s_l\\}_{l=0}^L \\), where \\( s_0 < s_1 < \\dots < s_L \\), for each OoD sample \\( x \\), DSI begins with the smallest \\( s_0 \\), uses the diffusion model to transfer the combination \\( \\hat{x} \\), and lets the predictor output the prediction result \\( h \\) together with the confidence score \\( c \\) of the prediction. If the \\( c \\) is greater than a predefined threshold \\( k \\), the prediction is accepted. Otherwise, DSI rejects the prediction, move to the next time index, and repeats the above procedure (transfer, prediction, and then using confidence score to make a judgment). If the prediction confidence score still does not meet the threshold at time index \\( s_L \\), the last prediction is accepted. By doing so, DSI allocates a small starting time index to the samples close to the source distribution and a larger one to the samples far from the" + }, + { + "type": "code_caption", + "bbox": [ + 0.501, + 0.42, + 0.773, + 0.435 + ], + "angle": 0, + "content": "Algorithm 1 Distribution Shift Inversion" + }, + { + "type": "algorithm", + "bbox": [ + 0.5, + 0.438, + 0.895, + 0.735 + ], + "angle": 0, + "content": "Input: Predictor: \\(f\\), Diffusion Models: \\(\\{g_m\\}_{m=1}^M\\), Function for calculating \\(\\alpha\\) and \\(\\beta\\): \\(\\phi\\), Ensemble function: \\(\\xi\\), Confidence score function: \\(\\psi\\) \nInput: Starting time series: \\(\\{s_l\\}_{l=0}^L\\), Threshold: \\(k\\) \nInput: OoD sample: \\(x\\) \n1: \\(h_0 \\gets f(x)\\) \\(\\triangleright\\) Draw prediction from original sample \n2: for \\(l\\) in \\(1, \\dots, L\\) do \n3: \\(\\alpha, \\beta \\gets \\phi(t_l)\\) \n4: \\(\\hat{x} \\gets \\beta x + \\alpha \\epsilon\\) \n5: for \\(m\\) in \\(1, \\dots, M\\) do \n6: \\(\\tilde{x} \\gets g_m(\\hat{x})\\) \\(\\triangleright\\) Transfer \n7: \\(h_m \\gets f(\\tilde{x})\\) \n8: end for \n9: \\(h \\gets \\xi(h_0, \\dots, h_M)\\) \\(\\triangleright\\) Ensemble \n10: if \\(\\psi(h) > k\\) then \\(\\triangleright\\) Confidence Filtering \n11: break \n12: end if \n13: end for \n14: output prediction \\(h\\) \\(\\triangleright\\) Accept the last prediction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.763, + 0.895, + 0.869 + ], + "angle": 0, + "content": "source distribution. Thus, this adaptation procedure avoids the use of a uniformly small time step which causes some samples to not be fully transferred, or a uniformly large time steps to cause the diffusion model to take too long to proceed. In our experiments, we use the maximum class probability as the confidence score and set the confidence threshold as hyperparameter." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Usually, under the setting of OoD prediction, multiple training domains are available. The majority of the OoD" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.517, + 0.958 + ], + "angle": 0, + "content": "3596" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.078, + 0.089, + 0.892, + 0.348 + ], + "angle": 0, + "content": "
DatasetPACSOfficeHome
Testing DomainACPSAverageACPRAverage
ERM76.24±0.4467.90±0.6494.47±0.4460.32±0.8574.73±0.5960.81±0.5154.17±0.1774.80±0.3576.11±0.4066.47±0.36
ERM*78.52±0.8170.90±0.7695.80±0.1667.97±0.6878.30±0.6061.15±0.5655.96±0.7675.55±0.2376.56±0.2967.31±0.46
ANDMask [50]67.35±0.5163.22±2.2393.98±0.2660.35±1.0571.23±1.0160.84±0.6055.73±0.6073.80±0.4475.88±0.0866.56±0.43
ANDMask*69.43±0.4068.23±2.2994.99±0.2469.63±0.5775.57±0.8861.18±0.6556.80±0.4174.35±0.4076.40±0.5467.18±0.50
CAD [58]75.42±0.5168.20±0.6495.02±0.5559.77±2.1474.60±0.9660.71±0.6453.39±0.1874.41±0.2975.36±0.3965.97±0.38
CAD*76.11±0.8171.81±0.5996.09±0.1669.56±1.6978.39±0.8161.04±0.6355.08±0.4475.20±0.2976.14±0.2866.87±0.41
CondCAD [58]75.55±0.3867.77±0.5095.57±0.1259.99±1.9074.72±0.7360.74±0.3755.27±0.8374.64±0.2675.42±0.2066.52±0.42
CondCAD*77.12±0.3671.61±0.3796.03±0.0969.79±1.9678.64±0.7061.15±0.2856.09±0.5875.52±0.4176.43±0.1767.30±0.36
GroupDRO [59]69.56±1.0163.77±3.7493.16±0.7764.16±1.7872.66±1.8360.32±0.2653.12±0.6471.61±0.6675.68±0.2165.18±0.44
GroupDRO*71.61±0.8167.45±2.7593.78±0.4071.88±1.0276.18±1.2560.73±0.2655.83±0.7973.01±0.9276.14±0.1866.43±0.54
IB_ERM [1]77.18±0.2069.76±0.2494.82±0.8061.26±0.5875.76±0.4658.30±0.7854.39±0.1070.36±0.0572.02±0.4463.77±0.34
IB_ERM*79.07±0.2071.88±0.4495.83±0.3069.95±0.8879.18±0.4658.66±0.8155.66±0.3971.29±0.0172.90±0.3464.63±0.39
IB_IRM [1]75.26±1.0967.77±0.9794.76±0.4560.25±2.4074.51±1.2358.01±0.4452.60±1.0072.75±0.6074.90±0.6564.57±0.67
IB_IRM*77.31±1.0870.70±0.6395.96±0.1268.03±1.6778.00±0.8858.37±0.3953.68±0.4472.95±0.8475.55±0.7965.14±0.62
Mixup [74]71.29±0.4966.11±2.3294.08±0.4764.81±2.8874.07±1.5461.46±0.2055.83±0.6574.06±0.4476.73±0.4167.02±0.43
Mixup*73.18±0.1769.63±2.3594.56±0.4071.45±2.7477.21±1.4262.25±0.3157.85±0.8575.10±0.4077.21±0.2668.10±0.46
SANDMask [63]67.35±0.5162.50±3.8594.17±0.6264.58±0.5872.15±1.3961.78±0.3655.24±0.1273.34±0.4075.68±0.3766.51±0.31
SANDMask*69.43±0.4067.42±2.9694.73±0.4272.66±0.6376.06±1.1062.14±0.3556.58±0.2873.50±0.2376.27±0.2967.12±0.29
SelfReg [27]76.86±0.0868.62±0.7496.09±0.1461.39±0.8175.74±0.4462.50±0.7656.09±0.2375.52±0.3875.75±0.2467.47±0.40
SelfReg*78.61±0.4171.55±0.7496.39±0.2171.19±0.2179.44±0.3962.90±0.8257.52±0.1476.37±0.3776.79±0.2068.40±0.38
Average Gain1.83±0.433.55±0.850.80±0.348.52±1.063.68±0.670.41±0.131.52±0.520.75±0.350.69±0.210.84±0.30
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.36, + 0.892, + 0.389 + ], + "angle": 0, + "content": "Table 1. The average accuracy \\( \\pm \\) the standard deviation of base algorithms w/o our method on PACS and OfficeHome datasets. The performance is generally boosted when our method is plugged in, whichever base algorithm is used." + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.406, + 0.473, + 0.678 + ], + "angle": 0, + "content": "prediction algorithms are based on this multiple-training domain assumption to extract stable features and establish a uniform predictor. Consistent with this common setting, for the multiple training domain problem, we use a unified predictor \\( f \\) trained on all available training domains. However, a mixture of multiple distributions increases the difficulty of training for the diffusion model, which leads to a slower convergence and domain collapse (only generating samples from easy domains). Given consideration to these undesired phenomena, for the multiple training domain problem, we train individual diffusion model \\( g_{m} \\), where \\( m = 1,\\dots ,M \\) is the training domain index, on each training domain, use every \\( g_{m} \\) to transfer the OoD sample, and then obtain the prediction \\( h_m \\) from every transferred sample using \\( f \\). Finally, we ensemble the predictions \\( \\{h_m\\}_{m = 1}^M \\) together to get the overall prediction. In our experiments, the ensemble is conducted by averaging the logits (the inputs of the softmax layer) in the predictor neural network." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.679, + 0.466, + 0.694 + ], + "angle": 0, + "content": "The overall framework of DSI is shown in Algorithm 1." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.709, + 0.21, + 0.725 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.734, + 0.471, + 0.84 + ], + "angle": 0, + "content": "Datasets. In the main text, experiments on the following datasets are reported. More experiments can be found in supplementary materials. (1) PACS [33] contains 999,1 colored images from 7 classes and 4 domains (art painting, cartoon, photo, and sketch); (2) Office-Home [69] contains around 15,500 images from 65 different classes and 4 domains (artistic, clip art, product, and real-world)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.472, + 0.902 + ], + "angle": 0, + "content": "Base Methods. Based on the taxonomy in Sec. 2, we select one (or two) up-to-date or representative algorithm(s) from each category as the base methods in the experiments with multiple training domains. For experiments with a" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.406, + 0.895, + 0.572 + ], + "angle": 0, + "content": "single training domain, we adjust the list of base methods by only choosing the algorithms without multi-domain assumption. For each experimental configuration (dataset and training-testing split), the hyperparameters of each algorithm are optimized based on the performance metric on the testing set over 10 random searches. The searching regions are reported in supplementary materials. Fixing the optimal hyperparameters, we repeat the experimental pipeline three times and report the average results together with the standard deviations to alleviate the influence of the lucky weight initialization and dataset split." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.574, + 0.895, + 0.651 + ], + "angle": 0, + "content": "In Tabs. 1 and 2, we use [algorithm]* to indicate the use of DSI, the green cells to indicate our method improves the base method, and the green cells with text in bold to indicate our method improves the base method with non-overlapped confidence interval." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.664, + 0.833, + 0.681 + ], + "angle": 0, + "content": "5.1. Multi-training Domain Generalization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.895, + 0.901 + ], + "angle": 0, + "content": "The experiments for multi-training domain generalization are conducted on PACS and OfficeHome. For each dataset, one domain is left as the testing domain and the other three are used for training. The performance comparison of base methods with and without our method are listed in Tab. 1. Our method generally enhances the OoD prediction of all types of base methods by \\(3.68\\%\\) on PACS and \\(0.84\\%\\) on OfficeHome, which indicates DSI successfully closes the distance between the OoD samples and the training distribution. The significance of the improvements varies among different leave-one-out settings, because the accuracy of the base methods varies. When the accuracy of the base method is low (e.g., the average accuracy of the base methods is \\(61.88\\%\\) for S of PACS), more \\((8.22\\%)\\) improvement is achieved. When" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.958 + ], + "angle": 0, + "content": "3597" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.089, + 0.287, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.124, + 0.216, + 0.253, + 0.228 + ], + "angle": 0, + "content": "(a) Testing Domain: Art" + }, + { + "type": "image", + "bbox": [ + 0.287, + 0.089, + 0.485, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.309, + 0.216, + 0.463, + 0.228 + ], + "angle": 0, + "content": "(b) Testing Domain: Cartoon" + }, + { + "type": "image", + "bbox": [ + 0.087, + 0.229, + 0.285, + 0.354 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.121, + 0.359, + 0.251, + 0.371 + ], + "angle": 0, + "content": "(e) Testing Domain: Art" + }, + { + "type": "image", + "bbox": [ + 0.287, + 0.229, + 0.482, + 0.354 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.308, + 0.359, + 0.461, + 0.371 + ], + "angle": 0, + "content": "(f) Testing Domain: Cartoon" + }, + { + "type": "image", + "bbox": [ + 0.485, + 0.089, + 0.683, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.514, + 0.216, + 0.655, + 0.228 + ], + "angle": 0, + "content": "(c) Testing Domain: Photo" + }, + { + "type": "image", + "bbox": [ + 0.485, + 0.229, + 0.681, + 0.354 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.511, + 0.359, + 0.653, + 0.371 + ], + "angle": 0, + "content": "(g) Testing Domain: Photo" + }, + { + "type": "image", + "bbox": [ + 0.685, + 0.089, + 0.883, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.709, + 0.216, + 0.856, + 0.228 + ], + "angle": 0, + "content": "(d) Testing Domain: Sketch" + }, + { + "type": "image", + "bbox": [ + 0.684, + 0.229, + 0.88, + 0.354 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.707, + 0.359, + 0.854, + 0.371 + ], + "angle": 0, + "content": "(h) Testing Domain: Sketch" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.377, + 0.894, + 0.418 + ], + "angle": 0, + "content": "Figure 4. The percentage of correct prediction when using our method among the samples which are correctly predicted by the base method (in Fig. 4a to Fig. 4d), or wrongly predicted by the base method (in Fig. 4e to Fig. 4h). The plot is separately drawn for each leave-one-out setting and each class." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.427, + 0.471, + 0.532 + ], + "angle": 0, + "content": "the accuracy of the base method is high (e.g., the average accuracy of the base methods is \\(94.61\\%\\) for P of PACS), the absolute value of the improvement is less \\((0.89\\%)\\). We also notice that the rise in performance on OfficeHome dataset is less than the PACS, which can be attributed to that the larger number of classes in OfficeHome increases the hardness of the semantic label preservation of our method." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.535, + 0.473, + 0.901 + ], + "angle": 0, + "content": "We further analyze whether the performance gain depends on a certain class or domain. We count, for each class in each testing domain, (1) the number of samples correctly predicted by both the base methods and the base methods with DSI(# Both Correct), (2) the number of samples correctly predicted by the base methods with DSI but wrongly predicted by base methods (# Only Ours Correct), (3) the number of samples correctly predicted by the base methods (# Base Correct), and (4) the number of samples wrongly predicted by the base methods (# Base Wrong). Fig. 4 shows the preservation ratio calculated by \\(\\frac{\\# \\text{Both Correct}}{\\# \\text{Base Correct}}\\) and the correction ratio calculated by \\(\\frac{\\# \\text{Only Ours Correct}}{\\# \\text{Base Wrong}}\\). The preservation ratio indicates the percentage of the correct predictions that are still correct when our method is used. The correction ratio indicates the percentage of the wrong predictions that are corrected when our method is used. Averaging over testing domains and classes, \\(94.52\\%\\) of the correct predictions are still correct when our method is used. The highest preservation ratio is \\(95.95\\%\\) appearing when photo is the testing domain. Among the testing domains and the classes, our method can at least correct \\(8.57\\%\\) wrong predictions and averagely \\(28.17\\%\\). These results prove the general effectiveness of our methods across different domains and classes." + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.427, + 0.889, + 0.571 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.585, + 0.892, + 0.613 + ], + "angle": 0, + "content": "Figure 5. Accuracy v.s. Starting Time \\( s \\) on PACS dataset with the testing domain of \"Cartoon\"." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.615, + 0.836, + 0.632 + ], + "angle": 0, + "content": "5.2. Single-training Domain Generalization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.639, + 0.894, + 0.76 + ], + "angle": 0, + "content": "To cover the harder single training domain generalization, we do experiments on PACS datasets in which we use each domain as the training domain and test on the other three. The performance comparison of base methods with and without our method on the dataset with single training domains are listed in Tab. 2. With our method, irrelevant to the training and testing domain, general performance gains are achieved and the average performance gain is \\(2.42\\%\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.771, + 0.783, + 0.788 + ], + "angle": 0, + "content": "5.3. Discussion on the starting time \\(s\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Transforming the distribution closer to the source distribution increases the confidence of the prediction based on the transformed image. On the other hand, the well-preserved label information guarantees the prediction of the generated image has the same label as its origin. However, increasing \\( s \\) to get further distribution transformation will destroy the label information, contrarily, decreasing \\( s \\) to preserve the" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3598" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.078, + 0.09, + 0.892, + 0.245 + ], + "angle": 0, + "content": "
DatasetPACS
Training DomainACPS
Testing DomainCPSAPSACSACP
ERM55.37±0.3297.92±0.0542.84±1.6855.63±0.2683.43±0.3257.42±2.2764.84±1.0228.26±3.8623.24±4.8815.82±1.3314.26±0.7012.66±0.49
ERM*57.58±0.2697.90±0.0348.54±1.1257.03±0.4483.98±0.5663.74±2.0065.92±0.3732.75±3.7825.68±4.7816.41±1.5116.80±0.7612.92±0.20
CORAL56.35±2.6396.68±0.6342.32±2.6055.47±0.5284.15±0.7057.81±1.6562.04±0.7432.16±5.8426.33±8.4615.27±0.6815.76±1.1611.65±0.81
CORAL*58.76±2.9696.84±0.5347.56±1.1656.87±0.0984.38±0.8364.65±2.0163.90±1.0135.97±4.8029.23±7.9915.98±0.6616.50±1.0412.27±0.92
RSC55.21±0.2898.18±0.1744.66±1.6954.36±1.0683.79±0.6259.41±2.3363.05±0.9631.61±6.7524.90±5.1216.57±0.5916.37±0.2613.77±1.92
RSC*57.39±0.4598.24±0.1550.39±1.2555.70±0.7483.95±0.5665.98±1.6064.13±1.6435.29±5.7728.22±4.8717.68±0.6817.45±0.6914.49±1.88
SagNet56.41±0.4797.95±0.0846.81±3.3358.82±1.1886.95±0.7957.91±2.6267.32±0.9941.76±2.3535.77±2.4815.76±0.9114.23±2.4516.76±1.51
SagNet*58.85±0.5197.96±0.0853.48±3.3059.51±1.4087.14±0.9764.71±3.5067.74±0.7544.34±2.0038.64±1.8418.03±0.6715.95±2.1718.26±1.90
Average Gain2.31±0.120.05±0.075.83±0.521.20±0.300.28±0.166.63±0.211.11±0.513.64±0.692.88±0.311.17±0.671.52±0.680.77±0.45
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.256, + 0.893, + 0.286 + ], + "angle": 0, + "content": "Table 2. The average accuracy \\( \\pm \\) the standard deviation of base algorithms w/o our method on PACS datasets with single training domain setting. The performance is generally boosted when our method is plugged in, whichever base algorithm used." + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.293, + 0.465, + 0.417 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.191, + 0.422, + 0.358, + 0.434 + ], + "angle": 0, + "content": "(a) Accuracy v.s. Ensemble Set" + }, + { + "type": "image", + "bbox": [ + 0.092, + 0.436, + 0.45, + 0.541 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.197, + 0.547, + 0.347, + 0.559 + ], + "angle": 0, + "content": "(b) Accuracy v.s. Threshold" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.566, + 0.47, + 0.678 + ], + "angle": 0, + "content": "Figure 6. Discussion about the influence of hyperparameters: Ensemble set (Fig. 6a) and Threshold (Fig. 6b) on the PACS dataset with the testing domain of \"Cartoon\". The y-axis label of Fig. 6a indicates the components of the ensemble set with the corresponding accuracy's show on the right. The row of \"C\" corresponds to the setting using the original testing images alone. The areas below(above) correspond to the ensembles with(without) the original testing images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.685, + 0.47, + 0.716 + ], + "angle": 0, + "content": "label information will limit the distribution transformation. Thus, an optimal \\(s\\) exists for each algorithm. (see Fig. 5)" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.727, + 0.363, + 0.743 + ], + "angle": 0, + "content": "5.4. Discussions on hyperparameters" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.901 + ], + "angle": 0, + "content": "**Ensemble.** We analyze whether only transforming the testing domain data to a subset of the training domains influences the performance gain or not. Fig. 6a shows the accuracy with different ensemble sets on PACS with the multi-training domain setting and Cartoon is the testing domain. Each row corresponds to one kind of ensemble. For example, row \"C\" shows the accuracy when the prediction is only based on the original testing image, which is the accuracy of the base methods; row \"C,A\" shows the accuracy when the prediction based on the original testing image and" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.293, + 0.895, + 0.428 + ], + "angle": 0, + "content": "prediction based on the image transformed towards the domain Art are considered together. As shown from the figure, including more components in the ensemble set increases the average performance and reduces its variance; ensembles without the original prediction can perform comparably with the base method; the ensembles with the original prediction and any (one, two, or all) of the predictions based on the transformed image is statistically better than the base methods." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.429, + 0.895, + 0.534 + ], + "angle": 0, + "content": "**Confidence Threshold.** We analyze the influence of the confidence threshold \\( k \\), and the performance with varying \\( k \\) are shown in 6b. Base methods are special cases when \\( k = 0 \\), their performances are shown along the red vertical line. Though tuning \\( k \\) enlarges the performance gain, when \\( k > 0 \\), our method is activated and there are always performance improvements." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.542, + 0.619, + 0.557 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.561, + 0.895, + 0.803 + ], + "angle": 0, + "content": "In this paper, we investigate a novel task, termed unseen distribution transformation, which aims at transforming the unseen distribution towards the seen distribution. We frame the first solution to unseen distribution transformation, in which the unseen distribution is first linearly combined with the Gaussian noise and then transformed by a diffusion model trained on the seen domain. By solving this task, we provide a new perspective for addressing the OoD prediction task by first closing the distance between the testing domain and the training domain and then drawing prediction. We propose the portable DSI, which conducts sample adaptive unseen distribution transformation to enhance the OoD prediction algorithms. Experimental results show that our method results in general performance gains when inserted into various types of base methods under multi-training and single-training domain generalization problems." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.816, + 0.671, + 0.833 + ], + "angle": 0, + "content": "7. Acknowledgment" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.901 + ], + "angle": 0, + "content": "This project is supported by the Singapore Ministry of Education Academic Research Fund Tier 1 (Grantor's Reference Number: 23-0306-A0001), a project titled \"Towards Robust Single Domain Generalization in Deep Learning\"." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3599" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.472, + 0.169 + ], + "angle": 0, + "content": "[1] Kartik Ahuja, Ethan Caballero, Dinghuai Zhang, Yoshua Bengio, Ioannis Mitliagkas, and Irina Rish. 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Transformed OoD samples from PACS dataset. Odd rows show the original OoD images, and even rows show their transformation results to the source distribution, obtained by the proposed DSI. Please zoom in for better visualization. + +# Abstract + +Machine learning society has witnessed the emergence of a myriad of Out-of-Distribution (OoD) algorithms, which address the distribution shift between the training and the testing distribution by searching for a unified predictor or invariant feature representation. However, the task of directly mitigating the distribution shift in the unseen testing set is rarely investigated, due to the unavailability of the testing distribution during the training phase and thus the impossibility of training a distribution translator mapping between the training and testing distribution. In this paper, we explore how to bypass the requirement of testing distribution for distribution translator training and make the distribution translation useful for OoD prediction. We propose a portable Distribution Shift Inversion (DSI) algorithm, in which, before being fed into the prediction model, the OoD testing samples are first linearly combined with additional Gaussian noise and then transferred back towards the training distribution using a diffusion model trained only on the source distribution. Theoretical analysis reveals the feasibility of our method. Experimental results, on both multiple-domain generalization datasets and single-domain generalization datasets, show that our method provides a general performance gain when plugged into a wide range of commonly used OoD algorithms. Our code is available at https://github.com/yu-rp/Distribution-Shift-Iverson. + +# 1. Introduction + +The ubiquity of the distribution shift between the training and testing data in the real-world application of machine + +learning systems induces the study of Out-of-Distribution (OoD) generalization (or domain generalization). [18, 64, 71, 79] Within the scope of OoD generalization, machine learning algorithms are required to generalize from the seen training domain to the unseen testing domain without the independent and identically distributed assumption. The bulk of the OoD algorithms in previous literature focuses on promoting the generalization capability of the machine learning models themselves by utilizing the domain invariant feature [2, 13, 36], context-based data augmentation [47, 74], distributionally robust optimization [59], subnetwork searching [81], neural network calibration [70], etc. + +In this work, orthogonal to enhancing the generalization capability of the model, we consider a novel pathway to OoD prediction. On the way, the testing(target) distribution is explicitly transformed towards the training.source) distribution to straightforwardly mitigate the distribution shift between the testing and the training distribution. Therein, the OoD prediction can be regarded as a two-step procedure, (1) transferring testing samples back towards training distribution, and (2) drawing prediction. The second step can be implemented by any OoD prediction algorithm. In this paper, we concentrate on the exploration of the first step, the distribution transformation. + +Unlike previous works on distribution translation and domain transformation, in which certain target distribution is accessible during the training phase, here the target distribution is arbitrary and unavailable during the training. We term this new task as Unseen Distribution Transformation (UDT), in which a domain translator is trained on the source distribution and works to transform unseen target distribution towards the source distribution. The uniqueness, as well as the superiority, of UDT is listed as followings. + +![](images/d3b3409097f1042a2e129adde8fa4f1fc40f31f3937c1441e9f7dc59bd6ef724.jpg) +Figure 2. Using a Diffusion Model to solve the one-dimensional UDT. OoD samples are transformed to the source distribution with limited failure of label preservation. + +- UDT puts no requirements on the data from both source and testing distribution like previous works do. This is practically valuable, because the real-world testing distributions are uncountable and dynamically changing. +- UDT is able to transform various distributions using only one model. However, the previous distribution translator works for the translation between certain source and target distributions. With a different source-target pair, a new translator is required. +- Considering the application of UDT in OoD prediction, it is free from the extra assumptions commonly used by the OoD generalization algorithms, such as the multi-training domain assumption and the various forms of the domain invariant assumption. + +Despite the advantages, the unavailability of the testing distribution poses new difficulty. Releasing this constraint, the idea of distribution alignment is well established in domain adaptation (DA). Wherein, a distribution translator is trained with the (pixel, feature, and semantic level) cycle consistency loss [23, 38, 82]. However, the training of such distribution transfer modules necessitates the testing distribution, which is unsuitable under the setting of OoD prediction and makes the transplant of the methods in DA to OoD even impossible. + +To circumvent the requirement of testing distribution during training time, we propose a novel method, named Distribution Shift Inversion (DSI). Instead of using a model transferring from testing distribution to training distribution, an unconditional generative model, trained only on the source distribution, is used, which transfers data from a reference noise distribution to the source distribution. The method operates in two successive parts. First, the OoD target distribution is transferred to the neighborhood of the noise distribution and aligned with the input of the generative model, thereafter we refer to this process as the forward transformation. The crux of this step is designing to what degree the target distribution is aligned to the noise distribution. In our implementation, the forward transformation is conducted by linearly combining the OoD samples and random noise with + +the weights controlling the alignment. Then, in the second step, the outcome of the first step is transferred towards the source distribution by a generative model, thereafter we refer to this process as the backward transformation. In this paper, the generative model is chosen to be the diffusion model [21]. The superiority of the diffusion model is that its input is the linear combination of the source sample and the noise with varying magnitude, which is in accord with our design of the forward transformation and naturally allows strength control. Comparatively, VAE [28] and GAN [16] have a fixed level of noise in their input, which makes the forward transformation strength control indirect. Our theoretical analyses of the diffusion model also show the feasibility of using the diffusion model for UDT. + +Illustrative Example. A one-dimensional example is shown in Fig. 2. The example considers a binary classification problem, in which, given label, the conditional distributions of the samples are Gaussian in both the source and the testing domain. The testing distribution is constructed to be OoD and located in the region where the source distribution has a low density. The diffusion model is trained only on the source distribution. Passing through the noise space alignment and diffusion model transformation, the OoD samples are transformed to the source distribution with limited failure of label preservation. + +Transformed Images. Fig. 1 shows some transformation results of OoD images towards the source distribution. The observation is twofold. (1) The distribution (here is the style) of the images is successfully transformed. All of the transferred images can be correctly classified by the ERM model trained on the source domain. (2) The transformed images are correlated to the original images. Some structural and color characteristics are mutually shared between them. This indicates that the diffusion model has extracted some low-level information and is capable to preserve it during the transformation. We would like to highlight again that, during the training, the diffusion model is isolated from the testing domain. + +Our contributions are therefore summarized as: + +- We put forward the unseen distribution transformation (UDT) and study its application to OoD prediction. +- We offer theoretical analyses of the feasibility of UDT. +- we propose DSI, a sample adaptive distribution transformation algorithm for efficient distribution adaptation and semantic information preservation. +- We perform extensive experiments to demonstrate that our method is suitable for various OoD algorithms to achieve performance gain on diversified OoD benchmarks. On average, adding in our method produces $2.26\%$ accuracy gain on multi-training domain generalization datasets and $2.28\%$ on single-training domain generalization datasets. + +# 2. Related Work + +# 2.1. Out-of-Distribution Generalization + +To achieve OoD generalization, diverse methods have been proposed. + +Causal inference methods extract the invariant feature among training domains and build up a unified predictor for all domains. For example, CNBB [19] down-weights the samples which introduce big changes to the feature space by evaluating the causal effect of each sample; ICP [51] find the subset of features satisfying the property that the conditional probability of the target given this set of features is invariant among the domains; IRM [2] regularizes the ERM loss with the norm of the gradient of loss corresponding to the latent features; IB-IRM [1] extends the IRM to the case, where the invariant features are only partially informative, by adding an extra entropy loss term of the latent feature. + +Context-based data augmentation methods enrich the training feature space by linear interpolation between the features of inter-domain and intra-domain samples [74]; or combining the normalized feature of one sample with the mean and variance of the feature of another sample [47]. + +Distributional Robust Optimization method, like Group-DRO [59], theoretically formulates the OoD generalization as a min-max optimization and practically up-weights the domains with large losses in an online learning style to guarantee the model fit on all domains. + +Feature alignment methods learn a unified feature representation among all training domains with the assumption that this representation is shared by the testing domain data. For example, DANN [13] and CDANN [36] align the marginal and conditional feature distribution by domain adversarial training, respectively; CORAL [67] matches the covariance of the features in every training domain; MASF [11] proposes model-agnostic episodic learning to regularize the semantic structure of the feature space; using the contrastive learning as the regularization term, SelfReg [27] minimizes the distance between the features of the samples within the sample class; CAD and ConCAD [58] minimize the mutual information between the feature and domain variable as well as the negative mutual information between the feature of original samples and the feature of augmented samples. + +Context feature separation methods recognize the context feature by an extra context discriminator and disentangle them from the category feature by orthogonality penalty [4]. + +Gradient manipulation methods are designed based on the intuitions that (1) to train a unified predictor, only the gradient common across all domains should be used; or the intuition that (2) the spurious correlation, which leads to larger gradients, is easier to be fitted to and prevent the algorithm from learning other features. For example, IGA [30] and SD [52] penalize the variance of the gradients and the $l_{2}$ norm of the logits, respectively; RSC [25] only takes + +the samples whose gradients are small into consideration; MLDG [34] updates the parameters only when there are performance gains in two separated parts of the training dataset; ANDMask [50] and its ReLU-smoothed version SANDMask [63] only update the parameter whose gradients in most of the domains have the same sign. + +Different from the previous works, DSI tackles the OoD generalization problem by test time sample adaption. Instead of increasing the OoD generalization ability of the model, DSI aims to mitigate the distribution shift of the testing samples by shifting them back towards the source distribution. Though input enhancing is investigated in dataset distillation [39] and domain adaptation [23, 38, 82], we are the first to test this idea in OoD generalization. Besides its novelty, DSI is orthogonal to the previous algorithms, which allows it to be portably used as a common technique for OoD tasks. + +# 2.2. Diffusion Model + +Neural network reuse has drawn recent interest [75-78]. In this work, we consider reusing pre-trained diffusion models. With promising performance and theoretical explanation, the diffusion model has been intensively investigated in the field of time series generalization/imputation/prediction [29, 32, 56, 68], image generalization/editing/inpainting [3, 6-8, 41, 44, 54, 61], text generalization/modeling [35, 80], text2image generalization [17, 48, 55, 60], text2speech generalization [53], video generalization [22], graph generalization [24, 73], 3D point cloud generalization [42, 43, 83]. Besides, these generation tasks, diffusion model conduces to the downstream tasks such as image segmenting [5], testing time sample adaptation for corrupted images [14], and adversarial attack defense [49]. In DSI, we explore a new application of the diffusion model in which it enhances the OoD prediction by transferring the OoD samples towards the source distribution. + +# 2.3. Prediction Confidence Estimation + +In DSI, the prediction confidence score is used for selecting poorly predicted samples and achieving an adaptive distribution shift inversion at the sample level. By satisfying the partial order relationship of uncertainty, commonly used loss functions, such as softmax cross entropy, are suitable confidence metrics. [31] Other softmax-based scores, such as the maximum class probability [15, 20], true class probability [10] and the KL-divergence between the softmax distribution and the uniform distribution [20] are also widely used. Based on the Bayesian method, Monte Carlo dropout [12], use the standard uncertainty criteria (e.g., variance, entropy) of the stochastic network predictions as the confidence score. Taking a modified nearest-neighbor classifier as the reference, trust score [26] uses a minimal distance ratio as the confidence score. We note that measurements in the field of OoD detection [37,40,46,57,62] and sample + +difficulty estimation may also serve as proper filtering metrics for DSI. But, in this paper, we prefer to establish a new OoD prediction framework and leave the discovery of the potential filtering metrics as future work. + +# 3. Preliminary + +The task of sampling an instance $\pmb{x}$ of a random variable $\pmb{X} \in \mathcal{R}^d$ with distribution $p(\pmb{x})$ is generally intractable due to the fact that $p(\pmb{x})$ is complex or unknown. Diffusion model, such as ScoreFlow [66] and DDPM [21], first samples from an simple distribution $\rho(\pmb{x})$ and then iteratively transforms sample $\pmb{x}$ to make its distribution consistent with $p(\pmb{x})$ . + +Under the continuous time setting, diffusion model formulates the forward transformation from $p(\pmb{x})$ to $\rho(\pmb{x})$ as a stochastic process $\{x_t\}_{t=0}^T$ following the Stochastic Differential Equation (SDE) + +$$ +d \boldsymbol {x} = f (\boldsymbol {x}, t) d t + g (t) d \boldsymbol {w}, \tag {1} +$$ + +where $f(\cdot, t): \mathcal{R}^d \to \mathcal{R}^d$ is named drift coefficient, $g(t) \in \mathcal{R}$ is named diffusion coefficient, and $\pmb{w}$ is the Wiener process whose derivative $d\pmb{w}$ is characterized by a standard Gaussian random variable (white Gaussian noise). The corresponding marginal distribution $p_t(\pmb{x})$ at time $t$ satisfies $p_0(\pmb{x}) = p(\pmb{x})$ and $p_T(\pmb{x}) \approx \rho(\pmb{x})$ . To sample from $p(\pmb{x})$ , the diffusion model first samples from $\rho(\pmb{x})$ and then transforms $\pmb{x}$ backward according to the inverse SDE associated with Eq. (1) + +$$ +d \boldsymbol {x} = [ f (\boldsymbol {x}, t) - g ^ {2} (t) \nabla_ {\boldsymbol {x}} \log p _ {t} (\boldsymbol {x}) ] d t + g (t) d \bar {\boldsymbol {w}}, \tag {2} +$$ + +where $dt$ is the negative time flow, evolving from $t = T$ to $t = 0$ , and $\bar{w}$ is the Wiener process in the inverse time direction whose derivative $d\bar{w}$ is again a standard Gaussian random variable because of the Gaussian increment characterization of Wiener process. In Eq. (2), $\nabla_{\pmb{x}}\log p_t(\pmb {x})$ is the unknown score function of $\pmb{x}$ at time $t$ , which is estimated by a neural network $s_{\theta}(\pmb {x},t)$ with the weighted score matching loss + +$$ +\begin{array}{l} \mathcal {J} _ {S M} (\boldsymbol {\theta}; \lambda (\cdot)) \\ = \frac {1}{2} \int_ {0} ^ {T} \mathbb {E} _ {p _ {t} (\boldsymbol {x})} [ \lambda (t) | | \nabla_ {\boldsymbol {x}} \log p _ {t} (\boldsymbol {x}) - s _ {\boldsymbol {\theta}} (\boldsymbol {x}, t) | | _ {2} ^ {2} ] d t. \tag {3} \\ \end{array} +$$ + +# 4. Unseen Distribution Transformation + +First, we motivate our method by analyzing why the diffusion model helps promote the OoD generalization. + +Here, we proof that, by feeding a linear combination of the OoD samples and the standard Gaussian noise to a diffusion model, the OoD samples can be transformed to the ID samples. + +Theorem 1. Given a diffusion model trained on the source distribution $p(x)$ , let $p_t$ denote the distribution at time $t$ in the forward transformation, let $\bar{p}(x)$ denote the output distribution when the input of the backward process is standard Gaussian noise $\epsilon$ whose distribution is denoted by $\rho(x)$ , let $\omega(x)$ denote the output distribution when the input of backward process is a convex combination $(1 - \alpha)X' + \alpha\epsilon$ , where random variable $X'$ is sampled following the target distribution $q(x)$ and $\alpha \in (0,1)$ . Under some regularity conditions detailed in Appendix, we have + +$$ +K L (p \mid \mid \omega) \leqslant \mathcal {J} _ {S M} + K L (p _ {T} \mid \mid \rho) + \mathcal {F} (\alpha) \tag {4} +$$ + +Theorem 1 proves that the testing distribution can be transformed to the source distribution and the convergence is controlled by $\alpha$ . The first terms in the inequality are introduced by the pretrained diffusion model. The loss term $\mathcal{I}_{SM}$ is small after sufficient training and can be reduced if the training procedure is further optimized. The KL-divergence term $KL(p_{T}||\rho)$ indicates the distance between the real distribution achieved by the forward transformation and the manually chosen standard Gaussian distribution, which is monotonically decreasing as the $T$ goes larger and converges to 0 as the $T$ is sufficient large. The third term (detailed in Appendix) is introduced by the distribution of the OOD testing samples, which is controlled by $\alpha$ and converges to 0 as $\alpha$ goes to 1. + +# 4.1. Implementation + +In this part, we describe DSI to realize the idea of shifting testing image towards the training distribution to boost the OoD generalization. The entire workflow is illustrated in Fig. 3. + +In the previous analysis, by constructing a linear combination of the OoD input and the noise, the alignment between the testing and the training distributions is converted to an alignment problem in the noise space. To be consistent with the diffusion model literature, we rewrite the linear combination as $\hat{x} = \beta x + \alpha \epsilon$ . By adjusting the coefficients $\alpha$ , $\beta$ and the starting time $s$ , the distance between the distribution of $\hat{x}$ (i.e., $w(\hat{x})$ ) and the input distribution of the diffusion model (during the training time) at time $s$ (i.e., $p_s(x)$ ) is controlled. To better match $w(\hat{x})$ to $p_s(x)$ , utilizing the common practice [21, 65] that $x_s$ is designed to be a linear combination of $x$ and Gaussian noise, we keep $s$ as a hyperparameter and calculate $\alpha$ and $\beta$ from $s$ . Conditioned on the diffusion model, the maps from $s$ to $\alpha$ and $\beta$ vary. Taking DDPM as an example, the calculations can be written as $\alpha = \sqrt{1 - \prod_{l=1}^{s}(1 - \sigma_l)}$ and $\beta = \sqrt{\prod_{l=1}^{s}(1 - \sigma_l)}$ , where $\sigma_l$ is the standard deviation of the noise in the forward process at time $l$ . + +Next, we look into the schedule of starting time $s$ . Two factors are taken into consideration. First is the time efficiency. The generation of the diffusion model requires an + +![](images/99eacc1478574a02f4741191d676d3bb9ade6871d4b7b5895ede64ac63678d9e.jpg) +Figure 3. Illustrative example of DSI finished in two iterations. In the first iteration, insufficient transformation leads to wrong prediction with low confidence. Our algorithm rejects the prediction and continues the second iteration. In the second iteration, with proper transformation, the correct prediction is drawn and accepted. Then, the algorithm finished. + +iterative sampling in which the total sampling steps (thus the sampling time) are controlled by the starting time $s$ . Though providing more sufficient distribution transformation, using a large $s$ is time-consuming and inappropriate for the online testing environment. [9, 72] Second is the sample differences. As discovered in image editing [45] using the diffusion model, the starting time controls the faithfulness and reality of the generated images. Analogically, in using the diffusion model to transfer the OoD data, $s$ is a controller of the degree of distribution transformation and the preservation of semantic information, which are both crucial to OoD prediction. In practice, the distance from different samples to the training distribution is different and the difficulty of the semantic label preservation varies among the samples, which makes a uniform starting time schedule improper. + +Thus, in DSI, a sample adaptive schedule of the starting time index is used, in which $s$ increases gradually. Specifically, given a predefined starting time sequence $\{s_l\}_{l=0}^L$ , where $s_0 < s_1 < \dots < s_L$ , for each OoD sample $x$ , DSI begins with the smallest $s_0$ , uses the diffusion model to transfer the combination $\hat{x}$ , and lets the predictor output the prediction result $h$ together with the confidence score $c$ of the prediction. If the $c$ is greater than a predefined threshold $k$ , the prediction is accepted. Otherwise, DSI rejects the prediction, move to the next time index, and repeats the above procedure (transfer, prediction, and then using confidence score to make a judgment). If the prediction confidence score still does not meet the threshold at time index $s_L$ , the last prediction is accepted. By doing so, DSI allocates a small starting time index to the samples close to the source distribution and a larger one to the samples far from the + +Algorithm 1 Distribution Shift Inversion +Input: Predictor: $f$ , Diffusion Models: $\{g_m\}_{m=1}^M$ , Function for calculating $\alpha$ and $\beta$ : $\phi$ , Ensemble function: $\xi$ , Confidence score function: $\psi$ +Input: Starting time series: $\{s_l\}_{l=0}^L$ , Threshold: $k$ +Input: OoD sample: $x$ +1: $h_0 \gets f(x)$ $\triangleright$ Draw prediction from original sample +2: for $l$ in $1, \dots, L$ do +3: $\alpha, \beta \gets \phi(t_l)$ +4: $\hat{x} \gets \beta x + \alpha \epsilon$ +5: for $m$ in $1, \dots, M$ do +6: $\tilde{x} \gets g_m(\hat{x})$ $\triangleright$ Transfer +7: $h_m \gets f(\tilde{x})$ +8: end for +9: $h \gets \xi(h_0, \dots, h_M)$ $\triangleright$ Ensemble +10: if $\psi(h) > k$ then $\triangleright$ Confidence Filtering +11: break +12: end if +13: end for +14: output prediction $h$ $\triangleright$ Accept the last prediction + +source distribution. Thus, this adaptation procedure avoids the use of a uniformly small time step which causes some samples to not be fully transferred, or a uniformly large time steps to cause the diffusion model to take too long to proceed. In our experiments, we use the maximum class probability as the confidence score and set the confidence threshold as hyperparameter. + +Usually, under the setting of OoD prediction, multiple training domains are available. The majority of the OoD + +
DatasetPACSOfficeHome
Testing DomainACPSAverageACPRAverage
ERM76.24±0.4467.90±0.6494.47±0.4460.32±0.8574.73±0.5960.81±0.5154.17±0.1774.80±0.3576.11±0.4066.47±0.36
ERM*78.52±0.8170.90±0.7695.80±0.1667.97±0.6878.30±0.6061.15±0.5655.96±0.7675.55±0.2376.56±0.2967.31±0.46
ANDMask [50]67.35±0.5163.22±2.2393.98±0.2660.35±1.0571.23±1.0160.84±0.6055.73±0.6073.80±0.4475.88±0.0866.56±0.43
ANDMask*69.43±0.4068.23±2.2994.99±0.2469.63±0.5775.57±0.8861.18±0.6556.80±0.4174.35±0.4076.40±0.5467.18±0.50
CAD [58]75.42±0.5168.20±0.6495.02±0.5559.77±2.1474.60±0.9660.71±0.6453.39±0.1874.41±0.2975.36±0.3965.97±0.38
CAD*76.11±0.8171.81±0.5996.09±0.1669.56±1.6978.39±0.8161.04±0.6355.08±0.4475.20±0.2976.14±0.2866.87±0.41
CondCAD [58]75.55±0.3867.77±0.5095.57±0.1259.99±1.9074.72±0.7360.74±0.3755.27±0.8374.64±0.2675.42±0.2066.52±0.42
CondCAD*77.12±0.3671.61±0.3796.03±0.0969.79±1.9678.64±0.7061.15±0.2856.09±0.5875.52±0.4176.43±0.1767.30±0.36
GroupDRO [59]69.56±1.0163.77±3.7493.16±0.7764.16±1.7872.66±1.8360.32±0.2653.12±0.6471.61±0.6675.68±0.2165.18±0.44
GroupDRO*71.61±0.8167.45±2.7593.78±0.4071.88±1.0276.18±1.2560.73±0.2655.83±0.7973.01±0.9276.14±0.1866.43±0.54
IB_ERM [1]77.18±0.2069.76±0.2494.82±0.8061.26±0.5875.76±0.4658.30±0.7854.39±0.1070.36±0.0572.02±0.4463.77±0.34
IB_ERM*79.07±0.2071.88±0.4495.83±0.3069.95±0.8879.18±0.4658.66±0.8155.66±0.3971.29±0.0172.90±0.3464.63±0.39
IB_IRM [1]75.26±1.0967.77±0.9794.76±0.4560.25±2.4074.51±1.2358.01±0.4452.60±1.0072.75±0.6074.90±0.6564.57±0.67
IB_IRM*77.31±1.0870.70±0.6395.96±0.1268.03±1.6778.00±0.8858.37±0.3953.68±0.4472.95±0.8475.55±0.7965.14±0.62
Mixup [74]71.29±0.4966.11±2.3294.08±0.4764.81±2.8874.07±1.5461.46±0.2055.83±0.6574.06±0.4476.73±0.4167.02±0.43
Mixup*73.18±0.1769.63±2.3594.56±0.4071.45±2.7477.21±1.4262.25±0.3157.85±0.8575.10±0.4077.21±0.2668.10±0.46
SANDMask [63]67.35±0.5162.50±3.8594.17±0.6264.58±0.5872.15±1.3961.78±0.3655.24±0.1273.34±0.4075.68±0.3766.51±0.31
SANDMask*69.43±0.4067.42±2.9694.73±0.4272.66±0.6376.06±1.1062.14±0.3556.58±0.2873.50±0.2376.27±0.2967.12±0.29
SelfReg [27]76.86±0.0868.62±0.7496.09±0.1461.39±0.8175.74±0.4462.50±0.7656.09±0.2375.52±0.3875.75±0.2467.47±0.40
SelfReg*78.61±0.4171.55±0.7496.39±0.2171.19±0.2179.44±0.3962.90±0.8257.52±0.1476.37±0.3776.79±0.2068.40±0.38
Average Gain1.83±0.433.55±0.850.80±0.348.52±1.063.68±0.670.41±0.131.52±0.520.75±0.350.69±0.210.84±0.30
+ +Table 1. The average accuracy $\pm$ the standard deviation of base algorithms w/o our method on PACS and OfficeHome datasets. The performance is generally boosted when our method is plugged in, whichever base algorithm is used. + +prediction algorithms are based on this multiple-training domain assumption to extract stable features and establish a uniform predictor. Consistent with this common setting, for the multiple training domain problem, we use a unified predictor $f$ trained on all available training domains. However, a mixture of multiple distributions increases the difficulty of training for the diffusion model, which leads to a slower convergence and domain collapse (only generating samples from easy domains). Given consideration to these undesired phenomena, for the multiple training domain problem, we train individual diffusion model $g_{m}$ , where $m = 1,\dots ,M$ is the training domain index, on each training domain, use every $g_{m}$ to transfer the OoD sample, and then obtain the prediction $h_m$ from every transferred sample using $f$ . Finally, we ensemble the predictions $\{h_m\}_{m = 1}^M$ together to get the overall prediction. In our experiments, the ensemble is conducted by averaging the logits (the inputs of the softmax layer) in the predictor neural network. + +The overall framework of DSI is shown in Algorithm 1. + +# 5. Experiments + +Datasets. In the main text, experiments on the following datasets are reported. More experiments can be found in supplementary materials. (1) PACS [33] contains 999,1 colored images from 7 classes and 4 domains (art painting, cartoon, photo, and sketch); (2) Office-Home [69] contains around 15,500 images from 65 different classes and 4 domains (artistic, clip art, product, and real-world). + +Base Methods. Based on the taxonomy in Sec. 2, we select one (or two) up-to-date or representative algorithm(s) from each category as the base methods in the experiments with multiple training domains. For experiments with a + +single training domain, we adjust the list of base methods by only choosing the algorithms without multi-domain assumption. For each experimental configuration (dataset and training-testing split), the hyperparameters of each algorithm are optimized based on the performance metric on the testing set over 10 random searches. The searching regions are reported in supplementary materials. Fixing the optimal hyperparameters, we repeat the experimental pipeline three times and report the average results together with the standard deviations to alleviate the influence of the lucky weight initialization and dataset split. + +In Tabs. 1 and 2, we use [algorithm]* to indicate the use of DSI, the green cells to indicate our method improves the base method, and the green cells with text in bold to indicate our method improves the base method with non-overlapped confidence interval. + +# 5.1. Multi-training Domain Generalization + +The experiments for multi-training domain generalization are conducted on PACS and OfficeHome. For each dataset, one domain is left as the testing domain and the other three are used for training. The performance comparison of base methods with and without our method are listed in Tab. 1. Our method generally enhances the OoD prediction of all types of base methods by $3.68\%$ on PACS and $0.84\%$ on OfficeHome, which indicates DSI successfully closes the distance between the OoD samples and the training distribution. The significance of the improvements varies among different leave-one-out settings, because the accuracy of the base methods varies. When the accuracy of the base method is low (e.g., the average accuracy of the base methods is $61.88\%$ for S of PACS), more $(8.22\%)$ improvement is achieved. When + +![](images/70088e06ce5bf277c1e9cb102615e93aa6f2ef442e63e07be6d4936309a0faa6.jpg) + +![](images/655137bc8068ff47a55d854fd950e24ba04e80dde50938442b83f2fd92d34cba.jpg) + +![](images/ec1a14765d5a5e4627dc90d065d471d22c7053f7c4ad9aae4722adfd064de1b9.jpg) +(a) Testing Domain: Art +(e) Testing Domain: Art + +![](images/4a75f29c16c22d22f66cf3b066dd758daa510d4fee43b7ef9a3a1d8624c65100.jpg) +(b) Testing Domain: Cartoon +(f) Testing Domain: Cartoon + +![](images/ba9abe231334927a55c18704cedc53f602271c98cb6a17115186d39f284ccadc.jpg) + +![](images/5366802d15f708ad4b32f8ebf6d893ab6651f25c813f7d05eb0df6a371d933a5.jpg) +(c) Testing Domain: Photo +(g) Testing Domain: Photo + +![](images/5795729edff7d571812b33f38bbcbcf1ab1f459f32accdcdc072889caf16a18a.jpg) + +![](images/a9f0285724b3b97b9e69f011f7e5bd121a7e295921ecf14f7fc5fc671f1a31fe.jpg) +(d) Testing Domain: Sketch +(h) Testing Domain: Sketch + +the accuracy of the base method is high (e.g., the average accuracy of the base methods is $94.61\%$ for P of PACS), the absolute value of the improvement is less $(0.89\%)$ . We also notice that the rise in performance on OfficeHome dataset is less than the PACS, which can be attributed to that the larger number of classes in OfficeHome increases the hardness of the semantic label preservation of our method. + +We further analyze whether the performance gain depends on a certain class or domain. We count, for each class in each testing domain, (1) the number of samples correctly predicted by both the base methods and the base methods with DSI(# Both Correct), (2) the number of samples correctly predicted by the base methods with DSI but wrongly predicted by base methods (# Only Ours Correct), (3) the number of samples correctly predicted by the base methods (# Base Correct), and (4) the number of samples wrongly predicted by the base methods (# Base Wrong). Fig. 4 shows the preservation ratio calculated by $\frac{\# \text{Both Correct}}{\# \text{Base Correct}}$ and the correction ratio calculated by $\frac{\# \text{Only Ours Correct}}{\# \text{Base Wrong}}$ . The preservation ratio indicates the percentage of the correct predictions that are still correct when our method is used. The correction ratio indicates the percentage of the wrong predictions that are corrected when our method is used. Averaging over testing domains and classes, $94.52\%$ of the correct predictions are still correct when our method is used. The highest preservation ratio is $95.95\%$ appearing when photo is the testing domain. Among the testing domains and the classes, our method can at least correct $8.57\%$ wrong predictions and averagely $28.17\%$ . These results prove the general effectiveness of our methods across different domains and classes. + +![](images/636c714e2f68cde0e10dc7ad9767c1d1e0412c3a61a996b9782761dd4212ee2f.jpg) +Figure 4. The percentage of correct prediction when using our method among the samples which are correctly predicted by the base method (in Fig. 4a to Fig. 4d), or wrongly predicted by the base method (in Fig. 4e to Fig. 4h). The plot is separately drawn for each leave-one-out setting and each class. +Figure 5. Accuracy v.s. Starting Time $s$ on PACS dataset with the testing domain of "Cartoon". + +# 5.2. Single-training Domain Generalization + +To cover the harder single training domain generalization, we do experiments on PACS datasets in which we use each domain as the training domain and test on the other three. The performance comparison of base methods with and without our method on the dataset with single training domains are listed in Tab. 2. With our method, irrelevant to the training and testing domain, general performance gains are achieved and the average performance gain is $2.42\%$ . + +# 5.3. Discussion on the starting time $s$ + +Transforming the distribution closer to the source distribution increases the confidence of the prediction based on the transformed image. On the other hand, the well-preserved label information guarantees the prediction of the generated image has the same label as its origin. However, increasing $s$ to get further distribution transformation will destroy the label information, contrarily, decreasing $s$ to preserve the + +
DatasetPACS
Training DomainACPS
Testing DomainCPSAPSACSACP
ERM55.37±0.3297.92±0.0542.84±1.6855.63±0.2683.43±0.3257.42±2.2764.84±1.0228.26±3.8623.24±4.8815.82±1.3314.26±0.7012.66±0.49
ERM*57.58±0.2697.90±0.0348.54±1.1257.03±0.4483.98±0.5663.74±2.0065.92±0.3732.75±3.7825.68±4.7816.41±1.5116.80±0.7612.92±0.20
CORAL56.35±2.6396.68±0.6342.32±2.6055.47±0.5284.15±0.7057.81±1.6562.04±0.7432.16±5.8426.33±8.4615.27±0.6815.76±1.1611.65±0.81
CORAL*58.76±2.9696.84±0.5347.56±1.1656.87±0.0984.38±0.8364.65±2.0163.90±1.0135.97±4.8029.23±7.9915.98±0.6616.50±1.0412.27±0.92
RSC55.21±0.2898.18±0.1744.66±1.6954.36±1.0683.79±0.6259.41±2.3363.05±0.9631.61±6.7524.90±5.1216.57±0.5916.37±0.2613.77±1.92
RSC*57.39±0.4598.24±0.1550.39±1.2555.70±0.7483.95±0.5665.98±1.6064.13±1.6435.29±5.7728.22±4.8717.68±0.6817.45±0.6914.49±1.88
SagNet56.41±0.4797.95±0.0846.81±3.3358.82±1.1886.95±0.7957.91±2.6267.32±0.9941.76±2.3535.77±2.4815.76±0.9114.23±2.4516.76±1.51
SagNet*58.85±0.5197.96±0.0853.48±3.3059.51±1.4087.14±0.9764.71±3.5067.74±0.7544.34±2.0038.64±1.8418.03±0.6715.95±2.1718.26±1.90
Average Gain2.31±0.120.05±0.075.83±0.521.20±0.300.28±0.166.63±0.211.11±0.513.64±0.692.88±0.311.17±0.671.52±0.680.77±0.45
+ +Table 2. The average accuracy $\pm$ the standard deviation of base algorithms w/o our method on PACS datasets with single training domain setting. The performance is generally boosted when our method is plugged in, whichever base algorithm used. + +![](images/08087e127fd3fd318a5f1c871cde0e1c7ba016d49781fe1f41669647276ef705.jpg) +(a) Accuracy v.s. Ensemble Set + +![](images/6c2990f47ab1d9bd4de9f486c5dfd3e816ad567ae6725d7893eaef02a3f2f784.jpg) +(b) Accuracy v.s. Threshold +Figure 6. Discussion about the influence of hyperparameters: Ensemble set (Fig. 6a) and Threshold (Fig. 6b) on the PACS dataset with the testing domain of "Cartoon". The y-axis label of Fig. 6a indicates the components of the ensemble set with the corresponding accuracy's show on the right. The row of "C" corresponds to the setting using the original testing images alone. The areas below(above) correspond to the ensembles with(without) the original testing images. + +label information will limit the distribution transformation. Thus, an optimal $s$ exists for each algorithm. (see Fig. 5) + +# 5.4. Discussions on hyperparameters + +**Ensemble.** We analyze whether only transforming the testing domain data to a subset of the training domains influences the performance gain or not. Fig. 6a shows the accuracy with different ensemble sets on PACS with the multi-training domain setting and Cartoon is the testing domain. Each row corresponds to one kind of ensemble. For example, row "C" shows the accuracy when the prediction is only based on the original testing image, which is the accuracy of the base methods; row "C,A" shows the accuracy when the prediction based on the original testing image and + +prediction based on the image transformed towards the domain Art are considered together. As shown from the figure, including more components in the ensemble set increases the average performance and reduces its variance; ensembles without the original prediction can perform comparably with the base method; the ensembles with the original prediction and any (one, two, or all) of the predictions based on the transformed image is statistically better than the base methods. + +**Confidence Threshold.** We analyze the influence of the confidence threshold $k$ , and the performance with varying $k$ are shown in 6b. Base methods are special cases when $k = 0$ , their performances are shown along the red vertical line. Though tuning $k$ enlarges the performance gain, when $k > 0$ , our method is activated and there are always performance improvements. + +# 6. Conclusion + +In this paper, we investigate a novel task, termed unseen distribution transformation, which aims at transforming the unseen distribution towards the seen distribution. We frame the first solution to unseen distribution transformation, in which the unseen distribution is first linearly combined with the Gaussian noise and then transformed by a diffusion model trained on the seen domain. By solving this task, we provide a new perspective for addressing the OoD prediction task by first closing the distance between the testing domain and the training domain and then drawing prediction. We propose the portable DSI, which conducts sample adaptive unseen distribution transformation to enhance the OoD prediction algorithms. Experimental results show that our method results in general performance gains when inserted into various types of base methods under multi-training and single-training domain generalization problems. + +# 7. Acknowledgment + +This project is supported by the Singapore Ministry of Education Academic Research Fund Tier 1 (Grantor's Reference Number: 23-0306-A0001), a project titled "Towards Robust Single Domain Generalization in Deep Learning". + +# References + +[1] Kartik Ahuja, Ethan Caballero, Dinghuai Zhang, Yoshua Bengio, Ioannis Mitliagkas, and Irina Rish. Invariance principle meets information bottleneck for out-of-distribution generalization. arXiv:2106.06607, 2021. 3, 6 +[2] Martin Arjovsky, León Bottou, Ishaan Gulrajani, and David Lopez-Paz. Invariant risk minimization. arXiv:1907.02893, 2019. 1, 3 +[3] Omri Avrahami, Dani Lischinski, and Ohad Fried. Blended diffusion for text-driven editing of natural images. In CVPR, 2022. 3 +[4] Haoyue Bai, Rui Sun, Lanqing Hong, Fengwei Zhou, Nanyang Ye, Han-Jia Ye, S.-H. Gary Chan, and Zhenguo Li. Decaug: Out-of-distribution generalization via decomposed feature representation and semantic augmentation. 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In ICCV, 2021. 3 \ No newline at end of file diff --git a/2023/Distribution Shift Inversion for Out-of-Distribution Prediction/images.zip b/2023/Distribution Shift Inversion for Out-of-Distribution Prediction/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..6bcb5dd38e6776f240eaceb31d054e748a55ad07 --- /dev/null +++ b/2023/Distribution Shift Inversion for Out-of-Distribution Prediction/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:d3c5d4817762ec0e86208022ca56db09d12080599fa5258841dccf7c1fc2ea48 +size 733993 diff --git a/2023/Distribution Shift Inversion for Out-of-Distribution Prediction/layout.json b/2023/Distribution Shift Inversion for Out-of-Distribution Prediction/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..59cee90ff906cea0741f14154e0e0e88f15e7433 --- /dev/null +++ b/2023/Distribution Shift Inversion for Out-of-Distribution Prediction/layout.json @@ -0,0 +1,10573 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 104, + 103, + 489, + 119 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 103, + 489, + 119 + ], + "spans": [ + { + "bbox": [ + 104, + 103, + 489, + 119 + ], + "type": "text", + "content": "Distribution Shift Inversion for Out-of-Distribution Prediction" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 136, + 142, + 455, + 172 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 136, + 142, + 455, + 172 + ], + "spans": [ + { + "bbox": [ + 136, + 142, + 455, + 172 + ], + "type": "text", + "content": "Runpeng Yu Songhua Liu Xingyi Yang Xinchao Wang† National University of Singapore" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 147, + 174, + 443, + 186 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 147, + 174, + 443, + 186 + ], + "spans": [ + { + "bbox": [ + 147, + 174, + 443, + 186 + ], + "type": "text", + "content": "{r.yu, songhua.liu, xyang}@u.nus.edu xinchao@nus.edu.sg" + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 56, + 193, + 537, + 276 + ], + "blocks": [ + { + "bbox": [ + 56, + 193, + 537, + 276 + ], + "lines": [ + { + "bbox": [ + 56, + 193, + 537, + 276 + ], + "spans": [ + { + "bbox": [ + 56, + 193, + 537, + 276 + ], + "type": "image", + "image_path": "57a1db31e16982ae638b70d944f7d20809162ed97d4528fd9f70b6b9e13f1cbf.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 284, + 546, + 307 + ], + "lines": [ + { + "bbox": [ + 46, + 284, + 546, + 307 + ], + "spans": [ + { + "bbox": [ + 46, + 284, + 546, + 307 + ], + "type": "text", + "content": "Figure 1. Transformed OoD samples from PACS dataset. Odd rows show the original OoD images, and even rows show their transformation results to the source distribution, obtained by the proposed DSI. Please zoom in for better visualization." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 143, + 316, + 192, + 329 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 316, + 192, + 329 + ], + "spans": [ + { + "bbox": [ + 143, + 316, + 192, + 329 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 332, + 290, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 332, + 290, + 632 + ], + "spans": [ + { + "bbox": [ + 46, + 332, + 290, + 632 + ], + "type": "text", + "content": "Machine learning society has witnessed the emergence of a myriad of Out-of-Distribution (OoD) algorithms, which address the distribution shift between the training and the testing distribution by searching for a unified predictor or invariant feature representation. However, the task of directly mitigating the distribution shift in the unseen testing set is rarely investigated, due to the unavailability of the testing distribution during the training phase and thus the impossibility of training a distribution translator mapping between the training and testing distribution. In this paper, we explore how to bypass the requirement of testing distribution for distribution translator training and make the distribution translation useful for OoD prediction. We propose a portable Distribution Shift Inversion (DSI) algorithm, in which, before being fed into the prediction model, the OoD testing samples are first linearly combined with additional Gaussian noise and then transferred back towards the training distribution using a diffusion model trained only on the source distribution. Theoretical analysis reveals the feasibility of our method. Experimental results, on both multiple-domain generalization datasets and single-domain generalization datasets, show that our method provides a general performance gain when plugged into a wide range of commonly used OoD algorithms. Our code is available at https://github.com/yu-rp/Distribution-Shift-Iverson." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 653, + 128, + 665 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 653, + 128, + 665 + ], + "spans": [ + { + "bbox": [ + 47, + 653, + 128, + 665 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 672, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 672, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 47, + 672, + 287, + 696 + ], + "type": "text", + "content": "The ubiquity of the distribution shift between the training and testing data in the real-world application of machine" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 318, + 547, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 318, + 547, + 461 + ], + "spans": [ + { + "bbox": [ + 306, + 318, + 547, + 461 + ], + "type": "text", + "content": "learning systems induces the study of Out-of-Distribution (OoD) generalization (or domain generalization). [18, 64, 71, 79] Within the scope of OoD generalization, machine learning algorithms are required to generalize from the seen training domain to the unseen testing domain without the independent and identically distributed assumption. The bulk of the OoD algorithms in previous literature focuses on promoting the generalization capability of the machine learning models themselves by utilizing the domain invariant feature [2, 13, 36], context-based data augmentation [47, 74], distributionally robust optimization [59], subnetwork searching [81], neural network calibration [70], etc." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 462, + 548, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 548, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 548, + 605 + ], + "type": "text", + "content": "In this work, orthogonal to enhancing the generalization capability of the model, we consider a novel pathway to OoD prediction. On the way, the testing(target) distribution is explicitly transformed towards the training.source) distribution to straightforwardly mitigate the distribution shift between the testing and the training distribution. Therein, the OoD prediction can be regarded as a two-step procedure, (1) transferring testing samples back towards training distribution, and (2) drawing prediction. The second step can be implemented by any OoD prediction algorithm. In this paper, we concentrate on the exploration of the first step, the distribution transformation." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 605, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 548, + 714 + ], + "type": "text", + "content": "Unlike previous works on distribution translation and domain transformation, in which certain target distribution is accessible during the training phase, here the target distribution is arbitrary and unavailable during the training. We term this new task as Unseen Distribution Transformation (UDT), in which a domain translator is trained on the source distribution and works to transform unseen target distribution towards the source distribution. The uniqueness, as well as the superiority, of UDT is listed as followings." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 1, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 1, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 1, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "type": "text", + "content": "† Corresponding author." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "type": "text", + "content": "3592" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 70, + 286, + 195 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 286, + 195 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 286, + 195 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 286, + 195 + ], + "type": "image", + "image_path": "d3b3409097f1042a2e129adde8fa4f1fc40f31f3937c1441e9f7dc59bd6ef724.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 205, + 287, + 239 + ], + "lines": [ + { + "bbox": [ + 46, + 205, + 287, + 239 + ], + "spans": [ + { + "bbox": [ + 46, + 205, + 287, + 239 + ], + "type": "text", + "content": "Figure 2. Using a Diffusion Model to solve the one-dimensional UDT. OoD samples are transformed to the source distribution with limited failure of label preservation." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 59, + 242, + 287, + 413 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 59, + 242, + 287, + 290 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 242, + 287, + 290 + ], + "spans": [ + { + "bbox": [ + 59, + 242, + 287, + 290 + ], + "type": "text", + "content": "- UDT puts no requirements on the data from both source and testing distribution like previous works do. This is practically valuable, because the real-world testing distributions are uncountable and dynamically changing." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 291, + 287, + 351 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 291, + 287, + 351 + ], + "spans": [ + { + "bbox": [ + 59, + 291, + 287, + 351 + ], + "type": "text", + "content": "- UDT is able to transform various distributions using only one model. However, the previous distribution translator works for the translation between certain source and target distributions. With a different source-target pair, a new translator is required." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 59, + 354, + 287, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 354, + 287, + 413 + ], + "spans": [ + { + "bbox": [ + 59, + 354, + 287, + 413 + ], + "type": "text", + "content": "- Considering the application of UDT in OoD prediction, it is free from the extra assumptions commonly used by the OoD generalization algorithms, such as the multi-training domain assumption and the various forms of the domain invariant assumption." + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 46, + 414, + 287, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 414, + 287, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 414, + 287, + 533 + ], + "type": "text", + "content": "Despite the advantages, the unavailability of the testing distribution poses new difficulty. Releasing this constraint, the idea of distribution alignment is well established in domain adaptation (DA). Wherein, a distribution translator is trained with the (pixel, feature, and semantic level) cycle consistency loss [23, 38, 82]. However, the training of such distribution transfer modules necessitates the testing distribution, which is unsuitable under the setting of OoD prediction and makes the transplant of the methods in DA to OoD even impossible." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 534, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 534, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 534, + 288, + 713 + ], + "type": "text", + "content": "To circumvent the requirement of testing distribution during training time, we propose a novel method, named Distribution Shift Inversion (DSI). Instead of using a model transferring from testing distribution to training distribution, an unconditional generative model, trained only on the source distribution, is used, which transfers data from a reference noise distribution to the source distribution. The method operates in two successive parts. First, the OoD target distribution is transferred to the neighborhood of the noise distribution and aligned with the input of the generative model, thereafter we refer to this process as the forward transformation. The crux of this step is designing to what degree the target distribution is aligned to the noise distribution. In our implementation, the forward transformation is conducted by linearly combining the OoD samples and random noise with" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 547, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 239 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 239 + ], + "type": "text", + "content": "the weights controlling the alignment. Then, in the second step, the outcome of the first step is transferred towards the source distribution by a generative model, thereafter we refer to this process as the backward transformation. In this paper, the generative model is chosen to be the diffusion model [21]. The superiority of the diffusion model is that its input is the linear combination of the source sample and the noise with varying magnitude, which is in accord with our design of the forward transformation and naturally allows strength control. Comparatively, VAE [28] and GAN [16] have a fixed level of noise in their input, which makes the forward transformation strength control indirect. Our theoretical analyses of the diffusion model also show the feasibility of using the diffusion model for UDT." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 242, + 547, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 242, + 547, + 373 + ], + "spans": [ + { + "bbox": [ + 304, + 242, + 547, + 373 + ], + "type": "text", + "content": "Illustrative Example. A one-dimensional example is shown in Fig. 2. The example considers a binary classification problem, in which, given label, the conditional distributions of the samples are Gaussian in both the source and the testing domain. The testing distribution is constructed to be OoD and located in the region where the source distribution has a low density. The diffusion model is trained only on the source distribution. Passing through the noise space alignment and diffusion model transformation, the OoD samples are transformed to the source distribution with limited failure of label preservation." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 376, + 547, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 376, + 547, + 533 + ], + "spans": [ + { + "bbox": [ + 304, + 376, + 547, + 533 + ], + "type": "text", + "content": "Transformed Images. Fig. 1 shows some transformation results of OoD images towards the source distribution. The observation is twofold. (1) The distribution (here is the style) of the images is successfully transformed. All of the transferred images can be correctly classified by the ERM model trained on the source domain. (2) The transformed images are correlated to the original images. Some structural and color characteristics are mutually shared between them. This indicates that the diffusion model has extracted some low-level information and is capable to preserve it during the transformation. We would like to highlight again that, during the training, the diffusion model is isolated from the testing domain." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 317, + 535, + 509, + 546 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 535, + 509, + 546 + ], + "spans": [ + { + "bbox": [ + 317, + 535, + 509, + 546 + ], + "type": "text", + "content": "Our contributions are therefore summarized as:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 317, + 550, + 547, + 711 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 317, + 550, + 545, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 550, + 545, + 574 + ], + "spans": [ + { + "bbox": [ + 317, + 550, + 545, + 574 + ], + "type": "text", + "content": "- We put forward the unseen distribution transformation (UDT) and study its application to OoD prediction." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 317, + 575, + 547, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 575, + 547, + 588 + ], + "spans": [ + { + "bbox": [ + 317, + 575, + 547, + 588 + ], + "type": "text", + "content": "- We offer theoretical analyses of the feasibility of UDT." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 317, + 590, + 547, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 590, + 547, + 625 + ], + "spans": [ + { + "bbox": [ + 317, + 590, + 547, + 625 + ], + "type": "text", + "content": "- we propose DSI, a sample adaptive distribution transformation algorithm for efficient distribution adaptation and semantic information preservation." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 317, + 628, + 547, + 711 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 628, + 547, + 711 + ], + "spans": [ + { + "bbox": [ + 317, + 628, + 547, + 711 + ], + "type": "text", + "content": "- We perform extensive experiments to demonstrate that our method is suitable for various OoD algorithms to achieve performance gain on diversified OoD benchmarks. On average, adding in our method produces " + }, + { + "bbox": [ + 317, + 628, + 547, + 711 + ], + "type": "inline_equation", + "content": "2.26\\%" + }, + { + "bbox": [ + 317, + 628, + 547, + 711 + ], + "type": "text", + "content": " accuracy gain on multi-training domain generalization datasets and " + }, + { + "bbox": [ + 317, + 628, + 547, + 711 + ], + "type": "inline_equation", + "content": "2.28\\%" + }, + { + "bbox": [ + 317, + 628, + 547, + 711 + ], + "type": "text", + "content": " on single-training domain generalization datasets." + } + ] + } + ], + "index": 15 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3593" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 49, + 71, + 133, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 71, + 133, + 83 + ], + "spans": [ + { + "bbox": [ + 49, + 71, + 133, + 83 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 49, + 91, + 232, + 103 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 91, + 232, + 103 + ], + "spans": [ + { + "bbox": [ + 49, + 91, + 232, + 103 + ], + "type": "text", + "content": "2.1. Out-of-Distribution Generalization" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 49, + 110, + 286, + 134 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 110, + 286, + 134 + ], + "spans": [ + { + "bbox": [ + 49, + 110, + 286, + 134 + ], + "type": "text", + "content": "To achieve OoD generalization, diverse methods have been proposed." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 49, + 136, + 286, + 278 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 136, + 286, + 278 + ], + "spans": [ + { + "bbox": [ + 49, + 136, + 286, + 278 + ], + "type": "text", + "content": "Causal inference methods extract the invariant feature among training domains and build up a unified predictor for all domains. For example, CNBB [19] down-weights the samples which introduce big changes to the feature space by evaluating the causal effect of each sample; ICP [51] find the subset of features satisfying the property that the conditional probability of the target given this set of features is invariant among the domains; IRM [2] regularizes the ERM loss with the norm of the gradient of loss corresponding to the latent features; IB-IRM [1] extends the IRM to the case, where the invariant features are only partially informative, by adding an extra entropy loss term of the latent feature." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 49, + 280, + 286, + 339 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 280, + 286, + 339 + ], + "spans": [ + { + "bbox": [ + 49, + 280, + 286, + 339 + ], + "type": "text", + "content": "Context-based data augmentation methods enrich the training feature space by linear interpolation between the features of inter-domain and intra-domain samples [74]; or combining the normalized feature of one sample with the mean and variance of the feature of another sample [47]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 49, + 340, + 286, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 340, + 286, + 399 + ], + "spans": [ + { + "bbox": [ + 49, + 340, + 286, + 399 + ], + "type": "text", + "content": "Distributional Robust Optimization method, like Group-DRO [59], theoretically formulates the OoD generalization as a min-max optimization and practically up-weights the domains with large losses in an online learning style to guarantee the model fit on all domains." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 49, + 401, + 286, + 580 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 401, + 286, + 580 + ], + "spans": [ + { + "bbox": [ + 49, + 401, + 286, + 580 + ], + "type": "text", + "content": "Feature alignment methods learn a unified feature representation among all training domains with the assumption that this representation is shared by the testing domain data. For example, DANN [13] and CDANN [36] align the marginal and conditional feature distribution by domain adversarial training, respectively; CORAL [67] matches the covariance of the features in every training domain; MASF [11] proposes model-agnostic episodic learning to regularize the semantic structure of the feature space; using the contrastive learning as the regularization term, SelfReg [27] minimizes the distance between the features of the samples within the sample class; CAD and ConCAD [58] minimize the mutual information between the feature and domain variable as well as the negative mutual information between the feature of original samples and the feature of augmented samples." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 49, + 582, + 286, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 582, + 286, + 616 + ], + "spans": [ + { + "bbox": [ + 49, + 582, + 286, + 616 + ], + "type": "text", + "content": "Context feature separation methods recognize the context feature by an extra context discriminator and disentangle them from the category feature by orthogonality penalty [4]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 49, + 618, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 618, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 49, + 618, + 286, + 712 + ], + "type": "text", + "content": "Gradient manipulation methods are designed based on the intuitions that (1) to train a unified predictor, only the gradient common across all domains should be used; or the intuition that (2) the spurious correlation, which leads to larger gradients, is easier to be fitted to and prevent the algorithm from learning other features. For example, IGA [30] and SD [52] penalize the variance of the gradients and the " + }, + { + "bbox": [ + 49, + 618, + 286, + 712 + ], + "type": "inline_equation", + "content": "l_{2}" + }, + { + "bbox": [ + 49, + 618, + 286, + 712 + ], + "type": "text", + "content": " norm of the logits, respectively; RSC [25] only takes" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 308, + 72, + 545, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 72, + 545, + 144 + ], + "spans": [ + { + "bbox": [ + 308, + 72, + 545, + 144 + ], + "type": "text", + "content": "the samples whose gradients are small into consideration; MLDG [34] updates the parameters only when there are performance gains in two separated parts of the training dataset; ANDMask [50] and its ReLU-smoothed version SANDMask [63] only update the parameter whose gradients in most of the domains have the same sign." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 308, + 144, + 545, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 144, + 545, + 263 + ], + "spans": [ + { + "bbox": [ + 308, + 144, + 545, + 263 + ], + "type": "text", + "content": "Different from the previous works, DSI tackles the OoD generalization problem by test time sample adaption. Instead of increasing the OoD generalization ability of the model, DSI aims to mitigate the distribution shift of the testing samples by shifting them back towards the source distribution. Though input enhancing is investigated in dataset distillation [39] and domain adaptation [23, 38, 82], we are the first to test this idea in OoD generalization. Besides its novelty, DSI is orthogonal to the previous algorithms, which allows it to be portably used as a common technique for OoD tasks." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 308, + 272, + 403, + 284 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 272, + 403, + 284 + ], + "spans": [ + { + "bbox": [ + 308, + 272, + 403, + 284 + ], + "type": "text", + "content": "2.2. Diffusion Model" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 308, + 291, + 545, + 493 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 291, + 545, + 493 + ], + "spans": [ + { + "bbox": [ + 308, + 291, + 545, + 493 + ], + "type": "text", + "content": "Neural network reuse has drawn recent interest [75-78]. In this work, we consider reusing pre-trained diffusion models. With promising performance and theoretical explanation, the diffusion model has been intensively investigated in the field of time series generalization/imputation/prediction [29, 32, 56, 68], image generalization/editing/inpainting [3, 6-8, 41, 44, 54, 61], text generalization/modeling [35, 80], text2image generalization [17, 48, 55, 60], text2speech generalization [53], video generalization [22], graph generalization [24, 73], 3D point cloud generalization [42, 43, 83]. Besides, these generation tasks, diffusion model conduces to the downstream tasks such as image segmenting [5], testing time sample adaptation for corrupted images [14], and adversarial attack defense [49]. In DSI, we explore a new application of the diffusion model in which it enhances the OoD prediction by transferring the OoD samples towards the source distribution." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 308, + 502, + 484, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 502, + 484, + 514 + ], + "spans": [ + { + "bbox": [ + 308, + 502, + 484, + 514 + ], + "type": "text", + "content": "2.3. Prediction Confidence Estimation" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 308, + 522, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 522, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 308, + 522, + 545, + 712 + ], + "type": "text", + "content": "In DSI, the prediction confidence score is used for selecting poorly predicted samples and achieving an adaptive distribution shift inversion at the sample level. By satisfying the partial order relationship of uncertainty, commonly used loss functions, such as softmax cross entropy, are suitable confidence metrics. [31] Other softmax-based scores, such as the maximum class probability [15, 20], true class probability [10] and the KL-divergence between the softmax distribution and the uniform distribution [20] are also widely used. Based on the Bayesian method, Monte Carlo dropout [12], use the standard uncertainty criteria (e.g., variance, entropy) of the stochastic network predictions as the confidence score. Taking a modified nearest-neighbor classifier as the reference, trust score [26] uses a minimal distance ratio as the confidence score. We note that measurements in the field of OoD detection [37,40,46,57,62] and sample" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 750, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 750, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 750, + 314, + 757 + ], + "type": "text", + "content": "3594" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "type": "text", + "content": "difficulty estimation may also serve as proper filtering metrics for DSI. But, in this paper, we prefer to establish a new OoD prediction framework and leave the discovery of the potential filtering metrics as future work." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 131, + 124, + 144 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 131, + 124, + 144 + ], + "spans": [ + { + "bbox": [ + 47, + 131, + 124, + 144 + ], + "type": "text", + "content": "3. Preliminary" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 151, + 287, + 234 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 151, + 287, + 234 + ], + "spans": [ + { + "bbox": [ + 46, + 151, + 287, + 234 + ], + "type": "text", + "content": "The task of sampling an instance " + }, + { + "bbox": [ + 46, + 151, + 287, + 234 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 46, + 151, + 287, + 234 + ], + "type": "text", + "content": " of a random variable " + }, + { + "bbox": [ + 46, + 151, + 287, + 234 + ], + "type": "inline_equation", + "content": "\\pmb{X} \\in \\mathcal{R}^d" + }, + { + "bbox": [ + 46, + 151, + 287, + 234 + ], + "type": "text", + "content": " with distribution " + }, + { + "bbox": [ + 46, + 151, + 287, + 234 + ], + "type": "inline_equation", + "content": "p(\\pmb{x})" + }, + { + "bbox": [ + 46, + 151, + 287, + 234 + ], + "type": "text", + "content": " is generally intractable due to the fact that " + }, + { + "bbox": [ + 46, + 151, + 287, + 234 + ], + "type": "inline_equation", + "content": "p(\\pmb{x})" + }, + { + "bbox": [ + 46, + 151, + 287, + 234 + ], + "type": "text", + "content": " is complex or unknown. Diffusion model, such as ScoreFlow [66] and DDPM [21], first samples from an simple distribution " + }, + { + "bbox": [ + 46, + 151, + 287, + 234 + ], + "type": "inline_equation", + "content": "\\rho(\\pmb{x})" + }, + { + "bbox": [ + 46, + 151, + 287, + 234 + ], + "type": "text", + "content": " and then iteratively transforms sample " + }, + { + "bbox": [ + 46, + 151, + 287, + 234 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 46, + 151, + 287, + 234 + ], + "type": "text", + "content": " to make its distribution consistent with " + }, + { + "bbox": [ + 46, + 151, + 287, + 234 + ], + "type": "inline_equation", + "content": "p(\\pmb{x})" + }, + { + "bbox": [ + 46, + 151, + 287, + 234 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 235, + 288, + 282 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 235, + 288, + 282 + ], + "spans": [ + { + "bbox": [ + 46, + 235, + 288, + 282 + ], + "type": "text", + "content": "Under the continuous time setting, diffusion model formulates the forward transformation from " + }, + { + "bbox": [ + 46, + 235, + 288, + 282 + ], + "type": "inline_equation", + "content": "p(\\pmb{x})" + }, + { + "bbox": [ + 46, + 235, + 288, + 282 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 235, + 288, + 282 + ], + "type": "inline_equation", + "content": "\\rho(\\pmb{x})" + }, + { + "bbox": [ + 46, + 235, + 288, + 282 + ], + "type": "text", + "content": " as a stochastic process " + }, + { + "bbox": [ + 46, + 235, + 288, + 282 + ], + "type": "inline_equation", + "content": "\\{x_t\\}_{t=0}^T" + }, + { + "bbox": [ + 46, + 235, + 288, + 282 + ], + "type": "text", + "content": " following the Stochastic Differential Equation (SDE)" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 111, + 292, + 287, + 304 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 292, + 287, + 304 + ], + "spans": [ + { + "bbox": [ + 111, + 292, + 287, + 304 + ], + "type": "interline_equation", + "content": "d \\boldsymbol {x} = f (\\boldsymbol {x}, t) d t + g (t) d \\boldsymbol {w}, \\tag {1}", + "image_path": "a30a49a094553dcde67938f4ae66bcf3f5d763a45305cc2b34edec1b4319e88d.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 314, + 288, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 314, + 288, + 422 + ], + "spans": [ + { + "bbox": [ + 46, + 314, + 288, + 422 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 314, + 288, + 422 + ], + "type": "inline_equation", + "content": "f(\\cdot, t): \\mathcal{R}^d \\to \\mathcal{R}^d" + }, + { + "bbox": [ + 46, + 314, + 288, + 422 + ], + "type": "text", + "content": " is named drift coefficient, " + }, + { + "bbox": [ + 46, + 314, + 288, + 422 + ], + "type": "inline_equation", + "content": "g(t) \\in \\mathcal{R}" + }, + { + "bbox": [ + 46, + 314, + 288, + 422 + ], + "type": "text", + "content": " is named diffusion coefficient, and " + }, + { + "bbox": [ + 46, + 314, + 288, + 422 + ], + "type": "inline_equation", + "content": "\\pmb{w}" + }, + { + "bbox": [ + 46, + 314, + 288, + 422 + ], + "type": "text", + "content": " is the Wiener process whose derivative " + }, + { + "bbox": [ + 46, + 314, + 288, + 422 + ], + "type": "inline_equation", + "content": "d\\pmb{w}" + }, + { + "bbox": [ + 46, + 314, + 288, + 422 + ], + "type": "text", + "content": " is characterized by a standard Gaussian random variable (white Gaussian noise). The corresponding marginal distribution " + }, + { + "bbox": [ + 46, + 314, + 288, + 422 + ], + "type": "inline_equation", + "content": "p_t(\\pmb{x})" + }, + { + "bbox": [ + 46, + 314, + 288, + 422 + ], + "type": "text", + "content": " at time " + }, + { + "bbox": [ + 46, + 314, + 288, + 422 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 314, + 288, + 422 + ], + "type": "text", + "content": " satisfies " + }, + { + "bbox": [ + 46, + 314, + 288, + 422 + ], + "type": "inline_equation", + "content": "p_0(\\pmb{x}) = p(\\pmb{x})" + }, + { + "bbox": [ + 46, + 314, + 288, + 422 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 314, + 288, + 422 + ], + "type": "inline_equation", + "content": "p_T(\\pmb{x}) \\approx \\rho(\\pmb{x})" + }, + { + "bbox": [ + 46, + 314, + 288, + 422 + ], + "type": "text", + "content": ". To sample from " + }, + { + "bbox": [ + 46, + 314, + 288, + 422 + ], + "type": "inline_equation", + "content": "p(\\pmb{x})" + }, + { + "bbox": [ + 46, + 314, + 288, + 422 + ], + "type": "text", + "content": ", the diffusion model first samples from " + }, + { + "bbox": [ + 46, + 314, + 288, + 422 + ], + "type": "inline_equation", + "content": "\\rho(\\pmb{x})" + }, + { + "bbox": [ + 46, + 314, + 288, + 422 + ], + "type": "text", + "content": " and then transforms " + }, + { + "bbox": [ + 46, + 314, + 288, + 422 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 46, + 314, + 288, + 422 + ], + "type": "text", + "content": " backward according to the inverse SDE associated with Eq. (1)" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 59, + 430, + 287, + 444 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 430, + 287, + 444 + ], + "spans": [ + { + "bbox": [ + 59, + 430, + 287, + 444 + ], + "type": "interline_equation", + "content": "d \\boldsymbol {x} = [ f (\\boldsymbol {x}, t) - g ^ {2} (t) \\nabla_ {\\boldsymbol {x}} \\log p _ {t} (\\boldsymbol {x}) ] d t + g (t) d \\bar {\\boldsymbol {w}}, \\tag {2}", + "image_path": "6227a9c5e17cdd445b21aef64d157d6c79ca3ce0b7284aeef44e3ad6a2debc31.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 453, + 287, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 453, + 287, + 548 + ], + "spans": [ + { + "bbox": [ + 46, + 453, + 287, + 548 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 453, + 287, + 548 + ], + "type": "inline_equation", + "content": "dt" + }, + { + "bbox": [ + 46, + 453, + 287, + 548 + ], + "type": "text", + "content": " is the negative time flow, evolving from " + }, + { + "bbox": [ + 46, + 453, + 287, + 548 + ], + "type": "inline_equation", + "content": "t = T" + }, + { + "bbox": [ + 46, + 453, + 287, + 548 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 453, + 287, + 548 + ], + "type": "inline_equation", + "content": "t = 0" + }, + { + "bbox": [ + 46, + 453, + 287, + 548 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 453, + 287, + 548 + ], + "type": "inline_equation", + "content": "\\bar{w}" + }, + { + "bbox": [ + 46, + 453, + 287, + 548 + ], + "type": "text", + "content": " is the Wiener process in the inverse time direction whose derivative " + }, + { + "bbox": [ + 46, + 453, + 287, + 548 + ], + "type": "inline_equation", + "content": "d\\bar{w}" + }, + { + "bbox": [ + 46, + 453, + 287, + 548 + ], + "type": "text", + "content": " is again a standard Gaussian random variable because of the Gaussian increment characterization of Wiener process. In Eq. (2), " + }, + { + "bbox": [ + 46, + 453, + 287, + 548 + ], + "type": "inline_equation", + "content": "\\nabla_{\\pmb{x}}\\log p_t(\\pmb {x})" + }, + { + "bbox": [ + 46, + 453, + 287, + 548 + ], + "type": "text", + "content": " is the unknown score function of " + }, + { + "bbox": [ + 46, + 453, + 287, + 548 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 46, + 453, + 287, + 548 + ], + "type": "text", + "content": " at time " + }, + { + "bbox": [ + 46, + 453, + 287, + 548 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 453, + 287, + 548 + ], + "type": "text", + "content": ", which is estimated by a neural network " + }, + { + "bbox": [ + 46, + 453, + 287, + 548 + ], + "type": "inline_equation", + "content": "s_{\\theta}(\\pmb {x},t)" + }, + { + "bbox": [ + 46, + 453, + 287, + 548 + ], + "type": "text", + "content": " with the weighted score matching loss" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 54, + 558, + 287, + 612 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 558, + 287, + 612 + ], + "spans": [ + { + "bbox": [ + 54, + 558, + 287, + 612 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {J} _ {S M} (\\boldsymbol {\\theta}; \\lambda (\\cdot)) \\\\ = \\frac {1}{2} \\int_ {0} ^ {T} \\mathbb {E} _ {p _ {t} (\\boldsymbol {x})} [ \\lambda (t) | | \\nabla_ {\\boldsymbol {x}} \\log p _ {t} (\\boldsymbol {x}) - s _ {\\boldsymbol {\\theta}} (\\boldsymbol {x}, t) | | _ {2} ^ {2} ] d t. \\tag {3} \\\\ \\end{array}", + "image_path": "cd9a01072103b994d1c8a503708ae99e065bb47bff97a48667e3c9f6ff048d12.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 621, + 248, + 634 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 621, + 248, + 634 + ], + "spans": [ + { + "bbox": [ + 47, + 621, + 248, + 634 + ], + "type": "text", + "content": "4. Unseen Distribution Transformation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 641, + 288, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 641, + 288, + 666 + ], + "spans": [ + { + "bbox": [ + 47, + 641, + 288, + 666 + ], + "type": "text", + "content": "First, we motivate our method by analyzing why the diffusion model helps promote the OoD generalization." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 666, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 666, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 666, + 287, + 713 + ], + "type": "text", + "content": "Here, we proof that, by feeding a linear combination of the OoD samples and the standard Gaussian noise to a diffusion model, the OoD samples can be transformed to the ID samples." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "text", + "content": "Theorem 1. Given a diffusion model trained on the source distribution " + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "inline_equation", + "content": "p(x)" + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "text", + "content": ", let " + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "inline_equation", + "content": "p_t" + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "text", + "content": " denote the distribution at time " + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "text", + "content": " in the forward transformation, let " + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "inline_equation", + "content": "\\bar{p}(x)" + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "text", + "content": " denote the output distribution when the input of the backward process is standard Gaussian noise " + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "text", + "content": " whose distribution is denoted by " + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "inline_equation", + "content": "\\rho(x)" + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "text", + "content": ", let " + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "inline_equation", + "content": "\\omega(x)" + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "text", + "content": " denote the output distribution when the input of backward process is a convex combination " + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "inline_equation", + "content": "(1 - \\alpha)X' + \\alpha\\epsilon" + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "text", + "content": ", where random variable " + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "inline_equation", + "content": "X'" + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "text", + "content": " is sampled following the target distribution " + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "inline_equation", + "content": "q(x)" + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "inline_equation", + "content": "\\alpha \\in (0,1)" + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "text", + "content": ". Under some regularity conditions detailed in Appendix, we have" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 340, + 200, + 545, + 213 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 340, + 200, + 545, + 213 + ], + "spans": [ + { + "bbox": [ + 340, + 200, + 545, + 213 + ], + "type": "interline_equation", + "content": "K L (p \\mid \\mid \\omega) \\leqslant \\mathcal {J} _ {S M} + K L (p _ {T} \\mid \\mid \\rho) + \\mathcal {F} (\\alpha) \\tag {4}", + "image_path": "21db81d3b524dea5d406200dcda2fb12e8d549db1cf117ec7423dca665389ae4.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 221, + 547, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 221, + 547, + 389 + ], + "spans": [ + { + "bbox": [ + 304, + 221, + 547, + 389 + ], + "type": "text", + "content": "Theorem 1 proves that the testing distribution can be transformed to the source distribution and the convergence is controlled by " + }, + { + "bbox": [ + 304, + 221, + 547, + 389 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 221, + 547, + 389 + ], + "type": "text", + "content": ". The first terms in the inequality are introduced by the pretrained diffusion model. The loss term " + }, + { + "bbox": [ + 304, + 221, + 547, + 389 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_{SM}" + }, + { + "bbox": [ + 304, + 221, + 547, + 389 + ], + "type": "text", + "content": " is small after sufficient training and can be reduced if the training procedure is further optimized. The KL-divergence term " + }, + { + "bbox": [ + 304, + 221, + 547, + 389 + ], + "type": "inline_equation", + "content": "KL(p_{T}||\\rho)" + }, + { + "bbox": [ + 304, + 221, + 547, + 389 + ], + "type": "text", + "content": " indicates the distance between the real distribution achieved by the forward transformation and the manually chosen standard Gaussian distribution, which is monotonically decreasing as the " + }, + { + "bbox": [ + 304, + 221, + 547, + 389 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 221, + 547, + 389 + ], + "type": "text", + "content": " goes larger and converges to 0 as the " + }, + { + "bbox": [ + 304, + 221, + 547, + 389 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 221, + 547, + 389 + ], + "type": "text", + "content": " is sufficient large. The third term (detailed in Appendix) is introduced by the distribution of the OOD testing samples, which is controlled by " + }, + { + "bbox": [ + 304, + 221, + 547, + 389 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 221, + 547, + 389 + ], + "type": "text", + "content": " and converges to 0 as " + }, + { + "bbox": [ + 304, + 221, + 547, + 389 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 221, + 547, + 389 + ], + "type": "text", + "content": " goes to 1." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 396, + 403, + 408 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 396, + 403, + 408 + ], + "spans": [ + { + "bbox": [ + 306, + 396, + 403, + 408 + ], + "type": "text", + "content": "4.1. Implementation" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 415, + 545, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 415, + 545, + 461 + ], + "spans": [ + { + "bbox": [ + 304, + 415, + 545, + 461 + ], + "type": "text", + "content": "In this part, we describe DSI to realize the idea of shifting testing image towards the training distribution to boost the OoD generalization. The entire workflow is illustrated in Fig. 3." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 463, + 547, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 463, + 547, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 463, + 547, + 676 + ], + "type": "text", + "content": "In the previous analysis, by constructing a linear combination of the OoD input and the noise, the alignment between the testing and the training distributions is converted to an alignment problem in the noise space. To be consistent with the diffusion model literature, we rewrite the linear combination as " + }, + { + "bbox": [ + 304, + 463, + 547, + 676 + ], + "type": "inline_equation", + "content": "\\hat{x} = \\beta x + \\alpha \\epsilon" + }, + { + "bbox": [ + 304, + 463, + 547, + 676 + ], + "type": "text", + "content": ". By adjusting the coefficients " + }, + { + "bbox": [ + 304, + 463, + 547, + 676 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 463, + 547, + 676 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 463, + 547, + 676 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 463, + 547, + 676 + ], + "type": "text", + "content": " and the starting time " + }, + { + "bbox": [ + 304, + 463, + 547, + 676 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 463, + 547, + 676 + ], + "type": "text", + "content": ", the distance between the distribution of " + }, + { + "bbox": [ + 304, + 463, + 547, + 676 + ], + "type": "inline_equation", + "content": "\\hat{x}" + }, + { + "bbox": [ + 304, + 463, + 547, + 676 + ], + "type": "text", + "content": " (i.e., " + }, + { + "bbox": [ + 304, + 463, + 547, + 676 + ], + "type": "inline_equation", + "content": "w(\\hat{x})" + }, + { + "bbox": [ + 304, + 463, + 547, + 676 + ], + "type": "text", + "content": ") and the input distribution of the diffusion model (during the training time) at time " + }, + { + "bbox": [ + 304, + 463, + 547, + 676 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 463, + 547, + 676 + ], + "type": "text", + "content": " (i.e., " + }, + { + "bbox": [ + 304, + 463, + 547, + 676 + ], + "type": "inline_equation", + "content": "p_s(x)" + }, + { + "bbox": [ + 304, + 463, + 547, + 676 + ], + "type": "text", + "content": ") is controlled. To better match " + }, + { + "bbox": [ + 304, + 463, + 547, + 676 + ], + "type": "inline_equation", + "content": "w(\\hat{x})" + }, + { + "bbox": [ + 304, + 463, + 547, + 676 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 463, + 547, + 676 + ], + "type": "inline_equation", + "content": "p_s(x)" + }, + { + "bbox": [ + 304, + 463, + 547, + 676 + ], + "type": "text", + "content": ", utilizing the common practice [21, 65] that " + }, + { + "bbox": [ + 304, + 463, + 547, + 676 + ], + "type": "inline_equation", + "content": "x_s" + }, + { + "bbox": [ + 304, + 463, + 547, + 676 + ], + "type": "text", + "content": " is designed to be a linear combination of " + }, + { + "bbox": [ + 304, + 463, + 547, + 676 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 463, + 547, + 676 + ], + "type": "text", + "content": " and Gaussian noise, we keep " + }, + { + "bbox": [ + 304, + 463, + 547, + 676 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 463, + 547, + 676 + ], + "type": "text", + "content": " as a hyperparameter and calculate " + }, + { + "bbox": [ + 304, + 463, + 547, + 676 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 463, + 547, + 676 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 463, + 547, + 676 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 463, + 547, + 676 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 304, + 463, + 547, + 676 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 463, + 547, + 676 + ], + "type": "text", + "content": ". Conditioned on the diffusion model, the maps from " + }, + { + "bbox": [ + 304, + 463, + 547, + 676 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 463, + 547, + 676 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 463, + 547, + 676 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 463, + 547, + 676 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 463, + 547, + 676 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 463, + 547, + 676 + ], + "type": "text", + "content": " vary. Taking DDPM as an example, the calculations can be written as " + }, + { + "bbox": [ + 304, + 463, + 547, + 676 + ], + "type": "inline_equation", + "content": "\\alpha = \\sqrt{1 - \\prod_{l=1}^{s}(1 - \\sigma_l)}" + }, + { + "bbox": [ + 304, + 463, + 547, + 676 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 463, + 547, + 676 + ], + "type": "inline_equation", + "content": "\\beta = \\sqrt{\\prod_{l=1}^{s}(1 - \\sigma_l)}" + }, + { + "bbox": [ + 304, + 463, + 547, + 676 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 463, + 547, + 676 + ], + "type": "inline_equation", + "content": "\\sigma_l" + }, + { + "bbox": [ + 304, + 463, + 547, + 676 + ], + "type": "text", + "content": " is the standard deviation of the noise in the forward process at time " + }, + { + "bbox": [ + 304, + 463, + 547, + 676 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 463, + 547, + 676 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "content": "Next, we look into the schedule of starting time " + }, + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "content": ". Two factors are taken into consideration. First is the time efficiency. The generation of the diffusion model requires an" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3595" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 78, + 537, + 259 + ], + "blocks": [ + { + "bbox": [ + 51, + 78, + 537, + 259 + ], + "lines": [ + { + "bbox": [ + 51, + 78, + 537, + 259 + ], + "spans": [ + { + "bbox": [ + 51, + 78, + 537, + 259 + ], + "type": "image", + "image_path": "99eacc1478574a02f4741191d676d3bb9ade6871d4b7b5895ede64ac63678d9e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 278, + 547, + 313 + ], + "lines": [ + { + "bbox": [ + 46, + 278, + 547, + 313 + ], + "spans": [ + { + "bbox": [ + 46, + 278, + 547, + 313 + ], + "type": "text", + "content": "Figure 3. Illustrative example of DSI finished in two iterations. In the first iteration, insufficient transformation leads to wrong prediction with low confidence. Our algorithm rejects the prediction and continues the second iteration. In the second iteration, with proper transformation, the correct prediction is drawn and accepted. Then, the algorithm finished." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 333, + 290, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 333, + 290, + 514 + ], + "spans": [ + { + "bbox": [ + 46, + 333, + 290, + 514 + ], + "type": "text", + "content": "iterative sampling in which the total sampling steps (thus the sampling time) are controlled by the starting time " + }, + { + "bbox": [ + 46, + 333, + 290, + 514 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 333, + 290, + 514 + ], + "type": "text", + "content": ". Though providing more sufficient distribution transformation, using a large " + }, + { + "bbox": [ + 46, + 333, + 290, + 514 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 333, + 290, + 514 + ], + "type": "text", + "content": " is time-consuming and inappropriate for the online testing environment. [9, 72] Second is the sample differences. As discovered in image editing [45] using the diffusion model, the starting time controls the faithfulness and reality of the generated images. Analogically, in using the diffusion model to transfer the OoD data, " + }, + { + "bbox": [ + 46, + 333, + 290, + 514 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 333, + 290, + 514 + ], + "type": "text", + "content": " is a controller of the degree of distribution transformation and the preservation of semantic information, which are both crucial to OoD prediction. In practice, the distance from different samples to the training distribution is different and the difficulty of the semantic label preservation varies among the samples, which makes a uniform starting time schedule improper." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 521, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 289, + 714 + ], + "type": "text", + "content": "Thus, in DSI, a sample adaptive schedule of the starting time index is used, in which " + }, + { + "bbox": [ + 46, + 521, + 289, + 714 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 521, + 289, + 714 + ], + "type": "text", + "content": " increases gradually. Specifically, given a predefined starting time sequence " + }, + { + "bbox": [ + 46, + 521, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\{s_l\\}_{l=0}^L" + }, + { + "bbox": [ + 46, + 521, + 289, + 714 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 521, + 289, + 714 + ], + "type": "inline_equation", + "content": "s_0 < s_1 < \\dots < s_L" + }, + { + "bbox": [ + 46, + 521, + 289, + 714 + ], + "type": "text", + "content": ", for each OoD sample " + }, + { + "bbox": [ + 46, + 521, + 289, + 714 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 521, + 289, + 714 + ], + "type": "text", + "content": ", DSI begins with the smallest " + }, + { + "bbox": [ + 46, + 521, + 289, + 714 + ], + "type": "inline_equation", + "content": "s_0" + }, + { + "bbox": [ + 46, + 521, + 289, + 714 + ], + "type": "text", + "content": ", uses the diffusion model to transfer the combination " + }, + { + "bbox": [ + 46, + 521, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\hat{x}" + }, + { + "bbox": [ + 46, + 521, + 289, + 714 + ], + "type": "text", + "content": ", and lets the predictor output the prediction result " + }, + { + "bbox": [ + 46, + 521, + 289, + 714 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 46, + 521, + 289, + 714 + ], + "type": "text", + "content": " together with the confidence score " + }, + { + "bbox": [ + 46, + 521, + 289, + 714 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 521, + 289, + 714 + ], + "type": "text", + "content": " of the prediction. If the " + }, + { + "bbox": [ + 46, + 521, + 289, + 714 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 521, + 289, + 714 + ], + "type": "text", + "content": " is greater than a predefined threshold " + }, + { + "bbox": [ + 46, + 521, + 289, + 714 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 521, + 289, + 714 + ], + "type": "text", + "content": ", the prediction is accepted. Otherwise, DSI rejects the prediction, move to the next time index, and repeats the above procedure (transfer, prediction, and then using confidence score to make a judgment). If the prediction confidence score still does not meet the threshold at time index " + }, + { + "bbox": [ + 46, + 521, + 289, + 714 + ], + "type": "inline_equation", + "content": "s_L" + }, + { + "bbox": [ + 46, + 521, + 289, + 714 + ], + "type": "text", + "content": ", the last prediction is accepted. By doing so, DSI allocates a small starting time index to the samples close to the source distribution and a larger one to the samples far from the" + } + ] + } + ], + "index": 3 + }, + { + "type": "code", + "bbox": [ + 306, + 346, + 547, + 582 + ], + "blocks": [ + { + "bbox": [ + 306, + 332, + 473, + 344 + ], + "lines": [ + { + "bbox": [ + 306, + 332, + 473, + 344 + ], + "spans": [ + { + "bbox": [ + 306, + 332, + 473, + 344 + ], + "type": "text", + "content": "Algorithm 1 Distribution Shift Inversion" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 306, + 346, + 547, + 582 + ], + "lines": [ + { + "bbox": [ + 306, + 346, + 547, + 582 + ], + "spans": [ + { + "bbox": [ + 306, + 346, + 547, + 582 + ], + "type": "text", + "content": "Input: Predictor: " + }, + { + "bbox": [ + 306, + 346, + 547, + 582 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 306, + 346, + 547, + 582 + ], + "type": "text", + "content": ", Diffusion 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"type": "text", + "content": ", Confidence score function: " + }, + { + "bbox": [ + 306, + 346, + 547, + 582 + ], + "type": "inline_equation", + "content": "\\psi" + }, + { + "bbox": [ + 306, + 346, + 547, + 582 + ], + "type": "text", + "content": " \nInput: Starting time series: " + }, + { + "bbox": [ + 306, + 346, + 547, + 582 + ], + "type": "inline_equation", + "content": "\\{s_l\\}_{l=0}^L" + }, + { + "bbox": [ + 306, + 346, + 547, + 582 + ], + "type": "text", + "content": ", Threshold: " + }, + { + "bbox": [ + 306, + 346, + 547, + 582 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 306, + 346, + 547, + 582 + ], + "type": "text", + "content": " \nInput: OoD sample: " + }, + { + "bbox": [ + 306, + 346, + 547, + 582 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 306, + 346, + 547, + 582 + ], + "type": "text", + "content": " \n1: " + }, + { + "bbox": [ + 306, + 346, + 547, + 582 + ], + "type": "inline_equation", + "content": "h_0 \\gets f(x)" + }, + { + "bbox": [ + 306, + 346, + 547, + 582 + ], + "type": "inline_equation", + "content": "\\triangleright" + }, + { + "bbox": [ + 306, + 346, + 547, + 582 + ], + "type": "text", + "content": " Draw prediction from original sample \n2: for " + }, + { + "bbox": [ + 306, + 346, + 547, + 582 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 306, + 346, + 547, + 582 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 306, + 346, + 547, + 582 + ], + "type": "inline_equation", + "content": "1, \\dots, L" + }, + { + "bbox": [ + 306, + 346, + 547, + 582 + ], + "type": "text", + "content": " do \n3: " + }, + { + "bbox": [ + 306, + 346, + 547, + 582 + ], + "type": "inline_equation", + "content": "\\alpha, \\beta \\gets \\phi(t_l)" + }, + { + "bbox": [ + 306, + 346, + 547, + 582 + ], + "type": "text", + "content": " \n4: " + }, + { + "bbox": [ + 306, + 346, + 547, + 582 + ], + "type": "inline_equation", + "content": "\\hat{x} \\gets \\beta x + \\alpha \\epsilon" + }, + { + "bbox": [ + 306, + 346, + 547, + 582 + ], + "type": "text", + "content": " \n5: for " + }, + { + "bbox": [ + 306, + 346, + 547, + 582 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 306, + 346, + 547, + 582 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 306, + 346, + 547, + 582 + ], + "type": "inline_equation", + "content": "1, \\dots, M" + }, + { + "bbox": [ + 306, + 346, + 547, + 582 + ], + "type": "text", + "content": " do \n6: " + }, + { + "bbox": [ + 306, + 346, + 547, + 582 + ], + "type": "inline_equation", + "content": "\\tilde{x} \\gets g_m(\\hat{x})" + }, + { + "bbox": [ + 306, + 346, + 547, + 582 + ], + "type": "inline_equation", + "content": "\\triangleright" + }, + { + "bbox": [ + 306, + 346, + 547, + 582 + ], + "type": "text", + "content": " Transfer \n7: " + }, + { + "bbox": [ + 306, + 346, + 547, + 582 + ], + "type": "inline_equation", + "content": "h_m \\gets f(\\tilde{x})" + }, + { + "bbox": [ 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"inline_equation", + "content": "h" + }, + { + "bbox": [ + 306, + 346, + 547, + 582 + ], + "type": "inline_equation", + "content": "\\triangleright" + }, + { + "bbox": [ + 306, + 346, + 547, + 582 + ], + "type": "text", + "content": " Accept the last prediction" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "code_body" + } + ], + "index": 5, + "sub_type": "algorithm" + }, + { + "bbox": [ + 304, + 604, + 547, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 604, + 547, + 688 + ], + "spans": [ + { + "bbox": [ + 304, + 604, + 547, + 688 + ], + "type": "text", + "content": "source distribution. Thus, this adaptation procedure avoids the use of a uniformly small time step which causes some samples to not be fully transferred, or a uniformly large time steps to cause the diffusion model to take too long to proceed. In our experiments, we use the maximum class probability as the confidence score and set the confidence threshold as hyperparameter." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 689, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 547, + 715 + ], + "type": "text", + "content": "Usually, under the setting of OoD prediction, multiple training domains are available. The majority of the OoD" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 316, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 316, + 758 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 316, + 758 + ], + "type": "text", + "content": "3596" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 70, + 545, + 275 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 545, + 275 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 545, + 275 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 545, + 275 + ], + "type": "table", + "html": "
DatasetPACSOfficeHome
Testing DomainACPSAverageACPRAverage
ERM76.24±0.4467.90±0.6494.47±0.4460.32±0.8574.73±0.5960.81±0.5154.17±0.1774.80±0.3576.11±0.4066.47±0.36
ERM*78.52±0.8170.90±0.7695.80±0.1667.97±0.6878.30±0.6061.15±0.5655.96±0.7675.55±0.2376.56±0.2967.31±0.46
ANDMask [50]67.35±0.5163.22±2.2393.98±0.2660.35±1.0571.23±1.0160.84±0.6055.73±0.6073.80±0.4475.88±0.0866.56±0.43
ANDMask*69.43±0.4068.23±2.2994.99±0.2469.63±0.5775.57±0.8861.18±0.6556.80±0.4174.35±0.4076.40±0.5467.18±0.50
CAD [58]75.42±0.5168.20±0.6495.02±0.5559.77±2.1474.60±0.9660.71±0.6453.39±0.1874.41±0.2975.36±0.3965.97±0.38
CAD*76.11±0.8171.81±0.5996.09±0.1669.56±1.6978.39±0.8161.04±0.6355.08±0.4475.20±0.2976.14±0.2866.87±0.41
CondCAD [58]75.55±0.3867.77±0.5095.57±0.1259.99±1.9074.72±0.7360.74±0.3755.27±0.8374.64±0.2675.42±0.2066.52±0.42
CondCAD*77.12±0.3671.61±0.3796.03±0.0969.79±1.9678.64±0.7061.15±0.2856.09±0.5875.52±0.4176.43±0.1767.30±0.36
GroupDRO [59]69.56±1.0163.77±3.7493.16±0.7764.16±1.7872.66±1.8360.32±0.2653.12±0.6471.61±0.6675.68±0.2165.18±0.44
GroupDRO*71.61±0.8167.45±2.7593.78±0.4071.88±1.0276.18±1.2560.73±0.2655.83±0.7973.01±0.9276.14±0.1866.43±0.54
IB_ERM [1]77.18±0.2069.76±0.2494.82±0.8061.26±0.5875.76±0.4658.30±0.7854.39±0.1070.36±0.0572.02±0.4463.77±0.34
IB_ERM*79.07±0.2071.88±0.4495.83±0.3069.95±0.8879.18±0.4658.66±0.8155.66±0.3971.29±0.0172.90±0.3464.63±0.39
IB_IRM [1]75.26±1.0967.77±0.9794.76±0.4560.25±2.4074.51±1.2358.01±0.4452.60±1.0072.75±0.6074.90±0.6564.57±0.67
IB_IRM*77.31±1.0870.70±0.6395.96±0.1268.03±1.6778.00±0.8858.37±0.3953.68±0.4472.95±0.8475.55±0.7965.14±0.62
Mixup [74]71.29±0.4966.11±2.3294.08±0.4764.81±2.8874.07±1.5461.46±0.2055.83±0.6574.06±0.4476.73±0.4167.02±0.43
Mixup*73.18±0.1769.63±2.3594.56±0.4071.45±2.7477.21±1.4262.25±0.3157.85±0.8575.10±0.4077.21±0.2668.10±0.46
SANDMask [63]67.35±0.5162.50±3.8594.17±0.6264.58±0.5872.15±1.3961.78±0.3655.24±0.1273.34±0.4075.68±0.3766.51±0.31
SANDMask*69.43±0.4067.42±2.9694.73±0.4272.66±0.6376.06±1.1062.14±0.3556.58±0.2873.50±0.2376.27±0.2967.12±0.29
SelfReg [27]76.86±0.0868.62±0.7496.09±0.1461.39±0.8175.74±0.4462.50±0.7656.09±0.2375.52±0.3875.75±0.2467.47±0.40
SelfReg*78.61±0.4171.55±0.7496.39±0.2171.19±0.2179.44±0.3962.90±0.8257.52±0.1476.37±0.3776.79±0.2068.40±0.38
Average Gain1.83±0.433.55±0.850.80±0.348.52±1.063.68±0.670.41±0.131.52±0.520.75±0.350.69±0.210.84±0.30
", + "image_path": "c6116856a12d7cc6bdc95890b5540962b4e5024decc5fcddc5fc35c20e3786ff.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 285, + 545, + 308 + ], + "lines": [ + { + "bbox": [ + 46, + 285, + 545, + 308 + ], + "spans": [ + { + "bbox": [ + 46, + 285, + 545, + 308 + ], + "type": "text", + "content": "Table 1. The average accuracy " + }, + { + "bbox": [ + 46, + 285, + 545, + 308 + ], + "type": "inline_equation", + "content": "\\pm" + }, + { + "bbox": [ + 46, + 285, + 545, + 308 + ], + "type": "text", + "content": " the standard deviation of base algorithms w/o our method on PACS and OfficeHome datasets. The performance is generally boosted when our method is plugged in, whichever base algorithm is used." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 45, + 321, + 289, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 321, + 289, + 536 + ], + "spans": [ + { + "bbox": [ + 45, + 321, + 289, + 536 + ], + "type": "text", + "content": "prediction algorithms are based on this multiple-training domain assumption to extract stable features and establish a uniform predictor. Consistent with this common setting, for the multiple training domain problem, we use a unified predictor " + }, + { + "bbox": [ + 45, + 321, + 289, + 536 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 45, + 321, + 289, + 536 + ], + "type": "text", + "content": " trained on all available training domains. However, a mixture of multiple distributions increases the difficulty of training for the diffusion model, which leads to a slower convergence and domain collapse (only generating samples from easy domains). Given consideration to these undesired phenomena, for the multiple training domain problem, we train individual diffusion model " + }, + { + "bbox": [ + 45, + 321, + 289, + 536 + ], + "type": "inline_equation", + "content": "g_{m}" + }, + { + "bbox": [ + 45, + 321, + 289, + 536 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 45, + 321, + 289, + 536 + ], + "type": "inline_equation", + "content": "m = 1,\\dots ,M" + }, + { + "bbox": [ + 45, + 321, + 289, + 536 + ], + "type": "text", + "content": " is the training domain index, on each training domain, use every " + }, + { + "bbox": [ + 45, + 321, + 289, + 536 + ], + "type": "inline_equation", + "content": "g_{m}" + }, + { + "bbox": [ + 45, + 321, + 289, + 536 + ], + "type": "text", + "content": " to transfer the OoD sample, and then obtain the prediction " + }, + { + "bbox": [ + 45, + 321, + 289, + 536 + ], + "type": "inline_equation", + "content": "h_m" + }, + { + "bbox": [ + 45, + 321, + 289, + 536 + ], + "type": "text", + "content": " from every transferred sample using " + }, + { + "bbox": [ + 45, + 321, + 289, + 536 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 45, + 321, + 289, + 536 + ], + "type": "text", + "content": ". Finally, we ensemble the predictions " + }, + { + "bbox": [ + 45, + 321, + 289, + 536 + ], + "type": "inline_equation", + "content": "\\{h_m\\}_{m = 1}^M" + }, + { + "bbox": [ + 45, + 321, + 289, + 536 + ], + "type": "text", + "content": " together to get the overall prediction. In our experiments, the ensemble is conducted by averaging the logits (the inputs of the softmax layer) in the predictor neural network." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 537, + 285, + 549 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 537, + 285, + 549 + ], + "spans": [ + { + "bbox": [ + 59, + 537, + 285, + 549 + ], + "type": "text", + "content": "The overall framework of DSI is shown in Algorithm 1." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 561, + 128, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 561, + 128, + 574 + ], + "spans": [ + { + "bbox": [ + 47, + 561, + 128, + 574 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 581, + 288, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 581, + 288, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 581, + 288, + 665 + ], + "type": "text", + "content": "Datasets. In the main text, experiments on the following datasets are reported. More experiments can be found in supplementary materials. (1) PACS [33] contains 999,1 colored images from 7 classes and 4 domains (art painting, cartoon, photo, and sketch); (2) Office-Home [69] contains around 15,500 images from 65 different classes and 4 domains (artistic, clip art, product, and real-world)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": "Base Methods. Based on the taxonomy in Sec. 2, we select one (or two) up-to-date or representative algorithm(s) from each category as the base methods in the experiments with multiple training domains. For experiments with a" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 321, + 547, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 321, + 547, + 453 + ], + "spans": [ + { + "bbox": [ + 304, + 321, + 547, + 453 + ], + "type": "text", + "content": "single training domain, we adjust the list of base methods by only choosing the algorithms without multi-domain assumption. For each experimental configuration (dataset and training-testing split), the hyperparameters of each algorithm are optimized based on the performance metric on the testing set over 10 random searches. The searching regions are reported in supplementary materials. Fixing the optimal hyperparameters, we repeat the experimental pipeline three times and report the average results together with the standard deviations to alleviate the influence of the lucky weight initialization and dataset split." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 454, + 547, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 454, + 547, + 515 + ], + "spans": [ + { + "bbox": [ + 304, + 454, + 547, + 515 + ], + "type": "text", + "content": "In Tabs. 1 and 2, we use [algorithm]* to indicate the use of DSI, the green cells to indicate our method improves the base method, and the green cells with text in bold to indicate our method improves the base method with non-overlapped confidence interval." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 525, + 509, + 539 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 525, + 509, + 539 + ], + "spans": [ + { + "bbox": [ + 305, + 525, + 509, + 539 + ], + "type": "text", + "content": "5.1. Multi-training Domain Generalization" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 545, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 547, + 713 + ], + "type": "text", + "content": "The experiments for multi-training domain generalization are conducted on PACS and OfficeHome. For each dataset, one domain is left as the testing domain and the other three are used for training. The performance comparison of base methods with and without our method are listed in Tab. 1. Our method generally enhances the OoD prediction of all types of base methods by " + }, + { + "bbox": [ + 304, + 545, + 547, + 713 + ], + "type": "inline_equation", + "content": "3.68\\%" + }, + { + "bbox": [ + 304, + 545, + 547, + 713 + ], + "type": "text", + "content": " on PACS and " + }, + { + "bbox": [ + 304, + 545, + 547, + 713 + ], + "type": "inline_equation", + "content": "0.84\\%" + }, + { + "bbox": [ + 304, + 545, + 547, + 713 + ], + "type": "text", + "content": " on OfficeHome, which indicates DSI successfully closes the distance between the OoD samples and the training distribution. The significance of the improvements varies among different leave-one-out settings, because the accuracy of the base methods varies. When the accuracy of the base method is low (e.g., the average accuracy of the base methods is " + }, + { + "bbox": [ + 304, + 545, + 547, + 713 + ], + "type": "inline_equation", + "content": "61.88\\%" + }, + { + "bbox": [ + 304, + 545, + 547, + 713 + ], + "type": "text", + "content": " for S of PACS), more " + }, + { + "bbox": [ + 304, + 545, + 547, + 713 + ], + "type": "inline_equation", + "content": "(8.22\\%)" + }, + { + "bbox": [ + 304, + 545, + 547, + 713 + ], + "type": "text", + "content": " improvement is achieved. When" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "type": "text", + "content": "3597" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 70, + 175, + 167 + ], + "blocks": [ + { + "bbox": [ + 53, + 70, + 175, + 167 + ], + "lines": [ + { + "bbox": [ + 53, + 70, + 175, + 167 + ], + "spans": [ + { + "bbox": [ + 53, + 70, + 175, + 167 + ], + "type": "image", + "image_path": "70088e06ce5bf277c1e9cb102615e93aa6f2ef442e63e07be6d4936309a0faa6.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 175, + 70, + 296, + 167 + ], + "blocks": [ + { + "bbox": [ + 175, + 70, + 296, + 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"type": "image", + "image_path": "a9f0285724b3b97b9e69f011f7e5bd121a7e295921ecf14f7fc5fc671f1a31fe.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 432, + 284, + 522, + 293 + ], + "lines": [ + { + "bbox": [ + 432, + 284, + 522, + 293 + ], + "spans": [ + { + "bbox": [ + 432, + 284, + 522, + 293 + ], + "type": "text", + "content": "(h) Testing Domain: Sketch" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 338, + 288, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 338, + 288, + 421 + ], + "spans": [ + { + "bbox": [ + 46, + 338, + 288, + 421 + ], + "type": "text", + "content": "the accuracy of the base method is high (e.g., the average accuracy of the base methods is " + }, + { + "bbox": [ + 46, + 338, + 288, + 421 + ], + "type": "inline_equation", + "content": "94.61\\%" + }, + { + "bbox": [ + 46, + 338, + 288, + 421 + ], + "type": "text", + "content": " for P of PACS), the absolute value of the improvement is less " + }, + { + "bbox": [ + 46, + 338, + 288, + 421 + ], + "type": "inline_equation", + "content": "(0.89\\%)" + }, + { + "bbox": [ + 46, + 338, + 288, + 421 + ], + "type": "text", + "content": ". We also notice that the rise in performance on OfficeHome dataset is less than the PACS, which can be attributed to that the larger number of classes in OfficeHome increases the hardness of the semantic label preservation of our method." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 46, + 423, + 289, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 423, + 289, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 423, + 289, + 713 + ], + "type": "text", + "content": "We further analyze whether the performance gain depends on a certain class or domain. We count, for each class in each testing domain, (1) the number of samples correctly predicted by both the base methods and the base methods with DSI(# Both Correct), (2) the number of samples correctly predicted by the base methods with DSI but wrongly predicted by base methods (# Only Ours Correct), (3) the number of samples correctly predicted by the base methods (# Base Correct), and (4) the number of samples wrongly predicted by the base methods (# Base Wrong). Fig. 4 shows the preservation ratio calculated by " + }, + { + "bbox": [ + 46, + 423, + 289, + 713 + ], + "type": "inline_equation", + "content": "\\frac{\\# \\text{Both Correct}}{\\# \\text{Base Correct}}" + }, + { + "bbox": [ + 46, + 423, + 289, + 713 + ], + "type": "text", + "content": " and the correction ratio calculated by " + }, + { + "bbox": [ + 46, + 423, + 289, + 713 + ], + "type": "inline_equation", + "content": "\\frac{\\# \\text{Only Ours Correct}}{\\# \\text{Base Wrong}}" + }, + { + "bbox": [ + 46, + 423, + 289, + 713 + ], + "type": "text", + "content": ". The preservation ratio indicates the percentage of the correct predictions that are still correct when our method is used. The correction ratio indicates the percentage of the wrong predictions that are corrected when our method is used. Averaging over testing domains and classes, " + }, + { + "bbox": [ + 46, + 423, + 289, + 713 + ], + "type": "inline_equation", + "content": "94.52\\%" + }, + { + "bbox": [ + 46, + 423, + 289, + 713 + ], + "type": "text", + "content": " of the correct predictions are still correct when our method is used. The highest preservation ratio is " + }, + { + "bbox": [ + 46, + 423, + 289, + 713 + ], + "type": "inline_equation", + "content": "95.95\\%" + }, + { + "bbox": [ + 46, + 423, + 289, + 713 + ], + "type": "text", + "content": " appearing when photo is the testing domain. Among the testing domains and the classes, our method can at least correct " + }, + { + "bbox": [ + 46, + 423, + 289, + 713 + ], + "type": "inline_equation", + "content": "8.57\\%" + }, + { + "bbox": [ + 46, + 423, + 289, + 713 + ], + "type": "text", + "content": " wrong predictions and averagely " + }, + { + "bbox": [ + 46, + 423, + 289, + 713 + ], + "type": "inline_equation", + "content": "28.17\\%" + }, + { + "bbox": [ + 46, + 423, + 289, + 713 + ], + "type": "text", + "content": ". These results prove the general effectiveness of our methods across different domains and classes." + } + ] + } + ], + "index": 18 + }, + { + "type": "image", + "bbox": [ + 309, + 338, + 544, + 452 + ], + "blocks": [ + { + "bbox": [ + 46, + 298, + 547, + 331 + ], + "lines": [ + { + "bbox": [ + 46, + 298, + 547, + 331 + ], + "spans": [ + { + "bbox": [ + 46, + 298, + 547, + 331 + ], + "type": "text", + "content": "Figure 4. The percentage of correct prediction when using our method among the samples which are correctly predicted by the base method (in Fig. 4a to Fig. 4d), or wrongly predicted by the base method (in Fig. 4e to Fig. 4h). The plot is separately drawn for each leave-one-out setting and each class." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 309, + 338, + 544, + 452 + ], + "lines": [ + { + "bbox": [ + 309, + 338, + 544, + 452 + ], + "spans": [ + { + "bbox": [ + 309, + 338, + 544, + 452 + ], + "type": "image", + "image_path": "636c714e2f68cde0e10dc7ad9767c1d1e0412c3a61a996b9782761dd4212ee2f.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 463, + 545, + 485 + ], + "lines": [ + { + "bbox": [ + 305, + 463, + 545, + 485 + ], + "spans": [ + { + "bbox": [ + 305, + 463, + 545, + 485 + ], + "type": "text", + "content": "Figure 5. Accuracy v.s. Starting Time " + }, + { + "bbox": [ + 305, + 463, + 545, + 485 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 305, + 463, + 545, + 485 + ], + "type": "text", + "content": " on PACS dataset with the testing domain of \"Cartoon\"." + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 487, + 511, + 500 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 487, + 511, + 500 + ], + "spans": [ + { + "bbox": [ + 306, + 487, + 511, + 500 + ], + "type": "text", + "content": "5.2. Single-training Domain Generalization" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 506, + 547, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 506, + 547, + 601 + ], + "spans": [ + { + "bbox": [ + 304, + 506, + 547, + 601 + ], + "type": "text", + "content": "To cover the harder single training domain generalization, we do experiments on PACS datasets in which we use each domain as the training domain and test on the other three. The performance comparison of base methods with and without our method on the dataset with single training domains are listed in Tab. 2. With our method, irrelevant to the training and testing domain, general performance gains are achieved and the average performance gain is " + }, + { + "bbox": [ + 304, + 506, + 547, + 601 + ], + "type": "inline_equation", + "content": "2.42\\%" + }, + { + "bbox": [ + 304, + 506, + 547, + 601 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 610, + 479, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 610, + 479, + 624 + ], + "spans": [ + { + "bbox": [ + 306, + 610, + 479, + 624 + ], + "type": "text", + "content": "5.3. Discussion on the starting time " + }, + { + "bbox": [ + 306, + 610, + 479, + 624 + ], + "type": "inline_equation", + "content": "s" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 629, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 547, + 713 + ], + "type": "text", + "content": "Transforming the distribution closer to the source distribution increases the confidence of the prediction based on the transformed image. On the other hand, the well-preserved label information guarantees the prediction of the generated image has the same label as its origin. However, increasing " + }, + { + "bbox": [ + 304, + 629, + 547, + 713 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 629, + 547, + 713 + ], + "type": "text", + "content": " to get further distribution transformation will destroy the label information, contrarily, decreasing " + }, + { + "bbox": [ + 304, + 629, + 547, + 713 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 629, + 547, + 713 + ], + "type": "text", + "content": " to preserve the" + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3598" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 71, + 545, + 194 + ], + "blocks": [ + { + "bbox": [ + 47, + 71, + 545, + 194 + ], + "lines": [ + { + "bbox": [ + 47, + 71, + 545, + 194 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 545, + 194 + ], + "type": "table", + "html": "
DatasetPACS
Training DomainACPS
Testing DomainCPSAPSACSACP
ERM55.37±0.3297.92±0.0542.84±1.6855.63±0.2683.43±0.3257.42±2.2764.84±1.0228.26±3.8623.24±4.8815.82±1.3314.26±0.7012.66±0.49
ERM*57.58±0.2697.90±0.0348.54±1.1257.03±0.4483.98±0.5663.74±2.0065.92±0.3732.75±3.7825.68±4.7816.41±1.5116.80±0.7612.92±0.20
CORAL56.35±2.6396.68±0.6342.32±2.6055.47±0.5284.15±0.7057.81±1.6562.04±0.7432.16±5.8426.33±8.4615.27±0.6815.76±1.1611.65±0.81
CORAL*58.76±2.9696.84±0.5347.56±1.1656.87±0.0984.38±0.8364.65±2.0163.90±1.0135.97±4.8029.23±7.9915.98±0.6616.50±1.0412.27±0.92
RSC55.21±0.2898.18±0.1744.66±1.6954.36±1.0683.79±0.6259.41±2.3363.05±0.9631.61±6.7524.90±5.1216.57±0.5916.37±0.2613.77±1.92
RSC*57.39±0.4598.24±0.1550.39±1.2555.70±0.7483.95±0.5665.98±1.6064.13±1.6435.29±5.7728.22±4.8717.68±0.6817.45±0.6914.49±1.88
SagNet56.41±0.4797.95±0.0846.81±3.3358.82±1.1886.95±0.7957.91±2.6267.32±0.9941.76±2.3535.77±2.4815.76±0.9114.23±2.4516.76±1.51
SagNet*58.85±0.5197.96±0.0853.48±3.3059.51±1.4087.14±0.9764.71±3.5067.74±0.7544.34±2.0038.64±1.8418.03±0.6715.95±2.1718.26±1.90
Average Gain2.31±0.120.05±0.075.83±0.521.20±0.300.28±0.166.63±0.211.11±0.513.64±0.692.88±0.311.17±0.671.52±0.680.77±0.45
", + "image_path": "62d3367c0df0bd15d57d30aa3c76c0aa495486cb425141d67b4e99f04e099f7d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 202, + 546, + 226 + ], + "lines": [ + { + "bbox": [ + 46, + 202, + 546, + 226 + ], + "spans": [ + { + "bbox": [ + 46, + 202, + 546, + 226 + ], + "type": "text", + "content": "Table 2. The average accuracy " + }, + { + "bbox": [ + 46, + 202, + 546, + 226 + ], + "type": "inline_equation", + "content": "\\pm" + }, + { + "bbox": [ + 46, + 202, + 546, + 226 + ], + "type": "text", + "content": " the standard deviation of base algorithms w/o our method on PACS datasets with single training domain setting. The performance is generally boosted when our method is plugged in, whichever base algorithm used." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 51, + 232, + 284, + 330 + ], + "blocks": [ + { + "bbox": [ + 51, + 232, + 284, + 330 + ], + "lines": [ + { + "bbox": [ + 51, + 232, + 284, + 330 + ], + "spans": [ + { + "bbox": [ + 51, + 232, + 284, + 330 + ], + "type": "image", + "image_path": "08087e127fd3fd318a5f1c871cde0e1c7ba016d49781fe1f41669647276ef705.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 116, + 334, + 219, + 343 + ], + "lines": [ + { + "bbox": [ + 116, + 334, + 219, + 343 + ], + "spans": [ + { + "bbox": [ + 116, + 334, + 219, + 343 + ], + "type": "text", + "content": "(a) Accuracy v.s. Ensemble Set" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 56, + 345, + 275, + 428 + ], + "blocks": [ + { + "bbox": [ + 56, + 345, + 275, + 428 + ], + "lines": [ + { + "bbox": [ + 56, + 345, + 275, + 428 + ], + "spans": [ + { + "bbox": [ + 56, + 345, + 275, + 428 + ], + "type": "image", + "image_path": "6c2990f47ab1d9bd4de9f486c5dfd3e816ad567ae6725d7893eaef02a3f2f784.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 120, + 433, + 212, + 442 + ], + "lines": [ + { + "bbox": [ + 120, + 433, + 212, + 442 + ], + "spans": [ + { + "bbox": [ + 120, + 433, + 212, + 442 + ], + "type": "text", + "content": "(b) Accuracy v.s. Threshold" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 448, + 287, + 536 + ], + "lines": [ + { + "bbox": [ + 46, + 448, + 287, + 536 + ], + "spans": [ + { + "bbox": [ + 46, + 448, + 287, + 536 + ], + "type": "text", + "content": "Figure 6. Discussion about the influence of hyperparameters: Ensemble set (Fig. 6a) and Threshold (Fig. 6b) on the PACS dataset with the testing domain of \"Cartoon\". The y-axis label of Fig. 6a indicates the components of the ensemble set with the corresponding accuracy's show on the right. The row of \"C\" corresponds to the setting using the original testing images alone. The areas below(above) correspond to the ensembles with(without) the original testing images." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 542, + 287, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 542, + 287, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 542, + 287, + 567 + ], + "type": "text", + "content": "label information will limit the distribution transformation. Thus, an optimal " + }, + { + "bbox": [ + 46, + 542, + 287, + 567 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 542, + 287, + 567 + ], + "type": "text", + "content": " exists for each algorithm. (see Fig. 5)" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 575, + 222, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 575, + 222, + 588 + ], + "spans": [ + { + "bbox": [ + 47, + 575, + 222, + 588 + ], + "type": "text", + "content": "5.4. Discussions on hyperparameters" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 594, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 713 + ], + "type": "text", + "content": "**Ensemble.** We analyze whether only transforming the testing domain data to a subset of the training domains influences the performance gain or not. Fig. 6a shows the accuracy with different ensemble sets on PACS with the multi-training domain setting and Cartoon is the testing domain. Each row corresponds to one kind of ensemble. For example, row \"C\" shows the accuracy when the prediction is only based on the original testing image, which is the accuracy of the base methods; row \"C,A\" shows the accuracy when the prediction based on the original testing image and" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 232, + 547, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 232, + 547, + 338 + ], + "spans": [ + { + "bbox": [ + 304, + 232, + 547, + 338 + ], + "type": "text", + "content": "prediction based on the image transformed towards the domain Art are considered together. As shown from the figure, including more components in the ensemble set increases the average performance and reduces its variance; ensembles without the original prediction can perform comparably with the base method; the ensembles with the original prediction and any (one, two, or all) of the predictions based on the transformed image is statistically better than the base methods." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 339, + 547, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 339, + 547, + 422 + ], + "spans": [ + { + "bbox": [ + 304, + 339, + 547, + 422 + ], + "type": "text", + "content": "**Confidence Threshold.** We analyze the influence of the confidence threshold " + }, + { + "bbox": [ + 304, + 339, + 547, + 422 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 339, + 547, + 422 + ], + "type": "text", + "content": ", and the performance with varying " + }, + { + "bbox": [ + 304, + 339, + 547, + 422 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 339, + 547, + 422 + ], + "type": "text", + "content": " are shown in 6b. Base methods are special cases when " + }, + { + "bbox": [ + 304, + 339, + 547, + 422 + ], + "type": "inline_equation", + "content": "k = 0" + }, + { + "bbox": [ + 304, + 339, + 547, + 422 + ], + "type": "text", + "content": ", their performances are shown along the red vertical line. Though tuning " + }, + { + "bbox": [ + 304, + 339, + 547, + 422 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 339, + 547, + 422 + ], + "type": "text", + "content": " enlarges the performance gain, when " + }, + { + "bbox": [ + 304, + 339, + 547, + 422 + ], + "type": "inline_equation", + "content": "k > 0" + }, + { + "bbox": [ + 304, + 339, + 547, + 422 + ], + "type": "text", + "content": ", our method is activated and there are always performance improvements." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 429, + 378, + 441 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 429, + 378, + 441 + ], + "spans": [ + { + "bbox": [ + 306, + 429, + 378, + 441 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 444, + 547, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 444, + 547, + 635 + ], + "spans": [ + { + "bbox": [ + 304, + 444, + 547, + 635 + ], + "type": "text", + "content": "In this paper, we investigate a novel task, termed unseen distribution transformation, which aims at transforming the unseen distribution towards the seen distribution. We frame the first solution to unseen distribution transformation, in which the unseen distribution is first linearly combined with the Gaussian noise and then transformed by a diffusion model trained on the seen domain. By solving this task, we provide a new perspective for addressing the OoD prediction task by first closing the distance between the testing domain and the training domain and then drawing prediction. We propose the portable DSI, which conducts sample adaptive unseen distribution transformation to enhance the OoD prediction algorithms. Experimental results show that our method results in general performance gains when inserted into various types of base methods under multi-training and single-training domain generalization problems." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 646, + 410, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 646, + 410, + 659 + ], + "spans": [ + { + "bbox": [ + 306, + 646, + 410, + 659 + ], + "type": "text", + "content": "7. Acknowledgment" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "content": "This project is supported by the Singapore Ministry of Education Academic Research Fund Tier 1 (Grantor's Reference Number: 23-0306-A0001), a project titled \"Towards Robust Single Domain Generalization in Deep Learning\"." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3599" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 18, + "blocks": [ + { + "bbox": [ + 53, + 91, + 288, + 133 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 288, + 133 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 288, + 133 + ], + "type": "text", + "content": "[1] Kartik Ahuja, Ethan Caballero, Dinghuai Zhang, Yoshua Bengio, Ioannis Mitliagkas, and Irina Rish. 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However, an aspect of clustering that is not addressed by existing deep clustering methods, is that of efficiently producing multiple, diverse partitionings for a given dataset. This is particularly important, as a diverse set of base clusterings are necessary for consensus clustering, which has been found to produce better and more robust results than relying on a single clustering. To address this gap, we propose DivClust, a diversity controlling loss that can be incorporated into existing deep clustering frameworks to produce multiple clusterings with the desired degree of diversity. We conduct experiments with multiple datasets and deep clustering frameworks and show that: a) our method effectively controls diversity across frameworks and datasets with very small additional computational cost, b) the sets of clusterings learned by DivClust include solutions that significantly outperform single-clustering baselines, and c) using an off-the-shelf consensus clustering algorithm, DivClust produces consensus clustering solutions that consistently outperform single-clustering baselines, effectively improving the performance of the base deep clustering framework. Code is available at https://github.com/ManiadisG/DivClust.", + "bbox": [ + 76, + 318, + 472, + 696 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 727, + 209, + 742 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The exponentially increasing volume of visual data, along with advances in computing power and the development of powerful Deep Neural Network architectures, have revived the interest in unsupervised learning with visual data. Deep clustering in particular has been an area where significant progress has been made in the recent years. Existing works focus on producing a single clustering, which is evaluated in terms of how well that clustering matches", + "bbox": [ + 75, + 753, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "the ground truth labels of the dataset in question. However, consensus, or ensemble, clustering remains under-studied in the context of deep clustering, despite the fact that it has been found to consistently improve performance over single clustering outcomes [3, 17, 45, 73].", + "bbox": [ + 496, + 287, + 893, + 363 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Consensus clustering consists of two stages, specifically generating a set of base clusterings, and then applying a consensus algorithm to aggregate them. Identifying what properties ensembles should have in order to produce better outcomes in each setting has been an open problem [18]. However, research has found that inter-clustering diversity within the ensemble is an important, desirable factor [14,20,24,34,51], along with individual clustering quality, and that diversity should be moderated [15,22,51]. Furthermore, several works suggest that controlling diversity in ensembles is important toward studying its impact and determining its optimal level in each setting [22, 51].", + "bbox": [ + 496, + 367, + 893, + 549 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The typical way to produce diverse clusterings is to promote diversity by clustering the data multiple times with different initializations/hyperparameters or subsets of the data [3, 17]. This approach, however, does not guarantee or control the degree of diversity, and is computationally costly, particularly in the context of deep clustering, where it would require the training of multiple models. Some methods have been proposed that find diverse clusterings by including diversity-related objectives to the clustering process, but those methods have only been applied to clustering precomputed features and cannot be trivially incorporated into Deep Learning frameworks. Other methods tackle diverse clustering by creating and clustering diverse feature subspaces, including some that apply this approach in the context of deep clustering [48, 61]. Those methods, however, do not control inter-clustering diversity. Rather, they influence it indirectly through the properties of the subspaces they create. Furthermore, typically, existing methods have been focusing on producing orthogonal clusterings or identifying clusterings based on independent attributes of relatively simple visual data (e.g. color/shape). Consequently, they are oriented toward maximizing inter-clustering diversity, which is not appropriate for consensus", + "bbox": [ + 496, + 553, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author", + "bbox": [ + 94, + 886, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "3418", + "bbox": [ + 482, + 944, + 516, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3854d879e68eaf112ae12cad4955dc4f2262eca9e19bdcfb6434c317436d84e1.jpg", + "image_caption": [ + "Figure 1. Overview of DivClust. Assuming clusterings $A$ and $B$ , the proposed diversity loss $L_{div}$ calculates their similarity matrix $S_{AB}$ and restricts the similarity between cluster pairs to be lower than a similarity upper bound $d$ . In the figure, this is represented by the model adjusting the cluster boundaries to produce more diverse clusterings. Best seen in color." + ], + "image_footnote": [], + "bbox": [ + 81, + 90, + 893, + 205 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "clustering [15,22,51].", + "bbox": [ + 76, + 303, + 225, + 318 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To tackle this gap, namely generating multiple clusterings with deep clustering frameworks efficiently and with the desired degree of diversity, we propose DivClust. Our method can be straightforwardly incorporated into existing deep clustering frameworks to learn multiple clusterings whose diversity is explicitly controlled. Specifically, the proposed method uses a single backbone for feature extraction, followed by multiple projection heads, each producing cluster assignments for a corresponding clustering. Given a user defined diversity target, in this work expressed in terms of the average NMI between clusterings, DivClust restricts inter-clustering similarity to be below an appropriate, dynamically estimated threshold. This is achieved with a novel loss component, which estimates inter-clustering similarity based on soft cluster assignments produced by the model, and penalizes values exceeding the threshold. Importantly, DivClust introduces minimal computational cost and requires no hyperparameter tuning with respect to the base deep clustering framework, which makes its use simple and computationally efficient.", + "bbox": [ + 75, + 320, + 472, + 622 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Experiments on four datasets (CIFAR10, CIFAR100, Imagenet-10, Imagenet-Dogs) with three recent deep clustering methods (IIC [37], PICA [32], CC [44]) show that DivClust can effectively control inter-clustering diversity without reducing the quality of the clusterings. Furthermore, we demonstrate that, with the use of an off-the-shelf consensus clustering algorithm, the diverse base clusterings learned by DivClust produce consensus clustering solutions that outperform the base frameworks, effectively improving them with minimal computational cost. Notably, despite the sensitivity of consensus clustering to the properties of the ensemble, our method is robust across various diversity levels, outperforming baselines in most settings, often by large margins. Our work then provides a straightforward way for improving the performance of deep clustering frameworks, as well as a new tool for studying the impact of diversity in deep clustering ensembles [51].", + "bbox": [ + 75, + 626, + 468, + 882 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, DivClust: a) can be incorporated in ex", + "bbox": [ + 96, + 885, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "isting deep clustering frameworks in a plug-and-play way with very small computational cost, b) can explicitly and effectively control inter-clustering diversity to satisfy user-defined targets, and c) learns clusterings that can improve the performance of deep clustering frameworks via consensus clustering.", + "bbox": [ + 496, + 303, + 893, + 393 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 500, + 410, + 648, + 426 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Deep Clustering", + "text_level": 1, + "bbox": [ + 500, + 436, + 661, + 452 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The term deep clustering refers to methods that cluster data while learning their features. They are generally divided into two categories, namely those that alternate training between clustering and feature learning and those that train both simultaneously.", + "bbox": [ + 496, + 460, + 893, + 535 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Alternate learning: Methods following this approach generally utilize a two-step training regime repeated in regular intervals (e.g. per-epoch or per-step). First, sample pseudo-labels are produced based on representations extracted by the model (e.g. by feature clustering). Second, those pseudo-labels are utilized to improve the learned representations, typically by training the feature extraction model as a classifier. Those methods include DEC [64], DAC [8], DCCM [63], DDC [7], JULE [66], SCAN [57], ProPos [33] and SPICE [49], as well as DSC-N [36], IDFD [65] and MIX'EM [58], which propose ways to train models whose representations produce better outcomes when clustered. Other works in this area are DeepCluster [5], SeLa [1], PCL [42] and HCSC [21], though their primary focus is on representation learning.", + "bbox": [ + 496, + 537, + 893, + 763 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Simultaneous learning: These methods jointly learn features and cluster assignments. They include ADC [23], IIC [37] and PICA [32], which train clustering models end-to-end with loss functions that enforce desired properties on the clusters assignments, ConCURL [11, 52], which builds on BYOL [19] with a loss maximizing the agreement of clusterings from transformed embeddings, DCCS [71], which leverages an adversarial component in the clustering process, and GatCluster [50], which proposes an attention", + "bbox": [ + 496, + 765, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "3419", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "mechanism combined with four self-learning tasks. Finally, methods such as SCL [31], CC [44], GCC [72], TCC [53] and MiCE [56] leverage contrastive learning.", + "bbox": [ + 76, + 90, + 467, + 136 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Although some deep clustering methods [1, 37, 52] use multiple clusterings, most do not explore the prevalence and impact of inter-clustering diversity, and none proposes ways to control it. Our work is, to the best of our knowledge, the first that addresses both issues.", + "bbox": [ + 76, + 137, + 467, + 212 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Diverse Clustering", + "text_level": 1, + "bbox": [ + 76, + 224, + 256, + 242 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The most straightforward way of producing multiple, diverse clusterings is clustering the data multiple times. Typical methods to increase diversity include varying the clustering algorithm or its hyperparameters, using different initializations, and clustering a subset of the samples or features [3]. This approach, however, is a) computationally costly, in that it requires clustering the data multiple times, b) unreliable, as some ways to increase diversity might decrease the quality of clusters (e.g. using a subset of the data), and c) ineffective, as there is no guarantee that the desired degree of diversity will be achieved.", + "bbox": [ + 75, + 250, + 467, + 412 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To tackle this, several methods have been proposed to create multiple, diverse clusterings [25]. We identify two main approaches of promoting inter-clustering diversity: a) explicitly, by optimizing for appropriate objectives, and b) implicitly, by optimizing for decorrelated/orthogonal feature subspaces, which, when clustered, lead to diverse clusterings. Methods in the first category include COALA [2], Meta Clustering [6], Dec-kmeans [35], MNMF [67], MSC [26], ADFT [10] and MultiCC [60]. Subspace clustering methods include MISC [59], ISAAC [69], NR-kmeans [47], RAOSC [70] and ENRC [48]. Distinctly, diverse clustering has also been explored in the context of multi-view data by OSC [9], MVMC [68], DMSMF [46], DMClusts [62], DiMSC [4], and DiVMC [61].", + "bbox": [ + 75, + 416, + 467, + 626 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To the best of our knowledge, except for DiMVMC and ENRC, none of the existing methods are compatible with Deep Learning, they require a learned feature space on which to be applied, and most have quadratic complexity relative to the number of samples. This restricts their use on real-life high dimensional data, where deep clustering produces better outcomes [56, 57]. Regarding DiMVMC and ENRC, they depend on autoencoder-based architectures and adapting them to more recent deep clustering frameworks, which perform significantly better, is not trivial. More importantly, they utilize subspace clustering, inheriting its limitations regarding controlling diversity. Specifically: a) no method has been proposed to infer how different the subspaces must be in order to lead to a specific degree of interclustering diversity, and b) subspace clustering methods inherit the randomness of the clustering algorithm applied to the subspaces (K-means for DiMVMC and ENRC), which further limits their control over the outcomes.", + "bbox": [ + 75, + 628, + 467, + 898 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Consensus Clustering", + "text_level": 1, + "bbox": [ + 500, + 90, + 702, + 107 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The performance of clustering algorithms varies depending on the data and their properties, the algorithm itself, and its hyperparameters. This makes finding reliable clustering solutions particularly difficult. Consensus, or ensemble, clustering has emerged as a solution to this problem, specifically by combining the results of multiple, different clusterings, rather than relying on a single solution. This has been found to produce better and more robust outcomes than single-clustering approaches [3, 17, 18, 45]. The process of consensus clustering happens in two stages: a) multiple, diverse base clusterings are generated and b) those clusterings are aggregated using a consensus algorithm.", + "bbox": [ + 496, + 113, + 890, + 294 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Generating diverse clusterings: The properties of the set of clusterings used by the consensus algorithm is a key factor for obtaining good performance. Multiple works [24, 40, 51] have found that both the quality of individual base clusterings and their diversity is critical, and that, indeed, clustering ensembles with a moderate degree of diversity lead to better outcomes [15, 20, 22]. Typical methods for ensemble generation include using different clustering algorithms [13], using different initializations of the same clustering algorithm or different hyperparameters (e.g. the number of clusters) [16, 22, 41], clustering with different subsets of the features [54], using random projections to diversify the feature space [14], and clustering with different subsets of the dataset [12, 13]. However, concrete methods for identifying optimal hyperparameters, such as the degree of diversity, the number of clusterings in the ensemble, and the method by which the ensemble is generated, remain elusive.", + "bbox": [ + 496, + 296, + 890, + 551 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Consensus algorithms: Consensus algorithms aim to aggregate multiple, diverse clusterings to produce a single, robust solution. Various approaches to this problem have been proposed, such as using matrix factorization [43], distance minimization between clusterings [75], utilizing multiple views [55], graph learning [28, 73, 74] and matrix coassociation [29, 38]. We note that, while improving consensus algorithms increase the robustness of consensus clustering overall, the stages of ensemble generation and its aggregation with consensus algorithms are largely independent.", + "bbox": [ + 496, + 553, + 890, + 703 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Consensus Clustering & Deep Learning: Despite the established advantages of consensus clustering over single-clustering approaches, consensus clustering has not been explored in the context of deep clustering. A possible reason is the computational cost of generating multiple, diverse base clusterings, which would require training multiple models. The only work that has, to the best of our knowledge, applied consensus clustering in the deep clustering setting is DeepCluE [27]. Notably, however, the base clusterings used by DeepCluE are not all learned by the model. Rather, a single-clustering model is trained, and an ensemble is generated by clustering features from multiple layers of the model with U-SPEC [30]. Our work addresses", + "bbox": [ + 496, + 704, + 890, + 898 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "3420", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "this gap, by proposing a way to train a single deep clustering model to generate multiple clusterings with controlled diversity and with minimal computational overhead.", + "bbox": [ + 75, + 90, + 468, + 137 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 150, + 168, + 166 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Overview: Our method consists of two components: a) A novel loss function that can be incorporated in deep clustering frameworks to control inter-clustering diversity by applying a threshold to cluster-wise similarities, and b) a method for dynamically estimating that threshold so that the clusterings learned by the model are sufficiently diverse, according to a user-defined metric.", + "bbox": [ + 75, + 176, + 468, + 281 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "More concretely, we assume a deep clustering model that learns $K$ clusterings (typically a backbone encoder followed by $K$ projection heads), a deep clustering framework and its loss function $L_{\\text{main}}$ , and a diversity target $D^T$ set by the user, expressed as an upper bound to inter-clustering similarity1 (i.e. the maximum acceptable similarity). In order to control the inter-clustering similarity $D^R$ of the learned clusterings so that $D^T \\leq D^R$ , we propose a complementary loss $L_{\\text{div}}$ . Specifically, given soft cluster assignments for a pair of clusterings $A, B \\in K$ , we define the inter-clustering similarity matrix $S_{AB} \\in \\mathbb{R}^{C_A \\times C_B}$ , where $C_A$ and $C_B$ is the number of clusters in each clustering, and $S_{AB}(i,j) \\in [0,1]$ measures the similarity between clusters $i \\in C_A$ and $j \\in C_B$ . It follows that decreasing the values of $S_{AB}$ reduces the similarity between the clusters of $A$ and $B$ , and therefore increases their diversity. Accordingly, $L_{\\text{div}}$ utilizes $S_{AB}$ in order to restrict inter-clustering similarity to be under an upper similarity bound $d$ . The value of $d$ is dynamically adjusted during training, decreasing when $D^R > D^T$ and increasing when $D^R \\leq D^T$ , thereby tightening and relaxing the loss function so that, overall and throughout training, inter-clustering similarity $D^R$ remains at or under the desired level $D^T$ .", + "bbox": [ + 75, + 282, + 468, + 628 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Defining the inter-clustering similarity matrix: Our method assumes a standard deep clustering architecture, consisting of an encoder $f$ , followed by $K$ projection heads $h_1, \\ldots, h_K$ , each of which produces assignments for a clustering $k$ . Specifically, let $X$ be a set of $N$ unlabeled samples. The encoder maps each sample $x \\in X$ to a representation $f(x)$ , and each projection head $h_k$ maps $f(x)$ to $C_k$ clusters, so that $p_k(x) = h_k(f(x)) \\in \\mathbb{R}^{C_k \\times 1}$ represents a probability assignment vector mapping sample $x \\in X$ to $C_k$ clusters in clustering $k$ . Without loss of generality, we assume that $C = C_k \\forall k \\in K$ . Each clustering can then be represented by a cluster assignment matrix $P_k(X) = [p_k(x_1), p_k(x_2), \\dots, p_k(x_N)] \\in \\mathbb{R}^{C \\times N}$ . The column $p_k(n)$ , that is the probability assignment vector for the", + "bbox": [ + 75, + 628, + 468, + 840 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$n$ -th sample, encodes the degrees to which sample $x_{n}$ is assigned to different clusters. The row vector $q_{k}(i)\\in \\mathbb{R}^{N}$ shows which samples are softly assigned to cluster $i\\in C$ . We refer to $q_{k}(i)$ as the cluster membership vector.", + "bbox": [ + 500, + 90, + 890, + 151 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To quantify the similarity between clusterings $A$ and $B$ we define the inter-clustering similarity matrix $S_{AB} \\in \\mathbb{R}^{C \\times C}$ . We define each element $S_{AB}(i,j)$ as the cosine similarity between the cluster membership vector $q_{A}(i)$ of cluster $i \\in A$ and the cluster membership vector $q_{B}(j)$ of cluster $j \\in B$ :", + "bbox": [ + 500, + 151, + 893, + 242 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nS _ {A B} (i, j) = \\frac {q _ {A} (i) \\cdot q _ {B} (j)}{\\left| \\left| q _ {A} (i) \\right| \\right| _ {2} \\left| \\left| q _ {B} (j) \\right| \\right| _ {2}} \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 253, + 890, + 286 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This measure expresses the degree to which samples in the dataset are assigned similarly to clusters $i$ and $j$ . Specifically, $S_{AB}(i,j) = 0$ if $q_A(i) \\perp q_B(j)$ and $S_{AB}(i,j) = 1$ if $q_A(i) = q_B(j)$ . It is, therefore, a differentiable measure of the similarity of clusters $i$ and $j$ .", + "bbox": [ + 498, + 295, + 890, + 369 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Defining the loss function: Based on the inter-clustering similarity matrix $S_{AB}$ , we define DivClust's loss to softly enforce that a clustering $A$ does not have an aggregate cluster similarity with a clustering $B$ greater than a similarity upper bound $d$ . The aggregate similarity $S_{AB}^{aggr}$ is defined as the average similarity of clustering $A$ 's clusters with their most similar cluster of clustering $B$ (Eq. (2)). Using this metric, we propose $L_{div}$ (Eq. (3)), a loss that regulates diversity between clusterings $A$ and $B$ by forcing that $S_{AB}^{aggr} < d$ , for $d \\in [0,1]$ . It is clear from Eq. (3) that $S_{AB}^{aggr} < d \\Rightarrow L_{div}(A,B) = 0$ , in which case the diversity requirement is satisfied and the loss has no impact. Conversely, $S_{AB}^{aggr} \\geq d \\Rightarrow L_{div}(A,B) > 0$ , in which case the loss requires that inter-clustering similarity decreases.", + "bbox": [ + 498, + 371, + 892, + 583 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nS _ {A B} ^ {a q g r} = \\frac {1}{C} \\sum_ {i = 1} ^ {C} \\max _ {j} \\left(S _ {A B} (i, j)\\right) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 593, + 890, + 635 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {d i v} (A, B) = \\left[ S _ {A B} ^ {a g g r} - d \\right] _ {+} \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 599, + 646, + 890, + 665 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Having defined the diversity loss $L_{div}$ between two clusterings, we extend it to multiple clusterings $K$ and combine it with the base deep clustering framework's objective. For a clustering $k \\in K$ , we denote with $L_{main}(k)$ the loss of the base deep clustering framework for that clustering, and with $L_{div}(k, k')$ the diversity controlling loss between clusterings $k$ and $k'$ . We present the joint loss $L_{joint}(k)$ for each clustering $k$ in Eq. (4), where $L_{main}(k)$ depends on cluster assignment matrix $P_k$ , while $L_{div}(k, k')$ depends on $P_k$ and $P_{k'}$ . Accordingly, the model's training loss $L_{total}$ seen in Eq. (5), is the average of $L_{joint}$ over all clusterings.", + "bbox": [ + 498, + 670, + 892, + 838 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\text {j o i n t}} (k) = L _ {\\text {m a i n}} (k) + \\frac {1}{K - 1} \\sum_ {k ^ {\\prime} = 1, k ^ {\\prime} \\neq k} ^ {K} L _ {\\text {d i v}} \\left(k, k ^ {\\prime}\\right) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 506, + 859, + 890, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "1It is trivial to modify our formulation to enforce a lower bound. However, experiments (see Sec. 4.2) showed that, when learning multiple clusterings, deep clustering frameworks inherently tend to converge to near-identical solutions, which made the lower bound scenario redundant.", + "bbox": [ + 75, + 849, + 468, + 898 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "3421", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/fb1bf011e4bf13ee2aecb61723189e753b0db2299b4a94bc4c8b383850601c9a.jpg", + "image_caption": [ + "(a) Cluster assignments $P_A$ for clustering A" + ], + "image_footnote": [], + "bbox": [ + 156, + 88, + 339, + 218 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/6a89254c2b2683cca9e8ccdc2cec4d6e6f1cc58cb664cc6d453f485d2989447c.jpg", + "image_caption": [ + "Figure 2. Examples of synthetic cluster assignments $P_A$ , $P_B$ and similarity matrix $S_{AB}$ . Note that clusters $i \\in A$ and $j \\in B$ are softly assigned the same samples. Correspondingly, their similarity score $S_{AB}(i,j)$ is high (highlighted with red in Fig. 2c). Best seen in color." + ], + "image_footnote": [], + "bbox": [ + 388, + 87, + 571, + 218 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/9592883f221f5b157afa885a3f275a26ad33452a5e8ef36c7418bdb435d892ca.jpg", + "image_caption": [ + "(b) Cluster assignments $P_B$ for clustering B", + "(c) Similarity matrix $S_{AB}$" + ], + "image_footnote": [], + "bbox": [ + 625, + 88, + 799, + 218 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {t o t a l} = \\frac {1}{K} \\sum_ {k = 1} ^ {K} L _ {\\text {j o i n t}} (k) \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 183, + 323, + 468, + 364 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The loss $L_{total}$ is therefore a combination of the base deep clustering framework's loss $L_{main}$ for each clustering $k \\in K$ and the loss $L_{div}$ , which is used to control interclustering diversity. The proposed loss formulation is applicable to any deep clustering framework that produces cluster assignments through the model (as opposed to frameworks using offline methods such as MIX'EM [58]), which covers the majority of deep clustering frameworks outlined in Sec. 2.", + "bbox": [ + 75, + 369, + 468, + 503 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Dynamic upper bound $d$ : The proposed loss $L_{div}$ controls inter-clustering diversity by restricting the values of $S_{AB}$ according to the similarity upper bound $d$ . However, the values of $S_{AB}$ are calculated based on the cosine similarity of soft cluster assignments. This means that pairs of cluster assignment vectors $i$ , $j$ will have different similarity values $S_{AB}(i,j)$ depending on their sharpness, even if they point to the same cluster in terms of their corresponding hard assignment. It follows that $S_{AB}$ and, accordingly, the impact of $d$ , are dependent on the confidence of cluster assignments and vary throughout training and between experiments (as factors like the number of clusters and model capacity influence the confidence of cluster assignments). Therefore, $d$ is an ambiguous and unintuitive metric for users to define diversity targets with.", + "bbox": [ + 75, + 506, + 468, + 733 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To tackle this issue and to provide a reliable and intuitive method for defining diversity objectives, we propose dynamically determining the value of the threshold $d$ during training. Concretely, let $D$ be an inter-clustering similarity metric chosen by the user. In this work, we use avg. Normalized Mutual Information (NMI), a well established metric for estimating inter-clustering similarity.", + "bbox": [ + 75, + 732, + 468, + 838 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nD = \\frac {1}{(K - 1) (K / 2)} \\sum_ {k = 1} ^ {K - 1} \\sum_ {k ^ {\\prime} = k + 1} ^ {K} N M I \\left(P _ {k} ^ {h}, P _ {k ^ {\\prime}} ^ {h}\\right) \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 859, + 468, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $P_{k}^{h} \\in \\mathbb{Z}^{N}$ is the hard cluster assignment vector for $N$ samples in clustering $k \\in K$ and $NMI(P_{k}^{h}, P_{k^{\\prime}}^{h})$ represents the NMI between $k$ and $k^{\\prime}$ . $D \\in [0,1]$ , with higher values indicating more similar clusterings.", + "bbox": [ + 496, + 311, + 890, + 372 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Assuming a user-defined similarity target $D^T$ , expressed as a value of metric $D$ , we denote with $D^R$ the measured inter-clustering similarity of the clusterings learned by the model, expressed in the same metric. DivClust's objective is to control inter-clustering diversity, which translates to learning clusterings such that $D^R \\leq D^T$ . Accordingly, appropriate thresholds $d$ must be used during training. Under the assumption that $D^R$ decreases monotonically w.r.t. $d$ , we propose the following update rule for $d$ :", + "bbox": [ + 496, + 372, + 892, + 508 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nd _ {s + 1} = \\left\\{ \\begin{array}{l l} \\max \\left(d _ {s} (1 - m), 0\\right), & \\text {i f} D ^ {R} > D ^ {T} \\\\ \\min \\left(d _ {s} (1 + m), 1\\right), & \\text {i f} D ^ {R} \\leq D ^ {T} \\end{array} , \\right. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 526, + 521, + 890, + 561 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $d_{s}$ and $d_{s+1}$ are the values of the threshold $d$ for the current and the next steps, and $m \\in (0,1)$ regulates the magnitude of the update steps. Following this update rule, we decrease $d$ when the measured inter-clustering similarity $D^{R}$ needs to decrease, and increase it otherwise. For computational efficiency, instead of calculating $D^{R}$ over the entire dataset in every training step, we do so every 20 iterations on a memory bank of $M = 10,000$ cluster assignments – the latter is updated at every step in a FIFO manner. We set the hyperparameter $m$ to $m = 0.01$ in all experiments.", + "bbox": [ + 496, + 571, + 892, + 739 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 753, + 632, + 771 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We conduct several experiments to evaluate DivClust's adaptability, its effectiveness in controlling diversity, and the quality of the resulting clusterings. First, to show that DivClust effectively controls inter-clustering diversity and produces high quality clusterings with various frameworks, we combine it with IIC [37], PICA [32] and CC [44], and apply it to CIFAR10 with various diversity targets $D^{T}$ . Subsequently, we focus on the best framework of the", + "bbox": [ + 496, + 779, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "3422", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/be34e2b6b4258eaec6640b31bdb32d250424f68298148186f6f607c29d8c7fe3.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
FrameworkClusteringsDTDRCNFMean Acc.Max. Acc.DivClust Acc.
IIC1--0.9970.4420.4420.442
201.0.9830.9960.5260.5260.526
200.950.9390.9980.5310.5370.533
200.90.8880.9970.5680.590.578
200.80.80.9970.6110.6780.653
200.70.6940.9960.5660.6370.685
PICA1--0.9060.5330.5330.533
201.0.9910.8140.5970.5970.596
200.950.9310.8260.6240.6310.625
200.90.8910.8410.6480.6650.652
200.80.8170.8280.5980.6350.595
200.70.7030.8240.6250.6910.671
CC1--0.9360.7640.7640.764
201.0.9760.9340.7630.7630.763
200.950.9460.9340.7620.7730.76
200.90.90.9310.7940.8180.789
200.80.8140.930.7620.8470.819
200.70.6990.9270.7030.8180.815
", + "bbox": [ + 133, + 88, + 831, + 380 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/605e969e75020ac35182492683ab126289e796512e027e795c8b6b6f6cf3319d.jpg", + "table_caption": [ + "Table 1. Results for IIC, PICA and CC applied on CIFAR10 with DivClust. CNF and Mean Acc. are calculated by averaging the corresponding metrics over all clusterings, while Max Acc. refers to the best performing base clustering. The DivClust Acc. metric measures the accuracy of a consensus clustering produced with the DivClust C method." + ], + "table_footnote": [], + "table_body": "
DTDR
CIFAR10CIFAR100ImageNet-10ImageNet-Dogs
1.0.9760.9390.9870.941
0.950.9460.9260.9480.945
0.90.90.8480.8970.87
0.80.8140.8060.8070.795
0.70.6990.7050.6960.702
", + "bbox": [ + 78, + 457, + 470, + 577 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Avg. inter-clustering similarity scores $D^{R}$ for clustering sets produced by DivClust combined with CC for various diversity targets $D^{T}$ . The objective of DivClust is that $D^{R} \\leq D^{T}$ .", + "bbox": [ + 75, + 587, + 468, + 631 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "three, namely CC, and conduct experiments on 4 datasets (CIFAR10, CIFAR100,Imagenet-10 andImagenet-Dogs). Our findings demonstrate that, across frameworks and datasets, DivClust can: a) effectively control diversity and b) improve clustering outcomes over the base frameworks and alternative ensembling methods.", + "bbox": [ + 75, + 656, + 468, + 748 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Experiments setup", + "text_level": 1, + "bbox": [ + 76, + 756, + 256, + 773 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets: We conduct experiments with 4 standard datasets in deep clustering: CIFAR10, CIFAR100 [39] (evaluating on the 20 superclasses), ImageNet-10 and ImageNet-Dogs [8].", + "bbox": [ + 75, + 779, + 468, + 840 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Metrics: Inter-clustering similarity is measured by averaging the NMI between clusterings to calculate the interclustering NMI metric $D$ (Eq. (6)), with higher values indicating more similar clusterings. We denote with $D^T$ the", + "bbox": [ + 75, + 839, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "diversity target set by the user and with $D^{R}$ the measured inter-clustering similarity after training. When DivClust is applied we want that $D^{R} \\leq D^{T}$ . Clustering quality is evaluated based on overlap of the clusterings with the dataset's ground truth labels, using the Accuracy (ACC), Normalized Mutual Information (NMI) and Adjusted Rand Index (ARI) metrics. We also report the avg. cluster assignment confidence (CNF), which measures cluster separability. For all four metrics greater values are better, 1 being optimal.", + "bbox": [ + 496, + 459, + 890, + 595 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation & Training: DivClust is incorporated into the base frameworks as described in Sec. 3, by adding DivClust's loss to their objective and duplicating projection heads $h$ to produce multiple clusterings. The models were trained following the configurations (model architecture, training duration, hyperparameters etc.) suggested in their respective papers [32, 37, 44], unless stated otherwise. PICA and IIC were trained without overclustering. We set the number of clusterings to $K = 20$ , following convention in consensus clustering [73], and the number of clusters $C$ to the number of classes for each dataset, following convention for deep clustering evaluation [32, 37, 44].", + "bbox": [ + 496, + 597, + 892, + 777 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Consensus Clustering: To extract single clustering solutions we examine three methods: a) selecting the clustering $k$ with the lowest corresponding loss $L_{\\text{main}}(k)$ (DivClust A), b) using the consensus clustering algorithm SCCBG [73] to aggregate clusterings (DivClust B), and c) a combination of the two, where we select the 10 best clusterings with regard to their loss and then apply SCCBG (DivClust C). For clarity and space, we present in the paper", + "bbox": [ + 496, + 779, + 890, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "3423", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/09779981f2e802d88b0734376a0263881c626b43238e09de7387054d09a02fc3.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DatasetDTCIFAR10CIFAR100ImageNet-10ImageNet-Dogs
MetricNMINMIACCARINMIACCARINMIACCARINMIACCARI
K-means-0.0870.2290.0490.0840.1300.0280.1190.2410.0570.550.1050.020
AC-0.1050.2280.0650.0980.1380.0340.1380.2420.0670.0370.1390.021
NMF-0.0810.1900.0340.0790.1180.0260.1320.2300.0650.0440.1180.016
AE-0.2370.3140.1690.1000.1650.0480.2100.3170.1520.1040.1850.073
DAE-0.2510.2970.1630.1110.1510.0460.2060.3040.1380.1040.1900.078
DCGAN-0.2650.3150.1760.1200.1510.0450.2250.3460.1570.1210.1740.078
DeCNN-0.2400.2820.1740.0920.1330.0380.1860.3130.1420.0980.1750.073
VAE-0.2450.2910.1670.1080.1520.0400.1930.3340.1680.1070.1790.079
JULE-0.1920.2720.1380.1030.1370.0330.1750.3000.1380.0540.1380.028
DEC-0.2570.3010.1610.1360.1850.0500.2820.3810.2030.1220.1950.079
DAC-0.3960.5220.3060.1850.2380.0880.3940.5270.3020.2190.2750.111
ADC--0.325--0.160--0.530----
DDC-0.4240.5240.329---0.4330.5770.345---
DCCM-0.4960.6230.4080.2850.3270.1730.6080.7100.5550.3210.3830.182
IIC--0.617--0.257-------
PICA-0.5910.6960.5120.3100.3370.1710.8020.8700.7610.3520.3520.201
CC-0.7050.7900.6370.4310.4290.2660.8590.8930.8220.4450.4290.274
CC-Kmeans-0.6540.6980.5230.4290.4050.2350.7920.8410.6690.4570.4440.284
CC-Kmeans/S-0.6740.690.5540.4280.4020.2280.7920.8420.6730.4560.4440.283
CC-Kmeans/F-0.6840.7620.5990.4380.4090.2100.7970.8470.6850.4580.4440.285
DeepCluE-0.7270.7640.6460.4720.4570.2880.8820.9240.8560.4480.4160.273
DivClust C1.0.6780.7630.6040.4180.4240.2570.860.8950.8250.4590.4510.298
0.950.6770.760.6020.4310.4340.2760.8910.9360.8780.4610.4510.297
0.90.6780.7890.6410.4220.4260.2580.8790.920.8590.480.4870.332
0.80.7240.8190.6810.4220.4140.260.8790.9180.8510.4580.4480.296
0.70.710.8150.6750.440.4370.2830.850.900.8190.5160.5290.376
", + "bbox": [ + 76, + 88, + 890, + 512 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Results combining DivClust with CC for various diversity targets $D^T$ . We underline DivClust results that outperform the single-clustering baseline CC, and note with bold the best results for each metric across all methods and diversity levels. We emphasize that the NMI in this table measures the similarity between the single clustering produced by each method and the ground truth classes. The NMI values representing inter-clustering similarity $D^R$ in ensembles produced by DivClust for the same experiments are presented in Tab. 2.", + "bbox": [ + 75, + 521, + 892, + 580 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "results only for the hybrid aggregation method DivClust C, which we found to be the most robust. Detailed results for all three approaches are provided in supplementary Tab. 5.", + "bbox": [ + 75, + 604, + 470, + 652 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Results", + "text_level": 1, + "bbox": [ + 76, + 664, + 171, + 679 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Initially, we apply IIC, PICA and CC on CIFAR10, and present the outcomes in Tab. 1. We find that, for all three frameworks, DivClust effectively controls diversity, as $D^{R}$ is consistently close to or lower than $D^{T}$ . Furthermore, results indicate that DivClust is necessary to produce diverse clusterings in deep clustering frameworks, as, without it, they tend to converge to near identical solutions (when $D^{T} = 1$ , $D^{R} \\rightarrow 1$ ). Regarding cluster separability, assignment confidence $CNF$ remains high for various diversity targets $D^{T}$ , despite the increased complexity of optimizing both the main deep clustering loss and DivClust's objective. Finally, we observe that, for most diversity targets $D^{T}$ , the mean and max. accuracy, as well as the consensus clustering accuracy produced by the aggregation method DivClust", + "bbox": [ + 75, + 688, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "C, increase relative to the single clustering model. Notably, consensus clustering accuracy is higher than the mean clustering accuracy for most cases, which highlights the effectiveness of our approach. We stress that identifying clusterings in the ensemble whose performance matches the mean or max. accuracy is not trivial, which is why consensus clustering is necessary to reach a single clustering solution.", + "bbox": [ + 496, + 604, + 890, + 712 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Having established that DivClust is effective across frameworks, we focus on CC and apply it on CIFAR10, CIFAR100, ImageNet-Dogs and Imagenet-10. We compare DivClust with the standard implementation of CC, which is trained to learn a single clustering (CC), as well as with alternative methods of ensemble clustering. Specifically, we apply the typical methods of ensemble generation by extracting the features learned by the single-clustering CC model and running K-means 20 times on the entire dataset (CC-Kmeans), on random subsets of the dataset (CC-Kmeans/S) and on random subsets of the feature space (CC-Kmeans/F), following [3]. In all three cases, SCCBG", + "bbox": [ + 496, + 719, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "3424", + "bbox": [ + 482, + 944, + 516, + 955 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "is used to aggregate the resulting clusterings. Furthermore, we compare with DeepCluE [27], to the best of our knowledge the only other work that examines consensus clustering in the context of deep clustering, and which is also built on top of CC, allowing for a fair comparison. We note that DeepCluE is not mutually exclusive with DivClust, and could be used jointly with it.", + "bbox": [ + 75, + 90, + 468, + 196 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Inter-clustering similarity scores $D^{R}$ for this set of experiments are presented in Tab. 2, where it is seen that DivClust successfully controls diversity. Results for consensus clustering, the main task for which DivClust is intended, are presented in Tab. 3 for CC across 4 datasets, where we also include results from other deep clustering frameworks for reference. Detailed results, including aggregation methods DivClust A and DivClust B, as well as mean/max scores for DivClust's clustering ensembles, are provided in supplementary Tab. 5. Results in Tab. 3 demonstrate that, for most diversity targets $D^{T}$ , DivClust outperforms the single-clustering baseline CC and typical ensemble generation methods, and is competitive with the alternative consensus clustering method DeepCluE. Notably, DivClust is competitive with the baseline across diversity levels. This robustness is very significant, given that identifying what properties (including diversity) lead to optimal outcomes in clustering ensembles is an open problem [15, 22].", + "bbox": [ + 75, + 198, + 470, + 469 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To summarize, the results of Tabs. 1 to 3 demonstrate that DivClust: a) effectively controls inter-clustering diversity in deep clustering frameworks in accordance with user-defined objectives, b) does not degrade the quality of the clusterings and in fact produces better solutions than single-clustering models, and c), it can be used with consensus clustering to identify single-clustering solutions superior to those of the corresponding single-clustering frameworks.", + "bbox": [ + 75, + 470, + 468, + 592 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Discussion", + "text_level": 1, + "bbox": [ + 76, + 607, + 191, + 623 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.1. Diversity Control & Consensus Clustering Performance", + "text_level": 1, + "bbox": [ + 76, + 633, + 467, + 664 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Results presented in Sec. 4 demonstrate the effectiveness of DivClust both in controlling inter-clustering diversity and in producing clustering ensembles that lead to consensus clustering outcomes superior to single clustering baselines.", + "bbox": [ + 75, + 672, + 467, + 734 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Specifically, Tabs. 1 and 2 show that the inter-clustering similarity $D^{R}$ of ensembles produced by DivClust is consistently lower than the targets $D^{T}$ . In the few cases where $D^{R} \\geq D^{T}$ , it is by very small margins (the greatest deviation was +0.017), which may be attributed to our use of a memory bank to estimate $D^{R}$ for the update rule of the threshold $d$ . Regarding consensus clustering accuracy, despite the sensitivity of consensus clustering to the properties of the ensembles and, specifically, to different inter-clustering diversity levels, our method proves particularly robust to varying the diversity targets $D^{T}$ , outperforming", + "bbox": [ + 75, + 734, + 467, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "bases for most settings. This indicates that DivClust learns clusterings with a good quality-diversity trade-off and can be reliably used for consensus clustering.", + "bbox": [ + 496, + 90, + 890, + 136 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Finally, we note that DivClust's ability to explicitly control inter-clustering diversity can facilitate future research on the impact of diversity in clustering ensembles and toward methodologies that determine desirable diversity levels for specific settings [51].", + "bbox": [ + 496, + 138, + 890, + 215 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.2. Complexity & Computational Cost", + "text_level": 1, + "bbox": [ + 498, + 232, + 805, + 250 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The complexity of DivClust's objective is $O(nK^2 C^2)$ , where $n$ is the batch size, $K$ is the number of clusterings, and $C$ is the number of clusters in each clustering. Importantly, the cost of DivClust relates only to the computation of the loss and the additional projection heads, and is therefore fixed for fixed $n$ , $K$ , $C$ values, regardless of model size and data dimensionality, which are generally the computational bottleneck in Deep Learning applications. Therefore, DivClust is scalable to large datasets. Finally, we note that, in practice, the computational overhead introduced by DivClust is minimal. Specifically, for experiments in this work, DivClust learned ensembles with $K = 20$ clusterings, with training time increasing between $10\\% - 50\\%$ relative to the time it took to train the baseline single-clustering models. Contrasted with the alternative of training a single-clustering model 20 times (which would not allow for controlling diversity), DivClust provides an efficient approach for applying consensus clustering with deep clustering frameworks. A detailed analysis on complexity and runtimes is provided in supplementary Sec. 3.", + "bbox": [ + 496, + 257, + 890, + 561 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 582, + 617, + 598 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We introduce DivClust, a method that can be incorporated into existing deep clustering frameworks to learn multiple clusterings while controlling inter-clustering diversity. To the best of our knowledge, this is the first method that can explicitly control inter-clustering diversity based on user-defined targets, and that is compatible with deep clustering frameworks that learn features and clusters end-to-end. Our experiments, conducted with multiple datasets and deep clustering frameworks, confirm the effectiveness of DivClust in controlling inter-clustering diversity and its adaptability, in terms of it being compatible with various frameworks without requiring modifications and/or hyperparameter tuning. Furthermore, results demonstrate that DivClust learns high quality clusterings, which, in the context of consensus clustering, lead to improved performance compared to single clustering baselines and alternative ensemble clustering methods.", + "bbox": [ + 496, + 609, + 890, + 867 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments: This work was supported by the EU H2020 AI4Media No. 951911 project.", + "bbox": [ + 498, + 869, + 890, + 901 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "3425", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Yuki M. Asano, Christian Rupprecht, and Andrea Vedaldi. Self-labelling via simultaneous clustering and representation learning. 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In Twenty-Fourth International Joint Conference on Artificial Intelligence, 2015. 3" + ], + "bbox": [ + 503, + 92, + 890, + 330 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "3428", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/DivClust_ Controlling Diversity in Deep Clustering/66ea5bda-5daa-4792-a2cb-68e8650cf8e9_model.json b/2023/DivClust_ Controlling Diversity in Deep Clustering/66ea5bda-5daa-4792-a2cb-68e8650cf8e9_model.json new file mode 100644 index 0000000000000000000000000000000000000000..652610ecb4288d4e511c95d327efb4d2f2385c7c --- /dev/null +++ b/2023/DivClust_ Controlling Diversity in Deep Clustering/66ea5bda-5daa-4792-a2cb-68e8650cf8e9_model.json @@ -0,0 +1,2169 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.229, + 0.131, + 0.745, + 0.154 + ], + "angle": 0, + "content": "DivClust: Controlling Diversity in Deep Clustering" + }, + { + "type": "text", + "bbox": [ + 0.219, + 0.181, + 0.751, + 0.233 + ], + "angle": 0, + "content": "Ioannis Maniadis Metaxas,\\* Georgios Tzimiropoulos, Ioannis Patras Queen Mary University of London Mile End road, E1 4NS London, UK" + }, + { + "type": "text", + "bbox": [ + 0.23, + 0.237, + 0.735, + 0.253 + ], + "angle": 0, + "content": "{i.maniadismetaxas，g.tzimiropoulos，i.patras}@qmul.ac.uk" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.287, + 0.314, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.319, + 0.473, + 0.697 + ], + "angle": 0, + "content": "Clustering has been a major research topic in the field of machine learning, one to which Deep Learning has recently been applied with significant success. However, an aspect of clustering that is not addressed by existing deep clustering methods, is that of efficiently producing multiple, diverse partitionings for a given dataset. This is particularly important, as a diverse set of base clusterings are necessary for consensus clustering, which has been found to produce better and more robust results than relying on a single clustering. To address this gap, we propose DivClust, a diversity controlling loss that can be incorporated into existing deep clustering frameworks to produce multiple clusterings with the desired degree of diversity. We conduct experiments with multiple datasets and deep clustering frameworks and show that: a) our method effectively controls diversity across frameworks and datasets with very small additional computational cost, b) the sets of clusterings learned by DivClust include solutions that significantly outperform single-clustering baselines, and c) using an off-the-shelf consensus clustering algorithm, DivClust produces consensus clustering solutions that consistently outperform single-clustering baselines, effectively improving the performance of the base deep clustering framework. Code is available at https://github.com/ManiadisG/DivClust." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.728, + 0.21, + 0.743 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.754, + 0.47, + 0.876 + ], + "angle": 0, + "content": "The exponentially increasing volume of visual data, along with advances in computing power and the development of powerful Deep Neural Network architectures, have revived the interest in unsupervised learning with visual data. Deep clustering in particular has been an area where significant progress has been made in the recent years. Existing works focus on producing a single clustering, which is evaluated in terms of how well that clustering matches" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.288, + 0.895, + 0.364 + ], + "angle": 0, + "content": "the ground truth labels of the dataset in question. However, consensus, or ensemble, clustering remains under-studied in the context of deep clustering, despite the fact that it has been found to consistently improve performance over single clustering outcomes [3, 17, 45, 73]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.368, + 0.895, + 0.55 + ], + "angle": 0, + "content": "Consensus clustering consists of two stages, specifically generating a set of base clusterings, and then applying a consensus algorithm to aggregate them. Identifying what properties ensembles should have in order to produce better outcomes in each setting has been an open problem [18]. However, research has found that inter-clustering diversity within the ensemble is an important, desirable factor [14,20,24,34,51], along with individual clustering quality, and that diversity should be moderated [15,22,51]. Furthermore, several works suggest that controlling diversity in ensembles is important toward studying its impact and determining its optimal level in each setting [22, 51]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.554, + 0.895, + 0.903 + ], + "angle": 0, + "content": "The typical way to produce diverse clusterings is to promote diversity by clustering the data multiple times with different initializations/hyperparameters or subsets of the data [3, 17]. This approach, however, does not guarantee or control the degree of diversity, and is computationally costly, particularly in the context of deep clustering, where it would require the training of multiple models. Some methods have been proposed that find diverse clusterings by including diversity-related objectives to the clustering process, but those methods have only been applied to clustering precomputed features and cannot be trivially incorporated into Deep Learning frameworks. Other methods tackle diverse clustering by creating and clustering diverse feature subspaces, including some that apply this approach in the context of deep clustering [48, 61]. Those methods, however, do not control inter-clustering diversity. Rather, they influence it indirectly through the properties of the subspaces they create. Furthermore, typically, existing methods have been focusing on producing orthogonal clusterings or identifying clusterings based on independent attributes of relatively simple visual data (e.g. color/shape). Consequently, they are oriented toward maximizing inter-clustering diversity, which is not appropriate for consensus" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.221, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.517, + 0.957 + ], + "angle": 0, + "content": "3418" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.092, + 0.895, + 0.207 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.235, + 0.895, + 0.278 + ], + "angle": 0, + "content": "Figure 1. Overview of DivClust. Assuming clusterings \\( A \\) and \\( B \\), the proposed diversity loss \\( L_{div} \\) calculates their similarity matrix \\( S_{AB} \\) and restricts the similarity between cluster pairs to be lower than a similarity upper bound \\( d \\). In the figure, this is represented by the model adjusting the cluster boundaries to produce more diverse clusterings. Best seen in color." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.304, + 0.226, + 0.319 + ], + "angle": 0, + "content": "clustering [15,22,51]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.321, + 0.473, + 0.623 + ], + "angle": 0, + "content": "To tackle this gap, namely generating multiple clusterings with deep clustering frameworks efficiently and with the desired degree of diversity, we propose DivClust. Our method can be straightforwardly incorporated into existing deep clustering frameworks to learn multiple clusterings whose diversity is explicitly controlled. Specifically, the proposed method uses a single backbone for feature extraction, followed by multiple projection heads, each producing cluster assignments for a corresponding clustering. Given a user defined diversity target, in this work expressed in terms of the average NMI between clusterings, DivClust restricts inter-clustering similarity to be below an appropriate, dynamically estimated threshold. This is achieved with a novel loss component, which estimates inter-clustering similarity based on soft cluster assignments produced by the model, and penalizes values exceeding the threshold. Importantly, DivClust introduces minimal computational cost and requires no hyperparameter tuning with respect to the base deep clustering framework, which makes its use simple and computationally efficient." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.627, + 0.47, + 0.883 + ], + "angle": 0, + "content": "Experiments on four datasets (CIFAR10, CIFAR100, Imagenet-10, Imagenet-Dogs) with three recent deep clustering methods (IIC [37], PICA [32], CC [44]) show that DivClust can effectively control inter-clustering diversity without reducing the quality of the clusterings. Furthermore, we demonstrate that, with the use of an off-the-shelf consensus clustering algorithm, the diverse base clusterings learned by DivClust produce consensus clustering solutions that outperform the base frameworks, effectively improving them with minimal computational cost. Notably, despite the sensitivity of consensus clustering to the properties of the ensemble, our method is robust across various diversity levels, outperforming baselines in most settings, often by large margins. Our work then provides a straightforward way for improving the performance of deep clustering frameworks, as well as a new tool for studying the impact of diversity in deep clustering ensembles [51]." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.468, + 0.901 + ], + "angle": 0, + "content": "In summary, DivClust: a) can be incorporated in ex" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.304, + 0.895, + 0.395 + ], + "angle": 0, + "content": "isting deep clustering frameworks in a plug-and-play way with very small computational cost, b) can explicitly and effectively control inter-clustering diversity to satisfy user-defined targets, and c) learns clusterings that can improve the performance of deep clustering frameworks via consensus clustering." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.411, + 0.65, + 0.427 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.437, + 0.662, + 0.453 + ], + "angle": 0, + "content": "2.1. Deep Clustering" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.461, + 0.894, + 0.536 + ], + "angle": 0, + "content": "The term deep clustering refers to methods that cluster data while learning their features. They are generally divided into two categories, namely those that alternate training between clustering and feature learning and those that train both simultaneously." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.538, + 0.895, + 0.765 + ], + "angle": 0, + "content": "Alternate learning: Methods following this approach generally utilize a two-step training regime repeated in regular intervals (e.g. per-epoch or per-step). First, sample pseudo-labels are produced based on representations extracted by the model (e.g. by feature clustering). Second, those pseudo-labels are utilized to improve the learned representations, typically by training the feature extraction model as a classifier. Those methods include DEC [64], DAC [8], DCCM [63], DDC [7], JULE [66], SCAN [57], ProPos [33] and SPICE [49], as well as DSC-N [36], IDFD [65] and MIX'EM [58], which propose ways to train models whose representations produce better outcomes when clustered. Other works in this area are DeepCluster [5], SeLa [1], PCL [42] and HCSC [21], though their primary focus is on representation learning." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.766, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Simultaneous learning: These methods jointly learn features and cluster assignments. They include ADC [23], IIC [37] and PICA [32], which train clustering models end-to-end with loss functions that enforce desired properties on the clusters assignments, ConCURL [11, 52], which builds on BYOL [19] with a loss maximizing the agreement of clusterings from transformed embeddings, DCCS [71], which leverages an adversarial component in the clustering process, and GatCluster [50], which proposes an attention" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3419" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.468, + 0.137 + ], + "angle": 0, + "content": "mechanism combined with four self-learning tasks. Finally, methods such as SCL [31], CC [44], GCC [72], TCC [53] and MiCE [56] leverage contrastive learning." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.138, + 0.468, + 0.213 + ], + "angle": 0, + "content": "Although some deep clustering methods [1, 37, 52] use multiple clusterings, most do not explore the prevalence and impact of inter-clustering diversity, and none proposes ways to control it. Our work is, to the best of our knowledge, the first that addresses both issues." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.226, + 0.258, + 0.243 + ], + "angle": 0, + "content": "2.2. Diverse Clustering" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.25, + 0.468, + 0.414 + ], + "angle": 0, + "content": "The most straightforward way of producing multiple, diverse clusterings is clustering the data multiple times. Typical methods to increase diversity include varying the clustering algorithm or its hyperparameters, using different initializations, and clustering a subset of the samples or features [3]. This approach, however, is a) computationally costly, in that it requires clustering the data multiple times, b) unreliable, as some ways to increase diversity might decrease the quality of clusters (e.g. using a subset of the data), and c) ineffective, as there is no guarantee that the desired degree of diversity will be achieved." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.417, + 0.468, + 0.627 + ], + "angle": 0, + "content": "To tackle this, several methods have been proposed to create multiple, diverse clusterings [25]. We identify two main approaches of promoting inter-clustering diversity: a) explicitly, by optimizing for appropriate objectives, and b) implicitly, by optimizing for decorrelated/orthogonal feature subspaces, which, when clustered, lead to diverse clusterings. Methods in the first category include COALA [2], Meta Clustering [6], Dec-kmeans [35], MNMF [67], MSC [26], ADFT [10] and MultiCC [60]. Subspace clustering methods include MISC [59], ISAAC [69], NR-kmeans [47], RAOSC [70] and ENRC [48]. Distinctly, diverse clustering has also been explored in the context of multi-view data by OSC [9], MVMC [68], DMSMF [46], DMClusts [62], DiMSC [4], and DiVMC [61]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.468, + 0.899 + ], + "angle": 0, + "content": "To the best of our knowledge, except for DiMVMC and ENRC, none of the existing methods are compatible with Deep Learning, they require a learned feature space on which to be applied, and most have quadratic complexity relative to the number of samples. This restricts their use on real-life high dimensional data, where deep clustering produces better outcomes [56, 57]. Regarding DiMVMC and ENRC, they depend on autoencoder-based architectures and adapting them to more recent deep clustering frameworks, which perform significantly better, is not trivial. More importantly, they utilize subspace clustering, inheriting its limitations regarding controlling diversity. Specifically: a) no method has been proposed to infer how different the subspaces must be in order to lead to a specific degree of interclustering diversity, and b) subspace clustering methods inherit the randomness of the clustering algorithm applied to the subspaces (K-means for DiMVMC and ENRC), which further limits their control over the outcomes." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.092, + 0.704, + 0.108 + ], + "angle": 0, + "content": "2.3. Consensus Clustering" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.114, + 0.892, + 0.295 + ], + "angle": 0, + "content": "The performance of clustering algorithms varies depending on the data and their properties, the algorithm itself, and its hyperparameters. This makes finding reliable clustering solutions particularly difficult. Consensus, or ensemble, clustering has emerged as a solution to this problem, specifically by combining the results of multiple, different clusterings, rather than relying on a single solution. This has been found to produce better and more robust outcomes than single-clustering approaches [3, 17, 18, 45]. The process of consensus clustering happens in two stages: a) multiple, diverse base clusterings are generated and b) those clusterings are aggregated using a consensus algorithm." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.297, + 0.892, + 0.552 + ], + "angle": 0, + "content": "Generating diverse clusterings: The properties of the set of clusterings used by the consensus algorithm is a key factor for obtaining good performance. Multiple works [24, 40, 51] have found that both the quality of individual base clusterings and their diversity is critical, and that, indeed, clustering ensembles with a moderate degree of diversity lead to better outcomes [15, 20, 22]. Typical methods for ensemble generation include using different clustering algorithms [13], using different initializations of the same clustering algorithm or different hyperparameters (e.g. the number of clusters) [16, 22, 41], clustering with different subsets of the features [54], using random projections to diversify the feature space [14], and clustering with different subsets of the dataset [12, 13]. However, concrete methods for identifying optimal hyperparameters, such as the degree of diversity, the number of clusterings in the ensemble, and the method by which the ensemble is generated, remain elusive." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.554, + 0.892, + 0.704 + ], + "angle": 0, + "content": "Consensus algorithms: Consensus algorithms aim to aggregate multiple, diverse clusterings to produce a single, robust solution. Various approaches to this problem have been proposed, such as using matrix factorization [43], distance minimization between clusterings [75], utilizing multiple views [55], graph learning [28, 73, 74] and matrix coassociation [29, 38]. We note that, while improving consensus algorithms increase the robustness of consensus clustering overall, the stages of ensemble generation and its aggregation with consensus algorithms are largely independent." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Consensus Clustering & Deep Learning: Despite the established advantages of consensus clustering over single-clustering approaches, consensus clustering has not been explored in the context of deep clustering. A possible reason is the computational cost of generating multiple, diverse base clusterings, which would require training multiple models. The only work that has, to the best of our knowledge, applied consensus clustering in the deep clustering setting is DeepCluE [27]. Notably, however, the base clusterings used by DeepCluE are not all learned by the model. Rather, a single-clustering model is trained, and an ensemble is generated by clustering features from multiple layers of the model with U-SPEC [30]. Our work addresses" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "3420" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.138 + ], + "angle": 0, + "content": "this gap, by proposing a way to train a single deep clustering model to generate multiple clusterings with controlled diversity and with minimal computational overhead." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.151, + 0.169, + 0.167 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.177, + 0.469, + 0.282 + ], + "angle": 0, + "content": "Overview: Our method consists of two components: a) A novel loss function that can be incorporated in deep clustering frameworks to control inter-clustering diversity by applying a threshold to cluster-wise similarities, and b) a method for dynamically estimating that threshold so that the clusterings learned by the model are sufficiently diverse, according to a user-defined metric." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.283, + 0.47, + 0.629 + ], + "angle": 0, + "content": "More concretely, we assume a deep clustering model that learns \\(K\\) clusterings (typically a backbone encoder followed by \\(K\\) projection heads), a deep clustering framework and its loss function \\(L_{\\text{main}}\\), and a diversity target \\(D^T\\) set by the user, expressed as an upper bound to inter-clustering similarity1 (i.e. the maximum acceptable similarity). In order to control the inter-clustering similarity \\(D^R\\) of the learned clusterings so that \\(D^T \\leq D^R\\), we propose a complementary loss \\(L_{\\text{div}}\\). Specifically, given soft cluster assignments for a pair of clusterings \\(A, B \\in K\\), we define the inter-clustering similarity matrix \\(S_{AB} \\in \\mathbb{R}^{C_A \\times C_B}\\), where \\(C_A\\) and \\(C_B\\) is the number of clusters in each clustering, and \\(S_{AB}(i,j) \\in [0,1]\\) measures the similarity between clusters \\(i \\in C_A\\) and \\(j \\in C_B\\). It follows that decreasing the values of \\(S_{AB}\\) reduces the similarity between the clusters of \\(A\\) and \\(B\\), and therefore increases their diversity. Accordingly, \\(L_{\\text{div}}\\) utilizes \\(S_{AB}\\) in order to restrict inter-clustering similarity to be under an upper similarity bound \\(d\\). The value of \\(d\\) is dynamically adjusted during training, decreasing when \\(D^R > D^T\\) and increasing when \\(D^R \\leq D^T\\), thereby tightening and relaxing the loss function so that, overall and throughout training, inter-clustering similarity \\(D^R\\) remains at or under the desired level \\(D^T\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.63, + 0.469, + 0.842 + ], + "angle": 0, + "content": "Defining the inter-clustering similarity matrix: Our method assumes a standard deep clustering architecture, consisting of an encoder \\( f \\), followed by \\( K \\) projection heads \\( h_1, \\ldots, h_K \\), each of which produces assignments for a clustering \\( k \\). Specifically, let \\( X \\) be a set of \\( N \\) unlabeled samples. The encoder maps each sample \\( x \\in X \\) to a representation \\( f(x) \\), and each projection head \\( h_k \\) maps \\( f(x) \\) to \\( C_k \\) clusters, so that \\( p_k(x) = h_k(f(x)) \\in \\mathbb{R}^{C_k \\times 1} \\) represents a probability assignment vector mapping sample \\( x \\in X \\) to \\( C_k \\) clusters in clustering \\( k \\). Without loss of generality, we assume that \\( C = C_k \\forall k \\in K \\). Each clustering can then be represented by a cluster assignment matrix \\( P_k(X) = [p_k(x_1), p_k(x_2), \\dots, p_k(x_N)] \\in \\mathbb{R}^{C \\times N} \\). The column \\( p_k(n) \\), that is the probability assignment vector for the" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.892, + 0.152 + ], + "angle": 0, + "content": "\\(n\\)-th sample, encodes the degrees to which sample \\(x_{n}\\) is assigned to different clusters. The row vector \\(q_{k}(i)\\in \\mathbb{R}^{N}\\) shows which samples are softly assigned to cluster \\(i\\in C\\). We refer to \\(q_{k}(i)\\) as the cluster membership vector." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.152, + 0.894, + 0.243 + ], + "angle": 0, + "content": "To quantify the similarity between clusterings \\(A\\) and \\(B\\) we define the inter-clustering similarity matrix \\(S_{AB} \\in \\mathbb{R}^{C \\times C}\\). We define each element \\(S_{AB}(i,j)\\) as the cosine similarity between the cluster membership vector \\(q_{A}(i)\\) of cluster \\(i \\in A\\) and the cluster membership vector \\(q_{B}(j)\\) of cluster \\(j \\in B\\):" + }, + { + "type": "equation", + "bbox": [ + 0.585, + 0.254, + 0.892, + 0.287 + ], + "angle": 0, + "content": "\\[\nS _ {A B} (i, j) = \\frac {q _ {A} (i) \\cdot q _ {B} (j)}{\\left| \\left| q _ {A} (i) \\right| \\right| _ {2} \\left| \\left| q _ {B} (j) \\right| \\right| _ {2}} \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.296, + 0.892, + 0.371 + ], + "angle": 0, + "content": "This measure expresses the degree to which samples in the dataset are assigned similarly to clusters \\( i \\) and \\( j \\). Specifically, \\( S_{AB}(i,j) = 0 \\) if \\( q_A(i) \\perp q_B(j) \\) and \\( S_{AB}(i,j) = 1 \\) if \\( q_A(i) = q_B(j) \\). It is, therefore, a differentiable measure of the similarity of clusters \\( i \\) and \\( j \\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.372, + 0.893, + 0.584 + ], + "angle": 0, + "content": "Defining the loss function: Based on the inter-clustering similarity matrix \\( S_{AB} \\), we define DivClust's loss to softly enforce that a clustering \\( A \\) does not have an aggregate cluster similarity with a clustering \\( B \\) greater than a similarity upper bound \\( d \\). The aggregate similarity \\( S_{AB}^{aggr} \\) is defined as the average similarity of clustering \\( A \\)'s clusters with their most similar cluster of clustering \\( B \\) (Eq. (2)). Using this metric, we propose \\( L_{div} \\) (Eq. (3)), a loss that regulates diversity between clusterings \\( A \\) and \\( B \\) by forcing that \\( S_{AB}^{aggr} < d \\), for \\( d \\in [0,1] \\). It is clear from Eq. (3) that \\( S_{AB}^{aggr} < d \\Rightarrow L_{div}(A,B) = 0 \\), in which case the diversity requirement is satisfied and the loss has no impact. Conversely, \\( S_{AB}^{aggr} \\geq d \\Rightarrow L_{div}(A,B) > 0 \\), in which case the loss requires that inter-clustering similarity decreases." + }, + { + "type": "equation", + "bbox": [ + 0.585, + 0.594, + 0.892, + 0.636 + ], + "angle": 0, + "content": "\\[\nS _ {A B} ^ {a q g r} = \\frac {1}{C} \\sum_ {i = 1} ^ {C} \\max _ {j} \\left(S _ {A B} (i, j)\\right) \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.601, + 0.647, + 0.892, + 0.666 + ], + "angle": 0, + "content": "\\[\nL _ {d i v} (A, B) = \\left[ S _ {A B} ^ {a g g r} - d \\right] _ {+} \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.671, + 0.893, + 0.839 + ], + "angle": 0, + "content": "Having defined the diversity loss \\( L_{div} \\) between two clusterings, we extend it to multiple clusterings \\( K \\) and combine it with the base deep clustering framework's objective. For a clustering \\( k \\in K \\), we denote with \\( L_{main}(k) \\) the loss of the base deep clustering framework for that clustering, and with \\( L_{div}(k, k') \\) the diversity controlling loss between clusterings \\( k \\) and \\( k' \\). We present the joint loss \\( L_{joint}(k) \\) for each clustering \\( k \\) in Eq. (4), where \\( L_{main}(k) \\) depends on cluster assignment matrix \\( P_k \\), while \\( L_{div}(k, k') \\) depends on \\( P_k \\) and \\( P_{k'} \\). Accordingly, the model's training loss \\( L_{total} \\) seen in Eq. (5), is the average of \\( L_{joint} \\) over all clusterings." + }, + { + "type": "equation", + "bbox": [ + 0.508, + 0.861, + 0.892, + 0.904 + ], + "angle": 0, + "content": "\\[\nL _ {\\text {j o i n t}} (k) = L _ {\\text {m a i n}} (k) + \\frac {1}{K - 1} \\sum_ {k ^ {\\prime} = 1, k ^ {\\prime} \\neq k} ^ {K} L _ {\\text {d i v}} \\left(k, k ^ {\\prime}\\right) \\tag {4}\n\\]" + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.851, + 0.469, + 0.9 + ], + "angle": 0, + "content": "1It is trivial to modify our formulation to enforce a lower bound. However, experiments (see Sec. 4.2) showed that, when learning multiple clusterings, deep clustering frameworks inherently tend to converge to near-identical solutions, which made the lower bound scenario redundant." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "3421" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.157, + 0.089, + 0.341, + 0.219 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.152, + 0.235, + 0.358, + 0.247 + ], + "angle": 0, + "content": "(a) Cluster assignments \\(P_A\\) for clustering A" + }, + { + "type": "image", + "bbox": [ + 0.389, + 0.088, + 0.572, + 0.219 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.382, + 0.235, + 0.589, + 0.248 + ], + "angle": 0, + "content": "(b) Cluster assignments \\(P_B\\) for clustering B" + }, + { + "type": "image", + "bbox": [ + 0.626, + 0.089, + 0.8, + 0.219 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.653, + 0.235, + 0.778, + 0.247 + ], + "angle": 0, + "content": "(c) Similarity matrix \\(S_{AB}\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.258, + 0.892, + 0.288 + ], + "angle": 0, + "content": "Figure 2. Examples of synthetic cluster assignments \\( P_A \\), \\( P_B \\) and similarity matrix \\( S_{AB} \\). Note that clusters \\( i \\in A \\) and \\( j \\in B \\) are softly assigned the same samples. Correspondingly, their similarity score \\( S_{AB}(i,j) \\) is high (highlighted with red in Fig. 2c). Best seen in color." + }, + { + "type": "equation", + "bbox": [ + 0.184, + 0.324, + 0.469, + 0.365 + ], + "angle": 0, + "content": "\\[\nL _ {t o t a l} = \\frac {1}{K} \\sum_ {k = 1} ^ {K} L _ {\\text {j o i n t}} (k) \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.371, + 0.469, + 0.505 + ], + "angle": 0, + "content": "The loss \\( L_{total} \\) is therefore a combination of the base deep clustering framework's loss \\( L_{main} \\) for each clustering \\( k \\in K \\) and the loss \\( L_{div} \\), which is used to control interclustering diversity. The proposed loss formulation is applicable to any deep clustering framework that produces cluster assignments through the model (as opposed to frameworks using offline methods such as MIX'EM [58]), which covers the majority of deep clustering frameworks outlined in Sec. 2." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.507, + 0.47, + 0.734 + ], + "angle": 0, + "content": "Dynamic upper bound \\( d \\): The proposed loss \\( L_{div} \\) controls inter-clustering diversity by restricting the values of \\( S_{AB} \\) according to the similarity upper bound \\( d \\). However, the values of \\( S_{AB} \\) are calculated based on the cosine similarity of soft cluster assignments. This means that pairs of cluster assignment vectors \\( i \\), \\( j \\) will have different similarity values \\( S_{AB}(i,j) \\) depending on their sharpness, even if they point to the same cluster in terms of their corresponding hard assignment. It follows that \\( S_{AB} \\) and, accordingly, the impact of \\( d \\), are dependent on the confidence of cluster assignments and vary throughout training and between experiments (as factors like the number of clusters and model capacity influence the confidence of cluster assignments). Therefore, \\( d \\) is an ambiguous and unintuitive metric for users to define diversity targets with." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.733, + 0.469, + 0.839 + ], + "angle": 0, + "content": "To tackle this issue and to provide a reliable and intuitive method for defining diversity objectives, we propose dynamically determining the value of the threshold \\(d\\) during training. Concretely, let \\(D\\) be an inter-clustering similarity metric chosen by the user. In this work, we use avg. Normalized Mutual Information (NMI), a well established metric for estimating inter-clustering similarity." + }, + { + "type": "equation", + "bbox": [ + 0.098, + 0.861, + 0.469, + 0.904 + ], + "angle": 0, + "content": "\\[\nD = \\frac {1}{(K - 1) (K / 2)} \\sum_ {k = 1} ^ {K - 1} \\sum_ {k ^ {\\prime} = k + 1} ^ {K} N M I \\left(P _ {k} ^ {h}, P _ {k ^ {\\prime}} ^ {h}\\right) \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.312, + 0.892, + 0.373 + ], + "angle": 0, + "content": "where \\( P_{k}^{h} \\in \\mathbb{Z}^{N} \\) is the hard cluster assignment vector for \\( N \\) samples in clustering \\( k \\in K \\) and \\( NMI(P_{k}^{h}, P_{k^{\\prime}}^{h}) \\) represents the NMI between \\( k \\) and \\( k^{\\prime} \\). \\( D \\in [0,1] \\), with higher values indicating more similar clusterings." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.373, + 0.893, + 0.51 + ], + "angle": 0, + "content": "Assuming a user-defined similarity target \\( D^T \\), expressed as a value of metric \\( D \\), we denote with \\( D^R \\) the measured inter-clustering similarity of the clusterings learned by the model, expressed in the same metric. DivClust's objective is to control inter-clustering diversity, which translates to learning clusterings such that \\( D^R \\leq D^T \\). Accordingly, appropriate thresholds \\( d \\) must be used during training. Under the assumption that \\( D^R \\) decreases monotonically w.r.t. \\( d \\), we propose the following update rule for \\( d \\):" + }, + { + "type": "equation", + "bbox": [ + 0.527, + 0.522, + 0.892, + 0.562 + ], + "angle": 0, + "content": "\\[\nd _ {s + 1} = \\left\\{ \\begin{array}{l l} \\max \\left(d _ {s} (1 - m), 0\\right), & \\text {i f} D ^ {R} > D ^ {T} \\\\ \\min \\left(d _ {s} (1 + m), 1\\right), & \\text {i f} D ^ {R} \\leq D ^ {T} \\end{array} , \\right. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.573, + 0.893, + 0.74 + ], + "angle": 0, + "content": "where \\( d_{s} \\) and \\( d_{s+1} \\) are the values of the threshold \\( d \\) for the current and the next steps, and \\( m \\in (0,1) \\) regulates the magnitude of the update steps. Following this update rule, we decrease \\( d \\) when the measured inter-clustering similarity \\( D^{R} \\) needs to decrease, and increase it otherwise. For computational efficiency, instead of calculating \\( D^{R} \\) over the entire dataset in every training step, we do so every 20 iterations on a memory bank of \\( M = 10,000 \\) cluster assignments – the latter is updated at every step in a FIFO manner. We set the hyperparameter \\( m \\) to \\( m = 0.01 \\) in all experiments." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.755, + 0.633, + 0.772 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We conduct several experiments to evaluate DivClust's adaptability, its effectiveness in controlling diversity, and the quality of the resulting clusterings. First, to show that DivClust effectively controls inter-clustering diversity and produces high quality clusterings with various frameworks, we combine it with IIC [37], PICA [32] and CC [44], and apply it to CIFAR10 with various diversity targets \\( D^{T} \\). Subsequently, we focus on the best framework of the" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3422" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.134, + 0.089, + 0.833, + 0.381 + ], + "angle": 0, + "content": "
FrameworkClusteringsDTDRCNFMean Acc.Max. Acc.DivClust Acc.
IIC1--0.9970.4420.4420.442
201.0.9830.9960.5260.5260.526
200.950.9390.9980.5310.5370.533
200.90.8880.9970.5680.590.578
200.80.80.9970.6110.6780.653
200.70.6940.9960.5660.6370.685
PICA1--0.9060.5330.5330.533
201.0.9910.8140.5970.5970.596
200.950.9310.8260.6240.6310.625
200.90.8910.8410.6480.6650.652
200.80.8170.8280.5980.6350.595
200.70.7030.8240.6250.6910.671
CC1--0.9360.7640.7640.764
201.0.9760.9340.7630.7630.763
200.950.9460.9340.7620.7730.76
200.90.90.9310.7940.8180.789
200.80.8140.930.7620.8470.819
200.70.6990.9270.7030.8180.815
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.392, + 0.893, + 0.435 + ], + "angle": 0, + "content": "Table 1. Results for IIC, PICA and CC applied on CIFAR10 with DivClust. CNF and Mean Acc. are calculated by averaging the corresponding metrics over all clusterings, while Max Acc. refers to the best performing base clustering. The DivClust Acc. metric measures the accuracy of a consensus clustering produced with the DivClust C method." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.458, + 0.472, + 0.578 + ], + "angle": 0, + "content": "
DTDR
CIFAR10CIFAR100ImageNet-10ImageNet-Dogs
1.0.9760.9390.9870.941
0.950.9460.9260.9480.945
0.90.90.8480.8970.87
0.80.8140.8060.8070.795
0.70.6990.7050.6960.702
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.588, + 0.47, + 0.632 + ], + "angle": 0, + "content": "Table 2. Avg. inter-clustering similarity scores \\( D^{R} \\) for clustering sets produced by DivClust combined with CC for various diversity targets \\( D^{T} \\). The objective of DivClust is that \\( D^{R} \\leq D^{T} \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.657, + 0.47, + 0.749 + ], + "angle": 0, + "content": "three, namely CC, and conduct experiments on 4 datasets (CIFAR10, CIFAR100,Imagenet-10 andImagenet-Dogs). Our findings demonstrate that, across frameworks and datasets, DivClust can: a) effectively control diversity and b) improve clustering outcomes over the base frameworks and alternative ensembling methods." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.757, + 0.258, + 0.774 + ], + "angle": 0, + "content": "4.1. Experiments setup" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.469, + 0.841 + ], + "angle": 0, + "content": "Datasets: We conduct experiments with 4 standard datasets in deep clustering: CIFAR10, CIFAR100 [39] (evaluating on the 20 superclasses), ImageNet-10 and ImageNet-Dogs [8]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Metrics: Inter-clustering similarity is measured by averaging the NMI between clusterings to calculate the interclustering NMI metric \\( D \\) (Eq. (6)), with higher values indicating more similar clusterings. We denote with \\( D^T \\) the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.46, + 0.892, + 0.596 + ], + "angle": 0, + "content": "diversity target set by the user and with \\( D^{R} \\) the measured inter-clustering similarity after training. When DivClust is applied we want that \\( D^{R} \\leq D^{T} \\). Clustering quality is evaluated based on overlap of the clusterings with the dataset's ground truth labels, using the Accuracy (ACC), Normalized Mutual Information (NMI) and Adjusted Rand Index (ARI) metrics. We also report the avg. cluster assignment confidence (CNF), which measures cluster separability. For all four metrics greater values are better, 1 being optimal." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.598, + 0.893, + 0.779 + ], + "angle": 0, + "content": "Implementation & Training: DivClust is incorporated into the base frameworks as described in Sec. 3, by adding DivClust's loss to their objective and duplicating projection heads \\( h \\) to produce multiple clusterings. The models were trained following the configurations (model architecture, training duration, hyperparameters etc.) suggested in their respective papers [32, 37, 44], unless stated otherwise. PICA and IIC were trained without overclustering. We set the number of clusterings to \\( K = 20 \\), following convention in consensus clustering [73], and the number of clusters \\( C \\) to the number of classes for each dataset, following convention for deep clustering evaluation [32, 37, 44]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Consensus Clustering: To extract single clustering solutions we examine three methods: a) selecting the clustering \\( k \\) with the lowest corresponding loss \\( L_{\\text{main}}(k) \\) (DivClust A), b) using the consensus clustering algorithm SCCBG [73] to aggregate clusterings (DivClust B), and c) a combination of the two, where we select the 10 best clusterings with regard to their loss and then apply SCCBG (DivClust C). For clarity and space, we present in the paper" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "3423" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.078, + 0.089, + 0.892, + 0.513 + ], + "angle": 0, + "content": "
DatasetDTCIFAR10CIFAR100ImageNet-10ImageNet-Dogs
MetricNMINMIACCARINMIACCARINMIACCARINMIACCARI
K-means-0.0870.2290.0490.0840.1300.0280.1190.2410.0570.550.1050.020
AC-0.1050.2280.0650.0980.1380.0340.1380.2420.0670.0370.1390.021
NMF-0.0810.1900.0340.0790.1180.0260.1320.2300.0650.0440.1180.016
AE-0.2370.3140.1690.1000.1650.0480.2100.3170.1520.1040.1850.073
DAE-0.2510.2970.1630.1110.1510.0460.2060.3040.1380.1040.1900.078
DCGAN-0.2650.3150.1760.1200.1510.0450.2250.3460.1570.1210.1740.078
DeCNN-0.2400.2820.1740.0920.1330.0380.1860.3130.1420.0980.1750.073
VAE-0.2450.2910.1670.1080.1520.0400.1930.3340.1680.1070.1790.079
JULE-0.1920.2720.1380.1030.1370.0330.1750.3000.1380.0540.1380.028
DEC-0.2570.3010.1610.1360.1850.0500.2820.3810.2030.1220.1950.079
DAC-0.3960.5220.3060.1850.2380.0880.3940.5270.3020.2190.2750.111
ADC--0.325--0.160--0.530----
DDC-0.4240.5240.329---0.4330.5770.345---
DCCM-0.4960.6230.4080.2850.3270.1730.6080.7100.5550.3210.3830.182
IIC--0.617--0.257-------
PICA-0.5910.6960.5120.3100.3370.1710.8020.8700.7610.3520.3520.201
CC-0.7050.7900.6370.4310.4290.2660.8590.8930.8220.4450.4290.274
CC-Kmeans-0.6540.6980.5230.4290.4050.2350.7920.8410.6690.4570.4440.284
CC-Kmeans/S-0.6740.690.5540.4280.4020.2280.7920.8420.6730.4560.4440.283
CC-Kmeans/F-0.6840.7620.5990.4380.4090.2100.7970.8470.6850.4580.4440.285
DeepCluE-0.7270.7640.6460.4720.4570.2880.8820.9240.8560.4480.4160.273
DivClust C1.0.6780.7630.6040.4180.4240.2570.860.8950.8250.4590.4510.298
0.950.6770.760.6020.4310.4340.2760.8910.9360.8780.4610.4510.297
0.90.6780.7890.6410.4220.4260.2580.8790.920.8590.480.4870.332
0.80.7240.8190.6810.4220.4140.260.8790.9180.8510.4580.4480.296
0.70.710.8150.6750.440.4370.2830.850.900.8190.5160.5290.376
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.522, + 0.893, + 0.581 + ], + "angle": 0, + "content": "Table 3. Results combining DivClust with CC for various diversity targets \\( D^T \\). We underline DivClust results that outperform the single-clustering baseline CC, and note with bold the best results for each metric across all methods and diversity levels. We emphasize that the NMI in this table measures the similarity between the single clustering produced by each method and the ground truth classes. The NMI values representing inter-clustering similarity \\( D^R \\) in ensembles produced by DivClust for the same experiments are presented in Tab. 2." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.606, + 0.471, + 0.653 + ], + "angle": 0, + "content": "results only for the hybrid aggregation method DivClust C, which we found to be the most robust. Detailed results for all three approaches are provided in supplementary Tab. 5." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.665, + 0.172, + 0.68 + ], + "angle": 0, + "content": "4.2. Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Initially, we apply IIC, PICA and CC on CIFAR10, and present the outcomes in Tab. 1. We find that, for all three frameworks, DivClust effectively controls diversity, as \\( D^{R} \\) is consistently close to or lower than \\( D^{T} \\). Furthermore, results indicate that DivClust is necessary to produce diverse clusterings in deep clustering frameworks, as, without it, they tend to converge to near identical solutions (when \\( D^{T} = 1 \\), \\( D^{R} \\rightarrow 1 \\)). Regarding cluster separability, assignment confidence \\( CNF \\) remains high for various diversity targets \\( D^{T} \\), despite the increased complexity of optimizing both the main deep clustering loss and DivClust's objective. Finally, we observe that, for most diversity targets \\( D^{T} \\), the mean and max. accuracy, as well as the consensus clustering accuracy produced by the aggregation method DivClust" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.606, + 0.892, + 0.713 + ], + "angle": 0, + "content": "C, increase relative to the single clustering model. Notably, consensus clustering accuracy is higher than the mean clustering accuracy for most cases, which highlights the effectiveness of our approach. We stress that identifying clusterings in the ensemble whose performance matches the mean or max. accuracy is not trivial, which is why consensus clustering is necessary to reach a single clustering solution." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Having established that DivClust is effective across frameworks, we focus on CC and apply it on CIFAR10, CIFAR100, ImageNet-Dogs and Imagenet-10. We compare DivClust with the standard implementation of CC, which is trained to learn a single clustering (CC), as well as with alternative methods of ensemble clustering. Specifically, we apply the typical methods of ensemble generation by extracting the features learned by the single-clustering CC model and running K-means 20 times on the entire dataset (CC-Kmeans), on random subsets of the dataset (CC-Kmeans/S) and on random subsets of the feature space (CC-Kmeans/F), following [3]. In all three cases, SCCBG" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.517, + 0.957 + ], + "angle": 0, + "content": "3424" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.198 + ], + "angle": 0, + "content": "is used to aggregate the resulting clusterings. Furthermore, we compare with DeepCluE [27], to the best of our knowledge the only other work that examines consensus clustering in the context of deep clustering, and which is also built on top of CC, allowing for a fair comparison. We note that DeepCluE is not mutually exclusive with DivClust, and could be used jointly with it." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.199, + 0.471, + 0.47 + ], + "angle": 0, + "content": "Inter-clustering similarity scores \\( D^{R} \\) for this set of experiments are presented in Tab. 2, where it is seen that DivClust successfully controls diversity. Results for consensus clustering, the main task for which DivClust is intended, are presented in Tab. 3 for CC across 4 datasets, where we also include results from other deep clustering frameworks for reference. Detailed results, including aggregation methods DivClust A and DivClust B, as well as mean/max scores for DivClust's clustering ensembles, are provided in supplementary Tab. 5. Results in Tab. 3 demonstrate that, for most diversity targets \\( D^{T} \\), DivClust outperforms the single-clustering baseline CC and typical ensemble generation methods, and is competitive with the alternative consensus clustering method DeepCluE. Notably, DivClust is competitive with the baseline across diversity levels. This robustness is very significant, given that identifying what properties (including diversity) lead to optimal outcomes in clustering ensembles is an open problem [15, 22]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.471, + 0.47, + 0.593 + ], + "angle": 0, + "content": "To summarize, the results of Tabs. 1 to 3 demonstrate that DivClust: a) effectively controls inter-clustering diversity in deep clustering frameworks in accordance with user-defined objectives, b) does not degrade the quality of the clusterings and in fact produces better solutions than single-clustering models, and c), it can be used with consensus clustering to identify single-clustering solutions superior to those of the corresponding single-clustering frameworks." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.608, + 0.192, + 0.624 + ], + "angle": 0, + "content": "5. Discussion" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.634, + 0.468, + 0.665 + ], + "angle": 0, + "content": "5.1. Diversity Control & Consensus Clustering Performance" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.674, + 0.468, + 0.735 + ], + "angle": 0, + "content": "Results presented in Sec. 4 demonstrate the effectiveness of DivClust both in controlling inter-clustering diversity and in producing clustering ensembles that lead to consensus clustering outcomes superior to single clustering baselines." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.468, + 0.902 + ], + "angle": 0, + "content": "Specifically, Tabs. 1 and 2 show that the inter-clustering similarity \\( D^{R} \\) of ensembles produced by DivClust is consistently lower than the targets \\( D^{T} \\). In the few cases where \\( D^{R} \\geq D^{T} \\), it is by very small margins (the greatest deviation was +0.017), which may be attributed to our use of a memory bank to estimate \\( D^{R} \\) for the update rule of the threshold \\( d \\). Regarding consensus clustering accuracy, despite the sensitivity of consensus clustering to the properties of the ensembles and, specifically, to different inter-clustering diversity levels, our method proves particularly robust to varying the diversity targets \\( D^{T} \\), outperforming" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.137 + ], + "angle": 0, + "content": "bases for most settings. This indicates that DivClust learns clusterings with a good quality-diversity trade-off and can be reliably used for consensus clustering." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.139, + 0.892, + 0.216 + ], + "angle": 0, + "content": "Finally, we note that DivClust's ability to explicitly control inter-clustering diversity can facilitate future research on the impact of diversity in clustering ensembles and toward methodologies that determine desirable diversity levels for specific settings [51]." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.233, + 0.806, + 0.25 + ], + "angle": 0, + "content": "5.2. Complexity & Computational Cost" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.258, + 0.892, + 0.562 + ], + "angle": 0, + "content": "The complexity of DivClust's objective is \\( O(nK^2 C^2) \\), where \\( n \\) is the batch size, \\( K \\) is the number of clusterings, and \\( C \\) is the number of clusters in each clustering. Importantly, the cost of DivClust relates only to the computation of the loss and the additional projection heads, and is therefore fixed for fixed \\( n \\), \\( K \\), \\( C \\) values, regardless of model size and data dimensionality, which are generally the computational bottleneck in Deep Learning applications. Therefore, DivClust is scalable to large datasets. Finally, we note that, in practice, the computational overhead introduced by DivClust is minimal. Specifically, for experiments in this work, DivClust learned ensembles with \\( K = 20 \\) clusterings, with training time increasing between \\( 10\\% - 50\\% \\) relative to the time it took to train the baseline single-clustering models. Contrasted with the alternative of training a single-clustering model 20 times (which would not allow for controlling diversity), DivClust provides an efficient approach for applying consensus clustering with deep clustering frameworks. A detailed analysis on complexity and runtimes is provided in supplementary Sec. 3." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.583, + 0.619, + 0.599 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.611, + 0.892, + 0.868 + ], + "angle": 0, + "content": "We introduce DivClust, a method that can be incorporated into existing deep clustering frameworks to learn multiple clusterings while controlling inter-clustering diversity. To the best of our knowledge, this is the first method that can explicitly control inter-clustering diversity based on user-defined targets, and that is compatible with deep clustering frameworks that learn features and clusters end-to-end. Our experiments, conducted with multiple datasets and deep clustering frameworks, confirm the effectiveness of DivClust in controlling inter-clustering diversity and its adaptability, in terms of it being compatible with various frameworks without requiring modifications and/or hyperparameter tuning. Furthermore, results demonstrate that DivClust learns high quality clusterings, which, in the context of consensus clustering, lead to improved performance compared to single clustering baselines and alternative ensemble clustering methods." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Acknowledgments: This work was supported by the EU H2020 AI4Media No. 951911 project." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3425" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.17 + ], + "angle": 0, + "content": "[1] Yuki M. Asano, Christian Rupprecht, and Andrea Vedaldi. Self-labelling via simultaneous clustering and representation learning. 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In Twenty-Fourth International Joint Conference on Artificial Intelligence, 2015. 3" + }, + { + "type": "list", + "bbox": [ + 0.504, + 0.093, + 0.892, + 0.331 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.515, + 0.956 + ], + "angle": 0, + "content": "3428" + } + ] +] \ No newline at end of file diff --git a/2023/DivClust_ Controlling Diversity in Deep Clustering/66ea5bda-5daa-4792-a2cb-68e8650cf8e9_origin.pdf b/2023/DivClust_ Controlling Diversity in Deep Clustering/66ea5bda-5daa-4792-a2cb-68e8650cf8e9_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..525a33ac5df73a305d5c75c267fc150b2d347cac --- /dev/null +++ b/2023/DivClust_ Controlling Diversity in Deep Clustering/66ea5bda-5daa-4792-a2cb-68e8650cf8e9_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:61937d629fa8b38ebacca2dea029797e24cee0b8218cef3fdbd31abafd383460 +size 471793 diff --git a/2023/DivClust_ Controlling Diversity in Deep Clustering/full.md b/2023/DivClust_ Controlling Diversity in Deep Clustering/full.md new file mode 100644 index 0000000000000000000000000000000000000000..09b0e125ccd86ea588e940ca5ef5bd82cae9fef2 --- /dev/null +++ b/2023/DivClust_ Controlling Diversity in Deep Clustering/full.md @@ -0,0 +1,286 @@ +# DivClust: Controlling Diversity in Deep Clustering + +Ioannis Maniadis Metaxas,\* Georgios Tzimiropoulos, Ioannis Patras Queen Mary University of London Mile End road, E1 4NS London, UK + +{i.maniadismetaxas，g.tzimiropoulos，i.patras}@qmul.ac.uk + +# Abstract + +Clustering has been a major research topic in the field of machine learning, one to which Deep Learning has recently been applied with significant success. However, an aspect of clustering that is not addressed by existing deep clustering methods, is that of efficiently producing multiple, diverse partitionings for a given dataset. This is particularly important, as a diverse set of base clusterings are necessary for consensus clustering, which has been found to produce better and more robust results than relying on a single clustering. To address this gap, we propose DivClust, a diversity controlling loss that can be incorporated into existing deep clustering frameworks to produce multiple clusterings with the desired degree of diversity. We conduct experiments with multiple datasets and deep clustering frameworks and show that: a) our method effectively controls diversity across frameworks and datasets with very small additional computational cost, b) the sets of clusterings learned by DivClust include solutions that significantly outperform single-clustering baselines, and c) using an off-the-shelf consensus clustering algorithm, DivClust produces consensus clustering solutions that consistently outperform single-clustering baselines, effectively improving the performance of the base deep clustering framework. Code is available at https://github.com/ManiadisG/DivClust. + +# 1. Introduction + +The exponentially increasing volume of visual data, along with advances in computing power and the development of powerful Deep Neural Network architectures, have revived the interest in unsupervised learning with visual data. Deep clustering in particular has been an area where significant progress has been made in the recent years. Existing works focus on producing a single clustering, which is evaluated in terms of how well that clustering matches + +the ground truth labels of the dataset in question. However, consensus, or ensemble, clustering remains under-studied in the context of deep clustering, despite the fact that it has been found to consistently improve performance over single clustering outcomes [3, 17, 45, 73]. + +Consensus clustering consists of two stages, specifically generating a set of base clusterings, and then applying a consensus algorithm to aggregate them. Identifying what properties ensembles should have in order to produce better outcomes in each setting has been an open problem [18]. However, research has found that inter-clustering diversity within the ensemble is an important, desirable factor [14,20,24,34,51], along with individual clustering quality, and that diversity should be moderated [15,22,51]. Furthermore, several works suggest that controlling diversity in ensembles is important toward studying its impact and determining its optimal level in each setting [22, 51]. + +The typical way to produce diverse clusterings is to promote diversity by clustering the data multiple times with different initializations/hyperparameters or subsets of the data [3, 17]. This approach, however, does not guarantee or control the degree of diversity, and is computationally costly, particularly in the context of deep clustering, where it would require the training of multiple models. Some methods have been proposed that find diverse clusterings by including diversity-related objectives to the clustering process, but those methods have only been applied to clustering precomputed features and cannot be trivially incorporated into Deep Learning frameworks. Other methods tackle diverse clustering by creating and clustering diverse feature subspaces, including some that apply this approach in the context of deep clustering [48, 61]. Those methods, however, do not control inter-clustering diversity. Rather, they influence it indirectly through the properties of the subspaces they create. Furthermore, typically, existing methods have been focusing on producing orthogonal clusterings or identifying clusterings based on independent attributes of relatively simple visual data (e.g. color/shape). Consequently, they are oriented toward maximizing inter-clustering diversity, which is not appropriate for consensus + +![](images/3854d879e68eaf112ae12cad4955dc4f2262eca9e19bdcfb6434c317436d84e1.jpg) +Figure 1. Overview of DivClust. Assuming clusterings $A$ and $B$ , the proposed diversity loss $L_{div}$ calculates their similarity matrix $S_{AB}$ and restricts the similarity between cluster pairs to be lower than a similarity upper bound $d$ . In the figure, this is represented by the model adjusting the cluster boundaries to produce more diverse clusterings. Best seen in color. + +clustering [15,22,51]. + +To tackle this gap, namely generating multiple clusterings with deep clustering frameworks efficiently and with the desired degree of diversity, we propose DivClust. Our method can be straightforwardly incorporated into existing deep clustering frameworks to learn multiple clusterings whose diversity is explicitly controlled. Specifically, the proposed method uses a single backbone for feature extraction, followed by multiple projection heads, each producing cluster assignments for a corresponding clustering. Given a user defined diversity target, in this work expressed in terms of the average NMI between clusterings, DivClust restricts inter-clustering similarity to be below an appropriate, dynamically estimated threshold. This is achieved with a novel loss component, which estimates inter-clustering similarity based on soft cluster assignments produced by the model, and penalizes values exceeding the threshold. Importantly, DivClust introduces minimal computational cost and requires no hyperparameter tuning with respect to the base deep clustering framework, which makes its use simple and computationally efficient. + +Experiments on four datasets (CIFAR10, CIFAR100, Imagenet-10, Imagenet-Dogs) with three recent deep clustering methods (IIC [37], PICA [32], CC [44]) show that DivClust can effectively control inter-clustering diversity without reducing the quality of the clusterings. Furthermore, we demonstrate that, with the use of an off-the-shelf consensus clustering algorithm, the diverse base clusterings learned by DivClust produce consensus clustering solutions that outperform the base frameworks, effectively improving them with minimal computational cost. Notably, despite the sensitivity of consensus clustering to the properties of the ensemble, our method is robust across various diversity levels, outperforming baselines in most settings, often by large margins. Our work then provides a straightforward way for improving the performance of deep clustering frameworks, as well as a new tool for studying the impact of diversity in deep clustering ensembles [51]. + +In summary, DivClust: a) can be incorporated in ex + +isting deep clustering frameworks in a plug-and-play way with very small computational cost, b) can explicitly and effectively control inter-clustering diversity to satisfy user-defined targets, and c) learns clusterings that can improve the performance of deep clustering frameworks via consensus clustering. + +# 2. Related Works + +# 2.1. Deep Clustering + +The term deep clustering refers to methods that cluster data while learning their features. They are generally divided into two categories, namely those that alternate training between clustering and feature learning and those that train both simultaneously. + +Alternate learning: Methods following this approach generally utilize a two-step training regime repeated in regular intervals (e.g. per-epoch or per-step). First, sample pseudo-labels are produced based on representations extracted by the model (e.g. by feature clustering). Second, those pseudo-labels are utilized to improve the learned representations, typically by training the feature extraction model as a classifier. Those methods include DEC [64], DAC [8], DCCM [63], DDC [7], JULE [66], SCAN [57], ProPos [33] and SPICE [49], as well as DSC-N [36], IDFD [65] and MIX'EM [58], which propose ways to train models whose representations produce better outcomes when clustered. Other works in this area are DeepCluster [5], SeLa [1], PCL [42] and HCSC [21], though their primary focus is on representation learning. + +Simultaneous learning: These methods jointly learn features and cluster assignments. They include ADC [23], IIC [37] and PICA [32], which train clustering models end-to-end with loss functions that enforce desired properties on the clusters assignments, ConCURL [11, 52], which builds on BYOL [19] with a loss maximizing the agreement of clusterings from transformed embeddings, DCCS [71], which leverages an adversarial component in the clustering process, and GatCluster [50], which proposes an attention + +mechanism combined with four self-learning tasks. Finally, methods such as SCL [31], CC [44], GCC [72], TCC [53] and MiCE [56] leverage contrastive learning. + +Although some deep clustering methods [1, 37, 52] use multiple clusterings, most do not explore the prevalence and impact of inter-clustering diversity, and none proposes ways to control it. Our work is, to the best of our knowledge, the first that addresses both issues. + +# 2.2. Diverse Clustering + +The most straightforward way of producing multiple, diverse clusterings is clustering the data multiple times. Typical methods to increase diversity include varying the clustering algorithm or its hyperparameters, using different initializations, and clustering a subset of the samples or features [3]. This approach, however, is a) computationally costly, in that it requires clustering the data multiple times, b) unreliable, as some ways to increase diversity might decrease the quality of clusters (e.g. using a subset of the data), and c) ineffective, as there is no guarantee that the desired degree of diversity will be achieved. + +To tackle this, several methods have been proposed to create multiple, diverse clusterings [25]. We identify two main approaches of promoting inter-clustering diversity: a) explicitly, by optimizing for appropriate objectives, and b) implicitly, by optimizing for decorrelated/orthogonal feature subspaces, which, when clustered, lead to diverse clusterings. Methods in the first category include COALA [2], Meta Clustering [6], Dec-kmeans [35], MNMF [67], MSC [26], ADFT [10] and MultiCC [60]. Subspace clustering methods include MISC [59], ISAAC [69], NR-kmeans [47], RAOSC [70] and ENRC [48]. Distinctly, diverse clustering has also been explored in the context of multi-view data by OSC [9], MVMC [68], DMSMF [46], DMClusts [62], DiMSC [4], and DiVMC [61]. + +To the best of our knowledge, except for DiMVMC and ENRC, none of the existing methods are compatible with Deep Learning, they require a learned feature space on which to be applied, and most have quadratic complexity relative to the number of samples. This restricts their use on real-life high dimensional data, where deep clustering produces better outcomes [56, 57]. Regarding DiMVMC and ENRC, they depend on autoencoder-based architectures and adapting them to more recent deep clustering frameworks, which perform significantly better, is not trivial. More importantly, they utilize subspace clustering, inheriting its limitations regarding controlling diversity. Specifically: a) no method has been proposed to infer how different the subspaces must be in order to lead to a specific degree of interclustering diversity, and b) subspace clustering methods inherit the randomness of the clustering algorithm applied to the subspaces (K-means for DiMVMC and ENRC), which further limits their control over the outcomes. + +# 2.3. Consensus Clustering + +The performance of clustering algorithms varies depending on the data and their properties, the algorithm itself, and its hyperparameters. This makes finding reliable clustering solutions particularly difficult. Consensus, or ensemble, clustering has emerged as a solution to this problem, specifically by combining the results of multiple, different clusterings, rather than relying on a single solution. This has been found to produce better and more robust outcomes than single-clustering approaches [3, 17, 18, 45]. The process of consensus clustering happens in two stages: a) multiple, diverse base clusterings are generated and b) those clusterings are aggregated using a consensus algorithm. + +Generating diverse clusterings: The properties of the set of clusterings used by the consensus algorithm is a key factor for obtaining good performance. Multiple works [24, 40, 51] have found that both the quality of individual base clusterings and their diversity is critical, and that, indeed, clustering ensembles with a moderate degree of diversity lead to better outcomes [15, 20, 22]. Typical methods for ensemble generation include using different clustering algorithms [13], using different initializations of the same clustering algorithm or different hyperparameters (e.g. the number of clusters) [16, 22, 41], clustering with different subsets of the features [54], using random projections to diversify the feature space [14], and clustering with different subsets of the dataset [12, 13]. However, concrete methods for identifying optimal hyperparameters, such as the degree of diversity, the number of clusterings in the ensemble, and the method by which the ensemble is generated, remain elusive. + +Consensus algorithms: Consensus algorithms aim to aggregate multiple, diverse clusterings to produce a single, robust solution. Various approaches to this problem have been proposed, such as using matrix factorization [43], distance minimization between clusterings [75], utilizing multiple views [55], graph learning [28, 73, 74] and matrix coassociation [29, 38]. We note that, while improving consensus algorithms increase the robustness of consensus clustering overall, the stages of ensemble generation and its aggregation with consensus algorithms are largely independent. + +Consensus Clustering & Deep Learning: Despite the established advantages of consensus clustering over single-clustering approaches, consensus clustering has not been explored in the context of deep clustering. A possible reason is the computational cost of generating multiple, diverse base clusterings, which would require training multiple models. The only work that has, to the best of our knowledge, applied consensus clustering in the deep clustering setting is DeepCluE [27]. Notably, however, the base clusterings used by DeepCluE are not all learned by the model. Rather, a single-clustering model is trained, and an ensemble is generated by clustering features from multiple layers of the model with U-SPEC [30]. Our work addresses + +this gap, by proposing a way to train a single deep clustering model to generate multiple clusterings with controlled diversity and with minimal computational overhead. + +# 3. Method + +Overview: Our method consists of two components: a) A novel loss function that can be incorporated in deep clustering frameworks to control inter-clustering diversity by applying a threshold to cluster-wise similarities, and b) a method for dynamically estimating that threshold so that the clusterings learned by the model are sufficiently diverse, according to a user-defined metric. + +More concretely, we assume a deep clustering model that learns $K$ clusterings (typically a backbone encoder followed by $K$ projection heads), a deep clustering framework and its loss function $L_{\text{main}}$ , and a diversity target $D^T$ set by the user, expressed as an upper bound to inter-clustering similarity1 (i.e. the maximum acceptable similarity). In order to control the inter-clustering similarity $D^R$ of the learned clusterings so that $D^T \leq D^R$ , we propose a complementary loss $L_{\text{div}}$ . Specifically, given soft cluster assignments for a pair of clusterings $A, B \in K$ , we define the inter-clustering similarity matrix $S_{AB} \in \mathbb{R}^{C_A \times C_B}$ , where $C_A$ and $C_B$ is the number of clusters in each clustering, and $S_{AB}(i,j) \in [0,1]$ measures the similarity between clusters $i \in C_A$ and $j \in C_B$ . It follows that decreasing the values of $S_{AB}$ reduces the similarity between the clusters of $A$ and $B$ , and therefore increases their diversity. Accordingly, $L_{\text{div}}$ utilizes $S_{AB}$ in order to restrict inter-clustering similarity to be under an upper similarity bound $d$ . The value of $d$ is dynamically adjusted during training, decreasing when $D^R > D^T$ and increasing when $D^R \leq D^T$ , thereby tightening and relaxing the loss function so that, overall and throughout training, inter-clustering similarity $D^R$ remains at or under the desired level $D^T$ . + +Defining the inter-clustering similarity matrix: Our method assumes a standard deep clustering architecture, consisting of an encoder $f$ , followed by $K$ projection heads $h_1, \ldots, h_K$ , each of which produces assignments for a clustering $k$ . Specifically, let $X$ be a set of $N$ unlabeled samples. The encoder maps each sample $x \in X$ to a representation $f(x)$ , and each projection head $h_k$ maps $f(x)$ to $C_k$ clusters, so that $p_k(x) = h_k(f(x)) \in \mathbb{R}^{C_k \times 1}$ represents a probability assignment vector mapping sample $x \in X$ to $C_k$ clusters in clustering $k$ . Without loss of generality, we assume that $C = C_k \forall k \in K$ . Each clustering can then be represented by a cluster assignment matrix $P_k(X) = [p_k(x_1), p_k(x_2), \dots, p_k(x_N)] \in \mathbb{R}^{C \times N}$ . The column $p_k(n)$ , that is the probability assignment vector for the + +$n$ -th sample, encodes the degrees to which sample $x_{n}$ is assigned to different clusters. The row vector $q_{k}(i)\in \mathbb{R}^{N}$ shows which samples are softly assigned to cluster $i\in C$ . We refer to $q_{k}(i)$ as the cluster membership vector. + +To quantify the similarity between clusterings $A$ and $B$ we define the inter-clustering similarity matrix $S_{AB} \in \mathbb{R}^{C \times C}$ . We define each element $S_{AB}(i,j)$ as the cosine similarity between the cluster membership vector $q_{A}(i)$ of cluster $i \in A$ and the cluster membership vector $q_{B}(j)$ of cluster $j \in B$ : + +$$ +S _ {A B} (i, j) = \frac {q _ {A} (i) \cdot q _ {B} (j)}{\left| \left| q _ {A} (i) \right| \right| _ {2} \left| \left| q _ {B} (j) \right| \right| _ {2}} \tag {1} +$$ + +This measure expresses the degree to which samples in the dataset are assigned similarly to clusters $i$ and $j$ . Specifically, $S_{AB}(i,j) = 0$ if $q_A(i) \perp q_B(j)$ and $S_{AB}(i,j) = 1$ if $q_A(i) = q_B(j)$ . It is, therefore, a differentiable measure of the similarity of clusters $i$ and $j$ . + +Defining the loss function: Based on the inter-clustering similarity matrix $S_{AB}$ , we define DivClust's loss to softly enforce that a clustering $A$ does not have an aggregate cluster similarity with a clustering $B$ greater than a similarity upper bound $d$ . The aggregate similarity $S_{AB}^{aggr}$ is defined as the average similarity of clustering $A$ 's clusters with their most similar cluster of clustering $B$ (Eq. (2)). Using this metric, we propose $L_{div}$ (Eq. (3)), a loss that regulates diversity between clusterings $A$ and $B$ by forcing that $S_{AB}^{aggr} < d$ , for $d \in [0,1]$ . It is clear from Eq. (3) that $S_{AB}^{aggr} < d \Rightarrow L_{div}(A,B) = 0$ , in which case the diversity requirement is satisfied and the loss has no impact. Conversely, $S_{AB}^{aggr} \geq d \Rightarrow L_{div}(A,B) > 0$ , in which case the loss requires that inter-clustering similarity decreases. + +$$ +S _ {A B} ^ {a q g r} = \frac {1}{C} \sum_ {i = 1} ^ {C} \max _ {j} \left(S _ {A B} (i, j)\right) \tag {2} +$$ + +$$ +L _ {d i v} (A, B) = \left[ S _ {A B} ^ {a g g r} - d \right] _ {+} \tag {3} +$$ + +Having defined the diversity loss $L_{div}$ between two clusterings, we extend it to multiple clusterings $K$ and combine it with the base deep clustering framework's objective. For a clustering $k \in K$ , we denote with $L_{main}(k)$ the loss of the base deep clustering framework for that clustering, and with $L_{div}(k, k')$ the diversity controlling loss between clusterings $k$ and $k'$ . We present the joint loss $L_{joint}(k)$ for each clustering $k$ in Eq. (4), where $L_{main}(k)$ depends on cluster assignment matrix $P_k$ , while $L_{div}(k, k')$ depends on $P_k$ and $P_{k'}$ . Accordingly, the model's training loss $L_{total}$ seen in Eq. (5), is the average of $L_{joint}$ over all clusterings. + +$$ +L _ {\text {j o i n t}} (k) = L _ {\text {m a i n}} (k) + \frac {1}{K - 1} \sum_ {k ^ {\prime} = 1, k ^ {\prime} \neq k} ^ {K} L _ {\text {d i v}} \left(k, k ^ {\prime}\right) \tag {4} +$$ + +![](images/fb1bf011e4bf13ee2aecb61723189e753b0db2299b4a94bc4c8b383850601c9a.jpg) +(a) Cluster assignments $P_A$ for clustering A + +![](images/6a89254c2b2683cca9e8ccdc2cec4d6e6f1cc58cb664cc6d453f485d2989447c.jpg) +Figure 2. Examples of synthetic cluster assignments $P_A$ , $P_B$ and similarity matrix $S_{AB}$ . Note that clusters $i \in A$ and $j \in B$ are softly assigned the same samples. Correspondingly, their similarity score $S_{AB}(i,j)$ is high (highlighted with red in Fig. 2c). Best seen in color. + +![](images/9592883f221f5b157afa885a3f275a26ad33452a5e8ef36c7418bdb435d892ca.jpg) +(b) Cluster assignments $P_B$ for clustering B +(c) Similarity matrix $S_{AB}$ + +$$ +L _ {t o t a l} = \frac {1}{K} \sum_ {k = 1} ^ {K} L _ {\text {j o i n t}} (k) \tag {5} +$$ + +The loss $L_{total}$ is therefore a combination of the base deep clustering framework's loss $L_{main}$ for each clustering $k \in K$ and the loss $L_{div}$ , which is used to control interclustering diversity. The proposed loss formulation is applicable to any deep clustering framework that produces cluster assignments through the model (as opposed to frameworks using offline methods such as MIX'EM [58]), which covers the majority of deep clustering frameworks outlined in Sec. 2. + +Dynamic upper bound $d$ : The proposed loss $L_{div}$ controls inter-clustering diversity by restricting the values of $S_{AB}$ according to the similarity upper bound $d$ . However, the values of $S_{AB}$ are calculated based on the cosine similarity of soft cluster assignments. This means that pairs of cluster assignment vectors $i$ , $j$ will have different similarity values $S_{AB}(i,j)$ depending on their sharpness, even if they point to the same cluster in terms of their corresponding hard assignment. It follows that $S_{AB}$ and, accordingly, the impact of $d$ , are dependent on the confidence of cluster assignments and vary throughout training and between experiments (as factors like the number of clusters and model capacity influence the confidence of cluster assignments). Therefore, $d$ is an ambiguous and unintuitive metric for users to define diversity targets with. + +To tackle this issue and to provide a reliable and intuitive method for defining diversity objectives, we propose dynamically determining the value of the threshold $d$ during training. Concretely, let $D$ be an inter-clustering similarity metric chosen by the user. In this work, we use avg. Normalized Mutual Information (NMI), a well established metric for estimating inter-clustering similarity. + +$$ +D = \frac {1}{(K - 1) (K / 2)} \sum_ {k = 1} ^ {K - 1} \sum_ {k ^ {\prime} = k + 1} ^ {K} N M I \left(P _ {k} ^ {h}, P _ {k ^ {\prime}} ^ {h}\right) \tag {6} +$$ + +where $P_{k}^{h} \in \mathbb{Z}^{N}$ is the hard cluster assignment vector for $N$ samples in clustering $k \in K$ and $NMI(P_{k}^{h}, P_{k^{\prime}}^{h})$ represents the NMI between $k$ and $k^{\prime}$ . $D \in [0,1]$ , with higher values indicating more similar clusterings. + +Assuming a user-defined similarity target $D^T$ , expressed as a value of metric $D$ , we denote with $D^R$ the measured inter-clustering similarity of the clusterings learned by the model, expressed in the same metric. DivClust's objective is to control inter-clustering diversity, which translates to learning clusterings such that $D^R \leq D^T$ . Accordingly, appropriate thresholds $d$ must be used during training. Under the assumption that $D^R$ decreases monotonically w.r.t. $d$ , we propose the following update rule for $d$ : + +$$ +d _ {s + 1} = \left\{ \begin{array}{l l} \max \left(d _ {s} (1 - m), 0\right), & \text {i f} D ^ {R} > D ^ {T} \\ \min \left(d _ {s} (1 + m), 1\right), & \text {i f} D ^ {R} \leq D ^ {T} \end{array} , \right. \tag {7} +$$ + +where $d_{s}$ and $d_{s+1}$ are the values of the threshold $d$ for the current and the next steps, and $m \in (0,1)$ regulates the magnitude of the update steps. Following this update rule, we decrease $d$ when the measured inter-clustering similarity $D^{R}$ needs to decrease, and increase it otherwise. For computational efficiency, instead of calculating $D^{R}$ over the entire dataset in every training step, we do so every 20 iterations on a memory bank of $M = 10,000$ cluster assignments – the latter is updated at every step in a FIFO manner. We set the hyperparameter $m$ to $m = 0.01$ in all experiments. + +# 4. Experiments + +We conduct several experiments to evaluate DivClust's adaptability, its effectiveness in controlling diversity, and the quality of the resulting clusterings. First, to show that DivClust effectively controls inter-clustering diversity and produces high quality clusterings with various frameworks, we combine it with IIC [37], PICA [32] and CC [44], and apply it to CIFAR10 with various diversity targets $D^{T}$ . Subsequently, we focus on the best framework of the + +
FrameworkClusteringsDTDRCNFMean Acc.Max. Acc.DivClust Acc.
IIC1--0.9970.4420.4420.442
201.0.9830.9960.5260.5260.526
200.950.9390.9980.5310.5370.533
200.90.8880.9970.5680.590.578
200.80.80.9970.6110.6780.653
200.70.6940.9960.5660.6370.685
PICA1--0.9060.5330.5330.533
201.0.9910.8140.5970.5970.596
200.950.9310.8260.6240.6310.625
200.90.8910.8410.6480.6650.652
200.80.8170.8280.5980.6350.595
200.70.7030.8240.6250.6910.671
CC1--0.9360.7640.7640.764
201.0.9760.9340.7630.7630.763
200.950.9460.9340.7620.7730.76
200.90.90.9310.7940.8180.789
200.80.8140.930.7620.8470.819
200.70.6990.9270.7030.8180.815
+ +Table 1. Results for IIC, PICA and CC applied on CIFAR10 with DivClust. CNF and Mean Acc. are calculated by averaging the corresponding metrics over all clusterings, while Max Acc. refers to the best performing base clustering. The DivClust Acc. metric measures the accuracy of a consensus clustering produced with the DivClust C method. + +
DTDR
CIFAR10CIFAR100ImageNet-10ImageNet-Dogs
1.0.9760.9390.9870.941
0.950.9460.9260.9480.945
0.90.90.8480.8970.87
0.80.8140.8060.8070.795
0.70.6990.7050.6960.702
+ +Table 2. Avg. inter-clustering similarity scores $D^{R}$ for clustering sets produced by DivClust combined with CC for various diversity targets $D^{T}$ . The objective of DivClust is that $D^{R} \leq D^{T}$ . + +three, namely CC, and conduct experiments on 4 datasets (CIFAR10, CIFAR100,Imagenet-10 andImagenet-Dogs). Our findings demonstrate that, across frameworks and datasets, DivClust can: a) effectively control diversity and b) improve clustering outcomes over the base frameworks and alternative ensembling methods. + +# 4.1. Experiments setup + +Datasets: We conduct experiments with 4 standard datasets in deep clustering: CIFAR10, CIFAR100 [39] (evaluating on the 20 superclasses), ImageNet-10 and ImageNet-Dogs [8]. + +Metrics: Inter-clustering similarity is measured by averaging the NMI between clusterings to calculate the interclustering NMI metric $D$ (Eq. (6)), with higher values indicating more similar clusterings. We denote with $D^T$ the + +diversity target set by the user and with $D^{R}$ the measured inter-clustering similarity after training. When DivClust is applied we want that $D^{R} \leq D^{T}$ . Clustering quality is evaluated based on overlap of the clusterings with the dataset's ground truth labels, using the Accuracy (ACC), Normalized Mutual Information (NMI) and Adjusted Rand Index (ARI) metrics. We also report the avg. cluster assignment confidence (CNF), which measures cluster separability. For all four metrics greater values are better, 1 being optimal. + +Implementation & Training: DivClust is incorporated into the base frameworks as described in Sec. 3, by adding DivClust's loss to their objective and duplicating projection heads $h$ to produce multiple clusterings. The models were trained following the configurations (model architecture, training duration, hyperparameters etc.) suggested in their respective papers [32, 37, 44], unless stated otherwise. PICA and IIC were trained without overclustering. We set the number of clusterings to $K = 20$ , following convention in consensus clustering [73], and the number of clusters $C$ to the number of classes for each dataset, following convention for deep clustering evaluation [32, 37, 44]. + +Consensus Clustering: To extract single clustering solutions we examine three methods: a) selecting the clustering $k$ with the lowest corresponding loss $L_{\text{main}}(k)$ (DivClust A), b) using the consensus clustering algorithm SCCBG [73] to aggregate clusterings (DivClust B), and c) a combination of the two, where we select the 10 best clusterings with regard to their loss and then apply SCCBG (DivClust C). For clarity and space, we present in the paper + +
DatasetDTCIFAR10CIFAR100ImageNet-10ImageNet-Dogs
MetricNMINMIACCARINMIACCARINMIACCARINMIACCARI
K-means-0.0870.2290.0490.0840.1300.0280.1190.2410.0570.550.1050.020
AC-0.1050.2280.0650.0980.1380.0340.1380.2420.0670.0370.1390.021
NMF-0.0810.1900.0340.0790.1180.0260.1320.2300.0650.0440.1180.016
AE-0.2370.3140.1690.1000.1650.0480.2100.3170.1520.1040.1850.073
DAE-0.2510.2970.1630.1110.1510.0460.2060.3040.1380.1040.1900.078
DCGAN-0.2650.3150.1760.1200.1510.0450.2250.3460.1570.1210.1740.078
DeCNN-0.2400.2820.1740.0920.1330.0380.1860.3130.1420.0980.1750.073
VAE-0.2450.2910.1670.1080.1520.0400.1930.3340.1680.1070.1790.079
JULE-0.1920.2720.1380.1030.1370.0330.1750.3000.1380.0540.1380.028
DEC-0.2570.3010.1610.1360.1850.0500.2820.3810.2030.1220.1950.079
DAC-0.3960.5220.3060.1850.2380.0880.3940.5270.3020.2190.2750.111
ADC--0.325--0.160--0.530----
DDC-0.4240.5240.329---0.4330.5770.345---
DCCM-0.4960.6230.4080.2850.3270.1730.6080.7100.5550.3210.3830.182
IIC--0.617--0.257-------
PICA-0.5910.6960.5120.3100.3370.1710.8020.8700.7610.3520.3520.201
CC-0.7050.7900.6370.4310.4290.2660.8590.8930.8220.4450.4290.274
CC-Kmeans-0.6540.6980.5230.4290.4050.2350.7920.8410.6690.4570.4440.284
CC-Kmeans/S-0.6740.690.5540.4280.4020.2280.7920.8420.6730.4560.4440.283
CC-Kmeans/F-0.6840.7620.5990.4380.4090.2100.7970.8470.6850.4580.4440.285
DeepCluE-0.7270.7640.6460.4720.4570.2880.8820.9240.8560.4480.4160.273
DivClust C1.0.6780.7630.6040.4180.4240.2570.860.8950.8250.4590.4510.298
0.950.6770.760.6020.4310.4340.2760.8910.9360.8780.4610.4510.297
0.90.6780.7890.6410.4220.4260.2580.8790.920.8590.480.4870.332
0.80.7240.8190.6810.4220.4140.260.8790.9180.8510.4580.4480.296
0.70.710.8150.6750.440.4370.2830.850.900.8190.5160.5290.376
+ +Table 3. Results combining DivClust with CC for various diversity targets $D^T$ . We underline DivClust results that outperform the single-clustering baseline CC, and note with bold the best results for each metric across all methods and diversity levels. We emphasize that the NMI in this table measures the similarity between the single clustering produced by each method and the ground truth classes. The NMI values representing inter-clustering similarity $D^R$ in ensembles produced by DivClust for the same experiments are presented in Tab. 2. + +results only for the hybrid aggregation method DivClust C, which we found to be the most robust. Detailed results for all three approaches are provided in supplementary Tab. 5. + +# 4.2. Results + +Initially, we apply IIC, PICA and CC on CIFAR10, and present the outcomes in Tab. 1. We find that, for all three frameworks, DivClust effectively controls diversity, as $D^{R}$ is consistently close to or lower than $D^{T}$ . Furthermore, results indicate that DivClust is necessary to produce diverse clusterings in deep clustering frameworks, as, without it, they tend to converge to near identical solutions (when $D^{T} = 1$ , $D^{R} \rightarrow 1$ ). Regarding cluster separability, assignment confidence $CNF$ remains high for various diversity targets $D^{T}$ , despite the increased complexity of optimizing both the main deep clustering loss and DivClust's objective. Finally, we observe that, for most diversity targets $D^{T}$ , the mean and max. accuracy, as well as the consensus clustering accuracy produced by the aggregation method DivClust + +C, increase relative to the single clustering model. Notably, consensus clustering accuracy is higher than the mean clustering accuracy for most cases, which highlights the effectiveness of our approach. We stress that identifying clusterings in the ensemble whose performance matches the mean or max. accuracy is not trivial, which is why consensus clustering is necessary to reach a single clustering solution. + +Having established that DivClust is effective across frameworks, we focus on CC and apply it on CIFAR10, CIFAR100, ImageNet-Dogs and Imagenet-10. We compare DivClust with the standard implementation of CC, which is trained to learn a single clustering (CC), as well as with alternative methods of ensemble clustering. Specifically, we apply the typical methods of ensemble generation by extracting the features learned by the single-clustering CC model and running K-means 20 times on the entire dataset (CC-Kmeans), on random subsets of the dataset (CC-Kmeans/S) and on random subsets of the feature space (CC-Kmeans/F), following [3]. In all three cases, SCCBG + +is used to aggregate the resulting clusterings. Furthermore, we compare with DeepCluE [27], to the best of our knowledge the only other work that examines consensus clustering in the context of deep clustering, and which is also built on top of CC, allowing for a fair comparison. We note that DeepCluE is not mutually exclusive with DivClust, and could be used jointly with it. + +Inter-clustering similarity scores $D^{R}$ for this set of experiments are presented in Tab. 2, where it is seen that DivClust successfully controls diversity. Results for consensus clustering, the main task for which DivClust is intended, are presented in Tab. 3 for CC across 4 datasets, where we also include results from other deep clustering frameworks for reference. Detailed results, including aggregation methods DivClust A and DivClust B, as well as mean/max scores for DivClust's clustering ensembles, are provided in supplementary Tab. 5. Results in Tab. 3 demonstrate that, for most diversity targets $D^{T}$ , DivClust outperforms the single-clustering baseline CC and typical ensemble generation methods, and is competitive with the alternative consensus clustering method DeepCluE. Notably, DivClust is competitive with the baseline across diversity levels. This robustness is very significant, given that identifying what properties (including diversity) lead to optimal outcomes in clustering ensembles is an open problem [15, 22]. + +To summarize, the results of Tabs. 1 to 3 demonstrate that DivClust: a) effectively controls inter-clustering diversity in deep clustering frameworks in accordance with user-defined objectives, b) does not degrade the quality of the clusterings and in fact produces better solutions than single-clustering models, and c), it can be used with consensus clustering to identify single-clustering solutions superior to those of the corresponding single-clustering frameworks. + +# 5. Discussion + +# 5.1. Diversity Control & Consensus Clustering Performance + +Results presented in Sec. 4 demonstrate the effectiveness of DivClust both in controlling inter-clustering diversity and in producing clustering ensembles that lead to consensus clustering outcomes superior to single clustering baselines. + +Specifically, Tabs. 1 and 2 show that the inter-clustering similarity $D^{R}$ of ensembles produced by DivClust is consistently lower than the targets $D^{T}$ . In the few cases where $D^{R} \geq D^{T}$ , it is by very small margins (the greatest deviation was +0.017), which may be attributed to our use of a memory bank to estimate $D^{R}$ for the update rule of the threshold $d$ . Regarding consensus clustering accuracy, despite the sensitivity of consensus clustering to the properties of the ensembles and, specifically, to different inter-clustering diversity levels, our method proves particularly robust to varying the diversity targets $D^{T}$ , outperforming + +bases for most settings. This indicates that DivClust learns clusterings with a good quality-diversity trade-off and can be reliably used for consensus clustering. + +Finally, we note that DivClust's ability to explicitly control inter-clustering diversity can facilitate future research on the impact of diversity in clustering ensembles and toward methodologies that determine desirable diversity levels for specific settings [51]. + +# 5.2. Complexity & Computational Cost + +The complexity of DivClust's objective is $O(nK^2 C^2)$ , where $n$ is the batch size, $K$ is the number of clusterings, and $C$ is the number of clusters in each clustering. Importantly, the cost of DivClust relates only to the computation of the loss and the additional projection heads, and is therefore fixed for fixed $n$ , $K$ , $C$ values, regardless of model size and data dimensionality, which are generally the computational bottleneck in Deep Learning applications. Therefore, DivClust is scalable to large datasets. Finally, we note that, in practice, the computational overhead introduced by DivClust is minimal. Specifically, for experiments in this work, DivClust learned ensembles with $K = 20$ clusterings, with training time increasing between $10\% - 50\%$ relative to the time it took to train the baseline single-clustering models. Contrasted with the alternative of training a single-clustering model 20 times (which would not allow for controlling diversity), DivClust provides an efficient approach for applying consensus clustering with deep clustering frameworks. A detailed analysis on complexity and runtimes is provided in supplementary Sec. 3. + +# 6. Conclusion + +We introduce DivClust, a method that can be incorporated into existing deep clustering frameworks to learn multiple clusterings while controlling inter-clustering diversity. To the best of our knowledge, this is the first method that can explicitly control inter-clustering diversity based on user-defined targets, and that is compatible with deep clustering frameworks that learn features and clusters end-to-end. Our experiments, conducted with multiple datasets and deep clustering frameworks, confirm the effectiveness of DivClust in controlling inter-clustering diversity and its adaptability, in terms of it being compatible with various frameworks without requiring modifications and/or hyperparameter tuning. 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In Twenty-Fourth International Joint Conference on Artificial Intelligence, 2015. 3 \ No newline at end of file diff --git a/2023/DivClust_ Controlling Diversity in Deep Clustering/images.zip b/2023/DivClust_ Controlling Diversity in Deep Clustering/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..d8e945bfc6434515bbaa950e1fb1b88174dfeb5b --- /dev/null +++ b/2023/DivClust_ Controlling Diversity in Deep Clustering/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:45bd3f443fdf16040f394bdf4a5813a9a5e3ff85c393dd5a8132c90330a82e97 +size 435637 diff --git a/2023/DivClust_ Controlling Diversity in Deep Clustering/layout.json b/2023/DivClust_ Controlling Diversity in Deep Clustering/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..fff4f1dec86e4991e16b93605629a7ab5da54d89 --- /dev/null +++ b/2023/DivClust_ Controlling Diversity in Deep Clustering/layout.json @@ -0,0 +1,10302 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 140, + 103, + 455, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 140, + 103, + 455, + 121 + ], + "spans": [ + { + "bbox": [ + 140, + 103, + 455, + 121 + ], + "type": "text", + "content": "DivClust: Controlling Diversity in Deep Clustering" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 134, + 143, + 459, + 184 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 134, + 143, + 459, + 184 + ], + "spans": [ + { + "bbox": [ + 134, + 143, + 459, + 184 + ], + "type": "text", + "content": "Ioannis Maniadis Metaxas,\\* Georgios Tzimiropoulos, Ioannis Patras Queen Mary University of London Mile End road, E1 4NS London, UK" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 140, + 187, + 449, + 200 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 140, + 187, + 449, + 200 + ], + "spans": [ + { + "bbox": [ + 140, + 187, + 449, + 200 + ], + "type": "text", + "content": "{i.maniadismetaxas，g.tzimiropoulos，i.patras}@qmul.ac.uk" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 227, + 192, + 239 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 227, + 192, + 239 + ], + "spans": [ + { + "bbox": [ + 143, + 227, + 192, + 239 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 252, + 289, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 252, + 289, + 552 + ], + "spans": [ + { + "bbox": [ + 47, + 252, + 289, + 552 + ], + "type": "text", + "content": "Clustering has been a major research topic in the field of machine learning, one to which Deep Learning has recently been applied with significant success. However, an aspect of clustering that is not addressed by existing deep clustering methods, is that of efficiently producing multiple, diverse partitionings for a given dataset. This is particularly important, as a diverse set of base clusterings are necessary for consensus clustering, which has been found to produce better and more robust results than relying on a single clustering. To address this gap, we propose DivClust, a diversity controlling loss that can be incorporated into existing deep clustering frameworks to produce multiple clusterings with the desired degree of diversity. We conduct experiments with multiple datasets and deep clustering frameworks and show that: a) our method effectively controls diversity across frameworks and datasets with very small additional computational cost, b) the sets of clusterings learned by DivClust include solutions that significantly outperform single-clustering baselines, and c) using an off-the-shelf consensus clustering algorithm, DivClust produces consensus clustering solutions that consistently outperform single-clustering baselines, effectively improving the performance of the base deep clustering framework. Code is available at https://github.com/ManiadisG/DivClust." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 576, + 128, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 576, + 128, + 588 + ], + "spans": [ + { + "bbox": [ + 47, + 576, + 128, + 588 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 597, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 597, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 597, + 287, + 693 + ], + "type": "text", + "content": "The exponentially increasing volume of visual data, along with advances in computing power and the development of powerful Deep Neural Network architectures, have revived the interest in unsupervised learning with visual data. Deep clustering in particular has been an area where significant progress has been made in the recent years. Existing works focus on producing a single clustering, which is evaluated in terms of how well that clustering matches" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 228, + 547, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 228, + 547, + 288 + ], + "spans": [ + { + "bbox": [ + 304, + 228, + 547, + 288 + ], + "type": "text", + "content": "the ground truth labels of the dataset in question. However, consensus, or ensemble, clustering remains under-studied in the context of deep clustering, despite the fact that it has been found to consistently improve performance over single clustering outcomes [3, 17, 45, 73]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 291, + 547, + 435 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 291, + 547, + 435 + ], + "spans": [ + { + "bbox": [ + 304, + 291, + 547, + 435 + ], + "type": "text", + "content": "Consensus clustering consists of two stages, specifically generating a set of base clusterings, and then applying a consensus algorithm to aggregate them. Identifying what properties ensembles should have in order to produce better outcomes in each setting has been an open problem [18]. However, research has found that inter-clustering diversity within the ensemble is an important, desirable factor [14,20,24,34,51], along with individual clustering quality, and that diversity should be moderated [15,22,51]. Furthermore, several works suggest that controlling diversity in ensembles is important toward studying its impact and determining its optimal level in each setting [22, 51]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 438, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 438, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 438, + 547, + 715 + ], + "type": "text", + "content": "The typical way to produce diverse clusterings is to promote diversity by clustering the data multiple times with different initializations/hyperparameters or subsets of the data [3, 17]. This approach, however, does not guarantee or control the degree of diversity, and is computationally costly, particularly in the context of deep clustering, where it would require the training of multiple models. Some methods have been proposed that find diverse clusterings by including diversity-related objectives to the clustering process, but those methods have only been applied to clustering precomputed features and cannot be trivially incorporated into Deep Learning frameworks. Other methods tackle diverse clustering by creating and clustering diverse feature subspaces, including some that apply this approach in the context of deep clustering [48, 61]. Those methods, however, do not control inter-clustering diversity. Rather, they influence it indirectly through the properties of the subspaces they create. Furthermore, typically, existing methods have been focusing on producing orthogonal clusterings or identifying clusterings based on independent attributes of relatively simple visual data (e.g. color/shape). Consequently, they are oriented toward maximizing inter-clustering diversity, which is not appropriate for consensus" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "type": "text", + "content": "*Corresponding author" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "text", + "content": "3418" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 72, + 547, + 163 + ], + "blocks": [ + { + "bbox": [ + 50, + 72, + 547, + 163 + ], + "lines": [ + { + "bbox": [ + 50, + 72, + 547, + 163 + ], + "spans": [ + { + "bbox": [ + 50, + 72, + 547, + 163 + ], + "type": "image", + "image_path": "3854d879e68eaf112ae12cad4955dc4f2262eca9e19bdcfb6434c317436d84e1.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 186, + 547, + 220 + ], + "lines": [ + { + "bbox": [ + 46, + 186, + 547, + 220 + ], + "spans": [ + { + "bbox": [ + 46, + 186, + 547, + 220 + ], + "type": "text", + "content": "Figure 1. Overview of DivClust. Assuming clusterings " + }, + { + "bbox": [ + 46, + 186, + 547, + 220 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 186, + 547, + 220 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 186, + 547, + 220 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 46, + 186, + 547, + 220 + ], + "type": "text", + "content": ", the proposed diversity loss " + }, + { + "bbox": [ + 46, + 186, + 547, + 220 + ], + "type": "inline_equation", + "content": "L_{div}" + }, + { + "bbox": [ + 46, + 186, + 547, + 220 + ], + "type": "text", + "content": " calculates their similarity matrix " + }, + { + "bbox": [ + 46, + 186, + 547, + 220 + ], + "type": "inline_equation", + "content": "S_{AB}" + }, + { + "bbox": [ + 46, + 186, + 547, + 220 + ], + "type": "text", + "content": " and restricts the similarity between cluster pairs to be lower than a similarity upper bound " + }, + { + "bbox": [ + 46, + 186, + 547, + 220 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 186, + 547, + 220 + ], + "type": "text", + "content": ". In the figure, this is represented by the model adjusting the cluster boundaries to produce more diverse clusterings. Best seen in color." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 240, + 138, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 240, + 138, + 252 + ], + "spans": [ + { + "bbox": [ + 47, + 240, + 138, + 252 + ], + "type": "text", + "content": "clustering [15,22,51]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 254, + 289, + 493 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 254, + 289, + 493 + ], + "spans": [ + { + "bbox": [ + 46, + 254, + 289, + 493 + ], + "type": "text", + "content": "To tackle this gap, namely generating multiple clusterings with deep clustering frameworks efficiently and with the desired degree of diversity, we propose DivClust. Our method can be straightforwardly incorporated into existing deep clustering frameworks to learn multiple clusterings whose diversity is explicitly controlled. Specifically, the proposed method uses a single backbone for feature extraction, followed by multiple projection heads, each producing cluster assignments for a corresponding clustering. Given a user defined diversity target, in this work expressed in terms of the average NMI between clusterings, DivClust restricts inter-clustering similarity to be below an appropriate, dynamically estimated threshold. This is achieved with a novel loss component, which estimates inter-clustering similarity based on soft cluster assignments produced by the model, and penalizes values exceeding the threshold. Importantly, DivClust introduces minimal computational cost and requires no hyperparameter tuning with respect to the base deep clustering framework, which makes its use simple and computationally efficient." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 496, + 287, + 699 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 496, + 287, + 699 + ], + "spans": [ + { + "bbox": [ + 46, + 496, + 287, + 699 + ], + "type": "text", + "content": "Experiments on four datasets (CIFAR10, CIFAR100, Imagenet-10, Imagenet-Dogs) with three recent deep clustering methods (IIC [37], PICA [32], CC [44]) show that DivClust can effectively control inter-clustering diversity without reducing the quality of the clusterings. Furthermore, we demonstrate that, with the use of an off-the-shelf consensus clustering algorithm, the diverse base clusterings learned by DivClust produce consensus clustering solutions that outperform the base frameworks, effectively improving them with minimal computational cost. Notably, despite the sensitivity of consensus clustering to the properties of the ensemble, our method is robust across various diversity levels, outperforming baselines in most settings, often by large margins. Our work then provides a straightforward way for improving the performance of deep clustering frameworks, as well as a new tool for studying the impact of diversity in deep clustering ensembles [51]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 59, + 701, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 286, + 713 + ], + "type": "text", + "content": "In summary, DivClust: a) can be incorporated in ex" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 240, + 547, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 240, + 547, + 312 + ], + "spans": [ + { + "bbox": [ + 304, + 240, + 547, + 312 + ], + "type": "text", + "content": "isting deep clustering frameworks in a plug-and-play way with very small computational cost, b) can explicitly and effectively control inter-clustering diversity to satisfy user-defined targets, and c) learns clusterings that can improve the performance of deep clustering frameworks via consensus clustering." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 325, + 397, + 338 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 325, + 397, + 338 + ], + "spans": [ + { + "bbox": [ + 306, + 325, + 397, + 338 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 346, + 405, + 358 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 346, + 405, + 358 + ], + "spans": [ + { + "bbox": [ + 306, + 346, + 405, + 358 + ], + "type": "text", + "content": "2.1. Deep Clustering" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 365, + 547, + 424 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 365, + 547, + 424 + ], + "spans": [ + { + "bbox": [ + 304, + 365, + 547, + 424 + ], + "type": "text", + "content": "The term deep clustering refers to methods that cluster data while learning their features. They are generally divided into two categories, namely those that alternate training between clustering and feature learning and those that train both simultaneously." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 426, + 547, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 547, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 547, + 605 + ], + "type": "text", + "content": "Alternate learning: Methods following this approach generally utilize a two-step training regime repeated in regular intervals (e.g. per-epoch or per-step). First, sample pseudo-labels are produced based on representations extracted by the model (e.g. by feature clustering). Second, those pseudo-labels are utilized to improve the learned representations, typically by training the feature extraction model as a classifier. Those methods include DEC [64], DAC [8], DCCM [63], DDC [7], JULE [66], SCAN [57], ProPos [33] and SPICE [49], as well as DSC-N [36], IDFD [65] and MIX'EM [58], which propose ways to train models whose representations produce better outcomes when clustered. Other works in this area are DeepCluster [5], SeLa [1], PCL [42] and HCSC [21], though their primary focus is on representation learning." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 606, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 606, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 606, + 547, + 715 + ], + "type": "text", + "content": "Simultaneous learning: These methods jointly learn features and cluster assignments. They include ADC [23], IIC [37] and PICA [32], which train clustering models end-to-end with loss functions that enforce desired properties on the clusters assignments, ConCURL [11, 52], which builds on BYOL [19] with a loss maximizing the agreement of clusterings from transformed embeddings, DCCS [71], which leverages an adversarial component in the clustering process, and GatCluster [50], which proposes an attention" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3419" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 286, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 286, + 108 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 286, + 108 + ], + "type": "text", + "content": "mechanism combined with four self-learning tasks. Finally, methods such as SCL [31], CC [44], GCC [72], TCC [53] and MiCE [56] leverage contrastive learning." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 109, + 286, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 109, + 286, + 168 + ], + "spans": [ + { + "bbox": [ + 47, + 109, + 286, + 168 + ], + "type": "text", + "content": "Although some deep clustering methods [1, 37, 52] use multiple clusterings, most do not explore the prevalence and impact of inter-clustering diversity, and none proposes ways to control it. Our work is, to the best of our knowledge, the first that addresses both issues." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 178, + 157, + 192 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 178, + 157, + 192 + ], + "spans": [ + { + "bbox": [ + 47, + 178, + 157, + 192 + ], + "type": "text", + "content": "2.2. Diverse Clustering" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 198, + 286, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 198, + 286, + 327 + ], + "spans": [ + { + "bbox": [ + 46, + 198, + 286, + 327 + ], + "type": "text", + "content": "The most straightforward way of producing multiple, diverse clusterings is clustering the data multiple times. Typical methods to increase diversity include varying the clustering algorithm or its hyperparameters, using different initializations, and clustering a subset of the samples or features [3]. This approach, however, is a) computationally costly, in that it requires clustering the data multiple times, b) unreliable, as some ways to increase diversity might decrease the quality of clusters (e.g. using a subset of the data), and c) ineffective, as there is no guarantee that the desired degree of diversity will be achieved." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 330, + 286, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 330, + 286, + 496 + ], + "spans": [ + { + "bbox": [ + 46, + 330, + 286, + 496 + ], + "type": "text", + "content": "To tackle this, several methods have been proposed to create multiple, diverse clusterings [25]. We identify two main approaches of promoting inter-clustering diversity: a) explicitly, by optimizing for appropriate objectives, and b) implicitly, by optimizing for decorrelated/orthogonal feature subspaces, which, when clustered, lead to diverse clusterings. Methods in the first category include COALA [2], Meta Clustering [6], Dec-kmeans [35], MNMF [67], MSC [26], ADFT [10] and MultiCC [60]. Subspace clustering methods include MISC [59], ISAAC [69], NR-kmeans [47], RAOSC [70] and ENRC [48]. Distinctly, diverse clustering has also been explored in the context of multi-view data by OSC [9], MVMC [68], DMSMF [46], DMClusts [62], DiMSC [4], and DiVMC [61]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 498, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 286, + 712 + ], + "type": "text", + "content": "To the best of our knowledge, except for DiMVMC and ENRC, none of the existing methods are compatible with Deep Learning, they require a learned feature space on which to be applied, and most have quadratic complexity relative to the number of samples. This restricts their use on real-life high dimensional data, where deep clustering produces better outcomes [56, 57]. Regarding DiMVMC and ENRC, they depend on autoencoder-based architectures and adapting them to more recent deep clustering frameworks, which perform significantly better, is not trivial. More importantly, they utilize subspace clustering, inheriting its limitations regarding controlling diversity. Specifically: a) no method has been proposed to infer how different the subspaces must be in order to lead to a specific degree of interclustering diversity, and b) subspace clustering methods inherit the randomness of the clustering algorithm applied to the subspaces (K-means for DiMVMC and ENRC), which further limits their control over the outcomes." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 72, + 430, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 430, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 430, + 85 + ], + "type": "text", + "content": "2.3. Consensus Clustering" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 90, + 545, + 233 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 90, + 545, + 233 + ], + "spans": [ + { + "bbox": [ + 304, + 90, + 545, + 233 + ], + "type": "text", + "content": "The performance of clustering algorithms varies depending on the data and their properties, the algorithm itself, and its hyperparameters. This makes finding reliable clustering solutions particularly difficult. Consensus, or ensemble, clustering has emerged as a solution to this problem, specifically by combining the results of multiple, different clusterings, rather than relying on a single solution. This has been found to produce better and more robust outcomes than single-clustering approaches [3, 17, 18, 45]. The process of consensus clustering happens in two stages: a) multiple, diverse base clusterings are generated and b) those clusterings are aggregated using a consensus algorithm." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 235, + 545, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 235, + 545, + 437 + ], + "spans": [ + { + "bbox": [ + 304, + 235, + 545, + 437 + ], + "type": "text", + "content": "Generating diverse clusterings: The properties of the set of clusterings used by the consensus algorithm is a key factor for obtaining good performance. Multiple works [24, 40, 51] have found that both the quality of individual base clusterings and their diversity is critical, and that, indeed, clustering ensembles with a moderate degree of diversity lead to better outcomes [15, 20, 22]. Typical methods for ensemble generation include using different clustering algorithms [13], using different initializations of the same clustering algorithm or different hyperparameters (e.g. the number of clusters) [16, 22, 41], clustering with different subsets of the features [54], using random projections to diversify the feature space [14], and clustering with different subsets of the dataset [12, 13]. However, concrete methods for identifying optimal hyperparameters, such as the degree of diversity, the number of clusterings in the ensemble, and the method by which the ensemble is generated, remain elusive." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 438, + 545, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 438, + 545, + 557 + ], + "spans": [ + { + "bbox": [ + 304, + 438, + 545, + 557 + ], + "type": "text", + "content": "Consensus algorithms: Consensus algorithms aim to aggregate multiple, diverse clusterings to produce a single, robust solution. Various approaches to this problem have been proposed, such as using matrix factorization [43], distance minimization between clusterings [75], utilizing multiple views [55], graph learning [28, 73, 74] and matrix coassociation [29, 38]. We note that, while improving consensus algorithms increase the robustness of consensus clustering overall, the stages of ensemble generation and its aggregation with consensus algorithms are largely independent." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 558, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 545, + 712 + ], + "type": "text", + "content": "Consensus Clustering & Deep Learning: Despite the established advantages of consensus clustering over single-clustering approaches, consensus clustering has not been explored in the context of deep clustering. A possible reason is the computational cost of generating multiple, diverse base clusterings, which would require training multiple models. The only work that has, to the best of our knowledge, applied consensus clustering in the deep clustering setting is DeepCluE [27]. Notably, however, the base clusterings used by DeepCluE are not all learned by the model. Rather, a single-clustering model is trained, and an ensemble is generated by clustering features from multiple layers of the model with U-SPEC [30]. Our work addresses" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3420" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "text", + "content": "this gap, by proposing a way to train a single deep clustering model to generate multiple clusterings with controlled diversity and with minimal computational overhead." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 119, + 103, + 132 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 119, + 103, + 132 + ], + "spans": [ + { + "bbox": [ + 47, + 119, + 103, + 132 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 140, + 287, + 223 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 140, + 287, + 223 + ], + "spans": [ + { + "bbox": [ + 46, + 140, + 287, + 223 + ], + "type": "text", + "content": "Overview: Our method consists of two components: a) A novel loss function that can be incorporated in deep clustering frameworks to control inter-clustering diversity by applying a threshold to cluster-wise similarities, and b) a method for dynamically estimating that threshold so that the clusterings learned by the model are sufficiently diverse, according to a user-defined metric." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "spans": [ + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "text", + "content": "More concretely, we assume a deep clustering model that learns " + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "text", + "content": " clusterings (typically a backbone encoder followed by " + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "text", + "content": " projection heads), a deep clustering framework and its loss function " + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "inline_equation", + "content": "L_{\\text{main}}" + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "text", + "content": ", and a diversity target " + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "inline_equation", + "content": "D^T" + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "text", + "content": " set by the user, expressed as an upper bound to inter-clustering similarity1 (i.e. the maximum acceptable similarity). In order to control the inter-clustering similarity " + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "inline_equation", + "content": "D^R" + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "text", + "content": " of the learned clusterings so that " + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "inline_equation", + "content": "D^T \\leq D^R" + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "text", + "content": ", we propose a complementary loss " + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "inline_equation", + "content": "L_{\\text{div}}" + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "text", + "content": ". Specifically, given soft cluster assignments for a pair of clusterings " + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "inline_equation", + "content": "A, B \\in K" + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "text", + "content": ", we define the inter-clustering similarity matrix " + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "inline_equation", + "content": "S_{AB} \\in \\mathbb{R}^{C_A \\times C_B}" + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "inline_equation", + "content": "C_A" + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "inline_equation", + "content": "C_B" + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "text", + "content": " is the number of clusters in each clustering, and " + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "inline_equation", + "content": "S_{AB}(i,j) \\in [0,1]" + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "text", + "content": " measures the similarity between clusters " + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "inline_equation", + "content": "i \\in C_A" + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "inline_equation", + "content": "j \\in C_B" + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "text", + "content": ". It follows that decreasing the values of " + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "inline_equation", + "content": "S_{AB}" + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "text", + "content": " reduces the similarity between the clusters of " + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "text", + "content": ", and therefore increases their diversity. Accordingly, " + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "inline_equation", + "content": "L_{\\text{div}}" + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "text", + "content": " utilizes " + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "inline_equation", + "content": "S_{AB}" + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "text", + "content": " in order to restrict inter-clustering similarity to be under an upper similarity bound " + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "text", + "content": ". The value of " + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "text", + "content": " is dynamically adjusted during training, decreasing when " + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "inline_equation", + "content": "D^R > D^T" + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "text", + "content": " and increasing when " + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "inline_equation", + "content": "D^R \\leq D^T" + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "text", + "content": ", thereby tightening and relaxing the loss function so that, overall and throughout training, inter-clustering similarity " + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "inline_equation", + "content": "D^R" + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "text", + "content": " remains at or under the desired level " + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "inline_equation", + "content": "D^T" + }, + { + "bbox": [ + 46, + 224, + 287, + 498 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 498, + 287, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 287, + 666 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 287, + 666 + ], + "type": "text", + "content": "Defining the inter-clustering similarity matrix: Our method assumes a standard deep clustering architecture, consisting of an encoder " + }, + { + "bbox": [ + 46, + 498, + 287, + 666 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 498, + 287, + 666 + ], + "type": "text", + "content": ", followed by " + }, + { + "bbox": [ + 46, + 498, + 287, + 666 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 498, + 287, + 666 + ], + "type": "text", + "content": " projection heads " + }, + { + "bbox": [ + 46, + 498, + 287, + 666 + ], + "type": "inline_equation", + "content": "h_1, \\ldots, h_K" + }, + { + "bbox": [ + 46, + 498, + 287, + 666 + ], + "type": "text", + "content": ", each of which produces assignments for a clustering " + }, + { + "bbox": [ + 46, + 498, + 287, + 666 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 498, + 287, + 666 + ], + "type": "text", + "content": ". Specifically, let " + }, + { + "bbox": [ + 46, + 498, + 287, + 666 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 498, + 287, + 666 + ], + "type": "text", + "content": " be a set of " + }, + { + "bbox": [ + 46, + 498, + 287, + 666 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 498, + 287, + 666 + ], + "type": "text", + "content": " unlabeled samples. The encoder maps each sample " + }, + { + "bbox": [ + 46, + 498, + 287, + 666 + ], + "type": "inline_equation", + "content": "x \\in X" + }, + { + "bbox": [ + 46, + 498, + 287, + 666 + ], + "type": "text", + "content": " to a representation " + }, + { + "bbox": [ + 46, + 498, + 287, + 666 + ], + "type": "inline_equation", + "content": "f(x)" + }, + { + "bbox": [ + 46, + 498, + 287, + 666 + ], + "type": "text", + "content": ", and each projection head " + }, + { + "bbox": [ + 46, + 498, + 287, + 666 + ], + "type": "inline_equation", + "content": "h_k" + }, + { + "bbox": [ + 46, + 498, + 287, + 666 + ], + "type": "text", + "content": " maps " + }, + { + "bbox": [ + 46, + 498, + 287, + 666 + ], + "type": "inline_equation", + "content": "f(x)" + }, + { + "bbox": [ + 46, + 498, + 287, + 666 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 498, + 287, + 666 + ], + "type": "inline_equation", + "content": "C_k" + }, + { + "bbox": [ + 46, + 498, + 287, + 666 + ], + "type": "text", + "content": " clusters, so that " + }, + { + "bbox": [ + 46, + 498, + 287, + 666 + ], + "type": "inline_equation", + "content": "p_k(x) = h_k(f(x)) \\in \\mathbb{R}^{C_k \\times 1}" + }, + { + "bbox": [ + 46, + 498, + 287, + 666 + ], + "type": "text", + "content": " represents a probability assignment vector mapping sample " + }, + { + "bbox": [ + 46, + 498, + 287, + 666 + ], + "type": "inline_equation", + "content": "x \\in X" + }, + { + "bbox": [ + 46, + 498, + 287, + 666 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 498, + 287, + 666 + ], + "type": "inline_equation", + "content": "C_k" + }, + { + "bbox": [ + 46, + 498, + 287, + 666 + ], + "type": "text", + "content": " clusters in clustering " + }, + { + "bbox": [ + 46, + 498, + 287, + 666 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 498, + 287, + 666 + ], + "type": "text", + "content": ". Without loss of generality, we assume that " + }, + { + "bbox": [ + 46, + 498, + 287, + 666 + ], + "type": "inline_equation", + "content": "C = C_k \\forall k \\in K" + }, + { + "bbox": [ + 46, + 498, + 287, + 666 + ], + "type": "text", + "content": ". Each clustering can then be represented by a cluster assignment matrix " + }, + { + "bbox": [ + 46, + 498, + 287, + 666 + ], + "type": "inline_equation", + "content": "P_k(X) = [p_k(x_1), p_k(x_2), \\dots, p_k(x_N)] \\in \\mathbb{R}^{C \\times N}" + }, + { + "bbox": [ + 46, + 498, + 287, + 666 + ], + "type": "text", + "content": ". The column " + }, + { + "bbox": [ + 46, + 498, + 287, + 666 + ], + "type": "inline_equation", + "content": "p_k(n)" + }, + { + "bbox": [ + 46, + 498, + 287, + 666 + ], + "type": "text", + "content": ", that is the probability assignment vector for the" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 306, + 72, + 545, + 120 + ], + "type": "text", + "content": "-th sample, encodes the degrees to which sample " + }, + { + "bbox": [ + 306, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "x_{n}" + }, + { + "bbox": [ + 306, + 72, + 545, + 120 + ], + "type": "text", + "content": " is assigned to different clusters. The row vector " + }, + { + "bbox": [ + 306, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "q_{k}(i)\\in \\mathbb{R}^{N}" + }, + { + "bbox": [ + 306, + 72, + 545, + 120 + ], + "type": "text", + "content": " shows which samples are softly assigned to cluster " + }, + { + "bbox": [ + 306, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "i\\in C" + }, + { + "bbox": [ + 306, + 72, + 545, + 120 + ], + "type": "text", + "content": ". We refer to " + }, + { + "bbox": [ + 306, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "q_{k}(i)" + }, + { + "bbox": [ + 306, + 72, + 545, + 120 + ], + "type": "text", + "content": " as the cluster membership vector." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 120, + 547, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 120, + 547, + 192 + ], + "spans": [ + { + "bbox": [ + 306, + 120, + 547, + 192 + ], + "type": "text", + "content": "To quantify the similarity between clusterings " + }, + { + "bbox": [ + 306, + 120, + 547, + 192 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 306, + 120, + 547, + 192 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 120, + 547, + 192 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 306, + 120, + 547, + 192 + ], + "type": "text", + "content": " we define the inter-clustering similarity matrix " + }, + { + "bbox": [ + 306, + 120, + 547, + 192 + ], + "type": "inline_equation", + "content": "S_{AB} \\in \\mathbb{R}^{C \\times C}" + }, + { + "bbox": [ + 306, + 120, + 547, + 192 + ], + "type": "text", + "content": ". We define each element " + }, + { + "bbox": [ + 306, + 120, + 547, + 192 + ], + "type": "inline_equation", + "content": "S_{AB}(i,j)" + }, + { + "bbox": [ + 306, + 120, + 547, + 192 + ], + "type": "text", + "content": " as the cosine similarity between the cluster membership vector " + }, + { + "bbox": [ + 306, + 120, + 547, + 192 + ], + "type": "inline_equation", + "content": "q_{A}(i)" + }, + { + "bbox": [ + 306, + 120, + 547, + 192 + ], + "type": "text", + "content": " of cluster " + }, + { + "bbox": [ + 306, + 120, + 547, + 192 + ], + "type": "inline_equation", + "content": "i \\in A" + }, + { + "bbox": [ + 306, + 120, + 547, + 192 + ], + "type": "text", + "content": " and the cluster membership vector " + }, + { + "bbox": [ + 306, + 120, + 547, + 192 + ], + "type": "inline_equation", + "content": "q_{B}(j)" + }, + { + "bbox": [ + 306, + 120, + 547, + 192 + ], + "type": "text", + "content": " of cluster " + }, + { + "bbox": [ + 306, + 120, + 547, + 192 + ], + "type": "inline_equation", + "content": "j \\in B" + }, + { + "bbox": [ + 306, + 120, + 547, + 192 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 358, + 201, + 545, + 227 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 201, + 545, + 227 + ], + "spans": [ + { + "bbox": [ + 358, + 201, + 545, + 227 + ], + "type": "interline_equation", + "content": "S _ {A B} (i, j) = \\frac {q _ {A} (i) \\cdot q _ {B} (j)}{\\left| \\left| q _ {A} (i) \\right| \\right| _ {2} \\left| \\left| q _ {B} (j) \\right| \\right| _ {2}} \\tag {1}", + "image_path": "3ef2cae6d3d689acc345721829cf28e08fe5d4811858ce502fc4e385101015c6.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 234, + 545, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 234, + 545, + 293 + ], + "spans": [ + { + "bbox": [ + 305, + 234, + 545, + 293 + ], + "type": "text", + "content": "This measure expresses the degree to which samples in the dataset are assigned similarly to clusters " + }, + { + "bbox": [ + 305, + 234, + 545, + 293 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 305, + 234, + 545, + 293 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 234, + 545, + 293 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 305, + 234, + 545, + 293 + ], + "type": "text", + "content": ". Specifically, " + }, + { + "bbox": [ + 305, + 234, + 545, + 293 + ], + "type": "inline_equation", + "content": "S_{AB}(i,j) = 0" + }, + { + "bbox": [ + 305, + 234, + 545, + 293 + ], + "type": "text", + "content": " if " + }, + { + "bbox": [ + 305, + 234, + 545, + 293 + ], + "type": "inline_equation", + "content": "q_A(i) \\perp q_B(j)" + }, + { + "bbox": [ + 305, + 234, + 545, + 293 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 234, + 545, + 293 + ], + "type": "inline_equation", + "content": "S_{AB}(i,j) = 1" + }, + { + "bbox": [ + 305, + 234, + 545, + 293 + ], + "type": "text", + "content": " if " + }, + { + "bbox": [ + 305, + 234, + 545, + 293 + ], + "type": "inline_equation", + "content": "q_A(i) = q_B(j)" + }, + { + "bbox": [ + 305, + 234, + 545, + 293 + ], + "type": "text", + "content": ". It is, therefore, a differentiable measure of the similarity of clusters " + }, + { + "bbox": [ + 305, + 234, + 545, + 293 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 305, + 234, + 545, + 293 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 234, + 545, + 293 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 305, + 234, + 545, + 293 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 294, + 546, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 294, + 546, + 462 + ], + "spans": [ + { + "bbox": [ + 305, + 294, + 546, + 462 + ], + "type": "text", + "content": "Defining the loss function: Based on the inter-clustering similarity matrix " + }, + { + "bbox": [ + 305, + 294, + 546, + 462 + ], + "type": "inline_equation", + "content": "S_{AB}" + }, + { + "bbox": [ + 305, + 294, + 546, + 462 + ], + "type": "text", + "content": ", we define DivClust's loss to softly enforce that a clustering " + }, + { + "bbox": [ + 305, + 294, + 546, + 462 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 305, + 294, + 546, + 462 + ], + "type": "text", + "content": " does not have an aggregate cluster similarity with a clustering " + }, + { + "bbox": [ + 305, + 294, + 546, + 462 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 305, + 294, + 546, + 462 + ], + "type": "text", + "content": " greater than a similarity upper bound " + }, + { + "bbox": [ + 305, + 294, + 546, + 462 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 305, + 294, + 546, + 462 + ], + "type": "text", + "content": ". The aggregate similarity " + }, + { + "bbox": [ + 305, + 294, + 546, + 462 + ], + "type": "inline_equation", + "content": "S_{AB}^{aggr}" + }, + { + "bbox": [ + 305, + 294, + 546, + 462 + ], + "type": "text", + "content": " is defined as the average similarity of clustering " + }, + { + "bbox": [ + 305, + 294, + 546, + 462 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 305, + 294, + 546, + 462 + ], + "type": "text", + "content": "'s clusters with their most similar cluster of clustering " + }, + { + "bbox": [ + 305, + 294, + 546, + 462 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 305, + 294, + 546, + 462 + ], + "type": "text", + "content": " (Eq. (2)). Using this metric, we propose " + }, + { + "bbox": [ + 305, + 294, + 546, + 462 + ], + "type": "inline_equation", + "content": "L_{div}" + }, + { + "bbox": [ + 305, + 294, + 546, + 462 + ], + "type": "text", + "content": " (Eq. (3)), a loss that regulates diversity between clusterings " + }, + { + "bbox": [ + 305, + 294, + 546, + 462 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 305, + 294, + 546, + 462 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 294, + 546, + 462 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 305, + 294, + 546, + 462 + ], + "type": "text", + "content": " by forcing that " + }, + { + "bbox": [ + 305, + 294, + 546, + 462 + ], + "type": "inline_equation", + "content": "S_{AB}^{aggr} < d" + }, + { + "bbox": [ + 305, + 294, + 546, + 462 + ], + "type": "text", + "content": ", for " + }, + { + "bbox": [ + 305, + 294, + 546, + 462 + ], + "type": "inline_equation", + "content": "d \\in [0,1]" + }, + { + "bbox": [ + 305, + 294, + 546, + 462 + ], + "type": "text", + "content": ". It is clear from Eq. (3) that " + }, + { + "bbox": [ + 305, + 294, + 546, + 462 + ], + "type": "inline_equation", + "content": "S_{AB}^{aggr} < d \\Rightarrow L_{div}(A,B) = 0" + }, + { + "bbox": [ + 305, + 294, + 546, + 462 + ], + "type": "text", + "content": ", in which case the diversity requirement is satisfied and the loss has no impact. Conversely, " + }, + { + "bbox": [ + 305, + 294, + 546, + 462 + ], + "type": "inline_equation", + "content": "S_{AB}^{aggr} \\geq d \\Rightarrow L_{div}(A,B) > 0" + }, + { + "bbox": [ + 305, + 294, + 546, + 462 + ], + "type": "text", + "content": ", in which case the loss requires that inter-clustering similarity decreases." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 358, + 470, + 545, + 503 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 470, + 545, + 503 + ], + "spans": [ + { + "bbox": [ + 358, + 470, + 545, + 503 + ], + "type": "interline_equation", + "content": "S _ {A B} ^ {a q g r} = \\frac {1}{C} \\sum_ {i = 1} ^ {C} \\max _ {j} \\left(S _ {A B} (i, j)\\right) \\tag {2}", + "image_path": "3acc1932bf43fd669eb24f3075533f320ca2ff6210b3792c6d87041e093e2e8f.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 367, + 512, + 545, + 527 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 367, + 512, + 545, + 527 + ], + "spans": [ + { + "bbox": [ + 367, + 512, + 545, + 527 + ], + "type": "interline_equation", + "content": "L _ {d i v} (A, B) = \\left[ S _ {A B} ^ {a g g r} - d \\right] _ {+} \\tag {3}", + "image_path": "d93fe2bbc415c4ee5b1c19a43323b95e01d40ad46bacf75030125e6f9d5ed9e0.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 531, + 546, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 531, + 546, + 664 + ], + "spans": [ + { + "bbox": [ + 305, + 531, + 546, + 664 + ], + "type": "text", + "content": "Having defined the diversity loss " + }, + { + "bbox": [ + 305, + 531, + 546, + 664 + ], + "type": "inline_equation", + "content": "L_{div}" + }, + { + "bbox": [ + 305, + 531, + 546, + 664 + ], + "type": "text", + "content": " between two clusterings, we extend it to multiple clusterings " + }, + { + "bbox": [ + 305, + 531, + 546, + 664 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 305, + 531, + 546, + 664 + ], + "type": "text", + "content": " and combine it with the base deep clustering framework's objective. For a clustering " + }, + { + "bbox": [ + 305, + 531, + 546, + 664 + ], + "type": "inline_equation", + "content": "k \\in K" + }, + { + "bbox": [ + 305, + 531, + 546, + 664 + ], + "type": "text", + "content": ", we denote with " + }, + { + "bbox": [ + 305, + 531, + 546, + 664 + ], + "type": "inline_equation", + "content": "L_{main}(k)" + }, + { + "bbox": [ + 305, + 531, + 546, + 664 + ], + "type": "text", + "content": " the loss of the base deep clustering framework for that clustering, and with " + }, + { + "bbox": [ + 305, + 531, + 546, + 664 + ], + "type": "inline_equation", + "content": "L_{div}(k, k')" + }, + { + "bbox": [ + 305, + 531, + 546, + 664 + ], + "type": "text", + "content": " the diversity controlling loss between clusterings " + }, + { + "bbox": [ + 305, + 531, + 546, + 664 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 531, + 546, + 664 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 531, + 546, + 664 + ], + "type": "inline_equation", + "content": "k'" + }, + { + "bbox": [ + 305, + 531, + 546, + 664 + ], + "type": "text", + "content": ". We present the joint loss " + }, + { + "bbox": [ + 305, + 531, + 546, + 664 + ], + "type": "inline_equation", + "content": "L_{joint}(k)" + }, + { + "bbox": [ + 305, + 531, + 546, + 664 + ], + "type": "text", + "content": " for each clustering " + }, + { + "bbox": [ + 305, + 531, + 546, + 664 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 531, + 546, + 664 + ], + "type": "text", + "content": " in Eq. (4), where " + }, + { + "bbox": [ + 305, + 531, + 546, + 664 + ], + "type": "inline_equation", + "content": "L_{main}(k)" + }, + { + "bbox": [ + 305, + 531, + 546, + 664 + ], + "type": "text", + "content": " depends on cluster assignment matrix " + }, + { + "bbox": [ + 305, + 531, + 546, + 664 + ], + "type": "inline_equation", + "content": "P_k" + }, + { + "bbox": [ + 305, + 531, + 546, + 664 + ], + "type": "text", + "content": ", while " + }, + { + "bbox": [ + 305, + 531, + 546, + 664 + ], + "type": "inline_equation", + "content": "L_{div}(k, k')" + }, + { + "bbox": [ + 305, + 531, + 546, + 664 + ], + "type": "text", + "content": " depends on " + }, + { + "bbox": [ + 305, + 531, + 546, + 664 + ], + "type": "inline_equation", + "content": "P_k" + }, + { + "bbox": [ + 305, + 531, + 546, + 664 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 531, + 546, + 664 + ], + "type": "inline_equation", + "content": "P_{k'}" + }, + { + "bbox": [ + 305, + 531, + 546, + 664 + ], + "type": "text", + "content": ". Accordingly, the model's training loss " + }, + { + "bbox": [ + 305, + 531, + 546, + 664 + ], + "type": "inline_equation", + "content": "L_{total}" + }, + { + "bbox": [ + 305, + 531, + 546, + 664 + ], + "type": "text", + "content": " seen in Eq. (5), is the average of " + }, + { + "bbox": [ + 305, + 531, + 546, + 664 + ], + "type": "inline_equation", + "content": "L_{joint}" + }, + { + "bbox": [ + 305, + 531, + 546, + 664 + ], + "type": "text", + "content": " over all clusterings." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 310, + 681, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 681, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 310, + 681, + 545, + 715 + ], + "type": "interline_equation", + "content": "L _ {\\text {j o i n t}} (k) = L _ {\\text {m a i n}} (k) + \\frac {1}{K - 1} \\sum_ {k ^ {\\prime} = 1, k ^ {\\prime} \\neq k} ^ {K} L _ {\\text {d i v}} \\left(k, k ^ {\\prime}\\right) \\tag {4}", + "image_path": "d5147d5d3bbea5893e7d034bbb5878dedde6043e211d99d3709c98087565b43b.jpg" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 46, + 673, + 287, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 673, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 673, + 287, + 712 + ], + "type": "text", + "content": "1It is trivial to modify our formulation to enforce a lower bound. However, experiments (see Sec. 4.2) showed that, when learning multiple clusterings, deep clustering frameworks inherently tend to converge to near-identical solutions, which made the lower bound scenario redundant." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "3421" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 96, + 70, + 208, + 173 + ], + "blocks": [ + { + "bbox": [ + 96, + 70, + 208, + 173 + ], + "lines": [ + { + "bbox": [ + 96, + 70, + 208, + 173 + ], + "spans": [ + { + "bbox": [ + 96, + 70, + 208, + 173 + ], + "type": "image", + "image_path": "fb1bf011e4bf13ee2aecb61723189e753b0db2299b4a94bc4c8b383850601c9a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 93, + 186, + 219, + 195 + ], + "lines": [ + { + "bbox": [ + 93, + 186, + 219, + 195 + ], + "spans": [ + { + "bbox": [ + 93, + 186, + 219, + 195 + ], + "type": "text", + "content": "(a) Cluster assignments " + }, + { + "bbox": [ + 93, + 186, + 219, + 195 + ], + "type": "inline_equation", + "content": "P_A" + }, + { + "bbox": [ + 93, + 186, + 219, + 195 + ], + "type": "text", + "content": " for clustering A" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 238, + 69, + 350, + 173 + ], + "blocks": [ + { + "bbox": [ + 238, + 69, + 350, + 173 + ], + "lines": [ + { + "bbox": [ + 238, + 69, + 350, + 173 + ], + "spans": [ + { + "bbox": [ + 238, + 69, + 350, + 173 + ], + "type": "image", + "image_path": "6a89254c2b2683cca9e8ccdc2cec4d6e6f1cc58cb664cc6d453f485d2989447c.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 204, + 545, + 228 + ], + "lines": [ + { + "bbox": [ + 46, + 204, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 46, + 204, + 545, + 228 + ], + "type": "text", + "content": "Figure 2. Examples of synthetic cluster assignments " + }, + { + "bbox": [ + 46, + 204, + 545, + 228 + ], + "type": "inline_equation", + "content": "P_A" + }, + { + "bbox": [ + 46, + 204, + 545, + 228 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 204, + 545, + 228 + ], + "type": "inline_equation", + "content": "P_B" + }, + { + "bbox": [ + 46, + 204, + 545, + 228 + ], + "type": "text", + "content": " and similarity matrix " + }, + { + "bbox": [ + 46, + 204, + 545, + 228 + ], + "type": "inline_equation", + "content": "S_{AB}" + }, + { + "bbox": [ + 46, + 204, + 545, + 228 + ], + "type": "text", + "content": ". Note that clusters " + }, + { + "bbox": [ + 46, + 204, + 545, + 228 + ], + "type": "inline_equation", + "content": "i \\in A" + }, + { + "bbox": [ + 46, + 204, + 545, + 228 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 204, + 545, + 228 + ], + "type": "inline_equation", + "content": "j \\in B" + }, + { + "bbox": [ + 46, + 204, + 545, + 228 + ], + "type": "text", + "content": " are softly assigned the same samples. Correspondingly, their similarity score " + }, + { + "bbox": [ + 46, + 204, + 545, + 228 + ], + "type": "inline_equation", + "content": "S_{AB}(i,j)" + }, + { + "bbox": [ + 46, + 204, + 545, + 228 + ], + "type": "text", + "content": " is high (highlighted with red in Fig. 2c). Best seen in color." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 383, + 70, + 489, + 173 + ], + "blocks": [ + { + "bbox": [ + 233, + 186, + 360, + 196 + ], + "lines": [ + { + "bbox": [ + 233, + 186, + 360, + 196 + ], + "spans": [ + { + "bbox": [ + 233, + 186, + 360, + 196 + ], + "type": "text", + "content": "(b) Cluster assignments " + }, + { + "bbox": [ + 233, + 186, + 360, + 196 + ], + "type": "inline_equation", + "content": "P_B" + }, + { + "bbox": [ + 233, + 186, + 360, + 196 + ], + "type": "text", + "content": " for clustering B" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 383, + 70, + 489, + 173 + ], + "lines": [ + { + "bbox": [ + 383, + 70, + 489, + 173 + ], + "spans": [ + { + "bbox": [ + 383, + 70, + 489, + 173 + ], + "type": "image", + "image_path": "9592883f221f5b157afa885a3f275a26ad33452a5e8ef36c7418bdb435d892ca.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 399, + 186, + 476, + 195 + ], + "lines": [ + { + "bbox": [ + 399, + 186, + 476, + 195 + ], + "spans": [ + { + "bbox": [ + 399, + 186, + 476, + 195 + ], + "type": "text", + "content": "(c) Similarity matrix " + }, + { + "bbox": [ + 399, + 186, + 476, + 195 + ], + "type": "inline_equation", + "content": "S_{AB}" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 112, + 256, + 287, + 289 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 112, + 256, + 287, + 289 + ], + "spans": [ + { + "bbox": [ + 112, + 256, + 287, + 289 + ], + "type": "interline_equation", + "content": "L _ {t o t a l} = \\frac {1}{K} \\sum_ {k = 1} ^ {K} L _ {\\text {j o i n t}} (k) \\tag {5}", + "image_path": "50421c831c10dfc828f9cf62810e661ebf7c888bbe5c3369819f7e4504d51f8d.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 293, + 287, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 293, + 287, + 399 + ], + "spans": [ + { + "bbox": [ + 46, + 293, + 287, + 399 + ], + "type": "text", + "content": "The loss " + }, + { + "bbox": [ + 46, + 293, + 287, + 399 + ], + "type": "inline_equation", + "content": "L_{total}" + }, + { + "bbox": [ + 46, + 293, + 287, + 399 + ], + "type": "text", + "content": " is therefore a combination of the base deep clustering framework's loss " + }, + { + "bbox": [ + 46, + 293, + 287, + 399 + ], + "type": "inline_equation", + "content": "L_{main}" + }, + { + "bbox": [ + 46, + 293, + 287, + 399 + ], + "type": "text", + "content": " for each clustering " + }, + { + "bbox": [ + 46, + 293, + 287, + 399 + ], + "type": "inline_equation", + "content": "k \\in K" + }, + { + "bbox": [ + 46, + 293, + 287, + 399 + ], + "type": "text", + "content": " and the loss " + }, + { + "bbox": [ + 46, + 293, + 287, + 399 + ], + "type": "inline_equation", + "content": "L_{div}" + }, + { + "bbox": [ + 46, + 293, + 287, + 399 + ], + "type": "text", + "content": ", which is used to control interclustering diversity. The proposed loss formulation is applicable to any deep clustering framework that produces cluster assignments through the model (as opposed to frameworks using offline methods such as MIX'EM [58]), which covers the majority of deep clustering frameworks outlined in Sec. 2." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 401, + 287, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 401, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 401, + 287, + 581 + ], + "type": "text", + "content": "Dynamic upper bound " + }, + { + "bbox": [ + 46, + 401, + 287, + 581 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 401, + 287, + 581 + ], + "type": "text", + "content": ": The proposed loss " + }, + { + "bbox": [ + 46, + 401, + 287, + 581 + ], + "type": "inline_equation", + "content": "L_{div}" + }, + { + "bbox": [ + 46, + 401, + 287, + 581 + ], + "type": "text", + "content": " controls inter-clustering diversity by restricting the values of " + }, + { + "bbox": [ + 46, + 401, + 287, + 581 + ], + "type": "inline_equation", + "content": "S_{AB}" + }, + { + "bbox": [ + 46, + 401, + 287, + 581 + ], + "type": "text", + "content": " according to the similarity upper bound " + }, + { + "bbox": [ + 46, + 401, + 287, + 581 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 401, + 287, + 581 + ], + "type": "text", + "content": ". However, the values of " + }, + { + "bbox": [ + 46, + 401, + 287, + 581 + ], + "type": "inline_equation", + "content": "S_{AB}" + }, + { + "bbox": [ + 46, + 401, + 287, + 581 + ], + "type": "text", + "content": " are calculated based on the cosine similarity of soft cluster assignments. This means that pairs of cluster assignment vectors " + }, + { + "bbox": [ + 46, + 401, + 287, + 581 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 401, + 287, + 581 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 401, + 287, + 581 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 401, + 287, + 581 + ], + "type": "text", + "content": " will have different similarity values " + }, + { + "bbox": [ + 46, + 401, + 287, + 581 + ], + "type": "inline_equation", + "content": "S_{AB}(i,j)" + }, + { + "bbox": [ + 46, + 401, + 287, + 581 + ], + "type": "text", + "content": " depending on their sharpness, even if they point to the same cluster in terms of their corresponding hard assignment. It follows that " + }, + { + "bbox": [ + 46, + 401, + 287, + 581 + ], + "type": "inline_equation", + "content": "S_{AB}" + }, + { + "bbox": [ + 46, + 401, + 287, + 581 + ], + "type": "text", + "content": " and, accordingly, the impact of " + }, + { + "bbox": [ + 46, + 401, + 287, + 581 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 401, + 287, + 581 + ], + "type": "text", + "content": ", are dependent on the confidence of cluster assignments and vary throughout training and between experiments (as factors like the number of clusters and model capacity influence the confidence of cluster assignments). Therefore, " + }, + { + "bbox": [ + 46, + 401, + 287, + 581 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 401, + 287, + 581 + ], + "type": "text", + "content": " is an ambiguous and unintuitive metric for users to define diversity targets with." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 580, + 287, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 580, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 580, + 287, + 664 + ], + "type": "text", + "content": "To tackle this issue and to provide a reliable and intuitive method for defining diversity objectives, we propose dynamically determining the value of the threshold " + }, + { + "bbox": [ + 46, + 580, + 287, + 664 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 580, + 287, + 664 + ], + "type": "text", + "content": " during training. Concretely, let " + }, + { + "bbox": [ + 46, + 580, + 287, + 664 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 580, + 287, + 664 + ], + "type": "text", + "content": " be an inter-clustering similarity metric chosen by the user. In this work, we use avg. Normalized Mutual Information (NMI), a well established metric for estimating inter-clustering similarity." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 59, + 681, + 287, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 681, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 59, + 681, + 287, + 715 + ], + "type": "interline_equation", + "content": "D = \\frac {1}{(K - 1) (K / 2)} \\sum_ {k = 1} ^ {K - 1} \\sum_ {k ^ {\\prime} = k + 1} ^ {K} N M I \\left(P _ {k} ^ {h}, P _ {k ^ {\\prime}} ^ {h}\\right) \\tag {6}", + "image_path": "ab3954acfa174399c5fa860be6857d5129ebd3ff10978f50b8221791a97dfd10.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 247, + 545, + 295 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 247, + 545, + 295 + ], + "spans": [ + { + "bbox": [ + 304, + 247, + 545, + 295 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 247, + 545, + 295 + ], + "type": "inline_equation", + "content": "P_{k}^{h} \\in \\mathbb{Z}^{N}" + }, + { + "bbox": [ + 304, + 247, + 545, + 295 + ], + "type": "text", + "content": " is the hard cluster assignment vector for " + }, + { + "bbox": [ + 304, + 247, + 545, + 295 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 247, + 545, + 295 + ], + "type": "text", + "content": " samples in clustering " + }, + { + "bbox": [ + 304, + 247, + 545, + 295 + ], + "type": "inline_equation", + "content": "k \\in K" + }, + { + "bbox": [ + 304, + 247, + 545, + 295 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 247, + 545, + 295 + ], + "type": "inline_equation", + "content": "NMI(P_{k}^{h}, P_{k^{\\prime}}^{h})" + }, + { + "bbox": [ + 304, + 247, + 545, + 295 + ], + "type": "text", + "content": " represents the NMI between " + }, + { + "bbox": [ + 304, + 247, + 545, + 295 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 247, + 545, + 295 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 247, + 545, + 295 + ], + "type": "inline_equation", + "content": "k^{\\prime}" + }, + { + "bbox": [ + 304, + 247, + 545, + 295 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 247, + 545, + 295 + ], + "type": "inline_equation", + "content": "D \\in [0,1]" + }, + { + "bbox": [ + 304, + 247, + 545, + 295 + ], + "type": "text", + "content": ", with higher values indicating more similar clusterings." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 295, + 546, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 295, + 546, + 403 + ], + "spans": [ + { + "bbox": [ + 304, + 295, + 546, + 403 + ], + "type": "text", + "content": "Assuming a user-defined similarity target " + }, + { + "bbox": [ + 304, + 295, + 546, + 403 + ], + "type": "inline_equation", + "content": "D^T" + }, + { + "bbox": [ + 304, + 295, + 546, + 403 + ], + "type": "text", + "content": ", expressed as a value of metric " + }, + { + "bbox": [ + 304, + 295, + 546, + 403 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 295, + 546, + 403 + ], + "type": "text", + "content": ", we denote with " + }, + { + "bbox": [ + 304, + 295, + 546, + 403 + ], + "type": "inline_equation", + "content": "D^R" + }, + { + "bbox": [ + 304, + 295, + 546, + 403 + ], + "type": "text", + "content": " the measured inter-clustering similarity of the clusterings learned by the model, expressed in the same metric. DivClust's objective is to control inter-clustering diversity, which translates to learning clusterings such that " + }, + { + "bbox": [ + 304, + 295, + 546, + 403 + ], + "type": "inline_equation", + "content": "D^R \\leq D^T" + }, + { + "bbox": [ + 304, + 295, + 546, + 403 + ], + "type": "text", + "content": ". Accordingly, appropriate thresholds " + }, + { + "bbox": [ + 304, + 295, + 546, + 403 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 295, + 546, + 403 + ], + "type": "text", + "content": " must be used during training. Under the assumption that " + }, + { + "bbox": [ + 304, + 295, + 546, + 403 + ], + "type": "inline_equation", + "content": "D^R" + }, + { + "bbox": [ + 304, + 295, + 546, + 403 + ], + "type": "text", + "content": " decreases monotonically w.r.t. " + }, + { + "bbox": [ + 304, + 295, + 546, + 403 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 295, + 546, + 403 + ], + "type": "text", + "content": ", we propose the following update rule for " + }, + { + "bbox": [ + 304, + 295, + 546, + 403 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 295, + 546, + 403 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 322, + 413, + 545, + 445 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 322, + 413, + 545, + 445 + ], + "spans": [ + { + "bbox": [ + 322, + 413, + 545, + 445 + ], + "type": "interline_equation", + "content": "d _ {s + 1} = \\left\\{ \\begin{array}{l l} \\max \\left(d _ {s} (1 - m), 0\\right), & \\text {i f} D ^ {R} > D ^ {T} \\\\ \\min \\left(d _ {s} (1 + m), 1\\right), & \\text {i f} D ^ {R} \\leq D ^ {T} \\end{array} , \\right. \\tag {7}", + "image_path": "f9f43e2312dd443a64f47069e3835d34a887491291420e7f43063355ad2d61de.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 453, + 546, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 453, + 546, + 586 + ], + "spans": [ + { + "bbox": [ + 304, + 453, + 546, + 586 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 453, + 546, + 586 + ], + "type": "inline_equation", + "content": "d_{s}" + }, + { + "bbox": [ + 304, + 453, + 546, + 586 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 453, + 546, + 586 + ], + "type": "inline_equation", + "content": "d_{s+1}" + }, + { + "bbox": [ + 304, + 453, + 546, + 586 + ], + "type": "text", + "content": " are the values of the threshold " + }, + { + "bbox": [ + 304, + 453, + 546, + 586 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 453, + 546, + 586 + ], + "type": "text", + "content": " for the current and the next steps, and " + }, + { + "bbox": [ + 304, + 453, + 546, + 586 + ], + "type": "inline_equation", + "content": "m \\in (0,1)" + }, + { + "bbox": [ + 304, + 453, + 546, + 586 + ], + "type": "text", + "content": " regulates the magnitude of the update steps. Following this update rule, we decrease " + }, + { + "bbox": [ + 304, + 453, + 546, + 586 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 453, + 546, + 586 + ], + "type": "text", + "content": " when the measured inter-clustering similarity " + }, + { + "bbox": [ + 304, + 453, + 546, + 586 + ], + "type": "inline_equation", + "content": "D^{R}" + }, + { + "bbox": [ + 304, + 453, + 546, + 586 + ], + "type": "text", + "content": " needs to decrease, and increase it otherwise. For computational efficiency, instead of calculating " + }, + { + "bbox": [ + 304, + 453, + 546, + 586 + ], + "type": "inline_equation", + "content": "D^{R}" + }, + { + "bbox": [ + 304, + 453, + 546, + 586 + ], + "type": "text", + "content": " over the entire dataset in every training step, we do so every 20 iterations on a memory bank of " + }, + { + "bbox": [ + 304, + 453, + 546, + 586 + ], + "type": "inline_equation", + "content": "M = 10,000" + }, + { + "bbox": [ + 304, + 453, + 546, + 586 + ], + "type": "text", + "content": " cluster assignments – the latter is updated at every step in a FIFO manner. We set the hyperparameter " + }, + { + "bbox": [ + 304, + 453, + 546, + 586 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 453, + 546, + 586 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 453, + 546, + 586 + ], + "type": "inline_equation", + "content": "m = 0.01" + }, + { + "bbox": [ + 304, + 453, + 546, + 586 + ], + "type": "text", + "content": " in all experiments." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 597, + 387, + 611 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 597, + 387, + 611 + ], + "spans": [ + { + "bbox": [ + 306, + 597, + 387, + 611 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "We conduct several experiments to evaluate DivClust's adaptability, its effectiveness in controlling diversity, and the quality of the resulting clusterings. First, to show that DivClust effectively controls inter-clustering diversity and produces high quality clusterings with various frameworks, we combine it with IIC [37], PICA [32] and CC [44], and apply it to CIFAR10 with various diversity targets " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "D^{T}" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": ". Subsequently, we focus on the best framework of the" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3422" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 82, + 70, + 509, + 301 + ], + "blocks": [ + { + "bbox": [ + 82, + 70, + 509, + 301 + ], + "lines": [ + { + "bbox": [ + 82, + 70, + 509, + 301 + ], + "spans": [ + { + "bbox": [ + 82, + 70, + 509, + 301 + ], + "type": "table", + "html": "
FrameworkClusteringsDTDRCNFMean Acc.Max. Acc.DivClust Acc.
IIC1--0.9970.4420.4420.442
201.0.9830.9960.5260.5260.526
200.950.9390.9980.5310.5370.533
200.90.8880.9970.5680.590.578
200.80.80.9970.6110.6780.653
200.70.6940.9960.5660.6370.685
PICA1--0.9060.5330.5330.533
201.0.9910.8140.5970.5970.596
200.950.9310.8260.6240.6310.625
200.90.8910.8410.6480.6650.652
200.80.8170.8280.5980.6350.595
200.70.7030.8240.6250.6910.671
CC1--0.9360.7640.7640.764
201.0.9760.9340.7630.7630.763
200.950.9460.9340.7620.7730.76
200.90.90.9310.7940.8180.789
200.80.8140.930.7620.8470.819
200.70.6990.9270.7030.8180.815
", + "image_path": "be34e2b6b4258eaec6640b31bdb32d250424f68298148186f6f607c29d8c7fe3.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 48, + 362, + 288, + 457 + ], + "blocks": [ + { + "bbox": [ + 46, + 310, + 546, + 344 + ], + "lines": [ + { + "bbox": [ + 46, + 310, + 546, + 344 + ], + "spans": [ + { + "bbox": [ + 46, + 310, + 546, + 344 + ], + "type": "text", + "content": "Table 1. Results for IIC, PICA and CC applied on CIFAR10 with DivClust. CNF and Mean Acc. are calculated by averaging the corresponding metrics over all clusterings, while Max Acc. refers to the best performing base clustering. The DivClust Acc. metric measures the accuracy of a consensus clustering produced with the DivClust C method." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 362, + 288, + 457 + ], + "lines": [ + { + "bbox": [ + 48, + 362, + 288, + 457 + ], + "spans": [ + { + "bbox": [ + 48, + 362, + 288, + 457 + ], + "type": "table", + "html": "
DTDR
CIFAR10CIFAR100ImageNet-10ImageNet-Dogs
1.0.9760.9390.9870.941
0.950.9460.9260.9480.945
0.90.90.8480.8970.87
0.80.8140.8060.8070.795
0.70.6990.7050.6960.702
", + "image_path": "605e969e75020ac35182492683ab126289e796512e027e795c8b6b6f6cf3319d.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 465, + 287, + 500 + ], + "lines": [ + { + "bbox": [ + 46, + 465, + 287, + 500 + ], + "spans": [ + { + "bbox": [ + 46, + 465, + 287, + 500 + ], + "type": "text", + "content": "Table 2. Avg. inter-clustering similarity scores " + }, + { + "bbox": [ + 46, + 465, + 287, + 500 + ], + "type": "inline_equation", + "content": "D^{R}" + }, + { + "bbox": [ + 46, + 465, + 287, + 500 + ], + "type": "text", + "content": " for clustering sets produced by DivClust combined with CC for various diversity targets " + }, + { + "bbox": [ + 46, + 465, + 287, + 500 + ], + "type": "inline_equation", + "content": "D^{T}" + }, + { + "bbox": [ + 46, + 465, + 287, + 500 + ], + "type": "text", + "content": ". The objective of DivClust is that " + }, + { + "bbox": [ + 46, + 465, + 287, + 500 + ], + "type": "inline_equation", + "content": "D^{R} \\leq D^{T}" + }, + { + "bbox": [ + 46, + 465, + 287, + 500 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 520, + 287, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 520, + 287, + 593 + ], + "spans": [ + { + "bbox": [ + 46, + 520, + 287, + 593 + ], + "type": "text", + "content": "three, namely CC, and conduct experiments on 4 datasets (CIFAR10, CIFAR100,Imagenet-10 andImagenet-Dogs). Our findings demonstrate that, across frameworks and datasets, DivClust can: a) effectively control diversity and b) improve clustering outcomes over the base frameworks and alternative ensembling methods." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 599, + 157, + 613 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 599, + 157, + 613 + ], + "spans": [ + { + "bbox": [ + 47, + 599, + 157, + 613 + ], + "type": "text", + "content": "4.1. Experiments setup" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 617, + 287, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 666 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 666 + ], + "type": "text", + "content": "Datasets: We conduct experiments with 4 standard datasets in deep clustering: CIFAR10, CIFAR100 [39] (evaluating on the 20 superclasses), ImageNet-10 and ImageNet-Dogs [8]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "content": "Metrics: Inter-clustering similarity is measured by averaging the NMI between clusterings to calculate the interclustering NMI metric " + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "content": " (Eq. (6)), with higher values indicating more similar clusterings. We denote with " + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "inline_equation", + "content": "D^T" + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "content": " the" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 364, + 545, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 364, + 545, + 472 + ], + "spans": [ + { + "bbox": [ + 304, + 364, + 545, + 472 + ], + "type": "text", + "content": "diversity target set by the user and with " + }, + { + "bbox": [ + 304, + 364, + 545, + 472 + ], + "type": "inline_equation", + "content": "D^{R}" + }, + { + "bbox": [ + 304, + 364, + 545, + 472 + ], + "type": "text", + "content": " the measured inter-clustering similarity after training. When DivClust is applied we want that " + }, + { + "bbox": [ + 304, + 364, + 545, + 472 + ], + "type": "inline_equation", + "content": "D^{R} \\leq D^{T}" + }, + { + "bbox": [ + 304, + 364, + 545, + 472 + ], + "type": "text", + "content": ". Clustering quality is evaluated based on overlap of the clusterings with the dataset's ground truth labels, using the Accuracy (ACC), Normalized Mutual Information (NMI) and Adjusted Rand Index (ARI) metrics. We also report the avg. cluster assignment confidence (CNF), which measures cluster separability. For all four metrics greater values are better, 1 being optimal." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 473, + 546, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 473, + 546, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 473, + 546, + 616 + ], + "type": "text", + "content": "Implementation & Training: DivClust is incorporated into the base frameworks as described in Sec. 3, by adding DivClust's loss to their objective and duplicating projection heads " + }, + { + "bbox": [ + 304, + 473, + 546, + 616 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 304, + 473, + 546, + 616 + ], + "type": "text", + "content": " to produce multiple clusterings. The models were trained following the configurations (model architecture, training duration, hyperparameters etc.) suggested in their respective papers [32, 37, 44], unless stated otherwise. PICA and IIC were trained without overclustering. We set the number of clusterings to " + }, + { + "bbox": [ + 304, + 473, + 546, + 616 + ], + "type": "inline_equation", + "content": "K = 20" + }, + { + "bbox": [ + 304, + 473, + 546, + 616 + ], + "type": "text", + "content": ", following convention in consensus clustering [73], and the number of clusters " + }, + { + "bbox": [ + 304, + 473, + 546, + 616 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 473, + 546, + 616 + ], + "type": "text", + "content": " to the number of classes for each dataset, following convention for deep clustering evaluation [32, 37, 44]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 617, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 714 + ], + "type": "text", + "content": "Consensus Clustering: To extract single clustering solutions we examine three methods: a) selecting the clustering " + }, + { + "bbox": [ + 304, + 617, + 545, + 714 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 617, + 545, + 714 + ], + "type": "text", + "content": " with the lowest corresponding loss " + }, + { + "bbox": [ + 304, + 617, + 545, + 714 + ], + "type": "inline_equation", + "content": "L_{\\text{main}}(k)" + }, + { + "bbox": [ + 304, + 617, + 545, + 714 + ], + "type": "text", + "content": " (DivClust A), b) using the consensus clustering algorithm SCCBG [73] to aggregate clusterings (DivClust B), and c) a combination of the two, where we select the 10 best clusterings with regard to their loss and then apply SCCBG (DivClust C). For clarity and space, we present in the paper" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3423" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 70, + 545, + 406 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 545, + 406 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 545, + 406 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 545, + 406 + ], + "type": "table", + "html": "
DatasetDTCIFAR10CIFAR100ImageNet-10ImageNet-Dogs
MetricNMINMIACCARINMIACCARINMIACCARINMIACCARI
K-means-0.0870.2290.0490.0840.1300.0280.1190.2410.0570.550.1050.020
AC-0.1050.2280.0650.0980.1380.0340.1380.2420.0670.0370.1390.021
NMF-0.0810.1900.0340.0790.1180.0260.1320.2300.0650.0440.1180.016
AE-0.2370.3140.1690.1000.1650.0480.2100.3170.1520.1040.1850.073
DAE-0.2510.2970.1630.1110.1510.0460.2060.3040.1380.1040.1900.078
DCGAN-0.2650.3150.1760.1200.1510.0450.2250.3460.1570.1210.1740.078
DeCNN-0.2400.2820.1740.0920.1330.0380.1860.3130.1420.0980.1750.073
VAE-0.2450.2910.1670.1080.1520.0400.1930.3340.1680.1070.1790.079
JULE-0.1920.2720.1380.1030.1370.0330.1750.3000.1380.0540.1380.028
DEC-0.2570.3010.1610.1360.1850.0500.2820.3810.2030.1220.1950.079
DAC-0.3960.5220.3060.1850.2380.0880.3940.5270.3020.2190.2750.111
ADC--0.325--0.160--0.530----
DDC-0.4240.5240.329---0.4330.5770.345---
DCCM-0.4960.6230.4080.2850.3270.1730.6080.7100.5550.3210.3830.182
IIC--0.617--0.257-------
PICA-0.5910.6960.5120.3100.3370.1710.8020.8700.7610.3520.3520.201
CC-0.7050.7900.6370.4310.4290.2660.8590.8930.8220.4450.4290.274
CC-Kmeans-0.6540.6980.5230.4290.4050.2350.7920.8410.6690.4570.4440.284
CC-Kmeans/S-0.6740.690.5540.4280.4020.2280.7920.8420.6730.4560.4440.283
CC-Kmeans/F-0.6840.7620.5990.4380.4090.2100.7970.8470.6850.4580.4440.285
DeepCluE-0.7270.7640.6460.4720.4570.2880.8820.9240.8560.4480.4160.273
DivClust C1.0.6780.7630.6040.4180.4240.2570.860.8950.8250.4590.4510.298
0.950.6770.760.6020.4310.4340.2760.8910.9360.8780.4610.4510.297
0.90.6780.7890.6410.4220.4260.2580.8790.920.8590.480.4870.332
0.80.7240.8190.6810.4220.4140.260.8790.9180.8510.4580.4480.296
0.70.710.8150.6750.440.4370.2830.850.900.8190.5160.5290.376
", + "image_path": "09779981f2e802d88b0734376a0263881c626b43238e09de7387054d09a02fc3.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 413, + 546, + 460 + ], + "lines": [ + { + "bbox": [ + 46, + 413, + 546, + 460 + ], + "spans": [ + { + "bbox": [ + 46, + 413, + 546, + 460 + ], + "type": "text", + "content": "Table 3. Results combining DivClust with CC for various diversity targets " + }, + { + "bbox": [ + 46, + 413, + 546, + 460 + ], + "type": "inline_equation", + "content": "D^T" + }, + { + "bbox": [ + 46, + 413, + 546, + 460 + ], + "type": "text", + "content": ". We underline DivClust results that outperform the single-clustering baseline CC, and note with bold the best results for each metric across all methods and diversity levels. We emphasize that the NMI in this table measures the similarity between the single clustering produced by each method and the ground truth classes. The NMI values representing inter-clustering similarity " + }, + { + "bbox": [ + 46, + 413, + 546, + 460 + ], + "type": "inline_equation", + "content": "D^R" + }, + { + "bbox": [ + 46, + 413, + 546, + 460 + ], + "type": "text", + "content": " in ensembles produced by DivClust for the same experiments are presented in Tab. 2." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 479, + 288, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 479, + 288, + 517 + ], + "spans": [ + { + "bbox": [ + 46, + 479, + 288, + 517 + ], + "type": "text", + "content": "results only for the hybrid aggregation method DivClust C, which we found to be the most robust. Detailed results for all three approaches are provided in supplementary Tab. 5." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 526, + 105, + 538 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 526, + 105, + 538 + ], + "spans": [ + { + "bbox": [ + 47, + 526, + 105, + 538 + ], + "type": "text", + "content": "4.2. Results" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "text", + "content": "Initially, we apply IIC, PICA and CC on CIFAR10, and present the outcomes in Tab. 1. We find that, for all three frameworks, DivClust effectively controls diversity, as " + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "inline_equation", + "content": "D^{R}" + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "text", + "content": " is consistently close to or lower than " + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "inline_equation", + "content": "D^{T}" + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "text", + "content": ". Furthermore, results indicate that DivClust is necessary to produce diverse clusterings in deep clustering frameworks, as, without it, they tend to converge to near identical solutions (when " + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "inline_equation", + "content": "D^{T} = 1" + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "inline_equation", + "content": "D^{R} \\rightarrow 1" + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "text", + "content": "). Regarding cluster separability, assignment confidence " + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "inline_equation", + "content": "CNF" + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "text", + "content": " remains high for various diversity targets " + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "inline_equation", + "content": "D^{T}" + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "text", + "content": ", despite the increased complexity of optimizing both the main deep clustering loss and DivClust's objective. Finally, we observe that, for most diversity targets " + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "inline_equation", + "content": "D^{T}" + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "text", + "content": ", the mean and max. accuracy, as well as the consensus clustering accuracy produced by the aggregation method DivClust" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 479, + 545, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 479, + 545, + 564 + ], + "spans": [ + { + "bbox": [ + 304, + 479, + 545, + 564 + ], + "type": "text", + "content": "C, increase relative to the single clustering model. Notably, consensus clustering accuracy is higher than the mean clustering accuracy for most cases, which highlights the effectiveness of our approach. We stress that identifying clusterings in the ensemble whose performance matches the mean or max. accuracy is not trivial, which is why consensus clustering is necessary to reach a single clustering solution." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": "Having established that DivClust is effective across frameworks, we focus on CC and apply it on CIFAR10, CIFAR100, ImageNet-Dogs and Imagenet-10. We compare DivClust with the standard implementation of CC, which is trained to learn a single clustering (CC), as well as with alternative methods of ensemble clustering. Specifically, we apply the typical methods of ensemble generation by extracting the features learned by the single-clustering CC model and running K-means 20 times on the entire dataset (CC-Kmeans), on random subsets of the dataset (CC-Kmeans/S) and on random subsets of the feature space (CC-Kmeans/F), following [3]. In all three cases, SCCBG" + } + ] + } + ], + "index": 6 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "text", + "content": "3424" + } + ] + } + ], + "index": 7 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "text", + "content": "is used to aggregate the resulting clusterings. Furthermore, we compare with DeepCluE [27], to the best of our knowledge the only other work that examines consensus clustering in the context of deep clustering, and which is also built on top of CC, allowing for a fair comparison. We note that DeepCluE is not mutually exclusive with DivClust, and could be used jointly with it." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 157, + 288, + 372 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 157, + 288, + 372 + ], + "spans": [ + { + "bbox": [ + 46, + 157, + 288, + 372 + ], + "type": "text", + "content": "Inter-clustering similarity scores " + }, + { + "bbox": [ + 46, + 157, + 288, + 372 + ], + "type": "inline_equation", + "content": "D^{R}" + }, + { + "bbox": [ + 46, + 157, + 288, + 372 + ], + "type": "text", + "content": " for this set of experiments are presented in Tab. 2, where it is seen that DivClust successfully controls diversity. Results for consensus clustering, the main task for which DivClust is intended, are presented in Tab. 3 for CC across 4 datasets, where we also include results from other deep clustering frameworks for reference. Detailed results, including aggregation methods DivClust A and DivClust B, as well as mean/max scores for DivClust's clustering ensembles, are provided in supplementary Tab. 5. Results in Tab. 3 demonstrate that, for most diversity targets " + }, + { + "bbox": [ + 46, + 157, + 288, + 372 + ], + "type": "inline_equation", + "content": "D^{T}" + }, + { + "bbox": [ + 46, + 157, + 288, + 372 + ], + "type": "text", + "content": ", DivClust outperforms the single-clustering baseline CC and typical ensemble generation methods, and is competitive with the alternative consensus clustering method DeepCluE. Notably, DivClust is competitive with the baseline across diversity levels. This robustness is very significant, given that identifying what properties (including diversity) lead to optimal outcomes in clustering ensembles is an open problem [15, 22]." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 373, + 287, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 373, + 287, + 469 + ], + "spans": [ + { + "bbox": [ + 46, + 373, + 287, + 469 + ], + "type": "text", + "content": "To summarize, the results of Tabs. 1 to 3 demonstrate that DivClust: a) effectively controls inter-clustering diversity in deep clustering frameworks in accordance with user-defined objectives, b) does not degrade the quality of the clusterings and in fact produces better solutions than single-clustering models, and c), it can be used with consensus clustering to identify single-clustering solutions superior to those of the corresponding single-clustering frameworks." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 481, + 117, + 494 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 481, + 117, + 494 + ], + "spans": [ + { + "bbox": [ + 47, + 481, + 117, + 494 + ], + "type": "text", + "content": "5. Discussion" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 502, + 286, + 526 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 502, + 286, + 526 + ], + "spans": [ + { + "bbox": [ + 47, + 502, + 286, + 526 + ], + "type": "text", + "content": "5.1. Diversity Control & Consensus Clustering Performance" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 533, + 286, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 286, + 582 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 286, + 582 + ], + "type": "text", + "content": "Results presented in Sec. 4 demonstrate the effectiveness of DivClust both in controlling inter-clustering diversity and in producing clustering ensembles that lead to consensus clustering outcomes superior to single clustering baselines." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 582, + 286, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 286, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 286, + 714 + ], + "type": "text", + "content": "Specifically, Tabs. 1 and 2 show that the inter-clustering similarity " + }, + { + "bbox": [ + 46, + 582, + 286, + 714 + ], + "type": "inline_equation", + "content": "D^{R}" + }, + { + "bbox": [ + 46, + 582, + 286, + 714 + ], + "type": "text", + "content": " of ensembles produced by DivClust is consistently lower than the targets " + }, + { + "bbox": [ + 46, + 582, + 286, + 714 + ], + "type": "inline_equation", + "content": "D^{T}" + }, + { + "bbox": [ + 46, + 582, + 286, + 714 + ], + "type": "text", + "content": ". In the few cases where " + }, + { + "bbox": [ + 46, + 582, + 286, + 714 + ], + "type": "inline_equation", + "content": "D^{R} \\geq D^{T}" + }, + { + "bbox": [ + 46, + 582, + 286, + 714 + ], + "type": "text", + "content": ", it is by very small margins (the greatest deviation was +0.017), which may be attributed to our use of a memory bank to estimate " + }, + { + "bbox": [ + 46, + 582, + 286, + 714 + ], + "type": "inline_equation", + "content": "D^{R}" + }, + { + "bbox": [ + 46, + 582, + 286, + 714 + ], + "type": "text", + "content": " for the update rule of the threshold " + }, + { + "bbox": [ + 46, + 582, + 286, + 714 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 582, + 286, + 714 + ], + "type": "text", + "content": ". Regarding consensus clustering accuracy, despite the sensitivity of consensus clustering to the properties of the ensembles and, specifically, to different inter-clustering diversity levels, our method proves particularly robust to varying the diversity targets " + }, + { + "bbox": [ + 46, + 582, + 286, + 714 + ], + "type": "inline_equation", + "content": "D^{T}" + }, + { + "bbox": [ + 46, + 582, + 286, + 714 + ], + "type": "text", + "content": ", outperforming" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "content": "bases for most settings. This indicates that DivClust learns clusterings with a good quality-diversity trade-off and can be reliably used for consensus clustering." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 110, + 545, + 171 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 110, + 545, + 171 + ], + "spans": [ + { + "bbox": [ + 304, + 110, + 545, + 171 + ], + "type": "text", + "content": "Finally, we note that DivClust's ability to explicitly control inter-clustering diversity can facilitate future research on the impact of diversity in clustering ensembles and toward methodologies that determine desirable diversity levels for specific settings [51]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 184, + 493, + 198 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 184, + 493, + 198 + ], + "spans": [ + { + "bbox": [ + 305, + 184, + 493, + 198 + ], + "type": "text", + "content": "5.2. Complexity & Computational Cost" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 204, + 545, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 204, + 545, + 445 + ], + "spans": [ + { + "bbox": [ + 304, + 204, + 545, + 445 + ], + "type": "text", + "content": "The complexity of DivClust's objective is " + }, + { + "bbox": [ + 304, + 204, + 545, + 445 + ], + "type": "inline_equation", + "content": "O(nK^2 C^2)" + }, + { + "bbox": [ + 304, + 204, + 545, + 445 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 204, + 545, + 445 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 204, + 545, + 445 + ], + "type": "text", + "content": " is the batch size, " + }, + { + "bbox": [ + 304, + 204, + 545, + 445 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 204, + 545, + 445 + ], + "type": "text", + "content": " is the number of clusterings, and " + }, + { + "bbox": [ + 304, + 204, + 545, + 445 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 204, + 545, + 445 + ], + "type": "text", + "content": " is the number of clusters in each clustering. Importantly, the cost of DivClust relates only to the computation of the loss and the additional projection heads, and is therefore fixed for fixed " + }, + { + "bbox": [ + 304, + 204, + 545, + 445 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 204, + 545, + 445 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 204, + 545, + 445 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 204, + 545, + 445 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 204, + 545, + 445 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 204, + 545, + 445 + ], + "type": "text", + "content": " values, regardless of model size and data dimensionality, which are generally the computational bottleneck in Deep Learning applications. Therefore, DivClust is scalable to large datasets. Finally, we note that, in practice, the computational overhead introduced by DivClust is minimal. Specifically, for experiments in this work, DivClust learned ensembles with " + }, + { + "bbox": [ + 304, + 204, + 545, + 445 + ], + "type": "inline_equation", + "content": "K = 20" + }, + { + "bbox": [ + 304, + 204, + 545, + 445 + ], + "type": "text", + "content": " clusterings, with training time increasing between " + }, + { + "bbox": [ + 304, + 204, + 545, + 445 + ], + "type": "inline_equation", + "content": "10\\% - 50\\%" + }, + { + "bbox": [ + 304, + 204, + 545, + 445 + ], + "type": "text", + "content": " relative to the time it took to train the baseline single-clustering models. Contrasted with the alternative of training a single-clustering model 20 times (which would not allow for controlling diversity), DivClust provides an efficient approach for applying consensus clustering with deep clustering frameworks. A detailed analysis on complexity and runtimes is provided in supplementary Sec. 3." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 461, + 378, + 474 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 461, + 378, + 474 + ], + "spans": [ + { + "bbox": [ + 306, + 461, + 378, + 474 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 483, + 545, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 483, + 545, + 687 + ], + "spans": [ + { + "bbox": [ + 304, + 483, + 545, + 687 + ], + "type": "text", + "content": "We introduce DivClust, a method that can be incorporated into existing deep clustering frameworks to learn multiple clusterings while controlling inter-clustering diversity. To the best of our knowledge, this is the first method that can explicitly control inter-clustering diversity based on user-defined targets, and that is compatible with deep clustering frameworks that learn features and clusters end-to-end. Our experiments, conducted with multiple datasets and deep clustering frameworks, confirm the effectiveness of DivClust in controlling inter-clustering diversity and its adaptability, in terms of it being compatible with various frameworks without requiring modifications and/or hyperparameter tuning. Furthermore, results demonstrate that DivClust learns high quality clusterings, which, in the context of consensus clustering, lead to improved performance compared to single clustering baselines and alternative ensemble clustering methods." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": "Acknowledgments: This work was supported by the EU H2020 AI4Media No. 951911 project." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3425" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "text", + "content": "[1] Yuki M. 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In Twenty-Fourth International Joint Conference on Artificial Intelligence, 2015. 3" + } + ] + } + ], + "index": 18 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "3428" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Diverse 3D Hand Gesture Prediction From Body Dynamics by Bilateral Hand Disentanglement/d0994cbf-d27b-45f6-a350-1ef9d2d99ed2_content_list.json b/2023/Diverse 3D Hand Gesture Prediction From Body Dynamics by Bilateral Hand Disentanglement/d0994cbf-d27b-45f6-a350-1ef9d2d99ed2_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..08ff0e82492fa907d638c662a237922cb5988341 --- /dev/null +++ b/2023/Diverse 3D Hand Gesture Prediction From Body Dynamics by Bilateral Hand Disentanglement/d0994cbf-d27b-45f6-a350-1ef9d2d99ed2_content_list.json @@ -0,0 +1,1935 @@ +[ + { + "type": "text", + "text": "Diverse 3D Hand Gesture Prediction from Body Dynamics by Bilateral Hand Disentanglement", + "text_level": 1, + "bbox": [ + 174, + 130, + 794, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Xingqun Qi $^{1,4}$ , Chen Liu $^{2}$ , Muyi Sun $^{3}$ , Lincheng Li $^{4}$ , Changjie Fan $^{4}$ , Xin Yu $^{1,2*}$ $^{1}$ AAII, University of Technology Sydney \n $^{2}$ The University of Queensland \n $^{3}$ CRIPAC, NLPR, Institute of Automation, Chinese Academy of Sciences \n $^{4}$ Netease Fuxi AI Lab", + "bbox": [ + 173, + 202, + 802, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{xingqunqi, yenanliu36}@gmail.com, muyi.sun@cripac.ia.ac.cn", + "bbox": [ + 217, + 276, + 746, + 292 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{lilincheng, fanchangjie}@corp.netease.com, xin.yu@uq.edu.au", + "bbox": [ + 217, + 295, + 746, + 309 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8c235fe8833189cba313f653e69c78635c8ab566c1f7c966275ae2063a39de78.jpg", + "image_caption": [ + "Figure 1. Diverse exemplary clips sampled by our method from our newly collected TED Hands Dataset. The vital frames are visualized to demonstrate that the hand gestures change with the upper body dynamics, synchronously. Best view on screen." + ], + "image_footnote": [], + "bbox": [ + 135, + 321, + 828, + 449 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 491, + 313, + 507 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Predicting natural and diverse 3D hand gestures from the upper body dynamics is a practical yet challenging task in virtual avatar creation. Previous works usually overlook the asymmetric motions between two hands and generate two hands in a holistic manner, leading to unnatural results. In this work, we introduce a novel bilateral hand disentanglement based two-stage 3D hand generation method to achieve natural and diverse 3D hand prediction from body dynamics. In the first stage, we intend to generate natural hand gestures by two hand-disentanglement branches. Considering the asymmetric gestures and motions of two hands, we introduce a Spatial-Residual Memory (SRM) module to model spatial interaction between the body and each hand by residual learning. To enhance the coordination of two hand motions wrt. body dynamics holistically, we then present a Temporal-Motion Memory (TMM) module. TMM can effectively model the temporal association between body dynamics and two hand motions. The second stage is built upon the insight that 3D hand predictions should be non-deterministic given the sequential body postures. Thus, we further diversify our 3D hand predictions based on the initial output from the stage one. Concretely, we propose a Prototypical-Memory Sampling Strategy (PSS) to generate the non-deterministic hand gestures by gradient", + "bbox": [ + 75, + 511, + 473, + 875 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "based Markov Chain Monte Carlo (MCMC) sampling. Extensive experiments demonstrate that our method outperforms the state-of-the-art models on the B2H dataset and our newly collected TED Hands dataset. The dataset and code are available at: https://github.com/XingqunQilab/Diverse-3D-Hand-Gesture-Prediction.", + "bbox": [ + 496, + 492, + 893, + 583 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 599, + 632, + 616 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Given a sequence of upper body skeletons, our task aims at predicting natural and diverse 3D hand gestures. Such non-verbal body-hand coordination plays an important role in various virtual avatar scenarios, including human-agent interface [13, 17, 35, 40, 41], co-speech gesture synthesis [5, 20, 24, 46, 47], holoportation [29].", + "bbox": [ + 496, + 626, + 893, + 717 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, it is quite difficult to predict the natural and diverse 3D hand gestures due to three major challenges: (1) Spatially asymmetric motions: Asymmetric motions of two hands have been overlooked by previous works [28], e.g., when one hand moves, the other could be static or moving slowly. (2) Temporal consistency wrt. body dynamics: Predicted sequential hand gestures should be temporally consistent with respect to the body dynamics. (3) Non-deterministic hand prediction: Given the upper body dynamics, various 3D hand gestures can match the body postures rather than a deterministic result. Since the existing dataset has only a few avatar identities, the generated hands", + "bbox": [ + 496, + 719, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author.", + "bbox": [ + 94, + 886, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "4616", + "bbox": [ + 482, + 944, + 516, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "often lack diversity.", + "bbox": [ + 76, + 90, + 210, + 106 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Due to complex body-hand interaction and asymmetric movements of two hands, directly predicting the natural and diverse 3D hand is rather difficult. Therefore, we propose to address the aforementioned challenges in a prediction followed by a diversification paradigm. To be specific, we propose a novel bilateral hand disentanglement based two-stage method, to generate natural and diverse 3D hand gestures from upper body dynamics.", + "bbox": [ + 75, + 108, + 468, + 228 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In the first stage, we aim to predict the natural 3D hand gestures. Our key insight is to establish the bilateral hand disentanglement for asymmetric motions of two hands. We construct two hand-disentangled branches that interact with a body-specific branch to initially predict natural 3D hands. Here, we leverage a single-hand autoencoder to extract each hand feature respectively, thus achieving the effects of two hands disentanglement. Furthermore, we propose a Spatial-Residual Memory (SRM) module to model the spatial relation between the body and each hand via residual learning. Specifically, we employ a spatial memory bank to store the spatial residual deformation representations of each hand. Then, we leverage the current upper body embedding as a query to retrieve the most relevant spatial residual deformation. The queried spatial residual deformation and the synchronized hand embedding vector are used to generate the next step hand representation.", + "bbox": [ + 75, + 229, + 470, + 487 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To ensure the motions of both hands are temporally consistent with the upper body sequence, we present a Temporal-Motion Memory (TMM) module. TMM models the correlation between body dynamics and hand gestures. Similar to SRM, we utilize a temporal memory bank to store the motion features of each hand at the sequence level. Moreover, we employ a motion encoder to acquire the input body dynamics representation, and then use the body dynamics representation as a query to produce temporally consistent hand motion features. In this fashion, we can effectively synchronize hand motions with body dynamics.", + "bbox": [ + 75, + 489, + 468, + 655 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In the second stage, we develop a Prototypical-Memory Sampling Strategy (PSS) to diversify our 3D hand predictions based on the initial prediction at stage one. Here, we leverage an external memory that stores realistic hand prototypes, and then search a prototype that is closest to our initial predicted hands. Once we obtain the prototype, we project it into the feature space. To increase the diversity while preserving the authenticity of generated hand gestures, we perturb the prototype feature via gradient-based Markov Chain Monte Carlo (MCMC) sampling [23]. Specifically, a random noise is first sampled from a Gaussian distribution as a prior perturbation and then we update its posterior via Langevin dynamics based MCMC [4, 27]. Then, the perturbation is concatenated with the prototype feature to produce realistic new hand gestures.", + "bbox": [ + 75, + 657, + 468, + 883 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Moreover, the existing 3D hand prediction dataset [28]", + "bbox": [ + 96, + 885, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "contains less than 10 avatar identities, resulting in insufficient diversity of gestures. Therefore, we newly collect a large-scale 3D hand gestures dataset (dubbed TED Hands) with more than 1.7K avatar identities from in-the-wild scenarios. Our dataset contains around 100 hours of TED talk speeches, enabling research on diverse 3D hand gesture predictions. Extensive experiments conducted on the B2H dataset [28] and our TED Hands dataset demonstrate our method outperforms the state-of-the-art.", + "bbox": [ + 496, + 90, + 890, + 226 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Overall, our contributions are summarized as follows:", + "bbox": [ + 500, + 227, + 854, + 242 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a novel bilateral hand disentanglement based two-stage 3D hand generation method to predict diverse 3D hand gestures from body dynamics in a prediction followed by diversification paradigm.", + "- We present a Spatial-Residual Memory (SRM) module to predict authentic hand poses from disentangled hand representations and a Temporal-Motion Memory (TMM) module to ensure temporal consistency of generated 3D hands.", + "- We design a Prototypical-Memory Sampling Strategy (PSS) to diversify our initial 3D hand prediction, thus obtaining natural and diverse hand gestures.", + "- We collect a new large-scale sequential 3D hand dataset from 1.7K persons' hand gestures, significantly facilitating research on diverse 3D hands generation." + ], + "bbox": [ + 500, + 247, + 890, + 488 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 503, + 640, + 520 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Since our method predicts the 3D hand motions from upper body skeletons, we briefly review the approaches of 3D hand pose estimation and 3D human motion prediction.", + "bbox": [ + 496, + 530, + 890, + 575 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3D hand pose estimation: 3D hand estimation has received impressive attention for its wide applications in virtual reality, augmented reality, and robotics. Recently, parametric 3D hand model MANO [33] and various mocap-captured 3D hand datasets [2,9,26,52] significantly improve the performance of 3D hand pose estimation from the single image [6,18,32,37,49,51]. Among various image-based 3D hand estimation approaches, transformer-based models [10,18,21] have demonstrated outstanding performance. For instance, Li et al. [18] propose an interacting attention graph transformer to estimate two-hand poses from a single image. Shreyas et al. [10] present a hand keypoint based transformer combined with convolutional networks to establish the association among different joints.", + "bbox": [ + 496, + 582, + 890, + 792 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Since our task aims to predict the 3D hand motions from upper body skeletons, these single-image-based methods [10, 18, 21] cannot be directly employed. However, their excellent performance in 3D hand estimation inspires us to model the body-hand interaction via transformer-based architectures. Besides, Ng et al. [28] generate the hand gestures from body dynamics in a holistic manner. As the", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "4617", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/75149e03bc849e65e8e9dc8ef26c726a504a4a47887a94b49003659c1df7a9cd.jpg", + "image_caption": [ + "Figure 2. The pipeline of our proposed method. In stage one, we generate the natural initial 3D hands from sequential upper body skeletons. In stage two, we diversify our 3D hand predictions based on the initial gestures at stage one." + ], + "image_footnote": [], + "bbox": [ + 112, + 90, + 859, + 325 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "asymmetric motions of two hands, their method might produce some unnatural hand gestures. This also motivates us to disentangle two hands in hand pose estimation and then synchronize two-hands motions.", + "bbox": [ + 75, + 377, + 470, + 439 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3D human motion prediction: Predicting human future motions from existing 3D poses has been widely studied [1, 8, 19, 25, 39]. Wang et al. [39] leverage a multi-range transformer that attends learn local-global features for multi-person motion prediction. Bouazizi et al. [1] introduce a multi-layer perception based human motion prediction network to learn spatio-temporal pose relation. Due to the similar nature between 3D human motion prediction and hand pose prediction, these models [1, 8, 19, 25, 39] can be easily adopted as our baselines. Moreover, we notice that memory based networks [3, 42, 43, 48] achieve promising performance in long-sequence modeling tasks. Motivated by this, we introduce external memories into our network to facilitate our long-range hand pose generation.", + "bbox": [ + 75, + 444, + 470, + 656 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Proposed Method", + "text_level": 1, + "bbox": [ + 76, + 666, + 250, + 683 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem Formulation", + "text_level": 1, + "bbox": [ + 76, + 691, + 279, + 705 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a sequence of 3D upper body skeletons $\\mathcal{B} = \\{b^t\\}_{t=0}^T$ , our goal is to predict the natural and diverse 3D hand poses $\\mathcal{H} = \\{h^t\\}_{t=0}^T$ , where $T$ is the sequence length. Specifically, we define each step body skeleton (i.e., collars, shoulders, elbows, and wrists) $b^t \\in \\mathbb{R}^{24}$ as 8 joints. Each joint is represented by a 3D axis-angle representation. Meanwhile, the 3D hand pose at time $t$ , $h^t \\in \\mathbb{R}^{90}$ , is described as 30 joints with 3D axis-angle representation.", + "bbox": [ + 76, + 714, + 468, + 840 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Stage One: Natural Hand Prediction", + "text_level": 1, + "bbox": [ + 76, + 847, + 397, + 863 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Due to complex body-hand interaction and asymmetric motions of two hands, we leverage the bilateral hand disen", + "bbox": [ + 76, + 869, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "tanglement branches and a body-specific branch to generate the natural 3D hands. Specifically, as depicted in Fig. 2 (stage one), our method mainly consists of a Bilateral Hand Disentanglement (BHD) module, a Spatial-Residual Memory (SRM) module, a Temporal-Motion Memory (TMM) module, and a transformer-based backbone. Firstly, we leverage a body encoder to obtain the body features $F_{\\mathcal{B}} = \\{F_{\\mathcal{B}}^{t}\\}_{t=0}^{T}$ , where $F_{\\mathcal{B}}^{t} \\in \\mathbb{R}^{1 \\times C}$ denotes a body feature at time $t$ , and $C$ is the feature dimension. Then, the body features are disentangled by BHD to acquire the single hand features $F_{\\mathcal{SH}} = \\{F_{\\mathcal{SH}}^{t}\\}_{t=0}^{T}$ , where $F_{\\mathcal{SH}}^{t} \\in \\mathbb{R}^{1 \\times C}$ . Considering the asymmetry motions of two hands, we exploit SRM to model the spatial interaction between the body and each hand, respectively. Besides, we further develop TMM to keep the two hand gestures temporal consistent with body dynamics.", + "bbox": [ + 496, + 377, + 893, + 609 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Bilateral Hand Disentangle Module: Due to the asymmetric motions of two hands, we employ a single hand autoencoder as the feature extractor to disentangle two hands. We firstly train an autoencoder on 3D single hands. As shown in Fig. 3 (a), we then utilize a Multilayer Perceptron (MLP) to project the body features into the single hand features $F_{\\mathcal{SH}}$ . To ensure these single hand features represent each disentangled hand separately, we conduct the feature level and 3D representation level constraints by the single hand autoencoder, as follows:", + "bbox": [ + 496, + 628, + 893, + 779 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {d i s} = \\left\\| \\widetilde {F _ {S H} ^ {t}} - F _ {\\mathcal {S H}} ^ {t} \\right\\| _ {1} + \\left\\| \\mathbb {D} \\left(\\widetilde {F _ {S H} ^ {t}}\\right) - \\mathbb {D} \\left(F _ {\\mathcal {S H}} ^ {t}\\right) \\right\\| _ {1}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 790, + 890, + 819 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\widetilde{F_{SH}^{t}}$ denotes reconstructed hand feature at time $t$ , and $\\mathbb{D}$ is the pre-trained decoder.", + "bbox": [ + 498, + 830, + 890, + 864 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Spatial-Residual Memory Module: After obtaining the disentangled single hand features, we introduce a Spatial-", + "bbox": [ + 498, + 869, + 890, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "4618", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/78ba7a6f3e4d99372ca280f6dc2b48c3d5e6db1cd244048e13824fefb5e5deb6.jpg", + "image_caption": [ + "Figure 3. Details of three sub-modules in the first stage. For brevity, we only show them in terms of single-branch view." + ], + "image_footnote": [], + "bbox": [ + 99, + 90, + 614, + 209 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/92977298826388df9bc0781c682cf7bdc2383e230e38dad29dd3ca67967c258f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 617, + 95, + 864, + 209 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Residual Memory (SRM) module to model the spatial interaction between the body and each hand by residual learning. As illustrated in Fig. 3 (b), we leverage a spatial memory bank to store the spatial residual deformation representation between the current hand feature and the next step hand feature. Initially, each slot of the spatial memory bank is randomized as $m_j \\in \\mathbb{R}^{1 \\times C}$ , where $j$ denotes slot index. To model the body-hand correlation, the current body feature is exploited as a query to retrieve the most relevant memory slot by calculating the cosine similarity.", + "bbox": [ + 75, + 253, + 468, + 405 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In particular, we represent the relevance between the query and memory slots via cosine similarity. Then we leverage the argmax operation to acquire the most relevant memory slot $m_r$ . Intuitively, the retrieved most relevant memory slot is leveraged as the spatial residual deformation between the current feature and the next step hand feature. However, it is intractable for argmax operation to back-propagate gradients. Thus, we conduct the softmax operation on the above calculated cosine similarity matrix to obtain the slot-wise affinity matrix. Then we acquire the learnable spatial residual deformation $F_{\\mathcal{SH}}^{\\Delta t}$ by aggregation between the slot-wise affinity matrix and each memory slot. We apply the above reading process to allow gradient back-propagation. In the training phase, we utilize the current hand feature to update the retrieved memory slot as $m_r = \\gamma m_r + (1 - \\gamma)F_{\\mathcal{SH}}^t$ , where $\\gamma = 0.8$ in our experiments.", + "bbox": [ + 75, + 406, + 468, + 648 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Different from obtaining the next hand feature by simple addition between the spatial residual deformation and current hand feature, we claim the spatial residual deformation refers to local spatial dependency from the current feature to the next time feature. This spatial dependency $S$ is formulated as:", + "bbox": [ + 75, + 648, + 468, + 736 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nS _ {t} ^ {t + 1} = \\operatorname {s o f t m a x} \\left(F _ {\\mathcal {S H}} ^ {\\Delta t ^ {\\prime}} \\otimes F _ {\\mathcal {S H}} ^ {t}\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 160, + 743, + 468, + 766 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\otimes$ indicates matrix multiplication, and $^{\\prime}$ indicates the transpose operation. With the help of the spatial dependency, the next step hand feature is represented as $F_{\\mathcal{SH}}^{t + 1} = F_{\\mathcal{SH}}^{t} + F_{\\mathcal{SH}}^{t}\\otimes S_{t}^{t + 1}$ . Through SRM, we obtain the spatial-enhanced single-hand feature.", + "bbox": [ + 76, + 773, + 468, + 849 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Temporal-Motion Memory Module: We further propose a Temporal-Motion Memory (TMM) module to ensure the single hand motions consistent with the body dynamics,", + "bbox": [ + 75, + 854, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "globally. As depicted in Fig. 3 (c), we develop a motion encoder to obtain the sequence-aware body motion embedding as $F_{\\mathcal{B}\\mathcal{M}} \\in \\mathcal{R}^{T \\times 1}$ . Here, we use body motion embedding to represent temporal changes among body skeletons in a sequence. Then, we leverage the body motion embedding as a query to retrieve the most consistent single hand motion embedding $F_{\\mathcal{S}\\mathcal{H}\\mathcal{M}} \\in \\mathcal{R}^{T \\times 1}$ stored in a temporal memory bank. The initialization and reading processes of the temporal memory bank are similar to SRM. We utilize the body motion embedding to update the retrieved slot of the temporal memory bank in the same manner as SRM.", + "bbox": [ + 496, + 253, + 890, + 419 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Afterward, we utilize the retrieved hand motion embedding to boost the body-hand temporal consistency. Specifically, we leverage the retrieved temporal embedding to represent the temporal correlation of hand gesture changes in a sequence. Then, the temporal-consistent enhanced sequential hand gestures are attained by: $F_{\\mathcal{SH}} = F_{\\mathcal{SH}} + F_{\\mathcal{SH}} \\odot \\text{softmax}(F_{\\mathcal{SHM}})$ , where $\\odot$ means dot product.", + "bbox": [ + 496, + 421, + 890, + 527 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Transformer-based Backbone: As illustrated in Fig. 2 (stage one), to further enhance the body-hand interaction, we construct the bilateral hand disentanglement branches that interact with a body-specific branch to predict 3D hands. In particular, we introduce a body-specific transformer to generate body features as query $Q$ . Then, through 3 times Multi-Head Attention (MHA) [38], we use $Q$ to match the key features $K$ and value features $V$ in each hand transformer branch, respectively.", + "bbox": [ + 496, + 532, + 890, + 669 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Furthermore, we feed the concatenation of bilateral hand features into an MLP, thus obtaining the merged two-hand features. Similarly, we conduct 3 times MHA in the transformer-based decoder. This encourages the merged two-hand features to be more temporal consistent with body dynamics, holistically. At the end of the decoder, we adopt two fully-connected layers to obtain the 3D two hands sequence. Additionally, similar to [28], we employ a motion discriminator to ensure the natural and continuous initial prediction at stage one.", + "bbox": [ + 496, + 670, + 890, + 821 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Stage Two: Diverse Sampling", + "text_level": 1, + "bbox": [ + 500, + 830, + 763, + 848 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We leverage a Prototypical-Memory Sampling Strategy (PSS) to achieve hands diversification based on our initial predictions from stage one. Specifically, we first con", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "4619", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "struct a prototypical memory to store the realistic two hands prototypes. Then, we obtain the retrieved realistic prototype representation based on the initial prediction at stage one. Meanwhile, as shown in Fig. 2 (stage two), we propose a sampling header to obtain the hand-informative perturbation via gradient-based Markov Chain Monte Carlo (MCMC) sampling. Finally, we concatenate the retrieved realistic hand prototype representation and perturbation to generate the diverse 3D two hands.", + "bbox": [ + 75, + 90, + 472, + 227 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Hands Prototypical Memory Construction: Inspired by [50], we reformulate the two hands diversification as a generation task. Instead of directly sampling the prior of the perturbation from the isotropic Gaussian distribution [7, 11, 16, 36], we assume the sampling space follows a learnable realistic prior distribution [30, 31, 50]. Since the existing 3D hand prediction dataset is noisy due to the automated annotation process, we propose a prototypical memory bank to store the realistic hand prototype representations encoded from real 3D hands. These 3D hands are captured from a studio-based mocap-captured dataset, named BEAT [22]. The reading and updating strategies of hands prototypical memory are the same as TMM.", + "bbox": [ + 75, + 233, + 472, + 431 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Gradient-based MCMC Sampling: We exploit the retrieved hand prototype representation concatenated with sampled perturbation vector $w$ to predict the diverse hand gestures. Given the observed 3D two hands $h \\in \\mathbb{R}^{90}$ , the $\\tilde{h}$ is expressed as:", + "bbox": [ + 75, + 436, + 472, + 513 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {h} = R _ {\\theta} (h, w) + \\epsilon , w \\sim p _ {\\alpha} (w), \\epsilon \\sim \\mathcal {N} (0, \\sigma_ {\\epsilon} ^ {2} I), \\qquad (3)\n$$\n", + "text_format": "latex", + "bbox": [ + 104, + 523, + 468, + 544 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $p_{\\alpha}(w)$ is the prior distribution of perturbation with parameters $\\alpha$ , and $\\epsilon \\sim \\mathcal{N}(0, \\sigma_{\\epsilon}^{2}I)$ is the observation noise of hand gestures with $\\sigma_{\\epsilon}$ being given, $R_{\\theta}$ is the generation model with parameters $\\theta$ .", + "bbox": [ + 75, + 556, + 468, + 614 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Inspired by [11], we leverage an MLP-based sampling header $S_{\\alpha}(w)$ to model the diversification sampling process, as illustrated in Fig. 2 (stage two). The prior distribution of perturbation is initialized from an isotropic Gaussian reference distribution, expressed as:", + "bbox": [ + 75, + 617, + 468, + 694 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\alpha} (w) \\propto e x p \\left[ - S _ {\\alpha} (w) - \\frac {1}{2 \\sigma_ {w} ^ {2}} \\| w \\| ^ {2} \\right], \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 137, + 704, + 468, + 739 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where the $M_{\\alpha}(w) = S_{\\alpha}(w) + \\frac{1}{2\\sigma_w^2}\\| w\\|^2$ is defined as the whole sampling function, and $\\alpha$ is the learnable parameters of sampling header. The hyperparameter $\\sigma_w$ denotes the standard deviation. For notation simplicity, let $\\beta = \\{\\theta ,\\alpha \\}$ . For the $i$ th sample in a training mini-batch with size $n$ , the log-likelihood function of $\\beta$ is defined as:", + "bbox": [ + 75, + 752, + 468, + 845 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL (\\beta) = \\sum_ {i = 1} ^ {n} \\log \\left[ \\int p _ {\\alpha} \\left(w _ {i}\\right) p _ {\\theta} \\left(\\tilde {h} _ {i} \\mid h _ {i}, w _ {i}\\right) d w _ {i} \\right]. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 114, + 858, + 468, + 897 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Thus the gradient of $L(\\beta)$ is computed as:", + "bbox": [ + 500, + 90, + 781, + 106 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\bigtriangledown L (\\beta) = E _ {p _ {\\beta (w | \\tilde {h}, h)}} \\left[ \\bigtriangledown_ {\\alpha} \\operatorname {l o g p} _ {\\alpha} (w) + \\bigtriangledown_ {\\theta} \\operatorname {l o g p} _ {\\theta} (\\tilde {h} | h, w) \\right]. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 501, + 109, + 890, + 152 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The intractable expectation term $E_{p}(\\cdot)$ in Eq. (6) is approximately solved by a gradient-based MCMC (Langevin dynamics) [4, 27]. In particular, the initial state of perturbation $p_0(w)$ is sampled from the Gaussian distribution. Through MCMC, the perturbation from the prior distribution and posterior distribution are represented as $\\{w_i^-\\}$ and $\\{w_i^+\\}$ , respectively. The detailed calculation process is in [27]. Therefore, the gradients of the generation model and sampling header are updated by:", + "bbox": [ + 498, + 157, + 893, + 296 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\nabla_ {\\theta} R _ {\\theta} = \\frac {1}{n} \\sum_ {i = 1} ^ {n} \\left[ \\frac {1}{\\sigma_ {\\epsilon} ^ {2}} \\left(\\tilde {h} _ {i} - R _ {\\theta} \\left(h _ {i}, w _ {i} ^ {+}\\right)\\right) \\nabla_ {\\theta} R _ {\\theta} \\left(h _ {i}, w _ {i} ^ {+}\\right) \\right], \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 508, + 300, + 890, + 354 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\nabla_ {\\alpha} S _ {\\alpha} = \\frac {1}{n} \\sum_ {i = 1} ^ {n} \\left[ \\nabla_ {\\alpha} S _ {\\alpha} \\left(w _ {i} ^ {-}\\right) \\right] - \\frac {1}{n} \\sum_ {i = 1} ^ {n} \\left[ \\nabla_ {\\alpha} S _ {\\alpha} \\left(w _ {i} ^ {+}\\right) \\right]. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 508, + 358, + 890, + 397 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Objective Functions", + "text_level": 1, + "bbox": [ + 500, + 409, + 691, + 425 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In stage one, we apply the following loss functions to constrain the initial prediction process of hand gestures.", + "bbox": [ + 498, + 431, + 890, + 463 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Reconstruction Loss: We use the ground truth to supervise the predicted two hands as $\\mathcal{L}_{rec} = \\left\\| \\mathcal{H} - \\tilde{\\mathcal{H}} \\right\\|_1$ , where $\\tilde{\\mathcal{H}}$ denotes generated hands.", + "bbox": [ + 498, + 469, + 890, + 521 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Perceptual Loss: Inspired by [15], we leverage the studio-based 3D hands dataset BEAT to pre-train an MLP-based autoencoder as a feature extractor $\\phi(\\cdot)$ . We utilize the $L1$ loss to constrain the difference between the extracted features of $\\mathcal{H}$ and $\\tilde{\\mathcal{H}}$ , as formulated: $\\mathcal{L}_{perc} = \\left\\| \\phi(\\mathcal{H}) - \\phi(\\tilde{\\mathcal{H}}) \\right\\|_1$ .", + "bbox": [ + 498, + 527, + 890, + 628 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Adversarial Learning: Following the configuration of [28], we employ the adversarial training loss as:", + "bbox": [ + 500, + 632, + 890, + 662 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {a d v} = \\mathbb {E} _ {\\mathcal {H}} \\left[ \\log D (\\mathcal {H}) \\right] + \\mathbb {E} _ {\\mathcal {B}} \\left[ \\log \\left(1 - (G (\\mathcal {B}))\\right) \\right], \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 667, + 890, + 686 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $D$ denotes the discriminator and $G$ means hands generator. Finally, the overall objective in stage one is:", + "bbox": [ + 498, + 690, + 890, + 720 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {G} \\max _ {D} \\mathcal {L} _ {\\text {t o t a l}} ^ {\\text {s t a g e 1}} = \\mathcal {L} _ {\\text {r e c}} + \\mathcal {L} _ {\\text {a d v}} + \\mathcal {L} _ {\\text {p e r c}} + 0. 5 \\mathcal {L} _ {\\text {d i s}}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 503, + 724, + 890, + 748 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{dis}$ denotes disentanglement constraint in Eq. ((1)).", + "bbox": [ + 500, + 752, + 888, + 767 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In the second stage, the overall objective to train our model is defined as follows:", + "bbox": [ + 498, + 768, + 890, + 795 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {t o t a l}} ^ {\\text {s t a g e 2}} = \\left\\| h - R _ {\\theta} \\left(h, w ^ {+}\\right) \\right\\| _ {1}, \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 589, + 800, + 890, + 821 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $w^{+}$ is the posterior distribution of the perturbation. We conduct the frame-level diversification based on the initial prediction at stage one. To ensure temporal smoothness, we further apply temporal smoothness [45] to the diversified 3D hand gestures as a post processing.", + "bbox": [ + 498, + 824, + 890, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "4620", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/deb86d155219d00b379e2575ab74ff74134dc5930a7954b4082c69d5c8771052.jpg", + "table_caption": [ + "Table 1. Comparison with the state-of-the-art methods on B2H dataset and our proposed TED Hands dataset of the first stage initial prediction. $\\downarrow$ indicates the lower the better." + ], + "table_footnote": [], + "table_body": "
MethodsB2H Dataset [28]TED Hands Dataset
L2↓FHD↓MPJRE↓L2↓FHD↓MPJRE↓
Body2Hands [28]CVPR'213.7601.10313.1482.5511.17411.371
MRT [39]NeurIPS'213.6340.97312.5762.3250.87710.314
BTM [8]WACV'233.6571.26312.6962.3501.11110.440
LTD [25]ICCV'193.7551.07313.3152.4821.36711.078
MotionMixer [1]IJCAI'223.6160.98612.7022.3240.91010.427
SPGSN [19]ECCV'223.6560.96212.7572.4350.99010.887
Ours (stage one)3.4200.47111.4062.0370.2588.888
", + "bbox": [ + 135, + 122, + 834, + 253 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/7aa3bf0e42316c3174021ff0264a67d9aa405d521370c5dcc8c9e0dc99bfa59d.jpg", + "table_caption": [ + "Table 2. Sampling experiment results on B2H dataset. $\\downarrow$ indicates the lower the better, and $\\uparrow$ indicates the higher the better. $\\pm$ means 95% confidence interval." + ], + "table_footnote": [], + "table_body": "
MethodsFHD↓Diversity↑
Body2hands [28] w/ PSS2.5040.497±0.028
MRT [39] w/ PSS1.9820.698±0.031
BTM [8] w/ PSS2.3790.703±0.038
LTD [25] w/ PSS1.8930.577±0.028
MotionMixer [1] w/ PSS2.1690.869±0.055
SPGSN [19] w/ PSS2.0040.874±0.046
Ours w/ VAE [36]1.6171.001±0.061
Ours (stage two)1.2391.324±0.066
", + "bbox": [ + 84, + 313, + 460, + 444 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 467, + 209, + 484 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Datasets and Experimental Setting", + "text_level": 1, + "bbox": [ + 76, + 492, + 380, + 508 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "B2H Dataset: The B2H dataset [28] is automatically annotated by a monocular-based 3D pose estimation model [44], including the gestures of 8 speakers from in-the-wild talk show videos. In the original B2H dataset, there are more than 139K sequences. Each sequence includes 64 frames, with 32 frames overlapping between every two sequences. However, due to the noisiness and unavailable videos, we obtain 120,188 sequences finally. In our work, we adopt the same division criteria as [28] to split the training and testing dataset.", + "bbox": [ + 75, + 515, + 468, + 667 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "TED Hands Dataset: Due to the limited avatar identities in the existing 3D hand prediction dataset, we newly collect a large-scale 3D hands dataset (dubbed TED Hands) based on the TED Gesture [46, 47]. The original TED Gesture dataset only contains 10 upper body joints without elaborate fingers of two hands. Hence, we leverage a state-of-the-art 3D pose estimator FrankMocap [34] to extract the whole body-hand joints as pseudo ground truth from the video links provided by TED Gesture. Concretely, each joint of our dataset is normalized as the 3D axis-angle representation in a fixed kinematic structure [33]. In this fashion, our dataset is invariant to root joint motion and body shape. Finally, we acquired the 134,456 sequences from 1,755 different speakers, with 99.6 hours of TED talking speeches. Each sequence includes 64 frames without over", + "bbox": [ + 75, + 672, + 470, + 901 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/ebeacb6d561a4291537fac960d0f236916083a9779bbe4b130157238b07d10c8.jpg", + "table_caption": [ + "Table 3. Sampling experiment results on our proposed TED Hands dataset. $\\downarrow$ indicates the lower the better, and $\\uparrow$ indicates the higher the better. $\\pm$ means ${95}\\%$ confidence interval." + ], + "table_footnote": [], + "table_body": "
MethodsFHD↓Diversity↑
Body2hands [28] w/ PSS2.0052.705±0.153
MRT [39] w/ PSS1.1884.954±0.190
BTM [8] w/ PSS1.2243.632±0.150
LTD [25] w/ PSS1.3852.851±0.101
MotionMixer [1] w/ PSS1.6133.487±0.208
SPGSN [19] w/ PSS1.5653.812±0.219
Ours w/ VAE [36]1.0334.018±0.190
Ours (stage two)0.9386.426±0.300
", + "bbox": [ + 506, + 313, + 883, + 444 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "lap. We randomly spit the dataset into the $70\\%$ training set, $10\\%$ validation set, and $20\\%$ testing set. Please refer to the supplementary material for more details.", + "bbox": [ + 498, + 468, + 890, + 513 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details: Our model is implemented on the PyTorch platform with 2 NVIDIA RTX 2080Ti GPUs. We train the model utilizing Adam optimizer with an initial learning rate of 0.003. The whole training takes 30 epochs with a batch size of 64. We set $\\sigma_{\\epsilon} = 1$ in Eq. (3), and $\\sigma_w = 1$ in Eq. (4).", + "bbox": [ + 496, + 520, + 890, + 611 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation Metrics: To fully evaluate the naturalness of initial predictions at stage one and the diversity of sampled hand gestures at stage two, we employ various metrics:", + "bbox": [ + 496, + 617, + 893, + 662 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- $L2$ Distance: Distance between the generated whole two hand poses and pseudo ground truth.", + "- FHD: Inspired by FGD [46, 47], we propose a hand-specific metric (named FHD) to measure the Fréchet distance between the features of generated hands and pseudo ground truth. The feature extractors of FHD are pretrained by B2H and TED Hands datasets, respectively.", + "- MPJRE: We leverage the Mean Per Joint Rotation Error [○] (MPJRE) [14] to measure the absolute distance between predicted 3D representation joints and pseudo ground truth.", + "- Diversity: To verify the diversity of sampled hand gestures, we calculate the average feature distance between 500 random combined sequential pairs [20, 24]. The feature extractor is the same as FHD." + ], + "bbox": [ + 500, + 665, + 890, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "4621", + "bbox": [ + 480, + 944, + 513, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/2290dbd9d564554c0fe51b067396e5daa3c2fbab229283564ed2f0b99ad88726.jpg", + "table_caption": [ + "Table 4. Ablation study on different loss functions and different components of the proposed method. $\\downarrow$ indicates the lower the better. ✓ indicates the employment of a certain module or loss function. # means the temporal-motion memory module is adopted before the spatial-residual memory module. † denotes the weights of the two hands transformers are shared." + ], + "table_footnote": [], + "table_body": "
Model VariationsB2H Dataset [28]TED Hands Dataset
BaselineFull Model\\( \\mathcal{L}_{dis} \\)\\( \\mathcal{L}_{perc} \\)SRMTMML2 ↓FHD ↓MPJRE ↓L2 ↓FHD ↓MPJRE ↓
✓3.6501.09112.6902.3660.97710.531
✓3.6040.77312.4532.3030.73110.250
✓✓3.5520.68212.0372.2160.5959.786
✓✓3.5630.65712.0852.2610.69910.026
✓✓✓3.5040.64011.8282.1610.4959.508
✓✓✓✓3.4570.58011.6872.1000.3939.209
#✓✓✓✓✓3.4840.61411.7582.1240.4639.311
†✓✓✓✓✓3.4760.59811.7482.1560.3809.467
✓✓✓✓✓3.4200.47111.4062.0370.2588.888
", + "bbox": [ + 114, + 136, + 854, + 292 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Quantitative Results", + "text_level": 1, + "bbox": [ + 76, + 309, + 272, + 325 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparisons with the state-of-the-art: We compare our method with the pioneering 3D hands prediction work, named Body2hands [28]. Moreover, to fully verify the superiority of our method, we implement various state-of-the-art (SOTA) human motion prediction models: MTR [39], BTM [8], LTD [25], MotionMixer [1], and SPGSN [19]. For fair comparisons, all methods are implemented by source codes or pre-trained models released by authors. Since the above counterparts are designed without the diversification setting, the comparison is divided into two parts.", + "bbox": [ + 75, + 335, + 470, + 487 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In the first part, we leverage our stage one initial prediction to compare with other competitors. We adopt the $L2$ distance, FHD, and MPJRE to provide a well-rounded view of comparisons. As reported in Tab. 1, our method outperforms all the counterparts by a large margin. Remarkably, our method achieves the lowest FHD and MPJRE sores on both datasets. Concretely, on FHD scores of the TED Hands dataset, our method performs even $70.6\\%$ lower than the optimal results of other competitors (e.g., $(0.877 - 0.258) / 0.877 \\approx 70.6\\%$ ).", + "bbox": [ + 75, + 489, + 468, + 641 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To demonstrate the effectiveness of the diversification process in our method, we compare the diversified results based on the various predictions from above mentioned competitive methods. Meanwhile, we replace our MCMC-based sampling strategy with CVAE [36] to diversify our initial prediction at stage one. We exploit the FHD and Diversity metrics in the second part. As shown in Tab. 2 and Tab. 3, our method achieves superior performance from the perspective of diversity. Although the FHD is slightly worse than stage one due to the sampled perturbation, our method still achieves the optimal result. Compared with CVAE, our method effectively avoids the potential posterior collapse problem [12]. Moreover, we observe that the diversity scores on our TED Hands dataset are much higher than the B2H dataset with all the counterparts. It applies that our newly collected TED Hands dataset includes more diverse hand gestures.", + "bbox": [ + 75, + 643, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ablation Study: We further conduct the ablation study based on stage one to verify the effectiveness of each module and different loss functions, as indicated in Tab. 4. The baseline model is implemented by a simple transformer-based pipeline without bilateral hand branches. Our full model adopts the bilateral hand branches interacting with a body-specific transformer to produce the 3D hand gestures.", + "bbox": [ + 496, + 309, + 893, + 416 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As shown in Tab. 4, all combinations of the different loss functions and components have positive impacts on 3D hand predictions. The most complete combination attains the best results. Even though we directly construct the bilateral branches without disentanglement constraints (i.e., $\\mathcal{L}_{dis}$ ) as full model, our method achieves comparable performance against the simple baseline. This indicates the global body-hand interaction are effectively modeled by bilateral hand transformers and a body-specific transformer. Then, we observe that after adding the loss functions $\\mathcal{L}_{dis}$ and $\\mathcal{L}_{perc}$ , the performance of our method is significantly improved, especially in MPJRE scores on both datasets (e.g., $10.250 \\rightarrow 9.508$ on TED Hands).", + "bbox": [ + 496, + 416, + 893, + 611 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To verify the effectiveness of SRM and TMM, we conduct plenty of experiments on both datasets. As reported in Tab. 4, when we first employ the SRM, our method achieves the lower $L2$ distance and FHD scores on both datasets. Then, after adding TMM, our method achieves the best performance. This result proves that TMM effectively models the body-hand temporal association. Besides, we find that when TMM is adopted before SRM, the model performance decreases slightly (the third row from bottom to top in Tab. 4). This corresponds to both TMM and transformer-based backbone (i.e. body-transformer, bilateral hand branches) focus on modeling the body-hand temporal correlation. Both of them encourage the two hands to be more temporal consistent with body dynamics. Employing the SRM between them leads to worse spatial-temporal modeling for body-hand interaction.", + "bbox": [ + 496, + 613, + 893, + 853 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Moreover, we conduct experiments that the parameter weights of bilateral hand transformers are shared. As shown in Tab. 4 (the second row from bottom to top), the per", + "bbox": [ + 496, + 854, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "4622", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5fc72cec39abbb050f84fae479cd09eed107d4fa7638467cc8fad837aafaccd7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 109, + 87, + 181, + 150 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1558c91852efe02a108b243696baf43346c23f9f2ac4359a39ffb8a9764c4a21.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 183, + 88, + 256, + 148 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f15a464f111ecb454ead8f604c3acf7dba97f5691f7f79e9f25a8ef12975004d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 259, + 88, + 330, + 148 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": 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"image_caption": [ + "(a) GT" + ], + "image_footnote": [], + "bbox": [ + 109, + 215, + 181, + 276 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/393206eb6fc1eaa22a646e58a93e3e0c4078cdc23f126b251979fae62df784cc.jpg", + "image_caption": [ + "(b) Body2hands" + ], + "image_footnote": [], + "bbox": [ + 183, + 215, + 256, + 276 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f07b9788321ea595118d0fd06af8bd840ce6405821a6eb9388230e9055050ad4.jpg", + "image_caption": [ + "(c) BTM" + ], + "image_footnote": [], + "bbox": [ + 259, + 215, + 330, + 276 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d05db83f94cfea742ccd4d35552dbea83171ce8290039ac739bcaed2fa74ddd4.jpg", + "image_caption": [ + "(d) MRT" + ], + "image_footnote": [], + "bbox": [ + 333, + 215, + 405, + 276 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/dd207b3dec3f5cf64b33fbfde1845e0fd29c533ec47bd1bce5bd2a7a637cdcbc.jpg", + "image_caption": [ + "(e) LTD" + ], + "image_footnote": [], + "bbox": [ + 408, + 215, + 478, + 276 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b52b50db39dac9f29742cdc1c2c8f6f0726e36389bfa98ba46fc2beac6fae602.jpg", + "image_caption": [ + "(f) MotionMixer" + ], + "image_footnote": [], + "bbox": [ + 480, + 215, + 553, + 276 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0371e0ce936f7a7b3d399f3ad39a7f7a38dbb180b744ec3a5ded4898c91db40e.jpg", + "image_caption": [ + "(g) SPGSN" + ], + "image_footnote": [], + "bbox": [ + 555, + 215, + 627, + 276 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/41fc0f062c0403672db79fc89c731d583edfa617f6dfbd1125005c303c26b4ee.jpg", + "image_caption": [ + "(h) Ours (h) Ours (h) Ours (w/o Sampling) (w/ Sampling) (w/ Sampling)" + ], + "image_footnote": [], + "bbox": [ + 630, + 215, + 700, + 276 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f91978b5ca83bbdce43821324824f3a655b1ad45c5a318b92462e301dd1a9659.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 704, + 215, + 776, + 276 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f4c8ce356583382e8bb654d844f519e8ebcfcf659a3ff9b912e1fc68a8dae4c7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 779, + 215, + 851, + 276 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/78ec315dcbf9d040db00935726f7602563e4afd77f184d05ecdffb77e7b25040.jpg", + "image_caption": [ + "Figure 4. Visualization of our predicted 3D hand gestures against various state-of-the-art methods [1,8,19,25,28,39]. From top to bottom, samples of the first row are from the B2H dataset, and the others are from our TED Hands dataset. Best view on screen.", + "Figure 5. User study on the motion naturalness, smoothness, and body-hand temporal consistency. $\\uparrow$ indicates the higher the better." + ], + "image_footnote": [], + "bbox": [ + 96, + 349, + 449, + 463 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "formance is decreased due to the spatial-temporal interaction between the body and single-hand-specific branch being merged here. This supports our key technical insight on bilateral hand disentanglement. Additionally, to verify the practical ability of our method, we conduct experiments on model complexity and inference time, more details are presented in the supplementary material.", + "bbox": [ + 75, + 511, + 468, + 617 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Qualitative Evaluation", + "text_level": 1, + "bbox": [ + 76, + 628, + 287, + 645 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "User Study: To further analyze the visual quality of the predicted 3D hand gestures by different methods, we recruit 15 volunteers to participate in the user study. We take the naturalness, smoothness, and body-hand temporal consistency as three evaluation perceptions and the range of grades is from 0 to 5 (the higher, the better). The statistical results are reported in Fig. 5. Our method shows the best performance in all three metrics. Especially in the naturalness and body-hand temporal consistency, our method achieves remarkable advantages among all the methods due to the body-hand interaction modeling by SRM and TMM.", + "bbox": [ + 75, + 652, + 468, + 819 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Visualization: To fully verify the performance of our method, we show the visualization of generated 3D hands from the first and second stages, respectively. As depicted in Fig. 4, we compare our initial predictions (from stage one) with various SOTA approaches. The avatars are ren-", + "bbox": [ + 75, + 824, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "dered from ground truth speakers in B2H and TED Hands datasets. We observe that Body2hands, BTM, and LTD generate unreasonable hand gestures (e.g., in the third row of Body2hands, left-hand gestures of avatar). MRT, Motion-Mixer, and SPGSN predict the natural results, but the finger gestures are less consistent with the upper body dynamics. In contrast, our method successfully predicts the perceptually convincing 3D hand gestures from the body dynamics. This supports our key insight to build the bilateral hand disentanglement branches since the asymmetric motions of two hands. We further visualize the diversification results generated by our method at stage two. As shown in Fig. 1 and Fig. 4, with the same upper body dynamics as input, our method obtains the natural and diverse 3D hand gestures on B2H and TED Hands datasets, respectively. Please refer to the supplementary material for more visualization results.", + "bbox": [ + 496, + 351, + 893, + 593 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 606, + 617, + 622 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we present a novel bilateral hand disentanglement based two-stage method towards natural and diverse 3D hand prediction from body dynamics. In the first stage, upon the bilateral hand branches, we fully take advantage of the spatial-temporal body-hand interaction for generating natural initial 3D hand gestures. Then, in the second stage, we further diversify our natural initial 3D hand gestures by gradient-based markov chain monte carlo sampling. Extensive experiments conducted on B2H and our newly collected TED Hands datasets demonstrate the superiority of our method. As our method aims at generating diverse 3D avatar hand postures, in future work, we will investigate sampling diverse 3D hand gestures with temporal smoothness, instead of frame-wise sampling.", + "bbox": [ + 496, + 631, + 890, + 843 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. This research is funded in part by ARC-Discovery grant (DP220100800 to XY) and ARC-DECRA grant (DE230100477 to XY).", + "bbox": [ + 498, + 849, + 890, + 895 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "4623", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 106 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Arij Bouazizi, Adrian Holzbock, Ulrich Kressel, Klaus Dietmayer, and Vasileios Belagiannis. Motionmixer: Mlp-based 3d human body pose forecasting. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 813-822, 2019. 2" + ], + "bbox": [ + 78, + 90, + 468, + 287 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "4626", + "bbox": [ + 482, + 945, + 516, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Diverse 3D Hand Gesture Prediction From Body Dynamics by Bilateral Hand Disentanglement/d0994cbf-d27b-45f6-a350-1ef9d2d99ed2_model.json b/2023/Diverse 3D Hand Gesture Prediction From Body Dynamics by Bilateral Hand Disentanglement/d0994cbf-d27b-45f6-a350-1ef9d2d99ed2_model.json new file mode 100644 index 0000000000000000000000000000000000000000..1ea6b6e5dc36c10a5d5f5a7a545cdf30de96f9eb --- /dev/null +++ b/2023/Diverse 3D Hand Gesture Prediction From Body Dynamics by Bilateral Hand Disentanglement/d0994cbf-d27b-45f6-a350-1ef9d2d99ed2_model.json @@ -0,0 +1,2609 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.176, + 0.131, + 0.795, + 0.177 + ], + "angle": 0, + "content": "Diverse 3D Hand Gesture Prediction from Body Dynamics by Bilateral Hand Disentanglement" + }, + { + "type": "text", + "bbox": [ + 0.174, + 0.203, + 0.803, + 0.274 + ], + "angle": 0, + "content": "Xingqun Qi\\(^{1,4}\\), Chen Liu\\(^{2}\\), Muyi Sun\\(^{3}\\), Lincheng Li\\(^{4}\\), Changjie Fan\\(^{4}\\), Xin Yu\\(^{1,2*}\\) \n\\(^{1}\\)AAII, University of Technology Sydney \n\\(^{2}\\)The University of Queensland \n\\(^{3}\\)CRIPAC, NLPR, Institute of Automation, Chinese Academy of Sciences \n\\(^{4}\\)Netease Fuxi AI Lab" + }, + { + "type": "text", + "bbox": [ + 0.218, + 0.277, + 0.748, + 0.293 + ], + "angle": 0, + "content": "{xingqunqi, yenanliu36}@gmail.com, muyi.sun@cripac.ia.ac.cn" + }, + { + "type": "text", + "bbox": [ + 0.218, + 0.296, + 0.748, + 0.31 + ], + "angle": 0, + "content": "{lilincheng, fanchangjie}@corp.netease.com, xin.yu@uq.edu.au" + }, + { + "type": "image", + "bbox": [ + 0.137, + 0.322, + 0.83, + 0.45 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.451, + 0.894, + 0.48 + ], + "angle": 0, + "content": "Figure 1. Diverse exemplary clips sampled by our method from our newly collected TED Hands Dataset. The vital frames are visualized to demonstrate that the hand gestures change with the upper body dynamics, synchronously. Best view on screen." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.492, + 0.314, + 0.508 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.512, + 0.474, + 0.875 + ], + "angle": 0, + "content": "Predicting natural and diverse 3D hand gestures from the upper body dynamics is a practical yet challenging task in virtual avatar creation. Previous works usually overlook the asymmetric motions between two hands and generate two hands in a holistic manner, leading to unnatural results. In this work, we introduce a novel bilateral hand disentanglement based two-stage 3D hand generation method to achieve natural and diverse 3D hand prediction from body dynamics. In the first stage, we intend to generate natural hand gestures by two hand-disentanglement branches. Considering the asymmetric gestures and motions of two hands, we introduce a Spatial-Residual Memory (SRM) module to model spatial interaction between the body and each hand by residual learning. To enhance the coordination of two hand motions wrt. body dynamics holistically, we then present a Temporal-Motion Memory (TMM) module. TMM can effectively model the temporal association between body dynamics and two hand motions. The second stage is built upon the insight that 3D hand predictions should be non-deterministic given the sequential body postures. Thus, we further diversify our 3D hand predictions based on the initial output from the stage one. Concretely, we propose a Prototypical-Memory Sampling Strategy (PSS) to generate the non-deterministic hand gestures by gradient" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.493, + 0.895, + 0.584 + ], + "angle": 0, + "content": "based Markov Chain Monte Carlo (MCMC) sampling. Extensive experiments demonstrate that our method outperforms the state-of-the-art models on the B2H dataset and our newly collected TED Hands dataset. The dataset and code are available at: https://github.com/XingqunQilab/Diverse-3D-Hand-Gesture-Prediction." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.601, + 0.633, + 0.617 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.627, + 0.894, + 0.718 + ], + "angle": 0, + "content": "Given a sequence of upper body skeletons, our task aims at predicting natural and diverse 3D hand gestures. Such non-verbal body-hand coordination plays an important role in various virtual avatar scenarios, including human-agent interface [13, 17, 35, 40, 41], co-speech gesture synthesis [5, 20, 24, 46, 47], holoportation [29]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.902 + ], + "angle": 0, + "content": "However, it is quite difficult to predict the natural and diverse 3D hand gestures due to three major challenges: (1) Spatially asymmetric motions: Asymmetric motions of two hands have been overlooked by previous works [28], e.g., when one hand moves, the other could be static or moving slowly. (2) Temporal consistency wrt. body dynamics: Predicted sequential hand gestures should be temporally consistent with respect to the body dynamics. (3) Non-deterministic hand prediction: Given the upper body dynamics, various 3D hand gestures can match the body postures rather than a deterministic result. Since the existing dataset has only a few avatar identities, the generated hands" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.222, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.517, + 0.957 + ], + "angle": 0, + "content": "4616" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.212, + 0.107 + ], + "angle": 0, + "content": "often lack diversity." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.109, + 0.47, + 0.229 + ], + "angle": 0, + "content": "Due to complex body-hand interaction and asymmetric movements of two hands, directly predicting the natural and diverse 3D hand is rather difficult. Therefore, we propose to address the aforementioned challenges in a prediction followed by a diversification paradigm. To be specific, we propose a novel bilateral hand disentanglement based two-stage method, to generate natural and diverse 3D hand gestures from upper body dynamics." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.231, + 0.471, + 0.488 + ], + "angle": 0, + "content": "In the first stage, we aim to predict the natural 3D hand gestures. Our key insight is to establish the bilateral hand disentanglement for asymmetric motions of two hands. We construct two hand-disentangled branches that interact with a body-specific branch to initially predict natural 3D hands. Here, we leverage a single-hand autoencoder to extract each hand feature respectively, thus achieving the effects of two hands disentanglement. Furthermore, we propose a Spatial-Residual Memory (SRM) module to model the spatial relation between the body and each hand via residual learning. Specifically, we employ a spatial memory bank to store the spatial residual deformation representations of each hand. Then, we leverage the current upper body embedding as a query to retrieve the most relevant spatial residual deformation. The queried spatial residual deformation and the synchronized hand embedding vector are used to generate the next step hand representation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.49, + 0.47, + 0.656 + ], + "angle": 0, + "content": "To ensure the motions of both hands are temporally consistent with the upper body sequence, we present a Temporal-Motion Memory (TMM) module. TMM models the correlation between body dynamics and hand gestures. Similar to SRM, we utilize a temporal memory bank to store the motion features of each hand at the sequence level. Moreover, we employ a motion encoder to acquire the input body dynamics representation, and then use the body dynamics representation as a query to produce temporally consistent hand motion features. In this fashion, we can effectively synchronize hand motions with body dynamics." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.658, + 0.47, + 0.884 + ], + "angle": 0, + "content": "In the second stage, we develop a Prototypical-Memory Sampling Strategy (PSS) to diversify our 3D hand predictions based on the initial prediction at stage one. Here, we leverage an external memory that stores realistic hand prototypes, and then search a prototype that is closest to our initial predicted hands. Once we obtain the prototype, we project it into the feature space. To increase the diversity while preserving the authenticity of generated hand gestures, we perturb the prototype feature via gradient-based Markov Chain Monte Carlo (MCMC) sampling [23]. Specifically, a random noise is first sampled from a Gaussian distribution as a prior perturbation and then we update its posterior via Langevin dynamics based MCMC [4, 27]. Then, the perturbation is concatenated with the prototype feature to produce realistic new hand gestures." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Moreover, the existing 3D hand prediction dataset [28]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.227 + ], + "angle": 0, + "content": "contains less than 10 avatar identities, resulting in insufficient diversity of gestures. Therefore, we newly collect a large-scale 3D hand gestures dataset (dubbed TED Hands) with more than 1.7K avatar identities from in-the-wild scenarios. Our dataset contains around 100 hours of TED talk speeches, enabling research on diverse 3D hand gesture predictions. Extensive experiments conducted on the B2H dataset [28] and our TED Hands dataset demonstrate our method outperforms the state-of-the-art." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.228, + 0.855, + 0.243 + ], + "angle": 0, + "content": "Overall, our contributions are summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.248, + 0.892, + 0.309 + ], + "angle": 0, + "content": "- We propose a novel bilateral hand disentanglement based two-stage 3D hand generation method to predict diverse 3D hand gestures from body dynamics in a prediction followed by diversification paradigm." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.313, + 0.892, + 0.388 + ], + "angle": 0, + "content": "- We present a Spatial-Residual Memory (SRM) module to predict authentic hand poses from disentangled hand representations and a Temporal-Motion Memory (TMM) module to ensure temporal consistency of generated 3D hands." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.394, + 0.892, + 0.44 + ], + "angle": 0, + "content": "- We design a Prototypical-Memory Sampling Strategy (PSS) to diversify our initial 3D hand prediction, thus obtaining natural and diverse hand gestures." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.444, + 0.892, + 0.489 + ], + "angle": 0, + "content": "- We collect a new large-scale sequential 3D hand dataset from 1.7K persons' hand gestures, significantly facilitating research on diverse 3D hands generation." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.248, + 0.892, + 0.489 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.505, + 0.642, + 0.521 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.531, + 0.892, + 0.577 + ], + "angle": 0, + "content": "Since our method predicts the 3D hand motions from upper body skeletons, we briefly review the approaches of 3D hand pose estimation and 3D human motion prediction." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.583, + 0.892, + 0.794 + ], + "angle": 0, + "content": "3D hand pose estimation: 3D hand estimation has received impressive attention for its wide applications in virtual reality, augmented reality, and robotics. Recently, parametric 3D hand model MANO [33] and various mocap-captured 3D hand datasets [2,9,26,52] significantly improve the performance of 3D hand pose estimation from the single image [6,18,32,37,49,51]. Among various image-based 3D hand estimation approaches, transformer-based models [10,18,21] have demonstrated outstanding performance. For instance, Li et al. [18] propose an interacting attention graph transformer to estimate two-hand poses from a single image. Shreyas et al. [10] present a hand keypoint based transformer combined with convolutional networks to establish the association among different joints." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Since our task aims to predict the 3D hand motions from upper body skeletons, these single-image-based methods [10, 18, 21] cannot be directly employed. However, their excellent performance in 3D hand estimation inspires us to model the body-hand interaction via transformer-based architectures. Besides, Ng et al. [28] generate the hand gestures from body dynamics in a holistic manner. As the" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4617" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.113, + 0.091, + 0.861, + 0.326 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.329, + 0.895, + 0.361 + ], + "angle": 0, + "content": "Figure 2. The pipeline of our proposed method. In stage one, we generate the natural initial 3D hands from sequential upper body skeletons. In stage two, we diversify our 3D hand predictions based on the initial gestures at stage one." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.378, + 0.471, + 0.44 + ], + "angle": 0, + "content": "asymmetric motions of two hands, their method might produce some unnatural hand gestures. This also motivates us to disentangle two hands in hand pose estimation and then synchronize two-hands motions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.445, + 0.471, + 0.657 + ], + "angle": 0, + "content": "3D human motion prediction: Predicting human future motions from existing 3D poses has been widely studied [1, 8, 19, 25, 39]. Wang et al. [39] leverage a multi-range transformer that attends learn local-global features for multi-person motion prediction. Bouazizi et al. [1] introduce a multi-layer perception based human motion prediction network to learn spatio-temporal pose relation. Due to the similar nature between 3D human motion prediction and hand pose prediction, these models [1, 8, 19, 25, 39] can be easily adopted as our baselines. Moreover, we notice that memory based networks [3, 42, 43, 48] achieve promising performance in long-sequence modeling tasks. Motivated by this, we introduce external memories into our network to facilitate our long-range hand pose generation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.667, + 0.251, + 0.684 + ], + "angle": 0, + "content": "3. Proposed Method" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.692, + 0.281, + 0.707 + ], + "angle": 0, + "content": "3.1. Problem Formulation" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.715, + 0.47, + 0.842 + ], + "angle": 0, + "content": "Given a sequence of 3D upper body skeletons \\(\\mathcal{B} = \\{b^t\\}_{t=0}^T\\), our goal is to predict the natural and diverse 3D hand poses \\(\\mathcal{H} = \\{h^t\\}_{t=0}^T\\), where \\(T\\) is the sequence length. Specifically, we define each step body skeleton (i.e., collars, shoulders, elbows, and wrists) \\(b^t \\in \\mathbb{R}^{24}\\) as 8 joints. Each joint is represented by a 3D axis-angle representation. Meanwhile, the 3D hand pose at time \\(t\\), \\(h^t \\in \\mathbb{R}^{90}\\), is described as 30 joints with 3D axis-angle representation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.848, + 0.398, + 0.864 + ], + "angle": 0, + "content": "3.2. Stage One: Natural Hand Prediction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Due to complex body-hand interaction and asymmetric motions of two hands, we leverage the bilateral hand disen" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.378, + 0.895, + 0.61 + ], + "angle": 0, + "content": "tanglement branches and a body-specific branch to generate the natural 3D hands. Specifically, as depicted in Fig. 2 (stage one), our method mainly consists of a Bilateral Hand Disentanglement (BHD) module, a Spatial-Residual Memory (SRM) module, a Temporal-Motion Memory (TMM) module, and a transformer-based backbone. Firstly, we leverage a body encoder to obtain the body features \\( F_{\\mathcal{B}} = \\{F_{\\mathcal{B}}^{t}\\}_{t=0}^{T} \\), where \\( F_{\\mathcal{B}}^{t} \\in \\mathbb{R}^{1 \\times C} \\) denotes a body feature at time \\( t \\), and \\( C \\) is the feature dimension. Then, the body features are disentangled by BHD to acquire the single hand features \\( F_{\\mathcal{SH}} = \\{F_{\\mathcal{SH}}^{t}\\}_{t=0}^{T} \\), where \\( F_{\\mathcal{SH}}^{t} \\in \\mathbb{R}^{1 \\times C} \\). Considering the asymmetry motions of two hands, we exploit SRM to model the spatial interaction between the body and each hand, respectively. Besides, we further develop TMM to keep the two hand gestures temporal consistent with body dynamics." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.894, + 0.78 + ], + "angle": 0, + "content": "Bilateral Hand Disentangle Module: Due to the asymmetric motions of two hands, we employ a single hand autoencoder as the feature extractor to disentangle two hands. We firstly train an autoencoder on 3D single hands. As shown in Fig. 3 (a), we then utilize a Multilayer Perceptron (MLP) to project the body features into the single hand features \\( F_{\\mathcal{SH}} \\). To ensure these single hand features represent each disentangled hand separately, we conduct the feature level and 3D representation level constraints by the single hand autoencoder, as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.791, + 0.892, + 0.82 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {d i s} = \\left\\| \\widetilde {F _ {S H} ^ {t}} - F _ {\\mathcal {S H}} ^ {t} \\right\\| _ {1} + \\left\\| \\mathbb {D} \\left(\\widetilde {F _ {S H} ^ {t}}\\right) - \\mathbb {D} \\left(F _ {\\mathcal {S H}} ^ {t}\\right) \\right\\| _ {1}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.832, + 0.892, + 0.865 + ], + "angle": 0, + "content": "where \\(\\widetilde{F_{SH}^{t}}\\) denotes reconstructed hand feature at time \\(t\\), and \\(\\mathbb{D}\\) is the pre-trained decoder." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Spatial-Residual Memory Module: After obtaining the disentangled single hand features, we introduce a Spatial-" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4618" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.1, + 0.092, + 0.615, + 0.21 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.618, + 0.097, + 0.865, + 0.21 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.13, + 0.215, + 0.838, + 0.228 + ], + "angle": 0, + "content": "Figure 3. Details of three sub-modules in the first stage. For brevity, we only show them in terms of single-branch view." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.255, + 0.47, + 0.406 + ], + "angle": 0, + "content": "Residual Memory (SRM) module to model the spatial interaction between the body and each hand by residual learning. As illustrated in Fig. 3 (b), we leverage a spatial memory bank to store the spatial residual deformation representation between the current hand feature and the next step hand feature. Initially, each slot of the spatial memory bank is randomized as \\( m_j \\in \\mathbb{R}^{1 \\times C} \\), where \\( j \\) denotes slot index. To model the body-hand correlation, the current body feature is exploited as a query to retrieve the most relevant memory slot by calculating the cosine similarity." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.407, + 0.47, + 0.649 + ], + "angle": 0, + "content": "In particular, we represent the relevance between the query and memory slots via cosine similarity. Then we leverage the argmax operation to acquire the most relevant memory slot \\( m_r \\). Intuitively, the retrieved most relevant memory slot is leveraged as the spatial residual deformation between the current feature and the next step hand feature. However, it is intractable for argmax operation to back-propagate gradients. Thus, we conduct the softmax operation on the above calculated cosine similarity matrix to obtain the slot-wise affinity matrix. Then we acquire the learnable spatial residual deformation \\( F_{\\mathcal{SH}}^{\\Delta t} \\) by aggregation between the slot-wise affinity matrix and each memory slot. We apply the above reading process to allow gradient back-propagation. In the training phase, we utilize the current hand feature to update the retrieved memory slot as \\( m_r = \\gamma m_r + (1 - \\gamma)F_{\\mathcal{SH}}^t \\), where \\( \\gamma = 0.8 \\) in our experiments." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.649, + 0.47, + 0.737 + ], + "angle": 0, + "content": "Different from obtaining the next hand feature by simple addition between the spatial residual deformation and current hand feature, we claim the spatial residual deformation refers to local spatial dependency from the current feature to the next time feature. This spatial dependency \\( S \\) is formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.161, + 0.744, + 0.469, + 0.767 + ], + "angle": 0, + "content": "\\[\nS _ {t} ^ {t + 1} = \\operatorname {s o f t m a x} \\left(F _ {\\mathcal {S H}} ^ {\\Delta t ^ {\\prime}} \\otimes F _ {\\mathcal {S H}} ^ {t}\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.774, + 0.469, + 0.85 + ], + "angle": 0, + "content": "where \\(\\otimes\\) indicates matrix multiplication, and \\(^{\\prime}\\) indicates the transpose operation. With the help of the spatial dependency, the next step hand feature is represented as \\(F_{\\mathcal{SH}}^{t + 1} = F_{\\mathcal{SH}}^{t} + F_{\\mathcal{SH}}^{t}\\otimes S_{t}^{t + 1}\\). Through SRM, we obtain the spatial-enhanced single-hand feature." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Temporal-Motion Memory Module: We further propose a Temporal-Motion Memory (TMM) module to ensure the single hand motions consistent with the body dynamics," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.255, + 0.892, + 0.42 + ], + "angle": 0, + "content": "globally. As depicted in Fig. 3 (c), we develop a motion encoder to obtain the sequence-aware body motion embedding as \\( F_{\\mathcal{B}\\mathcal{M}} \\in \\mathcal{R}^{T \\times 1} \\). Here, we use body motion embedding to represent temporal changes among body skeletons in a sequence. Then, we leverage the body motion embedding as a query to retrieve the most consistent single hand motion embedding \\( F_{\\mathcal{S}\\mathcal{H}\\mathcal{M}} \\in \\mathcal{R}^{T \\times 1} \\) stored in a temporal memory bank. The initialization and reading processes of the temporal memory bank are similar to SRM. We utilize the body motion embedding to update the retrieved slot of the temporal memory bank in the same manner as SRM." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.422, + 0.892, + 0.528 + ], + "angle": 0, + "content": "Afterward, we utilize the retrieved hand motion embedding to boost the body-hand temporal consistency. Specifically, we leverage the retrieved temporal embedding to represent the temporal correlation of hand gesture changes in a sequence. Then, the temporal-consistent enhanced sequential hand gestures are attained by: \\( F_{\\mathcal{SH}} = F_{\\mathcal{SH}} + F_{\\mathcal{SH}} \\odot \\text{softmax}(F_{\\mathcal{SHM}}) \\), where \\( \\odot \\) means dot product." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.534, + 0.892, + 0.67 + ], + "angle": 0, + "content": "Transformer-based Backbone: As illustrated in Fig. 2 (stage one), to further enhance the body-hand interaction, we construct the bilateral hand disentanglement branches that interact with a body-specific branch to predict 3D hands. In particular, we introduce a body-specific transformer to generate body features as query \\( Q \\). Then, through 3 times Multi-Head Attention (MHA) [38], we use \\( Q \\) to match the key features \\( K \\) and value features \\( V \\) in each hand transformer branch, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.671, + 0.892, + 0.822 + ], + "angle": 0, + "content": "Furthermore, we feed the concatenation of bilateral hand features into an MLP, thus obtaining the merged two-hand features. Similarly, we conduct 3 times MHA in the transformer-based decoder. This encourages the merged two-hand features to be more temporal consistent with body dynamics, holistically. At the end of the decoder, we adopt two fully-connected layers to obtain the 3D two hands sequence. Additionally, similar to [28], we employ a motion discriminator to ensure the natural and continuous initial prediction at stage one." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.832, + 0.764, + 0.849 + ], + "angle": 0, + "content": "3.3. Stage Two: Diverse Sampling" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We leverage a Prototypical-Memory Sampling Strategy (PSS) to achieve hands diversification based on our initial predictions from stage one. Specifically, we first con" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4619" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.228 + ], + "angle": 0, + "content": "struct a prototypical memory to store the realistic two hands prototypes. Then, we obtain the retrieved realistic prototype representation based on the initial prediction at stage one. Meanwhile, as shown in Fig. 2 (stage two), we propose a sampling header to obtain the hand-informative perturbation via gradient-based Markov Chain Monte Carlo (MCMC) sampling. Finally, we concatenate the retrieved realistic hand prototype representation and perturbation to generate the diverse 3D two hands." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.234, + 0.473, + 0.432 + ], + "angle": 0, + "content": "Hands Prototypical Memory Construction: Inspired by [50], we reformulate the two hands diversification as a generation task. Instead of directly sampling the prior of the perturbation from the isotropic Gaussian distribution [7, 11, 16, 36], we assume the sampling space follows a learnable realistic prior distribution [30, 31, 50]. Since the existing 3D hand prediction dataset is noisy due to the automated annotation process, we propose a prototypical memory bank to store the realistic hand prototype representations encoded from real 3D hands. These 3D hands are captured from a studio-based mocap-captured dataset, named BEAT [22]. The reading and updating strategies of hands prototypical memory are the same as TMM." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.438, + 0.473, + 0.514 + ], + "angle": 0, + "content": "Gradient-based MCMC Sampling: We exploit the retrieved hand prototype representation concatenated with sampled perturbation vector \\( w \\) to predict the diverse hand gestures. Given the observed 3D two hands \\( h \\in \\mathbb{R}^{90} \\), the \\( \\tilde{h} \\) is expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.105, + 0.525, + 0.47, + 0.545 + ], + "angle": 0, + "content": "\\[\n\\tilde {h} = R _ {\\theta} (h, w) + \\epsilon , w \\sim p _ {\\alpha} (w), \\epsilon \\sim \\mathcal {N} (0, \\sigma_ {\\epsilon} ^ {2} I), \\qquad (3)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.557, + 0.47, + 0.616 + ], + "angle": 0, + "content": "where \\(p_{\\alpha}(w)\\) is the prior distribution of perturbation with parameters \\(\\alpha\\), and \\(\\epsilon \\sim \\mathcal{N}(0, \\sigma_{\\epsilon}^{2}I)\\) is the observation noise of hand gestures with \\(\\sigma_{\\epsilon}\\) being given, \\(R_{\\theta}\\) is the generation model with parameters \\(\\theta\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.618, + 0.47, + 0.695 + ], + "angle": 0, + "content": "Inspired by [11], we leverage an MLP-based sampling header \\( S_{\\alpha}(w) \\) to model the diversification sampling process, as illustrated in Fig. 2 (stage two). The prior distribution of perturbation is initialized from an isotropic Gaussian reference distribution, expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.138, + 0.705, + 0.47, + 0.74 + ], + "angle": 0, + "content": "\\[\np _ {\\alpha} (w) \\propto e x p \\left[ - S _ {\\alpha} (w) - \\frac {1}{2 \\sigma_ {w} ^ {2}} \\| w \\| ^ {2} \\right], \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.753, + 0.47, + 0.846 + ], + "angle": 0, + "content": "where the \\(M_{\\alpha}(w) = S_{\\alpha}(w) + \\frac{1}{2\\sigma_w^2}\\| w\\|^2\\) is defined as the whole sampling function, and \\(\\alpha\\) is the learnable parameters of sampling header. The hyperparameter \\(\\sigma_w\\) denotes the standard deviation. For notation simplicity, let \\(\\beta = \\{\\theta ,\\alpha \\}\\). For the \\(i\\) th sample in a training mini-batch with size \\(n\\), the log-likelihood function of \\(\\beta\\) is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.116, + 0.859, + 0.47, + 0.898 + ], + "angle": 0, + "content": "\\[\nL (\\beta) = \\sum_ {i = 1} ^ {n} \\log \\left[ \\int p _ {\\alpha} \\left(w _ {i}\\right) p _ {\\theta} \\left(\\tilde {h} _ {i} \\mid h _ {i}, w _ {i}\\right) d w _ {i} \\right]. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.782, + 0.107 + ], + "angle": 0, + "content": "Thus the gradient of \\(L(\\beta)\\) is computed as:" + }, + { + "type": "equation", + "bbox": [ + 0.502, + 0.111, + 0.892, + 0.153 + ], + "angle": 0, + "content": "\\[\n\\bigtriangledown L (\\beta) = E _ {p _ {\\beta (w | \\tilde {h}, h)}} \\left[ \\bigtriangledown_ {\\alpha} \\operatorname {l o g p} _ {\\alpha} (w) + \\bigtriangledown_ {\\theta} \\operatorname {l o g p} _ {\\theta} (\\tilde {h} | h, w) \\right]. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.158, + 0.894, + 0.297 + ], + "angle": 0, + "content": "The intractable expectation term \\( E_{p}(\\cdot) \\) in Eq. (6) is approximately solved by a gradient-based MCMC (Langevin dynamics) [4, 27]. In particular, the initial state of perturbation \\( p_0(w) \\) is sampled from the Gaussian distribution. Through MCMC, the perturbation from the prior distribution and posterior distribution are represented as \\( \\{w_i^-\\} \\) and \\( \\{w_i^+\\} \\), respectively. The detailed calculation process is in [27]. Therefore, the gradients of the generation model and sampling header are updated by:" + }, + { + "type": "equation", + "bbox": [ + 0.509, + 0.301, + 0.892, + 0.356 + ], + "angle": 0, + "content": "\\[\n\\nabla_ {\\theta} R _ {\\theta} = \\frac {1}{n} \\sum_ {i = 1} ^ {n} \\left[ \\frac {1}{\\sigma_ {\\epsilon} ^ {2}} \\left(\\tilde {h} _ {i} - R _ {\\theta} \\left(h _ {i}, w _ {i} ^ {+}\\right)\\right) \\nabla_ {\\theta} R _ {\\theta} \\left(h _ {i}, w _ {i} ^ {+}\\right) \\right], \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.509, + 0.359, + 0.892, + 0.398 + ], + "angle": 0, + "content": "\\[\n\\nabla_ {\\alpha} S _ {\\alpha} = \\frac {1}{n} \\sum_ {i = 1} ^ {n} \\left[ \\nabla_ {\\alpha} S _ {\\alpha} \\left(w _ {i} ^ {-}\\right) \\right] - \\frac {1}{n} \\sum_ {i = 1} ^ {n} \\left[ \\nabla_ {\\alpha} S _ {\\alpha} \\left(w _ {i} ^ {+}\\right) \\right]. \\tag {8}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.41, + 0.692, + 0.426 + ], + "angle": 0, + "content": "3.4. Objective Functions" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.433, + 0.892, + 0.464 + ], + "angle": 0, + "content": "In stage one, we apply the following loss functions to constrain the initial prediction process of hand gestures." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.47, + 0.892, + 0.522 + ], + "angle": 0, + "content": "Reconstruction Loss: We use the ground truth to supervise the predicted two hands as \\(\\mathcal{L}_{rec} = \\left\\| \\mathcal{H} - \\tilde{\\mathcal{H}} \\right\\|_1\\), where \\(\\tilde{\\mathcal{H}}\\) denotes generated hands." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.528, + 0.892, + 0.629 + ], + "angle": 0, + "content": "Perceptual Loss: Inspired by [15], we leverage the studio-based 3D hands dataset BEAT to pre-train an MLP-based autoencoder as a feature extractor \\(\\phi(\\cdot)\\). We utilize the \\(L1\\) loss to constrain the difference between the extracted features of \\(\\mathcal{H}\\) and \\(\\tilde{\\mathcal{H}}\\), as formulated: \\(\\mathcal{L}_{perc} = \\left\\| \\phi(\\mathcal{H}) - \\phi(\\tilde{\\mathcal{H}}) \\right\\|_1\\)." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.633, + 0.892, + 0.663 + ], + "angle": 0, + "content": "Adversarial Learning: Following the configuration of [28], we employ the adversarial training loss as:" + }, + { + "type": "equation", + "bbox": [ + 0.525, + 0.668, + 0.892, + 0.687 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {a d v} = \\mathbb {E} _ {\\mathcal {H}} \\left[ \\log D (\\mathcal {H}) \\right] + \\mathbb {E} _ {\\mathcal {B}} \\left[ \\log \\left(1 - (G (\\mathcal {B}))\\right) \\right], \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.691, + 0.892, + 0.721 + ], + "angle": 0, + "content": "where \\(D\\) denotes the discriminator and \\(G\\) means hands generator. Finally, the overall objective in stage one is:" + }, + { + "type": "equation", + "bbox": [ + 0.504, + 0.725, + 0.892, + 0.749 + ], + "angle": 0, + "content": "\\[\n\\min _ {G} \\max _ {D} \\mathcal {L} _ {\\text {t o t a l}} ^ {\\text {s t a g e 1}} = \\mathcal {L} _ {\\text {r e c}} + \\mathcal {L} _ {\\text {a d v}} + \\mathcal {L} _ {\\text {p e r c}} + 0. 5 \\mathcal {L} _ {\\text {d i s}}, \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.753, + 0.89, + 0.768 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{dis}\\) denotes disentanglement constraint in Eq. ((1))." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.769, + 0.892, + 0.796 + ], + "angle": 0, + "content": "In the second stage, the overall objective to train our model is defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.591, + 0.801, + 0.892, + 0.822 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {t o t a l}} ^ {\\text {s t a g e 2}} = \\left\\| h - R _ {\\theta} \\left(h, w ^ {+}\\right) \\right\\| _ {1}, \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.825, + 0.892, + 0.902 + ], + "angle": 0, + "content": "where \\( w^{+} \\) is the posterior distribution of the perturbation. We conduct the frame-level diversification based on the initial prediction at stage one. To ensure temporal smoothness, we further apply temporal smoothness [45] to the diversified 3D hand gestures as a post processing." + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4620" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.119 + ], + "angle": 0, + "content": "Table 1. Comparison with the state-of-the-art methods on B2H dataset and our proposed TED Hands dataset of the first stage initial prediction. \\( \\downarrow \\) indicates the lower the better." + }, + { + "type": "table", + "bbox": [ + 0.136, + 0.123, + 0.835, + 0.254 + ], + "angle": 0, + "content": "
MethodsB2H Dataset [28]TED Hands Dataset
L2↓FHD↓MPJRE↓L2↓FHD↓MPJRE↓
Body2Hands [28]CVPR'213.7601.10313.1482.5511.17411.371
MRT [39]NeurIPS'213.6340.97312.5762.3250.87710.314
BTM [8]WACV'233.6571.26312.6962.3501.11110.440
LTD [25]ICCV'193.7551.07313.3152.4821.36711.078
MotionMixer [1]IJCAI'223.6160.98612.7022.3240.91010.427
SPGSN [19]ECCV'223.6560.96212.7572.4350.99010.887
Ours (stage one)3.4200.47111.4062.0370.2588.888
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.267, + 0.471, + 0.308 + ], + "angle": 0, + "content": "Table 2. Sampling experiment results on B2H dataset. \\( \\downarrow \\) indicates the lower the better, and \\( \\uparrow \\) indicates the higher the better. \\( \\pm \\) means 95% confidence interval." + }, + { + "type": "table", + "bbox": [ + 0.086, + 0.314, + 0.462, + 0.445 + ], + "angle": 0, + "content": "
MethodsFHD↓Diversity↑
Body2hands [28] w/ PSS2.5040.497±0.028
MRT [39] w/ PSS1.9820.698±0.031
BTM [8] w/ PSS2.3790.703±0.038
LTD [25] w/ PSS1.8930.577±0.028
MotionMixer [1] w/ PSS2.1690.869±0.055
SPGSN [19] w/ PSS2.0040.874±0.046
Ours w/ VAE [36]1.6171.001±0.061
Ours (stage two)1.2391.324±0.066
" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.468, + 0.21, + 0.485 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.493, + 0.381, + 0.51 + ], + "angle": 0, + "content": "4.1. Datasets and Experimental Setting" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.516, + 0.47, + 0.668 + ], + "angle": 0, + "content": "B2H Dataset: The B2H dataset [28] is automatically annotated by a monocular-based 3D pose estimation model [44], including the gestures of 8 speakers from in-the-wild talk show videos. In the original B2H dataset, there are more than 139K sequences. Each sequence includes 64 frames, with 32 frames overlapping between every two sequences. However, due to the noisiness and unavailable videos, we obtain 120,188 sequences finally. In our work, we adopt the same division criteria as [28] to split the training and testing dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.674, + 0.471, + 0.902 + ], + "angle": 0, + "content": "TED Hands Dataset: Due to the limited avatar identities in the existing 3D hand prediction dataset, we newly collect a large-scale 3D hands dataset (dubbed TED Hands) based on the TED Gesture [46, 47]. The original TED Gesture dataset only contains 10 upper body joints without elaborate fingers of two hands. Hence, we leverage a state-of-the-art 3D pose estimator FrankMocap [34] to extract the whole body-hand joints as pseudo ground truth from the video links provided by TED Gesture. Concretely, each joint of our dataset is normalized as the 3D axis-angle representation in a fixed kinematic structure [33]. In this fashion, our dataset is invariant to root joint motion and body shape. Finally, we acquired the 134,456 sequences from 1,755 different speakers, with 99.6 hours of TED talking speeches. Each sequence includes 64 frames without over" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.267, + 0.892, + 0.308 + ], + "angle": 0, + "content": "Table 3. Sampling experiment results on our proposed TED Hands dataset. \\( \\downarrow \\) indicates the lower the better, and \\( \\uparrow \\) indicates the higher the better. \\( \\pm \\) means \\( {95}\\% \\) confidence interval." + }, + { + "type": "table", + "bbox": [ + 0.508, + 0.314, + 0.885, + 0.445 + ], + "angle": 0, + "content": "
MethodsFHD↓Diversity↑
Body2hands [28] w/ PSS2.0052.705±0.153
MRT [39] w/ PSS1.1884.954±0.190
BTM [8] w/ PSS1.2243.632±0.150
LTD [25] w/ PSS1.3852.851±0.101
MotionMixer [1] w/ PSS1.6133.487±0.208
SPGSN [19] w/ PSS1.5653.812±0.219
Ours w/ VAE [36]1.0334.018±0.190
Ours (stage two)0.9386.426±0.300
" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.469, + 0.892, + 0.515 + ], + "angle": 0, + "content": "lap. We randomly spit the dataset into the \\(70\\%\\) training set, \\(10\\%\\) validation set, and \\(20\\%\\) testing set. Please refer to the supplementary material for more details." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.521, + 0.892, + 0.612 + ], + "angle": 0, + "content": "Implementation Details: Our model is implemented on the PyTorch platform with 2 NVIDIA RTX 2080Ti GPUs. We train the model utilizing Adam optimizer with an initial learning rate of 0.003. The whole training takes 30 epochs with a batch size of 64. We set \\(\\sigma_{\\epsilon} = 1\\) in Eq. (3), and \\(\\sigma_w = 1\\) in Eq. (4)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.618, + 0.894, + 0.663 + ], + "angle": 0, + "content": "Evaluation Metrics: To fully evaluate the naturalness of initial predictions at stage one and the diversity of sampled hand gestures at stage two, we employ various metrics:" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.666, + 0.892, + 0.696 + ], + "angle": 0, + "content": "- \\(L2\\) Distance: Distance between the generated whole two hand poses and pseudo ground truth." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.699, + 0.892, + 0.775 + ], + "angle": 0, + "content": "- FHD: Inspired by FGD [46, 47], we propose a hand-specific metric (named FHD) to measure the Fréchet distance between the features of generated hands and pseudo ground truth. The feature extractors of FHD are pretrained by B2H and TED Hands datasets, respectively." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.777, + 0.892, + 0.838 + ], + "angle": 0, + "content": "- MPJRE: We leverage the Mean Per Joint Rotation Error [○] (MPJRE) [14] to measure the absolute distance between predicted 3D representation joints and pseudo ground truth." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.84, + 0.892, + 0.9 + ], + "angle": 0, + "content": "- Diversity: To verify the diversity of sampled hand gestures, we calculate the average feature distance between 500 random combined sequential pairs [20, 24]. The feature extractor is the same as FHD." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.666, + 0.892, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "4621" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.133 + ], + "angle": 0, + "content": "Table 4. Ablation study on different loss functions and different components of the proposed method. \\( \\downarrow \\) indicates the lower the better. ✓ indicates the employment of a certain module or loss function. # means the temporal-motion memory module is adopted before the spatial-residual memory module. † denotes the weights of the two hands transformers are shared." + }, + { + "type": "table", + "bbox": [ + 0.115, + 0.137, + 0.855, + 0.293 + ], + "angle": 0, + "content": "
Model VariationsB2H Dataset [28]TED Hands Dataset
BaselineFull Model\\( \\mathcal{L}_{dis} \\)\\( \\mathcal{L}_{perc} \\)SRMTMML2 ↓FHD ↓MPJRE ↓L2 ↓FHD ↓MPJRE ↓
✓3.6501.09112.6902.3660.97710.531
✓3.6040.77312.4532.3030.73110.250
✓✓3.5520.68212.0372.2160.5959.786
✓✓3.5630.65712.0852.2610.69910.026
✓✓✓3.5040.64011.8282.1610.4959.508
✓✓✓✓3.4570.58011.6872.1000.3939.209
#✓✓✓✓✓3.4840.61411.7582.1240.4639.311
†✓✓✓✓✓3.4760.59811.7482.1560.3809.467
✓✓✓✓✓3.4200.47111.4062.0370.2588.888
" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.31, + 0.273, + 0.327 + ], + "angle": 0, + "content": "4.2. Quantitative Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.337, + 0.471, + 0.488 + ], + "angle": 0, + "content": "Comparisons with the state-of-the-art: We compare our method with the pioneering 3D hands prediction work, named Body2hands [28]. Moreover, to fully verify the superiority of our method, we implement various state-of-the-art (SOTA) human motion prediction models: MTR [39], BTM [8], LTD [25], MotionMixer [1], and SPGSN [19]. For fair comparisons, all methods are implemented by source codes or pre-trained models released by authors. Since the above counterparts are designed without the diversification setting, the comparison is divided into two parts." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.49, + 0.47, + 0.642 + ], + "angle": 0, + "content": "In the first part, we leverage our stage one initial prediction to compare with other competitors. We adopt the \\(L2\\) distance, FHD, and MPJRE to provide a well-rounded view of comparisons. As reported in Tab. 1, our method outperforms all the counterparts by a large margin. Remarkably, our method achieves the lowest FHD and MPJRE sores on both datasets. Concretely, on FHD scores of the TED Hands dataset, our method performs even \\(70.6\\%\\) lower than the optimal results of other competitors (e.g., \\((0.877 - 0.258) / 0.877 \\approx 70.6\\%\\))." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.644, + 0.471, + 0.903 + ], + "angle": 0, + "content": "To demonstrate the effectiveness of the diversification process in our method, we compare the diversified results based on the various predictions from above mentioned competitive methods. Meanwhile, we replace our MCMC-based sampling strategy with CVAE [36] to diversify our initial prediction at stage one. We exploit the FHD and Diversity metrics in the second part. As shown in Tab. 2 and Tab. 3, our method achieves superior performance from the perspective of diversity. Although the FHD is slightly worse than stage one due to the sampled perturbation, our method still achieves the optimal result. Compared with CVAE, our method effectively avoids the potential posterior collapse problem [12]. Moreover, we observe that the diversity scores on our TED Hands dataset are much higher than the B2H dataset with all the counterparts. It applies that our newly collected TED Hands dataset includes more diverse hand gestures." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.31, + 0.895, + 0.417 + ], + "angle": 0, + "content": "Ablation Study: We further conduct the ablation study based on stage one to verify the effectiveness of each module and different loss functions, as indicated in Tab. 4. The baseline model is implemented by a simple transformer-based pipeline without bilateral hand branches. Our full model adopts the bilateral hand branches interacting with a body-specific transformer to produce the 3D hand gestures." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.417, + 0.895, + 0.612 + ], + "angle": 0, + "content": "As shown in Tab. 4, all combinations of the different loss functions and components have positive impacts on 3D hand predictions. The most complete combination attains the best results. Even though we directly construct the bilateral branches without disentanglement constraints (i.e., \\(\\mathcal{L}_{dis}\\)) as full model, our method achieves comparable performance against the simple baseline. This indicates the global body-hand interaction are effectively modeled by bilateral hand transformers and a body-specific transformer. Then, we observe that after adding the loss functions \\(\\mathcal{L}_{dis}\\) and \\(\\mathcal{L}_{perc}\\), the performance of our method is significantly improved, especially in MPJRE scores on both datasets (e.g., \\(10.250 \\rightarrow 9.508\\) on TED Hands)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.895, + 0.854 + ], + "angle": 0, + "content": "To verify the effectiveness of SRM and TMM, we conduct plenty of experiments on both datasets. As reported in Tab. 4, when we first employ the SRM, our method achieves the lower \\( L2 \\) distance and FHD scores on both datasets. Then, after adding TMM, our method achieves the best performance. This result proves that TMM effectively models the body-hand temporal association. Besides, we find that when TMM is adopted before SRM, the model performance decreases slightly (the third row from bottom to top in Tab. 4). This corresponds to both TMM and transformer-based backbone (i.e. body-transformer, bilateral hand branches) focus on modeling the body-hand temporal correlation. Both of them encourage the two hands to be more temporal consistent with body dynamics. Employing the SRM between them leads to worse spatial-temporal modeling for body-hand interaction." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Moreover, we conduct experiments that the parameter weights of bilateral hand transformers are shared. As shown in Tab. 4 (the second row from bottom to top), the per" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "4622" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.111, + 0.088, + 0.182, + 0.151 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.184, + 0.089, + 0.257, + 0.15 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.26, + 0.089, + 0.331, + 0.15 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.333, + 0.089, + 0.406, + 0.15 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.41, + 0.089, + 0.48, + 0.15 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.482, + 0.089, + 0.554, + 0.15 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.557, + 0.089, + 0.629, + 0.15 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.631, + 0.089, + 0.702, + 0.15 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.705, + 0.089, + 0.777, + 0.15 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.781, + 0.089, + 0.852, + 0.15 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.111, + 0.153, + 0.182, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.184, + 0.153, + 0.257, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.26, + 0.153, + 0.331, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.334, + 0.153, + 0.406, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.41, + 0.153, + 0.48, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.482, + 0.153, + 0.554, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.557, + 0.153, + 0.629, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.631, + 0.153, + 0.702, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.705, + 0.153, + 0.777, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.781, + 0.153, + 0.852, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.111, + 0.217, + 0.182, + 0.277 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.184, + 0.217, + 0.257, + 0.277 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.26, + 0.217, + 0.331, + 0.277 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.334, + 0.217, + 0.406, + 0.277 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.41, + 0.217, + 0.48, + 0.277 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.482, + 0.217, + 0.554, + 0.277 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.557, + 0.217, + 0.629, + 0.277 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.631, + 0.217, + 0.702, + 0.277 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.705, + 0.217, + 0.777, + 0.277 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.781, + 0.217, + 0.852, + 0.277 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.125, + 0.282, + 0.16, + 0.293 + ], + "angle": 0, + "content": "(a) GT" + }, + { + "type": "image_caption", + "bbox": [ + 0.184, + 0.282, + 0.26, + 0.293 + ], + "angle": 0, + "content": "(b) Body2hands" + }, + { + "type": "image_caption", + "bbox": [ + 0.269, + 0.282, + 0.313, + 0.293 + ], + "angle": 0, + "content": "(c) BTM" + }, + { + "type": "image_caption", + "bbox": [ + 0.342, + 0.282, + 0.385, + 0.293 + ], + "angle": 0, + "content": "(d) MRT" + }, + { + "type": "image_caption", + "bbox": [ + 0.42, + 0.282, + 0.46, + 0.293 + ], + "angle": 0, + "content": "(e) LTD" + }, + { + "type": "image_caption", + "bbox": [ + 0.478, + 0.282, + 0.557, + 0.293 + ], + "angle": 0, + "content": "(f) MotionMixer" + }, + { + "type": "image_caption", + "bbox": [ + 0.568, + 0.282, + 0.617, + 0.293 + ], + "angle": 0, + "content": "(g) SPGSN" + }, + { + "type": "image_caption", + "bbox": [ + 0.631, + 0.281, + 0.855, + 0.302 + ], + "angle": 0, + "content": "(h) Ours (h) Ours (h) Ours (w/o Sampling) (w/ Sampling) (w/ Sampling)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.303, + 0.892, + 0.332 + ], + "angle": 0, + "content": "Figure 4. Visualization of our predicted 3D hand gestures against various state-of-the-art methods [1,8,19,25,28,39]. From top to bottom, samples of the first row are from the B2H dataset, and the others are from our TED Hands dataset. Best view on screen." + }, + { + "type": "image", + "bbox": [ + 0.098, + 0.35, + 0.45, + 0.464 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.469, + 0.47, + 0.497 + ], + "angle": 0, + "content": "Figure 5. User study on the motion naturalness, smoothness, and body-hand temporal consistency. \\(\\uparrow\\) indicates the higher the better." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.512, + 0.47, + 0.618 + ], + "angle": 0, + "content": "formance is decreased due to the spatial-temporal interaction between the body and single-hand-specific branch being merged here. This supports our key technical insight on bilateral hand disentanglement. Additionally, to verify the practical ability of our method, we conduct experiments on model complexity and inference time, more details are presented in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.63, + 0.288, + 0.646 + ], + "angle": 0, + "content": "4.3. Qualitative Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.653, + 0.47, + 0.82 + ], + "angle": 0, + "content": "User Study: To further analyze the visual quality of the predicted 3D hand gestures by different methods, we recruit 15 volunteers to participate in the user study. We take the naturalness, smoothness, and body-hand temporal consistency as three evaluation perceptions and the range of grades is from 0 to 5 (the higher, the better). The statistical results are reported in Fig. 5. Our method shows the best performance in all three metrics. Especially in the naturalness and body-hand temporal consistency, our method achieves remarkable advantages among all the methods due to the body-hand interaction modeling by SRM and TMM." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Visualization: To fully verify the performance of our method, we show the visualization of generated 3D hands from the first and second stages, respectively. As depicted in Fig. 4, we compare our initial predictions (from stage one) with various SOTA approaches. The avatars are ren-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.352, + 0.895, + 0.594 + ], + "angle": 0, + "content": "dered from ground truth speakers in B2H and TED Hands datasets. We observe that Body2hands, BTM, and LTD generate unreasonable hand gestures (e.g., in the third row of Body2hands, left-hand gestures of avatar). MRT, Motion-Mixer, and SPGSN predict the natural results, but the finger gestures are less consistent with the upper body dynamics. In contrast, our method successfully predicts the perceptually convincing 3D hand gestures from the body dynamics. This supports our key insight to build the bilateral hand disentanglement branches since the asymmetric motions of two hands. We further visualize the diversification results generated by our method at stage two. As shown in Fig. 1 and Fig. 4, with the same upper body dynamics as input, our method obtains the natural and diverse 3D hand gestures on B2H and TED Hands datasets, respectively. Please refer to the supplementary material for more visualization results." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.607, + 0.619, + 0.623 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.632, + 0.892, + 0.844 + ], + "angle": 0, + "content": "In this paper, we present a novel bilateral hand disentanglement based two-stage method towards natural and diverse 3D hand prediction from body dynamics. In the first stage, upon the bilateral hand branches, we fully take advantage of the spatial-temporal body-hand interaction for generating natural initial 3D hand gestures. Then, in the second stage, we further diversify our natural initial 3D hand gestures by gradient-based markov chain monte carlo sampling. Extensive experiments conducted on B2H and our newly collected TED Hands datasets demonstrate the superiority of our method. As our method aims at generating diverse 3D avatar hand postures, in future work, we will investigate sampling diverse 3D hand gestures with temporal smoothness, instead of frame-wise sampling." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.85, + 0.892, + 0.896 + ], + "angle": 0, + "content": "Acknowledgements. This research is funded in part by ARC-Discovery grant (DP220100800 to XY) and ARC-DECRA grant (DE230100477 to XY)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4623" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.09, + 0.176, + 0.107 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.473, + 0.213 + ], + "angle": 0, + "content": "[1] Arij Bouazizi, Adrian Holzbock, Ulrich Kressel, Klaus Dietmayer, and Vasileios Belagiannis. Motionmixer: Mlp-based 3d human body pose forecasting. 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Diverse exemplary clips sampled by our method from our newly collected TED Hands Dataset. The vital frames are visualized to demonstrate that the hand gestures change with the upper body dynamics, synchronously. Best view on screen. + +# Abstract + +Predicting natural and diverse 3D hand gestures from the upper body dynamics is a practical yet challenging task in virtual avatar creation. Previous works usually overlook the asymmetric motions between two hands and generate two hands in a holistic manner, leading to unnatural results. In this work, we introduce a novel bilateral hand disentanglement based two-stage 3D hand generation method to achieve natural and diverse 3D hand prediction from body dynamics. In the first stage, we intend to generate natural hand gestures by two hand-disentanglement branches. Considering the asymmetric gestures and motions of two hands, we introduce a Spatial-Residual Memory (SRM) module to model spatial interaction between the body and each hand by residual learning. To enhance the coordination of two hand motions wrt. body dynamics holistically, we then present a Temporal-Motion Memory (TMM) module. TMM can effectively model the temporal association between body dynamics and two hand motions. The second stage is built upon the insight that 3D hand predictions should be non-deterministic given the sequential body postures. Thus, we further diversify our 3D hand predictions based on the initial output from the stage one. Concretely, we propose a Prototypical-Memory Sampling Strategy (PSS) to generate the non-deterministic hand gestures by gradient + +based Markov Chain Monte Carlo (MCMC) sampling. Extensive experiments demonstrate that our method outperforms the state-of-the-art models on the B2H dataset and our newly collected TED Hands dataset. The dataset and code are available at: https://github.com/XingqunQilab/Diverse-3D-Hand-Gesture-Prediction. + +# 1. Introduction + +Given a sequence of upper body skeletons, our task aims at predicting natural and diverse 3D hand gestures. Such non-verbal body-hand coordination plays an important role in various virtual avatar scenarios, including human-agent interface [13, 17, 35, 40, 41], co-speech gesture synthesis [5, 20, 24, 46, 47], holoportation [29]. + +However, it is quite difficult to predict the natural and diverse 3D hand gestures due to three major challenges: (1) Spatially asymmetric motions: Asymmetric motions of two hands have been overlooked by previous works [28], e.g., when one hand moves, the other could be static or moving slowly. (2) Temporal consistency wrt. body dynamics: Predicted sequential hand gestures should be temporally consistent with respect to the body dynamics. (3) Non-deterministic hand prediction: Given the upper body dynamics, various 3D hand gestures can match the body postures rather than a deterministic result. Since the existing dataset has only a few avatar identities, the generated hands + +often lack diversity. + +Due to complex body-hand interaction and asymmetric movements of two hands, directly predicting the natural and diverse 3D hand is rather difficult. Therefore, we propose to address the aforementioned challenges in a prediction followed by a diversification paradigm. To be specific, we propose a novel bilateral hand disentanglement based two-stage method, to generate natural and diverse 3D hand gestures from upper body dynamics. + +In the first stage, we aim to predict the natural 3D hand gestures. Our key insight is to establish the bilateral hand disentanglement for asymmetric motions of two hands. We construct two hand-disentangled branches that interact with a body-specific branch to initially predict natural 3D hands. Here, we leverage a single-hand autoencoder to extract each hand feature respectively, thus achieving the effects of two hands disentanglement. Furthermore, we propose a Spatial-Residual Memory (SRM) module to model the spatial relation between the body and each hand via residual learning. Specifically, we employ a spatial memory bank to store the spatial residual deformation representations of each hand. Then, we leverage the current upper body embedding as a query to retrieve the most relevant spatial residual deformation. The queried spatial residual deformation and the synchronized hand embedding vector are used to generate the next step hand representation. + +To ensure the motions of both hands are temporally consistent with the upper body sequence, we present a Temporal-Motion Memory (TMM) module. TMM models the correlation between body dynamics and hand gestures. Similar to SRM, we utilize a temporal memory bank to store the motion features of each hand at the sequence level. Moreover, we employ a motion encoder to acquire the input body dynamics representation, and then use the body dynamics representation as a query to produce temporally consistent hand motion features. In this fashion, we can effectively synchronize hand motions with body dynamics. + +In the second stage, we develop a Prototypical-Memory Sampling Strategy (PSS) to diversify our 3D hand predictions based on the initial prediction at stage one. Here, we leverage an external memory that stores realistic hand prototypes, and then search a prototype that is closest to our initial predicted hands. Once we obtain the prototype, we project it into the feature space. To increase the diversity while preserving the authenticity of generated hand gestures, we perturb the prototype feature via gradient-based Markov Chain Monte Carlo (MCMC) sampling [23]. Specifically, a random noise is first sampled from a Gaussian distribution as a prior perturbation and then we update its posterior via Langevin dynamics based MCMC [4, 27]. Then, the perturbation is concatenated with the prototype feature to produce realistic new hand gestures. + +Moreover, the existing 3D hand prediction dataset [28] + +contains less than 10 avatar identities, resulting in insufficient diversity of gestures. Therefore, we newly collect a large-scale 3D hand gestures dataset (dubbed TED Hands) with more than 1.7K avatar identities from in-the-wild scenarios. Our dataset contains around 100 hours of TED talk speeches, enabling research on diverse 3D hand gesture predictions. Extensive experiments conducted on the B2H dataset [28] and our TED Hands dataset demonstrate our method outperforms the state-of-the-art. + +Overall, our contributions are summarized as follows: + +- We propose a novel bilateral hand disentanglement based two-stage 3D hand generation method to predict diverse 3D hand gestures from body dynamics in a prediction followed by diversification paradigm. +- We present a Spatial-Residual Memory (SRM) module to predict authentic hand poses from disentangled hand representations and a Temporal-Motion Memory (TMM) module to ensure temporal consistency of generated 3D hands. +- We design a Prototypical-Memory Sampling Strategy (PSS) to diversify our initial 3D hand prediction, thus obtaining natural and diverse hand gestures. +- We collect a new large-scale sequential 3D hand dataset from 1.7K persons' hand gestures, significantly facilitating research on diverse 3D hands generation. + +# 2. Related Work + +Since our method predicts the 3D hand motions from upper body skeletons, we briefly review the approaches of 3D hand pose estimation and 3D human motion prediction. + +3D hand pose estimation: 3D hand estimation has received impressive attention for its wide applications in virtual reality, augmented reality, and robotics. Recently, parametric 3D hand model MANO [33] and various mocap-captured 3D hand datasets [2,9,26,52] significantly improve the performance of 3D hand pose estimation from the single image [6,18,32,37,49,51]. Among various image-based 3D hand estimation approaches, transformer-based models [10,18,21] have demonstrated outstanding performance. For instance, Li et al. [18] propose an interacting attention graph transformer to estimate two-hand poses from a single image. Shreyas et al. [10] present a hand keypoint based transformer combined with convolutional networks to establish the association among different joints. + +Since our task aims to predict the 3D hand motions from upper body skeletons, these single-image-based methods [10, 18, 21] cannot be directly employed. However, their excellent performance in 3D hand estimation inspires us to model the body-hand interaction via transformer-based architectures. Besides, Ng et al. [28] generate the hand gestures from body dynamics in a holistic manner. As the + +![](images/75149e03bc849e65e8e9dc8ef26c726a504a4a47887a94b49003659c1df7a9cd.jpg) +Figure 2. The pipeline of our proposed method. In stage one, we generate the natural initial 3D hands from sequential upper body skeletons. In stage two, we diversify our 3D hand predictions based on the initial gestures at stage one. + +asymmetric motions of two hands, their method might produce some unnatural hand gestures. This also motivates us to disentangle two hands in hand pose estimation and then synchronize two-hands motions. + +3D human motion prediction: Predicting human future motions from existing 3D poses has been widely studied [1, 8, 19, 25, 39]. Wang et al. [39] leverage a multi-range transformer that attends learn local-global features for multi-person motion prediction. Bouazizi et al. [1] introduce a multi-layer perception based human motion prediction network to learn spatio-temporal pose relation. Due to the similar nature between 3D human motion prediction and hand pose prediction, these models [1, 8, 19, 25, 39] can be easily adopted as our baselines. Moreover, we notice that memory based networks [3, 42, 43, 48] achieve promising performance in long-sequence modeling tasks. Motivated by this, we introduce external memories into our network to facilitate our long-range hand pose generation. + +# 3. Proposed Method + +# 3.1. Problem Formulation + +Given a sequence of 3D upper body skeletons $\mathcal{B} = \{b^t\}_{t=0}^T$ , our goal is to predict the natural and diverse 3D hand poses $\mathcal{H} = \{h^t\}_{t=0}^T$ , where $T$ is the sequence length. Specifically, we define each step body skeleton (i.e., collars, shoulders, elbows, and wrists) $b^t \in \mathbb{R}^{24}$ as 8 joints. Each joint is represented by a 3D axis-angle representation. Meanwhile, the 3D hand pose at time $t$ , $h^t \in \mathbb{R}^{90}$ , is described as 30 joints with 3D axis-angle representation. + +# 3.2. Stage One: Natural Hand Prediction + +Due to complex body-hand interaction and asymmetric motions of two hands, we leverage the bilateral hand disen + +tanglement branches and a body-specific branch to generate the natural 3D hands. Specifically, as depicted in Fig. 2 (stage one), our method mainly consists of a Bilateral Hand Disentanglement (BHD) module, a Spatial-Residual Memory (SRM) module, a Temporal-Motion Memory (TMM) module, and a transformer-based backbone. Firstly, we leverage a body encoder to obtain the body features $F_{\mathcal{B}} = \{F_{\mathcal{B}}^{t}\}_{t=0}^{T}$ , where $F_{\mathcal{B}}^{t} \in \mathbb{R}^{1 \times C}$ denotes a body feature at time $t$ , and $C$ is the feature dimension. Then, the body features are disentangled by BHD to acquire the single hand features $F_{\mathcal{SH}} = \{F_{\mathcal{SH}}^{t}\}_{t=0}^{T}$ , where $F_{\mathcal{SH}}^{t} \in \mathbb{R}^{1 \times C}$ . Considering the asymmetry motions of two hands, we exploit SRM to model the spatial interaction between the body and each hand, respectively. Besides, we further develop TMM to keep the two hand gestures temporal consistent with body dynamics. + +Bilateral Hand Disentangle Module: Due to the asymmetric motions of two hands, we employ a single hand autoencoder as the feature extractor to disentangle two hands. We firstly train an autoencoder on 3D single hands. As shown in Fig. 3 (a), we then utilize a Multilayer Perceptron (MLP) to project the body features into the single hand features $F_{\mathcal{SH}}$ . To ensure these single hand features represent each disentangled hand separately, we conduct the feature level and 3D representation level constraints by the single hand autoencoder, as follows: + +$$ +\mathcal {L} _ {d i s} = \left\| \widetilde {F _ {S H} ^ {t}} - F _ {\mathcal {S H}} ^ {t} \right\| _ {1} + \left\| \mathbb {D} \left(\widetilde {F _ {S H} ^ {t}}\right) - \mathbb {D} \left(F _ {\mathcal {S H}} ^ {t}\right) \right\| _ {1}, \tag {1} +$$ + +where $\widetilde{F_{SH}^{t}}$ denotes reconstructed hand feature at time $t$ , and $\mathbb{D}$ is the pre-trained decoder. + +Spatial-Residual Memory Module: After obtaining the disentangled single hand features, we introduce a Spatial- + +![](images/78ba7a6f3e4d99372ca280f6dc2b48c3d5e6db1cd244048e13824fefb5e5deb6.jpg) +Figure 3. Details of three sub-modules in the first stage. For brevity, we only show them in terms of single-branch view. + +![](images/92977298826388df9bc0781c682cf7bdc2383e230e38dad29dd3ca67967c258f.jpg) + +Residual Memory (SRM) module to model the spatial interaction between the body and each hand by residual learning. As illustrated in Fig. 3 (b), we leverage a spatial memory bank to store the spatial residual deformation representation between the current hand feature and the next step hand feature. Initially, each slot of the spatial memory bank is randomized as $m_j \in \mathbb{R}^{1 \times C}$ , where $j$ denotes slot index. To model the body-hand correlation, the current body feature is exploited as a query to retrieve the most relevant memory slot by calculating the cosine similarity. + +In particular, we represent the relevance between the query and memory slots via cosine similarity. Then we leverage the argmax operation to acquire the most relevant memory slot $m_r$ . Intuitively, the retrieved most relevant memory slot is leveraged as the spatial residual deformation between the current feature and the next step hand feature. However, it is intractable for argmax operation to back-propagate gradients. Thus, we conduct the softmax operation on the above calculated cosine similarity matrix to obtain the slot-wise affinity matrix. Then we acquire the learnable spatial residual deformation $F_{\mathcal{SH}}^{\Delta t}$ by aggregation between the slot-wise affinity matrix and each memory slot. We apply the above reading process to allow gradient back-propagation. In the training phase, we utilize the current hand feature to update the retrieved memory slot as $m_r = \gamma m_r + (1 - \gamma)F_{\mathcal{SH}}^t$ , where $\gamma = 0.8$ in our experiments. + +Different from obtaining the next hand feature by simple addition between the spatial residual deformation and current hand feature, we claim the spatial residual deformation refers to local spatial dependency from the current feature to the next time feature. This spatial dependency $S$ is formulated as: + +$$ +S _ {t} ^ {t + 1} = \operatorname {s o f t m a x} \left(F _ {\mathcal {S H}} ^ {\Delta t ^ {\prime}} \otimes F _ {\mathcal {S H}} ^ {t}\right), \tag {2} +$$ + +where $\otimes$ indicates matrix multiplication, and $^{\prime}$ indicates the transpose operation. With the help of the spatial dependency, the next step hand feature is represented as $F_{\mathcal{SH}}^{t + 1} = F_{\mathcal{SH}}^{t} + F_{\mathcal{SH}}^{t}\otimes S_{t}^{t + 1}$ . Through SRM, we obtain the spatial-enhanced single-hand feature. + +Temporal-Motion Memory Module: We further propose a Temporal-Motion Memory (TMM) module to ensure the single hand motions consistent with the body dynamics, + +globally. As depicted in Fig. 3 (c), we develop a motion encoder to obtain the sequence-aware body motion embedding as $F_{\mathcal{B}\mathcal{M}} \in \mathcal{R}^{T \times 1}$ . Here, we use body motion embedding to represent temporal changes among body skeletons in a sequence. Then, we leverage the body motion embedding as a query to retrieve the most consistent single hand motion embedding $F_{\mathcal{S}\mathcal{H}\mathcal{M}} \in \mathcal{R}^{T \times 1}$ stored in a temporal memory bank. The initialization and reading processes of the temporal memory bank are similar to SRM. We utilize the body motion embedding to update the retrieved slot of the temporal memory bank in the same manner as SRM. + +Afterward, we utilize the retrieved hand motion embedding to boost the body-hand temporal consistency. Specifically, we leverage the retrieved temporal embedding to represent the temporal correlation of hand gesture changes in a sequence. Then, the temporal-consistent enhanced sequential hand gestures are attained by: $F_{\mathcal{SH}} = F_{\mathcal{SH}} + F_{\mathcal{SH}} \odot \text{softmax}(F_{\mathcal{SHM}})$ , where $\odot$ means dot product. + +Transformer-based Backbone: As illustrated in Fig. 2 (stage one), to further enhance the body-hand interaction, we construct the bilateral hand disentanglement branches that interact with a body-specific branch to predict 3D hands. In particular, we introduce a body-specific transformer to generate body features as query $Q$ . Then, through 3 times Multi-Head Attention (MHA) [38], we use $Q$ to match the key features $K$ and value features $V$ in each hand transformer branch, respectively. + +Furthermore, we feed the concatenation of bilateral hand features into an MLP, thus obtaining the merged two-hand features. Similarly, we conduct 3 times MHA in the transformer-based decoder. This encourages the merged two-hand features to be more temporal consistent with body dynamics, holistically. At the end of the decoder, we adopt two fully-connected layers to obtain the 3D two hands sequence. Additionally, similar to [28], we employ a motion discriminator to ensure the natural and continuous initial prediction at stage one. + +# 3.3. Stage Two: Diverse Sampling + +We leverage a Prototypical-Memory Sampling Strategy (PSS) to achieve hands diversification based on our initial predictions from stage one. Specifically, we first con + +struct a prototypical memory to store the realistic two hands prototypes. Then, we obtain the retrieved realistic prototype representation based on the initial prediction at stage one. Meanwhile, as shown in Fig. 2 (stage two), we propose a sampling header to obtain the hand-informative perturbation via gradient-based Markov Chain Monte Carlo (MCMC) sampling. Finally, we concatenate the retrieved realistic hand prototype representation and perturbation to generate the diverse 3D two hands. + +Hands Prototypical Memory Construction: Inspired by [50], we reformulate the two hands diversification as a generation task. Instead of directly sampling the prior of the perturbation from the isotropic Gaussian distribution [7, 11, 16, 36], we assume the sampling space follows a learnable realistic prior distribution [30, 31, 50]. Since the existing 3D hand prediction dataset is noisy due to the automated annotation process, we propose a prototypical memory bank to store the realistic hand prototype representations encoded from real 3D hands. These 3D hands are captured from a studio-based mocap-captured dataset, named BEAT [22]. The reading and updating strategies of hands prototypical memory are the same as TMM. + +Gradient-based MCMC Sampling: We exploit the retrieved hand prototype representation concatenated with sampled perturbation vector $w$ to predict the diverse hand gestures. Given the observed 3D two hands $h \in \mathbb{R}^{90}$ , the $\tilde{h}$ is expressed as: + +$$ +\tilde {h} = R _ {\theta} (h, w) + \epsilon , w \sim p _ {\alpha} (w), \epsilon \sim \mathcal {N} (0, \sigma_ {\epsilon} ^ {2} I), \qquad (3) +$$ + +where $p_{\alpha}(w)$ is the prior distribution of perturbation with parameters $\alpha$ , and $\epsilon \sim \mathcal{N}(0, \sigma_{\epsilon}^{2}I)$ is the observation noise of hand gestures with $\sigma_{\epsilon}$ being given, $R_{\theta}$ is the generation model with parameters $\theta$ . + +Inspired by [11], we leverage an MLP-based sampling header $S_{\alpha}(w)$ to model the diversification sampling process, as illustrated in Fig. 2 (stage two). The prior distribution of perturbation is initialized from an isotropic Gaussian reference distribution, expressed as: + +$$ +p _ {\alpha} (w) \propto e x p \left[ - S _ {\alpha} (w) - \frac {1}{2 \sigma_ {w} ^ {2}} \| w \| ^ {2} \right], \tag {4} +$$ + +where the $M_{\alpha}(w) = S_{\alpha}(w) + \frac{1}{2\sigma_w^2}\| w\|^2$ is defined as the whole sampling function, and $\alpha$ is the learnable parameters of sampling header. The hyperparameter $\sigma_w$ denotes the standard deviation. For notation simplicity, let $\beta = \{\theta ,\alpha \}$ . For the $i$ th sample in a training mini-batch with size $n$ , the log-likelihood function of $\beta$ is defined as: + +$$ +L (\beta) = \sum_ {i = 1} ^ {n} \log \left[ \int p _ {\alpha} \left(w _ {i}\right) p _ {\theta} \left(\tilde {h} _ {i} \mid h _ {i}, w _ {i}\right) d w _ {i} \right]. \tag {5} +$$ + +Thus the gradient of $L(\beta)$ is computed as: + +$$ +\bigtriangledown L (\beta) = E _ {p _ {\beta (w | \tilde {h}, h)}} \left[ \bigtriangledown_ {\alpha} \operatorname {l o g p} _ {\alpha} (w) + \bigtriangledown_ {\theta} \operatorname {l o g p} _ {\theta} (\tilde {h} | h, w) \right]. \tag {6} +$$ + +The intractable expectation term $E_{p}(\cdot)$ in Eq. (6) is approximately solved by a gradient-based MCMC (Langevin dynamics) [4, 27]. In particular, the initial state of perturbation $p_0(w)$ is sampled from the Gaussian distribution. Through MCMC, the perturbation from the prior distribution and posterior distribution are represented as $\{w_i^-\}$ and $\{w_i^+\}$ , respectively. The detailed calculation process is in [27]. Therefore, the gradients of the generation model and sampling header are updated by: + +$$ +\nabla_ {\theta} R _ {\theta} = \frac {1}{n} \sum_ {i = 1} ^ {n} \left[ \frac {1}{\sigma_ {\epsilon} ^ {2}} \left(\tilde {h} _ {i} - R _ {\theta} \left(h _ {i}, w _ {i} ^ {+}\right)\right) \nabla_ {\theta} R _ {\theta} \left(h _ {i}, w _ {i} ^ {+}\right) \right], \tag {7} +$$ + +$$ +\nabla_ {\alpha} S _ {\alpha} = \frac {1}{n} \sum_ {i = 1} ^ {n} \left[ \nabla_ {\alpha} S _ {\alpha} \left(w _ {i} ^ {-}\right) \right] - \frac {1}{n} \sum_ {i = 1} ^ {n} \left[ \nabla_ {\alpha} S _ {\alpha} \left(w _ {i} ^ {+}\right) \right]. \tag {8} +$$ + +# 3.4. Objective Functions + +In stage one, we apply the following loss functions to constrain the initial prediction process of hand gestures. + +Reconstruction Loss: We use the ground truth to supervise the predicted two hands as $\mathcal{L}_{rec} = \left\| \mathcal{H} - \tilde{\mathcal{H}} \right\|_1$ , where $\tilde{\mathcal{H}}$ denotes generated hands. + +Perceptual Loss: Inspired by [15], we leverage the studio-based 3D hands dataset BEAT to pre-train an MLP-based autoencoder as a feature extractor $\phi(\cdot)$ . We utilize the $L1$ loss to constrain the difference between the extracted features of $\mathcal{H}$ and $\tilde{\mathcal{H}}$ , as formulated: $\mathcal{L}_{perc} = \left\| \phi(\mathcal{H}) - \phi(\tilde{\mathcal{H}}) \right\|_1$ . + +Adversarial Learning: Following the configuration of [28], we employ the adversarial training loss as: + +$$ +\mathcal {L} _ {a d v} = \mathbb {E} _ {\mathcal {H}} \left[ \log D (\mathcal {H}) \right] + \mathbb {E} _ {\mathcal {B}} \left[ \log \left(1 - (G (\mathcal {B}))\right) \right], \tag {9} +$$ + +where $D$ denotes the discriminator and $G$ means hands generator. Finally, the overall objective in stage one is: + +$$ +\min _ {G} \max _ {D} \mathcal {L} _ {\text {t o t a l}} ^ {\text {s t a g e 1}} = \mathcal {L} _ {\text {r e c}} + \mathcal {L} _ {\text {a d v}} + \mathcal {L} _ {\text {p e r c}} + 0. 5 \mathcal {L} _ {\text {d i s}}, \tag {10} +$$ + +where $\mathcal{L}_{dis}$ denotes disentanglement constraint in Eq. ((1)). + +In the second stage, the overall objective to train our model is defined as follows: + +$$ +\mathcal {L} _ {\text {t o t a l}} ^ {\text {s t a g e 2}} = \left\| h - R _ {\theta} \left(h, w ^ {+}\right) \right\| _ {1}, \tag {11} +$$ + +where $w^{+}$ is the posterior distribution of the perturbation. We conduct the frame-level diversification based on the initial prediction at stage one. To ensure temporal smoothness, we further apply temporal smoothness [45] to the diversified 3D hand gestures as a post processing. + +Table 1. Comparison with the state-of-the-art methods on B2H dataset and our proposed TED Hands dataset of the first stage initial prediction. $\downarrow$ indicates the lower the better. + +
MethodsB2H Dataset [28]TED Hands Dataset
L2↓FHD↓MPJRE↓L2↓FHD↓MPJRE↓
Body2Hands [28]CVPR'213.7601.10313.1482.5511.17411.371
MRT [39]NeurIPS'213.6340.97312.5762.3250.87710.314
BTM [8]WACV'233.6571.26312.6962.3501.11110.440
LTD [25]ICCV'193.7551.07313.3152.4821.36711.078
MotionMixer [1]IJCAI'223.6160.98612.7022.3240.91010.427
SPGSN [19]ECCV'223.6560.96212.7572.4350.99010.887
Ours (stage one)3.4200.47111.4062.0370.2588.888
+ +Table 2. Sampling experiment results on B2H dataset. $\downarrow$ indicates the lower the better, and $\uparrow$ indicates the higher the better. $\pm$ means 95% confidence interval. + +
MethodsFHD↓Diversity↑
Body2hands [28] w/ PSS2.5040.497±0.028
MRT [39] w/ PSS1.9820.698±0.031
BTM [8] w/ PSS2.3790.703±0.038
LTD [25] w/ PSS1.8930.577±0.028
MotionMixer [1] w/ PSS2.1690.869±0.055
SPGSN [19] w/ PSS2.0040.874±0.046
Ours w/ VAE [36]1.6171.001±0.061
Ours (stage two)1.2391.324±0.066
+ +# 4. Experiments + +# 4.1. Datasets and Experimental Setting + +B2H Dataset: The B2H dataset [28] is automatically annotated by a monocular-based 3D pose estimation model [44], including the gestures of 8 speakers from in-the-wild talk show videos. In the original B2H dataset, there are more than 139K sequences. Each sequence includes 64 frames, with 32 frames overlapping between every two sequences. However, due to the noisiness and unavailable videos, we obtain 120,188 sequences finally. In our work, we adopt the same division criteria as [28] to split the training and testing dataset. + +TED Hands Dataset: Due to the limited avatar identities in the existing 3D hand prediction dataset, we newly collect a large-scale 3D hands dataset (dubbed TED Hands) based on the TED Gesture [46, 47]. The original TED Gesture dataset only contains 10 upper body joints without elaborate fingers of two hands. Hence, we leverage a state-of-the-art 3D pose estimator FrankMocap [34] to extract the whole body-hand joints as pseudo ground truth from the video links provided by TED Gesture. Concretely, each joint of our dataset is normalized as the 3D axis-angle representation in a fixed kinematic structure [33]. In this fashion, our dataset is invariant to root joint motion and body shape. Finally, we acquired the 134,456 sequences from 1,755 different speakers, with 99.6 hours of TED talking speeches. Each sequence includes 64 frames without over + +Table 3. Sampling experiment results on our proposed TED Hands dataset. $\downarrow$ indicates the lower the better, and $\uparrow$ indicates the higher the better. $\pm$ means ${95}\%$ confidence interval. + +
MethodsFHD↓Diversity↑
Body2hands [28] w/ PSS2.0052.705±0.153
MRT [39] w/ PSS1.1884.954±0.190
BTM [8] w/ PSS1.2243.632±0.150
LTD [25] w/ PSS1.3852.851±0.101
MotionMixer [1] w/ PSS1.6133.487±0.208
SPGSN [19] w/ PSS1.5653.812±0.219
Ours w/ VAE [36]1.0334.018±0.190
Ours (stage two)0.9386.426±0.300
+ +lap. We randomly spit the dataset into the $70\%$ training set, $10\%$ validation set, and $20\%$ testing set. Please refer to the supplementary material for more details. + +Implementation Details: Our model is implemented on the PyTorch platform with 2 NVIDIA RTX 2080Ti GPUs. We train the model utilizing Adam optimizer with an initial learning rate of 0.003. The whole training takes 30 epochs with a batch size of 64. We set $\sigma_{\epsilon} = 1$ in Eq. (3), and $\sigma_w = 1$ in Eq. (4). + +Evaluation Metrics: To fully evaluate the naturalness of initial predictions at stage one and the diversity of sampled hand gestures at stage two, we employ various metrics: + +- $L2$ Distance: Distance between the generated whole two hand poses and pseudo ground truth. +- FHD: Inspired by FGD [46, 47], we propose a hand-specific metric (named FHD) to measure the Fréchet distance between the features of generated hands and pseudo ground truth. The feature extractors of FHD are pretrained by B2H and TED Hands datasets, respectively. +- MPJRE: We leverage the Mean Per Joint Rotation Error [○] (MPJRE) [14] to measure the absolute distance between predicted 3D representation joints and pseudo ground truth. +- Diversity: To verify the diversity of sampled hand gestures, we calculate the average feature distance between 500 random combined sequential pairs [20, 24]. The feature extractor is the same as FHD. + +Table 4. Ablation study on different loss functions and different components of the proposed method. $\downarrow$ indicates the lower the better. ✓ indicates the employment of a certain module or loss function. # means the temporal-motion memory module is adopted before the spatial-residual memory module. † denotes the weights of the two hands transformers are shared. + +
Model VariationsB2H Dataset [28]TED Hands Dataset
BaselineFull Model\( \mathcal{L}_{dis} \)\( \mathcal{L}_{perc} \)SRMTMML2 ↓FHD ↓MPJRE ↓L2 ↓FHD ↓MPJRE ↓
✓3.6501.09112.6902.3660.97710.531
✓3.6040.77312.4532.3030.73110.250
✓✓3.5520.68212.0372.2160.5959.786
✓✓3.5630.65712.0852.2610.69910.026
✓✓✓3.5040.64011.8282.1610.4959.508
✓✓✓✓3.4570.58011.6872.1000.3939.209
#✓✓✓✓✓3.4840.61411.7582.1240.4639.311
†✓✓✓✓✓3.4760.59811.7482.1560.3809.467
✓✓✓✓✓3.4200.47111.4062.0370.2588.888
+ +# 4.2. Quantitative Results + +Comparisons with the state-of-the-art: We compare our method with the pioneering 3D hands prediction work, named Body2hands [28]. Moreover, to fully verify the superiority of our method, we implement various state-of-the-art (SOTA) human motion prediction models: MTR [39], BTM [8], LTD [25], MotionMixer [1], and SPGSN [19]. For fair comparisons, all methods are implemented by source codes or pre-trained models released by authors. Since the above counterparts are designed without the diversification setting, the comparison is divided into two parts. + +In the first part, we leverage our stage one initial prediction to compare with other competitors. We adopt the $L2$ distance, FHD, and MPJRE to provide a well-rounded view of comparisons. As reported in Tab. 1, our method outperforms all the counterparts by a large margin. Remarkably, our method achieves the lowest FHD and MPJRE sores on both datasets. Concretely, on FHD scores of the TED Hands dataset, our method performs even $70.6\%$ lower than the optimal results of other competitors (e.g., $(0.877 - 0.258) / 0.877 \approx 70.6\%$ ). + +To demonstrate the effectiveness of the diversification process in our method, we compare the diversified results based on the various predictions from above mentioned competitive methods. Meanwhile, we replace our MCMC-based sampling strategy with CVAE [36] to diversify our initial prediction at stage one. We exploit the FHD and Diversity metrics in the second part. As shown in Tab. 2 and Tab. 3, our method achieves superior performance from the perspective of diversity. Although the FHD is slightly worse than stage one due to the sampled perturbation, our method still achieves the optimal result. Compared with CVAE, our method effectively avoids the potential posterior collapse problem [12]. Moreover, we observe that the diversity scores on our TED Hands dataset are much higher than the B2H dataset with all the counterparts. It applies that our newly collected TED Hands dataset includes more diverse hand gestures. + +Ablation Study: We further conduct the ablation study based on stage one to verify the effectiveness of each module and different loss functions, as indicated in Tab. 4. The baseline model is implemented by a simple transformer-based pipeline without bilateral hand branches. Our full model adopts the bilateral hand branches interacting with a body-specific transformer to produce the 3D hand gestures. + +As shown in Tab. 4, all combinations of the different loss functions and components have positive impacts on 3D hand predictions. The most complete combination attains the best results. Even though we directly construct the bilateral branches without disentanglement constraints (i.e., $\mathcal{L}_{dis}$ ) as full model, our method achieves comparable performance against the simple baseline. This indicates the global body-hand interaction are effectively modeled by bilateral hand transformers and a body-specific transformer. Then, we observe that after adding the loss functions $\mathcal{L}_{dis}$ and $\mathcal{L}_{perc}$ , the performance of our method is significantly improved, especially in MPJRE scores on both datasets (e.g., $10.250 \rightarrow 9.508$ on TED Hands). + +To verify the effectiveness of SRM and TMM, we conduct plenty of experiments on both datasets. As reported in Tab. 4, when we first employ the SRM, our method achieves the lower $L2$ distance and FHD scores on both datasets. Then, after adding TMM, our method achieves the best performance. This result proves that TMM effectively models the body-hand temporal association. Besides, we find that when TMM is adopted before SRM, the model performance decreases slightly (the third row from bottom to top in Tab. 4). This corresponds to both TMM and transformer-based backbone (i.e. body-transformer, bilateral hand branches) focus on modeling the body-hand temporal correlation. Both of them encourage the two hands to be more temporal consistent with body dynamics. Employing the SRM between them leads to worse spatial-temporal modeling for body-hand interaction. + +Moreover, we conduct experiments that the parameter weights of bilateral hand transformers are shared. As shown in Tab. 4 (the second row from bottom to top), the per + +![](images/5fc72cec39abbb050f84fae479cd09eed107d4fa7638467cc8fad837aafaccd7.jpg) + +![](images/1558c91852efe02a108b243696baf43346c23f9f2ac4359a39ffb8a9764c4a21.jpg) + +![](images/f15a464f111ecb454ead8f604c3acf7dba97f5691f7f79e9f25a8ef12975004d.jpg) + +![](images/d2e3e551457400722ddffaa442cb22d0d9c09b91cad2f37d9fab73205c713f98.jpg) + +![](images/7d576cac27ff7bbbc03ca3e6d61d2ce9287176e3b0900e877432108118d30c34.jpg) + +![](images/39e9e478473bbbaf337cf17e9be36a958569b8bfb9ac75330f9279a9ca607500.jpg) + +![](images/134c7e5710416f9426df6ef2f96f488a6221a906cf1b0d1018b0c6d97c5d5dca.jpg) + +![](images/057f40ba25ec8738cdd94c526eaca47a217bf6def6cf4eb65f17460da4773879.jpg) + +![](images/adb0d9d2812e21e95d9281341d8c70b732342885eb5bdba424959269d6df81f2.jpg) + +![](images/8fd36176c75fde745759a8e8c66b066837838d1cb0d7c74f9436f6a22bea1027.jpg) + +![](images/7a1582506941d0e5d3cd02f995a04ae64578c14b169037357596c1524555f3cd.jpg) + +![](images/9e50ca21b714be7281d78ae78bbf89a77f83aab2e0c07fd3caecc0ac1e1de12e.jpg) + +![](images/dcab86d6126b9d1ffc46b8575cca2ba322edf5120870b12cbc6f080c49fc8c5c.jpg) + +![](images/173ed2513979b223bcdc2267c914ff7f92e557e62609caffe32514e8f8bd3d5c.jpg) + +![](images/d52a8acc84d033ce196d70556fb40d6a75618cd6d0e684da430e76875a577423.jpg) + +![](images/9bfbd2e0aff1d88632a8295a06280874ffb6e42d8eb08ed5016af365ed30714b.jpg) + +![](images/ea2c8da5a8fea9caba47da437a6c617af8b63365da96a6c88562856333177a10.jpg) + +![](images/3f4e2d6acc899a590b48916c9fad223a7a6d455326e29160ade3a94821aa3c24.jpg) + +![](images/cb346ee03fd67e1264ae60f4153880eee9c66ec91b48c1478510f03375c693b4.jpg) + +![](images/cbb30a71b92e775b610899b99bacaae47258bb7fe70a0e4bc0f691e3813da643.jpg) + +![](images/b268d999e05435a599324e6bb1cc1c00c17e970f232009a353efca713a82c202.jpg) +(a) GT + +![](images/393206eb6fc1eaa22a646e58a93e3e0c4078cdc23f126b251979fae62df784cc.jpg) +(b) Body2hands + +![](images/f07b9788321ea595118d0fd06af8bd840ce6405821a6eb9388230e9055050ad4.jpg) +(c) BTM + +![](images/d05db83f94cfea742ccd4d35552dbea83171ce8290039ac739bcaed2fa74ddd4.jpg) +(d) MRT + +![](images/dd207b3dec3f5cf64b33fbfde1845e0fd29c533ec47bd1bce5bd2a7a637cdcbc.jpg) +(e) LTD + +![](images/b52b50db39dac9f29742cdc1c2c8f6f0726e36389bfa98ba46fc2beac6fae602.jpg) +(f) MotionMixer + +![](images/0371e0ce936f7a7b3d399f3ad39a7f7a38dbb180b744ec3a5ded4898c91db40e.jpg) +(g) SPGSN + +![](images/41fc0f062c0403672db79fc89c731d583edfa617f6dfbd1125005c303c26b4ee.jpg) +(h) Ours (h) Ours (h) Ours (w/o Sampling) (w/ Sampling) (w/ Sampling) + +![](images/f91978b5ca83bbdce43821324824f3a655b1ad45c5a318b92462e301dd1a9659.jpg) + +![](images/f4c8ce356583382e8bb654d844f519e8ebcfcf659a3ff9b912e1fc68a8dae4c7.jpg) + +![](images/78ec315dcbf9d040db00935726f7602563e4afd77f184d05ecdffb77e7b25040.jpg) +Figure 4. Visualization of our predicted 3D hand gestures against various state-of-the-art methods [1,8,19,25,28,39]. From top to bottom, samples of the first row are from the B2H dataset, and the others are from our TED Hands dataset. Best view on screen. +Figure 5. User study on the motion naturalness, smoothness, and body-hand temporal consistency. $\uparrow$ indicates the higher the better. + +formance is decreased due to the spatial-temporal interaction between the body and single-hand-specific branch being merged here. This supports our key technical insight on bilateral hand disentanglement. Additionally, to verify the practical ability of our method, we conduct experiments on model complexity and inference time, more details are presented in the supplementary material. + +# 4.3. Qualitative Evaluation + +User Study: To further analyze the visual quality of the predicted 3D hand gestures by different methods, we recruit 15 volunteers to participate in the user study. We take the naturalness, smoothness, and body-hand temporal consistency as three evaluation perceptions and the range of grades is from 0 to 5 (the higher, the better). The statistical results are reported in Fig. 5. Our method shows the best performance in all three metrics. Especially in the naturalness and body-hand temporal consistency, our method achieves remarkable advantages among all the methods due to the body-hand interaction modeling by SRM and TMM. + +Visualization: To fully verify the performance of our method, we show the visualization of generated 3D hands from the first and second stages, respectively. As depicted in Fig. 4, we compare our initial predictions (from stage one) with various SOTA approaches. The avatars are ren- + +dered from ground truth speakers in B2H and TED Hands datasets. We observe that Body2hands, BTM, and LTD generate unreasonable hand gestures (e.g., in the third row of Body2hands, left-hand gestures of avatar). MRT, Motion-Mixer, and SPGSN predict the natural results, but the finger gestures are less consistent with the upper body dynamics. In contrast, our method successfully predicts the perceptually convincing 3D hand gestures from the body dynamics. This supports our key insight to build the bilateral hand disentanglement branches since the asymmetric motions of two hands. We further visualize the diversification results generated by our method at stage two. As shown in Fig. 1 and Fig. 4, with the same upper body dynamics as input, our method obtains the natural and diverse 3D hand gestures on B2H and TED Hands datasets, respectively. Please refer to the supplementary material for more visualization results. + +# 5. Conclusion + +In this paper, we present a novel bilateral hand disentanglement based two-stage method towards natural and diverse 3D hand prediction from body dynamics. In the first stage, upon the bilateral hand branches, we fully take advantage of the spatial-temporal body-hand interaction for generating natural initial 3D hand gestures. Then, in the second stage, we further diversify our natural initial 3D hand gestures by gradient-based markov chain monte carlo sampling. Extensive experiments conducted on B2H and our newly collected TED Hands datasets demonstrate the superiority of our method. As our method aims at generating diverse 3D avatar hand postures, in future work, we will investigate sampling diverse 3D hand gestures with temporal smoothness, instead of frame-wise sampling. + +Acknowledgements. This research is funded in part by ARC-Discovery grant (DP220100800 to XY) and ARC-DECRA grant (DE230100477 to XY). + +# References + +[1] Arij Bouazizi, Adrian Holzbock, Ulrich Kressel, Klaus Dietmayer, and Vasileios Belagiannis. Motionmixer: Mlp-based 3d human body pose forecasting. 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"image_body" + }, + { + "bbox": [ + 45, + 357, + 547, + 380 + ], + "lines": [ + { + "bbox": [ + 45, + 357, + 547, + 380 + ], + "spans": [ + { + "bbox": [ + 45, + 357, + 547, + 380 + ], + "type": "text", + "content": "Figure 1. Diverse exemplary clips sampled by our method from our newly collected TED Hands Dataset. The vital frames are visualized to demonstrate that the hand gestures change with the upper body dynamics, synchronously. Best view on screen." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 143, + 389, + 192, + 402 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 389, + 192, + 402 + ], + "spans": [ + { + "bbox": [ + 143, + 389, + 192, + 402 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 405, + 290, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 405, + 290, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 405, + 290, + 693 + ], + "type": "text", + "content": "Predicting natural and diverse 3D hand gestures from the upper body dynamics is a practical yet challenging task in virtual avatar creation. Previous works usually overlook the asymmetric motions between two hands and generate two hands in a holistic manner, leading to unnatural results. In this work, we introduce a novel bilateral hand disentanglement based two-stage 3D hand generation method to achieve natural and diverse 3D hand prediction from body dynamics. In the first stage, we intend to generate natural hand gestures by two hand-disentanglement branches. Considering the asymmetric gestures and motions of two hands, we introduce a Spatial-Residual Memory (SRM) module to model spatial interaction between the body and each hand by residual learning. To enhance the coordination of two hand motions wrt. body dynamics holistically, we then present a Temporal-Motion Memory (TMM) module. TMM can effectively model the temporal association between body dynamics and two hand motions. The second stage is built upon the insight that 3D hand predictions should be non-deterministic given the sequential body postures. Thus, we further diversify our 3D hand predictions based on the initial output from the stage one. Concretely, we propose a Prototypical-Memory Sampling Strategy (PSS) to generate the non-deterministic hand gestures by gradient" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 390, + 547, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 390, + 547, + 462 + ], + "spans": [ + { + "bbox": [ + 304, + 390, + 547, + 462 + ], + "type": "text", + "content": "based Markov Chain Monte Carlo (MCMC) sampling. Extensive experiments demonstrate that our method outperforms the state-of-the-art models on the B2H dataset and our newly collected TED Hands dataset. The dataset and code are available at: https://github.com/XingqunQilab/Diverse-3D-Hand-Gesture-Prediction." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 475, + 387, + 488 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 475, + 387, + 488 + ], + "spans": [ + { + "bbox": [ + 306, + 475, + 387, + 488 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 496, + 547, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 496, + 547, + 568 + ], + "spans": [ + { + "bbox": [ + 304, + 496, + 547, + 568 + ], + "type": "text", + "content": "Given a sequence of upper body skeletons, our task aims at predicting natural and diverse 3D hand gestures. Such non-verbal body-hand coordination plays an important role in various virtual avatar scenarios, including human-agent interface [13, 17, 35, 40, 41], co-speech gesture synthesis [5, 20, 24, 46, 47], holoportation [29]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 570, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 714 + ], + "type": "text", + "content": "However, it is quite difficult to predict the natural and diverse 3D hand gestures due to three major challenges: (1) Spatially asymmetric motions: Asymmetric motions of two hands have been overlooked by previous works [28], e.g., when one hand moves, the other could be static or moving slowly. (2) Temporal consistency wrt. body dynamics: Predicted sequential hand gestures should be temporally consistent with respect to the body dynamics. (3) Non-deterministic hand prediction: Given the upper body dynamics, various 3D hand gestures can match the body postures rather than a deterministic result. Since the existing dataset has only a few avatar identities, the generated hands" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "type": "text", + "content": "*Corresponding author." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "text", + "content": "4616" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 129, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 129, + 84 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 129, + 84 + ], + "type": "text", + "content": "often lack diversity." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 86, + 287, + 181 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 86, + 287, + 181 + ], + "spans": [ + { + "bbox": [ + 46, + 86, + 287, + 181 + ], + "type": "text", + "content": "Due to complex body-hand interaction and asymmetric movements of two hands, directly predicting the natural and diverse 3D hand is rather difficult. Therefore, we propose to address the aforementioned challenges in a prediction followed by a diversification paradigm. To be specific, we propose a novel bilateral hand disentanglement based two-stage method, to generate natural and diverse 3D hand gestures from upper body dynamics." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 182, + 288, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 182, + 288, + 386 + ], + "spans": [ + { + "bbox": [ + 46, + 182, + 288, + 386 + ], + "type": "text", + "content": "In the first stage, we aim to predict the natural 3D hand gestures. Our key insight is to establish the bilateral hand disentanglement for asymmetric motions of two hands. We construct two hand-disentangled branches that interact with a body-specific branch to initially predict natural 3D hands. Here, we leverage a single-hand autoencoder to extract each hand feature respectively, thus achieving the effects of two hands disentanglement. Furthermore, we propose a Spatial-Residual Memory (SRM) module to model the spatial relation between the body and each hand via residual learning. Specifically, we employ a spatial memory bank to store the spatial residual deformation representations of each hand. Then, we leverage the current upper body embedding as a query to retrieve the most relevant spatial residual deformation. The queried spatial residual deformation and the synchronized hand embedding vector are used to generate the next step hand representation." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 388, + 287, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 388, + 287, + 519 + ], + "spans": [ + { + "bbox": [ + 46, + 388, + 287, + 519 + ], + "type": "text", + "content": "To ensure the motions of both hands are temporally consistent with the upper body sequence, we present a Temporal-Motion Memory (TMM) module. TMM models the correlation between body dynamics and hand gestures. Similar to SRM, we utilize a temporal memory bank to store the motion features of each hand at the sequence level. Moreover, we employ a motion encoder to acquire the input body dynamics representation, and then use the body dynamics representation as a query to produce temporally consistent hand motion features. In this fashion, we can effectively synchronize hand motions with body dynamics." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 521, + 287, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 700 + ], + "type": "text", + "content": "In the second stage, we develop a Prototypical-Memory Sampling Strategy (PSS) to diversify our 3D hand predictions based on the initial prediction at stage one. Here, we leverage an external memory that stores realistic hand prototypes, and then search a prototype that is closest to our initial predicted hands. Once we obtain the prototype, we project it into the feature space. To increase the diversity while preserving the authenticity of generated hand gestures, we perturb the prototype feature via gradient-based Markov Chain Monte Carlo (MCMC) sampling [23]. Specifically, a random noise is first sampled from a Gaussian distribution as a prior perturbation and then we update its posterior via Langevin dynamics based MCMC [4, 27]. Then, the perturbation is concatenated with the prototype feature to produce realistic new hand gestures." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 59, + 701, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 286, + 713 + ], + "type": "text", + "content": "Moreover, the existing 3D hand prediction dataset [28]" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "text", + "content": "contains less than 10 avatar identities, resulting in insufficient diversity of gestures. Therefore, we newly collect a large-scale 3D hand gestures dataset (dubbed TED Hands) with more than 1.7K avatar identities from in-the-wild scenarios. Our dataset contains around 100 hours of TED talk speeches, enabling research on diverse 3D hand gesture predictions. Extensive experiments conducted on the B2H dataset [28] and our TED Hands dataset demonstrate our method outperforms the state-of-the-art." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 180, + 523, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 180, + 523, + 192 + ], + "spans": [ + { + "bbox": [ + 306, + 180, + 523, + 192 + ], + "type": "text", + "content": "Overall, our contributions are summarized as follows:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 196, + 545, + 387 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 306, + 196, + 545, + 244 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 196, + 545, + 244 + ], + "spans": [ + { + "bbox": [ + 306, + 196, + 545, + 244 + ], + "type": "text", + "content": "- We propose a novel bilateral hand disentanglement based two-stage 3D hand generation method to predict diverse 3D hand gestures from body dynamics in a prediction followed by diversification paradigm." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 247, + 545, + 307 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 247, + 545, + 307 + ], + "spans": [ + { + "bbox": [ + 306, + 247, + 545, + 307 + ], + "type": "text", + "content": "- We present a Spatial-Residual Memory (SRM) module to predict authentic hand poses from disentangled hand representations and a Temporal-Motion Memory (TMM) module to ensure temporal consistency of generated 3D hands." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 312, + 545, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 312, + 545, + 348 + ], + "spans": [ + { + "bbox": [ + 306, + 312, + 545, + 348 + ], + "type": "text", + "content": "- We design a Prototypical-Memory Sampling Strategy (PSS) to diversify our initial 3D hand prediction, thus obtaining natural and diverse hand gestures." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 351, + 545, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 351, + 545, + 387 + ], + "spans": [ + { + "bbox": [ + 306, + 351, + 545, + 387 + ], + "type": "text", + "content": "- We collect a new large-scale sequential 3D hand dataset from 1.7K persons' hand gestures, significantly facilitating research on diverse 3D hands generation." + } + ] + } + ], + "index": 11 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 399, + 392, + 412 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 399, + 392, + 412 + ], + "spans": [ + { + "bbox": [ + 306, + 399, + 392, + 412 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 420, + 545, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 420, + 545, + 456 + ], + "spans": [ + { + "bbox": [ + 304, + 420, + 545, + 456 + ], + "type": "text", + "content": "Since our method predicts the 3D hand motions from upper body skeletons, we briefly review the approaches of 3D hand pose estimation and 3D human motion prediction." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 461, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 461, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 461, + 545, + 628 + ], + "type": "text", + "content": "3D hand pose estimation: 3D hand estimation has received impressive attention for its wide applications in virtual reality, augmented reality, and robotics. Recently, parametric 3D hand model MANO [33] and various mocap-captured 3D hand datasets [2,9,26,52] significantly improve the performance of 3D hand pose estimation from the single image [6,18,32,37,49,51]. Among various image-based 3D hand estimation approaches, transformer-based models [10,18,21] have demonstrated outstanding performance. For instance, Li et al. [18] propose an interacting attention graph transformer to estimate two-hand poses from a single image. Shreyas et al. [10] present a hand keypoint based transformer combined with convolutional networks to establish the association among different joints." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "Since our task aims to predict the 3D hand motions from upper body skeletons, these single-image-based methods [10, 18, 21] cannot be directly employed. However, their excellent performance in 3D hand estimation inspires us to model the body-hand interaction via transformer-based architectures. Besides, Ng et al. [28] generate the hand gestures from body dynamics in a holistic manner. As the" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "4617" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 69, + 72, + 526, + 258 + ], + "blocks": [ + { + "bbox": [ + 69, + 72, + 526, + 258 + ], + "lines": [ + { + "bbox": [ + 69, + 72, + 526, + 258 + ], + "spans": [ + { + "bbox": [ + 69, + 72, + 526, + 258 + ], + "type": "image", + "image_path": "75149e03bc849e65e8e9dc8ef26c726a504a4a47887a94b49003659c1df7a9cd.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 260, + 547, + 285 + ], + "lines": [ + { + "bbox": [ + 46, + 260, + 547, + 285 + ], + "spans": [ + { + "bbox": [ + 46, + 260, + 547, + 285 + ], + "type": "text", + "content": "Figure 2. The pipeline of our proposed method. In stage one, we generate the natural initial 3D hands from sequential upper body skeletons. In stage two, we diversify our 3D hand predictions based on the initial gestures at stage one." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 299, + 288, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 299, + 288, + 348 + ], + "spans": [ + { + "bbox": [ + 46, + 299, + 288, + 348 + ], + "type": "text", + "content": "asymmetric motions of two hands, their method might produce some unnatural hand gestures. This also motivates us to disentangle two hands in hand pose estimation and then synchronize two-hands motions." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 352, + 288, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 352, + 288, + 520 + ], + "spans": [ + { + "bbox": [ + 46, + 352, + 288, + 520 + ], + "type": "text", + "content": "3D human motion prediction: Predicting human future motions from existing 3D poses has been widely studied [1, 8, 19, 25, 39]. Wang et al. [39] leverage a multi-range transformer that attends learn local-global features for multi-person motion prediction. Bouazizi et al. [1] introduce a multi-layer perception based human motion prediction network to learn spatio-temporal pose relation. Due to the similar nature between 3D human motion prediction and hand pose prediction, these models [1, 8, 19, 25, 39] can be easily adopted as our baselines. Moreover, we notice that memory based networks [3, 42, 43, 48] achieve promising performance in long-sequence modeling tasks. Motivated by this, we introduce external memories into our network to facilitate our long-range hand pose generation." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 528, + 153, + 541 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 528, + 153, + 541 + ], + "spans": [ + { + "bbox": [ + 47, + 528, + 153, + 541 + ], + "type": "text", + "content": "3. Proposed Method" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 548, + 171, + 559 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 548, + 171, + 559 + ], + "spans": [ + { + "bbox": [ + 47, + 548, + 171, + 559 + ], + "type": "text", + "content": "3.1. Problem Formulation" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 566, + 287, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 566, + 287, + 666 + ], + "spans": [ + { + "bbox": [ + 47, + 566, + 287, + 666 + ], + "type": "text", + "content": "Given a sequence of 3D upper body skeletons " + }, + { + "bbox": [ + 47, + 566, + 287, + 666 + ], + "type": "inline_equation", + "content": "\\mathcal{B} = \\{b^t\\}_{t=0}^T" + }, + { + "bbox": [ + 47, + 566, + 287, + 666 + ], + "type": "text", + "content": ", our goal is to predict the natural and diverse 3D hand poses " + }, + { + "bbox": [ + 47, + 566, + 287, + 666 + ], + "type": "inline_equation", + "content": "\\mathcal{H} = \\{h^t\\}_{t=0}^T" + }, + { + "bbox": [ + 47, + 566, + 287, + 666 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 566, + 287, + 666 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 47, + 566, + 287, + 666 + ], + "type": "text", + "content": " is the sequence length. Specifically, we define each step body skeleton (i.e., collars, shoulders, elbows, and wrists) " + }, + { + "bbox": [ + 47, + 566, + 287, + 666 + ], + "type": "inline_equation", + "content": "b^t \\in \\mathbb{R}^{24}" + }, + { + "bbox": [ + 47, + 566, + 287, + 666 + ], + "type": "text", + "content": " as 8 joints. Each joint is represented by a 3D axis-angle representation. Meanwhile, the 3D hand pose at time " + }, + { + "bbox": [ + 47, + 566, + 287, + 666 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 566, + 287, + 666 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 566, + 287, + 666 + ], + "type": "inline_equation", + "content": "h^t \\in \\mathbb{R}^{90}" + }, + { + "bbox": [ + 47, + 566, + 287, + 666 + ], + "type": "text", + "content": ", is described as 30 joints with 3D axis-angle representation." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 671, + 243, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 243, + 684 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 243, + 684 + ], + "type": "text", + "content": "3.2. Stage One: Natural Hand Prediction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "text", + "content": "Due to complex body-hand interaction and asymmetric motions of two hands, we leverage the bilateral hand disen" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 299, + 547, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 299, + 547, + 483 + ], + "spans": [ + { + "bbox": [ + 304, + 299, + 547, + 483 + ], + "type": "text", + "content": "tanglement branches and a body-specific branch to generate the natural 3D hands. Specifically, as depicted in Fig. 2 (stage one), our method mainly consists of a Bilateral Hand Disentanglement (BHD) module, a Spatial-Residual Memory (SRM) module, a Temporal-Motion Memory (TMM) module, and a transformer-based backbone. Firstly, we leverage a body encoder to obtain the body features " + }, + { + "bbox": [ + 304, + 299, + 547, + 483 + ], + "type": "inline_equation", + "content": "F_{\\mathcal{B}} = \\{F_{\\mathcal{B}}^{t}\\}_{t=0}^{T}" + }, + { + "bbox": [ + 304, + 299, + 547, + 483 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 299, + 547, + 483 + ], + "type": "inline_equation", + "content": "F_{\\mathcal{B}}^{t} \\in \\mathbb{R}^{1 \\times C}" + }, + { + "bbox": [ + 304, + 299, + 547, + 483 + ], + "type": "text", + "content": " denotes a body feature at time " + }, + { + "bbox": [ + 304, + 299, + 547, + 483 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 299, + 547, + 483 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 299, + 547, + 483 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 299, + 547, + 483 + ], + "type": "text", + "content": " is the feature dimension. Then, the body features are disentangled by BHD to acquire the single hand features " + }, + { + "bbox": [ + 304, + 299, + 547, + 483 + ], + "type": "inline_equation", + "content": "F_{\\mathcal{SH}} = \\{F_{\\mathcal{SH}}^{t}\\}_{t=0}^{T}" + }, + { + "bbox": [ + 304, + 299, + 547, + 483 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 299, + 547, + 483 + ], + "type": "inline_equation", + "content": "F_{\\mathcal{SH}}^{t} \\in \\mathbb{R}^{1 \\times C}" + }, + { + "bbox": [ + 304, + 299, + 547, + 483 + ], + "type": "text", + "content": ". Considering the asymmetry motions of two hands, we exploit SRM to model the spatial interaction between the body and each hand, respectively. Besides, we further develop TMM to keep the two hand gestures temporal consistent with body dynamics." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 498, + 547, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 547, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 547, + 617 + ], + "type": "text", + "content": "Bilateral Hand Disentangle Module: Due to the asymmetric motions of two hands, we employ a single hand autoencoder as the feature extractor to disentangle two hands. We firstly train an autoencoder on 3D single hands. As shown in Fig. 3 (a), we then utilize a Multilayer Perceptron (MLP) to project the body features into the single hand features " + }, + { + "bbox": [ + 304, + 498, + 547, + 617 + ], + "type": "inline_equation", + "content": "F_{\\mathcal{SH}}" + }, + { + "bbox": [ + 304, + 498, + 547, + 617 + ], + "type": "text", + "content": ". To ensure these single hand features represent each disentangled hand separately, we conduct the feature level and 3D representation level constraints by the single hand autoencoder, as follows:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 315, + 626, + 545, + 649 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 626, + 545, + 649 + ], + "spans": [ + { + "bbox": [ + 315, + 626, + 545, + 649 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {d i s} = \\left\\| \\widetilde {F _ {S H} ^ {t}} - F _ {\\mathcal {S H}} ^ {t} \\right\\| _ {1} + \\left\\| \\mathbb {D} \\left(\\widetilde {F _ {S H} ^ {t}}\\right) - \\mathbb {D} \\left(F _ {\\mathcal {S H}} ^ {t}\\right) \\right\\| _ {1}, \\tag {1}", + "image_path": "971676de40554e780d62a67b9039c4de4e06ada3c1055f1e3a019b4b2701cbcd.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 658, + 545, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 658, + 545, + 685 + ], + "spans": [ + { + "bbox": [ + 305, + 658, + 545, + 685 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 658, + 545, + 685 + ], + "type": "inline_equation", + "content": "\\widetilde{F_{SH}^{t}}" + }, + { + "bbox": [ + 305, + 658, + 545, + 685 + ], + "type": "text", + "content": " denotes reconstructed hand feature at time " + }, + { + "bbox": [ + 305, + 658, + 545, + 685 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 305, + 658, + 545, + 685 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 658, + 545, + 685 + ], + "type": "inline_equation", + "content": "\\mathbb{D}" + }, + { + "bbox": [ + 305, + 658, + 545, + 685 + ], + "type": "text", + "content": " is the pre-trained decoder." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 689, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 715 + ], + "type": "text", + "content": "Spatial-Residual Memory Module: After obtaining the disentangled single hand features, we introduce a Spatial-" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4618" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 72, + 376, + 166 + ], + "blocks": [ + { + "bbox": [ + 61, + 72, + 376, + 166 + ], + "lines": [ + { + "bbox": [ + 61, + 72, + 376, + 166 + ], + "spans": [ + { + "bbox": [ + 61, + 72, + 376, + 166 + ], + "type": "image", + "image_path": "78ba7a6f3e4d99372ca280f6dc2b48c3d5e6db1cd244048e13824fefb5e5deb6.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 79, + 170, + 512, + 180 + ], + "lines": [ + { + "bbox": [ + 79, + 170, + 512, + 180 + ], + "spans": [ + { + "bbox": [ + 79, + 170, + 512, + 180 + ], + "type": "text", + "content": "Figure 3. Details of three sub-modules in the first stage. For brevity, we only show them in terms of single-branch view." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 378, + 76, + 529, + 166 + ], + "blocks": [ + { + "bbox": [ + 378, + 76, + 529, + 166 + ], + "lines": [ + { + "bbox": [ + 378, + 76, + 529, + 166 + ], + "spans": [ + { + "bbox": [ + 378, + 76, + 529, + 166 + ], + "type": "image", + "image_path": "92977298826388df9bc0781c682cf7bdc2383e230e38dad29dd3ca67967c258f.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 201, + 287, + 321 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 201, + 287, + 321 + ], + "spans": [ + { + "bbox": [ + 46, + 201, + 287, + 321 + ], + "type": "text", + "content": "Residual Memory (SRM) module to model the spatial interaction between the body and each hand by residual learning. As illustrated in Fig. 3 (b), we leverage a spatial memory bank to store the spatial residual deformation representation between the current hand feature and the next step hand feature. Initially, each slot of the spatial memory bank is randomized as " + }, + { + "bbox": [ + 46, + 201, + 287, + 321 + ], + "type": "inline_equation", + "content": "m_j \\in \\mathbb{R}^{1 \\times C}" + }, + { + "bbox": [ + 46, + 201, + 287, + 321 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 201, + 287, + 321 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 201, + 287, + 321 + ], + "type": "text", + "content": " denotes slot index. To model the body-hand correlation, the current body feature is exploited as a query to retrieve the most relevant memory slot by calculating the cosine similarity." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 322, + 287, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 322, + 287, + 514 + ], + "spans": [ + { + "bbox": [ + 46, + 322, + 287, + 514 + ], + "type": "text", + "content": "In particular, we represent the relevance between the query and memory slots via cosine similarity. Then we leverage the argmax operation to acquire the most relevant memory slot " + }, + { + "bbox": [ + 46, + 322, + 287, + 514 + ], + "type": "inline_equation", + "content": "m_r" + }, + { + "bbox": [ + 46, + 322, + 287, + 514 + ], + "type": "text", + "content": ". Intuitively, the retrieved most relevant memory slot is leveraged as the spatial residual deformation between the current feature and the next step hand feature. However, it is intractable for argmax operation to back-propagate gradients. Thus, we conduct the softmax operation on the above calculated cosine similarity matrix to obtain the slot-wise affinity matrix. Then we acquire the learnable spatial residual deformation " + }, + { + "bbox": [ + 46, + 322, + 287, + 514 + ], + "type": "inline_equation", + "content": "F_{\\mathcal{SH}}^{\\Delta t}" + }, + { + "bbox": [ + 46, + 322, + 287, + 514 + ], + "type": "text", + "content": " by aggregation between the slot-wise affinity matrix and each memory slot. We apply the above reading process to allow gradient back-propagation. In the training phase, we utilize the current hand feature to update the retrieved memory slot as " + }, + { + "bbox": [ + 46, + 322, + 287, + 514 + ], + "type": "inline_equation", + "content": "m_r = \\gamma m_r + (1 - \\gamma)F_{\\mathcal{SH}}^t" + }, + { + "bbox": [ + 46, + 322, + 287, + 514 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 322, + 287, + 514 + ], + "type": "inline_equation", + "content": "\\gamma = 0.8" + }, + { + "bbox": [ + 46, + 322, + 287, + 514 + ], + "type": "text", + "content": " in our experiments." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 514, + 287, + 583 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 514, + 287, + 583 + ], + "spans": [ + { + "bbox": [ + 46, + 514, + 287, + 583 + ], + "type": "text", + "content": "Different from obtaining the next hand feature by simple addition between the spatial residual deformation and current hand feature, we claim the spatial residual deformation refers to local spatial dependency from the current feature to the next time feature. This spatial dependency " + }, + { + "bbox": [ + 46, + 514, + 287, + 583 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 514, + 287, + 583 + ], + "type": "text", + "content": " is formulated as:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 98, + 589, + 287, + 607 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 98, + 589, + 287, + 607 + ], + "spans": [ + { + "bbox": [ + 98, + 589, + 287, + 607 + ], + "type": "interline_equation", + "content": "S _ {t} ^ {t + 1} = \\operatorname {s o f t m a x} \\left(F _ {\\mathcal {S H}} ^ {\\Delta t ^ {\\prime}} \\otimes F _ {\\mathcal {S H}} ^ {t}\\right), \\tag {2}", + "image_path": "0dc5727e09f30e29b617a769db4e16782c1634fef691707ba5b1f125e5a55a79.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 613, + 287, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 613, + 287, + 673 + ], + "spans": [ + { + "bbox": [ + 47, + 613, + 287, + 673 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 613, + 287, + 673 + ], + "type": "inline_equation", + "content": "\\otimes" + }, + { + "bbox": [ + 47, + 613, + 287, + 673 + ], + "type": "text", + "content": " indicates matrix multiplication, and " + }, + { + "bbox": [ + 47, + 613, + 287, + 673 + ], + "type": "inline_equation", + "content": "^{\\prime}" + }, + { + "bbox": [ + 47, + 613, + 287, + 673 + ], + "type": "text", + "content": " indicates the transpose operation. With the help of the spatial dependency, the next step hand feature is represented as " + }, + { + "bbox": [ + 47, + 613, + 287, + 673 + ], + "type": "inline_equation", + "content": "F_{\\mathcal{SH}}^{t + 1} = F_{\\mathcal{SH}}^{t} + F_{\\mathcal{SH}}^{t}\\otimes S_{t}^{t + 1}" + }, + { + "bbox": [ + 47, + 613, + 287, + 673 + ], + "type": "text", + "content": ". Through SRM, we obtain the spatial-enhanced single-hand feature." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "content": "Temporal-Motion Memory Module: We further propose a Temporal-Motion Memory (TMM) module to ensure the single hand motions consistent with the body dynamics," + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 201, + 545, + 332 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 201, + 545, + 332 + ], + "spans": [ + { + "bbox": [ + 304, + 201, + 545, + 332 + ], + "type": "text", + "content": "globally. As depicted in Fig. 3 (c), we develop a motion encoder to obtain the sequence-aware body motion embedding as " + }, + { + "bbox": [ + 304, + 201, + 545, + 332 + ], + "type": "inline_equation", + "content": "F_{\\mathcal{B}\\mathcal{M}} \\in \\mathcal{R}^{T \\times 1}" + }, + { + "bbox": [ + 304, + 201, + 545, + 332 + ], + "type": "text", + "content": ". Here, we use body motion embedding to represent temporal changes among body skeletons in a sequence. Then, we leverage the body motion embedding as a query to retrieve the most consistent single hand motion embedding " + }, + { + "bbox": [ + 304, + 201, + 545, + 332 + ], + "type": "inline_equation", + "content": "F_{\\mathcal{S}\\mathcal{H}\\mathcal{M}} \\in \\mathcal{R}^{T \\times 1}" + }, + { + "bbox": [ + 304, + 201, + 545, + 332 + ], + "type": "text", + "content": " stored in a temporal memory bank. The initialization and reading processes of the temporal memory bank are similar to SRM. We utilize the body motion embedding to update the retrieved slot of the temporal memory bank in the same manner as SRM." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 334, + 545, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 334, + 545, + 418 + ], + "spans": [ + { + "bbox": [ + 304, + 334, + 545, + 418 + ], + "type": "text", + "content": "Afterward, we utilize the retrieved hand motion embedding to boost the body-hand temporal consistency. Specifically, we leverage the retrieved temporal embedding to represent the temporal correlation of hand gesture changes in a sequence. Then, the temporal-consistent enhanced sequential hand gestures are attained by: " + }, + { + "bbox": [ + 304, + 334, + 545, + 418 + ], + "type": "inline_equation", + "content": "F_{\\mathcal{SH}} = F_{\\mathcal{SH}} + F_{\\mathcal{SH}} \\odot \\text{softmax}(F_{\\mathcal{SHM}})" + }, + { + "bbox": [ + 304, + 334, + 545, + 418 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 334, + 545, + 418 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 304, + 334, + 545, + 418 + ], + "type": "text", + "content": " means dot product." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 422, + 545, + 530 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 422, + 545, + 530 + ], + "spans": [ + { + "bbox": [ + 304, + 422, + 545, + 530 + ], + "type": "text", + "content": "Transformer-based Backbone: As illustrated in Fig. 2 (stage one), to further enhance the body-hand interaction, we construct the bilateral hand disentanglement branches that interact with a body-specific branch to predict 3D hands. In particular, we introduce a body-specific transformer to generate body features as query " + }, + { + "bbox": [ + 304, + 422, + 545, + 530 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 304, + 422, + 545, + 530 + ], + "type": "text", + "content": ". Then, through 3 times Multi-Head Attention (MHA) [38], we use " + }, + { + "bbox": [ + 304, + 422, + 545, + 530 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 304, + 422, + 545, + 530 + ], + "type": "text", + "content": " to match the key features " + }, + { + "bbox": [ + 304, + 422, + 545, + 530 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 422, + 545, + 530 + ], + "type": "text", + "content": " and value features " + }, + { + "bbox": [ + 304, + 422, + 545, + 530 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 304, + 422, + 545, + 530 + ], + "type": "text", + "content": " in each hand transformer branch, respectively." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 531, + 545, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 531, + 545, + 651 + ], + "spans": [ + { + "bbox": [ + 304, + 531, + 545, + 651 + ], + "type": "text", + "content": "Furthermore, we feed the concatenation of bilateral hand features into an MLP, thus obtaining the merged two-hand features. Similarly, we conduct 3 times MHA in the transformer-based decoder. This encourages the merged two-hand features to be more temporal consistent with body dynamics, holistically. At the end of the decoder, we adopt two fully-connected layers to obtain the 3D two hands sequence. Additionally, similar to [28], we employ a motion discriminator to ensure the natural and continuous initial prediction at stage one." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 658, + 467, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 658, + 467, + 672 + ], + "spans": [ + { + "bbox": [ + 306, + 658, + 467, + 672 + ], + "type": "text", + "content": "3.3. Stage Two: Diverse Sampling" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "We leverage a Prototypical-Memory Sampling Strategy (PSS) to achieve hands diversification based on our initial predictions from stage one. Specifically, we first con" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4619" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "type": "text", + "content": "struct a prototypical memory to store the realistic two hands prototypes. Then, we obtain the retrieved realistic prototype representation based on the initial prediction at stage one. Meanwhile, as shown in Fig. 2 (stage two), we propose a sampling header to obtain the hand-informative perturbation via gradient-based Markov Chain Monte Carlo (MCMC) sampling. Finally, we concatenate the retrieved realistic hand prototype representation and perturbation to generate the diverse 3D two hands." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 185, + 289, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 185, + 289, + 342 + ], + "spans": [ + { + "bbox": [ + 46, + 185, + 289, + 342 + ], + "type": "text", + "content": "Hands Prototypical Memory Construction: Inspired by [50], we reformulate the two hands diversification as a generation task. Instead of directly sampling the prior of the perturbation from the isotropic Gaussian distribution [7, 11, 16, 36], we assume the sampling space follows a learnable realistic prior distribution [30, 31, 50]. Since the existing 3D hand prediction dataset is noisy due to the automated annotation process, we propose a prototypical memory bank to store the realistic hand prototype representations encoded from real 3D hands. These 3D hands are captured from a studio-based mocap-captured dataset, named BEAT [22]. The reading and updating strategies of hands prototypical memory are the same as TMM." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 346, + 289, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 346, + 289, + 407 + ], + "spans": [ + { + "bbox": [ + 46, + 346, + 289, + 407 + ], + "type": "text", + "content": "Gradient-based MCMC Sampling: We exploit the retrieved hand prototype representation concatenated with sampled perturbation vector " + }, + { + "bbox": [ + 46, + 346, + 289, + 407 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 46, + 346, + 289, + 407 + ], + "type": "text", + "content": " to predict the diverse hand gestures. Given the observed 3D two hands " + }, + { + "bbox": [ + 46, + 346, + 289, + 407 + ], + "type": "inline_equation", + "content": "h \\in \\mathbb{R}^{90}" + }, + { + "bbox": [ + 46, + 346, + 289, + 407 + ], + "type": "text", + "content": ", the " + }, + { + "bbox": [ + 46, + 346, + 289, + 407 + ], + "type": "inline_equation", + "content": "\\tilde{h}" + }, + { + "bbox": [ + 46, + 346, + 289, + 407 + ], + "type": "text", + "content": " is expressed as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 64, + 415, + 287, + 431 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 415, + 287, + 431 + ], + "spans": [ + { + "bbox": [ + 64, + 415, + 287, + 431 + ], + "type": "interline_equation", + "content": "\\tilde {h} = R _ {\\theta} (h, w) + \\epsilon , w \\sim p _ {\\alpha} (w), \\epsilon \\sim \\mathcal {N} (0, \\sigma_ {\\epsilon} ^ {2} I), \\qquad (3)", + "image_path": "e28db69fe00b2473f037db3951c54f57444940a67dbbc77105ff53ee702b8180.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 441, + 287, + 487 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 441, + 287, + 487 + ], + "spans": [ + { + "bbox": [ + 46, + 441, + 287, + 487 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 441, + 287, + 487 + ], + "type": "inline_equation", + "content": "p_{\\alpha}(w)" + }, + { + "bbox": [ + 46, + 441, + 287, + 487 + ], + "type": "text", + "content": " is the prior distribution of perturbation with parameters " + }, + { + "bbox": [ + 46, + 441, + 287, + 487 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 441, + 287, + 487 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 441, + 287, + 487 + ], + "type": "inline_equation", + "content": "\\epsilon \\sim \\mathcal{N}(0, \\sigma_{\\epsilon}^{2}I)" + }, + { + "bbox": [ + 46, + 441, + 287, + 487 + ], + "type": "text", + "content": " is the observation noise of hand gestures with " + }, + { + "bbox": [ + 46, + 441, + 287, + 487 + ], + "type": "inline_equation", + "content": "\\sigma_{\\epsilon}" + }, + { + "bbox": [ + 46, + 441, + 287, + 487 + ], + "type": "text", + "content": " being given, " + }, + { + "bbox": [ + 46, + 441, + 287, + 487 + ], + "type": "inline_equation", + "content": "R_{\\theta}" + }, + { + "bbox": [ + 46, + 441, + 287, + 487 + ], + "type": "text", + "content": " is the generation model with parameters " + }, + { + "bbox": [ + 46, + 441, + 287, + 487 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 441, + 287, + 487 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 489, + 287, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 489, + 287, + 550 + ], + "spans": [ + { + "bbox": [ + 46, + 489, + 287, + 550 + ], + "type": "text", + "content": "Inspired by [11], we leverage an MLP-based sampling header " + }, + { + "bbox": [ + 46, + 489, + 287, + 550 + ], + "type": "inline_equation", + "content": "S_{\\alpha}(w)" + }, + { + "bbox": [ + 46, + 489, + 287, + 550 + ], + "type": "text", + "content": " to model the diversification sampling process, as illustrated in Fig. 2 (stage two). The prior distribution of perturbation is initialized from an isotropic Gaussian reference distribution, expressed as:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 84, + 558, + 287, + 586 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 84, + 558, + 287, + 586 + ], + "spans": [ + { + "bbox": [ + 84, + 558, + 287, + 586 + ], + "type": "interline_equation", + "content": "p _ {\\alpha} (w) \\propto e x p \\left[ - S _ {\\alpha} (w) - \\frac {1}{2 \\sigma_ {w} ^ {2}} \\| w \\| ^ {2} \\right], \\tag {4}", + "image_path": "26720b94f152391ee2dfee13dfce8d274215e8ae7bf02620b89f0feaa489ebb5.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 596, + 287, + 670 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 596, + 287, + 670 + ], + "spans": [ + { + "bbox": [ + 46, + 596, + 287, + 670 + ], + "type": "text", + "content": "where the " + }, + { + "bbox": [ + 46, + 596, + 287, + 670 + ], + "type": "inline_equation", + "content": "M_{\\alpha}(w) = S_{\\alpha}(w) + \\frac{1}{2\\sigma_w^2}\\| w\\|^2" + }, + { + "bbox": [ + 46, + 596, + 287, + 670 + ], + "type": "text", + "content": " is defined as the whole sampling function, and " + }, + { + "bbox": [ + 46, + 596, + 287, + 670 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 596, + 287, + 670 + ], + "type": "text", + "content": " is the learnable parameters of sampling header. The hyperparameter " + }, + { + "bbox": [ + 46, + 596, + 287, + 670 + ], + "type": "inline_equation", + "content": "\\sigma_w" + }, + { + "bbox": [ + 46, + 596, + 287, + 670 + ], + "type": "text", + "content": " denotes the standard deviation. For notation simplicity, let " + }, + { + "bbox": [ + 46, + 596, + 287, + 670 + ], + "type": "inline_equation", + "content": "\\beta = \\{\\theta ,\\alpha \\}" + }, + { + "bbox": [ + 46, + 596, + 287, + 670 + ], + "type": "text", + "content": ". For the " + }, + { + "bbox": [ + 46, + 596, + 287, + 670 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 596, + 287, + 670 + ], + "type": "text", + "content": " th sample in a training mini-batch with size " + }, + { + "bbox": [ + 46, + 596, + 287, + 670 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 596, + 287, + 670 + ], + "type": "text", + "content": ", the log-likelihood function of " + }, + { + "bbox": [ + 46, + 596, + 287, + 670 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 596, + 287, + 670 + ], + "type": "text", + "content": " is defined as:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 70, + 680, + 287, + 711 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 680, + 287, + 711 + ], + "spans": [ + { + "bbox": [ + 70, + 680, + 287, + 711 + ], + "type": "interline_equation", + "content": "L (\\beta) = \\sum_ {i = 1} ^ {n} \\log \\left[ \\int p _ {\\alpha} \\left(w _ {i}\\right) p _ {\\theta} \\left(\\tilde {h} _ {i} \\mid h _ {i}, w _ {i}\\right) d w _ {i} \\right]. \\tag {5}", + "image_path": "5c9303b40252b64bba5263046032ecdbf7701de1cb56fc402f9dc0825f7388d6.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 72, + 478, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 478, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 478, + 84 + ], + "type": "text", + "content": "Thus the gradient of " + }, + { + "bbox": [ + 306, + 72, + 478, + 84 + ], + "type": "inline_equation", + "content": "L(\\beta)" + }, + { + "bbox": [ + 306, + 72, + 478, + 84 + ], + "type": "text", + "content": " is computed as:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 307, + 87, + 545, + 121 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 87, + 545, + 121 + ], + "spans": [ + { + "bbox": [ + 307, + 87, + 545, + 121 + ], + "type": "interline_equation", + "content": "\\bigtriangledown L (\\beta) = E _ {p _ {\\beta (w | \\tilde {h}, h)}} \\left[ \\bigtriangledown_ {\\alpha} \\operatorname {l o g p} _ {\\alpha} (w) + \\bigtriangledown_ {\\theta} \\operatorname {l o g p} _ {\\theta} (\\tilde {h} | h, w) \\right]. \\tag {6}", + "image_path": "d19dffdf472dc6e3983dd8df33cd7cbe6d0bad0b6710912d664d1bcdef411194.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 125, + 547, + 235 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 125, + 547, + 235 + ], + "spans": [ + { + "bbox": [ + 305, + 125, + 547, + 235 + ], + "type": "text", + "content": "The intractable expectation term " + }, + { + "bbox": [ + 305, + 125, + 547, + 235 + ], + "type": "inline_equation", + "content": "E_{p}(\\cdot)" + }, + { + "bbox": [ + 305, + 125, + 547, + 235 + ], + "type": "text", + "content": " in Eq. (6) is approximately solved by a gradient-based MCMC (Langevin dynamics) [4, 27]. In particular, the initial state of perturbation " + }, + { + "bbox": [ + 305, + 125, + 547, + 235 + ], + "type": "inline_equation", + "content": "p_0(w)" + }, + { + "bbox": [ + 305, + 125, + 547, + 235 + ], + "type": "text", + "content": " is sampled from the Gaussian distribution. Through MCMC, the perturbation from the prior distribution and posterior distribution are represented as " + }, + { + "bbox": [ + 305, + 125, + 547, + 235 + ], + "type": "inline_equation", + "content": "\\{w_i^-\\}" + }, + { + "bbox": [ + 305, + 125, + 547, + 235 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 125, + 547, + 235 + ], + "type": "inline_equation", + "content": "\\{w_i^+\\}" + }, + { + "bbox": [ + 305, + 125, + 547, + 235 + ], + "type": "text", + "content": ", respectively. The detailed calculation process is in [27]. Therefore, the gradients of the generation model and sampling header are updated by:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 311, + 238, + 545, + 281 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 238, + 545, + 281 + ], + "spans": [ + { + "bbox": [ + 311, + 238, + 545, + 281 + ], + "type": "interline_equation", + "content": "\\nabla_ {\\theta} R _ {\\theta} = \\frac {1}{n} \\sum_ {i = 1} ^ {n} \\left[ \\frac {1}{\\sigma_ {\\epsilon} ^ {2}} \\left(\\tilde {h} _ {i} - R _ {\\theta} \\left(h _ {i}, w _ {i} ^ {+}\\right)\\right) \\nabla_ {\\theta} R _ {\\theta} \\left(h _ {i}, w _ {i} ^ {+}\\right) \\right], \\tag {7}", + "image_path": "e8ee724faa0e58a77e22e5941a2ae31a33e8d3c9bf1aa8d96e82f380e88e9081.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 311, + 284, + 545, + 315 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 284, + 545, + 315 + ], + "spans": [ + { + "bbox": [ + 311, + 284, + 545, + 315 + ], + "type": "interline_equation", + "content": "\\nabla_ {\\alpha} S _ {\\alpha} = \\frac {1}{n} \\sum_ {i = 1} ^ {n} \\left[ \\nabla_ {\\alpha} S _ {\\alpha} \\left(w _ {i} ^ {-}\\right) \\right] - \\frac {1}{n} \\sum_ {i = 1} ^ {n} \\left[ \\nabla_ {\\alpha} S _ {\\alpha} \\left(w _ {i} ^ {+}\\right) \\right]. \\tag {8}", + "image_path": "7b808a4880589129e2e18a1a2bc9dedba2af3113e832a5392f99f89c41e4be08.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 324, + 423, + 337 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 324, + 423, + 337 + ], + "spans": [ + { + "bbox": [ + 306, + 324, + 423, + 337 + ], + "type": "text", + "content": "3.4. Objective Functions" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 342, + 545, + 367 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 342, + 545, + 367 + ], + "spans": [ + { + "bbox": [ + 305, + 342, + 545, + 367 + ], + "type": "text", + "content": "In stage one, we apply the following loss functions to constrain the initial prediction process of hand gestures." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 372, + 545, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 372, + 545, + 413 + ], + "spans": [ + { + "bbox": [ + 305, + 372, + 545, + 413 + ], + "type": "text", + "content": "Reconstruction Loss: We use the ground truth to supervise the predicted two hands as " + }, + { + "bbox": [ + 305, + 372, + 545, + 413 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rec} = \\left\\| \\mathcal{H} - \\tilde{\\mathcal{H}} \\right\\|_1" + }, + { + "bbox": [ + 305, + 372, + 545, + 413 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 305, + 372, + 545, + 413 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathcal{H}}" + }, + { + "bbox": [ + 305, + 372, + 545, + 413 + ], + "type": "text", + "content": " denotes generated hands." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 418, + 545, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 418, + 545, + 498 + ], + "spans": [ + { + "bbox": [ + 305, + 418, + 545, + 498 + ], + "type": "text", + "content": "Perceptual Loss: Inspired by [15], we leverage the studio-based 3D hands dataset BEAT to pre-train an MLP-based autoencoder as a feature extractor " + }, + { + "bbox": [ + 305, + 418, + 545, + 498 + ], + "type": "inline_equation", + "content": "\\phi(\\cdot)" + }, + { + "bbox": [ + 305, + 418, + 545, + 498 + ], + "type": "text", + "content": ". We utilize the " + }, + { + "bbox": [ + 305, + 418, + 545, + 498 + ], + "type": "inline_equation", + "content": "L1" + }, + { + "bbox": [ + 305, + 418, + 545, + 498 + ], + "type": "text", + "content": " loss to constrain the difference between the extracted features of " + }, + { + "bbox": [ + 305, + 418, + 545, + 498 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 305, + 418, + 545, + 498 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 418, + 545, + 498 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathcal{H}}" + }, + { + "bbox": [ + 305, + 418, + 545, + 498 + ], + "type": "text", + "content": ", as formulated: " + }, + { + "bbox": [ + 305, + 418, + 545, + 498 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{perc} = \\left\\| \\phi(\\mathcal{H}) - \\phi(\\tilde{\\mathcal{H}}) \\right\\|_1" + }, + { + "bbox": [ + 305, + 418, + 545, + 498 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 501, + 545, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 501, + 545, + 525 + ], + "spans": [ + { + "bbox": [ + 306, + 501, + 545, + 525 + ], + "type": "text", + "content": "Adversarial Learning: Following the configuration of [28], we employ the adversarial training loss as:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 321, + 529, + 545, + 544 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 529, + 545, + 544 + ], + "spans": [ + { + "bbox": [ + 321, + 529, + 545, + 544 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {a d v} = \\mathbb {E} _ {\\mathcal {H}} \\left[ \\log D (\\mathcal {H}) \\right] + \\mathbb {E} _ {\\mathcal {B}} \\left[ \\log \\left(1 - (G (\\mathcal {B}))\\right) \\right], \\tag {9}", + "image_path": "6f7454e306a1b07a8c9d741bac943dacdbf2e9b2e84798cbecd077f6fd814c19.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 547, + 545, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 547, + 545, + 571 + ], + "spans": [ + { + "bbox": [ + 305, + 547, + 545, + 571 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 547, + 545, + 571 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 305, + 547, + 545, + 571 + ], + "type": "text", + "content": " denotes the discriminator and " + }, + { + "bbox": [ + 305, + 547, + 545, + 571 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 305, + 547, + 545, + 571 + ], + "type": "text", + "content": " means hands generator. Finally, the overall objective in stage one is:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 308, + 574, + 545, + 593 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 574, + 545, + 593 + ], + "spans": [ + { + "bbox": [ + 308, + 574, + 545, + 593 + ], + "type": "interline_equation", + "content": "\\min _ {G} \\max _ {D} \\mathcal {L} _ {\\text {t o t a l}} ^ {\\text {s t a g e 1}} = \\mathcal {L} _ {\\text {r e c}} + \\mathcal {L} _ {\\text {a d v}} + \\mathcal {L} _ {\\text {p e r c}} + 0. 5 \\mathcal {L} _ {\\text {d i s}}, \\tag {10}", + "image_path": "df45dabd3cc81533319c4f6b36696c466ecf7721e6777700e936adbbc8115903.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 596, + 544, + 608 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 596, + 544, + 608 + ], + "spans": [ + { + "bbox": [ + 306, + 596, + 544, + 608 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 596, + 544, + 608 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{dis}" + }, + { + "bbox": [ + 306, + 596, + 544, + 608 + ], + "type": "text", + "content": " denotes disentanglement constraint in Eq. ((1))." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 305, + 609, + 545, + 630 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 609, + 545, + 630 + ], + "spans": [ + { + "bbox": [ + 305, + 609, + 545, + 630 + ], + "type": "text", + "content": "In the second stage, the overall objective to train our model is defined as follows:" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 361, + 634, + 545, + 651 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 361, + 634, + 545, + 651 + ], + "spans": [ + { + "bbox": [ + 361, + 634, + 545, + 651 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {t o t a l}} ^ {\\text {s t a g e 2}} = \\left\\| h - R _ {\\theta} \\left(h, w ^ {+}\\right) \\right\\| _ {1}, \\tag {11}", + "image_path": "831826fccfaad2ff07c59789e242187c4ec190171676941c9953be804aab66b9.jpg" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 305, + 653, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 653, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 653, + 545, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 653, + 545, + 714 + ], + "type": "inline_equation", + "content": "w^{+}" + }, + { + "bbox": [ + 305, + 653, + 545, + 714 + ], + "type": "text", + "content": " is the posterior distribution of the perturbation. We conduct the frame-level diversification based on the initial prediction at stage one. To ensure temporal smoothness, we further apply temporal smoothness [45] to the diversified 3D hand gestures as a post processing." + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "4620" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 83, + 97, + 511, + 201 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "type": "text", + "content": "Table 1. Comparison with the state-of-the-art methods on B2H dataset and our proposed TED Hands dataset of the first stage initial prediction. " + }, + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "type": "inline_equation", + "content": "\\downarrow" + }, + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "type": "text", + "content": " indicates the lower the better." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 83, + 97, + 511, + 201 + ], + "lines": [ + { + "bbox": [ + 83, + 97, + 511, + 201 + ], + "spans": [ + { + "bbox": [ + 83, + 97, + 511, + 201 + ], + "type": "table", + "html": "
MethodsB2H Dataset [28]TED Hands Dataset
L2↓FHD↓MPJRE↓L2↓FHD↓MPJRE↓
Body2Hands [28]CVPR'213.7601.10313.1482.5511.17411.371
MRT [39]NeurIPS'213.6340.97312.5762.3250.87710.314
BTM [8]WACV'233.6571.26312.6962.3501.11110.440
LTD [25]ICCV'193.7551.07313.3152.4821.36711.078
MotionMixer [1]IJCAI'223.6160.98612.7022.3240.91010.427
SPGSN [19]ECCV'223.6560.96212.7572.4350.99010.887
Ours (stage one)3.4200.47111.4062.0370.2588.888
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MethodsFHD↓Diversity↑
Body2hands [28] w/ PSS2.5040.497±0.028
MRT [39] w/ PSS1.9820.698±0.031
BTM [8] w/ PSS2.3790.703±0.038
LTD [25] w/ PSS1.8930.577±0.028
MotionMixer [1] w/ PSS2.1690.869±0.055
SPGSN [19] w/ PSS2.0040.874±0.046
Ours w/ VAE [36]1.6171.001±0.061
Ours (stage two)1.2391.324±0.066
", + "image_path": "7aa3bf0e42316c3174021ff0264a67d9aa405d521370c5dcc8c9e0dc99bfa59d.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 370, + 128, + 384 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 370, + 128, + 384 + ], + "spans": [ + { + "bbox": [ + 47, + 370, + 128, + 384 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 390, + 233, + 403 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 390, + 233, + 403 + ], + "spans": [ + { + "bbox": [ + 47, + 390, + 233, + 403 + ], + "type": "text", + "content": "4.1. Datasets and Experimental Setting" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 408, + 287, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 408, + 287, + 529 + ], + "spans": [ + { + "bbox": [ + 46, + 408, + 287, + 529 + ], + "type": "text", + "content": "B2H Dataset: The B2H dataset [28] is automatically annotated by a monocular-based 3D pose estimation model [44], including the gestures of 8 speakers from in-the-wild talk show videos. In the original B2H dataset, there are more than 139K sequences. Each sequence includes 64 frames, with 32 frames overlapping between every two sequences. However, due to the noisiness and unavailable videos, we obtain 120,188 sequences finally. In our work, we adopt the same division criteria as [28] to split the training and testing dataset." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 533, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 288, + 714 + ], + "type": "text", + "content": "TED Hands Dataset: Due to the limited avatar identities in the existing 3D hand prediction dataset, we newly collect a large-scale 3D hands dataset (dubbed TED Hands) based on the TED Gesture [46, 47]. The original TED Gesture dataset only contains 10 upper body joints without elaborate fingers of two hands. Hence, we leverage a state-of-the-art 3D pose estimator FrankMocap [34] to extract the whole body-hand joints as pseudo ground truth from the video links provided by TED Gesture. Concretely, each joint of our dataset is normalized as the 3D axis-angle representation in a fixed kinematic structure [33]. In this fashion, our dataset is invariant to root joint motion and body shape. Finally, we acquired the 134,456 sequences from 1,755 different speakers, with 99.6 hours of TED talking speeches. Each sequence includes 64 frames without over" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 310, + 248, + 541, + 352 + ], + "blocks": [ + { + "bbox": [ + 305, + 211, + 545, + 243 + ], + "lines": [ + { + "bbox": [ + 305, + 211, + 545, + 243 + ], + "spans": [ + { + "bbox": [ + 305, + 211, + 545, + 243 + ], + "type": "text", + "content": "Table 3. Sampling experiment results on our proposed TED Hands dataset. " + }, + { + "bbox": [ + 305, + 211, + 545, + 243 + ], + "type": "inline_equation", + "content": "\\downarrow" + }, + { + "bbox": [ + 305, + 211, + 545, + 243 + ], + "type": "text", + "content": " indicates the lower the better, and " + }, + { + "bbox": [ + 305, + 211, + 545, + 243 + ], + "type": "inline_equation", + "content": "\\uparrow" + }, + { + "bbox": [ + 305, + 211, + 545, + 243 + ], + "type": "text", + "content": " indicates the higher the better. " + }, + { + "bbox": [ + 305, + 211, + 545, + 243 + ], + "type": "inline_equation", + "content": "\\pm" + }, + { + "bbox": [ + 305, + 211, + 545, + 243 + ], + "type": "text", + "content": " means " + }, + { + "bbox": [ + 305, + 211, + 545, + 243 + ], + "type": "inline_equation", + "content": "{95}\\%" + }, + { + "bbox": [ + 305, + 211, + 545, + 243 + ], + "type": "text", + "content": " confidence interval." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 310, + 248, + 541, + 352 + ], + "lines": [ + { + "bbox": [ + 310, + 248, + 541, + 352 + ], + "spans": [ + { + "bbox": [ + 310, + 248, + 541, + 352 + ], + "type": "table", + "html": "
MethodsFHD↓Diversity↑
Body2hands [28] w/ PSS2.0052.705±0.153
MRT [39] w/ PSS1.1884.954±0.190
BTM [8] w/ PSS1.2243.632±0.150
LTD [25] w/ PSS1.3852.851±0.101
MotionMixer [1] w/ PSS1.6133.487±0.208
SPGSN [19] w/ PSS1.5653.812±0.219
Ours w/ VAE [36]1.0334.018±0.190
Ours (stage two)0.9386.426±0.300
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We randomly spit the dataset into the " + }, + { + "bbox": [ + 305, + 371, + 545, + 407 + ], + "type": "inline_equation", + "content": "70\\%" + }, + { + "bbox": [ + 305, + 371, + 545, + 407 + ], + "type": "text", + "content": " training set, " + }, + { + "bbox": [ + 305, + 371, + 545, + 407 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 305, + 371, + 545, + 407 + ], + "type": "text", + "content": " validation set, and " + }, + { + "bbox": [ + 305, + 371, + 545, + 407 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 305, + 371, + 545, + 407 + ], + "type": "text", + "content": " testing set. Please refer to the supplementary material for more details." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 412, + 545, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 412, + 545, + 484 + ], + "spans": [ + { + "bbox": [ + 304, + 412, + 545, + 484 + ], + "type": "text", + "content": "Implementation Details: Our model is implemented on the PyTorch platform with 2 NVIDIA RTX 2080Ti GPUs. We train the model utilizing Adam optimizer with an initial learning rate of 0.003. The whole training takes 30 epochs with a batch size of 64. We set " + }, + { + "bbox": [ + 304, + 412, + 545, + 484 + ], + "type": "inline_equation", + "content": "\\sigma_{\\epsilon} = 1" + }, + { + "bbox": [ + 304, + 412, + 545, + 484 + ], + "type": "text", + "content": " in Eq. (3), and " + }, + { + "bbox": [ + 304, + 412, + 545, + 484 + ], + "type": "inline_equation", + "content": "\\sigma_w = 1" + }, + { + "bbox": [ + 304, + 412, + 545, + 484 + ], + "type": "text", + "content": " in Eq. (4)." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 489, + 547, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 489, + 547, + 525 + ], + "spans": [ + { + "bbox": [ + 304, + 489, + 547, + 525 + ], + "type": "text", + "content": "Evaluation Metrics: To fully evaluate the naturalness of initial predictions at stage one and the diversity of sampled hand gestures at stage two, we employ various metrics:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 527, + 545, + 712 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 306, + 527, + 545, + 551 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 527, + 545, + 551 + ], + "spans": [ + { + "bbox": [ + 306, + 527, + 545, + 551 + ], + "type": "text", + "content": "- " + }, + { + "bbox": [ + 306, + 527, + 545, + 551 + ], + "type": "inline_equation", + "content": "L2" + }, + { + "bbox": [ + 306, + 527, + 545, + 551 + ], + "type": "text", + "content": " Distance: Distance between the generated whole two hand poses and pseudo ground truth." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 553, + 545, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 553, + 545, + 613 + ], + "spans": [ + { + "bbox": [ + 306, + 553, + 545, + 613 + ], + "type": "text", + "content": "- FHD: Inspired by FGD [46, 47], we propose a hand-specific metric (named FHD) to measure the Fréchet distance between the features of generated hands and pseudo ground truth. The feature extractors of FHD are pretrained by B2H and TED Hands datasets, respectively." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 615, + 545, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 615, + 545, + 663 + ], + "spans": [ + { + "bbox": [ + 306, + 615, + 545, + 663 + ], + "type": "text", + "content": "- MPJRE: We leverage the Mean Per Joint Rotation Error [○] (MPJRE) [14] to measure the absolute distance between predicted 3D representation joints and pseudo ground truth." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 665, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 665, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 306, + 665, + 545, + 712 + ], + "type": "text", + "content": "- Diversity: To verify the diversity of sampled hand gestures, we calculate the average feature distance between 500 random combined sequential pairs [20, 24]. The feature extractor is the same as FHD." + } + ] + } + ], + "index": 16 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 314, + 757 + ], + "type": "text", + "content": "4621" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 70, + 108, + 523, + 232 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "text", + "content": "Table 4. Ablation study on different loss functions and different components of the proposed method. " + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "inline_equation", + "content": "\\downarrow" + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "text", + "content": " indicates the lower the better. ✓ indicates the employment of a certain module or loss function. # means the temporal-motion memory module is adopted before the spatial-residual memory module. † denotes the weights of the two hands transformers are shared." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 70, + 108, + 523, + 232 + ], + "lines": [ + { + "bbox": [ + 70, + 108, + 523, + 232 + ], + "spans": [ + { + "bbox": [ + 70, + 108, + 523, + 232 + ], + "type": "table", + "html": "
Model VariationsB2H Dataset [28]TED Hands Dataset
BaselineFull Model\\( \\mathcal{L}_{dis} \\)\\( \\mathcal{L}_{perc} \\)SRMTMML2 ↓FHD ↓MPJRE ↓L2 ↓FHD ↓MPJRE ↓
✓3.6501.09112.6902.3660.97710.531
✓3.6040.77312.4532.3030.73110.250
✓✓3.5520.68212.0372.2160.5959.786
✓✓3.5630.65712.0852.2610.69910.026
✓✓✓3.5040.64011.8282.1610.4959.508
✓✓✓✓3.4570.58011.6872.1000.3939.209
#✓✓✓✓✓3.4840.61411.7582.1240.4639.311
†✓✓✓✓✓3.4760.59811.7482.1560.3809.467
✓✓✓✓✓3.4200.47111.4062.0370.2588.888
", + "image_path": "2290dbd9d564554c0fe51b067396e5daa3c2fbab229283564ed2f0b99ad88726.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 245, + 167, + 258 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 245, + 167, + 258 + ], + "spans": [ + { + "bbox": [ + 47, + 245, + 167, + 258 + ], + "type": "text", + "content": "4.2. Quantitative Results" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 266, + 288, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 266, + 288, + 386 + ], + "spans": [ + { + "bbox": [ + 46, + 266, + 288, + 386 + ], + "type": "text", + "content": "Comparisons with the state-of-the-art: We compare our method with the pioneering 3D hands prediction work, named Body2hands [28]. Moreover, to fully verify the superiority of our method, we implement various state-of-the-art (SOTA) human motion prediction models: MTR [39], BTM [8], LTD [25], MotionMixer [1], and SPGSN [19]. For fair comparisons, all methods are implemented by source codes or pre-trained models released by authors. Since the above counterparts are designed without the diversification setting, the comparison is divided into two parts." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 388, + 287, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 388, + 287, + 508 + ], + "spans": [ + { + "bbox": [ + 46, + 388, + 287, + 508 + ], + "type": "text", + "content": "In the first part, we leverage our stage one initial prediction to compare with other competitors. We adopt the " + }, + { + "bbox": [ + 46, + 388, + 287, + 508 + ], + "type": "inline_equation", + "content": "L2" + }, + { + "bbox": [ + 46, + 388, + 287, + 508 + ], + "type": "text", + "content": " distance, FHD, and MPJRE to provide a well-rounded view of comparisons. As reported in Tab. 1, our method outperforms all the counterparts by a large margin. Remarkably, our method achieves the lowest FHD and MPJRE sores on both datasets. Concretely, on FHD scores of the TED Hands dataset, our method performs even " + }, + { + "bbox": [ + 46, + 388, + 287, + 508 + ], + "type": "inline_equation", + "content": "70.6\\%" + }, + { + "bbox": [ + 46, + 388, + 287, + 508 + ], + "type": "text", + "content": " lower than the optimal results of other competitors (e.g., " + }, + { + "bbox": [ + 46, + 388, + 287, + 508 + ], + "type": "inline_equation", + "content": "(0.877 - 0.258) / 0.877 \\approx 70.6\\%" + }, + { + "bbox": [ + 46, + 388, + 287, + 508 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 510, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 288, + 715 + ], + "type": "text", + "content": "To demonstrate the effectiveness of the diversification process in our method, we compare the diversified results based on the various predictions from above mentioned competitive methods. Meanwhile, we replace our MCMC-based sampling strategy with CVAE [36] to diversify our initial prediction at stage one. We exploit the FHD and Diversity metrics in the second part. As shown in Tab. 2 and Tab. 3, our method achieves superior performance from the perspective of diversity. Although the FHD is slightly worse than stage one due to the sampled perturbation, our method still achieves the optimal result. Compared with CVAE, our method effectively avoids the potential posterior collapse problem [12]. Moreover, we observe that the diversity scores on our TED Hands dataset are much higher than the B2H dataset with all the counterparts. It applies that our newly collected TED Hands dataset includes more diverse hand gestures." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 245, + 547, + 330 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 245, + 547, + 330 + ], + "spans": [ + { + "bbox": [ + 304, + 245, + 547, + 330 + ], + "type": "text", + "content": "Ablation Study: We further conduct the ablation study based on stage one to verify the effectiveness of each module and different loss functions, as indicated in Tab. 4. The baseline model is implemented by a simple transformer-based pipeline without bilateral hand branches. Our full model adopts the bilateral hand branches interacting with a body-specific transformer to produce the 3D hand gestures." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 330, + 547, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 330, + 547, + 484 + ], + "spans": [ + { + "bbox": [ + 304, + 330, + 547, + 484 + ], + "type": "text", + "content": "As shown in Tab. 4, all combinations of the different loss functions and components have positive impacts on 3D hand predictions. The most complete combination attains the best results. Even though we directly construct the bilateral branches without disentanglement constraints (i.e., " + }, + { + "bbox": [ + 304, + 330, + 547, + 484 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{dis}" + }, + { + "bbox": [ + 304, + 330, + 547, + 484 + ], + "type": "text", + "content": ") as full model, our method achieves comparable performance against the simple baseline. This indicates the global body-hand interaction are effectively modeled by bilateral hand transformers and a body-specific transformer. Then, we observe that after adding the loss functions " + }, + { + "bbox": [ + 304, + 330, + 547, + 484 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{dis}" + }, + { + "bbox": [ + 304, + 330, + 547, + 484 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 330, + 547, + 484 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{perc}" + }, + { + "bbox": [ + 304, + 330, + 547, + 484 + ], + "type": "text", + "content": ", the performance of our method is significantly improved, especially in MPJRE scores on both datasets (e.g., " + }, + { + "bbox": [ + 304, + 330, + 547, + 484 + ], + "type": "inline_equation", + "content": "10.250 \\rightarrow 9.508" + }, + { + "bbox": [ + 304, + 330, + 547, + 484 + ], + "type": "text", + "content": " on TED Hands)." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 486, + 547, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 547, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 547, + 676 + ], + "type": "text", + "content": "To verify the effectiveness of SRM and TMM, we conduct plenty of experiments on both datasets. As reported in Tab. 4, when we first employ the SRM, our method achieves the lower " + }, + { + "bbox": [ + 304, + 486, + 547, + 676 + ], + "type": "inline_equation", + "content": "L2" + }, + { + "bbox": [ + 304, + 486, + 547, + 676 + ], + "type": "text", + "content": " distance and FHD scores on both datasets. Then, after adding TMM, our method achieves the best performance. This result proves that TMM effectively models the body-hand temporal association. Besides, we find that when TMM is adopted before SRM, the model performance decreases slightly (the third row from bottom to top in Tab. 4). This corresponds to both TMM and transformer-based backbone (i.e. body-transformer, bilateral hand branches) focus on modeling the body-hand temporal correlation. Both of them encourage the two hands to be more temporal consistent with body dynamics. Employing the SRM between them leads to worse spatial-temporal modeling for body-hand interaction." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "content": "Moreover, we conduct experiments that the parameter weights of bilateral hand transformers are shared. 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+ "type": "image", + "bbox": [ + 477, + 171, + 521, + 219 + ], + "blocks": [ + { + "bbox": [ + 477, + 171, + 521, + 219 + ], + "lines": [ + { + "bbox": [ + 477, + 171, + 521, + 219 + ], + "spans": [ + { + "bbox": [ + 477, + 171, + 521, + 219 + ], + "type": "image", + "image_path": "f4c8ce356583382e8bb654d844f519e8ebcfcf659a3ff9b912e1fc68a8dae4c7.jpg" + } + ] + } + ], + "index": 29, + "angle": 0, + "type": "image_body" + } + ], + "index": 29 + }, + { + "type": "image", + "bbox": [ + 59, + 277, + 275, + 367 + ], + "blocks": [ + { + "bbox": [ + 46, + 239, + 545, + 262 + ], + "lines": [ + { + "bbox": [ + 46, + 239, + 545, + 262 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 545, + 262 + ], + "type": "text", + "content": "Figure 4. Visualization of our predicted 3D hand gestures against various state-of-the-art methods [1,8,19,25,28,39]. From top to bottom, samples of the first row are from the B2H dataset, and the others are from our TED Hands dataset. Best view on screen." + } + ] + } + ], + "index": 38, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 59, + 277, + 275, + 367 + ], + "lines": [ + { + "bbox": [ + 59, + 277, + 275, + 367 + ], + "spans": [ + { + "bbox": [ + 59, + 277, + 275, + 367 + ], + "type": "image", + "image_path": "78ec315dcbf9d040db00935726f7602563e4afd77f184d05ecdffb77e7b25040.jpg" + } + ] + } + ], + "index": 39, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 371, + 287, + 393 + ], + "lines": [ + { + "bbox": [ + 46, + 371, + 287, + 393 + ], + "spans": [ + { + "bbox": [ + 46, + 371, + 287, + 393 + ], + "type": "text", + "content": "Figure 5. User study on the motion naturalness, smoothness, and body-hand temporal consistency. " + }, + { + "bbox": [ + 46, + 371, + 287, + 393 + ], + "type": "inline_equation", + "content": "\\uparrow" + }, + { + "bbox": [ + 46, + 371, + 287, + 393 + ], + "type": "text", + "content": " indicates the higher the better." + } + ] + } + ], + "index": 40, + "angle": 0, + "type": "image_caption" + } + ], + "index": 39 + }, + { + "bbox": [ + 46, + 405, + 287, + 489 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 405, + 287, + 489 + ], + "spans": [ + { + "bbox": [ + 46, + 405, + 287, + 489 + ], + "type": "text", + "content": "formance is decreased due to the spatial-temporal interaction between the body and single-hand-specific branch being merged here. This supports our key technical insight on bilateral hand disentanglement. Additionally, to verify the practical ability of our method, we conduct experiments on model complexity and inference time, more details are presented in the supplementary material." + } + ] + } + ], + "index": 41 + }, + { + "bbox": [ + 47, + 498, + 176, + 511 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 498, + 176, + 511 + ], + "spans": [ + { + "bbox": [ + 47, + 498, + 176, + 511 + ], + "type": "text", + "content": "4.3. Qualitative Evaluation" + } + ] + } + ], + "index": 42 + }, + { + "bbox": [ + 46, + 517, + 287, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 517, + 287, + 649 + ], + "spans": [ + { + "bbox": [ + 46, + 517, + 287, + 649 + ], + "type": "text", + "content": "User Study: To further analyze the visual quality of the predicted 3D hand gestures by different methods, we recruit 15 volunteers to participate in the user study. We take the naturalness, smoothness, and body-hand temporal consistency as three evaluation perceptions and the range of grades is from 0 to 5 (the higher, the better). The statistical results are reported in Fig. 5. Our method shows the best performance in all three metrics. Especially in the naturalness and body-hand temporal consistency, our method achieves remarkable advantages among all the methods due to the body-hand interaction modeling by SRM and TMM." + } + ] + } + ], + "index": 43 + }, + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "content": "Visualization: To fully verify the performance of our method, we show the visualization of generated 3D hands from the first and second stages, respectively. As depicted in Fig. 4, we compare our initial predictions (from stage one) with various SOTA approaches. The avatars are ren-" + } + ] + } + ], + "index": 44 + }, + { + "bbox": [ + 304, + 278, + 547, + 470 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 278, + 547, + 470 + ], + "spans": [ + { + "bbox": [ + 304, + 278, + 547, + 470 + ], + "type": "text", + "content": "dered from ground truth speakers in B2H and TED Hands datasets. We observe that Body2hands, BTM, and LTD generate unreasonable hand gestures (e.g., in the third row of Body2hands, left-hand gestures of avatar). MRT, Motion-Mixer, and SPGSN predict the natural results, but the finger gestures are less consistent with the upper body dynamics. In contrast, our method successfully predicts the perceptually convincing 3D hand gestures from the body dynamics. This supports our key insight to build the bilateral hand disentanglement branches since the asymmetric motions of two hands. We further visualize the diversification results generated by our method at stage two. As shown in Fig. 1 and Fig. 4, with the same upper body dynamics as input, our method obtains the natural and diverse 3D hand gestures on B2H and TED Hands datasets, respectively. Please refer to the supplementary material for more visualization results." + } + ] + } + ], + "index": 45 + }, + { + "bbox": [ + 306, + 480, + 378, + 493 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 480, + 378, + 493 + ], + "spans": [ + { + "bbox": [ + 306, + 480, + 378, + 493 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 46 + }, + { + "bbox": [ + 304, + 500, + 545, + 668 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 500, + 545, + 668 + ], + "spans": [ + { + "bbox": [ + 304, + 500, + 545, + 668 + ], + "type": "text", + "content": "In this paper, we present a novel bilateral hand disentanglement based two-stage method towards natural and diverse 3D hand prediction from body dynamics. In the first stage, upon the bilateral hand branches, we fully take advantage of the spatial-temporal body-hand interaction for generating natural initial 3D hand gestures. Then, in the second stage, we further diversify our natural initial 3D hand gestures by gradient-based markov chain monte carlo sampling. Extensive experiments conducted on B2H and our newly collected TED Hands datasets demonstrate the superiority of our method. As our method aims at generating diverse 3D avatar hand postures, in future work, we will investigate sampling diverse 3D hand gestures with temporal smoothness, instead of frame-wise sampling." + } + ] + } + ], + "index": 47 + }, + { + "bbox": [ + 305, + 673, + 545, + 709 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 673, + 545, + 709 + ], + "spans": [ + { + "bbox": [ + 305, + 673, + 545, + 709 + ], + "type": "text", + "content": "Acknowledgements. 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China.", + "bbox": [ + 205, + 220, + 730, + 255 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ Key Laboratory of Multimedia Trusted Perception and Efficient Computing,", + "bbox": [ + 163, + 256, + 771, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Ministry of Education of China, Xiamen University, 361005, P.R. China.", + "bbox": [ + 181, + 275, + 753, + 291 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "3Shanghai Artificial Intelligence Laboratory, Shanghai, 200232, China.", + "bbox": [ + 187, + 292, + 746, + 309 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "zhangyk@stu.xmu.edu.cn, hanzi.wang@xmu.edu.cn", + "bbox": [ + 267, + 311, + 666, + 325 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 361, + 313, + 378 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "For the visible-infrared person re-identification (ViReID) task, one of the major challenges is the modality gaps between visible (VIS) and infrared (IR) images. However, the training samples are usually limited, while the modality gaps are too large, which leads that the existing methods cannot effectively mine diverse cross-modality clues. To handle this limitation, we propose a novel augmentation network in the embedding space, called diverse embedding expansion network (DEEN). The proposed DEEN can effectively generate diverse embeddings to learn the informative feature representations and reduce the modality discrepancy between the VIS and IR images. Moreover, the ViReID model may be seriously affected by drastic illumination changes, while all the existing ViReID datasets are captured under sufficient illumination without significant light changes. Thus, we provide a low-light cross-modality (LLCM) dataset, which contains 46,767 bounding boxes of 1,064 identities captured by 9 RGB/IR cameras. Extensive experiments on the SYSU-MM01, RegDB and LLCM datasets show the superiority of the proposed DEEN over several other state-of-the-art methods. The code and dataset are released at: https://github.com/ZYK100/LLCM", + "bbox": [ + 76, + 393, + 473, + 741 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 772, + 209, + 787 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Person re-identification (ReID) aims to match a given person with gallery images captured by different cameras [3, 9, 52]. Most existing ReID methods [22, 24, 30, 38, 50] only focus on matching RGB images captured by visible cameras at daytime. However, these methods may fail", + "bbox": [ + 76, + 799, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8b4f0a3de20e164309fccc573936a144cd5708769783484a5c52a6fbf4b8e4ab.jpg", + "image_caption": [ + "Figure 1. Motivation of the proposed DEEN, which aims to generate diverse embeddings to make the network focus on learning with the informative feature representations to reduce the modality gaps between the VIS and IR images." + ], + "image_footnote": [], + "bbox": [ + 504, + 361, + 883, + 518 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "to achieve encouraging results when visible cameras cannot effectively capture person's information under complex conditions, such as at night or low-light environments. To solve this problem, some visible (VIS)-infrared (IR) person re-identification (VIREID) methods [15,39,41,48] have been proposed to retrieve the VIS (IR) images according to the corresponding IR (VIS) images.", + "bbox": [ + 496, + 597, + 892, + 703 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Compared with the widely studied person ReID task, the VIREID task is much more challenging due to the additional cross-modality discrepancy between the VIS and IR images [33, 45, 49, 51]. Typically, there are two popular types of methods to reduce this modality discrepancy. One type is the feature-level methods [5, 11, 16, 35, 40, 42], which try to project the VIS and IR features into a common embedding space, where the modality discrepancy can be minimized. However, the large modality discrepancy makes these methods difficult to project the cross-modality images into a common feature space directly. The other type is the image-level methods [4, 28, 29, 32], which aim to reduce the modality discrepancy by translating an IR (or VIS) image", + "bbox": [ + 496, + 704, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author.", + "bbox": [ + 94, + 886, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "2153", + "bbox": [ + 480, + 924, + 514, + 936 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a5754c3b8954ae0bd7df54064b5555f1c416d38a3a9f66f318db5541fbd231ec.jpg", + "image_caption": [ + "Figure 2. Comparison of person images on the SYSU-MM01 (1st row), RegDB (2nd row), and LLCM (3rd-5th rows) datasets. Each row shows four VIS images and four IR images of two identities. It is obvious that our LLCM contains a more challenging and realistic VIREID environment." + ], + "image_footnote": [], + "bbox": [ + 80, + 89, + 465, + 292 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "into its VIS (or IR) counterpart by using the GANs [8]. Despite their success in reducing the modality gaps, the generated cross-modality images are usually accompanied by some noises due to the lack of the VIS-IR image pairs.", + "bbox": [ + 75, + 385, + 468, + 445 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we propose a novel augmentation network in the embedding space for the VIREID task, called diverse embedding expansion network (DEEN), which consists of a diverse embedding expansion (DEE) module and a multistage feature aggregation (MFA) block. The proposed DEE module can generate more embeddings followed by a novel center-guided pair mining (CPM) loss to drive the DEE module to focus on learning with the diverse feature representations. As illustrated in Fig. 1, by exploiting the generated embeddings with diverse information, the proposed DEE module can achieve the performance improvement by using more diverse embeddings. The proposed MFA block can aggregate the features from different stages for mining potential channel-wise and spatial feature representations, which increases the network's capacity for mining different-level diverse embeddings.", + "bbox": [ + 75, + 446, + 468, + 686 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Moreover, we observe that the existing VIREID datasets are captured under the environments with sufficient illumination. However, the performance of the VIREID methods may be seriously affected by drastic illumination changes or low illuminations. Therefore, we collect a challenging low-light cross-modality dataset, called LLCM dataset, which is shown in Fig. 2. Compared with the other VIREID datasets, the LLCM dataset contains a larger number of identities and images captured under low-light scenes, which introduces more challenges to the real-world VIREID task.", + "bbox": [ + 75, + 688, + 468, + 838 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, the main contributions are as follows:", + "bbox": [ + 96, + 839, + 431, + 853 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- We propose a novel diverse embedding expansion (DEE) module with a center-guided pair mining (CPM) loss to generate more embeddings for learning the diverse fea", + "bbox": [ + 76, + 854, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ture representations. We are the first to augment the embeddings in the embedding space in VIREID. Besides, we also propose an effective multistage feature aggregation (MFA) block to mine potential channel-wise and spatial feature representations.", + "bbox": [ + 496, + 90, + 890, + 165 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- With the incorporation of DEE, CPM loss and MFA into an end-to-end learning framework, we propose an effective diverse embedding expansion network (DEEN), which can effectively reduce the modality discrepancy between the VIS and IR images.", + "- We collect a low-light cross-modality (LLCM) dataset, which contains 46,767 images of 1,064 identities captured under the environments with illumination changes and low illuminations. The LLCM dataset has more new and important features, which can facilitate the research of VIREID towards practical applications.", + "- Extensive experiments show that the proposed DEEN outperforms the other state-of-the-art methods for the VIReID task on three challenging datasets." + ], + "bbox": [ + 496, + 166, + 890, + 378 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 392, + 640, + 407 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Generally speaking, there are two main categories of methods in VIREID: the image-level methods and the feature-level methods.", + "bbox": [ + 496, + 417, + 890, + 460 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The image-level VIREID methods try to transform one modality into the other for reducing the modality discrepancy between the VIS and IR images in the image space. For this purpose, some GANs-based [4, 28, 29, 32] methods are proposed to perform identity-preserving person image style transformation for aligning cross-modality images and alleviating the problem of limited data. These methods often design complex generative models to align cross-modality images. However, due to the lack of VIS-IR image pairs, the generated images are unavoidably accompanied by some noises. X-modality [14] and its variations [34, 49] apply a lightweight network to introduce an auxiliary middle modality to assist the cross-modality search task. However, there is still a modality gap between this middle modality and the VIS / IR modality.", + "bbox": [ + 496, + 462, + 890, + 688 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The feature-level methods aim to find a modality-shared and modality-specific feature space, where the modality gaps can be minimized. For this purpose, MAUM [15] tries to learn cross-modality metrics in two uni-directions to further enhance them with memory-based augmentation. RFM [25] introduces a cross-center loss to explore a more compact intra-class distribution. DCLNet [23] encourages the positive pixels with the same semantic information to be close, while it simultaneously pushes the negative pixels away. cmGAN [5] designs a cutting-edge discriminator to learn discriminative representations from different modalities. However, the large modality gaps between the VIS and IR images make it difficult to project the cross-modality images into a common space directly [7, 18, 21, 26].", + "bbox": [ + 496, + 688, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "2154", + "bbox": [ + 480, + 924, + 514, + 936 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/5a6d7dc627e1ca9f46910048e7aab6295ecdca80cc1888dec9aa8450ee8cc4a4.jpg", + "image_caption": [ + "Figure 3. The pipeline of the proposed network, which includes a DEE module and a MFA block. The DEE module can generate more embeddings with a novel CPM loss to learn diverse feature representations. The MFA block can aggregate the embeddings from different stages for mining diverse channel-wise and spatial feature representations." + ], + "image_footnote": [], + "bbox": [ + 101, + 90, + 862, + 362 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 422, + 169, + 436 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Model Architecture", + "text_level": 1, + "bbox": [ + 76, + 448, + 264, + 462 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Fig. 3 provides an overview of the proposed diverse embedding expansion network (DEEN), which utilizes a two-stream ResNet-50 network [12, 44] as the backbone. The VIS-IR features are fed into the proposed diverse embedding expansion (DEE) module to generate more embeddings. Then, a center-guided pair mining (CPM) loss is proposed to make the generated embeddings as diverse as possible for learning informative feature representations. Besides, we incorporate an effective MFA block to aggregate the features from different stages for mining diverse channel-wise and spatial feature representations. During the training stage, all the features before and after the batch normalization (BN) layer are fed into different losses to jointly optimize DEEN.", + "bbox": [ + 75, + 472, + 470, + 683 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Diverse Embedding Expansion Module", + "text_level": 1, + "bbox": [ + 76, + 695, + 413, + 710 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The proposed DEE module is used to generate more embeddings to alleviate the problem of insufficient training data by using a multi-branch convolutional generation structure. Specifically, for each branch of DEE, we firstly use three $3 \\times 3$ dilated convolutional layers $\\varphi_{3 \\times 3}^{1}, \\varphi_{3 \\times 3}^{2}, \\varphi_{3 \\times 3}^{3}$ with different dilation ratios (1, 2, 3) to reduce the number of feature maps $\\mathbf{f}$ to $1 / 4$ of its own size, and then we obtain the feature maps by combining them into one feature map, followed by a ReLU activation layer $\\mathbf{F}_{ReLU}$ to improve the non-linear representation capability of the DEE. Then, another convolutional layer $\\theta_{1 \\times 1}$ with a kernel in size of $1 \\times 1$ is applied to the obtained feature map to change its dimension as same as $\\mathbf{f}$ . Thus, the generated embeddings $\\mathbf{f}_{+}^{i}$ of the", + "bbox": [ + 75, + 717, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$i$ -th branch can be written as follows:", + "bbox": [ + 500, + 425, + 746, + 438 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {f} _ {+} ^ {i} = \\theta_ {1 \\times 1} \\left(\\mathbf {F} _ {R e L U} \\left(\\varphi_ {3 \\times 3} ^ {1} (\\mathbf {f}) + \\varphi_ {3 \\times 3} ^ {2} (\\mathbf {f}) + \\varphi_ {3 \\times 3} ^ {3} (\\mathbf {f})\\right)\\right). \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 532, + 446, + 890, + 465 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Then, all the generated embeddings are concatenated together and used as the input to the next stage of the backbone network.", + "bbox": [ + 498, + 474, + 890, + 518 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Center-Guided Pair Mining Loss", + "text_level": 1, + "bbox": [ + 500, + 530, + 787, + 545 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As we can see from the above operation, the DEE module can only generate more embeddings using a multibranch convolutional block. However, this operation cannot effectively obtain diverse embeddings. Thus, we apply the following three properties to constrain the generated embeddings as diverse as possible to effectively reduce the modality discrepancy between the VIS and IR images:", + "bbox": [ + 496, + 553, + 890, + 657 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Property 1: The generated embeddings should be as diverse as possible to effectively learn the informative feature representations. This means that we need to push away the distances between the generated embeddings and the original embeddings to learn diverse features and mine diverse cross-modality clues.", + "bbox": [ + 496, + 659, + 890, + 750 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Property 2: The generated embeddings should facilitate reducing the modality discrepancy between the VIS and IR images. This means that we need to pull close the distances between the embeddings generated from the VIS modality and the original IR embeddings. Similarly, we also need to pull close the distances between the embeddings generated from the IR modality and the original VIS embeddings.", + "bbox": [ + 496, + 750, + 890, + 869 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Property 3: The intra-class distance should be less than the inter-class one. By Property 2, it pushes close the", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "2155", + "bbox": [ + 480, + 926, + 514, + 936 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/95fa4c5421bc831bdffb9003d74f1685971dbeda5868d519c363e33310c1ea0b.jpg", + "image_caption": [ + "Figure 4. Illustration of the proposed CPM loss for DEE." + ], + "image_footnote": [], + "bbox": [ + 93, + 90, + 455, + 218 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "distance between the generated embeddings and the original ones, which may cause the embeddings of different classes to become close. Thus, it is necessary to keep the intra-class distance less than the inter-class distance.", + "bbox": [ + 75, + 250, + 468, + 306 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As shown in Fig. 4, for embeddings generated from the VIS modality, the CPM loss can be formulated as follows:", + "bbox": [ + 76, + 309, + 468, + 338 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} \\left(\\mathbf {f} _ {v}, \\mathbf {f} _ {n}, \\mathbf {f} _ {v +} ^ {i}\\right) = \\left[ \\boldsymbol {D} \\left(\\mathbf {f} _ {n} ^ {j}, \\mathbf {f} _ {v +} ^ {i, j}\\right) - \\boldsymbol {D} \\left(\\mathbf {f} _ {v} ^ {j}, \\mathbf {f} _ {v +} ^ {i, j}\\right) - \\boldsymbol {D} \\left(\\mathbf {f} _ {v} ^ {j}, \\mathbf {f} _ {v} ^ {k}\\right) \\right] _ {+}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 344, + 468, + 362 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $D(\\cdot, \\cdot)$ is the Euclidean distance between two embeddings. $\\mathbf{f}_v$ and $\\mathbf{f}_n$ are the original embeddings from the VIS and IR modalities, and $\\mathbf{f}_{v+}^i$ is the embeddings generated from the $i$ -th branch of the VIS modality. $j, k$ are different identities in a minibatch and $[z]_+ = \\max(z, 0)$ . In Eq. (2), the first term can pull the generated embeddings $\\mathbf{f}_{v+}^i$ towards the original IR's embeddings $\\mathbf{f}_n$ to reduce the modality discrepancy between $\\mathbf{f}_{v+}^i, j$ and $\\mathbf{f}_n^j$ . The second term can push the generated embeddings $\\mathbf{f}_{v+}$ away from the VIS's embeddings $\\mathbf{f}_v$ to enable $\\mathbf{f}_{v+}$ to learn informative feature representations. The third term can make the intra-class distance less than the inter-class distance.", + "bbox": [ + 75, + 369, + 468, + 547 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Then, we use the embedding centers $\\mathbf{c}_v$ and $\\mathbf{c}_n$ of each class to make the centers of generated embeddings $\\mathbf{c}_{v+}^i$ and $\\mathbf{c}_{n+}^i$ more discriminative, and introduce a margin term $\\alpha$ to balance the three terms in Eq. (2). Thus, for the embeddings from VIS, the CPM loss is formulated as follows:", + "bbox": [ + 75, + 549, + 468, + 621 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} \\left(\\mathbf {c} _ {v}, \\mathbf {c} _ {n}, \\mathbf {c} _ {v +} ^ {i}\\right) = \\left[ \\boldsymbol {D} \\left(\\mathbf {c} _ {n} ^ {j}, \\mathbf {c} _ {v +} ^ {i, j}\\right) - \\boldsymbol {D} \\left(\\mathbf {c} _ {v} ^ {j}, \\mathbf {c} _ {v +} ^ {i, j}\\right) - \\boldsymbol {D} \\left(\\mathbf {c} _ {v} ^ {j}, \\mathbf {c} _ {v} ^ {k}\\right) + \\alpha \\right] _ {+}. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 78, + 626, + 468, + 656 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Similarly, for the class centers $\\mathbf{c}_{n + }^{i}$ of embeddings generated from IR, we have:", + "bbox": [ + 76, + 665, + 468, + 693 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} \\left(\\mathbf {c} _ {v}, \\mathbf {c} _ {n}, \\mathbf {c} _ {n +} ^ {i}\\right) = \\left[ \\boldsymbol {D} \\left(\\mathbf {c} _ {v} ^ {j}, \\mathbf {c} _ {n +} ^ {i, j}\\right) - \\boldsymbol {D} \\left(\\mathbf {c} _ {n} ^ {j}, \\mathbf {c} _ {n +} ^ {i, j}\\right) - \\boldsymbol {D} \\left(\\mathbf {c} _ {n} ^ {j}, \\mathbf {c} _ {n} ^ {k}\\right) + \\alpha \\right] _ {+}. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 698, + 468, + 729 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Thus, the final CPM loss can be formulated as follows:", + "bbox": [ + 96, + 736, + 459, + 750 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {c p m} = \\mathcal {L} \\left(\\mathbf {c} _ {v}, \\mathbf {c} _ {n}, \\mathbf {c} _ {v +} ^ {i}\\right) + \\mathcal {L} \\left(\\mathbf {c} _ {v}, \\mathbf {c} _ {n}, \\mathbf {c} _ {n +} ^ {i}\\right). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 143, + 757, + 468, + 773 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Besides, to ensure that the generated embeddings from different branches can capture different informative feature representations, we force these different embeddings generated by different branches orthogonal to minimize the overlapping elements. Therefore, the orthogonal loss can be formulated as follows:", + "bbox": [ + 75, + 777, + 468, + 859 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {o r t} = \\sum_ {m = 1} ^ {i - 1} \\sum_ {n = m + 1} ^ {i} \\left(\\mathbf {f} _ {+} ^ {m T} \\mathbf {f} _ {+} ^ {n}\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 866, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $m$ and $n$ are the $m$ -th and $n$ -th generated embeddings from the original embeddings, respectively. The orthogonal loss can enforce the generated embeddings to learn more informative feature representations.", + "bbox": [ + 498, + 90, + 890, + 151 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Multistage Feature Aggregation Block", + "text_level": 1, + "bbox": [ + 500, + 159, + 828, + 176 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Features aggregation of different levels has been demonstrated to be helpful to semantic segmentation, classification and detection task [1, 54, 55]. To aggregate the features from different stages for mining diverse channel-wise and spatial feature representations, we incorporate an effective channel-spatial multistage feature aggregation (MFA) block to aggregate multi-stage features inspired by [31].", + "bbox": [ + 496, + 181, + 890, + 287 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Next, we elaborate on the detail of the MFA block, which is shown in Fig. 3. Specifically, we consider two types of source features for the channel-spatial aggregation block in each stage of the backbone network: low-level feature maps $\\mathbf{f}_l\\in \\mathbb{R}^{C_l\\times H_l\\times W_l}$ before the stage and high-level feature maps $\\mathbf{f}_h\\in \\mathbb{R}^{C_h\\times H_h\\times W_h}$ after the stage, where C, W and H denote the number of the channel, width and height of features, respectively. First, we employ three $1\\times 1$ convolutional layers $\\psi_q^1,\\psi_v^1,\\psi_k^1$ to transform $\\mathbf{f}$ into three compact embeddings: $\\psi_q^1 (\\mathbf{f}_h)$ , $\\psi_v^1 (\\mathbf{f}_l)$ and $\\psi_k^1 (\\mathbf{f}_l)$ . Then, we compute the channel-wise similarity matrix $\\mathbf{M}^c\\in \\mathbb{R}^{C'\\times C'}$ by matrix multiplication followed by softmax:", + "bbox": [ + 496, + 287, + 892, + 464 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {M} ^ {c} = \\mathbf {F} _ {\\text {s o f t m a x}} \\left(\\psi_ {q} ^ {1} \\left(\\mathbf {f} _ {h}\\right) \\times \\psi_ {k} ^ {1} \\left(\\mathbf {f} _ {l}\\right)\\right). \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 470, + 890, + 487 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Consequently, we implement the channel-wise multistage feature aggregation by restoring the channel dimension by the matrix multiplication of $\\psi_v^1 (\\mathbf{f}_l)$ and $\\mathbf{M}^c$ . After that, another $1\\times 1$ convolutional layer $\\omega^c$ is applied to transform the size of the above feature maps to that of $\\mathbf{f}_h$ . Finally, we get the output by adding $\\mathbf{f}_h$ to it by matrix addition:", + "bbox": [ + 496, + 493, + 890, + 577 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {f} _ {h} ^ {c} = \\omega^ {c} \\left(\\psi_ {v} ^ {1} (\\mathbf {f} _ {l}) \\times \\mathbf {M} ^ {c}\\right) + \\mathbf {f} _ {h}. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 604, + 584, + 890, + 599 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "After that, $\\mathbf{f}_h^c$ obtained from the above operations and the low-level feature map $\\mathbf{f}_l$ are used to perform the spatial feature aggregation operation, which is similar to the channelwise multistage feature aggregation operation. Finally, we get the MFA's output as follows:", + "bbox": [ + 496, + 607, + 890, + 676 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {f} _ {h} ^ {s} = \\omega^ {s} \\left(\\psi_ {v} ^ {2} \\left(\\mathbf {f} _ {l}\\right) \\times \\mathbf {M} ^ {s}\\right) + \\mathbf {f} _ {h} ^ {c}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 604, + 684, + 890, + 700 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\omega^s$ and $\\psi_v^2$ are two $1\\times 1$ convolutional layers, and $\\mathbf{M}^s$ is the spatial similarity matrix.", + "bbox": [ + 500, + 708, + 890, + 738 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.5. Multi-Loss Optimization", + "text_level": 1, + "bbox": [ + 500, + 747, + 725, + 763 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Besides the proposed $\\mathcal{L}_{cpm}$ and $\\mathcal{L}_{ort}$ , we also combine the cross-entropy loss $\\mathcal{L}_{ce}$ [17] and the triplet loss $\\mathcal{L}_{tri}$ [13] to jointly optimize the network in an end-to-end manner by minimizing the sum of these four losses $\\mathcal{L}_{total}$ , which can be formulated as follows:", + "bbox": [ + 496, + 768, + 890, + 838 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {c e} + \\mathcal {L} _ {\\text {t r i}} + \\lambda_ {1} \\mathcal {L} _ {\\text {c p m}} + \\lambda_ {2} \\mathcal {L} _ {\\text {o r t}}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 563, + 847, + 890, + 862 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\lambda_{1}$ and $\\lambda_{2}$ are the coefficients to control the relative importance of the loss terms.", + "bbox": [ + 496, + 869, + 890, + 898 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "2156", + "bbox": [ + 480, + 924, + 514, + 936 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/c4add90f66c6cc7be38d6add23a3a03e8542422f4ab04ffb8cc73a262b847679.jpg", + "image_caption": [ + "Figure 5. The distribution of the LLCM's images in the 2D space. It can be seen that the images under different light conditions present different styles, which further increases the modality discrepancy between the VIS and IR images." + ], + "image_footnote": [], + "bbox": [ + 86, + 89, + 459, + 267 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. LLCM Dataset", + "text_level": 1, + "bbox": [ + 76, + 347, + 230, + 362 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Dataset Description", + "text_level": 1, + "bbox": [ + 76, + 373, + 264, + 390 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this paper, we collect a new challenging low-light cross-modality dataset, called LLCM dataset. The LLCM dataset utilizes a 9-camera network deployed in low-light environments, which can capture the VIS images in daytime and capture the IR images at night. For protecting the personal privacy information, we utilize MTCNN [47] to get the bounding boxes of persons' faces and blur those regions. We make sure that each annotated identity is captured by both the VIS and IR cameras. Some examples from the LLCM dataset are shown in Fig. 2. As shown in Tab. 1, compared with the existing VIREID datasets, the LLCM dataset has the following new and important features:", + "bbox": [ + 75, + 398, + 468, + 580 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "First, the images in the LLCM dataset are captured under complex low-light environment for both the VIS and IR modalities, which contains severe illumination changes and is a common problem in the real scenes. As Fig. 2 and Fig. 5 shown, the severe light conditions can change the color of persons' clothes and cause the loss of texture information of the clothes, which introduces great challenges to VIReID. Second, the LLCM dataset has a larger number of identities and bounding boxes. This dataset contains 46,767 bounding boxes of 1,064 identities, making it the largest VIReID dataset at present (see Tab 1). Third, the LLCM dataset is collected in over 100 days from January to April, and different climate conditions and cloth styles are considered. Long-term data collection helps to study the VIReID task in different climates and clothing styles, which increases the generalization of the VIReID model.", + "bbox": [ + 75, + 580, + 468, + 823 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Besides, considering the real-world applications, the LLCM dataset also contains many images that suffer from various challenges, such as motion blurring, pose variation, camera view changes, occlusion, low resolution and others. All in all, the LLCM dataset is a challenging dataset for", + "bbox": [ + 75, + 824, + 468, + 902 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/0f58e0dd830411856bc5750b32558c7c65bce8f49d9c1386858daf7859ad50b1.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DatasetsIDsImagesVIS / IR cam.low-light
RegDB [19]4128,2401 / 1X
SYSU-MM01 [36]49138,2714 / 2X
LLCM1,06446,7679 / 9✓
", + "bbox": [ + 500, + 88, + 890, + 143 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 1. Comparison between the LLCM and other two popular VIREID datasets.", + "bbox": [ + 500, + 148, + 890, + 175 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "the VIREID task, which can further facilitate the research of VIREID towards practical applications.", + "bbox": [ + 498, + 184, + 890, + 215 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Evaluation Protocol", + "text_level": 1, + "bbox": [ + 500, + 224, + 689, + 239 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We divide the LLCM dataset into a training set and a testing set at a ratio about 2:1. The training set contains 30,921 bounding boxes of 713 identities (16,946 bounding boxes are from the VIS modality and 13,975 bounding boxes are from the IR modality), and the testing set contains 13,909 bounding boxes of 351 identities (8,680 bounding boxes are from the VIS modality and 7,166 bounding boxes are from the IR modality). Similar to the RegDB [19] dataset, both the VIS to IR mode and the IR to VIS mode are used to evaluate the performance of the VIREID models. During the testing stage, for each camera, we randomly choose one image from the images of each identity to form the gallery set for evaluation the performance of the models. We repeat the above evaluation 10 times with random split of the gallery set and report the average performance.", + "bbox": [ + 496, + 247, + 890, + 474 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 500, + 488, + 632, + 505 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Datasets", + "text_level": 1, + "bbox": [ + 500, + 512, + 602, + 527 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The SYSU-MM01 dataset [36] contains 491 identities captured by 4 VIS cameras and 2 IR cameras, including the All-Search and Indoor-Search modes. For the All-Search mode, all the images captured by all the VIS cameras are used as the gallery set. For the Indoor-Search mode, only the images captured by two indoor VIS cameras are used as the gallery set. The RegDB dataset [19] consists of 412 identities, and each identity has 10 VIS images and 10 IR images captured by a pair of overlapping cameras.", + "bbox": [ + 496, + 535, + 890, + 672 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.2. Implementation Details", + "text_level": 1, + "bbox": [ + 500, + 681, + 718, + 696 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "All the input images are firstly resized to $3 \\times 384 \\times 144$ , and the random horizontal flip and random erasing [53] techniques are adopted during the training phase. The initial learning rate is set to $1 \\times 10^{-2}$ and then it increases to $1 \\times 10^{-1}$ after 10 epochs with a warm-up strategy. After that, we decay the learning rate to $1 \\times 10^{-2}$ at 20 epoch, and further decay to $1 \\times 10^{-3}$ and $1 \\times 10^{-4}$ at epoch 60 and epoch 120, respectively, until a total of 150 epochs. In each mini-batch, we randomly select 4 VIS images and 4 IR images of 6 identities for training. The SGD optimizer is adopted for training, where the momentum is set to 0.9. For the RegDB dataset, we remove stage-4 and plug the proposed DEE module into the DEEN after stage-2.", + "bbox": [ + 496, + 703, + 890, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "2157", + "bbox": [ + 480, + 925, + 514, + 936 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/e156bccdbc711f9e505af7017847104e586e2c0e3e5f7fd591b63e5f2d7d3a7c.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsSYSU-MM01RegDB
All SearchIndoor SearchVIS to IRIR to VIS
R-1R-10R-20mAPR-1R-10R-20mAPR-1R-10R-20mAPR-1R-10R-20mAP
BDTR [46]17.055.472.019.7----33.658.667.432.832.958.568.432.0
D2RL [32]28.970.682.429.2----43.466.176.344.1----
Hi-CMD [4]34.977.6-35.9----70.986.4-66.0----
JSIA-ReID [29]38.180.789.936.943.886.294.252.948.1--48.948.5--49.3
AlignGAN [28]42.485.093.740.745.987.694.454.357.9--53.656.3--53.4
X-Modality [14]49.989.896.050.7----62.283.191.760.2----
DDAG [44]54.890.495.853.061.094.198.468.069.386.291.563.568.185.290.361.8
LbA [20]55.4--54.158.5--66.374.2--67.667.5--72.4
NFS [2]56.991.396.555.562.896.599.169.880.591.695.172.178.090.593.669.8
CM-NAS [6]60.892.196.858.968.094.897.952.482.895.197.779.381.794.196.977.6
MCLNet [10]65.493.397.162.072.697.099.276.680.392.796.073.175.990.994.669.5
FMCNet [48]66.3--62.568.2--74.189.1--84.488.4--83.9
SMCL [34]67.492.996.861.868.896.698.875.683.9--79.883.1--78.6
DART [41]68.796.499.066.372.597.899.578.283.6--75.782.0--73.8
CAJ [43]69.995.798.566.976.397.999.580.485.095.597.579.184.895.397.577.8
MPANet [37]70.696.298.868.276.798.299.681.082.8--80.783.7--80.9
MMN [49]70.696.299.066.976.297.299.379.691.697.798.984.187.596.098.180.5
DCLNet [23]70.8--65.373.5--76.881.2--74.378.0--70.6
MAUM [15]71.7--68.877.0--81.987.9--85.187.0--84.3
DEEN (ours)74.797.699.271.880.399.099.883.391.197.898.985.189.596.898.483.4
", + "bbox": [ + 81, + 87, + 893, + 361 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.3. Comparison with State-of-the-art Methods", + "text_level": 1, + "bbox": [ + 76, + 395, + 441, + 411 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We firstly compare the proposed DEEN with several state-of-the-art methods to demonstrate the superiority of our method. The experimental results on the SYSU-MM01 and RegDB datasets are reported in Tab. 2, and the results on our LLCM dataset are reported in Tab. 3.", + "bbox": [ + 76, + 422, + 468, + 500 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "SYSU-MM01 and RegDB: From Tab. 2, we can see that the results on the two datasets show that the proposed DEEN achieves the best performance against all other state-of-the-art methods. Specifically, for the All-Search mode on SYSU-MM01, DEEN achieves $74.7\\%$ Rank-1 accuracy and $71.8\\%$ mAP. For the Indoor-Search mode, DEEN achieves $80.3\\%$ Rank-1 accuracy and $83.3\\%$ mAP. For the VIS to IR mode on RegDB, DEEN achieves $91.1\\%$ Rank-1 accuracy and $85.1\\%$ mAP. For the IR to VIS mode, the proposed DEEN also obtains $89.5\\%$ Rank-1 accuracy and $83.4\\%$ mAP. The results validate the effectiveness of our method. Moreover, the results also demonstrate that the proposed DEEN can effectively reduce the modality discrepancy between the VIS and IR modalities.", + "bbox": [ + 75, + 503, + 468, + 715 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "LLCM: Tab. 3 shows the results on our LLCM dataset. Here, we use several representative open-source methods to evaluate our LLCM dataset and compare them with our method. From Tab. 3 we can draw the following conclusions: the best method only obtains $54.9\\%$ Rank-1 accuracy and $62.9\\%$ mAP under the IR to VIS mode. The results of the existing methods on our LLCM dataset are generally unsatisfactory. This shows that, on one hand, our LLCM dataset is a very challenging dataset. On the other hand, the change of light has serious influence on the VIREID model. Besides, the proposed DEEN achieves the best performance under both the VIS to IR mode and the IR to VIS", + "bbox": [ + 75, + 719, + 470, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/4826c9fa003af2e0c359becc510162b5aca395bc7614424ec55567f182628438.jpg", + "table_caption": [ + "Table 2. Comparisons between the proposed DEEN and some state-of-the-art methods on the SYSU-MM01 and RegDB datasets." + ], + "table_footnote": [], + "table_body": "
ModelLLCM
IR to VISVIS to IR
R-1R-10R-20mAPR-1R-10R-20mAP
DDAG [44]40.371.479.648.448.079.286.152.3
DDAG* [44]41.073.481.949.648.581.087.853.0
AGW [45]43.674.682.451.851.581.587.955.3
LbA [20]43.878.286.653.150.884.391.155.6
LbA* [20]44.678.286.853.850.884.691.155.9
AGW* [45]46.477.885.254.856.084.990.659.1
CAJ [43]48.879.585.356.656.585.390.959.8
DART [41]52.280.787.059.860.487.191.963.2
MMN [49]52.581.688.458.959.988.593.662.7
DEEN (ours)54.984.990.962.962.590.394.765.8
", + "bbox": [ + 501, + 393, + 897, + 545 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 3. Performance obtained by the competing methods on our LLCM dataset. The symbol of “*” represents the methods that we reproduced with the random erasing technique.", + "bbox": [ + 498, + 547, + 893, + 590 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "mode, which demonstrates the effectiveness of the proposed DEEN to reduce the modality gaps between the VIS and IR images.", + "bbox": [ + 498, + 608, + 892, + 654 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.4. Ablation Studies", + "text_level": 1, + "bbox": [ + 500, + 665, + 663, + 680 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Effectiveness of each component: To evaluate the contribution of each component to DEEN, we conduct some ablation studies on the LLCM and SYSU-MM01 datasets by removing certain modules from DEEN and evaluate the influence on the performance. The overall settings remain the same, while only the module under evaluation is used in or removed from DEEN. As shown in Tab. 4, although the DEE module can generate more embeddings using a multibranch convolutional block, which slightly improves the performance of the baseline, the results are not satisfactory. After being constrained by the proposed CPM loss to generate diverse embeddings, DEE can greatly improve the performance of the model and effectively reduce the modality discrepancy between the VIS and IR images. Besides, the", + "bbox": [ + 496, + 688, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "2158", + "bbox": [ + 480, + 926, + 514, + 936 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/8cb4221b7e13814328c79cc1a64c5298f967f1da0ddd0cb7ffa463fab2b847ea.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
SettingsLLCMSYSU-MM01
DEE\\( \\mathcal{L}_{cpm} \\)\\( \\mathcal{L}_{ort} \\)MFAR-1mAPR-1mAP
45.453.660.757.7
✓50.559.064.762.0
✓✓53.161.169.266.2
✓✓51.560.165.363.2
✓✓✓53.962.369.866.7
✓51.259.664.762.0
✓✓✓✓54.962.974.771.8
", + "bbox": [ + 78, + 88, + 468, + 200 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/a39b8edbb7629ad62a88b805b4a044caeaa539ba71ebbc43072811f06c4526ee.jpg", + "table_caption": [ + "Table 4. The influence of each component on the performance of the proposed DEEN." + ], + "table_footnote": [], + "table_body": "
MethodsLLCMSYSU-MM01
R-1mAPR-1mAP
DEE after stage-048.557.163.459.4
DEE after stage-149.457.863.760.8
DEE after stage-249.657.965.361.7
DEE after stage-353.962.369.866.7
DEE after stage-450.959.660.058.0
", + "bbox": [ + 83, + 237, + 460, + 321 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/b2a0b4df3a7bde673ed51367ab04c6676fcc1d976a592a62cb79663c7ac45de6.jpg", + "table_caption": [ + "Table 5. The influence of which stage of ResNet-50 to plug the DEE module." + ], + "table_footnote": [], + "table_body": "
MethodsLLCMSYSU-MM01
R-1mAPR-1mAP
Two branches52.660.967.564.6
Three branches53.962.369.266.2
Four branches52.460.767.664.6
", + "bbox": [ + 94, + 358, + 447, + 419 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/22553b020d31923e0767ec331c5d0677a3d0555500d8001842b95b3569e28df0.jpg", + "table_caption": [ + "Table 6. Study about how many branches are suitable for DEE." + ], + "table_footnote": [], + "table_body": "
MethodsLLCMSYSU-MM01
R-1mAPR-1mAP
NL50.157.463.860.7
MFA51.259.664.762.0
NL + DEE54.262.473.470.3
MFA+ DEE54.962.974.771.8
", + "bbox": [ + 96, + 443, + 447, + 506 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 7. Comparison with the Non-Local (NL) block.", + "bbox": [ + 114, + 507, + 431, + 520 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "proposed MFA block can improve the performance of the baseline by aggregating the features from different stages for mining diverse channel-wise and spatial feature representations. With the incorporation of DEE, CPM and MFA into an end-to-end learning framework, DEEN achieves an impressive performance improvement on two challenging VIREID datasets, which shows DEE and MFA can benefit from each other for generating diverse embeddings.", + "bbox": [ + 75, + 536, + 467, + 657 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The influence of which stage of ResNet-50 to plug the DEE module. The proposed DEE can be plugged after any stage of the backbone network. In our experiments, we use ResNet-50 as the backbone, which has five stages: stage-0 to stage-4. We plug DEE after different stages of the ResNet-50 to study how it will affect the performance of the DEEN. As shown in Tab. 5, when DEE is plugged after stage-0 to stage-3, the performance gradually increases, which shows the modality gaps become smaller and the generative ability of DEE becomes stronger at deeper layers of the network. When DEE is plugged after stage-3, it can achieve the best results on both LLCM and SYSU-MM01. However, when DEE is plugged after stage-4, the performance drops rapidly because the CPM loss works directly on the embeddings, enlarging the distances between the generated embeddings and the original embeddings, which", + "bbox": [ + 75, + 657, + 468, + 901 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/cbb256044aab84a426d8d7ec851b9deb188085eabbd4bbef62b8513e4ea33f44.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 90, + 883, + 185 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c47c54c5534c8e7ebefca599e8e74b1900b1eb13851f926bca6c2a140439a016.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 504, + 186, + 883, + 282 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5277400684fa2cd5732cc2c261f3763583a78b3e5a4d138a7ff5e3432f554ecf.jpg", + "image_caption": [ + "Figure 6. Influence of different $\\lambda_{1}$ , $\\lambda_{2}$ and $\\alpha$ values on our LLCM." + ], + "image_footnote": [], + "bbox": [ + 504, + 282, + 883, + 377 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "increases the difficulty of model optimization. Based on the above analysis, we plug DEE after stage-3 of the backbone if not specified.", + "bbox": [ + 498, + 401, + 890, + 445 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness on how many branches are more suitable for DEE. The proposed DEE module utilizes a multibranch convolutional block to generate diverse embeddings. Here, we study how many branches are suitable for DEE. As shown in Tab. 6, with the increase of the number of DEE's branches from 2 to 3, more embeddings are generated to reduce the modality gaps, so the performance gradually increases. However, the increase of performance has an upper limit when the number of branches is more than 3, because DEE generates too many redundant features, which leads to the drop of performance. As a result, DEE with three branches can achieve the best performances both on the LLCM and SYSU-MM01 datasets. It indicates that DEE with 3 branches is more suitable for generating diverse embeddings. Thus, we use 3 branches for DEE if not specified.", + "bbox": [ + 496, + 446, + 890, + 672 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison with the Non-Local block. In this paper, we propose a MFA block to mine diverse channel-wise and spatial feature representations inspired by the Non-local (NL) block in [31]. Thus, we compare these two blocks to investigate which block is more effective. As shown in Tab. 7, the MFA block outperforms the NL block by $1.1\\%$ Rank-1 accuracy and $2.2\\%$ mAP, respectively. The results validate the effectiveness of our MFA block. Moreover, the results also show that the MFA block and the DEE module are complementary for generating diverse embeddings to reduce the modality gaps between the VIS and IR images.", + "bbox": [ + 496, + 672, + 890, + 839 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The influence of the hyperparameters $\\lambda_{1},\\lambda_{2}$ and $\\alpha$ To evaluate the influence of the three hyperparameters, we give quantitative comparisons and report the results in Fig. 6. As we can see, the best performance is achieved when $\\lambda_{1}$", + "bbox": [ + 498, + 839, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "2159", + "bbox": [ + 482, + 926, + 514, + 936 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d22dae04bf26f1f9b5330cc7ced2b0e5db3f913d5fa54cda41d89effd56e3a17.jpg", + "image_caption": [ + "(a) Initial Distance" + ], + "image_footnote": [], + "bbox": [ + 81, + 90, + 243, + 193 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c31395fd3c8b755262de2302efb9cb613bd891c6e32972d73f96a7ada4729de6.jpg", + "image_caption": [ + "(b) Baseline Distance" + ], + "image_footnote": [], + "bbox": [ + 248, + 90, + 403, + 193 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d48c69ce132b505229d53b7c82f7d634cbbb03bc4bc5590009fe547da78edc9e.jpg", + "image_caption": [ + "(c) MFA Distance" + ], + "image_footnote": [], + "bbox": [ + 411, + 90, + 565, + 193 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f2bd4084d1428221c41b771e75f63fa04a8862e4f1cf32633c983017d992d6ff.jpg", + "image_caption": [ + "(d) DEE Distance" + ], + "image_footnote": [], + "bbox": [ + 571, + 90, + 725, + 193 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ed878afc2e4c2a7ea244e1c90b6379380f448c245e7e16c54bd30267076c2ac2.jpg", + "image_caption": [ + "(e) DEEN Distance" + ], + "image_footnote": [], + "bbox": [ + 733, + 90, + 887, + 193 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/aa3843b9b2185bc6406c0bb19c6a63a136ecf4bd7a6a8521097581ddb4d07c61.jpg", + "image_caption": [ + "(f) Initial Distribution" + ], + "image_footnote": [], + "bbox": [ + 86, + 209, + 243, + 306 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8ada288b53c84d6fd5f8d2d9692c233a98f6b12bb79b880b01eff8cd3265b413.jpg", + "image_caption": [ + "(g) Baseline Distribution" + ], + "image_footnote": [], + "bbox": [ + 248, + 209, + 401, + 306 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/db2c7afafa38584fa208a5a6e129441e4753298a08328e54178a01dccabfd2d3.jpg", + "image_caption": [ + "(h) MFA Distribution" + ], + "image_footnote": [], + "bbox": [ + 410, + 209, + 563, + 306 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/533a0a697eb19a863f6553c94a356474d12e806af8c610cf52bb02a5424f5677.jpg", + "image_caption": [ + "(i) DEE Distribution" + ], + "image_footnote": [], + "bbox": [ + 571, + 209, + 725, + 306 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1ad6ef42a52a3d838709aadc5e50e664a976eb407363e08eaea2885c0aa179e1.jpg", + "image_caption": [ + "(j) DEEN Distribution" + ], + "image_footnote": [], + "bbox": [ + 733, + 209, + 887, + 306 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ed65ca563b4aa23779780bed5bee80d6171b4c2223fb32c6899856d37f997fe6.jpg", + "image_caption": [ + "Figure 7. (a-e) show the intra-class and inter-class distances of cross-modality features. The intra-class and inter-class distances are indicated in blue and green colors, respectively. (f-j) show the distribution of feature embeddings in the 2D feature space, where circles and triangles in different colors denote visible and infrared modalities. A total of 20 persons are selected from the test set. The samples with the same color are from the same person. The \"dot\" and \"cross\" markers denote the images from the VIS and IR modalities, respectively.", + "Baseline", + "Figure 8. Some Rank-8 retrieval results obtained by the baseline and the proposed DEEN on our LLCM dataset." + ], + "image_footnote": [], + "bbox": [ + 81, + 398, + 274, + 553 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/fe893f377d67383f12d638d1543ddd6406521366a8a8dcbad063255c906ce48d.jpg", + "image_caption": [ + "DEEN" + ], + "image_footnote": [], + "bbox": [ + 279, + 398, + 473, + 553 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "is set to 0.8, $\\lambda_{2}$ is set to 0.1 and $\\alpha$ is set to 0.2, respectively.", + "bbox": [ + 75, + 611, + 467, + 628 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.5. Visualization", + "text_level": 1, + "bbox": [ + 76, + 635, + 212, + 648 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Feature distribution. To investigate the reason why DEEN is effective, we visualize the inter-class and intra-class distances on our LLCM dataset as shown in Fig. 7 (a-e). Comparing Fig. 7 (c-e) with Fig. 7 (a-b), the means (i.e., the vertical lines) of inter-class and intra-class distances are pushed away by MFA, DEE and DEEN, where $\\delta_1 < \\delta_2 < \\delta_3$ and $\\delta_1 < \\delta_2 < \\delta_4 < \\delta_5$ . This shows that the intra-class distance of DEEN is significantly reduced compared with the intra-class distance of the initial features (Fig. 7 (a)) and the baseline features (Fig. 7 (b)). Thus, DEEN can effectively reduce the modality discrepancy between the VIS and the IR images. Meanwhile, we also visualize the feature distribution with t-SNE [27] in the 2D feature space in Fig. 7 (f-j), which shows that MFA, DEE and DEEN can effectively discriminate and aggregate feature embeddings of the same person, and reduce the modality discrepancy.", + "bbox": [ + 75, + 659, + 468, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Retrieval result. To further show the effectiveness of DEEN, we also show some retrieval results of DEEN on our LLCM dataset in Fig. 8. For each retrieval case, the retrieved images with green boxes mean the correct matches corresponding the given query, while the red ones mean the incorrect matches. In general, DEEN can effectively improve the ranking results with more correctly matched images ranked in the top positions than the baseline.", + "bbox": [ + 496, + 398, + 890, + 521 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. CONCLUSION", + "text_level": 1, + "bbox": [ + 500, + 534, + 656, + 549 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose a novel diverse embedding expansion network (DEEN) in the embedding space for the VIREID task. The proposed DEEN can generate diverse embeddings and mine diverse channel-wise and spatial embeddings to learn the informative feature representations for reducing the modality discrepancy between the VIS and IR images. Moreover, we also provide a challenging low-light cross-modality (LLCM) dataset, which has more new and important features and can further facilitate the research of VIREID towards practical applications. Extensive experiments on the SYSU-MM01, RegDB and LLCM datasets show the superiority of the proposed DEEN over several other state-of-the-art methods.", + "bbox": [ + 496, + 559, + 890, + 755 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Acknowledgments", + "text_level": 1, + "bbox": [ + 500, + 768, + 678, + 787 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported by the National Key Research and Development Program of China under Grant 2022ZD0160402, by the National Natural Science Foundation of China under Grant U21A20514, and by the FuXiaQuan National Independent Innovation Demonstration Zone Collaborative Innovation Platform Project under Grant 3502ZCQXT2022008.", + "bbox": [ + 496, + 794, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "2160", + "bbox": [ + 480, + 926, + 514, + 936 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Xuesong Chen, Canmiao Fu, Yong Zhao, Feng Zheng, Jingkuan Song, Rongrong Ji, and Yi Yang. 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In Proceedings of the ICCV, pages 593–602, 2019. 4" + ], + "bbox": [ + 501, + 92, + 893, + 825 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "2162", + "bbox": [ + 482, + 926, + 514, + 936 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Diverse Embedding Expansion Network and Low-Light Cross-Modality Benchmark for Visible-Infrared Person Re-Identification/fe5b9645-eedb-4dae-90a3-37c29c7fb846_model.json b/2023/Diverse Embedding Expansion Network and Low-Light Cross-Modality Benchmark for Visible-Infrared Person Re-Identification/fe5b9645-eedb-4dae-90a3-37c29c7fb846_model.json new file mode 100644 index 0000000000000000000000000000000000000000..309ff89a80695f0f04f84cea0124010df4c38074 --- /dev/null +++ b/2023/Diverse Embedding Expansion Network and Low-Light Cross-Modality Benchmark for Visible-Infrared Person Re-Identification/fe5b9645-eedb-4dae-90a3-37c29c7fb846_model.json @@ -0,0 +1,2530 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.124, + 0.13, + 0.848, + 0.175 + ], + "angle": 0, + "content": "Diverse Embedding Expansion Network and Low-Light Cross-Modality Benchmark for Visible-Infrared Person Re-identification" + }, + { + "type": "text", + "bbox": [ + 0.334, + 0.203, + 0.61, + 0.221 + ], + "angle": 0, + "content": "Yukang Zhang\\(^{1,2}\\), Hanzi Wang\\(^{1,2,3*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.207, + 0.222, + 0.732, + 0.256 + ], + "angle": 0, + "content": "\\(^{1}\\)Fujian Key Laboratory of Sensing and Computing for Smart City, School of Informatics, Xiamen University, 361005, P.R. China." + }, + { + "type": "text", + "bbox": [ + 0.165, + 0.257, + 0.772, + 0.275 + ], + "angle": 0, + "content": "\\(^{2}\\)Key Laboratory of Multimedia Trusted Perception and Efficient Computing," + }, + { + "type": "text", + "bbox": [ + 0.182, + 0.276, + 0.754, + 0.292 + ], + "angle": 0, + "content": "Ministry of Education of China, Xiamen University, 361005, P.R. China." + }, + { + "type": "text", + "bbox": [ + 0.189, + 0.293, + 0.748, + 0.31 + ], + "angle": 0, + "content": "3Shanghai Artificial Intelligence Laboratory, Shanghai, 200232, China." + }, + { + "type": "text", + "bbox": [ + 0.268, + 0.313, + 0.668, + 0.327 + ], + "angle": 0, + "content": "zhangyk@stu.xmu.edu.cn, hanzi.wang@xmu.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.362, + 0.314, + 0.379 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.395, + 0.474, + 0.742 + ], + "angle": 0, + "content": "For the visible-infrared person re-identification (ViReID) task, one of the major challenges is the modality gaps between visible (VIS) and infrared (IR) images. However, the training samples are usually limited, while the modality gaps are too large, which leads that the existing methods cannot effectively mine diverse cross-modality clues. To handle this limitation, we propose a novel augmentation network in the embedding space, called diverse embedding expansion network (DEEN). The proposed DEEN can effectively generate diverse embeddings to learn the informative feature representations and reduce the modality discrepancy between the VIS and IR images. Moreover, the ViReID model may be seriously affected by drastic illumination changes, while all the existing ViReID datasets are captured under sufficient illumination without significant light changes. Thus, we provide a low-light cross-modality (LLCM) dataset, which contains 46,767 bounding boxes of 1,064 identities captured by 9 RGB/IR cameras. Extensive experiments on the SYSU-MM01, RegDB and LLCM datasets show the superiority of the proposed DEEN over several other state-of-the-art methods. The code and dataset are released at: https://github.com/ZYK100/LLCM" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.773, + 0.21, + 0.789 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.8, + 0.47, + 0.876 + ], + "angle": 0, + "content": "Person re-identification (ReID) aims to match a given person with gallery images captured by different cameras [3, 9, 52]. Most existing ReID methods [22, 24, 30, 38, 50] only focus on matching RGB images captured by visible cameras at daytime. However, these methods may fail" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.362, + 0.885, + 0.52 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.524, + 0.893, + 0.581 + ], + "angle": 0, + "content": "Figure 1. Motivation of the proposed DEEN, which aims to generate diverse embeddings to make the network focus on learning with the informative feature representations to reduce the modality gaps between the VIS and IR images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.598, + 0.893, + 0.704 + ], + "angle": 0, + "content": "to achieve encouraging results when visible cameras cannot effectively capture person's information under complex conditions, such as at night or low-light environments. To solve this problem, some visible (VIS)-infrared (IR) person re-identification (VIREID) methods [15,39,41,48] have been proposed to retrieve the VIS (IR) images according to the corresponding IR (VIS) images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Compared with the widely studied person ReID task, the VIREID task is much more challenging due to the additional cross-modality discrepancy between the VIS and IR images [33, 45, 49, 51]. Typically, there are two popular types of methods to reduce this modality discrepancy. One type is the feature-level methods [5, 11, 16, 35, 40, 42], which try to project the VIS and IR features into a common embedding space, where the modality discrepancy can be minimized. However, the large modality discrepancy makes these methods difficult to project the cross-modality images into a common feature space directly. The other type is the image-level methods [4, 28, 29, 32], which aim to reduce the modality discrepancy by translating an IR (or VIS) image" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.222, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.925, + 0.516, + 0.937 + ], + "angle": 0, + "content": "2153" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.09, + 0.466, + 0.294 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.299, + 0.47, + 0.368 + ], + "angle": 0, + "content": "Figure 2. Comparison of person images on the SYSU-MM01 (1st row), RegDB (2nd row), and LLCM (3rd-5th rows) datasets. Each row shows four VIS images and four IR images of two identities. It is obvious that our LLCM contains a more challenging and realistic VIREID environment." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.386, + 0.469, + 0.446 + ], + "angle": 0, + "content": "into its VIS (or IR) counterpart by using the GANs [8]. Despite their success in reducing the modality gaps, the generated cross-modality images are usually accompanied by some noises due to the lack of the VIS-IR image pairs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.447, + 0.469, + 0.688 + ], + "angle": 0, + "content": "In this paper, we propose a novel augmentation network in the embedding space for the VIREID task, called diverse embedding expansion network (DEEN), which consists of a diverse embedding expansion (DEE) module and a multistage feature aggregation (MFA) block. The proposed DEE module can generate more embeddings followed by a novel center-guided pair mining (CPM) loss to drive the DEE module to focus on learning with the diverse feature representations. As illustrated in Fig. 1, by exploiting the generated embeddings with diverse information, the proposed DEE module can achieve the performance improvement by using more diverse embeddings. The proposed MFA block can aggregate the features from different stages for mining potential channel-wise and spatial feature representations, which increases the network's capacity for mining different-level diverse embeddings." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.469, + 0.839 + ], + "angle": 0, + "content": "Moreover, we observe that the existing VIREID datasets are captured under the environments with sufficient illumination. However, the performance of the VIREID methods may be seriously affected by drastic illumination changes or low illuminations. Therefore, we collect a challenging low-light cross-modality dataset, called LLCM dataset, which is shown in Fig. 2. Compared with the other VIREID datasets, the LLCM dataset contains a larger number of identities and images captured under low-light scenes, which introduces more challenges to the real-world VIREID task." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.84, + 0.433, + 0.854 + ], + "angle": 0, + "content": "In summary, the main contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.47, + 0.901 + ], + "angle": 0, + "content": "- We propose a novel diverse embedding expansion (DEE) module with a center-guided pair mining (CPM) loss to generate more embeddings for learning the diverse fea" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.166 + ], + "angle": 0, + "content": "ture representations. We are the first to augment the embeddings in the embedding space in VIREID. Besides, we also propose an effective multistage feature aggregation (MFA) block to mine potential channel-wise and spatial feature representations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.167, + 0.892, + 0.242 + ], + "angle": 0, + "content": "- With the incorporation of DEE, CPM loss and MFA into an end-to-end learning framework, we propose an effective diverse embedding expansion network (DEEN), which can effectively reduce the modality discrepancy between the VIS and IR images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.243, + 0.892, + 0.333 + ], + "angle": 0, + "content": "- We collect a low-light cross-modality (LLCM) dataset, which contains 46,767 images of 1,064 identities captured under the environments with illumination changes and low illuminations. The LLCM dataset has more new and important features, which can facilitate the research of VIREID towards practical applications." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.333, + 0.892, + 0.379 + ], + "angle": 0, + "content": "- Extensive experiments show that the proposed DEEN outperforms the other state-of-the-art methods for the VIReID task on three challenging datasets." + }, + { + "type": "list", + "bbox": [ + 0.498, + 0.167, + 0.892, + 0.379 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.393, + 0.642, + 0.408 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.418, + 0.892, + 0.462 + ], + "angle": 0, + "content": "Generally speaking, there are two main categories of methods in VIREID: the image-level methods and the feature-level methods." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.463, + 0.892, + 0.689 + ], + "angle": 0, + "content": "The image-level VIREID methods try to transform one modality into the other for reducing the modality discrepancy between the VIS and IR images in the image space. For this purpose, some GANs-based [4, 28, 29, 32] methods are proposed to perform identity-preserving person image style transformation for aligning cross-modality images and alleviating the problem of limited data. These methods often design complex generative models to align cross-modality images. However, due to the lack of VIS-IR image pairs, the generated images are unavoidably accompanied by some noises. X-modality [14] and its variations [34, 49] apply a lightweight network to introduce an auxiliary middle modality to assist the cross-modality search task. However, there is still a modality gap between this middle modality and the VIS / IR modality." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The feature-level methods aim to find a modality-shared and modality-specific feature space, where the modality gaps can be minimized. For this purpose, MAUM [15] tries to learn cross-modality metrics in two uni-directions to further enhance them with memory-based augmentation. RFM [25] introduces a cross-center loss to explore a more compact intra-class distribution. DCLNet [23] encourages the positive pixels with the same semantic information to be close, while it simultaneously pushes the negative pixels away. cmGAN [5] designs a cutting-edge discriminator to learn discriminative representations from different modalities. However, the large modality gaps between the VIS and IR images make it difficult to project the cross-modality images into a common space directly [7, 18, 21, 26]." + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.925, + 0.516, + 0.937 + ], + "angle": 0, + "content": "2154" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.102, + 0.092, + 0.864, + 0.363 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.367, + 0.895, + 0.41 + ], + "angle": 0, + "content": "Figure 3. The pipeline of the proposed network, which includes a DEE module and a MFA block. The DEE module can generate more embeddings with a novel CPM loss to learn diverse feature representations. The MFA block can aggregate the embeddings from different stages for mining diverse channel-wise and spatial feature representations." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.424, + 0.17, + 0.438 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.449, + 0.265, + 0.463 + ], + "angle": 0, + "content": "3.1. Model Architecture" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.473, + 0.471, + 0.684 + ], + "angle": 0, + "content": "Fig. 3 provides an overview of the proposed diverse embedding expansion network (DEEN), which utilizes a two-stream ResNet-50 network [12, 44] as the backbone. The VIS-IR features are fed into the proposed diverse embedding expansion (DEE) module to generate more embeddings. Then, a center-guided pair mining (CPM) loss is proposed to make the generated embeddings as diverse as possible for learning informative feature representations. Besides, we incorporate an effective MFA block to aggregate the features from different stages for mining diverse channel-wise and spatial feature representations. During the training stage, all the features before and after the batch normalization (BN) layer are fed into different losses to jointly optimize DEEN." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.696, + 0.414, + 0.712 + ], + "angle": 0, + "content": "3.2. Diverse Embedding Expansion Module" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.718, + 0.47, + 0.902 + ], + "angle": 0, + "content": "The proposed DEE module is used to generate more embeddings to alleviate the problem of insufficient training data by using a multi-branch convolutional generation structure. Specifically, for each branch of DEE, we firstly use three \\(3 \\times 3\\) dilated convolutional layers \\(\\varphi_{3 \\times 3}^{1}, \\varphi_{3 \\times 3}^{2}, \\varphi_{3 \\times 3}^{3}\\) with different dilation ratios (1, 2, 3) to reduce the number of feature maps \\(\\mathbf{f}\\) to \\(1 / 4\\) of its own size, and then we obtain the feature maps by combining them into one feature map, followed by a ReLU activation layer \\(\\mathbf{F}_{ReLU}\\) to improve the non-linear representation capability of the DEE. Then, another convolutional layer \\(\\theta_{1 \\times 1}\\) with a kernel in size of \\(1 \\times 1\\) is applied to the obtained feature map to change its dimension as same as \\(\\mathbf{f}\\). Thus, the generated embeddings \\(\\mathbf{f}_{+}^{i}\\) of the" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.426, + 0.747, + 0.439 + ], + "angle": 0, + "content": "\\(i\\)-th branch can be written as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.534, + 0.448, + 0.892, + 0.466 + ], + "angle": 0, + "content": "\\[\n\\mathbf {f} _ {+} ^ {i} = \\theta_ {1 \\times 1} \\left(\\mathbf {F} _ {R e L U} \\left(\\varphi_ {3 \\times 3} ^ {1} (\\mathbf {f}) + \\varphi_ {3 \\times 3} ^ {2} (\\mathbf {f}) + \\varphi_ {3 \\times 3} ^ {3} (\\mathbf {f})\\right)\\right). \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.476, + 0.892, + 0.52 + ], + "angle": 0, + "content": "Then, all the generated embeddings are concatenated together and used as the input to the next stage of the backbone network." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.531, + 0.788, + 0.546 + ], + "angle": 0, + "content": "3.3. Center-Guided Pair Mining Loss" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.554, + 0.892, + 0.659 + ], + "angle": 0, + "content": "As we can see from the above operation, the DEE module can only generate more embeddings using a multibranch convolutional block. However, this operation cannot effectively obtain diverse embeddings. Thus, we apply the following three properties to constrain the generated embeddings as diverse as possible to effectively reduce the modality discrepancy between the VIS and IR images:" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.892, + 0.75 + ], + "angle": 0, + "content": "Property 1: The generated embeddings should be as diverse as possible to effectively learn the informative feature representations. This means that we need to push away the distances between the generated embeddings and the original embeddings to learn diverse features and mine diverse cross-modality clues." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.871 + ], + "angle": 0, + "content": "Property 2: The generated embeddings should facilitate reducing the modality discrepancy between the VIS and IR images. This means that we need to pull close the distances between the embeddings generated from the VIS modality and the original IR embeddings. Similarly, we also need to pull close the distances between the embeddings generated from the IR modality and the original VIS embeddings." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Property 3: The intra-class distance should be less than the inter-class one. By Property 2, it pushes close the" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.927, + 0.516, + 0.938 + ], + "angle": 0, + "content": "2155" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.094, + 0.092, + 0.457, + 0.219 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.103, + 0.224, + 0.443, + 0.239 + ], + "angle": 0, + "content": "Figure 4. Illustration of the proposed CPM loss for DEE." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.25, + 0.47, + 0.308 + ], + "angle": 0, + "content": "distance between the generated embeddings and the original ones, which may cause the embeddings of different classes to become close. Thus, it is necessary to keep the intra-class distance less than the inter-class distance." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.31, + 0.469, + 0.339 + ], + "angle": 0, + "content": "As shown in Fig. 4, for embeddings generated from the VIS modality, the CPM loss can be formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.091, + 0.345, + 0.47, + 0.363 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} \\left(\\mathbf {f} _ {v}, \\mathbf {f} _ {n}, \\mathbf {f} _ {v +} ^ {i}\\right) = \\left[ \\boldsymbol {D} \\left(\\mathbf {f} _ {n} ^ {j}, \\mathbf {f} _ {v +} ^ {i, j}\\right) - \\boldsymbol {D} \\left(\\mathbf {f} _ {v} ^ {j}, \\mathbf {f} _ {v +} ^ {i, j}\\right) - \\boldsymbol {D} \\left(\\mathbf {f} _ {v} ^ {j}, \\mathbf {f} _ {v} ^ {k}\\right) \\right] _ {+}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.37, + 0.469, + 0.549 + ], + "angle": 0, + "content": "where \\(D(\\cdot, \\cdot)\\) is the Euclidean distance between two embeddings. \\(\\mathbf{f}_v\\) and \\(\\mathbf{f}_n\\) are the original embeddings from the VIS and IR modalities, and \\(\\mathbf{f}_{v+}^i\\) is the embeddings generated from the \\(i\\)-th branch of the VIS modality. \\(j, k\\) are different identities in a minibatch and \\([z]_+ = \\max(z, 0)\\). In Eq. (2), the first term can pull the generated embeddings \\(\\mathbf{f}_{v+}^i\\) towards the original IR's embeddings \\(\\mathbf{f}_n\\) to reduce the modality discrepancy between \\(\\mathbf{f}_{v+}^i, j\\) and \\(\\mathbf{f}_n^j\\). The second term can push the generated embeddings \\(\\mathbf{f}_{v+}\\) away from the VIS's embeddings \\(\\mathbf{f}_v\\) to enable \\(\\mathbf{f}_{v+}\\) to learn informative feature representations. The third term can make the intra-class distance less than the inter-class distance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.55, + 0.47, + 0.622 + ], + "angle": 0, + "content": "Then, we use the embedding centers \\(\\mathbf{c}_v\\) and \\(\\mathbf{c}_n\\) of each class to make the centers of generated embeddings \\(\\mathbf{c}_{v+}^i\\) and \\(\\mathbf{c}_{n+}^i\\) more discriminative, and introduce a margin term \\(\\alpha\\) to balance the three terms in Eq. (2). Thus, for the embeddings from VIS, the CPM loss is formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.079, + 0.627, + 0.469, + 0.657 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} \\left(\\mathbf {c} _ {v}, \\mathbf {c} _ {n}, \\mathbf {c} _ {v +} ^ {i}\\right) = \\left[ \\boldsymbol {D} \\left(\\mathbf {c} _ {n} ^ {j}, \\mathbf {c} _ {v +} ^ {i, j}\\right) - \\boldsymbol {D} \\left(\\mathbf {c} _ {v} ^ {j}, \\mathbf {c} _ {v +} ^ {i, j}\\right) - \\boldsymbol {D} \\left(\\mathbf {c} _ {v} ^ {j}, \\mathbf {c} _ {v} ^ {k}\\right) + \\alpha \\right] _ {+}. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.666, + 0.469, + 0.694 + ], + "angle": 0, + "content": "Similarly, for the class centers \\(\\mathbf{c}_{n + }^{i}\\) of embeddings generated from IR, we have:" + }, + { + "type": "equation", + "bbox": [ + 0.078, + 0.699, + 0.47, + 0.731 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} \\left(\\mathbf {c} _ {v}, \\mathbf {c} _ {n}, \\mathbf {c} _ {n +} ^ {i}\\right) = \\left[ \\boldsymbol {D} \\left(\\mathbf {c} _ {v} ^ {j}, \\mathbf {c} _ {n +} ^ {i, j}\\right) - \\boldsymbol {D} \\left(\\mathbf {c} _ {n} ^ {j}, \\mathbf {c} _ {n +} ^ {i, j}\\right) - \\boldsymbol {D} \\left(\\mathbf {c} _ {n} ^ {j}, \\mathbf {c} _ {n} ^ {k}\\right) + \\alpha \\right] _ {+}. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.737, + 0.46, + 0.751 + ], + "angle": 0, + "content": "Thus, the final CPM loss can be formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.145, + 0.758, + 0.469, + 0.774 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {c p m} = \\mathcal {L} \\left(\\mathbf {c} _ {v}, \\mathbf {c} _ {n}, \\mathbf {c} _ {v +} ^ {i}\\right) + \\mathcal {L} \\left(\\mathbf {c} _ {v}, \\mathbf {c} _ {n}, \\mathbf {c} _ {n +} ^ {i}\\right). \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.779, + 0.469, + 0.861 + ], + "angle": 0, + "content": "Besides, to ensure that the generated embeddings from different branches can capture different informative feature representations, we force these different embeddings generated by different branches orthogonal to minimize the overlapping elements. Therefore, the orthogonal loss can be formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.182, + 0.867, + 0.469, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {o r t} = \\sum_ {m = 1} ^ {i - 1} \\sum_ {n = m + 1} ^ {i} \\left(\\mathbf {f} _ {+} ^ {m T} \\mathbf {f} _ {+} ^ {n}\\right), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.152 + ], + "angle": 0, + "content": "where \\( m \\) and \\( n \\) are the \\( m \\)-th and \\( n \\)-th generated embeddings from the original embeddings, respectively. The orthogonal loss can enforce the generated embeddings to learn more informative feature representations." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.16, + 0.83, + 0.177 + ], + "angle": 0, + "content": "3.4. Multistage Feature Aggregation Block" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.183, + 0.892, + 0.289 + ], + "angle": 0, + "content": "Features aggregation of different levels has been demonstrated to be helpful to semantic segmentation, classification and detection task [1, 54, 55]. To aggregate the features from different stages for mining diverse channel-wise and spatial feature representations, we incorporate an effective channel-spatial multistage feature aggregation (MFA) block to aggregate multi-stage features inspired by [31]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.289, + 0.893, + 0.465 + ], + "angle": 0, + "content": "Next, we elaborate on the detail of the MFA block, which is shown in Fig. 3. Specifically, we consider two types of source features for the channel-spatial aggregation block in each stage of the backbone network: low-level feature maps \\(\\mathbf{f}_l\\in \\mathbb{R}^{C_l\\times H_l\\times W_l}\\) before the stage and high-level feature maps \\(\\mathbf{f}_h\\in \\mathbb{R}^{C_h\\times H_h\\times W_h}\\) after the stage, where C, W and H denote the number of the channel, width and height of features, respectively. First, we employ three \\(1\\times 1\\) convolutional layers \\(\\psi_q^1,\\psi_v^1,\\psi_k^1\\) to transform \\(\\mathbf{f}\\) into three compact embeddings: \\(\\psi_q^1 (\\mathbf{f}_h)\\), \\(\\psi_v^1 (\\mathbf{f}_l)\\) and \\(\\psi_k^1 (\\mathbf{f}_l)\\). Then, we compute the channel-wise similarity matrix \\(\\mathbf{M}^c\\in \\mathbb{R}^{C'\\times C'}\\) by matrix multiplication followed by softmax:" + }, + { + "type": "equation", + "bbox": [ + 0.586, + 0.471, + 0.891, + 0.488 + ], + "angle": 0, + "content": "\\[\n\\mathbf {M} ^ {c} = \\mathbf {F} _ {\\text {s o f t m a x}} \\left(\\psi_ {q} ^ {1} \\left(\\mathbf {f} _ {h}\\right) \\times \\psi_ {k} ^ {1} \\left(\\mathbf {f} _ {l}\\right)\\right). \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.494, + 0.892, + 0.578 + ], + "angle": 0, + "content": "Consequently, we implement the channel-wise multistage feature aggregation by restoring the channel dimension by the matrix multiplication of \\(\\psi_v^1 (\\mathbf{f}_l)\\) and \\(\\mathbf{M}^c\\). After that, another \\(1\\times 1\\) convolutional layer \\(\\omega^c\\) is applied to transform the size of the above feature maps to that of \\(\\mathbf{f}_h\\). Finally, we get the output by adding \\(\\mathbf{f}_h\\) to it by matrix addition:" + }, + { + "type": "equation", + "bbox": [ + 0.605, + 0.585, + 0.891, + 0.601 + ], + "angle": 0, + "content": "\\[\n\\mathbf {f} _ {h} ^ {c} = \\omega^ {c} \\left(\\psi_ {v} ^ {1} (\\mathbf {f} _ {l}) \\times \\mathbf {M} ^ {c}\\right) + \\mathbf {f} _ {h}. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.608, + 0.892, + 0.678 + ], + "angle": 0, + "content": "After that, \\(\\mathbf{f}_h^c\\) obtained from the above operations and the low-level feature map \\(\\mathbf{f}_l\\) are used to perform the spatial feature aggregation operation, which is similar to the channelwise multistage feature aggregation operation. Finally, we get the MFA's output as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.605, + 0.685, + 0.891, + 0.701 + ], + "angle": 0, + "content": "\\[\n\\mathbf {f} _ {h} ^ {s} = \\omega^ {s} \\left(\\psi_ {v} ^ {2} \\left(\\mathbf {f} _ {l}\\right) \\times \\mathbf {M} ^ {s}\\right) + \\mathbf {f} _ {h} ^ {c}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.709, + 0.892, + 0.739 + ], + "angle": 0, + "content": "where \\(\\omega^s\\) and \\(\\psi_v^2\\) are two \\(1\\times 1\\) convolutional layers, and \\(\\mathbf{M}^s\\) is the spatial similarity matrix." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.748, + 0.727, + 0.764 + ], + "angle": 0, + "content": "3.5. Multi-Loss Optimization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.77, + 0.892, + 0.839 + ], + "angle": 0, + "content": "Besides the proposed \\(\\mathcal{L}_{cpm}\\) and \\(\\mathcal{L}_{ort}\\), we also combine the cross-entropy loss \\(\\mathcal{L}_{ce}\\) [17] and the triplet loss \\(\\mathcal{L}_{tri}\\) [13] to jointly optimize the network in an end-to-end manner by minimizing the sum of these four losses \\(\\mathcal{L}_{total}\\), which can be formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.564, + 0.848, + 0.891, + 0.863 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {c e} + \\mathcal {L} _ {\\text {t r i}} + \\lambda_ {1} \\mathcal {L} _ {\\text {c p m}} + \\lambda_ {2} \\mathcal {L} _ {\\text {o r t}}, \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.892, + 0.9 + ], + "angle": 0, + "content": "where \\(\\lambda_{1}\\) and \\(\\lambda_{2}\\) are the coefficients to control the relative importance of the loss terms." + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.925, + 0.516, + 0.937 + ], + "angle": 0, + "content": "2156" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.09, + 0.46, + 0.268 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.274, + 0.47, + 0.332 + ], + "angle": 0, + "content": "Figure 5. The distribution of the LLCM's images in the 2D space. It can be seen that the images under different light conditions present different styles, which further increases the modality discrepancy between the VIS and IR images." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.348, + 0.231, + 0.363 + ], + "angle": 0, + "content": "4. LLCM Dataset" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.374, + 0.266, + 0.391 + ], + "angle": 0, + "content": "4.1. Dataset Description" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.399, + 0.47, + 0.581 + ], + "angle": 0, + "content": "In this paper, we collect a new challenging low-light cross-modality dataset, called LLCM dataset. The LLCM dataset utilizes a 9-camera network deployed in low-light environments, which can capture the VIS images in daytime and capture the IR images at night. For protecting the personal privacy information, we utilize MTCNN [47] to get the bounding boxes of persons' faces and blur those regions. We make sure that each annotated identity is captured by both the VIS and IR cameras. Some examples from the LLCM dataset are shown in Fig. 2. As shown in Tab. 1, compared with the existing VIREID datasets, the LLCM dataset has the following new and important features:" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.582, + 0.47, + 0.824 + ], + "angle": 0, + "content": "First, the images in the LLCM dataset are captured under complex low-light environment for both the VIS and IR modalities, which contains severe illumination changes and is a common problem in the real scenes. As Fig. 2 and Fig. 5 shown, the severe light conditions can change the color of persons' clothes and cause the loss of texture information of the clothes, which introduces great challenges to VIReID. Second, the LLCM dataset has a larger number of identities and bounding boxes. This dataset contains 46,767 bounding boxes of 1,064 identities, making it the largest VIReID dataset at present (see Tab 1). Third, the LLCM dataset is collected in over 100 days from January to April, and different climate conditions and cloth styles are considered. Long-term data collection helps to study the VIReID task in different climates and clothing styles, which increases the generalization of the VIReID model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Besides, considering the real-world applications, the LLCM dataset also contains many images that suffer from various challenges, such as motion blurring, pose variation, camera view changes, occlusion, low resolution and others. All in all, the LLCM dataset is a challenging dataset for" + }, + { + "type": "table", + "bbox": [ + 0.501, + 0.089, + 0.892, + 0.145 + ], + "angle": 0, + "content": "
DatasetsIDsImagesVIS / IR cam.low-light
RegDB [19]4128,2401 / 1X
SYSU-MM01 [36]49138,2714 / 2X
LLCM1,06446,7679 / 9✓
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.149, + 0.892, + 0.176 + ], + "angle": 0, + "content": "Table 1. Comparison between the LLCM and other two popular VIREID datasets." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.185, + 0.892, + 0.217 + ], + "angle": 0, + "content": "the VIREID task, which can further facilitate the research of VIREID towards practical applications." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.225, + 0.691, + 0.24 + ], + "angle": 0, + "content": "4.2. Evaluation Protocol" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.248, + 0.892, + 0.476 + ], + "angle": 0, + "content": "We divide the LLCM dataset into a training set and a testing set at a ratio about 2:1. The training set contains 30,921 bounding boxes of 713 identities (16,946 bounding boxes are from the VIS modality and 13,975 bounding boxes are from the IR modality), and the testing set contains 13,909 bounding boxes of 351 identities (8,680 bounding boxes are from the VIS modality and 7,166 bounding boxes are from the IR modality). Similar to the RegDB [19] dataset, both the VIS to IR mode and the IR to VIS mode are used to evaluate the performance of the VIREID models. During the testing stage, for each camera, we randomly choose one image from the images of each identity to form the gallery set for evaluation the performance of the models. We repeat the above evaluation 10 times with random split of the gallery set and report the average performance." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.489, + 0.633, + 0.506 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.513, + 0.603, + 0.528 + ], + "angle": 0, + "content": "5.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.536, + 0.892, + 0.674 + ], + "angle": 0, + "content": "The SYSU-MM01 dataset [36] contains 491 identities captured by 4 VIS cameras and 2 IR cameras, including the All-Search and Indoor-Search modes. For the All-Search mode, all the images captured by all the VIS cameras are used as the gallery set. For the Indoor-Search mode, only the images captured by two indoor VIS cameras are used as the gallery set. The RegDB dataset [19] consists of 412 identities, and each identity has 10 VIS images and 10 IR images captured by a pair of overlapping cameras." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.682, + 0.719, + 0.698 + ], + "angle": 0, + "content": "5.2. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.892, + 0.903 + ], + "angle": 0, + "content": "All the input images are firstly resized to \\(3 \\times 384 \\times 144\\), and the random horizontal flip and random erasing [53] techniques are adopted during the training phase. The initial learning rate is set to \\(1 \\times 10^{-2}\\) and then it increases to \\(1 \\times 10^{-1}\\) after 10 epochs with a warm-up strategy. After that, we decay the learning rate to \\(1 \\times 10^{-2}\\) at 20 epoch, and further decay to \\(1 \\times 10^{-3}\\) and \\(1 \\times 10^{-4}\\) at epoch 60 and epoch 120, respectively, until a total of 150 epochs. In each mini-batch, we randomly select 4 VIS images and 4 IR images of 6 identities for training. The SGD optimizer is adopted for training, where the momentum is set to 0.9. For the RegDB dataset, we remove stage-4 and plug the proposed DEE module into the DEEN after stage-2." + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.926, + 0.516, + 0.938 + ], + "angle": 0, + "content": "2157" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.088, + 0.894, + 0.362 + ], + "angle": 0, + "content": "
MethodsSYSU-MM01RegDB
All SearchIndoor SearchVIS to IRIR to VIS
R-1R-10R-20mAPR-1R-10R-20mAPR-1R-10R-20mAPR-1R-10R-20mAP
BDTR [46]17.055.472.019.7----33.658.667.432.832.958.568.432.0
D2RL [32]28.970.682.429.2----43.466.176.344.1----
Hi-CMD [4]34.977.6-35.9----70.986.4-66.0----
JSIA-ReID [29]38.180.789.936.943.886.294.252.948.1--48.948.5--49.3
AlignGAN [28]42.485.093.740.745.987.694.454.357.9--53.656.3--53.4
X-Modality [14]49.989.896.050.7----62.283.191.760.2----
DDAG [44]54.890.495.853.061.094.198.468.069.386.291.563.568.185.290.361.8
LbA [20]55.4--54.158.5--66.374.2--67.667.5--72.4
NFS [2]56.991.396.555.562.896.599.169.880.591.695.172.178.090.593.669.8
CM-NAS [6]60.892.196.858.968.094.897.952.482.895.197.779.381.794.196.977.6
MCLNet [10]65.493.397.162.072.697.099.276.680.392.796.073.175.990.994.669.5
FMCNet [48]66.3--62.568.2--74.189.1--84.488.4--83.9
SMCL [34]67.492.996.861.868.896.698.875.683.9--79.883.1--78.6
DART [41]68.796.499.066.372.597.899.578.283.6--75.782.0--73.8
CAJ [43]69.995.798.566.976.397.999.580.485.095.597.579.184.895.397.577.8
MPANet [37]70.696.298.868.276.798.299.681.082.8--80.783.7--80.9
MMN [49]70.696.299.066.976.297.299.379.691.697.798.984.187.596.098.180.5
DCLNet [23]70.8--65.373.5--76.881.2--74.378.0--70.6
MAUM [15]71.7--68.877.0--81.987.9--85.187.0--84.3
DEEN (ours)74.797.699.271.880.399.099.883.391.197.898.985.189.596.898.483.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.102, + 0.367, + 0.866, + 0.381 + ], + "angle": 0, + "content": "Table 2. Comparisons between the proposed DEEN and some state-of-the-art methods on the SYSU-MM01 and RegDB datasets." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.396, + 0.442, + 0.412 + ], + "angle": 0, + "content": "5.3. Comparison with State-of-the-art Methods" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.424, + 0.47, + 0.5 + ], + "angle": 0, + "content": "We firstly compare the proposed DEEN with several state-of-the-art methods to demonstrate the superiority of our method. The experimental results on the SYSU-MM01 and RegDB datasets are reported in Tab. 2, and the results on our LLCM dataset are reported in Tab. 3." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.504, + 0.47, + 0.716 + ], + "angle": 0, + "content": "SYSU-MM01 and RegDB: From Tab. 2, we can see that the results on the two datasets show that the proposed DEEN achieves the best performance against all other state-of-the-art methods. Specifically, for the All-Search mode on SYSU-MM01, DEEN achieves \\(74.7\\%\\) Rank-1 accuracy and \\(71.8\\%\\) mAP. For the Indoor-Search mode, DEEN achieves \\(80.3\\%\\) Rank-1 accuracy and \\(83.3\\%\\) mAP. For the VIS to IR mode on RegDB, DEEN achieves \\(91.1\\%\\) Rank-1 accuracy and \\(85.1\\%\\) mAP. For the IR to VIS mode, the proposed DEEN also obtains \\(89.5\\%\\) Rank-1 accuracy and \\(83.4\\%\\) mAP. The results validate the effectiveness of our method. Moreover, the results also demonstrate that the proposed DEEN can effectively reduce the modality discrepancy between the VIS and IR modalities." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.471, + 0.901 + ], + "angle": 0, + "content": "LLCM: Tab. 3 shows the results on our LLCM dataset. Here, we use several representative open-source methods to evaluate our LLCM dataset and compare them with our method. From Tab. 3 we can draw the following conclusions: the best method only obtains \\(54.9\\%\\) Rank-1 accuracy and \\(62.9\\%\\) mAP under the IR to VIS mode. The results of the existing methods on our LLCM dataset are generally unsatisfactory. This shows that, on one hand, our LLCM dataset is a very challenging dataset. On the other hand, the change of light has serious influence on the VIREID model. Besides, the proposed DEEN achieves the best performance under both the VIS to IR mode and the IR to VIS" + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.394, + 0.898, + 0.546 + ], + "angle": 0, + "content": "
ModelLLCM
IR to VISVIS to IR
R-1R-10R-20mAPR-1R-10R-20mAP
DDAG [44]40.371.479.648.448.079.286.152.3
DDAG* [44]41.073.481.949.648.581.087.853.0
AGW [45]43.674.682.451.851.581.587.955.3
LbA [20]43.878.286.653.150.884.391.155.6
LbA* [20]44.678.286.853.850.884.691.155.9
AGW* [45]46.477.885.254.856.084.990.659.1
CAJ [43]48.879.585.356.656.585.390.959.8
DART [41]52.280.787.059.860.487.191.963.2
MMN [49]52.581.688.458.959.988.593.662.7
DEEN (ours)54.984.990.962.962.590.394.765.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.549, + 0.894, + 0.592 + ], + "angle": 0, + "content": "Table 3. Performance obtained by the competing methods on our LLCM dataset. The symbol of “*” represents the methods that we reproduced with the random erasing technique." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.609, + 0.893, + 0.655 + ], + "angle": 0, + "content": "mode, which demonstrates the effectiveness of the proposed DEEN to reduce the modality gaps between the VIS and IR images." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.666, + 0.665, + 0.681 + ], + "angle": 0, + "content": "5.4. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Effectiveness of each component: To evaluate the contribution of each component to DEEN, we conduct some ablation studies on the LLCM and SYSU-MM01 datasets by removing certain modules from DEEN and evaluate the influence on the performance. The overall settings remain the same, while only the module under evaluation is used in or removed from DEEN. As shown in Tab. 4, although the DEE module can generate more embeddings using a multibranch convolutional block, which slightly improves the performance of the baseline, the results are not satisfactory. After being constrained by the proposed CPM loss to generate diverse embeddings, DEE can greatly improve the performance of the model and effectively reduce the modality discrepancy between the VIS and IR images. Besides, the" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.927, + 0.516, + 0.938 + ], + "angle": 0, + "content": "2158" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.08, + 0.089, + 0.47, + 0.201 + ], + "angle": 0, + "content": "
SettingsLLCMSYSU-MM01
DEE\\( \\mathcal{L}_{cpm} \\)\\( \\mathcal{L}_{ort} \\)MFAR-1mAPR-1mAP
45.453.660.757.7
✓50.559.064.762.0
✓✓53.161.169.266.2
✓✓51.560.165.363.2
✓✓✓53.962.369.866.7
✓51.259.664.762.0
✓✓✓✓54.962.974.771.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.204, + 0.47, + 0.233 + ], + "angle": 0, + "content": "Table 4. The influence of each component on the performance of the proposed DEEN." + }, + { + "type": "table", + "bbox": [ + 0.084, + 0.238, + 0.462, + 0.322 + ], + "angle": 0, + "content": "
MethodsLLCMSYSU-MM01
R-1mAPR-1mAP
DEE after stage-048.557.163.459.4
DEE after stage-149.457.863.760.8
DEE after stage-249.657.965.361.7
DEE after stage-353.962.369.866.7
DEE after stage-450.959.660.058.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.325, + 0.468, + 0.354 + ], + "angle": 0, + "content": "Table 5. The influence of which stage of ResNet-50 to plug the DEE module." + }, + { + "type": "table", + "bbox": [ + 0.096, + 0.359, + 0.449, + 0.42 + ], + "angle": 0, + "content": "
MethodsLLCMSYSU-MM01
R-1mAPR-1mAP
Two branches52.660.967.564.6
Three branches53.962.369.266.2
Four branches52.460.767.664.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.087, + 0.424, + 0.46, + 0.438 + ], + "angle": 0, + "content": "Table 6. Study about how many branches are suitable for DEE." + }, + { + "type": "table", + "bbox": [ + 0.097, + 0.444, + 0.449, + 0.507 + ], + "angle": 0, + "content": "
MethodsLLCMSYSU-MM01
R-1mAPR-1mAP
NL50.157.463.860.7
MFA51.259.664.762.0
NL + DEE54.262.473.470.3
MFA+ DEE54.962.974.771.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.115, + 0.508, + 0.432, + 0.521 + ], + "angle": 0, + "content": "Table 7. Comparison with the Non-Local (NL) block." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.537, + 0.468, + 0.658 + ], + "angle": 0, + "content": "proposed MFA block can improve the performance of the baseline by aggregating the features from different stages for mining diverse channel-wise and spatial feature representations. With the incorporation of DEE, CPM and MFA into an end-to-end learning framework, DEEN achieves an impressive performance improvement on two challenging VIREID datasets, which shows DEE and MFA can benefit from each other for generating diverse embeddings." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.659, + 0.47, + 0.902 + ], + "angle": 0, + "content": "The influence of which stage of ResNet-50 to plug the DEE module. The proposed DEE can be plugged after any stage of the backbone network. In our experiments, we use ResNet-50 as the backbone, which has five stages: stage-0 to stage-4. We plug DEE after different stages of the ResNet-50 to study how it will affect the performance of the DEEN. As shown in Tab. 5, when DEE is plugged after stage-0 to stage-3, the performance gradually increases, which shows the modality gaps become smaller and the generative ability of DEE becomes stronger at deeper layers of the network. When DEE is plugged after stage-3, it can achieve the best results on both LLCM and SYSU-MM01. However, when DEE is plugged after stage-4, the performance drops rapidly because the CPM loss works directly on the embeddings, enlarging the distances between the generated embeddings and the original embeddings, which" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.091, + 0.885, + 0.186 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.187, + 0.884, + 0.283 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.283, + 0.884, + 0.378 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.378, + 0.89, + 0.392 + ], + "angle": 0, + "content": "Figure 6. Influence of different \\(\\lambda_{1}\\), \\(\\lambda_{2}\\) and \\(\\alpha\\) values on our LLCM." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.402, + 0.892, + 0.446 + ], + "angle": 0, + "content": "increases the difficulty of model optimization. Based on the above analysis, we plug DEE after stage-3 of the backbone if not specified." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.448, + 0.892, + 0.674 + ], + "angle": 0, + "content": "Effectiveness on how many branches are more suitable for DEE. The proposed DEE module utilizes a multibranch convolutional block to generate diverse embeddings. Here, we study how many branches are suitable for DEE. As shown in Tab. 6, with the increase of the number of DEE's branches from 2 to 3, more embeddings are generated to reduce the modality gaps, so the performance gradually increases. However, the increase of performance has an upper limit when the number of branches is more than 3, because DEE generates too many redundant features, which leads to the drop of performance. As a result, DEE with three branches can achieve the best performances both on the LLCM and SYSU-MM01 datasets. It indicates that DEE with 3 branches is more suitable for generating diverse embeddings. Thus, we use 3 branches for DEE if not specified." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.674, + 0.892, + 0.84 + ], + "angle": 0, + "content": "Comparison with the Non-Local block. In this paper, we propose a MFA block to mine diverse channel-wise and spatial feature representations inspired by the Non-local (NL) block in [31]. Thus, we compare these two blocks to investigate which block is more effective. As shown in Tab. 7, the MFA block outperforms the NL block by \\(1.1\\%\\) Rank-1 accuracy and \\(2.2\\%\\) mAP, respectively. The results validate the effectiveness of our MFA block. Moreover, the results also show that the MFA block and the DEE module are complementary for generating diverse embeddings to reduce the modality gaps between the VIS and IR images." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The influence of the hyperparameters \\(\\lambda_{1},\\lambda_{2}\\) and \\(\\alpha\\) To evaluate the influence of the three hyperparameters, we give quantitative comparisons and report the results in Fig. 6. As we can see, the best performance is achieved when \\(\\lambda_{1}\\)" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.927, + 0.516, + 0.938 + ], + "angle": 0, + "content": "2159" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.092, + 0.245, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.128, + 0.196, + 0.208, + 0.205 + ], + "angle": 0, + "content": "(a) Initial Distance" + }, + { + "type": "image", + "bbox": [ + 0.249, + 0.092, + 0.404, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.281, + 0.196, + 0.372, + 0.206 + ], + "angle": 0, + "content": "(b) Baseline Distance" + }, + { + "type": "image", + "bbox": [ + 0.412, + 0.092, + 0.566, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.45, + 0.196, + 0.528, + 0.206 + ], + "angle": 0, + "content": "(c) MFA Distance" + }, + { + "type": "image", + "bbox": [ + 0.572, + 0.092, + 0.727, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.613, + 0.196, + 0.689, + 0.206 + ], + "angle": 0, + "content": "(d) DEE Distance" + }, + { + "type": "image", + "bbox": [ + 0.734, + 0.092, + 0.888, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.771, + 0.196, + 0.853, + 0.206 + ], + "angle": 0, + "content": "(e) DEEN Distance" + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.21, + 0.244, + 0.307 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.12, + 0.308, + 0.215, + 0.318 + ], + "angle": 0, + "content": "(f) Initial Distribution" + }, + { + "type": "image", + "bbox": [ + 0.249, + 0.21, + 0.403, + 0.308 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.274, + 0.309, + 0.38, + 0.318 + ], + "angle": 0, + "content": "(g) Baseline Distribution" + }, + { + "type": "image", + "bbox": [ + 0.411, + 0.21, + 0.565, + 0.308 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.442, + 0.308, + 0.535, + 0.318 + ], + "angle": 0, + "content": "(h) MFA Distribution" + }, + { + "type": "image", + "bbox": [ + 0.573, + 0.21, + 0.727, + 0.308 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.606, + 0.309, + 0.695, + 0.318 + ], + "angle": 0, + "content": "(i) DEE Distribution" + }, + { + "type": "image", + "bbox": [ + 0.734, + 0.21, + 0.888, + 0.308 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.763, + 0.309, + 0.859, + 0.319 + ], + "angle": 0, + "content": "(j) DEEN Distribution" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.329, + 0.892, + 0.385 + ], + "angle": 0, + "content": "Figure 7. (a-e) show the intra-class and inter-class distances of cross-modality features. The intra-class and inter-class distances are indicated in blue and green colors, respectively. (f-j) show the distribution of feature embeddings in the 2D feature space, where circles and triangles in different colors denote visible and infrared modalities. A total of 20 persons are selected from the test set. The samples with the same color are from the same person. The \"dot\" and \"cross\" markers denote the images from the VIS and IR modalities, respectively." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.399, + 0.276, + 0.554 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.174, + 0.556, + 0.212, + 0.565 + ], + "angle": 0, + "content": "Baseline" + }, + { + "type": "image", + "bbox": [ + 0.28, + 0.399, + 0.474, + 0.554 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.378, + 0.555, + 0.409, + 0.565 + ], + "angle": 0, + "content": "DEEN" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.573, + 0.469, + 0.601 + ], + "angle": 0, + "content": "Figure 8. Some Rank-8 retrieval results obtained by the baseline and the proposed DEEN on our LLCM dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.612, + 0.468, + 0.629 + ], + "angle": 0, + "content": "is set to 0.8, \\(\\lambda_{2}\\) is set to 0.1 and \\(\\alpha\\) is set to 0.2, respectively." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.636, + 0.214, + 0.65 + ], + "angle": 0, + "content": "5.5. Visualization" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.66, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Feature distribution. To investigate the reason why DEEN is effective, we visualize the inter-class and intra-class distances on our LLCM dataset as shown in Fig. 7 (a-e). Comparing Fig. 7 (c-e) with Fig. 7 (a-b), the means (i.e., the vertical lines) of inter-class and intra-class distances are pushed away by MFA, DEE and DEEN, where \\(\\delta_1 < \\delta_2 < \\delta_3\\) and \\(\\delta_1 < \\delta_2 < \\delta_4 < \\delta_5\\). This shows that the intra-class distance of DEEN is significantly reduced compared with the intra-class distance of the initial features (Fig. 7 (a)) and the baseline features (Fig. 7 (b)). Thus, DEEN can effectively reduce the modality discrepancy between the VIS and the IR images. Meanwhile, we also visualize the feature distribution with t-SNE [27] in the 2D feature space in Fig. 7 (f-j), which shows that MFA, DEE and DEEN can effectively discriminate and aggregate feature embeddings of the same person, and reduce the modality discrepancy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.4, + 0.892, + 0.522 + ], + "angle": 0, + "content": "Retrieval result. To further show the effectiveness of DEEN, we also show some retrieval results of DEEN on our LLCM dataset in Fig. 8. For each retrieval case, the retrieved images with green boxes mean the correct matches corresponding the given query, while the red ones mean the incorrect matches. In general, DEEN can effectively improve the ranking results with more correctly matched images ranked in the top positions than the baseline." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.535, + 0.657, + 0.55 + ], + "angle": 0, + "content": "6. CONCLUSION" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.56, + 0.892, + 0.756 + ], + "angle": 0, + "content": "In this paper, we propose a novel diverse embedding expansion network (DEEN) in the embedding space for the VIREID task. The proposed DEEN can generate diverse embeddings and mine diverse channel-wise and spatial embeddings to learn the informative feature representations for reducing the modality discrepancy between the VIS and IR images. Moreover, we also provide a challenging low-light cross-modality (LLCM) dataset, which has more new and important features and can further facilitate the research of VIREID towards practical applications. Extensive experiments on the SYSU-MM01, RegDB and LLCM datasets show the superiority of the proposed DEEN over several other state-of-the-art methods." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.77, + 0.679, + 0.788 + ], + "angle": 0, + "content": "7. Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.901 + ], + "angle": 0, + "content": "This work was supported by the National Key Research and Development Program of China under Grant 2022ZD0160402, by the National Natural Science Foundation of China under Grant U21A20514, and by the FuXiaQuan National Independent Innovation Demonstration Zone Collaborative Innovation Platform Project under Grant 3502ZCQXT2022008." + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.927, + 0.516, + 0.938 + ], + "angle": 0, + "content": "2160" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Xuesong Chen, Canmiao Fu, Yong Zhao, Feng Zheng, Jingkuan Song, Rongrong Ji, and Yi Yang. Salience-guided cascaded suppression network for person re-identification. 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China. + +$^{2}$ Key Laboratory of Multimedia Trusted Perception and Efficient Computing, + +Ministry of Education of China, Xiamen University, 361005, P.R. China. + +3Shanghai Artificial Intelligence Laboratory, Shanghai, 200232, China. + +zhangyk@stu.xmu.edu.cn, hanzi.wang@xmu.edu.cn + +# Abstract + +For the visible-infrared person re-identification (ViReID) task, one of the major challenges is the modality gaps between visible (VIS) and infrared (IR) images. However, the training samples are usually limited, while the modality gaps are too large, which leads that the existing methods cannot effectively mine diverse cross-modality clues. To handle this limitation, we propose a novel augmentation network in the embedding space, called diverse embedding expansion network (DEEN). The proposed DEEN can effectively generate diverse embeddings to learn the informative feature representations and reduce the modality discrepancy between the VIS and IR images. Moreover, the ViReID model may be seriously affected by drastic illumination changes, while all the existing ViReID datasets are captured under sufficient illumination without significant light changes. Thus, we provide a low-light cross-modality (LLCM) dataset, which contains 46,767 bounding boxes of 1,064 identities captured by 9 RGB/IR cameras. Extensive experiments on the SYSU-MM01, RegDB and LLCM datasets show the superiority of the proposed DEEN over several other state-of-the-art methods. The code and dataset are released at: https://github.com/ZYK100/LLCM + +# 1. Introduction + +Person re-identification (ReID) aims to match a given person with gallery images captured by different cameras [3, 9, 52]. Most existing ReID methods [22, 24, 30, 38, 50] only focus on matching RGB images captured by visible cameras at daytime. However, these methods may fail + +![](images/8b4f0a3de20e164309fccc573936a144cd5708769783484a5c52a6fbf4b8e4ab.jpg) +Figure 1. Motivation of the proposed DEEN, which aims to generate diverse embeddings to make the network focus on learning with the informative feature representations to reduce the modality gaps between the VIS and IR images. + +to achieve encouraging results when visible cameras cannot effectively capture person's information under complex conditions, such as at night or low-light environments. To solve this problem, some visible (VIS)-infrared (IR) person re-identification (VIREID) methods [15,39,41,48] have been proposed to retrieve the VIS (IR) images according to the corresponding IR (VIS) images. + +Compared with the widely studied person ReID task, the VIREID task is much more challenging due to the additional cross-modality discrepancy between the VIS and IR images [33, 45, 49, 51]. Typically, there are two popular types of methods to reduce this modality discrepancy. One type is the feature-level methods [5, 11, 16, 35, 40, 42], which try to project the VIS and IR features into a common embedding space, where the modality discrepancy can be minimized. However, the large modality discrepancy makes these methods difficult to project the cross-modality images into a common feature space directly. The other type is the image-level methods [4, 28, 29, 32], which aim to reduce the modality discrepancy by translating an IR (or VIS) image + +![](images/a5754c3b8954ae0bd7df54064b5555f1c416d38a3a9f66f318db5541fbd231ec.jpg) +Figure 2. Comparison of person images on the SYSU-MM01 (1st row), RegDB (2nd row), and LLCM (3rd-5th rows) datasets. Each row shows four VIS images and four IR images of two identities. It is obvious that our LLCM contains a more challenging and realistic VIREID environment. + +into its VIS (or IR) counterpart by using the GANs [8]. Despite their success in reducing the modality gaps, the generated cross-modality images are usually accompanied by some noises due to the lack of the VIS-IR image pairs. + +In this paper, we propose a novel augmentation network in the embedding space for the VIREID task, called diverse embedding expansion network (DEEN), which consists of a diverse embedding expansion (DEE) module and a multistage feature aggregation (MFA) block. The proposed DEE module can generate more embeddings followed by a novel center-guided pair mining (CPM) loss to drive the DEE module to focus on learning with the diverse feature representations. As illustrated in Fig. 1, by exploiting the generated embeddings with diverse information, the proposed DEE module can achieve the performance improvement by using more diverse embeddings. The proposed MFA block can aggregate the features from different stages for mining potential channel-wise and spatial feature representations, which increases the network's capacity for mining different-level diverse embeddings. + +Moreover, we observe that the existing VIREID datasets are captured under the environments with sufficient illumination. However, the performance of the VIREID methods may be seriously affected by drastic illumination changes or low illuminations. Therefore, we collect a challenging low-light cross-modality dataset, called LLCM dataset, which is shown in Fig. 2. Compared with the other VIREID datasets, the LLCM dataset contains a larger number of identities and images captured under low-light scenes, which introduces more challenges to the real-world VIREID task. + +In summary, the main contributions are as follows: + +- We propose a novel diverse embedding expansion (DEE) module with a center-guided pair mining (CPM) loss to generate more embeddings for learning the diverse fea + +ture representations. We are the first to augment the embeddings in the embedding space in VIREID. Besides, we also propose an effective multistage feature aggregation (MFA) block to mine potential channel-wise and spatial feature representations. + +- With the incorporation of DEE, CPM loss and MFA into an end-to-end learning framework, we propose an effective diverse embedding expansion network (DEEN), which can effectively reduce the modality discrepancy between the VIS and IR images. +- We collect a low-light cross-modality (LLCM) dataset, which contains 46,767 images of 1,064 identities captured under the environments with illumination changes and low illuminations. The LLCM dataset has more new and important features, which can facilitate the research of VIREID towards practical applications. +- Extensive experiments show that the proposed DEEN outperforms the other state-of-the-art methods for the VIReID task on three challenging datasets. + +# 2. Related Work + +Generally speaking, there are two main categories of methods in VIREID: the image-level methods and the feature-level methods. + +The image-level VIREID methods try to transform one modality into the other for reducing the modality discrepancy between the VIS and IR images in the image space. For this purpose, some GANs-based [4, 28, 29, 32] methods are proposed to perform identity-preserving person image style transformation for aligning cross-modality images and alleviating the problem of limited data. These methods often design complex generative models to align cross-modality images. However, due to the lack of VIS-IR image pairs, the generated images are unavoidably accompanied by some noises. X-modality [14] and its variations [34, 49] apply a lightweight network to introduce an auxiliary middle modality to assist the cross-modality search task. However, there is still a modality gap between this middle modality and the VIS / IR modality. + +The feature-level methods aim to find a modality-shared and modality-specific feature space, where the modality gaps can be minimized. For this purpose, MAUM [15] tries to learn cross-modality metrics in two uni-directions to further enhance them with memory-based augmentation. RFM [25] introduces a cross-center loss to explore a more compact intra-class distribution. DCLNet [23] encourages the positive pixels with the same semantic information to be close, while it simultaneously pushes the negative pixels away. cmGAN [5] designs a cutting-edge discriminator to learn discriminative representations from different modalities. However, the large modality gaps between the VIS and IR images make it difficult to project the cross-modality images into a common space directly [7, 18, 21, 26]. + +![](images/5a6d7dc627e1ca9f46910048e7aab6295ecdca80cc1888dec9aa8450ee8cc4a4.jpg) +Figure 3. The pipeline of the proposed network, which includes a DEE module and a MFA block. The DEE module can generate more embeddings with a novel CPM loss to learn diverse feature representations. The MFA block can aggregate the embeddings from different stages for mining diverse channel-wise and spatial feature representations. + +# 3. Method + +# 3.1. Model Architecture + +Fig. 3 provides an overview of the proposed diverse embedding expansion network (DEEN), which utilizes a two-stream ResNet-50 network [12, 44] as the backbone. The VIS-IR features are fed into the proposed diverse embedding expansion (DEE) module to generate more embeddings. Then, a center-guided pair mining (CPM) loss is proposed to make the generated embeddings as diverse as possible for learning informative feature representations. Besides, we incorporate an effective MFA block to aggregate the features from different stages for mining diverse channel-wise and spatial feature representations. During the training stage, all the features before and after the batch normalization (BN) layer are fed into different losses to jointly optimize DEEN. + +# 3.2. Diverse Embedding Expansion Module + +The proposed DEE module is used to generate more embeddings to alleviate the problem of insufficient training data by using a multi-branch convolutional generation structure. Specifically, for each branch of DEE, we firstly use three $3 \times 3$ dilated convolutional layers $\varphi_{3 \times 3}^{1}, \varphi_{3 \times 3}^{2}, \varphi_{3 \times 3}^{3}$ with different dilation ratios (1, 2, 3) to reduce the number of feature maps $\mathbf{f}$ to $1 / 4$ of its own size, and then we obtain the feature maps by combining them into one feature map, followed by a ReLU activation layer $\mathbf{F}_{ReLU}$ to improve the non-linear representation capability of the DEE. Then, another convolutional layer $\theta_{1 \times 1}$ with a kernel in size of $1 \times 1$ is applied to the obtained feature map to change its dimension as same as $\mathbf{f}$ . Thus, the generated embeddings $\mathbf{f}_{+}^{i}$ of the + +$i$ -th branch can be written as follows: + +$$ +\mathbf {f} _ {+} ^ {i} = \theta_ {1 \times 1} \left(\mathbf {F} _ {R e L U} \left(\varphi_ {3 \times 3} ^ {1} (\mathbf {f}) + \varphi_ {3 \times 3} ^ {2} (\mathbf {f}) + \varphi_ {3 \times 3} ^ {3} (\mathbf {f})\right)\right). \tag {1} +$$ + +Then, all the generated embeddings are concatenated together and used as the input to the next stage of the backbone network. + +# 3.3. Center-Guided Pair Mining Loss + +As we can see from the above operation, the DEE module can only generate more embeddings using a multibranch convolutional block. However, this operation cannot effectively obtain diverse embeddings. Thus, we apply the following three properties to constrain the generated embeddings as diverse as possible to effectively reduce the modality discrepancy between the VIS and IR images: + +Property 1: The generated embeddings should be as diverse as possible to effectively learn the informative feature representations. This means that we need to push away the distances between the generated embeddings and the original embeddings to learn diverse features and mine diverse cross-modality clues. + +Property 2: The generated embeddings should facilitate reducing the modality discrepancy between the VIS and IR images. This means that we need to pull close the distances between the embeddings generated from the VIS modality and the original IR embeddings. Similarly, we also need to pull close the distances between the embeddings generated from the IR modality and the original VIS embeddings. + +Property 3: The intra-class distance should be less than the inter-class one. By Property 2, it pushes close the + +![](images/95fa4c5421bc831bdffb9003d74f1685971dbeda5868d519c363e33310c1ea0b.jpg) +Figure 4. Illustration of the proposed CPM loss for DEE. + +distance between the generated embeddings and the original ones, which may cause the embeddings of different classes to become close. Thus, it is necessary to keep the intra-class distance less than the inter-class distance. + +As shown in Fig. 4, for embeddings generated from the VIS modality, the CPM loss can be formulated as follows: + +$$ +\mathcal {L} \left(\mathbf {f} _ {v}, \mathbf {f} _ {n}, \mathbf {f} _ {v +} ^ {i}\right) = \left[ \boldsymbol {D} \left(\mathbf {f} _ {n} ^ {j}, \mathbf {f} _ {v +} ^ {i, j}\right) - \boldsymbol {D} \left(\mathbf {f} _ {v} ^ {j}, \mathbf {f} _ {v +} ^ {i, j}\right) - \boldsymbol {D} \left(\mathbf {f} _ {v} ^ {j}, \mathbf {f} _ {v} ^ {k}\right) \right] _ {+}, \tag {2} +$$ + +where $D(\cdot, \cdot)$ is the Euclidean distance between two embeddings. $\mathbf{f}_v$ and $\mathbf{f}_n$ are the original embeddings from the VIS and IR modalities, and $\mathbf{f}_{v+}^i$ is the embeddings generated from the $i$ -th branch of the VIS modality. $j, k$ are different identities in a minibatch and $[z]_+ = \max(z, 0)$ . In Eq. (2), the first term can pull the generated embeddings $\mathbf{f}_{v+}^i$ towards the original IR's embeddings $\mathbf{f}_n$ to reduce the modality discrepancy between $\mathbf{f}_{v+}^i, j$ and $\mathbf{f}_n^j$ . The second term can push the generated embeddings $\mathbf{f}_{v+}$ away from the VIS's embeddings $\mathbf{f}_v$ to enable $\mathbf{f}_{v+}$ to learn informative feature representations. The third term can make the intra-class distance less than the inter-class distance. + +Then, we use the embedding centers $\mathbf{c}_v$ and $\mathbf{c}_n$ of each class to make the centers of generated embeddings $\mathbf{c}_{v+}^i$ and $\mathbf{c}_{n+}^i$ more discriminative, and introduce a margin term $\alpha$ to balance the three terms in Eq. (2). Thus, for the embeddings from VIS, the CPM loss is formulated as follows: + +$$ +\mathcal {L} \left(\mathbf {c} _ {v}, \mathbf {c} _ {n}, \mathbf {c} _ {v +} ^ {i}\right) = \left[ \boldsymbol {D} \left(\mathbf {c} _ {n} ^ {j}, \mathbf {c} _ {v +} ^ {i, j}\right) - \boldsymbol {D} \left(\mathbf {c} _ {v} ^ {j}, \mathbf {c} _ {v +} ^ {i, j}\right) - \boldsymbol {D} \left(\mathbf {c} _ {v} ^ {j}, \mathbf {c} _ {v} ^ {k}\right) + \alpha \right] _ {+}. \tag {3} +$$ + +Similarly, for the class centers $\mathbf{c}_{n + }^{i}$ of embeddings generated from IR, we have: + +$$ +\mathcal {L} \left(\mathbf {c} _ {v}, \mathbf {c} _ {n}, \mathbf {c} _ {n +} ^ {i}\right) = \left[ \boldsymbol {D} \left(\mathbf {c} _ {v} ^ {j}, \mathbf {c} _ {n +} ^ {i, j}\right) - \boldsymbol {D} \left(\mathbf {c} _ {n} ^ {j}, \mathbf {c} _ {n +} ^ {i, j}\right) - \boldsymbol {D} \left(\mathbf {c} _ {n} ^ {j}, \mathbf {c} _ {n} ^ {k}\right) + \alpha \right] _ {+}. \tag {4} +$$ + +Thus, the final CPM loss can be formulated as follows: + +$$ +\mathcal {L} _ {c p m} = \mathcal {L} \left(\mathbf {c} _ {v}, \mathbf {c} _ {n}, \mathbf {c} _ {v +} ^ {i}\right) + \mathcal {L} \left(\mathbf {c} _ {v}, \mathbf {c} _ {n}, \mathbf {c} _ {n +} ^ {i}\right). \tag {5} +$$ + +Besides, to ensure that the generated embeddings from different branches can capture different informative feature representations, we force these different embeddings generated by different branches orthogonal to minimize the overlapping elements. Therefore, the orthogonal loss can be formulated as follows: + +$$ +\mathcal {L} _ {o r t} = \sum_ {m = 1} ^ {i - 1} \sum_ {n = m + 1} ^ {i} \left(\mathbf {f} _ {+} ^ {m T} \mathbf {f} _ {+} ^ {n}\right), \tag {6} +$$ + +where $m$ and $n$ are the $m$ -th and $n$ -th generated embeddings from the original embeddings, respectively. The orthogonal loss can enforce the generated embeddings to learn more informative feature representations. + +# 3.4. Multistage Feature Aggregation Block + +Features aggregation of different levels has been demonstrated to be helpful to semantic segmentation, classification and detection task [1, 54, 55]. To aggregate the features from different stages for mining diverse channel-wise and spatial feature representations, we incorporate an effective channel-spatial multistage feature aggregation (MFA) block to aggregate multi-stage features inspired by [31]. + +Next, we elaborate on the detail of the MFA block, which is shown in Fig. 3. Specifically, we consider two types of source features for the channel-spatial aggregation block in each stage of the backbone network: low-level feature maps $\mathbf{f}_l\in \mathbb{R}^{C_l\times H_l\times W_l}$ before the stage and high-level feature maps $\mathbf{f}_h\in \mathbb{R}^{C_h\times H_h\times W_h}$ after the stage, where C, W and H denote the number of the channel, width and height of features, respectively. First, we employ three $1\times 1$ convolutional layers $\psi_q^1,\psi_v^1,\psi_k^1$ to transform $\mathbf{f}$ into three compact embeddings: $\psi_q^1 (\mathbf{f}_h)$ , $\psi_v^1 (\mathbf{f}_l)$ and $\psi_k^1 (\mathbf{f}_l)$ . Then, we compute the channel-wise similarity matrix $\mathbf{M}^c\in \mathbb{R}^{C'\times C'}$ by matrix multiplication followed by softmax: + +$$ +\mathbf {M} ^ {c} = \mathbf {F} _ {\text {s o f t m a x}} \left(\psi_ {q} ^ {1} \left(\mathbf {f} _ {h}\right) \times \psi_ {k} ^ {1} \left(\mathbf {f} _ {l}\right)\right). \tag {7} +$$ + +Consequently, we implement the channel-wise multistage feature aggregation by restoring the channel dimension by the matrix multiplication of $\psi_v^1 (\mathbf{f}_l)$ and $\mathbf{M}^c$ . After that, another $1\times 1$ convolutional layer $\omega^c$ is applied to transform the size of the above feature maps to that of $\mathbf{f}_h$ . Finally, we get the output by adding $\mathbf{f}_h$ to it by matrix addition: + +$$ +\mathbf {f} _ {h} ^ {c} = \omega^ {c} \left(\psi_ {v} ^ {1} (\mathbf {f} _ {l}) \times \mathbf {M} ^ {c}\right) + \mathbf {f} _ {h}. \tag {8} +$$ + +After that, $\mathbf{f}_h^c$ obtained from the above operations and the low-level feature map $\mathbf{f}_l$ are used to perform the spatial feature aggregation operation, which is similar to the channelwise multistage feature aggregation operation. Finally, we get the MFA's output as follows: + +$$ +\mathbf {f} _ {h} ^ {s} = \omega^ {s} \left(\psi_ {v} ^ {2} \left(\mathbf {f} _ {l}\right) \times \mathbf {M} ^ {s}\right) + \mathbf {f} _ {h} ^ {c}, \tag {9} +$$ + +where $\omega^s$ and $\psi_v^2$ are two $1\times 1$ convolutional layers, and $\mathbf{M}^s$ is the spatial similarity matrix. + +# 3.5. Multi-Loss Optimization + +Besides the proposed $\mathcal{L}_{cpm}$ and $\mathcal{L}_{ort}$ , we also combine the cross-entropy loss $\mathcal{L}_{ce}$ [17] and the triplet loss $\mathcal{L}_{tri}$ [13] to jointly optimize the network in an end-to-end manner by minimizing the sum of these four losses $\mathcal{L}_{total}$ , which can be formulated as follows: + +$$ +\mathcal {L} _ {\text {t o t a l}} = \mathcal {L} _ {c e} + \mathcal {L} _ {\text {t r i}} + \lambda_ {1} \mathcal {L} _ {\text {c p m}} + \lambda_ {2} \mathcal {L} _ {\text {o r t}}, \tag {10} +$$ + +where $\lambda_{1}$ and $\lambda_{2}$ are the coefficients to control the relative importance of the loss terms. + +![](images/c4add90f66c6cc7be38d6add23a3a03e8542422f4ab04ffb8cc73a262b847679.jpg) +Figure 5. The distribution of the LLCM's images in the 2D space. It can be seen that the images under different light conditions present different styles, which further increases the modality discrepancy between the VIS and IR images. + +# 4. LLCM Dataset + +# 4.1. Dataset Description + +In this paper, we collect a new challenging low-light cross-modality dataset, called LLCM dataset. The LLCM dataset utilizes a 9-camera network deployed in low-light environments, which can capture the VIS images in daytime and capture the IR images at night. For protecting the personal privacy information, we utilize MTCNN [47] to get the bounding boxes of persons' faces and blur those regions. We make sure that each annotated identity is captured by both the VIS and IR cameras. Some examples from the LLCM dataset are shown in Fig. 2. As shown in Tab. 1, compared with the existing VIREID datasets, the LLCM dataset has the following new and important features: + +First, the images in the LLCM dataset are captured under complex low-light environment for both the VIS and IR modalities, which contains severe illumination changes and is a common problem in the real scenes. As Fig. 2 and Fig. 5 shown, the severe light conditions can change the color of persons' clothes and cause the loss of texture information of the clothes, which introduces great challenges to VIReID. Second, the LLCM dataset has a larger number of identities and bounding boxes. This dataset contains 46,767 bounding boxes of 1,064 identities, making it the largest VIReID dataset at present (see Tab 1). Third, the LLCM dataset is collected in over 100 days from January to April, and different climate conditions and cloth styles are considered. Long-term data collection helps to study the VIReID task in different climates and clothing styles, which increases the generalization of the VIReID model. + +Besides, considering the real-world applications, the LLCM dataset also contains many images that suffer from various challenges, such as motion blurring, pose variation, camera view changes, occlusion, low resolution and others. All in all, the LLCM dataset is a challenging dataset for + +
DatasetsIDsImagesVIS / IR cam.low-light
RegDB [19]4128,2401 / 1X
SYSU-MM01 [36]49138,2714 / 2X
LLCM1,06446,7679 / 9✓
+ +Table 1. Comparison between the LLCM and other two popular VIREID datasets. + +the VIREID task, which can further facilitate the research of VIREID towards practical applications. + +# 4.2. Evaluation Protocol + +We divide the LLCM dataset into a training set and a testing set at a ratio about 2:1. The training set contains 30,921 bounding boxes of 713 identities (16,946 bounding boxes are from the VIS modality and 13,975 bounding boxes are from the IR modality), and the testing set contains 13,909 bounding boxes of 351 identities (8,680 bounding boxes are from the VIS modality and 7,166 bounding boxes are from the IR modality). Similar to the RegDB [19] dataset, both the VIS to IR mode and the IR to VIS mode are used to evaluate the performance of the VIREID models. During the testing stage, for each camera, we randomly choose one image from the images of each identity to form the gallery set for evaluation the performance of the models. We repeat the above evaluation 10 times with random split of the gallery set and report the average performance. + +# 5. Experiments + +# 5.1. Datasets + +The SYSU-MM01 dataset [36] contains 491 identities captured by 4 VIS cameras and 2 IR cameras, including the All-Search and Indoor-Search modes. For the All-Search mode, all the images captured by all the VIS cameras are used as the gallery set. For the Indoor-Search mode, only the images captured by two indoor VIS cameras are used as the gallery set. The RegDB dataset [19] consists of 412 identities, and each identity has 10 VIS images and 10 IR images captured by a pair of overlapping cameras. + +# 5.2. Implementation Details + +All the input images are firstly resized to $3 \times 384 \times 144$ , and the random horizontal flip and random erasing [53] techniques are adopted during the training phase. The initial learning rate is set to $1 \times 10^{-2}$ and then it increases to $1 \times 10^{-1}$ after 10 epochs with a warm-up strategy. After that, we decay the learning rate to $1 \times 10^{-2}$ at 20 epoch, and further decay to $1 \times 10^{-3}$ and $1 \times 10^{-4}$ at epoch 60 and epoch 120, respectively, until a total of 150 epochs. In each mini-batch, we randomly select 4 VIS images and 4 IR images of 6 identities for training. The SGD optimizer is adopted for training, where the momentum is set to 0.9. For the RegDB dataset, we remove stage-4 and plug the proposed DEE module into the DEEN after stage-2. + +
MethodsSYSU-MM01RegDB
All SearchIndoor SearchVIS to IRIR to VIS
R-1R-10R-20mAPR-1R-10R-20mAPR-1R-10R-20mAPR-1R-10R-20mAP
BDTR [46]17.055.472.019.7----33.658.667.432.832.958.568.432.0
D2RL [32]28.970.682.429.2----43.466.176.344.1----
Hi-CMD [4]34.977.6-35.9----70.986.4-66.0----
JSIA-ReID [29]38.180.789.936.943.886.294.252.948.1--48.948.5--49.3
AlignGAN [28]42.485.093.740.745.987.694.454.357.9--53.656.3--53.4
X-Modality [14]49.989.896.050.7----62.283.191.760.2----
DDAG [44]54.890.495.853.061.094.198.468.069.386.291.563.568.185.290.361.8
LbA [20]55.4--54.158.5--66.374.2--67.667.5--72.4
NFS [2]56.991.396.555.562.896.599.169.880.591.695.172.178.090.593.669.8
CM-NAS [6]60.892.196.858.968.094.897.952.482.895.197.779.381.794.196.977.6
MCLNet [10]65.493.397.162.072.697.099.276.680.392.796.073.175.990.994.669.5
FMCNet [48]66.3--62.568.2--74.189.1--84.488.4--83.9
SMCL [34]67.492.996.861.868.896.698.875.683.9--79.883.1--78.6
DART [41]68.796.499.066.372.597.899.578.283.6--75.782.0--73.8
CAJ [43]69.995.798.566.976.397.999.580.485.095.597.579.184.895.397.577.8
MPANet [37]70.696.298.868.276.798.299.681.082.8--80.783.7--80.9
MMN [49]70.696.299.066.976.297.299.379.691.697.798.984.187.596.098.180.5
DCLNet [23]70.8--65.373.5--76.881.2--74.378.0--70.6
MAUM [15]71.7--68.877.0--81.987.9--85.187.0--84.3
DEEN (ours)74.797.699.271.880.399.099.883.391.197.898.985.189.596.898.483.4
+ +# 5.3. Comparison with State-of-the-art Methods + +We firstly compare the proposed DEEN with several state-of-the-art methods to demonstrate the superiority of our method. The experimental results on the SYSU-MM01 and RegDB datasets are reported in Tab. 2, and the results on our LLCM dataset are reported in Tab. 3. + +SYSU-MM01 and RegDB: From Tab. 2, we can see that the results on the two datasets show that the proposed DEEN achieves the best performance against all other state-of-the-art methods. Specifically, for the All-Search mode on SYSU-MM01, DEEN achieves $74.7\%$ Rank-1 accuracy and $71.8\%$ mAP. For the Indoor-Search mode, DEEN achieves $80.3\%$ Rank-1 accuracy and $83.3\%$ mAP. For the VIS to IR mode on RegDB, DEEN achieves $91.1\%$ Rank-1 accuracy and $85.1\%$ mAP. For the IR to VIS mode, the proposed DEEN also obtains $89.5\%$ Rank-1 accuracy and $83.4\%$ mAP. The results validate the effectiveness of our method. Moreover, the results also demonstrate that the proposed DEEN can effectively reduce the modality discrepancy between the VIS and IR modalities. + +LLCM: Tab. 3 shows the results on our LLCM dataset. Here, we use several representative open-source methods to evaluate our LLCM dataset and compare them with our method. From Tab. 3 we can draw the following conclusions: the best method only obtains $54.9\%$ Rank-1 accuracy and $62.9\%$ mAP under the IR to VIS mode. The results of the existing methods on our LLCM dataset are generally unsatisfactory. This shows that, on one hand, our LLCM dataset is a very challenging dataset. On the other hand, the change of light has serious influence on the VIREID model. Besides, the proposed DEEN achieves the best performance under both the VIS to IR mode and the IR to VIS + +Table 2. Comparisons between the proposed DEEN and some state-of-the-art methods on the SYSU-MM01 and RegDB datasets. + +
ModelLLCM
IR to VISVIS to IR
R-1R-10R-20mAPR-1R-10R-20mAP
DDAG [44]40.371.479.648.448.079.286.152.3
DDAG* [44]41.073.481.949.648.581.087.853.0
AGW [45]43.674.682.451.851.581.587.955.3
LbA [20]43.878.286.653.150.884.391.155.6
LbA* [20]44.678.286.853.850.884.691.155.9
AGW* [45]46.477.885.254.856.084.990.659.1
CAJ [43]48.879.585.356.656.585.390.959.8
DART [41]52.280.787.059.860.487.191.963.2
MMN [49]52.581.688.458.959.988.593.662.7
DEEN (ours)54.984.990.962.962.590.394.765.8
+ +Table 3. Performance obtained by the competing methods on our LLCM dataset. The symbol of “*” represents the methods that we reproduced with the random erasing technique. + +mode, which demonstrates the effectiveness of the proposed DEEN to reduce the modality gaps between the VIS and IR images. + +# 5.4. Ablation Studies + +Effectiveness of each component: To evaluate the contribution of each component to DEEN, we conduct some ablation studies on the LLCM and SYSU-MM01 datasets by removing certain modules from DEEN and evaluate the influence on the performance. The overall settings remain the same, while only the module under evaluation is used in or removed from DEEN. As shown in Tab. 4, although the DEE module can generate more embeddings using a multibranch convolutional block, which slightly improves the performance of the baseline, the results are not satisfactory. After being constrained by the proposed CPM loss to generate diverse embeddings, DEE can greatly improve the performance of the model and effectively reduce the modality discrepancy between the VIS and IR images. Besides, the + +
SettingsLLCMSYSU-MM01
DEE\( \mathcal{L}_{cpm} \)\( \mathcal{L}_{ort} \)MFAR-1mAPR-1mAP
45.453.660.757.7
✓50.559.064.762.0
✓✓53.161.169.266.2
✓✓51.560.165.363.2
✓✓✓53.962.369.866.7
✓51.259.664.762.0
✓✓✓✓54.962.974.771.8
+ +Table 4. The influence of each component on the performance of the proposed DEEN. + +
MethodsLLCMSYSU-MM01
R-1mAPR-1mAP
DEE after stage-048.557.163.459.4
DEE after stage-149.457.863.760.8
DEE after stage-249.657.965.361.7
DEE after stage-353.962.369.866.7
DEE after stage-450.959.660.058.0
+ +Table 5. The influence of which stage of ResNet-50 to plug the DEE module. + +
MethodsLLCMSYSU-MM01
R-1mAPR-1mAP
Two branches52.660.967.564.6
Three branches53.962.369.266.2
Four branches52.460.767.664.6
+ +Table 6. Study about how many branches are suitable for DEE. + +
MethodsLLCMSYSU-MM01
R-1mAPR-1mAP
NL50.157.463.860.7
MFA51.259.664.762.0
NL + DEE54.262.473.470.3
MFA+ DEE54.962.974.771.8
+ +Table 7. Comparison with the Non-Local (NL) block. + +proposed MFA block can improve the performance of the baseline by aggregating the features from different stages for mining diverse channel-wise and spatial feature representations. With the incorporation of DEE, CPM and MFA into an end-to-end learning framework, DEEN achieves an impressive performance improvement on two challenging VIREID datasets, which shows DEE and MFA can benefit from each other for generating diverse embeddings. + +The influence of which stage of ResNet-50 to plug the DEE module. The proposed DEE can be plugged after any stage of the backbone network. In our experiments, we use ResNet-50 as the backbone, which has five stages: stage-0 to stage-4. We plug DEE after different stages of the ResNet-50 to study how it will affect the performance of the DEEN. As shown in Tab. 5, when DEE is plugged after stage-0 to stage-3, the performance gradually increases, which shows the modality gaps become smaller and the generative ability of DEE becomes stronger at deeper layers of the network. When DEE is plugged after stage-3, it can achieve the best results on both LLCM and SYSU-MM01. However, when DEE is plugged after stage-4, the performance drops rapidly because the CPM loss works directly on the embeddings, enlarging the distances between the generated embeddings and the original embeddings, which + +![](images/cbb256044aab84a426d8d7ec851b9deb188085eabbd4bbef62b8513e4ea33f44.jpg) + +![](images/c47c54c5534c8e7ebefca599e8e74b1900b1eb13851f926bca6c2a140439a016.jpg) + +![](images/5277400684fa2cd5732cc2c261f3763583a78b3e5a4d138a7ff5e3432f554ecf.jpg) +Figure 6. Influence of different $\lambda_{1}$ , $\lambda_{2}$ and $\alpha$ values on our LLCM. + +increases the difficulty of model optimization. Based on the above analysis, we plug DEE after stage-3 of the backbone if not specified. + +Effectiveness on how many branches are more suitable for DEE. The proposed DEE module utilizes a multibranch convolutional block to generate diverse embeddings. Here, we study how many branches are suitable for DEE. As shown in Tab. 6, with the increase of the number of DEE's branches from 2 to 3, more embeddings are generated to reduce the modality gaps, so the performance gradually increases. However, the increase of performance has an upper limit when the number of branches is more than 3, because DEE generates too many redundant features, which leads to the drop of performance. As a result, DEE with three branches can achieve the best performances both on the LLCM and SYSU-MM01 datasets. It indicates that DEE with 3 branches is more suitable for generating diverse embeddings. Thus, we use 3 branches for DEE if not specified. + +Comparison with the Non-Local block. In this paper, we propose a MFA block to mine diverse channel-wise and spatial feature representations inspired by the Non-local (NL) block in [31]. Thus, we compare these two blocks to investigate which block is more effective. As shown in Tab. 7, the MFA block outperforms the NL block by $1.1\%$ Rank-1 accuracy and $2.2\%$ mAP, respectively. The results validate the effectiveness of our MFA block. Moreover, the results also show that the MFA block and the DEE module are complementary for generating diverse embeddings to reduce the modality gaps between the VIS and IR images. + +The influence of the hyperparameters $\lambda_{1},\lambda_{2}$ and $\alpha$ To evaluate the influence of the three hyperparameters, we give quantitative comparisons and report the results in Fig. 6. As we can see, the best performance is achieved when $\lambda_{1}$ + +![](images/d22dae04bf26f1f9b5330cc7ced2b0e5db3f913d5fa54cda41d89effd56e3a17.jpg) +(a) Initial Distance + +![](images/c31395fd3c8b755262de2302efb9cb613bd891c6e32972d73f96a7ada4729de6.jpg) +(b) Baseline Distance + +![](images/d48c69ce132b505229d53b7c82f7d634cbbb03bc4bc5590009fe547da78edc9e.jpg) +(c) MFA Distance + +![](images/f2bd4084d1428221c41b771e75f63fa04a8862e4f1cf32633c983017d992d6ff.jpg) +(d) DEE Distance + +![](images/ed878afc2e4c2a7ea244e1c90b6379380f448c245e7e16c54bd30267076c2ac2.jpg) +(e) DEEN Distance + +![](images/aa3843b9b2185bc6406c0bb19c6a63a136ecf4bd7a6a8521097581ddb4d07c61.jpg) +(f) Initial Distribution + +![](images/8ada288b53c84d6fd5f8d2d9692c233a98f6b12bb79b880b01eff8cd3265b413.jpg) +(g) Baseline Distribution + +![](images/db2c7afafa38584fa208a5a6e129441e4753298a08328e54178a01dccabfd2d3.jpg) +(h) MFA Distribution + +![](images/533a0a697eb19a863f6553c94a356474d12e806af8c610cf52bb02a5424f5677.jpg) +(i) DEE Distribution + +![](images/1ad6ef42a52a3d838709aadc5e50e664a976eb407363e08eaea2885c0aa179e1.jpg) +(j) DEEN Distribution + +![](images/ed65ca563b4aa23779780bed5bee80d6171b4c2223fb32c6899856d37f997fe6.jpg) +Figure 7. (a-e) show the intra-class and inter-class distances of cross-modality features. The intra-class and inter-class distances are indicated in blue and green colors, respectively. (f-j) show the distribution of feature embeddings in the 2D feature space, where circles and triangles in different colors denote visible and infrared modalities. A total of 20 persons are selected from the test set. The samples with the same color are from the same person. The "dot" and "cross" markers denote the images from the VIS and IR modalities, respectively. +Baseline +Figure 8. Some Rank-8 retrieval results obtained by the baseline and the proposed DEEN on our LLCM dataset. + +![](images/fe893f377d67383f12d638d1543ddd6406521366a8a8dcbad063255c906ce48d.jpg) +DEEN + +is set to 0.8, $\lambda_{2}$ is set to 0.1 and $\alpha$ is set to 0.2, respectively. + +# 5.5. Visualization + +Feature distribution. To investigate the reason why DEEN is effective, we visualize the inter-class and intra-class distances on our LLCM dataset as shown in Fig. 7 (a-e). Comparing Fig. 7 (c-e) with Fig. 7 (a-b), the means (i.e., the vertical lines) of inter-class and intra-class distances are pushed away by MFA, DEE and DEEN, where $\delta_1 < \delta_2 < \delta_3$ and $\delta_1 < \delta_2 < \delta_4 < \delta_5$ . This shows that the intra-class distance of DEEN is significantly reduced compared with the intra-class distance of the initial features (Fig. 7 (a)) and the baseline features (Fig. 7 (b)). Thus, DEEN can effectively reduce the modality discrepancy between the VIS and the IR images. Meanwhile, we also visualize the feature distribution with t-SNE [27] in the 2D feature space in Fig. 7 (f-j), which shows that MFA, DEE and DEEN can effectively discriminate and aggregate feature embeddings of the same person, and reduce the modality discrepancy. + +Retrieval result. To further show the effectiveness of DEEN, we also show some retrieval results of DEEN on our LLCM dataset in Fig. 8. For each retrieval case, the retrieved images with green boxes mean the correct matches corresponding the given query, while the red ones mean the incorrect matches. In general, DEEN can effectively improve the ranking results with more correctly matched images ranked in the top positions than the baseline. + +# 6. CONCLUSION + +In this paper, we propose a novel diverse embedding expansion network (DEEN) in the embedding space for the VIREID task. The proposed DEEN can generate diverse embeddings and mine diverse channel-wise and spatial embeddings to learn the informative feature representations for reducing the modality discrepancy between the VIS and IR images. Moreover, we also provide a challenging low-light cross-modality (LLCM) dataset, which has more new and important features and can further facilitate the research of VIREID towards practical applications. Extensive experiments on the SYSU-MM01, RegDB and LLCM datasets show the superiority of the proposed DEEN over several other state-of-the-art methods. + +# 7. Acknowledgments + +This work was supported by the National Key Research and Development Program of China under Grant 2022ZD0160402, by the National Natural Science Foundation of China under Grant U21A20514, and by the FuXiaQuan National Independent Innovation Demonstration Zone Collaborative Innovation Platform Project under Grant 3502ZCQXT2022008. + +# References + +[1] Xuesong Chen, Canmiao Fu, Yong Zhao, Feng Zheng, Jingkuan Song, Rongrong Ji, and Yi Yang. Salience-guided cascaded suppression network for person re-identification. In Proceedings of the CVPR, pages 3300–3310, 2020. 4 +[2] Yehansen Chen, Lin Wan, Zhihang Li, Qianyan Jing, and Zongyuan Sun. Neural feature search for rgb-infrared person re-identification. 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In Proceedings of the ICCV, pages 593–602, 2019. 4 \ No newline at end of file diff --git a/2023/Diverse Embedding Expansion Network and Low-Light Cross-Modality Benchmark for Visible-Infrared Person Re-Identification/images.zip b/2023/Diverse Embedding Expansion Network and Low-Light Cross-Modality Benchmark for Visible-Infrared Person Re-Identification/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..5d56f059e38b59affef0d69923bc91be82deb205 --- /dev/null +++ b/2023/Diverse Embedding Expansion Network and Low-Light Cross-Modality Benchmark for Visible-Infrared Person Re-Identification/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:02b4393ce005a382b24107ae60fa601dafa4d4d43da8c4d613fe0f5f232cd649 +size 840702 diff --git a/2023/Diverse Embedding Expansion Network and Low-Light Cross-Modality Benchmark for Visible-Infrared Person Re-Identification/layout.json b/2023/Diverse Embedding Expansion Network and Low-Light Cross-Modality Benchmark for Visible-Infrared Person Re-Identification/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..1e5edb5d81654e20508f0cd2821ce41b5487394d --- /dev/null +++ b/2023/Diverse Embedding Expansion Network and Low-Light Cross-Modality Benchmark for Visible-Infrared Person Re-Identification/layout.json @@ -0,0 +1,9716 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 75, + 102, + 518, + 138 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 75, + 102, + 518, + 138 + ], + "spans": [ + { + "bbox": [ + 75, + 102, + 518, + 138 + ], + "type": "text", + "content": "Diverse Embedding Expansion Network and Low-Light Cross-Modality Benchmark for Visible-Infrared Person Re-identification" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 204, + 160, + 373, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 204, + 160, + 373, + 175 + ], + "spans": [ + { + "bbox": [ + 204, + 160, + 373, + 175 + ], + "type": "text", + "content": "Yukang Zhang" + }, + { + "bbox": [ + 204, + 160, + 373, + 175 + ], + "type": "inline_equation", + "content": "^{1,2}" + }, + { + "bbox": [ + 204, + 160, + 373, + 175 + ], + "type": "text", + "content": ", Hanzi Wang" + }, + { + "bbox": [ + 204, + 160, + 373, + 175 + ], + "type": "inline_equation", + "content": "^{1,2,3*}" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 126, + 175, + 447, + 202 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 126, + 175, + 447, + 202 + ], + "spans": [ + { + "bbox": [ + 126, + 175, + 447, + 202 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 126, + 175, + 447, + 202 + ], + "type": "text", + "content": "Fujian Key Laboratory of Sensing and Computing for Smart City, School of Informatics, Xiamen University, 361005, P.R. 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China." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 115, + 232, + 457, + 245 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 232, + 457, + 245 + ], + "spans": [ + { + "bbox": [ + 115, + 232, + 457, + 245 + ], + "type": "text", + "content": "3Shanghai Artificial Intelligence Laboratory, Shanghai, 200232, China." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 164, + 247, + 408, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 164, + 247, + 408, + 258 + ], + "spans": [ + { + "bbox": [ + 164, + 247, + 408, + 258 + ], + "type": "text", + "content": "zhangyk@stu.xmu.edu.cn, hanzi.wang@xmu.edu.cn" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 143, + 286, + 192, + 300 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 286, + 192, + 300 + ], + "spans": [ + { + "bbox": [ + 143, + 286, + 192, + 300 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 312, + 290, + 587 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 312, + 290, + 587 + ], + "spans": [ + { + "bbox": [ + 47, + 312, + 290, + 587 + ], + "type": "text", + "content": "For the visible-infrared person re-identification (ViReID) task, one of the major challenges is the modality gaps between visible (VIS) and infrared (IR) images. However, the training samples are usually limited, while the modality gaps are too large, which leads that the existing methods cannot effectively mine diverse cross-modality clues. To handle this limitation, we propose a novel augmentation network in the embedding space, called diverse embedding expansion network (DEEN). The proposed DEEN can effectively generate diverse embeddings to learn the informative feature representations and reduce the modality discrepancy between the VIS and IR images. Moreover, the ViReID model may be seriously affected by drastic illumination changes, while all the existing ViReID datasets are captured under sufficient illumination without significant light changes. Thus, we provide a low-light cross-modality (LLCM) dataset, which contains 46,767 bounding boxes of 1,064 identities captured by 9 RGB/IR cameras. Extensive experiments on the SYSU-MM01, RegDB and LLCM datasets show the superiority of the proposed DEEN over several other state-of-the-art methods. The code and dataset are released at: https://github.com/ZYK100/LLCM" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 612, + 128, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 612, + 128, + 624 + ], + "spans": [ + { + "bbox": [ + 47, + 612, + 128, + 624 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 633, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 633, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 47, + 633, + 287, + 693 + ], + "type": "text", + "content": "Person re-identification (ReID) aims to match a given person with gallery images captured by different cameras [3, 9, 52]. Most existing ReID methods [22, 24, 30, 38, 50] only focus on matching RGB images captured by visible cameras at daytime. However, these methods may fail" + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 309, + 286, + 541, + 411 + ], + "blocks": [ + { + "bbox": [ + 309, + 286, + 541, + 411 + ], + "lines": [ + { + "bbox": [ + 309, + 286, + 541, + 411 + ], + "spans": [ + { + "bbox": [ + 309, + 286, + 541, + 411 + ], + "type": "image", + "image_path": "8b4f0a3de20e164309fccc573936a144cd5708769783484a5c52a6fbf4b8e4ab.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 415, + 546, + 460 + ], + "lines": [ + { + "bbox": [ + 305, + 415, + 546, + 460 + ], + "spans": [ + { + "bbox": [ + 305, + 415, + 546, + 460 + ], + "type": "text", + "content": "Figure 1. Motivation of the proposed DEEN, which aims to generate diverse embeddings to make the network focus on learning with the informative feature representations to reduce the modality gaps between the VIS and IR images." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 473, + 546, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 473, + 546, + 557 + ], + "spans": [ + { + "bbox": [ + 304, + 473, + 546, + 557 + ], + "type": "text", + "content": "to achieve encouraging results when visible cameras cannot effectively capture person's information under complex conditions, such as at night or low-light environments. To solve this problem, some visible (VIS)-infrared (IR) person re-identification (VIREID) methods [15,39,41,48] have been proposed to retrieve the VIS (IR) images according to the corresponding IR (VIS) images." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "text", + "content": "Compared with the widely studied person ReID task, the VIREID task is much more challenging due to the additional cross-modality discrepancy between the VIS and IR images [33, 45, 49, 51]. Typically, there are two popular types of methods to reduce this modality discrepancy. One type is the feature-level methods [5, 11, 16, 35, 40, 42], which try to project the VIS and IR features into a common embedding space, where the modality discrepancy can be minimized. However, the large modality discrepancy makes these methods difficult to project the cross-modality images into a common feature space directly. The other type is the image-level methods [4, 28, 29, 32], which aim to reduce the modality discrepancy by translating an IR (or VIS) image" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "type": "text", + "content": "*Corresponding author." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 294, + 732, + 315, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 732, + 315, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 732, + 315, + 742 + ], + "type": "text", + "content": "2153" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 71, + 285, + 232 + ], + "blocks": [ + { + "bbox": [ + 49, + 71, + 285, + 232 + ], + "lines": [ + { + "bbox": [ + 49, + 71, + 285, + 232 + ], + "spans": [ + { + "bbox": [ + 49, + 71, + 285, + 232 + ], + "type": "image", + "image_path": "a5754c3b8954ae0bd7df54064b5555f1c416d38a3a9f66f318db5541fbd231ec.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 236, + 287, + 291 + ], + "lines": [ + { + "bbox": [ + 46, + 236, + 287, + 291 + ], + "spans": [ + { + "bbox": [ + 46, + 236, + 287, + 291 + ], + "type": "text", + "content": "Figure 2. Comparison of person images on the SYSU-MM01 (1st row), RegDB (2nd row), and LLCM (3rd-5th rows) datasets. Each row shows four VIS images and four IR images of two identities. It is obvious that our LLCM contains a more challenging and realistic VIREID environment." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 305, + 287, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 305, + 287, + 353 + ], + "spans": [ + { + "bbox": [ + 46, + 305, + 287, + 353 + ], + "type": "text", + "content": "into its VIS (or IR) counterpart by using the GANs [8]. Despite their success in reducing the modality gaps, the generated cross-modality images are usually accompanied by some noises due to the lack of the VIS-IR image pairs." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 354, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 354, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 354, + 287, + 544 + ], + "type": "text", + "content": "In this paper, we propose a novel augmentation network in the embedding space for the VIREID task, called diverse embedding expansion network (DEEN), which consists of a diverse embedding expansion (DEE) module and a multistage feature aggregation (MFA) block. The proposed DEE module can generate more embeddings followed by a novel center-guided pair mining (CPM) loss to drive the DEE module to focus on learning with the diverse feature representations. As illustrated in Fig. 1, by exploiting the generated embeddings with diverse information, the proposed DEE module can achieve the performance improvement by using more diverse embeddings. The proposed MFA block can aggregate the features from different stages for mining potential channel-wise and spatial feature representations, which increases the network's capacity for mining different-level diverse embeddings." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 545, + 287, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 287, + 664 + ], + "type": "text", + "content": "Moreover, we observe that the existing VIREID datasets are captured under the environments with sufficient illumination. However, the performance of the VIREID methods may be seriously affected by drastic illumination changes or low illuminations. Therefore, we collect a challenging low-light cross-modality dataset, called LLCM dataset, which is shown in Fig. 2. Compared with the other VIREID datasets, the LLCM dataset contains a larger number of identities and images captured under low-light scenes, which introduces more challenges to the real-world VIREID task." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 59, + 665, + 264, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 665, + 264, + 676 + ], + "spans": [ + { + "bbox": [ + 59, + 665, + 264, + 676 + ], + "type": "text", + "content": "In summary, the main contributions are as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": "- We propose a novel diverse embedding expansion (DEE) module with a center-guided pair mining (CPM) loss to generate more embeddings for learning the diverse fea" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 545, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 131 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 131 + ], + "type": "text", + "content": "ture representations. We are the first to augment the embeddings in the embedding space in VIREID. Besides, we also propose an effective multistage feature aggregation (MFA) block to mine potential channel-wise and spatial feature representations." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 132, + 545, + 300 + ], + "type": "list", + "angle": 0, + "index": 11, + "blocks": [ + { + "bbox": [ + 304, + 132, + 545, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 132, + 545, + 191 + ], + "spans": [ + { + "bbox": [ + 304, + 132, + 545, + 191 + ], + "type": "text", + "content": "- With the incorporation of DEE, CPM loss and MFA into an end-to-end learning framework, we propose an effective diverse embedding expansion network (DEEN), which can effectively reduce the modality discrepancy between the VIS and IR images." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 192, + 545, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 192, + 545, + 263 + ], + "spans": [ + { + "bbox": [ + 304, + 192, + 545, + 263 + ], + "type": "text", + "content": "- We collect a low-light cross-modality (LLCM) dataset, which contains 46,767 images of 1,064 identities captured under the environments with illumination changes and low illuminations. The LLCM dataset has more new and important features, which can facilitate the research of VIREID towards practical applications." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 263, + 545, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 263, + 545, + 300 + ], + "spans": [ + { + "bbox": [ + 304, + 263, + 545, + 300 + ], + "type": "text", + "content": "- Extensive experiments show that the proposed DEEN outperforms the other state-of-the-art methods for the VIReID task on three challenging datasets." + } + ] + } + ], + "index": 10 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 311, + 392, + 323 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 311, + 392, + 323 + ], + "spans": [ + { + "bbox": [ + 306, + 311, + 392, + 323 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 331, + 545, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 331, + 545, + 365 + ], + "spans": [ + { + "bbox": [ + 304, + 331, + 545, + 365 + ], + "type": "text", + "content": "Generally speaking, there are two main categories of methods in VIREID: the image-level methods and the feature-level methods." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 366, + 545, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 366, + 545, + 545 + ], + "spans": [ + { + "bbox": [ + 304, + 366, + 545, + 545 + ], + "type": "text", + "content": "The image-level VIREID methods try to transform one modality into the other for reducing the modality discrepancy between the VIS and IR images in the image space. For this purpose, some GANs-based [4, 28, 29, 32] methods are proposed to perform identity-preserving person image style transformation for aligning cross-modality images and alleviating the problem of limited data. These methods often design complex generative models to align cross-modality images. However, due to the lack of VIS-IR image pairs, the generated images are unavoidably accompanied by some noises. X-modality [14] and its variations [34, 49] apply a lightweight network to introduce an auxiliary middle modality to assist the cross-modality search task. However, there is still a modality gap between this middle modality and the VIS / IR modality." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": "The feature-level methods aim to find a modality-shared and modality-specific feature space, where the modality gaps can be minimized. For this purpose, MAUM [15] tries to learn cross-modality metrics in two uni-directions to further enhance them with memory-based augmentation. RFM [25] introduces a cross-center loss to explore a more compact intra-class distribution. DCLNet [23] encourages the positive pixels with the same semantic information to be close, while it simultaneously pushes the negative pixels away. cmGAN [5] designs a cutting-edge discriminator to learn discriminative representations from different modalities. However, the large modality gaps between the VIS and IR images make it difficult to project the cross-modality images into a common space directly [7, 18, 21, 26]." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 732, + 315, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 732, + 315, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 732, + 315, + 742 + ], + "type": "text", + "content": "2154" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 62, + 72, + 528, + 287 + ], + "blocks": [ + { + "bbox": [ + 62, + 72, + 528, + 287 + ], + "lines": [ + { + "bbox": [ + 62, + 72, + 528, + 287 + ], + "spans": [ + { + "bbox": [ + 62, + 72, + 528, + 287 + ], + "type": "image", + "image_path": "5a6d7dc627e1ca9f46910048e7aab6295ecdca80cc1888dec9aa8450ee8cc4a4.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 290, + 547, + 324 + ], + "lines": [ + { + "bbox": [ + 46, + 290, + 547, + 324 + ], + "spans": [ + { + "bbox": [ + 46, + 290, + 547, + 324 + ], + "type": "text", + "content": "Figure 3. The pipeline of the proposed network, which includes a DEE module and a MFA block. The DEE module can generate more embeddings with a novel CPM loss to learn diverse feature representations. The MFA block can aggregate the embeddings from different stages for mining diverse channel-wise and spatial feature representations." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 335, + 104, + 346 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 335, + 104, + 346 + ], + "spans": [ + { + "bbox": [ + 47, + 335, + 104, + 346 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 355, + 162, + 366 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 355, + 162, + 366 + ], + "spans": [ + { + "bbox": [ + 47, + 355, + 162, + 366 + ], + "type": "text", + "content": "3.1. Model Architecture" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 374, + 288, + 541 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 374, + 288, + 541 + ], + "spans": [ + { + "bbox": [ + 46, + 374, + 288, + 541 + ], + "type": "text", + "content": "Fig. 3 provides an overview of the proposed diverse embedding expansion network (DEEN), which utilizes a two-stream ResNet-50 network [12, 44] as the backbone. The VIS-IR features are fed into the proposed diverse embedding expansion (DEE) module to generate more embeddings. Then, a center-guided pair mining (CPM) loss is proposed to make the generated embeddings as diverse as possible for learning informative feature representations. Besides, we incorporate an effective MFA block to aggregate the features from different stages for mining diverse channel-wise and spatial feature representations. During the training stage, all the features before and after the batch normalization (BN) layer are fed into different losses to jointly optimize DEEN." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 551, + 253, + 563 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 551, + 253, + 563 + ], + "spans": [ + { + "bbox": [ + 47, + 551, + 253, + 563 + ], + "type": "text", + "content": "3.2. Diverse Embedding Expansion Module" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 568, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 568, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 568, + 287, + 714 + ], + "type": "text", + "content": "The proposed DEE module is used to generate more embeddings to alleviate the problem of insufficient training data by using a multi-branch convolutional generation structure. Specifically, for each branch of DEE, we firstly use three " + }, + { + "bbox": [ + 46, + 568, + 287, + 714 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 46, + 568, + 287, + 714 + ], + "type": "text", + "content": " dilated convolutional layers " + }, + { + "bbox": [ + 46, + 568, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\varphi_{3 \\times 3}^{1}, \\varphi_{3 \\times 3}^{2}, \\varphi_{3 \\times 3}^{3}" + }, + { + "bbox": [ + 46, + 568, + 287, + 714 + ], + "type": "text", + "content": " with different dilation ratios (1, 2, 3) to reduce the number of feature maps " + }, + { + "bbox": [ + 46, + 568, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{f}" + }, + { + "bbox": [ + 46, + 568, + 287, + 714 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 568, + 287, + 714 + ], + "type": "inline_equation", + "content": "1 / 4" + }, + { + "bbox": [ + 46, + 568, + 287, + 714 + ], + "type": "text", + "content": " of its own size, and then we obtain the feature maps by combining them into one feature map, followed by a ReLU activation layer " + }, + { + "bbox": [ + 46, + 568, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{ReLU}" + }, + { + "bbox": [ + 46, + 568, + 287, + 714 + ], + "type": "text", + "content": " to improve the non-linear representation capability of the DEE. Then, another convolutional layer " + }, + { + "bbox": [ + 46, + 568, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\theta_{1 \\times 1}" + }, + { + "bbox": [ + 46, + 568, + 287, + 714 + ], + "type": "text", + "content": " with a kernel in size of " + }, + { + "bbox": [ + 46, + 568, + 287, + 714 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 46, + 568, + 287, + 714 + ], + "type": "text", + "content": " is applied to the obtained feature map to change its dimension as same as " + }, + { + "bbox": [ + 46, + 568, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{f}" + }, + { + "bbox": [ + 46, + 568, + 287, + 714 + ], + "type": "text", + "content": ". Thus, the generated embeddings " + }, + { + "bbox": [ + 46, + 568, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{+}^{i}" + }, + { + "bbox": [ + 46, + 568, + 287, + 714 + ], + "type": "text", + "content": " of the" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 337, + 457, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 337, + 457, + 347 + ], + "spans": [ + { + "bbox": [ + 306, + 337, + 457, + 347 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 306, + 337, + 457, + 347 + ], + "type": "text", + "content": "-th branch can be written as follows:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 326, + 354, + 545, + 369 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 354, + 545, + 369 + ], + "spans": [ + { + "bbox": [ + 326, + 354, + 545, + 369 + ], + "type": "interline_equation", + "content": "\\mathbf {f} _ {+} ^ {i} = \\theta_ {1 \\times 1} \\left(\\mathbf {F} _ {R e L U} \\left(\\varphi_ {3 \\times 3} ^ {1} (\\mathbf {f}) + \\varphi_ {3 \\times 3} ^ {2} (\\mathbf {f}) + \\varphi_ {3 \\times 3} ^ {3} (\\mathbf {f})\\right)\\right). \\tag {1}", + "image_path": "07884461449516f82b9ad6ee997677a89ac7808dce0b18939bdf6d8ad0f0a1b2.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 376, + 545, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 376, + 545, + 411 + ], + "spans": [ + { + "bbox": [ + 305, + 376, + 545, + 411 + ], + "type": "text", + "content": "Then, all the generated embeddings are concatenated together and used as the input to the next stage of the backbone network." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 420, + 482, + 432 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 420, + 482, + 432 + ], + "spans": [ + { + "bbox": [ + 306, + 420, + 482, + 432 + ], + "type": "text", + "content": "3.3. Center-Guided Pair Mining Loss" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 438, + 545, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 438, + 545, + 521 + ], + "spans": [ + { + "bbox": [ + 304, + 438, + 545, + 521 + ], + "type": "text", + "content": "As we can see from the above operation, the DEE module can only generate more embeddings using a multibranch convolutional block. However, this operation cannot effectively obtain diverse embeddings. Thus, we apply the following three properties to constrain the generated embeddings as diverse as possible to effectively reduce the modality discrepancy between the VIS and IR images:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 522, + 545, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 545, + 594 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 545, + 594 + ], + "type": "text", + "content": "Property 1: The generated embeddings should be as diverse as possible to effectively learn the informative feature representations. This means that we need to push away the distances between the generated embeddings and the original embeddings to learn diverse features and mine diverse cross-modality clues." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 594, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 689 + ], + "type": "text", + "content": "Property 2: The generated embeddings should facilitate reducing the modality discrepancy between the VIS and IR images. This means that we need to pull close the distances between the embeddings generated from the VIS modality and the original IR embeddings. Similarly, we also need to pull close the distances between the embeddings generated from the IR modality and the original VIS embeddings." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "Property 3: The intra-class distance should be less than the inter-class one. By Property 2, it pushes close the" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 734, + 315, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 734, + 315, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 734, + 315, + 742 + ], + "type": "text", + "content": "2155" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 57, + 72, + 279, + 173 + ], + "blocks": [ + { + "bbox": [ + 57, + 72, + 279, + 173 + ], + "lines": [ + { + "bbox": [ + 57, + 72, + 279, + 173 + ], + "spans": [ + { + "bbox": [ + 57, + 72, + 279, + 173 + ], + "type": "image", + "image_path": "95fa4c5421bc831bdffb9003d74f1685971dbeda5868d519c363e33310c1ea0b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 63, + 177, + 271, + 189 + ], + "lines": [ + { + "bbox": [ + 63, + 177, + 271, + 189 + ], + "spans": [ + { + "bbox": [ + 63, + 177, + 271, + 189 + ], + "type": "text", + "content": "Figure 4. Illustration of the proposed CPM loss for DEE." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 198, + 287, + 243 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 198, + 287, + 243 + ], + "spans": [ + { + "bbox": [ + 46, + 198, + 287, + 243 + ], + "type": "text", + "content": "distance between the generated embeddings and the original ones, which may cause the embeddings of different classes to become close. Thus, it is necessary to keep the intra-class distance less than the inter-class distance." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 245, + 287, + 268 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 245, + 287, + 268 + ], + "spans": [ + { + "bbox": [ + 47, + 245, + 287, + 268 + ], + "type": "text", + "content": "As shown in Fig. 4, for embeddings generated from the VIS modality, the CPM loss can be formulated as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 273, + 287, + 287 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 273, + 287, + 287 + ], + "spans": [ + { + "bbox": [ + 55, + 273, + 287, + 287 + ], + "type": "interline_equation", + "content": "\\mathcal {L} \\left(\\mathbf {f} _ {v}, \\mathbf {f} _ {n}, \\mathbf {f} _ {v +} ^ {i}\\right) = \\left[ \\boldsymbol {D} \\left(\\mathbf {f} _ {n} ^ {j}, \\mathbf {f} _ {v +} ^ {i, j}\\right) - \\boldsymbol {D} \\left(\\mathbf {f} _ {v} ^ {j}, \\mathbf {f} _ {v +} ^ {i, j}\\right) - \\boldsymbol {D} \\left(\\mathbf {f} _ {v} ^ {j}, \\mathbf {f} _ {v} ^ {k}\\right) \\right] _ {+}, \\tag {2}", + "image_path": "45d90002900390ca42215c5bea33042ffd3c081e95891a332ad7f4e0d345fb07.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 293, + 287, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 293, + 287, + 434 + ], + "spans": [ + { + "bbox": [ + 46, + 293, + 287, + 434 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 293, + 287, + 434 + ], + "type": "inline_equation", + "content": "D(\\cdot, \\cdot)" + }, + { + "bbox": [ + 46, + 293, + 287, + 434 + ], + "type": "text", + "content": " is the Euclidean distance between two embeddings. " + }, + { + "bbox": [ + 46, + 293, + 287, + 434 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_v" + }, + { + "bbox": [ + 46, + 293, + 287, + 434 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 293, + 287, + 434 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_n" + }, + { + "bbox": [ + 46, + 293, + 287, + 434 + ], + "type": "text", + "content": " are the original embeddings from the VIS and IR modalities, and " + }, + { + "bbox": [ + 46, + 293, + 287, + 434 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{v+}^i" + }, + { + "bbox": [ + 46, + 293, + 287, + 434 + ], + "type": "text", + "content": " is the embeddings generated from the " + }, + { + "bbox": [ + 46, + 293, + 287, + 434 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 293, + 287, + 434 + ], + "type": "text", + "content": "-th branch of the VIS modality. " + }, + { + "bbox": [ + 46, + 293, + 287, + 434 + ], + "type": "inline_equation", + "content": "j, k" + }, + { + "bbox": [ + 46, + 293, + 287, + 434 + ], + "type": "text", + "content": " are different identities in a minibatch and " + }, + { + "bbox": [ + 46, + 293, + 287, + 434 + ], + "type": "inline_equation", + "content": "[z]_+ = \\max(z, 0)" + }, + { + "bbox": [ + 46, + 293, + 287, + 434 + ], + "type": "text", + "content": ". In Eq. (2), the first term can pull the generated embeddings " + }, + { + "bbox": [ + 46, + 293, + 287, + 434 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{v+}^i" + }, + { + "bbox": [ + 46, + 293, + 287, + 434 + ], + "type": "text", + "content": " towards the original IR's embeddings " + }, + { + "bbox": [ + 46, + 293, + 287, + 434 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_n" + }, + { + "bbox": [ + 46, + 293, + 287, + 434 + ], + "type": "text", + "content": " to reduce the modality discrepancy between " + }, + { + "bbox": [ + 46, + 293, + 287, + 434 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{v+}^i, j" + }, + { + "bbox": [ + 46, + 293, + 287, + 434 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 293, + 287, + 434 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_n^j" + }, + { + "bbox": [ + 46, + 293, + 287, + 434 + ], + "type": "text", + "content": ". The second term can push the generated embeddings " + }, + { + "bbox": [ + 46, + 293, + 287, + 434 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{v+}" + }, + { + "bbox": [ + 46, + 293, + 287, + 434 + ], + "type": "text", + "content": " away from the VIS's embeddings " + }, + { + "bbox": [ + 46, + 293, + 287, + 434 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_v" + }, + { + "bbox": [ + 46, + 293, + 287, + 434 + ], + "type": "text", + "content": " to enable " + }, + { + "bbox": [ + 46, + 293, + 287, + 434 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{v+}" + }, + { + "bbox": [ + 46, + 293, + 287, + 434 + ], + "type": "text", + "content": " to learn informative feature representations. The third term can make the intra-class distance less than the inter-class distance." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 435, + 287, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 435, + 287, + 492 + ], + "spans": [ + { + "bbox": [ + 46, + 435, + 287, + 492 + ], + "type": "text", + "content": "Then, we use the embedding centers " + }, + { + "bbox": [ + 46, + 435, + 287, + 492 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_v" + }, + { + "bbox": [ + 46, + 435, + 287, + 492 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 435, + 287, + 492 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_n" + }, + { + "bbox": [ + 46, + 435, + 287, + 492 + ], + "type": "text", + "content": " of each class to make the centers of generated embeddings " + }, + { + "bbox": [ + 46, + 435, + 287, + 492 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_{v+}^i" + }, + { + "bbox": [ + 46, + 435, + 287, + 492 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 435, + 287, + 492 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_{n+}^i" + }, + { + "bbox": [ + 46, + 435, + 287, + 492 + ], + "type": "text", + "content": " more discriminative, and introduce a margin term " + }, + { + "bbox": [ + 46, + 435, + 287, + 492 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 435, + 287, + 492 + ], + "type": "text", + "content": " to balance the three terms in Eq. (2). Thus, for the embeddings from VIS, the CPM loss is formulated as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 48, + 496, + 287, + 520 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 496, + 287, + 520 + ], + "spans": [ + { + "bbox": [ + 48, + 496, + 287, + 520 + ], + "type": "interline_equation", + "content": "\\mathcal {L} \\left(\\mathbf {c} _ {v}, \\mathbf {c} _ {n}, \\mathbf {c} _ {v +} ^ {i}\\right) = \\left[ \\boldsymbol {D} \\left(\\mathbf {c} _ {n} ^ {j}, \\mathbf {c} _ {v +} ^ {i, j}\\right) - \\boldsymbol {D} \\left(\\mathbf {c} _ {v} ^ {j}, \\mathbf {c} _ {v +} ^ {i, j}\\right) - \\boldsymbol {D} \\left(\\mathbf {c} _ {v} ^ {j}, \\mathbf {c} _ {v} ^ {k}\\right) + \\alpha \\right] _ {+}. \\tag {3}", + "image_path": "16cf6137c150d55266396b9afe0aad6334cb44b76eddd33fe6ffe2bec0482e95.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 527, + 287, + 549 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 527, + 287, + 549 + ], + "spans": [ + { + "bbox": [ + 47, + 527, + 287, + 549 + ], + "type": "text", + "content": "Similarly, for the class centers " + }, + { + "bbox": [ + 47, + 527, + 287, + 549 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_{n + }^{i}" + }, + { + "bbox": [ + 47, + 527, + 287, + 549 + ], + "type": "text", + "content": " of embeddings generated from IR, we have:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 553, + 287, + 578 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 553, + 287, + 578 + ], + "spans": [ + { + "bbox": [ + 47, + 553, + 287, + 578 + ], + "type": "interline_equation", + "content": "\\mathcal {L} \\left(\\mathbf {c} _ {v}, \\mathbf {c} _ {n}, \\mathbf {c} _ {n +} ^ {i}\\right) = \\left[ \\boldsymbol {D} \\left(\\mathbf {c} _ {v} ^ {j}, \\mathbf {c} _ {n +} ^ {i, j}\\right) - \\boldsymbol {D} \\left(\\mathbf {c} _ {n} ^ {j}, \\mathbf {c} _ {n +} ^ {i, j}\\right) - \\boldsymbol {D} \\left(\\mathbf {c} _ {n} ^ {j}, \\mathbf {c} _ {n} ^ {k}\\right) + \\alpha \\right] _ {+}. \\tag {4}", + "image_path": "00978da784519d7af08f2988e00ccf602824d41204ef78070571eb4c8fc0d7d2.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 59, + 583, + 281, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 583, + 281, + 594 + ], + "spans": [ + { + "bbox": [ + 59, + 583, + 281, + 594 + ], + "type": "text", + "content": "Thus, the final CPM loss can be formulated as follows:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 88, + 600, + 287, + 613 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 600, + 287, + 613 + ], + "spans": [ + { + "bbox": [ + 88, + 600, + 287, + 613 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {c p m} = \\mathcal {L} \\left(\\mathbf {c} _ {v}, \\mathbf {c} _ {n}, \\mathbf {c} _ {v +} ^ {i}\\right) + \\mathcal {L} \\left(\\mathbf {c} _ {v}, \\mathbf {c} _ {n}, \\mathbf {c} _ {n +} ^ {i}\\right). \\tag {5}", + "image_path": "e55c65f24ed2bb419d13f48d47eb191ac2b5961d8a7794428e87308635a311e1.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 616, + 287, + 681 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 616, + 287, + 681 + ], + "spans": [ + { + "bbox": [ + 46, + 616, + 287, + 681 + ], + "type": "text", + "content": "Besides, to ensure that the generated embeddings from different branches can capture different informative feature representations, we force these different embeddings generated by different branches orthogonal to minimize the overlapping elements. Therefore, the orthogonal loss can be formulated as follows:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 111, + 686, + 287, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 686, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 111, + 686, + 287, + 715 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {o r t} = \\sum_ {m = 1} ^ {i - 1} \\sum_ {n = m + 1} ^ {i} \\left(\\mathbf {f} _ {+} ^ {m T} \\mathbf {f} _ {+} ^ {n}\\right), \\tag {6}", + "image_path": "3fe55c3743c8defdcf442f9b31df28cf6038965e5eb85cfcc9d9f51336987e54.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "text", + "content": " are the " + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "text", + "content": "-th and " + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "text", + "content": "-th generated embeddings from the original embeddings, respectively. The orthogonal loss can enforce the generated embeddings to learn more informative feature representations." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 126, + 507, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 126, + 507, + 140 + ], + "spans": [ + { + "bbox": [ + 306, + 126, + 507, + 140 + ], + "type": "text", + "content": "3.4. Multistage Feature Aggregation Block" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 144, + 545, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 144, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 304, + 144, + 545, + 228 + ], + "type": "text", + "content": "Features aggregation of different levels has been demonstrated to be helpful to semantic segmentation, classification and detection task [1, 54, 55]. To aggregate the features from different stages for mining diverse channel-wise and spatial feature representations, we incorporate an effective channel-spatial multistage feature aggregation (MFA) block to aggregate multi-stage features inspired by [31]." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 228, + 546, + 368 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 228, + 546, + 368 + ], + "spans": [ + { + "bbox": [ + 304, + 228, + 546, + 368 + ], + "type": "text", + "content": "Next, we elaborate on the detail of the MFA block, which is shown in Fig. 3. Specifically, we consider two types of source features for the channel-spatial aggregation block in each stage of the backbone network: low-level feature maps " + }, + { + "bbox": [ + 304, + 228, + 546, + 368 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_l\\in \\mathbb{R}^{C_l\\times H_l\\times W_l}" + }, + { + "bbox": [ + 304, + 228, + 546, + 368 + ], + "type": "text", + "content": " before the stage and high-level feature maps " + }, + { + "bbox": [ + 304, + 228, + 546, + 368 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_h\\in \\mathbb{R}^{C_h\\times H_h\\times W_h}" + }, + { + "bbox": [ + 304, + 228, + 546, + 368 + ], + "type": "text", + "content": " after the stage, where C, W and H denote the number of the channel, width and height of features, respectively. First, we employ three " + }, + { + "bbox": [ + 304, + 228, + 546, + 368 + ], + "type": "inline_equation", + "content": "1\\times 1" + }, + { + "bbox": [ + 304, + 228, + 546, + 368 + ], + "type": "text", + "content": " convolutional layers " + }, + { + "bbox": [ + 304, + 228, + 546, + 368 + ], + "type": "inline_equation", + "content": "\\psi_q^1,\\psi_v^1,\\psi_k^1" + }, + { + "bbox": [ + 304, + 228, + 546, + 368 + ], + "type": "text", + "content": " to transform " + }, + { + "bbox": [ + 304, + 228, + 546, + 368 + ], + "type": "inline_equation", + "content": "\\mathbf{f}" + }, + { + "bbox": [ + 304, + 228, + 546, + 368 + ], + "type": "text", + "content": " into three compact embeddings: " + }, + { + "bbox": [ + 304, + 228, + 546, + 368 + ], + "type": "inline_equation", + "content": "\\psi_q^1 (\\mathbf{f}_h)" + }, + { + "bbox": [ + 304, + 228, + 546, + 368 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 228, + 546, + 368 + ], + "type": "inline_equation", + "content": "\\psi_v^1 (\\mathbf{f}_l)" + }, + { + "bbox": [ + 304, + 228, + 546, + 368 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 228, + 546, + 368 + ], + "type": "inline_equation", + "content": "\\psi_k^1 (\\mathbf{f}_l)" + }, + { + "bbox": [ + 304, + 228, + 546, + 368 + ], + "type": "text", + "content": ". Then, we compute the channel-wise similarity matrix " + }, + { + "bbox": [ + 304, + 228, + 546, + 368 + ], + "type": "inline_equation", + "content": "\\mathbf{M}^c\\in \\mathbb{R}^{C'\\times C'}" + }, + { + "bbox": [ + 304, + 228, + 546, + 368 + ], + "type": "text", + "content": " by matrix multiplication followed by softmax:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 358, + 373, + 545, + 386 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 373, + 545, + 386 + ], + "spans": [ + { + "bbox": [ + 358, + 373, + 545, + 386 + ], + "type": "interline_equation", + "content": "\\mathbf {M} ^ {c} = \\mathbf {F} _ {\\text {s o f t m a x}} \\left(\\psi_ {q} ^ {1} \\left(\\mathbf {f} _ {h}\\right) \\times \\psi_ {k} ^ {1} \\left(\\mathbf {f} _ {l}\\right)\\right). \\tag {7}", + "image_path": "1384c4b56246b955c38b817eb468ee71f499a3e5c9aec58bb9c8855a23864c2a.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 391, + 545, + 457 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 391, + 545, + 457 + ], + "spans": [ + { + "bbox": [ + 304, + 391, + 545, + 457 + ], + "type": "text", + "content": "Consequently, we implement the channel-wise multistage feature aggregation by restoring the channel dimension by the matrix multiplication of " + }, + { + "bbox": [ + 304, + 391, + 545, + 457 + ], + "type": "inline_equation", + "content": "\\psi_v^1 (\\mathbf{f}_l)" + }, + { + "bbox": [ + 304, + 391, + 545, + 457 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 391, + 545, + 457 + ], + "type": "inline_equation", + "content": "\\mathbf{M}^c" + }, + { + "bbox": [ + 304, + 391, + 545, + 457 + ], + "type": "text", + "content": ". After that, another " + }, + { + "bbox": [ + 304, + 391, + 545, + 457 + ], + "type": "inline_equation", + "content": "1\\times 1" + }, + { + "bbox": [ + 304, + 391, + 545, + 457 + ], + "type": "text", + "content": " convolutional layer " + }, + { + "bbox": [ + 304, + 391, + 545, + 457 + ], + "type": "inline_equation", + "content": "\\omega^c" + }, + { + "bbox": [ + 304, + 391, + 545, + 457 + ], + "type": "text", + "content": " is applied to transform the size of the above feature maps to that of " + }, + { + "bbox": [ + 304, + 391, + 545, + 457 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_h" + }, + { + "bbox": [ + 304, + 391, + 545, + 457 + ], + "type": "text", + "content": ". Finally, we get the output by adding " + }, + { + "bbox": [ + 304, + 391, + 545, + 457 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_h" + }, + { + "bbox": [ + 304, + 391, + 545, + 457 + ], + "type": "text", + "content": " to it by matrix addition:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 370, + 463, + 545, + 475 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 370, + 463, + 545, + 475 + ], + "spans": [ + { + "bbox": [ + 370, + 463, + 545, + 475 + ], + "type": "interline_equation", + "content": "\\mathbf {f} _ {h} ^ {c} = \\omega^ {c} \\left(\\psi_ {v} ^ {1} (\\mathbf {f} _ {l}) \\times \\mathbf {M} ^ {c}\\right) + \\mathbf {f} _ {h}. \\tag {8}", + "image_path": "8c10930c92e1135a2282957f373a64b2f24cc26500b723a007b62aab3846e036.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 481, + 545, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 481, + 545, + 536 + ], + "spans": [ + { + "bbox": [ + 304, + 481, + 545, + 536 + ], + "type": "text", + "content": "After that, " + }, + { + "bbox": [ + 304, + 481, + 545, + 536 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_h^c" + }, + { + "bbox": [ + 304, + 481, + 545, + 536 + ], + "type": "text", + "content": " obtained from the above operations and the low-level feature map " + }, + { + "bbox": [ + 304, + 481, + 545, + 536 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_l" + }, + { + "bbox": [ + 304, + 481, + 545, + 536 + ], + "type": "text", + "content": " are used to perform the spatial feature aggregation operation, which is similar to the channelwise multistage feature aggregation operation. Finally, we get the MFA's output as follows:" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 370, + 542, + 545, + 555 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 370, + 542, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 370, + 542, + 545, + 555 + ], + "type": "interline_equation", + "content": "\\mathbf {f} _ {h} ^ {s} = \\omega^ {s} \\left(\\psi_ {v} ^ {2} \\left(\\mathbf {f} _ {l}\\right) \\times \\mathbf {M} ^ {s}\\right) + \\mathbf {f} _ {h} ^ {c}, \\tag {9}", + "image_path": "746a5c9d428f254040fd85eed936116818d3d9573febc8ebfb4efe9dd3afdd5a.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 561, + 545, + 585 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 561, + 545, + 585 + ], + "spans": [ + { + "bbox": [ + 306, + 561, + 545, + 585 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 561, + 545, + 585 + ], + "type": "inline_equation", + "content": "\\omega^s" + }, + { + "bbox": [ + 306, + 561, + 545, + 585 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 561, + 545, + 585 + ], + "type": "inline_equation", + "content": "\\psi_v^2" + }, + { + "bbox": [ + 306, + 561, + 545, + 585 + ], + "type": "text", + "content": " are two " + }, + { + "bbox": [ + 306, + 561, + 545, + 585 + ], + "type": "inline_equation", + "content": "1\\times 1" + }, + { + "bbox": [ + 306, + 561, + 545, + 585 + ], + "type": "text", + "content": " convolutional layers, and " + }, + { + "bbox": [ + 306, + 561, + 545, + 585 + ], + "type": "inline_equation", + "content": "\\mathbf{M}^s" + }, + { + "bbox": [ + 306, + 561, + 545, + 585 + ], + "type": "text", + "content": " is the spatial similarity matrix." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 592, + 444, + 605 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 592, + 444, + 605 + ], + "spans": [ + { + "bbox": [ + 306, + 592, + 444, + 605 + ], + "type": "text", + "content": "3.5. Multi-Loss Optimization" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 609, + 545, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 609, + 545, + 664 + ], + "spans": [ + { + "bbox": [ + 304, + 609, + 545, + 664 + ], + "type": "text", + "content": "Besides the proposed " + }, + { + "bbox": [ + 304, + 609, + 545, + 664 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cpm}" + }, + { + "bbox": [ + 304, + 609, + 545, + 664 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 609, + 545, + 664 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{ort}" + }, + { + "bbox": [ + 304, + 609, + 545, + 664 + ], + "type": "text", + "content": ", we also combine the cross-entropy loss " + }, + { + "bbox": [ + 304, + 609, + 545, + 664 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{ce}" + }, + { + "bbox": [ + 304, + 609, + 545, + 664 + ], + "type": "text", + "content": " [17] and the triplet loss " + }, + { + "bbox": [ + 304, + 609, + 545, + 664 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{tri}" + }, + { + "bbox": [ + 304, + 609, + 545, + 664 + ], + "type": "text", + "content": " [13] to jointly optimize the network in an end-to-end manner by minimizing the sum of these four losses " + }, + { + "bbox": [ + 304, + 609, + 545, + 664 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{total}" + }, + { + "bbox": [ + 304, + 609, + 545, + 664 + ], + "type": "text", + "content": ", which can be formulated as follows:" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 345, + 671, + 545, + 683 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 671, + 545, + 683 + ], + "spans": [ + { + "bbox": [ + 345, + 671, + 545, + 683 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {c e} + \\mathcal {L} _ {\\text {t r i}} + \\lambda_ {1} \\mathcal {L} _ {\\text {c p m}} + \\lambda_ {2} \\mathcal {L} _ {\\text {o r t}}, \\tag {10}", + "image_path": "4638d6c6a3794d2d0af18c0f9c0968deec2c7d944a144fb46d61f4e4ea609241.jpg" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 689, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 545, + 712 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 689, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\lambda_{1}" + }, + { + "bbox": [ + 304, + 689, + 545, + 712 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 689, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\lambda_{2}" + }, + { + "bbox": [ + 304, + 689, + 545, + 712 + ], + "type": "text", + "content": " are the coefficients to control the relative importance of the loss terms." + } + ] + } + ], + "index": 27 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 732, + 315, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 732, + 315, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 732, + 315, + 742 + ], + "type": "text", + "content": "2156" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 71, + 281, + 212 + ], + "blocks": [ + { + "bbox": [ + 53, + 71, + 281, + 212 + ], + "lines": [ + { + "bbox": [ + 53, + 71, + 281, + 212 + ], + "spans": [ + { + "bbox": [ + 53, + 71, + 281, + 212 + ], + "type": "image", + "image_path": "c4add90f66c6cc7be38d6add23a3a03e8542422f4ab04ffb8cc73a262b847679.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 217, + 287, + 262 + ], + "lines": [ + { + "bbox": [ + 46, + 217, + 287, + 262 + ], + "spans": [ + { + "bbox": [ + 46, + 217, + 287, + 262 + ], + "type": "text", + "content": "Figure 5. The distribution of the LLCM's images in the 2D space. It can be seen that the images under different light conditions present different styles, which further increases the modality discrepancy between the VIS and IR images." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 275, + 141, + 287 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 275, + 141, + 287 + ], + "spans": [ + { + "bbox": [ + 47, + 275, + 141, + 287 + ], + "type": "text", + "content": "4. LLCM Dataset" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 296, + 162, + 309 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 296, + 162, + 309 + ], + "spans": [ + { + "bbox": [ + 47, + 296, + 162, + 309 + ], + "type": "text", + "content": "4.1. Dataset Description" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 316, + 287, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 316, + 287, + 460 + ], + "spans": [ + { + "bbox": [ + 46, + 316, + 287, + 460 + ], + "type": "text", + "content": "In this paper, we collect a new challenging low-light cross-modality dataset, called LLCM dataset. The LLCM dataset utilizes a 9-camera network deployed in low-light environments, which can capture the VIS images in daytime and capture the IR images at night. For protecting the personal privacy information, we utilize MTCNN [47] to get the bounding boxes of persons' faces and blur those regions. We make sure that each annotated identity is captured by both the VIS and IR cameras. Some examples from the LLCM dataset are shown in Fig. 2. As shown in Tab. 1, compared with the existing VIREID datasets, the LLCM dataset has the following new and important features:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 460, + 287, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 460, + 287, + 652 + ], + "spans": [ + { + "bbox": [ + 46, + 460, + 287, + 652 + ], + "type": "text", + "content": "First, the images in the LLCM dataset are captured under complex low-light environment for both the VIS and IR modalities, which contains severe illumination changes and is a common problem in the real scenes. As Fig. 2 and Fig. 5 shown, the severe light conditions can change the color of persons' clothes and cause the loss of texture information of the clothes, which introduces great challenges to VIReID. Second, the LLCM dataset has a larger number of identities and bounding boxes. This dataset contains 46,767 bounding boxes of 1,064 identities, making it the largest VIReID dataset at present (see Tab 1). Third, the LLCM dataset is collected in over 100 days from January to April, and different climate conditions and cloth styles are considered. Long-term data collection helps to study the VIReID task in different climates and clothing styles, which increases the generalization of the VIReID model." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": "Besides, considering the real-world applications, the LLCM dataset also contains many images that suffer from various challenges, such as motion blurring, pose variation, camera view changes, occlusion, low resolution and others. All in all, the LLCM dataset is a challenging dataset for" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 306, + 70, + 545, + 114 + ], + "blocks": [ + { + "bbox": [ + 306, + 70, + 545, + 114 + ], + "lines": [ + { + "bbox": [ + 306, + 70, + 545, + 114 + ], + "spans": [ + { + "bbox": [ + 306, + 70, + 545, + 114 + ], + "type": "table", + "html": "
DatasetsIDsImagesVIS / IR cam.low-light
RegDB [19]4128,2401 / 1X
SYSU-MM01 [36]49138,2714 / 2X
LLCM1,06446,7679 / 9✓
", + "image_path": "0f58e0dd830411856bc5750b32558c7c65bce8f49d9c1386858daf7859ad50b1.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 118, + 545, + 139 + ], + "lines": [ + { + "bbox": [ + 306, + 118, + 545, + 139 + ], + "spans": [ + { + "bbox": [ + 306, + 118, + 545, + 139 + ], + "type": "text", + "content": "Table 1. Comparison between the LLCM and other two popular VIREID datasets." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 146, + 545, + 171 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 146, + 545, + 171 + ], + "spans": [ + { + "bbox": [ + 305, + 146, + 545, + 171 + ], + "type": "text", + "content": "the VIREID task, which can further facilitate the research of VIREID towards practical applications." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 178, + 422, + 190 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 178, + 422, + 190 + ], + "spans": [ + { + "bbox": [ + 306, + 178, + 422, + 190 + ], + "type": "text", + "content": "4.2. Evaluation Protocol" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 196, + 545, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 196, + 545, + 376 + ], + "spans": [ + { + "bbox": [ + 304, + 196, + 545, + 376 + ], + "type": "text", + "content": "We divide the LLCM dataset into a training set and a testing set at a ratio about 2:1. The training set contains 30,921 bounding boxes of 713 identities (16,946 bounding boxes are from the VIS modality and 13,975 bounding boxes are from the IR modality), and the testing set contains 13,909 bounding boxes of 351 identities (8,680 bounding boxes are from the VIS modality and 7,166 bounding boxes are from the IR modality). Similar to the RegDB [19] dataset, both the VIS to IR mode and the IR to VIS mode are used to evaluate the performance of the VIREID models. During the testing stage, for each camera, we randomly choose one image from the images of each identity to form the gallery set for evaluation the performance of the models. We repeat the above evaluation 10 times with random split of the gallery set and report the average performance." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 387, + 387, + 400 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 387, + 387, + 400 + ], + "spans": [ + { + "bbox": [ + 306, + 387, + 387, + 400 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 406, + 369, + 418 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 406, + 369, + 418 + ], + "spans": [ + { + "bbox": [ + 306, + 406, + 369, + 418 + ], + "type": "text", + "content": "5.1. Datasets" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 424, + 545, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 424, + 545, + 533 + ], + "spans": [ + { + "bbox": [ + 304, + 424, + 545, + 533 + ], + "type": "text", + "content": "The SYSU-MM01 dataset [36] contains 491 identities captured by 4 VIS cameras and 2 IR cameras, including the All-Search and Indoor-Search modes. For the All-Search mode, all the images captured by all the VIS cameras are used as the gallery set. For the Indoor-Search mode, only the images captured by two indoor VIS cameras are used as the gallery set. The RegDB dataset [19] consists of 412 identities, and each identity has 10 VIS images and 10 IR images captured by a pair of overlapping cameras." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 540, + 440, + 552 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 540, + 440, + 552 + ], + "spans": [ + { + "bbox": [ + 306, + 540, + 440, + 552 + ], + "type": "text", + "content": "5.2. Implementation Details" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 557, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 545, + 715 + ], + "type": "text", + "content": "All the input images are firstly resized to " + }, + { + "bbox": [ + 304, + 557, + 545, + 715 + ], + "type": "inline_equation", + "content": "3 \\times 384 \\times 144" + }, + { + "bbox": [ + 304, + 557, + 545, + 715 + ], + "type": "text", + "content": ", and the random horizontal flip and random erasing [53] techniques are adopted during the training phase. The initial learning rate is set to " + }, + { + "bbox": [ + 304, + 557, + 545, + 715 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-2}" + }, + { + "bbox": [ + 304, + 557, + 545, + 715 + ], + "type": "text", + "content": " and then it increases to " + }, + { + "bbox": [ + 304, + 557, + 545, + 715 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-1}" + }, + { + "bbox": [ + 304, + 557, + 545, + 715 + ], + "type": "text", + "content": " after 10 epochs with a warm-up strategy. After that, we decay the learning rate to " + }, + { + "bbox": [ + 304, + 557, + 545, + 715 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-2}" + }, + { + "bbox": [ + 304, + 557, + 545, + 715 + ], + "type": "text", + "content": " at 20 epoch, and further decay to " + }, + { + "bbox": [ + 304, + 557, + 545, + 715 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-3}" + }, + { + "bbox": [ + 304, + 557, + 545, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 557, + 545, + 715 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-4}" + }, + { + "bbox": [ + 304, + 557, + 545, + 715 + ], + "type": "text", + "content": " at epoch 60 and epoch 120, respectively, until a total of 150 epochs. In each mini-batch, we randomly select 4 VIS images and 4 IR images of 6 identities for training. The SGD optimizer is adopted for training, where the momentum is set to 0.9. For the RegDB dataset, we remove stage-4 and plug the proposed DEE module into the DEEN after stage-2." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 733, + 315, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 733, + 315, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 733, + 315, + 742 + ], + "type": "text", + "content": "2157" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 69, + 547, + 286 + ], + "blocks": [ + { + "bbox": [ + 50, + 69, + 547, + 286 + ], + "lines": [ + { + "bbox": [ + 50, + 69, + 547, + 286 + ], + "spans": [ + { + "bbox": [ + 50, + 69, + 547, + 286 + ], + "type": "table", + "html": "
MethodsSYSU-MM01RegDB
All SearchIndoor SearchVIS to IRIR to VIS
R-1R-10R-20mAPR-1R-10R-20mAPR-1R-10R-20mAPR-1R-10R-20mAP
BDTR [46]17.055.472.019.7----33.658.667.432.832.958.568.432.0
D2RL [32]28.970.682.429.2----43.466.176.344.1----
Hi-CMD [4]34.977.6-35.9----70.986.4-66.0----
JSIA-ReID [29]38.180.789.936.943.886.294.252.948.1--48.948.5--49.3
AlignGAN [28]42.485.093.740.745.987.694.454.357.9--53.656.3--53.4
X-Modality [14]49.989.896.050.7----62.283.191.760.2----
DDAG [44]54.890.495.853.061.094.198.468.069.386.291.563.568.185.290.361.8
LbA [20]55.4--54.158.5--66.374.2--67.667.5--72.4
NFS [2]56.991.396.555.562.896.599.169.880.591.695.172.178.090.593.669.8
CM-NAS [6]60.892.196.858.968.094.897.952.482.895.197.779.381.794.196.977.6
MCLNet [10]65.493.397.162.072.697.099.276.680.392.796.073.175.990.994.669.5
FMCNet [48]66.3--62.568.2--74.189.1--84.488.4--83.9
SMCL [34]67.492.996.861.868.896.698.875.683.9--79.883.1--78.6
DART [41]68.796.499.066.372.597.899.578.283.6--75.782.0--73.8
CAJ [43]69.995.798.566.976.397.999.580.485.095.597.579.184.895.397.577.8
MPANet [37]70.696.298.868.276.798.299.681.082.8--80.783.7--80.9
MMN [49]70.696.299.066.976.297.299.379.691.697.798.984.187.596.098.180.5
DCLNet [23]70.8--65.373.5--76.881.2--74.378.0--70.6
MAUM [15]71.7--68.877.0--81.987.9--85.187.0--84.3
DEEN (ours)74.797.699.271.880.399.099.883.391.197.898.985.189.596.898.483.4
", + "image_path": "e156bccdbc711f9e505af7017847104e586e2c0e3e5f7fd591b63e5f2d7d3a7c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 313, + 270, + 326 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 313, + 270, + 326 + ], + "spans": [ + { + "bbox": [ + 47, + 313, + 270, + 326 + ], + "type": "text", + "content": "5.3. Comparison with State-of-the-art Methods" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 335, + 287, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 335, + 287, + 396 + ], + "spans": [ + { + "bbox": [ + 47, + 335, + 287, + 396 + ], + "type": "text", + "content": "We firstly compare the proposed DEEN with several state-of-the-art methods to demonstrate the superiority of our method. The experimental results on the SYSU-MM01 and RegDB datasets are reported in Tab. 2, and the results on our LLCM dataset are reported in Tab. 3." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 399, + 287, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 399, + 287, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 399, + 287, + 567 + ], + "type": "text", + "content": "SYSU-MM01 and RegDB: From Tab. 2, we can see that the results on the two datasets show that the proposed DEEN achieves the best performance against all other state-of-the-art methods. Specifically, for the All-Search mode on SYSU-MM01, DEEN achieves " + }, + { + "bbox": [ + 46, + 399, + 287, + 567 + ], + "type": "inline_equation", + "content": "74.7\\%" + }, + { + "bbox": [ + 46, + 399, + 287, + 567 + ], + "type": "text", + "content": " Rank-1 accuracy and " + }, + { + "bbox": [ + 46, + 399, + 287, + 567 + ], + "type": "inline_equation", + "content": "71.8\\%" + }, + { + "bbox": [ + 46, + 399, + 287, + 567 + ], + "type": "text", + "content": " mAP. For the Indoor-Search mode, DEEN achieves " + }, + { + "bbox": [ + 46, + 399, + 287, + 567 + ], + "type": "inline_equation", + "content": "80.3\\%" + }, + { + "bbox": [ + 46, + 399, + 287, + 567 + ], + "type": "text", + "content": " Rank-1 accuracy and " + }, + { + "bbox": [ + 46, + 399, + 287, + 567 + ], + "type": "inline_equation", + "content": "83.3\\%" + }, + { + "bbox": [ + 46, + 399, + 287, + 567 + ], + "type": "text", + "content": " mAP. For the VIS to IR mode on RegDB, DEEN achieves " + }, + { + "bbox": [ + 46, + 399, + 287, + 567 + ], + "type": "inline_equation", + "content": "91.1\\%" + }, + { + "bbox": [ + 46, + 399, + 287, + 567 + ], + "type": "text", + "content": " Rank-1 accuracy and " + }, + { + "bbox": [ + 46, + 399, + 287, + 567 + ], + "type": "inline_equation", + "content": "85.1\\%" + }, + { + "bbox": [ + 46, + 399, + 287, + 567 + ], + "type": "text", + "content": " mAP. For the IR to VIS mode, the proposed DEEN also obtains " + }, + { + "bbox": [ + 46, + 399, + 287, + 567 + ], + "type": "inline_equation", + "content": "89.5\\%" + }, + { + "bbox": [ + 46, + 399, + 287, + 567 + ], + "type": "text", + "content": " Rank-1 accuracy and " + }, + { + "bbox": [ + 46, + 399, + 287, + 567 + ], + "type": "inline_equation", + "content": "83.4\\%" + }, + { + "bbox": [ + 46, + 399, + 287, + 567 + ], + "type": "text", + "content": " mAP. The results validate the effectiveness of our method. Moreover, the results also demonstrate that the proposed DEEN can effectively reduce the modality discrepancy between the VIS and IR modalities." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 570, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 288, + 713 + ], + "type": "text", + "content": "LLCM: Tab. 3 shows the results on our LLCM dataset. Here, we use several representative open-source methods to evaluate our LLCM dataset and compare them with our method. From Tab. 3 we can draw the following conclusions: the best method only obtains " + }, + { + "bbox": [ + 46, + 570, + 288, + 713 + ], + "type": "inline_equation", + "content": "54.9\\%" + }, + { + "bbox": [ + 46, + 570, + 288, + 713 + ], + "type": "text", + "content": " Rank-1 accuracy and " + }, + { + "bbox": [ + 46, + 570, + 288, + 713 + ], + "type": "inline_equation", + "content": "62.9\\%" + }, + { + "bbox": [ + 46, + 570, + 288, + 713 + ], + "type": "text", + "content": " mAP under the IR to VIS mode. The results of the existing methods on our LLCM dataset are generally unsatisfactory. This shows that, on one hand, our LLCM dataset is a very challenging dataset. On the other hand, the change of light has serious influence on the VIREID model. Besides, the proposed DEEN achieves the best performance under both the VIS to IR mode and the IR to VIS" + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 307, + 312, + 549, + 432 + ], + "blocks": [ + { + "bbox": [ + 62, + 290, + 529, + 301 + ], + "lines": [ + { + "bbox": [ + 62, + 290, + 529, + 301 + ], + "spans": [ + { + "bbox": [ + 62, + 290, + 529, + 301 + ], + "type": "text", + "content": "Table 2. Comparisons between the proposed DEEN and some state-of-the-art methods on the SYSU-MM01 and RegDB datasets." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 312, + 549, + 432 + ], + "lines": [ + { + "bbox": [ + 307, + 312, + 549, + 432 + ], + "spans": [ + { + "bbox": [ + 307, + 312, + 549, + 432 + ], + "type": "table", + "html": "
ModelLLCM
IR to VISVIS to IR
R-1R-10R-20mAPR-1R-10R-20mAP
DDAG [44]40.371.479.648.448.079.286.152.3
DDAG* [44]41.073.481.949.648.581.087.853.0
AGW [45]43.674.682.451.851.581.587.955.3
LbA [20]43.878.286.653.150.884.391.155.6
LbA* [20]44.678.286.853.850.884.691.155.9
AGW* [45]46.477.885.254.856.084.990.659.1
CAJ [43]48.879.585.356.656.585.390.959.8
DART [41]52.280.787.059.860.487.191.963.2
MMN [49]52.581.688.458.959.988.593.662.7
DEEN (ours)54.984.990.962.962.590.394.765.8
", + "image_path": "4826c9fa003af2e0c359becc510162b5aca395bc7614424ec55567f182628438.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 434, + 547, + 468 + ], + "lines": [ + { + "bbox": [ + 305, + 434, + 547, + 468 + ], + "spans": [ + { + "bbox": [ + 305, + 434, + 547, + 468 + ], + "type": "text", + "content": "Table 3. Performance obtained by the competing methods on our LLCM dataset. The symbol of “*” represents the methods that we reproduced with the random erasing technique." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 482, + 546, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 482, + 546, + 518 + ], + "spans": [ + { + "bbox": [ + 305, + 482, + 546, + 518 + ], + "type": "text", + "content": "mode, which demonstrates the effectiveness of the proposed DEEN to reduce the modality gaps between the VIS and IR images." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 527, + 406, + 539 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 527, + 406, + 539 + ], + "spans": [ + { + "bbox": [ + 306, + 527, + 406, + 539 + ], + "type": "text", + "content": "5.4. Ablation Studies" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": "Effectiveness of each component: To evaluate the contribution of each component to DEEN, we conduct some ablation studies on the LLCM and SYSU-MM01 datasets by removing certain modules from DEEN and evaluate the influence on the performance. The overall settings remain the same, while only the module under evaluation is used in or removed from DEEN. As shown in Tab. 4, although the DEE module can generate more embeddings using a multibranch convolutional block, which slightly improves the performance of the baseline, the results are not satisfactory. After being constrained by the proposed CPM loss to generate diverse embeddings, DEE can greatly improve the performance of the model and effectively reduce the modality discrepancy between the VIS and IR images. Besides, the" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 734, + 315, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 734, + 315, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 734, + 315, + 742 + ], + "type": "text", + "content": "2158" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 70, + 287, + 159 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 287, + 159 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 287, + 159 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 287, + 159 + ], + "type": "table", + "html": "
SettingsLLCMSYSU-MM01
DEE\\( \\mathcal{L}_{cpm} \\)\\( \\mathcal{L}_{ort} \\)MFAR-1mAPR-1mAP
45.453.660.757.7
✓50.559.064.762.0
✓✓53.161.169.266.2
✓✓51.560.165.363.2
✓✓✓53.962.369.866.7
✓51.259.664.762.0
✓✓✓✓54.962.974.771.8
", + "image_path": "8cb4221b7e13814328c79cc1a64c5298f967f1da0ddd0cb7ffa463fab2b847ea.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 51, + 188, + 282, + 255 + ], + "blocks": [ + { + "bbox": [ + 47, + 161, + 287, + 184 + ], + "lines": [ + { + "bbox": [ + 47, + 161, + 287, + 184 + ], + "spans": [ + { + "bbox": [ + 47, + 161, + 287, + 184 + ], + "type": "text", + "content": "Table 4. The influence of each component on the performance of the proposed DEEN." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 51, + 188, + 282, + 255 + ], + "lines": [ + { + "bbox": [ + 51, + 188, + 282, + 255 + ], + "spans": [ + { + "bbox": [ + 51, + 188, + 282, + 255 + ], + "type": "table", + "html": "
MethodsLLCMSYSU-MM01
R-1mAPR-1mAP
DEE after stage-048.557.163.459.4
DEE after stage-149.457.863.760.8
DEE after stage-249.657.965.361.7
DEE after stage-353.962.369.866.7
DEE after stage-450.959.660.058.0
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MethodsLLCMSYSU-MM01
R-1mAPR-1mAP
Two branches52.660.967.564.6
Three branches53.962.369.266.2
Four branches52.460.767.664.6
", + "image_path": "b2a0b4df3a7bde673ed51367ab04c6676fcc1d976a592a62cb79663c7ac45de6.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 59, + 351, + 274, + 401 + ], + "blocks": [ + { + "bbox": [ + 53, + 335, + 281, + 346 + ], + "lines": [ + { + "bbox": [ + 53, + 335, + 281, + 346 + ], + "spans": [ + { + "bbox": [ + 53, + 335, + 281, + 346 + ], + "type": "text", + "content": "Table 6. Study about how many branches are suitable for DEE." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 59, + 351, + 274, + 401 + ], + "lines": [ + { + "bbox": [ + 59, + 351, + 274, + 401 + ], + "spans": [ + { + "bbox": [ + 59, + 351, + 274, + 401 + ], + "type": "table", + "html": "
MethodsLLCMSYSU-MM01
R-1mAPR-1mAP
NL50.157.463.860.7
MFA51.259.664.762.0
NL + DEE54.262.473.470.3
MFA+ DEE54.962.974.771.8
", + "image_path": "22553b020d31923e0767ec331c5d0677a3d0555500d8001842b95b3569e28df0.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 70, + 402, + 264, + 412 + ], + "lines": [ + { + "bbox": [ + 70, + 402, + 264, + 412 + ], + "spans": [ + { + "bbox": [ + 70, + 402, + 264, + 412 + ], + "type": "text", + "content": "Table 7. Comparison with the Non-Local (NL) block." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 425, + 286, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 425, + 286, + 521 + ], + "spans": [ + { + "bbox": [ + 46, + 425, + 286, + 521 + ], + "type": "text", + "content": "proposed MFA block can improve the performance of the baseline by aggregating the features from different stages for mining diverse channel-wise and spatial feature representations. With the incorporation of DEE, CPM and MFA into an end-to-end learning framework, DEEN achieves an impressive performance improvement on two challenging VIREID datasets, which shows DEE and MFA can benefit from each other for generating diverse embeddings." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 521, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 714 + ], + "type": "text", + "content": "The influence of which stage of ResNet-50 to plug the DEE module. The proposed DEE can be plugged after any stage of the backbone network. In our experiments, we use ResNet-50 as the backbone, which has five stages: stage-0 to stage-4. We plug DEE after different stages of the ResNet-50 to study how it will affect the performance of the DEEN. As shown in Tab. 5, when DEE is plugged after stage-0 to stage-3, the performance gradually increases, which shows the modality gaps become smaller and the generative ability of DEE becomes stronger at deeper layers of the network. When DEE is plugged after stage-3, it can achieve the best results on both LLCM and SYSU-MM01. However, when DEE is plugged after stage-4, the performance drops rapidly because the CPM loss works directly on the embeddings, enlarging the distances between the generated embeddings and the original embeddings, which" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 310, + 72, + 541, + 147 + ], + "blocks": [ + { + "bbox": [ + 310, + 72, + 541, + 147 + ], + "lines": [ + { + "bbox": [ + 310, + 72, + 541, + 147 + ], + "spans": [ + { + "bbox": [ + 310, + 72, + 541, + 147 + ], + "type": "image", + "image_path": "cbb256044aab84a426d8d7ec851b9deb188085eabbd4bbef62b8513e4ea33f44.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 309, + 148, + 541, + 224 + ], + "blocks": [ + { + "bbox": [ + 309, + 148, + 541, + 224 + ], + "lines": [ + { + "bbox": [ + 309, + 148, + 541, + 224 + ], + "spans": [ + { + "bbox": [ + 309, + 148, + 541, + 224 + ], + "type": "image", + "image_path": "c47c54c5534c8e7ebefca599e8e74b1900b1eb13851f926bca6c2a140439a016.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 309, + 224, + 541, + 299 + ], + "blocks": [ + { + "bbox": [ + 309, + 224, + 541, + 299 + ], + "lines": [ + { + "bbox": [ + 309, + 224, + 541, + 299 + ], + "spans": [ + { + "bbox": [ + 309, + 224, + 541, + 299 + ], + "type": "image", + "image_path": "5277400684fa2cd5732cc2c261f3763583a78b3e5a4d138a7ff5e3432f554ecf.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 299, + 544, + 310 + ], + "lines": [ + { + "bbox": [ + 306, + 299, + 544, + 310 + ], + "spans": [ + { + "bbox": [ + 306, + 299, + 544, + 310 + ], + "type": "text", + "content": "Figure 6. Influence of different " + }, + { + "bbox": [ + 306, + 299, + 544, + 310 + ], + "type": "inline_equation", + "content": "\\lambda_{1}" + }, + { + "bbox": [ + 306, + 299, + 544, + 310 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 306, + 299, + 544, + 310 + ], + "type": "inline_equation", + "content": "\\lambda_{2}" + }, + { + "bbox": [ + 306, + 299, + 544, + 310 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 299, + 544, + 310 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 306, + 299, + 544, + 310 + ], + "type": "text", + "content": " values on our LLCM." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 318, + 545, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 318, + 545, + 353 + ], + "spans": [ + { + "bbox": [ + 305, + 318, + 545, + 353 + ], + "type": "text", + "content": "increases the difficulty of model optimization. Based on the above analysis, we plug DEE after stage-3 of the backbone if not specified." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 354, + 545, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 354, + 545, + 533 + ], + "spans": [ + { + "bbox": [ + 304, + 354, + 545, + 533 + ], + "type": "text", + "content": "Effectiveness on how many branches are more suitable for DEE. The proposed DEE module utilizes a multibranch convolutional block to generate diverse embeddings. Here, we study how many branches are suitable for DEE. As shown in Tab. 6, with the increase of the number of DEE's branches from 2 to 3, more embeddings are generated to reduce the modality gaps, so the performance gradually increases. However, the increase of performance has an upper limit when the number of branches is more than 3, because DEE generates too many redundant features, which leads to the drop of performance. As a result, DEE with three branches can achieve the best performances both on the LLCM and SYSU-MM01 datasets. It indicates that DEE with 3 branches is more suitable for generating diverse embeddings. Thus, we use 3 branches for DEE if not specified." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 533, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 545, + 665 + ], + "type": "text", + "content": "Comparison with the Non-Local block. In this paper, we propose a MFA block to mine diverse channel-wise and spatial feature representations inspired by the Non-local (NL) block in [31]. Thus, we compare these two blocks to investigate which block is more effective. As shown in Tab. 7, the MFA block outperforms the NL block by " + }, + { + "bbox": [ + 304, + 533, + 545, + 665 + ], + "type": "inline_equation", + "content": "1.1\\%" + }, + { + "bbox": [ + 304, + 533, + 545, + 665 + ], + "type": "text", + "content": " Rank-1 accuracy and " + }, + { + "bbox": [ + 304, + 533, + 545, + 665 + ], + "type": "inline_equation", + "content": "2.2\\%" + }, + { + "bbox": [ + 304, + 533, + 545, + 665 + ], + "type": "text", + "content": " mAP, respectively. The results validate the effectiveness of our MFA block. Moreover, the results also show that the MFA block and the DEE module are complementary for generating diverse embeddings to reduce the modality gaps between the VIS and IR images." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "text", + "content": "The influence of the hyperparameters " + }, + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\lambda_{1},\\lambda_{2}" + }, + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "text", + "content": " To evaluate the influence of the three hyperparameters, we give quantitative comparisons and report the results in Fig. 6. As we can see, the best performance is achieved when " + }, + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\lambda_{1}" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 734, + 315, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 734, + 315, + 742 + ], + "spans": [ + { + "bbox": [ + 295, + 734, + 315, + 742 + ], + "type": "text", + "content": "2159" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 72, + 149, + 153 + ], + "blocks": [ + { + "bbox": [ + 50, + 72, + 149, + 153 + ], + "lines": [ + { + "bbox": [ + 50, + 72, + 149, + 153 + ], + "spans": [ + { + "bbox": [ + 50, + 72, + 149, + 153 + ], + "type": "image", + "image_path": "d22dae04bf26f1f9b5330cc7ced2b0e5db3f913d5fa54cda41d89effd56e3a17.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": 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} + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "type": "image", + "bbox": [ + 50, + 316, + 168, + 438 + ], + "blocks": [ + { + "bbox": [ + 46, + 260, + 545, + 304 + ], + "lines": [ + { + "bbox": [ + 46, + 260, + 545, + 304 + ], + "spans": [ + { + "bbox": [ + 46, + 260, + 545, + 304 + ], + "type": "text", + "content": "Figure 7. (a-e) show the intra-class and inter-class distances of cross-modality features. The intra-class and inter-class distances are indicated in blue and green colors, respectively. (f-j) show the distribution of feature embeddings in the 2D feature space, where circles and triangles in different colors denote visible and infrared modalities. A total of 20 persons are selected from the test set. The samples with the same color are from the same person. The \"dot\" and \"cross\" markers denote the images from the VIS and IR modalities, respectively." + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 50, + 316, + 168, + 438 + ], + "lines": [ + { + "bbox": [ + 50, + 316, + 168, + 438 + ], + "spans": [ + { + "bbox": [ + 50, + 316, + 168, + 438 + ], + "type": "image", + "image_path": "ed65ca563b4aa23779780bed5bee80d6171b4c2223fb32c6899856d37f997fe6.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 106, + 440, + 129, + 447 + ], + "lines": [ + { + "bbox": [ + 106, + 440, + 129, + 447 + ], + "spans": [ + { + "bbox": [ + 106, + 440, + 129, + 447 + ], + "type": "text", + "content": "Baseline" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 453, + 287, + 475 + ], + "lines": [ + { + "bbox": [ + 46, + 453, + 287, + 475 + ], + "spans": [ + { + "bbox": [ + 46, + 453, + 287, + 475 + ], + "type": "text", + "content": "Figure 8. Some Rank-8 retrieval results obtained by the baseline and the proposed DEEN on our LLCM dataset." + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_caption" + } + ], + "index": 21 + }, + { + "type": "image", + "bbox": [ + 171, + 316, + 290, + 438 + ], + "blocks": [ + { + "bbox": [ + 171, + 316, + 290, + 438 + ], + "lines": [ + { + "bbox": [ + 171, + 316, + 290, + 438 + ], + "spans": [ + { + "bbox": [ + 171, + 316, + 290, + 438 + ], + "type": "image", + "image_path": "fe893f377d67383f12d638d1543ddd6406521366a8a8dcbad063255c906ce48d.jpg" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 231, + 439, + 250, + 447 + ], + "lines": [ + { + "bbox": [ + 231, + 439, + 250, + 447 + ], + "spans": [ + { + "bbox": [ + 231, + 439, + 250, + 447 + ], + "type": "text", + "content": "DEEN" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_caption" + } + ], + "index": 23 + }, + { + "bbox": [ + 46, + 484, + 286, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 484, + 286, + 498 + ], + "spans": [ + { + "bbox": [ + 46, + 484, + 286, + 498 + ], + "type": "text", + "content": "is set to 0.8, " + }, + { + "bbox": [ + 46, + 484, + 286, + 498 + ], + "type": "inline_equation", + "content": "\\lambda_{2}" + }, + { + "bbox": [ + 46, + 484, + 286, + 498 + ], + "type": "text", + "content": " is set to 0.1 and " + }, + { + "bbox": [ + 46, + 484, + 286, + 498 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 484, + 286, + 498 + ], + "type": "text", + "content": " is set to 0.2, respectively." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 47, + 503, + 130, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 503, + 130, + 514 + ], + "spans": [ + { + "bbox": [ + 47, + 503, + 130, + 514 + ], + "type": "text", + "content": "5.5. Visualization" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 46, + 522, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 522, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 522, + 287, + 714 + ], + "type": "text", + "content": "Feature distribution. To investigate the reason why DEEN is effective, we visualize the inter-class and intra-class distances on our LLCM dataset as shown in Fig. 7 (a-e). Comparing Fig. 7 (c-e) with Fig. 7 (a-b), the means (i.e., the vertical lines) of inter-class and intra-class distances are pushed away by MFA, DEE and DEEN, where " + }, + { + "bbox": [ + 46, + 522, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\delta_1 < \\delta_2 < \\delta_3" + }, + { + "bbox": [ + 46, + 522, + 287, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 522, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\delta_1 < \\delta_2 < \\delta_4 < \\delta_5" + }, + { + "bbox": [ + 46, + 522, + 287, + 714 + ], + "type": "text", + "content": ". This shows that the intra-class distance of DEEN is significantly reduced compared with the intra-class distance of the initial features (Fig. 7 (a)) and the baseline features (Fig. 7 (b)). Thus, DEEN can effectively reduce the modality discrepancy between the VIS and the IR images. Meanwhile, we also visualize the feature distribution with t-SNE [27] in the 2D feature space in Fig. 7 (f-j), which shows that MFA, DEE and DEEN can effectively discriminate and aggregate feature embeddings of the same person, and reduce the modality discrepancy." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 304, + 316, + 545, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 316, + 545, + 413 + ], + "spans": [ + { + "bbox": [ + 304, + 316, + 545, + 413 + ], + "type": "text", + "content": "Retrieval result. To further show the effectiveness of DEEN, we also show some retrieval results of DEEN on our LLCM dataset in Fig. 8. For each retrieval case, the retrieved images with green boxes mean the correct matches corresponding the given query, while the red ones mean the incorrect matches. In general, DEEN can effectively improve the ranking results with more correctly matched images ranked in the top positions than the baseline." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 306, + 423, + 402, + 435 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 423, + 402, + 435 + ], + "spans": [ + { + "bbox": [ + 306, + 423, + 402, + 435 + ], + "type": "text", + "content": "6. CONCLUSION" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 304, + 443, + 545, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 443, + 545, + 598 + ], + "spans": [ + { + "bbox": [ + 304, + 443, + 545, + 598 + ], + "type": "text", + "content": "In this paper, we propose a novel diverse embedding expansion network (DEEN) in the embedding space for the VIREID task. The proposed DEEN can generate diverse embeddings and mine diverse channel-wise and spatial embeddings to learn the informative feature representations for reducing the modality discrepancy between the VIS and IR images. Moreover, we also provide a challenging low-light cross-modality (LLCM) dataset, which has more new and important features and can further facilitate the research of VIREID towards practical applications. Extensive experiments on the SYSU-MM01, RegDB and LLCM datasets show the superiority of the proposed DEEN over several other state-of-the-art methods." + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 306, + 609, + 415, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 609, + 415, + 624 + ], + "spans": [ + { + "bbox": [ + 306, + 609, + 415, + 624 + ], + "type": "text", + "content": "7. Acknowledgments" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": "This work was supported by the National Key Research and Development Program of China under Grant 2022ZD0160402, by the National Natural Science Foundation of China under Grant U21A20514, and by the FuXiaQuan National Independent Innovation Demonstration Zone Collaborative Innovation Platform Project under Grant 3502ZCQXT2022008." + } + ] + } + ], + "index": 33 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 734, + 315, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 734, + 315, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 734, + 315, + 742 + ], + "type": "text", + "content": "2160" + } + ] + } + ], + "index": 34 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "text", + "content": "[1] Xuesong Chen, Canmiao Fu, Yong Zhao, Feng Zheng, Jingkuan Song, Rongrong Ji, and Yi Yang. 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A challenging issue in visual prompting is that image datasets sometimes have a large data diversity whereas a per-dataset generic prompt can hardly handle the complex distribution shift toward the original pretraining data distribution properly. To address this issue, we propose a dataset Diversity-Aware prompting strategy whose initialization is realized by a Meta-prompt. Specifically, we cluster the downstream dataset into small homogeneity subsets in a diversity-adaptive way, with each subset has its own prompt optimized separately. Such a divide-and-conquer design reduces the optimization difficulty greatly and significantly boosts the prompting performance. Furthermore, all the prompts are initialized with a meta-prompt, which is learned across several datasets. It is a bootstrapped paradigm, with the key observation that the prompting knowledge learned from previous datasets could help the prompt to converge faster and perform better on a new dataset. During inference, we dynamically select a proper prompt for each input, based on the feature distance between the input and each subset. Through extensive experiments, our DAM-VP demonstrates superior efficiency and effectiveness, clearly surpassing previous prompting methods in a series of downstream datasets for different pretraining models. Our code is available at: https://github.com/shikiw/DAM-VP.", + "bbox": [ + 76, + 335, + 473, + 760 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 789, + 209, + 806 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "With the increasing scale of training data and model size, the pretraining-finetuning paradigm has shown remarkable achievement in many areas, including natural language processing (NLP) [4, 13] and computer vision (CV) [2,7,8,19].", + "bbox": [ + 76, + 815, + 468, + 877 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/abafc6ff1f6bac34c17bdd9e7abfb951fad4628ac6ce0d82864e3ebe7eca070a.jpg", + "image_caption": [ + "Figure 1. Relation between dataset diversity and the performance gain got by using prompting. The gain is the performance improvement when compared with the linear-probing accuracy, under the head-tuning setting. Both previous methods get a large performance gain on low-diversity datasets, while failing to boost the transfer performance on high-diversity datasets." + ], + "image_footnote": [], + "bbox": [ + 508, + 303, + 885, + 436 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, fully finetuning a large pre-trained model for each small downstream task still has some problems in real-world usage. The most practical one is the storage and distribution problem that we have to maintain an independent copy of the model for each task, which is quite expensive and inflexible, especially for increasing numbers of downstream tasks [9].", + "bbox": [ + 496, + 563, + 893, + 669 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To break the dilemma, many efforts [6,17,18,25,51] have been paid to efficiently transfer the given pre-trained models into a particular dataset. Prompting is an extensively studied method in the NLP area, which appends a few tokens before the input sequence to provide some task-specific knowledge to the pre-trained model, so that the model could adapt well on the downstream tasks without the fully-finetuning. Inspired by the success of prompting in NLP, some recent works [1, 26] propose visual prompting for vision models. By adding some learnable noise onto the input image or appending some learnable tokens to the model input sequence, the pre-trained models show promising results on different kinds of downstream tasks.", + "bbox": [ + 496, + 671, + 895, + 867 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, we argue that these methods ignore the diverse distribution property of the image dataset and using a sin-", + "bbox": [ + 500, + 869, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author.", + "bbox": [ + 94, + 886, + 223, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "10878", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "gle prompt for all the images in each dataset is not optimal. In Figure 1, we show the relationship between the gain from prompting and the diversity of the dataset. Here the gain represents the accuracy improvement compared with the linear probing setting. We find that both VP [1] and VPT [26] improve the model accuracy by a large margin on the low-diversity dataset, but relatively small gains on the high-diversity datasets, which is intuitively sensible. For low-diversity datasets, such as the street view house number dataset (SVHN) [37], all the images have similar content so a unified prompt is sufficient. On the contrary, when it comes to high-diversity datasets, such as the ImageNet [12] dataset, it covers very diverse classes from the wordnet and there is not any pre-defined relationship between the classes, so it is hard to use a single prompt to provide the prior for all the images, such as for \"car\" and \"dog\".", + "bbox": [ + 75, + 90, + 472, + 332 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Motivated by this observation, we propose our Diversity-Aware Meta Visual Prompting (DAM-VP). It has two core designs. Firstly, to provide a proper prompt for each image from high-diversity datasets, we propose a clustering-based prompt selection method. In detail, given a pre-trained visual model and a downstream dataset, we use the off-the-shelf clustering method to cluster the feature of the downstream data into several coarse-grained subsets, and guide each cluster to learn its own prompt separately. Based on the strong homogeneity of the same clustered data, the optimization of cluster-specific visual prompts can be greatly facilitated and the data commonalities can be also easily covered. Secondly, we argue the prompt across different clusters or datasets may have some shared pattern, from which the model can be adapted to a new dataset faster and get better performance. This motivates us to introduce a meta-learning-based method that learns a meta prompt and initializes the prompt of each cluster with it.", + "bbox": [ + 75, + 333, + 472, + 604 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We conduct our experiments on datasets with different data diversity and evaluate the transfer performance with different pre-trained models. We report the performance on both the widely used head-tuning setting and a more challenging head-freezing/missing setting. Our DAM-VP outperforms previous methods by a large margin, especially on high-diversity datasets. For example, with the ImageNet22k pre-trained ViT-B model, DAM-VP gets $73.1\\%$ top-1 accuracy under the head-tuning setting on the diverse DTD [10] dataset, surpassing previous methods VP [1] and VPT [26] with $+13.6\\%$ and $+7.3\\%$ respectively. Meanwhile, we find DAM-VP is quite efficient that with only 10 epoch tuning, it gets $85.7\\%$ average top-1 accuracy over the 10 datasets, comparable with previous methods that tunes 100 epochs (83.4% for VP [1] and 85.5% for VPT [26]). Our contributions can be summarized as follows:", + "bbox": [ + 75, + 604, + 472, + 845 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- We analyze the limitation of previous visual prompting methods, and point out that vision-suitable prompting should consider the dataset diversity.", + "bbox": [ + 94, + 854, + 470, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- Accordingly, we propose a novel Diversity-Aware Meta Visual Prompting (DAM-VP) method. It uses the divide-and-conquer idea by clustering high-diversity datasets into subsets and learning separate prompts for each subset, in cooperation with a meta-prompt learning design.", + "bbox": [ + 517, + 90, + 890, + 181 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- Through extensive experiments, our DAM-VP demonstrates superior performance, achieving SOTA performance in a series of downstream datasets for different pretraining models.", + "bbox": [ + 517, + 194, + 893, + 255 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 270, + 640, + 286 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Prompt learning. Served as a new paradigm, prompting [33] originally emerges in NLP for adapting pre-trained language models (PLM) [4, 13] to downstream tasks. Its principle idea is to reformulate downstream data into the model knowledge learned during the pretraining phase, enabling the frozen pre-trained model to understand the task rather than tuning the model parameters for adaption. This goal has been initially reached through constructing pure text prompts that contains task-specific templates and label words to perform cloze test, e.g., hand-craft prompts [16] and generative text prompts [27, 45], but unfortunately, still requiring specialized linguistic expertise for preparation. To alleviate this, recent efforts have been paid on prompt tuning (PT) [30, 31] that learns a task-specific continuous vector as tunable prefix tokens. These tokens can be optimized via gradients to act as prompts in task adaptation while maintaining the pre-trained model untouched. Driven by the success of language prompts, a lot of works [35, 38, 43, 47, 50, 55], like CoOP [57] and CoCoOP [56], have been mushroomed to explore vision-related prompting especially in multi-modal scenarios, while still concentrating on text prompting in practice. Due to the gap of information density [19] between languages and images, prompting for vision models is more challenging and complex. Inspired by prefix tuning, VPT [26] takes the first step to adapt vision transformers to downstream tasks by preponding a set of learnable tokens at the model input. Concurrently, VP [1] follows the pixel-level perspective to optimize task-specific patches that are incorporated with input images. Despite the pioneering successes of VP and VPT, we find that they need to pre-assign the number of prompts, which is not flexible to handle the datasets with different diversities. In contrast, our method uses a diversity-adaptive solution to well address this issue.", + "bbox": [ + 496, + 296, + 893, + 809 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Transfer learning. Typically, transfer learning focuses on how to efficiently fine-tune the supervised or un-/self-supervised pre-trained model when tackling with a new task. A conventional art of transfer learning is to fully fine-tune all of the model parameters on training data of the new task, using the pretraining knowledge as model initializa", + "bbox": [ + 496, + 810, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "10879", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/ddc5462d2f02d2c5061160ca7f66786aca87b2471c65cf0ec2f397f34a7a4284.jpg", + "image_caption": [ + "Figure 2. The pipeline of our diversity-aware adaption for frozen pre-trained encoder $\\mathcal{M}$ on new task $\\mathcal{T}$ . We randomly select a little subset $S_{\\mathcal{T}}$ from the training data of task $\\mathcal{T}$ to implement agglomerative clustering and simulate prototypes of clusters. These prototypes are utilized to partition the whole training set into different subsets, so that we can optimize the prompt for each subset separately." + ], + "image_footnote": [], + "bbox": [ + 76, + 88, + 888, + 313 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "tion. However, the growing model capacity has exposed the inefficiency of fully fine-tuning, simulating the demand of parameter-efficient learning on downstream tasks, i.e., selecting or appending a few parameters for tuning and freezing the remaining of the model meanwhile. This topic has been widely explored in NLP by prepending extra learnable tokens or feature vectors [30, 31] at transformer input, whereas limited in vision which still focuses on ConvNets [5, 44, 53] and rarely on the emerging vision transformers. To mitigate this gap, recent efforts have explored to efficiently transfer vision transformers by introducing a parallel trainable down-to-up branch into the MLP module of self-attention blocks [6] or scaling and shifting the learned features [32]. VPT [26] is the pioneer work to leverage learnable prefix tokens/features for visual prompting, but still not efficient in terms of convergence time. Driven by this, our DAM-VP strives to learn faster during tuning with comparable amount of learnable parameters introduced.", + "bbox": [ + 75, + 386, + 472, + 657 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 675, + 168, + 690 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We introduce our Diversity-Aware Meta Visual Prompting (DAM-VP), a novel prompting method that is adaptive to diverse downstream datasets effectively and efficiently. As shown in Figure 2, with a given dataset, DAM-VP first extracts its specific prototypes in an unsupervised and adaptive manner as the pre-processing. Then we split the dataset into different subsets, according to the prototypes. For each subset, we assign a specific prompt to it and optimize it with the tuning loss. Rather than random initialization, all of the prompts are initialized by a meta prompt learned across different datasets, as shown in Figure 4.", + "bbox": [ + 75, + 702, + 468, + 868 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Diversity-adaptive dataset partition. As we briefly introduced in Sec. 1, different image datasets have different dis", + "bbox": [ + 75, + 869, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/f07464ec026420ba68c6cde1f4c1bdbdab8d1574937d8d5f03f3ca6271d3de33.jpg", + "image_caption": [ + "Figure 3. Examples of GTSRB (top) and SUN397 (bottom)." + ], + "image_footnote": [], + "bbox": [ + 501, + 382, + 576, + 501 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/27c6c18a514406b5773040efd14706be42fe6bc3fcbe22331196e8a4d4f15ae4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 578, + 382, + 656, + 501 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/a3c260b701b1593bf2ec4c4d0059640233bdf8dd9ea82215f053b778b4c0caff.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 658, + 382, + 735, + 501 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/7dff336bb259ab651138e4306f9bf03ebd5fdbb0641949cc58f001bbe5ba3330.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 736, + 382, + 813, + 501 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/14caf462091be32c303219021b11b53873699b9856b009fc8b94fb5caab02fef.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 813, + 382, + 892, + 501 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ribution diversity. Take Figure 3 as an example, when comparing with the traffic sign dataset [46], the data in the scene dataset [49] is more diverse in terms of angle, illumination, the complexity of content, etc. The prompting is designed to reduce the distribution gap between the target downstream dataset and the model pretraining data, and it is intuitive that a dataset with similar content is easy to transfer. So it is a straightforward idea to split a diverse dataset into small subsets and apply different prompts to each subset.", + "bbox": [ + 496, + 551, + 892, + 688 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To this end, we consider the diversity property in our visual prompting design and propose an adaptive dataset partition strategy to suit the diversity of task data automatically. Specifically, when adapting the frozen pre-trained backbone $\\mathcal{M}$ to the new task $\\mathcal{T}$ , we first randomly sample a small subset $S_{\\mathcal{T}}$ from the training set of $\\mathcal{T}$ . Then we extract the feature of subset $S_{\\mathcal{T}}$ with the frozen $\\mathcal{M}$ without any prompting. We denote the features as $\\{\\mathcal{M}(s)|s\\in S_{\\mathcal{T}}\\}$ and use an off-the-shelf clustering method [36] to aggregate them into several clusters. The clustering procedure is time-efficient (less than $1\\%$ of total tuning time) and the number of clusters $N$ is auto-adaptive to the dataset diversity by a pre-defined threshold. Once the clusters are constructed, we compute the average values for features of each cluster", + "bbox": [ + 496, + 689, + 893, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "10880", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/8f16d9eb7f77c3df1bedc155979d1606075e167876b955ae49842875ed210b43.jpg", + "image_caption": [ + "Figure 4. The pipeline of meta-learning-based prompt initialization. We partition each task dataset into subsets and regard each subset as a single meta task. During meta training on each meta batch, we continuously update the temporary prompt on each meta task set and finally apply moving average to get the updated meta prompt." + ], + "image_footnote": [], + "bbox": [ + 76, + 88, + 624, + 354 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/3bb7f79d7025e778e8b8e8a144ba5d6bb8f0303ffe3eb80f68ad9ba5c31e1bef.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 691, + 128, + 890, + 315 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "as the cluster-specific prototypes $\\{c_i\\}_{i = 1}^N$ , i.e.,", + "bbox": [ + 76, + 431, + 382, + 450 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nc _ {i} = \\frac {1}{\\left| \\mathcal {S} _ {i} \\right|} \\sum_ {s \\in \\mathcal {S} _ {i}} \\mathcal {M} (s), \\quad i = 1, \\dots , N, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 142, + 459, + 468, + 496 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $S_{i}$ is the data samples corresponding to the $i^{th}$ cluster that satisfies $|S_1| + |S_2| + \\dots + |S_N| = |S_{\\mathcal{T}}|$ . The unsupervised mechanism naturally guarantees that the dataset with a higher diversity can be divided into more clusters, and the dataset with a lower diversity can be divided into fewer clusters or even just a single cluster. In practice, we configure the threshold of clustering properly to keep $N$ in a reasonable range, usually less than the data category number.", + "bbox": [ + 75, + 507, + 468, + 628 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Diversity-aware prompt selection. With the simulated prototypes $\\{c_i\\}_{i=1}^N$ , it is easy to partition the whole training dataset $\\mathcal{D}_{\\mathcal{T}}$ of task $\\mathcal{T}$ into small subsets $\\{\\mathcal{D}_i\\}_{i=1}^N$ . Correspondingly, we assign one visual prompt for each subset and get $N$ visual prompts $\\{p_i\\}_{i=1}^N$ in total. Similar to the design in [1], we use a photo-frame-like pixel-level prompting. It has the same size as the model input and we add it to the input image directly. Such a design has two advantages: Firstly, it does not introduce additional computation cost during inference, while the prefix-token prompting used in VPT [26] increases the input length and leads to a larger computation cost. Secondly, such pixel-level prompting is irrelevant to the model type, so it could be used in both recent popular Vision Transformer models and traditional convolution networks. On the contrary, the prefix-token prompting is specifically designed for token-list-type input so that could only be used for Vision Transformer.", + "bbox": [ + 75, + 628, + 468, + 883 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given an image-label pair $(x,y)$ from the training set,", + "bbox": [ + 96, + 885, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "we forward $x$ on the frozen $\\mathcal{M}$ without prompting to get its original feature and compute the euclidean distances between the feature and each aforementioned prototype. The prompt that corresponds to the minimal distance is considered as the prompt added on $x$ . Formally, prompted image $x^p$ is defined as", + "bbox": [ + 498, + 433, + 890, + 523 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nx ^ {p} \\triangleq x + p _ {t}, \\quad \\text {s . t .} \\quad t = \\underset {i} {\\arg \\min } \\| \\mathcal {M} (x) - c _ {i} \\| _ {2} ^ {2}. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 532, + 890, + 558 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "which indicates the input image $x$ is assigned into the $t^{th}$ image subset $\\mathcal{D}_t$ .", + "bbox": [ + 498, + 566, + 888, + 598 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Prompt learning. In this paper, we seek a more general prompting format that could be utilized in different settings. 1) The head-tuning setting used in VPT [26] that a learnable classification head is optimized with the prompt jointly. 2) The head-freezing/missing setting that only the prompt is learnable. The second one is a more challenging task, but it is also a more flexible real-world usage format: we only need to add different prompts on the input for different tasks, maintaining an end-to-end frozen pre-trained model.", + "bbox": [ + 498, + 599, + 890, + 734 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For the head-tuning setting, we follow the design in VPT [26] that optimize a new $k$ -class classification head for the target task with $k$ categories. Similarly, for the head-freezing case, we assign the first $k$ classes in the frozen head to the new task. When it comes to the head-missing case that the pre-trained model does not have a classification head (such as self-supervised pre-trained models), a simple hard-coded mapping solution [1] is converted the output feature (e.g., 768 channels output feature of ViT/16-Base [14] encoder) to classification logits. However, we argue such hard-coded mapping is inefficient, because the optimization", + "bbox": [ + 496, + 734, + 892, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "10881", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "might be limited if the neurons at these fixed positions are not active enough. So we propose an active-based mapping method, which selects the most active top- $k$ neurons of the output layer of $\\mathcal{M}$ by measuring the variances of each position output when confronted with random noise inputs.", + "bbox": [ + 75, + 90, + 467, + 166 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Based on the above designs, we can minimize the cross-entropy loss between the logits of prompted image $x^p$ and ground-truth label $y$ to tune our visual prompts on $\\mathcal{D}_{\\mathcal{T}}$ , i.e.,", + "bbox": [ + 75, + 167, + 467, + 212 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\np _ {1} ^ {*}, \\dots , p _ {N} ^ {*} = \\underset {p _ {1}, \\dots , p _ {N}} {\\arg \\min } \\frac {1}{| \\mathcal {D} _ {\\mathcal {T}} |} \\sum_ {i = 1} ^ {N} \\sum_ {x \\in \\mathcal {D} _ {i}} \\mathcal {L} _ {C E} (\\mathcal {M} (x + p _ {i}), y). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 75, + 224, + 467, + 279 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Once the prompts are well-optimized, we can utilize prototypes to categorize the input image and assign it to its belonging subset during inference. The corresponding prompt is subsequently incorporated with the input image as prompted input to get the classification logits.", + "bbox": [ + 75, + 280, + 467, + 354 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Prompt boosting via Meta-learning. In real-world usage, a frozen model $\\mathcal{M}$ needs to be transferred to a bunch of downstream tasks, this leads to two desired favorable properties of the prompting method. First, it should be efficient that only a few epochs tuning could get a good result. Second, the prompts learned from previous tasks could help the new tasks learn better prompts so that the method is bootstrapped.", + "bbox": [ + 75, + 356, + 467, + 474 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In light of meta-learning [15, 39], we integrate a quick algorithm Reptile [39] into our diversity-aware learning to boost the prompting learning. The principle idea is to learn a meta prompt $p^m$ on several task datasets $\\{\\mathcal{D}_i^m\\}_{i=1}^M$ that are prepared as the meta training data, and adopt the well-trained $p^m$ as the initial prompt for diversity-aware adaption. Specifically, we first partition each task dataset into subsets, e.g., dataset $\\mathcal{D}_i^m$ is divided into $\\mathcal{D}_{i,1}^m, \\mathcal{D}_{i,2}^m, \\ldots, \\mathcal{D}_{i,K_i}^m$ . Then, we regard each subset as a single meta task and sample images from each subset to form the meta training batch $\\mathcal{B}$ , i.e., dataset $\\mathcal{D}_i^m$ contributes total $K_i$ meta task sets for $\\mathcal{B}$ . Formally, a meta training batch is constructed by", + "bbox": [ + 75, + 477, + 467, + 672 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {B} = \\bigcup_ {j = 1} ^ {K} \\mathcal {B} _ {j} \\quad \\text {s . t .} \\quad \\mathcal {B} _ {j} \\in \\mathcal {G} _ {j}. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 176, + 684, + 467, + 727 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $K$ is the total number of subsets that satisfies $K = K_{1} + K_{2} + \\dots + K_{M}$ and we rename each subset as group $\\mathcal{G}_j$ for convenience, satisfying $\\bigcup_{i=1}^{M} \\bigcup_{k=1}^{K_i} \\mathcal{D}_{i,k}^m = \\bigcup_{j=1}^{K} \\mathcal{G}_j$ .", + "bbox": [ + 76, + 738, + 467, + 787 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "With the sampled meta training batch $\\mathcal{B}$ , we can update the temporary prompt $p_j^m$ on each meta task set $\\mathcal{B}_j$ by minimizing cross-entropy loss $\\mathcal{L}_j^m$ , i.e.,", + "bbox": [ + 75, + 787, + 467, + 833 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\np _ {j} ^ {m} = p _ {j - 1} ^ {m} - \\eta \\nabla_ {p _ {j - 1} ^ {m}} \\frac {1}{| \\mathcal {B} _ {j} |} \\sum_ {x \\in \\mathcal {B} _ {j}} \\mathcal {L} _ {j} ^ {m}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 166, + 844, + 467, + 882 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\text {s . t .} \\quad \\mathcal {L} _ {j} ^ {m} = \\mathcal {L} _ {C E} (\\mathcal {M} (x + p _ {j - 1} ^ {m}), y), \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 130, + 886, + 375, + 904 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $y$ is the ground-truth label of $x$ . Finally, we implement meta update to get the new meta prompt after training on meta batch $\\mathcal{B}$ by moving average,", + "bbox": [ + 500, + 90, + 890, + 136 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\np ^ {m} \\leftarrow p ^ {m} + \\gamma \\frac {1}{K} \\sum_ {j = 1} ^ {K} \\left(p _ {j} ^ {m} - p ^ {m}\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 581, + 142, + 890, + 185 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\gamma$ is the meta update step that varies within $(0,1)$ .", + "bbox": [ + 500, + 191, + 870, + 207 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 218, + 630, + 234 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Setup", + "text_level": 1, + "bbox": [ + 500, + 243, + 580, + 258 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. Here we select 16 popular image datasets for the experiments including CIFAR10 [29], CIFAR100 [29], DTD [10], CUB200 [48], NABirds [22], Stanford-Dogs [28], Oxford-Flowers [40], Food101 [3], GTSRB [46], SVHN [37], SUN397 [49], STL10 [11], Fru92 [23], Veg200 [23], Oxford-IIIT Pet [41] and EuroSAT [21], where the first 10 datasets are used for prompt evaluation and the remaining 6 are prepared for our meta prompt initialization. For data preprocessing, we randomly resize the input image into the size of $256 \\times 256$ and subsequently crop it into $224 \\times 224$ . More details including the performance on VTAB-1k benchmark [52] are provided in supplementary.", + "bbox": [ + 498, + 266, + 890, + 446 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Models. Our experiments involve six pre-trained vision models including ImageNet-1k [12] supervised ViT-B/16 [14], supervised ResNet-50 [20], MoCo v3 [8] learned ViT-B/16; ImageNet-22k supervised ViT-B/16 and SwinBase [34]; 400m web data contrastive learning ViT-B/16 model CLIP [43]. As we illustrated above, our DAM-VP could be used for models without classification heads and traditional convolution networks, we discuss these settings in the supplementary materials.", + "bbox": [ + 498, + 448, + 890, + 582 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Baselines. We compare our method with both parameter-tuning methods and prompt-tuning methods. For parameter-tuning, we report the fully-tuning, linear probing results as baseline, and the efficient-tuning method Adapter [24, 42]. For prompt-tuning, we compare with the VP [1] and VPT [26].", + "bbox": [ + 498, + 583, + 890, + 672 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Diversity metrics. To quantitatively measure the data diversity of a given dataset, we follow [1] to randomly sample 10,000 image pairs in each dataset and compute the LPIPS distance [54] of each pair. The average LPIPS is regarded to measure the perceptual diversity of the given dataset.", + "bbox": [ + 498, + 674, + 890, + 750 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation details. For meta learning based prompt initialization, we unify update learning rate $\\eta$ (in Eq. (5)) as 0.5 and meta step size $\\gamma$ (in Eq. (6)) as 0.5. Our meta prompts of different pre-trained backbones are equally trained for 200 epochs by Adam optimizer with a cosine annealing schedule. The step number for updating the temporary prompt on each meta task is set as 4. For diversity-aware adaption, we set the subset size $|S_{\\mathcal{T}}|$ as 1000 by default. More implementation details, such as training or clustering configurations, are provided in our supplementary.", + "bbox": [ + 498, + 750, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "10882", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/b89ca6df6b1cfb4c1273a704233870862aec19b632fbe109baf00da2845e6593.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Extra HeadDTD [10]CUB200 [48]NABirds [22]Dogs [28]Flowers [40]Food101 [3]CIFAR100 [29]CIFAR10 [29]GTSRB [46]SVHN [37]Average
Data diversity-78.776.074.873.472.772.770.970.267.561.8-
Fully-Tuning✓70.684.772.384.698.383.087.597.496.896.987.2
Linear✓68.783.569.384.497.778.577.692.965.661.177.9
Adapter [24, 42]X47.717.53.832.040.146.143.072.882.219.640.5
VP [1]X47.840.613.861.956.555.754.492.986.087.859.7
VPT [26]X27.810.91.336.79.363.031.846.184.328.233.9
DAM-VP (10 epochs)X51.343.622.370.865.961.561.590.579.785.763.3
DAM-VP (50 epochs)X53.964.638.675.584.166.667.292.486.288.471.8
", + "bbox": [ + 86, + 88, + 883, + 224 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/69ff0aec04c0a43f567b7e43232908e448d4bb37186ed08b0b298e60f6d869b5.jpg", + "table_caption": [ + "Table 1. Head-freezing/missing adaption performance of different methods on ViT-B-1K, where we report image classification accuracy and all of baseline methods are trained for 50 epochs." + ], + "table_footnote": [], + "table_body": "
Extra HeadDTD [10]CUB200 [48]NABirds [22]Dogs [28]Flowers [40]Food101 [3]CIFAR100 [29]CIFAR10 [29]GTSRB [46]SVHN [37]Average
Data diversity-78.776.074.873.472.772.770.970.267.561.8-
Fully-Tuning✓78.681.972.680.597.391.880.996.395.395.787.1
Linear✓77.081.572.479.595.892.279.895.085.669.282.8
TP [43]X41.855.544.762.565.587.764.687.540.213.756.4
VP [1]X54.356.846.363.571.786.570.793.290.590.473.4
DAM-VP (10 epochs)X58.461.149.668.684.585.068.392.787.687.974.4
DAM-VP (50 epochs)X63.765.954.871.587.087.772.293.792.390.477.9
", + "bbox": [ + 86, + 276, + 883, + 402 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Comparison with Baseline Methods", + "text_level": 1, + "bbox": [ + 76, + 479, + 387, + 494 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Quantitative results. We comprehensively compare our method with the baselines mentioned in Section 4.1. Two scenarios are taken into our consideration: 1) head-freezing/missing adaption, i.e., only tuning the introduced modules like prompts without any extra task-specific head. 2) head-tuning adaption, i.e., tuning the introduced modules like prompts along with learning a task-specific head. Table 1 and 2 show the quantitative comparison results of the head-freezing/missing setting between our DAM-VP and other adaption methods. We can find that our method significantly outperforms baseline methods even when our prompts are just trained for 10 epochs. Table 4 and 5 show the quantitative comparison results of the head-tuning setting between our DAM-VP and other adaption methods. It is easy to discover that DAM-VP presents its strong ability to help pre-trained models generalize on various image datasets, surpassing other methods with fewer training epochs and higher recognition accuracy. Furthermore, our DAM-VP even outperforms the fully-tuning setting on both the ViT-B-22K model and the Swin-B-22K model with only 50 epochs tuning.", + "bbox": [ + 75, + 505, + 472, + 823 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Qualitative results. To better observe the adaption performance of each method, we depict the Top-1 accuracy curve of the first 50 training epochs to investigate the differences. Figure 7 shows the curve results of DAM-VP and the other three baselines in both head-freezing/missing and", + "bbox": [ + 75, + 824, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/05cd0cf6bb286da99c2b4b37f386fabb84dabdad1b50e122c45f13f050d11580.jpg", + "table_caption": [ + "Table 2. Head-freezing/missing adaption performance of different methods on CLIP-ViT-B, where we report image classification accuracy and all of baseline methods are trained for 50 epochs. \"TP\" denotes text prompting that directly adopts zero-shot classification head of CLIP. Here \"VP\" and our method also use this fixed head rather than particular mapping to get output logits." + ], + "table_footnote": [], + "table_body": "
SettingMetaDiversityCUB200 [48]Flowers [40]CIFAR100 [29]SVHN [37]
AXX41.259.955.187.9
B✓X43.965.759.488.1
CX✓63.381.566.988.2
D✓✓64.684.167.288.4
", + "bbox": [ + 509, + 477, + 880, + 563 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 3. Ablation results of diversity-aware strategy and metaprompt initialization. We report Top-1 accuracy on ViT-B-1K.", + "bbox": [ + 498, + 571, + 890, + 602 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "head-tuning scenarios, where four datasets with different diversities are selected. It is obvious that, the performance of DAM-VP is far ahead in the early stage, especially in the first 10 epochs. This phenomenon indicates our diversity-aware strategy can boost the efficiency of prompt optimization, since each prompt just need to learn from a group of images that already have considerable homogeneity. The design of meta-prompt initialization also benefits this quick converging of our method with a good start point.", + "bbox": [ + 496, + 626, + 893, + 763 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 771, + 653, + 787 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Component ablation. We first verify the significance of the proposed diversity-aware strategy and the meta-prompt initialization on four aforementioned datasets that have different diversities. As listed in Table 3, both two components contribute a lot to boosting prompting performance, especially when dealing with task data that has high diversity.", + "bbox": [ + 496, + 794, + 893, + 885 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Prompt learning stability. Previous methods mainly ini-", + "bbox": [ + 500, + 885, + 890, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "10883", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/430543b5698421e1944da9da6bf34fcb438ad9930ab2aa40b935bc862ca9f67f.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Extra HeadDTD [10]CUB200 [48]NABirds [22]Dogs [28]Flowers [40]Food101 [3]CIFAR100 [29]CIFAR10 [29]GTSRB [46]SVHN [37]Average
Data diversity-78.776.074.873.472.772.770.970.267.561.8-
Fully-Tuning✓64.387.382.789.498.884.968.997.497.187.485.8
Linear✓63.285.375.986.297.984.463.496.368.036.675.7
Adapter [24, 42]✓62.787.184.389.898.586.074.297.791.136.380.8
VP [1]✓59.584.677.784.597.780.578.794.289.487.683.4
VPT [26]✓65.888.584.290.299.083.378.896.890.778.185.5
DAM-VP (10 epochs)✓72.486.381.592.298.686.280.190.587.881.185.7
DAM-VP (50 epochs)✓73.187.582.192.399.286.988.197.390.687.988.5
", + "bbox": [ + 86, + 88, + 883, + 224 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/51ce5ced9d012ea4dea878ae7e4cde9a4e8b805de6eadd44cee410e59e6ca261.jpg", + "table_caption": [ + "Table 4. Head-tuning adaption performance of different methods on ViT-B-22K, where we report image classification accuracy and all of baseline methods are trained for 100 epochs." + ], + "table_footnote": [], + "table_body": "
Extra HeadDTD [10]CUB200 [48]NABirds [22]Dogs [28]Flowers [40]Food101 [3]CIFAR100 [29]CIFAR10 [29]GTSRB [46]SVHN [37]Average
Data diversity-78.776.074.873.472.772.770.970.267.561.8-
Fully-Tuning✓72.489.786.886.298.391.773.398.397.191.288.5
Linear✓73.688.685.285.999.488.261.696.383.843.580.6
Adapter [24, 42]✓73.988.584.686.898.988.785.796.583.671.385.9
VP [1]✓75.186.582.981.398.683.480.694.882.480.384.6
VPT [26]✓78.590.085.484.899.390.180.596.986.287.887.9
DAM-VP (10 epochs)✓77.089.486.888.399.690.285.596.484.779.087.7
DAM-VP (50 epochs)✓80.090.486.988.599.690.588.197.386.881.789.0
", + "bbox": [ + 86, + 276, + 883, + 414 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 5. Head-tuning adaption performance of different methods on Swin-B-22K, where we report image classification accuracy and all of baseline methods are trained for 100 epochs.", + "bbox": [ + 75, + 422, + 892, + 454 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e0171f5e7993f9c6bbff894f9d0b5c5e256adda68990a0487e5d372dfa305671.jpg", + "image_caption": [ + "Figure 5. Meta-prompt initialization makes prompt tuning more robust to the random factor. We test in both head-freezing/missing (ViT-B-1K, left) and head-tuning (ViT-B-22K, right) cases." + ], + "image_footnote": [], + "bbox": [ + 81, + 460, + 256, + 566 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/79bf899e77d719cda20f16fcfe6b41700cb79fda5a1e4a95b7338bec2871d935.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 272, + 460, + 450, + 566 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "tialize the prompt randomly, this leads to the instability of the performance caused by different random seeds. On the contrary, our meta-prompt design provides a good initialization point for optimization, which not only boosts the prompting performance but also improves the training stability. To eliminate the impact of random seeds, we test on 5 random seeds in experiments and report the results in Figure 5. It can be found that our meta-prompt initialization provides superb robustness across different training random seeds, while the randomly initialized prompt is unstable.", + "bbox": [ + 75, + 656, + 468, + 808 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Meta-prompt dataset number. As we elaborated in Sec. 4.1, there are 6 datasets prepared for our meta-prompt learning, which is also the default setting we used. Here we ablate this setting by reducing the number of meta datasets. As shown in Figure 6, when the meta dataset number is 0, i.e., no meta-prompt is used, our DVM-VP gets a rea", + "bbox": [ + 75, + 810, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/1e99316bbed12710dd07868dfa18894eb1a8aa157afe91b302195b90254b6a13.jpg", + "image_caption": [ + "Figure 6. Ablating meta-prompt dataset number on DTD in the head-freezing/missing setting (ViT-B-1K, left) and the head-tuning (ViT-B-22K, right) setting." + ], + "image_footnote": [], + "bbox": [ + 504, + 463, + 679, + 566 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f1ddfe7250423d35f4017643622cbdd2727b2d2ff08ea8677fe053ae5779cdeb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 697, + 462, + 872, + 566 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "sonable result that performs better than previous baseline methods. With the number of meta datasets increases, the prompting performance in both head-freezing/missing and head-tuning scenarios generally gets boosted. It proves that more prompting knowledge obtained from previous data is quite helpful for visual prompts to reduce the data distribution gap between downstream tasks and pretraining tasks.", + "bbox": [ + 496, + 651, + 890, + 758 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Meta-prompt update step size $\\eta$ . The step size $\\eta$ is a crucial hyper-parameter applied in the meta-prompt update. Here we ablate different step sizes that vary from 0.1 to 0.7 with the results given in Figure 8. Compared with baselines, the performance is relatively robust to different step sizes. We choose $\\eta = 0.5$ as the default configuration.", + "bbox": [ + 496, + 761, + 890, + 851 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Different size of subset $S_{\\mathcal{T}}$ . The size of subset $S_{\\mathcal{T}}$ can directly influence the clustering result and further affects the partition result during our diversity-adaptive dataset parti", + "bbox": [ + 496, + 854, + 890, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "10884", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/855aa2839977320ee5f1afe35f7ccbfdc3ab402c74df33ac795694fd8ad6d2b4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 76, + 84, + 269, + 213 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/81907a6fcc7fa754bfce2ab23582433d8dd46682efa6da643e11b78ac745d1a2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 279, + 85, + 470, + 213 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e3ca337eb47fd5b6f44c2033d365c952920b9c5e1ae19073f9fc00c9d6a4d76d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 483, + 85, + 671, + 213 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b6a91973aead1036ddd9592bddd69f4073edfc73260cc146a2cca41515aa39df.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 687, + 85, + 875, + 213 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b57aab5d9b3026440ffbc54e19aef4ee797c74b0c94019d37c5dddd9a0ddefe9.jpg", + "image_caption": [ + "Figure 7. Test accuracy curves of different adaption methods when adapting pre-trained ViT-B-1K to different datasets in head-freezing/missing scenario (top row) and adapting pre-trained ViT-B-22K to different datasets head-tuning scenario (bottom row)." + ], + "image_footnote": [], + "bbox": [ + 76, + 222, + 267, + 351 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5afecc478053bcc0f9945b81902c0c99251ee90271dce06861bd9cd2bdd3e6ba.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 281, + 222, + 468, + 351 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f04f2ff2bfe014b5d7b4ef40d1b503077b2962ca94c62f0d24da34d210bc26df.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 483, + 222, + 673, + 351 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/658b3fa38396dde180ad06a181399b9bd69e2c1886cea99a2883ab86e5e08924.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 687, + 222, + 875, + 351 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d6cd6ade1929a2934cf2f561a7ca2b99cacd772b9f95e8ed0303989a9ae7480f.jpg", + "image_caption": [ + "Figure 8. Ablating step size $\\eta$ on DTD in head-freezing/missing (ViT-B-1K, left) and head-tuning (ViT-B-22K, right) cases." + ], + "image_footnote": [], + "bbox": [ + 81, + 400, + 254, + 503 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d3385c8b9e70e325bcd883aeaf43c1f70745903897972c608c8da1ea3cd2d491.jpg", + "image_caption": [ + "Figure 9. (Left) Ablating the size of subset $S_{\\mathcal{T}}$ in both head-freezing/missing (ViT-B-1K) and head-tuning (ViT-B-22K) cases. (Right) Comparison between hard-coded mapping and our active-based mapping used for head-freezing/missing case." + ], + "image_footnote": [], + "bbox": [ + 277, + 400, + 450, + 503 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "tion. Therefore, we apply different subset size that varies from 200 to 1000 to explore how it affects the prompting ability. From Figure 9 (left), we find that as the size of $S_{\\mathcal{T}}$ increases, we can get higher performance in both scenarios. Meanwhile, we find our divide-and-conquer design is quite efficient that even with only 200 images, our DAM-VP still outperforms previous methods by a large margin. Considering the training images of some datasets are limited, we adopt 1,000 as the default size of $S_{\\mathcal{T}}$ in this work.", + "bbox": [ + 75, + 570, + 468, + 705 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Hard-coded mapping vs. Active-based mapping. As we discussed in Sec. 3, we argue the hard-coded mapping used by [1] for head-freezing/missing scenario is inefficient, since it might optimize some not active enough channels of the output feature (i.e., relatively robust to diverse model input), thus we propose active-based mapping to alleviate this issue. Figure 9 (right) show the comparison between these two mapping methods on VP, tested on ViT-B-1K.", + "bbox": [ + 75, + 707, + 470, + 829 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 844, + 194, + 859 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper considers the data diversity property in downstream task adaption for prompting pre-trained vision mod", + "bbox": [ + 76, + 869, + 468, + 902 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/51acf8463bbd579ba26bb727998517dd03fc400378bf0fc932d699e267088f89.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 501, + 400, + 696, + 503 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1def4f4642983b51b438edf51c1b924f032369450ffa6a15705bfeac967432a5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 700, + 400, + 872, + 503 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "els. We argue that the per-dataset generic prompt adopt in previous methods can hardly handle the dataset of large data diversity. To address this, we propose DAM-VP based on diversity-adaptive dataset partition and prompt selection, where our prompts is initialized by a meta-prompt that learns through a quick meta learning algorithm. Extensive experiments prove the superior performance of DAM-VP in both head-freezing/missing and head-tuning cases.", + "bbox": [ + 496, + 598, + 890, + 719 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement. This work was supported in part by the Natural Science Foundation of China under Grant U20B2047, 62072421, 62002334, 62102386 and 62121002, Key Research and Development program of Anhui Province under Grant 2022k07020008, the Fundamental Research Funds for the Central Universities under Grant WK5290000003, Ant Group through CCF-Ant Innovative Research Program CCF-AFSG RF20210025, Alibaba Group through Alibaba Innovative Research Program. This work was also partly supported by Shenzhen Key Laboratory of Media Security, Shenzhen University, Shenzhen 518060, China.", + "bbox": [ + 496, + 719, + 892, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "10885", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Hyojin Bahng, Ali Jahanian, Swami Sankaranarayanan, and Phillip Isola. Exploring visual prompts for adapting large-scale models. arXiv preprint arXiv:2203.17274, 2022. 1, 2, 4, 5, 6, 7, 8", + "[2] Hangbo Bao, Li Dong, Songhao Piao, and Furu Wei. Beit: Bert pre-training of image transformers. In ICLR, 2021. 1", + "[3] Lukas Bossard, Matthieu Guillaumin, and Luc Van Gool. Food-101 - mining discriminative components with random forests. 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IJCV, 2022. 2" + ], + "bbox": [ + 501, + 90, + 890, + 458 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "10887", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Diversity-Aware Meta Visual Prompting/ab39c456-2bd7-4413-8ddf-e238b3250192_model.json b/2023/Diversity-Aware Meta Visual Prompting/ab39c456-2bd7-4413-8ddf-e238b3250192_model.json new file mode 100644 index 0000000000000000000000000000000000000000..e8884ca6cf496ba31a21c7d6a4e220bde6eab5f4 --- /dev/null +++ b/2023/Diversity-Aware Meta Visual Prompting/ab39c456-2bd7-4413-8ddf-e238b3250192_model.json @@ -0,0 +1,2134 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.282, + 0.131, + 0.69, + 0.154 + ], + "angle": 0, + "content": "Diversity-Aware Meta Visual Prompting" + }, + { + "type": "text", + "bbox": [ + 0.094, + 0.179, + 0.874, + 0.273 + ], + "angle": 0, + "content": "Qidong Huang\\(^{1}\\) Xiaoyi Dong\\(^{1}\\) Dongdong Chen\\(^{2}\\) Weiming Zhang\\(^{1,*}\\) Feifei Wang\\(^{1}\\) Gang Hua\\(^{3}\\) Nenghai Yu\\(^{1}\\) \n\\(^{1}\\)University of Science and Technology of China \\(^{2}\\)Microsoft Cloud AI \\(^{3}\\)Wormpex AI Research {hqd0037@mail., dlight@mail., zhangwm@, wangfeifei@mail., ynh@}ustc.edu.cn {cddlyf@, ganghua@}gmail.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.304, + 0.314, + 0.321 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.337, + 0.474, + 0.761 + ], + "angle": 0, + "content": "We present Diversity-Aware Meta Visual Prompting (DAM-VP), an efficient and effective prompting method for transferring pre-trained models to downstream tasks with frozen backbone. A challenging issue in visual prompting is that image datasets sometimes have a large data diversity whereas a per-dataset generic prompt can hardly handle the complex distribution shift toward the original pretraining data distribution properly. To address this issue, we propose a dataset Diversity-Aware prompting strategy whose initialization is realized by a Meta-prompt. Specifically, we cluster the downstream dataset into small homogeneity subsets in a diversity-adaptive way, with each subset has its own prompt optimized separately. Such a divide-and-conquer design reduces the optimization difficulty greatly and significantly boosts the prompting performance. Furthermore, all the prompts are initialized with a meta-prompt, which is learned across several datasets. It is a bootstrapped paradigm, with the key observation that the prompting knowledge learned from previous datasets could help the prompt to converge faster and perform better on a new dataset. During inference, we dynamically select a proper prompt for each input, based on the feature distance between the input and each subset. Through extensive experiments, our DAM-VP demonstrates superior efficiency and effectiveness, clearly surpassing previous prompting methods in a series of downstream datasets for different pretraining models. Our code is available at: https://github.com/shikiw/DAM-VP." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.79, + 0.21, + 0.807 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.816, + 0.47, + 0.878 + ], + "angle": 0, + "content": "With the increasing scale of training data and model size, the pretraining-finetuning paradigm has shown remarkable achievement in many areas, including natural language processing (NLP) [4, 13] and computer vision (CV) [2,7,8,19]." + }, + { + "type": "image", + "bbox": [ + 0.509, + 0.304, + 0.887, + 0.438 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.449, + 0.895, + 0.534 + ], + "angle": 0, + "content": "Figure 1. Relation between dataset diversity and the performance gain got by using prompting. The gain is the performance improvement when compared with the linear-probing accuracy, under the head-tuning setting. Both previous methods get a large performance gain on low-diversity datasets, while failing to boost the transfer performance on high-diversity datasets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.564, + 0.895, + 0.67 + ], + "angle": 0, + "content": "However, fully finetuning a large pre-trained model for each small downstream task still has some problems in real-world usage. The most practical one is the storage and distribution problem that we have to maintain an independent copy of the model for each task, which is quite expensive and inflexible, especially for increasing numbers of downstream tasks [9]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.672, + 0.896, + 0.868 + ], + "angle": 0, + "content": "To break the dilemma, many efforts [6,17,18,25,51] have been paid to efficiently transfer the given pre-trained models into a particular dataset. Prompting is an extensively studied method in the NLP area, which appends a few tokens before the input sequence to provide some task-specific knowledge to the pre-trained model, so that the model could adapt well on the downstream tasks without the fully-finetuning. Inspired by the success of prompting in NLP, some recent works [1, 26] propose visual prompting for vision models. By adding some learnable noise onto the input image or appending some learnable tokens to the model input sequence, the pre-trained models show promising results on different kinds of downstream tasks." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.895, + 0.903 + ], + "angle": 0, + "content": "However, we argue that these methods ignore the diverse distribution property of the image dataset and using a sin-" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.224, + 0.901 + ], + "angle": 0, + "content": "*Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "10878" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.333 + ], + "angle": 0, + "content": "gle prompt for all the images in each dataset is not optimal. In Figure 1, we show the relationship between the gain from prompting and the diversity of the dataset. Here the gain represents the accuracy improvement compared with the linear probing setting. We find that both VP [1] and VPT [26] improve the model accuracy by a large margin on the low-diversity dataset, but relatively small gains on the high-diversity datasets, which is intuitively sensible. For low-diversity datasets, such as the street view house number dataset (SVHN) [37], all the images have similar content so a unified prompt is sufficient. On the contrary, when it comes to high-diversity datasets, such as the ImageNet [12] dataset, it covers very diverse classes from the wordnet and there is not any pre-defined relationship between the classes, so it is hard to use a single prompt to provide the prior for all the images, such as for \"car\" and \"dog\"." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.334, + 0.473, + 0.605 + ], + "angle": 0, + "content": "Motivated by this observation, we propose our Diversity-Aware Meta Visual Prompting (DAM-VP). It has two core designs. Firstly, to provide a proper prompt for each image from high-diversity datasets, we propose a clustering-based prompt selection method. In detail, given a pre-trained visual model and a downstream dataset, we use the off-the-shelf clustering method to cluster the feature of the downstream data into several coarse-grained subsets, and guide each cluster to learn its own prompt separately. Based on the strong homogeneity of the same clustered data, the optimization of cluster-specific visual prompts can be greatly facilitated and the data commonalities can be also easily covered. Secondly, we argue the prompt across different clusters or datasets may have some shared pattern, from which the model can be adapted to a new dataset faster and get better performance. This motivates us to introduce a meta-learning-based method that learns a meta prompt and initializes the prompt of each cluster with it." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.606, + 0.473, + 0.846 + ], + "angle": 0, + "content": "We conduct our experiments on datasets with different data diversity and evaluate the transfer performance with different pre-trained models. We report the performance on both the widely used head-tuning setting and a more challenging head-freezing/missing setting. Our DAM-VP outperforms previous methods by a large margin, especially on high-diversity datasets. For example, with the ImageNet22k pre-trained ViT-B model, DAM-VP gets \\(73.1\\%\\) top-1 accuracy under the head-tuning setting on the diverse DTD [10] dataset, surpassing previous methods VP [1] and VPT [26] with \\(+13.6\\%\\) and \\(+7.3\\%\\) respectively. Meanwhile, we find DAM-VP is quite efficient that with only 10 epoch tuning, it gets \\(85.7\\%\\) average top-1 accuracy over the 10 datasets, comparable with previous methods that tunes 100 epochs (83.4% for VP [1] and 85.5% for VPT [26]). Our contributions can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.856, + 0.472, + 0.903 + ], + "angle": 0, + "content": "- We analyze the limitation of previous visual prompting methods, and point out that vision-suitable prompting should consider the dataset diversity." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.092, + 0.892, + 0.182 + ], + "angle": 0, + "content": "- Accordingly, we propose a novel Diversity-Aware Meta Visual Prompting (DAM-VP) method. It uses the divide-and-conquer idea by clustering high-diversity datasets into subsets and learning separate prompts for each subset, in cooperation with a meta-prompt learning design." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.195, + 0.894, + 0.256 + ], + "angle": 0, + "content": "- Through extensive experiments, our DAM-VP demonstrates superior performance, achieving SOTA performance in a series of downstream datasets for different pretraining models." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.271, + 0.642, + 0.287 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.297, + 0.895, + 0.81 + ], + "angle": 0, + "content": "Prompt learning. Served as a new paradigm, prompting [33] originally emerges in NLP for adapting pre-trained language models (PLM) [4, 13] to downstream tasks. Its principle idea is to reformulate downstream data into the model knowledge learned during the pretraining phase, enabling the frozen pre-trained model to understand the task rather than tuning the model parameters for adaption. This goal has been initially reached through constructing pure text prompts that contains task-specific templates and label words to perform cloze test, e.g., hand-craft prompts [16] and generative text prompts [27, 45], but unfortunately, still requiring specialized linguistic expertise for preparation. To alleviate this, recent efforts have been paid on prompt tuning (PT) [30, 31] that learns a task-specific continuous vector as tunable prefix tokens. These tokens can be optimized via gradients to act as prompts in task adaptation while maintaining the pre-trained model untouched. Driven by the success of language prompts, a lot of works [35, 38, 43, 47, 50, 55], like CoOP [57] and CoCoOP [56], have been mushroomed to explore vision-related prompting especially in multi-modal scenarios, while still concentrating on text prompting in practice. Due to the gap of information density [19] between languages and images, prompting for vision models is more challenging and complex. Inspired by prefix tuning, VPT [26] takes the first step to adapt vision transformers to downstream tasks by preponding a set of learnable tokens at the model input. Concurrently, VP [1] follows the pixel-level perspective to optimize task-specific patches that are incorporated with input images. Despite the pioneering successes of VP and VPT, we find that they need to pre-assign the number of prompts, which is not flexible to handle the datasets with different diversities. In contrast, our method uses a diversity-adaptive solution to well address this issue." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Transfer learning. Typically, transfer learning focuses on how to efficiently fine-tune the supervised or un-/self-supervised pre-trained model when tackling with a new task. A conventional art of transfer learning is to fully fine-tune all of the model parameters on training data of the new task, using the pretraining knowledge as model initializa" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "10879" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.089, + 0.889, + 0.314 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.318, + 0.893, + 0.361 + ], + "angle": 0, + "content": "Figure 2. The pipeline of our diversity-aware adaption for frozen pre-trained encoder \\(\\mathcal{M}\\) on new task \\(\\mathcal{T}\\). We randomly select a little subset \\(S_{\\mathcal{T}}\\) from the training data of task \\(\\mathcal{T}\\) to implement agglomerative clustering and simulate prototypes of clusters. These prototypes are utilized to partition the whole training set into different subsets, so that we can optimize the prompt for each subset separately." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.387, + 0.473, + 0.659 + ], + "angle": 0, + "content": "tion. However, the growing model capacity has exposed the inefficiency of fully fine-tuning, simulating the demand of parameter-efficient learning on downstream tasks, i.e., selecting or appending a few parameters for tuning and freezing the remaining of the model meanwhile. This topic has been widely explored in NLP by prepending extra learnable tokens or feature vectors [30, 31] at transformer input, whereas limited in vision which still focuses on ConvNets [5, 44, 53] and rarely on the emerging vision transformers. To mitigate this gap, recent efforts have explored to efficiently transfer vision transformers by introducing a parallel trainable down-to-up branch into the MLP module of self-attention blocks [6] or scaling and shifting the learned features [32]. VPT [26] is the pioneer work to leverage learnable prefix tokens/features for visual prompting, but still not efficient in terms of convergence time. Driven by this, our DAM-VP strives to learn faster during tuning with comparable amount of learnable parameters introduced." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.676, + 0.169, + 0.691 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.703, + 0.47, + 0.869 + ], + "angle": 0, + "content": "We introduce our Diversity-Aware Meta Visual Prompting (DAM-VP), a novel prompting method that is adaptive to diverse downstream datasets effectively and efficiently. As shown in Figure 2, with a given dataset, DAM-VP first extracts its specific prototypes in an unsupervised and adaptive manner as the pre-processing. Then we split the dataset into different subsets, according to the prototypes. For each subset, we assign a specific prompt to it and optimize it with the tuning loss. Rather than random initialization, all of the prompts are initialized by a meta prompt learned across different datasets, as shown in Figure 4." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Diversity-adaptive dataset partition. As we briefly introduced in Sec. 1, different image datasets have different dis" + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.383, + 0.578, + 0.502 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.58, + 0.383, + 0.657, + 0.502 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.659, + 0.383, + 0.736, + 0.502 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.737, + 0.383, + 0.814, + 0.502 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.815, + 0.383, + 0.893, + 0.502 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.514, + 0.512, + 0.877, + 0.527 + ], + "angle": 0, + "content": "Figure 3. Examples of GTSRB (top) and SUN397 (bottom)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.553, + 0.893, + 0.689 + ], + "angle": 0, + "content": "ribution diversity. Take Figure 3 as an example, when comparing with the traffic sign dataset [46], the data in the scene dataset [49] is more diverse in terms of angle, illumination, the complexity of content, etc. The prompting is designed to reduce the distribution gap between the target downstream dataset and the model pretraining data, and it is intuitive that a dataset with similar content is easy to transfer. So it is a straightforward idea to split a diverse dataset into small subsets and apply different prompts to each subset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.69, + 0.895, + 0.901 + ], + "angle": 0, + "content": "To this end, we consider the diversity property in our visual prompting design and propose an adaptive dataset partition strategy to suit the diversity of task data automatically. Specifically, when adapting the frozen pre-trained backbone \\(\\mathcal{M}\\) to the new task \\(\\mathcal{T}\\), we first randomly sample a small subset \\(S_{\\mathcal{T}}\\) from the training set of \\(\\mathcal{T}\\). Then we extract the feature of subset \\(S_{\\mathcal{T}}\\) with the frozen \\(\\mathcal{M}\\) without any prompting. We denote the features as \\(\\{\\mathcal{M}(s)|s\\in S_{\\mathcal{T}}\\}\\) and use an off-the-shelf clustering method [36] to aggregate them into several clusters. The clustering procedure is time-efficient (less than \\(1\\%\\) of total tuning time) and the number of clusters \\(N\\) is auto-adaptive to the dataset diversity by a pre-defined threshold. Once the clusters are constructed, we compute the average values for features of each cluster" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10880" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.089, + 0.625, + 0.356 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.692, + 0.129, + 0.891, + 0.316 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.365, + 0.893, + 0.409 + ], + "angle": 0, + "content": "Figure 4. The pipeline of meta-learning-based prompt initialization. We partition each task dataset into subsets and regard each subset as a single meta task. During meta training on each meta batch, we continuously update the temporary prompt on each meta task set and finally apply moving average to get the updated meta prompt." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.433, + 0.383, + 0.451 + ], + "angle": 0, + "content": "as the cluster-specific prototypes \\(\\{c_i\\}_{i = 1}^N\\) , i.e.," + }, + { + "type": "equation", + "bbox": [ + 0.143, + 0.46, + 0.469, + 0.497 + ], + "angle": 0, + "content": "\\[\nc _ {i} = \\frac {1}{\\left| \\mathcal {S} _ {i} \\right|} \\sum_ {s \\in \\mathcal {S} _ {i}} \\mathcal {M} (s), \\quad i = 1, \\dots , N, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.508, + 0.469, + 0.629 + ], + "angle": 0, + "content": "where \\( S_{i} \\) is the data samples corresponding to the \\( i^{th} \\) cluster that satisfies \\( |S_1| + |S_2| + \\dots + |S_N| = |S_{\\mathcal{T}}| \\). The unsupervised mechanism naturally guarantees that the dataset with a higher diversity can be divided into more clusters, and the dataset with a lower diversity can be divided into fewer clusters or even just a single cluster. In practice, we configure the threshold of clustering properly to keep \\( N \\) in a reasonable range, usually less than the data category number." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.63, + 0.469, + 0.885 + ], + "angle": 0, + "content": "Diversity-aware prompt selection. With the simulated prototypes \\(\\{c_i\\}_{i=1}^N\\), it is easy to partition the whole training dataset \\(\\mathcal{D}_{\\mathcal{T}}\\) of task \\(\\mathcal{T}\\) into small subsets \\(\\{\\mathcal{D}_i\\}_{i=1}^N\\). Correspondingly, we assign one visual prompt for each subset and get \\(N\\) visual prompts \\(\\{p_i\\}_{i=1}^N\\) in total. Similar to the design in [1], we use a photo-frame-like pixel-level prompting. It has the same size as the model input and we add it to the input image directly. Such a design has two advantages: Firstly, it does not introduce additional computation cost during inference, while the prefix-token prompting used in VPT [26] increases the input length and leads to a larger computation cost. Secondly, such pixel-level prompting is irrelevant to the model type, so it could be used in both recent popular Vision Transformer models and traditional convolution networks. On the contrary, the prefix-token prompting is specifically designed for token-list-type input so that could only be used for Vision Transformer." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.469, + 0.902 + ], + "angle": 0, + "content": "Given an image-label pair \\((x,y)\\) from the training set," + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.434, + 0.892, + 0.524 + ], + "angle": 0, + "content": "we forward \\( x \\) on the frozen \\( \\mathcal{M} \\) without prompting to get its original feature and compute the euclidean distances between the feature and each aforementioned prototype. The prompt that corresponds to the minimal distance is considered as the prompt added on \\( x \\). Formally, prompted image \\( x^p \\) is defined as" + }, + { + "type": "equation", + "bbox": [ + 0.52, + 0.533, + 0.892, + 0.559 + ], + "angle": 0, + "content": "\\[\nx ^ {p} \\triangleq x + p _ {t}, \\quad \\text {s . t .} \\quad t = \\underset {i} {\\arg \\min } \\| \\mathcal {M} (x) - c _ {i} \\| _ {2} ^ {2}. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.568, + 0.89, + 0.599 + ], + "angle": 0, + "content": "which indicates the input image \\( x \\) is assigned into the \\( t^{th} \\) image subset \\( \\mathcal{D}_t \\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.6, + 0.892, + 0.735 + ], + "angle": 0, + "content": "Prompt learning. In this paper, we seek a more general prompting format that could be utilized in different settings. 1) The head-tuning setting used in VPT [26] that a learnable classification head is optimized with the prompt jointly. 2) The head-freezing/missing setting that only the prompt is learnable. The second one is a more challenging task, but it is also a more flexible real-world usage format: we only need to add different prompts on the input for different tasks, maintaining an end-to-end frozen pre-trained model." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.893, + 0.901 + ], + "angle": 0, + "content": "For the head-tuning setting, we follow the design in VPT [26] that optimize a new \\(k\\)-class classification head for the target task with \\(k\\) categories. Similarly, for the head-freezing case, we assign the first \\(k\\) classes in the frozen head to the new task. When it comes to the head-missing case that the pre-trained model does not have a classification head (such as self-supervised pre-trained models), a simple hard-coded mapping solution [1] is converted the output feature (e.g., 768 channels output feature of ViT/16-Base [14] encoder) to classification logits. However, we argue such hard-coded mapping is inefficient, because the optimization" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "10881" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.468, + 0.167 + ], + "angle": 0, + "content": "might be limited if the neurons at these fixed positions are not active enough. So we propose an active-based mapping method, which selects the most active top-\\(k\\) neurons of the output layer of \\(\\mathcal{M}\\) by measuring the variances of each position output when confronted with random noise inputs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.168, + 0.468, + 0.213 + ], + "angle": 0, + "content": "Based on the above designs, we can minimize the cross-entropy loss between the logits of prompted image \\( x^p \\) and ground-truth label \\( y \\) to tune our visual prompts on \\( \\mathcal{D}_{\\mathcal{T}} \\), i.e.," + }, + { + "type": "equation", + "bbox": [ + 0.076, + 0.225, + 0.468, + 0.28 + ], + "angle": 0, + "content": "\\[\np _ {1} ^ {*}, \\dots , p _ {N} ^ {*} = \\underset {p _ {1}, \\dots , p _ {N}} {\\arg \\min } \\frac {1}{| \\mathcal {D} _ {\\mathcal {T}} |} \\sum_ {i = 1} ^ {N} \\sum_ {x \\in \\mathcal {D} _ {i}} \\mathcal {L} _ {C E} (\\mathcal {M} (x + p _ {i}), y). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.281, + 0.468, + 0.356 + ], + "angle": 0, + "content": "Once the prompts are well-optimized, we can utilize prototypes to categorize the input image and assign it to its belonging subset during inference. The corresponding prompt is subsequently incorporated with the input image as prompted input to get the classification logits." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.357, + 0.468, + 0.476 + ], + "angle": 0, + "content": "Prompt boosting via Meta-learning. In real-world usage, a frozen model \\(\\mathcal{M}\\) needs to be transferred to a bunch of downstream tasks, this leads to two desired favorable properties of the prompting method. First, it should be efficient that only a few epochs tuning could get a good result. Second, the prompts learned from previous tasks could help the new tasks learn better prompts so that the method is bootstrapped." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.478, + 0.468, + 0.673 + ], + "angle": 0, + "content": "In light of meta-learning [15, 39], we integrate a quick algorithm Reptile [39] into our diversity-aware learning to boost the prompting learning. The principle idea is to learn a meta prompt \\( p^m \\) on several task datasets \\( \\{\\mathcal{D}_i^m\\}_{i=1}^M \\) that are prepared as the meta training data, and adopt the well-trained \\( p^m \\) as the initial prompt for diversity-aware adaption. Specifically, we first partition each task dataset into subsets, e.g., dataset \\( \\mathcal{D}_i^m \\) is divided into \\( \\mathcal{D}_{i,1}^m, \\mathcal{D}_{i,2}^m, \\ldots, \\mathcal{D}_{i,K_i}^m \\). Then, we regard each subset as a single meta task and sample images from each subset to form the meta training batch \\( \\mathcal{B} \\), i.e., dataset \\( \\mathcal{D}_i^m \\) contributes total \\( K_i \\) meta task sets for \\( \\mathcal{B} \\). Formally, a meta training batch is constructed by" + }, + { + "type": "equation", + "bbox": [ + 0.177, + 0.685, + 0.468, + 0.728 + ], + "angle": 0, + "content": "\\[\n\\mathcal {B} = \\bigcup_ {j = 1} ^ {K} \\mathcal {B} _ {j} \\quad \\text {s . t .} \\quad \\mathcal {B} _ {j} \\in \\mathcal {G} _ {j}. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.739, + 0.468, + 0.788 + ], + "angle": 0, + "content": "where \\(K\\) is the total number of subsets that satisfies \\(K = K_{1} + K_{2} + \\dots + K_{M}\\) and we rename each subset as group \\(\\mathcal{G}_j\\) for convenience, satisfying \\(\\bigcup_{i=1}^{M} \\bigcup_{k=1}^{K_i} \\mathcal{D}_{i,k}^m = \\bigcup_{j=1}^{K} \\mathcal{G}_j\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.788, + 0.468, + 0.834 + ], + "angle": 0, + "content": "With the sampled meta training batch \\(\\mathcal{B}\\), we can update the temporary prompt \\(p_j^m\\) on each meta task set \\(\\mathcal{B}_j\\) by minimizing cross-entropy loss \\(\\mathcal{L}_j^m\\), i.e.," + }, + { + "type": "equation", + "bbox": [ + 0.168, + 0.845, + 0.468, + 0.883 + ], + "angle": 0, + "content": "\\[\np _ {j} ^ {m} = p _ {j - 1} ^ {m} - \\eta \\nabla_ {p _ {j - 1} ^ {m}} \\frac {1}{| \\mathcal {B} _ {j} |} \\sum_ {x \\in \\mathcal {B} _ {j}} \\mathcal {L} _ {j} ^ {m}, \\tag {5}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.132, + 0.887, + 0.376, + 0.905 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\text {s . t .} \\quad \\mathcal {L} _ {j} ^ {m} = \\mathcal {L} _ {C E} (\\mathcal {M} (x + p _ {j - 1} ^ {m}), y), \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.891, + 0.137 + ], + "angle": 0, + "content": "where \\(y\\) is the ground-truth label of \\(x\\). Finally, we implement meta update to get the new meta prompt after training on meta batch \\(\\mathcal{B}\\) by moving average," + }, + { + "type": "equation", + "bbox": [ + 0.583, + 0.143, + 0.891, + 0.186 + ], + "angle": 0, + "content": "\\[\np ^ {m} \\leftarrow p ^ {m} + \\gamma \\frac {1}{K} \\sum_ {j = 1} ^ {K} \\left(p _ {j} ^ {m} - p ^ {m}\\right), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.192, + 0.871, + 0.208 + ], + "angle": 0, + "content": "where \\(\\gamma\\) is the meta update step that varies within \\((0,1)\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.219, + 0.632, + 0.236 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.244, + 0.581, + 0.26 + ], + "angle": 0, + "content": "4.1. Setup" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.267, + 0.892, + 0.448 + ], + "angle": 0, + "content": "Datasets. Here we select 16 popular image datasets for the experiments including CIFAR10 [29], CIFAR100 [29], DTD [10], CUB200 [48], NABirds [22], Stanford-Dogs [28], Oxford-Flowers [40], Food101 [3], GTSRB [46], SVHN [37], SUN397 [49], STL10 [11], Fru92 [23], Veg200 [23], Oxford-IIIT Pet [41] and EuroSAT [21], where the first 10 datasets are used for prompt evaluation and the remaining 6 are prepared for our meta prompt initialization. For data preprocessing, we randomly resize the input image into the size of \\(256 \\times 256\\) and subsequently crop it into \\(224 \\times 224\\). More details including the performance on VTAB-1k benchmark [52] are provided in supplementary." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.449, + 0.892, + 0.583 + ], + "angle": 0, + "content": "Models. Our experiments involve six pre-trained vision models including ImageNet-1k [12] supervised ViT-B/16 [14], supervised ResNet-50 [20], MoCo v3 [8] learned ViT-B/16; ImageNet-22k supervised ViT-B/16 and SwinBase [34]; 400m web data contrastive learning ViT-B/16 model CLIP [43]. As we illustrated above, our DAM-VP could be used for models without classification heads and traditional convolution networks, we discuss these settings in the supplementary materials." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.584, + 0.891, + 0.674 + ], + "angle": 0, + "content": "Baselines. We compare our method with both parameter-tuning methods and prompt-tuning methods. For parameter-tuning, we report the fully-tuning, linear probing results as baseline, and the efficient-tuning method Adapter [24, 42]. For prompt-tuning, we compare with the VP [1] and VPT [26]." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.675, + 0.891, + 0.75 + ], + "angle": 0, + "content": "Diversity metrics. To quantitatively measure the data diversity of a given dataset, we follow [1] to randomly sample 10,000 image pairs in each dataset and compute the LPIPS distance [54] of each pair. The average LPIPS is regarded to measure the perceptual diversity of the given dataset." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Implementation details. For meta learning based prompt initialization, we unify update learning rate \\(\\eta\\) (in Eq. (5)) as 0.5 and meta step size \\(\\gamma\\) (in Eq. (6)) as 0.5. Our meta prompts of different pre-trained backbones are equally trained for 200 epochs by Adam optimizer with a cosine annealing schedule. The step number for updating the temporary prompt on each meta task is set as 4. For diversity-aware adaption, we set the subset size \\(|S_{\\mathcal{T}}|\\) as 1000 by default. More implementation details, such as training or clustering configurations, are provided in our supplementary." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10882" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.087, + 0.089, + 0.885, + 0.226 + ], + "angle": 0, + "content": "
Extra HeadDTD [10]CUB200 [48]NABirds [22]Dogs [28]Flowers [40]Food101 [3]CIFAR100 [29]CIFAR10 [29]GTSRB [46]SVHN [37]Average
Data diversity-78.776.074.873.472.772.770.970.267.561.8-
Fully-Tuning✓70.684.772.384.698.383.087.597.496.896.987.2
Linear✓68.783.569.384.497.778.577.692.965.661.177.9
Adapter [24, 42]X47.717.53.832.040.146.143.072.882.219.640.5
VP [1]X47.840.613.861.956.555.754.492.986.087.859.7
VPT [26]X27.810.91.336.79.363.031.846.184.328.233.9
DAM-VP (10 epochs)X51.343.622.370.865.961.561.590.579.785.763.3
DAM-VP (50 epochs)X53.964.638.675.584.166.667.292.486.288.471.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.235, + 0.893, + 0.266 + ], + "angle": 0, + "content": "Table 1. Head-freezing/missing adaption performance of different methods on ViT-B-1K, where we report image classification accuracy and all of baseline methods are trained for 50 epochs." + }, + { + "type": "table", + "bbox": [ + 0.087, + 0.277, + 0.885, + 0.403 + ], + "angle": 0, + "content": "
Extra HeadDTD [10]CUB200 [48]NABirds [22]Dogs [28]Flowers [40]Food101 [3]CIFAR100 [29]CIFAR10 [29]GTSRB [46]SVHN [37]Average
Data diversity-78.776.074.873.472.772.770.970.267.561.8-
Fully-Tuning✓78.681.972.680.597.391.880.996.395.395.787.1
Linear✓77.081.572.479.595.892.279.895.085.669.282.8
TP [43]X41.855.544.762.565.587.764.687.540.213.756.4
VP [1]X54.356.846.363.571.786.570.793.290.590.473.4
DAM-VP (10 epochs)X58.461.149.668.684.585.068.392.787.687.974.4
DAM-VP (50 epochs)X63.765.954.871.587.087.772.293.792.390.477.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.412, + 0.893, + 0.456 + ], + "angle": 0, + "content": "Table 2. Head-freezing/missing adaption performance of different methods on CLIP-ViT-B, where we report image classification accuracy and all of baseline methods are trained for 50 epochs. \"TP\" denotes text prompting that directly adopts zero-shot classification head of CLIP. Here \"VP\" and our method also use this fixed head rather than particular mapping to get output logits." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.48, + 0.388, + 0.496 + ], + "angle": 0, + "content": "4.2. Comparison with Baseline Methods" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.506, + 0.473, + 0.824 + ], + "angle": 0, + "content": "Quantitative results. We comprehensively compare our method with the baselines mentioned in Section 4.1. Two scenarios are taken into our consideration: 1) head-freezing/missing adaption, i.e., only tuning the introduced modules like prompts without any extra task-specific head. 2) head-tuning adaption, i.e., tuning the introduced modules like prompts along with learning a task-specific head. Table 1 and 2 show the quantitative comparison results of the head-freezing/missing setting between our DAM-VP and other adaption methods. We can find that our method significantly outperforms baseline methods even when our prompts are just trained for 10 epochs. Table 4 and 5 show the quantitative comparison results of the head-tuning setting between our DAM-VP and other adaption methods. It is easy to discover that DAM-VP presents its strong ability to help pre-trained models generalize on various image datasets, surpassing other methods with fewer training epochs and higher recognition accuracy. Furthermore, our DAM-VP even outperforms the fully-tuning setting on both the ViT-B-22K model and the Swin-B-22K model with only 50 epochs tuning." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Qualitative results. To better observe the adaption performance of each method, we depict the Top-1 accuracy curve of the first 50 training epochs to investigate the differences. Figure 7 shows the curve results of DAM-VP and the other three baselines in both head-freezing/missing and" + }, + { + "type": "table", + "bbox": [ + 0.51, + 0.478, + 0.882, + 0.564 + ], + "angle": 0, + "content": "
SettingMetaDiversityCUB200 [48]Flowers [40]CIFAR100 [29]SVHN [37]
AXX41.259.955.187.9
B✓X43.965.759.488.1
CX✓63.381.566.988.2
D✓✓64.684.167.288.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.573, + 0.892, + 0.603 + ], + "angle": 0, + "content": "Table 3. Ablation results of diversity-aware strategy and metaprompt initialization. We report Top-1 accuracy on ViT-B-1K." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.627, + 0.895, + 0.765 + ], + "angle": 0, + "content": "head-tuning scenarios, where four datasets with different diversities are selected. It is obvious that, the performance of DAM-VP is far ahead in the early stage, especially in the first 10 epochs. This phenomenon indicates our diversity-aware strategy can boost the efficiency of prompt optimization, since each prompt just need to learn from a group of images that already have considerable homogeneity. The design of meta-prompt initialization also benefits this quick converging of our method with a good start point." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.772, + 0.655, + 0.789 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.894, + 0.886 + ], + "angle": 0, + "content": "Component ablation. We first verify the significance of the proposed diversity-aware strategy and the meta-prompt initialization on four aforementioned datasets that have different diversities. As listed in Table 3, both two components contribute a lot to boosting prompting performance, especially when dealing with task data that has high diversity." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Prompt learning stability. Previous methods mainly ini-" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10883" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.088, + 0.089, + 0.885, + 0.226 + ], + "angle": 0, + "content": "
Extra HeadDTD [10]CUB200 [48]NABirds [22]Dogs [28]Flowers [40]Food101 [3]CIFAR100 [29]CIFAR10 [29]GTSRB [46]SVHN [37]Average
Data diversity-78.776.074.873.472.772.770.970.267.561.8-
Fully-Tuning✓64.387.382.789.498.884.968.997.497.187.485.8
Linear✓63.285.375.986.297.984.463.496.368.036.675.7
Adapter [24, 42]✓62.787.184.389.898.586.074.297.791.136.380.8
VP [1]✓59.584.677.784.597.780.578.794.289.487.683.4
VPT [26]✓65.888.584.290.299.083.378.896.890.778.185.5
DAM-VP (10 epochs)✓72.486.381.592.298.686.280.190.587.881.185.7
DAM-VP (50 epochs)✓73.187.582.192.399.286.988.197.390.687.988.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.235, + 0.895, + 0.266 + ], + "angle": 0, + "content": "Table 4. Head-tuning adaption performance of different methods on ViT-B-22K, where we report image classification accuracy and all of baseline methods are trained for 100 epochs." + }, + { + "type": "table", + "bbox": [ + 0.088, + 0.277, + 0.885, + 0.415 + ], + "angle": 0, + "content": "
Extra HeadDTD [10]CUB200 [48]NABirds [22]Dogs [28]Flowers [40]Food101 [3]CIFAR100 [29]CIFAR10 [29]GTSRB [46]SVHN [37]Average
Data diversity-78.776.074.873.472.772.770.970.267.561.8-
Fully-Tuning✓72.489.786.886.298.391.773.398.397.191.288.5
Linear✓73.688.685.285.999.488.261.696.383.843.580.6
Adapter [24, 42]✓73.988.584.686.898.988.785.796.583.671.385.9
VP [1]✓75.186.582.981.398.683.480.694.882.480.384.6
VPT [26]✓78.590.085.484.899.390.180.596.986.287.887.9
DAM-VP (10 epochs)✓77.089.486.888.399.690.285.596.484.779.087.7
DAM-VP (50 epochs)✓80.090.486.988.599.690.588.197.386.881.789.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.424, + 0.893, + 0.455 + ], + "angle": 0, + "content": "Table 5. Head-tuning adaption performance of different methods on Swin-B-22K, where we report image classification accuracy and all of baseline methods are trained for 100 epochs." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.462, + 0.258, + 0.568 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.274, + 0.462, + 0.452, + 0.567 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.584, + 0.471, + 0.629 + ], + "angle": 0, + "content": "Figure 5. Meta-prompt initialization makes prompt tuning more robust to the random factor. We test in both head-freezing/missing (ViT-B-1K, left) and head-tuning (ViT-B-22K, right) cases." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.657, + 0.47, + 0.809 + ], + "angle": 0, + "content": "tialize the prompt randomly, this leads to the instability of the performance caused by different random seeds. On the contrary, our meta-prompt design provides a good initialization point for optimization, which not only boosts the prompting performance but also improves the training stability. To eliminate the impact of random seeds, we test on 5 random seeds in experiments and report the results in Figure 5. It can be found that our meta-prompt initialization provides superb robustness across different training random seeds, while the randomly initialized prompt is unstable." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Meta-prompt dataset number. As we elaborated in Sec. 4.1, there are 6 datasets prepared for our meta-prompt learning, which is also the default setting we used. Here we ablate this setting by reducing the number of meta datasets. As shown in Figure 6, when the meta dataset number is 0, i.e., no meta-prompt is used, our DVM-VP gets a rea" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.464, + 0.68, + 0.567 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.463, + 0.874, + 0.567 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.576, + 0.892, + 0.618 + ], + "angle": 0, + "content": "Figure 6. Ablating meta-prompt dataset number on DTD in the head-freezing/missing setting (ViT-B-1K, left) and the head-tuning (ViT-B-22K, right) setting." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.652, + 0.892, + 0.759 + ], + "angle": 0, + "content": "sonable result that performs better than previous baseline methods. With the number of meta datasets increases, the prompting performance in both head-freezing/missing and head-tuning scenarios generally gets boosted. It proves that more prompting knowledge obtained from previous data is quite helpful for visual prompts to reduce the data distribution gap between downstream tasks and pretraining tasks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.762, + 0.892, + 0.852 + ], + "angle": 0, + "content": "Meta-prompt update step size \\(\\eta\\). The step size \\(\\eta\\) is a crucial hyper-parameter applied in the meta-prompt update. Here we ablate different step sizes that vary from 0.1 to 0.7 with the results given in Figure 8. Compared with baselines, the performance is relatively robust to different step sizes. We choose \\(\\eta = 0.5\\) as the default configuration." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Different size of subset \\( S_{\\mathcal{T}} \\). The size of subset \\( S_{\\mathcal{T}} \\) can directly influence the clustering result and further affects the partition result during our diversity-adaptive dataset parti" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "10884" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.085, + 0.271, + 0.214 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.281, + 0.086, + 0.471, + 0.214 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.484, + 0.086, + 0.673, + 0.214 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.688, + 0.086, + 0.877, + 0.214 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.077, + 0.223, + 0.268, + 0.352 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.282, + 0.223, + 0.47, + 0.352 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.485, + 0.223, + 0.674, + 0.352 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.689, + 0.223, + 0.877, + 0.352 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.361, + 0.892, + 0.391 + ], + "angle": 0, + "content": "Figure 7. Test accuracy curves of different adaption methods when adapting pre-trained ViT-B-1K to different datasets in head-freezing/missing scenario (top row) and adapting pre-trained ViT-B-22K to different datasets head-tuning scenario (bottom row)." + }, + { + "type": "image", + "bbox": [ + 0.083, + 0.401, + 0.256, + 0.504 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.278, + 0.401, + 0.451, + 0.505 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.515, + 0.47, + 0.545 + ], + "angle": 0, + "content": "Figure 8. Ablating step size \\(\\eta\\) on DTD in head-freezing/missing (ViT-B-1K, left) and head-tuning (ViT-B-22K, right) cases." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.571, + 0.47, + 0.707 + ], + "angle": 0, + "content": "tion. Therefore, we apply different subset size that varies from 200 to 1000 to explore how it affects the prompting ability. From Figure 9 (left), we find that as the size of \\( S_{\\mathcal{T}} \\) increases, we can get higher performance in both scenarios. Meanwhile, we find our divide-and-conquer design is quite efficient that even with only 200 images, our DAM-VP still outperforms previous methods by a large margin. Considering the training images of some datasets are limited, we adopt 1,000 as the default size of \\( S_{\\mathcal{T}} \\) in this work." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.708, + 0.471, + 0.83 + ], + "angle": 0, + "content": "Hard-coded mapping vs. Active-based mapping. As we discussed in Sec. 3, we argue the hard-coded mapping used by [1] for head-freezing/missing scenario is inefficient, since it might optimize some not active enough channels of the output feature (i.e., relatively robust to diverse model input), thus we propose active-based mapping to alleviate this issue. Figure 9 (right) show the comparison between these two mapping methods on VP, tested on ViT-B-1K." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.845, + 0.196, + 0.86 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.903 + ], + "angle": 0, + "content": "This paper considers the data diversity property in downstream task adaption for prompting pre-trained vision mod" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.401, + 0.697, + 0.505 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.701, + 0.401, + 0.874, + 0.505 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.522, + 0.892, + 0.579 + ], + "angle": 0, + "content": "Figure 9. (Left) Ablating the size of subset \\( S_{\\mathcal{T}} \\) in both head-freezing/missing (ViT-B-1K) and head-tuning (ViT-B-22K) cases. (Right) Comparison between hard-coded mapping and our active-based mapping used for head-freezing/missing case." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.892, + 0.72 + ], + "angle": 0, + "content": "els. We argue that the per-dataset generic prompt adopt in previous methods can hardly handle the dataset of large data diversity. To address this, we propose DAM-VP based on diversity-adaptive dataset partition and prompt selection, where our prompts is initialized by a meta-prompt that learns through a quick meta learning algorithm. Extensive experiments prove the superior performance of DAM-VP in both head-freezing/missing and head-tuning cases." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.893, + 0.9 + ], + "angle": 0, + "content": "Acknowledgement. This work was supported in part by the Natural Science Foundation of China under Grant U20B2047, 62072421, 62002334, 62102386 and 62121002, Key Research and Development program of Anhui Province under Grant 2022k07020008, the Fundamental Research Funds for the Central Universities under Grant WK5290000003, Ant Group through CCF-Ant Innovative Research Program CCF-AFSG RF20210025, Alibaba Group through Alibaba Innovative Research Program. This work was also partly supported by Shenzhen Key Laboratory of Media Security, Shenzhen University, Shenzhen 518060, China." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10885" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.117, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Hyojin Bahng, Ali Jahanian, Swami Sankaranarayanan, and Phillip Isola. Exploring visual prompts for adapting large-scale models. arXiv preprint arXiv:2203.17274, 2022. 1, 2, 4, 5, 6, 7, 8" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.174, + 0.468, + 0.202 + ], + "angle": 0, + "content": "[2] Hangbo Bao, Li Dong, Songhao Piao, and Furu Wei. Beit: Bert pre-training of image transformers. 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IJCV, 2022. 2" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.092, + 0.892, + 0.459 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.956 + ], + "angle": 0, + "content": "10887" + } + ] +] \ No newline at end of file diff --git a/2023/Diversity-Aware Meta Visual Prompting/ab39c456-2bd7-4413-8ddf-e238b3250192_origin.pdf b/2023/Diversity-Aware Meta Visual Prompting/ab39c456-2bd7-4413-8ddf-e238b3250192_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..39042ca57acb7ebcfb911d3b06f935aeb98d3b48 --- /dev/null +++ b/2023/Diversity-Aware Meta Visual Prompting/ab39c456-2bd7-4413-8ddf-e238b3250192_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:fa5e22c39cc4edf21df894551266787ca5fea84f8ff892c008c9401e3cd32e50 +size 1311190 diff --git a/2023/Diversity-Aware Meta Visual Prompting/full.md b/2023/Diversity-Aware Meta Visual Prompting/full.md new file mode 100644 index 0000000000000000000000000000000000000000..6eb2725db270df7545561b502ad7289524eb65f2 --- /dev/null +++ b/2023/Diversity-Aware Meta Visual Prompting/full.md @@ -0,0 +1,301 @@ +# Diversity-Aware Meta Visual Prompting + +Qidong Huang $^{1}$ Xiaoyi Dong $^{1}$ Dongdong Chen $^{2}$ Weiming Zhang $^{1,*}$ Feifei Wang $^{1}$ Gang Hua $^{3}$ Nenghai Yu $^{1}$ $^{1}$ University of Science and Technology of China $^{2}$ Microsoft Cloud AI $^{3}$ Wormpex AI Research {hqd0037@mail., dlight@mail., zhangwm@, wangfeifei@mail., ynh@}ustc.edu.cn {cddlyf@, ganghua@}gmail.com + +# Abstract + +We present Diversity-Aware Meta Visual Prompting (DAM-VP), an efficient and effective prompting method for transferring pre-trained models to downstream tasks with frozen backbone. A challenging issue in visual prompting is that image datasets sometimes have a large data diversity whereas a per-dataset generic prompt can hardly handle the complex distribution shift toward the original pretraining data distribution properly. To address this issue, we propose a dataset Diversity-Aware prompting strategy whose initialization is realized by a Meta-prompt. Specifically, we cluster the downstream dataset into small homogeneity subsets in a diversity-adaptive way, with each subset has its own prompt optimized separately. Such a divide-and-conquer design reduces the optimization difficulty greatly and significantly boosts the prompting performance. Furthermore, all the prompts are initialized with a meta-prompt, which is learned across several datasets. It is a bootstrapped paradigm, with the key observation that the prompting knowledge learned from previous datasets could help the prompt to converge faster and perform better on a new dataset. During inference, we dynamically select a proper prompt for each input, based on the feature distance between the input and each subset. Through extensive experiments, our DAM-VP demonstrates superior efficiency and effectiveness, clearly surpassing previous prompting methods in a series of downstream datasets for different pretraining models. Our code is available at: https://github.com/shikiw/DAM-VP. + +# 1. Introduction + +With the increasing scale of training data and model size, the pretraining-finetuning paradigm has shown remarkable achievement in many areas, including natural language processing (NLP) [4, 13] and computer vision (CV) [2,7,8,19]. + +![](images/abafc6ff1f6bac34c17bdd9e7abfb951fad4628ac6ce0d82864e3ebe7eca070a.jpg) +Figure 1. Relation between dataset diversity and the performance gain got by using prompting. The gain is the performance improvement when compared with the linear-probing accuracy, under the head-tuning setting. Both previous methods get a large performance gain on low-diversity datasets, while failing to boost the transfer performance on high-diversity datasets. + +However, fully finetuning a large pre-trained model for each small downstream task still has some problems in real-world usage. The most practical one is the storage and distribution problem that we have to maintain an independent copy of the model for each task, which is quite expensive and inflexible, especially for increasing numbers of downstream tasks [9]. + +To break the dilemma, many efforts [6,17,18,25,51] have been paid to efficiently transfer the given pre-trained models into a particular dataset. Prompting is an extensively studied method in the NLP area, which appends a few tokens before the input sequence to provide some task-specific knowledge to the pre-trained model, so that the model could adapt well on the downstream tasks without the fully-finetuning. Inspired by the success of prompting in NLP, some recent works [1, 26] propose visual prompting for vision models. By adding some learnable noise onto the input image or appending some learnable tokens to the model input sequence, the pre-trained models show promising results on different kinds of downstream tasks. + +However, we argue that these methods ignore the diverse distribution property of the image dataset and using a sin- + +gle prompt for all the images in each dataset is not optimal. In Figure 1, we show the relationship between the gain from prompting and the diversity of the dataset. Here the gain represents the accuracy improvement compared with the linear probing setting. We find that both VP [1] and VPT [26] improve the model accuracy by a large margin on the low-diversity dataset, but relatively small gains on the high-diversity datasets, which is intuitively sensible. For low-diversity datasets, such as the street view house number dataset (SVHN) [37], all the images have similar content so a unified prompt is sufficient. On the contrary, when it comes to high-diversity datasets, such as the ImageNet [12] dataset, it covers very diverse classes from the wordnet and there is not any pre-defined relationship between the classes, so it is hard to use a single prompt to provide the prior for all the images, such as for "car" and "dog". + +Motivated by this observation, we propose our Diversity-Aware Meta Visual Prompting (DAM-VP). It has two core designs. Firstly, to provide a proper prompt for each image from high-diversity datasets, we propose a clustering-based prompt selection method. In detail, given a pre-trained visual model and a downstream dataset, we use the off-the-shelf clustering method to cluster the feature of the downstream data into several coarse-grained subsets, and guide each cluster to learn its own prompt separately. Based on the strong homogeneity of the same clustered data, the optimization of cluster-specific visual prompts can be greatly facilitated and the data commonalities can be also easily covered. Secondly, we argue the prompt across different clusters or datasets may have some shared pattern, from which the model can be adapted to a new dataset faster and get better performance. This motivates us to introduce a meta-learning-based method that learns a meta prompt and initializes the prompt of each cluster with it. + +We conduct our experiments on datasets with different data diversity and evaluate the transfer performance with different pre-trained models. We report the performance on both the widely used head-tuning setting and a more challenging head-freezing/missing setting. Our DAM-VP outperforms previous methods by a large margin, especially on high-diversity datasets. For example, with the ImageNet22k pre-trained ViT-B model, DAM-VP gets $73.1\%$ top-1 accuracy under the head-tuning setting on the diverse DTD [10] dataset, surpassing previous methods VP [1] and VPT [26] with $+13.6\%$ and $+7.3\%$ respectively. Meanwhile, we find DAM-VP is quite efficient that with only 10 epoch tuning, it gets $85.7\%$ average top-1 accuracy over the 10 datasets, comparable with previous methods that tunes 100 epochs (83.4% for VP [1] and 85.5% for VPT [26]). Our contributions can be summarized as follows: + +- We analyze the limitation of previous visual prompting methods, and point out that vision-suitable prompting should consider the dataset diversity. + +- Accordingly, we propose a novel Diversity-Aware Meta Visual Prompting (DAM-VP) method. It uses the divide-and-conquer idea by clustering high-diversity datasets into subsets and learning separate prompts for each subset, in cooperation with a meta-prompt learning design. + +- Through extensive experiments, our DAM-VP demonstrates superior performance, achieving SOTA performance in a series of downstream datasets for different pretraining models. + +# 2. Related Work + +Prompt learning. Served as a new paradigm, prompting [33] originally emerges in NLP for adapting pre-trained language models (PLM) [4, 13] to downstream tasks. Its principle idea is to reformulate downstream data into the model knowledge learned during the pretraining phase, enabling the frozen pre-trained model to understand the task rather than tuning the model parameters for adaption. This goal has been initially reached through constructing pure text prompts that contains task-specific templates and label words to perform cloze test, e.g., hand-craft prompts [16] and generative text prompts [27, 45], but unfortunately, still requiring specialized linguistic expertise for preparation. To alleviate this, recent efforts have been paid on prompt tuning (PT) [30, 31] that learns a task-specific continuous vector as tunable prefix tokens. These tokens can be optimized via gradients to act as prompts in task adaptation while maintaining the pre-trained model untouched. Driven by the success of language prompts, a lot of works [35, 38, 43, 47, 50, 55], like CoOP [57] and CoCoOP [56], have been mushroomed to explore vision-related prompting especially in multi-modal scenarios, while still concentrating on text prompting in practice. Due to the gap of information density [19] between languages and images, prompting for vision models is more challenging and complex. Inspired by prefix tuning, VPT [26] takes the first step to adapt vision transformers to downstream tasks by preponding a set of learnable tokens at the model input. Concurrently, VP [1] follows the pixel-level perspective to optimize task-specific patches that are incorporated with input images. Despite the pioneering successes of VP and VPT, we find that they need to pre-assign the number of prompts, which is not flexible to handle the datasets with different diversities. In contrast, our method uses a diversity-adaptive solution to well address this issue. + +Transfer learning. Typically, transfer learning focuses on how to efficiently fine-tune the supervised or un-/self-supervised pre-trained model when tackling with a new task. A conventional art of transfer learning is to fully fine-tune all of the model parameters on training data of the new task, using the pretraining knowledge as model initializa + +![](images/ddc5462d2f02d2c5061160ca7f66786aca87b2471c65cf0ec2f397f34a7a4284.jpg) +Figure 2. The pipeline of our diversity-aware adaption for frozen pre-trained encoder $\mathcal{M}$ on new task $\mathcal{T}$ . We randomly select a little subset $S_{\mathcal{T}}$ from the training data of task $\mathcal{T}$ to implement agglomerative clustering and simulate prototypes of clusters. These prototypes are utilized to partition the whole training set into different subsets, so that we can optimize the prompt for each subset separately. + +tion. However, the growing model capacity has exposed the inefficiency of fully fine-tuning, simulating the demand of parameter-efficient learning on downstream tasks, i.e., selecting or appending a few parameters for tuning and freezing the remaining of the model meanwhile. This topic has been widely explored in NLP by prepending extra learnable tokens or feature vectors [30, 31] at transformer input, whereas limited in vision which still focuses on ConvNets [5, 44, 53] and rarely on the emerging vision transformers. To mitigate this gap, recent efforts have explored to efficiently transfer vision transformers by introducing a parallel trainable down-to-up branch into the MLP module of self-attention blocks [6] or scaling and shifting the learned features [32]. VPT [26] is the pioneer work to leverage learnable prefix tokens/features for visual prompting, but still not efficient in terms of convergence time. Driven by this, our DAM-VP strives to learn faster during tuning with comparable amount of learnable parameters introduced. + +# 3. Method + +We introduce our Diversity-Aware Meta Visual Prompting (DAM-VP), a novel prompting method that is adaptive to diverse downstream datasets effectively and efficiently. As shown in Figure 2, with a given dataset, DAM-VP first extracts its specific prototypes in an unsupervised and adaptive manner as the pre-processing. Then we split the dataset into different subsets, according to the prototypes. For each subset, we assign a specific prompt to it and optimize it with the tuning loss. Rather than random initialization, all of the prompts are initialized by a meta prompt learned across different datasets, as shown in Figure 4. + +Diversity-adaptive dataset partition. As we briefly introduced in Sec. 1, different image datasets have different dis + +![](images/f07464ec026420ba68c6cde1f4c1bdbdab8d1574937d8d5f03f3ca6271d3de33.jpg) +Figure 3. Examples of GTSRB (top) and SUN397 (bottom). + +![](images/27c6c18a514406b5773040efd14706be42fe6bc3fcbe22331196e8a4d4f15ae4.jpg) + +![](images/a3c260b701b1593bf2ec4c4d0059640233bdf8dd9ea82215f053b778b4c0caff.jpg) + +![](images/7dff336bb259ab651138e4306f9bf03ebd5fdbb0641949cc58f001bbe5ba3330.jpg) + +![](images/14caf462091be32c303219021b11b53873699b9856b009fc8b94fb5caab02fef.jpg) + +ribution diversity. Take Figure 3 as an example, when comparing with the traffic sign dataset [46], the data in the scene dataset [49] is more diverse in terms of angle, illumination, the complexity of content, etc. The prompting is designed to reduce the distribution gap between the target downstream dataset and the model pretraining data, and it is intuitive that a dataset with similar content is easy to transfer. So it is a straightforward idea to split a diverse dataset into small subsets and apply different prompts to each subset. + +To this end, we consider the diversity property in our visual prompting design and propose an adaptive dataset partition strategy to suit the diversity of task data automatically. Specifically, when adapting the frozen pre-trained backbone $\mathcal{M}$ to the new task $\mathcal{T}$ , we first randomly sample a small subset $S_{\mathcal{T}}$ from the training set of $\mathcal{T}$ . Then we extract the feature of subset $S_{\mathcal{T}}$ with the frozen $\mathcal{M}$ without any prompting. We denote the features as $\{\mathcal{M}(s)|s\in S_{\mathcal{T}}\}$ and use an off-the-shelf clustering method [36] to aggregate them into several clusters. The clustering procedure is time-efficient (less than $1\%$ of total tuning time) and the number of clusters $N$ is auto-adaptive to the dataset diversity by a pre-defined threshold. Once the clusters are constructed, we compute the average values for features of each cluster + +![](images/8f16d9eb7f77c3df1bedc155979d1606075e167876b955ae49842875ed210b43.jpg) +Figure 4. The pipeline of meta-learning-based prompt initialization. We partition each task dataset into subsets and regard each subset as a single meta task. During meta training on each meta batch, we continuously update the temporary prompt on each meta task set and finally apply moving average to get the updated meta prompt. + +![](images/3bb7f79d7025e778e8b8e8a144ba5d6bb8f0303ffe3eb80f68ad9ba5c31e1bef.jpg) + +as the cluster-specific prototypes $\{c_i\}_{i = 1}^N$ , i.e., + +$$ +c _ {i} = \frac {1}{\left| \mathcal {S} _ {i} \right|} \sum_ {s \in \mathcal {S} _ {i}} \mathcal {M} (s), \quad i = 1, \dots , N, \tag {1} +$$ + +where $S_{i}$ is the data samples corresponding to the $i^{th}$ cluster that satisfies $|S_1| + |S_2| + \dots + |S_N| = |S_{\mathcal{T}}|$ . The unsupervised mechanism naturally guarantees that the dataset with a higher diversity can be divided into more clusters, and the dataset with a lower diversity can be divided into fewer clusters or even just a single cluster. In practice, we configure the threshold of clustering properly to keep $N$ in a reasonable range, usually less than the data category number. + +Diversity-aware prompt selection. With the simulated prototypes $\{c_i\}_{i=1}^N$ , it is easy to partition the whole training dataset $\mathcal{D}_{\mathcal{T}}$ of task $\mathcal{T}$ into small subsets $\{\mathcal{D}_i\}_{i=1}^N$ . Correspondingly, we assign one visual prompt for each subset and get $N$ visual prompts $\{p_i\}_{i=1}^N$ in total. Similar to the design in [1], we use a photo-frame-like pixel-level prompting. It has the same size as the model input and we add it to the input image directly. Such a design has two advantages: Firstly, it does not introduce additional computation cost during inference, while the prefix-token prompting used in VPT [26] increases the input length and leads to a larger computation cost. Secondly, such pixel-level prompting is irrelevant to the model type, so it could be used in both recent popular Vision Transformer models and traditional convolution networks. On the contrary, the prefix-token prompting is specifically designed for token-list-type input so that could only be used for Vision Transformer. + +Given an image-label pair $(x,y)$ from the training set, + +we forward $x$ on the frozen $\mathcal{M}$ without prompting to get its original feature and compute the euclidean distances between the feature and each aforementioned prototype. The prompt that corresponds to the minimal distance is considered as the prompt added on $x$ . Formally, prompted image $x^p$ is defined as + +$$ +x ^ {p} \triangleq x + p _ {t}, \quad \text {s . t .} \quad t = \underset {i} {\arg \min } \| \mathcal {M} (x) - c _ {i} \| _ {2} ^ {2}. \tag {2} +$$ + +which indicates the input image $x$ is assigned into the $t^{th}$ image subset $\mathcal{D}_t$ . + +Prompt learning. In this paper, we seek a more general prompting format that could be utilized in different settings. 1) The head-tuning setting used in VPT [26] that a learnable classification head is optimized with the prompt jointly. 2) The head-freezing/missing setting that only the prompt is learnable. The second one is a more challenging task, but it is also a more flexible real-world usage format: we only need to add different prompts on the input for different tasks, maintaining an end-to-end frozen pre-trained model. + +For the head-tuning setting, we follow the design in VPT [26] that optimize a new $k$ -class classification head for the target task with $k$ categories. Similarly, for the head-freezing case, we assign the first $k$ classes in the frozen head to the new task. When it comes to the head-missing case that the pre-trained model does not have a classification head (such as self-supervised pre-trained models), a simple hard-coded mapping solution [1] is converted the output feature (e.g., 768 channels output feature of ViT/16-Base [14] encoder) to classification logits. However, we argue such hard-coded mapping is inefficient, because the optimization + +might be limited if the neurons at these fixed positions are not active enough. So we propose an active-based mapping method, which selects the most active top- $k$ neurons of the output layer of $\mathcal{M}$ by measuring the variances of each position output when confronted with random noise inputs. + +Based on the above designs, we can minimize the cross-entropy loss between the logits of prompted image $x^p$ and ground-truth label $y$ to tune our visual prompts on $\mathcal{D}_{\mathcal{T}}$ , i.e., + +$$ +p _ {1} ^ {*}, \dots , p _ {N} ^ {*} = \underset {p _ {1}, \dots , p _ {N}} {\arg \min } \frac {1}{| \mathcal {D} _ {\mathcal {T}} |} \sum_ {i = 1} ^ {N} \sum_ {x \in \mathcal {D} _ {i}} \mathcal {L} _ {C E} (\mathcal {M} (x + p _ {i}), y). \tag {3} +$$ + +Once the prompts are well-optimized, we can utilize prototypes to categorize the input image and assign it to its belonging subset during inference. The corresponding prompt is subsequently incorporated with the input image as prompted input to get the classification logits. + +Prompt boosting via Meta-learning. In real-world usage, a frozen model $\mathcal{M}$ needs to be transferred to a bunch of downstream tasks, this leads to two desired favorable properties of the prompting method. First, it should be efficient that only a few epochs tuning could get a good result. Second, the prompts learned from previous tasks could help the new tasks learn better prompts so that the method is bootstrapped. + +In light of meta-learning [15, 39], we integrate a quick algorithm Reptile [39] into our diversity-aware learning to boost the prompting learning. The principle idea is to learn a meta prompt $p^m$ on several task datasets $\{\mathcal{D}_i^m\}_{i=1}^M$ that are prepared as the meta training data, and adopt the well-trained $p^m$ as the initial prompt for diversity-aware adaption. Specifically, we first partition each task dataset into subsets, e.g., dataset $\mathcal{D}_i^m$ is divided into $\mathcal{D}_{i,1}^m, \mathcal{D}_{i,2}^m, \ldots, \mathcal{D}_{i,K_i}^m$ . Then, we regard each subset as a single meta task and sample images from each subset to form the meta training batch $\mathcal{B}$ , i.e., dataset $\mathcal{D}_i^m$ contributes total $K_i$ meta task sets for $\mathcal{B}$ . Formally, a meta training batch is constructed by + +$$ +\mathcal {B} = \bigcup_ {j = 1} ^ {K} \mathcal {B} _ {j} \quad \text {s . t .} \quad \mathcal {B} _ {j} \in \mathcal {G} _ {j}. \tag {4} +$$ + +where $K$ is the total number of subsets that satisfies $K = K_{1} + K_{2} + \dots + K_{M}$ and we rename each subset as group $\mathcal{G}_j$ for convenience, satisfying $\bigcup_{i=1}^{M} \bigcup_{k=1}^{K_i} \mathcal{D}_{i,k}^m = \bigcup_{j=1}^{K} \mathcal{G}_j$ . + +With the sampled meta training batch $\mathcal{B}$ , we can update the temporary prompt $p_j^m$ on each meta task set $\mathcal{B}_j$ by minimizing cross-entropy loss $\mathcal{L}_j^m$ , i.e., + +$$ +p _ {j} ^ {m} = p _ {j - 1} ^ {m} - \eta \nabla_ {p _ {j - 1} ^ {m}} \frac {1}{| \mathcal {B} _ {j} |} \sum_ {x \in \mathcal {B} _ {j}} \mathcal {L} _ {j} ^ {m}, \tag {5} +$$ + +$$ +\begin{array}{l} \text {s . t .} \quad \mathcal {L} _ {j} ^ {m} = \mathcal {L} _ {C E} (\mathcal {M} (x + p _ {j - 1} ^ {m}), y), \end{array} +$$ + +where $y$ is the ground-truth label of $x$ . Finally, we implement meta update to get the new meta prompt after training on meta batch $\mathcal{B}$ by moving average, + +$$ +p ^ {m} \leftarrow p ^ {m} + \gamma \frac {1}{K} \sum_ {j = 1} ^ {K} \left(p _ {j} ^ {m} - p ^ {m}\right), \tag {6} +$$ + +where $\gamma$ is the meta update step that varies within $(0,1)$ . + +# 4. Experiments + +# 4.1. Setup + +Datasets. Here we select 16 popular image datasets for the experiments including CIFAR10 [29], CIFAR100 [29], DTD [10], CUB200 [48], NABirds [22], Stanford-Dogs [28], Oxford-Flowers [40], Food101 [3], GTSRB [46], SVHN [37], SUN397 [49], STL10 [11], Fru92 [23], Veg200 [23], Oxford-IIIT Pet [41] and EuroSAT [21], where the first 10 datasets are used for prompt evaluation and the remaining 6 are prepared for our meta prompt initialization. For data preprocessing, we randomly resize the input image into the size of $256 \times 256$ and subsequently crop it into $224 \times 224$ . More details including the performance on VTAB-1k benchmark [52] are provided in supplementary. + +Models. Our experiments involve six pre-trained vision models including ImageNet-1k [12] supervised ViT-B/16 [14], supervised ResNet-50 [20], MoCo v3 [8] learned ViT-B/16; ImageNet-22k supervised ViT-B/16 and SwinBase [34]; 400m web data contrastive learning ViT-B/16 model CLIP [43]. As we illustrated above, our DAM-VP could be used for models without classification heads and traditional convolution networks, we discuss these settings in the supplementary materials. + +Baselines. We compare our method with both parameter-tuning methods and prompt-tuning methods. For parameter-tuning, we report the fully-tuning, linear probing results as baseline, and the efficient-tuning method Adapter [24, 42]. For prompt-tuning, we compare with the VP [1] and VPT [26]. + +Diversity metrics. To quantitatively measure the data diversity of a given dataset, we follow [1] to randomly sample 10,000 image pairs in each dataset and compute the LPIPS distance [54] of each pair. The average LPIPS is regarded to measure the perceptual diversity of the given dataset. + +Implementation details. For meta learning based prompt initialization, we unify update learning rate $\eta$ (in Eq. (5)) as 0.5 and meta step size $\gamma$ (in Eq. (6)) as 0.5. Our meta prompts of different pre-trained backbones are equally trained for 200 epochs by Adam optimizer with a cosine annealing schedule. The step number for updating the temporary prompt on each meta task is set as 4. For diversity-aware adaption, we set the subset size $|S_{\mathcal{T}}|$ as 1000 by default. More implementation details, such as training or clustering configurations, are provided in our supplementary. + +
Extra HeadDTD [10]CUB200 [48]NABirds [22]Dogs [28]Flowers [40]Food101 [3]CIFAR100 [29]CIFAR10 [29]GTSRB [46]SVHN [37]Average
Data diversity-78.776.074.873.472.772.770.970.267.561.8-
Fully-Tuning✓70.684.772.384.698.383.087.597.496.896.987.2
Linear✓68.783.569.384.497.778.577.692.965.661.177.9
Adapter [24, 42]X47.717.53.832.040.146.143.072.882.219.640.5
VP [1]X47.840.613.861.956.555.754.492.986.087.859.7
VPT [26]X27.810.91.336.79.363.031.846.184.328.233.9
DAM-VP (10 epochs)X51.343.622.370.865.961.561.590.579.785.763.3
DAM-VP (50 epochs)X53.964.638.675.584.166.667.292.486.288.471.8
+ +Table 1. Head-freezing/missing adaption performance of different methods on ViT-B-1K, where we report image classification accuracy and all of baseline methods are trained for 50 epochs. + +
Extra HeadDTD [10]CUB200 [48]NABirds [22]Dogs [28]Flowers [40]Food101 [3]CIFAR100 [29]CIFAR10 [29]GTSRB [46]SVHN [37]Average
Data diversity-78.776.074.873.472.772.770.970.267.561.8-
Fully-Tuning✓78.681.972.680.597.391.880.996.395.395.787.1
Linear✓77.081.572.479.595.892.279.895.085.669.282.8
TP [43]X41.855.544.762.565.587.764.687.540.213.756.4
VP [1]X54.356.846.363.571.786.570.793.290.590.473.4
DAM-VP (10 epochs)X58.461.149.668.684.585.068.392.787.687.974.4
DAM-VP (50 epochs)X63.765.954.871.587.087.772.293.792.390.477.9
+ +# 4.2. Comparison with Baseline Methods + +Quantitative results. We comprehensively compare our method with the baselines mentioned in Section 4.1. Two scenarios are taken into our consideration: 1) head-freezing/missing adaption, i.e., only tuning the introduced modules like prompts without any extra task-specific head. 2) head-tuning adaption, i.e., tuning the introduced modules like prompts along with learning a task-specific head. Table 1 and 2 show the quantitative comparison results of the head-freezing/missing setting between our DAM-VP and other adaption methods. We can find that our method significantly outperforms baseline methods even when our prompts are just trained for 10 epochs. Table 4 and 5 show the quantitative comparison results of the head-tuning setting between our DAM-VP and other adaption methods. It is easy to discover that DAM-VP presents its strong ability to help pre-trained models generalize on various image datasets, surpassing other methods with fewer training epochs and higher recognition accuracy. Furthermore, our DAM-VP even outperforms the fully-tuning setting on both the ViT-B-22K model and the Swin-B-22K model with only 50 epochs tuning. + +Qualitative results. To better observe the adaption performance of each method, we depict the Top-1 accuracy curve of the first 50 training epochs to investigate the differences. Figure 7 shows the curve results of DAM-VP and the other three baselines in both head-freezing/missing and + +Table 2. Head-freezing/missing adaption performance of different methods on CLIP-ViT-B, where we report image classification accuracy and all of baseline methods are trained for 50 epochs. "TP" denotes text prompting that directly adopts zero-shot classification head of CLIP. Here "VP" and our method also use this fixed head rather than particular mapping to get output logits. + +
SettingMetaDiversityCUB200 [48]Flowers [40]CIFAR100 [29]SVHN [37]
AXX41.259.955.187.9
B✓X43.965.759.488.1
CX✓63.381.566.988.2
D✓✓64.684.167.288.4
+ +Table 3. Ablation results of diversity-aware strategy and metaprompt initialization. We report Top-1 accuracy on ViT-B-1K. + +head-tuning scenarios, where four datasets with different diversities are selected. It is obvious that, the performance of DAM-VP is far ahead in the early stage, especially in the first 10 epochs. This phenomenon indicates our diversity-aware strategy can boost the efficiency of prompt optimization, since each prompt just need to learn from a group of images that already have considerable homogeneity. The design of meta-prompt initialization also benefits this quick converging of our method with a good start point. + +# 4.3. Ablation Study + +Component ablation. We first verify the significance of the proposed diversity-aware strategy and the meta-prompt initialization on four aforementioned datasets that have different diversities. As listed in Table 3, both two components contribute a lot to boosting prompting performance, especially when dealing with task data that has high diversity. + +Prompt learning stability. Previous methods mainly ini- + +
Extra HeadDTD [10]CUB200 [48]NABirds [22]Dogs [28]Flowers [40]Food101 [3]CIFAR100 [29]CIFAR10 [29]GTSRB [46]SVHN [37]Average
Data diversity-78.776.074.873.472.772.770.970.267.561.8-
Fully-Tuning✓64.387.382.789.498.884.968.997.497.187.485.8
Linear✓63.285.375.986.297.984.463.496.368.036.675.7
Adapter [24, 42]✓62.787.184.389.898.586.074.297.791.136.380.8
VP [1]✓59.584.677.784.597.780.578.794.289.487.683.4
VPT [26]✓65.888.584.290.299.083.378.896.890.778.185.5
DAM-VP (10 epochs)✓72.486.381.592.298.686.280.190.587.881.185.7
DAM-VP (50 epochs)✓73.187.582.192.399.286.988.197.390.687.988.5
+ +Table 4. Head-tuning adaption performance of different methods on ViT-B-22K, where we report image classification accuracy and all of baseline methods are trained for 100 epochs. + +
Extra HeadDTD [10]CUB200 [48]NABirds [22]Dogs [28]Flowers [40]Food101 [3]CIFAR100 [29]CIFAR10 [29]GTSRB [46]SVHN [37]Average
Data diversity-78.776.074.873.472.772.770.970.267.561.8-
Fully-Tuning✓72.489.786.886.298.391.773.398.397.191.288.5
Linear✓73.688.685.285.999.488.261.696.383.843.580.6
Adapter [24, 42]✓73.988.584.686.898.988.785.796.583.671.385.9
VP [1]✓75.186.582.981.398.683.480.694.882.480.384.6
VPT [26]✓78.590.085.484.899.390.180.596.986.287.887.9
DAM-VP (10 epochs)✓77.089.486.888.399.690.285.596.484.779.087.7
DAM-VP (50 epochs)✓80.090.486.988.599.690.588.197.386.881.789.0
+ +Table 5. Head-tuning adaption performance of different methods on Swin-B-22K, where we report image classification accuracy and all of baseline methods are trained for 100 epochs. + +![](images/e0171f5e7993f9c6bbff894f9d0b5c5e256adda68990a0487e5d372dfa305671.jpg) +Figure 5. Meta-prompt initialization makes prompt tuning more robust to the random factor. We test in both head-freezing/missing (ViT-B-1K, left) and head-tuning (ViT-B-22K, right) cases. + +![](images/79bf899e77d719cda20f16fcfe6b41700cb79fda5a1e4a95b7338bec2871d935.jpg) + +tialize the prompt randomly, this leads to the instability of the performance caused by different random seeds. On the contrary, our meta-prompt design provides a good initialization point for optimization, which not only boosts the prompting performance but also improves the training stability. To eliminate the impact of random seeds, we test on 5 random seeds in experiments and report the results in Figure 5. It can be found that our meta-prompt initialization provides superb robustness across different training random seeds, while the randomly initialized prompt is unstable. + +Meta-prompt dataset number. As we elaborated in Sec. 4.1, there are 6 datasets prepared for our meta-prompt learning, which is also the default setting we used. Here we ablate this setting by reducing the number of meta datasets. As shown in Figure 6, when the meta dataset number is 0, i.e., no meta-prompt is used, our DVM-VP gets a rea + +![](images/1e99316bbed12710dd07868dfa18894eb1a8aa157afe91b302195b90254b6a13.jpg) +Figure 6. Ablating meta-prompt dataset number on DTD in the head-freezing/missing setting (ViT-B-1K, left) and the head-tuning (ViT-B-22K, right) setting. + +![](images/f1ddfe7250423d35f4017643622cbdd2727b2d2ff08ea8677fe053ae5779cdeb.jpg) + +sonable result that performs better than previous baseline methods. With the number of meta datasets increases, the prompting performance in both head-freezing/missing and head-tuning scenarios generally gets boosted. It proves that more prompting knowledge obtained from previous data is quite helpful for visual prompts to reduce the data distribution gap between downstream tasks and pretraining tasks. + +Meta-prompt update step size $\eta$ . The step size $\eta$ is a crucial hyper-parameter applied in the meta-prompt update. Here we ablate different step sizes that vary from 0.1 to 0.7 with the results given in Figure 8. Compared with baselines, the performance is relatively robust to different step sizes. We choose $\eta = 0.5$ as the default configuration. + +Different size of subset $S_{\mathcal{T}}$ . The size of subset $S_{\mathcal{T}}$ can directly influence the clustering result and further affects the partition result during our diversity-adaptive dataset parti + +![](images/855aa2839977320ee5f1afe35f7ccbfdc3ab402c74df33ac795694fd8ad6d2b4.jpg) + +![](images/81907a6fcc7fa754bfce2ab23582433d8dd46682efa6da643e11b78ac745d1a2.jpg) + +![](images/e3ca337eb47fd5b6f44c2033d365c952920b9c5e1ae19073f9fc00c9d6a4d76d.jpg) + +![](images/b6a91973aead1036ddd9592bddd69f4073edfc73260cc146a2cca41515aa39df.jpg) + +![](images/b57aab5d9b3026440ffbc54e19aef4ee797c74b0c94019d37c5dddd9a0ddefe9.jpg) +Figure 7. Test accuracy curves of different adaption methods when adapting pre-trained ViT-B-1K to different datasets in head-freezing/missing scenario (top row) and adapting pre-trained ViT-B-22K to different datasets head-tuning scenario (bottom row). + +![](images/5afecc478053bcc0f9945b81902c0c99251ee90271dce06861bd9cd2bdd3e6ba.jpg) + +![](images/f04f2ff2bfe014b5d7b4ef40d1b503077b2962ca94c62f0d24da34d210bc26df.jpg) + +![](images/658b3fa38396dde180ad06a181399b9bd69e2c1886cea99a2883ab86e5e08924.jpg) + +![](images/d6cd6ade1929a2934cf2f561a7ca2b99cacd772b9f95e8ed0303989a9ae7480f.jpg) +Figure 8. Ablating step size $\eta$ on DTD in head-freezing/missing (ViT-B-1K, left) and head-tuning (ViT-B-22K, right) cases. + +![](images/d3385c8b9e70e325bcd883aeaf43c1f70745903897972c608c8da1ea3cd2d491.jpg) +Figure 9. (Left) Ablating the size of subset $S_{\mathcal{T}}$ in both head-freezing/missing (ViT-B-1K) and head-tuning (ViT-B-22K) cases. (Right) Comparison between hard-coded mapping and our active-based mapping used for head-freezing/missing case. + +tion. Therefore, we apply different subset size that varies from 200 to 1000 to explore how it affects the prompting ability. From Figure 9 (left), we find that as the size of $S_{\mathcal{T}}$ increases, we can get higher performance in both scenarios. Meanwhile, we find our divide-and-conquer design is quite efficient that even with only 200 images, our DAM-VP still outperforms previous methods by a large margin. Considering the training images of some datasets are limited, we adopt 1,000 as the default size of $S_{\mathcal{T}}$ in this work. + +Hard-coded mapping vs. Active-based mapping. As we discussed in Sec. 3, we argue the hard-coded mapping used by [1] for head-freezing/missing scenario is inefficient, since it might optimize some not active enough channels of the output feature (i.e., relatively robust to diverse model input), thus we propose active-based mapping to alleviate this issue. Figure 9 (right) show the comparison between these two mapping methods on VP, tested on ViT-B-1K. + +# 5. Conclusion + +This paper considers the data diversity property in downstream task adaption for prompting pre-trained vision mod + +![](images/51acf8463bbd579ba26bb727998517dd03fc400378bf0fc932d699e267088f89.jpg) + +![](images/1def4f4642983b51b438edf51c1b924f032369450ffa6a15705bfeac967432a5.jpg) + +els. We argue that the per-dataset generic prompt adopt in previous methods can hardly handle the dataset of large data diversity. To address this, we propose DAM-VP based on diversity-adaptive dataset partition and prompt selection, where our prompts is initialized by a meta-prompt that learns through a quick meta learning algorithm. Extensive experiments prove the superior performance of DAM-VP in both head-freezing/missing and head-tuning cases. + +Acknowledgement. This work was supported in part by the Natural Science Foundation of China under Grant U20B2047, 62072421, 62002334, 62102386 and 62121002, Key Research and Development program of Anhui Province under Grant 2022k07020008, the Fundamental Research Funds for the Central Universities under Grant WK5290000003, Ant Group through CCF-Ant Innovative Research Program CCF-AFSG RF20210025, Alibaba Group through Alibaba Innovative Research Program. 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Bitfit: Simple parameter-efficient fine-tuning for transformer-based masked language-models. In ACL, 2022. 1 +[52] Xiaohua Zhai, Joan Puigcerver, Alexander Kolesnikov, Pierre Ruyssen, Carlos Riquelme, Mario Lucic, Josip Djolonga, Andre Susano Pinto, Maxim Neumann, Alexey Dosovitskiy, et al. A large-scale study of representation learning with the visual task adaptation benchmark. arXiv preprint arXiv:1910.04867, 2019. 5 +[53] Jeffrey O Zhang, Alexander Sax, Amir Zamir, Leonidas Guibas, and Jitendra Malik. Side-tuning: a baseline for network adaptation via additive side networks. In ECCV, 2020. 3 +[54] Richard Zhang, Phillip Isola, Alexei A Efros, Eli Shechtman, and Oliver Wang. The unreasonable effectiveness of deep features as a perceptual metric. In CVPR, 2018. 5 +[55] Renrui Zhang, Zhang Wei, Rongyao Fang, Peng Gao, Kunchang Li, Jifeng Dai, Yu Qiao, and Hongsheng Li. Tip-adapter: Training-free adaption of clip for few-shot classification. In ECCV, 2022. 2 +[56] Kaiyang Zhou, Jingkang Yang, Chen Change Loy, and Zwei Liu. Conditional prompt learning for vision-language models. In CVPR, 2022. 2 +[57] Kaiyang Zhou, Jingkang Yang, Chen Change Loy, and Ziwei Liu. Learning to prompt for vision-language models. IJCV, 2022. 2 \ No newline at end of file diff --git a/2023/Diversity-Aware Meta Visual Prompting/images.zip b/2023/Diversity-Aware Meta Visual Prompting/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..26a2a579cb4b2cac612355be4954a4930f1f19cd --- /dev/null +++ b/2023/Diversity-Aware Meta Visual Prompting/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:84cdf6a5719512ec80fbcb74b61dc9e38153ed280af79f049fb90a4130ef23dc +size 663691 diff --git a/2023/Diversity-Aware Meta Visual Prompting/layout.json b/2023/Diversity-Aware Meta Visual Prompting/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..3ffd16499e7f837db6a29cc6b1e182264e0f5396 --- /dev/null +++ b/2023/Diversity-Aware Meta Visual Prompting/layout.json @@ -0,0 +1,8558 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 172, + 103, + 422, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 172, + 103, + 422, + 121 + ], + "spans": [ + { + "bbox": [ + 172, + 103, + 422, + 121 + ], + "type": "text", + "content": "Diversity-Aware Meta Visual Prompting" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 57, + 141, + 534, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 141, + 534, + 216 + ], + "spans": [ + { + "bbox": [ + 57, + 141, + 534, + 216 + ], + "type": "text", + "content": "Qidong Huang" + }, + { + "bbox": [ + 57, + 141, + 534, + 216 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 57, + 141, + 534, + 216 + ], + "type": "text", + "content": " Xiaoyi Dong" + }, + { + "bbox": [ + 57, + 141, + 534, + 216 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 57, + 141, + 534, + 216 + ], + "type": "text", + "content": " Dongdong Chen" + }, + { + "bbox": [ + 57, + 141, + 534, + 216 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 57, + 141, + 534, + 216 + ], + "type": "text", + "content": " Weiming Zhang" + }, + { + "bbox": [ + 57, + 141, + 534, + 216 + ], + "type": "inline_equation", + "content": "^{1,*}" + }, + { + "bbox": [ + 57, + 141, + 534, + 216 + ], + "type": "text", + "content": " Feifei Wang" + }, + { + "bbox": [ + 57, + 141, + 534, + 216 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 57, + 141, + 534, + 216 + ], + "type": "text", + "content": " Gang Hua" + }, + { + "bbox": [ + 57, + 141, + 534, + 216 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 57, + 141, + 534, + 216 + ], + "type": "text", + "content": " Nenghai Yu" + }, + { + "bbox": [ + 57, + 141, + 534, + 216 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 57, + 141, + 534, + 216 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 57, + 141, + 534, + 216 + ], + "type": "text", + "content": "University of Science and Technology of China " + }, + { + "bbox": [ + 57, + 141, + 534, + 216 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 57, + 141, + 534, + 216 + ], + "type": "text", + "content": "Microsoft Cloud AI " + }, + { + "bbox": [ + 57, + 141, + 534, + 216 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 57, + 141, + 534, + 216 + ], + "type": "text", + "content": "Wormpex AI Research {hqd0037@mail., dlight@mail., zhangwm@, wangfeifei@mail., ynh@}ustc.edu.cn {cddlyf@, ganghua@}gmail.com" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 240, + 192, + 254 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 240, + 192, + 254 + ], + "spans": [ + { + "bbox": [ + 143, + 240, + 192, + 254 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 266, + 290, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 266, + 290, + 602 + ], + "spans": [ + { + "bbox": [ + 47, + 266, + 290, + 602 + ], + "type": "text", + "content": "We present Diversity-Aware Meta Visual Prompting (DAM-VP), an efficient and effective prompting method for transferring pre-trained models to downstream tasks with frozen backbone. A challenging issue in visual prompting is that image datasets sometimes have a large data diversity whereas a per-dataset generic prompt can hardly handle the complex distribution shift toward the original pretraining data distribution properly. To address this issue, we propose a dataset Diversity-Aware prompting strategy whose initialization is realized by a Meta-prompt. Specifically, we cluster the downstream dataset into small homogeneity subsets in a diversity-adaptive way, with each subset has its own prompt optimized separately. Such a divide-and-conquer design reduces the optimization difficulty greatly and significantly boosts the prompting performance. Furthermore, all the prompts are initialized with a meta-prompt, which is learned across several datasets. It is a bootstrapped paradigm, with the key observation that the prompting knowledge learned from previous datasets could help the prompt to converge faster and perform better on a new dataset. During inference, we dynamically select a proper prompt for each input, based on the feature distance between the input and each subset. Through extensive experiments, our DAM-VP demonstrates superior efficiency and effectiveness, clearly surpassing previous prompting methods in a series of downstream datasets for different pretraining models. Our code is available at: https://github.com/shikiw/DAM-VP." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 625, + 128, + 639 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 625, + 128, + 639 + ], + "spans": [ + { + "bbox": [ + 47, + 625, + 128, + 639 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 646, + 287, + 695 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 646, + 287, + 695 + ], + "spans": [ + { + "bbox": [ + 47, + 646, + 287, + 695 + ], + "type": "text", + "content": "With the increasing scale of training data and model size, the pretraining-finetuning paradigm has shown remarkable achievement in many areas, including natural language processing (NLP) [4, 13] and computer vision (CV) [2,7,8,19]." + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 311, + 240, + 542, + 346 + ], + "blocks": [ + { + "bbox": [ + 311, + 240, + 542, + 346 + ], + "lines": [ + { + "bbox": [ + 311, + 240, + 542, + 346 + ], + "spans": [ + { + "bbox": [ + 311, + 240, + 542, + 346 + ], + "type": "image", + "image_path": "abafc6ff1f6bac34c17bdd9e7abfb951fad4628ac6ce0d82864e3ebe7eca070a.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 355, + 547, + 422 + ], + "lines": [ + { + "bbox": [ + 304, + 355, + 547, + 422 + ], + "spans": [ + { + "bbox": [ + 304, + 355, + 547, + 422 + ], + "type": "text", + "content": "Figure 1. Relation between dataset diversity and the performance gain got by using prompting. The gain is the performance improvement when compared with the linear-probing accuracy, under the head-tuning setting. Both previous methods get a large performance gain on low-diversity datasets, while failing to boost the transfer performance on high-diversity datasets." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 446, + 547, + 530 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 446, + 547, + 530 + ], + "spans": [ + { + "bbox": [ + 304, + 446, + 547, + 530 + ], + "type": "text", + "content": "However, fully finetuning a large pre-trained model for each small downstream task still has some problems in real-world usage. The most practical one is the storage and distribution problem that we have to maintain an independent copy of the model for each task, which is quite expensive and inflexible, especially for increasing numbers of downstream tasks [9]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 532, + 548, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 532, + 548, + 687 + ], + "spans": [ + { + "bbox": [ + 304, + 532, + 548, + 687 + ], + "type": "text", + "content": "To break the dilemma, many efforts [6,17,18,25,51] have been paid to efficiently transfer the given pre-trained models into a particular dataset. Prompting is an extensively studied method in the NLP area, which appends a few tokens before the input sequence to provide some task-specific knowledge to the pre-trained model, so that the model could adapt well on the downstream tasks without the fully-finetuning. Inspired by the success of prompting in NLP, some recent works [1, 26] propose visual prompting for vision models. By adding some learnable noise onto the input image or appending some learnable tokens to the model input sequence, the pre-trained models show promising results on different kinds of downstream tasks." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 689, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 547, + 715 + ], + "type": "text", + "content": "However, we argue that these methods ignore the diverse distribution property of the image dataset and using a sin-" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 137, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 137, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 137, + 713 + ], + "type": "text", + "content": "*Corresponding author." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "10878" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 263 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 263 + ], + "type": "text", + "content": "gle prompt for all the images in each dataset is not optimal. In Figure 1, we show the relationship between the gain from prompting and the diversity of the dataset. Here the gain represents the accuracy improvement compared with the linear probing setting. We find that both VP [1] and VPT [26] improve the model accuracy by a large margin on the low-diversity dataset, but relatively small gains on the high-diversity datasets, which is intuitively sensible. For low-diversity datasets, such as the street view house number dataset (SVHN) [37], all the images have similar content so a unified prompt is sufficient. On the contrary, when it comes to high-diversity datasets, such as the ImageNet [12] dataset, it covers very diverse classes from the wordnet and there is not any pre-defined relationship between the classes, so it is hard to use a single prompt to provide the prior for all the images, such as for \"car\" and \"dog\"." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 264, + 289, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 264, + 289, + 479 + ], + "spans": [ + { + "bbox": [ + 46, + 264, + 289, + 479 + ], + "type": "text", + "content": "Motivated by this observation, we propose our Diversity-Aware Meta Visual Prompting (DAM-VP). It has two core designs. Firstly, to provide a proper prompt for each image from high-diversity datasets, we propose a clustering-based prompt selection method. In detail, given a pre-trained visual model and a downstream dataset, we use the off-the-shelf clustering method to cluster the feature of the downstream data into several coarse-grained subsets, and guide each cluster to learn its own prompt separately. Based on the strong homogeneity of the same clustered data, the optimization of cluster-specific visual prompts can be greatly facilitated and the data commonalities can be also easily covered. Secondly, we argue the prompt across different clusters or datasets may have some shared pattern, from which the model can be adapted to a new dataset faster and get better performance. This motivates us to introduce a meta-learning-based method that learns a meta prompt and initializes the prompt of each cluster with it." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 479, + 289, + 670 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 479, + 289, + 670 + ], + "spans": [ + { + "bbox": [ + 46, + 479, + 289, + 670 + ], + "type": "text", + "content": "We conduct our experiments on datasets with different data diversity and evaluate the transfer performance with different pre-trained models. We report the performance on both the widely used head-tuning setting and a more challenging head-freezing/missing setting. Our DAM-VP outperforms previous methods by a large margin, especially on high-diversity datasets. For example, with the ImageNet22k pre-trained ViT-B model, DAM-VP gets " + }, + { + "bbox": [ + 46, + 479, + 289, + 670 + ], + "type": "inline_equation", + "content": "73.1\\%" + }, + { + "bbox": [ + 46, + 479, + 289, + 670 + ], + "type": "text", + "content": " top-1 accuracy under the head-tuning setting on the diverse DTD [10] dataset, surpassing previous methods VP [1] and VPT [26] with " + }, + { + "bbox": [ + 46, + 479, + 289, + 670 + ], + "type": "inline_equation", + "content": "+13.6\\%" + }, + { + "bbox": [ + 46, + 479, + 289, + 670 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 479, + 289, + 670 + ], + "type": "inline_equation", + "content": "+7.3\\%" + }, + { + "bbox": [ + 46, + 479, + 289, + 670 + ], + "type": "text", + "content": " respectively. Meanwhile, we find DAM-VP is quite efficient that with only 10 epoch tuning, it gets " + }, + { + "bbox": [ + 46, + 479, + 289, + 670 + ], + "type": "inline_equation", + "content": "85.7\\%" + }, + { + "bbox": [ + 46, + 479, + 289, + 670 + ], + "type": "text", + "content": " average top-1 accuracy over the 10 datasets, comparable with previous methods that tunes 100 epochs (83.4% for VP [1] and 85.5% for VPT [26]). Our contributions can be summarized as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 58, + 677, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 677, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 58, + 677, + 288, + 715 + ], + "type": "text", + "content": "- We analyze the limitation of previous visual prompting methods, and point out that vision-suitable prompting should consider the dataset diversity." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 317, + 72, + 545, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 72, + 545, + 144 + ], + "spans": [ + { + "bbox": [ + 317, + 72, + 545, + 144 + ], + "type": "text", + "content": "- Accordingly, we propose a novel Diversity-Aware Meta Visual Prompting (DAM-VP) method. It uses the divide-and-conquer idea by clustering high-diversity datasets into subsets and learning separate prompts for each subset, in cooperation with a meta-prompt learning design." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 317, + 154, + 547, + 202 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 154, + 547, + 202 + ], + "spans": [ + { + "bbox": [ + 317, + 154, + 547, + 202 + ], + "type": "text", + "content": "- Through extensive experiments, our DAM-VP demonstrates superior performance, achieving SOTA performance in a series of downstream datasets for different pretraining models." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 214, + 392, + 227 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 214, + 392, + 227 + ], + "spans": [ + { + "bbox": [ + 306, + 214, + 392, + 227 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 235, + 547, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 235, + 547, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 235, + 547, + 641 + ], + "type": "text", + "content": "Prompt learning. Served as a new paradigm, prompting [33] originally emerges in NLP for adapting pre-trained language models (PLM) [4, 13] to downstream tasks. Its principle idea is to reformulate downstream data into the model knowledge learned during the pretraining phase, enabling the frozen pre-trained model to understand the task rather than tuning the model parameters for adaption. This goal has been initially reached through constructing pure text prompts that contains task-specific templates and label words to perform cloze test, e.g., hand-craft prompts [16] and generative text prompts [27, 45], but unfortunately, still requiring specialized linguistic expertise for preparation. To alleviate this, recent efforts have been paid on prompt tuning (PT) [30, 31] that learns a task-specific continuous vector as tunable prefix tokens. These tokens can be optimized via gradients to act as prompts in task adaptation while maintaining the pre-trained model untouched. Driven by the success of language prompts, a lot of works [35, 38, 43, 47, 50, 55], like CoOP [57] and CoCoOP [56], have been mushroomed to explore vision-related prompting especially in multi-modal scenarios, while still concentrating on text prompting in practice. Due to the gap of information density [19] between languages and images, prompting for vision models is more challenging and complex. Inspired by prefix tuning, VPT [26] takes the first step to adapt vision transformers to downstream tasks by preponding a set of learnable tokens at the model input. Concurrently, VP [1] follows the pixel-level perspective to optimize task-specific patches that are incorporated with input images. Despite the pioneering successes of VP and VPT, we find that they need to pre-assign the number of prompts, which is not flexible to handle the datasets with different diversities. In contrast, our method uses a diversity-adaptive solution to well address this issue." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "text", + "content": "Transfer learning. Typically, transfer learning focuses on how to efficiently fine-tune the supervised or un-/self-supervised pre-trained model when tackling with a new task. A conventional art of transfer learning is to fully fine-tune all of the model parameters on training data of the new task, using the pretraining knowledge as model initializa" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "10879" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 70, + 544, + 248 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 544, + 248 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 544, + 248 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 544, + 248 + ], + "type": "image", + "image_path": "ddc5462d2f02d2c5061160ca7f66786aca87b2471c65cf0ec2f397f34a7a4284.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 251, + 546, + 285 + ], + "lines": [ + { + "bbox": [ + 46, + 251, + 546, + 285 + ], + "spans": [ + { + "bbox": [ + 46, + 251, + 546, + 285 + ], + "type": "text", + "content": "Figure 2. The pipeline of our diversity-aware adaption for frozen pre-trained encoder " + }, + { + "bbox": [ + 46, + 251, + 546, + 285 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 46, + 251, + 546, + 285 + ], + "type": "text", + "content": " on new task " + }, + { + "bbox": [ + 46, + 251, + 546, + 285 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 46, + 251, + 546, + 285 + ], + "type": "text", + "content": ". We randomly select a little subset " + }, + { + "bbox": [ + 46, + 251, + 546, + 285 + ], + "type": "inline_equation", + "content": "S_{\\mathcal{T}}" + }, + { + "bbox": [ + 46, + 251, + 546, + 285 + ], + "type": "text", + "content": " from the training data of task " + }, + { + "bbox": [ + 46, + 251, + 546, + 285 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 46, + 251, + 546, + 285 + ], + "type": "text", + "content": " to implement agglomerative clustering and simulate prototypes of clusters. These prototypes are utilized to partition the whole training set into different subsets, so that we can optimize the prompt for each subset separately." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 306, + 289, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 306, + 289, + 521 + ], + "spans": [ + { + "bbox": [ + 46, + 306, + 289, + 521 + ], + "type": "text", + "content": "tion. However, the growing model capacity has exposed the inefficiency of fully fine-tuning, simulating the demand of parameter-efficient learning on downstream tasks, i.e., selecting or appending a few parameters for tuning and freezing the remaining of the model meanwhile. This topic has been widely explored in NLP by prepending extra learnable tokens or feature vectors [30, 31] at transformer input, whereas limited in vision which still focuses on ConvNets [5, 44, 53] and rarely on the emerging vision transformers. To mitigate this gap, recent efforts have explored to efficiently transfer vision transformers by introducing a parallel trainable down-to-up branch into the MLP module of self-attention blocks [6] or scaling and shifting the learned features [32]. VPT [26] is the pioneer work to leverage learnable prefix tokens/features for visual prompting, but still not efficient in terms of convergence time. Driven by this, our DAM-VP strives to learn faster during tuning with comparable amount of learnable parameters introduced." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 535, + 103, + 547 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 535, + 103, + 547 + ], + "spans": [ + { + "bbox": [ + 47, + 535, + 103, + 547 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 556, + 287, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 556, + 287, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 556, + 287, + 688 + ], + "type": "text", + "content": "We introduce our Diversity-Aware Meta Visual Prompting (DAM-VP), a novel prompting method that is adaptive to diverse downstream datasets effectively and efficiently. As shown in Figure 2, with a given dataset, DAM-VP first extracts its specific prototypes in an unsupervised and adaptive manner as the pre-processing. Then we split the dataset into different subsets, according to the prototypes. For each subset, we assign a specific prompt to it and optimize it with the tuning loss. Rather than random initialization, all of the prompts are initialized by a meta prompt learned across different datasets, as shown in Figure 4." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "content": "Diversity-adaptive dataset partition. As we briefly introduced in Sec. 1, different image datasets have different dis" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 307, + 303, + 353, + 397 + ], + "blocks": [ + { + "bbox": [ + 307, + 303, + 353, + 397 + ], + "lines": [ + { + "bbox": [ + 307, + 303, + 353, + 397 + ], + "spans": [ + { + "bbox": [ + 307, + 303, + 353, + 397 + ], + "type": "image", + "image_path": "f07464ec026420ba68c6cde1f4c1bdbdab8d1574937d8d5f03f3ca6271d3de33.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 314, + 405, + 536, + 417 + ], + "lines": [ + { + "bbox": [ + 314, + 405, + 536, + 417 + ], + "spans": [ + { + "bbox": [ + 314, + 405, + 536, + 417 + ], + "type": "text", + "content": "Figure 3. Examples of GTSRB (top) and SUN397 (bottom)." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 354, + 303, + 402, + 397 + ], + "blocks": [ + { + "bbox": [ + 354, + 303, + 402, + 397 + ], + "lines": [ + { + "bbox": [ + 354, + 303, + 402, + 397 + ], + "spans": [ + { + "bbox": [ + 354, + 303, + 402, + 397 + ], + "type": "image", + "image_path": "27c6c18a514406b5773040efd14706be42fe6bc3fcbe22331196e8a4d4f15ae4.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 403, + 303, + 450, + 397 + ], + "blocks": [ + { + "bbox": [ + 403, + 303, + 450, + 397 + ], + "lines": [ + { + "bbox": [ + 403, + 303, + 450, + 397 + ], + "spans": [ + { + "bbox": [ + 403, + 303, + 450, + 397 + ], + "type": "image", + "image_path": "a3c260b701b1593bf2ec4c4d0059640233bdf8dd9ea82215f053b778b4c0caff.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 451, + 303, + 498, + 397 + ], + "blocks": [ + { + "bbox": [ + 451, + 303, + 498, + 397 + ], + "lines": [ + { + "bbox": [ + 451, + 303, + 498, + 397 + ], + "spans": [ + { + "bbox": [ + 451, + 303, + 498, + 397 + ], + "type": "image", + "image_path": "7dff336bb259ab651138e4306f9bf03ebd5fdbb0641949cc58f001bbe5ba3330.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 498, + 303, + 546, + 397 + ], + "blocks": [ + { + "bbox": [ + 498, + 303, + 546, + 397 + ], + "lines": [ + { + "bbox": [ + 498, + 303, + 546, + 397 + ], + "spans": [ + { + "bbox": [ + 498, + 303, + 546, + 397 + ], + "type": "image", + "image_path": "14caf462091be32c303219021b11b53873699b9856b009fc8b94fb5caab02fef.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 437, + 546, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 546, + 545 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 546, + 545 + ], + "type": "text", + "content": "ribution diversity. Take Figure 3 as an example, when comparing with the traffic sign dataset [46], the data in the scene dataset [49] is more diverse in terms of angle, illumination, the complexity of content, etc. The prompting is designed to reduce the distribution gap between the target downstream dataset and the model pretraining data, and it is intuitive that a dataset with similar content is easy to transfer. So it is a straightforward idea to split a diverse dataset into small subsets and apply different prompts to each subset." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "type": "text", + "content": "To this end, we consider the diversity property in our visual prompting design and propose an adaptive dataset partition strategy to suit the diversity of task data automatically. Specifically, when adapting the frozen pre-trained backbone " + }, + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "type": "text", + "content": " to the new task " + }, + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "type": "text", + "content": ", we first randomly sample a small subset " + }, + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "type": "inline_equation", + "content": "S_{\\mathcal{T}}" + }, + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "type": "text", + "content": " from the training set of " + }, + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "type": "text", + "content": ". Then we extract the feature of subset " + }, + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "type": "inline_equation", + "content": "S_{\\mathcal{T}}" + }, + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "type": "text", + "content": " with the frozen " + }, + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "type": "text", + "content": " without any prompting. We denote the features as " + }, + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{M}(s)|s\\in S_{\\mathcal{T}}\\}" + }, + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "type": "text", + "content": " and use an off-the-shelf clustering method [36] to aggregate them into several clusters. The clustering procedure is time-efficient (less than " + }, + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "type": "text", + "content": " of total tuning time) and the number of clusters " + }, + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "type": "text", + "content": " is auto-adaptive to the dataset diversity by a pre-defined threshold. Once the clusters are constructed, we compute the average values for features of each cluster" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10880" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 70, + 382, + 281 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 382, + 281 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 382, + 281 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 382, + 281 + ], + "type": "image", + "image_path": "8f16d9eb7f77c3df1bedc155979d1606075e167876b955ae49842875ed210b43.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 289, + 546, + 323 + ], + "lines": [ + { + "bbox": [ + 46, + 289, + 546, + 323 + ], + "spans": [ + { + "bbox": [ + 46, + 289, + 546, + 323 + ], + "type": "text", + "content": "Figure 4. The pipeline of meta-learning-based prompt initialization. We partition each task dataset into subsets and regard each subset as a single meta task. During meta training on each meta batch, we continuously update the temporary prompt on each meta task set and finally apply moving average to get the updated meta prompt." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 423, + 102, + 545, + 250 + ], + "blocks": [ + { + "bbox": [ + 423, + 102, + 545, + 250 + ], + "lines": [ + { + "bbox": [ + 423, + 102, + 545, + 250 + ], + "spans": [ + { + "bbox": [ + 423, + 102, + 545, + 250 + ], + "type": "image", + "image_path": "3bb7f79d7025e778e8b8e8a144ba5d6bb8f0303ffe3eb80f68ad9ba5c31e1bef.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 342, + 234, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 342, + 234, + 357 + ], + "spans": [ + { + "bbox": [ + 47, + 342, + 234, + 357 + ], + "type": "text", + "content": "as the cluster-specific prototypes " + }, + { + "bbox": [ + 47, + 342, + 234, + 357 + ], + "type": "inline_equation", + "content": "\\{c_i\\}_{i = 1}^N" + }, + { + "bbox": [ + 47, + 342, + 234, + 357 + ], + "type": "text", + "content": " , i.e.," + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 87, + 364, + 287, + 393 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 364, + 287, + 393 + ], + "spans": [ + { + "bbox": [ + 87, + 364, + 287, + 393 + ], + "type": "interline_equation", + "content": "c _ {i} = \\frac {1}{\\left| \\mathcal {S} _ {i} \\right|} \\sum_ {s \\in \\mathcal {S} _ {i}} \\mathcal {M} (s), \\quad i = 1, \\dots , N, \\tag {1}", + "image_path": "3f555686c646b12ce7d3111255ec1664fd2075d93d95312f3cba528409d99ca9.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 402, + 287, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 402, + 287, + 498 + ], + "spans": [ + { + "bbox": [ + 46, + 402, + 287, + 498 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 402, + 287, + 498 + ], + "type": "inline_equation", + "content": "S_{i}" + }, + { + "bbox": [ + 46, + 402, + 287, + 498 + ], + "type": "text", + "content": " is the data samples corresponding to the " + }, + { + "bbox": [ + 46, + 402, + 287, + 498 + ], + "type": "inline_equation", + "content": "i^{th}" + }, + { + "bbox": [ + 46, + 402, + 287, + 498 + ], + "type": "text", + "content": " cluster that satisfies " + }, + { + "bbox": [ + 46, + 402, + 287, + 498 + ], + "type": "inline_equation", + "content": "|S_1| + |S_2| + \\dots + |S_N| = |S_{\\mathcal{T}}|" + }, + { + "bbox": [ + 46, + 402, + 287, + 498 + ], + "type": "text", + "content": ". The unsupervised mechanism naturally guarantees that the dataset with a higher diversity can be divided into more clusters, and the dataset with a lower diversity can be divided into fewer clusters or even just a single cluster. In practice, we configure the threshold of clustering properly to keep " + }, + { + "bbox": [ + 46, + 402, + 287, + 498 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 402, + 287, + 498 + ], + "type": "text", + "content": " in a reasonable range, usually less than the data category number." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 498, + 287, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 287, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 287, + 700 + ], + "type": "text", + "content": "Diversity-aware prompt selection. With the simulated prototypes " + }, + { + "bbox": [ + 46, + 498, + 287, + 700 + ], + "type": "inline_equation", + "content": "\\{c_i\\}_{i=1}^N" + }, + { + "bbox": [ + 46, + 498, + 287, + 700 + ], + "type": "text", + "content": ", it is easy to partition the whole training dataset " + }, + { + "bbox": [ + 46, + 498, + 287, + 700 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathcal{T}}" + }, + { + "bbox": [ + 46, + 498, + 287, + 700 + ], + "type": "text", + "content": " of task " + }, + { + "bbox": [ + 46, + 498, + 287, + 700 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 46, + 498, + 287, + 700 + ], + "type": "text", + "content": " into small subsets " + }, + { + "bbox": [ + 46, + 498, + 287, + 700 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{D}_i\\}_{i=1}^N" + }, + { + "bbox": [ + 46, + 498, + 287, + 700 + ], + "type": "text", + "content": ". Correspondingly, we assign one visual prompt for each subset and get " + }, + { + "bbox": [ + 46, + 498, + 287, + 700 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 498, + 287, + 700 + ], + "type": "text", + "content": " visual prompts " + }, + { + "bbox": [ + 46, + 498, + 287, + 700 + ], + "type": "inline_equation", + "content": "\\{p_i\\}_{i=1}^N" + }, + { + "bbox": [ + 46, + 498, + 287, + 700 + ], + "type": "text", + "content": " in total. Similar to the design in [1], we use a photo-frame-like pixel-level prompting. It has the same size as the model input and we add it to the input image directly. Such a design has two advantages: Firstly, it does not introduce additional computation cost during inference, while the prefix-token prompting used in VPT [26] increases the input length and leads to a larger computation cost. Secondly, such pixel-level prompting is irrelevant to the model type, so it could be used in both recent popular Vision Transformer models and traditional convolution networks. On the contrary, the prefix-token prompting is specifically designed for token-list-type input so that could only be used for Vision Transformer." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 59, + 701, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 287, + 714 + ], + "type": "text", + "content": "Given an image-label pair " + }, + { + "bbox": [ + 59, + 701, + 287, + 714 + ], + "type": "inline_equation", + "content": "(x,y)" + }, + { + "bbox": [ + 59, + 701, + 287, + 714 + ], + "type": "text", + "content": " from the training set," + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 343, + 545, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 343, + 545, + 415 + ], + "spans": [ + { + "bbox": [ + 305, + 343, + 545, + 415 + ], + "type": "text", + "content": "we forward " + }, + { + "bbox": [ + 305, + 343, + 545, + 415 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 305, + 343, + 545, + 415 + ], + "type": "text", + "content": " on the frozen " + }, + { + "bbox": [ + 305, + 343, + 545, + 415 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 305, + 343, + 545, + 415 + ], + "type": "text", + "content": " without prompting to get its original feature and compute the euclidean distances between the feature and each aforementioned prototype. The prompt that corresponds to the minimal distance is considered as the prompt added on " + }, + { + "bbox": [ + 305, + 343, + 545, + 415 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 305, + 343, + 545, + 415 + ], + "type": "text", + "content": ". Formally, prompted image " + }, + { + "bbox": [ + 305, + 343, + 545, + 415 + ], + "type": "inline_equation", + "content": "x^p" + }, + { + "bbox": [ + 305, + 343, + 545, + 415 + ], + "type": "text", + "content": " is defined as" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 318, + 422, + 545, + 442 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 422, + 545, + 442 + ], + "spans": [ + { + "bbox": [ + 318, + 422, + 545, + 442 + ], + "type": "interline_equation", + "content": "x ^ {p} \\triangleq x + p _ {t}, \\quad \\text {s . t .} \\quad t = \\underset {i} {\\arg \\min } \\| \\mathcal {M} (x) - c _ {i} \\| _ {2} ^ {2}. \\tag {2}", + "image_path": "a08bfb35067dcfeacc532386d12355ff5cddebebf83621ed2d961f4969c65aec.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 449, + 544, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 449, + 544, + 474 + ], + "spans": [ + { + "bbox": [ + 305, + 449, + 544, + 474 + ], + "type": "text", + "content": "which indicates the input image " + }, + { + "bbox": [ + 305, + 449, + 544, + 474 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 305, + 449, + 544, + 474 + ], + "type": "text", + "content": " is assigned into the " + }, + { + "bbox": [ + 305, + 449, + 544, + 474 + ], + "type": "inline_equation", + "content": "t^{th}" + }, + { + "bbox": [ + 305, + 449, + 544, + 474 + ], + "type": "text", + "content": " image subset " + }, + { + "bbox": [ + 305, + 449, + 544, + 474 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_t" + }, + { + "bbox": [ + 305, + 449, + 544, + 474 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 475, + 545, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 475, + 545, + 582 + ], + "spans": [ + { + "bbox": [ + 305, + 475, + 545, + 582 + ], + "type": "text", + "content": "Prompt learning. In this paper, we seek a more general prompting format that could be utilized in different settings. 1) The head-tuning setting used in VPT [26] that a learnable classification head is optimized with the prompt jointly. 2) The head-freezing/missing setting that only the prompt is learnable. The second one is a more challenging task, but it is also a more flexible real-world usage format: we only need to add different prompts on the input for different tasks, maintaining an end-to-end frozen pre-trained model." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "type": "text", + "content": "For the head-tuning setting, we follow the design in VPT [26] that optimize a new " + }, + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "type": "text", + "content": "-class classification head for the target task with " + }, + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "type": "text", + "content": " categories. Similarly, for the head-freezing case, we assign the first " + }, + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "type": "text", + "content": " classes in the frozen head to the new task. When it comes to the head-missing case that the pre-trained model does not have a classification head (such as self-supervised pre-trained models), a simple hard-coded mapping solution [1] is converted the output feature (e.g., 768 channels output feature of ViT/16-Base [14] encoder) to classification logits. However, we argue such hard-coded mapping is inefficient, because the optimization" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10881" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 286, + 132 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 286, + 132 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 286, + 132 + ], + "type": "text", + "content": "might be limited if the neurons at these fixed positions are not active enough. So we propose an active-based mapping method, which selects the most active top-" + }, + { + "bbox": [ + 46, + 72, + 286, + 132 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 72, + 286, + 132 + ], + "type": "text", + "content": " neurons of the output layer of " + }, + { + "bbox": [ + 46, + 72, + 286, + 132 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 46, + 72, + 286, + 132 + ], + "type": "text", + "content": " by measuring the variances of each position output when confronted with random noise inputs." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 133, + 286, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 133, + 286, + 168 + ], + "spans": [ + { + "bbox": [ + 46, + 133, + 286, + 168 + ], + "type": "text", + "content": "Based on the above designs, we can minimize the cross-entropy loss between the logits of prompted image " + }, + { + "bbox": [ + 46, + 133, + 286, + 168 + ], + "type": "inline_equation", + "content": "x^p" + }, + { + "bbox": [ + 46, + 133, + 286, + 168 + ], + "type": "text", + "content": " and ground-truth label " + }, + { + "bbox": [ + 46, + 133, + 286, + 168 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 133, + 286, + 168 + ], + "type": "text", + "content": " to tune our visual prompts on " + }, + { + "bbox": [ + 46, + 133, + 286, + 168 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathcal{T}}" + }, + { + "bbox": [ + 46, + 133, + 286, + 168 + ], + "type": "text", + "content": ", i.e.," + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 178, + 286, + 221 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 178, + 286, + 221 + ], + "spans": [ + { + "bbox": [ + 46, + 178, + 286, + 221 + ], + "type": "interline_equation", + "content": "p _ {1} ^ {*}, \\dots , p _ {N} ^ {*} = \\underset {p _ {1}, \\dots , p _ {N}} {\\arg \\min } \\frac {1}{| \\mathcal {D} _ {\\mathcal {T}} |} \\sum_ {i = 1} ^ {N} \\sum_ {x \\in \\mathcal {D} _ {i}} \\mathcal {L} _ {C E} (\\mathcal {M} (x + p _ {i}), y). \\tag {3}", + "image_path": "692d1c56f0af552067ec5101bc43bd273a22c7ab827279867c3ae6c476b02c5a.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 222, + 286, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 222, + 286, + 281 + ], + "spans": [ + { + "bbox": [ + 46, + 222, + 286, + 281 + ], + "type": "text", + "content": "Once the prompts are well-optimized, we can utilize prototypes to categorize the input image and assign it to its belonging subset during inference. The corresponding prompt is subsequently incorporated with the input image as prompted input to get the classification logits." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 282, + 286, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 282, + 286, + 376 + ], + "spans": [ + { + "bbox": [ + 46, + 282, + 286, + 376 + ], + "type": "text", + "content": "Prompt boosting via Meta-learning. In real-world usage, a frozen model " + }, + { + "bbox": [ + 46, + 282, + 286, + 376 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 46, + 282, + 286, + 376 + ], + "type": "text", + "content": " needs to be transferred to a bunch of downstream tasks, this leads to two desired favorable properties of the prompting method. First, it should be efficient that only a few epochs tuning could get a good result. Second, the prompts learned from previous tasks could help the new tasks learn better prompts so that the method is bootstrapped." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 378, + 286, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 378, + 286, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 378, + 286, + 533 + ], + "type": "text", + "content": "In light of meta-learning [15, 39], we integrate a quick algorithm Reptile [39] into our diversity-aware learning to boost the prompting learning. The principle idea is to learn a meta prompt " + }, + { + "bbox": [ + 46, + 378, + 286, + 533 + ], + "type": "inline_equation", + "content": "p^m" + }, + { + "bbox": [ + 46, + 378, + 286, + 533 + ], + "type": "text", + "content": " on several task datasets " + }, + { + "bbox": [ + 46, + 378, + 286, + 533 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{D}_i^m\\}_{i=1}^M" + }, + { + "bbox": [ + 46, + 378, + 286, + 533 + ], + "type": "text", + "content": " that are prepared as the meta training data, and adopt the well-trained " + }, + { + "bbox": [ + 46, + 378, + 286, + 533 + ], + "type": "inline_equation", + "content": "p^m" + }, + { + "bbox": [ + 46, + 378, + 286, + 533 + ], + "type": "text", + "content": " as the initial prompt for diversity-aware adaption. Specifically, we first partition each task dataset into subsets, e.g., dataset " + }, + { + "bbox": [ + 46, + 378, + 286, + 533 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_i^m" + }, + { + "bbox": [ + 46, + 378, + 286, + 533 + ], + "type": "text", + "content": " is divided into " + }, + { + "bbox": [ + 46, + 378, + 286, + 533 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{i,1}^m, \\mathcal{D}_{i,2}^m, \\ldots, \\mathcal{D}_{i,K_i}^m" + }, + { + "bbox": [ + 46, + 378, + 286, + 533 + ], + "type": "text", + "content": ". Then, we regard each subset as a single meta task and sample images from each subset to form the meta training batch " + }, + { + "bbox": [ + 46, + 378, + 286, + 533 + ], + "type": "inline_equation", + "content": "\\mathcal{B}" + }, + { + "bbox": [ + 46, + 378, + 286, + 533 + ], + "type": "text", + "content": ", i.e., dataset " + }, + { + "bbox": [ + 46, + 378, + 286, + 533 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_i^m" + }, + { + "bbox": [ + 46, + 378, + 286, + 533 + ], + "type": "text", + "content": " contributes total " + }, + { + "bbox": [ + 46, + 378, + 286, + 533 + ], + "type": "inline_equation", + "content": "K_i" + }, + { + "bbox": [ + 46, + 378, + 286, + 533 + ], + "type": "text", + "content": " meta task sets for " + }, + { + "bbox": [ + 46, + 378, + 286, + 533 + ], + "type": "inline_equation", + "content": "\\mathcal{B}" + }, + { + "bbox": [ + 46, + 378, + 286, + 533 + ], + "type": "text", + "content": ". Formally, a meta training batch is constructed by" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 108, + 542, + 286, + 576 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 542, + 286, + 576 + ], + "spans": [ + { + "bbox": [ + 108, + 542, + 286, + 576 + ], + "type": "interline_equation", + "content": "\\mathcal {B} = \\bigcup_ {j = 1} ^ {K} \\mathcal {B} _ {j} \\quad \\text {s . t .} \\quad \\mathcal {B} _ {j} \\in \\mathcal {G} _ {j}. \\tag {4}", + "image_path": "0d074003d503788281d0880631c8cc217a59177fe3d5dbf713942d0fcce12e07.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 585, + 286, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 585, + 286, + 624 + ], + "spans": [ + { + "bbox": [ + 47, + 585, + 286, + 624 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 585, + 286, + 624 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 47, + 585, + 286, + 624 + ], + "type": "text", + "content": " is the total number of subsets that satisfies " + }, + { + "bbox": [ + 47, + 585, + 286, + 624 + ], + "type": "inline_equation", + "content": "K = K_{1} + K_{2} + \\dots + K_{M}" + }, + { + "bbox": [ + 47, + 585, + 286, + 624 + ], + "type": "text", + "content": " and we rename each subset as group " + }, + { + "bbox": [ + 47, + 585, + 286, + 624 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_j" + }, + { + "bbox": [ + 47, + 585, + 286, + 624 + ], + "type": "text", + "content": " for convenience, satisfying " + }, + { + "bbox": [ + 47, + 585, + 286, + 624 + ], + "type": "inline_equation", + "content": "\\bigcup_{i=1}^{M} \\bigcup_{k=1}^{K_i} \\mathcal{D}_{i,k}^m = \\bigcup_{j=1}^{K} \\mathcal{G}_j" + }, + { + "bbox": [ + 47, + 585, + 286, + 624 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 624, + 286, + 660 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 624, + 286, + 660 + ], + "spans": [ + { + "bbox": [ + 46, + 624, + 286, + 660 + ], + "type": "text", + "content": "With the sampled meta training batch " + }, + { + "bbox": [ + 46, + 624, + 286, + 660 + ], + "type": "inline_equation", + "content": "\\mathcal{B}" + }, + { + "bbox": [ + 46, + 624, + 286, + 660 + ], + "type": "text", + "content": ", we can update the temporary prompt " + }, + { + "bbox": [ + 46, + 624, + 286, + 660 + ], + "type": "inline_equation", + "content": "p_j^m" + }, + { + "bbox": [ + 46, + 624, + 286, + 660 + ], + "type": "text", + "content": " on each meta task set " + }, + { + "bbox": [ + 46, + 624, + 286, + 660 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_j" + }, + { + "bbox": [ + 46, + 624, + 286, + 660 + ], + "type": "text", + "content": " by minimizing cross-entropy loss " + }, + { + "bbox": [ + 46, + 624, + 286, + 660 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_j^m" + }, + { + "bbox": [ + 46, + 624, + 286, + 660 + ], + "type": "text", + "content": ", i.e.," + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 102, + 669, + 286, + 699 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 669, + 286, + 699 + ], + "spans": [ + { + "bbox": [ + 102, + 669, + 286, + 699 + ], + "type": "interline_equation", + "content": "p _ {j} ^ {m} = p _ {j - 1} ^ {m} - \\eta \\nabla_ {p _ {j - 1} ^ {m}} \\frac {1}{| \\mathcal {B} _ {j} |} \\sum_ {x \\in \\mathcal {B} _ {j}} \\mathcal {L} _ {j} ^ {m}, \\tag {5}", + "image_path": "10e8b89146fb7eb015d5635bb6fa7acf8cb6156e254f0102843f33b2292d212b.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 80, + 702, + 230, + 716 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 702, + 230, + 716 + ], + "spans": [ + { + "bbox": [ + 80, + 702, + 230, + 716 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\text {s . t .} \\quad \\mathcal {L} _ {j} ^ {m} = \\mathcal {L} _ {C E} (\\mathcal {M} (x + p _ {j - 1} ^ {m}), y), \\end{array}", + "image_path": "4983663a9e71b457e1159734c352be36bd0341916e92f222576c9f6133952068.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 72, + 545, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 545, + 108 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 545, + 108 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 72, + 545, + 108 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 306, + 72, + 545, + 108 + ], + "type": "text", + "content": " is the ground-truth label of " + }, + { + "bbox": [ + 306, + 72, + 545, + 108 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 306, + 72, + 545, + 108 + ], + "type": "text", + "content": ". Finally, we implement meta update to get the new meta prompt after training on meta batch " + }, + { + "bbox": [ + 306, + 72, + 545, + 108 + ], + "type": "inline_equation", + "content": "\\mathcal{B}" + }, + { + "bbox": [ + 306, + 72, + 545, + 108 + ], + "type": "text", + "content": " by moving average," + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 356, + 113, + 545, + 147 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 356, + 113, + 545, + 147 + ], + "spans": [ + { + "bbox": [ + 356, + 113, + 545, + 147 + ], + "type": "interline_equation", + "content": "p ^ {m} \\leftarrow p ^ {m} + \\gamma \\frac {1}{K} \\sum_ {j = 1} ^ {K} \\left(p _ {j} ^ {m} - p ^ {m}\\right), \\tag {6}", + "image_path": "04fe6da5582c78760e693813b5ba207a6a55611599884da6596fadb5b1f0ab56.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 152, + 533, + 164 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 152, + 533, + 164 + ], + "spans": [ + { + "bbox": [ + 306, + 152, + 533, + 164 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 152, + 533, + 164 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 306, + 152, + 533, + 164 + ], + "type": "text", + "content": " is the meta update step that varies within " + }, + { + "bbox": [ + 306, + 152, + 533, + 164 + ], + "type": "inline_equation", + "content": "(0,1)" + }, + { + "bbox": [ + 306, + 152, + 533, + 164 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 173, + 386, + 186 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 173, + 386, + 186 + ], + "spans": [ + { + "bbox": [ + 306, + 173, + 386, + 186 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 193, + 355, + 205 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 193, + 355, + 205 + ], + "spans": [ + { + "bbox": [ + 306, + 193, + 355, + 205 + ], + "type": "text", + "content": "4.1. Setup" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 211, + 545, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 211, + 545, + 354 + ], + "spans": [ + { + "bbox": [ + 305, + 211, + 545, + 354 + ], + "type": "text", + "content": "Datasets. Here we select 16 popular image datasets for the experiments including CIFAR10 [29], CIFAR100 [29], DTD [10], CUB200 [48], NABirds [22], Stanford-Dogs [28], Oxford-Flowers [40], Food101 [3], GTSRB [46], SVHN [37], SUN397 [49], STL10 [11], Fru92 [23], Veg200 [23], Oxford-IIIT Pet [41] and EuroSAT [21], where the first 10 datasets are used for prompt evaluation and the remaining 6 are prepared for our meta prompt initialization. For data preprocessing, we randomly resize the input image into the size of " + }, + { + "bbox": [ + 305, + 211, + 545, + 354 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 305, + 211, + 545, + 354 + ], + "type": "text", + "content": " and subsequently crop it into " + }, + { + "bbox": [ + 305, + 211, + 545, + 354 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 305, + 211, + 545, + 354 + ], + "type": "text", + "content": ". More details including the performance on VTAB-1k benchmark [52] are provided in supplementary." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 355, + 545, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 355, + 545, + 461 + ], + "spans": [ + { + "bbox": [ + 305, + 355, + 545, + 461 + ], + "type": "text", + "content": "Models. Our experiments involve six pre-trained vision models including ImageNet-1k [12] supervised ViT-B/16 [14], supervised ResNet-50 [20], MoCo v3 [8] learned ViT-B/16; ImageNet-22k supervised ViT-B/16 and SwinBase [34]; 400m web data contrastive learning ViT-B/16 model CLIP [43]. As we illustrated above, our DAM-VP could be used for models without classification heads and traditional convolution networks, we discuss these settings in the supplementary materials." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 462, + 545, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 462, + 545, + 533 + ], + "spans": [ + { + "bbox": [ + 305, + 462, + 545, + 533 + ], + "type": "text", + "content": "Baselines. We compare our method with both parameter-tuning methods and prompt-tuning methods. For parameter-tuning, we report the fully-tuning, linear probing results as baseline, and the efficient-tuning method Adapter [24, 42]. For prompt-tuning, we compare with the VP [1] and VPT [26]." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 534, + 545, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 534, + 545, + 594 + ], + "spans": [ + { + "bbox": [ + 305, + 534, + 545, + 594 + ], + "type": "text", + "content": "Diversity metrics. To quantitatively measure the data diversity of a given dataset, we follow [1] to randomly sample 10,000 image pairs in each dataset and compute the LPIPS distance [54] of each pair. The average LPIPS is regarded to measure the perceptual diversity of the given dataset." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 594, + 545, + 713 + ], + "type": "text", + "content": "Implementation details. For meta learning based prompt initialization, we unify update learning rate " + }, + { + "bbox": [ + 305, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 305, + 594, + 545, + 713 + ], + "type": "text", + "content": " (in Eq. (5)) as 0.5 and meta step size " + }, + { + "bbox": [ + 305, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 305, + 594, + 545, + 713 + ], + "type": "text", + "content": " (in Eq. (6)) as 0.5. Our meta prompts of different pre-trained backbones are equally trained for 200 epochs by Adam optimizer with a cosine annealing schedule. The step number for updating the temporary prompt on each meta task is set as 4. For diversity-aware adaption, we set the subset size " + }, + { + "bbox": [ + 305, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "|S_{\\mathcal{T}}|" + }, + { + "bbox": [ + 305, + 594, + 545, + 713 + ], + "type": "text", + "content": " as 1000 by default. More implementation details, such as training or clustering configurations, are provided in our supplementary." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10882" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 53, + 70, + 541, + 178 + ], + "blocks": [ + { + "bbox": [ + 53, + 70, + 541, + 178 + ], + "lines": [ + { + "bbox": [ + 53, + 70, + 541, + 178 + ], + "spans": [ + { + "bbox": [ + 53, + 70, + 541, + 178 + ], + "type": "table", + "html": "
Extra HeadDTD [10]CUB200 [48]NABirds [22]Dogs [28]Flowers [40]Food101 [3]CIFAR100 [29]CIFAR10 [29]GTSRB [46]SVHN [37]Average
Data diversity-78.776.074.873.472.772.770.970.267.561.8-
Fully-Tuning✓70.684.772.384.698.383.087.597.496.896.987.2
Linear✓68.783.569.384.497.778.577.692.965.661.177.9
Adapter [24, 42]X47.717.53.832.040.146.143.072.882.219.640.5
VP [1]X47.840.613.861.956.555.754.492.986.087.859.7
VPT [26]X27.810.91.336.79.363.031.846.184.328.233.9
DAM-VP (10 epochs)X51.343.622.370.865.961.561.590.579.785.763.3
DAM-VP (50 epochs)X53.964.638.675.584.166.667.292.486.288.471.8
", + "image_path": "b89ca6df6b1cfb4c1273a704233870862aec19b632fbe109baf00da2845e6593.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 53, + 219, + 541, + 319 + ], + "blocks": [ + { + "bbox": [ + 46, + 186, + 546, + 210 + ], + "lines": [ + { + "bbox": [ + 46, + 186, + 546, + 210 + ], + "spans": [ + { + "bbox": [ + 46, + 186, + 546, + 210 + ], + "type": "text", + "content": "Table 1. Head-freezing/missing adaption performance of different methods on ViT-B-1K, where we report image classification accuracy and all of baseline methods are trained for 50 epochs." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 53, + 219, + 541, + 319 + ], + "lines": [ + { + "bbox": [ + 53, + 219, + 541, + 319 + ], + "spans": [ + { + "bbox": [ + 53, + 219, + 541, + 319 + ], + "type": "table", + "html": "
Extra HeadDTD [10]CUB200 [48]NABirds [22]Dogs [28]Flowers [40]Food101 [3]CIFAR100 [29]CIFAR10 [29]GTSRB [46]SVHN [37]Average
Data diversity-78.776.074.873.472.772.770.970.267.561.8-
Fully-Tuning✓78.681.972.680.597.391.880.996.395.395.787.1
Linear✓77.081.572.479.595.892.279.895.085.669.282.8
TP [43]X41.855.544.762.565.587.764.687.540.213.756.4
VP [1]X54.356.846.363.571.786.570.793.290.590.473.4
DAM-VP (10 epochs)X58.461.149.668.684.585.068.392.787.687.974.4
DAM-VP (50 epochs)X63.765.954.871.587.087.772.293.792.390.477.9
", + "image_path": "69ff0aec04c0a43f567b7e43232908e448d4bb37186ed08b0b298e60f6d869b5.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 380, + 237, + 392 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 380, + 237, + 392 + ], + "spans": [ + { + "bbox": [ + 47, + 380, + 237, + 392 + ], + "type": "text", + "content": "4.2. Comparison with Baseline Methods" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 400, + 289, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 400, + 289, + 652 + ], + "spans": [ + { + "bbox": [ + 46, + 400, + 289, + 652 + ], + "type": "text", + "content": "Quantitative results. We comprehensively compare our method with the baselines mentioned in Section 4.1. Two scenarios are taken into our consideration: 1) head-freezing/missing adaption, i.e., only tuning the introduced modules like prompts without any extra task-specific head. 2) head-tuning adaption, i.e., tuning the introduced modules like prompts along with learning a task-specific head. Table 1 and 2 show the quantitative comparison results of the head-freezing/missing setting between our DAM-VP and other adaption methods. We can find that our method significantly outperforms baseline methods even when our prompts are just trained for 10 epochs. Table 4 and 5 show the quantitative comparison results of the head-tuning setting between our DAM-VP and other adaption methods. It is easy to discover that DAM-VP presents its strong ability to help pre-trained models generalize on various image datasets, surpassing other methods with fewer training epochs and higher recognition accuracy. Furthermore, our DAM-VP even outperforms the fully-tuning setting on both the ViT-B-22K model and the Swin-B-22K model with only 50 epochs tuning." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "content": "Qualitative results. To better observe the adaption performance of each method, we depict the Top-1 accuracy curve of the first 50 training epochs to investigate the differences. Figure 7 shows the curve results of DAM-VP and the other three baselines in both head-freezing/missing and" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 312, + 378, + 539, + 446 + ], + "blocks": [ + { + "bbox": [ + 46, + 326, + 546, + 361 + ], + "lines": [ + { + "bbox": [ + 46, + 326, + 546, + 361 + ], + "spans": [ + { + "bbox": [ + 46, + 326, + 546, + 361 + ], + "type": "text", + "content": "Table 2. Head-freezing/missing adaption performance of different methods on CLIP-ViT-B, where we report image classification accuracy and all of baseline methods are trained for 50 epochs. \"TP\" denotes text prompting that directly adopts zero-shot classification head of CLIP. Here \"VP\" and our method also use this fixed head rather than particular mapping to get output logits." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 312, + 378, + 539, + 446 + ], + "lines": [ + { + "bbox": [ + 312, + 378, + 539, + 446 + ], + "spans": [ + { + "bbox": [ + 312, + 378, + 539, + 446 + ], + "type": "table", + "html": "
SettingMetaDiversityCUB200 [48]Flowers [40]CIFAR100 [29]SVHN [37]
AXX41.259.955.187.9
B✓X43.965.759.488.1
CX✓63.381.566.988.2
D✓✓64.684.167.288.4
", + "image_path": "05cd0cf6bb286da99c2b4b37f386fabb84dabdad1b50e122c45f13f050d11580.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 453, + 545, + 477 + ], + "lines": [ + { + "bbox": [ + 305, + 453, + 545, + 477 + ], + "spans": [ + { + "bbox": [ + 305, + 453, + 545, + 477 + ], + "type": "text", + "content": "Table 3. Ablation results of diversity-aware strategy and metaprompt initialization. We report Top-1 accuracy on ViT-B-1K." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 496, + 547, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 496, + 547, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 496, + 547, + 605 + ], + "type": "text", + "content": "head-tuning scenarios, where four datasets with different diversities are selected. It is obvious that, the performance of DAM-VP is far ahead in the early stage, especially in the first 10 epochs. This phenomenon indicates our diversity-aware strategy can boost the efficiency of prompt optimization, since each prompt just need to learn from a group of images that already have considerable homogeneity. The design of meta-prompt initialization also benefits this quick converging of our method with a good start point." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 611, + 400, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 611, + 400, + 624 + ], + "spans": [ + { + "bbox": [ + 306, + 611, + 400, + 624 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 629, + 547, + 701 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 547, + 701 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 547, + 701 + ], + "type": "text", + "content": "Component ablation. We first verify the significance of the proposed diversity-aware strategy and the meta-prompt initialization on four aforementioned datasets that have different diversities. As listed in Table 3, both two components contribute a lot to boosting prompting performance, especially when dealing with task data that has high diversity." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "type": "text", + "content": "Prompt learning stability. Previous methods mainly ini-" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10883" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 53, + 70, + 541, + 178 + ], + "blocks": [ + { + "bbox": [ + 53, + 70, + 541, + 178 + ], + "lines": [ + { + "bbox": [ + 53, + 70, + 541, + 178 + ], + "spans": [ + { + "bbox": [ + 53, + 70, + 541, + 178 + ], + "type": "table", + "html": "
Extra HeadDTD [10]CUB200 [48]NABirds [22]Dogs [28]Flowers [40]Food101 [3]CIFAR100 [29]CIFAR10 [29]GTSRB [46]SVHN [37]Average
Data diversity-78.776.074.873.472.772.770.970.267.561.8-
Fully-Tuning✓64.387.382.789.498.884.968.997.497.187.485.8
Linear✓63.285.375.986.297.984.463.496.368.036.675.7
Adapter [24, 42]✓62.787.184.389.898.586.074.297.791.136.380.8
VP [1]✓59.584.677.784.597.780.578.794.289.487.683.4
VPT [26]✓65.888.584.290.299.083.378.896.890.778.185.5
DAM-VP (10 epochs)✓72.486.381.592.298.686.280.190.587.881.185.7
DAM-VP (50 epochs)✓73.187.582.192.399.286.988.197.390.687.988.5
", + "image_path": "430543b5698421e1944da9da6bf34fcb438ad9930ab2aa40b935bc862ca9f67f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 53, + 219, + 541, + 328 + ], + "blocks": [ + { + "bbox": [ + 46, + 186, + 547, + 210 + ], + "lines": [ + { + "bbox": [ + 46, + 186, + 547, + 210 + ], + "spans": [ + { + "bbox": [ + 46, + 186, + 547, + 210 + ], + "type": "text", + "content": "Table 4. Head-tuning adaption performance of different methods on ViT-B-22K, where we report image classification accuracy and all of baseline methods are trained for 100 epochs." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 53, + 219, + 541, + 328 + ], + "lines": [ + { + "bbox": [ + 53, + 219, + 541, + 328 + ], + "spans": [ + { + "bbox": [ + 53, + 219, + 541, + 328 + ], + "type": "table", + "html": "
Extra HeadDTD [10]CUB200 [48]NABirds [22]Dogs [28]Flowers [40]Food101 [3]CIFAR100 [29]CIFAR10 [29]GTSRB [46]SVHN [37]Average
Data diversity-78.776.074.873.472.772.770.970.267.561.8-
Fully-Tuning✓72.489.786.886.298.391.773.398.397.191.288.5
Linear✓73.688.685.285.999.488.261.696.383.843.580.6
Adapter [24, 42]✓73.988.584.686.898.988.785.796.583.671.385.9
VP [1]✓75.186.582.981.398.683.480.694.882.480.384.6
VPT [26]✓78.590.085.484.899.390.180.596.986.287.887.9
DAM-VP (10 epochs)✓77.089.486.888.399.690.285.596.484.779.087.7
DAM-VP (50 epochs)✓80.090.486.988.599.690.588.197.386.881.789.0
", + "image_path": "51ce5ced9d012ea4dea878ae7e4cde9a4e8b805de6eadd44cee410e59e6ca261.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 335, + 546, + 360 + ], + "lines": [ + { + "bbox": [ + 46, + 335, + 546, + 360 + ], + "spans": [ + { + "bbox": [ + 46, + 335, + 546, + 360 + ], + "type": "text", + "content": "Table 5. Head-tuning adaption performance of different methods on Swin-B-22K, where we report image classification accuracy and all of baseline methods are trained for 100 epochs." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 50, + 365, + 157, + 449 + ], + "blocks": [ + { + "bbox": [ + 50, + 365, + 157, + 449 + ], + "lines": [ + { + "bbox": [ + 50, + 365, + 157, + 449 + ], + "spans": [ + { + "bbox": [ + 50, + 365, + 157, + 449 + ], + "type": "image", + "image_path": "e0171f5e7993f9c6bbff894f9d0b5c5e256adda68990a0487e5d372dfa305671.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 462, + 288, + 498 + ], + "lines": [ + { + "bbox": [ + 46, + 462, + 288, + 498 + ], + "spans": [ + { + "bbox": [ + 46, + 462, + 288, + 498 + ], + "type": "text", + "content": "Figure 5. Meta-prompt initialization makes prompt tuning more robust to the random factor. We test in both head-freezing/missing (ViT-B-1K, left) and head-tuning (ViT-B-22K, right) cases." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 167, + 365, + 276, + 449 + ], + "blocks": [ + { + "bbox": [ + 167, + 365, + 276, + 449 + ], + "lines": [ + { + "bbox": [ + 167, + 365, + 276, + 449 + ], + "spans": [ + { + "bbox": [ + 167, + 365, + 276, + 449 + ], + "type": "image", + "image_path": "79bf899e77d719cda20f16fcfe6b41700cb79fda5a1e4a95b7338bec2871d935.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 520, + 287, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 520, + 287, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 520, + 287, + 640 + ], + "type": "text", + "content": "tialize the prompt randomly, this leads to the instability of the performance caused by different random seeds. On the contrary, our meta-prompt design provides a good initialization point for optimization, which not only boosts the prompting performance but also improves the training stability. To eliminate the impact of random seeds, we test on 5 random seeds in experiments and report the results in Figure 5. It can be found that our meta-prompt initialization provides superb robustness across different training random seeds, while the randomly initialized prompt is unstable." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": "Meta-prompt dataset number. As we elaborated in Sec. 4.1, there are 6 datasets prepared for our meta-prompt learning, which is also the default setting we used. Here we ablate this setting by reducing the number of meta datasets. As shown in Figure 6, when the meta dataset number is 0, i.e., no meta-prompt is used, our DVM-VP gets a rea" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 309, + 367, + 416, + 449 + ], + "blocks": [ + { + "bbox": [ + 309, + 367, + 416, + 449 + ], + "lines": [ + { + "bbox": [ + 309, + 367, + 416, + 449 + ], + "spans": [ + { + "bbox": [ + 309, + 367, + 416, + 449 + ], + "type": "image", + "image_path": "1e99316bbed12710dd07868dfa18894eb1a8aa157afe91b302195b90254b6a13.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 456, + 545, + 489 + ], + "lines": [ + { + "bbox": [ + 305, + 456, + 545, + 489 + ], + "spans": [ + { + "bbox": [ + 305, + 456, + 545, + 489 + ], + "type": "text", + "content": "Figure 6. Ablating meta-prompt dataset number on DTD in the head-freezing/missing setting (ViT-B-1K, left) and the head-tuning (ViT-B-22K, right) setting." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 427, + 366, + 534, + 449 + ], + "blocks": [ + { + "bbox": [ + 427, + 366, + 534, + 449 + ], + "lines": [ + { + "bbox": [ + 427, + 366, + 534, + 449 + ], + "spans": [ + { + "bbox": [ + 427, + 366, + 534, + 449 + ], + "type": "image", + "image_path": "f1ddfe7250423d35f4017643622cbdd2727b2d2ff08ea8677fe053ae5779cdeb.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 516, + 545, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 516, + 545, + 601 + ], + "spans": [ + { + "bbox": [ + 304, + 516, + 545, + 601 + ], + "type": "text", + "content": "sonable result that performs better than previous baseline methods. With the number of meta datasets increases, the prompting performance in both head-freezing/missing and head-tuning scenarios generally gets boosted. It proves that more prompting knowledge obtained from previous data is quite helpful for visual prompts to reduce the data distribution gap between downstream tasks and pretraining tasks." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 603, + 545, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 603, + 545, + 674 + ], + "spans": [ + { + "bbox": [ + 304, + 603, + 545, + 674 + ], + "type": "text", + "content": "Meta-prompt update step size " + }, + { + "bbox": [ + 304, + 603, + 545, + 674 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 304, + 603, + 545, + 674 + ], + "type": "text", + "content": ". The step size " + }, + { + "bbox": [ + 304, + 603, + 545, + 674 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 304, + 603, + 545, + 674 + ], + "type": "text", + "content": " is a crucial hyper-parameter applied in the meta-prompt update. Here we ablate different step sizes that vary from 0.1 to 0.7 with the results given in Figure 8. Compared with baselines, the performance is relatively robust to different step sizes. We choose " + }, + { + "bbox": [ + 304, + 603, + 545, + 674 + ], + "type": "inline_equation", + "content": "\\eta = 0.5" + }, + { + "bbox": [ + 304, + 603, + 545, + 674 + ], + "type": "text", + "content": " as the default configuration." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 677, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 715 + ], + "type": "text", + "content": "Different size of subset " + }, + { + "bbox": [ + 304, + 677, + 545, + 715 + ], + "type": "inline_equation", + "content": "S_{\\mathcal{T}}" + }, + { + "bbox": [ + 304, + 677, + 545, + 715 + ], + "type": "text", + "content": ". 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Test accuracy curves of different adaption methods when adapting pre-trained ViT-B-1K to different datasets in head-freezing/missing scenario (top row) and adapting pre-trained ViT-B-22K to different datasets head-tuning scenario (bottom row)." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 172, + 176, + 287, + 278 + ], + "blocks": [ + { + "bbox": [ + 172, + 176, + 287, + 278 + ], + "lines": [ + { + "bbox": [ + 172, + 176, + 287, + 278 + ], + "spans": [ + { + "bbox": [ + 172, + 176, + 287, + 278 + ], + "type": "image", + "image_path": "5afecc478053bcc0f9945b81902c0c99251ee90271dce06861bd9cd2bdd3e6ba.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 296, + 176, + 412, + 278 + ], + "blocks": [ + { + "bbox": [ + 296, + 176, + 412, + 278 + ], + "lines": [ + { + "bbox": [ + 296, + 176, + 412, + 278 + ], + "spans": [ + { + "bbox": [ + 296, + 176, + 412, + 278 + ], + "type": "image", + "image_path": "f04f2ff2bfe014b5d7b4ef40d1b503077b2962ca94c62f0d24da34d210bc26df.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 421, + 176, + 536, + 278 + ], + "blocks": [ + { + "bbox": [ + 421, + 176, + 536, + 278 + ], + "lines": [ + { + "bbox": [ + 421, + 176, + 536, + 278 + ], + "spans": [ + { + "bbox": [ + 421, + 176, + 536, + 278 + ], + "type": "image", + "image_path": "658b3fa38396dde180ad06a181399b9bd69e2c1886cea99a2883ab86e5e08924.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 50, + 317, + 156, + 399 + ], + "blocks": [ + { + "bbox": [ + 50, + 317, + 156, + 399 + ], + "lines": [ + { + "bbox": [ + 50, + 317, + 156, + 399 + ], + "spans": [ + { + "bbox": [ + 50, + 317, + 156, + 399 + ], + "type": "image", + "image_path": "d6cd6ade1929a2934cf2f561a7ca2b99cacd772b9f95e8ed0303989a9ae7480f.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 407, + 287, + 431 + ], + "lines": [ + { + "bbox": [ + 46, + 407, + 287, + 431 + ], + "spans": [ + { + "bbox": [ + 46, + 407, + 287, + 431 + ], + "type": "text", + "content": "Figure 8. Ablating step size " + }, + { + "bbox": [ + 46, + 407, + 287, + 431 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 46, + 407, + 287, + 431 + ], + "type": "text", + "content": " on DTD in head-freezing/missing (ViT-B-1K, left) and head-tuning (ViT-B-22K, right) cases." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 170, + 317, + 276, + 399 + ], + "blocks": [ + { + "bbox": [ + 170, + 317, + 276, + 399 + ], + "lines": [ + { + "bbox": [ + 170, + 317, + 276, + 399 + ], + "spans": [ + { + "bbox": [ + 170, + 317, + 276, + 399 + ], + "type": "image", + "image_path": "d3385c8b9e70e325bcd883aeaf43c1f70745903897972c608c8da1ea3cd2d491.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 413, + 545, + 458 + ], + "lines": [ + { + "bbox": [ + 305, + 413, + 545, + 458 + ], + "spans": [ + { + "bbox": [ + 305, + 413, + 545, + 458 + ], + "type": "text", + "content": "Figure 9. (Left) Ablating the size of subset " + }, + { + "bbox": [ + 305, + 413, + 545, + 458 + ], + "type": "inline_equation", + "content": "S_{\\mathcal{T}}" + }, + { + "bbox": [ + 305, + 413, + 545, + 458 + ], + "type": "text", + "content": " in both head-freezing/missing (ViT-B-1K) and head-tuning (ViT-B-22K) cases. (Right) Comparison between hard-coded mapping and our active-based mapping used for head-freezing/missing case." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 452, + 287, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 452, + 287, + 559 + ], + "spans": [ + { + "bbox": [ + 46, + 452, + 287, + 559 + ], + "type": "text", + "content": "tion. Therefore, we apply different subset size that varies from 200 to 1000 to explore how it affects the prompting ability. From Figure 9 (left), we find that as the size of " + }, + { + "bbox": [ + 46, + 452, + 287, + 559 + ], + "type": "inline_equation", + "content": "S_{\\mathcal{T}}" + }, + { + "bbox": [ + 46, + 452, + 287, + 559 + ], + "type": "text", + "content": " increases, we can get higher performance in both scenarios. Meanwhile, we find our divide-and-conquer design is quite efficient that even with only 200 images, our DAM-VP still outperforms previous methods by a large margin. Considering the training images of some datasets are limited, we adopt 1,000 as the default size of " + }, + { + "bbox": [ + 46, + 452, + 287, + 559 + ], + "type": "inline_equation", + "content": "S_{\\mathcal{T}}" + }, + { + "bbox": [ + 46, + 452, + 287, + 559 + ], + "type": "text", + "content": " in this work." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 560, + 288, + 657 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 560, + 288, + 657 + ], + "spans": [ + { + "bbox": [ + 46, + 560, + 288, + 657 + ], + "type": "text", + "content": "Hard-coded mapping vs. Active-based mapping. As we discussed in Sec. 3, we argue the hard-coded mapping used by [1] for head-freezing/missing scenario is inefficient, since it might optimize some not active enough channels of the output feature (i.e., relatively robust to diverse model input), thus we propose active-based mapping to alleviate this issue. Figure 9 (right) show the comparison between these two mapping methods on VP, tested on ViT-B-1K." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 669, + 119, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 669, + 119, + 681 + ], + "spans": [ + { + "bbox": [ + 47, + 669, + 119, + 681 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "content": "This paper considers the data diversity property in downstream task adaption for prompting pre-trained vision mod" + } + ] + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 307, + 317, + 426, + 399 + ], + "blocks": [ + { + "bbox": [ + 307, + 317, + 426, + 399 + ], + "lines": [ + { + "bbox": [ + 307, + 317, + 426, + 399 + ], + "spans": [ + { + "bbox": [ + 307, + 317, + 426, + 399 + ], + "type": "image", + "image_path": "51acf8463bbd579ba26bb727998517dd03fc400378bf0fc932d699e267088f89.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 429, + 317, + 534, + 399 + ], + "blocks": [ + { + "bbox": [ + 429, + 317, + 534, + 399 + ], + "lines": [ + { + "bbox": [ + 429, + 317, + 534, + 399 + ], + "spans": [ + { + "bbox": [ + 429, + 317, + 534, + 399 + ], + "type": "image", + "image_path": "1def4f4642983b51b438edf51c1b924f032369450ffa6a15705bfeac967432a5.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 474, + 545, + 570 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 545, + 570 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 545, + 570 + ], + "type": "text", + "content": "els. We argue that the per-dataset generic prompt adopt in previous methods can hardly handle the dataset of large data diversity. To address this, we propose DAM-VP based on diversity-adaptive dataset partition and prompt selection, where our prompts is initialized by a meta-prompt that learns through a quick meta learning algorithm. Extensive experiments prove the superior performance of DAM-VP in both head-freezing/missing and head-tuning cases." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 570, + 546, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 546, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 546, + 712 + ], + "type": "text", + "content": "Acknowledgement. This work was supported in part by the Natural Science Foundation of China under Grant U20B2047, 62072421, 62002334, 62102386 and 62121002, Key Research and Development program of Anhui Province under Grant 2022k07020008, the Fundamental Research Funds for the Central Universities under Grant WK5290000003, Ant Group through CCF-Ant Innovative Research Program CCF-AFSG RF20210025, Alibaba Group through Alibaba Innovative Research Program. This work was also partly supported by Shenzhen Key Laboratory of Media Security, Shenzhen University, Shenzhen 518060, China." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10885" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 92, + 287, + 712 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 53, + 92, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 92, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 92, + 287, + 135 + ], + "type": "text", + "content": "[1] Hyojin Bahng, Ali Jahanian, Swami Sankaranarayanan, and Phillip Isola. 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IJCV, 2022. 2" + } + ] + } + ], + "index": 24 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10887" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Diversity-Measurable Anomaly Detection/43dbf769-f361-451d-b986-1893419fc738_content_list.json b/2023/Diversity-Measurable Anomaly Detection/43dbf769-f361-451d-b986-1893419fc738_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..52e667d4a47f8e7b97ef19fdbc5cf0a5a77e923f --- /dev/null +++ b/2023/Diversity-Measurable Anomaly Detection/43dbf769-f361-451d-b986-1893419fc738_content_list.json @@ -0,0 +1,1879 @@ +[ + { + "type": "text", + "text": "Diversity-Measurable Anomaly Detection", + "text_level": 1, + "bbox": [ + 274, + 130, + 694, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Wenrui Liu $^{1,2}$ , Hong Chang $^{1,2}$ , Bingpeng Ma $^{2}$ , Shiguang Shan $^{1,2}$ , Xilin Chen $^{1,2}$ $^{1}$ Institute of Computing Technology, Chinese Academy of Sciences, China \n $^{2}$ University of Chinese Academy of Sciences, China", + "bbox": [ + 171, + 179, + 795, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "wenrui.liu@vipl.ict.ac.cn, {changhong, sgshan, xlchen}@ict.ac.cn, bpma@ucas.ac.cn", + "bbox": [ + 120, + 236, + 841, + 252 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 286, + 313, + 301 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Reconstruction-based anomaly detection models achieve their purpose by suppressing the generalization ability for anomaly. However, diverse normal patterns are consequently not well reconstructed as well. Although some efforts have been made to alleviate this problem by modeling sample diversity, they suffer from shortcut learning due to undesired transmission of abnormal information. In this paper, to better handle the tradeoff problem, we propose Diversity-Measurable Anomaly Detection (DMAD) framework to enhance reconstruction diversity while avoid the undesired generalization on anomalies. To this end, we design Pyramid Deformation Module (PDM), which models diverse normals and measures the severity of anomaly by estimating multi-scale deformation fields from reconstructed reference to original input. Integrated with an information compression module, PDM essentially decouples deformation from prototypical embedding and makes the final anomaly score more reliable. Experimental results on both surveillance videos and industrial images demonstrate the effectiveness of our method. In addition, DMAD works equally well in front of contaminated data and anomaly-like normal samples.", + "bbox": [ + 75, + 316, + 473, + 650 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 679, + 209, + 695 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Visual anomaly detection is a fundamental and important problem in computer vision community, with wide applications in video surveillance and industrial inspection. It aims to detect outliers from seen classes and novel patterns from unseen classes. This task is very challenging because abnormal data is diversely distributed and expensive to collect. So we have to construct models based on only normal samples under unsupervised setting, targeting at high discrimination between normal and abnormal samples.", + "bbox": [ + 75, + 703, + 468, + 839 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "During the past decade, reconstruction-based methods have achieved great progress in anomaly detection. These methods use Autoencoders (AEs) [8,9,20,24,26,29,40] or Generative Adversarial Networks (GANs) [1, 19, 32] to re", + "bbox": [ + 75, + 839, + 470, + 901 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/7fe06ff0a8c5dfa5980addc51c64fe1415e2d3e8e9db3cb007947e25488f08a9.jpg", + "image_caption": [ + "Figure 1. Illustration of difficulty in anomaly detection in MNIST dataset. The prototype is indicated by orange triangle and the anomaly by red point. In this case, the anomaly can hardly be detected based on reconstruction error or distance in high-dimensional feature space. Our solution is illustrated in Fig. 2." + ], + "image_footnote": [], + "bbox": [ + 568, + 284, + 823, + 398 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "construct the normal counterparts from any input images or video frames. AE-based methods firstly compress the inputs to discard the information beyond normal prototypes, and then decode the embedding to reconstruct the inputs. According to the estimated reconstruction error, the anomalies can be detected.", + "bbox": [ + 496, + 507, + 890, + 595 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, the performance of reconstruction-based methods for anomaly detection has long been limited by a tough problem, i.e. the tradeoff between reconstructing diverse normals and detecting unknown anomalies. In order to discriminate anomalies more easily, previous works [8] imposes more constraints to suppress abnormal information during autoencoding, which leads to high reconstruction error for diverse normal instances. For example, in Figs. 1 and $2\\mathbf{g}$ , the severely deformed normal (a.k.a. anomaly-like) sample \"7\" has even higher error than the abnormal sample \"4\". To better reconstruct diverse normals, each query vector corresponds to multiple prototypes in the memory, which may be combined into abnormal embedding even if abnormal projection is far away from the prototype. As a consequence, anomalies that distribute in low likelihood area between prototypical embedding are difficult to identify from diverse normals. MNAD [29] introduces skipconnection for diverse reconstruction and additional constraints to get round the incorrect combination problem. But the latter forces model transmit more unrestrained in", + "bbox": [ + 496, + 598, + 892, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "12147", + "bbox": [ + 478, + 943, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3fd76b582e9bafb4bf2dff2c0675c3c5f31ec99cfce2667ad25fd7b40c78e662.jpg", + "image_caption": [ + "Figure 2. Illustration of our diversity-measurable method in addressing the detection difficulty. Numbers in white are anomaly scores. a) Original input; b) Reconstructed reference; c) Coarse deformation; d) Fine deformation; e) Measurement of diversity1; f) Deformation-augmented error map assigns lower anomaly score to the anomaly-like sample than the true anomaly; g) Pixel-wise reconstruction error yields incorrect anomaly scores." + ], + "image_footnote": [], + "bbox": [ + 76, + 87, + 468, + 223 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "formation with abnormal part by skip-connection, resulting in shortcut learning and undesired reconstruction of anomalies.", + "bbox": [ + 75, + 356, + 468, + 398 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "A key to address the above tradeoff problem is to find a proper measurement of diversity that normal and abnormal samples have, which is positively correlated with the severity of anomaly. With such a measure, we do not need to fight against imperfect reconstruction of normals or undesired reconstruction of anomalies, because anomalies can be detected more accurately by the diversity measure together with the reconstruction error. Note that pixel-wise reconstruction error is not an ideal measurement of diversity, because the high-error region often confuses anomalies with diverse normals, e.g. normals with structural deformation and anomalies with colors close to the background may yield unreliable reconstruction error.", + "bbox": [ + 75, + 401, + 468, + 595 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we propose a Diversity-Measurable Anomaly Detection (DMAD) framework to enhance the measurability of reconstruction diversity so as to measure abnormality more accurately. Our basic idea is to decouple the reconstruction into compact representation of prototypical normals and measurable deformations of more diverse normals and anomalies. The under-estimated reconstruction error can be compensated by the diversity, which can be properly measured. To this end, the DMAD framework includes a Pyramid Deformation Module (PDM) to model and measure the diversity and an Information Compression Module (ICM) to learn the prototypical normal patterns.", + "bbox": [ + 75, + 598, + 468, + 777 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Inspired by [4, 15], we assume anomalies (e.g. in video surveillance) can be represented as significant deformation of appearances, including positional changes and fine motions. In contrast, diverse normal samples can be represented as weaker deformations thus easily distinguished", + "bbox": [ + 75, + 779, + 468, + 854 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "from the abnormal ones. Therefore, we design PDM to model the diversity of normals as well as the severity of anomalies. More specifically, PDM learns hierarchical two-dimensional deformation fields (Fig. 2c,d) that describe the pixel-level transformation direction and distance from reference (Fig. 2b, which is reconstructed from prototypes in memory) to original input. In ICM, we learns compressed representation as sparse prototypes. As a result, a single memory item is enough to represent each normal cluster. This is more compact than other memory-based works which require multiple memory items. Integrating PDM with ICM, DMAD essentially decouples the deformation information (Fig. 2e) from class prototypes and makes the final anomaly score more discriminative (Fig. 2f).", + "bbox": [ + 500, + 90, + 890, + 301 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We evaluate our anomaly detection framework in scenarios of video surveillance and industrial defect detection. To apply DMAD in the latter scenario, we propose a variant of PDM, PPDM, to deal with the false positive issue in texture reconstruction. Extensive experimental results verify the efficacy of our approach. Moreover, our method works well even in front of contaminated data and anomaly-like normals. The main contributions of our work are as follows:", + "bbox": [ + 498, + 303, + 890, + 422 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We introduce diversity-measurable anomaly detection framework which allows reconstruction-based models to achieve better tradeoff between reconstructing diverse normals and detecting unknown anomalies.", + "- We propose pyramid deformation module to implement diversity measurement, in which the deformation information is explicitly separated from compact class prototypes and the resulting diversity measure is positively correlated to abnormality.", + "- Our approach outperforms previous works on video anomaly detection and industrial defect detection, and works well in front of contaminated data and anomaly-like normals, demonstrating its broad suitability and robustness." + ], + "bbox": [ + 501, + 428, + 890, + 643 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 662, + 640, + 678 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Anomaly detection. Reconstruction-based methods model the distribution of normal data and assign anomalies with high reconstruction error, because models trained with only normal data cannot reconstruct anomalies. Some works use autoencoder to detect anomalies, such as convolutional autoencoder [9] and the variants [24, 40]. Other approaches introduce additional constraints or memory to make the model more discriminative. For example, sparse coding [25, 39] reduces representation redundancy with regularization; memory-augmented autoencoder (MemAE) [8] memorizes the normal patterns appearing in training dataset with external memory bank; variational autoencoder [10, 35] assumes a prior distribution of normal data to constrain the nonlinear representation capacity; $\\mathrm{HF}^2\\mathrm{VAD}$ [20]", + "bbox": [ + 498, + 688, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_footnote", + "text": "1In this case, we only count fine deformation because deformations in position and angle are considered as normal. In real-world experiments, we consider both coarse and fine deformations.", + "bbox": [ + 75, + 862, + 468, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "12148", + "bbox": [ + 480, + 943, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "uses CVAE [33] to capture the correlation among motions. Frame prediction [19] assumes that abnormal samples in videos cannot be represented by past frames that do not contain unseen information and forces the model to encode changes among different frames. In addition, autoencoders can also be combined with external object detectors [7, 14, 20] to capture background-invariant appearance.", + "bbox": [ + 75, + 90, + 467, + 196 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Although these methods generally work well, they often have difficulty in discriminating abnormal samples from anomaly-like normals due to the tradeoff between reconstruction and discrimination. In our framework, pyramid deformation module and information compression module are leveraged to address the trade-off problem, significantly improving the performance in anomaly detection.", + "bbox": [ + 75, + 198, + 467, + 303 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Memory network. Generative models map continuously in feature space and they may assign higher probabilities to anomalies than normal ones [28]. Recent research [8, 11, 20, 29] has explored the application of discrete external memory to generate seen normal patterns even if the input is abnormal. MemAE [8] proposes a memory-augmented autoencoder, which uses information from encoder as a query and obtains a normal pattern retrieved from memory module. MNAD [29] introduces skip-connection to alleviate the problem that diverse normal patterns may yield high reconstruction errors. $\\mathrm{HF^2VAD}$ [20] extends the memory module to multi-level memory, and uses additional estimators [3, 13] to explicitly model the motion information and filter the noise from background. DAAD [11] uses block-wise memory to increase the specificity of memory.", + "bbox": [ + 75, + 306, + 467, + 532 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In most existing works, the memory module outputs a linear combination of memory items which may lead to undesired reconstruction of normal-like anomalies. And they do not explicitly consider that instances corresponding to the same memory grid may be located at different positions of the receptive field. In our approach, we alleviate these problems via compressing embedding into a single memory item to ensure that the output is absolutely normal.", + "bbox": [ + 75, + 535, + 467, + 654 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Transformation modeling. The transformation between video frames is a key clue for anomaly detection. Some methods [7, 14, 19, 20] use external object detectors or optical-flow estimators to model the motion information implicitly or explicitly. Among the transformation estimators, optical-flow estimation [13] is widely studied, which aims to estimate the pixel-wise motions between consecutive frames. In addition, correspondence modeling between pair-wise images is also applied to 2D geometric matching [30] and 3D image registration [36] to obtain image deformation fields. STN [15] learns to transform the original images themselves to benefit identification algorithm. RegAD [12] uses feature-level affine registration to relocate features without changing the embeddings.", + "bbox": [ + 75, + 657, + 467, + 867 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "However, pairwise transformation modeling only focus on pattern changes thus cannot detect static anomalies. And", + "bbox": [ + 76, + 869, + 467, + 898 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/0ab9514c0ff3786bac933b6a545f46d20aef4b977f82968b3a9fd7c454f4f4b8.jpg", + "image_caption": [ + "Figure 3. Three conditions for DMAD framework. The colors of lines represent the measurements of diversity (severity of anomaly); The gray area represents uncertainty in the measure; Double dashed arrows indicate possible ranges of the boundary. The last two lines denote DMAD and traditional reconstruction-based method respectively." + ], + "image_footnote": [], + "bbox": [ + 500, + 85, + 890, + 223 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "pretrained transformation estimators introduce generalization error in different scenarios. In contrast, we address these problems by separating and measuring the transformation from prototypical memory in end-to-end training.", + "bbox": [ + 498, + 342, + 890, + 402 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Diversity-Measurable Anomaly Detection", + "text_level": 1, + "bbox": [ + 500, + 415, + 869, + 431 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we first analyze the objective of reconstruction-based anomaly detection and propose a diversity-measurable framework to address the tradeoff problem in existing works. Then, we introduce information compression module and pyramid deformation module (PDM) as an implementation of the framework. Finally, we explain the training and inference process and how to apply the framework to defect detection with a variant of PDM.", + "bbox": [ + 498, + 440, + 890, + 559 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. The framework", + "text_level": 1, + "bbox": [ + 500, + 569, + 656, + 583 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given input $x$ , autoencoder-based methods aim to model normal data distribution by minimizing the following reconstruction loss $(\\| \\cdot \\|_2$ is just one type of reconstruction loss):", + "bbox": [ + 498, + 592, + 890, + 638 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nL = \\| x - g (\\phi (f (x), z)) \\| _ {2} + \\gamma_ {1} R _ {1} (\\phi), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 563, + 646, + 890, + 664 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "with respect to encoder $f(\\cdot)$ , decoder $g(\\cdot)$ , latent variable $z$ (referring to discrete memory items in these cases) and a constrained feature mapping function $\\phi(\\cdot)$ corresponding to its constraint $R_1(\\phi)$ . Skip-connection and concatenation $[\\cdot, \\cdot]$ are introduced to generate diverse normal patterns [29]:", + "bbox": [ + 498, + 670, + 890, + 747 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nL = \\| x - g ([ \\phi (f (x), z), f (x) ]) \\| _ {2} + \\gamma_ {1} R _ {1} (\\phi). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 539, + 753, + 890, + 772 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "However, due to diverse data distribution, previous methods have to face the conflict between representing diverse normals and detecting anomalies. The intrinsic reason lies in that the encoding of diversity $[\\cdot ,f(x)]$ contains redundant information that cannot be measured accurately.", + "bbox": [ + 498, + 779, + 890, + 853 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this work, we propose a principled framework, Diversity-Measurable Anomaly Detection (DMAD), to alleviate the conflict. The basic idea is to restrict the anomaly", + "bbox": [ + 498, + 854, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "12149", + "bbox": [ + 478, + 943, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/8f7b4f6390eecdfad989b5ccda968651119a9a84d06ee3ffe2c9a11e9f607409.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 81, + 85, + 436, + 282 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/55440356652e7e8fd158ef7f0561bd0b784bf88f0ed21f997d0a3e8046543e6c.jpg", + "image_caption": [ + "(b)", + "Figure 4. Two versions of diversity-measurable anomaly detection framework. Multi-scale pyramid deformation fields are estimated as $\\mathbf{O}$ and the reverse processes are $\\mathbf{O}^T$ . a) PDM version computes forward deformation $\\mathbf{O}$ after reconstruction. b) PPDM version employs cycle-consistent forward-backward deformations and the forward deformation is applied on the input." + ], + "image_footnote": [], + "bbox": [ + 439, + 87, + 883, + 284 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "information transmitted to $g(\\cdot)$ while measuring and modeling the diversity of the remaining part. To this end, we design information compression module $\\phi(\\cdot)$ and diversity-aware module $\\psi(\\cdot)$ under DMAD framework:", + "bbox": [ + 75, + 372, + 468, + 434 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL = \\| x - g (\\phi (f (x), z)) \\circ \\psi (x) \\| _ {2} + \\gamma_ {1} R _ {1} (\\phi) + \\gamma_ {2} R _ {2} (\\psi), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 445, + 468, + 477 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\circ$ refers to aggregation operator. With appropriate design of $\\phi(\\cdot), \\psi(\\cdot)$ and the constraints, optimization of the reconstruction loss can improve the compactness of feature embedding. So that diverse representations are mapped via $\\phi(\\cdot)$ to compact prototypes in the memory. The diversity of input $x$ relative to its reconstruction is represented by $\\psi(\\cdot)$ . The under-estimated reconstruction error can be compensated by the diversity measured in $\\psi(\\cdot)$ , a key factor contributing to accurate anomaly scores.", + "bbox": [ + 75, + 477, + 468, + 611 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This framework can achieve our target on the premise that the following conditions (Fig. 3) are met: 1. $\\psi(\\cdot)$ can learn all diverse information from prototypical patterns to any normal inputs to ensure normal samples do not yield high anomaly score; 2. Deformation generated by $\\psi(\\cdot)$ is positively correlated to diversity measure; 3. Prototypical information about $x$ represented by $\\psi(\\cdot)$ needs to be minimized. In the following subsections, we explain how to design modules to fulfill these conditions.", + "bbox": [ + 75, + 612, + 470, + 748 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Information compression module", + "text_level": 1, + "bbox": [ + 76, + 758, + 369, + 773 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "According to [35], we adapt VQ-Layer as an information compression module to learn $\\phi(\\cdot)$ given embedding $f(x) \\in R^{D \\times H' \\times W'}$ as a query $z^e = f(x)$ and memory $z \\in R^{D \\times N}$ . Then, we quantize $z^e$ into a single-memory feature cube $z^q \\in R^{D \\times H' \\times W'}$ by seeking for memory item with minimum $L2$ distance (\"Search\" in Fig. 4):", + "bbox": [ + 76, + 781, + 470, + 875 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nz _ {h, w} ^ {q} = \\operatorname {a r g m i n} _ {z _ {n}} \\left\\| z _ {h, w} ^ {e} - z _ {n} \\right\\| _ {2}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 161, + 883, + 468, + 904 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $z_{n}$ is the $n^{th}$ memory item, $h\\in \\{1,\\dots ,H^{\\prime}\\} ,w\\in$ $\\{1,\\dots ,W^{\\prime}\\}$ indicates the same location in both $z^q$ and $z^{e}$ . The compression loss $L_{com}$ with stop-gradient operator $SG(\\cdot)$ that updates its parameters separately [35] is combined by a hyperparameter $\\beta$ :", + "bbox": [ + 498, + 372, + 893, + 449 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {c o m} = \\left\\| S G \\left(z ^ {e}\\right) - z ^ {q} \\right\\| _ {2} + \\beta \\left\\| z ^ {e} - S G \\left(z ^ {q}\\right) \\right\\| _ {2}. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 527, + 460, + 890, + 479 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Skip-connection with low information capacity (Fig. 4 \"Comp.\") is also allowed to further improve the reconstruction quality without bringing excessive generalization (i.e. Conv-Layer with stop-gradient operator for intermediate features whose reduction factor is 16 or larger).", + "bbox": [ + 498, + 489, + 893, + 566 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Pyramid deformation module", + "text_level": 1, + "bbox": [ + 500, + 575, + 764, + 593 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We categorize the unknown anomalies into the following three types: unseen class (e.g. novel objects), global anomaly (e.g. unexpected movement) and local anomaly (e.g. strange behavior and workpiece damage) of seen class. The unseen class is easy to be detected based on reconstruction result, but the latter two types are usually confused with diverse normals. To discriminate these anomalies from normal ones, we represent the diversity using measurable deformation between reconstructed reference and original input, so that slight deformations occur in normals while drastic deformations occur in anomalies.", + "bbox": [ + 496, + 599, + 890, + 763 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Inspired by STN and DCN [4, 15], we introduce Pyramid Deformation Module (PDM) which explicitly learn deformation fields with hierarchical scales to model the motion, behavior and defect of different anomaly types, as shown in Fig. 4a. Specifically, after feature extraction, $\\psi(\\cdot)$ uses $K$ -heads to compute offsets $\\mathbf{O} = \\{O_1, \\dots, O_K\\}$ , corresponding to $K$ coarse-to-fine deformations:", + "bbox": [ + 496, + 766, + 893, + 873 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\psi (x) = U p \\left(h \\left(P E (x)\\right)\\right) = \\mathbf {O}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 883, + 890, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "12150", + "bbox": [ + 478, + 943, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $PE(\\cdot)$ is positional embedding operator [18], $h: R^{C \\times H \\times W} \\to R^{2 \\times \\{H_1 \\times W_1, \\dots, H_K \\times W_K\\}}$ is the deformation estimator that generates offset vectors, $Up(\\cdot)$ is upsampling function that resizes the outputs of $K$ -heads to the same size with the original image. In our experiments, we set $K = 2$ , with $O_1$ used to estimate coarse deformation (e.g. corresponding to the position of pedestrians or the placement of workpieces) and $O_2$ used to estimate fine deformation (e.g. corresponding to pedestrian behaviors or workpiece details).", + "bbox": [ + 76, + 90, + 468, + 241 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Considering that quantized embedding without positional information may lead to inaccurate reconstruction, we also introduce position embedding operator for the decoder $g(\\cdot)$ . We then aggregate $\\mathbf{O}$ onto the reconstructed reference $g(PE(z^q))$ , and obtain $\\tilde{x}_k(k = 1,\\dots ,K)$ which is calibrated by the $k^{th}$ layer of deformation fields:", + "bbox": [ + 76, + 242, + 468, + 332 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {x} _ {k} = g \\left(P E \\left(z ^ {q}\\right)\\right) \\circ O _ {1} \\dots \\circ O _ {k}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 163, + 343, + 468, + 359 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\circ$ is grid-sampling function with a reference coordinate in this implementation (\"Agg.\" and \"Coord.\" in Fig. 4). However, minimizing the unconstrained reconstruction loss with respect to $\\psi(x)$ may cause degenerate solution of the encoder $f(\\cdot)$ . To address this problem, we add constraint using smoothness loss via gradient operation and strength loss as:", + "bbox": [ + 76, + 369, + 468, + 472 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {d f} = \\sum_ {k} \\| \\nabla O _ {k} \\| _ {1} + \\| O _ {k} \\| _ {2}. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 171, + 472, + 468, + 503 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Foreground-background selection", + "text_level": 1, + "bbox": [ + 76, + 511, + 372, + 526 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Storing the background information in memory will break the compactness of embedding and require plenty of memory items. Besides, the deformation estimation should not be applied to the background. Some approaches use external estimators to remove interference from background, but the generalization in different scenarios cannot be guaranteed and extra noise will inevitably be introduced. Benefiting from the strong prior of fixed-view videos, we model the background with a learnable template $x_{bg}$ and generate a binary mask to indicate whether a pixel belongs to foreground or background with $f_{m}(\\cdot)$ . The final reconstruction $\\hat{x}_k$ of $k^{th}$ head is:", + "bbox": [ + 76, + 534, + 468, + 715 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {x} _ {k} = f _ {m} (x) \\tilde {x} _ {k} + (1 - f _ {m} (x)) x _ {b g}. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 726, + 468, + 742 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Training and inference", + "text_level": 1, + "bbox": [ + 76, + 751, + 289, + 767 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training phase. Once we obtain the reconstruction $\\hat{x}_k$ , we can calculate reconstruction loss $L_{rec}$ as:", + "bbox": [ + 76, + 773, + 467, + 804 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {r e c} = \\sum_ {k} D i s (x, \\hat {x} _ {k}), \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 191, + 813, + 468, + 844 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $Dis(\\cdot)$ refers to a distance function in sample space. Reminding of the optimization objective in Eq. 3, we implement the two constraints using $L_{com}$ and $L_{df}$ respectively.", + "bbox": [ + 76, + 854, + 468, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finally, training is performed by minimizing the overall loss:", + "bbox": [ + 498, + 90, + 890, + 119 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {a l l} = L _ {r e c} + \\gamma_ {1} L _ {c o m} + \\gamma_ {2} L _ {d f}. \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 121, + 890, + 137 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Inference phase. In the inference phase, we use $\\mathbf{O}$ and the reconstruction loss to calculate the error maps of input sample $x$ :", + "bbox": [ + 498, + 143, + 890, + 186 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nA _ {r e c} = \\operatorname {D i s} (x, \\hat {x} _ {K}), \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 624, + 188, + 890, + 204 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nA _ {d f} = \\sum_ {k} \\| O _ {k} \\| _ {2}. \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 632, + 210, + 890, + 241 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Image-level anomaly score is computed based on local maxima:", + "bbox": [ + 498, + 246, + 890, + 273 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {S c o r e} _ {I} = \\max \\left(A _ {r e c} \\otimes k ^ {\\star}\\right) + \\alpha \\max \\left(A _ {d f} \\otimes k ^ {\\star}\\right). \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 286, + 890, + 303 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\otimes$ is convolution operator and $k^{\\star}$ is convolution kernel for anomaly maps. $\\alpha$ is a tradeoff parameter. That is, the reconstruction loss and deformation jointly determine the anomaly score, which is much more effective than traditional reconstruction-based methods, as illustrated in Fig. 3.", + "bbox": [ + 498, + 314, + 890, + 388 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.6. Variant of PDM", + "text_level": 1, + "bbox": [ + 500, + 398, + 660, + 412 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Modified framework with Pre-PDM. The DMAD framework together with ICM and PDM modules proposed above are suitable in many anomaly detection scenarios including video surveillance. However, for industrial defect detection, texture reconstruction may be harmful (such as spots on \"Pill\"), and we should reconstruct high-level semantic features instead. Since PDM does not work in high-dimensional feature space and interferes with the training process, we propose variant of PDM, Pre-PDM (PPDM), as a solution. PPDM works in sample space, and is applied to the input sample rather than the reconstructed one. Eq. (3) is modified naturally as follows:", + "bbox": [ + 498, + 421, + 890, + 602 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} L = \\| x \\circ \\psi^ {\\prime} (x) - g (\\phi (f (x \\circ \\psi^ {\\prime} (x)), z)) \\| _ {2} \\tag {15} \\\\ + \\gamma_ {1} R _ {1} (\\phi) + \\gamma_ {2} R _ {2} (\\psi^ {\\prime}). \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 539, + 612, + 890, + 647 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Since we do not reconstruct the original samples, reconstruction loss cannot constrain PPDM to maintain information diversity. In order to prevent $x \\circ \\psi'(x)$ in Eq. (15) from shortcut learning, we propose to add the inversion of forward deformation, backward deformation $\\mathbf{O}^T$ , based on cycle-consistency principle to maintain the diversity of appearance information:", + "bbox": [ + 498, + 657, + 890, + 763 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\psi^ {\\prime} (x) = U p \\left(h ^ {\\prime} \\left(P E (x)\\right)\\right) = \\left\\{\\mathbf {O}, \\mathbf {O} ^ {T} \\right\\}. \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 562, + 773, + 890, + 792 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training phase. The cycle-consistency losses $L_{cyc}$ and constraint for forward-backward deformation $L_{df}^{+}$ are:", + "bbox": [ + 500, + 801, + 890, + 834 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {c y c} = \\left\\| x - x \\circ O _ {1} \\dots \\circ O _ {K} \\circ O _ {K} ^ {T} \\dots \\circ O _ {1} ^ {T} \\right\\| _ {2}, \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 843, + 890, + 862 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {d f} ^ {+} = \\sum_ {k} \\| \\nabla O _ {k} \\| _ {1} + \\| \\nabla O _ {k} ^ {T} \\| _ {1} + \\| O _ {k} \\| _ {2} + \\| O _ {k} ^ {T} \\| _ {2}. \\tag {18}\n$$\n", + "text_format": "latex", + "bbox": [ + 508, + 871, + 890, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "12151", + "bbox": [ + 480, + 943, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/a703299c6ba384a505806b5c930756533f9b4011baeba486e495268c12752045.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 125, + 87, + 220, + 159 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/9375a064bf96cd6308fc2040ef2d1df6eb2fd94e3a4e897ceb29bbed3e8a8869.jpg", + "image_caption": [ + "(c)" + ], + "image_footnote": [], + "bbox": [ + 222, + 88, + 318, + 159 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/77d46b807abbb1d1514c1d77f481ee36c77c41b7cbef694b08c28c6a813259ab.jpg", + "image_caption": [ + "(d)" + ], + "image_footnote": [], + "bbox": [ + 321, + 88, + 416, + 159 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/92473f40e1dcea88bdc757e73784259310b03092f15f81e27290d1d9183974fc.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 125, + 172, + 218, + 244 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/781344392755dc0ebd9733a999b3e6c742f1a3c407ace778e0da0aa25a41601f.jpg", + "image_caption": [ + "(e)" + ], + "image_footnote": [], + "bbox": [ + 223, + 172, + 316, + 244 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/103eee2e2081a875d19cc15e67f17de4b1f70e39801ad7a1b028b79884830ec6.jpg", + "image_caption": [ + "(f)", + "Figure 5. The process of forward and backward deformation: a) The pattern of original image. Red indicates high error regions and black indicates low error regions; b) The normal pattern; c) The coarse estimation $O_{1}$ (dark blue) and $O_{1}^{T}$ (light blue); d) The fine estimation $O_{2}$ (dark blue) and $O_{2}^{T}$ (light blue); e) Using $\\hat{x}$ simply causes high anomaly score at the wrong location (solid cross). Ground-truth is shown as hollow cross; f) $\\hat{x} \\circ O_{2}^{T} \\circ O_{1}^{T}$ adjusts the high reconstruction error to original position." + ], + "image_footnote": [], + "bbox": [ + 321, + 172, + 416, + 244 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "So we train our anomaly detection model with PPDM by minimizing the following loss:", + "bbox": [ + 75, + 400, + 468, + 431 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nL _ {a l l} ^ {+} = L _ {r e c} + \\gamma_ {1} L _ {c o m} + \\gamma_ {2} L _ {d f} ^ {+} + \\gamma_ {3} L _ {c y c}. \\tag {19}\n$$\n", + "text_format": "latex", + "bbox": [ + 114, + 436, + 468, + 455 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The modified DMAD framework (i.e. with PPDM and Reverse Distribution [6]) is shown in in Fig. 4b.", + "bbox": [ + 75, + 460, + 468, + 489 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Inference phase. The result of PPDM is not aligned with the position of original input, which may reduce the performance of anomaly localization. In order to obtain the anomaly map of real location, we use backward deformation to perform inverse sampling (Fig. 5):", + "bbox": [ + 75, + 489, + 468, + 563 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nA _ {r e c} ^ {+} = \\operatorname {D i s} \\left(x, \\hat {x} _ {K}\\right) \\circ O _ {K} ^ {T} \\dots \\circ O _ {1} ^ {T}, \\tag {20}\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 568, + 468, + 587 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} A _ {d f} ^ {+} = \\sum_ {k} \\| O _ {k} \\circ O _ {k + 1} \\dots \\circ O _ {K} \\| _ {2} \\tag {21} \\\\ + \\sum_ {k} \\| O _ {k} ^ {T} \\circ O _ {k - 1} ^ {T} \\dots \\circ O _ {1} ^ {T} \\| _ {2}. \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 592, + 468, + 657 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The image-level anomaly score $Score_{I}^{+}$ and pixel-level anomaly score $Score_{P}^{+}$ are calculated respectively as:", + "bbox": [ + 75, + 662, + 468, + 694 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {S c o r e} _ {I} ^ {+} = \\max \\left(A _ {\\text {r e c}} ^ {+} \\otimes k ^ {\\star}\\right) + \\alpha \\max \\left(A _ {d f} ^ {+} \\otimes k ^ {\\star}\\right), \\tag {22}\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 699, + 468, + 718 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {S c o r e} _ {P} ^ {+} = A _ {r e c} ^ {+} + \\alpha A _ {d f} ^ {+}. \\tag {23}\n$$\n", + "text_format": "latex", + "bbox": [ + 187, + 723, + 468, + 743 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments and Analysis", + "text_level": 1, + "bbox": [ + 76, + 752, + 318, + 768 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Firstly, we perform toy experiment on MNIST to illustrate our approach. Then the quantitative and qualitative results of two versions our DMAD framework are reported in video anomaly detection and industrial surface defect detection respectively2. Finally, we conduct ablation experiments and analyze the results.", + "bbox": [ + 75, + 777, + 468, + 867 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/6b99b30160a86a98f1ac07a81ded836fd211a7464247f53aa2e38bbb658e5efc.jpg", + "image_caption": [ + "Figure 6. Visualization of toy experiment. The last three rows are: reference reconstructed from memory, reference after coarse deformation, and final output after applying fine deformation." + ], + "image_footnote": [], + "bbox": [ + 529, + 85, + 864, + 239 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Datasets", + "text_level": 1, + "bbox": [ + 500, + 314, + 601, + 329 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Surveillance Videos. Ped2 [27], Avenue [23] and ShanghaiTech [25] are fixed-view videos. The anomalies include driving, cycling, running, throwing stuff, etc. Mutual occlusion, anomaly-like behavior, contaminated data and different scenes occur frequently in these datasets.", + "bbox": [ + 498, + 337, + 890, + 412 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Industrial Images. MVtec [2] contains 15 types of industrial images, which are divided into 5 types of textures and 10 types of objects. The defects include crack, scratch, etc. The normal workpiece has different positions, angles and textures. It is used for detection and localization task.", + "bbox": [ + 498, + 412, + 890, + 488 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Toy experiment", + "text_level": 1, + "bbox": [ + 500, + 498, + 656, + 513 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As shown in Fig. 6, we perform a toy experiment on MNIST dataset [16] with setting analogous to out-of-distribution (OOD) detection (i.e. training on \"1, 3, 5, 7, 9\" and test on all classes). Our model searches separate memory items for each digital category to reconstruct it into class-specific reference and uses the deformation fields from PDM to adjust it hierarchically. When tested with seen and unseen classes, the model adjusts reconstructed references to normal inputs, but fails on the abnormal ones.", + "bbox": [ + 496, + 521, + 890, + 656 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In contrast, memory network without diversity-aware module cannot guarantee the intra-class compactness and the reconstruction diversity, which misdirects the model to obtain dataset-optimal \"average memory\", leading to fuzzy reconstruction and lower discrimination ability. The model with full-channel skip-connection suffers from shortcut learning and reconstruct anomalies successfully which weakens the ability to identify anomalies.", + "bbox": [ + 496, + 657, + 890, + 777 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Implementation details", + "text_level": 1, + "bbox": [ + 500, + 786, + 714, + 801 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The input images are resized into $256 \\times 256$ and normalized to the value in range of $[-1,1]$ . According to frame-pred strategy [19], the history length is set to 4 in video anomaly detection and 0 for images. After feature extraction with a backbone, PDM and PPDM obtain different heads by stacking stride-2 convolution layers. Then", + "bbox": [ + 496, + 809, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "2Our code will be available at https://github.com/FlappyPeggy/DMAD.", + "bbox": [ + 76, + 875, + 467, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "12152", + "bbox": [ + 480, + 943, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "we use $\\text{Tanh}$ as the activation function of output layer and clipping function to ensure the value of deformation is between $[-1, 1]$ . Unless otherwise noted, the architecture of autoencoder complies with the settings of MNAD [29] and RD [6] for PDM and PPDM respectively. The function $\\text{Dis}(\\cdot)$ in Eq. (10) is a combination of $MSE$ loss and $Grad$ loss for reconstruction in sample space, and $COS$ loss for deep features. We set $(\\gamma_1, \\gamma_2) = (1, 0.25)$ for PDM, $(1, 1)$ for PPDM $(\\gamma_3$ is discussed in Sec. 4.5), and $\\beta = 0.25$ as in [35]. During post-processing, we use average kernel for surveillance videos and Gaussian kernel with $\\sigma = 4$ for industrial images as in [6]. Frame-difference method is applied to remove static anomalies for Avenue, because our method detects all anomalies which may be labeled as normal ones in [23]. And we use the mask calculated in Eq. (9) to normalize anomaly map in [25] due to the scale changes. Besides, we set $\\alpha = 0.2$ for three video tasks and an additional option $\\alpha = 0.05$ for defect detection, depending on whether the defect includes geometrical changes. The model is optimized by AdamW [21] and the learning rate is 2e-4 and 5e-3 as in [6, 29] respectively, being decayed by CosineAnnealingLR [22] strategy. We adopt 60, 60, 60, 10, 400 epochs for MNIST, Ped2, Avenue, Shanghai and MVTec respectively with batch size of 8.", + "bbox": [ + 76, + 90, + 472, + 454 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Main results", + "text_level": 1, + "bbox": [ + 76, + 464, + 210, + 479 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Surveillance Videos. We compare our method with SOTA works on video anomaly detection in Tab. 1. Our method outperforms comparative approaches even though we neither use external estimators nor remove abnormal frames in training data. In additional, if we detect global offset for camera jitter in [23], there will be extra $0.1\\%$ gain.", + "bbox": [ + 75, + 487, + 468, + 578 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The qualitative results are shown in Fig. 7. We find that: anomalies are over-reconstructed in (b); normals are not reconstructed well in (c); (d) greatly improves normal reconstruction with slightly less inhibition ability for anomalies.", + "bbox": [ + 75, + 579, + 468, + 638 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Industrial Images. Anomaly detection results on MVTec are shown in Tab. 2 and localization results are shown in Tab. 3. With the deformation from PPDM, texture anomalies are detected with high performance and our method outperforms SOTA methods in both detection and localization tasks without memorizing an enormous number of embedding from training data.", + "bbox": [ + 75, + 640, + 470, + 747 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Ablation study", + "text_level": 1, + "bbox": [ + 76, + 756, + 227, + 772 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As shown in Tab. 4, single-output memory module without PDM suppresses diverse normal patterns seriously, while separate PDM without memory provides comparable performance gains as the previous SOTA works because the module \"Comp.\" serves as an information compression module instead. The number of multi-scale deformation fields also have a modest effect on performance. We suggest that \"K\" should at least make the scale of control grid", + "bbox": [ + 75, + 780, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/1566b8f9c01a4e4422258f21d38e13a0d0f63323a25ab1fe4cfac04f56b5dcef.jpg", + "table_caption": [ + "Table 1. Video anomaly detection results on Ped2 [27], Avenue [23] and Shanghai [25]. We calculate $AUC(\\%)$ with all frames together. Numbers in bold indicate the best performance and the underlined ones are the second best. $^+$ indicates that we reproduce the result due to higher performance or absence of implementation." + ], + "table_footnote": [], + "table_body": "
MethodsPed2 [27]Avenue [23]Shanghai [25]
Conv2D [9]90.070.2-
Conv3D [40]91.277.1-
ConvLSTM [24]88.177.0-
FramePred [19]95.484.972.8
ConvVQ+90.284.3-
MemAE [8]94.183.371.2
MPN [26]96.989.573.8
MNAD+ [29]97.888.570.5
HF2VAD [20]99.391.176.2
Ours99.792.878.8
", + "bbox": [ + 501, + 169, + 893, + 339 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6b61aa6e1d6614ebf12b7b7df27453b04c569312a12e22d2faa8464a3a1b84d0.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 586, + 352, + 694, + 436 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b52cbfc92f067605d8f1c08d5f8b9cd2643494a2e61afea4e86960988cdac7f4.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 697, + 352, + 805, + 436 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b25a96436442e303c791566a7e8b9722cf5af0e09af855f004763626c4c577e9.jpg", + "image_caption": [ + "(c)", + "Figure 7. Qualitative results on Ped2. a) Original image; b) Memory network with skip-connection [29]; c) PDM with VQ-Layer [35]; d) PDM with ICM. Green box indicates negative, red box indicates positive, and yellow box indicates weak positive." + ], + "image_footnote": [], + "bbox": [ + 586, + 445, + 694, + 527 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/cf9dcc661808b1bf3bcca66f6f740605d4fbf83ef63ed90217c07e5507e7c83a.jpg", + "image_caption": [ + "(d)" + ], + "image_footnote": [], + "bbox": [ + 697, + 445, + 805, + 527 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "cover the size of base elements (e.g. pedestrian limbs). Besides, the foreground-background selection module further improves the compactness of memory embedding. Moreover, if any constraint for PDM is missing, the abnormal information will be transmitted and cause shortcut learning. Especially, the cycle-consistency constraint $L_{cyc}$ is also a necessary part for PPDM to avoid degenerated solution $(-1.7\\%)$ , because the feature reconstruction error can be minimized by eliminating all necessary information.", + "bbox": [ + 496, + 628, + 890, + 763 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As shown in Tab. 5, the proposed method is robust to hyperparameter $\\gamma_{3}$ in Eq. (19). On condition that degenerated solution will not be formed, weakening the constraint makes model restore images from reference with less detail more easily and perceive the position of anomalies more accurately by transforming anomalies to normal patterns which benefits localization task. On the contrary, strengthening the constraint alleviates shortcut learning and improves image-level result by maintaining more abnormal details.", + "bbox": [ + 496, + 765, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "12153", + "bbox": [ + 480, + 941, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/f21f680dbc2154c1034b31856994eb1ce3482d09b412c7919f3e8d3fa032a1c9.jpg", + "table_caption": [ + "Table 2. Image-level ${AUC}\\left( \\% \\right)$ of anomaly detection on MVTec [2]." + ], + "table_footnote": [], + "table_body": "
Class\\MethodsGN [1]PSVDD [37]DAAD [11]CutPaste [17]PaDiM [5]PatchCore [31]DRAEM [38]RD [6]Ours
AvgTextures77.594.591.097.598.899.099.199.599.9
AvgObjects75.590.888.895.593.899.297.498.099.3
AvgAll76.292.189.596.195.599.198.098.599.5
", + "bbox": [ + 76, + 109, + 893, + 188 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/1e3ae388c13ff2f6133ae958fb088c11adba560bec1692044312657da557fbe4.jpg", + "table_caption": [ + "Table 3. Pixel-level ${AUC}\\left( \\% \\right)$ of anomaly localization on MVtec [2]." + ], + "table_footnote": [], + "table_body": "
Class\\MethodsPSVDD [37]CutPaste [17]PaDiM [5]PatchCore [31]DRAEM [38]TMAE [34]RD [6]Ours
AvgTextures93.796.396.997.697.993.897.797.8
AvgObjects96.795.897.898.497.094.097.998.3
AvgAll95.796.097.598.197.393.997.898.2
", + "bbox": [ + 78, + 220, + 892, + 297 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/b396e05335f914db70f5ac581570a1c9771bb9ae49630a8851a52bf8dbc71a44.jpg", + "table_caption": [ + "Table 4. Ablation study of proposed module and loss on Ped2 [27]. From left to right: without PDM; with only one head of PDM $(K = 1)$ ; without memory module; without background template; removing strength constraint; removing smoothness constraint." + ], + "table_footnote": [], + "table_body": "
w/oPDMK>1Memxbg|O|2|∇O|2
AUC%-9.4-0.4-1.8-1.6-1.4-1.4
", + "bbox": [ + 78, + 375, + 468, + 417 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/d5aa08139c8bf74464370d59575bffade79b852ddb72a30bc5a743f85f230385.jpg", + "table_caption": [ + "Table 5. Ablation study of deformation constraint on MVTec [2]." + ], + "table_footnote": [], + "table_body": "
Task\\γ300.10.250.512
Det.97.999.499.499.599.699.4
Loc.96.698.098.298.097.797.6
", + "bbox": [ + 78, + 448, + 468, + 508 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.6. Discussion", + "text_level": 1, + "bbox": [ + 76, + 529, + 192, + 544 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Contaminated data assumption. Assuming that training data only contains completely normal data is unrealistic, because the workload of natural data cleansing is considerable, even has same cost as data annotations. We mix training data with abnormal events in Ped2 to simulate contaminated data and find performance drop of MNAD [29] is $-3.7\\%$ while ours is $-1.8\\%$ . The reason why DMAD is less affected may be that PDM can encode and transmit residual abnormal representation of mixed anomalies and anomaly-like normal samples, thus strictly maintaining representation compactness of the main encoder and low generalization ability on abnormal samples.", + "bbox": [ + 75, + 551, + 468, + 733 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Two DMAD implementations. As introduced earlier, our DMAD framework is implemented by two versions using PDM and PPDM respectively, corresponding to different detection targets. As shown in Fig. 8, PDM learns measurable quantization error (caused by ICM) from memory embedding to diverse patterns which enhances the potential of ICM to keep intra-class compactness without generating unmeasurable reconstruction loss. Unlike PDM, PPDM is partially in charge of the information compression, i.e. PPDM removes the diverse appearance by using the reverse deformation process from inputs to reference.", + "bbox": [ + 75, + 734, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/98ff6ab2411d041b029fb61d759369f6cf89beba1530821c6909541d80658b10.jpg", + "image_caption": [ + "Figure 8. Illustration of two DMAD implementations with PDM and PPDM respectively." + ], + "image_footnote": [], + "bbox": [ + 517, + 309, + 875, + 450 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 506, + 617, + 522 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we present a reconstruction-based diversity-measurable anomaly detection framework, which simultaneously enhances anomaly discrimination and reconstruction diversity. Pyramid deformation module is proposed to be used together with information compression module for this purpose. PDM models multi-scale transformation fields from reference to original input explicitly without relying on external estimators. Therefore, diverse normal patterns can be reconstructed and anomaly severity can be measured accurately. Empirical studies on both videos and images benchmarks show the effectiveness and applicability of our work. In future research, we will further explore diversity-aware models for anomaly detection.", + "bbox": [ + 496, + 532, + 890, + 729 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations. Our method focuses on anomaly with measurable geometrical diversity, the most common type in anomaly detection. However, as for anomaly with other kind of diversities, e.g. colors, the proposed diversity measure may not be positively correlated to anomaly severity.", + "bbox": [ + 496, + 746, + 890, + 821 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement. This work is partially supported by National Key R&D Program of China (No. 2018AAA0102402), and National Natural Science Foundation of China (NSFC): 61976203 and 62276246.", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "12154", + "bbox": [ + 480, + 943, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Samet Akcay, Amir Atapour Abarghouei, and Toby P. Breckon. Ganomaly: Semi-supervised anomaly detection via adversarial training. 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In Proceedings of the 2017 ACM on Multimedia Conference, pages 1933-1941, 2017. 1, 2, 7" + ], + "bbox": [ + 501, + 92, + 890, + 233 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "12156", + "bbox": [ + 480, + 943, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Diversity-Measurable Anomaly Detection/43dbf769-f361-451d-b986-1893419fc738_model.json b/2023/Diversity-Measurable Anomaly Detection/43dbf769-f361-451d-b986-1893419fc738_model.json new file mode 100644 index 0000000000000000000000000000000000000000..471600c742331e00705d9f61c34c0721e05cb431 --- /dev/null +++ b/2023/Diversity-Measurable Anomaly Detection/43dbf769-f361-451d-b986-1893419fc738_model.json @@ -0,0 +1,2475 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.275, + 0.131, + 0.696, + 0.154 + ], + "angle": 0, + "content": "Diversity-Measurable Anomaly Detection" + }, + { + "type": "text", + "bbox": [ + 0.172, + 0.18, + 0.796, + 0.234 + ], + "angle": 0, + "content": "Wenrui Liu\\(^{1,2}\\), Hong Chang\\(^{1,2}\\), Bingpeng Ma\\(^{2}\\), Shiguang Shan\\(^{1,2}\\), Xilin Chen\\(^{1,2}\\) \n\\(^{1}\\)Institute of Computing Technology, Chinese Academy of Sciences, China \n\\(^{2}\\)University of Chinese Academy of Sciences, China" + }, + { + "type": "text", + "bbox": [ + 0.122, + 0.237, + 0.842, + 0.253 + ], + "angle": 0, + "content": "wenrui.liu@vipl.ict.ac.cn, {changhong, sgshan, xlchen}@ict.ac.cn, bpma@ucas.ac.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.287, + 0.314, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.318, + 0.474, + 0.651 + ], + "angle": 0, + "content": "Reconstruction-based anomaly detection models achieve their purpose by suppressing the generalization ability for anomaly. However, diverse normal patterns are consequently not well reconstructed as well. Although some efforts have been made to alleviate this problem by modeling sample diversity, they suffer from shortcut learning due to undesired transmission of abnormal information. In this paper, to better handle the tradeoff problem, we propose Diversity-Measurable Anomaly Detection (DMAD) framework to enhance reconstruction diversity while avoid the undesired generalization on anomalies. To this end, we design Pyramid Deformation Module (PDM), which models diverse normals and measures the severity of anomaly by estimating multi-scale deformation fields from reconstructed reference to original input. Integrated with an information compression module, PDM essentially decouples deformation from prototypical embedding and makes the final anomaly score more reliable. Experimental results on both surveillance videos and industrial images demonstrate the effectiveness of our method. In addition, DMAD works equally well in front of contaminated data and anomaly-like normal samples." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.68, + 0.21, + 0.696 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.47, + 0.84 + ], + "angle": 0, + "content": "Visual anomaly detection is a fundamental and important problem in computer vision community, with wide applications in video surveillance and industrial inspection. It aims to detect outliers from seen classes and novel patterns from unseen classes. This task is very challenging because abnormal data is diversely distributed and expensive to collect. So we have to construct models based on only normal samples under unsupervised setting, targeting at high discrimination between normal and abnormal samples." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.902 + ], + "angle": 0, + "content": "During the past decade, reconstruction-based methods have achieved great progress in anomaly detection. These methods use Autoencoders (AEs) [8,9,20,24,26,29,40] or Generative Adversarial Networks (GANs) [1, 19, 32] to re" + }, + { + "type": "image", + "bbox": [ + 0.57, + 0.285, + 0.825, + 0.4 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.411, + 0.895, + 0.482 + ], + "angle": 0, + "content": "Figure 1. Illustration of difficulty in anomaly detection in MNIST dataset. The prototype is indicated by orange triangle and the anomaly by red point. In this case, the anomaly can hardly be detected based on reconstruction error or distance in high-dimensional feature space. Our solution is illustrated in Fig. 2." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.508, + 0.892, + 0.597 + ], + "angle": 0, + "content": "construct the normal counterparts from any input images or video frames. AE-based methods firstly compress the inputs to discard the information beyond normal prototypes, and then decode the embedding to reconstruct the inputs. According to the estimated reconstruction error, the anomalies can be detected." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.893, + 0.901 + ], + "angle": 0, + "content": "However, the performance of reconstruction-based methods for anomaly detection has long been limited by a tough problem, i.e. the tradeoff between reconstructing diverse normals and detecting unknown anomalies. In order to discriminate anomalies more easily, previous works [8] imposes more constraints to suppress abnormal information during autoencoding, which leads to high reconstruction error for diverse normal instances. For example, in Figs. 1 and \\(2\\mathbf{g}\\), the severely deformed normal (a.k.a. anomaly-like) sample \"7\" has even higher error than the abnormal sample \"4\". To better reconstruct diverse normals, each query vector corresponds to multiple prototypes in the memory, which may be combined into abnormal embedding even if abnormal projection is far away from the prototype. As a consequence, anomalies that distribute in low likelihood area between prototypical embedding are difficult to identify from diverse normals. MNAD [29] introduces skipconnection for diverse reconstruction and additional constraints to get round the incorrect combination problem. But the latter forces model transmit more unrestrained in" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.944, + 0.52, + 0.956 + ], + "angle": 0, + "content": "12147" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.088, + 0.47, + 0.224 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.235, + 0.47, + 0.332 + ], + "angle": 0, + "content": "Figure 2. Illustration of our diversity-measurable method in addressing the detection difficulty. Numbers in white are anomaly scores. a) Original input; b) Reconstructed reference; c) Coarse deformation; d) Fine deformation; e) Measurement of diversity1; f) Deformation-augmented error map assigns lower anomaly score to the anomaly-like sample than the true anomaly; g) Pixel-wise reconstruction error yields incorrect anomaly scores." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.357, + 0.469, + 0.4 + ], + "angle": 0, + "content": "formation with abnormal part by skip-connection, resulting in shortcut learning and undesired reconstruction of anomalies." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.402, + 0.469, + 0.597 + ], + "angle": 0, + "content": "A key to address the above tradeoff problem is to find a proper measurement of diversity that normal and abnormal samples have, which is positively correlated with the severity of anomaly. With such a measure, we do not need to fight against imperfect reconstruction of normals or undesired reconstruction of anomalies, because anomalies can be detected more accurately by the diversity measure together with the reconstruction error. Note that pixel-wise reconstruction error is not an ideal measurement of diversity, because the high-error region often confuses anomalies with diverse normals, e.g. normals with structural deformation and anomalies with colors close to the background may yield unreliable reconstruction error." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.469, + 0.779 + ], + "angle": 0, + "content": "In this paper, we propose a Diversity-Measurable Anomaly Detection (DMAD) framework to enhance the measurability of reconstruction diversity so as to measure abnormality more accurately. Our basic idea is to decouple the reconstruction into compact representation of prototypical normals and measurable deformations of more diverse normals and anomalies. The under-estimated reconstruction error can be compensated by the diversity, which can be properly measured. To this end, the DMAD framework includes a Pyramid Deformation Module (PDM) to model and measure the diversity and an Information Compression Module (ICM) to learn the prototypical normal patterns." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.469, + 0.855 + ], + "angle": 0, + "content": "Inspired by [4, 15], we assume anomalies (e.g. in video surveillance) can be represented as significant deformation of appearances, including positional changes and fine motions. In contrast, diverse normal samples can be represented as weaker deformations thus easily distinguished" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.892, + 0.303 + ], + "angle": 0, + "content": "from the abnormal ones. Therefore, we design PDM to model the diversity of normals as well as the severity of anomalies. More specifically, PDM learns hierarchical two-dimensional deformation fields (Fig. 2c,d) that describe the pixel-level transformation direction and distance from reference (Fig. 2b, which is reconstructed from prototypes in memory) to original input. In ICM, we learns compressed representation as sparse prototypes. As a result, a single memory item is enough to represent each normal cluster. This is more compact than other memory-based works which require multiple memory items. Integrating PDM with ICM, DMAD essentially decouples the deformation information (Fig. 2e) from class prototypes and makes the final anomaly score more discriminative (Fig. 2f)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.304, + 0.892, + 0.424 + ], + "angle": 0, + "content": "We evaluate our anomaly detection framework in scenarios of video surveillance and industrial defect detection. To apply DMAD in the latter scenario, we propose a variant of PDM, PPDM, to deal with the false positive issue in texture reconstruction. Extensive experimental results verify the efficacy of our approach. Moreover, our method works well even in front of contaminated data and anomaly-like normals. The main contributions of our work are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.429, + 0.892, + 0.489 + ], + "angle": 0, + "content": "- We introduce diversity-measurable anomaly detection framework which allows reconstruction-based models to achieve better tradeoff between reconstructing diverse normals and detecting unknown anomalies." + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.492, + 0.892, + 0.567 + ], + "angle": 0, + "content": "- We propose pyramid deformation module to implement diversity measurement, in which the deformation information is explicitly separated from compact class prototypes and the resulting diversity measure is positively correlated to abnormality." + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.57, + 0.892, + 0.644 + ], + "angle": 0, + "content": "- Our approach outperforms previous works on video anomaly detection and industrial defect detection, and works well in front of contaminated data and anomaly-like normals, demonstrating its broad suitability and robustness." + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.429, + 0.892, + 0.644 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.663, + 0.642, + 0.679 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.689, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Anomaly detection. Reconstruction-based methods model the distribution of normal data and assign anomalies with high reconstruction error, because models trained with only normal data cannot reconstruct anomalies. Some works use autoencoder to detect anomalies, such as convolutional autoencoder [9] and the variants [24, 40]. Other approaches introduce additional constraints or memory to make the model more discriminative. For example, sparse coding [25, 39] reduces representation redundancy with regularization; memory-augmented autoencoder (MemAE) [8] memorizes the normal patterns appearing in training dataset with external memory bank; variational autoencoder [10, 35] assumes a prior distribution of normal data to constrain the nonlinear representation capacity; \\(\\mathrm{HF}^2\\mathrm{VAD}\\) [20]" + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.863, + 0.469, + 0.9 + ], + "angle": 0, + "content": "1In this case, we only count fine deformation because deformations in position and angle are considered as normal. In real-world experiments, we consider both coarse and fine deformations." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.944, + 0.519, + 0.956 + ], + "angle": 0, + "content": "12148" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.468, + 0.198 + ], + "angle": 0, + "content": "uses CVAE [33] to capture the correlation among motions. Frame prediction [19] assumes that abnormal samples in videos cannot be represented by past frames that do not contain unseen information and forces the model to encode changes among different frames. In addition, autoencoders can also be combined with external object detectors [7, 14, 20] to capture background-invariant appearance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.199, + 0.468, + 0.304 + ], + "angle": 0, + "content": "Although these methods generally work well, they often have difficulty in discriminating abnormal samples from anomaly-like normals due to the tradeoff between reconstruction and discrimination. In our framework, pyramid deformation module and information compression module are leveraged to address the trade-off problem, significantly improving the performance in anomaly detection." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.307, + 0.468, + 0.533 + ], + "angle": 0, + "content": "Memory network. Generative models map continuously in feature space and they may assign higher probabilities to anomalies than normal ones [28]. Recent research [8, 11, 20, 29] has explored the application of discrete external memory to generate seen normal patterns even if the input is abnormal. MemAE [8] proposes a memory-augmented autoencoder, which uses information from encoder as a query and obtains a normal pattern retrieved from memory module. MNAD [29] introduces skip-connection to alleviate the problem that diverse normal patterns may yield high reconstruction errors. \\(\\mathrm{HF^2VAD}\\) [20] extends the memory module to multi-level memory, and uses additional estimators [3, 13] to explicitly model the motion information and filter the noise from background. DAAD [11] uses block-wise memory to increase the specificity of memory." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.536, + 0.468, + 0.655 + ], + "angle": 0, + "content": "In most existing works, the memory module outputs a linear combination of memory items which may lead to undesired reconstruction of normal-like anomalies. And they do not explicitly consider that instances corresponding to the same memory grid may be located at different positions of the receptive field. In our approach, we alleviate these problems via compressing embedding into a single memory item to ensure that the output is absolutely normal." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.658, + 0.468, + 0.868 + ], + "angle": 0, + "content": "Transformation modeling. The transformation between video frames is a key clue for anomaly detection. Some methods [7, 14, 19, 20] use external object detectors or optical-flow estimators to model the motion information implicitly or explicitly. Among the transformation estimators, optical-flow estimation [13] is widely studied, which aims to estimate the pixel-wise motions between consecutive frames. In addition, correspondence modeling between pair-wise images is also applied to 2D geometric matching [30] and 3D image registration [36] to obtain image deformation fields. STN [15] learns to transform the original images themselves to benefit identification algorithm. RegAD [12] uses feature-level affine registration to relocate features without changing the embeddings." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.468, + 0.9 + ], + "angle": 0, + "content": "However, pairwise transformation modeling only focus on pattern changes thus cannot detect static anomalies. And" + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.087, + 0.892, + 0.224 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.236, + 0.892, + 0.32 + ], + "angle": 0, + "content": "Figure 3. Three conditions for DMAD framework. The colors of lines represent the measurements of diversity (severity of anomaly); The gray area represents uncertainty in the measure; Double dashed arrows indicate possible ranges of the boundary. The last two lines denote DMAD and traditional reconstruction-based method respectively." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.343, + 0.891, + 0.403 + ], + "angle": 0, + "content": "pretrained transformation estimators introduce generalization error in different scenarios. In contrast, we address these problems by separating and measuring the transformation from prototypical memory in end-to-end training." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.416, + 0.87, + 0.433 + ], + "angle": 0, + "content": "3. Diversity-Measurable Anomaly Detection" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.441, + 0.892, + 0.56 + ], + "angle": 0, + "content": "In this section, we first analyze the objective of reconstruction-based anomaly detection and propose a diversity-measurable framework to address the tradeoff problem in existing works. Then, we introduce information compression module and pyramid deformation module (PDM) as an implementation of the framework. Finally, we explain the training and inference process and how to apply the framework to defect detection with a variant of PDM." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.57, + 0.657, + 0.584 + ], + "angle": 0, + "content": "3.1. The framework" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.593, + 0.891, + 0.639 + ], + "angle": 0, + "content": "Given input \\( x \\), autoencoder-based methods aim to model normal data distribution by minimizing the following reconstruction loss \\( (\\| \\cdot \\|_2 \\) is just one type of reconstruction loss):" + }, + { + "type": "equation", + "bbox": [ + 0.564, + 0.647, + 0.891, + 0.665 + ], + "angle": 0, + "content": "\\[\nL = \\| x - g (\\phi (f (x), z)) \\| _ {2} + \\gamma_ {1} R _ {1} (\\phi), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.671, + 0.892, + 0.748 + ], + "angle": 0, + "content": "with respect to encoder \\( f(\\cdot) \\), decoder \\( g(\\cdot) \\), latent variable \\( z \\) (referring to discrete memory items in these cases) and a constrained feature mapping function \\( \\phi(\\cdot) \\) corresponding to its constraint \\( R_1(\\phi) \\). Skip-connection and concatenation \\( [\\cdot, \\cdot] \\) are introduced to generate diverse normal patterns [29]:" + }, + { + "type": "equation", + "bbox": [ + 0.54, + 0.755, + 0.891, + 0.773 + ], + "angle": 0, + "content": "\\[\nL = \\| x - g ([ \\phi (f (x), z), f (x) ]) \\| _ {2} + \\gamma_ {1} R _ {1} (\\phi). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.78, + 0.891, + 0.854 + ], + "angle": 0, + "content": "However, due to diverse data distribution, previous methods have to face the conflict between representing diverse normals and detecting anomalies. The intrinsic reason lies in that the encoding of diversity \\([\\cdot ,f(x)]\\) contains redundant information that cannot be measured accurately." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.891, + 0.901 + ], + "angle": 0, + "content": "In this work, we propose a principled framework, Diversity-Measurable Anomaly Detection (DMAD), to alleviate the conflict. The basic idea is to restrict the anomaly" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.944, + 0.519, + 0.956 + ], + "angle": 0, + "content": "12149" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.087, + 0.437, + 0.283 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.26, + 0.286, + 0.282, + 0.3 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.441, + 0.088, + 0.885, + 0.285 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.671, + 0.286, + 0.693, + 0.3 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.305, + 0.894, + 0.351 + ], + "angle": 0, + "content": "Figure 4. Two versions of diversity-measurable anomaly detection framework. Multi-scale pyramid deformation fields are estimated as \\(\\mathbf{O}\\) and the reverse processes are \\(\\mathbf{O}^T\\). a) PDM version computes forward deformation \\(\\mathbf{O}\\) after reconstruction. b) PPDM version employs cycle-consistent forward-backward deformations and the forward deformation is applied on the input." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.373, + 0.47, + 0.435 + ], + "angle": 0, + "content": "information transmitted to \\( g(\\cdot) \\) while measuring and modeling the diversity of the remaining part. To this end, we design information compression module \\( \\phi(\\cdot) \\) and diversity-aware module \\( \\psi(\\cdot) \\) under DMAD framework:" + }, + { + "type": "equation", + "bbox": [ + 0.078, + 0.446, + 0.47, + 0.478 + ], + "angle": 0, + "content": "\\[\nL = \\| x - g (\\phi (f (x), z)) \\circ \\psi (x) \\| _ {2} + \\gamma_ {1} R _ {1} (\\phi) + \\gamma_ {2} R _ {2} (\\psi), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.478, + 0.47, + 0.612 + ], + "angle": 0, + "content": "where \\(\\circ\\) refers to aggregation operator. With appropriate design of \\(\\phi(\\cdot), \\psi(\\cdot)\\) and the constraints, optimization of the reconstruction loss can improve the compactness of feature embedding. So that diverse representations are mapped via \\(\\phi(\\cdot)\\) to compact prototypes in the memory. The diversity of input \\(x\\) relative to its reconstruction is represented by \\(\\psi(\\cdot)\\). The under-estimated reconstruction error can be compensated by the diversity measured in \\(\\psi(\\cdot)\\), a key factor contributing to accurate anomaly scores." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.613, + 0.471, + 0.749 + ], + "angle": 0, + "content": "This framework can achieve our target on the premise that the following conditions (Fig. 3) are met: 1. \\(\\psi(\\cdot)\\) can learn all diverse information from prototypical patterns to any normal inputs to ensure normal samples do not yield high anomaly score; 2. Deformation generated by \\(\\psi(\\cdot)\\) is positively correlated to diversity measure; 3. Prototypical information about \\(x\\) represented by \\(\\psi(\\cdot)\\) needs to be minimized. In the following subsections, we explain how to design modules to fulfill these conditions." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.759, + 0.37, + 0.775 + ], + "angle": 0, + "content": "3.2. Information compression module" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.782, + 0.471, + 0.875 + ], + "angle": 0, + "content": "According to [35], we adapt VQ-Layer as an information compression module to learn \\(\\phi(\\cdot)\\) given embedding \\(f(x) \\in R^{D \\times H' \\times W'}\\) as a query \\(z^e = f(x)\\) and memory \\(z \\in R^{D \\times N}\\). Then, we quantize \\(z^e\\) into a single-memory feature cube \\(z^q \\in R^{D \\times H' \\times W'}\\) by seeking for memory item with minimum \\(L2\\) distance (\"Search\" in Fig. 4):" + }, + { + "type": "equation", + "bbox": [ + 0.162, + 0.885, + 0.47, + 0.905 + ], + "angle": 0, + "content": "\\[\nz _ {h, w} ^ {q} = \\operatorname {a r g m i n} _ {z _ {n}} \\left\\| z _ {h, w} ^ {e} - z _ {n} \\right\\| _ {2}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.373, + 0.895, + 0.45 + ], + "angle": 0, + "content": "where \\(z_{n}\\) is the \\(n^{th}\\) memory item, \\(h\\in \\{1,\\dots ,H^{\\prime}\\} ,w\\in\\) \\(\\{1,\\dots ,W^{\\prime}\\}\\) indicates the same location in both \\(z^q\\) and \\(z^{e}\\). The compression loss \\(L_{com}\\) with stop-gradient operator \\(SG(\\cdot)\\) that updates its parameters separately [35] is combined by a hyperparameter \\(\\beta\\):" + }, + { + "type": "equation", + "bbox": [ + 0.528, + 0.461, + 0.892, + 0.48 + ], + "angle": 0, + "content": "\\[\nL _ {c o m} = \\left\\| S G \\left(z ^ {e}\\right) - z ^ {q} \\right\\| _ {2} + \\beta \\left\\| z ^ {e} - S G \\left(z ^ {q}\\right) \\right\\| _ {2}. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.491, + 0.894, + 0.568 + ], + "angle": 0, + "content": "Skip-connection with low information capacity (Fig. 4 \"Comp.\") is also allowed to further improve the reconstruction quality without bringing excessive generalization (i.e. Conv-Layer with stop-gradient operator for intermediate features whose reduction factor is 16 or larger)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.577, + 0.766, + 0.594 + ], + "angle": 0, + "content": "3.3. Pyramid deformation module" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.6, + 0.892, + 0.765 + ], + "angle": 0, + "content": "We categorize the unknown anomalies into the following three types: unseen class (e.g. novel objects), global anomaly (e.g. unexpected movement) and local anomaly (e.g. strange behavior and workpiece damage) of seen class. The unseen class is easy to be detected based on reconstruction result, but the latter two types are usually confused with diverse normals. To discriminate these anomalies from normal ones, we represent the diversity using measurable deformation between reconstructed reference and original input, so that slight deformations occur in normals while drastic deformations occur in anomalies." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.767, + 0.894, + 0.874 + ], + "angle": 0, + "content": "Inspired by STN and DCN [4, 15], we introduce Pyramid Deformation Module (PDM) which explicitly learn deformation fields with hierarchical scales to model the motion, behavior and defect of different anomaly types, as shown in Fig. 4a. Specifically, after feature extraction, \\(\\psi(\\cdot)\\) uses \\(K\\)-heads to compute offsets \\(\\mathbf{O} = \\{O_1, \\dots, O_K\\}\\), corresponding to \\(K\\) coarse-to-fine deformations:" + }, + { + "type": "equation", + "bbox": [ + 0.595, + 0.885, + 0.892, + 0.903 + ], + "angle": 0, + "content": "\\[\n\\psi (x) = U p \\left(h \\left(P E (x)\\right)\\right) = \\mathbf {O}, \\tag {6}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.944, + 0.52, + 0.956 + ], + "angle": 0, + "content": "12150" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.242 + ], + "angle": 0, + "content": "where \\(PE(\\cdot)\\) is positional embedding operator [18], \\(h: R^{C \\times H \\times W} \\to R^{2 \\times \\{H_1 \\times W_1, \\dots, H_K \\times W_K\\}}\\) is the deformation estimator that generates offset vectors, \\(Up(\\cdot)\\) is upsampling function that resizes the outputs of \\(K\\)-heads to the same size with the original image. In our experiments, we set \\(K = 2\\), with \\(O_1\\) used to estimate coarse deformation (e.g. corresponding to the position of pedestrians or the placement of workpieces) and \\(O_2\\) used to estimate fine deformation (e.g. corresponding to pedestrian behaviors or workpiece details)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.243, + 0.469, + 0.333 + ], + "angle": 0, + "content": "Considering that quantized embedding without positional information may lead to inaccurate reconstruction, we also introduce position embedding operator for the decoder \\( g(\\cdot) \\). We then aggregate \\( \\mathbf{O} \\) onto the reconstructed reference \\( g(PE(z^q)) \\), and obtain \\( \\tilde{x}_k(k = 1,\\dots ,K) \\) which is calibrated by the \\( k^{th} \\) layer of deformation fields:" + }, + { + "type": "equation", + "bbox": [ + 0.165, + 0.344, + 0.469, + 0.36 + ], + "angle": 0, + "content": "\\[\n\\tilde {x} _ {k} = g \\left(P E \\left(z ^ {q}\\right)\\right) \\circ O _ {1} \\dots \\circ O _ {k}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.37, + 0.469, + 0.473 + ], + "angle": 0, + "content": "where \\( \\circ \\) is grid-sampling function with a reference coordinate in this implementation (\"Agg.\" and \"Coord.\" in Fig. 4). However, minimizing the unconstrained reconstruction loss with respect to \\( \\psi(x) \\) may cause degenerate solution of the encoder \\( f(\\cdot) \\). To address this problem, we add constraint using smoothness loss via gradient operation and strength loss as:" + }, + { + "type": "equation", + "bbox": [ + 0.172, + 0.473, + 0.469, + 0.504 + ], + "angle": 0, + "content": "\\[\nL _ {d f} = \\sum_ {k} \\| \\nabla O _ {k} \\| _ {1} + \\| O _ {k} \\| _ {2}. \\tag {8}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.512, + 0.373, + 0.527 + ], + "angle": 0, + "content": "3.4. Foreground-background selection" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.535, + 0.47, + 0.716 + ], + "angle": 0, + "content": "Storing the background information in memory will break the compactness of embedding and require plenty of memory items. Besides, the deformation estimation should not be applied to the background. Some approaches use external estimators to remove interference from background, but the generalization in different scenarios cannot be guaranteed and extra noise will inevitably be introduced. Benefiting from the strong prior of fixed-view videos, we model the background with a learnable template \\( x_{bg} \\) and generate a binary mask to indicate whether a pixel belongs to foreground or background with \\( f_{m}(\\cdot) \\). The final reconstruction \\( \\hat{x}_k \\) of \\( k^{th} \\) head is:" + }, + { + "type": "equation", + "bbox": [ + 0.155, + 0.727, + 0.469, + 0.743 + ], + "angle": 0, + "content": "\\[\n\\hat {x} _ {k} = f _ {m} (x) \\tilde {x} _ {k} + (1 - f _ {m} (x)) x _ {b g}. \\tag {9}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.752, + 0.29, + 0.768 + ], + "angle": 0, + "content": "3.5. Training and inference" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.775, + 0.468, + 0.805 + ], + "angle": 0, + "content": "Training phase. Once we obtain the reconstruction \\(\\hat{x}_k\\), we can calculate reconstruction loss \\(L_{rec}\\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.192, + 0.814, + 0.469, + 0.845 + ], + "angle": 0, + "content": "\\[\nL _ {r e c} = \\sum_ {k} D i s (x, \\hat {x} _ {k}), \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.469, + 0.903 + ], + "angle": 0, + "content": "where \\( Dis(\\cdot) \\) refers to a distance function in sample space. Reminding of the optimization objective in Eq. 3, we implement the two constraints using \\( L_{com} \\) and \\( L_{df} \\) respectively." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.12 + ], + "angle": 0, + "content": "Finally, training is performed by minimizing the overall loss:" + }, + { + "type": "equation", + "bbox": [ + 0.587, + 0.122, + 0.892, + 0.138 + ], + "angle": 0, + "content": "\\[\nL _ {a l l} = L _ {r e c} + \\gamma_ {1} L _ {c o m} + \\gamma_ {2} L _ {d f}. \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.144, + 0.892, + 0.188 + ], + "angle": 0, + "content": "Inference phase. In the inference phase, we use \\(\\mathbf{O}\\) and the reconstruction loss to calculate the error maps of input sample \\(x\\):" + }, + { + "type": "equation", + "bbox": [ + 0.625, + 0.189, + 0.892, + 0.205 + ], + "angle": 0, + "content": "\\[\nA _ {r e c} = \\operatorname {D i s} (x, \\hat {x} _ {K}), \\tag {12}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.633, + 0.211, + 0.892, + 0.242 + ], + "angle": 0, + "content": "\\[\nA _ {d f} = \\sum_ {k} \\| O _ {k} \\| _ {2}. \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.247, + 0.892, + 0.275 + ], + "angle": 0, + "content": "Image-level anomaly score is computed based on local maxima:" + }, + { + "type": "equation", + "bbox": [ + 0.518, + 0.287, + 0.892, + 0.304 + ], + "angle": 0, + "content": "\\[\n\\operatorname {S c o r e} _ {I} = \\max \\left(A _ {r e c} \\otimes k ^ {\\star}\\right) + \\alpha \\max \\left(A _ {d f} \\otimes k ^ {\\star}\\right). \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.315, + 0.892, + 0.39 + ], + "angle": 0, + "content": "where \\(\\otimes\\) is convolution operator and \\(k^{\\star}\\) is convolution kernel for anomaly maps. \\(\\alpha\\) is a tradeoff parameter. That is, the reconstruction loss and deformation jointly determine the anomaly score, which is much more effective than traditional reconstruction-based methods, as illustrated in Fig. 3." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.399, + 0.661, + 0.414 + ], + "angle": 0, + "content": "3.6. Variant of PDM" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.422, + 0.892, + 0.603 + ], + "angle": 0, + "content": "Modified framework with Pre-PDM. The DMAD framework together with ICM and PDM modules proposed above are suitable in many anomaly detection scenarios including video surveillance. However, for industrial defect detection, texture reconstruction may be harmful (such as spots on \"Pill\"), and we should reconstruct high-level semantic features instead. Since PDM does not work in high-dimensional feature space and interferes with the training process, we propose variant of PDM, Pre-PDM (PPDM), as a solution. PPDM works in sample space, and is applied to the input sample rather than the reconstructed one. Eq. (3) is modified naturally as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.54, + 0.613, + 0.892, + 0.648 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} L = \\| x \\circ \\psi^ {\\prime} (x) - g (\\phi (f (x \\circ \\psi^ {\\prime} (x)), z)) \\| _ {2} \\tag {15} \\\\ + \\gamma_ {1} R _ {1} (\\phi) + \\gamma_ {2} R _ {2} (\\psi^ {\\prime}). \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.659, + 0.892, + 0.764 + ], + "angle": 0, + "content": "Since we do not reconstruct the original samples, reconstruction loss cannot constrain PPDM to maintain information diversity. In order to prevent \\( x \\circ \\psi'(x) \\) in Eq. (15) from shortcut learning, we propose to add the inversion of forward deformation, backward deformation \\( \\mathbf{O}^T \\), based on cycle-consistency principle to maintain the diversity of appearance information:" + }, + { + "type": "equation", + "bbox": [ + 0.563, + 0.774, + 0.892, + 0.793 + ], + "angle": 0, + "content": "\\[\n\\psi^ {\\prime} (x) = U p \\left(h ^ {\\prime} \\left(P E (x)\\right)\\right) = \\left\\{\\mathbf {O}, \\mathbf {O} ^ {T} \\right\\}. \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.802, + 0.892, + 0.835 + ], + "angle": 0, + "content": "Training phase. The cycle-consistency losses \\( L_{cyc} \\) and constraint for forward-backward deformation \\( L_{df}^{+} \\) are:" + }, + { + "type": "equation", + "bbox": [ + 0.521, + 0.844, + 0.892, + 0.863 + ], + "angle": 0, + "content": "\\[\nL _ {c y c} = \\left\\| x - x \\circ O _ {1} \\dots \\circ O _ {K} \\circ O _ {K} ^ {T} \\dots \\circ O _ {1} ^ {T} \\right\\| _ {2}, \\tag {17}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.509, + 0.872, + 0.892, + 0.904 + ], + "angle": 0, + "content": "\\[\nL _ {d f} ^ {+} = \\sum_ {k} \\| \\nabla O _ {k} \\| _ {1} + \\| \\nabla O _ {k} ^ {T} \\| _ {1} + \\| O _ {k} \\| _ {2} + \\| O _ {k} ^ {T} \\| _ {2}. \\tag {18}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.944, + 0.518, + 0.956 + ], + "angle": 0, + "content": "12151" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.127, + 0.088, + 0.221, + 0.16 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.165, + 0.161, + 0.184, + 0.172 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.223, + 0.089, + 0.319, + 0.16 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.262, + 0.161, + 0.281, + 0.172 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image", + "bbox": [ + 0.323, + 0.089, + 0.418, + 0.16 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.361, + 0.161, + 0.382, + 0.172 + ], + "angle": 0, + "content": "(d)" + }, + { + "type": "image", + "bbox": [ + 0.126, + 0.174, + 0.219, + 0.246 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.165, + 0.247, + 0.184, + 0.259 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.224, + 0.174, + 0.318, + 0.246 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.262, + 0.247, + 0.282, + 0.259 + ], + "angle": 0, + "content": "(e)" + }, + { + "type": "image", + "bbox": [ + 0.323, + 0.174, + 0.417, + 0.246 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.362, + 0.247, + 0.381, + 0.259 + ], + "angle": 0, + "content": "(f)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.268, + 0.47, + 0.379 + ], + "angle": 0, + "content": "Figure 5. The process of forward and backward deformation: a) The pattern of original image. Red indicates high error regions and black indicates low error regions; b) The normal pattern; c) The coarse estimation \\( O_{1} \\) (dark blue) and \\( O_{1}^{T} \\) (light blue); d) The fine estimation \\( O_{2} \\) (dark blue) and \\( O_{2}^{T} \\) (light blue); e) Using \\( \\hat{x} \\) simply causes high anomaly score at the wrong location (solid cross). Ground-truth is shown as hollow cross; f) \\( \\hat{x} \\circ O_{2}^{T} \\circ O_{1}^{T} \\) adjusts the high reconstruction error to original position." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.401, + 0.469, + 0.432 + ], + "angle": 0, + "content": "So we train our anomaly detection model with PPDM by minimizing the following loss:" + }, + { + "type": "equation", + "bbox": [ + 0.116, + 0.438, + 0.469, + 0.457 + ], + "angle": 0, + "content": "\\[\nL _ {a l l} ^ {+} = L _ {r e c} + \\gamma_ {1} L _ {c o m} + \\gamma_ {2} L _ {d f} ^ {+} + \\gamma_ {3} L _ {c y c}. \\tag {19}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.461, + 0.469, + 0.49 + ], + "angle": 0, + "content": "The modified DMAD framework (i.e. with PPDM and Reverse Distribution [6]) is shown in in Fig. 4b." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.49, + 0.469, + 0.564 + ], + "angle": 0, + "content": "Inference phase. The result of PPDM is not aligned with the position of original input, which may reduce the performance of anomaly localization. In order to obtain the anomaly map of real location, we use backward deformation to perform inverse sampling (Fig. 5):" + }, + { + "type": "equation", + "bbox": [ + 0.152, + 0.569, + 0.469, + 0.588 + ], + "angle": 0, + "content": "\\[\nA _ {r e c} ^ {+} = \\operatorname {D i s} \\left(x, \\hat {x} _ {K}\\right) \\circ O _ {K} ^ {T} \\dots \\circ O _ {1} ^ {T}, \\tag {20}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.154, + 0.593, + 0.469, + 0.658 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} A _ {d f} ^ {+} = \\sum_ {k} \\| O _ {k} \\circ O _ {k + 1} \\dots \\circ O _ {K} \\| _ {2} \\tag {21} \\\\ + \\sum_ {k} \\| O _ {k} ^ {T} \\circ O _ {k - 1} ^ {T} \\dots \\circ O _ {1} ^ {T} \\| _ {2}. \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.663, + 0.469, + 0.695 + ], + "angle": 0, + "content": "The image-level anomaly score \\(Score_{I}^{+}\\) and pixel-level anomaly score \\(Score_{P}^{+}\\) are calculated respectively as:" + }, + { + "type": "equation", + "bbox": [ + 0.093, + 0.7, + 0.469, + 0.719 + ], + "angle": 0, + "content": "\\[\n\\operatorname {S c o r e} _ {I} ^ {+} = \\max \\left(A _ {\\text {r e c}} ^ {+} \\otimes k ^ {\\star}\\right) + \\alpha \\max \\left(A _ {d f} ^ {+} \\otimes k ^ {\\star}\\right), \\tag {22}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.188, + 0.724, + 0.469, + 0.744 + ], + "angle": 0, + "content": "\\[\n\\operatorname {S c o r e} _ {P} ^ {+} = A _ {r e c} ^ {+} + \\alpha A _ {d f} ^ {+}. \\tag {23}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.753, + 0.32, + 0.77 + ], + "angle": 0, + "content": "4. Experiments and Analysis" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.778, + 0.469, + 0.868 + ], + "angle": 0, + "content": "Firstly, we perform toy experiment on MNIST to illustrate our approach. Then the quantitative and qualitative results of two versions our DMAD framework are reported in video anomaly detection and industrial surface defect detection respectively2. Finally, we conduct ablation experiments and analyze the results." + }, + { + "type": "page_footnote", + "bbox": [ + 0.077, + 0.875, + 0.468, + 0.901 + ], + "angle": 0, + "content": "2Our code will be available at https://github.com/FlappyPeggy/DMAD." + }, + { + "type": "image", + "bbox": [ + 0.53, + 0.087, + 0.865, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.25, + 0.892, + 0.292 + ], + "angle": 0, + "content": "Figure 6. Visualization of toy experiment. The last three rows are: reference reconstructed from memory, reference after coarse deformation, and final output after applying fine deformation." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.315, + 0.602, + 0.33 + ], + "angle": 0, + "content": "4.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.338, + 0.892, + 0.414 + ], + "angle": 0, + "content": "Surveillance Videos. Ped2 [27], Avenue [23] and ShanghaiTech [25] are fixed-view videos. The anomalies include driving, cycling, running, throwing stuff, etc. Mutual occlusion, anomaly-like behavior, contaminated data and different scenes occur frequently in these datasets." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.414, + 0.892, + 0.489 + ], + "angle": 0, + "content": "Industrial Images. MVtec [2] contains 15 types of industrial images, which are divided into 5 types of textures and 10 types of objects. The defects include crack, scratch, etc. The normal workpiece has different positions, angles and textures. It is used for detection and localization task." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.499, + 0.657, + 0.515 + ], + "angle": 0, + "content": "4.2. Toy experiment" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.522, + 0.892, + 0.657 + ], + "angle": 0, + "content": "As shown in Fig. 6, we perform a toy experiment on MNIST dataset [16] with setting analogous to out-of-distribution (OOD) detection (i.e. training on \"1, 3, 5, 7, 9\" and test on all classes). Our model searches separate memory items for each digital category to reconstruct it into class-specific reference and uses the deformation fields from PDM to adjust it hierarchically. When tested with seen and unseen classes, the model adjusts reconstructed references to normal inputs, but fails on the abnormal ones." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.658, + 0.892, + 0.779 + ], + "angle": 0, + "content": "In contrast, memory network without diversity-aware module cannot guarantee the intra-class compactness and the reconstruction diversity, which misdirects the model to obtain dataset-optimal \"average memory\", leading to fuzzy reconstruction and lower discrimination ability. The model with full-channel skip-connection suffers from shortcut learning and reconstruct anomalies successfully which weakens the ability to identify anomalies." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.787, + 0.715, + 0.803 + ], + "angle": 0, + "content": "4.3. Implementation details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The input images are resized into \\(256 \\times 256\\) and normalized to the value in range of \\([-1,1]\\). According to frame-pred strategy [19], the history length is set to 4 in video anomaly detection and 0 for images. After feature extraction with a backbone, PDM and PPDM obtain different heads by stacking stride-2 convolution layers. Then" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.944, + 0.519, + 0.956 + ], + "angle": 0, + "content": "12152" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.455 + ], + "angle": 0, + "content": "we use \\( \\text{Tanh} \\) as the activation function of output layer and clipping function to ensure the value of deformation is between \\([-1, 1]\\). Unless otherwise noted, the architecture of autoencoder complies with the settings of MNAD [29] and RD [6] for PDM and PPDM respectively. The function \\( \\text{Dis}(\\cdot) \\) in Eq. (10) is a combination of \\( MSE \\) loss and \\( Grad \\) loss for reconstruction in sample space, and \\( COS \\) loss for deep features. We set \\( (\\gamma_1, \\gamma_2) = (1, 0.25) \\) for PDM, \\( (1, 1) \\) for PPDM \\( (\\gamma_3 \\) is discussed in Sec. 4.5), and \\( \\beta = 0.25 \\) as in [35]. During post-processing, we use average kernel for surveillance videos and Gaussian kernel with \\( \\sigma = 4 \\) for industrial images as in [6]. Frame-difference method is applied to remove static anomalies for Avenue, because our method detects all anomalies which may be labeled as normal ones in [23]. And we use the mask calculated in Eq. (9) to normalize anomaly map in [25] due to the scale changes. Besides, we set \\( \\alpha = 0.2 \\) for three video tasks and an additional option \\( \\alpha = 0.05 \\) for defect detection, depending on whether the defect includes geometrical changes. The model is optimized by AdamW [21] and the learning rate is 2e-4 and 5e-3 as in [6, 29] respectively, being decayed by CosineAnnealingLR [22] strategy. We adopt 60, 60, 60, 10, 400 epochs for MNIST, Ped2, Avenue, Shanghai and MVTec respectively with batch size of 8." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.465, + 0.212, + 0.48 + ], + "angle": 0, + "content": "4.4. Main results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.488, + 0.47, + 0.579 + ], + "angle": 0, + "content": "Surveillance Videos. We compare our method with SOTA works on video anomaly detection in Tab. 1. Our method outperforms comparative approaches even though we neither use external estimators nor remove abnormal frames in training data. In additional, if we detect global offset for camera jitter in [23], there will be extra \\(0.1\\%\\) gain." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.58, + 0.47, + 0.64 + ], + "angle": 0, + "content": "The qualitative results are shown in Fig. 7. We find that: anomalies are over-reconstructed in (b); normals are not reconstructed well in (c); (d) greatly improves normal reconstruction with slightly less inhibition ability for anomalies." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.641, + 0.471, + 0.748 + ], + "angle": 0, + "content": "Industrial Images. Anomaly detection results on MVTec are shown in Tab. 2 and localization results are shown in Tab. 3. With the deformation from PPDM, texture anomalies are detected with high performance and our method outperforms SOTA methods in both detection and localization tasks without memorizing an enormous number of embedding from training data." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.757, + 0.228, + 0.773 + ], + "angle": 0, + "content": "4.5. Ablation study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.471, + 0.903 + ], + "angle": 0, + "content": "As shown in Tab. 4, single-output memory module without PDM suppresses diverse normal patterns seriously, while separate PDM without memory provides comparable performance gains as the previous SOTA works because the module \"Comp.\" serves as an information compression module instead. The number of multi-scale deformation fields also have a modest effect on performance. We suggest that \"K\" should at least make the scale of control grid" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.089, + 0.894, + 0.161 + ], + "angle": 0, + "content": "Table 1. Video anomaly detection results on Ped2 [27], Avenue [23] and Shanghai [25]. We calculate \\(AUC(\\%)\\) with all frames together. Numbers in bold indicate the best performance and the underlined ones are the second best. \\(^+\\) indicates that we reproduce the result due to higher performance or absence of implementation." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.17, + 0.895, + 0.34 + ], + "angle": 0, + "content": "
MethodsPed2 [27]Avenue [23]Shanghai [25]
Conv2D [9]90.070.2-
Conv3D [40]91.277.1-
ConvLSTM [24]88.177.0-
FramePred [19]95.484.972.8
ConvVQ+90.284.3-
MemAE [8]94.183.371.2
MPN [26]96.989.573.8
MNAD+ [29]97.888.570.5
HF2VAD [20]99.391.176.2
Ours99.792.878.8
" + }, + { + "type": "image", + "bbox": [ + 0.588, + 0.353, + 0.695, + 0.437 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.634, + 0.437, + 0.649, + 0.445 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.698, + 0.353, + 0.807, + 0.437 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.747, + 0.438, + 0.762, + 0.445 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.588, + 0.446, + 0.695, + 0.528 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.637, + 0.528, + 0.652, + 0.537 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image", + "bbox": [ + 0.698, + 0.446, + 0.807, + 0.528 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.746, + 0.528, + 0.761, + 0.537 + ], + "angle": 0, + "content": "(d)" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.547, + 0.894, + 0.604 + ], + "angle": 0, + "content": "Figure 7. Qualitative results on Ped2. a) Original image; b) Memory network with skip-connection [29]; c) PDM with VQ-Layer [35]; d) PDM with ICM. Green box indicates negative, red box indicates positive, and yellow box indicates weak positive." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.892, + 0.765 + ], + "angle": 0, + "content": "cover the size of base elements (e.g. pedestrian limbs). Besides, the foreground-background selection module further improves the compactness of memory embedding. Moreover, if any constraint for PDM is missing, the abnormal information will be transmitted and cause shortcut learning. Especially, the cycle-consistency constraint \\( L_{cyc} \\) is also a necessary part for PPDM to avoid degenerated solution \\((-1.7\\%)\\), because the feature reconstruction error can be minimized by eliminating all necessary information." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.766, + 0.895, + 0.903 + ], + "angle": 0, + "content": "As shown in Tab. 5, the proposed method is robust to hyperparameter \\(\\gamma_{3}\\) in Eq. (19). On condition that degenerated solution will not be formed, weakening the constraint makes model restore images from reference with less detail more easily and perceive the position of anomalies more accurately by transforming anomalies to normal patterns which benefits localization task. On the contrary, strengthening the constraint alleviates shortcut learning and improves image-level result by maintaining more abnormal details." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.943, + 0.519, + 0.956 + ], + "angle": 0, + "content": "12153" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.281, + 0.089, + 0.687, + 0.104 + ], + "angle": 0, + "content": "Table 2. Image-level \\( {AUC}\\left( \\% \\right) \\) of anomaly detection on MVTec [2]." + }, + { + "type": "table", + "bbox": [ + 0.078, + 0.111, + 0.894, + 0.189 + ], + "angle": 0, + "content": "
Class\\MethodsGN [1]PSVDD [37]DAAD [11]CutPaste [17]PaDiM [5]PatchCore [31]DRAEM [38]RD [6]Ours
AvgTextures77.594.591.097.598.899.099.199.599.9
AvgObjects75.590.888.895.593.899.297.498.099.3
AvgAll76.292.189.596.195.599.198.098.599.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.276, + 0.199, + 0.692, + 0.213 + ], + "angle": 0, + "content": "Table 3. Pixel-level \\( {AUC}\\left( \\% \\right) \\) of anomaly localization on MVtec [2]." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.221, + 0.893, + 0.298 + ], + "angle": 0, + "content": "
Class\\MethodsPSVDD [37]CutPaste [17]PaDiM [5]PatchCore [31]DRAEM [38]TMAE [34]RD [6]Ours
AvgTextures93.796.396.997.697.993.897.797.8
AvgObjects96.795.897.898.497.094.097.998.3
AvgAll95.796.097.598.197.393.997.898.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.313, + 0.468, + 0.368 + ], + "angle": 0, + "content": "Table 4. Ablation study of proposed module and loss on Ped2 [27]. From left to right: without PDM; with only one head of PDM \\((K = 1)\\); without memory module; without background template; removing strength constraint; removing smoothness constraint." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.375, + 0.47, + 0.419 + ], + "angle": 0, + "content": "
w/oPDMK>1Memxbg|O|2|∇O|2
AUC%-9.4-0.4-1.8-1.6-1.4-1.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.08, + 0.428, + 0.466, + 0.442 + ], + "angle": 0, + "content": "Table 5. Ablation study of deformation constraint on MVTec [2]." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.449, + 0.47, + 0.509 + ], + "angle": 0, + "content": "
Task\\γ300.10.250.512
Det.97.999.499.499.599.699.4
Loc.96.698.098.298.097.797.6
" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.53, + 0.194, + 0.545 + ], + "angle": 0, + "content": "4.6. Discussion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.553, + 0.47, + 0.734 + ], + "angle": 0, + "content": "Contaminated data assumption. Assuming that training data only contains completely normal data is unrealistic, because the workload of natural data cleansing is considerable, even has same cost as data annotations. We mix training data with abnormal events in Ped2 to simulate contaminated data and find performance drop of MNAD [29] is \\(-3.7\\%\\) while ours is \\(-1.8\\%\\). The reason why DMAD is less affected may be that PDM can encode and transmit residual abnormal representation of mixed anomalies and anomaly-like normal samples, thus strictly maintaining representation compactness of the main encoder and low generalization ability on abnormal samples." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Two DMAD implementations. As introduced earlier, our DMAD framework is implemented by two versions using PDM and PPDM respectively, corresponding to different detection targets. As shown in Fig. 8, PDM learns measurable quantization error (caused by ICM) from memory embedding to diverse patterns which enhances the potential of ICM to keep intra-class compactness without generating unmeasurable reconstruction loss. Unlike PDM, PPDM is partially in charge of the information compression, i.e. PPDM removes the diverse appearance by using the reverse deformation process from inputs to reference." + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.31, + 0.877, + 0.452 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.46, + 0.892, + 0.489 + ], + "angle": 0, + "content": "Figure 8. Illustration of two DMAD implementations with PDM and PPDM respectively." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.507, + 0.618, + 0.523 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.533, + 0.892, + 0.73 + ], + "angle": 0, + "content": "In this paper, we present a reconstruction-based diversity-measurable anomaly detection framework, which simultaneously enhances anomaly discrimination and reconstruction diversity. Pyramid deformation module is proposed to be used together with information compression module for this purpose. PDM models multi-scale transformation fields from reference to original input explicitly without relying on external estimators. Therefore, diverse normal patterns can be reconstructed and anomaly severity can be measured accurately. Empirical studies on both videos and images benchmarks show the effectiveness and applicability of our work. In future research, we will further explore diversity-aware models for anomaly detection." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.747, + 0.892, + 0.823 + ], + "angle": 0, + "content": "Limitations. Our method focuses on anomaly with measurable geometrical diversity, the most common type in anomaly detection. However, as for anomaly with other kind of diversities, e.g. colors, the proposed diversity measure may not be positively correlated to anomaly severity." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgement. This work is partially supported by National Key R&D Program of China (No. 2018AAA0102402), and National Natural Science Foundation of China (NSFC): 61976203 and 62276246." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.944, + 0.519, + 0.956 + ], + "angle": 0, + "content": "12154" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.117, + 0.47, + 0.185 + ], + "angle": 0, + "content": "[1] Samet Akcay, Amir Atapour Abarghouei, and Toby P. Breckon. Ganomaly: Semi-supervised anomaly detection via adversarial training. 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In Proceedings of the 2017 ACM on Multimedia Conference, pages 1933-1941, 2017. 1, 2, 7" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.234 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.944, + 0.52, + 0.956 + ], + "angle": 0, + "content": "12156" + } + ] +] \ No newline at end of file diff --git a/2023/Diversity-Measurable Anomaly Detection/43dbf769-f361-451d-b986-1893419fc738_origin.pdf b/2023/Diversity-Measurable Anomaly Detection/43dbf769-f361-451d-b986-1893419fc738_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..705ac321372dd8ba5760424ebe2621531378bbad --- /dev/null +++ b/2023/Diversity-Measurable Anomaly Detection/43dbf769-f361-451d-b986-1893419fc738_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:ce43626993838fb47eb213a662cfe7416ed101c2b8fd4e5ee53647aa78bdc52b +size 4328005 diff --git a/2023/Diversity-Measurable Anomaly Detection/full.md b/2023/Diversity-Measurable Anomaly Detection/full.md new file mode 100644 index 0000000000000000000000000000000000000000..b82063d96a49c9cda890f37d6e1356930f94af08 --- /dev/null +++ b/2023/Diversity-Measurable Anomaly Detection/full.md @@ -0,0 +1,394 @@ +# Diversity-Measurable Anomaly Detection + +Wenrui Liu $^{1,2}$ , Hong Chang $^{1,2}$ , Bingpeng Ma $^{2}$ , Shiguang Shan $^{1,2}$ , Xilin Chen $^{1,2}$ $^{1}$ Institute of Computing Technology, Chinese Academy of Sciences, China + $^{2}$ University of Chinese Academy of Sciences, China + +wenrui.liu@vipl.ict.ac.cn, {changhong, sgshan, xlchen}@ict.ac.cn, bpma@ucas.ac.cn + +# Abstract + +Reconstruction-based anomaly detection models achieve their purpose by suppressing the generalization ability for anomaly. However, diverse normal patterns are consequently not well reconstructed as well. Although some efforts have been made to alleviate this problem by modeling sample diversity, they suffer from shortcut learning due to undesired transmission of abnormal information. In this paper, to better handle the tradeoff problem, we propose Diversity-Measurable Anomaly Detection (DMAD) framework to enhance reconstruction diversity while avoid the undesired generalization on anomalies. To this end, we design Pyramid Deformation Module (PDM), which models diverse normals and measures the severity of anomaly by estimating multi-scale deformation fields from reconstructed reference to original input. Integrated with an information compression module, PDM essentially decouples deformation from prototypical embedding and makes the final anomaly score more reliable. Experimental results on both surveillance videos and industrial images demonstrate the effectiveness of our method. In addition, DMAD works equally well in front of contaminated data and anomaly-like normal samples. + +# 1. Introduction + +Visual anomaly detection is a fundamental and important problem in computer vision community, with wide applications in video surveillance and industrial inspection. It aims to detect outliers from seen classes and novel patterns from unseen classes. This task is very challenging because abnormal data is diversely distributed and expensive to collect. So we have to construct models based on only normal samples under unsupervised setting, targeting at high discrimination between normal and abnormal samples. + +During the past decade, reconstruction-based methods have achieved great progress in anomaly detection. These methods use Autoencoders (AEs) [8,9,20,24,26,29,40] or Generative Adversarial Networks (GANs) [1, 19, 32] to re + +![](images/7fe06ff0a8c5dfa5980addc51c64fe1415e2d3e8e9db3cb007947e25488f08a9.jpg) +Figure 1. Illustration of difficulty in anomaly detection in MNIST dataset. The prototype is indicated by orange triangle and the anomaly by red point. In this case, the anomaly can hardly be detected based on reconstruction error or distance in high-dimensional feature space. Our solution is illustrated in Fig. 2. + +construct the normal counterparts from any input images or video frames. AE-based methods firstly compress the inputs to discard the information beyond normal prototypes, and then decode the embedding to reconstruct the inputs. According to the estimated reconstruction error, the anomalies can be detected. + +However, the performance of reconstruction-based methods for anomaly detection has long been limited by a tough problem, i.e. the tradeoff between reconstructing diverse normals and detecting unknown anomalies. In order to discriminate anomalies more easily, previous works [8] imposes more constraints to suppress abnormal information during autoencoding, which leads to high reconstruction error for diverse normal instances. For example, in Figs. 1 and $2\mathbf{g}$ , the severely deformed normal (a.k.a. anomaly-like) sample "7" has even higher error than the abnormal sample "4". To better reconstruct diverse normals, each query vector corresponds to multiple prototypes in the memory, which may be combined into abnormal embedding even if abnormal projection is far away from the prototype. As a consequence, anomalies that distribute in low likelihood area between prototypical embedding are difficult to identify from diverse normals. MNAD [29] introduces skipconnection for diverse reconstruction and additional constraints to get round the incorrect combination problem. But the latter forces model transmit more unrestrained in + +![](images/3fd76b582e9bafb4bf2dff2c0675c3c5f31ec99cfce2667ad25fd7b40c78e662.jpg) +Figure 2. Illustration of our diversity-measurable method in addressing the detection difficulty. Numbers in white are anomaly scores. a) Original input; b) Reconstructed reference; c) Coarse deformation; d) Fine deformation; e) Measurement of diversity1; f) Deformation-augmented error map assigns lower anomaly score to the anomaly-like sample than the true anomaly; g) Pixel-wise reconstruction error yields incorrect anomaly scores. + +formation with abnormal part by skip-connection, resulting in shortcut learning and undesired reconstruction of anomalies. + +A key to address the above tradeoff problem is to find a proper measurement of diversity that normal and abnormal samples have, which is positively correlated with the severity of anomaly. With such a measure, we do not need to fight against imperfect reconstruction of normals or undesired reconstruction of anomalies, because anomalies can be detected more accurately by the diversity measure together with the reconstruction error. Note that pixel-wise reconstruction error is not an ideal measurement of diversity, because the high-error region often confuses anomalies with diverse normals, e.g. normals with structural deformation and anomalies with colors close to the background may yield unreliable reconstruction error. + +In this paper, we propose a Diversity-Measurable Anomaly Detection (DMAD) framework to enhance the measurability of reconstruction diversity so as to measure abnormality more accurately. Our basic idea is to decouple the reconstruction into compact representation of prototypical normals and measurable deformations of more diverse normals and anomalies. The under-estimated reconstruction error can be compensated by the diversity, which can be properly measured. To this end, the DMAD framework includes a Pyramid Deformation Module (PDM) to model and measure the diversity and an Information Compression Module (ICM) to learn the prototypical normal patterns. + +Inspired by [4, 15], we assume anomalies (e.g. in video surveillance) can be represented as significant deformation of appearances, including positional changes and fine motions. In contrast, diverse normal samples can be represented as weaker deformations thus easily distinguished + +from the abnormal ones. Therefore, we design PDM to model the diversity of normals as well as the severity of anomalies. More specifically, PDM learns hierarchical two-dimensional deformation fields (Fig. 2c,d) that describe the pixel-level transformation direction and distance from reference (Fig. 2b, which is reconstructed from prototypes in memory) to original input. In ICM, we learns compressed representation as sparse prototypes. As a result, a single memory item is enough to represent each normal cluster. This is more compact than other memory-based works which require multiple memory items. Integrating PDM with ICM, DMAD essentially decouples the deformation information (Fig. 2e) from class prototypes and makes the final anomaly score more discriminative (Fig. 2f). + +We evaluate our anomaly detection framework in scenarios of video surveillance and industrial defect detection. To apply DMAD in the latter scenario, we propose a variant of PDM, PPDM, to deal with the false positive issue in texture reconstruction. Extensive experimental results verify the efficacy of our approach. Moreover, our method works well even in front of contaminated data and anomaly-like normals. The main contributions of our work are as follows: + +- We introduce diversity-measurable anomaly detection framework which allows reconstruction-based models to achieve better tradeoff between reconstructing diverse normals and detecting unknown anomalies. +- We propose pyramid deformation module to implement diversity measurement, in which the deformation information is explicitly separated from compact class prototypes and the resulting diversity measure is positively correlated to abnormality. +- Our approach outperforms previous works on video anomaly detection and industrial defect detection, and works well in front of contaminated data and anomaly-like normals, demonstrating its broad suitability and robustness. + +# 2. Related Work + +Anomaly detection. Reconstruction-based methods model the distribution of normal data and assign anomalies with high reconstruction error, because models trained with only normal data cannot reconstruct anomalies. Some works use autoencoder to detect anomalies, such as convolutional autoencoder [9] and the variants [24, 40]. Other approaches introduce additional constraints or memory to make the model more discriminative. For example, sparse coding [25, 39] reduces representation redundancy with regularization; memory-augmented autoencoder (MemAE) [8] memorizes the normal patterns appearing in training dataset with external memory bank; variational autoencoder [10, 35] assumes a prior distribution of normal data to constrain the nonlinear representation capacity; $\mathrm{HF}^2\mathrm{VAD}$ [20] + +uses CVAE [33] to capture the correlation among motions. Frame prediction [19] assumes that abnormal samples in videos cannot be represented by past frames that do not contain unseen information and forces the model to encode changes among different frames. In addition, autoencoders can also be combined with external object detectors [7, 14, 20] to capture background-invariant appearance. + +Although these methods generally work well, they often have difficulty in discriminating abnormal samples from anomaly-like normals due to the tradeoff between reconstruction and discrimination. In our framework, pyramid deformation module and information compression module are leveraged to address the trade-off problem, significantly improving the performance in anomaly detection. + +Memory network. Generative models map continuously in feature space and they may assign higher probabilities to anomalies than normal ones [28]. Recent research [8, 11, 20, 29] has explored the application of discrete external memory to generate seen normal patterns even if the input is abnormal. MemAE [8] proposes a memory-augmented autoencoder, which uses information from encoder as a query and obtains a normal pattern retrieved from memory module. MNAD [29] introduces skip-connection to alleviate the problem that diverse normal patterns may yield high reconstruction errors. $\mathrm{HF^2VAD}$ [20] extends the memory module to multi-level memory, and uses additional estimators [3, 13] to explicitly model the motion information and filter the noise from background. DAAD [11] uses block-wise memory to increase the specificity of memory. + +In most existing works, the memory module outputs a linear combination of memory items which may lead to undesired reconstruction of normal-like anomalies. And they do not explicitly consider that instances corresponding to the same memory grid may be located at different positions of the receptive field. In our approach, we alleviate these problems via compressing embedding into a single memory item to ensure that the output is absolutely normal. + +Transformation modeling. The transformation between video frames is a key clue for anomaly detection. Some methods [7, 14, 19, 20] use external object detectors or optical-flow estimators to model the motion information implicitly or explicitly. Among the transformation estimators, optical-flow estimation [13] is widely studied, which aims to estimate the pixel-wise motions between consecutive frames. In addition, correspondence modeling between pair-wise images is also applied to 2D geometric matching [30] and 3D image registration [36] to obtain image deformation fields. STN [15] learns to transform the original images themselves to benefit identification algorithm. RegAD [12] uses feature-level affine registration to relocate features without changing the embeddings. + +However, pairwise transformation modeling only focus on pattern changes thus cannot detect static anomalies. And + +![](images/0ab9514c0ff3786bac933b6a545f46d20aef4b977f82968b3a9fd7c454f4f4b8.jpg) +Figure 3. Three conditions for DMAD framework. The colors of lines represent the measurements of diversity (severity of anomaly); The gray area represents uncertainty in the measure; Double dashed arrows indicate possible ranges of the boundary. The last two lines denote DMAD and traditional reconstruction-based method respectively. + +pretrained transformation estimators introduce generalization error in different scenarios. In contrast, we address these problems by separating and measuring the transformation from prototypical memory in end-to-end training. + +# 3. Diversity-Measurable Anomaly Detection + +In this section, we first analyze the objective of reconstruction-based anomaly detection and propose a diversity-measurable framework to address the tradeoff problem in existing works. Then, we introduce information compression module and pyramid deformation module (PDM) as an implementation of the framework. Finally, we explain the training and inference process and how to apply the framework to defect detection with a variant of PDM. + +# 3.1. The framework + +Given input $x$ , autoencoder-based methods aim to model normal data distribution by minimizing the following reconstruction loss $(\| \cdot \|_2$ is just one type of reconstruction loss): + +$$ +L = \| x - g (\phi (f (x), z)) \| _ {2} + \gamma_ {1} R _ {1} (\phi), \tag {1} +$$ + +with respect to encoder $f(\cdot)$ , decoder $g(\cdot)$ , latent variable $z$ (referring to discrete memory items in these cases) and a constrained feature mapping function $\phi(\cdot)$ corresponding to its constraint $R_1(\phi)$ . Skip-connection and concatenation $[\cdot, \cdot]$ are introduced to generate diverse normal patterns [29]: + +$$ +L = \| x - g ([ \phi (f (x), z), f (x) ]) \| _ {2} + \gamma_ {1} R _ {1} (\phi). \tag {2} +$$ + +However, due to diverse data distribution, previous methods have to face the conflict between representing diverse normals and detecting anomalies. The intrinsic reason lies in that the encoding of diversity $[\cdot ,f(x)]$ contains redundant information that cannot be measured accurately. + +In this work, we propose a principled framework, Diversity-Measurable Anomaly Detection (DMAD), to alleviate the conflict. The basic idea is to restrict the anomaly + +![](images/8f7b4f6390eecdfad989b5ccda968651119a9a84d06ee3ffe2c9a11e9f607409.jpg) +(a) + +![](images/55440356652e7e8fd158ef7f0561bd0b784bf88f0ed21f997d0a3e8046543e6c.jpg) +(b) +Figure 4. Two versions of diversity-measurable anomaly detection framework. Multi-scale pyramid deformation fields are estimated as $\mathbf{O}$ and the reverse processes are $\mathbf{O}^T$ . a) PDM version computes forward deformation $\mathbf{O}$ after reconstruction. b) PPDM version employs cycle-consistent forward-backward deformations and the forward deformation is applied on the input. + +information transmitted to $g(\cdot)$ while measuring and modeling the diversity of the remaining part. To this end, we design information compression module $\phi(\cdot)$ and diversity-aware module $\psi(\cdot)$ under DMAD framework: + +$$ +L = \| x - g (\phi (f (x), z)) \circ \psi (x) \| _ {2} + \gamma_ {1} R _ {1} (\phi) + \gamma_ {2} R _ {2} (\psi), \tag {3} +$$ + +where $\circ$ refers to aggregation operator. With appropriate design of $\phi(\cdot), \psi(\cdot)$ and the constraints, optimization of the reconstruction loss can improve the compactness of feature embedding. So that diverse representations are mapped via $\phi(\cdot)$ to compact prototypes in the memory. The diversity of input $x$ relative to its reconstruction is represented by $\psi(\cdot)$ . The under-estimated reconstruction error can be compensated by the diversity measured in $\psi(\cdot)$ , a key factor contributing to accurate anomaly scores. + +This framework can achieve our target on the premise that the following conditions (Fig. 3) are met: 1. $\psi(\cdot)$ can learn all diverse information from prototypical patterns to any normal inputs to ensure normal samples do not yield high anomaly score; 2. Deformation generated by $\psi(\cdot)$ is positively correlated to diversity measure; 3. Prototypical information about $x$ represented by $\psi(\cdot)$ needs to be minimized. In the following subsections, we explain how to design modules to fulfill these conditions. + +# 3.2. Information compression module + +According to [35], we adapt VQ-Layer as an information compression module to learn $\phi(\cdot)$ given embedding $f(x) \in R^{D \times H' \times W'}$ as a query $z^e = f(x)$ and memory $z \in R^{D \times N}$ . Then, we quantize $z^e$ into a single-memory feature cube $z^q \in R^{D \times H' \times W'}$ by seeking for memory item with minimum $L2$ distance ("Search" in Fig. 4): + +$$ +z _ {h, w} ^ {q} = \operatorname {a r g m i n} _ {z _ {n}} \left\| z _ {h, w} ^ {e} - z _ {n} \right\| _ {2}, \tag {4} +$$ + +where $z_{n}$ is the $n^{th}$ memory item, $h\in \{1,\dots ,H^{\prime}\} ,w\in$ $\{1,\dots ,W^{\prime}\}$ indicates the same location in both $z^q$ and $z^{e}$ . The compression loss $L_{com}$ with stop-gradient operator $SG(\cdot)$ that updates its parameters separately [35] is combined by a hyperparameter $\beta$ : + +$$ +L _ {c o m} = \left\| S G \left(z ^ {e}\right) - z ^ {q} \right\| _ {2} + \beta \left\| z ^ {e} - S G \left(z ^ {q}\right) \right\| _ {2}. \tag {5} +$$ + +Skip-connection with low information capacity (Fig. 4 "Comp.") is also allowed to further improve the reconstruction quality without bringing excessive generalization (i.e. Conv-Layer with stop-gradient operator for intermediate features whose reduction factor is 16 or larger). + +# 3.3. Pyramid deformation module + +We categorize the unknown anomalies into the following three types: unseen class (e.g. novel objects), global anomaly (e.g. unexpected movement) and local anomaly (e.g. strange behavior and workpiece damage) of seen class. The unseen class is easy to be detected based on reconstruction result, but the latter two types are usually confused with diverse normals. To discriminate these anomalies from normal ones, we represent the diversity using measurable deformation between reconstructed reference and original input, so that slight deformations occur in normals while drastic deformations occur in anomalies. + +Inspired by STN and DCN [4, 15], we introduce Pyramid Deformation Module (PDM) which explicitly learn deformation fields with hierarchical scales to model the motion, behavior and defect of different anomaly types, as shown in Fig. 4a. Specifically, after feature extraction, $\psi(\cdot)$ uses $K$ -heads to compute offsets $\mathbf{O} = \{O_1, \dots, O_K\}$ , corresponding to $K$ coarse-to-fine deformations: + +$$ +\psi (x) = U p \left(h \left(P E (x)\right)\right) = \mathbf {O}, \tag {6} +$$ + +where $PE(\cdot)$ is positional embedding operator [18], $h: R^{C \times H \times W} \to R^{2 \times \{H_1 \times W_1, \dots, H_K \times W_K\}}$ is the deformation estimator that generates offset vectors, $Up(\cdot)$ is upsampling function that resizes the outputs of $K$ -heads to the same size with the original image. In our experiments, we set $K = 2$ , with $O_1$ used to estimate coarse deformation (e.g. corresponding to the position of pedestrians or the placement of workpieces) and $O_2$ used to estimate fine deformation (e.g. corresponding to pedestrian behaviors or workpiece details). + +Considering that quantized embedding without positional information may lead to inaccurate reconstruction, we also introduce position embedding operator for the decoder $g(\cdot)$ . We then aggregate $\mathbf{O}$ onto the reconstructed reference $g(PE(z^q))$ , and obtain $\tilde{x}_k(k = 1,\dots ,K)$ which is calibrated by the $k^{th}$ layer of deformation fields: + +$$ +\tilde {x} _ {k} = g \left(P E \left(z ^ {q}\right)\right) \circ O _ {1} \dots \circ O _ {k}, \tag {7} +$$ + +where $\circ$ is grid-sampling function with a reference coordinate in this implementation ("Agg." and "Coord." in Fig. 4). However, minimizing the unconstrained reconstruction loss with respect to $\psi(x)$ may cause degenerate solution of the encoder $f(\cdot)$ . To address this problem, we add constraint using smoothness loss via gradient operation and strength loss as: + +$$ +L _ {d f} = \sum_ {k} \| \nabla O _ {k} \| _ {1} + \| O _ {k} \| _ {2}. \tag {8} +$$ + +# 3.4. Foreground-background selection + +Storing the background information in memory will break the compactness of embedding and require plenty of memory items. Besides, the deformation estimation should not be applied to the background. Some approaches use external estimators to remove interference from background, but the generalization in different scenarios cannot be guaranteed and extra noise will inevitably be introduced. Benefiting from the strong prior of fixed-view videos, we model the background with a learnable template $x_{bg}$ and generate a binary mask to indicate whether a pixel belongs to foreground or background with $f_{m}(\cdot)$ . The final reconstruction $\hat{x}_k$ of $k^{th}$ head is: + +$$ +\hat {x} _ {k} = f _ {m} (x) \tilde {x} _ {k} + (1 - f _ {m} (x)) x _ {b g}. \tag {9} +$$ + +# 3.5. Training and inference + +Training phase. Once we obtain the reconstruction $\hat{x}_k$ , we can calculate reconstruction loss $L_{rec}$ as: + +$$ +L _ {r e c} = \sum_ {k} D i s (x, \hat {x} _ {k}), \tag {10} +$$ + +where $Dis(\cdot)$ refers to a distance function in sample space. Reminding of the optimization objective in Eq. 3, we implement the two constraints using $L_{com}$ and $L_{df}$ respectively. + +Finally, training is performed by minimizing the overall loss: + +$$ +L _ {a l l} = L _ {r e c} + \gamma_ {1} L _ {c o m} + \gamma_ {2} L _ {d f}. \tag {11} +$$ + +Inference phase. In the inference phase, we use $\mathbf{O}$ and the reconstruction loss to calculate the error maps of input sample $x$ : + +$$ +A _ {r e c} = \operatorname {D i s} (x, \hat {x} _ {K}), \tag {12} +$$ + +$$ +A _ {d f} = \sum_ {k} \| O _ {k} \| _ {2}. \tag {13} +$$ + +Image-level anomaly score is computed based on local maxima: + +$$ +\operatorname {S c o r e} _ {I} = \max \left(A _ {r e c} \otimes k ^ {\star}\right) + \alpha \max \left(A _ {d f} \otimes k ^ {\star}\right). \tag {14} +$$ + +where $\otimes$ is convolution operator and $k^{\star}$ is convolution kernel for anomaly maps. $\alpha$ is a tradeoff parameter. That is, the reconstruction loss and deformation jointly determine the anomaly score, which is much more effective than traditional reconstruction-based methods, as illustrated in Fig. 3. + +# 3.6. Variant of PDM + +Modified framework with Pre-PDM. The DMAD framework together with ICM and PDM modules proposed above are suitable in many anomaly detection scenarios including video surveillance. However, for industrial defect detection, texture reconstruction may be harmful (such as spots on "Pill"), and we should reconstruct high-level semantic features instead. Since PDM does not work in high-dimensional feature space and interferes with the training process, we propose variant of PDM, Pre-PDM (PPDM), as a solution. PPDM works in sample space, and is applied to the input sample rather than the reconstructed one. Eq. (3) is modified naturally as follows: + +$$ +\begin{array}{l} L = \| x \circ \psi^ {\prime} (x) - g (\phi (f (x \circ \psi^ {\prime} (x)), z)) \| _ {2} \tag {15} \\ + \gamma_ {1} R _ {1} (\phi) + \gamma_ {2} R _ {2} (\psi^ {\prime}). \\ \end{array} +$$ + +Since we do not reconstruct the original samples, reconstruction loss cannot constrain PPDM to maintain information diversity. In order to prevent $x \circ \psi'(x)$ in Eq. (15) from shortcut learning, we propose to add the inversion of forward deformation, backward deformation $\mathbf{O}^T$ , based on cycle-consistency principle to maintain the diversity of appearance information: + +$$ +\psi^ {\prime} (x) = U p \left(h ^ {\prime} \left(P E (x)\right)\right) = \left\{\mathbf {O}, \mathbf {O} ^ {T} \right\}. \tag {16} +$$ + +Training phase. The cycle-consistency losses $L_{cyc}$ and constraint for forward-backward deformation $L_{df}^{+}$ are: + +$$ +L _ {c y c} = \left\| x - x \circ O _ {1} \dots \circ O _ {K} \circ O _ {K} ^ {T} \dots \circ O _ {1} ^ {T} \right\| _ {2}, \tag {17} +$$ + +$$ +L _ {d f} ^ {+} = \sum_ {k} \| \nabla O _ {k} \| _ {1} + \| \nabla O _ {k} ^ {T} \| _ {1} + \| O _ {k} \| _ {2} + \| O _ {k} ^ {T} \| _ {2}. \tag {18} +$$ + +![](images/a703299c6ba384a505806b5c930756533f9b4011baeba486e495268c12752045.jpg) +(a) + +![](images/9375a064bf96cd6308fc2040ef2d1df6eb2fd94e3a4e897ceb29bbed3e8a8869.jpg) +(c) + +![](images/77d46b807abbb1d1514c1d77f481ee36c77c41b7cbef694b08c28c6a813259ab.jpg) +(d) + +![](images/92473f40e1dcea88bdc757e73784259310b03092f15f81e27290d1d9183974fc.jpg) +(b) + +![](images/781344392755dc0ebd9733a999b3e6c742f1a3c407ace778e0da0aa25a41601f.jpg) +(e) + +![](images/103eee2e2081a875d19cc15e67f17de4b1f70e39801ad7a1b028b79884830ec6.jpg) +(f) +Figure 5. The process of forward and backward deformation: a) The pattern of original image. Red indicates high error regions and black indicates low error regions; b) The normal pattern; c) The coarse estimation $O_{1}$ (dark blue) and $O_{1}^{T}$ (light blue); d) The fine estimation $O_{2}$ (dark blue) and $O_{2}^{T}$ (light blue); e) Using $\hat{x}$ simply causes high anomaly score at the wrong location (solid cross). Ground-truth is shown as hollow cross; f) $\hat{x} \circ O_{2}^{T} \circ O_{1}^{T}$ adjusts the high reconstruction error to original position. + +So we train our anomaly detection model with PPDM by minimizing the following loss: + +$$ +L _ {a l l} ^ {+} = L _ {r e c} + \gamma_ {1} L _ {c o m} + \gamma_ {2} L _ {d f} ^ {+} + \gamma_ {3} L _ {c y c}. \tag {19} +$$ + +The modified DMAD framework (i.e. with PPDM and Reverse Distribution [6]) is shown in in Fig. 4b. + +Inference phase. The result of PPDM is not aligned with the position of original input, which may reduce the performance of anomaly localization. In order to obtain the anomaly map of real location, we use backward deformation to perform inverse sampling (Fig. 5): + +$$ +A _ {r e c} ^ {+} = \operatorname {D i s} \left(x, \hat {x} _ {K}\right) \circ O _ {K} ^ {T} \dots \circ O _ {1} ^ {T}, \tag {20} +$$ + +$$ +\begin{array}{l} A _ {d f} ^ {+} = \sum_ {k} \| O _ {k} \circ O _ {k + 1} \dots \circ O _ {K} \| _ {2} \tag {21} \\ + \sum_ {k} \| O _ {k} ^ {T} \circ O _ {k - 1} ^ {T} \dots \circ O _ {1} ^ {T} \| _ {2}. \\ \end{array} +$$ + +The image-level anomaly score $Score_{I}^{+}$ and pixel-level anomaly score $Score_{P}^{+}$ are calculated respectively as: + +$$ +\operatorname {S c o r e} _ {I} ^ {+} = \max \left(A _ {\text {r e c}} ^ {+} \otimes k ^ {\star}\right) + \alpha \max \left(A _ {d f} ^ {+} \otimes k ^ {\star}\right), \tag {22} +$$ + +$$ +\operatorname {S c o r e} _ {P} ^ {+} = A _ {r e c} ^ {+} + \alpha A _ {d f} ^ {+}. \tag {23} +$$ + +# 4. Experiments and Analysis + +Firstly, we perform toy experiment on MNIST to illustrate our approach. Then the quantitative and qualitative results of two versions our DMAD framework are reported in video anomaly detection and industrial surface defect detection respectively2. Finally, we conduct ablation experiments and analyze the results. + +![](images/6b99b30160a86a98f1ac07a81ded836fd211a7464247f53aa2e38bbb658e5efc.jpg) +Figure 6. Visualization of toy experiment. The last three rows are: reference reconstructed from memory, reference after coarse deformation, and final output after applying fine deformation. + +# 4.1. Datasets + +Surveillance Videos. Ped2 [27], Avenue [23] and ShanghaiTech [25] are fixed-view videos. The anomalies include driving, cycling, running, throwing stuff, etc. Mutual occlusion, anomaly-like behavior, contaminated data and different scenes occur frequently in these datasets. + +Industrial Images. MVtec [2] contains 15 types of industrial images, which are divided into 5 types of textures and 10 types of objects. The defects include crack, scratch, etc. The normal workpiece has different positions, angles and textures. It is used for detection and localization task. + +# 4.2. Toy experiment + +As shown in Fig. 6, we perform a toy experiment on MNIST dataset [16] with setting analogous to out-of-distribution (OOD) detection (i.e. training on "1, 3, 5, 7, 9" and test on all classes). Our model searches separate memory items for each digital category to reconstruct it into class-specific reference and uses the deformation fields from PDM to adjust it hierarchically. When tested with seen and unseen classes, the model adjusts reconstructed references to normal inputs, but fails on the abnormal ones. + +In contrast, memory network without diversity-aware module cannot guarantee the intra-class compactness and the reconstruction diversity, which misdirects the model to obtain dataset-optimal "average memory", leading to fuzzy reconstruction and lower discrimination ability. The model with full-channel skip-connection suffers from shortcut learning and reconstruct anomalies successfully which weakens the ability to identify anomalies. + +# 4.3. Implementation details + +The input images are resized into $256 \times 256$ and normalized to the value in range of $[-1,1]$ . According to frame-pred strategy [19], the history length is set to 4 in video anomaly detection and 0 for images. After feature extraction with a backbone, PDM and PPDM obtain different heads by stacking stride-2 convolution layers. Then + +we use $\text{Tanh}$ as the activation function of output layer and clipping function to ensure the value of deformation is between $[-1, 1]$ . Unless otherwise noted, the architecture of autoencoder complies with the settings of MNAD [29] and RD [6] for PDM and PPDM respectively. The function $\text{Dis}(\cdot)$ in Eq. (10) is a combination of $MSE$ loss and $Grad$ loss for reconstruction in sample space, and $COS$ loss for deep features. We set $(\gamma_1, \gamma_2) = (1, 0.25)$ for PDM, $(1, 1)$ for PPDM $(\gamma_3$ is discussed in Sec. 4.5), and $\beta = 0.25$ as in [35]. During post-processing, we use average kernel for surveillance videos and Gaussian kernel with $\sigma = 4$ for industrial images as in [6]. Frame-difference method is applied to remove static anomalies for Avenue, because our method detects all anomalies which may be labeled as normal ones in [23]. And we use the mask calculated in Eq. (9) to normalize anomaly map in [25] due to the scale changes. Besides, we set $\alpha = 0.2$ for three video tasks and an additional option $\alpha = 0.05$ for defect detection, depending on whether the defect includes geometrical changes. The model is optimized by AdamW [21] and the learning rate is 2e-4 and 5e-3 as in [6, 29] respectively, being decayed by CosineAnnealingLR [22] strategy. We adopt 60, 60, 60, 10, 400 epochs for MNIST, Ped2, Avenue, Shanghai and MVTec respectively with batch size of 8. + +# 4.4. Main results + +Surveillance Videos. We compare our method with SOTA works on video anomaly detection in Tab. 1. Our method outperforms comparative approaches even though we neither use external estimators nor remove abnormal frames in training data. In additional, if we detect global offset for camera jitter in [23], there will be extra $0.1\%$ gain. + +The qualitative results are shown in Fig. 7. We find that: anomalies are over-reconstructed in (b); normals are not reconstructed well in (c); (d) greatly improves normal reconstruction with slightly less inhibition ability for anomalies. + +Industrial Images. Anomaly detection results on MVTec are shown in Tab. 2 and localization results are shown in Tab. 3. With the deformation from PPDM, texture anomalies are detected with high performance and our method outperforms SOTA methods in both detection and localization tasks without memorizing an enormous number of embedding from training data. + +# 4.5. Ablation study + +As shown in Tab. 4, single-output memory module without PDM suppresses diverse normal patterns seriously, while separate PDM without memory provides comparable performance gains as the previous SOTA works because the module "Comp." serves as an information compression module instead. The number of multi-scale deformation fields also have a modest effect on performance. We suggest that "K" should at least make the scale of control grid + +Table 1. Video anomaly detection results on Ped2 [27], Avenue [23] and Shanghai [25]. We calculate $AUC(\%)$ with all frames together. Numbers in bold indicate the best performance and the underlined ones are the second best. $^+$ indicates that we reproduce the result due to higher performance or absence of implementation. + +
MethodsPed2 [27]Avenue [23]Shanghai [25]
Conv2D [9]90.070.2-
Conv3D [40]91.277.1-
ConvLSTM [24]88.177.0-
FramePred [19]95.484.972.8
ConvVQ+90.284.3-
MemAE [8]94.183.371.2
MPN [26]96.989.573.8
MNAD+ [29]97.888.570.5
HF2VAD [20]99.391.176.2
Ours99.792.878.8
+ +![](images/6b61aa6e1d6614ebf12b7b7df27453b04c569312a12e22d2faa8464a3a1b84d0.jpg) +(a) + +![](images/b52cbfc92f067605d8f1c08d5f8b9cd2643494a2e61afea4e86960988cdac7f4.jpg) +(b) + +![](images/b25a96436442e303c791566a7e8b9722cf5af0e09af855f004763626c4c577e9.jpg) +(c) +Figure 7. Qualitative results on Ped2. a) Original image; b) Memory network with skip-connection [29]; c) PDM with VQ-Layer [35]; d) PDM with ICM. Green box indicates negative, red box indicates positive, and yellow box indicates weak positive. + +![](images/cf9dcc661808b1bf3bcca66f6f740605d4fbf83ef63ed90217c07e5507e7c83a.jpg) +(d) + +cover the size of base elements (e.g. pedestrian limbs). Besides, the foreground-background selection module further improves the compactness of memory embedding. Moreover, if any constraint for PDM is missing, the abnormal information will be transmitted and cause shortcut learning. Especially, the cycle-consistency constraint $L_{cyc}$ is also a necessary part for PPDM to avoid degenerated solution $(-1.7\%)$ , because the feature reconstruction error can be minimized by eliminating all necessary information. + +As shown in Tab. 5, the proposed method is robust to hyperparameter $\gamma_{3}$ in Eq. (19). On condition that degenerated solution will not be formed, weakening the constraint makes model restore images from reference with less detail more easily and perceive the position of anomalies more accurately by transforming anomalies to normal patterns which benefits localization task. On the contrary, strengthening the constraint alleviates shortcut learning and improves image-level result by maintaining more abnormal details. + +Table 2. Image-level ${AUC}\left( \% \right)$ of anomaly detection on MVTec [2]. + +
Class\MethodsGN [1]PSVDD [37]DAAD [11]CutPaste [17]PaDiM [5]PatchCore [31]DRAEM [38]RD [6]Ours
AvgTextures77.594.591.097.598.899.099.199.599.9
AvgObjects75.590.888.895.593.899.297.498.099.3
AvgAll76.292.189.596.195.599.198.098.599.5
+ +Table 3. Pixel-level ${AUC}\left( \% \right)$ of anomaly localization on MVtec [2]. + +
Class\MethodsPSVDD [37]CutPaste [17]PaDiM [5]PatchCore [31]DRAEM [38]TMAE [34]RD [6]Ours
AvgTextures93.796.396.997.697.993.897.797.8
AvgObjects96.795.897.898.497.094.097.998.3
AvgAll95.796.097.598.197.393.997.898.2
+ +Table 4. Ablation study of proposed module and loss on Ped2 [27]. From left to right: without PDM; with only one head of PDM $(K = 1)$ ; without memory module; without background template; removing strength constraint; removing smoothness constraint. + +
w/oPDMK>1Memxbg|O|2|∇O|2
AUC%-9.4-0.4-1.8-1.6-1.4-1.4
+ +Table 5. Ablation study of deformation constraint on MVTec [2]. + +
Task\γ300.10.250.512
Det.97.999.499.499.599.699.4
Loc.96.698.098.298.097.797.6
+ +# 4.6. Discussion + +Contaminated data assumption. Assuming that training data only contains completely normal data is unrealistic, because the workload of natural data cleansing is considerable, even has same cost as data annotations. We mix training data with abnormal events in Ped2 to simulate contaminated data and find performance drop of MNAD [29] is $-3.7\%$ while ours is $-1.8\%$ . The reason why DMAD is less affected may be that PDM can encode and transmit residual abnormal representation of mixed anomalies and anomaly-like normal samples, thus strictly maintaining representation compactness of the main encoder and low generalization ability on abnormal samples. + +Two DMAD implementations. As introduced earlier, our DMAD framework is implemented by two versions using PDM and PPDM respectively, corresponding to different detection targets. As shown in Fig. 8, PDM learns measurable quantization error (caused by ICM) from memory embedding to diverse patterns which enhances the potential of ICM to keep intra-class compactness without generating unmeasurable reconstruction loss. Unlike PDM, PPDM is partially in charge of the information compression, i.e. PPDM removes the diverse appearance by using the reverse deformation process from inputs to reference. + +![](images/98ff6ab2411d041b029fb61d759369f6cf89beba1530821c6909541d80658b10.jpg) +Figure 8. Illustration of two DMAD implementations with PDM and PPDM respectively. + +# 5. Conclusion + +In this paper, we present a reconstruction-based diversity-measurable anomaly detection framework, which simultaneously enhances anomaly discrimination and reconstruction diversity. Pyramid deformation module is proposed to be used together with information compression module for this purpose. PDM models multi-scale transformation fields from reference to original input explicitly without relying on external estimators. Therefore, diverse normal patterns can be reconstructed and anomaly severity can be measured accurately. Empirical studies on both videos and images benchmarks show the effectiveness and applicability of our work. In future research, we will further explore diversity-aware models for anomaly detection. + +Limitations. Our method focuses on anomaly with measurable geometrical diversity, the most common type in anomaly detection. However, as for anomaly with other kind of diversities, e.g. colors, the proposed diversity measure may not be positively correlated to anomaly severity. + +Acknowledgement. This work is partially supported by National Key R&D Program of China (No. 2018AAA0102402), and National Natural Science Foundation of China (NSFC): 61976203 and 62276246. + +# References + +[1] Samet Akcay, Amir Atapour Abarghouei, and Toby P. Breckon. 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However, diverse normal patterns are consequently not well reconstructed as well. Although some efforts have been made to alleviate this problem by modeling sample diversity, they suffer from shortcut learning due to undesired transmission of abnormal information. In this paper, to better handle the tradeoff problem, we propose Diversity-Measurable Anomaly Detection (DMAD) framework to enhance reconstruction diversity while avoid the undesired generalization on anomalies. To this end, we design Pyramid Deformation Module (PDM), which models diverse normals and measures the severity of anomaly by estimating multi-scale deformation fields from reconstructed reference to original input. Integrated with an information compression module, PDM essentially decouples deformation from prototypical embedding and makes the final anomaly score more reliable. Experimental results on both surveillance videos and industrial images demonstrate the effectiveness of our method. In addition, DMAD works equally well in front of contaminated data and anomaly-like normal samples." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 538, + 128, + 551 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 538, + 128, + 551 + ], + "spans": [ + { + "bbox": [ + 47, + 538, + 128, + 551 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 557, + 287, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 287, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 287, + 665 + ], + "type": "text", + "content": "Visual anomaly detection is a fundamental and important problem in computer vision community, with wide applications in video surveillance and industrial inspection. It aims to detect outliers from seen classes and novel patterns from unseen classes. This task is very challenging because abnormal data is diversely distributed and expensive to collect. So we have to construct models based on only normal samples under unsupervised setting, targeting at high discrimination between normal and abnormal samples." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": "During the past decade, reconstruction-based methods have achieved great progress in anomaly detection. These methods use Autoencoders (AEs) [8,9,20,24,26,29,40] or Generative Adversarial Networks (GANs) [1, 19, 32] to re" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 348, + 225, + 504, + 316 + ], + "blocks": [ + { + "bbox": [ + 348, + 225, + 504, + 316 + ], + "lines": [ + { + "bbox": [ + 348, + 225, + 504, + 316 + ], + "spans": [ + { + "bbox": [ + 348, + 225, + 504, + 316 + ], + "type": "image", + "image_path": "7fe06ff0a8c5dfa5980addc51c64fe1415e2d3e8e9db3cb007947e25488f08a9.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 325, + 547, + 381 + ], + "lines": [ + { + "bbox": [ + 305, + 325, + 547, + 381 + ], + "spans": [ + { + "bbox": [ + 305, + 325, + 547, + 381 + ], + "type": "text", + "content": "Figure 1. Illustration of difficulty in anomaly detection in MNIST dataset. The prototype is indicated by orange triangle and the anomaly by red point. In this case, the anomaly can hardly be detected based on reconstruction error or distance in high-dimensional feature space. Our solution is illustrated in Fig. 2." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 402, + 545, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 402, + 545, + 472 + ], + "spans": [ + { + "bbox": [ + 304, + 402, + 545, + 472 + ], + "type": "text", + "content": "construct the normal counterparts from any input images or video frames. AE-based methods firstly compress the inputs to discard the information beyond normal prototypes, and then decode the embedding to reconstruct the inputs. According to the estimated reconstruction error, the anomalies can be detected." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 474, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 546, + 713 + ], + "type": "text", + "content": "However, the performance of reconstruction-based methods for anomaly detection has long been limited by a tough problem, i.e. the tradeoff between reconstructing diverse normals and detecting unknown anomalies. In order to discriminate anomalies more easily, previous works [8] imposes more constraints to suppress abnormal information during autoencoding, which leads to high reconstruction error for diverse normal instances. For example, in Figs. 1 and " + }, + { + "bbox": [ + 304, + 474, + 546, + 713 + ], + "type": "inline_equation", + "content": "2\\mathbf{g}" + }, + { + "bbox": [ + 304, + 474, + 546, + 713 + ], + "type": "text", + "content": ", the severely deformed normal (a.k.a. anomaly-like) sample \"7\" has even higher error than the abnormal sample \"4\". To better reconstruct diverse normals, each query vector corresponds to multiple prototypes in the memory, which may be combined into abnormal embedding even if abnormal projection is far away from the prototype. As a consequence, anomalies that distribute in low likelihood area between prototypical embedding are difficult to identify from diverse normals. MNAD [29] introduces skipconnection for diverse reconstruction and additional constraints to get round the incorrect combination problem. But the latter forces model transmit more unrestrained in" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 747, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 747, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 747, + 318, + 757 + ], + "type": "text", + "content": "12147" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 69, + 287, + 177 + ], + "blocks": [ + { + "bbox": [ + 47, + 69, + 287, + 177 + ], + "lines": [ + { + "bbox": [ + 47, + 69, + 287, + 177 + ], + "spans": [ + { + "bbox": [ + 47, + 69, + 287, + 177 + ], + "type": "image", + "image_path": "3fd76b582e9bafb4bf2dff2c0675c3c5f31ec99cfce2667ad25fd7b40c78e662.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 186, + 287, + 262 + ], + "lines": [ + { + "bbox": [ + 46, + 186, + 287, + 262 + ], + "spans": [ + { + "bbox": [ + 46, + 186, + 287, + 262 + ], + "type": "text", + "content": "Figure 2. Illustration of our diversity-measurable method in addressing the detection difficulty. Numbers in white are anomaly scores. a) Original input; b) Reconstructed reference; c) Coarse deformation; d) Fine deformation; e) Measurement of diversity1; f) Deformation-augmented error map assigns lower anomaly score to the anomaly-like sample than the true anomaly; g) Pixel-wise reconstruction error yields incorrect anomaly scores." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 282, + 287, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 282, + 287, + 316 + ], + "spans": [ + { + "bbox": [ + 46, + 282, + 287, + 316 + ], + "type": "text", + "content": "formation with abnormal part by skip-connection, resulting in shortcut learning and undesired reconstruction of anomalies." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 318, + 287, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 318, + 287, + 472 + ], + "spans": [ + { + "bbox": [ + 46, + 318, + 287, + 472 + ], + "type": "text", + "content": "A key to address the above tradeoff problem is to find a proper measurement of diversity that normal and abnormal samples have, which is positively correlated with the severity of anomaly. With such a measure, we do not need to fight against imperfect reconstruction of normals or undesired reconstruction of anomalies, because anomalies can be detected more accurately by the diversity measure together with the reconstruction error. Note that pixel-wise reconstruction error is not an ideal measurement of diversity, because the high-error region often confuses anomalies with diverse normals, e.g. normals with structural deformation and anomalies with colors close to the background may yield unreliable reconstruction error." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 474, + 287, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 287, + 616 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 287, + 616 + ], + "type": "text", + "content": "In this paper, we propose a Diversity-Measurable Anomaly Detection (DMAD) framework to enhance the measurability of reconstruction diversity so as to measure abnormality more accurately. Our basic idea is to decouple the reconstruction into compact representation of prototypical normals and measurable deformations of more diverse normals and anomalies. The under-estimated reconstruction error can be compensated by the diversity, which can be properly measured. To this end, the DMAD framework includes a Pyramid Deformation Module (PDM) to model and measure the diversity and an Information Compression Module (ICM) to learn the prototypical normal patterns." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 617, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 677 + ], + "type": "text", + "content": "Inspired by [4, 15], we assume anomalies (e.g. in video surveillance) can be represented as significant deformation of appearances, including positional changes and fine motions. In contrast, diverse normal samples can be represented as weaker deformations thus easily distinguished" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 72, + 545, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 545, + 239 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 545, + 239 + ], + "type": "text", + "content": "from the abnormal ones. Therefore, we design PDM to model the diversity of normals as well as the severity of anomalies. More specifically, PDM learns hierarchical two-dimensional deformation fields (Fig. 2c,d) that describe the pixel-level transformation direction and distance from reference (Fig. 2b, which is reconstructed from prototypes in memory) to original input. In ICM, we learns compressed representation as sparse prototypes. As a result, a single memory item is enough to represent each normal cluster. This is more compact than other memory-based works which require multiple memory items. Integrating PDM with ICM, DMAD essentially decouples the deformation information (Fig. 2e) from class prototypes and makes the final anomaly score more discriminative (Fig. 2f)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 240, + 545, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 240, + 545, + 335 + ], + "spans": [ + { + "bbox": [ + 305, + 240, + 545, + 335 + ], + "type": "text", + "content": "We evaluate our anomaly detection framework in scenarios of video surveillance and industrial defect detection. To apply DMAD in the latter scenario, we propose a variant of PDM, PPDM, to deal with the false positive issue in texture reconstruction. Extensive experimental results verify the efficacy of our approach. Moreover, our method works well even in front of contaminated data and anomaly-like normals. The main contributions of our work are as follows:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 307, + 339, + 545, + 510 + ], + "type": "list", + "angle": 0, + "index": 11, + "blocks": [ + { + "bbox": [ + 307, + 339, + 545, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 339, + 545, + 387 + ], + "spans": [ + { + "bbox": [ + 307, + 339, + 545, + 387 + ], + "type": "text", + "content": "- We introduce diversity-measurable anomaly detection framework which allows reconstruction-based models to achieve better tradeoff between reconstructing diverse normals and detecting unknown anomalies." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 307, + 389, + 545, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 389, + 545, + 449 + ], + "spans": [ + { + "bbox": [ + 307, + 389, + 545, + 449 + ], + "type": "text", + "content": "- We propose pyramid deformation module to implement diversity measurement, in which the deformation information is explicitly separated from compact class prototypes and the resulting diversity measure is positively correlated to abnormality." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 307, + 451, + 545, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 451, + 545, + 510 + ], + "spans": [ + { + "bbox": [ + 307, + 451, + 545, + 510 + ], + "type": "text", + "content": "- Our approach outperforms previous works on video anomaly detection and industrial defect detection, and works well in front of contaminated data and anomaly-like normals, demonstrating its broad suitability and robustness." + } + ] + } + ], + "index": 10 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 525, + 392, + 537 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 525, + 392, + 537 + ], + "spans": [ + { + "bbox": [ + 306, + 525, + 392, + 537 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 545, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 545, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 545, + 545, + 713 + ], + "type": "text", + "content": "Anomaly detection. Reconstruction-based methods model the distribution of normal data and assign anomalies with high reconstruction error, because models trained with only normal data cannot reconstruct anomalies. Some works use autoencoder to detect anomalies, such as convolutional autoencoder [9] and the variants [24, 40]. Other approaches introduce additional constraints or memory to make the model more discriminative. For example, sparse coding [25, 39] reduces representation redundancy with regularization; memory-augmented autoencoder (MemAE) [8] memorizes the normal patterns appearing in training dataset with external memory bank; variational autoencoder [10, 35] assumes a prior distribution of normal data to constrain the nonlinear representation capacity; " + }, + { + "bbox": [ + 305, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{HF}^2\\mathrm{VAD}" + }, + { + "bbox": [ + 305, + 545, + 545, + 713 + ], + "type": "text", + "content": " [20]" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 46, + 683, + 287, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 683, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 683, + 287, + 712 + ], + "type": "text", + "content": "1In this case, we only count fine deformation because deformations in position and angle are considered as normal. In real-world experiments, we consider both coarse and fine deformations." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 294, + 747, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 747, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 747, + 317, + 757 + ], + "type": "text", + "content": "12148" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 286, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 286, + 156 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 286, + 156 + ], + "type": "text", + "content": "uses CVAE [33] to capture the correlation among motions. Frame prediction [19] assumes that abnormal samples in videos cannot be represented by past frames that do not contain unseen information and forces the model to encode changes among different frames. In addition, autoencoders can also be combined with external object detectors [7, 14, 20] to capture background-invariant appearance." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 157, + 286, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 157, + 286, + 240 + ], + "spans": [ + { + "bbox": [ + 46, + 157, + 286, + 240 + ], + "type": "text", + "content": "Although these methods generally work well, they often have difficulty in discriminating abnormal samples from anomaly-like normals due to the tradeoff between reconstruction and discrimination. In our framework, pyramid deformation module and information compression module are leveraged to address the trade-off problem, significantly improving the performance in anomaly detection." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 243, + 286, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 243, + 286, + 422 + ], + "spans": [ + { + "bbox": [ + 46, + 243, + 286, + 422 + ], + "type": "text", + "content": "Memory network. Generative models map continuously in feature space and they may assign higher probabilities to anomalies than normal ones [28]. Recent research [8, 11, 20, 29] has explored the application of discrete external memory to generate seen normal patterns even if the input is abnormal. MemAE [8] proposes a memory-augmented autoencoder, which uses information from encoder as a query and obtains a normal pattern retrieved from memory module. MNAD [29] introduces skip-connection to alleviate the problem that diverse normal patterns may yield high reconstruction errors. " + }, + { + "bbox": [ + 46, + 243, + 286, + 422 + ], + "type": "inline_equation", + "content": "\\mathrm{HF^2VAD}" + }, + { + "bbox": [ + 46, + 243, + 286, + 422 + ], + "type": "text", + "content": " [20] extends the memory module to multi-level memory, and uses additional estimators [3, 13] to explicitly model the motion information and filter the noise from background. DAAD [11] uses block-wise memory to increase the specificity of memory." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 424, + 286, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 424, + 286, + 518 + ], + "spans": [ + { + "bbox": [ + 46, + 424, + 286, + 518 + ], + "type": "text", + "content": "In most existing works, the memory module outputs a linear combination of memory items which may lead to undesired reconstruction of normal-like anomalies. And they do not explicitly consider that instances corresponding to the same memory grid may be located at different positions of the receptive field. In our approach, we alleviate these problems via compressing embedding into a single memory item to ensure that the output is absolutely normal." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 521, + 286, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 286, + 687 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 286, + 687 + ], + "type": "text", + "content": "Transformation modeling. The transformation between video frames is a key clue for anomaly detection. Some methods [7, 14, 19, 20] use external object detectors or optical-flow estimators to model the motion information implicitly or explicitly. Among the transformation estimators, optical-flow estimation [13] is widely studied, which aims to estimate the pixel-wise motions between consecutive frames. In addition, correspondence modeling between pair-wise images is also applied to 2D geometric matching [30] and 3D image registration [36] to obtain image deformation fields. STN [15] learns to transform the original images themselves to benefit identification algorithm. RegAD [12] uses feature-level affine registration to relocate features without changing the embeddings." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 689, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 286, + 712 + ], + "type": "text", + "content": "However, pairwise transformation modeling only focus on pattern changes thus cannot detect static anomalies. And" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 306, + 68, + 545, + 177 + ], + "blocks": [ + { + "bbox": [ + 306, + 68, + 545, + 177 + ], + "lines": [ + { + "bbox": [ + 306, + 68, + 545, + 177 + ], + "spans": [ + { + "bbox": [ + 306, + 68, + 545, + 177 + ], + "type": "image", + "image_path": "0ab9514c0ff3786bac933b6a545f46d20aef4b977f82968b3a9fd7c454f4f4b8.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 186, + 545, + 253 + ], + "lines": [ + { + "bbox": [ + 305, + 186, + 545, + 253 + ], + "spans": [ + { + "bbox": [ + 305, + 186, + 545, + 253 + ], + "type": "text", + "content": "Figure 3. Three conditions for DMAD framework. The colors of lines represent the measurements of diversity (severity of anomaly); The gray area represents uncertainty in the measure; Double dashed arrows indicate possible ranges of the boundary. The last two lines denote DMAD and traditional reconstruction-based method respectively." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 271, + 545, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 271, + 545, + 319 + ], + "spans": [ + { + "bbox": [ + 305, + 271, + 545, + 319 + ], + "type": "text", + "content": "pretrained transformation estimators introduce generalization error in different scenarios. In contrast, we address these problems by separating and measuring the transformation from prototypical memory in end-to-end training." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 329, + 532, + 342 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 329, + 532, + 342 + ], + "spans": [ + { + "bbox": [ + 306, + 329, + 532, + 342 + ], + "type": "text", + "content": "3. Diversity-Measurable Anomaly Detection" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 349, + 545, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 349, + 545, + 443 + ], + "spans": [ + { + "bbox": [ + 305, + 349, + 545, + 443 + ], + "type": "text", + "content": "In this section, we first analyze the objective of reconstruction-based anomaly detection and propose a diversity-measurable framework to address the tradeoff problem in existing works. Then, we introduce information compression module and pyramid deformation module (PDM) as an implementation of the framework. Finally, we explain the training and inference process and how to apply the framework to defect detection with a variant of PDM." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 451, + 402, + 462 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 451, + 402, + 462 + ], + "spans": [ + { + "bbox": [ + 306, + 451, + 402, + 462 + ], + "type": "text", + "content": "3.1. The framework" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 469, + 545, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 469, + 545, + 506 + ], + "spans": [ + { + "bbox": [ + 305, + 469, + 545, + 506 + ], + "type": "text", + "content": "Given input " + }, + { + "bbox": [ + 305, + 469, + 545, + 506 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 305, + 469, + 545, + 506 + ], + "type": "text", + "content": ", autoencoder-based methods aim to model normal data distribution by minimizing the following reconstruction loss " + }, + { + "bbox": [ + 305, + 469, + 545, + 506 + ], + "type": "inline_equation", + "content": "(\\| \\cdot \\|_2" + }, + { + "bbox": [ + 305, + 469, + 545, + 506 + ], + "type": "text", + "content": " is just one type of reconstruction loss):" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 345, + 512, + 545, + 526 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 512, + 545, + 526 + ], + "spans": [ + { + "bbox": [ + 345, + 512, + 545, + 526 + ], + "type": "interline_equation", + "content": "L = \\| x - g (\\phi (f (x), z)) \\| _ {2} + \\gamma_ {1} R _ {1} (\\phi), \\tag {1}", + "image_path": "b19a05e590ecb49ec50973c56ce7b67db76b606e1e7609e91c12776543c7bf9e.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 531, + 545, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 531, + 545, + 592 + ], + "spans": [ + { + "bbox": [ + 305, + 531, + 545, + 592 + ], + "type": "text", + "content": "with respect to encoder " + }, + { + "bbox": [ + 305, + 531, + 545, + 592 + ], + "type": "inline_equation", + "content": "f(\\cdot)" + }, + { + "bbox": [ + 305, + 531, + 545, + 592 + ], + "type": "text", + "content": ", decoder " + }, + { + "bbox": [ + 305, + 531, + 545, + 592 + ], + "type": "inline_equation", + "content": "g(\\cdot)" + }, + { + "bbox": [ + 305, + 531, + 545, + 592 + ], + "type": "text", + "content": ", latent variable " + }, + { + "bbox": [ + 305, + 531, + 545, + 592 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 305, + 531, + 545, + 592 + ], + "type": "text", + "content": " (referring to discrete memory items in these cases) and a constrained feature mapping function " + }, + { + "bbox": [ + 305, + 531, + 545, + 592 + ], + "type": "inline_equation", + "content": "\\phi(\\cdot)" + }, + { + "bbox": [ + 305, + 531, + 545, + 592 + ], + "type": "text", + "content": " corresponding to its constraint " + }, + { + "bbox": [ + 305, + 531, + 545, + 592 + ], + "type": "inline_equation", + "content": "R_1(\\phi)" + }, + { + "bbox": [ + 305, + 531, + 545, + 592 + ], + "type": "text", + "content": ". Skip-connection and concatenation " + }, + { + "bbox": [ + 305, + 531, + 545, + 592 + ], + "type": "inline_equation", + "content": "[\\cdot, \\cdot]" + }, + { + "bbox": [ + 305, + 531, + 545, + 592 + ], + "type": "text", + "content": " are introduced to generate diverse normal patterns [29]:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 330, + 597, + 545, + 612 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 597, + 545, + 612 + ], + "spans": [ + { + "bbox": [ + 330, + 597, + 545, + 612 + ], + "type": "interline_equation", + "content": "L = \\| x - g ([ \\phi (f (x), z), f (x) ]) \\| _ {2} + \\gamma_ {1} R _ {1} (\\phi). \\tag {2}", + "image_path": "816a13d467da8b72d113603f922653c6256dda173df1db2c255dfaf742cd87be.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 617, + 545, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 617, + 545, + 676 + ], + "spans": [ + { + "bbox": [ + 305, + 617, + 545, + 676 + ], + "type": "text", + "content": "However, due to diverse data distribution, previous methods have to face the conflict between representing diverse normals and detecting anomalies. The intrinsic reason lies in that the encoding of diversity " + }, + { + "bbox": [ + 305, + 617, + 545, + 676 + ], + "type": "inline_equation", + "content": "[\\cdot ,f(x)]" + }, + { + "bbox": [ + 305, + 617, + 545, + 676 + ], + "type": "text", + "content": " contains redundant information that cannot be measured accurately." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": "In this work, we propose a principled framework, Diversity-Measurable Anomaly Detection (DMAD), to alleviate the conflict. The basic idea is to restrict the anomaly" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 747, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 747, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 747, + 317, + 757 + ], + "type": "text", + "content": "12149" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 68, + 267, + 224 + ], + "blocks": [ + { + "bbox": [ + 50, + 68, + 267, + 224 + ], + "lines": [ + { + "bbox": [ + 50, + 68, + 267, + 224 + ], + "spans": [ + { + "bbox": [ + 50, + 68, + 267, + 224 + ], + "type": "image", + "image_path": "8f7b4f6390eecdfad989b5ccda968651119a9a84d06ee3ffe2c9a11e9f607409.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 159, + 226, + 172, + 237 + ], + "lines": [ + { + "bbox": [ + 159, + 226, + 172, + 237 + ], + "spans": [ + { + "bbox": [ + 159, + 226, + 172, + 237 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 269, + 69, + 541, + 225 + ], + "blocks": [ + { + "bbox": [ + 269, + 69, + 541, + 225 + ], + "lines": [ + { + "bbox": [ + 269, + 69, + 541, + 225 + ], + "spans": [ + { + "bbox": [ + 269, + 69, + 541, + 225 + ], + "type": "image", + "image_path": "55440356652e7e8fd158ef7f0561bd0b784bf88f0ed21f997d0a3e8046543e6c.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 410, + 226, + 424, + 237 + ], + "lines": [ + { + "bbox": [ + 410, + 226, + 424, + 237 + ], + "spans": [ + { + "bbox": [ + 410, + 226, + 424, + 237 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 241, + 547, + 277 + ], + "lines": [ + { + "bbox": [ + 46, + 241, + 547, + 277 + ], + "spans": [ + { + "bbox": [ + 46, + 241, + 547, + 277 + ], + "type": "text", + "content": "Figure 4. Two versions of diversity-measurable anomaly detection framework. Multi-scale pyramid deformation fields are estimated as " + }, + { + "bbox": [ + 46, + 241, + 547, + 277 + ], + "type": "inline_equation", + "content": "\\mathbf{O}" + }, + { + "bbox": [ + 46, + 241, + 547, + 277 + ], + "type": "text", + "content": " and the reverse processes are " + }, + { + "bbox": [ + 46, + 241, + 547, + 277 + ], + "type": "inline_equation", + "content": "\\mathbf{O}^T" + }, + { + "bbox": [ + 46, + 241, + 547, + 277 + ], + "type": "text", + "content": ". a) PDM version computes forward deformation " + }, + { + "bbox": [ + 46, + 241, + 547, + 277 + ], + "type": "inline_equation", + "content": "\\mathbf{O}" + }, + { + "bbox": [ + 46, + 241, + 547, + 277 + ], + "type": "text", + "content": " after reconstruction. b) PPDM version employs cycle-consistent forward-backward deformations and the forward deformation is applied on the input." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 295, + 287, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 295, + 287, + 344 + ], + "spans": [ + { + "bbox": [ + 46, + 295, + 287, + 344 + ], + "type": "text", + "content": "information transmitted to " + }, + { + "bbox": [ + 46, + 295, + 287, + 344 + ], + "type": "inline_equation", + "content": "g(\\cdot)" + }, + { + "bbox": [ + 46, + 295, + 287, + 344 + ], + "type": "text", + "content": " while measuring and modeling the diversity of the remaining part. To this end, we design information compression module " + }, + { + "bbox": [ + 46, + 295, + 287, + 344 + ], + "type": "inline_equation", + "content": "\\phi(\\cdot)" + }, + { + "bbox": [ + 46, + 295, + 287, + 344 + ], + "type": "text", + "content": " and diversity-aware module " + }, + { + "bbox": [ + 46, + 295, + 287, + 344 + ], + "type": "inline_equation", + "content": "\\psi(\\cdot)" + }, + { + "bbox": [ + 46, + 295, + 287, + 344 + ], + "type": "text", + "content": " under DMAD framework:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 353, + 287, + 378 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 353, + 287, + 378 + ], + "spans": [ + { + "bbox": [ + 47, + 353, + 287, + 378 + ], + "type": "interline_equation", + "content": "L = \\| x - g (\\phi (f (x), z)) \\circ \\psi (x) \\| _ {2} + \\gamma_ {1} R _ {1} (\\phi) + \\gamma_ {2} R _ {2} (\\psi), \\tag {3}", + "image_path": "5748103c4af6e8fbf2fba5f04a298701c81a70e9a857d3220c98515930f71c54.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 378, + 287, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 378, + 287, + 484 + ], + "spans": [ + { + "bbox": [ + 46, + 378, + 287, + 484 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 378, + 287, + 484 + ], + "type": "inline_equation", + "content": "\\circ" + }, + { + "bbox": [ + 46, + 378, + 287, + 484 + ], + "type": "text", + "content": " refers to aggregation operator. With appropriate design of " + }, + { + "bbox": [ + 46, + 378, + 287, + 484 + ], + "type": "inline_equation", + "content": "\\phi(\\cdot), \\psi(\\cdot)" + }, + { + "bbox": [ + 46, + 378, + 287, + 484 + ], + "type": "text", + "content": " and the constraints, optimization of the reconstruction loss can improve the compactness of feature embedding. So that diverse representations are mapped via " + }, + { + "bbox": [ + 46, + 378, + 287, + 484 + ], + "type": "inline_equation", + "content": "\\phi(\\cdot)" + }, + { + "bbox": [ + 46, + 378, + 287, + 484 + ], + "type": "text", + "content": " to compact prototypes in the memory. The diversity of input " + }, + { + "bbox": [ + 46, + 378, + 287, + 484 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 378, + 287, + 484 + ], + "type": "text", + "content": " relative to its reconstruction is represented by " + }, + { + "bbox": [ + 46, + 378, + 287, + 484 + ], + "type": "inline_equation", + "content": "\\psi(\\cdot)" + }, + { + "bbox": [ + 46, + 378, + 287, + 484 + ], + "type": "text", + "content": ". The under-estimated reconstruction error can be compensated by the diversity measured in " + }, + { + "bbox": [ + 46, + 378, + 287, + 484 + ], + "type": "inline_equation", + "content": "\\psi(\\cdot)" + }, + { + "bbox": [ + 46, + 378, + 287, + 484 + ], + "type": "text", + "content": ", a key factor contributing to accurate anomaly scores." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 485, + 288, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 485, + 288, + 593 + ], + "spans": [ + { + "bbox": [ + 46, + 485, + 288, + 593 + ], + "type": "text", + "content": "This framework can achieve our target on the premise that the following conditions (Fig. 3) are met: 1. " + }, + { + "bbox": [ + 46, + 485, + 288, + 593 + ], + "type": "inline_equation", + "content": "\\psi(\\cdot)" + }, + { + "bbox": [ + 46, + 485, + 288, + 593 + ], + "type": "text", + "content": " can learn all diverse information from prototypical patterns to any normal inputs to ensure normal samples do not yield high anomaly score; 2. Deformation generated by " + }, + { + "bbox": [ + 46, + 485, + 288, + 593 + ], + "type": "inline_equation", + "content": "\\psi(\\cdot)" + }, + { + "bbox": [ + 46, + 485, + 288, + 593 + ], + "type": "text", + "content": " is positively correlated to diversity measure; 3. Prototypical information about " + }, + { + "bbox": [ + 46, + 485, + 288, + 593 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 485, + 288, + 593 + ], + "type": "text", + "content": " represented by " + }, + { + "bbox": [ + 46, + 485, + 288, + 593 + ], + "type": "inline_equation", + "content": "\\psi(\\cdot)" + }, + { + "bbox": [ + 46, + 485, + 288, + 593 + ], + "type": "text", + "content": " needs to be minimized. In the following subsections, we explain how to design modules to fulfill these conditions." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 601, + 226, + 613 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 601, + 226, + 613 + ], + "spans": [ + { + "bbox": [ + 47, + 601, + 226, + 613 + ], + "type": "text", + "content": "3.2. Information compression module" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 619, + 288, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 619, + 288, + 693 + ], + "spans": [ + { + "bbox": [ + 47, + 619, + 288, + 693 + ], + "type": "text", + "content": "According to [35], we adapt VQ-Layer as an information compression module to learn " + }, + { + "bbox": [ + 47, + 619, + 288, + 693 + ], + "type": "inline_equation", + "content": "\\phi(\\cdot)" + }, + { + "bbox": [ + 47, + 619, + 288, + 693 + ], + "type": "text", + "content": " given embedding " + }, + { + "bbox": [ + 47, + 619, + 288, + 693 + ], + "type": "inline_equation", + "content": "f(x) \\in R^{D \\times H' \\times W'}" + }, + { + "bbox": [ + 47, + 619, + 288, + 693 + ], + "type": "text", + "content": " as a query " + }, + { + "bbox": [ + 47, + 619, + 288, + 693 + ], + "type": "inline_equation", + "content": "z^e = f(x)" + }, + { + "bbox": [ + 47, + 619, + 288, + 693 + ], + "type": "text", + "content": " and memory " + }, + { + "bbox": [ + 47, + 619, + 288, + 693 + ], + "type": "inline_equation", + "content": "z \\in R^{D \\times N}" + }, + { + "bbox": [ + 47, + 619, + 288, + 693 + ], + "type": "text", + "content": ". Then, we quantize " + }, + { + "bbox": [ + 47, + 619, + 288, + 693 + ], + "type": "inline_equation", + "content": "z^e" + }, + { + "bbox": [ + 47, + 619, + 288, + 693 + ], + "type": "text", + "content": " into a single-memory feature cube " + }, + { + "bbox": [ + 47, + 619, + 288, + 693 + ], + "type": "inline_equation", + "content": "z^q \\in R^{D \\times H' \\times W'}" + }, + { + "bbox": [ + 47, + 619, + 288, + 693 + ], + "type": "text", + "content": " by seeking for memory item with minimum " + }, + { + "bbox": [ + 47, + 619, + 288, + 693 + ], + "type": "inline_equation", + "content": "L2" + }, + { + "bbox": [ + 47, + 619, + 288, + 693 + ], + "type": "text", + "content": " distance (\"Search\" in Fig. 4):" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 99, + 700, + 287, + 716 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 99, + 700, + 287, + 716 + ], + "spans": [ + { + "bbox": [ + 99, + 700, + 287, + 716 + ], + "type": "interline_equation", + "content": "z _ {h, w} ^ {q} = \\operatorname {a r g m i n} _ {z _ {n}} \\left\\| z _ {h, w} ^ {e} - z _ {n} \\right\\| _ {2}, \\tag {4}", + "image_path": "94d49df29b0ebb4e68098300268dcd6ee17eb19e3ba2ca064b3424a551938c37.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 295, + 547, + 356 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 295, + 547, + 356 + ], + "spans": [ + { + "bbox": [ + 305, + 295, + 547, + 356 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 295, + 547, + 356 + ], + "type": "inline_equation", + "content": "z_{n}" + }, + { + "bbox": [ + 305, + 295, + 547, + 356 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 305, + 295, + 547, + 356 + ], + "type": "inline_equation", + "content": "n^{th}" + }, + { + "bbox": [ + 305, + 295, + 547, + 356 + ], + "type": "text", + "content": " memory item, " + }, + { + "bbox": [ + 305, + 295, + 547, + 356 + ], + "type": "inline_equation", + "content": "h\\in \\{1,\\dots ,H^{\\prime}\\} ,w\\in" + }, + { + "bbox": [ + 305, + 295, + 547, + 356 + ], + "type": "inline_equation", + "content": "\\{1,\\dots ,W^{\\prime}\\}" + }, + { + "bbox": [ + 305, + 295, + 547, + 356 + ], + "type": "text", + "content": " indicates the same location in both " + }, + { + "bbox": [ + 305, + 295, + 547, + 356 + ], + "type": "inline_equation", + "content": "z^q" + }, + { + "bbox": [ + 305, + 295, + 547, + 356 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 295, + 547, + 356 + ], + "type": "inline_equation", + "content": "z^{e}" + }, + { + "bbox": [ + 305, + 295, + 547, + 356 + ], + "type": "text", + "content": ". The compression loss " + }, + { + "bbox": [ + 305, + 295, + 547, + 356 + ], + "type": "inline_equation", + "content": "L_{com}" + }, + { + "bbox": [ + 305, + 295, + 547, + 356 + ], + "type": "text", + "content": " with stop-gradient operator " + }, + { + "bbox": [ + 305, + 295, + 547, + 356 + ], + "type": "inline_equation", + "content": "SG(\\cdot)" + }, + { + "bbox": [ + 305, + 295, + 547, + 356 + ], + "type": "text", + "content": " that updates its parameters separately [35] is combined by a hyperparameter " + }, + { + "bbox": [ + 305, + 295, + 547, + 356 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 305, + 295, + 547, + 356 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 323, + 365, + 545, + 380 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 365, + 545, + 380 + ], + "spans": [ + { + "bbox": [ + 323, + 365, + 545, + 380 + ], + "type": "interline_equation", + "content": "L _ {c o m} = \\left\\| S G \\left(z ^ {e}\\right) - z ^ {q} \\right\\| _ {2} + \\beta \\left\\| z ^ {e} - S G \\left(z ^ {q}\\right) \\right\\| _ {2}. \\tag {5}", + "image_path": "cc13ba32614c4c575d4819aedd68b218c75a58406d21f9fa48eccd4d26917478.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 388, + 547, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 388, + 547, + 449 + ], + "spans": [ + { + "bbox": [ + 305, + 388, + 547, + 449 + ], + "type": "text", + "content": "Skip-connection with low information capacity (Fig. 4 \"Comp.\") is also allowed to further improve the reconstruction quality without bringing excessive generalization (i.e. Conv-Layer with stop-gradient operator for intermediate features whose reduction factor is 16 or larger)." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 456, + 468, + 470 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 456, + 468, + 470 + ], + "spans": [ + { + "bbox": [ + 306, + 456, + 468, + 470 + ], + "type": "text", + "content": "3.3. Pyramid deformation module" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 475, + 545, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 475, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 475, + 545, + 605 + ], + "type": "text", + "content": "We categorize the unknown anomalies into the following three types: unseen class (e.g. novel objects), global anomaly (e.g. unexpected movement) and local anomaly (e.g. strange behavior and workpiece damage) of seen class. The unseen class is easy to be detected based on reconstruction result, but the latter two types are usually confused with diverse normals. To discriminate these anomalies from normal ones, we represent the diversity using measurable deformation between reconstructed reference and original input, so that slight deformations occur in normals while drastic deformations occur in anomalies." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 607, + 547, + 692 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 607, + 547, + 692 + ], + "spans": [ + { + "bbox": [ + 304, + 607, + 547, + 692 + ], + "type": "text", + "content": "Inspired by STN and DCN [4, 15], we introduce Pyramid Deformation Module (PDM) which explicitly learn deformation fields with hierarchical scales to model the motion, behavior and defect of different anomaly types, as shown in Fig. 4a. Specifically, after feature extraction, " + }, + { + "bbox": [ + 304, + 607, + 547, + 692 + ], + "type": "inline_equation", + "content": "\\psi(\\cdot)" + }, + { + "bbox": [ + 304, + 607, + 547, + 692 + ], + "type": "text", + "content": " uses " + }, + { + "bbox": [ + 304, + 607, + 547, + 692 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 607, + 547, + 692 + ], + "type": "text", + "content": "-heads to compute offsets " + }, + { + "bbox": [ + 304, + 607, + 547, + 692 + ], + "type": "inline_equation", + "content": "\\mathbf{O} = \\{O_1, \\dots, O_K\\}" + }, + { + "bbox": [ + 304, + 607, + 547, + 692 + ], + "type": "text", + "content": ", corresponding to " + }, + { + "bbox": [ + 304, + 607, + 547, + 692 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 607, + 547, + 692 + ], + "type": "text", + "content": " coarse-to-fine deformations:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 364, + 700, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 700, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 364, + 700, + 545, + 715 + ], + "type": "interline_equation", + "content": "\\psi (x) = U p \\left(h \\left(P E (x)\\right)\\right) = \\mathbf {O}, \\tag {6}", + "image_path": "76e4de892af7c8a4babe93e60a37c36c2730916b3f0c40c8c29ef2e1dca3897b.jpg" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 747, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 747, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 747, + 318, + 757 + ], + "type": "text", + "content": "12150" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 191 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 191 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 72, + 287, + 191 + ], + "type": "inline_equation", + "content": "PE(\\cdot)" + }, + { + "bbox": [ + 47, + 72, + 287, + 191 + ], + "type": "text", + "content": " is positional embedding operator [18], " + }, + { + "bbox": [ + 47, + 72, + 287, + 191 + ], + "type": "inline_equation", + "content": "h: R^{C \\times H \\times W} \\to R^{2 \\times \\{H_1 \\times W_1, \\dots, H_K \\times W_K\\}}" + }, + { + "bbox": [ + 47, + 72, + 287, + 191 + ], + "type": "text", + "content": " is the deformation estimator that generates offset vectors, " + }, + { + "bbox": [ + 47, + 72, + 287, + 191 + ], + "type": "inline_equation", + "content": "Up(\\cdot)" + }, + { + "bbox": [ + 47, + 72, + 287, + 191 + ], + "type": "text", + "content": " is upsampling function that resizes the outputs of " + }, + { + "bbox": [ + 47, + 72, + 287, + 191 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 47, + 72, + 287, + 191 + ], + "type": "text", + "content": "-heads to the same size with the original image. In our experiments, we set " + }, + { + "bbox": [ + 47, + 72, + 287, + 191 + ], + "type": "inline_equation", + "content": "K = 2" + }, + { + "bbox": [ + 47, + 72, + 287, + 191 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 47, + 72, + 287, + 191 + ], + "type": "inline_equation", + "content": "O_1" + }, + { + "bbox": [ + 47, + 72, + 287, + 191 + ], + "type": "text", + "content": " used to estimate coarse deformation (e.g. corresponding to the position of pedestrians or the placement of workpieces) and " + }, + { + "bbox": [ + 47, + 72, + 287, + 191 + ], + "type": "inline_equation", + "content": "O_2" + }, + { + "bbox": [ + 47, + 72, + 287, + 191 + ], + "type": "text", + "content": " used to estimate fine deformation (e.g. corresponding to pedestrian behaviors or workpiece details)." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 192, + 287, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 192, + 287, + 263 + ], + "spans": [ + { + "bbox": [ + 47, + 192, + 287, + 263 + ], + "type": "text", + "content": "Considering that quantized embedding without positional information may lead to inaccurate reconstruction, we also introduce position embedding operator for the decoder " + }, + { + "bbox": [ + 47, + 192, + 287, + 263 + ], + "type": "inline_equation", + "content": "g(\\cdot)" + }, + { + "bbox": [ + 47, + 192, + 287, + 263 + ], + "type": "text", + "content": ". We then aggregate " + }, + { + "bbox": [ + 47, + 192, + 287, + 263 + ], + "type": "inline_equation", + "content": "\\mathbf{O}" + }, + { + "bbox": [ + 47, + 192, + 287, + 263 + ], + "type": "text", + "content": " onto the reconstructed reference " + }, + { + "bbox": [ + 47, + 192, + 287, + 263 + ], + "type": "inline_equation", + "content": "g(PE(z^q))" + }, + { + "bbox": [ + 47, + 192, + 287, + 263 + ], + "type": "text", + "content": ", and obtain " + }, + { + "bbox": [ + 47, + 192, + 287, + 263 + ], + "type": "inline_equation", + "content": "\\tilde{x}_k(k = 1,\\dots ,K)" + }, + { + "bbox": [ + 47, + 192, + 287, + 263 + ], + "type": "text", + "content": " which is calibrated by the " + }, + { + "bbox": [ + 47, + 192, + 287, + 263 + ], + "type": "inline_equation", + "content": "k^{th}" + }, + { + "bbox": [ + 47, + 192, + 287, + 263 + ], + "type": "text", + "content": " layer of deformation fields:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 100, + 272, + 287, + 285 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 100, + 272, + 287, + 285 + ], + "spans": [ + { + "bbox": [ + 100, + 272, + 287, + 285 + ], + "type": "interline_equation", + "content": "\\tilde {x} _ {k} = g \\left(P E \\left(z ^ {q}\\right)\\right) \\circ O _ {1} \\dots \\circ O _ {k}, \\tag {7}", + "image_path": "5ef2b878815e246c85055ee22dedf7e8c4bd43403eff76c9c33291a292fa870f.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 293, + 287, + 374 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 293, + 287, + 374 + ], + "spans": [ + { + "bbox": [ + 47, + 293, + 287, + 374 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 293, + 287, + 374 + ], + "type": "inline_equation", + "content": "\\circ" + }, + { + "bbox": [ + 47, + 293, + 287, + 374 + ], + "type": "text", + "content": " is grid-sampling function with a reference coordinate in this implementation (\"Agg.\" and \"Coord.\" in Fig. 4). However, minimizing the unconstrained reconstruction loss with respect to " + }, + { + "bbox": [ + 47, + 293, + 287, + 374 + ], + "type": "inline_equation", + "content": "\\psi(x)" + }, + { + "bbox": [ + 47, + 293, + 287, + 374 + ], + "type": "text", + "content": " may cause degenerate solution of the encoder " + }, + { + "bbox": [ + 47, + 293, + 287, + 374 + ], + "type": "inline_equation", + "content": "f(\\cdot)" + }, + { + "bbox": [ + 47, + 293, + 287, + 374 + ], + "type": "text", + "content": ". To address this problem, we add constraint using smoothness loss via gradient operation and strength loss as:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 374, + 287, + 399 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 374, + 287, + 399 + ], + "spans": [ + { + "bbox": [ + 105, + 374, + 287, + 399 + ], + "type": "interline_equation", + "content": "L _ {d f} = \\sum_ {k} \\| \\nabla O _ {k} \\| _ {1} + \\| O _ {k} \\| _ {2}. \\tag {8}", + "image_path": "2f1929cf8ba31f14b1c51311dd379569e02d334201bd0bbb57f0d1f0b8864f4d.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 405, + 228, + 417 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 405, + 228, + 417 + ], + "spans": [ + { + "bbox": [ + 47, + 405, + 228, + 417 + ], + "type": "text", + "content": "3.4. Foreground-background selection" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 423, + 287, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 423, + 287, + 567 + ], + "spans": [ + { + "bbox": [ + 47, + 423, + 287, + 567 + ], + "type": "text", + "content": "Storing the background information in memory will break the compactness of embedding and require plenty of memory items. Besides, the deformation estimation should not be applied to the background. Some approaches use external estimators to remove interference from background, but the generalization in different scenarios cannot be guaranteed and extra noise will inevitably be introduced. Benefiting from the strong prior of fixed-view videos, we model the background with a learnable template " + }, + { + "bbox": [ + 47, + 423, + 287, + 567 + ], + "type": "inline_equation", + "content": "x_{bg}" + }, + { + "bbox": [ + 47, + 423, + 287, + 567 + ], + "type": "text", + "content": " and generate a binary mask to indicate whether a pixel belongs to foreground or background with " + }, + { + "bbox": [ + 47, + 423, + 287, + 567 + ], + "type": "inline_equation", + "content": "f_{m}(\\cdot)" + }, + { + "bbox": [ + 47, + 423, + 287, + 567 + ], + "type": "text", + "content": ". The final reconstruction " + }, + { + "bbox": [ + 47, + 423, + 287, + 567 + ], + "type": "inline_equation", + "content": "\\hat{x}_k" + }, + { + "bbox": [ + 47, + 423, + 287, + 567 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 47, + 423, + 287, + 567 + ], + "type": "inline_equation", + "content": "k^{th}" + }, + { + "bbox": [ + 47, + 423, + 287, + 567 + ], + "type": "text", + "content": " head is:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 94, + 575, + 287, + 588 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 575, + 287, + 588 + ], + "spans": [ + { + "bbox": [ + 94, + 575, + 287, + 588 + ], + "type": "interline_equation", + "content": "\\hat {x} _ {k} = f _ {m} (x) \\tilde {x} _ {k} + (1 - f _ {m} (x)) x _ {b g}. \\tag {9}", + "image_path": "bac62d8c54cef6461fb79471dd061d5d0c320a4aa9be738a039bdf16b0ed4dce.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 595, + 177, + 608 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 595, + 177, + 608 + ], + "spans": [ + { + "bbox": [ + 47, + 595, + 177, + 608 + ], + "type": "text", + "content": "3.5. Training and inference" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 613, + 286, + 637 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 613, + 286, + 637 + ], + "spans": [ + { + "bbox": [ + 47, + 613, + 286, + 637 + ], + "type": "text", + "content": "Training phase. Once we obtain the reconstruction " + }, + { + "bbox": [ + 47, + 613, + 286, + 637 + ], + "type": "inline_equation", + "content": "\\hat{x}_k" + }, + { + "bbox": [ + 47, + 613, + 286, + 637 + ], + "type": "text", + "content": ", we can calculate reconstruction loss " + }, + { + "bbox": [ + 47, + 613, + 286, + 637 + ], + "type": "inline_equation", + "content": "L_{rec}" + }, + { + "bbox": [ + 47, + 613, + 286, + 637 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 117, + 644, + 287, + 669 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 117, + 644, + 287, + 669 + ], + "spans": [ + { + "bbox": [ + 117, + 644, + 287, + 669 + ], + "type": "interline_equation", + "content": "L _ {r e c} = \\sum_ {k} D i s (x, \\hat {x} _ {k}), \\tag {10}", + "image_path": "0beff2d86ed40db221f24fd5292ee6d680fc1ee9329db55a410700fd74c86545.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "inline_equation", + "content": "Dis(\\cdot)" + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "content": " refers to a distance function in sample space. Reminding of the optimization objective in Eq. 3, we implement the two constraints using " + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "inline_equation", + "content": "L_{com}" + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "inline_equation", + "content": "L_{df}" + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "content": " respectively." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "text", + "content": "Finally, training is performed by minimizing the overall loss:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 359, + 96, + 545, + 109 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 96, + 545, + 109 + ], + "spans": [ + { + "bbox": [ + 359, + 96, + 545, + 109 + ], + "type": "interline_equation", + "content": "L _ {a l l} = L _ {r e c} + \\gamma_ {1} L _ {c o m} + \\gamma_ {2} L _ {d f}. \\tag {11}", + "image_path": "049f9601693837a49dfaf187f1c5fcbec045951052ec5cbb106dc6f8959f20ea.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 114, + 545, + 148 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 114, + 545, + 148 + ], + "spans": [ + { + "bbox": [ + 305, + 114, + 545, + 148 + ], + "type": "text", + "content": "Inference phase. In the inference phase, we use " + }, + { + "bbox": [ + 305, + 114, + 545, + 148 + ], + "type": "inline_equation", + "content": "\\mathbf{O}" + }, + { + "bbox": [ + 305, + 114, + 545, + 148 + ], + "type": "text", + "content": " and the reconstruction loss to calculate the error maps of input sample " + }, + { + "bbox": [ + 305, + 114, + 545, + 148 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 305, + 114, + 545, + 148 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 382, + 149, + 545, + 162 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 382, + 149, + 545, + 162 + ], + "spans": [ + { + "bbox": [ + 382, + 149, + 545, + 162 + ], + "type": "interline_equation", + "content": "A _ {r e c} = \\operatorname {D i s} (x, \\hat {x} _ {K}), \\tag {12}", + "image_path": "8a5b4248919434d2c75a0eeb36bcd6799055202011694bc21441c8c36479bc5b.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 387, + 167, + 545, + 191 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 387, + 167, + 545, + 191 + ], + "spans": [ + { + "bbox": [ + 387, + 167, + 545, + 191 + ], + "type": "interline_equation", + "content": "A _ {d f} = \\sum_ {k} \\| O _ {k} \\| _ {2}. \\tag {13}", + "image_path": "91e0e80d8d464b3e5a3d0428f5cac909f63e47d822cdfee169d91585a05f9ff7.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 195, + 545, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 195, + 545, + 217 + ], + "spans": [ + { + "bbox": [ + 305, + 195, + 545, + 217 + ], + "type": "text", + "content": "Image-level anomaly score is computed based on local maxima:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 317, + 227, + 545, + 240 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 227, + 545, + 240 + ], + "spans": [ + { + "bbox": [ + 317, + 227, + 545, + 240 + ], + "type": "interline_equation", + "content": "\\operatorname {S c o r e} _ {I} = \\max \\left(A _ {r e c} \\otimes k ^ {\\star}\\right) + \\alpha \\max \\left(A _ {d f} \\otimes k ^ {\\star}\\right). \\tag {14}", + "image_path": "57cd203bedd1265476fe1e17733ba9a3c46d3857bb7894d9b7d490f1b7b4ae9a.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 249, + 545, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 249, + 545, + 308 + ], + "spans": [ + { + "bbox": [ + 305, + 249, + 545, + 308 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 249, + 545, + 308 + ], + "type": "inline_equation", + "content": "\\otimes" + }, + { + "bbox": [ + 305, + 249, + 545, + 308 + ], + "type": "text", + "content": " is convolution operator and " + }, + { + "bbox": [ + 305, + 249, + 545, + 308 + ], + "type": "inline_equation", + "content": "k^{\\star}" + }, + { + "bbox": [ + 305, + 249, + 545, + 308 + ], + "type": "text", + "content": " is convolution kernel for anomaly maps. " + }, + { + "bbox": [ + 305, + 249, + 545, + 308 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 305, + 249, + 545, + 308 + ], + "type": "text", + "content": " is a tradeoff parameter. That is, the reconstruction loss and deformation jointly determine the anomaly score, which is much more effective than traditional reconstruction-based methods, as illustrated in Fig. 3." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 316, + 404, + 327 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 316, + 404, + 327 + ], + "spans": [ + { + "bbox": [ + 306, + 316, + 404, + 327 + ], + "type": "text", + "content": "3.6. Variant of PDM" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 334, + 545, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 334, + 545, + 477 + ], + "spans": [ + { + "bbox": [ + 305, + 334, + 545, + 477 + ], + "type": "text", + "content": "Modified framework with Pre-PDM. The DMAD framework together with ICM and PDM modules proposed above are suitable in many anomaly detection scenarios including video surveillance. However, for industrial defect detection, texture reconstruction may be harmful (such as spots on \"Pill\"), and we should reconstruct high-level semantic features instead. Since PDM does not work in high-dimensional feature space and interferes with the training process, we propose variant of PDM, Pre-PDM (PPDM), as a solution. PPDM works in sample space, and is applied to the input sample rather than the reconstructed one. Eq. (3) is modified naturally as follows:" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 330, + 485, + 545, + 513 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 485, + 545, + 513 + ], + "spans": [ + { + "bbox": [ + 330, + 485, + 545, + 513 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} L = \\| x \\circ \\psi^ {\\prime} (x) - g (\\phi (f (x \\circ \\psi^ {\\prime} (x)), z)) \\| _ {2} \\tag {15} \\\\ + \\gamma_ {1} R _ {1} (\\phi) + \\gamma_ {2} R _ {2} (\\psi^ {\\prime}). \\\\ \\end{array}", + "image_path": "954706abf42158408e9b3cc4c7cd9c8fe960adc89b3fcb45a4866a5eba1629f2.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 305, + 521, + 545, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 521, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 305, + 521, + 545, + 605 + ], + "type": "text", + "content": "Since we do not reconstruct the original samples, reconstruction loss cannot constrain PPDM to maintain information diversity. In order to prevent " + }, + { + "bbox": [ + 305, + 521, + 545, + 605 + ], + "type": "inline_equation", + "content": "x \\circ \\psi'(x)" + }, + { + "bbox": [ + 305, + 521, + 545, + 605 + ], + "type": "text", + "content": " in Eq. (15) from shortcut learning, we propose to add the inversion of forward deformation, backward deformation " + }, + { + "bbox": [ + 305, + 521, + 545, + 605 + ], + "type": "inline_equation", + "content": "\\mathbf{O}^T" + }, + { + "bbox": [ + 305, + 521, + 545, + 605 + ], + "type": "text", + "content": ", based on cycle-consistency principle to maintain the diversity of appearance information:" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 344, + 613, + 545, + 628 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 344, + 613, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 344, + 613, + 545, + 628 + ], + "type": "interline_equation", + "content": "\\psi^ {\\prime} (x) = U p \\left(h ^ {\\prime} \\left(P E (x)\\right)\\right) = \\left\\{\\mathbf {O}, \\mathbf {O} ^ {T} \\right\\}. \\tag {16}", + "image_path": "d6c05b54566b0b880b9d01297d1ba9765548a7911f86db9e547b90502cad53a4.jpg" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 306, + 635, + 545, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 635, + 545, + 661 + ], + "spans": [ + { + "bbox": [ + 306, + 635, + 545, + 661 + ], + "type": "text", + "content": "Training phase. The cycle-consistency losses " + }, + { + "bbox": [ + 306, + 635, + 545, + 661 + ], + "type": "inline_equation", + "content": "L_{cyc}" + }, + { + "bbox": [ + 306, + 635, + 545, + 661 + ], + "type": "text", + "content": " and constraint for forward-backward deformation " + }, + { + "bbox": [ + 306, + 635, + 545, + 661 + ], + "type": "inline_equation", + "content": "L_{df}^{+}" + }, + { + "bbox": [ + 306, + 635, + 545, + 661 + ], + "type": "text", + "content": " are:" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 318, + 668, + 545, + 683 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 668, + 545, + 683 + ], + "spans": [ + { + "bbox": [ + 318, + 668, + 545, + 683 + ], + "type": "interline_equation", + "content": "L _ {c y c} = \\left\\| x - x \\circ O _ {1} \\dots \\circ O _ {K} \\circ O _ {K} ^ {T} \\dots \\circ O _ {1} ^ {T} \\right\\| _ {2}, \\tag {17}", + "image_path": "fc05b8f504132f4d430baa861e40d76f2da6758b5470c9c1414b5bb063249a4d.jpg" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 311, + 690, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 690, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 311, + 690, + 545, + 715 + ], + "type": "interline_equation", + "content": "L _ {d f} ^ {+} = \\sum_ {k} \\| \\nabla O _ {k} \\| _ {1} + \\| \\nabla O _ {k} ^ {T} \\| _ {1} + \\| O _ {k} \\| _ {2} + \\| O _ {k} ^ {T} \\| _ {2}. \\tag {18}", + "image_path": "5fb63ff8750543c75782ab42c33ca709fcfd0e724ffb72d37aebd26e62731424.jpg" + } + ] + } + ], + "index": 27 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 747, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 747, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 747, + 317, + 757 + ], + "type": "text", + "content": "12151" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 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The process of forward and backward deformation: a) The pattern of original image. Red indicates high error regions and black indicates low error regions; b) The normal pattern; c) The coarse estimation " + }, + { + "bbox": [ + 46, + 212, + 287, + 300 + ], + "type": "inline_equation", + "content": "O_{1}" + }, + { + "bbox": [ + 46, + 212, + 287, + 300 + ], + "type": "text", + "content": " (dark blue) and " + }, + { + "bbox": [ + 46, + 212, + 287, + 300 + ], + "type": "inline_equation", + "content": "O_{1}^{T}" + }, + { + "bbox": [ + 46, + 212, + 287, + 300 + ], + "type": "text", + "content": " (light blue); d) The fine estimation " + }, + { + "bbox": [ + 46, + 212, + 287, + 300 + ], + "type": "inline_equation", + "content": "O_{2}" + }, + { + "bbox": [ + 46, + 212, + 287, + 300 + ], + "type": "text", + "content": " (dark blue) and " + }, + { + "bbox": [ + 46, + 212, + 287, + 300 + ], + "type": "inline_equation", + "content": "O_{2}^{T}" + }, + { + "bbox": [ + 46, + 212, + 287, + 300 + ], + "type": "text", + "content": " (light blue); e) Using " + }, + { + "bbox": [ + 46, + 212, + 287, + 300 + ], + "type": "inline_equation", + "content": "\\hat{x}" + }, + { + "bbox": [ + 46, + 212, + 287, + 300 + ], + "type": "text", + "content": " simply causes high anomaly score at the wrong location (solid cross). Ground-truth is shown as hollow cross; f) " + }, + { + "bbox": [ + 46, + 212, + 287, + 300 + ], + "type": "inline_equation", + "content": "\\hat{x} \\circ O_{2}^{T} \\circ O_{1}^{T}" + }, + { + "bbox": [ + 46, + 212, + 287, + 300 + ], + "type": "text", + "content": " adjusts the high reconstruction error to original position." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 317, + 287, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 317, + 287, + 342 + ], + "spans": [ + { + "bbox": [ + 46, + 317, + 287, + 342 + ], + "type": "text", + "content": "So we train our anomaly detection model with PPDM by minimizing the following loss:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 70, + 346, + 287, + 361 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 346, + 287, + 361 + ], + "spans": [ + { + "bbox": [ + 70, + 346, + 287, + 361 + ], + "type": "interline_equation", + "content": "L _ {a l l} ^ {+} = L _ {r e c} + \\gamma_ {1} L _ {c o m} + \\gamma_ {2} L _ {d f} ^ {+} + \\gamma_ {3} L _ {c y c}. \\tag {19}", + "image_path": "49bb442dc476458e0303fe908c575160f64d783b2b1b489bf7717c860f0c45d8.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 365, + 287, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 365, + 287, + 388 + ], + "spans": [ + { + "bbox": [ + 46, + 365, + 287, + 388 + ], + "type": "text", + "content": "The modified DMAD framework (i.e. with PPDM and Reverse Distribution [6]) is shown in in Fig. 4b." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 388, + 287, + 446 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 388, + 287, + 446 + ], + "spans": [ + { + "bbox": [ + 46, + 388, + 287, + 446 + ], + "type": "text", + "content": "Inference phase. The result of PPDM is not aligned with the position of original input, which may reduce the performance of anomaly localization. In order to obtain the anomaly map of real location, we use backward deformation to perform inverse sampling (Fig. 5):" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 93, + 450, + 287, + 465 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 450, + 287, + 465 + ], + "spans": [ + { + "bbox": [ + 93, + 450, + 287, + 465 + ], + "type": "interline_equation", + "content": "A _ {r e c} ^ {+} = \\operatorname {D i s} \\left(x, \\hat {x} _ {K}\\right) \\circ O _ {K} ^ {T} \\dots \\circ O _ {1} ^ {T}, \\tag {20}", + "image_path": "935cf83d9c573ae768dff35fa8e7b2ac85b557be4cd80fe94e1401e6fa9f6299.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 94, + 469, + 287, + 521 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 469, + 287, + 521 + ], + "spans": [ + { + "bbox": [ + 94, + 469, + 287, + 521 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} A _ {d f} ^ {+} = \\sum_ {k} \\| O _ {k} \\circ O _ {k + 1} \\dots \\circ O _ {K} \\| _ {2} \\tag {21} \\\\ + \\sum_ {k} \\| O _ {k} ^ {T} \\circ O _ {k - 1} ^ {T} \\dots \\circ O _ {1} ^ {T} \\| _ {2}. \\\\ \\end{array}", + "image_path": "f0cd17d10a3f77fa67daeee14390102272f775ab6fad763ef5a7454fab413ec5.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 46, + 525, + 287, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 525, + 287, + 550 + ], + "spans": [ + { + "bbox": [ + 46, + 525, + 287, + 550 + ], + "type": "text", + "content": "The image-level anomaly score " + }, + { + "bbox": [ + 46, + 525, + 287, + 550 + ], + "type": "inline_equation", + "content": "Score_{I}^{+}" + }, + { + "bbox": [ + 46, + 525, + 287, + 550 + ], + "type": "text", + "content": " and pixel-level anomaly score " + }, + { + "bbox": [ + 46, + 525, + 287, + 550 + ], + "type": "inline_equation", + "content": "Score_{P}^{+}" + }, + { + "bbox": [ + 46, + 525, + 287, + 550 + ], + "type": "text", + "content": " are calculated respectively as:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 56, + 554, + 287, + 569 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 554, + 287, + 569 + ], + "spans": [ + { + "bbox": [ + 56, + 554, + 287, + 569 + ], + "type": "interline_equation", + "content": "\\operatorname {S c o r e} _ {I} ^ {+} = \\max \\left(A _ {\\text {r e c}} ^ {+} \\otimes k ^ {\\star}\\right) + \\alpha \\max \\left(A _ {d f} ^ {+} \\otimes k ^ {\\star}\\right), \\tag {22}", + "image_path": "89e982cdf782c7504a9a40795a946f81c6d47d45874d31455be281a7a043e4b4.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 115, + 573, + 287, + 589 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 573, + 287, + 589 + ], + "spans": [ + { + "bbox": [ + 115, + 573, + 287, + 589 + ], + "type": "interline_equation", + "content": "\\operatorname {S c o r e} _ {P} ^ {+} = A _ {r e c} ^ {+} + \\alpha A _ {d f} ^ {+}. \\tag {23}", + "image_path": "b0b1e87f2dffe0d293582baaf19960ca3d75080f9ea19baaf36ea4cf15dc7a5c.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 47, + 596, + 195, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 596, + 195, + 609 + ], + "spans": [ + { + "bbox": [ + 47, + 596, + 195, + 609 + ], + "type": "text", + "content": "4. Experiments and Analysis" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 46, + 616, + 287, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 616, + 287, + 687 + ], + "spans": [ + { + "bbox": [ + 46, + 616, + 287, + 687 + ], + "type": "text", + "content": "Firstly, we perform toy experiment on MNIST to illustrate our approach. Then the quantitative and qualitative results of two versions our DMAD framework are reported in video anomaly detection and industrial surface defect detection respectively2. Finally, we conduct ablation experiments and analyze the results." + } + ] + } + ], + "index": 23 + }, + { + "type": "image", + "bbox": [ + 324, + 68, + 529, + 190 + ], + "blocks": [ + { + "bbox": [ + 324, + 68, + 529, + 190 + ], + "lines": [ + { + "bbox": [ + 324, + 68, + 529, + 190 + ], + "spans": [ + { + "bbox": [ + 324, + 68, + 529, + 190 + ], + "type": "image", + "image_path": "6b99b30160a86a98f1ac07a81ded836fd211a7464247f53aa2e38bbb658e5efc.jpg" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 198, + 545, + 231 + ], + "lines": [ + { + "bbox": [ + 305, + 198, + 545, + 231 + ], + "spans": [ + { + "bbox": [ + 305, + 198, + 545, + 231 + ], + "type": "text", + "content": "Figure 6. Visualization of toy experiment. The last three rows are: reference reconstructed from memory, reference after coarse deformation, and final output after applying fine deformation." + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "image_caption" + } + ], + "index": 25 + }, + { + "bbox": [ + 306, + 249, + 368, + 261 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 249, + 368, + 261 + ], + "spans": [ + { + "bbox": [ + 306, + 249, + 368, + 261 + ], + "type": "text", + "content": "4.1. Datasets" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 305, + 267, + 545, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 267, + 545, + 327 + ], + "spans": [ + { + "bbox": [ + 305, + 267, + 545, + 327 + ], + "type": "text", + "content": "Surveillance Videos. Ped2 [27], Avenue [23] and ShanghaiTech [25] are fixed-view videos. The anomalies include driving, cycling, running, throwing stuff, etc. Mutual occlusion, anomaly-like behavior, contaminated data and different scenes occur frequently in these datasets." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 305, + 327, + 545, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 327, + 545, + 387 + ], + "spans": [ + { + "bbox": [ + 305, + 327, + 545, + 387 + ], + "type": "text", + "content": "Industrial Images. MVtec [2] contains 15 types of industrial images, which are divided into 5 types of textures and 10 types of objects. The defects include crack, scratch, etc. The normal workpiece has different positions, angles and textures. It is used for detection and localization task." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 306, + 395, + 402, + 407 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 395, + 402, + 407 + ], + "spans": [ + { + "bbox": [ + 306, + 395, + 402, + 407 + ], + "type": "text", + "content": "4.2. Toy experiment" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 304, + 413, + 545, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 413, + 545, + 520 + ], + "spans": [ + { + "bbox": [ + 304, + 413, + 545, + 520 + ], + "type": "text", + "content": "As shown in Fig. 6, we perform a toy experiment on MNIST dataset [16] with setting analogous to out-of-distribution (OOD) detection (i.e. training on \"1, 3, 5, 7, 9\" and test on all classes). Our model searches separate memory items for each digital category to reconstruct it into class-specific reference and uses the deformation fields from PDM to adjust it hierarchically. When tested with seen and unseen classes, the model adjusts reconstructed references to normal inputs, but fails on the abnormal ones." + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 304, + 521, + 545, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 545, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 545, + 616 + ], + "type": "text", + "content": "In contrast, memory network without diversity-aware module cannot guarantee the intra-class compactness and the reconstruction diversity, which misdirects the model to obtain dataset-optimal \"average memory\", leading to fuzzy reconstruction and lower discrimination ability. The model with full-channel skip-connection suffers from shortcut learning and reconstruct anomalies successfully which weakens the ability to identify anomalies." + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 306, + 623, + 437, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 623, + 437, + 635 + ], + "spans": [ + { + "bbox": [ + 306, + 623, + 437, + 635 + ], + "type": "text", + "content": "4.3. Implementation details" + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": "The input images are resized into " + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": " and normalized to the value in range of " + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "inline_equation", + "content": "[-1,1]" + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": ". According to frame-pred strategy [19], the history length is set to 4 in video anomaly detection and 0 for images. After feature extraction with a backbone, PDM and PPDM obtain different heads by stacking stride-2 convolution layers. Then" + } + ] + } + ], + "index": 34 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 47, + 693, + 286, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 286, + 713 + ], + "type": "text", + "content": "2Our code will be available at https://github.com/FlappyPeggy/DMAD." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 294, + 747, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 747, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 747, + 317, + 757 + ], + "type": "text", + "content": "12152" + } + ] + } + ], + "index": 35 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 360 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 360 + ], + "type": "text", + "content": "we use " + }, + { + "bbox": [ + 47, + 72, + 289, + 360 + ], + "type": "inline_equation", + "content": "\\text{Tanh}" + }, + { + "bbox": [ + 47, + 72, + 289, + 360 + ], + "type": "text", + "content": " as the activation function of output layer and clipping function to ensure the value of deformation is between " + }, + { + "bbox": [ + 47, + 72, + 289, + 360 + ], + "type": "inline_equation", + "content": "[-1, 1]" + }, + { + "bbox": [ + 47, + 72, + 289, + 360 + ], + "type": "text", + "content": ". Unless otherwise noted, the architecture of autoencoder complies with the settings of MNAD [29] and RD [6] for PDM and PPDM respectively. The function " + }, + { + "bbox": [ + 47, + 72, + 289, + 360 + ], + "type": "inline_equation", + "content": "\\text{Dis}(\\cdot)" + }, + { + "bbox": [ + 47, + 72, + 289, + 360 + ], + "type": "text", + "content": " in Eq. (10) is a combination of " + }, + { + "bbox": [ + 47, + 72, + 289, + 360 + ], + "type": "inline_equation", + "content": "MSE" + }, + { + "bbox": [ + 47, + 72, + 289, + 360 + ], + "type": "text", + "content": " loss and " + }, + { + "bbox": [ + 47, + 72, + 289, + 360 + ], + "type": "inline_equation", + "content": "Grad" + }, + { + "bbox": [ + 47, + 72, + 289, + 360 + ], + "type": "text", + "content": " loss for reconstruction in sample space, and " + }, + { + "bbox": [ + 47, + 72, + 289, + 360 + ], + "type": "inline_equation", + "content": "COS" + }, + { + "bbox": [ + 47, + 72, + 289, + 360 + ], + "type": "text", + "content": " loss for deep features. We set " + }, + { + "bbox": [ + 47, + 72, + 289, + 360 + ], + "type": "inline_equation", + "content": "(\\gamma_1, \\gamma_2) = (1, 0.25)" + }, + { + "bbox": [ + 47, + 72, + 289, + 360 + ], + "type": "text", + "content": " for PDM, " + }, + { + "bbox": [ + 47, + 72, + 289, + 360 + ], + "type": "inline_equation", + "content": "(1, 1)" + }, + { + "bbox": [ + 47, + 72, + 289, + 360 + ], + "type": "text", + "content": " for PPDM " + }, + { + "bbox": [ + 47, + 72, + 289, + 360 + ], + "type": "inline_equation", + "content": "(\\gamma_3" + }, + { + "bbox": [ + 47, + 72, + 289, + 360 + ], + "type": "text", + "content": " is discussed in Sec. 4.5), and " + }, + { + "bbox": [ + 47, + 72, + 289, + 360 + ], + "type": "inline_equation", + "content": "\\beta = 0.25" + }, + { + "bbox": [ + 47, + 72, + 289, + 360 + ], + "type": "text", + "content": " as in [35]. During post-processing, we use average kernel for surveillance videos and Gaussian kernel with " + }, + { + "bbox": [ + 47, + 72, + 289, + 360 + ], + "type": "inline_equation", + "content": "\\sigma = 4" + }, + { + "bbox": [ + 47, + 72, + 289, + 360 + ], + "type": "text", + "content": " for industrial images as in [6]. Frame-difference method is applied to remove static anomalies for Avenue, because our method detects all anomalies which may be labeled as normal ones in [23]. And we use the mask calculated in Eq. (9) to normalize anomaly map in [25] due to the scale changes. Besides, we set " + }, + { + "bbox": [ + 47, + 72, + 289, + 360 + ], + "type": "inline_equation", + "content": "\\alpha = 0.2" + }, + { + "bbox": [ + 47, + 72, + 289, + 360 + ], + "type": "text", + "content": " for three video tasks and an additional option " + }, + { + "bbox": [ + 47, + 72, + 289, + 360 + ], + "type": "inline_equation", + "content": "\\alpha = 0.05" + }, + { + "bbox": [ + 47, + 72, + 289, + 360 + ], + "type": "text", + "content": " for defect detection, depending on whether the defect includes geometrical changes. The model is optimized by AdamW [21] and the learning rate is 2e-4 and 5e-3 as in [6, 29] respectively, being decayed by CosineAnnealingLR [22] strategy. We adopt 60, 60, 60, 10, 400 epochs for MNIST, Ped2, Avenue, Shanghai and MVTec respectively with batch size of 8." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 368, + 129, + 380 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 368, + 129, + 380 + ], + "spans": [ + { + "bbox": [ + 47, + 368, + 129, + 380 + ], + "type": "text", + "content": "4.4. Main results" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 386, + 287, + 458 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 386, + 287, + 458 + ], + "spans": [ + { + "bbox": [ + 46, + 386, + 287, + 458 + ], + "type": "text", + "content": "Surveillance Videos. We compare our method with SOTA works on video anomaly detection in Tab. 1. Our method outperforms comparative approaches even though we neither use external estimators nor remove abnormal frames in training data. In additional, if we detect global offset for camera jitter in [23], there will be extra " + }, + { + "bbox": [ + 46, + 386, + 287, + 458 + ], + "type": "inline_equation", + "content": "0.1\\%" + }, + { + "bbox": [ + 46, + 386, + 287, + 458 + ], + "type": "text", + "content": " gain." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 459, + 287, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 459, + 287, + 506 + ], + "spans": [ + { + "bbox": [ + 46, + 459, + 287, + 506 + ], + "type": "text", + "content": "The qualitative results are shown in Fig. 7. We find that: anomalies are over-reconstructed in (b); normals are not reconstructed well in (c); (d) greatly improves normal reconstruction with slightly less inhibition ability for anomalies." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 507, + 288, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 507, + 288, + 592 + ], + "spans": [ + { + "bbox": [ + 46, + 507, + 288, + 592 + ], + "type": "text", + "content": "Industrial Images. Anomaly detection results on MVTec are shown in Tab. 2 and localization results are shown in Tab. 3. With the deformation from PPDM, texture anomalies are detected with high performance and our method outperforms SOTA methods in both detection and localization tasks without memorizing an enormous number of embedding from training data." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 599, + 139, + 612 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 599, + 139, + 612 + ], + "spans": [ + { + "bbox": [ + 47, + 599, + 139, + 612 + ], + "type": "text", + "content": "4.5. Ablation study" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "type": "text", + "content": "As shown in Tab. 4, single-output memory module without PDM suppresses diverse normal patterns seriously, while separate PDM without memory provides comparable performance gains as the previous SOTA works because the module \"Comp.\" serves as an information compression module instead. The number of multi-scale deformation fields also have a modest effect on performance. We suggest that \"K\" should at least make the scale of control grid" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 307, + 134, + 547, + 269 + ], + "blocks": [ + { + "bbox": [ + 305, + 70, + 547, + 127 + ], + "lines": [ + { + "bbox": [ + 305, + 70, + 547, + 127 + ], + "spans": [ + { + "bbox": [ + 305, + 70, + 547, + 127 + ], + "type": "text", + "content": "Table 1. Video anomaly detection results on Ped2 [27], Avenue [23] and Shanghai [25]. We calculate " + }, + { + "bbox": [ + 305, + 70, + 547, + 127 + ], + "type": "inline_equation", + "content": "AUC(\\%)" + }, + { + "bbox": [ + 305, + 70, + 547, + 127 + ], + "type": "text", + "content": " with all frames together. Numbers in bold indicate the best performance and the underlined ones are the second best. " + }, + { + "bbox": [ + 305, + 70, + 547, + 127 + ], + "type": "inline_equation", + "content": "^+" + }, + { + "bbox": [ + 305, + 70, + 547, + 127 + ], + "type": "text", + "content": " indicates that we reproduce the result due to higher performance or absence of implementation." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 134, + 547, + 269 + ], + "lines": [ + { + "bbox": [ + 307, + 134, + 547, + 269 + ], + "spans": [ + { + "bbox": [ + 307, + 134, + 547, + 269 + ], + "type": "table", + "html": "
MethodsPed2 [27]Avenue [23]Shanghai [25]
Conv2D [9]90.070.2-
Conv3D [40]91.277.1-
ConvLSTM [24]88.177.0-
FramePred [19]95.484.972.8
ConvVQ+90.284.3-
MemAE [8]94.183.371.2
MPN [26]96.989.573.8
MNAD+ [29]97.888.570.5
HF2VAD [20]99.391.176.2
Ours99.792.878.8
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Qualitative results on Ped2. a) Original image; b) Memory network with skip-connection [29]; c) PDM with VQ-Layer [35]; d) PDM with ICM. Green box indicates negative, red box indicates positive, and yellow box indicates weak positive." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 427, + 353, + 493, + 418 + ], + "blocks": [ + { + "bbox": [ + 427, + 353, + 493, + 418 + ], + "lines": [ + { + "bbox": [ + 427, + 353, + 493, + 418 + ], + "spans": [ + { + "bbox": [ + 427, + 353, + 493, + 418 + ], + "type": "image", + "image_path": "cf9dcc661808b1bf3bcca66f6f740605d4fbf83ef63ed90217c07e5507e7c83a.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 456, + 418, + 465, + 425 + ], + "lines": [ + { + "bbox": [ + 456, + 418, + 465, + 425 + ], + "spans": [ + { + "bbox": [ + 456, + 418, + 465, + 425 + ], + "type": "text", + "content": "(d)" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 498, + 545, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 605 + ], + "type": "text", + "content": "cover the size of base elements (e.g. pedestrian limbs). Besides, the foreground-background selection module further improves the compactness of memory embedding. Moreover, if any constraint for PDM is missing, the abnormal information will be transmitted and cause shortcut learning. Especially, the cycle-consistency constraint " + }, + { + "bbox": [ + 304, + 498, + 545, + 605 + ], + "type": "inline_equation", + "content": "L_{cyc}" + }, + { + "bbox": [ + 304, + 498, + 545, + 605 + ], + "type": "text", + "content": " is also a necessary part for PPDM to avoid degenerated solution " + }, + { + "bbox": [ + 304, + 498, + 545, + 605 + ], + "type": "inline_equation", + "content": "(-1.7\\%)" + }, + { + "bbox": [ + 304, + 498, + 545, + 605 + ], + "type": "text", + "content": ", because the feature reconstruction error can be minimized by eliminating all necessary information." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 606, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 606, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 606, + 547, + 715 + ], + "type": "text", + "content": "As shown in Tab. 5, the proposed method is robust to hyperparameter " + }, + { + "bbox": [ + 304, + 606, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\gamma_{3}" + }, + { + "bbox": [ + 304, + 606, + 547, + 715 + ], + "type": "text", + "content": " in Eq. (19). On condition that degenerated solution will not be formed, weakening the constraint makes model restore images from reference with less detail more easily and perceive the position of anomalies more accurately by transforming anomalies to normal patterns which benefits localization task. On the contrary, strengthening the constraint alleviates shortcut learning and improves image-level result by maintaining more abnormal details." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 746, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 746, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 746, + 317, + 757 + ], + "type": "text", + "content": "12153" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 87, + 547, + 149 + ], + "blocks": [ + { + "bbox": [ + 171, + 70, + 420, + 82 + ], + "lines": [ + { + "bbox": [ + 171, + 70, + 420, + 82 + ], + "spans": [ + { + "bbox": [ + 171, + 70, + 420, + 82 + ], + "type": "text", + "content": "Table 2. Image-level " + }, + { + "bbox": [ + 171, + 70, + 420, + 82 + ], + "type": "inline_equation", + "content": "{AUC}\\left( \\% \\right)" + }, + { + "bbox": [ + 171, + 70, + 420, + 82 + ], + "type": "text", + "content": " of anomaly detection on MVTec [2]." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 47, + 87, + 547, + 149 + ], + "lines": [ + { + "bbox": [ + 47, + 87, + 547, + 149 + ], + "spans": [ + { + "bbox": [ + 47, + 87, + 547, + 149 + ], + "type": "table", + "html": "
Class\\MethodsGN [1]PSVDD [37]DAAD [11]CutPaste [17]PaDiM [5]PatchCore [31]DRAEM [38]RD [6]Ours
AvgTextures77.594.591.097.598.899.099.199.599.9
AvgObjects75.590.888.895.593.899.297.498.099.3
AvgAll76.292.189.596.195.599.198.098.599.5
", + "image_path": "f21f680dbc2154c1034b31856994eb1ce3482d09b412c7919f3e8d3fa032a1c9.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 48, + 175, + 546, + 236 + ], + "blocks": [ + { + "bbox": [ + 168, + 157, + 423, + 168 + ], + "lines": [ + { + "bbox": [ + 168, + 157, + 423, + 168 + ], + "spans": [ + { + "bbox": [ + 168, + 157, + 423, + 168 + ], + "type": "text", + "content": "Table 3. Pixel-level " + }, + { + "bbox": [ + 168, + 157, + 423, + 168 + ], + "type": "inline_equation", + "content": "{AUC}\\left( \\% \\right)" + }, + { + "bbox": [ + 168, + 157, + 423, + 168 + ], + "type": "text", + "content": " of anomaly localization on MVtec [2]." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 175, + 546, + 236 + ], + "lines": [ + { + "bbox": [ + 48, + 175, + 546, + 236 + ], + "spans": [ + { + "bbox": [ + 48, + 175, + 546, + 236 + ], + "type": "table", + "html": "
Class\\MethodsPSVDD [37]CutPaste [17]PaDiM [5]PatchCore [31]DRAEM [38]TMAE [34]RD [6]Ours
AvgTextures93.796.396.997.697.993.897.797.8
AvgObjects96.795.897.898.497.094.097.998.3
AvgAll95.796.097.598.197.393.997.898.2
", + "image_path": "1e3ae388c13ff2f6133ae958fb088c11adba560bec1692044312657da557fbe4.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 48, + 297, + 287, + 331 + ], + "blocks": [ + { + "bbox": [ + 46, + 247, + 286, + 291 + ], + "lines": [ + { + "bbox": [ + 46, + 247, + 286, + 291 + ], + "spans": [ + { + "bbox": [ + 46, + 247, + 286, + 291 + ], + "type": "text", + "content": "Table 4. Ablation study of proposed module and loss on Ped2 [27]. From left to right: without PDM; with only one head of PDM " + }, + { + "bbox": [ + 46, + 247, + 286, + 291 + ], + "type": "inline_equation", + "content": "(K = 1)" + }, + { + "bbox": [ + 46, + 247, + 286, + 291 + ], + "type": "text", + "content": "; without memory module; without background template; removing strength constraint; removing smoothness constraint." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 297, + 287, + 331 + ], + "lines": [ + { + "bbox": [ + 48, + 297, + 287, + 331 + ], + "spans": [ + { + "bbox": [ + 48, + 297, + 287, + 331 + ], + "type": "table", + "html": "
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Task\\γ300.10.250.512
Det.97.999.499.499.599.699.4
Loc.96.698.098.298.097.797.6
", + "image_path": "d5aa08139c8bf74464370d59575bffade79b852ddb72a30bc5a743f85f230385.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 419, + 118, + 431 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 419, + 118, + 431 + ], + "spans": [ + { + "bbox": [ + 47, + 419, + 118, + 431 + ], + "type": "text", + "content": "4.6. Discussion" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 437, + 287, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 437, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 287, + 581 + ], + "type": "text", + "content": "Contaminated data assumption. Assuming that training data only contains completely normal data is unrealistic, because the workload of natural data cleansing is considerable, even has same cost as data annotations. We mix training data with abnormal events in Ped2 to simulate contaminated data and find performance drop of MNAD [29] is " + }, + { + "bbox": [ + 46, + 437, + 287, + 581 + ], + "type": "inline_equation", + "content": "-3.7\\%" + }, + { + "bbox": [ + 46, + 437, + 287, + 581 + ], + "type": "text", + "content": " while ours is " + }, + { + "bbox": [ + 46, + 437, + 287, + 581 + ], + "type": "inline_equation", + "content": "-1.8\\%" + }, + { + "bbox": [ + 46, + 437, + 287, + 581 + ], + "type": "text", + "content": ". The reason why DMAD is less affected may be that PDM can encode and transmit residual abnormal representation of mixed anomalies and anomaly-like normal samples, thus strictly maintaining representation compactness of the main encoder and low generalization ability on abnormal samples." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "content": "Two DMAD implementations. As introduced earlier, our DMAD framework is implemented by two versions using PDM and PPDM respectively, corresponding to different detection targets. As shown in Fig. 8, PDM learns measurable quantization error (caused by ICM) from memory embedding to diverse patterns which enhances the potential of ICM to keep intra-class compactness without generating unmeasurable reconstruction loss. Unlike PDM, PPDM is partially in charge of the information compression, i.e. PPDM removes the diverse appearance by using the reverse deformation process from inputs to reference." + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 317, + 245, + 536, + 357 + ], + "blocks": [ + { + "bbox": [ + 317, + 245, + 536, + 357 + ], + "lines": [ + { + "bbox": [ + 317, + 245, + 536, + 357 + ], + "spans": [ + { + "bbox": [ + 317, + 245, + 536, + 357 + ], + "type": "image", + "image_path": "98ff6ab2411d041b029fb61d759369f6cf89beba1530821c6909541d80658b10.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 364, + 545, + 387 + ], + "lines": [ + { + "bbox": [ + 306, + 364, + 545, + 387 + ], + "spans": [ + { + "bbox": [ + 306, + 364, + 545, + 387 + ], + "type": "text", + "content": "Figure 8. Illustration of two DMAD implementations with PDM and PPDM respectively." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 401, + 378, + 414 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 401, + 378, + 414 + ], + "spans": [ + { + "bbox": [ + 306, + 401, + 378, + 414 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 422, + 545, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 422, + 545, + 578 + ], + "spans": [ + { + "bbox": [ + 304, + 422, + 545, + 578 + ], + "type": "text", + "content": "In this paper, we present a reconstruction-based diversity-measurable anomaly detection framework, which simultaneously enhances anomaly discrimination and reconstruction diversity. Pyramid deformation module is proposed to be used together with information compression module for this purpose. PDM models multi-scale transformation fields from reference to original input explicitly without relying on external estimators. Therefore, diverse normal patterns can be reconstructed and anomaly severity can be measured accurately. Empirical studies on both videos and images benchmarks show the effectiveness and applicability of our work. In future research, we will further explore diversity-aware models for anomaly detection." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 591, + 545, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 591, + 545, + 651 + ], + "spans": [ + { + "bbox": [ + 304, + 591, + 545, + 651 + ], + "type": "text", + "content": "Limitations. Our method focuses on anomaly with measurable geometrical diversity, the most common type in anomaly detection. However, as for anomaly with other kind of diversities, e.g. colors, the proposed diversity measure may not be positively correlated to anomaly severity." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgement. This work is partially supported by National Key R&D Program of China (No. 2018AAA0102402), and National Natural Science Foundation of China (NSFC): 61976203 and 62276246." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 747, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 747, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 747, + 317, + 757 + ], + "type": "text", + "content": "12154" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 92, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 53, + 92, + 287, + 146 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 92, + 287, + 146 + ], + "spans": [ + { + "bbox": [ + 53, + 92, + 287, + 146 + ], + "type": "text", + "content": "[1] Samet Akcay, Amir Atapour Abarghouei, and Toby P. 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Conventional AL methods do not consider the existence of domain shift, and hence, fail to identify the truly valuable samples in the context of domain adaptation. To accommodate active learning and domain adaption, the two naturally different tasks, in a collaborative framework, we advocate that a customized learning strategy for the target data is the key to the success of ADA solutions. We present Divide-and-Adapt (DiaNA), a new ADA framework that partitions the target instances into four categories with stratified transferable properties. With a novel data subdivision protocol based on uncertainty and domaininess, DiaNA can accurately recognize the most gainful samples. While sending the informative instances for annotation, DiaNA employs tailored learning strategies for the remaining categories. Furthermore, we propose an informativeness score that unifies the data partitioning criteria. This enables the use of a Gaussian mixture model (GMM) to automatically sample unlabeled data into the proposed four categories. Thanks to the \"divide-and-adapt\" spirit, DiaNA can handle data with large variations of domain gap. In addition, we show that DiaNA can generalize to different domain adaptation settings, such as unsupervised domain adaptation (UDA), semi-supervised domain adaptation (SSDA), source-free domain adaptation (SFDA), etc.", + "bbox": [ + 75, + 366, + 472, + 752 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 78, + 779, + 208, + 793 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Domain adaptation (DA) approaches strive to generalize model trained on a labeled source domain to a target domain with rare annotation [5, 13, 16, 24] by coping with", + "bbox": [ + 75, + 802, + 468, + 845 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/bcfd5e369887bee3927030178c8d339728135c12341d4b5917fc15f93b109b43.jpg", + "image_caption": [ + "Figure 1. The illustration of our proposed Divide-and-Adapt mechanism to divide target samples into different data subsets for customized learning." + ], + "image_footnote": [], + "bbox": [ + 512, + 343, + 878, + 523 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "the domain disparity. Nevertheless, DA methods are significantly outperformed by their supervised counterparts due to the scariness of annotation as demonstrated in [4, 14, 27]. In practice, it is cost-effective to get a moderate amount of target samples labeled to boost the performance of domain adaptation. Active learning (AL) approaches seek to select samples with uncertainty [9, 12, 29, 30] and diversity [19, 25] to best benefit the model, which properly matches the demand. However, previous AL methods assume that both the labeled and unlabeled data follow the same distribution, such a strategy may become ineffective to the DA scenarios where the target data suffer from domain shift. The recently proposed active domain adaptation (ADA) [4, 22, 31] aims to resolve this issue by actively selecting the maximally-informative instances such that the performance of the transferred model can be best boosted with a limited annotation budget.", + "bbox": [ + 497, + 574, + 890, + 809 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The key to the success of ADA is to strike a good balance between the highly coupled yet inherently different tasks: active learning and domain adaptation. The real-world target data typically exhibit either of the two characteristics:", + "bbox": [ + 497, + 811, + 890, + 866 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 129, + 49, + 200, + 84 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 252, + 48, + 791, + 87 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding author is Guanbin Li.", + "bbox": [ + 94, + 852, + 297, + 866 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "7651", + "bbox": [ + 468, + 885, + 500, + 897 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "source-like or target-specific. While the former has similar feature distribution with the source data, the latter tends to be the unique part of target domain and deviates greatly from the source distribution [4, 26, 38]. On one hand, to achieve domain adaptation, applying the same adaptation strategy to all target data equally cannot generalize well to scenarios with varying degrees of domain shift. This is particularly true when the gap between the source-like and target-specific data is unknown. On the other hand, in active learning tasks, the samples with a learning difficulty will be more likely to be selected for labeling. Nonetheless, with large domain gap, incorporating such difficult samples in the adaptation task would hamper the learning of the adaptation model, making the training highly unstable. However, despite the impressive progress that has been made, none of the existing works has fully addressed the above issues.", + "bbox": [ + 75, + 125, + 472, + 347 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we propose Divide-And-Adapt (DiaNA), a novel ADA framework that can scale to large variations of domain gaps while achieving cost-effective data labeling with a significant performance boost for domain adaptation. Our key observation is that customized learning strategies are vital for target data with different characteristics. In particular, DiaNA divides the target data into four subsets with different levels of transferable properties (see Figure 1), each of which is handled with a customized learning strategy. Unlike traditional AL methods that would simply label the most uncertain data [29, 30, 37], we propose to withhold the most challenging samples (Figure 1 category (4)) for training the domain adaption models. Instead, the selected samples for active annotation would maintain a proper stimulus for the source model, providing informative domain knowledge without jeopardizing the training stability. The subdivision of target data is dynamically updated as the domain disparity is gradually mitigated with more labeled data. Hence, the previous challenging samples could be classified as transferable in the later stage and exploited in the network training.", + "bbox": [ + 75, + 350, + 472, + 642 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We introduce a novel protocol for subdividing the target samples for customized learning. In addition to the uncertainty of model prediction, we advocate that the consistency with the learned prior distribution, i.e. the domainness, is another key criterion for active domain adaptation [4, 26]. To this end, we divide the target data into four categories as shown in Figure 1 according to the domainness and uncertainty of the instances. We further propose that the samples with 1) being uncertain to the model and 2) having inconsistent prediction with the label of its closest category prototype in the learned feature space (i.e. high domainness) are the most \"profitable\" instances for bringing informative knowledge of target domain if annotated. Thereby, we identify the uncertain inconsistent samples for labeling while applying tailored learning strategies for the remaining categories to boost the selectivity of the sampling.", + "bbox": [ + 75, + 644, + 472, + 866 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To avoid heuristic thresholding for data subdivision, we propose an automatic data sampling mechanism based on Gaussian mixture model (GMM). In particular, we propose an informativeness function that incorporates the domainness and uncertainty in a unified scoring system. The computed informativeness score of the labeled data is used to train a four-component GMM model, which is then applied to sample the unlabeled target data into four categories.", + "bbox": [ + 497, + 125, + 890, + 236 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We evaluate DiaNA over a large variety of domain shift scenarios on DomainNet [21], Office-Home [28] and CIFAR-10 [11]. Furthermore, the proposed sampling strategy of DiaNA can be generalized to various domain adaptation problems with different supervision settings, including unsupervised domain adaptation (UDA), semi-supervised domain adaptation (SSDA), and source-free domain adaptation (SFDA).", + "bbox": [ + 497, + 236, + 892, + 346 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We summarize our contributions as follows:", + "bbox": [ + 517, + 347, + 811, + 359 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- A general \"divide-and-adapt\" framework, coded DiaNA, for active domain adaptation that can handle diversified degrees of domain gaps while being able to generalize to different domain adaptation problems, including UDA, SSDA, and SFDA.", + "- A new target data partition strategy based on domaininess and uncertainty that enables stratified learning to achieve more stable training, superior adaptation performance, and better generality.", + "- A novel informativeness scoring system and the corresponding sampling paradigm based on GMM model for automatic data partitioning.", + "- New state-of-the-art performance over the mainstream public datasets in the task of active domain adaptation." + ], + "bbox": [ + 515, + 362, + 890, + 561 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 499, + 580, + 640, + 593 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Domain adaptation (DA). Most of the prior methods involving domain adaptation follow the unsupervised domain adaptation (UDA) paradigm that only unlabeled data is accessible in the target domain. Early UDA approaches [16, 18, 32] utilized maximum mean discrepancy (MMD) to minimize the discrepancy of features from different domains to address the domain shift, while recent adversarial learning based methods [5, 17] have become popular solutions for UDA. Despite effectiveness, UDA is still significantly outperformed by its supervised variant as indicated in [4, 14, 27]. Semi-supervised domain adaptation (SSDA) [13, 24, 35] allows a few target instances to be labeled and generally achieves improved performance. However, SSDA assumes that the labeled instances are passively provided in advance, depriving the choice of informative samples beneficial to the model. In this work, we propose an active domain adaption method to select the most informative samples, which can be incorporated into other DA methods to further boost their performance.", + "bbox": [ + 497, + 603, + 890, + 866 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "7652", + "bbox": [ + 468, + 885, + 500, + 897 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/20d6a4f16aa87216c84fb34818c4095c959ca3d727ad9bacb0dcdd697bb1e382.jpg", + "image_caption": [ + "Figure 2. We propose a general \"divide-and-adapt\" framework, named DiaNA, for active domain adaptation. (a) A new target data partition strategy is presented to divide target data into four categories via building an informativeness scoring function that incorporates both domainness and uncertainty metrics. Besides, an automatic data partitioning function based on a learned four-component GMM model is applied to adaptively separate four sample categories from unlabeled target data. (b) To achieve customized learning, different auxiliary techniques are integrated into model fine-tuning w.r.t the four categories of unlabeled target data." + ], + "image_footnote": [], + "bbox": [ + 146, + 124, + 821, + 304 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Active Learning (AL). Active learning is proposed to select a maximally-informative subset of unlabeled data for annotation via a query function, in an effort to best improve the model performance with a limited annotation budget. There exist several efforts to tackle the challenges involving active learning. For example, the uncertainty-based AL methods mainly focus on designing query functions based on prediction confidence [30], entropy [9, 29], or margin [10, 23] of the posterior probabilities. On the other hand, the diversity-based approaches [6, 19, 25] concentrate on selecting samples that can well represent the entire dataset. Meanwhile, expected model change-based methods [3, 15] aim to query the instances that would lead to a significant change to the current model. Recently proposed active learning approaches attain better performance by utilizing hybrid strategies which taking multiple metrics into consideration [1, 20]. Notwithstanding, the efficacy of previous AL resources may falter in DA scenarios as their selection strategy fails to meticulously consider the implications of the domain gap.", + "bbox": [ + 75, + 383, + 472, + 660 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Active Domain Adaptation (ADA). Early ADA researches [4,26] propose to measure the uncertainty and domaininess of each target instance via a domain discriminator with adversarial training. CLUE [22] presents an entropy-weighted clustering algorithm to query uncertain and diverse samples in the target domain. Recently, SDM [33] is proposed to optimize a margin loss function for exploring target instances similar to potential hard samples in the source domain. Nevertheless, the majority of existing ADA methods deliberately design hand-crafted query functions to evaluate sample's annotation value and apply the same adaptation strategy to all target data equally [4,26,31]. The rigid criteria make them easily overfit to certain domain adaption scenarios, which limits the generalization of the", + "bbox": [ + 75, + 672, + 472, + 866 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "method. In contrast, we propose to integrate uncertainty and domainness metrics within a unified scoring function to select informative samples. Moreover, we apply tailored learning strategies for target data with different characteristics, constructing an effective framework capable of generalizing across large variations of domain shifts.", + "bbox": [ + 497, + 383, + 890, + 467 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Divide-and-Adapt Framework", + "text_level": 1, + "bbox": [ + 497, + 480, + 779, + 498 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Problem formulation. Active domain adaptation aims at seeking an optimal model for a target domain when given labeled source data $S = \\{(x_s, y_s)\\}$ as well as unlabeled target data $\\mathcal{U} = \\{x_u\\}$ , assisted by the iteratively queried labeled data $\\mathcal{T} = \\{(x_t, y_t)\\}$ of the target domain. Here, $S, \\mathcal{U},$ and $\\mathcal{T}$ share the same label space over $C$ categories. Initially, $\\mathcal{T}$ is an empty set. The model is iteratively trained using $S, \\mathcal{T},$ and $\\mathcal{U}$ for $R$ active learning loops until a given annotation budget $B$ is reached. In each active learning loop, $b = B / R$ samples from $\\mathcal{U}$ would be selected, labeled by human experts, and then moved into $\\mathcal{T}$ . The proposed Divide-and-Adapt framework consists of a feature extractor and a classifier. Our goal is to design a query function to identify informative samples to annotate and utilize limited amount of labeled samples to best enhance the classification performance for the target domain.", + "bbox": [ + 497, + 505, + 890, + 726 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Overview. In this paper, we propose Divide-And-Adapt, coded DiaNA, to tackle the problem of active domain adaptation. In detail, we first propose to design an informativeness function for subdividing the target samples into four categories, one of which is the informative target samples used for actively annotating. Such a function is a unified scoring system that incorporates the domainness and the uncertainty. To avoid heuristic thresholding for data subdivision, we propose an automatic data sampling mechanism to divide the unlabeled target data into four", + "bbox": [ + 497, + 728, + 892, + 866 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "7653", + "bbox": [ + 468, + 885, + 500, + 897 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/56fa990c17f659cb8dfda4a2e61e1bb7d6e5bdccba44bcf853a1c98adfbc0b73.jpg", + "image_caption": [ + "Figure 3. (a) Source-like target samples are more likely to be close to the source centroid in the feature space with respect to its predicted category. (b) Target-specific target samples are prone to be inconsistent between model predictions and similarity-based labels." + ], + "image_footnote": [], + "bbox": [ + 102, + 127, + 442, + 267 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "sample categories. This is achieved by learning a four-component Gaussian mixture model using semi-supervised Expectation-Maximization algorithm. Finally, we design tailored learning strategies for different categories of target samples during model fine-tuning, thus further improving the model performance. The overview of the proposed algorithm has been summarized in Figure 2.", + "bbox": [ + 75, + 344, + 468, + 441 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1. Informativeness Scoring Mechanism", + "text_level": 1, + "bbox": [ + 75, + 450, + 391, + 465 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Following previous ADA works [4, 26, 31], we aim to search for the target instances with high domainness and uncertainty. To achieve this goal, we propose to first estimate category-wise centroids based on the labeled samples, and then define a similarity-based label for each unlabeled target sample by computing its top- $k$ feature similarity with the categorical centroids. Finally, we integrate both the domainness and the uncertainty metrics into an informativeness function, which is formulated as the consistency between model prediction and similarity-based label.", + "bbox": [ + 75, + 470, + 468, + 609 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Categorical centroids. We propose to average the features of labeled samples to estimate the category-specific data distribution, i.e., category prototype. Here, we formulate the centroid with respect to the $c$ -th category as follows,", + "bbox": [ + 75, + 625, + 468, + 681 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nA ^ {c} = \\frac {\\sum_ {(x , y) \\in \\mathcal {S}} \\mathbb {1} \\{y = c \\} \\cdot G (x)}{\\sum_ {(x , y) \\in \\mathcal {S}} \\mathbb {1} \\{y = c \\}}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 688, + 468, + 725 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbb{1}\\{\\cdot\\}$ is an indicator function, and $G(x)$ is a feature extractor that outputs the sample feature of $x$ . Note that, as the active learning loops proceed, labeled target samples would be incorporated into the calculation of categorical centroids to mitigate the impact of distribution change.", + "bbox": [ + 75, + 733, + 468, + 804 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Similarity-based data label. As introduced in the works [7, 13], samples share more top- $k$ indices in their respective lists of rank-ordered feature elements would have a higher probability of being the same category. To obtain the", + "bbox": [ + 75, + 809, + 468, + 866 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "similarity-based label for each target instance, we first measure pairwise similarity of the indices of the sorted feature elements based on the magnitude. Then, we can formulate a similarity-based label for a sample $x$ from $\\mathcal{U}$ as follows,", + "bbox": [ + 497, + 125, + 890, + 181 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\ddot {y} (x) = \\underset {1 \\leq c \\leq C} {\\operatorname {a r g m a x}} \\mathbf {I o U} (\\operatorname {t o p} k (G (x)), \\operatorname {t o p} k \\left(A ^ {c}\\right)), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 542, + 190, + 890, + 214 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathrm{top}k(\\cdot)$ computes the top- $k$ feature element indices ranked according to their magnitudes. In addition, $\\mathbf{IoU}(\\cdot ,\\cdot)$ denotes an Intersection-over-Union function, which returns the extent of overlap of the two respective index lists.", + "bbox": [ + 497, + 223, + 890, + 277 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We set the value of $k$ to be significantly smaller than the full dimension of the feature vector. In this way, the function $\\mathrm{top}k(\\cdot)$ only extracts the principle components of the feature of sample. Therefore, the IoU function in Eq. 2 is equivalent to measuring pairwise image sample similarity under a low-resolution condition. In ADA tasks, the training of model is inevitably dominated by the source domain especially in the early stage [33]. Therefore, source-like target samples that are similar to the source domain would naturally have more accurate representation than the target-specific ones that are distinct from the source. Under the low-resolution condition, i.e., $k$ set to be small, source-like samples tend to have the same similarity-based label as the model predicted class thanks to their reliable and discriminative features extracted by the model. In contrast, target-specific samples are prone to produce inconsistent results since they are typically underfitted by the current model as shown in Figure 3. Based on the analysis above, we utilize the consistency of the model predicted class and similarity-based label to evaluate the domainness of each target sample. Detailed theoretical and experimental supports are demonstrated in our supplementary.", + "bbox": [ + 497, + 279, + 890, + 583 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Informativeness function. To explore the most informative target samples, we integrate the domainness and uncertainty into a unified informativeness function (InfoF). The informativeness score for a sample $x$ from unlabeled target domain can be formulated as follows,", + "bbox": [ + 497, + 590, + 890, + 657 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\ell_ {u} (x) = - \\sum_ {c = 1} ^ {C} \\mathbb {1} \\{c = \\ddot {y} (x) \\} \\cdot \\log P _ {c} (x), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 559, + 667, + 890, + 705 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $P(x)$ denotes the probabilistic prediction of a sample $x$ from the network model and $P_{c}(x)$ is the $c$ -th element of the vector $P(x)$ . According to Eq. 3, we can divide unlabeled target samples into two subsets depending on whether the model predicted class and the similarity-based label are identical: consistent and inconsistent subsets, while both sets have confident samples and uncertain samples depending on whether the predicted probability is greater than a given confidence threshold. We name these four categories of unlabeled target data as confident-consistent (CC), uncertain-consistent (UC), uncertain-inconsistent (UI) and", + "bbox": [ + 497, + 713, + 890, + 866 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "7654", + "bbox": [ + 468, + 885, + 500, + 897 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Algorithm 1: The training procedure of four-component Gaussian Mixture Model (GMM) using semi-supervised Expectation-Maximization", + "bbox": [ + 84, + 128, + 423, + 169 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Input: $\\mathcal{D}_L;\\mathcal{D}_U;\\alpha$", + "bbox": [ + 97, + 172, + 228, + 186 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Output: Optimal GMM parameters $\\mathcal{W}$", + "bbox": [ + 97, + 186, + 357, + 199 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1 Initialize $\\mathcal{W} = \\{(\\pi_k,\\mu_k,\\sigma_k)|1\\leq k\\leq K\\}$ using $\\mathcal{D}_L$ via Bayes estimation.", + "2 while $\\mathcal{W}$ is not converged do", + "3 $\\{(\\ell_g^i,p_g^i)\\}_{i = 1}^{|\\mathcal{D}_L|}\\gets \\mathcal{D}_L$", + "4 $\\{(\\ell_u^i),\\})_{j = 1}^{|\\mathcal{D}_U|}\\gets \\mathcal{D}_U$", + "//Estep:", + "5 $\\gamma_{gk}(\\ell_g^i) = \\mathbb{1}\\{p_g^i = k\\} ,$", + "6 $\\gamma_{uk}(\\ell_u^j) = \\frac{\\pi_k\\mathcal{N}(\\ell_u^j;\\mu_k,\\sigma_k)}{\\sum_{k' = 1}^{K}\\pi_{k'}\\mathcal{N}(\\ell_u^j;\\mu_{k'}\\sigma_{k'})},$", + "//Mstep:", + "7 $\\pi_{k} = \\frac{\\alpha\\sum_{i}\\gamma_{gk}(\\ell_{g}^{i}) + (1 - \\alpha)\\sum_{j}\\gamma_{uk}(\\ell_{u}^{j})}{\\alpha|\\mathcal{D}_{L}| + (1 - \\alpha)|\\mathcal{D}_{U}|};$", + "8 $\\mu_{k} = \\frac{\\alpha\\sum_{i}\\gamma_{gk}(\\ell_{g}^{i})\\cdot\\ell_{g}^{i} + (1 - \\alpha)\\sum_{j}\\gamma_{uk}^{j}\\cdot\\ell_{u}^{j}}{\\alpha\\sum_{i}\\gamma_{gk}(\\ell_{g}^{i}) + (1 - \\alpha)\\sum_{j}\\gamma_{uk}(\\ell_{u}^{j})};$", + "9 $\\sigma_{k} =$" + ], + "bbox": [ + 84, + 200, + 436, + 399 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {\\alpha \\sum_ {i} \\gamma_ {g k} (\\ell_ {g} ^ {i}) \\cdot (\\ell_ {g} ^ {i} - \\mu_ {k}) ^ {2} + (1 - \\alpha) \\sum_ {j} \\gamma_ {u k} \\cdot (\\ell_ {u} ^ {j}) (\\ell_ {u} ^ {j} - \\mu_ {k}) ^ {2}}{\\alpha \\sum_ {i} \\gamma_ {g k} (\\ell_ {g} ^ {i}) + (1 - \\alpha) \\sum_ {j} \\gamma_ {u k} (\\ell_ {u} ^ {j})};\n$$\n", + "text_format": "latex", + "bbox": [ + 132, + 400, + 447, + 427 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "confident-inconsistent (CI), respectively. In this way, samples that are both uncertain to the model and contain target-specific knowledge can be extracted based on the InfoF score. In next section, we devise a strategy for informative sampling to adaptatively distinguish those subsets from unlabeled target samples.", + "bbox": [ + 75, + 461, + 468, + 545 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2. Informative Sampling Function", + "text_level": 1, + "bbox": [ + 75, + 553, + 354, + 568 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "During training, the varying scale of InfoF scores obtained above would hinder accurate data categorization using manual data division, leading to a biased sampling strategy and degraded performance. Therefore, our work here formulates an Informative Sampling Function to achieve the goal of adaptively selecting informative target samples. In general, it can be observed that the four categories of unlabeled target data as stated above are significantly separable in the distributions of the InfoF scores, making it possible to learn mixture models to separate four sample partitioning from unlabeled target data. Thereafter, by learning the distribution of InfoF scores using a four-component Gaussian mixture model (GMM), the target data can be adaptively mapped to the probability distribution of four categories and then be separated, thereby avoiding sampling bias that may be created by manual division.", + "bbox": [ + 75, + 576, + 468, + 796 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In specific, we first take inspiration from [34] that labeled samples can be used to construct supervision information, therefore building a more trustworthy GMM model with $K$ Gaussian components (namely $K = 4$ in this work) via a semi-supervised Expectation-Maximization al", + "bbox": [ + 75, + 796, + 468, + 866 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "gorthm. To this end, we then calculate the InfoF score for a labeled sample with $(x,y)$ from $S$ or $\\mathcal{T}$ as follows,", + "bbox": [ + 497, + 125, + 890, + 153 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\ell_ {g} (x, y) = - \\sum_ {c = 1} ^ {C} \\mathbb {1} \\{c = y \\} \\cdot \\log P _ {c} (x). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 563, + 161, + 890, + 199 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The similarity-based label is determined using categorical centroids of the labeled data, resulting in the totally identical similarity-based label and model prediction for labeled samples. In order to obtain reliable supervision and build a better GMM model, we have replaced the similarity-based label with the ground-truth class label here.", + "bbox": [ + 497, + 206, + 890, + 289 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Afterwards, to obtain the supervision information for training GMM, we here define a piecewise function to obtain the observation labels that assign all labeled samples across domains to the corresponding Gaussian components. Thus, the observation label of a candidate instance $x$ can be computed as,", + "bbox": [ + 497, + 290, + 890, + 372 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nq (x, y) = \\left\\{ \\begin{array}{l l} 1, & \\max P (x) \\geq \\tau \\text {a n d} y = \\arg \\max P (x), \\\\ 2, & \\max P (x) < \\tau \\text {a n d} y = \\arg \\max P (x), \\\\ 3, & \\max P (x) < \\tau \\text {a n d} y \\neq \\arg \\max P (x), \\\\ 4, & \\max P (x) \\geq \\tau \\text {a n d} y \\neq \\arg \\max P (x), \\end{array} \\right. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 497, + 380, + 890, + 448 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where the numbers, i.e., $k = 1,\\dots ,4$ , indicate the indices of different Gaussian components corresponding to the CC, UC, UI and CI sample subsets, respectively. As well, $\\tau$ is a confidence threshold to classify labeled samples into the confident subset and the uncertain subset. Furthermore, the comparison between the ground-truth and predicted class labels is used to divide them into the consistent subset and the inconsistent subset of labeled training samples.", + "bbox": [ + 497, + 450, + 890, + 559 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Once we obtain $\\{\\ell_g(x,y)|(x,y)\\in S\\cup \\mathcal{T}\\}$ $\\{\\ell_u(x)|x\\in$ $\\mathcal{U}\\}$ , and $q(x,y)$ , we incorporate them into building training instances for learning the GMM model as follows,", + "bbox": [ + 497, + 560, + 890, + 600 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {D} _ {L} \\leftarrow \\left\\{\\left(\\ell_ {g} (x, y), q (x, y)\\right) | (x, y) \\in \\mathcal {S} \\cup \\mathcal {T} \\right\\}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 546, + 612, + 890, + 628 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {D} _ {U} \\leftarrow \\left\\{\\left(\\ell_ {u} (x),\\right) \\mid x \\in \\mathcal {U} \\right\\}. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 606, + 638, + 890, + 654 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For convenience, we denote the GMM model by $\\mathcal{W} = \\{(\\pi_k,\\mu_k,\\sigma_k)|1\\leq k\\leq K\\}$ . Afterwards, given a training instance $\\ell_{x}$ from $\\mathcal{D}_L$ or $\\mathcal{D}_U$ , the output of the probability density functions of the GMM model regarding $\\ell_{x}$ can be computed as", + "bbox": [ + 497, + 660, + 890, + 730 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\np \\left(\\ell_ {x}\\right) = \\sum_ {k = 1} ^ {K} \\pi_ {k} \\mathcal {N} \\left(\\ell_ {x}; \\mu_ {k}, \\sigma_ {k}\\right), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 591, + 737, + 890, + 775 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\pi_{k}$ represents the weight of the $k$ -th Gaussian component subject to $\\sum_{k=1}^{K} \\pi_{k} = 1$ and $0 \\leq \\pi_{k} \\leq 1$ for $k = 1, \\dots, K$ , while $\\mu_{k}$ and $\\sigma_{k}$ are vectors denoting the mean and variance of such a component. Here, $\\mathcal{N}(\\cdot; \\mu_{k}, \\sigma_{k})$ is used to model the Gaussian distribution of the $k$ -th component. Note that a given coefficient $\\alpha = |\\mathcal{D}_{L}| / |\\mathcal{D}_{U}|$ is", + "bbox": [ + 497, + 783, + 890, + 866 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "7655", + "bbox": [ + 468, + 885, + 500, + 897 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "used for the weighted integration of the labeled and unlabeled training instances. Thus, we can summarize the training procedure of the GMM model using a semi-supervised EM algorithm in Algorithm 1 according to [34].", + "bbox": [ + 75, + 125, + 468, + 181 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "After obtaining the trained GMM parameters $\\mathcal{W}$ , the probability of a sample $x$ from $\\mathcal{U}$ being classified into the $k$ -th component can be computed as follows,", + "bbox": [ + 75, + 182, + 468, + 223 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\Pr (z = k | x, \\mathcal {W}) = \\frac {\\pi_ {k} \\mathcal {N} \\left(\\ell_ {u} (x) ; \\mu_ {k} , \\sigma_ {k}\\right)}{\\sum_ {k ^ {\\prime} = 1} ^ {K} \\pi_ {k ^ {\\prime}} \\mathcal {N} \\left(\\ell_ {u} (x) ; \\mu_ {k ^ {\\prime}} , \\sigma_ {k ^ {\\prime}}\\right)}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 95, + 233, + 468, + 268 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $z$ is a discrete variable to infer which component the sample $x$ belongs to.", + "bbox": [ + 75, + 277, + 468, + 306 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.3. Candidate Selection and Training Objectives", + "text_level": 1, + "bbox": [ + 75, + 315, + 455, + 331 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "After acquiring the informativeness sampling function, it is utilized for carrying out data partitioning. For ADA, the main focus should be on annotating samples that are uncertain to the model and can effectively represent the target dataset, which is termed as uncertain-inconsistent samples within our subdivision framework. Therefore, during each sampling step, we first rank the unlabeled target samples in descending order according to the scores predicted by $\\operatorname{Pr}(z = 3|\\cdot ,\\mathcal{W})$ and then the top $b$ examples are selected to annotate and moved into labeled target data. Following previous ADA works, we apply the standard cross-entropy loss to the labeled data as follows:", + "bbox": [ + 75, + 338, + 468, + 503 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {s u p} = \\underset {(x, y) \\sim \\mathcal {S} \\cup \\mathcal {T}} {\\mathbb {E}} \\left[ - \\sum_ {c = 1} ^ {C} \\mathbb {1} \\{c = y \\} \\cdot \\log P _ {c} (x) \\right]. \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 92, + 514, + 468, + 551 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To boost the selectivity of the sampling strategy, we further design tailored training techniques for the other data subsets with varied transferable properties. We perform data partitioning on the remaining unlabeled target samples, i.e., $\\mathcal{U}\\gets \\mathcal{U}\\backslash \\mathcal{T}$ , according to the posterior probabilities regarding the rest of Gaussian components.", + "bbox": [ + 75, + 562, + 468, + 644 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathcal {U}} _ {k} = \\{x \\mid \\arg \\max \\mathbf {P r} (x) = k, \\forall (x,) \\in \\mathcal {U} \\}, \\text {f o r} k = 1, 2, 4, \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 77, + 656, + 467, + 684 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\hat{\\mathcal{U}}_1, \\hat{\\mathcal{U}}_2$ and $\\hat{\\mathcal{U}}_4$ refer to $\\hat{\\mathcal{U}}_{\\mathrm{CC}}, \\hat{\\mathcal{U}}_{\\mathrm{UC}}, \\hat{\\mathcal{U}}_{\\mathrm{CI}}$ . Here, $\\mathbf{Pr}(x)$ is the concatenated probability vector corresponding to different components, i.e., $\\mathbf{Pr}(x) = [\\operatorname{Pr}(z = 1|x, \\mathcal{W}), \\operatorname{Pr}(z = 2|x, \\mathcal{W}), \\operatorname{Pr}(z = 3|x, \\mathcal{W}), \\operatorname{Pr}(z = 4|x, \\mathcal{W})]$ w.r.t the sample $x$ .", + "bbox": [ + 75, + 685, + 468, + 752 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As shown in Figure 1(4), the source-oriented model could produce confident but unreliable predictions for some target samples having large domain gap with the source. Samples from $\\hat{\\mathcal{U}}_{\\mathrm{CI}}$ have extremely controversial results between model prediction and similarity-based label, which are most likely to be some excessively challenging instances. Therefore, we withhold them in the current stage to avoid jeopardizing the training stability.", + "bbox": [ + 75, + 755, + 468, + 866 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The samples in $\\hat{\\mathcal{U}}_{\\mathrm{CC}}$ have confident and reliable predictions, which tend to be some class centroid in the target feature space. Therefore, we apply consistency regularization to them to enforce the prediction consistency under different perturbations, which can be formulated as follows:", + "bbox": [ + 497, + 125, + 890, + 195 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {c o n} = \\underset {(x, \\cdot) \\sim \\hat {\\mathcal {U}} _ {\\mathrm {C C}}} {\\mathbb {E}} \\left[ - \\sum_ {c = 1} ^ {C} \\mathbb {1} \\{c = \\ddot {y} (x) \\} \\cdot \\log P _ {c} (\\mathbf {A u g} (x)) \\right], \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 505, + 209, + 890, + 258 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathbf{Aug}(\\cdot)$ is a function to create perturbations for the sample $x$ using classic data augmentation techniques such as AutoAugment [2].", + "bbox": [ + 497, + 258, + 890, + 300 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For data group $\\hat{\\mathcal{U}}_{\\mathrm{UC}}$ whose prediction tend to be reliable but uncertain, we directly minimize the entropy of the predictions to using the following conditional entropy loss:", + "bbox": [ + 497, + 302, + 890, + 343 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {e n t} = \\underset {(x, \\cdot) \\sim \\hat {\\mathcal {U}} _ {U C}} {\\mathbb {E}} \\left[ - \\sum_ {c = 1} ^ {C} P _ {c} (x) \\log P _ {c} (x) \\right]. \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 537, + 357, + 890, + 395 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In summary, the overall loss functions used to further optimize the model can be formulated as follows,", + "bbox": [ + 499, + 410, + 890, + 438 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {\\text {s u p}} + \\lambda_ {c} \\mathcal {L} _ {\\text {c o n}} + \\lambda_ {e} \\mathcal {L} _ {\\text {e n t}} \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 591, + 453, + 890, + 467 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\lambda_{c}$ and $\\lambda_{e}$ are the weights to trade off different loss terms during the training process. As shown in Figure 2, $\\mathcal{L}_{sup}$ can calibrate the potentially underfitting of uncertain and target-specific samples. $\\mathcal{L}_{con}$ can guide the model to learn global cross-domain clustering while $\\mathcal{L}_{ent}$ serves to minimize the distance of data from the same class. As demonstrated in Sec. 4.3, these training objectives are complementary to each other to best adapt the model to the target domain.", + "bbox": [ + 497, + 482, + 890, + 606 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.4. Compatibility with UDA/SSDA/SFDA", + "text_level": 1, + "bbox": [ + 499, + 622, + 823, + 636 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The proposed sampling strategy of DiaNA requires no additional network modules like a domain discriminator or multiple classifiers [4, 26], making it easy to be integrated into existing DA frameworks, such as unsupervised domain adaptation (UDA), semi-supervised domain adaptation (SSDA), and source-free domain adaptation (SFDA); see supplementary document for the implementation details. It should be noted that we further design a variant of DiaNA for the SFDA settings, due to the unavailability of source data. As evidenced by Sec. 4.3, when integrated into diverse DA techniques, the proposed sampling strategy can deliver more performance improvement than random sample selection, thereby demonstrating its compatibility in various DA settings. To the best of our knowledge, we are the first to propose an active selection strategy that can generalize to UDA, SSDA, and SFDA methods.", + "bbox": [ + 497, + 644, + 890, + 866 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "7656", + "bbox": [ + 468, + 885, + 500, + 897 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/131967745c0a90a3cd5a97ff67487878e911cf50028c81acd62c0a296c24ee30.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodR → CC → SS → PC → QR → SR → PAVG
1k2k5k1k2k5k1k2k5k1k2k5k1k2k5k1k2k5k1k2k5k
Random50.955.261.542.644.849.441.044.450.126.333.243.038.240.746.946.548.853.740.944.550.8
CONF48.654.261.341.943.648.041.644.248.525.532.742.836.939.445.347.147.851.240.343.649.5
Entropy [29]48.054.261.942.745.248.941.143.748.724.631.042.137.040.445.746.548.452.240.043.849.9
Coreset [25]49.152.559.840.642.245.839.141.544.824.730.339.736.738.343.345.146.850.339.241.947.3
BADGE [1]51.755.462.543.645.750.142.345.549.726.034.343.937.841.547.848.050.154.241.645.451.4
Alpha [20]52.056.362.844.346.850.541.944.949.727.234.644.438.641.347.947.650.453.241.945.751.4
AADA [26]50.856.364.742.845.751.041.845.650.825.231.340.838.541.749.546.549.755.140.945.152.0
SDM [33]51.055.462.343.145.249.641.944.949.326.935.043.837.340.246.547.449.753.241.345.150.8
EADA [31]51.556.163.944.246.351.743.846.150.327.534.842.939.041.546.448.650.454.142.445.951.2
CLUE [22]54.159.466.045.348.753.744.048.053.228.835.543.240.444.451.150.052.756.443.848.153.9
DiaNA(Ours)55.660.468.747.050.856.644.249.055.430.239.552.142.447.955.050.553.659.145.050.257.8
", + "bbox": [ + 80, + 123, + 889, + 251 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/6f2d1d60e3a89901dc9c88d28a1f9affebb1a538c803b284f1d80fd4e0516255.jpg", + "table_caption": [ + "Table 1. Comparison results (Accuracy: %) on DomainNet with 1k, 2k and 5k labeling budgets. \"Random\" and \"CONF\" correspond to the classic AL approaches \"Random Sampling\" and \"Least-Confidence Sampling\"." + ], + "table_footnote": [], + "table_body": "
MethodOffice-Home
A → CA → PA → RC → AC → PC → RP → AP → CP → RR → AR → CR → PAVG
Random52.574.377.456.369.768.957.750.975.870.054.681.365.8
Entropy [29]51.372.776.461.774.172.957.651.176.669.857.182.367.0
Coreset [25]52.873.375.559.873.470.858.152.675.869.356.582.566.7
BADGE [1]57.275.276.961.577.271.960.453.678.070.861.184.369.0
Alpha [20]57.079.478.261.678.074.158.954.278.171.761.184.669.7
AADA [26]56.678.179.058.573.771.060.153.177.070.657.084.568.3
CLUE [22]58.079.177.061.378.073.160.455.977.970.960.384.169.7
TQS [4]58.681.181.561.176.173.361.254.779.773.458.986.170.5
SDM [33]61.282.282.766.177.976.166.158.481.076.062.587.073.1
EADA [31]63.684.483.570.783.780.573.063.585.278.465.488.676.7
DiaNA(Ours)64.586.084.972.384.682.573.363.785.678.567.289.577.7
", + "bbox": [ + 99, + 288, + 867, + 434 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Comparison results (Accuracy: %) on Office-Home with $5\\%$ labeling budget.", + "bbox": [ + 226, + 435, + 739, + 448 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 75, + 454, + 208, + 469 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.1. Dataset", + "text_level": 1, + "bbox": [ + 77, + 478, + 171, + 491 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We validate the effectiveness of the proposed approach DiaNA on three standard benchmark datasets: DomainNet [21], Office-Home [28] and CIFAR-10 [11]. On DomainNet, we select five domains namley Real (R), Clipart (C), Sketch (S), Painting (P), and Quikdraw (Q), while we hire these domains to construct 6 adaptation scenarios. As in [4, 31, 33], we report 12 different adaptation scenarios on Office-Home, constructed from four domains: Real (R), Clipart (C), Art (A), and Product (P). To further evaluate the generalization of the proposed sample selection strategy, we additionally report the classification results on CIFAR-10 with a standard active learning setting.", + "bbox": [ + 75, + 500, + 468, + 667 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Implementation", + "text_level": 1, + "bbox": [ + 75, + 676, + 236, + 691 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Here, we mainly focus on the detailed descriptions of the settings involving active learning on DomainNet, OfficeHome, and CIFAR-10, while more implementation details can be found in the supplementary material. In each adaptation scenario, we report the average accuracy over 3 trials.", + "bbox": [ + 75, + 699, + 468, + 768 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "DomainNet. Similar to CLUE [22], we consider ResNet-34 [8] as the network backbone, where such network model is pre-trained on all labeled source samples over 50 training epochs through standard supervision. In all adaptation cases, we set $B = 5000$ and $R = 10$ .", + "bbox": [ + 75, + 769, + 468, + 836 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Office-Home. To be fair, we follow the experimental settings of existing ADA works [4, 31, 33] to conduct", + "bbox": [ + 75, + 838, + 468, + 866 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "performance comparison. In particular, we also use ResNet-50 [8] as the backbone model, while we choose a $5\\%$ proportion of unlabeled target data to set the labeling budget $B$ , and $R$ is set to 5.", + "bbox": [ + 497, + 456, + 890, + 510 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "CIFAR-10. On this dataset, we select ResNet-34 [8] as the backbone model. We randomly choose select $10\\%$ training samples at random as the initially labeled data set, and we then annotate $4\\%$ at each sampling step with a total annotation budget $30\\%$ .", + "bbox": [ + 497, + 511, + 890, + 580 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Main Results", + "text_level": 1, + "bbox": [ + 499, + 592, + 636, + 606 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results on DomainNet and Office-Home. We summarize the comparison with baselines in Table 1 and Table 2 on both datasets respectively. Note that we consider varying label budgets, namely i.e., 1k, 2k, and 5k, on DomainNet. We can see that DiaNA achieves the highest average accuracy in all cases on both datasets for solving the ADA tasks. Especially in the most difficult adaptation scenarios, e.g., $\\mathrm{C} \\rightarrow \\mathrm{A}$ and $\\mathrm{R} \\rightarrow \\mathrm{C}$ , on Office-Home, the proposed method can still exceed all the other methods by more than $1.6\\%$ and $1.8\\%$ respectively, demonstrating the effectiveness of DiaNA on the commonly used DA benchmark datasets.", + "bbox": [ + 497, + 615, + 890, + 767 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results on CIFAR-10. We also extend the proposed method to standard AL tasks on CIFAR-10, where the domain gap between labeled and unlabeled ones is minor. Figure 4(a) lists the comparisons of DiaNA against classic AL strategies involving [1, 20, 25, 29]. It can be observed that compared to classic AL algorithms, with fewer labeling budgets, the effect of the proposed method is still notice", + "bbox": [ + 497, + 769, + 890, + 866 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "7657", + "bbox": [ + 468, + 885, + 500, + 897 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6c40e6776152b9f71cc6483d832a9524546a5744ffbf1190a42c04ab29760f6b.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 131, + 123, + 329, + 231 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/58165b18c7ff42a478d960ffe659a9109ca8a281ecadafa211cfd737796c6e71.jpg", + "image_caption": [ + "(b)", + "Figure 4. (a) Comparison results on CIFAR-10. (b) Combination with UDA/SSDA methods. (c) Combination with SFDA methods." + ], + "image_footnote": [], + "bbox": [ + 383, + 122, + 576, + 232 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9052ba9140705fe2d1e084df96ff77789bfcb359c2d9a0202e16a70236faa774.jpg", + "image_caption": [ + "(c)" + ], + "image_footnote": [], + "bbox": [ + 606, + 122, + 803, + 232 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/b14513d4968adb1a01bcf4c0cb3e39398428709cdf3c0941689aa62b1fae80b9.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodALLconLentGMMAVG
DiaNAUI✓✓✓77.7±0.2
DiaNA w/o ALR✓✓✓74.8±0.4
DiaNA w/o LconUI✓✓76.9±0.3
DiaNA w/o LentUI✓✓75.8±0.3
DiaNA w/o GMMUI✓✓74.0±0.2
DiaNA-UIUI✓72.1±0.4
DiaNA-UCUC✓68.3±0.6
DiaNA-CICI✓66.4±0.8
DiaNA-CCCC✓63.0±0.3
Random (Baseline)R65.8±0.5
", + "bbox": [ + 132, + 263, + 411, + 358 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 3. Ablation study results of DiaNA. The \"AL\" column indicates which type of data subset should be selected to be annotated during each sampling step. We evaluated the performance of all adaptation scenarios on Office-Home by averaging their accuracy.", + "bbox": [ + 75, + 358, + 468, + 410 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "able, resulting from its significant performance improvement. This also indicates that our sampling strategy can be effectively applied to general active learning.", + "bbox": [ + 75, + 418, + 468, + 460 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Combination with UDA/SSDA/SFDA methods. To validate the compatibility of the proposed DiaNA with existing UDA, SSDA, and SFDA algorithms, we conduct the experiments for UDA and SSDA in the adaptation $\\mathrm{C} \\rightarrow \\mathrm{S}$ on DomainNet, and for SFDA in $\\mathrm{C} \\rightarrow \\mathrm{A}$ and $\\mathrm{R} \\rightarrow \\mathrm{C}$ on OfficeHome. DANN [5], MME [24], and NRC [36] correspond to the SOTA methods towards UDA, SSDA, and SFDA, respectively. As shown in Figure 4(b) and Figure 4(c), combining the selection strategy of DiaNA with other DA methods, i.e., DANN+Ours, MME+Ours, and NRC+Ours, significantly increases the performance of existing DA algorithms that select labeled target samples via random selection, namely DANN+Random, MME+Random and NRC+Random. This suggests that, adaptively considering both the domaininess and uncertainty, DiaNA is beneficial for the selection of informative target sample searching, while combined into diverse domain adaptation techniques.", + "bbox": [ + 75, + 461, + 468, + 695 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Ablation study", + "text_level": 1, + "bbox": [ + 75, + 706, + 226, + 720 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Efficacy of the targeted training strategies. To illustrate the effect of each component of the proposed DiaNA, we conduct ablation study by removing the corresponding individual components. As displayed in Table 3, the proposed method exceeds all of the model variants by a large accuracy margin on average, demonstrating the effectiveness of each component. By comparing our proposed entire approach with DiaNA w/o GMM, manual data division strategy might considerably cause performance degradation, thereby in turn emphasizing the need for adaptive", + "bbox": [ + 75, + 726, + 468, + 866 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "data subdivision protocol. Furthermore, as demonstrated, disrupting the correspondence between targeted data subsets provides empirical evidence supporting the validity of our proposed customized learning techniques; see supplementary document for more details.", + "bbox": [ + 497, + 264, + 890, + 334 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Efficacy of the sampling strategy. To provide insights into how effectively the domaininess-based metric and the uncertainty-based metric work in the sampling step, we use different data subsets to replace the UI subset as active samples for annotation. To eliminate the influence of $\\mathcal{L}_{con}$ and $\\mathcal{L}_{ent}$ , we remove these two terms but only retain $\\mathcal{L}_{sup}$ during training. As shown in Table 3, both DiaNA-UC and DiaNA-CI achieve better classification performance than baseline selection, thereby showing the effect of the proposed uncertainty metric and domainness metric. Moreover, active sampling on UI samples (DiaNA-UI) obtains the best performance among all the variants, further illustrating the superiority of the integration of both metrics.", + "bbox": [ + 497, + 334, + 892, + 515 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusions", + "text_level": 1, + "bbox": [ + 499, + 528, + 626, + 542 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we introduce a \"divide-and-adapt\" framework, named DiaNA, to address the problem of active domain adaptation. Specifically, we first design an informativeness function that jointly captures sample's uncertainty and domainness. Moreover, we devise an automatic data subdivision protocol to partition the target instances into four categories with different characteristics. While selecting the most informative samples to annotate, we also design tailored learning strategies for the other target data subsets with stratified transferable properties. Extensive experimental results, as well as ablation studies, have confirmed the superiority of the proposed approach.", + "bbox": [ + 497, + 551, + 890, + 719 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments", + "text_level": 1, + "bbox": [ + 499, + 732, + 658, + 748 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported in part by the Guangdong Basic and Applied Basic Research Foundation (NO. 2020B1515020048), in part by the National Natural Science Foundation of China (NO. 61976250), in part by the Shenzhen Science and Technology Program (NO. JCYJ20220530141211024) and in part by the Fundamental Research Funds for the Central Universities under Grant 22lgqb25.", + "bbox": [ + 497, + 755, + 890, + 866 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "7658", + "bbox": [ + 468, + 885, + 500, + 897 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 124, + 173, + 138 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Jordan T Ash, Chicheng Zhang, Akshay Krishnamurthy, John Langford, and Alekh Agarwal. Deep batch active learning by diverse, uncertain gradient lower bounds. In International Conference on Learning Representations, 2019.", + "[2] Ekin D Cubuk, Barret Zoph, Dandelion Mane, Vijay Vasudevan, and Quoc V Le. Autoaugment: Learning augmentation strategies from data. 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Divide and contrast: Source-free domain adaptation via adaptive contrastive learning. arXiv preprint arXiv:2211.06612, 2022." + ], + "bbox": [ + 78, + 125, + 470, + 745 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "7660", + "bbox": [ + 468, + 885, + 500, + 897 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Divide and Adapt_ Active Domain Adaptation via Customized Learning/86a989bf-4e7d-4c1f-bfb3-37887b13a20b_model.json b/2023/Divide and Adapt_ Active Domain Adaptation via Customized Learning/86a989bf-4e7d-4c1f-bfb3-37887b13a20b_model.json new file mode 100644 index 0000000000000000000000000000000000000000..64c937248fc19bc9752746f010ed5076eef64609 --- /dev/null +++ b/2023/Divide and Adapt_ Active Domain Adaptation via Customized Learning/86a989bf-4e7d-4c1f-bfb3-37887b13a20b_model.json @@ -0,0 +1,2134 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.13, + 0.051, + 0.201, + 0.085 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.253, + 0.049, + 0.792, + 0.088 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.123, + 0.162, + 0.848, + 0.183 + ], + "angle": 0, + "content": "Divide and Adapt: Active Domain Adaptation via Customized Learning" + }, + { + "type": "text", + "bbox": [ + 0.099, + 0.207, + 0.877, + 0.274 + ], + "angle": 0, + "content": "Duojun Huang\\(^{1,2}\\) Jichang Li\\(^{3}\\) Weikai Chen\\(^{4}\\) Junshi Huang\\(^{5}\\) Zhenhua Chai\\(^{5}\\) Guanbin Li\\(^{1,2\\dagger}\\) \n\\(^{1}\\)School of Computer Science and Engineering, Sun Yat-sen University, Guangzhou, China \n\\(^{2}\\)Research Institute, Sun Yat-sen University, Shenzhen, China \n\\(^{3}\\)The University of Hong Kong \\({}^{4}\\)Tencent America \\({}^{5}\\)Meituan" + }, + { + "type": "text", + "bbox": [ + 0.174, + 0.276, + 0.796, + 0.306 + ], + "angle": 0, + "content": "huangdj9@mail2.sysu.edu.cn, csjcli@connect.hku.hk, chenwk891@gmail.com {huangjunshi,chaizhenhua}@meituan.com, liguanbin@mail.sysu.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.337, + 0.314, + 0.352 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.367, + 0.473, + 0.754 + ], + "angle": 0, + "content": "Active domain adaptation (ADA) aims to improve the model adaptation performance by incorporating active learning (AL) techniques to label a maximally-informative subset of target samples. Conventional AL methods do not consider the existence of domain shift, and hence, fail to identify the truly valuable samples in the context of domain adaptation. To accommodate active learning and domain adaption, the two naturally different tasks, in a collaborative framework, we advocate that a customized learning strategy for the target data is the key to the success of ADA solutions. We present Divide-and-Adapt (DiaNA), a new ADA framework that partitions the target instances into four categories with stratified transferable properties. With a novel data subdivision protocol based on uncertainty and domaininess, DiaNA can accurately recognize the most gainful samples. While sending the informative instances for annotation, DiaNA employs tailored learning strategies for the remaining categories. Furthermore, we propose an informativeness score that unifies the data partitioning criteria. This enables the use of a Gaussian mixture model (GMM) to automatically sample unlabeled data into the proposed four categories. Thanks to the \"divide-and-adapt\" spirit, DiaNA can handle data with large variations of domain gap. In addition, we show that DiaNA can generalize to different domain adaptation settings, such as unsupervised domain adaptation (UDA), semi-supervised domain adaptation (SSDA), source-free domain adaptation (SFDA), etc." + }, + { + "type": "title", + "bbox": [ + 0.079, + 0.78, + 0.21, + 0.794 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.803, + 0.47, + 0.846 + ], + "angle": 0, + "content": "Domain adaptation (DA) approaches strive to generalize model trained on a labeled source domain to a target domain with rare annotation [5, 13, 16, 24] by coping with" + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.344, + 0.88, + 0.524 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.527, + 0.893, + 0.567 + ], + "angle": 0, + "content": "Figure 1. The illustration of our proposed Divide-and-Adapt mechanism to divide target samples into different data subsets for customized learning." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.576, + 0.892, + 0.811 + ], + "angle": 0, + "content": "the domain disparity. Nevertheless, DA methods are significantly outperformed by their supervised counterparts due to the scariness of annotation as demonstrated in [4, 14, 27]. In practice, it is cost-effective to get a moderate amount of target samples labeled to boost the performance of domain adaptation. Active learning (AL) approaches seek to select samples with uncertainty [9, 12, 29, 30] and diversity [19, 25] to best benefit the model, which properly matches the demand. However, previous AL methods assume that both the labeled and unlabeled data follow the same distribution, such a strategy may become ineffective to the DA scenarios where the target data suffer from domain shift. The recently proposed active domain adaptation (ADA) [4, 22, 31] aims to resolve this issue by actively selecting the maximally-informative instances such that the performance of the transferred model can be best boosted with a limited annotation budget." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.812, + 0.892, + 0.868 + ], + "angle": 0, + "content": "The key to the success of ADA is to strike a good balance between the highly coupled yet inherently different tasks: active learning and domain adaptation. The real-world target data typically exhibit either of the two characteristics:" + }, + { + "type": "page_footnote", + "bbox": [ + 0.095, + 0.853, + 0.298, + 0.867 + ], + "angle": 0, + "content": "† Corresponding author is Guanbin Li." + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.887, + 0.501, + 0.898 + ], + "angle": 0, + "content": "7651" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.126, + 0.473, + 0.348 + ], + "angle": 0, + "content": "source-like or target-specific. While the former has similar feature distribution with the source data, the latter tends to be the unique part of target domain and deviates greatly from the source distribution [4, 26, 38]. On one hand, to achieve domain adaptation, applying the same adaptation strategy to all target data equally cannot generalize well to scenarios with varying degrees of domain shift. This is particularly true when the gap between the source-like and target-specific data is unknown. On the other hand, in active learning tasks, the samples with a learning difficulty will be more likely to be selected for labeling. Nonetheless, with large domain gap, incorporating such difficult samples in the adaptation task would hamper the learning of the adaptation model, making the training highly unstable. However, despite the impressive progress that has been made, none of the existing works has fully addressed the above issues." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.351, + 0.473, + 0.643 + ], + "angle": 0, + "content": "In this work, we propose Divide-And-Adapt (DiaNA), a novel ADA framework that can scale to large variations of domain gaps while achieving cost-effective data labeling with a significant performance boost for domain adaptation. Our key observation is that customized learning strategies are vital for target data with different characteristics. In particular, DiaNA divides the target data into four subsets with different levels of transferable properties (see Figure 1), each of which is handled with a customized learning strategy. Unlike traditional AL methods that would simply label the most uncertain data [29, 30, 37], we propose to withhold the most challenging samples (Figure 1 category (4)) for training the domain adaption models. Instead, the selected samples for active annotation would maintain a proper stimulus for the source model, providing informative domain knowledge without jeopardizing the training stability. The subdivision of target data is dynamically updated as the domain disparity is gradually mitigated with more labeled data. Hence, the previous challenging samples could be classified as transferable in the later stage and exploited in the network training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.646, + 0.473, + 0.868 + ], + "angle": 0, + "content": "We introduce a novel protocol for subdividing the target samples for customized learning. In addition to the uncertainty of model prediction, we advocate that the consistency with the learned prior distribution, i.e. the domainness, is another key criterion for active domain adaptation [4, 26]. To this end, we divide the target data into four categories as shown in Figure 1 according to the domainness and uncertainty of the instances. We further propose that the samples with 1) being uncertain to the model and 2) having inconsistent prediction with the label of its closest category prototype in the learned feature space (i.e. high domainness) are the most \"profitable\" instances for bringing informative knowledge of target domain if annotated. Thereby, we identify the uncertain inconsistent samples for labeling while applying tailored learning strategies for the remaining categories to boost the selectivity of the sampling." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.126, + 0.892, + 0.237 + ], + "angle": 0, + "content": "To avoid heuristic thresholding for data subdivision, we propose an automatic data sampling mechanism based on Gaussian mixture model (GMM). In particular, we propose an informativeness function that incorporates the domainness and uncertainty in a unified scoring system. The computed informativeness score of the labeled data is used to train a four-component GMM model, which is then applied to sample the unlabeled target data into four categories." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.237, + 0.893, + 0.347 + ], + "angle": 0, + "content": "We evaluate DiaNA over a large variety of domain shift scenarios on DomainNet [21], Office-Home [28] and CIFAR-10 [11]. Furthermore, the proposed sampling strategy of DiaNA can be generalized to various domain adaptation problems with different supervision settings, including unsupervised domain adaptation (UDA), semi-supervised domain adaptation (SSDA), and source-free domain adaptation (SFDA)." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.348, + 0.812, + 0.361 + ], + "angle": 0, + "content": "We summarize our contributions as follows:" + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.363, + 0.892, + 0.431 + ], + "angle": 0, + "content": "- A general \"divide-and-adapt\" framework, coded DiaNA, for active domain adaptation that can handle diversified degrees of domain gaps while being able to generalize to different domain adaptation problems, including UDA, SSDA, and SFDA." + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.434, + 0.892, + 0.489 + ], + "angle": 0, + "content": "- A new target data partition strategy based on domaininess and uncertainty that enables stratified learning to achieve more stable training, superior adaptation performance, and better generality." + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.491, + 0.892, + 0.533 + ], + "angle": 0, + "content": "- A novel informativeness scoring system and the corresponding sampling paradigm based on GMM model for automatic data partitioning." + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.534, + 0.892, + 0.562 + ], + "angle": 0, + "content": "- New state-of-the-art performance over the mainstream public datasets in the task of active domain adaptation." + }, + { + "type": "list", + "bbox": [ + 0.517, + 0.363, + 0.892, + 0.562 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.581, + 0.642, + 0.595 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.604, + 0.892, + 0.868 + ], + "angle": 0, + "content": "Domain adaptation (DA). Most of the prior methods involving domain adaptation follow the unsupervised domain adaptation (UDA) paradigm that only unlabeled data is accessible in the target domain. Early UDA approaches [16, 18, 32] utilized maximum mean discrepancy (MMD) to minimize the discrepancy of features from different domains to address the domain shift, while recent adversarial learning based methods [5, 17] have become popular solutions for UDA. Despite effectiveness, UDA is still significantly outperformed by its supervised variant as indicated in [4, 14, 27]. Semi-supervised domain adaptation (SSDA) [13, 24, 35] allows a few target instances to be labeled and generally achieves improved performance. However, SSDA assumes that the labeled instances are passively provided in advance, depriving the choice of informative samples beneficial to the model. In this work, we propose an active domain adaption method to select the most informative samples, which can be incorporated into other DA methods to further boost their performance." + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.887, + 0.502, + 0.898 + ], + "angle": 0, + "content": "7652" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.147, + 0.125, + 0.823, + 0.305 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.306, + 0.895, + 0.371 + ], + "angle": 0, + "content": "Figure 2. We propose a general \"divide-and-adapt\" framework, named DiaNA, for active domain adaptation. (a) A new target data partition strategy is presented to divide target data into four categories via building an informativeness scoring function that incorporates both domainness and uncertainty metrics. Besides, an automatic data partitioning function based on a learned four-component GMM model is applied to adaptively separate four sample categories from unlabeled target data. (b) To achieve customized learning, different auxiliary techniques are integrated into model fine-tuning w.r.t the four categories of unlabeled target data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.384, + 0.473, + 0.661 + ], + "angle": 0, + "content": "Active Learning (AL). Active learning is proposed to select a maximally-informative subset of unlabeled data for annotation via a query function, in an effort to best improve the model performance with a limited annotation budget. There exist several efforts to tackle the challenges involving active learning. For example, the uncertainty-based AL methods mainly focus on designing query functions based on prediction confidence [30], entropy [9, 29], or margin [10, 23] of the posterior probabilities. On the other hand, the diversity-based approaches [6, 19, 25] concentrate on selecting samples that can well represent the entire dataset. Meanwhile, expected model change-based methods [3, 15] aim to query the instances that would lead to a significant change to the current model. Recently proposed active learning approaches attain better performance by utilizing hybrid strategies which taking multiple metrics into consideration [1, 20]. Notwithstanding, the efficacy of previous AL resources may falter in DA scenarios as their selection strategy fails to meticulously consider the implications of the domain gap." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.673, + 0.473, + 0.868 + ], + "angle": 0, + "content": "Active Domain Adaptation (ADA). Early ADA researches [4,26] propose to measure the uncertainty and domaininess of each target instance via a domain discriminator with adversarial training. CLUE [22] presents an entropy-weighted clustering algorithm to query uncertain and diverse samples in the target domain. Recently, SDM [33] is proposed to optimize a margin loss function for exploring target instances similar to potential hard samples in the source domain. Nevertheless, the majority of existing ADA methods deliberately design hand-crafted query functions to evaluate sample's annotation value and apply the same adaptation strategy to all target data equally [4,26,31]. The rigid criteria make them easily overfit to certain domain adaption scenarios, which limits the generalization of the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.384, + 0.892, + 0.468 + ], + "angle": 0, + "content": "method. In contrast, we propose to integrate uncertainty and domainness metrics within a unified scoring function to select informative samples. Moreover, we apply tailored learning strategies for target data with different characteristics, constructing an effective framework capable of generalizing across large variations of domain shifts." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.482, + 0.78, + 0.499 + ], + "angle": 0, + "content": "3. Divide-and-Adapt Framework" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.507, + 0.892, + 0.728 + ], + "angle": 0, + "content": "Problem formulation. Active domain adaptation aims at seeking an optimal model for a target domain when given labeled source data \\( S = \\{(x_s, y_s)\\} \\) as well as unlabeled target data \\( \\mathcal{U} = \\{x_u\\} \\), assisted by the iteratively queried labeled data \\( \\mathcal{T} = \\{(x_t, y_t)\\} \\) of the target domain. Here, \\( S, \\mathcal{U}, \\) and \\( \\mathcal{T} \\) share the same label space over \\( C \\) categories. Initially, \\( \\mathcal{T} \\) is an empty set. The model is iteratively trained using \\( S, \\mathcal{T}, \\) and \\( \\mathcal{U} \\) for \\( R \\) active learning loops until a given annotation budget \\( B \\) is reached. In each active learning loop, \\( b = B / R \\) samples from \\( \\mathcal{U} \\) would be selected, labeled by human experts, and then moved into \\( \\mathcal{T} \\). The proposed Divide-and-Adapt framework consists of a feature extractor and a classifier. Our goal is to design a query function to identify informative samples to annotate and utilize limited amount of labeled samples to best enhance the classification performance for the target domain." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.729, + 0.893, + 0.867 + ], + "angle": 0, + "content": "Overview. In this paper, we propose Divide-And-Adapt, coded DiaNA, to tackle the problem of active domain adaptation. In detail, we first propose to design an informativeness function for subdividing the target samples into four categories, one of which is the informative target samples used for actively annotating. Such a function is a unified scoring system that incorporates the domainness and the uncertainty. To avoid heuristic thresholding for data subdivision, we propose an automatic data sampling mechanism to divide the unlabeled target data into four" + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.887, + 0.501, + 0.898 + ], + "angle": 0, + "content": "7653" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.104, + 0.128, + 0.443, + 0.268 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.268, + 0.47, + 0.33 + ], + "angle": 0, + "content": "Figure 3. (a) Source-like target samples are more likely to be close to the source centroid in the feature space with respect to its predicted category. (b) Target-specific target samples are prone to be inconsistent between model predictions and similarity-based labels." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.345, + 0.47, + 0.442 + ], + "angle": 0, + "content": "sample categories. This is achieved by learning a four-component Gaussian mixture model using semi-supervised Expectation-Maximization algorithm. Finally, we design tailored learning strategies for different categories of target samples during model fine-tuning, thus further improving the model performance. The overview of the proposed algorithm has been summarized in Figure 2." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.451, + 0.393, + 0.466 + ], + "angle": 0, + "content": "3.1. Informativeness Scoring Mechanism" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.471, + 0.469, + 0.61 + ], + "angle": 0, + "content": "Following previous ADA works [4, 26, 31], we aim to search for the target instances with high domainness and uncertainty. To achieve this goal, we propose to first estimate category-wise centroids based on the labeled samples, and then define a similarity-based label for each unlabeled target sample by computing its top-\\(k\\) feature similarity with the categorical centroids. Finally, we integrate both the domainness and the uncertainty metrics into an informativeness function, which is formulated as the consistency between model prediction and similarity-based label." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.626, + 0.469, + 0.682 + ], + "angle": 0, + "content": "Categorical centroids. We propose to average the features of labeled samples to estimate the category-specific data distribution, i.e., category prototype. Here, we formulate the centroid with respect to the \\(c\\)-th category as follows," + }, + { + "type": "equation", + "bbox": [ + 0.157, + 0.69, + 0.469, + 0.726 + ], + "angle": 0, + "content": "\\[\nA ^ {c} = \\frac {\\sum_ {(x , y) \\in \\mathcal {S}} \\mathbb {1} \\{y = c \\} \\cdot G (x)}{\\sum_ {(x , y) \\in \\mathcal {S}} \\mathbb {1} \\{y = c \\}}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.469, + 0.805 + ], + "angle": 0, + "content": "where \\(\\mathbb{1}\\{\\cdot\\}\\) is an indicator function, and \\(G(x)\\) is a feature extractor that outputs the sample feature of \\(x\\). Note that, as the active learning loops proceed, labeled target samples would be incorporated into the calculation of categorical centroids to mitigate the impact of distribution change." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.469, + 0.867 + ], + "angle": 0, + "content": "Similarity-based data label. As introduced in the works [7, 13], samples share more top-\\(k\\) indices in their respective lists of rank-ordered feature elements would have a higher probability of being the same category. To obtain the" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.127, + 0.892, + 0.182 + ], + "angle": 0, + "content": "similarity-based label for each target instance, we first measure pairwise similarity of the indices of the sorted feature elements based on the magnitude. Then, we can formulate a similarity-based label for a sample \\( x \\) from \\( \\mathcal{U} \\) as follows," + }, + { + "type": "equation", + "bbox": [ + 0.543, + 0.191, + 0.892, + 0.216 + ], + "angle": 0, + "content": "\\[\n\\ddot {y} (x) = \\underset {1 \\leq c \\leq C} {\\operatorname {a r g m a x}} \\mathbf {I o U} (\\operatorname {t o p} k (G (x)), \\operatorname {t o p} k \\left(A ^ {c}\\right)), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.224, + 0.891, + 0.279 + ], + "angle": 0, + "content": "where \\(\\mathrm{top}k(\\cdot)\\) computes the top- \\(k\\) feature element indices ranked according to their magnitudes. In addition, \\(\\mathbf{IoU}(\\cdot ,\\cdot)\\) denotes an Intersection-over-Union function, which returns the extent of overlap of the two respective index lists." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.28, + 0.892, + 0.584 + ], + "angle": 0, + "content": "We set the value of \\( k \\) to be significantly smaller than the full dimension of the feature vector. In this way, the function \\( \\mathrm{top}k(\\cdot) \\) only extracts the principle components of the feature of sample. Therefore, the IoU function in Eq. 2 is equivalent to measuring pairwise image sample similarity under a low-resolution condition. In ADA tasks, the training of model is inevitably dominated by the source domain especially in the early stage [33]. Therefore, source-like target samples that are similar to the source domain would naturally have more accurate representation than the target-specific ones that are distinct from the source. Under the low-resolution condition, i.e., \\( k \\) set to be small, source-like samples tend to have the same similarity-based label as the model predicted class thanks to their reliable and discriminative features extracted by the model. In contrast, target-specific samples are prone to produce inconsistent results since they are typically underfitted by the current model as shown in Figure 3. Based on the analysis above, we utilize the consistency of the model predicted class and similarity-based label to evaluate the domainness of each target sample. Detailed theoretical and experimental supports are demonstrated in our supplementary." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.591, + 0.891, + 0.659 + ], + "angle": 0, + "content": "Informativeness function. To explore the most informative target samples, we integrate the domainness and uncertainty into a unified informativeness function (InfoF). The informativeness score for a sample \\( x \\) from unlabeled target domain can be formulated as follows," + }, + { + "type": "equation", + "bbox": [ + 0.56, + 0.668, + 0.891, + 0.706 + ], + "angle": 0, + "content": "\\[\n\\ell_ {u} (x) = - \\sum_ {c = 1} ^ {C} \\mathbb {1} \\{c = \\ddot {y} (x) \\} \\cdot \\log P _ {c} (x), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.714, + 0.892, + 0.867 + ], + "angle": 0, + "content": "where \\(P(x)\\) denotes the probabilistic prediction of a sample \\(x\\) from the network model and \\(P_{c}(x)\\) is the \\(c\\)-th element of the vector \\(P(x)\\). According to Eq. 3, we can divide unlabeled target samples into two subsets depending on whether the model predicted class and the similarity-based label are identical: consistent and inconsistent subsets, while both sets have confident samples and uncertain samples depending on whether the predicted probability is greater than a given confidence threshold. We name these four categories of unlabeled target data as confident-consistent (CC), uncertain-consistent (UC), uncertain-inconsistent (UI) and" + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.887, + 0.501, + 0.898 + ], + "angle": 0, + "content": "7654" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.085, + 0.129, + 0.425, + 0.171 + ], + "angle": 0, + "content": "Algorithm 1: The training procedure of four-component Gaussian Mixture Model (GMM) using semi-supervised Expectation-Maximization" + }, + { + "type": "text", + "bbox": [ + 0.098, + 0.173, + 0.229, + 0.187 + ], + "angle": 0, + "content": "Input: \\(\\mathcal{D}_L;\\mathcal{D}_U;\\alpha\\)" + }, + { + "type": "text", + "bbox": [ + 0.099, + 0.187, + 0.358, + 0.2 + ], + "angle": 0, + "content": "Output: Optimal GMM parameters \\(\\mathcal{W}\\)" + }, + { + "type": "text", + "bbox": [ + 0.086, + 0.201, + 0.438, + 0.228 + ], + "angle": 0, + "content": "1 Initialize \\(\\mathcal{W} = \\{(\\pi_k,\\mu_k,\\sigma_k)|1\\leq k\\leq K\\}\\) using \\(\\mathcal{D}_L\\) via Bayes estimation." + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.229, + 0.293, + 0.242 + ], + "angle": 0, + "content": "2 while \\(\\mathcal{W}\\) is not converged do" + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.242, + 0.267, + 0.261 + ], + "angle": 0, + "content": "3 \\(\\{(\\ell_g^i,p_g^i)\\}_{i = 1}^{|\\mathcal{D}_L|}\\gets \\mathcal{D}_L\\)" + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.261, + 0.254, + 0.278 + ], + "angle": 0, + "content": "4 \\(\\{(\\ell_u^i),\\})_{j = 1}^{|\\mathcal{D}_U|}\\gets \\mathcal{D}_U\\)" + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.278, + 0.204, + 0.288 + ], + "angle": 0, + "content": "//Estep:" + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.289, + 0.276, + 0.306 + ], + "angle": 0, + "content": "5 \\(\\gamma_{gk}(\\ell_g^i) = \\mathbb{1}\\{p_g^i = k\\} ,\\)" + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.306, + 0.351, + 0.328 + ], + "angle": 0, + "content": "6 \\(\\gamma_{uk}(\\ell_u^j) = \\frac{\\pi_k\\mathcal{N}(\\ell_u^j;\\mu_k,\\sigma_k)}{\\sum_{k' = 1}^{K}\\pi_{k'}\\mathcal{N}(\\ell_u^j;\\mu_{k'}\\sigma_{k'})},\\)" + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.328, + 0.203, + 0.34 + ], + "angle": 0, + "content": "//Mstep:" + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.341, + 0.362, + 0.362 + ], + "angle": 0, + "content": "7 \\(\\pi_{k} = \\frac{\\alpha\\sum_{i}\\gamma_{gk}(\\ell_{g}^{i}) + (1 - \\alpha)\\sum_{j}\\gamma_{uk}(\\ell_{u}^{j})}{\\alpha|\\mathcal{D}_{L}| + (1 - \\alpha)|\\mathcal{D}_{U}|};\\)" + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.362, + 0.373, + 0.388 + ], + "angle": 0, + "content": "8 \\(\\mu_{k} = \\frac{\\alpha\\sum_{i}\\gamma_{gk}(\\ell_{g}^{i})\\cdot\\ell_{g}^{i} + (1 - \\alpha)\\sum_{j}\\gamma_{uk}^{j}\\cdot\\ell_{u}^{j}}{\\alpha\\sum_{i}\\gamma_{gk}(\\ell_{g}^{i}) + (1 - \\alpha)\\sum_{j}\\gamma_{uk}(\\ell_{u}^{j})};\\)" + }, + { + "type": "text", + "bbox": [ + 0.085, + 0.389, + 0.162, + 0.4 + ], + "angle": 0, + "content": "9 \\(\\sigma_{k} =\\)" + }, + { + "type": "list", + "bbox": [ + 0.085, + 0.201, + 0.438, + 0.4 + ], + "angle": 0, + "content": null + }, + { + "type": "equation", + "bbox": [ + 0.133, + 0.401, + 0.448, + 0.428 + ], + "angle": 0, + "content": "\\[\n\\frac {\\alpha \\sum_ {i} \\gamma_ {g k} (\\ell_ {g} ^ {i}) \\cdot (\\ell_ {g} ^ {i} - \\mu_ {k}) ^ {2} + (1 - \\alpha) \\sum_ {j} \\gamma_ {u k} \\cdot (\\ell_ {u} ^ {j}) (\\ell_ {u} ^ {j} - \\mu_ {k}) ^ {2}}{\\alpha \\sum_ {i} \\gamma_ {g k} (\\ell_ {g} ^ {i}) + (1 - \\alpha) \\sum_ {j} \\gamma_ {u k} (\\ell_ {u} ^ {j})};\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.462, + 0.47, + 0.546 + ], + "angle": 0, + "content": "confident-inconsistent (CI), respectively. In this way, samples that are both uncertain to the model and contain target-specific knowledge can be extracted based on the InfoF score. In next section, we devise a strategy for informative sampling to adaptatively distinguish those subsets from unlabeled target samples." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.554, + 0.356, + 0.57 + ], + "angle": 0, + "content": "3.2. Informative Sampling Function" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.577, + 0.469, + 0.797 + ], + "angle": 0, + "content": "During training, the varying scale of InfoF scores obtained above would hinder accurate data categorization using manual data division, leading to a biased sampling strategy and degraded performance. Therefore, our work here formulates an Informative Sampling Function to achieve the goal of adaptively selecting informative target samples. In general, it can be observed that the four categories of unlabeled target data as stated above are significantly separable in the distributions of the InfoF scores, making it possible to learn mixture models to separate four sample partitioning from unlabeled target data. Thereafter, by learning the distribution of InfoF scores using a four-component Gaussian mixture model (GMM), the target data can be adaptively mapped to the probability distribution of four categories and then be separated, thereby avoiding sampling bias that may be created by manual division." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.798, + 0.469, + 0.867 + ], + "angle": 0, + "content": "In specific, we first take inspiration from [34] that labeled samples can be used to construct supervision information, therefore building a more trustworthy GMM model with \\(K\\) Gaussian components (namely \\(K = 4\\) in this work) via a semi-supervised Expectation-Maximization al" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.126, + 0.892, + 0.154 + ], + "angle": 0, + "content": "gorthm. To this end, we then calculate the InfoF score for a labeled sample with \\((x,y)\\) from \\(S\\) or \\(\\mathcal{T}\\) as follows," + }, + { + "type": "equation", + "bbox": [ + 0.564, + 0.162, + 0.892, + 0.2 + ], + "angle": 0, + "content": "\\[\n\\ell_ {g} (x, y) = - \\sum_ {c = 1} ^ {C} \\mathbb {1} \\{c = y \\} \\cdot \\log P _ {c} (x). \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.207, + 0.892, + 0.29 + ], + "angle": 0, + "content": "The similarity-based label is determined using categorical centroids of the labeled data, resulting in the totally identical similarity-based label and model prediction for labeled samples. In order to obtain reliable supervision and build a better GMM model, we have replaced the similarity-based label with the ground-truth class label here." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.291, + 0.892, + 0.373 + ], + "angle": 0, + "content": "Afterwards, to obtain the supervision information for training GMM, we here define a piecewise function to obtain the observation labels that assign all labeled samples across domains to the corresponding Gaussian components. Thus, the observation label of a candidate instance \\( x \\) can be computed as," + }, + { + "type": "equation", + "bbox": [ + 0.499, + 0.381, + 0.891, + 0.45 + ], + "angle": 0, + "content": "\\[\nq (x, y) = \\left\\{ \\begin{array}{l l} 1, & \\max P (x) \\geq \\tau \\text {a n d} y = \\arg \\max P (x), \\\\ 2, & \\max P (x) < \\tau \\text {a n d} y = \\arg \\max P (x), \\\\ 3, & \\max P (x) < \\tau \\text {a n d} y \\neq \\arg \\max P (x), \\\\ 4, & \\max P (x) \\geq \\tau \\text {a n d} y \\neq \\arg \\max P (x), \\end{array} \\right. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.451, + 0.892, + 0.56 + ], + "angle": 0, + "content": "where the numbers, i.e., \\( k = 1,\\dots ,4 \\), indicate the indices of different Gaussian components corresponding to the CC, UC, UI and CI sample subsets, respectively. As well, \\( \\tau \\) is a confidence threshold to classify labeled samples into the confident subset and the uncertain subset. Furthermore, the comparison between the ground-truth and predicted class labels is used to divide them into the consistent subset and the inconsistent subset of labeled training samples." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.561, + 0.892, + 0.602 + ], + "angle": 0, + "content": "Once we obtain \\(\\{\\ell_g(x,y)|(x,y)\\in S\\cup \\mathcal{T}\\}\\) \\(\\{\\ell_u(x)|x\\in\\) \\(\\mathcal{U}\\}\\) , and \\(q(x,y)\\) , we incorporate them into building training instances for learning the GMM model as follows," + }, + { + "type": "equation", + "bbox": [ + 0.547, + 0.613, + 0.891, + 0.629 + ], + "angle": 0, + "content": "\\[\n\\mathcal {D} _ {L} \\leftarrow \\left\\{\\left(\\ell_ {g} (x, y), q (x, y)\\right) | (x, y) \\in \\mathcal {S} \\cup \\mathcal {T} \\right\\}, \\tag {6}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.607, + 0.64, + 0.891, + 0.655 + ], + "angle": 0, + "content": "\\[\n\\mathcal {D} _ {U} \\leftarrow \\left\\{\\left(\\ell_ {u} (x),\\right) \\mid x \\in \\mathcal {U} \\right\\}. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.661, + 0.892, + 0.731 + ], + "angle": 0, + "content": "For convenience, we denote the GMM model by \\(\\mathcal{W} = \\{(\\pi_k,\\mu_k,\\sigma_k)|1\\leq k\\leq K\\}\\). Afterwards, given a training instance \\(\\ell_{x}\\) from \\(\\mathcal{D}_L\\) or \\(\\mathcal{D}_U\\), the output of the probability density functions of the GMM model regarding \\(\\ell_{x}\\) can be computed as" + }, + { + "type": "equation", + "bbox": [ + 0.592, + 0.738, + 0.891, + 0.776 + ], + "angle": 0, + "content": "\\[\np \\left(\\ell_ {x}\\right) = \\sum_ {k = 1} ^ {K} \\pi_ {k} \\mathcal {N} \\left(\\ell_ {x}; \\mu_ {k}, \\sigma_ {k}\\right), \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.784, + 0.892, + 0.867 + ], + "angle": 0, + "content": "where \\(\\pi_{k}\\) represents the weight of the \\(k\\)-th Gaussian component subject to \\(\\sum_{k=1}^{K} \\pi_{k} = 1\\) and \\(0 \\leq \\pi_{k} \\leq 1\\) for \\(k = 1, \\dots, K\\), while \\(\\mu_{k}\\) and \\(\\sigma_{k}\\) are vectors denoting the mean and variance of such a component. Here, \\(\\mathcal{N}(\\cdot; \\mu_{k}, \\sigma_{k})\\) is used to model the Gaussian distribution of the \\(k\\)-th component. Note that a given coefficient \\(\\alpha = |\\mathcal{D}_{L}| / |\\mathcal{D}_{U}|\\) is" + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.887, + 0.501, + 0.898 + ], + "angle": 0, + "content": "7655" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.126, + 0.47, + 0.182 + ], + "angle": 0, + "content": "used for the weighted integration of the labeled and unlabeled training instances. Thus, we can summarize the training procedure of the GMM model using a semi-supervised EM algorithm in Algorithm 1 according to [34]." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.183, + 0.47, + 0.224 + ], + "angle": 0, + "content": "After obtaining the trained GMM parameters \\(\\mathcal{W}\\), the probability of a sample \\(x\\) from \\(\\mathcal{U}\\) being classified into the \\(k\\)-th component can be computed as follows," + }, + { + "type": "equation", + "bbox": [ + 0.096, + 0.235, + 0.469, + 0.269 + ], + "angle": 0, + "content": "\\[\n\\Pr (z = k | x, \\mathcal {W}) = \\frac {\\pi_ {k} \\mathcal {N} \\left(\\ell_ {u} (x) ; \\mu_ {k} , \\sigma_ {k}\\right)}{\\sum_ {k ^ {\\prime} = 1} ^ {K} \\pi_ {k ^ {\\prime}} \\mathcal {N} \\left(\\ell_ {u} (x) ; \\mu_ {k ^ {\\prime}} , \\sigma_ {k ^ {\\prime}}\\right)}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.278, + 0.469, + 0.307 + ], + "angle": 0, + "content": "where \\(z\\) is a discrete variable to infer which component the sample \\(x\\) belongs to." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.317, + 0.457, + 0.332 + ], + "angle": 0, + "content": "3.3. Candidate Selection and Training Objectives" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.339, + 0.47, + 0.504 + ], + "angle": 0, + "content": "After acquiring the informativeness sampling function, it is utilized for carrying out data partitioning. For ADA, the main focus should be on annotating samples that are uncertain to the model and can effectively represent the target dataset, which is termed as uncertain-inconsistent samples within our subdivision framework. Therefore, during each sampling step, we first rank the unlabeled target samples in descending order according to the scores predicted by \\(\\operatorname{Pr}(z = 3|\\cdot ,\\mathcal{W})\\) and then the top \\(b\\) examples are selected to annotate and moved into labeled target data. Following previous ADA works, we apply the standard cross-entropy loss to the labeled data as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.093, + 0.515, + 0.469, + 0.552 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {s u p} = \\underset {(x, y) \\sim \\mathcal {S} \\cup \\mathcal {T}} {\\mathbb {E}} \\left[ - \\sum_ {c = 1} ^ {C} \\mathbb {1} \\{c = y \\} \\cdot \\log P _ {c} (x) \\right]. \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.563, + 0.469, + 0.646 + ], + "angle": 0, + "content": "To boost the selectivity of the sampling strategy, we further design tailored training techniques for the other data subsets with varied transferable properties. We perform data partitioning on the remaining unlabeled target samples, i.e., \\(\\mathcal{U}\\gets \\mathcal{U}\\backslash \\mathcal{T}\\), according to the posterior probabilities regarding the rest of Gaussian components." + }, + { + "type": "equation", + "bbox": [ + 0.078, + 0.657, + 0.468, + 0.685 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathcal {U}} _ {k} = \\{x \\mid \\arg \\max \\mathbf {P r} (x) = k, \\forall (x,) \\in \\mathcal {U} \\}, \\text {f o r} k = 1, 2, 4, \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.686, + 0.469, + 0.754 + ], + "angle": 0, + "content": "where \\(\\hat{\\mathcal{U}}_1, \\hat{\\mathcal{U}}_2\\) and \\(\\hat{\\mathcal{U}}_4\\) refer to \\(\\hat{\\mathcal{U}}_{\\mathrm{CC}}, \\hat{\\mathcal{U}}_{\\mathrm{UC}}, \\hat{\\mathcal{U}}_{\\mathrm{CI}}\\). Here, \\(\\mathbf{Pr}(x)\\) is the concatenated probability vector corresponding to different components, i.e., \\(\\mathbf{Pr}(x) = [\\operatorname{Pr}(z = 1|x, \\mathcal{W}), \\operatorname{Pr}(z = 2|x, \\mathcal{W}), \\operatorname{Pr}(z = 3|x, \\mathcal{W}), \\operatorname{Pr}(z = 4|x, \\mathcal{W})]\\) w.r.t the sample \\(x\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.756, + 0.469, + 0.867 + ], + "angle": 0, + "content": "As shown in Figure 1(4), the source-oriented model could produce confident but unreliable predictions for some target samples having large domain gap with the source. Samples from \\(\\hat{\\mathcal{U}}_{\\mathrm{CI}}\\) have extremely controversial results between model prediction and similarity-based label, which are most likely to be some excessively challenging instances. Therefore, we withhold them in the current stage to avoid jeopardizing the training stability." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.126, + 0.892, + 0.196 + ], + "angle": 0, + "content": "The samples in \\(\\hat{\\mathcal{U}}_{\\mathrm{CC}}\\) have confident and reliable predictions, which tend to be some class centroid in the target feature space. Therefore, we apply consistency regularization to them to enforce the prediction consistency under different perturbations, which can be formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.506, + 0.21, + 0.891, + 0.259 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {c o n} = \\underset {(x, \\cdot) \\sim \\hat {\\mathcal {U}} _ {\\mathrm {C C}}} {\\mathbb {E}} \\left[ - \\sum_ {c = 1} ^ {C} \\mathbb {1} \\{c = \\ddot {y} (x) \\} \\cdot \\log P _ {c} (\\mathbf {A u g} (x)) \\right], \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.26, + 0.892, + 0.301 + ], + "angle": 0, + "content": "where \\(\\mathbf{Aug}(\\cdot)\\) is a function to create perturbations for the sample \\(x\\) using classic data augmentation techniques such as AutoAugment [2]." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.303, + 0.892, + 0.344 + ], + "angle": 0, + "content": "For data group \\(\\hat{\\mathcal{U}}_{\\mathrm{UC}}\\) whose prediction tend to be reliable but uncertain, we directly minimize the entropy of the predictions to using the following conditional entropy loss:" + }, + { + "type": "equation", + "bbox": [ + 0.538, + 0.358, + 0.891, + 0.396 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {e n t} = \\underset {(x, \\cdot) \\sim \\hat {\\mathcal {U}} _ {U C}} {\\mathbb {E}} \\left[ - \\sum_ {c = 1} ^ {C} P _ {c} (x) \\log P _ {c} (x) \\right]. \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.411, + 0.892, + 0.439 + ], + "angle": 0, + "content": "In summary, the overall loss functions used to further optimize the model can be formulated as follows," + }, + { + "type": "equation", + "bbox": [ + 0.592, + 0.454, + 0.891, + 0.469 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {\\text {s u p}} + \\lambda_ {c} \\mathcal {L} _ {\\text {c o n}} + \\lambda_ {e} \\mathcal {L} _ {\\text {e n t}} \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.483, + 0.892, + 0.608 + ], + "angle": 0, + "content": "where \\(\\lambda_{c}\\) and \\(\\lambda_{e}\\) are the weights to trade off different loss terms during the training process. As shown in Figure 2, \\(\\mathcal{L}_{sup}\\) can calibrate the potentially underfitting of uncertain and target-specific samples. \\(\\mathcal{L}_{con}\\) can guide the model to learn global cross-domain clustering while \\(\\mathcal{L}_{ent}\\) serves to minimize the distance of data from the same class. As demonstrated in Sec. 4.3, these training objectives are complementary to each other to best adapt the model to the target domain." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.623, + 0.825, + 0.637 + ], + "angle": 0, + "content": "3.4. Compatibility with UDA/SSDA/SFDA" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.646, + 0.892, + 0.867 + ], + "angle": 0, + "content": "The proposed sampling strategy of DiaNA requires no additional network modules like a domain discriminator or multiple classifiers [4, 26], making it easy to be integrated into existing DA frameworks, such as unsupervised domain adaptation (UDA), semi-supervised domain adaptation (SSDA), and source-free domain adaptation (SFDA); see supplementary document for the implementation details. It should be noted that we further design a variant of DiaNA for the SFDA settings, due to the unavailability of source data. As evidenced by Sec. 4.3, when integrated into diverse DA techniques, the proposed sampling strategy can deliver more performance improvement than random sample selection, thereby demonstrating its compatibility in various DA settings. To the best of our knowledge, we are the first to propose an active selection strategy that can generalize to UDA, SSDA, and SFDA methods." + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.887, + 0.502, + 0.898 + ], + "angle": 0, + "content": "7656" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.124, + 0.89, + 0.252 + ], + "angle": 0, + "content": "
MethodR → CC → SS → PC → QR → SR → PAVG
1k2k5k1k2k5k1k2k5k1k2k5k1k2k5k1k2k5k1k2k5k
Random50.955.261.542.644.849.441.044.450.126.333.243.038.240.746.946.548.853.740.944.550.8
CONF48.654.261.341.943.648.041.644.248.525.532.742.836.939.445.347.147.851.240.343.649.5
Entropy [29]48.054.261.942.745.248.941.143.748.724.631.042.137.040.445.746.548.452.240.043.849.9
Coreset [25]49.152.559.840.642.245.839.141.544.824.730.339.736.738.343.345.146.850.339.241.947.3
BADGE [1]51.755.462.543.645.750.142.345.549.726.034.343.937.841.547.848.050.154.241.645.451.4
Alpha [20]52.056.362.844.346.850.541.944.949.727.234.644.438.641.347.947.650.453.241.945.751.4
AADA [26]50.856.364.742.845.751.041.845.650.825.231.340.838.541.749.546.549.755.140.945.152.0
SDM [33]51.055.462.343.145.249.641.944.949.326.935.043.837.340.246.547.449.753.241.345.150.8
EADA [31]51.556.163.944.246.351.743.846.150.327.534.842.939.041.546.448.650.454.142.445.951.2
CLUE [22]54.159.466.045.348.753.744.048.053.228.835.543.240.444.451.150.052.756.443.848.153.9
DiaNA(Ours)55.660.468.747.050.856.644.249.055.430.239.552.142.447.955.050.553.659.145.050.257.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.254, + 0.893, + 0.281 + ], + "angle": 0, + "content": "Table 1. Comparison results (Accuracy: %) on DomainNet with 1k, 2k and 5k labeling budgets. \"Random\" and \"CONF\" correspond to the classic AL approaches \"Random Sampling\" and \"Least-Confidence Sampling\"." + }, + { + "type": "table", + "bbox": [ + 0.1, + 0.289, + 0.868, + 0.435 + ], + "angle": 0, + "content": "
MethodOffice-Home
A → CA → PA → RC → AC → PC → RP → AP → CP → RR → AR → CR → PAVG
Random52.574.377.456.369.768.957.750.975.870.054.681.365.8
Entropy [29]51.372.776.461.774.172.957.651.176.669.857.182.367.0
Coreset [25]52.873.375.559.873.470.858.152.675.869.356.582.566.7
BADGE [1]57.275.276.961.577.271.960.453.678.070.861.184.369.0
Alpha [20]57.079.478.261.678.074.158.954.278.171.761.184.669.7
AADA [26]56.678.179.058.573.771.060.153.177.070.657.084.568.3
CLUE [22]58.079.177.061.378.073.160.455.977.970.960.384.169.7
TQS [4]58.681.181.561.176.173.361.254.779.773.458.986.170.5
SDM [33]61.282.282.766.177.976.166.158.481.076.062.587.073.1
EADA [31]63.684.483.570.783.780.573.063.585.278.465.488.676.7
DiaNA(Ours)64.586.084.972.384.682.573.363.785.678.567.289.577.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.228, + 0.436, + 0.74, + 0.449 + ], + "angle": 0, + "content": "Table 2. Comparison results (Accuracy: %) on Office-Home with \\(5\\%\\) labeling budget." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.455, + 0.21, + 0.47 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.479, + 0.173, + 0.492 + ], + "angle": 0, + "content": "4.1. Dataset" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.501, + 0.47, + 0.668 + ], + "angle": 0, + "content": "We validate the effectiveness of the proposed approach DiaNA on three standard benchmark datasets: DomainNet [21], Office-Home [28] and CIFAR-10 [11]. On DomainNet, we select five domains namley Real (R), Clipart (C), Sketch (S), Painting (P), and Quikdraw (Q), while we hire these domains to construct 6 adaptation scenarios. As in [4, 31, 33], we report 12 different adaptation scenarios on Office-Home, constructed from four domains: Real (R), Clipart (C), Art (A), and Product (P). To further evaluate the generalization of the proposed sample selection strategy, we additionally report the classification results on CIFAR-10 with a standard active learning setting." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.678, + 0.237, + 0.692 + ], + "angle": 0, + "content": "4.2. Implementation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.7, + 0.469, + 0.769 + ], + "angle": 0, + "content": "Here, we mainly focus on the detailed descriptions of the settings involving active learning on DomainNet, OfficeHome, and CIFAR-10, while more implementation details can be found in the supplementary material. In each adaptation scenario, we report the average accuracy over 3 trials." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.77, + 0.469, + 0.837 + ], + "angle": 0, + "content": "DomainNet. Similar to CLUE [22], we consider ResNet-34 [8] as the network backbone, where such network model is pre-trained on all labeled source samples over 50 training epochs through standard supervision. In all adaptation cases, we set \\( B = 5000 \\) and \\( R = 10 \\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.839, + 0.469, + 0.867 + ], + "angle": 0, + "content": "Office-Home. To be fair, we follow the experimental settings of existing ADA works [4, 31, 33] to conduct" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.457, + 0.892, + 0.511 + ], + "angle": 0, + "content": "performance comparison. In particular, we also use ResNet-50 [8] as the backbone model, while we choose a \\(5\\%\\) proportion of unlabeled target data to set the labeling budget \\(B\\), and \\(R\\) is set to 5." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.512, + 0.892, + 0.581 + ], + "angle": 0, + "content": "CIFAR-10. On this dataset, we select ResNet-34 [8] as the backbone model. We randomly choose select \\(10\\%\\) training samples at random as the initially labeled data set, and we then annotate \\(4\\%\\) at each sampling step with a total annotation budget \\(30\\%\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.593, + 0.638, + 0.607 + ], + "angle": 0, + "content": "4.3. Main Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.616, + 0.892, + 0.768 + ], + "angle": 0, + "content": "Results on DomainNet and Office-Home. We summarize the comparison with baselines in Table 1 and Table 2 on both datasets respectively. Note that we consider varying label budgets, namely i.e., 1k, 2k, and 5k, on DomainNet. We can see that DiaNA achieves the highest average accuracy in all cases on both datasets for solving the ADA tasks. Especially in the most difficult adaptation scenarios, e.g., \\(\\mathrm{C} \\rightarrow \\mathrm{A}\\) and \\(\\mathrm{R} \\rightarrow \\mathrm{C}\\), on Office-Home, the proposed method can still exceed all the other methods by more than \\(1.6\\%\\) and \\(1.8\\%\\) respectively, demonstrating the effectiveness of DiaNA on the commonly used DA benchmark datasets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.77, + 0.892, + 0.867 + ], + "angle": 0, + "content": "Results on CIFAR-10. We also extend the proposed method to standard AL tasks on CIFAR-10, where the domain gap between labeled and unlabeled ones is minor. Figure 4(a) lists the comparisons of DiaNA against classic AL strategies involving [1, 20, 25, 29]. It can be observed that compared to classic AL algorithms, with fewer labeling budgets, the effect of the proposed method is still notice" + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.887, + 0.502, + 0.898 + ], + "angle": 0, + "content": "7657" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.132, + 0.124, + 0.331, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.223, + 0.235, + 0.238, + 0.243 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.384, + 0.123, + 0.578, + 0.233 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.472, + 0.235, + 0.489, + 0.244 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.607, + 0.123, + 0.804, + 0.233 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.719, + 0.235, + 0.735, + 0.244 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image_caption", + "bbox": [ + 0.096, + 0.245, + 0.871, + 0.258 + ], + "angle": 0, + "content": "Figure 4. (a) Comparison results on CIFAR-10. (b) Combination with UDA/SSDA methods. (c) Combination with SFDA methods." + }, + { + "type": "table", + "bbox": [ + 0.134, + 0.264, + 0.413, + 0.359 + ], + "angle": 0, + "content": "
MethodALLconLentGMMAVG
DiaNAUI✓✓✓77.7±0.2
DiaNA w/o ALR✓✓✓74.8±0.4
DiaNA w/o LconUI✓✓76.9±0.3
DiaNA w/o LentUI✓✓75.8±0.3
DiaNA w/o GMMUI✓✓74.0±0.2
DiaNA-UIUI✓72.1±0.4
DiaNA-UCUC✓68.3±0.6
DiaNA-CICI✓66.4±0.8
DiaNA-CCCC✓63.0±0.3
Random (Baseline)R65.8±0.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.359, + 0.47, + 0.412 + ], + "angle": 0, + "content": "Table 3. Ablation study results of DiaNA. The \"AL\" column indicates which type of data subset should be selected to be annotated during each sampling step. We evaluated the performance of all adaptation scenarios on Office-Home by averaging their accuracy." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.419, + 0.469, + 0.461 + ], + "angle": 0, + "content": "able, resulting from its significant performance improvement. This also indicates that our sampling strategy can be effectively applied to general active learning." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.462, + 0.47, + 0.697 + ], + "angle": 0, + "content": "Combination with UDA/SSDA/SFDA methods. To validate the compatibility of the proposed DiaNA with existing UDA, SSDA, and SFDA algorithms, we conduct the experiments for UDA and SSDA in the adaptation \\(\\mathrm{C} \\rightarrow \\mathrm{S}\\) on DomainNet, and for SFDA in \\(\\mathrm{C} \\rightarrow \\mathrm{A}\\) and \\(\\mathrm{R} \\rightarrow \\mathrm{C}\\) on OfficeHome. DANN [5], MME [24], and NRC [36] correspond to the SOTA methods towards UDA, SSDA, and SFDA, respectively. As shown in Figure 4(b) and Figure 4(c), combining the selection strategy of DiaNA with other DA methods, i.e., DANN+Ours, MME+Ours, and NRC+Ours, significantly increases the performance of existing DA algorithms that select labeled target samples via random selection, namely DANN+Random, MME+Random and NRC+Random. This suggests that, adaptively considering both the domaininess and uncertainty, DiaNA is beneficial for the selection of informative target sample searching, while combined into diverse domain adaptation techniques." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.707, + 0.227, + 0.722 + ], + "angle": 0, + "content": "4.4. Ablation study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.728, + 0.469, + 0.867 + ], + "angle": 0, + "content": "Efficacy of the targeted training strategies. To illustrate the effect of each component of the proposed DiaNA, we conduct ablation study by removing the corresponding individual components. As displayed in Table 3, the proposed method exceeds all of the model variants by a large accuracy margin on average, demonstrating the effectiveness of each component. By comparing our proposed entire approach with DiaNA w/o GMM, manual data division strategy might considerably cause performance degradation, thereby in turn emphasizing the need for adaptive" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.266, + 0.892, + 0.335 + ], + "angle": 0, + "content": "data subdivision protocol. Furthermore, as demonstrated, disrupting the correspondence between targeted data subsets provides empirical evidence supporting the validity of our proposed customized learning techniques; see supplementary document for more details." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.336, + 0.893, + 0.516 + ], + "angle": 0, + "content": "Efficacy of the sampling strategy. To provide insights into how effectively the domaininess-based metric and the uncertainty-based metric work in the sampling step, we use different data subsets to replace the UI subset as active samples for annotation. To eliminate the influence of \\(\\mathcal{L}_{con}\\) and \\(\\mathcal{L}_{ent}\\), we remove these two terms but only retain \\(\\mathcal{L}_{sup}\\) during training. As shown in Table 3, both DiaNA-UC and DiaNA-CI achieve better classification performance than baseline selection, thereby showing the effect of the proposed uncertainty metric and domainness metric. Moreover, active sampling on UI samples (DiaNA-UI) obtains the best performance among all the variants, further illustrating the superiority of the integration of both metrics." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.529, + 0.627, + 0.543 + ], + "angle": 0, + "content": "5. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.552, + 0.892, + 0.72 + ], + "angle": 0, + "content": "In this paper, we introduce a \"divide-and-adapt\" framework, named DiaNA, to address the problem of active domain adaptation. Specifically, we first design an informativeness function that jointly captures sample's uncertainty and domainness. Moreover, we devise an automatic data subdivision protocol to partition the target instances into four categories with different characteristics. While selecting the most informative samples to annotate, we also design tailored learning strategies for the other target data subsets with stratified transferable properties. Extensive experimental results, as well as ablation studies, have confirmed the superiority of the proposed approach." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.733, + 0.66, + 0.749 + ], + "angle": 0, + "content": "Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.756, + 0.892, + 0.868 + ], + "angle": 0, + "content": "This work was supported in part by the Guangdong Basic and Applied Basic Research Foundation (NO. 2020B1515020048), in part by the National Natural Science Foundation of China (NO. 61976250), in part by the Shenzhen Science and Technology Program (NO. JCYJ20220530141211024) and in part by the Fundamental Research Funds for the Central Universities under Grant 22lgqb25." + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.887, + 0.502, + 0.898 + ], + "angle": 0, + "content": "7658" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.125, + 0.174, + 0.14 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.148, + 0.47, + 0.2 + ], + "angle": 0, + "content": "[1] Jordan T Ash, Chicheng Zhang, Akshay Krishnamurthy, John Langford, and Alekh Agarwal. Deep batch active learning by diverse, uncertain gradient lower bounds. In International Conference on Learning Representations, 2019." + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.201, + 0.472, + 0.263 + ], + "angle": 0, + "content": "[2] Ekin D Cubuk, Barret Zoph, Dandelion Mane, Vijay Vasudevan, and Quoc V Le. Autoaugment: Learning augmentation strategies from data. 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Divide and contrast: Source-free domain adaptation via adaptive contrastive learning. arXiv preprint arXiv:2211.06612, 2022." + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.127, + 0.471, + 0.747 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.887, + 0.502, + 0.898 + ], + "angle": 0, + "content": "7660" + } + ] +] \ No newline at end of file diff --git a/2023/Divide and Adapt_ Active Domain Adaptation via Customized Learning/86a989bf-4e7d-4c1f-bfb3-37887b13a20b_origin.pdf b/2023/Divide and Adapt_ Active Domain Adaptation via Customized Learning/86a989bf-4e7d-4c1f-bfb3-37887b13a20b_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..ac280f8f35bd326594f99ce2a99cdf632958781a --- /dev/null +++ b/2023/Divide and Adapt_ Active Domain Adaptation via Customized Learning/86a989bf-4e7d-4c1f-bfb3-37887b13a20b_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:eefaaba631afaa6ee6972fb006fa5a5af2345e24890619d9575c20f280ac4095 +size 308996 diff --git a/2023/Divide and Adapt_ Active Domain Adaptation via Customized Learning/full.md b/2023/Divide and Adapt_ Active Domain Adaptation via Customized Learning/full.md new file mode 100644 index 0000000000000000000000000000000000000000..061e00f3f868da8c53c01e3ab73e8d5bca953b3b --- /dev/null +++ b/2023/Divide and Adapt_ Active Domain Adaptation via Customized Learning/full.md @@ -0,0 +1,323 @@ +# Divide and Adapt: Active Domain Adaptation via Customized Learning + +Duojun Huang $^{1,2}$ Jichang Li $^{3}$ Weikai Chen $^{4}$ Junshi Huang $^{5}$ Zhenhua Chai $^{5}$ Guanbin Li $^{1,2\dagger}$ $^{1}$ School of Computer Science and Engineering, Sun Yat-sen University, Guangzhou, China + $^{2}$ Research Institute, Sun Yat-sen University, Shenzhen, China + $^{3}$ The University of Hong Kong ${}^{4}$ Tencent America ${}^{5}$ Meituan + +huangdj9@mail2.sysu.edu.cn, csjcli@connect.hku.hk, chenwk891@gmail.com {huangjunshi,chaizhenhua}@meituan.com, liguanbin@mail.sysu.edu.cn + +# Abstract + +Active domain adaptation (ADA) aims to improve the model adaptation performance by incorporating active learning (AL) techniques to label a maximally-informative subset of target samples. Conventional AL methods do not consider the existence of domain shift, and hence, fail to identify the truly valuable samples in the context of domain adaptation. To accommodate active learning and domain adaption, the two naturally different tasks, in a collaborative framework, we advocate that a customized learning strategy for the target data is the key to the success of ADA solutions. We present Divide-and-Adapt (DiaNA), a new ADA framework that partitions the target instances into four categories with stratified transferable properties. With a novel data subdivision protocol based on uncertainty and domaininess, DiaNA can accurately recognize the most gainful samples. While sending the informative instances for annotation, DiaNA employs tailored learning strategies for the remaining categories. Furthermore, we propose an informativeness score that unifies the data partitioning criteria. This enables the use of a Gaussian mixture model (GMM) to automatically sample unlabeled data into the proposed four categories. Thanks to the "divide-and-adapt" spirit, DiaNA can handle data with large variations of domain gap. In addition, we show that DiaNA can generalize to different domain adaptation settings, such as unsupervised domain adaptation (UDA), semi-supervised domain adaptation (SSDA), source-free domain adaptation (SFDA), etc. + +# 1. Introduction + +Domain adaptation (DA) approaches strive to generalize model trained on a labeled source domain to a target domain with rare annotation [5, 13, 16, 24] by coping with + +![](images/bcfd5e369887bee3927030178c8d339728135c12341d4b5917fc15f93b109b43.jpg) +Figure 1. The illustration of our proposed Divide-and-Adapt mechanism to divide target samples into different data subsets for customized learning. + +the domain disparity. Nevertheless, DA methods are significantly outperformed by their supervised counterparts due to the scariness of annotation as demonstrated in [4, 14, 27]. In practice, it is cost-effective to get a moderate amount of target samples labeled to boost the performance of domain adaptation. Active learning (AL) approaches seek to select samples with uncertainty [9, 12, 29, 30] and diversity [19, 25] to best benefit the model, which properly matches the demand. However, previous AL methods assume that both the labeled and unlabeled data follow the same distribution, such a strategy may become ineffective to the DA scenarios where the target data suffer from domain shift. The recently proposed active domain adaptation (ADA) [4, 22, 31] aims to resolve this issue by actively selecting the maximally-informative instances such that the performance of the transferred model can be best boosted with a limited annotation budget. + +The key to the success of ADA is to strike a good balance between the highly coupled yet inherently different tasks: active learning and domain adaptation. The real-world target data typically exhibit either of the two characteristics: + +source-like or target-specific. While the former has similar feature distribution with the source data, the latter tends to be the unique part of target domain and deviates greatly from the source distribution [4, 26, 38]. On one hand, to achieve domain adaptation, applying the same adaptation strategy to all target data equally cannot generalize well to scenarios with varying degrees of domain shift. This is particularly true when the gap between the source-like and target-specific data is unknown. On the other hand, in active learning tasks, the samples with a learning difficulty will be more likely to be selected for labeling. Nonetheless, with large domain gap, incorporating such difficult samples in the adaptation task would hamper the learning of the adaptation model, making the training highly unstable. However, despite the impressive progress that has been made, none of the existing works has fully addressed the above issues. + +In this work, we propose Divide-And-Adapt (DiaNA), a novel ADA framework that can scale to large variations of domain gaps while achieving cost-effective data labeling with a significant performance boost for domain adaptation. Our key observation is that customized learning strategies are vital for target data with different characteristics. In particular, DiaNA divides the target data into four subsets with different levels of transferable properties (see Figure 1), each of which is handled with a customized learning strategy. Unlike traditional AL methods that would simply label the most uncertain data [29, 30, 37], we propose to withhold the most challenging samples (Figure 1 category (4)) for training the domain adaption models. Instead, the selected samples for active annotation would maintain a proper stimulus for the source model, providing informative domain knowledge without jeopardizing the training stability. The subdivision of target data is dynamically updated as the domain disparity is gradually mitigated with more labeled data. Hence, the previous challenging samples could be classified as transferable in the later stage and exploited in the network training. + +We introduce a novel protocol for subdividing the target samples for customized learning. In addition to the uncertainty of model prediction, we advocate that the consistency with the learned prior distribution, i.e. the domainness, is another key criterion for active domain adaptation [4, 26]. To this end, we divide the target data into four categories as shown in Figure 1 according to the domainness and uncertainty of the instances. We further propose that the samples with 1) being uncertain to the model and 2) having inconsistent prediction with the label of its closest category prototype in the learned feature space (i.e. high domainness) are the most "profitable" instances for bringing informative knowledge of target domain if annotated. Thereby, we identify the uncertain inconsistent samples for labeling while applying tailored learning strategies for the remaining categories to boost the selectivity of the sampling. + +To avoid heuristic thresholding for data subdivision, we propose an automatic data sampling mechanism based on Gaussian mixture model (GMM). In particular, we propose an informativeness function that incorporates the domainness and uncertainty in a unified scoring system. The computed informativeness score of the labeled data is used to train a four-component GMM model, which is then applied to sample the unlabeled target data into four categories. + +We evaluate DiaNA over a large variety of domain shift scenarios on DomainNet [21], Office-Home [28] and CIFAR-10 [11]. Furthermore, the proposed sampling strategy of DiaNA can be generalized to various domain adaptation problems with different supervision settings, including unsupervised domain adaptation (UDA), semi-supervised domain adaptation (SSDA), and source-free domain adaptation (SFDA). + +We summarize our contributions as follows: + +- A general "divide-and-adapt" framework, coded DiaNA, for active domain adaptation that can handle diversified degrees of domain gaps while being able to generalize to different domain adaptation problems, including UDA, SSDA, and SFDA. +- A new target data partition strategy based on domaininess and uncertainty that enables stratified learning to achieve more stable training, superior adaptation performance, and better generality. +- A novel informativeness scoring system and the corresponding sampling paradigm based on GMM model for automatic data partitioning. +- New state-of-the-art performance over the mainstream public datasets in the task of active domain adaptation. + +# 2. Related Work + +Domain adaptation (DA). Most of the prior methods involving domain adaptation follow the unsupervised domain adaptation (UDA) paradigm that only unlabeled data is accessible in the target domain. Early UDA approaches [16, 18, 32] utilized maximum mean discrepancy (MMD) to minimize the discrepancy of features from different domains to address the domain shift, while recent adversarial learning based methods [5, 17] have become popular solutions for UDA. Despite effectiveness, UDA is still significantly outperformed by its supervised variant as indicated in [4, 14, 27]. Semi-supervised domain adaptation (SSDA) [13, 24, 35] allows a few target instances to be labeled and generally achieves improved performance. However, SSDA assumes that the labeled instances are passively provided in advance, depriving the choice of informative samples beneficial to the model. In this work, we propose an active domain adaption method to select the most informative samples, which can be incorporated into other DA methods to further boost their performance. + +![](images/20d6a4f16aa87216c84fb34818c4095c959ca3d727ad9bacb0dcdd697bb1e382.jpg) +Figure 2. We propose a general "divide-and-adapt" framework, named DiaNA, for active domain adaptation. (a) A new target data partition strategy is presented to divide target data into four categories via building an informativeness scoring function that incorporates both domainness and uncertainty metrics. Besides, an automatic data partitioning function based on a learned four-component GMM model is applied to adaptively separate four sample categories from unlabeled target data. (b) To achieve customized learning, different auxiliary techniques are integrated into model fine-tuning w.r.t the four categories of unlabeled target data. + +Active Learning (AL). Active learning is proposed to select a maximally-informative subset of unlabeled data for annotation via a query function, in an effort to best improve the model performance with a limited annotation budget. There exist several efforts to tackle the challenges involving active learning. For example, the uncertainty-based AL methods mainly focus on designing query functions based on prediction confidence [30], entropy [9, 29], or margin [10, 23] of the posterior probabilities. On the other hand, the diversity-based approaches [6, 19, 25] concentrate on selecting samples that can well represent the entire dataset. Meanwhile, expected model change-based methods [3, 15] aim to query the instances that would lead to a significant change to the current model. Recently proposed active learning approaches attain better performance by utilizing hybrid strategies which taking multiple metrics into consideration [1, 20]. Notwithstanding, the efficacy of previous AL resources may falter in DA scenarios as their selection strategy fails to meticulously consider the implications of the domain gap. + +Active Domain Adaptation (ADA). Early ADA researches [4,26] propose to measure the uncertainty and domaininess of each target instance via a domain discriminator with adversarial training. CLUE [22] presents an entropy-weighted clustering algorithm to query uncertain and diverse samples in the target domain. Recently, SDM [33] is proposed to optimize a margin loss function for exploring target instances similar to potential hard samples in the source domain. Nevertheless, the majority of existing ADA methods deliberately design hand-crafted query functions to evaluate sample's annotation value and apply the same adaptation strategy to all target data equally [4,26,31]. The rigid criteria make them easily overfit to certain domain adaption scenarios, which limits the generalization of the + +method. In contrast, we propose to integrate uncertainty and domainness metrics within a unified scoring function to select informative samples. Moreover, we apply tailored learning strategies for target data with different characteristics, constructing an effective framework capable of generalizing across large variations of domain shifts. + +# 3. Divide-and-Adapt Framework + +Problem formulation. Active domain adaptation aims at seeking an optimal model for a target domain when given labeled source data $S = \{(x_s, y_s)\}$ as well as unlabeled target data $\mathcal{U} = \{x_u\}$ , assisted by the iteratively queried labeled data $\mathcal{T} = \{(x_t, y_t)\}$ of the target domain. Here, $S, \mathcal{U},$ and $\mathcal{T}$ share the same label space over $C$ categories. Initially, $\mathcal{T}$ is an empty set. The model is iteratively trained using $S, \mathcal{T},$ and $\mathcal{U}$ for $R$ active learning loops until a given annotation budget $B$ is reached. In each active learning loop, $b = B / R$ samples from $\mathcal{U}$ would be selected, labeled by human experts, and then moved into $\mathcal{T}$ . The proposed Divide-and-Adapt framework consists of a feature extractor and a classifier. Our goal is to design a query function to identify informative samples to annotate and utilize limited amount of labeled samples to best enhance the classification performance for the target domain. + +Overview. In this paper, we propose Divide-And-Adapt, coded DiaNA, to tackle the problem of active domain adaptation. In detail, we first propose to design an informativeness function for subdividing the target samples into four categories, one of which is the informative target samples used for actively annotating. Such a function is a unified scoring system that incorporates the domainness and the uncertainty. To avoid heuristic thresholding for data subdivision, we propose an automatic data sampling mechanism to divide the unlabeled target data into four + +![](images/56fa990c17f659cb8dfda4a2e61e1bb7d6e5bdccba44bcf853a1c98adfbc0b73.jpg) +Figure 3. (a) Source-like target samples are more likely to be close to the source centroid in the feature space with respect to its predicted category. (b) Target-specific target samples are prone to be inconsistent between model predictions and similarity-based labels. + +sample categories. This is achieved by learning a four-component Gaussian mixture model using semi-supervised Expectation-Maximization algorithm. Finally, we design tailored learning strategies for different categories of target samples during model fine-tuning, thus further improving the model performance. The overview of the proposed algorithm has been summarized in Figure 2. + +# 3.1. Informativeness Scoring Mechanism + +Following previous ADA works [4, 26, 31], we aim to search for the target instances with high domainness and uncertainty. To achieve this goal, we propose to first estimate category-wise centroids based on the labeled samples, and then define a similarity-based label for each unlabeled target sample by computing its top- $k$ feature similarity with the categorical centroids. Finally, we integrate both the domainness and the uncertainty metrics into an informativeness function, which is formulated as the consistency between model prediction and similarity-based label. + +Categorical centroids. We propose to average the features of labeled samples to estimate the category-specific data distribution, i.e., category prototype. Here, we formulate the centroid with respect to the $c$ -th category as follows, + +$$ +A ^ {c} = \frac {\sum_ {(x , y) \in \mathcal {S}} \mathbb {1} \{y = c \} \cdot G (x)}{\sum_ {(x , y) \in \mathcal {S}} \mathbb {1} \{y = c \}}, \tag {1} +$$ + +where $\mathbb{1}\{\cdot\}$ is an indicator function, and $G(x)$ is a feature extractor that outputs the sample feature of $x$ . Note that, as the active learning loops proceed, labeled target samples would be incorporated into the calculation of categorical centroids to mitigate the impact of distribution change. + +Similarity-based data label. As introduced in the works [7, 13], samples share more top- $k$ indices in their respective lists of rank-ordered feature elements would have a higher probability of being the same category. To obtain the + +similarity-based label for each target instance, we first measure pairwise similarity of the indices of the sorted feature elements based on the magnitude. Then, we can formulate a similarity-based label for a sample $x$ from $\mathcal{U}$ as follows, + +$$ +\ddot {y} (x) = \underset {1 \leq c \leq C} {\operatorname {a r g m a x}} \mathbf {I o U} (\operatorname {t o p} k (G (x)), \operatorname {t o p} k \left(A ^ {c}\right)), \tag {2} +$$ + +where $\mathrm{top}k(\cdot)$ computes the top- $k$ feature element indices ranked according to their magnitudes. In addition, $\mathbf{IoU}(\cdot ,\cdot)$ denotes an Intersection-over-Union function, which returns the extent of overlap of the two respective index lists. + +We set the value of $k$ to be significantly smaller than the full dimension of the feature vector. In this way, the function $\mathrm{top}k(\cdot)$ only extracts the principle components of the feature of sample. Therefore, the IoU function in Eq. 2 is equivalent to measuring pairwise image sample similarity under a low-resolution condition. In ADA tasks, the training of model is inevitably dominated by the source domain especially in the early stage [33]. Therefore, source-like target samples that are similar to the source domain would naturally have more accurate representation than the target-specific ones that are distinct from the source. Under the low-resolution condition, i.e., $k$ set to be small, source-like samples tend to have the same similarity-based label as the model predicted class thanks to their reliable and discriminative features extracted by the model. In contrast, target-specific samples are prone to produce inconsistent results since they are typically underfitted by the current model as shown in Figure 3. Based on the analysis above, we utilize the consistency of the model predicted class and similarity-based label to evaluate the domainness of each target sample. Detailed theoretical and experimental supports are demonstrated in our supplementary. + +Informativeness function. To explore the most informative target samples, we integrate the domainness and uncertainty into a unified informativeness function (InfoF). The informativeness score for a sample $x$ from unlabeled target domain can be formulated as follows, + +$$ +\ell_ {u} (x) = - \sum_ {c = 1} ^ {C} \mathbb {1} \{c = \ddot {y} (x) \} \cdot \log P _ {c} (x), \tag {3} +$$ + +where $P(x)$ denotes the probabilistic prediction of a sample $x$ from the network model and $P_{c}(x)$ is the $c$ -th element of the vector $P(x)$ . According to Eq. 3, we can divide unlabeled target samples into two subsets depending on whether the model predicted class and the similarity-based label are identical: consistent and inconsistent subsets, while both sets have confident samples and uncertain samples depending on whether the predicted probability is greater than a given confidence threshold. We name these four categories of unlabeled target data as confident-consistent (CC), uncertain-consistent (UC), uncertain-inconsistent (UI) and + +Algorithm 1: The training procedure of four-component Gaussian Mixture Model (GMM) using semi-supervised Expectation-Maximization + +Input: $\mathcal{D}_L;\mathcal{D}_U;\alpha$ + +Output: Optimal GMM parameters $\mathcal{W}$ + +1 Initialize $\mathcal{W} = \{(\pi_k,\mu_k,\sigma_k)|1\leq k\leq K\}$ using $\mathcal{D}_L$ via Bayes estimation. +2 while $\mathcal{W}$ is not converged do +3 $\{(\ell_g^i,p_g^i)\}_{i = 1}^{|\mathcal{D}_L|}\gets \mathcal{D}_L$ +4 $\{(\ell_u^i),\})_{j = 1}^{|\mathcal{D}_U|}\gets \mathcal{D}_U$ +//Estep: +5 $\gamma_{gk}(\ell_g^i) = \mathbb{1}\{p_g^i = k\} ,$ +6 $\gamma_{uk}(\ell_u^j) = \frac{\pi_k\mathcal{N}(\ell_u^j;\mu_k,\sigma_k)}{\sum_{k' = 1}^{K}\pi_{k'}\mathcal{N}(\ell_u^j;\mu_{k'}\sigma_{k'})},$ +//Mstep: +7 $\pi_{k} = \frac{\alpha\sum_{i}\gamma_{gk}(\ell_{g}^{i}) + (1 - \alpha)\sum_{j}\gamma_{uk}(\ell_{u}^{j})}{\alpha|\mathcal{D}_{L}| + (1 - \alpha)|\mathcal{D}_{U}|};$ +8 $\mu_{k} = \frac{\alpha\sum_{i}\gamma_{gk}(\ell_{g}^{i})\cdot\ell_{g}^{i} + (1 - \alpha)\sum_{j}\gamma_{uk}^{j}\cdot\ell_{u}^{j}}{\alpha\sum_{i}\gamma_{gk}(\ell_{g}^{i}) + (1 - \alpha)\sum_{j}\gamma_{uk}(\ell_{u}^{j})};$ +9 $\sigma_{k} =$ + +$$ +\frac {\alpha \sum_ {i} \gamma_ {g k} (\ell_ {g} ^ {i}) \cdot (\ell_ {g} ^ {i} - \mu_ {k}) ^ {2} + (1 - \alpha) \sum_ {j} \gamma_ {u k} \cdot (\ell_ {u} ^ {j}) (\ell_ {u} ^ {j} - \mu_ {k}) ^ {2}}{\alpha \sum_ {i} \gamma_ {g k} (\ell_ {g} ^ {i}) + (1 - \alpha) \sum_ {j} \gamma_ {u k} (\ell_ {u} ^ {j})}; +$$ + +confident-inconsistent (CI), respectively. In this way, samples that are both uncertain to the model and contain target-specific knowledge can be extracted based on the InfoF score. In next section, we devise a strategy for informative sampling to adaptatively distinguish those subsets from unlabeled target samples. + +# 3.2. Informative Sampling Function + +During training, the varying scale of InfoF scores obtained above would hinder accurate data categorization using manual data division, leading to a biased sampling strategy and degraded performance. Therefore, our work here formulates an Informative Sampling Function to achieve the goal of adaptively selecting informative target samples. In general, it can be observed that the four categories of unlabeled target data as stated above are significantly separable in the distributions of the InfoF scores, making it possible to learn mixture models to separate four sample partitioning from unlabeled target data. Thereafter, by learning the distribution of InfoF scores using a four-component Gaussian mixture model (GMM), the target data can be adaptively mapped to the probability distribution of four categories and then be separated, thereby avoiding sampling bias that may be created by manual division. + +In specific, we first take inspiration from [34] that labeled samples can be used to construct supervision information, therefore building a more trustworthy GMM model with $K$ Gaussian components (namely $K = 4$ in this work) via a semi-supervised Expectation-Maximization al + +gorthm. To this end, we then calculate the InfoF score for a labeled sample with $(x,y)$ from $S$ or $\mathcal{T}$ as follows, + +$$ +\ell_ {g} (x, y) = - \sum_ {c = 1} ^ {C} \mathbb {1} \{c = y \} \cdot \log P _ {c} (x). \tag {4} +$$ + +The similarity-based label is determined using categorical centroids of the labeled data, resulting in the totally identical similarity-based label and model prediction for labeled samples. In order to obtain reliable supervision and build a better GMM model, we have replaced the similarity-based label with the ground-truth class label here. + +Afterwards, to obtain the supervision information for training GMM, we here define a piecewise function to obtain the observation labels that assign all labeled samples across domains to the corresponding Gaussian components. Thus, the observation label of a candidate instance $x$ can be computed as, + +$$ +q (x, y) = \left\{ \begin{array}{l l} 1, & \max P (x) \geq \tau \text {a n d} y = \arg \max P (x), \\ 2, & \max P (x) < \tau \text {a n d} y = \arg \max P (x), \\ 3, & \max P (x) < \tau \text {a n d} y \neq \arg \max P (x), \\ 4, & \max P (x) \geq \tau \text {a n d} y \neq \arg \max P (x), \end{array} \right. \tag {5} +$$ + +where the numbers, i.e., $k = 1,\dots ,4$ , indicate the indices of different Gaussian components corresponding to the CC, UC, UI and CI sample subsets, respectively. As well, $\tau$ is a confidence threshold to classify labeled samples into the confident subset and the uncertain subset. Furthermore, the comparison between the ground-truth and predicted class labels is used to divide them into the consistent subset and the inconsistent subset of labeled training samples. + +Once we obtain $\{\ell_g(x,y)|(x,y)\in S\cup \mathcal{T}\}$ $\{\ell_u(x)|x\in$ $\mathcal{U}\}$ , and $q(x,y)$ , we incorporate them into building training instances for learning the GMM model as follows, + +$$ +\mathcal {D} _ {L} \leftarrow \left\{\left(\ell_ {g} (x, y), q (x, y)\right) | (x, y) \in \mathcal {S} \cup \mathcal {T} \right\}, \tag {6} +$$ + +$$ +\mathcal {D} _ {U} \leftarrow \left\{\left(\ell_ {u} (x),\right) \mid x \in \mathcal {U} \right\}. \tag {7} +$$ + +For convenience, we denote the GMM model by $\mathcal{W} = \{(\pi_k,\mu_k,\sigma_k)|1\leq k\leq K\}$ . Afterwards, given a training instance $\ell_{x}$ from $\mathcal{D}_L$ or $\mathcal{D}_U$ , the output of the probability density functions of the GMM model regarding $\ell_{x}$ can be computed as + +$$ +p \left(\ell_ {x}\right) = \sum_ {k = 1} ^ {K} \pi_ {k} \mathcal {N} \left(\ell_ {x}; \mu_ {k}, \sigma_ {k}\right), \tag {8} +$$ + +where $\pi_{k}$ represents the weight of the $k$ -th Gaussian component subject to $\sum_{k=1}^{K} \pi_{k} = 1$ and $0 \leq \pi_{k} \leq 1$ for $k = 1, \dots, K$ , while $\mu_{k}$ and $\sigma_{k}$ are vectors denoting the mean and variance of such a component. Here, $\mathcal{N}(\cdot; \mu_{k}, \sigma_{k})$ is used to model the Gaussian distribution of the $k$ -th component. Note that a given coefficient $\alpha = |\mathcal{D}_{L}| / |\mathcal{D}_{U}|$ is + +used for the weighted integration of the labeled and unlabeled training instances. Thus, we can summarize the training procedure of the GMM model using a semi-supervised EM algorithm in Algorithm 1 according to [34]. + +After obtaining the trained GMM parameters $\mathcal{W}$ , the probability of a sample $x$ from $\mathcal{U}$ being classified into the $k$ -th component can be computed as follows, + +$$ +\Pr (z = k | x, \mathcal {W}) = \frac {\pi_ {k} \mathcal {N} \left(\ell_ {u} (x) ; \mu_ {k} , \sigma_ {k}\right)}{\sum_ {k ^ {\prime} = 1} ^ {K} \pi_ {k ^ {\prime}} \mathcal {N} \left(\ell_ {u} (x) ; \mu_ {k ^ {\prime}} , \sigma_ {k ^ {\prime}}\right)}, \tag {9} +$$ + +where $z$ is a discrete variable to infer which component the sample $x$ belongs to. + +# 3.3. Candidate Selection and Training Objectives + +After acquiring the informativeness sampling function, it is utilized for carrying out data partitioning. For ADA, the main focus should be on annotating samples that are uncertain to the model and can effectively represent the target dataset, which is termed as uncertain-inconsistent samples within our subdivision framework. Therefore, during each sampling step, we first rank the unlabeled target samples in descending order according to the scores predicted by $\operatorname{Pr}(z = 3|\cdot ,\mathcal{W})$ and then the top $b$ examples are selected to annotate and moved into labeled target data. Following previous ADA works, we apply the standard cross-entropy loss to the labeled data as follows: + +$$ +\mathcal {L} _ {s u p} = \underset {(x, y) \sim \mathcal {S} \cup \mathcal {T}} {\mathbb {E}} \left[ - \sum_ {c = 1} ^ {C} \mathbb {1} \{c = y \} \cdot \log P _ {c} (x) \right]. \tag {10} +$$ + +To boost the selectivity of the sampling strategy, we further design tailored training techniques for the other data subsets with varied transferable properties. We perform data partitioning on the remaining unlabeled target samples, i.e., $\mathcal{U}\gets \mathcal{U}\backslash \mathcal{T}$ , according to the posterior probabilities regarding the rest of Gaussian components. + +$$ +\hat {\mathcal {U}} _ {k} = \{x \mid \arg \max \mathbf {P r} (x) = k, \forall (x,) \in \mathcal {U} \}, \text {f o r} k = 1, 2, 4, \tag {11} +$$ + +where $\hat{\mathcal{U}}_1, \hat{\mathcal{U}}_2$ and $\hat{\mathcal{U}}_4$ refer to $\hat{\mathcal{U}}_{\mathrm{CC}}, \hat{\mathcal{U}}_{\mathrm{UC}}, \hat{\mathcal{U}}_{\mathrm{CI}}$ . Here, $\mathbf{Pr}(x)$ is the concatenated probability vector corresponding to different components, i.e., $\mathbf{Pr}(x) = [\operatorname{Pr}(z = 1|x, \mathcal{W}), \operatorname{Pr}(z = 2|x, \mathcal{W}), \operatorname{Pr}(z = 3|x, \mathcal{W}), \operatorname{Pr}(z = 4|x, \mathcal{W})]$ w.r.t the sample $x$ . + +As shown in Figure 1(4), the source-oriented model could produce confident but unreliable predictions for some target samples having large domain gap with the source. Samples from $\hat{\mathcal{U}}_{\mathrm{CI}}$ have extremely controversial results between model prediction and similarity-based label, which are most likely to be some excessively challenging instances. Therefore, we withhold them in the current stage to avoid jeopardizing the training stability. + +The samples in $\hat{\mathcal{U}}_{\mathrm{CC}}$ have confident and reliable predictions, which tend to be some class centroid in the target feature space. Therefore, we apply consistency regularization to them to enforce the prediction consistency under different perturbations, which can be formulated as follows: + +$$ +\mathcal {L} _ {c o n} = \underset {(x, \cdot) \sim \hat {\mathcal {U}} _ {\mathrm {C C}}} {\mathbb {E}} \left[ - \sum_ {c = 1} ^ {C} \mathbb {1} \{c = \ddot {y} (x) \} \cdot \log P _ {c} (\mathbf {A u g} (x)) \right], \tag {12} +$$ + +where $\mathbf{Aug}(\cdot)$ is a function to create perturbations for the sample $x$ using classic data augmentation techniques such as AutoAugment [2]. + +For data group $\hat{\mathcal{U}}_{\mathrm{UC}}$ whose prediction tend to be reliable but uncertain, we directly minimize the entropy of the predictions to using the following conditional entropy loss: + +$$ +\mathcal {L} _ {e n t} = \underset {(x, \cdot) \sim \hat {\mathcal {U}} _ {U C}} {\mathbb {E}} \left[ - \sum_ {c = 1} ^ {C} P _ {c} (x) \log P _ {c} (x) \right]. \tag {13} +$$ + +In summary, the overall loss functions used to further optimize the model can be formulated as follows, + +$$ +\mathcal {L} = \mathcal {L} _ {\text {s u p}} + \lambda_ {c} \mathcal {L} _ {\text {c o n}} + \lambda_ {e} \mathcal {L} _ {\text {e n t}} \tag {14} +$$ + +where $\lambda_{c}$ and $\lambda_{e}$ are the weights to trade off different loss terms during the training process. As shown in Figure 2, $\mathcal{L}_{sup}$ can calibrate the potentially underfitting of uncertain and target-specific samples. $\mathcal{L}_{con}$ can guide the model to learn global cross-domain clustering while $\mathcal{L}_{ent}$ serves to minimize the distance of data from the same class. As demonstrated in Sec. 4.3, these training objectives are complementary to each other to best adapt the model to the target domain. + +# 3.4. Compatibility with UDA/SSDA/SFDA + +The proposed sampling strategy of DiaNA requires no additional network modules like a domain discriminator or multiple classifiers [4, 26], making it easy to be integrated into existing DA frameworks, such as unsupervised domain adaptation (UDA), semi-supervised domain adaptation (SSDA), and source-free domain adaptation (SFDA); see supplementary document for the implementation details. It should be noted that we further design a variant of DiaNA for the SFDA settings, due to the unavailability of source data. As evidenced by Sec. 4.3, when integrated into diverse DA techniques, the proposed sampling strategy can deliver more performance improvement than random sample selection, thereby demonstrating its compatibility in various DA settings. To the best of our knowledge, we are the first to propose an active selection strategy that can generalize to UDA, SSDA, and SFDA methods. + +
MethodR → CC → SS → PC → QR → SR → PAVG
1k2k5k1k2k5k1k2k5k1k2k5k1k2k5k1k2k5k1k2k5k
Random50.955.261.542.644.849.441.044.450.126.333.243.038.240.746.946.548.853.740.944.550.8
CONF48.654.261.341.943.648.041.644.248.525.532.742.836.939.445.347.147.851.240.343.649.5
Entropy [29]48.054.261.942.745.248.941.143.748.724.631.042.137.040.445.746.548.452.240.043.849.9
Coreset [25]49.152.559.840.642.245.839.141.544.824.730.339.736.738.343.345.146.850.339.241.947.3
BADGE [1]51.755.462.543.645.750.142.345.549.726.034.343.937.841.547.848.050.154.241.645.451.4
Alpha [20]52.056.362.844.346.850.541.944.949.727.234.644.438.641.347.947.650.453.241.945.751.4
AADA [26]50.856.364.742.845.751.041.845.650.825.231.340.838.541.749.546.549.755.140.945.152.0
SDM [33]51.055.462.343.145.249.641.944.949.326.935.043.837.340.246.547.449.753.241.345.150.8
EADA [31]51.556.163.944.246.351.743.846.150.327.534.842.939.041.546.448.650.454.142.445.951.2
CLUE [22]54.159.466.045.348.753.744.048.053.228.835.543.240.444.451.150.052.756.443.848.153.9
DiaNA(Ours)55.660.468.747.050.856.644.249.055.430.239.552.142.447.955.050.553.659.145.050.257.8
+ +Table 1. Comparison results (Accuracy: %) on DomainNet with 1k, 2k and 5k labeling budgets. "Random" and "CONF" correspond to the classic AL approaches "Random Sampling" and "Least-Confidence Sampling". + +
MethodOffice-Home
A → CA → PA → RC → AC → PC → RP → AP → CP → RR → AR → CR → PAVG
Random52.574.377.456.369.768.957.750.975.870.054.681.365.8
Entropy [29]51.372.776.461.774.172.957.651.176.669.857.182.367.0
Coreset [25]52.873.375.559.873.470.858.152.675.869.356.582.566.7
BADGE [1]57.275.276.961.577.271.960.453.678.070.861.184.369.0
Alpha [20]57.079.478.261.678.074.158.954.278.171.761.184.669.7
AADA [26]56.678.179.058.573.771.060.153.177.070.657.084.568.3
CLUE [22]58.079.177.061.378.073.160.455.977.970.960.384.169.7
TQS [4]58.681.181.561.176.173.361.254.779.773.458.986.170.5
SDM [33]61.282.282.766.177.976.166.158.481.076.062.587.073.1
EADA [31]63.684.483.570.783.780.573.063.585.278.465.488.676.7
DiaNA(Ours)64.586.084.972.384.682.573.363.785.678.567.289.577.7
+ +Table 2. Comparison results (Accuracy: %) on Office-Home with $5\%$ labeling budget. + +# 4. Experiments + +# 4.1. Dataset + +We validate the effectiveness of the proposed approach DiaNA on three standard benchmark datasets: DomainNet [21], Office-Home [28] and CIFAR-10 [11]. On DomainNet, we select five domains namley Real (R), Clipart (C), Sketch (S), Painting (P), and Quikdraw (Q), while we hire these domains to construct 6 adaptation scenarios. As in [4, 31, 33], we report 12 different adaptation scenarios on Office-Home, constructed from four domains: Real (R), Clipart (C), Art (A), and Product (P). To further evaluate the generalization of the proposed sample selection strategy, we additionally report the classification results on CIFAR-10 with a standard active learning setting. + +# 4.2. Implementation + +Here, we mainly focus on the detailed descriptions of the settings involving active learning on DomainNet, OfficeHome, and CIFAR-10, while more implementation details can be found in the supplementary material. In each adaptation scenario, we report the average accuracy over 3 trials. + +DomainNet. Similar to CLUE [22], we consider ResNet-34 [8] as the network backbone, where such network model is pre-trained on all labeled source samples over 50 training epochs through standard supervision. In all adaptation cases, we set $B = 5000$ and $R = 10$ . + +Office-Home. To be fair, we follow the experimental settings of existing ADA works [4, 31, 33] to conduct + +performance comparison. In particular, we also use ResNet-50 [8] as the backbone model, while we choose a $5\%$ proportion of unlabeled target data to set the labeling budget $B$ , and $R$ is set to 5. + +CIFAR-10. On this dataset, we select ResNet-34 [8] as the backbone model. We randomly choose select $10\%$ training samples at random as the initially labeled data set, and we then annotate $4\%$ at each sampling step with a total annotation budget $30\%$ . + +# 4.3. Main Results + +Results on DomainNet and Office-Home. We summarize the comparison with baselines in Table 1 and Table 2 on both datasets respectively. Note that we consider varying label budgets, namely i.e., 1k, 2k, and 5k, on DomainNet. We can see that DiaNA achieves the highest average accuracy in all cases on both datasets for solving the ADA tasks. Especially in the most difficult adaptation scenarios, e.g., $\mathrm{C} \rightarrow \mathrm{A}$ and $\mathrm{R} \rightarrow \mathrm{C}$ , on Office-Home, the proposed method can still exceed all the other methods by more than $1.6\%$ and $1.8\%$ respectively, demonstrating the effectiveness of DiaNA on the commonly used DA benchmark datasets. + +Results on CIFAR-10. We also extend the proposed method to standard AL tasks on CIFAR-10, where the domain gap between labeled and unlabeled ones is minor. Figure 4(a) lists the comparisons of DiaNA against classic AL strategies involving [1, 20, 25, 29]. It can be observed that compared to classic AL algorithms, with fewer labeling budgets, the effect of the proposed method is still notice + +![](images/6c40e6776152b9f71cc6483d832a9524546a5744ffbf1190a42c04ab29760f6b.jpg) +(a) + +![](images/58165b18c7ff42a478d960ffe659a9109ca8a281ecadafa211cfd737796c6e71.jpg) +(b) +Figure 4. (a) Comparison results on CIFAR-10. (b) Combination with UDA/SSDA methods. (c) Combination with SFDA methods. + +![](images/9052ba9140705fe2d1e084df96ff77789bfcb359c2d9a0202e16a70236faa774.jpg) +(c) + +
MethodALLconLentGMMAVG
DiaNAUI✓✓✓77.7±0.2
DiaNA w/o ALR✓✓✓74.8±0.4
DiaNA w/o LconUI✓✓76.9±0.3
DiaNA w/o LentUI✓✓75.8±0.3
DiaNA w/o GMMUI✓✓74.0±0.2
DiaNA-UIUI✓72.1±0.4
DiaNA-UCUC✓68.3±0.6
DiaNA-CICI✓66.4±0.8
DiaNA-CCCC✓63.0±0.3
Random (Baseline)R65.8±0.5
+ +Table 3. Ablation study results of DiaNA. The "AL" column indicates which type of data subset should be selected to be annotated during each sampling step. We evaluated the performance of all adaptation scenarios on Office-Home by averaging their accuracy. + +able, resulting from its significant performance improvement. This also indicates that our sampling strategy can be effectively applied to general active learning. + +Combination with UDA/SSDA/SFDA methods. To validate the compatibility of the proposed DiaNA with existing UDA, SSDA, and SFDA algorithms, we conduct the experiments for UDA and SSDA in the adaptation $\mathrm{C} \rightarrow \mathrm{S}$ on DomainNet, and for SFDA in $\mathrm{C} \rightarrow \mathrm{A}$ and $\mathrm{R} \rightarrow \mathrm{C}$ on OfficeHome. DANN [5], MME [24], and NRC [36] correspond to the SOTA methods towards UDA, SSDA, and SFDA, respectively. As shown in Figure 4(b) and Figure 4(c), combining the selection strategy of DiaNA with other DA methods, i.e., DANN+Ours, MME+Ours, and NRC+Ours, significantly increases the performance of existing DA algorithms that select labeled target samples via random selection, namely DANN+Random, MME+Random and NRC+Random. This suggests that, adaptively considering both the domaininess and uncertainty, DiaNA is beneficial for the selection of informative target sample searching, while combined into diverse domain adaptation techniques. + +# 4.4. Ablation study + +Efficacy of the targeted training strategies. To illustrate the effect of each component of the proposed DiaNA, we conduct ablation study by removing the corresponding individual components. As displayed in Table 3, the proposed method exceeds all of the model variants by a large accuracy margin on average, demonstrating the effectiveness of each component. By comparing our proposed entire approach with DiaNA w/o GMM, manual data division strategy might considerably cause performance degradation, thereby in turn emphasizing the need for adaptive + +data subdivision protocol. Furthermore, as demonstrated, disrupting the correspondence between targeted data subsets provides empirical evidence supporting the validity of our proposed customized learning techniques; see supplementary document for more details. + +Efficacy of the sampling strategy. To provide insights into how effectively the domaininess-based metric and the uncertainty-based metric work in the sampling step, we use different data subsets to replace the UI subset as active samples for annotation. To eliminate the influence of $\mathcal{L}_{con}$ and $\mathcal{L}_{ent}$ , we remove these two terms but only retain $\mathcal{L}_{sup}$ during training. As shown in Table 3, both DiaNA-UC and DiaNA-CI achieve better classification performance than baseline selection, thereby showing the effect of the proposed uncertainty metric and domainness metric. Moreover, active sampling on UI samples (DiaNA-UI) obtains the best performance among all the variants, further illustrating the superiority of the integration of both metrics. + +# 5. Conclusions + +In this paper, we introduce a "divide-and-adapt" framework, named DiaNA, to address the problem of active domain adaptation. Specifically, we first design an informativeness function that jointly captures sample's uncertainty and domainness. Moreover, we devise an automatic data subdivision protocol to partition the target instances into four categories with different characteristics. While selecting the most informative samples to annotate, we also design tailored learning strategies for the other target data subsets with stratified transferable properties. Extensive experimental results, as well as ablation studies, have confirmed the superiority of the proposed approach. + +# Acknowledgments + +This work was supported in part by the Guangdong Basic and Applied Basic Research Foundation (NO. 2020B1515020048), in part by the National Natural Science Foundation of China (NO. 61976250), in part by the Shenzhen Science and Technology Program (NO. JCYJ20220530141211024) and in part by the Fundamental Research Funds for the Central Universities under Grant 22lgqb25. + +# References + +[1] Jordan T Ash, Chicheng Zhang, Akshay Krishnamurthy, John Langford, and Alekh Agarwal. Deep batch active learning by diverse, uncertain gradient lower bounds. In International Conference on Learning Representations, 2019. +[2] Ekin D Cubuk, Barret Zoph, Dandelion Mane, Vijay Vasudevan, and Quoc V Le. Autoaugment: Learning augmentation strategies from data. 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230 + ], + "type": "text", + "content": "School of Computer Science and Engineering, Sun Yat-sen University, Guangzhou, China \n" + }, + { + "bbox": [ + 58, + 174, + 521, + 230 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 58, + 174, + 521, + 230 + ], + "type": "text", + "content": "Research Institute, Sun Yat-sen University, Shenzhen, China \n" + }, + { + "bbox": [ + 58, + 174, + 521, + 230 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 58, + 174, + 521, + 230 + ], + "type": "text", + "content": "The University of Hong Kong " + }, + { + "bbox": [ + 58, + 174, + 521, + 230 + ], + "type": "inline_equation", + "content": "{}^{4}" + }, + { + "bbox": [ + 58, + 174, + 521, + 230 + ], + "type": "text", + "content": "Tencent America " + }, + { + "bbox": [ + 58, + 174, + 521, + 230 + ], + "type": "inline_equation", + "content": "{}^{5}" + }, + { + "bbox": [ + 58, + 174, + 521, + 230 + ], + "type": "text", + "content": "Meituan" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 103, + 232, + 473, + 257 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 103, + 232, + 473, + 257 + ], + "spans": [ + { + "bbox": [ + 103, + 232, + 473, + 257 + ], + "type": "text", + "content": "huangdj9@mail2.sysu.edu.cn, csjcli@connect.hku.hk, chenwk891@gmail.com {huangjunshi,chaizhenhua}@meituan.com, liguanbin@mail.sysu.edu.cn" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 139, + 283, + 186, + 296 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 139, + 283, + 186, + 296 + ], + "spans": [ + { + "bbox": [ + 139, + 283, + 186, + 296 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 309, + 281, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 309, + 281, + 634 + ], + "spans": [ + { + "bbox": [ + 45, + 309, + 281, + 634 + ], + "type": "text", + "content": "Active domain adaptation (ADA) aims to improve the model adaptation performance by incorporating active learning (AL) techniques to label a maximally-informative subset of target samples. Conventional AL methods do not consider the existence of domain shift, and hence, fail to identify the truly valuable samples in the context of domain adaptation. To accommodate active learning and domain adaption, the two naturally different tasks, in a collaborative framework, we advocate that a customized learning strategy for the target data is the key to the success of ADA solutions. We present Divide-and-Adapt (DiaNA), a new ADA framework that partitions the target instances into four categories with stratified transferable properties. With a novel data subdivision protocol based on uncertainty and domaininess, DiaNA can accurately recognize the most gainful samples. While sending the informative instances for annotation, DiaNA employs tailored learning strategies for the remaining categories. Furthermore, we propose an informativeness score that unifies the data partitioning criteria. This enables the use of a Gaussian mixture model (GMM) to automatically sample unlabeled data into the proposed four categories. Thanks to the \"divide-and-adapt\" spirit, DiaNA can handle data with large variations of domain gap. In addition, we show that DiaNA can generalize to different domain adaptation settings, such as unsupervised domain adaptation (UDA), semi-supervised domain adaptation (SSDA), source-free domain adaptation (SFDA), etc." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 656, + 124, + 668 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 656, + 124, + 668 + ], + "spans": [ + { + "bbox": [ + 47, + 656, + 124, + 668 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 676, + 279, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 676, + 279, + 712 + ], + "spans": [ + { + "bbox": [ + 45, + 676, + 279, + 712 + ], + "type": "text", + "content": "Domain adaptation (DA) approaches strive to generalize model trained on a labeled source domain to a target domain with rare annotation [5, 13, 16, 24] by coping with" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 305, + 289, + 523, + 441 + ], + "blocks": [ + { + "bbox": [ + 305, + 289, + 523, + 441 + ], + "lines": [ + { + "bbox": [ + 305, + 289, + 523, + 441 + ], + "spans": [ + { + "bbox": [ + 305, + 289, + 523, + 441 + ], + "type": "image", + "image_path": "bcfd5e369887bee3927030178c8d339728135c12341d4b5917fc15f93b109b43.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 296, + 443, + 531, + 477 + ], + "lines": [ + { + "bbox": [ + 296, + 443, + 531, + 477 + ], + "spans": [ + { + "bbox": [ + 296, + 443, + 531, + 477 + ], + "type": "text", + "content": "Figure 1. The illustration of our proposed Divide-and-Adapt mechanism to divide target samples into different data subsets for customized learning." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 296, + 484, + 530, + 682 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 484, + 530, + 682 + ], + "spans": [ + { + "bbox": [ + 296, + 484, + 530, + 682 + ], + "type": "text", + "content": "the domain disparity. Nevertheless, DA methods are significantly outperformed by their supervised counterparts due to the scariness of annotation as demonstrated in [4, 14, 27]. In practice, it is cost-effective to get a moderate amount of target samples labeled to boost the performance of domain adaptation. Active learning (AL) approaches seek to select samples with uncertainty [9, 12, 29, 30] and diversity [19, 25] to best benefit the model, which properly matches the demand. However, previous AL methods assume that both the labeled and unlabeled data follow the same distribution, such a strategy may become ineffective to the DA scenarios where the target data suffer from domain shift. The recently proposed active domain adaptation (ADA) [4, 22, 31] aims to resolve this issue by actively selecting the maximally-informative instances such that the performance of the transferred model can be best boosted with a limited annotation budget." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 296, + 683, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 683, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 683, + 530, + 730 + ], + "type": "text", + "content": "The key to the success of ADA is to strike a good balance between the highly coupled yet inherently different tasks: active learning and domain adaptation. The real-world target data typically exhibit either of the two characteristics:" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 77, + 42, + 119, + 71 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 42, + 119, + 71 + ], + "spans": [ + { + "bbox": [ + 77, + 42, + 119, + 71 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 150, + 41, + 471, + 74 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 150, + 41, + 471, + 74 + ], + "spans": [ + { + "bbox": [ + 150, + 41, + 471, + 74 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 718, + 177, + 730 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 718, + 177, + 730 + ], + "spans": [ + { + "bbox": [ + 56, + 718, + 177, + 730 + ], + "type": "text", + "content": "† Corresponding author is Guanbin Li." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "text", + "content": "7651" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 45, + 106, + 281, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 106, + 281, + 293 + ], + "spans": [ + { + "bbox": [ + 45, + 106, + 281, + 293 + ], + "type": "text", + "content": "source-like or target-specific. While the former has similar feature distribution with the source data, the latter tends to be the unique part of target domain and deviates greatly from the source distribution [4, 26, 38]. On one hand, to achieve domain adaptation, applying the same adaptation strategy to all target data equally cannot generalize well to scenarios with varying degrees of domain shift. This is particularly true when the gap between the source-like and target-specific data is unknown. On the other hand, in active learning tasks, the samples with a learning difficulty will be more likely to be selected for labeling. Nonetheless, with large domain gap, incorporating such difficult samples in the adaptation task would hamper the learning of the adaptation model, making the training highly unstable. However, despite the impressive progress that has been made, none of the existing works has fully addressed the above issues." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 295, + 281, + 541 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 295, + 281, + 541 + ], + "spans": [ + { + "bbox": [ + 45, + 295, + 281, + 541 + ], + "type": "text", + "content": "In this work, we propose Divide-And-Adapt (DiaNA), a novel ADA framework that can scale to large variations of domain gaps while achieving cost-effective data labeling with a significant performance boost for domain adaptation. Our key observation is that customized learning strategies are vital for target data with different characteristics. In particular, DiaNA divides the target data into four subsets with different levels of transferable properties (see Figure 1), each of which is handled with a customized learning strategy. Unlike traditional AL methods that would simply label the most uncertain data [29, 30, 37], we propose to withhold the most challenging samples (Figure 1 category (4)) for training the domain adaption models. Instead, the selected samples for active annotation would maintain a proper stimulus for the source model, providing informative domain knowledge without jeopardizing the training stability. The subdivision of target data is dynamically updated as the domain disparity is gradually mitigated with more labeled data. Hence, the previous challenging samples could be classified as transferable in the later stage and exploited in the network training." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 543, + 281, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 543, + 281, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 543, + 281, + 730 + ], + "type": "text", + "content": "We introduce a novel protocol for subdividing the target samples for customized learning. In addition to the uncertainty of model prediction, we advocate that the consistency with the learned prior distribution, i.e. the domainness, is another key criterion for active domain adaptation [4, 26]. To this end, we divide the target data into four categories as shown in Figure 1 according to the domainness and uncertainty of the instances. We further propose that the samples with 1) being uncertain to the model and 2) having inconsistent prediction with the label of its closest category prototype in the learned feature space (i.e. high domainness) are the most \"profitable\" instances for bringing informative knowledge of target domain if annotated. Thereby, we identify the uncertain inconsistent samples for labeling while applying tailored learning strategies for the remaining categories to boost the selectivity of the sampling." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 296, + 106, + 530, + 199 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 106, + 530, + 199 + ], + "spans": [ + { + "bbox": [ + 296, + 106, + 530, + 199 + ], + "type": "text", + "content": "To avoid heuristic thresholding for data subdivision, we propose an automatic data sampling mechanism based on Gaussian mixture model (GMM). In particular, we propose an informativeness function that incorporates the domainness and uncertainty in a unified scoring system. The computed informativeness score of the labeled data is used to train a four-component GMM model, which is then applied to sample the unlabeled target data into four categories." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 296, + 199, + 531, + 292 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 199, + 531, + 292 + ], + "spans": [ + { + "bbox": [ + 296, + 199, + 531, + 292 + ], + "type": "text", + "content": "We evaluate DiaNA over a large variety of domain shift scenarios on DomainNet [21], Office-Home [28] and CIFAR-10 [11]. Furthermore, the proposed sampling strategy of DiaNA can be generalized to various domain adaptation problems with different supervision settings, including unsupervised domain adaptation (UDA), semi-supervised domain adaptation (SSDA), and source-free domain adaptation (SFDA)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 308, + 293, + 483, + 303 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 293, + 483, + 303 + ], + "spans": [ + { + "bbox": [ + 308, + 293, + 483, + 303 + ], + "type": "text", + "content": "We summarize our contributions as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 307, + 305, + 530, + 473 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 307, + 305, + 530, + 362 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 305, + 530, + 362 + ], + "spans": [ + { + "bbox": [ + 307, + 305, + 530, + 362 + ], + "type": "text", + "content": "- A general \"divide-and-adapt\" framework, coded DiaNA, for active domain adaptation that can handle diversified degrees of domain gaps while being able to generalize to different domain adaptation problems, including UDA, SSDA, and SFDA." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 307, + 365, + 530, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 365, + 530, + 411 + ], + "spans": [ + { + "bbox": [ + 307, + 365, + 530, + 411 + ], + "type": "text", + "content": "- A new target data partition strategy based on domaininess and uncertainty that enables stratified learning to achieve more stable training, superior adaptation performance, and better generality." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 307, + 413, + 530, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 413, + 530, + 448 + ], + "spans": [ + { + "bbox": [ + 307, + 413, + 530, + 448 + ], + "type": "text", + "content": "- A novel informativeness scoring system and the corresponding sampling paradigm based on GMM model for automatic data partitioning." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 307, + 449, + 530, + 473 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 449, + 530, + 473 + ], + "spans": [ + { + "bbox": [ + 307, + 449, + 530, + 473 + ], + "type": "text", + "content": "- New state-of-the-art performance over the mainstream public datasets in the task of active domain adaptation." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 297, + 489, + 381, + 500 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 489, + 381, + 500 + ], + "spans": [ + { + "bbox": [ + 297, + 489, + 381, + 500 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 296, + 508, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 508, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 508, + 530, + 730 + ], + "type": "text", + "content": "Domain adaptation (DA). Most of the prior methods involving domain adaptation follow the unsupervised domain adaptation (UDA) paradigm that only unlabeled data is accessible in the target domain. Early UDA approaches [16, 18, 32] utilized maximum mean discrepancy (MMD) to minimize the discrepancy of features from different domains to address the domain shift, while recent adversarial learning based methods [5, 17] have become popular solutions for UDA. Despite effectiveness, UDA is still significantly outperformed by its supervised variant as indicated in [4, 14, 27]. Semi-supervised domain adaptation (SSDA) [13, 24, 35] allows a few target instances to be labeled and generally achieves improved performance. However, SSDA assumes that the labeled instances are passively provided in advance, depriving the choice of informative samples beneficial to the model. In this work, we propose an active domain adaption method to select the most informative samples, which can be incorporated into other DA methods to further boost their performance." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "text", + "content": "7652" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 87, + 105, + 489, + 256 + ], + "blocks": [ + { + "bbox": [ + 87, + 105, + 489, + 256 + ], + "lines": [ + { + "bbox": [ + 87, + 105, + 489, + 256 + ], + "spans": [ + { + "bbox": [ + 87, + 105, + 489, + 256 + ], + "type": "image", + "image_path": "20d6a4f16aa87216c84fb34818c4095c959ca3d727ad9bacb0dcdd697bb1e382.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 257, + 532, + 312 + ], + "lines": [ + { + "bbox": [ + 45, + 257, + 532, + 312 + ], + "spans": [ + { + "bbox": [ + 45, + 257, + 532, + 312 + ], + "type": "text", + "content": "Figure 2. We propose a general \"divide-and-adapt\" framework, named DiaNA, for active domain adaptation. (a) A new target data partition strategy is presented to divide target data into four categories via building an informativeness scoring function that incorporates both domainness and uncertainty metrics. Besides, an automatic data partitioning function based on a learned four-component GMM model is applied to adaptively separate four sample categories from unlabeled target data. (b) To achieve customized learning, different auxiliary techniques are integrated into model fine-tuning w.r.t the four categories of unlabeled target data." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 323, + 281, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 323, + 281, + 556 + ], + "spans": [ + { + "bbox": [ + 45, + 323, + 281, + 556 + ], + "type": "text", + "content": "Active Learning (AL). Active learning is proposed to select a maximally-informative subset of unlabeled data for annotation via a query function, in an effort to best improve the model performance with a limited annotation budget. There exist several efforts to tackle the challenges involving active learning. For example, the uncertainty-based AL methods mainly focus on designing query functions based on prediction confidence [30], entropy [9, 29], or margin [10, 23] of the posterior probabilities. On the other hand, the diversity-based approaches [6, 19, 25] concentrate on selecting samples that can well represent the entire dataset. Meanwhile, expected model change-based methods [3, 15] aim to query the instances that would lead to a significant change to the current model. Recently proposed active learning approaches attain better performance by utilizing hybrid strategies which taking multiple metrics into consideration [1, 20]. Notwithstanding, the efficacy of previous AL resources may falter in DA scenarios as their selection strategy fails to meticulously consider the implications of the domain gap." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 566, + 281, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 566, + 281, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 566, + 281, + 730 + ], + "type": "text", + "content": "Active Domain Adaptation (ADA). Early ADA researches [4,26] propose to measure the uncertainty and domaininess of each target instance via a domain discriminator with adversarial training. CLUE [22] presents an entropy-weighted clustering algorithm to query uncertain and diverse samples in the target domain. Recently, SDM [33] is proposed to optimize a margin loss function for exploring target instances similar to potential hard samples in the source domain. Nevertheless, the majority of existing ADA methods deliberately design hand-crafted query functions to evaluate sample's annotation value and apply the same adaptation strategy to all target data equally [4,26,31]. The rigid criteria make them easily overfit to certain domain adaption scenarios, which limits the generalization of the" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 296, + 323, + 530, + 394 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 323, + 530, + 394 + ], + "spans": [ + { + "bbox": [ + 296, + 323, + 530, + 394 + ], + "type": "text", + "content": "method. In contrast, we propose to integrate uncertainty and domainness metrics within a unified scoring function to select informative samples. Moreover, we apply tailored learning strategies for target data with different characteristics, constructing an effective framework capable of generalizing across large variations of domain shifts." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 296, + 405, + 464, + 420 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 405, + 464, + 420 + ], + "spans": [ + { + "bbox": [ + 296, + 405, + 464, + 420 + ], + "type": "text", + "content": "3. Divide-and-Adapt Framework" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 296, + 426, + 530, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 426, + 530, + 612 + ], + "spans": [ + { + "bbox": [ + 296, + 426, + 530, + 612 + ], + "type": "text", + "content": "Problem formulation. Active domain adaptation aims at seeking an optimal model for a target domain when given labeled source data " + }, + { + "bbox": [ + 296, + 426, + 530, + 612 + ], + "type": "inline_equation", + "content": "S = \\{(x_s, y_s)\\}" + }, + { + "bbox": [ + 296, + 426, + 530, + 612 + ], + "type": "text", + "content": " as well as unlabeled target data " + }, + { + "bbox": [ + 296, + 426, + 530, + 612 + ], + "type": "inline_equation", + "content": "\\mathcal{U} = \\{x_u\\}" + }, + { + "bbox": [ + 296, + 426, + 530, + 612 + ], + "type": "text", + "content": ", assisted by the iteratively queried labeled data " + }, + { + "bbox": [ + 296, + 426, + 530, + 612 + ], + "type": "inline_equation", + "content": "\\mathcal{T} = \\{(x_t, y_t)\\}" + }, + { + "bbox": [ + 296, + 426, + 530, + 612 + ], + "type": "text", + "content": " of the target domain. Here, " + }, + { + "bbox": [ + 296, + 426, + 530, + 612 + ], + "type": "inline_equation", + "content": "S, \\mathcal{U}," + }, + { + "bbox": [ + 296, + 426, + 530, + 612 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 426, + 530, + 612 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 296, + 426, + 530, + 612 + ], + "type": "text", + "content": " share the same label space over " + }, + { + "bbox": [ + 296, + 426, + 530, + 612 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 296, + 426, + 530, + 612 + ], + "type": "text", + "content": " categories. Initially, " + }, + { + "bbox": [ + 296, + 426, + 530, + 612 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 296, + 426, + 530, + 612 + ], + "type": "text", + "content": " is an empty set. The model is iteratively trained using " + }, + { + "bbox": [ + 296, + 426, + 530, + 612 + ], + "type": "inline_equation", + "content": "S, \\mathcal{T}," + }, + { + "bbox": [ + 296, + 426, + 530, + 612 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 426, + 530, + 612 + ], + "type": "inline_equation", + "content": "\\mathcal{U}" + }, + { + "bbox": [ + 296, + 426, + 530, + 612 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 296, + 426, + 530, + 612 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 296, + 426, + 530, + 612 + ], + "type": "text", + "content": " active learning loops until a given annotation budget " + }, + { + "bbox": [ + 296, + 426, + 530, + 612 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 296, + 426, + 530, + 612 + ], + "type": "text", + "content": " is reached. In each active learning loop, " + }, + { + "bbox": [ + 296, + 426, + 530, + 612 + ], + "type": "inline_equation", + "content": "b = B / R" + }, + { + "bbox": [ + 296, + 426, + 530, + 612 + ], + "type": "text", + "content": " samples from " + }, + { + "bbox": [ + 296, + 426, + 530, + 612 + ], + "type": "inline_equation", + "content": "\\mathcal{U}" + }, + { + "bbox": [ + 296, + 426, + 530, + 612 + ], + "type": "text", + "content": " would be selected, labeled by human experts, and then moved into " + }, + { + "bbox": [ + 296, + 426, + 530, + 612 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 296, + 426, + 530, + 612 + ], + "type": "text", + "content": ". The proposed Divide-and-Adapt framework consists of a feature extractor and a classifier. Our goal is to design a query function to identify informative samples to annotate and utilize limited amount of labeled samples to best enhance the classification performance for the target domain." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 296, + 613, + 531, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 613, + 531, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 613, + 531, + 730 + ], + "type": "text", + "content": "Overview. In this paper, we propose Divide-And-Adapt, coded DiaNA, to tackle the problem of active domain adaptation. In detail, we first propose to design an informativeness function for subdividing the target samples into four categories, one of which is the informative target samples used for actively annotating. Such a function is a unified scoring system that incorporates the domainness and the uncertainty. To avoid heuristic thresholding for data subdivision, we propose an automatic data sampling mechanism to divide the unlabeled target data into four" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "text", + "content": "7653" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 107, + 263, + 225 + ], + "blocks": [ + { + "bbox": [ + 61, + 107, + 263, + 225 + ], + "lines": [ + { + "bbox": [ + 61, + 107, + 263, + 225 + ], + "spans": [ + { + "bbox": [ + 61, + 107, + 263, + 225 + ], + "type": "image", + "image_path": "56fa990c17f659cb8dfda4a2e61e1bb7d6e5bdccba44bcf853a1c98adfbc0b73.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 225, + 279, + 277 + ], + "lines": [ + { + "bbox": [ + 45, + 225, + 279, + 277 + ], + "spans": [ + { + "bbox": [ + 45, + 225, + 279, + 277 + ], + "type": "text", + "content": "Figure 3. (a) Source-like target samples are more likely to be close to the source centroid in the feature space with respect to its predicted category. (b) Target-specific target samples are prone to be inconsistent between model predictions and similarity-based labels." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 290, + 279, + 372 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 290, + 279, + 372 + ], + "spans": [ + { + "bbox": [ + 45, + 290, + 279, + 372 + ], + "type": "text", + "content": "sample categories. This is achieved by learning a four-component Gaussian mixture model using semi-supervised Expectation-Maximization algorithm. Finally, we design tailored learning strategies for different categories of target samples during model fine-tuning, thus further improving the model performance. The overview of the proposed algorithm has been summarized in Figure 2." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 379, + 233, + 392 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 379, + 233, + 392 + ], + "spans": [ + { + "bbox": [ + 45, + 379, + 233, + 392 + ], + "type": "text", + "content": "3.1. Informativeness Scoring Mechanism" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 396, + 279, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 396, + 279, + 513 + ], + "spans": [ + { + "bbox": [ + 45, + 396, + 279, + 513 + ], + "type": "text", + "content": "Following previous ADA works [4, 26, 31], we aim to search for the target instances with high domainness and uncertainty. To achieve this goal, we propose to first estimate category-wise centroids based on the labeled samples, and then define a similarity-based label for each unlabeled target sample by computing its top-" + }, + { + "bbox": [ + 45, + 396, + 279, + 513 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 45, + 396, + 279, + 513 + ], + "type": "text", + "content": " feature similarity with the categorical centroids. Finally, we integrate both the domainness and the uncertainty metrics into an informativeness function, which is formulated as the consistency between model prediction and similarity-based label." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 527, + 279, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 527, + 279, + 574 + ], + "spans": [ + { + "bbox": [ + 45, + 527, + 279, + 574 + ], + "type": "text", + "content": "Categorical centroids. We propose to average the features of labeled samples to estimate the category-specific data distribution, i.e., category prototype. Here, we formulate the centroid with respect to the " + }, + { + "bbox": [ + 45, + 527, + 279, + 574 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 45, + 527, + 279, + 574 + ], + "type": "text", + "content": "-th category as follows," + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 93, + 580, + 279, + 611 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 580, + 279, + 611 + ], + "spans": [ + { + "bbox": [ + 93, + 580, + 279, + 611 + ], + "type": "interline_equation", + "content": "A ^ {c} = \\frac {\\sum_ {(x , y) \\in \\mathcal {S}} \\mathbb {1} \\{y = c \\} \\cdot G (x)}{\\sum_ {(x , y) \\in \\mathcal {S}} \\mathbb {1} \\{y = c \\}}, \\tag {1}", + "image_path": "329279dd2a5fbb5e0d9b5928b52534bb15e79c4c29ae251a801eddb94c5afa60.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 618, + 279, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 618, + 279, + 677 + ], + "spans": [ + { + "bbox": [ + 45, + 618, + 279, + 677 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 45, + 618, + 279, + 677 + ], + "type": "inline_equation", + "content": "\\mathbb{1}\\{\\cdot\\}" + }, + { + "bbox": [ + 45, + 618, + 279, + 677 + ], + "type": "text", + "content": " is an indicator function, and " + }, + { + "bbox": [ + 45, + 618, + 279, + 677 + ], + "type": "inline_equation", + "content": "G(x)" + }, + { + "bbox": [ + 45, + 618, + 279, + 677 + ], + "type": "text", + "content": " is a feature extractor that outputs the sample feature of " + }, + { + "bbox": [ + 45, + 618, + 279, + 677 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 45, + 618, + 279, + 677 + ], + "type": "text", + "content": ". Note that, as the active learning loops proceed, labeled target samples would be incorporated into the calculation of categorical centroids to mitigate the impact of distribution change." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 682, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 682, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 682, + 279, + 730 + ], + "type": "text", + "content": "Similarity-based data label. As introduced in the works [7, 13], samples share more top-" + }, + { + "bbox": [ + 45, + 682, + 279, + 730 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 45, + 682, + 279, + 730 + ], + "type": "text", + "content": " indices in their respective lists of rank-ordered feature elements would have a higher probability of being the same category. To obtain the" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 296, + 106, + 530, + 153 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 106, + 530, + 153 + ], + "spans": [ + { + "bbox": [ + 296, + 106, + 530, + 153 + ], + "type": "text", + "content": "similarity-based label for each target instance, we first measure pairwise similarity of the indices of the sorted feature elements based on the magnitude. Then, we can formulate a similarity-based label for a sample " + }, + { + "bbox": [ + 296, + 106, + 530, + 153 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 296, + 106, + 530, + 153 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 296, + 106, + 530, + 153 + ], + "type": "inline_equation", + "content": "\\mathcal{U}" + }, + { + "bbox": [ + 296, + 106, + 530, + 153 + ], + "type": "text", + "content": " as follows," + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 323, + 160, + 530, + 181 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 160, + 530, + 181 + ], + "spans": [ + { + "bbox": [ + 323, + 160, + 530, + 181 + ], + "type": "interline_equation", + "content": "\\ddot {y} (x) = \\underset {1 \\leq c \\leq C} {\\operatorname {a r g m a x}} \\mathbf {I o U} (\\operatorname {t o p} k (G (x)), \\operatorname {t o p} k \\left(A ^ {c}\\right)), \\tag {2}", + "image_path": "54dbb321aa3e090dbacce1265720565d331c03d5595cb83292a59f96d68582b7.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 296, + 188, + 530, + 234 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 188, + 530, + 234 + ], + "spans": [ + { + "bbox": [ + 296, + 188, + 530, + 234 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 296, + 188, + 530, + 234 + ], + "type": "inline_equation", + "content": "\\mathrm{top}k(\\cdot)" + }, + { + "bbox": [ + 296, + 188, + 530, + 234 + ], + "type": "text", + "content": " computes the top- " + }, + { + "bbox": [ + 296, + 188, + 530, + 234 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 296, + 188, + 530, + 234 + ], + "type": "text", + "content": " feature element indices ranked according to their magnitudes. In addition, " + }, + { + "bbox": [ + 296, + 188, + 530, + 234 + ], + "type": "inline_equation", + "content": "\\mathbf{IoU}(\\cdot ,\\cdot)" + }, + { + "bbox": [ + 296, + 188, + 530, + 234 + ], + "type": "text", + "content": " denotes an Intersection-over-Union function, which returns the extent of overlap of the two respective index lists." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 296, + 235, + 530, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 235, + 530, + 491 + ], + "spans": [ + { + "bbox": [ + 296, + 235, + 530, + 491 + ], + "type": "text", + "content": "We set the value of " + }, + { + "bbox": [ + 296, + 235, + 530, + 491 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 296, + 235, + 530, + 491 + ], + "type": "text", + "content": " to be significantly smaller than the full dimension of the feature vector. In this way, the function " + }, + { + "bbox": [ + 296, + 235, + 530, + 491 + ], + "type": "inline_equation", + "content": "\\mathrm{top}k(\\cdot)" + }, + { + "bbox": [ + 296, + 235, + 530, + 491 + ], + "type": "text", + "content": " only extracts the principle components of the feature of sample. Therefore, the IoU function in Eq. 2 is equivalent to measuring pairwise image sample similarity under a low-resolution condition. In ADA tasks, the training of model is inevitably dominated by the source domain especially in the early stage [33]. Therefore, source-like target samples that are similar to the source domain would naturally have more accurate representation than the target-specific ones that are distinct from the source. Under the low-resolution condition, i.e., " + }, + { + "bbox": [ + 296, + 235, + 530, + 491 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 296, + 235, + 530, + 491 + ], + "type": "text", + "content": " set to be small, source-like samples tend to have the same similarity-based label as the model predicted class thanks to their reliable and discriminative features extracted by the model. In contrast, target-specific samples are prone to produce inconsistent results since they are typically underfitted by the current model as shown in Figure 3. Based on the analysis above, we utilize the consistency of the model predicted class and similarity-based label to evaluate the domainness of each target sample. Detailed theoretical and experimental supports are demonstrated in our supplementary." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 296, + 497, + 530, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 497, + 530, + 554 + ], + "spans": [ + { + "bbox": [ + 296, + 497, + 530, + 554 + ], + "type": "text", + "content": "Informativeness function. To explore the most informative target samples, we integrate the domainness and uncertainty into a unified informativeness function (InfoF). The informativeness score for a sample " + }, + { + "bbox": [ + 296, + 497, + 530, + 554 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 296, + 497, + 530, + 554 + ], + "type": "text", + "content": " from unlabeled target domain can be formulated as follows," + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 333, + 562, + 530, + 594 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 333, + 562, + 530, + 594 + ], + "spans": [ + { + "bbox": [ + 333, + 562, + 530, + 594 + ], + "type": "interline_equation", + "content": "\\ell_ {u} (x) = - \\sum_ {c = 1} ^ {C} \\mathbb {1} \\{c = \\ddot {y} (x) \\} \\cdot \\log P _ {c} (x), \\tag {3}", + "image_path": "786afba450607f719234bf96b9cfd9ceb589f955f3eec2f5a5db84f844a30106.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 296, + 601, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 601, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 601, + 530, + 730 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 296, + 601, + 530, + 730 + ], + "type": "inline_equation", + "content": "P(x)" + }, + { + "bbox": [ + 296, + 601, + 530, + 730 + ], + "type": "text", + "content": " denotes the probabilistic prediction of a sample " + }, + { + "bbox": [ + 296, + 601, + 530, + 730 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 296, + 601, + 530, + 730 + ], + "type": "text", + "content": " from the network model and " + }, + { + "bbox": [ + 296, + 601, + 530, + 730 + ], + "type": "inline_equation", + "content": "P_{c}(x)" + }, + { + "bbox": [ + 296, + 601, + 530, + 730 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 296, + 601, + 530, + 730 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 296, + 601, + 530, + 730 + ], + "type": "text", + "content": "-th element of the vector " + }, + { + "bbox": [ + 296, + 601, + 530, + 730 + ], + "type": "inline_equation", + "content": "P(x)" + }, + { + "bbox": [ + 296, + 601, + 530, + 730 + ], + "type": "text", + "content": ". According to Eq. 3, we can divide unlabeled target samples into two subsets depending on whether the model predicted class and the similarity-based label are identical: consistent and inconsistent subsets, while both sets have confident samples and uncertain samples depending on whether the predicted probability is greater than a given confidence threshold. We name these four categories of unlabeled target data as confident-consistent (CC), uncertain-consistent (UC), uncertain-inconsistent (UI) and" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "text", + "content": "7654" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 50, + 108, + 252, + 143 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 108, + 252, + 143 + ], + "spans": [ + { + "bbox": [ + 50, + 108, + 252, + 143 + ], + "type": "text", + "content": "Algorithm 1: The training procedure of four-component Gaussian Mixture Model (GMM) using semi-supervised Expectation-Maximization" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 58, + 145, 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"\\mathcal{W}" + }, + { + "bbox": [ + 50, + 192, + 174, + 203 + ], + "type": "text", + "content": " is not converged do" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 50, + 203, + 158, + 219 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 203, + 158, + 219 + ], + "spans": [ + { + "bbox": [ + 50, + 203, + 158, + 219 + ], + "type": "text", + "content": "3 " + }, + { + "bbox": [ + 50, + 203, + 158, + 219 + ], + "type": "inline_equation", + "content": "\\{(\\ell_g^i,p_g^i)\\}_{i = 1}^{|\\mathcal{D}_L|}\\gets \\mathcal{D}_L" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 50, + 219, + 151, + 234 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 219, + 151, + 234 + ], + "spans": [ + { + "bbox": [ + 50, + 219, + 151, + 234 + ], + "type": "text", + "content": "4 " + }, + { + "bbox": [ + 50, + 219, + 151, + 234 + ], + "type": "inline_equation", + "content": "\\{(\\ell_u^i),\\})_{j = 1}^{|\\mathcal{D}_U|}\\gets \\mathcal{D}_U" + } + ] 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\\alpha)|\\mathcal{D}_{U}|};" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 50, + 304, + 221, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 304, + 221, + 326 + ], + "spans": [ + { + "bbox": [ + 50, + 304, + 221, + 326 + ], + "type": "text", + "content": "8 " + }, + { + "bbox": [ + 50, + 304, + 221, + 326 + ], + "type": "inline_equation", + "content": "\\mu_{k} = \\frac{\\alpha\\sum_{i}\\gamma_{gk}(\\ell_{g}^{i})\\cdot\\ell_{g}^{i} + (1 - \\alpha)\\sum_{j}\\gamma_{uk}^{j}\\cdot\\ell_{u}^{j}}{\\alpha\\sum_{i}\\gamma_{gk}(\\ell_{g}^{i}) + (1 - \\alpha)\\sum_{j}\\gamma_{uk}(\\ell_{u}^{j})};" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 50, + 327, + 96, + 336 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 327, + 96, + 336 + ], + "spans": [ + { + "bbox": [ + 50, + 327, + 96, + 336 + ], + "type": "text", + "content": "9 " + }, + { + "bbox": [ + 50, + 327, + 96, + 336 + ], + "type": "inline_equation", + "content": "\\sigma_{k} =" + } + ] + } + ], + "index": 13 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 79, + 337, + 266, + 360 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 79, + 337, + 266, + 360 + ], + "spans": [ + { + "bbox": [ + 79, + 337, + 266, + 360 + ], + "type": "interline_equation", + "content": "\\frac {\\alpha \\sum_ {i} \\gamma_ {g k} (\\ell_ {g} ^ {i}) \\cdot (\\ell_ {g} ^ {i} - \\mu_ {k}) ^ {2} + (1 - \\alpha) \\sum_ {j} \\gamma_ {u k} \\cdot (\\ell_ {u} ^ {j}) (\\ell_ {u} ^ {j} - \\mu_ {k}) ^ {2}}{\\alpha \\sum_ {i} \\gamma_ {g k} (\\ell_ {g} ^ {i}) + (1 - \\alpha) \\sum_ {j} \\gamma_ {u k} (\\ell_ {u} ^ {j})};", + "image_path": "22916057d52d6a0fa12c6c5d64d1142307be005ec5691cb3d4c6159bd694d093.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 45, + 389, + 279, + 459 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 389, + 279, + 459 + ], + "spans": [ + { + "bbox": [ + 45, + 389, + 279, + 459 + ], + "type": "text", + "content": "confident-inconsistent (CI), respectively. In this way, samples that are both uncertain to the model and contain target-specific knowledge can be extracted based on the InfoF score. In next section, we devise a strategy for informative sampling to adaptatively distinguish those subsets from unlabeled target samples." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 45, + 466, + 211, + 479 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 466, + 211, + 479 + ], + "spans": [ + { + "bbox": [ + 45, + 466, + 211, + 479 + ], + "type": "text", + "content": "3.2. Informative Sampling Function" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 45, + 485, + 279, + 671 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 485, + 279, + 671 + ], + "spans": [ + { + "bbox": [ + 45, + 485, + 279, + 671 + ], + "type": "text", + "content": "During training, the varying scale of InfoF scores obtained above would hinder accurate data categorization using manual data division, leading to a biased sampling strategy and degraded performance. Therefore, our work here formulates an Informative Sampling Function to achieve the goal of adaptively selecting informative target samples. In general, it can be observed that the four categories of unlabeled target data as stated above are significantly separable in the distributions of the InfoF scores, making it possible to learn mixture models to separate four sample partitioning from unlabeled target data. Thereafter, by learning the distribution of InfoF scores using a four-component Gaussian mixture model (GMM), the target data can be adaptively mapped to the probability distribution of four categories and then be separated, thereby avoiding sampling bias that may be created by manual division." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 45, + 671, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 671, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 671, + 279, + 730 + ], + "type": "text", + "content": "In specific, we first take inspiration from [34] that labeled samples can be used to construct supervision information, therefore building a more trustworthy GMM model with " + }, + { + "bbox": [ + 45, + 671, + 279, + 730 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 45, + 671, + 279, + 730 + ], + "type": "text", + "content": " Gaussian components (namely " + }, + { + "bbox": [ + 45, + 671, + 279, + 730 + ], + "type": "inline_equation", + "content": "K = 4" + }, + { + "bbox": [ + 45, + 671, + 279, + 730 + ], + "type": "text", + "content": " in this work) via a semi-supervised Expectation-Maximization al" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 296, + 106, + 530, + 129 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 106, + 530, + 129 + ], + "spans": [ + { + "bbox": [ + 296, + 106, + 530, + 129 + ], + "type": "text", + "content": "gorthm. To this end, we then calculate the InfoF score for a labeled sample with " + }, + { + "bbox": [ + 296, + 106, + 530, + 129 + ], + "type": "inline_equation", + "content": "(x,y)" + }, + { + "bbox": [ + 296, + 106, + 530, + 129 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 296, + 106, + 530, + 129 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 296, + 106, + 530, + 129 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 296, + 106, + 530, + 129 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 296, + 106, + 530, + 129 + ], + "type": "text", + "content": " as follows," + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 335, + 136, + 530, + 168 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 335, + 136, + 530, + 168 + ], + "spans": [ + { + "bbox": [ + 335, + 136, + 530, + 168 + ], + "type": "interline_equation", + "content": "\\ell_ {g} (x, y) = - \\sum_ {c = 1} ^ {C} \\mathbb {1} \\{c = y \\} \\cdot \\log P _ {c} (x). \\tag {4}", + "image_path": "2c8984c2553767b602875548226decc4358ecc5f0d68d07eb346d70568614cd6.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 296, + 174, + 530, + 244 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 174, + 530, + 244 + ], + "spans": [ + { + "bbox": [ + 296, + 174, + 530, + 244 + ], + "type": "text", + "content": "The similarity-based label is determined using categorical centroids of the labeled data, resulting in the totally identical similarity-based label and model prediction for labeled samples. In order to obtain reliable supervision and build a better GMM model, we have replaced the similarity-based label with the ground-truth class label here." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 296, + 245, + 530, + 314 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 245, + 530, + 314 + ], + "spans": [ + { + "bbox": [ + 296, + 245, + 530, + 314 + ], + "type": "text", + "content": "Afterwards, to obtain the supervision information for training GMM, we here define a piecewise function to obtain the observation labels that assign all labeled samples across domains to the corresponding Gaussian components. Thus, the observation label of a candidate instance " + }, + { + "bbox": [ + 296, + 245, + 530, + 314 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 296, + 245, + 530, + 314 + ], + "type": "text", + "content": " can be computed as," + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 296, + 320, + 530, + 378 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 320, + 530, + 378 + ], + "spans": [ + { + "bbox": [ + 296, + 320, + 530, + 378 + ], + "type": "interline_equation", + "content": "q (x, y) = \\left\\{ \\begin{array}{l l} 1, & \\max P (x) \\geq \\tau \\text {a n d} y = \\arg \\max P (x), \\\\ 2, & \\max P (x) < \\tau \\text {a n d} y = \\arg \\max P (x), \\\\ 3, & \\max P (x) < \\tau \\text {a n d} y \\neq \\arg \\max P (x), \\\\ 4, & \\max P (x) \\geq \\tau \\text {a n d} y \\neq \\arg \\max P (x), \\end{array} \\right. \\tag {5}", + "image_path": "829c71fcd06d0540733abf83b2ac725ec72e495655cdec86747e6647ed8c6412.jpg" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 296, + 379, + 530, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 379, + 530, + 471 + ], + "spans": [ + { + "bbox": [ + 296, + 379, + 530, + 471 + ], + "type": "text", + "content": "where the numbers, i.e., " + }, + { + "bbox": [ + 296, + 379, + 530, + 471 + ], + "type": "inline_equation", + "content": "k = 1,\\dots ,4" + }, + { + "bbox": [ + 296, + 379, + 530, + 471 + ], + "type": "text", + "content": ", indicate the indices of different Gaussian components corresponding to the CC, UC, UI and CI sample subsets, respectively. As well, " + }, + { + "bbox": [ + 296, + 379, + 530, + 471 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 296, + 379, + 530, + 471 + ], + "type": "text", + "content": " is a confidence threshold to classify labeled samples into the confident subset and the uncertain subset. Furthermore, the comparison between the ground-truth and predicted class labels is used to divide them into the consistent subset and the inconsistent subset of labeled training samples." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 296, + 472, + 530, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 472, + 530, + 506 + ], + "spans": [ + { + "bbox": [ + 296, + 472, + 530, + 506 + ], + "type": "text", + "content": "Once we obtain " + }, + { + "bbox": [ + 296, + 472, + 530, + 506 + ], + "type": "inline_equation", + "content": "\\{\\ell_g(x,y)|(x,y)\\in S\\cup \\mathcal{T}\\}" + }, + { + "bbox": [ + 296, + 472, + 530, + 506 + ], + "type": "inline_equation", + "content": "\\{\\ell_u(x)|x\\in" + }, + { + "bbox": [ + 296, + 472, + 530, + 506 + ], + "type": "inline_equation", + "content": "\\mathcal{U}\\}" + }, + { + "bbox": [ + 296, + 472, + 530, + 506 + ], + "type": "text", + "content": " , and " + }, + { + "bbox": [ + 296, + 472, + 530, + 506 + ], + "type": "inline_equation", + "content": "q(x,y)" + }, + { + "bbox": [ + 296, + 472, + 530, + 506 + ], + "type": "text", + "content": " , we incorporate them into building training instances for learning the GMM model as follows," + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 325, + 516, + 530, + 529 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 516, + 530, + 529 + ], + "spans": [ + { + "bbox": [ + 325, + 516, + 530, + 529 + ], + "type": "interline_equation", + "content": "\\mathcal {D} _ {L} \\leftarrow \\left\\{\\left(\\ell_ {g} (x, y), q (x, y)\\right) | (x, y) \\in \\mathcal {S} \\cup \\mathcal {T} \\right\\}, \\tag {6}", + "image_path": "b0a222e751d5f62f2265088a6e9a95b88e6c9f61dff932b6038d3201d1731b9b.jpg" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 361, + 538, + 530, + 551 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 361, + 538, + 530, + 551 + ], + "spans": [ + { + "bbox": [ + 361, + 538, + 530, + 551 + ], + "type": "interline_equation", + "content": "\\mathcal {D} _ {U} \\leftarrow \\left\\{\\left(\\ell_ {u} (x),\\right) \\mid x \\in \\mathcal {U} \\right\\}. \\tag {7}", + "image_path": "18a67129b12cb21e5afd495dd4c8fb8a9d70c05eed5cb88148d3f9c010e6b708.jpg" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 296, + 556, + 530, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 556, + 530, + 615 + ], + "spans": [ + { + "bbox": [ + 296, + 556, + 530, + 615 + ], + "type": "text", + "content": "For convenience, we denote the GMM model by " + }, + { + "bbox": [ + 296, + 556, + 530, + 615 + ], + "type": "inline_equation", + "content": "\\mathcal{W} = \\{(\\pi_k,\\mu_k,\\sigma_k)|1\\leq k\\leq K\\}" + }, + { + "bbox": [ + 296, + 556, + 530, + 615 + ], + "type": "text", + "content": ". Afterwards, given a training instance " + }, + { + "bbox": [ + 296, + 556, + 530, + 615 + ], + "type": "inline_equation", + "content": "\\ell_{x}" + }, + { + "bbox": [ + 296, + 556, + 530, + 615 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 296, + 556, + 530, + 615 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_L" + }, + { + "bbox": [ + 296, + 556, + 530, + 615 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 296, + 556, + 530, + 615 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_U" + }, + { + "bbox": [ + 296, + 556, + 530, + 615 + ], + "type": "text", + "content": ", the output of the probability density functions of the GMM model regarding " + }, + { + "bbox": [ + 296, + 556, + 530, + 615 + ], + "type": "inline_equation", + "content": "\\ell_{x}" + }, + { + "bbox": [ + 296, + 556, + 530, + 615 + ], + "type": "text", + "content": " can be computed as" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 352, + 621, + 530, + 653 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 352, + 621, + 530, + 653 + ], + "spans": [ + { + "bbox": [ + 352, + 621, + 530, + 653 + ], + "type": "interline_equation", + "content": "p \\left(\\ell_ {x}\\right) = \\sum_ {k = 1} ^ {K} \\pi_ {k} \\mathcal {N} \\left(\\ell_ {x}; \\mu_ {k}, \\sigma_ {k}\\right), \\tag {8}", + "image_path": "b3c1e40a5ccf50f7a25a50b29b2dc074665f64b0e14d2fdc21a6135697d213cd.jpg" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 296, + 660, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 660, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 660, + 530, + 730 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 296, + 660, + 530, + 730 + ], + "type": "inline_equation", + "content": "\\pi_{k}" + }, + { + "bbox": [ + 296, + 660, + 530, + 730 + ], + "type": "text", + "content": " represents the weight of the " + }, + { + "bbox": [ + 296, + 660, + 530, + 730 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 296, + 660, + 530, + 730 + ], + "type": "text", + "content": "-th Gaussian component subject to " + }, + { + "bbox": [ + 296, + 660, + 530, + 730 + ], + "type": "inline_equation", + "content": "\\sum_{k=1}^{K} \\pi_{k} = 1" + }, + { + "bbox": [ + 296, + 660, + 530, + 730 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 660, + 530, + 730 + ], + "type": "inline_equation", + "content": "0 \\leq \\pi_{k} \\leq 1" + }, + { + "bbox": [ + 296, + 660, + 530, + 730 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 296, + 660, + 530, + 730 + ], + "type": "inline_equation", + "content": "k = 1, \\dots, K" + }, + { + "bbox": [ + 296, + 660, + 530, + 730 + ], + "type": "text", + "content": ", while " + }, + { + "bbox": [ + 296, + 660, + 530, + 730 + ], + "type": "inline_equation", + "content": "\\mu_{k}" + }, + { + "bbox": [ + 296, + 660, + 530, + 730 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 660, + 530, + 730 + ], + "type": "inline_equation", + "content": "\\sigma_{k}" + }, + { + "bbox": [ + 296, + 660, + 530, + 730 + ], + "type": "text", + "content": " are vectors denoting the mean and variance of such a component. Here, " + }, + { + "bbox": [ + 296, + 660, + 530, + 730 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(\\cdot; \\mu_{k}, \\sigma_{k})" + }, + { + "bbox": [ + 296, + 660, + 530, + 730 + ], + "type": "text", + "content": " is used to model the Gaussian distribution of the " + }, + { + "bbox": [ + 296, + 660, + 530, + 730 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 296, + 660, + 530, + 730 + ], + "type": "text", + "content": "-th component. Note that a given coefficient " + }, + { + "bbox": [ + 296, + 660, + 530, + 730 + ], + "type": "inline_equation", + "content": "\\alpha = |\\mathcal{D}_{L}| / |\\mathcal{D}_{U}|" + }, + { + "bbox": [ + 296, + 660, + 530, + 730 + ], + "type": "text", + "content": " is" + } + ] + } + ], + "index": 31 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "text", + "content": "7655" + } + ] + } + ], + "index": 32 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 45, + 106, + 279, + 153 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 106, + 279, + 153 + ], + "spans": [ + { + "bbox": [ + 45, + 106, + 279, + 153 + ], + "type": "text", + "content": "used for the weighted integration of the labeled and unlabeled training instances. Thus, we can summarize the training procedure of the GMM model using a semi-supervised EM algorithm in Algorithm 1 according to [34]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 154, + 279, + 188 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 154, + 279, + 188 + ], + "spans": [ + { + "bbox": [ + 45, + 154, + 279, + 188 + ], + "type": "text", + "content": "After obtaining the trained GMM parameters " + }, + { + "bbox": [ + 45, + 154, + 279, + 188 + ], + "type": "inline_equation", + "content": "\\mathcal{W}" + }, + { + "bbox": [ + 45, + 154, + 279, + 188 + ], + "type": "text", + "content": ", the probability of a sample " + }, + { + "bbox": [ + 45, + 154, + 279, + 188 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 45, + 154, + 279, + 188 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 45, + 154, + 279, + 188 + ], + "type": "inline_equation", + "content": "\\mathcal{U}" + }, + { + "bbox": [ + 45, + 154, + 279, + 188 + ], + "type": "text", + "content": " being classified into the " + }, + { + "bbox": [ + 45, + 154, + 279, + 188 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 45, + 154, + 279, + 188 + ], + "type": "text", + "content": "-th component can be computed as follows," + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 57, + 197, + 279, + 226 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 197, + 279, + 226 + ], + "spans": [ + { + "bbox": [ + 57, + 197, + 279, + 226 + ], + "type": "interline_equation", + "content": "\\Pr (z = k | x, \\mathcal {W}) = \\frac {\\pi_ {k} \\mathcal {N} \\left(\\ell_ {u} (x) ; \\mu_ {k} , \\sigma_ {k}\\right)}{\\sum_ {k ^ {\\prime} = 1} ^ {K} \\pi_ {k ^ {\\prime}} \\mathcal {N} \\left(\\ell_ {u} (x) ; \\mu_ {k ^ {\\prime}} , \\sigma_ {k ^ {\\prime}}\\right)}, \\tag {9}", + "image_path": "35aebd1db2200b7e251337db8d1f4130c8dec1aad061c5d7827d49d6a0228a69.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 234, + 279, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 234, + 279, + 258 + ], + "spans": [ + { + "bbox": [ + 45, + 234, + 279, + 258 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 45, + 234, + 279, + 258 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 45, + 234, + 279, + 258 + ], + "type": "text", + "content": " is a discrete variable to infer which component the sample " + }, + { + "bbox": [ + 45, + 234, + 279, + 258 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 45, + 234, + 279, + 258 + ], + "type": "text", + "content": " belongs to." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 266, + 271, + 279 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 266, + 271, + 279 + ], + "spans": [ + { + "bbox": [ + 45, + 266, + 271, + 279 + ], + "type": "text", + "content": "3.3. Candidate Selection and Training Objectives" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 285, + 279, + 424 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 285, + 279, + 424 + ], + "spans": [ + { + "bbox": [ + 45, + 285, + 279, + 424 + ], + "type": "text", + "content": "After acquiring the informativeness sampling function, it is utilized for carrying out data partitioning. For ADA, the main focus should be on annotating samples that are uncertain to the model and can effectively represent the target dataset, which is termed as uncertain-inconsistent samples within our subdivision framework. Therefore, during each sampling step, we first rank the unlabeled target samples in descending order according to the scores predicted by " + }, + { + "bbox": [ + 45, + 285, + 279, + 424 + ], + "type": "inline_equation", + "content": "\\operatorname{Pr}(z = 3|\\cdot ,\\mathcal{W})" + }, + { + "bbox": [ + 45, + 285, + 279, + 424 + ], + "type": "text", + "content": " and then the top " + }, + { + "bbox": [ + 45, + 285, + 279, + 424 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 45, + 285, + 279, + 424 + ], + "type": "text", + "content": " examples are selected to annotate and moved into labeled target data. Following previous ADA works, we apply the standard cross-entropy loss to the labeled data as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 433, + 279, + 464 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 433, + 279, + 464 + ], + "spans": [ + { + "bbox": [ + 55, + 433, + 279, + 464 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {s u p} = \\underset {(x, y) \\sim \\mathcal {S} \\cup \\mathcal {T}} {\\mathbb {E}} \\left[ - \\sum_ {c = 1} ^ {C} \\mathbb {1} \\{c = y \\} \\cdot \\log P _ {c} (x) \\right]. \\tag {10}", + "image_path": "332f204bb7bba4a0e888eb68e0a5a8ed446558c8b639ecb5804f4d801649b113.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 474, + 279, + 543 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 474, + 279, + 543 + ], + "spans": [ + { + "bbox": [ + 45, + 474, + 279, + 543 + ], + "type": "text", + "content": "To boost the selectivity of the sampling strategy, we further design tailored training techniques for the other data subsets with varied transferable properties. We perform data partitioning on the remaining unlabeled target samples, i.e., " + }, + { + "bbox": [ + 45, + 474, + 279, + 543 + ], + "type": "inline_equation", + "content": "\\mathcal{U}\\gets \\mathcal{U}\\backslash \\mathcal{T}" + }, + { + "bbox": [ + 45, + 474, + 279, + 543 + ], + "type": "text", + "content": ", according to the posterior probabilities regarding the rest of Gaussian components." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 553, + 278, + 576 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 553, + 278, + 576 + ], + "spans": [ + { + "bbox": [ + 46, + 553, + 278, + 576 + ], + "type": "interline_equation", + "content": "\\hat {\\mathcal {U}} _ {k} = \\{x \\mid \\arg \\max \\mathbf {P r} (x) = k, \\forall (x,) \\in \\mathcal {U} \\}, \\text {f o r} k = 1, 2, 4, \\tag {11}", + "image_path": "65909491a7deb9089523d9a8371db0d0fa7a7289174d42e55d5526527ade362d.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 45, + 577, + 279, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 577, + 279, + 634 + ], + "spans": [ + { + "bbox": [ + 45, + 577, + 279, + 634 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 45, + 577, + 279, + 634 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{U}}_1, \\hat{\\mathcal{U}}_2" + }, + { + "bbox": [ + 45, + 577, + 279, + 634 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 577, + 279, + 634 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{U}}_4" + }, + { + "bbox": [ + 45, + 577, + 279, + 634 + ], + "type": "text", + "content": " refer to " + }, + { + "bbox": [ + 45, + 577, + 279, + 634 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{U}}_{\\mathrm{CC}}, \\hat{\\mathcal{U}}_{\\mathrm{UC}}, \\hat{\\mathcal{U}}_{\\mathrm{CI}}" + }, + { + "bbox": [ + 45, + 577, + 279, + 634 + ], + "type": "text", + "content": ". Here, " + }, + { + "bbox": [ + 45, + 577, + 279, + 634 + ], + "type": "inline_equation", + "content": "\\mathbf{Pr}(x)" + }, + { + "bbox": [ + 45, + 577, + 279, + 634 + ], + "type": "text", + "content": " is the concatenated probability vector corresponding to different components, i.e., " + }, + { + "bbox": [ + 45, + 577, + 279, + 634 + ], + "type": "inline_equation", + "content": "\\mathbf{Pr}(x) = [\\operatorname{Pr}(z = 1|x, \\mathcal{W}), \\operatorname{Pr}(z = 2|x, \\mathcal{W}), \\operatorname{Pr}(z = 3|x, \\mathcal{W}), \\operatorname{Pr}(z = 4|x, \\mathcal{W})]" + }, + { + "bbox": [ + 45, + 577, + 279, + 634 + ], + "type": "text", + "content": " w.r.t the sample " + }, + { + "bbox": [ + 45, + 577, + 279, + 634 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 45, + 577, + 279, + 634 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 45, + 636, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 636, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 636, + 279, + 730 + ], + "type": "text", + "content": "As shown in Figure 1(4), the source-oriented model could produce confident but unreliable predictions for some target samples having large domain gap with the source. Samples from " + }, + { + "bbox": [ + 45, + 636, + 279, + 730 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{U}}_{\\mathrm{CI}}" + }, + { + "bbox": [ + 45, + 636, + 279, + 730 + ], + "type": "text", + "content": " have extremely controversial results between model prediction and similarity-based label, which are most likely to be some excessively challenging instances. Therefore, we withhold them in the current stage to avoid jeopardizing the training stability." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 296, + 106, + 530, + 165 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 106, + 530, + 165 + ], + "spans": [ + { + "bbox": [ + 296, + 106, + 530, + 165 + ], + "type": "text", + "content": "The samples in " + }, + { + "bbox": [ + 296, + 106, + 530, + 165 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{U}}_{\\mathrm{CC}}" + }, + { + "bbox": [ + 296, + 106, + 530, + 165 + ], + "type": "text", + "content": " have confident and reliable predictions, which tend to be some class centroid in the target feature space. Therefore, we apply consistency regularization to them to enforce the prediction consistency under different perturbations, which can be formulated as follows:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 301, + 176, + 530, + 218 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 301, + 176, + 530, + 218 + ], + "spans": [ + { + "bbox": [ + 301, + 176, + 530, + 218 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {c o n} = \\underset {(x, \\cdot) \\sim \\hat {\\mathcal {U}} _ {\\mathrm {C C}}} {\\mathbb {E}} \\left[ - \\sum_ {c = 1} ^ {C} \\mathbb {1} \\{c = \\ddot {y} (x) \\} \\cdot \\log P _ {c} (\\mathbf {A u g} (x)) \\right], \\tag {12}", + "image_path": "61d6b68d5b9189c09958e17019e5d7b25b3851e0e74fb32552f004c6236d0a0c.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 296, + 218, + 530, + 253 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 218, + 530, + 253 + ], + "spans": [ + { + "bbox": [ + 296, + 218, + 530, + 253 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 296, + 218, + 530, + 253 + ], + "type": "inline_equation", + "content": "\\mathbf{Aug}(\\cdot)" + }, + { + "bbox": [ + 296, + 218, + 530, + 253 + ], + "type": "text", + "content": " is a function to create perturbations for the sample " + }, + { + "bbox": [ + 296, + 218, + 530, + 253 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 296, + 218, + 530, + 253 + ], + "type": "text", + "content": " using classic data augmentation techniques such as AutoAugment [2]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 296, + 255, + 530, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 255, + 530, + 289 + ], + "spans": [ + { + "bbox": [ + 296, + 255, + 530, + 289 + ], + "type": "text", + "content": "For data group " + }, + { + "bbox": [ + 296, + 255, + 530, + 289 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{U}}_{\\mathrm{UC}}" + }, + { + "bbox": [ + 296, + 255, + 530, + 289 + ], + "type": "text", + "content": " whose prediction tend to be reliable but uncertain, we directly minimize the entropy of the predictions to using the following conditional entropy loss:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 320, + 301, + 530, + 333 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 301, + 530, + 333 + ], + "spans": [ + { + "bbox": [ + 320, + 301, + 530, + 333 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {e n t} = \\underset {(x, \\cdot) \\sim \\hat {\\mathcal {U}} _ {U C}} {\\mathbb {E}} \\left[ - \\sum_ {c = 1} ^ {C} P _ {c} (x) \\log P _ {c} (x) \\right]. \\tag {13}", + "image_path": "fc959926226e263e0f0a6735f719ad52b94d7455c381b79ae24f64a5000f9e5f.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 297, + 346, + 530, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 346, + 530, + 369 + ], + "spans": [ + { + "bbox": [ + 297, + 346, + 530, + 369 + ], + "type": "text", + "content": "In summary, the overall loss functions used to further optimize the model can be formulated as follows," + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 352, + 382, + 530, + 394 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 352, + 382, + 530, + 394 + ], + "spans": [ + { + "bbox": [ + 352, + 382, + 530, + 394 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {\\text {s u p}} + \\lambda_ {c} \\mathcal {L} _ {\\text {c o n}} + \\lambda_ {e} \\mathcal {L} _ {\\text {e n t}} \\tag {14}", + "image_path": "67c2814eb0119fa5fe0038953111f3035d0a58a08f68a356b4c3adb80c622206.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 296, + 406, + 530, + 511 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 406, + 530, + 511 + ], + "spans": [ + { + "bbox": [ + 296, + 406, + 530, + 511 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 296, + 406, + 530, + 511 + ], + "type": "inline_equation", + "content": "\\lambda_{c}" + }, + { + "bbox": [ + 296, + 406, + 530, + 511 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 406, + 530, + 511 + ], + "type": "inline_equation", + "content": "\\lambda_{e}" + }, + { + "bbox": [ + 296, + 406, + 530, + 511 + ], + "type": "text", + "content": " are the weights to trade off different loss terms during the training process. As shown in Figure 2, " + }, + { + "bbox": [ + 296, + 406, + 530, + 511 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{sup}" + }, + { + "bbox": [ + 296, + 406, + 530, + 511 + ], + "type": "text", + "content": " can calibrate the potentially underfitting of uncertain and target-specific samples. " + }, + { + "bbox": [ + 296, + 406, + 530, + 511 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{con}" + }, + { + "bbox": [ + 296, + 406, + 530, + 511 + ], + "type": "text", + "content": " can guide the model to learn global cross-domain clustering while " + }, + { + "bbox": [ + 296, + 406, + 530, + 511 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{ent}" + }, + { + "bbox": [ + 296, + 406, + 530, + 511 + ], + "type": "text", + "content": " serves to minimize the distance of data from the same class. As demonstrated in Sec. 4.3, these training objectives are complementary to each other to best adapt the model to the target domain." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 297, + 524, + 490, + 536 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 524, + 490, + 536 + ], + "spans": [ + { + "bbox": [ + 297, + 524, + 490, + 536 + ], + "type": "text", + "content": "3.4. Compatibility with UDA/SSDA/SFDA" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 296, + 543, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 543, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 543, + 530, + 730 + ], + "type": "text", + "content": "The proposed sampling strategy of DiaNA requires no additional network modules like a domain discriminator or multiple classifiers [4, 26], making it easy to be integrated into existing DA frameworks, such as unsupervised domain adaptation (UDA), semi-supervised domain adaptation (SSDA), and source-free domain adaptation (SFDA); see supplementary document for the implementation details. It should be noted that we further design a variant of DiaNA for the SFDA settings, due to the unavailability of source data. As evidenced by Sec. 4.3, when integrated into diverse DA techniques, the proposed sampling strategy can deliver more performance improvement than random sample selection, thereby demonstrating its compatibility in various DA settings. To the best of our knowledge, we are the first to propose an active selection strategy that can generalize to UDA, SSDA, and SFDA methods." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "text", + "content": "7656" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 104, + 529, + 212 + ], + "blocks": [ + { + "bbox": [ + 48, + 104, + 529, + 212 + ], + "lines": [ + { + "bbox": [ + 48, + 104, + 529, + 212 + ], + "spans": [ + { + "bbox": [ + 48, + 104, + 529, + 212 + ], + "type": "table", + "html": "
MethodR → CC → SS → PC → QR → SR → PAVG
1k2k5k1k2k5k1k2k5k1k2k5k1k2k5k1k2k5k1k2k5k
Random50.955.261.542.644.849.441.044.450.126.333.243.038.240.746.946.548.853.740.944.550.8
CONF48.654.261.341.943.648.041.644.248.525.532.742.836.939.445.347.147.851.240.343.649.5
Entropy [29]48.054.261.942.745.248.941.143.748.724.631.042.137.040.445.746.548.452.240.043.849.9
Coreset [25]49.152.559.840.642.245.839.141.544.824.730.339.736.738.343.345.146.850.339.241.947.3
BADGE [1]51.755.462.543.645.750.142.345.549.726.034.343.937.841.547.848.050.154.241.645.451.4
Alpha [20]52.056.362.844.346.850.541.944.949.727.234.644.438.641.347.947.650.453.241.945.751.4
AADA [26]50.856.364.742.845.751.041.845.650.825.231.340.838.541.749.546.549.755.140.945.152.0
SDM [33]51.055.462.343.145.249.641.944.949.326.935.043.837.340.246.547.449.753.241.345.150.8
EADA [31]51.556.163.944.246.351.743.846.150.327.534.842.939.041.546.448.650.454.142.445.951.2
CLUE [22]54.159.466.045.348.753.744.048.053.228.835.543.240.444.451.150.052.756.443.848.153.9
DiaNA(Ours)55.660.468.747.050.856.644.249.055.430.239.552.142.447.955.050.553.659.145.050.257.8
", + "image_path": "131967745c0a90a3cd5a97ff67487878e911cf50028c81acd62c0a296c24ee30.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 59, + 243, + 516, + 366 + ], + "blocks": [ + { + "bbox": [ + 45, + 213, + 531, + 236 + ], + "lines": [ + { + "bbox": [ + 45, + 213, + 531, + 236 + ], + "spans": [ + { + "bbox": [ + 45, + 213, + 531, + 236 + ], + "type": "text", + "content": "Table 1. Comparison results (Accuracy: %) on DomainNet with 1k, 2k and 5k labeling budgets. \"Random\" and \"CONF\" correspond to the classic AL approaches \"Random Sampling\" and \"Least-Confidence Sampling\"." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 59, + 243, + 516, + 366 + ], + "lines": [ + { + "bbox": [ + 59, + 243, + 516, + 366 + ], + "spans": [ + { + "bbox": [ + 59, + 243, + 516, + 366 + ], + "type": "table", + "html": "
MethodOffice-Home
A → CA → PA → RC → AC → PC → RP → AP → CP → RR → AR → CR → PAVG
Random52.574.377.456.369.768.957.750.975.870.054.681.365.8
Entropy [29]51.372.776.461.774.172.957.651.176.669.857.182.367.0
Coreset [25]52.873.375.559.873.470.858.152.675.869.356.582.566.7
BADGE [1]57.275.276.961.577.271.960.453.678.070.861.184.369.0
Alpha [20]57.079.478.261.678.074.158.954.278.171.761.184.669.7
AADA [26]56.678.179.058.573.771.060.153.177.070.657.084.568.3
CLUE [22]58.079.177.061.378.073.160.455.977.970.960.384.169.7
TQS [4]58.681.181.561.176.173.361.254.779.773.458.986.170.5
SDM [33]61.282.282.766.177.976.166.158.481.076.062.587.073.1
EADA [31]63.684.483.570.783.780.573.063.585.278.465.488.676.7
DiaNA(Ours)64.586.084.972.384.682.573.363.785.678.567.289.577.7
", + "image_path": "6f2d1d60e3a89901dc9c88d28a1f9affebb1a538c803b284f1d80fd4e0516255.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 135, + 367, + 440, + 378 + ], + "lines": [ + { + "bbox": [ + 135, + 367, + 440, + 378 + ], + "spans": [ + { + "bbox": [ + 135, + 367, + 440, + 378 + ], + "type": "text", + "content": "Table 2. Comparison results (Accuracy: %) on Office-Home with " + }, + { + "bbox": [ + 135, + 367, + 440, + 378 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 135, + 367, + 440, + 378 + ], + "type": "text", + "content": " labeling budget." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 45, + 383, + 124, + 395 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 383, + 124, + 395 + ], + "spans": [ + { + "bbox": [ + 45, + 383, + 124, + 395 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 403, + 102, + 414 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 403, + 102, + 414 + ], + "spans": [ + { + "bbox": [ + 46, + 403, + 102, + 414 + ], + "type": "text", + "content": "4.1. Dataset" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 421, + 279, + 562 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 421, + 279, + 562 + ], + "spans": [ + { + "bbox": [ + 45, + 421, + 279, + 562 + ], + "type": "text", + "content": "We validate the effectiveness of the proposed approach DiaNA on three standard benchmark datasets: DomainNet [21], Office-Home [28] and CIFAR-10 [11]. On DomainNet, we select five domains namley Real (R), Clipart (C), Sketch (S), Painting (P), and Quikdraw (Q), while we hire these domains to construct 6 adaptation scenarios. As in [4, 31, 33], we report 12 different adaptation scenarios on Office-Home, constructed from four domains: Real (R), Clipart (C), Art (A), and Product (P). To further evaluate the generalization of the proposed sample selection strategy, we additionally report the classification results on CIFAR-10 with a standard active learning setting." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 570, + 141, + 582 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 570, + 141, + 582 + ], + "spans": [ + { + "bbox": [ + 45, + 570, + 141, + 582 + ], + "type": "text", + "content": "4.2. Implementation" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 589, + 279, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 589, + 279, + 647 + ], + "spans": [ + { + "bbox": [ + 45, + 589, + 279, + 647 + ], + "type": "text", + "content": "Here, we mainly focus on the detailed descriptions of the settings involving active learning on DomainNet, OfficeHome, and CIFAR-10, while more implementation details can be found in the supplementary material. In each adaptation scenario, we report the average accuracy over 3 trials." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 45, + 648, + 279, + 704 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 648, + 279, + 704 + ], + "spans": [ + { + "bbox": [ + 45, + 648, + 279, + 704 + ], + "type": "text", + "content": "DomainNet. Similar to CLUE [22], we consider ResNet-34 [8] as the network backbone, where such network model is pre-trained on all labeled source samples over 50 training epochs through standard supervision. In all adaptation cases, we set " + }, + { + "bbox": [ + 45, + 648, + 279, + 704 + ], + "type": "inline_equation", + "content": "B = 5000" + }, + { + "bbox": [ + 45, + 648, + 279, + 704 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 648, + 279, + 704 + ], + "type": "inline_equation", + "content": "R = 10" + }, + { + "bbox": [ + 45, + 648, + 279, + 704 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 45, + 706, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 706, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 706, + 279, + 730 + ], + "type": "text", + "content": "Office-Home. To be fair, we follow the experimental settings of existing ADA works [4, 31, 33] to conduct" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 296, + 384, + 530, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 384, + 530, + 430 + ], + "spans": [ + { + "bbox": [ + 296, + 384, + 530, + 430 + ], + "type": "text", + "content": "performance comparison. In particular, we also use ResNet-50 [8] as the backbone model, while we choose a " + }, + { + "bbox": [ + 296, + 384, + 530, + 430 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 296, + 384, + 530, + 430 + ], + "type": "text", + "content": " proportion of unlabeled target data to set the labeling budget " + }, + { + "bbox": [ + 296, + 384, + 530, + 430 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 296, + 384, + 530, + 430 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 296, + 384, + 530, + 430 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 296, + 384, + 530, + 430 + ], + "type": "text", + "content": " is set to 5." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 296, + 431, + 530, + 489 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 431, + 530, + 489 + ], + "spans": [ + { + "bbox": [ + 296, + 431, + 530, + 489 + ], + "type": "text", + "content": "CIFAR-10. On this dataset, we select ResNet-34 [8] as the backbone model. We randomly choose select " + }, + { + "bbox": [ + 296, + 431, + 530, + 489 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 296, + 431, + 530, + 489 + ], + "type": "text", + "content": " training samples at random as the initially labeled data set, and we then annotate " + }, + { + "bbox": [ + 296, + 431, + 530, + 489 + ], + "type": "inline_equation", + "content": "4\\%" + }, + { + "bbox": [ + 296, + 431, + 530, + 489 + ], + "type": "text", + "content": " at each sampling step with a total annotation budget " + }, + { + "bbox": [ + 296, + 431, + 530, + 489 + ], + "type": "inline_equation", + "content": "30\\%" + }, + { + "bbox": [ + 296, + 431, + 530, + 489 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 297, + 499, + 379, + 511 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 499, + 379, + 511 + ], + "spans": [ + { + "bbox": [ + 297, + 499, + 379, + 511 + ], + "type": "text", + "content": "4.3. Main Results" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 296, + 518, + 530, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 518, + 530, + 646 + ], + "spans": [ + { + "bbox": [ + 296, + 518, + 530, + 646 + ], + "type": "text", + "content": "Results on DomainNet and Office-Home. We summarize the comparison with baselines in Table 1 and Table 2 on both datasets respectively. Note that we consider varying label budgets, namely i.e., 1k, 2k, and 5k, on DomainNet. We can see that DiaNA achieves the highest average accuracy in all cases on both datasets for solving the ADA tasks. Especially in the most difficult adaptation scenarios, e.g., " + }, + { + "bbox": [ + 296, + 518, + 530, + 646 + ], + "type": "inline_equation", + "content": "\\mathrm{C} \\rightarrow \\mathrm{A}" + }, + { + "bbox": [ + 296, + 518, + 530, + 646 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 518, + 530, + 646 + ], + "type": "inline_equation", + "content": "\\mathrm{R} \\rightarrow \\mathrm{C}" + }, + { + "bbox": [ + 296, + 518, + 530, + 646 + ], + "type": "text", + "content": ", on Office-Home, the proposed method can still exceed all the other methods by more than " + }, + { + "bbox": [ + 296, + 518, + 530, + 646 + ], + "type": "inline_equation", + "content": "1.6\\%" + }, + { + "bbox": [ + 296, + 518, + 530, + 646 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 518, + 530, + 646 + ], + "type": "inline_equation", + "content": "1.8\\%" + }, + { + "bbox": [ + 296, + 518, + 530, + 646 + ], + "type": "text", + "content": " respectively, demonstrating the effectiveness of DiaNA on the commonly used DA benchmark datasets." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 296, + 648, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 648, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 648, + 530, + 730 + ], + "type": "text", + "content": "Results on CIFAR-10. We also extend the proposed method to standard AL tasks on CIFAR-10, where the domain gap between labeled and unlabeled ones is minor. Figure 4(a) lists the comparisons of DiaNA against classic AL strategies involving [1, 20, 25, 29]. It can be observed that compared to classic AL algorithms, with fewer labeling budgets, the effect of the proposed method is still notice" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "text", + "content": "7657" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 78, + 104, + 196, + 195 + ], + "blocks": [ + { + "bbox": [ + 78, + 104, + 196, + 195 + ], + "lines": [ + { + "bbox": [ + 78, + 104, + 196, + 195 + ], + "spans": [ + { + "bbox": [ + 78, + 104, + 196, + 195 + ], + "type": "image", + "image_path": "6c40e6776152b9f71cc6483d832a9524546a5744ffbf1190a42c04ab29760f6b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 132, + 197, + 141, + 204 + ], + "lines": [ + { + "bbox": [ + 132, + 197, + 141, + 204 + ], + "spans": [ + { + "bbox": [ + 132, + 197, + 141, + 204 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 228, + 103, + 343, + 196 + ], + "blocks": [ + { + "bbox": [ + 228, + 103, + 343, + 196 + ], + "lines": [ + { + "bbox": [ + 228, + 103, + 343, + 196 + ], + "spans": [ + { + "bbox": [ + 228, + 103, + 343, + 196 + ], + "type": "image", + "image_path": "58165b18c7ff42a478d960ffe659a9109ca8a281ecadafa211cfd737796c6e71.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 280, + 197, + 290, + 205 + ], + "lines": [ + { + "bbox": [ + 280, + 197, + 290, + 205 + ], + "spans": [ + { + "bbox": [ + 280, + 197, + 290, + 205 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 57, + 206, + 518, + 217 + ], + "lines": [ + { + "bbox": [ + 57, + 206, + 518, + 217 + ], + "spans": [ + { + "bbox": [ + 57, + 206, + 518, + 217 + ], + "type": "text", + "content": "Figure 4. (a) Comparison results on CIFAR-10. (b) Combination with UDA/SSDA methods. (c) Combination with SFDA methods." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 361, + 103, + 478, + 196 + ], + "blocks": [ + { + "bbox": [ + 361, + 103, + 478, + 196 + ], + "lines": [ + { + "bbox": [ + 361, + 103, + 478, + 196 + ], + "spans": [ + { + "bbox": [ + 361, + 103, + 478, + 196 + ], + "type": "image", + "image_path": "9052ba9140705fe2d1e084df96ff77789bfcb359c2d9a0202e16a70236faa774.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 427, + 197, + 437, + 205 + ], + "lines": [ + { + "bbox": [ + 427, + 197, + 437, + 205 + ], + "spans": [ + { + "bbox": [ + 427, + 197, + 437, + 205 + ], + "type": "text", + "content": "(c)" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 79, + 222, + 245, + 302 + ], + "blocks": [ + { + "bbox": [ + 79, + 222, + 245, + 302 + ], + "lines": [ + { + "bbox": [ + 79, + 222, + 245, + 302 + ], + "spans": [ + { + "bbox": [ + 79, + 222, + 245, + 302 + ], + "type": "table", + "html": "
MethodALLconLentGMMAVG
DiaNAUI✓✓✓77.7±0.2
DiaNA w/o ALR✓✓✓74.8±0.4
DiaNA w/o LconUI✓✓76.9±0.3
DiaNA w/o LentUI✓✓75.8±0.3
DiaNA w/o GMMUI✓✓74.0±0.2
DiaNA-UIUI✓72.1±0.4
DiaNA-UCUC✓68.3±0.6
DiaNA-CICI✓66.4±0.8
DiaNA-CCCC✓63.0±0.3
Random (Baseline)R65.8±0.5
", + "image_path": "b14513d4968adb1a01bcf4c0cb3e39398428709cdf3c0941689aa62b1fae80b9.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 302, + 279, + 346 + ], + "lines": [ + { + "bbox": [ + 45, + 302, + 279, + 346 + ], + "spans": [ + { + "bbox": [ + 45, + 302, + 279, + 346 + ], + "type": "text", + "content": "Table 3. Ablation study results of DiaNA. The \"AL\" column indicates which type of data subset should be selected to be annotated during each sampling step. We evaluated the performance of all adaptation scenarios on Office-Home by averaging their accuracy." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 45, + 352, + 279, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 352, + 279, + 388 + ], + "spans": [ + { + "bbox": [ + 45, + 352, + 279, + 388 + ], + "type": "text", + "content": "able, resulting from its significant performance improvement. This also indicates that our sampling strategy can be effectively applied to general active learning." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 45, + 389, + 279, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 389, + 279, + 586 + ], + "spans": [ + { + "bbox": [ + 45, + 389, + 279, + 586 + ], + "type": "text", + "content": "Combination with UDA/SSDA/SFDA methods. To validate the compatibility of the proposed DiaNA with existing UDA, SSDA, and SFDA algorithms, we conduct the experiments for UDA and SSDA in the adaptation " + }, + { + "bbox": [ + 45, + 389, + 279, + 586 + ], + "type": "inline_equation", + "content": "\\mathrm{C} \\rightarrow \\mathrm{S}" + }, + { + "bbox": [ + 45, + 389, + 279, + 586 + ], + "type": "text", + "content": " on DomainNet, and for SFDA in " + }, + { + "bbox": [ + 45, + 389, + 279, + 586 + ], + "type": "inline_equation", + "content": "\\mathrm{C} \\rightarrow \\mathrm{A}" + }, + { + "bbox": [ + 45, + 389, + 279, + 586 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 389, + 279, + 586 + ], + "type": "inline_equation", + "content": "\\mathrm{R} \\rightarrow \\mathrm{C}" + }, + { + "bbox": [ + 45, + 389, + 279, + 586 + ], + "type": "text", + "content": " on OfficeHome. DANN [5], MME [24], and NRC [36] correspond to the SOTA methods towards UDA, SSDA, and SFDA, respectively. As shown in Figure 4(b) and Figure 4(c), combining the selection strategy of DiaNA with other DA methods, i.e., DANN+Ours, MME+Ours, and NRC+Ours, significantly increases the performance of existing DA algorithms that select labeled target samples via random selection, namely DANN+Random, MME+Random and NRC+Random. This suggests that, adaptively considering both the domaininess and uncertainty, DiaNA is beneficial for the selection of informative target sample searching, while combined into diverse domain adaptation techniques." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 45, + 595, + 135, + 607 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 595, + 135, + 607 + ], + "spans": [ + { + "bbox": [ + 45, + 595, + 135, + 607 + ], + "type": "text", + "content": "4.4. Ablation study" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 45, + 612, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 612, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 612, + 279, + 730 + ], + "type": "text", + "content": "Efficacy of the targeted training strategies. To illustrate the effect of each component of the proposed DiaNA, we conduct ablation study by removing the corresponding individual components. As displayed in Table 3, the proposed method exceeds all of the model variants by a large accuracy margin on average, demonstrating the effectiveness of each component. By comparing our proposed entire approach with DiaNA w/o GMM, manual data division strategy might considerably cause performance degradation, thereby in turn emphasizing the need for adaptive" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 296, + 223, + 530, + 282 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 223, + 530, + 282 + ], + "spans": [ + { + "bbox": [ + 296, + 223, + 530, + 282 + ], + "type": "text", + "content": "data subdivision protocol. Furthermore, as demonstrated, disrupting the correspondence between targeted data subsets provides empirical evidence supporting the validity of our proposed customized learning techniques; see supplementary document for more details." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 296, + 282, + 531, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 282, + 531, + 434 + ], + "spans": [ + { + "bbox": [ + 296, + 282, + 531, + 434 + ], + "type": "text", + "content": "Efficacy of the sampling strategy. To provide insights into how effectively the domaininess-based metric and the uncertainty-based metric work in the sampling step, we use different data subsets to replace the UI subset as active samples for annotation. To eliminate the influence of " + }, + { + "bbox": [ + 296, + 282, + 531, + 434 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{con}" + }, + { + "bbox": [ + 296, + 282, + 531, + 434 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 282, + 531, + 434 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{ent}" + }, + { + "bbox": [ + 296, + 282, + 531, + 434 + ], + "type": "text", + "content": ", we remove these two terms but only retain " + }, + { + "bbox": [ + 296, + 282, + 531, + 434 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{sup}" + }, + { + "bbox": [ + 296, + 282, + 531, + 434 + ], + "type": "text", + "content": " during training. As shown in Table 3, both DiaNA-UC and DiaNA-CI achieve better classification performance than baseline selection, thereby showing the effect of the proposed uncertainty metric and domainness metric. Moreover, active sampling on UI samples (DiaNA-UI) obtains the best performance among all the variants, further illustrating the superiority of the integration of both metrics." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 297, + 445, + 373, + 457 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 445, + 373, + 457 + ], + "spans": [ + { + "bbox": [ + 297, + 445, + 373, + 457 + ], + "type": "text", + "content": "5. Conclusions" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 296, + 464, + 530, + 606 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 464, + 530, + 606 + ], + "spans": [ + { + "bbox": [ + 296, + 464, + 530, + 606 + ], + "type": "text", + "content": "In this paper, we introduce a \"divide-and-adapt\" framework, named DiaNA, to address the problem of active domain adaptation. Specifically, we first design an informativeness function that jointly captures sample's uncertainty and domainness. Moreover, we devise an automatic data subdivision protocol to partition the target instances into four categories with different characteristics. While selecting the most informative samples to annotate, we also design tailored learning strategies for the other target data subsets with stratified transferable properties. Extensive experimental results, as well as ablation studies, have confirmed the superiority of the proposed approach." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 297, + 617, + 392, + 630 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 617, + 392, + 630 + ], + "spans": [ + { + "bbox": [ + 297, + 617, + 392, + 630 + ], + "type": "text", + "content": "Acknowledgments" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 296, + 636, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 636, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 636, + 530, + 730 + ], + "type": "text", + "content": "This work was supported in part by the Guangdong Basic and Applied Basic Research Foundation (NO. 2020B1515020048), in part by the National Natural Science Foundation of China (NO. 61976250), in part by the Shenzhen Science and Technology Program (NO. JCYJ20220530141211024) and in part by the Fundamental Research Funds for the Central Universities under Grant 22lgqb25." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "text", + "content": "7658" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 105, + 103, + 117 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 105, + 103, + 117 + ], + "spans": [ + { + "bbox": [ + 47, + 105, + 103, + 117 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 124, + 280, + 730 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 51, + 124, + 279, + 168 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 124, + 279, + 168 + ], + "spans": [ + { + "bbox": [ + 51, + 124, + 279, + 168 + ], + "type": "text", + "content": "[1] Jordan T Ash, Chicheng Zhang, Akshay Krishnamurthy, John Langford, and Alekh Agarwal. 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On the contrary, existing visual reasoning methods assume training samples that capture every possible object and reasoning problem, and rely on black-boxed models that commonly exploit statistical priors. They have yet to develop the capability to address novel objects or spurious biases in real-world scenarios, and also fall short of interpreting the rationales behind their decisions. Inspired by humans' reasoning of the visual world, we tackle the aforementioned challenges from a compositional perspective, and propose an integral framework consisting of a principled object factorization method and a novel neural module network. Our factorization method decomposes objects based on their key characteristics, and automatically derives prototypes that represent a wide range of objects. With these prototypes encoding important semantics, the proposed network then correlates objects by measuring their similarity on a common semantic space and makes decisions with a compositional reasoning process. It is capable of answering questions with diverse objects regardless of their availability during training, and overcoming the issues of biased question-answer distributions. In addition to the enhanced generalizability, our framework also provides an interpretable interface for understanding the decision-making process of models. Our code is available at https://github.com/szzexpoi/POEM.", + "bbox": [ + 76, + 342, + 472, + 781 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 813, + 209, + 829 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "One of the fundamental goals in artificial intelligence is to develop systems that are able to reason with the complexity of real-world data to make decisions. Most existing visual question answering (VQA) methods [2, 13, 28, 29, 33,", + "bbox": [ + 75, + 839, + 470, + 902 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "34, 38, 49, 57] assume a complete overlap between objects involved in training and testing, and commonly rely on the spurious distributions of questions and answers [39]. As a result, they have limited generalizability toward real-life visual reasoning, and also lack the ability to justify the reasoning process that leads to the answers.", + "bbox": [ + 496, + 309, + 890, + 400 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "\"All mammals are animals. All elephants are mammals. Therefore, all elephants are animals [5].\" The wide application of syllogistic logic reflects key characteristics of the ways humans reason about the world. Unlike models [2, 38, 49] that utilize implicit features and heavily exploit statistical priors, humans correlate diverse objects from the compositional perspective based on their shared characteristics [26] and tackle problems with a structured reasoning process, which is both generalizable and interpretable.", + "bbox": [ + 496, + 401, + 892, + 537 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To address the complexity of real-world problems, this study aims to develop object factorization and compositional reasoning capabilities in models. As shown in Figure 1, our approach bridges diverse objects by projecting them onto a common space formed by discriminative prototypes (e.g., round shape, stuffed toy), and formulates the reasoning process with atomic steps [48] representing essential reasoning skills (e.g., Find, Relate). The prototypes are derived with object factorization, and they represent important semantics of objects (e.g., honey jar $\\rightarrow$ , teddy bear $\\rightarrow$ ). With an improved understanding of semantic relationships, our framework correlates objects (e.g., honey jar and container, stuffed toy and teddy bear) based on their commonalities in characteristics, leading to enhanced robustness against the diversity of objects and data biases. It also allows interpretations of the model's reasoning process consistent with the ways humans describe their own thinking [8].", + "bbox": [ + 496, + 537, + 893, + 809 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Compared to previous studies [2, 21, 33, 34, 48, 49], our major distinction lies in (1) the composition in two important dimensions of visual reasoning, i.e., objects and the reasoning process, and (2) a tight coupling between them. Instead of using black-boxed features or a direct mapping between question and answer that is vulnerable to object di", + "bbox": [ + 496, + 810, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "6736", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/51edc9c75a6dc04100daca80082332f5ba0e75b34e2ba54808cba21540f501c8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 86, + 88, + 240, + 244 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/2de158b8cb41b7c6354de56d9535bd8df5c7a51124fa053ffbb69821f2446740.jpg", + "image_caption": [ + "Question: Do you see a stuffed toy behind the honey jar to the left of the sandwich?", + "Figure 1. Overview of our method that represents objects with semantically meaningful prototypes and makes decisions via an explicit reasoning process. Honey jar is a novel object unseen during training. Note that our prototypes are not limited to a set of manually defined categories, but learned from factorizing objects to encode broader characteristics (e.g., shapes, colors, object categories)." + ], + "image_footnote": [], + "bbox": [ + 248, + 87, + 890, + 290 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "versity or data biases, our method decomposes objects into bases representing discriminative semantics, and develops a prototypical neural module network to explicitly bridge objects with a compositional reasoning paradigm. The proposed method naturally approaches generalizability with its compositional nature, handling novel objects and variable data distributions. It also provides a transparent interface for interpreting how models parse objects based on their characteristics and incorporate them for visual reasoning.", + "bbox": [ + 75, + 369, + 467, + 503 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To summarize, our major contributions are as follows:", + "bbox": [ + 96, + 506, + 454, + 520 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. We identify the significance of tightly coupling the compositionality between objects and the reasoning process, and for the first time investigate its effectiveness in generalizable and interpretable reasoning.", + "2. We propose a principled method that automatically derives prototypes with object factorization, which plays a key role in encoding key characteristics of objects.", + "3. We develop a new neural module network that adaptively reasons on the commonalities of different objects along a structured decision-making process.", + "4. We perform extensive analyses to shed light on the roles of compositionality in reasoning with novel objects and variable data distributions." + ], + "bbox": [ + 88, + 530, + 468, + 755 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 76, + 768, + 225, + 784 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our study is most related to previous efforts on visual question answering, zero-short learning for VQA, and VQA with out-of-distribution (OOD) questions.", + "bbox": [ + 76, + 794, + 467, + 839 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Visual question answering. With the diversity in language and visual semantics, visual question answering has become a popular task for studying models' reasoning capability [16]. A large body of research develops datasets", + "bbox": [ + 76, + 839, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "[4,6,18,24,25,40,42,58] and models [2,3,21,22,28,33,34, 38,48,49] for VQA. Early datasets typically rely on crowdsourcing [4, 18, 58] to collect human-annotated questions. Several recent studies [24,25,53] use functional programs to automatically generate questions based on pre-defined rules and enable more balanced data distributions. There is also an increasing interest in investigating different types of reasoning, e.g., scene text understanding [6], reasoning on context [42], and knowledge-based reasoning [40]. These data efforts lead to the development of methods that advance VQA models from different perspectives, including multi-modal fusion [13,29,57], attention mechanism [2,28], structured inference [21-23, 48], and vision-and-language pretraining [33,34,38,49]. The aforementioned studies assume that every semantic in the test questions is well illustrated during training, and pay little attention to the models' generalizability to real-world scenarios that inevitably involve novel objects and diverse question-answer distributions. Our study aims to fill the gap with an integral framework that develops generalizable decision making capability with object factorization and compositional reasoning.", + "bbox": [ + 496, + 369, + 890, + 686 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Zero-shot learning for VQA. Zero-shot VQA aims to answer questions with novel objects. The pioneering work [51] proposes the zero-shot setting for the VQA task, and benchmarks several techniques for improving the models' generalizability, including explicit object detector [2] and pretrained word embeddings [43]. Ramakrishnan et al. [45] leverage self-supervised pretraining to learn more generalizable features with external data. Wang et al. [54] combine visual models trained on different datasets with an attention mechanism. Whitehead et al. [55] decompose VQA into two sub-problems, i.e., concept grounding and skill matching, and propose additional training objectives to address unseen objects in the questions. Besides the above stud", + "bbox": [ + 496, + 703, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "6737", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/574b9e2c6779563d75f6d03bc589af1abe8e1b9eae08e9eb1d10dcc26a11a238.jpg", + "image_caption": [ + "Figure 2. Overview of our prototype learning paradigm based on object factorization." + ], + "image_footnote": [], + "bbox": [ + 78, + 85, + 893, + 234 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ies concerning novel concepts in language, there are also attempts [12, 52] that leverage exemplar-based methods to address novel concepts in both visual and textual modalities. While showing usefulness, these studies either leverage external data, which violates zero-shot assumption [32], or require memorizing a vast amount of supporting samples. As a result, they have yet to develop the capability of generalizing toward real-world scenarios. The key differentiators of our method lie in its ability to connect novel and known objects and the use of an explicit reasoning process. By bridging objects based on their commonalities and decomposing the decision-making process into atomic reasoning steps, it improves the generalizability and interpretability without relying on external data or memorizing samples.", + "bbox": [ + 75, + 287, + 468, + 498 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "VQA with OOD questions. To develop models that can truly reason on the visual-textual inputs instead of relying on statistical priors, VQA with out-of-distribution questions has gained considerable attention. In particular, Agrawal et al. [1] present the first VQA dataset with adversarial distributions between the training and validation data. A more recent study [27] analyzes models' robustness against biases by differentiating evaluation questions based on their question-answer distributions. To tackle the issues of harmful biases, a series of studies make progresses by improving visual attention [47, 56], reducing biases toward individual modalities [7, 15, 44], and leveraging ensemble techniques [11, 20]. There are also attempts [9, 17, 35] that use data augmentation to increase accuracy on biased data. However, they alter the distributions of training samples with additional data, and violate the original intent of the VQA with OOD questions task [50]. Our study is complementary to existing efforts, and it differentiates itself by investigating the usefulness of object factorization and compositional reasoning for addressing biases. It does not balance training samples to remove data biases, but instead focuses on enhancing models' own reasoning capabilities.", + "bbox": [ + 75, + 500, + 470, + 832 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 76, + 845, + 210, + 862 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Visual reasoning would benefit from capabilities of correlating objects based on their characteristics and decom", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "posing problems into atomic steps [19]. This section presents a new framework for improving the robustness against questions with novel objects and diverse question-answer distributions. It consists of two novel components: (1) a principled method that automatically derives semantically plausible prototypes to represent different objects, and (2) a neural module network that bridges objects by incorporating discriminative prototypes in an explicit reasoning process. Besides the enhanced generalizability, the method also provides an interpretable interface for elaborating on the rationales behind the model's decisions.", + "bbox": [ + 496, + 287, + 890, + 452 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Bridging Diverse Objects with Factorization", + "text_level": 1, + "bbox": [ + 500, + 460, + 874, + 477 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Inspired by humans' reasoning process that classifies objects based on their semantics similarity, a primary goal of our study is to derive semantic prototypes that can represent a vast amount of objects. The prototypes encode different aspects of the objects, and augment models with the capability to bridge diverse objects for more generalizable reasoning. Unlike previous studies [14, 41] that construct prototypes based on manually annotations and have difficulties scaling to different scenarios, we propose to automatically learn discriminative prototypes by factorizing various objects. Object factorization plays a key role in parsing the fine-grained characteristics of objects (e.g., shapes, textures, and super-categories), which facilitates understanding of the semantic relationships between objects.", + "bbox": [ + 496, + 484, + 890, + 696 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As illustrated in Figure 2, our prototype learning method leverages the multi-label classification task [10, 46, 59, 61] to discover discriminative prototypes in a data-driven manner. Given an input image, we train a deep neural network that predicts all object categories in the visual scene. Different from conventional approaches that recognize objects based on their visual features $O$ , we decompose objects with trainable prototypes $P$ and utilize the combinations of their matched prototypes for classification:", + "bbox": [ + 496, + 696, + 890, + 830 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\alpha_ {p} = \\delta \\left(O _ {i} \\cdot P\\right) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 640, + 838, + 890, + 856 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nC ^ {i} = C l s \\left(\\sum_ {k = 1} ^ {K} \\alpha_ {p} ^ {k} P ^ {k}\\right) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 620, + 861, + 890, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "6738", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/d367db23030cf9002029c3007d4d8cabfc0f6a00bdb6e1b02b77556124e96b44.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 76, + 137, + 274, + 258 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/86133129317079c4de2ed52f9d02721784bb960d672748c5067244b1606f1548.jpg", + "image_caption": [ + "Question: Are there any people to the left of the frisbee that the dog catches?", + "Figure 3. Illustration of the proposed prototypical neural module network. $\\otimes$ and $\\oplus$ denote dot product and concatenation, respectively." + ], + "image_footnote": [], + "bbox": [ + 279, + 88, + 890, + 292 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\alpha_{p} \\in \\mathbb{R}^{1 \\times K}$ denotes relevance scores between the $i^{th}$ object and $K$ prototypes. $O_{i} \\cdot P$ is the dot product between features and prototypes, which corresponds to their cosine similarity. $\\delta$ is the sigmoid activation function for normalization. $C^{i}$ is the prediction for the current object and $Cls$ is the classification module. To facilitate optimization without expensive instance-level annotations, we leverage an attention module $A_{cls}$ to dynamically aggregate instance-level predictions into the image-wise prediction $C$ :", + "bbox": [ + 75, + 340, + 473, + 479 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\alpha_ {c} ^ {i} = A _ {c l s} \\left(\\sum_ {k = 1} ^ {K} \\alpha_ {p} ^ {k} P ^ {k}\\right) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 196, + 489, + 468, + 532 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nC = \\sum_ {i = 1} ^ {N} \\alpha_ {c} ^ {i} C ^ {i} \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 220, + 546, + 468, + 587 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $N$ is the number of objects. We train the network with a standard binary cross-entropy loss, and select prototypes $P$ that provide the highest validation performance.", + "bbox": [ + 75, + 593, + 468, + 638 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The aforementioned paradigm factorizes objects into a set of bases formed by different prototypes. The prototypes encode important semantics of objects (see Section 4.5), and serve as critical components of our reasoning model, as detailed in the next subsection.", + "bbox": [ + 75, + 640, + 468, + 714 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Prototypical Neural Module Network", + "text_level": 1, + "bbox": [ + 76, + 724, + 398, + 742 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "With our prototypes constructing the common semantic space for bridging diverse objects, we further propose a novel prototypical neural module network to adaptively incorporate the correlation between objects with a compositional reasoning process. Compared to previous VQA methods [2,12,33,45,48,49,52,55], the advantages of our model lie in (1) its capability to generalize to both known and novel objects in the visual-textual domains, (2) the enhanced robustness against the spurious data biases, and (3) the interpretability of the decision-making procedure.", + "bbox": [ + 75, + 750, + 470, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Figure 3 provides an overview of the proposed neural module network with prototype matching and a semantic memory module. The principal idea behind our model is to take advantage of semantic relationships encoded in our learned prototypes (Section 3.1), and reason with a structured decision-making procedure. Neural module networks [3,21,48] are a body of interpretable reasoning methods that perform visual reasoning with two steps: (1) decomposing the reasoning process into discrete reasoning steps, where each step is associated with an atomic module (e.g., Find module for locating regions of interest), and (2) sequentially executing the modules on visual-textual inputs and gathering information to predict the answer. In addition to the use of an explicit reasoning process, our model utilizes prototype matching to project features of diverse objects onto the semantic space formed by prototypes, enabling it to measure their semantic relationships and tightly couple relevant objects. A semantic memory module is also proposed to adaptively combine important semantics captured at different reasoning steps, which facilitates joint reasoning throughout the whole reasoning process.", + "bbox": [ + 496, + 342, + 893, + 660 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Specifically, unlike conventional methods that rely on raw visual features and pay little attention to semantic relationships between objects, our model leverages the learned prototypes to parse different objects and correlate them based on their fine-grained characteristics. At each $t^{th}$ reasoning step, our network computes the similarity between visual features and prototypes, explicitly representing objects based on their corresponding characteristics, and uses the similarity scores $S^t \\in \\mathbb{R}^{N \\times K}$ for decision making:", + "bbox": [ + 496, + 660, + 893, + 797 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nS _ {i} ^ {t} = \\phi \\left(V _ {i} \\cdot P ^ {t}\\right) \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 640, + 809, + 890, + 827 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $V_{i}\\in \\mathbb{R}^{1\\times D}$ is $D$ dimensional visual features for the $i^{th}$ visual regions ( $N$ regions in total), and $P^t\\in \\mathbb{R}^{D\\times K}$ represents the $K$ prototypes. $V_{i}\\cdot P^{t}$ is the dot product between features and prototypes. $\\phi$ is the hyperbolic tangent", + "bbox": [ + 496, + 839, + 893, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "6739", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "activation function for normalizing the scores. Upon obtaining the similarity scores, we then locate the regions of interest for the current reasoning step:", + "bbox": [ + 75, + 90, + 472, + 137 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\alpha^ {t} = A ^ {t} \\left(F ^ {t} \\left(S ^ {t}, q ^ {t}\\right)\\right) \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 200, + 142, + 468, + 160 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\alpha^t\\in \\mathbb{R}^{1\\times N}$ is the attention map highlighting the important regions, $F^t$ and $A^t$ are the multi-modal fusion and attention module, respectively. $q^{t}$ is the query information derived from the question.", + "bbox": [ + 75, + 167, + 468, + 227 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Another key differentiator between our proposed model and existing neural module networks [21, 48] is the incorporation of semantic memory. Instead of determining the answer solely based on the question $Q$ and attended visual features $V'$ , we further take into account the prototypes attended over time $p^t = \\alpha^t \\cdot S^t$ , and bridge objects of interest at different reasoning steps. Our semantic memory module uses an attention mechanism to adaptively incorporate key prototypes at different steps:", + "bbox": [ + 75, + 228, + 468, + 364 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\alpha_ {s} = A _ {s} (Q) \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 227, + 371, + 468, + 388 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {y} = A n s \\left(\\left[ V ^ {\\prime}; \\sum_ {t = 1} ^ {T} \\alpha_ {s} ^ {t} p ^ {t} \\right], Q\\right) \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 176, + 395, + 468, + 435 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\alpha_{s} \\in \\mathbb{R}^{1 \\times T}$ represents attention weights for $T$ reasoning steps, and $A_{s}$ is the module for attention computation. $\\hat{y}$ is the predicted answer, and $Ans$ is the answer prediction module. $[\\cdot]$ denotes the concatenation of features.", + "bbox": [ + 75, + 439, + 468, + 500 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our proposed model associates objects based on their relationships with distinct prototypes, and adaptively combines important prototypes captured throughout the reasoning process. It takes advantage of the compositionality in both objects involved during visual reasoning (i.e., from objects to their characteristics) and the reasoning process (i.e., from questions to reasoning steps), which plays an essential role in addressing the diversity of objects and the spurious data biases. The compositional nature of the model also allows better interpretation of the underlying decision-making procedure (Section 4.6).", + "bbox": [ + 75, + 501, + 468, + 667 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 679, + 207, + 695 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This section presents implementation details (Section 4.1) and experiments to analyze the proposed method. We experiment with two different settings of VQA, including zero-shot VQA (Section 4.2) and VQA with out-of-distribution questions (Section 4.3), to validate the robustness of our method. We also provide an ablation study with different prototypes (Section 4.4) to demonstrate the advantages of object factorization. Besides examining the effectiveness of our method, we perform extensive analyses to shed light on the following questions: (1) What do prototypes learn? Do they encode common characteristics among objects? (Section 4.5); and (2) How do models reason to answer diverse questions? (Section 4.6)", + "bbox": [ + 75, + 704, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Implementations", + "text_level": 1, + "bbox": [ + 500, + 90, + 666, + 106 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. The primary goal of our experiments is to study models' generalizability to tackle real-world problems. We experiment with two different settings, each representing a common type of generalization: (1) Zeroshot VQA estimates models' generalizability toward both known and novel objects. Three popular datasets are used in our experiments, including VQA [18], GQA [24] and the recently introduced Novel-VQA [55]. Following [45, 55], for the VQA and GQA datasets, we reconstruct their training and validation sets to have a disjoint set of objects. For each dataset, we randomly select ten objects from the object pools and use them as novel objects unavailable during training. Similar to [12, 45, 51], we exclude all training questions that either contain words related to the selected objects or use images with the objects, and divide the original validation sets into Known and Novel splits based on objects required for reasoning. For the Novel-VQA dataset, we adopt the original training and test sets [55], which only considers novel objects in the questions (Novel-Q); (2) VQA with OOD questions focuses on evaluating models' generalizability to data with diverse question-answer distributions. We experiment with two popular datasets, including VQA-CP [1] with adversarial distributions between training and evaluation, and GQA-OOD [27] that utilizes balanced training questions but differentiates evaluation questions based on their question-answer distributions.", + "bbox": [ + 496, + 113, + 890, + 505 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation. We evaluate models with common metrics for visual question answering. For the VQA, Novel-VQA, and VQA-CP datasets, we adopt VQA accuracy [4] as the evaluation metric, which considers multiple candidate answers. For the GQA and GQA-OOD datasets, we use the standard accuracy since each question has an unique answer. We also follow [27] and consider differences in accuracy when answering in-distribution and out-of-distribution questions (i.e., $\\triangle$ ) on the GQA-OOD dataset.", + "bbox": [ + 496, + 507, + 890, + 643 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Model specification. We use the state-of-the-art neural module network XNM [48] as our baseline, which provides competitive performance on multiple datasets without loss of interpretability. We follow [60] and replace the Transform module with the Relate module to improve attention propagation. Following [34, 49, 55], we adopt the UpDown features [2] that capture 36 semantically meaningful regions (i.e., $N = 36$ ) as the visual inputs. To enable understanding of unseen vocabulary, we follow [51, 55] and use Glove vectors [43] to initialize the word embeddings. Other settings, e.g., network specification and training configuration, are the same as those defined in the original papers [48, 60] without tuning. The aforementioned baseline is incorporated with our method discussed in Section 3.2 to enable object factorization and compositional reasoning.", + "bbox": [ + 496, + 643, + 890, + 869 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Prototype learning. We derive our prototypes with the multi-label classification task [59, 61], which aims to pre", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "6740", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/5135943a4de3accb67f281ebd58110a8c61ffbf95dc581f37a0028d65b9c7d8c.jpg", + "table_caption": [ + "Table 1. Comparative results on zero-shot VQA." + ], + "table_footnote": [], + "table_body": "
VQAGQANovel-VQA
KnownNovelKnownNovelNovel-Q
UpDown [2]55.6548.5352.7351.3551.40
VisualBert [33]--59.8558.80-
Skill-Concept [55]----59.80
XNM [48]62.0552.8159.3957.5457.54
XNM+POEM63.8054.8260.6059.7160.73
", + "bbox": [ + 81, + 114, + 460, + 234 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "dict all object categories that exist in an image. The image-wise ground truth is constructed with object detection labels (VQA, VQA-CP and Novel-VQA) or scene graphs (GQA and GQA-OOD). UpDown features are used as inputs to the classification network, which encode semantic information of different objects. For zero-shot VQA, we train the model on each dataset with training images that do not contain the selected novel objects, and evaluate it on validation images with only known objects. For VQA with OOD questions, we use the original training and validation sets without excluding samples. We set the number of prototypes in our experiments to 1000 (i.e., $K = 1000$ ), which is comparable to the number of fine-grained objects in GQA (i.e., $\\sim 1000$ object categories). The network is trained with Adam [30] optimizer for 60 epochs, the learning rate and batch size are set to $4 \\times 10^{-4}$ and 128, respectively. Prototypes with the best validation performance are used in our VQA model.", + "bbox": [ + 75, + 261, + 468, + 518 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Results on Zero-shot VQA", + "text_level": 1, + "bbox": [ + 76, + 529, + 315, + 545 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We first demonstrate the effectiveness of our prototypical neural module (POEM) network on answering questions with both known and novel objects. We compare it with four approaches, including (1) UpDown [2] that does not explicitly model the reasoning process, (2) Our baseline XNM [48] with an explicitly reasoning process, (3) VisualBert [33] that utilizes vision-and-language pretraining on external data containing the novel objects (i.e., MSCOCO [36]), and (4) Skill-Concept [55] that is the current state-of-the-art on Novel-VQA dataset, which explicitly exploits novel objects in images with around $97\\%$ of them covered in a handcrafted reference training set. All of the models are trained with UpDown visual features and initialized with pretrained word embeddings.", + "bbox": [ + 75, + 551, + 468, + 763 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We draw three key observations from the results in Table 1: (1) While Updown and XNM show similar accuracy under the standard VQA setting [2, 48], the latter provides stronger performance on zero-shot VQA. The results indicate that the compositional reasoning process is not only helpful in interpretability, but also important for model performance and generalizability; (2) By leveraging external data, VisualBert provides better performance than both aforementioned models. However, it violates the original", + "bbox": [ + 75, + 763, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/9741aebff794f76278bae559f139dacaa24bf1b12510b5b43b0e72b8d51c9b93.jpg", + "table_caption": [ + "Table 2. Comparative results on VQA with OOD questions." + ], + "table_footnote": [], + "table_body": "
VQA-CPGQA-OOD
acc ↑acc-tail ↑△↓
Bias Product [11]39.9330.812.0
AdvReg [44]41.17--
Hint [47]46.73--
RUBi [7]47.1135.714.3
SCR [56]49.45--
LMH [11]52.0532.211.5
LMH+Entropies [15]54.55--
XNM [48]51.5446.1414.4
XNM+POEM53.9946.8910.7
", + "bbox": [ + 531, + 114, + 854, + 325 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "intent of zero-shot VQA with novel objects actually covered in the external data, making them impractical for real-world scenarios with unseen objects; and (3) Differently, with our prototypes bridging different objects and the reasoning process, the proposed method improves the performance of the XNM baseline without relying on external data, and achieves overall the best results in answering questions with both known and novel objects in the visual-textual data. It also outperforms Skill-Concept on the Novel-VQA dataset that only considers novel objects in the questions. Note that Skill-Concept assumes the availability of novel objects in training images and is not applicable to zero-shot setting on VQA and GQA datasets, while our method has the capability to generalize toward broader scenarios.", + "bbox": [ + 496, + 352, + 890, + 564 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Results on VQA with OOD Questions", + "text_level": 1, + "bbox": [ + 500, + 574, + 823, + 590 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Next, we investigate the robustness of our method against spurious data biases. We compare our method with eight approaches that do not exploit additional data, including Bias Product [11], AdvReg [44], RUBi [7], and LMH+Entropies [15] for reducing single-modal biases, Hint [47] and SCR [56] for boosting visual attention, LMH [11] for learning the residual of biases, and our baseline XNM. Following [11, 15, 20], when experimenting on the VQA-CP dataset [1], both XNM and our model incorporate the learned mixed-in module [11] to address known biases.", + "bbox": [ + 496, + 598, + 890, + 748 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results in Table 2 show that our method is able to improve the XNM baseline by a considerable margin. With object factorization and compositional reasoning, it not only improves the robustness against adversarial distributions (i.e., VQA-CP), but also reduces the performance gap between answering in-distribution and out-of-distribution questions (i.e., $\\triangle$ for GQA-OOD). Compared to existing methods that introduce additional regularization and have difficulties generalizing to different datasets [7, 11, 15], our method augments models' reasoning capability without im", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "6741", + "bbox": [ + 482, + 945, + 513, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/80381474976b2764a5e8152e06ef39e994919026e58f6069ed51cf63423f79f9.jpg", + "table_caption": [ + "Table 3. Comparative results for different prototypes." + ], + "table_footnote": [], + "table_body": "
VQAGQANovel-VQAVQA-CP
KnownNovelKnownNovelNovel-QOOD
Scratch62.6653.6658.8757.6959.4850.39
Object62.5653.2360.4859.4656.6752.23
Textual60.6152.3355.3153.2259.1751.09
Ours63.8054.8260.6059.7160.7353.99
", + "bbox": [ + 81, + 114, + 464, + 217 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "posing data-specific constrains and thus enjoys better generalizability. The aforementioned observations suggest the significance of explicitly bridging objects with their fine-grained characteristics for overcoming data biases.", + "bbox": [ + 75, + 244, + 468, + 305 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Ablation Study on Object Factorization", + "text_level": 1, + "bbox": [ + 76, + 316, + 416, + 333 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "A key component of our framework is the proposed method for learning discriminative prototypes with object factorization. In this section, we perform an ablation study to investigate the usefulness of different prototypes (see our supplementary materials for additional ablation studies on model design). Specifically, we consider three types of alternative prototypes: (1) Prototypes that are randomly initialized and learned from scratch on the VQA task (Scratch); (2) Prototypes specific to manually defined objects (Object), which are learned with the same multi-label classification task as our approach but without object factorization; and (3) Prototypes derived from Glove [43] word embeddings of concepts covered in the Visual Genome [31] dataset (Textual), including objects, attributes, and relationships.", + "bbox": [ + 75, + 340, + 468, + 566 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We made three observations from results in Table 3: (1) Randomly initialized prototypes lead to inferior performance among all datasets, indicating the significance of explicitly learning semantically plausible prototypes; (2) While object-based prototypes show reasonable performance on the GQA dataset with detailed annotations (i.e., $\\sim 1000$ object categories), they have negligible improvements on the VQA, Novel-VQA, and VQA-CP datasets with abstract-level annotations (i.e., 80 object categories). The large gap in performance gain across datasets demonstrates the advantages of fine-grained categorization, and more importantly, highlights the need to learn discriminative prototypes without relying on extensive annotations. For this, our method utilizes object factorization to automatically decompose objects into more elaborated semantics, and brings considerable improvements among datasets with both abstract and detailed object annotations; (3) Textual prototypes result in a visible drop in accuracy, despite the consideration of various concepts. This is likely caused by the difficulty of correlating objects across the visual and textual domains. Differently, our method directly captures diverse characteristics of objects from visual data and does", + "bbox": [ + 75, + 568, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4169df35cbbb9683445160f9c51fec2ac58fc3d97a0b96df10f6311eb9507013.jpg", + "image_caption": [ + "Figure 4. Examples of semantics encoded in diverse prototypes." + ], + "image_footnote": [], + "bbox": [ + 501, + 88, + 890, + 333 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "not suffer from the discrepancies between modalities.", + "bbox": [ + 500, + 385, + 854, + 400 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. What Do Prototypes Learn? Do They Encode Common Characteristics among Objects?", + "text_level": 1, + "bbox": [ + 500, + 409, + 890, + 441 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results in the previous sections demonstrate that our method learns discriminative prototypes to represent a variety of objects and bring enhanced generalizability across various settings. This section further demonstrates its effectiveness by investigating how our prototypes correlate different objects.", + "bbox": [ + 496, + 446, + 890, + 537 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We first study what each individual prototype learns. In Figure 4, we visualize instances (regions inside bounding boxes) most relevant to the prototypes (measured with their relevance scores on different prototypes, i.e., $\\alpha_{p}^{k}$ in Equation 2, $k$ denotes the indices of prototypes). The results show that our prototypes learn to represent a diverse pool of semantics. They not only capture low-level visual cues, such as shapes (e.g., round objects in the $1^{st}$ row), textures (e.g., objects with jagged texture in the $2^{nd}$ row), and patterns (e.g., objects with stripes in the $3^{rd}$ row), but also encode high-level semantics including object categories (e.g., wheels in the $4^{th}$ row) and commonalities in semantics (e.g., all objects in the $5^{th}$ row are displaying text).", + "bbox": [ + 496, + 537, + 892, + 734 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "With our prototypes encoding abundant semantics, we further analyze their effectiveness in correlating relevant objects based on their characteristics. Specifically, we calculate the average relevance scores $\\alpha_{p}$ (see Equation 1) between objects in the GQA dataset and all prototypes, and then apply k-means algorithm [37] ( $k = 30$ ) to cluster objects using the scores. As shown in Table 4, by representing objects based on the prototypes, we can correlate objects that belong to similar categories (e.g., drinks and utensils in the $1^{st}$ and $2^{nd}$ rows), commonly appear in the same scenarios (e.g., baseball games and bedrooms in the $3^{rd}$ and $4^{th}$ rows).", + "bbox": [ + 496, + 734, + 893, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "6742", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/dc227c2d8b627e8ba6af26e02937d6706ccb276a0a305b8e97669177404c0e8b.jpg", + "table_caption": [ + "Table 4. Different groups of objects that are clustered based on their relevance to prototypes. Please refer to our supplementary materials for the complete results with 30 groups." + ], + "table_footnote": [], + "table_body": "
GroupObjects
1cup, saucer, glass, beer, mug, juice, beverage, liquid, smoothie, coffee
2fork, spoon, knife, silverware, utensil, ladle, chopstick, tongs, spatula, butter knife
3spectator,UMPire, batter, catcher, crowd, net, player, baseball, stadium, bleachers
4bed, sofa, pillow, bedspread, headboard, comforter, couch, sheet, ottoman, mattress
5sticker, newspaper, paper, sign, book, tape, drawing, CD, letter, label
6water, sand, sea, rock, ocean, boulders, lake, beach, shore, river
", + "bbox": [ + 83, + 142, + 459, + 351 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "or share similar characteristics (e.g., objects related to text and landscape in the $5^{th}$ and $6^{th}$ rows). The results demonstrate the effectiveness of our prototypes in parsing objects based on their commonalities in the semantic space.", + "bbox": [ + 75, + 378, + 468, + 441 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.6. How Do Models Reason to Answer Questions?", + "text_level": 1, + "bbox": [ + 76, + 452, + 467, + 469 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Besides improving the generalizability, our method also enables interpretation of the decision-making process by visualizing the regions of interest (ROIs) at each reasoning step and prototypes matched with the observations. In this section, we provide qualitative examples to study the underlying rationales behind the derivation of answers.", + "bbox": [ + 75, + 476, + 468, + 566 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Figure 5 shows the reasoning process of our method. For each question, we visualize the reasoning steps represented by neural modules (top), attention maps highlighting the ROIs (middle, $\\alpha^t$ in Equation 6), and images associated to prototypes matched with the observations (bottom). It shows that our method can correlate objects based on various characteristics and locate those important ones. In the $1^{st}$ example, while the apples are not explicitly mentioned in the question, our model correlates them with prototypes for different fruits (\"fruit\" is a keyword in the question) and pays focused attention in the Find step. Besides capturing semantic relationships about object categories, prototypes also help identify the cat based on its attribute (i.e., brown color) within the Filter step, and enable the model to reason on the relative position between objects (i.e., Relate step). In the $2^{nd}$ example, our model not only highlights the correct objects in the first two Find steps (i.e., the banana and the mat), but also identifies the key characteristics that contribute to reasoning (i.e., matching observations with prototypes related to colors instead of object categories or other attributes). In the $3^{rd}$ example, woman in the question is an unseen object during training. With object factorization,", + "bbox": [ + 75, + 568, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/12c6f55d3e7ff510369b48984ebab3feee9026788c79e3d9b3322cc36a315f87.jpg", + "image_caption": [ + "Question: How is the fruit to the right of the brown animal called? Answer: Apple" + ], + "image_footnote": [], + "bbox": [ + 506, + 95, + 591, + 137 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/99208baa5b0f84ca49a2f59dc6ef935e8b52bc78f72c7eb68499ef80b7c3ce03.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 606, + 89, + 689, + 165 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f85dcb78305a5a19456de178d672fa09df1938f94fb88045a075ad06495c80f3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 606, + 167, + 691, + 250 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/dc928e931be11ff88cb5a7ed8f1c11b71f28ba6994e558242b50b2f4e32ac5ec.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 692, + 89, + 785, + 165 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7b71e9e189913e384cb86b8c5dc8a4d373f45b622dc6d58f8132d5ec16ffe0f5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 785, + 89, + 882, + 165 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4543385112d474e56b5c73757a9d5955dce78de2be7ca2c48113da8496eead35.jpg", + "image_caption": [ + "Question: Are both the banana and the place mat the same color? Answer: no" + ], + "image_footnote": [], + "bbox": [ + 517, + 258, + 583, + 321 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1bf0c21e9de0806b45981c0e85479d1bf6ff55afaa61c04bc44e6fc4c9681dbd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 602, + 169, + 689, + 250 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8ab06514a278703cf82b72ed7b2c2b1150bbc4d6e9a5111db8dd050049f66069.jpg", + "image_caption": [ + "Question: Do you see a woman near the water bottle in the bottom? Answer: yes" + ], + "image_footnote": [], + "bbox": [ + 602, + 251, + 679, + 356 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8e2b80b073cb3b3eaae152acb245a14a93d28befb7cb40b81ca14c4dca3982dd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 689, + 169, + 795, + 250 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/11d919d2ed29181ed3a9b59264679e691f74be2ece6737e1a6744a407f5c6142.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 795, + 169, + 885, + 250 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b54eb062fedf73518ca9e2f0d2efc3347dc02d2486b24206587c23feb96bf0fa.jpg", + "image_caption": [ + "Figure 5. Illustrations of the reasoning process. From left to right are the input images together with questions and predicted answers, and sequences of reasoning steps." + ], + "image_footnote": [], + "bbox": [ + 691, + 323, + 790, + 356 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/abf107185ea3bd1a39703a97333bb477b80a12875a9aae8c5858c20753f83c74.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 792, + 323, + 890, + 356 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "our model successfully associates it to known objects (i.e., men) based on the similarity in clothing, and progressively shifts the attention from both women (i.e., Find step) to the one lying next to the bottle (i.e., Filter and Relate steps).", + "bbox": [ + 498, + 439, + 890, + 501 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 516, + 617, + 532 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This study is an effort toward generalizable and interpretable AI systems for real-world applications. It draws inspiration from the ways humans reason with the visual world, and investigates the effectiveness of integrating the compositionality of objects and the reasoning process. Our work distinguishes itself with a principled method for automatically factorizing objects into fine-grained semantics, bridging novel and known objects, and a new neural module network with a compositional decision-making process. The compositionality in both dimensions addresses object diversity and spurious data biases, enhancing model generalizability toward a broad range of scenarios. It also enables interpretation of the rationales behind the model's decisions. Experimental results demonstrate the advantages of our method under diverse settings, and provide insights on how our model reasons with the visual-textual inputs. We hope that this study can be useful for future developments of trustworthy visual reasoning models with more human-like intelligence and generalizability.", + "bbox": [ + 496, + 541, + 892, + 829 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements", + "text_level": 1, + "bbox": [ + 500, + 844, + 666, + 861 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work is supported by NSF Grants 2143197 and 2227450.", + "bbox": [ + 500, + 869, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "6743", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Aishwarya Agrawal, Dhruv Batra, Devi Parikh, and Aniruddha Kembhavi. Don't just assume; look and answer: Overcoming priors for visual question answering. 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Learning spatial regularization with image-level supervisions for multi-label image classification. In CVPR, pages 2027-2036, 2017. 3, 5" + ], + "bbox": [ + 501, + 90, + 890, + 829 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "6745", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Divide and Conquer_ Answering Questions With Object Factorization and Compositional Reasoning/9361ff3c-8aee-49ab-8084-0a759e885614_model.json b/2023/Divide and Conquer_ Answering Questions With Object Factorization and Compositional Reasoning/9361ff3c-8aee-49ab-8084-0a759e885614_model.json new file mode 100644 index 0000000000000000000000000000000000000000..c53c342e6d6ee05ef365cd23ed0fe2bee9f25a76 --- /dev/null +++ b/2023/Divide and Conquer_ Answering Questions With Object Factorization and Compositional Reasoning/9361ff3c-8aee-49ab-8084-0a759e885614_model.json @@ -0,0 +1,2244 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.115, + 0.13, + 0.856, + 0.177 + ], + "angle": 0, + "content": "Divide and Conquer: Answering Questions with Object Factorization and Compositional Reasoning" + }, + { + "type": "text", + "bbox": [ + 0.393, + 0.204, + 0.578, + 0.221 + ], + "angle": 0, + "content": "Shi Chen Qi Zhao" + }, + { + "type": "text", + "bbox": [ + 0.284, + 0.223, + 0.686, + 0.24 + ], + "angle": 0, + "content": "Department of Computer Science and Engineering," + }, + { + "type": "text", + "bbox": [ + 0.39, + 0.24, + 0.582, + 0.257 + ], + "angle": 0, + "content": "University of Minnesota" + }, + { + "type": "text", + "bbox": [ + 0.377, + 0.26, + 0.596, + 0.275 + ], + "angle": 0, + "content": "{chen4595，qzhao}@umn.edu" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.309, + 0.314, + 0.327 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.343, + 0.473, + 0.782 + ], + "angle": 0, + "content": "Humans have the innate capability to answer diverse questions, which is rooted in the natural ability to correlate different concepts based on their semantic relationships and decompose difficult problems into sub-tasks. On the contrary, existing visual reasoning methods assume training samples that capture every possible object and reasoning problem, and rely on black-boxed models that commonly exploit statistical priors. They have yet to develop the capability to address novel objects or spurious biases in real-world scenarios, and also fall short of interpreting the rationales behind their decisions. Inspired by humans' reasoning of the visual world, we tackle the aforementioned challenges from a compositional perspective, and propose an integral framework consisting of a principled object factorization method and a novel neural module network. Our factorization method decomposes objects based on their key characteristics, and automatically derives prototypes that represent a wide range of objects. With these prototypes encoding important semantics, the proposed network then correlates objects by measuring their similarity on a common semantic space and makes decisions with a compositional reasoning process. It is capable of answering questions with diverse objects regardless of their availability during training, and overcoming the issues of biased question-answer distributions. In addition to the enhanced generalizability, our framework also provides an interpretable interface for understanding the decision-making process of models. Our code is available at https://github.com/szzexpoi/POEM." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.814, + 0.21, + 0.83 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.903 + ], + "angle": 0, + "content": "One of the fundamental goals in artificial intelligence is to develop systems that are able to reason with the complexity of real-world data to make decisions. Most existing visual question answering (VQA) methods [2, 13, 28, 29, 33," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.31, + 0.892, + 0.401 + ], + "angle": 0, + "content": "34, 38, 49, 57] assume a complete overlap between objects involved in training and testing, and commonly rely on the spurious distributions of questions and answers [39]. As a result, they have limited generalizability toward real-life visual reasoning, and also lack the ability to justify the reasoning process that leads to the answers." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.402, + 0.893, + 0.538 + ], + "angle": 0, + "content": "\"All mammals are animals. All elephants are mammals. Therefore, all elephants are animals [5].\" The wide application of syllogistic logic reflects key characteristics of the ways humans reason about the world. Unlike models [2, 38, 49] that utilize implicit features and heavily exploit statistical priors, humans correlate diverse objects from the compositional perspective based on their shared characteristics [26] and tackle problems with a structured reasoning process, which is both generalizable and interpretable." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.539, + 0.895, + 0.81 + ], + "angle": 0, + "content": "To address the complexity of real-world problems, this study aims to develop object factorization and compositional reasoning capabilities in models. As shown in Figure 1, our approach bridges diverse objects by projecting them onto a common space formed by discriminative prototypes (e.g., round shape, stuffed toy), and formulates the reasoning process with atomic steps [48] representing essential reasoning skills (e.g., Find, Relate). The prototypes are derived with object factorization, and they represent important semantics of objects (e.g., honey jar \\(\\rightarrow\\) , teddy bear \\(\\rightarrow\\) ). With an improved understanding of semantic relationships, our framework correlates objects (e.g., honey jar and container, stuffed toy and teddy bear) based on their commonalities in characteristics, leading to enhanced robustness against the diversity of objects and data biases. It also allows interpretations of the model's reasoning process consistent with the ways humans describe their own thinking [8]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Compared to previous studies [2, 21, 33, 34, 48, 49], our major distinction lies in (1) the composition in two important dimensions of visual reasoning, i.e., objects and the reasoning process, and (2) a tight coupling between them. Instead of using black-boxed features or a direct mapping between question and answer that is vulnerable to object di" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6736" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.089, + 0.241, + 0.246 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.08, + 0.249, + 0.248, + 0.287 + ], + "angle": 0, + "content": "Question: Do you see a stuffed toy behind the honey jar to the left of the sandwich?" + }, + { + "type": "image", + "bbox": [ + 0.249, + 0.088, + 0.891, + 0.291 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.302, + 0.893, + 0.345 + ], + "angle": 0, + "content": "Figure 1. Overview of our method that represents objects with semantically meaningful prototypes and makes decisions via an explicit reasoning process. Honey jar is a novel object unseen during training. Note that our prototypes are not limited to a set of manually defined categories, but learned from factorizing objects to encode broader characteristics (e.g., shapes, colors, object categories)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.371, + 0.468, + 0.505 + ], + "angle": 0, + "content": "versity or data biases, our method decomposes objects into bases representing discriminative semantics, and develops a prototypical neural module network to explicitly bridge objects with a compositional reasoning paradigm. The proposed method naturally approaches generalizability with its compositional nature, handling novel objects and variable data distributions. It also provides a transparent interface for interpreting how models parse objects based on their characteristics and incorporate them for visual reasoning." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.507, + 0.455, + 0.521 + ], + "angle": 0, + "content": "To summarize, our major contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.531, + 0.469, + 0.592 + ], + "angle": 0, + "content": "1. We identify the significance of tightly coupling the compositionality between objects and the reasoning process, and for the first time investigate its effectiveness in generalizable and interpretable reasoning." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.601, + 0.469, + 0.647 + ], + "angle": 0, + "content": "2. We propose a principled method that automatically derives prototypes with object factorization, which plays a key role in encoding key characteristics of objects." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.657, + 0.469, + 0.702 + ], + "angle": 0, + "content": "3. We develop a new neural module network that adaptively reasons on the commonalities of different objects along a structured decision-making process." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.711, + 0.469, + 0.756 + ], + "angle": 0, + "content": "4. We perform extensive analyses to shed light on the roles of compositionality in reasoning with novel objects and variable data distributions." + }, + { + "type": "list", + "bbox": [ + 0.089, + 0.531, + 0.469, + 0.756 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.77, + 0.227, + 0.785 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.795, + 0.468, + 0.84 + ], + "angle": 0, + "content": "Our study is most related to previous efforts on visual question answering, zero-short learning for VQA, and VQA with out-of-distribution (OOD) questions." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.84, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Visual question answering. With the diversity in language and visual semantics, visual question answering has become a popular task for studying models' reasoning capability [16]. A large body of research develops datasets" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.37, + 0.892, + 0.688 + ], + "angle": 0, + "content": "[4,6,18,24,25,40,42,58] and models [2,3,21,22,28,33,34, 38,48,49] for VQA. Early datasets typically rely on crowdsourcing [4, 18, 58] to collect human-annotated questions. Several recent studies [24,25,53] use functional programs to automatically generate questions based on pre-defined rules and enable more balanced data distributions. There is also an increasing interest in investigating different types of reasoning, e.g., scene text understanding [6], reasoning on context [42], and knowledge-based reasoning [40]. These data efforts lead to the development of methods that advance VQA models from different perspectives, including multi-modal fusion [13,29,57], attention mechanism [2,28], structured inference [21-23, 48], and vision-and-language pretraining [33,34,38,49]. The aforementioned studies assume that every semantic in the test questions is well illustrated during training, and pay little attention to the models' generalizability to real-world scenarios that inevitably involve novel objects and diverse question-answer distributions. Our study aims to fill the gap with an integral framework that develops generalizable decision making capability with object factorization and compositional reasoning." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Zero-shot learning for VQA. Zero-shot VQA aims to answer questions with novel objects. The pioneering work [51] proposes the zero-shot setting for the VQA task, and benchmarks several techniques for improving the models' generalizability, including explicit object detector [2] and pretrained word embeddings [43]. Ramakrishnan et al. [45] leverage self-supervised pretraining to learn more generalizable features with external data. Wang et al. [54] combine visual models trained on different datasets with an attention mechanism. Whitehead et al. [55] decompose VQA into two sub-problems, i.e., concept grounding and skill matching, and propose additional training objectives to address unseen objects in the questions. Besides the above stud" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6737" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.087, + 0.895, + 0.235 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.231, + 0.247, + 0.738, + 0.262 + ], + "angle": 0, + "content": "Figure 2. Overview of our prototype learning paradigm based on object factorization." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.288, + 0.47, + 0.499 + ], + "angle": 0, + "content": "ies concerning novel concepts in language, there are also attempts [12, 52] that leverage exemplar-based methods to address novel concepts in both visual and textual modalities. While showing usefulness, these studies either leverage external data, which violates zero-shot assumption [32], or require memorizing a vast amount of supporting samples. As a result, they have yet to develop the capability of generalizing toward real-world scenarios. The key differentiators of our method lie in its ability to connect novel and known objects and the use of an explicit reasoning process. By bridging objects based on their commonalities and decomposing the decision-making process into atomic reasoning steps, it improves the generalizability and interpretability without relying on external data or memorizing samples." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.5, + 0.471, + 0.833 + ], + "angle": 0, + "content": "VQA with OOD questions. To develop models that can truly reason on the visual-textual inputs instead of relying on statistical priors, VQA with out-of-distribution questions has gained considerable attention. In particular, Agrawal et al. [1] present the first VQA dataset with adversarial distributions between the training and validation data. A more recent study [27] analyzes models' robustness against biases by differentiating evaluation questions based on their question-answer distributions. To tackle the issues of harmful biases, a series of studies make progresses by improving visual attention [47, 56], reducing biases toward individual modalities [7, 15, 44], and leveraging ensemble techniques [11, 20]. There are also attempts [9, 17, 35] that use data augmentation to increase accuracy on biased data. However, they alter the distributions of training samples with additional data, and violate the original intent of the VQA with OOD questions task [50]. Our study is complementary to existing efforts, and it differentiates itself by investigating the usefulness of object factorization and compositional reasoning for addressing biases. It does not balance training samples to remove data biases, but instead focuses on enhancing models' own reasoning capabilities." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.846, + 0.212, + 0.863 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Visual reasoning would benefit from capabilities of correlating objects based on their characteristics and decom" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.288, + 0.892, + 0.453 + ], + "angle": 0, + "content": "posing problems into atomic steps [19]. This section presents a new framework for improving the robustness against questions with novel objects and diverse question-answer distributions. It consists of two novel components: (1) a principled method that automatically derives semantically plausible prototypes to represent different objects, and (2) a neural module network that bridges objects by incorporating discriminative prototypes in an explicit reasoning process. Besides the enhanced generalizability, the method also provides an interpretable interface for elaborating on the rationales behind the model's decisions." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.461, + 0.875, + 0.478 + ], + "angle": 0, + "content": "3.1. Bridging Diverse Objects with Factorization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.485, + 0.892, + 0.697 + ], + "angle": 0, + "content": "Inspired by humans' reasoning process that classifies objects based on their semantics similarity, a primary goal of our study is to derive semantic prototypes that can represent a vast amount of objects. The prototypes encode different aspects of the objects, and augment models with the capability to bridge diverse objects for more generalizable reasoning. Unlike previous studies [14, 41] that construct prototypes based on manually annotations and have difficulties scaling to different scenarios, we propose to automatically learn discriminative prototypes by factorizing various objects. Object factorization plays a key role in parsing the fine-grained characteristics of objects (e.g., shapes, textures, and super-categories), which facilitates understanding of the semantic relationships between objects." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.697, + 0.892, + 0.832 + ], + "angle": 0, + "content": "As illustrated in Figure 2, our prototype learning method leverages the multi-label classification task [10, 46, 59, 61] to discover discriminative prototypes in a data-driven manner. Given an input image, we train a deep neural network that predicts all object categories in the visual scene. Different from conventional approaches that recognize objects based on their visual features \\( O \\), we decompose objects with trainable prototypes \\( P \\) and utilize the combinations of their matched prototypes for classification:" + }, + { + "type": "equation", + "bbox": [ + 0.641, + 0.839, + 0.892, + 0.857 + ], + "angle": 0, + "content": "\\[\n\\alpha_ {p} = \\delta \\left(O _ {i} \\cdot P\\right) \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.621, + 0.862, + 0.892, + 0.904 + ], + "angle": 0, + "content": "\\[\nC ^ {i} = C l s \\left(\\sum_ {k = 1} ^ {K} \\alpha_ {p} ^ {k} P ^ {k}\\right) \\tag {2}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6738" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.08, + 0.089, + 0.273, + 0.13 + ], + "angle": 0, + "content": "Question: Are there any people to the left of the frisbee that the dog catches?" + }, + { + "type": "image", + "bbox": [ + 0.078, + 0.138, + 0.276, + 0.26 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.28, + 0.089, + 0.891, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.083, + 0.302, + 0.885, + 0.318 + ], + "angle": 0, + "content": "Figure 3. Illustration of the proposed prototypical neural module network. \\(\\otimes\\) and \\(\\oplus\\) denote dot product and concatenation, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.342, + 0.474, + 0.481 + ], + "angle": 0, + "content": "where \\(\\alpha_{p} \\in \\mathbb{R}^{1 \\times K}\\) denotes relevance scores between the \\(i^{th}\\) object and \\(K\\) prototypes. \\(O_{i} \\cdot P\\) is the dot product between features and prototypes, which corresponds to their cosine similarity. \\(\\delta\\) is the sigmoid activation function for normalization. \\(C^{i}\\) is the prediction for the current object and \\(Cls\\) is the classification module. To facilitate optimization without expensive instance-level annotations, we leverage an attention module \\(A_{cls}\\) to dynamically aggregate instance-level predictions into the image-wise prediction \\(C\\):" + }, + { + "type": "equation", + "bbox": [ + 0.197, + 0.491, + 0.47, + 0.533 + ], + "angle": 0, + "content": "\\[\n\\alpha_ {c} ^ {i} = A _ {c l s} \\left(\\sum_ {k = 1} ^ {K} \\alpha_ {p} ^ {k} P ^ {k}\\right) \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.222, + 0.547, + 0.47, + 0.588 + ], + "angle": 0, + "content": "\\[\nC = \\sum_ {i = 1} ^ {N} \\alpha_ {c} ^ {i} C ^ {i} \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.594, + 0.47, + 0.64 + ], + "angle": 0, + "content": "where \\(N\\) is the number of objects. We train the network with a standard binary cross-entropy loss, and select prototypes \\(P\\) that provide the highest validation performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.641, + 0.47, + 0.715 + ], + "angle": 0, + "content": "The aforementioned paradigm factorizes objects into a set of bases formed by different prototypes. The prototypes encode important semantics of objects (see Section 4.5), and serve as critical components of our reasoning model, as detailed in the next subsection." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.726, + 0.4, + 0.743 + ], + "angle": 0, + "content": "3.2. Prototypical Neural Module Network" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.903 + ], + "angle": 0, + "content": "With our prototypes constructing the common semantic space for bridging diverse objects, we further propose a novel prototypical neural module network to adaptively incorporate the correlation between objects with a compositional reasoning process. Compared to previous VQA methods [2,12,33,45,48,49,52,55], the advantages of our model lie in (1) its capability to generalize to both known and novel objects in the visual-textual domains, (2) the enhanced robustness against the spurious data biases, and (3) the interpretability of the decision-making procedure." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.343, + 0.895, + 0.661 + ], + "angle": 0, + "content": "Figure 3 provides an overview of the proposed neural module network with prototype matching and a semantic memory module. The principal idea behind our model is to take advantage of semantic relationships encoded in our learned prototypes (Section 3.1), and reason with a structured decision-making procedure. Neural module networks [3,21,48] are a body of interpretable reasoning methods that perform visual reasoning with two steps: (1) decomposing the reasoning process into discrete reasoning steps, where each step is associated with an atomic module (e.g., Find module for locating regions of interest), and (2) sequentially executing the modules on visual-textual inputs and gathering information to predict the answer. In addition to the use of an explicit reasoning process, our model utilizes prototype matching to project features of diverse objects onto the semantic space formed by prototypes, enabling it to measure their semantic relationships and tightly couple relevant objects. A semantic memory module is also proposed to adaptively combine important semantics captured at different reasoning steps, which facilitates joint reasoning throughout the whole reasoning process." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.661, + 0.894, + 0.798 + ], + "angle": 0, + "content": "Specifically, unlike conventional methods that rely on raw visual features and pay little attention to semantic relationships between objects, our model leverages the learned prototypes to parse different objects and correlate them based on their fine-grained characteristics. At each \\( t^{th} \\) reasoning step, our network computes the similarity between visual features and prototypes, explicitly representing objects based on their corresponding characteristics, and uses the similarity scores \\( S^t \\in \\mathbb{R}^{N \\times K} \\) for decision making:" + }, + { + "type": "equation", + "bbox": [ + 0.641, + 0.81, + 0.892, + 0.828 + ], + "angle": 0, + "content": "\\[\nS _ {i} ^ {t} = \\phi \\left(V _ {i} \\cdot P ^ {t}\\right) \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.903 + ], + "angle": 0, + "content": "where \\(V_{i}\\in \\mathbb{R}^{1\\times D}\\) is \\(D\\) dimensional visual features for the \\(i^{th}\\) visual regions ( \\(N\\) regions in total), and \\(P^t\\in \\mathbb{R}^{D\\times K}\\) represents the \\(K\\) prototypes. \\(V_{i}\\cdot P^{t}\\) is the dot product between features and prototypes. \\(\\phi\\) is the hyperbolic tangent" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6739" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.138 + ], + "angle": 0, + "content": "activation function for normalizing the scores. Upon obtaining the similarity scores, we then locate the regions of interest for the current reasoning step:" + }, + { + "type": "equation", + "bbox": [ + 0.202, + 0.143, + 0.47, + 0.161 + ], + "angle": 0, + "content": "\\[\n\\alpha^ {t} = A ^ {t} \\left(F ^ {t} \\left(S ^ {t}, q ^ {t}\\right)\\right) \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.168, + 0.469, + 0.228 + ], + "angle": 0, + "content": "where \\(\\alpha^t\\in \\mathbb{R}^{1\\times N}\\) is the attention map highlighting the important regions, \\(F^t\\) and \\(A^t\\) are the multi-modal fusion and attention module, respectively. \\(q^{t}\\) is the query information derived from the question." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.229, + 0.47, + 0.365 + ], + "angle": 0, + "content": "Another key differentiator between our proposed model and existing neural module networks [21, 48] is the incorporation of semantic memory. Instead of determining the answer solely based on the question \\( Q \\) and attended visual features \\( V' \\), we further take into account the prototypes attended over time \\( p^t = \\alpha^t \\cdot S^t \\), and bridge objects of interest at different reasoning steps. Our semantic memory module uses an attention mechanism to adaptively incorporate key prototypes at different steps:" + }, + { + "type": "equation", + "bbox": [ + 0.228, + 0.372, + 0.469, + 0.389 + ], + "angle": 0, + "content": "\\[\n\\alpha_ {s} = A _ {s} (Q) \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.177, + 0.396, + 0.469, + 0.436 + ], + "angle": 0, + "content": "\\[\n\\hat {y} = A n s \\left(\\left[ V ^ {\\prime}; \\sum_ {t = 1} ^ {T} \\alpha_ {s} ^ {t} p ^ {t} \\right], Q\\right) \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.44, + 0.469, + 0.501 + ], + "angle": 0, + "content": "where \\(\\alpha_{s} \\in \\mathbb{R}^{1 \\times T}\\) represents attention weights for \\(T\\) reasoning steps, and \\(A_{s}\\) is the module for attention computation. \\(\\hat{y}\\) is the predicted answer, and \\(Ans\\) is the answer prediction module. \\([\\cdot]\\) denotes the concatenation of features." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.502, + 0.469, + 0.668 + ], + "angle": 0, + "content": "Our proposed model associates objects based on their relationships with distinct prototypes, and adaptively combines important prototypes captured throughout the reasoning process. It takes advantage of the compositionality in both objects involved during visual reasoning (i.e., from objects to their characteristics) and the reasoning process (i.e., from questions to reasoning steps), which plays an essential role in addressing the diversity of objects and the spurious data biases. The compositional nature of the model also allows better interpretation of the underlying decision-making procedure (Section 4.6)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.68, + 0.209, + 0.696 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.469, + 0.901 + ], + "angle": 0, + "content": "This section presents implementation details (Section 4.1) and experiments to analyze the proposed method. We experiment with two different settings of VQA, including zero-shot VQA (Section 4.2) and VQA with out-of-distribution questions (Section 4.3), to validate the robustness of our method. We also provide an ablation study with different prototypes (Section 4.4) to demonstrate the advantages of object factorization. Besides examining the effectiveness of our method, we perform extensive analyses to shed light on the following questions: (1) What do prototypes learn? Do they encode common characteristics among objects? (Section 4.5); and (2) How do models reason to answer diverse questions? (Section 4.6)" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.092, + 0.667, + 0.107 + ], + "angle": 0, + "content": "4.1. Implementations" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.114, + 0.892, + 0.506 + ], + "angle": 0, + "content": "Datasets. The primary goal of our experiments is to study models' generalizability to tackle real-world problems. We experiment with two different settings, each representing a common type of generalization: (1) Zeroshot VQA estimates models' generalizability toward both known and novel objects. Three popular datasets are used in our experiments, including VQA [18], GQA [24] and the recently introduced Novel-VQA [55]. Following [45, 55], for the VQA and GQA datasets, we reconstruct their training and validation sets to have a disjoint set of objects. For each dataset, we randomly select ten objects from the object pools and use them as novel objects unavailable during training. Similar to [12, 45, 51], we exclude all training questions that either contain words related to the selected objects or use images with the objects, and divide the original validation sets into Known and Novel splits based on objects required for reasoning. For the Novel-VQA dataset, we adopt the original training and test sets [55], which only considers novel objects in the questions (Novel-Q); (2) VQA with OOD questions focuses on evaluating models' generalizability to data with diverse question-answer distributions. We experiment with two popular datasets, including VQA-CP [1] with adversarial distributions between training and evaluation, and GQA-OOD [27] that utilizes balanced training questions but differentiates evaluation questions based on their question-answer distributions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.508, + 0.892, + 0.644 + ], + "angle": 0, + "content": "Evaluation. We evaluate models with common metrics for visual question answering. For the VQA, Novel-VQA, and VQA-CP datasets, we adopt VQA accuracy [4] as the evaluation metric, which considers multiple candidate answers. For the GQA and GQA-OOD datasets, we use the standard accuracy since each question has an unique answer. We also follow [27] and consider differences in accuracy when answering in-distribution and out-of-distribution questions (i.e., \\(\\triangle\\)) on the GQA-OOD dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.892, + 0.87 + ], + "angle": 0, + "content": "Model specification. We use the state-of-the-art neural module network XNM [48] as our baseline, which provides competitive performance on multiple datasets without loss of interpretability. We follow [60] and replace the Transform module with the Relate module to improve attention propagation. Following [34, 49, 55], we adopt the UpDown features [2] that capture 36 semantically meaningful regions (i.e., \\( N = 36 \\)) as the visual inputs. To enable understanding of unseen vocabulary, we follow [51, 55] and use Glove vectors [43] to initialize the word embeddings. Other settings, e.g., network specification and training configuration, are the same as those defined in the original papers [48, 60] without tuning. The aforementioned baseline is incorporated with our method discussed in Section 3.2 to enable object factorization and compositional reasoning." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Prototype learning. We derive our prototypes with the multi-label classification task [59, 61], which aims to pre" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6740" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.13, + 0.09, + 0.417, + 0.104 + ], + "angle": 0, + "content": "Table 1. Comparative results on zero-shot VQA." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.115, + 0.462, + 0.235 + ], + "angle": 0, + "content": "
VQAGQANovel-VQA
KnownNovelKnownNovelNovel-Q
UpDown [2]55.6548.5352.7351.3551.40
VisualBert [33]--59.8558.80-
Skill-Concept [55]----59.80
XNM [48]62.0552.8159.3957.5457.54
XNM+POEM63.8054.8260.6059.7160.73
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.262, + 0.47, + 0.519 + ], + "angle": 0, + "content": "dict all object categories that exist in an image. The image-wise ground truth is constructed with object detection labels (VQA, VQA-CP and Novel-VQA) or scene graphs (GQA and GQA-OOD). UpDown features are used as inputs to the classification network, which encode semantic information of different objects. For zero-shot VQA, we train the model on each dataset with training images that do not contain the selected novel objects, and evaluate it on validation images with only known objects. For VQA with OOD questions, we use the original training and validation sets without excluding samples. We set the number of prototypes in our experiments to 1000 (i.e., \\( K = 1000 \\)), which is comparable to the number of fine-grained objects in GQA (i.e., \\( \\sim 1000 \\) object categories). The network is trained with Adam [30] optimizer for 60 epochs, the learning rate and batch size are set to \\( 4 \\times 10^{-4} \\) and 128, respectively. Prototypes with the best validation performance are used in our VQA model." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.53, + 0.316, + 0.546 + ], + "angle": 0, + "content": "4.2. Results on Zero-shot VQA" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.553, + 0.469, + 0.764 + ], + "angle": 0, + "content": "We first demonstrate the effectiveness of our prototypical neural module (POEM) network on answering questions with both known and novel objects. We compare it with four approaches, including (1) UpDown [2] that does not explicitly model the reasoning process, (2) Our baseline XNM [48] with an explicitly reasoning process, (3) VisualBert [33] that utilizes vision-and-language pretraining on external data containing the novel objects (i.e., MSCOCO [36]), and (4) Skill-Concept [55] that is the current state-of-the-art on Novel-VQA dataset, which explicitly exploits novel objects in images with around \\(97\\%\\) of them covered in a handcrafted reference training set. All of the models are trained with UpDown visual features and initialized with pretrained word embeddings." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.469, + 0.901 + ], + "angle": 0, + "content": "We draw three key observations from the results in Table 1: (1) While Updown and XNM show similar accuracy under the standard VQA setting [2, 48], the latter provides stronger performance on zero-shot VQA. The results indicate that the compositional reasoning process is not only helpful in interpretability, but also important for model performance and generalizability; (2) By leveraging external data, VisualBert provides better performance than both aforementioned models. However, it violates the original" + }, + { + "type": "table_caption", + "bbox": [ + 0.519, + 0.09, + 0.872, + 0.104 + ], + "angle": 0, + "content": "Table 2. Comparative results on VQA with OOD questions." + }, + { + "type": "table", + "bbox": [ + 0.532, + 0.115, + 0.855, + 0.327 + ], + "angle": 0, + "content": "
VQA-CPGQA-OOD
acc ↑acc-tail ↑△↓
Bias Product [11]39.9330.812.0
AdvReg [44]41.17--
Hint [47]46.73--
RUBi [7]47.1135.714.3
SCR [56]49.45--
LMH [11]52.0532.211.5
LMH+Entropies [15]54.55--
XNM [48]51.5446.1414.4
XNM+POEM53.9946.8910.7
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.353, + 0.892, + 0.565 + ], + "angle": 0, + "content": "intent of zero-shot VQA with novel objects actually covered in the external data, making them impractical for real-world scenarios with unseen objects; and (3) Differently, with our prototypes bridging different objects and the reasoning process, the proposed method improves the performance of the XNM baseline without relying on external data, and achieves overall the best results in answering questions with both known and novel objects in the visual-textual data. It also outperforms Skill-Concept on the Novel-VQA dataset that only considers novel objects in the questions. Note that Skill-Concept assumes the availability of novel objects in training images and is not applicable to zero-shot setting on VQA and GQA datasets, while our method has the capability to generalize toward broader scenarios." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.575, + 0.825, + 0.592 + ], + "angle": 0, + "content": "4.3. Results on VQA with OOD Questions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.892, + 0.749 + ], + "angle": 0, + "content": "Next, we investigate the robustness of our method against spurious data biases. We compare our method with eight approaches that do not exploit additional data, including Bias Product [11], AdvReg [44], RUBi [7], and LMH+Entropies [15] for reducing single-modal biases, Hint [47] and SCR [56] for boosting visual attention, LMH [11] for learning the residual of biases, and our baseline XNM. Following [11, 15, 20], when experimenting on the VQA-CP dataset [1], both XNM and our model incorporate the learned mixed-in module [11] to address known biases." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Results in Table 2 show that our method is able to improve the XNM baseline by a considerable margin. With object factorization and compositional reasoning, it not only improves the robustness against adversarial distributions (i.e., VQA-CP), but also reduces the performance gap between answering in-distribution and out-of-distribution questions (i.e., \\(\\triangle\\) for GQA-OOD). Compared to existing methods that introduce additional regularization and have difficulties generalizing to different datasets [7, 11, 15], our method augments models' reasoning capability without im" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.514, + 0.957 + ], + "angle": 0, + "content": "6741" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.115, + 0.09, + 0.432, + 0.104 + ], + "angle": 0, + "content": "Table 3. Comparative results for different prototypes." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.115, + 0.465, + 0.218 + ], + "angle": 0, + "content": "
VQAGQANovel-VQAVQA-CP
KnownNovelKnownNovelNovel-QOOD
Scratch62.6653.6658.8757.6959.4850.39
Object62.5653.2360.4859.4656.6752.23
Textual60.6152.3355.3153.2259.1751.09
Ours63.8054.8260.6059.7160.7353.99
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.246, + 0.47, + 0.306 + ], + "angle": 0, + "content": "posing data-specific constrains and thus enjoys better generalizability. The aforementioned observations suggest the significance of explicitly bridging objects with their fine-grained characteristics for overcoming data biases." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.318, + 0.418, + 0.334 + ], + "angle": 0, + "content": "4.4. Ablation Study on Object Factorization" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.342, + 0.47, + 0.568 + ], + "angle": 0, + "content": "A key component of our framework is the proposed method for learning discriminative prototypes with object factorization. In this section, we perform an ablation study to investigate the usefulness of different prototypes (see our supplementary materials for additional ablation studies on model design). Specifically, we consider three types of alternative prototypes: (1) Prototypes that are randomly initialized and learned from scratch on the VQA task (Scratch); (2) Prototypes specific to manually defined objects (Object), which are learned with the same multi-label classification task as our approach but without object factorization; and (3) Prototypes derived from Glove [43] word embeddings of concepts covered in the Visual Genome [31] dataset (Textual), including objects, attributes, and relationships." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.569, + 0.471, + 0.902 + ], + "angle": 0, + "content": "We made three observations from results in Table 3: (1) Randomly initialized prototypes lead to inferior performance among all datasets, indicating the significance of explicitly learning semantically plausible prototypes; (2) While object-based prototypes show reasonable performance on the GQA dataset with detailed annotations (i.e., \\(\\sim 1000\\) object categories), they have negligible improvements on the VQA, Novel-VQA, and VQA-CP datasets with abstract-level annotations (i.e., 80 object categories). The large gap in performance gain across datasets demonstrates the advantages of fine-grained categorization, and more importantly, highlights the need to learn discriminative prototypes without relying on extensive annotations. For this, our method utilizes object factorization to automatically decompose objects into more elaborated semantics, and brings considerable improvements among datasets with both abstract and detailed object annotations; (3) Textual prototypes result in a visible drop in accuracy, despite the consideration of various concepts. This is likely caused by the difficulty of correlating objects across the visual and textual domains. Differently, our method directly captures diverse characteristics of objects from visual data and does" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.089, + 0.892, + 0.334 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.505, + 0.345, + 0.885, + 0.359 + ], + "angle": 0, + "content": "Figure 4. Examples of semantics encoded in diverse prototypes." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.386, + 0.855, + 0.401 + ], + "angle": 0, + "content": "not suffer from the discrepancies between modalities." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.41, + 0.892, + 0.442 + ], + "angle": 0, + "content": "4.5. What Do Prototypes Learn? Do They Encode Common Characteristics among Objects?" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.448, + 0.892, + 0.538 + ], + "angle": 0, + "content": "Results in the previous sections demonstrate that our method learns discriminative prototypes to represent a variety of objects and bring enhanced generalizability across various settings. This section further demonstrates its effectiveness by investigating how our prototypes correlate different objects." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.539, + 0.893, + 0.736 + ], + "angle": 0, + "content": "We first study what each individual prototype learns. In Figure 4, we visualize instances (regions inside bounding boxes) most relevant to the prototypes (measured with their relevance scores on different prototypes, i.e., \\(\\alpha_{p}^{k}\\) in Equation 2, \\(k\\) denotes the indices of prototypes). The results show that our prototypes learn to represent a diverse pool of semantics. They not only capture low-level visual cues, such as shapes (e.g., round objects in the \\(1^{st}\\) row), textures (e.g., objects with jagged texture in the \\(2^{nd}\\) row), and patterns (e.g., objects with stripes in the \\(3^{rd}\\) row), but also encode high-level semantics including object categories (e.g., wheels in the \\(4^{th}\\) row) and commonalities in semantics (e.g., all objects in the \\(5^{th}\\) row are displaying text)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.736, + 0.894, + 0.902 + ], + "angle": 0, + "content": "With our prototypes encoding abundant semantics, we further analyze their effectiveness in correlating relevant objects based on their characteristics. Specifically, we calculate the average relevance scores \\(\\alpha_{p}\\) (see Equation 1) between objects in the GQA dataset and all prototypes, and then apply k-means algorithm [37] (\\(k = 30\\)) to cluster objects using the scores. As shown in Table 4, by representing objects based on the prototypes, we can correlate objects that belong to similar categories (e.g., drinks and utensils in the \\(1^{st}\\) and \\(2^{nd}\\) rows), commonly appear in the same scenarios (e.g., baseball games and bedrooms in the \\(3^{rd}\\) and \\(4^{th}\\) rows)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6742" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.471, + 0.132 + ], + "angle": 0, + "content": "Table 4. Different groups of objects that are clustered based on their relevance to prototypes. Please refer to our supplementary materials for the complete results with 30 groups." + }, + { + "type": "table", + "bbox": [ + 0.084, + 0.143, + 0.46, + 0.352 + ], + "angle": 0, + "content": "
GroupObjects
1cup, saucer, glass, beer, mug, juice, beverage, liquid, smoothie, coffee
2fork, spoon, knife, silverware, utensil, ladle, chopstick, tongs, spatula, butter knife
3spectator,UMPire, batter, catcher, crowd, net, player, baseball, stadium, bleachers
4bed, sofa, pillow, bedspread, headboard, comforter, couch, sheet, ottoman, mattress
5sticker, newspaper, paper, sign, book, tape, drawing, CD, letter, label
6water, sand, sea, rock, ocean, boulders, lake, beach, shore, river
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.38, + 0.47, + 0.442 + ], + "angle": 0, + "content": "or share similar characteristics (e.g., objects related to text and landscape in the \\(5^{th}\\) and \\(6^{th}\\) rows). The results demonstrate the effectiveness of our prototypes in parsing objects based on their commonalities in the semantic space." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.453, + 0.468, + 0.47 + ], + "angle": 0, + "content": "4.6. How Do Models Reason to Answer Questions?" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.477, + 0.47, + 0.568 + ], + "angle": 0, + "content": "Besides improving the generalizability, our method also enables interpretation of the decision-making process by visualizing the regions of interest (ROIs) at each reasoning step and prototypes matched with the observations. In this section, we provide qualitative examples to study the underlying rationales behind the derivation of answers." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.569, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Figure 5 shows the reasoning process of our method. For each question, we visualize the reasoning steps represented by neural modules (top), attention maps highlighting the ROIs (middle, \\(\\alpha^t\\) in Equation 6), and images associated to prototypes matched with the observations (bottom). It shows that our method can correlate objects based on various characteristics and locate those important ones. In the \\(1^{st}\\) example, while the apples are not explicitly mentioned in the question, our model correlates them with prototypes for different fruits (\"fruit\" is a keyword in the question) and pays focused attention in the Find step. Besides capturing semantic relationships about object categories, prototypes also help identify the cat based on its attribute (i.e., brown color) within the Filter step, and enable the model to reason on the relative position between objects (i.e., Relate step). In the \\(2^{nd}\\) example, our model not only highlights the correct objects in the first two Find steps (i.e., the banana and the mat), but also identifies the key characteristics that contribute to reasoning (i.e., matching observations with prototypes related to colors instead of object categories or other attributes). In the \\(3^{rd}\\) example, woman in the question is an unseen object during training. With object factorization," + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.096, + 0.593, + 0.138 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.508, + 0.14, + 0.596, + 0.176 + ], + "angle": 0, + "content": "Question: How is the fruit to the right of the brown animal called? Answer: Apple" + }, + { + "type": "image", + "bbox": [ + 0.607, + 0.09, + 0.691, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.607, + 0.168, + 0.692, + 0.251 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.693, + 0.09, + 0.787, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.787, + 0.09, + 0.883, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.508, + 0.224, + 0.596, + 0.258 + ], + "angle": 0, + "content": "Question: Are both the banana and the place mat the same color? Answer: no" + }, + { + "type": "image", + "bbox": [ + 0.519, + 0.259, + 0.584, + 0.323 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.508, + 0.324, + 0.602, + 0.359 + ], + "angle": 0, + "content": "Question: Do you see a woman near the water bottle in the bottom? Answer: yes" + }, + { + "type": "image", + "bbox": [ + 0.603, + 0.17, + 0.69, + 0.251 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.603, + 0.252, + 0.68, + 0.357 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.691, + 0.17, + 0.796, + 0.251 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.797, + 0.17, + 0.887, + 0.251 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.692, + 0.324, + 0.792, + 0.357 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.794, + 0.324, + 0.892, + 0.357 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.371, + 0.892, + 0.414 + ], + "angle": 0, + "content": "Figure 5. Illustrations of the reasoning process. From left to right are the input images together with questions and predicted answers, and sequences of reasoning steps." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.44, + 0.892, + 0.502 + ], + "angle": 0, + "content": "our model successfully associates it to known objects (i.e., men) based on the similarity in clothing, and progressively shifts the attention from both women (i.e., Find step) to the one lying next to the bottle (i.e., Filter and Relate steps)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.517, + 0.619, + 0.533 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.542, + 0.893, + 0.83 + ], + "angle": 0, + "content": "This study is an effort toward generalizable and interpretable AI systems for real-world applications. It draws inspiration from the ways humans reason with the visual world, and investigates the effectiveness of integrating the compositionality of objects and the reasoning process. Our work distinguishes itself with a principled method for automatically factorizing objects into fine-grained semantics, bridging novel and known objects, and a new neural module network with a compositional decision-making process. The compositionality in both dimensions addresses object diversity and spurious data biases, enhancing model generalizability toward a broad range of scenarios. It also enables interpretation of the rationales behind the model's decisions. Experimental results demonstrate the advantages of our method under diverse settings, and provide insights on how our model reasons with the visual-textual inputs. We hope that this study can be useful for future developments of trustworthy visual reasoning models with more human-like intelligence and generalizability." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.845, + 0.667, + 0.862 + ], + "angle": 0, + "content": "Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.9 + ], + "angle": 0, + "content": "This work is supported by NSF Grants 2143197 and 2227450." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6743" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.17 + ], + "angle": 0, + "content": "[1] Aishwarya Agrawal, Dhruv Batra, Devi Parikh, and Aniruddha Kembhavi. Don't just assume; look and answer: Overcoming priors for visual question answering. 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On the contrary, existing visual reasoning methods assume training samples that capture every possible object and reasoning problem, and rely on black-boxed models that commonly exploit statistical priors. They have yet to develop the capability to address novel objects or spurious biases in real-world scenarios, and also fall short of interpreting the rationales behind their decisions. Inspired by humans' reasoning of the visual world, we tackle the aforementioned challenges from a compositional perspective, and propose an integral framework consisting of a principled object factorization method and a novel neural module network. Our factorization method decomposes objects based on their key characteristics, and automatically derives prototypes that represent a wide range of objects. With these prototypes encoding important semantics, the proposed network then correlates objects by measuring their similarity on a common semantic space and makes decisions with a compositional reasoning process. It is capable of answering questions with diverse objects regardless of their availability during training, and overcoming the issues of biased question-answer distributions. In addition to the enhanced generalizability, our framework also provides an interpretable interface for understanding the decision-making process of models. Our code is available at https://github.com/szzexpoi/POEM. + +# 1. Introduction + +One of the fundamental goals in artificial intelligence is to develop systems that are able to reason with the complexity of real-world data to make decisions. Most existing visual question answering (VQA) methods [2, 13, 28, 29, 33, + +34, 38, 49, 57] assume a complete overlap between objects involved in training and testing, and commonly rely on the spurious distributions of questions and answers [39]. As a result, they have limited generalizability toward real-life visual reasoning, and also lack the ability to justify the reasoning process that leads to the answers. + +"All mammals are animals. All elephants are mammals. Therefore, all elephants are animals [5]." The wide application of syllogistic logic reflects key characteristics of the ways humans reason about the world. Unlike models [2, 38, 49] that utilize implicit features and heavily exploit statistical priors, humans correlate diverse objects from the compositional perspective based on their shared characteristics [26] and tackle problems with a structured reasoning process, which is both generalizable and interpretable. + +To address the complexity of real-world problems, this study aims to develop object factorization and compositional reasoning capabilities in models. As shown in Figure 1, our approach bridges diverse objects by projecting them onto a common space formed by discriminative prototypes (e.g., round shape, stuffed toy), and formulates the reasoning process with atomic steps [48] representing essential reasoning skills (e.g., Find, Relate). The prototypes are derived with object factorization, and they represent important semantics of objects (e.g., honey jar $\rightarrow$ , teddy bear $\rightarrow$ ). With an improved understanding of semantic relationships, our framework correlates objects (e.g., honey jar and container, stuffed toy and teddy bear) based on their commonalities in characteristics, leading to enhanced robustness against the diversity of objects and data biases. It also allows interpretations of the model's reasoning process consistent with the ways humans describe their own thinking [8]. + +Compared to previous studies [2, 21, 33, 34, 48, 49], our major distinction lies in (1) the composition in two important dimensions of visual reasoning, i.e., objects and the reasoning process, and (2) a tight coupling between them. Instead of using black-boxed features or a direct mapping between question and answer that is vulnerable to object di + +![](images/51edc9c75a6dc04100daca80082332f5ba0e75b34e2ba54808cba21540f501c8.jpg) + +![](images/2de158b8cb41b7c6354de56d9535bd8df5c7a51124fa053ffbb69821f2446740.jpg) +Question: Do you see a stuffed toy behind the honey jar to the left of the sandwich? +Figure 1. Overview of our method that represents objects with semantically meaningful prototypes and makes decisions via an explicit reasoning process. Honey jar is a novel object unseen during training. Note that our prototypes are not limited to a set of manually defined categories, but learned from factorizing objects to encode broader characteristics (e.g., shapes, colors, object categories). + +versity or data biases, our method decomposes objects into bases representing discriminative semantics, and develops a prototypical neural module network to explicitly bridge objects with a compositional reasoning paradigm. The proposed method naturally approaches generalizability with its compositional nature, handling novel objects and variable data distributions. It also provides a transparent interface for interpreting how models parse objects based on their characteristics and incorporate them for visual reasoning. + +To summarize, our major contributions are as follows: + +1. We identify the significance of tightly coupling the compositionality between objects and the reasoning process, and for the first time investigate its effectiveness in generalizable and interpretable reasoning. +2. We propose a principled method that automatically derives prototypes with object factorization, which plays a key role in encoding key characteristics of objects. +3. We develop a new neural module network that adaptively reasons on the commonalities of different objects along a structured decision-making process. +4. We perform extensive analyses to shed light on the roles of compositionality in reasoning with novel objects and variable data distributions. + +# 2. Related Works + +Our study is most related to previous efforts on visual question answering, zero-short learning for VQA, and VQA with out-of-distribution (OOD) questions. + +Visual question answering. With the diversity in language and visual semantics, visual question answering has become a popular task for studying models' reasoning capability [16]. A large body of research develops datasets + +[4,6,18,24,25,40,42,58] and models [2,3,21,22,28,33,34, 38,48,49] for VQA. Early datasets typically rely on crowdsourcing [4, 18, 58] to collect human-annotated questions. Several recent studies [24,25,53] use functional programs to automatically generate questions based on pre-defined rules and enable more balanced data distributions. There is also an increasing interest in investigating different types of reasoning, e.g., scene text understanding [6], reasoning on context [42], and knowledge-based reasoning [40]. These data efforts lead to the development of methods that advance VQA models from different perspectives, including multi-modal fusion [13,29,57], attention mechanism [2,28], structured inference [21-23, 48], and vision-and-language pretraining [33,34,38,49]. The aforementioned studies assume that every semantic in the test questions is well illustrated during training, and pay little attention to the models' generalizability to real-world scenarios that inevitably involve novel objects and diverse question-answer distributions. Our study aims to fill the gap with an integral framework that develops generalizable decision making capability with object factorization and compositional reasoning. + +Zero-shot learning for VQA. Zero-shot VQA aims to answer questions with novel objects. The pioneering work [51] proposes the zero-shot setting for the VQA task, and benchmarks several techniques for improving the models' generalizability, including explicit object detector [2] and pretrained word embeddings [43]. Ramakrishnan et al. [45] leverage self-supervised pretraining to learn more generalizable features with external data. Wang et al. [54] combine visual models trained on different datasets with an attention mechanism. Whitehead et al. [55] decompose VQA into two sub-problems, i.e., concept grounding and skill matching, and propose additional training objectives to address unseen objects in the questions. Besides the above stud + +![](images/574b9e2c6779563d75f6d03bc589af1abe8e1b9eae08e9eb1d10dcc26a11a238.jpg) +Figure 2. Overview of our prototype learning paradigm based on object factorization. + +ies concerning novel concepts in language, there are also attempts [12, 52] that leverage exemplar-based methods to address novel concepts in both visual and textual modalities. While showing usefulness, these studies either leverage external data, which violates zero-shot assumption [32], or require memorizing a vast amount of supporting samples. As a result, they have yet to develop the capability of generalizing toward real-world scenarios. The key differentiators of our method lie in its ability to connect novel and known objects and the use of an explicit reasoning process. By bridging objects based on their commonalities and decomposing the decision-making process into atomic reasoning steps, it improves the generalizability and interpretability without relying on external data or memorizing samples. + +VQA with OOD questions. To develop models that can truly reason on the visual-textual inputs instead of relying on statistical priors, VQA with out-of-distribution questions has gained considerable attention. In particular, Agrawal et al. [1] present the first VQA dataset with adversarial distributions between the training and validation data. A more recent study [27] analyzes models' robustness against biases by differentiating evaluation questions based on their question-answer distributions. To tackle the issues of harmful biases, a series of studies make progresses by improving visual attention [47, 56], reducing biases toward individual modalities [7, 15, 44], and leveraging ensemble techniques [11, 20]. There are also attempts [9, 17, 35] that use data augmentation to increase accuracy on biased data. However, they alter the distributions of training samples with additional data, and violate the original intent of the VQA with OOD questions task [50]. Our study is complementary to existing efforts, and it differentiates itself by investigating the usefulness of object factorization and compositional reasoning for addressing biases. It does not balance training samples to remove data biases, but instead focuses on enhancing models' own reasoning capabilities. + +# 3. Methodology + +Visual reasoning would benefit from capabilities of correlating objects based on their characteristics and decom + +posing problems into atomic steps [19]. This section presents a new framework for improving the robustness against questions with novel objects and diverse question-answer distributions. It consists of two novel components: (1) a principled method that automatically derives semantically plausible prototypes to represent different objects, and (2) a neural module network that bridges objects by incorporating discriminative prototypes in an explicit reasoning process. Besides the enhanced generalizability, the method also provides an interpretable interface for elaborating on the rationales behind the model's decisions. + +# 3.1. Bridging Diverse Objects with Factorization + +Inspired by humans' reasoning process that classifies objects based on their semantics similarity, a primary goal of our study is to derive semantic prototypes that can represent a vast amount of objects. The prototypes encode different aspects of the objects, and augment models with the capability to bridge diverse objects for more generalizable reasoning. Unlike previous studies [14, 41] that construct prototypes based on manually annotations and have difficulties scaling to different scenarios, we propose to automatically learn discriminative prototypes by factorizing various objects. Object factorization plays a key role in parsing the fine-grained characteristics of objects (e.g., shapes, textures, and super-categories), which facilitates understanding of the semantic relationships between objects. + +As illustrated in Figure 2, our prototype learning method leverages the multi-label classification task [10, 46, 59, 61] to discover discriminative prototypes in a data-driven manner. Given an input image, we train a deep neural network that predicts all object categories in the visual scene. Different from conventional approaches that recognize objects based on their visual features $O$ , we decompose objects with trainable prototypes $P$ and utilize the combinations of their matched prototypes for classification: + +$$ +\alpha_ {p} = \delta \left(O _ {i} \cdot P\right) \tag {1} +$$ + +$$ +C ^ {i} = C l s \left(\sum_ {k = 1} ^ {K} \alpha_ {p} ^ {k} P ^ {k}\right) \tag {2} +$$ + +![](images/d367db23030cf9002029c3007d4d8cabfc0f6a00bdb6e1b02b77556124e96b44.jpg) + +![](images/86133129317079c4de2ed52f9d02721784bb960d672748c5067244b1606f1548.jpg) +Question: Are there any people to the left of the frisbee that the dog catches? +Figure 3. Illustration of the proposed prototypical neural module network. $\otimes$ and $\oplus$ denote dot product and concatenation, respectively. + +where $\alpha_{p} \in \mathbb{R}^{1 \times K}$ denotes relevance scores between the $i^{th}$ object and $K$ prototypes. $O_{i} \cdot P$ is the dot product between features and prototypes, which corresponds to their cosine similarity. $\delta$ is the sigmoid activation function for normalization. $C^{i}$ is the prediction for the current object and $Cls$ is the classification module. To facilitate optimization without expensive instance-level annotations, we leverage an attention module $A_{cls}$ to dynamically aggregate instance-level predictions into the image-wise prediction $C$ : + +$$ +\alpha_ {c} ^ {i} = A _ {c l s} \left(\sum_ {k = 1} ^ {K} \alpha_ {p} ^ {k} P ^ {k}\right) \tag {3} +$$ + +$$ +C = \sum_ {i = 1} ^ {N} \alpha_ {c} ^ {i} C ^ {i} \tag {4} +$$ + +where $N$ is the number of objects. We train the network with a standard binary cross-entropy loss, and select prototypes $P$ that provide the highest validation performance. + +The aforementioned paradigm factorizes objects into a set of bases formed by different prototypes. The prototypes encode important semantics of objects (see Section 4.5), and serve as critical components of our reasoning model, as detailed in the next subsection. + +# 3.2. Prototypical Neural Module Network + +With our prototypes constructing the common semantic space for bridging diverse objects, we further propose a novel prototypical neural module network to adaptively incorporate the correlation between objects with a compositional reasoning process. Compared to previous VQA methods [2,12,33,45,48,49,52,55], the advantages of our model lie in (1) its capability to generalize to both known and novel objects in the visual-textual domains, (2) the enhanced robustness against the spurious data biases, and (3) the interpretability of the decision-making procedure. + +Figure 3 provides an overview of the proposed neural module network with prototype matching and a semantic memory module. The principal idea behind our model is to take advantage of semantic relationships encoded in our learned prototypes (Section 3.1), and reason with a structured decision-making procedure. Neural module networks [3,21,48] are a body of interpretable reasoning methods that perform visual reasoning with two steps: (1) decomposing the reasoning process into discrete reasoning steps, where each step is associated with an atomic module (e.g., Find module for locating regions of interest), and (2) sequentially executing the modules on visual-textual inputs and gathering information to predict the answer. In addition to the use of an explicit reasoning process, our model utilizes prototype matching to project features of diverse objects onto the semantic space formed by prototypes, enabling it to measure their semantic relationships and tightly couple relevant objects. A semantic memory module is also proposed to adaptively combine important semantics captured at different reasoning steps, which facilitates joint reasoning throughout the whole reasoning process. + +Specifically, unlike conventional methods that rely on raw visual features and pay little attention to semantic relationships between objects, our model leverages the learned prototypes to parse different objects and correlate them based on their fine-grained characteristics. At each $t^{th}$ reasoning step, our network computes the similarity between visual features and prototypes, explicitly representing objects based on their corresponding characteristics, and uses the similarity scores $S^t \in \mathbb{R}^{N \times K}$ for decision making: + +$$ +S _ {i} ^ {t} = \phi \left(V _ {i} \cdot P ^ {t}\right) \tag {5} +$$ + +where $V_{i}\in \mathbb{R}^{1\times D}$ is $D$ dimensional visual features for the $i^{th}$ visual regions ( $N$ regions in total), and $P^t\in \mathbb{R}^{D\times K}$ represents the $K$ prototypes. $V_{i}\cdot P^{t}$ is the dot product between features and prototypes. $\phi$ is the hyperbolic tangent + +activation function for normalizing the scores. Upon obtaining the similarity scores, we then locate the regions of interest for the current reasoning step: + +$$ +\alpha^ {t} = A ^ {t} \left(F ^ {t} \left(S ^ {t}, q ^ {t}\right)\right) \tag {6} +$$ + +where $\alpha^t\in \mathbb{R}^{1\times N}$ is the attention map highlighting the important regions, $F^t$ and $A^t$ are the multi-modal fusion and attention module, respectively. $q^{t}$ is the query information derived from the question. + +Another key differentiator between our proposed model and existing neural module networks [21, 48] is the incorporation of semantic memory. Instead of determining the answer solely based on the question $Q$ and attended visual features $V'$ , we further take into account the prototypes attended over time $p^t = \alpha^t \cdot S^t$ , and bridge objects of interest at different reasoning steps. Our semantic memory module uses an attention mechanism to adaptively incorporate key prototypes at different steps: + +$$ +\alpha_ {s} = A _ {s} (Q) \tag {7} +$$ + +$$ +\hat {y} = A n s \left(\left[ V ^ {\prime}; \sum_ {t = 1} ^ {T} \alpha_ {s} ^ {t} p ^ {t} \right], Q\right) \tag {8} +$$ + +where $\alpha_{s} \in \mathbb{R}^{1 \times T}$ represents attention weights for $T$ reasoning steps, and $A_{s}$ is the module for attention computation. $\hat{y}$ is the predicted answer, and $Ans$ is the answer prediction module. $[\cdot]$ denotes the concatenation of features. + +Our proposed model associates objects based on their relationships with distinct prototypes, and adaptively combines important prototypes captured throughout the reasoning process. It takes advantage of the compositionality in both objects involved during visual reasoning (i.e., from objects to their characteristics) and the reasoning process (i.e., from questions to reasoning steps), which plays an essential role in addressing the diversity of objects and the spurious data biases. The compositional nature of the model also allows better interpretation of the underlying decision-making procedure (Section 4.6). + +# 4. Experiments + +This section presents implementation details (Section 4.1) and experiments to analyze the proposed method. We experiment with two different settings of VQA, including zero-shot VQA (Section 4.2) and VQA with out-of-distribution questions (Section 4.3), to validate the robustness of our method. We also provide an ablation study with different prototypes (Section 4.4) to demonstrate the advantages of object factorization. Besides examining the effectiveness of our method, we perform extensive analyses to shed light on the following questions: (1) What do prototypes learn? Do they encode common characteristics among objects? (Section 4.5); and (2) How do models reason to answer diverse questions? (Section 4.6) + +# 4.1. Implementations + +Datasets. The primary goal of our experiments is to study models' generalizability to tackle real-world problems. We experiment with two different settings, each representing a common type of generalization: (1) Zeroshot VQA estimates models' generalizability toward both known and novel objects. Three popular datasets are used in our experiments, including VQA [18], GQA [24] and the recently introduced Novel-VQA [55]. Following [45, 55], for the VQA and GQA datasets, we reconstruct their training and validation sets to have a disjoint set of objects. For each dataset, we randomly select ten objects from the object pools and use them as novel objects unavailable during training. Similar to [12, 45, 51], we exclude all training questions that either contain words related to the selected objects or use images with the objects, and divide the original validation sets into Known and Novel splits based on objects required for reasoning. For the Novel-VQA dataset, we adopt the original training and test sets [55], which only considers novel objects in the questions (Novel-Q); (2) VQA with OOD questions focuses on evaluating models' generalizability to data with diverse question-answer distributions. We experiment with two popular datasets, including VQA-CP [1] with adversarial distributions between training and evaluation, and GQA-OOD [27] that utilizes balanced training questions but differentiates evaluation questions based on their question-answer distributions. + +Evaluation. We evaluate models with common metrics for visual question answering. For the VQA, Novel-VQA, and VQA-CP datasets, we adopt VQA accuracy [4] as the evaluation metric, which considers multiple candidate answers. For the GQA and GQA-OOD datasets, we use the standard accuracy since each question has an unique answer. We also follow [27] and consider differences in accuracy when answering in-distribution and out-of-distribution questions (i.e., $\triangle$ ) on the GQA-OOD dataset. + +Model specification. We use the state-of-the-art neural module network XNM [48] as our baseline, which provides competitive performance on multiple datasets without loss of interpretability. We follow [60] and replace the Transform module with the Relate module to improve attention propagation. Following [34, 49, 55], we adopt the UpDown features [2] that capture 36 semantically meaningful regions (i.e., $N = 36$ ) as the visual inputs. To enable understanding of unseen vocabulary, we follow [51, 55] and use Glove vectors [43] to initialize the word embeddings. Other settings, e.g., network specification and training configuration, are the same as those defined in the original papers [48, 60] without tuning. The aforementioned baseline is incorporated with our method discussed in Section 3.2 to enable object factorization and compositional reasoning. + +Prototype learning. We derive our prototypes with the multi-label classification task [59, 61], which aims to pre + +Table 1. Comparative results on zero-shot VQA. + +
VQAGQANovel-VQA
KnownNovelKnownNovelNovel-Q
UpDown [2]55.6548.5352.7351.3551.40
VisualBert [33]--59.8558.80-
Skill-Concept [55]----59.80
XNM [48]62.0552.8159.3957.5457.54
XNM+POEM63.8054.8260.6059.7160.73
+ +dict all object categories that exist in an image. The image-wise ground truth is constructed with object detection labels (VQA, VQA-CP and Novel-VQA) or scene graphs (GQA and GQA-OOD). UpDown features are used as inputs to the classification network, which encode semantic information of different objects. For zero-shot VQA, we train the model on each dataset with training images that do not contain the selected novel objects, and evaluate it on validation images with only known objects. For VQA with OOD questions, we use the original training and validation sets without excluding samples. We set the number of prototypes in our experiments to 1000 (i.e., $K = 1000$ ), which is comparable to the number of fine-grained objects in GQA (i.e., $\sim 1000$ object categories). The network is trained with Adam [30] optimizer for 60 epochs, the learning rate and batch size are set to $4 \times 10^{-4}$ and 128, respectively. Prototypes with the best validation performance are used in our VQA model. + +# 4.2. Results on Zero-shot VQA + +We first demonstrate the effectiveness of our prototypical neural module (POEM) network on answering questions with both known and novel objects. We compare it with four approaches, including (1) UpDown [2] that does not explicitly model the reasoning process, (2) Our baseline XNM [48] with an explicitly reasoning process, (3) VisualBert [33] that utilizes vision-and-language pretraining on external data containing the novel objects (i.e., MSCOCO [36]), and (4) Skill-Concept [55] that is the current state-of-the-art on Novel-VQA dataset, which explicitly exploits novel objects in images with around $97\%$ of them covered in a handcrafted reference training set. All of the models are trained with UpDown visual features and initialized with pretrained word embeddings. + +We draw three key observations from the results in Table 1: (1) While Updown and XNM show similar accuracy under the standard VQA setting [2, 48], the latter provides stronger performance on zero-shot VQA. The results indicate that the compositional reasoning process is not only helpful in interpretability, but also important for model performance and generalizability; (2) By leveraging external data, VisualBert provides better performance than both aforementioned models. However, it violates the original + +Table 2. Comparative results on VQA with OOD questions. + +
VQA-CPGQA-OOD
acc ↑acc-tail ↑△↓
Bias Product [11]39.9330.812.0
AdvReg [44]41.17--
Hint [47]46.73--
RUBi [7]47.1135.714.3
SCR [56]49.45--
LMH [11]52.0532.211.5
LMH+Entropies [15]54.55--
XNM [48]51.5446.1414.4
XNM+POEM53.9946.8910.7
+ +intent of zero-shot VQA with novel objects actually covered in the external data, making them impractical for real-world scenarios with unseen objects; and (3) Differently, with our prototypes bridging different objects and the reasoning process, the proposed method improves the performance of the XNM baseline without relying on external data, and achieves overall the best results in answering questions with both known and novel objects in the visual-textual data. It also outperforms Skill-Concept on the Novel-VQA dataset that only considers novel objects in the questions. Note that Skill-Concept assumes the availability of novel objects in training images and is not applicable to zero-shot setting on VQA and GQA datasets, while our method has the capability to generalize toward broader scenarios. + +# 4.3. Results on VQA with OOD Questions + +Next, we investigate the robustness of our method against spurious data biases. We compare our method with eight approaches that do not exploit additional data, including Bias Product [11], AdvReg [44], RUBi [7], and LMH+Entropies [15] for reducing single-modal biases, Hint [47] and SCR [56] for boosting visual attention, LMH [11] for learning the residual of biases, and our baseline XNM. Following [11, 15, 20], when experimenting on the VQA-CP dataset [1], both XNM and our model incorporate the learned mixed-in module [11] to address known biases. + +Results in Table 2 show that our method is able to improve the XNM baseline by a considerable margin. With object factorization and compositional reasoning, it not only improves the robustness against adversarial distributions (i.e., VQA-CP), but also reduces the performance gap between answering in-distribution and out-of-distribution questions (i.e., $\triangle$ for GQA-OOD). Compared to existing methods that introduce additional regularization and have difficulties generalizing to different datasets [7, 11, 15], our method augments models' reasoning capability without im + +Table 3. Comparative results for different prototypes. + +
VQAGQANovel-VQAVQA-CP
KnownNovelKnownNovelNovel-QOOD
Scratch62.6653.6658.8757.6959.4850.39
Object62.5653.2360.4859.4656.6752.23
Textual60.6152.3355.3153.2259.1751.09
Ours63.8054.8260.6059.7160.7353.99
+ +posing data-specific constrains and thus enjoys better generalizability. The aforementioned observations suggest the significance of explicitly bridging objects with their fine-grained characteristics for overcoming data biases. + +# 4.4. Ablation Study on Object Factorization + +A key component of our framework is the proposed method for learning discriminative prototypes with object factorization. In this section, we perform an ablation study to investigate the usefulness of different prototypes (see our supplementary materials for additional ablation studies on model design). Specifically, we consider three types of alternative prototypes: (1) Prototypes that are randomly initialized and learned from scratch on the VQA task (Scratch); (2) Prototypes specific to manually defined objects (Object), which are learned with the same multi-label classification task as our approach but without object factorization; and (3) Prototypes derived from Glove [43] word embeddings of concepts covered in the Visual Genome [31] dataset (Textual), including objects, attributes, and relationships. + +We made three observations from results in Table 3: (1) Randomly initialized prototypes lead to inferior performance among all datasets, indicating the significance of explicitly learning semantically plausible prototypes; (2) While object-based prototypes show reasonable performance on the GQA dataset with detailed annotations (i.e., $\sim 1000$ object categories), they have negligible improvements on the VQA, Novel-VQA, and VQA-CP datasets with abstract-level annotations (i.e., 80 object categories). The large gap in performance gain across datasets demonstrates the advantages of fine-grained categorization, and more importantly, highlights the need to learn discriminative prototypes without relying on extensive annotations. For this, our method utilizes object factorization to automatically decompose objects into more elaborated semantics, and brings considerable improvements among datasets with both abstract and detailed object annotations; (3) Textual prototypes result in a visible drop in accuracy, despite the consideration of various concepts. This is likely caused by the difficulty of correlating objects across the visual and textual domains. Differently, our method directly captures diverse characteristics of objects from visual data and does + +![](images/4169df35cbbb9683445160f9c51fec2ac58fc3d97a0b96df10f6311eb9507013.jpg) +Figure 4. Examples of semantics encoded in diverse prototypes. + +not suffer from the discrepancies between modalities. + +# 4.5. What Do Prototypes Learn? Do They Encode Common Characteristics among Objects? + +Results in the previous sections demonstrate that our method learns discriminative prototypes to represent a variety of objects and bring enhanced generalizability across various settings. This section further demonstrates its effectiveness by investigating how our prototypes correlate different objects. + +We first study what each individual prototype learns. In Figure 4, we visualize instances (regions inside bounding boxes) most relevant to the prototypes (measured with their relevance scores on different prototypes, i.e., $\alpha_{p}^{k}$ in Equation 2, $k$ denotes the indices of prototypes). The results show that our prototypes learn to represent a diverse pool of semantics. They not only capture low-level visual cues, such as shapes (e.g., round objects in the $1^{st}$ row), textures (e.g., objects with jagged texture in the $2^{nd}$ row), and patterns (e.g., objects with stripes in the $3^{rd}$ row), but also encode high-level semantics including object categories (e.g., wheels in the $4^{th}$ row) and commonalities in semantics (e.g., all objects in the $5^{th}$ row are displaying text). + +With our prototypes encoding abundant semantics, we further analyze their effectiveness in correlating relevant objects based on their characteristics. Specifically, we calculate the average relevance scores $\alpha_{p}$ (see Equation 1) between objects in the GQA dataset and all prototypes, and then apply k-means algorithm [37] ( $k = 30$ ) to cluster objects using the scores. As shown in Table 4, by representing objects based on the prototypes, we can correlate objects that belong to similar categories (e.g., drinks and utensils in the $1^{st}$ and $2^{nd}$ rows), commonly appear in the same scenarios (e.g., baseball games and bedrooms in the $3^{rd}$ and $4^{th}$ rows). + +Table 4. Different groups of objects that are clustered based on their relevance to prototypes. Please refer to our supplementary materials for the complete results with 30 groups. + +
GroupObjects
1cup, saucer, glass, beer, mug, juice, beverage, liquid, smoothie, coffee
2fork, spoon, knife, silverware, utensil, ladle, chopstick, tongs, spatula, butter knife
3spectator,UMPire, batter, catcher, crowd, net, player, baseball, stadium, bleachers
4bed, sofa, pillow, bedspread, headboard, comforter, couch, sheet, ottoman, mattress
5sticker, newspaper, paper, sign, book, tape, drawing, CD, letter, label
6water, sand, sea, rock, ocean, boulders, lake, beach, shore, river
+ +or share similar characteristics (e.g., objects related to text and landscape in the $5^{th}$ and $6^{th}$ rows). The results demonstrate the effectiveness of our prototypes in parsing objects based on their commonalities in the semantic space. + +# 4.6. How Do Models Reason to Answer Questions? + +Besides improving the generalizability, our method also enables interpretation of the decision-making process by visualizing the regions of interest (ROIs) at each reasoning step and prototypes matched with the observations. In this section, we provide qualitative examples to study the underlying rationales behind the derivation of answers. + +Figure 5 shows the reasoning process of our method. For each question, we visualize the reasoning steps represented by neural modules (top), attention maps highlighting the ROIs (middle, $\alpha^t$ in Equation 6), and images associated to prototypes matched with the observations (bottom). It shows that our method can correlate objects based on various characteristics and locate those important ones. In the $1^{st}$ example, while the apples are not explicitly mentioned in the question, our model correlates them with prototypes for different fruits ("fruit" is a keyword in the question) and pays focused attention in the Find step. Besides capturing semantic relationships about object categories, prototypes also help identify the cat based on its attribute (i.e., brown color) within the Filter step, and enable the model to reason on the relative position between objects (i.e., Relate step). In the $2^{nd}$ example, our model not only highlights the correct objects in the first two Find steps (i.e., the banana and the mat), but also identifies the key characteristics that contribute to reasoning (i.e., matching observations with prototypes related to colors instead of object categories or other attributes). In the $3^{rd}$ example, woman in the question is an unseen object during training. With object factorization, + +![](images/12c6f55d3e7ff510369b48984ebab3feee9026788c79e3d9b3322cc36a315f87.jpg) +Question: How is the fruit to the right of the brown animal called? Answer: Apple + +![](images/99208baa5b0f84ca49a2f59dc6ef935e8b52bc78f72c7eb68499ef80b7c3ce03.jpg) + +![](images/f85dcb78305a5a19456de178d672fa09df1938f94fb88045a075ad06495c80f3.jpg) + +![](images/dc928e931be11ff88cb5a7ed8f1c11b71f28ba6994e558242b50b2f4e32ac5ec.jpg) + +![](images/7b71e9e189913e384cb86b8c5dc8a4d373f45b622dc6d58f8132d5ec16ffe0f5.jpg) + +![](images/4543385112d474e56b5c73757a9d5955dce78de2be7ca2c48113da8496eead35.jpg) +Question: Are both the banana and the place mat the same color? Answer: no + +![](images/1bf0c21e9de0806b45981c0e85479d1bf6ff55afaa61c04bc44e6fc4c9681dbd.jpg) + +![](images/8ab06514a278703cf82b72ed7b2c2b1150bbc4d6e9a5111db8dd050049f66069.jpg) +Question: Do you see a woman near the water bottle in the bottom? Answer: yes + +![](images/8e2b80b073cb3b3eaae152acb245a14a93d28befb7cb40b81ca14c4dca3982dd.jpg) + +![](images/11d919d2ed29181ed3a9b59264679e691f74be2ece6737e1a6744a407f5c6142.jpg) + +![](images/b54eb062fedf73518ca9e2f0d2efc3347dc02d2486b24206587c23feb96bf0fa.jpg) +Figure 5. Illustrations of the reasoning process. From left to right are the input images together with questions and predicted answers, and sequences of reasoning steps. + +![](images/abf107185ea3bd1a39703a97333bb477b80a12875a9aae8c5858c20753f83c74.jpg) + +our model successfully associates it to known objects (i.e., men) based on the similarity in clothing, and progressively shifts the attention from both women (i.e., Find step) to the one lying next to the bottle (i.e., Filter and Relate steps). + +# 5. Conclusion + +This study is an effort toward generalizable and interpretable AI systems for real-world applications. It draws inspiration from the ways humans reason with the visual world, and investigates the effectiveness of integrating the compositionality of objects and the reasoning process. Our work distinguishes itself with a principled method for automatically factorizing objects into fine-grained semantics, bridging novel and known objects, and a new neural module network with a compositional decision-making process. The compositionality in both dimensions addresses object diversity and spurious data biases, enhancing model generalizability toward a broad range of scenarios. It also enables interpretation of the rationales behind the model's decisions. Experimental results demonstrate the advantages of our method under diverse settings, and provide insights on how our model reasons with the visual-textual inputs. We hope that this study can be useful for future developments of trustworthy visual reasoning models with more human-like intelligence and generalizability. + +# Acknowledgements + +This work is supported by NSF Grants 2143197 and 2227450. + +# References + +[1] Aishwarya Agrawal, Dhruv Batra, Devi Parikh, and Aniruddha Kembhavi. Don't just assume; look and answer: Overcoming priors for visual question answering. In CVPR, pages 4971-4980, 2018. 3, 5, 6 +[2] Peter Anderson, Xiaodong He, Chris Buehler, Damien Teney, Mark Johnson, Stephen Gould, and Lei Zhang. 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In CVPR, pages 2027-2036, 2017. 3, 5 \ No newline at end of file diff --git a/2023/Divide and Conquer_ Answering Questions With Object Factorization and Compositional Reasoning/images.zip b/2023/Divide and Conquer_ Answering Questions With Object Factorization and Compositional Reasoning/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..d4635275c7de486936b7ff075d5f21fa6613aaa3 --- /dev/null +++ b/2023/Divide and Conquer_ Answering Questions With Object Factorization and Compositional Reasoning/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:a2db058ad2ec789473cbd9e36207f2ea578512297649fdbbddf2c95057fdb2e6 +size 524166 diff --git a/2023/Divide and Conquer_ Answering Questions With Object Factorization and Compositional Reasoning/layout.json b/2023/Divide and Conquer_ Answering Questions With Object Factorization and Compositional Reasoning/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..494fc161e534a3f7d6703b88ce8a0cfd0068dee7 --- /dev/null +++ b/2023/Divide and Conquer_ Answering Questions With Object Factorization and Compositional Reasoning/layout.json @@ -0,0 +1,8303 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 70, + 102, + 523, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 102, + 523, + 140 + ], + "spans": [ + { + "bbox": [ + 70, + 102, + 523, + 140 + ], + "type": "text", + "content": "Divide and Conquer: Answering Questions with Object Factorization and Compositional Reasoning" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 240, + 161, + 353, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 240, + 161, + 353, + 175 + ], + "spans": [ + { + "bbox": [ + 240, + 161, + 353, + 175 + ], + "type": "text", + "content": "Shi Chen Qi Zhao" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 173, + 176, + 419, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 173, + 176, + 419, + 190 + ], + "spans": [ + { + "bbox": [ + 173, + 176, + 419, + 190 + ], + "type": "text", + "content": "Department of Computer Science and Engineering," + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 238, + 190, + 356, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 238, + 190, + 356, + 203 + ], + "spans": [ + { + "bbox": [ + 238, + 190, + 356, + 203 + ], + "type": "text", + "content": "University of Minnesota" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 230, + 205, + 364, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 230, + 205, + 364, + 217 + ], + "spans": [ + { + "bbox": [ + 230, + 205, + 364, + 217 + ], + "type": "text", + "content": "{chen4595，qzhao}@umn.edu" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 143, + 244, + 192, + 258 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 244, + 192, + 258 + ], + "spans": [ + { + "bbox": [ + 143, + 244, + 192, + 258 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 271, + 289, + 619 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 271, + 289, + 619 + ], + "spans": [ + { + "bbox": [ + 47, + 271, + 289, + 619 + ], + "type": "text", + "content": "Humans have the innate capability to answer diverse questions, which is rooted in the natural ability to correlate different concepts based on their semantic relationships and decompose difficult problems into sub-tasks. On the contrary, existing visual reasoning methods assume training samples that capture every possible object and reasoning problem, and rely on black-boxed models that commonly exploit statistical priors. They have yet to develop the capability to address novel objects or spurious biases in real-world scenarios, and also fall short of interpreting the rationales behind their decisions. Inspired by humans' reasoning of the visual world, we tackle the aforementioned challenges from a compositional perspective, and propose an integral framework consisting of a principled object factorization method and a novel neural module network. Our factorization method decomposes objects based on their key characteristics, and automatically derives prototypes that represent a wide range of objects. With these prototypes encoding important semantics, the proposed network then correlates objects by measuring their similarity on a common semantic space and makes decisions with a compositional reasoning process. It is capable of answering questions with diverse objects regardless of their availability during training, and overcoming the issues of biased question-answer distributions. In addition to the enhanced generalizability, our framework also provides an interpretable interface for understanding the decision-making process of models. Our code is available at https://github.com/szzexpoi/POEM." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 644, + 128, + 657 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 644, + 128, + 657 + ], + "spans": [ + { + "bbox": [ + 47, + 644, + 128, + 657 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": "One of the fundamental goals in artificial intelligence is to develop systems that are able to reason with the complexity of real-world data to make decisions. Most existing visual question answering (VQA) methods [2, 13, 28, 29, 33," + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 245, + 545, + 317 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 245, + 545, + 317 + ], + "spans": [ + { + "bbox": [ + 304, + 245, + 545, + 317 + ], + "type": "text", + "content": "34, 38, 49, 57] assume a complete overlap between objects involved in training and testing, and commonly rely on the spurious distributions of questions and answers [39]. As a result, they have limited generalizability toward real-life visual reasoning, and also lack the ability to justify the reasoning process that leads to the answers." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 318, + 546, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 318, + 546, + 426 + ], + "spans": [ + { + "bbox": [ + 304, + 318, + 546, + 426 + ], + "type": "text", + "content": "\"All mammals are animals. All elephants are mammals. Therefore, all elephants are animals [5].\" The wide application of syllogistic logic reflects key characteristics of the ways humans reason about the world. Unlike models [2, 38, 49] that utilize implicit features and heavily exploit statistical priors, humans correlate diverse objects from the compositional perspective based on their shared characteristics [26] and tackle problems with a structured reasoning process, which is both generalizable and interpretable." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 426, + 547, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 547, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 547, + 641 + ], + "type": "text", + "content": "To address the complexity of real-world problems, this study aims to develop object factorization and compositional reasoning capabilities in models. As shown in Figure 1, our approach bridges diverse objects by projecting them onto a common space formed by discriminative prototypes (e.g., round shape, stuffed toy), and formulates the reasoning process with atomic steps [48] representing essential reasoning skills (e.g., Find, Relate). The prototypes are derived with object factorization, and they represent important semantics of objects (e.g., honey jar " + }, + { + "bbox": [ + 304, + 426, + 547, + 641 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 304, + 426, + 547, + 641 + ], + "type": "text", + "content": " , teddy bear " + }, + { + "bbox": [ + 304, + 426, + 547, + 641 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 304, + 426, + 547, + 641 + ], + "type": "text", + "content": " ). With an improved understanding of semantic relationships, our framework correlates objects (e.g., honey jar and container, stuffed toy and teddy bear) based on their commonalities in characteristics, leading to enhanced robustness against the diversity of objects and data biases. It also allows interpretations of the model's reasoning process consistent with the ways humans describe their own thinking [8]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "type": "text", + "content": "Compared to previous studies [2, 21, 33, 34, 48, 49], our major distinction lies in (1) the composition in two important dimensions of visual reasoning, i.e., objects and the reasoning process, and (2) a tight coupling between them. Instead of using black-boxed features or a direct mapping between question and answer that is vulnerable to object di" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "6736" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 70, + 147, + 194 + ], + "blocks": [ + { + "bbox": [ + 53, + 70, + 147, + 194 + ], + "lines": [ + { + "bbox": [ + 53, + 70, + 147, + 194 + ], + "spans": [ + { + "bbox": [ + 53, + 70, + 147, + 194 + ], + "type": "image", + "image_path": "51edc9c75a6dc04100daca80082332f5ba0e75b34e2ba54808cba21540f501c8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 152, + 69, + 545, + 230 + ], + "blocks": [ + { + "bbox": [ + 48, + 197, + 151, + 227 + ], + "lines": [ + { + "bbox": [ + 48, + 197, + 151, + 227 + ], + "spans": [ + { + "bbox": [ + 48, + 197, + 151, + 227 + ], + "type": "text", + "content": "Question: Do you see a stuffed toy behind the honey jar to the left of the sandwich?" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 152, + 69, + 545, + 230 + ], + "lines": [ + { + "bbox": [ + 152, + 69, + 545, + 230 + ], + "spans": [ + { + "bbox": [ + 152, + 69, + 545, + 230 + ], + "type": "image", + "image_path": "2de158b8cb41b7c6354de56d9535bd8df5c7a51124fa053ffbb69821f2446740.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 239, + 546, + 273 + ], + "lines": [ + { + "bbox": [ + 46, + 239, + 546, + 273 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 546, + 273 + ], + "type": "text", + "content": "Figure 1. Overview of our method that represents objects with semantically meaningful prototypes and makes decisions via an explicit reasoning process. Honey jar is a novel object unseen during training. Note that our prototypes are not limited to a set of manually defined categories, but learned from factorizing objects to encode broader characteristics (e.g., shapes, colors, object categories)." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 293, + 286, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 293, + 286, + 399 + ], + "spans": [ + { + "bbox": [ + 46, + 293, + 286, + 399 + ], + "type": "text", + "content": "versity or data biases, our method decomposes objects into bases representing discriminative semantics, and develops a prototypical neural module network to explicitly bridge objects with a compositional reasoning paradigm. The proposed method naturally approaches generalizability with its compositional nature, handling novel objects and variable data distributions. It also provides a transparent interface for interpreting how models parse objects based on their characteristics and incorporate them for visual reasoning." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 59, + 401, + 278, + 412 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 401, + 278, + 412 + ], + "spans": [ + { + "bbox": [ + 59, + 401, + 278, + 412 + ], + "type": "text", + "content": "To summarize, our major contributions are as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 54, + 420, + 287, + 598 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 55, + 420, + 287, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 420, + 287, + 468 + ], + "spans": [ + { + "bbox": [ + 55, + 420, + 287, + 468 + ], + "type": "text", + "content": "1. We identify the significance of tightly coupling the compositionality between objects and the reasoning process, and for the first time investigate its effectiveness in generalizable and interpretable reasoning." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 475, + 287, + 512 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 475, + 287, + 512 + ], + "spans": [ + { + "bbox": [ + 55, + 475, + 287, + 512 + ], + "type": "text", + "content": "2. We propose a principled method that automatically derives prototypes with object factorization, which plays a key role in encoding key characteristics of objects." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 520, + 287, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 520, + 287, + 555 + ], + "spans": [ + { + "bbox": [ + 55, + 520, + 287, + 555 + ], + "type": "text", + "content": "3. We develop a new neural module network that adaptively reasons on the commonalities of different objects along a structured decision-making process." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 54, + 563, + 287, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 563, + 287, + 598 + ], + "spans": [ + { + "bbox": [ + 54, + 563, + 287, + 598 + ], + "type": "text", + "content": "4. We perform extensive analyses to shed light on the roles of compositionality in reasoning with novel objects and variable data distributions." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 609, + 138, + 621 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 609, + 138, + 621 + ], + "spans": [ + { + "bbox": [ + 47, + 609, + 138, + 621 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 629, + 286, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 629, + 286, + 665 + ], + "spans": [ + { + "bbox": [ + 47, + 629, + 286, + 665 + ], + "type": "text", + "content": "Our study is most related to previous efforts on visual question answering, zero-short learning for VQA, and VQA with out-of-distribution (OOD) questions." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 665, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 665, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 665, + 287, + 713 + ], + "type": "text", + "content": "Visual question answering. With the diversity in language and visual semantics, visual question answering has become a popular task for studying models' reasoning capability [16]. A large body of research develops datasets" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 293, + 545, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 293, + 545, + 544 + ], + "spans": [ + { + "bbox": [ + 304, + 293, + 545, + 544 + ], + "type": "text", + "content": "[4,6,18,24,25,40,42,58] and models [2,3,21,22,28,33,34, 38,48,49] for VQA. Early datasets typically rely on crowdsourcing [4, 18, 58] to collect human-annotated questions. Several recent studies [24,25,53] use functional programs to automatically generate questions based on pre-defined rules and enable more balanced data distributions. There is also an increasing interest in investigating different types of reasoning, e.g., scene text understanding [6], reasoning on context [42], and knowledge-based reasoning [40]. These data efforts lead to the development of methods that advance VQA models from different perspectives, including multi-modal fusion [13,29,57], attention mechanism [2,28], structured inference [21-23, 48], and vision-and-language pretraining [33,34,38,49]. The aforementioned studies assume that every semantic in the test questions is well illustrated during training, and pay little attention to the models' generalizability to real-world scenarios that inevitably involve novel objects and diverse question-answer distributions. Our study aims to fill the gap with an integral framework that develops generalizable decision making capability with object factorization and compositional reasoning." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "type": "text", + "content": "Zero-shot learning for VQA. Zero-shot VQA aims to answer questions with novel objects. The pioneering work [51] proposes the zero-shot setting for the VQA task, and benchmarks several techniques for improving the models' generalizability, including explicit object detector [2] and pretrained word embeddings [43]. Ramakrishnan et al. [45] leverage self-supervised pretraining to learn more generalizable features with external data. Wang et al. [54] combine visual models trained on different datasets with an attention mechanism. Whitehead et al. [55] decompose VQA into two sub-problems, i.e., concept grounding and skill matching, and propose additional training objectives to address unseen objects in the questions. Besides the above stud" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6737" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 68, + 547, + 186 + ], + "blocks": [ + { + "bbox": [ + 48, + 68, + 547, + 186 + ], + "lines": [ + { + "bbox": [ + 48, + 68, + 547, + 186 + ], + "spans": [ + { + "bbox": [ + 48, + 68, + 547, + 186 + ], + "type": "image", + "image_path": "574b9e2c6779563d75f6d03bc589af1abe8e1b9eae08e9eb1d10dcc26a11a238.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 141, + 195, + 451, + 207 + ], + "lines": [ + { + "bbox": [ + 141, + 195, + 451, + 207 + ], + "spans": [ + { + "bbox": [ + 141, + 195, + 451, + 207 + ], + "type": "text", + "content": "Figure 2. Overview of our prototype learning paradigm based on object factorization." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 228, + 287, + 395 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 228, + 287, + 395 + ], + "spans": [ + { + "bbox": [ + 46, + 228, + 287, + 395 + ], + "type": "text", + "content": "ies concerning novel concepts in language, there are also attempts [12, 52] that leverage exemplar-based methods to address novel concepts in both visual and textual modalities. While showing usefulness, these studies either leverage external data, which violates zero-shot assumption [32], or require memorizing a vast amount of supporting samples. As a result, they have yet to develop the capability of generalizing toward real-world scenarios. The key differentiators of our method lie in its ability to connect novel and known objects and the use of an explicit reasoning process. By bridging objects based on their commonalities and decomposing the decision-making process into atomic reasoning steps, it improves the generalizability and interpretability without relying on external data or memorizing samples." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 396, + 288, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 396, + 288, + 659 + ], + "spans": [ + { + "bbox": [ + 46, + 396, + 288, + 659 + ], + "type": "text", + "content": "VQA with OOD questions. To develop models that can truly reason on the visual-textual inputs instead of relying on statistical priors, VQA with out-of-distribution questions has gained considerable attention. In particular, Agrawal et al. [1] present the first VQA dataset with adversarial distributions between the training and validation data. A more recent study [27] analyzes models' robustness against biases by differentiating evaluation questions based on their question-answer distributions. To tackle the issues of harmful biases, a series of studies make progresses by improving visual attention [47, 56], reducing biases toward individual modalities [7, 15, 44], and leveraging ensemble techniques [11, 20]. There are also attempts [9, 17, 35] that use data augmentation to increase accuracy on biased data. However, they alter the distributions of training samples with additional data, and violate the original intent of the VQA with OOD questions task [50]. Our study is complementary to existing efforts, and it differentiates itself by investigating the usefulness of object factorization and compositional reasoning for addressing biases. It does not balance training samples to remove data biases, but instead focuses on enhancing models' own reasoning capabilities." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 670, + 129, + 683 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 670, + 129, + 683 + ], + "spans": [ + { + "bbox": [ + 47, + 670, + 129, + 683 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "Visual reasoning would benefit from capabilities of correlating objects based on their characteristics and decom" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 228, + 545, + 358 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 228, + 545, + 358 + ], + "spans": [ + { + "bbox": [ + 304, + 228, + 545, + 358 + ], + "type": "text", + "content": "posing problems into atomic steps [19]. This section presents a new framework for improving the robustness against questions with novel objects and diverse question-answer distributions. It consists of two novel components: (1) a principled method that automatically derives semantically plausible prototypes to represent different objects, and (2) a neural module network that bridges objects by incorporating discriminative prototypes in an explicit reasoning process. Besides the enhanced generalizability, the method also provides an interpretable interface for elaborating on the rationales behind the model's decisions." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 365, + 535, + 378 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 365, + 535, + 378 + ], + "spans": [ + { + "bbox": [ + 306, + 365, + 535, + 378 + ], + "type": "text", + "content": "3.1. Bridging Diverse Objects with Factorization" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 384, + 545, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 384, + 545, + 552 + ], + "spans": [ + { + "bbox": [ + 304, + 384, + 545, + 552 + ], + "type": "text", + "content": "Inspired by humans' reasoning process that classifies objects based on their semantics similarity, a primary goal of our study is to derive semantic prototypes that can represent a vast amount of objects. The prototypes encode different aspects of the objects, and augment models with the capability to bridge diverse objects for more generalizable reasoning. Unlike previous studies [14, 41] that construct prototypes based on manually annotations and have difficulties scaling to different scenarios, we propose to automatically learn discriminative prototypes by factorizing various objects. Object factorization plays a key role in parsing the fine-grained characteristics of objects (e.g., shapes, textures, and super-categories), which facilitates understanding of the semantic relationships between objects." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 552, + 545, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 552, + 545, + 658 + ], + "spans": [ + { + "bbox": [ + 304, + 552, + 545, + 658 + ], + "type": "text", + "content": "As illustrated in Figure 2, our prototype learning method leverages the multi-label classification task [10, 46, 59, 61] to discover discriminative prototypes in a data-driven manner. Given an input image, we train a deep neural network that predicts all object categories in the visual scene. Different from conventional approaches that recognize objects based on their visual features " + }, + { + "bbox": [ + 304, + 552, + 545, + 658 + ], + "type": "inline_equation", + "content": "O" + }, + { + "bbox": [ + 304, + 552, + 545, + 658 + ], + "type": "text", + "content": ", we decompose objects with trainable prototypes " + }, + { + "bbox": [ + 304, + 552, + 545, + 658 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 552, + 545, + 658 + ], + "type": "text", + "content": " and utilize the combinations of their matched prototypes for classification:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 392, + 664, + 545, + 678 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 392, + 664, + 545, + 678 + ], + "spans": [ + { + "bbox": [ + 392, + 664, + 545, + 678 + ], + "type": "interline_equation", + "content": "\\alpha_ {p} = \\delta \\left(O _ {i} \\cdot P\\right) \\tag {1}", + "image_path": "cbc1b9b36171a6e2abf98de659e2feb9bf0b2f597a617152f86502ddfb449126.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 380, + 682, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 380, + 682, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 380, + 682, + 545, + 715 + ], + "type": "interline_equation", + "content": "C ^ {i} = C l s \\left(\\sum_ {k = 1} ^ {K} \\alpha_ {p} ^ {k} P ^ {k}\\right) \\tag {2}", + "image_path": "aa0b1787ec334faaa40de20acd421c9739227b556a97e39f19e8986a1aa925a1.jpg" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6738" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 109, + 168, + 205 + ], + "blocks": [ + { + "bbox": [ + 47, + 109, + 168, + 205 + ], + "lines": [ + { + "bbox": [ + 47, + 109, + 168, + 205 + ], + "spans": [ + { + "bbox": [ + 47, + 109, + 168, + 205 + ], + "type": "image", + "image_path": "d367db23030cf9002029c3007d4d8cabfc0f6a00bdb6e1b02b77556124e96b44.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 171, + 70, + 545, + 232 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 167, + 102 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 167, + 102 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 167, + 102 + ], + "type": "text", + "content": "Question: Are there any people to the left of the frisbee that the dog catches?" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 171, + 70, + 545, + 232 + ], + "lines": [ + { + "bbox": [ + 171, + 70, + 545, + 232 + ], + "spans": [ + { + "bbox": [ + 171, + 70, + 545, + 232 + ], + "type": "image", + "image_path": "86133129317079c4de2ed52f9d02721784bb960d672748c5067244b1606f1548.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 50, + 239, + 541, + 251 + ], + "lines": [ + { + "bbox": [ + 50, + 239, + 541, + 251 + ], + "spans": [ + { + "bbox": [ + 50, + 239, + 541, + 251 + ], + "type": "text", + "content": "Figure 3. Illustration of the proposed prototypical neural module network. " + }, + { + "bbox": [ + 50, + 239, + 541, + 251 + ], + "type": "inline_equation", + "content": "\\otimes" + }, + { + "bbox": [ + 50, + 239, + 541, + 251 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 50, + 239, + 541, + 251 + ], + "type": "inline_equation", + "content": "\\oplus" + }, + { + "bbox": [ + 50, + 239, + 541, + 251 + ], + "type": "text", + "content": " denote dot product and concatenation, respectively." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 270, + 290, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 270, + 290, + 380 + ], + "spans": [ + { + "bbox": [ + 46, + 270, + 290, + 380 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 270, + 290, + 380 + ], + "type": "inline_equation", + "content": "\\alpha_{p} \\in \\mathbb{R}^{1 \\times K}" + }, + { + "bbox": [ + 46, + 270, + 290, + 380 + ], + "type": "text", + "content": " denotes relevance scores between the " + }, + { + "bbox": [ + 46, + 270, + 290, + 380 + ], + "type": "inline_equation", + "content": "i^{th}" + }, + { + "bbox": [ + 46, + 270, + 290, + 380 + ], + "type": "text", + "content": " object and " + }, + { + "bbox": [ + 46, + 270, + 290, + 380 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 270, + 290, + 380 + ], + "type": "text", + "content": " prototypes. " + }, + { + "bbox": [ + 46, + 270, + 290, + 380 + ], + "type": "inline_equation", + "content": "O_{i} \\cdot P" + }, + { + "bbox": [ + 46, + 270, + 290, + 380 + ], + "type": "text", + "content": " is the dot product between features and prototypes, which corresponds to their cosine similarity. " + }, + { + "bbox": [ + 46, + 270, + 290, + 380 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 46, + 270, + 290, + 380 + ], + "type": "text", + "content": " is the sigmoid activation function for normalization. " + }, + { + "bbox": [ + 46, + 270, + 290, + 380 + ], + "type": "inline_equation", + "content": "C^{i}" + }, + { + "bbox": [ + 46, + 270, + 290, + 380 + ], + "type": "text", + "content": " is the prediction for the current object and " + }, + { + "bbox": [ + 46, + 270, + 290, + 380 + ], + "type": "inline_equation", + "content": "Cls" + }, + { + "bbox": [ + 46, + 270, + 290, + 380 + ], + "type": "text", + "content": " is the classification module. To facilitate optimization without expensive instance-level annotations, we leverage an attention module " + }, + { + "bbox": [ + 46, + 270, + 290, + 380 + ], + "type": "inline_equation", + "content": "A_{cls}" + }, + { + "bbox": [ + 46, + 270, + 290, + 380 + ], + "type": "text", + "content": " to dynamically aggregate instance-level predictions into the image-wise prediction " + }, + { + "bbox": [ + 46, + 270, + 290, + 380 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 270, + 290, + 380 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 120, + 388, + 287, + 422 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 120, + 388, + 287, + 422 + ], + "spans": [ + { + "bbox": [ + 120, + 388, + 287, + 422 + ], + "type": "interline_equation", + "content": "\\alpha_ {c} ^ {i} = A _ {c l s} \\left(\\sum_ {k = 1} ^ {K} \\alpha_ {p} ^ {k} P ^ {k}\\right) \\tag {3}", + "image_path": "6ed5198dc40e6d0571a7268433e601dedb0f85fcb68033c9ed4c2201aaba229a.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 135, + 433, + 287, + 465 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 135, + 433, + 287, + 465 + ], + "spans": [ + { + "bbox": [ + 135, + 433, + 287, + 465 + ], + "type": "interline_equation", + "content": "C = \\sum_ {i = 1} ^ {N} \\alpha_ {c} ^ {i} C ^ {i} \\tag {4}", + "image_path": "3a3c4379f73294d8a5e97356e3599e9968786282ea3ccd9d160bc37847b30467.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 470, + 287, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 470, + 287, + 506 + ], + "spans": [ + { + "bbox": [ + 46, + 470, + 287, + 506 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 470, + 287, + 506 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 470, + 287, + 506 + ], + "type": "text", + "content": " is the number of objects. We train the network with a standard binary cross-entropy loss, and select prototypes " + }, + { + "bbox": [ + 46, + 470, + 287, + 506 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 470, + 287, + 506 + ], + "type": "text", + "content": " that provide the highest validation performance." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 507, + 287, + 566 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 507, + 287, + 566 + ], + "spans": [ + { + "bbox": [ + 46, + 507, + 287, + 566 + ], + "type": "text", + "content": "The aforementioned paradigm factorizes objects into a set of bases formed by different prototypes. The prototypes encode important semantics of objects (see Section 4.5), and serve as critical components of our reasoning model, as detailed in the next subsection." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 574, + 244, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 574, + 244, + 588 + ], + "spans": [ + { + "bbox": [ + 47, + 574, + 244, + 588 + ], + "type": "text", + "content": "3.2. Prototypical Neural Module Network" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "content": "With our prototypes constructing the common semantic space for bridging diverse objects, we further propose a novel prototypical neural module network to adaptively incorporate the correlation between objects with a compositional reasoning process. Compared to previous VQA methods [2,12,33,45,48,49,52,55], the advantages of our model lie in (1) its capability to generalize to both known and novel objects in the visual-textual domains, (2) the enhanced robustness against the spurious data biases, and (3) the interpretability of the decision-making procedure." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 271, + 547, + 523 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 271, + 547, + 523 + ], + "spans": [ + { + "bbox": [ + 304, + 271, + 547, + 523 + ], + "type": "text", + "content": "Figure 3 provides an overview of the proposed neural module network with prototype matching and a semantic memory module. The principal idea behind our model is to take advantage of semantic relationships encoded in our learned prototypes (Section 3.1), and reason with a structured decision-making procedure. Neural module networks [3,21,48] are a body of interpretable reasoning methods that perform visual reasoning with two steps: (1) decomposing the reasoning process into discrete reasoning steps, where each step is associated with an atomic module (e.g., Find module for locating regions of interest), and (2) sequentially executing the modules on visual-textual inputs and gathering information to predict the answer. In addition to the use of an explicit reasoning process, our model utilizes prototype matching to project features of diverse objects onto the semantic space formed by prototypes, enabling it to measure their semantic relationships and tightly couple relevant objects. A semantic memory module is also proposed to adaptively combine important semantics captured at different reasoning steps, which facilitates joint reasoning throughout the whole reasoning process." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 523, + 547, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 523, + 547, + 632 + ], + "spans": [ + { + "bbox": [ + 304, + 523, + 547, + 632 + ], + "type": "text", + "content": "Specifically, unlike conventional methods that rely on raw visual features and pay little attention to semantic relationships between objects, our model leverages the learned prototypes to parse different objects and correlate them based on their fine-grained characteristics. At each " + }, + { + "bbox": [ + 304, + 523, + 547, + 632 + ], + "type": "inline_equation", + "content": "t^{th}" + }, + { + "bbox": [ + 304, + 523, + 547, + 632 + ], + "type": "text", + "content": " reasoning step, our network computes the similarity between visual features and prototypes, explicitly representing objects based on their corresponding characteristics, and uses the similarity scores " + }, + { + "bbox": [ + 304, + 523, + 547, + 632 + ], + "type": "inline_equation", + "content": "S^t \\in \\mathbb{R}^{N \\times K}" + }, + { + "bbox": [ + 304, + 523, + 547, + 632 + ], + "type": "text", + "content": " for decision making:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 392, + 641, + 545, + 655 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 392, + 641, + 545, + 655 + ], + "spans": [ + { + "bbox": [ + 392, + 641, + 545, + 655 + ], + "type": "interline_equation", + "content": "S _ {i} ^ {t} = \\phi \\left(V _ {i} \\cdot P ^ {t}\\right) \\tag {5}", + "image_path": "b9fe5546915cecb53391e60c1d2664df432d18967ce9d17b4abd88833aca33a2.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "inline_equation", + "content": "V_{i}\\in \\mathbb{R}^{1\\times D}" + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": " dimensional visual features for the " + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "inline_equation", + "content": "i^{th}" + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": " visual regions ( " + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": " regions in total), and " + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "inline_equation", + "content": "P^t\\in \\mathbb{R}^{D\\times K}" + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": " represents the " + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": " prototypes. " + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "inline_equation", + "content": "V_{i}\\cdot P^{t}" + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": " is the dot product between features and prototypes. " + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": " is the hyperbolic tangent" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6739" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 109 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 109 + ], + "type": "text", + "content": "activation function for normalizing the scores. Upon obtaining the similarity scores, we then locate the regions of interest for the current reasoning step:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 123, + 113, + 287, + 127 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 113, + 287, + 127 + ], + "spans": [ + { + "bbox": [ + 123, + 113, + 287, + 127 + ], + "type": "interline_equation", + "content": "\\alpha^ {t} = A ^ {t} \\left(F ^ {t} \\left(S ^ {t}, q ^ {t}\\right)\\right) \\tag {6}", + "image_path": "f893524c64aa8c94257a727ba1be4a17e124dadafd2c97e7b71d78595468d143.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 133, + 287, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 133, + 287, + 180 + ], + "spans": [ + { + "bbox": [ + 46, + 133, + 287, + 180 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 133, + 287, + 180 + ], + "type": "inline_equation", + "content": "\\alpha^t\\in \\mathbb{R}^{1\\times N}" + }, + { + "bbox": [ + 46, + 133, + 287, + 180 + ], + "type": "text", + "content": " is the attention map highlighting the important regions, " + }, + { + "bbox": [ + 46, + 133, + 287, + 180 + ], + "type": "inline_equation", + "content": "F^t" + }, + { + "bbox": [ + 46, + 133, + 287, + 180 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 133, + 287, + 180 + ], + "type": "inline_equation", + "content": "A^t" + }, + { + "bbox": [ + 46, + 133, + 287, + 180 + ], + "type": "text", + "content": " are the multi-modal fusion and attention module, respectively. " + }, + { + "bbox": [ + 46, + 133, + 287, + 180 + ], + "type": "inline_equation", + "content": "q^{t}" + }, + { + "bbox": [ + 46, + 133, + 287, + 180 + ], + "type": "text", + "content": " is the query information derived from the question." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 181, + 287, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 181, + 287, + 289 + ], + "spans": [ + { + "bbox": [ + 46, + 181, + 287, + 289 + ], + "type": "text", + "content": "Another key differentiator between our proposed model and existing neural module networks [21, 48] is the incorporation of semantic memory. Instead of determining the answer solely based on the question " + }, + { + "bbox": [ + 46, + 181, + 287, + 289 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 46, + 181, + 287, + 289 + ], + "type": "text", + "content": " and attended visual features " + }, + { + "bbox": [ + 46, + 181, + 287, + 289 + ], + "type": "inline_equation", + "content": "V'" + }, + { + "bbox": [ + 46, + 181, + 287, + 289 + ], + "type": "text", + "content": ", we further take into account the prototypes attended over time " + }, + { + "bbox": [ + 46, + 181, + 287, + 289 + ], + "type": "inline_equation", + "content": "p^t = \\alpha^t \\cdot S^t" + }, + { + "bbox": [ + 46, + 181, + 287, + 289 + ], + "type": "text", + "content": ", and bridge objects of interest at different reasoning steps. Our semantic memory module uses an attention mechanism to adaptively incorporate key prototypes at different steps:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 139, + 294, + 287, + 308 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 139, + 294, + 287, + 308 + ], + "spans": [ + { + "bbox": [ + 139, + 294, + 287, + 308 + ], + "type": "interline_equation", + "content": "\\alpha_ {s} = A _ {s} (Q) \\tag {7}", + "image_path": "5915a920fb3fb28254de845fa3db5807d7215bd192699cba02cf9482df7ab6fd.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 108, + 313, + 287, + 345 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 313, + 287, + 345 + ], + "spans": [ + { + "bbox": [ + 108, + 313, + 287, + 345 + ], + "type": "interline_equation", + "content": "\\hat {y} = A n s \\left(\\left[ V ^ {\\prime}; \\sum_ {t = 1} ^ {T} \\alpha_ {s} ^ {t} p ^ {t} \\right], Q\\right) \\tag {8}", + "image_path": "6040cd91d1988258e81392e020f34c7e10c717b6c55b53d89dcfb4c22cf6907a.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 348, + 287, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 348, + 287, + 396 + ], + "spans": [ + { + "bbox": [ + 46, + 348, + 287, + 396 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 348, + 287, + 396 + ], + "type": "inline_equation", + "content": "\\alpha_{s} \\in \\mathbb{R}^{1 \\times T}" + }, + { + "bbox": [ + 46, + 348, + 287, + 396 + ], + "type": "text", + "content": " represents attention weights for " + }, + { + "bbox": [ + 46, + 348, + 287, + 396 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 348, + 287, + 396 + ], + "type": "text", + "content": " reasoning steps, and " + }, + { + "bbox": [ + 46, + 348, + 287, + 396 + ], + "type": "inline_equation", + "content": "A_{s}" + }, + { + "bbox": [ + 46, + 348, + 287, + 396 + ], + "type": "text", + "content": " is the module for attention computation. " + }, + { + "bbox": [ + 46, + 348, + 287, + 396 + ], + "type": "inline_equation", + "content": "\\hat{y}" + }, + { + "bbox": [ + 46, + 348, + 287, + 396 + ], + "type": "text", + "content": " is the predicted answer, and " + }, + { + "bbox": [ + 46, + 348, + 287, + 396 + ], + "type": "inline_equation", + "content": "Ans" + }, + { + "bbox": [ + 46, + 348, + 287, + 396 + ], + "type": "text", + "content": " is the answer prediction module. " + }, + { + "bbox": [ + 46, + 348, + 287, + 396 + ], + "type": "inline_equation", + "content": "[\\cdot]" + }, + { + "bbox": [ + 46, + 348, + 287, + 396 + ], + "type": "text", + "content": " denotes the concatenation of features." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 397, + 287, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 397, + 287, + 529 + ], + "spans": [ + { + "bbox": [ + 46, + 397, + 287, + 529 + ], + "type": "text", + "content": "Our proposed model associates objects based on their relationships with distinct prototypes, and adaptively combines important prototypes captured throughout the reasoning process. It takes advantage of the compositionality in both objects involved during visual reasoning (i.e., from objects to their characteristics) and the reasoning process (i.e., from questions to reasoning steps), which plays an essential role in addressing the diversity of objects and the spurious data biases. The compositional nature of the model also allows better interpretation of the underlying decision-making procedure (Section 4.6)." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 538, + 127, + 551 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 538, + 127, + 551 + ], + "spans": [ + { + "bbox": [ + 47, + 538, + 127, + 551 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "type": "text", + "content": "This section presents implementation details (Section 4.1) and experiments to analyze the proposed method. We experiment with two different settings of VQA, including zero-shot VQA (Section 4.2) and VQA with out-of-distribution questions (Section 4.3), to validate the robustness of our method. We also provide an ablation study with different prototypes (Section 4.4) to demonstrate the advantages of object factorization. Besides examining the effectiveness of our method, we perform extensive analyses to shed light on the following questions: (1) What do prototypes learn? Do they encode common characteristics among objects? (Section 4.5); and (2) How do models reason to answer diverse questions? (Section 4.6)" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 72, + 408, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 408, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 408, + 84 + ], + "type": "text", + "content": "4.1. Implementations" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 90, + 545, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 90, + 545, + 400 + ], + "spans": [ + { + "bbox": [ + 304, + 90, + 545, + 400 + ], + "type": "text", + "content": "Datasets. The primary goal of our experiments is to study models' generalizability to tackle real-world problems. We experiment with two different settings, each representing a common type of generalization: (1) Zeroshot VQA estimates models' generalizability toward both known and novel objects. Three popular datasets are used in our experiments, including VQA [18], GQA [24] and the recently introduced Novel-VQA [55]. Following [45, 55], for the VQA and GQA datasets, we reconstruct their training and validation sets to have a disjoint set of objects. For each dataset, we randomly select ten objects from the object pools and use them as novel objects unavailable during training. Similar to [12, 45, 51], we exclude all training questions that either contain words related to the selected objects or use images with the objects, and divide the original validation sets into Known and Novel splits based on objects required for reasoning. For the Novel-VQA dataset, we adopt the original training and test sets [55], which only considers novel objects in the questions (Novel-Q); (2) VQA with OOD questions focuses on evaluating models' generalizability to data with diverse question-answer distributions. We experiment with two popular datasets, including VQA-CP [1] with adversarial distributions between training and evaluation, and GQA-OOD [27] that utilizes balanced training questions but differentiates evaluation questions based on their question-answer distributions." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 402, + 545, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 402, + 545, + 510 + ], + "spans": [ + { + "bbox": [ + 304, + 402, + 545, + 510 + ], + "type": "text", + "content": "Evaluation. We evaluate models with common metrics for visual question answering. For the VQA, Novel-VQA, and VQA-CP datasets, we adopt VQA accuracy [4] as the evaluation metric, which considers multiple candidate answers. For the GQA and GQA-OOD datasets, we use the standard accuracy since each question has an unique answer. We also follow [27] and consider differences in accuracy when answering in-distribution and out-of-distribution questions (i.e., " + }, + { + "bbox": [ + 304, + 402, + 545, + 510 + ], + "type": "inline_equation", + "content": "\\triangle" + }, + { + "bbox": [ + 304, + 402, + 545, + 510 + ], + "type": "text", + "content": ") on the GQA-OOD dataset." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 510, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 545, + 689 + ], + "type": "text", + "content": "Model specification. We use the state-of-the-art neural module network XNM [48] as our baseline, which provides competitive performance on multiple datasets without loss of interpretability. We follow [60] and replace the Transform module with the Relate module to improve attention propagation. Following [34, 49, 55], we adopt the UpDown features [2] that capture 36 semantically meaningful regions (i.e., " + }, + { + "bbox": [ + 304, + 510, + 545, + 689 + ], + "type": "inline_equation", + "content": "N = 36" + }, + { + "bbox": [ + 304, + 510, + 545, + 689 + ], + "type": "text", + "content": ") as the visual inputs. To enable understanding of unseen vocabulary, we follow [51, 55] and use Glove vectors [43] to initialize the word embeddings. Other settings, e.g., network specification and training configuration, are the same as those defined in the original papers [48, 60] without tuning. The aforementioned baseline is incorporated with our method discussed in Section 3.2 to enable object factorization and compositional reasoning." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "Prototype learning. We derive our prototypes with the multi-label classification task [59, 61], which aims to pre" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6740" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 91, + 282, + 186 + ], + "blocks": [ + { + "bbox": [ + 79, + 71, + 255, + 82 + ], + "lines": [ + { + "bbox": [ + 79, + 71, + 255, + 82 + ], + "spans": [ + { + "bbox": [ + 79, + 71, + 255, + 82 + ], + "type": "text", + "content": "Table 1. Comparative results on zero-shot VQA." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 91, + 282, + 186 + ], + "lines": [ + { + "bbox": [ + 50, + 91, + 282, + 186 + ], + "spans": [ + { + "bbox": [ + 50, + 91, + 282, + 186 + ], + "type": "table", + "html": "
VQAGQANovel-VQA
KnownNovelKnownNovelNovel-Q
UpDown [2]55.6548.5352.7351.3551.40
VisualBert [33]--59.8558.80-
Skill-Concept [55]----59.80
XNM [48]62.0552.8159.3957.5457.54
XNM+POEM63.8054.8260.6059.7160.73
", + "image_path": "5135943a4de3accb67f281ebd58110a8c61ffbf95dc581f37a0028d65b9c7d8c.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 207, + 287, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 207, + 287, + 411 + ], + "spans": [ + { + "bbox": [ + 46, + 207, + 287, + 411 + ], + "type": "text", + "content": "dict all object categories that exist in an image. The image-wise ground truth is constructed with object detection labels (VQA, VQA-CP and Novel-VQA) or scene graphs (GQA and GQA-OOD). UpDown features are used as inputs to the classification network, which encode semantic information of different objects. For zero-shot VQA, we train the model on each dataset with training images that do not contain the selected novel objects, and evaluate it on validation images with only known objects. For VQA with OOD questions, we use the original training and validation sets without excluding samples. We set the number of prototypes in our experiments to 1000 (i.e., " + }, + { + "bbox": [ + 46, + 207, + 287, + 411 + ], + "type": "inline_equation", + "content": "K = 1000" + }, + { + "bbox": [ + 46, + 207, + 287, + 411 + ], + "type": "text", + "content": "), which is comparable to the number of fine-grained objects in GQA (i.e., " + }, + { + "bbox": [ + 46, + 207, + 287, + 411 + ], + "type": "inline_equation", + "content": "\\sim 1000" + }, + { + "bbox": [ + 46, + 207, + 287, + 411 + ], + "type": "text", + "content": " object categories). The network is trained with Adam [30] optimizer for 60 epochs, the learning rate and batch size are set to " + }, + { + "bbox": [ + 46, + 207, + 287, + 411 + ], + "type": "inline_equation", + "content": "4 \\times 10^{-4}" + }, + { + "bbox": [ + 46, + 207, + 287, + 411 + ], + "type": "text", + "content": " and 128, respectively. Prototypes with the best validation performance are used in our VQA model." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 419, + 193, + 432 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 419, + 193, + 432 + ], + "spans": [ + { + "bbox": [ + 47, + 419, + 193, + 432 + ], + "type": "text", + "content": "4.2. Results on Zero-shot VQA" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 437, + 287, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 437, + 287, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 287, + 605 + ], + "type": "text", + "content": "We first demonstrate the effectiveness of our prototypical neural module (POEM) network on answering questions with both known and novel objects. We compare it with four approaches, including (1) UpDown [2] that does not explicitly model the reasoning process, (2) Our baseline XNM [48] with an explicitly reasoning process, (3) VisualBert [33] that utilizes vision-and-language pretraining on external data containing the novel objects (i.e., MSCOCO [36]), and (4) Skill-Concept [55] that is the current state-of-the-art on Novel-VQA dataset, which explicitly exploits novel objects in images with around " + }, + { + "bbox": [ + 46, + 437, + 287, + 605 + ], + "type": "inline_equation", + "content": "97\\%" + }, + { + "bbox": [ + 46, + 437, + 287, + 605 + ], + "type": "text", + "content": " of them covered in a handcrafted reference training set. All of the models are trained with UpDown visual features and initialized with pretrained word embeddings." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": "We draw three key observations from the results in Table 1: (1) While Updown and XNM show similar accuracy under the standard VQA setting [2, 48], the latter provides stronger performance on zero-shot VQA. The results indicate that the compositional reasoning process is not only helpful in interpretability, but also important for model performance and generalizability; (2) By leveraging external data, VisualBert provides better performance than both aforementioned models. However, it violates the original" + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 325, + 91, + 523, + 258 + ], + "blocks": [ + { + "bbox": [ + 317, + 71, + 533, + 82 + ], + "lines": [ + { + "bbox": [ + 317, + 71, + 533, + 82 + ], + "spans": [ + { + "bbox": [ + 317, + 71, + 533, + 82 + ], + "type": "text", + "content": "Table 2. Comparative results on VQA with OOD questions." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 325, + 91, + 523, + 258 + ], + "lines": [ + { + "bbox": [ + 325, + 91, + 523, + 258 + ], + "spans": [ + { + "bbox": [ + 325, + 91, + 523, + 258 + ], + "type": "table", + "html": "
VQA-CPGQA-OOD
acc ↑acc-tail ↑△↓
Bias Product [11]39.9330.812.0
AdvReg [44]41.17--
Hint [47]46.73--
RUBi [7]47.1135.714.3
SCR [56]49.45--
LMH [11]52.0532.211.5
LMH+Entropies [15]54.55--
XNM [48]51.5446.1414.4
XNM+POEM53.9946.8910.7
", + "image_path": "9741aebff794f76278bae559f139dacaa24bf1b12510b5b43b0e72b8d51c9b93.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 279, + 545, + 447 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 279, + 545, + 447 + ], + "spans": [ + { + "bbox": [ + 304, + 279, + 545, + 447 + ], + "type": "text", + "content": "intent of zero-shot VQA with novel objects actually covered in the external data, making them impractical for real-world scenarios with unseen objects; and (3) Differently, with our prototypes bridging different objects and the reasoning process, the proposed method improves the performance of the XNM baseline without relying on external data, and achieves overall the best results in answering questions with both known and novel objects in the visual-textual data. It also outperforms Skill-Concept on the Novel-VQA dataset that only considers novel objects in the questions. Note that Skill-Concept assumes the availability of novel objects in training images and is not applicable to zero-shot setting on VQA and GQA datasets, while our method has the capability to generalize toward broader scenarios." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 455, + 504, + 468 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 455, + 504, + 468 + ], + "spans": [ + { + "bbox": [ + 306, + 455, + 504, + 468 + ], + "type": "text", + "content": "4.3. Results on VQA with OOD Questions" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 474, + 545, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 545, + 593 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 545, + 593 + ], + "type": "text", + "content": "Next, we investigate the robustness of our method against spurious data biases. We compare our method with eight approaches that do not exploit additional data, including Bias Product [11], AdvReg [44], RUBi [7], and LMH+Entropies [15] for reducing single-modal biases, Hint [47] and SCR [56] for boosting visual attention, LMH [11] for learning the residual of biases, and our baseline XNM. Following [11, 15, 20], when experimenting on the VQA-CP dataset [1], both XNM and our model incorporate the learned mixed-in module [11] to address known biases." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "Results in Table 2 show that our method is able to improve the XNM baseline by a considerable margin. With object factorization and compositional reasoning, it not only improves the robustness against adversarial distributions (i.e., VQA-CP), but also reduces the performance gap between answering in-distribution and out-of-distribution questions (i.e., " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\triangle" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": " for GQA-OOD). Compared to existing methods that introduce additional regularization and have difficulties generalizing to different datasets [7, 11, 15], our method augments models' reasoning capability without im" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 314, + 757 + ], + "type": "text", + "content": "6741" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 91, + 284, + 172 + ], + "blocks": [ + { + "bbox": [ + 70, + 71, + 264, + 82 + ], + "lines": [ + { + "bbox": [ + 70, + 71, + 264, + 82 + ], + "spans": [ + { + "bbox": [ + 70, + 71, + 264, + 82 + ], + "type": "text", + "content": "Table 3. Comparative results for different prototypes." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 91, + 284, + 172 + ], + "lines": [ + { + "bbox": [ + 50, + 91, + 284, + 172 + ], + "spans": [ + { + "bbox": [ + 50, + 91, + 284, + 172 + ], + "type": "table", + "html": "
VQAGQANovel-VQAVQA-CP
KnownNovelKnownNovelNovel-QOOD
Scratch62.6653.6658.8757.6959.4850.39
Object62.5653.2360.4859.4656.6752.23
Textual60.6152.3355.3153.2259.1751.09
Ours63.8054.8260.6059.7160.7353.99
", + "image_path": "80381474976b2764a5e8152e06ef39e994919026e58f6069ed51cf63423f79f9.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 194, + 287, + 242 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 194, + 287, + 242 + ], + "spans": [ + { + "bbox": [ + 46, + 194, + 287, + 242 + ], + "type": "text", + "content": "posing data-specific constrains and thus enjoys better generalizability. The aforementioned observations suggest the significance of explicitly bridging objects with their fine-grained characteristics for overcoming data biases." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 251, + 255, + 264 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 251, + 255, + 264 + ], + "spans": [ + { + "bbox": [ + 47, + 251, + 255, + 264 + ], + "type": "text", + "content": "4.4. Ablation Study on Object Factorization" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 270, + 287, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 270, + 287, + 449 + ], + "spans": [ + { + "bbox": [ + 46, + 270, + 287, + 449 + ], + "type": "text", + "content": "A key component of our framework is the proposed method for learning discriminative prototypes with object factorization. In this section, we perform an ablation study to investigate the usefulness of different prototypes (see our supplementary materials for additional ablation studies on model design). Specifically, we consider three types of alternative prototypes: (1) Prototypes that are randomly initialized and learned from scratch on the VQA task (Scratch); (2) Prototypes specific to manually defined objects (Object), which are learned with the same multi-label classification task as our approach but without object factorization; and (3) Prototypes derived from Glove [43] word embeddings of concepts covered in the Visual Genome [31] dataset (Textual), including objects, attributes, and relationships." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 450, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 450, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 450, + 288, + 714 + ], + "type": "text", + "content": "We made three observations from results in Table 3: (1) Randomly initialized prototypes lead to inferior performance among all datasets, indicating the significance of explicitly learning semantically plausible prototypes; (2) While object-based prototypes show reasonable performance on the GQA dataset with detailed annotations (i.e., " + }, + { + "bbox": [ + 46, + 450, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\sim 1000" + }, + { + "bbox": [ + 46, + 450, + 288, + 714 + ], + "type": "text", + "content": " object categories), they have negligible improvements on the VQA, Novel-VQA, and VQA-CP datasets with abstract-level annotations (i.e., 80 object categories). The large gap in performance gain across datasets demonstrates the advantages of fine-grained categorization, and more importantly, highlights the need to learn discriminative prototypes without relying on extensive annotations. For this, our method utilizes object factorization to automatically decompose objects into more elaborated semantics, and brings considerable improvements among datasets with both abstract and detailed object annotations; (3) Textual prototypes result in a visible drop in accuracy, despite the consideration of various concepts. This is likely caused by the difficulty of correlating objects across the visual and textual domains. Differently, our method directly captures diverse characteristics of objects from visual data and does" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 307, + 70, + 545, + 264 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 545, + 264 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 545, + 264 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 545, + 264 + ], + "type": "image", + "image_path": "4169df35cbbb9683445160f9c51fec2ac58fc3d97a0b96df10f6311eb9507013.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 309, + 273, + 541, + 284 + ], + "lines": [ + { + "bbox": [ + 309, + 273, + 541, + 284 + ], + "spans": [ + { + "bbox": [ + 309, + 273, + 541, + 284 + ], + "type": "text", + "content": "Figure 4. Examples of semantics encoded in diverse prototypes." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 305, + 523, + 317 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 305, + 523, + 317 + ], + "spans": [ + { + "bbox": [ + 306, + 305, + 523, + 317 + ], + "type": "text", + "content": "not suffer from the discrepancies between modalities." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 324, + 545, + 350 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 324, + 545, + 350 + ], + "spans": [ + { + "bbox": [ + 306, + 324, + 545, + 350 + ], + "type": "text", + "content": "4.5. What Do Prototypes Learn? Do They Encode Common Characteristics among Objects?" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 354, + 545, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 354, + 545, + 426 + ], + "spans": [ + { + "bbox": [ + 304, + 354, + 545, + 426 + ], + "type": "text", + "content": "Results in the previous sections demonstrate that our method learns discriminative prototypes to represent a variety of objects and bring enhanced generalizability across various settings. This section further demonstrates its effectiveness by investigating how our prototypes correlate different objects." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 426, + 546, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 546, + 582 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 546, + 582 + ], + "type": "text", + "content": "We first study what each individual prototype learns. In Figure 4, we visualize instances (regions inside bounding boxes) most relevant to the prototypes (measured with their relevance scores on different prototypes, i.e., " + }, + { + "bbox": [ + 304, + 426, + 546, + 582 + ], + "type": "inline_equation", + "content": "\\alpha_{p}^{k}" + }, + { + "bbox": [ + 304, + 426, + 546, + 582 + ], + "type": "text", + "content": " in Equation 2, " + }, + { + "bbox": [ + 304, + 426, + 546, + 582 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 426, + 546, + 582 + ], + "type": "text", + "content": " denotes the indices of prototypes). The results show that our prototypes learn to represent a diverse pool of semantics. They not only capture low-level visual cues, such as shapes (e.g., round objects in the " + }, + { + "bbox": [ + 304, + 426, + 546, + 582 + ], + "type": "inline_equation", + "content": "1^{st}" + }, + { + "bbox": [ + 304, + 426, + 546, + 582 + ], + "type": "text", + "content": " row), textures (e.g., objects with jagged texture in the " + }, + { + "bbox": [ + 304, + 426, + 546, + 582 + ], + "type": "inline_equation", + "content": "2^{nd}" + }, + { + "bbox": [ + 304, + 426, + 546, + 582 + ], + "type": "text", + "content": " row), and patterns (e.g., objects with stripes in the " + }, + { + "bbox": [ + 304, + 426, + 546, + 582 + ], + "type": "inline_equation", + "content": "3^{rd}" + }, + { + "bbox": [ + 304, + 426, + 546, + 582 + ], + "type": "text", + "content": " row), but also encode high-level semantics including object categories (e.g., wheels in the " + }, + { + "bbox": [ + 304, + 426, + 546, + 582 + ], + "type": "inline_equation", + "content": "4^{th}" + }, + { + "bbox": [ + 304, + 426, + 546, + 582 + ], + "type": "text", + "content": " row) and commonalities in semantics (e.g., all objects in the " + }, + { + "bbox": [ + 304, + 426, + 546, + 582 + ], + "type": "inline_equation", + "content": "5^{th}" + }, + { + "bbox": [ + 304, + 426, + 546, + 582 + ], + "type": "text", + "content": " row are displaying text)." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 582, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 714 + ], + "type": "text", + "content": "With our prototypes encoding abundant semantics, we further analyze their effectiveness in correlating relevant objects based on their characteristics. Specifically, we calculate the average relevance scores " + }, + { + "bbox": [ + 304, + 582, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\alpha_{p}" + }, + { + "bbox": [ + 304, + 582, + 547, + 714 + ], + "type": "text", + "content": " (see Equation 1) between objects in the GQA dataset and all prototypes, and then apply k-means algorithm [37] (" + }, + { + "bbox": [ + 304, + 582, + 547, + 714 + ], + "type": "inline_equation", + "content": "k = 30" + }, + { + "bbox": [ + 304, + 582, + 547, + 714 + ], + "type": "text", + "content": ") to cluster objects using the scores. As shown in Table 4, by representing objects based on the prototypes, we can correlate objects that belong to similar categories (e.g., drinks and utensils in the " + }, + { + "bbox": [ + 304, + 582, + 547, + 714 + ], + "type": "inline_equation", + "content": "1^{st}" + }, + { + "bbox": [ + 304, + 582, + 547, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 582, + 547, + 714 + ], + "type": "inline_equation", + "content": "2^{nd}" + }, + { + "bbox": [ + 304, + 582, + 547, + 714 + ], + "type": "text", + "content": " rows), commonly appear in the same scenarios (e.g., baseball games and bedrooms in the " + }, + { + "bbox": [ + 304, + 582, + 547, + 714 + ], + "type": "inline_equation", + "content": "3^{rd}" + }, + { + "bbox": [ + 304, + 582, + 547, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 582, + 547, + 714 + ], + "type": "inline_equation", + "content": "4^{th}" + }, + { + "bbox": [ + 304, + 582, + 547, + 714 + ], + "type": "text", + "content": " rows)." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6742" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 51, + 113, + 281, + 278 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 288, + 104 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 288, + 104 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 288, + 104 + ], + "type": "text", + "content": "Table 4. Different groups of objects that are clustered based on their relevance to prototypes. Please refer to our supplementary materials for the complete results with 30 groups." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 51, + 113, + 281, + 278 + ], + "lines": [ + { + "bbox": [ + 51, + 113, + 281, + 278 + ], + "spans": [ + { + "bbox": [ + 51, + 113, + 281, + 278 + ], + "type": "table", + "html": "
GroupObjects
1cup, saucer, glass, beer, mug, juice, beverage, liquid, smoothie, coffee
2fork, spoon, knife, silverware, utensil, ladle, chopstick, tongs, spatula, butter knife
3spectator,UMPire, batter, catcher, crowd, net, player, baseball, stadium, bleachers
4bed, sofa, pillow, bedspread, headboard, comforter, couch, sheet, ottoman, mattress
5sticker, newspaper, paper, sign, book, tape, drawing, CD, letter, label
6water, sand, sea, rock, ocean, boulders, lake, beach, shore, river
", + "image_path": "dc227c2d8b627e8ba6af26e02937d6706ccb276a0a305b8e97669177404c0e8b.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 300, + 287, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 300, + 287, + 350 + ], + "spans": [ + { + "bbox": [ + 46, + 300, + 287, + 350 + ], + "type": "text", + "content": "or share similar characteristics (e.g., objects related to text and landscape in the " + }, + { + "bbox": [ + 46, + 300, + 287, + 350 + ], + "type": "inline_equation", + "content": "5^{th}" + }, + { + "bbox": [ + 46, + 300, + 287, + 350 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 300, + 287, + 350 + ], + "type": "inline_equation", + "content": "6^{th}" + }, + { + "bbox": [ + 46, + 300, + 287, + 350 + ], + "type": "text", + "content": " rows). The results demonstrate the effectiveness of our prototypes in parsing objects based on their commonalities in the semantic space." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 358, + 286, + 372 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 358, + 286, + 372 + ], + "spans": [ + { + "bbox": [ + 47, + 358, + 286, + 372 + ], + "type": "text", + "content": "4.6. How Do Models Reason to Answer Questions?" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 377, + 287, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 377, + 287, + 449 + ], + "spans": [ + { + "bbox": [ + 46, + 377, + 287, + 449 + ], + "type": "text", + "content": "Besides improving the generalizability, our method also enables interpretation of the decision-making process by visualizing the regions of interest (ROIs) at each reasoning step and prototypes matched with the observations. In this section, we provide qualitative examples to study the underlying rationales behind the derivation of answers." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 450, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 450, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 450, + 288, + 715 + ], + "type": "text", + "content": "Figure 5 shows the reasoning process of our method. For each question, we visualize the reasoning steps represented by neural modules (top), attention maps highlighting the ROIs (middle, " + }, + { + "bbox": [ + 46, + 450, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\alpha^t" + }, + { + "bbox": [ + 46, + 450, + 288, + 715 + ], + "type": "text", + "content": " in Equation 6), and images associated to prototypes matched with the observations (bottom). It shows that our method can correlate objects based on various characteristics and locate those important ones. In the " + }, + { + "bbox": [ + 46, + 450, + 288, + 715 + ], + "type": "inline_equation", + "content": "1^{st}" + }, + { + "bbox": [ + 46, + 450, + 288, + 715 + ], + "type": "text", + "content": " example, while the apples are not explicitly mentioned in the question, our model correlates them with prototypes for different fruits (\"fruit\" is a keyword in the question) and pays focused attention in the Find step. Besides capturing semantic relationships about object categories, prototypes also help identify the cat based on its attribute (i.e., brown color) within the Filter step, and enable the model to reason on the relative position between objects (i.e., Relate step). In the " + }, + { + "bbox": [ + 46, + 450, + 288, + 715 + ], + "type": "inline_equation", + "content": "2^{nd}" + }, + { + "bbox": [ + 46, + 450, + 288, + 715 + ], + "type": "text", + "content": " example, our model not only highlights the correct objects in the first two Find steps (i.e., the banana and the mat), but also identifies the key characteristics that contribute to reasoning (i.e., matching observations with prototypes related to colors instead of object categories or other attributes). In the " + }, + { + "bbox": [ + 46, + 450, + 288, + 715 + ], + "type": "inline_equation", + "content": "3^{rd}" + }, + { + "bbox": [ + 46, + 450, + 288, + 715 + ], + "type": "text", + "content": " example, woman in the question is an unseen object during training. With object factorization," + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 310, + 76, + 362, + 109 + ], + "blocks": [ + { + "bbox": [ + 310, + 76, + 362, + 109 + ], + "lines": [ + { + "bbox": [ + 310, + 76, + 362, + 109 + ], + "spans": [ + { + "bbox": [ + 310, + 76, + 362, + 109 + ], + "type": "image", + "image_path": "12c6f55d3e7ff510369b48984ebab3feee9026788c79e3d9b3322cc36a315f87.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 310, + 110, + 364, + 139 + ], + "lines": [ + { + "bbox": [ + 310, + 110, + 364, + 139 + ], + "spans": [ + { + "bbox": [ + 310, + 110, + 364, + 139 + ], + "type": "text", + "content": "Question: How is the fruit to the right of the brown animal called? 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Answer: no" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 317, + 205, + 357, + 255 + ], + "lines": [ + { + "bbox": [ + 317, + 205, + 357, + 255 + ], + "spans": [ + { + "bbox": [ + 317, + 205, + 357, + 255 + ], + "type": "image", + "image_path": "4543385112d474e56b5c73757a9d5955dce78de2be7ca2c48113da8496eead35.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 369, + 134, + 422, + 198 + ], + "blocks": [ + { + "bbox": [ + 369, + 134, + 422, + 198 + ], + "lines": [ + { + "bbox": [ + 369, + 134, + 422, + 198 + ], + "spans": [ + { + "bbox": [ + 369, + 134, + 422, + 198 + ], + "type": "image", + "image_path": "1bf0c21e9de0806b45981c0e85479d1bf6ff55afaa61c04bc44e6fc4c9681dbd.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 369, + 199, + 416, + 282 + ], + "blocks": [ + { + "bbox": [ + 310, + 256, + 368, + 284 + ], + "lines": [ + { + "bbox": [ + 310, + 256, + 368, + 284 + ], + "spans": [ + { + "bbox": [ + 310, + 256, + 368, + 284 + ], + "type": "text", + "content": "Question: Do you see a woman near the water bottle in the bottom? Answer: yes" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 369, + 199, + 416, + 282 + ], + "lines": [ + { + "bbox": [ + 369, + 199, + 416, + 282 + ], + "spans": [ + { + "bbox": [ + 369, + 199, + 416, + 282 + ], + "type": "image", + "image_path": "8ab06514a278703cf82b72ed7b2c2b1150bbc4d6e9a5111db8dd050049f66069.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 422, + 134, + 487, + 198 + ], + "blocks": [ + { + "bbox": [ + 422, + 134, + 487, + 198 + ], + "lines": [ + { + "bbox": [ + 422, + 134, + 487, + 198 + ], + "spans": [ + { + "bbox": [ + 422, + 134, + 487, + 198 + ], + "type": "image", + "image_path": "8e2b80b073cb3b3eaae152acb245a14a93d28befb7cb40b81ca14c4dca3982dd.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 487, + 134, + 542, + 198 + ], + "blocks": [ + { + "bbox": [ + 487, + 134, + 542, + 198 + ], + "lines": [ + { + "bbox": [ + 487, + 134, + 542, + 198 + ], + "spans": [ + { + "bbox": [ + 487, + 134, + 542, + 198 + ], + "type": "image", + "image_path": "11d919d2ed29181ed3a9b59264679e691f74be2ece6737e1a6744a407f5c6142.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + } + ], + "index": 18 + }, + { + "type": "image", + "bbox": [ + 423, + 256, + 484, + 282 + ], + "blocks": [ + { + "bbox": [ + 423, + 256, + 484, + 282 + ], + "lines": [ + { + "bbox": [ + 423, + 256, + 484, + 282 + ], + "spans": [ + { + "bbox": [ + 423, + 256, + 484, + 282 + ], + "type": "image", + "image_path": "b54eb062fedf73518ca9e2f0d2efc3347dc02d2486b24206587c23feb96bf0fa.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 293, + 545, + 327 + ], + "lines": [ + { + "bbox": [ + 306, + 293, + 545, + 327 + ], + "spans": [ + { + "bbox": [ + 306, + 293, + 545, + 327 + ], + "type": "text", + "content": "Figure 5. Illustrations of the reasoning process. From left to right are the input images together with questions and predicted answers, and sequences of reasoning steps." + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + } + ], + "index": 19 + }, + { + "type": "image", + "bbox": [ + 485, + 256, + 545, + 282 + ], + "blocks": [ + { + "bbox": [ + 485, + 256, + 545, + 282 + ], + "lines": [ + { + "bbox": [ + 485, + 256, + 545, + 282 + ], + "spans": [ + { + "bbox": [ + 485, + 256, + 545, + 282 + ], + "type": "image", + "image_path": "abf107185ea3bd1a39703a97333bb477b80a12875a9aae8c5858c20753f83c74.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_body" + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 348, + 545, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 348, + 545, + 397 + ], + "spans": [ + { + "bbox": [ + 305, + 348, + 545, + 397 + ], + "type": "text", + "content": "our model successfully associates it to known objects (i.e., men) based on the similarity in clothing, and progressively shifts the attention from both women (i.e., Find step) to the one lying next to the bottle (i.e., Filter and Relate steps)." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 409, + 378, + 422 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 409, + 378, + 422 + ], + "spans": [ + { + "bbox": [ + 306, + 409, + 378, + 422 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 429, + 546, + 657 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 429, + 546, + 657 + ], + "spans": [ + { + "bbox": [ + 304, + 429, + 546, + 657 + ], + "type": "text", + "content": "This study is an effort toward generalizable and interpretable AI systems for real-world applications. It draws inspiration from the ways humans reason with the visual world, and investigates the effectiveness of integrating the compositionality of objects and the reasoning process. Our work distinguishes itself with a principled method for automatically factorizing objects into fine-grained semantics, bridging novel and known objects, and a new neural module network with a compositional decision-making process. The compositionality in both dimensions addresses object diversity and spurious data biases, enhancing model generalizability toward a broad range of scenarios. It also enables interpretation of the rationales behind the model's decisions. Experimental results demonstrate the advantages of our method under diverse settings, and provide insights on how our model reasons with the visual-textual inputs. We hope that this study can be useful for future developments of trustworthy visual reasoning models with more human-like intelligence and generalizability." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 306, + 669, + 408, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 669, + 408, + 682 + ], + "spans": [ + { + "bbox": [ + 306, + 669, + 408, + 682 + ], + "type": "text", + "content": "Acknowledgements" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 306, + 689, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 712 + ], + "type": "text", + "content": "This work is supported by NSF Grants 2143197 and 2227450." + } + ] + } + ], + "index": 26 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6743" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "text", + "content": "[1] Aishwarya Agrawal, Dhruv Batra, Devi Parikh, and Aniruddha Kembhavi. 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In CVPR, pages 2027-2036, 2017. 3, 5" + } + ] + } + ], + "index": 30 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6745" + } + ] + } + ], + "index": 32 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/DoNet_ Deep De-Overlapping Network for Cytology Instance Segmentation/6ce3e51d-a82a-47f1-b18c-a1b3922a9d7f_content_list.json b/2023/DoNet_ Deep De-Overlapping Network for Cytology Instance Segmentation/6ce3e51d-a82a-47f1-b18c-a1b3922a9d7f_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..2caa7a8635bd8fb089884084a96fc338f4af4516 --- /dev/null +++ b/2023/DoNet_ Deep De-Overlapping Network for Cytology Instance Segmentation/6ce3e51d-a82a-47f1-b18c-a1b3922a9d7f_content_list.json @@ -0,0 +1,1475 @@ +[ + { + "type": "text", + "text": "DoNet: Deep De-overlapping Network for Cytology Instance Segmentation", + "text_level": 1, + "bbox": [ + 107, + 130, + 861, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Hao Jiang $^{1*}$ Rushan Zhang $^{1*}$ Yanning Zhou $^{2}$ Yumeng Wang $^{1}$ Hao Chen $^{1\\dagger}$ $^{1}$ The Hong Kong University of Science and Technology \n $^{2}$ Tencent AI Lab", + "bbox": [ + 104, + 179, + 869, + 217 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{hjiangaz, jhc}@cse.ust.hk, {rzhangbq,ywanglu}@connect.ust.hk, amandayzhou@tencent.com", + "bbox": [ + 150, + 219, + 818, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 268, + 313, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Cell instance segmentation in cytology images has significant importance for biology analysis and cancer screening, while remains challenging due to 1) the extensive overlapping translucent cell clusters that cause the ambiguous boundaries, and 2) the confusion of mimics and debris as nuclei. In this work, we proposed a De-overlapping Network (DoNet) in a decompose-and-recombined strategy. A Dual-path Region Segmentation Module (DRM) explicitly decomposes the cell clusters into intersection and complement regions, followed by a Semantic Consistency-guided Recombination Module (CRM) for integration. To further introduce the containment relationship of the nucleus in the cytoplasm, we design a Mask-guided Region Proposal Strategy (MRP) that integrates the cell attention maps for inner-cell instance prediction. We validate the proposed approach on ISBI2014 and CPS datasets. Experiments show that our proposed DoNet significantly outperforms other state-of-the-art (SOTA) cell instance segmentation methods. The code is available at https://github.com/DeepDoNet/DoNet.", + "bbox": [ + 75, + 301, + 473, + 604 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 637, + 209, + 652 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Cytology image has been essential for cancer screening and earlier diagnosis, such as qualitative and quantitative identification of cellular morphology, nuclei size, nuclear-cytoplasmic ratio, and other cytological features [12, 15, 25]. However, examining tens of thousands of cells under the microscope visually is inherently tedious and suffers from inter-/intra-observer variability. Computational techniques enable efficient and accurate characterization of cells from cytology images [12, 16]. Among all computational techniques, cell segmentation has been a fundamental and widely-studied task, since the acquisition of cell-level identification is a pre-requisition for further assessment and analysis [3, 23].", + "bbox": [ + 75, + 662, + 468, + 861 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/6bc4bb6363aa0f89207f07da4edf2b136940cc0adfb0680e5812b27f2cf1d5b2.jpg", + "image_caption": [ + "Figure 1. The schematic illustration of proposed DoNet with decompose-and-recombined strategy, which maps each overlapping cell into the intersection, complement, and instance layers to address the overlapping issue in cytology instance segmentation." + ], + "image_footnote": [], + "bbox": [ + 531, + 267, + 861, + 458 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Deep Learning (DL) methods show promising results for cell-nuclei segmentation in the histopathology image [5,6,14,17]. However, cytology segmentation remains challenging for the following two reasons. Firstly, cells in a cytology image are prone to cluster with each other, leading to the overlapping issue. In the cytology images, the translucent cytoplasm of the cell (seen in Figure 1) tends to occlude each other with low contrast staining, leading to ambiguous cellular boundary predictions. This phenomenon is particularly evident in cervical cell images. Secondly, hard mimics, are widespread in the background, along with other technical artefacts such as bubbles, which could mislead the instance segmentation models [4]. Take the cervical cell image as an example, the widespread white blood cells and mucus stains lead to false predictions for nuclei. To address these challenges, several works [24, 33] propose the segment-then-refine paradigm, while others [39, 40] utilize the detection-based framework, e.g., Mask R-CNN [11]. However, they fail to model the interaction between intersection and complement sub-regions within the translucent cell cluster explicitly, resulting in a limited understanding of cross-region relationships.", + "bbox": [ + 496, + 551, + 892, + 883 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Amodal instance segmentation tackles the occlusion", + "bbox": [ + 519, + 885, + 890, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal contribution", + "bbox": [ + 94, + 875, + 202, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding author", + "bbox": [ + 96, + 887, + 218, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "15641", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "problem by inferring the integral object based on the partially visible region [22]. Based on the fact that humans can infer the occluded region of an object despite the ambiguity, these methods attempt to learn the integrated object mask (amodal mask) for better occlusion reasoning capability [9, 37] via synthesizing occluded data label pairs and aggregating global information to enhance perceptual ability. Compared to natural scenes, cell instances in cytology images are mostly semi-transparent. Therefore, an occlusion (overlapping) region exits in both the occluding and occluded instances. However, treating semi-transparent overlapping regions as general occlusion regions is not optimal, since they have different appearances compared to non-overlapping regions, and could in fact provide richer shape information than general occlusion regions.", + "bbox": [ + 75, + 90, + 472, + 316 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Motivated by the amodal perception, we propose a decompose-and-recombine strategy for translucent cell instance segmentation, named De-overlapping Network (DoNet). Figure 1 provides the schematic diagram. For each cell cluster with more than one cellular sub-region, DoNet starts from implicitly learning the hidden interaction of sub-regions by predicting instance masks from clusters. Then, it explicitly models the components and their relationships via the intersection layer, complement layer, and instance layer, to enhance its perceptual capability.", + "bbox": [ + 75, + 318, + 472, + 469 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Initially, we adopt Mask R-CNN to get the coarse predictions, followed by a novel Dual-path Region segmentation Module (DRM) that combines features and coarse masks from the first stage to decompose cell clusters into intersection and complement sub-regions. Then, the semantic Consistency-guided Recombination Module (CRM) is designed to encourage consistency between the refined instances and integral sub-region predictions. Furthermore, to impose the morphological constraint that nuclei stay inside the cellular regions, we propose a Mask-guided Region Proposal Module (MRP) to encourage the model to focus on the intra-cellular area during nuclei segmentation.", + "bbox": [ + 75, + 469, + 472, + 650 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The overall contributions are summarized as follows:", + "bbox": [ + 96, + 651, + 447, + 665 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- A novel de-overlapping network for cell instance segmentation with a decompose-and-recombined strategy, decomposing the cell regions with the DRM, as well as implicitly and explicitly modeling the semantic relationship between intersection, complement, and instance (cell) components via the CRM. These designs equip the network with enhanced perceptual capability in overlapping cellular sub-regions.", + "- A mask-guided region proposal module (MRP) that leverages the cytoplasm attention map for the intracellular nuclei refinement, which imposes the biology prior of cellular instances into the module, effectively mitigating the influence of mimickers widespread in the background." + ], + "bbox": [ + 94, + 676, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- Extensive experiments on two overlapping cytology image segmentation datasets, namely ISBI2014 [24] and CPS [39], demonstrating that our proposed DoNet outperforms other state-of-the-art (SOTA) methods by a large margin.", + "bbox": [ + 517, + 90, + 890, + 167 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 191, + 640, + 209 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Cytology Instance Segmentation: Challenges such as cell clustering, hard mimics, and semi-transparent overlapping cytoplasm regions pose in the segmentation of cellular instance (e.g., cell, nuclei, cytoplasm) from cytology images. These challenges inspired numerous insightful works, especially after the publication of ISBI2014 [33]. Two mainstream approaches are proposed to tackle the overlapping cell segmentation challenge: the segment-then-refine stream and the end-to-end training stream.", + "bbox": [ + 496, + 218, + 890, + 354 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Early approaches tackling this challenge are primarily the combination of pixel-level segmentation models and additional post-processing techniques, such as seeded watershed algorithm [19], random walk [38], conditional random field algorithms [35], and star-convex parameterization [34]. To further improve the segmentation performance, some other methods introduce morphological prior. Song et al. design a dynamic multi-template deformation model, which leverages case-specific shape constraints to guide the inference of overlapping cell boundaries [30]. Tareef et al. propose to refine cytoplasm boundary via a learnable shape prior, which is dynamically modeled as the fusion of shape templates [32].", + "bbox": [ + 496, + 354, + 892, + 551 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Escaping from the complex post-processing procedure, many later works turn to end-to-end training. These approaches typically adopt Mask R-CNN as their baseline. The first attempt following this approach was [29], a model for nuclear instance segmentation from liquid-based cytology smears. Based on the appearance similarity between different cells, Zhou et al. propose the IRNet to explore instance relation during overlapping cervical cell segmentation [40]. To leverage information from unlabeled data, Zhou et al. provide a mean-teacher-based semi-supervised learning scheme, MMT-PSM [39].", + "bbox": [ + 496, + 551, + 890, + 717 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The above two methods have achieved notable performance improvements, yet still lack the necessary perceptual capability for overlapping regions, leading to sub-optimal results, i.e., ambiguous cell boundaries. In this study, we propose a de-overlapping network, named DoNet, to implicitly and explicitly model the interaction between the integral instance and its sub-regions.", + "bbox": [ + 496, + 718, + 890, + 824 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Occluded Instance Segmentation: Instance segmentation, a typical task in computer vision, refers to the inference of bounding boxes and instance segmentation masks. Most notable approaches follow the detect-then-segment paradigm, such as Mask R-CNN [11] and its following variants [2, 13].", + "bbox": [ + 496, + 825, + 892, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "15642", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/0aee67d7d1e86c6a8cab86b20261ca11a7c821c58641118d4abfff63da87b3c1.jpg", + "image_caption": [ + "Figure 2. The flowchart of the proposed DoNet. It consists of four main parts: (1) baseline for coarse mask segmentation; (2) DRM to simultaneously regress intersection and complement regions which provides cues for final mask refinement; (3) CRM to explicitly refine the final mask and encourage the semantic consistency; (4) MRP to mitigate the effect of background noise." + ], + "image_footnote": [], + "bbox": [ + 84, + 90, + 885, + 404 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "However, these approaches could not handle the occlusion problem, common in visual application scenarios like robotic manipulations, scene parsing, and autonomous driving [1, 10]. Due to the inconsistencies within a Regions of Interest (RoI), these models suffer from the limited perceptual capability, leading to ambiguous segmentation boundaries. To tackle this issue, a specific task, occluded instance segmentation aims at leveraging visible regions to perceive the entirety of the occluded instance accurately. This capability of inferring and reasoning occluded objects is defined as amodal perception [9], thus occluded instance segmentation is also called amodal instance segmentation.", + "bbox": [ + 75, + 486, + 472, + 667 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Research on amodal instance segmentation starts from [22], which poses this challenging task and gives a synthesis-based solution. In this work, the first amodal instance segmentation dataset, the COCOA dataset, is established based on the COCO dataset. Afterward, some notable solutions accomplish this task and achieve state-of-the-art performance. Previous approaches tackle this challenge by leveraging information from visible instance segmentation, then inferring the amodal mask [1,9]. For example, Occlusion R-CNN (ORCNN) is built on R-CNN with two mask heads, the visible mask head, and the amodal mask head, which directly predict the amodal mask and the visible mask, inferring the visible mask through the subtraction of these two masks [9]. Qi et al. [28] perform amodal instance segmentation with multi-level coding and establish", + "bbox": [ + 75, + 674, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "a large-scale amodal instance segmentation dataset. Xiao et al. [37] leverage shape prior knowledge to infer amodal mask using memory codebook. Some other models, like BCNet [18] abandon the visible instance prediction based manner and directly models the relationship between the occluder and the occludee. To address the lack of amodal mask ground truth, ASBU [26] introduces a weakly supervised amodal segmenter, which generates pseudo-ground truth by boundary uncertainty estimation.", + "bbox": [ + 496, + 486, + 890, + 621 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Essentially, the above occluded instance segmentation methods aim to enhance the amodal perception and reasoning capability, inspiring us to explore the interaction between instance sub-regions and the integral instance. Compared to amodal segmentation, whose focus on inferring the invisible region from the partially visible regions, our focus is to resolve the inconsistency between the intersection and complement regions.", + "bbox": [ + 496, + 622, + 890, + 743 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 500, + 756, + 635, + 773 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Overview", + "text_level": 1, + "bbox": [ + 500, + 781, + 609, + 796 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Problem formulation: Following the setting of cell instance segmentation, we are provided with a dataset with $K$ images and the corresponding annotations $\\mathcal{D} = \\{(\\mathcal{X}_k,\\mathcal{Y}_k)\\}_{k = 1}^K$ , each of which contains annotations of bounding boxes $\\mathcal{B}_k = \\{b_{k,i}\\}_{i = 1}^{N_k}$ , object categories $\\mathcal{C}_k = \\{c_{k,i}\\}_{i = 1}^{N_k}$ , and instance masks $\\mathcal{E}_k = \\{e_{k,i}\\}_{i = 1}^{N_k}$ , where $N_{k}$", + "bbox": [ + 496, + 804, + 893, + 904 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "15643", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "denotes the number of instances in the $k$ -th image. Here, we focus on segmenting the nucleus and cytoplasm for cell instance $c_{k,i} \\in \\{\\text{nuclei}, \\text{cytoplasm}\\}$ . For each cell cluster, based on the localization relationship among the cells, we decompose the instance mask into the intersection region $\\mathcal{O}_k = \\{o_{k,i}\\}_{i=1}^{N_k}$ and the complement region $\\mathcal{M}_k = \\{m_{k,i}\\}_{i=1}^{N_k}$ via the logical operation (see in Figure 1), which is used to model their relationship in the DoNet.", + "bbox": [ + 76, + 90, + 468, + 214 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "**Workflow:** The flowchart of the proposed DoNet is provided in Figure 2. It takes Mask R-CNN [11] as the base model, followed by a Dual-path Region segmentation Module (DRM) which takes the instance features as input to predict intersection regions $\\hat{o}_{k,i}$ and complement regions $\\hat{m}_{k,i}$ of cytoplasm via the intersection and complement layers (Section 3.2). After decomposing cell clusters according to the position relationship, a Consistency-guided Recombination Module (CRM) takes instance features from DRM and RoIAlign layer to generate the recombined masks $\\hat{e}_{k,i}^{r}$ for consistency regularization (Section 3.2). Then, the recombined cytoplasm prediction is utilized as prior knowledge for intra-cellular object prediction throughout the Mask-guided Region Proposal (MRP) (Section 3.3). We will present the details of our framework in the following sections.", + "bbox": [ + 76, + 215, + 470, + 455 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Coarse Mask Segmentation: Previous research works on Mask R-CNN has shown competitive performance in instance segmentation [9, 11, 13], adopted into the proposed DoNet for coarse mask segmentation. Mask R-CNN consists of two stages. The first stage utilizes Feature Pyramid Network (FPN) for feature extraction and a Region Proposal Network (RPN) for candidate object bounding boxes generation. The second stage generates Region-of-Interest (RoI) features $f_{k,i}^{roi}$ via the RoIAngle layer and predicts object classes $\\hat{c}_{k,i}$ and bounding boxes $\\hat{b}_{k,i}$ from the detection head, and semantic masks $\\hat{e}_{k,i}^{c}$ from the Instance Mask Head $(H_{i})$ , respectively. Due to limited perception capability in overlapping regions, $\\hat{e}_{k,i}^{c}$ may contain ambiguous boundaries. Thus, we denote $\\hat{e}_{k,i}^{c}$ as the coarse mask, which provides information for sub-region decomposition in DRM and suppresses the interference from background mimics. Following standard losses in [11], a multi-task loss $\\mathcal{L}_{\\text{coarse}}$ for coarse mask segmentation is formed as,", + "bbox": [ + 76, + 457, + 470, + 733 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {c o a r s e}} = \\mathcal {L} _ {\\text {r e g}} + \\mathcal {L} _ {\\text {c l s}} + \\mathcal {L} _ {\\text {c m a s k}}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 746, + 468, + 762 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{reg}$ denotes the smooth-L1 loss for bounding box regression, $\\mathcal{L}_{cls}$ denotes cross-entropy (CE) loss for classification, and $\\mathcal{L}_{cmask}$ denotes pixel-wise CE loss for segmentation.", + "bbox": [ + 76, + 773, + 468, + 834 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Decompose-and-recombined Strategy", + "text_level": 1, + "bbox": [ + 76, + 845, + 401, + 864 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Previous solutions for amodal perception infer the integral structure of occluded instances using visible regions", + "bbox": [ + 76, + 869, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "[9, 37]. However, they ignore information from overlapping regions, which tend to be sub-optimal in the case of complex superposition of translucent objects. To empower the perception capability of model for overlapping translucent regions, we specifically design the decompose-and-recombined strategy.", + "bbox": [ + 496, + 90, + 890, + 181 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Dual-path Region Segmentation Module (DRM): As shown in Figure 2, DRM consists of an Intersection Mask Head $H_{o}$ and a Complement Mask Head $H_{m}$ with the same architecture. Let $f_{k,i}^{c}$ denotes the rich semantic feature before the coarse mask prediction in the Instance Mask Head. Both $H_{o}$ and $H_{m}$ take the concatenation of $f_{k,i}^{roi}$ and $f_{k,i}^{c}$ as input to predict the intersection and complement regions $\\hat{o}_{k,i}, \\hat{m}_{k,i}$ in clusters. See the supplementary material for details of the Concatenation Unit. Specifically, each head consists of 4 convolutional layers to generate features in $14 \\times 14 \\times 256$ , followed by one deconvolutional layer to get the semantic mask with a resolution of $28 \\times 28 \\times 1$ . Here, we add the pixel-wise CE loss to both heads as the explicit constraint for decomposition,", + "bbox": [ + 496, + 181, + 892, + 393 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {d e c} = \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\frac {1}{N _ {k}} \\sum_ {i = 1} ^ {N _ {k}} \\left(\\mathcal {L} _ {c e} \\left(\\hat {o} _ {k, i}, o _ {k, i}\\right) + \\mathcal {L} _ {c e} \\left(\\hat {m} _ {k, i}, m _ {k, i}\\right)\\right). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 406, + 895, + 460 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Semantic Consistency-guided Recombination Module (CRM): To further enhance the perception capability for overlapping instances, CRM is designed to encourage DoNet to perceive integral instances. Specifically, let $f_{k,i}^{o}$ and $f_{k,i}^{m}$ denote the features before the last layer in the intersection mask head and the complement mask head. The rich semantic feature for the overlapping and non-overlapping region is considered as the residual information for the complex areas which is fused with $f_{k,i}^{roi}$ and then fed into the recombined mask head. See the supplementary material for details of the Fusion Unit. Noted that we reuse the Instance Mask Head $(H_{i})$ here to predict the integral instance. This combination facilitates CRM to leverage contextual information of overlapping instances, leading to the improvement of perception capability. The refined mask $\\hat{e}_{k,i}^{r}$ from CRM is optimized by segmentation loss $\\mathcal{L}_{rmask}$ ,", + "bbox": [ + 496, + 462, + 892, + 705 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {r m a s k} = \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\frac {1}{N _ {k}} \\sum_ {i = 1} ^ {N _ {k}} \\mathcal {L} _ {c e} \\left(\\hat {e} _ {k, i} ^ {r}, e _ {k, i}\\right). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 557, + 715, + 890, + 758 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To further enhance the feature representation capacity for the relationship of components, we add semantic consistency regularization between the recombination $\\hat{e}_{k,i}^{r}$ and merged predictions of $\\hat{o}_{k,i}$ and $\\hat{m}_{k,i}$ ,", + "bbox": [ + 496, + 771, + 890, + 832 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {c o n s}} = \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\frac {1}{N _ {k}} \\sum_ {i = 1} ^ {N _ {k}} \\mathcal {L} _ {\\text {c e}} \\left(\\hat {e} _ {k, i} ^ {r}, \\mathcal {F} _ {\\text {m e r g e}} \\left(\\hat {o} _ {k, i}, \\hat {m} _ {k, i}\\right)\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 508, + 845, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "15644", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{F}_{\\text{merge}}(\\cdot)$ represents the merging operation for the intersection region and the complement region in Mergence Unit, which is $xor()$ , two sub-region masks are passed through Sigmoid function for normalization. Then, we calculate the Mask Exclusive-OR of two mask logits for merging them and suppressing redundant predicted pixels.", + "bbox": [ + 75, + 90, + 472, + 183 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Mask-guided Region Proposal", + "text_level": 1, + "bbox": [ + 76, + 191, + 346, + 209 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "It is inevitable for cytology images to exist abundant cellular debris and non-target objects, e.g., white blood cells and mucus. These objects often have a similar appearance as the nuclei, with small round surfaces stained in dark purple, which increases the model identification difficulty. To avoid the interference it brings, we further propose a Mask-guided Region Proposal module (MRP) to encourage the model to generate nuclei proposals in intra-cellular regions.", + "bbox": [ + 75, + 215, + 468, + 335 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For each image, we can aggregate all the recombined instance predictions $\\hat{e}_{k,i}^{r}$ in CRM together into a semantic mask $\\hat{M}_k$ . The raw predictions are first mapped back and then summed up according to their bounding boxes predictions $\\hat{b}_{k,i}$ in the detection head, followed by a Sigmoid function to normalize them into probabilities. $\\hat{M}_k$ is considered as the attention score to re-weight features $f_{k}$ in origin FPN via element-wise multiplication:", + "bbox": [ + 75, + 337, + 472, + 464 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nf _ {k} ^ {w} = \\hat {M} _ {k} \\circ f _ {k}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 218, + 474, + 468, + 492 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $f_{k}^{w}$ denotes the re-weighted features for nuclei proposal predictions in MRP. Thus, extracellular pixels with a lower probability to be cytoplasm are suppressed, which reduces the false positives for background instances (i.e., blood, mucus, and others). In addition, MRP also builds information interaction between different stages, which naturally encourages feature representation ability.", + "bbox": [ + 75, + 503, + 468, + 609 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. End-to-end Learning", + "text_level": 1, + "bbox": [ + 76, + 619, + 276, + 636 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Extended dataset with synthetic clusters: The semitransparency characteristic of cytoplasm alleviates the effect of high overlap, allowing cytologists to delineate the contour of cellular instances based on expert knowledge. However, extremely challenging labeling and unavoidable label noise limit the availability of large-scale annotated datasets. To tackle this problem, we propose an instance-level data augmentor for overlapping cell data augmentation, which can generate large-scale synthetic cell clusters with controllable overlapping ratios and transparency based on the annotated cellular instances. This synthetic dataset further facilitates the generalization ability, by providing more diverse data to implicitly learn the concept of instance and its components. See the supplementary material for details of the synthetic pipeline. Unless otherwise specified, we do not use this synthetic dataset in the following comparison.", + "bbox": [ + 75, + 643, + 472, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Overall Loss Function: The proposed cell instance segmentation framework can be trained in a supervised manner. The overall objective $\\mathcal{L}$ is as follows,", + "bbox": [ + 498, + 90, + 890, + 137 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {\\text {c o a r s e}} + \\lambda_ {\\text {d e c}} \\mathcal {L} _ {\\text {d e c}} + \\lambda_ {\\text {r m a s k}} \\mathcal {L} _ {\\text {r m a s k}} + \\lambda_ {\\text {c o n s}} \\mathcal {L} _ {\\text {c o n s}}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 501, + 154, + 890, + 184 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{\\text{coarse}}$ denotes losses for RoI extraction and coarse mask prediction, $\\mathcal{L}_{dec}$ denotes the decomposition loss for intersection and complement regions segmentation, $\\mathcal{L}_{rmask}$ is the segmentation loss for refined masks, $\\mathcal{L}_{cons}$ supervises the semantic consistency between integral instance and subregions. $\\lambda_{dec}, \\lambda_{rmask},$ and $\\lambda_{cons}$ are trade-off parameters controlling the importance of each component.", + "bbox": [ + 498, + 185, + 892, + 291 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 311, + 633, + 329 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 500, + 338, + 689, + 356 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We evaluate our proposed DoNet in two cytology image datasets for overlapping cell instance segmentation:", + "bbox": [ + 498, + 364, + 890, + 395 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "ISBI2014 [24]: This is a widely-used dataset from Overlapping Cervical Cytology Image Segmentation Challenge1, which consists of 8 extended depth-of-focus (EDF) real cervical cytology images and corresponding synthetic images. It contains high-quality pixel-level annotations for both nuclei and cytoplasm with a resolution of $512 \\times 512$ . We follow the setting in this challenge [24] to use 45, 90 and 810 images for training, validation and testing to evaluate our proposed DoNet in a supervised setting.", + "bbox": [ + 498, + 397, + 892, + 532 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "CPS [39]: This liquid-based cytology dataset contains 137 labeled images with a resolution of $1000 \\times 1000$ . In total, it contains 4439 cytoplasm and 4789 nuclei annotations. We conduct 3-fold cross-validation on this dataset.", + "bbox": [ + 498, + 535, + 893, + 595 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation metrics: To measure the overall performance of the proposed DoNet, we utilize four commonly-used evaluation metrics in instance segmentation: aggregated Jaccard index (AJI), average Dice coefficient (Dice), F1-score (F1) [20], mean of Average Precision (mAP) [11]. In order to compare our result on the ISBI2014 with previous studies [24], we further adopt evaluation metrics including Dice, object-based false negative rate $(\\mathrm{FN}_o)$ , and pixel-based true positive rate $(\\mathrm{TP}_p)$ .", + "bbox": [ + 498, + 598, + 893, + 734 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation details: We utilize the Mask R-CNN [11] in Detector2 [36] as the baseline model. We use the ResNet-50-based FPN network in all experiments. During training, we adopt SGD with 0.9 momentum as the optimizer. We set the initial learning rate to 0.001 and add the linear warm-up in the first 1k iterations. We train the network for 60k iterations, decreasing the learning rate by a factor of 0.1 after 50k and 55k iterations.", + "bbox": [ + 498, + 737, + 893, + 857 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "1 https://cs.adelaide.edu.au/~carneiro/isbil4_challenge/index.html", + "bbox": [ + 500, + 875, + 892, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "15645", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/67351f6d2a4a2ffecdcd6c0e04085004a460451ebbd121b77c705099e79cac59.jpg", + "table_caption": [ + "Table 1. Quantitative segmentation results of DoNet and other state-of-the-art methods on CPS and ISBI2014." + ], + "table_footnote": [], + "table_body": "
MethodsISBI2014CPS
mAP↑Dice↑F1↑AJI↑mAP↑Dice↑F1↑AJI↑
Mask R-CNN [11]59.0991.1592.5477.0748.28 ± 3.1089.32 ± 0.5085.07 ± 2.0169.20 ± 2.27
Cascade R-CNN [2]62.4591.2992.5177.9147.87 ± 3.2789.24 ± 0.4483.33 ± 1.6568.86 ± 3.55
Mask Scoring R-CNN [13]63.5691.2891.8775.1448.38 ± 3.1389.39 ± 0.2482.98 ± 1.8667.45 ± 2.45
HTC [8]59.6291.3988.0875.0047.60 ± 3.5689.08 ± 0.5181.30 ± 2.5666.35 ± 2.84
Occlusion R-CNN [9]62.3591.7593.1878.6448.14 ± 2.8489.08 ± 0.2885.69 ± 2.2869.51 ± 2.45
Xiao et al. [37]57.3491.7092.7578.2948.53 ± 2.8589.29 ± 0.2485.46 ± 2.6069.37 ± 2.88
DoNet64.0292.1393.2379.0549.43 ± 3.8389.54 ± 0.2585.51 ± 2.3370.08 ± 2.84
DoNet w/ Aug.----49.65 ± 3.5289.50 ± 0.3886.30 ± 2.0170.56 ± 2.34
", + "bbox": [ + 102, + 109, + 874, + 250 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Results", + "text_level": 1, + "bbox": [ + 76, + 285, + 171, + 300 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We quantitatively compare the cell instance segmentation results from the ISBI2014 and CPS in Table 1 with state-of-the-art methods in the field of general instance segmentation (Mask R-CNN [11], Cascade R-CNN [2], Mask Scoring R-CNN [13], HTC [8]) and amodal instance segmentation (Occlusion R-CNN [9], Xiao et al. [37]). Noted that the amodal instance segmentation methods and general instance segmentation methods perform differently on two datasets due to the varying degrees of overlapping. Our method achieves the highest scores among all metrics. Specifically, it gains $2.68\\%$ and $0.52\\%$ improvements for mAP and AJI compared with the best of others [9] on the ISBI2014 dataset, as well as $1.85\\%$ and $1.02\\%$ improvements compared with the best [37] on the CPS dataset. We also evaluate $TP_{p}$ and $FN_{o}$ for DoNet to compare results against winners of the ISBI2014 challenge [27,33] and their following works [21, 31], which are mostly the segment-then-refine manners (Seen in Table 2).", + "bbox": [ + 75, + 316, + 473, + 588 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Furthermore, by introducing the synthetic clusters as instance-level augmentation, DoNet further has $0.45\\%$ and $0.68\\%$ improvements for mAP and AJI on the CPS dataset. This is mainly because the synthetic overlapping cells can further enhance the model's occlusion reasoning capability, which is consistent with the conclusions in [22].", + "bbox": [ + 75, + 595, + 470, + 686 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/bdf573bdf5439f1ab79c2ce7c30adddc0ebb10f84e3f345c0d61d8010b3f2e51.jpg", + "table_caption": [ + "Table 2. Comparison with other methods on ISBI2014." + ], + "table_footnote": [], + "table_body": "
MethodsISBI2014
Dice↑TPp↑FN0↓
Ushizima et al. [33]0.8720.8410.265
Nosrati et al. [27]0.8710.8750.110
Walter et al. [34]0.8600.8300.310
Lu et al. [24]0.8930.9050.315
Lee et al. [21]0.8970.8820.137
Tareef et al. [31]0.8980.9460.161
Chen et al. [7]0.9200.9000.020
DoNet0.9210.9480.162
", + "bbox": [ + 107, + 729, + 437, + 885 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 285, + 653, + 301 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Effects of Network Components: We perform ablation studies to investigate the effects of the different components of our proposed pipeline for DoNet. The comparison results can be seen in Table 3. By adding DRM for explicit decomposing integral instances into intersection and complement sub-regions, we observe a $3.25\\%$ increase in the average mAP of cytoplasm and nuclei on ISBI2014. However, directly adding DRM without the fusion of structural and morphological information, may mislead the model. This issue is observed in the more complex CPS dataset. To alleviate this problem, DoNet takes advantage of the decompose-and-recombined strategy by adding CRM after DRM. This strategy brings a total of $7.34\\%$ and $1.74\\%$ mAP improvements on two datasets by strengthening the model's perception of overlapping regions while preserving morphological information.", + "bbox": [ + 496, + 309, + 893, + 551 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a2cad089aac2a11a6f5e56ce3b2bef867e086488e2ca42f1a57c569d745ff696.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 513, + 566, + 602, + 637 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2bf66742e99cdb45a3a1cdb1d2c88dc7a72e150e89f1c8009452f57418c6661a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 604, + 566, + 694, + 637 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/930409e24a14aaa5f632c5b0b0f7e2374f6f3bc7c2acfe43a8a8ea1d60b8a91b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 697, + 566, + 787, + 638 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f44c4454170ec449bad6861d7f66f9764616b3cdf36ed99979f6c78aa04ae6fd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 789, + 566, + 877, + 638 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/5636e93e3201def7dc5504aa664177d7a9c2180c88813b37471483ccef8de177.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 513, + 638, + 602, + 708 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/132ab24df7d23a20086d2ab93646472d0ecf86146e49ace860d29ab4912a5a04.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 604, + 638, + 694, + 708 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/6c376490f200b5826e3caa3af15fc247572b05ce86304ad8c2da08393989906f.jpg", + "image_caption": [ + "(c)", + "Figure 3. Illustration of background noise suppression in MRP: (a) the original image, (b) the origin feature map for region proposal, (c) the attention map from cytoplasm prediction, and (d) the re-weighted feature map for nuclei proposal generation." + ], + "image_footnote": [], + "bbox": [ + 697, + 638, + 785, + 708 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/4fedc8e070c55e2ba07048ab56b12bcb9621d05637ba84469d09e84f2c15ef16.jpg", + "image_caption": [ + "(d)" + ], + "image_footnote": [], + "bbox": [ + 787, + 638, + 877, + 708 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Applying MRP for mitigating the side effects from background mimics yields a further improvement of $0.59\\%$ mAP and $0.31\\%$ mAP on ISBI2014 and CPS datasets. Figure 3 provides the visualization of MRP operation, where background instances (e.g., mucus, karyoclasis, pointed by red arrow) are suppressed with strong responses in the feature", + "bbox": [ + 496, + 809, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "15646", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/c6c4ed5b9e9b0c718f50f0885124a5efe906da488a3a72961543f5ec53bb97ee.jpg", + "table_caption": [ + "Table 3. Effect of each proposed module on CPS and ISBI2014 datasets. $\\checkmark$ denotes adding the corresponding module." + ], + "table_footnote": [], + "table_body": "
BaseDRMCRMMRPISBI2014CPS
mAP↑Dice↑F1↑AJI↑mAP↑Dice↑F1↑AJI↑
✓59.0991.1592.5477.0748.28 ± 3.1089.32 ± 0.5085.07 ± 2.0169.20 ± 2.27
✓✓61.0191.6192.8678.0648.03 ± 3.4889.13 ± 0.3084.63 ± 2.5768.56 ± 2.57
✓✓✓63.4391.8794.1679.8849.12 ± 3.2689.47 ± 0.3184.82 ± 2.7369.26 ± 2.63
✓✓✓✓64.0292.1393.2379.0549.43 ± 3.8389.54 ± 0.2585.51 ± 2.3370.08 ± 2.84
", + "bbox": [ + 99, + 104, + 870, + 189 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/2e1a93f4450a7d2feddb7eeed809c7927924fe9dbc3958b1645b884cc3ce42d9.jpg", + "table_caption": [ + "Table 4. Ablation study of DRM and CRM on the ISBI2014 dataset. $\\checkmark$ denotes adding the corresponding component or strategy." + ], + "table_footnote": [], + "table_body": "
\\(H_i\\)\\(H_o\\)\\(H_m\\)FU\\(\\mathcal{L}_{cons}\\)mAP↑Dice↑F1↑AJI↑
Cyt.Nuc.Avg.Cyt.Nuc.Avg.Cyt.Nuc.Avg.Cyt.Nuc.Avg.
✓50.7167.4659.0990.7291.5991.1586.9698.1392.5470.5583.6077.07
✓✓54.8465.9460.3991.5691.5491.5587.0097.6892.3472.0782.6777.37
✓✓✓57.4166.4961.9591.7991.5391.6688.6797.9893.3274.0083.2778.63
✓✓✓✓58.4067.8263.1192.2291.7491.9889.2198.0793.6474.9483.7079.32
✓✓✓✓✓59.3167.5663.4392.0391.7191.8790.1398.1894.1675.8683.9179.88
", + "bbox": [ + 81, + 227, + 893, + 330 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "map, encouraging the RPN to concentrate on cellular instance during nuclei region proposal.", + "bbox": [ + 75, + 367, + 468, + 398 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Design Choice for DRM: We provide detailed comparisons on the ISBI2014 dataset to demonstrate the effectiveness of different components in DRM: 1) $H_{i}$ : instance mask head for coarse segmentation only; 2) $H_{o}$ : intersection mask head for overlapping region segmentation; 3) $H_{m}$ : complement mask head for non-overlapping region segmentation;", + "bbox": [ + 75, + 402, + 468, + 494 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As seen in Table 4, adding $H_{o}$ yields an improvement of $2.20\\%$ in average mAP, with a further $2.64\\%$ gains from the additional $H_{m}$ . We notice that cytoplasm results have a more significant improvement of $13.2\\%$ in mAP, which is indeed in line with our design intent.", + "bbox": [ + 75, + 497, + 468, + 574 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Design Choice for CRM: The goal of semantic consistency regularization is to enhance the model's overlapping reasoning capability by learning the concept of recombined instances from sub-regions. We provide comparisons to demonstrate the design choice (Table 4): 1) $\\mathrm{CU} + \\mathrm{FU}$ : integration of rich semantic features as inputs via Concatenation Unit and Fusion Unit. 2) $\\mathcal{L}_{\\text{cons}}$ : consistency regularization between the recombined prediction $\\hat{e}_{k,i}^{r}$ and the fusion of sub-regions $\\hat{o}_{k,i}, \\hat{m}_{k,i}$ . As seen in Table 4, by aggregating the rich semantic feature for overlapping and non-overlapping region via Fusion Unit, we observe an increase of $1.52\\%$ average mAP on the ISBI2014 dataset. Adding consistency regularization further improves $0.91\\%$ mAP for cytoplasm.", + "bbox": [ + 75, + 578, + 468, + 790 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Figure 4 visualizes the results of the DoNet and other typical instance segmentation methods, including standard (Mask R-CNN), multi-task (DoNet w/o CRM), and amodal (Occlusion R-CNN) instance segmentation model. It demonstrates the importance of adding interaction among sub-regions via CRM and the strong perceptual capability of DoNet in overlapping regions.", + "bbox": [ + 75, + 794, + 468, + 902 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b09fe0056960c8d0ad6c0a9e364c8242fdc8f79892e84b579c1567cf4dde3a7a.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 542, + 367, + 694, + 484 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/09e7b7bc850093e4f7e29963d21d3d907d9d2fdb2761673684d5075491a7a5e2.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 697, + 367, + 851, + 484 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d7b74a07a7304ecd717b6ea08a4f40cda3d62be8688decd3a54f2c9f692dbf87.jpg", + "image_caption": [ + "(c)" + ], + "image_footnote": [], + "bbox": [ + 540, + 505, + 694, + 622 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/dd16129c8c8f28d059c83dfafcb507d127866dcb96be69beb144d57642f99434.jpg", + "image_caption": [ + "(d)", + "Figure 4. Qualitative results from (a) standard [11], (b) multitask (DoNet w/o CRM), (c) amodal [9], and (d) proposed deoverlapping instance segmentation method." + ], + "image_footnote": [], + "bbox": [ + 697, + 505, + 851, + 622 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Qualitative Analysis and Discussion", + "text_level": 1, + "bbox": [ + 500, + 722, + 808, + 739 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We visualize the heatmap of the intersection region, the complement region, and the integral instance in Figure 6. The proposed method successfully identifies sub-regions based on the overlapping concept, even in low-resolution areas with high transparency.", + "bbox": [ + 496, + 747, + 890, + 824 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Furthermore, we provide qualitative comparisons on CPS (top) and ISBI2014 (bottom) datasets in Figure 5. Our proposed DoNet outperforms other instance segmentation methods. Specifically, red rectangles provide details and highlight the main difference among these results. In the", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "15647", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/46caceede9d40b1308808bc786c999a63f21a07a16952601a70079dd09368ae1.jpg", + "image_caption": [ + "Figure 5. Qualitative results of our DoNet and other SOTA methods on CPS (top) and ISBI2014 (bottom) datasets. (a) Ground Truth; (b) Mask R-CNN [11]; (c) Occlusion R-CNN [9]; (d) Xiao et al. [37]; (e) Cascade R-CNN [2]; (f) Hybrid Task Cascade [8]; (g) Mask Scoring R-CNN [13]; (h) Our proposed DoNet." + ], + "image_footnote": [], + "bbox": [ + 80, + 90, + 890, + 424 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/83864683f617ac17ff886e8841d0900fe3b16b4be7e00ca9977bb414e0711867.jpg", + "image_caption": [ + "Figure 6. Heatmaps of the intersection region, the complement region, and the integral instance on CPS (top) and ISBI2014 (bottom) datasets, including (a) the original instance, the prediction heatmap of (b) intersection regions, (c) complement regions, and (d) the integral instance." + ], + "image_footnote": [], + "bbox": [ + 117, + 496, + 424, + 756 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "segmentation results of the CPS data, it can be seen that overlapped cells with different staining (e.g., dark red and blue) show significant appearance inconsistency between cellular sub-regions. Previous works (e.g., Mask R-CNN", + "bbox": [ + 75, + 839, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "[11] and Occlusion R-CNN [9]) with limited perceptual capability have difficulty capturing the relationship between pixels in the intersection and complement sub-regions, leading to ambiguous segmentation contours. In contrast, our DoNet can effectively distinguish different instance boundaries and can better perceive the integrality of cells. This generalized superiority is also observed in the ISBI2014 dataset with low-contrast cellular instances.", + "bbox": [ + 498, + 496, + 890, + 618 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 631, + 617, + 645 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose a de-overlapping network (DoNet) to address the overlapping challenges in cytology instance segmentation. The proposed DoNet enhances the model's perception of overlapping regions by implicitly and explicitly modeling the interaction between cellular regions and the integral instance. Extensive experiments reveal the superiorities of the proposed DoNet, which not only provides immense potential for overlapping object perception in the medical domain but also occluded instance segmentation in general vision application scenarios.", + "bbox": [ + 496, + 657, + 890, + 808 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 500, + 821, + 660, + 838 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported by National Natural Science Foundation of China (No. 62202403) and Beijing Institute of Collaborative Innovation Program (No. BICI22EG01).", + "bbox": [ + 496, + 845, + 890, + 892 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "15648", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Seunghyeok Back, Joosoon Lee, Taewon Kim, Sangjun Noh, Raeyoung Kang, Seongho Bak, and Kyoobin Lee. 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Springer, 2019. 1, 2" + ], + "bbox": [ + 501, + 90, + 890, + 244 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "15650", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/DoNet_ Deep De-Overlapping Network for Cytology Instance Segmentation/6ce3e51d-a82a-47f1-b18c-a1b3922a9d7f_model.json b/2023/DoNet_ Deep De-Overlapping Network for Cytology Instance Segmentation/6ce3e51d-a82a-47f1-b18c-a1b3922a9d7f_model.json new file mode 100644 index 0000000000000000000000000000000000000000..692abf72aaf46f73f55ec89c66f80d9d21878077 --- /dev/null +++ b/2023/DoNet_ Deep De-Overlapping Network for Cytology Instance Segmentation/6ce3e51d-a82a-47f1-b18c-a1b3922a9d7f_model.json @@ -0,0 +1,2013 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.109, + 0.131, + 0.862, + 0.154 + ], + "angle": 0, + "content": "DoNet: Deep De-overlapping Network for Cytology Instance Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.106, + 0.18, + 0.87, + 0.218 + ], + "angle": 0, + "content": "Hao Jiang\\(^{1*}\\) Rushan Zhang\\(^{1*}\\) Yanning Zhou\\(^{2}\\) Yumeng Wang\\(^{1}\\) Hao Chen\\(^{1\\dagger}\\) \n\\(^{1}\\)The Hong Kong University of Science and Technology \n\\(^{2}\\)Tencent AI Lab" + }, + { + "type": "text", + "bbox": [ + 0.151, + 0.22, + 0.819, + 0.234 + ], + "angle": 0, + "content": "{hjiangaz, jhc}@cse.ust.hk, {rzhangbq,ywanglu}@connect.ust.hk, amandayzhou@tencent.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.302, + 0.474, + 0.605 + ], + "angle": 0, + "content": "Cell instance segmentation in cytology images has significant importance for biology analysis and cancer screening, while remains challenging due to 1) the extensive overlapping translucent cell clusters that cause the ambiguous boundaries, and 2) the confusion of mimics and debris as nuclei. In this work, we proposed a De-overlapping Network (DoNet) in a decompose-and-recombined strategy. A Dual-path Region Segmentation Module (DRM) explicitly decomposes the cell clusters into intersection and complement regions, followed by a Semantic Consistency-guided Recombination Module (CRM) for integration. To further introduce the containment relationship of the nucleus in the cytoplasm, we design a Mask-guided Region Proposal Strategy (MRP) that integrates the cell attention maps for inner-cell instance prediction. We validate the proposed approach on ISBI2014 and CPS datasets. Experiments show that our proposed DoNet significantly outperforms other state-of-the-art (SOTA) cell instance segmentation methods. The code is available at https://github.com/DeepDoNet/DoNet." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.638, + 0.21, + 0.654 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.664, + 0.47, + 0.862 + ], + "angle": 0, + "content": "Cytology image has been essential for cancer screening and earlier diagnosis, such as qualitative and quantitative identification of cellular morphology, nuclei size, nuclear-cytoplasmic ratio, and other cytological features [12, 15, 25]. However, examining tens of thousands of cells under the microscope visually is inherently tedious and suffers from inter-/intra-observer variability. Computational techniques enable efficient and accurate characterization of cells from cytology images [12, 16]. Among all computational techniques, cell segmentation has been a fundamental and widely-studied task, since the acquisition of cell-level identification is a pre-requisition for further assessment and analysis [3, 23]." + }, + { + "type": "image", + "bbox": [ + 0.532, + 0.268, + 0.862, + 0.459 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.467, + 0.895, + 0.523 + ], + "angle": 0, + "content": "Figure 1. The schematic illustration of proposed DoNet with decompose-and-recombined strategy, which maps each overlapping cell into the intersection, complement, and instance layers to address the overlapping issue in cytology instance segmentation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.552, + 0.893, + 0.884 + ], + "angle": 0, + "content": "Deep Learning (DL) methods show promising results for cell-nuclei segmentation in the histopathology image [5,6,14,17]. However, cytology segmentation remains challenging for the following two reasons. Firstly, cells in a cytology image are prone to cluster with each other, leading to the overlapping issue. In the cytology images, the translucent cytoplasm of the cell (seen in Figure 1) tends to occlude each other with low contrast staining, leading to ambiguous cellular boundary predictions. This phenomenon is particularly evident in cervical cell images. Secondly, hard mimics, are widespread in the background, along with other technical artefacts such as bubbles, which could mislead the instance segmentation models [4]. Take the cervical cell image as an example, the widespread white blood cells and mucus stains lead to false predictions for nuclei. To address these challenges, several works [24, 33] propose the segment-then-refine paradigm, while others [39, 40] utilize the detection-based framework, e.g., Mask R-CNN [11]. However, they fail to model the interaction between intersection and complement sub-regions within the translucent cell cluster explicitly, resulting in a limited understanding of cross-region relationships." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.886, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Amodal instance segmentation tackles the occlusion" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.875, + 0.204, + 0.888 + ], + "angle": 0, + "content": "*Equal contribution" + }, + { + "type": "page_footnote", + "bbox": [ + 0.098, + 0.888, + 0.22, + 0.9 + ], + "angle": 0, + "content": "† Corresponding author" + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.875, + 0.22, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "15641" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.318 + ], + "angle": 0, + "content": "problem by inferring the integral object based on the partially visible region [22]. Based on the fact that humans can infer the occluded region of an object despite the ambiguity, these methods attempt to learn the integrated object mask (amodal mask) for better occlusion reasoning capability [9, 37] via synthesizing occluded data label pairs and aggregating global information to enhance perceptual ability. Compared to natural scenes, cell instances in cytology images are mostly semi-transparent. Therefore, an occlusion (overlapping) region exits in both the occluding and occluded instances. However, treating semi-transparent overlapping regions as general occlusion regions is not optimal, since they have different appearances compared to non-overlapping regions, and could in fact provide richer shape information than general occlusion regions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.319, + 0.473, + 0.47 + ], + "angle": 0, + "content": "Motivated by the amodal perception, we propose a decompose-and-recombine strategy for translucent cell instance segmentation, named De-overlapping Network (DoNet). Figure 1 provides the schematic diagram. For each cell cluster with more than one cellular sub-region, DoNet starts from implicitly learning the hidden interaction of sub-regions by predicting instance masks from clusters. Then, it explicitly models the components and their relationships via the intersection layer, complement layer, and instance layer, to enhance its perceptual capability." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.47, + 0.473, + 0.651 + ], + "angle": 0, + "content": "Initially, we adopt Mask R-CNN to get the coarse predictions, followed by a novel Dual-path Region segmentation Module (DRM) that combines features and coarse masks from the first stage to decompose cell clusters into intersection and complement sub-regions. Then, the semantic Consistency-guided Recombination Module (CRM) is designed to encourage consistency between the refined instances and integral sub-region predictions. Furthermore, to impose the morphological constraint that nuclei stay inside the cellular regions, we propose a Mask-guided Region Proposal Module (MRP) to encourage the model to focus on the intra-cellular area during nuclei segmentation." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.652, + 0.449, + 0.666 + ], + "angle": 0, + "content": "The overall contributions are summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.678, + 0.47, + 0.8 + ], + "angle": 0, + "content": "- A novel de-overlapping network for cell instance segmentation with a decompose-and-recombined strategy, decomposing the cell regions with the DRM, as well as implicitly and explicitly modeling the semantic relationship between intersection, complement, and instance (cell) components via the CRM. These designs equip the network with enhanced perceptual capability in overlapping cellular sub-regions." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.81, + 0.471, + 0.902 + ], + "angle": 0, + "content": "- A mask-guided region proposal module (MRP) that leverages the cytoplasm attention map for the intracellular nuclei refinement, which imposes the biology prior of cellular instances into the module, effectively mitigating the influence of mimickers widespread in the background." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.678, + 0.471, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.092, + 0.892, + 0.168 + ], + "angle": 0, + "content": "- Extensive experiments on two overlapping cytology image segmentation datasets, namely ISBI2014 [24] and CPS [39], demonstrating that our proposed DoNet outperforms other state-of-the-art (SOTA) methods by a large margin." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.193, + 0.642, + 0.21 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.219, + 0.892, + 0.355 + ], + "angle": 0, + "content": "Cytology Instance Segmentation: Challenges such as cell clustering, hard mimics, and semi-transparent overlapping cytoplasm regions pose in the segmentation of cellular instance (e.g., cell, nuclei, cytoplasm) from cytology images. These challenges inspired numerous insightful works, especially after the publication of ISBI2014 [33]. Two mainstream approaches are proposed to tackle the overlapping cell segmentation challenge: the segment-then-refine stream and the end-to-end training stream." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.356, + 0.893, + 0.552 + ], + "angle": 0, + "content": "Early approaches tackling this challenge are primarily the combination of pixel-level segmentation models and additional post-processing techniques, such as seeded watershed algorithm [19], random walk [38], conditional random field algorithms [35], and star-convex parameterization [34]. To further improve the segmentation performance, some other methods introduce morphological prior. Song et al. design a dynamic multi-template deformation model, which leverages case-specific shape constraints to guide the inference of overlapping cell boundaries [30]. Tareef et al. propose to refine cytoplasm boundary via a learnable shape prior, which is dynamically modeled as the fusion of shape templates [32]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.553, + 0.892, + 0.718 + ], + "angle": 0, + "content": "Escaping from the complex post-processing procedure, many later works turn to end-to-end training. These approaches typically adopt Mask R-CNN as their baseline. The first attempt following this approach was [29], a model for nuclear instance segmentation from liquid-based cytology smears. Based on the appearance similarity between different cells, Zhou et al. propose the IRNet to explore instance relation during overlapping cervical cell segmentation [40]. To leverage information from unlabeled data, Zhou et al. provide a mean-teacher-based semi-supervised learning scheme, MMT-PSM [39]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.719, + 0.892, + 0.825 + ], + "angle": 0, + "content": "The above two methods have achieved notable performance improvements, yet still lack the necessary perceptual capability for overlapping regions, leading to sub-optimal results, i.e., ambiguous cell boundaries. In this study, we propose a de-overlapping network, named DoNet, to implicitly and explicitly model the interaction between the integral instance and its sub-regions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Occluded Instance Segmentation: Instance segmentation, a typical task in computer vision, refers to the inference of bounding boxes and instance segmentation masks. Most notable approaches follow the detect-then-segment paradigm, such as Mask R-CNN [11] and its following variants [2, 13]." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "15642" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.085, + 0.092, + 0.887, + 0.405 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.418, + 0.895, + 0.463 + ], + "angle": 0, + "content": "Figure 2. The flowchart of the proposed DoNet. It consists of four main parts: (1) baseline for coarse mask segmentation; (2) DRM to simultaneously regress intersection and complement regions which provides cues for final mask refinement; (3) CRM to explicitly refine the final mask and encourage the semantic consistency; (4) MRP to mitigate the effect of background noise." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.487, + 0.473, + 0.669 + ], + "angle": 0, + "content": "However, these approaches could not handle the occlusion problem, common in visual application scenarios like robotic manipulations, scene parsing, and autonomous driving [1, 10]. Due to the inconsistencies within a Regions of Interest (RoI), these models suffer from the limited perceptual capability, leading to ambiguous segmentation boundaries. To tackle this issue, a specific task, occluded instance segmentation aims at leveraging visible regions to perceive the entirety of the occluded instance accurately. This capability of inferring and reasoning occluded objects is defined as amodal perception [9], thus occluded instance segmentation is also called amodal instance segmentation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.675, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Research on amodal instance segmentation starts from [22], which poses this challenging task and gives a synthesis-based solution. In this work, the first amodal instance segmentation dataset, the COCOA dataset, is established based on the COCO dataset. Afterward, some notable solutions accomplish this task and achieve state-of-the-art performance. Previous approaches tackle this challenge by leveraging information from visible instance segmentation, then inferring the amodal mask [1,9]. For example, Occlusion R-CNN (ORCNN) is built on R-CNN with two mask heads, the visible mask head, and the amodal mask head, which directly predict the amodal mask and the visible mask, inferring the visible mask through the subtraction of these two masks [9]. Qi et al. [28] perform amodal instance segmentation with multi-level coding and establish" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.487, + 0.892, + 0.622 + ], + "angle": 0, + "content": "a large-scale amodal instance segmentation dataset. Xiao et al. [37] leverage shape prior knowledge to infer amodal mask using memory codebook. Some other models, like BCNet [18] abandon the visible instance prediction based manner and directly models the relationship between the occluder and the occludee. To address the lack of amodal mask ground truth, ASBU [26] introduces a weakly supervised amodal segmenter, which generates pseudo-ground truth by boundary uncertainty estimation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.623, + 0.892, + 0.744 + ], + "angle": 0, + "content": "Essentially, the above occluded instance segmentation methods aim to enhance the amodal perception and reasoning capability, inspiring us to explore the interaction between instance sub-regions and the integral instance. Compared to amodal segmentation, whose focus on inferring the invisible region from the partially visible regions, our focus is to resolve the inconsistency between the intersection and complement regions." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.757, + 0.637, + 0.775 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.782, + 0.611, + 0.797 + ], + "angle": 0, + "content": "3.1. Overview" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.805, + 0.895, + 0.905 + ], + "angle": 0, + "content": "Problem formulation: Following the setting of cell instance segmentation, we are provided with a dataset with \\(K\\) images and the corresponding annotations \\(\\mathcal{D} = \\{(\\mathcal{X}_k,\\mathcal{Y}_k)\\}_{k = 1}^K\\), each of which contains annotations of bounding boxes \\(\\mathcal{B}_k = \\{b_{k,i}\\}_{i = 1}^{N_k}\\), object categories \\(\\mathcal{C}_k = \\{c_{k,i}\\}_{i = 1}^{N_k}\\), and instance masks \\(\\mathcal{E}_k = \\{e_{k,i}\\}_{i = 1}^{N_k}\\), where \\(N_{k}\\)" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15643" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.215 + ], + "angle": 0, + "content": "denotes the number of instances in the \\(k\\)-th image. Here, we focus on segmenting the nucleus and cytoplasm for cell instance \\(c_{k,i} \\in \\{\\text{nuclei}, \\text{cytoplasm}\\}\\). For each cell cluster, based on the localization relationship among the cells, we decompose the instance mask into the intersection region \\(\\mathcal{O}_k = \\{o_{k,i}\\}_{i=1}^{N_k}\\) and the complement region \\(\\mathcal{M}_k = \\{m_{k,i}\\}_{i=1}^{N_k}\\) via the logical operation (see in Figure 1), which is used to model their relationship in the DoNet." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.216, + 0.471, + 0.456 + ], + "angle": 0, + "content": "**Workflow:** The flowchart of the proposed DoNet is provided in Figure 2. It takes Mask R-CNN [11] as the base model, followed by a Dual-path Region segmentation Module (DRM) which takes the instance features as input to predict intersection regions \\(\\hat{o}_{k,i}\\) and complement regions \\(\\hat{m}_{k,i}\\) of cytoplasm via the intersection and complement layers (Section 3.2). After decomposing cell clusters according to the position relationship, a Consistency-guided Recombination Module (CRM) takes instance features from DRM and RoIAlign layer to generate the recombined masks \\(\\hat{e}_{k,i}^{r}\\) for consistency regularization (Section 3.2). Then, the recombined cytoplasm prediction is utilized as prior knowledge for intra-cellular object prediction throughout the Mask-guided Region Proposal (MRP) (Section 3.3). We will present the details of our framework in the following sections." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.458, + 0.471, + 0.734 + ], + "angle": 0, + "content": "Coarse Mask Segmentation: Previous research works on Mask R-CNN has shown competitive performance in instance segmentation [9, 11, 13], adopted into the proposed DoNet for coarse mask segmentation. Mask R-CNN consists of two stages. The first stage utilizes Feature Pyramid Network (FPN) for feature extraction and a Region Proposal Network (RPN) for candidate object bounding boxes generation. The second stage generates Region-of-Interest (RoI) features \\( f_{k,i}^{roi} \\) via the RoIAngle layer and predicts object classes \\( \\hat{c}_{k,i} \\) and bounding boxes \\( \\hat{b}_{k,i} \\) from the detection head, and semantic masks \\( \\hat{e}_{k,i}^{c} \\) from the Instance Mask Head \\( (H_{i}) \\), respectively. Due to limited perception capability in overlapping regions, \\( \\hat{e}_{k,i}^{c} \\) may contain ambiguous boundaries. Thus, we denote \\( \\hat{e}_{k,i}^{c} \\) as the coarse mask, which provides information for sub-region decomposition in DRM and suppresses the interference from background mimics. Following standard losses in [11], a multi-task loss \\( \\mathcal{L}_{\\text{coarse}} \\) for coarse mask segmentation is formed as," + }, + { + "type": "equation", + "bbox": [ + 0.158, + 0.747, + 0.469, + 0.763 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {c o a r s e}} = \\mathcal {L} _ {\\text {r e g}} + \\mathcal {L} _ {\\text {c l s}} + \\mathcal {L} _ {\\text {c m a s k}}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.775, + 0.469, + 0.835 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{reg}\\) denotes the smooth-L1 loss for bounding box regression, \\(\\mathcal{L}_{cls}\\) denotes cross-entropy (CE) loss for classification, and \\(\\mathcal{L}_{cmask}\\) denotes pixel-wise CE loss for segmentation." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.847, + 0.402, + 0.865 + ], + "angle": 0, + "content": "3.2. Decompose-and-recombined Strategy" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.902 + ], + "angle": 0, + "content": "Previous solutions for amodal perception infer the integral structure of occluded instances using visible regions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.182 + ], + "angle": 0, + "content": "[9, 37]. However, they ignore information from overlapping regions, which tend to be sub-optimal in the case of complex superposition of translucent objects. To empower the perception capability of model for overlapping translucent regions, we specifically design the decompose-and-recombined strategy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.183, + 0.893, + 0.395 + ], + "angle": 0, + "content": "Dual-path Region Segmentation Module (DRM): As shown in Figure 2, DRM consists of an Intersection Mask Head \\( H_{o} \\) and a Complement Mask Head \\( H_{m} \\) with the same architecture. Let \\( f_{k,i}^{c} \\) denotes the rich semantic feature before the coarse mask prediction in the Instance Mask Head. Both \\( H_{o} \\) and \\( H_{m} \\) take the concatenation of \\( f_{k,i}^{roi} \\) and \\( f_{k,i}^{c} \\) as input to predict the intersection and complement regions \\( \\hat{o}_{k,i}, \\hat{m}_{k,i} \\) in clusters. See the supplementary material for details of the Concatenation Unit. Specifically, each head consists of 4 convolutional layers to generate features in \\( 14 \\times 14 \\times 256 \\), followed by one deconvolutional layer to get the semantic mask with a resolution of \\( 28 \\times 28 \\times 1 \\). Here, we add the pixel-wise CE loss to both heads as the explicit constraint for decomposition," + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.407, + 0.896, + 0.462 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {d e c} = \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\frac {1}{N _ {k}} \\sum_ {i = 1} ^ {N _ {k}} \\left(\\mathcal {L} _ {c e} \\left(\\hat {o} _ {k, i}, o _ {k, i}\\right) + \\mathcal {L} _ {c e} \\left(\\hat {m} _ {k, i}, m _ {k, i}\\right)\\right). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.463, + 0.893, + 0.706 + ], + "angle": 0, + "content": "Semantic Consistency-guided Recombination Module (CRM): To further enhance the perception capability for overlapping instances, CRM is designed to encourage DoNet to perceive integral instances. Specifically, let \\( f_{k,i}^{o} \\) and \\( f_{k,i}^{m} \\) denote the features before the last layer in the intersection mask head and the complement mask head. The rich semantic feature for the overlapping and non-overlapping region is considered as the residual information for the complex areas which is fused with \\( f_{k,i}^{roi} \\) and then fed into the recombined mask head. See the supplementary material for details of the Fusion Unit. Noted that we reuse the Instance Mask Head \\( (H_{i}) \\) here to predict the integral instance. This combination facilitates CRM to leverage contextual information of overlapping instances, leading to the improvement of perception capability. The refined mask \\( \\hat{e}_{k,i}^{r} \\) from CRM is optimized by segmentation loss \\( \\mathcal{L}_{rmask} \\)," + }, + { + "type": "equation", + "bbox": [ + 0.558, + 0.717, + 0.892, + 0.76 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {r m a s k} = \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\frac {1}{N _ {k}} \\sum_ {i = 1} ^ {N _ {k}} \\mathcal {L} _ {c e} \\left(\\hat {e} _ {k, i} ^ {r}, e _ {k, i}\\right). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.772, + 0.892, + 0.833 + ], + "angle": 0, + "content": "To further enhance the feature representation capacity for the relationship of components, we add semantic consistency regularization between the recombination \\(\\hat{e}_{k,i}^{r}\\) and merged predictions of \\(\\hat{o}_{k,i}\\) and \\(\\hat{m}_{k,i}\\)," + }, + { + "type": "equation", + "bbox": [ + 0.509, + 0.846, + 0.892, + 0.901 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {c o n s}} = \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\frac {1}{N _ {k}} \\sum_ {i = 1} ^ {N _ {k}} \\mathcal {L} _ {\\text {c e}} \\left(\\hat {e} _ {k, i} ^ {r}, \\mathcal {F} _ {\\text {m e r g e}} \\left(\\hat {o} _ {k, i}, \\hat {m} _ {k, i}\\right)\\right), \\tag {4}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15644" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.473, + 0.184 + ], + "angle": 0, + "content": "where \\(\\mathcal{F}_{\\text{merge}}(\\cdot)\\) represents the merging operation for the intersection region and the complement region in Mergence Unit, which is \\(xor()\\), two sub-region masks are passed through Sigmoid function for normalization. Then, we calculate the Mask Exclusive-OR of two mask logits for merging them and suppressing redundant predicted pixels." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.192, + 0.347, + 0.21 + ], + "angle": 0, + "content": "3.3. Mask-guided Region Proposal" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.216, + 0.47, + 0.337 + ], + "angle": 0, + "content": "It is inevitable for cytology images to exist abundant cellular debris and non-target objects, e.g., white blood cells and mucus. These objects often have a similar appearance as the nuclei, with small round surfaces stained in dark purple, which increases the model identification difficulty. To avoid the interference it brings, we further propose a Mask-guided Region Proposal module (MRP) to encourage the model to generate nuclei proposals in intra-cellular regions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.338, + 0.473, + 0.465 + ], + "angle": 0, + "content": "For each image, we can aggregate all the recombined instance predictions \\(\\hat{e}_{k,i}^{r}\\) in CRM together into a semantic mask \\(\\hat{M}_k\\). The raw predictions are first mapped back and then summed up according to their bounding boxes predictions \\(\\hat{b}_{k,i}\\) in the detection head, followed by a Sigmoid function to normalize them into probabilities. \\(\\hat{M}_k\\) is considered as the attention score to re-weight features \\(f_{k}\\) in origin FPN via element-wise multiplication:" + }, + { + "type": "equation", + "bbox": [ + 0.22, + 0.475, + 0.47, + 0.493 + ], + "angle": 0, + "content": "\\[\nf _ {k} ^ {w} = \\hat {M} _ {k} \\circ f _ {k}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.504, + 0.47, + 0.611 + ], + "angle": 0, + "content": "where \\( f_{k}^{w} \\) denotes the re-weighted features for nuclei proposal predictions in MRP. Thus, extracellular pixels with a lower probability to be cytoplasm are suppressed, which reduces the false positives for background instances (i.e., blood, mucus, and others). In addition, MRP also builds information interaction between different stages, which naturally encourages feature representation ability." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.621, + 0.277, + 0.637 + ], + "angle": 0, + "content": "3.4. End-to-end Learning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.644, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Extended dataset with synthetic clusters: The semitransparency characteristic of cytoplasm alleviates the effect of high overlap, allowing cytologists to delineate the contour of cellular instances based on expert knowledge. However, extremely challenging labeling and unavoidable label noise limit the availability of large-scale annotated datasets. To tackle this problem, we propose an instance-level data augmentor for overlapping cell data augmentation, which can generate large-scale synthetic cell clusters with controllable overlapping ratios and transparency based on the annotated cellular instances. This synthetic dataset further facilitates the generalization ability, by providing more diverse data to implicitly learn the concept of instance and its components. See the supplementary material for details of the synthetic pipeline. Unless otherwise specified, we do not use this synthetic dataset in the following comparison." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.138 + ], + "angle": 0, + "content": "Overall Loss Function: The proposed cell instance segmentation framework can be trained in a supervised manner. The overall objective \\(\\mathcal{L}\\) is as follows," + }, + { + "type": "equation", + "bbox": [ + 0.502, + 0.155, + 0.892, + 0.185 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {\\text {c o a r s e}} + \\lambda_ {\\text {d e c}} \\mathcal {L} _ {\\text {d e c}} + \\lambda_ {\\text {r m a s k}} \\mathcal {L} _ {\\text {r m a s k}} + \\lambda_ {\\text {c o n s}} \\mathcal {L} _ {\\text {c o n s}}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.186, + 0.893, + 0.292 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{\\text{coarse}}\\) denotes losses for RoI extraction and coarse mask prediction, \\(\\mathcal{L}_{dec}\\) denotes the decomposition loss for intersection and complement regions segmentation, \\(\\mathcal{L}_{rmask}\\) is the segmentation loss for refined masks, \\(\\mathcal{L}_{cons}\\) supervises the semantic consistency between integral instance and subregions. \\(\\lambda_{dec}, \\lambda_{rmask},\\) and \\(\\lambda_{cons}\\) are trade-off parameters controlling the importance of each component." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.312, + 0.634, + 0.33 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.339, + 0.691, + 0.357 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.365, + 0.892, + 0.396 + ], + "angle": 0, + "content": "We evaluate our proposed DoNet in two cytology image datasets for overlapping cell instance segmentation:" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.398, + 0.893, + 0.534 + ], + "angle": 0, + "content": "ISBI2014 [24]: This is a widely-used dataset from Overlapping Cervical Cytology Image Segmentation Challenge1, which consists of 8 extended depth-of-focus (EDF) real cervical cytology images and corresponding synthetic images. It contains high-quality pixel-level annotations for both nuclei and cytoplasm with a resolution of \\(512 \\times 512\\). We follow the setting in this challenge [24] to use 45, 90 and 810 images for training, validation and testing to evaluate our proposed DoNet in a supervised setting." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.536, + 0.894, + 0.597 + ], + "angle": 0, + "content": "CPS [39]: This liquid-based cytology dataset contains 137 labeled images with a resolution of \\(1000 \\times 1000\\). In total, it contains 4439 cytoplasm and 4789 nuclei annotations. We conduct 3-fold cross-validation on this dataset." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.599, + 0.894, + 0.736 + ], + "angle": 0, + "content": "Evaluation metrics: To measure the overall performance of the proposed DoNet, we utilize four commonly-used evaluation metrics in instance segmentation: aggregated Jaccard index (AJI), average Dice coefficient (Dice), F1-score (F1) [20], mean of Average Precision (mAP) [11]. In order to compare our result on the ISBI2014 with previous studies [24], we further adopt evaluation metrics including Dice, object-based false negative rate \\((\\mathrm{FN}_o)\\), and pixel-based true positive rate \\((\\mathrm{TP}_p)\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.738, + 0.894, + 0.858 + ], + "angle": 0, + "content": "Implementation details: We utilize the Mask R-CNN [11] in Detector2 [36] as the baseline model. We use the ResNet-50-based FPN network in all experiments. During training, we adopt SGD with 0.9 momentum as the optimizer. We set the initial learning rate to 0.001 and add the linear warm-up in the first 1k iterations. We train the network for 60k iterations, decreasing the learning rate by a factor of 0.1 after 50k and 55k iterations." + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.875, + 0.893, + 0.901 + ], + "angle": 0, + "content": "1 https://cs.adelaide.edu.au/~carneiro/isbil4_challenge/index.html" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15645" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.16, + 0.089, + 0.812, + 0.104 + ], + "angle": 0, + "content": "Table 1. Quantitative segmentation results of DoNet and other state-of-the-art methods on CPS and ISBI2014." + }, + { + "type": "table", + "bbox": [ + 0.104, + 0.11, + 0.875, + 0.25 + ], + "angle": 0, + "content": "
MethodsISBI2014CPS
mAP↑Dice↑F1↑AJI↑mAP↑Dice↑F1↑AJI↑
Mask R-CNN [11]59.0991.1592.5477.0748.28 ± 3.1089.32 ± 0.5085.07 ± 2.0169.20 ± 2.27
Cascade R-CNN [2]62.4591.2992.5177.9147.87 ± 3.2789.24 ± 0.4483.33 ± 1.6568.86 ± 3.55
Mask Scoring R-CNN [13]63.5691.2891.8775.1448.38 ± 3.1389.39 ± 0.2482.98 ± 1.8667.45 ± 2.45
HTC [8]59.6291.3988.0875.0047.60 ± 3.5689.08 ± 0.5181.30 ± 2.5666.35 ± 2.84
Occlusion R-CNN [9]62.3591.7593.1878.6448.14 ± 2.8489.08 ± 0.2885.69 ± 2.2869.51 ± 2.45
Xiao et al. [37]57.3491.7092.7578.2948.53 ± 2.8589.29 ± 0.2485.46 ± 2.6069.37 ± 2.88
DoNet64.0292.1393.2379.0549.43 ± 3.8389.54 ± 0.2585.51 ± 2.3370.08 ± 2.84
DoNet w/ Aug.----49.65 ± 3.5289.50 ± 0.3886.30 ± 2.0170.56 ± 2.34
" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.286, + 0.172, + 0.301 + ], + "angle": 0, + "content": "4.2. Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.317, + 0.474, + 0.589 + ], + "angle": 0, + "content": "We quantitatively compare the cell instance segmentation results from the ISBI2014 and CPS in Table 1 with state-of-the-art methods in the field of general instance segmentation (Mask R-CNN [11], Cascade R-CNN [2], Mask Scoring R-CNN [13], HTC [8]) and amodal instance segmentation (Occlusion R-CNN [9], Xiao et al. [37]). Noted that the amodal instance segmentation methods and general instance segmentation methods perform differently on two datasets due to the varying degrees of overlapping. Our method achieves the highest scores among all metrics. Specifically, it gains \\(2.68\\%\\) and \\(0.52\\%\\) improvements for mAP and AJI compared with the best of others [9] on the ISBI2014 dataset, as well as \\(1.85\\%\\) and \\(1.02\\%\\) improvements compared with the best [37] on the CPS dataset. We also evaluate \\(TP_{p}\\) and \\(FN_{o}\\) for DoNet to compare results against winners of the ISBI2014 challenge [27,33] and their following works [21, 31], which are mostly the segment-then-refine manners (Seen in Table 2)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.596, + 0.471, + 0.687 + ], + "angle": 0, + "content": "Furthermore, by introducing the synthetic clusters as instance-level augmentation, DoNet further has \\(0.45\\%\\) and \\(0.68\\%\\) improvements for mAP and AJI on the CPS dataset. This is mainly because the synthetic overlapping cells can further enhance the model's occlusion reasoning capability, which is consistent with the conclusions in [22]." + }, + { + "type": "table_caption", + "bbox": [ + 0.109, + 0.705, + 0.438, + 0.719 + ], + "angle": 0, + "content": "Table 2. Comparison with other methods on ISBI2014." + }, + { + "type": "table", + "bbox": [ + 0.109, + 0.73, + 0.438, + 0.886 + ], + "angle": 0, + "content": "
MethodsISBI2014
Dice↑TPp↑FN0↓
Ushizima et al. [33]0.8720.8410.265
Nosrati et al. [27]0.8710.8750.110
Walter et al. [34]0.8600.8300.310
Lu et al. [24]0.8930.9050.315
Lee et al. [21]0.8970.8820.137
Tareef et al. [31]0.8980.9460.161
Chen et al. [7]0.9200.9000.020
DoNet0.9210.9480.162
" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.286, + 0.655, + 0.303 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.31, + 0.895, + 0.553 + ], + "angle": 0, + "content": "Effects of Network Components: We perform ablation studies to investigate the effects of the different components of our proposed pipeline for DoNet. The comparison results can be seen in Table 3. By adding DRM for explicit decomposing integral instances into intersection and complement sub-regions, we observe a \\(3.25\\%\\) increase in the average mAP of cytoplasm and nuclei on ISBI2014. However, directly adding DRM without the fusion of structural and morphological information, may mislead the model. This issue is observed in the more complex CPS dataset. To alleviate this problem, DoNet takes advantage of the decompose-and-recombined strategy by adding CRM after DRM. This strategy brings a total of \\(7.34\\%\\) and \\(1.74\\%\\) mAP improvements on two datasets by strengthening the model's perception of overlapping regions while preserving morphological information." + }, + { + "type": "image", + "bbox": [ + 0.514, + 0.568, + 0.603, + 0.638 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.606, + 0.568, + 0.696, + 0.638 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.698, + 0.568, + 0.788, + 0.639 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.79, + 0.568, + 0.879, + 0.639 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.514, + 0.639, + 0.603, + 0.709 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.606, + 0.639, + 0.696, + 0.709 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.698, + 0.639, + 0.787, + 0.709 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.789, + 0.639, + 0.879, + 0.709 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.553, + 0.713, + 0.567, + 0.723 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image_caption", + "bbox": [ + 0.64, + 0.712, + 0.655, + 0.723 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.735, + 0.713, + 0.748, + 0.723 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image_caption", + "bbox": [ + 0.828, + 0.713, + 0.842, + 0.723 + ], + "angle": 0, + "content": "(d)" + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.736, + 0.894, + 0.793 + ], + "angle": 0, + "content": "Figure 3. Illustration of background noise suppression in MRP: (a) the original image, (b) the origin feature map for region proposal, (c) the attention map from cytoplasm prediction, and (d) the re-weighted feature map for nuclei proposal generation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Applying MRP for mitigating the side effects from background mimics yields a further improvement of \\(0.59\\%\\) mAP and \\(0.31\\%\\) mAP on ISBI2014 and CPS datasets. Figure 3 provides the visualization of MRP operation, where background instances (e.g., mucus, karyoclasis, pointed by red arrow) are suppressed with strong responses in the feature" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "15646" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.136, + 0.08, + 0.832, + 0.096 + ], + "angle": 0, + "content": "Table 3. Effect of each proposed module on CPS and ISBI2014 datasets. \\( \\checkmark \\) denotes adding the corresponding module." + }, + { + "type": "table", + "bbox": [ + 0.101, + 0.106, + 0.871, + 0.19 + ], + "angle": 0, + "content": "
BaseDRMCRMMRPISBI2014CPS
mAP↑Dice↑F1↑AJI↑mAP↑Dice↑F1↑AJI↑
✓59.0991.1592.5477.0748.28 ± 3.1089.32 ± 0.5085.07 ± 2.0169.20 ± 2.27
✓✓61.0191.6192.8678.0648.03 ± 3.4889.13 ± 0.3084.63 ± 2.5768.56 ± 2.57
✓✓✓63.4391.8794.1679.8849.12 ± 3.2689.47 ± 0.3184.82 ± 2.7369.26 ± 2.63
✓✓✓✓64.0292.1393.2379.0549.43 ± 3.8389.54 ± 0.2585.51 ± 2.3370.08 ± 2.84
" + }, + { + "type": "table_caption", + "bbox": [ + 0.107, + 0.202, + 0.86, + 0.217 + ], + "angle": 0, + "content": "Table 4. Ablation study of DRM and CRM on the ISBI2014 dataset. \\( \\checkmark \\) denotes adding the corresponding component or strategy." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.228, + 0.895, + 0.332 + ], + "angle": 0, + "content": "
\\(H_i\\)\\(H_o\\)\\(H_m\\)FU\\(\\mathcal{L}_{cons}\\)mAP↑Dice↑F1↑AJI↑
Cyt.Nuc.Avg.Cyt.Nuc.Avg.Cyt.Nuc.Avg.Cyt.Nuc.Avg.
✓50.7167.4659.0990.7291.5991.1586.9698.1392.5470.5583.6077.07
✓✓54.8465.9460.3991.5691.5491.5587.0097.6892.3472.0782.6777.37
✓✓✓57.4166.4961.9591.7991.5391.6688.6797.9893.3274.0083.2778.63
✓✓✓✓58.4067.8263.1192.2291.7491.9889.2198.0793.6474.9483.7079.32
✓✓✓✓✓59.3167.5663.4392.0391.7191.8790.1398.1894.1675.8683.9179.88
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.368, + 0.47, + 0.399 + ], + "angle": 0, + "content": "map, encouraging the RPN to concentrate on cellular instance during nuclei region proposal." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.403, + 0.47, + 0.495 + ], + "angle": 0, + "content": "Design Choice for DRM: We provide detailed comparisons on the ISBI2014 dataset to demonstrate the effectiveness of different components in DRM: 1) \\( H_{i} \\): instance mask head for coarse segmentation only; 2) \\( H_{o} \\): intersection mask head for overlapping region segmentation; 3) \\( H_{m} \\): complement mask head for non-overlapping region segmentation;" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.498, + 0.47, + 0.575 + ], + "angle": 0, + "content": "As seen in Table 4, adding \\( H_{o} \\) yields an improvement of \\( 2.20\\% \\) in average mAP, with a further \\( 2.64\\% \\) gains from the additional \\( H_{m} \\). We notice that cytoplasm results have a more significant improvement of \\( 13.2\\% \\) in mAP, which is indeed in line with our design intent." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.579, + 0.47, + 0.791 + ], + "angle": 0, + "content": "Design Choice for CRM: The goal of semantic consistency regularization is to enhance the model's overlapping reasoning capability by learning the concept of recombined instances from sub-regions. We provide comparisons to demonstrate the design choice (Table 4): 1) \\(\\mathrm{CU} + \\mathrm{FU}\\): integration of rich semantic features as inputs via Concatenation Unit and Fusion Unit. 2) \\(\\mathcal{L}_{\\text{cons}}\\): consistency regularization between the recombined prediction \\(\\hat{e}_{k,i}^{r}\\) and the fusion of sub-regions \\(\\hat{o}_{k,i}, \\hat{m}_{k,i}\\). As seen in Table 4, by aggregating the rich semantic feature for overlapping and non-overlapping region via Fusion Unit, we observe an increase of \\(1.52\\%\\) average mAP on the ISBI2014 dataset. Adding consistency regularization further improves \\(0.91\\%\\) mAP for cytoplasm." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Figure 4 visualizes the results of the DoNet and other typical instance segmentation methods, including standard (Mask R-CNN), multi-task (DoNet w/o CRM), and amodal (Occlusion R-CNN) instance segmentation model. It demonstrates the importance of adding interaction among sub-regions via CRM and the strong perceptual capability of DoNet in overlapping regions." + }, + { + "type": "image", + "bbox": [ + 0.543, + 0.368, + 0.695, + 0.485 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.61, + 0.489, + 0.627, + 0.5 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.698, + 0.368, + 0.852, + 0.485 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.762, + 0.488, + 0.78, + 0.5 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.542, + 0.506, + 0.696, + 0.623 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.611, + 0.627, + 0.628, + 0.638 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image", + "bbox": [ + 0.698, + 0.506, + 0.852, + 0.623 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.759, + 0.627, + 0.777, + 0.638 + ], + "angle": 0, + "content": "(d)" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.651, + 0.892, + 0.694 + ], + "angle": 0, + "content": "Figure 4. Qualitative results from (a) standard [11], (b) multitask (DoNet w/o CRM), (c) amodal [9], and (d) proposed deoverlapping instance segmentation method." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.723, + 0.81, + 0.74 + ], + "angle": 0, + "content": "4.4. Qualitative Analysis and Discussion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.748, + 0.892, + 0.825 + ], + "angle": 0, + "content": "We visualize the heatmap of the intersection region, the complement region, and the integral instance in Figure 6. The proposed method successfully identifies sub-regions based on the overlapping concept, even in low-resolution areas with high transparency." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Furthermore, we provide qualitative comparisons on CPS (top) and ISBI2014 (bottom) datasets in Figure 5. Our proposed DoNet outperforms other instance segmentation methods. Specifically, red rectangles provide details and highlight the main difference among these results. In the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15647" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.091, + 0.891, + 0.425 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.438, + 0.893, + 0.482 + ], + "angle": 0, + "content": "Figure 5. Qualitative results of our DoNet and other SOTA methods on CPS (top) and ISBI2014 (bottom) datasets. (a) Ground Truth; (b) Mask R-CNN [11]; (c) Occlusion R-CNN [9]; (d) Xiao et al. [37]; (e) Cascade R-CNN [2]; (f) Hybrid Task Cascade [8]; (g) Mask Scoring R-CNN [13]; (h) Our proposed DoNet." + }, + { + "type": "image", + "bbox": [ + 0.119, + 0.497, + 0.426, + 0.757 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.761, + 0.47, + 0.83 + ], + "angle": 0, + "content": "Figure 6. Heatmaps of the intersection region, the complement region, and the integral instance on CPS (top) and ISBI2014 (bottom) datasets, including (a) the original instance, the prediction heatmap of (b) intersection regions, (c) complement regions, and (d) the integral instance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.903 + ], + "angle": 0, + "content": "segmentation results of the CPS data, it can be seen that overlapped cells with different staining (e.g., dark red and blue) show significant appearance inconsistency between cellular sub-regions. Previous works (e.g., Mask R-CNN" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.497, + 0.892, + 0.619 + ], + "angle": 0, + "content": "[11] and Occlusion R-CNN [9]) with limited perceptual capability have difficulty capturing the relationship between pixels in the intersection and complement sub-regions, leading to ambiguous segmentation contours. In contrast, our DoNet can effectively distinguish different instance boundaries and can better perceive the integrality of cells. This generalized superiority is also observed in the ISBI2014 dataset with low-contrast cellular instances." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.632, + 0.619, + 0.646 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.658, + 0.892, + 0.809 + ], + "angle": 0, + "content": "In this paper, we propose a de-overlapping network (DoNet) to address the overlapping challenges in cytology instance segmentation. The proposed DoNet enhances the model's perception of overlapping regions by implicitly and explicitly modeling the interaction between cellular regions and the integral instance. Extensive experiments reveal the superiorities of the proposed DoNet, which not only provides immense potential for overlapping object perception in the medical domain but also occluded instance segmentation in general vision application scenarios." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.822, + 0.661, + 0.839 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.847, + 0.892, + 0.893 + ], + "angle": 0, + "content": "This work was supported by National Natural Science Foundation of China (No. 62202403) and Beijing Institute of Collaborative Innovation Program (No. BICI22EG01)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15648" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.117, + 0.47, + 0.198 + ], + "angle": 0, + "content": "[1] Seunghyeok Back, Joosoon Lee, Taewon Kim, Sangjun Noh, Raeyoung Kang, Seongho Bak, and Kyoobin Lee. 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In this work, we proposed a De-overlapping Network (DoNet) in a decompose-and-recombined strategy. A Dual-path Region Segmentation Module (DRM) explicitly decomposes the cell clusters into intersection and complement regions, followed by a Semantic Consistency-guided Recombination Module (CRM) for integration. To further introduce the containment relationship of the nucleus in the cytoplasm, we design a Mask-guided Region Proposal Strategy (MRP) that integrates the cell attention maps for inner-cell instance prediction. We validate the proposed approach on ISBI2014 and CPS datasets. Experiments show that our proposed DoNet significantly outperforms other state-of-the-art (SOTA) cell instance segmentation methods. The code is available at https://github.com/DeepDoNet/DoNet. + +# 1. Introduction + +Cytology image has been essential for cancer screening and earlier diagnosis, such as qualitative and quantitative identification of cellular morphology, nuclei size, nuclear-cytoplasmic ratio, and other cytological features [12, 15, 25]. However, examining tens of thousands of cells under the microscope visually is inherently tedious and suffers from inter-/intra-observer variability. Computational techniques enable efficient and accurate characterization of cells from cytology images [12, 16]. Among all computational techniques, cell segmentation has been a fundamental and widely-studied task, since the acquisition of cell-level identification is a pre-requisition for further assessment and analysis [3, 23]. + +![](images/6bc4bb6363aa0f89207f07da4edf2b136940cc0adfb0680e5812b27f2cf1d5b2.jpg) +Figure 1. The schematic illustration of proposed DoNet with decompose-and-recombined strategy, which maps each overlapping cell into the intersection, complement, and instance layers to address the overlapping issue in cytology instance segmentation. + +Deep Learning (DL) methods show promising results for cell-nuclei segmentation in the histopathology image [5,6,14,17]. However, cytology segmentation remains challenging for the following two reasons. Firstly, cells in a cytology image are prone to cluster with each other, leading to the overlapping issue. In the cytology images, the translucent cytoplasm of the cell (seen in Figure 1) tends to occlude each other with low contrast staining, leading to ambiguous cellular boundary predictions. This phenomenon is particularly evident in cervical cell images. Secondly, hard mimics, are widespread in the background, along with other technical artefacts such as bubbles, which could mislead the instance segmentation models [4]. Take the cervical cell image as an example, the widespread white blood cells and mucus stains lead to false predictions for nuclei. To address these challenges, several works [24, 33] propose the segment-then-refine paradigm, while others [39, 40] utilize the detection-based framework, e.g., Mask R-CNN [11]. However, they fail to model the interaction between intersection and complement sub-regions within the translucent cell cluster explicitly, resulting in a limited understanding of cross-region relationships. + +Amodal instance segmentation tackles the occlusion + +problem by inferring the integral object based on the partially visible region [22]. Based on the fact that humans can infer the occluded region of an object despite the ambiguity, these methods attempt to learn the integrated object mask (amodal mask) for better occlusion reasoning capability [9, 37] via synthesizing occluded data label pairs and aggregating global information to enhance perceptual ability. Compared to natural scenes, cell instances in cytology images are mostly semi-transparent. Therefore, an occlusion (overlapping) region exits in both the occluding and occluded instances. However, treating semi-transparent overlapping regions as general occlusion regions is not optimal, since they have different appearances compared to non-overlapping regions, and could in fact provide richer shape information than general occlusion regions. + +Motivated by the amodal perception, we propose a decompose-and-recombine strategy for translucent cell instance segmentation, named De-overlapping Network (DoNet). Figure 1 provides the schematic diagram. For each cell cluster with more than one cellular sub-region, DoNet starts from implicitly learning the hidden interaction of sub-regions by predicting instance masks from clusters. Then, it explicitly models the components and their relationships via the intersection layer, complement layer, and instance layer, to enhance its perceptual capability. + +Initially, we adopt Mask R-CNN to get the coarse predictions, followed by a novel Dual-path Region segmentation Module (DRM) that combines features and coarse masks from the first stage to decompose cell clusters into intersection and complement sub-regions. Then, the semantic Consistency-guided Recombination Module (CRM) is designed to encourage consistency between the refined instances and integral sub-region predictions. Furthermore, to impose the morphological constraint that nuclei stay inside the cellular regions, we propose a Mask-guided Region Proposal Module (MRP) to encourage the model to focus on the intra-cellular area during nuclei segmentation. + +The overall contributions are summarized as follows: + +- A novel de-overlapping network for cell instance segmentation with a decompose-and-recombined strategy, decomposing the cell regions with the DRM, as well as implicitly and explicitly modeling the semantic relationship between intersection, complement, and instance (cell) components via the CRM. These designs equip the network with enhanced perceptual capability in overlapping cellular sub-regions. +- A mask-guided region proposal module (MRP) that leverages the cytoplasm attention map for the intracellular nuclei refinement, which imposes the biology prior of cellular instances into the module, effectively mitigating the influence of mimickers widespread in the background. + +- Extensive experiments on two overlapping cytology image segmentation datasets, namely ISBI2014 [24] and CPS [39], demonstrating that our proposed DoNet outperforms other state-of-the-art (SOTA) methods by a large margin. + +# 2. Related Work + +Cytology Instance Segmentation: Challenges such as cell clustering, hard mimics, and semi-transparent overlapping cytoplasm regions pose in the segmentation of cellular instance (e.g., cell, nuclei, cytoplasm) from cytology images. These challenges inspired numerous insightful works, especially after the publication of ISBI2014 [33]. Two mainstream approaches are proposed to tackle the overlapping cell segmentation challenge: the segment-then-refine stream and the end-to-end training stream. + +Early approaches tackling this challenge are primarily the combination of pixel-level segmentation models and additional post-processing techniques, such as seeded watershed algorithm [19], random walk [38], conditional random field algorithms [35], and star-convex parameterization [34]. To further improve the segmentation performance, some other methods introduce morphological prior. Song et al. design a dynamic multi-template deformation model, which leverages case-specific shape constraints to guide the inference of overlapping cell boundaries [30]. Tareef et al. propose to refine cytoplasm boundary via a learnable shape prior, which is dynamically modeled as the fusion of shape templates [32]. + +Escaping from the complex post-processing procedure, many later works turn to end-to-end training. These approaches typically adopt Mask R-CNN as their baseline. The first attempt following this approach was [29], a model for nuclear instance segmentation from liquid-based cytology smears. Based on the appearance similarity between different cells, Zhou et al. propose the IRNet to explore instance relation during overlapping cervical cell segmentation [40]. To leverage information from unlabeled data, Zhou et al. provide a mean-teacher-based semi-supervised learning scheme, MMT-PSM [39]. + +The above two methods have achieved notable performance improvements, yet still lack the necessary perceptual capability for overlapping regions, leading to sub-optimal results, i.e., ambiguous cell boundaries. In this study, we propose a de-overlapping network, named DoNet, to implicitly and explicitly model the interaction between the integral instance and its sub-regions. + +Occluded Instance Segmentation: Instance segmentation, a typical task in computer vision, refers to the inference of bounding boxes and instance segmentation masks. Most notable approaches follow the detect-then-segment paradigm, such as Mask R-CNN [11] and its following variants [2, 13]. + +![](images/0aee67d7d1e86c6a8cab86b20261ca11a7c821c58641118d4abfff63da87b3c1.jpg) +Figure 2. The flowchart of the proposed DoNet. It consists of four main parts: (1) baseline for coarse mask segmentation; (2) DRM to simultaneously regress intersection and complement regions which provides cues for final mask refinement; (3) CRM to explicitly refine the final mask and encourage the semantic consistency; (4) MRP to mitigate the effect of background noise. + +However, these approaches could not handle the occlusion problem, common in visual application scenarios like robotic manipulations, scene parsing, and autonomous driving [1, 10]. Due to the inconsistencies within a Regions of Interest (RoI), these models suffer from the limited perceptual capability, leading to ambiguous segmentation boundaries. To tackle this issue, a specific task, occluded instance segmentation aims at leveraging visible regions to perceive the entirety of the occluded instance accurately. This capability of inferring and reasoning occluded objects is defined as amodal perception [9], thus occluded instance segmentation is also called amodal instance segmentation. + +Research on amodal instance segmentation starts from [22], which poses this challenging task and gives a synthesis-based solution. In this work, the first amodal instance segmentation dataset, the COCOA dataset, is established based on the COCO dataset. Afterward, some notable solutions accomplish this task and achieve state-of-the-art performance. Previous approaches tackle this challenge by leveraging information from visible instance segmentation, then inferring the amodal mask [1,9]. For example, Occlusion R-CNN (ORCNN) is built on R-CNN with two mask heads, the visible mask head, and the amodal mask head, which directly predict the amodal mask and the visible mask, inferring the visible mask through the subtraction of these two masks [9]. Qi et al. [28] perform amodal instance segmentation with multi-level coding and establish + +a large-scale amodal instance segmentation dataset. Xiao et al. [37] leverage shape prior knowledge to infer amodal mask using memory codebook. Some other models, like BCNet [18] abandon the visible instance prediction based manner and directly models the relationship between the occluder and the occludee. To address the lack of amodal mask ground truth, ASBU [26] introduces a weakly supervised amodal segmenter, which generates pseudo-ground truth by boundary uncertainty estimation. + +Essentially, the above occluded instance segmentation methods aim to enhance the amodal perception and reasoning capability, inspiring us to explore the interaction between instance sub-regions and the integral instance. Compared to amodal segmentation, whose focus on inferring the invisible region from the partially visible regions, our focus is to resolve the inconsistency between the intersection and complement regions. + +# 3. Methodology + +# 3.1. Overview + +Problem formulation: Following the setting of cell instance segmentation, we are provided with a dataset with $K$ images and the corresponding annotations $\mathcal{D} = \{(\mathcal{X}_k,\mathcal{Y}_k)\}_{k = 1}^K$ , each of which contains annotations of bounding boxes $\mathcal{B}_k = \{b_{k,i}\}_{i = 1}^{N_k}$ , object categories $\mathcal{C}_k = \{c_{k,i}\}_{i = 1}^{N_k}$ , and instance masks $\mathcal{E}_k = \{e_{k,i}\}_{i = 1}^{N_k}$ , where $N_{k}$ + +denotes the number of instances in the $k$ -th image. Here, we focus on segmenting the nucleus and cytoplasm for cell instance $c_{k,i} \in \{\text{nuclei}, \text{cytoplasm}\}$ . For each cell cluster, based on the localization relationship among the cells, we decompose the instance mask into the intersection region $\mathcal{O}_k = \{o_{k,i}\}_{i=1}^{N_k}$ and the complement region $\mathcal{M}_k = \{m_{k,i}\}_{i=1}^{N_k}$ via the logical operation (see in Figure 1), which is used to model their relationship in the DoNet. + +**Workflow:** The flowchart of the proposed DoNet is provided in Figure 2. It takes Mask R-CNN [11] as the base model, followed by a Dual-path Region segmentation Module (DRM) which takes the instance features as input to predict intersection regions $\hat{o}_{k,i}$ and complement regions $\hat{m}_{k,i}$ of cytoplasm via the intersection and complement layers (Section 3.2). After decomposing cell clusters according to the position relationship, a Consistency-guided Recombination Module (CRM) takes instance features from DRM and RoIAlign layer to generate the recombined masks $\hat{e}_{k,i}^{r}$ for consistency regularization (Section 3.2). Then, the recombined cytoplasm prediction is utilized as prior knowledge for intra-cellular object prediction throughout the Mask-guided Region Proposal (MRP) (Section 3.3). We will present the details of our framework in the following sections. + +Coarse Mask Segmentation: Previous research works on Mask R-CNN has shown competitive performance in instance segmentation [9, 11, 13], adopted into the proposed DoNet for coarse mask segmentation. Mask R-CNN consists of two stages. The first stage utilizes Feature Pyramid Network (FPN) for feature extraction and a Region Proposal Network (RPN) for candidate object bounding boxes generation. The second stage generates Region-of-Interest (RoI) features $f_{k,i}^{roi}$ via the RoIAngle layer and predicts object classes $\hat{c}_{k,i}$ and bounding boxes $\hat{b}_{k,i}$ from the detection head, and semantic masks $\hat{e}_{k,i}^{c}$ from the Instance Mask Head $(H_{i})$ , respectively. Due to limited perception capability in overlapping regions, $\hat{e}_{k,i}^{c}$ may contain ambiguous boundaries. Thus, we denote $\hat{e}_{k,i}^{c}$ as the coarse mask, which provides information for sub-region decomposition in DRM and suppresses the interference from background mimics. Following standard losses in [11], a multi-task loss $\mathcal{L}_{\text{coarse}}$ for coarse mask segmentation is formed as, + +$$ +\mathcal {L} _ {\text {c o a r s e}} = \mathcal {L} _ {\text {r e g}} + \mathcal {L} _ {\text {c l s}} + \mathcal {L} _ {\text {c m a s k}}, \tag {1} +$$ + +where $\mathcal{L}_{reg}$ denotes the smooth-L1 loss for bounding box regression, $\mathcal{L}_{cls}$ denotes cross-entropy (CE) loss for classification, and $\mathcal{L}_{cmask}$ denotes pixel-wise CE loss for segmentation. + +# 3.2. Decompose-and-recombined Strategy + +Previous solutions for amodal perception infer the integral structure of occluded instances using visible regions + +[9, 37]. However, they ignore information from overlapping regions, which tend to be sub-optimal in the case of complex superposition of translucent objects. To empower the perception capability of model for overlapping translucent regions, we specifically design the decompose-and-recombined strategy. + +Dual-path Region Segmentation Module (DRM): As shown in Figure 2, DRM consists of an Intersection Mask Head $H_{o}$ and a Complement Mask Head $H_{m}$ with the same architecture. Let $f_{k,i}^{c}$ denotes the rich semantic feature before the coarse mask prediction in the Instance Mask Head. Both $H_{o}$ and $H_{m}$ take the concatenation of $f_{k,i}^{roi}$ and $f_{k,i}^{c}$ as input to predict the intersection and complement regions $\hat{o}_{k,i}, \hat{m}_{k,i}$ in clusters. See the supplementary material for details of the Concatenation Unit. Specifically, each head consists of 4 convolutional layers to generate features in $14 \times 14 \times 256$ , followed by one deconvolutional layer to get the semantic mask with a resolution of $28 \times 28 \times 1$ . Here, we add the pixel-wise CE loss to both heads as the explicit constraint for decomposition, + +$$ +\mathcal {L} _ {d e c} = \frac {1}{K} \sum_ {k = 1} ^ {K} \frac {1}{N _ {k}} \sum_ {i = 1} ^ {N _ {k}} \left(\mathcal {L} _ {c e} \left(\hat {o} _ {k, i}, o _ {k, i}\right) + \mathcal {L} _ {c e} \left(\hat {m} _ {k, i}, m _ {k, i}\right)\right). \tag {2} +$$ + +Semantic Consistency-guided Recombination Module (CRM): To further enhance the perception capability for overlapping instances, CRM is designed to encourage DoNet to perceive integral instances. Specifically, let $f_{k,i}^{o}$ and $f_{k,i}^{m}$ denote the features before the last layer in the intersection mask head and the complement mask head. The rich semantic feature for the overlapping and non-overlapping region is considered as the residual information for the complex areas which is fused with $f_{k,i}^{roi}$ and then fed into the recombined mask head. See the supplementary material for details of the Fusion Unit. Noted that we reuse the Instance Mask Head $(H_{i})$ here to predict the integral instance. This combination facilitates CRM to leverage contextual information of overlapping instances, leading to the improvement of perception capability. The refined mask $\hat{e}_{k,i}^{r}$ from CRM is optimized by segmentation loss $\mathcal{L}_{rmask}$ , + +$$ +\mathcal {L} _ {r m a s k} = \frac {1}{K} \sum_ {k = 1} ^ {K} \frac {1}{N _ {k}} \sum_ {i = 1} ^ {N _ {k}} \mathcal {L} _ {c e} \left(\hat {e} _ {k, i} ^ {r}, e _ {k, i}\right). \tag {3} +$$ + +To further enhance the feature representation capacity for the relationship of components, we add semantic consistency regularization between the recombination $\hat{e}_{k,i}^{r}$ and merged predictions of $\hat{o}_{k,i}$ and $\hat{m}_{k,i}$ , + +$$ +\mathcal {L} _ {\text {c o n s}} = \frac {1}{K} \sum_ {k = 1} ^ {K} \frac {1}{N _ {k}} \sum_ {i = 1} ^ {N _ {k}} \mathcal {L} _ {\text {c e}} \left(\hat {e} _ {k, i} ^ {r}, \mathcal {F} _ {\text {m e r g e}} \left(\hat {o} _ {k, i}, \hat {m} _ {k, i}\right)\right), \tag {4} +$$ + +where $\mathcal{F}_{\text{merge}}(\cdot)$ represents the merging operation for the intersection region and the complement region in Mergence Unit, which is $xor()$ , two sub-region masks are passed through Sigmoid function for normalization. Then, we calculate the Mask Exclusive-OR of two mask logits for merging them and suppressing redundant predicted pixels. + +# 3.3. Mask-guided Region Proposal + +It is inevitable for cytology images to exist abundant cellular debris and non-target objects, e.g., white blood cells and mucus. These objects often have a similar appearance as the nuclei, with small round surfaces stained in dark purple, which increases the model identification difficulty. To avoid the interference it brings, we further propose a Mask-guided Region Proposal module (MRP) to encourage the model to generate nuclei proposals in intra-cellular regions. + +For each image, we can aggregate all the recombined instance predictions $\hat{e}_{k,i}^{r}$ in CRM together into a semantic mask $\hat{M}_k$ . The raw predictions are first mapped back and then summed up according to their bounding boxes predictions $\hat{b}_{k,i}$ in the detection head, followed by a Sigmoid function to normalize them into probabilities. $\hat{M}_k$ is considered as the attention score to re-weight features $f_{k}$ in origin FPN via element-wise multiplication: + +$$ +f _ {k} ^ {w} = \hat {M} _ {k} \circ f _ {k}, \tag {5} +$$ + +where $f_{k}^{w}$ denotes the re-weighted features for nuclei proposal predictions in MRP. Thus, extracellular pixels with a lower probability to be cytoplasm are suppressed, which reduces the false positives for background instances (i.e., blood, mucus, and others). In addition, MRP also builds information interaction between different stages, which naturally encourages feature representation ability. + +# 3.4. End-to-end Learning + +Extended dataset with synthetic clusters: The semitransparency characteristic of cytoplasm alleviates the effect of high overlap, allowing cytologists to delineate the contour of cellular instances based on expert knowledge. However, extremely challenging labeling and unavoidable label noise limit the availability of large-scale annotated datasets. To tackle this problem, we propose an instance-level data augmentor for overlapping cell data augmentation, which can generate large-scale synthetic cell clusters with controllable overlapping ratios and transparency based on the annotated cellular instances. This synthetic dataset further facilitates the generalization ability, by providing more diverse data to implicitly learn the concept of instance and its components. See the supplementary material for details of the synthetic pipeline. Unless otherwise specified, we do not use this synthetic dataset in the following comparison. + +Overall Loss Function: The proposed cell instance segmentation framework can be trained in a supervised manner. The overall objective $\mathcal{L}$ is as follows, + +$$ +\mathcal {L} = \mathcal {L} _ {\text {c o a r s e}} + \lambda_ {\text {d e c}} \mathcal {L} _ {\text {d e c}} + \lambda_ {\text {r m a s k}} \mathcal {L} _ {\text {r m a s k}} + \lambda_ {\text {c o n s}} \mathcal {L} _ {\text {c o n s}}, \tag {6} +$$ + +where $\mathcal{L}_{\text{coarse}}$ denotes losses for RoI extraction and coarse mask prediction, $\mathcal{L}_{dec}$ denotes the decomposition loss for intersection and complement regions segmentation, $\mathcal{L}_{rmask}$ is the segmentation loss for refined masks, $\mathcal{L}_{cons}$ supervises the semantic consistency between integral instance and subregions. $\lambda_{dec}, \lambda_{rmask},$ and $\lambda_{cons}$ are trade-off parameters controlling the importance of each component. + +# 4. Experiments + +# 4.1. Experimental Setup + +We evaluate our proposed DoNet in two cytology image datasets for overlapping cell instance segmentation: + +ISBI2014 [24]: This is a widely-used dataset from Overlapping Cervical Cytology Image Segmentation Challenge1, which consists of 8 extended depth-of-focus (EDF) real cervical cytology images and corresponding synthetic images. It contains high-quality pixel-level annotations for both nuclei and cytoplasm with a resolution of $512 \times 512$ . We follow the setting in this challenge [24] to use 45, 90 and 810 images for training, validation and testing to evaluate our proposed DoNet in a supervised setting. + +CPS [39]: This liquid-based cytology dataset contains 137 labeled images with a resolution of $1000 \times 1000$ . In total, it contains 4439 cytoplasm and 4789 nuclei annotations. We conduct 3-fold cross-validation on this dataset. + +Evaluation metrics: To measure the overall performance of the proposed DoNet, we utilize four commonly-used evaluation metrics in instance segmentation: aggregated Jaccard index (AJI), average Dice coefficient (Dice), F1-score (F1) [20], mean of Average Precision (mAP) [11]. In order to compare our result on the ISBI2014 with previous studies [24], we further adopt evaluation metrics including Dice, object-based false negative rate $(\mathrm{FN}_o)$ , and pixel-based true positive rate $(\mathrm{TP}_p)$ . + +Implementation details: We utilize the Mask R-CNN [11] in Detector2 [36] as the baseline model. We use the ResNet-50-based FPN network in all experiments. During training, we adopt SGD with 0.9 momentum as the optimizer. We set the initial learning rate to 0.001 and add the linear warm-up in the first 1k iterations. We train the network for 60k iterations, decreasing the learning rate by a factor of 0.1 after 50k and 55k iterations. + +Table 1. Quantitative segmentation results of DoNet and other state-of-the-art methods on CPS and ISBI2014. + +
MethodsISBI2014CPS
mAP↑Dice↑F1↑AJI↑mAP↑Dice↑F1↑AJI↑
Mask R-CNN [11]59.0991.1592.5477.0748.28 ± 3.1089.32 ± 0.5085.07 ± 2.0169.20 ± 2.27
Cascade R-CNN [2]62.4591.2992.5177.9147.87 ± 3.2789.24 ± 0.4483.33 ± 1.6568.86 ± 3.55
Mask Scoring R-CNN [13]63.5691.2891.8775.1448.38 ± 3.1389.39 ± 0.2482.98 ± 1.8667.45 ± 2.45
HTC [8]59.6291.3988.0875.0047.60 ± 3.5689.08 ± 0.5181.30 ± 2.5666.35 ± 2.84
Occlusion R-CNN [9]62.3591.7593.1878.6448.14 ± 2.8489.08 ± 0.2885.69 ± 2.2869.51 ± 2.45
Xiao et al. [37]57.3491.7092.7578.2948.53 ± 2.8589.29 ± 0.2485.46 ± 2.6069.37 ± 2.88
DoNet64.0292.1393.2379.0549.43 ± 3.8389.54 ± 0.2585.51 ± 2.3370.08 ± 2.84
DoNet w/ Aug.----49.65 ± 3.5289.50 ± 0.3886.30 ± 2.0170.56 ± 2.34
+ +# 4.2. Results + +We quantitatively compare the cell instance segmentation results from the ISBI2014 and CPS in Table 1 with state-of-the-art methods in the field of general instance segmentation (Mask R-CNN [11], Cascade R-CNN [2], Mask Scoring R-CNN [13], HTC [8]) and amodal instance segmentation (Occlusion R-CNN [9], Xiao et al. [37]). Noted that the amodal instance segmentation methods and general instance segmentation methods perform differently on two datasets due to the varying degrees of overlapping. Our method achieves the highest scores among all metrics. Specifically, it gains $2.68\%$ and $0.52\%$ improvements for mAP and AJI compared with the best of others [9] on the ISBI2014 dataset, as well as $1.85\%$ and $1.02\%$ improvements compared with the best [37] on the CPS dataset. We also evaluate $TP_{p}$ and $FN_{o}$ for DoNet to compare results against winners of the ISBI2014 challenge [27,33] and their following works [21, 31], which are mostly the segment-then-refine manners (Seen in Table 2). + +Furthermore, by introducing the synthetic clusters as instance-level augmentation, DoNet further has $0.45\%$ and $0.68\%$ improvements for mAP and AJI on the CPS dataset. This is mainly because the synthetic overlapping cells can further enhance the model's occlusion reasoning capability, which is consistent with the conclusions in [22]. + +Table 2. Comparison with other methods on ISBI2014. + +
MethodsISBI2014
Dice↑TPp↑FN0↓
Ushizima et al. [33]0.8720.8410.265
Nosrati et al. [27]0.8710.8750.110
Walter et al. [34]0.8600.8300.310
Lu et al. [24]0.8930.9050.315
Lee et al. [21]0.8970.8820.137
Tareef et al. [31]0.8980.9460.161
Chen et al. [7]0.9200.9000.020
DoNet0.9210.9480.162
+ +# 4.3. Ablation Study + +Effects of Network Components: We perform ablation studies to investigate the effects of the different components of our proposed pipeline for DoNet. The comparison results can be seen in Table 3. By adding DRM for explicit decomposing integral instances into intersection and complement sub-regions, we observe a $3.25\%$ increase in the average mAP of cytoplasm and nuclei on ISBI2014. However, directly adding DRM without the fusion of structural and morphological information, may mislead the model. This issue is observed in the more complex CPS dataset. To alleviate this problem, DoNet takes advantage of the decompose-and-recombined strategy by adding CRM after DRM. This strategy brings a total of $7.34\%$ and $1.74\%$ mAP improvements on two datasets by strengthening the model's perception of overlapping regions while preserving morphological information. + +![](images/a2cad089aac2a11a6f5e56ce3b2bef867e086488e2ca42f1a57c569d745ff696.jpg) + +![](images/2bf66742e99cdb45a3a1cdb1d2c88dc7a72e150e89f1c8009452f57418c6661a.jpg) + +![](images/930409e24a14aaa5f632c5b0b0f7e2374f6f3bc7c2acfe43a8a8ea1d60b8a91b.jpg) + +![](images/f44c4454170ec449bad6861d7f66f9764616b3cdf36ed99979f6c78aa04ae6fd.jpg) + +![](images/5636e93e3201def7dc5504aa664177d7a9c2180c88813b37471483ccef8de177.jpg) +(a) + +![](images/132ab24df7d23a20086d2ab93646472d0ecf86146e49ace860d29ab4912a5a04.jpg) +(b) + +![](images/6c376490f200b5826e3caa3af15fc247572b05ce86304ad8c2da08393989906f.jpg) +(c) +Figure 3. Illustration of background noise suppression in MRP: (a) the original image, (b) the origin feature map for region proposal, (c) the attention map from cytoplasm prediction, and (d) the re-weighted feature map for nuclei proposal generation. + +![](images/4fedc8e070c55e2ba07048ab56b12bcb9621d05637ba84469d09e84f2c15ef16.jpg) +(d) + +Applying MRP for mitigating the side effects from background mimics yields a further improvement of $0.59\%$ mAP and $0.31\%$ mAP on ISBI2014 and CPS datasets. Figure 3 provides the visualization of MRP operation, where background instances (e.g., mucus, karyoclasis, pointed by red arrow) are suppressed with strong responses in the feature + +Table 3. Effect of each proposed module on CPS and ISBI2014 datasets. $\checkmark$ denotes adding the corresponding module. + +
BaseDRMCRMMRPISBI2014CPS
mAP↑Dice↑F1↑AJI↑mAP↑Dice↑F1↑AJI↑
✓59.0991.1592.5477.0748.28 ± 3.1089.32 ± 0.5085.07 ± 2.0169.20 ± 2.27
✓✓61.0191.6192.8678.0648.03 ± 3.4889.13 ± 0.3084.63 ± 2.5768.56 ± 2.57
✓✓✓63.4391.8794.1679.8849.12 ± 3.2689.47 ± 0.3184.82 ± 2.7369.26 ± 2.63
✓✓✓✓64.0292.1393.2379.0549.43 ± 3.8389.54 ± 0.2585.51 ± 2.3370.08 ± 2.84
+ +Table 4. Ablation study of DRM and CRM on the ISBI2014 dataset. $\checkmark$ denotes adding the corresponding component or strategy. + +
\(H_i\)\(H_o\)\(H_m\)FU\(\mathcal{L}_{cons}\)mAP↑Dice↑F1↑AJI↑
Cyt.Nuc.Avg.Cyt.Nuc.Avg.Cyt.Nuc.Avg.Cyt.Nuc.Avg.
✓50.7167.4659.0990.7291.5991.1586.9698.1392.5470.5583.6077.07
✓✓54.8465.9460.3991.5691.5491.5587.0097.6892.3472.0782.6777.37
✓✓✓57.4166.4961.9591.7991.5391.6688.6797.9893.3274.0083.2778.63
✓✓✓✓58.4067.8263.1192.2291.7491.9889.2198.0793.6474.9483.7079.32
✓✓✓✓✓59.3167.5663.4392.0391.7191.8790.1398.1894.1675.8683.9179.88
+ +map, encouraging the RPN to concentrate on cellular instance during nuclei region proposal. + +Design Choice for DRM: We provide detailed comparisons on the ISBI2014 dataset to demonstrate the effectiveness of different components in DRM: 1) $H_{i}$ : instance mask head for coarse segmentation only; 2) $H_{o}$ : intersection mask head for overlapping region segmentation; 3) $H_{m}$ : complement mask head for non-overlapping region segmentation; + +As seen in Table 4, adding $H_{o}$ yields an improvement of $2.20\%$ in average mAP, with a further $2.64\%$ gains from the additional $H_{m}$ . We notice that cytoplasm results have a more significant improvement of $13.2\%$ in mAP, which is indeed in line with our design intent. + +Design Choice for CRM: The goal of semantic consistency regularization is to enhance the model's overlapping reasoning capability by learning the concept of recombined instances from sub-regions. We provide comparisons to demonstrate the design choice (Table 4): 1) $\mathrm{CU} + \mathrm{FU}$ : integration of rich semantic features as inputs via Concatenation Unit and Fusion Unit. 2) $\mathcal{L}_{\text{cons}}$ : consistency regularization between the recombined prediction $\hat{e}_{k,i}^{r}$ and the fusion of sub-regions $\hat{o}_{k,i}, \hat{m}_{k,i}$ . As seen in Table 4, by aggregating the rich semantic feature for overlapping and non-overlapping region via Fusion Unit, we observe an increase of $1.52\%$ average mAP on the ISBI2014 dataset. Adding consistency regularization further improves $0.91\%$ mAP for cytoplasm. + +Figure 4 visualizes the results of the DoNet and other typical instance segmentation methods, including standard (Mask R-CNN), multi-task (DoNet w/o CRM), and amodal (Occlusion R-CNN) instance segmentation model. It demonstrates the importance of adding interaction among sub-regions via CRM and the strong perceptual capability of DoNet in overlapping regions. + +![](images/b09fe0056960c8d0ad6c0a9e364c8242fdc8f79892e84b579c1567cf4dde3a7a.jpg) +(a) + +![](images/09e7b7bc850093e4f7e29963d21d3d907d9d2fdb2761673684d5075491a7a5e2.jpg) +(b) + +![](images/d7b74a07a7304ecd717b6ea08a4f40cda3d62be8688decd3a54f2c9f692dbf87.jpg) +(c) + +![](images/dd16129c8c8f28d059c83dfafcb507d127866dcb96be69beb144d57642f99434.jpg) +(d) +Figure 4. Qualitative results from (a) standard [11], (b) multitask (DoNet w/o CRM), (c) amodal [9], and (d) proposed deoverlapping instance segmentation method. + +# 4.4. Qualitative Analysis and Discussion + +We visualize the heatmap of the intersection region, the complement region, and the integral instance in Figure 6. The proposed method successfully identifies sub-regions based on the overlapping concept, even in low-resolution areas with high transparency. + +Furthermore, we provide qualitative comparisons on CPS (top) and ISBI2014 (bottom) datasets in Figure 5. Our proposed DoNet outperforms other instance segmentation methods. Specifically, red rectangles provide details and highlight the main difference among these results. In the + +![](images/46caceede9d40b1308808bc786c999a63f21a07a16952601a70079dd09368ae1.jpg) +Figure 5. Qualitative results of our DoNet and other SOTA methods on CPS (top) and ISBI2014 (bottom) datasets. (a) Ground Truth; (b) Mask R-CNN [11]; (c) Occlusion R-CNN [9]; (d) Xiao et al. [37]; (e) Cascade R-CNN [2]; (f) Hybrid Task Cascade [8]; (g) Mask Scoring R-CNN [13]; (h) Our proposed DoNet. + +![](images/83864683f617ac17ff886e8841d0900fe3b16b4be7e00ca9977bb414e0711867.jpg) +Figure 6. Heatmaps of the intersection region, the complement region, and the integral instance on CPS (top) and ISBI2014 (bottom) datasets, including (a) the original instance, the prediction heatmap of (b) intersection regions, (c) complement regions, and (d) the integral instance. + +segmentation results of the CPS data, it can be seen that overlapped cells with different staining (e.g., dark red and blue) show significant appearance inconsistency between cellular sub-regions. Previous works (e.g., Mask R-CNN + +[11] and Occlusion R-CNN [9]) with limited perceptual capability have difficulty capturing the relationship between pixels in the intersection and complement sub-regions, leading to ambiguous segmentation contours. In contrast, our DoNet can effectively distinguish different instance boundaries and can better perceive the integrality of cells. This generalized superiority is also observed in the ISBI2014 dataset with low-contrast cellular instances. + +# 5. Conclusion + +In this paper, we propose a de-overlapping network (DoNet) to address the overlapping challenges in cytology instance segmentation. The proposed DoNet enhances the model's perception of overlapping regions by implicitly and explicitly modeling the interaction between cellular regions and the integral instance. Extensive experiments reveal the superiorities of the proposed DoNet, which not only provides immense potential for overlapping object perception in the medical domain but also occluded instance segmentation in general vision application scenarios. + +# Acknowledgement + +This work was supported by National Natural Science Foundation of China (No. 62202403) and Beijing Institute of Collaborative Innovation Program (No. BICI22EG01). + +# References + +[1] Seunghyeok Back, Joosoon Lee, Taewon Kim, Sangjun Noh, Raeyoung Kang, Seongho Bak, and Kyoobin Lee. Unseen object amodal instance segmentation via hierarchical occlusion modeling. 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Springer, 2019. 1, 2 \ No newline at end of file diff --git a/2023/DoNet_ Deep De-Overlapping Network for Cytology Instance Segmentation/images.zip b/2023/DoNet_ Deep De-Overlapping Network for Cytology Instance Segmentation/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..39b8db6a39d1251e1b912f03e21112392e4d70bf --- /dev/null +++ b/2023/DoNet_ Deep De-Overlapping Network for Cytology Instance Segmentation/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:6c5eec9f1c5259b87dff0d63c19b58ac74cc1d5bf1242c1c1a7a73a46922fa8f +size 708125 diff --git a/2023/DoNet_ Deep De-Overlapping Network for Cytology Instance Segmentation/layout.json b/2023/DoNet_ Deep De-Overlapping Network for Cytology Instance Segmentation/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..cf16dc024c0147e1135c59dfd198f51b323913a9 --- /dev/null +++ b/2023/DoNet_ Deep De-Overlapping Network for Cytology Instance Segmentation/layout.json @@ -0,0 +1,8151 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 66, + 103, + 527, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 103, + 527, + 121 + ], + "spans": [ + { + "bbox": [ + 66, + 103, + 527, + 121 + ], + "type": "text", + "content": "DoNet: Deep De-overlapping Network for Cytology Instance Segmentation" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 64, + 142, + 532, + 172 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 142, + 532, + 172 + ], + "spans": [ + { + "bbox": [ + 64, + 142, + 532, + 172 + ], + "type": "text", + "content": "Hao Jiang" + }, + { + "bbox": [ + 64, + 142, + 532, + 172 + ], + "type": "inline_equation", + "content": "^{1*}" + }, + { + "bbox": [ + 64, + 142, + 532, + 172 + ], + "type": "text", + "content": " Rushan Zhang" + }, + { + "bbox": [ + 64, + 142, + 532, + 172 + ], + "type": "inline_equation", + "content": "^{1*}" + }, + { + "bbox": [ + 64, + 142, + 532, + 172 + ], + "type": "text", + "content": " Yanning Zhou" + }, + { + "bbox": [ + 64, + 142, + 532, + 172 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 64, + 142, + 532, + 172 + ], + "type": "text", + "content": " Yumeng Wang" + }, + { + "bbox": [ + 64, + 142, + 532, + 172 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 64, + 142, + 532, + 172 + ], + "type": "text", + "content": " Hao Chen" + }, + { + "bbox": [ + 64, + 142, + 532, + 172 + ], + "type": "inline_equation", + "content": "^{1\\dagger}" + }, + { + "bbox": [ + 64, + 142, + 532, + 172 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 64, + 142, + 532, + 172 + ], + "type": "text", + "content": "The Hong Kong University of Science and Technology \n" + }, + { + "bbox": [ + 64, + 142, + 532, + 172 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 64, + 142, + 532, + 172 + ], + "type": "text", + "content": "Tencent AI Lab" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 92, + 174, + 501, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 92, + 174, + 501, + 185 + ], + "spans": [ + { + "bbox": [ + 92, + 174, + 501, + 185 + ], + "type": "text", + "content": "{hjiangaz, jhc}@cse.ust.hk, {rzhangbq,ywanglu}@connect.ust.hk, amandayzhou@tencent.com" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "spans": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 239, + 290, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 239, + 290, + 479 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 290, + 479 + ], + "type": "text", + "content": "Cell instance segmentation in cytology images has significant importance for biology analysis and cancer screening, while remains challenging due to 1) the extensive overlapping translucent cell clusters that cause the ambiguous boundaries, and 2) the confusion of mimics and debris as nuclei. In this work, we proposed a De-overlapping Network (DoNet) in a decompose-and-recombined strategy. A Dual-path Region Segmentation Module (DRM) explicitly decomposes the cell clusters into intersection and complement regions, followed by a Semantic Consistency-guided Recombination Module (CRM) for integration. To further introduce the containment relationship of the nucleus in the cytoplasm, we design a Mask-guided Region Proposal Strategy (MRP) that integrates the cell attention maps for inner-cell instance prediction. We validate the proposed approach on ISBI2014 and CPS datasets. Experiments show that our proposed DoNet significantly outperforms other state-of-the-art (SOTA) cell instance segmentation methods. The code is available at https://github.com/DeepDoNet/DoNet." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 505, + 128, + 517 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 505, + 128, + 517 + ], + "spans": [ + { + "bbox": [ + 47, + 505, + 128, + 517 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 525, + 287, + 682 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 525, + 287, + 682 + ], + "spans": [ + { + "bbox": [ + 46, + 525, + 287, + 682 + ], + "type": "text", + "content": "Cytology image has been essential for cancer screening and earlier diagnosis, such as qualitative and quantitative identification of cellular morphology, nuclei size, nuclear-cytoplasmic ratio, and other cytological features [12, 15, 25]. However, examining tens of thousands of cells under the microscope visually is inherently tedious and suffers from inter-/intra-observer variability. Computational techniques enable efficient and accurate characterization of cells from cytology images [12, 16]. Among all computational techniques, cell segmentation has been a fundamental and widely-studied task, since the acquisition of cell-level identification is a pre-requisition for further assessment and analysis [3, 23]." + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 325, + 212, + 527, + 363 + ], + "blocks": [ + { + "bbox": [ + 325, + 212, + 527, + 363 + ], + "lines": [ + { + "bbox": [ + 325, + 212, + 527, + 363 + ], + "spans": [ + { + "bbox": [ + 325, + 212, + 527, + 363 + ], + "type": "image", + "image_path": "6bc4bb6363aa0f89207f07da4edf2b136940cc0adfb0680e5812b27f2cf1d5b2.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 369, + 547, + 414 + ], + "lines": [ + { + "bbox": [ + 305, + 369, + 547, + 414 + ], + "spans": [ + { + "bbox": [ + 305, + 369, + 547, + 414 + ], + "type": "text", + "content": "Figure 1. The schematic illustration of proposed DoNet with decompose-and-recombined strategy, which maps each overlapping cell into the intersection, complement, and instance layers to address the overlapping issue in cytology instance segmentation." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 437, + 546, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 546, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 546, + 700 + ], + "type": "text", + "content": "Deep Learning (DL) methods show promising results for cell-nuclei segmentation in the histopathology image [5,6,14,17]. However, cytology segmentation remains challenging for the following two reasons. Firstly, cells in a cytology image are prone to cluster with each other, leading to the overlapping issue. In the cytology images, the translucent cytoplasm of the cell (seen in Figure 1) tends to occlude each other with low contrast staining, leading to ambiguous cellular boundary predictions. This phenomenon is particularly evident in cervical cell images. Secondly, hard mimics, are widespread in the background, along with other technical artefacts such as bubbles, which could mislead the instance segmentation models [4]. Take the cervical cell image as an example, the widespread white blood cells and mucus stains lead to false predictions for nuclei. To address these challenges, several works [24, 33] propose the segment-then-refine paradigm, while others [39, 40] utilize the detection-based framework, e.g., Mask R-CNN [11]. However, they fail to model the interaction between intersection and complement sub-regions within the translucent cell cluster explicitly, resulting in a limited understanding of cross-region relationships." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 318, + 701, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 701, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 318, + 701, + 545, + 713 + ], + "type": "text", + "content": "Amodal instance segmentation tackles the occlusion" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 693, + 124, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 693, + 124, + 703 + ], + "spans": [ + { + "bbox": [ + 58, + 693, + 124, + 703 + ], + "type": "text", + "content": "*Equal contribution" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 59, + 703, + 134, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 703, + 134, + 712 + ], + "spans": [ + { + "bbox": [ + 59, + 703, + 134, + 712 + ], + "type": "text", + "content": "† Corresponding author" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15641" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": "problem by inferring the integral object based on the partially visible region [22]. Based on the fact that humans can infer the occluded region of an object despite the ambiguity, these methods attempt to learn the integrated object mask (amodal mask) for better occlusion reasoning capability [9, 37] via synthesizing occluded data label pairs and aggregating global information to enhance perceptual ability. Compared to natural scenes, cell instances in cytology images are mostly semi-transparent. Therefore, an occlusion (overlapping) region exits in both the occluding and occluded instances. However, treating semi-transparent overlapping regions as general occlusion regions is not optimal, since they have different appearances compared to non-overlapping regions, and could in fact provide richer shape information than general occlusion regions." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 252, + 289, + 372 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 252, + 289, + 372 + ], + "spans": [ + { + "bbox": [ + 46, + 252, + 289, + 372 + ], + "type": "text", + "content": "Motivated by the amodal perception, we propose a decompose-and-recombine strategy for translucent cell instance segmentation, named De-overlapping Network (DoNet). Figure 1 provides the schematic diagram. For each cell cluster with more than one cellular sub-region, DoNet starts from implicitly learning the hidden interaction of sub-regions by predicting instance masks from clusters. Then, it explicitly models the components and their relationships via the intersection layer, complement layer, and instance layer, to enhance its perceptual capability." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 372, + 289, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 372, + 289, + 515 + ], + "spans": [ + { + "bbox": [ + 46, + 372, + 289, + 515 + ], + "type": "text", + "content": "Initially, we adopt Mask R-CNN to get the coarse predictions, followed by a novel Dual-path Region segmentation Module (DRM) that combines features and coarse masks from the first stage to decompose cell clusters into intersection and complement sub-regions. Then, the semantic Consistency-guided Recombination Module (CRM) is designed to encourage consistency between the refined instances and integral sub-region predictions. Furthermore, to impose the morphological constraint that nuclei stay inside the cellular regions, we propose a Mask-guided Region Proposal Module (MRP) to encourage the model to focus on the intra-cellular area during nuclei segmentation." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 516, + 274, + 527 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 516, + 274, + 527 + ], + "spans": [ + { + "bbox": [ + 59, + 516, + 274, + 527 + ], + "type": "text", + "content": "The overall contributions are summarized as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 536, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 58, + 536, + 287, + 633 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 536, + 287, + 633 + ], + "spans": [ + { + "bbox": [ + 58, + 536, + 287, + 633 + ], + "type": "text", + "content": "- A novel de-overlapping network for cell instance segmentation with a decompose-and-recombined strategy, decomposing the cell regions with the DRM, as well as implicitly and explicitly modeling the semantic relationship between intersection, complement, and instance (cell) components via the CRM. These designs equip the network with enhanced perceptual capability in overlapping cellular sub-regions." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 58, + 641, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 641, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 58, + 641, + 288, + 714 + ], + "type": "text", + "content": "- A mask-guided region proposal module (MRP) that leverages the cytoplasm attention map for the intracellular nuclei refinement, which imposes the biology prior of cellular instances into the module, effectively mitigating the influence of mimickers widespread in the background." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 317, + 72, + 545, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 72, + 545, + 133 + ], + "spans": [ + { + "bbox": [ + 317, + 72, + 545, + 133 + ], + "type": "text", + "content": "- Extensive experiments on two overlapping cytology image segmentation datasets, namely ISBI2014 [24] and CPS [39], demonstrating that our proposed DoNet outperforms other state-of-the-art (SOTA) methods by a large margin." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 152, + 392, + 166 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 152, + 392, + 166 + ], + "spans": [ + { + "bbox": [ + 306, + 152, + 392, + 166 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 173, + 545, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 173, + 545, + 281 + ], + "spans": [ + { + "bbox": [ + 304, + 173, + 545, + 281 + ], + "type": "text", + "content": "Cytology Instance Segmentation: Challenges such as cell clustering, hard mimics, and semi-transparent overlapping cytoplasm regions pose in the segmentation of cellular instance (e.g., cell, nuclei, cytoplasm) from cytology images. These challenges inspired numerous insightful works, especially after the publication of ISBI2014 [33]. Two mainstream approaches are proposed to tackle the overlapping cell segmentation challenge: the segment-then-refine stream and the end-to-end training stream." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 281, + 546, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 281, + 546, + 437 + ], + "spans": [ + { + "bbox": [ + 304, + 281, + 546, + 437 + ], + "type": "text", + "content": "Early approaches tackling this challenge are primarily the combination of pixel-level segmentation models and additional post-processing techniques, such as seeded watershed algorithm [19], random walk [38], conditional random field algorithms [35], and star-convex parameterization [34]. To further improve the segmentation performance, some other methods introduce morphological prior. Song et al. design a dynamic multi-template deformation model, which leverages case-specific shape constraints to guide the inference of overlapping cell boundaries [30]. Tareef et al. propose to refine cytoplasm boundary via a learnable shape prior, which is dynamically modeled as the fusion of shape templates [32]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 437, + 545, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 545, + 568 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 545, + 568 + ], + "type": "text", + "content": "Escaping from the complex post-processing procedure, many later works turn to end-to-end training. These approaches typically adopt Mask R-CNN as their baseline. The first attempt following this approach was [29], a model for nuclear instance segmentation from liquid-based cytology smears. Based on the appearance similarity between different cells, Zhou et al. propose the IRNet to explore instance relation during overlapping cervical cell segmentation [40]. To leverage information from unlabeled data, Zhou et al. provide a mean-teacher-based semi-supervised learning scheme, MMT-PSM [39]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 569, + 545, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 569, + 545, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 569, + 545, + 653 + ], + "type": "text", + "content": "The above two methods have achieved notable performance improvements, yet still lack the necessary perceptual capability for overlapping regions, leading to sub-optimal results, i.e., ambiguous cell boundaries. In this study, we propose a de-overlapping network, named DoNet, to implicitly and explicitly model the interaction between the integral instance and its sub-regions." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 654, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 546, + 713 + ], + "type": "text", + "content": "Occluded Instance Segmentation: Instance segmentation, a typical task in computer vision, refers to the inference of bounding boxes and instance segmentation masks. Most notable approaches follow the detect-then-segment paradigm, such as Mask R-CNN [11] and its following variants [2, 13]." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "15642" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 72, + 542, + 320 + ], + "blocks": [ + { + "bbox": [ + 52, + 72, + 542, + 320 + ], + "lines": [ + { + "bbox": [ + 52, + 72, + 542, + 320 + ], + "spans": [ + { + "bbox": [ + 52, + 72, + 542, + 320 + ], + "type": "image", + "image_path": "0aee67d7d1e86c6a8cab86b20261ca11a7c821c58641118d4abfff63da87b3c1.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 331, + 547, + 366 + ], + "lines": [ + { + "bbox": [ + 46, + 331, + 547, + 366 + ], + "spans": [ + { + "bbox": [ + 46, + 331, + 547, + 366 + ], + "type": "text", + "content": "Figure 2. The flowchart of the proposed DoNet. It consists of four main parts: (1) baseline for coarse mask segmentation; (2) DRM to simultaneously regress intersection and complement regions which provides cues for final mask refinement; (3) CRM to explicitly refine the final mask and encourage the semantic consistency; (4) MRP to mitigate the effect of background noise." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 385, + 289, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 385, + 289, + 529 + ], + "spans": [ + { + "bbox": [ + 46, + 385, + 289, + 529 + ], + "type": "text", + "content": "However, these approaches could not handle the occlusion problem, common in visual application scenarios like robotic manipulations, scene parsing, and autonomous driving [1, 10]. Due to the inconsistencies within a Regions of Interest (RoI), these models suffer from the limited perceptual capability, leading to ambiguous segmentation boundaries. To tackle this issue, a specific task, occluded instance segmentation aims at leveraging visible regions to perceive the entirety of the occluded instance accurately. This capability of inferring and reasoning occluded objects is defined as amodal perception [9], thus occluded instance segmentation is also called amodal instance segmentation." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 534, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 534, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 534, + 289, + 715 + ], + "type": "text", + "content": "Research on amodal instance segmentation starts from [22], which poses this challenging task and gives a synthesis-based solution. In this work, the first amodal instance segmentation dataset, the COCOA dataset, is established based on the COCO dataset. Afterward, some notable solutions accomplish this task and achieve state-of-the-art performance. Previous approaches tackle this challenge by leveraging information from visible instance segmentation, then inferring the amodal mask [1,9]. For example, Occlusion R-CNN (ORCNN) is built on R-CNN with two mask heads, the visible mask head, and the amodal mask head, which directly predict the amodal mask and the visible mask, inferring the visible mask through the subtraction of these two masks [9]. Qi et al. [28] perform amodal instance segmentation with multi-level coding and establish" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 385, + 545, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 385, + 545, + 492 + ], + "spans": [ + { + "bbox": [ + 304, + 385, + 545, + 492 + ], + "type": "text", + "content": "a large-scale amodal instance segmentation dataset. Xiao et al. [37] leverage shape prior knowledge to infer amodal mask using memory codebook. Some other models, like BCNet [18] abandon the visible instance prediction based manner and directly models the relationship between the occluder and the occludee. To address the lack of amodal mask ground truth, ASBU [26] introduces a weakly supervised amodal segmenter, which generates pseudo-ground truth by boundary uncertainty estimation." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 493, + 545, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 493, + 545, + 589 + ], + "spans": [ + { + "bbox": [ + 304, + 493, + 545, + 589 + ], + "type": "text", + "content": "Essentially, the above occluded instance segmentation methods aim to enhance the amodal perception and reasoning capability, inspiring us to explore the interaction between instance sub-regions and the integral instance. Compared to amodal segmentation, whose focus on inferring the invisible region from the partially visible regions, our focus is to resolve the inconsistency between the intersection and complement regions." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 599, + 389, + 613 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 599, + 389, + 613 + ], + "spans": [ + { + "bbox": [ + 306, + 599, + 389, + 613 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 619, + 373, + 631 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 619, + 373, + 631 + ], + "spans": [ + { + "bbox": [ + 306, + 619, + 373, + 631 + ], + "type": "text", + "content": "3.1. Overview" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 637, + 547, + 716 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 637, + 547, + 716 + ], + "spans": [ + { + "bbox": [ + 304, + 637, + 547, + 716 + ], + "type": "text", + "content": "Problem formulation: Following the setting of cell instance segmentation, we are provided with a dataset with " + }, + { + "bbox": [ + 304, + 637, + 547, + 716 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 637, + 547, + 716 + ], + "type": "text", + "content": " images and the corresponding annotations " + }, + { + "bbox": [ + 304, + 637, + 547, + 716 + ], + "type": "inline_equation", + "content": "\\mathcal{D} = \\{(\\mathcal{X}_k,\\mathcal{Y}_k)\\}_{k = 1}^K" + }, + { + "bbox": [ + 304, + 637, + 547, + 716 + ], + "type": "text", + "content": ", each of which contains annotations of bounding boxes " + }, + { + "bbox": [ + 304, + 637, + 547, + 716 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_k = \\{b_{k,i}\\}_{i = 1}^{N_k}" + }, + { + "bbox": [ + 304, + 637, + 547, + 716 + ], + "type": "text", + "content": ", object categories " + }, + { + "bbox": [ + 304, + 637, + 547, + 716 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_k = \\{c_{k,i}\\}_{i = 1}^{N_k}" + }, + { + "bbox": [ + 304, + 637, + 547, + 716 + ], + "type": "text", + "content": ", and instance masks " + }, + { + "bbox": [ + 304, + 637, + 547, + 716 + ], + "type": "inline_equation", + "content": "\\mathcal{E}_k = \\{e_{k,i}\\}_{i = 1}^{N_k}" + }, + { + "bbox": [ + 304, + 637, + 547, + 716 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 637, + 547, + 716 + ], + "type": "inline_equation", + "content": "N_{k}" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15643" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 170 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 170 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 170 + ], + "type": "text", + "content": "denotes the number of instances in the " + }, + { + "bbox": [ + 47, + 72, + 287, + 170 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 72, + 287, + 170 + ], + "type": "text", + "content": "-th image. Here, we focus on segmenting the nucleus and cytoplasm for cell instance " + }, + { + "bbox": [ + 47, + 72, + 287, + 170 + ], + "type": "inline_equation", + "content": "c_{k,i} \\in \\{\\text{nuclei}, \\text{cytoplasm}\\}" + }, + { + "bbox": [ + 47, + 72, + 287, + 170 + ], + "type": "text", + "content": ". For each cell cluster, based on the localization relationship among the cells, we decompose the instance mask into the intersection region " + }, + { + "bbox": [ + 47, + 72, + 287, + 170 + ], + "type": "inline_equation", + "content": "\\mathcal{O}_k = \\{o_{k,i}\\}_{i=1}^{N_k}" + }, + { + "bbox": [ + 47, + 72, + 287, + 170 + ], + "type": "text", + "content": " and the complement region " + }, + { + "bbox": [ + 47, + 72, + 287, + 170 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_k = \\{m_{k,i}\\}_{i=1}^{N_k}" + }, + { + "bbox": [ + 47, + 72, + 287, + 170 + ], + "type": "text", + "content": " via the logical operation (see in Figure 1), which is used to model their relationship in the DoNet." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 171, + 288, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 171, + 288, + 361 + ], + "spans": [ + { + "bbox": [ + 47, + 171, + 288, + 361 + ], + "type": "text", + "content": "**Workflow:** The flowchart of the proposed DoNet is provided in Figure 2. It takes Mask R-CNN [11] as the base model, followed by a Dual-path Region segmentation Module (DRM) which takes the instance features as input to predict intersection regions " + }, + { + "bbox": [ + 47, + 171, + 288, + 361 + ], + "type": "inline_equation", + "content": "\\hat{o}_{k,i}" + }, + { + "bbox": [ + 47, + 171, + 288, + 361 + ], + "type": "text", + "content": " and complement regions " + }, + { + "bbox": [ + 47, + 171, + 288, + 361 + ], + "type": "inline_equation", + "content": "\\hat{m}_{k,i}" + }, + { + "bbox": [ + 47, + 171, + 288, + 361 + ], + "type": "text", + "content": " of cytoplasm via the intersection and complement layers (Section 3.2). After decomposing cell clusters according to the position relationship, a Consistency-guided Recombination Module (CRM) takes instance features from DRM and RoIAlign layer to generate the recombined masks " + }, + { + "bbox": [ + 47, + 171, + 288, + 361 + ], + "type": "inline_equation", + "content": "\\hat{e}_{k,i}^{r}" + }, + { + "bbox": [ + 47, + 171, + 288, + 361 + ], + "type": "text", + "content": " for consistency regularization (Section 3.2). Then, the recombined cytoplasm prediction is utilized as prior knowledge for intra-cellular object prediction throughout the Mask-guided Region Proposal (MRP) (Section 3.3). We will present the details of our framework in the following sections." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 362, + 288, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 362, + 288, + 581 + ], + "spans": [ + { + "bbox": [ + 47, + 362, + 288, + 581 + ], + "type": "text", + "content": "Coarse Mask Segmentation: Previous research works on Mask R-CNN has shown competitive performance in instance segmentation [9, 11, 13], adopted into the proposed DoNet for coarse mask segmentation. Mask R-CNN consists of two stages. The first stage utilizes Feature Pyramid Network (FPN) for feature extraction and a Region Proposal Network (RPN) for candidate object bounding boxes generation. The second stage generates Region-of-Interest (RoI) features " + }, + { + "bbox": [ + 47, + 362, + 288, + 581 + ], + "type": "inline_equation", + "content": "f_{k,i}^{roi}" + }, + { + "bbox": [ + 47, + 362, + 288, + 581 + ], + "type": "text", + "content": " via the RoIAngle layer and predicts object classes " + }, + { + "bbox": [ + 47, + 362, + 288, + 581 + ], + "type": "inline_equation", + "content": "\\hat{c}_{k,i}" + }, + { + "bbox": [ + 47, + 362, + 288, + 581 + ], + "type": "text", + "content": " and bounding boxes " + }, + { + "bbox": [ + 47, + 362, + 288, + 581 + ], + "type": "inline_equation", + "content": "\\hat{b}_{k,i}" + }, + { + "bbox": [ + 47, + 362, + 288, + 581 + ], + "type": "text", + "content": " from the detection head, and semantic masks " + }, + { + "bbox": [ + 47, + 362, + 288, + 581 + ], + "type": "inline_equation", + "content": "\\hat{e}_{k,i}^{c}" + }, + { + "bbox": [ + 47, + 362, + 288, + 581 + ], + "type": "text", + "content": " from the Instance Mask Head " + }, + { + "bbox": [ + 47, + 362, + 288, + 581 + ], + "type": "inline_equation", + "content": "(H_{i})" + }, + { + "bbox": [ + 47, + 362, + 288, + 581 + ], + "type": "text", + "content": ", respectively. Due to limited perception capability in overlapping regions, " + }, + { + "bbox": [ + 47, + 362, + 288, + 581 + ], + "type": "inline_equation", + "content": "\\hat{e}_{k,i}^{c}" + }, + { + "bbox": [ + 47, + 362, + 288, + 581 + ], + "type": "text", + "content": " may contain ambiguous boundaries. Thus, we denote " + }, + { + "bbox": [ + 47, + 362, + 288, + 581 + ], + "type": "inline_equation", + "content": "\\hat{e}_{k,i}^{c}" + }, + { + "bbox": [ + 47, + 362, + 288, + 581 + ], + "type": "text", + "content": " as the coarse mask, which provides information for sub-region decomposition in DRM and suppresses the interference from background mimics. Following standard losses in [11], a multi-task loss " + }, + { + "bbox": [ + 47, + 362, + 288, + 581 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{coarse}}" + }, + { + "bbox": [ + 47, + 362, + 288, + 581 + ], + "type": "text", + "content": " for coarse mask segmentation is formed as," + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 96, + 591, + 287, + 604 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 591, + 287, + 604 + ], + "spans": [ + { + "bbox": [ + 96, + 591, + 287, + 604 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {c o a r s e}} = \\mathcal {L} _ {\\text {r e g}} + \\mathcal {L} _ {\\text {c l s}} + \\mathcal {L} _ {\\text {c m a s k}}, \\tag {1}", + "image_path": "f3214f9cd9da507f835f78d522034c32ca738cfd70d0ecceaf29c3d8b04d1a5b.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 613, + 287, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 613, + 287, + 661 + ], + "spans": [ + { + "bbox": [ + 47, + 613, + 287, + 661 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 613, + 287, + 661 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{reg}" + }, + { + "bbox": [ + 47, + 613, + 287, + 661 + ], + "type": "text", + "content": " denotes the smooth-L1 loss for bounding box regression, " + }, + { + "bbox": [ + 47, + 613, + 287, + 661 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cls}" + }, + { + "bbox": [ + 47, + 613, + 287, + 661 + ], + "type": "text", + "content": " denotes cross-entropy (CE) loss for classification, and " + }, + { + "bbox": [ + 47, + 613, + 287, + 661 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cmask}" + }, + { + "bbox": [ + 47, + 613, + 287, + 661 + ], + "type": "text", + "content": " denotes pixel-wise CE loss for segmentation." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 670, + 246, + 685 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 670, + 246, + 685 + ], + "spans": [ + { + "bbox": [ + 47, + 670, + 246, + 685 + ], + "type": "text", + "content": "3.2. Decompose-and-recombined Strategy" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "Previous solutions for amodal perception infer the integral structure of occluded instances using visible regions" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": "[9, 37]. However, they ignore information from overlapping regions, which tend to be sub-optimal in the case of complex superposition of translucent objects. To empower the perception capability of model for overlapping translucent regions, we specifically design the decompose-and-recombined strategy." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 144, + 546, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 144, + 546, + 312 + ], + "spans": [ + { + "bbox": [ + 304, + 144, + 546, + 312 + ], + "type": "text", + "content": "Dual-path Region Segmentation Module (DRM): As shown in Figure 2, DRM consists of an Intersection Mask Head " + }, + { + "bbox": [ + 304, + 144, + 546, + 312 + ], + "type": "inline_equation", + "content": "H_{o}" + }, + { + "bbox": [ + 304, + 144, + 546, + 312 + ], + "type": "text", + "content": " and a Complement Mask Head " + }, + { + "bbox": [ + 304, + 144, + 546, + 312 + ], + "type": "inline_equation", + "content": "H_{m}" + }, + { + "bbox": [ + 304, + 144, + 546, + 312 + ], + "type": "text", + "content": " with the same architecture. Let " + }, + { + "bbox": [ + 304, + 144, + 546, + 312 + ], + "type": "inline_equation", + "content": "f_{k,i}^{c}" + }, + { + "bbox": [ + 304, + 144, + 546, + 312 + ], + "type": "text", + "content": " denotes the rich semantic feature before the coarse mask prediction in the Instance Mask Head. Both " + }, + { + "bbox": [ + 304, + 144, + 546, + 312 + ], + "type": "inline_equation", + "content": "H_{o}" + }, + { + "bbox": [ + 304, + 144, + 546, + 312 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 144, + 546, + 312 + ], + "type": "inline_equation", + "content": "H_{m}" + }, + { + "bbox": [ + 304, + 144, + 546, + 312 + ], + "type": "text", + "content": " take the concatenation of " + }, + { + "bbox": [ + 304, + 144, + 546, + 312 + ], + "type": "inline_equation", + "content": "f_{k,i}^{roi}" + }, + { + "bbox": [ + 304, + 144, + 546, + 312 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 144, + 546, + 312 + ], + "type": "inline_equation", + "content": "f_{k,i}^{c}" + }, + { + "bbox": [ + 304, + 144, + 546, + 312 + ], + "type": "text", + "content": " as input to predict the intersection and complement regions " + }, + { + "bbox": [ + 304, + 144, + 546, + 312 + ], + "type": "inline_equation", + "content": "\\hat{o}_{k,i}, \\hat{m}_{k,i}" + }, + { + "bbox": [ + 304, + 144, + 546, + 312 + ], + "type": "text", + "content": " in clusters. See the supplementary material for details of the Concatenation Unit. Specifically, each head consists of 4 convolutional layers to generate features in " + }, + { + "bbox": [ + 304, + 144, + 546, + 312 + ], + "type": "inline_equation", + "content": "14 \\times 14 \\times 256" + }, + { + "bbox": [ + 304, + 144, + 546, + 312 + ], + "type": "text", + "content": ", followed by one deconvolutional layer to get the semantic mask with a resolution of " + }, + { + "bbox": [ + 304, + 144, + 546, + 312 + ], + "type": "inline_equation", + "content": "28 \\times 28 \\times 1" + }, + { + "bbox": [ + 304, + 144, + 546, + 312 + ], + "type": "text", + "content": ". Here, we add the pixel-wise CE loss to both heads as the explicit constraint for decomposition," + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 322, + 548, + 365 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 322, + 548, + 365 + ], + "spans": [ + { + "bbox": [ + 306, + 322, + 548, + 365 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {d e c} = \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\frac {1}{N _ {k}} \\sum_ {i = 1} ^ {N _ {k}} \\left(\\mathcal {L} _ {c e} \\left(\\hat {o} _ {k, i}, o _ {k, i}\\right) + \\mathcal {L} _ {c e} \\left(\\hat {m} _ {k, i}, m _ {k, i}\\right)\\right). \\tag {2}", + "image_path": "a957cb5cf0c932084db6b85baa3b7be03050fac28a3bbdd56a7514ccdcc36c98.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 366, + 546, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 366, + 546, + 559 + ], + "spans": [ + { + "bbox": [ + 304, + 366, + 546, + 559 + ], + "type": "text", + "content": "Semantic Consistency-guided Recombination Module (CRM): To further enhance the perception capability for overlapping instances, CRM is designed to encourage DoNet to perceive integral instances. Specifically, let " + }, + { + "bbox": [ + 304, + 366, + 546, + 559 + ], + "type": "inline_equation", + "content": "f_{k,i}^{o}" + }, + { + "bbox": [ + 304, + 366, + 546, + 559 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 366, + 546, + 559 + ], + "type": "inline_equation", + "content": "f_{k,i}^{m}" + }, + { + "bbox": [ + 304, + 366, + 546, + 559 + ], + "type": "text", + "content": " denote the features before the last layer in the intersection mask head and the complement mask head. The rich semantic feature for the overlapping and non-overlapping region is considered as the residual information for the complex areas which is fused with " + }, + { + "bbox": [ + 304, + 366, + 546, + 559 + ], + "type": "inline_equation", + "content": "f_{k,i}^{roi}" + }, + { + "bbox": [ + 304, + 366, + 546, + 559 + ], + "type": "text", + "content": " and then fed into the recombined mask head. See the supplementary material for details of the Fusion Unit. Noted that we reuse the Instance Mask Head " + }, + { + "bbox": [ + 304, + 366, + 546, + 559 + ], + "type": "inline_equation", + "content": "(H_{i})" + }, + { + "bbox": [ + 304, + 366, + 546, + 559 + ], + "type": "text", + "content": " here to predict the integral instance. This combination facilitates CRM to leverage contextual information of overlapping instances, leading to the improvement of perception capability. The refined mask " + }, + { + "bbox": [ + 304, + 366, + 546, + 559 + ], + "type": "inline_equation", + "content": "\\hat{e}_{k,i}^{r}" + }, + { + "bbox": [ + 304, + 366, + 546, + 559 + ], + "type": "text", + "content": " from CRM is optimized by segmentation loss " + }, + { + "bbox": [ + 304, + 366, + 546, + 559 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rmask}" + }, + { + "bbox": [ + 304, + 366, + 546, + 559 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 341, + 567, + 545, + 601 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 341, + 567, + 545, + 601 + ], + "spans": [ + { + "bbox": [ + 341, + 567, + 545, + 601 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {r m a s k} = \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\frac {1}{N _ {k}} \\sum_ {i = 1} ^ {N _ {k}} \\mathcal {L} _ {c e} \\left(\\hat {e} _ {k, i} ^ {r}, e _ {k, i}\\right). \\tag {3}", + "image_path": "f6d098613ba319bf2e912c4c6075ed784b257841f4746ced74e8e416396beda3.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 611, + 545, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 611, + 545, + 659 + ], + "spans": [ + { + "bbox": [ + 304, + 611, + 545, + 659 + ], + "type": "text", + "content": "To further enhance the feature representation capacity for the relationship of components, we add semantic consistency regularization between the recombination " + }, + { + "bbox": [ + 304, + 611, + 545, + 659 + ], + "type": "inline_equation", + "content": "\\hat{e}_{k,i}^{r}" + }, + { + "bbox": [ + 304, + 611, + 545, + 659 + ], + "type": "text", + "content": " and merged predictions of " + }, + { + "bbox": [ + 304, + 611, + 545, + 659 + ], + "type": "inline_equation", + "content": "\\hat{o}_{k,i}" + }, + { + "bbox": [ + 304, + 611, + 545, + 659 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 611, + 545, + 659 + ], + "type": "inline_equation", + "content": "\\hat{m}_{k,i}" + }, + { + "bbox": [ + 304, + 611, + 545, + 659 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 311, + 670, + 545, + 713 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 670, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 311, + 670, + 545, + 713 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {c o n s}} = \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\frac {1}{N _ {k}} \\sum_ {i = 1} ^ {N _ {k}} \\mathcal {L} _ {\\text {c e}} \\left(\\hat {e} _ {k, i} ^ {r}, \\mathcal {F} _ {\\text {m e r g e}} \\left(\\hat {o} _ {k, i}, \\hat {m} _ {k, i}\\right)\\right), \\tag {4}", + "image_path": "5adb25097c9abfd5a5bb10b8192d98f5487e3ada3a603220aaceb68891430e69.jpg" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15644" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{\\text{merge}}(\\cdot)" + }, + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "text", + "content": " represents the merging operation for the intersection region and the complement region in Mergence Unit, which is " + }, + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "inline_equation", + "content": "xor()" + }, + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "text", + "content": ", two sub-region masks are passed through Sigmoid function for normalization. Then, we calculate the Mask Exclusive-OR of two mask logits for merging them and suppressing redundant predicted pixels." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 152, + 212, + 166 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 152, + 212, + 166 + ], + "spans": [ + { + "bbox": [ + 47, + 152, + 212, + 166 + ], + "type": "text", + "content": "3.3. Mask-guided Region Proposal" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 171, + 287, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 171, + 287, + 266 + ], + "spans": [ + { + "bbox": [ + 46, + 171, + 287, + 266 + ], + "type": "text", + "content": "It is inevitable for cytology images to exist abundant cellular debris and non-target objects, e.g., white blood cells and mucus. These objects often have a similar appearance as the nuclei, with small round surfaces stained in dark purple, which increases the model identification difficulty. To avoid the interference it brings, we further propose a Mask-guided Region Proposal module (MRP) to encourage the model to generate nuclei proposals in intra-cellular regions." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 267, + 289, + 368 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 267, + 289, + 368 + ], + "spans": [ + { + "bbox": [ + 46, + 267, + 289, + 368 + ], + "type": "text", + "content": "For each image, we can aggregate all the recombined instance predictions " + }, + { + "bbox": [ + 46, + 267, + 289, + 368 + ], + "type": "inline_equation", + "content": "\\hat{e}_{k,i}^{r}" + }, + { + "bbox": [ + 46, + 267, + 289, + 368 + ], + "type": "text", + "content": " in CRM together into a semantic mask " + }, + { + "bbox": [ + 46, + 267, + 289, + 368 + ], + "type": "inline_equation", + "content": "\\hat{M}_k" + }, + { + "bbox": [ + 46, + 267, + 289, + 368 + ], + "type": "text", + "content": ". The raw predictions are first mapped back and then summed up according to their bounding boxes predictions " + }, + { + "bbox": [ + 46, + 267, + 289, + 368 + ], + "type": "inline_equation", + "content": "\\hat{b}_{k,i}" + }, + { + "bbox": [ + 46, + 267, + 289, + 368 + ], + "type": "text", + "content": " in the detection head, followed by a Sigmoid function to normalize them into probabilities. " + }, + { + "bbox": [ + 46, + 267, + 289, + 368 + ], + "type": "inline_equation", + "content": "\\hat{M}_k" + }, + { + "bbox": [ + 46, + 267, + 289, + 368 + ], + "type": "text", + "content": " is considered as the attention score to re-weight features " + }, + { + "bbox": [ + 46, + 267, + 289, + 368 + ], + "type": "inline_equation", + "content": "f_{k}" + }, + { + "bbox": [ + 46, + 267, + 289, + 368 + ], + "type": "text", + "content": " in origin FPN via element-wise multiplication:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 134, + 376, + 287, + 390 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 134, + 376, + 287, + 390 + ], + "spans": [ + { + "bbox": [ + 134, + 376, + 287, + 390 + ], + "type": "interline_equation", + "content": "f _ {k} ^ {w} = \\hat {M} _ {k} \\circ f _ {k}, \\tag {5}", + "image_path": "1e5585f55833f69efcafea5a573f1b995f3e085fd631510528fd38ebc51a7a9b.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 399, + 287, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 399, + 287, + 483 + ], + "spans": [ + { + "bbox": [ + 46, + 399, + 287, + 483 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 399, + 287, + 483 + ], + "type": "inline_equation", + "content": "f_{k}^{w}" + }, + { + "bbox": [ + 46, + 399, + 287, + 483 + ], + "type": "text", + "content": " denotes the re-weighted features for nuclei proposal predictions in MRP. Thus, extracellular pixels with a lower probability to be cytoplasm are suppressed, which reduces the false positives for background instances (i.e., blood, mucus, and others). In addition, MRP also builds information interaction between different stages, which naturally encourages feature representation ability." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 491, + 169, + 504 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 491, + 169, + 504 + ], + "spans": [ + { + "bbox": [ + 47, + 491, + 169, + 504 + ], + "type": "text", + "content": "3.4. End-to-end Learning" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "text", + "content": "Extended dataset with synthetic clusters: The semitransparency characteristic of cytoplasm alleviates the effect of high overlap, allowing cytologists to delineate the contour of cellular instances based on expert knowledge. However, extremely challenging labeling and unavoidable label noise limit the availability of large-scale annotated datasets. To tackle this problem, we propose an instance-level data augmentor for overlapping cell data augmentation, which can generate large-scale synthetic cell clusters with controllable overlapping ratios and transparency based on the annotated cellular instances. This synthetic dataset further facilitates the generalization ability, by providing more diverse data to implicitly learn the concept of instance and its components. See the supplementary material for details of the synthetic pipeline. Unless otherwise specified, we do not use this synthetic dataset in the following comparison." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": "Overall Loss Function: The proposed cell instance segmentation framework can be trained in a supervised manner. The overall objective " + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": " is as follows," + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 307, + 122, + 545, + 146 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 122, + 545, + 146 + ], + "spans": [ + { + "bbox": [ + 307, + 122, + 545, + 146 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {\\text {c o a r s e}} + \\lambda_ {\\text {d e c}} \\mathcal {L} _ {\\text {d e c}} + \\lambda_ {\\text {r m a s k}} \\mathcal {L} _ {\\text {r m a s k}} + \\lambda_ {\\text {c o n s}} \\mathcal {L} _ {\\text {c o n s}}, \\tag {6}", + "image_path": "3fbf272bbbe1567cf2810dfa8e54bb20483045a9cd97f2a3877b3659563be7ca.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 147, + 546, + 231 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 147, + 546, + 231 + ], + "spans": [ + { + "bbox": [ + 305, + 147, + 546, + 231 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 147, + 546, + 231 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{coarse}}" + }, + { + "bbox": [ + 305, + 147, + 546, + 231 + ], + "type": "text", + "content": " denotes losses for RoI extraction and coarse mask prediction, " + }, + { + "bbox": [ + 305, + 147, + 546, + 231 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{dec}" + }, + { + "bbox": [ + 305, + 147, + 546, + 231 + ], + "type": "text", + "content": " denotes the decomposition loss for intersection and complement regions segmentation, " + }, + { + "bbox": [ + 305, + 147, + 546, + 231 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rmask}" + }, + { + "bbox": [ + 305, + 147, + 546, + 231 + ], + "type": "text", + "content": " is the segmentation loss for refined masks, " + }, + { + "bbox": [ + 305, + 147, + 546, + 231 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cons}" + }, + { + "bbox": [ + 305, + 147, + 546, + 231 + ], + "type": "text", + "content": " supervises the semantic consistency between integral instance and subregions. " + }, + { + "bbox": [ + 305, + 147, + 546, + 231 + ], + "type": "inline_equation", + "content": "\\lambda_{dec}, \\lambda_{rmask}," + }, + { + "bbox": [ + 305, + 147, + 546, + 231 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 147, + 546, + 231 + ], + "type": "inline_equation", + "content": "\\lambda_{cons}" + }, + { + "bbox": [ + 305, + 147, + 546, + 231 + ], + "type": "text", + "content": " are trade-off parameters controlling the importance of each component." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 247, + 388, + 261 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 247, + 388, + 261 + ], + "spans": [ + { + "bbox": [ + 306, + 247, + 388, + 261 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 268, + 422, + 282 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 268, + 422, + 282 + ], + "spans": [ + { + "bbox": [ + 306, + 268, + 422, + 282 + ], + "type": "text", + "content": "4.1. Experimental Setup" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 289, + 545, + 313 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 289, + 545, + 313 + ], + "spans": [ + { + "bbox": [ + 305, + 289, + 545, + 313 + ], + "type": "text", + "content": "We evaluate our proposed DoNet in two cytology image datasets for overlapping cell instance segmentation:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 315, + 546, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 315, + 546, + 422 + ], + "spans": [ + { + "bbox": [ + 305, + 315, + 546, + 422 + ], + "type": "text", + "content": "ISBI2014 [24]: This is a widely-used dataset from Overlapping Cervical Cytology Image Segmentation Challenge1, which consists of 8 extended depth-of-focus (EDF) real cervical cytology images and corresponding synthetic images. It contains high-quality pixel-level annotations for both nuclei and cytoplasm with a resolution of " + }, + { + "bbox": [ + 305, + 315, + 546, + 422 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 305, + 315, + 546, + 422 + ], + "type": "text", + "content": ". We follow the setting in this challenge [24] to use 45, 90 and 810 images for training, validation and testing to evaluate our proposed DoNet in a supervised setting." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 424, + 547, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 424, + 547, + 472 + ], + "spans": [ + { + "bbox": [ + 305, + 424, + 547, + 472 + ], + "type": "text", + "content": "CPS [39]: This liquid-based cytology dataset contains 137 labeled images with a resolution of " + }, + { + "bbox": [ + 305, + 424, + 547, + 472 + ], + "type": "inline_equation", + "content": "1000 \\times 1000" + }, + { + "bbox": [ + 305, + 424, + 547, + 472 + ], + "type": "text", + "content": ". In total, it contains 4439 cytoplasm and 4789 nuclei annotations. We conduct 3-fold cross-validation on this dataset." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 474, + 547, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 474, + 547, + 582 + ], + "spans": [ + { + "bbox": [ + 305, + 474, + 547, + 582 + ], + "type": "text", + "content": "Evaluation metrics: To measure the overall performance of the proposed DoNet, we utilize four commonly-used evaluation metrics in instance segmentation: aggregated Jaccard index (AJI), average Dice coefficient (Dice), F1-score (F1) [20], mean of Average Precision (mAP) [11]. In order to compare our result on the ISBI2014 with previous studies [24], we further adopt evaluation metrics including Dice, object-based false negative rate " + }, + { + "bbox": [ + 305, + 474, + 547, + 582 + ], + "type": "inline_equation", + "content": "(\\mathrm{FN}_o)" + }, + { + "bbox": [ + 305, + 474, + 547, + 582 + ], + "type": "text", + "content": ", and pixel-based true positive rate " + }, + { + "bbox": [ + 305, + 474, + 547, + 582 + ], + "type": "inline_equation", + "content": "(\\mathrm{TP}_p)" + }, + { + "bbox": [ + 305, + 474, + 547, + 582 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 584, + 547, + 679 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 584, + 547, + 679 + ], + "spans": [ + { + "bbox": [ + 305, + 584, + 547, + 679 + ], + "type": "text", + "content": "Implementation details: We utilize the Mask R-CNN [11] in Detector2 [36] as the baseline model. We use the ResNet-50-based FPN network in all experiments. During training, we adopt SGD with 0.9 momentum as the optimizer. We set the initial learning rate to 0.001 and add the linear warm-up in the first 1k iterations. We train the network for 60k iterations, decreasing the learning rate by a factor of 0.1 after 50k and 55k iterations." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 693, + 546, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 546, + 713 + ], + "type": "text", + "content": "1 https://cs.adelaide.edu.au/~carneiro/isbil4_challenge/index.html" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15645" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 63, + 87, + 535, + 198 + ], + "blocks": [ + { + "bbox": [ + 97, + 70, + 496, + 82 + ], + "lines": [ + { + "bbox": [ + 97, + 70, + 496, + 82 + ], + "spans": [ + { + "bbox": [ + 97, + 70, + 496, + 82 + ], + "type": "text", + "content": "Table 1. Quantitative segmentation results of DoNet and other state-of-the-art methods on CPS and ISBI2014." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 63, + 87, + 535, + 198 + ], + "lines": [ + { + "bbox": [ + 63, + 87, + 535, + 198 + ], + "spans": [ + { + "bbox": [ + 63, + 87, + 535, + 198 + ], + "type": "table", + "html": "
MethodsISBI2014CPS
mAP↑Dice↑F1↑AJI↑mAP↑Dice↑F1↑AJI↑
Mask R-CNN [11]59.0991.1592.5477.0748.28 ± 3.1089.32 ± 0.5085.07 ± 2.0169.20 ± 2.27
Cascade R-CNN [2]62.4591.2992.5177.9147.87 ± 3.2789.24 ± 0.4483.33 ± 1.6568.86 ± 3.55
Mask Scoring R-CNN [13]63.5691.2891.8775.1448.38 ± 3.1389.39 ± 0.2482.98 ± 1.8667.45 ± 2.45
HTC [8]59.6291.3988.0875.0047.60 ± 3.5689.08 ± 0.5181.30 ± 2.5666.35 ± 2.84
Occlusion R-CNN [9]62.3591.7593.1878.6448.14 ± 2.8489.08 ± 0.2885.69 ± 2.2869.51 ± 2.45
Xiao et al. [37]57.3491.7092.7578.2948.53 ± 2.8589.29 ± 0.2485.46 ± 2.6069.37 ± 2.88
DoNet64.0292.1393.2379.0549.43 ± 3.8389.54 ± 0.2585.51 ± 2.3370.08 ± 2.84
DoNet w/ Aug.----49.65 ± 3.5289.50 ± 0.3886.30 ± 2.0170.56 ± 2.34
", + "image_path": "67351f6d2a4a2ffecdcd6c0e04085004a460451ebbd121b77c705099e79cac59.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 226, + 105, + 238 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 226, + 105, + 238 + ], + "spans": [ + { + "bbox": [ + 47, + 226, + 105, + 238 + ], + "type": "text", + "content": "4.2. Results" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 251, + 290, + 466 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 251, + 290, + 466 + ], + "spans": [ + { + "bbox": [ + 46, + 251, + 290, + 466 + ], + "type": "text", + "content": "We quantitatively compare the cell instance segmentation results from the ISBI2014 and CPS in Table 1 with state-of-the-art methods in the field of general instance segmentation (Mask R-CNN [11], Cascade R-CNN [2], Mask Scoring R-CNN [13], HTC [8]) and amodal instance segmentation (Occlusion R-CNN [9], Xiao et al. [37]). Noted that the amodal instance segmentation methods and general instance segmentation methods perform differently on two datasets due to the varying degrees of overlapping. Our method achieves the highest scores among all metrics. Specifically, it gains " + }, + { + "bbox": [ + 46, + 251, + 290, + 466 + ], + "type": "inline_equation", + "content": "2.68\\%" + }, + { + "bbox": [ + 46, + 251, + 290, + 466 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 251, + 290, + 466 + ], + "type": "inline_equation", + "content": "0.52\\%" + }, + { + "bbox": [ + 46, + 251, + 290, + 466 + ], + "type": "text", + "content": " improvements for mAP and AJI compared with the best of others [9] on the ISBI2014 dataset, as well as " + }, + { + "bbox": [ + 46, + 251, + 290, + 466 + ], + "type": "inline_equation", + "content": "1.85\\%" + }, + { + "bbox": [ + 46, + 251, + 290, + 466 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 251, + 290, + 466 + ], + "type": "inline_equation", + "content": "1.02\\%" + }, + { + "bbox": [ + 46, + 251, + 290, + 466 + ], + "type": "text", + "content": " improvements compared with the best [37] on the CPS dataset. We also evaluate " + }, + { + "bbox": [ + 46, + 251, + 290, + 466 + ], + "type": "inline_equation", + "content": "TP_{p}" + }, + { + "bbox": [ + 46, + 251, + 290, + 466 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 251, + 290, + 466 + ], + "type": "inline_equation", + "content": "FN_{o}" + }, + { + "bbox": [ + 46, + 251, + 290, + 466 + ], + "type": "text", + "content": " for DoNet to compare results against winners of the ISBI2014 challenge [27,33] and their following works [21, 31], which are mostly the segment-then-refine manners (Seen in Table 2)." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 472, + 288, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 472, + 288, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 472, + 288, + 544 + ], + "type": "text", + "content": "Furthermore, by introducing the synthetic clusters as instance-level augmentation, DoNet further has " + }, + { + "bbox": [ + 46, + 472, + 288, + 544 + ], + "type": "inline_equation", + "content": "0.45\\%" + }, + { + "bbox": [ + 46, + 472, + 288, + 544 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 472, + 288, + 544 + ], + "type": "inline_equation", + "content": "0.68\\%" + }, + { + "bbox": [ + 46, + 472, + 288, + 544 + ], + "type": "text", + "content": " improvements for mAP and AJI on the CPS dataset. This is mainly because the synthetic overlapping cells can further enhance the model's occlusion reasoning capability, which is consistent with the conclusions in [22]." + } + ] + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 66, + 578, + 268, + 701 + ], + "blocks": [ + { + "bbox": [ + 66, + 558, + 268, + 569 + ], + "lines": [ + { + "bbox": [ + 66, + 558, + 268, + 569 + ], + "spans": [ + { + "bbox": [ + 66, + 558, + 268, + 569 + ], + "type": "text", + "content": "Table 2. Comparison with other methods on ISBI2014." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 66, + 578, + 268, + 701 + ], + "lines": [ + { + "bbox": [ + 66, + 578, + 268, + 701 + ], + "spans": [ + { + "bbox": [ + 66, + 578, + 268, + 701 + ], + "type": "table", + "html": "
MethodsISBI2014
Dice↑TPp↑FN0↓
Ushizima et al. [33]0.8720.8410.265
Nosrati et al. [27]0.8710.8750.110
Walter et al. [34]0.8600.8300.310
Lu et al. [24]0.8930.9050.315
Lee et al. [21]0.8970.8820.137
Tareef et al. [31]0.8980.9460.161
Chen et al. [7]0.9200.9000.020
DoNet0.9210.9480.162
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By adding DRM for explicit decomposing integral instances into intersection and complement sub-regions, we observe a " + }, + { + "bbox": [ + 304, + 245, + 547, + 437 + ], + "type": "inline_equation", + "content": "3.25\\%" + }, + { + "bbox": [ + 304, + 245, + 547, + 437 + ], + "type": "text", + "content": " increase in the average mAP of cytoplasm and nuclei on ISBI2014. However, directly adding DRM without the fusion of structural and morphological information, may mislead the model. This issue is observed in the more complex CPS dataset. To alleviate this problem, DoNet takes advantage of the decompose-and-recombined strategy by adding CRM after DRM. This strategy brings a total of " + }, + { + "bbox": [ + 304, + 245, + 547, + 437 + ], + "type": "inline_equation", + "content": "7.34\\%" + }, + { + "bbox": [ + 304, + 245, + 547, + 437 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 245, + 547, + 437 + ], + "type": "inline_equation", + "content": "1.74\\%" + }, + { + "bbox": [ + 304, + 245, + 547, + 437 + ], + "type": "text", + "content": " mAP improvements on two datasets by strengthening the model's perception of overlapping regions while preserving morphological information." + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 314, + 449, + 369, + 505 + ], + "blocks": [ + { + "bbox": [ + 314, + 449, + 369, + 505 + ], + "lines": [ + { + "bbox": [ + 314, + 449, + 369, + 505 + ], + "spans": [ + { + "bbox": [ + 314, + 449, + 369, + 505 + ], + "type": "image", + "image_path": "a2cad089aac2a11a6f5e56ce3b2bef867e086488e2ca42f1a57c569d745ff696.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 370, + 449, + 425, + 505 + ], + "blocks": [ + { + "bbox": [ + 370, + 449, + 425, + 505 + ], + "lines": [ + { + "bbox": [ + 370, + 449, + 425, + 505 + ], + "spans": [ + { + "bbox": [ + 370, + 449, + 425, + 505 + ], + "type": "image", + "image_path": "2bf66742e99cdb45a3a1cdb1d2c88dc7a72e150e89f1c8009452f57418c6661a.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 427, + 449, + 482, + 506 + ], + "blocks": [ + { + "bbox": [ + 427, + 449, + 482, + 506 + ], + "lines": [ + { + "bbox": [ + 427, + 449, + 482, + 506 + ], + "spans": [ + { + "bbox": [ + 427, + 449, + 482, + 506 + ], + "type": "image", + "image_path": "930409e24a14aaa5f632c5b0b0f7e2374f6f3bc7c2acfe43a8a8ea1d60b8a91b.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 483, + 449, + 537, + 506 + ], + "blocks": [ + { + "bbox": [ + 483, + 449, + 537, + 506 + ], + "lines": [ + { + "bbox": [ + 483, + 449, + 537, + 506 + ], + "spans": [ + { + "bbox": [ + 483, + 449, + 537, + 506 + ], + "type": "image", + "image_path": "f44c4454170ec449bad6861d7f66f9764616b3cdf36ed99979f6c78aa04ae6fd.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 314, + 506, + 369, + 561 + ], + "blocks": [ + { + "bbox": [ + 314, + 506, + 369, + 561 + ], + "lines": [ + { + "bbox": [ + 314, + 506, + 369, + 561 + ], + "spans": [ + { + "bbox": [ + 314, + 506, + 369, + 561 + ], + "type": "image", + "image_path": "5636e93e3201def7dc5504aa664177d7a9c2180c88813b37471483ccef8de177.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 338, + 564, + 347, + 572 + ], + "lines": [ + { + "bbox": [ + 338, + 564, + 347, + 572 + ], + "spans": [ + { + "bbox": [ + 338, + 564, + 347, + 572 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 370, + 506, + 425, + 561 + ], + "blocks": [ + { + "bbox": [ + 370, + 506, + 425, + 561 + ], + "lines": [ + { + "bbox": [ + 370, + 506, + 425, + 561 + ], + "spans": [ + { + "bbox": [ + 370, + 506, + 425, + 561 + ], + "type": "image", + "image_path": "132ab24df7d23a20086d2ab93646472d0ecf86146e49ace860d29ab4912a5a04.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 391, + 563, + 400, + 572 + ], + "lines": [ + { + "bbox": [ + 391, + 563, + 400, + 572 + ], + "spans": [ + { + "bbox": [ + 391, + 563, + 400, + 572 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 427, + 506, + 481, + 561 + ], + "blocks": [ + { + "bbox": [ + 427, + 506, + 481, + 561 + ], + "lines": [ + { + "bbox": [ + 427, + 506, + 481, + 561 + ], + "spans": [ + { + "bbox": [ + 427, + 506, + 481, + 561 + ], + "type": "image", + "image_path": "6c376490f200b5826e3caa3af15fc247572b05ce86304ad8c2da08393989906f.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 449, + 564, + 457, + 572 + ], + "lines": [ + { + "bbox": [ + 449, + 564, + 457, + 572 + ], + "spans": [ + { + "bbox": [ + 449, + 564, + 457, + 572 + ], + "type": "text", + "content": "(c)" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 306, + 582, + 547, + 628 + ], + "lines": [ + { + "bbox": [ + 306, + 582, + 547, + 628 + ], + "spans": [ + { + "bbox": [ + 306, + 582, + 547, + 628 + ], + "type": "text", + "content": "Figure 3. Illustration of background noise suppression in MRP: (a) the original image, (b) the origin feature map for region proposal, (c) the attention map from cytoplasm prediction, and (d) the re-weighted feature map for nuclei proposal generation." + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 482, + 506, + 537, + 561 + ], + "blocks": [ + { + "bbox": [ + 482, + 506, + 537, + 561 + ], + "lines": [ + { + "bbox": [ + 482, + 506, + 537, + 561 + ], + "spans": [ + { + "bbox": [ + 482, + 506, + 537, + 561 + ], + "type": "image", + "image_path": "4fedc8e070c55e2ba07048ab56b12bcb9621d05637ba84469d09e84f2c15ef16.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 506, + 564, + 515, + 572 + ], + "lines": [ + { + "bbox": [ + 506, + 564, + 515, + 572 + ], + "spans": [ + { + "bbox": [ + 506, + 564, + 515, + 572 + ], + "type": "text", + "content": "(d)" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": "Applying MRP for mitigating the side effects from background mimics yields a further improvement of " + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "inline_equation", + "content": "0.59\\%" + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": " mAP and " + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "inline_equation", + "content": "0.31\\%" + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": " mAP on ISBI2014 and CPS datasets. Figure 3 provides the visualization of MRP operation, where background instances (e.g., mucus, karyoclasis, pointed by red arrow) are suppressed with strong responses in the feature" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "15646" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 61, + 83, + 533, + 150 + ], + "blocks": [ + { + "bbox": [ + 83, + 63, + 509, + 76 + ], + "lines": [ + { + "bbox": [ + 83, + 63, + 509, + 76 + ], + "spans": [ + { + "bbox": [ + 83, + 63, + 509, + 76 + ], + "type": "text", + "content": "Table 3. Effect of each proposed module on CPS and ISBI2014 datasets. " + }, + { + "bbox": [ + 83, + 63, + 509, + 76 + ], + "type": "inline_equation", + "content": "\\checkmark" + }, + { + "bbox": [ + 83, + 63, + 509, + 76 + ], + "type": "text", + "content": " denotes adding the corresponding module." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 61, + 83, + 533, + 150 + ], + "lines": [ + { + "bbox": [ + 61, + 83, + 533, + 150 + ], + "spans": [ + { + "bbox": [ + 61, + 83, + 533, + 150 + ], + "type": "table", + "html": "
BaseDRMCRMMRPISBI2014CPS
mAP↑Dice↑F1↑AJI↑mAP↑Dice↑F1↑AJI↑
✓59.0991.1592.5477.0748.28 ± 3.1089.32 ± 0.5085.07 ± 2.0169.20 ± 2.27
✓✓61.0191.6192.8678.0648.03 ± 3.4889.13 ± 0.3084.63 ± 2.5768.56 ± 2.57
✓✓✓63.4391.8794.1679.8849.12 ± 3.2689.47 ± 0.3184.82 ± 2.7369.26 ± 2.63
✓✓✓✓64.0292.1393.2379.0549.43 ± 3.8389.54 ± 0.2585.51 ± 2.3370.08 ± 2.84
", + "image_path": "c6c4ed5b9e9b0c718f50f0885124a5efe906da488a3a72961543f5ec53bb97ee.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 50, + 180, + 547, + 262 + ], + "blocks": [ + { + "bbox": [ + 65, + 159, + 526, + 171 + ], + "lines": [ + { + "bbox": [ + 65, + 159, + 526, + 171 + ], + "spans": [ + { + "bbox": [ + 65, + 159, + 526, + 171 + ], + "type": "text", + "content": "Table 4. Ablation study of DRM and CRM on the ISBI2014 dataset. " + }, + { + "bbox": [ + 65, + 159, + 526, + 171 + ], + "type": "inline_equation", + "content": "\\checkmark" + }, + { + "bbox": [ + 65, + 159, + 526, + 171 + ], + "type": "text", + "content": " denotes adding the corresponding component or strategy." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 180, + 547, + 262 + ], + "lines": [ + { + "bbox": [ + 50, + 180, + 547, + 262 + ], + "spans": [ + { + "bbox": [ + 50, + 180, + 547, + 262 + ], + "type": "table", + "html": "
\\(H_i\\)\\(H_o\\)\\(H_m\\)FU\\(\\mathcal{L}_{cons}\\)mAP↑Dice↑F1↑AJI↑
Cyt.Nuc.Avg.Cyt.Nuc.Avg.Cyt.Nuc.Avg.Cyt.Nuc.Avg.
✓50.7167.4659.0990.7291.5991.1586.9698.1392.5470.5583.6077.07
✓✓54.8465.9460.3991.5691.5491.5587.0097.6892.3472.0782.6777.37
✓✓✓57.4166.4961.9591.7991.5391.6688.6797.9893.3274.0083.2778.63
✓✓✓✓58.4067.8263.1192.2291.7491.9889.2198.0793.6474.9483.7079.32
✓✓✓✓✓59.3167.5663.4392.0391.7191.8790.1398.1894.1675.8683.9179.88
", + "image_path": "2e1a93f4450a7d2feddb7eeed809c7927924fe9dbc3958b1645b884cc3ce42d9.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 291, + 287, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 291, + 287, + 316 + ], + "spans": [ + { + "bbox": [ + 46, + 291, + 287, + 316 + ], + "type": "text", + "content": "map, encouraging the RPN to concentrate on cellular instance during nuclei region proposal." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 319, + 287, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 319, + 287, + 392 + ], + "spans": [ + { + "bbox": [ + 46, + 319, + 287, + 392 + ], + "type": "text", + "content": "Design Choice for DRM: We provide detailed comparisons on the ISBI2014 dataset to demonstrate the effectiveness of different components in DRM: 1) " + }, + { + "bbox": [ + 46, + 319, + 287, + 392 + ], + "type": "inline_equation", + "content": "H_{i}" + }, + { + "bbox": [ + 46, + 319, + 287, + 392 + ], + "type": "text", + "content": ": instance mask head for coarse segmentation only; 2) " + }, + { + "bbox": [ + 46, + 319, + 287, + 392 + ], + "type": "inline_equation", + "content": "H_{o}" + }, + { + "bbox": [ + 46, + 319, + 287, + 392 + ], + "type": "text", + "content": ": intersection mask head for overlapping region segmentation; 3) " + }, + { + "bbox": [ + 46, + 319, + 287, + 392 + ], + "type": "inline_equation", + "content": "H_{m}" + }, + { + "bbox": [ + 46, + 319, + 287, + 392 + ], + "type": "text", + "content": ": complement mask head for non-overlapping region segmentation;" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 394, + 287, + 455 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 394, + 287, + 455 + ], + "spans": [ + { + "bbox": [ + 46, + 394, + 287, + 455 + ], + "type": "text", + "content": "As seen in Table 4, adding " + }, + { + "bbox": [ + 46, + 394, + 287, + 455 + ], + "type": "inline_equation", + "content": "H_{o}" + }, + { + "bbox": [ + 46, + 394, + 287, + 455 + ], + "type": "text", + "content": " yields an improvement of " + }, + { + "bbox": [ + 46, + 394, + 287, + 455 + ], + "type": "inline_equation", + "content": "2.20\\%" + }, + { + "bbox": [ + 46, + 394, + 287, + 455 + ], + "type": "text", + "content": " in average mAP, with a further " + }, + { + "bbox": [ + 46, + 394, + 287, + 455 + ], + "type": "inline_equation", + "content": "2.64\\%" + }, + { + "bbox": [ + 46, + 394, + 287, + 455 + ], + "type": "text", + "content": " gains from the additional " + }, + { + "bbox": [ + 46, + 394, + 287, + 455 + ], + "type": "inline_equation", + "content": "H_{m}" + }, + { + "bbox": [ + 46, + 394, + 287, + 455 + ], + "type": "text", + "content": ". We notice that cytoplasm results have a more significant improvement of " + }, + { + "bbox": [ + 46, + 394, + 287, + 455 + ], + "type": "inline_equation", + "content": "13.2\\%" + }, + { + "bbox": [ + 46, + 394, + 287, + 455 + ], + "type": "text", + "content": " in mAP, which is indeed in line with our design intent." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 458, + 287, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 458, + 287, + 626 + ], + "spans": [ + { + "bbox": [ + 46, + 458, + 287, + 626 + ], + "type": "text", + "content": "Design Choice for CRM: The goal of semantic consistency regularization is to enhance the model's overlapping reasoning capability by learning the concept of recombined instances from sub-regions. We provide comparisons to demonstrate the design choice (Table 4): 1) " + }, + { + "bbox": [ + 46, + 458, + 287, + 626 + ], + "type": "inline_equation", + "content": "\\mathrm{CU} + \\mathrm{FU}" + }, + { + "bbox": [ + 46, + 458, + 287, + 626 + ], + "type": "text", + "content": ": integration of rich semantic features as inputs via Concatenation Unit and Fusion Unit. 2) " + }, + { + "bbox": [ + 46, + 458, + 287, + 626 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{cons}}" + }, + { + "bbox": [ + 46, + 458, + 287, + 626 + ], + "type": "text", + "content": ": consistency regularization between the recombined prediction " + }, + { + "bbox": [ + 46, + 458, + 287, + 626 + ], + "type": "inline_equation", + "content": "\\hat{e}_{k,i}^{r}" + }, + { + "bbox": [ + 46, + 458, + 287, + 626 + ], + "type": "text", + "content": " and the fusion of sub-regions " + }, + { + "bbox": [ + 46, + 458, + 287, + 626 + ], + "type": "inline_equation", + "content": "\\hat{o}_{k,i}, \\hat{m}_{k,i}" + }, + { + "bbox": [ + 46, + 458, + 287, + 626 + ], + "type": "text", + "content": ". As seen in Table 4, by aggregating the rich semantic feature for overlapping and non-overlapping region via Fusion Unit, we observe an increase of " + }, + { + "bbox": [ + 46, + 458, + 287, + 626 + ], + "type": "inline_equation", + "content": "1.52\\%" + }, + { + "bbox": [ + 46, + 458, + 287, + 626 + ], + "type": "text", + "content": " average mAP on the ISBI2014 dataset. Adding consistency regularization further improves " + }, + { + "bbox": [ + 46, + 458, + 287, + 626 + ], + "type": "inline_equation", + "content": "0.91\\%" + }, + { + "bbox": [ + 46, + 458, + 287, + 626 + ], + "type": "text", + "content": " mAP for cytoplasm." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": "Figure 4 visualizes the results of the DoNet and other typical instance segmentation methods, including standard (Mask R-CNN), multi-task (DoNet w/o CRM), and amodal (Occlusion R-CNN) instance segmentation model. It demonstrates the importance of adding interaction among sub-regions via CRM and the strong perceptual capability of DoNet in overlapping regions." + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 332, + 291, + 425, + 384 + ], + "blocks": [ + { + "bbox": [ + 332, + 291, + 425, + 384 + ], + "lines": [ + { + "bbox": [ + 332, + 291, + 425, + 384 + ], + "spans": [ + { + "bbox": [ + 332, + 291, + 425, + 384 + ], + "type": "image", + "image_path": "b09fe0056960c8d0ad6c0a9e364c8242fdc8f79892e84b579c1567cf4dde3a7a.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 373, + 387, + 383, + 396 + ], + "lines": [ + { + "bbox": [ + 373, + 387, + 383, + 396 + ], + "spans": [ + { + "bbox": [ + 373, + 387, + 383, + 396 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 427, + 291, + 521, + 384 + ], + "blocks": [ + { + "bbox": [ + 427, + 291, + 521, + 384 + ], + "lines": [ + { + "bbox": [ + 427, + 291, + 521, + 384 + ], + "spans": [ + { + "bbox": [ + 427, + 291, + 521, + 384 + ], + "type": "image", + "image_path": "09e7b7bc850093e4f7e29963d21d3d907d9d2fdb2761673684d5075491a7a5e2.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 466, + 386, + 477, + 396 + ], + "lines": [ + { + "bbox": [ + 466, + 386, + 477, + 396 + ], + "spans": [ + { + "bbox": [ + 466, + 386, + 477, + 396 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 331, + 400, + 425, + 493 + ], + "blocks": [ + { + "bbox": [ + 331, + 400, + 425, + 493 + ], + "lines": [ + { + "bbox": [ + 331, + 400, + 425, + 493 + ], + "spans": [ + { + "bbox": [ + 331, + 400, + 425, + 493 + ], + "type": "image", + "image_path": "d7b74a07a7304ecd717b6ea08a4f40cda3d62be8688decd3a54f2c9f692dbf87.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 373, + 496, + 384, + 505 + ], + "lines": [ + { + "bbox": [ + 373, + 496, + 384, + 505 + ], + "spans": [ + { + "bbox": [ + 373, + 496, + 384, + 505 + ], + "type": "text", + "content": "(c)" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 427, + 400, + 521, + 493 + ], + "blocks": [ + { + "bbox": [ + 427, + 400, + 521, + 493 + ], + "lines": [ + { + "bbox": [ + 427, + 400, + 521, + 493 + ], + "spans": [ + { + "bbox": [ + 427, + 400, + 521, + 493 + ], + "type": "image", + "image_path": "dd16129c8c8f28d059c83dfafcb507d127866dcb96be69beb144d57642f99434.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 464, + 496, + 475, + 505 + ], + "lines": [ + { + "bbox": [ + 464, + 496, + 475, + 505 + ], + "spans": [ + { + "bbox": [ + 464, + 496, + 475, + 505 + ], + "type": "text", + "content": "(d)" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 304, + 515, + 545, + 549 + ], + "lines": [ + { + "bbox": [ + 304, + 515, + 545, + 549 + ], + "spans": [ + { + "bbox": [ + 304, + 515, + 545, + 549 + ], + "type": "text", + "content": "Figure 4. Qualitative results from (a) standard [11], (b) multitask (DoNet w/o CRM), (c) amodal [9], and (d) proposed deoverlapping instance segmentation method." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 572, + 495, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 572, + 495, + 586 + ], + "spans": [ + { + "bbox": [ + 306, + 572, + 495, + 586 + ], + "type": "text", + "content": "4.4. Qualitative Analysis and Discussion" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 592, + 545, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 592, + 545, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 592, + 545, + 653 + ], + "type": "text", + "content": "We visualize the heatmap of the intersection region, the complement region, and the integral instance in Figure 6. The proposed method successfully identifies sub-regions based on the overlapping concept, even in low-resolution areas with high transparency." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "Furthermore, we provide qualitative comparisons on CPS (top) and ISBI2014 (bottom) datasets in Figure 5. Our proposed DoNet outperforms other instance segmentation methods. Specifically, red rectangles provide details and highlight the main difference among these results. In the" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15647" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 72, + 545, + 336 + ], + "blocks": [ + { + "bbox": [ + 49, + 72, + 545, + 336 + ], + "lines": [ + { + "bbox": [ + 49, + 72, + 545, + 336 + ], + "spans": [ + { + "bbox": [ + 49, + 72, + 545, + 336 + ], + "type": "image", + "image_path": "46caceede9d40b1308808bc786c999a63f21a07a16952601a70079dd09368ae1.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 346, + 546, + 381 + ], + "lines": [ + { + "bbox": [ + 46, + 346, + 546, + 381 + ], + "spans": [ + { + "bbox": [ + 46, + 346, + 546, + 381 + ], + "type": "text", + "content": "Figure 5. Qualitative results of our DoNet and other SOTA methods on CPS (top) and ISBI2014 (bottom) datasets. (a) Ground Truth; (b) Mask R-CNN [11]; (c) Occlusion R-CNN [9]; (d) Xiao et al. [37]; (e) Cascade R-CNN [2]; (f) Hybrid Task Cascade [8]; (g) Mask Scoring R-CNN [13]; (h) Our proposed DoNet." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 72, + 393, + 260, + 599 + ], + "blocks": [ + { + "bbox": [ + 72, + 393, + 260, + 599 + ], + "lines": [ + { + "bbox": [ + 72, + 393, + 260, + 599 + ], + "spans": [ + { + "bbox": [ + 72, + 393, + 260, + 599 + ], + "type": "image", + "image_path": "83864683f617ac17ff886e8841d0900fe3b16b4be7e00ca9977bb414e0711867.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 602, + 287, + 657 + ], + "lines": [ + { + "bbox": [ + 46, + 602, + 287, + 657 + ], + "spans": [ + { + "bbox": [ + 46, + 602, + 287, + 657 + ], + "type": "text", + "content": "Figure 6. Heatmaps of the intersection region, the complement region, and the integral instance on CPS (top) and ISBI2014 (bottom) datasets, including (a) the original instance, the prediction heatmap of (b) intersection regions, (c) complement regions, and (d) the integral instance." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": "segmentation results of the CPS data, it can be seen that overlapped cells with different staining (e.g., dark red and blue) show significant appearance inconsistency between cellular sub-regions. Previous works (e.g., Mask R-CNN" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 393, + 545, + 490 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 393, + 545, + 490 + ], + "spans": [ + { + "bbox": [ + 305, + 393, + 545, + 490 + ], + "type": "text", + "content": "[11] and Occlusion R-CNN [9]) with limited perceptual capability have difficulty capturing the relationship between pixels in the intersection and complement sub-regions, leading to ambiguous segmentation contours. In contrast, our DoNet can effectively distinguish different instance boundaries and can better perceive the integrality of cells. This generalized superiority is also observed in the ISBI2014 dataset with low-contrast cellular instances." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 500, + 378, + 511 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 500, + 378, + 511 + ], + "spans": [ + { + "bbox": [ + 306, + 500, + 378, + 511 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 521, + 545, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 545, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 545, + 640 + ], + "type": "text", + "content": "In this paper, we propose a de-overlapping network (DoNet) to address the overlapping challenges in cytology instance segmentation. The proposed DoNet enhances the model's perception of overlapping regions by implicitly and explicitly modeling the interaction between cellular regions and the integral instance. Extensive experiments reveal the superiorities of the proposed DoNet, which not only provides immense potential for overlapping object perception in the medical domain but also occluded instance segmentation in general vision application scenarios." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 651, + 404, + 664 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 651, + 404, + 664 + ], + "spans": [ + { + "bbox": [ + 306, + 651, + 404, + 664 + ], + "type": "text", + "content": "Acknowledgement" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 670, + 545, + 707 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 670, + 545, + 707 + ], + "spans": [ + { + "bbox": [ + 304, + 670, + 545, + 707 + ], + "type": "text", + "content": "This work was supported by National Natural Science Foundation of China (No. 62202403) and Beijing Institute of Collaborative Innovation Program (No. BICI22EG01)." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15648" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 92, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 53, + 92, + 287, + 156 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 92, + 287, + 156 + ], + "spans": [ + { + "bbox": [ + 53, + 92, + 287, + 156 + ], + "type": "text", + "content": "[1] Seunghyeok Back, Joosoon Lee, Taewon Kim, Sangjun Noh, Raeyoung Kang, Seongho Bak, and Kyoobin Lee. 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Springer, 2019. 1, 2" + } + ] + } + ], + "index": 15 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "15650" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Document Image Shadow Removal Guided by Color-Aware Background/488a81e8-9aa8-4e58-aac0-74e15ffd5e40_content_list.json b/2023/Document Image Shadow Removal Guided by Color-Aware Background/488a81e8-9aa8-4e58-aac0-74e15ffd5e40_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..0a10dbaef1a64a7f078e5a8cb45a77c69bf325da --- /dev/null +++ b/2023/Document Image Shadow Removal Guided by Color-Aware Background/488a81e8-9aa8-4e58-aac0-74e15ffd5e40_content_list.json @@ -0,0 +1,2268 @@ +[ + { + "type": "text", + "text": "Document Image Shadow Removal Guided by Color-Aware Background", + "text_level": 1, + "bbox": [ + 119, + 130, + 849, + 151 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Ling Zhang $^{1}$ , Yinghao He $^{1}$ , Qing Zhang $^{2}$ , Zheng Liu $^{3}$ , Xiaolong Zhang $^{1}$ , Chunxia Xiao $^{4*}$ $^{1}$ School of Computer Science and Technology, Wuhan University of Science and Technology \n $^{2}$ School of Computer Science and Engineering, Sun Yat-Sen University \n $^{3}$ School of Computer Science, China University of Geosciences (Wuhan) \n $^{4}$ School of Computer Science, Wuhan University", + "bbox": [ + 117, + 179, + 851, + 268 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "zhling@wust.edu.cn, hyhwust@163.com, zhangqing.whu.cs@gmail.com \nliu.zheng.jojo@gmail.com, xiaolong.zhang@wust.edu.cn, cxxiao@whu.edu.cn", + "bbox": [ + 166, + 272, + 795, + 303 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 339, + 313, + 354 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Existing works on document image shadow removal mostly depend on learning and leveraging a constant background (the color of the paper) from the image. However, the constant background is less representative and frequently ignores other background colors, such as the printed colors, resulting in distorted results. In this paper, we present a color-aware background extraction network (CBENet) for extracting a spatially varying background image that accurately depicts the background colors of the document. Furthermore, we propose a background-guided document images shadow removal network (BGShadowNet) using the predicted spatially varying background as auxiliary information, which consists of two stages. At Stage I, a background-constrained decoder is designed to promote a coarse result. Then, the coarse result is refined with a background-based attention module (BAModule) to maintain a consistent appearance and a detail improvement module (DEModule) to enhance the texture details at Stage II. Experiments on two benchmark datasets qualitatively and quantitatively validate the superiority of the proposed approach over state-of-the-arts.", + "bbox": [ + 76, + 371, + 473, + 690 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 715, + 209, + 732 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Documents, such as textbooks, newspapers, leaflets, and receipts, are available daily, often saved as electronic documents for digital document archives or online message transfer. Since the wide use and convenience of mobile phones, people currently prefer to use mobile phones for digital document copying. However, the captured document images become highly susceptible to shadows when the light sources are blocked. The low brightness in shadow regions reduces the quality and readability of the documen", + "bbox": [ + 75, + 742, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4373280f1215c56af2b5a624561c598c1b0ffcac1f2aabb36175e706b0429203.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 509, + 338, + 633, + 438 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/1de4dc7fd787fb3dab303559dd7bdf2d428a30fbe7de6db77b5def07b2418f79.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 635, + 338, + 756, + 438 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/9a694d29b78bbda99e7cc048399da32d590c3f36da28a00adfc7d1977bfa4fd8.jpg", + "image_caption": [ + "(c) Our result" + ], + "image_footnote": [], + "bbox": [ + 759, + 338, + 883, + 438 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/1429bd00a9274a9814570e528df70846f3737460f0fdc024c8ced3894ceaf194.jpg", + "image_caption": [ + "(a) Shadow image", + "(d) Result of [2]" + ], + "image_footnote": [], + "bbox": [ + 509, + 453, + 633, + 553 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/cf133f6a966bb0ba45e55638f72416af648403f364509d1ebc88bb07587d3f44.jpg", + "image_caption": [ + "(b) Our background", + "(e) Background of [24]", + "Figure 1. Document image shadow removal. With the assumption of constant background, results of [2] and [24] may cause color distortion or shadow remnant. By using a spatially varying background, our method can produce more desirable result." + ], + "image_footnote": [], + "bbox": [ + 635, + 453, + 756, + 554 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/424b31d9fa6cbaf0014dce66e3d21cc91141c557bffee6b24a45d0c0390ab92e.jpg", + "image_caption": [ + "(f) Result of [24]" + ], + "image_footnote": [], + "bbox": [ + 759, + 453, + 883, + 554 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "t image, resulting in illegible content and unpleasant user experience [2, 10, 12, 19, 28, 29]. Thus, shadow removal for document images is a required image processing task in various vision applications [3, 4, 33, 37, 46, 48].", + "bbox": [ + 496, + 640, + 893, + 700 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Although natural image shadow removal has made substantial progress [16, 20, 22, 40, 44, 45], these approaches generally perform poorly on document pictures due to their drastically different features from natural images. Natural image, for example, emphasizes background content (shadow-free image) without a shadow layer [6, 7, 13, 27, 41], whereas document image emphasizes text content [2, 19, 30]. Without considering the particular properties of the document image, traditional approaches to natural image generally yield incorrect result when they are applied to document image, as well as learning-based methods (see Figure 9(c-f)) due to the less attention to the content structures.", + "bbox": [ + 496, + 704, + 893, + 898 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author: Chunxia Xiao (cxxiao@whu.edu.cn).", + "bbox": [ + 94, + 886, + 421, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "1818", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Several approaches on document image shadow removal are currently available, which dig into the specific characteristics of the document image [3, 21, 30, 49]. However, these approaches may cause color distortion or shadow remnant for image with complex backgrounds, as illustrated in Figure 1(d). Recently, Lin et al. [24] estimate a constant background for the image and propose BEDSR-Net for document image shadow removal. The constant background is the color of the paper (see Figure 1(e)), which ignores some other background colors, such as the printed colors. The constant background may provide inaccurate information for the shadow removal task, resulting in unsatisfactory results (see Figure 1(f)). To address this problem, we propose a color-aware background extraction network (CBENet) to extract a spatially varying background, which can preserve various background colors of the original image (see Figure 1(b)). The spatially varying background can provide more useful color information, which contributes to image shadow removal, as shown in Figure 1(c).", + "bbox": [ + 76, + 90, + 472, + 378 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "With the background image, we propose a background-guided shadow removal network (BGShadowNet) for document image that exploits the background image as auxiliary information. Figure 2 presents the framework of the proposed BGShadowNet, which removes shadows in a two-stage process. First, we introduce a background-constrained decoder to combine background features with image features, which can help to promote the realistic coarse shadow-removal result. Then, we refine the coarse result with a background-based attention module (BAModule) and a detail enhancement module (DEModule). In particular, BAModule is designed to eliminate the illumination and color inconsistency in the image by using the attention mechanism. Inspired by image histogram equalization, DE-Module aims to enhance the detail features at low-level scales.", + "bbox": [ + 76, + 378, + 472, + 618 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Due to the lack of large-scale real document image datasets, we construct a new dataset comprised of real document images to facilitate the performance of document image shadow removal. Experiments on extensive document images and evaluations on two datasets verify that our BGShadowNet outperforms existing approaches.", + "bbox": [ + 76, + 619, + 472, + 710 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our main contributions are three-fold:", + "bbox": [ + 94, + 710, + 431, + 724 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We present a color-aware background extraction network (CBENet) for estimating a spatially varying background image that guides the shadow removal of document image.", + "- We propose a framework named BGShadowNet for document image shadow removal, which takes full advantage of the background image and is able to robustly produce high-quality shadow removal results.", + "- We design a background-based attention module (BAModule) to maintain a consistent appearance and a detail enhancement module (DEModule) to enhance texture details." + ], + "bbox": [ + 93, + 724, + 468, + 898 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 89, + 640, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Shadow removal for natural image", + "text_level": 1, + "bbox": [ + 500, + 114, + 803, + 132 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Traditional methods for natural image shadow removal usually focus on studying the different physical properties of shadows [1, 9, 25]. Finlayson et al. [8, 9] reconstructed shadow removal images based on gradient consistency. However, these methods can incur obvious shadow boundary artifacts due to the change of illumination. Shor et al. [34] defined an affine relationship between the shadow and non-shadow areas. Xiao et al. [34, 42, 43] and Zhang et al. [50] removed shadows by transforming illumination from non-shadow regions to shadow regions. However, these methods depended on the reference non-shadow areas, and often resulted in inconsistent illumination when the reference areas are unfortunate.", + "bbox": [ + 496, + 138, + 890, + 333 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Numerous learning-based methods have been proposed for natural image shadow removal [6,11,15,16,18,23,26,27, 31, 35]. For example, Deshadow-Net [31] extracted multicontext features to predict shadow matte layers for shadow removal. Wang et al. [38] employed stacked conditional GANs for joint shadow detection and removal. Zhang et al. [47] explored residual and illumination with GANs for shadow removal. ARGAN [7] proposed a attentive recurrent generative adversarial network for shadow detection and removal. Liu et al. [27] utilized shadow generation for weakly-supervised shadow removal. More recently, Chen et al. [5] transferred the contextual information from nonshadow regions to shadow regions in the embedded feature spaces.", + "bbox": [ + 496, + 335, + 890, + 547 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Although these methods are effective for natural images, they do not generalize well to document image shadow removal due to the difference characteristics between natural images and document images.", + "bbox": [ + 496, + 547, + 890, + 609 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Shadow removal for document image", + "text_level": 1, + "bbox": [ + 500, + 619, + 821, + 635 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Most existing document shadow removal algorithms [2,3,19,21,30] use heuristics algorithms to dig into specific features of the document image. Bako et al. [2] removed shadows using the estimated shadow map. This method leaves slight trace at the boundary under strong shadows. Oliveira et al. [30] used natural neighborhood interpolation to estimate shadow image. Jung et al. [19] explored a waterfilling method for correcting the illumination of document image by converting the input image to a topographic surface. This method can achieve good performance in weak or moderate level of shadows, but tends to produce color degraded results for scenes with heavy shadows.", + "bbox": [ + 496, + 642, + 890, + 824 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recently, Lin et al. [24] proposed a BEDSR-Net for document image shadow removal by estimating a constant background. It is the first deep network specifically designed for document image shadow removal, which takes advantage of specific properties of document images. Due", + "bbox": [ + 496, + 824, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "1819", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/32bc17d1a938b2b7731de30b00a7733dd3c7e209bb4239905b4f70030cbf7fae.jpg", + "image_caption": [ + "Figure 2. The framework of the proposed CBENet and BGShadowNet. Spatially varying background estimated by CBENet is used to help BGShadowNet produce a high-quality shadow removal result. With a background-constrained decoder, BGShadowNet first predicts a coarse shadow-removal result. Then, the coarse result is refined with a BAModule and a DEModule." + ], + "image_footnote": [], + "bbox": [ + 127, + 80, + 834, + 297 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "to ignoring some other background colors in the image, this method may introduce artifacts, such as shadow boundaries or unremoved shadows.", + "bbox": [ + 75, + 352, + 470, + 397 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Document Dataset Construction", + "text_level": 1, + "bbox": [ + 76, + 412, + 372, + 428 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Although there are several document shadow removal datasets, such as Bako [2], Kligler [21], Jung [19], RDSRD [24], SDSRD [24], they mostly have some limitations. Bako, Kligler, Jung, and RDSRD are small-scale evaluation datasets that are unsuitable for training a deep model. While SDSRD is a large-scale dataset, it is a synthetic dataset.", + "bbox": [ + 75, + 438, + 468, + 529 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/0f020264082efec4598bda3f1006aebe06986b6618c1e215f40fa7306510ca9e.jpg", + "image_caption": [ + "Figure 3. Illustration of several captured shadow and shadow-free image pairs in RDD. The first row shows shadow images, and the second row demonstrates the corresponding shadow-free images." + ], + "image_footnote": [], + "bbox": [ + 80, + 534, + 465, + 626 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Imaging is a physical generation process by the interaction between light and material. Light environments in the real world usually contains multiple different lights, which are difficult to simulate in synthetic environments accurately. The statistical features of the synthetic and real images are often different. To facilitate the performance of document image shadow removal, we construct a new real document dataset, named RDD, for shadow removal.", + "bbox": [ + 75, + 674, + 468, + 792 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Concretely, we use documents as the background scene to construct our dataset, such as papers, books, publicity pamphlets, etc. We first capture a shadow image with illumination blocked by an object. Then, we obtain the corresponding shadow-free image by removing the occluder. Our RDD collects 4916 pairs of shadow and shadow-free images, divided into two groups, 4371 for training and 545", + "bbox": [ + 75, + 795, + 468, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "for testing. Figure 3 presents some shadow and shadow-free image pairs in our RDD. To the best of our knowledge, RD-D is the first large-scale real document dataset for shadow removal.", + "bbox": [ + 496, + 352, + 890, + 412 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Methodology", + "text_level": 1, + "bbox": [ + 500, + 429, + 635, + 446 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We first introduce a color-aware background extraction network (CBENet) to estimate a spatially varying background for shadow image. Then, we propose a background-guided shadow removal network (BGShadowNet) for document image, which uses the estimated background as auxiliary information to facilitate shadow removal task. Figure 2 presents the framework of our CBENet and BGShadowNet.", + "bbox": [ + 496, + 455, + 892, + 561 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Color-aware Background Extraction Network", + "text_level": 1, + "bbox": [ + 498, + 573, + 888, + 589 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As document image focuses mostly on the text content, a common strategy [2, 24] to perform document image shadow removal is to utilize the background layer extracted from the image, that only contains the color information for the image without text content. These methods assume the document has a constant color background (the color of the paper), as shown in Figure 4(b). But discrepancy may exist between a constant color background and the image. For example, there may be other background colors due to color printing, as shown in Figure 4(a). The constant background will result in unsatisfactory results, as shown in Figure 4(c).", + "bbox": [ + 496, + 598, + 890, + 763 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To address this problem, we propose a color-aware background extraction network (CBENet) to extract a spatially varying color background $\\hat{B}$ for the document image, which preserves different background colors in the image, as shown in Figure 4(d). Compared with the constant background, our spatially varying background can provide more useful color information for the following shadow removal network. Note that our background is shadow-free, which can help BGShadowNet learn more shadow-free features,", + "bbox": [ + 496, + 763, + 892, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "1820", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/dd1e2d3804452d1c9e60db319ff63b55383af07a2f9fb877ccf4dc8c5d267915.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 120, + 80, + 240, + 151 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/0e706225fe3e22e7e9dc1910a717bc9db53cfb6f772a87f536b7aea87c206b86.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 120, + 152, + 240, + 223 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/67658ea56a6958f387d82793929f9f5c9aa7a2a40e815606efe76ee67a810914.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 243, + 80, + 359, + 152 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/b337ee676c963de12f3d94fdd57854c226674c17fb6d33f1d60055588beec3f5.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 243, + 152, + 359, + 222 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/93f46694b0072fdee56e8233b14a67846a8e948843bc55d54fd94f7ab83de6b2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 364, + 80, + 483, + 151 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/cbb7364638ec9e62446ea57dd39495b9820a49ac0f6cfd6cf123b3549658dd4a.jpg", + "image_caption": [ + "(c)" + ], + "image_footnote": [], + "bbox": [ + 364, + 152, + 483, + 222 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/516574efd8c5ceda46dafa432ae5ce0f7172ed34d242ab89ff39ab1b50ec5fd4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 486, + 80, + 604, + 151 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/245db0bddcf48c155468e7106676e601ff15b6844da5fcdf0e71c40d3a5784fb.jpg", + "image_caption": [ + "(d)" + ], + "image_footnote": [], + "bbox": [ + 486, + 152, + 604, + 222 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/d296d71e2699e1adde19b906b2f150d9ced2dab00abdf327f0a029f32defab4e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 607, + 80, + 725, + 151 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/9a0bf31584baac15ac4d11eca79bb4958824cc46763beeda5e94fa17550fe8cd.jpg", + "image_caption": [ + "(e)" + ], + "image_footnote": [], + "bbox": [ + 607, + 152, + 725, + 222 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/d748cb292909c28d5b11266776ed6d74a76273adfcde35fb10b190d7871a0bad.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 727, + 80, + 848, + 151 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/aa5cf4a0905d4cbbcc50f917eb5f2d03f8845564502b6f0f5ca9524cf88bfd73.jpg", + "image_caption": [ + "(f)" + ], + "image_footnote": [], + "bbox": [ + 728, + 152, + 848, + 222 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/005650f6f196b7414f50025ac41050c2b4efcb2b4aeaa675ba3176029b7a9278.jpg", + "image_caption": [ + "Figure 4. Extracted background images and the corresponding shadow removal images. (a) is input images. (b) and (c) are the background images and shadow removal results predicted by BEDSR-Net [24]. (d) and (e) are our spatially varying background images and shadow removal results. (f) is the corresponding ground-truth images." + ], + "image_footnote": [], + "bbox": [ + 104, + 286, + 217, + 352 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/e889b1dc623fc7c7e8a23ed2f65b7df7c73510f1b11bea0bcdbe2c32ff616888.jpg", + "image_caption": [ + "(a)", + "Figure 5. Visualization of background: (a) shadow images, (b) local background images, and (c) final background images." + ], + "image_footnote": [], + "bbox": [ + 106, + 354, + 217, + 417 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/c6f1666d66fe9ad71624dce077baa25aa33342cb4010933321a2ea974133d202.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 220, + 287, + 328, + 352 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/f06670a2e3e181a241bc43a1e3f0632e59670f065e899100ff1c88b5fab5519f.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 220, + 353, + 328, + 417 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/328e22de7a7b17cfb18a4d9e9ebba5dc3231581d6b598e2af29d711e392c9983.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 331, + 287, + 439, + 352 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/dd700d0682199e9a74bbf212dc5bdf2887a38d65f4dcb62a20af70d52d2b239b.jpg", + "image_caption": [ + "(c)" + ], + "image_footnote": [], + "bbox": [ + 331, + 353, + 439, + 417 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "contributing to shadow removal while better avoiding illumination or color artifacts in the image (see Figure 4(e)).", + "bbox": [ + 75, + 470, + 467, + 500 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To train our CBENet, we employ a background calculator with local-to-global strategy to construct the ground-truth background as the supervisor. Specifically, we first divide the ground-truth shadow-free image $I_{gt}$ into $16 \\times 16$ patches to obtain the local background $\\overline{B}$ . For each patch, we use the Gaussian Mixture Model (GMM) to cluster it into two clusters according to the pixel intensity of the image [2], corresponding to text content and background, respectively. With the observation that the background color of the document is usually brighter [2, 24], we consider the cluster with a higher intensity as the background cluster and apply the average color of the background cluster as the background of the patch. Since different patches have different background colors, the local background $\\overline{B}$ usually has obvious patch boundaries, as shown in Figure 5(b). Thus, inspired by the guided filter for edge-preserving image smoothing [14], we employ a color-preserving smoothing operator to refine $\\overline{B}$ and get a desired ground-truth background image $B$ for the image, as shown in Figure 5(c).", + "bbox": [ + 75, + 500, + 467, + 787 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The value of pixel $i$ in $B$ can be expressed as:", + "bbox": [ + 96, + 787, + 398, + 801 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nB _ {i} = \\sum_ {j \\in N (i)} W _ {i j} \\bar {B} _ {j}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 202, + 804, + 468, + 839 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $N(i)$ is a local neighborhood of pixel i. $W_{ij}$ is the filter kernel, which measures the color similarity between pixel $i$ and pixel $j$ . Due to the original image has the edge information, we use $I^{gt}$ as the guidance image to calculate", + "bbox": [ + 75, + 839, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the filter kernel $W_{ij}$ , that is,", + "bbox": [ + 500, + 292, + 687, + 309 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nW _ {i j} = \\frac {1}{| \\omega | ^ {2}} \\sum_ {i, j} (1 + \\frac {\\left(I _ {i} ^ {g t} - \\mu_ {k}\\right) \\left(I _ {j} ^ {g t} - \\mu_ {k}\\right)}{\\sigma_ {k} ^ {2} + \\epsilon}), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 542, + 314, + 890, + 357 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mu_{k}$ and $\\sigma_k^2$ are the mean and variance of $I^{gt}$ in $N(i)$ , $|\\omega|$ is the number of pixels in $N(i)$ , and $\\epsilon$ is a regularization parameter preventing $W_{ij}$ from being too large.", + "bbox": [ + 498, + 363, + 890, + 409 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We adopt the U-Net structure to implement our CBENet. The U-Net first applies five Conv+BN+LReLU to extract features from the image. Then, it takes five deconvolutional layers with batch normalization and ReLU activation function to predict the background image. Skip connection is applied between convolutional layers and deconvolutional layers, increasing the number of channels in the network and preserving the context information of the front layer.", + "bbox": [ + 498, + 410, + 890, + 531 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Background-guided Shadow Removal Network", + "text_level": 1, + "bbox": [ + 500, + 542, + 890, + 559 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As aforementioned, the background can provide some useful information to facilitate shadow removal. Thus, we propose a background-guided shadow removal network (BGShadowNet) exploiting the background image as supplementary information. As shown in Figure 2, our BGShadowNet includes two stages. At Stage I, besides an image encoder, a background-constrained decoder is introduced to produce a coarse shadow-removal result. At Stage II, to improve the coarse result and produce the final shadow-free image, a background-based attention module (BAModule) and a detail enhancement module (DEModule) are embedded into an encoder-decoder network. A discriminator is stacked at the end to distinguish whether the produced image is real or not. We choose DenseUnet [32] and Markovian discriminator [17] as our encoder-decoder structure and discriminator.", + "bbox": [ + 496, + 566, + 890, + 808 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Background-constrained Decoder. To take full advantage of the features from background image, we replace the common decoder with a background-constrained decoder at Stage I. Concretely, features from the background encoder are integrated into the background-constrained decoder at each corresponding level. The integrated features can com", + "bbox": [ + 496, + 810, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "1821", + "bbox": [ + 483, + 944, + 513, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/af7ce88daa283bd3d23167ec74c1da8879a3f2a48495aa0a001e80a1ac2dd6ac.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 81, + 84, + 158, + 143 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/7287e2fb57b7299c2927703edecb9a38cbda134b506d37768325227a4fd92b32.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 158, + 84, + 235, + 143 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/ae015b0c0d9ba39f4b84546641a2a7e0c71e1ecdde02a35f8853c517766da693.jpg", + "image_caption": [ + "(c)", + "Figure 6. Results of stage I and II. (a): Input. (b): Coarse result at stage I. (d): Result at stage II. (c)&(e): close-ups of (b) and (d)." + ], + "image_footnote": [], + "bbox": [ + 236, + 84, + 312, + 143 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/9d9b937716d7170722ffe646ee343bd974855f9188326359fa1b0db636bb845e.jpg", + "image_caption": [ + "(d)" + ], + "image_footnote": [], + "bbox": [ + 313, + 84, + 388, + 143 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/795e3bd5e32b11025642bf79bde06ab786766ff1f3eb15a7800e20404ffe24fc.jpg", + "image_caption": [ + "(e)" + ], + "image_footnote": [], + "bbox": [ + 390, + 84, + 465, + 143 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "plement the image features and help to produce a satisfactory shadow-removal result.", + "bbox": [ + 75, + 200, + 468, + 229 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Background-based Attention Module. Generally, areas with a similar background should have a similar appearance (color and illumination) in an image. However, there might be illumination or color artifacts in the coarse shadow-removal result (see Figure 6(b)). To preserve the overall consistency of the image, we introduce a background-based attention module (BAModule). Using the learned background features and attention mechanism, the BAModule helps to eliminate the appearance inconsistency in the image (see Figure 6(d)).", + "bbox": [ + 75, + 229, + 468, + 381 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/88675993d117bfdcae1c06de3d345e8206edd87090606257685050167afc5fcd.jpg", + "image_caption": [ + "Figure 7. The network of our background-based attention module (BAModule)." + ], + "image_footnote": [], + "bbox": [ + 125, + 386, + 421, + 473 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Figure 7 illustrates the architecture of the proposed BAModule. We first fuse the encoder and background features to obtain the integrated features by channel-wise concatenation. Then, the integrated features are fed into an attention computing unit to generate a color-aware attention map. The attention computing unit consists of a convolutional layer, a Leaky ReLu activation function, batch normalization, and a ResidualBlock Layer. Finally, we fuse the color-aware attention map and the integrated features by element-wise multiplication to reconstruct the features, and then embed these features into the corresponding decoder level. The color-aware attention map can make the network adaptively focus on the regions with a similar background, promoting a consistent appearance in these regions.", + "bbox": [ + 75, + 508, + 468, + 718 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Detail Enhancement Module. As multiple convolutions and downsampling operators in the network, partial detail information will be lost at high-level layers, resulting in detail-blurred results (see Figure 6(c)). Compared to the high-level features, low-level features in CNN layers usually contain more texture details. Thus, we introduce a detail enhancement module (DEModule) to restore the texture details of the coarse result by utilizing the low-level features of the network.", + "bbox": [ + 75, + 719, + 468, + 853 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As we know, the statistical texture information of the image reflects the texture intensities to some extent. Therefore, our DEModule is inspired by image histogram equalization,", + "bbox": [ + 76, + 854, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/3462e1758c0e58564de7ffa272fb10f23f2063e7d214b74e8e3ae2ded84f664a.jpg", + "image_caption": [ + "Figure 8. The pipeline of our detail enhancement module (DEM)." + ], + "image_footnote": [], + "bbox": [ + 545, + 84, + 844, + 306 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "consisting of two parts. One is feature counting to obtain the statistical information for low-level features, and the other is feature equalization to enhance texture details. Figure 8 illustrates the pipeline of the proposed DEModule. Specifically, we fuse the features of the first two low-level layers from the encoder to get the concatenated low-level features $F$ , which are fed into DEModule for statistical analysis.", + "bbox": [ + 498, + 337, + 890, + 443 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "(1) Feature Counting. The purpose of feature counting is to get the quantization encoding map and statistical feature. We first use two $2 \\times 2$ convolution layers to produce a feature map $M$ and perform global average pooling to obtain the global averaged features $\\overline{M}$ for $M$ . Next, we calculate the correlation between $M$ and $\\overline{M}$ by using cosine similarity, denoted as $S$ .", + "bbox": [ + 498, + 444, + 890, + 547 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To effectively conduct quantification and statistics, we construct a set of quantization levels $L$ , which divide the range of the minimum and maximum values of $S$ into $N$ equal parts. Then, the correlation matrix $S$ can be quantized to a quantization encoding matrix $E$ by using $L$ :", + "bbox": [ + 498, + 549, + 890, + 626 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nE _ {i, n} = \\left\\{ \\begin{array}{c c} 1 - | L _ {n} - S _ {i} |, & i f - \\frac {0 . 5}{N} \\leq L _ {n} - S _ {i} \\leq \\frac {0 . 5}{N} \\\\ 0, & e l s e \\end{array} , \\right. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 511, + 628, + 890, + 674 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $i \\in [1, HW]$ and $n \\in [1, N]$ . $H$ and $W$ are the length and width of the image. $L_{n}$ is the $n$ th level of $L$ , and $S_{i}$ is the $i$ th row of $S$ . In our experiments, we set $N = 128$ .", + "bbox": [ + 498, + 672, + 890, + 717 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To avoid eliminating gradient information, we perform a normalization operation for matrix $E$ . We integrate the normalized result and quantization levels $L$ into a quantization counting map $C$ , which reflects the relative statistics of the low-level input features. Due to the concatenation operation, the channel number of $C$ is 2. Thus, we perform two $1 \\times 1$ convolution operations for $C$ to increase the channel number, followed by a concatenation operation with $\\overline{M}$ to further get absolute statistical information $H$ . $H$ denotes the statistical features which play the role of the histogram.", + "bbox": [ + 496, + 719, + 890, + 869 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "(2) Feature Equalization. Feature equalization is used to enhance the texture details of low-level layers by recon", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "1822", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/5758acaaf0c037b311dbe1a7acc9adc381405ae3f1d5d7fe0099a48935bdaf5b.jpg", + "image_caption": [ + "(a)", + "(b)", + "(c)", + "(d)", + "(e)", + "(f)", + "(g)", + "(h)", + "Figure 9. Visual comparison among state-of-the-art shadow removal methods: (a) input images, (b) Jung [19], (c) DSC [15], (d) Fu [11], (e) DHAN [6], (f) CANet [5], (g) BEDSR-Net [24], (h) our BGShadowNet, and (i) ground-truth images." + ], + "image_footnote": [], + "bbox": [ + 99, + 88, + 872, + 289 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "structuring a new set of quantization levels. We first perform a $1 \\times 1$ convolution operation for $H$ to get $G$ . Inspired by the attention mechanism, we perform matrix multiplication of $G$ and its transposed matrix, followed by a softmax operation, to build a learned adjacent matrix $X$ . Matrix $X$ can be regarded as a similarity coefficient matrix. Then, we can reconstruct the new quantization levels $L'$ with a matrix multiplication for $X$ and $G$ .", + "bbox": [ + 75, + 344, + 467, + 463 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Based on the reconstructed quantization levels $L'$ , we conduct feature equalization for the original quantization encoding matrix $E$ to enhance the detail features. The enhanced features $R$ can be obtained using a matrix multiplication of quantization levels $L'$ and matrix $E$ . By using the enhanced texture details, the decoder can easily capture detail information.", + "bbox": [ + 75, + 465, + 467, + 568 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Loss Function", + "text_level": 1, + "bbox": [ + 76, + 578, + 220, + 590 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our loss functions for optimizing the proposed network contain four components: background reconstruction loss $\\mathcal{L}_{\\text {background }}$ , appearance consistency loss $\\mathcal{L}_{\\text {appearance }}$ , structure consistency loss $\\mathcal{L}_{\\text {structure }}$ and adversarial loss $\\mathcal{L}_{\\text {adv }}$ .", + "bbox": [ + 76, + 601, + 467, + 675 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Background reconstruction loss is used to constrain the CBENet to obtain the desirable background image, which uses the $\\ell_1$ distance between $\\hat{B}$ produced by CBENet and the ground-truth background image $B$ , that is,", + "bbox": [ + 76, + 676, + 467, + 736 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {b a c k g r o u n d}} = \\left\\| B - \\bar {B} \\right\\| _ {1}. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 739, + 467, + 753 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Appearance consistency loss evaluates the data loss between the predicted results and the ground-truth image, which is calculated in the $\\ell_1$ distance:", + "bbox": [ + 76, + 757, + 467, + 801 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\text {a p p e a r a n c e}} = \\lambda_ {1} \\mathcal {L} _ {\\text {c o a r s e}} + \\lambda_ {2} \\mathcal {L} _ {\\text {f i n a l}} \\\\ = \\lambda_ {1} \\| I _ {g t} - I _ {\\text {c o a r s e}} \\| _ {1} + \\lambda_ {2} \\| I _ {g t} - I _ {\\text {f r e e}} \\| _ {1}, \\tag {5} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 805, + 467, + 854 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\lambda_{1}$ and $\\lambda_{2}$ are the weight parameters. $I_{\\text{coarse}}$ is the coarse result produced at Stage I, and $I_{\\text{free}}$ is the final shadow-removal result produced at Stage II.", + "bbox": [ + 76, + 856, + 467, + 898 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Structure consistency loss aims to preserve image structure, which is calculated as,", + "bbox": [ + 500, + 344, + 888, + 372 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {s t u c t u r e}} = \\lambda_ {3} \\left| \\left| \\mathrm {V G G} \\left(I _ {g t}\\right) - \\mathrm {V G G} \\left(I _ {f r e e}\\right) \\right| \\right| _ {2} ^ {2}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 542, + 380, + 888, + 398 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\lambda_{3}$ is the weight parameter, and $\\mathrm{VGG}(\\cdot)$ is the feature extractor from the pre-trained VGG19 model.", + "bbox": [ + 498, + 406, + 888, + 434 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Adversarial loss is designed for the discriminator to judge whether the produced results are real or fake, which is described as:", + "bbox": [ + 498, + 436, + 888, + 479 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {a d v} = \\lambda_ {4} \\mathbb {E} _ {\\left(I, I _ {f r e e}, I _ {g t}\\right)} [ \\log (D (I _ {g t})) + \\log (1 - D (I)) ], \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 509, + 489, + 888, + 518 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $D$ is the discriminator, and $I$ is the shadow image.", + "bbox": [ + 500, + 518, + 874, + 532 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 500, + 547, + 630, + 564 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Implementation Detail", + "text_level": 1, + "bbox": [ + 500, + 571, + 707, + 587 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our network is implemented in Pytorch. In our experiments, CBENet and BGShadowNet are trained separately. We first train CBENet for 200 epochs using the background ground-truth as the supervisor. Next, we fix the CBENet and train BGShadowNet for 200 epochs on a NVIDIA GeForce RTX2080Ti. We use Adam optimizer to optimize our generator and the discriminator with attenuation rate $betas = (0.5, 0.999)$ . The initial learning rate is set to 0.0004. The weight parameters $\\lambda_1, \\lambda_2, \\lambda_3$ and $\\lambda_4$ are set to 1, 1, 0.05 and 0.01 in our experiments, respectively.", + "bbox": [ + 498, + 595, + 888, + 746 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Comparison with State-of-the-arts", + "text_level": 1, + "bbox": [ + 500, + 756, + 799, + 771 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. Since SDSRD dataset [24] is not available, we use the proposed RDD dataset to train and evaluate our BGShadowNet. Apart from RDD, we also use Kligler's dataset [21] for evaluation.", + "bbox": [ + 498, + 779, + 888, + 838 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Metrics. We utilize the root mean square error (RMSE) in LAB color space between the shadow removal result and the ground-truth shadow-free image to evaluate the shadow removal performance. In addition, we also report the PSNR", + "bbox": [ + 498, + 840, + 888, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "1823", + "bbox": [ + 483, + 945, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2871f3672a16a8fb549bd9fdfeb4d07dde0fe9ec4d8024240b9a446d1494c22f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 102, + 84, + 184, + 150 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4b21e99f116c87da6cf6a12c43246df64775b3c3566832aa18b6d561c593750c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 186, + 85, + 272, + 150 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9132ce5f3c1a43f95ba90a628534aca08bd8225a4378aeee5007a00975d3b708.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 274, + 85, + 356, + 148 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": 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"images/56b821f4f56d4ec20f979b149e574d56c6ac68e46984c6b83674cb643ff15dfc.jpg", + "image_caption": [ + "(c)" + ], + "image_footnote": [], + "bbox": [ + 274, + 220, + 356, + 279 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c503369c775cfb9ea82eed159720d95505a5acf3367b310599ec42428c896bd2.jpg", + "image_caption": [ + "(d)", + "Figure 10. Visual comparison among state-of-the-art shadow removal methods: (a) input images, (b) Jung [19], (c) DSC [15], (d) DHAN [6], (e) Fu [11], (f) BEDSR-Net [24], (g) CANet [5], (h) BMNet [51], and (i) our BGShadowNet." + ], + "image_footnote": [], + "bbox": [ + 357, + 220, + 441, + 279 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3d984dfeb79c992001fd4957bd45baf94d51376a911efb4c65b16c752f4930d1.jpg", + "image_caption": [ + "(e)" + ], + "image_footnote": [], + "bbox": [ + 442, + 220, + 526, + 279 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0f58f1030eb8911dcb6ceaac9067dbe8d90e915dcc4e69e286ed0afc5a57d716.jpg", + "image_caption": [ + "(f)" + ], + "image_footnote": [], + "bbox": [ + 527, + 220, + 612, + 279 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8d696028752242cf436632d86d3f5ec0289a4ace6e4232f9bbb1b33c113b50b3.jpg", + "image_caption": [ + "(g)" + ], + "image_footnote": [], + "bbox": [ + 612, + 220, + 696, + 279 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ef322d06ee9e4d017d996924347b79a3a38f13b4f9db05ae2e5d8e10f168a69d.jpg", + "image_caption": [ + "(h)" + ], + "image_footnote": [], + "bbox": [ + 697, + 220, + 779, + 279 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/472926062b03450497642eec3034d7f11600bfe0fe5440e22ac9ee13c4f1ba52.jpg", + "image_caption": [ + "(i)" + ], + "image_footnote": [], + "bbox": [ + 782, + 220, + 866, + 279 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/cff00e342ba93e7b73493e577d7df75e3d45a02717e2d58274041e92b72439bf.jpg", + "table_caption": [ + "Table 1. Quantitative comparisons of shadow removal on RDD and Kligler datasets in terms of RMSE, PSNR, and SSIM. All the learning-based methods are trained on RDD dataset. $\\uparrow$ means the larger the better while $\\downarrow$ means the smaller the better." + ], + "table_footnote": [], + "table_body": "
MethodsVenue/YearRDDKligler
RMSE↓PSNR↑SSIM ↑RMSE↓PSNR↑SSIM ↑
ST-CGAN [39]CVPR/20183.14334.3280.9746.82627.4330.931
DSC [15]PAMI/20206.35728.1510.9147.70525.6150.898
DHAN [6]AAAI/20202.46736.3370.9786.61027.7070.937
Fu [11]CVPR/20214.32831.3870.9467.10127.3620.914
CANet [5]ICCV/20215.56128.9510.9187.85525.6250.899
SG-ShadowNet [36]ECCV/20222.97434.7270.9726.82927.1410.920
BMNet [51]CVPR/20229.40924.2890.91516.45919.0310.874
Bako [2]ACCV/201614.64820.7410.8949.05824.7770.895
Jung [19]ACCV/201830.19014.3640.86128.24713.7260.852
BEDSR-Net [24]CVPR/20202.93734.9280.9736.53328.1240.932
BGShadowNetCVPR/20232.21937.5850.9835.37729.1760.948
", + "bbox": [ + 189, + 353, + 777, + 513 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "and SSIM in the RGB colour space to evaluate the performance of the proposed BGShadowNet.", + "bbox": [ + 75, + 521, + 467, + 550 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To verify the effectiveness of our method, we compare our results with various state-of-the-art shadow removal methods including three document image shadow removal methods (Bako [2], Jung [19] and BEDSR-Net [24]) and six natural image shadow removal methods (ST-CGAN [39], DSC [15], DHAN [6], Fu [11], CANet [5], SG-ShadowNet [36] and BMNet [51]). To make fair comparison, we use RDD dataset to train all the learning-based methods on the same hardware. Table 1 concludes the comparison results. From the table, we can observe that, our method achieves the best values for all metrics among all the comparing methods, clearly demonstrating the effectiveness.", + "bbox": [ + 75, + 551, + 467, + 733 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Figure 9 provides some visual shadow removal results to further demonstrate the superiority of our methods. It can be seen, DSC [15] fails in handling image with heavy shadows (see Figure 9(c)). The robustness of Fu [11] is limited, and their results may contain unremoved shadows, as shown in Figure 9(d). DHAN [6] and CANet [5] have the similar problem to Fu [11]. Ignoring the content characteristics of the documents, Jung [19] leads to obvious color and illumination distortion (see Figure 9(b)). With the constant background, results of BEDSR-Net [24] sometimes exhibit artifacts along the shadow boundaries (see Figure 9(g)).", + "bbox": [ + 75, + 734, + 467, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparatively, the proposed method effectively recovers illumination in shadow regions without artifacts, as shown in Figure 9(h), which is similar to the ground-truth image.", + "bbox": [ + 498, + 521, + 890, + 566 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To further verify the robustness and generalization ability of the proposed method, Figure 10 presents some other shadow removal results for document images, containing some challenging cases, such as heavy shadows and inconsistent illumination in shadow regions. Apparently, results recovered by our method look more natural and have little artifacts.", + "bbox": [ + 496, + 566, + 890, + 672 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "User Study. We conduct an user study to evaluate the visual performance of our method and some state-of-the-art shadow removal methods. We prepare 100 sets of shadow removal images. Each set contains seven shadow removal results of our BGShadowNet, CANet, DSC, DHAN, Fu, BEDSR-Net, and Jung, respectively. We randomly select 100 volunteers. For each volunteer, we randomly provide them twenty image sets. The volunteers are required to select the best shadow-free image for each set. Counting all the results, we find that $20.32\\%$ of shadow-removal images generated by our BGShadowNet are chosen as the best shadow-free images, while $11.92\\%$ , $11.67\\%$ , $16.72\\%$ , $13.25\\%$ , $15.91\\%$ , and $10.21\\%$ of shadow removal results are chosen by CANet, DSC, DHAN, Fu, BEDSR-Net, and Jung, respectively.", + "bbox": [ + 496, + 674, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "1824", + "bbox": [ + 483, + 945, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f4eff1a228cddea5eec519b29bf572f51e5948a9c1589c85d621922087f64668.jpg", + "image_caption": [ + "Figure 11. Visual comparison for ablation study: (a) input images, (b) BASE $_1$ , (c) BASE $_2$ , (d) BGShadowNet $_1$ , (e) BGShadowNet $_2$ , (f) BGShadowNet $_3$ , (g) BGShadowNet $_4$ , and (h) our BGShadowNet." + ], + "image_footnote": [], + "bbox": [ + 106, + 87, + 866, + 246 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/58f0a4be549848f6fe17e520ccd0e6224c0fbaaffef2a6478dbfd44060d17605.jpg", + "table_caption": [ + "Table 2. Quantitative results of ablation study on RDD and Kligler using RMSE, PSNR, and SSIM." + ], + "table_footnote": [], + "table_body": "
MethodsRDDKligler
RMSE ↓PSNR ↑SSIM ↑RMSE ↓PSNR ↑SSIM ↑
BASE12.94234.8210.9386.25328.2670.944
BASE22.89735.9760.9455.81128.8950.947
BGShadowNet12.60336.0520.9805.80528.3710.944
BGShadowNet22.58336.1350.9815.73129.0350.947
BGShadowNet32.43336.6810.9825.53829.1800.947
BGShadowNet42.34437.0490.9825.63328.8400.948
BGShadowNet2.21937.5850.9835.37729.1760.948
", + "bbox": [ + 241, + 294, + 725, + 406 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.3. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 417, + 228, + 431 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ablation of BGShadowNet. To further evaluate the performance of each component applied in our BGShadowNet, we perform ablation experiments using six variants (with or without the specific component) as follows:", + "bbox": [ + 76, + 441, + 468, + 502 + ], + "page_idx": 7 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "(1) $BASE_{1}$ : one DenseUnet;", + "(2) $BASE_2$ : two stacked DenseUnet;", + "(3) BGShadowNet1: BGShadowNet without StageII;", + "(4) $BGShadowNet_2$ : BGShadowNet without DEModule and BAModule;", + "(5) BGShadowNet3: BGShadowNet without BAModule;", + "(6) BGShadowNet ${}_{4}$ : BGShadowNet without DEModule." + ], + "bbox": [ + 76, + 503, + 468, + 607 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We train the six variants and evaluate the results on RDD and Kligler's datasets. The results are summarized in Table 2. From the table, we can observe that the components embedded in the two stages can improve the shadow removal results. We also provide qualitative results in Figure 11, which shows that our BGShadowNet with all the components can produce more realistic results.", + "bbox": [ + 75, + 611, + 468, + 715 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ablation of Background Image. To verify the effectiveness of the spatially varying background, we rebuild BGShadowNet exploiting the constant background (denoted as $\\mathrm{BGShadowNet}_b$ ) estimated by BEDSR-Net [24], and reorganize BEDSR-Net employing our spatially varying background (denoted as $\\mathrm{BEDSR}_b$ ). Table 3 summarizes the comparison results. From the results, we can observe that, variant $\\mathrm{BEDSR}_b$ using the spatially varying background can obtain better values than BEDSR-Net. Besides, our BGShadowNet can produce better results than that using the constant background. These results show that our spatially varying background contributes to superior results.", + "bbox": [ + 75, + 719, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/b89942403616a3bed163efe89aab2336119f56275bd5fb37b66c5024bac2c12f.jpg", + "table_caption": [ + "Table 3. Quantitative comparisons using different background images on RDD dataset." + ], + "table_footnote": [], + "table_body": "
MethodsRMSE ↓PSNR ↑SSIM ↑
BEDSR-Net2.93734.9280.973
BEDSRb2.77135.5550.976
BGShadowNetb2.74035.8210.980
BGShadowNet2.21937.5850.983
", + "bbox": [ + 545, + 444, + 843, + 508 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "**Limitation.** Our BGShadowNet can effectively remove shadows in document images. However, when the images are corrupted by heavy noise, our shadow removal results may contain some residual noise, resulting in uneven illumination with the surrounding environment.", + "bbox": [ + 498, + 520, + 890, + 595 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 609, + 617, + 625 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose a CBENet to estimate a spatially varying background for the shadow image, which can facilitate the proposed BGShadowNet performs document shadow removal. Our BGShadowNet first predicts a coarse shadow-removal result using a background-constrained decoder. Then, we embed a BAModule and a DEModule into the encoder-decoder network to improve the coarse result and produce the final shadow-free result with a consistent appearance and detail-rich texture. Experiments comparing our BGShadowNet to state-of-the-art approaches demonstrate its superiority.", + "bbox": [ + 496, + 635, + 890, + 801 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments", + "text_level": 1, + "bbox": [ + 500, + 815, + 658, + 830 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work is partially supported by NS-FC (No.61902286, No.61972299, No.U1803262, No.61972298) and CAAI-Huawei MindSpore Open Fund.", + "bbox": [ + 498, + 839, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "1825", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] E. Arbel and H. Hel-Or. Shadow removal using intensity surfaces and texture anchor points. 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In CVPR, pages 5627-5636, 2022. 7" + ], + "bbox": [ + 501, + 92, + 890, + 162 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "1827", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Document Image Shadow Removal Guided by Color-Aware Background/488a81e8-9aa8-4e58-aac0-74e15ffd5e40_model.json b/2023/Document Image Shadow Removal Guided by Color-Aware Background/488a81e8-9aa8-4e58-aac0-74e15ffd5e40_model.json new file mode 100644 index 0000000000000000000000000000000000000000..69f890c7d2d2f65ab8391798ae39c9eedcb9c68a --- /dev/null +++ b/2023/Document Image Shadow Removal Guided by Color-Aware Background/488a81e8-9aa8-4e58-aac0-74e15ffd5e40_model.json @@ -0,0 +1,3201 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.12, + 0.131, + 0.85, + 0.152 + ], + "angle": 0, + "content": "Document Image Shadow Removal Guided by Color-Aware Background" + }, + { + "type": "text", + "bbox": [ + 0.119, + 0.18, + 0.852, + 0.269 + ], + "angle": 0, + "content": "Ling Zhang\\(^{1}\\), Yinghao He\\(^{1}\\), Qing Zhang\\(^{2}\\), Zheng Liu\\(^{3}\\), Xiaolong Zhang\\(^{1}\\), Chunxia Xiao\\(^{4*}\\) \n\\(^{1}\\)School of Computer Science and Technology, Wuhan University of Science and Technology \n\\(^{2}\\)School of Computer Science and Engineering, Sun Yat-Sen University \n\\(^{3}\\)School of Computer Science, China University of Geosciences (Wuhan) \n\\(^{4}\\)School of Computer Science, Wuhan University" + }, + { + "type": "text", + "bbox": [ + 0.168, + 0.273, + 0.796, + 0.304 + ], + "angle": 0, + "content": "zhling@wust.edu.cn, hyhwust@163.com, zhangqing.whu.cs@gmail.com \nliu.zheng.jojo@gmail.com, xiaolong.zhang@wust.edu.cn, cxxiao@whu.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.34, + 0.314, + 0.356 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.372, + 0.474, + 0.691 + ], + "angle": 0, + "content": "Existing works on document image shadow removal mostly depend on learning and leveraging a constant background (the color of the paper) from the image. However, the constant background is less representative and frequently ignores other background colors, such as the printed colors, resulting in distorted results. In this paper, we present a color-aware background extraction network (CBENet) for extracting a spatially varying background image that accurately depicts the background colors of the document. Furthermore, we propose a background-guided document images shadow removal network (BGShadowNet) using the predicted spatially varying background as auxiliary information, which consists of two stages. At Stage I, a background-constrained decoder is designed to promote a coarse result. Then, the coarse result is refined with a background-based attention module (BAModule) to maintain a consistent appearance and a detail improvement module (DEModule) to enhance the texture details at Stage II. Experiments on two benchmark datasets qualitatively and quantitatively validate the superiority of the proposed approach over state-of-the-arts." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.717, + 0.21, + 0.733 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.743, + 0.47, + 0.879 + ], + "angle": 0, + "content": "Documents, such as textbooks, newspapers, leaflets, and receipts, are available daily, often saved as electronic documents for digital document archives or online message transfer. Since the wide use and convenience of mobile phones, people currently prefer to use mobile phones for digital document copying. However, the captured document images become highly susceptible to shadows when the light sources are blocked. The low brightness in shadow regions reduces the quality and readability of the documen" + }, + { + "type": "image", + "bbox": [ + 0.51, + 0.339, + 0.635, + 0.439 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.524, + 0.442, + 0.621, + 0.453 + ], + "angle": 0, + "content": "(a) Shadow image" + }, + { + "type": "image", + "bbox": [ + 0.636, + 0.339, + 0.758, + 0.439 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.645, + 0.442, + 0.75, + 0.453 + ], + "angle": 0, + "content": "(b) Our background" + }, + { + "type": "image", + "bbox": [ + 0.76, + 0.339, + 0.885, + 0.439 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.786, + 0.442, + 0.858, + 0.452 + ], + "angle": 0, + "content": "(c) Our result" + }, + { + "type": "image", + "bbox": [ + 0.51, + 0.454, + 0.634, + 0.554 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.528, + 0.557, + 0.615, + 0.57 + ], + "angle": 0, + "content": "(d) Result of [2]" + }, + { + "type": "image", + "bbox": [ + 0.636, + 0.454, + 0.758, + 0.555 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.635, + 0.557, + 0.758, + 0.57 + ], + "angle": 0, + "content": "(e) Background of [24]" + }, + { + "type": "image", + "bbox": [ + 0.76, + 0.454, + 0.885, + 0.555 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.776, + 0.557, + 0.867, + 0.57 + ], + "angle": 0, + "content": "(f) Result of [24]" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.571, + 0.892, + 0.627 + ], + "angle": 0, + "content": "Figure 1. Document image shadow removal. With the assumption of constant background, results of [2] and [24] may cause color distortion or shadow remnant. By using a spatially varying background, our method can produce more desirable result." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.641, + 0.894, + 0.701 + ], + "angle": 0, + "content": "t image, resulting in illegible content and unpleasant user experience [2, 10, 12, 19, 28, 29]. Thus, shadow removal for document images is a required image processing task in various vision applications [3, 4, 33, 37, 46, 48]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.895, + 0.9 + ], + "angle": 0, + "content": "Although natural image shadow removal has made substantial progress [16, 20, 22, 40, 44, 45], these approaches generally perform poorly on document pictures due to their drastically different features from natural images. Natural image, for example, emphasizes background content (shadow-free image) without a shadow layer [6, 7, 13, 27, 41], whereas document image emphasizes text content [2, 19, 30]. Without considering the particular properties of the document image, traditional approaches to natural image generally yield incorrect result when they are applied to document image, as well as learning-based methods (see Figure 9(c-f)) due to the less attention to the content structures." + }, + { + "type": "page_footnote", + "bbox": [ + 0.095, + 0.887, + 0.422, + 0.901 + ], + "angle": 0, + "content": "*Corresponding author: Chunxia Xiao (cxxiao@whu.edu.cn)." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1818" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.379 + ], + "angle": 0, + "content": "Several approaches on document image shadow removal are currently available, which dig into the specific characteristics of the document image [3, 21, 30, 49]. However, these approaches may cause color distortion or shadow remnant for image with complex backgrounds, as illustrated in Figure 1(d). Recently, Lin et al. [24] estimate a constant background for the image and propose BEDSR-Net for document image shadow removal. The constant background is the color of the paper (see Figure 1(e)), which ignores some other background colors, such as the printed colors. The constant background may provide inaccurate information for the shadow removal task, resulting in unsatisfactory results (see Figure 1(f)). To address this problem, we propose a color-aware background extraction network (CBENet) to extract a spatially varying background, which can preserve various background colors of the original image (see Figure 1(b)). The spatially varying background can provide more useful color information, which contributes to image shadow removal, as shown in Figure 1(c)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.379, + 0.473, + 0.619 + ], + "angle": 0, + "content": "With the background image, we propose a background-guided shadow removal network (BGShadowNet) for document image that exploits the background image as auxiliary information. Figure 2 presents the framework of the proposed BGShadowNet, which removes shadows in a two-stage process. First, we introduce a background-constrained decoder to combine background features with image features, which can help to promote the realistic coarse shadow-removal result. Then, we refine the coarse result with a background-based attention module (BAModule) and a detail enhancement module (DEModule). In particular, BAModule is designed to eliminate the illumination and color inconsistency in the image by using the attention mechanism. Inspired by image histogram equalization, DE-Module aims to enhance the detail features at low-level scales." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.62, + 0.473, + 0.711 + ], + "angle": 0, + "content": "Due to the lack of large-scale real document image datasets, we construct a new dataset comprised of real document images to facilitate the performance of document image shadow removal. Experiments on extensive document images and evaluations on two datasets verify that our BGShadowNet outperforms existing approaches." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.711, + 0.433, + 0.725 + ], + "angle": 0, + "content": "In summary, our main contributions are three-fold:" + }, + { + "type": "text", + "bbox": [ + 0.094, + 0.725, + 0.47, + 0.782 + ], + "angle": 0, + "content": "- We present a color-aware background extraction network (CBENet) for estimating a spatially varying background image that guides the shadow removal of document image." + }, + { + "type": "text", + "bbox": [ + 0.094, + 0.782, + 0.47, + 0.841 + ], + "angle": 0, + "content": "- We propose a framework named BGShadowNet for document image shadow removal, which takes full advantage of the background image and is able to robustly produce high-quality shadow removal results." + }, + { + "type": "text", + "bbox": [ + 0.094, + 0.841, + 0.47, + 0.9 + ], + "angle": 0, + "content": "- We design a background-based attention module (BAModule) to maintain a consistent appearance and a detail enhancement module (DEModule) to enhance texture details." + }, + { + "type": "list", + "bbox": [ + 0.094, + 0.725, + 0.47, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.09, + 0.642, + 0.106 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.115, + 0.805, + 0.133 + ], + "angle": 0, + "content": "2.1. Shadow removal for natural image" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.139, + 0.892, + 0.334 + ], + "angle": 0, + "content": "Traditional methods for natural image shadow removal usually focus on studying the different physical properties of shadows [1, 9, 25]. Finlayson et al. [8, 9] reconstructed shadow removal images based on gradient consistency. However, these methods can incur obvious shadow boundary artifacts due to the change of illumination. Shor et al. [34] defined an affine relationship between the shadow and non-shadow areas. Xiao et al. [34, 42, 43] and Zhang et al. [50] removed shadows by transforming illumination from non-shadow regions to shadow regions. However, these methods depended on the reference non-shadow areas, and often resulted in inconsistent illumination when the reference areas are unfortunate." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.336, + 0.892, + 0.548 + ], + "angle": 0, + "content": "Numerous learning-based methods have been proposed for natural image shadow removal [6,11,15,16,18,23,26,27, 31, 35]. For example, Deshadow-Net [31] extracted multicontext features to predict shadow matte layers for shadow removal. Wang et al. [38] employed stacked conditional GANs for joint shadow detection and removal. Zhang et al. [47] explored residual and illumination with GANs for shadow removal. ARGAN [7] proposed a attentive recurrent generative adversarial network for shadow detection and removal. Liu et al. [27] utilized shadow generation for weakly-supervised shadow removal. More recently, Chen et al. [5] transferred the contextual information from nonshadow regions to shadow regions in the embedded feature spaces." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.548, + 0.892, + 0.61 + ], + "angle": 0, + "content": "Although these methods are effective for natural images, they do not generalize well to document image shadow removal due to the difference characteristics between natural images and document images." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.62, + 0.822, + 0.636 + ], + "angle": 0, + "content": "2.2. Shadow removal for document image" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.643, + 0.892, + 0.825 + ], + "angle": 0, + "content": "Most existing document shadow removal algorithms [2,3,19,21,30] use heuristics algorithms to dig into specific features of the document image. Bako et al. [2] removed shadows using the estimated shadow map. This method leaves slight trace at the boundary under strong shadows. Oliveira et al. [30] used natural neighborhood interpolation to estimate shadow image. Jung et al. [19] explored a waterfilling method for correcting the illumination of document image by converting the input image to a topographic surface. This method can achieve good performance in weak or moderate level of shadows, but tends to produce color degraded results for scenes with heavy shadows." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Recently, Lin et al. [24] proposed a BEDSR-Net for document image shadow removal by estimating a constant background. It is the first deep network specifically designed for document image shadow removal, which takes advantage of specific properties of document images. Due" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1819" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.129, + 0.082, + 0.835, + 0.299 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.302, + 0.895, + 0.345 + ], + "angle": 0, + "content": "Figure 2. The framework of the proposed CBENet and BGShadowNet. Spatially varying background estimated by CBENet is used to help BGShadowNet produce a high-quality shadow removal result. With a background-constrained decoder, BGShadowNet first predicts a coarse shadow-removal result. Then, the coarse result is refined with a BAModule and a DEModule." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.353, + 0.471, + 0.398 + ], + "angle": 0, + "content": "to ignoring some other background colors in the image, this method may introduce artifacts, such as shadow boundaries or unremoved shadows." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.413, + 0.373, + 0.429 + ], + "angle": 0, + "content": "3. Document Dataset Construction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.439, + 0.47, + 0.53 + ], + "angle": 0, + "content": "Although there are several document shadow removal datasets, such as Bako [2], Kligler [21], Jung [19], RDSRD [24], SDSRD [24], they mostly have some limitations. Bako, Kligler, Jung, and RDSRD are small-scale evaluation datasets that are unsuitable for training a deep model. While SDSRD is a large-scale dataset, it is a synthetic dataset." + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.535, + 0.467, + 0.627 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.63, + 0.47, + 0.673 + ], + "angle": 0, + "content": "Figure 3. Illustration of several captured shadow and shadow-free image pairs in RDD. The first row shows shadow images, and the second row demonstrates the corresponding shadow-free images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.675, + 0.469, + 0.794 + ], + "angle": 0, + "content": "Imaging is a physical generation process by the interaction between light and material. Light environments in the real world usually contains multiple different lights, which are difficult to simulate in synthetic environments accurately. The statistical features of the synthetic and real images are often different. To facilitate the performance of document image shadow removal, we construct a new real document dataset, named RDD, for shadow removal." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Concretely, we use documents as the background scene to construct our dataset, such as papers, books, publicity pamphlets, etc. We first capture a shadow image with illumination blocked by an object. Then, we obtain the corresponding shadow-free image by removing the occluder. Our RDD collects 4916 pairs of shadow and shadow-free images, divided into two groups, 4371 for training and 545" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.353, + 0.892, + 0.413 + ], + "angle": 0, + "content": "for testing. Figure 3 presents some shadow and shadow-free image pairs in our RDD. To the best of our knowledge, RD-D is the first large-scale real document dataset for shadow removal." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.43, + 0.637, + 0.448 + ], + "angle": 0, + "content": "4. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.456, + 0.893, + 0.563 + ], + "angle": 0, + "content": "We first introduce a color-aware background extraction network (CBENet) to estimate a spatially varying background for shadow image. Then, we propose a background-guided shadow removal network (BGShadowNet) for document image, which uses the estimated background as auxiliary information to facilitate shadow removal task. Figure 2 presents the framework of our CBENet and BGShadowNet." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.574, + 0.889, + 0.59 + ], + "angle": 0, + "content": "4.1. Color-aware Background Extraction Network" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.892, + 0.764 + ], + "angle": 0, + "content": "As document image focuses mostly on the text content, a common strategy [2, 24] to perform document image shadow removal is to utilize the background layer extracted from the image, that only contains the color information for the image without text content. These methods assume the document has a constant color background (the color of the paper), as shown in Figure 4(b). But discrepancy may exist between a constant color background and the image. For example, there may be other background colors due to color printing, as shown in Figure 4(a). The constant background will result in unsatisfactory results, as shown in Figure 4(c)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.893, + 0.901 + ], + "angle": 0, + "content": "To address this problem, we propose a color-aware background extraction network (CBENet) to extract a spatially varying color background \\(\\hat{B}\\) for the document image, which preserves different background colors in the image, as shown in Figure 4(d). Compared with the constant background, our spatially varying background can provide more useful color information for the following shadow removal network. Note that our background is shadow-free, which can help BGShadowNet learn more shadow-free features," + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1820" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.122, + 0.082, + 0.241, + 0.152 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.122, + 0.154, + 0.241, + 0.224 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.173, + 0.226, + 0.191, + 0.237 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.245, + 0.082, + 0.361, + 0.153 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.245, + 0.154, + 0.361, + 0.223 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.295, + 0.226, + 0.313, + 0.237 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.365, + 0.082, + 0.484, + 0.152 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.365, + 0.154, + 0.484, + 0.223 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.417, + 0.226, + 0.433, + 0.237 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image", + "bbox": [ + 0.487, + 0.082, + 0.605, + 0.152 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.487, + 0.154, + 0.605, + 0.223 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.537, + 0.226, + 0.555, + 0.237 + ], + "angle": 0, + "content": "(d)" + }, + { + "type": "image", + "bbox": [ + 0.608, + 0.082, + 0.726, + 0.152 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.608, + 0.154, + 0.726, + 0.223 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.659, + 0.226, + 0.676, + 0.238 + ], + "angle": 0, + "content": "(e)" + }, + { + "type": "image", + "bbox": [ + 0.728, + 0.082, + 0.849, + 0.152 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.729, + 0.154, + 0.849, + 0.223 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.781, + 0.226, + 0.797, + 0.237 + ], + "angle": 0, + "content": "(f)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.237, + 0.894, + 0.278 + ], + "angle": 0, + "content": "Figure 4. Extracted background images and the corresponding shadow removal images. (a) is input images. (b) and (c) are the background images and shadow removal results predicted by BEDSR-Net [24]. (d) and (e) are our spatially varying background images and shadow removal results. (f) is the corresponding ground-truth images." + }, + { + "type": "image", + "bbox": [ + 0.105, + 0.287, + 0.218, + 0.353 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.107, + 0.355, + 0.218, + 0.419 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.154, + 0.423, + 0.171, + 0.432 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.221, + 0.288, + 0.33, + 0.353 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.221, + 0.354, + 0.33, + 0.419 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.266, + 0.422, + 0.283, + 0.432 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.332, + 0.288, + 0.441, + 0.353 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.332, + 0.354, + 0.441, + 0.419 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.378, + 0.422, + 0.395, + 0.433 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.433, + 0.468, + 0.46 + ], + "angle": 0, + "content": "Figure 5. Visualization of background: (a) shadow images, (b) local background images, and (c) final background images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.471, + 0.468, + 0.5 + ], + "angle": 0, + "content": "contributing to shadow removal while better avoiding illumination or color artifacts in the image (see Figure 4(e))." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.501, + 0.468, + 0.788 + ], + "angle": 0, + "content": "To train our CBENet, we employ a background calculator with local-to-global strategy to construct the ground-truth background as the supervisor. Specifically, we first divide the ground-truth shadow-free image \\( I_{gt} \\) into \\( 16 \\times 16 \\) patches to obtain the local background \\( \\overline{B} \\). For each patch, we use the Gaussian Mixture Model (GMM) to cluster it into two clusters according to the pixel intensity of the image [2], corresponding to text content and background, respectively. With the observation that the background color of the document is usually brighter [2, 24], we consider the cluster with a higher intensity as the background cluster and apply the average color of the background cluster as the background of the patch. Since different patches have different background colors, the local background \\( \\overline{B} \\) usually has obvious patch boundaries, as shown in Figure 5(b). Thus, inspired by the guided filter for edge-preserving image smoothing [14], we employ a color-preserving smoothing operator to refine \\( \\overline{B} \\) and get a desired ground-truth background image \\( B \\) for the image, as shown in Figure 5(c)." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.788, + 0.4, + 0.802 + ], + "angle": 0, + "content": "The value of pixel \\(i\\) in \\(B\\) can be expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.203, + 0.805, + 0.469, + 0.84 + ], + "angle": 0, + "content": "\\[\nB _ {i} = \\sum_ {j \\in N (i)} W _ {i j} \\bar {B} _ {j}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.469, + 0.901 + ], + "angle": 0, + "content": "where \\( N(i) \\) is a local neighborhood of pixel i. \\( W_{ij} \\) is the filter kernel, which measures the color similarity between pixel \\( i \\) and pixel \\( j \\). Due to the original image has the edge information, we use \\( I^{gt} \\) as the guidance image to calculate" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.294, + 0.688, + 0.31 + ], + "angle": 0, + "content": "the filter kernel \\(W_{ij}\\), that is," + }, + { + "type": "equation", + "bbox": [ + 0.544, + 0.315, + 0.892, + 0.358 + ], + "angle": 0, + "content": "\\[\nW _ {i j} = \\frac {1}{| \\omega | ^ {2}} \\sum_ {i, j} (1 + \\frac {\\left(I _ {i} ^ {g t} - \\mu_ {k}\\right) \\left(I _ {j} ^ {g t} - \\mu_ {k}\\right)}{\\sigma_ {k} ^ {2} + \\epsilon}), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.364, + 0.892, + 0.41 + ], + "angle": 0, + "content": "where \\(\\mu_{k}\\) and \\(\\sigma_k^2\\) are the mean and variance of \\(I^{gt}\\) in \\(N(i)\\), \\(|\\omega|\\) is the number of pixels in \\(N(i)\\), and \\(\\epsilon\\) is a regularization parameter preventing \\(W_{ij}\\) from being too large." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.411, + 0.892, + 0.532 + ], + "angle": 0, + "content": "We adopt the U-Net structure to implement our CBENet. The U-Net first applies five Conv+BN+LReLU to extract features from the image. Then, it takes five deconvolutional layers with batch normalization and ReLU activation function to predict the background image. Skip connection is applied between convolutional layers and deconvolutional layers, increasing the number of channels in the network and preserving the context information of the front layer." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.544, + 0.892, + 0.56 + ], + "angle": 0, + "content": "4.2. Background-guided Shadow Removal Network" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.568, + 0.892, + 0.809 + ], + "angle": 0, + "content": "As aforementioned, the background can provide some useful information to facilitate shadow removal. Thus, we propose a background-guided shadow removal network (BGShadowNet) exploiting the background image as supplementary information. As shown in Figure 2, our BGShadowNet includes two stages. At Stage I, besides an image encoder, a background-constrained decoder is introduced to produce a coarse shadow-removal result. At Stage II, to improve the coarse result and produce the final shadow-free image, a background-based attention module (BAModule) and a detail enhancement module (DEModule) are embedded into an encoder-decoder network. A discriminator is stacked at the end to distinguish whether the produced image is real or not. We choose DenseUnet [32] and Markovian discriminator [17] as our encoder-decoder structure and discriminator." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Background-constrained Decoder. To take full advantage of the features from background image, we replace the common decoder with a background-constrained decoder at Stage I. Concretely, features from the background encoder are integrated into the background-constrained decoder at each corresponding level. The integrated features can com" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "1821" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.083, + 0.085, + 0.159, + 0.145 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.113, + 0.147, + 0.13, + 0.157 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.16, + 0.085, + 0.236, + 0.144 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.19, + 0.147, + 0.207, + 0.157 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.238, + 0.085, + 0.313, + 0.145 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.267, + 0.147, + 0.283, + 0.158 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image", + "bbox": [ + 0.314, + 0.085, + 0.389, + 0.145 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.342, + 0.147, + 0.36, + 0.157 + ], + "angle": 0, + "content": "(d)" + }, + { + "type": "image", + "bbox": [ + 0.391, + 0.085, + 0.466, + 0.145 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.419, + 0.147, + 0.436, + 0.157 + ], + "angle": 0, + "content": "(e)" + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.159, + 0.47, + 0.187 + ], + "angle": 0, + "content": "Figure 6. Results of stage I and II. (a): Input. (b): Coarse result at stage I. (d): Result at stage II. (c)&(e): close-ups of (b) and (d)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.201, + 0.469, + 0.23 + ], + "angle": 0, + "content": "plement the image features and help to produce a satisfactory shadow-removal result." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.231, + 0.47, + 0.382 + ], + "angle": 0, + "content": "Background-based Attention Module. Generally, areas with a similar background should have a similar appearance (color and illumination) in an image. However, there might be illumination or color artifacts in the coarse shadow-removal result (see Figure 6(b)). To preserve the overall consistency of the image, we introduce a background-based attention module (BAModule). Using the learned background features and attention mechanism, the BAModule helps to eliminate the appearance inconsistency in the image (see Figure 6(d))." + }, + { + "type": "image", + "bbox": [ + 0.127, + 0.387, + 0.422, + 0.474 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.476, + 0.469, + 0.504 + ], + "angle": 0, + "content": "Figure 7. The network of our background-based attention module (BAModule)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.509, + 0.469, + 0.719 + ], + "angle": 0, + "content": "Figure 7 illustrates the architecture of the proposed BAModule. We first fuse the encoder and background features to obtain the integrated features by channel-wise concatenation. Then, the integrated features are fed into an attention computing unit to generate a color-aware attention map. The attention computing unit consists of a convolutional layer, a Leaky ReLu activation function, batch normalization, and a ResidualBlock Layer. Finally, we fuse the color-aware attention map and the integrated features by element-wise multiplication to reconstruct the features, and then embed these features into the corresponding decoder level. The color-aware attention map can make the network adaptively focus on the regions with a similar background, promoting a consistent appearance in these regions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.469, + 0.854 + ], + "angle": 0, + "content": "Detail Enhancement Module. As multiple convolutions and downsampling operators in the network, partial detail information will be lost at high-level layers, resulting in detail-blurred results (see Figure 6(c)). Compared to the high-level features, low-level features in CNN layers usually contain more texture details. Thus, we introduce a detail enhancement module (DEModule) to restore the texture details of the coarse result by utilizing the low-level features of the network." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.469, + 0.901 + ], + "angle": 0, + "content": "As we know, the statistical texture information of the image reflects the texture intensities to some extent. Therefore, our DEModule is inspired by image histogram equalization," + }, + { + "type": "image", + "bbox": [ + 0.547, + 0.085, + 0.845, + 0.308 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.311, + 0.89, + 0.325 + ], + "angle": 0, + "content": "Figure 8. The pipeline of our detail enhancement module (DEM)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.338, + 0.892, + 0.444 + ], + "angle": 0, + "content": "consisting of two parts. One is feature counting to obtain the statistical information for low-level features, and the other is feature equalization to enhance texture details. Figure 8 illustrates the pipeline of the proposed DEModule. Specifically, we fuse the features of the first two low-level layers from the encoder to get the concatenated low-level features \\( F \\), which are fed into DEModule for statistical analysis." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.445, + 0.892, + 0.548 + ], + "angle": 0, + "content": "(1) Feature Counting. The purpose of feature counting is to get the quantization encoding map and statistical feature. We first use two \\(2 \\times 2\\) convolution layers to produce a feature map \\(M\\) and perform global average pooling to obtain the global averaged features \\(\\overline{M}\\) for \\(M\\). Next, we calculate the correlation between \\(M\\) and \\(\\overline{M}\\) by using cosine similarity, denoted as \\(S\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.55, + 0.892, + 0.627 + ], + "angle": 0, + "content": "To effectively conduct quantification and statistics, we construct a set of quantization levels \\( L \\), which divide the range of the minimum and maximum values of \\( S \\) into \\( N \\) equal parts. Then, the correlation matrix \\( S \\) can be quantized to a quantization encoding matrix \\( E \\) by using \\( L \\):" + }, + { + "type": "equation", + "bbox": [ + 0.512, + 0.63, + 0.892, + 0.675 + ], + "angle": 0, + "content": "\\[\nE _ {i, n} = \\left\\{ \\begin{array}{c c} 1 - | L _ {n} - S _ {i} |, & i f - \\frac {0 . 5}{N} \\leq L _ {n} - S _ {i} \\leq \\frac {0 . 5}{N} \\\\ 0, & e l s e \\end{array} , \\right. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.673, + 0.891, + 0.718 + ], + "angle": 0, + "content": "where \\( i \\in [1, HW] \\) and \\( n \\in [1, N] \\). \\( H \\) and \\( W \\) are the length and width of the image. \\( L_{n} \\) is the \\( n \\)th level of \\( L \\), and \\( S_{i} \\) is the \\( i \\)th row of \\( S \\). In our experiments, we set \\( N = 128 \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.87 + ], + "angle": 0, + "content": "To avoid eliminating gradient information, we perform a normalization operation for matrix \\( E \\). We integrate the normalized result and quantization levels \\( L \\) into a quantization counting map \\( C \\), which reflects the relative statistics of the low-level input features. Due to the concatenation operation, the channel number of \\( C \\) is 2. Thus, we perform two \\( 1 \\times 1 \\) convolution operations for \\( C \\) to increase the channel number, followed by a concatenation operation with \\( \\overline{M} \\) to further get absolute statistical information \\( H \\). \\( H \\) denotes the statistical features which play the role of the histogram." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "(2) Feature Equalization. Feature equalization is used to enhance the texture details of low-level layers by recon" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1822" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.101, + 0.089, + 0.873, + 0.29 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.134, + 0.292, + 0.151, + 0.302 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image_caption", + "bbox": [ + 0.221, + 0.292, + 0.237, + 0.302 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.307, + 0.292, + 0.324, + 0.302 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image_caption", + "bbox": [ + 0.391, + 0.292, + 0.408, + 0.302 + ], + "angle": 0, + "content": "(d)" + }, + { + "type": "image_caption", + "bbox": [ + 0.48, + 0.292, + 0.494, + 0.302 + ], + "angle": 0, + "content": "(e)" + }, + { + "type": "image_caption", + "bbox": [ + 0.565, + 0.292, + 0.581, + 0.302 + ], + "angle": 0, + "content": "(f)" + }, + { + "type": "image_caption", + "bbox": [ + 0.648, + 0.292, + 0.666, + 0.302 + ], + "angle": 0, + "content": "(g)" + }, + { + "type": "image_caption", + "bbox": [ + 0.735, + 0.292, + 0.751, + 0.302 + ], + "angle": 0, + "content": "(h)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.302, + 0.891, + 0.329 + ], + "angle": 0, + "content": "Figure 9. Visual comparison among state-of-the-art shadow removal methods: (a) input images, (b) Jung [19], (c) DSC [15], (d) Fu [11], (e) DHAN [6], (f) CANet [5], (g) BEDSR-Net [24], (h) our BGShadowNet, and (i) ground-truth images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.345, + 0.468, + 0.464 + ], + "angle": 0, + "content": "structuring a new set of quantization levels. We first perform a \\(1 \\times 1\\) convolution operation for \\(H\\) to get \\(G\\). Inspired by the attention mechanism, we perform matrix multiplication of \\(G\\) and its transposed matrix, followed by a softmax operation, to build a learned adjacent matrix \\(X\\). Matrix \\(X\\) can be regarded as a similarity coefficient matrix. Then, we can reconstruct the new quantization levels \\(L'\\) with a matrix multiplication for \\(X\\) and \\(G\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.466, + 0.468, + 0.569 + ], + "angle": 0, + "content": "Based on the reconstructed quantization levels \\( L' \\), we conduct feature equalization for the original quantization encoding matrix \\( E \\) to enhance the detail features. The enhanced features \\( R \\) can be obtained using a matrix multiplication of quantization levels \\( L' \\) and matrix \\( E \\). By using the enhanced texture details, the decoder can easily capture detail information." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.579, + 0.221, + 0.592 + ], + "angle": 0, + "content": "4.3. Loss Function" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.602, + 0.468, + 0.676 + ], + "angle": 0, + "content": "Our loss functions for optimizing the proposed network contain four components: background reconstruction loss \\(\\mathcal{L}_{\\text {background }}\\), appearance consistency loss \\(\\mathcal{L}_{\\text {appearance }}\\), structure consistency loss \\(\\mathcal{L}_{\\text {structure }}\\) and adversarial loss \\(\\mathcal{L}_{\\text {adv }}\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.678, + 0.468, + 0.737 + ], + "angle": 0, + "content": "Background reconstruction loss is used to constrain the CBENet to obtain the desirable background image, which uses the \\(\\ell_1\\) distance between \\(\\hat{B}\\) produced by CBENet and the ground-truth background image \\(B\\), that is," + }, + { + "type": "equation", + "bbox": [ + 0.182, + 0.74, + 0.468, + 0.755 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {b a c k g r o u n d}} = \\left\\| B - \\bar {B} \\right\\| _ {1}. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.758, + 0.468, + 0.802 + ], + "angle": 0, + "content": "Appearance consistency loss evaluates the data loss between the predicted results and the ground-truth image, which is calculated in the \\(\\ell_1\\) distance:" + }, + { + "type": "equation", + "bbox": [ + 0.085, + 0.806, + 0.468, + 0.855 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\text {a p p e a r a n c e}} = \\lambda_ {1} \\mathcal {L} _ {\\text {c o a r s e}} + \\lambda_ {2} \\mathcal {L} _ {\\text {f i n a l}} \\\\ = \\lambda_ {1} \\| I _ {g t} - I _ {\\text {c o a r s e}} \\| _ {1} + \\lambda_ {2} \\| I _ {g t} - I _ {\\text {f r e e}} \\| _ {1}, \\tag {5} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.857, + 0.468, + 0.9 + ], + "angle": 0, + "content": "where \\(\\lambda_{1}\\) and \\(\\lambda_{2}\\) are the weight parameters. \\(I_{\\text{coarse}}\\) is the coarse result produced at Stage I, and \\(I_{\\text{free}}\\) is the final shadow-removal result produced at Stage II." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.345, + 0.89, + 0.373 + ], + "angle": 0, + "content": "Structure consistency loss aims to preserve image structure, which is calculated as," + }, + { + "type": "equation", + "bbox": [ + 0.543, + 0.381, + 0.89, + 0.399 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {s t u c t u r e}} = \\lambda_ {3} \\left| \\left| \\mathrm {V G G} \\left(I _ {g t}\\right) - \\mathrm {V G G} \\left(I _ {f r e e}\\right) \\right| \\right| _ {2} ^ {2}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.407, + 0.89, + 0.435 + ], + "angle": 0, + "content": "where \\(\\lambda_{3}\\) is the weight parameter, and \\(\\mathrm{VGG}(\\cdot)\\) is the feature extractor from the pre-trained VGG19 model." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.437, + 0.89, + 0.48 + ], + "angle": 0, + "content": "Adversarial loss is designed for the discriminator to judge whether the produced results are real or fake, which is described as:" + }, + { + "type": "equation", + "bbox": [ + 0.51, + 0.49, + 0.89, + 0.52 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {a d v} = \\lambda_ {4} \\mathbb {E} _ {\\left(I, I _ {f r e e}, I _ {g t}\\right)} [ \\log (D (I _ {g t})) + \\log (1 - D (I)) ], \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.52, + 0.875, + 0.534 + ], + "angle": 0, + "content": "where \\(D\\) is the discriminator, and \\(I\\) is the shadow image." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.548, + 0.632, + 0.565 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.573, + 0.709, + 0.588 + ], + "angle": 0, + "content": "5.1. Implementation Detail" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.596, + 0.89, + 0.747 + ], + "angle": 0, + "content": "Our network is implemented in Pytorch. In our experiments, CBENet and BGShadowNet are trained separately. We first train CBENet for 200 epochs using the background ground-truth as the supervisor. Next, we fix the CBENet and train BGShadowNet for 200 epochs on a NVIDIA GeForce RTX2080Ti. We use Adam optimizer to optimize our generator and the discriminator with attenuation rate \\( betas = (0.5, 0.999) \\). The initial learning rate is set to 0.0004. The weight parameters \\( \\lambda_1, \\lambda_2, \\lambda_3 \\) and \\( \\lambda_4 \\) are set to 1, 1, 0.05 and 0.01 in our experiments, respectively." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.757, + 0.8, + 0.772 + ], + "angle": 0, + "content": "5.2. Comparison with State-of-the-arts" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.78, + 0.89, + 0.839 + ], + "angle": 0, + "content": "Datasets. Since SDSRD dataset [24] is not available, we use the proposed RDD dataset to train and evaluate our BGShadowNet. Apart from RDD, we also use Kligler's dataset [21] for evaluation." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.841, + 0.89, + 0.9 + ], + "angle": 0, + "content": "Metrics. We utilize the root mean square error (RMSE) in LAB color space between the shadow removal result and the ground-truth shadow-free image to evaluate the shadow removal performance. In addition, we also report the PSNR" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.946, + 0.515, + 0.957 + ], + "angle": 0, + "content": "1823" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.104, + 0.085, + 0.186, + 0.151 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.187, + 0.086, + 0.273, + 0.151 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.275, + 0.086, + 0.357, + 0.15 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.358, + 0.086, + 0.442, + 0.15 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.444, + 0.086, + 0.527, + 0.15 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.528, + 0.086, + 0.612, + 0.15 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.613, + 0.086, + 0.696, + 0.15 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.698, + 0.086, + 0.781, + 0.15 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.783, + 0.086, + 0.867, + 0.15 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.104, + 0.152, + 0.186, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.187, + 0.152, + 0.273, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.275, + 0.152, + 0.357, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.358, + 0.152, + 0.442, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.444, + 0.152, + 0.528, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.529, + 0.152, + 0.613, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.614, + 0.152, + 0.697, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.698, + 0.152, + 0.781, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.783, + 0.152, + 0.867, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.104, + 0.221, + 0.186, + 0.28 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.187, + 0.221, + 0.273, + 0.279 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.275, + 0.221, + 0.357, + 0.28 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.358, + 0.221, + 0.442, + 0.28 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.444, + 0.221, + 0.527, + 0.28 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.528, + 0.221, + 0.613, + 0.28 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.614, + 0.221, + 0.697, + 0.28 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.698, + 0.221, + 0.781, + 0.28 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.783, + 0.221, + 0.867, + 0.28 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.137, + 0.282, + 0.155, + 0.293 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image_caption", + "bbox": [ + 0.166, + 0.282, + 0.24, + 0.293 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.308, + 0.282, + 0.324, + 0.293 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image_caption", + "bbox": [ + 0.392, + 0.282, + 0.409, + 0.293 + ], + "angle": 0, + "content": "(d)" + }, + { + "type": "image_caption", + "bbox": [ + 0.478, + 0.282, + 0.494, + 0.293 + ], + "angle": 0, + "content": "(e)" + }, + { + "type": "image_caption", + "bbox": [ + 0.564, + 0.282, + 0.579, + 0.293 + ], + "angle": 0, + "content": "(f)" + }, + { + "type": "image_caption", + "bbox": [ + 0.648, + 0.282, + 0.665, + 0.293 + ], + "angle": 0, + "content": "(g)" + }, + { + "type": "image_caption", + "bbox": [ + 0.732, + 0.282, + 0.749, + 0.293 + ], + "angle": 0, + "content": "(h)" + }, + { + "type": "image_caption", + "bbox": [ + 0.819, + 0.282, + 0.834, + 0.293 + ], + "angle": 0, + "content": "(i)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.293, + 0.891, + 0.32 + ], + "angle": 0, + "content": "Figure 10. Visual comparison among state-of-the-art shadow removal methods: (a) input images, (b) Jung [19], (c) DSC [15], (d) DHAN [6], (e) Fu [11], (f) BEDSR-Net [24], (g) CANet [5], (h) BMNet [51], and (i) our BGShadowNet." + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.325, + 0.891, + 0.352 + ], + "angle": 0, + "content": "Table 1. Quantitative comparisons of shadow removal on RDD and Kligler datasets in terms of RMSE, PSNR, and SSIM. All the learning-based methods are trained on RDD dataset. \\(\\uparrow\\) means the larger the better while \\(\\downarrow\\) means the smaller the better." + }, + { + "type": "table", + "bbox": [ + 0.191, + 0.354, + 0.778, + 0.514 + ], + "angle": 0, + "content": "
MethodsVenue/YearRDDKligler
RMSE↓PSNR↑SSIM ↑RMSE↓PSNR↑SSIM ↑
ST-CGAN [39]CVPR/20183.14334.3280.9746.82627.4330.931
DSC [15]PAMI/20206.35728.1510.9147.70525.6150.898
DHAN [6]AAAI/20202.46736.3370.9786.61027.7070.937
Fu [11]CVPR/20214.32831.3870.9467.10127.3620.914
CANet [5]ICCV/20215.56128.9510.9187.85525.6250.899
SG-ShadowNet [36]ECCV/20222.97434.7270.9726.82927.1410.920
BMNet [51]CVPR/20229.40924.2890.91516.45919.0310.874
Bako [2]ACCV/201614.64820.7410.8949.05824.7770.895
Jung [19]ACCV/201830.19014.3640.86128.24713.7260.852
BEDSR-Net [24]CVPR/20202.93734.9280.9736.53328.1240.932
BGShadowNetCVPR/20232.21937.5850.9835.37729.1760.948
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.522, + 0.468, + 0.551 + ], + "angle": 0, + "content": "and SSIM in the RGB colour space to evaluate the performance of the proposed BGShadowNet." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.553, + 0.468, + 0.734 + ], + "angle": 0, + "content": "To verify the effectiveness of our method, we compare our results with various state-of-the-art shadow removal methods including three document image shadow removal methods (Bako [2], Jung [19] and BEDSR-Net [24]) and six natural image shadow removal methods (ST-CGAN [39], DSC [15], DHAN [6], Fu [11], CANet [5], SG-ShadowNet [36] and BMNet [51]). To make fair comparison, we use RDD dataset to train all the learning-based methods on the same hardware. Table 1 concludes the comparison results. From the table, we can observe that, our method achieves the best values for all metrics among all the comparing methods, clearly demonstrating the effectiveness." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Figure 9 provides some visual shadow removal results to further demonstrate the superiority of our methods. It can be seen, DSC [15] fails in handling image with heavy shadows (see Figure 9(c)). The robustness of Fu [11] is limited, and their results may contain unremoved shadows, as shown in Figure 9(d). DHAN [6] and CANet [5] have the similar problem to Fu [11]. Ignoring the content characteristics of the documents, Jung [19] leads to obvious color and illumination distortion (see Figure 9(b)). With the constant background, results of BEDSR-Net [24] sometimes exhibit artifacts along the shadow boundaries (see Figure 9(g))." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.522, + 0.891, + 0.568 + ], + "angle": 0, + "content": "Comparatively, the proposed method effectively recovers illumination in shadow regions without artifacts, as shown in Figure 9(h), which is similar to the ground-truth image." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.568, + 0.891, + 0.673 + ], + "angle": 0, + "content": "To further verify the robustness and generalization ability of the proposed method, Figure 10 presents some other shadow removal results for document images, containing some challenging cases, such as heavy shadows and inconsistent illumination in shadow regions. Apparently, results recovered by our method look more natural and have little artifacts." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.901 + ], + "angle": 0, + "content": "User Study. We conduct an user study to evaluate the visual performance of our method and some state-of-the-art shadow removal methods. We prepare 100 sets of shadow removal images. Each set contains seven shadow removal results of our BGShadowNet, CANet, DSC, DHAN, Fu, BEDSR-Net, and Jung, respectively. We randomly select 100 volunteers. For each volunteer, we randomly provide them twenty image sets. The volunteers are required to select the best shadow-free image for each set. Counting all the results, we find that \\(20.32\\%\\) of shadow-removal images generated by our BGShadowNet are chosen as the best shadow-free images, while \\(11.92\\%\\), \\(11.67\\%\\), \\(16.72\\%\\), \\(13.25\\%\\), \\(15.91\\%\\), and \\(10.21\\%\\) of shadow removal results are chosen by CANet, DSC, DHAN, Fu, BEDSR-Net, and Jung, respectively." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1824" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.107, + 0.088, + 0.867, + 0.247 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.248, + 0.892, + 0.275 + ], + "angle": 0, + "content": "Figure 11. Visual comparison for ablation study: (a) input images, (b) BASE\\(_1\\), (c) BASE\\(_2\\), (d) BGShadowNet\\(_1\\), (e) BGShadowNet\\(_2\\), (f) BGShadowNet\\(_3\\), (g) BGShadowNet\\(_4\\), and (h) our BGShadowNet." + }, + { + "type": "table_caption", + "bbox": [ + 0.19, + 0.28, + 0.778, + 0.294 + ], + "angle": 0, + "content": "Table 2. Quantitative results of ablation study on RDD and Kligler using RMSE, PSNR, and SSIM." + }, + { + "type": "table", + "bbox": [ + 0.242, + 0.295, + 0.727, + 0.407 + ], + "angle": 0, + "content": "
MethodsRDDKligler
RMSE ↓PSNR ↑SSIM ↑RMSE ↓PSNR ↑SSIM ↑
BASE12.94234.8210.9386.25328.2670.944
BASE22.89735.9760.9455.81128.8950.947
BGShadowNet12.60336.0520.9805.80528.3710.944
BGShadowNet22.58336.1350.9815.73129.0350.947
BGShadowNet32.43336.6810.9825.53829.1800.947
BGShadowNet42.34437.0490.9825.63328.8400.948
BGShadowNet2.21937.5850.9835.37729.1760.948
" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.418, + 0.23, + 0.433 + ], + "angle": 0, + "content": "5.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.443, + 0.47, + 0.503 + ], + "angle": 0, + "content": "Ablation of BGShadowNet. To further evaluate the performance of each component applied in our BGShadowNet, we perform ablation experiments using six variants (with or without the specific component) as follows:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.504, + 0.265, + 0.518 + ], + "angle": 0, + "content": "(1) \\(BASE_{1}\\): one DenseUnet;" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.519, + 0.319, + 0.533 + ], + "angle": 0, + "content": "(2) \\(BASE_2\\): two stacked DenseUnet;" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.534, + 0.427, + 0.548 + ], + "angle": 0, + "content": "(3) BGShadowNet1: BGShadowNet without StageII;" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.549, + 0.469, + 0.578 + ], + "angle": 0, + "content": "(4) \\(BGShadowNet_2\\): BGShadowNet without DEModule and BAModule;" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.579, + 0.452, + 0.593 + ], + "angle": 0, + "content": "(5) BGShadowNet3: BGShadowNet without BAModule;" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.594, + 0.45, + 0.608 + ], + "angle": 0, + "content": "(6) BGShadowNet \\( {}_{4} \\) : BGShadowNet without DEModule." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.504, + 0.469, + 0.608 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.612, + 0.47, + 0.717 + ], + "angle": 0, + "content": "We train the six variants and evaluate the results on RDD and Kligler's datasets. The results are summarized in Table 2. From the table, we can observe that the components embedded in the two stages can improve the shadow removal results. We also provide qualitative results in Figure 11, which shows that our BGShadowNet with all the components can produce more realistic results." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Ablation of Background Image. To verify the effectiveness of the spatially varying background, we rebuild BGShadowNet exploiting the constant background (denoted as \\(\\mathrm{BGShadowNet}_b\\)) estimated by BEDSR-Net [24], and reorganize BEDSR-Net employing our spatially varying background (denoted as \\(\\mathrm{BEDSR}_b\\)). Table 3 summarizes the comparison results. From the results, we can observe that, variant \\(\\mathrm{BEDSR}_b\\) using the spatially varying background can obtain better values than BEDSR-Net. Besides, our BGShadowNet can produce better results than that using the constant background. These results show that our spatially varying background contributes to superior results." + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.416, + 0.892, + 0.443 + ], + "angle": 0, + "content": "Table 3. Quantitative comparisons using different background images on RDD dataset." + }, + { + "type": "table", + "bbox": [ + 0.547, + 0.445, + 0.844, + 0.51 + ], + "angle": 0, + "content": "
MethodsRMSE ↓PSNR ↑SSIM ↑
BEDSR-Net2.93734.9280.973
BEDSRb2.77135.5550.976
BGShadowNetb2.74035.8210.980
BGShadowNet2.21937.5850.983
" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.521, + 0.892, + 0.596 + ], + "angle": 0, + "content": "**Limitation.** Our BGShadowNet can effectively remove shadows in document images. However, when the images are corrupted by heavy noise, our shadow removal results may contain some residual noise, resulting in uneven illumination with the surrounding environment." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.61, + 0.619, + 0.626 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.636, + 0.892, + 0.802 + ], + "angle": 0, + "content": "In this paper, we propose a CBENet to estimate a spatially varying background for the shadow image, which can facilitate the proposed BGShadowNet performs document shadow removal. Our BGShadowNet first predicts a coarse shadow-removal result using a background-constrained decoder. Then, we embed a BAModule and a DEModule into the encoder-decoder network to improve the coarse result and produce the final shadow-free result with a consistent appearance and detail-rich texture. Experiments comparing our BGShadowNet to state-of-the-art approaches demonstrate its superiority." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.816, + 0.66, + 0.832 + ], + "angle": 0, + "content": "Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.892, + 0.9 + ], + "angle": 0, + "content": "This work is partially supported by NS-FC (No.61902286, No.61972299, No.U1803262, No.61972298) and CAAI-Huawei MindSpore Open Fund." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1825" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.169 + ], + "angle": 0, + "content": "[1] E. Arbel and H. Hel-Or. Shadow removal using intensity surfaces and texture anchor points. 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In CVPR, pages 5627-5636, 2022. 7" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.163 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "1827" + } + ] +] \ No newline at end of file diff --git a/2023/Document Image Shadow Removal Guided by Color-Aware Background/488a81e8-9aa8-4e58-aac0-74e15ffd5e40_origin.pdf b/2023/Document Image Shadow Removal Guided by Color-Aware Background/488a81e8-9aa8-4e58-aac0-74e15ffd5e40_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..975cfcecd65907d49bf9d3f5d8ec9874c2fd2fca --- /dev/null +++ b/2023/Document Image Shadow Removal Guided by Color-Aware Background/488a81e8-9aa8-4e58-aac0-74e15ffd5e40_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:4c798bfc2790195ffa380fb58c76dff1fab278c4171e50a5711cba5f0f93443d +size 9417911 diff --git a/2023/Document Image Shadow Removal Guided by Color-Aware Background/full.md b/2023/Document Image Shadow Removal Guided by Color-Aware Background/full.md new file mode 100644 index 0000000000000000000000000000000000000000..bb29ac295d250e2f0c0b5d07a5f5819b83900edd --- /dev/null +++ b/2023/Document Image Shadow Removal Guided by Color-Aware Background/full.md @@ -0,0 +1,454 @@ +# Document Image Shadow Removal Guided by Color-Aware Background + +Ling Zhang $^{1}$ , Yinghao He $^{1}$ , Qing Zhang $^{2}$ , Zheng Liu $^{3}$ , Xiaolong Zhang $^{1}$ , Chunxia Xiao $^{4*}$ $^{1}$ School of Computer Science and Technology, Wuhan University of Science and Technology + $^{2}$ School of Computer Science and Engineering, Sun Yat-Sen University + $^{3}$ School of Computer Science, China University of Geosciences (Wuhan) + $^{4}$ School of Computer Science, Wuhan University + +zhling@wust.edu.cn, hyhwust@163.com, zhangqing.whu.cs@gmail.com +liu.zheng.jojo@gmail.com, xiaolong.zhang@wust.edu.cn, cxxiao@whu.edu.cn + +# Abstract + +Existing works on document image shadow removal mostly depend on learning and leveraging a constant background (the color of the paper) from the image. However, the constant background is less representative and frequently ignores other background colors, such as the printed colors, resulting in distorted results. In this paper, we present a color-aware background extraction network (CBENet) for extracting a spatially varying background image that accurately depicts the background colors of the document. Furthermore, we propose a background-guided document images shadow removal network (BGShadowNet) using the predicted spatially varying background as auxiliary information, which consists of two stages. At Stage I, a background-constrained decoder is designed to promote a coarse result. Then, the coarse result is refined with a background-based attention module (BAModule) to maintain a consistent appearance and a detail improvement module (DEModule) to enhance the texture details at Stage II. Experiments on two benchmark datasets qualitatively and quantitatively validate the superiority of the proposed approach over state-of-the-arts. + +# 1. Introduction + +Documents, such as textbooks, newspapers, leaflets, and receipts, are available daily, often saved as electronic documents for digital document archives or online message transfer. Since the wide use and convenience of mobile phones, people currently prefer to use mobile phones for digital document copying. However, the captured document images become highly susceptible to shadows when the light sources are blocked. The low brightness in shadow regions reduces the quality and readability of the documen + +![](images/4373280f1215c56af2b5a624561c598c1b0ffcac1f2aabb36175e706b0429203.jpg) + +![](images/1de4dc7fd787fb3dab303559dd7bdf2d428a30fbe7de6db77b5def07b2418f79.jpg) + +![](images/9a694d29b78bbda99e7cc048399da32d590c3f36da28a00adfc7d1977bfa4fd8.jpg) +(c) Our result + +![](images/1429bd00a9274a9814570e528df70846f3737460f0fdc024c8ced3894ceaf194.jpg) +(a) Shadow image +(d) Result of [2] + +![](images/cf133f6a966bb0ba45e55638f72416af648403f364509d1ebc88bb07587d3f44.jpg) +(b) Our background +(e) Background of [24] +Figure 1. Document image shadow removal. With the assumption of constant background, results of [2] and [24] may cause color distortion or shadow remnant. By using a spatially varying background, our method can produce more desirable result. + +![](images/424b31d9fa6cbaf0014dce66e3d21cc91141c557bffee6b24a45d0c0390ab92e.jpg) +(f) Result of [24] + +t image, resulting in illegible content and unpleasant user experience [2, 10, 12, 19, 28, 29]. Thus, shadow removal for document images is a required image processing task in various vision applications [3, 4, 33, 37, 46, 48]. + +Although natural image shadow removal has made substantial progress [16, 20, 22, 40, 44, 45], these approaches generally perform poorly on document pictures due to their drastically different features from natural images. Natural image, for example, emphasizes background content (shadow-free image) without a shadow layer [6, 7, 13, 27, 41], whereas document image emphasizes text content [2, 19, 30]. Without considering the particular properties of the document image, traditional approaches to natural image generally yield incorrect result when they are applied to document image, as well as learning-based methods (see Figure 9(c-f)) due to the less attention to the content structures. + +Several approaches on document image shadow removal are currently available, which dig into the specific characteristics of the document image [3, 21, 30, 49]. However, these approaches may cause color distortion or shadow remnant for image with complex backgrounds, as illustrated in Figure 1(d). Recently, Lin et al. [24] estimate a constant background for the image and propose BEDSR-Net for document image shadow removal. The constant background is the color of the paper (see Figure 1(e)), which ignores some other background colors, such as the printed colors. The constant background may provide inaccurate information for the shadow removal task, resulting in unsatisfactory results (see Figure 1(f)). To address this problem, we propose a color-aware background extraction network (CBENet) to extract a spatially varying background, which can preserve various background colors of the original image (see Figure 1(b)). The spatially varying background can provide more useful color information, which contributes to image shadow removal, as shown in Figure 1(c). + +With the background image, we propose a background-guided shadow removal network (BGShadowNet) for document image that exploits the background image as auxiliary information. Figure 2 presents the framework of the proposed BGShadowNet, which removes shadows in a two-stage process. First, we introduce a background-constrained decoder to combine background features with image features, which can help to promote the realistic coarse shadow-removal result. Then, we refine the coarse result with a background-based attention module (BAModule) and a detail enhancement module (DEModule). In particular, BAModule is designed to eliminate the illumination and color inconsistency in the image by using the attention mechanism. Inspired by image histogram equalization, DE-Module aims to enhance the detail features at low-level scales. + +Due to the lack of large-scale real document image datasets, we construct a new dataset comprised of real document images to facilitate the performance of document image shadow removal. Experiments on extensive document images and evaluations on two datasets verify that our BGShadowNet outperforms existing approaches. + +In summary, our main contributions are three-fold: + +- We present a color-aware background extraction network (CBENet) for estimating a spatially varying background image that guides the shadow removal of document image. +- We propose a framework named BGShadowNet for document image shadow removal, which takes full advantage of the background image and is able to robustly produce high-quality shadow removal results. +- We design a background-based attention module (BAModule) to maintain a consistent appearance and a detail enhancement module (DEModule) to enhance texture details. + +# 2. Related Work + +# 2.1. Shadow removal for natural image + +Traditional methods for natural image shadow removal usually focus on studying the different physical properties of shadows [1, 9, 25]. Finlayson et al. [8, 9] reconstructed shadow removal images based on gradient consistency. However, these methods can incur obvious shadow boundary artifacts due to the change of illumination. Shor et al. [34] defined an affine relationship between the shadow and non-shadow areas. Xiao et al. [34, 42, 43] and Zhang et al. [50] removed shadows by transforming illumination from non-shadow regions to shadow regions. However, these methods depended on the reference non-shadow areas, and often resulted in inconsistent illumination when the reference areas are unfortunate. + +Numerous learning-based methods have been proposed for natural image shadow removal [6,11,15,16,18,23,26,27, 31, 35]. For example, Deshadow-Net [31] extracted multicontext features to predict shadow matte layers for shadow removal. Wang et al. [38] employed stacked conditional GANs for joint shadow detection and removal. Zhang et al. [47] explored residual and illumination with GANs for shadow removal. ARGAN [7] proposed a attentive recurrent generative adversarial network for shadow detection and removal. Liu et al. [27] utilized shadow generation for weakly-supervised shadow removal. More recently, Chen et al. [5] transferred the contextual information from nonshadow regions to shadow regions in the embedded feature spaces. + +Although these methods are effective for natural images, they do not generalize well to document image shadow removal due to the difference characteristics between natural images and document images. + +# 2.2. Shadow removal for document image + +Most existing document shadow removal algorithms [2,3,19,21,30] use heuristics algorithms to dig into specific features of the document image. Bako et al. [2] removed shadows using the estimated shadow map. This method leaves slight trace at the boundary under strong shadows. Oliveira et al. [30] used natural neighborhood interpolation to estimate shadow image. Jung et al. [19] explored a waterfilling method for correcting the illumination of document image by converting the input image to a topographic surface. This method can achieve good performance in weak or moderate level of shadows, but tends to produce color degraded results for scenes with heavy shadows. + +Recently, Lin et al. [24] proposed a BEDSR-Net for document image shadow removal by estimating a constant background. It is the first deep network specifically designed for document image shadow removal, which takes advantage of specific properties of document images. Due + +![](images/32bc17d1a938b2b7731de30b00a7733dd3c7e209bb4239905b4f70030cbf7fae.jpg) +Figure 2. The framework of the proposed CBENet and BGShadowNet. Spatially varying background estimated by CBENet is used to help BGShadowNet produce a high-quality shadow removal result. With a background-constrained decoder, BGShadowNet first predicts a coarse shadow-removal result. Then, the coarse result is refined with a BAModule and a DEModule. + +to ignoring some other background colors in the image, this method may introduce artifacts, such as shadow boundaries or unremoved shadows. + +# 3. Document Dataset Construction + +Although there are several document shadow removal datasets, such as Bako [2], Kligler [21], Jung [19], RDSRD [24], SDSRD [24], they mostly have some limitations. Bako, Kligler, Jung, and RDSRD are small-scale evaluation datasets that are unsuitable for training a deep model. While SDSRD is a large-scale dataset, it is a synthetic dataset. + +![](images/0f020264082efec4598bda3f1006aebe06986b6618c1e215f40fa7306510ca9e.jpg) +Figure 3. Illustration of several captured shadow and shadow-free image pairs in RDD. The first row shows shadow images, and the second row demonstrates the corresponding shadow-free images. + +Imaging is a physical generation process by the interaction between light and material. Light environments in the real world usually contains multiple different lights, which are difficult to simulate in synthetic environments accurately. The statistical features of the synthetic and real images are often different. To facilitate the performance of document image shadow removal, we construct a new real document dataset, named RDD, for shadow removal. + +Concretely, we use documents as the background scene to construct our dataset, such as papers, books, publicity pamphlets, etc. We first capture a shadow image with illumination blocked by an object. Then, we obtain the corresponding shadow-free image by removing the occluder. Our RDD collects 4916 pairs of shadow and shadow-free images, divided into two groups, 4371 for training and 545 + +for testing. Figure 3 presents some shadow and shadow-free image pairs in our RDD. To the best of our knowledge, RD-D is the first large-scale real document dataset for shadow removal. + +# 4. Methodology + +We first introduce a color-aware background extraction network (CBENet) to estimate a spatially varying background for shadow image. Then, we propose a background-guided shadow removal network (BGShadowNet) for document image, which uses the estimated background as auxiliary information to facilitate shadow removal task. Figure 2 presents the framework of our CBENet and BGShadowNet. + +# 4.1. Color-aware Background Extraction Network + +As document image focuses mostly on the text content, a common strategy [2, 24] to perform document image shadow removal is to utilize the background layer extracted from the image, that only contains the color information for the image without text content. These methods assume the document has a constant color background (the color of the paper), as shown in Figure 4(b). But discrepancy may exist between a constant color background and the image. For example, there may be other background colors due to color printing, as shown in Figure 4(a). The constant background will result in unsatisfactory results, as shown in Figure 4(c). + +To address this problem, we propose a color-aware background extraction network (CBENet) to extract a spatially varying color background $\hat{B}$ for the document image, which preserves different background colors in the image, as shown in Figure 4(d). Compared with the constant background, our spatially varying background can provide more useful color information for the following shadow removal network. Note that our background is shadow-free, which can help BGShadowNet learn more shadow-free features, + +![](images/dd1e2d3804452d1c9e60db319ff63b55383af07a2f9fb877ccf4dc8c5d267915.jpg) + +![](images/0e706225fe3e22e7e9dc1910a717bc9db53cfb6f772a87f536b7aea87c206b86.jpg) +(a) + +![](images/67658ea56a6958f387d82793929f9f5c9aa7a2a40e815606efe76ee67a810914.jpg) + +![](images/b337ee676c963de12f3d94fdd57854c226674c17fb6d33f1d60055588beec3f5.jpg) +(b) + +![](images/93f46694b0072fdee56e8233b14a67846a8e948843bc55d54fd94f7ab83de6b2.jpg) + +![](images/cbb7364638ec9e62446ea57dd39495b9820a49ac0f6cfd6cf123b3549658dd4a.jpg) +(c) + +![](images/516574efd8c5ceda46dafa432ae5ce0f7172ed34d242ab89ff39ab1b50ec5fd4.jpg) + +![](images/245db0bddcf48c155468e7106676e601ff15b6844da5fcdf0e71c40d3a5784fb.jpg) +(d) + +![](images/d296d71e2699e1adde19b906b2f150d9ced2dab00abdf327f0a029f32defab4e.jpg) + +![](images/9a0bf31584baac15ac4d11eca79bb4958824cc46763beeda5e94fa17550fe8cd.jpg) +(e) + +![](images/d748cb292909c28d5b11266776ed6d74a76273adfcde35fb10b190d7871a0bad.jpg) + +![](images/aa5cf4a0905d4cbbcc50f917eb5f2d03f8845564502b6f0f5ca9524cf88bfd73.jpg) +(f) + +![](images/005650f6f196b7414f50025ac41050c2b4efcb2b4aeaa675ba3176029b7a9278.jpg) +Figure 4. Extracted background images and the corresponding shadow removal images. (a) is input images. (b) and (c) are the background images and shadow removal results predicted by BEDSR-Net [24]. (d) and (e) are our spatially varying background images and shadow removal results. (f) is the corresponding ground-truth images. + +![](images/e889b1dc623fc7c7e8a23ed2f65b7df7c73510f1b11bea0bcdbe2c32ff616888.jpg) +(a) +Figure 5. Visualization of background: (a) shadow images, (b) local background images, and (c) final background images. + +![](images/c6f1666d66fe9ad71624dce077baa25aa33342cb4010933321a2ea974133d202.jpg) + +![](images/f06670a2e3e181a241bc43a1e3f0632e59670f065e899100ff1c88b5fab5519f.jpg) +(b) + +![](images/328e22de7a7b17cfb18a4d9e9ebba5dc3231581d6b598e2af29d711e392c9983.jpg) + +![](images/dd700d0682199e9a74bbf212dc5bdf2887a38d65f4dcb62a20af70d52d2b239b.jpg) +(c) + +contributing to shadow removal while better avoiding illumination or color artifacts in the image (see Figure 4(e)). + +To train our CBENet, we employ a background calculator with local-to-global strategy to construct the ground-truth background as the supervisor. Specifically, we first divide the ground-truth shadow-free image $I_{gt}$ into $16 \times 16$ patches to obtain the local background $\overline{B}$ . For each patch, we use the Gaussian Mixture Model (GMM) to cluster it into two clusters according to the pixel intensity of the image [2], corresponding to text content and background, respectively. With the observation that the background color of the document is usually brighter [2, 24], we consider the cluster with a higher intensity as the background cluster and apply the average color of the background cluster as the background of the patch. Since different patches have different background colors, the local background $\overline{B}$ usually has obvious patch boundaries, as shown in Figure 5(b). Thus, inspired by the guided filter for edge-preserving image smoothing [14], we employ a color-preserving smoothing operator to refine $\overline{B}$ and get a desired ground-truth background image $B$ for the image, as shown in Figure 5(c). + +The value of pixel $i$ in $B$ can be expressed as: + +$$ +B _ {i} = \sum_ {j \in N (i)} W _ {i j} \bar {B} _ {j}, \tag {1} +$$ + +where $N(i)$ is a local neighborhood of pixel i. $W_{ij}$ is the filter kernel, which measures the color similarity between pixel $i$ and pixel $j$ . Due to the original image has the edge information, we use $I^{gt}$ as the guidance image to calculate + +the filter kernel $W_{ij}$ , that is, + +$$ +W _ {i j} = \frac {1}{| \omega | ^ {2}} \sum_ {i, j} (1 + \frac {\left(I _ {i} ^ {g t} - \mu_ {k}\right) \left(I _ {j} ^ {g t} - \mu_ {k}\right)}{\sigma_ {k} ^ {2} + \epsilon}), \tag {2} +$$ + +where $\mu_{k}$ and $\sigma_k^2$ are the mean and variance of $I^{gt}$ in $N(i)$ , $|\omega|$ is the number of pixels in $N(i)$ , and $\epsilon$ is a regularization parameter preventing $W_{ij}$ from being too large. + +We adopt the U-Net structure to implement our CBENet. The U-Net first applies five Conv+BN+LReLU to extract features from the image. Then, it takes five deconvolutional layers with batch normalization and ReLU activation function to predict the background image. Skip connection is applied between convolutional layers and deconvolutional layers, increasing the number of channels in the network and preserving the context information of the front layer. + +# 4.2. Background-guided Shadow Removal Network + +As aforementioned, the background can provide some useful information to facilitate shadow removal. Thus, we propose a background-guided shadow removal network (BGShadowNet) exploiting the background image as supplementary information. As shown in Figure 2, our BGShadowNet includes two stages. At Stage I, besides an image encoder, a background-constrained decoder is introduced to produce a coarse shadow-removal result. At Stage II, to improve the coarse result and produce the final shadow-free image, a background-based attention module (BAModule) and a detail enhancement module (DEModule) are embedded into an encoder-decoder network. A discriminator is stacked at the end to distinguish whether the produced image is real or not. We choose DenseUnet [32] and Markovian discriminator [17] as our encoder-decoder structure and discriminator. + +Background-constrained Decoder. To take full advantage of the features from background image, we replace the common decoder with a background-constrained decoder at Stage I. Concretely, features from the background encoder are integrated into the background-constrained decoder at each corresponding level. The integrated features can com + +![](images/af7ce88daa283bd3d23167ec74c1da8879a3f2a48495aa0a001e80a1ac2dd6ac.jpg) +(a) + +![](images/7287e2fb57b7299c2927703edecb9a38cbda134b506d37768325227a4fd92b32.jpg) +(b) + +![](images/ae015b0c0d9ba39f4b84546641a2a7e0c71e1ecdde02a35f8853c517766da693.jpg) +(c) +Figure 6. Results of stage I and II. (a): Input. (b): Coarse result at stage I. (d): Result at stage II. (c)&(e): close-ups of (b) and (d). + +![](images/9d9b937716d7170722ffe646ee343bd974855f9188326359fa1b0db636bb845e.jpg) +(d) + +![](images/795e3bd5e32b11025642bf79bde06ab786766ff1f3eb15a7800e20404ffe24fc.jpg) +(e) + +plement the image features and help to produce a satisfactory shadow-removal result. + +Background-based Attention Module. Generally, areas with a similar background should have a similar appearance (color and illumination) in an image. However, there might be illumination or color artifacts in the coarse shadow-removal result (see Figure 6(b)). To preserve the overall consistency of the image, we introduce a background-based attention module (BAModule). Using the learned background features and attention mechanism, the BAModule helps to eliminate the appearance inconsistency in the image (see Figure 6(d)). + +![](images/88675993d117bfdcae1c06de3d345e8206edd87090606257685050167afc5fcd.jpg) +Figure 7. The network of our background-based attention module (BAModule). + +Figure 7 illustrates the architecture of the proposed BAModule. We first fuse the encoder and background features to obtain the integrated features by channel-wise concatenation. Then, the integrated features are fed into an attention computing unit to generate a color-aware attention map. The attention computing unit consists of a convolutional layer, a Leaky ReLu activation function, batch normalization, and a ResidualBlock Layer. Finally, we fuse the color-aware attention map and the integrated features by element-wise multiplication to reconstruct the features, and then embed these features into the corresponding decoder level. The color-aware attention map can make the network adaptively focus on the regions with a similar background, promoting a consistent appearance in these regions. + +Detail Enhancement Module. As multiple convolutions and downsampling operators in the network, partial detail information will be lost at high-level layers, resulting in detail-blurred results (see Figure 6(c)). Compared to the high-level features, low-level features in CNN layers usually contain more texture details. Thus, we introduce a detail enhancement module (DEModule) to restore the texture details of the coarse result by utilizing the low-level features of the network. + +As we know, the statistical texture information of the image reflects the texture intensities to some extent. Therefore, our DEModule is inspired by image histogram equalization, + +![](images/3462e1758c0e58564de7ffa272fb10f23f2063e7d214b74e8e3ae2ded84f664a.jpg) +Figure 8. The pipeline of our detail enhancement module (DEM). + +consisting of two parts. One is feature counting to obtain the statistical information for low-level features, and the other is feature equalization to enhance texture details. Figure 8 illustrates the pipeline of the proposed DEModule. Specifically, we fuse the features of the first two low-level layers from the encoder to get the concatenated low-level features $F$ , which are fed into DEModule for statistical analysis. + +(1) Feature Counting. The purpose of feature counting is to get the quantization encoding map and statistical feature. We first use two $2 \times 2$ convolution layers to produce a feature map $M$ and perform global average pooling to obtain the global averaged features $\overline{M}$ for $M$ . Next, we calculate the correlation between $M$ and $\overline{M}$ by using cosine similarity, denoted as $S$ . + +To effectively conduct quantification and statistics, we construct a set of quantization levels $L$ , which divide the range of the minimum and maximum values of $S$ into $N$ equal parts. Then, the correlation matrix $S$ can be quantized to a quantization encoding matrix $E$ by using $L$ : + +$$ +E _ {i, n} = \left\{ \begin{array}{c c} 1 - | L _ {n} - S _ {i} |, & i f - \frac {0 . 5}{N} \leq L _ {n} - S _ {i} \leq \frac {0 . 5}{N} \\ 0, & e l s e \end{array} , \right. \tag {3} +$$ + +where $i \in [1, HW]$ and $n \in [1, N]$ . $H$ and $W$ are the length and width of the image. $L_{n}$ is the $n$ th level of $L$ , and $S_{i}$ is the $i$ th row of $S$ . In our experiments, we set $N = 128$ . + +To avoid eliminating gradient information, we perform a normalization operation for matrix $E$ . We integrate the normalized result and quantization levels $L$ into a quantization counting map $C$ , which reflects the relative statistics of the low-level input features. Due to the concatenation operation, the channel number of $C$ is 2. Thus, we perform two $1 \times 1$ convolution operations for $C$ to increase the channel number, followed by a concatenation operation with $\overline{M}$ to further get absolute statistical information $H$ . $H$ denotes the statistical features which play the role of the histogram. + +(2) Feature Equalization. Feature equalization is used to enhance the texture details of low-level layers by recon + +![](images/5758acaaf0c037b311dbe1a7acc9adc381405ae3f1d5d7fe0099a48935bdaf5b.jpg) +(a) +(b) +(c) +(d) +(e) +(f) +(g) +(h) +Figure 9. Visual comparison among state-of-the-art shadow removal methods: (a) input images, (b) Jung [19], (c) DSC [15], (d) Fu [11], (e) DHAN [6], (f) CANet [5], (g) BEDSR-Net [24], (h) our BGShadowNet, and (i) ground-truth images. + +structuring a new set of quantization levels. We first perform a $1 \times 1$ convolution operation for $H$ to get $G$ . Inspired by the attention mechanism, we perform matrix multiplication of $G$ and its transposed matrix, followed by a softmax operation, to build a learned adjacent matrix $X$ . Matrix $X$ can be regarded as a similarity coefficient matrix. Then, we can reconstruct the new quantization levels $L'$ with a matrix multiplication for $X$ and $G$ . + +Based on the reconstructed quantization levels $L'$ , we conduct feature equalization for the original quantization encoding matrix $E$ to enhance the detail features. The enhanced features $R$ can be obtained using a matrix multiplication of quantization levels $L'$ and matrix $E$ . By using the enhanced texture details, the decoder can easily capture detail information. + +# 4.3. Loss Function + +Our loss functions for optimizing the proposed network contain four components: background reconstruction loss $\mathcal{L}_{\text {background }}$ , appearance consistency loss $\mathcal{L}_{\text {appearance }}$ , structure consistency loss $\mathcal{L}_{\text {structure }}$ and adversarial loss $\mathcal{L}_{\text {adv }}$ . + +Background reconstruction loss is used to constrain the CBENet to obtain the desirable background image, which uses the $\ell_1$ distance between $\hat{B}$ produced by CBENet and the ground-truth background image $B$ , that is, + +$$ +\mathcal {L} _ {\text {b a c k g r o u n d}} = \left\| B - \bar {B} \right\| _ {1}. \tag {4} +$$ + +Appearance consistency loss evaluates the data loss between the predicted results and the ground-truth image, which is calculated in the $\ell_1$ distance: + +$$ +\begin{array}{l} \mathcal {L} _ {\text {a p p e a r a n c e}} = \lambda_ {1} \mathcal {L} _ {\text {c o a r s e}} + \lambda_ {2} \mathcal {L} _ {\text {f i n a l}} \\ = \lambda_ {1} \| I _ {g t} - I _ {\text {c o a r s e}} \| _ {1} + \lambda_ {2} \| I _ {g t} - I _ {\text {f r e e}} \| _ {1}, \tag {5} \\ \end{array} +$$ + +where $\lambda_{1}$ and $\lambda_{2}$ are the weight parameters. $I_{\text{coarse}}$ is the coarse result produced at Stage I, and $I_{\text{free}}$ is the final shadow-removal result produced at Stage II. + +Structure consistency loss aims to preserve image structure, which is calculated as, + +$$ +\mathcal {L} _ {\text {s t u c t u r e}} = \lambda_ {3} \left| \left| \mathrm {V G G} \left(I _ {g t}\right) - \mathrm {V G G} \left(I _ {f r e e}\right) \right| \right| _ {2} ^ {2}, \tag {6} +$$ + +where $\lambda_{3}$ is the weight parameter, and $\mathrm{VGG}(\cdot)$ is the feature extractor from the pre-trained VGG19 model. + +Adversarial loss is designed for the discriminator to judge whether the produced results are real or fake, which is described as: + +$$ +\mathcal {L} _ {a d v} = \lambda_ {4} \mathbb {E} _ {\left(I, I _ {f r e e}, I _ {g t}\right)} [ \log (D (I _ {g t})) + \log (1 - D (I)) ], \tag {7} +$$ + +where $D$ is the discriminator, and $I$ is the shadow image. + +# 5. Experiments + +# 5.1. Implementation Detail + +Our network is implemented in Pytorch. In our experiments, CBENet and BGShadowNet are trained separately. We first train CBENet for 200 epochs using the background ground-truth as the supervisor. Next, we fix the CBENet and train BGShadowNet for 200 epochs on a NVIDIA GeForce RTX2080Ti. We use Adam optimizer to optimize our generator and the discriminator with attenuation rate $betas = (0.5, 0.999)$ . The initial learning rate is set to 0.0004. The weight parameters $\lambda_1, \lambda_2, \lambda_3$ and $\lambda_4$ are set to 1, 1, 0.05 and 0.01 in our experiments, respectively. + +# 5.2. Comparison with State-of-the-arts + +Datasets. Since SDSRD dataset [24] is not available, we use the proposed RDD dataset to train and evaluate our BGShadowNet. Apart from RDD, we also use Kligler's dataset [21] for evaluation. + +Metrics. We utilize the root mean square error (RMSE) in LAB color space between the shadow removal result and the ground-truth shadow-free image to evaluate the shadow removal performance. In addition, we also report the PSNR + +![](images/2871f3672a16a8fb549bd9fdfeb4d07dde0fe9ec4d8024240b9a446d1494c22f.jpg) + +![](images/4b21e99f116c87da6cf6a12c43246df64775b3c3566832aa18b6d561c593750c.jpg) + +![](images/9132ce5f3c1a43f95ba90a628534aca08bd8225a4378aeee5007a00975d3b708.jpg) + +![](images/19a5165d4b17901b84c8f0ffa76fdb0950dc3aba1b5b0978d4e660a70ca051fb.jpg) + +![](images/37839b619c6fc9b87ecb7f626624f813cf21d727937281dc9c6b03d0dca8f42f.jpg) + +![](images/cb4d2e7bf6584084524d9d1e808b9c17c767e9f1bc7dc18c182e3d622897ca60.jpg) + +![](images/2ff14e251de0966b4519aad5da9fce16fd0e6c1de38fd8f16dcd6212f50f7488.jpg) + +![](images/44398a58c51f09be6a1694527766dab1ba7a01fe148a8590dd43efee22f5d822.jpg) + +![](images/e71bf5390b662e19677f1f5c9850d79068c5d35e37a074faf847454390cb2c6a.jpg) + +![](images/0d28ce297fc796187ddcd25dd34b85138b16124679d19e51e788d55d243811e3.jpg) + +![](images/a82d7238c4df842923169ed7dfcf79f687785c69dcc38360781f68dee39790aa.jpg) + +![](images/b1201a5cdeb8e8cd42a42f41e045d9a0566f214daa4e2a9e61988be81308581e.jpg) + +![](images/67b0cf0465d334abe95b842c362a22aad02e11ebf45fec03de1839974d317542.jpg) + +![](images/19af414df0132a6a00000d4d1e79083d6cec162e69029e0d4029b8abd7cb79a2.jpg) + +![](images/4d718093b4da2170163beb37edd6bab8eab7e6fedb150d949f0770547b3bd289.jpg) + +![](images/36c0a42de41b89df799df5552278b3d9f135f61ec984abfe026a0fb4106e1b5f.jpg) + +![](images/169e40e60138729a51dd56856eaaa5eda74c5727332ae1443eaf52b2f3cc9207.jpg) + +![](images/b17aec3423681f4dabbe149f84e0bffbca44ce2720eb7d04b21329ab43856d49.jpg) + +![](images/7d6da37a060d1b67469e66464ee0f53a4ed5e43cfa9e5505f56ac511cb9f7795.jpg) +(a) + +![](images/08e5fd057b1ce5a7da90999bbee1fb71a0e180df234b1a44c98adcd802a5f8d8.jpg) +(b) + +![](images/56b821f4f56d4ec20f979b149e574d56c6ac68e46984c6b83674cb643ff15dfc.jpg) +(c) + +![](images/c503369c775cfb9ea82eed159720d95505a5acf3367b310599ec42428c896bd2.jpg) +(d) +Figure 10. Visual comparison among state-of-the-art shadow removal methods: (a) input images, (b) Jung [19], (c) DSC [15], (d) DHAN [6], (e) Fu [11], (f) BEDSR-Net [24], (g) CANet [5], (h) BMNet [51], and (i) our BGShadowNet. + +![](images/3d984dfeb79c992001fd4957bd45baf94d51376a911efb4c65b16c752f4930d1.jpg) +(e) + +![](images/0f58f1030eb8911dcb6ceaac9067dbe8d90e915dcc4e69e286ed0afc5a57d716.jpg) +(f) + +![](images/8d696028752242cf436632d86d3f5ec0289a4ace6e4232f9bbb1b33c113b50b3.jpg) +(g) + +![](images/ef322d06ee9e4d017d996924347b79a3a38f13b4f9db05ae2e5d8e10f168a69d.jpg) +(h) + +![](images/472926062b03450497642eec3034d7f11600bfe0fe5440e22ac9ee13c4f1ba52.jpg) +(i) + +Table 1. Quantitative comparisons of shadow removal on RDD and Kligler datasets in terms of RMSE, PSNR, and SSIM. All the learning-based methods are trained on RDD dataset. $\uparrow$ means the larger the better while $\downarrow$ means the smaller the better. + +
MethodsVenue/YearRDDKligler
RMSE↓PSNR↑SSIM ↑RMSE↓PSNR↑SSIM ↑
ST-CGAN [39]CVPR/20183.14334.3280.9746.82627.4330.931
DSC [15]PAMI/20206.35728.1510.9147.70525.6150.898
DHAN [6]AAAI/20202.46736.3370.9786.61027.7070.937
Fu [11]CVPR/20214.32831.3870.9467.10127.3620.914
CANet [5]ICCV/20215.56128.9510.9187.85525.6250.899
SG-ShadowNet [36]ECCV/20222.97434.7270.9726.82927.1410.920
BMNet [51]CVPR/20229.40924.2890.91516.45919.0310.874
Bako [2]ACCV/201614.64820.7410.8949.05824.7770.895
Jung [19]ACCV/201830.19014.3640.86128.24713.7260.852
BEDSR-Net [24]CVPR/20202.93734.9280.9736.53328.1240.932
BGShadowNetCVPR/20232.21937.5850.9835.37729.1760.948
+ +and SSIM in the RGB colour space to evaluate the performance of the proposed BGShadowNet. + +To verify the effectiveness of our method, we compare our results with various state-of-the-art shadow removal methods including three document image shadow removal methods (Bako [2], Jung [19] and BEDSR-Net [24]) and six natural image shadow removal methods (ST-CGAN [39], DSC [15], DHAN [6], Fu [11], CANet [5], SG-ShadowNet [36] and BMNet [51]). To make fair comparison, we use RDD dataset to train all the learning-based methods on the same hardware. Table 1 concludes the comparison results. From the table, we can observe that, our method achieves the best values for all metrics among all the comparing methods, clearly demonstrating the effectiveness. + +Figure 9 provides some visual shadow removal results to further demonstrate the superiority of our methods. It can be seen, DSC [15] fails in handling image with heavy shadows (see Figure 9(c)). The robustness of Fu [11] is limited, and their results may contain unremoved shadows, as shown in Figure 9(d). DHAN [6] and CANet [5] have the similar problem to Fu [11]. Ignoring the content characteristics of the documents, Jung [19] leads to obvious color and illumination distortion (see Figure 9(b)). With the constant background, results of BEDSR-Net [24] sometimes exhibit artifacts along the shadow boundaries (see Figure 9(g)). + +Comparatively, the proposed method effectively recovers illumination in shadow regions without artifacts, as shown in Figure 9(h), which is similar to the ground-truth image. + +To further verify the robustness and generalization ability of the proposed method, Figure 10 presents some other shadow removal results for document images, containing some challenging cases, such as heavy shadows and inconsistent illumination in shadow regions. Apparently, results recovered by our method look more natural and have little artifacts. + +User Study. We conduct an user study to evaluate the visual performance of our method and some state-of-the-art shadow removal methods. We prepare 100 sets of shadow removal images. Each set contains seven shadow removal results of our BGShadowNet, CANet, DSC, DHAN, Fu, BEDSR-Net, and Jung, respectively. We randomly select 100 volunteers. For each volunteer, we randomly provide them twenty image sets. The volunteers are required to select the best shadow-free image for each set. Counting all the results, we find that $20.32\%$ of shadow-removal images generated by our BGShadowNet are chosen as the best shadow-free images, while $11.92\%$ , $11.67\%$ , $16.72\%$ , $13.25\%$ , $15.91\%$ , and $10.21\%$ of shadow removal results are chosen by CANet, DSC, DHAN, Fu, BEDSR-Net, and Jung, respectively. + +![](images/f4eff1a228cddea5eec519b29bf572f51e5948a9c1589c85d621922087f64668.jpg) +Figure 11. Visual comparison for ablation study: (a) input images, (b) BASE $_1$ , (c) BASE $_2$ , (d) BGShadowNet $_1$ , (e) BGShadowNet $_2$ , (f) BGShadowNet $_3$ , (g) BGShadowNet $_4$ , and (h) our BGShadowNet. + +Table 2. Quantitative results of ablation study on RDD and Kligler using RMSE, PSNR, and SSIM. + +
MethodsRDDKligler
RMSE ↓PSNR ↑SSIM ↑RMSE ↓PSNR ↑SSIM ↑
BASE12.94234.8210.9386.25328.2670.944
BASE22.89735.9760.9455.81128.8950.947
BGShadowNet12.60336.0520.9805.80528.3710.944
BGShadowNet22.58336.1350.9815.73129.0350.947
BGShadowNet32.43336.6810.9825.53829.1800.947
BGShadowNet42.34437.0490.9825.63328.8400.948
BGShadowNet2.21937.5850.9835.37729.1760.948
+ +# 5.3. Ablation Study + +Ablation of BGShadowNet. To further evaluate the performance of each component applied in our BGShadowNet, we perform ablation experiments using six variants (with or without the specific component) as follows: + +(1) $BASE_{1}$ : one DenseUnet; +(2) $BASE_2$ : two stacked DenseUnet; +(3) BGShadowNet1: BGShadowNet without StageII; +(4) $BGShadowNet_2$ : BGShadowNet without DEModule and BAModule; +(5) BGShadowNet3: BGShadowNet without BAModule; +(6) BGShadowNet ${}_{4}$ : BGShadowNet without DEModule. + +We train the six variants and evaluate the results on RDD and Kligler's datasets. The results are summarized in Table 2. From the table, we can observe that the components embedded in the two stages can improve the shadow removal results. We also provide qualitative results in Figure 11, which shows that our BGShadowNet with all the components can produce more realistic results. + +Ablation of Background Image. To verify the effectiveness of the spatially varying background, we rebuild BGShadowNet exploiting the constant background (denoted as $\mathrm{BGShadowNet}_b$ ) estimated by BEDSR-Net [24], and reorganize BEDSR-Net employing our spatially varying background (denoted as $\mathrm{BEDSR}_b$ ). Table 3 summarizes the comparison results. From the results, we can observe that, variant $\mathrm{BEDSR}_b$ using the spatially varying background can obtain better values than BEDSR-Net. Besides, our BGShadowNet can produce better results than that using the constant background. These results show that our spatially varying background contributes to superior results. + +Table 3. Quantitative comparisons using different background images on RDD dataset. + +
MethodsRMSE ↓PSNR ↑SSIM ↑
BEDSR-Net2.93734.9280.973
BEDSRb2.77135.5550.976
BGShadowNetb2.74035.8210.980
BGShadowNet2.21937.5850.983
+ +**Limitation.** Our BGShadowNet can effectively remove shadows in document images. However, when the images are corrupted by heavy noise, our shadow removal results may contain some residual noise, resulting in uneven illumination with the surrounding environment. + +# 6. Conclusion + +In this paper, we propose a CBENet to estimate a spatially varying background for the shadow image, which can facilitate the proposed BGShadowNet performs document shadow removal. Our BGShadowNet first predicts a coarse shadow-removal result using a background-constrained decoder. Then, we embed a BAModule and a DEModule into the encoder-decoder network to improve the coarse result and produce the final shadow-free result with a consistent appearance and detail-rich texture. Experiments comparing our BGShadowNet to state-of-the-art approaches demonstrate its superiority. + +# Acknowledgments + +This work is partially supported by NS-FC (No.61902286, No.61972299, No.U1803262, No.61972298) and CAAI-Huawei MindSpore Open Fund. + +# References + +[1] E. Arbel and H. Hel-Or. Shadow removal using intensity surfaces and texture anchor points. IEEE Transactions on Pattern Analysis Machine Intelligence, 33(6):1202-1216, 2011. 2 +[2] S. Bako, S. Darabi, E. Shechtman, J. Wang, and P. Sen. Removing shadows from images of documents. In ACCV, pages 173-183, 2016. 1, 2, 3, 4, 7 +[3] M. S. Brown and Y. C. Tsoi. Geometric and shading correction for images of printed materials using boundary. IEEE Transactions on Image Processing, 15(6):1544-1554, 2006. 1, 2 +[4] Cen Chen, Kenli Li, Sin G Teo, Xiaofeng Zou, Keqin Li, and Zeng Zeng. Citywide traffic flow prediction based on multiple gated spatio-temporal convolutional neural networks. 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However, the constant background is less representative and frequently ignores other background colors, such as the printed colors, resulting in distorted results. In this paper, we present a color-aware background extraction network (CBENet) for extracting a spatially varying background image that accurately depicts the background colors of the document. Furthermore, we propose a background-guided document images shadow removal network (BGShadowNet) using the predicted spatially varying background as auxiliary information, which consists of two stages. At Stage I, a background-constrained decoder is designed to promote a coarse result. Then, the coarse result is refined with a background-based attention module (BAModule) to maintain a consistent appearance and a detail improvement module (DEModule) to enhance the texture details at Stage II. Experiments on two benchmark datasets qualitatively and quantitatively validate the superiority of the proposed approach over state-of-the-arts." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 567, + 128, + 580 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 567, + 128, + 580 + ], + "spans": [ + { + "bbox": [ + 47, + 567, + 128, + 580 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 588, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 588, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 588, + 287, + 696 + ], + "type": "text", + "content": "Documents, such as textbooks, newspapers, leaflets, and receipts, are available daily, often saved as electronic documents for digital document archives or online message transfer. Since the wide use and convenience of mobile phones, people currently prefer to use mobile phones for digital document copying. However, the captured document images become highly susceptible to shadows when the light sources are blocked. 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Document image shadow removal. With the assumption of constant background, results of [2] and [24] may cause color distortion or shadow remnant. By using a spatially varying background, our method can produce more desirable result." + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 465, + 359, + 541, + 439 + ], + "blocks": [ + { + "bbox": [ + 465, + 359, + 541, + 439 + ], + "lines": [ + { + "bbox": [ + 465, + 359, + 541, + 439 + ], + "spans": [ + { + "bbox": [ + 465, + 359, + 541, + 439 + ], + "type": "image", + "image_path": "424b31d9fa6cbaf0014dce66e3d21cc91141c557bffee6b24a45d0c0390ab92e.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 474, + 441, + 530, + 451 + ], + "lines": [ + { + "bbox": [ + 474, + 441, + 530, + 451 + ], + "spans": [ + { + "bbox": [ + 474, + 441, + 530, + 451 + ], + "type": "text", + "content": "(f) Result of [24]" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 507, + 547, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 507, + 547, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 507, + 547, + 555 + ], + "type": "text", + "content": "t image, resulting in illegible content and unpleasant user experience [2, 10, 12, 19, 28, 29]. Thus, shadow removal for document images is a required image processing task in various vision applications [3, 4, 33, 37, 46, 48]." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 558, + 547, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 547, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 547, + 712 + ], + "type": "text", + "content": "Although natural image shadow removal has made substantial progress [16, 20, 22, 40, 44, 45], these approaches generally perform poorly on document pictures due to their drastically different features from natural images. Natural image, for example, emphasizes background content (shadow-free image) without a shadow layer [6, 7, 13, 27, 41], whereas document image emphasizes text content [2, 19, 30]. Without considering the particular properties of the document image, traditional approaches to natural image generally yield incorrect result when they are applied to document image, as well as learning-based methods (see Figure 9(c-f)) due to the less attention to the content structures." + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 258, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 258, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 258, + 713 + ], + "type": "text", + "content": "*Corresponding author: Chunxia Xiao (cxxiao@whu.edu.cn)." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1818" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 300 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 300 + ], + "type": "text", + "content": "Several approaches on document image shadow removal are currently available, which dig into the specific characteristics of the document image [3, 21, 30, 49]. However, these approaches may cause color distortion or shadow remnant for image with complex backgrounds, as illustrated in Figure 1(d). Recently, Lin et al. [24] estimate a constant background for the image and propose BEDSR-Net for document image shadow removal. The constant background is the color of the paper (see Figure 1(e)), which ignores some other background colors, such as the printed colors. The constant background may provide inaccurate information for the shadow removal task, resulting in unsatisfactory results (see Figure 1(f)). To address this problem, we propose a color-aware background extraction network (CBENet) to extract a spatially varying background, which can preserve various background colors of the original image (see Figure 1(b)). The spatially varying background can provide more useful color information, which contributes to image shadow removal, as shown in Figure 1(c)." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 300, + 289, + 490 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 300, + 289, + 490 + ], + "spans": [ + { + "bbox": [ + 47, + 300, + 289, + 490 + ], + "type": "text", + "content": "With the background image, we propose a background-guided shadow removal network (BGShadowNet) for document image that exploits the background image as auxiliary information. Figure 2 presents the framework of the proposed BGShadowNet, which removes shadows in a two-stage process. First, we introduce a background-constrained decoder to combine background features with image features, which can help to promote the realistic coarse shadow-removal result. Then, we refine the coarse result with a background-based attention module (BAModule) and a detail enhancement module (DEModule). In particular, BAModule is designed to eliminate the illumination and color inconsistency in the image by using the attention mechanism. Inspired by image histogram equalization, DE-Module aims to enhance the detail features at low-level scales." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 491, + 289, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 491, + 289, + 563 + ], + "spans": [ + { + "bbox": [ + 47, + 491, + 289, + 563 + ], + "type": "text", + "content": "Due to the lack of large-scale real document image datasets, we construct a new dataset comprised of real document images to facilitate the performance of document image shadow removal. Experiments on extensive document images and evaluations on two datasets verify that our BGShadowNet outperforms existing approaches." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 58, + 563, + 264, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 563, + 264, + 574 + ], + "spans": [ + { + "bbox": [ + 58, + 563, + 264, + 574 + ], + "type": "text", + "content": "In summary, our main contributions are three-fold:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 57, + 574, + 287, + 712 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 57, + 574, + 287, + 619 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 574, + 287, + 619 + ], + "spans": [ + { + "bbox": [ + 57, + 574, + 287, + 619 + ], + "type": "text", + "content": "- We present a color-aware background extraction network (CBENet) for estimating a spatially varying background image that guides the shadow removal of document image." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 57, + 619, + 287, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 619, + 287, + 666 + ], + "spans": [ + { + "bbox": [ + 57, + 619, + 287, + 666 + ], + "type": "text", + "content": "- We propose a framework named BGShadowNet for document image shadow removal, which takes full advantage of the background image and is able to robustly produce high-quality shadow removal results." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 57, + 666, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 666, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 57, + 666, + 287, + 712 + ], + "type": "text", + "content": "- We design a background-based attention module (BAModule) to maintain a consistent appearance and a detail enhancement module (DEModule) to enhance texture details." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 71, + 392, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 71, + 392, + 83 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 392, + 83 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 91, + 492, + 105 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 91, + 492, + 105 + ], + "spans": [ + { + "bbox": [ + 306, + 91, + 492, + 105 + ], + "type": "text", + "content": "2.1. Shadow removal for natural image" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 110, + 545, + 264 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 110, + 545, + 264 + ], + "spans": [ + { + "bbox": [ + 304, + 110, + 545, + 264 + ], + "type": "text", + "content": "Traditional methods for natural image shadow removal usually focus on studying the different physical properties of shadows [1, 9, 25]. Finlayson et al. [8, 9] reconstructed shadow removal images based on gradient consistency. However, these methods can incur obvious shadow boundary artifacts due to the change of illumination. Shor et al. [34] defined an affine relationship between the shadow and non-shadow areas. Xiao et al. [34, 42, 43] and Zhang et al. [50] removed shadows by transforming illumination from non-shadow regions to shadow regions. However, these methods depended on the reference non-shadow areas, and often resulted in inconsistent illumination when the reference areas are unfortunate." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 266, + 545, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 266, + 545, + 434 + ], + "spans": [ + { + "bbox": [ + 304, + 266, + 545, + 434 + ], + "type": "text", + "content": "Numerous learning-based methods have been proposed for natural image shadow removal [6,11,15,16,18,23,26,27, 31, 35]. For example, Deshadow-Net [31] extracted multicontext features to predict shadow matte layers for shadow removal. Wang et al. [38] employed stacked conditional GANs for joint shadow detection and removal. Zhang et al. [47] explored residual and illumination with GANs for shadow removal. ARGAN [7] proposed a attentive recurrent generative adversarial network for shadow detection and removal. Liu et al. [27] utilized shadow generation for weakly-supervised shadow removal. More recently, Chen et al. [5] transferred the contextual information from nonshadow regions to shadow regions in the embedded feature spaces." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 434, + 545, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 434, + 545, + 483 + ], + "spans": [ + { + "bbox": [ + 304, + 434, + 545, + 483 + ], + "type": "text", + "content": "Although these methods are effective for natural images, they do not generalize well to document image shadow removal due to the difference characteristics between natural images and document images." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 491, + 503, + 503 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 491, + 503, + 503 + ], + "spans": [ + { + "bbox": [ + 306, + 491, + 503, + 503 + ], + "type": "text", + "content": "2.2. Shadow removal for document image" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 509, + 545, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 509, + 545, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 509, + 545, + 653 + ], + "type": "text", + "content": "Most existing document shadow removal algorithms [2,3,19,21,30] use heuristics algorithms to dig into specific features of the document image. Bako et al. [2] removed shadows using the estimated shadow map. This method leaves slight trace at the boundary under strong shadows. Oliveira et al. [30] used natural neighborhood interpolation to estimate shadow image. Jung et al. [19] explored a waterfilling method for correcting the illumination of document image by converting the input image to a topographic surface. This method can achieve good performance in weak or moderate level of shadows, but tends to produce color degraded results for scenes with heavy shadows." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": "Recently, Lin et al. [24] proposed a BEDSR-Net for document image shadow removal by estimating a constant background. It is the first deep network specifically designed for document image shadow removal, which takes advantage of specific properties of document images. Due" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1819" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 78, + 64, + 511, + 236 + ], + "blocks": [ + { + "bbox": [ + 78, + 64, + 511, + 236 + ], + "lines": [ + { + "bbox": [ + 78, + 64, + 511, + 236 + ], + "spans": [ + { + "bbox": [ + 78, + 64, + 511, + 236 + ], + "type": "image", + "image_path": "32bc17d1a938b2b7731de30b00a7733dd3c7e209bb4239905b4f70030cbf7fae.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 239, + 547, + 273 + ], + "lines": [ + { + "bbox": [ + 46, + 239, + 547, + 273 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 547, + 273 + ], + "type": "text", + "content": "Figure 2. The framework of the proposed CBENet and BGShadowNet. Spatially varying background estimated by CBENet is used to help BGShadowNet produce a high-quality shadow removal result. With a background-constrained decoder, BGShadowNet first predicts a coarse shadow-removal result. Then, the coarse result is refined with a BAModule and a DEModule." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 279, + 288, + 315 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 279, + 288, + 315 + ], + "spans": [ + { + "bbox": [ + 46, + 279, + 288, + 315 + ], + "type": "text", + "content": "to ignoring some other background colors in the image, this method may introduce artifacts, such as shadow boundaries or unremoved shadows." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 327, + 228, + 339 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 327, + 228, + 339 + ], + "spans": [ + { + "bbox": [ + 47, + 327, + 228, + 339 + ], + "type": "text", + "content": "3. Document Dataset Construction" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 347, + 287, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 347, + 287, + 419 + ], + "spans": [ + { + "bbox": [ + 46, + 347, + 287, + 419 + ], + "type": "text", + "content": "Although there are several document shadow removal datasets, such as Bako [2], Kligler [21], Jung [19], RDSRD [24], SDSRD [24], they mostly have some limitations. Bako, Kligler, Jung, and RDSRD are small-scale evaluation datasets that are unsuitable for training a deep model. While SDSRD is a large-scale dataset, it is a synthetic dataset." + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 49, + 423, + 285, + 496 + ], + "blocks": [ + { + "bbox": [ + 49, + 423, + 285, + 496 + ], + "lines": [ + { + "bbox": [ + 49, + 423, + 285, + 496 + ], + "spans": [ + { + "bbox": [ + 49, + 423, + 285, + 496 + ], + "type": "image", + "image_path": "0f020264082efec4598bda3f1006aebe06986b6618c1e215f40fa7306510ca9e.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 498, + 287, + 533 + ], + "lines": [ + { + "bbox": [ + 46, + 498, + 287, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 287, + 533 + ], + "type": "text", + "content": "Figure 3. Illustration of several captured shadow and shadow-free image pairs in RDD. The first row shows shadow images, and the second row demonstrates the corresponding shadow-free images." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 534, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 534, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 534, + 287, + 628 + ], + "type": "text", + "content": "Imaging is a physical generation process by the interaction between light and material. Light environments in the real world usually contains multiple different lights, which are difficult to simulate in synthetic environments accurately. The statistical features of the synthetic and real images are often different. To facilitate the performance of document image shadow removal, we construct a new real document dataset, named RDD, for shadow removal." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 630, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 287, + 715 + ], + "type": "text", + "content": "Concretely, we use documents as the background scene to construct our dataset, such as papers, books, publicity pamphlets, etc. We first capture a shadow image with illumination blocked by an object. Then, we obtain the corresponding shadow-free image by removing the occluder. Our RDD collects 4916 pairs of shadow and shadow-free images, divided into two groups, 4371 for training and 545" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 279, + 545, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 279, + 545, + 327 + ], + "spans": [ + { + "bbox": [ + 304, + 279, + 545, + 327 + ], + "type": "text", + "content": "for testing. Figure 3 presents some shadow and shadow-free image pairs in our RDD. To the best of our knowledge, RD-D is the first large-scale real document dataset for shadow removal." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 340, + 389, + 354 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 340, + 389, + 354 + ], + "spans": [ + { + "bbox": [ + 306, + 340, + 389, + 354 + ], + "type": "text", + "content": "4. Methodology" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 361, + 546, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 361, + 546, + 445 + ], + "spans": [ + { + "bbox": [ + 304, + 361, + 546, + 445 + ], + "type": "text", + "content": "We first introduce a color-aware background extraction network (CBENet) to estimate a spatially varying background for shadow image. Then, we propose a background-guided shadow removal network (BGShadowNet) for document image, which uses the estimated background as auxiliary information to facilitate shadow removal task. Figure 2 presents the framework of our CBENet and BGShadowNet." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 454, + 544, + 467 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 454, + 544, + 467 + ], + "spans": [ + { + "bbox": [ + 305, + 454, + 544, + 467 + ], + "type": "text", + "content": "4.1. Color-aware Background Extraction Network" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 474, + 545, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 545, + 605 + ], + "type": "text", + "content": "As document image focuses mostly on the text content, a common strategy [2, 24] to perform document image shadow removal is to utilize the background layer extracted from the image, that only contains the color information for the image without text content. These methods assume the document has a constant color background (the color of the paper), as shown in Figure 4(b). But discrepancy may exist between a constant color background and the image. For example, there may be other background colors due to color printing, as shown in Figure 4(a). The constant background will result in unsatisfactory results, as shown in Figure 4(c)." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 605, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 546, + 713 + ], + "type": "text", + "content": "To address this problem, we propose a color-aware background extraction network (CBENet) to extract a spatially varying color background " + }, + { + "bbox": [ + 304, + 605, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\hat{B}" + }, + { + "bbox": [ + 304, + 605, + 546, + 713 + ], + "type": "text", + "content": " for the document image, which preserves different background colors in the image, as shown in Figure 4(d). Compared with the constant background, our spatially varying background can provide more useful color information for the following shadow removal network. Note that our background is shadow-free, which can help BGShadowNet learn more shadow-free features," + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1820" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 74, + 64, + 147, + 120 + ], + "blocks": [ + { + "bbox": [ + 74, + 64, + 147, + 120 + ], + "lines": [ + { + "bbox": [ + 74, + 64, + 147, + 120 + ], + "spans": [ + { + "bbox": [ + 74, + 64, + 147, + 120 + ], + "type": "image", + "image_path": "dd1e2d3804452d1c9e60db319ff63b55383af07a2f9fb877ccf4dc8c5d267915.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + 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Extracted background images and the corresponding shadow removal images. (a) is input images. (b) and (c) are the background images and shadow removal results predicted by BEDSR-Net [24]. (d) and (e) are our spatially varying background images and shadow removal results. 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Specifically, we first divide the ground-truth shadow-free image " + }, + { + "bbox": [ + 46, + 396, + 286, + 624 + ], + "type": "inline_equation", + "content": "I_{gt}" + }, + { + "bbox": [ + 46, + 396, + 286, + 624 + ], + "type": "text", + "content": " into " + }, + { + "bbox": [ + 46, + 396, + 286, + 624 + ], + "type": "inline_equation", + "content": "16 \\times 16" + }, + { + "bbox": [ + 46, + 396, + 286, + 624 + ], + "type": "text", + "content": " patches to obtain the local background " + }, + { + "bbox": [ + 46, + 396, + 286, + 624 + ], + "type": "inline_equation", + "content": "\\overline{B}" + }, + { + "bbox": [ + 46, + 396, + 286, + 624 + ], + "type": "text", + "content": ". For each patch, we use the Gaussian Mixture Model (GMM) to cluster it into two clusters according to the pixel intensity of the image [2], corresponding to text content and background, respectively. With the observation that the background color of the document is usually brighter [2, 24], we consider the cluster with a higher intensity as the background cluster and apply the average color of the background cluster as the background of the patch. Since different patches have different background colors, the local background " + }, + { + "bbox": [ + 46, + 396, + 286, + 624 + ], + "type": "inline_equation", + "content": "\\overline{B}" + }, + { + "bbox": [ + 46, + 396, + 286, + 624 + ], + "type": "text", + "content": " usually has obvious patch boundaries, as shown in Figure 5(b). Thus, inspired by the guided filter for edge-preserving image smoothing [14], we employ a color-preserving smoothing operator to refine " + }, + { + "bbox": [ + 46, + 396, + 286, + 624 + ], + "type": "inline_equation", + "content": "\\overline{B}" + }, + { + "bbox": [ + 46, + 396, + 286, + 624 + ], + "type": "text", + "content": " and get a desired ground-truth background image " + }, + { + "bbox": [ + 46, + 396, + 286, + 624 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 46, + 396, + 286, + 624 + ], + "type": "text", + "content": " for the image, as shown in Figure 5(c)." + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 59, + 624, + 244, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 624, + 244, + 635 + ], + "spans": [ + { + "bbox": [ + 59, + 624, + 244, + 635 + ], + "type": "text", + "content": "The value of pixel " + }, + { + "bbox": [ + 59, + 624, + 244, + 635 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 59, + 624, + 244, + 635 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 59, + 624, + 244, + 635 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 59, + 624, + 244, + 635 + ], + "type": "text", + "content": " can be expressed as:" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 124, + 637, + 287, + 665 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 124, + 637, + 287, + 665 + ], + "spans": [ + { + "bbox": [ + 124, + 637, + 287, + 665 + ], + "type": "interline_equation", + "content": "B _ {i} = \\sum_ {j \\in N (i)} W _ {i j} \\bar {B} _ {j}, \\tag {1}", + "image_path": "19d28b3e6c805de1ed8d7cea92aadb45dc233a5f3c54df79e5d4063f2cab819b.jpg" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "inline_equation", + "content": "N(i)" + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "content": " is a local neighborhood of pixel i. " + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "inline_equation", + "content": "W_{ij}" + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "content": " is the filter kernel, which measures the color similarity between pixel " + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "content": " and pixel " + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "content": ". Due to the original image has the edge information, we use " + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "inline_equation", + "content": "I^{gt}" + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "content": " as the guidance image to calculate" + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 306, + 232, + 421, + 245 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 232, + 421, + 245 + ], + "spans": [ + { + "bbox": [ + 306, + 232, + 421, + 245 + ], + "type": "text", + "content": "the filter kernel " + }, + { + "bbox": [ + 306, + 232, + 421, + 245 + ], + "type": "inline_equation", + "content": "W_{ij}" + }, + { + "bbox": [ + 306, + 232, + 421, + 245 + ], + "type": "text", + "content": ", that is," + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 332, + 249, + 545, + 283 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 332, + 249, + 545, + 283 + ], + "spans": [ + { + "bbox": [ + 332, + 249, + 545, + 283 + ], + "type": "interline_equation", + "content": "W _ {i j} = \\frac {1}{| \\omega | ^ {2}} \\sum_ {i, j} (1 + \\frac {\\left(I _ {i} ^ {g t} - \\mu_ {k}\\right) \\left(I _ {j} ^ {g t} - \\mu_ {k}\\right)}{\\sigma_ {k} ^ {2} + \\epsilon}), \\tag {2}", + "image_path": "086a0d171e45f29732648a9dee59bb459f6256039f14b15c61cb2a7c6c74a3c7.jpg" + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 305, + 288, + 545, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 288, + 545, + 324 + ], + "spans": [ + { + "bbox": [ + 305, + 288, + 545, + 324 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 288, + 545, + 324 + ], + "type": "inline_equation", + "content": "\\mu_{k}" + }, + { + "bbox": [ + 305, + 288, + 545, + 324 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 288, + 545, + 324 + ], + "type": "inline_equation", + "content": "\\sigma_k^2" + }, + { + "bbox": [ + 305, + 288, + 545, + 324 + ], + "type": "text", + "content": " are the mean and variance of " + }, + { + "bbox": [ + 305, + 288, + 545, + 324 + ], + "type": "inline_equation", + "content": "I^{gt}" + }, + { + "bbox": [ + 305, + 288, + 545, + 324 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 305, + 288, + 545, + 324 + ], + "type": "inline_equation", + "content": "N(i)" + }, + { + "bbox": [ + 305, + 288, + 545, + 324 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 288, + 545, + 324 + ], + "type": "inline_equation", + "content": "|\\omega|" + }, + { + "bbox": [ + 305, + 288, + 545, + 324 + ], + "type": "text", + "content": " is the number of pixels in " + }, + { + "bbox": [ + 305, + 288, + 545, + 324 + ], + "type": "inline_equation", + "content": "N(i)" + }, + { + "bbox": [ + 305, + 288, + 545, + 324 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 288, + 545, + 324 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 305, + 288, + 545, + 324 + ], + "type": "text", + "content": " is a regularization parameter preventing " + }, + { + "bbox": [ + 305, + 288, + 545, + 324 + ], + "type": "inline_equation", + "content": "W_{ij}" + }, + { + "bbox": [ + 305, + 288, + 545, + 324 + ], + "type": "text", + "content": " from being too large." + } + ] + } + ], + "index": 36 + }, + { + "bbox": [ + 305, + 325, + 545, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 325, + 545, + 421 + ], + "spans": [ + { + "bbox": [ + 305, + 325, + 545, + 421 + ], + "type": "text", + "content": "We adopt the U-Net structure to implement our CBENet. The U-Net first applies five Conv+BN+LReLU to extract features from the image. Then, it takes five deconvolutional layers with batch normalization and ReLU activation function to predict the background image. Skip connection is applied between convolutional layers and deconvolutional layers, increasing the number of channels in the network and preserving the context information of the front layer." + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 306, + 430, + 545, + 443 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 430, + 545, + 443 + ], + "spans": [ + { + "bbox": [ + 306, + 430, + 545, + 443 + ], + "type": "text", + "content": "4.2. Background-guided Shadow Removal Network" + } + ] + } + ], + "index": 38 + }, + { + "bbox": [ + 304, + 449, + 545, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 545, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 545, + 640 + ], + "type": "text", + "content": "As aforementioned, the background can provide some useful information to facilitate shadow removal. Thus, we propose a background-guided shadow removal network (BGShadowNet) exploiting the background image as supplementary information. As shown in Figure 2, our BGShadowNet includes two stages. At Stage I, besides an image encoder, a background-constrained decoder is introduced to produce a coarse shadow-removal result. At Stage II, to improve the coarse result and produce the final shadow-free image, a background-based attention module (BAModule) and a detail enhancement module (DEModule) are embedded into an encoder-decoder network. A discriminator is stacked at the end to distinguish whether the produced image is real or not. We choose DenseUnet [32] and Markovian discriminator [17] as our encoder-decoder structure and discriminator." + } + ] + } + ], + "index": 39 + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": "Background-constrained Decoder. To take full advantage of the features from background image, we replace the common decoder with a background-constrained decoder at Stage I. Concretely, features from the background encoder are integrated into the background-constrained decoder at each corresponding level. The integrated features can com" + } + ] + } + ], + "index": 40 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 314, + 757 + ], + "type": "text", + "content": "1821" + } + ] + } + ], + "index": 41 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 67, + 97, + 114 + ], + "blocks": [ + { + "bbox": [ + 50, + 67, + 97, + 114 + ], + "lines": [ + { + "bbox": [ + 50, + 67, + 97, + 114 + ], + "spans": [ + { + "bbox": [ + 50, + 67, + 97, + 114 + ], + "type": "image", + "image_path": "af7ce88daa283bd3d23167ec74c1da8879a3f2a48495aa0a001e80a1ac2dd6ac.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 69, + 116, + 79, + 124 + ], + "lines": [ + { + "bbox": [ + 69, + 116, + 79, + 124 + ], + "spans": [ + { + "bbox": [ + 69, + 116, + 79, + 124 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 97, + 67, + 144, + 114 + ], + "blocks": [ + { + "bbox": [ + 97, + 67, + 144, + 114 + ], + "lines": [ + { + "bbox": [ + 97, + 67, + 144, + 114 + ], + "spans": [ + { + "bbox": [ + 97, + 67, + 144, + 114 + ], + "type": "image", + "image_path": "7287e2fb57b7299c2927703edecb9a38cbda134b506d37768325227a4fd92b32.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 116, + 116, + 126, + 124 + ], + "lines": [ + { + "bbox": [ + 116, + 116, + 126, + 124 + ], + "spans": [ + { + "bbox": [ + 116, + 116, + 126, + 124 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 145, + 67, + 191, + 114 + ], + "blocks": [ + { + "bbox": [ + 145, + 67, + 191, + 114 + ], + "lines": [ + { + "bbox": [ + 145, + 67, + 191, + 114 + ], + "spans": [ + { + "bbox": [ + 145, + 67, + 191, + 114 + ], + "type": "image", + "image_path": "ae015b0c0d9ba39f4b84546641a2a7e0c71e1ecdde02a35f8853c517766da693.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 163, + 116, + 173, + 125 + ], + "lines": [ + { + "bbox": [ + 163, + 116, + 173, + 125 + ], + "spans": [ + { + "bbox": [ + 163, + 116, + 173, + 125 + ], + "type": "text", + "content": "(c)" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 47, + 125, + 287, + 148 + ], + "lines": [ + { + "bbox": [ + 47, + 125, + 287, + 148 + ], + "spans": [ + { + "bbox": [ + 47, + 125, + 287, + 148 + ], + "type": "text", + "content": "Figure 6. Results of stage I and II. (a): Input. (b): Coarse result at stage I. (d): Result at stage II. (c)&(e): close-ups of (b) and (d)." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 192, + 67, + 238, + 114 + ], + "blocks": [ + { + "bbox": [ + 192, + 67, + 238, + 114 + ], + "lines": [ + { + "bbox": [ + 192, + 67, + 238, + 114 + ], + "spans": [ + { + "bbox": [ + 192, + 67, + 238, + 114 + ], + "type": "image", + "image_path": "9d9b937716d7170722ffe646ee343bd974855f9188326359fa1b0db636bb845e.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 209, + 116, + 220, + 124 + ], + "lines": [ + { + "bbox": [ + 209, + 116, + 220, + 124 + ], + "spans": [ + { + "bbox": [ + 209, + 116, + 220, + 124 + ], + "type": "text", + "content": "(d)" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 239, + 67, + 285, + 114 + ], + "blocks": [ + { + "bbox": [ + 239, + 67, + 285, + 114 + ], + "lines": [ + { + "bbox": [ + 239, + 67, + 285, + 114 + ], + "spans": [ + { + "bbox": [ + 239, + 67, + 285, + 114 + ], + "type": "image", + "image_path": "795e3bd5e32b11025642bf79bde06ab786766ff1f3eb15a7800e20404ffe24fc.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 256, + 116, + 266, + 124 + ], + "lines": [ + { + "bbox": [ + 256, + 116, + 266, + 124 + ], + "spans": [ + { + "bbox": [ + 256, + 116, + 266, + 124 + ], + "type": "text", + "content": "(e)" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 159, + 287, + 182 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 159, + 287, + 182 + ], + "spans": [ + { + "bbox": [ + 46, + 159, + 287, + 182 + ], + "type": "text", + "content": "plement the image features and help to produce a satisfactory shadow-removal result." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 182, + 287, + 302 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 182, + 287, + 302 + ], + "spans": [ + { + "bbox": [ + 46, + 182, + 287, + 302 + ], + "type": "text", + "content": "Background-based Attention Module. Generally, areas with a similar background should have a similar appearance (color and illumination) in an image. However, there might be illumination or color artifacts in the coarse shadow-removal result (see Figure 6(b)). To preserve the overall consistency of the image, we introduce a background-based attention module (BAModule). Using the learned background features and attention mechanism, the BAModule helps to eliminate the appearance inconsistency in the image (see Figure 6(d))." + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 77, + 306, + 258, + 375 + ], + "blocks": [ + { + "bbox": [ + 77, + 306, + 258, + 375 + ], + "lines": [ + { + "bbox": [ + 77, + 306, + 258, + 375 + ], + "spans": [ + { + "bbox": [ + 77, + 306, + 258, + 375 + ], + "type": "image", + "image_path": "88675993d117bfdcae1c06de3d345e8206edd87090606257685050167afc5fcd.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 376, + 287, + 399 + ], + "lines": [ + { + "bbox": [ + 47, + 376, + 287, + 399 + ], + "spans": [ + { + "bbox": [ + 47, + 376, + 287, + 399 + ], + "type": "text", + "content": "Figure 7. The network of our background-based attention module (BAModule)." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 403, + 287, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 403, + 287, + 569 + ], + "spans": [ + { + "bbox": [ + 46, + 403, + 287, + 569 + ], + "type": "text", + "content": "Figure 7 illustrates the architecture of the proposed BAModule. We first fuse the encoder and background features to obtain the integrated features by channel-wise concatenation. Then, the integrated features are fed into an attention computing unit to generate a color-aware attention map. The attention computing unit consists of a convolutional layer, a Leaky ReLu activation function, batch normalization, and a ResidualBlock Layer. Finally, we fuse the color-aware attention map and the integrated features by element-wise multiplication to reconstruct the features, and then embed these features into the corresponding decoder level. The color-aware attention map can make the network adaptively focus on the regions with a similar background, promoting a consistent appearance in these regions." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 570, + 287, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 287, + 676 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 287, + 676 + ], + "type": "text", + "content": "Detail Enhancement Module. As multiple convolutions and downsampling operators in the network, partial detail information will be lost at high-level layers, resulting in detail-blurred results (see Figure 6(c)). Compared to the high-level features, low-level features in CNN layers usually contain more texture details. Thus, we introduce a detail enhancement module (DEModule) to restore the texture details of the coarse result by utilizing the low-level features of the network." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": "As we know, the statistical texture information of the image reflects the texture intensities to some extent. Therefore, our DEModule is inspired by image histogram equalization," + } + ] + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 334, + 67, + 517, + 243 + ], + "blocks": [ + { + "bbox": [ + 334, + 67, + 517, + 243 + ], + "lines": [ + { + "bbox": [ + 334, + 67, + 517, + 243 + ], + "spans": [ + { + "bbox": [ + 334, + 67, + 517, + 243 + ], + "type": "image", + "image_path": "3462e1758c0e58564de7ffa272fb10f23f2063e7d214b74e8e3ae2ded84f664a.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 246, + 544, + 257 + ], + "lines": [ + { + "bbox": [ + 306, + 246, + 544, + 257 + ], + "spans": [ + { + "bbox": [ + 306, + 246, + 544, + 257 + ], + "type": "text", + "content": "Figure 8. The pipeline of our detail enhancement module (DEM)." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 267, + 545, + 351 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 267, + 545, + 351 + ], + "spans": [ + { + "bbox": [ + 305, + 267, + 545, + 351 + ], + "type": "text", + "content": "consisting of two parts. One is feature counting to obtain the statistical information for low-level features, and the other is feature equalization to enhance texture details. Figure 8 illustrates the pipeline of the proposed DEModule. Specifically, we fuse the features of the first two low-level layers from the encoder to get the concatenated low-level features " + }, + { + "bbox": [ + 305, + 267, + 545, + 351 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 305, + 267, + 545, + 351 + ], + "type": "text", + "content": ", which are fed into DEModule for statistical analysis." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 352, + 545, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 352, + 545, + 434 + ], + "spans": [ + { + "bbox": [ + 305, + 352, + 545, + 434 + ], + "type": "text", + "content": "(1) Feature Counting. The purpose of feature counting is to get the quantization encoding map and statistical feature. We first use two " + }, + { + "bbox": [ + 305, + 352, + 545, + 434 + ], + "type": "inline_equation", + "content": "2 \\times 2" + }, + { + "bbox": [ + 305, + 352, + 545, + 434 + ], + "type": "text", + "content": " convolution layers to produce a feature map " + }, + { + "bbox": [ + 305, + 352, + 545, + 434 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 305, + 352, + 545, + 434 + ], + "type": "text", + "content": " and perform global average pooling to obtain the global averaged features " + }, + { + "bbox": [ + 305, + 352, + 545, + 434 + ], + "type": "inline_equation", + "content": "\\overline{M}" + }, + { + "bbox": [ + 305, + 352, + 545, + 434 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 305, + 352, + 545, + 434 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 305, + 352, + 545, + 434 + ], + "type": "text", + "content": ". Next, we calculate the correlation between " + }, + { + "bbox": [ + 305, + 352, + 545, + 434 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 305, + 352, + 545, + 434 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 352, + 545, + 434 + ], + "type": "inline_equation", + "content": "\\overline{M}" + }, + { + "bbox": [ + 305, + 352, + 545, + 434 + ], + "type": "text", + "content": " by using cosine similarity, denoted as " + }, + { + "bbox": [ + 305, + 352, + 545, + 434 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 305, + 352, + 545, + 434 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 435, + 545, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 435, + 545, + 496 + ], + "spans": [ + { + "bbox": [ + 305, + 435, + 545, + 496 + ], + "type": "text", + "content": "To effectively conduct quantification and statistics, we construct a set of quantization levels " + }, + { + "bbox": [ + 305, + 435, + 545, + 496 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 305, + 435, + 545, + 496 + ], + "type": "text", + "content": ", which divide the range of the minimum and maximum values of " + }, + { + "bbox": [ + 305, + 435, + 545, + 496 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 305, + 435, + 545, + 496 + ], + "type": "text", + "content": " into " + }, + { + "bbox": [ + 305, + 435, + 545, + 496 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 305, + 435, + 545, + 496 + ], + "type": "text", + "content": " equal parts. Then, the correlation matrix " + }, + { + "bbox": [ + 305, + 435, + 545, + 496 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 305, + 435, + 545, + 496 + ], + "type": "text", + "content": " can be quantized to a quantization encoding matrix " + }, + { + "bbox": [ + 305, + 435, + 545, + 496 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 305, + 435, + 545, + 496 + ], + "type": "text", + "content": " by using " + }, + { + "bbox": [ + 305, + 435, + 545, + 496 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 305, + 435, + 545, + 496 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 498, + 545, + 534 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 498, + 545, + 534 + ], + "spans": [ + { + "bbox": [ + 313, + 498, + 545, + 534 + ], + "type": "interline_equation", + "content": "E _ {i, n} = \\left\\{ \\begin{array}{c c} 1 - | L _ {n} - S _ {i} |, & i f - \\frac {0 . 5}{N} \\leq L _ {n} - S _ {i} \\leq \\frac {0 . 5}{N} \\\\ 0, & e l s e \\end{array} , \\right. \\tag {3}", + "image_path": "9e109294e93b54e6a1c4bc2c0c42e807738c8e6b12b8404f01868c825f7e5316.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 305, + 533, + 545, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 533, + 545, + 568 + ], + "spans": [ + { + "bbox": [ + 305, + 533, + 545, + 568 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 533, + 545, + 568 + ], + "type": "inline_equation", + "content": "i \\in [1, HW]" + }, + { + "bbox": [ + 305, + 533, + 545, + 568 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 533, + 545, + 568 + ], + "type": "inline_equation", + "content": "n \\in [1, N]" + }, + { + "bbox": [ + 305, + 533, + 545, + 568 + ], + "type": "text", + "content": ". 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" + }, + { + "bbox": [ + 305, + 533, + 545, + 568 + ], + "type": "inline_equation", + "content": "L_{n}" + }, + { + "bbox": [ + 305, + 533, + 545, + 568 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 305, + 533, + 545, + 568 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 305, + 533, + 545, + 568 + ], + "type": "text", + "content": "th level of " + }, + { + "bbox": [ + 305, + 533, + 545, + 568 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 305, + 533, + 545, + 568 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 533, + 545, + 568 + ], + "type": "inline_equation", + "content": "S_{i}" + }, + { + "bbox": [ + 305, + 533, + 545, + 568 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 305, + 533, + 545, + 568 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 305, + 533, + 545, + 568 + ], + "type": "text", + "content": "th row of " + }, + { + "bbox": [ + 305, + 533, + 545, + 568 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 305, + 533, + 545, + 568 + ], + "type": "text", + "content": ". In our experiments, we set " + }, + { + "bbox": [ + 305, + 533, + 545, + 568 + ], + "type": "inline_equation", + "content": "N = 128" + }, + { + "bbox": [ + 305, + 533, + 545, + 568 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 570, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 689 + ], + "type": "text", + "content": "To avoid eliminating gradient information, we perform a normalization operation for matrix " + }, + { + "bbox": [ + 304, + 570, + 545, + 689 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 304, + 570, + 545, + 689 + ], + "type": "text", + "content": ". We integrate the normalized result and quantization levels " + }, + { + "bbox": [ + 304, + 570, + 545, + 689 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 304, + 570, + 545, + 689 + ], + "type": "text", + "content": " into a quantization counting map " + }, + { + "bbox": [ + 304, + 570, + 545, + 689 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 570, + 545, + 689 + ], + "type": "text", + "content": ", which reflects the relative statistics of the low-level input features. Due to the concatenation operation, the channel number of " + }, + { + "bbox": [ + 304, + 570, + 545, + 689 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 570, + 545, + 689 + ], + "type": "text", + "content": " is 2. Thus, we perform two " + }, + { + "bbox": [ + 304, + 570, + 545, + 689 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 304, + 570, + 545, + 689 + ], + "type": "text", + "content": " convolution operations for " + }, + { + "bbox": [ + 304, + 570, + 545, + 689 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 570, + 545, + 689 + ], + "type": "text", + "content": " to increase the channel number, followed by a concatenation operation with " + }, + { + "bbox": [ + 304, + 570, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\overline{M}" + }, + { + "bbox": [ + 304, + 570, + 545, + 689 + ], + "type": "text", + "content": " to further get absolute statistical information " + }, + { + "bbox": [ + 304, + 570, + 545, + 689 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 304, + 570, + 545, + 689 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 570, + 545, + 689 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 304, + 570, + 545, + 689 + ], + "type": "text", + "content": " denotes the statistical features which play the role of the histogram." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "(2) Feature Equalization. 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Visual comparison among state-of-the-art shadow removal methods: (a) input images, (b) Jung [19], (c) DSC [15], (d) Fu [11], (e) DHAN [6], (f) CANet [5], (g) BEDSR-Net [24], (h) our BGShadowNet, and (i) ground-truth images." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 273, + 286, + 367 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 273, + 286, + 367 + ], + "spans": [ + { + "bbox": [ + 46, + 273, + 286, + 367 + ], + "type": "text", + "content": "structuring a new set of quantization levels. We first perform a " + }, + { + "bbox": [ + 46, + 273, + 286, + 367 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 46, + 273, + 286, + 367 + ], + "type": "text", + "content": " convolution operation for " + }, + { + "bbox": [ + 46, + 273, + 286, + 367 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 46, + 273, + 286, + 367 + ], + "type": "text", + "content": " to get " + }, + { + "bbox": [ + 46, + 273, + 286, + 367 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 273, + 286, + 367 + ], + "type": "text", + "content": ". Inspired by the attention mechanism, we perform matrix multiplication of " + }, + { + "bbox": [ + 46, + 273, + 286, + 367 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 273, + 286, + 367 + ], + "type": "text", + "content": " and its transposed matrix, followed by a softmax operation, to build a learned adjacent matrix " + }, + { + "bbox": [ + 46, + 273, + 286, + 367 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 273, + 286, + 367 + ], + "type": "text", + "content": ". Matrix " + }, + { + "bbox": [ + 46, + 273, + 286, + 367 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 273, + 286, + 367 + ], + "type": "text", + "content": " can be regarded as a similarity coefficient matrix. Then, we can reconstruct the new quantization levels " + }, + { + "bbox": [ + 46, + 273, + 286, + 367 + ], + "type": "inline_equation", + "content": "L'" + }, + { + "bbox": [ + 46, + 273, + 286, + 367 + ], + "type": "text", + "content": " with a matrix multiplication for " + }, + { + "bbox": [ + 46, + 273, + 286, + 367 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 273, + 286, + 367 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 273, + 286, + 367 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 273, + 286, + 367 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 369, + 286, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 369, + 286, + 450 + ], + "spans": [ + { + "bbox": [ + 46, + 369, + 286, + 450 + ], + "type": "text", + "content": "Based on the reconstructed quantization levels " + }, + { + "bbox": [ + 46, + 369, + 286, + 450 + ], + "type": "inline_equation", + "content": "L'" + }, + { + "bbox": [ + 46, + 369, + 286, + 450 + ], + "type": "text", + "content": ", we conduct feature equalization for the original quantization encoding matrix " + }, + { + "bbox": [ + 46, + 369, + 286, + 450 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 46, + 369, + 286, + 450 + ], + "type": "text", + "content": " to enhance the detail features. The enhanced features " + }, + { + "bbox": [ + 46, + 369, + 286, + 450 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 46, + 369, + 286, + 450 + ], + "type": "text", + "content": " can be obtained using a matrix multiplication of quantization levels " + }, + { + "bbox": [ + 46, + 369, + 286, + 450 + ], + "type": "inline_equation", + "content": "L'" + }, + { + "bbox": [ + 46, + 369, + 286, + 450 + ], + "type": "text", + "content": " and matrix " + }, + { + "bbox": [ + 46, + 369, + 286, + 450 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 46, + 369, + 286, + 450 + ], + "type": "text", + "content": ". By using the enhanced texture details, the decoder can easily capture detail information." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 458, + 135, + 468 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 458, + 135, + 468 + ], + "spans": [ + { + "bbox": [ + 47, + 458, + 135, + 468 + ], + "type": "text", + "content": "4.3. 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Visual comparison among state-of-the-art shadow removal methods: (a) input images, (b) Jung [19], (c) DSC [15], (d) DHAN [6], (e) Fu [11], (f) BEDSR-Net [24], (g) CANet [5], (h) BMNet [51], and (i) our BGShadowNet." + } + ] + } + ], + "index": 36, + "angle": 0, + "type": "image_caption" + } + ], + "index": 21 + }, + { + "type": "image", + "bbox": [ + 271, + 175, + 322, + 221 + ], + "blocks": [ + { + "bbox": [ + 271, + 175, + 322, + 221 + ], + "lines": [ + { + "bbox": [ + 271, + 175, + 322, + 221 + ], + "spans": [ + { + "bbox": [ + 271, + 175, + 322, + 221 + ], + "type": "image", + "image_path": "3d984dfeb79c992001fd4957bd45baf94d51376a911efb4c65b16c752f4930d1.jpg" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 292, + 223, + 302, + 232 + ], + "lines": [ + { + "bbox": [ + 292, + 223, + 302, + 232 + ], + "spans": [ + { + "bbox": [ + 292, + 223, + 302, + 232 + ], + "type": "text", + "content": "(e)" + } + ] + } + ], + "index": 31, + "angle": 0, + "type": "image_caption" + } + ], + "index": 22 + }, + { + "type": "image", + "bbox": [ + 323, + 175, + 375, + 221 + ], + "blocks": [ + { + "bbox": [ + 323, + 175, + 375, + 221 + ], + "lines": [ + { + "bbox": [ + 323, + 175, + 375, + 221 + ], + "spans": [ + { + "bbox": [ + 323, + 175, + 375, + 221 + ], + "type": "image", + "image_path": "0f58f1030eb8911dcb6ceaac9067dbe8d90e915dcc4e69e286ed0afc5a57d716.jpg" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 345, + 223, + 354, + 232 + ], + "lines": [ + { + "bbox": [ + 345, + 223, + 354, + 232 + ], + "spans": [ + { + "bbox": [ + 345, + 223, + 354, + 232 + ], + "type": "text", + "content": "(f)" + } + ] + } + ], + "index": 32, + "angle": 0, + "type": "image_caption" + } + ], + "index": 23 + }, + { + "type": "image", + "bbox": [ + 375, + 175, + 426, + 221 + ], + "blocks": [ + { + "bbox": [ + 375, + 175, + 426, + 221 + ], + "lines": [ + { + "bbox": [ + 375, + 175, + 426, + 221 + ], + "spans": [ + { + "bbox": [ + 375, + 175, + 426, + 221 + ], + "type": "image", + "image_path": "8d696028752242cf436632d86d3f5ec0289a4ace6e4232f9bbb1b33c113b50b3.jpg" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 396, + 223, + 406, + 232 + ], + "lines": [ + { + "bbox": [ + 396, + 223, + 406, + 232 + ], + "spans": [ + { + "bbox": [ + 396, + 223, + 406, + 232 + ], + "type": "text", + "content": "(g)" + } + ] + } + ], + "index": 33, + "angle": 0, + "type": "image_caption" + } + ], + "index": 24 + }, + { + "type": "image", + "bbox": [ + 427, + 175, + 477, + 221 + ], + "blocks": [ + { + "bbox": [ + 427, + 175, + 477, + 221 + ], + "lines": [ + { + "bbox": [ + 427, + 175, + 477, + 221 + ], + "spans": [ + { + "bbox": [ + 427, + 175, + 477, + 221 + ], + "type": "image", + "image_path": "ef322d06ee9e4d017d996924347b79a3a38f13b4f9db05ae2e5d8e10f168a69d.jpg" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 447, + 223, + 458, + 232 + ], + "lines": [ + { + "bbox": [ + 447, + 223, + 458, + 232 + ], + "spans": [ + { + "bbox": [ + 447, + 223, + 458, + 232 + ], + "type": "text", + "content": "(h)" + } + ] + } + ], + "index": 34, + "angle": 0, + "type": "image_caption" + } + ], + "index": 25 + }, + { + "type": "image", + "bbox": [ + 479, + 175, + 530, + 221 + ], + "blocks": [ + { + "bbox": [ + 479, + 175, + 530, + 221 + ], + "lines": [ + { + "bbox": [ + 479, + 175, + 530, + 221 + ], + "spans": [ + { + "bbox": [ + 479, + 175, + 530, + 221 + ], + "type": "image", + "image_path": "472926062b03450497642eec3034d7f11600bfe0fe5440e22ac9ee13c4f1ba52.jpg" + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 501, + 223, + 510, + 232 + ], + "lines": [ + { + "bbox": [ + 501, + 223, + 510, + 232 + ], + "spans": [ + { + "bbox": [ + 501, + 223, + 510, + 232 + ], + "type": "text", + "content": "(i)" + } + ] + } + ], + "index": 35, + "angle": 0, + "type": "image_caption" + } + ], + "index": 26 + }, + { + "type": "table", + "bbox": [ + 116, + 280, + 476, + 407 + ], + "blocks": [ + { + "bbox": [ + 46, + 257, + 545, + 278 + ], + "lines": [ + { + "bbox": [ + 46, + 257, + 545, + 278 + ], + "spans": [ + { + "bbox": [ + 46, + 257, + 545, + 278 + ], + "type": "text", + "content": "Table 1. Quantitative comparisons of shadow removal on RDD and Kligler datasets in terms of RMSE, PSNR, and SSIM. All the learning-based methods are trained on RDD dataset. " + }, + { + "bbox": [ + 46, + 257, + 545, + 278 + ], + "type": "inline_equation", + "content": "\\uparrow" + }, + { + "bbox": [ + 46, + 257, + 545, + 278 + ], + "type": "text", + "content": " means the larger the better while " + }, + { + "bbox": [ + 46, + 257, + 545, + 278 + ], + "type": "inline_equation", + "content": "\\downarrow" + }, + { + "bbox": [ + 46, + 257, + 545, + 278 + ], + "type": "text", + "content": " means the smaller the better." + } + ] + } + ], + "index": 37, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 116, + 280, + 476, + 407 + ], + "lines": [ + { + "bbox": [ + 116, + 280, + 476, + 407 + ], + "spans": [ + { + "bbox": [ + 116, + 280, + 476, + 407 + ], + "type": "table", + "html": "
MethodsVenue/YearRDDKligler
RMSE↓PSNR↑SSIM ↑RMSE↓PSNR↑SSIM ↑
ST-CGAN [39]CVPR/20183.14334.3280.9746.82627.4330.931
DSC [15]PAMI/20206.35728.1510.9147.70525.6150.898
DHAN [6]AAAI/20202.46736.3370.9786.61027.7070.937
Fu [11]CVPR/20214.32831.3870.9467.10127.3620.914
CANet [5]ICCV/20215.56128.9510.9187.85525.6250.899
SG-ShadowNet [36]ECCV/20222.97434.7270.9726.82927.1410.920
BMNet [51]CVPR/20229.40924.2890.91516.45919.0310.874
Bako [2]ACCV/201614.64820.7410.8949.05824.7770.895
Jung [19]ACCV/201830.19014.3640.86128.24713.7260.852
BEDSR-Net [24]CVPR/20202.93734.9280.9736.53328.1240.932
BGShadowNetCVPR/20232.21937.5850.9835.37729.1760.948
", + "image_path": "cff00e342ba93e7b73493e577d7df75e3d45a02717e2d58274041e92b72439bf.jpg" + } + ] + } + ], + "index": 38, + "angle": 0, + "type": "table_body" + } + ], + "index": 38 + }, + { + "bbox": [ + 46, + 413, + 286, + 436 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 413, + 286, + 436 + ], + "spans": [ + { + "bbox": [ + 46, + 413, + 286, + 436 + ], + "type": "text", + "content": "and SSIM in the RGB colour space to evaluate the performance of the proposed BGShadowNet." + } + ] + } + ], + "index": 39 + }, + { + "bbox": [ + 46, + 437, + 286, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 437, + 286, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 286, + 581 + ], + "type": "text", + "content": "To verify the effectiveness of our method, we compare our results with various state-of-the-art shadow removal methods including three document image shadow removal methods (Bako [2], Jung [19] and BEDSR-Net [24]) and six natural image shadow removal methods (ST-CGAN [39], DSC [15], DHAN [6], Fu [11], CANet [5], SG-ShadowNet [36] and BMNet [51]). To make fair comparison, we use RDD dataset to train all the learning-based methods on the same hardware. Table 1 concludes the comparison results. From the table, we can observe that, our method achieves the best values for all metrics among all the comparing methods, clearly demonstrating the effectiveness." + } + ] + } + ], + "index": 40 + }, + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "type": "text", + "content": "Figure 9 provides some visual shadow removal results to further demonstrate the superiority of our methods. It can be seen, DSC [15] fails in handling image with heavy shadows (see Figure 9(c)). The robustness of Fu [11] is limited, and their results may contain unremoved shadows, as shown in Figure 9(d). DHAN [6] and CANet [5] have the similar problem to Fu [11]. Ignoring the content characteristics of the documents, Jung [19] leads to obvious color and illumination distortion (see Figure 9(b)). With the constant background, results of BEDSR-Net [24] sometimes exhibit artifacts along the shadow boundaries (see Figure 9(g))." + } + ] + } + ], + "index": 41 + }, + { + "bbox": [ + 305, + 413, + 545, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 413, + 545, + 449 + ], + "spans": [ + { + "bbox": [ + 305, + 413, + 545, + 449 + ], + "type": "text", + "content": "Comparatively, the proposed method effectively recovers illumination in shadow regions without artifacts, as shown in Figure 9(h), which is similar to the ground-truth image." + } + ] + } + ], + "index": 42 + }, + { + "bbox": [ + 304, + 449, + 545, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 545, + 533 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 545, + 533 + ], + "type": "text", + "content": "To further verify the robustness and generalization ability of the proposed method, Figure 10 presents some other shadow removal results for document images, containing some challenging cases, such as heavy shadows and inconsistent illumination in shadow regions. Apparently, results recovered by our method look more natural and have little artifacts." + } + ] + } + ], + "index": 43 + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": "User Study. We conduct an user study to evaluate the visual performance of our method and some state-of-the-art shadow removal methods. We prepare 100 sets of shadow removal images. Each set contains seven shadow removal results of our BGShadowNet, CANet, DSC, DHAN, Fu, BEDSR-Net, and Jung, respectively. We randomly select 100 volunteers. For each volunteer, we randomly provide them twenty image sets. The volunteers are required to select the best shadow-free image for each set. Counting all the results, we find that " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "20.32\\%" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": " of shadow-removal images generated by our BGShadowNet are chosen as the best shadow-free images, while " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "11.92\\%" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "11.67\\%" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "16.72\\%" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "13.25\\%" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "15.91\\%" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "10.21\\%" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": " of shadow removal results are chosen by CANet, DSC, DHAN, Fu, BEDSR-Net, and Jung, respectively." + } + ] + } + ], + "index": 44 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "type": "text", + "content": "1824" + } + ] + } + ], + "index": 45 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 65, + 69, + 530, + 195 + ], + "blocks": [ + { + "bbox": [ + 65, + 69, + 530, + 195 + ], + "lines": [ + { + "bbox": [ + 65, + 69, + 530, + 195 + ], + "spans": [ + { + "bbox": [ + 65, + 69, + 530, + 195 + ], + "type": "image", + "image_path": "f4eff1a228cddea5eec519b29bf572f51e5948a9c1589c85d621922087f64668.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 196, + 545, + 217 + ], + "lines": [ + { + "bbox": [ + 46, + 196, + 545, + 217 + ], + "spans": [ + { + "bbox": [ + 46, + 196, + 545, + 217 + ], + "type": "text", + "content": "Figure 11. Visual comparison for ablation study: (a) input images, (b) BASE" + }, + { + "bbox": [ + 46, + 196, + 545, + 217 + ], + "type": "inline_equation", + "content": "_1" + }, + { + "bbox": [ + 46, + 196, + 545, + 217 + ], + "type": "text", + "content": ", (c) BASE" + }, + { + "bbox": [ + 46, + 196, + 545, + 217 + ], + "type": "inline_equation", + "content": "_2" + }, + { + "bbox": [ + 46, + 196, + 545, + 217 + ], + "type": "text", + "content": ", (d) BGShadowNet" + }, + { + "bbox": [ + 46, + 196, + 545, + 217 + ], + "type": "inline_equation", + "content": "_1" + }, + { + "bbox": [ + 46, + 196, + 545, + 217 + ], + "type": "text", + "content": ", (e) BGShadowNet" + }, + { + "bbox": [ + 46, + 196, + 545, + 217 + ], + "type": "inline_equation", + "content": "_2" + }, + { + "bbox": [ + 46, + 196, + 545, + 217 + ], + "type": "text", + "content": ", (f) BGShadowNet" + }, + { + "bbox": [ + 46, + 196, + 545, + 217 + ], + "type": "inline_equation", + "content": "_3" + }, + { + "bbox": [ + 46, + 196, + 545, + 217 + ], + "type": "text", + "content": ", (g) BGShadowNet" + }, + { + "bbox": [ + 46, + 196, + 545, + 217 + ], + "type": "inline_equation", + "content": "_4" + }, + { + "bbox": [ + 46, + 196, + 545, + 217 + ], + "type": "text", + "content": ", and (h) our BGShadowNet." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 148, + 233, + 444, + 322 + ], + "blocks": [ + { + "bbox": [ + 116, + 221, + 476, + 232 + ], + "lines": [ + { + "bbox": [ + 116, + 221, + 476, + 232 + ], + "spans": [ + { + "bbox": [ + 116, + 221, + 476, + 232 + ], + "type": "text", + "content": "Table 2. Quantitative results of ablation study on RDD and Kligler using RMSE, PSNR, and SSIM." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 148, + 233, + 444, + 322 + ], + "lines": [ + { + "bbox": [ + 148, + 233, + 444, + 322 + ], + "spans": [ + { + "bbox": [ + 148, + 233, + 444, + 322 + ], + "type": "table", + "html": "
MethodsRDDKligler
RMSE ↓PSNR ↑SSIM ↑RMSE ↓PSNR ↑SSIM ↑
BASE12.94234.8210.9386.25328.2670.944
BASE22.89735.9760.9455.81128.8950.947
BGShadowNet12.60336.0520.9805.80528.3710.944
BGShadowNet22.58336.1350.9815.73129.0350.947
BGShadowNet32.43336.6810.9825.53829.1800.947
BGShadowNet42.34437.0490.9825.63328.8400.948
BGShadowNet2.21937.5850.9835.37729.1760.948
", + "image_path": "58f0a4be549848f6fe17e520ccd0e6224c0fbaaffef2a6478dbfd44060d17605.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 331, + 140, + 342 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 331, + 140, + 342 + ], + "spans": [ + { + "bbox": [ + 47, + 331, + 140, + 342 + ], + "type": "text", + "content": "5.3. Ablation Study" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 350, + 287, + 398 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 350, + 287, + 398 + ], + "spans": [ + { + "bbox": [ + 47, + 350, + 287, + 398 + ], + "type": "text", + "content": "Ablation of BGShadowNet. To further evaluate the performance of each component applied in our BGShadowNet, we perform ablation experiments using six variants (with or without the specific component) as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 399, + 287, + 481 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 47, + 399, + 162, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 399, + 162, + 410 + ], + "spans": [ + { + "bbox": [ + 47, + 399, + 162, + 410 + ], + "type": "text", + "content": "(1) " + }, + { + "bbox": [ + 47, + 399, + 162, + 410 + ], + "type": "inline_equation", + "content": "BASE_{1}" + }, + { + "bbox": [ + 47, + 399, + 162, + 410 + ], + "type": "text", + "content": ": one DenseUnet;" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 411, + 195, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 411, + 195, + 422 + ], + "spans": [ + { + "bbox": [ + 47, + 411, + 195, + 422 + ], + "type": "text", + "content": "(2) " + }, + { + "bbox": [ + 47, + 411, + 195, + 422 + ], + "type": "inline_equation", + "content": "BASE_2" + }, + { + "bbox": [ + 47, + 411, + 195, + 422 + ], + "type": "text", + "content": ": two stacked DenseUnet;" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 422, + 261, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 422, + 261, + 434 + ], + "spans": [ + { + "bbox": [ + 47, + 422, + 261, + 434 + ], + "type": "text", + "content": "(3) BGShadowNet1: BGShadowNet without StageII;" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 434, + 287, + 457 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 434, + 287, + 457 + ], + "spans": [ + { + "bbox": [ + 47, + 434, + 287, + 457 + ], + "type": "text", + "content": "(4) " + }, + { + "bbox": [ + 47, + 434, + 287, + 457 + ], + "type": "inline_equation", + "content": "BGShadowNet_2" + }, + { + "bbox": [ + 47, + 434, + 287, + 457 + ], + "type": "text", + "content": ": BGShadowNet without DEModule and BAModule;" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 458, + 276, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 458, + 276, + 469 + ], + "spans": [ + { + "bbox": [ + 47, + 458, + 276, + 469 + ], + "type": "text", + "content": "(5) BGShadowNet3: BGShadowNet without BAModule;" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 470, + 275, + 481 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 470, + 275, + 481 + ], + "spans": [ + { + "bbox": [ + 47, + 470, + 275, + 481 + ], + "type": "text", + "content": "(6) BGShadowNet " + }, + { + "bbox": [ + 47, + 470, + 275, + 481 + ], + "type": "inline_equation", + "content": "{}_{4}" + }, + { + "bbox": [ + 47, + 470, + 275, + 481 + ], + "type": "text", + "content": " : BGShadowNet without DEModule." + } + ] + } + ], + "index": 11 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 46, + 484, + 287, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 484, + 287, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 484, + 287, + 567 + ], + "type": "text", + "content": "We train the six variants and evaluate the results on RDD and Kligler's datasets. The results are summarized in Table 2. From the table, we can observe that the components embedded in the two stages can improve the shadow removal results. We also provide qualitative results in Figure 11, which shows that our BGShadowNet with all the components can produce more realistic results." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": "Ablation of Background Image. To verify the effectiveness of the spatially varying background, we rebuild BGShadowNet exploiting the constant background (denoted as " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{BGShadowNet}_b" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": ") estimated by BEDSR-Net [24], and reorganize BEDSR-Net employing our spatially varying background (denoted as " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{BEDSR}_b" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": "). Table 3 summarizes the comparison results. From the results, we can observe that, variant " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{BEDSR}_b" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": " using the spatially varying background can obtain better values than BEDSR-Net. Besides, our BGShadowNet can produce better results than that using the constant background. These results show that our spatially varying background contributes to superior results." + } + ] + } + ], + "index": 14 + }, + { + "type": "table", + "bbox": [ + 334, + 352, + 516, + 403 + ], + "blocks": [ + { + "bbox": [ + 305, + 329, + 545, + 350 + ], + "lines": [ + { + "bbox": [ + 305, + 329, + 545, + 350 + ], + "spans": [ + { + "bbox": [ + 305, + 329, + 545, + 350 + ], + "type": "text", + "content": "Table 3. Quantitative comparisons using different background images on RDD dataset." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 334, + 352, + 516, + 403 + ], + "lines": [ + { + "bbox": [ + 334, + 352, + 516, + 403 + ], + "spans": [ + { + "bbox": [ + 334, + 352, + 516, + 403 + ], + "type": "table", + "html": "
MethodsRMSE ↓PSNR ↑SSIM ↑
BEDSR-Net2.93734.9280.973
BEDSRb2.77135.5550.976
BGShadowNetb2.74035.8210.980
BGShadowNet2.21937.5850.983
", + "image_path": "b89942403616a3bed163efe89aab2336119f56275bd5fb37b66c5024bac2c12f.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "table_body" + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 412, + 545, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 412, + 545, + 472 + ], + "spans": [ + { + "bbox": [ + 305, + 412, + 545, + 472 + ], + "type": "text", + "content": "**Limitation.** Our BGShadowNet can effectively remove shadows in document images. However, when the images are corrupted by heavy noise, our shadow removal results may contain some residual noise, resulting in uneven illumination with the surrounding environment." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 483, + 378, + 495 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 483, + 378, + 495 + ], + "spans": [ + { + "bbox": [ + 306, + 483, + 378, + 495 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 503, + 545, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 503, + 545, + 635 + ], + "spans": [ + { + "bbox": [ + 304, + 503, + 545, + 635 + ], + "type": "text", + "content": "In this paper, we propose a CBENet to estimate a spatially varying background for the shadow image, which can facilitate the proposed BGShadowNet performs document shadow removal. Our BGShadowNet first predicts a coarse shadow-removal result using a background-constrained decoder. Then, we embed a BAModule and a DEModule into the encoder-decoder network to improve the coarse result and produce the final shadow-free result with a consistent appearance and detail-rich texture. Experiments comparing our BGShadowNet to state-of-the-art approaches demonstrate its superiority." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 646, + 403, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 646, + 403, + 658 + ], + "spans": [ + { + "bbox": [ + 306, + 646, + 403, + 658 + ], + "type": "text", + "content": "Acknowledgments" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 665, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 665, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 305, + 665, + 545, + 712 + ], + "type": "text", + "content": "This work is partially supported by NS-FC (No.61902286, No.61972299, No.U1803262, No.61972298) and CAAI-Huawei MindSpore Open Fund." + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1825" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "type": "text", + "content": "[1] E. 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In CVPR, pages 5627-5636, 2022. 7" + } + ] + } + ], + "index": 19 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1827" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Domain Expansion of Image Generators/d894b4ee-e2ae-449a-85b9-1c0622cd67b3_content_list.json b/2023/Domain Expansion of Image Generators/d894b4ee-e2ae-449a-85b9-1c0622cd67b3_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..bca2e5edf457a8b13c40d2fed1a4566cbc6549fc --- /dev/null +++ b/2023/Domain Expansion of Image Generators/d894b4ee-e2ae-449a-85b9-1c0622cd67b3_content_list.json @@ -0,0 +1,1858 @@ +[ + { + "type": "text", + "text": "Domain Expansion of Image Generators", + "text_level": 1, + "bbox": [ + 279, + 128, + 691, + 151 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yotam Nitzan $^{1,2}$", + "bbox": [ + 81, + 176, + 212, + 196 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Michaël Gharbi1", + "bbox": [ + 251, + 179, + 383, + 195 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Richard Zhang", + "bbox": [ + 424, + 179, + 552, + 196 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Taesung Park", + "bbox": [ + 589, + 179, + 707, + 196 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Jun-Yan Zhu3", + "bbox": [ + 746, + 179, + 859, + 196 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Daniel Cohen-Or²", + "bbox": [ + 310, + 203, + 459, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Eli Shechtman", + "bbox": [ + 531, + 203, + 656, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1 Adobe Research", + "bbox": [ + 166, + 237, + 313, + 253 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "2 Tel-Aviv University", + "bbox": [ + 351, + 237, + 522, + 256 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "3 Carnegie Mellon University", + "bbox": [ + 563, + 237, + 797, + 256 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4c53af4eb0676e4c0e686716b59fa3fab17309e493b70cdd098c09b5dc4fc667.jpg", + "image_caption": [ + "Domain Adaptation", + "Figure 1. (center) Traversing the latent space of generative models along some directions changes the image significantly while traversing others has no perceptible effect. We call such directions dormant. (left) Domain adaptation methods, transform the entire generator from a source domain to a target domain. (right) We introduce an approach for a new task - domain expansion. Rather than transforming the generator fully, we expand it to include new data domains. Our method learns to represent the new domain in a disentangled manner by repurposing a single dormant direction." + ], + "image_footnote": [], + "bbox": [ + 86, + 284, + 161, + 412 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a174e3f4135f34d4a5ba225e065949fbd049a393d8c99cd705ebebf99e58405f.jpg", + "image_caption": [ + "Dormant direction" + ], + "image_footnote": [], + "bbox": [ + 161, + 310, + 334, + 412 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/9ca450b64bedf4c309b959f624a01f3671a2e4607130747f3d70096ddf421c81.jpg", + "image_caption": [ + "Dormant direction" + ], + "image_footnote": [], + "bbox": [ + 370, + 282, + 444, + 339 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/da7d71321a9e0a508aa496a76bec194137b919fbfd9ebb95bf7fc2c95caf5ce4.jpg", + "image_caption": [ + "Source Generator" + ], + "image_footnote": [], + "bbox": [ + 372, + 354, + 444, + 410 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d48bb29ce21ec19d2e825c72e5b99d19f29434fdc9eaa96d89a39b1f2fd6837d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 447, + 333, + 593, + 410 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0e7420f437cc98ad3e4be91fb5bd2dd10393543273af7c1ca201b2d475543ac6.jpg", + "image_caption": [ + "Zombie direction" + ], + "image_footnote": [], + "bbox": [ + 656, + 282, + 728, + 339 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/dadb9bae29135c6319af8e5af0418976210611ab0734bbcbe9830b528f90605b.jpg", + "image_caption": [ + "Domain Expansion (Ours)" + ], + "image_footnote": [], + "bbox": [ + 658, + 354, + 728, + 410 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ed56b9d2d67ccd02948e82fbd47c4db7f7b7cfac4e684709fa5cab0dc01e2571.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 730, + 333, + 880, + 410 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 534, + 313, + 549 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Can one inject new concepts into an already trained generative model, while respecting its existing structure and knowledge? We propose a new task - domain expansion - to address this. Given a pretrained generator and novel (but related) domains, we expand the generator to jointly model all domains, old and new, harmoniously. First, we note the generator contains a meaningful, pretrained latent space. Is it possible to minimally perturb this hard-earned representation, while maximally representing the new domains? Interestingly, we find that the latent space offers unused, \"dormant\" directions, which do not affect the output. This provides an opportunity: By \"repurposing\" these directions, we can represent new domains without perturbing the original representation. In fact, we find that pretrained generators have the capacity to add several - even hundreds - of new domains! Using our expansion method, one \"expanded\" model can supersede numerous domain-specific models, without expanding the model size. Additionally, a single expanded generator natively supports smooth transitions between domains, as well as composition of domains.", + "bbox": [ + 75, + 564, + 472, + 857 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Code and project page available here.", + "bbox": [ + 96, + 868, + 349, + 883 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 501, + 534, + 630, + 549 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent domain adaptation techniques piggyback on the tremendous success of modern generative image models [3, 12, 32, 40], by adapting a pretrained generator so it can generate images from a new target domain. Oftentimes, the target domain is defined with respect to the source domain [5, 21, 22], e.g., changing the \"stylization\" from a photorealistic image to a sketch. When such a relationship holds, domain adaptation typically seeks to preserve the factors of variations learned in the source domain, and transfer them to the new one (e.g., making the human depicted in a sketch smile based on the prior from a face generator). With existing techniques, however, the adapted model loses the ability to generate images from the original domain.", + "bbox": [ + 496, + 561, + 890, + 751 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this work, we introduce a novel task — domain expansion. Unlike domain adaptation, we aim to augment the space of images a single model can generate, without overriding its original behavior (see Fig. 1). Rather than viewing similar image domains as disjoint data distributions, we treat them as different modes in a joint distribution. As a result, the domains share a semantic prior inherited from the original data domain. For example, the inherent factors of variation for photorealistic faces, such as pose and face shape, can equally apply to the domain of “zombies”.", + "bbox": [ + 496, + 753, + 890, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "15933", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/132a72b4a2928348d56858381fab15be1bbcfc526b61d677f68d6c20c52a9eb2.jpg", + "image_caption": [ + "Source Domain" + ], + "image_footnote": [], + "bbox": [ + 81, + 132, + 155, + 200 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/055e62ef34af5a041e401c0f577d141567bc5f0b63ac40d32e5223727383853e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 163, + 95, + 380, + 165 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/aba7cd94bb0576d686c3cb528e962b15006a7d053600ab8f657006638d212bac.jpg", + "image_caption": [ + "Happy", + "Expanded Domains", + "Figure 2. Example of a domain expansion result. Starting from dogs as the source domain, we expand a single generator to model new domains such as facial expressions, breeds of dogs and other animals, and artistic styles. Finally, as the representations are disentangled, the expanded generator is able to generalize and compose the different domains, although they were never seen jointly in training." + ], + "image_footnote": [], + "bbox": [ + 163, + 181, + 380, + 239 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/f5314b0fee02e676725a5f3ec7a00a85ecf53c2f55d5a14219a186383b43aaa1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 390, + 90, + 464, + 162 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/c930f459bdd27e2290f874943470ba02eddbd811eb44fc032fe2ea1778912c2e.jpg", + "image_caption": [ + "Boar + Happy + Pop Art", + "Domain Composition" + ], + "image_footnote": [], + "bbox": [ + 388, + 183, + 464, + 239 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To this end, we carefully structure the model training process for expansion, respecting the original data domain. It is well-known that modern generative models with low-dimensional latent spaces offer an intriguing, emergent property – through training, the latent spaces represent the factors of variation, in a linear and interpretable manner [3, 6, 10, 12, 28, 30, 39, 40]. We wish to extend this advantageous behavior and represent the new domains along linear and disentangled directions. Interestingly, it was previously shown that many latent directions have insignificant perceptible effect on generated images [6]. Taking advantage of this finding, we repurpose such directions to represent the new domains.", + "bbox": [ + 75, + 372, + 468, + 561 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In practice, we start from an orthogonal decomposition of the latent space [36] and identify a set of low-magnitude directions that have no perceptible effect on the generated images, which we call dormant. To add a new domain, we select a dormant direction to repurpose. Its orthogonal subspace, which we call base subspace, is sufficient to represent the original domain [6]. We aim to repurpose the dormant direction such that traversing it would now cause a transition between the original and the new domain. Specifically, the transition should be disentangled from the original domain's factors of variation. To this end, we define a repurposed affine subspace by transporting the base subspace along the chosen dormant direction, as shown in Fig. 3. We capture the new domain by applying a domain adaptation method, transformed to operate only on latent codes sampled from the repurposed subspace. A regularization loss is applied on the base subspace to ensure that the original domain is preserved. The original domain's factors of variation are implicitly preserved due to the subspaces being parallel and the latent space being disentangled. For multiple new domains, we simply repeat this procedure across multiple dormant directions.", + "bbox": [ + 75, + 564, + 468, + 883 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We apply our method to the StyleGAN [13] architecture,", + "bbox": [ + 96, + 885, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "with multiple datasets, and expand the generator with hundreds of new factors of variation. Crucially, we show our expanded model simultaneously generates high-quality images from both original and new domains, comparable to specialized, domain-specific generators. Thus, a single expanded generator supersedes hundreds of adapted generators, facilitating the deployment of generative models for real-world applications. We additionally demonstrate that the new domains are learned as global and disentangled factors of variation, alongside existing ones. This enables fine-grained control over the generative process and paves the way to new applications and capabilities, e.g., compositing multiple domains (See Fig. 2). Finally, we conduct a detailed analysis of key aspects of our method, such as the effect of the number of newly introduced domains, thus shedding light on our method and, in the process, on the nature of the latent space of generative models.", + "bbox": [ + 496, + 90, + 890, + 338 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To summarize, our contributions are as follows:", + "bbox": [ + 517, + 340, + 834, + 354 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We introduce a new task - domain expansion of a pretrained generative model.", + "- We propose a novel latent space structure that is amenable to representing new knowledge in a disentangled manner, while maintaining existing knowledge intact.", + "- We present a simple paradigm transforming domain adaptation methods into domain expansion methods.", + "- We demonstrate successful domain expansion to hundreds of new domains and illustrate its advantage over domain adaptation methods." + ], + "bbox": [ + 500, + 356, + 890, + 501 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 518, + 640, + 535 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Fine-tuning generative models. Starting from a generator pretrained on a source domain and training it for a target domain, often called fine-tuning, is a common technique applied for various purposes and settings.", + "bbox": [ + 496, + 537, + 890, + 595 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Some works wish to model only the target domain. In which case, the pretrained model is leveraged simply as an efficient initialization, shortening the training time, and improving image quality [11, 16, 19, 47, 50]. Others, wish to learn the target domain alongside the source domain, in a setting called continuous learning, and propose methods to ensure that the source domain is not forgotten [34, 44]. Although in a single generator, the domains are modeled separately, each as its own class.", + "bbox": [ + 496, + 597, + 890, + 728 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "A prominent line of works have sought to make the target domain inherit knowledge from the source domain [1,2,5, 14,17,21-23,31,33,42,43,51]. This approach allows generalization beyond the target domain per-se and is especially useful when training data is scarce.", + "bbox": [ + 496, + 729, + 890, + 803 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our work similarly involves fine-tuning, but for a novel purpose. Our perspective is that, since the target domain is introduced with knowledge from the source domain – it is in essence, an expansion of it. Therefore, in contrast to the aforementioned works, we aim to model the domains jointly. The proposed method does not replace previous fine-tuning methods, but allows applying them jointly.", + "bbox": [ + 496, + 804, + 890, + 906 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "15934", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Latent directions in generative models. Generative models learn to represent the factors of variation of observed data in their latent space. Disentangled representations are especially useful as they facilitate intuitive control over the generative process. With recent architectures, disentanglement miraculously emerges without intervention [12, 24, 28, 39]. In such models, disentanglement is manifested through the existence of linear latent directions, each ideally controlling a single factor of variation.", + "bbox": [ + 75, + 90, + 468, + 222 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Due to the spontaneous emergence of such directions, many works have been proposed to identify them after the model has been trained [6, 25, 35-37, 41, 45] and used them for downstream applications, most commonly semantic image editing. At the same time, it has also been observed that some latent directions have no perceptible effect on the generated images [6, 46]. These directions, which we call dormant, were not previously leveraged for any purpose.", + "bbox": [ + 75, + 222, + 468, + 339 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this work, we rely on existing methods to factorize the latent space into such linear directions. As we aim to expand the pretrained generator to additional domains, we decide to explicitly encode the \"new knowledge\" along the dormant directions, while keeping other directions intact. This design ensures that the original domain is preserved and that the different domains are represented in a disentangled fashion.", + "bbox": [ + 75, + 339, + 468, + 455 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 465, + 166, + 481 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We start with a pretrained generator $G_{\\mathrm{src}}$ that maps from latent codes $z \\in \\mathcal{Z} \\subseteq \\mathbb{R}^D$ to images in a source domain $\\mathcal{D}_{\\mathrm{src}}$ , and a set of $N$ domain adaptation tasks, each defined by a loss function $\\mathcal{L}_i$ , $i \\in \\{1, \\dots, N\\}$ . In domain adaptation, fine-tuning $G_{\\mathrm{src}}$ to minimize $\\mathcal{L}_i$ yields a generator $G_i$ that generates images from the new domain $\\mathcal{D}_i$ . In contrast, our goal is domain expansion, which aims at training a single expanded generator $G^+$ that can simultaneously model all the new domains $\\cup_{i=1}^{N} \\mathcal{D}_i$ , along with the original domain $\\mathcal{D}_{\\mathrm{src}}$ . We want to ensure that the new domains $\\mathcal{D}_i$ are disentangled from each other and also share the factors of variation from the source domain, which remain intact.", + "bbox": [ + 75, + 491, + 468, + 666 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our solution is to partition the latent space into disjoint subspaces, one for each new domain, and to restrict the effect of each domain adaptation to the corresponding subspace. To this end, we endow the latent space with an explicit structure that supports domain expansion (Sec. 3.1), and optimize each domain adaptation loss only using latents from specific subspace reserved for the new domain (Sec. 3.2). Our decomposition reserves a base subspace for the original domain $\\mathcal{D}_{\\mathrm{src}}$ , on which we impose a regularization objective to maintain the behavior of the source generator (Sec. 3.3). Fig. 3 gives an overview of our domain expansion algorithm.", + "bbox": [ + 75, + 667, + 468, + 840 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Structuring the Latent Space for Expansion", + "text_level": 1, + "bbox": [ + 76, + 848, + 447, + 864 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Modern generative models conveniently learn to represent the factors of variation along linear latent directions,", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/294e767875f6043b04b95bf53b332b9198c7323519c1fca0fdfdbd7099f48e36.jpg", + "image_caption": [ + "Figure 3. Our method transforms a domain adaptation task to a domain expansion task. (a) Generator $G$ is optimized to satisfy the loss $\\mathcal{L}_i$ for every latent code in space. The entire generator and latent space now represent the new domain, indicated with the color blue. (b) Generator $G$ is optimized to satisfy the same loss, $\\mathcal{L}_i$ , only on a subspace $\\mathcal{Z}_i$ , dedicated to the new domain. Simultaneously, $G$ is optimized to satisfy a regularization term $\\mathcal{L}_{\\mathrm{reg}}$ on a parallel subspace, $\\mathcal{Z}_{\\mathrm{base}}$ , ensuring the original knowledge is preserved there. The generator and latent space now represent both domains, indicated by being colored both blue and orange. The latent direction between the two spaces was originally dormant in generator $G$ , and now represents a transition between the domains." + ], + "image_footnote": [], + "bbox": [ + 501, + 89, + 684, + 189 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/10cb86f4adabeabefbb348630568c51213676604393cb6c1dc346bf106ec8d2a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 694, + 89, + 885, + 189 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "in a completely unsupervised manner [12, 26, 28, 39]. We decide to explicitly extend this model by structuring the latent space such that the effect defined by an adaptation task would be represented along a single linear direction. Formally, there should exist some scalar $s$ and latent direction $v_{i}$ , for which images generated from $G^{+}(z), G^{+}(z + sv_{i})$ , relate to each other as the corresponding images from the source and adapted generators $G_{\\mathrm{src}}(z), G_{i}(z)$ do.", + "bbox": [ + 496, + 371, + 890, + 489 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Concretely, following SeFA [36], we obtain a semantic and orthogonal basis $V$ of the latent space from the right singular vectors (produced by SVD) of the very first generator layer, which acts on the latent space $\\mathcal{Z}$ . With a similar factorization technique [6], it was observed that a relatively small subset of the basis vector is sufficient to represent most of the generators $G_{\\mathrm{src}}$ 's variability. Other basis vectors have barely any perceptible effect on the generated images. We find this to be the case with SeFA as well. We refer to vectors with no perceptible effect as dormant.", + "bbox": [ + 496, + 489, + 890, + 633 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As the dormant directions do not affect the model's generation capabilities, they are available to be repurposed with new desired behavior. We thus choose to represent the domains $\\mathcal{D}_{\\mathrm{src}}$ and $\\mathcal{D}_i$ in regions that are separated by only a dormant direction.", + "bbox": [ + 496, + 633, + 890, + 705 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Formally, for each of the $N$ adaptation tasks, we dedicate a single dormant direction, $v_{i}$ , that will be repurposed. The remaining directions $\\{v_{N + 1},\\ldots ,v_D\\}$ will remain intact. We finally define a subspace of $\\mathcal{Z}$ , dubbed the base subspace, as", + "bbox": [ + 496, + 705, + 890, + 780 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {Z} _ {\\text {b a s e}} = \\operatorname {s p a n} \\left(v _ {N + 1}, \\dots , v _ {D}\\right) + \\bar {z} \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 581, + 789, + 890, + 804 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\overline{z}$ is the mean of the distribution over the latents used to train the generator. Then, for each repurposed direction, $v_{i}$ , we define a repurposed subspace $\\mathcal{Z}_i$ that is the base subspace transported along direction $v_{i}$ by a predetermined scalar size $s$ .", + "bbox": [ + 496, + 811, + 890, + 883 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {Z} _ {i} = \\mathcal {Z} _ {\\text {b a s e}} + s v _ {i}. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 633, + 886, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "15935", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The choice of direction $v_{i}$ and scalar $s$ are discussed in Appendices C.2 and C.4.", + "bbox": [ + 75, + 90, + 468, + 119 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our domain expansion training procedure described hereafter will ensure subspace $\\mathcal{Z}_i$ is the only part of the latent space affected by the training objective $\\mathcal{L}_i$ , and is reserved to generate images from domain $\\mathcal{D}_i$ . Intuitively, shifting the base subspace along direction $v_i$ aims to achieve two goals: 1. preserve the factors of variations inherited from $\\mathcal{Z}_{\\mathrm{base}}$ , and 2. restrict the new factor of variation (corresponding to $\\mathcal{D}_i$ ) to a single latent direction, $v_i$ .", + "bbox": [ + 75, + 121, + 470, + 238 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. From Domain Adaptation to Expansion", + "text_level": 1, + "bbox": [ + 76, + 250, + 416, + 266 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Having defined disjoint affine subspaces $\\mathcal{Z}_i$ of the latent space $\\mathcal{Z}$ for our new domains $\\mathcal{D}_i$ , we now describe how we constrain each domain adaptation objective $\\mathcal{L}_i$ to affect only the corresponding subspace.", + "bbox": [ + 75, + 272, + 468, + 330 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The domain adaptation objective is applied to images generated from latent codes $z \\in \\mathcal{Z}$ , sampled from distribution $p(z)$ defined on the entire space $\\mathcal{Z}$ . Commonly the distribution is a Gaussian, or is derived from it [12] but some exceptions exist [21, 43]. Our strategy is to transform this sample distribution into one restricted to the affine subspace $\\mathcal{Z}_i$ . We do so by projecting the samples from $p(z)$ onto $\\mathcal{Z}_i$ , using a standard orthogonal projection operator", + "bbox": [ + 75, + 332, + 468, + 450 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {p r o j} _ {\\mathcal {Z} _ {i}} (z) = \\sum_ {j = N + 1} ^ {D} \\left(v _ {j} ^ {\\top} (z - \\bar {z})\\right) v _ {j} + \\bar {z} + s v _ {i}. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 119, + 462, + 468, + 505 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Denoting by $p_i$ the sampling distribution over $\\mathcal{Z}$ for each of the new domains we seek to adapt, the training loss over all tasks is defined as", + "bbox": [ + 75, + 518, + 468, + 561 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {e x p a n d}} = \\sum_ {i = 1} ^ {N} \\mathbb {E} _ {z \\sim p _ {i} (z)} \\mathcal {L} _ {i} \\left(G \\left(\\operatorname {p r o j} _ {\\mathcal {Z} _ {i}} (z)\\right)\\right). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 129, + 573, + 468, + 614 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Regularization", + "text_level": 1, + "bbox": [ + 76, + 627, + 227, + 643 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Optimizing $\\mathcal{L}_{\\mathrm{expand}}$ lets us learn to generate data from the new domains $\\mathcal{D}_i$ within a single generator, but unfortunately it leaves the base subspace $\\mathcal{Z}_{\\mathrm{base}}$ under-constrained and, therefore, does not guarantee it will remain unaltered during training. In practice, we observe that the effect of $\\mathcal{L}_i$ \"leaks\" outside $\\mathcal{Z}_i$ , causing catastrophic forgetting [18] in subspace $\\mathcal{Z}_{\\mathrm{base}}$ , and undesirably affecting other subspaces $\\mathcal{Z}_j$ . We show an example of this leakage in Fig. 4.", + "bbox": [ + 75, + 651, + 468, + 768 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To prevent this failure mode, we explicitly enforce the preservation of $G_{\\mathrm{src}}$ 's behavior over the base subspace $\\mathcal{Z}_{\\mathrm{base}}$ by regularization. We adopt two successful regularization techniques. First, we keep optimizing the generator with the loss it was originally trained on, $\\mathcal{L}_{\\mathrm{src}}$ , which is known to mitigate forgetting [15]. Second, we apply replay alignment [44], which is a reconstruction loss that compares the output of a frozen copy of the source generator to that produced by our generator. We use a weighted combination of", + "bbox": [ + 75, + 768, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/1c808ecbf299660494cda4f0573c1d23f70ea5c9aa564f685b773829adc50b50.jpg", + "image_caption": [ + "Figure 4. Regularization prevents leakage. Without regularization (top row), new factors of variation \"Sketch\" and \"Funny\" are leaking into the base subspace and the other repurposed subspace. Note, for example, that the image from the base subspace is both a sketch and depicts a smiling dog. Our regularization, described in Eq. (6), solves the issue (bottom row)." + ], + "image_footnote": [], + "bbox": [ + 501, + 88, + 890, + 251 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "an $L_{2}$ pixel loss and LPIPS [49]:", + "bbox": [ + 500, + 352, + 718, + 367 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {r e c o n}} = \\lambda_ {\\text {l p i p s}} \\mathcal {L} _ {\\text {l p i p s}} \\left(G _ {\\text {s r c}} (z), G (z)\\right) + \\lambda_ {L _ {2}} \\| G _ {\\text {s r c}} (z) - G (z) \\| _ {2}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 373, + 906, + 405 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\lambda_{\\mathrm{lpips}} = \\lambda_{L_2} = 10$ are weighting hyperparameters. Not only does replay alignment preserve the source domain $D_{\\mathrm{src}}$ , it also has the added benefit of aligning $G^{+}$ to the source generator $G_{\\mathrm{src}}$ , in the sense that they will produce similar outputs given the same latent code $z$ .", + "bbox": [ + 496, + 412, + 890, + 484 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Crucially, we only regularize the base subspace $\\mathcal{Z}_{\\mathrm{base}}$ , since the subspaces $\\mathcal{Z}_i$ should be allowed to change to learn the new behaviors. To this end, we project the latent codes to the base subspace $\\mathcal{Z}_{\\mathrm{base}}$ , before calculating the regularization terms. Our overall regularization objective is thus:", + "bbox": [ + 496, + 484, + 890, + 559 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {r e g}} = \\mathbb {E} _ {z \\sim p _ {\\text {s r c}} (z)} \\left[ \\lambda_ {\\text {s r c}} \\mathcal {L} _ {\\text {s r c}} \\left(G \\left(\\operatorname {p r o j} _ {\\mathcal {Z} _ {\\text {b a s e}}} (z)\\right)\\right) + \\right. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 542, + 564, + 890, + 590 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left. \\mathcal {L} _ {\\text {r e c o n}} \\left(G \\left(\\operatorname {p r o j} _ {\\mathcal {Z} _ {\\text {b a s e}}} (z)\\right)\\right) \\right],\n$$\n", + "text_format": "latex", + "bbox": [ + 679, + 585, + 844, + 603 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\lambda_{\\mathrm{src}} = 1$ balances the two terms and $p_{src}(z)$ is the latent distribution over $\\mathcal{Z}$ used to train $G_{\\mathrm{src}}$ . Our final, regularized domain expansion objective is, therefore:", + "bbox": [ + 500, + 609, + 890, + 654 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {f u l l}} = \\mathcal {L} _ {\\text {e x p a n d}} + \\mathcal {L} _ {\\text {r e g}}. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 620, + 661, + 890, + 678 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 686, + 632, + 702 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We evaluate our method and analyze its key characteristics. Sec. 4.1 first details the experimental setting, focusing on StyleGAN. We start by analyzing the knowledge encoded along repurposed directions and compare it to domain adaptation methods (Sec. 4.2). We then delve deeper and evaluate the effects (Sec. 4.3) and opportunities (Sec. 4.4) presented by expanding a generator to multiple domains simultaneously. Next, we demonstrate that the quality of the source domain is maintained in the base subspace (Sec. 4.5). Finally, we demonstrate that our method generalizes to other generators (Sec. 4.6).", + "bbox": [ + 496, + 710, + 890, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Further experiments, results, and details are provided in the supplementary.", + "bbox": [ + 498, + 871, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "15936", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Experimental Setting", + "text_level": 1, + "bbox": [ + 76, + 90, + 277, + 107 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We adopt StyleGAN2 [13] as the main generator architecture, for its disentangled latent space and because it has been the dominant test bed for generative domain adaptation methods in recent years [1,5,21,22,43,51].", + "bbox": [ + 75, + 113, + 468, + 172 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Latent space and subspaces. Several latent spaces have been considered in the context of StyleGAN. We use the intermediate latent space $\\mathcal{W}$ in all our experiments but note it as $\\mathcal{Z}$ for consistency. We use SeFA [36] for the orthogonal decomposition of $\\mathcal{Z}$ . As SeFA performs SVD, there is a native indication to how dormant is a given latent direction – the corresponding singular value. As singular values are commonly sorted in decreasing orders, the last basis vectors are most dormant. When expanding with $N$ new domains, unless specified otherwise, we repurpose the last $N$ basis vectors. We use $s = 20$ in all experiments. These decisions are evaluated in greater depth in Appendices C.2 and C.4.", + "bbox": [ + 75, + 185, + 470, + 361 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Adaptation methods. We demonstrate our expansion method with two domain adaptation tasks - StyleGAN-NADA [5] and MyStyle [21]. These two tasks were chosen as they differ significantly in key aspects - source of supervision, sampling distribution and loss.", + "bbox": [ + 75, + 375, + 468, + 446 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "StyleGAN-NADA is a zero-shot, text-guided, domain adaptation method. It takes as input a pair of text prompts, $t_{\\mathrm{source}}$ and $t_{\\mathrm{target}}$ , describing the desired transformation source $\\rightarrow$ target to be applied on the domain of the pretrained generator, $\\mathcal{D}_{\\mathrm{src}}$ . The loss function $\\mathcal{L}$ is given by", + "bbox": [ + 75, + 448, + 468, + 522 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\Delta T = E _ {T} \\left(t _ {\\text {t a r g e t}}\\right) - E _ {T} \\left(t _ {\\text {s o u r c e}}\\right),\n$$\n", + "text_format": "latex", + "bbox": [ + 158, + 532, + 385, + 550 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\Delta I = E _ {I} (G (z)) - E _ {I} \\left(G _ {\\text {s r c}} (z)\\right), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 551, + 468, + 575 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = 1 - \\frac {\\Delta I \\cdot \\Delta T}{| \\Delta I | | \\Delta T |},\n$$\n", + "text_format": "latex", + "bbox": [ + 200, + 570, + 344, + 604 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $E_{I}$ and $E_{T}$ are CLIP's [29] image and text encoders respectively.", + "bbox": [ + 76, + 614, + 468, + 643 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "MyStyle is a few-shot, image-supervised, domain adaptation method. As input, it takes a set of images $\\{x_{m}\\}_{m = 1}^{M}$ of an individual $(M\\sim 100)$ , and adapts $G_{\\mathrm{src}}$ to form a personalized prior for that individual. The generator is trained to better reconstruct $x_{m}$ from their original latent space inversions $z_{m}\\in \\mathcal{Z}$ [38]. Formally, the loss function is given by", + "bbox": [ + 76, + 645, + 468, + 748 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\sum_ {m = 1} ^ {M} \\left[ \\mathcal {L} _ {\\mathrm {l p i p s}} \\left(G \\left(z _ {m}\\right), x _ {m}\\right) + \\| G \\left(z _ {m}\\right) - x _ {m} \\| _ {2} \\right], \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 94, + 760, + 468, + 801 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{\\mathrm{lpips}}$ is again the LPIPS loss [49].", + "bbox": [ + 76, + 813, + 349, + 830 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets and models. We demonstrate our method on four datasets – FFHQ [12], AFHQ Dog [4], LSUN Church [48] and SD-Elephant [20]. The FFHQ model is expanded with 105 new domains, 100 introduced with the expanded", + "bbox": [ + 75, + 840, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/d85f841acc12bdc14200dea4c49e25e5cbd78e83c3bc5fb75aaa6f7ae664b435.jpg", + "image_caption": [ + "Figure 5. Continuous traversal along repurposed directions. As can be seen, the traversal between the base subspace $(\\alpha = 0)$ and repurposed subspace $(\\alpha = s)$ portrays a smooth transition between the source and newly introduced domains. Advantageously, the semantic meaning of the repurposed direction is preserved in the extrapolation, representing the opposite relationship between the domains $(\\alpha < 0)$ or exaggerations of it $(\\alpha > s)$ ." + ], + "image_footnote": [], + "bbox": [ + 501, + 87, + 890, + 247 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/2b0694848647996008daf23dd40abcf6cc61e1f1e7884053dda9e6ccc14be24b.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodUser % (↑)ID (↑)Diversity×10 (↑)
StyleGAN-NADA41.2%-2.42 ± 0.13
Ours w/ NADA58.8%-2.42 ± 0.13
MyStyle-0.80 ± 0.063.08 ± 0.15
Ours w/ MyStyle-0.76 ± 0.053.14 ± 0.14
", + "bbox": [ + 500, + 369, + 905, + 465 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 1. Quantitative comparison of images generated from our repurposed subspaces to those generated by corresponding domain adaptation methods - StyleGAN-NADA [5] and MyStyle [21]. We follow each adaptation method's quantitative evaluation protocol.", + "bbox": [ + 496, + 474, + 892, + 529 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "variant of StyleGAN-NADA and 5 from the expanded variant of MyStyle. The AFHQ Dog, LSUN Chruch and SD-Elephant are expanded with 50, 20, and 20 new domains correspondingly, all introduced from the expanded variant of StyleGAN-NADA.", + "bbox": [ + 496, + 556, + 890, + 630 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Evaluating Domains Individually", + "text_level": 1, + "bbox": [ + 500, + 641, + 790, + 657 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Traversing a repurposed direction. We start by investigating what knowledge, if any, is encoded along the repurposed latent directions. To this end, starting from a random latent code $z \\in \\mathcal{Z}_{\\mathrm{base}}$ , we individually traverse different repurposed directions, $v_{i}$ , and inspect the generated images $G^{+}(z + \\alpha v_{i})$ . Sample results from our dogs, elephants, and faces models are displayed in Fig. 5. We find that each individual repurposed direction now successfully encodes the desired factor of variation, in a global and continuous way.", + "bbox": [ + 496, + 666, + 890, + 797 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our training paradigm is inherently discrete - encouraging the source behavior on the base subspace $(\\alpha = 0)$ and the newly introduced effect on the repurposed space $(\\alpha = s)$ . Therefore, obtaining a smooth effect might seem surprising at first glance. Nevertheless, this phenomenon can be clearly traced to the well-established observation that generators are smooth with respect to their latent space [12].", + "bbox": [ + 496, + 797, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "15937", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/c4720fe2e45e053e88db0aeff3f97a9f60f795ced839a447bf938bf759e76b52.jpg", + "image_caption": [ + "Figure 6. A random set of images generated by our generator from repurposed subspaces (bottom) and by corresponding domain adaptation methods (top). The images are similar and differences are subtle." + ], + "image_footnote": [], + "bbox": [ + 76, + 88, + 472, + 244 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Behavior on the repurposed subspace. We have transformed adaptation tasks into expansion tasks by limiting the training effect to the repurposed subspaces only. But, for latents in repurposed subspaces $(\\alpha = s)$ , the domain adaptation could be considered to have been applied as-is.", + "bbox": [ + 75, + 320, + 468, + 393 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We next directly compare the images generated by our generator from the repurposed subspace to the corresponding images generated by the domain-adapted generator. We inherit and repeat the quantitative evaluation protocols performed by each of the adaption tasks. To compare quality with StyleGAN-NADA [5] we perform a two-alternative forced choice user study. Users were asked to pick the image that has higher-quality and better aligns with the target text used for training. We gathered 1440 responses from 32 unique users. To compare quality with MyStyle [21], we evaluate preservation of identity in generated images, as observed by a face recognition network [9]. For both methods, the diversity is compared based on intra-cluster LPIPS [49] distance, first suggested by Ojha et al. [22]. We use 10 domains for comparison with StyleGAN-NADA and 5 for comparison with MyStyle. Note that we use a single generator $G^{+}$ , expanded with 105 domains, while competing methods use a dedicated model per domain, 15, overall. We report the results in Tab. 1 and Fig. 6.", + "bbox": [ + 75, + 393, + 468, + 671 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As can be seen, on the repurposed subspaces, our method produces comparable images to that generated by the dedicated, domain-adapted generator. Perhaps surprisingly, users somewhat prefer our results over StyleGAN-NADA's. We speculate this is due to the significantly greater difficulty of choosing hyperparameters for their training.", + "bbox": [ + 75, + 672, + 468, + 761 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Effect of Domains on Each Other", + "text_level": 1, + "bbox": [ + 76, + 773, + 369, + 787 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Previous evaluation of individual repurposed directions already indicates disentanglement between different factors of variation. For example, \"Barbie\" images in Fig. 6 show no sign of being caricature, Barack Obama, or any of the other hundred factors of variation introduced to that generator. In this section, we delve deeper into evaluating the effects of expanding with multiple factors of variation.", + "bbox": [ + 75, + 797, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/3fd8760e5a9c24df1207a64948e8060994175e88673d3fe42cc70e0cdb54f16e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 501, + 87, + 890, + 224 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/af8beeadb270f008bb6e53293e5c8a35ad2f9ed04a66fd2d01d303df75f4dddc.jpg", + "image_caption": [ + "Figure 7. Investigating the effect of introducing multiple domains simultaneously. (a) Reports the CLIP error of generated images with the text \"a sketch\", as a function of training iterations. Images are generated from the \"Sketch\" and \"Sumo\" subspaces of models trained with a different number of domains. (b) Depicts generated images from models that have similar CLIP errors. As can be seen, the sketch domain does not \"leak\" into the sumo subspace. Additionally, introducing additional domains delays, but does not prevent, the introduction of sketch." + ], + "image_footnote": [], + "bbox": [ + 501, + 229, + 890, + 315 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To this end, we train three models to expand the FFHQ parent model with either 1, 5 or 50 new domains, all induced by StyleGAN-NADA [5]. All models are expanded with \"Sketch\", and the latter two with \"Sumo\" as well as other factors of variation. We quantify the strength of introduced factor of variation using CLIP error, the 1-complement of the score produced by CLIP [29]. We use the top-performing version of the CLIP encoder available, ViT-L/14, which is not used during training. We note that simply minimizing CLIP error is not the objective, as it might lead to favoring mode-collapsed and adversarial examples [5]. Nevertheless, together with qualitative inspection, it is useful for comparing different models.", + "bbox": [ + 496, + 472, + 892, + 662 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In Fig. 7a, we report the CLIP error of generated images with the text \"a sketch\", as a function of the training iterations. Images are generated from the \"Sketch\", and if exists, \"Sumo\" subspace. First, we observe that CLIP error is decreasing for \"Sketch\" subspaces in all models, as expected. Conversely, CLIP error in the \"Sumo\" subspace does not significantly change, indicating it is not becoming any more or less of a sketch. This result quantitatively supports our previous finding, that factors of variations do not interfere with each other, and demonstrates it is true regardless of the number of other factors of variations learned simultaneously. Additionally, we observe that expanding with additional factors of variation delays, but does not prevent, $G^{+}$ the introduction of \"Sketch\" effectively. The observed delay is expected, as expanding with more variations corresponds to $G^{+}$ optimizing and balancing additional loss functions.", + "bbox": [ + 496, + 666, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "15938", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/fd30c13017487f157b3646735b28d81d6f044895d415591c53df806eea1bb67f.jpg", + "image_caption": [ + "Figure 8. Composing multiple effects by simple latent traversal. In each grid, we start from the latent code that generates the top-left image and traverse along two latent directions, represented by advancement in rows and columns. For each direction, we note the associated domain, its ordinal number in the latent space's basis, and the training method used (\"NADA\" or \"MyStyle\") to learn the domain. As can be seen, $G^{+}$ has learned a disentangled representation, allowing meaningful composition of concepts. Specifically, note the disentanglement between directions, as traversing left-right does not affect the magnitude of the effect corresponding to up-down traversal, and vice versa." + ], + "image_footnote": [], + "bbox": [ + 91, + 88, + 352, + 291 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5fa012a44e98a27b784b56e900cc73407958cbaa77037421ea19b3f35e108584.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 352, + 88, + 614, + 290 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/12896c4e85efcbea1a411672291fe10e255df058128f9fd8f5a6704439e21213.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 617, + 88, + 880, + 290 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Generated samples from the sketch and sumo subspaces are provided in Fig. 7b.", + "bbox": [ + 75, + 388, + 470, + 420 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Compositionality", + "text_level": 1, + "bbox": [ + 76, + 428, + 245, + 444 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "While accidental \"leakage\" between latent directions during training is undesired, intentionally composing variations at test time is useful. For generative models with a disentangled latent space, summing together latent directions aggregates their semantic meaning, and should not affect the magnitude of their effects if applied separately. For example, if direction $v_{1}$ controls head pose and direction $v_{2}$ controls an unrelated variation, images $G(z + v_{1} + v_{2})$ and $G(z + v_{1})$ should depict the same head pose.", + "bbox": [ + 75, + 450, + 468, + 583 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We find that the latent space of the expanded generator $G^{+}$ is disentangled, and variations can indeed be composed effectively. Crucially, variations can be composed with each other regardless of their originating training task, including those on the base subspace, learned from the source domain. Fig. 8 shows a sample of gradual composition results across models and training tasks.", + "bbox": [ + 75, + 583, + 470, + 686 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison to existing techniques. Several domain adaptation methods have proposed techniques to combine multiple variations. These methods still train a separate generative model per variation, but combine their effects in test-time. Specifically, in the realm of CLIP-supervised training, StyleGAN-NADA [5] interpolates the generators' weights, while DiffusionCLIP [14] interpolates intermediate activations of the generators. Next, we compare the disentanglement of composition in our generator to that made possible using these techniques.", + "bbox": [ + 75, + 696, + 468, + 840 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For each method, we start with a setting that was optimized to generate images that align with one of two text prompts. In our case, this setting is $G^{+}$ with latent codes in certain subspaces. For the baselines, these settings are", + "bbox": [ + 75, + 842, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/a28625c2566eafd191c5df033f6f2b451c81104f9bd63eee98f901bf02f276f6.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelFFHQAFHQLSUN ChurchSD Elephant
Parent2.777.433.922.30
Ours2.807.513.762.70
Only Lsrc2.75±0.087.38±0.093.31±0.223.91±0.67
", + "bbox": [ + 500, + 386, + 893, + 479 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. We generate images from the base subspace and report FID [7] $(\\downarrow)$ with respect to source domain dataset. We compare our FID to that of the source generator $G_{\\mathrm{src}}$ . For reference, we also continue training the source generator for the same number of iterations with its original loss - $\\mathcal{L}_{\\mathrm{src}}$ , and report the mean and standard deviations of FID along the training. As can be seen, on the base subspace, our models have comparable FID scores to their parents. Furthermore, similar magnitude of change in FID are observed by simply continuing training, indicating that the change in FID might be, at least in part, due to \"random\" fluctuations.", + "bbox": [ + 496, + 488, + 893, + 625 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "dedicated generators with any latent code. Then, for each method, we gradually introduce the variation described by the other text prompt and generate the corresponding images. Finally, we measure normalized CLIP error between generated images and the two prompts. We normalize all errors by the error of the initial setting, to make the metric comparable across methods and text prompts. Fig. 9 reports the mean and standard deviation of the CLIP error, on 10 pairs of prompts, and provides a sample of qualitative results. As can be seen, both baseline methods directly trade-off one domain for the other, expressed by a linear-looking trend. Conversely, our method obtains significantly lower errors and allows for a true composition of concepts.", + "bbox": [ + 496, + 648, + 893, + 840 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Preservation of the Source Domain", + "text_level": 1, + "bbox": [ + 500, + 848, + 805, + 863 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We next evaluate the preservation of the source domain in $G^{+}$ . To this end, using FID [7], we compare the quality", + "bbox": [ + 498, + 869, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "15939", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2cba78b02d03b4a219dc751dc72c8469a503207f547a8a347e698aa6c116105d.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 86, + 79, + 468, + 277 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8cb69aa8c7aa40d6832967c4ac9405948d1964c2d2f79afacfa34559cb58bb6f.jpg", + "image_caption": [ + "(b)", + "Figure 9. Comparing compositionality in our generator to methods of combining multiple domains proposed by StyleGAN-NADA [5] and DiffusionCLIP [14]. Starting from a setting optimized for either text prompt #1 or #2, we gradually introduce the variation described by the other text. (a) Reports the CLIP error to both prompts along the gradual introduction, normalized to the error obtained for each text prompt in isolation. (b) Portrays a sample of qualitative results, where the composition is such that assigns equal strengths to both effects. As can be seen in, both quantitatively and qualitatively, NADA and DiffusionCLIP directly trade-off one effect for the other - strengthening the effect of one prompt directly lessens that of the other. In contrast, our generator allows true composition of modalities." + ], + "image_footnote": [], + "bbox": [ + 76, + 297, + 468, + 455 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "of images generated from the base subspace $\\mathcal{Z}_{\\mathrm{base}}$ of $G^{+}$ to those generated by the source generator $G_{src}$ . Since the generator is being trained, some change in FID is expected. Therefore, we also report the average and standard deviation over FID scores for a generator that simply continues training, i.e., using only the original loss $\\mathcal{L}_{\\mathrm{src}}$ . Results are reported in Tab. 2 and vary between datasets. Across all datasets, we observe that the FID from our base subspace is within $1\\sigma$ of the that obtained from either the parent or a generator that continues training. For reference, generator's adapted with StyleGAN-NADA and MyStyle have an average FID of 125 and 183, respectively. We conclude that the expansion method might have a slight impact on FID, but it is negligible.", + "bbox": [ + 75, + 695, + 472, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.6. Generalization Beyond StyleGAN", + "text_level": 1, + "bbox": [ + 500, + 90, + 794, + 107 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We finally demonstrate that our expansion method generalizes to other models, beyond StyleGAN. To this end, we experiment with Diffusion Autoencoder (DiffAE) [28]. Despite differences in architecture and training method, DiffAE also has a semantic latent space, marked with $z_{\\mathrm{sem}}$ . We apply our approach over DiffAE and its latent space, using StyleGAN-NADA [5] as the base adaptation method. We find that our expansion methods work as well with DiffAE, and provide a sample of qualitative results in Fig. 10.", + "bbox": [ + 496, + 114, + 893, + 250 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a53fc4b78b4110592716ea7d72a39f20fc4830a77a88841c2f0c203f626d371f.jpg", + "image_caption": [ + "Figure 10. Applying our domain expansion method with Diffusion Autoencoder [28]." + ], + "image_footnote": [], + "bbox": [ + 511, + 276, + 880, + 401 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusions", + "text_level": 1, + "bbox": [ + 500, + 470, + 627, + 486 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We present a new problem - domain expansion - and propose an approach to solve it. The core of our method is to carefully structure the latent space, such that it is amenable to learning additional knowledge, while keeping the existing knowledge intact. Our method takes advantage of the existence of dormant latent directions, and the task itself implicitly relies on the capacity of the model weights to represent more knowledge. If one of these assumptions does not hold, it might not be possible to apply domain expansion. However, the popularity of methods squeezing neural networks, such as Knowledge Distillation [8], and current estimates of the intrinsic dimensionality of image datasets [27], indicate that these assumptions commonly hold. In our experiments, we were able to expand to hundreds of directions. A plausible limitation is that the model can be expanded to a certain point but ultimately limited by factors such as the latent space or network capacity. Overcoming this limitation, perhaps by considering more complex latent space structures, is an avenue for future work.", + "bbox": [ + 496, + 498, + 893, + 776 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgment. This work was done while Yotam Nitzan was an intern at Adobe. This research was supported in part by the Israel Science Foundation (grants no. 2492/20 and 3441/21), Len Blavatnik and the Blavatnik family foundation, and The Tel Aviv University Innovation Laboratories (TILabs).", + "bbox": [ + 496, + 811, + 893, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "15940", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] David Bau, Steven Liu, Tongzhou Wang, Jun-Yan Zhu, and Antonio Torralba. Rewriting a deep generative model. In European conference on computer vision, pages 351-369. Springer, 2020. 2, 5", + "[2] David Bau, Hendrik Strobelt, William Peebles, Jonas Wulff, Bolei Zhou, Jun-Yan Zhu, and Antonio Torralba. 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Mind the gap: Domain gap control for single shot domain adaptation for generative adversarial networks. arXiv preprint arXiv:2110.08398, 2021. 2, 5" + ], + "bbox": [ + 501, + 92, + 890, + 392 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "15942", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Domain Expansion of Image Generators/d894b4ee-e2ae-449a-85b9-1c0622cd67b3_model.json b/2023/Domain Expansion of Image Generators/d894b4ee-e2ae-449a-85b9-1c0622cd67b3_model.json new file mode 100644 index 0000000000000000000000000000000000000000..e0503145562a6f9f4cfaef45af14385a62ac5a71 --- /dev/null +++ b/2023/Domain Expansion of Image Generators/d894b4ee-e2ae-449a-85b9-1c0622cd67b3_model.json @@ -0,0 +1,2563 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.281, + 0.13, + 0.692, + 0.152 + ], + "angle": 0, + "content": "Domain Expansion of Image Generators" + }, + { + "type": "text", + "bbox": [ + 0.082, + 0.178, + 0.213, + 0.197 + ], + "angle": 0, + "content": "Yotam Nitzan\\(^{1,2}\\)" + }, + { + "type": "text", + "bbox": [ + 0.252, + 0.18, + 0.385, + 0.196 + ], + "angle": 0, + "content": "Michaël Gharbi1" + }, + { + "type": "text", + "bbox": [ + 0.426, + 0.18, + 0.553, + 0.198 + ], + "angle": 0, + "content": "Richard Zhang" + }, + { + "type": "text", + "bbox": [ + 0.591, + 0.18, + 0.708, + 0.198 + ], + "angle": 0, + "content": "Taesung Park" + }, + { + "type": "text", + "bbox": [ + 0.748, + 0.18, + 0.86, + 0.197 + ], + "angle": 0, + "content": "Jun-Yan Zhu3" + }, + { + "type": "text", + "bbox": [ + 0.312, + 0.204, + 0.46, + 0.221 + ], + "angle": 0, + "content": "Daniel Cohen-Or²" + }, + { + "type": "text", + "bbox": [ + 0.532, + 0.204, + 0.657, + 0.221 + ], + "angle": 0, + "content": "Eli Shechtman" + }, + { + "type": "text", + "bbox": [ + 0.167, + 0.238, + 0.314, + 0.255 + ], + "angle": 0, + "content": "1 Adobe Research" + }, + { + "type": "text", + "bbox": [ + 0.352, + 0.238, + 0.523, + 0.257 + ], + "angle": 0, + "content": "2 Tel-Aviv University" + }, + { + "type": "text", + "bbox": [ + 0.564, + 0.238, + 0.798, + 0.257 + ], + "angle": 0, + "content": "3 Carnegie Mellon University" + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.285, + 0.162, + 0.414 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.185, + 0.29, + 0.243, + 0.314 + ], + "angle": 0, + "content": "Dormant direction" + }, + { + "type": "image", + "bbox": [ + 0.162, + 0.311, + 0.335, + 0.413 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.133, + 0.422, + 0.286, + 0.439 + ], + "angle": 0, + "content": "Domain Adaptation" + }, + { + "type": "image", + "bbox": [ + 0.371, + 0.283, + 0.445, + 0.34 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.462, + 0.286, + 0.521, + 0.311 + ], + "angle": 0, + "content": "Dormant direction" + }, + { + "type": "image", + "bbox": [ + 0.373, + 0.355, + 0.446, + 0.411 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.448, + 0.334, + 0.594, + 0.411 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.414, + 0.423, + 0.551, + 0.437 + ], + "angle": 0, + "content": "Source Generator" + }, + { + "type": "image", + "bbox": [ + 0.658, + 0.283, + 0.73, + 0.34 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.751, + 0.286, + 0.808, + 0.311 + ], + "angle": 0, + "content": "Zombie direction" + }, + { + "type": "image", + "bbox": [ + 0.659, + 0.355, + 0.73, + 0.411 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.732, + 0.334, + 0.882, + 0.411 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.669, + 0.422, + 0.875, + 0.44 + ], + "angle": 0, + "content": "Domain Expansion (Ours)" + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.454, + 0.894, + 0.522 + ], + "angle": 0, + "content": "Figure 1. (center) Traversing the latent space of generative models along some directions changes the image significantly while traversing others has no perceptible effect. We call such directions dormant. (left) Domain adaptation methods, transform the entire generator from a source domain to a target domain. (right) We introduce an approach for a new task - domain expansion. Rather than transforming the generator fully, we expand it to include new data domains. Our method learns to represent the new domain in a disentangled manner by repurposing a single dormant direction." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.535, + 0.314, + 0.55 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.565, + 0.473, + 0.858 + ], + "angle": 0, + "content": "Can one inject new concepts into an already trained generative model, while respecting its existing structure and knowledge? We propose a new task - domain expansion - to address this. Given a pretrained generator and novel (but related) domains, we expand the generator to jointly model all domains, old and new, harmoniously. First, we note the generator contains a meaningful, pretrained latent space. Is it possible to minimally perturb this hard-earned representation, while maximally representing the new domains? Interestingly, we find that the latent space offers unused, \"dormant\" directions, which do not affect the output. This provides an opportunity: By \"repurposing\" these directions, we can represent new domains without perturbing the original representation. In fact, we find that pretrained generators have the capacity to add several - even hundreds - of new domains! Using our expansion method, one \"expanded\" model can supersede numerous domain-specific models, without expanding the model size. Additionally, a single expanded generator natively supports smooth transitions between domains, as well as composition of domains." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.869, + 0.351, + 0.884 + ], + "angle": 0, + "content": "Code and project page available here." + }, + { + "type": "title", + "bbox": [ + 0.502, + 0.535, + 0.632, + 0.55 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.562, + 0.892, + 0.752 + ], + "angle": 0, + "content": "Recent domain adaptation techniques piggyback on the tremendous success of modern generative image models [3, 12, 32, 40], by adapting a pretrained generator so it can generate images from a new target domain. Oftentimes, the target domain is defined with respect to the source domain [5, 21, 22], e.g., changing the \"stylization\" from a photorealistic image to a sketch. When such a relationship holds, domain adaptation typically seeks to preserve the factors of variations learned in the source domain, and transfer them to the new one (e.g., making the human depicted in a sketch smile based on the prior from a face generator). With existing techniques, however, the adapted model loses the ability to generate images from the original domain." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.755, + 0.892, + 0.903 + ], + "angle": 0, + "content": "In this work, we introduce a novel task — domain expansion. Unlike domain adaptation, we aim to augment the space of images a single model can generate, without overriding its original behavior (see Fig. 1). Rather than viewing similar image domains as disjoint data distributions, we treat them as different modes in a joint distribution. As a result, the domains share a semantic prior inherited from the original data domain. For example, the inherent factors of variation for photorealistic faces, such as pose and face shape, can equally apply to the domain of “zombies”." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15933" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.133, + 0.156, + 0.201 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.202, + 0.15, + 0.209 + ], + "angle": 0, + "content": "Source Domain" + }, + { + "type": "image", + "bbox": [ + 0.164, + 0.097, + 0.382, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.235, + 0.173, + 0.31, + 0.182 + ], + "angle": 0, + "content": "Happy" + }, + { + "type": "image", + "bbox": [ + 0.164, + 0.183, + 0.382, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.237, + 0.241, + 0.311, + 0.249 + ], + "angle": 0, + "content": "Expanded Domains" + }, + { + "type": "image", + "bbox": [ + 0.391, + 0.091, + 0.465, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.396, + 0.166, + 0.458, + 0.183 + ], + "angle": 0, + "content": "Boar + Happy + Pop Art" + }, + { + "type": "image", + "bbox": [ + 0.389, + 0.184, + 0.465, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.387, + 0.241, + 0.468, + 0.249 + ], + "angle": 0, + "content": "Domain Composition" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.261, + 0.47, + 0.356 + ], + "angle": 0, + "content": "Figure 2. Example of a domain expansion result. Starting from dogs as the source domain, we expand a single generator to model new domains such as facial expressions, breeds of dogs and other animals, and artistic styles. Finally, as the representations are disentangled, the expanded generator is able to generalize and compose the different domains, although they were never seen jointly in training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.373, + 0.469, + 0.563 + ], + "angle": 0, + "content": "To this end, we carefully structure the model training process for expansion, respecting the original data domain. It is well-known that modern generative models with low-dimensional latent spaces offer an intriguing, emergent property – through training, the latent spaces represent the factors of variation, in a linear and interpretable manner [3, 6, 10, 12, 28, 30, 39, 40]. We wish to extend this advantageous behavior and represent the new domains along linear and disentangled directions. Interestingly, it was previously shown that many latent directions have insignificant perceptible effect on generated images [6]. Taking advantage of this finding, we repurpose such directions to represent the new domains." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.565, + 0.47, + 0.885 + ], + "angle": 0, + "content": "In practice, we start from an orthogonal decomposition of the latent space [36] and identify a set of low-magnitude directions that have no perceptible effect on the generated images, which we call dormant. To add a new domain, we select a dormant direction to repurpose. Its orthogonal subspace, which we call base subspace, is sufficient to represent the original domain [6]. We aim to repurpose the dormant direction such that traversing it would now cause a transition between the original and the new domain. Specifically, the transition should be disentangled from the original domain's factors of variation. To this end, we define a repurposed affine subspace by transporting the base subspace along the chosen dormant direction, as shown in Fig. 3. We capture the new domain by applying a domain adaptation method, transformed to operate only on latent codes sampled from the repurposed subspace. A regularization loss is applied on the base subspace to ensure that the original domain is preserved. The original domain's factors of variation are implicitly preserved due to the subspaces being parallel and the latent space being disentangled. For multiple new domains, we simply repeat this procedure across multiple dormant directions." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.469, + 0.901 + ], + "angle": 0, + "content": "We apply our method to the StyleGAN [13] architecture," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.339 + ], + "angle": 0, + "content": "with multiple datasets, and expand the generator with hundreds of new factors of variation. Crucially, we show our expanded model simultaneously generates high-quality images from both original and new domains, comparable to specialized, domain-specific generators. Thus, a single expanded generator supersedes hundreds of adapted generators, facilitating the deployment of generative models for real-world applications. We additionally demonstrate that the new domains are learned as global and disentangled factors of variation, alongside existing ones. This enables fine-grained control over the generative process and paves the way to new applications and capabilities, e.g., compositing multiple domains (See Fig. 2). Finally, we conduct a detailed analysis of key aspects of our method, such as the effect of the number of newly introduced domains, thus shedding light on our method and, in the process, on the nature of the latent space of generative models." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.341, + 0.836, + 0.355 + ], + "angle": 0, + "content": "To summarize, our contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.357, + 0.891, + 0.386 + ], + "angle": 0, + "content": "- We introduce a new task - domain expansion of a pretrained generative model." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.386, + 0.891, + 0.43 + ], + "angle": 0, + "content": "- We propose a novel latent space structure that is amenable to representing new knowledge in a disentangled manner, while maintaining existing knowledge intact." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.43, + 0.891, + 0.459 + ], + "angle": 0, + "content": "- We present a simple paradigm transforming domain adaptation methods into domain expansion methods." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.459, + 0.892, + 0.502 + ], + "angle": 0, + "content": "- We demonstrate successful domain expansion to hundreds of new domains and illustrate its advantage over domain adaptation methods." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.357, + 0.892, + 0.502 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.52, + 0.642, + 0.536 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.539, + 0.892, + 0.597 + ], + "angle": 0, + "content": "Fine-tuning generative models. Starting from a generator pretrained on a source domain and training it for a target domain, often called fine-tuning, is a common technique applied for various purposes and settings." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.598, + 0.892, + 0.729 + ], + "angle": 0, + "content": "Some works wish to model only the target domain. In which case, the pretrained model is leveraged simply as an efficient initialization, shortening the training time, and improving image quality [11, 16, 19, 47, 50]. Others, wish to learn the target domain alongside the source domain, in a setting called continuous learning, and propose methods to ensure that the source domain is not forgotten [34, 44]. Although in a single generator, the domains are modeled separately, each as its own class." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.731, + 0.892, + 0.804 + ], + "angle": 0, + "content": "A prominent line of works have sought to make the target domain inherit knowledge from the source domain [1,2,5, 14,17,21-23,31,33,42,43,51]. This approach allows generalization beyond the target domain per-se and is especially useful when training data is scarce." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.805, + 0.892, + 0.907 + ], + "angle": 0, + "content": "Our work similarly involves fine-tuning, but for a novel purpose. Our perspective is that, since the target domain is introduced with knowledge from the source domain – it is in essence, an expansion of it. Therefore, in contrast to the aforementioned works, we aim to model the domains jointly. The proposed method does not replace previous fine-tuning methods, but allows applying them jointly." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "15934" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.223 + ], + "angle": 0, + "content": "Latent directions in generative models. Generative models learn to represent the factors of variation of observed data in their latent space. Disentangled representations are especially useful as they facilitate intuitive control over the generative process. With recent architectures, disentanglement miraculously emerges without intervention [12, 24, 28, 39]. In such models, disentanglement is manifested through the existence of linear latent directions, each ideally controlling a single factor of variation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.223, + 0.469, + 0.34 + ], + "angle": 0, + "content": "Due to the spontaneous emergence of such directions, many works have been proposed to identify them after the model has been trained [6, 25, 35-37, 41, 45] and used them for downstream applications, most commonly semantic image editing. At the same time, it has also been observed that some latent directions have no perceptible effect on the generated images [6, 46]. These directions, which we call dormant, were not previously leveraged for any purpose." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.34, + 0.469, + 0.456 + ], + "angle": 0, + "content": "In this work, we rely on existing methods to factorize the latent space into such linear directions. As we aim to expand the pretrained generator to additional domains, we decide to explicitly encode the \"new knowledge\" along the dormant directions, while keeping other directions intact. This design ensures that the original domain is preserved and that the different domains are represented in a disentangled fashion." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.467, + 0.168, + 0.482 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.492, + 0.469, + 0.667 + ], + "angle": 0, + "content": "We start with a pretrained generator \\( G_{\\mathrm{src}} \\) that maps from latent codes \\( z \\in \\mathcal{Z} \\subseteq \\mathbb{R}^D \\) to images in a source domain \\( \\mathcal{D}_{\\mathrm{src}} \\), and a set of \\( N \\) domain adaptation tasks, each defined by a loss function \\( \\mathcal{L}_i \\), \\( i \\in \\{1, \\dots, N\\} \\). In domain adaptation, fine-tuning \\( G_{\\mathrm{src}} \\) to minimize \\( \\mathcal{L}_i \\) yields a generator \\( G_i \\) that generates images from the new domain \\( \\mathcal{D}_i \\). In contrast, our goal is domain expansion, which aims at training a single expanded generator \\( G^+ \\) that can simultaneously model all the new domains \\( \\cup_{i=1}^{N} \\mathcal{D}_i \\), along with the original domain \\( \\mathcal{D}_{\\mathrm{src}} \\). We want to ensure that the new domains \\( \\mathcal{D}_i \\) are disentangled from each other and also share the factors of variation from the source domain, which remain intact." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.668, + 0.469, + 0.842 + ], + "angle": 0, + "content": "Our solution is to partition the latent space into disjoint subspaces, one for each new domain, and to restrict the effect of each domain adaptation to the corresponding subspace. To this end, we endow the latent space with an explicit structure that supports domain expansion (Sec. 3.1), and optimize each domain adaptation loss only using latents from specific subspace reserved for the new domain (Sec. 3.2). Our decomposition reserves a base subspace for the original domain \\( \\mathcal{D}_{\\mathrm{src}} \\), on which we impose a regularization objective to maintain the behavior of the source generator (Sec. 3.3). Fig. 3 gives an overview of our domain expansion algorithm." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.849, + 0.449, + 0.866 + ], + "angle": 0, + "content": "3.1. Structuring the Latent Space for Expansion" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Modern generative models conveniently learn to represent the factors of variation along linear latent directions," + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.09, + 0.685, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.695, + 0.09, + 0.887, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.202, + 0.892, + 0.363 + ], + "angle": 0, + "content": "Figure 3. Our method transforms a domain adaptation task to a domain expansion task. (a) Generator \\( G \\) is optimized to satisfy the loss \\( \\mathcal{L}_i \\) for every latent code in space. The entire generator and latent space now represent the new domain, indicated with the color blue. (b) Generator \\( G \\) is optimized to satisfy the same loss, \\( \\mathcal{L}_i \\), only on a subspace \\( \\mathcal{Z}_i \\), dedicated to the new domain. Simultaneously, \\( G \\) is optimized to satisfy a regularization term \\( \\mathcal{L}_{\\mathrm{reg}} \\) on a parallel subspace, \\( \\mathcal{Z}_{\\mathrm{base}} \\), ensuring the original knowledge is preserved there. The generator and latent space now represent both domains, indicated by being colored both blue and orange. The latent direction between the two spaces was originally dormant in generator \\( G \\), and now represents a transition between the domains." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.372, + 0.892, + 0.49 + ], + "angle": 0, + "content": "in a completely unsupervised manner [12, 26, 28, 39]. We decide to explicitly extend this model by structuring the latent space such that the effect defined by an adaptation task would be represented along a single linear direction. Formally, there should exist some scalar \\( s \\) and latent direction \\( v_{i} \\), for which images generated from \\( G^{+}(z), G^{+}(z + sv_{i}) \\), relate to each other as the corresponding images from the source and adapted generators \\( G_{\\mathrm{src}}(z), G_{i}(z) \\) do." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.49, + 0.892, + 0.635 + ], + "angle": 0, + "content": "Concretely, following SeFA [36], we obtain a semantic and orthogonal basis \\(V\\) of the latent space from the right singular vectors (produced by SVD) of the very first generator layer, which acts on the latent space \\(\\mathcal{Z}\\). With a similar factorization technique [6], it was observed that a relatively small subset of the basis vector is sufficient to represent most of the generators \\(G_{\\mathrm{src}}\\)'s variability. Other basis vectors have barely any perceptible effect on the generated images. We find this to be the case with SeFA as well. We refer to vectors with no perceptible effect as dormant." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.635, + 0.892, + 0.707 + ], + "angle": 0, + "content": "As the dormant directions do not affect the model's generation capabilities, they are available to be repurposed with new desired behavior. We thus choose to represent the domains \\(\\mathcal{D}_{\\mathrm{src}}\\) and \\(\\mathcal{D}_i\\) in regions that are separated by only a dormant direction." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.707, + 0.892, + 0.781 + ], + "angle": 0, + "content": "Formally, for each of the \\(N\\) adaptation tasks, we dedicate a single dormant direction, \\(v_{i}\\), that will be repurposed. The remaining directions \\(\\{v_{N + 1},\\ldots ,v_D\\}\\) will remain intact. We finally define a subspace of \\(\\mathcal{Z}\\), dubbed the base subspace, as" + }, + { + "type": "equation", + "bbox": [ + 0.583, + 0.79, + 0.891, + 0.805 + ], + "angle": 0, + "content": "\\[\n\\mathcal {Z} _ {\\text {b a s e}} = \\operatorname {s p a n} \\left(v _ {N + 1}, \\dots , v _ {D}\\right) + \\bar {z} \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.813, + 0.892, + 0.884 + ], + "angle": 0, + "content": "where \\(\\overline{z}\\) is the mean of the distribution over the latents used to train the generator. Then, for each repurposed direction, \\(v_{i}\\), we define a repurposed subspace \\(\\mathcal{Z}_i\\) that is the base subspace transported along direction \\(v_{i}\\) by a predetermined scalar size \\(s\\)." + }, + { + "type": "equation", + "bbox": [ + 0.635, + 0.887, + 0.891, + 0.901 + ], + "angle": 0, + "content": "\\[\n\\mathcal {Z} _ {i} = \\mathcal {Z} _ {\\text {b a s e}} + s v _ {i}. \\tag {2}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "15935" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.12 + ], + "angle": 0, + "content": "The choice of direction \\( v_{i} \\) and scalar \\( s \\) are discussed in Appendices C.2 and C.4." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.122, + 0.471, + 0.239 + ], + "angle": 0, + "content": "Our domain expansion training procedure described hereafter will ensure subspace \\(\\mathcal{Z}_i\\) is the only part of the latent space affected by the training objective \\(\\mathcal{L}_i\\), and is reserved to generate images from domain \\(\\mathcal{D}_i\\). Intuitively, shifting the base subspace along direction \\(v_i\\) aims to achieve two goals: 1. preserve the factors of variations inherited from \\(\\mathcal{Z}_{\\mathrm{base}}\\), and 2. restrict the new factor of variation (corresponding to \\(\\mathcal{D}_i\\)) to a single latent direction, \\(v_i\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.25, + 0.418, + 0.267 + ], + "angle": 0, + "content": "3.2. From Domain Adaptation to Expansion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.273, + 0.47, + 0.332 + ], + "angle": 0, + "content": "Having defined disjoint affine subspaces \\(\\mathcal{Z}_i\\) of the latent space \\(\\mathcal{Z}\\) for our new domains \\(\\mathcal{D}_i\\), we now describe how we constrain each domain adaptation objective \\(\\mathcal{L}_i\\) to affect only the corresponding subspace." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.333, + 0.469, + 0.451 + ], + "angle": 0, + "content": "The domain adaptation objective is applied to images generated from latent codes \\( z \\in \\mathcal{Z} \\), sampled from distribution \\( p(z) \\) defined on the entire space \\( \\mathcal{Z} \\). Commonly the distribution is a Gaussian, or is derived from it [12] but some exceptions exist [21, 43]. Our strategy is to transform this sample distribution into one restricted to the affine subspace \\( \\mathcal{Z}_i \\). We do so by projecting the samples from \\( p(z) \\) onto \\( \\mathcal{Z}_i \\), using a standard orthogonal projection operator" + }, + { + "type": "equation", + "bbox": [ + 0.12, + 0.463, + 0.47, + 0.506 + ], + "angle": 0, + "content": "\\[\n\\operatorname {p r o j} _ {\\mathcal {Z} _ {i}} (z) = \\sum_ {j = N + 1} ^ {D} \\left(v _ {j} ^ {\\top} (z - \\bar {z})\\right) v _ {j} + \\bar {z} + s v _ {i}. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.519, + 0.47, + 0.562 + ], + "angle": 0, + "content": "Denoting by \\( p_i \\) the sampling distribution over \\( \\mathcal{Z} \\) for each of the new domains we seek to adapt, the training loss over all tasks is defined as" + }, + { + "type": "equation", + "bbox": [ + 0.13, + 0.574, + 0.47, + 0.615 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {e x p a n d}} = \\sum_ {i = 1} ^ {N} \\mathbb {E} _ {z \\sim p _ {i} (z)} \\mathcal {L} _ {i} \\left(G \\left(\\operatorname {p r o j} _ {\\mathcal {Z} _ {i}} (z)\\right)\\right). \\tag {4}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.628, + 0.228, + 0.644 + ], + "angle": 0, + "content": "3.3. Regularization" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.652, + 0.469, + 0.769 + ], + "angle": 0, + "content": "Optimizing \\(\\mathcal{L}_{\\mathrm{expand}}\\) lets us learn to generate data from the new domains \\(\\mathcal{D}_i\\) within a single generator, but unfortunately it leaves the base subspace \\(\\mathcal{Z}_{\\mathrm{base}}\\) under-constrained and, therefore, does not guarantee it will remain unaltered during training. In practice, we observe that the effect of \\(\\mathcal{L}_i\\) \"leaks\" outside \\(\\mathcal{Z}_i\\), causing catastrophic forgetting [18] in subspace \\(\\mathcal{Z}_{\\mathrm{base}}\\), and undesirably affecting other subspaces \\(\\mathcal{Z}_j\\). We show an example of this leakage in Fig. 4." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.77, + 0.47, + 0.901 + ], + "angle": 0, + "content": "To prevent this failure mode, we explicitly enforce the preservation of \\( G_{\\mathrm{src}} \\)'s behavior over the base subspace \\( \\mathcal{Z}_{\\mathrm{base}} \\) by regularization. We adopt two successful regularization techniques. First, we keep optimizing the generator with the loss it was originally trained on, \\( \\mathcal{L}_{\\mathrm{src}} \\), which is known to mitigate forgetting [15]. Second, we apply replay alignment [44], which is a reconstruction loss that compares the output of a frozen copy of the source generator to that produced by our generator. We use a weighted combination of" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.089, + 0.891, + 0.252 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.263, + 0.893, + 0.344 + ], + "angle": 0, + "content": "Figure 4. Regularization prevents leakage. Without regularization (top row), new factors of variation \"Sketch\" and \"Funny\" are leaking into the base subspace and the other repurposed subspace. Note, for example, that the image from the base subspace is both a sketch and depicts a smiling dog. Our regularization, described in Eq. (6), solves the issue (bottom row)." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.353, + 0.719, + 0.368 + ], + "angle": 0, + "content": "an \\(L_{2}\\) pixel loss and LPIPS [49]:" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.374, + 0.907, + 0.406 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {r e c o n}} = \\lambda_ {\\text {l p i p s}} \\mathcal {L} _ {\\text {l p i p s}} \\left(G _ {\\text {s r c}} (z), G (z)\\right) + \\lambda_ {L _ {2}} \\| G _ {\\text {s r c}} (z) - G (z) \\| _ {2}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.413, + 0.892, + 0.485 + ], + "angle": 0, + "content": "where \\(\\lambda_{\\mathrm{lpips}} = \\lambda_{L_2} = 10\\) are weighting hyperparameters. Not only does replay alignment preserve the source domain \\(D_{\\mathrm{src}}\\), it also has the added benefit of aligning \\(G^{+}\\) to the source generator \\(G_{\\mathrm{src}}\\), in the sense that they will produce similar outputs given the same latent code \\(z\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.486, + 0.892, + 0.56 + ], + "angle": 0, + "content": "Crucially, we only regularize the base subspace \\(\\mathcal{Z}_{\\mathrm{base}}\\), since the subspaces \\(\\mathcal{Z}_i\\) should be allowed to change to learn the new behaviors. To this end, we project the latent codes to the base subspace \\(\\mathcal{Z}_{\\mathrm{base}}\\), before calculating the regularization terms. Our overall regularization objective is thus:" + }, + { + "type": "equation", + "bbox": [ + 0.544, + 0.565, + 0.891, + 0.592 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {r e g}} = \\mathbb {E} _ {z \\sim p _ {\\text {s r c}} (z)} \\left[ \\lambda_ {\\text {s r c}} \\mathcal {L} _ {\\text {s r c}} \\left(G \\left(\\operatorname {p r o j} _ {\\mathcal {Z} _ {\\text {b a s e}}} (z)\\right)\\right) + \\right. \\tag {6}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.681, + 0.587, + 0.846, + 0.604 + ], + "angle": 0, + "content": "\\[\n\\left. \\mathcal {L} _ {\\text {r e c o n}} \\left(G \\left(\\operatorname {p r o j} _ {\\mathcal {Z} _ {\\text {b a s e}}} (z)\\right)\\right) \\right],\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.61, + 0.892, + 0.655 + ], + "angle": 0, + "content": "where \\(\\lambda_{\\mathrm{src}} = 1\\) balances the two terms and \\(p_{src}(z)\\) is the latent distribution over \\(\\mathcal{Z}\\) used to train \\(G_{\\mathrm{src}}\\). Our final, regularized domain expansion objective is, therefore:" + }, + { + "type": "equation", + "bbox": [ + 0.621, + 0.662, + 0.891, + 0.679 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {f u l l}} = \\mathcal {L} _ {\\text {e x p a n d}} + \\mathcal {L} _ {\\text {r e g}}. \\tag {7}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.687, + 0.633, + 0.703 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.711, + 0.892, + 0.871 + ], + "angle": 0, + "content": "We evaluate our method and analyze its key characteristics. Sec. 4.1 first details the experimental setting, focusing on StyleGAN. We start by analyzing the knowledge encoded along repurposed directions and compare it to domain adaptation methods (Sec. 4.2). We then delve deeper and evaluate the effects (Sec. 4.3) and opportunities (Sec. 4.4) presented by expanding a generator to multiple domains simultaneously. Next, we demonstrate that the quality of the source domain is maintained in the base subspace (Sec. 4.5). Finally, we demonstrate that our method generalizes to other generators (Sec. 4.6)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.872, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Further experiments, results, and details are provided in the supplementary." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15936" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.077, + 0.091, + 0.279, + 0.108 + ], + "angle": 0, + "content": "4.1. Experimental Setting" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.114, + 0.47, + 0.174 + ], + "angle": 0, + "content": "We adopt StyleGAN2 [13] as the main generator architecture, for its disentangled latent space and because it has been the dominant test bed for generative domain adaptation methods in recent years [1,5,21,22,43,51]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.186, + 0.471, + 0.362 + ], + "angle": 0, + "content": "Latent space and subspaces. Several latent spaces have been considered in the context of StyleGAN. We use the intermediate latent space \\(\\mathcal{W}\\) in all our experiments but note it as \\(\\mathcal{Z}\\) for consistency. We use SeFA [36] for the orthogonal decomposition of \\(\\mathcal{Z}\\). As SeFA performs SVD, there is a native indication to how dormant is a given latent direction – the corresponding singular value. As singular values are commonly sorted in decreasing orders, the last basis vectors are most dormant. When expanding with \\(N\\) new domains, unless specified otherwise, we repurpose the last \\(N\\) basis vectors. We use \\(s = 20\\) in all experiments. These decisions are evaluated in greater depth in Appendices C.2 and C.4." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.375, + 0.47, + 0.448 + ], + "angle": 0, + "content": "Adaptation methods. We demonstrate our expansion method with two domain adaptation tasks - StyleGAN-NADA [5] and MyStyle [21]. These two tasks were chosen as they differ significantly in key aspects - source of supervision, sampling distribution and loss." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.449, + 0.469, + 0.523 + ], + "angle": 0, + "content": "StyleGAN-NADA is a zero-shot, text-guided, domain adaptation method. It takes as input a pair of text prompts, \\( t_{\\mathrm{source}} \\) and \\( t_{\\mathrm{target}} \\), describing the desired transformation source \\( \\rightarrow \\) target to be applied on the domain of the pretrained generator, \\( \\mathcal{D}_{\\mathrm{src}} \\). The loss function \\( \\mathcal{L} \\) is given by" + }, + { + "type": "equation", + "bbox": [ + 0.16, + 0.534, + 0.386, + 0.551 + ], + "angle": 0, + "content": "\\[\n\\Delta T = E _ {T} \\left(t _ {\\text {t a r g e t}}\\right) - E _ {T} \\left(t _ {\\text {s o u r c e}}\\right),\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.158, + 0.553, + 0.469, + 0.576 + ], + "angle": 0, + "content": "\\[\n\\Delta I = E _ {I} (G (z)) - E _ {I} \\left(G _ {\\text {s r c}} (z)\\right), \\tag {8}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.202, + 0.571, + 0.346, + 0.605 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = 1 - \\frac {\\Delta I \\cdot \\Delta T}{| \\Delta I | | \\Delta T |},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.616, + 0.469, + 0.645 + ], + "angle": 0, + "content": "where \\( E_{I} \\) and \\( E_{T} \\) are CLIP's [29] image and text encoders respectively." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.646, + 0.47, + 0.749 + ], + "angle": 0, + "content": "MyStyle is a few-shot, image-supervised, domain adaptation method. As input, it takes a set of images \\(\\{x_{m}\\}_{m = 1}^{M}\\) of an individual \\((M\\sim 100)\\), and adapts \\(G_{\\mathrm{src}}\\) to form a personalized prior for that individual. The generator is trained to better reconstruct \\(x_{m}\\) from their original latent space inversions \\(z_{m}\\in \\mathcal{Z}\\) [38]. Formally, the loss function is given by" + }, + { + "type": "equation", + "bbox": [ + 0.095, + 0.761, + 0.47, + 0.802 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\sum_ {m = 1} ^ {M} \\left[ \\mathcal {L} _ {\\mathrm {l p i p s}} \\left(G \\left(z _ {m}\\right), x _ {m}\\right) + \\| G \\left(z _ {m}\\right) - x _ {m} \\| _ {2} \\right], \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.814, + 0.351, + 0.831 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{\\mathrm{lpips}}\\) is again the LPIPS loss [49]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.842, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Datasets and models. We demonstrate our method on four datasets – FFHQ [12], AFHQ Dog [4], LSUN Church [48] and SD-Elephant [20]. The FFHQ model is expanded with 105 new domains, 100 introduced with the expanded" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.088, + 0.891, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.26, + 0.894, + 0.355 + ], + "angle": 0, + "content": "Figure 5. Continuous traversal along repurposed directions. As can be seen, the traversal between the base subspace \\((\\alpha = 0)\\) and repurposed subspace \\((\\alpha = s)\\) portrays a smooth transition between the source and newly introduced domains. Advantageously, the semantic meaning of the repurposed direction is preserved in the extrapolation, representing the opposite relationship between the domains \\((\\alpha < 0)\\) or exaggerations of it \\((\\alpha > s)\\)." + }, + { + "type": "table", + "bbox": [ + 0.501, + 0.37, + 0.906, + 0.466 + ], + "angle": 0, + "content": "
MethodUser % (↑)ID (↑)Diversity×10 (↑)
StyleGAN-NADA41.2%-2.42 ± 0.13
Ours w/ NADA58.8%-2.42 ± 0.13
MyStyle-0.80 ± 0.063.08 ± 0.15
Ours w/ MyStyle-0.76 ± 0.053.14 ± 0.14
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.475, + 0.893, + 0.53 + ], + "angle": 0, + "content": "Table 1. Quantitative comparison of images generated from our repurposed subspaces to those generated by corresponding domain adaptation methods - StyleGAN-NADA [5] and MyStyle [21]. We follow each adaptation method's quantitative evaluation protocol." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.557, + 0.892, + 0.631 + ], + "angle": 0, + "content": "variant of StyleGAN-NADA and 5 from the expanded variant of MyStyle. The AFHQ Dog, LSUN Chruch and SD-Elephant are expanded with 50, 20, and 20 new domains correspondingly, all introduced from the expanded variant of StyleGAN-NADA." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.642, + 0.791, + 0.658 + ], + "angle": 0, + "content": "4.2. Evaluating Domains Individually" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.667, + 0.892, + 0.798 + ], + "angle": 0, + "content": "Traversing a repurposed direction. We start by investigating what knowledge, if any, is encoded along the repurposed latent directions. To this end, starting from a random latent code \\( z \\in \\mathcal{Z}_{\\mathrm{base}} \\), we individually traverse different repurposed directions, \\( v_{i} \\), and inspect the generated images \\( G^{+}(z + \\alpha v_{i}) \\). Sample results from our dogs, elephants, and faces models are displayed in Fig. 5. We find that each individual repurposed direction now successfully encodes the desired factor of variation, in a global and continuous way." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.799, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Our training paradigm is inherently discrete - encouraging the source behavior on the base subspace \\((\\alpha = 0)\\) and the newly introduced effect on the repurposed space \\((\\alpha = s)\\). Therefore, obtaining a smooth effect might seem surprising at first glance. Nevertheless, this phenomenon can be clearly traced to the well-established observation that generators are smooth with respect to their latent space [12]." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15937" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.089, + 0.473, + 0.246 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.255, + 0.47, + 0.308 + ], + "angle": 0, + "content": "Figure 6. A random set of images generated by our generator from repurposed subspaces (bottom) and by corresponding domain adaptation methods (top). The images are similar and differences are subtle." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.321, + 0.469, + 0.395 + ], + "angle": 0, + "content": "Behavior on the repurposed subspace. We have transformed adaptation tasks into expansion tasks by limiting the training effect to the repurposed subspaces only. But, for latents in repurposed subspaces \\((\\alpha = s)\\), the domain adaptation could be considered to have been applied as-is." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.395, + 0.47, + 0.672 + ], + "angle": 0, + "content": "We next directly compare the images generated by our generator from the repurposed subspace to the corresponding images generated by the domain-adapted generator. We inherit and repeat the quantitative evaluation protocols performed by each of the adaption tasks. To compare quality with StyleGAN-NADA [5] we perform a two-alternative forced choice user study. Users were asked to pick the image that has higher-quality and better aligns with the target text used for training. We gathered 1440 responses from 32 unique users. To compare quality with MyStyle [21], we evaluate preservation of identity in generated images, as observed by a face recognition network [9]. For both methods, the diversity is compared based on intra-cluster LPIPS [49] distance, first suggested by Ojha et al. [22]. We use 10 domains for comparison with StyleGAN-NADA and 5 for comparison with MyStyle. Note that we use a single generator \\( G^{+} \\), expanded with 105 domains, while competing methods use a dedicated model per domain, 15, overall. We report the results in Tab. 1 and Fig. 6." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.673, + 0.47, + 0.762 + ], + "angle": 0, + "content": "As can be seen, on the repurposed subspaces, our method produces comparable images to that generated by the dedicated, domain-adapted generator. Perhaps surprisingly, users somewhat prefer our results over StyleGAN-NADA's. We speculate this is due to the significantly greater difficulty of choosing hyperparameters for their training." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.774, + 0.37, + 0.789 + ], + "angle": 0, + "content": "4.3. Effect of Domains on Each Other" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.799, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Previous evaluation of individual repurposed directions already indicates disentanglement between different factors of variation. For example, \"Barbie\" images in Fig. 6 show no sign of being caricature, Barack Obama, or any of the other hundred factors of variation introduced to that generator. In this section, we delve deeper into evaluating the effects of expanding with multiple factors of variation." + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.088, + 0.891, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.231, + 0.891, + 0.316 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.327, + 0.892, + 0.448 + ], + "angle": 0, + "content": "Figure 7. Investigating the effect of introducing multiple domains simultaneously. (a) Reports the CLIP error of generated images with the text \"a sketch\", as a function of training iterations. Images are generated from the \"Sketch\" and \"Sumo\" subspaces of models trained with a different number of domains. (b) Depicts generated images from models that have similar CLIP errors. As can be seen, the sketch domain does not \"leak\" into the sumo subspace. Additionally, introducing additional domains delays, but does not prevent, the introduction of sketch." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.473, + 0.893, + 0.664 + ], + "angle": 0, + "content": "To this end, we train three models to expand the FFHQ parent model with either 1, 5 or 50 new domains, all induced by StyleGAN-NADA [5]. All models are expanded with \"Sketch\", and the latter two with \"Sumo\" as well as other factors of variation. We quantify the strength of introduced factor of variation using CLIP error, the 1-complement of the score produced by CLIP [29]. We use the top-performing version of the CLIP encoder available, ViT-L/14, which is not used during training. We note that simply minimizing CLIP error is not the objective, as it might lead to favoring mode-collapsed and adversarial examples [5]. Nevertheless, together with qualitative inspection, it is useful for comparing different models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.667, + 0.894, + 0.901 + ], + "angle": 0, + "content": "In Fig. 7a, we report the CLIP error of generated images with the text \"a sketch\", as a function of the training iterations. Images are generated from the \"Sketch\", and if exists, \"Sumo\" subspace. First, we observe that CLIP error is decreasing for \"Sketch\" subspaces in all models, as expected. Conversely, CLIP error in the \"Sumo\" subspace does not significantly change, indicating it is not becoming any more or less of a sketch. This result quantitatively supports our previous finding, that factors of variations do not interfere with each other, and demonstrates it is true regardless of the number of other factors of variations learned simultaneously. Additionally, we observe that expanding with additional factors of variation delays, but does not prevent, \\( G^{+} \\) the introduction of \"Sketch\" effectively. The observed delay is expected, as expanding with more variations corresponds to \\( G^{+} \\) optimizing and balancing additional loss functions." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15938" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.092, + 0.089, + 0.353, + 0.292 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.353, + 0.089, + 0.615, + 0.291 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.619, + 0.089, + 0.882, + 0.291 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.303, + 0.895, + 0.373 + ], + "angle": 0, + "content": "Figure 8. Composing multiple effects by simple latent traversal. In each grid, we start from the latent code that generates the top-left image and traverse along two latent directions, represented by advancement in rows and columns. For each direction, we note the associated domain, its ordinal number in the latent space's basis, and the training method used (\"NADA\" or \"MyStyle\") to learn the domain. As can be seen, \\( G^{+} \\) has learned a disentangled representation, allowing meaningful composition of concepts. Specifically, note the disentanglement between directions, as traversing left-right does not affect the magnitude of the effect corresponding to up-down traversal, and vice versa." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.39, + 0.471, + 0.421 + ], + "angle": 0, + "content": "Generated samples from the sketch and sumo subspaces are provided in Fig. 7b." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.429, + 0.246, + 0.445 + ], + "angle": 0, + "content": "4.4. Compositionality" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.452, + 0.47, + 0.584 + ], + "angle": 0, + "content": "While accidental \"leakage\" between latent directions during training is undesired, intentionally composing variations at test time is useful. For generative models with a disentangled latent space, summing together latent directions aggregates their semantic meaning, and should not affect the magnitude of their effects if applied separately. For example, if direction \\( v_{1} \\) controls head pose and direction \\( v_{2} \\) controls an unrelated variation, images \\( G(z + v_{1} + v_{2}) \\) and \\( G(z + v_{1}) \\) should depict the same head pose." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.584, + 0.471, + 0.687 + ], + "angle": 0, + "content": "We find that the latent space of the expanded generator \\( G^{+} \\) is disentangled, and variations can indeed be composed effectively. Crucially, variations can be composed with each other regardless of their originating training task, including those on the base subspace, learned from the source domain. Fig. 8 shows a sample of gradual composition results across models and training tasks." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.697, + 0.47, + 0.842 + ], + "angle": 0, + "content": "Comparison to existing techniques. Several domain adaptation methods have proposed techniques to combine multiple variations. These methods still train a separate generative model per variation, but combine their effects in test-time. Specifically, in the realm of CLIP-supervised training, StyleGAN-NADA [5] interpolates the generators' weights, while DiffusionCLIP [14] interpolates intermediate activations of the generators. Next, we compare the disentanglement of composition in our generator to that made possible using these techniques." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.843, + 0.471, + 0.903 + ], + "angle": 0, + "content": "For each method, we start with a setting that was optimized to generate images that align with one of two text prompts. In our case, this setting is \\( G^{+} \\) with latent codes in certain subspaces. For the baselines, these settings are" + }, + { + "type": "table", + "bbox": [ + 0.501, + 0.387, + 0.895, + 0.48 + ], + "angle": 0, + "content": "
ModelFFHQAFHQLSUN ChurchSD Elephant
Parent2.777.433.922.30
Ours2.807.513.762.70
Only Lsrc2.75±0.087.38±0.093.31±0.223.91±0.67
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.489, + 0.895, + 0.626 + ], + "angle": 0, + "content": "Table 2. We generate images from the base subspace and report FID [7] \\((\\downarrow)\\) with respect to source domain dataset. We compare our FID to that of the source generator \\(G_{\\mathrm{src}}\\). For reference, we also continue training the source generator for the same number of iterations with its original loss - \\(\\mathcal{L}_{\\mathrm{src}}\\), and report the mean and standard deviations of FID along the training. As can be seen, on the base subspace, our models have comparable FID scores to their parents. Furthermore, similar magnitude of change in FID are observed by simply continuing training, indicating that the change in FID might be, at least in part, due to \"random\" fluctuations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.65, + 0.895, + 0.842 + ], + "angle": 0, + "content": "dedicated generators with any latent code. Then, for each method, we gradually introduce the variation described by the other text prompt and generate the corresponding images. Finally, we measure normalized CLIP error between generated images and the two prompts. We normalize all errors by the error of the initial setting, to make the metric comparable across methods and text prompts. Fig. 9 reports the mean and standard deviation of the CLIP error, on 10 pairs of prompts, and provides a sample of qualitative results. As can be seen, both baseline methods directly trade-off one domain for the other, expressed by a linear-looking trend. Conversely, our method obtains significantly lower errors and allows for a true composition of concepts." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.849, + 0.806, + 0.864 + ], + "angle": 0, + "content": "4.5. Preservation of the Source Domain" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.894, + 0.903 + ], + "angle": 0, + "content": "We next evaluate the preservation of the source domain in \\( G^{+} \\). To this end, using FID [7], we compare the quality" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "15939" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.087, + 0.08, + 0.469, + 0.278 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.266, + 0.282, + 0.282, + 0.294 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.078, + 0.298, + 0.47, + 0.457 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.265, + 0.458, + 0.283, + 0.47 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.476, + 0.473, + 0.651 + ], + "angle": 0, + "content": "Figure 9. Comparing compositionality in our generator to methods of combining multiple domains proposed by StyleGAN-NADA [5] and DiffusionCLIP [14]. Starting from a setting optimized for either text prompt #1 or #2, we gradually introduce the variation described by the other text. (a) Reports the CLIP error to both prompts along the gradual introduction, normalized to the error obtained for each text prompt in isolation. (b) Portrays a sample of qualitative results, where the composition is such that assigns equal strengths to both effects. As can be seen in, both quantitatively and qualitatively, NADA and DiffusionCLIP directly trade-off one effect for the other - strengthening the effect of one prompt directly lessens that of the other. In contrast, our generator allows true composition of modalities." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.696, + 0.473, + 0.903 + ], + "angle": 0, + "content": "of images generated from the base subspace \\(\\mathcal{Z}_{\\mathrm{base}}\\) of \\(G^{+}\\) to those generated by the source generator \\(G_{src}\\). Since the generator is being trained, some change in FID is expected. Therefore, we also report the average and standard deviation over FID scores for a generator that simply continues training, i.e., using only the original loss \\(\\mathcal{L}_{\\mathrm{src}}\\). Results are reported in Tab. 2 and vary between datasets. Across all datasets, we observe that the FID from our base subspace is within \\(1\\sigma\\) of the that obtained from either the parent or a generator that continues training. For reference, generator's adapted with StyleGAN-NADA and MyStyle have an average FID of 125 and 183, respectively. We conclude that the expansion method might have a slight impact on FID, but it is negligible." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.795, + 0.108 + ], + "angle": 0, + "content": "4.6. Generalization Beyond StyleGAN" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.116, + 0.895, + 0.25 + ], + "angle": 0, + "content": "We finally demonstrate that our expansion method generalizes to other models, beyond StyleGAN. To this end, we experiment with Diffusion Autoencoder (DiffAE) [28]. Despite differences in architecture and training method, DiffAE also has a semantic latent space, marked with \\( z_{\\mathrm{sem}} \\). We apply our approach over DiffAE and its latent space, using StyleGAN-NADA [5] as the base adaptation method. We find that our expansion methods work as well with DiffAE, and provide a sample of qualitative results in Fig. 10." + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.277, + 0.882, + 0.402 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.413, + 0.893, + 0.441 + ], + "angle": 0, + "content": "Figure 10. Applying our domain expansion method with Diffusion Autoencoder [28]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.472, + 0.628, + 0.487 + ], + "angle": 0, + "content": "5. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.499, + 0.895, + 0.777 + ], + "angle": 0, + "content": "We present a new problem - domain expansion - and propose an approach to solve it. The core of our method is to carefully structure the latent space, such that it is amenable to learning additional knowledge, while keeping the existing knowledge intact. Our method takes advantage of the existence of dormant latent directions, and the task itself implicitly relies on the capacity of the model weights to represent more knowledge. If one of these assumptions does not hold, it might not be possible to apply domain expansion. However, the popularity of methods squeezing neural networks, such as Knowledge Distillation [8], and current estimates of the intrinsic dimensionality of image datasets [27], indicate that these assumptions commonly hold. In our experiments, we were able to expand to hundreds of directions. A plausible limitation is that the model can be expanded to a certain point but ultimately limited by factors such as the latent space or network capacity. Overcoming this limitation, perhaps by considering more complex latent space structures, is an avenue for future work." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.813, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Acknowledgment. This work was done while Yotam Nitzan was an intern at Adobe. This research was supported in part by the Israel Science Foundation (grants no. 2492/20 and 3441/21), Len Blavatnik and the Blavatnik family foundation, and The Tel Aviv University Innovation Laboratories (TILabs)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "15940" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.169 + ], + "angle": 0, + "content": "[1] David Bau, Steven Liu, Tongzhou Wang, Jun-Yan Zhu, and Antonio Torralba. Rewriting a deep generative model. In European conference on computer vision, pages 351-369. 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Mind the gap: Domain gap control for single shot domain adaptation for generative adversarial networks. arXiv preprint arXiv:2110.08398, 2021. 2, 5" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.393 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "15942" + } + ] +] \ No newline at end of file diff --git a/2023/Domain Expansion of Image Generators/d894b4ee-e2ae-449a-85b9-1c0622cd67b3_origin.pdf b/2023/Domain Expansion of Image Generators/d894b4ee-e2ae-449a-85b9-1c0622cd67b3_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..7732a0cc5be474a828d28df1ef81ede053ce6ffc --- /dev/null +++ b/2023/Domain Expansion of Image Generators/d894b4ee-e2ae-449a-85b9-1c0622cd67b3_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:b679105cbb1a70d89926dc626217ca08c1f34310b5b9155812aa81245484d93f +size 8055421 diff --git a/2023/Domain Expansion of Image Generators/full.md b/2023/Domain Expansion of Image Generators/full.md new file mode 100644 index 0000000000000000000000000000000000000000..b569f19382134946873a015ded2e8e2d2c47e8c6 --- /dev/null +++ b/2023/Domain Expansion of Image Generators/full.md @@ -0,0 +1,376 @@ +# Domain Expansion of Image Generators + +Yotam Nitzan $^{1,2}$ + +Michaël Gharbi1 + +Richard Zhang + +Taesung Park + +Jun-Yan Zhu3 + +Daniel Cohen-Or² + +Eli Shechtman + +1 Adobe Research + +2 Tel-Aviv University + +3 Carnegie Mellon University + +![](images/4c53af4eb0676e4c0e686716b59fa3fab17309e493b70cdd098c09b5dc4fc667.jpg) +Domain Adaptation +Figure 1. (center) Traversing the latent space of generative models along some directions changes the image significantly while traversing others has no perceptible effect. We call such directions dormant. (left) Domain adaptation methods, transform the entire generator from a source domain to a target domain. (right) We introduce an approach for a new task - domain expansion. Rather than transforming the generator fully, we expand it to include new data domains. Our method learns to represent the new domain in a disentangled manner by repurposing a single dormant direction. + +![](images/a174e3f4135f34d4a5ba225e065949fbd049a393d8c99cd705ebebf99e58405f.jpg) +Dormant direction + +![](images/9ca450b64bedf4c309b959f624a01f3671a2e4607130747f3d70096ddf421c81.jpg) +Dormant direction + +![](images/da7d71321a9e0a508aa496a76bec194137b919fbfd9ebb95bf7fc2c95caf5ce4.jpg) +Source Generator + +![](images/d48bb29ce21ec19d2e825c72e5b99d19f29434fdc9eaa96d89a39b1f2fd6837d.jpg) + +![](images/0e7420f437cc98ad3e4be91fb5bd2dd10393543273af7c1ca201b2d475543ac6.jpg) +Zombie direction + +![](images/dadb9bae29135c6319af8e5af0418976210611ab0734bbcbe9830b528f90605b.jpg) +Domain Expansion (Ours) + +![](images/ed56b9d2d67ccd02948e82fbd47c4db7f7b7cfac4e684709fa5cab0dc01e2571.jpg) + +# Abstract + +Can one inject new concepts into an already trained generative model, while respecting its existing structure and knowledge? We propose a new task - domain expansion - to address this. Given a pretrained generator and novel (but related) domains, we expand the generator to jointly model all domains, old and new, harmoniously. First, we note the generator contains a meaningful, pretrained latent space. Is it possible to minimally perturb this hard-earned representation, while maximally representing the new domains? Interestingly, we find that the latent space offers unused, "dormant" directions, which do not affect the output. This provides an opportunity: By "repurposing" these directions, we can represent new domains without perturbing the original representation. In fact, we find that pretrained generators have the capacity to add several - even hundreds - of new domains! Using our expansion method, one "expanded" model can supersede numerous domain-specific models, without expanding the model size. Additionally, a single expanded generator natively supports smooth transitions between domains, as well as composition of domains. + +Code and project page available here. + +# 1. Introduction + +Recent domain adaptation techniques piggyback on the tremendous success of modern generative image models [3, 12, 32, 40], by adapting a pretrained generator so it can generate images from a new target domain. Oftentimes, the target domain is defined with respect to the source domain [5, 21, 22], e.g., changing the "stylization" from a photorealistic image to a sketch. When such a relationship holds, domain adaptation typically seeks to preserve the factors of variations learned in the source domain, and transfer them to the new one (e.g., making the human depicted in a sketch smile based on the prior from a face generator). With existing techniques, however, the adapted model loses the ability to generate images from the original domain. + +In this work, we introduce a novel task — domain expansion. Unlike domain adaptation, we aim to augment the space of images a single model can generate, without overriding its original behavior (see Fig. 1). Rather than viewing similar image domains as disjoint data distributions, we treat them as different modes in a joint distribution. As a result, the domains share a semantic prior inherited from the original data domain. For example, the inherent factors of variation for photorealistic faces, such as pose and face shape, can equally apply to the domain of “zombies”. + +![](images/132a72b4a2928348d56858381fab15be1bbcfc526b61d677f68d6c20c52a9eb2.jpg) +Source Domain + +![](images/055e62ef34af5a041e401c0f577d141567bc5f0b63ac40d32e5223727383853e.jpg) + +![](images/aba7cd94bb0576d686c3cb528e962b15006a7d053600ab8f657006638d212bac.jpg) +Happy +Expanded Domains +Figure 2. Example of a domain expansion result. Starting from dogs as the source domain, we expand a single generator to model new domains such as facial expressions, breeds of dogs and other animals, and artistic styles. Finally, as the representations are disentangled, the expanded generator is able to generalize and compose the different domains, although they were never seen jointly in training. + +![](images/f5314b0fee02e676725a5f3ec7a00a85ecf53c2f55d5a14219a186383b43aaa1.jpg) + +![](images/c930f459bdd27e2290f874943470ba02eddbd811eb44fc032fe2ea1778912c2e.jpg) +Boar + Happy + Pop Art +Domain Composition + +To this end, we carefully structure the model training process for expansion, respecting the original data domain. It is well-known that modern generative models with low-dimensional latent spaces offer an intriguing, emergent property – through training, the latent spaces represent the factors of variation, in a linear and interpretable manner [3, 6, 10, 12, 28, 30, 39, 40]. We wish to extend this advantageous behavior and represent the new domains along linear and disentangled directions. Interestingly, it was previously shown that many latent directions have insignificant perceptible effect on generated images [6]. Taking advantage of this finding, we repurpose such directions to represent the new domains. + +In practice, we start from an orthogonal decomposition of the latent space [36] and identify a set of low-magnitude directions that have no perceptible effect on the generated images, which we call dormant. To add a new domain, we select a dormant direction to repurpose. Its orthogonal subspace, which we call base subspace, is sufficient to represent the original domain [6]. We aim to repurpose the dormant direction such that traversing it would now cause a transition between the original and the new domain. Specifically, the transition should be disentangled from the original domain's factors of variation. To this end, we define a repurposed affine subspace by transporting the base subspace along the chosen dormant direction, as shown in Fig. 3. We capture the new domain by applying a domain adaptation method, transformed to operate only on latent codes sampled from the repurposed subspace. A regularization loss is applied on the base subspace to ensure that the original domain is preserved. The original domain's factors of variation are implicitly preserved due to the subspaces being parallel and the latent space being disentangled. For multiple new domains, we simply repeat this procedure across multiple dormant directions. + +We apply our method to the StyleGAN [13] architecture, + +with multiple datasets, and expand the generator with hundreds of new factors of variation. Crucially, we show our expanded model simultaneously generates high-quality images from both original and new domains, comparable to specialized, domain-specific generators. Thus, a single expanded generator supersedes hundreds of adapted generators, facilitating the deployment of generative models for real-world applications. We additionally demonstrate that the new domains are learned as global and disentangled factors of variation, alongside existing ones. This enables fine-grained control over the generative process and paves the way to new applications and capabilities, e.g., compositing multiple domains (See Fig. 2). Finally, we conduct a detailed analysis of key aspects of our method, such as the effect of the number of newly introduced domains, thus shedding light on our method and, in the process, on the nature of the latent space of generative models. + +To summarize, our contributions are as follows: + +- We introduce a new task - domain expansion of a pretrained generative model. +- We propose a novel latent space structure that is amenable to representing new knowledge in a disentangled manner, while maintaining existing knowledge intact. +- We present a simple paradigm transforming domain adaptation methods into domain expansion methods. +- We demonstrate successful domain expansion to hundreds of new domains and illustrate its advantage over domain adaptation methods. + +# 2. Related Work + +Fine-tuning generative models. Starting from a generator pretrained on a source domain and training it for a target domain, often called fine-tuning, is a common technique applied for various purposes and settings. + +Some works wish to model only the target domain. In which case, the pretrained model is leveraged simply as an efficient initialization, shortening the training time, and improving image quality [11, 16, 19, 47, 50]. Others, wish to learn the target domain alongside the source domain, in a setting called continuous learning, and propose methods to ensure that the source domain is not forgotten [34, 44]. Although in a single generator, the domains are modeled separately, each as its own class. + +A prominent line of works have sought to make the target domain inherit knowledge from the source domain [1,2,5, 14,17,21-23,31,33,42,43,51]. This approach allows generalization beyond the target domain per-se and is especially useful when training data is scarce. + +Our work similarly involves fine-tuning, but for a novel purpose. Our perspective is that, since the target domain is introduced with knowledge from the source domain – it is in essence, an expansion of it. Therefore, in contrast to the aforementioned works, we aim to model the domains jointly. The proposed method does not replace previous fine-tuning methods, but allows applying them jointly. + +Latent directions in generative models. Generative models learn to represent the factors of variation of observed data in their latent space. Disentangled representations are especially useful as they facilitate intuitive control over the generative process. With recent architectures, disentanglement miraculously emerges without intervention [12, 24, 28, 39]. In such models, disentanglement is manifested through the existence of linear latent directions, each ideally controlling a single factor of variation. + +Due to the spontaneous emergence of such directions, many works have been proposed to identify them after the model has been trained [6, 25, 35-37, 41, 45] and used them for downstream applications, most commonly semantic image editing. At the same time, it has also been observed that some latent directions have no perceptible effect on the generated images [6, 46]. These directions, which we call dormant, were not previously leveraged for any purpose. + +In this work, we rely on existing methods to factorize the latent space into such linear directions. As we aim to expand the pretrained generator to additional domains, we decide to explicitly encode the "new knowledge" along the dormant directions, while keeping other directions intact. This design ensures that the original domain is preserved and that the different domains are represented in a disentangled fashion. + +# 3. Method + +We start with a pretrained generator $G_{\mathrm{src}}$ that maps from latent codes $z \in \mathcal{Z} \subseteq \mathbb{R}^D$ to images in a source domain $\mathcal{D}_{\mathrm{src}}$ , and a set of $N$ domain adaptation tasks, each defined by a loss function $\mathcal{L}_i$ , $i \in \{1, \dots, N\}$ . In domain adaptation, fine-tuning $G_{\mathrm{src}}$ to minimize $\mathcal{L}_i$ yields a generator $G_i$ that generates images from the new domain $\mathcal{D}_i$ . In contrast, our goal is domain expansion, which aims at training a single expanded generator $G^+$ that can simultaneously model all the new domains $\cup_{i=1}^{N} \mathcal{D}_i$ , along with the original domain $\mathcal{D}_{\mathrm{src}}$ . We want to ensure that the new domains $\mathcal{D}_i$ are disentangled from each other and also share the factors of variation from the source domain, which remain intact. + +Our solution is to partition the latent space into disjoint subspaces, one for each new domain, and to restrict the effect of each domain adaptation to the corresponding subspace. To this end, we endow the latent space with an explicit structure that supports domain expansion (Sec. 3.1), and optimize each domain adaptation loss only using latents from specific subspace reserved for the new domain (Sec. 3.2). Our decomposition reserves a base subspace for the original domain $\mathcal{D}_{\mathrm{src}}$ , on which we impose a regularization objective to maintain the behavior of the source generator (Sec. 3.3). Fig. 3 gives an overview of our domain expansion algorithm. + +# 3.1. Structuring the Latent Space for Expansion + +Modern generative models conveniently learn to represent the factors of variation along linear latent directions, + +![](images/294e767875f6043b04b95bf53b332b9198c7323519c1fca0fdfdbd7099f48e36.jpg) +Figure 3. Our method transforms a domain adaptation task to a domain expansion task. (a) Generator $G$ is optimized to satisfy the loss $\mathcal{L}_i$ for every latent code in space. The entire generator and latent space now represent the new domain, indicated with the color blue. (b) Generator $G$ is optimized to satisfy the same loss, $\mathcal{L}_i$ , only on a subspace $\mathcal{Z}_i$ , dedicated to the new domain. Simultaneously, $G$ is optimized to satisfy a regularization term $\mathcal{L}_{\mathrm{reg}}$ on a parallel subspace, $\mathcal{Z}_{\mathrm{base}}$ , ensuring the original knowledge is preserved there. The generator and latent space now represent both domains, indicated by being colored both blue and orange. The latent direction between the two spaces was originally dormant in generator $G$ , and now represents a transition between the domains. + +![](images/10cb86f4adabeabefbb348630568c51213676604393cb6c1dc346bf106ec8d2a.jpg) + +in a completely unsupervised manner [12, 26, 28, 39]. We decide to explicitly extend this model by structuring the latent space such that the effect defined by an adaptation task would be represented along a single linear direction. Formally, there should exist some scalar $s$ and latent direction $v_{i}$ , for which images generated from $G^{+}(z), G^{+}(z + sv_{i})$ , relate to each other as the corresponding images from the source and adapted generators $G_{\mathrm{src}}(z), G_{i}(z)$ do. + +Concretely, following SeFA [36], we obtain a semantic and orthogonal basis $V$ of the latent space from the right singular vectors (produced by SVD) of the very first generator layer, which acts on the latent space $\mathcal{Z}$ . With a similar factorization technique [6], it was observed that a relatively small subset of the basis vector is sufficient to represent most of the generators $G_{\mathrm{src}}$ 's variability. Other basis vectors have barely any perceptible effect on the generated images. We find this to be the case with SeFA as well. We refer to vectors with no perceptible effect as dormant. + +As the dormant directions do not affect the model's generation capabilities, they are available to be repurposed with new desired behavior. We thus choose to represent the domains $\mathcal{D}_{\mathrm{src}}$ and $\mathcal{D}_i$ in regions that are separated by only a dormant direction. + +Formally, for each of the $N$ adaptation tasks, we dedicate a single dormant direction, $v_{i}$ , that will be repurposed. The remaining directions $\{v_{N + 1},\ldots ,v_D\}$ will remain intact. We finally define a subspace of $\mathcal{Z}$ , dubbed the base subspace, as + +$$ +\mathcal {Z} _ {\text {b a s e}} = \operatorname {s p a n} \left(v _ {N + 1}, \dots , v _ {D}\right) + \bar {z} \tag {1} +$$ + +where $\overline{z}$ is the mean of the distribution over the latents used to train the generator. Then, for each repurposed direction, $v_{i}$ , we define a repurposed subspace $\mathcal{Z}_i$ that is the base subspace transported along direction $v_{i}$ by a predetermined scalar size $s$ . + +$$ +\mathcal {Z} _ {i} = \mathcal {Z} _ {\text {b a s e}} + s v _ {i}. \tag {2} +$$ + +The choice of direction $v_{i}$ and scalar $s$ are discussed in Appendices C.2 and C.4. + +Our domain expansion training procedure described hereafter will ensure subspace $\mathcal{Z}_i$ is the only part of the latent space affected by the training objective $\mathcal{L}_i$ , and is reserved to generate images from domain $\mathcal{D}_i$ . Intuitively, shifting the base subspace along direction $v_i$ aims to achieve two goals: 1. preserve the factors of variations inherited from $\mathcal{Z}_{\mathrm{base}}$ , and 2. restrict the new factor of variation (corresponding to $\mathcal{D}_i$ ) to a single latent direction, $v_i$ . + +# 3.2. From Domain Adaptation to Expansion + +Having defined disjoint affine subspaces $\mathcal{Z}_i$ of the latent space $\mathcal{Z}$ for our new domains $\mathcal{D}_i$ , we now describe how we constrain each domain adaptation objective $\mathcal{L}_i$ to affect only the corresponding subspace. + +The domain adaptation objective is applied to images generated from latent codes $z \in \mathcal{Z}$ , sampled from distribution $p(z)$ defined on the entire space $\mathcal{Z}$ . Commonly the distribution is a Gaussian, or is derived from it [12] but some exceptions exist [21, 43]. Our strategy is to transform this sample distribution into one restricted to the affine subspace $\mathcal{Z}_i$ . We do so by projecting the samples from $p(z)$ onto $\mathcal{Z}_i$ , using a standard orthogonal projection operator + +$$ +\operatorname {p r o j} _ {\mathcal {Z} _ {i}} (z) = \sum_ {j = N + 1} ^ {D} \left(v _ {j} ^ {\top} (z - \bar {z})\right) v _ {j} + \bar {z} + s v _ {i}. \tag {3} +$$ + +Denoting by $p_i$ the sampling distribution over $\mathcal{Z}$ for each of the new domains we seek to adapt, the training loss over all tasks is defined as + +$$ +\mathcal {L} _ {\text {e x p a n d}} = \sum_ {i = 1} ^ {N} \mathbb {E} _ {z \sim p _ {i} (z)} \mathcal {L} _ {i} \left(G \left(\operatorname {p r o j} _ {\mathcal {Z} _ {i}} (z)\right)\right). \tag {4} +$$ + +# 3.3. Regularization + +Optimizing $\mathcal{L}_{\mathrm{expand}}$ lets us learn to generate data from the new domains $\mathcal{D}_i$ within a single generator, but unfortunately it leaves the base subspace $\mathcal{Z}_{\mathrm{base}}$ under-constrained and, therefore, does not guarantee it will remain unaltered during training. In practice, we observe that the effect of $\mathcal{L}_i$ "leaks" outside $\mathcal{Z}_i$ , causing catastrophic forgetting [18] in subspace $\mathcal{Z}_{\mathrm{base}}$ , and undesirably affecting other subspaces $\mathcal{Z}_j$ . We show an example of this leakage in Fig. 4. + +To prevent this failure mode, we explicitly enforce the preservation of $G_{\mathrm{src}}$ 's behavior over the base subspace $\mathcal{Z}_{\mathrm{base}}$ by regularization. We adopt two successful regularization techniques. First, we keep optimizing the generator with the loss it was originally trained on, $\mathcal{L}_{\mathrm{src}}$ , which is known to mitigate forgetting [15]. Second, we apply replay alignment [44], which is a reconstruction loss that compares the output of a frozen copy of the source generator to that produced by our generator. We use a weighted combination of + +![](images/1c808ecbf299660494cda4f0573c1d23f70ea5c9aa564f685b773829adc50b50.jpg) +Figure 4. Regularization prevents leakage. Without regularization (top row), new factors of variation "Sketch" and "Funny" are leaking into the base subspace and the other repurposed subspace. Note, for example, that the image from the base subspace is both a sketch and depicts a smiling dog. Our regularization, described in Eq. (6), solves the issue (bottom row). + +an $L_{2}$ pixel loss and LPIPS [49]: + +$$ +\mathcal {L} _ {\text {r e c o n}} = \lambda_ {\text {l p i p s}} \mathcal {L} _ {\text {l p i p s}} \left(G _ {\text {s r c}} (z), G (z)\right) + \lambda_ {L _ {2}} \| G _ {\text {s r c}} (z) - G (z) \| _ {2}, \tag {5} +$$ + +where $\lambda_{\mathrm{lpips}} = \lambda_{L_2} = 10$ are weighting hyperparameters. Not only does replay alignment preserve the source domain $D_{\mathrm{src}}$ , it also has the added benefit of aligning $G^{+}$ to the source generator $G_{\mathrm{src}}$ , in the sense that they will produce similar outputs given the same latent code $z$ . + +Crucially, we only regularize the base subspace $\mathcal{Z}_{\mathrm{base}}$ , since the subspaces $\mathcal{Z}_i$ should be allowed to change to learn the new behaviors. To this end, we project the latent codes to the base subspace $\mathcal{Z}_{\mathrm{base}}$ , before calculating the regularization terms. Our overall regularization objective is thus: + +$$ +\mathcal {L} _ {\text {r e g}} = \mathbb {E} _ {z \sim p _ {\text {s r c}} (z)} \left[ \lambda_ {\text {s r c}} \mathcal {L} _ {\text {s r c}} \left(G \left(\operatorname {p r o j} _ {\mathcal {Z} _ {\text {b a s e}}} (z)\right)\right) + \right. \tag {6} +$$ + +$$ +\left. \mathcal {L} _ {\text {r e c o n}} \left(G \left(\operatorname {p r o j} _ {\mathcal {Z} _ {\text {b a s e}}} (z)\right)\right) \right], +$$ + +where $\lambda_{\mathrm{src}} = 1$ balances the two terms and $p_{src}(z)$ is the latent distribution over $\mathcal{Z}$ used to train $G_{\mathrm{src}}$ . Our final, regularized domain expansion objective is, therefore: + +$$ +\mathcal {L} _ {\text {f u l l}} = \mathcal {L} _ {\text {e x p a n d}} + \mathcal {L} _ {\text {r e g}}. \tag {7} +$$ + +# 4. Experiments + +We evaluate our method and analyze its key characteristics. Sec. 4.1 first details the experimental setting, focusing on StyleGAN. We start by analyzing the knowledge encoded along repurposed directions and compare it to domain adaptation methods (Sec. 4.2). We then delve deeper and evaluate the effects (Sec. 4.3) and opportunities (Sec. 4.4) presented by expanding a generator to multiple domains simultaneously. Next, we demonstrate that the quality of the source domain is maintained in the base subspace (Sec. 4.5). Finally, we demonstrate that our method generalizes to other generators (Sec. 4.6). + +Further experiments, results, and details are provided in the supplementary. + +# 4.1. Experimental Setting + +We adopt StyleGAN2 [13] as the main generator architecture, for its disentangled latent space and because it has been the dominant test bed for generative domain adaptation methods in recent years [1,5,21,22,43,51]. + +Latent space and subspaces. Several latent spaces have been considered in the context of StyleGAN. We use the intermediate latent space $\mathcal{W}$ in all our experiments but note it as $\mathcal{Z}$ for consistency. We use SeFA [36] for the orthogonal decomposition of $\mathcal{Z}$ . As SeFA performs SVD, there is a native indication to how dormant is a given latent direction – the corresponding singular value. As singular values are commonly sorted in decreasing orders, the last basis vectors are most dormant. When expanding with $N$ new domains, unless specified otherwise, we repurpose the last $N$ basis vectors. We use $s = 20$ in all experiments. These decisions are evaluated in greater depth in Appendices C.2 and C.4. + +Adaptation methods. We demonstrate our expansion method with two domain adaptation tasks - StyleGAN-NADA [5] and MyStyle [21]. These two tasks were chosen as they differ significantly in key aspects - source of supervision, sampling distribution and loss. + +StyleGAN-NADA is a zero-shot, text-guided, domain adaptation method. It takes as input a pair of text prompts, $t_{\mathrm{source}}$ and $t_{\mathrm{target}}$ , describing the desired transformation source $\rightarrow$ target to be applied on the domain of the pretrained generator, $\mathcal{D}_{\mathrm{src}}$ . The loss function $\mathcal{L}$ is given by + +$$ +\Delta T = E _ {T} \left(t _ {\text {t a r g e t}}\right) - E _ {T} \left(t _ {\text {s o u r c e}}\right), +$$ + +$$ +\Delta I = E _ {I} (G (z)) - E _ {I} \left(G _ {\text {s r c}} (z)\right), \tag {8} +$$ + +$$ +\mathcal {L} = 1 - \frac {\Delta I \cdot \Delta T}{| \Delta I | | \Delta T |}, +$$ + +where $E_{I}$ and $E_{T}$ are CLIP's [29] image and text encoders respectively. + +MyStyle is a few-shot, image-supervised, domain adaptation method. As input, it takes a set of images $\{x_{m}\}_{m = 1}^{M}$ of an individual $(M\sim 100)$ , and adapts $G_{\mathrm{src}}$ to form a personalized prior for that individual. The generator is trained to better reconstruct $x_{m}$ from their original latent space inversions $z_{m}\in \mathcal{Z}$ [38]. Formally, the loss function is given by + +$$ +\mathcal {L} = \sum_ {m = 1} ^ {M} \left[ \mathcal {L} _ {\mathrm {l p i p s}} \left(G \left(z _ {m}\right), x _ {m}\right) + \| G \left(z _ {m}\right) - x _ {m} \| _ {2} \right], \tag {9} +$$ + +where $\mathcal{L}_{\mathrm{lpips}}$ is again the LPIPS loss [49]. + +Datasets and models. We demonstrate our method on four datasets – FFHQ [12], AFHQ Dog [4], LSUN Church [48] and SD-Elephant [20]. The FFHQ model is expanded with 105 new domains, 100 introduced with the expanded + +![](images/d85f841acc12bdc14200dea4c49e25e5cbd78e83c3bc5fb75aaa6f7ae664b435.jpg) +Figure 5. Continuous traversal along repurposed directions. As can be seen, the traversal between the base subspace $(\alpha = 0)$ and repurposed subspace $(\alpha = s)$ portrays a smooth transition between the source and newly introduced domains. Advantageously, the semantic meaning of the repurposed direction is preserved in the extrapolation, representing the opposite relationship between the domains $(\alpha < 0)$ or exaggerations of it $(\alpha > s)$ . + +
MethodUser % (↑)ID (↑)Diversity×10 (↑)
StyleGAN-NADA41.2%-2.42 ± 0.13
Ours w/ NADA58.8%-2.42 ± 0.13
MyStyle-0.80 ± 0.063.08 ± 0.15
Ours w/ MyStyle-0.76 ± 0.053.14 ± 0.14
+ +Table 1. Quantitative comparison of images generated from our repurposed subspaces to those generated by corresponding domain adaptation methods - StyleGAN-NADA [5] and MyStyle [21]. We follow each adaptation method's quantitative evaluation protocol. + +variant of StyleGAN-NADA and 5 from the expanded variant of MyStyle. The AFHQ Dog, LSUN Chruch and SD-Elephant are expanded with 50, 20, and 20 new domains correspondingly, all introduced from the expanded variant of StyleGAN-NADA. + +# 4.2. Evaluating Domains Individually + +Traversing a repurposed direction. We start by investigating what knowledge, if any, is encoded along the repurposed latent directions. To this end, starting from a random latent code $z \in \mathcal{Z}_{\mathrm{base}}$ , we individually traverse different repurposed directions, $v_{i}$ , and inspect the generated images $G^{+}(z + \alpha v_{i})$ . Sample results from our dogs, elephants, and faces models are displayed in Fig. 5. We find that each individual repurposed direction now successfully encodes the desired factor of variation, in a global and continuous way. + +Our training paradigm is inherently discrete - encouraging the source behavior on the base subspace $(\alpha = 0)$ and the newly introduced effect on the repurposed space $(\alpha = s)$ . Therefore, obtaining a smooth effect might seem surprising at first glance. Nevertheless, this phenomenon can be clearly traced to the well-established observation that generators are smooth with respect to their latent space [12]. + +![](images/c4720fe2e45e053e88db0aeff3f97a9f60f795ced839a447bf938bf759e76b52.jpg) +Figure 6. A random set of images generated by our generator from repurposed subspaces (bottom) and by corresponding domain adaptation methods (top). The images are similar and differences are subtle. + +Behavior on the repurposed subspace. We have transformed adaptation tasks into expansion tasks by limiting the training effect to the repurposed subspaces only. But, for latents in repurposed subspaces $(\alpha = s)$ , the domain adaptation could be considered to have been applied as-is. + +We next directly compare the images generated by our generator from the repurposed subspace to the corresponding images generated by the domain-adapted generator. We inherit and repeat the quantitative evaluation protocols performed by each of the adaption tasks. To compare quality with StyleGAN-NADA [5] we perform a two-alternative forced choice user study. Users were asked to pick the image that has higher-quality and better aligns with the target text used for training. We gathered 1440 responses from 32 unique users. To compare quality with MyStyle [21], we evaluate preservation of identity in generated images, as observed by a face recognition network [9]. For both methods, the diversity is compared based on intra-cluster LPIPS [49] distance, first suggested by Ojha et al. [22]. We use 10 domains for comparison with StyleGAN-NADA and 5 for comparison with MyStyle. Note that we use a single generator $G^{+}$ , expanded with 105 domains, while competing methods use a dedicated model per domain, 15, overall. We report the results in Tab. 1 and Fig. 6. + +As can be seen, on the repurposed subspaces, our method produces comparable images to that generated by the dedicated, domain-adapted generator. Perhaps surprisingly, users somewhat prefer our results over StyleGAN-NADA's. We speculate this is due to the significantly greater difficulty of choosing hyperparameters for their training. + +# 4.3. Effect of Domains on Each Other + +Previous evaluation of individual repurposed directions already indicates disentanglement between different factors of variation. For example, "Barbie" images in Fig. 6 show no sign of being caricature, Barack Obama, or any of the other hundred factors of variation introduced to that generator. In this section, we delve deeper into evaluating the effects of expanding with multiple factors of variation. + +![](images/3fd8760e5a9c24df1207a64948e8060994175e88673d3fe42cc70e0cdb54f16e.jpg) + +![](images/af8beeadb270f008bb6e53293e5c8a35ad2f9ed04a66fd2d01d303df75f4dddc.jpg) +Figure 7. Investigating the effect of introducing multiple domains simultaneously. (a) Reports the CLIP error of generated images with the text "a sketch", as a function of training iterations. Images are generated from the "Sketch" and "Sumo" subspaces of models trained with a different number of domains. (b) Depicts generated images from models that have similar CLIP errors. As can be seen, the sketch domain does not "leak" into the sumo subspace. Additionally, introducing additional domains delays, but does not prevent, the introduction of sketch. + +To this end, we train three models to expand the FFHQ parent model with either 1, 5 or 50 new domains, all induced by StyleGAN-NADA [5]. All models are expanded with "Sketch", and the latter two with "Sumo" as well as other factors of variation. We quantify the strength of introduced factor of variation using CLIP error, the 1-complement of the score produced by CLIP [29]. We use the top-performing version of the CLIP encoder available, ViT-L/14, which is not used during training. We note that simply minimizing CLIP error is not the objective, as it might lead to favoring mode-collapsed and adversarial examples [5]. Nevertheless, together with qualitative inspection, it is useful for comparing different models. + +In Fig. 7a, we report the CLIP error of generated images with the text "a sketch", as a function of the training iterations. Images are generated from the "Sketch", and if exists, "Sumo" subspace. First, we observe that CLIP error is decreasing for "Sketch" subspaces in all models, as expected. Conversely, CLIP error in the "Sumo" subspace does not significantly change, indicating it is not becoming any more or less of a sketch. This result quantitatively supports our previous finding, that factors of variations do not interfere with each other, and demonstrates it is true regardless of the number of other factors of variations learned simultaneously. Additionally, we observe that expanding with additional factors of variation delays, but does not prevent, $G^{+}$ the introduction of "Sketch" effectively. The observed delay is expected, as expanding with more variations corresponds to $G^{+}$ optimizing and balancing additional loss functions. + +![](images/fd30c13017487f157b3646735b28d81d6f044895d415591c53df806eea1bb67f.jpg) +Figure 8. Composing multiple effects by simple latent traversal. In each grid, we start from the latent code that generates the top-left image and traverse along two latent directions, represented by advancement in rows and columns. For each direction, we note the associated domain, its ordinal number in the latent space's basis, and the training method used ("NADA" or "MyStyle") to learn the domain. As can be seen, $G^{+}$ has learned a disentangled representation, allowing meaningful composition of concepts. Specifically, note the disentanglement between directions, as traversing left-right does not affect the magnitude of the effect corresponding to up-down traversal, and vice versa. + +![](images/5fa012a44e98a27b784b56e900cc73407958cbaa77037421ea19b3f35e108584.jpg) + +![](images/12896c4e85efcbea1a411672291fe10e255df058128f9fd8f5a6704439e21213.jpg) + +Generated samples from the sketch and sumo subspaces are provided in Fig. 7b. + +# 4.4. Compositionality + +While accidental "leakage" between latent directions during training is undesired, intentionally composing variations at test time is useful. For generative models with a disentangled latent space, summing together latent directions aggregates their semantic meaning, and should not affect the magnitude of their effects if applied separately. For example, if direction $v_{1}$ controls head pose and direction $v_{2}$ controls an unrelated variation, images $G(z + v_{1} + v_{2})$ and $G(z + v_{1})$ should depict the same head pose. + +We find that the latent space of the expanded generator $G^{+}$ is disentangled, and variations can indeed be composed effectively. Crucially, variations can be composed with each other regardless of their originating training task, including those on the base subspace, learned from the source domain. Fig. 8 shows a sample of gradual composition results across models and training tasks. + +Comparison to existing techniques. Several domain adaptation methods have proposed techniques to combine multiple variations. These methods still train a separate generative model per variation, but combine their effects in test-time. Specifically, in the realm of CLIP-supervised training, StyleGAN-NADA [5] interpolates the generators' weights, while DiffusionCLIP [14] interpolates intermediate activations of the generators. Next, we compare the disentanglement of composition in our generator to that made possible using these techniques. + +For each method, we start with a setting that was optimized to generate images that align with one of two text prompts. In our case, this setting is $G^{+}$ with latent codes in certain subspaces. For the baselines, these settings are + +
ModelFFHQAFHQLSUN ChurchSD Elephant
Parent2.777.433.922.30
Ours2.807.513.762.70
Only Lsrc2.75±0.087.38±0.093.31±0.223.91±0.67
+ +Table 2. We generate images from the base subspace and report FID [7] $(\downarrow)$ with respect to source domain dataset. We compare our FID to that of the source generator $G_{\mathrm{src}}$ . For reference, we also continue training the source generator for the same number of iterations with its original loss - $\mathcal{L}_{\mathrm{src}}$ , and report the mean and standard deviations of FID along the training. As can be seen, on the base subspace, our models have comparable FID scores to their parents. Furthermore, similar magnitude of change in FID are observed by simply continuing training, indicating that the change in FID might be, at least in part, due to "random" fluctuations. + +dedicated generators with any latent code. Then, for each method, we gradually introduce the variation described by the other text prompt and generate the corresponding images. Finally, we measure normalized CLIP error between generated images and the two prompts. We normalize all errors by the error of the initial setting, to make the metric comparable across methods and text prompts. Fig. 9 reports the mean and standard deviation of the CLIP error, on 10 pairs of prompts, and provides a sample of qualitative results. As can be seen, both baseline methods directly trade-off one domain for the other, expressed by a linear-looking trend. Conversely, our method obtains significantly lower errors and allows for a true composition of concepts. + +# 4.5. Preservation of the Source Domain + +We next evaluate the preservation of the source domain in $G^{+}$ . To this end, using FID [7], we compare the quality + +![](images/2cba78b02d03b4a219dc751dc72c8469a503207f547a8a347e698aa6c116105d.jpg) +(a) + +![](images/8cb69aa8c7aa40d6832967c4ac9405948d1964c2d2f79afacfa34559cb58bb6f.jpg) +(b) +Figure 9. Comparing compositionality in our generator to methods of combining multiple domains proposed by StyleGAN-NADA [5] and DiffusionCLIP [14]. Starting from a setting optimized for either text prompt #1 or #2, we gradually introduce the variation described by the other text. (a) Reports the CLIP error to both prompts along the gradual introduction, normalized to the error obtained for each text prompt in isolation. (b) Portrays a sample of qualitative results, where the composition is such that assigns equal strengths to both effects. As can be seen in, both quantitatively and qualitatively, NADA and DiffusionCLIP directly trade-off one effect for the other - strengthening the effect of one prompt directly lessens that of the other. In contrast, our generator allows true composition of modalities. + +of images generated from the base subspace $\mathcal{Z}_{\mathrm{base}}$ of $G^{+}$ to those generated by the source generator $G_{src}$ . Since the generator is being trained, some change in FID is expected. Therefore, we also report the average and standard deviation over FID scores for a generator that simply continues training, i.e., using only the original loss $\mathcal{L}_{\mathrm{src}}$ . Results are reported in Tab. 2 and vary between datasets. Across all datasets, we observe that the FID from our base subspace is within $1\sigma$ of the that obtained from either the parent or a generator that continues training. For reference, generator's adapted with StyleGAN-NADA and MyStyle have an average FID of 125 and 183, respectively. We conclude that the expansion method might have a slight impact on FID, but it is negligible. + +# 4.6. Generalization Beyond StyleGAN + +We finally demonstrate that our expansion method generalizes to other models, beyond StyleGAN. To this end, we experiment with Diffusion Autoencoder (DiffAE) [28]. Despite differences in architecture and training method, DiffAE also has a semantic latent space, marked with $z_{\mathrm{sem}}$ . We apply our approach over DiffAE and its latent space, using StyleGAN-NADA [5] as the base adaptation method. We find that our expansion methods work as well with DiffAE, and provide a sample of qualitative results in Fig. 10. + +![](images/a53fc4b78b4110592716ea7d72a39f20fc4830a77a88841c2f0c203f626d371f.jpg) +Figure 10. Applying our domain expansion method with Diffusion Autoencoder [28]. + +# 5. Conclusions + +We present a new problem - domain expansion - and propose an approach to solve it. The core of our method is to carefully structure the latent space, such that it is amenable to learning additional knowledge, while keeping the existing knowledge intact. Our method takes advantage of the existence of dormant latent directions, and the task itself implicitly relies on the capacity of the model weights to represent more knowledge. If one of these assumptions does not hold, it might not be possible to apply domain expansion. However, the popularity of methods squeezing neural networks, such as Knowledge Distillation [8], and current estimates of the intrinsic dimensionality of image datasets [27], indicate that these assumptions commonly hold. In our experiments, we were able to expand to hundreds of directions. A plausible limitation is that the model can be expanded to a certain point but ultimately limited by factors such as the latent space or network capacity. Overcoming this limitation, perhaps by considering more complex latent space structures, is an avenue for future work. + +Acknowledgment. This work was done while Yotam Nitzan was an intern at Adobe. This research was supported in part by the Israel Science Foundation (grants no. 2492/20 and 3441/21), Len Blavatnik and the Blavatnik family foundation, and The Tel Aviv University Innovation Laboratories (TILabs). + +# References + +[1] David Bau, Steven Liu, Tongzhou Wang, Jun-Yan Zhu, and Antonio Torralba. Rewriting a deep generative model. 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(center) Traversing the latent space of generative models along some directions changes the image significantly while traversing others has no perceptible effect. We call such directions dormant. (left) Domain adaptation methods, transform the entire generator from a source domain to a target domain. (right) We introduce an approach for a new task - domain expansion. Rather than transforming the generator fully, we expand it to include new data domains. 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"angle": 0, + "lines": [ + { + "bbox": [ + 143, + 423, + 192, + 435 + ], + "spans": [ + { + "bbox": [ + 143, + 423, + 192, + 435 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 46, + 447, + 289, + 679 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 447, + 289, + 679 + ], + "spans": [ + { + "bbox": [ + 46, + 447, + 289, + 679 + ], + "type": "text", + "content": "Can one inject new concepts into an already trained generative model, while respecting its existing structure and knowledge? We propose a new task - domain expansion - to address this. Given a pretrained generator and novel (but related) domains, we expand the generator to jointly model all domains, old and new, harmoniously. First, we note the generator contains a meaningful, pretrained latent space. Is it possible to minimally perturb this hard-earned representation, while maximally representing the new domains? Interestingly, we find that the latent space offers unused, \"dormant\" directions, which do not affect the output. This provides an opportunity: By \"repurposing\" these directions, we can represent new domains without perturbing the original representation. In fact, we find that pretrained generators have the capacity to add several - even hundreds - of new domains! Using our expansion method, one \"expanded\" model can supersede numerous domain-specific models, without expanding the model size. Additionally, a single expanded generator natively supports smooth transitions between domains, as well as composition of domains." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 59, + 688, + 214, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 688, + 214, + 700 + ], + "spans": [ + { + "bbox": [ + 59, + 688, + 214, + 700 + ], + "type": "text", + "content": "Code and project page available here." + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 307, + 423, + 386, + 435 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 423, + 386, + 435 + ], + "spans": [ + { + "bbox": [ + 307, + 423, + 386, + 435 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 304, + 445, + 545, + 595 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 445, + 545, + 595 + ], + "spans": [ + { + "bbox": [ + 304, + 445, + 545, + 595 + ], + "type": "text", + "content": "Recent domain adaptation techniques piggyback on the tremendous success of modern generative image models [3, 12, 32, 40], by adapting a pretrained generator so it can generate images from a new target domain. Oftentimes, the target domain is defined with respect to the source domain [5, 21, 22], e.g., changing the \"stylization\" from a photorealistic image to a sketch. When such a relationship holds, domain adaptation typically seeks to preserve the factors of variations learned in the source domain, and transfer them to the new one (e.g., making the human depicted in a sketch smile based on the prior from a face generator). With existing techniques, however, the adapted model loses the ability to generate images from the original domain." + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 304, + 597, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 597, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 597, + 545, + 715 + ], + "type": "text", + "content": "In this work, we introduce a novel task — domain expansion. Unlike domain adaptation, we aim to augment the space of images a single model can generate, without overriding its original behavior (see Fig. 1). Rather than viewing similar image domains as disjoint data distributions, we treat them as different modes in a joint distribution. As a result, the domains share a semantic prior inherited from the original data domain. For example, the inherent factors of variation for photorealistic faces, such as pose and face shape, can equally apply to the domain of “zombies”." + } + ] + } + ], + "index": 33 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15933" + } + ] + } + ], + "index": 34 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 105, + 95, + 159 + ], + "blocks": [ + { + "bbox": [ + 50, + 105, + 95, + 159 + ], + "lines": [ + { + "bbox": [ + 50, + 105, + 95, + 159 + ], + "spans": [ + { + "bbox": [ + 50, + 105, + 95, + 159 + ], + "type": "image", + "image_path": "132a72b4a2928348d56858381fab15be1bbcfc526b61d677f68d6c20c52a9eb2.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 159, + 91, + 165 + ], + "lines": [ + { + "bbox": [ + 55, + 159, + 91, + 165 + ], + "spans": [ + { + "bbox": [ + 55, + 159, + 91, + 165 + ], + "type": "text", + "content": "Source Domain" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 100, + 76, + 233, + 131 + ], + "blocks": [ + { + "bbox": [ + 100, + 76, + 233, + 131 + ], + "lines": [ + { + "bbox": [ + 100, + 76, + 233, + 131 + ], + "spans": [ + { + "bbox": [ + 100, + 76, + 233, + 131 + ], + "type": "image", + "image_path": "055e62ef34af5a041e401c0f577d141567bc5f0b63ac40d32e5223727383853e.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 100, + 144, + 233, + 190 + ], + "blocks": [ + { + "bbox": [ + 143, + 137, + 189, + 144 + ], + "lines": [ + { + "bbox": [ + 143, + 137, + 189, + 144 + ], + "spans": [ + { + "bbox": [ + 143, + 137, + 189, + 144 + ], + "type": "text", + "content": "Happy" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 100, + 144, + 233, + 190 + ], + "lines": [ + { + "bbox": [ + 100, + 144, + 233, + 190 + ], + "spans": [ + { + "bbox": [ + 100, + 144, + 233, + 190 + ], + "type": "image", + "image_path": "aba7cd94bb0576d686c3cb528e962b15006a7d053600ab8f657006638d212bac.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 145, + 190, + 190, + 197 + ], + "lines": [ + { + "bbox": [ + 145, + 190, + 190, + 197 + ], + "spans": [ + { + "bbox": [ + 145, + 190, + 190, + 197 + ], + "type": "text", + "content": "Expanded Domains" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 206, + 287, + 281 + ], + "lines": [ + { + "bbox": [ + 46, + 206, + 287, + 281 + ], + "spans": [ + { + "bbox": [ + 46, + 206, + 287, + 281 + ], + "type": "text", + "content": "Figure 2. Example of a domain expansion result. Starting from dogs as the source domain, we expand a single generator to model new domains such as facial expressions, breeds of dogs and other animals, and artistic styles. Finally, as the representations are disentangled, the expanded generator is able to generalize and compose the different domains, although they were never seen jointly in training." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 239, + 72, + 284, + 129 + ], + "blocks": [ + { + "bbox": [ + 239, + 72, + 284, + 129 + ], + "lines": [ + { + "bbox": [ + 239, + 72, + 284, + 129 + ], + "spans": [ + { + "bbox": [ + 239, + 72, + 284, + 129 + ], + "type": "image", + "image_path": "f5314b0fee02e676725a5f3ec7a00a85ecf53c2f55d5a14219a186383b43aaa1.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 238, + 145, + 284, + 190 + ], + "blocks": [ + { + "bbox": [ + 242, + 131, + 280, + 144 + ], + "lines": [ + { + "bbox": [ + 242, + 131, + 280, + 144 + ], + "spans": [ + { + "bbox": [ + 242, + 131, + 280, + 144 + ], + "type": "text", + "content": "Boar + Happy + Pop Art" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 238, + 145, + 284, + 190 + ], + "lines": [ + { + "bbox": [ + 238, + 145, + 284, + 190 + ], + "spans": [ + { + "bbox": [ + 238, + 145, + 284, + 190 + ], + "type": "image", + "image_path": "c930f459bdd27e2290f874943470ba02eddbd811eb44fc032fe2ea1778912c2e.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 236, + 190, + 286, + 197 + ], + "lines": [ + { + "bbox": [ + 236, + 190, + 286, + 197 + ], + "spans": [ + { + "bbox": [ + 236, + 190, + 286, + 197 + ], + "type": "text", + "content": "Domain Composition" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 295, + 287, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 295, + 287, + 445 + ], + "spans": [ + { + "bbox": [ + 46, + 295, + 287, + 445 + ], + "type": "text", + "content": "To this end, we carefully structure the model training process for expansion, respecting the original data domain. It is well-known that modern generative models with low-dimensional latent spaces offer an intriguing, emergent property – through training, the latent spaces represent the factors of variation, in a linear and interpretable manner [3, 6, 10, 12, 28, 30, 39, 40]. We wish to extend this advantageous behavior and represent the new domains along linear and disentangled directions. Interestingly, it was previously shown that many latent directions have insignificant perceptible effect on generated images [6]. Taking advantage of this finding, we repurpose such directions to represent the new domains." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 447, + 287, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 447, + 287, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 447, + 287, + 700 + ], + "type": "text", + "content": "In practice, we start from an orthogonal decomposition of the latent space [36] and identify a set of low-magnitude directions that have no perceptible effect on the generated images, which we call dormant. To add a new domain, we select a dormant direction to repurpose. Its orthogonal subspace, which we call base subspace, is sufficient to represent the original domain [6]. We aim to repurpose the dormant direction such that traversing it would now cause a transition between the original and the new domain. Specifically, the transition should be disentangled from the original domain's factors of variation. To this end, we define a repurposed affine subspace by transporting the base subspace along the chosen dormant direction, as shown in Fig. 3. We capture the new domain by applying a domain adaptation method, transformed to operate only on latent codes sampled from the repurposed subspace. A regularization loss is applied on the base subspace to ensure that the original domain is preserved. The original domain's factors of variation are implicitly preserved due to the subspaces being parallel and the latent space being disentangled. For multiple new domains, we simply repeat this procedure across multiple dormant directions." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "type": "text", + "content": "We apply our method to the StyleGAN [13] architecture," + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 72, + 545, + 268 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 268 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 268 + ], + "type": "text", + "content": "with multiple datasets, and expand the generator with hundreds of new factors of variation. Crucially, we show our expanded model simultaneously generates high-quality images from both original and new domains, comparable to specialized, domain-specific generators. Thus, a single expanded generator supersedes hundreds of adapted generators, facilitating the deployment of generative models for real-world applications. We additionally demonstrate that the new domains are learned as global and disentangled factors of variation, alongside existing ones. This enables fine-grained control over the generative process and paves the way to new applications and capabilities, e.g., compositing multiple domains (See Fig. 2). Finally, we conduct a detailed analysis of key aspects of our method, such as the effect of the number of newly introduced domains, thus shedding light on our method and, in the process, on the nature of the latent space of generative models." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 317, + 270, + 511, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 270, + 511, + 281 + ], + "spans": [ + { + "bbox": [ + 317, + 270, + 511, + 281 + ], + "type": "text", + "content": "To summarize, our contributions are as follows:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 282, + 545, + 397 + ], + "type": "list", + "angle": 0, + "index": 20, + "blocks": [ + { + "bbox": [ + 306, + 282, + 545, + 305 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 282, + 545, + 305 + ], + "spans": [ + { + "bbox": [ + 306, + 282, + 545, + 305 + ], + "type": "text", + "content": "- We introduce a new task - domain expansion of a pretrained generative model." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 305, + 545, + 340 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 305, + 545, + 340 + ], + "spans": [ + { + "bbox": [ + 306, + 305, + 545, + 340 + ], + "type": "text", + "content": "- We propose a novel latent space structure that is amenable to representing new knowledge in a disentangled manner, while maintaining existing knowledge intact." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 340, + 545, + 363 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 340, + 545, + 363 + ], + "spans": [ + { + "bbox": [ + 306, + 340, + 545, + 363 + ], + "type": "text", + "content": "- We present a simple paradigm transforming domain adaptation methods into domain expansion methods." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 363, + 545, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 363, + 545, + 397 + ], + "spans": [ + { + "bbox": [ + 306, + 363, + 545, + 397 + ], + "type": "text", + "content": "- We demonstrate successful domain expansion to hundreds of new domains and illustrate its advantage over domain adaptation methods." + } + ] + } + ], + "index": 19 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 411, + 392, + 424 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 411, + 392, + 424 + ], + "spans": [ + { + "bbox": [ + 306, + 411, + 392, + 424 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 426, + 545, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 545, + 472 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 545, + 472 + ], + "type": "text", + "content": "Fine-tuning generative models. Starting from a generator pretrained on a source domain and training it for a target domain, often called fine-tuning, is a common technique applied for various purposes and settings." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 473, + 545, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 473, + 545, + 577 + ], + "spans": [ + { + "bbox": [ + 304, + 473, + 545, + 577 + ], + "type": "text", + "content": "Some works wish to model only the target domain. In which case, the pretrained model is leveraged simply as an efficient initialization, shortening the training time, and improving image quality [11, 16, 19, 47, 50]. Others, wish to learn the target domain alongside the source domain, in a setting called continuous learning, and propose methods to ensure that the source domain is not forgotten [34, 44]. Although in a single generator, the domains are modeled separately, each as its own class." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 578, + 545, + 636 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 578, + 545, + 636 + ], + "spans": [ + { + "bbox": [ + 304, + 578, + 545, + 636 + ], + "type": "text", + "content": "A prominent line of works have sought to make the target domain inherit knowledge from the source domain [1,2,5, 14,17,21-23,31,33,42,43,51]. This approach allows generalization beyond the target domain per-se and is especially useful when training data is scarce." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 637, + 545, + 718 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 637, + 545, + 718 + ], + "spans": [ + { + "bbox": [ + 304, + 637, + 545, + 718 + ], + "type": "text", + "content": "Our work similarly involves fine-tuning, but for a novel purpose. Our perspective is that, since the target domain is introduced with knowledge from the source domain – it is in essence, an expansion of it. Therefore, in contrast to the aforementioned works, we aim to model the domains jointly. The proposed method does not replace previous fine-tuning methods, but allows applying them jointly." + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "15934" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 176 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 176 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 176 + ], + "type": "text", + "content": "Latent directions in generative models. Generative models learn to represent the factors of variation of observed data in their latent space. Disentangled representations are especially useful as they facilitate intuitive control over the generative process. With recent architectures, disentanglement miraculously emerges without intervention [12, 24, 28, 39]. In such models, disentanglement is manifested through the existence of linear latent directions, each ideally controlling a single factor of variation." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 176, + 287, + 269 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 176, + 287, + 269 + ], + "spans": [ + { + "bbox": [ + 46, + 176, + 287, + 269 + ], + "type": "text", + "content": "Due to the spontaneous emergence of such directions, many works have been proposed to identify them after the model has been trained [6, 25, 35-37, 41, 45] and used them for downstream applications, most commonly semantic image editing. At the same time, it has also been observed that some latent directions have no perceptible effect on the generated images [6, 46]. These directions, which we call dormant, were not previously leveraged for any purpose." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 269, + 287, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 269, + 287, + 361 + ], + "spans": [ + { + "bbox": [ + 46, + 269, + 287, + 361 + ], + "type": "text", + "content": "In this work, we rely on existing methods to factorize the latent space into such linear directions. As we aim to expand the pretrained generator to additional domains, we decide to explicitly encode the \"new knowledge\" along the dormant directions, while keeping other directions intact. This design ensures that the original domain is preserved and that the different domains are represented in a disentangled fashion." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 369, + 102, + 381 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 369, + 102, + 381 + ], + "spans": [ + { + "bbox": [ + 47, + 369, + 102, + 381 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 389, + 287, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 389, + 287, + 528 + ], + "spans": [ + { + "bbox": [ + 46, + 389, + 287, + 528 + ], + "type": "text", + "content": "We start with a pretrained generator " + }, + { + "bbox": [ + 46, + 389, + 287, + 528 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{src}}" + }, + { + "bbox": [ + 46, + 389, + 287, + 528 + ], + "type": "text", + "content": " that maps from latent codes " + }, + { + "bbox": [ + 46, + 389, + 287, + 528 + ], + "type": "inline_equation", + "content": "z \\in \\mathcal{Z} \\subseteq \\mathbb{R}^D" + }, + { + "bbox": [ + 46, + 389, + 287, + 528 + ], + "type": "text", + "content": " to images in a source domain " + }, + { + "bbox": [ + 46, + 389, + 287, + 528 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{src}}" + }, + { + "bbox": [ + 46, + 389, + 287, + 528 + ], + "type": "text", + "content": ", and a set of " + }, + { + "bbox": [ + 46, + 389, + 287, + 528 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 389, + 287, + 528 + ], + "type": "text", + "content": " domain adaptation tasks, each defined by a loss function " + }, + { + "bbox": [ + 46, + 389, + 287, + 528 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_i" + }, + { + "bbox": [ + 46, + 389, + 287, + 528 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 389, + 287, + 528 + ], + "type": "inline_equation", + "content": "i \\in \\{1, \\dots, N\\}" + }, + { + "bbox": [ + 46, + 389, + 287, + 528 + ], + "type": "text", + "content": ". In domain adaptation, fine-tuning " + }, + { + "bbox": [ + 46, + 389, + 287, + 528 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{src}}" + }, + { + "bbox": [ + 46, + 389, + 287, + 528 + ], + "type": "text", + "content": " to minimize " + }, + { + "bbox": [ + 46, + 389, + 287, + 528 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_i" + }, + { + "bbox": [ + 46, + 389, + 287, + 528 + ], + "type": "text", + "content": " yields a generator " + }, + { + "bbox": [ + 46, + 389, + 287, + 528 + ], + "type": "inline_equation", + "content": "G_i" + }, + { + "bbox": [ + 46, + 389, + 287, + 528 + ], + "type": "text", + "content": " that generates images from the new domain " + }, + { + "bbox": [ + 46, + 389, + 287, + 528 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_i" + }, + { + "bbox": [ + 46, + 389, + 287, + 528 + ], + "type": "text", + "content": ". In contrast, our goal is domain expansion, which aims at training a single expanded generator " + }, + { + "bbox": [ + 46, + 389, + 287, + 528 + ], + "type": "inline_equation", + "content": "G^+" + }, + { + "bbox": [ + 46, + 389, + 287, + 528 + ], + "type": "text", + "content": " that can simultaneously model all the new domains " + }, + { + "bbox": [ + 46, + 389, + 287, + 528 + ], + "type": "inline_equation", + "content": "\\cup_{i=1}^{N} \\mathcal{D}_i" + }, + { + "bbox": [ + 46, + 389, + 287, + 528 + ], + "type": "text", + "content": ", along with the original domain " + }, + { + "bbox": [ + 46, + 389, + 287, + 528 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{src}}" + }, + { + "bbox": [ + 46, + 389, + 287, + 528 + ], + "type": "text", + "content": ". We want to ensure that the new domains " + }, + { + "bbox": [ + 46, + 389, + 287, + 528 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_i" + }, + { + "bbox": [ + 46, + 389, + 287, + 528 + ], + "type": "text", + "content": " are disentangled from each other and also share the factors of variation from the source domain, which remain intact." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 529, + 287, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 529, + 287, + 666 + ], + "spans": [ + { + "bbox": [ + 46, + 529, + 287, + 666 + ], + "type": "text", + "content": "Our solution is to partition the latent space into disjoint subspaces, one for each new domain, and to restrict the effect of each domain adaptation to the corresponding subspace. To this end, we endow the latent space with an explicit structure that supports domain expansion (Sec. 3.1), and optimize each domain adaptation loss only using latents from specific subspace reserved for the new domain (Sec. 3.2). Our decomposition reserves a base subspace for the original domain " + }, + { + "bbox": [ + 46, + 529, + 287, + 666 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{src}}" + }, + { + "bbox": [ + 46, + 529, + 287, + 666 + ], + "type": "text", + "content": ", on which we impose a regularization objective to maintain the behavior of the source generator (Sec. 3.3). Fig. 3 gives an overview of our domain expansion algorithm." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 672, + 274, + 685 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 672, + 274, + 685 + ], + "spans": [ + { + "bbox": [ + 47, + 672, + 274, + 685 + ], + "type": "text", + "content": "3.1. Structuring the Latent Space for Expansion" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "Modern generative models conveniently learn to represent the factors of variation along linear latent directions," + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 307, + 71, + 419, + 150 + ], + "blocks": [ + { + "bbox": [ + 307, + 71, + 419, + 150 + ], + "lines": [ + { + "bbox": [ + 307, + 71, + 419, + 150 + ], + "spans": [ + { + "bbox": [ + 307, + 71, + 419, + 150 + ], + "type": "image", + "image_path": "294e767875f6043b04b95bf53b332b9198c7323519c1fca0fdfdbd7099f48e36.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 159, + 545, + 287 + ], + "lines": [ + { + "bbox": [ + 304, + 159, + 545, + 287 + ], + "spans": [ + { + "bbox": [ + 304, + 159, + 545, + 287 + ], + "type": "text", + "content": "Figure 3. Our method transforms a domain adaptation task to a domain expansion task. (a) Generator " + }, + { + "bbox": [ + 304, + 159, + 545, + 287 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 159, + 545, + 287 + ], + "type": "text", + "content": " is optimized to satisfy the loss " + }, + { + "bbox": [ + 304, + 159, + 545, + 287 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_i" + }, + { + "bbox": [ + 304, + 159, + 545, + 287 + ], + "type": "text", + "content": " for every latent code in space. The entire generator and latent space now represent the new domain, indicated with the color blue. (b) Generator " + }, + { + "bbox": [ + 304, + 159, + 545, + 287 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 159, + 545, + 287 + ], + "type": "text", + "content": " is optimized to satisfy the same loss, " + }, + { + "bbox": [ + 304, + 159, + 545, + 287 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_i" + }, + { + "bbox": [ + 304, + 159, + 545, + 287 + ], + "type": "text", + "content": ", only on a subspace " + }, + { + "bbox": [ + 304, + 159, + 545, + 287 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}_i" + }, + { + "bbox": [ + 304, + 159, + 545, + 287 + ], + "type": "text", + "content": ", dedicated to the new domain. Simultaneously, " + }, + { + "bbox": [ + 304, + 159, + 545, + 287 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 159, + 545, + 287 + ], + "type": "text", + "content": " is optimized to satisfy a regularization term " + }, + { + "bbox": [ + 304, + 159, + 545, + 287 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{reg}}" + }, + { + "bbox": [ + 304, + 159, + 545, + 287 + ], + "type": "text", + "content": " on a parallel subspace, " + }, + { + "bbox": [ + 304, + 159, + 545, + 287 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}_{\\mathrm{base}}" + }, + { + "bbox": [ + 304, + 159, + 545, + 287 + ], + "type": "text", + "content": ", ensuring the original knowledge is preserved there. The generator and latent space now represent both domains, indicated by being colored both blue and orange. The latent direction between the two spaces was originally dormant in generator " + }, + { + "bbox": [ + 304, + 159, + 545, + 287 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 159, + 545, + 287 + ], + "type": "text", + "content": ", and now represents a transition between the domains." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 425, + 71, + 542, + 150 + ], + "blocks": [ + { + "bbox": [ + 425, + 71, + 542, + 150 + ], + "lines": [ + { + "bbox": [ + 425, + 71, + 542, + 150 + ], + "spans": [ + { + "bbox": [ + 425, + 71, + 542, + 150 + ], + "type": "image", + "image_path": "10cb86f4adabeabefbb348630568c51213676604393cb6c1dc346bf106ec8d2a.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 294, + 545, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 294, + 545, + 388 + ], + "spans": [ + { + "bbox": [ + 304, + 294, + 545, + 388 + ], + "type": "text", + "content": "in a completely unsupervised manner [12, 26, 28, 39]. We decide to explicitly extend this model by structuring the latent space such that the effect defined by an adaptation task would be represented along a single linear direction. Formally, there should exist some scalar " + }, + { + "bbox": [ + 304, + 294, + 545, + 388 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 294, + 545, + 388 + ], + "type": "text", + "content": " and latent direction " + }, + { + "bbox": [ + 304, + 294, + 545, + 388 + ], + "type": "inline_equation", + "content": "v_{i}" + }, + { + "bbox": [ + 304, + 294, + 545, + 388 + ], + "type": "text", + "content": ", for which images generated from " + }, + { + "bbox": [ + 304, + 294, + 545, + 388 + ], + "type": "inline_equation", + "content": "G^{+}(z), G^{+}(z + sv_{i})" + }, + { + "bbox": [ + 304, + 294, + 545, + 388 + ], + "type": "text", + "content": ", relate to each other as the corresponding images from the source and adapted generators " + }, + { + "bbox": [ + 304, + 294, + 545, + 388 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{src}}(z), G_{i}(z)" + }, + { + "bbox": [ + 304, + 294, + 545, + 388 + ], + "type": "text", + "content": " do." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 388, + 545, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 388, + 545, + 502 + ], + "spans": [ + { + "bbox": [ + 304, + 388, + 545, + 502 + ], + "type": "text", + "content": "Concretely, following SeFA [36], we obtain a semantic and orthogonal basis " + }, + { + "bbox": [ + 304, + 388, + 545, + 502 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 304, + 388, + 545, + 502 + ], + "type": "text", + "content": " of the latent space from the right singular vectors (produced by SVD) of the very first generator layer, which acts on the latent space " + }, + { + "bbox": [ + 304, + 388, + 545, + 502 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}" + }, + { + "bbox": [ + 304, + 388, + 545, + 502 + ], + "type": "text", + "content": ". With a similar factorization technique [6], it was observed that a relatively small subset of the basis vector is sufficient to represent most of the generators " + }, + { + "bbox": [ + 304, + 388, + 545, + 502 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{src}}" + }, + { + "bbox": [ + 304, + 388, + 545, + 502 + ], + "type": "text", + "content": "'s variability. Other basis vectors have barely any perceptible effect on the generated images. We find this to be the case with SeFA as well. We refer to vectors with no perceptible effect as dormant." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 502, + 545, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 502, + 545, + 559 + ], + "spans": [ + { + "bbox": [ + 304, + 502, + 545, + 559 + ], + "type": "text", + "content": "As the dormant directions do not affect the model's generation capabilities, they are available to be repurposed with new desired behavior. We thus choose to represent the domains " + }, + { + "bbox": [ + 304, + 502, + 545, + 559 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{src}}" + }, + { + "bbox": [ + 304, + 502, + 545, + 559 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 502, + 545, + 559 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_i" + }, + { + "bbox": [ + 304, + 502, + 545, + 559 + ], + "type": "text", + "content": " in regions that are separated by only a dormant direction." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 559, + 545, + 618 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 559, + 545, + 618 + ], + "spans": [ + { + "bbox": [ + 304, + 559, + 545, + 618 + ], + "type": "text", + "content": "Formally, for each of the " + }, + { + "bbox": [ + 304, + 559, + 545, + 618 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 559, + 545, + 618 + ], + "type": "text", + "content": " adaptation tasks, we dedicate a single dormant direction, " + }, + { + "bbox": [ + 304, + 559, + 545, + 618 + ], + "type": "inline_equation", + "content": "v_{i}" + }, + { + "bbox": [ + 304, + 559, + 545, + 618 + ], + "type": "text", + "content": ", that will be repurposed. The remaining directions " + }, + { + "bbox": [ + 304, + 559, + 545, + 618 + ], + "type": "inline_equation", + "content": "\\{v_{N + 1},\\ldots ,v_D\\}" + }, + { + "bbox": [ + 304, + 559, + 545, + 618 + ], + "type": "text", + "content": " will remain intact. We finally define a subspace of " + }, + { + "bbox": [ + 304, + 559, + 545, + 618 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}" + }, + { + "bbox": [ + 304, + 559, + 545, + 618 + ], + "type": "text", + "content": ", dubbed the base subspace, as" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 356, + 625, + 545, + 637 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 356, + 625, + 545, + 637 + ], + "spans": [ + { + "bbox": [ + 356, + 625, + 545, + 637 + ], + "type": "interline_equation", + "content": "\\mathcal {Z} _ {\\text {b a s e}} = \\operatorname {s p a n} \\left(v _ {N + 1}, \\dots , v _ {D}\\right) + \\bar {z} \\tag {1}", + "image_path": "424ab55a68e7a7de074495f7fcf3f08f7a03fa5d0052269d5d0e7882f0fb355e.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 643, + 545, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 643, + 545, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 643, + 545, + 700 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 643, + 545, + 700 + ], + "type": "inline_equation", + "content": "\\overline{z}" + }, + { + "bbox": [ + 304, + 643, + 545, + 700 + ], + "type": "text", + "content": " is the mean of the distribution over the latents used to train the generator. Then, for each repurposed direction, " + }, + { + "bbox": [ + 304, + 643, + 545, + 700 + ], + "type": "inline_equation", + "content": "v_{i}" + }, + { + "bbox": [ + 304, + 643, + 545, + 700 + ], + "type": "text", + "content": ", we define a repurposed subspace " + }, + { + "bbox": [ + 304, + 643, + 545, + 700 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}_i" + }, + { + "bbox": [ + 304, + 643, + 545, + 700 + ], + "type": "text", + "content": " that is the base subspace transported along direction " + }, + { + "bbox": [ + 304, + 643, + 545, + 700 + ], + "type": "inline_equation", + "content": "v_{i}" + }, + { + "bbox": [ + 304, + 643, + 545, + 700 + ], + "type": "text", + "content": " by a predetermined scalar size " + }, + { + "bbox": [ + 304, + 643, + 545, + 700 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 643, + 545, + 700 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 388, + 702, + 545, + 713 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 388, + 702, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 388, + 702, + 545, + 713 + ], + "type": "interline_equation", + "content": "\\mathcal {Z} _ {i} = \\mathcal {Z} _ {\\text {b a s e}} + s v _ {i}. \\tag {2}", + "image_path": "5825e11817cf8ff7ed88f80ad242cfd279bc72597b8f5e4908dad0e456b62870.jpg" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "15935" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": "The choice of direction " + }, + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "inline_equation", + "content": "v_{i}" + }, + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": " and scalar " + }, + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": " are discussed in Appendices C.2 and C.4." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 96, + 288, + 189 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 96, + 288, + 189 + ], + "spans": [ + { + "bbox": [ + 46, + 96, + 288, + 189 + ], + "type": "text", + "content": "Our domain expansion training procedure described hereafter will ensure subspace " + }, + { + "bbox": [ + 46, + 96, + 288, + 189 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}_i" + }, + { + "bbox": [ + 46, + 96, + 288, + 189 + ], + "type": "text", + "content": " is the only part of the latent space affected by the training objective " + }, + { + "bbox": [ + 46, + 96, + 288, + 189 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_i" + }, + { + "bbox": [ + 46, + 96, + 288, + 189 + ], + "type": "text", + "content": ", and is reserved to generate images from domain " + }, + { + "bbox": [ + 46, + 96, + 288, + 189 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_i" + }, + { + "bbox": [ + 46, + 96, + 288, + 189 + ], + "type": "text", + "content": ". Intuitively, shifting the base subspace along direction " + }, + { + "bbox": [ + 46, + 96, + 288, + 189 + ], + "type": "inline_equation", + "content": "v_i" + }, + { + "bbox": [ + 46, + 96, + 288, + 189 + ], + "type": "text", + "content": " aims to achieve two goals: 1. preserve the factors of variations inherited from " + }, + { + "bbox": [ + 46, + 96, + 288, + 189 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}_{\\mathrm{base}}" + }, + { + "bbox": [ + 46, + 96, + 288, + 189 + ], + "type": "text", + "content": ", and 2. restrict the new factor of variation (corresponding to " + }, + { + "bbox": [ + 46, + 96, + 288, + 189 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_i" + }, + { + "bbox": [ + 46, + 96, + 288, + 189 + ], + "type": "text", + "content": ") to a single latent direction, " + }, + { + "bbox": [ + 46, + 96, + 288, + 189 + ], + "type": "inline_equation", + "content": "v_i" + }, + { + "bbox": [ + 46, + 96, + 288, + 189 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 198, + 255, + 211 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 198, + 255, + 211 + ], + "spans": [ + { + "bbox": [ + 47, + 198, + 255, + 211 + ], + "type": "text", + "content": "3.2. From Domain Adaptation to Expansion" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 216, + 287, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 216, + 287, + 262 + ], + "spans": [ + { + "bbox": [ + 46, + 216, + 287, + 262 + ], + "type": "text", + "content": "Having defined disjoint affine subspaces " + }, + { + "bbox": [ + 46, + 216, + 287, + 262 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}_i" + }, + { + "bbox": [ + 46, + 216, + 287, + 262 + ], + "type": "text", + "content": " of the latent space " + }, + { + "bbox": [ + 46, + 216, + 287, + 262 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}" + }, + { + "bbox": [ + 46, + 216, + 287, + 262 + ], + "type": "text", + "content": " for our new domains " + }, + { + "bbox": [ + 46, + 216, + 287, + 262 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_i" + }, + { + "bbox": [ + 46, + 216, + 287, + 262 + ], + "type": "text", + "content": ", we now describe how we constrain each domain adaptation objective " + }, + { + "bbox": [ + 46, + 216, + 287, + 262 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_i" + }, + { + "bbox": [ + 46, + 216, + 287, + 262 + ], + "type": "text", + "content": " to affect only the corresponding subspace." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 263, + 287, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 263, + 287, + 357 + ], + "spans": [ + { + "bbox": [ + 46, + 263, + 287, + 357 + ], + "type": "text", + "content": "The domain adaptation objective is applied to images generated from latent codes " + }, + { + "bbox": [ + 46, + 263, + 287, + 357 + ], + "type": "inline_equation", + "content": "z \\in \\mathcal{Z}" + }, + { + "bbox": [ + 46, + 263, + 287, + 357 + ], + "type": "text", + "content": ", sampled from distribution " + }, + { + "bbox": [ + 46, + 263, + 287, + 357 + ], + "type": "inline_equation", + "content": "p(z)" + }, + { + "bbox": [ + 46, + 263, + 287, + 357 + ], + "type": "text", + "content": " defined on the entire space " + }, + { + "bbox": [ + 46, + 263, + 287, + 357 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}" + }, + { + "bbox": [ + 46, + 263, + 287, + 357 + ], + "type": "text", + "content": ". Commonly the distribution is a Gaussian, or is derived from it [12] but some exceptions exist [21, 43]. Our strategy is to transform this sample distribution into one restricted to the affine subspace " + }, + { + "bbox": [ + 46, + 263, + 287, + 357 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}_i" + }, + { + "bbox": [ + 46, + 263, + 287, + 357 + ], + "type": "text", + "content": ". We do so by projecting the samples from " + }, + { + "bbox": [ + 46, + 263, + 287, + 357 + ], + "type": "inline_equation", + "content": "p(z)" + }, + { + "bbox": [ + 46, + 263, + 287, + 357 + ], + "type": "text", + "content": " onto " + }, + { + "bbox": [ + 46, + 263, + 287, + 357 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}_i" + }, + { + "bbox": [ + 46, + 263, + 287, + 357 + ], + "type": "text", + "content": ", using a standard orthogonal projection operator" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 73, + 366, + 287, + 400 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 73, + 366, + 287, + 400 + ], + "spans": [ + { + "bbox": [ + 73, + 366, + 287, + 400 + ], + "type": "interline_equation", + "content": "\\operatorname {p r o j} _ {\\mathcal {Z} _ {i}} (z) = \\sum_ {j = N + 1} ^ {D} \\left(v _ {j} ^ {\\top} (z - \\bar {z})\\right) v _ {j} + \\bar {z} + s v _ {i}. \\tag {3}", + "image_path": "f8ae56df5064e4bc607c0c51968acd21b4d19a00d3b0dd1d21b41599c8a55bc5.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 411, + 287, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 411, + 287, + 445 + ], + "spans": [ + { + "bbox": [ + 46, + 411, + 287, + 445 + ], + "type": "text", + "content": "Denoting by " + }, + { + "bbox": [ + 46, + 411, + 287, + 445 + ], + "type": "inline_equation", + "content": "p_i" + }, + { + "bbox": [ + 46, + 411, + 287, + 445 + ], + "type": "text", + "content": " the sampling distribution over " + }, + { + "bbox": [ + 46, + 411, + 287, + 445 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}" + }, + { + "bbox": [ + 46, + 411, + 287, + 445 + ], + "type": "text", + "content": " for each of the new domains we seek to adapt, the training loss over all tasks is defined as" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 79, + 454, + 287, + 487 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 79, + 454, + 287, + 487 + ], + "spans": [ + { + "bbox": [ + 79, + 454, + 287, + 487 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {e x p a n d}} = \\sum_ {i = 1} ^ {N} \\mathbb {E} _ {z \\sim p _ {i} (z)} \\mathcal {L} _ {i} \\left(G \\left(\\operatorname {p r o j} _ {\\mathcal {Z} _ {i}} (z)\\right)\\right). \\tag {4}", + "image_path": "be6ad1a40ea44a9fac07332839a21fd46fa70faffe4795b12d9cd887aa3150e5.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 497, + 139, + 510 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 497, + 139, + 510 + ], + "spans": [ + { + "bbox": [ + 47, + 497, + 139, + 510 + ], + "type": "text", + "content": "3.3. Regularization" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 516, + 287, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 516, + 287, + 609 + ], + "spans": [ + { + "bbox": [ + 46, + 516, + 287, + 609 + ], + "type": "text", + "content": "Optimizing " + }, + { + "bbox": [ + 46, + 516, + 287, + 609 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{expand}}" + }, + { + "bbox": [ + 46, + 516, + 287, + 609 + ], + "type": "text", + "content": " lets us learn to generate data from the new domains " + }, + { + "bbox": [ + 46, + 516, + 287, + 609 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_i" + }, + { + "bbox": [ + 46, + 516, + 287, + 609 + ], + "type": "text", + "content": " within a single generator, but unfortunately it leaves the base subspace " + }, + { + "bbox": [ + 46, + 516, + 287, + 609 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}_{\\mathrm{base}}" + }, + { + "bbox": [ + 46, + 516, + 287, + 609 + ], + "type": "text", + "content": " under-constrained and, therefore, does not guarantee it will remain unaltered during training. In practice, we observe that the effect of " + }, + { + "bbox": [ + 46, + 516, + 287, + 609 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_i" + }, + { + "bbox": [ + 46, + 516, + 287, + 609 + ], + "type": "text", + "content": " \"leaks\" outside " + }, + { + "bbox": [ + 46, + 516, + 287, + 609 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}_i" + }, + { + "bbox": [ + 46, + 516, + 287, + 609 + ], + "type": "text", + "content": ", causing catastrophic forgetting [18] in subspace " + }, + { + "bbox": [ + 46, + 516, + 287, + 609 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}_{\\mathrm{base}}" + }, + { + "bbox": [ + 46, + 516, + 287, + 609 + ], + "type": "text", + "content": ", and undesirably affecting other subspaces " + }, + { + "bbox": [ + 46, + 516, + 287, + 609 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}_j" + }, + { + "bbox": [ + 46, + 516, + 287, + 609 + ], + "type": "text", + "content": ". We show an example of this leakage in Fig. 4." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 609, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 609, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 609, + 287, + 713 + ], + "type": "text", + "content": "To prevent this failure mode, we explicitly enforce the preservation of " + }, + { + "bbox": [ + 46, + 609, + 287, + 713 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{src}}" + }, + { + "bbox": [ + 46, + 609, + 287, + 713 + ], + "type": "text", + "content": "'s behavior over the base subspace " + }, + { + "bbox": [ + 46, + 609, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}_{\\mathrm{base}}" + }, + { + "bbox": [ + 46, + 609, + 287, + 713 + ], + "type": "text", + "content": " by regularization. We adopt two successful regularization techniques. First, we keep optimizing the generator with the loss it was originally trained on, " + }, + { + "bbox": [ + 46, + 609, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{src}}" + }, + { + "bbox": [ + 46, + 609, + 287, + 713 + ], + "type": "text", + "content": ", which is known to mitigate forgetting [15]. Second, we apply replay alignment [44], which is a reconstruction loss that compares the output of a frozen copy of the source generator to that produced by our generator. We use a weighted combination of" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 307, + 70, + 545, + 199 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 545, + 199 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 545, + 199 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 545, + 199 + ], + "type": "image", + "image_path": "1c808ecbf299660494cda4f0573c1d23f70ea5c9aa564f685b773829adc50b50.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 208, + 546, + 272 + ], + "lines": [ + { + "bbox": [ + 304, + 208, + 546, + 272 + ], + "spans": [ + { + "bbox": [ + 304, + 208, + 546, + 272 + ], + "type": "text", + "content": "Figure 4. Regularization prevents leakage. Without regularization (top row), new factors of variation \"Sketch\" and \"Funny\" are leaking into the base subspace and the other repurposed subspace. Note, for example, that the image from the base subspace is both a sketch and depicts a smiling dog. Our regularization, described in Eq. (6), solves the issue (bottom row)." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 279, + 440, + 291 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 279, + 440, + 291 + ], + "spans": [ + { + "bbox": [ + 306, + 279, + 440, + 291 + ], + "type": "text", + "content": "an " + }, + { + "bbox": [ + 306, + 279, + 440, + 291 + ], + "type": "inline_equation", + "content": "L_{2}" + }, + { + "bbox": [ + 306, + 279, + 440, + 291 + ], + "type": "text", + "content": " pixel loss and LPIPS [49]:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 296, + 555, + 321 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 296, + 555, + 321 + ], + "spans": [ + { + "bbox": [ + 306, + 296, + 555, + 321 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {r e c o n}} = \\lambda_ {\\text {l p i p s}} \\mathcal {L} _ {\\text {l p i p s}} \\left(G _ {\\text {s r c}} (z), G (z)\\right) + \\lambda_ {L _ {2}} \\| G _ {\\text {s r c}} (z) - G (z) \\| _ {2}, \\tag {5}", + "image_path": "8377eb00dec306230f408220297d91b46a4f1ce6148dc55bd667fdb5aa2bf743.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 327, + 545, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 327, + 545, + 384 + ], + "spans": [ + { + "bbox": [ + 304, + 327, + 545, + 384 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 327, + 545, + 384 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{lpips}} = \\lambda_{L_2} = 10" + }, + { + "bbox": [ + 304, + 327, + 545, + 384 + ], + "type": "text", + "content": " are weighting hyperparameters. Not only does replay alignment preserve the source domain " + }, + { + "bbox": [ + 304, + 327, + 545, + 384 + ], + "type": "inline_equation", + "content": "D_{\\mathrm{src}}" + }, + { + "bbox": [ + 304, + 327, + 545, + 384 + ], + "type": "text", + "content": ", it also has the added benefit of aligning " + }, + { + "bbox": [ + 304, + 327, + 545, + 384 + ], + "type": "inline_equation", + "content": "G^{+}" + }, + { + "bbox": [ + 304, + 327, + 545, + 384 + ], + "type": "text", + "content": " to the source generator " + }, + { + "bbox": [ + 304, + 327, + 545, + 384 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{src}}" + }, + { + "bbox": [ + 304, + 327, + 545, + 384 + ], + "type": "text", + "content": ", in the sense that they will produce similar outputs given the same latent code " + }, + { + "bbox": [ + 304, + 327, + 545, + 384 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 304, + 327, + 545, + 384 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 384, + 545, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 384, + 545, + 443 + ], + "spans": [ + { + "bbox": [ + 304, + 384, + 545, + 443 + ], + "type": "text", + "content": "Crucially, we only regularize the base subspace " + }, + { + "bbox": [ + 304, + 384, + 545, + 443 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}_{\\mathrm{base}}" + }, + { + "bbox": [ + 304, + 384, + 545, + 443 + ], + "type": "text", + "content": ", since the subspaces " + }, + { + "bbox": [ + 304, + 384, + 545, + 443 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}_i" + }, + { + "bbox": [ + 304, + 384, + 545, + 443 + ], + "type": "text", + "content": " should be allowed to change to learn the new behaviors. To this end, we project the latent codes to the base subspace " + }, + { + "bbox": [ + 304, + 384, + 545, + 443 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}_{\\mathrm{base}}" + }, + { + "bbox": [ + 304, + 384, + 545, + 443 + ], + "type": "text", + "content": ", before calculating the regularization terms. Our overall regularization objective is thus:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 332, + 447, + 545, + 468 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 332, + 447, + 545, + 468 + ], + "spans": [ + { + "bbox": [ + 332, + 447, + 545, + 468 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {r e g}} = \\mathbb {E} _ {z \\sim p _ {\\text {s r c}} (z)} \\left[ \\lambda_ {\\text {s r c}} \\mathcal {L} _ {\\text {s r c}} \\left(G \\left(\\operatorname {p r o j} _ {\\mathcal {Z} _ {\\text {b a s e}}} (z)\\right)\\right) + \\right. \\tag {6}", + "image_path": "7e227b3028b84a653aaa30d567df702e37cbec0438295a4646ab72a6b458b3c5.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 416, + 464, + 517, + 478 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 416, + 464, + 517, + 478 + ], + "spans": [ + { + "bbox": [ + 416, + 464, + 517, + 478 + ], + "type": "interline_equation", + "content": "\\left. \\mathcal {L} _ {\\text {r e c o n}} \\left(G \\left(\\operatorname {p r o j} _ {\\mathcal {Z} _ {\\text {b a s e}}} (z)\\right)\\right) \\right],", + "image_path": "682d8728355beeff6d4a182efba403cd9ad9bd0770c8a7ac4be6f17f638aa438.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 483, + 545, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 483, + 545, + 518 + ], + "spans": [ + { + "bbox": [ + 306, + 483, + 545, + 518 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 483, + 545, + 518 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{src}} = 1" + }, + { + "bbox": [ + 306, + 483, + 545, + 518 + ], + "type": "text", + "content": " balances the two terms and " + }, + { + "bbox": [ + 306, + 483, + 545, + 518 + ], + "type": "inline_equation", + "content": "p_{src}(z)" + }, + { + "bbox": [ + 306, + 483, + 545, + 518 + ], + "type": "text", + "content": " is the latent distribution over " + }, + { + "bbox": [ + 306, + 483, + 545, + 518 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}" + }, + { + "bbox": [ + 306, + 483, + 545, + 518 + ], + "type": "text", + "content": " used to train " + }, + { + "bbox": [ + 306, + 483, + 545, + 518 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{src}}" + }, + { + "bbox": [ + 306, + 483, + 545, + 518 + ], + "type": "text", + "content": ". Our final, regularized domain expansion objective is, therefore:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 380, + 524, + 545, + 537 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 380, + 524, + 545, + 537 + ], + "spans": [ + { + "bbox": [ + 380, + 524, + 545, + 537 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {f u l l}} = \\mathcal {L} _ {\\text {e x p a n d}} + \\mathcal {L} _ {\\text {r e g}}. \\tag {7}", + "image_path": "5e5b846fb156ed3424e8bfed6862e28c12247cf4439502e2eb287e24770dfebc.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 544, + 387, + 556 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 544, + 387, + 556 + ], + "spans": [ + { + "bbox": [ + 306, + 544, + 387, + 556 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 563, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 563, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 563, + 545, + 689 + ], + "type": "text", + "content": "We evaluate our method and analyze its key characteristics. Sec. 4.1 first details the experimental setting, focusing on StyleGAN. We start by analyzing the knowledge encoded along repurposed directions and compare it to domain adaptation methods (Sec. 4.2). We then delve deeper and evaluate the effects (Sec. 4.3) and opportunities (Sec. 4.4) presented by expanding a generator to multiple domains simultaneously. Next, we demonstrate that the quality of the source domain is maintained in the base subspace (Sec. 4.5). Finally, we demonstrate that our method generalizes to other generators (Sec. 4.6)." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 305, + 690, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 690, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 690, + 545, + 713 + ], + "type": "text", + "content": "Further experiments, results, and details are provided in the supplementary." + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15936" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 170, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 170, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 170, + 85 + ], + "type": "text", + "content": "4.1. Experimental Setting" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 90, + 287, + 137 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 90, + 287, + 137 + ], + "spans": [ + { + "bbox": [ + 46, + 90, + 287, + 137 + ], + "type": "text", + "content": "We adopt StyleGAN2 [13] as the main generator architecture, for its disentangled latent space and because it has been the dominant test bed for generative domain adaptation methods in recent years [1,5,21,22,43,51]." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 147, + 288, + 286 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 147, + 288, + 286 + ], + "spans": [ + { + "bbox": [ + 46, + 147, + 288, + 286 + ], + "type": "text", + "content": "Latent space and subspaces. Several latent spaces have been considered in the context of StyleGAN. We use the intermediate latent space " + }, + { + "bbox": [ + 46, + 147, + 288, + 286 + ], + "type": "inline_equation", + "content": "\\mathcal{W}" + }, + { + "bbox": [ + 46, + 147, + 288, + 286 + ], + "type": "text", + "content": " in all our experiments but note it as " + }, + { + "bbox": [ + 46, + 147, + 288, + 286 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}" + }, + { + "bbox": [ + 46, + 147, + 288, + 286 + ], + "type": "text", + "content": " for consistency. We use SeFA [36] for the orthogonal decomposition of " + }, + { + "bbox": [ + 46, + 147, + 288, + 286 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}" + }, + { + "bbox": [ + 46, + 147, + 288, + 286 + ], + "type": "text", + "content": ". As SeFA performs SVD, there is a native indication to how dormant is a given latent direction – the corresponding singular value. As singular values are commonly sorted in decreasing orders, the last basis vectors are most dormant. When expanding with " + }, + { + "bbox": [ + 46, + 147, + 288, + 286 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 147, + 288, + 286 + ], + "type": "text", + "content": " new domains, unless specified otherwise, we repurpose the last " + }, + { + "bbox": [ + 46, + 147, + 288, + 286 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 147, + 288, + 286 + ], + "type": "text", + "content": " basis vectors. We use " + }, + { + "bbox": [ + 46, + 147, + 288, + 286 + ], + "type": "inline_equation", + "content": "s = 20" + }, + { + "bbox": [ + 46, + 147, + 288, + 286 + ], + "type": "text", + "content": " in all experiments. These decisions are evaluated in greater depth in Appendices C.2 and C.4." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 297, + 287, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 297, + 287, + 354 + ], + "spans": [ + { + "bbox": [ + 46, + 297, + 287, + 354 + ], + "type": "text", + "content": "Adaptation methods. We demonstrate our expansion method with two domain adaptation tasks - StyleGAN-NADA [5] and MyStyle [21]. These two tasks were chosen as they differ significantly in key aspects - source of supervision, sampling distribution and loss." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 355, + 287, + 414 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 355, + 287, + 414 + ], + "spans": [ + { + "bbox": [ + 46, + 355, + 287, + 414 + ], + "type": "text", + "content": "StyleGAN-NADA is a zero-shot, text-guided, domain adaptation method. It takes as input a pair of text prompts, " + }, + { + "bbox": [ + 46, + 355, + 287, + 414 + ], + "type": "inline_equation", + "content": "t_{\\mathrm{source}}" + }, + { + "bbox": [ + 46, + 355, + 287, + 414 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 355, + 287, + 414 + ], + "type": "inline_equation", + "content": "t_{\\mathrm{target}}" + }, + { + "bbox": [ + 46, + 355, + 287, + 414 + ], + "type": "text", + "content": ", describing the desired transformation source " + }, + { + "bbox": [ + 46, + 355, + 287, + 414 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 46, + 355, + 287, + 414 + ], + "type": "text", + "content": " target to be applied on the domain of the pretrained generator, " + }, + { + "bbox": [ + 46, + 355, + 287, + 414 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{src}}" + }, + { + "bbox": [ + 46, + 355, + 287, + 414 + ], + "type": "text", + "content": ". The loss function " + }, + { + "bbox": [ + 46, + 355, + 287, + 414 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 46, + 355, + 287, + 414 + ], + "type": "text", + "content": " is given by" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 97, + 422, + 236, + 436 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 422, + 236, + 436 + ], + "spans": [ + { + "bbox": [ + 97, + 422, + 236, + 436 + ], + "type": "interline_equation", + "content": "\\Delta T = E _ {T} \\left(t _ {\\text {t a r g e t}}\\right) - E _ {T} \\left(t _ {\\text {s o u r c e}}\\right),", + "image_path": "bb66e9b455811f35b561bd0d85d0c88c65305bbedb0a9c31eaa4f2394e0c529e.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 96, + 437, + 287, + 456 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 437, + 287, + 456 + ], + "spans": [ + { + "bbox": [ + 96, + 437, + 287, + 456 + ], + "type": "interline_equation", + "content": "\\Delta I = E _ {I} (G (z)) - E _ {I} \\left(G _ {\\text {s r c}} (z)\\right), \\tag {8}", + "image_path": "9d0392663512e03f27ec7b2d61f70f4da01107206dedfedd20fc08f3f5ec5bc7.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 123, + 452, + 211, + 479 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 452, + 211, + 479 + ], + "spans": [ + { + "bbox": [ + 123, + 452, + 211, + 479 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = 1 - \\frac {\\Delta I \\cdot \\Delta T}{| \\Delta I | | \\Delta T |},", + "image_path": "0309dc42b7839a07f8cdc9b8f78f085d47d9577ad8ce59151f05eef972c13c81.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 487, + 287, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 487, + 287, + 510 + ], + "spans": [ + { + "bbox": [ + 47, + 487, + 287, + 510 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 487, + 287, + 510 + ], + "type": "inline_equation", + "content": "E_{I}" + }, + { + "bbox": [ + 47, + 487, + 287, + 510 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 487, + 287, + 510 + ], + "type": "inline_equation", + "content": "E_{T}" + }, + { + "bbox": [ + 47, + 487, + 287, + 510 + ], + "type": "text", + "content": " are CLIP's [29] image and text encoders respectively." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 511, + 287, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 511, + 287, + 593 + ], + "spans": [ + { + "bbox": [ + 47, + 511, + 287, + 593 + ], + "type": "text", + "content": "MyStyle is a few-shot, image-supervised, domain adaptation method. As input, it takes a set of images " + }, + { + "bbox": [ + 47, + 511, + 287, + 593 + ], + "type": "inline_equation", + "content": "\\{x_{m}\\}_{m = 1}^{M}" + }, + { + "bbox": [ + 47, + 511, + 287, + 593 + ], + "type": "text", + "content": " of an individual " + }, + { + "bbox": [ + 47, + 511, + 287, + 593 + ], + "type": "inline_equation", + "content": "(M\\sim 100)" + }, + { + "bbox": [ + 47, + 511, + 287, + 593 + ], + "type": "text", + "content": ", and adapts " + }, + { + "bbox": [ + 47, + 511, + 287, + 593 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{src}}" + }, + { + "bbox": [ + 47, + 511, + 287, + 593 + ], + "type": "text", + "content": " to form a personalized prior for that individual. The generator is trained to better reconstruct " + }, + { + "bbox": [ + 47, + 511, + 287, + 593 + ], + "type": "inline_equation", + "content": "x_{m}" + }, + { + "bbox": [ + 47, + 511, + 287, + 593 + ], + "type": "text", + "content": " from their original latent space inversions " + }, + { + "bbox": [ + 47, + 511, + 287, + 593 + ], + "type": "inline_equation", + "content": "z_{m}\\in \\mathcal{Z}" + }, + { + "bbox": [ + 47, + 511, + 287, + 593 + ], + "type": "text", + "content": " [38]. Formally, the loss function is given by" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 58, + 602, + 287, + 635 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 602, + 287, + 635 + ], + "spans": [ + { + "bbox": [ + 58, + 602, + 287, + 635 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\sum_ {m = 1} ^ {M} \\left[ \\mathcal {L} _ {\\mathrm {l p i p s}} \\left(G \\left(z _ {m}\\right), x _ {m}\\right) + \\| G \\left(z _ {m}\\right) - x _ {m} \\| _ {2} \\right], \\tag {9}", + "image_path": "5f8d30127469c316e4c4f729882250aa055b841a6b8ccdc096e18ce4c20358dd.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 644, + 214, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 644, + 214, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 644, + 214, + 658 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 644, + 214, + 658 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{lpips}}" + }, + { + "bbox": [ + 47, + 644, + 214, + 658 + ], + "type": "text", + "content": " is again the LPIPS loss [49]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 666, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 666, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 666, + 287, + 713 + ], + "type": "text", + "content": "Datasets and models. We demonstrate our method on four datasets – FFHQ [12], AFHQ Dog [4], LSUN Church [48] and SD-Elephant [20]. The FFHQ model is expanded with 105 new domains, 100 introduced with the expanded" + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 307, + 69, + 545, + 196 + ], + "blocks": [ + { + "bbox": [ + 307, + 69, + 545, + 196 + ], + "lines": [ + { + "bbox": [ + 307, + 69, + 545, + 196 + ], + "spans": [ + { + "bbox": [ + 307, + 69, + 545, + 196 + ], + "type": "image", + "image_path": "d85f841acc12bdc14200dea4c49e25e5cbd78e83c3bc5fb75aaa6f7ae664b435.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 205, + 547, + 281 + ], + "lines": [ + { + "bbox": [ + 304, + 205, + 547, + 281 + ], + "spans": [ + { + "bbox": [ + 304, + 205, + 547, + 281 + ], + "type": "text", + "content": "Figure 5. Continuous traversal along repurposed directions. As can be seen, the traversal between the base subspace " + }, + { + "bbox": [ + 304, + 205, + 547, + 281 + ], + "type": "inline_equation", + "content": "(\\alpha = 0)" + }, + { + "bbox": [ + 304, + 205, + 547, + 281 + ], + "type": "text", + "content": " and repurposed subspace " + }, + { + "bbox": [ + 304, + 205, + 547, + 281 + ], + "type": "inline_equation", + "content": "(\\alpha = s)" + }, + { + "bbox": [ + 304, + 205, + 547, + 281 + ], + "type": "text", + "content": " portrays a smooth transition between the source and newly introduced domains. Advantageously, the semantic meaning of the repurposed direction is preserved in the extrapolation, representing the opposite relationship between the domains " + }, + { + "bbox": [ + 304, + 205, + 547, + 281 + ], + "type": "inline_equation", + "content": "(\\alpha < 0)" + }, + { + "bbox": [ + 304, + 205, + 547, + 281 + ], + "type": "text", + "content": " or exaggerations of it " + }, + { + "bbox": [ + 304, + 205, + 547, + 281 + ], + "type": "inline_equation", + "content": "(\\alpha > s)" + }, + { + "bbox": [ + 304, + 205, + 547, + 281 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "table", + "bbox": [ + 306, + 293, + 554, + 369 + ], + "blocks": [ + { + "bbox": [ + 306, + 293, + 554, + 369 + ], + "lines": [ + { + "bbox": [ + 306, + 293, + 554, + 369 + ], + "spans": [ + { + "bbox": [ + 306, + 293, + 554, + 369 + ], + "type": "table", + "html": "
MethodUser % (↑)ID (↑)Diversity×10 (↑)
StyleGAN-NADA41.2%-2.42 ± 0.13
Ours w/ NADA58.8%-2.42 ± 0.13
MyStyle-0.80 ± 0.063.08 ± 0.15
Ours w/ MyStyle-0.76 ± 0.053.14 ± 0.14
", + "image_path": "2b0694848647996008daf23dd40abcf6cc61e1f1e7884053dda9e6ccc14be24b.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_body" + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 376, + 546, + 419 + ], + "lines": [ + { + "bbox": [ + 304, + 376, + 546, + 419 + ], + "spans": [ + { + "bbox": [ + 304, + 376, + 546, + 419 + ], + "type": "text", + "content": "Table 1. Quantitative comparison of images generated from our repurposed subspaces to those generated by corresponding domain adaptation methods - StyleGAN-NADA [5] and MyStyle [21]. We follow each adaptation method's quantitative evaluation protocol." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 441, + 545, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 441, + 545, + 499 + ], + "spans": [ + { + "bbox": [ + 304, + 441, + 545, + 499 + ], + "type": "text", + "content": "variant of StyleGAN-NADA and 5 from the expanded variant of MyStyle. The AFHQ Dog, LSUN Chruch and SD-Elephant are expanded with 50, 20, and 20 new domains correspondingly, all introduced from the expanded variant of StyleGAN-NADA." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 508, + 484, + 521 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 508, + 484, + 521 + ], + "spans": [ + { + "bbox": [ + 306, + 508, + 484, + 521 + ], + "type": "text", + "content": "4.2. Evaluating Domains Individually" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 528, + 545, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 528, + 545, + 632 + ], + "spans": [ + { + "bbox": [ + 304, + 528, + 545, + 632 + ], + "type": "text", + "content": "Traversing a repurposed direction. We start by investigating what knowledge, if any, is encoded along the repurposed latent directions. To this end, starting from a random latent code " + }, + { + "bbox": [ + 304, + 528, + 545, + 632 + ], + "type": "inline_equation", + "content": "z \\in \\mathcal{Z}_{\\mathrm{base}}" + }, + { + "bbox": [ + 304, + 528, + 545, + 632 + ], + "type": "text", + "content": ", we individually traverse different repurposed directions, " + }, + { + "bbox": [ + 304, + 528, + 545, + 632 + ], + "type": "inline_equation", + "content": "v_{i}" + }, + { + "bbox": [ + 304, + 528, + 545, + 632 + ], + "type": "text", + "content": ", and inspect the generated images " + }, + { + "bbox": [ + 304, + 528, + 545, + 632 + ], + "type": "inline_equation", + "content": "G^{+}(z + \\alpha v_{i})" + }, + { + "bbox": [ + 304, + 528, + 545, + 632 + ], + "type": "text", + "content": ". Sample results from our dogs, elephants, and faces models are displayed in Fig. 5. We find that each individual repurposed direction now successfully encodes the desired factor of variation, in a global and continuous way." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 632, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 632, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 632, + 545, + 713 + ], + "type": "text", + "content": "Our training paradigm is inherently discrete - encouraging the source behavior on the base subspace " + }, + { + "bbox": [ + 304, + 632, + 545, + 713 + ], + "type": "inline_equation", + "content": "(\\alpha = 0)" + }, + { + "bbox": [ + 304, + 632, + 545, + 713 + ], + "type": "text", + "content": " and the newly introduced effect on the repurposed space " + }, + { + "bbox": [ + 304, + 632, + 545, + 713 + ], + "type": "inline_equation", + "content": "(\\alpha = s)" + }, + { + "bbox": [ + 304, + 632, + 545, + 713 + ], + "type": "text", + "content": ". Therefore, obtaining a smooth effect might seem surprising at first glance. Nevertheless, this phenomenon can be clearly traced to the well-established observation that generators are smooth with respect to their latent space [12]." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15937" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 70, + 289, + 194 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 289, + 194 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 289, + 194 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 289, + 194 + ], + "type": "image", + "image_path": "c4720fe2e45e053e88db0aeff3f97a9f60f795ced839a447bf938bf759e76b52.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 201, + 287, + 243 + ], + "lines": [ + { + "bbox": [ + 46, + 201, + 287, + 243 + ], + "spans": [ + { + "bbox": [ + 46, + 201, + 287, + 243 + ], + "type": "text", + "content": "Figure 6. A random set of images generated by our generator from repurposed subspaces (bottom) and by corresponding domain adaptation methods (top). The images are similar and differences are subtle." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 254, + 287, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 254, + 287, + 312 + ], + "spans": [ + { + "bbox": [ + 46, + 254, + 287, + 312 + ], + "type": "text", + "content": "Behavior on the repurposed subspace. We have transformed adaptation tasks into expansion tasks by limiting the training effect to the repurposed subspaces only. But, for latents in repurposed subspaces " + }, + { + "bbox": [ + 46, + 254, + 287, + 312 + ], + "type": "inline_equation", + "content": "(\\alpha = s)" + }, + { + "bbox": [ + 46, + 254, + 287, + 312 + ], + "type": "text", + "content": ", the domain adaptation could be considered to have been applied as-is." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 312, + 287, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 312, + 287, + 532 + ], + "spans": [ + { + "bbox": [ + 46, + 312, + 287, + 532 + ], + "type": "text", + "content": "We next directly compare the images generated by our generator from the repurposed subspace to the corresponding images generated by the domain-adapted generator. We inherit and repeat the quantitative evaluation protocols performed by each of the adaption tasks. To compare quality with StyleGAN-NADA [5] we perform a two-alternative forced choice user study. Users were asked to pick the image that has higher-quality and better aligns with the target text used for training. We gathered 1440 responses from 32 unique users. To compare quality with MyStyle [21], we evaluate preservation of identity in generated images, as observed by a face recognition network [9]. For both methods, the diversity is compared based on intra-cluster LPIPS [49] distance, first suggested by Ojha et al. [22]. We use 10 domains for comparison with StyleGAN-NADA and 5 for comparison with MyStyle. Note that we use a single generator " + }, + { + "bbox": [ + 46, + 312, + 287, + 532 + ], + "type": "inline_equation", + "content": "G^{+}" + }, + { + "bbox": [ + 46, + 312, + 287, + 532 + ], + "type": "text", + "content": ", expanded with 105 domains, while competing methods use a dedicated model per domain, 15, overall. We report the results in Tab. 1 and Fig. 6." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 533, + 287, + 603 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 287, + 603 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 287, + 603 + ], + "type": "text", + "content": "As can be seen, on the repurposed subspaces, our method produces comparable images to that generated by the dedicated, domain-adapted generator. Perhaps surprisingly, users somewhat prefer our results over StyleGAN-NADA's. We speculate this is due to the significantly greater difficulty of choosing hyperparameters for their training." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 613, + 226, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 613, + 226, + 624 + ], + "spans": [ + { + "bbox": [ + 47, + 613, + 226, + 624 + ], + "type": "text", + "content": "4.3. Effect of Domains on Each Other" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 632, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 632, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 632, + 287, + 713 + ], + "type": "text", + "content": "Previous evaluation of individual repurposed directions already indicates disentanglement between different factors of variation. For example, \"Barbie\" images in Fig. 6 show no sign of being caricature, Barack Obama, or any of the other hundred factors of variation introduced to that generator. In this section, we delve deeper into evaluating the effects of expanding with multiple factors of variation." + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 307, + 69, + 545, + 178 + ], + "blocks": [ + { + "bbox": [ + 307, + 69, + 545, + 178 + ], + "lines": [ + { + "bbox": [ + 307, + 69, + 545, + 178 + ], + "spans": [ + { + "bbox": [ + 307, + 69, + 545, + 178 + ], + "type": "image", + "image_path": "3fd8760e5a9c24df1207a64948e8060994175e88673d3fe42cc70e0cdb54f16e.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 307, + 182, + 545, + 250 + ], + "blocks": [ + { + "bbox": [ + 307, + 182, + 545, + 250 + ], + "lines": [ + { + "bbox": [ + 307, + 182, + 545, + 250 + ], + "spans": [ + { + "bbox": [ + 307, + 182, + 545, + 250 + ], + "type": "image", + "image_path": "af8beeadb270f008bb6e53293e5c8a35ad2f9ed04a66fd2d01d303df75f4dddc.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 258, + 545, + 354 + ], + "lines": [ + { + "bbox": [ + 304, + 258, + 545, + 354 + ], + "spans": [ + { + "bbox": [ + 304, + 258, + 545, + 354 + ], + "type": "text", + "content": "Figure 7. Investigating the effect of introducing multiple domains simultaneously. (a) Reports the CLIP error of generated images with the text \"a sketch\", as a function of training iterations. Images are generated from the \"Sketch\" and \"Sumo\" subspaces of models trained with a different number of domains. (b) Depicts generated images from models that have similar CLIP errors. As can be seen, the sketch domain does not \"leak\" into the sumo subspace. Additionally, introducing additional domains delays, but does not prevent, the introduction of sketch." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 374, + 546, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 374, + 546, + 525 + ], + "spans": [ + { + "bbox": [ + 304, + 374, + 546, + 525 + ], + "type": "text", + "content": "To this end, we train three models to expand the FFHQ parent model with either 1, 5 or 50 new domains, all induced by StyleGAN-NADA [5]. All models are expanded with \"Sketch\", and the latter two with \"Sumo\" as well as other factors of variation. We quantify the strength of introduced factor of variation using CLIP error, the 1-complement of the score produced by CLIP [29]. We use the top-performing version of the CLIP encoder available, ViT-L/14, which is not used during training. We note that simply minimizing CLIP error is not the objective, as it might lead to favoring mode-collapsed and adversarial examples [5]. Nevertheless, together with qualitative inspection, it is useful for comparing different models." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 528, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 528, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 528, + 547, + 713 + ], + "type": "text", + "content": "In Fig. 7a, we report the CLIP error of generated images with the text \"a sketch\", as a function of the training iterations. Images are generated from the \"Sketch\", and if exists, \"Sumo\" subspace. First, we observe that CLIP error is decreasing for \"Sketch\" subspaces in all models, as expected. Conversely, CLIP error in the \"Sumo\" subspace does not significantly change, indicating it is not becoming any more or less of a sketch. This result quantitatively supports our previous finding, that factors of variations do not interfere with each other, and demonstrates it is true regardless of the number of other factors of variations learned simultaneously. Additionally, we observe that expanding with additional factors of variation delays, but does not prevent, " + }, + { + "bbox": [ + 304, + 528, + 547, + 713 + ], + "type": "inline_equation", + "content": "G^{+}" + }, + { + "bbox": [ + 304, + 528, + 547, + 713 + ], + "type": "text", + "content": " the introduction of \"Sketch\" effectively. The observed delay is expected, as expanding with more variations corresponds to " + }, + { + "bbox": [ + 304, + 528, + 547, + 713 + ], + "type": "inline_equation", + "content": "G^{+}" + }, + { + "bbox": [ + 304, + 528, + 547, + 713 + ], + "type": "text", + "content": " optimizing and balancing additional loss functions." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15938" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 70, + 216, + 231 + ], + "blocks": [ + { + "bbox": [ + 56, + 70, + 216, + 231 + ], + "lines": [ + { + "bbox": [ + 56, + 70, + 216, + 231 + ], + "spans": [ + { + "bbox": [ + 56, + 70, + 216, + 231 + ], + "type": "image", + "image_path": "fd30c13017487f157b3646735b28d81d6f044895d415591c53df806eea1bb67f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 239, + 547, + 295 + ], + "lines": [ + { + "bbox": [ + 46, + 239, + 547, + 295 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 547, + 295 + ], + "type": "text", + "content": "Figure 8. Composing multiple effects by simple latent traversal. In each grid, we start from the latent code that generates the top-left image and traverse along two latent directions, represented by advancement in rows and columns. For each direction, we note the associated domain, its ordinal number in the latent space's basis, and the training method used (\"NADA\" or \"MyStyle\") to learn the domain. As can be seen, " + }, + { + "bbox": [ + 46, + 239, + 547, + 295 + ], + "type": "inline_equation", + "content": "G^{+}" + }, + { + "bbox": [ + 46, + 239, + 547, + 295 + ], + "type": "text", + "content": " has learned a disentangled representation, allowing meaningful composition of concepts. Specifically, note the disentanglement between directions, as traversing left-right does not affect the magnitude of the effect corresponding to up-down traversal, and vice versa." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 216, + 70, + 376, + 230 + ], + "blocks": [ + { + "bbox": [ + 216, + 70, + 376, + 230 + ], + "lines": [ + { + "bbox": [ + 216, + 70, + 376, + 230 + ], + "spans": [ + { + "bbox": [ + 216, + 70, + 376, + 230 + ], + "type": "image", + "image_path": "5fa012a44e98a27b784b56e900cc73407958cbaa77037421ea19b3f35e108584.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 378, + 70, + 539, + 230 + ], + "blocks": [ + { + "bbox": [ + 378, + 70, + 539, + 230 + ], + "lines": [ + { + "bbox": [ + 378, + 70, + 539, + 230 + ], + "spans": [ + { + "bbox": [ + 378, + 70, + 539, + 230 + ], + "type": "image", + "image_path": "12896c4e85efcbea1a411672291fe10e255df058128f9fd8f5a6704439e21213.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 308, + 288, + 333 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 308, + 288, + 333 + ], + "spans": [ + { + "bbox": [ + 46, + 308, + 288, + 333 + ], + "type": "text", + "content": "Generated samples from the sketch and sumo subspaces are provided in Fig. 7b." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 339, + 150, + 352 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 339, + 150, + 352 + ], + "spans": [ + { + "bbox": [ + 47, + 339, + 150, + 352 + ], + "type": "text", + "content": "4.4. Compositionality" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 357, + 287, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 357, + 287, + 462 + ], + "spans": [ + { + "bbox": [ + 46, + 357, + 287, + 462 + ], + "type": "text", + "content": "While accidental \"leakage\" between latent directions during training is undesired, intentionally composing variations at test time is useful. For generative models with a disentangled latent space, summing together latent directions aggregates their semantic meaning, and should not affect the magnitude of their effects if applied separately. For example, if direction " + }, + { + "bbox": [ + 46, + 357, + 287, + 462 + ], + "type": "inline_equation", + "content": "v_{1}" + }, + { + "bbox": [ + 46, + 357, + 287, + 462 + ], + "type": "text", + "content": " controls head pose and direction " + }, + { + "bbox": [ + 46, + 357, + 287, + 462 + ], + "type": "inline_equation", + "content": "v_{2}" + }, + { + "bbox": [ + 46, + 357, + 287, + 462 + ], + "type": "text", + "content": " controls an unrelated variation, images " + }, + { + "bbox": [ + 46, + 357, + 287, + 462 + ], + "type": "inline_equation", + "content": "G(z + v_{1} + v_{2})" + }, + { + "bbox": [ + 46, + 357, + 287, + 462 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 357, + 287, + 462 + ], + "type": "inline_equation", + "content": "G(z + v_{1})" + }, + { + "bbox": [ + 46, + 357, + 287, + 462 + ], + "type": "text", + "content": " should depict the same head pose." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 462, + 288, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 462, + 288, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 462, + 288, + 544 + ], + "type": "text", + "content": "We find that the latent space of the expanded generator " + }, + { + "bbox": [ + 46, + 462, + 288, + 544 + ], + "type": "inline_equation", + "content": "G^{+}" + }, + { + "bbox": [ + 46, + 462, + 288, + 544 + ], + "type": "text", + "content": " is disentangled, and variations can indeed be composed effectively. Crucially, variations can be composed with each other regardless of their originating training task, including those on the base subspace, learned from the source domain. Fig. 8 shows a sample of gradual composition results across models and training tasks." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 552, + 287, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 552, + 287, + 666 + ], + "spans": [ + { + "bbox": [ + 46, + 552, + 287, + 666 + ], + "type": "text", + "content": "Comparison to existing techniques. Several domain adaptation methods have proposed techniques to combine multiple variations. These methods still train a separate generative model per variation, but combine their effects in test-time. Specifically, in the realm of CLIP-supervised training, StyleGAN-NADA [5] interpolates the generators' weights, while DiffusionCLIP [14] interpolates intermediate activations of the generators. Next, we compare the disentanglement of composition in our generator to that made possible using these techniques." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 667, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 667, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 667, + 288, + 715 + ], + "type": "text", + "content": "For each method, we start with a setting that was optimized to generate images that align with one of two text prompts. In our case, this setting is " + }, + { + "bbox": [ + 46, + 667, + 288, + 715 + ], + "type": "inline_equation", + "content": "G^{+}" + }, + { + "bbox": [ + 46, + 667, + 288, + 715 + ], + "type": "text", + "content": " with latent codes in certain subspaces. For the baselines, these settings are" + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 306, + 306, + 547, + 380 + ], + "blocks": [ + { + "bbox": [ + 306, + 306, + 547, + 380 + ], + "lines": [ + { + "bbox": [ + 306, + 306, + 547, + 380 + ], + "spans": [ + { + "bbox": [ + 306, + 306, + 547, + 380 + ], + "type": "table", + "html": "
ModelFFHQAFHQLSUN ChurchSD Elephant
Parent2.777.433.922.30
Ours2.807.513.762.70
Only Lsrc2.75±0.087.38±0.093.31±0.223.91±0.67
", + "image_path": "a28625c2566eafd191c5df033f6f2b451c81104f9bd63eee98f901bf02f276f6.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 387, + 547, + 495 + ], + "lines": [ + { + "bbox": [ + 304, + 387, + 547, + 495 + ], + "spans": [ + { + "bbox": [ + 304, + 387, + 547, + 495 + ], + "type": "text", + "content": "Table 2. We generate images from the base subspace and report FID [7] " + }, + { + "bbox": [ + 304, + 387, + 547, + 495 + ], + "type": "inline_equation", + "content": "(\\downarrow)" + }, + { + "bbox": [ + 304, + 387, + 547, + 495 + ], + "type": "text", + "content": " with respect to source domain dataset. We compare our FID to that of the source generator " + }, + { + "bbox": [ + 304, + 387, + 547, + 495 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{src}}" + }, + { + "bbox": [ + 304, + 387, + 547, + 495 + ], + "type": "text", + "content": ". For reference, we also continue training the source generator for the same number of iterations with its original loss - " + }, + { + "bbox": [ + 304, + 387, + 547, + 495 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{src}}" + }, + { + "bbox": [ + 304, + 387, + 547, + 495 + ], + "type": "text", + "content": ", and report the mean and standard deviations of FID along the training. As can be seen, on the base subspace, our models have comparable FID scores to their parents. Furthermore, similar magnitude of change in FID are observed by simply continuing training, indicating that the change in FID might be, at least in part, due to \"random\" fluctuations." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 514, + 547, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 514, + 547, + 666 + ], + "spans": [ + { + "bbox": [ + 304, + 514, + 547, + 666 + ], + "type": "text", + "content": "dedicated generators with any latent code. Then, for each method, we gradually introduce the variation described by the other text prompt and generate the corresponding images. Finally, we measure normalized CLIP error between generated images and the two prompts. We normalize all errors by the error of the initial setting, to make the metric comparable across methods and text prompts. Fig. 9 reports the mean and standard deviation of the CLIP error, on 10 pairs of prompts, and provides a sample of qualitative results. As can be seen, both baseline methods directly trade-off one domain for the other, expressed by a linear-looking trend. Conversely, our method obtains significantly lower errors and allows for a true composition of concepts." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 672, + 493, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 672, + 493, + 684 + ], + "spans": [ + { + "bbox": [ + 306, + 672, + 493, + 684 + ], + "type": "text", + "content": "4.5. Preservation of the Source Domain" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 689, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 547, + 715 + ], + "type": "text", + "content": "We next evaluate the preservation of the source domain in " + }, + { + "bbox": [ + 305, + 689, + 547, + 715 + ], + "type": "inline_equation", + "content": "G^{+}" + }, + { + "bbox": [ + 305, + 689, + 547, + 715 + ], + "type": "text", + "content": ". To this end, using FID [7], we compare the quality" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "15939" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 63, + 287, + 220 + ], + "blocks": [ + { + "bbox": [ + 53, + 63, + 287, + 220 + ], + "lines": [ + { + "bbox": [ + 53, + 63, + 287, + 220 + ], + "spans": [ + { + "bbox": [ + 53, + 63, + 287, + 220 + ], + "type": "image", + "image_path": "2cba78b02d03b4a219dc751dc72c8469a503207f547a8a347e698aa6c116105d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 162, + 223, + 172, + 232 + ], + "lines": [ + { + "bbox": [ + 162, + 223, + 172, + 232 + ], + "spans": [ + { + "bbox": [ + 162, + 223, + 172, + 232 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 47, + 236, + 287, + 361 + ], + "blocks": [ + { + "bbox": [ + 47, + 236, + 287, + 361 + ], + "lines": [ + { + "bbox": [ + 47, + 236, + 287, + 361 + ], + "spans": [ + { + "bbox": [ + 47, + 236, + 287, + 361 + ], + "type": "image", + "image_path": "8cb69aa8c7aa40d6832967c4ac9405948d1964c2d2f79afacfa34559cb58bb6f.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 162, + 362, + 173, + 372 + ], + "lines": [ + { + "bbox": [ + 162, + 362, + 173, + 372 + ], + "spans": [ + { + "bbox": [ + 162, + 362, + 173, + 372 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 376, + 289, + 515 + ], + "lines": [ + { + "bbox": [ + 46, + 376, + 289, + 515 + ], + "spans": [ + { + "bbox": [ + 46, + 376, + 289, + 515 + ], + "type": "text", + "content": "Figure 9. Comparing compositionality in our generator to methods of combining multiple domains proposed by StyleGAN-NADA [5] and DiffusionCLIP [14]. Starting from a setting optimized for either text prompt #1 or #2, we gradually introduce the variation described by the other text. (a) Reports the CLIP error to both prompts along the gradual introduction, normalized to the error obtained for each text prompt in isolation. (b) Portrays a sample of qualitative results, where the composition is such that assigns equal strengths to both effects. As can be seen in, both quantitatively and qualitatively, NADA and DiffusionCLIP directly trade-off one effect for the other - strengthening the effect of one prompt directly lessens that of the other. In contrast, our generator allows true composition of modalities." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 551, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 551, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 551, + 289, + 715 + ], + "type": "text", + "content": "of images generated from the base subspace " + }, + { + "bbox": [ + 46, + 551, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}_{\\mathrm{base}}" + }, + { + "bbox": [ + 46, + 551, + 289, + 715 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 46, + 551, + 289, + 715 + ], + "type": "inline_equation", + "content": "G^{+}" + }, + { + "bbox": [ + 46, + 551, + 289, + 715 + ], + "type": "text", + "content": " to those generated by the source generator " + }, + { + "bbox": [ + 46, + 551, + 289, + 715 + ], + "type": "inline_equation", + "content": "G_{src}" + }, + { + "bbox": [ + 46, + 551, + 289, + 715 + ], + "type": "text", + "content": ". Since the generator is being trained, some change in FID is expected. Therefore, we also report the average and standard deviation over FID scores for a generator that simply continues training, i.e., using only the original loss " + }, + { + "bbox": [ + 46, + 551, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{src}}" + }, + { + "bbox": [ + 46, + 551, + 289, + 715 + ], + "type": "text", + "content": ". Results are reported in Tab. 2 and vary between datasets. Across all datasets, we observe that the FID from our base subspace is within " + }, + { + "bbox": [ + 46, + 551, + 289, + 715 + ], + "type": "inline_equation", + "content": "1\\sigma" + }, + { + "bbox": [ + 46, + 551, + 289, + 715 + ], + "type": "text", + "content": " of the that obtained from either the parent or a generator that continues training. For reference, generator's adapted with StyleGAN-NADA and MyStyle have an average FID of 125 and 183, respectively. We conclude that the expansion method might have a slight impact on FID, but it is negligible." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 72, + 486, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 486, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 486, + 85 + ], + "type": "text", + "content": "4.6. Generalization Beyond StyleGAN" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 91, + 547, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 91, + 547, + 198 + ], + "spans": [ + { + "bbox": [ + 304, + 91, + 547, + 198 + ], + "type": "text", + "content": "We finally demonstrate that our expansion method generalizes to other models, beyond StyleGAN. To this end, we experiment with Diffusion Autoencoder (DiffAE) [28]. Despite differences in architecture and training method, DiffAE also has a semantic latent space, marked with " + }, + { + "bbox": [ + 304, + 91, + 547, + 198 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{sem}}" + }, + { + "bbox": [ + 304, + 91, + 547, + 198 + ], + "type": "text", + "content": ". We apply our approach over DiffAE and its latent space, using StyleGAN-NADA [5] as the base adaptation method. We find that our expansion methods work as well with DiffAE, and provide a sample of qualitative results in Fig. 10." + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 313, + 219, + 539, + 318 + ], + "blocks": [ + { + "bbox": [ + 313, + 219, + 539, + 318 + ], + "lines": [ + { + "bbox": [ + 313, + 219, + 539, + 318 + ], + "spans": [ + { + "bbox": [ + 313, + 219, + 539, + 318 + ], + "type": "image", + "image_path": "a53fc4b78b4110592716ea7d72a39f20fc4830a77a88841c2f0c203f626d371f.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 327, + 546, + 349 + ], + "lines": [ + { + "bbox": [ + 306, + 327, + 546, + 349 + ], + "spans": [ + { + "bbox": [ + 306, + 327, + 546, + 349 + ], + "type": "text", + "content": "Figure 10. Applying our domain expansion method with Diffusion Autoencoder [28]." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 373, + 384, + 385 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 373, + 384, + 385 + ], + "spans": [ + { + "bbox": [ + 306, + 373, + 384, + 385 + ], + "type": "text", + "content": "5. Conclusions" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 395, + 547, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 395, + 547, + 615 + ], + "spans": [ + { + "bbox": [ + 304, + 395, + 547, + 615 + ], + "type": "text", + "content": "We present a new problem - domain expansion - and propose an approach to solve it. The core of our method is to carefully structure the latent space, such that it is amenable to learning additional knowledge, while keeping the existing knowledge intact. Our method takes advantage of the existence of dormant latent directions, and the task itself implicitly relies on the capacity of the model weights to represent more knowledge. If one of these assumptions does not hold, it might not be possible to apply domain expansion. However, the popularity of methods squeezing neural networks, such as Knowledge Distillation [8], and current estimates of the intrinsic dimensionality of image datasets [27], indicate that these assumptions commonly hold. In our experiments, we were able to expand to hundreds of directions. A plausible limitation is that the model can be expanded to a certain point but ultimately limited by factors such as the latent space or network capacity. Overcoming this limitation, perhaps by considering more complex latent space structures, is an avenue for future work." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 643, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 643, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 643, + 547, + 713 + ], + "type": "text", + "content": "Acknowledgment. This work was done while Yotam Nitzan was an intern at Adobe. This research was supported in part by the Israel Science Foundation (grants no. 2492/20 and 3441/21), Len Blavatnik and the Blavatnik family foundation, and The Tel Aviv University Innovation Laboratories (TILabs)." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "15940" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "type": "text", + "content": "[1] David Bau, Steven Liu, Tongzhou Wang, Jun-Yan Zhu, and Antonio Torralba. 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However, existing deep SM networks are prone to learn dataset-dependent shortcuts, which fail to generalize well on unseen realistic datasets. This paper takes a step towards training robust models for the domain generalized SM task, which mainly focuses on learning shortcut-invariant representation from synthetic data to alleviate the domain shifts. Specifically, we propose a Hierarchical Visual Transformation (HVT) network to 1) first transform the training sample hierarchically into new domains with diverse distributions from three levels: Global, Local, and Pixel, 2) then maximize the visual discrepancy between the source domain and new domains, and minimize the cross-domain feature inconsistency to capture domain-invariant features. In this way, we can prevent the model from exploiting the artifacts of synthetic stereo images as shortcut features, thereby estimating the disparity maps more effectively based on the learned robust and shortcut-invariant representation. We integrate our proposed HVT network with SOTA SM networks and evaluate its effectiveness on several public SM benchmark datasets. Extensive experiments clearly show that the HVT network can substantially enhance the performance of existing SM networks in synthetic-to-realistic domain generalization.", + "bbox": [ + 75, + 316, + 473, + 696 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 717, + 209, + 733 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Stereo Matching (SM) [7,41,44] aims to find the matching correspondences between a given stereo image pair and then calculate the disparity for depth sensing in many applications, such as robot navigation and autonomous driving [1,28]. Recently, it attracts increasing attention in the computer vision community [4,27,30,42].", + "bbox": [ + 75, + 743, + 468, + 833 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "With the development of deep learning [6, 18, 34-38], Convolutional Neural Network (CNN) based deep SM networks have shown impressive performance benefiting from", + "bbox": [ + 75, + 834, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c09daecdb5f2f94dd35e0a62126038002e43271632d10986f205c91cdf694c9f.jpg", + "image_caption": [ + "Figure 1. Comparison of the cross-domain SM generalization. Columns from left to right denote a sample image, ground truth disparities, the predicted disparities of the pretrained PSMNet model and our HVT-PSMNet model. Both models are trained on the synthetic SceneFlow [19] dataset and evaluated on the realistic datasets: Middlebury, ETH3D, KITTI 2012 and KITTI 2015." + ], + "image_footnote": [], + "bbox": [ + 522, + 284, + 867, + 450 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "their strong ability of feature representation. However, due to the scarcity of sufficient labeled realistic training data, existing state-of-the-art (SOTA) SM networks usually are trained on synthetic data, e.g. SceneFlow [19], which fail to generalize well to unseen realistic domains as shown in Fig. 1. Generally, the generalizability of cross-domain deep SM networks is mainly hindered by a critical issue: SM networks usually learn superficial shortcut features [5] from synthetic data to estimate the disparity. Specifically, such shortcut features mainly include two types of artifacts: consistent local RGB color statistics and overreliance on local chromaticity features, which are domain-sensitive and nontransferable to unseen domain. The semantic and structural features that are truly desirable are ignored by most existing SM networks. Therefore, the key to addressing the challenging cross-domain SM task is how to effectively learn the domain-invariant representations of the given stereo image pair for synthetic-to-realistic generalization.", + "bbox": [ + 496, + 549, + 892, + 821 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Several attempts [3, 10, 15, 26, 45] have been made to minimize the synthetic-to-realistic domain gap and learn the domain-invariant representations for the SM task by either 1) exploiting labeled target-domain realistic data to fine-tune the SM network trained with synthetic data [3, 10]", + "bbox": [ + 496, + 824, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding Author", + "bbox": [ + 101, + 887, + 230, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "9559", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "or 2) jointly using the synthetic data and unlabeled target-domain realistic data to train domain adaptive SM networks [15,26,45]. Despite their performance improvement on realistic data, these attempts only work well when the target-domain realistic data is provided during training and thus can not improve the out-of-distribution (OOD) generalization of SM networks, which are less practically useful in real-world scenarios.", + "bbox": [ + 75, + 90, + 468, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we address the important but less explored challenging problem of single domain generalization in SM, where only the synthetic data is available for training. Considering the fact that most existing SM networks are susceptible to exploiting shortcut cues in synthetic data instead of the semantic and structural correspondences, we propose to learn shortcut-invariant robust representation from synthetic SM image pairs for OOD generalization. Specifically, this paper presents a Hierarchical Visual Transformation (HVT) network to 1) first transform the synthetic training sample hierarchically into new source domains with diverse distributions from three levels: Global, Local, and Pixel, 2) then maximize the image discrepancy between the synthetic source domain and new domains for significantly altering the original distribution, and minimize the cross-domain feature inconsistency to capture domain-invariant features. In this way, we are able to prevent the model from exploiting the artifacts of synthetic stereo images as shortcut features, thereby estimating the disparity maps more effectively based on the learned shortcut-invariant feature representation. Our basic idea is to diversify the distribution of training data and thus force the network to overlook the artifacts from synthetic domain. Note that our proposed HVT network is simple and can be plug-and-play. We integrate HVT with SOTA SM networks during training and evaluate its effectiveness on several challenging SM benchmark datasets. Extensive experiments clearly show that the HVT network can substantially enhance the performance of existing SM networks in synthetic-to-realistic domain generalization without using any auxiliary data or features [17].", + "bbox": [ + 75, + 212, + 472, + 664 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions can be briefly summarized as follows:", + "bbox": [ + 94, + 666, + 467, + 680 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We devise a simple yet effective domain generalized SM framework. It leverages a hierarchical visual transformation network to effectively diversify the distribution of training data which prevents the model from exploiting the artifacts in synthetic data as shortcuts.", + "- We formulate novel learning objectives that force the model to effectively optimize three complementary visual transformations by maximizing domain discrepancy and minimizing feature inconsistency between synthetic domain and new domains, thereby facilitating the learning of domain-invariant feature representation.", + "- Extensive experiments on four realistic SM datasets clearly demonstrate the effectiveness and robustness of our HVT network. The out-of-distribution generalization" + ], + "bbox": [ + 76, + 685, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ability of four SOTA SM methods has been significantly boosted, benefiting from our solution.", + "bbox": [ + 514, + 90, + 890, + 121 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 135, + 640, + 150 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "This section briefly introduces the learning based stereo matching (SM) methods from two perspectives: 1) In-Distribution SM and 2) Our-of-Distribution SM.", + "bbox": [ + 498, + 161, + 890, + 204 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In-Distribution SM. In the past decade, deep learning has triggered the fast development of the task of SM. Mayer et al. [19] introduced an end-to-end SM network which uses the correlation layer to generate the cost volume and the 2D-CNN to aggregate the cost volume. SegStereo [33] and EdgeStereo [27] exploit the semantic and edge cues to help the disparity prediction. To learn better features, AANet [30] integrates both normal convolution and deformable convolution for feature extraction. Furthermore, GCNet [14] concatenates left and right features for cost volume generation and aggregation with 3D convolutions. GwcNet [10] proposes the group-wise correlation to construct the cost volume with lower memory cost. PSM-Net [3] proposes the spatial pyramid pooling module and the stack hourglass network to expand the receptive field. GANet [42] designs the image content guided layers to globally and locally update the cost volume. LEAStereo [4] introduces the neural architecture searching into SM. In recent several years, the Cascade-based SM methods [9, 25, 39] first use the coarsest resolution feature maps to predict an initial disparity, and narrow down the disparity search range to refine the disparity based on the initial disparity. Despite the good performance of existing deep-learning based SM networks, their training set and testing set always follow the independent and identically distributed (IID) assumption. Most existing works usually fail to generalize well on unseen realistic data.", + "bbox": [ + 498, + 205, + 892, + 612 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Out-of-Distribution SM. Most recently, the synthetic-to-realistic generalized SM networks [5, 16, 25, 43] have received increasing attention. Different from those fine-tuning or adaptation-based methods [3, 15, 26, 42, 45], they aim to directly learn SM networks that can generalize to unseen domains. Some works propose to improve the generalization ability by devising novel network architectures. For example, DSMNet [43] proposes the domain normalization layer and the trainable non-local graph-based filter to learn domain-invariant structural feature. Besides, both CFNet [25] and RAFT-Stereo [16] introduce a network architecture with multi-scale cost volume fusion and aggregation to learn robust semantic or structural features. Some other efforts attempt to design flexible modules that can facilitate the cross-domain generalization of more existing SM networks. MS-Net [2] points out that learned feature is the core reason for the poor generalization performance, and proposes to use the traditional feature descriptors to construct the cost. FC-Net [46] uses the stereo contrastive", + "bbox": [ + 498, + 613, + 892, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "9560", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/093696791a5f78dc7b0ace1b6569150e9dbf275dfa357d1b87e3a48004e70d82.jpg", + "image_caption": [ + "Figure 2. The pipeline of our domain-generalized SM approach. It leverages a hierarchical visual transformation module to improve the diversity of training domain by training a domain discriminator $\\phi(\\cdot)$ . Its main goal is to optimize a feature extractor $f(\\cdot)$ that can learn shortcut-robust and domain-invariant representation, thereby facilitating the generalization of SM network in unseen realistic domains." + ], + "image_footnote": [], + "bbox": [ + 158, + 89, + 810, + 308 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "feature loss and the stereo selective whitening loss to encourage the stereo feature consistency across different domains. GraftNet [17] leverages the robust broad-spectrum feature which is trained on large-scale datasets to replace the original feature to improve the generalization ability. ITSA [5] generates the pixel-perturbed image through the gradient of the features with respect to the input image, and guides the network to learn shortcut-invariant feature.", + "bbox": [ + 75, + 359, + 472, + 479 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Different from these methods, we introduce a simple yet effective method to enhance the synthetic-to-realistic generalization. We design a hierarchical visual transformation module to diversify the training domain by maximizing the cross-domain visual discrepancy and propose to learn domain-invariant feature representation by minimizing the cross-domain feature inconsistency. ITSA [5] can be generally seen as a special case of our work that diversifies the distribution in the Pixel level. Experiments in the Sec. 4 have clearly validated the effectiveness of our method on improving the synthetic-to-realistic generalization of SM.", + "bbox": [ + 75, + 482, + 472, + 650 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. The Approach", + "text_level": 1, + "bbox": [ + 76, + 666, + 223, + 684 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem Overview", + "text_level": 1, + "bbox": [ + 76, + 691, + 256, + 708 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "This work aims to improve the synthetic-to-realistic domain generalization for SM. Given a synthetic training set $\\mathcal{D}_s$ as input, consisting of $|\\mathcal{D}_s|$ synthetic stereo image pairs $\\{\\mathbf{X}_i^l,\\mathbf{X}_i^r\\}_{i = 1}^{|\\mathcal{D}_s|}$ and the corresponding ground-truth disparity maps $\\{\\mathbf{Y}_i^{gt}\\}_{i = 1}^{|\\mathcal{D}_s|}$ , the goal is to learn a cross-domain SM network that can effectively predict the disparity between a pair of stereo images from unseen domains $\\mathcal{D}_r$ . A typical SM network $F_{\\Theta}(\\cdot ,\\cdot)$ can be formally formulated as:", + "bbox": [ + 76, + 717, + 468, + 844 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {Y}} = F _ {\\Theta} \\left(\\mathbf {X} ^ {l}, \\mathbf {X} ^ {r}\\right) = s \\left(g \\left(f \\left(\\mathbf {X} ^ {l}\\right), f \\left(\\mathbf {X} ^ {r}\\right)\\right)\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 127, + 848, + 468, + 867 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\Theta$ denotes the total network parameters and $f(\\cdot)$ is a feature extraction module that yields the feature map of", + "bbox": [ + 75, + 869, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "stereo images. $g(\\cdot)$ is a joint network module that first generates the cost volume by correlation or concatenation strategy, and then performs the cost aggregation and refinement. The final disparity map $\\hat{\\mathbf{Y}}$ is estimated by converting the refined cost volumes with the soft-argmin [14] operation $s(\\cdot)$ . The typical SM network $F_{\\Theta}(\\cdot,\\cdot)$ is optimized by minimizing the smooth- $\\ell_1$ loss $L_{\\mathrm{sm}-\\ell_1}\\left(F_{\\Theta}(\\mathbf{X}^l,\\mathbf{X}^r),\\mathbf{Y}^{gt}\\right)$ [3].", + "bbox": [ + 496, + 359, + 890, + 465 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the past years, existing efforts primarily focus on how to devise an effective sub-network $g(\\cdot)$ for cost volume generation and cost aggregation, while overlook the importance of learning robust feature representations of stereo images that can preserve the semantic and structural cues. Recent studies pointed out that most existing SM networks trained on synthetic data are susceptible to learn superficial shortcut features [5] instead of the desirable semantic and structural features, which leads to poor generalization performance in unseen (realistic) domain due to the significant synthetic-realistic domain gap. Therefore, the main research problem in this work is how to train an effective feature extraction network $f(\\cdot)$ on only synthetic data that can learn generalizable representation of stereo images, so as to estimate reliable disparity map on unseen domain.", + "bbox": [ + 496, + 465, + 892, + 691 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Our Proposed Method", + "text_level": 1, + "bbox": [ + 500, + 700, + 709, + 718 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our target is to tackle the synthetic-to-realistic generalization in SM. Its main challenge is that we only have synthetic data for training, which has the high risk of overfitting to synthetic data due to its limited diversity. Inspired by [13, 29, 40, 47], we address the domain generalized SM from a new perspective in this work. The rest of this section will introduce our proposed network for this task in detail. The pipeline of our proposed HVT is shown in Fig. 2", + "bbox": [ + 496, + 724, + 890, + 847 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2.1 Hierarchical Visual Transformation", + "text_level": 1, + "bbox": [ + 500, + 851, + 803, + 866 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As we know, the key to addressing domain generalization is learning domain-invariant feature, also called causal fea", + "bbox": [ + 500, + 869, + 890, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "9561", + "bbox": [ + 480, + 944, + 513, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Although the explicit form of causal feature is unknown in general, we have the prior that causal feature should remain invariant to certain transformations [29]. For example, the semantic and structural features can be treated as two domain-invariant (causal) features of stereo images for SM, while adjusting the luminance, contrast, or saturation of a stereo image pair will not affect the corresponding disparity map. Our intuitive idea is to leverage the visual transformations that do not change the underlying domain-invariant feature to increase the diversity of training domain, thereby enhancing the generalization performance of SM network. It is a straightforward but effective way. To this end, we design a Hierarchical Visual Transformation (HVT) network to diversify the distribution of training domain. Specifically, we learn a set of visual transformations $\\mathcal{T} = \\{T_1,\\dots ,T_M\\}$ at different levels to transform the original stereo image pairs as $(T(\\mathbf{X}^l),T(\\mathbf{X}^r))$ , where $T\\in \\mathcal{T}$ . We force the visual transformation $T(\\cdot)$ to meet the following three requirements:", + "bbox": [ + 75, + 90, + 472, + 378 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- $T(\\cdot)$ should induce large visual discrepancy between the original stereo image and the transformed images to enlarge the diversity of training domain.", + "- $T(\\cdot)$ should not change the target disparity map of the original stereo image pairs. We should minimize the smooth- $\\ell_1$ loss $L_{\\mathrm{sm}-\\ell_1}(F_\\Theta(T(\\mathbf{X}^l), T(\\mathbf{X}^r)), \\mathbf{Y}^{gt})$ where the transformed stereo images are fed into.", + "- The representation of the transformed stereo images $f(T(\\mathbf{X}))$ should be consistent with that of the original images $f(\\mathbf{X})$ , so as to learn domain-invariant features." + ], + "bbox": [ + 76, + 383, + 468, + 542 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Following the above-listed requirements, we describe the implementation of our proposed HVT network as follows.", + "bbox": [ + 75, + 546, + 468, + 578 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Implementation of HVT. To effectively learn domain-invariant feature representation for the challenging SM task, we transform the stereo image from three complementary perspectives: Global, Local, and Pixel.", + "bbox": [ + 75, + 585, + 468, + 645 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "(1) Global: The Global visual transformation $T_{G}(\\cdot)$ aims to globally change the distribution of stereo images by sequentially adjusting the basic visual attributes of images: Brightness, Contrast, Saturation, and Hue based on the four corresponding sub-transformations $\\{T_{G}^{B}, T_{G}^{C}, T_{G}^{S}, T_{G}^{H}\\}$ , following the pipeline of automatic image editing [12]. The three sub-transformations $\\{T_{G}^{B}, T_{G}^{C}, T_{G}^{S}\\}$ can be formulated as:", + "bbox": [ + 75, + 651, + 468, + 758 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nT _ {G} ^ {I} (\\mathbf {X}) = \\alpha_ {G} ^ {I} \\mathbf {X} + (1 - \\alpha_ {G} ^ {I}) o ^ {I} (\\mathbf {X}), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 761, + 468, + 779 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $I\\in \\{B,G,S\\}$ . The $\\alpha_{G}^{I}$ is a randomly selected positive constant in an adjustable range of $[\\tau_{\\mathrm{min}}^I,\\tau_{\\mathrm{max}}^I ]$", + "bbox": [ + 75, + 782, + 468, + 815 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{ \\begin{array}{l} \\tau_ {\\min } ^ {I} = 1 - \\left(\\mu \\sigma \\left(\\varrho_ {l} ^ {I}\\right) + \\beta\\right) \\\\ \\tau_ {\\max } ^ {I} = 1 + \\left(\\mu \\sigma \\left(\\varrho_ {h} ^ {I}\\right) + \\beta\\right) \\end{array} , \\right. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 166, + 816, + 468, + 849 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\sigma (\\cdot)$ denotes the sigmoid function, $\\varrho_l^I\\in \\mathbb{R}^1$ and $\\varrho_h^I\\in \\mathbb{R}^1$ are two learnable parameters, $\\mu$ and $\\beta$ are two positive hyper-parameters. The operation $o^{I}(\\cdot)$ in Eq. (2)", + "bbox": [ + 76, + 854, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "is customized as follows. Specifically, for the Brightness, $o^B (\\mathbf{X}) = \\mathbf{X}\\cdot \\mathbf{O}$ where $\\mathbf{O}$ denotes a zero matrix all of whose entries are zero. For the Contrast, $o^C (\\mathbf{X}) = \\mathrm{Avg}(\\mathrm{Gray}(\\mathbf{X}))$ where Gray(·) transforms the RGB image into a gray-scale image and $\\mathrm{Avg}(\\cdot)$ computes the mean value of all pixels. For the Saturation, $o^S (\\mathbf{X}) = \\mathrm{Gray}(\\mathbf{X})$ . The Hue adjustment is defined as:", + "bbox": [ + 496, + 90, + 890, + 195 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nT _ {G} ^ {H} (\\mathbf {X}) = \\operatorname {R g b} \\left(\\left[ \\mathbf {h} + \\alpha_ {G} ^ {H}, \\mathbf {s}, \\mathbf {v} \\right]\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 199, + 890, + 218 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $[\\mathbf{h},\\mathbf{s},\\mathbf{v}] = \\mathrm{Hsv}(\\mathbf{X})$ denotes the three components of $\\mathbf{X}$ in the HSV color space and $\\mathbf{h}$ denotes the Hue component. $\\operatorname {Rgb}(\\cdot)$ transforms the image from the HSV space into the RGB space. The $\\alpha_{G}^{H}\\in \\mathbb{R}^{1}$ is randomly selected from an adjustable range of $[\\tau_{\\min}^{H},\\tau_{\\max}^{H}]$ , where $\\tau_{\\mathrm{min}}^H = -\\mu \\sigma (\\varrho_l^H) - \\beta$ and $\\tau_{\\mathrm{max}}^H = \\mu \\sigma (\\varrho_h^H) + \\beta$", + "bbox": [ + 496, + 220, + 893, + 313 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Note that the order of the sequential sub-transformations $\\{T_G^B, T_G^C, T_G^S, T_G^H\\}$ is random to improve the diversity.", + "bbox": [ + 500, + 314, + 890, + 345 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "(2) Local: The Local visual transformation $T_{L}(\\cdot)$ aims to locally modify the distribution of stereo training images. The basic pipeline is that we first slice the given stereo image into $N' \\times N'$ non-overlapping patches $\\{\\mathbf{x}_1^p, \\dots, \\mathbf{x}_{N' \\times N'}^p\\}$ , then transform each image patch $\\mathbf{x}_i^p$ by a global transformation $T_{L}^{p}(\\cdot)$ , and finally merge these transformed image patches into the stereo image based on the original sequential order. The output can be described by", + "bbox": [ + 496, + 349, + 890, + 472 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nT _ {L} (\\mathbf {X}) = \\operatorname {M e r g e} \\left(\\left[ T _ {L} ^ {p} \\left(\\mathbf {x} _ {1} ^ {p}\\right), \\dots , T _ {L} ^ {p} \\left(\\mathbf {x} _ {N ^ {\\prime} \\times N ^ {\\prime}} ^ {p}\\right) \\right]\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 522, + 476, + 890, + 494 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\text{Merge}(\\cdot)$ denotes the Merge operation.", + "bbox": [ + 500, + 497, + 802, + 512 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Note that patch-level transformation $T_{L}^{p}(\\cdot)$ for each patch doesn't share parameters with each other to improve the diversity. $T_{L}^{p}(\\cdot)$ can be implemented by existing style transfer networks, e.g. Adain [22] or Fourier-based method [31]. To better complementing our Global transformation, patch-level transformation $T_{L}^{p}(\\cdot)$ is implemented by $T_{G}(\\cdot)$ in Eq.(2) and Eq.(4) for its simplicity and effectiveness.", + "bbox": [ + 496, + 513, + 890, + 619 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "(3) Pixel: The Pixel visual transformation $T_{P}(\\cdot)$ aims to perturb the given stereo images with a pixel-level perturbation matrix. It can be formulated as:", + "bbox": [ + 496, + 626, + 890, + 671 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nT _ {P} (\\mathbf {X}) = \\mathbf {X} + (\\mu \\sigma (\\mathbf {W}) + \\beta) \\mathbf {P} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 676, + 890, + 694 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{P} \\in \\mathbb{R}^{H \\times W \\times 3}$ is a randomly generated Gaussian matrix with the mean of 0 and the standard deviation of 1, and $\\mathbf{W} \\in \\mathbb{R}^{H \\times W \\times 3}$ is a learnable matrix. Different from the Global and Local transformations, $T_P(\\cdot)$ can alter the distribution of synthetic data in a more granular fashion.", + "bbox": [ + 496, + 696, + 890, + 773 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Remark: The implementation of HVT is mainly motivated by the empirically found evidence [5] that existing SM networks are susceptible to exploit common artifacts (e.g. consistent local RGB color statistics and overreliance on local chromaticity features) of synthetic stereo images as shortcuts, which can be clearly illustrated by Fig. 3. We observe from Fig. 3 that the PSMNet is quite sensitive to the different levels of perturbation. It reflects that PSM-", + "bbox": [ + 496, + 779, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "9562", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/2b495d2b09df787d7560c33a27869bea05d56f8f5aba6bab2b0b520fcc9c0624.jpg", + "image_caption": [ + "Figure 3. Examples of visualized output of three visual transformations (top-2 rows of (a) and (b)) and the corresponding disparity error maps $|\\dot{\\mathbf{Y}} - \\mathbf{Y}^{gt}|$ (the 3-rd row of (a) and (b)) of the PSMNet trained on the synthetic SceneFlow dataset. The EPE values are marked in the bottom of the 3-rd row for comparison." + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 467, + 378 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Net doesn't capture the robust semantic and structural features of stereo images. Our method is specially devised to improve the robustness and generalization ability of existing SM method. The design of the three different transformations $\\{T_{G}(\\mathbf{X}), T_{L}(\\mathbf{X}), T_{P}(\\mathbf{X})\\}$ can effectively diversify the training domain and prevent the shortcuts from being encoded into the stereo image representation $f(\\mathbf{X})$ .", + "bbox": [ + 75, + 465, + 468, + 571 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2.2 Learning Objectives", + "text_level": 1, + "bbox": [ + 76, + 601, + 272, + 617 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To effectively train our proposed HVT network for the domain generalized SM task, we introduce the following loss terms for network optimization.", + "bbox": [ + 75, + 628, + 468, + 674 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Maximizing Cross-Domain Visual Discrepancy: In this work, without having access to the target domain, we propose to improve the SM network's generalization by transforming the synthetic source domain data into several new source domains $\\{T_G(\\mathbf{X}), T_L(\\mathbf{X}), T_P(\\mathbf{X})\\}$ to diversify the training domain. Our first objective is to force the distributions of new source domains to be dissimilar as possible to the original distribution of synthetic data. Then we should maximize the following cross-domain visual discrepancy as", + "bbox": [ + 75, + 676, + 470, + 813 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\max L _ {\\text {d i s c}} (\\mathbf {X}) = \\frac {1}{3} \\sum_ {J} d \\left(T _ {J} (\\mathbf {X}), \\mathbf {X}\\right) \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 150, + 815, + 468, + 851 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $J \\in \\{G, L, P\\}$ , and $d(\\cdot)$ is a domain discrepancy measure. In this work, we introduce a specific feature extraction network $\\phi(\\cdot)$ for domain discriminating. Then we", + "bbox": [ + 75, + 854, + 468, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "implement Eq. (7) by minimizing the domain similarity as", + "bbox": [ + 498, + 90, + 885, + 106 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\min L _ {\\text {s i m}} (\\mathbf {X}) = \\frac {1}{3} \\sum_ {J} \\operatorname {C o s} \\left(\\phi \\left(T _ {J} (\\mathbf {X})\\right), \\phi (\\mathbf {X})\\right), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 539, + 108, + 890, + 142 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathrm{Cos}(\\cdot ,\\cdot)$ denotes the cosine similarity function. $\\phi (\\mathbf{X})$ denotes the pooled feature vector from the domain discriminating network $\\phi (\\cdot)$ . Besides, to further improve the domain discrepancy, we also minimize the following cross-entropy loss for domain classification:", + "bbox": [ + 496, + 146, + 890, + 220 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\min L _ {\\mathrm {c e}} (\\mathbf {X}) = \\operatorname {C E} \\left(\\left\\{\\phi \\left(T _ {J} (\\mathbf {X})\\right), \\phi (\\mathbf {X}) \\right\\}, \\mathcal {Y} _ {d}\\right), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 542, + 224, + 890, + 242 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathrm{CE}(\\cdot ,\\cdot)$ denotes the standard cross-entropy loss and $\\mathcal{V}_d$ denotes the domain labels of four source domains.", + "bbox": [ + 496, + 246, + 890, + 276 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Minimizing Cross-Domain Feature Inconsistency: To enhance the model's generalization ability, we need to learn domain-invariant representation of stereo images. We expect that our visual transformation $T(\\cdot)$ doesn't change the core features (e.g., semantic and structural features) of images for stereo matching. Therefore, our second objective is to force the feature representation of transformed stereo images to be consistent with that of original synthetic images. Then we minimize the following pairwise distance term:", + "bbox": [ + 496, + 281, + 890, + 417 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\min L _ {\\text {d i s t}} (\\mathbf {X}) = \\frac {1}{3} \\sum_ {J} \\| f (T _ {J} (\\mathbf {X})) - f (\\mathbf {X}) \\| _ {2}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 420, + 890, + 454 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "which facilitates the learning of shortcut-robust and domain invariant features for domain-generalized stereo matching. In summary, our model is trained by minimizing the linear combination of the above-mentioned learning objectives:", + "bbox": [ + 496, + 457, + 890, + 517 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\min \\mathcal {L} = L _ {\\mathrm {s m} - \\ell_ {1}} (\\hat {\\mathbf {Y}}, \\mathbf {Y} ^ {g t}) + \\\\ \\frac {1}{2} \\left(\\lambda_ {1} L _ {\\text {d i s t}} (\\mathbf {X}) + \\lambda_ {2} L _ {\\text {s i m}} (\\mathbf {X}) + \\lambda_ {3} L _ {\\text {c e}} (\\mathbf {X})\\right), \\tag {11} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 521, + 890, + 570 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The full loss $\\mathcal{L}$ is computed as the average over a training batch. The smooth- $\\ell_1$ loss $L_{\\mathrm{sm - }\\ell_1}$ is computed based on not only the original synthetic image pairs $\\{\\mathbf{X}^l,\\mathbf{X}^r\\}$ but also the transformed image pairs $\\{T_J(\\mathbf{X}^l),T_J(\\mathbf{X}^r)\\}$ . $\\lambda_{1},\\lambda_{2}$ and $\\lambda_{3}$ are three trade-off hyper-parameters.", + "bbox": [ + 496, + 573, + 890, + 648 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 661, + 632, + 679 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we quantitatively and qualitatively conduct extensive experiments to answer the following research questions: R1: Can the HVT effectively improve the generalization performance of existing SM networks? Can our performance reach the SOTA level? R2: Do the three transformations in the HVT effectively complement to each other? R3: Can our approach learn the domain-invariant features? R4: How is the robustness of our approach when tested in complex realistic scenarios?", + "bbox": [ + 496, + 686, + 890, + 821 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Dataset and Experimental Setting", + "text_level": 1, + "bbox": [ + 500, + 832, + 795, + 848 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. We use the SceneFlow [19] dataset for training and four realistic SM datasets (KITTI 2012 [8], KITTI 2015 [20], Middlebury [23] and ETH3D [24]) for e", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "9563", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/9afbc1b96748d394623d389f8772d7da7a6e3028fd9fdbf6eb675d81ee95116d.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
BaselinesMethodsKITTI 2015KITTI 2012Middlebury(H)ETH3DReferences
EPED1(3px)EPED1(3px)EPED1(2px)EPED1(1px)
-GANet [42]2.3111.71.9310.15.4120.31.3314.1CVPR 2019
CasStereo [9]2.4211.92.1211.83.7117.20.877.8CVPR 2020
DSMNet [43]1.466.51.266.22.6213.80.696.2ECCV 2020
PSMNet [3]PSMNet [3]3.1716.32.6915.17.6534.22.3323.8CVPR 2018
MS-PSMNet [2]1.64*7.82.33*14.04.72*19.81.42*16.83DV 2020
FC-PSMNet [46]1.58*7.51.42*7.04.14*18.31.25*12.8CVPR 2022
ITSA-PSMNet [5]1.39*5.81.09*5.23.25*12.70.94*9.8CVPR 2022
Graft-PSMNet [17]1.325.31.095.02.3410.91.1610.7CVPR 2022
HVT-PSMNet1.14±0.024.9±0.120.93±0.024.3±0.061.46±0.1310.2±0.160.47±0.036.9±0.23Ours
GwcNet [10]GwcNet [10]3.4322.72.7720.27.2337.92.7854.2CVPR 2019
FC-GwcNet [46]1.72*8.01.45*7.45.14*21.11.13*11.7CVPR 2022
ITSA-GwcNet [5]1.33*5.41.02*4.92.73*11.40.62*7.1CVPR 2022
HVT-GwcNet1.15±0.025.0±0.110.88±0.023.9±0.131.29±0.1310.3±0.210.46±0.085.9±0.26Ours
CFNet [25]CFNet [25]1.716.01.045.23.2415.40.485.72CVPR 2021
ITSA-CFNet [5]1.094.70.874.21.8710.40.455.1CVPR 2022
HVT-CFNet1.10±0.044.9±0.160.85±0.024.0±0.141.79±0.2210.2±0.160.39±0.024.5±0.24Ours
RAFT [16]RAFT [16]1.265.71.015.11.9212.60.363.33DV 2021
HVT-RAFT1.12±0.025.2±0.090.87±0.023.7±0.081.37±0.1110.4±0.140.29±0.013.0±0.09Ours
", + "bbox": [ + 106, + 88, + 859, + 333 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Performance comparison with SOTA domain generalized SM networks. The * denotes our reproduced EPE results since the authors only use the D1 metric. As we didn't have a validation set for model selection, we report the average result over last 5 epochs.", + "bbox": [ + 75, + 338, + 890, + 368 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "valuation. SceneFlow [19] is a large-scale synthetic SM dataset containing 35,454 training stereo image pairs and 4,370 testing image pairs with a resolution of $960 \\times 540$ . All the synthetic image pairs have dense annotations of ground-truth disparities. KITTI 2012 [8] and KITTI 2015 [20] consists of 194 and 200 training stereo image pairs collected in outdoor driving scenes with sparse annotations of disparities, respectively. Middlebury [23] includes 15 high-resolution stereo image pairs in indoor scenes. In our experiments, we use the half-resolution version (Middlebury(H)) for evaluation. ETH3D [24] has 27 grayscale stereo image pairs collected from both indoor and outdoor scenes.", + "bbox": [ + 75, + 380, + 468, + 561 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Metrics. Following the setting of [17], we use both EPE rate (End-Point Error) and D1 error rate $(\\%)$ with different pixel threshold $\\rho$ as the metrics to get a more comprehensive evaluation. The EPE measures the average disparity error over all pixels, which reflects the average disparity estimate. The D1 error rate computes the percentage of error pixels with absolute error larger than a specific threshold $\\rho$ . The pixel threshold is set as $\\rho = 3\\mathrm{px}$ for KITTI 2012 [8] and KITTI 2015 [20], $\\rho = 2\\mathrm{px}$ for Middlebury [23] and $\\rho = 1\\mathrm{px}$ for ETH3D [24], respectively, following recent works [17, 46].", + "bbox": [ + 75, + 563, + 468, + 715 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baselines. We select four SM networks as baselines, including two well-studied and commonly-used methods (PSMNet [3] and GwcNet [10]) and two SOTA methods (CFNet [25] and RAFT [16]), in our experiments. We will integrate our HVT networks with these baseline networks to validate the effectiveness of HVT on domain generalization.", + "bbox": [ + 75, + 717, + 468, + 808 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details. Following [43], we use the domain normalization technique in the feature extraction module for all baselines. Except the RAFT [16], all the baselines are implemented by PyTorch [21] with Adam $(\\beta_{1} = 0.9, \\beta_{2} = 0.999)$ optimizer. We train the model for 45 epochs with the batch size of 8. Besides, we introduce an incremen", + "bbox": [ + 75, + 810, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "tal training scheme to stably optimize the network in this work. Specifically, we train the model with $T_{G}(\\cdot)$ only for 15 epochs at Stage I, then we further train the model with $\\{T_G(\\cdot), T_L(\\cdot)\\}$ for another 15 epochs at Stage II, and finally we continually train the model with $\\{T_G(\\cdot), T_L(\\cdot), T_P(\\cdot)\\}$ for the remaining 15 epochs at Stage III. The learning rate is set to 0.001 and decreased by half after epoch 10, 20, 30 and 40. For the RAFT [16] baseline, we train the model for total 30K steps and train each stage 10K steps. The optimizer and learning rate follow its original setting. Besides, the asymmetric chromatic augmentation is not used in any models to avoid unfair experimental comparison. We select ResNet18 [11] as the domain discriminating network $\\phi(\\cdot)$ for its simplicity. For different hyper-parameters, the $\\mu$ and $\\beta$ in Eq. (3) and (6) are set as 0.1 and 0.15 respectively. The $\\lambda_1$ , $\\lambda_2$ and $\\lambda_3$ in Eq. (11) are set as 1, 0.5 and 0.5 respectively. The $N' = 4$ in $T_{L}(\\cdot)$ . Note that all the SM networks are only trained on the synthetic dataset, SceneFlow. The target data is strictly inaccessible during training.", + "bbox": [ + 496, + 380, + 890, + 667 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Overall Performance Comparison", + "text_level": 1, + "bbox": [ + 498, + 676, + 795, + 694 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "R1: Comparison with Baselines and SOTAs. In Tab. 1, we report the comparison of generalization performance between the baselines (PSMNet, GwcNet, CFNet, and RAFT) and our HVT-integrated methods, as well as the comparison between ours and the reported SOTA results, across the four realistic datasets. We have the following observations:", + "bbox": [ + 496, + 700, + 890, + 792 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "- The synthetic-to-realistic generalization performances of all the baselines are consistently improved by our HVT in all settings. Specifically, compared with the widely-used PSMNet [3], the performance improvements w.r.t. the D1 metric are $11.4\\%$ , $10.8\\%$ , $24\\%$ , and $16.9\\%$ , respectively on the four datasets. Similar improvement can also be observed on GwcNet [10]: $17.7\\%$ , $16.3\\%$ , $27.6\\%$ , and", + "bbox": [ + 500, + 795, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "9564", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/99dbf60f061aeff72355fc22f05e392518704e44612deb261ebdbfc6306d16d3.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
BaselinesGlobal Local PixelKITTI 2015MiddleburyETH3D
EPE3pxEPE2pxEPE1px
PSMNet [3]✓✗✗1.316.072.0413.70.489.4
✗✓✗1.286.031.6912.50.5910.7
✗✗✓1.276.292.3914.60.579.9
✓✓✗1.235.471.5711.10.539.1
✓✗✓1.195.571.4411.20.517.7
✗✓✓1.275.721.5810.90.627.9
✓✓✓1.144.931.4610.20.476.9
GwcNet [10]✓✗✗1.285.891.8812.60.748.2
✗✓✗1.265.881.6411.90.688.5
✗✗✓1.296.181.8312.40.718.3
✓✓✗1.235.381.5810.40.587.8
✓✗✓1.195.521.4910.70.557.1
✗✓✓1.185.471.5710.60.526.9
✓✓✓1.155.021.2910.30.465.9
", + "bbox": [ + 83, + 88, + 462, + 316 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "$48.3\\%$ w.r.t. the D1 metric. Even compared with the SOTA CFNet [25] and RAFT [16], the D1 error rates are still substantially decreased: $1.1\\%$ , $1.2\\%$ , $5.2\\%$ , and $1.2\\%$ for CFNet, and $0.5\\%$ , $1.4\\%$ , $2.2\\%$ , and $0.3\\%$ for RAFT. The quantitative comparison clearly shows the effectiveness of HVT on enhancing the robustness of SM models. The improvement can be mainly attributed to the fact that our HVT significantly diversify the visual distribution of original synthetic images, thus preventing the model from building the spurious relationship between the pairwise input and the target disparity. The model will not easily find the matching correspondences across the stereo images by just leveraging the shortcut cues, e.g., local RGB color statistics and chromaticity features.", + "bbox": [ + 91, + 377, + 468, + 589 + ], + "page_idx": 6 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- The improvements of generalization performance brought by HVT on the Middlebury and ETH3D datasets seem to be much larger than those on the KITTI 2012 and 2015 datasets. The reason is that Middlebury has higher resolution images in realistic scenarios than those in KITTI 2012 and 2015, and the images in ETH3D are all grayscale which are very different from the colorful synthetic training images. It reflects that our HVT can perform well in diverse realistic scenarios that differ from training domain in resolution and color distribution.", + "- Our HVT-enhanced methods almost outperform all the SOTA methods except ITSA-CFNet on KITTI 2015. It shows the strong potential of our HVT in improving the cross-domain generalization. Note that the three transformations devised in this work are all simple and straightforward. The performance can be further improved if we introduce more delicate transformations into our HVT. Besides, the performance of ITSA-CFNet on KITTI 2015 is already very high w.r.t. the EPE and D1 metrics, 1.09 and $4.7\\%$ . Our HVT-CFNet's performance is on a par" + ], + "bbox": [ + 76, + 594, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/4553da0f889957cb13293cb58d2db7b11198d10cde972e4a037b20f5687f055a.jpg", + "table_caption": [ + "Table 2. Ablation studies on the effect of three visual transformations (Global, Local, and Pixel) on three datasets using the two well-studied baselines, PSMNet [3] and GwcNet [10]." + ], + "table_footnote": [], + "table_body": "
BaselinesObj-1Obj-2KITTI 2015MiddleburyETH3D
EPE3pxEPE2pxEPE2px
PSMNet [3]XX1.677.742.8815.10.8913.2
X✓1.316.232.0411.70.6310.1
✓✓1.144.931.4610.20.476.9
GwcNet [10]XX1.647.582.6514.60.8612.4
X✓1.286.071.9311.30.579.2
✓✓1.155.021.2910.30.465.9
", + "bbox": [ + 524, + 88, + 867, + 196 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Ablation studies of our two main optimization objectives: Obj-1 (i.e., Eq. (8) and Eq. (9)) and Obj-2 (i.e., Eq. (10)).", + "bbox": [ + 500, + 196, + 888, + 226 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8eb31a533c24fdd6637a111a36f28d44403a5640a0da7371db01343d482f3226.jpg", + "image_caption": [ + "Figure 4. Visualization of RGB color histograms (see (b)) and visual feature histograms (see (c)) of original image and transformed images (see (a)) based on the HVT-PSMNet method. The original image is randomly selected from the realistic Middlebury dataset." + ], + "image_footnote": [], + "bbox": [ + 500, + 239, + 890, + 409 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "with that of the ITSA-CFNet.", + "bbox": [ + 514, + 484, + 712, + 498 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "- Benefiting from using HVT, the performances of weak baselines, i.e., PSMNet and GwcNet, have been increased to the SOTA level, especially on the top-three datasets. It reflects that the critical step for the domain-generalized SM task is to learn domain-invariant representation from diverse training domain instead of devising different complex network modules for cost volume generation or aggregation. It further validates the rationale of our HVT.", + "bbox": [ + 500, + 501, + 890, + 636 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Studies", + "text_level": 1, + "bbox": [ + 500, + 650, + 663, + 666 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "R2: The Complementation of HVTs. As shown in Tab. 2, we investigate the effect of the HVT module by gradually adding the visual transformations in two baselines, PSMNet [3] and GwcNet [10]. We observe that the three visual transformations can complement well to each other. Specifically, only using one of the three transformations can also facilitate the performance improvement of baselines. When using more visual transformations, we observe consistent performance gains across the three realistic datasets. For example, the D1 error rates of $T_{G}(\\cdot)$ -enhanced PSMNet have been decreased from $6.07\\%$ , $13.7\\%$ , and $9.4\\%$ to $5.57\\%$ , $11.2\\%$ , and $7.7\\%$ , respectively, when jointly using $T_{G}(\\cdot)$ and $T_{P}(\\cdot)$ . The best performances are observed when all the three transformations are jointly used. Similar performance improvements can also be observed when Gwc", + "bbox": [ + 496, + 674, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "9565", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/b8cc791800523e89f4c3d922267eb7ce71e5e25b09b5da55777d613960d72e93.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsSunnyCloudyRainyFoggyAvg.
PSMNet [3]62.560.160.568.663.9
FT-PSMNet [5]4.02.911.56.56.3
FC-PSMNet [46]4.94.37.26.25.7
ITSA-PSMNet [5]4.83.29.46.35.9
HVT-PSMNet4.23.18.75.65.4
GwcNet [10]18.124.728.228.324.8
FT-GwcNet [5]3.12.512.36.06.0
ITSA-GwcNet [5]4.43.39.85.95.9
HVT-GwcNet3.43.58.65.65.3
", + "bbox": [ + 99, + 88, + 444, + 237 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4. Robustness comparison of different methods on the DrivingStereo [32] dataset collected from complex realistic scenarios: Sunny, Cloudy, Rainy, and Foggy. The D1 (3px) metric is used.", + "bbox": [ + 76, + 241, + 467, + 284 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Net is used as the SM baseline.", + "bbox": [ + 76, + 294, + 285, + 306 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "R3: Learning Domain-Invariant features. The core of our approach is to learn shortcut-robust features that can generalize well to unseen domains. As illustrated in Fig. 4 (b), we observe that the hierarchical visual transformation's significantly alter the RGB color histograms of original stereo image in the levels of Global, Local, and Pixel. Benefiting from the minimization of cross-domain feature inconsistency in Eq. (10), the image representation $f(\\mathbf{X})$ seems to be invariant across different domains as shown in Fig. 4 (c). Tab. 3 quantitatively investigate the effect of learning objective in Eq. (10). We can observe a clear performance improvement by just minimizing the cross-domain feature inconsistency (Obj-2 in Tab. 3). Obviously, by jointly optimizing the two objectives, we obtain the best generalization performance. The quantitative and qualitative results clearly reflects the importance and efficacy of the two learning objectives in Sec. 3.2.2.", + "bbox": [ + 75, + 314, + 468, + 570 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "R4: Robustness to Complex Realistic Scenarios. In this section, we evaluate the generalization of our HVT-enhanced methods on the DrivingStereo [32] dataset which is collected from complex realistic scenarios: Sunny, Cloudy, Rainy, and Foggy, as shown in Fig. 5. We conduct experiments using the PSMNet [3] and GwcNet [10] as the baseline frameworks. The results of officially released fine-tuned (FT) networks of PSMNet and GwcNet on the realistic KITTI 2015 dataset are included for comparison. Besides, we also include the results of SOTA domain generalized SM methods [5, 46] in the Tab. 4. We have the following observations from Tab. 4 and Fig. 5:", + "bbox": [ + 75, + 577, + 467, + 758 + ], + "page_idx": 7 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Our methods (HVT-PSMNet and HVT-GwcNet) obtain the best overall performance $(5.4\\%$ and $5.3\\%)$ w.r.t. the average D1 error rate over the four groups of weather conditions, which demonstrates the efficacy of HVT and the strong robustness of HVT-based methods.", + "- HVT-PSMNet and HVT-GwcNet not only outperform the baselines PSMNet and GwcNet, respectively, by a large margin, but also decrease the error rates of the FT-PSMNet and FT-GwcNet on the Rainy and Foggy groups." + ], + "bbox": [ + 76, + 762, + 467, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e4ae0f8a73df010aa0b212d00aec450ff6ff296f74a58ccca5b69afb82d9d390.jpg", + "image_caption": [ + "Figure 5. Qualitative results on the DrivingStereo [32] dataset. For each group, top row shows the left image and the EPE error maps of PSMNet, fine-tuned (FT) PSMNet, and our HVT-PSMNet, respectively. Bottom row shows the GT disparity map and the predicted disparity maps of different methods. The EPE values are marked in the upper right corner of error maps." + ], + "image_footnote": [], + "bbox": [ + 521, + 88, + 864, + 284 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "On another two groups, both fine-tuned (FT) models perform slightly better than our HVT, since images in the two groups are similar to the KITTI training data. The results reflect that our HVT can effectively deal with the domain shift between the synthetic data and realistic data.", + "bbox": [ + 513, + 380, + 890, + 455 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "- Fig. 5 shows the qualitative robustness comparison in different weather conditions. The observation from Fig. 5 is consistent with that from Tab. 4, which further validates the potential of HVT in enhancing the model robustness.", + "bbox": [ + 500, + 458, + 890, + 517 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 534, + 617, + 549 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we have devised an effective HVT module for the problem of domain generalized SM. To prevent the network from exploiting the shortcut features for disparity estimation, we propose to 1) first diversify the training domain by leveraging the three complementary visual transformations, where the cross-domain visual discrepancy is maximized, and 2) minimize the cross-domain feature inconsistency to effectively capture domain-invariant features. Our proposed method is simple and can be flexibly integrated with most existing SM networks. Extensive experimental results show that our HVT consistently advances the learning of shortcut-robust features and substantially improves the generalization performance of SM networks in unseen realistic scenarios. In the future, we will attempt to design more delicate visual transformations to enhance HVT and extend HVT for addressing other 3D vision tasks.", + "bbox": [ + 496, + 559, + 890, + 815 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Acknowledgments", + "text_level": 1, + "bbox": [ + 500, + 830, + 678, + 847 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported by the National Natural Science Foundation of China (NSFC) under Grant 62272435, Grant U22A2094 and Grant 72188101.", + "bbox": [ + 498, + 854, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "9566", + "bbox": [ + 480, + 945, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Joydeep Biswas and Manuela Veloso. Depth camera based localization and navigation for indoor mobile robots. In RGB-D Workshop at RSS, volume 2011, 2011. 1", + "[2] Changjiang Cai, Matteo Poggi, Stefano Mattoccia, and Filippos Mordohai. Matching-space stereo networks for cross-domain generalization. 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Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.095, + 0.131, + 0.877, + 0.152 + ], + "angle": 0, + "content": "Domain Generalized Stereo Matching via Hierarchical Visual Transformation" + }, + { + "type": "text", + "bbox": [ + 0.241, + 0.18, + 0.728, + 0.199 + ], + "angle": 0, + "content": "Tianyu Chang\\(^{1,3}\\), Xun Yang\\(^{1*}\\), Tianzhu Zhang\\(^{1}\\), Meng Wang\\(^{2}\\)" + }, + { + "type": "text", + "bbox": [ + 0.145, + 0.199, + 0.826, + 0.234 + ], + "angle": 0, + "content": "1University of Science and Technology of China 2Hefei University of Technology Institute of Artificial Intelligence, Hefei Comprehensive National Science Center" + }, + { + "type": "text", + "bbox": [ + 0.111, + 0.238, + 0.853, + 0.251 + ], + "angle": 0, + "content": "cty8998@mail.ustc.edu.cn {xyang21, tzhang}@ustc.edu.cn wangmeng@h Fut.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.287, + 0.313, + 0.302 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.318, + 0.474, + 0.697 + ], + "angle": 0, + "content": "Recently, deep Stereo Matching (SM) networks have shown impressive performance and attracted increasing attention in computer vision. However, existing deep SM networks are prone to learn dataset-dependent shortcuts, which fail to generalize well on unseen realistic datasets. This paper takes a step towards training robust models for the domain generalized SM task, which mainly focuses on learning shortcut-invariant representation from synthetic data to alleviate the domain shifts. Specifically, we propose a Hierarchical Visual Transformation (HVT) network to 1) first transform the training sample hierarchically into new domains with diverse distributions from three levels: Global, Local, and Pixel, 2) then maximize the visual discrepancy between the source domain and new domains, and minimize the cross-domain feature inconsistency to capture domain-invariant features. In this way, we can prevent the model from exploiting the artifacts of synthetic stereo images as shortcut features, thereby estimating the disparity maps more effectively based on the learned robust and shortcut-invariant representation. We integrate our proposed HVT network with SOTA SM networks and evaluate its effectiveness on several public SM benchmark datasets. Extensive experiments clearly show that the HVT network can substantially enhance the performance of existing SM networks in synthetic-to-realistic domain generalization." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.718, + 0.21, + 0.734 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.744, + 0.47, + 0.834 + ], + "angle": 0, + "content": "Stereo Matching (SM) [7,41,44] aims to find the matching correspondences between a given stereo image pair and then calculate the disparity for depth sensing in many applications, such as robot navigation and autonomous driving [1,28]. Recently, it attracts increasing attention in the computer vision community [4,27,30,42]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.835, + 0.47, + 0.88 + ], + "angle": 0, + "content": "With the development of deep learning [6, 18, 34-38], Convolutional Neural Network (CNN) based deep SM networks have shown impressive performance benefiting from" + }, + { + "type": "image", + "bbox": [ + 0.523, + 0.285, + 0.869, + 0.452 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.455, + 0.892, + 0.537 + ], + "angle": 0, + "content": "Figure 1. Comparison of the cross-domain SM generalization. Columns from left to right denote a sample image, ground truth disparities, the predicted disparities of the pretrained PSMNet model and our HVT-PSMNet model. Both models are trained on the synthetic SceneFlow [19] dataset and evaluated on the realistic datasets: Middlebury, ETH3D, KITTI 2012 and KITTI 2015." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.55, + 0.893, + 0.822 + ], + "angle": 0, + "content": "their strong ability of feature representation. However, due to the scarcity of sufficient labeled realistic training data, existing state-of-the-art (SOTA) SM networks usually are trained on synthetic data, e.g. SceneFlow [19], which fail to generalize well to unseen realistic domains as shown in Fig. 1. Generally, the generalizability of cross-domain deep SM networks is mainly hindered by a critical issue: SM networks usually learn superficial shortcut features [5] from synthetic data to estimate the disparity. Specifically, such shortcut features mainly include two types of artifacts: consistent local RGB color statistics and overreliance on local chromaticity features, which are domain-sensitive and nontransferable to unseen domain. The semantic and structural features that are truly desirable are ignored by most existing SM networks. Therefore, the key to addressing the challenging cross-domain SM task is how to effectively learn the domain-invariant representations of the given stereo image pair for synthetic-to-realistic generalization." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Several attempts [3, 10, 15, 26, 45] have been made to minimize the synthetic-to-realistic domain gap and learn the domain-invariant representations for the SM task by either 1) exploiting labeled target-domain realistic data to fine-tune the SM network trained with synthetic data [3, 10]" + }, + { + "type": "page_footnote", + "bbox": [ + 0.102, + 0.888, + 0.232, + 0.9 + ], + "angle": 0, + "content": "*Corresponding Author" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9559" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.211 + ], + "angle": 0, + "content": "or 2) jointly using the synthetic data and unlabeled target-domain realistic data to train domain adaptive SM networks [15,26,45]. Despite their performance improvement on realistic data, these attempts only work well when the target-domain realistic data is provided during training and thus can not improve the out-of-distribution (OOD) generalization of SM networks, which are less practically useful in real-world scenarios." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.213, + 0.473, + 0.665 + ], + "angle": 0, + "content": "In this work, we address the important but less explored challenging problem of single domain generalization in SM, where only the synthetic data is available for training. Considering the fact that most existing SM networks are susceptible to exploiting shortcut cues in synthetic data instead of the semantic and structural correspondences, we propose to learn shortcut-invariant robust representation from synthetic SM image pairs for OOD generalization. Specifically, this paper presents a Hierarchical Visual Transformation (HVT) network to 1) first transform the synthetic training sample hierarchically into new source domains with diverse distributions from three levels: Global, Local, and Pixel, 2) then maximize the image discrepancy between the synthetic source domain and new domains for significantly altering the original distribution, and minimize the cross-domain feature inconsistency to capture domain-invariant features. In this way, we are able to prevent the model from exploiting the artifacts of synthetic stereo images as shortcut features, thereby estimating the disparity maps more effectively based on the learned shortcut-invariant feature representation. Our basic idea is to diversify the distribution of training data and thus force the network to overlook the artifacts from synthetic domain. Note that our proposed HVT network is simple and can be plug-and-play. We integrate HVT with SOTA SM networks during training and evaluate its effectiveness on several challenging SM benchmark datasets. Extensive experiments clearly show that the HVT network can substantially enhance the performance of existing SM networks in synthetic-to-realistic domain generalization without using any auxiliary data or features [17]." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.667, + 0.468, + 0.681 + ], + "angle": 0, + "content": "Our contributions can be briefly summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.686, + 0.47, + 0.76 + ], + "angle": 0, + "content": "- We devise a simple yet effective domain generalized SM framework. It leverages a hierarchical visual transformation network to effectively diversify the distribution of training data which prevents the model from exploiting the artifacts in synthetic data as shortcuts." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.763, + 0.468, + 0.853 + ], + "angle": 0, + "content": "- We formulate novel learning objectives that force the model to effectively optimize three complementary visual transformations by maximizing domain discrepancy and minimizing feature inconsistency between synthetic domain and new domains, thereby facilitating the learning of domain-invariant feature representation." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.856, + 0.468, + 0.901 + ], + "angle": 0, + "content": "- Extensive experiments on four realistic SM datasets clearly demonstrate the effectiveness and robustness of our HVT network. The out-of-distribution generalization" + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.686, + 0.47, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "ability of four SOTA SM methods has been significantly boosted, benefiting from our solution." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.136, + 0.642, + 0.151 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.162, + 0.892, + 0.205 + ], + "angle": 0, + "content": "This section briefly introduces the learning based stereo matching (SM) methods from two perspectives: 1) In-Distribution SM and 2) Our-of-Distribution SM." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.207, + 0.893, + 0.613 + ], + "angle": 0, + "content": "In-Distribution SM. In the past decade, deep learning has triggered the fast development of the task of SM. Mayer et al. [19] introduced an end-to-end SM network which uses the correlation layer to generate the cost volume and the 2D-CNN to aggregate the cost volume. SegStereo [33] and EdgeStereo [27] exploit the semantic and edge cues to help the disparity prediction. To learn better features, AANet [30] integrates both normal convolution and deformable convolution for feature extraction. Furthermore, GCNet [14] concatenates left and right features for cost volume generation and aggregation with 3D convolutions. GwcNet [10] proposes the group-wise correlation to construct the cost volume with lower memory cost. PSM-Net [3] proposes the spatial pyramid pooling module and the stack hourglass network to expand the receptive field. GANet [42] designs the image content guided layers to globally and locally update the cost volume. LEAStereo [4] introduces the neural architecture searching into SM. In recent several years, the Cascade-based SM methods [9, 25, 39] first use the coarsest resolution feature maps to predict an initial disparity, and narrow down the disparity search range to refine the disparity based on the initial disparity. Despite the good performance of existing deep-learning based SM networks, their training set and testing set always follow the independent and identically distributed (IID) assumption. Most existing works usually fail to generalize well on unseen realistic data." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.614, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Out-of-Distribution SM. Most recently, the synthetic-to-realistic generalized SM networks [5, 16, 25, 43] have received increasing attention. Different from those fine-tuning or adaptation-based methods [3, 15, 26, 42, 45], they aim to directly learn SM networks that can generalize to unseen domains. Some works propose to improve the generalization ability by devising novel network architectures. For example, DSMNet [43] proposes the domain normalization layer and the trainable non-local graph-based filter to learn domain-invariant structural feature. Besides, both CFNet [25] and RAFT-Stereo [16] introduce a network architecture with multi-scale cost volume fusion and aggregation to learn robust semantic or structural features. Some other efforts attempt to design flexible modules that can facilitate the cross-domain generalization of more existing SM networks. MS-Net [2] points out that learned feature is the core reason for the poor generalization performance, and proposes to use the traditional feature descriptors to construct the cost. FC-Net [46] uses the stereo contrastive" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "9560" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.16, + 0.09, + 0.812, + 0.309 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.31, + 0.895, + 0.355 + ], + "angle": 0, + "content": "Figure 2. The pipeline of our domain-generalized SM approach. It leverages a hierarchical visual transformation module to improve the diversity of training domain by training a domain discriminator \\(\\phi(\\cdot)\\). Its main goal is to optimize a feature extractor \\(f(\\cdot)\\) that can learn shortcut-robust and domain-invariant representation, thereby facilitating the generalization of SM network in unseen realistic domains." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.36, + 0.473, + 0.481 + ], + "angle": 0, + "content": "feature loss and the stereo selective whitening loss to encourage the stereo feature consistency across different domains. GraftNet [17] leverages the robust broad-spectrum feature which is trained on large-scale datasets to replace the original feature to improve the generalization ability. ITSA [5] generates the pixel-perturbed image through the gradient of the features with respect to the input image, and guides the network to learn shortcut-invariant feature." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.483, + 0.473, + 0.651 + ], + "angle": 0, + "content": "Different from these methods, we introduce a simple yet effective method to enhance the synthetic-to-realistic generalization. We design a hierarchical visual transformation module to diversify the training domain by maximizing the cross-domain visual discrepancy and propose to learn domain-invariant feature representation by minimizing the cross-domain feature inconsistency. ITSA [5] can be generally seen as a special case of our work that diversifies the distribution in the Pixel level. Experiments in the Sec. 4 have clearly validated the effectiveness of our method on improving the synthetic-to-realistic generalization of SM." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.667, + 0.224, + 0.685 + ], + "angle": 0, + "content": "3. The Approach" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.693, + 0.258, + 0.709 + ], + "angle": 0, + "content": "3.1. Problem Overview" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.718, + 0.47, + 0.845 + ], + "angle": 0, + "content": "This work aims to improve the synthetic-to-realistic domain generalization for SM. Given a synthetic training set \\(\\mathcal{D}_s\\) as input, consisting of \\(|\\mathcal{D}_s|\\) synthetic stereo image pairs \\(\\{\\mathbf{X}_i^l,\\mathbf{X}_i^r\\}_{i = 1}^{|\\mathcal{D}_s|}\\) and the corresponding ground-truth disparity maps \\(\\{\\mathbf{Y}_i^{gt}\\}_{i = 1}^{|\\mathcal{D}_s|}\\), the goal is to learn a cross-domain SM network that can effectively predict the disparity between a pair of stereo images from unseen domains \\(\\mathcal{D}_r\\). A typical SM network \\(F_{\\Theta}(\\cdot ,\\cdot)\\) can be formally formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.129, + 0.849, + 0.47, + 0.868 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {Y}} = F _ {\\Theta} \\left(\\mathbf {X} ^ {l}, \\mathbf {X} ^ {r}\\right) = s \\left(g \\left(f \\left(\\mathbf {X} ^ {l}\\right), f \\left(\\mathbf {X} ^ {r}\\right)\\right)\\right), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.473, + 0.903 + ], + "angle": 0, + "content": "where \\(\\Theta\\) denotes the total network parameters and \\(f(\\cdot)\\) is a feature extraction module that yields the feature map of" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.36, + 0.892, + 0.467 + ], + "angle": 0, + "content": "stereo images. \\( g(\\cdot) \\) is a joint network module that first generates the cost volume by correlation or concatenation strategy, and then performs the cost aggregation and refinement. The final disparity map \\( \\hat{\\mathbf{Y}} \\) is estimated by converting the refined cost volumes with the soft-argmin [14] operation \\( s(\\cdot) \\). The typical SM network \\( F_{\\Theta}(\\cdot,\\cdot) \\) is optimized by minimizing the smooth-\\( \\ell_1 \\) loss \\( L_{\\mathrm{sm}-\\ell_1}\\left(F_{\\Theta}(\\mathbf{X}^l,\\mathbf{X}^r),\\mathbf{Y}^{gt}\\right) \\) [3]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.467, + 0.893, + 0.693 + ], + "angle": 0, + "content": "In the past years, existing efforts primarily focus on how to devise an effective sub-network \\( g(\\cdot) \\) for cost volume generation and cost aggregation, while overlook the importance of learning robust feature representations of stereo images that can preserve the semantic and structural cues. Recent studies pointed out that most existing SM networks trained on synthetic data are susceptible to learn superficial shortcut features [5] instead of the desirable semantic and structural features, which leads to poor generalization performance in unseen (realistic) domain due to the significant synthetic-realistic domain gap. Therefore, the main research problem in this work is how to train an effective feature extraction network \\( f(\\cdot) \\) on only synthetic data that can learn generalizable representation of stereo images, so as to estimate reliable disparity map on unseen domain." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.702, + 0.71, + 0.719 + ], + "angle": 0, + "content": "3.2. Our Proposed Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.725, + 0.892, + 0.848 + ], + "angle": 0, + "content": "Our target is to tackle the synthetic-to-realistic generalization in SM. Its main challenge is that we only have synthetic data for training, which has the high risk of overfitting to synthetic data due to its limited diversity. Inspired by [13, 29, 40, 47], we address the domain generalized SM from a new perspective in this work. The rest of this section will introduce our proposed network for this task in detail. The pipeline of our proposed HVT is shown in Fig. 2" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.852, + 0.805, + 0.867 + ], + "angle": 0, + "content": "3.2.1 Hierarchical Visual Transformation" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.903 + ], + "angle": 0, + "content": "As we know, the key to addressing domain generalization is learning domain-invariant feature, also called causal fea" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "9561" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.38 + ], + "angle": 0, + "content": "Although the explicit form of causal feature is unknown in general, we have the prior that causal feature should remain invariant to certain transformations [29]. For example, the semantic and structural features can be treated as two domain-invariant (causal) features of stereo images for SM, while adjusting the luminance, contrast, or saturation of a stereo image pair will not affect the corresponding disparity map. Our intuitive idea is to leverage the visual transformations that do not change the underlying domain-invariant feature to increase the diversity of training domain, thereby enhancing the generalization performance of SM network. It is a straightforward but effective way. To this end, we design a Hierarchical Visual Transformation (HVT) network to diversify the distribution of training domain. Specifically, we learn a set of visual transformations \\(\\mathcal{T} = \\{T_1,\\dots ,T_M\\}\\) at different levels to transform the original stereo image pairs as \\((T(\\mathbf{X}^l),T(\\mathbf{X}^r))\\) , where \\(T\\in \\mathcal{T}\\) . We force the visual transformation \\(T(\\cdot)\\) to meet the following three requirements:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.385, + 0.47, + 0.43 + ], + "angle": 0, + "content": "- \\( T(\\cdot) \\) should induce large visual discrepancy between the original stereo image and the transformed images to enlarge the diversity of training domain." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.433, + 0.47, + 0.493 + ], + "angle": 0, + "content": "- \\(T(\\cdot)\\) should not change the target disparity map of the original stereo image pairs. We should minimize the smooth-\\(\\ell_1\\) loss \\(L_{\\mathrm{sm}-\\ell_1}(F_\\Theta(T(\\mathbf{X}^l), T(\\mathbf{X}^r)), \\mathbf{Y}^{gt})\\) where the transformed stereo images are fed into." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.498, + 0.469, + 0.543 + ], + "angle": 0, + "content": "- The representation of the transformed stereo images \\( f(T(\\mathbf{X})) \\) should be consistent with that of the original images \\( f(\\mathbf{X}) \\), so as to learn domain-invariant features." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.385, + 0.47, + 0.543 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.547, + 0.47, + 0.579 + ], + "angle": 0, + "content": "Following the above-listed requirements, we describe the implementation of our proposed HVT network as follows." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.586, + 0.47, + 0.646 + ], + "angle": 0, + "content": "Implementation of HVT. To effectively learn domain-invariant feature representation for the challenging SM task, we transform the stereo image from three complementary perspectives: Global, Local, and Pixel." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.652, + 0.469, + 0.759 + ], + "angle": 0, + "content": "(1) Global: The Global visual transformation \\( T_{G}(\\cdot) \\) aims to globally change the distribution of stereo images by sequentially adjusting the basic visual attributes of images: Brightness, Contrast, Saturation, and Hue based on the four corresponding sub-transformations \\( \\{T_{G}^{B}, T_{G}^{C}, T_{G}^{S}, T_{G}^{H}\\} \\), following the pipeline of automatic image editing [12]. The three sub-transformations \\( \\{T_{G}^{B}, T_{G}^{C}, T_{G}^{S}\\} \\) can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.154, + 0.762, + 0.469, + 0.78 + ], + "angle": 0, + "content": "\\[\nT _ {G} ^ {I} (\\mathbf {X}) = \\alpha_ {G} ^ {I} \\mathbf {X} + (1 - \\alpha_ {G} ^ {I}) o ^ {I} (\\mathbf {X}), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.783, + 0.469, + 0.816 + ], + "angle": 0, + "content": "where \\(I\\in \\{B,G,S\\}\\) . The \\(\\alpha_{G}^{I}\\) is a randomly selected positive constant in an adjustable range of \\([\\tau_{\\mathrm{min}}^I,\\tau_{\\mathrm{max}}^I ]\\)" + }, + { + "type": "equation", + "bbox": [ + 0.168, + 0.818, + 0.469, + 0.851 + ], + "angle": 0, + "content": "\\[\n\\left\\{ \\begin{array}{l} \\tau_ {\\min } ^ {I} = 1 - \\left(\\mu \\sigma \\left(\\varrho_ {l} ^ {I}\\right) + \\beta\\right) \\\\ \\tau_ {\\max } ^ {I} = 1 + \\left(\\mu \\sigma \\left(\\varrho_ {h} ^ {I}\\right) + \\beta\\right) \\end{array} , \\right. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.855, + 0.47, + 0.903 + ], + "angle": 0, + "content": "where \\(\\sigma (\\cdot)\\) denotes the sigmoid function, \\(\\varrho_l^I\\in \\mathbb{R}^1\\) and \\(\\varrho_h^I\\in \\mathbb{R}^1\\) are two learnable parameters, \\(\\mu\\) and \\(\\beta\\) are two positive hyper-parameters. The operation \\(o^{I}(\\cdot)\\) in Eq. (2)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.196 + ], + "angle": 0, + "content": "is customized as follows. Specifically, for the Brightness, \\(o^B (\\mathbf{X}) = \\mathbf{X}\\cdot \\mathbf{O}\\) where \\(\\mathbf{O}\\) denotes a zero matrix all of whose entries are zero. For the Contrast, \\(o^C (\\mathbf{X}) = \\mathrm{Avg}(\\mathrm{Gray}(\\mathbf{X}))\\) where Gray(·) transforms the RGB image into a gray-scale image and \\(\\mathrm{Avg}(\\cdot)\\) computes the mean value of all pixels. For the Saturation, \\(o^S (\\mathbf{X}) = \\mathrm{Gray}(\\mathbf{X})\\). The Hue adjustment is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.587, + 0.2, + 0.892, + 0.219 + ], + "angle": 0, + "content": "\\[\nT _ {G} ^ {H} (\\mathbf {X}) = \\operatorname {R g b} \\left(\\left[ \\mathbf {h} + \\alpha_ {G} ^ {H}, \\mathbf {s}, \\mathbf {v} \\right]\\right), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.222, + 0.894, + 0.314 + ], + "angle": 0, + "content": "where \\([\\mathbf{h},\\mathbf{s},\\mathbf{v}] = \\mathrm{Hsv}(\\mathbf{X})\\) denotes the three components of \\(\\mathbf{X}\\) in the HSV color space and \\(\\mathbf{h}\\) denotes the Hue component. \\(\\operatorname {Rgb}(\\cdot)\\) transforms the image from the HSV space into the RGB space. The \\(\\alpha_{G}^{H}\\in \\mathbb{R}^{1}\\) is randomly selected from an adjustable range of \\([\\tau_{\\min}^{H},\\tau_{\\max}^{H}]\\), where \\(\\tau_{\\mathrm{min}}^H = -\\mu \\sigma (\\varrho_l^H) - \\beta\\) and \\(\\tau_{\\mathrm{max}}^H = \\mu \\sigma (\\varrho_h^H) + \\beta\\)" + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.315, + 0.892, + 0.347 + ], + "angle": 0, + "content": "Note that the order of the sequential sub-transformations \\(\\{T_G^B, T_G^C, T_G^S, T_G^H\\}\\) is random to improve the diversity." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.351, + 0.892, + 0.473 + ], + "angle": 0, + "content": "(2) Local: The Local visual transformation \\( T_{L}(\\cdot) \\) aims to locally modify the distribution of stereo training images. The basic pipeline is that we first slice the given stereo image into \\( N' \\times N' \\) non-overlapping patches \\( \\{\\mathbf{x}_1^p, \\dots, \\mathbf{x}_{N' \\times N'}^p\\} \\), then transform each image patch \\( \\mathbf{x}_i^p \\) by a global transformation \\( T_{L}^{p}(\\cdot) \\), and finally merge these transformed image patches into the stereo image based on the original sequential order. The output can be described by" + }, + { + "type": "equation", + "bbox": [ + 0.524, + 0.477, + 0.892, + 0.495 + ], + "angle": 0, + "content": "\\[\nT _ {L} (\\mathbf {X}) = \\operatorname {M e r g e} \\left(\\left[ T _ {L} ^ {p} \\left(\\mathbf {x} _ {1} ^ {p}\\right), \\dots , T _ {L} ^ {p} \\left(\\mathbf {x} _ {N ^ {\\prime} \\times N ^ {\\prime}} ^ {p}\\right) \\right]\\right), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.498, + 0.803, + 0.513 + ], + "angle": 0, + "content": "where \\( \\text{Merge}(\\cdot) \\) denotes the Merge operation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.515, + 0.892, + 0.621 + ], + "angle": 0, + "content": "Note that patch-level transformation \\( T_{L}^{p}(\\cdot) \\) for each patch doesn't share parameters with each other to improve the diversity. \\( T_{L}^{p}(\\cdot) \\) can be implemented by existing style transfer networks, e.g. Adain [22] or Fourier-based method [31]. To better complementing our Global transformation, patch-level transformation \\( T_{L}^{p}(\\cdot) \\) is implemented by \\( T_{G}(\\cdot) \\) in Eq.(2) and Eq.(4) for its simplicity and effectiveness." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.627, + 0.892, + 0.672 + ], + "angle": 0, + "content": "(3) Pixel: The Pixel visual transformation \\( T_{P}(\\cdot) \\) aims to perturb the given stereo images with a pixel-level perturbation matrix. It can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.586, + 0.677, + 0.892, + 0.695 + ], + "angle": 0, + "content": "\\[\nT _ {P} (\\mathbf {X}) = \\mathbf {X} + (\\mu \\sigma (\\mathbf {W}) + \\beta) \\mathbf {P} \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.697, + 0.892, + 0.774 + ], + "angle": 0, + "content": "where \\(\\mathbf{P} \\in \\mathbb{R}^{H \\times W \\times 3}\\) is a randomly generated Gaussian matrix with the mean of 0 and the standard deviation of 1, and \\(\\mathbf{W} \\in \\mathbb{R}^{H \\times W \\times 3}\\) is a learnable matrix. Different from the Global and Local transformations, \\(T_P(\\cdot)\\) can alter the distribution of synthetic data in a more granular fashion." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Remark: The implementation of HVT is mainly motivated by the empirically found evidence [5] that existing SM networks are susceptible to exploit common artifacts (e.g. consistent local RGB color statistics and overreliance on local chromaticity features) of synthetic stereo images as shortcuts, which can be clearly illustrated by Fig. 3. We observe from Fig. 3 that the PSMNet is quite sensitive to the different levels of perturbation. It reflects that PSM-" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9562" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.468, + 0.38 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.383, + 0.47, + 0.452 + ], + "angle": 0, + "content": "Figure 3. Examples of visualized output of three visual transformations (top-2 rows of (a) and (b)) and the corresponding disparity error maps \\( |\\dot{\\mathbf{Y}} - \\mathbf{Y}^{gt}| \\) (the 3-rd row of (a) and (b)) of the PSMNet trained on the synthetic SceneFlow dataset. The EPE values are marked in the bottom of the 3-rd row for comparison." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.466, + 0.47, + 0.573 + ], + "angle": 0, + "content": "Net doesn't capture the robust semantic and structural features of stereo images. Our method is specially devised to improve the robustness and generalization ability of existing SM method. The design of the three different transformations \\(\\{T_{G}(\\mathbf{X}), T_{L}(\\mathbf{X}), T_{P}(\\mathbf{X})\\}\\) can effectively diversify the training domain and prevent the shortcuts from being encoded into the stereo image representation \\(f(\\mathbf{X})\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.602, + 0.273, + 0.618 + ], + "angle": 0, + "content": "3.2.2 Learning Objectives" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.63, + 0.47, + 0.675 + ], + "angle": 0, + "content": "To effectively train our proposed HVT network for the domain generalized SM task, we introduce the following loss terms for network optimization." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.677, + 0.471, + 0.814 + ], + "angle": 0, + "content": "Maximizing Cross-Domain Visual Discrepancy: In this work, without having access to the target domain, we propose to improve the SM network's generalization by transforming the synthetic source domain data into several new source domains \\(\\{T_G(\\mathbf{X}), T_L(\\mathbf{X}), T_P(\\mathbf{X})\\}\\) to diversify the training domain. Our first objective is to force the distributions of new source domains to be dissimilar as possible to the original distribution of synthetic data. Then we should maximize the following cross-domain visual discrepancy as" + }, + { + "type": "equation", + "bbox": [ + 0.151, + 0.816, + 0.469, + 0.852 + ], + "angle": 0, + "content": "\\[\n\\max L _ {\\text {d i s c}} (\\mathbf {X}) = \\frac {1}{3} \\sum_ {J} d \\left(T _ {J} (\\mathbf {X}), \\mathbf {X}\\right) \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.855, + 0.47, + 0.903 + ], + "angle": 0, + "content": "where \\( J \\in \\{G, L, P\\} \\), and \\( d(\\cdot) \\) is a domain discrepancy measure. In this work, we introduce a specific feature extraction network \\( \\phi(\\cdot) \\) for domain discriminating. Then we" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.886, + 0.107 + ], + "angle": 0, + "content": "implement Eq. (7) by minimizing the domain similarity as" + }, + { + "type": "equation", + "bbox": [ + 0.54, + 0.109, + 0.892, + 0.143 + ], + "angle": 0, + "content": "\\[\n\\min L _ {\\text {s i m}} (\\mathbf {X}) = \\frac {1}{3} \\sum_ {J} \\operatorname {C o s} \\left(\\phi \\left(T _ {J} (\\mathbf {X})\\right), \\phi (\\mathbf {X})\\right), \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.147, + 0.892, + 0.222 + ], + "angle": 0, + "content": "where \\(\\mathrm{Cos}(\\cdot ,\\cdot)\\) denotes the cosine similarity function. \\(\\phi (\\mathbf{X})\\) denotes the pooled feature vector from the domain discriminating network \\(\\phi (\\cdot)\\). Besides, to further improve the domain discrepancy, we also minimize the following cross-entropy loss for domain classification:" + }, + { + "type": "equation", + "bbox": [ + 0.544, + 0.226, + 0.892, + 0.243 + ], + "angle": 0, + "content": "\\[\n\\min L _ {\\mathrm {c e}} (\\mathbf {X}) = \\operatorname {C E} \\left(\\left\\{\\phi \\left(T _ {J} (\\mathbf {X})\\right), \\phi (\\mathbf {X}) \\right\\}, \\mathcal {Y} _ {d}\\right), \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.247, + 0.892, + 0.277 + ], + "angle": 0, + "content": "where \\(\\mathrm{CE}(\\cdot ,\\cdot)\\) denotes the standard cross-entropy loss and \\(\\mathcal{V}_d\\) denotes the domain labels of four source domains." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.282, + 0.892, + 0.419 + ], + "angle": 0, + "content": "Minimizing Cross-Domain Feature Inconsistency: To enhance the model's generalization ability, we need to learn domain-invariant representation of stereo images. We expect that our visual transformation \\( T(\\cdot) \\) doesn't change the core features (e.g., semantic and structural features) of images for stereo matching. Therefore, our second objective is to force the feature representation of transformed stereo images to be consistent with that of original synthetic images. Then we minimize the following pairwise distance term:" + }, + { + "type": "equation", + "bbox": [ + 0.526, + 0.421, + 0.892, + 0.455 + ], + "angle": 0, + "content": "\\[\n\\min L _ {\\text {d i s t}} (\\mathbf {X}) = \\frac {1}{3} \\sum_ {J} \\| f (T _ {J} (\\mathbf {X})) - f (\\mathbf {X}) \\| _ {2}, \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.458, + 0.892, + 0.518 + ], + "angle": 0, + "content": "which facilitates the learning of shortcut-robust and domain invariant features for domain-generalized stereo matching. In summary, our model is trained by minimizing the linear combination of the above-mentioned learning objectives:" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.522, + 0.891, + 0.571 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\min \\mathcal {L} = L _ {\\mathrm {s m} - \\ell_ {1}} (\\hat {\\mathbf {Y}}, \\mathbf {Y} ^ {g t}) + \\\\ \\frac {1}{2} \\left(\\lambda_ {1} L _ {\\text {d i s t}} (\\mathbf {X}) + \\lambda_ {2} L _ {\\text {s i m}} (\\mathbf {X}) + \\lambda_ {3} L _ {\\text {c e}} (\\mathbf {X})\\right), \\tag {11} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.574, + 0.892, + 0.65 + ], + "angle": 0, + "content": "The full loss \\(\\mathcal{L}\\) is computed as the average over a training batch. The smooth-\\(\\ell_1\\) loss \\(L_{\\mathrm{sm - }\\ell_1}\\) is computed based on not only the original synthetic image pairs \\(\\{\\mathbf{X}^l,\\mathbf{X}^r\\}\\) but also the transformed image pairs \\(\\{T_J(\\mathbf{X}^l),T_J(\\mathbf{X}^r)\\}\\). \\(\\lambda_{1},\\lambda_{2}\\) and \\(\\lambda_{3}\\) are three trade-off hyper-parameters." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.662, + 0.633, + 0.68 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.688, + 0.892, + 0.823 + ], + "angle": 0, + "content": "In this section, we quantitatively and qualitatively conduct extensive experiments to answer the following research questions: R1: Can the HVT effectively improve the generalization performance of existing SM networks? Can our performance reach the SOTA level? R2: Do the three transformations in the HVT effectively complement to each other? R3: Can our approach learn the domain-invariant features? R4: How is the robustness of our approach when tested in complex realistic scenarios?" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.833, + 0.796, + 0.849 + ], + "angle": 0, + "content": "4.1. Dataset and Experimental Setting" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Datasets. We use the SceneFlow [19] dataset for training and four realistic SM datasets (KITTI 2012 [8], KITTI 2015 [20], Middlebury [23] and ETH3D [24]) for e" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9563" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.107, + 0.089, + 0.861, + 0.334 + ], + "angle": 0, + "content": "
BaselinesMethodsKITTI 2015KITTI 2012Middlebury(H)ETH3DReferences
EPED1(3px)EPED1(3px)EPED1(2px)EPED1(1px)
-GANet [42]2.3111.71.9310.15.4120.31.3314.1CVPR 2019
CasStereo [9]2.4211.92.1211.83.7117.20.877.8CVPR 2020
DSMNet [43]1.466.51.266.22.6213.80.696.2ECCV 2020
PSMNet [3]PSMNet [3]3.1716.32.6915.17.6534.22.3323.8CVPR 2018
MS-PSMNet [2]1.64*7.82.33*14.04.72*19.81.42*16.83DV 2020
FC-PSMNet [46]1.58*7.51.42*7.04.14*18.31.25*12.8CVPR 2022
ITSA-PSMNet [5]1.39*5.81.09*5.23.25*12.70.94*9.8CVPR 2022
Graft-PSMNet [17]1.325.31.095.02.3410.91.1610.7CVPR 2022
HVT-PSMNet1.14±0.024.9±0.120.93±0.024.3±0.061.46±0.1310.2±0.160.47±0.036.9±0.23Ours
GwcNet [10]GwcNet [10]3.4322.72.7720.27.2337.92.7854.2CVPR 2019
FC-GwcNet [46]1.72*8.01.45*7.45.14*21.11.13*11.7CVPR 2022
ITSA-GwcNet [5]1.33*5.41.02*4.92.73*11.40.62*7.1CVPR 2022
HVT-GwcNet1.15±0.025.0±0.110.88±0.023.9±0.131.29±0.1310.3±0.210.46±0.085.9±0.26Ours
CFNet [25]CFNet [25]1.716.01.045.23.2415.40.485.72CVPR 2021
ITSA-CFNet [5]1.094.70.874.21.8710.40.455.1CVPR 2022
HVT-CFNet1.10±0.044.9±0.160.85±0.024.0±0.141.79±0.2210.2±0.160.39±0.024.5±0.24Ours
RAFT [16]RAFT [16]1.265.71.015.11.9212.60.363.33DV 2021
HVT-RAFT1.12±0.025.2±0.090.87±0.023.7±0.081.37±0.1110.4±0.140.29±0.013.0±0.09Ours
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.339, + 0.892, + 0.369 + ], + "angle": 0, + "content": "Table 1. Performance comparison with SOTA domain generalized SM networks. The * denotes our reproduced EPE results since the authors only use the D1 metric. As we didn't have a validation set for model selection, we report the average result over last 5 epochs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.381, + 0.47, + 0.562 + ], + "angle": 0, + "content": "valuation. SceneFlow [19] is a large-scale synthetic SM dataset containing 35,454 training stereo image pairs and 4,370 testing image pairs with a resolution of \\(960 \\times 540\\). All the synthetic image pairs have dense annotations of ground-truth disparities. KITTI 2012 [8] and KITTI 2015 [20] consists of 194 and 200 training stereo image pairs collected in outdoor driving scenes with sparse annotations of disparities, respectively. Middlebury [23] includes 15 high-resolution stereo image pairs in indoor scenes. In our experiments, we use the half-resolution version (Middlebury(H)) for evaluation. ETH3D [24] has 27 grayscale stereo image pairs collected from both indoor and outdoor scenes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.564, + 0.47, + 0.716 + ], + "angle": 0, + "content": "Metrics. Following the setting of [17], we use both EPE rate (End-Point Error) and D1 error rate \\((\\%)\\) with different pixel threshold \\(\\rho\\) as the metrics to get a more comprehensive evaluation. The EPE measures the average disparity error over all pixels, which reflects the average disparity estimate. The D1 error rate computes the percentage of error pixels with absolute error larger than a specific threshold \\(\\rho\\). The pixel threshold is set as \\(\\rho = 3\\mathrm{px}\\) for KITTI 2012 [8] and KITTI 2015 [20], \\(\\rho = 2\\mathrm{px}\\) for Middlebury [23] and \\(\\rho = 1\\mathrm{px}\\) for ETH3D [24], respectively, following recent works [17, 46]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.718, + 0.469, + 0.809 + ], + "angle": 0, + "content": "Baselines. We select four SM networks as baselines, including two well-studied and commonly-used methods (PSMNet [3] and GwcNet [10]) and two SOTA methods (CFNet [25] and RAFT [16]), in our experiments. We will integrate our HVT networks with these baseline networks to validate the effectiveness of HVT on domain generalization." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Implementation Details. Following [43], we use the domain normalization technique in the feature extraction module for all baselines. Except the RAFT [16], all the baselines are implemented by PyTorch [21] with Adam \\((\\beta_{1} = 0.9, \\beta_{2} = 0.999)\\) optimizer. We train the model for 45 epochs with the batch size of 8. Besides, we introduce an incremen" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.381, + 0.892, + 0.669 + ], + "angle": 0, + "content": "tal training scheme to stably optimize the network in this work. Specifically, we train the model with \\(T_{G}(\\cdot)\\) only for 15 epochs at Stage I, then we further train the model with \\(\\{T_G(\\cdot), T_L(\\cdot)\\}\\) for another 15 epochs at Stage II, and finally we continually train the model with \\(\\{T_G(\\cdot), T_L(\\cdot), T_P(\\cdot)\\}\\) for the remaining 15 epochs at Stage III. The learning rate is set to 0.001 and decreased by half after epoch 10, 20, 30 and 40. For the RAFT [16] baseline, we train the model for total 30K steps and train each stage 10K steps. The optimizer and learning rate follow its original setting. Besides, the asymmetric chromatic augmentation is not used in any models to avoid unfair experimental comparison. We select ResNet18 [11] as the domain discriminating network \\(\\phi(\\cdot)\\) for its simplicity. For different hyper-parameters, the \\(\\mu\\) and \\(\\beta\\) in Eq. (3) and (6) are set as 0.1 and 0.15 respectively. The \\(\\lambda_1\\), \\(\\lambda_2\\) and \\(\\lambda_3\\) in Eq. (11) are set as 1, 0.5 and 0.5 respectively. The \\(N' = 4\\) in \\(T_{L}(\\cdot)\\). Note that all the SM networks are only trained on the synthetic dataset, SceneFlow. The target data is strictly inaccessible during training." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.678, + 0.797, + 0.695 + ], + "angle": 0, + "content": "4.2. Overall Performance Comparison" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.702, + 0.892, + 0.793 + ], + "angle": 0, + "content": "R1: Comparison with Baselines and SOTAs. In Tab. 1, we report the comparison of generalization performance between the baselines (PSMNet, GwcNet, CFNet, and RAFT) and our HVT-integrated methods, as well as the comparison between ours and the reported SOTA results, across the four realistic datasets. We have the following observations:" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "- The synthetic-to-realistic generalization performances of all the baselines are consistently improved by our HVT in all settings. Specifically, compared with the widely-used PSMNet [3], the performance improvements w.r.t. the D1 metric are \\(11.4\\%\\), \\(10.8\\%\\), \\(24\\%\\), and \\(16.9\\%\\), respectively on the four datasets. Similar improvement can also be observed on GwcNet [10]: \\(17.7\\%\\), \\(16.3\\%\\), \\(27.6\\%\\), and" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "9564" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.084, + 0.089, + 0.464, + 0.317 + ], + "angle": 0, + "content": "
BaselinesGlobal Local PixelKITTI 2015MiddleburyETH3D
EPE3pxEPE2pxEPE1px
PSMNet [3]✓✗✗1.316.072.0413.70.489.4
✗✓✗1.286.031.6912.50.5910.7
✗✗✓1.276.292.3914.60.579.9
✓✓✗1.235.471.5711.10.539.1
✓✗✓1.195.571.4411.20.517.7
✗✓✓1.275.721.5810.90.627.9
✓✓✓1.144.931.4610.20.476.9
GwcNet [10]✓✗✗1.285.891.8812.60.748.2
✗✓✗1.265.881.6411.90.688.5
✗✗✓1.296.181.8312.40.718.3
✓✓✗1.235.381.5810.40.587.8
✓✗✓1.195.521.4910.70.557.1
✗✓✓1.185.471.5710.60.526.9
✓✓✓1.155.021.2910.30.465.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.324, + 0.47, + 0.366 + ], + "angle": 0, + "content": "Table 2. Ablation studies on the effect of three visual transformations (Global, Local, and Pixel) on three datasets using the two well-studied baselines, PSMNet [3] and GwcNet [10]." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.378, + 0.47, + 0.59 + ], + "angle": 0, + "content": "\\(48.3\\%\\) w.r.t. the D1 metric. Even compared with the SOTA CFNet [25] and RAFT [16], the D1 error rates are still substantially decreased: \\(1.1\\%\\), \\(1.2\\%\\), \\(5.2\\%\\), and \\(1.2\\%\\) for CFNet, and \\(0.5\\%\\), \\(1.4\\%\\), \\(2.2\\%\\), and \\(0.3\\%\\) for RAFT. The quantitative comparison clearly shows the effectiveness of HVT on enhancing the robustness of SM models. The improvement can be mainly attributed to the fact that our HVT significantly diversify the visual distribution of original synthetic images, thus preventing the model from building the spurious relationship between the pairwise input and the target disparity. The model will not easily find the matching correspondences across the stereo images by just leveraging the shortcut cues, e.g., local RGB color statistics and chromaticity features." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.595, + 0.47, + 0.745 + ], + "angle": 0, + "content": "- The improvements of generalization performance brought by HVT on the Middlebury and ETH3D datasets seem to be much larger than those on the KITTI 2012 and 2015 datasets. The reason is that Middlebury has higher resolution images in realistic scenarios than those in KITTI 2012 and 2015, and the images in ETH3D are all grayscale which are very different from the colorful synthetic training images. It reflects that our HVT can perform well in diverse realistic scenarios that differ from training domain in resolution and color distribution." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.75, + 0.471, + 0.902 + ], + "angle": 0, + "content": "- Our HVT-enhanced methods almost outperform all the SOTA methods except ITSA-CFNet on KITTI 2015. It shows the strong potential of our HVT in improving the cross-domain generalization. Note that the three transformations devised in this work are all simple and straightforward. The performance can be further improved if we introduce more delicate transformations into our HVT. Besides, the performance of ITSA-CFNet on KITTI 2015 is already very high w.r.t. the EPE and D1 metrics, 1.09 and \\(4.7\\%\\). Our HVT-CFNet's performance is on a par" + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.595, + 0.471, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "table", + "bbox": [ + 0.526, + 0.089, + 0.868, + 0.197 + ], + "angle": 0, + "content": "
BaselinesObj-1Obj-2KITTI 2015MiddleburyETH3D
EPE3pxEPE2pxEPE2px
PSMNet [3]XX1.677.742.8815.10.8913.2
X✓1.316.232.0411.70.6310.1
✓✓1.144.931.4610.20.476.9
GwcNet [10]XX1.647.582.6514.60.8612.4
X✓1.286.071.9311.30.579.2
✓✓1.155.021.2910.30.465.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.198, + 0.89, + 0.227 + ], + "angle": 0, + "content": "Table 3. Ablation studies of our two main optimization objectives: Obj-1 (i.e., Eq. (8) and Eq. (9)) and Obj-2 (i.e., Eq. (10))." + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.24, + 0.892, + 0.41 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.416, + 0.892, + 0.472 + ], + "angle": 0, + "content": "Figure 4. Visualization of RGB color histograms (see (b)) and visual feature histograms (see (c)) of original image and transformed images (see (a)) based on the HVT-PSMNet method. The original image is randomly selected from the realistic Middlebury dataset." + }, + { + "type": "text", + "bbox": [ + 0.516, + 0.486, + 0.714, + 0.499 + ], + "angle": 0, + "content": "with that of the ITSA-CFNet." + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.502, + 0.892, + 0.637 + ], + "angle": 0, + "content": "- Benefiting from using HVT, the performances of weak baselines, i.e., PSMNet and GwcNet, have been increased to the SOTA level, especially on the top-three datasets. It reflects that the critical step for the domain-generalized SM task is to learn domain-invariant representation from diverse training domain instead of devising different complex network modules for cost volume generation or aggregation. It further validates the rationale of our HVT." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.651, + 0.665, + 0.667 + ], + "angle": 0, + "content": "4.3. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.901 + ], + "angle": 0, + "content": "R2: The Complementation of HVTs. As shown in Tab. 2, we investigate the effect of the HVT module by gradually adding the visual transformations in two baselines, PSMNet [3] and GwcNet [10]. We observe that the three visual transformations can complement well to each other. Specifically, only using one of the three transformations can also facilitate the performance improvement of baselines. When using more visual transformations, we observe consistent performance gains across the three realistic datasets. For example, the D1 error rates of \\( T_{G}(\\cdot) \\)-enhanced PSMNet have been decreased from \\( 6.07\\% \\), \\( 13.7\\% \\), and \\( 9.4\\% \\) to \\( 5.57\\% \\), \\( 11.2\\% \\), and \\( 7.7\\% \\), respectively, when jointly using \\( T_{G}(\\cdot) \\) and \\( T_{P}(\\cdot) \\). The best performances are observed when all the three transformations are jointly used. Similar performance improvements can also be observed when Gwc" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9565" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.1, + 0.089, + 0.445, + 0.238 + ], + "angle": 0, + "content": "
MethodsSunnyCloudyRainyFoggyAvg.
PSMNet [3]62.560.160.568.663.9
FT-PSMNet [5]4.02.911.56.56.3
FC-PSMNet [46]4.94.37.26.25.7
ITSA-PSMNet [5]4.83.29.46.35.9
HVT-PSMNet4.23.18.75.65.4
GwcNet [10]18.124.728.228.324.8
FT-GwcNet [5]3.12.512.36.06.0
ITSA-GwcNet [5]4.43.39.85.95.9
HVT-GwcNet3.43.58.65.65.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.242, + 0.468, + 0.285 + ], + "angle": 0, + "content": "Table 4. Robustness comparison of different methods on the DrivingStereo [32] dataset collected from complex realistic scenarios: Sunny, Cloudy, Rainy, and Foggy. The D1 (3px) metric is used." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.295, + 0.286, + 0.308 + ], + "angle": 0, + "content": "Net is used as the SM baseline." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.315, + 0.47, + 0.571 + ], + "angle": 0, + "content": "R3: Learning Domain-Invariant features. The core of our approach is to learn shortcut-robust features that can generalize well to unseen domains. As illustrated in Fig. 4 (b), we observe that the hierarchical visual transformation's significantly alter the RGB color histograms of original stereo image in the levels of Global, Local, and Pixel. Benefiting from the minimization of cross-domain feature inconsistency in Eq. (10), the image representation \\( f(\\mathbf{X}) \\) seems to be invariant across different domains as shown in Fig. 4 (c). Tab. 3 quantitatively investigate the effect of learning objective in Eq. (10). We can observe a clear performance improvement by just minimizing the cross-domain feature inconsistency (Obj-2 in Tab. 3). Obviously, by jointly optimizing the two objectives, we obtain the best generalization performance. The quantitative and qualitative results clearly reflects the importance and efficacy of the two learning objectives in Sec. 3.2.2." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.578, + 0.468, + 0.759 + ], + "angle": 0, + "content": "R4: Robustness to Complex Realistic Scenarios. In this section, we evaluate the generalization of our HVT-enhanced methods on the DrivingStereo [32] dataset which is collected from complex realistic scenarios: Sunny, Cloudy, Rainy, and Foggy, as shown in Fig. 5. We conduct experiments using the PSMNet [3] and GwcNet [10] as the baseline frameworks. The results of officially released fine-tuned (FT) networks of PSMNet and GwcNet on the realistic KITTI 2015 dataset are included for comparison. Besides, we also include the results of SOTA domain generalized SM methods [5, 46] in the Tab. 4. We have the following observations from Tab. 4 and Fig. 5:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.763, + 0.468, + 0.837 + ], + "angle": 0, + "content": "- Our methods (HVT-PSMNet and HVT-GwcNet) obtain the best overall performance \\((5.4\\%\\) and \\(5.3\\%)\\) w.r.t. the average D1 error rate over the four groups of weather conditions, which demonstrates the efficacy of HVT and the strong robustness of HVT-based methods." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.84, + 0.468, + 0.901 + ], + "angle": 0, + "content": "- HVT-PSMNet and HVT-GwcNet not only outperform the baselines PSMNet and GwcNet, respectively, by a large margin, but also decrease the error rates of the FT-PSMNet and FT-GwcNet on the Rainy and Foggy groups." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.763, + 0.468, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.089, + 0.866, + 0.285 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.289, + 0.892, + 0.372 + ], + "angle": 0, + "content": "Figure 5. Qualitative results on the DrivingStereo [32] dataset. For each group, top row shows the left image and the EPE error maps of PSMNet, fine-tuned (FT) PSMNet, and our HVT-PSMNet, respectively. Bottom row shows the GT disparity map and the predicted disparity maps of different methods. The EPE values are marked in the upper right corner of error maps." + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.381, + 0.891, + 0.456 + ], + "angle": 0, + "content": "On another two groups, both fine-tuned (FT) models perform slightly better than our HVT, since images in the two groups are similar to the KITTI training data. The results reflect that our HVT can effectively deal with the domain shift between the synthetic data and realistic data." + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.459, + 0.891, + 0.518 + ], + "angle": 0, + "content": "- Fig. 5 shows the qualitative robustness comparison in different weather conditions. The observation from Fig. 5 is consistent with that from Tab. 4, which further validates the potential of HVT in enhancing the model robustness." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.535, + 0.618, + 0.55 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.56, + 0.892, + 0.816 + ], + "angle": 0, + "content": "In this work, we have devised an effective HVT module for the problem of domain generalized SM. To prevent the network from exploiting the shortcut features for disparity estimation, we propose to 1) first diversify the training domain by leveraging the three complementary visual transformations, where the cross-domain visual discrepancy is maximized, and 2) minimize the cross-domain feature inconsistency to effectively capture domain-invariant features. Our proposed method is simple and can be flexibly integrated with most existing SM networks. Extensive experimental results show that our HVT consistently advances the learning of shortcut-robust features and substantially improves the generalization performance of SM networks in unseen realistic scenarios. In the future, we will attempt to design more delicate visual transformations to enhance HVT and extend HVT for addressing other 3D vision tasks." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.831, + 0.679, + 0.848 + ], + "angle": 0, + "content": "6. Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.891, + 0.9 + ], + "angle": 0, + "content": "This work was supported by the National Natural Science Foundation of China (NSFC) under Grant 62272435, Grant U22A2094 and Grant 72188101." + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9566" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.158 + ], + "angle": 0, + "content": "[1] Joydeep Biswas and Manuela Veloso. Depth camera based localization and navigation for indoor mobile robots. In RGB-D Workshop at RSS, volume 2011, 2011. 1" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.16, + 0.472, + 0.228 + ], + "angle": 0, + "content": "[2] Changjiang Cai, Matteo Poggi, Stefano Mattoccia, and Filippos Mordohai. 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Springer, 2020. 3" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.686 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.956 + ], + "angle": 0, + "content": "9568" + } + ] +] \ No newline at end of file diff --git a/2023/Domain Generalized Stereo Matching via Hierarchical Visual Transformation/9850d655-e7cd-45f5-81bc-ed4d96ec4425_origin.pdf b/2023/Domain Generalized Stereo Matching via Hierarchical Visual Transformation/9850d655-e7cd-45f5-81bc-ed4d96ec4425_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..8f6e435ce2ef874d5d59592e99d08b0b91aea014 --- /dev/null +++ b/2023/Domain Generalized Stereo Matching via Hierarchical Visual Transformation/9850d655-e7cd-45f5-81bc-ed4d96ec4425_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:8d33b68c42c5ab7d4e50011dadb80cb17d8acb4adc50ceaf4cd93266d6f95fa7 +size 6353439 diff --git a/2023/Domain Generalized Stereo Matching via Hierarchical Visual Transformation/full.md b/2023/Domain Generalized Stereo Matching via Hierarchical Visual Transformation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..7b076e59314c90ca9fa12a7019b1f29aa4a01802 --- /dev/null +++ b/2023/Domain Generalized Stereo Matching via Hierarchical Visual Transformation/full.md @@ -0,0 +1,308 @@ +# Domain Generalized Stereo Matching via Hierarchical Visual Transformation + +Tianyu Chang $^{1,3}$ , Xun Yang $^{1*}$ , Tianzhu Zhang $^{1}$ , Meng Wang $^{2}$ + +1University of Science and Technology of China 2Hefei University of Technology Institute of Artificial Intelligence, Hefei Comprehensive National Science Center + +cty8998@mail.ustc.edu.cn {xyang21, tzhang}@ustc.edu.cn wangmeng@h Fut.edu.cn + +# Abstract + +Recently, deep Stereo Matching (SM) networks have shown impressive performance and attracted increasing attention in computer vision. However, existing deep SM networks are prone to learn dataset-dependent shortcuts, which fail to generalize well on unseen realistic datasets. This paper takes a step towards training robust models for the domain generalized SM task, which mainly focuses on learning shortcut-invariant representation from synthetic data to alleviate the domain shifts. Specifically, we propose a Hierarchical Visual Transformation (HVT) network to 1) first transform the training sample hierarchically into new domains with diverse distributions from three levels: Global, Local, and Pixel, 2) then maximize the visual discrepancy between the source domain and new domains, and minimize the cross-domain feature inconsistency to capture domain-invariant features. In this way, we can prevent the model from exploiting the artifacts of synthetic stereo images as shortcut features, thereby estimating the disparity maps more effectively based on the learned robust and shortcut-invariant representation. We integrate our proposed HVT network with SOTA SM networks and evaluate its effectiveness on several public SM benchmark datasets. Extensive experiments clearly show that the HVT network can substantially enhance the performance of existing SM networks in synthetic-to-realistic domain generalization. + +# 1. Introduction + +Stereo Matching (SM) [7,41,44] aims to find the matching correspondences between a given stereo image pair and then calculate the disparity for depth sensing in many applications, such as robot navigation and autonomous driving [1,28]. Recently, it attracts increasing attention in the computer vision community [4,27,30,42]. + +With the development of deep learning [6, 18, 34-38], Convolutional Neural Network (CNN) based deep SM networks have shown impressive performance benefiting from + +![](images/c09daecdb5f2f94dd35e0a62126038002e43271632d10986f205c91cdf694c9f.jpg) +Figure 1. Comparison of the cross-domain SM generalization. Columns from left to right denote a sample image, ground truth disparities, the predicted disparities of the pretrained PSMNet model and our HVT-PSMNet model. Both models are trained on the synthetic SceneFlow [19] dataset and evaluated on the realistic datasets: Middlebury, ETH3D, KITTI 2012 and KITTI 2015. + +their strong ability of feature representation. However, due to the scarcity of sufficient labeled realistic training data, existing state-of-the-art (SOTA) SM networks usually are trained on synthetic data, e.g. SceneFlow [19], which fail to generalize well to unseen realistic domains as shown in Fig. 1. Generally, the generalizability of cross-domain deep SM networks is mainly hindered by a critical issue: SM networks usually learn superficial shortcut features [5] from synthetic data to estimate the disparity. Specifically, such shortcut features mainly include two types of artifacts: consistent local RGB color statistics and overreliance on local chromaticity features, which are domain-sensitive and nontransferable to unseen domain. The semantic and structural features that are truly desirable are ignored by most existing SM networks. Therefore, the key to addressing the challenging cross-domain SM task is how to effectively learn the domain-invariant representations of the given stereo image pair for synthetic-to-realistic generalization. + +Several attempts [3, 10, 15, 26, 45] have been made to minimize the synthetic-to-realistic domain gap and learn the domain-invariant representations for the SM task by either 1) exploiting labeled target-domain realistic data to fine-tune the SM network trained with synthetic data [3, 10] + +or 2) jointly using the synthetic data and unlabeled target-domain realistic data to train domain adaptive SM networks [15,26,45]. Despite their performance improvement on realistic data, these attempts only work well when the target-domain realistic data is provided during training and thus can not improve the out-of-distribution (OOD) generalization of SM networks, which are less practically useful in real-world scenarios. + +In this work, we address the important but less explored challenging problem of single domain generalization in SM, where only the synthetic data is available for training. Considering the fact that most existing SM networks are susceptible to exploiting shortcut cues in synthetic data instead of the semantic and structural correspondences, we propose to learn shortcut-invariant robust representation from synthetic SM image pairs for OOD generalization. Specifically, this paper presents a Hierarchical Visual Transformation (HVT) network to 1) first transform the synthetic training sample hierarchically into new source domains with diverse distributions from three levels: Global, Local, and Pixel, 2) then maximize the image discrepancy between the synthetic source domain and new domains for significantly altering the original distribution, and minimize the cross-domain feature inconsistency to capture domain-invariant features. In this way, we are able to prevent the model from exploiting the artifacts of synthetic stereo images as shortcut features, thereby estimating the disparity maps more effectively based on the learned shortcut-invariant feature representation. Our basic idea is to diversify the distribution of training data and thus force the network to overlook the artifacts from synthetic domain. Note that our proposed HVT network is simple and can be plug-and-play. We integrate HVT with SOTA SM networks during training and evaluate its effectiveness on several challenging SM benchmark datasets. Extensive experiments clearly show that the HVT network can substantially enhance the performance of existing SM networks in synthetic-to-realistic domain generalization without using any auxiliary data or features [17]. + +Our contributions can be briefly summarized as follows: + +- We devise a simple yet effective domain generalized SM framework. It leverages a hierarchical visual transformation network to effectively diversify the distribution of training data which prevents the model from exploiting the artifacts in synthetic data as shortcuts. +- We formulate novel learning objectives that force the model to effectively optimize three complementary visual transformations by maximizing domain discrepancy and minimizing feature inconsistency between synthetic domain and new domains, thereby facilitating the learning of domain-invariant feature representation. +- Extensive experiments on four realistic SM datasets clearly demonstrate the effectiveness and robustness of our HVT network. The out-of-distribution generalization + +ability of four SOTA SM methods has been significantly boosted, benefiting from our solution. + +# 2. Related Work + +This section briefly introduces the learning based stereo matching (SM) methods from two perspectives: 1) In-Distribution SM and 2) Our-of-Distribution SM. + +In-Distribution SM. In the past decade, deep learning has triggered the fast development of the task of SM. Mayer et al. [19] introduced an end-to-end SM network which uses the correlation layer to generate the cost volume and the 2D-CNN to aggregate the cost volume. SegStereo [33] and EdgeStereo [27] exploit the semantic and edge cues to help the disparity prediction. To learn better features, AANet [30] integrates both normal convolution and deformable convolution for feature extraction. Furthermore, GCNet [14] concatenates left and right features for cost volume generation and aggregation with 3D convolutions. GwcNet [10] proposes the group-wise correlation to construct the cost volume with lower memory cost. PSM-Net [3] proposes the spatial pyramid pooling module and the stack hourglass network to expand the receptive field. GANet [42] designs the image content guided layers to globally and locally update the cost volume. LEAStereo [4] introduces the neural architecture searching into SM. In recent several years, the Cascade-based SM methods [9, 25, 39] first use the coarsest resolution feature maps to predict an initial disparity, and narrow down the disparity search range to refine the disparity based on the initial disparity. Despite the good performance of existing deep-learning based SM networks, their training set and testing set always follow the independent and identically distributed (IID) assumption. Most existing works usually fail to generalize well on unseen realistic data. + +Out-of-Distribution SM. Most recently, the synthetic-to-realistic generalized SM networks [5, 16, 25, 43] have received increasing attention. Different from those fine-tuning or adaptation-based methods [3, 15, 26, 42, 45], they aim to directly learn SM networks that can generalize to unseen domains. Some works propose to improve the generalization ability by devising novel network architectures. For example, DSMNet [43] proposes the domain normalization layer and the trainable non-local graph-based filter to learn domain-invariant structural feature. Besides, both CFNet [25] and RAFT-Stereo [16] introduce a network architecture with multi-scale cost volume fusion and aggregation to learn robust semantic or structural features. Some other efforts attempt to design flexible modules that can facilitate the cross-domain generalization of more existing SM networks. MS-Net [2] points out that learned feature is the core reason for the poor generalization performance, and proposes to use the traditional feature descriptors to construct the cost. FC-Net [46] uses the stereo contrastive + +![](images/093696791a5f78dc7b0ace1b6569150e9dbf275dfa357d1b87e3a48004e70d82.jpg) +Figure 2. The pipeline of our domain-generalized SM approach. It leverages a hierarchical visual transformation module to improve the diversity of training domain by training a domain discriminator $\phi(\cdot)$ . Its main goal is to optimize a feature extractor $f(\cdot)$ that can learn shortcut-robust and domain-invariant representation, thereby facilitating the generalization of SM network in unseen realistic domains. + +feature loss and the stereo selective whitening loss to encourage the stereo feature consistency across different domains. GraftNet [17] leverages the robust broad-spectrum feature which is trained on large-scale datasets to replace the original feature to improve the generalization ability. ITSA [5] generates the pixel-perturbed image through the gradient of the features with respect to the input image, and guides the network to learn shortcut-invariant feature. + +Different from these methods, we introduce a simple yet effective method to enhance the synthetic-to-realistic generalization. We design a hierarchical visual transformation module to diversify the training domain by maximizing the cross-domain visual discrepancy and propose to learn domain-invariant feature representation by minimizing the cross-domain feature inconsistency. ITSA [5] can be generally seen as a special case of our work that diversifies the distribution in the Pixel level. Experiments in the Sec. 4 have clearly validated the effectiveness of our method on improving the synthetic-to-realistic generalization of SM. + +# 3. The Approach + +# 3.1. Problem Overview + +This work aims to improve the synthetic-to-realistic domain generalization for SM. Given a synthetic training set $\mathcal{D}_s$ as input, consisting of $|\mathcal{D}_s|$ synthetic stereo image pairs $\{\mathbf{X}_i^l,\mathbf{X}_i^r\}_{i = 1}^{|\mathcal{D}_s|}$ and the corresponding ground-truth disparity maps $\{\mathbf{Y}_i^{gt}\}_{i = 1}^{|\mathcal{D}_s|}$ , the goal is to learn a cross-domain SM network that can effectively predict the disparity between a pair of stereo images from unseen domains $\mathcal{D}_r$ . A typical SM network $F_{\Theta}(\cdot ,\cdot)$ can be formally formulated as: + +$$ +\hat {\mathbf {Y}} = F _ {\Theta} \left(\mathbf {X} ^ {l}, \mathbf {X} ^ {r}\right) = s \left(g \left(f \left(\mathbf {X} ^ {l}\right), f \left(\mathbf {X} ^ {r}\right)\right)\right), \tag {1} +$$ + +where $\Theta$ denotes the total network parameters and $f(\cdot)$ is a feature extraction module that yields the feature map of + +stereo images. $g(\cdot)$ is a joint network module that first generates the cost volume by correlation or concatenation strategy, and then performs the cost aggregation and refinement. The final disparity map $\hat{\mathbf{Y}}$ is estimated by converting the refined cost volumes with the soft-argmin [14] operation $s(\cdot)$ . The typical SM network $F_{\Theta}(\cdot,\cdot)$ is optimized by minimizing the smooth- $\ell_1$ loss $L_{\mathrm{sm}-\ell_1}\left(F_{\Theta}(\mathbf{X}^l,\mathbf{X}^r),\mathbf{Y}^{gt}\right)$ [3]. + +In the past years, existing efforts primarily focus on how to devise an effective sub-network $g(\cdot)$ for cost volume generation and cost aggregation, while overlook the importance of learning robust feature representations of stereo images that can preserve the semantic and structural cues. Recent studies pointed out that most existing SM networks trained on synthetic data are susceptible to learn superficial shortcut features [5] instead of the desirable semantic and structural features, which leads to poor generalization performance in unseen (realistic) domain due to the significant synthetic-realistic domain gap. Therefore, the main research problem in this work is how to train an effective feature extraction network $f(\cdot)$ on only synthetic data that can learn generalizable representation of stereo images, so as to estimate reliable disparity map on unseen domain. + +# 3.2. Our Proposed Method + +Our target is to tackle the synthetic-to-realistic generalization in SM. Its main challenge is that we only have synthetic data for training, which has the high risk of overfitting to synthetic data due to its limited diversity. Inspired by [13, 29, 40, 47], we address the domain generalized SM from a new perspective in this work. The rest of this section will introduce our proposed network for this task in detail. The pipeline of our proposed HVT is shown in Fig. 2 + +# 3.2.1 Hierarchical Visual Transformation + +As we know, the key to addressing domain generalization is learning domain-invariant feature, also called causal fea + +Although the explicit form of causal feature is unknown in general, we have the prior that causal feature should remain invariant to certain transformations [29]. For example, the semantic and structural features can be treated as two domain-invariant (causal) features of stereo images for SM, while adjusting the luminance, contrast, or saturation of a stereo image pair will not affect the corresponding disparity map. Our intuitive idea is to leverage the visual transformations that do not change the underlying domain-invariant feature to increase the diversity of training domain, thereby enhancing the generalization performance of SM network. It is a straightforward but effective way. To this end, we design a Hierarchical Visual Transformation (HVT) network to diversify the distribution of training domain. Specifically, we learn a set of visual transformations $\mathcal{T} = \{T_1,\dots ,T_M\}$ at different levels to transform the original stereo image pairs as $(T(\mathbf{X}^l),T(\mathbf{X}^r))$ , where $T\in \mathcal{T}$ . We force the visual transformation $T(\cdot)$ to meet the following three requirements: + +- $T(\cdot)$ should induce large visual discrepancy between the original stereo image and the transformed images to enlarge the diversity of training domain. +- $T(\cdot)$ should not change the target disparity map of the original stereo image pairs. We should minimize the smooth- $\ell_1$ loss $L_{\mathrm{sm}-\ell_1}(F_\Theta(T(\mathbf{X}^l), T(\mathbf{X}^r)), \mathbf{Y}^{gt})$ where the transformed stereo images are fed into. +- The representation of the transformed stereo images $f(T(\mathbf{X}))$ should be consistent with that of the original images $f(\mathbf{X})$ , so as to learn domain-invariant features. + +Following the above-listed requirements, we describe the implementation of our proposed HVT network as follows. + +Implementation of HVT. To effectively learn domain-invariant feature representation for the challenging SM task, we transform the stereo image from three complementary perspectives: Global, Local, and Pixel. + +(1) Global: The Global visual transformation $T_{G}(\cdot)$ aims to globally change the distribution of stereo images by sequentially adjusting the basic visual attributes of images: Brightness, Contrast, Saturation, and Hue based on the four corresponding sub-transformations $\{T_{G}^{B}, T_{G}^{C}, T_{G}^{S}, T_{G}^{H}\}$ , following the pipeline of automatic image editing [12]. The three sub-transformations $\{T_{G}^{B}, T_{G}^{C}, T_{G}^{S}\}$ can be formulated as: + +$$ +T _ {G} ^ {I} (\mathbf {X}) = \alpha_ {G} ^ {I} \mathbf {X} + (1 - \alpha_ {G} ^ {I}) o ^ {I} (\mathbf {X}), \tag {2} +$$ + +where $I\in \{B,G,S\}$ . The $\alpha_{G}^{I}$ is a randomly selected positive constant in an adjustable range of $[\tau_{\mathrm{min}}^I,\tau_{\mathrm{max}}^I ]$ + +$$ +\left\{ \begin{array}{l} \tau_ {\min } ^ {I} = 1 - \left(\mu \sigma \left(\varrho_ {l} ^ {I}\right) + \beta\right) \\ \tau_ {\max } ^ {I} = 1 + \left(\mu \sigma \left(\varrho_ {h} ^ {I}\right) + \beta\right) \end{array} , \right. \tag {3} +$$ + +where $\sigma (\cdot)$ denotes the sigmoid function, $\varrho_l^I\in \mathbb{R}^1$ and $\varrho_h^I\in \mathbb{R}^1$ are two learnable parameters, $\mu$ and $\beta$ are two positive hyper-parameters. The operation $o^{I}(\cdot)$ in Eq. (2) + +is customized as follows. Specifically, for the Brightness, $o^B (\mathbf{X}) = \mathbf{X}\cdot \mathbf{O}$ where $\mathbf{O}$ denotes a zero matrix all of whose entries are zero. For the Contrast, $o^C (\mathbf{X}) = \mathrm{Avg}(\mathrm{Gray}(\mathbf{X}))$ where Gray(·) transforms the RGB image into a gray-scale image and $\mathrm{Avg}(\cdot)$ computes the mean value of all pixels. For the Saturation, $o^S (\mathbf{X}) = \mathrm{Gray}(\mathbf{X})$ . The Hue adjustment is defined as: + +$$ +T _ {G} ^ {H} (\mathbf {X}) = \operatorname {R g b} \left(\left[ \mathbf {h} + \alpha_ {G} ^ {H}, \mathbf {s}, \mathbf {v} \right]\right), \tag {4} +$$ + +where $[\mathbf{h},\mathbf{s},\mathbf{v}] = \mathrm{Hsv}(\mathbf{X})$ denotes the three components of $\mathbf{X}$ in the HSV color space and $\mathbf{h}$ denotes the Hue component. $\operatorname {Rgb}(\cdot)$ transforms the image from the HSV space into the RGB space. The $\alpha_{G}^{H}\in \mathbb{R}^{1}$ is randomly selected from an adjustable range of $[\tau_{\min}^{H},\tau_{\max}^{H}]$ , where $\tau_{\mathrm{min}}^H = -\mu \sigma (\varrho_l^H) - \beta$ and $\tau_{\mathrm{max}}^H = \mu \sigma (\varrho_h^H) + \beta$ + +Note that the order of the sequential sub-transformations $\{T_G^B, T_G^C, T_G^S, T_G^H\}$ is random to improve the diversity. + +(2) Local: The Local visual transformation $T_{L}(\cdot)$ aims to locally modify the distribution of stereo training images. The basic pipeline is that we first slice the given stereo image into $N' \times N'$ non-overlapping patches $\{\mathbf{x}_1^p, \dots, \mathbf{x}_{N' \times N'}^p\}$ , then transform each image patch $\mathbf{x}_i^p$ by a global transformation $T_{L}^{p}(\cdot)$ , and finally merge these transformed image patches into the stereo image based on the original sequential order. The output can be described by + +$$ +T _ {L} (\mathbf {X}) = \operatorname {M e r g e} \left(\left[ T _ {L} ^ {p} \left(\mathbf {x} _ {1} ^ {p}\right), \dots , T _ {L} ^ {p} \left(\mathbf {x} _ {N ^ {\prime} \times N ^ {\prime}} ^ {p}\right) \right]\right), \tag {5} +$$ + +where $\text{Merge}(\cdot)$ denotes the Merge operation. + +Note that patch-level transformation $T_{L}^{p}(\cdot)$ for each patch doesn't share parameters with each other to improve the diversity. $T_{L}^{p}(\cdot)$ can be implemented by existing style transfer networks, e.g. Adain [22] or Fourier-based method [31]. To better complementing our Global transformation, patch-level transformation $T_{L}^{p}(\cdot)$ is implemented by $T_{G}(\cdot)$ in Eq.(2) and Eq.(4) for its simplicity and effectiveness. + +(3) Pixel: The Pixel visual transformation $T_{P}(\cdot)$ aims to perturb the given stereo images with a pixel-level perturbation matrix. It can be formulated as: + +$$ +T _ {P} (\mathbf {X}) = \mathbf {X} + (\mu \sigma (\mathbf {W}) + \beta) \mathbf {P} \tag {6} +$$ + +where $\mathbf{P} \in \mathbb{R}^{H \times W \times 3}$ is a randomly generated Gaussian matrix with the mean of 0 and the standard deviation of 1, and $\mathbf{W} \in \mathbb{R}^{H \times W \times 3}$ is a learnable matrix. Different from the Global and Local transformations, $T_P(\cdot)$ can alter the distribution of synthetic data in a more granular fashion. + +Remark: The implementation of HVT is mainly motivated by the empirically found evidence [5] that existing SM networks are susceptible to exploit common artifacts (e.g. consistent local RGB color statistics and overreliance on local chromaticity features) of synthetic stereo images as shortcuts, which can be clearly illustrated by Fig. 3. We observe from Fig. 3 that the PSMNet is quite sensitive to the different levels of perturbation. It reflects that PSM- + +![](images/2b495d2b09df787d7560c33a27869bea05d56f8f5aba6bab2b0b520fcc9c0624.jpg) +Figure 3. Examples of visualized output of three visual transformations (top-2 rows of (a) and (b)) and the corresponding disparity error maps $|\dot{\mathbf{Y}} - \mathbf{Y}^{gt}|$ (the 3-rd row of (a) and (b)) of the PSMNet trained on the synthetic SceneFlow dataset. The EPE values are marked in the bottom of the 3-rd row for comparison. + +Net doesn't capture the robust semantic and structural features of stereo images. Our method is specially devised to improve the robustness and generalization ability of existing SM method. The design of the three different transformations $\{T_{G}(\mathbf{X}), T_{L}(\mathbf{X}), T_{P}(\mathbf{X})\}$ can effectively diversify the training domain and prevent the shortcuts from being encoded into the stereo image representation $f(\mathbf{X})$ . + +# 3.2.2 Learning Objectives + +To effectively train our proposed HVT network for the domain generalized SM task, we introduce the following loss terms for network optimization. + +Maximizing Cross-Domain Visual Discrepancy: In this work, without having access to the target domain, we propose to improve the SM network's generalization by transforming the synthetic source domain data into several new source domains $\{T_G(\mathbf{X}), T_L(\mathbf{X}), T_P(\mathbf{X})\}$ to diversify the training domain. Our first objective is to force the distributions of new source domains to be dissimilar as possible to the original distribution of synthetic data. Then we should maximize the following cross-domain visual discrepancy as + +$$ +\max L _ {\text {d i s c}} (\mathbf {X}) = \frac {1}{3} \sum_ {J} d \left(T _ {J} (\mathbf {X}), \mathbf {X}\right) \tag {7} +$$ + +where $J \in \{G, L, P\}$ , and $d(\cdot)$ is a domain discrepancy measure. In this work, we introduce a specific feature extraction network $\phi(\cdot)$ for domain discriminating. Then we + +implement Eq. (7) by minimizing the domain similarity as + +$$ +\min L _ {\text {s i m}} (\mathbf {X}) = \frac {1}{3} \sum_ {J} \operatorname {C o s} \left(\phi \left(T _ {J} (\mathbf {X})\right), \phi (\mathbf {X})\right), \tag {8} +$$ + +where $\mathrm{Cos}(\cdot ,\cdot)$ denotes the cosine similarity function. $\phi (\mathbf{X})$ denotes the pooled feature vector from the domain discriminating network $\phi (\cdot)$ . Besides, to further improve the domain discrepancy, we also minimize the following cross-entropy loss for domain classification: + +$$ +\min L _ {\mathrm {c e}} (\mathbf {X}) = \operatorname {C E} \left(\left\{\phi \left(T _ {J} (\mathbf {X})\right), \phi (\mathbf {X}) \right\}, \mathcal {Y} _ {d}\right), \tag {9} +$$ + +where $\mathrm{CE}(\cdot ,\cdot)$ denotes the standard cross-entropy loss and $\mathcal{V}_d$ denotes the domain labels of four source domains. + +Minimizing Cross-Domain Feature Inconsistency: To enhance the model's generalization ability, we need to learn domain-invariant representation of stereo images. We expect that our visual transformation $T(\cdot)$ doesn't change the core features (e.g., semantic and structural features) of images for stereo matching. Therefore, our second objective is to force the feature representation of transformed stereo images to be consistent with that of original synthetic images. Then we minimize the following pairwise distance term: + +$$ +\min L _ {\text {d i s t}} (\mathbf {X}) = \frac {1}{3} \sum_ {J} \| f (T _ {J} (\mathbf {X})) - f (\mathbf {X}) \| _ {2}, \tag {10} +$$ + +which facilitates the learning of shortcut-robust and domain invariant features for domain-generalized stereo matching. In summary, our model is trained by minimizing the linear combination of the above-mentioned learning objectives: + +$$ +\begin{array}{l} \min \mathcal {L} = L _ {\mathrm {s m} - \ell_ {1}} (\hat {\mathbf {Y}}, \mathbf {Y} ^ {g t}) + \\ \frac {1}{2} \left(\lambda_ {1} L _ {\text {d i s t}} (\mathbf {X}) + \lambda_ {2} L _ {\text {s i m}} (\mathbf {X}) + \lambda_ {3} L _ {\text {c e}} (\mathbf {X})\right), \tag {11} \\ \end{array} +$$ + +The full loss $\mathcal{L}$ is computed as the average over a training batch. The smooth- $\ell_1$ loss $L_{\mathrm{sm - }\ell_1}$ is computed based on not only the original synthetic image pairs $\{\mathbf{X}^l,\mathbf{X}^r\}$ but also the transformed image pairs $\{T_J(\mathbf{X}^l),T_J(\mathbf{X}^r)\}$ . $\lambda_{1},\lambda_{2}$ and $\lambda_{3}$ are three trade-off hyper-parameters. + +# 4. Experiments + +In this section, we quantitatively and qualitatively conduct extensive experiments to answer the following research questions: R1: Can the HVT effectively improve the generalization performance of existing SM networks? Can our performance reach the SOTA level? R2: Do the three transformations in the HVT effectively complement to each other? R3: Can our approach learn the domain-invariant features? R4: How is the robustness of our approach when tested in complex realistic scenarios? + +# 4.1. Dataset and Experimental Setting + +Datasets. We use the SceneFlow [19] dataset for training and four realistic SM datasets (KITTI 2012 [8], KITTI 2015 [20], Middlebury [23] and ETH3D [24]) for e + +
BaselinesMethodsKITTI 2015KITTI 2012Middlebury(H)ETH3DReferences
EPED1(3px)EPED1(3px)EPED1(2px)EPED1(1px)
-GANet [42]2.3111.71.9310.15.4120.31.3314.1CVPR 2019
CasStereo [9]2.4211.92.1211.83.7117.20.877.8CVPR 2020
DSMNet [43]1.466.51.266.22.6213.80.696.2ECCV 2020
PSMNet [3]PSMNet [3]3.1716.32.6915.17.6534.22.3323.8CVPR 2018
MS-PSMNet [2]1.64*7.82.33*14.04.72*19.81.42*16.83DV 2020
FC-PSMNet [46]1.58*7.51.42*7.04.14*18.31.25*12.8CVPR 2022
ITSA-PSMNet [5]1.39*5.81.09*5.23.25*12.70.94*9.8CVPR 2022
Graft-PSMNet [17]1.325.31.095.02.3410.91.1610.7CVPR 2022
HVT-PSMNet1.14±0.024.9±0.120.93±0.024.3±0.061.46±0.1310.2±0.160.47±0.036.9±0.23Ours
GwcNet [10]GwcNet [10]3.4322.72.7720.27.2337.92.7854.2CVPR 2019
FC-GwcNet [46]1.72*8.01.45*7.45.14*21.11.13*11.7CVPR 2022
ITSA-GwcNet [5]1.33*5.41.02*4.92.73*11.40.62*7.1CVPR 2022
HVT-GwcNet1.15±0.025.0±0.110.88±0.023.9±0.131.29±0.1310.3±0.210.46±0.085.9±0.26Ours
CFNet [25]CFNet [25]1.716.01.045.23.2415.40.485.72CVPR 2021
ITSA-CFNet [5]1.094.70.874.21.8710.40.455.1CVPR 2022
HVT-CFNet1.10±0.044.9±0.160.85±0.024.0±0.141.79±0.2210.2±0.160.39±0.024.5±0.24Ours
RAFT [16]RAFT [16]1.265.71.015.11.9212.60.363.33DV 2021
HVT-RAFT1.12±0.025.2±0.090.87±0.023.7±0.081.37±0.1110.4±0.140.29±0.013.0±0.09Ours
+ +Table 1. Performance comparison with SOTA domain generalized SM networks. The * denotes our reproduced EPE results since the authors only use the D1 metric. As we didn't have a validation set for model selection, we report the average result over last 5 epochs. + +valuation. SceneFlow [19] is a large-scale synthetic SM dataset containing 35,454 training stereo image pairs and 4,370 testing image pairs with a resolution of $960 \times 540$ . All the synthetic image pairs have dense annotations of ground-truth disparities. KITTI 2012 [8] and KITTI 2015 [20] consists of 194 and 200 training stereo image pairs collected in outdoor driving scenes with sparse annotations of disparities, respectively. Middlebury [23] includes 15 high-resolution stereo image pairs in indoor scenes. In our experiments, we use the half-resolution version (Middlebury(H)) for evaluation. ETH3D [24] has 27 grayscale stereo image pairs collected from both indoor and outdoor scenes. + +Metrics. Following the setting of [17], we use both EPE rate (End-Point Error) and D1 error rate $(\%)$ with different pixel threshold $\rho$ as the metrics to get a more comprehensive evaluation. The EPE measures the average disparity error over all pixels, which reflects the average disparity estimate. The D1 error rate computes the percentage of error pixels with absolute error larger than a specific threshold $\rho$ . The pixel threshold is set as $\rho = 3\mathrm{px}$ for KITTI 2012 [8] and KITTI 2015 [20], $\rho = 2\mathrm{px}$ for Middlebury [23] and $\rho = 1\mathrm{px}$ for ETH3D [24], respectively, following recent works [17, 46]. + +Baselines. We select four SM networks as baselines, including two well-studied and commonly-used methods (PSMNet [3] and GwcNet [10]) and two SOTA methods (CFNet [25] and RAFT [16]), in our experiments. We will integrate our HVT networks with these baseline networks to validate the effectiveness of HVT on domain generalization. + +Implementation Details. Following [43], we use the domain normalization technique in the feature extraction module for all baselines. Except the RAFT [16], all the baselines are implemented by PyTorch [21] with Adam $(\beta_{1} = 0.9, \beta_{2} = 0.999)$ optimizer. We train the model for 45 epochs with the batch size of 8. Besides, we introduce an incremen + +tal training scheme to stably optimize the network in this work. Specifically, we train the model with $T_{G}(\cdot)$ only for 15 epochs at Stage I, then we further train the model with $\{T_G(\cdot), T_L(\cdot)\}$ for another 15 epochs at Stage II, and finally we continually train the model with $\{T_G(\cdot), T_L(\cdot), T_P(\cdot)\}$ for the remaining 15 epochs at Stage III. The learning rate is set to 0.001 and decreased by half after epoch 10, 20, 30 and 40. For the RAFT [16] baseline, we train the model for total 30K steps and train each stage 10K steps. The optimizer and learning rate follow its original setting. Besides, the asymmetric chromatic augmentation is not used in any models to avoid unfair experimental comparison. We select ResNet18 [11] as the domain discriminating network $\phi(\cdot)$ for its simplicity. For different hyper-parameters, the $\mu$ and $\beta$ in Eq. (3) and (6) are set as 0.1 and 0.15 respectively. The $\lambda_1$ , $\lambda_2$ and $\lambda_3$ in Eq. (11) are set as 1, 0.5 and 0.5 respectively. The $N' = 4$ in $T_{L}(\cdot)$ . Note that all the SM networks are only trained on the synthetic dataset, SceneFlow. The target data is strictly inaccessible during training. + +# 4.2. Overall Performance Comparison + +R1: Comparison with Baselines and SOTAs. In Tab. 1, we report the comparison of generalization performance between the baselines (PSMNet, GwcNet, CFNet, and RAFT) and our HVT-integrated methods, as well as the comparison between ours and the reported SOTA results, across the four realistic datasets. We have the following observations: + +- The synthetic-to-realistic generalization performances of all the baselines are consistently improved by our HVT in all settings. Specifically, compared with the widely-used PSMNet [3], the performance improvements w.r.t. the D1 metric are $11.4\%$ , $10.8\%$ , $24\%$ , and $16.9\%$ , respectively on the four datasets. Similar improvement can also be observed on GwcNet [10]: $17.7\%$ , $16.3\%$ , $27.6\%$ , and + +
BaselinesGlobal Local PixelKITTI 2015MiddleburyETH3D
EPE3pxEPE2pxEPE1px
PSMNet [3]✓✗✗1.316.072.0413.70.489.4
✗✓✗1.286.031.6912.50.5910.7
✗✗✓1.276.292.3914.60.579.9
✓✓✗1.235.471.5711.10.539.1
✓✗✓1.195.571.4411.20.517.7
✗✓✓1.275.721.5810.90.627.9
✓✓✓1.144.931.4610.20.476.9
GwcNet [10]✓✗✗1.285.891.8812.60.748.2
✗✓✗1.265.881.6411.90.688.5
✗✗✓1.296.181.8312.40.718.3
✓✓✗1.235.381.5810.40.587.8
✓✗✓1.195.521.4910.70.557.1
✗✓✓1.185.471.5710.60.526.9
✓✓✓1.155.021.2910.30.465.9
+ +$48.3\%$ w.r.t. the D1 metric. Even compared with the SOTA CFNet [25] and RAFT [16], the D1 error rates are still substantially decreased: $1.1\%$ , $1.2\%$ , $5.2\%$ , and $1.2\%$ for CFNet, and $0.5\%$ , $1.4\%$ , $2.2\%$ , and $0.3\%$ for RAFT. The quantitative comparison clearly shows the effectiveness of HVT on enhancing the robustness of SM models. The improvement can be mainly attributed to the fact that our HVT significantly diversify the visual distribution of original synthetic images, thus preventing the model from building the spurious relationship between the pairwise input and the target disparity. The model will not easily find the matching correspondences across the stereo images by just leveraging the shortcut cues, e.g., local RGB color statistics and chromaticity features. + +- The improvements of generalization performance brought by HVT on the Middlebury and ETH3D datasets seem to be much larger than those on the KITTI 2012 and 2015 datasets. The reason is that Middlebury has higher resolution images in realistic scenarios than those in KITTI 2012 and 2015, and the images in ETH3D are all grayscale which are very different from the colorful synthetic training images. It reflects that our HVT can perform well in diverse realistic scenarios that differ from training domain in resolution and color distribution. +- Our HVT-enhanced methods almost outperform all the SOTA methods except ITSA-CFNet on KITTI 2015. It shows the strong potential of our HVT in improving the cross-domain generalization. Note that the three transformations devised in this work are all simple and straightforward. The performance can be further improved if we introduce more delicate transformations into our HVT. Besides, the performance of ITSA-CFNet on KITTI 2015 is already very high w.r.t. the EPE and D1 metrics, 1.09 and $4.7\%$ . Our HVT-CFNet's performance is on a par + +Table 2. Ablation studies on the effect of three visual transformations (Global, Local, and Pixel) on three datasets using the two well-studied baselines, PSMNet [3] and GwcNet [10]. + +
BaselinesObj-1Obj-2KITTI 2015MiddleburyETH3D
EPE3pxEPE2pxEPE2px
PSMNet [3]XX1.677.742.8815.10.8913.2
X✓1.316.232.0411.70.6310.1
✓✓1.144.931.4610.20.476.9
GwcNet [10]XX1.647.582.6514.60.8612.4
X✓1.286.071.9311.30.579.2
✓✓1.155.021.2910.30.465.9
+ +Table 3. Ablation studies of our two main optimization objectives: Obj-1 (i.e., Eq. (8) and Eq. (9)) and Obj-2 (i.e., Eq. (10)). + +![](images/8eb31a533c24fdd6637a111a36f28d44403a5640a0da7371db01343d482f3226.jpg) +Figure 4. Visualization of RGB color histograms (see (b)) and visual feature histograms (see (c)) of original image and transformed images (see (a)) based on the HVT-PSMNet method. The original image is randomly selected from the realistic Middlebury dataset. + +with that of the ITSA-CFNet. + +- Benefiting from using HVT, the performances of weak baselines, i.e., PSMNet and GwcNet, have been increased to the SOTA level, especially on the top-three datasets. It reflects that the critical step for the domain-generalized SM task is to learn domain-invariant representation from diverse training domain instead of devising different complex network modules for cost volume generation or aggregation. It further validates the rationale of our HVT. + +# 4.3. Ablation Studies + +R2: The Complementation of HVTs. As shown in Tab. 2, we investigate the effect of the HVT module by gradually adding the visual transformations in two baselines, PSMNet [3] and GwcNet [10]. We observe that the three visual transformations can complement well to each other. Specifically, only using one of the three transformations can also facilitate the performance improvement of baselines. When using more visual transformations, we observe consistent performance gains across the three realistic datasets. For example, the D1 error rates of $T_{G}(\cdot)$ -enhanced PSMNet have been decreased from $6.07\%$ , $13.7\%$ , and $9.4\%$ to $5.57\%$ , $11.2\%$ , and $7.7\%$ , respectively, when jointly using $T_{G}(\cdot)$ and $T_{P}(\cdot)$ . The best performances are observed when all the three transformations are jointly used. Similar performance improvements can also be observed when Gwc + +
MethodsSunnyCloudyRainyFoggyAvg.
PSMNet [3]62.560.160.568.663.9
FT-PSMNet [5]4.02.911.56.56.3
FC-PSMNet [46]4.94.37.26.25.7
ITSA-PSMNet [5]4.83.29.46.35.9
HVT-PSMNet4.23.18.75.65.4
GwcNet [10]18.124.728.228.324.8
FT-GwcNet [5]3.12.512.36.06.0
ITSA-GwcNet [5]4.43.39.85.95.9
HVT-GwcNet3.43.58.65.65.3
+ +Table 4. Robustness comparison of different methods on the DrivingStereo [32] dataset collected from complex realistic scenarios: Sunny, Cloudy, Rainy, and Foggy. The D1 (3px) metric is used. + +Net is used as the SM baseline. + +R3: Learning Domain-Invariant features. The core of our approach is to learn shortcut-robust features that can generalize well to unseen domains. As illustrated in Fig. 4 (b), we observe that the hierarchical visual transformation's significantly alter the RGB color histograms of original stereo image in the levels of Global, Local, and Pixel. Benefiting from the minimization of cross-domain feature inconsistency in Eq. (10), the image representation $f(\mathbf{X})$ seems to be invariant across different domains as shown in Fig. 4 (c). Tab. 3 quantitatively investigate the effect of learning objective in Eq. (10). We can observe a clear performance improvement by just minimizing the cross-domain feature inconsistency (Obj-2 in Tab. 3). Obviously, by jointly optimizing the two objectives, we obtain the best generalization performance. The quantitative and qualitative results clearly reflects the importance and efficacy of the two learning objectives in Sec. 3.2.2. + +R4: Robustness to Complex Realistic Scenarios. In this section, we evaluate the generalization of our HVT-enhanced methods on the DrivingStereo [32] dataset which is collected from complex realistic scenarios: Sunny, Cloudy, Rainy, and Foggy, as shown in Fig. 5. We conduct experiments using the PSMNet [3] and GwcNet [10] as the baseline frameworks. The results of officially released fine-tuned (FT) networks of PSMNet and GwcNet on the realistic KITTI 2015 dataset are included for comparison. Besides, we also include the results of SOTA domain generalized SM methods [5, 46] in the Tab. 4. We have the following observations from Tab. 4 and Fig. 5: + +- Our methods (HVT-PSMNet and HVT-GwcNet) obtain the best overall performance $(5.4\%$ and $5.3\%)$ w.r.t. the average D1 error rate over the four groups of weather conditions, which demonstrates the efficacy of HVT and the strong robustness of HVT-based methods. +- HVT-PSMNet and HVT-GwcNet not only outperform the baselines PSMNet and GwcNet, respectively, by a large margin, but also decrease the error rates of the FT-PSMNet and FT-GwcNet on the Rainy and Foggy groups. + +![](images/e4ae0f8a73df010aa0b212d00aec450ff6ff296f74a58ccca5b69afb82d9d390.jpg) +Figure 5. Qualitative results on the DrivingStereo [32] dataset. For each group, top row shows the left image and the EPE error maps of PSMNet, fine-tuned (FT) PSMNet, and our HVT-PSMNet, respectively. Bottom row shows the GT disparity map and the predicted disparity maps of different methods. The EPE values are marked in the upper right corner of error maps. + +On another two groups, both fine-tuned (FT) models perform slightly better than our HVT, since images in the two groups are similar to the KITTI training data. The results reflect that our HVT can effectively deal with the domain shift between the synthetic data and realistic data. + +- Fig. 5 shows the qualitative robustness comparison in different weather conditions. The observation from Fig. 5 is consistent with that from Tab. 4, which further validates the potential of HVT in enhancing the model robustness. + +# 5. Conclusion + +In this work, we have devised an effective HVT module for the problem of domain generalized SM. To prevent the network from exploiting the shortcut features for disparity estimation, we propose to 1) first diversify the training domain by leveraging the three complementary visual transformations, where the cross-domain visual discrepancy is maximized, and 2) minimize the cross-domain feature inconsistency to effectively capture domain-invariant features. Our proposed method is simple and can be flexibly integrated with most existing SM networks. Extensive experimental results show that our HVT consistently advances the learning of shortcut-robust features and substantially improves the generalization performance of SM networks in unseen realistic scenarios. In the future, we will attempt to design more delicate visual transformations to enhance HVT and extend HVT for addressing other 3D vision tasks. + +# 6. Acknowledgments + +This work was supported by the National Natural Science Foundation of China (NSFC) under Grant 62272435, Grant U22A2094 and Grant 72188101. + +# References + +[1] Joydeep Biswas and Manuela Veloso. Depth camera based localization and navigation for indoor mobile robots. In RGB-D Workshop at RSS, volume 2011, 2011. 1 +[2] Changjiang Cai, Matteo Poggi, Stefano Mattoccia, and Filippos Mordohai. Matching-space stereo networks for cross-domain generalization. In 2020 International Conference on 3D Vision (3DV), pages 364-373. IEEE, 2020. 2, 6 +[3] Jia-Ren Chang and Yong-Sheng Chen. Pyramid stereo matching network. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 5410-5418, 2018. 1, 2, 3, 6, 7, 8 +[4] Xuelian Cheng, Yiran Zhong, Mehrtash Harandi, Yuchao Dai, Xiaojun Chang, Hongdong Li, Tom Drummond, and Zongyuan Ge. Hierarchical neural architecture search for deep stereo matching. 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Springer, 2020. 3 \ No newline at end of file diff --git a/2023/Domain Generalized Stereo Matching via Hierarchical Visual Transformation/images.zip b/2023/Domain Generalized Stereo Matching via Hierarchical Visual Transformation/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..08ddc74d13c665178e8d3295f13d8d58456fe893 --- /dev/null +++ b/2023/Domain Generalized Stereo Matching via Hierarchical Visual Transformation/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:56b419dd9cc9342681c56640193d6e41661db966d8be9a1a940d74e5fb6d2404 +size 706888 diff --git a/2023/Domain Generalized Stereo Matching via Hierarchical Visual Transformation/layout.json b/2023/Domain Generalized Stereo Matching via Hierarchical Visual Transformation/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..f229ffec3960286e16ad2b850a52660224bc2448 --- /dev/null +++ b/2023/Domain Generalized Stereo Matching via Hierarchical Visual Transformation/layout.json @@ -0,0 +1,9183 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 58, + 103, + 536, + 120 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 103, + 536, + 120 + ], + "spans": [ + { + "bbox": [ + 58, + 103, + 536, + 120 + ], + "type": "text", + "content": "Domain Generalized Stereo Matching via Hierarchical Visual Transformation" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 147, + 142, + 445, + 157 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 147, + 142, + 445, + 157 + ], + "spans": [ + { + "bbox": [ + 147, + 142, + 445, + 157 + ], + "type": "text", + "content": "Tianyu Chang" + }, + { + "bbox": [ + 147, + 142, + 445, + 157 + ], + "type": "inline_equation", + "content": "^{1,3}" + }, + { + "bbox": [ + 147, + 142, + 445, + 157 + ], + "type": "text", + "content": ", Xun Yang" + }, + { + "bbox": [ + 147, + 142, + 445, + 157 + ], + "type": "inline_equation", + "content": "^{1*}" + }, + { + "bbox": [ + 147, + 142, + 445, + 157 + ], + "type": "text", + "content": ", Tianzhu Zhang" + }, + { + "bbox": [ + 147, + 142, + 445, + 157 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 147, + 142, + 445, + 157 + ], + "type": "text", + "content": ", Meng Wang" + }, + { + "bbox": [ + 147, + 142, + 445, + 157 + ], + "type": "inline_equation", + "content": "^{2}" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 88, + 157, + 505, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 157, + 505, + 185 + ], + "spans": [ + { + "bbox": [ + 88, + 157, + 505, + 185 + ], + "type": "text", + "content": "1University of Science and Technology of China 2Hefei University of Technology Institute of Artificial Intelligence, Hefei Comprehensive National Science Center" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 67, + 188, + 522, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 188, + 522, + 198 + ], + "spans": [ + { + "bbox": [ + 67, + 188, + 522, + 198 + ], + "type": "text", + "content": "cty8998@mail.ustc.edu.cn {xyang21, tzhang}@ustc.edu.cn wangmeng@h Fut.edu.cn" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 143, + 227, + 191, + 239 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 227, + 191, + 239 + ], + "spans": [ + { + "bbox": [ + 143, + 227, + 191, + 239 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 251, + 290, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 251, + 290, + 552 + ], + "spans": [ + { + "bbox": [ + 46, + 251, + 290, + 552 + ], + "type": "text", + "content": "Recently, deep Stereo Matching (SM) networks have shown impressive performance and attracted increasing attention in computer vision. However, existing deep SM networks are prone to learn dataset-dependent shortcuts, which fail to generalize well on unseen realistic datasets. This paper takes a step towards training robust models for the domain generalized SM task, which mainly focuses on learning shortcut-invariant representation from synthetic data to alleviate the domain shifts. Specifically, we propose a Hierarchical Visual Transformation (HVT) network to 1) first transform the training sample hierarchically into new domains with diverse distributions from three levels: Global, Local, and Pixel, 2) then maximize the visual discrepancy between the source domain and new domains, and minimize the cross-domain feature inconsistency to capture domain-invariant features. In this way, we can prevent the model from exploiting the artifacts of synthetic stereo images as shortcut features, thereby estimating the disparity maps more effectively based on the learned robust and shortcut-invariant representation. We integrate our proposed HVT network with SOTA SM networks and evaluate its effectiveness on several public SM benchmark datasets. Extensive experiments clearly show that the HVT network can substantially enhance the performance of existing SM networks in synthetic-to-realistic domain generalization." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 568, + 128, + 581 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 568, + 128, + 581 + ], + "spans": [ + { + "bbox": [ + 47, + 568, + 128, + 581 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 589, + 287, + 660 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 589, + 287, + 660 + ], + "spans": [ + { + "bbox": [ + 46, + 589, + 287, + 660 + ], + "type": "text", + "content": "Stereo Matching (SM) [7,41,44] aims to find the matching correspondences between a given stereo image pair and then calculate the disparity for depth sensing in many applications, such as robot navigation and autonomous driving [1,28]. Recently, it attracts increasing attention in the computer vision community [4,27,30,42]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 661, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 661, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 661, + 287, + 696 + ], + "type": "text", + "content": "With the development of deep learning [6, 18, 34-38], Convolutional Neural Network (CNN) based deep SM networks have shown impressive performance benefiting from" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 320, + 225, + 531, + 357 + ], + "blocks": [ + { + "bbox": [ + 320, + 225, + 531, + 357 + ], + "lines": [ + { + "bbox": [ + 320, + 225, + 531, + 357 + ], + "spans": [ + { + "bbox": [ + 320, + 225, + 531, + 357 + ], + "type": "image", + "image_path": "c09daecdb5f2f94dd35e0a62126038002e43271632d10986f205c91cdf694c9f.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 360, + 545, + 425 + ], + "lines": [ + { + "bbox": [ + 305, + 360, + 545, + 425 + ], + "spans": [ + { + "bbox": [ + 305, + 360, + 545, + 425 + ], + "type": "text", + "content": "Figure 1. Comparison of the cross-domain SM generalization. Columns from left to right denote a sample image, ground truth disparities, the predicted disparities of the pretrained PSMNet model and our HVT-PSMNet model. Both models are trained on the synthetic SceneFlow [19] dataset and evaluated on the realistic datasets: Middlebury, ETH3D, KITTI 2012 and KITTI 2015." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 435, + 546, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 435, + 546, + 651 + ], + "spans": [ + { + "bbox": [ + 304, + 435, + 546, + 651 + ], + "type": "text", + "content": "their strong ability of feature representation. However, due to the scarcity of sufficient labeled realistic training data, existing state-of-the-art (SOTA) SM networks usually are trained on synthetic data, e.g. SceneFlow [19], which fail to generalize well to unseen realistic domains as shown in Fig. 1. Generally, the generalizability of cross-domain deep SM networks is mainly hindered by a critical issue: SM networks usually learn superficial shortcut features [5] from synthetic data to estimate the disparity. Specifically, such shortcut features mainly include two types of artifacts: consistent local RGB color statistics and overreliance on local chromaticity features, which are domain-sensitive and nontransferable to unseen domain. The semantic and structural features that are truly desirable are ignored by most existing SM networks. Therefore, the key to addressing the challenging cross-domain SM task is how to effectively learn the domain-invariant representations of the given stereo image pair for synthetic-to-realistic generalization." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 653, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 547, + 713 + ], + "type": "text", + "content": "Several attempts [3, 10, 15, 26, 45] have been made to minimize the synthetic-to-realistic domain gap and learn the domain-invariant representations for the SM task by either 1) exploiting labeled target-domain realistic data to fine-tune the SM network trained with synthetic data [3, 10]" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 62, + 703, + 141, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 703, + 141, + 712 + ], + "spans": [ + { + "bbox": [ + 62, + 703, + 141, + 712 + ], + "type": "text", + "content": "*Corresponding Author" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "9559" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "type": "text", + "content": "or 2) jointly using the synthetic data and unlabeled target-domain realistic data to train domain adaptive SM networks [15,26,45]. Despite their performance improvement on realistic data, these attempts only work well when the target-domain realistic data is provided during training and thus can not improve the out-of-distribution (OOD) generalization of SM networks, which are less practically useful in real-world scenarios." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 168, + 289, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 168, + 289, + 526 + ], + "spans": [ + { + "bbox": [ + 46, + 168, + 289, + 526 + ], + "type": "text", + "content": "In this work, we address the important but less explored challenging problem of single domain generalization in SM, where only the synthetic data is available for training. Considering the fact that most existing SM networks are susceptible to exploiting shortcut cues in synthetic data instead of the semantic and structural correspondences, we propose to learn shortcut-invariant robust representation from synthetic SM image pairs for OOD generalization. Specifically, this paper presents a Hierarchical Visual Transformation (HVT) network to 1) first transform the synthetic training sample hierarchically into new source domains with diverse distributions from three levels: Global, Local, and Pixel, 2) then maximize the image discrepancy between the synthetic source domain and new domains for significantly altering the original distribution, and minimize the cross-domain feature inconsistency to capture domain-invariant features. In this way, we are able to prevent the model from exploiting the artifacts of synthetic stereo images as shortcut features, thereby estimating the disparity maps more effectively based on the learned shortcut-invariant feature representation. Our basic idea is to diversify the distribution of training data and thus force the network to overlook the artifacts from synthetic domain. Note that our proposed HVT network is simple and can be plug-and-play. We integrate HVT with SOTA SM networks during training and evaluate its effectiveness on several challenging SM benchmark datasets. Extensive experiments clearly show that the HVT network can substantially enhance the performance of existing SM networks in synthetic-to-realistic domain generalization without using any auxiliary data or features [17]." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 528, + 286, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 528, + 286, + 539 + ], + "spans": [ + { + "bbox": [ + 58, + 528, + 286, + 539 + ], + "type": "text", + "content": "Our contributions can be briefly summarized as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 543, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 47, + 543, + 287, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 543, + 287, + 601 + ], + "spans": [ + { + "bbox": [ + 47, + 543, + 287, + 601 + ], + "type": "text", + "content": "- We devise a simple yet effective domain generalized SM framework. It leverages a hierarchical visual transformation network to effectively diversify the distribution of training data which prevents the model from exploiting the artifacts in synthetic data as shortcuts." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 604, + 286, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 604, + 286, + 675 + ], + "spans": [ + { + "bbox": [ + 47, + 604, + 286, + 675 + ], + "type": "text", + "content": "- We formulate novel learning objectives that force the model to effectively optimize three complementary visual transformations by maximizing domain discrepancy and minimizing feature inconsistency between synthetic domain and new domains, thereby facilitating the learning of domain-invariant feature representation." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "type": "text", + "content": "- Extensive experiments on four realistic SM datasets clearly demonstrate the effectiveness and robustness of our HVT network. The out-of-distribution generalization" + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 315, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 315, + 72, + 545, + 96 + ], + "type": "text", + "content": "ability of four SOTA SM methods has been significantly boosted, benefiting from our solution." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 107, + 392, + 119 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 107, + 392, + 119 + ], + "spans": [ + { + "bbox": [ + 306, + 107, + 392, + 119 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 128, + 545, + 162 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 128, + 545, + 162 + ], + "spans": [ + { + "bbox": [ + 305, + 128, + 545, + 162 + ], + "type": "text", + "content": "This section briefly introduces the learning based stereo matching (SM) methods from two perspectives: 1) In-Distribution SM and 2) Our-of-Distribution SM." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 163, + 546, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 163, + 546, + 485 + ], + "spans": [ + { + "bbox": [ + 305, + 163, + 546, + 485 + ], + "type": "text", + "content": "In-Distribution SM. In the past decade, deep learning has triggered the fast development of the task of SM. Mayer et al. [19] introduced an end-to-end SM network which uses the correlation layer to generate the cost volume and the 2D-CNN to aggregate the cost volume. SegStereo [33] and EdgeStereo [27] exploit the semantic and edge cues to help the disparity prediction. To learn better features, AANet [30] integrates both normal convolution and deformable convolution for feature extraction. Furthermore, GCNet [14] concatenates left and right features for cost volume generation and aggregation with 3D convolutions. GwcNet [10] proposes the group-wise correlation to construct the cost volume with lower memory cost. PSM-Net [3] proposes the spatial pyramid pooling module and the stack hourglass network to expand the receptive field. GANet [42] designs the image content guided layers to globally and locally update the cost volume. LEAStereo [4] introduces the neural architecture searching into SM. In recent several years, the Cascade-based SM methods [9, 25, 39] first use the coarsest resolution feature maps to predict an initial disparity, and narrow down the disparity search range to refine the disparity based on the initial disparity. Despite the good performance of existing deep-learning based SM networks, their training set and testing set always follow the independent and identically distributed (IID) assumption. Most existing works usually fail to generalize well on unseen realistic data." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 486, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 486, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 486, + 546, + 713 + ], + "type": "text", + "content": "Out-of-Distribution SM. Most recently, the synthetic-to-realistic generalized SM networks [5, 16, 25, 43] have received increasing attention. Different from those fine-tuning or adaptation-based methods [3, 15, 26, 42, 45], they aim to directly learn SM networks that can generalize to unseen domains. Some works propose to improve the generalization ability by devising novel network architectures. For example, DSMNet [43] proposes the domain normalization layer and the trainable non-local graph-based filter to learn domain-invariant structural feature. Besides, both CFNet [25] and RAFT-Stereo [16] introduce a network architecture with multi-scale cost volume fusion and aggregation to learn robust semantic or structural features. Some other efforts attempt to design flexible modules that can facilitate the cross-domain generalization of more existing SM networks. MS-Net [2] points out that learned feature is the core reason for the poor generalization performance, and proposes to use the traditional feature descriptors to construct the cost. FC-Net [46] uses the stereo contrastive" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "9560" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 97, + 71, + 496, + 244 + ], + "blocks": [ + { + "bbox": [ + 97, + 71, + 496, + 244 + ], + "lines": [ + { + "bbox": [ + 97, + 71, + 496, + 244 + ], + "spans": [ + { + "bbox": [ + 97, + 71, + 496, + 244 + ], + "type": "image", + "image_path": "093696791a5f78dc7b0ace1b6569150e9dbf275dfa357d1b87e3a48004e70d82.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 245, + 547, + 281 + ], + "lines": [ + { + "bbox": [ + 46, + 245, + 547, + 281 + ], + "spans": [ + { + "bbox": [ + 46, + 245, + 547, + 281 + ], + "type": "text", + "content": "Figure 2. The pipeline of our domain-generalized SM approach. It leverages a hierarchical visual transformation module to improve the diversity of training domain by training a domain discriminator " + }, + { + "bbox": [ + 46, + 245, + 547, + 281 + ], + "type": "inline_equation", + "content": "\\phi(\\cdot)" + }, + { + "bbox": [ + 46, + 245, + 547, + 281 + ], + "type": "text", + "content": ". Its main goal is to optimize a feature extractor " + }, + { + "bbox": [ + 46, + 245, + 547, + 281 + ], + "type": "inline_equation", + "content": "f(\\cdot)" + }, + { + "bbox": [ + 46, + 245, + 547, + 281 + ], + "type": "text", + "content": " that can learn shortcut-robust and domain-invariant representation, thereby facilitating the generalization of SM network in unseen realistic domains." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 285, + 289, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 285, + 289, + 380 + ], + "spans": [ + { + "bbox": [ + 46, + 285, + 289, + 380 + ], + "type": "text", + "content": "feature loss and the stereo selective whitening loss to encourage the stereo feature consistency across different domains. GraftNet [17] leverages the robust broad-spectrum feature which is trained on large-scale datasets to replace the original feature to improve the generalization ability. ITSA [5] generates the pixel-perturbed image through the gradient of the features with respect to the input image, and guides the network to learn shortcut-invariant feature." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 382, + 289, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 382, + 289, + 515 + ], + "spans": [ + { + "bbox": [ + 46, + 382, + 289, + 515 + ], + "type": "text", + "content": "Different from these methods, we introduce a simple yet effective method to enhance the synthetic-to-realistic generalization. We design a hierarchical visual transformation module to diversify the training domain by maximizing the cross-domain visual discrepancy and propose to learn domain-invariant feature representation by minimizing the cross-domain feature inconsistency. ITSA [5] can be generally seen as a special case of our work that diversifies the distribution in the Pixel level. Experiments in the Sec. 4 have clearly validated the effectiveness of our method on improving the synthetic-to-realistic generalization of SM." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 528, + 137, + 542 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 528, + 137, + 542 + ], + "spans": [ + { + "bbox": [ + 47, + 528, + 137, + 542 + ], + "type": "text", + "content": "3. The Approach" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 548, + 157, + 561 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 548, + 157, + 561 + ], + "spans": [ + { + "bbox": [ + 47, + 548, + 157, + 561 + ], + "type": "text", + "content": "3.1. Problem Overview" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 568, + 287, + 669 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 568, + 287, + 669 + ], + "spans": [ + { + "bbox": [ + 47, + 568, + 287, + 669 + ], + "type": "text", + "content": "This work aims to improve the synthetic-to-realistic domain generalization for SM. Given a synthetic training set " + }, + { + "bbox": [ + 47, + 568, + 287, + 669 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_s" + }, + { + "bbox": [ + 47, + 568, + 287, + 669 + ], + "type": "text", + "content": " as input, consisting of " + }, + { + "bbox": [ + 47, + 568, + 287, + 669 + ], + "type": "inline_equation", + "content": "|\\mathcal{D}_s|" + }, + { + "bbox": [ + 47, + 568, + 287, + 669 + ], + "type": "text", + "content": " synthetic stereo image pairs " + }, + { + "bbox": [ + 47, + 568, + 287, + 669 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{X}_i^l,\\mathbf{X}_i^r\\}_{i = 1}^{|\\mathcal{D}_s|}" + }, + { + "bbox": [ + 47, + 568, + 287, + 669 + ], + "type": "text", + "content": " and the corresponding ground-truth disparity maps " + }, + { + "bbox": [ + 47, + 568, + 287, + 669 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{Y}_i^{gt}\\}_{i = 1}^{|\\mathcal{D}_s|}" + }, + { + "bbox": [ + 47, + 568, + 287, + 669 + ], + "type": "text", + "content": ", the goal is to learn a cross-domain SM network that can effectively predict the disparity between a pair of stereo images from unseen domains " + }, + { + "bbox": [ + 47, + 568, + 287, + 669 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_r" + }, + { + "bbox": [ + 47, + 568, + 287, + 669 + ], + "type": "text", + "content": ". A typical SM network " + }, + { + "bbox": [ + 47, + 568, + 287, + 669 + ], + "type": "inline_equation", + "content": "F_{\\Theta}(\\cdot ,\\cdot)" + }, + { + "bbox": [ + 47, + 568, + 287, + 669 + ], + "type": "text", + "content": " can be formally formulated as:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 78, + 672, + 287, + 687 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 672, + 287, + 687 + ], + "spans": [ + { + "bbox": [ + 78, + 672, + 287, + 687 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {Y}} = F _ {\\Theta} \\left(\\mathbf {X} ^ {l}, \\mathbf {X} ^ {r}\\right) = s \\left(g \\left(f \\left(\\mathbf {X} ^ {l}\\right), f \\left(\\mathbf {X} ^ {r}\\right)\\right)\\right), \\tag {1}", + "image_path": "2e0736410115a79ede830ed27674f414784ce4e89f2ae72fd63208894b34c8ed.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "text", + "content": " denotes the total network parameters and " + }, + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "inline_equation", + "content": "f(\\cdot)" + }, + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "text", + "content": " is a feature extraction module that yields the feature map of" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 285, + 545, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 285, + 545, + 369 + ], + "spans": [ + { + "bbox": [ + 304, + 285, + 545, + 369 + ], + "type": "text", + "content": "stereo images. " + }, + { + "bbox": [ + 304, + 285, + 545, + 369 + ], + "type": "inline_equation", + "content": "g(\\cdot)" + }, + { + "bbox": [ + 304, + 285, + 545, + 369 + ], + "type": "text", + "content": " is a joint network module that first generates the cost volume by correlation or concatenation strategy, and then performs the cost aggregation and refinement. The final disparity map " + }, + { + "bbox": [ + 304, + 285, + 545, + 369 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{Y}}" + }, + { + "bbox": [ + 304, + 285, + 545, + 369 + ], + "type": "text", + "content": " is estimated by converting the refined cost volumes with the soft-argmin [14] operation " + }, + { + "bbox": [ + 304, + 285, + 545, + 369 + ], + "type": "inline_equation", + "content": "s(\\cdot)" + }, + { + "bbox": [ + 304, + 285, + 545, + 369 + ], + "type": "text", + "content": ". The typical SM network " + }, + { + "bbox": [ + 304, + 285, + 545, + 369 + ], + "type": "inline_equation", + "content": "F_{\\Theta}(\\cdot,\\cdot)" + }, + { + "bbox": [ + 304, + 285, + 545, + 369 + ], + "type": "text", + "content": " is optimized by minimizing the smooth-" + }, + { + "bbox": [ + 304, + 285, + 545, + 369 + ], + "type": "inline_equation", + "content": "\\ell_1" + }, + { + "bbox": [ + 304, + 285, + 545, + 369 + ], + "type": "text", + "content": " loss " + }, + { + "bbox": [ + 304, + 285, + 545, + 369 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{sm}-\\ell_1}\\left(F_{\\Theta}(\\mathbf{X}^l,\\mathbf{X}^r),\\mathbf{Y}^{gt}\\right)" + }, + { + "bbox": [ + 304, + 285, + 545, + 369 + ], + "type": "text", + "content": " [3]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 369, + 546, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 369, + 546, + 548 + ], + "spans": [ + { + "bbox": [ + 304, + 369, + 546, + 548 + ], + "type": "text", + "content": "In the past years, existing efforts primarily focus on how to devise an effective sub-network " + }, + { + "bbox": [ + 304, + 369, + 546, + 548 + ], + "type": "inline_equation", + "content": "g(\\cdot)" + }, + { + "bbox": [ + 304, + 369, + 546, + 548 + ], + "type": "text", + "content": " for cost volume generation and cost aggregation, while overlook the importance of learning robust feature representations of stereo images that can preserve the semantic and structural cues. Recent studies pointed out that most existing SM networks trained on synthetic data are susceptible to learn superficial shortcut features [5] instead of the desirable semantic and structural features, which leads to poor generalization performance in unseen (realistic) domain due to the significant synthetic-realistic domain gap. Therefore, the main research problem in this work is how to train an effective feature extraction network " + }, + { + "bbox": [ + 304, + 369, + 546, + 548 + ], + "type": "inline_equation", + "content": "f(\\cdot)" + }, + { + "bbox": [ + 304, + 369, + 546, + 548 + ], + "type": "text", + "content": " on only synthetic data that can learn generalizable representation of stereo images, so as to estimate reliable disparity map on unseen domain." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 555, + 434, + 569 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 555, + 434, + 569 + ], + "spans": [ + { + "bbox": [ + 306, + 555, + 434, + 569 + ], + "type": "text", + "content": "3.2. Our Proposed Method" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 574, + 545, + 671 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 574, + 545, + 671 + ], + "spans": [ + { + "bbox": [ + 304, + 574, + 545, + 671 + ], + "type": "text", + "content": "Our target is to tackle the synthetic-to-realistic generalization in SM. Its main challenge is that we only have synthetic data for training, which has the high risk of overfitting to synthetic data due to its limited diversity. Inspired by [13, 29, 40, 47], we address the domain generalized SM from a new perspective in this work. The rest of this section will introduce our proposed network for this task in detail. The pipeline of our proposed HVT is shown in Fig. 2" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 674, + 492, + 686 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 674, + 492, + 686 + ], + "spans": [ + { + "bbox": [ + 306, + 674, + 492, + 686 + ], + "type": "text", + "content": "3.2.1 Hierarchical Visual Transformation" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 689, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 715 + ], + "type": "text", + "content": "As we know, the key to addressing domain generalization is learning domain-invariant feature, also called causal fea" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 314, + 757 + ], + "type": "text", + "content": "9561" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 300 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 300 + ], + "type": "text", + "content": "Although the explicit form of causal feature is unknown in general, we have the prior that causal feature should remain invariant to certain transformations [29]. For example, the semantic and structural features can be treated as two domain-invariant (causal) features of stereo images for SM, while adjusting the luminance, contrast, or saturation of a stereo image pair will not affect the corresponding disparity map. Our intuitive idea is to leverage the visual transformations that do not change the underlying domain-invariant feature to increase the diversity of training domain, thereby enhancing the generalization performance of SM network. It is a straightforward but effective way. To this end, we design a Hierarchical Visual Transformation (HVT) network to diversify the distribution of training domain. Specifically, we learn a set of visual transformations " + }, + { + "bbox": [ + 46, + 72, + 289, + 300 + ], + "type": "inline_equation", + "content": "\\mathcal{T} = \\{T_1,\\dots ,T_M\\}" + }, + { + "bbox": [ + 46, + 72, + 289, + 300 + ], + "type": "text", + "content": " at different levels to transform the original stereo image pairs as " + }, + { + "bbox": [ + 46, + 72, + 289, + 300 + ], + "type": "inline_equation", + "content": "(T(\\mathbf{X}^l),T(\\mathbf{X}^r))" + }, + { + "bbox": [ + 46, + 72, + 289, + 300 + ], + "type": "text", + "content": " , where " + }, + { + "bbox": [ + 46, + 72, + 289, + 300 + ], + "type": "inline_equation", + "content": "T\\in \\mathcal{T}" + }, + { + "bbox": [ + 46, + 72, + 289, + 300 + ], + "type": "text", + "content": " . We force the visual transformation " + }, + { + "bbox": [ + 46, + 72, + 289, + 300 + ], + "type": "inline_equation", + "content": "T(\\cdot)" + }, + { + "bbox": [ + 46, + 72, + 289, + 300 + ], + "type": "text", + "content": " to meet the following three requirements:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 304, + 287, + 430 + ], + "type": "list", + "angle": 0, + "index": 4, + "blocks": [ + { + "bbox": [ + 47, + 304, + 287, + 340 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 304, + 287, + 340 + ], + "spans": [ + { + "bbox": [ + 47, + 304, + 287, + 340 + ], + "type": "text", + "content": "- " + }, + { + "bbox": [ + 47, + 304, + 287, + 340 + ], + "type": "inline_equation", + "content": "T(\\cdot)" + }, + { + "bbox": [ + 47, + 304, + 287, + 340 + ], + "type": "text", + "content": " should induce large visual discrepancy between the original stereo image and the transformed images to enlarge the diversity of training domain." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 342, + 287, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 342, + 287, + 390 + ], + "spans": [ + { + "bbox": [ + 47, + 342, + 287, + 390 + ], + "type": "text", + "content": "- " + }, + { + "bbox": [ + 47, + 342, + 287, + 390 + ], + "type": "inline_equation", + "content": "T(\\cdot)" + }, + { + "bbox": [ + 47, + 342, + 287, + 390 + ], + "type": "text", + "content": " should not change the target disparity map of the original stereo image pairs. We should minimize the smooth-" + }, + { + "bbox": [ + 47, + 342, + 287, + 390 + ], + "type": "inline_equation", + "content": "\\ell_1" + }, + { + "bbox": [ + 47, + 342, + 287, + 390 + ], + "type": "text", + "content": " loss " + }, + { + "bbox": [ + 47, + 342, + 287, + 390 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{sm}-\\ell_1}(F_\\Theta(T(\\mathbf{X}^l), T(\\mathbf{X}^r)), \\mathbf{Y}^{gt})" + }, + { + "bbox": [ + 47, + 342, + 287, + 390 + ], + "type": "text", + "content": " where the transformed stereo images are fed into." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 394, + 287, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 394, + 287, + 430 + ], + "spans": [ + { + "bbox": [ + 47, + 394, + 287, + 430 + ], + "type": "text", + "content": "- The representation of the transformed stereo images " + }, + { + "bbox": [ + 47, + 394, + 287, + 430 + ], + "type": "inline_equation", + "content": "f(T(\\mathbf{X}))" + }, + { + "bbox": [ + 47, + 394, + 287, + 430 + ], + "type": "text", + "content": " should be consistent with that of the original images " + }, + { + "bbox": [ + 47, + 394, + 287, + 430 + ], + "type": "inline_equation", + "content": "f(\\mathbf{X})" + }, + { + "bbox": [ + 47, + 394, + 287, + 430 + ], + "type": "text", + "content": ", so as to learn domain-invariant features." + } + ] + } + ], + "index": 3 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 46, + 433, + 287, + 458 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 433, + 287, + 458 + ], + "spans": [ + { + "bbox": [ + 46, + 433, + 287, + 458 + ], + "type": "text", + "content": "Following the above-listed requirements, we describe the implementation of our proposed HVT network as follows." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 464, + 287, + 511 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 464, + 287, + 511 + ], + "spans": [ + { + "bbox": [ + 46, + 464, + 287, + 511 + ], + "type": "text", + "content": "Implementation of HVT. To effectively learn domain-invariant feature representation for the challenging SM task, we transform the stereo image from three complementary perspectives: Global, Local, and Pixel." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 516, + 287, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 516, + 287, + 601 + ], + "spans": [ + { + "bbox": [ + 46, + 516, + 287, + 601 + ], + "type": "text", + "content": "(1) Global: The Global visual transformation " + }, + { + "bbox": [ + 46, + 516, + 287, + 601 + ], + "type": "inline_equation", + "content": "T_{G}(\\cdot)" + }, + { + "bbox": [ + 46, + 516, + 287, + 601 + ], + "type": "text", + "content": " aims to globally change the distribution of stereo images by sequentially adjusting the basic visual attributes of images: Brightness, Contrast, Saturation, and Hue based on the four corresponding sub-transformations " + }, + { + "bbox": [ + 46, + 516, + 287, + 601 + ], + "type": "inline_equation", + "content": "\\{T_{G}^{B}, T_{G}^{C}, T_{G}^{S}, T_{G}^{H}\\}" + }, + { + "bbox": [ + 46, + 516, + 287, + 601 + ], + "type": "text", + "content": ", following the pipeline of automatic image editing [12]. The three sub-transformations " + }, + { + "bbox": [ + 46, + 516, + 287, + 601 + ], + "type": "inline_equation", + "content": "\\{T_{G}^{B}, T_{G}^{C}, T_{G}^{S}\\}" + }, + { + "bbox": [ + 46, + 516, + 287, + 601 + ], + "type": "text", + "content": " can be formulated as:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 94, + 603, + 287, + 617 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 603, + 287, + 617 + ], + "spans": [ + { + "bbox": [ + 94, + 603, + 287, + 617 + ], + "type": "interline_equation", + "content": "T _ {G} ^ {I} (\\mathbf {X}) = \\alpha_ {G} ^ {I} \\mathbf {X} + (1 - \\alpha_ {G} ^ {I}) o ^ {I} (\\mathbf {X}), \\tag {2}", + "image_path": "bed8b790dcbf32379f9cfac39c3cb1881955cb6459e5513ca273fdbb8c10132d.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 620, + 287, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 620, + 287, + 646 + ], + "spans": [ + { + "bbox": [ + 46, + 620, + 287, + 646 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 620, + 287, + 646 + ], + "type": "inline_equation", + "content": "I\\in \\{B,G,S\\}" + }, + { + "bbox": [ + 46, + 620, + 287, + 646 + ], + "type": "text", + "content": " . The " + }, + { + "bbox": [ + 46, + 620, + 287, + 646 + ], + "type": "inline_equation", + "content": "\\alpha_{G}^{I}" + }, + { + "bbox": [ + 46, + 620, + 287, + 646 + ], + "type": "text", + "content": " is a randomly selected positive constant in an adjustable range of " + }, + { + "bbox": [ + 46, + 620, + 287, + 646 + ], + "type": "inline_equation", + "content": "[\\tau_{\\mathrm{min}}^I,\\tau_{\\mathrm{max}}^I ]" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 102, + 647, + 287, + 673 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 647, + 287, + 673 + ], + "spans": [ + { + "bbox": [ + 102, + 647, + 287, + 673 + ], + "type": "interline_equation", + "content": "\\left\\{ \\begin{array}{l} \\tau_ {\\min } ^ {I} = 1 - \\left(\\mu \\sigma \\left(\\varrho_ {l} ^ {I}\\right) + \\beta\\right) \\\\ \\tau_ {\\max } ^ {I} = 1 + \\left(\\mu \\sigma \\left(\\varrho_ {h} ^ {I}\\right) + \\beta\\right) \\end{array} , \\right. \\tag {3}", + "image_path": "006d53f9e2f83cc9eb0b9a05623996e23de1183b8bf1107c4093cc2c44cdc9cc.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\sigma (\\cdot)" + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "content": " denotes the sigmoid function, " + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\varrho_l^I\\in \\mathbb{R}^1" + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\varrho_h^I\\in \\mathbb{R}^1" + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "content": " are two learnable parameters, " + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "content": " are two positive hyper-parameters. The operation " + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "inline_equation", + "content": "o^{I}(\\cdot)" + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "content": " in Eq. (2)" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 72, + 545, + 155 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 155 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 155 + ], + "type": "text", + "content": "is customized as follows. Specifically, for the Brightness, " + }, + { + "bbox": [ + 304, + 72, + 545, + 155 + ], + "type": "inline_equation", + "content": "o^B (\\mathbf{X}) = \\mathbf{X}\\cdot \\mathbf{O}" + }, + { + "bbox": [ + 304, + 72, + 545, + 155 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 72, + 545, + 155 + ], + "type": "inline_equation", + "content": "\\mathbf{O}" + }, + { + "bbox": [ + 304, + 72, + 545, + 155 + ], + "type": "text", + "content": " denotes a zero matrix all of whose entries are zero. For the Contrast, " + }, + { + "bbox": [ + 304, + 72, + 545, + 155 + ], + "type": "inline_equation", + "content": "o^C (\\mathbf{X}) = \\mathrm{Avg}(\\mathrm{Gray}(\\mathbf{X}))" + }, + { + "bbox": [ + 304, + 72, + 545, + 155 + ], + "type": "text", + "content": " where Gray(·) transforms the RGB image into a gray-scale image and " + }, + { + "bbox": [ + 304, + 72, + 545, + 155 + ], + "type": "inline_equation", + "content": "\\mathrm{Avg}(\\cdot)" + }, + { + "bbox": [ + 304, + 72, + 545, + 155 + ], + "type": "text", + "content": " computes the mean value of all pixels. For the Saturation, " + }, + { + "bbox": [ + 304, + 72, + 545, + 155 + ], + "type": "inline_equation", + "content": "o^S (\\mathbf{X}) = \\mathrm{Gray}(\\mathbf{X})" + }, + { + "bbox": [ + 304, + 72, + 545, + 155 + ], + "type": "text", + "content": ". The Hue adjustment is defined as:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 359, + 158, + 545, + 173 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 158, + 545, + 173 + ], + "spans": [ + { + "bbox": [ + 359, + 158, + 545, + 173 + ], + "type": "interline_equation", + "content": "T _ {G} ^ {H} (\\mathbf {X}) = \\operatorname {R g b} \\left(\\left[ \\mathbf {h} + \\alpha_ {G} ^ {H}, \\mathbf {s}, \\mathbf {v} \\right]\\right), \\tag {4}", + "image_path": "a9e095403bde1723fbef1fd96845fb3defc5f491e74795d0c686c1d11b0b89c7.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 175, + 547, + 248 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 175, + 547, + 248 + ], + "spans": [ + { + "bbox": [ + 304, + 175, + 547, + 248 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 175, + 547, + 248 + ], + "type": "inline_equation", + "content": "[\\mathbf{h},\\mathbf{s},\\mathbf{v}] = \\mathrm{Hsv}(\\mathbf{X})" + }, + { + "bbox": [ + 304, + 175, + 547, + 248 + ], + "type": "text", + "content": " denotes the three components of " + }, + { + "bbox": [ + 304, + 175, + 547, + 248 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 304, + 175, + 547, + 248 + ], + "type": "text", + "content": " in the HSV color space and " + }, + { + "bbox": [ + 304, + 175, + 547, + 248 + ], + "type": "inline_equation", + "content": "\\mathbf{h}" + }, + { + "bbox": [ + 304, + 175, + 547, + 248 + ], + "type": "text", + "content": " denotes the Hue component. " + }, + { + "bbox": [ + 304, + 175, + 547, + 248 + ], + "type": "inline_equation", + "content": "\\operatorname {Rgb}(\\cdot)" + }, + { + "bbox": [ + 304, + 175, + 547, + 248 + ], + "type": "text", + "content": " transforms the image from the HSV space into the RGB space. The " + }, + { + "bbox": [ + 304, + 175, + 547, + 248 + ], + "type": "inline_equation", + "content": "\\alpha_{G}^{H}\\in \\mathbb{R}^{1}" + }, + { + "bbox": [ + 304, + 175, + 547, + 248 + ], + "type": "text", + "content": " is randomly selected from an adjustable range of " + }, + { + "bbox": [ + 304, + 175, + 547, + 248 + ], + "type": "inline_equation", + "content": "[\\tau_{\\min}^{H},\\tau_{\\max}^{H}]" + }, + { + "bbox": [ + 304, + 175, + 547, + 248 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 175, + 547, + 248 + ], + "type": "inline_equation", + "content": "\\tau_{\\mathrm{min}}^H = -\\mu \\sigma (\\varrho_l^H) - \\beta" + }, + { + "bbox": [ + 304, + 175, + 547, + 248 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 175, + 547, + 248 + ], + "type": "inline_equation", + "content": "\\tau_{\\mathrm{max}}^H = \\mu \\sigma (\\varrho_h^H) + \\beta" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 249, + 545, + 274 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 249, + 545, + 274 + ], + "spans": [ + { + "bbox": [ + 306, + 249, + 545, + 274 + ], + "type": "text", + "content": "Note that the order of the sequential sub-transformations " + }, + { + "bbox": [ + 306, + 249, + 545, + 274 + ], + "type": "inline_equation", + "content": "\\{T_G^B, T_G^C, T_G^S, T_G^H\\}" + }, + { + "bbox": [ + 306, + 249, + 545, + 274 + ], + "type": "text", + "content": " is random to improve the diversity." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 277, + 545, + 374 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 277, + 545, + 374 + ], + "spans": [ + { + "bbox": [ + 304, + 277, + 545, + 374 + ], + "type": "text", + "content": "(2) Local: The Local visual transformation " + }, + { + "bbox": [ + 304, + 277, + 545, + 374 + ], + "type": "inline_equation", + "content": "T_{L}(\\cdot)" + }, + { + "bbox": [ + 304, + 277, + 545, + 374 + ], + "type": "text", + "content": " aims to locally modify the distribution of stereo training images. The basic pipeline is that we first slice the given stereo image into " + }, + { + "bbox": [ + 304, + 277, + 545, + 374 + ], + "type": "inline_equation", + "content": "N' \\times N'" + }, + { + "bbox": [ + 304, + 277, + 545, + 374 + ], + "type": "text", + "content": " non-overlapping patches " + }, + { + "bbox": [ + 304, + 277, + 545, + 374 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{x}_1^p, \\dots, \\mathbf{x}_{N' \\times N'}^p\\}" + }, + { + "bbox": [ + 304, + 277, + 545, + 374 + ], + "type": "text", + "content": ", then transform each image patch " + }, + { + "bbox": [ + 304, + 277, + 545, + 374 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i^p" + }, + { + "bbox": [ + 304, + 277, + 545, + 374 + ], + "type": "text", + "content": " by a global transformation " + }, + { + "bbox": [ + 304, + 277, + 545, + 374 + ], + "type": "inline_equation", + "content": "T_{L}^{p}(\\cdot)" + }, + { + "bbox": [ + 304, + 277, + 545, + 374 + ], + "type": "text", + "content": ", and finally merge these transformed image patches into the stereo image based on the original sequential order. The output can be described by" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 320, + 377, + 545, + 392 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 377, + 545, + 392 + ], + "spans": [ + { + "bbox": [ + 320, + 377, + 545, + 392 + ], + "type": "interline_equation", + "content": "T _ {L} (\\mathbf {X}) = \\operatorname {M e r g e} \\left(\\left[ T _ {L} ^ {p} \\left(\\mathbf {x} _ {1} ^ {p}\\right), \\dots , T _ {L} ^ {p} \\left(\\mathbf {x} _ {N ^ {\\prime} \\times N ^ {\\prime}} ^ {p}\\right) \\right]\\right), \\tag {5}", + "image_path": "d7fd12a31579d68751ce52528fc7c00068fd1a42b8e5c7f91039a3c15e730d2f.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 394, + 491, + 406 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 394, + 491, + 406 + ], + "spans": [ + { + "bbox": [ + 306, + 394, + 491, + 406 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 394, + 491, + 406 + ], + "type": "inline_equation", + "content": "\\text{Merge}(\\cdot)" + }, + { + "bbox": [ + 306, + 394, + 491, + 406 + ], + "type": "text", + "content": " denotes the Merge operation." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 407, + 545, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 407, + 545, + 491 + ], + "spans": [ + { + "bbox": [ + 304, + 407, + 545, + 491 + ], + "type": "text", + "content": "Note that patch-level transformation " + }, + { + "bbox": [ + 304, + 407, + 545, + 491 + ], + "type": "inline_equation", + "content": "T_{L}^{p}(\\cdot)" + }, + { + "bbox": [ + 304, + 407, + 545, + 491 + ], + "type": "text", + "content": " for each patch doesn't share parameters with each other to improve the diversity. " + }, + { + "bbox": [ + 304, + 407, + 545, + 491 + ], + "type": "inline_equation", + "content": "T_{L}^{p}(\\cdot)" + }, + { + "bbox": [ + 304, + 407, + 545, + 491 + ], + "type": "text", + "content": " can be implemented by existing style transfer networks, e.g. Adain [22] or Fourier-based method [31]. To better complementing our Global transformation, patch-level transformation " + }, + { + "bbox": [ + 304, + 407, + 545, + 491 + ], + "type": "inline_equation", + "content": "T_{L}^{p}(\\cdot)" + }, + { + "bbox": [ + 304, + 407, + 545, + 491 + ], + "type": "text", + "content": " is implemented by " + }, + { + "bbox": [ + 304, + 407, + 545, + 491 + ], + "type": "inline_equation", + "content": "T_{G}(\\cdot)" + }, + { + "bbox": [ + 304, + 407, + 545, + 491 + ], + "type": "text", + "content": " in Eq.(2) and Eq.(4) for its simplicity and effectiveness." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 496, + 545, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 496, + 545, + 532 + ], + "spans": [ + { + "bbox": [ + 304, + 496, + 545, + 532 + ], + "type": "text", + "content": "(3) Pixel: The Pixel visual transformation " + }, + { + "bbox": [ + 304, + 496, + 545, + 532 + ], + "type": "inline_equation", + "content": "T_{P}(\\cdot)" + }, + { + "bbox": [ + 304, + 496, + 545, + 532 + ], + "type": "text", + "content": " aims to perturb the given stereo images with a pixel-level perturbation matrix. It can be formulated as:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 358, + 536, + 545, + 550 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 536, + 545, + 550 + ], + "spans": [ + { + "bbox": [ + 358, + 536, + 545, + 550 + ], + "type": "interline_equation", + "content": "T _ {P} (\\mathbf {X}) = \\mathbf {X} + (\\mu \\sigma (\\mathbf {W}) + \\beta) \\mathbf {P} \\tag {6}", + "image_path": "0e70bc1ddd9202fd63b51c34ad609626354616dd8b18cba038fed7438b1be517.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 552, + 545, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 552, + 545, + 613 + ], + "spans": [ + { + "bbox": [ + 304, + 552, + 545, + 613 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 552, + 545, + 613 + ], + "type": "inline_equation", + "content": "\\mathbf{P} \\in \\mathbb{R}^{H \\times W \\times 3}" + }, + { + "bbox": [ + 304, + 552, + 545, + 613 + ], + "type": "text", + "content": " is a randomly generated Gaussian matrix with the mean of 0 and the standard deviation of 1, and " + }, + { + "bbox": [ + 304, + 552, + 545, + 613 + ], + "type": "inline_equation", + "content": "\\mathbf{W} \\in \\mathbb{R}^{H \\times W \\times 3}" + }, + { + "bbox": [ + 304, + 552, + 545, + 613 + ], + "type": "text", + "content": " is a learnable matrix. Different from the Global and Local transformations, " + }, + { + "bbox": [ + 304, + 552, + 545, + 613 + ], + "type": "inline_equation", + "content": "T_P(\\cdot)" + }, + { + "bbox": [ + 304, + 552, + 545, + 613 + ], + "type": "text", + "content": " can alter the distribution of synthetic data in a more granular fashion." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "Remark: The implementation of HVT is mainly motivated by the empirically found evidence [5] that existing SM networks are susceptible to exploit common artifacts (e.g. consistent local RGB color statistics and overreliance on local chromaticity features) of synthetic stereo images as shortcuts, which can be clearly illustrated by Fig. 3. We observe from Fig. 3 that the PSMNet is quite sensitive to the different levels of perturbation. It reflects that PSM-" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "9562" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 70, + 286, + 300 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 286, + 300 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 286, + 300 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 286, + 300 + ], + "type": "image", + "image_path": "2b495d2b09df787d7560c33a27869bea05d56f8f5aba6bab2b0b520fcc9c0624.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 303, + 287, + 357 + ], + "lines": [ + { + "bbox": [ + 46, + 303, + 287, + 357 + ], + "spans": [ + { + "bbox": [ + 46, + 303, + 287, + 357 + ], + "type": "text", + "content": "Figure 3. Examples of visualized output of three visual transformations (top-2 rows of (a) and (b)) and the corresponding disparity error maps " + }, + { + "bbox": [ + 46, + 303, + 287, + 357 + ], + "type": "inline_equation", + "content": "|\\dot{\\mathbf{Y}} - \\mathbf{Y}^{gt}|" + }, + { + "bbox": [ + 46, + 303, + 287, + 357 + ], + "type": "text", + "content": " (the 3-rd row of (a) and (b)) of the PSMNet trained on the synthetic SceneFlow dataset. The EPE values are marked in the bottom of the 3-rd row for comparison." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 369, + 287, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 369, + 287, + 453 + ], + "spans": [ + { + "bbox": [ + 46, + 369, + 287, + 453 + ], + "type": "text", + "content": "Net doesn't capture the robust semantic and structural features of stereo images. Our method is specially devised to improve the robustness and generalization ability of existing SM method. The design of the three different transformations " + }, + { + "bbox": [ + 46, + 369, + 287, + 453 + ], + "type": "inline_equation", + "content": "\\{T_{G}(\\mathbf{X}), T_{L}(\\mathbf{X}), T_{P}(\\mathbf{X})\\}" + }, + { + "bbox": [ + 46, + 369, + 287, + 453 + ], + "type": "text", + "content": " can effectively diversify the training domain and prevent the shortcuts from being encoded into the stereo image representation " + }, + { + "bbox": [ + 46, + 369, + 287, + 453 + ], + "type": "inline_equation", + "content": "f(\\mathbf{X})" + }, + { + "bbox": [ + 46, + 369, + 287, + 453 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 476, + 167, + 489 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 476, + 167, + 489 + ], + "spans": [ + { + "bbox": [ + 47, + 476, + 167, + 489 + ], + "type": "text", + "content": "3.2.2 Learning Objectives" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 498, + 287, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 287, + 534 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 287, + 534 + ], + "type": "text", + "content": "To effectively train our proposed HVT network for the domain generalized SM task, we introduce the following loss terms for network optimization." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 536, + 288, + 644 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 536, + 288, + 644 + ], + "spans": [ + { + "bbox": [ + 46, + 536, + 288, + 644 + ], + "type": "text", + "content": "Maximizing Cross-Domain Visual Discrepancy: In this work, without having access to the target domain, we propose to improve the SM network's generalization by transforming the synthetic source domain data into several new source domains " + }, + { + "bbox": [ + 46, + 536, + 288, + 644 + ], + "type": "inline_equation", + "content": "\\{T_G(\\mathbf{X}), T_L(\\mathbf{X}), T_P(\\mathbf{X})\\}" + }, + { + "bbox": [ + 46, + 536, + 288, + 644 + ], + "type": "text", + "content": " to diversify the training domain. Our first objective is to force the distributions of new source domains to be dissimilar as possible to the original distribution of synthetic data. Then we should maximize the following cross-domain visual discrepancy as" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 92, + 646, + 287, + 674 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 92, + 646, + 287, + 674 + ], + "spans": [ + { + "bbox": [ + 92, + 646, + 287, + 674 + ], + "type": "interline_equation", + "content": "\\max L _ {\\text {d i s c}} (\\mathbf {X}) = \\frac {1}{3} \\sum_ {J} d \\left(T _ {J} (\\mathbf {X}), \\mathbf {X}\\right) \\tag {7}", + "image_path": "4bf00849262ba7dc39af80316478ee1a1f40ffd23547f10213626ea53c08cb71.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "inline_equation", + "content": "J \\in \\{G, L, P\\}" + }, + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "inline_equation", + "content": "d(\\cdot)" + }, + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "text", + "content": " is a domain discrepancy measure. In this work, we introduce a specific feature extraction network " + }, + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\phi(\\cdot)" + }, + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "text", + "content": " for domain discriminating. Then we" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 72, + 542, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 542, + 84 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 542, + 84 + ], + "type": "text", + "content": "implement Eq. (7) by minimizing the domain similarity as" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 330, + 86, + 545, + 113 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 86, + 545, + 113 + ], + "spans": [ + { + "bbox": [ + 330, + 86, + 545, + 113 + ], + "type": "interline_equation", + "content": "\\min L _ {\\text {s i m}} (\\mathbf {X}) = \\frac {1}{3} \\sum_ {J} \\operatorname {C o s} \\left(\\phi \\left(T _ {J} (\\mathbf {X})\\right), \\phi (\\mathbf {X})\\right), \\tag {8}", + "image_path": "062f9932a8eebc2e89e7bd86fed0b0376b50e7d6d224137c4bbeba2dfb7f663b.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 116, + 545, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 116, + 545, + 175 + ], + "spans": [ + { + "bbox": [ + 304, + 116, + 545, + 175 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 116, + 545, + 175 + ], + "type": "inline_equation", + "content": "\\mathrm{Cos}(\\cdot ,\\cdot)" + }, + { + "bbox": [ + 304, + 116, + 545, + 175 + ], + "type": "text", + "content": " denotes the cosine similarity function. " + }, + { + "bbox": [ + 304, + 116, + 545, + 175 + ], + "type": "inline_equation", + "content": "\\phi (\\mathbf{X})" + }, + { + "bbox": [ + 304, + 116, + 545, + 175 + ], + "type": "text", + "content": " denotes the pooled feature vector from the domain discriminating network " + }, + { + "bbox": [ + 304, + 116, + 545, + 175 + ], + "type": "inline_equation", + "content": "\\phi (\\cdot)" + }, + { + "bbox": [ + 304, + 116, + 545, + 175 + ], + "type": "text", + "content": ". Besides, to further improve the domain discrepancy, we also minimize the following cross-entropy loss for domain classification:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 332, + 178, + 545, + 192 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 332, + 178, + 545, + 192 + ], + "spans": [ + { + "bbox": [ + 332, + 178, + 545, + 192 + ], + "type": "interline_equation", + "content": "\\min L _ {\\mathrm {c e}} (\\mathbf {X}) = \\operatorname {C E} \\left(\\left\\{\\phi \\left(T _ {J} (\\mathbf {X})\\right), \\phi (\\mathbf {X}) \\right\\}, \\mathcal {Y} _ {d}\\right), \\tag {9}", + "image_path": "d1a6207afd9e9d427f50e55b6288c4c6b8ff010ad23f26a27fce79eb669e526a.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 195, + 545, + 219 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 195, + 545, + 219 + ], + "spans": [ + { + "bbox": [ + 304, + 195, + 545, + 219 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 195, + 545, + 219 + ], + "type": "inline_equation", + "content": "\\mathrm{CE}(\\cdot ,\\cdot)" + }, + { + "bbox": [ + 304, + 195, + 545, + 219 + ], + "type": "text", + "content": " denotes the standard cross-entropy loss and " + }, + { + "bbox": [ + 304, + 195, + 545, + 219 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_d" + }, + { + "bbox": [ + 304, + 195, + 545, + 219 + ], + "type": "text", + "content": " denotes the domain labels of four source domains." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 223, + 545, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 223, + 545, + 331 + ], + "spans": [ + { + "bbox": [ + 304, + 223, + 545, + 331 + ], + "type": "text", + "content": "Minimizing Cross-Domain Feature Inconsistency: To enhance the model's generalization ability, we need to learn domain-invariant representation of stereo images. We expect that our visual transformation " + }, + { + "bbox": [ + 304, + 223, + 545, + 331 + ], + "type": "inline_equation", + "content": "T(\\cdot)" + }, + { + "bbox": [ + 304, + 223, + 545, + 331 + ], + "type": "text", + "content": " doesn't change the core features (e.g., semantic and structural features) of images for stereo matching. Therefore, our second objective is to force the feature representation of transformed stereo images to be consistent with that of original synthetic images. Then we minimize the following pairwise distance term:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 321, + 333, + 545, + 360 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 333, + 545, + 360 + ], + "spans": [ + { + "bbox": [ + 321, + 333, + 545, + 360 + ], + "type": "interline_equation", + "content": "\\min L _ {\\text {d i s t}} (\\mathbf {X}) = \\frac {1}{3} \\sum_ {J} \\| f (T _ {J} (\\mathbf {X})) - f (\\mathbf {X}) \\| _ {2}, \\tag {10}", + "image_path": "9a1df3f16e2ae3522a0fdf24bab544488ebda30c93a121a8eadb4cc114088459.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 362, + 545, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 362, + 545, + 410 + ], + "spans": [ + { + "bbox": [ + 304, + 362, + 545, + 410 + ], + "type": "text", + "content": "which facilitates the learning of shortcut-robust and domain invariant features for domain-generalized stereo matching. In summary, our model is trained by minimizing the linear combination of the above-mentioned learning objectives:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 315, + 413, + 545, + 452 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 413, + 545, + 452 + ], + "spans": [ + { + "bbox": [ + 315, + 413, + 545, + 452 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\min \\mathcal {L} = L _ {\\mathrm {s m} - \\ell_ {1}} (\\hat {\\mathbf {Y}}, \\mathbf {Y} ^ {g t}) + \\\\ \\frac {1}{2} \\left(\\lambda_ {1} L _ {\\text {d i s t}} (\\mathbf {X}) + \\lambda_ {2} L _ {\\text {s i m}} (\\mathbf {X}) + \\lambda_ {3} L _ {\\text {c e}} (\\mathbf {X})\\right), \\tag {11} \\\\ \\end{array}", + "image_path": "f3dc95d4b7c1ca6d96c44ab381225c9835fd2054a0ec7db6531149f9edbc93e0.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 454, + 545, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 454, + 545, + 514 + ], + "spans": [ + { + "bbox": [ + 304, + 454, + 545, + 514 + ], + "type": "text", + "content": "The full loss " + }, + { + "bbox": [ + 304, + 454, + 545, + 514 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 304, + 454, + 545, + 514 + ], + "type": "text", + "content": " is computed as the average over a training batch. The smooth-" + }, + { + "bbox": [ + 304, + 454, + 545, + 514 + ], + "type": "inline_equation", + "content": "\\ell_1" + }, + { + "bbox": [ + 304, + 454, + 545, + 514 + ], + "type": "text", + "content": " loss " + }, + { + "bbox": [ + 304, + 454, + 545, + 514 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{sm - }\\ell_1}" + }, + { + "bbox": [ + 304, + 454, + 545, + 514 + ], + "type": "text", + "content": " is computed based on not only the original synthetic image pairs " + }, + { + "bbox": [ + 304, + 454, + 545, + 514 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{X}^l,\\mathbf{X}^r\\}" + }, + { + "bbox": [ + 304, + 454, + 545, + 514 + ], + "type": "text", + "content": " but also the transformed image pairs " + }, + { + "bbox": [ + 304, + 454, + 545, + 514 + ], + "type": "inline_equation", + "content": "\\{T_J(\\mathbf{X}^l),T_J(\\mathbf{X}^r)\\}" + }, + { + "bbox": [ + 304, + 454, + 545, + 514 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 454, + 545, + 514 + ], + "type": "inline_equation", + "content": "\\lambda_{1},\\lambda_{2}" + }, + { + "bbox": [ + 304, + 454, + 545, + 514 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 454, + 545, + 514 + ], + "type": "inline_equation", + "content": "\\lambda_{3}" + }, + { + "bbox": [ + 304, + 454, + 545, + 514 + ], + "type": "text", + "content": " are three trade-off hyper-parameters." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 524, + 387, + 538 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 524, + 387, + 538 + ], + "spans": [ + { + "bbox": [ + 306, + 524, + 387, + 538 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 544, + 545, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 544, + 545, + 651 + ], + "spans": [ + { + "bbox": [ + 304, + 544, + 545, + 651 + ], + "type": "text", + "content": "In this section, we quantitatively and qualitatively conduct extensive experiments to answer the following research questions: R1: Can the HVT effectively improve the generalization performance of existing SM networks? Can our performance reach the SOTA level? R2: Do the three transformations in the HVT effectively complement to each other? R3: Can our approach learn the domain-invariant features? R4: How is the robustness of our approach when tested in complex realistic scenarios?" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 659, + 487, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 659, + 487, + 672 + ], + "spans": [ + { + "bbox": [ + 306, + 659, + 487, + 672 + ], + "type": "text", + "content": "4.1. Dataset and Experimental Setting" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "Datasets. We use the SceneFlow [19] dataset for training and four realistic SM datasets (KITTI 2012 [8], KITTI 2015 [20], Middlebury [23] and ETH3D [24]) for e" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "9563" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 65, + 70, + 526, + 264 + ], + "blocks": [ + { + "bbox": [ + 65, + 70, + 526, + 264 + ], + "lines": [ + { + "bbox": [ + 65, + 70, + 526, + 264 + ], + "spans": [ + { + "bbox": [ + 65, + 70, + 526, + 264 + ], + "type": "table", + "html": "
BaselinesMethodsKITTI 2015KITTI 2012Middlebury(H)ETH3DReferences
EPED1(3px)EPED1(3px)EPED1(2px)EPED1(1px)
-GANet [42]2.3111.71.9310.15.4120.31.3314.1CVPR 2019
CasStereo [9]2.4211.92.1211.83.7117.20.877.8CVPR 2020
DSMNet [43]1.466.51.266.22.6213.80.696.2ECCV 2020
PSMNet [3]PSMNet [3]3.1716.32.6915.17.6534.22.3323.8CVPR 2018
MS-PSMNet [2]1.64*7.82.33*14.04.72*19.81.42*16.83DV 2020
FC-PSMNet [46]1.58*7.51.42*7.04.14*18.31.25*12.8CVPR 2022
ITSA-PSMNet [5]1.39*5.81.09*5.23.25*12.70.94*9.8CVPR 2022
Graft-PSMNet [17]1.325.31.095.02.3410.91.1610.7CVPR 2022
HVT-PSMNet1.14±0.024.9±0.120.93±0.024.3±0.061.46±0.1310.2±0.160.47±0.036.9±0.23Ours
GwcNet [10]GwcNet [10]3.4322.72.7720.27.2337.92.7854.2CVPR 2019
FC-GwcNet [46]1.72*8.01.45*7.45.14*21.11.13*11.7CVPR 2022
ITSA-GwcNet [5]1.33*5.41.02*4.92.73*11.40.62*7.1CVPR 2022
HVT-GwcNet1.15±0.025.0±0.110.88±0.023.9±0.131.29±0.1310.3±0.210.46±0.085.9±0.26Ours
CFNet [25]CFNet [25]1.716.01.045.23.2415.40.485.72CVPR 2021
ITSA-CFNet [5]1.094.70.874.21.8710.40.455.1CVPR 2022
HVT-CFNet1.10±0.044.9±0.160.85±0.024.0±0.141.79±0.2210.2±0.160.39±0.024.5±0.24Ours
RAFT [16]RAFT [16]1.265.71.015.11.9212.60.363.33DV 2021
HVT-RAFT1.12±0.025.2±0.090.87±0.023.7±0.081.37±0.1110.4±0.140.29±0.013.0±0.09Ours
", + "image_path": "9afbc1b96748d394623d389f8772d7da7a6e3028fd9fdbf6eb675d81ee95116d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 268, + 545, + 292 + ], + "lines": [ + { + "bbox": [ + 46, + 268, + 545, + 292 + ], + "spans": [ + { + "bbox": [ + 46, + 268, + 545, + 292 + ], + "type": "text", + "content": "Table 1. Performance comparison with SOTA domain generalized SM networks. The * denotes our reproduced EPE results since the authors only use the D1 metric. As we didn't have a validation set for model selection, we report the average result over last 5 epochs." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 301, + 287, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 301, + 287, + 445 + ], + "spans": [ + { + "bbox": [ + 46, + 301, + 287, + 445 + ], + "type": "text", + "content": "valuation. SceneFlow [19] is a large-scale synthetic SM dataset containing 35,454 training stereo image pairs and 4,370 testing image pairs with a resolution of " + }, + { + "bbox": [ + 46, + 301, + 287, + 445 + ], + "type": "inline_equation", + "content": "960 \\times 540" + }, + { + "bbox": [ + 46, + 301, + 287, + 445 + ], + "type": "text", + "content": ". All the synthetic image pairs have dense annotations of ground-truth disparities. KITTI 2012 [8] and KITTI 2015 [20] consists of 194 and 200 training stereo image pairs collected in outdoor driving scenes with sparse annotations of disparities, respectively. Middlebury [23] includes 15 high-resolution stereo image pairs in indoor scenes. In our experiments, we use the half-resolution version (Middlebury(H)) for evaluation. ETH3D [24] has 27 grayscale stereo image pairs collected from both indoor and outdoor scenes." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 446, + 287, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 446, + 287, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 446, + 287, + 567 + ], + "type": "text", + "content": "Metrics. Following the setting of [17], we use both EPE rate (End-Point Error) and D1 error rate " + }, + { + "bbox": [ + 46, + 446, + 287, + 567 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 46, + 446, + 287, + 567 + ], + "type": "text", + "content": " with different pixel threshold " + }, + { + "bbox": [ + 46, + 446, + 287, + 567 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 46, + 446, + 287, + 567 + ], + "type": "text", + "content": " as the metrics to get a more comprehensive evaluation. The EPE measures the average disparity error over all pixels, which reflects the average disparity estimate. The D1 error rate computes the percentage of error pixels with absolute error larger than a specific threshold " + }, + { + "bbox": [ + 46, + 446, + 287, + 567 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 46, + 446, + 287, + 567 + ], + "type": "text", + "content": ". The pixel threshold is set as " + }, + { + "bbox": [ + 46, + 446, + 287, + 567 + ], + "type": "inline_equation", + "content": "\\rho = 3\\mathrm{px}" + }, + { + "bbox": [ + 46, + 446, + 287, + 567 + ], + "type": "text", + "content": " for KITTI 2012 [8] and KITTI 2015 [20], " + }, + { + "bbox": [ + 46, + 446, + 287, + 567 + ], + "type": "inline_equation", + "content": "\\rho = 2\\mathrm{px}" + }, + { + "bbox": [ + 46, + 446, + 287, + 567 + ], + "type": "text", + "content": " for Middlebury [23] and " + }, + { + "bbox": [ + 46, + 446, + 287, + 567 + ], + "type": "inline_equation", + "content": "\\rho = 1\\mathrm{px}" + }, + { + "bbox": [ + 46, + 446, + 287, + 567 + ], + "type": "text", + "content": " for ETH3D [24], respectively, following recent works [17, 46]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 568, + 287, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 568, + 287, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 568, + 287, + 640 + ], + "type": "text", + "content": "Baselines. We select four SM networks as baselines, including two well-studied and commonly-used methods (PSMNet [3] and GwcNet [10]) and two SOTA methods (CFNet [25] and RAFT [16]), in our experiments. We will integrate our HVT networks with these baseline networks to validate the effectiveness of HVT on domain generalization." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 642, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 287, + 713 + ], + "type": "text", + "content": "Implementation Details. Following [43], we use the domain normalization technique in the feature extraction module for all baselines. Except the RAFT [16], all the baselines are implemented by PyTorch [21] with Adam " + }, + { + "bbox": [ + 46, + 642, + 287, + 713 + ], + "type": "inline_equation", + "content": "(\\beta_{1} = 0.9, \\beta_{2} = 0.999)" + }, + { + "bbox": [ + 46, + 642, + 287, + 713 + ], + "type": "text", + "content": " optimizer. We train the model for 45 epochs with the batch size of 8. Besides, we introduce an incremen" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 301, + 545, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 301, + 545, + 529 + ], + "spans": [ + { + "bbox": [ + 304, + 301, + 545, + 529 + ], + "type": "text", + "content": "tal training scheme to stably optimize the network in this work. Specifically, we train the model with " + }, + { + "bbox": [ + 304, + 301, + 545, + 529 + ], + "type": "inline_equation", + "content": "T_{G}(\\cdot)" + }, + { + "bbox": [ + 304, + 301, + 545, + 529 + ], + "type": "text", + "content": " only for 15 epochs at Stage I, then we further train the model with " + }, + { + "bbox": [ + 304, + 301, + 545, + 529 + ], + "type": "inline_equation", + "content": "\\{T_G(\\cdot), T_L(\\cdot)\\}" + }, + { + "bbox": [ + 304, + 301, + 545, + 529 + ], + "type": "text", + "content": " for another 15 epochs at Stage II, and finally we continually train the model with " + }, + { + "bbox": [ + 304, + 301, + 545, + 529 + ], + "type": "inline_equation", + "content": "\\{T_G(\\cdot), T_L(\\cdot), T_P(\\cdot)\\}" + }, + { + "bbox": [ + 304, + 301, + 545, + 529 + ], + "type": "text", + "content": " for the remaining 15 epochs at Stage III. The learning rate is set to 0.001 and decreased by half after epoch 10, 20, 30 and 40. For the RAFT [16] baseline, we train the model for total 30K steps and train each stage 10K steps. The optimizer and learning rate follow its original setting. Besides, the asymmetric chromatic augmentation is not used in any models to avoid unfair experimental comparison. We select ResNet18 [11] as the domain discriminating network " + }, + { + "bbox": [ + 304, + 301, + 545, + 529 + ], + "type": "inline_equation", + "content": "\\phi(\\cdot)" + }, + { + "bbox": [ + 304, + 301, + 545, + 529 + ], + "type": "text", + "content": " for its simplicity. For different hyper-parameters, the " + }, + { + "bbox": [ + 304, + 301, + 545, + 529 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 304, + 301, + 545, + 529 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 301, + 545, + 529 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 301, + 545, + 529 + ], + "type": "text", + "content": " in Eq. (3) and (6) are set as 0.1 and 0.15 respectively. The " + }, + { + "bbox": [ + 304, + 301, + 545, + 529 + ], + "type": "inline_equation", + "content": "\\lambda_1" + }, + { + "bbox": [ + 304, + 301, + 545, + 529 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 301, + 545, + 529 + ], + "type": "inline_equation", + "content": "\\lambda_2" + }, + { + "bbox": [ + 304, + 301, + 545, + 529 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 301, + 545, + 529 + ], + "type": "inline_equation", + "content": "\\lambda_3" + }, + { + "bbox": [ + 304, + 301, + 545, + 529 + ], + "type": "text", + "content": " in Eq. (11) are set as 1, 0.5 and 0.5 respectively. The " + }, + { + "bbox": [ + 304, + 301, + 545, + 529 + ], + "type": "inline_equation", + "content": "N' = 4" + }, + { + "bbox": [ + 304, + 301, + 545, + 529 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 304, + 301, + 545, + 529 + ], + "type": "inline_equation", + "content": "T_{L}(\\cdot)" + }, + { + "bbox": [ + 304, + 301, + 545, + 529 + ], + "type": "text", + "content": ". Note that all the SM networks are only trained on the synthetic dataset, SceneFlow. The target data is strictly inaccessible during training." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 536, + 487, + 550 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 536, + 487, + 550 + ], + "spans": [ + { + "bbox": [ + 305, + 536, + 487, + 550 + ], + "type": "text", + "content": "4.2. Overall Performance Comparison" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 555, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 555, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 555, + 545, + 628 + ], + "type": "text", + "content": "R1: Comparison with Baselines and SOTAs. In Tab. 1, we report the comparison of generalization performance between the baselines (PSMNet, GwcNet, CFNet, and RAFT) and our HVT-integrated methods, as well as the comparison between ours and the reported SOTA results, across the four realistic datasets. We have the following observations:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 630, + 545, + 713 + ], + "type": "text", + "content": "- The synthetic-to-realistic generalization performances of all the baselines are consistently improved by our HVT in all settings. Specifically, compared with the widely-used PSMNet [3], the performance improvements w.r.t. the D1 metric are " + }, + { + "bbox": [ + 306, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "11.4\\%" + }, + { + "bbox": [ + 306, + 630, + 545, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 306, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "10.8\\%" + }, + { + "bbox": [ + 306, + 630, + 545, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 306, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "24\\%" + }, + { + "bbox": [ + 306, + 630, + 545, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 306, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "16.9\\%" + }, + { + "bbox": [ + 306, + 630, + 545, + 713 + ], + "type": "text", + "content": ", respectively on the four datasets. Similar improvement can also be observed on GwcNet [10]: " + }, + { + "bbox": [ + 306, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "17.7\\%" + }, + { + "bbox": [ + 306, + 630, + 545, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 306, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "16.3\\%" + }, + { + "bbox": [ + 306, + 630, + 545, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 306, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "27.6\\%" + }, + { + "bbox": [ + 306, + 630, + 545, + 713 + ], + "type": "text", + "content": ", and" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "9564" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 51, + 70, + 283, + 251 + ], + "blocks": [ + { + "bbox": [ + 51, + 70, + 283, + 251 + ], + "lines": [ + { + "bbox": [ + 51, + 70, + 283, + 251 + ], + "spans": [ + { + "bbox": [ + 51, + 70, + 283, + 251 + ], + "type": "table", + "html": "
BaselinesGlobal Local PixelKITTI 2015MiddleburyETH3D
EPE3pxEPE2pxEPE1px
PSMNet [3]✓✗✗1.316.072.0413.70.489.4
✗✓✗1.286.031.6912.50.5910.7
✗✗✓1.276.292.3914.60.579.9
✓✓✗1.235.471.5711.10.539.1
✓✗✓1.195.571.4411.20.517.7
✗✓✓1.275.721.5810.90.627.9
✓✓✓1.144.931.4610.20.476.9
GwcNet [10]✓✗✗1.285.891.8812.60.748.2
✗✓✗1.265.881.6411.90.688.5
✗✗✓1.296.181.8312.40.718.3
✓✓✗1.235.381.5810.40.587.8
✓✗✓1.195.521.4910.70.557.1
✗✓✓1.185.471.5710.60.526.9
✓✓✓1.155.021.2910.30.465.9
", + "image_path": "99dbf60f061aeff72355fc22f05e392518704e44612deb261ebdbfc6306d16d3.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 299, + 287, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 299, + 287, + 467 + ], + "spans": [ + { + "bbox": [ + 56, + 299, + 287, + 467 + ], + "type": "inline_equation", + "content": "48.3\\%" + }, + { + "bbox": [ + 56, + 299, + 287, + 467 + ], + "type": "text", + "content": " w.r.t. the D1 metric. Even compared with the SOTA CFNet [25] and RAFT [16], the D1 error rates are still substantially decreased: " + }, + { + "bbox": [ + 56, + 299, + 287, + 467 + ], + "type": "inline_equation", + "content": "1.1\\%" + }, + { + "bbox": [ + 56, + 299, + 287, + 467 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 56, + 299, + 287, + 467 + ], + "type": "inline_equation", + "content": "1.2\\%" + }, + { + "bbox": [ + 56, + 299, + 287, + 467 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 56, + 299, + 287, + 467 + ], + "type": "inline_equation", + "content": "5.2\\%" + }, + { + "bbox": [ + 56, + 299, + 287, + 467 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 56, + 299, + 287, + 467 + ], + "type": "inline_equation", + "content": "1.2\\%" + }, + { + "bbox": [ + 56, + 299, + 287, + 467 + ], + "type": "text", + "content": " for CFNet, and " + }, + { + "bbox": [ + 56, + 299, + 287, + 467 + ], + "type": "inline_equation", + "content": "0.5\\%" + }, + { + "bbox": [ + 56, + 299, + 287, + 467 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 56, + 299, + 287, + 467 + ], + "type": "inline_equation", + "content": "1.4\\%" + }, + { + "bbox": [ + 56, + 299, + 287, + 467 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 56, + 299, + 287, + 467 + ], + "type": "inline_equation", + "content": "2.2\\%" + }, + { + "bbox": [ + 56, + 299, + 287, + 467 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 56, + 299, + 287, + 467 + ], + "type": "inline_equation", + "content": "0.3\\%" + }, + { + "bbox": [ + 56, + 299, + 287, + 467 + ], + "type": "text", + "content": " for RAFT. The quantitative comparison clearly shows the effectiveness of HVT on enhancing the robustness of SM models. The improvement can be mainly attributed to the fact that our HVT significantly diversify the visual distribution of original synthetic images, thus preventing the model from building the spurious relationship between the pairwise input and the target disparity. The model will not easily find the matching correspondences across the stereo images by just leveraging the shortcut cues, e.g., local RGB color statistics and chromaticity features." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 471, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 47, + 471, + 287, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 471, + 287, + 590 + ], + "spans": [ + { + "bbox": [ + 47, + 471, + 287, + 590 + ], + "type": "text", + "content": "- The improvements of generalization performance brought by HVT on the Middlebury and ETH3D datasets seem to be much larger than those on the KITTI 2012 and 2015 datasets. The reason is that Middlebury has higher resolution images in realistic scenarios than those in KITTI 2012 and 2015, and the images in ETH3D are all grayscale which are very different from the colorful synthetic training images. It reflects that our HVT can perform well in diverse realistic scenarios that differ from training domain in resolution and color distribution." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 594, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 594, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 594, + 288, + 714 + ], + "type": "text", + "content": "- Our HVT-enhanced methods almost outperform all the SOTA methods except ITSA-CFNet on KITTI 2015. It shows the strong potential of our HVT in improving the cross-domain generalization. Note that the three transformations devised in this work are all simple and straightforward. The performance can be further improved if we introduce more delicate transformations into our HVT. Besides, the performance of ITSA-CFNet on KITTI 2015 is already very high w.r.t. the EPE and D1 metrics, 1.09 and " + }, + { + "bbox": [ + 47, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "4.7\\%" + }, + { + "bbox": [ + 47, + 594, + 288, + 714 + ], + "type": "text", + "content": ". Our HVT-CFNet's performance is on a par" + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "type": "table", + "bbox": [ + 321, + 70, + 531, + 156 + ], + "blocks": [ + { + "bbox": [ + 47, + 256, + 287, + 289 + ], + "lines": [ + { + "bbox": [ + 47, + 256, + 287, + 289 + ], + "spans": [ + { + "bbox": [ + 47, + 256, + 287, + 289 + ], + "type": "text", + "content": "Table 2. Ablation studies on the effect of three visual transformations (Global, Local, and Pixel) on three datasets using the two well-studied baselines, PSMNet [3] and GwcNet [10]." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 321, + 70, + 531, + 156 + ], + "lines": [ + { + "bbox": [ + 321, + 70, + 531, + 156 + ], + "spans": [ + { + "bbox": [ + 321, + 70, + 531, + 156 + ], + "type": "table", + "html": "
BaselinesObj-1Obj-2KITTI 2015MiddleburyETH3D
EPE3pxEPE2pxEPE2px
PSMNet [3]XX1.677.742.8815.10.8913.2
X✓1.316.232.0411.70.6310.1
✓✓1.144.931.4610.20.476.9
GwcNet [10]XX1.647.582.6514.60.8612.4
X✓1.286.071.9311.30.579.2
✓✓1.155.021.2910.30.465.9
", + "image_path": "4553da0f889957cb13293cb58d2db7b11198d10cde972e4a037b20f5687f055a.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 156, + 544, + 179 + ], + "lines": [ + { + "bbox": [ + 306, + 156, + 544, + 179 + ], + "spans": [ + { + "bbox": [ + 306, + 156, + 544, + 179 + ], + "type": "text", + "content": "Table 3. Ablation studies of our two main optimization objectives: Obj-1 (i.e., Eq. (8) and Eq. (9)) and Obj-2 (i.e., Eq. (10))." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 306, + 190, + 545, + 324 + ], + "blocks": [ + { + "bbox": [ + 306, + 190, + 545, + 324 + ], + "lines": [ + { + "bbox": [ + 306, + 190, + 545, + 324 + ], + "spans": [ + { + "bbox": [ + 306, + 190, + 545, + 324 + ], + "type": "image", + "image_path": "8eb31a533c24fdd6637a111a36f28d44403a5640a0da7371db01343d482f3226.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 329, + 545, + 373 + ], + "lines": [ + { + "bbox": [ + 305, + 329, + 545, + 373 + ], + "spans": [ + { + "bbox": [ + 305, + 329, + 545, + 373 + ], + "type": "text", + "content": "Figure 4. Visualization of RGB color histograms (see (b)) and visual feature histograms (see (c)) of original image and transformed images (see (a)) based on the HVT-PSMNet method. The original image is randomly selected from the realistic Middlebury dataset." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 315, + 384, + 436, + 395 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 384, + 436, + 395 + ], + "spans": [ + { + "bbox": [ + 315, + 384, + 436, + 395 + ], + "type": "text", + "content": "with that of the ITSA-CFNet." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 397, + 545, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 397, + 545, + 504 + ], + "spans": [ + { + "bbox": [ + 306, + 397, + 545, + 504 + ], + "type": "text", + "content": "- Benefiting from using HVT, the performances of weak baselines, i.e., PSMNet and GwcNet, have been increased to the SOTA level, especially on the top-three datasets. It reflects that the critical step for the domain-generalized SM task is to learn domain-invariant representation from diverse training domain instead of devising different complex network modules for cost volume generation or aggregation. It further validates the rationale of our HVT." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 515, + 406, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 515, + 406, + 528 + ], + "spans": [ + { + "bbox": [ + 306, + 515, + 406, + 528 + ], + "type": "text", + "content": "4.3. Ablation Studies" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": "R2: The Complementation of HVTs. As shown in Tab. 2, we investigate the effect of the HVT module by gradually adding the visual transformations in two baselines, PSMNet [3] and GwcNet [10]. We observe that the three visual transformations can complement well to each other. Specifically, only using one of the three transformations can also facilitate the performance improvement of baselines. When using more visual transformations, we observe consistent performance gains across the three realistic datasets. For example, the D1 error rates of " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "T_{G}(\\cdot)" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": "-enhanced PSMNet have been decreased from " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "6.07\\%" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "13.7\\%" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "9.4\\%" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "5.57\\%" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "11.2\\%" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "7.7\\%" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": ", respectively, when jointly using " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "T_{G}(\\cdot)" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "T_{P}(\\cdot)" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": ". The best performances are observed when all the three transformations are jointly used. Similar performance improvements can also be observed when Gwc" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "9565" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 61, + 70, + 272, + 188 + ], + "blocks": [ + { + "bbox": [ + 61, + 70, + 272, + 188 + ], + "lines": [ + { + "bbox": [ + 61, + 70, + 272, + 188 + ], + "spans": [ + { + "bbox": [ + 61, + 70, + 272, + 188 + ], + "type": "table", + "html": "
MethodsSunnyCloudyRainyFoggyAvg.
PSMNet [3]62.560.160.568.663.9
FT-PSMNet [5]4.02.911.56.56.3
FC-PSMNet [46]4.94.37.26.25.7
ITSA-PSMNet [5]4.83.29.46.35.9
HVT-PSMNet4.23.18.75.65.4
GwcNet [10]18.124.728.228.324.8
FT-GwcNet [5]3.12.512.36.06.0
ITSA-GwcNet [5]4.43.39.85.95.9
HVT-GwcNet3.43.58.65.65.3
", + "image_path": "b8cc791800523e89f4c3d922267eb7ce71e5e25b09b5da55777d613960d72e93.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 191, + 286, + 225 + ], + "lines": [ + { + "bbox": [ + 47, + 191, + 286, + 225 + ], + "spans": [ + { + "bbox": [ + 47, + 191, + 286, + 225 + ], + "type": "text", + "content": "Table 4. Robustness comparison of different methods on the DrivingStereo [32] dataset collected from complex realistic scenarios: Sunny, Cloudy, Rainy, and Foggy. The D1 (3px) metric is used." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 233, + 175, + 243 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 233, + 175, + 243 + ], + "spans": [ + { + "bbox": [ + 47, + 233, + 175, + 243 + ], + "type": "text", + "content": "Net is used as the SM baseline." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 249, + 287, + 452 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 249, + 287, + 452 + ], + "spans": [ + { + "bbox": [ + 46, + 249, + 287, + 452 + ], + "type": "text", + "content": "R3: Learning Domain-Invariant features. The core of our approach is to learn shortcut-robust features that can generalize well to unseen domains. As illustrated in Fig. 4 (b), we observe that the hierarchical visual transformation's significantly alter the RGB color histograms of original stereo image in the levels of Global, Local, and Pixel. Benefiting from the minimization of cross-domain feature inconsistency in Eq. (10), the image representation " + }, + { + "bbox": [ + 46, + 249, + 287, + 452 + ], + "type": "inline_equation", + "content": "f(\\mathbf{X})" + }, + { + "bbox": [ + 46, + 249, + 287, + 452 + ], + "type": "text", + "content": " seems to be invariant across different domains as shown in Fig. 4 (c). Tab. 3 quantitatively investigate the effect of learning objective in Eq. (10). We can observe a clear performance improvement by just minimizing the cross-domain feature inconsistency (Obj-2 in Tab. 3). Obviously, by jointly optimizing the two objectives, we obtain the best generalization performance. The quantitative and qualitative results clearly reflects the importance and efficacy of the two learning objectives in Sec. 3.2.2." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 457, + 286, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 457, + 286, + 601 + ], + "spans": [ + { + "bbox": [ + 46, + 457, + 286, + 601 + ], + "type": "text", + "content": "R4: Robustness to Complex Realistic Scenarios. In this section, we evaluate the generalization of our HVT-enhanced methods on the DrivingStereo [32] dataset which is collected from complex realistic scenarios: Sunny, Cloudy, Rainy, and Foggy, as shown in Fig. 5. We conduct experiments using the PSMNet [3] and GwcNet [10] as the baseline frameworks. The results of officially released fine-tuned (FT) networks of PSMNet and GwcNet on the realistic KITTI 2015 dataset are included for comparison. Besides, we also include the results of SOTA domain generalized SM methods [5, 46] in the Tab. 4. We have the following observations from Tab. 4 and Fig. 5:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 604, + 286, + 713 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 47, + 604, + 286, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 604, + 286, + 662 + ], + "spans": [ + { + "bbox": [ + 47, + 604, + 286, + 662 + ], + "type": "text", + "content": "- Our methods (HVT-PSMNet and HVT-GwcNet) obtain the best overall performance " + }, + { + "bbox": [ + 47, + 604, + 286, + 662 + ], + "type": "inline_equation", + "content": "(5.4\\%" + }, + { + "bbox": [ + 47, + 604, + 286, + 662 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 604, + 286, + 662 + ], + "type": "inline_equation", + "content": "5.3\\%)" + }, + { + "bbox": [ + 47, + 604, + 286, + 662 + ], + "type": "text", + "content": " w.r.t. the average D1 error rate over the four groups of weather conditions, which demonstrates the efficacy of HVT and the strong robustness of HVT-based methods." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 665, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 665, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 665, + 286, + 713 + ], + "type": "text", + "content": "- HVT-PSMNet and HVT-GwcNet not only outperform the baselines PSMNet and GwcNet, respectively, by a large margin, but also decrease the error rates of the FT-PSMNet and FT-GwcNet on the Rainy and Foggy groups." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "type": "image", + "bbox": [ + 319, + 70, + 529, + 225 + ], + "blocks": [ + { + "bbox": [ + 319, + 70, + 529, + 225 + ], + "lines": [ + { + "bbox": [ + 319, + 70, + 529, + 225 + ], + "spans": [ + { + "bbox": [ + 319, + 70, + 529, + 225 + ], + "type": "image", + "image_path": "e4ae0f8a73df010aa0b212d00aec450ff6ff296f74a58ccca5b69afb82d9d390.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 228, + 545, + 294 + ], + "lines": [ + { + "bbox": [ + 305, + 228, + 545, + 294 + ], + "spans": [ + { + "bbox": [ + 305, + 228, + 545, + 294 + ], + "type": "text", + "content": "Figure 5. Qualitative results on the DrivingStereo [32] dataset. For each group, top row shows the left image and the EPE error maps of PSMNet, fine-tuned (FT) PSMNet, and our HVT-PSMNet, respectively. Bottom row shows the GT disparity map and the predicted disparity maps of different methods. The EPE values are marked in the upper right corner of error maps." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 314, + 301, + 545, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 301, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 314, + 301, + 545, + 361 + ], + "type": "text", + "content": "On another two groups, both fine-tuned (FT) models perform slightly better than our HVT, since images in the two groups are similar to the KITTI training data. The results reflect that our HVT can effectively deal with the domain shift between the synthetic data and realistic data." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 363, + 545, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 363, + 545, + 410 + ], + "spans": [ + { + "bbox": [ + 306, + 363, + 545, + 410 + ], + "type": "text", + "content": "- Fig. 5 shows the qualitative robustness comparison in different weather conditions. The observation from Fig. 5 is consistent with that from Tab. 4, which further validates the potential of HVT in enhancing the model robustness." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 423, + 378, + 435 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 423, + 378, + 435 + ], + "spans": [ + { + "bbox": [ + 306, + 423, + 378, + 435 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 443, + 545, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 443, + 545, + 646 + ], + "spans": [ + { + "bbox": [ + 304, + 443, + 545, + 646 + ], + "type": "text", + "content": "In this work, we have devised an effective HVT module for the problem of domain generalized SM. To prevent the network from exploiting the shortcut features for disparity estimation, we propose to 1) first diversify the training domain by leveraging the three complementary visual transformations, where the cross-domain visual discrepancy is maximized, and 2) minimize the cross-domain feature inconsistency to effectively capture domain-invariant features. Our proposed method is simple and can be flexibly integrated with most existing SM networks. Extensive experimental results show that our HVT consistently advances the learning of shortcut-robust features and substantially improves the generalization performance of SM networks in unseen realistic scenarios. In the future, we will attempt to design more delicate visual transformations to enhance HVT and extend HVT for addressing other 3D vision tasks." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 658, + 415, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 658, + 415, + 671 + ], + "spans": [ + { + "bbox": [ + 306, + 658, + 415, + 671 + ], + "type": "text", + "content": "6. Acknowledgments" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 677, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 712 + ], + "type": "text", + "content": "This work was supported by the National Natural Science Foundation of China (NSFC) under Grant 62272435, Grant U22A2094 and Grant 72188101." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 315, + 757 + ], + "type": "text", + "content": "9566" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 125 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 125 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 125 + ], + "type": "text", + "content": "[1] Joydeep Biswas and Manuela Veloso. 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Robust and Efficient Explainability with Verified Perturbation Analysis", + "text_level": 1, + "bbox": [ + 125, + 130, + 844, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Thomas Fel $^{1,2,5\\dagger}$ Melanie Ducoffe $^{2,7\\dagger}$ David Vigouroux $^{2,4\\dagger}$ Rémi Cadène $^{1,3}$ Mikael Capelle $^{6}$ Claire Nicodème $^{5}$ Thomas Serre $^{1,2}$", + "bbox": [ + 161, + 200, + 797, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ Carney Institute for Brain Science, Brown University, USA $^{2}$ Artificial and Natural Intelligence Toulouse Institute", + "bbox": [ + 245, + 255, + 723, + 291 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{3}$ Sorbonne Université, CNRS, France $^{4}$ IRT Saint-Exupery, France $^{5}$ Innovation & Research Division, SNCF $^{6}$ Thales Alenia Space, France $^{7}$ Airbus AI Research", + "bbox": [ + 199, + 291, + 769, + 344 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 378, + 313, + 395 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "A plethora of attribution methods have recently been developed to explain deep neural networks. These methods use different classes of perturbations (e.g., occlusion, blurring, masking, etc) to estimate the importance of individual image pixels to drive a model's decision. Nevertheless, the space of possible perturbations is vast and current attribution methods typically require significant computation time to accurately sample the space in order to achieve high-quality explanations. In this work, we introduce EVA (Explaining using Verified Perturbation Analysis) – the first explainability method which comes with guarantees that an entire set of possible perturbations has been exhaustively searched. We leverage recent progress in verified perturbation analysis methods to directly propagate bounds through a neural network to exhaustively probe a – potentially infinite-size – set of perturbations in a single forward pass. Our approach takes advantage of the beneficial properties of verified perturbation analysis, i.e., time efficiency and guaranteed complete – sampling agnostic – coverage of the perturbation space – to identify image pixels that drive a model's decision. We evaluate EVA systematically and demonstrate state-of-the-art results on multiple benchmarks. Our code is freely available: github.com/deel-ai/formal-explainability", + "bbox": [ + 75, + 412, + 473, + 777 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 78, + 797, + 209, + 814 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Deep neural networks are now being widely deployed in many applications from medicine, transportation, and security to finance, with broad societal implications [40]. They are routinely used to making safety-critical decisions – often without an explanation as their decisions are notoriously", + "bbox": [ + 75, + 824, + 468, + 902 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d84cf3ad071e906cd321d87ed3c5dc6904cca47f8c114ba7d204acd356420ed8.jpg", + "image_caption": [ + "Figure 1. Manifold exploration of current attribution methods. Current methods assign an importance score to individual pixels using perturbations around a given input image $\\pmb{x}$ . Saliency [56] uses infinitesimal perturbations around $\\pmb{x}$ , Occlusion [71] switches individual pixel intensities on/off. More recent approaches [17,43,46,48,49] use (Quasi-) random sampling methods in specific perturbation spaces (occlusion of segments of pixels, blurring, ...). However, the choice of the perturbation space undoubtedly biases the results – potentially even introducing serious artifacts [26, 29, 38, 64]. We propose to use verified perturbation analysis to efficiently perform a complete coverage of a perturbation space around $\\pmb{x}$ to produce reliable and faithful explanations." + ], + "image_footnote": [], + "bbox": [ + 500, + 380, + 910, + 551 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "hard to interpret.", + "text_level": 1, + "bbox": [ + 500, + 761, + 612, + 776 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Many explainability methods have been proposed to gain insight into how network models arrive at a particular decision [17,24,43,46,48,49,53,55,61,65,71]. The applications of these methods are multiple - from helping to improve or debug their decisions to helping instill confidence in the reliability of their decisions [14]. Unfortunately, a severe limitation of these approaches is that they are subject to a confirmation bias: while they appear to offer useful expla", + "bbox": [ + 496, + 779, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "16153", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "nations to a human experimenter, they may produce incorrect explanations [2, 23, 59]. In other words, just because the explanations make sense to humans does not mean that they actually convey what is actually happening within the model. Therefore, the community is actively seeking for better benchmarks involving humans [12, 29, 37, 45].", + "bbox": [ + 75, + 90, + 470, + 181 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In the meantime, it has been shown that some of our current and commonly used benchmarks are biased and that explainability methods reflect these biases - ultimately providing the wrong explanation for the behavior of the model [25, 29, 64]. For example, some of the current fidelity metrics [7, 18, 27, 34, 48] mask one or a few of the input variables (with a fixed value such as a gray mask) in order to assess how much they contribute to the output of the system. Trivially, if these variables are already set to the mask value in a given image (e.g., gray), masking these variables will not yield any effect on the model's output and the importance of these variables is poised to be underestimated. Finally, these methods rely on sampling a space of perturbations that is far too vast to be fully explored - e.g., LIME on a image divided in 64 segments image would need more than $10^{19}$ samples to test all possible perturbations. As a result, current attribution methods may be subject to bias and are potentially not entirely reliable.", + "bbox": [ + 75, + 184, + 473, + 455 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address the baseline issue, a growing body of work is starting to leverage adversarial methods [8, 29, 31, 42, 50] to derive explanations that reflect the robustness of the model to local adversarial perturbations. Specifically, a pixel or an image region is considered important if it allows the easy generation of an adversarial example. That is if a small perturbation of that pixel or image region yields a large change in the model's output. This idea has led to the design of several novel robustness metrics to evaluate the quality of explanations, such as Robustness- $S_r$ [29]. For a better ranking on those robustness metrics, several methods have been proposed that make intensive use of adversarial attacks [29, 70], such as Greedy-AS for Robustness- $S_r$ . However, these methods are computationally very costly – in some cases, requiring over 50 000 adversarial attacks per explanation – severely limiting the widespread adoption of these methods in real-world scenarios.", + "bbox": [ + 75, + 459, + 470, + 715 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we propose to address this limitation by introducing EVA (Explaining using Verified perturbation Analysis), a new explainability method based on robustness analysis. Verified perturbation analysis is a rapidly growing toolkit of methods to derive bounds on the outputs of neural networks in the presence of input perturbations. In contrast to current attributions methods based on gradient estimation or sampling, verified perturbation analysis allows the full exploration of the perturbation space, see Fig. 1. We use a tractable certified upper bound of robustness confidence to derive a new estimator to help quantify the importance of input variables (i.e., those that matter the most). That is, the", + "bbox": [ + 75, + 719, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "variables most likely to change the predictor's decision.", + "bbox": [ + 498, + 90, + 867, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We can summarize our main contributions as follows:", + "bbox": [ + 517, + 107, + 874, + 119 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We introduce EVA, the first explainability method guaranteed to explore its entire set of perturbations using Verified Perturbation Analysis.", + "- We propose a method to scale EVA to large vision models and show that the exhaustive exploration of all possible perturbations can be done efficiently.", + "- We systematically evaluate our approach using several image datasets and show that it yields convincing results on a large range of explainability metrics", + "- Finally, we demonstrate that we can use the proposed method to generate class-specific explanations, and we study the effects of several verified perturbation analysis methods as a hyperparameter of the generated explanations." + ], + "bbox": [ + 500, + 125, + 890, + 347 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 363, + 640, + 378 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Attribution Methods. Our approach builds on prior attribution methods in order to explain the prediction of a deep neural network via the identification of input variables that support the prediction (typically pixels or image regions for images – which lead to importance maps shown in Fig. 1). \"Saliency\" was first introduced in [4] and consists in using the gradient of a classification score. It was later refined in [57, 61, 63, 65, 72] in the context of deep convolutional networks for classification. However, the image gradient only reflects the model's operation within an infinitesimal neighborhood around an input. Hence, it can yield misleading importance estimates [22] since gradients of the current large vision models are noisy [61]. Other methods rely on different image perturbations applied to images to produce importance maps that reflect the corresponding change in classification score resulting from the perturbation. Methods such as \"Occlusion\" [72], \"LIME\" [49], \"RISE\" [48], \"Sobol\" [17] or \"HSIC\" [46] leverage different sampling strategies to explore the space of perturbations around the image. For instance, Occlusion uses binary masks to occlude individual image regions, one at a time. RISE and HSIC combines these discrete masks to perturb multiple regions simultaneously. Sobol uses continuous masks for a finer exploration of the perturbation space.", + "bbox": [ + 496, + 388, + 890, + 751 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Nevertheless, none of these methods are able to systematically cover the full space of perturbations. As a result, the corresponding explanations may not reliably reflect the true importance of pixels. In contrast, our approach comes with strong guarantees that can be derived from the verified perturbation analysis framework as it provides bounds on the perturbation space.", + "bbox": [ + 496, + 751, + 890, + 857 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Robustness-based Explanation. To try to address the aforementioned limitations, several groups [8,19,29,32,33,", + "bbox": [ + 498, + 869, + 890, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "16154", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "42, 60] have focused on the development of a new set of robustness-based evaluation metrics for trustworthy explanations. These new metrics are in contrast with the previous ones, which consisted in removing the pixels considered important in an explanation by substituting them with a fixed baseline – which inevitably introduces bias and artifacts [25, 26, 29, 38, 64]. Key to these new metrics is the assumption that when the important pixels are in their nominal (fixed) state, then perturbations applied to the complementary pixels – deemed unimportant – should not affect the model's decision to any great extent. The corollary that follows is that perturbations limited to the pixels considered important should easily influence the model's decision [29, 42]. Going further along the path of robustness, abductive reasoning was used in [32] to compute optimal subsets with guarantees. The challenge consists in looking for the subset with the smallest possible cardinality – to guarantee the decision of the model. This work constituted one of the early successes of formal methods for explainability, but the approach was limited to low-dimensional problems and shallow neural networks. It was later extended to relax the subset minimum explanation by either providing multiple explanations, aggregating pixels in bundles [6] or by using local surrogates [9].", + "bbox": [ + 76, + 90, + 472, + 454 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Some heuristics-oriented works also propose to optimize these new robustness based criteria and design new methods using a generative model [47] or adversarial attacks [29]. The latter approach requires searching for the existence or lack of an adversarial example for a multitude of $\\ell_p$ balls around the input of interest. As a result, the induced computational cost is quite high as the authors used more than 50000 computations of adversarial examples to generate a single explanation.", + "bbox": [ + 76, + 455, + 472, + 590 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "More importantly, a failure to find an adversarial perturbation for a given radius does not guarantee that none exists. In fact, it is not uncommon for adversarial attacks to fail to converge – or fail to find an adversarial example – which will result in a failure to output an importance score. Our method addresses these issues while drastically reducing the computation cost. An added benefit of our approach is that verified perturbation analysis provides additional guarantees and hence opens the doors of certification which is a necessity for safety-critical applications.", + "bbox": [ + 76, + 593, + 472, + 744 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Verified Perturbation Analysis. This growing field of research focuses on the development of methods that outerapproximate neural network outputs given some input perturbations. Simply put, for a given input $\\pmb{x}$ and a bounded perturbation $\\delta$ , verification methods yield minimum $\\underline{f}(\\pmb{x})$ and maximum $\\overline{f}(\\pmb{x})$ bounds on the output of a model. Formally $\\forall \\delta s.t \\|\\delta\\|_p \\leq \\varepsilon$ :", + "bbox": [ + 76, + 761, + 470, + 872 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\underline {{\\boldsymbol {f}}} (\\boldsymbol {x}) \\leq \\boldsymbol {f} (\\boldsymbol {x} + \\boldsymbol {\\delta}) \\leq \\overline {{\\boldsymbol {f}}} (\\boldsymbol {x}).\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 883, + 367, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "This allows us to explore the whole perturbation space without having to explicitly sample points in that space.", + "bbox": [ + 498, + 90, + 890, + 121 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Early works focused on computing reachable lower and upper bounds based on satisfiability modulo theories [16, 36], and mixed-integer linear programming problems [66]. While these early results were encouraging, the proposed methods struggled even for small networks and image datasets. More recent work has led to the independent development of methods for computing looser certified lower and upper bounds more efficiently thanks to convex linear relaxations either in the primal or dual space [51]. While looser, those bounds remain tight enough to yield non-ubiquitous robustness properties on medium size neural networks. CROWN (hereafter called Backward) uses Linear Relaxation-based Perturbation Analysis (LiRPA) and achieves the tightest bound for efficient single neuron linear relaxation [58, 67, 73]. In addition, linear relaxation methods offer a wide range of possibilities with a vast trade-off between \"tightness\" of the bounds and efficiency. These methods form two broad classes: 'forward' methods which propagate constant bounds (more generally affine relaxations from the input to the output of the network) also called Interval Bound Propagation (IBP, Forward, IBP+Forward) vs. 'backward' methods which bound the output of the network by affine relaxations given the internal layers of the network, starting from the output to the input. Note that these methods can be combined, e.g. $(\\mathrm{CROWN} + \\mathrm{IBP} + \\mathrm{Forward})$ . For a thorough description of the LiRPA framework and theoretical analysis of the worst-case complexities of each variant, see [68]. In this work, we remain purposefully agnostic to the verification method used and opt for the most accurate LiRPA method applicable to the predictor. Our approach is based on the formal verification framework DecoMon, based on Keras [15].", + "bbox": [ + 496, + 123, + 893, + 609 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Explainability with Verified Perturbation Analysis", + "text_level": 1, + "bbox": [ + 498, + 626, + 890, + 662 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Notation. We consider a standard supervised machine-learning classification setting with input space $\\mathcal{X} \\subseteq \\mathbb{R}^d$ , an output space $\\mathcal{Y} \\subseteq \\mathbb{R}^c$ , and a predictor function $f: \\mathcal{X} \\to \\mathcal{Y}$ that maps an input vector $\\boldsymbol{x} = (x_1, \\ldots, x_d)$ to an output $\\boldsymbol{f}(\\boldsymbol{x}) = (\\boldsymbol{f}_1(\\boldsymbol{x}), \\ldots, \\boldsymbol{f}_c(\\boldsymbol{x}))$ . We denote $\\mathcal{B} = \\{\\delta \\in \\mathbb{R}^d : ||\\delta||_p \\leq \\varepsilon\\}$ the perturbation ball with radius $\\varepsilon > 0$ with $p \\in \\{1, 2, \\infty\\}$ . For any subset of indices $\\boldsymbol{u} \\subseteq \\{1, \\ldots, d\\}$ , we denote $\\mathcal{B}_u$ the ball without perturbation on the variables in $\\boldsymbol{u}$ : $\\mathcal{B}_u = \\{\\delta : \\delta \\in \\mathcal{B}, \\delta_u = 0\\}$ and $\\mathcal{B}(\\boldsymbol{x})$ the perturbation ball centered on $\\boldsymbol{x}$ . We denote the lower (resp. upper) bounds obtained with verification perturbation analysis as $\\underline{\\boldsymbol{f}}(\\boldsymbol{x}, \\mathcal{B}) = (\\underline{\\boldsymbol{f}}_1(\\boldsymbol{x}, \\mathcal{B}), \\ldots, \\underline{\\boldsymbol{f}}_c(\\boldsymbol{x}, \\mathcal{B}))$ , and $\\overline{\\boldsymbol{f}}(\\boldsymbol{x}, \\mathcal{B}) = (\\overline{\\boldsymbol{f}}_1(\\boldsymbol{x}, \\mathcal{B}), \\ldots, \\overline{\\boldsymbol{f}}_c(\\boldsymbol{x}, \\mathcal{B}))$ . Intuitively, these bounds delimit the output prediction for any perturbed sample in $\\mathcal{B}(\\boldsymbol{x})$ .", + "bbox": [ + 496, + 665, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "16155", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. The importance of setting the importance right", + "text_level": 1, + "bbox": [ + 76, + 90, + 468, + 107 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Different attribution methods implicitly assume different definitions of the notion of importance for input variables based either on game theory [43], the notion of conditional expectation of the score logits [48], their variance [17] or on some measure of statistical dependency between different areas of an input image and the output of the model [46]. In this work, we build on robustness-based explainability methods [29] which assume that a variable is important if small perturbations of this variable lead to large changes in the model decision. Conversely, a variable is said to be unimportant if changes to this variable only yield small changes in the model decision. From this intuitive assertion, we construct an estimator that we call Adversarial overlap.", + "bbox": [ + 75, + 113, + 470, + 311 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Adversarial overlap", + "text_level": 1, + "bbox": [ + 76, + 316, + 266, + 333 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We go one step beyond previous work and propose to compute importance by taking into account not only the ability of individual variables to change the network's decision but also its confidence in the prediction. Adversarial overlap measures the extent to which a modification on a group of pixels can generate overlap between classes, i.e. generate a point close to $x$ such that the attainable maximum of an unfavorable class $c'$ can match the minimum of the initially predicted class $c$ .", + "bbox": [ + 75, + 337, + 468, + 473 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Indeed, if a modification of a pixel – or group of pixels – allows generating a new image that changes the decision of $f$ , this variable must be considered important. Conversely, if the decision does not change regardless of the value of the pixel, then the pixel can be left at its nominal value and should be considered unimportant.", + "bbox": [ + 75, + 473, + 470, + 563 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Among the set of possible variable perturbations $\\delta$ around a point $x$ , we, therefore, look for points that can modify the decision with the most confidence. Hence our scoring criterion can be formulated as follows:", + "bbox": [ + 75, + 564, + 468, + 622 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nA O _ {c} (\\boldsymbol {x}, \\mathcal {B}) = \\max _ {\\substack {\\boldsymbol {\\delta} \\in \\mathcal {B} \\\\ c ^ {\\prime} \\neq c}} \\boldsymbol {f} _ {c ^ {\\prime}} (\\boldsymbol {x} + \\boldsymbol {\\delta}) - \\boldsymbol {f} _ {c} (\\boldsymbol {x} + \\boldsymbol {\\delta}). \\tag{1}\n$$\n", + "text_format": "latex", + "bbox": [ + 122, + 623, + 468, + 656 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Intuitively, this score represents the confidence of the \"best\" adversarial perturbation that can be found in the perturbation ball $\\mathcal{B}$ around $\\pmb{x}$ . Throughout the article, when $c$ is not specified, it is assumed that $c = \\arg \\max f(\\pmb{x})$ .", + "bbox": [ + 75, + 659, + 468, + 719 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In order to estimate this criterion, a naive strategy could be to use adversarial attacks to search within $\\mathcal{B}$ . However, when they converge - which is not ensured, such methods only explore certain points of the considered space, thus giving no guarantee regarding the optimality of the solution. Moreover, adversarial methods have no guarantee of success and therefore cannot ensure a valid score under every circumstance. Finally, the large dimensions of the current datasets make exhaustive searches impossible.", + "bbox": [ + 75, + 719, + 468, + 854 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To overcome these issues, we take advantage of one of the main results from verified perturbation analysis to derive a guaranteed upper bound on the criterion introduced", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "in Eq. 1. We can upper bound the adversarial overlap criterion as follows:", + "bbox": [ + 496, + 90, + 888, + 119 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nA O (\\boldsymbol {x}, \\mathcal {B}) \\leq \\overline {{A O}} (\\boldsymbol {x}, \\mathcal {B}) = \\max _ {c ^ {\\prime} \\neq c} \\overline {{\\boldsymbol {f}}} _ {c ^ {\\prime}} (\\boldsymbol {x}, \\mathcal {B}) - \\underline {{\\boldsymbol {f}}} _ {c} (\\boldsymbol {x}, \\mathcal {B}).\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 128, + 870, + 154 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The computation of this upper bound becomes tractable using any verified perturbation analysis method.", + "bbox": [ + 496, + 162, + 888, + 193 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For example, $\\overline{AO}(\\boldsymbol{x},\\mathcal{B}) \\leq 0$ guarantees that no adversarial perturbation is possible in the perturbation space. Our upper bound $\\overline{AO}(\\boldsymbol{x},\\mathcal{B})$ corresponds to the difference between the verified lower bound of the class of interest $c$ and the maximum over the verified upper bounds among the other classes. Thus, when important variables are modified (e.g. the head of the dog in Fig. 2, using $\\mathcal{B}$ ), the lower bound for the class of interest will get smaller than the upper bound of the adversary class. On the other hand, this overlap is not possible when important variables are fixed (e.g. in Fig. 2 when the head of the dog is fixed, using $\\mathcal{B}_u$ ). We now demonstrate how to leverage this score to derive an efficient estimator of variable importance.", + "bbox": [ + 496, + 193, + 890, + 388 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3.EVA", + "text_level": 1, + "bbox": [ + 500, + 398, + 571, + 412 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We are willing to assign a higher importance score for a variable allowing (1) a change in a decision, (2) a greater adversarial – thus a solid change of decision. Modifying all variables gives us an idea of the robustness of the model. In the same way, the modification of all variables without the subset $\\mathbf{u}$ allows quantifying the change of the strongest adversarial perturbation and thus quantifies the importance of the variables $\\mathbf{u}$ . Intuitively, if an important variable $\\mathbf{u}$ is discarded, then it will be more difficult, if not impossible, to succeed in finding any adversarial perturbation. Specifically, removing the possibility to modify $x_{\\mathbf{u}}$ allows us to reveal its importance by taking into account its possible interactions.", + "bbox": [ + 496, + 421, + 890, + 616 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The complexity of current models means that the variables are not only treated individually in neural network models but collectively. In order to capture these higher-order interactions, our method consists in measuring the adversarial overlap allowed by all the variables together $\\overline{AO}(\\boldsymbol{x},\\mathcal{B})$ - thus taking into account their interactions - and then forbidding to play on a group of variables $\\overline{AO}(\\boldsymbol{x},\\mathcal{B}_{\\boldsymbol{u}})$ to estimate the importance of $\\boldsymbol{u}$ . Making the interactions of $\\boldsymbol{u}$ disappear reveals their importance. Note that several works have mentioned the importance of taking into account the interactions of the variables when calculating the importance [17, 20, 30, 48]. Formally, we introduce EVA (Explainability using Verified perturbation Analysis) that measure the drop in adversarial overlap when we fixed the variables $\\boldsymbol{u}$ :", + "bbox": [ + 496, + 618, + 890, + 843 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {E V A} (\\boldsymbol {x}, \\boldsymbol {u}, \\mathcal {B}) \\equiv \\overline {{A O}} (\\boldsymbol {x}, \\mathcal {B}) - \\overline {{A O}} (\\boldsymbol {x}, \\mathcal {B} _ {\\boldsymbol {u}}). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 555, + 849, + 890, + 867 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "1Note that with adversarial attacks, failure to find an adversarial example does not guarantee that it does not exist.", + "bbox": [ + 500, + 875, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "16156", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/171579447d1d3cf83d529ff64613d46ef4021e7051c273505a253c5746a73701.jpg", + "image_caption": [ + "(1) $\\mathcal{B}(\\pmb{x})$ are the points around $\\pmb{x}$ in a ball of radius $\\pmb{\\varepsilon}$ . $\\mathcal{B}_u(\\pmb{x})$ is a subset of $\\mathcal{B}(\\pmb{x})$ where the variables $\\pmb{u}$ (the dog head) are left untouched", + "(2) Without perturbating $\\mathbf{u}$ , we can't reach any adversarial input, thus $\\mathbf{u}$ is important", + "(3) Attribution after computing importance of each variables", + "Figure 2. EVA attribution method. In order to compute the importance for a group of variables $\\mathbf{u}$ – for instance the dog's head – the first step (1) consists in designing the perturbation ball $\\mathcal{B}_u(\\mathbf{x})$ . This ball is centered in $\\mathbf{x}$ and contains all the possible images perturbed by $\\delta$ s.t $||\\delta||_p \\leq \\varepsilon$ , $||\\delta_{\\mathbf{u}}||_p = 0$ which do not perturb the variables $\\mathbf{u}$ . Using verified perturbation analysis, we then compute the adversarial overlap $\\overline{AO}(\\mathbf{x}, \\mathcal{B}_u)$ which corresponds to the overlapping between the class $c$ – here $\\mathrm{dog}$ – and $c'$ , the maximum among the other classes. Finally, the importance score for the variable $\\mathbf{u}$ corresponds to the drop in adversarial overlap when $\\mathbf{u}$ cannot be perturbed, thus the difference between $\\overline{AO}(\\mathbf{x}, \\mathcal{B})$ and $\\overline{AO}(\\mathbf{x}, \\mathcal{B}_u)$ . Specifically, this measures how important the variables $\\mathbf{u}$ are for changing the model's decision." + ], + "image_footnote": [], + "bbox": [ + 81, + 85, + 674, + 333 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {E V A} (\\boldsymbol {x}, \\boldsymbol {u}) = \\overline {{A O}} (\\boldsymbol {x}, \\mathcal {B}) - \\overline {{A O}} (\\boldsymbol {x}, \\mathcal {B} _ {\\boldsymbol {u}})\n$$\n", + "text_format": "latex", + "bbox": [ + 666, + 143, + 875, + 161 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/dfed16fb608d2c6002757407a643119019b79e6ab14c2e37ae1657559304e872.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 686, + 174, + 864, + 311 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As explained in Fig. 2, the estimator requires two passes of the perturbation analysis method; one for $\\overline{AO}(\\mathcal{B})$ , and the other for $\\overline{AO}(\\mathcal{B}_u)$ : the first term consists in measuring the adversarial overlap by modifying all the variables, the second term measures the adversarial surface when fixing the variables of interest $u$ . In other words, EVA measures the adversarial overlap that would be left if the variables $u$ were to be fixed.", + "bbox": [ + 75, + 501, + 468, + 621 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "From a theoretical point of view, we notice that EVA - under reasonable assumptions - yield the optimal subset of variables to minimize the theoretical Robustness- $S_{\\mathrm{r}}$ metric (see Theorem C.6). From a computational point of view, we can note that the first term of the adversarial overlap $\\overline{AO}(\\boldsymbol{x}, \\mathcal{B})$ - as it does not depend on $\\boldsymbol{u}$ - can be calculated once and re-used to evaluate the importance of any other variables considered. Moreover, contrary to an iterative process method [21, 29, 32], each importance can be evaluated independently and thus benefit from the parallelization of modern neural networks. Finally, the experiments in Section 4 show that even with two calls to $\\overline{AO}$ per variables, our method remains much faster than the one based on sampling or on adversarial attacks (such as Greedy-AS or Greedy-AO, see appendix B).", + "bbox": [ + 75, + 625, + 470, + 852 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this work, the verified perturbation-based analysis considered is not always adapted to high dimensional models, especially those running on ImageNet [13]. We are con", + "bbox": [ + 75, + 854, + 468, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "fident that the verification methods will progress towards more scalability in the near future, enabling the original version of EVA on deeper models.", + "bbox": [ + 496, + 500, + 888, + 545 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In the meantime, we introduce an empirical method that allows to scale EVA to high dimensional models. This method sacrifices theoretical guarantees, but the results section reveals that it may be a good compromise.", + "bbox": [ + 496, + 547, + 890, + 608 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Scaling to larger models", + "text_level": 1, + "bbox": [ + 500, + 619, + 720, + 636 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We propose a second version of EVA, which is a combination of sampling and verification perturbation analysis. The aim of this hybrid method is twofold: $(i)$ take advantage of sampling to approach the bounds of an intermediate layer in a potentially very large model, $(ii)$ then complete only the rest of the propagations with verified perturbation analysis and thus move towards the native EVA method which benefits from theoretical guarantees. Note that, combining verification methods with empirical methods (a.k.a adversarial training) has notably been proposed in [5] for robust training.", + "bbox": [ + 496, + 641, + 890, + 806 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Specifically, our technique consists of splitting the model into two parts, and $(i)$ estimating the bounds of an intermediate layer using sampling, $(ii)$ propagating these empirical intermediate bounds onto the second part of the model with verified perturbation analysis methods.", + "bbox": [ + 496, + 808, + 890, + 883 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For the first step $(i)$ we consider the original predictor $\\pmb{f}$", + "bbox": [ + 517, + 885, + 890, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "16157", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/605f2cb5a3388f521f50f67aded1751ef31e3dbe49a037ee14656d590d4fc072.jpg", + "image_caption": [ + "Figure 3. Scaling strategy. In order to scale to very large models, we propose to estimate the bounds of an intermediate layer's activations empirically by (1) Sampling $N$ input perturbations and (2) calculating empirical bounds on the resulting activations for the layer $\\pmb{h}(\\cdot)$ . We can then form the set $\\mathcal{P}_B^x$ which is a subset of the true bounds $\\mathcal{H}_B^x$ since the sampling is never exhaustive. We can then plug this set into a verified perturbation analysis method (3) and continue the forward propagation of the inputs through the rest of the network." + ], + "image_footnote": [], + "bbox": [ + 89, + 89, + 803, + 292 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "as a composition of functions $f(x) = g \\circ h(x)$ . For deep neural networks, $h(\\cdot)$ is a function that maps input to an intermediate feature space and $g(\\cdot)$ is a function that maps this same feature space to the classification.", + "bbox": [ + 75, + 380, + 468, + 438 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We propose to empirically estimate bounds $(\\underline{h}_{\\mathcal{B}}^x,\\overline{h}_{\\mathcal{B}}^x)$ for the intermediate activations $h(\\cdot)\\in \\mathbb{R}^{d'}$ using Monte-Carlo sampling on the perturbation $\\delta \\in \\mathcal{B}$ . Formally:", + "bbox": [ + 75, + 436, + 468, + 484 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\forall j \\in [ 0, \\dots , d ^ {\\prime} ], \\underline {{h}} _ {\\mathcal {B}} ^ {\\boldsymbol {x}} [ j ] = \\min _ {\\delta_ {1}, \\dots \\delta_ {i}, \\dots \\delta_ {n} \\stackrel {\\mathrm {i i d}} {\\sim} U (\\mathcal {B})} \\boldsymbol {h} (\\boldsymbol {x} + \\boldsymbol {\\delta} _ {i}) [ j ]\n$$\n", + "text_format": "latex", + "bbox": [ + 78, + 492, + 460, + 521 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\overline{\\boldsymbol{h}}_{\\mathcal{B}}^{\\boldsymbol{x}}[j] = \\max_{\\substack{\\boldsymbol{\\delta}_{1},\\ldots \\boldsymbol{\\delta}_{i},\\ldots \\boldsymbol{\\delta}_{n}\\stackrel {\\mathrm{iid}}{\\sim}U(\\mathcal{B})}}\\boldsymbol {h}(\\boldsymbol {x} + \\boldsymbol{\\delta}_{i})[j].\n$$\n", + "text_format": "latex", + "bbox": [ + 196, + 523, + 464, + 555 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Obviously, since the sampling is never exhaustive, the bounds obtained underestimate the true maximum $\\overline{h}_{\\mathcal{B}}^x \\leq \\max h(x + \\delta)$ and overestimates the true minimum $h_{\\mathcal{B}}^x \\geq \\min h(x + \\delta)$ as illustrated in the Fig. 3. In a similar way, we define $\\underline{h}_{\\mathcal{B}_u}^x$ and $\\overline{h}_{\\mathcal{B}_u}^x$ when $\\delta \\in \\mathcal{B}_u$ . Once the empirical bounds are estimated, we may proceed to the second step and use the obtained bounds to form the new perturbation set", + "bbox": [ + 75, + 568, + 468, + 686 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {P} _ {\\mathcal {B}} ^ {\\boldsymbol {x}} = [ \\underline {{\\boldsymbol {h}}} _ {\\mathcal {B}} ^ {\\boldsymbol {x}} - \\boldsymbol {h} (\\boldsymbol {x}), \\overline {{\\boldsymbol {h}}} _ {\\mathcal {B}} ^ {\\boldsymbol {x}} - \\boldsymbol {h} (\\boldsymbol {x}) ].\n$$\n", + "text_format": "latex", + "bbox": [ + 161, + 684, + 382, + 703 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Intuitively, this set bounds the intermediate activations obtained empirically and can then be fed to a verified perturbation verification method.", + "bbox": [ + 75, + 710, + 468, + 755 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We then carry out the end of the bounds propagation in the usual way, using verified perturbation analysis. This amounts to computing bounds for the outputs of the network for all possible activations contained in our empirical bounds. The only change is that we no longer operate in the pixel space $\\pmb{x}$ with the ball $\\mathcal{B}$ , but in the activation space $h(\\cdot)$ with the perturbations set $\\mathcal{P}_{\\mathcal{B}}^{\\pmb{x}}$ . The importance score of a set of variables $\\pmb{u}$ is then:", + "bbox": [ + 75, + 757, + 470, + 877 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {E V A} _ {\\text {h y b r i d}} (\\boldsymbol {x}, \\boldsymbol {u}, \\mathcal {B}) \\equiv \\operatorname {E V A} (\\boldsymbol {h} (\\boldsymbol {x}), \\boldsymbol {u}, \\mathcal {P} _ {\\mathcal {B}} ^ {\\boldsymbol {x}}).\n$$\n", + "text_format": "latex", + "bbox": [ + 130, + 883, + 413, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "This hybrid approach allows us to use EVA on state-of-the-art models and thus to benefit from our method while remaining tractable. We believe this extension to be a promising step towards robust explanations on deeper networks.", + "bbox": [ + 498, + 380, + 892, + 441 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 498, + 462, + 633, + 479 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To evaluate the benefits and reliability of our explainability method, we performed several experiments on a standard dataset, using a set of common explainability metrics against EVA. In order to test the fidelity of the explanations produced by our method, we compare them to that of 10 other explainability methods using the (1) Deletion, (2) Insertion, and (3) MuFidelity metrics. As it has been shown that these metrics can exhibit biases, we completed the benchmark by adding the (4) Robustness- $\\mathrm{S_r}$ metric. Each score is averaged over 500 samples.", + "bbox": [ + 496, + 489, + 892, + 641 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We evaluated these 4 metrics on 3 image classification datasets, namely MNIST [41], CIFAR-10 [39] and ImageNet [13]. Through these experiments, the explanations were generated using EVA estimator introduced in Equation 2. The importance scores were not evaluated pixelwise but on each cell of the image after having cut it into a grid of 12 sides (see Fig. 2). For MNIST and Cifar-10, we used $\\varepsilon = 0.5$ , whereas for ImageNet $\\varepsilon = 5$ . Concerning the verified perturbation analysis method, we used (IBP+Forward+Backward) for MNIST, and (IBP+Forward) on Cifar-10 and $p = \\infty$ . For computational purposes, we used the hybrid approach to introduce in Section 3.4 for ImageNet using the penultimate layer (FC-4096) as the intermediate layer $h(\\cdot)$ . We give in Appendix the complete set of hyperparameters used for the other explainability methods, metrics considered as well as the architecture of the models used on MNIST and Cifar-10.", + "bbox": [ + 496, + 643, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "16158", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/9d014b5b0b05905ce450dc7abd2f48fc2a596fa867a3252acde0dbc9f7543ee1.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MNISTCifar-10ImageNet
Del.↓Ins.↑Fid.↑Rob.↓TimeDel.↓Ins.↑Fid.↑Rob.↓TimeDel.↓Ins.↑Fid.↑Rob.↓Time
Saliency [56].193.633.378.0710.04.171.172-.021.0260.16.057.126.035.7690.36
GradInput [3].222.611.107.0740.04.200.143-.018.0950.17.057.050.023.8140.36
SmoothGrad [61].185.621.331.0701.91.174.181.092.0489.07.051.069.019.8099.63
VarGrad [54].207.555.216.0771.76.183.211-.012.1939.07.098.201.021.7879.62
InteGrad [65].209.615.108.0741.77.194.171-.016.1547.19.058.052.023.8138.39
Occlusion [3].247.545.137.0820.04.217.290.105.2321.13.100.266.026.8214.97
GradCAM [53]n/an/an/an/an/a.297.282.056.1950.39.073.232.036.8170.18
GradCAM++ [10]n/an/an/an/an/a.270.326.102.0940.39.074.285.054.8000.19
RISE [48].248.558.133.0932.26.196.273.157.38520.5.074.276.154.8181215
Greedy-AS [29].260.497.110.061335.205.264-.003.0134618.088.047.023.612180056
EVA (ours).089.736.428.0691.29.164.290.352.02512.7.070.289.048.7586454
", + "bbox": [ + 98, + 88, + 890, + 287 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 1. Results on Deletion (Del.), Insertion (Ins.), $\\mu$ Fidelity (Fid.) and Robustness- $S_{\\mathrm{r}}$ (Rob.) metrics. Time in seconds corresponds to the generation of 500 (MNIST/CIFAR-10) and 100 (ImageNet) explanations on an Nvidia P100. Note that EVA is the only method with guarantees that the entire set of possible perturbations has been exhaustively searched. Verified perturbation analysis with IBP + Forward + Backward is used for MNIST, with Forward only for CIFAR-10 and with our hybrid strategy described in Section3.4 for ImageNet. Grad-CAM and Grad-CAM++ are not calculated on the MNIST dataset since the network only has dense layers. The first and second best results are in bold and underlined, respectively.", + "bbox": [ + 75, + 308, + 895, + 395 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.1. Comparison with the state of the art", + "text_level": 1, + "bbox": [ + 76, + 407, + 393, + 424 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "There is a general consensus that fidelity is a crucial criterion for an explanation method. That is, if an explanation is used to make a critical decision, then users are expecting it to reflect the true decision-making process underlying the model and not just a consensus with humans. Failure to do so could have disastrous consequences. Pragmatically, these metrics assume that the more faithful an explanation is, the faster the prediction score should drop when pixels considered important are changed. In Table 1, we present the results of the Deletion [48] (or $1 - AOPC$ [52]) metric for the MNIST and Cifar-10 datasets on 500 images sampled from the test set. TensorFlow [1] and the Keras API [11] were used to run the models and Xplique [18] for the explainability methods. In order to evaluate the methods, the metrics require a baseline and several were proposed [29,64], but we chose to keep the choice of [29] using their random baseline.", + "bbox": [ + 75, + 431, + 470, + 686 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We observe that EVA is the explainability method getting the best Deletion, Insertion, and $\\mu$ Fidelity scores on MNIST, and is just behind Greedy-AS on Robustness- $S_{\\mathrm{r}}$ . This can be explained by the fact that the Robustness metric uses the adversarial attack PGD [44], which is the same one used to generate Greedy-AS, thus biasing the adversarial search. Indeed, if PGD does not find an adversarial perturbation using a subset $u$ does not give a guarantee of the robustness of the model, just that the adversarial perturbation could be difficult to reach with PGD.", + "bbox": [ + 75, + 688, + 468, + 838 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For Cifar-10, EVA remains overall the most faithful method according to Deletion and $\\mu$ Fidelity, and obtains the second score in Insertion behind Grad-Cam++ [10]. Finally, we notice that if Greedy-AS [29] allows us to ob", + "bbox": [ + 75, + 839, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "tain a good Robustness- $S_r$ score, but this comes with a considerable computation time, which is not the case of EVA which is much more efficient. Eventually, EVA is a very good compromise for its relevance to commonly accepted explainability metrics and more recent robustness metrics.", + "bbox": [ + 496, + 407, + 893, + 484 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ImageNet After having demonstrated the potential of the method on vision datasets of limited size, we consider the case of ImageNet which has a significantly higher level of dimension. The use of verified perturbation analysis methods other than IBP is not easily scalable on these datasets. We, therefore, used the hybrid method introduced in Section 3.4 in order to estimate the bounds in a latent space and then plug those bounds into the perturbation analysis to get the final adversarial overlap score.", + "bbox": [ + 496, + 489, + 893, + 627 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 1 shows the results obtained with the empirical method proposed in Section 3.4. We observe that even with this relaxed estimation, EVA is able to score high on all the metrics. Indeed, EVA obtains the best score on the Insertion metric and ranks second on $\\mu$ Fidelity and Robustness- $S_{\\mathrm{r}}$ . Greedy-AS ranks first on Robustness- $S_{\\mathrm{r}}$ at the expense of the other scores where it performs poorly. Finally, both RISE and SmoothGrad perform well on all the fidelity metrics but collapse on the robustness metric. Extending results with ablations of EVA, including Greedy-AO, are available in Table 3.", + "bbox": [ + 496, + 627, + 895, + 792 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Qualitatively, Fig. 5 shows examples of explanations produced on the ImageNet VGG-16 model. The explanations produced by EVA are more localized than Grad-CAM or RISE, while being less noisy than the gradient-based or Greedy-AS methods.", + "bbox": [ + 496, + 792, + 893, + 869 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In addition, as the literature on verified perturbation analysis is evolving rapidly we can conjecture that the advances", + "bbox": [ + 496, + 869, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "16159", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "will benefit the proposed explainability method. Indeed, EVA proved to be the most effective on the benchmark when an accurate formal method was used. After demonstrating the performance of the proposed method, we study its ability to generate class explanations specific.", + "bbox": [ + 75, + 90, + 468, + 167 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.2. Tighter bounds lead to improved explanations", + "text_level": 1, + "bbox": [ + 76, + 175, + 465, + 191 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/9d579bd25bd184336a8ba2cd7456bc4c391026519c414482d2d75894fda89b2e.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Tightness↓Del.↓Ins.↑Fid.↑Rob.↓
IBP4.58.148.588.222.077
Forward2.66.150.580.209.078
Backward2.36.115.607.274.074
IBP + Fo. + Ba.1.55.089.736.428.069
", + "bbox": [ + 98, + 207, + 452, + 291 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 2. Impact of the verified perturbation analysis method on EVA. Results of EVAon Tightness, Deletion (Del.), Insertion (Ins.), Fidelity (Fid.) and Robustness- $S_{\\mathrm{r}}$ (Rob.) metrics obtained on MNIST. The Tightness score corresponds to the average adversarial surface. A lower Tightness score indicates that the method is more precise: it reaches tighter bound, resulting in better explanations and superior scores on the other metrics. The first and second best results are respectively in bold and underlined.", + "bbox": [ + 75, + 301, + 467, + 412 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The choice of the verified perturbation analysis method is a hyperparameter of EVA. Hence, it is interesting to see the effect of the choice of this hyperparameter on the previous benchmark. We recall that only the MNIST dataset could benefit from the (IBP+Forward+Backward) combo. Table 2 reports the results of the fidelity metrics using other verified perturbation analysis methods. We also report a tightness score which corresponds to the average of the adversarial overlap: $\\mathbb{E}_{\\boldsymbol{x} \\sim \\mathcal{X}}(\\overline{AO}(\\boldsymbol{x}, \\mathcal{B}))$ . Specifically, a low score indicates that the verification method is precise, meaning that the over-approximation is closer to the actual value. It should be noted that the true value is intractable, but remains the same across all three tested cases. We observe that the tighter the bounds, the higher the scores. This allows us to conjecture that the more scalable the formal methods will become, the better the quality of the generated explanations will be. We perform additional experiments to ensure that the certified component of EVA score is significant by comparing EVA to a sampling-based version of EVA. The details of these experiments are available in Appendix B.", + "bbox": [ + 75, + 414, + 467, + 732 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Targeted Explanations", + "text_level": 1, + "bbox": [ + 76, + 741, + 287, + 758 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In some cases, it is instructive to look at the explanations for unpredicted classes in order to get information about the internal mechanisms of the models studied. Such explanations allow us to highlight contrastive features: elements that should be changed or whose absence is critical. Our method allows us to obtain such explanations: for a given input, we are then exclusively interested in the class we are trying to explain, without looking at the other decisions. Formally, for a given tar", + "bbox": [ + 75, + 763, + 467, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1808d15479652d969fafca461f6ba04d6439efdc8e09c20613781320dc70413a.jpg", + "image_caption": [ + "9" + ], + "image_footnote": [], + "bbox": [ + 501, + 88, + 581, + 148 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4efdad90b7e6955cb77c898687b0fc1da94c4701e0cbed95d92ef861b04d958a.jpg", + "image_caption": [ + "3" + ], + "image_footnote": [], + "bbox": [ + 596, + 89, + 676, + 148 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ceef5c2e90890e093aaa45dc27668a52f6e03110c4267edd747100917c8e138b.jpg", + "image_caption": [ + "8", + "Figure 4. Targeted explanations. Generated explanations for a decision other than the one predicted by the model. The class explained is indicated at the bottom of each sample, e.g., the first sample is a '4' and the explanation is for the class '9'. As indicated in section 4.3, the red areas indicate that a black line should be added and the blue areas that it should be removed. More examples are available in the Appendix." + ], + "image_footnote": [], + "bbox": [ + 694, + 88, + 772, + 148 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3bb55b5e2a3f873fdc33740a355c098fa0d6330baaa1d1d77ad63913b93866fa.jpg", + "image_caption": [ + "8" + ], + "image_footnote": [], + "bbox": [ + 790, + 88, + 867, + 148 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "geted class $c'$ the adversarial overlap (Equation 1) become $AO(\\pmb{x},\\mathcal{B}) = \\max_{\\delta \\in \\mathcal{B}}\\pmb{f}_{c'}(\\pmb{x} + \\delta) - \\pmb{f}_c(\\pmb{x} + \\delta)$ . Moreover, by splitting the perturbation ball into a positive one $\\mathcal{B}^{(+)} = \\{\\pmb{\\delta}\\in \\mathcal{B}:\\pmb{\\delta}_i\\geq 0,\\forall i\\in \\{1,\\dots,d\\}\\}$ and a negative one $\\mathcal{B}^{(-)} = \\{\\pmb {\\delta}\\in \\mathcal{B}:\\pmb {\\delta}_i\\leq 0,\\forall i\\in \\{1,\\dots,d\\}\\}$ , one can deduce which direction - adding or removing the black line in the case of gray-scaled images - will impact the most the model decision.", + "bbox": [ + 496, + 279, + 890, + 400 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We generate targeted explanations on the MNIST dataset using (IBP+Forward+Backward). For several inputs, we generate the explanation for the 10 classes. Fig. 7 shows 4 examples of targeted explanations, the target class $c'$ is indicated at the bottom. The red areas indicate that adding a black line increases the adversarial overlap with the target class. Conversely, the blue areas indicate where the increase of the score requires removing black lines. All other results can be found in the Appendix. In addition to favorable results on the fidelity metrics and guarantees provided by the verification methods, EVA can provide targeted explanations that are easily understandable by humans, which are two qualities that make them a candidate of choice to meet the recent General Data Protection Regulation (GDPR) adopted in Europe [35]. More examples are available in the Appendix H.", + "bbox": [ + 496, + 402, + 890, + 643 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 650, + 617, + 666 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we presented the first explainability method that uses verification perturbation analysis that exhaustively explores the perturbation space to generate explanations. We presented an efficient estimator that yields explanations that are state-of-the-art on current metrics. We also described a simple strategy to scale up perturbation verification methods to complex models. Finally, we showed that this estimator can be used to form easily interpretable targeted explanations.", + "bbox": [ + 496, + 675, + 890, + 810 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We hope that this work will for searching for safer and more efficient explanation methods for neural networks – and that it will inspire further synergies with the field of formal verification.", + "bbox": [ + 496, + 811, + 890, + 869 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "16160", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 106 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Martin Abadi, Ashish Agarwal, Paul Barham, Eugene Brevdo, Zhifeng Chen, Craig Citro, Greg S. 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Advances in Neural Information Processing Systems (NeurIPS), 2018. 3" + ], + "bbox": [ + 501, + 92, + 890, + 710 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "16163", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Don't Lie to Me! Robust and Efficient Explainability With Verified Perturbation Analysis/b65bbb01-b52c-43c2-b278-f068bfd77b29_model.json b/2023/Don't Lie to Me! Robust and Efficient Explainability With Verified Perturbation Analysis/b65bbb01-b52c-43c2-b278-f068bfd77b29_model.json new file mode 100644 index 0000000000000000000000000000000000000000..c60a5147e5a07b035e30c805ecf81f1102401cbd --- /dev/null +++ b/2023/Don't Lie to Me! Robust and Efficient Explainability With Verified Perturbation Analysis/b65bbb01-b52c-43c2-b278-f068bfd77b29_model.json @@ -0,0 +1,2378 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.126, + 0.131, + 0.845, + 0.177 + ], + "angle": 0, + "content": "Don’t Lie to Me! Robust and Efficient Explainability with Verified Perturbation Analysis" + }, + { + "type": "text", + "bbox": [ + 0.163, + 0.202, + 0.798, + 0.24 + ], + "angle": 0, + "content": "Thomas Fel\\(^{1,2,5\\dagger}\\) Melanie Ducoffe\\(^{2,7\\dagger}\\) David Vigouroux\\(^{2,4\\dagger}\\) Rémi Cadène\\(^{1,3}\\) Mikael Capelle\\(^{6}\\) Claire Nicodème\\(^{5}\\) Thomas Serre\\(^{1,2}\\)" + }, + { + "type": "text", + "bbox": [ + 0.246, + 0.256, + 0.725, + 0.292 + ], + "angle": 0, + "content": "\\(^{1}\\)Carney Institute for Brain Science, Brown University, USA \\(^{2}\\)Artificial and Natural Intelligence Toulouse Institute" + }, + { + "type": "text", + "bbox": [ + 0.2, + 0.292, + 0.77, + 0.345 + ], + "angle": 0, + "content": "\\(^{3}\\)Sorbonne Université, CNRS, France \\(^{4}\\)IRT Saint-Exupery, France \\(^{5}\\)Innovation & Research Division, SNCF \\(^{6}\\)Thales Alenia Space, France \\(^{7}\\)Airbus AI Research" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.38, + 0.314, + 0.396 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.413, + 0.474, + 0.778 + ], + "angle": 0, + "content": "A plethora of attribution methods have recently been developed to explain deep neural networks. These methods use different classes of perturbations (e.g., occlusion, blurring, masking, etc) to estimate the importance of individual image pixels to drive a model's decision. Nevertheless, the space of possible perturbations is vast and current attribution methods typically require significant computation time to accurately sample the space in order to achieve high-quality explanations. In this work, we introduce EVA (Explaining using Verified Perturbation Analysis) – the first explainability method which comes with guarantees that an entire set of possible perturbations has been exhaustively searched. We leverage recent progress in verified perturbation analysis methods to directly propagate bounds through a neural network to exhaustively probe a – potentially infinite-size – set of perturbations in a single forward pass. Our approach takes advantage of the beneficial properties of verified perturbation analysis, i.e., time efficiency and guaranteed complete – sampling agnostic – coverage of the perturbation space – to identify image pixels that drive a model's decision. We evaluate EVA systematically and demonstrate state-of-the-art results on multiple benchmarks. Our code is freely available: github.com/deel-ai/formal-explainability" + }, + { + "type": "title", + "bbox": [ + 0.079, + 0.799, + 0.21, + 0.815 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Deep neural networks are now being widely deployed in many applications from medicine, transportation, and security to finance, with broad societal implications [40]. They are routinely used to making safety-critical decisions – often without an explanation as their decisions are notoriously" + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.381, + 0.911, + 0.553 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.561, + 0.895, + 0.73 + ], + "angle": 0, + "content": "Figure 1. Manifold exploration of current attribution methods. Current methods assign an importance score to individual pixels using perturbations around a given input image \\( \\pmb{x} \\). Saliency [56] uses infinitesimal perturbations around \\( \\pmb{x} \\), Occlusion [71] switches individual pixel intensities on/off. More recent approaches [17,43,46,48,49] use (Quasi-) random sampling methods in specific perturbation spaces (occlusion of segments of pixels, blurring, ...). However, the choice of the perturbation space undoubtedly biases the results – potentially even introducing serious artifacts [26, 29, 38, 64]. We propose to use verified perturbation analysis to efficiently perform a complete coverage of a perturbation space around \\( \\pmb{x} \\) to produce reliable and faithful explanations." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.762, + 0.614, + 0.777 + ], + "angle": 0, + "content": "hard to interpret." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Many explainability methods have been proposed to gain insight into how network models arrive at a particular decision [17,24,43,46,48,49,53,55,61,65,71]. The applications of these methods are multiple - from helping to improve or debug their decisions to helping instill confidence in the reliability of their decisions [14]. Unfortunately, a severe limitation of these approaches is that they are subject to a confirmation bias: while they appear to offer useful expla" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16153" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.182 + ], + "angle": 0, + "content": "nations to a human experimenter, they may produce incorrect explanations [2, 23, 59]. In other words, just because the explanations make sense to humans does not mean that they actually convey what is actually happening within the model. Therefore, the community is actively seeking for better benchmarks involving humans [12, 29, 37, 45]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.185, + 0.474, + 0.457 + ], + "angle": 0, + "content": "In the meantime, it has been shown that some of our current and commonly used benchmarks are biased and that explainability methods reflect these biases - ultimately providing the wrong explanation for the behavior of the model [25, 29, 64]. For example, some of the current fidelity metrics [7, 18, 27, 34, 48] mask one or a few of the input variables (with a fixed value such as a gray mask) in order to assess how much they contribute to the output of the system. Trivially, if these variables are already set to the mask value in a given image (e.g., gray), masking these variables will not yield any effect on the model's output and the importance of these variables is poised to be underestimated. Finally, these methods rely on sampling a space of perturbations that is far too vast to be fully explored - e.g., LIME on a image divided in 64 segments image would need more than \\(10^{19}\\) samples to test all possible perturbations. As a result, current attribution methods may be subject to bias and are potentially not entirely reliable." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.46, + 0.471, + 0.717 + ], + "angle": 0, + "content": "To address the baseline issue, a growing body of work is starting to leverage adversarial methods [8, 29, 31, 42, 50] to derive explanations that reflect the robustness of the model to local adversarial perturbations. Specifically, a pixel or an image region is considered important if it allows the easy generation of an adversarial example. That is if a small perturbation of that pixel or image region yields a large change in the model's output. This idea has led to the design of several novel robustness metrics to evaluate the quality of explanations, such as Robustness-\\( S_r \\) [29]. For a better ranking on those robustness metrics, several methods have been proposed that make intensive use of adversarial attacks [29, 70], such as Greedy-AS for Robustness-\\( S_r \\). However, these methods are computationally very costly – in some cases, requiring over 50 000 adversarial attacks per explanation – severely limiting the widespread adoption of these methods in real-world scenarios." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.472, + 0.902 + ], + "angle": 0, + "content": "In this work, we propose to address this limitation by introducing EVA (Explaining using Verified perturbation Analysis), a new explainability method based on robustness analysis. Verified perturbation analysis is a rapidly growing toolkit of methods to derive bounds on the outputs of neural networks in the presence of input perturbations. In contrast to current attributions methods based on gradient estimation or sampling, verified perturbation analysis allows the full exploration of the perturbation space, see Fig. 1. We use a tractable certified upper bound of robustness confidence to derive a new estimator to help quantify the importance of input variables (i.e., those that matter the most). That is, the" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.868, + 0.106 + ], + "angle": 0, + "content": "variables most likely to change the predictor's decision." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.108, + 0.875, + 0.121 + ], + "angle": 0, + "content": "We can summarize our main contributions as follows:" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.126, + 0.892, + 0.171 + ], + "angle": 0, + "content": "- We introduce EVA, the first explainability method guaranteed to explore its entire set of perturbations using Verified Perturbation Analysis." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.175, + 0.892, + 0.22 + ], + "angle": 0, + "content": "- We propose a method to scale EVA to large vision models and show that the exhaustive exploration of all possible perturbations can be done efficiently." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.225, + 0.892, + 0.27 + ], + "angle": 0, + "content": "- We systematically evaluate our approach using several image datasets and show that it yields convincing results on a large range of explainability metrics" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.274, + 0.892, + 0.348 + ], + "angle": 0, + "content": "- Finally, we demonstrate that we can use the proposed method to generate class-specific explanations, and we study the effects of several verified perturbation analysis methods as a hyperparameter of the generated explanations." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.126, + 0.892, + 0.348 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.364, + 0.642, + 0.38 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.389, + 0.892, + 0.752 + ], + "angle": 0, + "content": "Attribution Methods. Our approach builds on prior attribution methods in order to explain the prediction of a deep neural network via the identification of input variables that support the prediction (typically pixels or image regions for images – which lead to importance maps shown in Fig. 1). \"Saliency\" was first introduced in [4] and consists in using the gradient of a classification score. It was later refined in [57, 61, 63, 65, 72] in the context of deep convolutional networks for classification. However, the image gradient only reflects the model's operation within an infinitesimal neighborhood around an input. Hence, it can yield misleading importance estimates [22] since gradients of the current large vision models are noisy [61]. Other methods rely on different image perturbations applied to images to produce importance maps that reflect the corresponding change in classification score resulting from the perturbation. Methods such as \"Occlusion\" [72], \"LIME\" [49], \"RISE\" [48], \"Sobol\" [17] or \"HSIC\" [46] leverage different sampling strategies to explore the space of perturbations around the image. For instance, Occlusion uses binary masks to occlude individual image regions, one at a time. RISE and HSIC combines these discrete masks to perturb multiple regions simultaneously. Sobol uses continuous masks for a finer exploration of the perturbation space." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.752, + 0.892, + 0.858 + ], + "angle": 0, + "content": "Nevertheless, none of these methods are able to systematically cover the full space of perturbations. As a result, the corresponding explanations may not reliably reflect the true importance of pixels. In contrast, our approach comes with strong guarantees that can be derived from the verified perturbation analysis framework as it provides bounds on the perturbation space." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Robustness-based Explanation. To try to address the aforementioned limitations, several groups [8,19,29,32,33," + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "16154" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.455 + ], + "angle": 0, + "content": "42, 60] have focused on the development of a new set of robustness-based evaluation metrics for trustworthy explanations. These new metrics are in contrast with the previous ones, which consisted in removing the pixels considered important in an explanation by substituting them with a fixed baseline – which inevitably introduces bias and artifacts [25, 26, 29, 38, 64]. Key to these new metrics is the assumption that when the important pixels are in their nominal (fixed) state, then perturbations applied to the complementary pixels – deemed unimportant – should not affect the model's decision to any great extent. The corollary that follows is that perturbations limited to the pixels considered important should easily influence the model's decision [29, 42]. Going further along the path of robustness, abductive reasoning was used in [32] to compute optimal subsets with guarantees. The challenge consists in looking for the subset with the smallest possible cardinality – to guarantee the decision of the model. This work constituted one of the early successes of formal methods for explainability, but the approach was limited to low-dimensional problems and shallow neural networks. It was later extended to relax the subset minimum explanation by either providing multiple explanations, aggregating pixels in bundles [6] or by using local surrogates [9]." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.456, + 0.473, + 0.592 + ], + "angle": 0, + "content": "Some heuristics-oriented works also propose to optimize these new robustness based criteria and design new methods using a generative model [47] or adversarial attacks [29]. The latter approach requires searching for the existence or lack of an adversarial example for a multitude of \\(\\ell_p\\) balls around the input of interest. As a result, the induced computational cost is quite high as the authors used more than 50000 computations of adversarial examples to generate a single explanation." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.594, + 0.473, + 0.746 + ], + "angle": 0, + "content": "More importantly, a failure to find an adversarial perturbation for a given radius does not guarantee that none exists. In fact, it is not uncommon for adversarial attacks to fail to converge – or fail to find an adversarial example – which will result in a failure to output an importance score. Our method addresses these issues while drastically reducing the computation cost. An added benefit of our approach is that verified perturbation analysis provides additional guarantees and hence opens the doors of certification which is a necessity for safety-critical applications." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.762, + 0.472, + 0.873 + ], + "angle": 0, + "content": "Verified Perturbation Analysis. This growing field of research focuses on the development of methods that outerapproximate neural network outputs given some input perturbations. Simply put, for a given input \\(\\pmb{x}\\) and a bounded perturbation \\(\\delta\\), verification methods yield minimum \\(\\underline{f}(\\pmb{x})\\) and maximum \\(\\overline{f}(\\pmb{x})\\) bounds on the output of a model. Formally \\(\\forall \\delta s.t \\|\\delta\\|_p \\leq \\varepsilon\\):" + }, + { + "type": "equation", + "bbox": [ + 0.18, + 0.884, + 0.368, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\underline {{\\boldsymbol {f}}} (\\boldsymbol {x}) \\leq \\boldsymbol {f} (\\boldsymbol {x} + \\boldsymbol {\\delta}) \\leq \\overline {{\\boldsymbol {f}}} (\\boldsymbol {x}).\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "This allows us to explore the whole perturbation space without having to explicitly sample points in that space." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.124, + 0.895, + 0.61 + ], + "angle": 0, + "content": "Early works focused on computing reachable lower and upper bounds based on satisfiability modulo theories [16, 36], and mixed-integer linear programming problems [66]. While these early results were encouraging, the proposed methods struggled even for small networks and image datasets. More recent work has led to the independent development of methods for computing looser certified lower and upper bounds more efficiently thanks to convex linear relaxations either in the primal or dual space [51]. While looser, those bounds remain tight enough to yield non-ubiquitous robustness properties on medium size neural networks. CROWN (hereafter called Backward) uses Linear Relaxation-based Perturbation Analysis (LiRPA) and achieves the tightest bound for efficient single neuron linear relaxation [58, 67, 73]. In addition, linear relaxation methods offer a wide range of possibilities with a vast trade-off between \"tightness\" of the bounds and efficiency. These methods form two broad classes: 'forward' methods which propagate constant bounds (more generally affine relaxations from the input to the output of the network) also called Interval Bound Propagation (IBP, Forward, IBP+Forward) vs. 'backward' methods which bound the output of the network by affine relaxations given the internal layers of the network, starting from the output to the input. Note that these methods can be combined, e.g. \\((\\mathrm{CROWN} + \\mathrm{IBP} + \\mathrm{Forward})\\). For a thorough description of the LiRPA framework and theoretical analysis of the worst-case complexities of each variant, see [68]. In this work, we remain purposefully agnostic to the verification method used and opt for the most accurate LiRPA method applicable to the predictor. Our approach is based on the formal verification framework DecoMon, based on Keras [15]." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.627, + 0.892, + 0.663 + ], + "angle": 0, + "content": "3. Explainability with Verified Perturbation Analysis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.666, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Notation. We consider a standard supervised machine-learning classification setting with input space \\(\\mathcal{X} \\subseteq \\mathbb{R}^d\\), an output space \\(\\mathcal{Y} \\subseteq \\mathbb{R}^c\\), and a predictor function \\(f: \\mathcal{X} \\to \\mathcal{Y}\\) that maps an input vector \\(\\boldsymbol{x} = (x_1, \\ldots, x_d)\\) to an output \\(\\boldsymbol{f}(\\boldsymbol{x}) = (\\boldsymbol{f}_1(\\boldsymbol{x}), \\ldots, \\boldsymbol{f}_c(\\boldsymbol{x}))\\). We denote \\(\\mathcal{B} = \\{\\delta \\in \\mathbb{R}^d : ||\\delta||_p \\leq \\varepsilon\\}\\) the perturbation ball with radius \\(\\varepsilon > 0\\) with \\(p \\in \\{1, 2, \\infty\\}\\). For any subset of indices \\(\\boldsymbol{u} \\subseteq \\{1, \\ldots, d\\}\\), we denote \\(\\mathcal{B}_u\\) the ball without perturbation on the variables in \\(\\boldsymbol{u}\\): \\(\\mathcal{B}_u = \\{\\delta : \\delta \\in \\mathcal{B}, \\delta_u = 0\\}\\) and \\(\\mathcal{B}(\\boldsymbol{x})\\) the perturbation ball centered on \\(\\boldsymbol{x}\\). We denote the lower (resp. upper) bounds obtained with verification perturbation analysis as \\(\\underline{\\boldsymbol{f}}(\\boldsymbol{x}, \\mathcal{B}) = (\\underline{\\boldsymbol{f}}_1(\\boldsymbol{x}, \\mathcal{B}), \\ldots, \\underline{\\boldsymbol{f}}_c(\\boldsymbol{x}, \\mathcal{B}))\\), and \\(\\overline{\\boldsymbol{f}}(\\boldsymbol{x}, \\mathcal{B}) = (\\overline{\\boldsymbol{f}}_1(\\boldsymbol{x}, \\mathcal{B}), \\ldots, \\overline{\\boldsymbol{f}}_c(\\boldsymbol{x}, \\mathcal{B}))\\). Intuitively, these bounds delimit the output prediction for any perturbed sample in \\(\\mathcal{B}(\\boldsymbol{x})\\)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "16155" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.077, + 0.091, + 0.47, + 0.108 + ], + "angle": 0, + "content": "3.1. The importance of setting the importance right" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.114, + 0.471, + 0.312 + ], + "angle": 0, + "content": "Different attribution methods implicitly assume different definitions of the notion of importance for input variables based either on game theory [43], the notion of conditional expectation of the score logits [48], their variance [17] or on some measure of statistical dependency between different areas of an input image and the output of the model [46]. In this work, we build on robustness-based explainability methods [29] which assume that a variable is important if small perturbations of this variable lead to large changes in the model decision. Conversely, a variable is said to be unimportant if changes to this variable only yield small changes in the model decision. From this intuitive assertion, we construct an estimator that we call Adversarial overlap." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.318, + 0.267, + 0.334 + ], + "angle": 0, + "content": "3.2. Adversarial overlap" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.338, + 0.47, + 0.474 + ], + "angle": 0, + "content": "We go one step beyond previous work and propose to compute importance by taking into account not only the ability of individual variables to change the network's decision but also its confidence in the prediction. Adversarial overlap measures the extent to which a modification on a group of pixels can generate overlap between classes, i.e. generate a point close to \\( x \\) such that the attainable maximum of an unfavorable class \\( c' \\) can match the minimum of the initially predicted class \\( c \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.474, + 0.472, + 0.564 + ], + "angle": 0, + "content": "Indeed, if a modification of a pixel – or group of pixels – allows generating a new image that changes the decision of \\( f \\), this variable must be considered important. Conversely, if the decision does not change regardless of the value of the pixel, then the pixel can be left at its nominal value and should be considered unimportant." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.565, + 0.47, + 0.623 + ], + "angle": 0, + "content": "Among the set of possible variable perturbations \\(\\delta\\) around a point \\(x\\), we, therefore, look for points that can modify the decision with the most confidence. Hence our scoring criterion can be formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.124, + 0.624, + 0.469, + 0.657 + ], + "angle": 0, + "content": "\\[\nA O _ {c} (\\boldsymbol {x}, \\mathcal {B}) = \\max _ {\\substack {\\boldsymbol {\\delta} \\in \\mathcal {B} \\\\ c ^ {\\prime} \\neq c}} \\boldsymbol {f} _ {c ^ {\\prime}} (\\boldsymbol {x} + \\boldsymbol {\\delta}) - \\boldsymbol {f} _ {c} (\\boldsymbol {x} + \\boldsymbol {\\delta}). \\tag{1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.66, + 0.469, + 0.72 + ], + "angle": 0, + "content": "Intuitively, this score represents the confidence of the \"best\" adversarial perturbation that can be found in the perturbation ball \\(\\mathcal{B}\\) around \\(\\pmb{x}\\). Throughout the article, when \\(c\\) is not specified, it is assumed that \\(c = \\arg \\max f(\\pmb{x})\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.469, + 0.856 + ], + "angle": 0, + "content": "In order to estimate this criterion, a naive strategy could be to use adversarial attacks to search within \\(\\mathcal{B}\\). However, when they converge - which is not ensured, such methods only explore certain points of the considered space, thus giving no guarantee regarding the optimality of the solution. Moreover, adversarial methods have no guarantee of success and therefore cannot ensure a valid score under every circumstance. Finally, the large dimensions of the current datasets make exhaustive searches impossible." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.901 + ], + "angle": 0, + "content": "To overcome these issues, we take advantage of one of the main results from verified perturbation analysis to derive a guaranteed upper bound on the criterion introduced" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.89, + 0.121 + ], + "angle": 0, + "content": "in Eq. 1. We can upper bound the adversarial overlap criterion as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.516, + 0.13, + 0.872, + 0.155 + ], + "angle": 0, + "content": "\\[\nA O (\\boldsymbol {x}, \\mathcal {B}) \\leq \\overline {{A O}} (\\boldsymbol {x}, \\mathcal {B}) = \\max _ {c ^ {\\prime} \\neq c} \\overline {{\\boldsymbol {f}}} _ {c ^ {\\prime}} (\\boldsymbol {x}, \\mathcal {B}) - \\underline {{\\boldsymbol {f}}} _ {c} (\\boldsymbol {x}, \\mathcal {B}).\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.164, + 0.89, + 0.194 + ], + "angle": 0, + "content": "The computation of this upper bound becomes tractable using any verified perturbation analysis method." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.194, + 0.892, + 0.39 + ], + "angle": 0, + "content": "For example, \\(\\overline{AO}(\\boldsymbol{x},\\mathcal{B}) \\leq 0\\) guarantees that no adversarial perturbation is possible in the perturbation space. Our upper bound \\(\\overline{AO}(\\boldsymbol{x},\\mathcal{B})\\) corresponds to the difference between the verified lower bound of the class of interest \\(c\\) and the maximum over the verified upper bounds among the other classes. Thus, when important variables are modified (e.g. the head of the dog in Fig. 2, using \\(\\mathcal{B}\\)), the lower bound for the class of interest will get smaller than the upper bound of the adversary class. On the other hand, this overlap is not possible when important variables are fixed (e.g. in Fig. 2 when the head of the dog is fixed, using \\(\\mathcal{B}_u\\)). We now demonstrate how to leverage this score to derive an efficient estimator of variable importance." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.399, + 0.573, + 0.413 + ], + "angle": 0, + "content": "3.3.EVA" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.422, + 0.892, + 0.617 + ], + "angle": 0, + "content": "We are willing to assign a higher importance score for a variable allowing (1) a change in a decision, (2) a greater adversarial – thus a solid change of decision. Modifying all variables gives us an idea of the robustness of the model. In the same way, the modification of all variables without the subset \\( \\mathbf{u} \\) allows quantifying the change of the strongest adversarial perturbation and thus quantifies the importance of the variables \\( \\mathbf{u} \\). Intuitively, if an important variable \\( \\mathbf{u} \\) is discarded, then it will be more difficult, if not impossible, to succeed in finding any adversarial perturbation. Specifically, removing the possibility to modify \\( x_{\\mathbf{u}} \\) allows us to reveal its importance by taking into account its possible interactions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.619, + 0.892, + 0.844 + ], + "angle": 0, + "content": "The complexity of current models means that the variables are not only treated individually in neural network models but collectively. In order to capture these higher-order interactions, our method consists in measuring the adversarial overlap allowed by all the variables together \\(\\overline{AO}(\\boldsymbol{x},\\mathcal{B})\\) - thus taking into account their interactions - and then forbidding to play on a group of variables \\(\\overline{AO}(\\boldsymbol{x},\\mathcal{B}_{\\boldsymbol{u}})\\) to estimate the importance of \\(\\boldsymbol{u}\\). Making the interactions of \\(\\boldsymbol{u}\\) disappear reveals their importance. Note that several works have mentioned the importance of taking into account the interactions of the variables when calculating the importance [17, 20, 30, 48]. Formally, we introduce EVA (Explainability using Verified perturbation Analysis) that measure the drop in adversarial overlap when we fixed the variables \\(\\boldsymbol{u}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.557, + 0.85, + 0.892, + 0.868 + ], + "angle": 0, + "content": "\\[\n\\operatorname {E V A} (\\boldsymbol {x}, \\boldsymbol {u}, \\mathcal {B}) \\equiv \\overline {{A O}} (\\boldsymbol {x}, \\mathcal {B}) - \\overline {{A O}} (\\boldsymbol {x}, \\mathcal {B} _ {\\boldsymbol {u}}). \\tag {2}\n\\]" + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.875, + 0.892, + 0.901 + ], + "angle": 0, + "content": "1Note that with adversarial attacks, failure to find an adversarial example does not guarantee that it does not exist." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "16156" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.083, + 0.087, + 0.675, + 0.334 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.086, + 0.334, + 0.416, + 0.371 + ], + "angle": 0, + "content": "(1) \\(\\mathcal{B}(\\pmb{x})\\) are the points around \\(\\pmb{x}\\) in a ball of radius \\(\\pmb{\\varepsilon}\\). \\(\\mathcal{B}_u(\\pmb{x})\\) is a subset of \\(\\mathcal{B}(\\pmb{x})\\) where the variables \\(\\pmb{u}\\) (the dog head) are left untouched" + }, + { + "type": "image_caption", + "bbox": [ + 0.424, + 0.334, + 0.648, + 0.36 + ], + "angle": 0, + "content": "(2) Without perturbating \\(\\mathbf{u}\\), we can't reach any adversarial input, thus \\(\\mathbf{u}\\) is important" + }, + { + "type": "equation", + "bbox": [ + 0.668, + 0.144, + 0.877, + 0.162 + ], + "angle": 0, + "content": "\\[\n\\operatorname {E V A} (\\boldsymbol {x}, \\boldsymbol {u}) = \\overline {{A O}} (\\boldsymbol {x}, \\mathcal {B}) - \\overline {{A O}} (\\boldsymbol {x}, \\mathcal {B} _ {\\boldsymbol {u}})\n\\]" + }, + { + "type": "image", + "bbox": [ + 0.687, + 0.175, + 0.866, + 0.313 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.682, + 0.333, + 0.846, + 0.357 + ], + "angle": 0, + "content": "(3) Attribution after computing importance of each variables" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.388, + 0.892, + 0.485 + ], + "angle": 0, + "content": "Figure 2. EVA attribution method. In order to compute the importance for a group of variables \\( \\mathbf{u} \\) – for instance the dog's head – the first step (1) consists in designing the perturbation ball \\( \\mathcal{B}_u(\\mathbf{x}) \\). This ball is centered in \\( \\mathbf{x} \\) and contains all the possible images perturbed by \\( \\delta \\) s.t \\( ||\\delta||_p \\leq \\varepsilon \\), \\( ||\\delta_{\\mathbf{u}}||_p = 0 \\) which do not perturb the variables \\( \\mathbf{u} \\). Using verified perturbation analysis, we then compute the adversarial overlap \\( \\overline{AO}(\\mathbf{x}, \\mathcal{B}_u) \\) which corresponds to the overlapping between the class \\( c \\) – here \\( \\mathrm{dog} \\) – and \\( c' \\), the maximum among the other classes. Finally, the importance score for the variable \\( \\mathbf{u} \\) corresponds to the drop in adversarial overlap when \\( \\mathbf{u} \\) cannot be perturbed, thus the difference between \\( \\overline{AO}(\\mathbf{x}, \\mathcal{B}) \\) and \\( \\overline{AO}(\\mathbf{x}, \\mathcal{B}_u) \\). Specifically, this measures how important the variables \\( \\mathbf{u} \\) are for changing the model's decision." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.502, + 0.47, + 0.622 + ], + "angle": 0, + "content": "As explained in Fig. 2, the estimator requires two passes of the perturbation analysis method; one for \\(\\overline{AO}(\\mathcal{B})\\), and the other for \\(\\overline{AO}(\\mathcal{B}_u)\\): the first term consists in measuring the adversarial overlap by modifying all the variables, the second term measures the adversarial surface when fixing the variables of interest \\(u\\). In other words, EVA measures the adversarial overlap that would be left if the variables \\(u\\) were to be fixed." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.626, + 0.471, + 0.853 + ], + "angle": 0, + "content": "From a theoretical point of view, we notice that EVA - under reasonable assumptions - yield the optimal subset of variables to minimize the theoretical Robustness-\\(S_{\\mathrm{r}}\\) metric (see Theorem C.6). From a computational point of view, we can note that the first term of the adversarial overlap \\(\\overline{AO}(\\boldsymbol{x}, \\mathcal{B})\\) - as it does not depend on \\(\\boldsymbol{u}\\) - can be calculated once and re-used to evaluate the importance of any other variables considered. Moreover, contrary to an iterative process method [21, 29, 32], each importance can be evaluated independently and thus benefit from the parallelization of modern neural networks. Finally, the experiments in Section 4 show that even with two calls to \\(\\overline{AO}\\) per variables, our method remains much faster than the one based on sampling or on adversarial attacks (such as Greedy-AS or Greedy-AO, see appendix B)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.903 + ], + "angle": 0, + "content": "In this work, the verified perturbation-based analysis considered is not always adapted to high dimensional models, especially those running on ImageNet [13]. We are con" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.501, + 0.89, + 0.546 + ], + "angle": 0, + "content": "fident that the verification methods will progress towards more scalability in the near future, enabling the original version of EVA on deeper models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.548, + 0.892, + 0.609 + ], + "angle": 0, + "content": "In the meantime, we introduce an empirical method that allows to scale EVA to high dimensional models. This method sacrifices theoretical guarantees, but the results section reveals that it may be a good compromise." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.621, + 0.722, + 0.637 + ], + "angle": 0, + "content": "3.4. Scaling to larger models" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.642, + 0.892, + 0.808 + ], + "angle": 0, + "content": "We propose a second version of EVA, which is a combination of sampling and verification perturbation analysis. The aim of this hybrid method is twofold: \\((i)\\) take advantage of sampling to approach the bounds of an intermediate layer in a potentially very large model, \\((ii)\\) then complete only the rest of the propagations with verified perturbation analysis and thus move towards the native EVA method which benefits from theoretical guarantees. Note that, combining verification methods with empirical methods (a.k.a adversarial training) has notably been proposed in [5] for robust training." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.809, + 0.892, + 0.884 + ], + "angle": 0, + "content": "Specifically, our technique consists of splitting the model into two parts, and \\((i)\\) estimating the bounds of an intermediate layer using sampling, \\((ii)\\) propagating these empirical intermediate bounds onto the second part of the model with verified perturbation analysis methods." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "For the first step \\((i)\\) we consider the original predictor \\(\\pmb{f}\\)" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16157" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.09, + 0.09, + 0.805, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.299, + 0.895, + 0.356 + ], + "angle": 0, + "content": "Figure 3. Scaling strategy. In order to scale to very large models, we propose to estimate the bounds of an intermediate layer's activations empirically by (1) Sampling \\(N\\) input perturbations and (2) calculating empirical bounds on the resulting activations for the layer \\(\\pmb{h}(\\cdot)\\). We can then form the set \\(\\mathcal{P}_B^x\\) which is a subset of the true bounds \\(\\mathcal{H}_B^x\\) since the sampling is never exhaustive. We can then plug this set into a verified perturbation analysis method (3) and continue the forward propagation of the inputs through the rest of the network." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.381, + 0.47, + 0.439 + ], + "angle": 0, + "content": "as a composition of functions \\( f(x) = g \\circ h(x) \\). For deep neural networks, \\( h(\\cdot) \\) is a function that maps input to an intermediate feature space and \\( g(\\cdot) \\) is a function that maps this same feature space to the classification." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.438, + 0.47, + 0.485 + ], + "angle": 0, + "content": "We propose to empirically estimate bounds \\((\\underline{h}_{\\mathcal{B}}^x,\\overline{h}_{\\mathcal{B}}^x)\\) for the intermediate activations \\(h(\\cdot)\\in \\mathbb{R}^{d'}\\) using Monte-Carlo sampling on the perturbation \\(\\delta \\in \\mathcal{B}\\). Formally:" + }, + { + "type": "equation", + "bbox": [ + 0.08, + 0.493, + 0.462, + 0.522 + ], + "angle": 0, + "content": "\\[\n\\forall j \\in [ 0, \\dots , d ^ {\\prime} ], \\underline {{h}} _ {\\mathcal {B}} ^ {\\boldsymbol {x}} [ j ] = \\min _ {\\delta_ {1}, \\dots \\delta_ {i}, \\dots \\delta_ {n} \\stackrel {\\mathrm {i i d}} {\\sim} U (\\mathcal {B})} \\boldsymbol {h} (\\boldsymbol {x} + \\boldsymbol {\\delta} _ {i}) [ j ]\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.197, + 0.525, + 0.465, + 0.556 + ], + "angle": 0, + "content": "\\[\n\\overline{\\boldsymbol{h}}_{\\mathcal{B}}^{\\boldsymbol{x}}[j] = \\max_{\\substack{\\boldsymbol{\\delta}_{1},\\ldots \\boldsymbol{\\delta}_{i},\\ldots \\boldsymbol{\\delta}_{n}\\stackrel {\\mathrm{iid}}{\\sim}U(\\mathcal{B})}}\\boldsymbol {h}(\\boldsymbol {x} + \\boldsymbol{\\delta}_{i})[j].\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.569, + 0.47, + 0.688 + ], + "angle": 0, + "content": "Obviously, since the sampling is never exhaustive, the bounds obtained underestimate the true maximum \\(\\overline{h}_{\\mathcal{B}}^x \\leq \\max h(x + \\delta)\\) and overestimates the true minimum \\(h_{\\mathcal{B}}^x \\geq \\min h(x + \\delta)\\) as illustrated in the Fig. 3. In a similar way, we define \\(\\underline{h}_{\\mathcal{B}_u}^x\\) and \\(\\overline{h}_{\\mathcal{B}_u}^x\\) when \\(\\delta \\in \\mathcal{B}_u\\). Once the empirical bounds are estimated, we may proceed to the second step and use the obtained bounds to form the new perturbation set" + }, + { + "type": "equation", + "bbox": [ + 0.163, + 0.685, + 0.383, + 0.704 + ], + "angle": 0, + "content": "\\[\n\\mathcal {P} _ {\\mathcal {B}} ^ {\\boldsymbol {x}} = [ \\underline {{\\boldsymbol {h}}} _ {\\mathcal {B}} ^ {\\boldsymbol {x}} - \\boldsymbol {h} (\\boldsymbol {x}), \\overline {{\\boldsymbol {h}}} _ {\\mathcal {B}} ^ {\\boldsymbol {x}} - \\boldsymbol {h} (\\boldsymbol {x}) ].\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.712, + 0.47, + 0.756 + ], + "angle": 0, + "content": "Intuitively, this set bounds the intermediate activations obtained empirically and can then be fed to a verified perturbation verification method." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.758, + 0.471, + 0.878 + ], + "angle": 0, + "content": "We then carry out the end of the bounds propagation in the usual way, using verified perturbation analysis. This amounts to computing bounds for the outputs of the network for all possible activations contained in our empirical bounds. The only change is that we no longer operate in the pixel space \\( \\pmb{x} \\) with the ball \\( \\mathcal{B} \\), but in the activation space \\( h(\\cdot) \\) with the perturbations set \\( \\mathcal{P}_{\\mathcal{B}}^{\\pmb{x}} \\). The importance score of a set of variables \\( \\pmb{u} \\) is then:" + }, + { + "type": "equation", + "bbox": [ + 0.132, + 0.885, + 0.414, + 0.903 + ], + "angle": 0, + "content": "\\[\n\\operatorname {E V A} _ {\\text {h y b r i d}} (\\boldsymbol {x}, \\boldsymbol {u}, \\mathcal {B}) \\equiv \\operatorname {E V A} (\\boldsymbol {h} (\\boldsymbol {x}), \\boldsymbol {u}, \\mathcal {P} _ {\\mathcal {B}} ^ {\\boldsymbol {x}}).\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.381, + 0.893, + 0.442 + ], + "angle": 0, + "content": "This hybrid approach allows us to use EVA on state-of-the-art models and thus to benefit from our method while remaining tractable. We believe this extension to be a promising step towards robust explanations on deeper networks." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.463, + 0.634, + 0.481 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.491, + 0.893, + 0.642 + ], + "angle": 0, + "content": "To evaluate the benefits and reliability of our explainability method, we performed several experiments on a standard dataset, using a set of common explainability metrics against EVA. In order to test the fidelity of the explanations produced by our method, we compare them to that of 10 other explainability methods using the (1) Deletion, (2) Insertion, and (3) MuFidelity metrics. As it has been shown that these metrics can exhibit biases, we completed the benchmark by adding the (4) Robustness-\\(\\mathrm{S_r}\\) metric. Each score is averaged over 500 samples." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.895, + 0.901 + ], + "angle": 0, + "content": "We evaluated these 4 metrics on 3 image classification datasets, namely MNIST [41], CIFAR-10 [39] and ImageNet [13]. Through these experiments, the explanations were generated using EVA estimator introduced in Equation 2. The importance scores were not evaluated pixelwise but on each cell of the image after having cut it into a grid of 12 sides (see Fig. 2). For MNIST and Cifar-10, we used \\(\\varepsilon = 0.5\\), whereas for ImageNet \\(\\varepsilon = 5\\). Concerning the verified perturbation analysis method, we used (IBP+Forward+Backward) for MNIST, and (IBP+Forward) on Cifar-10 and \\(p = \\infty\\). For computational purposes, we used the hybrid approach to introduce in Section 3.4 for ImageNet using the penultimate layer (FC-4096) as the intermediate layer \\(h(\\cdot)\\). We give in Appendix the complete set of hyperparameters used for the other explainability methods, metrics considered as well as the architecture of the models used on MNIST and Cifar-10." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "16158" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.099, + 0.089, + 0.891, + 0.288 + ], + "angle": 0, + "content": "
MNISTCifar-10ImageNet
Del.↓Ins.↑Fid.↑Rob.↓TimeDel.↓Ins.↑Fid.↑Rob.↓TimeDel.↓Ins.↑Fid.↑Rob.↓Time
Saliency [56].193.633.378.0710.04.171.172-.021.0260.16.057.126.035.7690.36
GradInput [3].222.611.107.0740.04.200.143-.018.0950.17.057.050.023.8140.36
SmoothGrad [61].185.621.331.0701.91.174.181.092.0489.07.051.069.019.8099.63
VarGrad [54].207.555.216.0771.76.183.211-.012.1939.07.098.201.021.7879.62
InteGrad [65].209.615.108.0741.77.194.171-.016.1547.19.058.052.023.8138.39
Occlusion [3].247.545.137.0820.04.217.290.105.2321.13.100.266.026.8214.97
GradCAM [53]n/an/an/an/an/a.297.282.056.1950.39.073.232.036.8170.18
GradCAM++ [10]n/an/an/an/an/a.270.326.102.0940.39.074.285.054.8000.19
RISE [48].248.558.133.0932.26.196.273.157.38520.5.074.276.154.8181215
Greedy-AS [29].260.497.110.061335.205.264-.003.0134618.088.047.023.612180056
EVA (ours).089.736.428.0691.29.164.290.352.02512.7.070.289.048.7586454
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.309, + 0.896, + 0.396 + ], + "angle": 0, + "content": "Table 1. Results on Deletion (Del.), Insertion (Ins.), \\(\\mu\\)Fidelity (Fid.) and Robustness-\\(S_{\\mathrm{r}}\\) (Rob.) metrics. Time in seconds corresponds to the generation of 500 (MNIST/CIFAR-10) and 100 (ImageNet) explanations on an Nvidia P100. Note that EVA is the only method with guarantees that the entire set of possible perturbations has been exhaustively searched. Verified perturbation analysis with IBP + Forward + Backward is used for MNIST, with Forward only for CIFAR-10 and with our hybrid strategy described in Section3.4 for ImageNet. Grad-CAM and Grad-CAM++ are not calculated on the MNIST dataset since the network only has dense layers. The first and second best results are in bold and underlined, respectively." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.408, + 0.395, + 0.425 + ], + "angle": 0, + "content": "4.1. Comparison with the state of the art" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.432, + 0.471, + 0.688 + ], + "angle": 0, + "content": "There is a general consensus that fidelity is a crucial criterion for an explanation method. That is, if an explanation is used to make a critical decision, then users are expecting it to reflect the true decision-making process underlying the model and not just a consensus with humans. Failure to do so could have disastrous consequences. Pragmatically, these metrics assume that the more faithful an explanation is, the faster the prediction score should drop when pixels considered important are changed. In Table 1, we present the results of the Deletion [48] (or \\(1 - AOPC\\) [52]) metric for the MNIST and Cifar-10 datasets on 500 images sampled from the test set. TensorFlow [1] and the Keras API [11] were used to run the models and Xplique [18] for the explainability methods. In order to evaluate the methods, the metrics require a baseline and several were proposed [29,64], but we chose to keep the choice of [29] using their random baseline." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.47, + 0.839 + ], + "angle": 0, + "content": "We observe that EVA is the explainability method getting the best Deletion, Insertion, and \\(\\mu\\) Fidelity scores on MNIST, and is just behind Greedy-AS on Robustness-\\(S_{\\mathrm{r}}\\). This can be explained by the fact that the Robustness metric uses the adversarial attack PGD [44], which is the same one used to generate Greedy-AS, thus biasing the adversarial search. Indeed, if PGD does not find an adversarial perturbation using a subset \\(u\\) does not give a guarantee of the robustness of the model, just that the adversarial perturbation could be difficult to reach with PGD." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.903 + ], + "angle": 0, + "content": "For Cifar-10, EVA remains overall the most faithful method according to Deletion and \\(\\mu\\) Fidelity, and obtains the second score in Insertion behind Grad-Cam++ [10]. Finally, we notice that if Greedy-AS [29] allows us to ob" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.409, + 0.895, + 0.485 + ], + "angle": 0, + "content": "tain a good Robustness-\\( S_r \\) score, but this comes with a considerable computation time, which is not the case of EVA which is much more efficient. Eventually, EVA is a very good compromise for its relevance to commonly accepted explainability metrics and more recent robustness metrics." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.491, + 0.895, + 0.628 + ], + "angle": 0, + "content": "ImageNet After having demonstrated the potential of the method on vision datasets of limited size, we consider the case of ImageNet which has a significantly higher level of dimension. The use of verified perturbation analysis methods other than IBP is not easily scalable on these datasets. We, therefore, used the hybrid method introduced in Section 3.4 in order to estimate the bounds in a latent space and then plug those bounds into the perturbation analysis to get the final adversarial overlap score." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.628, + 0.896, + 0.793 + ], + "angle": 0, + "content": "Table 1 shows the results obtained with the empirical method proposed in Section 3.4. We observe that even with this relaxed estimation, EVA is able to score high on all the metrics. Indeed, EVA obtains the best score on the Insertion metric and ranks second on \\(\\mu\\) Fidelity and Robustness-\\(S_{\\mathrm{r}}\\). Greedy-AS ranks first on Robustness-\\(S_{\\mathrm{r}}\\) at the expense of the other scores where it performs poorly. Finally, both RISE and SmoothGrad perform well on all the fidelity metrics but collapse on the robustness metric. Extending results with ablations of EVA, including Greedy-AO, are available in Table 3." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.794, + 0.895, + 0.87 + ], + "angle": 0, + "content": "Qualitatively, Fig. 5 shows examples of explanations produced on the ImageNet VGG-16 model. The explanations produced by EVA are more localized than Grad-CAM or RISE, while being less noisy than the gradient-based or Greedy-AS methods." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.895, + 0.903 + ], + "angle": 0, + "content": "In addition, as the literature on verified perturbation analysis is evolving rapidly we can conjecture that the advances" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "16159" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.47, + 0.168 + ], + "angle": 0, + "content": "will benefit the proposed explainability method. Indeed, EVA proved to be the most effective on the benchmark when an accurate formal method was used. After demonstrating the performance of the proposed method, we study its ability to generate class explanations specific." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.176, + 0.466, + 0.193 + ], + "angle": 0, + "content": "4.2. Tighter bounds lead to improved explanations" + }, + { + "type": "table", + "bbox": [ + 0.099, + 0.208, + 0.454, + 0.292 + ], + "angle": 0, + "content": "
Tightness↓Del.↓Ins.↑Fid.↑Rob.↓
IBP4.58.148.588.222.077
Forward2.66.150.580.209.078
Backward2.36.115.607.274.074
IBP + Fo. + Ba.1.55.089.736.428.069
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.303, + 0.468, + 0.414 + ], + "angle": 0, + "content": "Table 2. Impact of the verified perturbation analysis method on EVA. Results of EVAon Tightness, Deletion (Del.), Insertion (Ins.), Fidelity (Fid.) and Robustness- \\( S_{\\mathrm{r}} \\) (Rob.) metrics obtained on MNIST. The Tightness score corresponds to the average adversarial surface. A lower Tightness score indicates that the method is more precise: it reaches tighter bound, resulting in better explanations and superior scores on the other metrics. The first and second best results are respectively in bold and underlined." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.415, + 0.468, + 0.733 + ], + "angle": 0, + "content": "The choice of the verified perturbation analysis method is a hyperparameter of EVA. Hence, it is interesting to see the effect of the choice of this hyperparameter on the previous benchmark. We recall that only the MNIST dataset could benefit from the (IBP+Forward+Backward) combo. Table 2 reports the results of the fidelity metrics using other verified perturbation analysis methods. We also report a tightness score which corresponds to the average of the adversarial overlap: \\(\\mathbb{E}_{\\boldsymbol{x} \\sim \\mathcal{X}}(\\overline{AO}(\\boldsymbol{x}, \\mathcal{B}))\\). Specifically, a low score indicates that the verification method is precise, meaning that the over-approximation is closer to the actual value. It should be noted that the true value is intractable, but remains the same across all three tested cases. We observe that the tighter the bounds, the higher the scores. This allows us to conjecture that the more scalable the formal methods will become, the better the quality of the generated explanations will be. We perform additional experiments to ensure that the certified component of EVA score is significant by comparing EVA to a sampling-based version of EVA. The details of these experiments are available in Appendix B." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.742, + 0.288, + 0.759 + ], + "angle": 0, + "content": "4.3. Targeted Explanations" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.468, + 0.901 + ], + "angle": 0, + "content": "In some cases, it is instructive to look at the explanations for unpredicted classes in order to get information about the internal mechanisms of the models studied. Such explanations allow us to highlight contrastive features: elements that should be changed or whose absence is critical. Our method allows us to obtain such explanations: for a given input, we are then exclusively interested in the class we are trying to explain, without looking at the other decisions. Formally, for a given tar" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.089, + 0.582, + 0.15 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.536, + 0.153, + 0.548, + 0.166 + ], + "angle": 0, + "content": "9" + }, + { + "type": "image", + "bbox": [ + 0.598, + 0.09, + 0.677, + 0.15 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.632, + 0.154, + 0.644, + 0.166 + ], + "angle": 0, + "content": "3" + }, + { + "type": "image", + "bbox": [ + 0.695, + 0.089, + 0.773, + 0.15 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.728, + 0.154, + 0.74, + 0.166 + ], + "angle": 0, + "content": "8" + }, + { + "type": "image", + "bbox": [ + 0.791, + 0.089, + 0.869, + 0.15 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.825, + 0.154, + 0.837, + 0.166 + ], + "angle": 0, + "content": "8" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.17, + 0.892, + 0.268 + ], + "angle": 0, + "content": "Figure 4. Targeted explanations. Generated explanations for a decision other than the one predicted by the model. The class explained is indicated at the bottom of each sample, e.g., the first sample is a '4' and the explanation is for the class '9'. As indicated in section 4.3, the red areas indicate that a black line should be added and the blue areas that it should be removed. More examples are available in the Appendix." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.28, + 0.892, + 0.401 + ], + "angle": 0, + "content": "geted class \\(c'\\) the adversarial overlap (Equation 1) become \\(AO(\\pmb{x},\\mathcal{B}) = \\max_{\\delta \\in \\mathcal{B}}\\pmb{f}_{c'}(\\pmb{x} + \\delta) - \\pmb{f}_c(\\pmb{x} + \\delta)\\). Moreover, by splitting the perturbation ball into a positive one \\(\\mathcal{B}^{(+)} = \\{\\pmb{\\delta}\\in \\mathcal{B}:\\pmb{\\delta}_i\\geq 0,\\forall i\\in \\{1,\\dots,d\\}\\}\\) and a negative one \\(\\mathcal{B}^{(-)} = \\{\\pmb {\\delta}\\in \\mathcal{B}:\\pmb {\\delta}_i\\leq 0,\\forall i\\in \\{1,\\dots,d\\}\\}\\), one can deduce which direction - adding or removing the black line in the case of gray-scaled images - will impact the most the model decision." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.403, + 0.892, + 0.644 + ], + "angle": 0, + "content": "We generate targeted explanations on the MNIST dataset using (IBP+Forward+Backward). For several inputs, we generate the explanation for the 10 classes. Fig. 7 shows 4 examples of targeted explanations, the target class \\( c' \\) is indicated at the bottom. The red areas indicate that adding a black line increases the adversarial overlap with the target class. Conversely, the blue areas indicate where the increase of the score requires removing black lines. All other results can be found in the Appendix. In addition to favorable results on the fidelity metrics and guarantees provided by the verification methods, EVA can provide targeted explanations that are easily understandable by humans, which are two qualities that make them a candidate of choice to meet the recent General Data Protection Regulation (GDPR) adopted in Europe [35]. More examples are available in the Appendix H." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.651, + 0.619, + 0.667 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.676, + 0.892, + 0.811 + ], + "angle": 0, + "content": "In this work, we presented the first explainability method that uses verification perturbation analysis that exhaustively explores the perturbation space to generate explanations. We presented an efficient estimator that yields explanations that are state-of-the-art on current metrics. We also described a simple strategy to scale up perturbation verification methods to complex models. Finally, we showed that this estimator can be used to form easily interpretable targeted explanations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.812, + 0.892, + 0.871 + ], + "angle": 0, + "content": "We hope that this work will for searching for safer and more efficient explanation methods for neural networks – and that it will inspire further synergies with the field of formal verification." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16160" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.09, + 0.176, + 0.107 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.293 + ], + "angle": 0, + "content": "[1] Martin Abadi, Ashish Agarwal, Paul Barham, Eugene Brevdo, Zhifeng Chen, Craig Citro, Greg S. 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Robust and Efficient Explainability with Verified Perturbation Analysis + +Thomas Fel $^{1,2,5\dagger}$ Melanie Ducoffe $^{2,7\dagger}$ David Vigouroux $^{2,4\dagger}$ Rémi Cadène $^{1,3}$ Mikael Capelle $^{6}$ Claire Nicodème $^{5}$ Thomas Serre $^{1,2}$ + +$^{1}$ Carney Institute for Brain Science, Brown University, USA $^{2}$ Artificial and Natural Intelligence Toulouse Institute + +$^{3}$ Sorbonne Université, CNRS, France $^{4}$ IRT Saint-Exupery, France $^{5}$ Innovation & Research Division, SNCF $^{6}$ Thales Alenia Space, France $^{7}$ Airbus AI Research + +# Abstract + +A plethora of attribution methods have recently been developed to explain deep neural networks. These methods use different classes of perturbations (e.g., occlusion, blurring, masking, etc) to estimate the importance of individual image pixels to drive a model's decision. Nevertheless, the space of possible perturbations is vast and current attribution methods typically require significant computation time to accurately sample the space in order to achieve high-quality explanations. In this work, we introduce EVA (Explaining using Verified Perturbation Analysis) – the first explainability method which comes with guarantees that an entire set of possible perturbations has been exhaustively searched. We leverage recent progress in verified perturbation analysis methods to directly propagate bounds through a neural network to exhaustively probe a – potentially infinite-size – set of perturbations in a single forward pass. Our approach takes advantage of the beneficial properties of verified perturbation analysis, i.e., time efficiency and guaranteed complete – sampling agnostic – coverage of the perturbation space – to identify image pixels that drive a model's decision. We evaluate EVA systematically and demonstrate state-of-the-art results on multiple benchmarks. Our code is freely available: github.com/deel-ai/formal-explainability + +# 1. Introduction + +Deep neural networks are now being widely deployed in many applications from medicine, transportation, and security to finance, with broad societal implications [40]. They are routinely used to making safety-critical decisions – often without an explanation as their decisions are notoriously + +![](images/d84cf3ad071e906cd321d87ed3c5dc6904cca47f8c114ba7d204acd356420ed8.jpg) +Figure 1. Manifold exploration of current attribution methods. Current methods assign an importance score to individual pixels using perturbations around a given input image $\pmb{x}$ . Saliency [56] uses infinitesimal perturbations around $\pmb{x}$ , Occlusion [71] switches individual pixel intensities on/off. More recent approaches [17,43,46,48,49] use (Quasi-) random sampling methods in specific perturbation spaces (occlusion of segments of pixels, blurring, ...). However, the choice of the perturbation space undoubtedly biases the results – potentially even introducing serious artifacts [26, 29, 38, 64]. We propose to use verified perturbation analysis to efficiently perform a complete coverage of a perturbation space around $\pmb{x}$ to produce reliable and faithful explanations. + +# hard to interpret. + +Many explainability methods have been proposed to gain insight into how network models arrive at a particular decision [17,24,43,46,48,49,53,55,61,65,71]. The applications of these methods are multiple - from helping to improve or debug their decisions to helping instill confidence in the reliability of their decisions [14]. Unfortunately, a severe limitation of these approaches is that they are subject to a confirmation bias: while they appear to offer useful expla + +nations to a human experimenter, they may produce incorrect explanations [2, 23, 59]. In other words, just because the explanations make sense to humans does not mean that they actually convey what is actually happening within the model. Therefore, the community is actively seeking for better benchmarks involving humans [12, 29, 37, 45]. + +In the meantime, it has been shown that some of our current and commonly used benchmarks are biased and that explainability methods reflect these biases - ultimately providing the wrong explanation for the behavior of the model [25, 29, 64]. For example, some of the current fidelity metrics [7, 18, 27, 34, 48] mask one or a few of the input variables (with a fixed value such as a gray mask) in order to assess how much they contribute to the output of the system. Trivially, if these variables are already set to the mask value in a given image (e.g., gray), masking these variables will not yield any effect on the model's output and the importance of these variables is poised to be underestimated. Finally, these methods rely on sampling a space of perturbations that is far too vast to be fully explored - e.g., LIME on a image divided in 64 segments image would need more than $10^{19}$ samples to test all possible perturbations. As a result, current attribution methods may be subject to bias and are potentially not entirely reliable. + +To address the baseline issue, a growing body of work is starting to leverage adversarial methods [8, 29, 31, 42, 50] to derive explanations that reflect the robustness of the model to local adversarial perturbations. Specifically, a pixel or an image region is considered important if it allows the easy generation of an adversarial example. That is if a small perturbation of that pixel or image region yields a large change in the model's output. This idea has led to the design of several novel robustness metrics to evaluate the quality of explanations, such as Robustness- $S_r$ [29]. For a better ranking on those robustness metrics, several methods have been proposed that make intensive use of adversarial attacks [29, 70], such as Greedy-AS for Robustness- $S_r$ . However, these methods are computationally very costly – in some cases, requiring over 50 000 adversarial attacks per explanation – severely limiting the widespread adoption of these methods in real-world scenarios. + +In this work, we propose to address this limitation by introducing EVA (Explaining using Verified perturbation Analysis), a new explainability method based on robustness analysis. Verified perturbation analysis is a rapidly growing toolkit of methods to derive bounds on the outputs of neural networks in the presence of input perturbations. In contrast to current attributions methods based on gradient estimation or sampling, verified perturbation analysis allows the full exploration of the perturbation space, see Fig. 1. We use a tractable certified upper bound of robustness confidence to derive a new estimator to help quantify the importance of input variables (i.e., those that matter the most). That is, the + +variables most likely to change the predictor's decision. + +We can summarize our main contributions as follows: + +- We introduce EVA, the first explainability method guaranteed to explore its entire set of perturbations using Verified Perturbation Analysis. +- We propose a method to scale EVA to large vision models and show that the exhaustive exploration of all possible perturbations can be done efficiently. +- We systematically evaluate our approach using several image datasets and show that it yields convincing results on a large range of explainability metrics +- Finally, we demonstrate that we can use the proposed method to generate class-specific explanations, and we study the effects of several verified perturbation analysis methods as a hyperparameter of the generated explanations. + +# 2. Related Work + +Attribution Methods. Our approach builds on prior attribution methods in order to explain the prediction of a deep neural network via the identification of input variables that support the prediction (typically pixels or image regions for images – which lead to importance maps shown in Fig. 1). "Saliency" was first introduced in [4] and consists in using the gradient of a classification score. It was later refined in [57, 61, 63, 65, 72] in the context of deep convolutional networks for classification. However, the image gradient only reflects the model's operation within an infinitesimal neighborhood around an input. Hence, it can yield misleading importance estimates [22] since gradients of the current large vision models are noisy [61]. Other methods rely on different image perturbations applied to images to produce importance maps that reflect the corresponding change in classification score resulting from the perturbation. Methods such as "Occlusion" [72], "LIME" [49], "RISE" [48], "Sobol" [17] or "HSIC" [46] leverage different sampling strategies to explore the space of perturbations around the image. For instance, Occlusion uses binary masks to occlude individual image regions, one at a time. RISE and HSIC combines these discrete masks to perturb multiple regions simultaneously. Sobol uses continuous masks for a finer exploration of the perturbation space. + +Nevertheless, none of these methods are able to systematically cover the full space of perturbations. As a result, the corresponding explanations may not reliably reflect the true importance of pixels. In contrast, our approach comes with strong guarantees that can be derived from the verified perturbation analysis framework as it provides bounds on the perturbation space. + +Robustness-based Explanation. To try to address the aforementioned limitations, several groups [8,19,29,32,33, + +42, 60] have focused on the development of a new set of robustness-based evaluation metrics for trustworthy explanations. These new metrics are in contrast with the previous ones, which consisted in removing the pixels considered important in an explanation by substituting them with a fixed baseline – which inevitably introduces bias and artifacts [25, 26, 29, 38, 64]. Key to these new metrics is the assumption that when the important pixels are in their nominal (fixed) state, then perturbations applied to the complementary pixels – deemed unimportant – should not affect the model's decision to any great extent. The corollary that follows is that perturbations limited to the pixels considered important should easily influence the model's decision [29, 42]. Going further along the path of robustness, abductive reasoning was used in [32] to compute optimal subsets with guarantees. The challenge consists in looking for the subset with the smallest possible cardinality – to guarantee the decision of the model. This work constituted one of the early successes of formal methods for explainability, but the approach was limited to low-dimensional problems and shallow neural networks. It was later extended to relax the subset minimum explanation by either providing multiple explanations, aggregating pixels in bundles [6] or by using local surrogates [9]. + +Some heuristics-oriented works also propose to optimize these new robustness based criteria and design new methods using a generative model [47] or adversarial attacks [29]. The latter approach requires searching for the existence or lack of an adversarial example for a multitude of $\ell_p$ balls around the input of interest. As a result, the induced computational cost is quite high as the authors used more than 50000 computations of adversarial examples to generate a single explanation. + +More importantly, a failure to find an adversarial perturbation for a given radius does not guarantee that none exists. In fact, it is not uncommon for adversarial attacks to fail to converge – or fail to find an adversarial example – which will result in a failure to output an importance score. Our method addresses these issues while drastically reducing the computation cost. An added benefit of our approach is that verified perturbation analysis provides additional guarantees and hence opens the doors of certification which is a necessity for safety-critical applications. + +Verified Perturbation Analysis. This growing field of research focuses on the development of methods that outerapproximate neural network outputs given some input perturbations. Simply put, for a given input $\pmb{x}$ and a bounded perturbation $\delta$ , verification methods yield minimum $\underline{f}(\pmb{x})$ and maximum $\overline{f}(\pmb{x})$ bounds on the output of a model. Formally $\forall \delta s.t \|\delta\|_p \leq \varepsilon$ : + +$$ +\underline {{\boldsymbol {f}}} (\boldsymbol {x}) \leq \boldsymbol {f} (\boldsymbol {x} + \boldsymbol {\delta}) \leq \overline {{\boldsymbol {f}}} (\boldsymbol {x}). +$$ + +This allows us to explore the whole perturbation space without having to explicitly sample points in that space. + +Early works focused on computing reachable lower and upper bounds based on satisfiability modulo theories [16, 36], and mixed-integer linear programming problems [66]. While these early results were encouraging, the proposed methods struggled even for small networks and image datasets. More recent work has led to the independent development of methods for computing looser certified lower and upper bounds more efficiently thanks to convex linear relaxations either in the primal or dual space [51]. While looser, those bounds remain tight enough to yield non-ubiquitous robustness properties on medium size neural networks. CROWN (hereafter called Backward) uses Linear Relaxation-based Perturbation Analysis (LiRPA) and achieves the tightest bound for efficient single neuron linear relaxation [58, 67, 73]. In addition, linear relaxation methods offer a wide range of possibilities with a vast trade-off between "tightness" of the bounds and efficiency. These methods form two broad classes: 'forward' methods which propagate constant bounds (more generally affine relaxations from the input to the output of the network) also called Interval Bound Propagation (IBP, Forward, IBP+Forward) vs. 'backward' methods which bound the output of the network by affine relaxations given the internal layers of the network, starting from the output to the input. Note that these methods can be combined, e.g. $(\mathrm{CROWN} + \mathrm{IBP} + \mathrm{Forward})$ . For a thorough description of the LiRPA framework and theoretical analysis of the worst-case complexities of each variant, see [68]. In this work, we remain purposefully agnostic to the verification method used and opt for the most accurate LiRPA method applicable to the predictor. Our approach is based on the formal verification framework DecoMon, based on Keras [15]. + +# 3. Explainability with Verified Perturbation Analysis + +Notation. We consider a standard supervised machine-learning classification setting with input space $\mathcal{X} \subseteq \mathbb{R}^d$ , an output space $\mathcal{Y} \subseteq \mathbb{R}^c$ , and a predictor function $f: \mathcal{X} \to \mathcal{Y}$ that maps an input vector $\boldsymbol{x} = (x_1, \ldots, x_d)$ to an output $\boldsymbol{f}(\boldsymbol{x}) = (\boldsymbol{f}_1(\boldsymbol{x}), \ldots, \boldsymbol{f}_c(\boldsymbol{x}))$ . We denote $\mathcal{B} = \{\delta \in \mathbb{R}^d : ||\delta||_p \leq \varepsilon\}$ the perturbation ball with radius $\varepsilon > 0$ with $p \in \{1, 2, \infty\}$ . For any subset of indices $\boldsymbol{u} \subseteq \{1, \ldots, d\}$ , we denote $\mathcal{B}_u$ the ball without perturbation on the variables in $\boldsymbol{u}$ : $\mathcal{B}_u = \{\delta : \delta \in \mathcal{B}, \delta_u = 0\}$ and $\mathcal{B}(\boldsymbol{x})$ the perturbation ball centered on $\boldsymbol{x}$ . We denote the lower (resp. upper) bounds obtained with verification perturbation analysis as $\underline{\boldsymbol{f}}(\boldsymbol{x}, \mathcal{B}) = (\underline{\boldsymbol{f}}_1(\boldsymbol{x}, \mathcal{B}), \ldots, \underline{\boldsymbol{f}}_c(\boldsymbol{x}, \mathcal{B}))$ , and $\overline{\boldsymbol{f}}(\boldsymbol{x}, \mathcal{B}) = (\overline{\boldsymbol{f}}_1(\boldsymbol{x}, \mathcal{B}), \ldots, \overline{\boldsymbol{f}}_c(\boldsymbol{x}, \mathcal{B}))$ . Intuitively, these bounds delimit the output prediction for any perturbed sample in $\mathcal{B}(\boldsymbol{x})$ . + +# 3.1. The importance of setting the importance right + +Different attribution methods implicitly assume different definitions of the notion of importance for input variables based either on game theory [43], the notion of conditional expectation of the score logits [48], their variance [17] or on some measure of statistical dependency between different areas of an input image and the output of the model [46]. In this work, we build on robustness-based explainability methods [29] which assume that a variable is important if small perturbations of this variable lead to large changes in the model decision. Conversely, a variable is said to be unimportant if changes to this variable only yield small changes in the model decision. From this intuitive assertion, we construct an estimator that we call Adversarial overlap. + +# 3.2. Adversarial overlap + +We go one step beyond previous work and propose to compute importance by taking into account not only the ability of individual variables to change the network's decision but also its confidence in the prediction. Adversarial overlap measures the extent to which a modification on a group of pixels can generate overlap between classes, i.e. generate a point close to $x$ such that the attainable maximum of an unfavorable class $c'$ can match the minimum of the initially predicted class $c$ . + +Indeed, if a modification of a pixel – or group of pixels – allows generating a new image that changes the decision of $f$ , this variable must be considered important. Conversely, if the decision does not change regardless of the value of the pixel, then the pixel can be left at its nominal value and should be considered unimportant. + +Among the set of possible variable perturbations $\delta$ around a point $x$ , we, therefore, look for points that can modify the decision with the most confidence. Hence our scoring criterion can be formulated as follows: + +$$ +A O _ {c} (\boldsymbol {x}, \mathcal {B}) = \max _ {\substack {\boldsymbol {\delta} \in \mathcal {B} \\ c ^ {\prime} \neq c}} \boldsymbol {f} _ {c ^ {\prime}} (\boldsymbol {x} + \boldsymbol {\delta}) - \boldsymbol {f} _ {c} (\boldsymbol {x} + \boldsymbol {\delta}). \tag{1} +$$ + +Intuitively, this score represents the confidence of the "best" adversarial perturbation that can be found in the perturbation ball $\mathcal{B}$ around $\pmb{x}$ . Throughout the article, when $c$ is not specified, it is assumed that $c = \arg \max f(\pmb{x})$ . + +In order to estimate this criterion, a naive strategy could be to use adversarial attacks to search within $\mathcal{B}$ . However, when they converge - which is not ensured, such methods only explore certain points of the considered space, thus giving no guarantee regarding the optimality of the solution. Moreover, adversarial methods have no guarantee of success and therefore cannot ensure a valid score under every circumstance. Finally, the large dimensions of the current datasets make exhaustive searches impossible. + +To overcome these issues, we take advantage of one of the main results from verified perturbation analysis to derive a guaranteed upper bound on the criterion introduced + +in Eq. 1. We can upper bound the adversarial overlap criterion as follows: + +$$ +A O (\boldsymbol {x}, \mathcal {B}) \leq \overline {{A O}} (\boldsymbol {x}, \mathcal {B}) = \max _ {c ^ {\prime} \neq c} \overline {{\boldsymbol {f}}} _ {c ^ {\prime}} (\boldsymbol {x}, \mathcal {B}) - \underline {{\boldsymbol {f}}} _ {c} (\boldsymbol {x}, \mathcal {B}). +$$ + +The computation of this upper bound becomes tractable using any verified perturbation analysis method. + +For example, $\overline{AO}(\boldsymbol{x},\mathcal{B}) \leq 0$ guarantees that no adversarial perturbation is possible in the perturbation space. Our upper bound $\overline{AO}(\boldsymbol{x},\mathcal{B})$ corresponds to the difference between the verified lower bound of the class of interest $c$ and the maximum over the verified upper bounds among the other classes. Thus, when important variables are modified (e.g. the head of the dog in Fig. 2, using $\mathcal{B}$ ), the lower bound for the class of interest will get smaller than the upper bound of the adversary class. On the other hand, this overlap is not possible when important variables are fixed (e.g. in Fig. 2 when the head of the dog is fixed, using $\mathcal{B}_u$ ). We now demonstrate how to leverage this score to derive an efficient estimator of variable importance. + +# 3.3.EVA + +We are willing to assign a higher importance score for a variable allowing (1) a change in a decision, (2) a greater adversarial – thus a solid change of decision. Modifying all variables gives us an idea of the robustness of the model. In the same way, the modification of all variables without the subset $\mathbf{u}$ allows quantifying the change of the strongest adversarial perturbation and thus quantifies the importance of the variables $\mathbf{u}$ . Intuitively, if an important variable $\mathbf{u}$ is discarded, then it will be more difficult, if not impossible, to succeed in finding any adversarial perturbation. Specifically, removing the possibility to modify $x_{\mathbf{u}}$ allows us to reveal its importance by taking into account its possible interactions. + +The complexity of current models means that the variables are not only treated individually in neural network models but collectively. In order to capture these higher-order interactions, our method consists in measuring the adversarial overlap allowed by all the variables together $\overline{AO}(\boldsymbol{x},\mathcal{B})$ - thus taking into account their interactions - and then forbidding to play on a group of variables $\overline{AO}(\boldsymbol{x},\mathcal{B}_{\boldsymbol{u}})$ to estimate the importance of $\boldsymbol{u}$ . Making the interactions of $\boldsymbol{u}$ disappear reveals their importance. Note that several works have mentioned the importance of taking into account the interactions of the variables when calculating the importance [17, 20, 30, 48]. Formally, we introduce EVA (Explainability using Verified perturbation Analysis) that measure the drop in adversarial overlap when we fixed the variables $\boldsymbol{u}$ : + +$$ +\operatorname {E V A} (\boldsymbol {x}, \boldsymbol {u}, \mathcal {B}) \equiv \overline {{A O}} (\boldsymbol {x}, \mathcal {B}) - \overline {{A O}} (\boldsymbol {x}, \mathcal {B} _ {\boldsymbol {u}}). \tag {2} +$$ + +![](images/171579447d1d3cf83d529ff64613d46ef4021e7051c273505a253c5746a73701.jpg) +(1) $\mathcal{B}(\pmb{x})$ are the points around $\pmb{x}$ in a ball of radius $\pmb{\varepsilon}$ . $\mathcal{B}_u(\pmb{x})$ is a subset of $\mathcal{B}(\pmb{x})$ where the variables $\pmb{u}$ (the dog head) are left untouched +(2) Without perturbating $\mathbf{u}$ , we can't reach any adversarial input, thus $\mathbf{u}$ is important +(3) Attribution after computing importance of each variables +Figure 2. EVA attribution method. In order to compute the importance for a group of variables $\mathbf{u}$ – for instance the dog's head – the first step (1) consists in designing the perturbation ball $\mathcal{B}_u(\mathbf{x})$ . This ball is centered in $\mathbf{x}$ and contains all the possible images perturbed by $\delta$ s.t $||\delta||_p \leq \varepsilon$ , $||\delta_{\mathbf{u}}||_p = 0$ which do not perturb the variables $\mathbf{u}$ . Using verified perturbation analysis, we then compute the adversarial overlap $\overline{AO}(\mathbf{x}, \mathcal{B}_u)$ which corresponds to the overlapping between the class $c$ – here $\mathrm{dog}$ – and $c'$ , the maximum among the other classes. Finally, the importance score for the variable $\mathbf{u}$ corresponds to the drop in adversarial overlap when $\mathbf{u}$ cannot be perturbed, thus the difference between $\overline{AO}(\mathbf{x}, \mathcal{B})$ and $\overline{AO}(\mathbf{x}, \mathcal{B}_u)$ . Specifically, this measures how important the variables $\mathbf{u}$ are for changing the model's decision. + +$$ +\operatorname {E V A} (\boldsymbol {x}, \boldsymbol {u}) = \overline {{A O}} (\boldsymbol {x}, \mathcal {B}) - \overline {{A O}} (\boldsymbol {x}, \mathcal {B} _ {\boldsymbol {u}}) +$$ + +![](images/dfed16fb608d2c6002757407a643119019b79e6ab14c2e37ae1657559304e872.jpg) + +As explained in Fig. 2, the estimator requires two passes of the perturbation analysis method; one for $\overline{AO}(\mathcal{B})$ , and the other for $\overline{AO}(\mathcal{B}_u)$ : the first term consists in measuring the adversarial overlap by modifying all the variables, the second term measures the adversarial surface when fixing the variables of interest $u$ . In other words, EVA measures the adversarial overlap that would be left if the variables $u$ were to be fixed. + +From a theoretical point of view, we notice that EVA - under reasonable assumptions - yield the optimal subset of variables to minimize the theoretical Robustness- $S_{\mathrm{r}}$ metric (see Theorem C.6). From a computational point of view, we can note that the first term of the adversarial overlap $\overline{AO}(\boldsymbol{x}, \mathcal{B})$ - as it does not depend on $\boldsymbol{u}$ - can be calculated once and re-used to evaluate the importance of any other variables considered. Moreover, contrary to an iterative process method [21, 29, 32], each importance can be evaluated independently and thus benefit from the parallelization of modern neural networks. Finally, the experiments in Section 4 show that even with two calls to $\overline{AO}$ per variables, our method remains much faster than the one based on sampling or on adversarial attacks (such as Greedy-AS or Greedy-AO, see appendix B). + +In this work, the verified perturbation-based analysis considered is not always adapted to high dimensional models, especially those running on ImageNet [13]. We are con + +fident that the verification methods will progress towards more scalability in the near future, enabling the original version of EVA on deeper models. + +In the meantime, we introduce an empirical method that allows to scale EVA to high dimensional models. This method sacrifices theoretical guarantees, but the results section reveals that it may be a good compromise. + +# 3.4. Scaling to larger models + +We propose a second version of EVA, which is a combination of sampling and verification perturbation analysis. The aim of this hybrid method is twofold: $(i)$ take advantage of sampling to approach the bounds of an intermediate layer in a potentially very large model, $(ii)$ then complete only the rest of the propagations with verified perturbation analysis and thus move towards the native EVA method which benefits from theoretical guarantees. Note that, combining verification methods with empirical methods (a.k.a adversarial training) has notably been proposed in [5] for robust training. + +Specifically, our technique consists of splitting the model into two parts, and $(i)$ estimating the bounds of an intermediate layer using sampling, $(ii)$ propagating these empirical intermediate bounds onto the second part of the model with verified perturbation analysis methods. + +For the first step $(i)$ we consider the original predictor $\pmb{f}$ + +![](images/605f2cb5a3388f521f50f67aded1751ef31e3dbe49a037ee14656d590d4fc072.jpg) +Figure 3. Scaling strategy. In order to scale to very large models, we propose to estimate the bounds of an intermediate layer's activations empirically by (1) Sampling $N$ input perturbations and (2) calculating empirical bounds on the resulting activations for the layer $\pmb{h}(\cdot)$ . We can then form the set $\mathcal{P}_B^x$ which is a subset of the true bounds $\mathcal{H}_B^x$ since the sampling is never exhaustive. We can then plug this set into a verified perturbation analysis method (3) and continue the forward propagation of the inputs through the rest of the network. + +as a composition of functions $f(x) = g \circ h(x)$ . For deep neural networks, $h(\cdot)$ is a function that maps input to an intermediate feature space and $g(\cdot)$ is a function that maps this same feature space to the classification. + +We propose to empirically estimate bounds $(\underline{h}_{\mathcal{B}}^x,\overline{h}_{\mathcal{B}}^x)$ for the intermediate activations $h(\cdot)\in \mathbb{R}^{d'}$ using Monte-Carlo sampling on the perturbation $\delta \in \mathcal{B}$ . Formally: + +$$ +\forall j \in [ 0, \dots , d ^ {\prime} ], \underline {{h}} _ {\mathcal {B}} ^ {\boldsymbol {x}} [ j ] = \min _ {\delta_ {1}, \dots \delta_ {i}, \dots \delta_ {n} \stackrel {\mathrm {i i d}} {\sim} U (\mathcal {B})} \boldsymbol {h} (\boldsymbol {x} + \boldsymbol {\delta} _ {i}) [ j ] +$$ + +$$ +\overline{\boldsymbol{h}}_{\mathcal{B}}^{\boldsymbol{x}}[j] = \max_{\substack{\boldsymbol{\delta}_{1},\ldots \boldsymbol{\delta}_{i},\ldots \boldsymbol{\delta}_{n}\stackrel {\mathrm{iid}}{\sim}U(\mathcal{B})}}\boldsymbol {h}(\boldsymbol {x} + \boldsymbol{\delta}_{i})[j]. +$$ + +Obviously, since the sampling is never exhaustive, the bounds obtained underestimate the true maximum $\overline{h}_{\mathcal{B}}^x \leq \max h(x + \delta)$ and overestimates the true minimum $h_{\mathcal{B}}^x \geq \min h(x + \delta)$ as illustrated in the Fig. 3. In a similar way, we define $\underline{h}_{\mathcal{B}_u}^x$ and $\overline{h}_{\mathcal{B}_u}^x$ when $\delta \in \mathcal{B}_u$ . Once the empirical bounds are estimated, we may proceed to the second step and use the obtained bounds to form the new perturbation set + +$$ +\mathcal {P} _ {\mathcal {B}} ^ {\boldsymbol {x}} = [ \underline {{\boldsymbol {h}}} _ {\mathcal {B}} ^ {\boldsymbol {x}} - \boldsymbol {h} (\boldsymbol {x}), \overline {{\boldsymbol {h}}} _ {\mathcal {B}} ^ {\boldsymbol {x}} - \boldsymbol {h} (\boldsymbol {x}) ]. +$$ + +Intuitively, this set bounds the intermediate activations obtained empirically and can then be fed to a verified perturbation verification method. + +We then carry out the end of the bounds propagation in the usual way, using verified perturbation analysis. This amounts to computing bounds for the outputs of the network for all possible activations contained in our empirical bounds. The only change is that we no longer operate in the pixel space $\pmb{x}$ with the ball $\mathcal{B}$ , but in the activation space $h(\cdot)$ with the perturbations set $\mathcal{P}_{\mathcal{B}}^{\pmb{x}}$ . The importance score of a set of variables $\pmb{u}$ is then: + +$$ +\operatorname {E V A} _ {\text {h y b r i d}} (\boldsymbol {x}, \boldsymbol {u}, \mathcal {B}) \equiv \operatorname {E V A} (\boldsymbol {h} (\boldsymbol {x}), \boldsymbol {u}, \mathcal {P} _ {\mathcal {B}} ^ {\boldsymbol {x}}). +$$ + +This hybrid approach allows us to use EVA on state-of-the-art models and thus to benefit from our method while remaining tractable. We believe this extension to be a promising step towards robust explanations on deeper networks. + +# 4. Experiments + +To evaluate the benefits and reliability of our explainability method, we performed several experiments on a standard dataset, using a set of common explainability metrics against EVA. In order to test the fidelity of the explanations produced by our method, we compare them to that of 10 other explainability methods using the (1) Deletion, (2) Insertion, and (3) MuFidelity metrics. As it has been shown that these metrics can exhibit biases, we completed the benchmark by adding the (4) Robustness- $\mathrm{S_r}$ metric. Each score is averaged over 500 samples. + +We evaluated these 4 metrics on 3 image classification datasets, namely MNIST [41], CIFAR-10 [39] and ImageNet [13]. Through these experiments, the explanations were generated using EVA estimator introduced in Equation 2. The importance scores were not evaluated pixelwise but on each cell of the image after having cut it into a grid of 12 sides (see Fig. 2). For MNIST and Cifar-10, we used $\varepsilon = 0.5$ , whereas for ImageNet $\varepsilon = 5$ . Concerning the verified perturbation analysis method, we used (IBP+Forward+Backward) for MNIST, and (IBP+Forward) on Cifar-10 and $p = \infty$ . For computational purposes, we used the hybrid approach to introduce in Section 3.4 for ImageNet using the penultimate layer (FC-4096) as the intermediate layer $h(\cdot)$ . We give in Appendix the complete set of hyperparameters used for the other explainability methods, metrics considered as well as the architecture of the models used on MNIST and Cifar-10. + +
MNISTCifar-10ImageNet
Del.↓Ins.↑Fid.↑Rob.↓TimeDel.↓Ins.↑Fid.↑Rob.↓TimeDel.↓Ins.↑Fid.↑Rob.↓Time
Saliency [56].193.633.378.0710.04.171.172-.021.0260.16.057.126.035.7690.36
GradInput [3].222.611.107.0740.04.200.143-.018.0950.17.057.050.023.8140.36
SmoothGrad [61].185.621.331.0701.91.174.181.092.0489.07.051.069.019.8099.63
VarGrad [54].207.555.216.0771.76.183.211-.012.1939.07.098.201.021.7879.62
InteGrad [65].209.615.108.0741.77.194.171-.016.1547.19.058.052.023.8138.39
Occlusion [3].247.545.137.0820.04.217.290.105.2321.13.100.266.026.8214.97
GradCAM [53]n/an/an/an/an/a.297.282.056.1950.39.073.232.036.8170.18
GradCAM++ [10]n/an/an/an/an/a.270.326.102.0940.39.074.285.054.8000.19
RISE [48].248.558.133.0932.26.196.273.157.38520.5.074.276.154.8181215
Greedy-AS [29].260.497.110.061335.205.264-.003.0134618.088.047.023.612180056
EVA (ours).089.736.428.0691.29.164.290.352.02512.7.070.289.048.7586454
+ +Table 1. Results on Deletion (Del.), Insertion (Ins.), $\mu$ Fidelity (Fid.) and Robustness- $S_{\mathrm{r}}$ (Rob.) metrics. Time in seconds corresponds to the generation of 500 (MNIST/CIFAR-10) and 100 (ImageNet) explanations on an Nvidia P100. Note that EVA is the only method with guarantees that the entire set of possible perturbations has been exhaustively searched. Verified perturbation analysis with IBP + Forward + Backward is used for MNIST, with Forward only for CIFAR-10 and with our hybrid strategy described in Section3.4 for ImageNet. Grad-CAM and Grad-CAM++ are not calculated on the MNIST dataset since the network only has dense layers. The first and second best results are in bold and underlined, respectively. + +# 4.1. Comparison with the state of the art + +There is a general consensus that fidelity is a crucial criterion for an explanation method. That is, if an explanation is used to make a critical decision, then users are expecting it to reflect the true decision-making process underlying the model and not just a consensus with humans. Failure to do so could have disastrous consequences. Pragmatically, these metrics assume that the more faithful an explanation is, the faster the prediction score should drop when pixels considered important are changed. In Table 1, we present the results of the Deletion [48] (or $1 - AOPC$ [52]) metric for the MNIST and Cifar-10 datasets on 500 images sampled from the test set. TensorFlow [1] and the Keras API [11] were used to run the models and Xplique [18] for the explainability methods. In order to evaluate the methods, the metrics require a baseline and several were proposed [29,64], but we chose to keep the choice of [29] using their random baseline. + +We observe that EVA is the explainability method getting the best Deletion, Insertion, and $\mu$ Fidelity scores on MNIST, and is just behind Greedy-AS on Robustness- $S_{\mathrm{r}}$ . This can be explained by the fact that the Robustness metric uses the adversarial attack PGD [44], which is the same one used to generate Greedy-AS, thus biasing the adversarial search. Indeed, if PGD does not find an adversarial perturbation using a subset $u$ does not give a guarantee of the robustness of the model, just that the adversarial perturbation could be difficult to reach with PGD. + +For Cifar-10, EVA remains overall the most faithful method according to Deletion and $\mu$ Fidelity, and obtains the second score in Insertion behind Grad-Cam++ [10]. Finally, we notice that if Greedy-AS [29] allows us to ob + +tain a good Robustness- $S_r$ score, but this comes with a considerable computation time, which is not the case of EVA which is much more efficient. Eventually, EVA is a very good compromise for its relevance to commonly accepted explainability metrics and more recent robustness metrics. + +ImageNet After having demonstrated the potential of the method on vision datasets of limited size, we consider the case of ImageNet which has a significantly higher level of dimension. The use of verified perturbation analysis methods other than IBP is not easily scalable on these datasets. We, therefore, used the hybrid method introduced in Section 3.4 in order to estimate the bounds in a latent space and then plug those bounds into the perturbation analysis to get the final adversarial overlap score. + +Table 1 shows the results obtained with the empirical method proposed in Section 3.4. We observe that even with this relaxed estimation, EVA is able to score high on all the metrics. Indeed, EVA obtains the best score on the Insertion metric and ranks second on $\mu$ Fidelity and Robustness- $S_{\mathrm{r}}$ . Greedy-AS ranks first on Robustness- $S_{\mathrm{r}}$ at the expense of the other scores where it performs poorly. Finally, both RISE and SmoothGrad perform well on all the fidelity metrics but collapse on the robustness metric. Extending results with ablations of EVA, including Greedy-AO, are available in Table 3. + +Qualitatively, Fig. 5 shows examples of explanations produced on the ImageNet VGG-16 model. The explanations produced by EVA are more localized than Grad-CAM or RISE, while being less noisy than the gradient-based or Greedy-AS methods. + +In addition, as the literature on verified perturbation analysis is evolving rapidly we can conjecture that the advances + +will benefit the proposed explainability method. Indeed, EVA proved to be the most effective on the benchmark when an accurate formal method was used. After demonstrating the performance of the proposed method, we study its ability to generate class explanations specific. + +# 4.2. Tighter bounds lead to improved explanations + +
Tightness↓Del.↓Ins.↑Fid.↑Rob.↓
IBP4.58.148.588.222.077
Forward2.66.150.580.209.078
Backward2.36.115.607.274.074
IBP + Fo. + Ba.1.55.089.736.428.069
+ +Table 2. Impact of the verified perturbation analysis method on EVA. Results of EVAon Tightness, Deletion (Del.), Insertion (Ins.), Fidelity (Fid.) and Robustness- $S_{\mathrm{r}}$ (Rob.) metrics obtained on MNIST. The Tightness score corresponds to the average adversarial surface. A lower Tightness score indicates that the method is more precise: it reaches tighter bound, resulting in better explanations and superior scores on the other metrics. The first and second best results are respectively in bold and underlined. + +The choice of the verified perturbation analysis method is a hyperparameter of EVA. Hence, it is interesting to see the effect of the choice of this hyperparameter on the previous benchmark. We recall that only the MNIST dataset could benefit from the (IBP+Forward+Backward) combo. Table 2 reports the results of the fidelity metrics using other verified perturbation analysis methods. We also report a tightness score which corresponds to the average of the adversarial overlap: $\mathbb{E}_{\boldsymbol{x} \sim \mathcal{X}}(\overline{AO}(\boldsymbol{x}, \mathcal{B}))$ . Specifically, a low score indicates that the verification method is precise, meaning that the over-approximation is closer to the actual value. It should be noted that the true value is intractable, but remains the same across all three tested cases. We observe that the tighter the bounds, the higher the scores. This allows us to conjecture that the more scalable the formal methods will become, the better the quality of the generated explanations will be. We perform additional experiments to ensure that the certified component of EVA score is significant by comparing EVA to a sampling-based version of EVA. The details of these experiments are available in Appendix B. + +# 4.3. Targeted Explanations + +In some cases, it is instructive to look at the explanations for unpredicted classes in order to get information about the internal mechanisms of the models studied. Such explanations allow us to highlight contrastive features: elements that should be changed or whose absence is critical. Our method allows us to obtain such explanations: for a given input, we are then exclusively interested in the class we are trying to explain, without looking at the other decisions. Formally, for a given tar + +![](images/1808d15479652d969fafca461f6ba04d6439efdc8e09c20613781320dc70413a.jpg) +9 + +![](images/4efdad90b7e6955cb77c898687b0fc1da94c4701e0cbed95d92ef861b04d958a.jpg) +3 + +![](images/ceef5c2e90890e093aaa45dc27668a52f6e03110c4267edd747100917c8e138b.jpg) +8 +Figure 4. Targeted explanations. Generated explanations for a decision other than the one predicted by the model. The class explained is indicated at the bottom of each sample, e.g., the first sample is a '4' and the explanation is for the class '9'. As indicated in section 4.3, the red areas indicate that a black line should be added and the blue areas that it should be removed. More examples are available in the Appendix. + +![](images/3bb55b5e2a3f873fdc33740a355c098fa0d6330baaa1d1d77ad63913b93866fa.jpg) +8 + +geted class $c'$ the adversarial overlap (Equation 1) become $AO(\pmb{x},\mathcal{B}) = \max_{\delta \in \mathcal{B}}\pmb{f}_{c'}(\pmb{x} + \delta) - \pmb{f}_c(\pmb{x} + \delta)$ . Moreover, by splitting the perturbation ball into a positive one $\mathcal{B}^{(+)} = \{\pmb{\delta}\in \mathcal{B}:\pmb{\delta}_i\geq 0,\forall i\in \{1,\dots,d\}\}$ and a negative one $\mathcal{B}^{(-)} = \{\pmb {\delta}\in \mathcal{B}:\pmb {\delta}_i\leq 0,\forall i\in \{1,\dots,d\}\}$ , one can deduce which direction - adding or removing the black line in the case of gray-scaled images - will impact the most the model decision. + +We generate targeted explanations on the MNIST dataset using (IBP+Forward+Backward). For several inputs, we generate the explanation for the 10 classes. Fig. 7 shows 4 examples of targeted explanations, the target class $c'$ is indicated at the bottom. The red areas indicate that adding a black line increases the adversarial overlap with the target class. Conversely, the blue areas indicate where the increase of the score requires removing black lines. All other results can be found in the Appendix. In addition to favorable results on the fidelity metrics and guarantees provided by the verification methods, EVA can provide targeted explanations that are easily understandable by humans, which are two qualities that make them a candidate of choice to meet the recent General Data Protection Regulation (GDPR) adopted in Europe [35]. More examples are available in the Appendix H. + +# 5. Conclusion + +In this work, we presented the first explainability method that uses verification perturbation analysis that exhaustively explores the perturbation space to generate explanations. We presented an efficient estimator that yields explanations that are state-of-the-art on current metrics. We also described a simple strategy to scale up perturbation verification methods to complex models. 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These methods use different classes of perturbations (e.g., occlusion, blurring, masking, etc) to estimate the importance of individual image pixels to drive a model's decision. Nevertheless, the space of possible perturbations is vast and current attribution methods typically require significant computation time to accurately sample the space in order to achieve high-quality explanations. In this work, we introduce EVA (Explaining using Verified Perturbation Analysis) – the first explainability method which comes with guarantees that an entire set of possible perturbations has been exhaustively searched. We leverage recent progress in verified perturbation analysis methods to directly propagate bounds through a neural network to exhaustively probe a – potentially infinite-size – set of perturbations in a single forward pass. Our approach takes advantage of the beneficial properties of verified perturbation analysis, i.e., time efficiency and guaranteed complete – sampling agnostic – coverage of the perturbation space – to identify image pixels that drive a model's decision. We evaluate EVA systematically and demonstrate state-of-the-art results on multiple benchmarks. Our code is freely available: github.com/deel-ai/formal-explainability" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 48, + 632, + 128, + 645 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 632, + 128, + 645 + ], + "spans": [ + { + "bbox": [ + 48, + 632, + 128, + 645 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": "Deep neural networks are now being widely deployed in many applications from medicine, transportation, and security to finance, with broad societal implications [40]. They are routinely used to making safety-critical decisions – often without an explanation as their decisions are notoriously" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 306, + 301, + 557, + 437 + ], + "blocks": [ + { + "bbox": [ + 306, + 301, + 557, + 437 + ], + "lines": [ + { + "bbox": [ + 306, + 301, + 557, + 437 + ], + "spans": [ + { + "bbox": [ + 306, + 301, + 557, + 437 + ], + "type": "image", + "image_path": "d84cf3ad071e906cd321d87ed3c5dc6904cca47f8c114ba7d204acd356420ed8.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 444, + 547, + 578 + ], + "lines": [ + { + "bbox": [ + 304, + 444, + 547, + 578 + ], + "spans": [ + { + "bbox": [ + 304, + 444, + 547, + 578 + ], + "type": "text", + "content": "Figure 1. Manifold exploration of current attribution methods. Current methods assign an importance score to individual pixels using perturbations around a given input image " + }, + { + "bbox": [ + 304, + 444, + 547, + 578 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 304, + 444, + 547, + 578 + ], + "type": "text", + "content": ". Saliency [56] uses infinitesimal perturbations around " + }, + { + "bbox": [ + 304, + 444, + 547, + 578 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 304, + 444, + 547, + 578 + ], + "type": "text", + "content": ", Occlusion [71] switches individual pixel intensities on/off. More recent approaches [17,43,46,48,49] use (Quasi-) random sampling methods in specific perturbation spaces (occlusion of segments of pixels, blurring, ...). However, the choice of the perturbation space undoubtedly biases the results – potentially even introducing serious artifacts [26, 29, 38, 64]. We propose to use verified perturbation analysis to efficiently perform a complete coverage of a perturbation space around " + }, + { + "bbox": [ + 304, + 444, + 547, + 578 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 304, + 444, + 547, + 578 + ], + "type": "text", + "content": " to produce reliable and faithful explanations." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 603, + 375, + 615 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 603, + 375, + 615 + ], + "spans": [ + { + "bbox": [ + 306, + 603, + 375, + 615 + ], + "type": "text", + "content": "hard to interpret." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "type": "text", + "content": "Many explainability methods have been proposed to gain insight into how network models arrive at a particular decision [17,24,43,46,48,49,53,55,61,65,71]. The applications of these methods are multiple - from helping to improve or debug their decisions to helping instill confidence in the reliability of their decisions [14]. Unfortunately, a severe limitation of these approaches is that they are subject to a confirmation bias: while they appear to offer useful expla" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16153" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 144 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 144 + ], + "type": "text", + "content": "nations to a human experimenter, they may produce incorrect explanations [2, 23, 59]. In other words, just because the explanations make sense to humans does not mean that they actually convey what is actually happening within the model. Therefore, the community is actively seeking for better benchmarks involving humans [12, 29, 37, 45]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 146, + 290, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 146, + 290, + 361 + ], + "spans": [ + { + "bbox": [ + 46, + 146, + 290, + 361 + ], + "type": "text", + "content": "In the meantime, it has been shown that some of our current and commonly used benchmarks are biased and that explainability methods reflect these biases - ultimately providing the wrong explanation for the behavior of the model [25, 29, 64]. For example, some of the current fidelity metrics [7, 18, 27, 34, 48] mask one or a few of the input variables (with a fixed value such as a gray mask) in order to assess how much they contribute to the output of the system. Trivially, if these variables are already set to the mask value in a given image (e.g., gray), masking these variables will not yield any effect on the model's output and the importance of these variables is poised to be underestimated. Finally, these methods rely on sampling a space of perturbations that is far too vast to be fully explored - e.g., LIME on a image divided in 64 segments image would need more than " + }, + { + "bbox": [ + 46, + 146, + 290, + 361 + ], + "type": "inline_equation", + "content": "10^{19}" + }, + { + "bbox": [ + 46, + 146, + 290, + 361 + ], + "type": "text", + "content": " samples to test all possible perturbations. As a result, current attribution methods may be subject to bias and are potentially not entirely reliable." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 364, + 288, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 364, + 288, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 364, + 288, + 567 + ], + "type": "text", + "content": "To address the baseline issue, a growing body of work is starting to leverage adversarial methods [8, 29, 31, 42, 50] to derive explanations that reflect the robustness of the model to local adversarial perturbations. Specifically, a pixel or an image region is considered important if it allows the easy generation of an adversarial example. That is if a small perturbation of that pixel or image region yields a large change in the model's output. This idea has led to the design of several novel robustness metrics to evaluate the quality of explanations, such as Robustness-" + }, + { + "bbox": [ + 46, + 364, + 288, + 567 + ], + "type": "inline_equation", + "content": "S_r" + }, + { + "bbox": [ + 46, + 364, + 288, + 567 + ], + "type": "text", + "content": " [29]. For a better ranking on those robustness metrics, several methods have been proposed that make intensive use of adversarial attacks [29, 70], such as Greedy-AS for Robustness-" + }, + { + "bbox": [ + 46, + 364, + 288, + 567 + ], + "type": "inline_equation", + "content": "S_r" + }, + { + "bbox": [ + 46, + 364, + 288, + 567 + ], + "type": "text", + "content": ". However, these methods are computationally very costly – in some cases, requiring over 50 000 adversarial attacks per explanation – severely limiting the widespread adoption of these methods in real-world scenarios." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": "In this work, we propose to address this limitation by introducing EVA (Explaining using Verified perturbation Analysis), a new explainability method based on robustness analysis. Verified perturbation analysis is a rapidly growing toolkit of methods to derive bounds on the outputs of neural networks in the presence of input perturbations. In contrast to current attributions methods based on gradient estimation or sampling, verified perturbation analysis allows the full exploration of the perturbation space, see Fig. 1. We use a tractable certified upper bound of robustness confidence to derive a new estimator to help quantify the importance of input variables (i.e., those that matter the most). That is, the" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 305, + 72, + 531, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 531, + 83 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 531, + 83 + ], + "type": "text", + "content": "variables most likely to change the predictor's decision." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 317, + 85, + 535, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 85, + 535, + 95 + ], + "spans": [ + { + "bbox": [ + 317, + 85, + 535, + 95 + ], + "type": "text", + "content": "We can summarize our main contributions as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 99, + 545, + 275 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 306, + 99, + 545, + 135 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 99, + 545, + 135 + ], + "spans": [ + { + "bbox": [ + 306, + 99, + 545, + 135 + ], + "type": "text", + "content": "- We introduce EVA, the first explainability method guaranteed to explore its entire set of perturbations using Verified Perturbation Analysis." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 138, + 545, + 174 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 138, + 545, + 174 + ], + "spans": [ + { + "bbox": [ + 306, + 138, + 545, + 174 + ], + "type": "text", + "content": "- We propose a method to scale EVA to large vision models and show that the exhaustive exploration of all possible perturbations can be done efficiently." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 178, + 545, + 213 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 178, + 545, + 213 + ], + "spans": [ + { + "bbox": [ + 306, + 178, + 545, + 213 + ], + "type": "text", + "content": "- We systematically evaluate our approach using several image datasets and show that it yields convincing results on a large range of explainability metrics" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 217, + 545, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 217, + 545, + 275 + ], + "spans": [ + { + "bbox": [ + 306, + 217, + 545, + 275 + ], + "type": "text", + "content": "- Finally, we demonstrate that we can use the proposed method to generate class-specific explanations, and we study the effects of several verified perturbation analysis methods as a hyperparameter of the generated explanations." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 288, + 392, + 300 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 288, + 392, + 300 + ], + "spans": [ + { + "bbox": [ + 306, + 288, + 392, + 300 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 308, + 545, + 595 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 308, + 545, + 595 + ], + "spans": [ + { + "bbox": [ + 304, + 308, + 545, + 595 + ], + "type": "text", + "content": "Attribution Methods. Our approach builds on prior attribution methods in order to explain the prediction of a deep neural network via the identification of input variables that support the prediction (typically pixels or image regions for images – which lead to importance maps shown in Fig. 1). \"Saliency\" was first introduced in [4] and consists in using the gradient of a classification score. It was later refined in [57, 61, 63, 65, 72] in the context of deep convolutional networks for classification. However, the image gradient only reflects the model's operation within an infinitesimal neighborhood around an input. Hence, it can yield misleading importance estimates [22] since gradients of the current large vision models are noisy [61]. Other methods rely on different image perturbations applied to images to produce importance maps that reflect the corresponding change in classification score resulting from the perturbation. Methods such as \"Occlusion\" [72], \"LIME\" [49], \"RISE\" [48], \"Sobol\" [17] or \"HSIC\" [46] leverage different sampling strategies to explore the space of perturbations around the image. For instance, Occlusion uses binary masks to occlude individual image regions, one at a time. RISE and HSIC combines these discrete masks to perturb multiple regions simultaneously. Sobol uses continuous masks for a finer exploration of the perturbation space." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 595, + 545, + 679 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 595, + 545, + 679 + ], + "spans": [ + { + "bbox": [ + 304, + 595, + 545, + 679 + ], + "type": "text", + "content": "Nevertheless, none of these methods are able to systematically cover the full space of perturbations. As a result, the corresponding explanations may not reliably reflect the true importance of pixels. In contrast, our approach comes with strong guarantees that can be derived from the verified perturbation analysis framework as it provides bounds on the perturbation space." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": "Robustness-based Explanation. To try to address the aforementioned limitations, several groups [8,19,29,32,33," + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "16154" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 360 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 360 + ], + "type": "text", + "content": "42, 60] have focused on the development of a new set of robustness-based evaluation metrics for trustworthy explanations. These new metrics are in contrast with the previous ones, which consisted in removing the pixels considered important in an explanation by substituting them with a fixed baseline – which inevitably introduces bias and artifacts [25, 26, 29, 38, 64]. Key to these new metrics is the assumption that when the important pixels are in their nominal (fixed) state, then perturbations applied to the complementary pixels – deemed unimportant – should not affect the model's decision to any great extent. The corollary that follows is that perturbations limited to the pixels considered important should easily influence the model's decision [29, 42]. Going further along the path of robustness, abductive reasoning was used in [32] to compute optimal subsets with guarantees. The challenge consists in looking for the subset with the smallest possible cardinality – to guarantee the decision of the model. This work constituted one of the early successes of formal methods for explainability, but the approach was limited to low-dimensional problems and shallow neural networks. It was later extended to relax the subset minimum explanation by either providing multiple explanations, aggregating pixels in bundles [6] or by using local surrogates [9]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 361, + 289, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 361, + 289, + 468 + ], + "spans": [ + { + "bbox": [ + 47, + 361, + 289, + 468 + ], + "type": "text", + "content": "Some heuristics-oriented works also propose to optimize these new robustness based criteria and design new methods using a generative model [47] or adversarial attacks [29]. The latter approach requires searching for the existence or lack of an adversarial example for a multitude of " + }, + { + "bbox": [ + 47, + 361, + 289, + 468 + ], + "type": "inline_equation", + "content": "\\ell_p" + }, + { + "bbox": [ + 47, + 361, + 289, + 468 + ], + "type": "text", + "content": " balls around the input of interest. As a result, the induced computational cost is quite high as the authors used more than 50000 computations of adversarial examples to generate a single explanation." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 470, + 289, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 470, + 289, + 590 + ], + "spans": [ + { + "bbox": [ + 47, + 470, + 289, + 590 + ], + "type": "text", + "content": "More importantly, a failure to find an adversarial perturbation for a given radius does not guarantee that none exists. In fact, it is not uncommon for adversarial attacks to fail to converge – or fail to find an adversarial example – which will result in a failure to output an importance score. Our method addresses these issues while drastically reducing the computation cost. An added benefit of our approach is that verified perturbation analysis provides additional guarantees and hence opens the doors of certification which is a necessity for safety-critical applications." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 603, + 288, + 691 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 603, + 288, + 691 + ], + "spans": [ + { + "bbox": [ + 47, + 603, + 288, + 691 + ], + "type": "text", + "content": "Verified Perturbation Analysis. This growing field of research focuses on the development of methods that outerapproximate neural network outputs given some input perturbations. Simply put, for a given input " + }, + { + "bbox": [ + 47, + 603, + 288, + 691 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 47, + 603, + 288, + 691 + ], + "type": "text", + "content": " and a bounded perturbation " + }, + { + "bbox": [ + 47, + 603, + 288, + 691 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 47, + 603, + 288, + 691 + ], + "type": "text", + "content": ", verification methods yield minimum " + }, + { + "bbox": [ + 47, + 603, + 288, + 691 + ], + "type": "inline_equation", + "content": "\\underline{f}(\\pmb{x})" + }, + { + "bbox": [ + 47, + 603, + 288, + 691 + ], + "type": "text", + "content": " and maximum " + }, + { + "bbox": [ + 47, + 603, + 288, + 691 + ], + "type": "inline_equation", + "content": "\\overline{f}(\\pmb{x})" + }, + { + "bbox": [ + 47, + 603, + 288, + 691 + ], + "type": "text", + "content": " bounds on the output of a model. Formally " + }, + { + "bbox": [ + 47, + 603, + 288, + 691 + ], + "type": "inline_equation", + "content": "\\forall \\delta s.t \\|\\delta\\|_p \\leq \\varepsilon" + }, + { + "bbox": [ + 47, + 603, + 288, + 691 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 110, + 700, + 225, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 700, + 225, + 715 + ], + "spans": [ + { + "bbox": [ + 110, + 700, + 225, + 715 + ], + "type": "interline_equation", + "content": "\\underline {{\\boldsymbol {f}}} (\\boldsymbol {x}) \\leq \\boldsymbol {f} (\\boldsymbol {x} + \\boldsymbol {\\delta}) \\leq \\overline {{\\boldsymbol {f}}} (\\boldsymbol {x}).", + "image_path": "528246f650698e23fc3e7ec64ad7c24f713b02a8ec4e84920722786ea91fe67e.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": "This allows us to explore the whole perturbation space without having to explicitly sample points in that space." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 98, + 547, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 98, + 547, + 483 + ], + "spans": [ + { + "bbox": [ + 304, + 98, + 547, + 483 + ], + "type": "text", + "content": "Early works focused on computing reachable lower and upper bounds based on satisfiability modulo theories [16, 36], and mixed-integer linear programming problems [66]. While these early results were encouraging, the proposed methods struggled even for small networks and image datasets. More recent work has led to the independent development of methods for computing looser certified lower and upper bounds more efficiently thanks to convex linear relaxations either in the primal or dual space [51]. While looser, those bounds remain tight enough to yield non-ubiquitous robustness properties on medium size neural networks. CROWN (hereafter called Backward) uses Linear Relaxation-based Perturbation Analysis (LiRPA) and achieves the tightest bound for efficient single neuron linear relaxation [58, 67, 73]. In addition, linear relaxation methods offer a wide range of possibilities with a vast trade-off between \"tightness\" of the bounds and efficiency. These methods form two broad classes: 'forward' methods which propagate constant bounds (more generally affine relaxations from the input to the output of the network) also called Interval Bound Propagation (IBP, Forward, IBP+Forward) vs. 'backward' methods which bound the output of the network by affine relaxations given the internal layers of the network, starting from the output to the input. Note that these methods can be combined, e.g. " + }, + { + "bbox": [ + 304, + 98, + 547, + 483 + ], + "type": "inline_equation", + "content": "(\\mathrm{CROWN} + \\mathrm{IBP} + \\mathrm{Forward})" + }, + { + "bbox": [ + 304, + 98, + 547, + 483 + ], + "type": "text", + "content": ". For a thorough description of the LiRPA framework and theoretical analysis of the worst-case complexities of each variant, see [68]. In this work, we remain purposefully agnostic to the verification method used and opt for the most accurate LiRPA method applicable to the predictor. Our approach is based on the formal verification framework DecoMon, based on Keras [15]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 496, + 545, + 525 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 496, + 545, + 525 + ], + "spans": [ + { + "bbox": [ + 305, + 496, + 545, + 525 + ], + "type": "text", + "content": "3. Explainability with Verified Perturbation Analysis" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 527, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 527, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 527, + 547, + 715 + ], + "type": "text", + "content": "Notation. We consider a standard supervised machine-learning classification setting with input space " + }, + { + "bbox": [ + 304, + 527, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{X} \\subseteq \\mathbb{R}^d" + }, + { + "bbox": [ + 304, + 527, + 547, + 715 + ], + "type": "text", + "content": ", an output space " + }, + { + "bbox": [ + 304, + 527, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{Y} \\subseteq \\mathbb{R}^c" + }, + { + "bbox": [ + 304, + 527, + 547, + 715 + ], + "type": "text", + "content": ", and a predictor function " + }, + { + "bbox": [ + 304, + 527, + 547, + 715 + ], + "type": "inline_equation", + "content": "f: \\mathcal{X} \\to \\mathcal{Y}" + }, + { + "bbox": [ + 304, + 527, + 547, + 715 + ], + "type": "text", + "content": " that maps an input vector " + }, + { + "bbox": [ + 304, + 527, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x} = (x_1, \\ldots, x_d)" + }, + { + "bbox": [ + 304, + 527, + 547, + 715 + ], + "type": "text", + "content": " to an output " + }, + { + "bbox": [ + 304, + 527, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\boldsymbol{f}(\\boldsymbol{x}) = (\\boldsymbol{f}_1(\\boldsymbol{x}), \\ldots, \\boldsymbol{f}_c(\\boldsymbol{x}))" + }, + { + "bbox": [ + 304, + 527, + 547, + 715 + ], + "type": "text", + "content": ". We denote " + }, + { + "bbox": [ + 304, + 527, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{B} = \\{\\delta \\in \\mathbb{R}^d : ||\\delta||_p \\leq \\varepsilon\\}" + }, + { + "bbox": [ + 304, + 527, + 547, + 715 + ], + "type": "text", + "content": " the perturbation ball with radius " + }, + { + "bbox": [ + 304, + 527, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\varepsilon > 0" + }, + { + "bbox": [ + 304, + 527, + 547, + 715 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 527, + 547, + 715 + ], + "type": "inline_equation", + "content": "p \\in \\{1, 2, \\infty\\}" + }, + { + "bbox": [ + 304, + 527, + 547, + 715 + ], + "type": "text", + "content": ". For any subset of indices " + }, + { + "bbox": [ + 304, + 527, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\boldsymbol{u} \\subseteq \\{1, \\ldots, d\\}" + }, + { + "bbox": [ + 304, + 527, + 547, + 715 + ], + "type": "text", + "content": ", we denote " + }, + { + "bbox": [ + 304, + 527, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_u" + }, + { + "bbox": [ + 304, + 527, + 547, + 715 + ], + "type": "text", + "content": " the ball without perturbation on the variables in " + }, + { + "bbox": [ + 304, + 527, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\boldsymbol{u}" + }, + { + "bbox": [ + 304, + 527, + 547, + 715 + ], + "type": "text", + "content": ": " + }, + { + "bbox": [ + 304, + 527, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_u = \\{\\delta : \\delta \\in \\mathcal{B}, \\delta_u = 0\\}" + }, + { + "bbox": [ + 304, + 527, + 547, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 527, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{B}(\\boldsymbol{x})" + }, + { + "bbox": [ + 304, + 527, + 547, + 715 + ], + "type": "text", + "content": " the perturbation ball centered on " + }, + { + "bbox": [ + 304, + 527, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}" + }, + { + "bbox": [ + 304, + 527, + 547, + 715 + ], + "type": "text", + "content": ". We denote the lower (resp. upper) bounds obtained with verification perturbation analysis as " + }, + { + "bbox": [ + 304, + 527, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\underline{\\boldsymbol{f}}(\\boldsymbol{x}, \\mathcal{B}) = (\\underline{\\boldsymbol{f}}_1(\\boldsymbol{x}, \\mathcal{B}), \\ldots, \\underline{\\boldsymbol{f}}_c(\\boldsymbol{x}, \\mathcal{B}))" + }, + { + "bbox": [ + 304, + 527, + 547, + 715 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 527, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\overline{\\boldsymbol{f}}(\\boldsymbol{x}, \\mathcal{B}) = (\\overline{\\boldsymbol{f}}_1(\\boldsymbol{x}, \\mathcal{B}), \\ldots, \\overline{\\boldsymbol{f}}_c(\\boldsymbol{x}, \\mathcal{B}))" + }, + { + "bbox": [ + 304, + 527, + 547, + 715 + ], + "type": "text", + "content": ". Intuitively, these bounds delimit the output prediction for any perturbed sample in " + }, + { + "bbox": [ + 304, + 527, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{B}(\\boldsymbol{x})" + }, + { + "bbox": [ + 304, + 527, + 547, + 715 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "16155" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 85 + ], + "type": "text", + "content": "3.1. The importance of setting the importance right" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 90, + 288, + 247 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 90, + 288, + 247 + ], + "spans": [ + { + "bbox": [ + 46, + 90, + 288, + 247 + ], + "type": "text", + "content": "Different attribution methods implicitly assume different definitions of the notion of importance for input variables based either on game theory [43], the notion of conditional expectation of the score logits [48], their variance [17] or on some measure of statistical dependency between different areas of an input image and the output of the model [46]. In this work, we build on robustness-based explainability methods [29] which assume that a variable is important if small perturbations of this variable lead to large changes in the model decision. Conversely, a variable is said to be unimportant if changes to this variable only yield small changes in the model decision. From this intuitive assertion, we construct an estimator that we call Adversarial overlap." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 251, + 163, + 264 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 251, + 163, + 264 + ], + "spans": [ + { + "bbox": [ + 47, + 251, + 163, + 264 + ], + "type": "text", + "content": "3.2. Adversarial overlap" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 267, + 287, + 375 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 267, + 287, + 375 + ], + "spans": [ + { + "bbox": [ + 46, + 267, + 287, + 375 + ], + "type": "text", + "content": "We go one step beyond previous work and propose to compute importance by taking into account not only the ability of individual variables to change the network's decision but also its confidence in the prediction. Adversarial overlap measures the extent to which a modification on a group of pixels can generate overlap between classes, i.e. generate a point close to " + }, + { + "bbox": [ + 46, + 267, + 287, + 375 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 267, + 287, + 375 + ], + "type": "text", + "content": " such that the attainable maximum of an unfavorable class " + }, + { + "bbox": [ + 46, + 267, + 287, + 375 + ], + "type": "inline_equation", + "content": "c'" + }, + { + "bbox": [ + 46, + 267, + 287, + 375 + ], + "type": "text", + "content": " can match the minimum of the initially predicted class " + }, + { + "bbox": [ + 46, + 267, + 287, + 375 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 267, + 287, + 375 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 375, + 288, + 446 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 375, + 288, + 446 + ], + "spans": [ + { + "bbox": [ + 46, + 375, + 288, + 446 + ], + "type": "text", + "content": "Indeed, if a modification of a pixel – or group of pixels – allows generating a new image that changes the decision of " + }, + { + "bbox": [ + 46, + 375, + 288, + 446 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 375, + 288, + 446 + ], + "type": "text", + "content": ", this variable must be considered important. Conversely, if the decision does not change regardless of the value of the pixel, then the pixel can be left at its nominal value and should be considered unimportant." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 447, + 287, + 493 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 447, + 287, + 493 + ], + "spans": [ + { + "bbox": [ + 46, + 447, + 287, + 493 + ], + "type": "text", + "content": "Among the set of possible variable perturbations " + }, + { + "bbox": [ + 46, + 447, + 287, + 493 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 46, + 447, + 287, + 493 + ], + "type": "text", + "content": " around a point " + }, + { + "bbox": [ + 46, + 447, + 287, + 493 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 447, + 287, + 493 + ], + "type": "text", + "content": ", we, therefore, look for points that can modify the decision with the most confidence. Hence our scoring criterion can be formulated as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 75, + 494, + 287, + 520 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 75, + 494, + 287, + 520 + ], + "spans": [ + { + "bbox": [ + 75, + 494, + 287, + 520 + ], + "type": "interline_equation", + "content": "A O _ {c} (\\boldsymbol {x}, \\mathcal {B}) = \\max _ {\\substack {\\boldsymbol {\\delta} \\in \\mathcal {B} \\\\ c ^ {\\prime} \\neq c}} \\boldsymbol {f} _ {c ^ {\\prime}} (\\boldsymbol {x} + \\boldsymbol {\\delta}) - \\boldsymbol {f} _ {c} (\\boldsymbol {x} + \\boldsymbol {\\delta}). \\tag{1}", + "image_path": "8351d94b13b865101cc1d09a95db5bafdbd171595dec86cc16473f38d13acdf4.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 522, + 287, + 570 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 522, + 287, + 570 + ], + "spans": [ + { + "bbox": [ + 46, + 522, + 287, + 570 + ], + "type": "text", + "content": "Intuitively, this score represents the confidence of the \"best\" adversarial perturbation that can be found in the perturbation ball " + }, + { + "bbox": [ + 46, + 522, + 287, + 570 + ], + "type": "inline_equation", + "content": "\\mathcal{B}" + }, + { + "bbox": [ + 46, + 522, + 287, + 570 + ], + "type": "text", + "content": " around " + }, + { + "bbox": [ + 46, + 522, + 287, + 570 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 46, + 522, + 287, + 570 + ], + "type": "text", + "content": ". Throughout the article, when " + }, + { + "bbox": [ + 46, + 522, + 287, + 570 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 522, + 287, + 570 + ], + "type": "text", + "content": " is not specified, it is assumed that " + }, + { + "bbox": [ + 46, + 522, + 287, + 570 + ], + "type": "inline_equation", + "content": "c = \\arg \\max f(\\pmb{x})" + }, + { + "bbox": [ + 46, + 522, + 287, + 570 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 570, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 287, + 677 + ], + "type": "text", + "content": "In order to estimate this criterion, a naive strategy could be to use adversarial attacks to search within " + }, + { + "bbox": [ + 46, + 570, + 287, + 677 + ], + "type": "inline_equation", + "content": "\\mathcal{B}" + }, + { + "bbox": [ + 46, + 570, + 287, + 677 + ], + "type": "text", + "content": ". However, when they converge - which is not ensured, such methods only explore certain points of the considered space, thus giving no guarantee regarding the optimality of the solution. Moreover, adversarial methods have no guarantee of success and therefore cannot ensure a valid score under every circumstance. Finally, the large dimensions of the current datasets make exhaustive searches impossible." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "To overcome these issues, we take advantage of one of the main results from verified perturbation analysis to derive a guaranteed upper bound on the criterion introduced" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 544, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 544, + 95 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 544, + 95 + ], + "type": "text", + "content": "in Eq. 1. We can upper bound the adversarial overlap criterion as follows:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 315, + 102, + 533, + 122 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 102, + 533, + 122 + ], + "spans": [ + { + "bbox": [ + 315, + 102, + 533, + 122 + ], + "type": "interline_equation", + "content": "A O (\\boldsymbol {x}, \\mathcal {B}) \\leq \\overline {{A O}} (\\boldsymbol {x}, \\mathcal {B}) = \\max _ {c ^ {\\prime} \\neq c} \\overline {{\\boldsymbol {f}}} _ {c ^ {\\prime}} (\\boldsymbol {x}, \\mathcal {B}) - \\underline {{\\boldsymbol {f}}} _ {c} (\\boldsymbol {x}, \\mathcal {B}).", + "image_path": "0ffffccb92ca9346441db201827ad0365934a3462321bcc6177d8210d7dd1196.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 129, + 544, + 153 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 129, + 544, + 153 + ], + "spans": [ + { + "bbox": [ + 304, + 129, + 544, + 153 + ], + "type": "text", + "content": "The computation of this upper bound becomes tractable using any verified perturbation analysis method." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 153, + 545, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 153, + 545, + 308 + ], + "spans": [ + { + "bbox": [ + 304, + 153, + 545, + 308 + ], + "type": "text", + "content": "For example, " + }, + { + "bbox": [ + 304, + 153, + 545, + 308 + ], + "type": "inline_equation", + "content": "\\overline{AO}(\\boldsymbol{x},\\mathcal{B}) \\leq 0" + }, + { + "bbox": [ + 304, + 153, + 545, + 308 + ], + "type": "text", + "content": " guarantees that no adversarial perturbation is possible in the perturbation space. Our upper bound " + }, + { + "bbox": [ + 304, + 153, + 545, + 308 + ], + "type": "inline_equation", + "content": "\\overline{AO}(\\boldsymbol{x},\\mathcal{B})" + }, + { + "bbox": [ + 304, + 153, + 545, + 308 + ], + "type": "text", + "content": " corresponds to the difference between the verified lower bound of the class of interest " + }, + { + "bbox": [ + 304, + 153, + 545, + 308 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 153, + 545, + 308 + ], + "type": "text", + "content": " and the maximum over the verified upper bounds among the other classes. Thus, when important variables are modified (e.g. the head of the dog in Fig. 2, using " + }, + { + "bbox": [ + 304, + 153, + 545, + 308 + ], + "type": "inline_equation", + "content": "\\mathcal{B}" + }, + { + "bbox": [ + 304, + 153, + 545, + 308 + ], + "type": "text", + "content": "), the lower bound for the class of interest will get smaller than the upper bound of the adversary class. On the other hand, this overlap is not possible when important variables are fixed (e.g. in Fig. 2 when the head of the dog is fixed, using " + }, + { + "bbox": [ + 304, + 153, + 545, + 308 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_u" + }, + { + "bbox": [ + 304, + 153, + 545, + 308 + ], + "type": "text", + "content": "). We now demonstrate how to leverage this score to derive an efficient estimator of variable importance." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 316, + 350, + 327 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 316, + 350, + 327 + ], + "spans": [ + { + "bbox": [ + 306, + 316, + 350, + 327 + ], + "type": "text", + "content": "3.3.EVA" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 334, + 545, + 488 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 334, + 545, + 488 + ], + "spans": [ + { + "bbox": [ + 304, + 334, + 545, + 488 + ], + "type": "text", + "content": "We are willing to assign a higher importance score for a variable allowing (1) a change in a decision, (2) a greater adversarial – thus a solid change of decision. Modifying all variables gives us an idea of the robustness of the model. In the same way, the modification of all variables without the subset " + }, + { + "bbox": [ + 304, + 334, + 545, + 488 + ], + "type": "inline_equation", + "content": "\\mathbf{u}" + }, + { + "bbox": [ + 304, + 334, + 545, + 488 + ], + "type": "text", + "content": " allows quantifying the change of the strongest adversarial perturbation and thus quantifies the importance of the variables " + }, + { + "bbox": [ + 304, + 334, + 545, + 488 + ], + "type": "inline_equation", + "content": "\\mathbf{u}" + }, + { + "bbox": [ + 304, + 334, + 545, + 488 + ], + "type": "text", + "content": ". Intuitively, if an important variable " + }, + { + "bbox": [ + 304, + 334, + 545, + 488 + ], + "type": "inline_equation", + "content": "\\mathbf{u}" + }, + { + "bbox": [ + 304, + 334, + 545, + 488 + ], + "type": "text", + "content": " is discarded, then it will be more difficult, if not impossible, to succeed in finding any adversarial perturbation. Specifically, removing the possibility to modify " + }, + { + "bbox": [ + 304, + 334, + 545, + 488 + ], + "type": "inline_equation", + "content": "x_{\\mathbf{u}}" + }, + { + "bbox": [ + 304, + 334, + 545, + 488 + ], + "type": "text", + "content": " allows us to reveal its importance by taking into account its possible interactions." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 490, + 545, + 668 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 490, + 545, + 668 + ], + "spans": [ + { + "bbox": [ + 304, + 490, + 545, + 668 + ], + "type": "text", + "content": "The complexity of current models means that the variables are not only treated individually in neural network models but collectively. In order to capture these higher-order interactions, our method consists in measuring the adversarial overlap allowed by all the variables together " + }, + { + "bbox": [ + 304, + 490, + 545, + 668 + ], + "type": "inline_equation", + "content": "\\overline{AO}(\\boldsymbol{x},\\mathcal{B})" + }, + { + "bbox": [ + 304, + 490, + 545, + 668 + ], + "type": "text", + "content": " - thus taking into account their interactions - and then forbidding to play on a group of variables " + }, + { + "bbox": [ + 304, + 490, + 545, + 668 + ], + "type": "inline_equation", + "content": "\\overline{AO}(\\boldsymbol{x},\\mathcal{B}_{\\boldsymbol{u}})" + }, + { + "bbox": [ + 304, + 490, + 545, + 668 + ], + "type": "text", + "content": " to estimate the importance of " + }, + { + "bbox": [ + 304, + 490, + 545, + 668 + ], + "type": "inline_equation", + "content": "\\boldsymbol{u}" + }, + { + "bbox": [ + 304, + 490, + 545, + 668 + ], + "type": "text", + "content": ". Making the interactions of " + }, + { + "bbox": [ + 304, + 490, + 545, + 668 + ], + "type": "inline_equation", + "content": "\\boldsymbol{u}" + }, + { + "bbox": [ + 304, + 490, + 545, + 668 + ], + "type": "text", + "content": " disappear reveals their importance. Note that several works have mentioned the importance of taking into account the interactions of the variables when calculating the importance [17, 20, 30, 48]. Formally, we introduce EVA (Explainability using Verified perturbation Analysis) that measure the drop in adversarial overlap when we fixed the variables " + }, + { + "bbox": [ + 304, + 490, + 545, + 668 + ], + "type": "inline_equation", + "content": "\\boldsymbol{u}" + }, + { + "bbox": [ + 304, + 490, + 545, + 668 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 340, + 673, + 545, + 687 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 340, + 673, + 545, + 687 + ], + "spans": [ + { + "bbox": [ + 340, + 673, + 545, + 687 + ], + "type": "interline_equation", + "content": "\\operatorname {E V A} (\\boldsymbol {x}, \\boldsymbol {u}, \\mathcal {B}) \\equiv \\overline {{A O}} (\\boldsymbol {x}, \\mathcal {B}) - \\overline {{A O}} (\\boldsymbol {x}, \\mathcal {B} _ {\\boldsymbol {u}}). \\tag {2}", + "image_path": "430ef934a2172fb32ab5af28f9f87b108f368e8325c2048d643a8f2f38a57e41.jpg" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "text", + "content": "1Note that with adversarial attacks, failure to find an adversarial example does not guarantee that it does not exist." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "16156" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 68, + 413, + 264 + ], + "blocks": [ + { + "bbox": [ + 50, + 68, + 413, + 264 + ], + "lines": [ + { + "bbox": [ + 50, + 68, + 413, + 264 + ], + "spans": [ + { + "bbox": [ + 50, + 68, + 413, + 264 + ], + "type": "image", + "image_path": "171579447d1d3cf83d529ff64613d46ef4021e7051c273505a253c5746a73701.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 52, + 264, + 254, + 293 + ], + "lines": [ + { + "bbox": [ + 52, + 264, + 254, + 293 + ], + "spans": [ + { + "bbox": [ + 52, + 264, + 254, + 293 + ], + "type": "text", + "content": "(1) " + }, + { + "bbox": [ + 52, + 264, + 254, + 293 + ], + "type": "inline_equation", + "content": "\\mathcal{B}(\\pmb{x})" + }, + { + "bbox": [ + 52, + 264, + 254, + 293 + ], + "type": "text", + "content": " are the points around " + }, + { + "bbox": [ + 52, + 264, + 254, + 293 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 52, + 264, + 254, + 293 + ], + "type": "text", + "content": " in a ball of radius " + }, + { + "bbox": [ + 52, + 264, + 254, + 293 + ], + "type": "inline_equation", + "content": "\\pmb{\\varepsilon}" + }, + { + "bbox": [ + 52, + 264, + 254, + 293 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 52, + 264, + 254, + 293 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_u(\\pmb{x})" + }, + { + "bbox": [ + 52, + 264, + 254, + 293 + ], + "type": "text", + "content": " is a subset of " + }, + { + "bbox": [ + 52, + 264, + 254, + 293 + ], + "type": "inline_equation", + "content": "\\mathcal{B}(\\pmb{x})" + }, + { + "bbox": [ + 52, + 264, + 254, + 293 + ], + "type": "text", + "content": " where the variables " + }, + { + "bbox": [ + 52, + 264, + 254, + 293 + ], + "type": "inline_equation", + "content": "\\pmb{u}" + }, + { + "bbox": [ + 52, + 264, + 254, + 293 + ], + "type": "text", + "content": " (the dog head) are left untouched" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 259, + 264, + 396, + 285 + ], + "lines": [ + { + "bbox": [ + 259, + 264, + 396, + 285 + ], + "spans": [ + { + "bbox": [ + 259, + 264, + 396, + 285 + ], + "type": "text", + "content": "(2) Without perturbating " + }, + { + "bbox": [ + 259, + 264, + 396, + 285 + ], + "type": "inline_equation", + "content": "\\mathbf{u}" + }, + { + "bbox": [ + 259, + 264, + 396, + 285 + ], + "type": "text", + "content": ", we can't reach any adversarial input, thus " + }, + { + "bbox": [ + 259, + 264, + 396, + 285 + ], + "type": "inline_equation", + "content": "\\mathbf{u}" + }, + { + "bbox": [ + 259, + 264, + 396, + 285 + ], + "type": "text", + "content": " is important" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 417, + 263, + 517, + 282 + ], + "lines": [ + { + "bbox": [ + 417, + 263, + 517, + 282 + ], + "spans": [ + { + "bbox": [ + 417, + 263, + 517, + 282 + ], + "type": "text", + "content": "(3) Attribution after computing importance of each variables" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 307, + 545, + 384 + ], + "lines": [ + { + "bbox": [ + 46, + 307, + 545, + 384 + ], + "spans": [ + { + "bbox": [ + 46, + 307, + 545, + 384 + ], + "type": "text", + "content": "Figure 2. EVA attribution method. In order to compute the importance for a group of variables " + }, + { + "bbox": [ + 46, + 307, + 545, + 384 + ], + "type": "inline_equation", + "content": "\\mathbf{u}" + }, + { + "bbox": [ + 46, + 307, + 545, + 384 + ], + "type": "text", + "content": " – for instance the dog's head – the first step (1) consists in designing the perturbation ball " + }, + { + "bbox": [ + 46, + 307, + 545, + 384 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_u(\\mathbf{x})" + }, + { + "bbox": [ + 46, + 307, + 545, + 384 + ], + "type": "text", + "content": ". This ball is centered in " + }, + { + "bbox": [ + 46, + 307, + 545, + 384 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 307, + 545, + 384 + ], + "type": "text", + "content": " and contains all the possible images perturbed by " + }, + { + "bbox": [ + 46, + 307, + 545, + 384 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 46, + 307, + 545, + 384 + ], + "type": "text", + "content": " s.t " + }, + { + "bbox": [ + 46, + 307, + 545, + 384 + ], + "type": "inline_equation", + "content": "||\\delta||_p \\leq \\varepsilon" + }, + { + "bbox": [ + 46, + 307, + 545, + 384 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 307, + 545, + 384 + ], + "type": "inline_equation", + "content": "||\\delta_{\\mathbf{u}}||_p = 0" + }, + { + "bbox": [ + 46, + 307, + 545, + 384 + ], + "type": "text", + "content": " which do not perturb the variables " + }, + { + "bbox": [ + 46, + 307, + 545, + 384 + ], + "type": "inline_equation", + "content": "\\mathbf{u}" + }, + { + "bbox": [ + 46, + 307, + 545, + 384 + ], + "type": "text", + "content": ". Using verified perturbation analysis, we then compute the adversarial overlap " + }, + { + "bbox": [ + 46, + 307, + 545, + 384 + ], + "type": "inline_equation", + "content": "\\overline{AO}(\\mathbf{x}, \\mathcal{B}_u)" + }, + { + "bbox": [ + 46, + 307, + 545, + 384 + ], + "type": "text", + "content": " which corresponds to the overlapping between the class " + }, + { + "bbox": [ + 46, + 307, + 545, + 384 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 307, + 545, + 384 + ], + "type": "text", + "content": " – here " + }, + { + "bbox": [ + 46, + 307, + 545, + 384 + ], + "type": "inline_equation", + "content": "\\mathrm{dog}" + }, + { + "bbox": [ + 46, + 307, + 545, + 384 + ], + "type": "text", + "content": " – and " + }, + { + "bbox": [ + 46, + 307, + 545, + 384 + ], + "type": "inline_equation", + "content": "c'" + }, + { + "bbox": [ + 46, + 307, + 545, + 384 + ], + "type": "text", + "content": ", the maximum among the other classes. Finally, the importance score for the variable " + }, + { + "bbox": [ + 46, + 307, + 545, + 384 + ], + "type": "inline_equation", + "content": "\\mathbf{u}" + }, + { + "bbox": [ + 46, + 307, + 545, + 384 + ], + "type": "text", + "content": " corresponds to the drop in adversarial overlap when " + }, + { + "bbox": [ + 46, + 307, + 545, + 384 + ], + "type": "inline_equation", + "content": "\\mathbf{u}" + }, + { + "bbox": [ + 46, + 307, + 545, + 384 + ], + "type": "text", + "content": " cannot be perturbed, thus the difference between " + }, + { + "bbox": [ + 46, + 307, + 545, + 384 + ], + "type": "inline_equation", + "content": "\\overline{AO}(\\mathbf{x}, \\mathcal{B})" + }, + { + "bbox": [ + 46, + 307, + 545, + 384 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 307, + 545, + 384 + ], + "type": "inline_equation", + "content": "\\overline{AO}(\\mathbf{x}, \\mathcal{B}_u)" + }, + { + "bbox": [ + 46, + 307, + 545, + 384 + ], + "type": "text", + "content": ". Specifically, this measures how important the variables " + }, + { + "bbox": [ + 46, + 307, + 545, + 384 + ], + "type": "inline_equation", + "content": "\\mathbf{u}" + }, + { + "bbox": [ + 46, + 307, + 545, + 384 + ], + "type": "text", + "content": " are for changing the model's decision." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 408, + 114, + 536, + 128 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 408, + 114, + 536, + 128 + ], + "spans": [ + { + "bbox": [ + 408, + 114, + 536, + 128 + ], + "type": "interline_equation", + "content": "\\operatorname {E V A} (\\boldsymbol {x}, \\boldsymbol {u}) = \\overline {{A O}} (\\boldsymbol {x}, \\mathcal {B}) - \\overline {{A O}} (\\boldsymbol {x}, \\mathcal {B} _ {\\boldsymbol {u}})", + "image_path": "044814e2cde09d52323a3481fd533fe73b8e32059197c68f71ef0333651e9205.jpg" + } + ] + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 420, + 138, + 529, + 247 + ], + "blocks": [ + { + "bbox": [ + 420, + 138, + 529, + 247 + ], + "lines": [ + { + "bbox": [ + 420, + 138, + 529, + 247 + ], + "spans": [ + { + "bbox": [ + 420, + 138, + 529, + 247 + ], + "type": "image", + "image_path": "dfed16fb608d2c6002757407a643119019b79e6ab14c2e37ae1657559304e872.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 397, + 287, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 397, + 287, + 492 + ], + "spans": [ + { + "bbox": [ + 46, + 397, + 287, + 492 + ], + "type": "text", + "content": "As explained in Fig. 2, the estimator requires two passes of the perturbation analysis method; one for " + }, + { + "bbox": [ + 46, + 397, + 287, + 492 + ], + "type": "inline_equation", + "content": "\\overline{AO}(\\mathcal{B})" + }, + { + "bbox": [ + 46, + 397, + 287, + 492 + ], + "type": "text", + "content": ", and the other for " + }, + { + "bbox": [ + 46, + 397, + 287, + 492 + ], + "type": "inline_equation", + "content": "\\overline{AO}(\\mathcal{B}_u)" + }, + { + "bbox": [ + 46, + 397, + 287, + 492 + ], + "type": "text", + "content": ": the first term consists in measuring the adversarial overlap by modifying all the variables, the second term measures the adversarial surface when fixing the variables of interest " + }, + { + "bbox": [ + 46, + 397, + 287, + 492 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 46, + 397, + 287, + 492 + ], + "type": "text", + "content": ". In other words, EVA measures the adversarial overlap that would be left if the variables " + }, + { + "bbox": [ + 46, + 397, + 287, + 492 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 46, + 397, + 287, + 492 + ], + "type": "text", + "content": " were to be fixed." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 495, + 288, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 495, + 288, + 675 + ], + "spans": [ + { + "bbox": [ + 46, + 495, + 288, + 675 + ], + "type": "text", + "content": "From a theoretical point of view, we notice that EVA - under reasonable assumptions - yield the optimal subset of variables to minimize the theoretical Robustness-" + }, + { + "bbox": [ + 46, + 495, + 288, + 675 + ], + "type": "inline_equation", + "content": "S_{\\mathrm{r}}" + }, + { + "bbox": [ + 46, + 495, + 288, + 675 + ], + "type": "text", + "content": " metric (see Theorem C.6). From a computational point of view, we can note that the first term of the adversarial overlap " + }, + { + "bbox": [ + 46, + 495, + 288, + 675 + ], + "type": "inline_equation", + "content": "\\overline{AO}(\\boldsymbol{x}, \\mathcal{B})" + }, + { + "bbox": [ + 46, + 495, + 288, + 675 + ], + "type": "text", + "content": " - as it does not depend on " + }, + { + "bbox": [ + 46, + 495, + 288, + 675 + ], + "type": "inline_equation", + "content": "\\boldsymbol{u}" + }, + { + "bbox": [ + 46, + 495, + 288, + 675 + ], + "type": "text", + "content": " - can be calculated once and re-used to evaluate the importance of any other variables considered. Moreover, contrary to an iterative process method [21, 29, 32], each importance can be evaluated independently and thus benefit from the parallelization of modern neural networks. Finally, the experiments in Section 4 show that even with two calls to " + }, + { + "bbox": [ + 46, + 495, + 288, + 675 + ], + "type": "inline_equation", + "content": "\\overline{AO}" + }, + { + "bbox": [ + 46, + 495, + 288, + 675 + ], + "type": "text", + "content": " per variables, our method remains much faster than the one based on sampling or on adversarial attacks (such as Greedy-AS or Greedy-AO, see appendix B)." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "text", + "content": "In this work, the verified perturbation-based analysis considered is not always adapted to high dimensional models, especially those running on ImageNet [13]. We are con" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 396, + 544, + 432 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 396, + 544, + 432 + ], + "spans": [ + { + "bbox": [ + 304, + 396, + 544, + 432 + ], + "type": "text", + "content": "fident that the verification methods will progress towards more scalability in the near future, enabling the original version of EVA on deeper models." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 434, + 545, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 434, + 545, + 482 + ], + "spans": [ + { + "bbox": [ + 304, + 434, + 545, + 482 + ], + "type": "text", + "content": "In the meantime, we introduce an empirical method that allows to scale EVA to high dimensional models. This method sacrifices theoretical guarantees, but the results section reveals that it may be a good compromise." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 491, + 441, + 504 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 491, + 441, + 504 + ], + "spans": [ + { + "bbox": [ + 306, + 491, + 441, + 504 + ], + "type": "text", + "content": "3.4. Scaling to larger models" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 508, + 545, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 508, + 545, + 639 + ], + "spans": [ + { + "bbox": [ + 304, + 508, + 545, + 639 + ], + "type": "text", + "content": "We propose a second version of EVA, which is a combination of sampling and verification perturbation analysis. The aim of this hybrid method is twofold: " + }, + { + "bbox": [ + 304, + 508, + 545, + 639 + ], + "type": "inline_equation", + "content": "(i)" + }, + { + "bbox": [ + 304, + 508, + 545, + 639 + ], + "type": "text", + "content": " take advantage of sampling to approach the bounds of an intermediate layer in a potentially very large model, " + }, + { + "bbox": [ + 304, + 508, + 545, + 639 + ], + "type": "inline_equation", + "content": "(ii)" + }, + { + "bbox": [ + 304, + 508, + 545, + 639 + ], + "type": "text", + "content": " then complete only the rest of the propagations with verified perturbation analysis and thus move towards the native EVA method which benefits from theoretical guarantees. Note that, combining verification methods with empirical methods (a.k.a adversarial training) has notably been proposed in [5] for robust training." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 640, + 545, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 640, + 545, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 640, + 545, + 700 + ], + "type": "text", + "content": "Specifically, our technique consists of splitting the model into two parts, and " + }, + { + "bbox": [ + 304, + 640, + 545, + 700 + ], + "type": "inline_equation", + "content": "(i)" + }, + { + "bbox": [ + 304, + 640, + 545, + 700 + ], + "type": "text", + "content": " estimating the bounds of an intermediate layer using sampling, " + }, + { + "bbox": [ + 304, + 640, + 545, + 700 + ], + "type": "inline_equation", + "content": "(ii)" + }, + { + "bbox": [ + 304, + 640, + 545, + 700 + ], + "type": "text", + "content": " propagating these empirical intermediate bounds onto the second part of the model with verified perturbation analysis methods." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "text", + "content": "For the first step " + }, + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "inline_equation", + "content": "(i)" + }, + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "text", + "content": " we consider the original predictor " + }, + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\pmb{f}" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16157" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 55, + 71, + 492, + 232 + ], + "blocks": [ + { + "bbox": [ + 55, + 71, + 492, + 232 + ], + "lines": [ + { + "bbox": [ + 55, + 71, + 492, + 232 + ], + "spans": [ + { + "bbox": [ + 55, + 71, + 492, + 232 + ], + "type": "image", + "image_path": "605f2cb5a3388f521f50f67aded1751ef31e3dbe49a037ee14656d590d4fc072.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 236, + 547, + 281 + ], + "lines": [ + { + "bbox": [ + 46, + 236, + 547, + 281 + ], + "spans": [ + { + "bbox": [ + 46, + 236, + 547, + 281 + ], + "type": "text", + "content": "Figure 3. Scaling strategy. In order to scale to very large models, we propose to estimate the bounds of an intermediate layer's activations empirically by (1) Sampling " + }, + { + "bbox": [ + 46, + 236, + 547, + 281 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 236, + 547, + 281 + ], + "type": "text", + "content": " input perturbations and (2) calculating empirical bounds on the resulting activations for the layer " + }, + { + "bbox": [ + 46, + 236, + 547, + 281 + ], + "type": "inline_equation", + "content": "\\pmb{h}(\\cdot)" + }, + { + "bbox": [ + 46, + 236, + 547, + 281 + ], + "type": "text", + "content": ". We can then form the set " + }, + { + "bbox": [ + 46, + 236, + 547, + 281 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_B^x" + }, + { + "bbox": [ + 46, + 236, + 547, + 281 + ], + "type": "text", + "content": " which is a subset of the true bounds " + }, + { + "bbox": [ + 46, + 236, + 547, + 281 + ], + "type": "inline_equation", + "content": "\\mathcal{H}_B^x" + }, + { + "bbox": [ + 46, + 236, + 547, + 281 + ], + "type": "text", + "content": " since the sampling is never exhaustive. We can then plug this set into a verified perturbation analysis method (3) and continue the forward propagation of the inputs through the rest of the network." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 301, + 287, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 301, + 287, + 347 + ], + "spans": [ + { + "bbox": [ + 46, + 301, + 287, + 347 + ], + "type": "text", + "content": "as a composition of functions " + }, + { + "bbox": [ + 46, + 301, + 287, + 347 + ], + "type": "inline_equation", + "content": "f(x) = g \\circ h(x)" + }, + { + "bbox": [ + 46, + 301, + 287, + 347 + ], + "type": "text", + "content": ". For deep neural networks, " + }, + { + "bbox": [ + 46, + 301, + 287, + 347 + ], + "type": "inline_equation", + "content": "h(\\cdot)" + }, + { + "bbox": [ + 46, + 301, + 287, + 347 + ], + "type": "text", + "content": " is a function that maps input to an intermediate feature space and " + }, + { + "bbox": [ + 46, + 301, + 287, + 347 + ], + "type": "inline_equation", + "content": "g(\\cdot)" + }, + { + "bbox": [ + 46, + 301, + 287, + 347 + ], + "type": "text", + "content": " is a function that maps this same feature space to the classification." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 346, + 287, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 346, + 287, + 384 + ], + "spans": [ + { + "bbox": [ + 46, + 346, + 287, + 384 + ], + "type": "text", + "content": "We propose to empirically estimate bounds " + }, + { + "bbox": [ + 46, + 346, + 287, + 384 + ], + "type": "inline_equation", + "content": "(\\underline{h}_{\\mathcal{B}}^x,\\overline{h}_{\\mathcal{B}}^x)" + }, + { + "bbox": [ + 46, + 346, + 287, + 384 + ], + "type": "text", + "content": " for the intermediate activations " + }, + { + "bbox": [ + 46, + 346, + 287, + 384 + ], + "type": "inline_equation", + "content": "h(\\cdot)\\in \\mathbb{R}^{d'}" + }, + { + "bbox": [ + 46, + 346, + 287, + 384 + ], + "type": "text", + "content": " using Monte-Carlo sampling on the perturbation " + }, + { + "bbox": [ + 46, + 346, + 287, + 384 + ], + "type": "inline_equation", + "content": "\\delta \\in \\mathcal{B}" + }, + { + "bbox": [ + 46, + 346, + 287, + 384 + ], + "type": "text", + "content": ". Formally:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 48, + 390, + 282, + 413 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 390, + 282, + 413 + ], + "spans": [ + { + "bbox": [ + 48, + 390, + 282, + 413 + ], + "type": "interline_equation", + "content": "\\forall j \\in [ 0, \\dots , d ^ {\\prime} ], \\underline {{h}} _ {\\mathcal {B}} ^ {\\boldsymbol {x}} [ j ] = \\min _ {\\delta_ {1}, \\dots \\delta_ {i}, \\dots \\delta_ {n} \\stackrel {\\mathrm {i i d}} {\\sim} U (\\mathcal {B})} \\boldsymbol {h} (\\boldsymbol {x} + \\boldsymbol {\\delta} _ {i}) [ j ]", + "image_path": "129f86d5d2304c40806db38efb74597690c4357c5e2a8b176abc7c6cb249d37a.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 120, + 415, + 284, + 440 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 120, + 415, + 284, + 440 + ], + "spans": [ + { + "bbox": [ + 120, + 415, + 284, + 440 + ], + "type": "interline_equation", + "content": "\\overline{\\boldsymbol{h}}_{\\mathcal{B}}^{\\boldsymbol{x}}[j] = \\max_{\\substack{\\boldsymbol{\\delta}_{1},\\ldots \\boldsymbol{\\delta}_{i},\\ldots \\boldsymbol{\\delta}_{n}\\stackrel {\\mathrm{iid}}{\\sim}U(\\mathcal{B})}}\\boldsymbol {h}(\\boldsymbol {x} + \\boldsymbol{\\delta}_{i})[j].", + "image_path": "7a61dc2fd3f6fad22faf4ad4f15234c54c4820d41bef5dfa90203ff4d8e39bfb.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 450, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 450, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 450, + 287, + 544 + ], + "type": "text", + "content": "Obviously, since the sampling is never exhaustive, the bounds obtained underestimate the true maximum " + }, + { + "bbox": [ + 46, + 450, + 287, + 544 + ], + "type": "inline_equation", + "content": "\\overline{h}_{\\mathcal{B}}^x \\leq \\max h(x + \\delta)" + }, + { + "bbox": [ + 46, + 450, + 287, + 544 + ], + "type": "text", + "content": " and overestimates the true minimum " + }, + { + "bbox": [ + 46, + 450, + 287, + 544 + ], + "type": "inline_equation", + "content": "h_{\\mathcal{B}}^x \\geq \\min h(x + \\delta)" + }, + { + "bbox": [ + 46, + 450, + 287, + 544 + ], + "type": "text", + "content": " as illustrated in the Fig. 3. In a similar way, we define " + }, + { + "bbox": [ + 46, + 450, + 287, + 544 + ], + "type": "inline_equation", + "content": "\\underline{h}_{\\mathcal{B}_u}^x" + }, + { + "bbox": [ + 46, + 450, + 287, + 544 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 450, + 287, + 544 + ], + "type": "inline_equation", + "content": "\\overline{h}_{\\mathcal{B}_u}^x" + }, + { + "bbox": [ + 46, + 450, + 287, + 544 + ], + "type": "text", + "content": " when " + }, + { + "bbox": [ + 46, + 450, + 287, + 544 + ], + "type": "inline_equation", + "content": "\\delta \\in \\mathcal{B}_u" + }, + { + "bbox": [ + 46, + 450, + 287, + 544 + ], + "type": "text", + "content": ". Once the empirical bounds are estimated, we may proceed to the second step and use the obtained bounds to form the new perturbation set" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 99, + 542, + 234, + 557 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 99, + 542, + 234, + 557 + ], + "spans": [ + { + "bbox": [ + 99, + 542, + 234, + 557 + ], + "type": "interline_equation", + "content": "\\mathcal {P} _ {\\mathcal {B}} ^ {\\boldsymbol {x}} = [ \\underline {{\\boldsymbol {h}}} _ {\\mathcal {B}} ^ {\\boldsymbol {x}} - \\boldsymbol {h} (\\boldsymbol {x}), \\overline {{\\boldsymbol {h}}} _ {\\mathcal {B}} ^ {\\boldsymbol {x}} - \\boldsymbol {h} (\\boldsymbol {x}) ].", + "image_path": "678d0ed20ac32279bb69e469aecbdd25e4d4e3b81dc3ee2bbbb751966b52322d.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 563, + 287, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 563, + 287, + 598 + ], + "spans": [ + { + "bbox": [ + 46, + 563, + 287, + 598 + ], + "type": "text", + "content": "Intuitively, this set bounds the intermediate activations obtained empirically and can then be fed to a verified perturbation verification method." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 600, + 288, + 695 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 600, + 288, + 695 + ], + "spans": [ + { + "bbox": [ + 46, + 600, + 288, + 695 + ], + "type": "text", + "content": "We then carry out the end of the bounds propagation in the usual way, using verified perturbation analysis. This amounts to computing bounds for the outputs of the network for all possible activations contained in our empirical bounds. The only change is that we no longer operate in the pixel space " + }, + { + "bbox": [ + 46, + 600, + 288, + 695 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 46, + 600, + 288, + 695 + ], + "type": "text", + "content": " with the ball " + }, + { + "bbox": [ + 46, + 600, + 288, + 695 + ], + "type": "inline_equation", + "content": "\\mathcal{B}" + }, + { + "bbox": [ + 46, + 600, + 288, + 695 + ], + "type": "text", + "content": ", but in the activation space " + }, + { + "bbox": [ + 46, + 600, + 288, + 695 + ], + "type": "inline_equation", + "content": "h(\\cdot)" + }, + { + "bbox": [ + 46, + 600, + 288, + 695 + ], + "type": "text", + "content": " with the perturbations set " + }, + { + "bbox": [ + 46, + 600, + 288, + 695 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_{\\mathcal{B}}^{\\pmb{x}}" + }, + { + "bbox": [ + 46, + 600, + 288, + 695 + ], + "type": "text", + "content": ". The importance score of a set of variables " + }, + { + "bbox": [ + 46, + 600, + 288, + 695 + ], + "type": "inline_equation", + "content": "\\pmb{u}" + }, + { + "bbox": [ + 46, + 600, + 288, + 695 + ], + "type": "text", + "content": " is then:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 80, + 700, + 253, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 700, + 253, + 715 + ], + "spans": [ + { + "bbox": [ + 80, + 700, + 253, + 715 + ], + "type": "interline_equation", + "content": "\\operatorname {E V A} _ {\\text {h y b r i d}} (\\boldsymbol {x}, \\boldsymbol {u}, \\mathcal {B}) \\equiv \\operatorname {E V A} (\\boldsymbol {h} (\\boldsymbol {x}), \\boldsymbol {u}, \\mathcal {P} _ {\\mathcal {B}} ^ {\\boldsymbol {x}}).", + "image_path": "5acd6a58a734c917088b6df9b2ac034560f789228b2916113c7829439f8b82e8.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 301, + 546, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 301, + 546, + 350 + ], + "spans": [ + { + "bbox": [ + 305, + 301, + 546, + 350 + ], + "type": "text", + "content": "This hybrid approach allows us to use EVA on state-of-the-art models and thus to benefit from our method while remaining tractable. We believe this extension to be a promising step towards robust explanations on deeper networks." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 366, + 388, + 380 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 366, + 388, + 380 + ], + "spans": [ + { + "bbox": [ + 305, + 366, + 388, + 380 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 388, + 546, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 388, + 546, + 508 + ], + "spans": [ + { + "bbox": [ + 304, + 388, + 546, + 508 + ], + "type": "text", + "content": "To evaluate the benefits and reliability of our explainability method, we performed several experiments on a standard dataset, using a set of common explainability metrics against EVA. In order to test the fidelity of the explanations produced by our method, we compare them to that of 10 other explainability methods using the (1) Deletion, (2) Insertion, and (3) MuFidelity metrics. As it has been shown that these metrics can exhibit biases, we completed the benchmark by adding the (4) Robustness-" + }, + { + "bbox": [ + 304, + 388, + 546, + 508 + ], + "type": "inline_equation", + "content": "\\mathrm{S_r}" + }, + { + "bbox": [ + 304, + 388, + 546, + 508 + ], + "type": "text", + "content": " metric. Each score is averaged over 500 samples." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 510, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 547, + 713 + ], + "type": "text", + "content": "We evaluated these 4 metrics on 3 image classification datasets, namely MNIST [41], CIFAR-10 [39] and ImageNet [13]. Through these experiments, the explanations were generated using EVA estimator introduced in Equation 2. The importance scores were not evaluated pixelwise but on each cell of the image after having cut it into a grid of 12 sides (see Fig. 2). For MNIST and Cifar-10, we used " + }, + { + "bbox": [ + 304, + 510, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\varepsilon = 0.5" + }, + { + "bbox": [ + 304, + 510, + 547, + 713 + ], + "type": "text", + "content": ", whereas for ImageNet " + }, + { + "bbox": [ + 304, + 510, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\varepsilon = 5" + }, + { + "bbox": [ + 304, + 510, + 547, + 713 + ], + "type": "text", + "content": ". Concerning the verified perturbation analysis method, we used (IBP+Forward+Backward) for MNIST, and (IBP+Forward) on Cifar-10 and " + }, + { + "bbox": [ + 304, + 510, + 547, + 713 + ], + "type": "inline_equation", + "content": "p = \\infty" + }, + { + "bbox": [ + 304, + 510, + 547, + 713 + ], + "type": "text", + "content": ". For computational purposes, we used the hybrid approach to introduce in Section 3.4 for ImageNet using the penultimate layer (FC-4096) as the intermediate layer " + }, + { + "bbox": [ + 304, + 510, + 547, + 713 + ], + "type": "inline_equation", + "content": "h(\\cdot)" + }, + { + "bbox": [ + 304, + 510, + 547, + 713 + ], + "type": "text", + "content": ". We give in Appendix the complete set of hyperparameters used for the other explainability methods, metrics considered as well as the architecture of the models used on MNIST and Cifar-10." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "16158" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 60, + 70, + 545, + 228 + ], + "blocks": [ + { + "bbox": [ + 60, + 70, + 545, + 228 + ], + "lines": [ + { + "bbox": [ + 60, + 70, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 60, + 70, + 545, + 228 + ], + "type": "table", + "html": "
MNISTCifar-10ImageNet
Del.↓Ins.↑Fid.↑Rob.↓TimeDel.↓Ins.↑Fid.↑Rob.↓TimeDel.↓Ins.↑Fid.↑Rob.↓Time
Saliency [56].193.633.378.0710.04.171.172-.021.0260.16.057.126.035.7690.36
GradInput [3].222.611.107.0740.04.200.143-.018.0950.17.057.050.023.8140.36
SmoothGrad [61].185.621.331.0701.91.174.181.092.0489.07.051.069.019.8099.63
VarGrad [54].207.555.216.0771.76.183.211-.012.1939.07.098.201.021.7879.62
InteGrad [65].209.615.108.0741.77.194.171-.016.1547.19.058.052.023.8138.39
Occlusion [3].247.545.137.0820.04.217.290.105.2321.13.100.266.026.8214.97
GradCAM [53]n/an/an/an/an/a.297.282.056.1950.39.073.232.036.8170.18
GradCAM++ [10]n/an/an/an/an/a.270.326.102.0940.39.074.285.054.8000.19
RISE [48].248.558.133.0932.26.196.273.157.38520.5.074.276.154.8181215
Greedy-AS [29].260.497.110.061335.205.264-.003.0134618.088.047.023.612180056
EVA (ours).089.736.428.0691.29.164.290.352.02512.7.070.289.048.7586454
", + "image_path": "9d014b5b0b05905ce450dc7abd2f48fc2a596fa867a3252acde0dbc9f7543ee1.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 244, + 548, + 313 + ], + "lines": [ + { + "bbox": [ + 46, + 244, + 548, + 313 + ], + "spans": [ + { + "bbox": [ + 46, + 244, + 548, + 313 + ], + "type": "text", + "content": "Table 1. Results on Deletion (Del.), Insertion (Ins.), " + }, + { + "bbox": [ + 46, + 244, + 548, + 313 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 46, + 244, + 548, + 313 + ], + "type": "text", + "content": "Fidelity (Fid.) and Robustness-" + }, + { + "bbox": [ + 46, + 244, + 548, + 313 + ], + "type": "inline_equation", + "content": "S_{\\mathrm{r}}" + }, + { + "bbox": [ + 46, + 244, + 548, + 313 + ], + "type": "text", + "content": " (Rob.) metrics. Time in seconds corresponds to the generation of 500 (MNIST/CIFAR-10) and 100 (ImageNet) explanations on an Nvidia P100. Note that EVA is the only method with guarantees that the entire set of possible perturbations has been exhaustively searched. Verified perturbation analysis with IBP + Forward + Backward is used for MNIST, with Forward only for CIFAR-10 and with our hybrid strategy described in Section3.4 for ImageNet. Grad-CAM and Grad-CAM++ are not calculated on the MNIST dataset since the network only has dense layers. The first and second best results are in bold and underlined, respectively." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 323, + 241, + 336 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 323, + 241, + 336 + ], + "spans": [ + { + "bbox": [ + 47, + 323, + 241, + 336 + ], + "type": "text", + "content": "4.1. Comparison with the state of the art" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 342, + 288, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 342, + 288, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 342, + 288, + 544 + ], + "type": "text", + "content": "There is a general consensus that fidelity is a crucial criterion for an explanation method. That is, if an explanation is used to make a critical decision, then users are expecting it to reflect the true decision-making process underlying the model and not just a consensus with humans. Failure to do so could have disastrous consequences. Pragmatically, these metrics assume that the more faithful an explanation is, the faster the prediction score should drop when pixels considered important are changed. In Table 1, we present the results of the Deletion [48] (or " + }, + { + "bbox": [ + 46, + 342, + 288, + 544 + ], + "type": "inline_equation", + "content": "1 - AOPC" + }, + { + "bbox": [ + 46, + 342, + 288, + 544 + ], + "type": "text", + "content": " [52]) metric for the MNIST and Cifar-10 datasets on 500 images sampled from the test set. TensorFlow [1] and the Keras API [11] were used to run the models and Xplique [18] for the explainability methods. In order to evaluate the methods, the metrics require a baseline and several were proposed [29,64], but we chose to keep the choice of [29] using their random baseline." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 545, + 287, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 287, + 664 + ], + "type": "text", + "content": "We observe that EVA is the explainability method getting the best Deletion, Insertion, and " + }, + { + "bbox": [ + 46, + 545, + 287, + 664 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 46, + 545, + 287, + 664 + ], + "type": "text", + "content": " Fidelity scores on MNIST, and is just behind Greedy-AS on Robustness-" + }, + { + "bbox": [ + 46, + 545, + 287, + 664 + ], + "type": "inline_equation", + "content": "S_{\\mathrm{r}}" + }, + { + "bbox": [ + 46, + 545, + 287, + 664 + ], + "type": "text", + "content": ". This can be explained by the fact that the Robustness metric uses the adversarial attack PGD [44], which is the same one used to generate Greedy-AS, thus biasing the adversarial search. Indeed, if PGD does not find an adversarial perturbation using a subset " + }, + { + "bbox": [ + 46, + 545, + 287, + 664 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 46, + 545, + 287, + 664 + ], + "type": "text", + "content": " does not give a guarantee of the robustness of the model, just that the adversarial perturbation could be difficult to reach with PGD." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": "For Cifar-10, EVA remains overall the most faithful method according to Deletion and " + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": " Fidelity, and obtains the second score in Insertion behind Grad-Cam++ [10]. Finally, we notice that if Greedy-AS [29] allows us to ob" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 323, + 547, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 323, + 547, + 384 + ], + "spans": [ + { + "bbox": [ + 304, + 323, + 547, + 384 + ], + "type": "text", + "content": "tain a good Robustness-" + }, + { + "bbox": [ + 304, + 323, + 547, + 384 + ], + "type": "inline_equation", + "content": "S_r" + }, + { + "bbox": [ + 304, + 323, + 547, + 384 + ], + "type": "text", + "content": " score, but this comes with a considerable computation time, which is not the case of EVA which is much more efficient. Eventually, EVA is a very good compromise for its relevance to commonly accepted explainability metrics and more recent robustness metrics." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 388, + 547, + 497 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 388, + 547, + 497 + ], + "spans": [ + { + "bbox": [ + 304, + 388, + 547, + 497 + ], + "type": "text", + "content": "ImageNet After having demonstrated the potential of the method on vision datasets of limited size, we consider the case of ImageNet which has a significantly higher level of dimension. The use of verified perturbation analysis methods other than IBP is not easily scalable on these datasets. We, therefore, used the hybrid method introduced in Section 3.4 in order to estimate the bounds in a latent space and then plug those bounds into the perturbation analysis to get the final adversarial overlap score." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 497, + 548, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 497, + 548, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 497, + 548, + 628 + ], + "type": "text", + "content": "Table 1 shows the results obtained with the empirical method proposed in Section 3.4. We observe that even with this relaxed estimation, EVA is able to score high on all the metrics. Indeed, EVA obtains the best score on the Insertion metric and ranks second on " + }, + { + "bbox": [ + 304, + 497, + 548, + 628 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 304, + 497, + 548, + 628 + ], + "type": "text", + "content": " Fidelity and Robustness-" + }, + { + "bbox": [ + 304, + 497, + 548, + 628 + ], + "type": "inline_equation", + "content": "S_{\\mathrm{r}}" + }, + { + "bbox": [ + 304, + 497, + 548, + 628 + ], + "type": "text", + "content": ". Greedy-AS ranks first on Robustness-" + }, + { + "bbox": [ + 304, + 497, + 548, + 628 + ], + "type": "inline_equation", + "content": "S_{\\mathrm{r}}" + }, + { + "bbox": [ + 304, + 497, + 548, + 628 + ], + "type": "text", + "content": " at the expense of the other scores where it performs poorly. Finally, both RISE and SmoothGrad perform well on all the fidelity metrics but collapse on the robustness metric. Extending results with ablations of EVA, including Greedy-AO, are available in Table 3." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 628, + 547, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 628, + 547, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 628, + 547, + 689 + ], + "type": "text", + "content": "Qualitatively, Fig. 5 shows examples of explanations produced on the ImageNet VGG-16 model. The explanations produced by EVA are more localized than Grad-CAM or RISE, while being less noisy than the gradient-based or Greedy-AS methods." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 689, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 547, + 715 + ], + "type": "text", + "content": "In addition, as the literature on verified perturbation analysis is evolving rapidly we can conjecture that the advances" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "16159" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "content": "will benefit the proposed explainability method. Indeed, EVA proved to be the most effective on the benchmark when an accurate formal method was used. After demonstrating the performance of the proposed method, we study its ability to generate class explanations specific." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 139, + 285, + 152 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 139, + 285, + 152 + ], + "spans": [ + { + "bbox": [ + 47, + 139, + 285, + 152 + ], + "type": "text", + "content": "4.2. Tighter bounds lead to improved explanations" + } + ] + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 60, + 164, + 277, + 231 + ], + "blocks": [ + { + "bbox": [ + 60, + 164, + 277, + 231 + ], + "lines": [ + { + "bbox": [ + 60, + 164, + 277, + 231 + ], + "spans": [ + { + "bbox": [ + 60, + 164, + 277, + 231 + ], + "type": "table", + "html": "
Tightness↓Del.↓Ins.↑Fid.↑Rob.↓
IBP4.58.148.588.222.077
Forward2.66.150.580.209.078
Backward2.36.115.607.274.074
IBP + Fo. + Ba.1.55.089.736.428.069
", + "image_path": "9d579bd25bd184336a8ba2cd7456bc4c391026519c414482d2d75894fda89b2e.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 239, + 286, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 239, + 286, + 327 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 286, + 327 + ], + "type": "text", + "content": "Table 2. Impact of the verified perturbation analysis method on EVA. Results of EVAon Tightness, Deletion (Del.), Insertion (Ins.), Fidelity (Fid.) and Robustness- " + }, + { + "bbox": [ + 46, + 239, + 286, + 327 + ], + "type": "inline_equation", + "content": "S_{\\mathrm{r}}" + }, + { + "bbox": [ + 46, + 239, + 286, + 327 + ], + "type": "text", + "content": " (Rob.) metrics obtained on MNIST. The Tightness score corresponds to the average adversarial surface. A lower Tightness score indicates that the method is more precise: it reaches tighter bound, resulting in better explanations and superior scores on the other metrics. The first and second best results are respectively in bold and underlined." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 328, + 286, + 580 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 328, + 286, + 580 + ], + "spans": [ + { + "bbox": [ + 46, + 328, + 286, + 580 + ], + "type": "text", + "content": "The choice of the verified perturbation analysis method is a hyperparameter of EVA. Hence, it is interesting to see the effect of the choice of this hyperparameter on the previous benchmark. We recall that only the MNIST dataset could benefit from the (IBP+Forward+Backward) combo. Table 2 reports the results of the fidelity metrics using other verified perturbation analysis methods. We also report a tightness score which corresponds to the average of the adversarial overlap: " + }, + { + "bbox": [ + 46, + 328, + 286, + 580 + ], + "type": "inline_equation", + "content": "\\mathbb{E}_{\\boldsymbol{x} \\sim \\mathcal{X}}(\\overline{AO}(\\boldsymbol{x}, \\mathcal{B}))" + }, + { + "bbox": [ + 46, + 328, + 286, + 580 + ], + "type": "text", + "content": ". Specifically, a low score indicates that the verification method is precise, meaning that the over-approximation is closer to the actual value. It should be noted that the true value is intractable, but remains the same across all three tested cases. We observe that the tighter the bounds, the higher the scores. This allows us to conjecture that the more scalable the formal methods will become, the better the quality of the generated explanations will be. We perform additional experiments to ensure that the certified component of EVA score is significant by comparing EVA to a sampling-based version of EVA. The details of these experiments are available in Appendix B." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 587, + 176, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 587, + 176, + 601 + ], + "spans": [ + { + "bbox": [ + 47, + 587, + 176, + 601 + ], + "type": "text", + "content": "4.3. Targeted Explanations" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "text", + "content": "In some cases, it is instructive to look at the explanations for unpredicted classes in order to get information about the internal mechanisms of the models studied. Such explanations allow us to highlight contrastive features: elements that should be changed or whose absence is critical. Our method allows us to obtain such explanations: for a given input, we are then exclusively interested in the class we are trying to explain, without looking at the other decisions. Formally, for a given tar" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 307, + 70, + 356, + 118 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 356, + 118 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 356, + 118 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 356, + 118 + ], + "type": "image", + "image_path": "1808d15479652d969fafca461f6ba04d6439efdc8e09c20613781320dc70413a.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 328, + 121, + 335, + 131 + ], + "lines": [ + { + "bbox": [ + 328, + 121, + 335, + 131 + ], + "spans": [ + { + "bbox": [ + 328, + 121, + 335, + 131 + ], + "type": "text", + "content": "9" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 365, + 71, + 414, + 118 + ], + "blocks": [ + { + "bbox": [ + 365, + 71, + 414, + 118 + ], + "lines": [ + { + "bbox": [ + 365, + 71, + 414, + 118 + ], + "spans": [ + { + "bbox": [ + 365, + 71, + 414, + 118 + ], + "type": "image", + "image_path": "4efdad90b7e6955cb77c898687b0fc1da94c4701e0cbed95d92ef861b04d958a.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 386, + 121, + 394, + 131 + ], + "lines": [ + { + "bbox": [ + 386, + 121, + 394, + 131 + ], + "spans": [ + { + "bbox": [ + 386, + 121, + 394, + 131 + ], + "type": "text", + "content": "3" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 425, + 70, + 473, + 118 + ], + "blocks": [ + { + "bbox": [ + 425, + 70, + 473, + 118 + ], + "lines": [ + { + "bbox": [ + 425, + 70, + 473, + 118 + ], + "spans": [ + { + "bbox": [ + 425, + 70, + 473, + 118 + ], + "type": "image", + "image_path": "ceef5c2e90890e093aaa45dc27668a52f6e03110c4267edd747100917c8e138b.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 445, + 121, + 452, + 131 + ], + "lines": [ + { + "bbox": [ + 445, + 121, + 452, + 131 + ], + "spans": [ + { + "bbox": [ + 445, + 121, + 452, + 131 + ], + "type": "text", + "content": "8" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 304, + 134, + 545, + 212 + ], + "lines": [ + { + "bbox": [ + 304, + 134, + 545, + 212 + ], + "spans": [ + { + "bbox": [ + 304, + 134, + 545, + 212 + ], + "type": "text", + "content": "Figure 4. Targeted explanations. Generated explanations for a decision other than the one predicted by the model. The class explained is indicated at the bottom of each sample, e.g., the first sample is a '4' and the explanation is for the class '9'. As indicated in section 4.3, the red areas indicate that a black line should be added and the blue areas that it should be removed. More examples are available in the Appendix." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 484, + 70, + 531, + 118 + ], + "blocks": [ + { + "bbox": [ + 484, + 70, + 531, + 118 + ], + "lines": [ + { + "bbox": [ + 484, + 70, + 531, + 118 + ], + "spans": [ + { + "bbox": [ + 484, + 70, + 531, + 118 + ], + "type": "image", + "image_path": "3bb55b5e2a3f873fdc33740a355c098fa0d6330baaa1d1d77ad63913b93866fa.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 504, + 121, + 512, + 131 + ], + "lines": [ + { + "bbox": [ + 504, + 121, + 512, + 131 + ], + "spans": [ + { + "bbox": [ + 504, + 121, + 512, + 131 + ], + "type": "text", + "content": "8" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 221, + 545, + 317 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 221, + 545, + 317 + ], + "spans": [ + { + "bbox": [ + 304, + 221, + 545, + 317 + ], + "type": "text", + "content": "geted class " + }, + { + "bbox": [ + 304, + 221, + 545, + 317 + ], + "type": "inline_equation", + "content": "c'" + }, + { + "bbox": [ + 304, + 221, + 545, + 317 + ], + "type": "text", + "content": " the adversarial overlap (Equation 1) become " + }, + { + "bbox": [ + 304, + 221, + 545, + 317 + ], + "type": "inline_equation", + "content": "AO(\\pmb{x},\\mathcal{B}) = \\max_{\\delta \\in \\mathcal{B}}\\pmb{f}_{c'}(\\pmb{x} + \\delta) - \\pmb{f}_c(\\pmb{x} + \\delta)" + }, + { + "bbox": [ + 304, + 221, + 545, + 317 + ], + "type": "text", + "content": ". Moreover, by splitting the perturbation ball into a positive one " + }, + { + "bbox": [ + 304, + 221, + 545, + 317 + ], + "type": "inline_equation", + "content": "\\mathcal{B}^{(+)} = \\{\\pmb{\\delta}\\in \\mathcal{B}:\\pmb{\\delta}_i\\geq 0,\\forall i\\in \\{1,\\dots,d\\}\\}" + }, + { + "bbox": [ + 304, + 221, + 545, + 317 + ], + "type": "text", + "content": " and a negative one " + }, + { + "bbox": [ + 304, + 221, + 545, + 317 + ], + "type": "inline_equation", + "content": "\\mathcal{B}^{(-)} = \\{\\pmb {\\delta}\\in \\mathcal{B}:\\pmb {\\delta}_i\\leq 0,\\forall i\\in \\{1,\\dots,d\\}\\}" + }, + { + "bbox": [ + 304, + 221, + 545, + 317 + ], + "type": "text", + "content": ", one can deduce which direction - adding or removing the black line in the case of gray-scaled images - will impact the most the model decision." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 319, + 545, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 319, + 545, + 510 + ], + "spans": [ + { + "bbox": [ + 304, + 319, + 545, + 510 + ], + "type": "text", + "content": "We generate targeted explanations on the MNIST dataset using (IBP+Forward+Backward). For several inputs, we generate the explanation for the 10 classes. Fig. 7 shows 4 examples of targeted explanations, the target class " + }, + { + "bbox": [ + 304, + 319, + 545, + 510 + ], + "type": "inline_equation", + "content": "c'" + }, + { + "bbox": [ + 304, + 319, + 545, + 510 + ], + "type": "text", + "content": " is indicated at the bottom. The red areas indicate that adding a black line increases the adversarial overlap with the target class. Conversely, the blue areas indicate where the increase of the score requires removing black lines. All other results can be found in the Appendix. In addition to favorable results on the fidelity metrics and guarantees provided by the verification methods, EVA can provide targeted explanations that are easily understandable by humans, which are two qualities that make them a candidate of choice to meet the recent General Data Protection Regulation (GDPR) adopted in Europe [35]. More examples are available in the Appendix H." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 515, + 378, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 515, + 378, + 528 + ], + "spans": [ + { + "bbox": [ + 306, + 515, + 378, + 528 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 535, + 545, + 642 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 535, + 545, + 642 + ], + "spans": [ + { + "bbox": [ + 304, + 535, + 545, + 642 + ], + "type": "text", + "content": "In this work, we presented the first explainability method that uses verification perturbation analysis that exhaustively explores the perturbation space to generate explanations. We presented an efficient estimator that yields explanations that are state-of-the-art on current metrics. We also described a simple strategy to scale up perturbation verification methods to complex models. Finally, we showed that this estimator can be used to form easily interpretable targeted explanations." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 643, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 643, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 643, + 545, + 689 + ], + "type": "text", + "content": "We hope that this work will for searching for safer and more efficient explanation methods for neural networks – and that it will inspire further synergies with the field of formal verification." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16160" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 715 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 232 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 232 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 232 + ], + "type": "text", + "content": "[1] Martin Abadi, Ashish Agarwal, Paul Barham, Eugene Brevdo, Zhifeng Chen, Craig Citro, Greg S. 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In this paper, we investigate whether computer vision models can also provide correct rationales for their predictions. We propose a \"doubly right\" object recognition benchmark, where the metric requires the model to simultaneously produce both the right labels as well as the right rationales. We find that state-of-the-art visual models, such as CLIP, often provide incorrect rationales for their categorical predictions. However, by transferring the rationales from language models into visual representations through a tailored dataset, we show that we can learn a \"why prompt,\" which adapts large visual representations to produce correct rationales. Visualizations and empirical experiments show that our prompts significantly improve performance on doubly right object recognition, in addition to zero-shot transfer to unseen tasks and datasets.", + "bbox": [ + 73, + 316, + 473, + 575 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 603, + 207, + 618 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Computer vision models today are able to achieve high accuracy – sometimes super-human – at correctly recognizing objects in images. However, most models today are not evaluated on whether they get the prediction right for the right reasons [14, 19, 48, 53]. Learning models that can explain their own decision is important for building trustworthy systems, especially in applications that require human-machine interactions [2, 15, 37, 50]. Rationales that justify the prediction can largely improve user trust [54], which is a crucial metric that the visual recognition field should push forward in the future.", + "bbox": [ + 75, + 628, + 468, + 792 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Existing methods in interpretability have investigated how to understand which features contribute to the models' prediction [33, 34, 44, 46, 47, 52, 60]. However, saliency explanations are often imprecise, require domain expertise to understand, and also cannot be evaluated. [20, 22] have instead explored verbal rationales to justify the decision-making. However, they require manual collections of the", + "bbox": [ + 75, + 795, + 470, + 901 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/7b9867f4f63f610f8d0921009fa765c556696293e74fddec536488d03308bd09.jpg", + "image_caption": [ + "Figure 1. Visual reasoning for doubly right object recognition task. Motivated by prompting in NLP, we learn a why prompt from multimodal data, which allows us to instruct visual models to predict both the right category and the correct rationales that justify the prediction." + ], + "image_footnote": [], + "bbox": [ + 514, + 268, + 874, + 406 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "plausible rationales in the first place, which subsequently are limited to small-scale datasets and tasks [24, 56].", + "bbox": [ + 498, + 503, + 890, + 532 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Scalable methods for explainability have been developed in natural language processing (NLP) through prompting. By adding additional instructions to the input, such as the sentence \"think step-by-step,\" language models then output descriptions of their reasoning through the chain of thought process [57]. Since the explanations are verbal, they are easily understandable by people, and since the mechanism emerges without explicit supervision, it is highly scalable. In this paper, we investigate whether visual representations can also explain their reasoning through visual chain-of-thought prompts.", + "bbox": [ + 496, + 536, + 890, + 700 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Our paper first introduces a benchmark for doubly right object recognition, where computer vision models must predict both correct categorical labels as well as correct rationales. Our benchmark is large, and covers many categories and datasets. We found that the visual representations do not have double right capability out-of-the-box on our benchmark. The recent large-scale image-language pretrained models [41, 49] can retrieve open-world language descriptions that are closest to the image embedding in the feature space, serving as verbal explanations. However, the models often select the wrong rationales.", + "bbox": [ + 496, + 703, + 890, + 868 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Instead, we propose a framework to explicitly transfer the chain-of-thought reasoning from NLP models into", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "2722", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "vision models. We first query the large-scale language model [9] via the chain-of-thought reasoning for object category, where we obtain language rationales that explain discriminative features for an object. We then collect images containing both the category and the rationale features using Google image search. We then train visual prompts to transfer the verbal chain of thought to visual chain of thought with contrastive learning, where features of images and their rationales are pulled together. Our \"why\" prompts obtain up to 26 points gain at doubly right performance when evaluated on our benchmark. In addition, visualizations and quantitative results show that our why prompts zero-shot transfer to unseen tasks and datasets. We believe this \"doubly right\" object recognition task is a future direction which the visual recognition field should go forward for. Our data and code is available at https://github.com/cvlab-columbia/DoubleRight.", + "bbox": [ + 80, + 90, + 467, + 345 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 80, + 361, + 215, + 376 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Explainability. Visual recognition models achieve high performance on the classification tasks, yet they often provide vague and unreliable interpretations and rationales [8]. There are two lines of research for interpreting image classification using neural networks: feature visualization and language explanation. Feature visualization methods [6, 32-34] find the inputs that maximize the outputs of learned features. Gradient-based feature visualization [28, 42, 44, 46, 47, 52, 60] highlight the input features/pixels in images that are most important for the network to make decisions. Since the visualizations are often abstract, it is hard for a non-expert to understand. In addition, saliency map [44] highlights regions that may contain overlapping concepts such as color, texture, and shape, which is hard to disentangle. The second line of research uses language-based explanation methods [20, 22] to generate visual explanations. However, those methods require human annotations, which limits their ability to evaluate on a larger scale.", + "bbox": [ + 80, + 386, + 467, + 672 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "External Knowledge. Visual models often learn spurious correlations without external knowledge [29]. External knowledge allows models to learn the right features and obtain better transferability [26, 45]. Large-scale pretrained language models, such as GPT-3 [9], contains knowledge and commonsense learned from the Internet [38]. [57] shows that designing the right prompt, such as the chain of thought, improves the model's ability for language reasoning, which we leverage as an external knowledge source. Other sources of external knowledge include interactions [1, 11, 55], physics [31, 59], etc. [30] provides descriptions together with the objective category, which improves recognition performance. However, since they do not annotate rationales in their approach, they cannot measure CLIP's ability to produce the right rationales.", + "bbox": [ + 80, + 674, + 467, + 898 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Visual Attributes Several works have studied visual attributes in images [17,25,27,35,36,39,63]. [58] used the visual attributes for animal classification and [23] used them for face verification. However, some of the attributes are spurious correlated [51] with the prediction task. In this work, we aim to generate visual rationales that produce robust visual attributes like shape and parts, instead of spurious features such as the background.", + "bbox": [ + 503, + 90, + 888, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Visual Reasoning. [61] proposed a new cognition benchmark that the model needs to predict both the answer and the rationale to be correct. Visual Question Answering [3] performs visual understanding as a QA task, such as questions about COCO images. However, the questions are not asking for rationales to justify object recognition. [62] shows that multi-modal vision language models can perform zero-shot image-language tasks, such as image captioning. However, all existing visual reasoning work does not directly evaluate object recognition on the rationales they provided.", + "bbox": [ + 503, + 213, + 888, + 364 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Prompting. Prompt tuning is a lightweight adaptation method for language task [64-66]. Recently, the computer vision field has adapted the language and proposed the visual prompts to adapt vision models [4, 5, 21, 43]. Due to their lightweight, it has been shown effective for continuous learning [12]. One advantage of the visual prompt is that it does not require model access at test time, which is flexible [4]. While existing visual prompt methods focus on improving the recognition task performance, we propose to use this lightweight prompt to improve the models' ability to provide visual rationales.", + "bbox": [ + 503, + 364, + 888, + 530 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Language Rationales to Visual Rationales", + "text_level": 1, + "bbox": [ + 503, + 549, + 869, + 565 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We first introduce how to obtain the language rationales for discriminating an object. We then show how we translate the language descriptions into visual images and construct the dataset. We then propose to construct a \"why prompt\" to adapt the large visual models to produce the right rationales for their predictions.", + "bbox": [ + 503, + 575, + 888, + 665 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3.1. Rationale from Language Model", + "text_level": 1, + "bbox": [ + 503, + 680, + 784, + 695 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "A standard way of getting visual rationales for image predictions is through manual annotation. However, manual annotation is expensive, especially when applied to large-scale datasets. Recent advances in large-scale language models, such as the GPT3, demonstrate the ability to provide various commonsense knowledge in language. By providing chain-of-thought instructions to the language model, [57] shows that language models can perform the task of interest as well as produce explanations. We can use large-scale language models as a tool to collect rationales by asking the right language prompts. In addition, since the rationales are presented in language, it is easy to understand, even for non-experts.", + "bbox": [ + 503, + 704, + 888, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "2723", + "bbox": [ + 483, + 946, + 513, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/71c2cddc1c083ed7df2421914f3a98118ce57f9700e3acd970cddec84c19541e.jpg", + "image_caption": [ + "Figure 2. Examples of the rationales generated by prompting GPT3 with the chain of thought reasoning on the features of objects. We show one example from each of the six datasets—CIFAR10, CIFAR100, Food101, Caltech101, SUN, and ImageNet—we studied. The bold word is the category, and the list follows is the generated rationales. GPT3 can produce reasoning for why an object is as predicted." + ], + "image_footnote": [], + "bbox": [ + 83, + 90, + 883, + 150 + ], + "page_idx": 2 + }, + { + "type": "table", + "img_path": "images/f2fd7dcde204093ec2758cda6b82368102fe60e6e2929698939e9ba7f5155c2d.jpg", + "table_caption": [ + "Table 1. List of datasets that include both the model prediction and rationales. Animals with attributes (AWA) collects discriminative attributes for animals. CUB collects verbal rationales on only birds. BDD-X collects rationales for explaining driving scenarios. VAW and Broaden collect a large number of attributes. However, they are often not the right rationales for explaining why objects are classified, such as color. The * indicates the number of annotated video frames. The existing datasets are often small-scale, limited in domains, and not annotating rationales for the object recognition task. Our framework allows the automatic collection of diversified categories over a large scale. Note that the $^+$ name in our dataset, such as CIFAR- $10^{+}$ , indicates that we collect the same set of categories in CIFAR-10 from google with our pipeline. Our benchmark is large, containing more categories and dataset variants than prior methods." + ], + "table_footnote": [], + "table_body": "
Dataset NameNumber of CategoriesNumber of DescriptionsNumber of ImagesFor Right Rationales
AWA [24]508530,475Yes
CUB [20,56]200N/A11,788Yes
BDD-X [22]9061,66826,000*Yes
VAW [40]N/A65072,274No
Broaden [7]5841,30062,476No
Ours CIFAR-10+10632,201Yes
Ours CIFAR-100+10054018,318Yes
Ours Food101+10143515,212Yes
Ours Caltech101+10151616,849Yes
Ours SUN+3972,17075,381Yes
Ours ImageNet+10005,810271,016Yes
", + "bbox": [ + 78, + 426, + 473, + 588 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Motivated by the recent work in language prompting [9, 30], we propose to ask the language model: what are the valid rationales for an object prediction? Specifically, to obtain rationales for visual objects, we ask GPT3 the following question:", + "bbox": [ + 75, + 614, + 468, + 691 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "Q: What are useful visual features for distinguishing a {category name} in a photo?", + "A: There are several useful visual features to tell there is a {category name} in a photo:" + ], + "bbox": [ + 76, + 700, + 439, + 785 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where GPT3 automatically generates the answer for us, which scales to large, unseen categories. In Figure 2, we show random examples of the rationales generated by querying GPT3. Each category is provided with a list of discriminative features for the category, which is consistent with how people explain their predictions.", + "bbox": [ + 75, + 809, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/17db92a069c2437730cc42cac4a5360c6eddc5978ca1e74e3d72cf9bdf1d3728.jpg", + "image_caption": [ + "Figure 3. Histogram of the number of images per ImageNet category retrieved by Google search. There are natural imbalances in the data. Learning model under such imbalanced natural data distribution is an interesting problem to study." + ], + "image_footnote": [], + "bbox": [ + 513, + 208, + 880, + 356 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Knowledge Transfer to Visual Domain", + "text_level": 1, + "bbox": [ + 500, + 431, + 830, + 449 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Since not every rationale exists in every image of the given object, we cannot directly apply this list of rationales to images based on their category. We need external knowledge to collect images containing specified rationales, so that we can correspond the language rationales to the visual rationals in images. Prior work [45] uses structured external knowledge from Wiktionary and WordNet to obtain images with text descriptions.", + "bbox": [ + 496, + 455, + 890, + 575 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the era of the Internet, people often Google a new word if they don't know what the object — the word refers to — looks like. Once people see the image examples from Google, they quickly understand what the word refers to in the real world. Our method is motivated by this natural procedure, where our system Googles \"what the rationales look like\" to visually understand them.", + "bbox": [ + 496, + 578, + 890, + 683 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We propose to leverage this external knowledge from web search engines, a larger-scale knowledge base than Wiktionary [45]. We use Google image search to obtain images that contain our specified visual features, and we find that the returned images match the language queries with high accuracy. The search engine serves as a cross-modal translator, translating the knowledge from the language domain to the visual domain by retrieving images.", + "bbox": [ + 496, + 684, + 890, + 805 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We use the following queries to query images that belong to our specified category and contain our specified attribute:", + "bbox": [ + 496, + 806, + 890, + 837 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. {category name} which has {attribute name}", + "2. {attribute name} of {category name}", + "3. a photo of {category name} because" + ], + "bbox": [ + 500, + 845, + 846, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "2724", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/08f662d5a1cc47dc7a81c1b8e5d31a3365f20f3723ccbc08666e9168be7d11cb.jpg", + "image_caption": [ + "Figure 4. Examples for the images in our collected ImageNet $^+$ dataset, where each image corresponds to one category label and one rationale. We show three random categories, and for each category, we show three random rationales. The rationales are consistent with the image features that decide the object's category." + ], + "image_footnote": [], + "bbox": [ + 84, + 89, + 885, + 260 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "there is {attribute name}", + "text_level": 1, + "bbox": [ + 109, + 321, + 331, + 335 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "and we retrieve the top 50 images returned by Google search. More query sentences can be constructed if more images are needed, which we leave for future work. We remove the duplicated and incorrect images in preprocessing.", + "bbox": [ + 75, + 347, + 468, + 407 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Google image search allows us to obtain images containing specific attributes. We perform the above automatic pipeline on ImageNet categories and obtain a dataset that contains images and the rationales that explain why this image is a particular category. For the dataset collected with our framework, we show a histogram of the number of images per ImageNet category in Figure 3. The data is S-curved due to the natural, non-interventional collection procedure. We also show examples of rationales and the retrieved images in Figure 4, where images can often be explained by rationales. Since our system is automatic, we in addition run our pipeline on the categories in CIFAR-10, CIFAR-100, Food101, Caltech101, and SUN datasets. Table 1 shows the scale of our collected images and compares them with prior datasets that are related to our work. Our pipeline allows richer rationales and is more extensive in the number of images and categories. To evaluate how accurate the Google image search can retrieve the images with the specified attribute as well as the category, we conduct a human study on the quality and consistency, which we describe in Section 4.4.", + "bbox": [ + 75, + 409, + 473, + 726 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Learning the Why Prompt", + "text_level": 1, + "bbox": [ + 76, + 738, + 316, + 755 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Using external knowledge from both the language model and Google, we show we can collect image datasets containing both the category and rationales. Our pipeline allows us to evaluate the quality of this doubly right task on a large scale over several datasets for the first time. Our results show that doubly right object recognition is a challenging task for large visual models, such as CLIP.", + "bbox": [ + 75, + 763, + 468, + 868 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We then seek a way to adapt and improve large pretrained models so that they can provide the correct rationale", + "bbox": [ + 76, + 869, + 470, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "for the predictions. Motivated by the prompting in natural language processing, we propose constructing a visual \"why\" prompt that instructs the model to produce the right rationales for the prediction. We optimize the visual prompt to ask \"what are the visual rationales that explains the prediction of this image\". We use the following input prompts or deep prompts to adapt the model.", + "bbox": [ + 496, + 321, + 890, + 426 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Prompt Design. We study how to adapt transformer-based models since they are state-of-the-art. Our visual why prompts append additional tokens $P_{k}$ to the input sequence of the vision transformer:", + "bbox": [ + 496, + 426, + 890, + 486 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} = \\left[ \\mathbf {x}; P _ {0}, P _ {1}, \\dots , P _ {k} \\right] \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 617, + 500, + 890, + 515 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The remaining transformer parameters and computations are kept the same as the original.", + "bbox": [ + 496, + 526, + 890, + 556 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Deep prompt. Besides adding context to the input sequence, the deep prompting method [21] adds prompts to the intermediate layers in the transformer, which is a more powerful adaptation method than single-layer input prompt. Let $\\mathbf{x}_i$ be the latent token sequence of the $i$ -th layer in the transformer. We can add a prompt to each latent layer:", + "bbox": [ + 496, + 556, + 890, + 648 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} _ {i} = \\left[ \\mathbf {x} _ {i} ^ {0}; P _ {i}, P _ {i} ^ {1}, \\dots , P _ {i} ^ {k} \\right] \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 609, + 657, + 890, + 676 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} _ {i + 1} = \\operatorname {H e a d} \\left(\\mathbf {x} _ {i}\\right) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 611, + 678, + 890, + 694 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the Head indicates the transformer block. We find deep prompt is particularly useful for learning on large-scale datasets, such as ImageNet.", + "bbox": [ + 496, + 705, + 890, + 750 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Learning Objective. We now introduce the training objective to instruct models for doubly right object recognition. We use cross-modal image-to-text contrastive learning to train the model for the right rationales. Using our above pipeline, we have collected a set of images and their rationales, which we denote as $\\{(\\mathbf{x}_i, \\mathbf{t}_i)\\}$ . In contrast to the prior text prompts for object recognition, which uses:", + "bbox": [ + 496, + 751, + 890, + 857 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This is a photo of [CATEGORY]", + "text_level": 1, + "bbox": [ + 500, + 864, + 756, + 878 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "we instead create the training text prompt to be:", + "bbox": [ + 500, + 885, + 815, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "2725", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Table 2. Benchmarking six large-scale image-language pretrained models on doubly right recognition over six datasets. The accuracy for doubly right is gray-scaled. We bold the best accuracy. $\\uparrow$ indicates higher number is better. For the same CLIP model, when model capacity increases from Res50 to H/14, the models' ability to get doubly right also increases, even though CLIP has never been trained on this metric. However, the doubly right accuracy on large-scale datasets is still low. For example, the double right accuracy is less than $1\\%$ on ImageNet. While larger model provides higher accuracy for object classification, they often provide wrong rationales, as indicated by the increase in RW percentage. Our evaluation suggests that this new doubly right object recognition task is challenging for existing large-scale visual models.", + "bbox": [ + 75, + 88, + 893, + 186 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/8ddbada9bd3f0b904a3fca01d6cfcde1c7c2fa81eabb75f683073dd9d1ad4a69.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelCIFAR-10+CIFAR-100+Food101+
RR↑RW↓WR↓WW↓RR↑RW↓WR↓WW↓RR↑RW↓WR↓
FLAVA29.4453.045.8311.683.5759.725.4431.263.9555.784.86
CLIP-Res5030.6550.858.519.974.5158.947.7628.786.5361.475.31
CLIP-Res10130.4150.618.7610.215.0960.317.4127.195.2364.654.61
CLIP-B/3236.9846.719.007.305.2359.937.3027.535.4863.575.41
CLIP-B/1635.2849.639.255.835.6164.096.1624.136.0467.654.26
CLIP-L/1442.5744.527.065.846.4363.717.7322.135.7370.074.30
ModelCaltech101+SUN+ImageNet+
RR↑RW↓WR↓WW↓RR↑RW↓WR↓WW↓RR↑RW↓WR↓
FLAVA2.2161.573.8532.380.9514.6210.7273.700.4028.313.58
CLIP-Res504.1361.605.3126.690.7819.8710.9368.410.6140.423.69
CLIP-Res1014.5764.244.6125.460.8921.2911.6866.750.6542.743.64
CLIP-B/324.5165.925.4224.150.8623.3210.7265.160.6842.693.87
CLIP-B/164.6068.304.8422.250.8123.4110.5065.680.6346.733.41
CLIP-L/145.9966.555.9621.500.9424.2711.2163.580.7250.004.34
", + "bbox": [ + 163, + 196, + 805, + 393 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 3. Gain of using why prompt to adapt models to perform doubly right object recognition. We evaluate the CLIP-H/14 model, except for ImageNet, where we use CLIP-B/32 due to the large dataset size. We use a deep prompt on ImageNet, which is indicated by *. We bold the best doubly right accuracy. Learning a why prompt significantly improves the models' ability to predict the right category as well as the right rationales, reducing the failures when the model predicts the right category with wrong rationales.", + "bbox": [ + 75, + 406, + 893, + 464 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/e738144926c5135bae4cb3d87523597e7ba92f9ce00c2cefb391e75a645ad443.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DatasetsPrompt LengthRR↑RW↓WR↓WW↓
BaselineOursBaselineOursBaselineOursBaselineOurs
CIFAR-10+342.5770.8244.5218.257.066.325.844.62
CIFAR-100+36.4322.2763.7144.617.739.9722.1323.14
Food101+35.7325.2570.0751.834.305.8319.9117.08
Caltech101+35.9923.6466.5552.435.965.8621.5018.06
SUN+1000.946.7024.278.2911.2123.7663.5861.24
ImageNet+30*0.683.6342.6921.703.877.6652.7625.34
", + "bbox": [ + 187, + 474, + 782, + 577 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This is a photo of [CATEGORY] because there is [RATIONALE]", + "text_level": 1, + "bbox": [ + 76, + 603, + 408, + 630 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This allows the model to learn what is the correct rationales that explain the category prediction.", + "bbox": [ + 75, + 638, + 468, + 667 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We use the pretrained image-language model, where we encode the image with an image encoder $F_{\\theta}$ and the corresponding rationale with a text encoder $T$ . To train the model to rank the correct rationales higher than the other negative rationales, we minimize the following image-to-text contrastive loss function,", + "bbox": [ + 75, + 667, + 472, + 758 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {s} (\\mathbf {x}, \\mathbf {t}, \\mathbf {y}) = - \\mathbb {E} _ {i, j} \\left[ \\mathbf {y} _ {i j} \\log \\frac {\\exp \\left(\\cos \\left(\\mathbf {z} _ {i} ^ {(I)} , \\mathbf {z} _ {j} ^ {(T)}\\right) / \\tau\\right)}{\\sum_ {k} \\exp \\left(\\cos \\left(\\mathbf {z} _ {i} ^ {(I)} , \\mathbf {z} _ {k} ^ {(T)}\\right) / \\tau\\right)} \\right], \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 768, + 473, + 821 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{z}_i^{(I)} = F_\\theta (\\mathbf{x}_i)$ and $\\mathbf{z}_i^{(T)} = T(\\mathbf{t}_i)$ are the features from the image and text, respectively. $\\mathbf{y}_{ij}$ indicates which image-text are paired in the dataset and which are not. We set $\\mathbf{y}_{ij} = 1$ when the image and text are from the same data point. cos denotes the cosine similarity function. $\\tau$ is the", + "bbox": [ + 75, + 821, + 472, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "temperature hyperparameter to scale the confidence of the prediction. We then use gradient descent to optimize the visual prompt such that this loss is minimal.", + "bbox": [ + 496, + 602, + 892, + 647 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Evaluation Metric", + "text_level": 1, + "bbox": [ + 498, + 655, + 676, + 670 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We define the following metric to evaluate the models' predictions as well as their rationales. We formulate producing the rationales as a ranking task, where we provide the model sentence descriptions containing a pair-wise combination of all the categories and rationales, and the image-language model will retrieve the closer ones. Specifically, we present the model with a sentence in this format:", + "bbox": [ + 496, + 678, + 890, + 785 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This is a photo of [CATEGORY] because there is [RATIONALE]", + "text_level": 1, + "bbox": [ + 500, + 790, + 830, + 819 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "and ask the model to return the sentence that has the closest representation to the visual embeddings. Since one image may have multiple rationales to explain the category, following the standard practice [16], we use a top-K accuracy — if the top K rationales include the ground truth, then it is", + "bbox": [ + 496, + 824, + 893, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "2726", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/5a1784510e7840134d6e7ebdee25442bf9dccb294528ac77a050b6e67a34f8d3.jpg", + "table_caption": [ + "Table 4. Zero-shot gain of using why prompt to adapt models to perform doubly right object recognition. For all datasets we use CLIP-H/14 model, except for ImageNet, where we use CLIP-B/32. We bold the best accuracy for doubly right object recognition. Our method can obtain better rationales on unseen datasets than baseline (CLIP) model." + ], + "table_footnote": [], + "table_body": "
Zero-Shot TransferRR↑RW↓WR↓WW↓
Training DatasetsTesting DatasetsBaselineOursBaselineOursBaselineOursBaselineOurs
CIFAR-100+CIFAR-10+42.4754.9944.5233.587.064.875.846.57
CIFAR-100+Food101+5.738.3570.0744.614.309.9719.9123.14
CIFAR-100+Caltech101+5.9915.0766.5556.345.966.2121.5022.38
Caltech101+CIFAR-10+42.4749.6344.5239.177.065.605.845.60
Caltech101+CIFAR-100+6.4313.2063.7149.117.7310.3822.1327.30
Caltech101+Food101+5.737.3670.0761.054.304.4919.9126.69
SUN+CIFAR-10+42.4749.0044.5240.047.065.785.845.18
SUN+CIFAR-100+6.4313.1163.7149.637.738.3222.1328.93
SUN+Food101+5.738.9470.0751.904.306.6719.9132.48
SUN+Caltech101+5.9913.5866.5555.145.965.3921.5025.88
ImageNet+CIFAR-10+36.9838.6846.7143.809.009.257.308.27
ImageNet+CIFAR-100+5.2315.6759.9339.897.309.5127.5355.57
ImageNet+Food101+5.488.3163.5746.595.415.9725.5339.12
ImageNet+Caltech101+4.5116.7165.9245.425.427.6624.1530.20
ImageNet+SUN+0.861.9823.327.0210.7214.9665.1676.90
", + "bbox": [ + 176, + 142, + 795, + 363 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "counted as correct. The predicted category is based on the majority vote of the top-K retrieved categories [30]. We denote the metric as follows:", + "bbox": [ + 75, + 388, + 470, + 434 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "(1) Right classification with right rationale (RR);", + "(2) Right classification with wrong rationale (RW);", + "(3) Wrong classification with right rationale (WR);", + "(4) Wrong classification with wrong rationale (WW)" + ], + "bbox": [ + 81, + 443, + 434, + 518 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We desire a high accuracy for RR and a low percentage for RW, WR, and WW. We will evaluate the above metric on our collected dataset where rationale ground truth is provided. We select $20\\%$ of the data as the hold-out test set. We will train the model on the remaining $80\\%$ data.", + "bbox": [ + 75, + 527, + 468, + 603 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiment", + "text_level": 1, + "bbox": [ + 76, + 616, + 202, + 633 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We evaluate six large-scale image-language pretrained models on our doubly right benchmark. We find that the model often produces the wrong rationales for the predictions. We then show that our why prompts significantly improves the models' ability to produce the right rationales quantitatively and qualitatively. Lastly, we show that we can have a hierarchy of visual rationales where the model can provide sub-rationales.", + "bbox": [ + 75, + 641, + 470, + 762 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Benchmark Existing Models", + "text_level": 1, + "bbox": [ + 76, + 771, + 333, + 787 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We start our investigation by evaluating existing large-scale image language models [41, 49] on our collected doubly right dataset. Our evaluation includes images in the category of CIFAR-10, CIFAR-100, Food101, Caltech101, SUN, and ImageNet. Since we recollect the image based on the category name of those dataset, we use $^+$ to denote our collected dataset. We set $K = 5$ for the top-K accuracy", + "bbox": [ + 75, + 795, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "of the doubly right prediction. We study FLAVA [49] and five variants of CLIP [41], where evaluation results are in Table 2. We find that for the same CLIP model, increasing their capacity from Resnet 50 [18] to ViT Huge/14 [13] generally improves performance in retrieving the right rationales, even if the model has never been trained on the doubly right task. FLAVA model performs worse than all CLIP model variants, except on $\\mathrm{SUN^{+}}$ . Despite the high classification accuracy, doubly right object recognition is challenging for all models, where models produce incorrect rationales more often than the correct ones. Specifically, the best CLIP-H/14 model only obtains $1\\%$ accuracy on $\\mathrm{ImageNet^{+}}$ doubly right recognition task. Our evaluation shows that doubly right object recognition is still an open challenge for the large-scale dataset.", + "bbox": [ + 496, + 388, + 893, + 616 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Why Prompt for Visual Rationales", + "text_level": 1, + "bbox": [ + 498, + 631, + 802, + 647 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To adapt the vision model so that they can perform doubly right object recognition, we apply our \"why\" prompting to visual foundation models. On ImageNet $^{+}$ , we adapt the CLIP-B/32 due to the large size of the dataset. We use deep prompt with prompt length 30 for each of the 12 layers. We train 10 epochs with a learning rate of 10. For all the other datasets, we adapt the best CLIP-H/14 model. We train model for 100 epochs with a learning rate of 40. We use a prompt size of 3, except for SUN where we use 100. For each dataset, we train on $80\\%$ of the data and test on the hold out $20\\%$ test data.", + "bbox": [ + 496, + 656, + 890, + 821 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We show our results in Table 3. By finding a why prompt to adapt the visual model, we significantly improve the models' ability to produce the right predictions as well as the right rationales, up to 28 points. Using our prompt, the model also sometimes predicts the wrong categories when", + "bbox": [ + 496, + 824, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "2727", + "bbox": [ + 482, + 944, + 514, + 957 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/849930d11443da8be7a95fff2c25fa170fd1bc7aecdb61fa30fad70d11e1cf26.jpg", + "image_caption": [ + "Figure 5. Visualization for the doubly right recognition task. For each row, we show image examples from categories of one dataset. In columns 2, 4, 7, and 9, we show the rationales produced by the model to explain the prediction. In column 3, 5, 8, and 10, we show the saliency map [10] that models look to produce the prediction and rationales. While the state-of-the-art H/14 CLIP model produces the correct category with the wrong rationales, our method can produce the correct category with the right rationales. In addition, our visual prompt also adapts the model to use the right image region to produce the prediction." + ], + "image_footnote": [], + "bbox": [ + 80, + 70, + 885, + 452 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/553625481af16056b30a5f16160099e45a09230d00b0f31b2f4085aa69e91091.jpg", + "image_caption": [ + "Figure 6. Visualization for top 3 rationales. We show the original examples from SUN, Caltech101, Food101, and ImageNet datasets with high-resolution images. Even though we do not annotate rationales for images in these datasets, our method can successfully transfer the rationales learned from our data and apply them." + ], + "image_footnote": [], + "bbox": [ + 81, + 529, + 890, + 656 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "the rationales are wrong (higher WW), suggesting our why prompt achieve higher consistency in reasoning between category and rationales. Our prompt method is still effective when the prompt size is as small as 3, containing minimal parameters, which is lightweight to apply. In addition, learning our why prompt can maintain the classification accuracy on the original ImageNet validation set, where CLIP-B/32 obtains an accuracy of $59.16\\%$ , and we obtain an accuracy of $59.20\\%$ .", + "bbox": [ + 75, + 708, + 470, + 843 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Zero-shot Transferability for Why Prompt. We find that the above generated \"why\" also transfers to unseen datasets and categories. In Table 4, we show the doubly right accu", + "bbox": [ + 75, + 854, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "racy obtained by zero-shot transfer, where we obtain up to 12 points gain. For example, by learning the model on the $\\mathrm{SUN}^{+}$ dataset which contains natural scenes, our method can teach CLIP to provide the correct rationales for food images $(\\mathrm{Food101}^{+})$ , by 3 points better. This experiment shows our why prompt can adapt large scale models to produce correct predictions with right rationales, and generalize to novel categories, suggesting the effectiveness of our method.", + "bbox": [ + 496, + 708, + 890, + 843 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Visualizations on Doubly Right dataset. We visualize images from the test set of our benchmark. In Figure 5, we show the top 1 rationales retrieved by the baseline and our", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "2728", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a420b0e1096b391a73f3383c86b5f43477e20e4be9402e519d5299c050885369.jpg", + "image_caption": [ + "Figure 7. Visualizations for the hierarchical rationales on CIFAR $^{10^{+}}$ . Our method obtains reasonable sub-rationales by learning an additional sub why prompt." + ], + "image_footnote": [], + "bbox": [ + 89, + 89, + 269, + 176 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Sub-Rationales", + "text_level": 1, + "bbox": [ + 334, + 97, + 401, + 106 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Why this is a tail of a dog?", + "bbox": [ + 282, + 116, + 387, + 125 + ], + "page_idx": 7 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "Because it is thin Because it is Long", + "Why this is four legs of a dog?", + "Because it is furry - Because it is long" + ], + "bbox": [ + 282, + 126, + 441, + 154 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Why this is ears of a dog?", + "bbox": [ + 282, + 157, + 382, + 167 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "- Because it is short - Because it is wet", + "bbox": [ + 282, + 167, + 437, + 176 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "prompted model. Our method often produces a correct explanation, while the baseline does not. We also visualize the saliency map corresponding to the rationales [10], where we can also see that the why prompt instructs the model to look at the right region to explain the prediction.", + "bbox": [ + 75, + 231, + 468, + 306 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Qualitative results on the original dataset. In addition to evaluating the doubly right performance on our collected dataset above, we also evaluate the established, original data. We study ImageNet, SUN, Caltech, and Food101 datasets since they contain high-resolution images that allow detailed explanations. Though we cannot directly evaluate the doubly right accuracy of those dataset images since they do not contain annotated ground truth, we show visualizations for the rationales generated on those datasets. In Figure 6, we find our learned \"why\" prompt also transfers well in improving the doubly right performance on images in those datasets.", + "bbox": [ + 75, + 306, + 468, + 487 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Analyzing Hierarchical Rationales", + "text_level": 1, + "bbox": [ + 76, + 497, + 377, + 512 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The rationales provided by our approach may not be the basic explanations. For example, with the above method, we can explain that this is a photo of a dog because there are four legs. We are curious whether the model can also provide another level of visual reasoning for why the four legs cause the image to be a dog. We explore whether our framework can provide even more fundamental explanations for the generated rationales.", + "bbox": [ + 75, + 520, + 468, + 640 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To obtain sub-rationales, we query GPT3 with:", + "bbox": [ + 96, + 641, + 406, + 656 + ], + "page_idx": 7 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "Q: What are useful visual features for distinguishing a {attribute name} of a {category name} in a photo?", + "A: There are several useful visual features to tell there is a {attribute name} of a {category name} in a photo:" + ], + "bbox": [ + 76, + 662, + 447, + 746 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "After getting the sub-rationales through language chain of thought, we transfer the knowledge to visual domain by Google query:", + "bbox": [ + 75, + 753, + 468, + 799 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "A photo of {CATEGORY}, because there is {sub-level attribute name} {attribute name}", + "bbox": [ + 76, + 806, + 439, + 845 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "where we collect 10583 images that contain attributes of specific patterns denoted by the sub-rationales. We split the dataset into an $80\\%$ training set and $20\\%$ of testing set.", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5. Accuracy for hierarchical visual rationales. On CIFAR $^{-10^{+}}$ categories, we evaluate CLIP and our models' ability to get the category, the rationales, and the rationales' explanations correct (RR). Our method produces better sub-rationales than CLIP.", + "bbox": [ + 498, + 89, + 890, + 143 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/a1d79a1f7426d948c5d9d7db9abdad7dca022cb5b0279b5e87c4e6b5786bb91f.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
RRRWWRWW
CLIP-H/140.0538.140.2061.61
Ours26.1953.861.5818.35
", + "bbox": [ + 547, + 155, + 841, + 215 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We train our why prompt with the same objective in Equation 4. We then evaluate the correctness of the rationales and the sub-rationales. We experiment on CIFAR- $10^{+}$ and train the model for 25 epochs. When categories, rationales, and sub-rationales are correct, it is counted as doubly right (RR). In Table 5, baseline CLIP has 0 accuracy. Our method improves RR by 26 points. In Figure 7, we visualize this hierarchical rationale, where our method can produce sub-rationales that explains the rationales hierarchically.", + "bbox": [ + 496, + 224, + 890, + 361 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. User Study", + "text_level": 1, + "bbox": [ + 500, + 376, + 620, + 391 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To evaluate the quality of our doubly right dataset, we conduct a human study. We show 200 images randomly sampled from our dataset and ask the user to check whether the category and rationales match what's inside the image. We conduct this study on 20 participants. Since the task requires visual reasoning, it takes 20 to 40 minutes for one participant to complete the study. On average, the user thinks $86.2\\%$ of the annotation is correct, with a standard deviation of 8.5. This shows our pipeline can collect visual data with visual rationales of reasonably high quality.", + "bbox": [ + 496, + 400, + 890, + 551 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 571, + 617, + 585 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, We study an essential yet under-explored visual problem, getting the correct rationales for the predictions, which we name as the \"doubly right\" object recognition task. We construct large-scale datasets containing categories from various datasets with rich rationales, which allows us to evaluate this doubly right metric directly. Our work proposes a pipeline that transfers the rationales knowledge from language models to visual models, which significantly improves the doubly right object recognition accuracy on both seen and unseen categories. Our work provides a benchmark and algorithm that allows the visual recognition field to push this doubly right task forward.", + "bbox": [ + 496, + 597, + 890, + 779 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 500, + 797, + 658, + 814 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This research is based on work partially supported by the DARPA GAILA program, the DARPA KAIROS program, the NSF NRI Award #2132519, a GE/DARPA grant, a CAIT grant, and gifts from JP Morgan, DiDi, and Accenture. 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Prompt consistency for zero-shot task generalization. arXiv preprint arXiv:2205.00049, 2022.", + "[65] Kaiyang Zhou, Jingkang Yang, Chen Change Loy, and Ziwei Liu. Conditional prompt learning for vision-language models. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 16816-16825, 2022.", + "[66] Kaiyang Zhou, Jingkang Yang, Chen Change Loy, and Ziwei Liu. Learning to prompt for vision-language models. International Journal of Computer Vision, 130(9):2337-2348, 2022." + ], + "bbox": [ + 501, + 92, + 890, + 837 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "2732", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Doubly Right Object Recognition_ A Why Prompt for Visual Rationales/3e3819d8-6dd5-452f-ae03-010df00b34bb_model.json b/2023/Doubly Right Object Recognition_ A Why Prompt for Visual Rationales/3e3819d8-6dd5-452f-ae03-010df00b34bb_model.json new file mode 100644 index 0000000000000000000000000000000000000000..c1b2765bc65192ca5e04afb484a299f85bee70c2 --- /dev/null +++ b/2023/Doubly Right Object Recognition_ A Why Prompt for Visual Rationales/3e3819d8-6dd5-452f-ae03-010df00b34bb_model.json @@ -0,0 +1,2477 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.126, + 0.131, + 0.844, + 0.152 + ], + "angle": 0, + "content": "Doubly Right Object Recognition: A Why Prompt for Visual Rationales" + }, + { + "type": "text", + "bbox": [ + 0.191, + 0.179, + 0.777, + 0.234 + ], + "angle": 0, + "content": "Chengzhi Mao1 \nRevant Teotia1 \nAmrutha Sundar1 \nSachit Menon1 \nJunfeng Yang1 \nXin Wang2 \nCarl Vondrick1 \n1Columbia University \n2Microsoft Research" + }, + { + "type": "text", + "bbox": [ + 0.128, + 0.237, + 0.842, + 0.251 + ], + "angle": 0, + "content": "{mcz,rt2891,as6431,sm4934,junfeng,vondrick}@cs.columbia.edu，wanxin@microsoft.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.287, + 0.313, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.318, + 0.474, + 0.576 + ], + "angle": 0, + "content": "Many visual recognition models are evaluated only on their classification accuracy, a metric for which they obtain strong performance. In this paper, we investigate whether computer vision models can also provide correct rationales for their predictions. We propose a \"doubly right\" object recognition benchmark, where the metric requires the model to simultaneously produce both the right labels as well as the right rationales. We find that state-of-the-art visual models, such as CLIP, often provide incorrect rationales for their categorical predictions. However, by transferring the rationales from language models into visual representations through a tailored dataset, we show that we can learn a \"why prompt,\" which adapts large visual representations to produce correct rationales. Visualizations and empirical experiments show that our prompts significantly improve performance on doubly right object recognition, in addition to zero-shot transfer to unseen tasks and datasets." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.604, + 0.208, + 0.619 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.47, + 0.794 + ], + "angle": 0, + "content": "Computer vision models today are able to achieve high accuracy – sometimes super-human – at correctly recognizing objects in images. However, most models today are not evaluated on whether they get the prediction right for the right reasons [14, 19, 48, 53]. Learning models that can explain their own decision is important for building trustworthy systems, especially in applications that require human-machine interactions [2, 15, 37, 50]. Rationales that justify the prediction can largely improve user trust [54], which is a crucial metric that the visual recognition field should push forward in the future." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Existing methods in interpretability have investigated how to understand which features contribute to the models' prediction [33, 34, 44, 46, 47, 52, 60]. However, saliency explanations are often imprecise, require domain expertise to understand, and also cannot be evaluated. [20, 22] have instead explored verbal rationales to justify the decision-making. However, they require manual collections of the" + }, + { + "type": "image", + "bbox": [ + 0.516, + 0.269, + 0.875, + 0.407 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.423, + 0.892, + 0.493 + ], + "angle": 0, + "content": "Figure 1. Visual reasoning for doubly right object recognition task. Motivated by prompting in NLP, we learn a why prompt from multimodal data, which allows us to instruct visual models to predict both the right category and the correct rationales that justify the prediction." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.504, + 0.891, + 0.534 + ], + "angle": 0, + "content": "plausible rationales in the first place, which subsequently are limited to small-scale datasets and tasks [24, 56]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.537, + 0.892, + 0.702 + ], + "angle": 0, + "content": "Scalable methods for explainability have been developed in natural language processing (NLP) through prompting. By adding additional instructions to the input, such as the sentence \"think step-by-step,\" language models then output descriptions of their reasoning through the chain of thought process [57]. Since the explanations are verbal, they are easily understandable by people, and since the mechanism emerges without explicit supervision, it is highly scalable. In this paper, we investigate whether visual representations can also explain their reasoning through visual chain-of-thought prompts." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.892, + 0.869 + ], + "angle": 0, + "content": "Our paper first introduces a benchmark for doubly right object recognition, where computer vision models must predict both correct categorical labels as well as correct rationales. Our benchmark is large, and covers many categories and datasets. We found that the visual representations do not have double right capability out-of-the-box on our benchmark. The recent large-scale image-language pretrained models [41, 49] can retrieve open-world language descriptions that are closest to the image embedding in the feature space, serving as verbal explanations. However, the models often select the wrong rationales." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Instead, we propose a framework to explicitly transfer the chain-of-thought reasoning from NLP models into" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2722" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.081, + 0.092, + 0.468, + 0.347 + ], + "angle": 0, + "content": "vision models. We first query the large-scale language model [9] via the chain-of-thought reasoning for object category, where we obtain language rationales that explain discriminative features for an object. We then collect images containing both the category and the rationale features using Google image search. We then train visual prompts to transfer the verbal chain of thought to visual chain of thought with contrastive learning, where features of images and their rationales are pulled together. Our \"why\" prompts obtain up to 26 points gain at doubly right performance when evaluated on our benchmark. In addition, visualizations and quantitative results show that our why prompts zero-shot transfer to unseen tasks and datasets. We believe this \"doubly right\" object recognition task is a future direction which the visual recognition field should go forward for. Our data and code is available at https://github.com/cvlab-columbia/DoubleRight." + }, + { + "type": "title", + "bbox": [ + 0.081, + 0.362, + 0.217, + 0.377 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.387, + 0.468, + 0.673 + ], + "angle": 0, + "content": "Explainability. Visual recognition models achieve high performance on the classification tasks, yet they often provide vague and unreliable interpretations and rationales [8]. There are two lines of research for interpreting image classification using neural networks: feature visualization and language explanation. Feature visualization methods [6, 32-34] find the inputs that maximize the outputs of learned features. Gradient-based feature visualization [28, 42, 44, 46, 47, 52, 60] highlight the input features/pixels in images that are most important for the network to make decisions. Since the visualizations are often abstract, it is hard for a non-expert to understand. In addition, saliency map [44] highlights regions that may contain overlapping concepts such as color, texture, and shape, which is hard to disentangle. The second line of research uses language-based explanation methods [20, 22] to generate visual explanations. However, those methods require human annotations, which limits their ability to evaluate on a larger scale." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.675, + 0.468, + 0.9 + ], + "angle": 0, + "content": "External Knowledge. Visual models often learn spurious correlations without external knowledge [29]. External knowledge allows models to learn the right features and obtain better transferability [26, 45]. Large-scale pretrained language models, such as GPT-3 [9], contains knowledge and commonsense learned from the Internet [38]. [57] shows that designing the right prompt, such as the chain of thought, improves the model's ability for language reasoning, which we leverage as an external knowledge source. Other sources of external knowledge include interactions [1, 11, 55], physics [31, 59], etc. [30] provides descriptions together with the objective category, which improves recognition performance. However, since they do not annotate rationales in their approach, they cannot measure CLIP's ability to produce the right rationales." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.092, + 0.89, + 0.212 + ], + "angle": 0, + "content": "Visual Attributes Several works have studied visual attributes in images [17,25,27,35,36,39,63]. [58] used the visual attributes for animal classification and [23] used them for face verification. However, some of the attributes are spurious correlated [51] with the prediction task. In this work, we aim to generate visual rationales that produce robust visual attributes like shape and parts, instead of spurious features such as the background." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.214, + 0.89, + 0.365 + ], + "angle": 0, + "content": "Visual Reasoning. [61] proposed a new cognition benchmark that the model needs to predict both the answer and the rationale to be correct. Visual Question Answering [3] performs visual understanding as a QA task, such as questions about COCO images. However, the questions are not asking for rationales to justify object recognition. [62] shows that multi-modal vision language models can perform zero-shot image-language tasks, such as image captioning. However, all existing visual reasoning work does not directly evaluate object recognition on the rationales they provided." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.366, + 0.89, + 0.531 + ], + "angle": 0, + "content": "Prompting. Prompt tuning is a lightweight adaptation method for language task [64-66]. Recently, the computer vision field has adapted the language and proposed the visual prompts to adapt vision models [4, 5, 21, 43]. Due to their lightweight, it has been shown effective for continuous learning [12]. One advantage of the visual prompt is that it does not require model access at test time, which is flexible [4]. While existing visual prompt methods focus on improving the recognition task performance, we propose to use this lightweight prompt to improve the models' ability to provide visual rationales." + }, + { + "type": "title", + "bbox": [ + 0.504, + 0.55, + 0.87, + 0.566 + ], + "angle": 0, + "content": "3. Language Rationales to Visual Rationales" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.577, + 0.89, + 0.666 + ], + "angle": 0, + "content": "We first introduce how to obtain the language rationales for discriminating an object. We then show how we translate the language descriptions into visual images and construct the dataset. We then propose to construct a \"why prompt\" to adapt the large visual models to produce the right rationales for their predictions." + }, + { + "type": "title", + "bbox": [ + 0.504, + 0.681, + 0.785, + 0.696 + ], + "angle": 0, + "content": "3.1. Rationale from Language Model" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.705, + 0.89, + 0.9 + ], + "angle": 0, + "content": "A standard way of getting visual rationales for image predictions is through manual annotation. However, manual annotation is expensive, especially when applied to large-scale datasets. Recent advances in large-scale language models, such as the GPT3, demonstrate the ability to provide various commonsense knowledge in language. By providing chain-of-thought instructions to the language model, [57] shows that language models can perform the task of interest as well as produce explanations. We can use large-scale language models as a tool to collect rationales by asking the right language prompts. In addition, since the rationales are presented in language, it is easy to understand, even for non-experts." + }, + { + "type": "page_number", + "bbox": [ + 0.485, + 0.947, + 0.514, + 0.957 + ], + "angle": 0, + "content": "2723" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.092, + 0.885, + 0.151 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.161, + 0.895, + 0.203 + ], + "angle": 0, + "content": "Figure 2. Examples of the rationales generated by prompting GPT3 with the chain of thought reasoning on the features of objects. We show one example from each of the six datasets—CIFAR10, CIFAR100, Food101, Caltech101, SUN, and ImageNet—we studied. The bold word is the category, and the list follows is the generated rationales. GPT3 can produce reasoning for why an object is as predicted." + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.209, + 0.473, + 0.419 + ], + "angle": 0, + "content": "Table 1. List of datasets that include both the model prediction and rationales. Animals with attributes (AWA) collects discriminative attributes for animals. CUB collects verbal rationales on only birds. BDD-X collects rationales for explaining driving scenarios. VAW and Broaden collect a large number of attributes. However, they are often not the right rationales for explaining why objects are classified, such as color. The * indicates the number of annotated video frames. The existing datasets are often small-scale, limited in domains, and not annotating rationales for the object recognition task. Our framework allows the automatic collection of diversified categories over a large scale. Note that the \\(^+\\) name in our dataset, such as CIFAR- \\(10^{+}\\), indicates that we collect the same set of categories in CIFAR-10 from google with our pipeline. Our benchmark is large, containing more categories and dataset variants than prior methods." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.428, + 0.474, + 0.589 + ], + "angle": 0, + "content": "
Dataset NameNumber of CategoriesNumber of DescriptionsNumber of ImagesFor Right Rationales
AWA [24]508530,475Yes
CUB [20,56]200N/A11,788Yes
BDD-X [22]9061,66826,000*Yes
VAW [40]N/A65072,274No
Broaden [7]5841,30062,476No
Ours CIFAR-10+10632,201Yes
Ours CIFAR-100+10054018,318Yes
Ours Food101+10143515,212Yes
Ours Caltech101+10151616,849Yes
Ours SUN+3972,17075,381Yes
Ours ImageNet+10005,810271,016Yes
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.616, + 0.47, + 0.692 + ], + "angle": 0, + "content": "Motivated by the recent work in language prompting [9, 30], we propose to ask the language model: what are the valid rationales for an object prediction? Specifically, to obtain rationales for visual objects, we ask GPT3 the following question:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.702, + 0.441, + 0.744 + ], + "angle": 0, + "content": "Q: What are useful visual features for distinguishing a {category name} in a photo?" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.745, + 0.441, + 0.786 + ], + "angle": 0, + "content": "A: There are several useful visual features to tell there is a {category name} in a photo:" + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.702, + 0.441, + 0.786 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.47, + 0.902 + ], + "angle": 0, + "content": "where GPT3 automatically generates the answer for us, which scales to large, unseen categories. In Figure 2, we show random examples of the rationales generated by querying GPT3. Each category is provided with a list of discriminative features for the category, which is consistent with how people explain their predictions." + }, + { + "type": "image", + "bbox": [ + 0.514, + 0.209, + 0.882, + 0.357 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.367, + 0.893, + 0.424 + ], + "angle": 0, + "content": "Figure 3. Histogram of the number of images per ImageNet category retrieved by Google search. There are natural imbalances in the data. Learning model under such imbalanced natural data distribution is an interesting problem to study." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.433, + 0.831, + 0.45 + ], + "angle": 0, + "content": "3.2. Knowledge Transfer to Visual Domain" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.457, + 0.892, + 0.577 + ], + "angle": 0, + "content": "Since not every rationale exists in every image of the given object, we cannot directly apply this list of rationales to images based on their category. We need external knowledge to collect images containing specified rationales, so that we can correspond the language rationales to the visual rationals in images. Prior work [45] uses structured external knowledge from Wiktionary and WordNet to obtain images with text descriptions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.579, + 0.892, + 0.684 + ], + "angle": 0, + "content": "In the era of the Internet, people often Google a new word if they don't know what the object — the word refers to — looks like. Once people see the image examples from Google, they quickly understand what the word refers to in the real world. Our method is motivated by this natural procedure, where our system Googles \"what the rationales look like\" to visually understand them." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.685, + 0.892, + 0.806 + ], + "angle": 0, + "content": "We propose to leverage this external knowledge from web search engines, a larger-scale knowledge base than Wiktionary [45]. We use Google image search to obtain images that contain our specified visual features, and we find that the returned images match the language queries with high accuracy. The search engine serves as a cross-modal translator, translating the knowledge from the language domain to the visual domain by retrieving images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.807, + 0.892, + 0.838 + ], + "angle": 0, + "content": "We use the following queries to query images that belong to our specified category and contain our specified attribute:" + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.846, + 0.848, + 0.873 + ], + "angle": 0, + "content": "1. {category name} which has {attribute name}" + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.874, + 0.837, + 0.888 + ], + "angle": 0, + "content": "2. {attribute name} of {category name}" + }, + { + "type": "text", + "bbox": [ + 0.502, + 0.888, + 0.83, + 0.901 + ], + "angle": 0, + "content": "3. a photo of {category name} because" + }, + { + "type": "list", + "bbox": [ + 0.501, + 0.846, + 0.848, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2724" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.09, + 0.887, + 0.261 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.271, + 0.895, + 0.314 + ], + "angle": 0, + "content": "Figure 4. Examples for the images in our collected ImageNet\\(^+\\) dataset, where each image corresponds to one category label and one rationale. We show three random categories, and for each category, we show three random rationales. The rationales are consistent with the image features that decide the object's category." + }, + { + "type": "title", + "bbox": [ + 0.11, + 0.323, + 0.333, + 0.336 + ], + "angle": 0, + "content": "there is {attribute name}" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.348, + 0.47, + 0.409 + ], + "angle": 0, + "content": "and we retrieve the top 50 images returned by Google search. More query sentences can be constructed if more images are needed, which we leave for future work. We remove the duplicated and incorrect images in preprocessing." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.41, + 0.474, + 0.727 + ], + "angle": 0, + "content": "Google image search allows us to obtain images containing specific attributes. We perform the above automatic pipeline on ImageNet categories and obtain a dataset that contains images and the rationales that explain why this image is a particular category. For the dataset collected with our framework, we show a histogram of the number of images per ImageNet category in Figure 3. The data is S-curved due to the natural, non-interventional collection procedure. We also show examples of rationales and the retrieved images in Figure 4, where images can often be explained by rationales. Since our system is automatic, we in addition run our pipeline on the categories in CIFAR-10, CIFAR-100, Food101, Caltech101, and SUN datasets. Table 1 shows the scale of our collected images and compares them with prior datasets that are related to our work. Our pipeline allows richer rationales and is more extensive in the number of images and categories. To evaluate how accurate the Google image search can retrieve the images with the specified attribute as well as the category, we conduct a human study on the quality and consistency, which we describe in Section 4.4." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.739, + 0.318, + 0.756 + ], + "angle": 0, + "content": "3.3. Learning the Why Prompt" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.764, + 0.47, + 0.869 + ], + "angle": 0, + "content": "Using external knowledge from both the language model and Google, we show we can collect image datasets containing both the category and rationales. Our pipeline allows us to evaluate the quality of this doubly right task on a large scale over several datasets for the first time. Our results show that doubly right object recognition is a challenging task for large visual models, such as CLIP." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.471, + 0.901 + ], + "angle": 0, + "content": "We then seek a way to adapt and improve large pretrained models so that they can provide the correct rationale" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.322, + 0.892, + 0.427 + ], + "angle": 0, + "content": "for the predictions. Motivated by the prompting in natural language processing, we propose constructing a visual \"why\" prompt that instructs the model to produce the right rationales for the prediction. We optimize the visual prompt to ask \"what are the visual rationales that explains the prediction of this image\". We use the following input prompts or deep prompts to adapt the model." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.428, + 0.892, + 0.487 + ], + "angle": 0, + "content": "Prompt Design. We study how to adapt transformer-based models since they are state-of-the-art. Our visual why prompts append additional tokens \\( P_{k} \\) to the input sequence of the vision transformer:" + }, + { + "type": "equation", + "bbox": [ + 0.619, + 0.5, + 0.892, + 0.516 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} = \\left[ \\mathbf {x}; P _ {0}, P _ {1}, \\dots , P _ {k} \\right] \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.527, + 0.892, + 0.557 + ], + "angle": 0, + "content": "The remaining transformer parameters and computations are kept the same as the original." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.558, + 0.892, + 0.649 + ], + "angle": 0, + "content": "Deep prompt. Besides adding context to the input sequence, the deep prompting method [21] adds prompts to the intermediate layers in the transformer, which is a more powerful adaptation method than single-layer input prompt. Let \\(\\mathbf{x}_i\\) be the latent token sequence of the \\(i\\)-th layer in the transformer. We can add a prompt to each latent layer:" + }, + { + "type": "equation", + "bbox": [ + 0.611, + 0.658, + 0.891, + 0.677 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} _ {i} = \\left[ \\mathbf {x} _ {i} ^ {0}; P _ {i}, P _ {i} ^ {1}, \\dots , P _ {i} ^ {k} \\right] \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.612, + 0.679, + 0.891, + 0.695 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} _ {i + 1} = \\operatorname {H e a d} \\left(\\mathbf {x} _ {i}\\right) \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.706, + 0.891, + 0.751 + ], + "angle": 0, + "content": "where the Head indicates the transformer block. We find deep prompt is particularly useful for learning on large-scale datasets, such as ImageNet." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.752, + 0.892, + 0.858 + ], + "angle": 0, + "content": "Learning Objective. We now introduce the training objective to instruct models for doubly right object recognition. We use cross-modal image-to-text contrastive learning to train the model for the right rationales. Using our above pipeline, we have collected a set of images and their rationales, which we denote as \\(\\{(\\mathbf{x}_i, \\mathbf{t}_i)\\}\\). In contrast to the prior text prompts for object recognition, which uses:" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.865, + 0.758, + 0.879 + ], + "angle": 0, + "content": "This is a photo of [CATEGORY]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.886, + 0.816, + 0.901 + ], + "angle": 0, + "content": "we instead create the training text prompt to be:" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2725" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.187 + ], + "angle": 0, + "content": "Table 2. Benchmarking six large-scale image-language pretrained models on doubly right recognition over six datasets. The accuracy for doubly right is gray-scaled. We bold the best accuracy. \\(\\uparrow\\) indicates higher number is better. For the same CLIP model, when model capacity increases from Res50 to H/14, the models' ability to get doubly right also increases, even though CLIP has never been trained on this metric. However, the doubly right accuracy on large-scale datasets is still low. For example, the double right accuracy is less than \\(1\\%\\) on ImageNet. While larger model provides higher accuracy for object classification, they often provide wrong rationales, as indicated by the increase in RW percentage. Our evaluation suggests that this new doubly right object recognition task is challenging for existing large-scale visual models." + }, + { + "type": "table", + "bbox": [ + 0.164, + 0.198, + 0.807, + 0.394 + ], + "angle": 0, + "content": "
ModelCIFAR-10+CIFAR-100+Food101+
RR↑RW↓WR↓WW↓RR↑RW↓WR↓WW↓RR↑RW↓WR↓
FLAVA29.4453.045.8311.683.5759.725.4431.263.9555.784.86
CLIP-Res5030.6550.858.519.974.5158.947.7628.786.5361.475.31
CLIP-Res10130.4150.618.7610.215.0960.317.4127.195.2364.654.61
CLIP-B/3236.9846.719.007.305.2359.937.3027.535.4863.575.41
CLIP-B/1635.2849.639.255.835.6164.096.1624.136.0467.654.26
CLIP-L/1442.5744.527.065.846.4363.717.7322.135.7370.074.30
ModelCaltech101+SUN+ImageNet+
RR↑RW↓WR↓WW↓RR↑RW↓WR↓WW↓RR↑RW↓WR↓
FLAVA2.2161.573.8532.380.9514.6210.7273.700.4028.313.58
CLIP-Res504.1361.605.3126.690.7819.8710.9368.410.6140.423.69
CLIP-Res1014.5764.244.6125.460.8921.2911.6866.750.6542.743.64
CLIP-B/324.5165.925.4224.150.8623.3210.7265.160.6842.693.87
CLIP-B/164.6068.304.8422.250.8123.4110.5065.680.6346.733.41
CLIP-L/145.9966.555.9621.500.9424.2711.2163.580.7250.004.34
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.407, + 0.895, + 0.465 + ], + "angle": 0, + "content": "Table 3. Gain of using why prompt to adapt models to perform doubly right object recognition. We evaluate the CLIP-H/14 model, except for ImageNet, where we use CLIP-B/32 due to the large dataset size. We use a deep prompt on ImageNet, which is indicated by *. We bold the best doubly right accuracy. Learning a why prompt significantly improves the models' ability to predict the right category as well as the right rationales, reducing the failures when the model predicts the right category with wrong rationales." + }, + { + "type": "table", + "bbox": [ + 0.188, + 0.475, + 0.784, + 0.578 + ], + "angle": 0, + "content": "
DatasetsPrompt LengthRR↑RW↓WR↓WW↓
BaselineOursBaselineOursBaselineOursBaselineOurs
CIFAR-10+342.5770.8244.5218.257.066.325.844.62
CIFAR-100+36.4322.2763.7144.617.739.9722.1323.14
Food101+35.7325.2570.0751.834.305.8319.9117.08
Caltech101+35.9923.6466.5552.435.965.8621.5018.06
SUN+1000.946.7024.278.2911.2123.7663.5861.24
ImageNet+30*0.683.6342.6921.703.877.6652.7625.34
" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.604, + 0.409, + 0.631 + ], + "angle": 0, + "content": "This is a photo of [CATEGORY] because there is [RATIONALE]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.639, + 0.47, + 0.669 + ], + "angle": 0, + "content": "This allows the model to learn what is the correct rationales that explain the category prediction." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.669, + 0.473, + 0.759 + ], + "angle": 0, + "content": "We use the pretrained image-language model, where we encode the image with an image encoder \\( F_{\\theta} \\) and the corresponding rationale with a text encoder \\( T \\). To train the model to rank the correct rationales higher than the other negative rationales, we minimize the following image-to-text contrastive loss function," + }, + { + "type": "equation", + "bbox": [ + 0.077, + 0.769, + 0.475, + 0.822 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {s} (\\mathbf {x}, \\mathbf {t}, \\mathbf {y}) = - \\mathbb {E} _ {i, j} \\left[ \\mathbf {y} _ {i j} \\log \\frac {\\exp \\left(\\cos \\left(\\mathbf {z} _ {i} ^ {(I)} , \\mathbf {z} _ {j} ^ {(T)}\\right) / \\tau\\right)}{\\sum_ {k} \\exp \\left(\\cos \\left(\\mathbf {z} _ {i} ^ {(I)} , \\mathbf {z} _ {k} ^ {(T)}\\right) / \\tau\\right)} \\right], \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.822, + 0.473, + 0.902 + ], + "angle": 0, + "content": "where \\(\\mathbf{z}_i^{(I)} = F_\\theta (\\mathbf{x}_i)\\) and \\(\\mathbf{z}_i^{(T)} = T(\\mathbf{t}_i)\\) are the features from the image and text, respectively. \\(\\mathbf{y}_{ij}\\) indicates which image-text are paired in the dataset and which are not. We set \\(\\mathbf{y}_{ij} = 1\\) when the image and text are from the same data point. cos denotes the cosine similarity function. \\(\\tau\\) is the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.603, + 0.893, + 0.648 + ], + "angle": 0, + "content": "temperature hyperparameter to scale the confidence of the prediction. We then use gradient descent to optimize the visual prompt such that this loss is minimal." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.656, + 0.677, + 0.671 + ], + "angle": 0, + "content": "3.4. Evaluation Metric" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.679, + 0.892, + 0.786 + ], + "angle": 0, + "content": "We define the following metric to evaluate the models' predictions as well as their rationales. We formulate producing the rationales as a ranking task, where we provide the model sentence descriptions containing a pair-wise combination of all the categories and rationales, and the image-language model will retrieve the closer ones. Specifically, we present the model with a sentence in this format:" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.791, + 0.831, + 0.82 + ], + "angle": 0, + "content": "This is a photo of [CATEGORY] because there is [RATIONALE]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.894, + 0.901 + ], + "angle": 0, + "content": "and ask the model to return the sentence that has the closest representation to the visual embeddings. Since one image may have multiple rationales to explain the category, following the standard practice [16], we use a top-K accuracy — if the top K rationales include the ground truth, then it is" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2726" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.133 + ], + "angle": 0, + "content": "Table 4. Zero-shot gain of using why prompt to adapt models to perform doubly right object recognition. For all datasets we use CLIP-H/14 model, except for ImageNet, where we use CLIP-B/32. We bold the best accuracy for doubly right object recognition. Our method can obtain better rationales on unseen datasets than baseline (CLIP) model." + }, + { + "type": "table", + "bbox": [ + 0.177, + 0.143, + 0.797, + 0.364 + ], + "angle": 0, + "content": "
Zero-Shot TransferRR↑RW↓WR↓WW↓
Training DatasetsTesting DatasetsBaselineOursBaselineOursBaselineOursBaselineOurs
CIFAR-100+CIFAR-10+42.4754.9944.5233.587.064.875.846.57
CIFAR-100+Food101+5.738.3570.0744.614.309.9719.9123.14
CIFAR-100+Caltech101+5.9915.0766.5556.345.966.2121.5022.38
Caltech101+CIFAR-10+42.4749.6344.5239.177.065.605.845.60
Caltech101+CIFAR-100+6.4313.2063.7149.117.7310.3822.1327.30
Caltech101+Food101+5.737.3670.0761.054.304.4919.9126.69
SUN+CIFAR-10+42.4749.0044.5240.047.065.785.845.18
SUN+CIFAR-100+6.4313.1163.7149.637.738.3222.1328.93
SUN+Food101+5.738.9470.0751.904.306.6719.9132.48
SUN+Caltech101+5.9913.5866.5555.145.965.3921.5025.88
ImageNet+CIFAR-10+36.9838.6846.7143.809.009.257.308.27
ImageNet+CIFAR-100+5.2315.6759.9339.897.309.5127.5355.57
ImageNet+Food101+5.488.3163.5746.595.415.9725.5339.12
ImageNet+Caltech101+4.5116.7165.9245.425.427.6624.1530.20
ImageNet+SUN+0.861.9823.327.0210.7214.9665.1676.90
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.389, + 0.471, + 0.435 + ], + "angle": 0, + "content": "counted as correct. The predicted category is based on the majority vote of the top-K retrieved categories [30]. We denote the metric as follows:" + }, + { + "type": "text", + "bbox": [ + 0.082, + 0.444, + 0.414, + 0.459 + ], + "angle": 0, + "content": "(1) Right classification with right rationale (RR);" + }, + { + "type": "text", + "bbox": [ + 0.082, + 0.464, + 0.427, + 0.479 + ], + "angle": 0, + "content": "(2) Right classification with wrong rationale (RW);" + }, + { + "type": "text", + "bbox": [ + 0.082, + 0.484, + 0.427, + 0.5 + ], + "angle": 0, + "content": "(3) Wrong classification with right rationale (WR);" + }, + { + "type": "text", + "bbox": [ + 0.082, + 0.504, + 0.436, + 0.52 + ], + "angle": 0, + "content": "(4) Wrong classification with wrong rationale (WW)" + }, + { + "type": "list", + "bbox": [ + 0.082, + 0.444, + 0.436, + 0.52 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.528, + 0.47, + 0.604 + ], + "angle": 0, + "content": "We desire a high accuracy for RR and a low percentage for RW, WR, and WW. We will evaluate the above metric on our collected dataset where rationale ground truth is provided. We select \\(20\\%\\) of the data as the hold-out test set. We will train the model on the remaining \\(80\\%\\) data." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.617, + 0.203, + 0.634 + ], + "angle": 0, + "content": "4. Experiment" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.642, + 0.471, + 0.763 + ], + "angle": 0, + "content": "We evaluate six large-scale image-language pretrained models on our doubly right benchmark. We find that the model often produces the wrong rationales for the predictions. We then show that our why prompts significantly improves the models' ability to produce the right rationales quantitatively and qualitatively. Lastly, we show that we can have a hierarchy of visual rationales where the model can provide sub-rationales." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.772, + 0.334, + 0.789 + ], + "angle": 0, + "content": "4.1. Benchmark Existing Models" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.471, + 0.903 + ], + "angle": 0, + "content": "We start our investigation by evaluating existing large-scale image language models [41, 49] on our collected doubly right dataset. Our evaluation includes images in the category of CIFAR-10, CIFAR-100, Food101, Caltech101, SUN, and ImageNet. Since we recollect the image based on the category name of those dataset, we use \\(^+\\) to denote our collected dataset. We set \\(K = 5\\) for the top-K accuracy" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.389, + 0.895, + 0.617 + ], + "angle": 0, + "content": "of the doubly right prediction. We study FLAVA [49] and five variants of CLIP [41], where evaluation results are in Table 2. We find that for the same CLIP model, increasing their capacity from Resnet 50 [18] to ViT Huge/14 [13] generally improves performance in retrieving the right rationales, even if the model has never been trained on the doubly right task. FLAVA model performs worse than all CLIP model variants, except on \\(\\mathrm{SUN^{+}}\\). Despite the high classification accuracy, doubly right object recognition is challenging for all models, where models produce incorrect rationales more often than the correct ones. Specifically, the best CLIP-H/14 model only obtains \\(1\\%\\) accuracy on \\(\\mathrm{ImageNet^{+}}\\) doubly right recognition task. Our evaluation shows that doubly right object recognition is still an open challenge for the large-scale dataset." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.632, + 0.803, + 0.648 + ], + "angle": 0, + "content": "4.2. Why Prompt for Visual Rationales" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.657, + 0.892, + 0.822 + ], + "angle": 0, + "content": "To adapt the vision model so that they can perform doubly right object recognition, we apply our \"why\" prompting to visual foundation models. On ImageNet\\(^{+}\\), we adapt the CLIP-B/32 due to the large size of the dataset. We use deep prompt with prompt length 30 for each of the 12 layers. We train 10 epochs with a learning rate of 10. For all the other datasets, we adapt the best CLIP-H/14 model. We train model for 100 epochs with a learning rate of 40. We use a prompt size of 3, except for SUN where we use 100. For each dataset, we train on \\(80\\%\\) of the data and test on the hold out \\(20\\%\\) test data." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.895, + 0.903 + ], + "angle": 0, + "content": "We show our results in Table 3. By finding a why prompt to adapt the visual model, we significantly improve the models' ability to produce the right predictions as well as the right rationales, up to 28 points. Using our prompt, the model also sometimes predicts the wrong categories when" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.958 + ], + "angle": 0, + "content": "2727" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.071, + 0.887, + 0.453 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.457, + 0.893, + 0.527 + ], + "angle": 0, + "content": "Figure 5. Visualization for the doubly right recognition task. For each row, we show image examples from categories of one dataset. In columns 2, 4, 7, and 9, we show the rationales produced by the model to explain the prediction. In column 3, 5, 8, and 10, we show the saliency map [10] that models look to produce the prediction and rationales. While the state-of-the-art H/14 CLIP model produces the correct category with the wrong rationales, our method can produce the correct category with the right rationales. In addition, our visual prompt also adapts the model to use the right image region to produce the prediction." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.53, + 0.892, + 0.657 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.658, + 0.893, + 0.701 + ], + "angle": 0, + "content": "Figure 6. Visualization for top 3 rationales. We show the original examples from SUN, Caltech101, Food101, and ImageNet datasets with high-resolution images. Even though we do not annotate rationales for images in these datasets, our method can successfully transfer the rationales learned from our data and apply them." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.709, + 0.471, + 0.844 + ], + "angle": 0, + "content": "the rationales are wrong (higher WW), suggesting our why prompt achieve higher consistency in reasoning between category and rationales. Our prompt method is still effective when the prompt size is as small as 3, containing minimal parameters, which is lightweight to apply. In addition, learning our why prompt can maintain the classification accuracy on the original ImageNet validation set, where CLIP-B/32 obtains an accuracy of \\(59.16\\%\\), and we obtain an accuracy of \\(59.20\\%\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Zero-shot Transferability for Why Prompt. We find that the above generated \"why\" also transfers to unseen datasets and categories. In Table 4, we show the doubly right accu" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.709, + 0.892, + 0.844 + ], + "angle": 0, + "content": "racy obtained by zero-shot transfer, where we obtain up to 12 points gain. For example, by learning the model on the \\(\\mathrm{SUN}^{+}\\) dataset which contains natural scenes, our method can teach CLIP to provide the correct rationales for food images \\((\\mathrm{Food101}^{+})\\), by 3 points better. This experiment shows our why prompt can adapt large scale models to produce correct predictions with right rationales, and generalize to novel categories, suggesting the effectiveness of our method." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Visualizations on Doubly Right dataset. We visualize images from the test set of our benchmark. In Figure 5, we show the top 1 rationales retrieved by the baseline and our" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2728" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.091, + 0.09, + 0.27, + 0.178 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.335, + 0.098, + 0.402, + 0.107 + ], + "angle": 0, + "content": "Sub-Rationales" + }, + { + "type": "text", + "bbox": [ + 0.283, + 0.117, + 0.388, + 0.126 + ], + "angle": 0, + "content": "Why this is a tail of a dog?" + }, + { + "type": "text", + "bbox": [ + 0.284, + 0.127, + 0.442, + 0.135 + ], + "angle": 0, + "content": "Because it is thin Because it is Long" + }, + { + "type": "text", + "bbox": [ + 0.284, + 0.136, + 0.402, + 0.145 + ], + "angle": 0, + "content": "Why this is four legs of a dog?" + }, + { + "type": "text", + "bbox": [ + 0.284, + 0.146, + 0.44, + 0.155 + ], + "angle": 0, + "content": "Because it is furry - Because it is long" + }, + { + "type": "list", + "bbox": [ + 0.284, + 0.127, + 0.442, + 0.155 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.283, + 0.159, + 0.383, + 0.168 + ], + "angle": 0, + "content": "Why this is ears of a dog?" + }, + { + "type": "text", + "bbox": [ + 0.283, + 0.169, + 0.439, + 0.177 + ], + "angle": 0, + "content": "- Because it is short - Because it is wet" + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.182, + 0.47, + 0.224 + ], + "angle": 0, + "content": "Figure 7. Visualizations for the hierarchical rationales on CIFAR\\(^{10^{+}}\\). Our method obtains reasonable sub-rationales by learning an additional sub why prompt." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.232, + 0.469, + 0.307 + ], + "angle": 0, + "content": "prompted model. Our method often produces a correct explanation, while the baseline does not. We also visualize the saliency map corresponding to the rationales [10], where we can also see that the why prompt instructs the model to look at the right region to explain the prediction." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.308, + 0.469, + 0.488 + ], + "angle": 0, + "content": "Qualitative results on the original dataset. In addition to evaluating the doubly right performance on our collected dataset above, we also evaluate the established, original data. We study ImageNet, SUN, Caltech, and Food101 datasets since they contain high-resolution images that allow detailed explanations. Though we cannot directly evaluate the doubly right accuracy of those dataset images since they do not contain annotated ground truth, we show visualizations for the rationales generated on those datasets. In Figure 6, we find our learned \"why\" prompt also transfers well in improving the doubly right performance on images in those datasets." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.498, + 0.378, + 0.513 + ], + "angle": 0, + "content": "4.3. Analyzing Hierarchical Rationales" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.521, + 0.469, + 0.641 + ], + "angle": 0, + "content": "The rationales provided by our approach may not be the basic explanations. For example, with the above method, we can explain that this is a photo of a dog because there are four legs. We are curious whether the model can also provide another level of visual reasoning for why the four legs cause the image to be a dog. We explore whether our framework can provide even more fundamental explanations for the generated rationales." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.642, + 0.408, + 0.657 + ], + "angle": 0, + "content": "To obtain sub-rationales, we query GPT3 with:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.664, + 0.449, + 0.706 + ], + "angle": 0, + "content": "Q: What are useful visual features for distinguishing a {attribute name} of a {category name} in a photo?" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.707, + 0.449, + 0.747 + ], + "angle": 0, + "content": "A: There are several useful visual features to tell there is a {attribute name} of a {category name} in a photo:" + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.664, + 0.449, + 0.747 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.755, + 0.469, + 0.8 + ], + "angle": 0, + "content": "After getting the sub-rationales through language chain of thought, we transfer the knowledge to visual domain by Google query:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.808, + 0.44, + 0.847 + ], + "angle": 0, + "content": "A photo of {CATEGORY}, because there is {sub-level attribute name} {attribute name}" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.469, + 0.901 + ], + "angle": 0, + "content": "where we collect 10583 images that contain attributes of specific patterns denoted by the sub-rationales. We split the dataset into an \\(80\\%\\) training set and \\(20\\%\\) of testing set." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.09, + 0.892, + 0.145 + ], + "angle": 0, + "content": "Table 5. Accuracy for hierarchical visual rationales. On CIFAR\\(^{-10^{+}}\\) categories, we evaluate CLIP and our models' ability to get the category, the rationales, and the rationales' explanations correct (RR). Our method produces better sub-rationales than CLIP." + }, + { + "type": "table", + "bbox": [ + 0.548, + 0.156, + 0.842, + 0.216 + ], + "angle": 0, + "content": "
RRRWWRWW
CLIP-H/140.0538.140.2061.61
Ours26.1953.861.5818.35
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.226, + 0.892, + 0.362 + ], + "angle": 0, + "content": "We train our why prompt with the same objective in Equation 4. We then evaluate the correctness of the rationales and the sub-rationales. We experiment on CIFAR- \\(10^{+}\\) and train the model for 25 epochs. When categories, rationales, and sub-rationales are correct, it is counted as doubly right (RR). In Table 5, baseline CLIP has 0 accuracy. Our method improves RR by 26 points. In Figure 7, we visualize this hierarchical rationale, where our method can produce sub-rationales that explains the rationales hierarchically." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.377, + 0.621, + 0.392 + ], + "angle": 0, + "content": "4.4. User Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.401, + 0.892, + 0.553 + ], + "angle": 0, + "content": "To evaluate the quality of our doubly right dataset, we conduct a human study. We show 200 images randomly sampled from our dataset and ask the user to check whether the category and rationales match what's inside the image. We conduct this study on 20 participants. Since the task requires visual reasoning, it takes 20 to 40 minutes for one participant to complete the study. On average, the user thinks \\(86.2\\%\\) of the annotation is correct, with a standard deviation of 8.5. This shows our pipeline can collect visual data with visual rationales of reasonably high quality." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.572, + 0.619, + 0.587 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.598, + 0.892, + 0.78 + ], + "angle": 0, + "content": "In this paper, We study an essential yet under-explored visual problem, getting the correct rationales for the predictions, which we name as the \"doubly right\" object recognition task. We construct large-scale datasets containing categories from various datasets with rich rationales, which allows us to evaluate this doubly right metric directly. Our work proposes a pipeline that transfers the rationales knowledge from language models to visual models, which significantly improves the doubly right object recognition accuracy on both seen and unseen categories. Our work provides a benchmark and algorithm that allows the visual recognition field to push this doubly right task forward." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.799, + 0.66, + 0.815 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "This research is based on work partially supported by the DARPA GAILA program, the DARPA KAIROS program, the NSF NRI Award #2132519, a GE/DARPA grant, a CAIT grant, and gifts from JP Morgan, DiDi, and Accenture. 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In this paper, we investigate whether computer vision models can also provide correct rationales for their predictions. We propose a "doubly right" object recognition benchmark, where the metric requires the model to simultaneously produce both the right labels as well as the right rationales. We find that state-of-the-art visual models, such as CLIP, often provide incorrect rationales for their categorical predictions. However, by transferring the rationales from language models into visual representations through a tailored dataset, we show that we can learn a "why prompt," which adapts large visual representations to produce correct rationales. Visualizations and empirical experiments show that our prompts significantly improve performance on doubly right object recognition, in addition to zero-shot transfer to unseen tasks and datasets. + +# 1. Introduction + +Computer vision models today are able to achieve high accuracy – sometimes super-human – at correctly recognizing objects in images. However, most models today are not evaluated on whether they get the prediction right for the right reasons [14, 19, 48, 53]. Learning models that can explain their own decision is important for building trustworthy systems, especially in applications that require human-machine interactions [2, 15, 37, 50]. Rationales that justify the prediction can largely improve user trust [54], which is a crucial metric that the visual recognition field should push forward in the future. + +Existing methods in interpretability have investigated how to understand which features contribute to the models' prediction [33, 34, 44, 46, 47, 52, 60]. However, saliency explanations are often imprecise, require domain expertise to understand, and also cannot be evaluated. [20, 22] have instead explored verbal rationales to justify the decision-making. However, they require manual collections of the + +![](images/7b9867f4f63f610f8d0921009fa765c556696293e74fddec536488d03308bd09.jpg) +Figure 1. Visual reasoning for doubly right object recognition task. Motivated by prompting in NLP, we learn a why prompt from multimodal data, which allows us to instruct visual models to predict both the right category and the correct rationales that justify the prediction. + +plausible rationales in the first place, which subsequently are limited to small-scale datasets and tasks [24, 56]. + +Scalable methods for explainability have been developed in natural language processing (NLP) through prompting. By adding additional instructions to the input, such as the sentence "think step-by-step," language models then output descriptions of their reasoning through the chain of thought process [57]. Since the explanations are verbal, they are easily understandable by people, and since the mechanism emerges without explicit supervision, it is highly scalable. In this paper, we investigate whether visual representations can also explain their reasoning through visual chain-of-thought prompts. + +Our paper first introduces a benchmark for doubly right object recognition, where computer vision models must predict both correct categorical labels as well as correct rationales. Our benchmark is large, and covers many categories and datasets. We found that the visual representations do not have double right capability out-of-the-box on our benchmark. The recent large-scale image-language pretrained models [41, 49] can retrieve open-world language descriptions that are closest to the image embedding in the feature space, serving as verbal explanations. However, the models often select the wrong rationales. + +Instead, we propose a framework to explicitly transfer the chain-of-thought reasoning from NLP models into + +vision models. We first query the large-scale language model [9] via the chain-of-thought reasoning for object category, where we obtain language rationales that explain discriminative features for an object. We then collect images containing both the category and the rationale features using Google image search. We then train visual prompts to transfer the verbal chain of thought to visual chain of thought with contrastive learning, where features of images and their rationales are pulled together. Our "why" prompts obtain up to 26 points gain at doubly right performance when evaluated on our benchmark. In addition, visualizations and quantitative results show that our why prompts zero-shot transfer to unseen tasks and datasets. We believe this "doubly right" object recognition task is a future direction which the visual recognition field should go forward for. Our data and code is available at https://github.com/cvlab-columbia/DoubleRight. + +# 2. Related Work + +Explainability. Visual recognition models achieve high performance on the classification tasks, yet they often provide vague and unreliable interpretations and rationales [8]. There are two lines of research for interpreting image classification using neural networks: feature visualization and language explanation. Feature visualization methods [6, 32-34] find the inputs that maximize the outputs of learned features. Gradient-based feature visualization [28, 42, 44, 46, 47, 52, 60] highlight the input features/pixels in images that are most important for the network to make decisions. Since the visualizations are often abstract, it is hard for a non-expert to understand. In addition, saliency map [44] highlights regions that may contain overlapping concepts such as color, texture, and shape, which is hard to disentangle. The second line of research uses language-based explanation methods [20, 22] to generate visual explanations. However, those methods require human annotations, which limits their ability to evaluate on a larger scale. + +External Knowledge. Visual models often learn spurious correlations without external knowledge [29]. External knowledge allows models to learn the right features and obtain better transferability [26, 45]. Large-scale pretrained language models, such as GPT-3 [9], contains knowledge and commonsense learned from the Internet [38]. [57] shows that designing the right prompt, such as the chain of thought, improves the model's ability for language reasoning, which we leverage as an external knowledge source. Other sources of external knowledge include interactions [1, 11, 55], physics [31, 59], etc. [30] provides descriptions together with the objective category, which improves recognition performance. However, since they do not annotate rationales in their approach, they cannot measure CLIP's ability to produce the right rationales. + +Visual Attributes Several works have studied visual attributes in images [17,25,27,35,36,39,63]. [58] used the visual attributes for animal classification and [23] used them for face verification. However, some of the attributes are spurious correlated [51] with the prediction task. In this work, we aim to generate visual rationales that produce robust visual attributes like shape and parts, instead of spurious features such as the background. + +Visual Reasoning. [61] proposed a new cognition benchmark that the model needs to predict both the answer and the rationale to be correct. Visual Question Answering [3] performs visual understanding as a QA task, such as questions about COCO images. However, the questions are not asking for rationales to justify object recognition. [62] shows that multi-modal vision language models can perform zero-shot image-language tasks, such as image captioning. However, all existing visual reasoning work does not directly evaluate object recognition on the rationales they provided. + +Prompting. Prompt tuning is a lightweight adaptation method for language task [64-66]. Recently, the computer vision field has adapted the language and proposed the visual prompts to adapt vision models [4, 5, 21, 43]. Due to their lightweight, it has been shown effective for continuous learning [12]. One advantage of the visual prompt is that it does not require model access at test time, which is flexible [4]. While existing visual prompt methods focus on improving the recognition task performance, we propose to use this lightweight prompt to improve the models' ability to provide visual rationales. + +# 3. Language Rationales to Visual Rationales + +We first introduce how to obtain the language rationales for discriminating an object. We then show how we translate the language descriptions into visual images and construct the dataset. We then propose to construct a "why prompt" to adapt the large visual models to produce the right rationales for their predictions. + +# 3.1. Rationale from Language Model + +A standard way of getting visual rationales for image predictions is through manual annotation. However, manual annotation is expensive, especially when applied to large-scale datasets. Recent advances in large-scale language models, such as the GPT3, demonstrate the ability to provide various commonsense knowledge in language. By providing chain-of-thought instructions to the language model, [57] shows that language models can perform the task of interest as well as produce explanations. We can use large-scale language models as a tool to collect rationales by asking the right language prompts. In addition, since the rationales are presented in language, it is easy to understand, even for non-experts. + +![](images/71c2cddc1c083ed7df2421914f3a98118ce57f9700e3acd970cddec84c19541e.jpg) +Figure 2. Examples of the rationales generated by prompting GPT3 with the chain of thought reasoning on the features of objects. We show one example from each of the six datasets—CIFAR10, CIFAR100, Food101, Caltech101, SUN, and ImageNet—we studied. The bold word is the category, and the list follows is the generated rationales. GPT3 can produce reasoning for why an object is as predicted. + +Table 1. List of datasets that include both the model prediction and rationales. Animals with attributes (AWA) collects discriminative attributes for animals. CUB collects verbal rationales on only birds. BDD-X collects rationales for explaining driving scenarios. VAW and Broaden collect a large number of attributes. However, they are often not the right rationales for explaining why objects are classified, such as color. The * indicates the number of annotated video frames. The existing datasets are often small-scale, limited in domains, and not annotating rationales for the object recognition task. Our framework allows the automatic collection of diversified categories over a large scale. Note that the $^+$ name in our dataset, such as CIFAR- $10^{+}$ , indicates that we collect the same set of categories in CIFAR-10 from google with our pipeline. Our benchmark is large, containing more categories and dataset variants than prior methods. + +
Dataset NameNumber of CategoriesNumber of DescriptionsNumber of ImagesFor Right Rationales
AWA [24]508530,475Yes
CUB [20,56]200N/A11,788Yes
BDD-X [22]9061,66826,000*Yes
VAW [40]N/A65072,274No
Broaden [7]5841,30062,476No
Ours CIFAR-10+10632,201Yes
Ours CIFAR-100+10054018,318Yes
Ours Food101+10143515,212Yes
Ours Caltech101+10151616,849Yes
Ours SUN+3972,17075,381Yes
Ours ImageNet+10005,810271,016Yes
+ +Motivated by the recent work in language prompting [9, 30], we propose to ask the language model: what are the valid rationales for an object prediction? Specifically, to obtain rationales for visual objects, we ask GPT3 the following question: + +Q: What are useful visual features for distinguishing a {category name} in a photo? +A: There are several useful visual features to tell there is a {category name} in a photo: + +where GPT3 automatically generates the answer for us, which scales to large, unseen categories. In Figure 2, we show random examples of the rationales generated by querying GPT3. Each category is provided with a list of discriminative features for the category, which is consistent with how people explain their predictions. + +![](images/17db92a069c2437730cc42cac4a5360c6eddc5978ca1e74e3d72cf9bdf1d3728.jpg) +Figure 3. Histogram of the number of images per ImageNet category retrieved by Google search. There are natural imbalances in the data. Learning model under such imbalanced natural data distribution is an interesting problem to study. + +# 3.2. Knowledge Transfer to Visual Domain + +Since not every rationale exists in every image of the given object, we cannot directly apply this list of rationales to images based on their category. We need external knowledge to collect images containing specified rationales, so that we can correspond the language rationales to the visual rationals in images. Prior work [45] uses structured external knowledge from Wiktionary and WordNet to obtain images with text descriptions. + +In the era of the Internet, people often Google a new word if they don't know what the object — the word refers to — looks like. Once people see the image examples from Google, they quickly understand what the word refers to in the real world. Our method is motivated by this natural procedure, where our system Googles "what the rationales look like" to visually understand them. + +We propose to leverage this external knowledge from web search engines, a larger-scale knowledge base than Wiktionary [45]. We use Google image search to obtain images that contain our specified visual features, and we find that the returned images match the language queries with high accuracy. The search engine serves as a cross-modal translator, translating the knowledge from the language domain to the visual domain by retrieving images. + +We use the following queries to query images that belong to our specified category and contain our specified attribute: + +1. {category name} which has {attribute name} +2. {attribute name} of {category name} +3. a photo of {category name} because + +![](images/08f662d5a1cc47dc7a81c1b8e5d31a3365f20f3723ccbc08666e9168be7d11cb.jpg) +Figure 4. Examples for the images in our collected ImageNet $^+$ dataset, where each image corresponds to one category label and one rationale. We show three random categories, and for each category, we show three random rationales. The rationales are consistent with the image features that decide the object's category. + +# there is {attribute name} + +and we retrieve the top 50 images returned by Google search. More query sentences can be constructed if more images are needed, which we leave for future work. We remove the duplicated and incorrect images in preprocessing. + +Google image search allows us to obtain images containing specific attributes. We perform the above automatic pipeline on ImageNet categories and obtain a dataset that contains images and the rationales that explain why this image is a particular category. For the dataset collected with our framework, we show a histogram of the number of images per ImageNet category in Figure 3. The data is S-curved due to the natural, non-interventional collection procedure. We also show examples of rationales and the retrieved images in Figure 4, where images can often be explained by rationales. Since our system is automatic, we in addition run our pipeline on the categories in CIFAR-10, CIFAR-100, Food101, Caltech101, and SUN datasets. Table 1 shows the scale of our collected images and compares them with prior datasets that are related to our work. Our pipeline allows richer rationales and is more extensive in the number of images and categories. To evaluate how accurate the Google image search can retrieve the images with the specified attribute as well as the category, we conduct a human study on the quality and consistency, which we describe in Section 4.4. + +# 3.3. Learning the Why Prompt + +Using external knowledge from both the language model and Google, we show we can collect image datasets containing both the category and rationales. Our pipeline allows us to evaluate the quality of this doubly right task on a large scale over several datasets for the first time. Our results show that doubly right object recognition is a challenging task for large visual models, such as CLIP. + +We then seek a way to adapt and improve large pretrained models so that they can provide the correct rationale + +for the predictions. Motivated by the prompting in natural language processing, we propose constructing a visual "why" prompt that instructs the model to produce the right rationales for the prediction. We optimize the visual prompt to ask "what are the visual rationales that explains the prediction of this image". We use the following input prompts or deep prompts to adapt the model. + +Prompt Design. We study how to adapt transformer-based models since they are state-of-the-art. Our visual why prompts append additional tokens $P_{k}$ to the input sequence of the vision transformer: + +$$ +\mathbf {x} = \left[ \mathbf {x}; P _ {0}, P _ {1}, \dots , P _ {k} \right] \tag {1} +$$ + +The remaining transformer parameters and computations are kept the same as the original. + +Deep prompt. Besides adding context to the input sequence, the deep prompting method [21] adds prompts to the intermediate layers in the transformer, which is a more powerful adaptation method than single-layer input prompt. Let $\mathbf{x}_i$ be the latent token sequence of the $i$ -th layer in the transformer. We can add a prompt to each latent layer: + +$$ +\mathbf {x} _ {i} = \left[ \mathbf {x} _ {i} ^ {0}; P _ {i}, P _ {i} ^ {1}, \dots , P _ {i} ^ {k} \right] \tag {2} +$$ + +$$ +\mathbf {x} _ {i + 1} = \operatorname {H e a d} \left(\mathbf {x} _ {i}\right) \tag {3} +$$ + +where the Head indicates the transformer block. We find deep prompt is particularly useful for learning on large-scale datasets, such as ImageNet. + +Learning Objective. We now introduce the training objective to instruct models for doubly right object recognition. We use cross-modal image-to-text contrastive learning to train the model for the right rationales. Using our above pipeline, we have collected a set of images and their rationales, which we denote as $\{(\mathbf{x}_i, \mathbf{t}_i)\}$ . In contrast to the prior text prompts for object recognition, which uses: + +# This is a photo of [CATEGORY] + +we instead create the training text prompt to be: + +Table 2. Benchmarking six large-scale image-language pretrained models on doubly right recognition over six datasets. The accuracy for doubly right is gray-scaled. We bold the best accuracy. $\uparrow$ indicates higher number is better. For the same CLIP model, when model capacity increases from Res50 to H/14, the models' ability to get doubly right also increases, even though CLIP has never been trained on this metric. However, the doubly right accuracy on large-scale datasets is still low. For example, the double right accuracy is less than $1\%$ on ImageNet. While larger model provides higher accuracy for object classification, they often provide wrong rationales, as indicated by the increase in RW percentage. Our evaluation suggests that this new doubly right object recognition task is challenging for existing large-scale visual models. + +
ModelCIFAR-10+CIFAR-100+Food101+
RR↑RW↓WR↓WW↓RR↑RW↓WR↓WW↓RR↑RW↓WR↓
FLAVA29.4453.045.8311.683.5759.725.4431.263.9555.784.86
CLIP-Res5030.6550.858.519.974.5158.947.7628.786.5361.475.31
CLIP-Res10130.4150.618.7610.215.0960.317.4127.195.2364.654.61
CLIP-B/3236.9846.719.007.305.2359.937.3027.535.4863.575.41
CLIP-B/1635.2849.639.255.835.6164.096.1624.136.0467.654.26
CLIP-L/1442.5744.527.065.846.4363.717.7322.135.7370.074.30
ModelCaltech101+SUN+ImageNet+
RR↑RW↓WR↓WW↓RR↑RW↓WR↓WW↓RR↑RW↓WR↓
FLAVA2.2161.573.8532.380.9514.6210.7273.700.4028.313.58
CLIP-Res504.1361.605.3126.690.7819.8710.9368.410.6140.423.69
CLIP-Res1014.5764.244.6125.460.8921.2911.6866.750.6542.743.64
CLIP-B/324.5165.925.4224.150.8623.3210.7265.160.6842.693.87
CLIP-B/164.6068.304.8422.250.8123.4110.5065.680.6346.733.41
CLIP-L/145.9966.555.9621.500.9424.2711.2163.580.7250.004.34
+ +Table 3. Gain of using why prompt to adapt models to perform doubly right object recognition. We evaluate the CLIP-H/14 model, except for ImageNet, where we use CLIP-B/32 due to the large dataset size. We use a deep prompt on ImageNet, which is indicated by *. We bold the best doubly right accuracy. Learning a why prompt significantly improves the models' ability to predict the right category as well as the right rationales, reducing the failures when the model predicts the right category with wrong rationales. + +
DatasetsPrompt LengthRR↑RW↓WR↓WW↓
BaselineOursBaselineOursBaselineOursBaselineOurs
CIFAR-10+342.5770.8244.5218.257.066.325.844.62
CIFAR-100+36.4322.2763.7144.617.739.9722.1323.14
Food101+35.7325.2570.0751.834.305.8319.9117.08
Caltech101+35.9923.6466.5552.435.965.8621.5018.06
SUN+1000.946.7024.278.2911.2123.7663.5861.24
ImageNet+30*0.683.6342.6921.703.877.6652.7625.34
+ +# This is a photo of [CATEGORY] because there is [RATIONALE] + +This allows the model to learn what is the correct rationales that explain the category prediction. + +We use the pretrained image-language model, where we encode the image with an image encoder $F_{\theta}$ and the corresponding rationale with a text encoder $T$ . To train the model to rank the correct rationales higher than the other negative rationales, we minimize the following image-to-text contrastive loss function, + +$$ +\mathcal {L} _ {s} (\mathbf {x}, \mathbf {t}, \mathbf {y}) = - \mathbb {E} _ {i, j} \left[ \mathbf {y} _ {i j} \log \frac {\exp \left(\cos \left(\mathbf {z} _ {i} ^ {(I)} , \mathbf {z} _ {j} ^ {(T)}\right) / \tau\right)}{\sum_ {k} \exp \left(\cos \left(\mathbf {z} _ {i} ^ {(I)} , \mathbf {z} _ {k} ^ {(T)}\right) / \tau\right)} \right], \tag {4} +$$ + +where $\mathbf{z}_i^{(I)} = F_\theta (\mathbf{x}_i)$ and $\mathbf{z}_i^{(T)} = T(\mathbf{t}_i)$ are the features from the image and text, respectively. $\mathbf{y}_{ij}$ indicates which image-text are paired in the dataset and which are not. We set $\mathbf{y}_{ij} = 1$ when the image and text are from the same data point. cos denotes the cosine similarity function. $\tau$ is the + +temperature hyperparameter to scale the confidence of the prediction. We then use gradient descent to optimize the visual prompt such that this loss is minimal. + +# 3.4. Evaluation Metric + +We define the following metric to evaluate the models' predictions as well as their rationales. We formulate producing the rationales as a ranking task, where we provide the model sentence descriptions containing a pair-wise combination of all the categories and rationales, and the image-language model will retrieve the closer ones. Specifically, we present the model with a sentence in this format: + +# This is a photo of [CATEGORY] because there is [RATIONALE] + +and ask the model to return the sentence that has the closest representation to the visual embeddings. Since one image may have multiple rationales to explain the category, following the standard practice [16], we use a top-K accuracy — if the top K rationales include the ground truth, then it is + +Table 4. Zero-shot gain of using why prompt to adapt models to perform doubly right object recognition. For all datasets we use CLIP-H/14 model, except for ImageNet, where we use CLIP-B/32. We bold the best accuracy for doubly right object recognition. Our method can obtain better rationales on unseen datasets than baseline (CLIP) model. + +
Zero-Shot TransferRR↑RW↓WR↓WW↓
Training DatasetsTesting DatasetsBaselineOursBaselineOursBaselineOursBaselineOurs
CIFAR-100+CIFAR-10+42.4754.9944.5233.587.064.875.846.57
CIFAR-100+Food101+5.738.3570.0744.614.309.9719.9123.14
CIFAR-100+Caltech101+5.9915.0766.5556.345.966.2121.5022.38
Caltech101+CIFAR-10+42.4749.6344.5239.177.065.605.845.60
Caltech101+CIFAR-100+6.4313.2063.7149.117.7310.3822.1327.30
Caltech101+Food101+5.737.3670.0761.054.304.4919.9126.69
SUN+CIFAR-10+42.4749.0044.5240.047.065.785.845.18
SUN+CIFAR-100+6.4313.1163.7149.637.738.3222.1328.93
SUN+Food101+5.738.9470.0751.904.306.6719.9132.48
SUN+Caltech101+5.9913.5866.5555.145.965.3921.5025.88
ImageNet+CIFAR-10+36.9838.6846.7143.809.009.257.308.27
ImageNet+CIFAR-100+5.2315.6759.9339.897.309.5127.5355.57
ImageNet+Food101+5.488.3163.5746.595.415.9725.5339.12
ImageNet+Caltech101+4.5116.7165.9245.425.427.6624.1530.20
ImageNet+SUN+0.861.9823.327.0210.7214.9665.1676.90
+ +counted as correct. The predicted category is based on the majority vote of the top-K retrieved categories [30]. We denote the metric as follows: + +(1) Right classification with right rationale (RR); +(2) Right classification with wrong rationale (RW); +(3) Wrong classification with right rationale (WR); +(4) Wrong classification with wrong rationale (WW) + +We desire a high accuracy for RR and a low percentage for RW, WR, and WW. We will evaluate the above metric on our collected dataset where rationale ground truth is provided. We select $20\%$ of the data as the hold-out test set. We will train the model on the remaining $80\%$ data. + +# 4. Experiment + +We evaluate six large-scale image-language pretrained models on our doubly right benchmark. We find that the model often produces the wrong rationales for the predictions. We then show that our why prompts significantly improves the models' ability to produce the right rationales quantitatively and qualitatively. Lastly, we show that we can have a hierarchy of visual rationales where the model can provide sub-rationales. + +# 4.1. Benchmark Existing Models + +We start our investigation by evaluating existing large-scale image language models [41, 49] on our collected doubly right dataset. Our evaluation includes images in the category of CIFAR-10, CIFAR-100, Food101, Caltech101, SUN, and ImageNet. Since we recollect the image based on the category name of those dataset, we use $^+$ to denote our collected dataset. We set $K = 5$ for the top-K accuracy + +of the doubly right prediction. We study FLAVA [49] and five variants of CLIP [41], where evaluation results are in Table 2. We find that for the same CLIP model, increasing their capacity from Resnet 50 [18] to ViT Huge/14 [13] generally improves performance in retrieving the right rationales, even if the model has never been trained on the doubly right task. FLAVA model performs worse than all CLIP model variants, except on $\mathrm{SUN^{+}}$ . Despite the high classification accuracy, doubly right object recognition is challenging for all models, where models produce incorrect rationales more often than the correct ones. Specifically, the best CLIP-H/14 model only obtains $1\%$ accuracy on $\mathrm{ImageNet^{+}}$ doubly right recognition task. Our evaluation shows that doubly right object recognition is still an open challenge for the large-scale dataset. + +# 4.2. Why Prompt for Visual Rationales + +To adapt the vision model so that they can perform doubly right object recognition, we apply our "why" prompting to visual foundation models. On ImageNet $^{+}$ , we adapt the CLIP-B/32 due to the large size of the dataset. We use deep prompt with prompt length 30 for each of the 12 layers. We train 10 epochs with a learning rate of 10. For all the other datasets, we adapt the best CLIP-H/14 model. We train model for 100 epochs with a learning rate of 40. We use a prompt size of 3, except for SUN where we use 100. For each dataset, we train on $80\%$ of the data and test on the hold out $20\%$ test data. + +We show our results in Table 3. By finding a why prompt to adapt the visual model, we significantly improve the models' ability to produce the right predictions as well as the right rationales, up to 28 points. Using our prompt, the model also sometimes predicts the wrong categories when + +![](images/849930d11443da8be7a95fff2c25fa170fd1bc7aecdb61fa30fad70d11e1cf26.jpg) +Figure 5. Visualization for the doubly right recognition task. For each row, we show image examples from categories of one dataset. In columns 2, 4, 7, and 9, we show the rationales produced by the model to explain the prediction. In column 3, 5, 8, and 10, we show the saliency map [10] that models look to produce the prediction and rationales. While the state-of-the-art H/14 CLIP model produces the correct category with the wrong rationales, our method can produce the correct category with the right rationales. In addition, our visual prompt also adapts the model to use the right image region to produce the prediction. + +![](images/553625481af16056b30a5f16160099e45a09230d00b0f31b2f4085aa69e91091.jpg) +Figure 6. Visualization for top 3 rationales. We show the original examples from SUN, Caltech101, Food101, and ImageNet datasets with high-resolution images. Even though we do not annotate rationales for images in these datasets, our method can successfully transfer the rationales learned from our data and apply them. + +the rationales are wrong (higher WW), suggesting our why prompt achieve higher consistency in reasoning between category and rationales. Our prompt method is still effective when the prompt size is as small as 3, containing minimal parameters, which is lightweight to apply. In addition, learning our why prompt can maintain the classification accuracy on the original ImageNet validation set, where CLIP-B/32 obtains an accuracy of $59.16\%$ , and we obtain an accuracy of $59.20\%$ . + +Zero-shot Transferability for Why Prompt. We find that the above generated "why" also transfers to unseen datasets and categories. In Table 4, we show the doubly right accu + +racy obtained by zero-shot transfer, where we obtain up to 12 points gain. For example, by learning the model on the $\mathrm{SUN}^{+}$ dataset which contains natural scenes, our method can teach CLIP to provide the correct rationales for food images $(\mathrm{Food101}^{+})$ , by 3 points better. This experiment shows our why prompt can adapt large scale models to produce correct predictions with right rationales, and generalize to novel categories, suggesting the effectiveness of our method. + +Visualizations on Doubly Right dataset. We visualize images from the test set of our benchmark. In Figure 5, we show the top 1 rationales retrieved by the baseline and our + +![](images/a420b0e1096b391a73f3383c86b5f43477e20e4be9402e519d5299c050885369.jpg) +Figure 7. Visualizations for the hierarchical rationales on CIFAR $^{10^{+}}$ . Our method obtains reasonable sub-rationales by learning an additional sub why prompt. + +# Sub-Rationales + +Why this is a tail of a dog? + +Because it is thin Because it is Long +Why this is four legs of a dog? +Because it is furry - Because it is long + +Why this is ears of a dog? + +- Because it is short - Because it is wet + +prompted model. Our method often produces a correct explanation, while the baseline does not. We also visualize the saliency map corresponding to the rationales [10], where we can also see that the why prompt instructs the model to look at the right region to explain the prediction. + +Qualitative results on the original dataset. In addition to evaluating the doubly right performance on our collected dataset above, we also evaluate the established, original data. We study ImageNet, SUN, Caltech, and Food101 datasets since they contain high-resolution images that allow detailed explanations. Though we cannot directly evaluate the doubly right accuracy of those dataset images since they do not contain annotated ground truth, we show visualizations for the rationales generated on those datasets. In Figure 6, we find our learned "why" prompt also transfers well in improving the doubly right performance on images in those datasets. + +# 4.3. Analyzing Hierarchical Rationales + +The rationales provided by our approach may not be the basic explanations. For example, with the above method, we can explain that this is a photo of a dog because there are four legs. We are curious whether the model can also provide another level of visual reasoning for why the four legs cause the image to be a dog. We explore whether our framework can provide even more fundamental explanations for the generated rationales. + +To obtain sub-rationales, we query GPT3 with: + +Q: What are useful visual features for distinguishing a {attribute name} of a {category name} in a photo? +A: There are several useful visual features to tell there is a {attribute name} of a {category name} in a photo: + +After getting the sub-rationales through language chain of thought, we transfer the knowledge to visual domain by Google query: + +A photo of {CATEGORY}, because there is {sub-level attribute name} {attribute name} + +where we collect 10583 images that contain attributes of specific patterns denoted by the sub-rationales. We split the dataset into an $80\%$ training set and $20\%$ of testing set. + +Table 5. Accuracy for hierarchical visual rationales. On CIFAR $^{-10^{+}}$ categories, we evaluate CLIP and our models' ability to get the category, the rationales, and the rationales' explanations correct (RR). Our method produces better sub-rationales than CLIP. + +
RRRWWRWW
CLIP-H/140.0538.140.2061.61
Ours26.1953.861.5818.35
+ +We train our why prompt with the same objective in Equation 4. We then evaluate the correctness of the rationales and the sub-rationales. We experiment on CIFAR- $10^{+}$ and train the model for 25 epochs. When categories, rationales, and sub-rationales are correct, it is counted as doubly right (RR). In Table 5, baseline CLIP has 0 accuracy. Our method improves RR by 26 points. In Figure 7, we visualize this hierarchical rationale, where our method can produce sub-rationales that explains the rationales hierarchically. + +# 4.4. User Study + +To evaluate the quality of our doubly right dataset, we conduct a human study. We show 200 images randomly sampled from our dataset and ask the user to check whether the category and rationales match what's inside the image. We conduct this study on 20 participants. Since the task requires visual reasoning, it takes 20 to 40 minutes for one participant to complete the study. On average, the user thinks $86.2\%$ of the annotation is correct, with a standard deviation of 8.5. This shows our pipeline can collect visual data with visual rationales of reasonably high quality. + +# 5. Conclusion + +In this paper, We study an essential yet under-explored visual problem, getting the correct rationales for the predictions, which we name as the "doubly right" object recognition task. We construct large-scale datasets containing categories from various datasets with rich rationales, which allows us to evaluate this doubly right metric directly. Our work proposes a pipeline that transfers the rationales knowledge from language models to visual models, which significantly improves the doubly right object recognition accuracy on both seen and unseen categories. Our work provides a benchmark and algorithm that allows the visual recognition field to push this doubly right task forward. + +# Acknowledgement + +This research is based on work partially supported by the DARPA GAILA program, the DARPA KAIROS program, the NSF NRI Award #2132519, a GE/DARPA grant, a CAIT grant, and gifts from JP Morgan, DiDi, and Accenture. We thank Jianan Yao on feedback for user study. + +# References + +[1] Alexandre Alahi, Kratarth Goel, Vignesh Ramanathan, Alexandre Robicquet, Li Fei-Fei, and Silvio Savarese. Social lstm: Human trajectory prediction in crowded spaces. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 961–971, 2016. +[2] Marco Ancona, Enea Ceolini, Cengiz Öztireli, and Markus Gross. Towards better understanding of gradient-based attribution methods for deep neural networks. 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International Journal of Computer Vision, 130(9):2337-2348, 2022. \ No newline at end of file diff --git a/2023/Doubly Right Object Recognition_ A Why Prompt for Visual Rationales/images.zip b/2023/Doubly Right Object Recognition_ A Why Prompt for Visual Rationales/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..d23d1b19c64509026addbc52efe9f0d60fe85dd5 --- /dev/null +++ b/2023/Doubly Right Object Recognition_ A Why Prompt for Visual Rationales/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:071cdc908ce0f6856d70132c124c0f789a62799a7a2a752a0eb46cba2aa975dc +size 829415 diff --git a/2023/Doubly Right Object Recognition_ A Why Prompt for Visual Rationales/layout.json b/2023/Doubly Right Object Recognition_ A Why Prompt for Visual Rationales/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..92ba98f2d2f1e8973f976e93899d04e296f75dce --- /dev/null +++ b/2023/Doubly Right Object Recognition_ A Why Prompt for Visual Rationales/layout.json @@ -0,0 +1,8150 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 77, + 103, + 516, + 120 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 103, + 516, + 120 + ], + "spans": [ + { + "bbox": [ + 77, + 103, + 516, + 120 + ], + "type": "text", + "content": "Doubly Right Object Recognition: A Why Prompt for Visual Rationales" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 116, + 141, + 475, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 141, + 475, + 185 + ], + "spans": [ + { + "bbox": [ + 116, + 141, + 475, + 185 + ], + "type": "text", + "content": "Chengzhi Mao1 \nRevant Teotia1 \nAmrutha Sundar1 \nSachit Menon1 \nJunfeng Yang1 \nXin Wang2 \nCarl Vondrick1 \n1Columbia University \n2Microsoft Research" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 78, + 187, + 515, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 187, + 515, + 198 + ], + "spans": [ + { + "bbox": [ + 78, + 187, + 515, + 198 + ], + "type": "text", + "content": "{mcz,rt2891,as6431,sm4934,junfeng,vondrick}@cs.columbia.edu，wanxin@microsoft.com" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 227, + 191, + 239 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 227, + 191, + 239 + ], + "spans": [ + { + "bbox": [ + 143, + 227, + 191, + 239 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 251, + 290, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 251, + 290, + 456 + ], + "spans": [ + { + "bbox": [ + 45, + 251, + 290, + 456 + ], + "type": "text", + "content": "Many visual recognition models are evaluated only on their classification accuracy, a metric for which they obtain strong performance. In this paper, we investigate whether computer vision models can also provide correct rationales for their predictions. We propose a \"doubly right\" object recognition benchmark, where the metric requires the model to simultaneously produce both the right labels as well as the right rationales. We find that state-of-the-art visual models, such as CLIP, often provide incorrect rationales for their categorical predictions. However, by transferring the rationales from language models into visual representations through a tailored dataset, we show that we can learn a \"why prompt,\" which adapts large visual representations to produce correct rationales. Visualizations and empirical experiments show that our prompts significantly improve performance on doubly right object recognition, in addition to zero-shot transfer to unseen tasks and datasets." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 478, + 127, + 490 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 478, + 127, + 490 + ], + "spans": [ + { + "bbox": [ + 47, + 478, + 127, + 490 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 498, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 287, + 628 + ], + "type": "text", + "content": "Computer vision models today are able to achieve high accuracy – sometimes super-human – at correctly recognizing objects in images. However, most models today are not evaluated on whether they get the prediction right for the right reasons [14, 19, 48, 53]. Learning models that can explain their own decision is important for building trustworthy systems, especially in applications that require human-machine interactions [2, 15, 37, 50]. Rationales that justify the prediction can largely improve user trust [54], which is a crucial metric that the visual recognition field should push forward in the future." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "content": "Existing methods in interpretability have investigated how to understand which features contribute to the models' prediction [33, 34, 44, 46, 47, 52, 60]. However, saliency explanations are often imprecise, require domain expertise to understand, and also cannot be evaluated. [20, 22] have instead explored verbal rationales to justify the decision-making. However, they require manual collections of the" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 315, + 213, + 535, + 322 + ], + "blocks": [ + { + "bbox": [ + 315, + 213, + 535, + 322 + ], + "lines": [ + { + "bbox": [ + 315, + 213, + 535, + 322 + ], + "spans": [ + { + "bbox": [ + 315, + 213, + 535, + 322 + ], + "type": "image", + "image_path": "7b9867f4f63f610f8d0921009fa765c556696293e74fddec536488d03308bd09.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 335, + 545, + 390 + ], + "lines": [ + { + "bbox": [ + 305, + 335, + 545, + 390 + ], + "spans": [ + { + "bbox": [ + 305, + 335, + 545, + 390 + ], + "type": "text", + "content": "Figure 1. Visual reasoning for doubly right object recognition task. Motivated by prompting in NLP, we learn a why prompt from multimodal data, which allows us to instruct visual models to predict both the right category and the correct rationales that justify the prediction." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 399, + 545, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 399, + 545, + 422 + ], + "spans": [ + { + "bbox": [ + 305, + 399, + 545, + 422 + ], + "type": "text", + "content": "plausible rationales in the first place, which subsequently are limited to small-scale datasets and tasks [24, 56]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 425, + 545, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 425, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 425, + 545, + 555 + ], + "type": "text", + "content": "Scalable methods for explainability have been developed in natural language processing (NLP) through prompting. By adding additional instructions to the input, such as the sentence \"think step-by-step,\" language models then output descriptions of their reasoning through the chain of thought process [57]. Since the explanations are verbal, they are easily understandable by people, and since the mechanism emerges without explicit supervision, it is highly scalable. In this paper, we investigate whether visual representations can also explain their reasoning through visual chain-of-thought prompts." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 557, + 545, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 545, + 688 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 545, + 688 + ], + "type": "text", + "content": "Our paper first introduces a benchmark for doubly right object recognition, where computer vision models must predict both correct categorical labels as well as correct rationales. Our benchmark is large, and covers many categories and datasets. We found that the visual representations do not have double right capability out-of-the-box on our benchmark. The recent large-scale image-language pretrained models [41, 49] can retrieve open-world language descriptions that are closest to the image embedding in the feature space, serving as verbal explanations. However, the models often select the wrong rationales." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "Instead, we propose a framework to explicitly transfer the chain-of-thought reasoning from NLP models into" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "2722" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 49, + 72, + 286, + 274 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 72, + 286, + 274 + ], + "spans": [ + { + "bbox": [ + 49, + 72, + 286, + 274 + ], + "type": "text", + "content": "vision models. We first query the large-scale language model [9] via the chain-of-thought reasoning for object category, where we obtain language rationales that explain discriminative features for an object. We then collect images containing both the category and the rationale features using Google image search. We then train visual prompts to transfer the verbal chain of thought to visual chain of thought with contrastive learning, where features of images and their rationales are pulled together. Our \"why\" prompts obtain up to 26 points gain at doubly right performance when evaluated on our benchmark. In addition, visualizations and quantitative results show that our why prompts zero-shot transfer to unseen tasks and datasets. We believe this \"doubly right\" object recognition task is a future direction which the visual recognition field should go forward for. Our data and code is available at https://github.com/cvlab-columbia/DoubleRight." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 49, + 286, + 132, + 298 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 286, + 132, + 298 + ], + "spans": [ + { + "bbox": [ + 49, + 286, + 132, + 298 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 49, + 306, + 286, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 306, + 286, + 533 + ], + "spans": [ + { + "bbox": [ + 49, + 306, + 286, + 533 + ], + "type": "text", + "content": "Explainability. Visual recognition models achieve high performance on the classification tasks, yet they often provide vague and unreliable interpretations and rationales [8]. There are two lines of research for interpreting image classification using neural networks: feature visualization and language explanation. Feature visualization methods [6, 32-34] find the inputs that maximize the outputs of learned features. Gradient-based feature visualization [28, 42, 44, 46, 47, 52, 60] highlight the input features/pixels in images that are most important for the network to make decisions. Since the visualizations are often abstract, it is hard for a non-expert to understand. In addition, saliency map [44] highlights regions that may contain overlapping concepts such as color, texture, and shape, which is hard to disentangle. The second line of research uses language-based explanation methods [20, 22] to generate visual explanations. However, those methods require human annotations, which limits their ability to evaluate on a larger scale." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 49, + 534, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 534, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 49, + 534, + 286, + 712 + ], + "type": "text", + "content": "External Knowledge. Visual models often learn spurious correlations without external knowledge [29]. External knowledge allows models to learn the right features and obtain better transferability [26, 45]. Large-scale pretrained language models, such as GPT-3 [9], contains knowledge and commonsense learned from the Internet [38]. [57] shows that designing the right prompt, such as the chain of thought, improves the model's ability for language reasoning, which we leverage as an external knowledge source. Other sources of external knowledge include interactions [1, 11, 55], physics [31, 59], etc. [30] provides descriptions together with the objective category, which improves recognition performance. However, since they do not annotate rationales in their approach, they cannot measure CLIP's ability to produce the right rationales." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 308, + 72, + 544, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 72, + 544, + 167 + ], + "spans": [ + { + "bbox": [ + 308, + 72, + 544, + 167 + ], + "type": "text", + "content": "Visual Attributes Several works have studied visual attributes in images [17,25,27,35,36,39,63]. [58] used the visual attributes for animal classification and [23] used them for face verification. However, some of the attributes are spurious correlated [51] with the prediction task. In this work, we aim to generate visual rationales that produce robust visual attributes like shape and parts, instead of spurious features such as the background." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 308, + 169, + 544, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 169, + 544, + 289 + ], + "spans": [ + { + "bbox": [ + 308, + 169, + 544, + 289 + ], + "type": "text", + "content": "Visual Reasoning. [61] proposed a new cognition benchmark that the model needs to predict both the answer and the rationale to be correct. Visual Question Answering [3] performs visual understanding as a QA task, such as questions about COCO images. However, the questions are not asking for rationales to justify object recognition. [62] shows that multi-modal vision language models can perform zero-shot image-language tasks, such as image captioning. However, all existing visual reasoning work does not directly evaluate object recognition on the rationales they provided." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 308, + 289, + 544, + 420 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 289, + 544, + 420 + ], + "spans": [ + { + "bbox": [ + 308, + 289, + 544, + 420 + ], + "type": "text", + "content": "Prompting. Prompt tuning is a lightweight adaptation method for language task [64-66]. Recently, the computer vision field has adapted the language and proposed the visual prompts to adapt vision models [4, 5, 21, 43]. Due to their lightweight, it has been shown effective for continuous learning [12]. One advantage of the visual prompt is that it does not require model access at test time, which is flexible [4]. While existing visual prompt methods focus on improving the recognition task performance, we propose to use this lightweight prompt to improve the models' ability to provide visual rationales." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 308, + 435, + 532, + 448 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 435, + 532, + 448 + ], + "spans": [ + { + "bbox": [ + 308, + 435, + 532, + 448 + ], + "type": "text", + "content": "3. Language Rationales to Visual Rationales" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 308, + 456, + 544, + 527 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 456, + 544, + 527 + ], + "spans": [ + { + "bbox": [ + 308, + 456, + 544, + 527 + ], + "type": "text", + "content": "We first introduce how to obtain the language rationales for discriminating an object. We then show how we translate the language descriptions into visual images and construct the dataset. We then propose to construct a \"why prompt\" to adapt the large visual models to produce the right rationales for their predictions." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 308, + 539, + 480, + 551 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 539, + 480, + 551 + ], + "spans": [ + { + "bbox": [ + 308, + 539, + 480, + 551 + ], + "type": "text", + "content": "3.1. Rationale from Language Model" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 308, + 558, + 544, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 558, + 544, + 712 + ], + "spans": [ + { + "bbox": [ + 308, + 558, + 544, + 712 + ], + "type": "text", + "content": "A standard way of getting visual rationales for image predictions is through manual annotation. However, manual annotation is expensive, especially when applied to large-scale datasets. Recent advances in large-scale language models, such as the GPT3, demonstrate the ability to provide various commonsense knowledge in language. By providing chain-of-thought instructions to the language model, [57] shows that language models can perform the task of interest as well as produce explanations. We can use large-scale language models as a tool to collect rationales by asking the right language prompts. In addition, since the rationales are presented in language, it is easy to understand, even for non-experts." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 750, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 750, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 750, + 314, + 757 + ], + "type": "text", + "content": "2723" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 72, + 541, + 119 + ], + "blocks": [ + { + "bbox": [ + 51, + 72, + 541, + 119 + ], + "lines": [ + { + "bbox": [ + 51, + 72, + 541, + 119 + ], + "spans": [ + { + "bbox": [ + 51, + 72, + 541, + 119 + ], + "type": "image", + "image_path": "71c2cddc1c083ed7df2421914f3a98118ce57f9700e3acd970cddec84c19541e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 127, + 547, + 160 + ], + "lines": [ + { + "bbox": [ + 46, + 127, + 547, + 160 + ], + "spans": [ + { + "bbox": [ + 46, + 127, + 547, + 160 + ], + "type": "text", + "content": "Figure 2. Examples of the rationales generated by prompting GPT3 with the chain of thought reasoning on the features of objects. We show one example from each of the six datasets—CIFAR10, CIFAR100, Food101, Caltech101, SUN, and ImageNet—we studied. The bold word is the category, and the list follows is the generated rationales. GPT3 can produce reasoning for why an object is as predicted." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 48, + 338, + 290, + 466 + ], + "blocks": [ + { + "bbox": [ + 46, + 165, + 289, + 331 + ], + "lines": [ + { + "bbox": [ + 46, + 165, + 289, + 331 + ], + "spans": [ + { + "bbox": [ + 46, + 165, + 289, + 331 + ], + "type": "text", + "content": "Table 1. List of datasets that include both the model prediction and rationales. Animals with attributes (AWA) collects discriminative attributes for animals. CUB collects verbal rationales on only birds. BDD-X collects rationales for explaining driving scenarios. VAW and Broaden collect a large number of attributes. However, they are often not the right rationales for explaining why objects are classified, such as color. The * indicates the number of annotated video frames. The existing datasets are often small-scale, limited in domains, and not annotating rationales for the object recognition task. Our framework allows the automatic collection of diversified categories over a large scale. Note that the " + }, + { + "bbox": [ + 46, + 165, + 289, + 331 + ], + "type": "inline_equation", + "content": "^+" + }, + { + "bbox": [ + 46, + 165, + 289, + 331 + ], + "type": "text", + "content": " name in our dataset, such as CIFAR- " + }, + { + "bbox": [ + 46, + 165, + 289, + 331 + ], + "type": "inline_equation", + "content": "10^{+}" + }, + { + "bbox": [ + 46, + 165, + 289, + 331 + ], + "type": "text", + "content": ", indicates that we collect the same set of categories in CIFAR-10 from google with our pipeline. Our benchmark is large, containing more categories and dataset variants than prior methods." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 338, + 290, + 466 + ], + "lines": [ + { + "bbox": [ + 48, + 338, + 290, + 466 + ], + "spans": [ + { + "bbox": [ + 48, + 338, + 290, + 466 + ], + "type": "table", + "html": "
Dataset NameNumber of CategoriesNumber of DescriptionsNumber of ImagesFor Right Rationales
AWA [24]508530,475Yes
CUB [20,56]200N/A11,788Yes
BDD-X [22]9061,66826,000*Yes
VAW [40]N/A65072,274No
Broaden [7]5841,30062,476No
Ours CIFAR-10+10632,201Yes
Ours CIFAR-100+10054018,318Yes
Ours Food101+10143515,212Yes
Ours Caltech101+10151616,849Yes
Ours SUN+3972,17075,381Yes
Ours ImageNet+10005,810271,016Yes
", + "image_path": "f2fd7dcde204093ec2758cda6b82368102fe60e6e2929698939e9ba7f5155c2d.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 487, + 287, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 487, + 287, + 548 + ], + "spans": [ + { + "bbox": [ + 46, + 487, + 287, + 548 + ], + "type": "text", + "content": "Motivated by the recent work in language prompting [9, 30], we propose to ask the language model: what are the valid rationales for an object prediction? Specifically, to obtain rationales for visual objects, we ask GPT3 the following question:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 555, + 269, + 622 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 47, + 555, + 269, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 555, + 269, + 589 + ], + "spans": [ + { + "bbox": [ + 47, + 555, + 269, + 589 + ], + "type": "text", + "content": "Q: What are useful visual features for distinguishing a {category name} in a photo?" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 590, + 269, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 590, + 269, + 622 + ], + "spans": [ + { + "bbox": [ + 47, + 590, + 269, + 622 + ], + "type": "text", + "content": "A: There are several useful visual features to tell there is a {category name} in a photo:" + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "type": "text", + "content": "where GPT3 automatically generates the answer for us, which scales to large, unseen categories. In Figure 2, we show random examples of the rationales generated by querying GPT3. Each category is provided with a list of discriminative features for the category, which is consistent with how people explain their predictions." + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 314, + 165, + 539, + 282 + ], + "blocks": [ + { + "bbox": [ + 314, + 165, + 539, + 282 + ], + "lines": [ + { + "bbox": [ + 314, + 165, + 539, + 282 + ], + "spans": [ + { + "bbox": [ + 314, + 165, + 539, + 282 + ], + "type": "image", + "image_path": "17db92a069c2437730cc42cac4a5360c6eddc5978ca1e74e3d72cf9bdf1d3728.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 290, + 546, + 335 + ], + "lines": [ + { + "bbox": [ + 304, + 290, + 546, + 335 + ], + "spans": [ + { + "bbox": [ + 304, + 290, + 546, + 335 + ], + "type": "text", + "content": "Figure 3. Histogram of the number of images per ImageNet category retrieved by Google search. There are natural imbalances in the data. Learning model under such imbalanced natural data distribution is an interesting problem to study." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 342, + 508, + 356 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 342, + 508, + 356 + ], + "spans": [ + { + "bbox": [ + 306, + 342, + 508, + 356 + ], + "type": "text", + "content": "3.2. Knowledge Transfer to Visual Domain" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 361, + 545, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 361, + 545, + 456 + ], + "spans": [ + { + "bbox": [ + 304, + 361, + 545, + 456 + ], + "type": "text", + "content": "Since not every rationale exists in every image of the given object, we cannot directly apply this list of rationales to images based on their category. We need external knowledge to collect images containing specified rationales, so that we can correspond the language rationales to the visual rationals in images. Prior work [45] uses structured external knowledge from Wiktionary and WordNet to obtain images with text descriptions." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 458, + 545, + 541 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 458, + 545, + 541 + ], + "spans": [ + { + "bbox": [ + 304, + 458, + 545, + 541 + ], + "type": "text", + "content": "In the era of the Internet, people often Google a new word if they don't know what the object — the word refers to — looks like. Once people see the image examples from Google, they quickly understand what the word refers to in the real world. Our method is motivated by this natural procedure, where our system Googles \"what the rationales look like\" to visually understand them." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 542, + 545, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 542, + 545, + 638 + ], + "spans": [ + { + "bbox": [ + 304, + 542, + 545, + 638 + ], + "type": "text", + "content": "We propose to leverage this external knowledge from web search engines, a larger-scale knowledge base than Wiktionary [45]. We use Google image search to obtain images that contain our specified visual features, and we find that the returned images match the language queries with high accuracy. The search engine serves as a cross-modal translator, translating the knowledge from the language domain to the visual domain by retrieving images." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 639, + 545, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 639, + 545, + 663 + ], + "spans": [ + { + "bbox": [ + 304, + 639, + 545, + 663 + ], + "type": "text", + "content": "We use the following queries to query images that belong to our specified category and contain our specified attribute:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 670, + 518, + 713 + ], + "type": "list", + "angle": 0, + "index": 19, + "blocks": [ + { + "bbox": [ + 306, + 670, + 518, + 691 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 670, + 518, + 691 + ], + "spans": [ + { + "bbox": [ + 306, + 670, + 518, + 691 + ], + "type": "text", + "content": "1. {category name} which has {attribute name}" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 692, + 512, + 703 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 692, + 512, + 703 + ], + "spans": [ + { + "bbox": [ + 306, + 692, + 512, + 703 + ], + "type": "text", + "content": "2. {attribute name} of {category name}" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 307, + 703, + 507, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 703, + 507, + 713 + ], + "spans": [ + { + "bbox": [ + 307, + 703, + 507, + 713 + ], + "type": "text", + "content": "3. a photo of {category name} because" + } + ] + } + ], + "index": 18 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2724" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 71, + 542, + 206 + ], + "blocks": [ + { + "bbox": [ + 52, + 71, + 542, + 206 + ], + "lines": [ + { + "bbox": [ + 52, + 71, + 542, + 206 + ], + "spans": [ + { + "bbox": [ + 52, + 71, + 542, + 206 + ], + "type": "image", + "image_path": "08f662d5a1cc47dc7a81c1b8e5d31a3365f20f3723ccbc08666e9168be7d11cb.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 214, + 547, + 248 + ], + "lines": [ + { + "bbox": [ + 46, + 214, + 547, + 248 + ], + "spans": [ + { + "bbox": [ + 46, + 214, + 547, + 248 + ], + "type": "text", + "content": "Figure 4. Examples for the images in our collected ImageNet" + }, + { + "bbox": [ + 46, + 214, + 547, + 248 + ], + "type": "inline_equation", + "content": "^+" + }, + { + "bbox": [ + 46, + 214, + 547, + 248 + ], + "type": "text", + "content": " dataset, where each image corresponds to one category label and one rationale. We show three random categories, and for each category, we show three random rationales. The rationales are consistent with the image features that decide the object's category." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 67, + 255, + 203, + 266 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 255, + 203, + 266 + ], + "spans": [ + { + "bbox": [ + 67, + 255, + 203, + 266 + ], + "type": "text", + "content": "there is {attribute name}" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 275, + 287, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 275, + 287, + 323 + ], + "spans": [ + { + "bbox": [ + 46, + 275, + 287, + 323 + ], + "type": "text", + "content": "and we retrieve the top 50 images returned by Google search. More query sentences can be constructed if more images are needed, which we leave for future work. We remove the duplicated and incorrect images in preprocessing." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 324, + 290, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 324, + 290, + 575 + ], + "spans": [ + { + "bbox": [ + 46, + 324, + 290, + 575 + ], + "type": "text", + "content": "Google image search allows us to obtain images containing specific attributes. We perform the above automatic pipeline on ImageNet categories and obtain a dataset that contains images and the rationales that explain why this image is a particular category. For the dataset collected with our framework, we show a histogram of the number of images per ImageNet category in Figure 3. The data is S-curved due to the natural, non-interventional collection procedure. We also show examples of rationales and the retrieved images in Figure 4, where images can often be explained by rationales. Since our system is automatic, we in addition run our pipeline on the categories in CIFAR-10, CIFAR-100, Food101, Caltech101, and SUN datasets. Table 1 shows the scale of our collected images and compares them with prior datasets that are related to our work. Our pipeline allows richer rationales and is more extensive in the number of images and categories. To evaluate how accurate the Google image search can retrieve the images with the specified attribute as well as the category, we conduct a human study on the quality and consistency, which we describe in Section 4.4." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 585, + 194, + 598 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 585, + 194, + 598 + ], + "spans": [ + { + "bbox": [ + 47, + 585, + 194, + 598 + ], + "type": "text", + "content": "3.3. Learning the Why Prompt" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 605, + 287, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 688 + ], + "type": "text", + "content": "Using external knowledge from both the language model and Google, we show we can collect image datasets containing both the category and rationales. Our pipeline allows us to evaluate the quality of this doubly right task on a large scale over several datasets for the first time. Our results show that doubly right object recognition is a challenging task for large visual models, such as CLIP." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 689, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 713 + ], + "type": "text", + "content": "We then seek a way to adapt and improve large pretrained models so that they can provide the correct rationale" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 255, + 545, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 255, + 545, + 338 + ], + "spans": [ + { + "bbox": [ + 304, + 255, + 545, + 338 + ], + "type": "text", + "content": "for the predictions. Motivated by the prompting in natural language processing, we propose constructing a visual \"why\" prompt that instructs the model to produce the right rationales for the prediction. We optimize the visual prompt to ask \"what are the visual rationales that explains the prediction of this image\". We use the following input prompts or deep prompts to adapt the model." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 338, + 545, + 385 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 338, + 545, + 385 + ], + "spans": [ + { + "bbox": [ + 304, + 338, + 545, + 385 + ], + "type": "text", + "content": "Prompt Design. We study how to adapt transformer-based models since they are state-of-the-art. Our visual why prompts append additional tokens " + }, + { + "bbox": [ + 304, + 338, + 545, + 385 + ], + "type": "inline_equation", + "content": "P_{k}" + }, + { + "bbox": [ + 304, + 338, + 545, + 385 + ], + "type": "text", + "content": " to the input sequence of the vision transformer:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 378, + 396, + 545, + 408 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 378, + 396, + 545, + 408 + ], + "spans": [ + { + "bbox": [ + 378, + 396, + 545, + 408 + ], + "type": "interline_equation", + "content": "\\mathbf {x} = \\left[ \\mathbf {x}; P _ {0}, P _ {1}, \\dots , P _ {k} \\right] \\tag {1}", + "image_path": "015d6f98e551216b86d3a2f80c040fec243d97fb87379a2c96d3c6ea6df8bf24.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 417, + 545, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 417, + 545, + 441 + ], + "spans": [ + { + "bbox": [ + 304, + 417, + 545, + 441 + ], + "type": "text", + "content": "The remaining transformer parameters and computations are kept the same as the original." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 441, + 545, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 441, + 545, + 514 + ], + "spans": [ + { + "bbox": [ + 304, + 441, + 545, + 514 + ], + "type": "text", + "content": "Deep prompt. Besides adding context to the input sequence, the deep prompting method [21] adds prompts to the intermediate layers in the transformer, which is a more powerful adaptation method than single-layer input prompt. Let " + }, + { + "bbox": [ + 304, + 441, + 545, + 514 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i" + }, + { + "bbox": [ + 304, + 441, + 545, + 514 + ], + "type": "text", + "content": " be the latent token sequence of the " + }, + { + "bbox": [ + 304, + 441, + 545, + 514 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 441, + 545, + 514 + ], + "type": "text", + "content": "-th layer in the transformer. We can add a prompt to each latent layer:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 373, + 521, + 545, + 536 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 373, + 521, + 545, + 536 + ], + "spans": [ + { + "bbox": [ + 373, + 521, + 545, + 536 + ], + "type": "interline_equation", + "content": "\\mathbf {x} _ {i} = \\left[ \\mathbf {x} _ {i} ^ {0}; P _ {i}, P _ {i} ^ {1}, \\dots , P _ {i} ^ {k} \\right] \\tag {2}", + "image_path": "ccdaa0258d2b9f479a42c23a7861d05b154c77c457865348b757f07dfb402d1a.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 374, + 537, + 545, + 550 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 374, + 537, + 545, + 550 + ], + "spans": [ + { + "bbox": [ + 374, + 537, + 545, + 550 + ], + "type": "interline_equation", + "content": "\\mathbf {x} _ {i + 1} = \\operatorname {H e a d} \\left(\\mathbf {x} _ {i}\\right) \\tag {3}", + "image_path": "87ef22c7c98d9af862edeb65b64bbd629e311337792253596624d52991116b15.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 559, + 545, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 559, + 545, + 594 + ], + "spans": [ + { + "bbox": [ + 304, + 559, + 545, + 594 + ], + "type": "text", + "content": "where the Head indicates the transformer block. We find deep prompt is particularly useful for learning on large-scale datasets, such as ImageNet." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 595, + 545, + 679 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 595, + 545, + 679 + ], + "spans": [ + { + "bbox": [ + 304, + 595, + 545, + 679 + ], + "type": "text", + "content": "Learning Objective. We now introduce the training objective to instruct models for doubly right object recognition. We use cross-modal image-to-text contrastive learning to train the model for the right rationales. Using our above pipeline, we have collected a set of images and their rationales, which we denote as " + }, + { + "bbox": [ + 304, + 595, + 545, + 679 + ], + "type": "inline_equation", + "content": "\\{(\\mathbf{x}_i, \\mathbf{t}_i)\\}" + }, + { + "bbox": [ + 304, + 595, + 545, + 679 + ], + "type": "text", + "content": ". In contrast to the prior text prompts for object recognition, which uses:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 685, + 463, + 696 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 685, + 463, + 696 + ], + "spans": [ + { + "bbox": [ + 306, + 685, + 463, + 696 + ], + "type": "text", + "content": "This is a photo of [CATEGORY]" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 701, + 499, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 701, + 499, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 701, + 499, + 713 + ], + "type": "text", + "content": "we instead create the training text prompt to be:" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2725" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 148 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 148 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 148 + ], + "type": "text", + "content": "Table 2. Benchmarking six large-scale image-language pretrained models on doubly right recognition over six datasets. The accuracy for doubly right is gray-scaled. We bold the best accuracy. " + }, + { + "bbox": [ + 46, + 70, + 547, + 148 + ], + "type": "inline_equation", + "content": "\\uparrow" + }, + { + "bbox": [ + 46, + 70, + 547, + 148 + ], + "type": "text", + "content": " indicates higher number is better. For the same CLIP model, when model capacity increases from Res50 to H/14, the models' ability to get doubly right also increases, even though CLIP has never been trained on this metric. However, the doubly right accuracy on large-scale datasets is still low. For example, the double right accuracy is less than " + }, + { + "bbox": [ + 46, + 70, + 547, + 148 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 46, + 70, + 547, + 148 + ], + "type": "text", + "content": " on ImageNet. While larger model provides higher accuracy for object classification, they often provide wrong rationales, as indicated by the increase in RW percentage. Our evaluation suggests that this new doubly right object recognition task is challenging for existing large-scale visual models." + } + ] + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 100, + 156, + 493, + 312 + ], + "blocks": [ + { + "bbox": [ + 100, + 156, + 493, + 312 + ], + "lines": [ + { + "bbox": [ + 100, + 156, + 493, + 312 + ], + "spans": [ + { + "bbox": [ + 100, + 156, + 493, + 312 + ], + "type": "table", + "html": "
ModelCIFAR-10+CIFAR-100+Food101+
RR↑RW↓WR↓WW↓RR↑RW↓WR↓WW↓RR↑RW↓WR↓
FLAVA29.4453.045.8311.683.5759.725.4431.263.9555.784.86
CLIP-Res5030.6550.858.519.974.5158.947.7628.786.5361.475.31
CLIP-Res10130.4150.618.7610.215.0960.317.4127.195.2364.654.61
CLIP-B/3236.9846.719.007.305.2359.937.3027.535.4863.575.41
CLIP-B/1635.2849.639.255.835.6164.096.1624.136.0467.654.26
CLIP-L/1442.5744.527.065.846.4363.717.7322.135.7370.074.30
ModelCaltech101+SUN+ImageNet+
RR↑RW↓WR↓WW↓RR↑RW↓WR↓WW↓RR↑RW↓WR↓
FLAVA2.2161.573.8532.380.9514.6210.7273.700.4028.313.58
CLIP-Res504.1361.605.3126.690.7819.8710.9368.410.6140.423.69
CLIP-Res1014.5764.244.6125.460.8921.2911.6866.750.6542.743.64
CLIP-B/324.5165.925.4224.150.8623.3210.7265.160.6842.693.87
CLIP-B/164.6068.304.8422.250.8123.4110.5065.680.6346.733.41
CLIP-L/145.9966.555.9621.500.9424.2711.2163.580.7250.004.34
", + "image_path": "8ddbada9bd3f0b904a3fca01d6cfcde1c7c2fa81eabb75f683073dd9d1ad4a69.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 322, + 547, + 368 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 322, + 547, + 368 + ], + "spans": [ + { + "bbox": [ + 46, + 322, + 547, + 368 + ], + "type": "text", + "content": "Table 3. Gain of using why prompt to adapt models to perform doubly right object recognition. We evaluate the CLIP-H/14 model, except for ImageNet, where we use CLIP-B/32 due to the large dataset size. We use a deep prompt on ImageNet, which is indicated by *. We bold the best doubly right accuracy. Learning a why prompt significantly improves the models' ability to predict the right category as well as the right rationales, reducing the failures when the model predicts the right category with wrong rationales." + } + ] + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 115, + 376, + 479, + 457 + ], + "blocks": [ + { + "bbox": [ + 115, + 376, + 479, + 457 + ], + "lines": [ + { + "bbox": [ + 115, + 376, + 479, + 457 + ], + "spans": [ + { + "bbox": [ + 115, + 376, + 479, + 457 + ], + "type": "table", + "html": "
DatasetsPrompt LengthRR↑RW↓WR↓WW↓
BaselineOursBaselineOursBaselineOursBaselineOurs
CIFAR-10+342.5770.8244.5218.257.066.325.844.62
CIFAR-100+36.4322.2763.7144.617.739.9722.1323.14
Food101+35.7325.2570.0751.834.305.8319.9117.08
Caltech101+35.9923.6466.5552.435.965.8621.5018.06
SUN+1000.946.7024.278.2911.2123.7663.5861.24
ImageNet+30*0.683.6342.6921.703.877.6652.7625.34
", + "image_path": "e738144926c5135bae4cb3d87523597e7ba92f9ce00c2cefb391e75a645ad443.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 478, + 250, + 499 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 478, + 250, + 499 + ], + "spans": [ + { + "bbox": [ + 47, + 478, + 250, + 499 + ], + "type": "text", + "content": "This is a photo of [CATEGORY] because there is [RATIONALE]" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 506, + 287, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 506, + 287, + 529 + ], + "spans": [ + { + "bbox": [ + 46, + 506, + 287, + 529 + ], + "type": "text", + "content": "This allows the model to learn what is the correct rationales that explain the category prediction." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 529, + 289, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 529, + 289, + 601 + ], + "spans": [ + { + "bbox": [ + 46, + 529, + 289, + 601 + ], + "type": "text", + "content": "We use the pretrained image-language model, where we encode the image with an image encoder " + }, + { + "bbox": [ + 46, + 529, + 289, + 601 + ], + "type": "inline_equation", + "content": "F_{\\theta}" + }, + { + "bbox": [ + 46, + 529, + 289, + 601 + ], + "type": "text", + "content": " and the corresponding rationale with a text encoder " + }, + { + "bbox": [ + 46, + 529, + 289, + 601 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 529, + 289, + 601 + ], + "type": "text", + "content": ". To train the model to rank the correct rationales higher than the other negative rationales, we minimize the following image-to-text contrastive loss function," + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 609, + 290, + 651 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 609, + 290, + 651 + ], + "spans": [ + { + "bbox": [ + 47, + 609, + 290, + 651 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {s} (\\mathbf {x}, \\mathbf {t}, \\mathbf {y}) = - \\mathbb {E} _ {i, j} \\left[ \\mathbf {y} _ {i j} \\log \\frac {\\exp \\left(\\cos \\left(\\mathbf {z} _ {i} ^ {(I)} , \\mathbf {z} _ {j} ^ {(T)}\\right) / \\tau\\right)}{\\sum_ {k} \\exp \\left(\\cos \\left(\\mathbf {z} _ {i} ^ {(I)} , \\mathbf {z} _ {k} ^ {(T)}\\right) / \\tau\\right)} \\right], \\tag {4}", + "image_path": "9f474c5c381e27565c63683096e597779b3a08aaabc0e7a4abe71010ccde5920.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 651, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 651, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 651, + 289, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 651, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_i^{(I)} = F_\\theta (\\mathbf{x}_i)" + }, + { + "bbox": [ + 46, + 651, + 289, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 651, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_i^{(T)} = T(\\mathbf{t}_i)" + }, + { + "bbox": [ + 46, + 651, + 289, + 714 + ], + "type": "text", + "content": " are the features from the image and text, respectively. " + }, + { + "bbox": [ + 46, + 651, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_{ij}" + }, + { + "bbox": [ + 46, + 651, + 289, + 714 + ], + "type": "text", + "content": " indicates which image-text are paired in the dataset and which are not. We set " + }, + { + "bbox": [ + 46, + 651, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_{ij} = 1" + }, + { + "bbox": [ + 46, + 651, + 289, + 714 + ], + "type": "text", + "content": " when the image and text are from the same data point. cos denotes the cosine similarity function. " + }, + { + "bbox": [ + 46, + 651, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 651, + 289, + 714 + ], + "type": "text", + "content": " is the" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 477, + 546, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 477, + 546, + 513 + ], + "spans": [ + { + "bbox": [ + 304, + 477, + 546, + 513 + ], + "type": "text", + "content": "temperature hyperparameter to scale the confidence of the prediction. We then use gradient descent to optimize the visual prompt such that this loss is minimal." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 519, + 414, + 531 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 519, + 414, + 531 + ], + "spans": [ + { + "bbox": [ + 305, + 519, + 414, + 531 + ], + "type": "text", + "content": "3.4. Evaluation Metric" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 537, + 545, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 537, + 545, + 622 + ], + "spans": [ + { + "bbox": [ + 304, + 537, + 545, + 622 + ], + "type": "text", + "content": "We define the following metric to evaluate the models' predictions as well as their rationales. We formulate producing the rationales as a ranking task, where we provide the model sentence descriptions containing a pair-wise combination of all the categories and rationales, and the image-language model will retrieve the closer ones. Specifically, we present the model with a sentence in this format:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 626, + 508, + 649 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 626, + 508, + 649 + ], + "spans": [ + { + "bbox": [ + 306, + 626, + 508, + 649 + ], + "type": "text", + "content": "This is a photo of [CATEGORY] because there is [RATIONALE]" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 653, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 547, + 713 + ], + "type": "text", + "content": "and ask the model to return the sentence that has the closest representation to the visual embeddings. Since one image may have multiple rationales to explain the category, following the standard practice [16], we use a top-K accuracy — if the top K rationales include the ground truth, then it is" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2726" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 108, + 113, + 487, + 288 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "text", + "content": "Table 4. Zero-shot gain of using why prompt to adapt models to perform doubly right object recognition. For all datasets we use CLIP-H/14 model, except for ImageNet, where we use CLIP-B/32. We bold the best accuracy for doubly right object recognition. Our method can obtain better rationales on unseen datasets than baseline (CLIP) model." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 108, + 113, + 487, + 288 + ], + "lines": [ + { + "bbox": [ + 108, + 113, + 487, + 288 + ], + "spans": [ + { + "bbox": [ + 108, + 113, + 487, + 288 + ], + "type": "table", + "html": "
Zero-Shot TransferRR↑RW↓WR↓WW↓
Training DatasetsTesting DatasetsBaselineOursBaselineOursBaselineOursBaselineOurs
CIFAR-100+CIFAR-10+42.4754.9944.5233.587.064.875.846.57
CIFAR-100+Food101+5.738.3570.0744.614.309.9719.9123.14
CIFAR-100+Caltech101+5.9915.0766.5556.345.966.2121.5022.38
Caltech101+CIFAR-10+42.4749.6344.5239.177.065.605.845.60
Caltech101+CIFAR-100+6.4313.2063.7149.117.7310.3822.1327.30
Caltech101+Food101+5.737.3670.0761.054.304.4919.9126.69
SUN+CIFAR-10+42.4749.0044.5240.047.065.785.845.18
SUN+CIFAR-100+6.4313.1163.7149.637.738.3222.1328.93
SUN+Food101+5.738.9470.0751.904.306.6719.9132.48
SUN+Caltech101+5.9913.5866.5555.145.965.3921.5025.88
ImageNet+CIFAR-10+36.9838.6846.7143.809.009.257.308.27
ImageNet+CIFAR-100+5.2315.6759.9339.897.309.5127.5355.57
ImageNet+Food101+5.488.3163.5746.595.415.9725.5339.12
ImageNet+Caltech101+4.5116.7165.9245.425.427.6624.1530.20
ImageNet+SUN+0.861.9823.327.0210.7214.9665.1676.90
", + "image_path": "5a1784510e7840134d6e7ebdee25442bf9dccb294528ac77a050b6e67a34f8d3.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 308, + 288, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 308, + 288, + 344 + ], + "spans": [ + { + "bbox": [ + 46, + 308, + 288, + 344 + ], + "type": "text", + "content": "counted as correct. The predicted category is based on the majority vote of the top-K retrieved categories [30]. We denote the metric as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 50, + 351, + 266, + 411 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 50, + 351, + 253, + 363 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 351, + 253, + 363 + ], + "spans": [ + { + "bbox": [ + 50, + 351, + 253, + 363 + ], + "type": "text", + "content": "(1) Right classification with right rationale (RR);" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 50, + 367, + 261, + 379 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 367, + 261, + 379 + ], + "spans": [ + { + "bbox": [ + 50, + 367, + 261, + 379 + ], + "type": "text", + "content": "(2) Right classification with wrong rationale (RW);" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 50, + 383, + 261, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 383, + 261, + 396 + ], + "spans": [ + { + "bbox": [ + 50, + 383, + 261, + 396 + ], + "type": "text", + "content": "(3) Wrong classification with right rationale (WR);" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 50, + 399, + 266, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 399, + 266, + 411 + ], + "spans": [ + { + "bbox": [ + 50, + 399, + 266, + 411 + ], + "type": "text", + "content": "(4) Wrong classification with wrong rationale (WW)" + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 46, + 418, + 287, + 478 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 418, + 287, + 478 + ], + "spans": [ + { + "bbox": [ + 46, + 418, + 287, + 478 + ], + "type": "text", + "content": "We desire a high accuracy for RR and a low percentage for RW, WR, and WW. We will evaluate the above metric on our collected dataset where rationale ground truth is provided. We select " + }, + { + "bbox": [ + 46, + 418, + 287, + 478 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 46, + 418, + 287, + 478 + ], + "type": "text", + "content": " of the data as the hold-out test set. We will train the model on the remaining " + }, + { + "bbox": [ + 46, + 418, + 287, + 478 + ], + "type": "inline_equation", + "content": "80\\%" + }, + { + "bbox": [ + 46, + 418, + 287, + 478 + ], + "type": "text", + "content": " data." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 488, + 124, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 488, + 124, + 502 + ], + "spans": [ + { + "bbox": [ + 47, + 488, + 124, + 502 + ], + "type": "text", + "content": "4. Experiment" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 508, + 288, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 508, + 288, + 604 + ], + "spans": [ + { + "bbox": [ + 46, + 508, + 288, + 604 + ], + "type": "text", + "content": "We evaluate six large-scale image-language pretrained models on our doubly right benchmark. We find that the model often produces the wrong rationales for the predictions. We then show that our why prompts significantly improves the models' ability to produce the right rationales quantitatively and qualitatively. Lastly, we show that we can have a hierarchy of visual rationales where the model can provide sub-rationales." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 611, + 204, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 611, + 204, + 624 + ], + "spans": [ + { + "bbox": [ + 47, + 611, + 204, + 624 + ], + "type": "text", + "content": "4.1. Benchmark Existing Models" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "type": "text", + "content": "We start our investigation by evaluating existing large-scale image language models [41, 49] on our collected doubly right dataset. Our evaluation includes images in the category of CIFAR-10, CIFAR-100, Food101, Caltech101, SUN, and ImageNet. Since we recollect the image based on the category name of those dataset, we use " + }, + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "type": "inline_equation", + "content": "^+" + }, + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "type": "text", + "content": " to denote our collected dataset. We set " + }, + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "type": "inline_equation", + "content": "K = 5" + }, + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "type": "text", + "content": " for the top-K accuracy" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 308, + 547, + 488 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 308, + 547, + 488 + ], + "spans": [ + { + "bbox": [ + 304, + 308, + 547, + 488 + ], + "type": "text", + "content": "of the doubly right prediction. We study FLAVA [49] and five variants of CLIP [41], where evaluation results are in Table 2. We find that for the same CLIP model, increasing their capacity from Resnet 50 [18] to ViT Huge/14 [13] generally improves performance in retrieving the right rationales, even if the model has never been trained on the doubly right task. FLAVA model performs worse than all CLIP model variants, except on " + }, + { + "bbox": [ + 304, + 308, + 547, + 488 + ], + "type": "inline_equation", + "content": "\\mathrm{SUN^{+}}" + }, + { + "bbox": [ + 304, + 308, + 547, + 488 + ], + "type": "text", + "content": ". Despite the high classification accuracy, doubly right object recognition is challenging for all models, where models produce incorrect rationales more often than the correct ones. Specifically, the best CLIP-H/14 model only obtains " + }, + { + "bbox": [ + 304, + 308, + 547, + 488 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 304, + 308, + 547, + 488 + ], + "type": "text", + "content": " accuracy on " + }, + { + "bbox": [ + 304, + 308, + 547, + 488 + ], + "type": "inline_equation", + "content": "\\mathrm{ImageNet^{+}}" + }, + { + "bbox": [ + 304, + 308, + 547, + 488 + ], + "type": "text", + "content": " doubly right recognition task. Our evaluation shows that doubly right object recognition is still an open challenge for the large-scale dataset." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 500, + 491, + 513 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 500, + 491, + 513 + ], + "spans": [ + { + "bbox": [ + 305, + 500, + 491, + 513 + ], + "type": "text", + "content": "4.2. Why Prompt for Visual Rationales" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 520, + 545, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 520, + 545, + 651 + ], + "spans": [ + { + "bbox": [ + 304, + 520, + 545, + 651 + ], + "type": "text", + "content": "To adapt the vision model so that they can perform doubly right object recognition, we apply our \"why\" prompting to visual foundation models. On ImageNet" + }, + { + "bbox": [ + 304, + 520, + 545, + 651 + ], + "type": "inline_equation", + "content": "^{+}" + }, + { + "bbox": [ + 304, + 520, + 545, + 651 + ], + "type": "text", + "content": ", we adapt the CLIP-B/32 due to the large size of the dataset. We use deep prompt with prompt length 30 for each of the 12 layers. We train 10 epochs with a learning rate of 10. For all the other datasets, we adapt the best CLIP-H/14 model. We train model for 100 epochs with a learning rate of 40. We use a prompt size of 3, except for SUN where we use 100. For each dataset, we train on " + }, + { + "bbox": [ + 304, + 520, + 545, + 651 + ], + "type": "inline_equation", + "content": "80\\%" + }, + { + "bbox": [ + 304, + 520, + 545, + 651 + ], + "type": "text", + "content": " of the data and test on the hold out " + }, + { + "bbox": [ + 304, + 520, + 545, + 651 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 304, + 520, + 545, + 651 + ], + "type": "text", + "content": " test data." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "content": "We show our results in Table 3. By finding a why prompt to adapt the visual model, we significantly improve the models' ability to produce the right predictions as well as the right rationales, up to 28 points. Using our prompt, the model also sometimes predicts the wrong categories when" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "type": "text", + "content": "2727" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 56, + 542, + 358 + ], + "blocks": [ + { + "bbox": [ + 49, + 56, + 542, + 358 + ], + "lines": [ + { + "bbox": [ + 49, + 56, + 542, + 358 + ], + "spans": [ + { + "bbox": [ + 49, + 56, + 542, + 358 + ], + "type": "image", + "image_path": "849930d11443da8be7a95fff2c25fa170fd1bc7aecdb61fa30fad70d11e1cf26.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 361, + 546, + 417 + ], + "lines": [ + { + "bbox": [ + 46, + 361, + 546, + 417 + ], + "spans": [ + { + "bbox": [ + 46, + 361, + 546, + 417 + ], + "type": "text", + "content": "Figure 5. Visualization for the doubly right recognition task. For each row, we show image examples from categories of one dataset. In columns 2, 4, 7, and 9, we show the rationales produced by the model to explain the prediction. In column 3, 5, 8, and 10, we show the saliency map [10] that models look to produce the prediction and rationales. While the state-of-the-art H/14 CLIP model produces the correct category with the wrong rationales, our method can produce the correct category with the right rationales. In addition, our visual prompt also adapts the model to use the right image region to produce the prediction." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 50, + 419, + 545, + 520 + ], + "blocks": [ + { + "bbox": [ + 50, + 419, + 545, + 520 + ], + "lines": [ + { + "bbox": [ + 50, + 419, + 545, + 520 + ], + "spans": [ + { + "bbox": [ + 50, + 419, + 545, + 520 + ], + "type": "image", + "image_path": "553625481af16056b30a5f16160099e45a09230d00b0f31b2f4085aa69e91091.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 521, + 546, + 555 + ], + "lines": [ + { + "bbox": [ + 46, + 521, + 546, + 555 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 546, + 555 + ], + "type": "text", + "content": "Figure 6. Visualization for top 3 rationales. We show the original examples from SUN, Caltech101, Food101, and ImageNet datasets with high-resolution images. Even though we do not annotate rationales for images in these datasets, our method can successfully transfer the rationales learned from our data and apply them." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 561, + 288, + 668 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 561, + 288, + 668 + ], + "spans": [ + { + "bbox": [ + 46, + 561, + 288, + 668 + ], + "type": "text", + "content": "the rationales are wrong (higher WW), suggesting our why prompt achieve higher consistency in reasoning between category and rationales. Our prompt method is still effective when the prompt size is as small as 3, containing minimal parameters, which is lightweight to apply. In addition, learning our why prompt can maintain the classification accuracy on the original ImageNet validation set, where CLIP-B/32 obtains an accuracy of " + }, + { + "bbox": [ + 46, + 561, + 288, + 668 + ], + "type": "inline_equation", + "content": "59.16\\%" + }, + { + "bbox": [ + 46, + 561, + 288, + 668 + ], + "type": "text", + "content": ", and we obtain an accuracy of " + }, + { + "bbox": [ + 46, + 561, + 288, + 668 + ], + "type": "inline_equation", + "content": "59.20\\%" + }, + { + "bbox": [ + 46, + 561, + 288, + 668 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "content": "Zero-shot Transferability for Why Prompt. We find that the above generated \"why\" also transfers to unseen datasets and categories. In Table 4, we show the doubly right accu" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 561, + 545, + 668 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 561, + 545, + 668 + ], + "spans": [ + { + "bbox": [ + 304, + 561, + 545, + 668 + ], + "type": "text", + "content": "racy obtained by zero-shot transfer, where we obtain up to 12 points gain. For example, by learning the model on the " + }, + { + "bbox": [ + 304, + 561, + 545, + 668 + ], + "type": "inline_equation", + "content": "\\mathrm{SUN}^{+}" + }, + { + "bbox": [ + 304, + 561, + 545, + 668 + ], + "type": "text", + "content": " dataset which contains natural scenes, our method can teach CLIP to provide the correct rationales for food images " + }, + { + "bbox": [ + 304, + 561, + 545, + 668 + ], + "type": "inline_equation", + "content": "(\\mathrm{Food101}^{+})" + }, + { + "bbox": [ + 304, + 561, + 545, + 668 + ], + "type": "text", + "content": ", by 3 points better. This experiment shows our why prompt can adapt large scale models to produce correct predictions with right rationales, and generalize to novel categories, suggesting the effectiveness of our method." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "Visualizations on Doubly Right dataset. We visualize images from the test set of our benchmark. In Figure 5, we show the top 1 rationales retrieved by the baseline and our" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2728" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 55, + 71, + 165, + 140 + ], + "blocks": [ + { + "bbox": [ + 55, + 71, + 165, + 140 + ], + "lines": [ + { + "bbox": [ + 55, + 71, + 165, + 140 + ], + "spans": [ + { + "bbox": [ + 55, + 71, + 165, + 140 + ], + "type": "image", + "image_path": "a420b0e1096b391a73f3383c86b5f43477e20e4be9402e519d5299c050885369.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 144, + 287, + 177 + ], + "lines": [ + { + "bbox": [ + 47, + 144, + 287, + 177 + ], + "spans": [ + { + "bbox": [ + 47, + 144, + 287, + 177 + ], + "type": "text", + "content": "Figure 7. Visualizations for the hierarchical rationales on CIFAR" + }, + { + "bbox": [ + 47, + 144, + 287, + 177 + ], + "type": "inline_equation", + "content": "^{10^{+}}" + }, + { + "bbox": [ + 47, + 144, + 287, + 177 + ], + "type": "text", + "content": ". Our method obtains reasonable sub-rationales by learning an additional sub why prompt." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 205, + 77, + 246, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 205, + 77, + 246, + 84 + ], + "spans": [ + { + "bbox": [ + 205, + 77, + 246, + 84 + ], + "type": "text", + "content": "Sub-Rationales" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 173, + 92, + 237, + 99 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 173, + 92, + 237, + 99 + ], + "spans": [ + { + "bbox": [ + 173, + 92, + 237, + 99 + ], + "type": "text", + "content": "Why this is a tail of a dog?" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 173, + 100, + 270, + 122 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 173, + 100, + 270, + 106 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 173, + 100, + 270, + 106 + ], + "spans": [ + { + "bbox": [ + 173, + 100, + 270, + 106 + ], + "type": "text", + "content": "Because it is thin Because it is Long" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 173, + 107, + 246, + 114 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 173, + 107, + 246, + 114 + ], + "spans": [ + { + "bbox": [ + 173, + 107, + 246, + 114 + ], + "type": "text", + "content": "Why this is four legs of a dog?" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 173, + 115, + 269, + 122 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 173, + 115, + 269, + 122 + ], + "spans": [ + { + "bbox": [ + 173, + 115, + 269, + 122 + ], + "type": "text", + "content": "Because it is furry - Because it is long" + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 173, + 125, + 234, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 173, + 125, + 234, + 133 + ], + "spans": [ + { + "bbox": [ + 173, + 125, + 234, + 133 + ], + "type": "text", + "content": "Why this is ears of a dog?" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 173, + 133, + 268, + 140 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 173, + 133, + 268, + 140 + ], + "spans": [ + { + "bbox": [ + 173, + 133, + 268, + 140 + ], + "type": "text", + "content": "- Because it is short - Because it is wet" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 183, + 287, + 243 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 183, + 287, + 243 + ], + "spans": [ + { + "bbox": [ + 46, + 183, + 287, + 243 + ], + "type": "text", + "content": "prompted model. Our method often produces a correct explanation, while the baseline does not. We also visualize the saliency map corresponding to the rationales [10], where we can also see that the why prompt instructs the model to look at the right region to explain the prediction." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 243, + 287, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 243, + 287, + 386 + ], + "spans": [ + { + "bbox": [ + 46, + 243, + 287, + 386 + ], + "type": "text", + "content": "Qualitative results on the original dataset. In addition to evaluating the doubly right performance on our collected dataset above, we also evaluate the established, original data. We study ImageNet, SUN, Caltech, and Food101 datasets since they contain high-resolution images that allow detailed explanations. Though we cannot directly evaluate the doubly right accuracy of those dataset images since they do not contain annotated ground truth, we show visualizations for the rationales generated on those datasets. In Figure 6, we find our learned \"why\" prompt also transfers well in improving the doubly right performance on images in those datasets." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 394, + 231, + 406 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 394, + 231, + 406 + ], + "spans": [ + { + "bbox": [ + 47, + 394, + 231, + 406 + ], + "type": "text", + "content": "4.3. Analyzing Hierarchical Rationales" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 412, + 287, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 412, + 287, + 507 + ], + "spans": [ + { + "bbox": [ + 46, + 412, + 287, + 507 + ], + "type": "text", + "content": "The rationales provided by our approach may not be the basic explanations. For example, with the above method, we can explain that this is a photo of a dog because there are four legs. We are curious whether the model can also provide another level of visual reasoning for why the four legs cause the image to be a dog. We explore whether our framework can provide even more fundamental explanations for the generated rationales." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 59, + 508, + 249, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 508, + 249, + 520 + ], + "spans": [ + { + "bbox": [ + 59, + 508, + 249, + 520 + ], + "type": "text", + "content": "To obtain sub-rationales, we query GPT3 with:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 47, + 525, + 274, + 591 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 47, + 525, + 274, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 525, + 274, + 559 + ], + "spans": [ + { + "bbox": [ + 47, + 525, + 274, + 559 + ], + "type": "text", + "content": "Q: What are useful visual features for distinguishing a {attribute name} of a {category name} in a photo?" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 47, + 559, + 274, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 559, + 274, + 591 + ], + "spans": [ + { + "bbox": [ + 47, + 559, + 274, + 591 + ], + "type": "text", + "content": "A: There are several useful visual features to tell there is a {attribute name} of a {category name} in a photo:" + } + ] + } + ], + "index": 16 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 46, + 597, + 287, + 633 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 597, + 287, + 633 + ], + "spans": [ + { + "bbox": [ + 46, + 597, + 287, + 633 + ], + "type": "text", + "content": "After getting the sub-rationales through language chain of thought, we transfer the knowledge to visual domain by Google query:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 47, + 639, + 269, + 670 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 639, + 269, + 670 + ], + "spans": [ + { + "bbox": [ + 47, + 639, + 269, + 670 + ], + "type": "text", + "content": "A photo of {CATEGORY}, because there is {sub-level attribute name} {attribute name}" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "where we collect 10583 images that contain attributes of specific patterns denoted by the sub-rationales. We split the dataset into an " + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "80\\%" + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": " training set and " + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": " of testing set." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 71, + 545, + 114 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 71, + 545, + 114 + ], + "spans": [ + { + "bbox": [ + 305, + 71, + 545, + 114 + ], + "type": "text", + "content": "Table 5. Accuracy for hierarchical visual rationales. On CIFAR" + }, + { + "bbox": [ + 305, + 71, + 545, + 114 + ], + "type": "inline_equation", + "content": "^{-10^{+}}" + }, + { + "bbox": [ + 305, + 71, + 545, + 114 + ], + "type": "text", + "content": " categories, we evaluate CLIP and our models' ability to get the category, the rationales, and the rationales' explanations correct (RR). Our method produces better sub-rationales than CLIP." + } + ] + } + ], + "index": 21 + }, + { + "type": "table", + "bbox": [ + 335, + 123, + 515, + 171 + ], + "blocks": [ + { + "bbox": [ + 335, + 123, + 515, + 171 + ], + "lines": [ + { + "bbox": [ + 335, + 123, + 515, + 171 + ], + "spans": [ + { + "bbox": [ + 335, + 123, + 515, + 171 + ], + "type": "table", + "html": "
RRRWWRWW
CLIP-H/140.0538.140.2061.61
Ours26.1953.861.5818.35
", + "image_path": "a1d79a1f7426d948c5d9d7db9abdad7dca022cb5b0279b5e87c4e6b5786bb91f.jpg" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "table_body" + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 178, + 545, + 286 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 178, + 545, + 286 + ], + "spans": [ + { + "bbox": [ + 304, + 178, + 545, + 286 + ], + "type": "text", + "content": "We train our why prompt with the same objective in Equation 4. We then evaluate the correctness of the rationales and the sub-rationales. We experiment on CIFAR- " + }, + { + "bbox": [ + 304, + 178, + 545, + 286 + ], + "type": "inline_equation", + "content": "10^{+}" + }, + { + "bbox": [ + 304, + 178, + 545, + 286 + ], + "type": "text", + "content": " and train the model for 25 epochs. When categories, rationales, and sub-rationales are correct, it is counted as doubly right (RR). In Table 5, baseline CLIP has 0 accuracy. Our method improves RR by 26 points. In Figure 7, we visualize this hierarchical rationale, where our method can produce sub-rationales that explains the rationales hierarchically." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 298, + 380, + 310 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 298, + 380, + 310 + ], + "spans": [ + { + "bbox": [ + 306, + 298, + 380, + 310 + ], + "type": "text", + "content": "4.4. User Study" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 317, + 545, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 317, + 545, + 437 + ], + "spans": [ + { + "bbox": [ + 304, + 317, + 545, + 437 + ], + "type": "text", + "content": "To evaluate the quality of our doubly right dataset, we conduct a human study. We show 200 images randomly sampled from our dataset and ask the user to check whether the category and rationales match what's inside the image. We conduct this study on 20 participants. Since the task requires visual reasoning, it takes 20 to 40 minutes for one participant to complete the study. On average, the user thinks " + }, + { + "bbox": [ + 304, + 317, + 545, + 437 + ], + "type": "inline_equation", + "content": "86.2\\%" + }, + { + "bbox": [ + 304, + 317, + 545, + 437 + ], + "type": "text", + "content": " of the annotation is correct, with a standard deviation of 8.5. This shows our pipeline can collect visual data with visual rationales of reasonably high quality." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 306, + 453, + 378, + 464 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 453, + 378, + 464 + ], + "spans": [ + { + "bbox": [ + 306, + 453, + 378, + 464 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 473, + 545, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 473, + 545, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 473, + 545, + 617 + ], + "type": "text", + "content": "In this paper, We study an essential yet under-explored visual problem, getting the correct rationales for the predictions, which we name as the \"doubly right\" object recognition task. We construct large-scale datasets containing categories from various datasets with rich rationales, which allows us to evaluate this doubly right metric directly. Our work proposes a pipeline that transfers the rationales knowledge from language models to visual models, which significantly improves the doubly right object recognition accuracy on both seen and unseen categories. Our work provides a benchmark and algorithm that allows the visual recognition field to push this doubly right task forward." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 306, + 632, + 403, + 645 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 632, + 403, + 645 + ], + "spans": [ + { + "bbox": [ + 306, + 632, + 403, + 645 + ], + "type": "text", + "content": "Acknowledgement" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "This research is based on work partially supported by the DARPA GAILA program, the DARPA KAIROS program, the NSF NRI Award #2132519, a GE/DARPA grant, a CAIT grant, and gifts from JP Morgan, DiDi, and Accenture. 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Our network can drape garments over bodies of different shapes in various poses. To minimize the required amount of supervision, our draping network is trained with physics-based self-supervision and generalizes to multiple garments by being conditioned on latent codes. These can be manipulated to edit specific features of the corresponding garments. Being fully differentiable, our pipeline makes it possible to recover 3D models of garments and bodies from observations such as images and 3D scans." + ], + "image_footnote": [], + "bbox": [ + 120, + 234, + 846, + 513 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 585, + 313, + 602 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent approaches to drape garments quickly over arbitrary human bodies leverage self-supervision to eliminate the need for large training sets. However, they are designed to train one network per clothing item, which severely limits their generalization abilities. In our work, we rely on self-supervision to train a single network to drape multiple garments. This is achieved by predicting a 3D deformation field conditioned on the latent codes of a generative network, which models garments as unsigned distance fields.", + "bbox": [ + 73, + 618, + 470, + 755 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Our pipeline can generate and drape previously unseen garments of any topology, whose shape can be edited by manipulating their latent codes. Being fully differentiable, our formulation makes it possible to recover accurate 3D models of garments from partial observations – images or 3D scans – via gradient descent. Our code is publicly available at https://github.com/liren2515/DrapeNet.", + "bbox": [ + 73, + 755, + 470, + 862 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 582, + 632, + 598 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Draping digital garments over differently-shaped bodies in random poses has been extensively studied due to its many applications such as fashion design, moviemaking, video gaming, virtual try-on and, nowadays, virtual and augmented reality. Physics-based simulation (PBS) [3, 12, 23, 32, 33, 38, 39, 47-49, 51, 60] can produce outstanding results, but at a high computational cost.", + "bbox": [ + 496, + 609, + 893, + 715 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent years have witnessed the emergence of deep neural networks aiming to achieve the quality of PBS draping while being much faster, easily differentiable, and offering new speed vs. accuracy tradeoffs [15, 16, 25, 36, 44, 46, 50, 53, 55]. These networks are often trained to produce garments that resemble ground-truth ones. While effective, this requires building training datasets, consisting of ground-truth meshes obtained either from computationally expensive simulations [31] or using complex 3D scanning setups [37]. Moreover, to generalize to unseen garments and poses, these supervised approaches require training databases encompassing a great variety of samples de", + "bbox": [ + 496, + 719, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* Equal contributions", + "bbox": [ + 101, + 886, + 218, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "1451", + "bbox": [ + 483, + 944, + 513, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "picting many combinations of garments, bodies and poses.", + "bbox": [ + 76, + 90, + 464, + 107 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The recent PBNS and SNUG approaches [5, 42] address this by casting the physical models adopted in PBS into constraints used for self-supervision of deep learning models. This makes it possible to train the network on a multitude of body shapes and poses without ground-truth draped garments. Instead, the predicted garments are constrained to obey physics-based rules. However, both PBNS and SNUG require training a separate network for each garment. They rely on mesh templates for garment representation and feature one output per mesh vertex. Thus, they cannot handle meshes with different topologies, even for the same garment. This makes them very specialized and limits their applicability to large garment collections as a new network must be trained for each new clothing item.", + "bbox": [ + 75, + 109, + 468, + 321 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we introduce DrapeNet, an approach that also relies on physics-based constraints to provide self-supervision but can handle generic garments by conditioning a single draping network with a latent code describing the garment to be draped. We achieve this by coupling the draping network with a garment generative network, composed of an encoder and a decoder. The encoder is trained to compress input garments into compact latent codes that are used as input condition for the draping network. The decoder, instead, reconstructs a 3D garment model from its latent code, thus allowing us to sample and edit new garments from the learned latent space.", + "bbox": [ + 75, + 325, + 470, + 507 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Specifically, we model the output of the garment decoder as an unsigned distance function (UDF), which were demonstrated [14] to yield better accuracy and fewer interpenetrations than the inflated signed distance functions often used for this purpose [10, 19]. Moreover, UDFs can be triangulated in a differentiable way [14] to produce explicit surfaces that can easily be post-processed, making our pipeline fully differentiable. Hence, DrapeNet can not only drape garments over given body shapes but can also perform gradient-based optimization to fit garments, along with body shapes and poses, to partial observations of clothed people, such as images or 3D scans.", + "bbox": [ + 75, + 511, + 468, + 691 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions are as follows:", + "bbox": [ + 96, + 696, + 316, + 710 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We introduce a single garment draping network conditioned on a latent code to handle generic garments from a large collection (e.g. top or bottom garments);", + "- By exploiting physics-based self-supervision, our pipeline only requires a few hundred garment meshes in a canonical pose for training;", + "- Our framework enables the fast draping of new garments with high fidelity, as well as the sampling and editing of new garments from the learned latent space;", + "- Being fully differentiable, our method can be used to recover accurate 3D models of clothed people from images and 3D scans." + ], + "bbox": [ + 94, + 715, + 467, + 896 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 89, + 640, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Implicit Neural Representations for 3D Surfaces. Implicit neural representations have emerged a few years ago as an effective tool to represent surfaces whose topology is not known a priori. They can be implemented using (clipped) signed distance functions (SDF) [35] or occupancies [28]. When an explicit representation is required, it can be obtained using Marching Cubes [18] and this can be done while preserving differentiability [1,27,41]. However, they can only represent watertight surfaces.", + "bbox": [ + 496, + 114, + 890, + 250 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Thus, to represent open surfaces, such as clothes, it is possible to use inflated SDFs surrounding them. However, this entails a loss in accuracy and there has been a recent push to replace SDFs by unsigned distance functions (UDFs) [9, 52, 61]. One difficulty in so doing was that Marching Cubes was not designed with UDFs in mind, and obtaining explicit surfaces from these UDFs was therefore non-trivial. This has been addressed in [14] by modifying the Marching Cubes algorithm to operate with UDFs. We model garment with UDFs and use [14] to mesh them. Other works augment signed distance fields with covariant fields to encode open surface garments [8, 43].", + "bbox": [ + 496, + 251, + 890, + 431 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Draping Garments over 3D Bodies. Two main classes of methods coexist, physics-based algorithms [3, 21, 22, 30, 31, 48] that produce high-quality draptings but at a high computational cost, and data-driven approaches that are faster but often at the cost of realism.", + "bbox": [ + 496, + 431, + 890, + 506 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Among the latter, template-based approaches [5,7,17,34, 36,42,45,50] are dominant. Each garment is modeled by a specific triangulated mesh and a draping function is learned for each one. In other words, they do not generalize. There are however a number of exceptions. In [6, 15] the mesh is replaced by 3D point clouds that can represent generic garments. This enables deforming garments with arbitrary topology and geometric complexity, by estimating the deformation separately for each point. [59] goes further and allows differentiable changes in garment topology by sampling a fixed number of points from the body mesh. Unfortunately, this point cloud representation severely limits possible downstream applications.", + "bbox": [ + 496, + 507, + 890, + 703 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In recent approaches [10, 19], a space of garments is learned with clothing items modeled as inflated SDFs and one single shared network to predict their deformations as a 3D displacement field. This makes deployment in real-world scenarios easier and allows the reconstruction of garments from images and 3D scans. However, the inflated SDF scheme reduces realism and precludes post-processing using standard physics-based simulators or other cloth-specific downstream applications. Furthermore, both models are fully supervised and require a dataset of draped garments whose collection is extremely time-consuming.", + "bbox": [ + 496, + 704, + 890, + 869 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Alleviating the need for costly ground-truth draped garments is tackled in [5, 42], by introducing physics-based", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "1452", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/fb1663b9a6bb537ab68eba8bf474a9cb30b28d145bb1733742d29b1ba81ccd24.jpg", + "image_caption": [ + "Figure 2. Overview of our framework. Left: Garment generative network, trained to embed garments into compact latent codes and predict their unsigned distance field (UDF) from such vectors. UDFs are then meshed using [14]. Right: Garment draping network, conditioned on the latent codes of the generative network. It is trained in a self-supervised way to predict the displacements $\\Delta x$ and $\\Delta x_{\\mathrm{ref}}$ to be applied to the vertices of given garments, before skinning them according to body shape and pose $(\\beta ,\\theta)$ with the predicted blending weights $\\mathcal{W}$ . It includes an Intersection Solver module to prevent intersection between top and bottom garments." + ], + "image_footnote": [], + "bbox": [ + 83, + 89, + 415, + 311 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/ace0a9c283926b20ff2f8f1d234a7196dc81569ce3618808b0156cff179156fd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 416, + 90, + 880, + 311 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "losses to train draping networks in a self-supervised manner. The approach of [42] relies on a mass spring model to enforce the physical consistency of static garments deformed by different body poses. The method of [5] also accounts for variable body shapes and dynamic effects; furthermore, it incorporates a more realistic and expressive material model. Both methods, however, require training one network per garment, a limitation we remove.", + "bbox": [ + 75, + 400, + 470, + 521 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 540, + 168, + 555 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We aim to realistically deform and drape generic garments over human bodies of various shapes and poses. To this end, we introduce the DrapeNet framework, presented in Fig. 2. It comprises a generative network shown on the left and a draping network shown on the right. Only the first is trained in a supervised manner, but using only static unposed garments meshes. This is key to avoiding having to run physics-based simulations to generate groundtruth data. Furthermore, we condition the draping network on latent vectors representing the input garments, which allows us to use the same network for very different garments, something that competing methods [5,42] cannot do.", + "bbox": [ + 75, + 566, + 468, + 747 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The generative network is a decoder trained using an encoder that turns a garment into a latent code $\\mathbf{z}$ that can then be decoded to an Unsigned Distance Function (UDF), from which a triangulated mesh can be extracted in a differentiable manner [14]. The UDF representation allows us to accurately represent open surfaces and the many openings that garments typically feature. Since the top and bottom garments - shirts and trousers - have different patterns, we train one generative model for each. Both networks have the same architecture but different weights.", + "bbox": [ + 75, + 750, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The resulting garment generative network is only trained to output garments in a canonical shape, pose, and size that fit a neutral SMPL [24] body. Draping the resulting garments to bodies in non-canonical poses is then entrusted to a draping network, again one for the top and one for the bottom. As in [5, 19, 42], this network predicts vertex displacements w.r.t. the neutral position. The deformed garment is then skinned onto the articulated body model. To enable generalization to different tops and bottoms, we condition the draping process on the garment latent codes of the generative network, shown as $\\mathbf{z}_{\\mathrm{top}}$ and $\\mathbf{z}_{\\mathrm{bot}}$ in Fig. 2.", + "bbox": [ + 496, + 400, + 890, + 566 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We use a small database of static unposed garments loosely aligned with bodies in the canonical position to train the two garment generating networks. This being done, we exploit physics-based constraints to train in a fully self-supervised manner the top and bottom draping networks for realism, without interpenetrations with the body and between the garments themselves.", + "bbox": [ + 496, + 566, + 890, + 672 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Garment Generative Network", + "text_level": 1, + "bbox": [ + 500, + 681, + 766, + 695 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To encode garments into latent codes that can then be decoded into UDFs, we rely on a point cloud encoder that embeds points sampled from the unposed garment surface into a compact vector. This lets us obtain latent codes for previously unseen garments in a single inference pass from points sampled from its surface. This can be done given any arbitrary surface triangulation. Hence, it gives us the flexibility to operate on any given garment mesh.", + "bbox": [ + 496, + 704, + 890, + 824 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We use DGCNN [56] as the encoder. It first propagates the features of points within the same local region at multiple scales and then aggregates them into a single global embedding by max pooling. We pair it with a decoder that takes as input a latent vector, along with a point in 3D space,", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "1453", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "and returns its (unsigned) distance to the garment. The decoder is a multi-layer perceptron (MLP) that relies on Conditional Batch Normalization [54] for conditioning on the input latent vector.", + "bbox": [ + 75, + 90, + 468, + 151 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We train the encoder and the decoder by encouraging them to jointly predict distances that are small near the training garments' surface and large elsewhere. Because the algorithm we use to compute triangulated meshes from the predicted distances [14] relies on the gradient vectors of the UDF field, we also want these gradients to be as accurate as possible [2, 61]. We therefore minimize the loss", + "bbox": [ + 75, + 151, + 470, + 257 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {g a r m} = L _ {d i s t} + \\lambda_ {g} L _ {g r a d}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 178, + 263, + 468, + 281 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $L_{dist}$ encodes our distance requirements, $L_{grad}$ the gradient ones, and $\\lambda_g$ is a weight balancing their influence.", + "bbox": [ + 76, + 286, + 468, + 316 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "More formally, at training time and given a mini-batch comprising $B$ garments, we sample a fixed number $P$ of points from the surface of each one. For each resulting point cloud $\\mathbf{p}_i$ ( $1 \\leq i \\leq B$ ), we use the garment encoder $E_G$ to compute the latent code", + "bbox": [ + 75, + 316, + 468, + 392 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {z} _ {i} = E _ {G} (\\mathbf {p} _ {i}) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 223, + 398, + 468, + 416 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "and use it as input to the decoder $D_G$ . It predicts an UDF field supervised with Eq. (1), whose terms we define below.", + "bbox": [ + 76, + 421, + 468, + 450 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Distance Loss. Having experimented with many different formulations of this loss, we found the following one both simple and effective. Given $N$ points $\\{\\mathbf{x}_{ij}\\}_{j\\leq N}$ sampled from the space surrounding the $i$ -th garment, we pick a distance threshold $\\delta$ , clip all the ground-truth distance values $\\{y_{ij}\\}$ to it, and linearly normalize the clipped values to the range [0, 1]. This yields normalized ground-truth values $\\bar{y}_{ij} = \\min(y_{ij}, \\delta) / \\delta$ . Similarly, we pass the output of the final layer of $D_G$ through a sigmoid function $\\sigma(\\cdot)$ to produce a prediction in the same range for point $\\mathbf{x}_{ij}$", + "bbox": [ + 75, + 452, + 468, + 604 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\widetilde {y} _ {i j} = \\sigma \\left(D _ {G} \\left(\\mathbf {x} _ {i j}, \\mathbf {z} _ {i}\\right)\\right). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 192, + 609, + 468, + 627 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Finally, we take the loss to be", + "bbox": [ + 76, + 633, + 274, + 647 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {d i s t}} = \\operatorname {B C E} \\left[ \\left(\\bar {y} _ {i j}\\right) _ {j \\leq N} ^ {i \\leq B}, \\left(\\tilde {y} _ {i j}\\right) _ {j \\leq N} ^ {i \\leq B} \\right], \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 143, + 652, + 468, + 680 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathrm{BCE}[\\cdot, \\cdot]$ stands for binary cross-entropy. As observed in [13], the sampling strategy used for points $\\mathbf{x}_{ij}$ strongly impacts training effectiveness. We describe ours in the supplementary. In our experiments, we set $\\delta = 0.1$ , being the top and bottom garments normalized respectively into the upper and lower halves of the $[-1, 1]^3$ cube.", + "bbox": [ + 75, + 684, + 468, + 775 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Gradient Loss. Given the same sample points as before, we take the gradient loss to be", + "bbox": [ + 76, + 775, + 468, + 805 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {g r a d}} = \\frac {1}{B N} \\sum_ {i, j} \\| \\mathbf {g} _ {i j} - \\widehat {\\mathbf {g} _ {i j}} \\| _ {2} ^ {2}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 160, + 811, + 468, + 848 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{g}_{ij} = \\nabla_{\\mathbf{x}}y_{ij}\\in \\mathbb{R}^3$ is the ground-truth gradient of the $i$ -th garment's UDF at $\\mathbf{x}_{ij}$ and $\\widehat{\\mathbf{g}_{ij}} = \\nabla_{\\mathbf{x}}D_G(\\mathbf{x}_{ij},\\mathbf{z}_i)$ the one of the predicted UDF, computed by backpropagation.", + "bbox": [ + 76, + 854, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Garment Draping Network", + "text_level": 1, + "bbox": [ + 500, + 90, + 745, + 107 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We describe our approach to draping generic garments as opposed to specific ones and our self-supervised scheme. We assume that all garments are made of a single common fabric material, and we drape them in a quasi-static manner.", + "bbox": [ + 498, + 113, + 890, + 174 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.1 Draping Generic Garments", + "text_level": 1, + "bbox": [ + 500, + 191, + 745, + 207 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We rely on SMPL [24] to parameterize the body in terms of shape $(\\beta)$ and pose $(\\theta)$ parameters. It uses Linear Blend Skinning to deform a body template. Since garments generally follow the pose of the underlying body, we extend the SMPL skinning procedure to the 3D volume around the body for garment draping. Given a point $\\mathbf{x} \\in \\mathbb{R}^3$ in the garment space, its position $D(\\mathbf{x}, \\beta, \\theta, \\mathbf{z})$ after draping becomes", + "bbox": [ + 498, + 215, + 890, + 321 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} D (\\mathbf {x}, \\beta , \\theta , \\mathbf {z}) = W \\left(\\mathbf {x} _ {\\left(\\beta , \\theta , \\mathbf {z}\\right)}, \\beta , \\theta , \\mathcal {W} (\\mathbf {x})\\right), \\tag {6} \\\\ \\mathbf {x} _ {(\\beta , \\theta , \\mathbf {z})} = \\mathbf {x} + \\Delta x (\\mathbf {x}, \\beta) + \\Delta x _ {\\mathrm {r e f}} (\\mathbf {x}, \\beta , \\theta , \\mathbf {z}), \\\\ \\Delta x _ {\\mathrm {r e f}} (\\mathbf {x}, \\beta , \\theta , \\mathbf {z}) = \\mathcal {B} (\\beta , \\theta) \\cdot \\mathcal {M} (x, \\mathbf {z}), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 330, + 890, + 386 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $W(\\cdot)$ is the SMPL skinning function, applied with blending weights $\\mathcal{W}(\\mathbf{x})$ , over the point displaced by $\\Delta x(\\mathbf{x},\\beta)$ and $\\Delta x_{\\mathrm{ref}}(\\mathbf{x},\\beta ,\\theta ,\\mathbf{z})$ . $\\mathcal{W}(\\mathbf{x})$ and $\\Delta x(\\mathbf{x},\\beta)$ are computed as in [19, 45]. However, they only give an initial deformation for garments that roughly fits the underlying body. To refine it, we introduce a new term, $\\Delta x_{\\mathrm{ref}}(\\mathbf{x},\\beta ,\\theta ,\\mathbf{z})$ . It is a deformation field conditioned on body parameters $\\beta$ and $\\theta$ , and on the garment latent code $\\mathbf{z}$ from the generative network. Following the linear decomposition of displacements in SMPL, it is the composition of an embedding $\\mathcal{B}(\\beta ,\\theta)\\in \\mathbb{R}^{N_B}$ of body parameters and a displacement matrix $\\mathcal{M}(x,\\mathbf{z})\\in \\mathbb{R}^{N_B\\times 3}$ conditioned on $\\mathbf{z}$ . Being conditioned on the latent code $\\mathbf{z}$ , $\\Delta x_{\\mathrm{ref}}$ can deform different garments differently, unlike the methods of [5, 42]. The number of vertices does not need to be fixed, since displacements are predicted separately for each vertex.", + "bbox": [ + 498, + 393, + 890, + 636 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Since we have distinct encodings for the top and bottom garments, for each one we train two MLPs $(\\mathcal{B},\\mathcal{M})$ to predict $\\Delta x_{\\mathrm{ref}}$ . The other MLPs for $\\mathcal{W}(\\cdot)$ and $\\Delta x(\\cdot)$ are shared.", + "bbox": [ + 498, + 637, + 890, + 683 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.2 Self-Supervised Training", + "text_level": 1, + "bbox": [ + 500, + 700, + 725, + 715 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We first learn the weights of $\\mathcal{W}(\\cdot)$ and $\\Delta x(\\cdot)$ as in [19, 45], which does not require any annotation or simulation data but only the blending weights and shape displacements of SMPL. We then train our deformation fields $\\Delta x_{\\mathrm{ref}}$ in a fully self-supervised fashion by minimizing the physics-based losses introduced below. In this way, we completely eliminate the huge cost that extensive simulations would entail.", + "bbox": [ + 498, + 723, + 890, + 828 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Top Garments. For upper body garments - shirts, t-shirts, vests, tank tops, etc. - the deformation field is trained using the loss from [42], expressed as", + "bbox": [ + 498, + 829, + 890, + 875 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {t o p}} = \\mathcal {L} _ {\\text {s t r a i n}} + \\mathcal {L} _ {\\text {b e n d}} + \\mathcal {L} _ {\\text {g r a v i t y}} + \\mathcal {L} _ {\\text {c o l}}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 545, + 885, + 890, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "1454", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{strain}$ is the membrane strain energy of the deformed garment, $\\mathcal{L}_{bend}$ the bending energy caused by the folding of adjacent faces, $\\mathcal{L}_{gravity}$ the gravitational potential energy, and $\\mathcal{L}_{col}$ a penalty for collisions between body and garment. Unlike in [42], we only consider the quasi-static state after draping, that is, without acceleration.", + "bbox": [ + 75, + 90, + 468, + 181 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Bottom Garments. Due to gravity, bottom garments, such as trousers, would drop onto the floors if we used only the loss terms of Eq. (7). We thus introduce an extra loss term to constrain the deformation of vertices around the waist and hips. The loss becomes", + "bbox": [ + 75, + 181, + 470, + 257 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {b o t t o m}} = \\mathcal {L} _ {\\text {s t r a i n}} + \\mathcal {L} _ {\\text {b e n d}} + \\mathcal {L} _ {\\text {g r a v i t y}} + \\mathcal {L} _ {\\text {c o l}} + \\mathcal {L} _ {\\text {p i n}},\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 267, + 455, + 284 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {p i n} = \\sum_ {v \\in V} | \\Delta x _ {y} | ^ {2} + \\lambda \\left(| \\Delta x _ {x} | ^ {2} + | \\Delta x _ {z} | ^ {2}\\right), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 109, + 286, + 468, + 319 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $V$ is the set of garment vertices whose closest body vertices are located in the region of the waist and hips. See supplementary material for details. The terms $\\Delta x_{x}$ , $\\Delta x_{y}$ and $\\Delta x_{z}$ are the deformations along the X, Y and Z axes, respectively. $\\lambda$ is a positive value smaller than 1 that penalizes deformations along the vertical direction (Y axis) and produces natural deformations along the other directions.", + "bbox": [ + 75, + 327, + 468, + 433 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Top-Bottom Intersection. To ensure that the top and bottom garments do not intersect with each other when we drape them on the same body, we define a loss $\\mathcal{L}_{IS}$ that ensures that when the top and the bottom garments overlap, the bottom garment vertices are closer to the body mesh than the top ones, which prevents them from intersecting – this is arbitrary, and the following could be formulated the other way around. To this end, we introduce an Intersection Solver (IS) network. It predicts a displacement correction $\\Delta x_{IS}$ , added only when draping bottom garments as", + "bbox": [ + 75, + 433, + 468, + 584 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {\\mathbf {x}} _ {(\\mathbf {z} _ {t o p}, \\mathbf {z} _ {b o t})} = \\mathbf {x} _ {(\\mathbf {z} _ {b o t})} + \\Delta x _ {I S} (\\mathbf {x}, \\mathbf {z} _ {t o p}, \\mathbf {z} _ {b o t}), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 120, + 594, + 468, + 612 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where we omit the dependency of $\\tilde{\\mathbf{x}}$ , $\\mathbf{x}$ and $\\Delta x_{IS}$ on the body parameters $(\\beta, \\theta)$ for simplicity. $\\mathbf{z}_{top}$ and $\\mathbf{z}_{bot}$ are the latent codes of the top and bottom garments, and $\\mathbf{x}_{(\\mathbf{z}_{bot})}$ is the input point displaced according to Eq. (6). The skinning function of Eq. (6) is then applied to $\\tilde{\\mathbf{x}}_{(\\mathbf{z}_{top}, \\mathbf{z}_{bot})}$ for draping. $\\Delta x_{IS}(\\cdot)$ is implemented as a simple MLP and trained with", + "bbox": [ + 75, + 619, + 468, + 710 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {I S} = \\mathcal {L} _ {\\text {b o t t o m}} + \\mathcal {L} _ {\\text {l a y e r}}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 186, + 720, + 468, + 738 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{layer}$ is a loss whose minimization requires the top and bottom garments to be separated from each other. We formulate it as", + "bbox": [ + 75, + 747, + 468, + 790 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {l a y e r}} = \\sum_ {v _ {B} \\in C} \\max \\left(d _ {\\text {b o t}} \\left(v _ {B}\\right) - \\gamma d _ {\\text {t o p}} \\left(v _ {B}\\right), 0\\right), \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 98, + 799, + 468, + 830 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $C$ is the set of body vertices covered by both the top and bottom garments, $d_{top}(\\cdot)$ and $d_{bot}(\\cdot)$ the distance to the top and the bottom garments respectively, and $\\gamma$ a positive value smaller than 1 (more details in the supplementary).", + "bbox": [ + 75, + 839, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/28e22ab3a7f4c64636468a4de69306098b1564ffc98234f14a0820683e567fe2.jpg", + "image_caption": [ + "Figure 3. Overview of DrapeNet applications. Top: New garments can be sampled from the latent spaces of the generative networks, and deformed by the draping networks to fit to a given body. Center: The garment encoders and the draping networks form a general purpose framework to drape any garment with a single forward pass. Bottom: Being a differentiable parametric model, our framework can reconstruct 3D garments by fitting observations such as images or 3D scans. The red boxes indicate the parameters optimized in this process." + ], + "image_footnote": [], + "bbox": [ + 514, + 90, + 874, + 404 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 550, + 632, + 566 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We first describe our experimental setup and test DrapeNet for the different purposes depicted by Fig. 3. They include reconstructing different kinds of garments and editing them by manipulating their latent codes. We then gauge the draping network both qualitatively and quantitatively. Finally, we use DrapeNet to reconstruct garments from images and 3D scans.", + "bbox": [ + 498, + 575, + 890, + 681 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Settings, Datasets and Metrics", + "text_level": 1, + "bbox": [ + 500, + 695, + 767, + 709 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. Both our generative and draping networks are trained with garments from CLOTH3D [4], a synthetic dataset that contains over 7K sequences of animated 3D humans parametrized used the SMPL model and wearing different garments. Each sequence comprises up to 300 frames and features garments coming from different templates. For training, we randomly selected 600 top garments (t-shirts, shirts, tank tops, etc.) and 300 bottom garments (both long and short trousers). Neither for the generative nor for the draping networks did we use the simulated deformations of the selected garments. Instead, we trained the networks using only garment meshes on average body shapes in T-pose.", + "bbox": [ + 498, + 719, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "1455", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/ae0e626c3a858f9609b0e393cfedc6f218da9b3b1801bc76e5bf9ad3a64e6fb6.jpg", + "image_caption": [ + "Figure 4. Generative network: reconstruction of unseen garments in neutral pose/shape. The latent codes are obtained with the garment encoder, then decoded into open surface meshes." + ], + "image_footnote": [], + "bbox": [ + 117, + 89, + 424, + 212 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "By contrast, for testing purposes, we selected random clothing items - 30 for top garments and 30 bottom ones - and considered whole simulated sequences.", + "bbox": [ + 75, + 263, + 468, + 309 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Training. We train two different models for top and bottom garments, both for the generative and for the draping parts of our framework. First, the generative models are trained on the 600/300 neutral garments Then, with the generative networks weights frozen, we train the draping networks by following [42]: body poses $\\theta$ are sampled randomly from the AMASS [26] dataset, and shapes $\\beta$ uniformly from $[-3,3]^{10}$ at each step. The other hyperparameters are given in the supplementary material.", + "bbox": [ + 75, + 310, + 468, + 445 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Metrics. We report the Euclidean distance (ED), interpenetration ratio between body and garment (B2G), and intersection between top and bottom garments (G2G). ED is computed between corresponding vertices of the considered meshes. B2G is the area ratio between the garment faces inside the body and the whole surface as in [19]. Since CLOTH3D exclusively features pairs of top/bottom garments with the bottom one closer to the body, G2G is computed by detecting faces of the bottom garment that are outside of the top one, and taking the area ratio between those and the overall bottom garment surface.", + "bbox": [ + 75, + 446, + 468, + 612 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Garment Parameterization", + "text_level": 1, + "bbox": [ + 76, + 619, + 307, + 635 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We first test the encoding-decoding scheme of Sec. 3.1.", + "bbox": [ + 94, + 643, + 462, + 657 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Encoding-Decoding Previously Unseen Garments. The generative network of Fig. 2 is designed to project garments into a latent space and to reconstruct them from the resulting latent vectors. In Fig. 4, we visualize reconstructed previously-unseen garments from CLOTH3D. The reconstructions are faithful to the input garments, including fine-grained details such as the shirt collar on the left or the shoulder straps of the tank top.", + "bbox": [ + 75, + 659, + 468, + 779 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Semantic Manipulation of Latent Codes. Our framework enables us to edit a garment by manipulating its latent code. For the resulting edits to have a semantic meaning, we assigned binary labels corresponding to features of interest to 100 training garments. For instance, we labeled garments as having \"short sleeves\" (label $= 0$ ) or \"long sleeves\" (label $= 1$ ). Then, we fit a linear logistic regressor to the garment latent codes. After training, the regressor weights indicate", + "bbox": [ + 75, + 780, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/7ad22a392c7aa6e292811396dd0cffaac703fdd5b0ba686c3018c05c0b58218a.jpg", + "image_caption": [ + "Figure 5. Garment editing. The latent codes produced by the garment encoder can be manipulated to edit specific features of the corresponding garments, without altering the overall geometry." + ], + "image_footnote": [], + "bbox": [ + 514, + 90, + 875, + 252 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/682a4b74a9833e87cb887eed491ec795c97ac69708b988385cdf622a028e1074.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DeePSDDIGOurs
ED-top (mm)28.129.647.9
ED-bottom (mm)18.320.027.3
B2G-top (%) ↓7.21.80.9
B2G-bottom (%) ↓3.40.80.3
G2G (%) ↓2.04.00.5
", + "bbox": [ + 566, + 304, + 826, + 395 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Draping unseen garment meshes. Comparison between DeePSD, DIG and our method, for top and bottom garments: Euclidean distance (ED), intersections with the body (B2G) and between garments (G2G) as ratio of intersection areas.", + "bbox": [ + 498, + 400, + 890, + 455 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "which dimensions of the latent space control the feature of interest. To this end, we first apply min-max normalization to the absolute weight values and then zero out the ones below a certain threshold, empirically set to 0.5. The remaining non-zero weights indicate which dimensions of the latent codes should be increased or decreased to edit the studied feature. To create Fig. 5, we applied this simple procedure to control the sleeve length and the front opening for top garments along with the length for bottom garments. As can be seen from the figure, our latent representations give us the ability to edit a specific garment feature while leaving other aspects of the garment geometry unchanged.", + "bbox": [ + 496, + 468, + 890, + 650 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Garment Draping", + "text_level": 1, + "bbox": [ + 500, + 662, + 674, + 679 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We now turn to the evaluation of the draping network and compare its performance to those of DeePSD [6] or DIG [19], two fully supervised learning methods trained on CLOTH3D. DeePSD takes the point cloud of the garment mesh as input and predicts blending weights and pose displacements for each point; DIG drapes garments with a learned skinning field that can be applied to generic 3D points, but is similar for all garments. We chose those because, like DrapeNet, they both can deform garments of arbitrary geometry and topology.", + "bbox": [ + 496, + 686, + 890, + 838 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Draping Unseen Meshes. We drape previously unseen garments on different bodies in random poses. We first encode the garments and use the resulting latent codes to condition the draping network, whose inference takes $\\sim 5\\mathrm{ms}$ .", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "1456", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c0421b1fdc2a817b966492349c4ecf41e46d906f1632b3d9f1d44f90574e8453.jpg", + "image_caption": [ + "Figure 6. Comparison between DeePSD, DIG and our method. Ours is more realistic despite having the highest Euclidean distance (ED) error (left), and has less intersection between garments (right). Left also shows that $\\Delta x_{\\mathrm{ref}}$ is necessary for realistic deformations." + ], + "image_footnote": [], + "bbox": [ + 133, + 87, + 836, + 247 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b023d2ba17e162d1d59bc2c87952cd8dcb8028060eac7b4720ef1752aba83524.jpg", + "image_caption": [ + "Figure 7. Human evaluation of draping results. When shown draping results of our method, DIG and DeePSD, evaluators selected ours as the most realistic one in more than half of the cases. None refers to the case when they had no clear preference." + ], + "image_footnote": [], + "bbox": [ + 89, + 289, + 455, + 354 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We provide qualitative results in Fig. 6 and report quantitative ones in Tab. 1. Despite being completely self-supervised, DrapeNet delivers the lowest ratio of body-garment interpenetrations (B2G) for both top and bottom garments and the least intersections between them (G2G).", + "bbox": [ + 75, + 430, + 468, + 505 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "However, DrapeNet also yields higher ED values, which makes sense because there is more than one way to satisfy the physical constraints and to achieve realism. Hence, in the absence of explicit supervision, there is no reason for the answer picked by DrapeNet to be exactly the same as the one picked by the simulator. In fact, as argued in [5] and illustrated by Fig. 6, which is representative in terms of ED, a low ED value does not necessarily correspond to a realistic draping. To confirm this, we conducted a human evaluation study by sharing a link to a website on friends groupchats. We gave no further instructions or details besides those given on the site and reproduced in the supplementary material. The website displays 3 drapings of the same garment over the same posed body, one computed using our method and the others using the other two. The users were asked to select which one of the three seemed more realistic and more pleasant, with a fourth potential response being \"none of them\". We obtained feedback from 187 different people. A total of 1258 individual examples were rated and we collected 3738 user opinions. In other words, each user expressed 20 opinions on average. The chart in Fig. 7 shows that our method was selected more than $50\\%$ of the times, with a large gap over the second best, DIG [19], selected less than $30\\%$ of the time. This result confirms that DrapeNet can drape garments with better perceptual quality than the competing methods.", + "bbox": [ + 75, + 508, + 472, + 902 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9ae7175e18a0fa1ba7e80404827e26a422ed16b2ae6eb4947aa3e338be0fda3b.jpg", + "image_caption": [ + "Figure 8. Switching input latent codes of the draping network. Draping the same shirt by conditioning the draping network with (a) the corresponding latent code, (b) the code of an open vest, (c) of a t-shirt and (d) of a tank top. Gray meshes in dashed boxed are the garments corresponding to the input latent codes." + ], + "image_footnote": [], + "bbox": [ + 506, + 287, + 879, + 352 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ablation Study. In Fig. 8, we show what happens when the draping network is conditioned with a latent code of a garment that does not match the input one. This creates unnatural deformations on the front when using the code of a shirt with a front opening to deform a shirt without an opening. Similarly, the sleeves penetrate the arms when conditioning with the code of a short sleeves shirt. This demonstrates that the draping network truly exploits the latent codes to predict garment-dependent deformation fields.", + "bbox": [ + 496, + 436, + 890, + 573 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In Fig. 6 left we show that removing our novel displacement term $\\Delta x_{\\mathrm{ref}}(\\cdot)$ from Eq. (6) leads to unrealistic results.", + "bbox": [ + 498, + 574, + 890, + 603 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We also ablate the influence of our Intersection Solver and observe that G2G increases from $0.5\\%$ to $1.1\\%$ without it. This demonstrates the effectiveness of this component at reducing collisions between top and bottom garments.", + "bbox": [ + 496, + 604, + 890, + 664 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Fitting Observations", + "text_level": 1, + "bbox": [ + 500, + 672, + 694, + 689 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Since our method is end-to-end differentiable, it can be used to reconstruct 3D models of people and their garments from partial observations, such as 2D images and 3D scans.", + "bbox": [ + 496, + 696, + 890, + 742 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Fitting Images. Given an image of a clothed person, we use the algorithm of [57, 58] to get initial estimates for the body parameters $(\\beta, \\theta)$ and a segmentation mask $\\mathbf{S}$ . Then, starting with the mean of the learned codes $\\mathbf{z}$ , we reconstruct a mesh for the body and its garments by minimizing", + "bbox": [ + 496, + 742, + 890, + 818 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} L (\\beta , \\theta , \\mathbf {z}) = L _ {\\mathrm {I o U}} \\left(R \\left(D (\\mathbf {G}, \\beta , \\theta , \\mathbf {z}), \\operatorname {S M P L} (\\beta , \\theta)\\right), \\mathbf {S}\\right), \\tag {12} \\\\ \\mathbf {G} = \\operatorname {M e s h U D F} \\left(D _ {G} (\\mathbf {z})\\right), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 827, + 890, + 859 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "w.r.t. $\\mathbf{z},\\beta$ and $\\theta$ , where $L_{\\mathrm{IoU}}$ is the IoU loss [20] in pixel space penalizing discrepancies between 2D masks, $R(\\cdot)$ is", + "bbox": [ + 498, + 869, + 890, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "1457", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2e1cb944ae2971f34b94fc85dce1a840e5cf3b8377004c909e09f52ec5cc85c7.jpg", + "image_caption": [ + "Figure 9. Recovering garments and bodies from images. From left to right we show the input image and the 3D models recovered with our method (without and with post-refinement), and competitors methods: SMPlicit [10], ClothWild [29], DIG [19]." + ], + "image_footnote": [], + "bbox": [ + 86, + 90, + 455, + 337 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "a differentiable mesh renderer [40], and $\\mathbf{G}$ is the set of vertices of the garment mesh reconstructed with our garment decoder using $\\mathbf{z}$ . $D(\\cdot)$ and $\\mathrm{SMPL}(\\cdot)$ are the garment and body skinning functions defined in Eq. (6) and in [24], respectively. To ensure pose plausibility, $\\theta$ is constrained by an adversarial pose prior [11].", + "bbox": [ + 75, + 400, + 467, + 491 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "For the sake of simplicity, Eq. (12) formulates the reconstruction of a single garment $\\mathbf{G}$ . In practice, we extend this formulation to both the top and the bottom garments shown in the target image. Fig. 9 depicts the results of minimizing this loss. It outperforms the state-of-the-art methods SMPLicit [10], ClothWild [29] and DIG [19]. The garments we recover follow the ones in the input image with higher fidelity and visual quality, without interpenetration between the body and the garments or between the two garments.", + "bbox": [ + 75, + 491, + 467, + 626 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "After this optimization, we can further refine the result by minimizing the physics-based objectives of Eq. (7) w.r.t. the per-vertex displacements of the reconstructed garments, as opposed to w.r.t. the latent vectors. We describe this procedure in the supplementary material. As shown in the third column of Fig. 9, this further boosts the realism of the reconstructed garments. Note that this refinement is feasible thanks to the open surface representation allowed by our UDF model. Applying these physically inspired losses to an inflated garment, as produced by SMPLlicit, ClothWild and DIG, yields poor results with many self-intersections, as shown in the supplementary material.", + "bbox": [ + 75, + 627, + 467, + 808 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Fitting 3D scans. Given a 3D scan of a clothed person and segmentation information, we apply a strategy similar to the one presented above and minimize", + "bbox": [ + 76, + 809, + 467, + 853 + ], + "page_idx": 7 + }, + { + "type": "equation", + "text": "\n$$\nL (\\beta , \\theta , \\mathbf {z}) = d (D (\\mathbf {G}, \\beta , \\theta , \\mathbf {z}), \\mathbf {S} _ {\\mathbf {G}}) + \\vec {d} (\\mathrm {S M P L} (\\beta , \\theta), \\mathbf {S} _ {\\mathbf {B}}), \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 861, + 467, + 878 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "w.r.t. $\\mathbf{z},\\beta$ and $\\theta$ , where $\\mathbf{S_G}$ and $\\mathbf{S_B}$ denote the segmented", + "bbox": [ + 76, + 885, + 467, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/983c9e39825d3e931aff373dfc3c5999041de27917cd7d6bc2a250050cac860d.jpg", + "image_caption": [ + "Figure 10. Recovering garments and bodies from 3D scans. We show 3D models recovered with our method from scans of the SIZER dataset [50]. Raw indicates the model recovered with Eq. (13) from the 3D scan. Post Refinement refers to the models further refined with the physics-based losses." + ], + "image_footnote": [], + "bbox": [ + 532, + 88, + 856, + 337 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "garment and body scan points, and $d(a,b)$ and $\\vec{d}(a,b)$ are the bidirectional and the one-directional Chamfer distance from $b$ to $a$ . Similarly to Eq. (12), we apply Eq. (13) to recover both the top and bottom garments. Fig. 10 shows our fitting results for some scans of the SIZER dataset [50]. The recovered 3D models closely match the input scans. Moreover, we can also apply a post-refinement procedure similar to the one described above, by minimizing both the physics-based losses from Eq. (7) and the Chamfer distance to the input scan w.r.t. the 3D coordinates of the vertices of the reconstructed models. This leads to even more realistic results, with fine wrinkles aligning to the input scans.", + "bbox": [ + 496, + 417, + 890, + 599 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 609, + 617, + 625 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We have shown that physics-based self-supervision can be leveraged to learn a single parameterization for many different garments to be draped on human bodies in arbitrary poses. Our approach relies on UDFs to represent garment surfaces and on a displacement field to drape them, which enables us to handle a continuous manifold of garments without restrictions on their topology. Our whole pipeline is differentiable, which makes it suitable for solving inverse problems and for modeling clothed people from image data.", + "bbox": [ + 496, + 628, + 890, + 763 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Future work will focus on modeling dynamic poses instead of only static ones. This is of particular relevance for loose clothes, where our reliance on the SMPL skinning prior should be relaxed. Moreover, we will investigate replacing our current global latent code by a set of local ones to yield finer-grained control both for garment editing and draping.", + "bbox": [ + 496, + 763, + 890, + 868 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement. This project was supported in part by the Swiss National Science Foundation.", + "bbox": [ + 498, + 869, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "1458", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] M. Atzmon, N. Haim, L. Yariv, O. Israelov, H. Maron, and Y. Lipman. Controlling Neural Level Sets. In Advances in Neural Information Processing Systems, 2019. 2", + "[2] M. Atzmon and Y. Lipman. SALD: Sign Agnostic Learning with Derivatives. In International Conference on Learning Representations, 2020. 4", + "[3] D. Baraff and A. Witkin. Large Steps in Cloth Simulation. In ACM SIGGRAPH, pages 43-54, 1998. 1, 2", + "[4] H. Bertiche, M. Madadi, and S. Escalera. CLOTH3D: Clothed 3D Humans. 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In International Conference on Computer Vision, 2021. 2, 4" + ], + "bbox": [ + 501, + 92, + 890, + 573 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "1460", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/DrapeNet_ Garment Generation and Self-Supervised Draping/bc8ad2b1-5bdc-4117-96e0-b09e43677d93_model.json b/2023/DrapeNet_ Garment Generation and Self-Supervised Draping/bc8ad2b1-5bdc-4117-96e0-b09e43677d93_model.json new file mode 100644 index 0000000000000000000000000000000000000000..1be0ded2c19513d41cc02d637a26e3cb17ea8b77 --- /dev/null +++ b/2023/DrapeNet_ Garment Generation and Self-Supervised Draping/bc8ad2b1-5bdc-4117-96e0-b09e43677d93_model.json @@ -0,0 +1,2398 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.173, + 0.131, + 0.798, + 0.154 + ], + "angle": 0, + "content": "DrapeNet: Garment Generation and Self-Supervised Draping" + }, + { + "type": "text", + "bbox": [ + 0.106, + 0.18, + 0.245, + 0.2 + ], + "angle": 0, + "content": "Luca De Luigi*,2" + }, + { + "type": "text", + "bbox": [ + 0.282, + 0.181, + 0.358, + 0.198 + ], + "angle": 0, + "content": "Ren Li\\*,1" + }, + { + "type": "text", + "bbox": [ + 0.398, + 0.181, + 0.53, + 0.198 + ], + "angle": 0, + "content": "Benoit Guillard" + }, + { + "type": "text", + "bbox": [ + 0.569, + 0.181, + 0.726, + 0.198 + ], + "angle": 0, + "content": "Mathieu Salzmann1" + }, + { + "type": "text", + "bbox": [ + 0.768, + 0.181, + 0.86, + 0.198 + ], + "angle": 0, + "content": "Pascal Fua1" + }, + { + "type": "text", + "bbox": [ + 0.154, + 0.204, + 0.808, + 0.22 + ], + "angle": 0, + "content": "1: CVLab, EPFL, {name.surname}@epfl.ch 2: University of Bologna, luca.deluigi4@unibo.it" + }, + { + "type": "image", + "bbox": [ + 0.122, + 0.236, + 0.847, + 0.515 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.518, + 0.895, + 0.575 + ], + "angle": 0, + "content": "Figure 1. Our network can drape garments over bodies of different shapes in various poses. To minimize the required amount of supervision, our draping network is trained with physics-based self-supervision and generalizes to multiple garments by being conditioned on latent codes. These can be manipulated to edit specific features of the corresponding garments. Being fully differentiable, our pipeline makes it possible to recover 3D models of garments and bodies from observations such as images and 3D scans." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.587, + 0.314, + 0.603 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.619, + 0.471, + 0.756 + ], + "angle": 0, + "content": "Recent approaches to drape garments quickly over arbitrary human bodies leverage self-supervision to eliminate the need for large training sets. However, they are designed to train one network per clothing item, which severely limits their generalization abilities. In our work, we rely on self-supervision to train a single network to drape multiple garments. This is achieved by predicting a 3D deformation field conditioned on the latent codes of a generative network, which models garments as unsigned distance fields." + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.756, + 0.471, + 0.863 + ], + "angle": 0, + "content": "Our pipeline can generate and drape previously unseen garments of any topology, whose shape can be edited by manipulating their latent codes. Being fully differentiable, our formulation makes it possible to recover accurate 3D models of garments from partial observations – images or 3D scans – via gradient descent. Our code is publicly available at https://github.com/liren2515/DrapeNet." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.583, + 0.633, + 0.599 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.611, + 0.894, + 0.717 + ], + "angle": 0, + "content": "Draping digital garments over differently-shaped bodies in random poses has been extensively studied due to its many applications such as fashion design, moviemaking, video gaming, virtual try-on and, nowadays, virtual and augmented reality. Physics-based simulation (PBS) [3, 12, 23, 32, 33, 38, 39, 47-49, 51, 60] can produce outstanding results, but at a high computational cost." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Recent years have witnessed the emergence of deep neural networks aiming to achieve the quality of PBS draping while being much faster, easily differentiable, and offering new speed vs. accuracy tradeoffs [15, 16, 25, 36, 44, 46, 50, 53, 55]. These networks are often trained to produce garments that resemble ground-truth ones. While effective, this requires building training datasets, consisting of ground-truth meshes obtained either from computationally expensive simulations [31] or using complex 3D scanning setups [37]. Moreover, to generalize to unseen garments and poses, these supervised approaches require training databases encompassing a great variety of samples de" + }, + { + "type": "page_footnote", + "bbox": [ + 0.102, + 0.887, + 0.219, + 0.9 + ], + "angle": 0, + "content": "* Equal contributions" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "1451" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.465, + 0.108 + ], + "angle": 0, + "content": "picting many combinations of garments, bodies and poses." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.111, + 0.47, + 0.323 + ], + "angle": 0, + "content": "The recent PBNS and SNUG approaches [5, 42] address this by casting the physical models adopted in PBS into constraints used for self-supervision of deep learning models. This makes it possible to train the network on a multitude of body shapes and poses without ground-truth draped garments. Instead, the predicted garments are constrained to obey physics-based rules. However, both PBNS and SNUG require training a separate network for each garment. They rely on mesh templates for garment representation and feature one output per mesh vertex. Thus, they cannot handle meshes with different topologies, even for the same garment. This makes them very specialized and limits their applicability to large garment collections as a new network must be trained for each new clothing item." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.327, + 0.471, + 0.508 + ], + "angle": 0, + "content": "In this work, we introduce DrapeNet, an approach that also relies on physics-based constraints to provide self-supervision but can handle generic garments by conditioning a single draping network with a latent code describing the garment to be draped. We achieve this by coupling the draping network with a garment generative network, composed of an encoder and a decoder. The encoder is trained to compress input garments into compact latent codes that are used as input condition for the draping network. The decoder, instead, reconstructs a 3D garment model from its latent code, thus allowing us to sample and edit new garments from the learned latent space." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.512, + 0.47, + 0.693 + ], + "angle": 0, + "content": "Specifically, we model the output of the garment decoder as an unsigned distance function (UDF), which were demonstrated [14] to yield better accuracy and fewer interpenetrations than the inflated signed distance functions often used for this purpose [10, 19]. Moreover, UDFs can be triangulated in a differentiable way [14] to produce explicit surfaces that can easily be post-processed, making our pipeline fully differentiable. Hence, DrapeNet can not only drape garments over given body shapes but can also perform gradient-based optimization to fit garments, along with body shapes and poses, to partial observations of clothed people, such as images or 3D scans." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.698, + 0.317, + 0.712 + ], + "angle": 0, + "content": "Our contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.717, + 0.468, + 0.761 + ], + "angle": 0, + "content": "- We introduce a single garment draping network conditioned on a latent code to handle generic garments from a large collection (e.g. top or bottom garments);" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.763, + 0.468, + 0.807 + ], + "angle": 0, + "content": "- By exploiting physics-based self-supervision, our pipeline only requires a few hundred garment meshes in a canonical pose for training;" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.808, + 0.468, + 0.852 + ], + "angle": 0, + "content": "- Our framework enables the fast draping of new garments with high fidelity, as well as the sampling and editing of new garments from the learned latent space;" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.853, + 0.468, + 0.897 + ], + "angle": 0, + "content": "- Being fully differentiable, our method can be used to recover accurate 3D models of clothed people from images and 3D scans." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.717, + 0.468, + 0.897 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.09, + 0.642, + 0.106 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.115, + 0.892, + 0.251 + ], + "angle": 0, + "content": "Implicit Neural Representations for 3D Surfaces. Implicit neural representations have emerged a few years ago as an effective tool to represent surfaces whose topology is not known a priori. They can be implemented using (clipped) signed distance functions (SDF) [35] or occupancies [28]. When an explicit representation is required, it can be obtained using Marching Cubes [18] and this can be done while preserving differentiability [1,27,41]. However, they can only represent watertight surfaces." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.252, + 0.892, + 0.432 + ], + "angle": 0, + "content": "Thus, to represent open surfaces, such as clothes, it is possible to use inflated SDFs surrounding them. However, this entails a loss in accuracy and there has been a recent push to replace SDFs by unsigned distance functions (UDFs) [9, 52, 61]. One difficulty in so doing was that Marching Cubes was not designed with UDFs in mind, and obtaining explicit surfaces from these UDFs was therefore non-trivial. This has been addressed in [14] by modifying the Marching Cubes algorithm to operate with UDFs. We model garment with UDFs and use [14] to mesh them. Other works augment signed distance fields with covariant fields to encode open surface garments [8, 43]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.433, + 0.892, + 0.507 + ], + "angle": 0, + "content": "Draping Garments over 3D Bodies. Two main classes of methods coexist, physics-based algorithms [3, 21, 22, 30, 31, 48] that produce high-quality draptings but at a high computational cost, and data-driven approaches that are faster but often at the cost of realism." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.508, + 0.892, + 0.704 + ], + "angle": 0, + "content": "Among the latter, template-based approaches [5,7,17,34, 36,42,45,50] are dominant. Each garment is modeled by a specific triangulated mesh and a draping function is learned for each one. In other words, they do not generalize. There are however a number of exceptions. In [6, 15] the mesh is replaced by 3D point clouds that can represent generic garments. This enables deforming garments with arbitrary topology and geometric complexity, by estimating the deformation separately for each point. [59] goes further and allows differentiable changes in garment topology by sampling a fixed number of points from the body mesh. Unfortunately, this point cloud representation severely limits possible downstream applications." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.892, + 0.87 + ], + "angle": 0, + "content": "In recent approaches [10, 19], a space of garments is learned with clothing items modeled as inflated SDFs and one single shared network to predict their deformations as a 3D displacement field. This makes deployment in real-world scenarios easier and allows the reconstruction of garments from images and 3D scans. However, the inflated SDF scheme reduces realism and precludes post-processing using standard physics-based simulators or other cloth-specific downstream applications. Furthermore, both models are fully supervised and require a dataset of draped garments whose collection is extremely time-consuming." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Alleviating the need for costly ground-truth draped garments is tackled in [5, 42], by introducing physics-based" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1452" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.09, + 0.416, + 0.312 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.418, + 0.091, + 0.882, + 0.312 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.318, + 0.894, + 0.388 + ], + "angle": 0, + "content": "Figure 2. Overview of our framework. Left: Garment generative network, trained to embed garments into compact latent codes and predict their unsigned distance field (UDF) from such vectors. UDFs are then meshed using [14]. Right: Garment draping network, conditioned on the latent codes of the generative network. It is trained in a self-supervised way to predict the displacements \\(\\Delta x\\) and \\(\\Delta x_{\\mathrm{ref}}\\) to be applied to the vertices of given garments, before skinning them according to body shape and pose \\((\\beta ,\\theta)\\) with the predicted blending weights \\(\\mathcal{W}\\). It includes an Intersection Solver module to prevent intersection between top and bottom garments." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.401, + 0.471, + 0.522 + ], + "angle": 0, + "content": "losses to train draping networks in a self-supervised manner. The approach of [42] relies on a mass spring model to enforce the physical consistency of static garments deformed by different body poses. The method of [5] also accounts for variable body shapes and dynamic effects; furthermore, it incorporates a more realistic and expressive material model. Both methods, however, require training one network per garment, a limitation we remove." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.541, + 0.169, + 0.556 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.568, + 0.47, + 0.748 + ], + "angle": 0, + "content": "We aim to realistically deform and drape generic garments over human bodies of various shapes and poses. To this end, we introduce the DrapeNet framework, presented in Fig. 2. It comprises a generative network shown on the left and a draping network shown on the right. Only the first is trained in a supervised manner, but using only static unposed garments meshes. This is key to avoiding having to run physics-based simulations to generate groundtruth data. Furthermore, we condition the draping network on latent vectors representing the input garments, which allows us to use the same network for very different garments, something that competing methods [5,42] cannot do." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.903 + ], + "angle": 0, + "content": "The generative network is a decoder trained using an encoder that turns a garment into a latent code \\(\\mathbf{z}\\) that can then be decoded to an Unsigned Distance Function (UDF), from which a triangulated mesh can be extracted in a differentiable manner [14]. The UDF representation allows us to accurately represent open surfaces and the many openings that garments typically feature. Since the top and bottom garments - shirts and trousers - have different patterns, we train one generative model for each. Both networks have the same architecture but different weights." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.401, + 0.892, + 0.568 + ], + "angle": 0, + "content": "The resulting garment generative network is only trained to output garments in a canonical shape, pose, and size that fit a neutral SMPL [24] body. Draping the resulting garments to bodies in non-canonical poses is then entrusted to a draping network, again one for the top and one for the bottom. As in [5, 19, 42], this network predicts vertex displacements w.r.t. the neutral position. The deformed garment is then skinned onto the articulated body model. To enable generalization to different tops and bottoms, we condition the draping process on the garment latent codes of the generative network, shown as \\(\\mathbf{z}_{\\mathrm{top}}\\) and \\(\\mathbf{z}_{\\mathrm{bot}}\\) in Fig. 2." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.568, + 0.892, + 0.673 + ], + "angle": 0, + "content": "We use a small database of static unposed garments loosely aligned with bodies in the canonical position to train the two garment generating networks. This being done, we exploit physics-based constraints to train in a fully self-supervised manner the top and bottom draping networks for realism, without interpenetrations with the body and between the garments themselves." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.682, + 0.767, + 0.696 + ], + "angle": 0, + "content": "3.1. Garment Generative Network" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.892, + 0.825 + ], + "angle": 0, + "content": "To encode garments into latent codes that can then be decoded into UDFs, we rely on a point cloud encoder that embeds points sampled from the unposed garment surface into a compact vector. This lets us obtain latent codes for previously unseen garments in a single inference pass from points sampled from its surface. This can be done given any arbitrary surface triangulation. Hence, it gives us the flexibility to operate on any given garment mesh." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We use DGCNN [56] as the encoder. It first propagates the features of points within the same local region at multiple scales and then aggregates them into a single global embedding by max pooling. We pair it with a decoder that takes as input a latent vector, along with a point in 3D space," + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1453" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.152 + ], + "angle": 0, + "content": "and returns its (unsigned) distance to the garment. The decoder is a multi-layer perceptron (MLP) that relies on Conditional Batch Normalization [54] for conditioning on the input latent vector." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.152, + 0.471, + 0.258 + ], + "angle": 0, + "content": "We train the encoder and the decoder by encouraging them to jointly predict distances that are small near the training garments' surface and large elsewhere. Because the algorithm we use to compute triangulated meshes from the predicted distances [14] relies on the gradient vectors of the UDF field, we also want these gradients to be as accurate as possible [2, 61]. We therefore minimize the loss" + }, + { + "type": "equation", + "bbox": [ + 0.179, + 0.265, + 0.47, + 0.282 + ], + "angle": 0, + "content": "\\[\nL _ {g a r m} = L _ {d i s t} + \\lambda_ {g} L _ {g r a d}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.287, + 0.469, + 0.318 + ], + "angle": 0, + "content": "where \\(L_{dist}\\) encodes our distance requirements, \\(L_{grad}\\) the gradient ones, and \\(\\lambda_g\\) is a weight balancing their influence." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.318, + 0.47, + 0.393 + ], + "angle": 0, + "content": "More formally, at training time and given a mini-batch comprising \\(B\\) garments, we sample a fixed number \\(P\\) of points from the surface of each one. For each resulting point cloud \\(\\mathbf{p}_i\\) (\\(1 \\leq i \\leq B\\)), we use the garment encoder \\(E_G\\) to compute the latent code" + }, + { + "type": "equation", + "bbox": [ + 0.224, + 0.4, + 0.469, + 0.417 + ], + "angle": 0, + "content": "\\[\n\\mathbf {z} _ {i} = E _ {G} (\\mathbf {p} _ {i}) \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.422, + 0.469, + 0.452 + ], + "angle": 0, + "content": "and use it as input to the decoder \\( D_G \\). It predicts an UDF field supervised with Eq. (1), whose terms we define below." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.453, + 0.47, + 0.606 + ], + "angle": 0, + "content": "Distance Loss. Having experimented with many different formulations of this loss, we found the following one both simple and effective. Given \\(N\\) points \\(\\{\\mathbf{x}_{ij}\\}_{j\\leq N}\\) sampled from the space surrounding the \\(i\\)-th garment, we pick a distance threshold \\(\\delta\\), clip all the ground-truth distance values \\(\\{y_{ij}\\}\\) to it, and linearly normalize the clipped values to the range [0, 1]. This yields normalized ground-truth values \\(\\bar{y}_{ij} = \\min(y_{ij}, \\delta) / \\delta\\). Similarly, we pass the output of the final layer of \\(D_G\\) through a sigmoid function \\(\\sigma(\\cdot)\\) to produce a prediction in the same range for point \\(\\mathbf{x}_{ij}\\)" + }, + { + "type": "equation", + "bbox": [ + 0.194, + 0.611, + 0.469, + 0.628 + ], + "angle": 0, + "content": "\\[\n\\widetilde {y} _ {i j} = \\sigma \\left(D _ {G} \\left(\\mathbf {x} _ {i j}, \\mathbf {z} _ {i}\\right)\\right). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.634, + 0.276, + 0.648 + ], + "angle": 0, + "content": "Finally, we take the loss to be" + }, + { + "type": "equation", + "bbox": [ + 0.144, + 0.654, + 0.469, + 0.681 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {d i s t}} = \\operatorname {B C E} \\left[ \\left(\\bar {y} _ {i j}\\right) _ {j \\leq N} ^ {i \\leq B}, \\left(\\tilde {y} _ {i j}\\right) _ {j \\leq N} ^ {i \\leq B} \\right], \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.685, + 0.469, + 0.776 + ], + "angle": 0, + "content": "where \\(\\mathrm{BCE}[\\cdot, \\cdot]\\) stands for binary cross-entropy. As observed in [13], the sampling strategy used for points \\(\\mathbf{x}_{ij}\\) strongly impacts training effectiveness. We describe ours in the supplementary. In our experiments, we set \\(\\delta = 0.1\\), being the top and bottom garments normalized respectively into the upper and lower halves of the \\([-1, 1]^3\\) cube." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.776, + 0.469, + 0.806 + ], + "angle": 0, + "content": "Gradient Loss. Given the same sample points as before, we take the gradient loss to be" + }, + { + "type": "equation", + "bbox": [ + 0.161, + 0.812, + 0.469, + 0.849 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {g r a d}} = \\frac {1}{B N} \\sum_ {i, j} \\| \\mathbf {g} _ {i j} - \\widehat {\\mathbf {g} _ {i j}} \\| _ {2} ^ {2}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.855, + 0.469, + 0.902 + ], + "angle": 0, + "content": "where \\(\\mathbf{g}_{ij} = \\nabla_{\\mathbf{x}}y_{ij}\\in \\mathbb{R}^3\\) is the ground-truth gradient of the \\(i\\)-th garment's UDF at \\(\\mathbf{x}_{ij}\\) and \\(\\widehat{\\mathbf{g}_{ij}} = \\nabla_{\\mathbf{x}}D_G(\\mathbf{x}_{ij},\\mathbf{z}_i)\\) the one of the predicted UDF, computed by backpropagation." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.746, + 0.108 + ], + "angle": 0, + "content": "3.2. Garment Draping Network" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.114, + 0.892, + 0.175 + ], + "angle": 0, + "content": "We describe our approach to draping generic garments as opposed to specific ones and our self-supervised scheme. We assume that all garments are made of a single common fabric material, and we drape them in a quasi-static manner." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.193, + 0.746, + 0.208 + ], + "angle": 0, + "content": "3.2.1 Draping Generic Garments" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.216, + 0.892, + 0.323 + ], + "angle": 0, + "content": "We rely on SMPL [24] to parameterize the body in terms of shape \\((\\beta)\\) and pose \\((\\theta)\\) parameters. It uses Linear Blend Skinning to deform a body template. Since garments generally follow the pose of the underlying body, we extend the SMPL skinning procedure to the 3D volume around the body for garment draping. Given a point \\(\\mathbf{x} \\in \\mathbb{R}^3\\) in the garment space, its position \\(D(\\mathbf{x}, \\beta, \\theta, \\mathbf{z})\\) after draping becomes" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.332, + 0.891, + 0.387 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} D (\\mathbf {x}, \\beta , \\theta , \\mathbf {z}) = W \\left(\\mathbf {x} _ {\\left(\\beta , \\theta , \\mathbf {z}\\right)}, \\beta , \\theta , \\mathcal {W} (\\mathbf {x})\\right), \\tag {6} \\\\ \\mathbf {x} _ {(\\beta , \\theta , \\mathbf {z})} = \\mathbf {x} + \\Delta x (\\mathbf {x}, \\beta) + \\Delta x _ {\\mathrm {r e f}} (\\mathbf {x}, \\beta , \\theta , \\mathbf {z}), \\\\ \\Delta x _ {\\mathrm {r e f}} (\\mathbf {x}, \\beta , \\theta , \\mathbf {z}) = \\mathcal {B} (\\beta , \\theta) \\cdot \\mathcal {M} (x, \\mathbf {z}), \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.395, + 0.892, + 0.637 + ], + "angle": 0, + "content": "where \\(W(\\cdot)\\) is the SMPL skinning function, applied with blending weights \\(\\mathcal{W}(\\mathbf{x})\\), over the point displaced by \\(\\Delta x(\\mathbf{x},\\beta)\\) and \\(\\Delta x_{\\mathrm{ref}}(\\mathbf{x},\\beta ,\\theta ,\\mathbf{z})\\). \\(\\mathcal{W}(\\mathbf{x})\\) and \\(\\Delta x(\\mathbf{x},\\beta)\\) are computed as in [19, 45]. However, they only give an initial deformation for garments that roughly fits the underlying body. To refine it, we introduce a new term, \\(\\Delta x_{\\mathrm{ref}}(\\mathbf{x},\\beta ,\\theta ,\\mathbf{z})\\). It is a deformation field conditioned on body parameters \\(\\beta\\) and \\(\\theta\\), and on the garment latent code \\(\\mathbf{z}\\) from the generative network. Following the linear decomposition of displacements in SMPL, it is the composition of an embedding \\(\\mathcal{B}(\\beta ,\\theta)\\in \\mathbb{R}^{N_B}\\) of body parameters and a displacement matrix \\(\\mathcal{M}(x,\\mathbf{z})\\in \\mathbb{R}^{N_B\\times 3}\\) conditioned on \\(\\mathbf{z}\\). Being conditioned on the latent code \\(\\mathbf{z}\\), \\(\\Delta x_{\\mathrm{ref}}\\) can deform different garments differently, unlike the methods of [5, 42]. The number of vertices does not need to be fixed, since displacements are predicted separately for each vertex." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.638, + 0.892, + 0.684 + ], + "angle": 0, + "content": "Since we have distinct encodings for the top and bottom garments, for each one we train two MLPs \\((\\mathcal{B},\\mathcal{M})\\) to predict \\(\\Delta x_{\\mathrm{ref}}\\). The other MLPs for \\(\\mathcal{W}(\\cdot)\\) and \\(\\Delta x(\\cdot)\\) are shared." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.701, + 0.727, + 0.716 + ], + "angle": 0, + "content": "3.2.2 Self-Supervised Training" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.724, + 0.892, + 0.829 + ], + "angle": 0, + "content": "We first learn the weights of \\(\\mathcal{W}(\\cdot)\\) and \\(\\Delta x(\\cdot)\\) as in [19, 45], which does not require any annotation or simulation data but only the blending weights and shape displacements of SMPL. We then train our deformation fields \\(\\Delta x_{\\mathrm{ref}}\\) in a fully self-supervised fashion by minimizing the physics-based losses introduced below. In this way, we completely eliminate the huge cost that extensive simulations would entail." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.83, + 0.892, + 0.876 + ], + "angle": 0, + "content": "Top Garments. For upper body garments - shirts, t-shirts, vests, tank tops, etc. - the deformation field is trained using the loss from [42], expressed as" + }, + { + "type": "equation", + "bbox": [ + 0.547, + 0.886, + 0.891, + 0.903 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {t o p}} = \\mathcal {L} _ {\\text {s t r a i n}} + \\mathcal {L} _ {\\text {b e n d}} + \\mathcal {L} _ {\\text {g r a v i t y}} + \\mathcal {L} _ {\\text {c o l}}, \\tag {7}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1454" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.182 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{strain}\\) is the membrane strain energy of the deformed garment, \\(\\mathcal{L}_{bend}\\) the bending energy caused by the folding of adjacent faces, \\(\\mathcal{L}_{gravity}\\) the gravitational potential energy, and \\(\\mathcal{L}_{col}\\) a penalty for collisions between body and garment. Unlike in [42], we only consider the quasi-static state after draping, that is, without acceleration." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.183, + 0.471, + 0.258 + ], + "angle": 0, + "content": "Bottom Garments. Due to gravity, bottom garments, such as trousers, would drop onto the floors if we used only the loss terms of Eq. (7). We thus introduce an extra loss term to constrain the deformation of vertices around the waist and hips. The loss becomes" + }, + { + "type": "equation", + "bbox": [ + 0.09, + 0.268, + 0.457, + 0.285 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {b o t t o m}} = \\mathcal {L} _ {\\text {s t r a i n}} + \\mathcal {L} _ {\\text {b e n d}} + \\mathcal {L} _ {\\text {g r a v i t y}} + \\mathcal {L} _ {\\text {c o l}} + \\mathcal {L} _ {\\text {p i n}},\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.11, + 0.287, + 0.47, + 0.32 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {p i n} = \\sum_ {v \\in V} | \\Delta x _ {y} | ^ {2} + \\lambda \\left(| \\Delta x _ {x} | ^ {2} + | \\Delta x _ {z} | ^ {2}\\right), \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.328, + 0.469, + 0.434 + ], + "angle": 0, + "content": "where \\(V\\) is the set of garment vertices whose closest body vertices are located in the region of the waist and hips. See supplementary material for details. The terms \\(\\Delta x_{x}\\), \\(\\Delta x_{y}\\) and \\(\\Delta x_{z}\\) are the deformations along the X, Y and Z axes, respectively. \\(\\lambda\\) is a positive value smaller than 1 that penalizes deformations along the vertical direction (Y axis) and produces natural deformations along the other directions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.434, + 0.47, + 0.585 + ], + "angle": 0, + "content": "Top-Bottom Intersection. To ensure that the top and bottom garments do not intersect with each other when we drape them on the same body, we define a loss \\(\\mathcal{L}_{IS}\\) that ensures that when the top and the bottom garments overlap, the bottom garment vertices are closer to the body mesh than the top ones, which prevents them from intersecting – this is arbitrary, and the following could be formulated the other way around. To this end, we introduce an Intersection Solver (IS) network. It predicts a displacement correction \\(\\Delta x_{IS}\\), added only when draping bottom garments as" + }, + { + "type": "equation", + "bbox": [ + 0.122, + 0.595, + 0.469, + 0.613 + ], + "angle": 0, + "content": "\\[\n\\tilde {\\mathbf {x}} _ {(\\mathbf {z} _ {t o p}, \\mathbf {z} _ {b o t})} = \\mathbf {x} _ {(\\mathbf {z} _ {b o t})} + \\Delta x _ {I S} (\\mathbf {x}, \\mathbf {z} _ {t o p}, \\mathbf {z} _ {b o t}), \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.62, + 0.469, + 0.711 + ], + "angle": 0, + "content": "where we omit the dependency of \\(\\tilde{\\mathbf{x}}\\), \\(\\mathbf{x}\\) and \\(\\Delta x_{IS}\\) on the body parameters \\((\\beta, \\theta)\\) for simplicity. \\(\\mathbf{z}_{top}\\) and \\(\\mathbf{z}_{bot}\\) are the latent codes of the top and bottom garments, and \\(\\mathbf{x}_{(\\mathbf{z}_{bot})}\\) is the input point displaced according to Eq. (6). The skinning function of Eq. (6) is then applied to \\(\\tilde{\\mathbf{x}}_{(\\mathbf{z}_{top}, \\mathbf{z}_{bot})}\\) for draping. \\(\\Delta x_{IS}(\\cdot)\\) is implemented as a simple MLP and trained with" + }, + { + "type": "equation", + "bbox": [ + 0.187, + 0.722, + 0.469, + 0.739 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {I S} = \\mathcal {L} _ {\\text {b o t t o m}} + \\mathcal {L} _ {\\text {l a y e r}}, \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.748, + 0.47, + 0.791 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{layer}\\) is a loss whose minimization requires the top and bottom garments to be separated from each other. We formulate it as" + }, + { + "type": "equation", + "bbox": [ + 0.099, + 0.8, + 0.469, + 0.832 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {l a y e r}} = \\sum_ {v _ {B} \\in C} \\max \\left(d _ {\\text {b o t}} \\left(v _ {B}\\right) - \\gamma d _ {\\text {t o p}} \\left(v _ {B}\\right), 0\\right), \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.47, + 0.902 + ], + "angle": 0, + "content": "where \\(C\\) is the set of body vertices covered by both the top and bottom garments, \\(d_{top}(\\cdot)\\) and \\(d_{bot}(\\cdot)\\) the distance to the top and the bottom garments respectively, and \\(\\gamma\\) a positive value smaller than 1 (more details in the supplementary)." + }, + { + "type": "image", + "bbox": [ + 0.515, + 0.092, + 0.875, + 0.405 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.41, + 0.892, + 0.536 + ], + "angle": 0, + "content": "Figure 3. Overview of DrapeNet applications. Top: New garments can be sampled from the latent spaces of the generative networks, and deformed by the draping networks to fit to a given body. Center: The garment encoders and the draping networks form a general purpose framework to drape any garment with a single forward pass. Bottom: Being a differentiable parametric model, our framework can reconstruct 3D garments by fitting observations such as images or 3D scans. The red boxes indicate the parameters optimized in this process." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.551, + 0.633, + 0.567 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.577, + 0.892, + 0.682 + ], + "angle": 0, + "content": "We first describe our experimental setup and test DrapeNet for the different purposes depicted by Fig. 3. They include reconstructing different kinds of garments and editing them by manipulating their latent codes. We then gauge the draping network both qualitatively and quantitatively. Finally, we use DrapeNet to reconstruct garments from images and 3D scans." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.696, + 0.768, + 0.71 + ], + "angle": 0, + "content": "4.1. Settings, Datasets and Metrics" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.72, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Datasets. Both our generative and draping networks are trained with garments from CLOTH3D [4], a synthetic dataset that contains over 7K sequences of animated 3D humans parametrized used the SMPL model and wearing different garments. Each sequence comprises up to 300 frames and features garments coming from different templates. For training, we randomly selected 600 top garments (t-shirts, shirts, tank tops, etc.) and 300 bottom garments (both long and short trousers). Neither for the generative nor for the draping networks did we use the simulated deformations of the selected garments. Instead, we trained the networks using only garment meshes on average body shapes in T-pose." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1455" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.118, + 0.09, + 0.426, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.215, + 0.47, + 0.256 + ], + "angle": 0, + "content": "Figure 4. Generative network: reconstruction of unseen garments in neutral pose/shape. The latent codes are obtained with the garment encoder, then decoded into open surface meshes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.265, + 0.469, + 0.31 + ], + "angle": 0, + "content": "By contrast, for testing purposes, we selected random clothing items - 30 for top garments and 30 bottom ones - and considered whole simulated sequences." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.311, + 0.469, + 0.446 + ], + "angle": 0, + "content": "Training. We train two different models for top and bottom garments, both for the generative and for the draping parts of our framework. First, the generative models are trained on the 600/300 neutral garments Then, with the generative networks weights frozen, we train the draping networks by following [42]: body poses \\(\\theta\\) are sampled randomly from the AMASS [26] dataset, and shapes \\(\\beta\\) uniformly from \\([-3,3]^{10}\\) at each step. The other hyperparameters are given in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.447, + 0.47, + 0.613 + ], + "angle": 0, + "content": "Metrics. We report the Euclidean distance (ED), interpenetration ratio between body and garment (B2G), and intersection between top and bottom garments (G2G). ED is computed between corresponding vertices of the considered meshes. B2G is the area ratio between the garment faces inside the body and the whole surface as in [19]. Since CLOTH3D exclusively features pairs of top/bottom garments with the bottom one closer to the body, G2G is computed by detecting faces of the bottom garment that are outside of the top one, and taking the area ratio between those and the overall bottom garment surface." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.621, + 0.308, + 0.636 + ], + "angle": 0, + "content": "4.2. Garment Parameterization" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.645, + 0.464, + 0.659 + ], + "angle": 0, + "content": "We first test the encoding-decoding scheme of Sec. 3.1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.66, + 0.469, + 0.78 + ], + "angle": 0, + "content": "Encoding-Decoding Previously Unseen Garments. The generative network of Fig. 2 is designed to project garments into a latent space and to reconstruct them from the resulting latent vectors. In Fig. 4, we visualize reconstructed previously-unseen garments from CLOTH3D. The reconstructions are faithful to the input garments, including fine-grained details such as the shirt collar on the left or the shoulder straps of the tank top." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Semantic Manipulation of Latent Codes. Our framework enables us to edit a garment by manipulating its latent code. For the resulting edits to have a semantic meaning, we assigned binary labels corresponding to features of interest to 100 training garments. For instance, we labeled garments as having \"short sleeves\" (label \\(= 0\\)) or \"long sleeves\" (label \\(= 1\\)). Then, we fit a linear logistic regressor to the garment latent codes. After training, the regressor weights indicate" + }, + { + "type": "image", + "bbox": [ + 0.515, + 0.092, + 0.877, + 0.253 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.253, + 0.892, + 0.296 + ], + "angle": 0, + "content": "Figure 5. Garment editing. The latent codes produced by the garment encoder can be manipulated to edit specific features of the corresponding garments, without altering the overall geometry." + }, + { + "type": "table", + "bbox": [ + 0.567, + 0.305, + 0.828, + 0.396 + ], + "angle": 0, + "content": "
DeePSDDIGOurs
ED-top (mm)28.129.647.9
ED-bottom (mm)18.320.027.3
B2G-top (%) ↓7.21.80.9
B2G-bottom (%) ↓3.40.80.3
G2G (%) ↓2.04.00.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.401, + 0.892, + 0.457 + ], + "angle": 0, + "content": "Table 1. Draping unseen garment meshes. Comparison between DeePSD, DIG and our method, for top and bottom garments: Euclidean distance (ED), intersections with the body (B2G) and between garments (G2G) as ratio of intersection areas." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.469, + 0.892, + 0.651 + ], + "angle": 0, + "content": "which dimensions of the latent space control the feature of interest. To this end, we first apply min-max normalization to the absolute weight values and then zero out the ones below a certain threshold, empirically set to 0.5. The remaining non-zero weights indicate which dimensions of the latent codes should be increased or decreased to edit the studied feature. To create Fig. 5, we applied this simple procedure to control the sleeve length and the front opening for top garments along with the length for bottom garments. As can be seen from the figure, our latent representations give us the ability to edit a specific garment feature while leaving other aspects of the garment geometry unchanged." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.664, + 0.675, + 0.68 + ], + "angle": 0, + "content": "4.3. Garment Draping" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.688, + 0.892, + 0.839 + ], + "angle": 0, + "content": "We now turn to the evaluation of the draping network and compare its performance to those of DeePSD [6] or DIG [19], two fully supervised learning methods trained on CLOTH3D. DeePSD takes the point cloud of the garment mesh as input and predicts blending weights and pose displacements for each point; DIG drapes garments with a learned skinning field that can be applied to generic 3D points, but is similar for all garments. We chose those because, like DrapeNet, they both can deform garments of arbitrary geometry and topology." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Draping Unseen Meshes. We drape previously unseen garments on different bodies in random poses. We first encode the garments and use the resulting latent codes to condition the draping network, whose inference takes \\(\\sim 5\\mathrm{ms}\\)." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "1456" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.134, + 0.088, + 0.837, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.252, + 0.895, + 0.281 + ], + "angle": 0, + "content": "Figure 6. Comparison between DeePSD, DIG and our method. Ours is more realistic despite having the highest Euclidean distance (ED) error (left), and has less intersection between garments (right). Left also shows that \\(\\Delta x_{\\mathrm{ref}}\\) is necessary for realistic deformations." + }, + { + "type": "image", + "bbox": [ + 0.09, + 0.29, + 0.456, + 0.356 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.359, + 0.471, + 0.416 + ], + "angle": 0, + "content": "Figure 7. Human evaluation of draping results. When shown draping results of our method, DIG and DeePSD, evaluators selected ours as the most realistic one in more than half of the cases. None refers to the case when they had no clear preference." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.431, + 0.47, + 0.506 + ], + "angle": 0, + "content": "We provide qualitative results in Fig. 6 and report quantitative ones in Tab. 1. Despite being completely self-supervised, DrapeNet delivers the lowest ratio of body-garment interpenetrations (B2G) for both top and bottom garments and the least intersections between them (G2G)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.509, + 0.473, + 0.903 + ], + "angle": 0, + "content": "However, DrapeNet also yields higher ED values, which makes sense because there is more than one way to satisfy the physical constraints and to achieve realism. Hence, in the absence of explicit supervision, there is no reason for the answer picked by DrapeNet to be exactly the same as the one picked by the simulator. In fact, as argued in [5] and illustrated by Fig. 6, which is representative in terms of ED, a low ED value does not necessarily correspond to a realistic draping. To confirm this, we conducted a human evaluation study by sharing a link to a website on friends groupchats. We gave no further instructions or details besides those given on the site and reproduced in the supplementary material. The website displays 3 drapings of the same garment over the same posed body, one computed using our method and the others using the other two. The users were asked to select which one of the three seemed more realistic and more pleasant, with a fourth potential response being \"none of them\". We obtained feedback from 187 different people. A total of 1258 individual examples were rated and we collected 3738 user opinions. In other words, each user expressed 20 opinions on average. The chart in Fig. 7 shows that our method was selected more than \\(50\\%\\) of the times, with a large gap over the second best, DIG [19], selected less than \\(30\\%\\) of the time. This result confirms that DrapeNet can drape garments with better perceptual quality than the competing methods." + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.289, + 0.88, + 0.353 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.355, + 0.892, + 0.426 + ], + "angle": 0, + "content": "Figure 8. Switching input latent codes of the draping network. Draping the same shirt by conditioning the draping network with (a) the corresponding latent code, (b) the code of an open vest, (c) of a t-shirt and (d) of a tank top. Gray meshes in dashed boxed are the garments corresponding to the input latent codes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.438, + 0.892, + 0.574 + ], + "angle": 0, + "content": "Ablation Study. In Fig. 8, we show what happens when the draping network is conditioned with a latent code of a garment that does not match the input one. This creates unnatural deformations on the front when using the code of a shirt with a front opening to deform a shirt without an opening. Similarly, the sleeves penetrate the arms when conditioning with the code of a short sleeves shirt. This demonstrates that the draping network truly exploits the latent codes to predict garment-dependent deformation fields." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.575, + 0.892, + 0.604 + ], + "angle": 0, + "content": "In Fig. 6 left we show that removing our novel displacement term \\(\\Delta x_{\\mathrm{ref}}(\\cdot)\\) from Eq. (6) leads to unrealistic results." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.605, + 0.892, + 0.665 + ], + "angle": 0, + "content": "We also ablate the influence of our Intersection Solver and observe that G2G increases from \\(0.5\\%\\) to \\(1.1\\%\\) without it. This demonstrates the effectiveness of this component at reducing collisions between top and bottom garments." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.674, + 0.695, + 0.69 + ], + "angle": 0, + "content": "4.4. Fitting Observations" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.697, + 0.892, + 0.743 + ], + "angle": 0, + "content": "Since our method is end-to-end differentiable, it can be used to reconstruct 3D models of people and their garments from partial observations, such as 2D images and 3D scans." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.743, + 0.892, + 0.819 + ], + "angle": 0, + "content": "Fitting Images. Given an image of a clothed person, we use the algorithm of [57, 58] to get initial estimates for the body parameters \\((\\beta, \\theta)\\) and a segmentation mask \\(\\mathbf{S}\\). Then, starting with the mean of the learned codes \\(\\mathbf{z}\\), we reconstruct a mesh for the body and its garments by minimizing" + }, + { + "type": "equation", + "bbox": [ + 0.518, + 0.828, + 0.892, + 0.86 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} L (\\beta , \\theta , \\mathbf {z}) = L _ {\\mathrm {I o U}} \\left(R \\left(D (\\mathbf {G}, \\beta , \\theta , \\mathbf {z}), \\operatorname {S M P L} (\\beta , \\theta)\\right), \\mathbf {S}\\right), \\tag {12} \\\\ \\mathbf {G} = \\operatorname {M e s h U D F} \\left(D _ {G} (\\mathbf {z})\\right), \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "w.r.t. \\(\\mathbf{z},\\beta\\) and \\(\\theta\\) , where \\(L_{\\mathrm{IoU}}\\) is the IoU loss [20] in pixel space penalizing discrepancies between 2D masks, \\(R(\\cdot)\\) is" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1457" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.087, + 0.092, + 0.457, + 0.338 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.34, + 0.47, + 0.395 + ], + "angle": 0, + "content": "Figure 9. Recovering garments and bodies from images. From left to right we show the input image and the 3D models recovered with our method (without and with post-refinement), and competitors methods: SMPlicit [10], ClothWild [29], DIG [19]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.401, + 0.468, + 0.492 + ], + "angle": 0, + "content": "a differentiable mesh renderer [40], and \\(\\mathbf{G}\\) is the set of vertices of the garment mesh reconstructed with our garment decoder using \\(\\mathbf{z}\\). \\(D(\\cdot)\\) and \\(\\mathrm{SMPL}(\\cdot)\\) are the garment and body skinning functions defined in Eq. (6) and in [24], respectively. To ensure pose plausibility, \\(\\theta\\) is constrained by an adversarial pose prior [11]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.492, + 0.468, + 0.627 + ], + "angle": 0, + "content": "For the sake of simplicity, Eq. (12) formulates the reconstruction of a single garment \\(\\mathbf{G}\\). In practice, we extend this formulation to both the top and the bottom garments shown in the target image. Fig. 9 depicts the results of minimizing this loss. It outperforms the state-of-the-art methods SMPLicit [10], ClothWild [29] and DIG [19]. The garments we recover follow the ones in the input image with higher fidelity and visual quality, without interpenetration between the body and the garments or between the two garments." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.628, + 0.468, + 0.809 + ], + "angle": 0, + "content": "After this optimization, we can further refine the result by minimizing the physics-based objectives of Eq. (7) w.r.t. the per-vertex displacements of the reconstructed garments, as opposed to w.r.t. the latent vectors. We describe this procedure in the supplementary material. As shown in the third column of Fig. 9, this further boosts the realism of the reconstructed garments. Note that this refinement is feasible thanks to the open surface representation allowed by our UDF model. Applying these physically inspired losses to an inflated garment, as produced by SMPLlicit, ClothWild and DIG, yields poor results with many self-intersections, as shown in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.81, + 0.468, + 0.854 + ], + "angle": 0, + "content": "Fitting 3D scans. Given a 3D scan of a clothed person and segmentation information, we apply a strategy similar to the one presented above and minimize" + }, + { + "type": "equation", + "bbox": [ + 0.085, + 0.862, + 0.468, + 0.879 + ], + "angle": 0, + "content": "\\[\nL (\\beta , \\theta , \\mathbf {z}) = d (D (\\mathbf {G}, \\beta , \\theta , \\mathbf {z}), \\mathbf {S} _ {\\mathbf {G}}) + \\vec {d} (\\mathrm {S M P L} (\\beta , \\theta), \\mathbf {S} _ {\\mathbf {B}}), \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.886, + 0.468, + 0.901 + ], + "angle": 0, + "content": "w.r.t. \\(\\mathbf{z},\\beta\\) and \\(\\theta\\) , where \\(\\mathbf{S_G}\\) and \\(\\mathbf{S_B}\\) denote the segmented" + }, + { + "type": "image", + "bbox": [ + 0.533, + 0.089, + 0.857, + 0.338 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.34, + 0.892, + 0.407 + ], + "angle": 0, + "content": "Figure 10. Recovering garments and bodies from 3D scans. We show 3D models recovered with our method from scans of the SIZER dataset [50]. Raw indicates the model recovered with Eq. (13) from the 3D scan. Post Refinement refers to the models further refined with the physics-based losses." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.418, + 0.892, + 0.6 + ], + "angle": 0, + "content": "garment and body scan points, and \\( d(a,b) \\) and \\( \\vec{d}(a,b) \\) are the bidirectional and the one-directional Chamfer distance from \\( b \\) to \\( a \\). Similarly to Eq. (12), we apply Eq. (13) to recover both the top and bottom garments. Fig. 10 shows our fitting results for some scans of the SIZER dataset [50]. The recovered 3D models closely match the input scans. Moreover, we can also apply a post-refinement procedure similar to the one described above, by minimizing both the physics-based losses from Eq. (7) and the Chamfer distance to the input scan w.r.t. the 3D coordinates of the vertices of the reconstructed models. This leads to even more realistic results, with fine wrinkles aligning to the input scans." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.611, + 0.619, + 0.625 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.892, + 0.764 + ], + "angle": 0, + "content": "We have shown that physics-based self-supervision can be leveraged to learn a single parameterization for many different garments to be draped on human bodies in arbitrary poses. Our approach relies on UDFs to represent garment surfaces and on a displacement field to drape them, which enables us to handle a continuous manifold of garments without restrictions on their topology. Our whole pipeline is differentiable, which makes it suitable for solving inverse problems and for modeling clothed people from image data." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.869 + ], + "angle": 0, + "content": "Future work will focus on modeling dynamic poses instead of only static ones. This is of particular relevance for loose clothes, where our reliance on the SMPL skinning prior should be relaxed. Moreover, we will investigate replacing our current global latent code by a set of local ones to yield finer-grained control both for garment editing and draping." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.87, + 0.892, + 0.899 + ], + "angle": 0, + "content": "Acknowledgement. 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In International Conference on Computer Vision, 2021. 2, 4" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.574 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "1460" + } + ] +] \ No newline at end of file diff --git a/2023/DrapeNet_ Garment Generation and Self-Supervised Draping/bc8ad2b1-5bdc-4117-96e0-b09e43677d93_origin.pdf b/2023/DrapeNet_ Garment Generation and Self-Supervised Draping/bc8ad2b1-5bdc-4117-96e0-b09e43677d93_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..df05ac324a7f37166eb3b1a7ae1789627b45e348 --- /dev/null +++ b/2023/DrapeNet_ Garment Generation and Self-Supervised Draping/bc8ad2b1-5bdc-4117-96e0-b09e43677d93_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:62114137e74d93323c751329e796e98374dc25b6182928636816fda32fa88004 +size 6304645 diff --git a/2023/DrapeNet_ Garment Generation and Self-Supervised Draping/full.md b/2023/DrapeNet_ Garment Generation and Self-Supervised Draping/full.md new file mode 100644 index 0000000000000000000000000000000000000000..feabef272f4f4f120fc8d96af9b92843512b200e --- /dev/null +++ b/2023/DrapeNet_ Garment Generation and Self-Supervised Draping/full.md @@ -0,0 +1,352 @@ +# DrapeNet: Garment Generation and Self-Supervised Draping + +Luca De Luigi*,2 + +Ren Li\*,1 + +Benoit Guillard + +Mathieu Salzmann1 + +Pascal Fua1 + +1: CVLab, EPFL, {name.surname}@epfl.ch 2: University of Bologna, luca.deluigi4@unibo.it + +![](images/d74685ce3404a283951a0a5cf66c28fac754f6260f35ca3fe2cf8f49d611fc76.jpg) +Figure 1. Our network can drape garments over bodies of different shapes in various poses. To minimize the required amount of supervision, our draping network is trained with physics-based self-supervision and generalizes to multiple garments by being conditioned on latent codes. These can be manipulated to edit specific features of the corresponding garments. Being fully differentiable, our pipeline makes it possible to recover 3D models of garments and bodies from observations such as images and 3D scans. + +# Abstract + +Recent approaches to drape garments quickly over arbitrary human bodies leverage self-supervision to eliminate the need for large training sets. However, they are designed to train one network per clothing item, which severely limits their generalization abilities. In our work, we rely on self-supervision to train a single network to drape multiple garments. This is achieved by predicting a 3D deformation field conditioned on the latent codes of a generative network, which models garments as unsigned distance fields. + +Our pipeline can generate and drape previously unseen garments of any topology, whose shape can be edited by manipulating their latent codes. Being fully differentiable, our formulation makes it possible to recover accurate 3D models of garments from partial observations – images or 3D scans – via gradient descent. Our code is publicly available at https://github.com/liren2515/DrapeNet. + +# 1. Introduction + +Draping digital garments over differently-shaped bodies in random poses has been extensively studied due to its many applications such as fashion design, moviemaking, video gaming, virtual try-on and, nowadays, virtual and augmented reality. Physics-based simulation (PBS) [3, 12, 23, 32, 33, 38, 39, 47-49, 51, 60] can produce outstanding results, but at a high computational cost. + +Recent years have witnessed the emergence of deep neural networks aiming to achieve the quality of PBS draping while being much faster, easily differentiable, and offering new speed vs. accuracy tradeoffs [15, 16, 25, 36, 44, 46, 50, 53, 55]. These networks are often trained to produce garments that resemble ground-truth ones. While effective, this requires building training datasets, consisting of ground-truth meshes obtained either from computationally expensive simulations [31] or using complex 3D scanning setups [37]. Moreover, to generalize to unseen garments and poses, these supervised approaches require training databases encompassing a great variety of samples de + +picting many combinations of garments, bodies and poses. + +The recent PBNS and SNUG approaches [5, 42] address this by casting the physical models adopted in PBS into constraints used for self-supervision of deep learning models. This makes it possible to train the network on a multitude of body shapes and poses without ground-truth draped garments. Instead, the predicted garments are constrained to obey physics-based rules. However, both PBNS and SNUG require training a separate network for each garment. They rely on mesh templates for garment representation and feature one output per mesh vertex. Thus, they cannot handle meshes with different topologies, even for the same garment. This makes them very specialized and limits their applicability to large garment collections as a new network must be trained for each new clothing item. + +In this work, we introduce DrapeNet, an approach that also relies on physics-based constraints to provide self-supervision but can handle generic garments by conditioning a single draping network with a latent code describing the garment to be draped. We achieve this by coupling the draping network with a garment generative network, composed of an encoder and a decoder. The encoder is trained to compress input garments into compact latent codes that are used as input condition for the draping network. The decoder, instead, reconstructs a 3D garment model from its latent code, thus allowing us to sample and edit new garments from the learned latent space. + +Specifically, we model the output of the garment decoder as an unsigned distance function (UDF), which were demonstrated [14] to yield better accuracy and fewer interpenetrations than the inflated signed distance functions often used for this purpose [10, 19]. Moreover, UDFs can be triangulated in a differentiable way [14] to produce explicit surfaces that can easily be post-processed, making our pipeline fully differentiable. Hence, DrapeNet can not only drape garments over given body shapes but can also perform gradient-based optimization to fit garments, along with body shapes and poses, to partial observations of clothed people, such as images or 3D scans. + +Our contributions are as follows: + +- We introduce a single garment draping network conditioned on a latent code to handle generic garments from a large collection (e.g. top or bottom garments); +- By exploiting physics-based self-supervision, our pipeline only requires a few hundred garment meshes in a canonical pose for training; +- Our framework enables the fast draping of new garments with high fidelity, as well as the sampling and editing of new garments from the learned latent space; +- Being fully differentiable, our method can be used to recover accurate 3D models of clothed people from images and 3D scans. + +# 2. Related Work + +Implicit Neural Representations for 3D Surfaces. Implicit neural representations have emerged a few years ago as an effective tool to represent surfaces whose topology is not known a priori. They can be implemented using (clipped) signed distance functions (SDF) [35] or occupancies [28]. When an explicit representation is required, it can be obtained using Marching Cubes [18] and this can be done while preserving differentiability [1,27,41]. However, they can only represent watertight surfaces. + +Thus, to represent open surfaces, such as clothes, it is possible to use inflated SDFs surrounding them. However, this entails a loss in accuracy and there has been a recent push to replace SDFs by unsigned distance functions (UDFs) [9, 52, 61]. One difficulty in so doing was that Marching Cubes was not designed with UDFs in mind, and obtaining explicit surfaces from these UDFs was therefore non-trivial. This has been addressed in [14] by modifying the Marching Cubes algorithm to operate with UDFs. We model garment with UDFs and use [14] to mesh them. Other works augment signed distance fields with covariant fields to encode open surface garments [8, 43]. + +Draping Garments over 3D Bodies. Two main classes of methods coexist, physics-based algorithms [3, 21, 22, 30, 31, 48] that produce high-quality draptings but at a high computational cost, and data-driven approaches that are faster but often at the cost of realism. + +Among the latter, template-based approaches [5,7,17,34, 36,42,45,50] are dominant. Each garment is modeled by a specific triangulated mesh and a draping function is learned for each one. In other words, they do not generalize. There are however a number of exceptions. In [6, 15] the mesh is replaced by 3D point clouds that can represent generic garments. This enables deforming garments with arbitrary topology and geometric complexity, by estimating the deformation separately for each point. [59] goes further and allows differentiable changes in garment topology by sampling a fixed number of points from the body mesh. Unfortunately, this point cloud representation severely limits possible downstream applications. + +In recent approaches [10, 19], a space of garments is learned with clothing items modeled as inflated SDFs and one single shared network to predict their deformations as a 3D displacement field. This makes deployment in real-world scenarios easier and allows the reconstruction of garments from images and 3D scans. However, the inflated SDF scheme reduces realism and precludes post-processing using standard physics-based simulators or other cloth-specific downstream applications. Furthermore, both models are fully supervised and require a dataset of draped garments whose collection is extremely time-consuming. + +Alleviating the need for costly ground-truth draped garments is tackled in [5, 42], by introducing physics-based + +![](images/fb1663b9a6bb537ab68eba8bf474a9cb30b28d145bb1733742d29b1ba81ccd24.jpg) +Figure 2. Overview of our framework. Left: Garment generative network, trained to embed garments into compact latent codes and predict their unsigned distance field (UDF) from such vectors. UDFs are then meshed using [14]. Right: Garment draping network, conditioned on the latent codes of the generative network. It is trained in a self-supervised way to predict the displacements $\Delta x$ and $\Delta x_{\mathrm{ref}}$ to be applied to the vertices of given garments, before skinning them according to body shape and pose $(\beta ,\theta)$ with the predicted blending weights $\mathcal{W}$ . It includes an Intersection Solver module to prevent intersection between top and bottom garments. + +![](images/ace0a9c283926b20ff2f8f1d234a7196dc81569ce3618808b0156cff179156fd.jpg) + +losses to train draping networks in a self-supervised manner. The approach of [42] relies on a mass spring model to enforce the physical consistency of static garments deformed by different body poses. The method of [5] also accounts for variable body shapes and dynamic effects; furthermore, it incorporates a more realistic and expressive material model. Both methods, however, require training one network per garment, a limitation we remove. + +# 3. Method + +We aim to realistically deform and drape generic garments over human bodies of various shapes and poses. To this end, we introduce the DrapeNet framework, presented in Fig. 2. It comprises a generative network shown on the left and a draping network shown on the right. Only the first is trained in a supervised manner, but using only static unposed garments meshes. This is key to avoiding having to run physics-based simulations to generate groundtruth data. Furthermore, we condition the draping network on latent vectors representing the input garments, which allows us to use the same network for very different garments, something that competing methods [5,42] cannot do. + +The generative network is a decoder trained using an encoder that turns a garment into a latent code $\mathbf{z}$ that can then be decoded to an Unsigned Distance Function (UDF), from which a triangulated mesh can be extracted in a differentiable manner [14]. The UDF representation allows us to accurately represent open surfaces and the many openings that garments typically feature. Since the top and bottom garments - shirts and trousers - have different patterns, we train one generative model for each. Both networks have the same architecture but different weights. + +The resulting garment generative network is only trained to output garments in a canonical shape, pose, and size that fit a neutral SMPL [24] body. Draping the resulting garments to bodies in non-canonical poses is then entrusted to a draping network, again one for the top and one for the bottom. As in [5, 19, 42], this network predicts vertex displacements w.r.t. the neutral position. The deformed garment is then skinned onto the articulated body model. To enable generalization to different tops and bottoms, we condition the draping process on the garment latent codes of the generative network, shown as $\mathbf{z}_{\mathrm{top}}$ and $\mathbf{z}_{\mathrm{bot}}$ in Fig. 2. + +We use a small database of static unposed garments loosely aligned with bodies in the canonical position to train the two garment generating networks. This being done, we exploit physics-based constraints to train in a fully self-supervised manner the top and bottom draping networks for realism, without interpenetrations with the body and between the garments themselves. + +# 3.1. Garment Generative Network + +To encode garments into latent codes that can then be decoded into UDFs, we rely on a point cloud encoder that embeds points sampled from the unposed garment surface into a compact vector. This lets us obtain latent codes for previously unseen garments in a single inference pass from points sampled from its surface. This can be done given any arbitrary surface triangulation. Hence, it gives us the flexibility to operate on any given garment mesh. + +We use DGCNN [56] as the encoder. It first propagates the features of points within the same local region at multiple scales and then aggregates them into a single global embedding by max pooling. We pair it with a decoder that takes as input a latent vector, along with a point in 3D space, + +and returns its (unsigned) distance to the garment. The decoder is a multi-layer perceptron (MLP) that relies on Conditional Batch Normalization [54] for conditioning on the input latent vector. + +We train the encoder and the decoder by encouraging them to jointly predict distances that are small near the training garments' surface and large elsewhere. Because the algorithm we use to compute triangulated meshes from the predicted distances [14] relies on the gradient vectors of the UDF field, we also want these gradients to be as accurate as possible [2, 61]. We therefore minimize the loss + +$$ +L _ {g a r m} = L _ {d i s t} + \lambda_ {g} L _ {g r a d}, \tag {1} +$$ + +where $L_{dist}$ encodes our distance requirements, $L_{grad}$ the gradient ones, and $\lambda_g$ is a weight balancing their influence. + +More formally, at training time and given a mini-batch comprising $B$ garments, we sample a fixed number $P$ of points from the surface of each one. For each resulting point cloud $\mathbf{p}_i$ ( $1 \leq i \leq B$ ), we use the garment encoder $E_G$ to compute the latent code + +$$ +\mathbf {z} _ {i} = E _ {G} (\mathbf {p} _ {i}) \tag {2} +$$ + +and use it as input to the decoder $D_G$ . It predicts an UDF field supervised with Eq. (1), whose terms we define below. + +Distance Loss. Having experimented with many different formulations of this loss, we found the following one both simple and effective. Given $N$ points $\{\mathbf{x}_{ij}\}_{j\leq N}$ sampled from the space surrounding the $i$ -th garment, we pick a distance threshold $\delta$ , clip all the ground-truth distance values $\{y_{ij}\}$ to it, and linearly normalize the clipped values to the range [0, 1]. This yields normalized ground-truth values $\bar{y}_{ij} = \min(y_{ij}, \delta) / \delta$ . Similarly, we pass the output of the final layer of $D_G$ through a sigmoid function $\sigma(\cdot)$ to produce a prediction in the same range for point $\mathbf{x}_{ij}$ + +$$ +\widetilde {y} _ {i j} = \sigma \left(D _ {G} \left(\mathbf {x} _ {i j}, \mathbf {z} _ {i}\right)\right). \tag {3} +$$ + +Finally, we take the loss to be + +$$ +\mathcal {L} _ {\text {d i s t}} = \operatorname {B C E} \left[ \left(\bar {y} _ {i j}\right) _ {j \leq N} ^ {i \leq B}, \left(\tilde {y} _ {i j}\right) _ {j \leq N} ^ {i \leq B} \right], \tag {4} +$$ + +where $\mathrm{BCE}[\cdot, \cdot]$ stands for binary cross-entropy. As observed in [13], the sampling strategy used for points $\mathbf{x}_{ij}$ strongly impacts training effectiveness. We describe ours in the supplementary. In our experiments, we set $\delta = 0.1$ , being the top and bottom garments normalized respectively into the upper and lower halves of the $[-1, 1]^3$ cube. + +Gradient Loss. Given the same sample points as before, we take the gradient loss to be + +$$ +\mathcal {L} _ {\text {g r a d}} = \frac {1}{B N} \sum_ {i, j} \| \mathbf {g} _ {i j} - \widehat {\mathbf {g} _ {i j}} \| _ {2} ^ {2}, \tag {5} +$$ + +where $\mathbf{g}_{ij} = \nabla_{\mathbf{x}}y_{ij}\in \mathbb{R}^3$ is the ground-truth gradient of the $i$ -th garment's UDF at $\mathbf{x}_{ij}$ and $\widehat{\mathbf{g}_{ij}} = \nabla_{\mathbf{x}}D_G(\mathbf{x}_{ij},\mathbf{z}_i)$ the one of the predicted UDF, computed by backpropagation. + +# 3.2. Garment Draping Network + +We describe our approach to draping generic garments as opposed to specific ones and our self-supervised scheme. We assume that all garments are made of a single common fabric material, and we drape them in a quasi-static manner. + +# 3.2.1 Draping Generic Garments + +We rely on SMPL [24] to parameterize the body in terms of shape $(\beta)$ and pose $(\theta)$ parameters. It uses Linear Blend Skinning to deform a body template. Since garments generally follow the pose of the underlying body, we extend the SMPL skinning procedure to the 3D volume around the body for garment draping. Given a point $\mathbf{x} \in \mathbb{R}^3$ in the garment space, its position $D(\mathbf{x}, \beta, \theta, \mathbf{z})$ after draping becomes + +$$ +\begin{array}{l} D (\mathbf {x}, \beta , \theta , \mathbf {z}) = W \left(\mathbf {x} _ {\left(\beta , \theta , \mathbf {z}\right)}, \beta , \theta , \mathcal {W} (\mathbf {x})\right), \tag {6} \\ \mathbf {x} _ {(\beta , \theta , \mathbf {z})} = \mathbf {x} + \Delta x (\mathbf {x}, \beta) + \Delta x _ {\mathrm {r e f}} (\mathbf {x}, \beta , \theta , \mathbf {z}), \\ \Delta x _ {\mathrm {r e f}} (\mathbf {x}, \beta , \theta , \mathbf {z}) = \mathcal {B} (\beta , \theta) \cdot \mathcal {M} (x, \mathbf {z}), \\ \end{array} +$$ + +where $W(\cdot)$ is the SMPL skinning function, applied with blending weights $\mathcal{W}(\mathbf{x})$ , over the point displaced by $\Delta x(\mathbf{x},\beta)$ and $\Delta x_{\mathrm{ref}}(\mathbf{x},\beta ,\theta ,\mathbf{z})$ . $\mathcal{W}(\mathbf{x})$ and $\Delta x(\mathbf{x},\beta)$ are computed as in [19, 45]. However, they only give an initial deformation for garments that roughly fits the underlying body. To refine it, we introduce a new term, $\Delta x_{\mathrm{ref}}(\mathbf{x},\beta ,\theta ,\mathbf{z})$ . It is a deformation field conditioned on body parameters $\beta$ and $\theta$ , and on the garment latent code $\mathbf{z}$ from the generative network. Following the linear decomposition of displacements in SMPL, it is the composition of an embedding $\mathcal{B}(\beta ,\theta)\in \mathbb{R}^{N_B}$ of body parameters and a displacement matrix $\mathcal{M}(x,\mathbf{z})\in \mathbb{R}^{N_B\times 3}$ conditioned on $\mathbf{z}$ . Being conditioned on the latent code $\mathbf{z}$ , $\Delta x_{\mathrm{ref}}$ can deform different garments differently, unlike the methods of [5, 42]. The number of vertices does not need to be fixed, since displacements are predicted separately for each vertex. + +Since we have distinct encodings for the top and bottom garments, for each one we train two MLPs $(\mathcal{B},\mathcal{M})$ to predict $\Delta x_{\mathrm{ref}}$ . The other MLPs for $\mathcal{W}(\cdot)$ and $\Delta x(\cdot)$ are shared. + +# 3.2.2 Self-Supervised Training + +We first learn the weights of $\mathcal{W}(\cdot)$ and $\Delta x(\cdot)$ as in [19, 45], which does not require any annotation or simulation data but only the blending weights and shape displacements of SMPL. We then train our deformation fields $\Delta x_{\mathrm{ref}}$ in a fully self-supervised fashion by minimizing the physics-based losses introduced below. In this way, we completely eliminate the huge cost that extensive simulations would entail. + +Top Garments. For upper body garments - shirts, t-shirts, vests, tank tops, etc. - the deformation field is trained using the loss from [42], expressed as + +$$ +\mathcal {L} _ {\text {t o p}} = \mathcal {L} _ {\text {s t r a i n}} + \mathcal {L} _ {\text {b e n d}} + \mathcal {L} _ {\text {g r a v i t y}} + \mathcal {L} _ {\text {c o l}}, \tag {7} +$$ + +where $\mathcal{L}_{strain}$ is the membrane strain energy of the deformed garment, $\mathcal{L}_{bend}$ the bending energy caused by the folding of adjacent faces, $\mathcal{L}_{gravity}$ the gravitational potential energy, and $\mathcal{L}_{col}$ a penalty for collisions between body and garment. Unlike in [42], we only consider the quasi-static state after draping, that is, without acceleration. + +Bottom Garments. Due to gravity, bottom garments, such as trousers, would drop onto the floors if we used only the loss terms of Eq. (7). We thus introduce an extra loss term to constrain the deformation of vertices around the waist and hips. The loss becomes + +$$ +\mathcal {L} _ {\text {b o t t o m}} = \mathcal {L} _ {\text {s t r a i n}} + \mathcal {L} _ {\text {b e n d}} + \mathcal {L} _ {\text {g r a v i t y}} + \mathcal {L} _ {\text {c o l}} + \mathcal {L} _ {\text {p i n}}, +$$ + +$$ +\mathcal {L} _ {p i n} = \sum_ {v \in V} | \Delta x _ {y} | ^ {2} + \lambda \left(| \Delta x _ {x} | ^ {2} + | \Delta x _ {z} | ^ {2}\right), \tag {8} +$$ + +where $V$ is the set of garment vertices whose closest body vertices are located in the region of the waist and hips. See supplementary material for details. The terms $\Delta x_{x}$ , $\Delta x_{y}$ and $\Delta x_{z}$ are the deformations along the X, Y and Z axes, respectively. $\lambda$ is a positive value smaller than 1 that penalizes deformations along the vertical direction (Y axis) and produces natural deformations along the other directions. + +Top-Bottom Intersection. To ensure that the top and bottom garments do not intersect with each other when we drape them on the same body, we define a loss $\mathcal{L}_{IS}$ that ensures that when the top and the bottom garments overlap, the bottom garment vertices are closer to the body mesh than the top ones, which prevents them from intersecting – this is arbitrary, and the following could be formulated the other way around. To this end, we introduce an Intersection Solver (IS) network. It predicts a displacement correction $\Delta x_{IS}$ , added only when draping bottom garments as + +$$ +\tilde {\mathbf {x}} _ {(\mathbf {z} _ {t o p}, \mathbf {z} _ {b o t})} = \mathbf {x} _ {(\mathbf {z} _ {b o t})} + \Delta x _ {I S} (\mathbf {x}, \mathbf {z} _ {t o p}, \mathbf {z} _ {b o t}), \tag {9} +$$ + +where we omit the dependency of $\tilde{\mathbf{x}}$ , $\mathbf{x}$ and $\Delta x_{IS}$ on the body parameters $(\beta, \theta)$ for simplicity. $\mathbf{z}_{top}$ and $\mathbf{z}_{bot}$ are the latent codes of the top and bottom garments, and $\mathbf{x}_{(\mathbf{z}_{bot})}$ is the input point displaced according to Eq. (6). The skinning function of Eq. (6) is then applied to $\tilde{\mathbf{x}}_{(\mathbf{z}_{top}, \mathbf{z}_{bot})}$ for draping. $\Delta x_{IS}(\cdot)$ is implemented as a simple MLP and trained with + +$$ +\mathcal {L} _ {I S} = \mathcal {L} _ {\text {b o t t o m}} + \mathcal {L} _ {\text {l a y e r}}, \tag {10} +$$ + +where $\mathcal{L}_{layer}$ is a loss whose minimization requires the top and bottom garments to be separated from each other. We formulate it as + +$$ +\mathcal {L} _ {\text {l a y e r}} = \sum_ {v _ {B} \in C} \max \left(d _ {\text {b o t}} \left(v _ {B}\right) - \gamma d _ {\text {t o p}} \left(v _ {B}\right), 0\right), \tag {11} +$$ + +where $C$ is the set of body vertices covered by both the top and bottom garments, $d_{top}(\cdot)$ and $d_{bot}(\cdot)$ the distance to the top and the bottom garments respectively, and $\gamma$ a positive value smaller than 1 (more details in the supplementary). + +![](images/28e22ab3a7f4c64636468a4de69306098b1564ffc98234f14a0820683e567fe2.jpg) +Figure 3. Overview of DrapeNet applications. Top: New garments can be sampled from the latent spaces of the generative networks, and deformed by the draping networks to fit to a given body. Center: The garment encoders and the draping networks form a general purpose framework to drape any garment with a single forward pass. Bottom: Being a differentiable parametric model, our framework can reconstruct 3D garments by fitting observations such as images or 3D scans. The red boxes indicate the parameters optimized in this process. + +# 4. Experiments + +We first describe our experimental setup and test DrapeNet for the different purposes depicted by Fig. 3. They include reconstructing different kinds of garments and editing them by manipulating their latent codes. We then gauge the draping network both qualitatively and quantitatively. Finally, we use DrapeNet to reconstruct garments from images and 3D scans. + +# 4.1. Settings, Datasets and Metrics + +Datasets. Both our generative and draping networks are trained with garments from CLOTH3D [4], a synthetic dataset that contains over 7K sequences of animated 3D humans parametrized used the SMPL model and wearing different garments. Each sequence comprises up to 300 frames and features garments coming from different templates. For training, we randomly selected 600 top garments (t-shirts, shirts, tank tops, etc.) and 300 bottom garments (both long and short trousers). Neither for the generative nor for the draping networks did we use the simulated deformations of the selected garments. Instead, we trained the networks using only garment meshes on average body shapes in T-pose. + +![](images/ae0e626c3a858f9609b0e393cfedc6f218da9b3b1801bc76e5bf9ad3a64e6fb6.jpg) +Figure 4. Generative network: reconstruction of unseen garments in neutral pose/shape. The latent codes are obtained with the garment encoder, then decoded into open surface meshes. + +By contrast, for testing purposes, we selected random clothing items - 30 for top garments and 30 bottom ones - and considered whole simulated sequences. + +Training. We train two different models for top and bottom garments, both for the generative and for the draping parts of our framework. First, the generative models are trained on the 600/300 neutral garments Then, with the generative networks weights frozen, we train the draping networks by following [42]: body poses $\theta$ are sampled randomly from the AMASS [26] dataset, and shapes $\beta$ uniformly from $[-3,3]^{10}$ at each step. The other hyperparameters are given in the supplementary material. + +Metrics. We report the Euclidean distance (ED), interpenetration ratio between body and garment (B2G), and intersection between top and bottom garments (G2G). ED is computed between corresponding vertices of the considered meshes. B2G is the area ratio between the garment faces inside the body and the whole surface as in [19]. Since CLOTH3D exclusively features pairs of top/bottom garments with the bottom one closer to the body, G2G is computed by detecting faces of the bottom garment that are outside of the top one, and taking the area ratio between those and the overall bottom garment surface. + +# 4.2. Garment Parameterization + +We first test the encoding-decoding scheme of Sec. 3.1. + +Encoding-Decoding Previously Unseen Garments. The generative network of Fig. 2 is designed to project garments into a latent space and to reconstruct them from the resulting latent vectors. In Fig. 4, we visualize reconstructed previously-unseen garments from CLOTH3D. The reconstructions are faithful to the input garments, including fine-grained details such as the shirt collar on the left or the shoulder straps of the tank top. + +Semantic Manipulation of Latent Codes. Our framework enables us to edit a garment by manipulating its latent code. For the resulting edits to have a semantic meaning, we assigned binary labels corresponding to features of interest to 100 training garments. For instance, we labeled garments as having "short sleeves" (label $= 0$ ) or "long sleeves" (label $= 1$ ). Then, we fit a linear logistic regressor to the garment latent codes. After training, the regressor weights indicate + +![](images/7ad22a392c7aa6e292811396dd0cffaac703fdd5b0ba686c3018c05c0b58218a.jpg) +Figure 5. Garment editing. The latent codes produced by the garment encoder can be manipulated to edit specific features of the corresponding garments, without altering the overall geometry. + +
DeePSDDIGOurs
ED-top (mm)28.129.647.9
ED-bottom (mm)18.320.027.3
B2G-top (%) ↓7.21.80.9
B2G-bottom (%) ↓3.40.80.3
G2G (%) ↓2.04.00.5
+ +Table 1. Draping unseen garment meshes. Comparison between DeePSD, DIG and our method, for top and bottom garments: Euclidean distance (ED), intersections with the body (B2G) and between garments (G2G) as ratio of intersection areas. + +which dimensions of the latent space control the feature of interest. To this end, we first apply min-max normalization to the absolute weight values and then zero out the ones below a certain threshold, empirically set to 0.5. The remaining non-zero weights indicate which dimensions of the latent codes should be increased or decreased to edit the studied feature. To create Fig. 5, we applied this simple procedure to control the sleeve length and the front opening for top garments along with the length for bottom garments. As can be seen from the figure, our latent representations give us the ability to edit a specific garment feature while leaving other aspects of the garment geometry unchanged. + +# 4.3. Garment Draping + +We now turn to the evaluation of the draping network and compare its performance to those of DeePSD [6] or DIG [19], two fully supervised learning methods trained on CLOTH3D. DeePSD takes the point cloud of the garment mesh as input and predicts blending weights and pose displacements for each point; DIG drapes garments with a learned skinning field that can be applied to generic 3D points, but is similar for all garments. We chose those because, like DrapeNet, they both can deform garments of arbitrary geometry and topology. + +Draping Unseen Meshes. We drape previously unseen garments on different bodies in random poses. We first encode the garments and use the resulting latent codes to condition the draping network, whose inference takes $\sim 5\mathrm{ms}$ . + +![](images/c0421b1fdc2a817b966492349c4ecf41e46d906f1632b3d9f1d44f90574e8453.jpg) +Figure 6. Comparison between DeePSD, DIG and our method. Ours is more realistic despite having the highest Euclidean distance (ED) error (left), and has less intersection between garments (right). Left also shows that $\Delta x_{\mathrm{ref}}$ is necessary for realistic deformations. + +![](images/b023d2ba17e162d1d59bc2c87952cd8dcb8028060eac7b4720ef1752aba83524.jpg) +Figure 7. Human evaluation of draping results. When shown draping results of our method, DIG and DeePSD, evaluators selected ours as the most realistic one in more than half of the cases. None refers to the case when they had no clear preference. + +We provide qualitative results in Fig. 6 and report quantitative ones in Tab. 1. Despite being completely self-supervised, DrapeNet delivers the lowest ratio of body-garment interpenetrations (B2G) for both top and bottom garments and the least intersections between them (G2G). + +However, DrapeNet also yields higher ED values, which makes sense because there is more than one way to satisfy the physical constraints and to achieve realism. Hence, in the absence of explicit supervision, there is no reason for the answer picked by DrapeNet to be exactly the same as the one picked by the simulator. In fact, as argued in [5] and illustrated by Fig. 6, which is representative in terms of ED, a low ED value does not necessarily correspond to a realistic draping. To confirm this, we conducted a human evaluation study by sharing a link to a website on friends groupchats. We gave no further instructions or details besides those given on the site and reproduced in the supplementary material. The website displays 3 drapings of the same garment over the same posed body, one computed using our method and the others using the other two. The users were asked to select which one of the three seemed more realistic and more pleasant, with a fourth potential response being "none of them". We obtained feedback from 187 different people. A total of 1258 individual examples were rated and we collected 3738 user opinions. In other words, each user expressed 20 opinions on average. The chart in Fig. 7 shows that our method was selected more than $50\%$ of the times, with a large gap over the second best, DIG [19], selected less than $30\%$ of the time. This result confirms that DrapeNet can drape garments with better perceptual quality than the competing methods. + +![](images/9ae7175e18a0fa1ba7e80404827e26a422ed16b2ae6eb4947aa3e338be0fda3b.jpg) +Figure 8. Switching input latent codes of the draping network. Draping the same shirt by conditioning the draping network with (a) the corresponding latent code, (b) the code of an open vest, (c) of a t-shirt and (d) of a tank top. Gray meshes in dashed boxed are the garments corresponding to the input latent codes. + +Ablation Study. In Fig. 8, we show what happens when the draping network is conditioned with a latent code of a garment that does not match the input one. This creates unnatural deformations on the front when using the code of a shirt with a front opening to deform a shirt without an opening. Similarly, the sleeves penetrate the arms when conditioning with the code of a short sleeves shirt. This demonstrates that the draping network truly exploits the latent codes to predict garment-dependent deformation fields. + +In Fig. 6 left we show that removing our novel displacement term $\Delta x_{\mathrm{ref}}(\cdot)$ from Eq. (6) leads to unrealistic results. + +We also ablate the influence of our Intersection Solver and observe that G2G increases from $0.5\%$ to $1.1\%$ without it. This demonstrates the effectiveness of this component at reducing collisions between top and bottom garments. + +# 4.4. Fitting Observations + +Since our method is end-to-end differentiable, it can be used to reconstruct 3D models of people and their garments from partial observations, such as 2D images and 3D scans. + +Fitting Images. Given an image of a clothed person, we use the algorithm of [57, 58] to get initial estimates for the body parameters $(\beta, \theta)$ and a segmentation mask $\mathbf{S}$ . Then, starting with the mean of the learned codes $\mathbf{z}$ , we reconstruct a mesh for the body and its garments by minimizing + +$$ +\begin{array}{l} L (\beta , \theta , \mathbf {z}) = L _ {\mathrm {I o U}} \left(R \left(D (\mathbf {G}, \beta , \theta , \mathbf {z}), \operatorname {S M P L} (\beta , \theta)\right), \mathbf {S}\right), \tag {12} \\ \mathbf {G} = \operatorname {M e s h U D F} \left(D _ {G} (\mathbf {z})\right), \\ \end{array} +$$ + +w.r.t. $\mathbf{z},\beta$ and $\theta$ , where $L_{\mathrm{IoU}}$ is the IoU loss [20] in pixel space penalizing discrepancies between 2D masks, $R(\cdot)$ is + +![](images/2e1cb944ae2971f34b94fc85dce1a840e5cf3b8377004c909e09f52ec5cc85c7.jpg) +Figure 9. Recovering garments and bodies from images. From left to right we show the input image and the 3D models recovered with our method (without and with post-refinement), and competitors methods: SMPlicit [10], ClothWild [29], DIG [19]. + +a differentiable mesh renderer [40], and $\mathbf{G}$ is the set of vertices of the garment mesh reconstructed with our garment decoder using $\mathbf{z}$ . $D(\cdot)$ and $\mathrm{SMPL}(\cdot)$ are the garment and body skinning functions defined in Eq. (6) and in [24], respectively. To ensure pose plausibility, $\theta$ is constrained by an adversarial pose prior [11]. + +For the sake of simplicity, Eq. (12) formulates the reconstruction of a single garment $\mathbf{G}$ . In practice, we extend this formulation to both the top and the bottom garments shown in the target image. Fig. 9 depicts the results of minimizing this loss. It outperforms the state-of-the-art methods SMPLicit [10], ClothWild [29] and DIG [19]. The garments we recover follow the ones in the input image with higher fidelity and visual quality, without interpenetration between the body and the garments or between the two garments. + +After this optimization, we can further refine the result by minimizing the physics-based objectives of Eq. (7) w.r.t. the per-vertex displacements of the reconstructed garments, as opposed to w.r.t. the latent vectors. We describe this procedure in the supplementary material. As shown in the third column of Fig. 9, this further boosts the realism of the reconstructed garments. Note that this refinement is feasible thanks to the open surface representation allowed by our UDF model. Applying these physically inspired losses to an inflated garment, as produced by SMPLlicit, ClothWild and DIG, yields poor results with many self-intersections, as shown in the supplementary material. + +Fitting 3D scans. Given a 3D scan of a clothed person and segmentation information, we apply a strategy similar to the one presented above and minimize + +$$ +L (\beta , \theta , \mathbf {z}) = d (D (\mathbf {G}, \beta , \theta , \mathbf {z}), \mathbf {S} _ {\mathbf {G}}) + \vec {d} (\mathrm {S M P L} (\beta , \theta), \mathbf {S} _ {\mathbf {B}}), \tag {13} +$$ + +w.r.t. $\mathbf{z},\beta$ and $\theta$ , where $\mathbf{S_G}$ and $\mathbf{S_B}$ denote the segmented + +![](images/983c9e39825d3e931aff373dfc3c5999041de27917cd7d6bc2a250050cac860d.jpg) +Figure 10. Recovering garments and bodies from 3D scans. We show 3D models recovered with our method from scans of the SIZER dataset [50]. Raw indicates the model recovered with Eq. (13) from the 3D scan. Post Refinement refers to the models further refined with the physics-based losses. + +garment and body scan points, and $d(a,b)$ and $\vec{d}(a,b)$ are the bidirectional and the one-directional Chamfer distance from $b$ to $a$ . Similarly to Eq. (12), we apply Eq. (13) to recover both the top and bottom garments. Fig. 10 shows our fitting results for some scans of the SIZER dataset [50]. The recovered 3D models closely match the input scans. Moreover, we can also apply a post-refinement procedure similar to the one described above, by minimizing both the physics-based losses from Eq. (7) and the Chamfer distance to the input scan w.r.t. the 3D coordinates of the vertices of the reconstructed models. This leads to even more realistic results, with fine wrinkles aligning to the input scans. + +# 5. Conclusion + +We have shown that physics-based self-supervision can be leveraged to learn a single parameterization for many different garments to be draped on human bodies in arbitrary poses. Our approach relies on UDFs to represent garment surfaces and on a displacement field to drape them, which enables us to handle a continuous manifold of garments without restrictions on their topology. 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In International Conference on Computer Vision, 2021. 2, 4 \ No newline at end of file diff --git a/2023/DrapeNet_ Garment Generation and Self-Supervised Draping/images.zip b/2023/DrapeNet_ Garment Generation and Self-Supervised Draping/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..389a8728f55a37873e8a76edd0365b8da175d4ef --- /dev/null +++ b/2023/DrapeNet_ Garment Generation and Self-Supervised Draping/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:cd489f947d4ba37fc85c494ea57a6cf608733b7fe030abb578c53311f08f3e71 +size 506939 diff --git a/2023/DrapeNet_ Garment Generation and Self-Supervised Draping/layout.json b/2023/DrapeNet_ Garment Generation and Self-Supervised Draping/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..72f6dca14bbdd0061743f7e4d48a4a3a1810d4cf --- /dev/null +++ b/2023/DrapeNet_ Garment Generation and Self-Supervised Draping/layout.json @@ -0,0 +1,9638 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 105, + 103, + 488, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 103, + 488, + 121 + ], + "spans": [ + { + "bbox": [ + 105, + 103, + 488, + 121 + ], + "type": "text", + "content": "DrapeNet: Garment Generation and Self-Supervised Draping" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 64, + 142, + 149, + 158 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 142, + 149, + 158 + ], + "spans": [ + { + "bbox": [ + 64, + 142, + 149, + 158 + ], + "type": "text", + "content": "Luca De Luigi*,2" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 172, + 143, + 219, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 172, + 143, + 219, + 156 + ], + "spans": [ + { + "bbox": [ + 172, + 143, + 219, + 156 + ], + "type": "text", + "content": "Ren Li\\*,1" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 243, + 143, + 324, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 243, + 143, + 324, + 156 + ], + "spans": [ + { + "bbox": [ + 243, + 143, + 324, + 156 + ], + "type": "text", + "content": "Benoit Guillard" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 348, + 143, + 444, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 143, + 444, + 156 + ], + "spans": [ + { + "bbox": [ + 348, + 143, + 444, + 156 + ], + "type": "text", + "content": "Mathieu Salzmann1" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 470, + 143, + 526, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 470, + 143, + 526, + 156 + ], + "spans": [ + { + "bbox": [ + 470, + 143, + 526, + 156 + ], + "type": "text", + "content": "Pascal Fua1" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 94, + 161, + 494, + 174 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 161, + 494, + 174 + ], + "spans": [ + { + "bbox": [ + 94, + 161, + 494, + 174 + ], + "type": "text", + "content": "1: CVLab, EPFL, {name.surname}@epfl.ch 2: University of Bologna, luca.deluigi4@unibo.it" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 74, + 186, + 518, + 407 + ], + "blocks": [ + { + "bbox": [ + 74, + 186, + 518, + 407 + ], + "lines": [ + { + "bbox": [ + 74, + 186, + 518, + 407 + ], + "spans": [ + { + "bbox": [ + 74, + 186, + 518, + 407 + ], + "type": "image", + "image_path": "d74685ce3404a283951a0a5cf66c28fac754f6260f35ca3fe2cf8f49d611fc76.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 410, + 547, + 455 + ], + "lines": [ + { + "bbox": [ + 45, + 410, + 547, + 455 + ], + "spans": [ + { + "bbox": [ + 45, + 410, + 547, + 455 + ], + "type": "text", + "content": "Figure 1. Our network can drape garments over bodies of different shapes in various poses. To minimize the required amount of supervision, our draping network is trained with physics-based self-supervision and generalizes to multiple garments by being conditioned on latent codes. These can be manipulated to edit specific features of the corresponding garments. Being fully differentiable, our pipeline makes it possible to recover 3D models of garments and bodies from observations such as images and 3D scans." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 143, + 464, + 192, + 477 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 464, + 192, + 477 + ], + "spans": [ + { + "bbox": [ + 143, + 464, + 192, + 477 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 45, + 490, + 288, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 490, + 288, + 598 + ], + "spans": [ + { + "bbox": [ + 45, + 490, + 288, + 598 + ], + "type": "text", + "content": "Recent approaches to drape garments quickly over arbitrary human bodies leverage self-supervision to eliminate the need for large training sets. However, they are designed to train one network per clothing item, which severely limits their generalization abilities. In our work, we rely on self-supervision to train a single network to drape multiple garments. This is achieved by predicting a 3D deformation field conditioned on the latent codes of a generative network, which models garments as unsigned distance fields." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 45, + 598, + 288, + 683 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 598, + 288, + 683 + ], + "spans": [ + { + "bbox": [ + 45, + 598, + 288, + 683 + ], + "type": "text", + "content": "Our pipeline can generate and drape previously unseen garments of any topology, whose shape can be edited by manipulating their latent codes. Being fully differentiable, our formulation makes it possible to recover accurate 3D models of garments from partial observations – images or 3D scans – via gradient descent. Our code is publicly available at https://github.com/liren2515/DrapeNet." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 461, + 387, + 474 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 461, + 387, + 474 + ], + "spans": [ + { + "bbox": [ + 306, + 461, + 387, + 474 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 483, + 547, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 483, + 547, + 567 + ], + "spans": [ + { + "bbox": [ + 304, + 483, + 547, + 567 + ], + "type": "text", + "content": "Draping digital garments over differently-shaped bodies in random poses has been extensively studied due to its many applications such as fashion design, moviemaking, video gaming, virtual try-on and, nowadays, virtual and augmented reality. Physics-based simulation (PBS) [3, 12, 23, 32, 33, 38, 39, 47-49, 51, 60] can produce outstanding results, but at a high computational cost." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": "Recent years have witnessed the emergence of deep neural networks aiming to achieve the quality of PBS draping while being much faster, easily differentiable, and offering new speed vs. accuracy tradeoffs [15, 16, 25, 36, 44, 46, 50, 53, 55]. These networks are often trained to produce garments that resemble ground-truth ones. While effective, this requires building training datasets, consisting of ground-truth meshes obtained either from computationally expensive simulations [31] or using complex 3D scanning setups [37]. Moreover, to generalize to unseen garments and poses, these supervised approaches require training databases encompassing a great variety of samples de" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 62, + 702, + 134, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 702, + 134, + 712 + ], + "spans": [ + { + "bbox": [ + 62, + 702, + 134, + 712 + ], + "type": "text", + "content": "* Equal contributions" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 296, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 314, + 757 + ], + "type": "text", + "content": "1451" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 284, + 85 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 284, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 284, + 85 + ], + "type": "text", + "content": "picting many combinations of garments, bodies and poses." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 87, + 287, + 255 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 87, + 287, + 255 + ], + "spans": [ + { + "bbox": [ + 46, + 87, + 287, + 255 + ], + "type": "text", + "content": "The recent PBNS and SNUG approaches [5, 42] address this by casting the physical models adopted in PBS into constraints used for self-supervision of deep learning models. This makes it possible to train the network on a multitude of body shapes and poses without ground-truth draped garments. Instead, the predicted garments are constrained to obey physics-based rules. However, both PBNS and SNUG require training a separate network for each garment. They rely on mesh templates for garment representation and feature one output per mesh vertex. Thus, they cannot handle meshes with different topologies, even for the same garment. This makes them very specialized and limits their applicability to large garment collections as a new network must be trained for each new clothing item." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 258, + 288, + 402 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 258, + 288, + 402 + ], + "spans": [ + { + "bbox": [ + 46, + 258, + 288, + 402 + ], + "type": "text", + "content": "In this work, we introduce DrapeNet, an approach that also relies on physics-based constraints to provide self-supervision but can handle generic garments by conditioning a single draping network with a latent code describing the garment to be draped. We achieve this by coupling the draping network with a garment generative network, composed of an encoder and a decoder. The encoder is trained to compress input garments into compact latent codes that are used as input condition for the draping network. The decoder, instead, reconstructs a 3D garment model from its latent code, thus allowing us to sample and edit new garments from the learned latent space." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 405, + 287, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 405, + 287, + 548 + ], + "spans": [ + { + "bbox": [ + 46, + 405, + 287, + 548 + ], + "type": "text", + "content": "Specifically, we model the output of the garment decoder as an unsigned distance function (UDF), which were demonstrated [14] to yield better accuracy and fewer interpenetrations than the inflated signed distance functions often used for this purpose [10, 19]. Moreover, UDFs can be triangulated in a differentiable way [14] to produce explicit surfaces that can easily be post-processed, making our pipeline fully differentiable. Hence, DrapeNet can not only drape garments over given body shapes but can also perform gradient-based optimization to fit garments, along with body shapes and poses, to partial observations of clothed people, such as images or 3D scans." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 59, + 552, + 194, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 552, + 194, + 563 + ], + "spans": [ + { + "bbox": [ + 59, + 552, + 194, + 563 + ], + "type": "text", + "content": "Our contributions are as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 58, + 567, + 286, + 710 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 58, + 567, + 286, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 567, + 286, + 602 + ], + "spans": [ + { + "bbox": [ + 58, + 567, + 286, + 602 + ], + "type": "text", + "content": "- We introduce a single garment draping network conditioned on a latent code to handle generic garments from a large collection (e.g. top or bottom garments);" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 58, + 604, + 286, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 604, + 286, + 639 + ], + "spans": [ + { + "bbox": [ + 58, + 604, + 286, + 639 + ], + "type": "text", + "content": "- By exploiting physics-based self-supervision, our pipeline only requires a few hundred garment meshes in a canonical pose for training;" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 58, + 639, + 286, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 639, + 286, + 674 + ], + "spans": [ + { + "bbox": [ + 58, + 639, + 286, + 674 + ], + "type": "text", + "content": "- Our framework enables the fast draping of new garments with high fidelity, as well as the sampling and editing of new garments from the learned latent space;" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 58, + 675, + 286, + 710 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 675, + 286, + 710 + ], + "spans": [ + { + "bbox": [ + 58, + 675, + 286, + 710 + ], + "type": "text", + "content": "- Being fully differentiable, our method can be used to recover accurate 3D models of clothed people from images and 3D scans." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 71, + 392, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 71, + 392, + 83 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 392, + 83 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 91, + 545, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 91, + 545, + 198 + ], + "spans": [ + { + "bbox": [ + 304, + 91, + 545, + 198 + ], + "type": "text", + "content": "Implicit Neural Representations for 3D Surfaces. Implicit neural representations have emerged a few years ago as an effective tool to represent surfaces whose topology is not known a priori. They can be implemented using (clipped) signed distance functions (SDF) [35] or occupancies [28]. When an explicit representation is required, it can be obtained using Marching Cubes [18] and this can be done while preserving differentiability [1,27,41]. However, they can only represent watertight surfaces." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 199, + 545, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 199, + 545, + 342 + ], + "spans": [ + { + "bbox": [ + 304, + 199, + 545, + 342 + ], + "type": "text", + "content": "Thus, to represent open surfaces, such as clothes, it is possible to use inflated SDFs surrounding them. However, this entails a loss in accuracy and there has been a recent push to replace SDFs by unsigned distance functions (UDFs) [9, 52, 61]. One difficulty in so doing was that Marching Cubes was not designed with UDFs in mind, and obtaining explicit surfaces from these UDFs was therefore non-trivial. This has been addressed in [14] by modifying the Marching Cubes algorithm to operate with UDFs. We model garment with UDFs and use [14] to mesh them. Other works augment signed distance fields with covariant fields to encode open surface garments [8, 43]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 342, + 545, + 401 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 342, + 545, + 401 + ], + "spans": [ + { + "bbox": [ + 304, + 342, + 545, + 401 + ], + "type": "text", + "content": "Draping Garments over 3D Bodies. Two main classes of methods coexist, physics-based algorithms [3, 21, 22, 30, 31, 48] that produce high-quality draptings but at a high computational cost, and data-driven approaches that are faster but often at the cost of realism." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 402, + 545, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 402, + 545, + 557 + ], + "spans": [ + { + "bbox": [ + 304, + 402, + 545, + 557 + ], + "type": "text", + "content": "Among the latter, template-based approaches [5,7,17,34, 36,42,45,50] are dominant. Each garment is modeled by a specific triangulated mesh and a draping function is learned for each one. In other words, they do not generalize. There are however a number of exceptions. In [6, 15] the mesh is replaced by 3D point clouds that can represent generic garments. This enables deforming garments with arbitrary topology and geometric complexity, by estimating the deformation separately for each point. [59] goes further and allows differentiable changes in garment topology by sampling a fixed number of points from the body mesh. Unfortunately, this point cloud representation severely limits possible downstream applications." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 558, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 545, + 689 + ], + "type": "text", + "content": "In recent approaches [10, 19], a space of garments is learned with clothing items modeled as inflated SDFs and one single shared network to predict their deformations as a 3D displacement field. This makes deployment in real-world scenarios easier and allows the reconstruction of garments from images and 3D scans. However, the inflated SDF scheme reduces realism and precludes post-processing using standard physics-based simulators or other cloth-specific downstream applications. Furthermore, both models are fully supervised and require a dataset of draped garments whose collection is extremely time-consuming." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "Alleviating the need for costly ground-truth draped garments is tackled in [5, 42], by introducing physics-based" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1452" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 71, + 254, + 247 + ], + "blocks": [ + { + "bbox": [ + 51, + 71, + 254, + 247 + ], + "lines": [ + { + "bbox": [ + 51, + 71, + 254, + 247 + ], + "spans": [ + { + "bbox": [ + 51, + 71, + 254, + 247 + ], + "type": "image", + "image_path": "fb1663b9a6bb537ab68eba8bf474a9cb30b28d145bb1733742d29b1ba81ccd24.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 251, + 547, + 307 + ], + "lines": [ + { + "bbox": [ + 46, + 251, + 547, + 307 + ], + "spans": [ + { + "bbox": [ + 46, + 251, + 547, + 307 + ], + "type": "text", + "content": "Figure 2. Overview of our framework. Left: Garment generative network, trained to embed garments into compact latent codes and predict their unsigned distance field (UDF) from such vectors. UDFs are then meshed using [14]. Right: Garment draping network, conditioned on the latent codes of the generative network. It is trained in a self-supervised way to predict the displacements " + }, + { + "bbox": [ + 46, + 251, + 547, + 307 + ], + "type": "inline_equation", + "content": "\\Delta x" + }, + { + "bbox": [ + 46, + 251, + 547, + 307 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 251, + 547, + 307 + ], + "type": "inline_equation", + "content": "\\Delta x_{\\mathrm{ref}}" + }, + { + "bbox": [ + 46, + 251, + 547, + 307 + ], + "type": "text", + "content": " to be applied to the vertices of given garments, before skinning them according to body shape and pose " + }, + { + "bbox": [ + 46, + 251, + 547, + 307 + ], + "type": "inline_equation", + "content": "(\\beta ,\\theta)" + }, + { + "bbox": [ + 46, + 251, + 547, + 307 + ], + "type": "text", + "content": " with the predicted blending weights " + }, + { + "bbox": [ + 46, + 251, + 547, + 307 + ], + "type": "inline_equation", + "content": "\\mathcal{W}" + }, + { + "bbox": [ + 46, + 251, + 547, + 307 + ], + "type": "text", + "content": ". It includes an Intersection Solver module to prevent intersection between top and bottom garments." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 255, + 72, + 539, + 247 + ], + "blocks": [ + { + "bbox": [ + 255, + 72, + 539, + 247 + ], + "lines": [ + { + "bbox": [ + 255, + 72, + 539, + 247 + ], + "spans": [ + { + "bbox": [ + 255, + 72, + 539, + 247 + ], + "type": "image", + "image_path": "ace0a9c283926b20ff2f8f1d234a7196dc81569ce3618808b0156cff179156fd.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 317, + 288, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 317, + 288, + 413 + ], + "spans": [ + { + "bbox": [ + 46, + 317, + 288, + 413 + ], + "type": "text", + "content": "losses to train draping networks in a self-supervised manner. The approach of [42] relies on a mass spring model to enforce the physical consistency of static garments deformed by different body poses. The method of [5] also accounts for variable body shapes and dynamic effects; furthermore, it incorporates a more realistic and expressive material model. Both methods, however, require training one network per garment, a limitation we remove." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 428, + 103, + 440 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 428, + 103, + 440 + ], + "spans": [ + { + "bbox": [ + 47, + 428, + 103, + 440 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 449, + 287, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 287, + 592 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 287, + 592 + ], + "type": "text", + "content": "We aim to realistically deform and drape generic garments over human bodies of various shapes and poses. To this end, we introduce the DrapeNet framework, presented in Fig. 2. It comprises a generative network shown on the left and a draping network shown on the right. Only the first is trained in a supervised manner, but using only static unposed garments meshes. This is key to avoiding having to run physics-based simulations to generate groundtruth data. Furthermore, we condition the draping network on latent vectors representing the input garments, which allows us to use the same network for very different garments, something that competing methods [5,42] cannot do." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "content": "The generative network is a decoder trained using an encoder that turns a garment into a latent code " + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "content": " that can then be decoded to an Unsigned Distance Function (UDF), from which a triangulated mesh can be extracted in a differentiable manner [14]. The UDF representation allows us to accurately represent open surfaces and the many openings that garments typically feature. Since the top and bottom garments - shirts and trousers - have different patterns, we train one generative model for each. Both networks have the same architecture but different weights." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 317, + 545, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 317, + 545, + 449 + ], + "spans": [ + { + "bbox": [ + 304, + 317, + 545, + 449 + ], + "type": "text", + "content": "The resulting garment generative network is only trained to output garments in a canonical shape, pose, and size that fit a neutral SMPL [24] body. Draping the resulting garments to bodies in non-canonical poses is then entrusted to a draping network, again one for the top and one for the bottom. As in [5, 19, 42], this network predicts vertex displacements w.r.t. the neutral position. The deformed garment is then skinned onto the articulated body model. To enable generalization to different tops and bottoms, we condition the draping process on the garment latent codes of the generative network, shown as " + }, + { + "bbox": [ + 304, + 317, + 545, + 449 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{\\mathrm{top}}" + }, + { + "bbox": [ + 304, + 317, + 545, + 449 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 317, + 545, + 449 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{\\mathrm{bot}}" + }, + { + "bbox": [ + 304, + 317, + 545, + 449 + ], + "type": "text", + "content": " in Fig. 2." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 449, + 545, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 545, + 533 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 545, + 533 + ], + "type": "text", + "content": "We use a small database of static unposed garments loosely aligned with bodies in the canonical position to train the two garment generating networks. This being done, we exploit physics-based constraints to train in a fully self-supervised manner the top and bottom draping networks for realism, without interpenetrations with the body and between the garments themselves." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 540, + 469, + 551 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 540, + 469, + 551 + ], + "spans": [ + { + "bbox": [ + 306, + 540, + 469, + 551 + ], + "type": "text", + "content": "3.1. Garment Generative Network" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 558, + 545, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 545, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 545, + 653 + ], + "type": "text", + "content": "To encode garments into latent codes that can then be decoded into UDFs, we rely on a point cloud encoder that embeds points sampled from the unposed garment surface into a compact vector. This lets us obtain latent codes for previously unseen garments in a single inference pass from points sampled from its surface. This can be done given any arbitrary surface triangulation. Hence, it gives us the flexibility to operate on any given garment mesh." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "We use DGCNN [56] as the encoder. It first propagates the features of points within the same local region at multiple scales and then aggregates them into a single global embedding by max pooling. We pair it with a decoder that takes as input a latent vector, along with a point in 3D space," + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1453" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": "and returns its (unsigned) distance to the garment. The decoder is a multi-layer perceptron (MLP) that relies on Conditional Batch Normalization [54] for conditioning on the input latent vector." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 120, + 288, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 120, + 288, + 204 + ], + "spans": [ + { + "bbox": [ + 46, + 120, + 288, + 204 + ], + "type": "text", + "content": "We train the encoder and the decoder by encouraging them to jointly predict distances that are small near the training garments' surface and large elsewhere. Because the algorithm we use to compute triangulated meshes from the predicted distances [14] relies on the gradient vectors of the UDF field, we also want these gradients to be as accurate as possible [2, 61]. We therefore minimize the loss" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 109, + 209, + 287, + 223 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 109, + 209, + 287, + 223 + ], + "spans": [ + { + "bbox": [ + 109, + 209, + 287, + 223 + ], + "type": "interline_equation", + "content": "L _ {g a r m} = L _ {d i s t} + \\lambda_ {g} L _ {g r a d}, \\tag {1}", + "image_path": "15b7e4ee67535763fb1399327fdd58b6fec33a79d2347cf12583007791635b4b.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 227, + 287, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 227, + 287, + 251 + ], + "spans": [ + { + "bbox": [ + 47, + 227, + 287, + 251 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 227, + 287, + 251 + ], + "type": "inline_equation", + "content": "L_{dist}" + }, + { + "bbox": [ + 47, + 227, + 287, + 251 + ], + "type": "text", + "content": " encodes our distance requirements, " + }, + { + "bbox": [ + 47, + 227, + 287, + 251 + ], + "type": "inline_equation", + "content": "L_{grad}" + }, + { + "bbox": [ + 47, + 227, + 287, + 251 + ], + "type": "text", + "content": " the gradient ones, and " + }, + { + "bbox": [ + 47, + 227, + 287, + 251 + ], + "type": "inline_equation", + "content": "\\lambda_g" + }, + { + "bbox": [ + 47, + 227, + 287, + 251 + ], + "type": "text", + "content": " is a weight balancing their influence." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 251, + 287, + 311 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 251, + 287, + 311 + ], + "spans": [ + { + "bbox": [ + 46, + 251, + 287, + 311 + ], + "type": "text", + "content": "More formally, at training time and given a mini-batch comprising " + }, + { + "bbox": [ + 46, + 251, + 287, + 311 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 46, + 251, + 287, + 311 + ], + "type": "text", + "content": " garments, we sample a fixed number " + }, + { + "bbox": [ + 46, + 251, + 287, + 311 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 251, + 287, + 311 + ], + "type": "text", + "content": " of points from the surface of each one. For each resulting point cloud " + }, + { + "bbox": [ + 46, + 251, + 287, + 311 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_i" + }, + { + "bbox": [ + 46, + 251, + 287, + 311 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 46, + 251, + 287, + 311 + ], + "type": "inline_equation", + "content": "1 \\leq i \\leq B" + }, + { + "bbox": [ + 46, + 251, + 287, + 311 + ], + "type": "text", + "content": "), we use the garment encoder " + }, + { + "bbox": [ + 46, + 251, + 287, + 311 + ], + "type": "inline_equation", + "content": "E_G" + }, + { + "bbox": [ + 46, + 251, + 287, + 311 + ], + "type": "text", + "content": " to compute the latent code" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 137, + 316, + 287, + 330 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 137, + 316, + 287, + 330 + ], + "spans": [ + { + "bbox": [ + 137, + 316, + 287, + 330 + ], + "type": "interline_equation", + "content": "\\mathbf {z} _ {i} = E _ {G} (\\mathbf {p} _ {i}) \\tag {2}", + "image_path": "0489a89f2655e17fee95059d21d6044d21f8fee2653aed36a13181797ec00d8d.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 334, + 287, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 334, + 287, + 357 + ], + "spans": [ + { + "bbox": [ + 47, + 334, + 287, + 357 + ], + "type": "text", + "content": "and use it as input to the decoder " + }, + { + "bbox": [ + 47, + 334, + 287, + 357 + ], + "type": "inline_equation", + "content": "D_G" + }, + { + "bbox": [ + 47, + 334, + 287, + 357 + ], + "type": "text", + "content": ". It predicts an UDF field supervised with Eq. (1), whose terms we define below." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 358, + 287, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 358, + 287, + 479 + ], + "spans": [ + { + "bbox": [ + 46, + 358, + 287, + 479 + ], + "type": "text", + "content": "Distance Loss. Having experimented with many different formulations of this loss, we found the following one both simple and effective. Given " + }, + { + "bbox": [ + 46, + 358, + 287, + 479 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 358, + 287, + 479 + ], + "type": "text", + "content": " points " + }, + { + "bbox": [ + 46, + 358, + 287, + 479 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{x}_{ij}\\}_{j\\leq N}" + }, + { + "bbox": [ + 46, + 358, + 287, + 479 + ], + "type": "text", + "content": " sampled from the space surrounding the " + }, + { + "bbox": [ + 46, + 358, + 287, + 479 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 358, + 287, + 479 + ], + "type": "text", + "content": "-th garment, we pick a distance threshold " + }, + { + "bbox": [ + 46, + 358, + 287, + 479 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 46, + 358, + 287, + 479 + ], + "type": "text", + "content": ", clip all the ground-truth distance values " + }, + { + "bbox": [ + 46, + 358, + 287, + 479 + ], + "type": "inline_equation", + "content": "\\{y_{ij}\\}" + }, + { + "bbox": [ + 46, + 358, + 287, + 479 + ], + "type": "text", + "content": " to it, and linearly normalize the clipped values to the range [0, 1]. This yields normalized ground-truth values " + }, + { + "bbox": [ + 46, + 358, + 287, + 479 + ], + "type": "inline_equation", + "content": "\\bar{y}_{ij} = \\min(y_{ij}, \\delta) / \\delta" + }, + { + "bbox": [ + 46, + 358, + 287, + 479 + ], + "type": "text", + "content": ". Similarly, we pass the output of the final layer of " + }, + { + "bbox": [ + 46, + 358, + 287, + 479 + ], + "type": "inline_equation", + "content": "D_G" + }, + { + "bbox": [ + 46, + 358, + 287, + 479 + ], + "type": "text", + "content": " through a sigmoid function " + }, + { + "bbox": [ + 46, + 358, + 287, + 479 + ], + "type": "inline_equation", + "content": "\\sigma(\\cdot)" + }, + { + "bbox": [ + 46, + 358, + 287, + 479 + ], + "type": "text", + "content": " to produce a prediction in the same range for point " + }, + { + "bbox": [ + 46, + 358, + 287, + 479 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{ij}" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 118, + 483, + 287, + 497 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 118, + 483, + 287, + 497 + ], + "spans": [ + { + "bbox": [ + 118, + 483, + 287, + 497 + ], + "type": "interline_equation", + "content": "\\widetilde {y} _ {i j} = \\sigma \\left(D _ {G} \\left(\\mathbf {x} _ {i j}, \\mathbf {z} _ {i}\\right)\\right). \\tag {3}", + "image_path": "c5b0afbaac1d99566b7197255e4b48c2a7ab002009731cab30aa88297905d826.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 502, + 168, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 502, + 168, + 513 + ], + "spans": [ + { + "bbox": [ + 47, + 502, + 168, + 513 + ], + "type": "text", + "content": "Finally, we take the loss to be" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 88, + 517, + 287, + 539 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 517, + 287, + 539 + ], + "spans": [ + { + "bbox": [ + 88, + 517, + 287, + 539 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {d i s t}} = \\operatorname {B C E} \\left[ \\left(\\bar {y} _ {i j}\\right) _ {j \\leq N} ^ {i \\leq B}, \\left(\\tilde {y} _ {i j}\\right) _ {j \\leq N} ^ {i \\leq B} \\right], \\tag {4}", + "image_path": "dd267975e82ced4b99057b268de3bb770fc0318213b7a9c8e580e3f6d12d62cb.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 542, + 287, + 614 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 542, + 287, + 614 + ], + "spans": [ + { + "bbox": [ + 46, + 542, + 287, + 614 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 542, + 287, + 614 + ], + "type": "inline_equation", + "content": "\\mathrm{BCE}[\\cdot, \\cdot]" + }, + { + "bbox": [ + 46, + 542, + 287, + 614 + ], + "type": "text", + "content": " stands for binary cross-entropy. As observed in [13], the sampling strategy used for points " + }, + { + "bbox": [ + 46, + 542, + 287, + 614 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{ij}" + }, + { + "bbox": [ + 46, + 542, + 287, + 614 + ], + "type": "text", + "content": " strongly impacts training effectiveness. We describe ours in the supplementary. In our experiments, we set " + }, + { + "bbox": [ + 46, + 542, + 287, + 614 + ], + "type": "inline_equation", + "content": "\\delta = 0.1" + }, + { + "bbox": [ + 46, + 542, + 287, + 614 + ], + "type": "text", + "content": ", being the top and bottom garments normalized respectively into the upper and lower halves of the " + }, + { + "bbox": [ + 46, + 542, + 287, + 614 + ], + "type": "inline_equation", + "content": "[-1, 1]^3" + }, + { + "bbox": [ + 46, + 542, + 287, + 614 + ], + "type": "text", + "content": " cube." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 614, + 287, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 614, + 287, + 638 + ], + "spans": [ + { + "bbox": [ + 47, + 614, + 287, + 638 + ], + "type": "text", + "content": "Gradient Loss. Given the same sample points as before, we take the gradient loss to be" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 98, + 643, + 287, + 672 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 98, + 643, + 287, + 672 + ], + "spans": [ + { + "bbox": [ + 98, + 643, + 287, + 672 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {g r a d}} = \\frac {1}{B N} \\sum_ {i, j} \\| \\mathbf {g} _ {i j} - \\widehat {\\mathbf {g} _ {i j}} \\| _ {2} ^ {2}, \\tag {5}", + "image_path": "90c05b7d584f10e0fcf84a7786094f30a2189b2d7d08d22e86ff03b147ef0a6b.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{g}_{ij} = \\nabla_{\\mathbf{x}}y_{ij}\\in \\mathbb{R}^3" + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "text", + "content": " is the ground-truth gradient of the " + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "text", + "content": "-th garment's UDF at " + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{ij}" + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathbf{g}_{ij}} = \\nabla_{\\mathbf{x}}D_G(\\mathbf{x}_{ij},\\mathbf{z}_i)" + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "text", + "content": " the one of the predicted UDF, computed by backpropagation." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 72, + 456, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 456, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 456, + 85 + ], + "type": "text", + "content": "3.2. Garment Draping Network" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 90, + 545, + 138 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 90, + 545, + 138 + ], + "spans": [ + { + "bbox": [ + 305, + 90, + 545, + 138 + ], + "type": "text", + "content": "We describe our approach to draping generic garments as opposed to specific ones and our self-supervised scheme. We assume that all garments are made of a single common fabric material, and we drape them in a quasi-static manner." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 152, + 456, + 164 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 152, + 456, + 164 + ], + "spans": [ + { + "bbox": [ + 306, + 152, + 456, + 164 + ], + "type": "text", + "content": "3.2.1 Draping Generic Garments" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 171, + 545, + 255 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 171, + 545, + 255 + ], + "spans": [ + { + "bbox": [ + 305, + 171, + 545, + 255 + ], + "type": "text", + "content": "We rely on SMPL [24] to parameterize the body in terms of shape " + }, + { + "bbox": [ + 305, + 171, + 545, + 255 + ], + "type": "inline_equation", + "content": "(\\beta)" + }, + { + "bbox": [ + 305, + 171, + 545, + 255 + ], + "type": "text", + "content": " and pose " + }, + { + "bbox": [ + 305, + 171, + 545, + 255 + ], + "type": "inline_equation", + "content": "(\\theta)" + }, + { + "bbox": [ + 305, + 171, + 545, + 255 + ], + "type": "text", + "content": " parameters. It uses Linear Blend Skinning to deform a body template. Since garments generally follow the pose of the underlying body, we extend the SMPL skinning procedure to the 3D volume around the body for garment draping. Given a point " + }, + { + "bbox": [ + 305, + 171, + 545, + 255 + ], + "type": "inline_equation", + "content": "\\mathbf{x} \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 305, + 171, + 545, + 255 + ], + "type": "text", + "content": " in the garment space, its position " + }, + { + "bbox": [ + 305, + 171, + 545, + 255 + ], + "type": "inline_equation", + "content": "D(\\mathbf{x}, \\beta, \\theta, \\mathbf{z})" + }, + { + "bbox": [ + 305, + 171, + 545, + 255 + ], + "type": "text", + "content": " after draping becomes" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 315, + 262, + 545, + 306 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 262, + 545, + 306 + ], + "spans": [ + { + "bbox": [ + 315, + 262, + 545, + 306 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} D (\\mathbf {x}, \\beta , \\theta , \\mathbf {z}) = W \\left(\\mathbf {x} _ {\\left(\\beta , \\theta , \\mathbf {z}\\right)}, \\beta , \\theta , \\mathcal {W} (\\mathbf {x})\\right), \\tag {6} \\\\ \\mathbf {x} _ {(\\beta , \\theta , \\mathbf {z})} = \\mathbf {x} + \\Delta x (\\mathbf {x}, \\beta) + \\Delta x _ {\\mathrm {r e f}} (\\mathbf {x}, \\beta , \\theta , \\mathbf {z}), \\\\ \\Delta x _ {\\mathrm {r e f}} (\\mathbf {x}, \\beta , \\theta , \\mathbf {z}) = \\mathcal {B} (\\beta , \\theta) \\cdot \\mathcal {M} (x, \\mathbf {z}), \\\\ \\end{array}", + "image_path": "a109889bf7f3b300800c3ae92401dab7f4f59f88a65dcc6cc650731bab12ae2c.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 312, + 545, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 312, + 545, + 504 + ], + "spans": [ + { + "bbox": [ + 305, + 312, + 545, + 504 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 312, + 545, + 504 + ], + "type": "inline_equation", + "content": "W(\\cdot)" + }, + { + "bbox": [ + 305, + 312, + 545, + 504 + ], + "type": "text", + "content": " is the SMPL skinning function, applied with blending weights " + }, + { + "bbox": [ + 305, + 312, + 545, + 504 + ], + "type": "inline_equation", + "content": "\\mathcal{W}(\\mathbf{x})" + }, + { + "bbox": [ + 305, + 312, + 545, + 504 + ], + "type": "text", + "content": ", over the point displaced by " + }, + { + "bbox": [ + 305, + 312, + 545, + 504 + ], + "type": "inline_equation", + "content": "\\Delta x(\\mathbf{x},\\beta)" + }, + { + "bbox": [ + 305, + 312, + 545, + 504 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 312, + 545, + 504 + ], + "type": "inline_equation", + "content": "\\Delta x_{\\mathrm{ref}}(\\mathbf{x},\\beta ,\\theta ,\\mathbf{z})" + }, + { + "bbox": [ + 305, + 312, + 545, + 504 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 305, + 312, + 545, + 504 + ], + "type": "inline_equation", + "content": "\\mathcal{W}(\\mathbf{x})" + }, + { + "bbox": [ + 305, + 312, + 545, + 504 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 312, + 545, + 504 + ], + "type": "inline_equation", + "content": "\\Delta x(\\mathbf{x},\\beta)" + }, + { + "bbox": [ + 305, + 312, + 545, + 504 + ], + "type": "text", + "content": " are computed as in [19, 45]. However, they only give an initial deformation for garments that roughly fits the underlying body. To refine it, we introduce a new term, " + }, + { + "bbox": [ + 305, + 312, + 545, + 504 + ], + "type": "inline_equation", + "content": "\\Delta x_{\\mathrm{ref}}(\\mathbf{x},\\beta ,\\theta ,\\mathbf{z})" + }, + { + "bbox": [ + 305, + 312, + 545, + 504 + ], + "type": "text", + "content": ". It is a deformation field conditioned on body parameters " + }, + { + "bbox": [ + 305, + 312, + 545, + 504 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 305, + 312, + 545, + 504 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 312, + 545, + 504 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 305, + 312, + 545, + 504 + ], + "type": "text", + "content": ", and on the garment latent code " + }, + { + "bbox": [ + 305, + 312, + 545, + 504 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 305, + 312, + 545, + 504 + ], + "type": "text", + "content": " from the generative network. Following the linear decomposition of displacements in SMPL, it is the composition of an embedding " + }, + { + "bbox": [ + 305, + 312, + 545, + 504 + ], + "type": "inline_equation", + "content": "\\mathcal{B}(\\beta ,\\theta)\\in \\mathbb{R}^{N_B}" + }, + { + "bbox": [ + 305, + 312, + 545, + 504 + ], + "type": "text", + "content": " of body parameters and a displacement matrix " + }, + { + "bbox": [ + 305, + 312, + 545, + 504 + ], + "type": "inline_equation", + "content": "\\mathcal{M}(x,\\mathbf{z})\\in \\mathbb{R}^{N_B\\times 3}" + }, + { + "bbox": [ + 305, + 312, + 545, + 504 + ], + "type": "text", + "content": " conditioned on " + }, + { + "bbox": [ + 305, + 312, + 545, + 504 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 305, + 312, + 545, + 504 + ], + "type": "text", + "content": ". Being conditioned on the latent code " + }, + { + "bbox": [ + 305, + 312, + 545, + 504 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 305, + 312, + 545, + 504 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 312, + 545, + 504 + ], + "type": "inline_equation", + "content": "\\Delta x_{\\mathrm{ref}}" + }, + { + "bbox": [ + 305, + 312, + 545, + 504 + ], + "type": "text", + "content": " can deform different garments differently, unlike the methods of [5, 42]. The number of vertices does not need to be fixed, since displacements are predicted separately for each vertex." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 505, + 545, + 541 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 505, + 545, + 541 + ], + "spans": [ + { + "bbox": [ + 305, + 505, + 545, + 541 + ], + "type": "text", + "content": "Since we have distinct encodings for the top and bottom garments, for each one we train two MLPs " + }, + { + "bbox": [ + 305, + 505, + 545, + 541 + ], + "type": "inline_equation", + "content": "(\\mathcal{B},\\mathcal{M})" + }, + { + "bbox": [ + 305, + 505, + 545, + 541 + ], + "type": "text", + "content": " to predict " + }, + { + "bbox": [ + 305, + 505, + 545, + 541 + ], + "type": "inline_equation", + "content": "\\Delta x_{\\mathrm{ref}}" + }, + { + "bbox": [ + 305, + 505, + 545, + 541 + ], + "type": "text", + "content": ". The other MLPs for " + }, + { + "bbox": [ + 305, + 505, + 545, + 541 + ], + "type": "inline_equation", + "content": "\\mathcal{W}(\\cdot)" + }, + { + "bbox": [ + 305, + 505, + 545, + 541 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 505, + 545, + 541 + ], + "type": "inline_equation", + "content": "\\Delta x(\\cdot)" + }, + { + "bbox": [ + 305, + 505, + 545, + 541 + ], + "type": "text", + "content": " are shared." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 555, + 444, + 567 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 555, + 444, + 567 + ], + "spans": [ + { + "bbox": [ + 306, + 555, + 444, + 567 + ], + "type": "text", + "content": "3.2.2 Self-Supervised Training" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 305, + 573, + 545, + 656 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 573, + 545, + 656 + ], + "spans": [ + { + "bbox": [ + 305, + 573, + 545, + 656 + ], + "type": "text", + "content": "We first learn the weights of " + }, + { + "bbox": [ + 305, + 573, + 545, + 656 + ], + "type": "inline_equation", + "content": "\\mathcal{W}(\\cdot)" + }, + { + "bbox": [ + 305, + 573, + 545, + 656 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 573, + 545, + 656 + ], + "type": "inline_equation", + "content": "\\Delta x(\\cdot)" + }, + { + "bbox": [ + 305, + 573, + 545, + 656 + ], + "type": "text", + "content": " as in [19, 45], which does not require any annotation or simulation data but only the blending weights and shape displacements of SMPL. We then train our deformation fields " + }, + { + "bbox": [ + 305, + 573, + 545, + 656 + ], + "type": "inline_equation", + "content": "\\Delta x_{\\mathrm{ref}}" + }, + { + "bbox": [ + 305, + 573, + 545, + 656 + ], + "type": "text", + "content": " in a fully self-supervised fashion by minimizing the physics-based losses introduced below. In this way, we completely eliminate the huge cost that extensive simulations would entail." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 305, + 657, + 545, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 657, + 545, + 693 + ], + "spans": [ + { + "bbox": [ + 305, + 657, + 545, + 693 + ], + "type": "text", + "content": "Top Garments. For upper body garments - shirts, t-shirts, vests, tank tops, etc. - the deformation field is trained using the loss from [42], expressed as" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 334, + 701, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 334, + 701, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 334, + 701, + 545, + 715 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {t o p}} = \\mathcal {L} _ {\\text {s t r a i n}} + \\mathcal {L} _ {\\text {b e n d}} + \\mathcal {L} _ {\\text {g r a v i t y}} + \\mathcal {L} _ {\\text {c o l}}, \\tag {7}", + "image_path": "76e9765bfbb99c5766a5a27de7f833f65a92fd82c8c0908380e19a627fa4f143.jpg" + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1454" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{strain}" + }, + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "content": " is the membrane strain energy of the deformed garment, " + }, + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{bend}" + }, + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "content": " the bending energy caused by the folding of adjacent faces, " + }, + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{gravity}" + }, + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "content": " the gravitational potential energy, and " + }, + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{col}" + }, + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "content": " a penalty for collisions between body and garment. Unlike in [42], we only consider the quasi-static state after draping, that is, without acceleration." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 144, + 288, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 144, + 288, + 204 + ], + "spans": [ + { + "bbox": [ + 46, + 144, + 288, + 204 + ], + "type": "text", + "content": "Bottom Garments. Due to gravity, bottom garments, such as trousers, would drop onto the floors if we used only the loss terms of Eq. (7). We thus introduce an extra loss term to constrain the deformation of vertices around the waist and hips. The loss becomes" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 212, + 279, + 225 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 212, + 279, + 225 + ], + "spans": [ + { + "bbox": [ + 55, + 212, + 279, + 225 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {b o t t o m}} = \\mathcal {L} _ {\\text {s t r a i n}} + \\mathcal {L} _ {\\text {b e n d}} + \\mathcal {L} _ {\\text {g r a v i t y}} + \\mathcal {L} _ {\\text {c o l}} + \\mathcal {L} _ {\\text {p i n}},", + "image_path": "d0133b299a9c27efe0e8b091be9b8d85c905ab471fcdabaa96339fe038948b41.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 67, + 227, + 287, + 253 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 227, + 287, + 253 + ], + "spans": [ + { + "bbox": [ + 67, + 227, + 287, + 253 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {p i n} = \\sum_ {v \\in V} | \\Delta x _ {y} | ^ {2} + \\lambda \\left(| \\Delta x _ {x} | ^ {2} + | \\Delta x _ {z} | ^ {2}\\right), \\tag {8}", + "image_path": "2758331b93906330d9555a907670a4328152e70a9eb393eb0cf0aa29c6c2bed4.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 259, + 287, + 343 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 259, + 287, + 343 + ], + "spans": [ + { + "bbox": [ + 46, + 259, + 287, + 343 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 259, + 287, + 343 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 46, + 259, + 287, + 343 + ], + "type": "text", + "content": " is the set of garment vertices whose closest body vertices are located in the region of the waist and hips. See supplementary material for details. The terms " + }, + { + "bbox": [ + 46, + 259, + 287, + 343 + ], + "type": "inline_equation", + "content": "\\Delta x_{x}" + }, + { + "bbox": [ + 46, + 259, + 287, + 343 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 259, + 287, + 343 + ], + "type": "inline_equation", + "content": "\\Delta x_{y}" + }, + { + "bbox": [ + 46, + 259, + 287, + 343 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 259, + 287, + 343 + ], + "type": "inline_equation", + "content": "\\Delta x_{z}" + }, + { + "bbox": [ + 46, + 259, + 287, + 343 + ], + "type": "text", + "content": " are the deformations along the X, Y and Z axes, respectively. " + }, + { + "bbox": [ + 46, + 259, + 287, + 343 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 259, + 287, + 343 + ], + "type": "text", + "content": " is a positive value smaller than 1 that penalizes deformations along the vertical direction (Y axis) and produces natural deformations along the other directions." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 343, + 287, + 463 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 343, + 287, + 463 + ], + "spans": [ + { + "bbox": [ + 46, + 343, + 287, + 463 + ], + "type": "text", + "content": "Top-Bottom Intersection. To ensure that the top and bottom garments do not intersect with each other when we drape them on the same body, we define a loss " + }, + { + "bbox": [ + 46, + 343, + 287, + 463 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{IS}" + }, + { + "bbox": [ + 46, + 343, + 287, + 463 + ], + "type": "text", + "content": " that ensures that when the top and the bottom garments overlap, the bottom garment vertices are closer to the body mesh than the top ones, which prevents them from intersecting – this is arbitrary, and the following could be formulated the other way around. To this end, we introduce an Intersection Solver (IS) network. It predicts a displacement correction " + }, + { + "bbox": [ + 46, + 343, + 287, + 463 + ], + "type": "inline_equation", + "content": "\\Delta x_{IS}" + }, + { + "bbox": [ + 46, + 343, + 287, + 463 + ], + "type": "text", + "content": ", added only when draping bottom garments as" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 74, + 471, + 287, + 485 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 74, + 471, + 287, + 485 + ], + "spans": [ + { + "bbox": [ + 74, + 471, + 287, + 485 + ], + "type": "interline_equation", + "content": "\\tilde {\\mathbf {x}} _ {(\\mathbf {z} _ {t o p}, \\mathbf {z} _ {b o t})} = \\mathbf {x} _ {(\\mathbf {z} _ {b o t})} + \\Delta x _ {I S} (\\mathbf {x}, \\mathbf {z} _ {t o p}, \\mathbf {z} _ {b o t}), \\tag {9}", + "image_path": "b9a01c8ca1d069039e800310d8e5bce4c5e3c96169d42fad8385546713a1aab5.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 491, + 287, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 491, + 287, + 563 + ], + "spans": [ + { + "bbox": [ + 46, + 491, + 287, + 563 + ], + "type": "text", + "content": "where we omit the dependency of " + }, + { + "bbox": [ + 46, + 491, + 287, + 563 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{x}}" + }, + { + "bbox": [ + 46, + 491, + 287, + 563 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 491, + 287, + 563 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 491, + 287, + 563 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 491, + 287, + 563 + ], + "type": "inline_equation", + "content": "\\Delta x_{IS}" + }, + { + "bbox": [ + 46, + 491, + 287, + 563 + ], + "type": "text", + "content": " on the body parameters " + }, + { + "bbox": [ + 46, + 491, + 287, + 563 + ], + "type": "inline_equation", + "content": "(\\beta, \\theta)" + }, + { + "bbox": [ + 46, + 491, + 287, + 563 + ], + "type": "text", + "content": " for simplicity. " + }, + { + "bbox": [ + 46, + 491, + 287, + 563 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{top}" + }, + { + "bbox": [ + 46, + 491, + 287, + 563 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 491, + 287, + 563 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{bot}" + }, + { + "bbox": [ + 46, + 491, + 287, + 563 + ], + "type": "text", + "content": " are the latent codes of the top and bottom garments, and " + }, + { + "bbox": [ + 46, + 491, + 287, + 563 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{(\\mathbf{z}_{bot})}" + }, + { + "bbox": [ + 46, + 491, + 287, + 563 + ], + "type": "text", + "content": " is the input point displaced according to Eq. (6). The skinning function of Eq. (6) is then applied to " + }, + { + "bbox": [ + 46, + 491, + 287, + 563 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{x}}_{(\\mathbf{z}_{top}, \\mathbf{z}_{bot})}" + }, + { + "bbox": [ + 46, + 491, + 287, + 563 + ], + "type": "text", + "content": " for draping. " + }, + { + "bbox": [ + 46, + 491, + 287, + 563 + ], + "type": "inline_equation", + "content": "\\Delta x_{IS}(\\cdot)" + }, + { + "bbox": [ + 46, + 491, + 287, + 563 + ], + "type": "text", + "content": " is implemented as a simple MLP and trained with" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 114, + 571, + 287, + 585 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 114, + 571, + 287, + 585 + ], + "spans": [ + { + "bbox": [ + 114, + 571, + 287, + 585 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {I S} = \\mathcal {L} _ {\\text {b o t t o m}} + \\mathcal {L} _ {\\text {l a y e r}}, \\tag {10}", + "image_path": "15ed113d338a4ae055ec1e949bc919fd52fe824825783883ce22634ca5369fc3.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 592, + 287, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 592, + 287, + 626 + ], + "spans": [ + { + "bbox": [ + 46, + 592, + 287, + 626 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 592, + 287, + 626 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{layer}" + }, + { + "bbox": [ + 46, + 592, + 287, + 626 + ], + "type": "text", + "content": " is a loss whose minimization requires the top and bottom garments to be separated from each other. We formulate it as" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 60, + 633, + 287, + 658 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 60, + 633, + 287, + 658 + ], + "spans": [ + { + "bbox": [ + 60, + 633, + 287, + 658 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {l a y e r}} = \\sum_ {v _ {B} \\in C} \\max \\left(d _ {\\text {b o t}} \\left(v _ {B}\\right) - \\gamma d _ {\\text {t o p}} \\left(v _ {B}\\right), 0\\right), \\tag {11}", + "image_path": "2bedaea3bf66a50fd1c657e07669be6579d904aac76487a5cbf7780366aeb6b4.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": " is the set of body vertices covered by both the top and bottom garments, " + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "d_{top}(\\cdot)" + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "d_{bot}(\\cdot)" + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": " the distance to the top and the bottom garments respectively, and " + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": " a positive value smaller than 1 (more details in the supplementary)." + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 315, + 72, + 535, + 320 + ], + "blocks": [ + { + "bbox": [ + 315, + 72, + 535, + 320 + ], + "lines": [ + { + "bbox": [ + 315, + 72, + 535, + 320 + ], + "spans": [ + { + "bbox": [ + 315, + 72, + 535, + 320 + ], + "type": "image", + "image_path": "28e22ab3a7f4c64636468a4de69306098b1564ffc98234f14a0820683e567fe2.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 324, + 545, + 424 + ], + "lines": [ + { + "bbox": [ + 305, + 324, + 545, + 424 + ], + "spans": [ + { + "bbox": [ + 305, + 324, + 545, + 424 + ], + "type": "text", + "content": "Figure 3. Overview of DrapeNet applications. Top: New garments can be sampled from the latent spaces of the generative networks, and deformed by the draping networks to fit to a given body. Center: The garment encoders and the draping networks form a general purpose framework to drape any garment with a single forward pass. Bottom: Being a differentiable parametric model, our framework can reconstruct 3D garments by fitting observations such as images or 3D scans. The red boxes indicate the parameters optimized in this process." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 436, + 387, + 449 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 436, + 387, + 449 + ], + "spans": [ + { + "bbox": [ + 306, + 436, + 387, + 449 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 456, + 545, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 456, + 545, + 540 + ], + "spans": [ + { + "bbox": [ + 305, + 456, + 545, + 540 + ], + "type": "text", + "content": "We first describe our experimental setup and test DrapeNet for the different purposes depicted by Fig. 3. They include reconstructing different kinds of garments and editing them by manipulating their latent codes. We then gauge the draping network both qualitatively and quantitatively. Finally, we use DrapeNet to reconstruct garments from images and 3D scans." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 551, + 470, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 551, + 470, + 562 + ], + "spans": [ + { + "bbox": [ + 306, + 551, + 470, + 562 + ], + "type": "text", + "content": "4.1. Settings, Datasets and Metrics" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 570, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 570, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 570, + 545, + 713 + ], + "type": "text", + "content": "Datasets. Both our generative and draping networks are trained with garments from CLOTH3D [4], a synthetic dataset that contains over 7K sequences of animated 3D humans parametrized used the SMPL model and wearing different garments. Each sequence comprises up to 300 frames and features garments coming from different templates. For training, we randomly selected 600 top garments (t-shirts, shirts, tank tops, etc.) and 300 bottom garments (both long and short trousers). Neither for the generative nor for the draping networks did we use the simulated deformations of the selected garments. Instead, we trained the networks using only garment meshes on average body shapes in T-pose." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1455" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 72, + 71, + 260, + 168 + ], + "blocks": [ + { + "bbox": [ + 72, + 71, + 260, + 168 + ], + "lines": [ + { + "bbox": [ + 72, + 71, + 260, + 168 + ], + "spans": [ + { + "bbox": [ + 72, + 71, + 260, + 168 + ], + "type": "image", + "image_path": "ae0e626c3a858f9609b0e393cfedc6f218da9b3b1801bc76e5bf9ad3a64e6fb6.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 170, + 287, + 202 + ], + "lines": [ + { + "bbox": [ + 46, + 170, + 287, + 202 + ], + "spans": [ + { + "bbox": [ + 46, + 170, + 287, + 202 + ], + "type": "text", + "content": "Figure 4. Generative network: reconstruction of unseen garments in neutral pose/shape. The latent codes are obtained with the garment encoder, then decoded into open surface meshes." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 209, + 287, + 245 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 209, + 287, + 245 + ], + "spans": [ + { + "bbox": [ + 46, + 209, + 287, + 245 + ], + "type": "text", + "content": "By contrast, for testing purposes, we selected random clothing items - 30 for top garments and 30 bottom ones - and considered whole simulated sequences." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 246, + 287, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 246, + 287, + 353 + ], + "spans": [ + { + "bbox": [ + 46, + 246, + 287, + 353 + ], + "type": "text", + "content": "Training. We train two different models for top and bottom garments, both for the generative and for the draping parts of our framework. First, the generative models are trained on the 600/300 neutral garments Then, with the generative networks weights frozen, we train the draping networks by following [42]: body poses " + }, + { + "bbox": [ + 46, + 246, + 287, + 353 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 246, + 287, + 353 + ], + "type": "text", + "content": " are sampled randomly from the AMASS [26] dataset, and shapes " + }, + { + "bbox": [ + 46, + 246, + 287, + 353 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 246, + 287, + 353 + ], + "type": "text", + "content": " uniformly from " + }, + { + "bbox": [ + 46, + 246, + 287, + 353 + ], + "type": "inline_equation", + "content": "[-3,3]^{10}" + }, + { + "bbox": [ + 46, + 246, + 287, + 353 + ], + "type": "text", + "content": " at each step. The other hyperparameters are given in the supplementary material." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 354, + 287, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 354, + 287, + 485 + ], + "spans": [ + { + "bbox": [ + 46, + 354, + 287, + 485 + ], + "type": "text", + "content": "Metrics. We report the Euclidean distance (ED), interpenetration ratio between body and garment (B2G), and intersection between top and bottom garments (G2G). ED is computed between corresponding vertices of the considered meshes. B2G is the area ratio between the garment faces inside the body and the whole surface as in [19]. Since CLOTH3D exclusively features pairs of top/bottom garments with the bottom one closer to the body, G2G is computed by detecting faces of the bottom garment that are outside of the top one, and taking the area ratio between those and the overall bottom garment surface." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 491, + 188, + 503 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 491, + 188, + 503 + ], + "spans": [ + { + "bbox": [ + 47, + 491, + 188, + 503 + ], + "type": "text", + "content": "4.2. Garment Parameterization" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 58, + 510, + 283, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 510, + 283, + 521 + ], + "spans": [ + { + "bbox": [ + 58, + 510, + 283, + 521 + ], + "type": "text", + "content": "We first test the encoding-decoding scheme of Sec. 3.1." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 522, + 287, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 522, + 287, + 617 + ], + "spans": [ + { + "bbox": [ + 46, + 522, + 287, + 617 + ], + "type": "text", + "content": "Encoding-Decoding Previously Unseen Garments. The generative network of Fig. 2 is designed to project garments into a latent space and to reconstruct them from the resulting latent vectors. In Fig. 4, we visualize reconstructed previously-unseen garments from CLOTH3D. The reconstructions are faithful to the input garments, including fine-grained details such as the shirt collar on the left or the shoulder straps of the tank top." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "type": "text", + "content": "Semantic Manipulation of Latent Codes. Our framework enables us to edit a garment by manipulating its latent code. For the resulting edits to have a semantic meaning, we assigned binary labels corresponding to features of interest to 100 training garments. For instance, we labeled garments as having \"short sleeves\" (label " + }, + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "type": "inline_equation", + "content": "= 0" + }, + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "type": "text", + "content": ") or \"long sleeves\" (label " + }, + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "type": "inline_equation", + "content": "= 1" + }, + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "type": "text", + "content": "). Then, we fit a linear logistic regressor to the garment latent codes. After training, the regressor weights indicate" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 315, + 72, + 536, + 200 + ], + "blocks": [ + { + "bbox": [ + 315, + 72, + 536, + 200 + ], + "lines": [ + { + "bbox": [ + 315, + 72, + 536, + 200 + ], + "spans": [ + { + "bbox": [ + 315, + 72, + 536, + 200 + ], + "type": "image", + "image_path": "7ad22a392c7aa6e292811396dd0cffaac703fdd5b0ba686c3018c05c0b58218a.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 200, + 545, + 234 + ], + "lines": [ + { + "bbox": [ + 305, + 200, + 545, + 234 + ], + "spans": [ + { + "bbox": [ + 305, + 200, + 545, + 234 + ], + "type": "text", + "content": "Figure 5. Garment editing. The latent codes produced by the garment encoder can be manipulated to edit specific features of the corresponding garments, without altering the overall geometry." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 347, + 241, + 506, + 313 + ], + "blocks": [ + { + "bbox": [ + 347, + 241, + 506, + 313 + ], + "lines": [ + { + "bbox": [ + 347, + 241, + 506, + 313 + ], + "spans": [ + { + "bbox": [ + 347, + 241, + 506, + 313 + ], + "type": "table", + "html": "
DeePSDDIGOurs
ED-top (mm)28.129.647.9
ED-bottom (mm)18.320.027.3
B2G-top (%) ↓7.21.80.9
B2G-bottom (%) ↓3.40.80.3
G2G (%) ↓2.04.00.5
", + "image_path": "682a4b74a9833e87cb887eed491ec795c97ac69708b988385cdf622a028e1074.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 317, + 545, + 361 + ], + "lines": [ + { + "bbox": [ + 305, + 317, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 305, + 317, + 545, + 361 + ], + "type": "text", + "content": "Table 1. Draping unseen garment meshes. Comparison between DeePSD, DIG and our method, for top and bottom garments: Euclidean distance (ED), intersections with the body (B2G) and between garments (G2G) as ratio of intersection areas." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 371, + 545, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 371, + 545, + 515 + ], + "spans": [ + { + "bbox": [ + 304, + 371, + 545, + 515 + ], + "type": "text", + "content": "which dimensions of the latent space control the feature of interest. To this end, we first apply min-max normalization to the absolute weight values and then zero out the ones below a certain threshold, empirically set to 0.5. The remaining non-zero weights indicate which dimensions of the latent codes should be increased or decreased to edit the studied feature. To create Fig. 5, we applied this simple procedure to control the sleeve length and the front opening for top garments along with the length for bottom garments. As can be seen from the figure, our latent representations give us the ability to edit a specific garment feature while leaving other aspects of the garment geometry unchanged." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 525, + 413, + 538 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 525, + 413, + 538 + ], + "spans": [ + { + "bbox": [ + 306, + 525, + 413, + 538 + ], + "type": "text", + "content": "4.3. Garment Draping" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 544, + 545, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 544, + 545, + 664 + ], + "spans": [ + { + "bbox": [ + 304, + 544, + 545, + 664 + ], + "type": "text", + "content": "We now turn to the evaluation of the draping network and compare its performance to those of DeePSD [6] or DIG [19], two fully supervised learning methods trained on CLOTH3D. DeePSD takes the point cloud of the garment mesh as input and predicts blending weights and pose displacements for each point; DIG drapes garments with a learned skinning field that can be applied to generic 3D points, but is similar for all garments. We chose those because, like DrapeNet, they both can deform garments of arbitrary geometry and topology." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "Draping Unseen Meshes. We drape previously unseen garments on different bodies in random poses. We first encode the garments and use the resulting latent codes to condition the draping network, whose inference takes " + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\sim 5\\mathrm{ms}" + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1456" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 82, + 69, + 512, + 196 + ], + "blocks": [ + { + "bbox": [ + 82, + 69, + 512, + 196 + ], + "lines": [ + { + "bbox": [ + 82, + 69, + 512, + 196 + ], + "spans": [ + { + "bbox": [ + 82, + 69, + 512, + 196 + ], + "type": "image", + "image_path": "c0421b1fdc2a817b966492349c4ecf41e46d906f1632b3d9f1d44f90574e8453.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 199, + 547, + 222 + ], + "lines": [ + { + "bbox": [ + 46, + 199, + 547, + 222 + ], + "spans": [ + { + "bbox": [ + 46, + 199, + 547, + 222 + ], + "type": "text", + "content": "Figure 6. Comparison between DeePSD, DIG and our method. Ours is more realistic despite having the highest Euclidean distance (ED) error (left), and has less intersection between garments (right). Left also shows that " + }, + { + "bbox": [ + 46, + 199, + 547, + 222 + ], + "type": "inline_equation", + "content": "\\Delta x_{\\mathrm{ref}}" + }, + { + "bbox": [ + 46, + 199, + 547, + 222 + ], + "type": "text", + "content": " is necessary for realistic deformations." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 55, + 229, + 279, + 281 + ], + "blocks": [ + { + "bbox": [ + 55, + 229, + 279, + 281 + ], + "lines": [ + { + "bbox": [ + 55, + 229, + 279, + 281 + ], + "spans": [ + { + "bbox": [ + 55, + 229, + 279, + 281 + ], + "type": "image", + "image_path": "b023d2ba17e162d1d59bc2c87952cd8dcb8028060eac7b4720ef1752aba83524.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 284, + 288, + 329 + ], + "lines": [ + { + "bbox": [ + 46, + 284, + 288, + 329 + ], + "spans": [ + { + "bbox": [ + 46, + 284, + 288, + 329 + ], + "type": "text", + "content": "Figure 7. Human evaluation of draping results. When shown draping results of our method, DIG and DeePSD, evaluators selected ours as the most realistic one in more than half of the cases. None refers to the case when they had no clear preference." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 341, + 287, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 341, + 287, + 400 + ], + "spans": [ + { + "bbox": [ + 46, + 341, + 287, + 400 + ], + "type": "text", + "content": "We provide qualitative results in Fig. 6 and report quantitative ones in Tab. 1. Despite being completely self-supervised, DrapeNet delivers the lowest ratio of body-garment interpenetrations (B2G) for both top and bottom garments and the least intersections between them (G2G)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "text", + "content": "However, DrapeNet also yields higher ED values, which makes sense because there is more than one way to satisfy the physical constraints and to achieve realism. Hence, in the absence of explicit supervision, there is no reason for the answer picked by DrapeNet to be exactly the same as the one picked by the simulator. In fact, as argued in [5] and illustrated by Fig. 6, which is representative in terms of ED, a low ED value does not necessarily correspond to a realistic draping. To confirm this, we conducted a human evaluation study by sharing a link to a website on friends groupchats. We gave no further instructions or details besides those given on the site and reproduced in the supplementary material. The website displays 3 drapings of the same garment over the same posed body, one computed using our method and the others using the other two. The users were asked to select which one of the three seemed more realistic and more pleasant, with a fourth potential response being \"none of them\". We obtained feedback from 187 different people. A total of 1258 individual examples were rated and we collected 3738 user opinions. In other words, each user expressed 20 opinions on average. The chart in Fig. 7 shows that our method was selected more than " + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "text", + "content": " of the times, with a large gap over the second best, DIG [19], selected less than " + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "inline_equation", + "content": "30\\%" + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "text", + "content": " of the time. This result confirms that DrapeNet can drape garments with better perceptual quality than the competing methods." + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 310, + 228, + 538, + 279 + ], + "blocks": [ + { + "bbox": [ + 310, + 228, + 538, + 279 + ], + "lines": [ + { + "bbox": [ + 310, + 228, + 538, + 279 + ], + "spans": [ + { + "bbox": [ + 310, + 228, + 538, + 279 + ], + "type": "image", + "image_path": "9ae7175e18a0fa1ba7e80404827e26a422ed16b2ae6eb4947aa3e338be0fda3b.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 281, + 545, + 337 + ], + "lines": [ + { + "bbox": [ + 304, + 281, + 545, + 337 + ], + "spans": [ + { + "bbox": [ + 304, + 281, + 545, + 337 + ], + "type": "text", + "content": "Figure 8. Switching input latent codes of the draping network. Draping the same shirt by conditioning the draping network with (a) the corresponding latent code, (b) the code of an open vest, (c) of a t-shirt and (d) of a tank top. Gray meshes in dashed boxed are the garments corresponding to the input latent codes." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 346, + 545, + 454 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 346, + 545, + 454 + ], + "spans": [ + { + "bbox": [ + 304, + 346, + 545, + 454 + ], + "type": "text", + "content": "Ablation Study. In Fig. 8, we show what happens when the draping network is conditioned with a latent code of a garment that does not match the input one. This creates unnatural deformations on the front when using the code of a shirt with a front opening to deform a shirt without an opening. Similarly, the sleeves penetrate the arms when conditioning with the code of a short sleeves shirt. This demonstrates that the draping network truly exploits the latent codes to predict garment-dependent deformation fields." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 455, + 545, + 478 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 455, + 545, + 478 + ], + "spans": [ + { + "bbox": [ + 305, + 455, + 545, + 478 + ], + "type": "text", + "content": "In Fig. 6 left we show that removing our novel displacement term " + }, + { + "bbox": [ + 305, + 455, + 545, + 478 + ], + "type": "inline_equation", + "content": "\\Delta x_{\\mathrm{ref}}(\\cdot)" + }, + { + "bbox": [ + 305, + 455, + 545, + 478 + ], + "type": "text", + "content": " from Eq. (6) leads to unrealistic results." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 479, + 545, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 479, + 545, + 526 + ], + "spans": [ + { + "bbox": [ + 304, + 479, + 545, + 526 + ], + "type": "text", + "content": "We also ablate the influence of our Intersection Solver and observe that G2G increases from " + }, + { + "bbox": [ + 304, + 479, + 545, + 526 + ], + "type": "inline_equation", + "content": "0.5\\%" + }, + { + "bbox": [ + 304, + 479, + 545, + 526 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 479, + 545, + 526 + ], + "type": "inline_equation", + "content": "1.1\\%" + }, + { + "bbox": [ + 304, + 479, + 545, + 526 + ], + "type": "text", + "content": " without it. This demonstrates the effectiveness of this component at reducing collisions between top and bottom garments." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 533, + 425, + 546 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 533, + 425, + 546 + ], + "spans": [ + { + "bbox": [ + 306, + 533, + 425, + 546 + ], + "type": "text", + "content": "4.4. Fitting Observations" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 552, + 545, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 552, + 545, + 588 + ], + "spans": [ + { + "bbox": [ + 304, + 552, + 545, + 588 + ], + "type": "text", + "content": "Since our method is end-to-end differentiable, it can be used to reconstruct 3D models of people and their garments from partial observations, such as 2D images and 3D scans." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 588, + 545, + 648 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 588, + 545, + 648 + ], + "spans": [ + { + "bbox": [ + 304, + 588, + 545, + 648 + ], + "type": "text", + "content": "Fitting Images. Given an image of a clothed person, we use the algorithm of [57, 58] to get initial estimates for the body parameters " + }, + { + "bbox": [ + 304, + 588, + 545, + 648 + ], + "type": "inline_equation", + "content": "(\\beta, \\theta)" + }, + { + "bbox": [ + 304, + 588, + 545, + 648 + ], + "type": "text", + "content": " and a segmentation mask " + }, + { + "bbox": [ + 304, + 588, + 545, + 648 + ], + "type": "inline_equation", + "content": "\\mathbf{S}" + }, + { + "bbox": [ + 304, + 588, + 545, + 648 + ], + "type": "text", + "content": ". Then, starting with the mean of the learned codes " + }, + { + "bbox": [ + 304, + 588, + 545, + 648 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 304, + 588, + 545, + 648 + ], + "type": "text", + "content": ", we reconstruct a mesh for the body and its garments by minimizing" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 317, + 655, + 545, + 681 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 655, + 545, + 681 + ], + "spans": [ + { + "bbox": [ + 317, + 655, + 545, + 681 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} L (\\beta , \\theta , \\mathbf {z}) = L _ {\\mathrm {I o U}} \\left(R \\left(D (\\mathbf {G}, \\beta , \\theta , \\mathbf {z}), \\operatorname {S M P L} (\\beta , \\theta)\\right), \\mathbf {S}\\right), \\tag {12} \\\\ \\mathbf {G} = \\operatorname {M e s h U D F} \\left(D _ {G} (\\mathbf {z})\\right), \\\\ \\end{array}", + "image_path": "3387d884bf271813d0adce218e86d2169354200745277cc921962d12a986bb6c.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": "w.r.t. " + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{z},\\beta" + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": " , where " + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{IoU}}" + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": " is the IoU loss [20] in pixel space penalizing discrepancies between 2D masks, " + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "R(\\cdot)" + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": " is" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1457" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 72, + 279, + 267 + ], + "blocks": [ + { + "bbox": [ + 53, + 72, + 279, + 267 + ], + "lines": [ + { + "bbox": [ + 53, + 72, + 279, + 267 + ], + "spans": [ + { + "bbox": [ + 53, + 72, + 279, + 267 + ], + "type": "image", + "image_path": "2e1cb944ae2971f34b94fc85dce1a840e5cf3b8377004c909e09f52ec5cc85c7.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 269, + 287, + 312 + ], + "lines": [ + { + "bbox": [ + 46, + 269, + 287, + 312 + ], + "spans": [ + { + "bbox": [ + 46, + 269, + 287, + 312 + ], + "type": "text", + "content": "Figure 9. Recovering garments and bodies from images. From left to right we show the input image and the 3D models recovered with our method (without and with post-refinement), and competitors methods: SMPlicit [10], ClothWild [29], DIG [19]." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 317, + 286, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 317, + 286, + 389 + ], + "spans": [ + { + "bbox": [ + 46, + 317, + 286, + 389 + ], + "type": "text", + "content": "a differentiable mesh renderer [40], and " + }, + { + "bbox": [ + 46, + 317, + 286, + 389 + ], + "type": "inline_equation", + "content": "\\mathbf{G}" + }, + { + "bbox": [ + 46, + 317, + 286, + 389 + ], + "type": "text", + "content": " is the set of vertices of the garment mesh reconstructed with our garment decoder using " + }, + { + "bbox": [ + 46, + 317, + 286, + 389 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 46, + 317, + 286, + 389 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 317, + 286, + 389 + ], + "type": "inline_equation", + "content": "D(\\cdot)" + }, + { + "bbox": [ + 46, + 317, + 286, + 389 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 317, + 286, + 389 + ], + "type": "inline_equation", + "content": "\\mathrm{SMPL}(\\cdot)" + }, + { + "bbox": [ + 46, + 317, + 286, + 389 + ], + "type": "text", + "content": " are the garment and body skinning functions defined in Eq. (6) and in [24], respectively. To ensure pose plausibility, " + }, + { + "bbox": [ + 46, + 317, + 286, + 389 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 317, + 286, + 389 + ], + "type": "text", + "content": " is constrained by an adversarial pose prior [11]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 389, + 286, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 389, + 286, + 496 + ], + "spans": [ + { + "bbox": [ + 46, + 389, + 286, + 496 + ], + "type": "text", + "content": "For the sake of simplicity, Eq. (12) formulates the reconstruction of a single garment " + }, + { + "bbox": [ + 46, + 389, + 286, + 496 + ], + "type": "inline_equation", + "content": "\\mathbf{G}" + }, + { + "bbox": [ + 46, + 389, + 286, + 496 + ], + "type": "text", + "content": ". In practice, we extend this formulation to both the top and the bottom garments shown in the target image. Fig. 9 depicts the results of minimizing this loss. It outperforms the state-of-the-art methods SMPLicit [10], ClothWild [29] and DIG [19]. The garments we recover follow the ones in the input image with higher fidelity and visual quality, without interpenetration between the body and the garments or between the two garments." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 497, + 286, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 497, + 286, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 497, + 286, + 640 + ], + "type": "text", + "content": "After this optimization, we can further refine the result by minimizing the physics-based objectives of Eq. (7) w.r.t. the per-vertex displacements of the reconstructed garments, as opposed to w.r.t. the latent vectors. We describe this procedure in the supplementary material. As shown in the third column of Fig. 9, this further boosts the realism of the reconstructed garments. Note that this refinement is feasible thanks to the open surface representation allowed by our UDF model. Applying these physically inspired losses to an inflated garment, as produced by SMPLlicit, ClothWild and DIG, yields poor results with many self-intersections, as shown in the supplementary material." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 641, + 286, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 641, + 286, + 676 + ], + "spans": [ + { + "bbox": [ + 47, + 641, + 286, + 676 + ], + "type": "text", + "content": "Fitting 3D scans. Given a 3D scan of a clothed person and segmentation information, we apply a strategy similar to the one presented above and minimize" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 52, + 682, + 286, + 696 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 682, + 286, + 696 + ], + "spans": [ + { + "bbox": [ + 52, + 682, + 286, + 696 + ], + "type": "interline_equation", + "content": "L (\\beta , \\theta , \\mathbf {z}) = d (D (\\mathbf {G}, \\beta , \\theta , \\mathbf {z}), \\mathbf {S} _ {\\mathbf {G}}) + \\vec {d} (\\mathrm {S M P L} (\\beta , \\theta), \\mathbf {S} _ {\\mathbf {B}}), \\tag {13}", + "image_path": "feab9a6fe16c64c155e10478a5b0eecf9701750a866f6801ce01fb839e383280.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 701, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 701, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 701, + 286, + 713 + ], + "type": "text", + "content": "w.r.t. " + }, + { + "bbox": [ + 47, + 701, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{z},\\beta" + }, + { + "bbox": [ + 47, + 701, + 286, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 701, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 47, + 701, + 286, + 713 + ], + "type": "text", + "content": " , where " + }, + { + "bbox": [ + 47, + 701, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{S_G}" + }, + { + "bbox": [ + 47, + 701, + 286, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 701, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{S_B}" + }, + { + "bbox": [ + 47, + 701, + 286, + 713 + ], + "type": "text", + "content": " denote the segmented" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 326, + 70, + 524, + 267 + ], + "blocks": [ + { + "bbox": [ + 326, + 70, + 524, + 267 + ], + "lines": [ + { + "bbox": [ + 326, + 70, + 524, + 267 + ], + "spans": [ + { + "bbox": [ + 326, + 70, + 524, + 267 + ], + "type": "image", + "image_path": "983c9e39825d3e931aff373dfc3c5999041de27917cd7d6bc2a250050cac860d.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 269, + 545, + 322 + ], + "lines": [ + { + "bbox": [ + 305, + 269, + 545, + 322 + ], + "spans": [ + { + "bbox": [ + 305, + 269, + 545, + 322 + ], + "type": "text", + "content": "Figure 10. Recovering garments and bodies from 3D scans. We show 3D models recovered with our method from scans of the SIZER dataset [50]. Raw indicates the model recovered with Eq. (13) from the 3D scan. Post Refinement refers to the models further refined with the physics-based losses." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 331, + 545, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 331, + 545, + 475 + ], + "spans": [ + { + "bbox": [ + 304, + 331, + 545, + 475 + ], + "type": "text", + "content": "garment and body scan points, and " + }, + { + "bbox": [ + 304, + 331, + 545, + 475 + ], + "type": "inline_equation", + "content": "d(a,b)" + }, + { + "bbox": [ + 304, + 331, + 545, + 475 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 331, + 545, + 475 + ], + "type": "inline_equation", + "content": "\\vec{d}(a,b)" + }, + { + "bbox": [ + 304, + 331, + 545, + 475 + ], + "type": "text", + "content": " are the bidirectional and the one-directional Chamfer distance from " + }, + { + "bbox": [ + 304, + 331, + 545, + 475 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 304, + 331, + 545, + 475 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 331, + 545, + 475 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 304, + 331, + 545, + 475 + ], + "type": "text", + "content": ". Similarly to Eq. (12), we apply Eq. (13) to recover both the top and bottom garments. Fig. 10 shows our fitting results for some scans of the SIZER dataset [50]. The recovered 3D models closely match the input scans. Moreover, we can also apply a post-refinement procedure similar to the one described above, by minimizing both the physics-based losses from Eq. (7) and the Chamfer distance to the input scan w.r.t. the 3D coordinates of the vertices of the reconstructed models. This leads to even more realistic results, with fine wrinkles aligning to the input scans." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 483, + 378, + 495 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 483, + 378, + 495 + ], + "spans": [ + { + "bbox": [ + 306, + 483, + 378, + 495 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 498, + 545, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 605 + ], + "type": "text", + "content": "We have shown that physics-based self-supervision can be leveraged to learn a single parameterization for many different garments to be draped on human bodies in arbitrary poses. Our approach relies on UDFs to represent garment surfaces and on a displacement field to drape them, which enables us to handle a continuous manifold of garments without restrictions on their topology. Our whole pipeline is differentiable, which makes it suitable for solving inverse problems and for modeling clothed people from image data." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 605, + 545, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 688 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 688 + ], + "type": "text", + "content": "Future work will focus on modeling dynamic poses instead of only static ones. This is of particular relevance for loose clothes, where our reliance on the SMPL skinning prior should be relaxed. Moreover, we will investigate replacing our current global latent code by a set of local ones to yield finer-grained control both for garment editing and draping." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 689, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 712 + ], + "type": "text", + "content": "Acknowledgement. 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By utilizing 3D shape priors and powerful text-to-image diffusion models, our Dream3D can generate 3D content that exhibits superior visual quality and shape accuracy in accordance with the text prompt when compared to PureCLIPNeRF [24]." + ], + "image_footnote": [], + "bbox": [ + 84, + 304, + 872, + 469 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 527, + 313, + 542 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent CLIP-guided 3D optimization methods, such as DreamFields [19] and PureCLIPNeRF [24], have achieved impressive results in zero-shot text-to-3D synthesis. However, due to scratch training and random initialization without prior knowledge, these methods often fail to generate accurate and faithful 3D structures that conform to the input text. In this paper, we make the first attempt to introduce explicit 3D shape priors into the CLIP-guided 3D optimization process. Specifically, we first generate a high-quality 3D shape from the input text in the text-to-shape stage as a 3D shape prior. We then use it as the initialization of a neural radiance field and optimize it with the full prompt. To address the challenging text-to-shape generation task, we present a simple yet effective approach that directly bridges the text and image modalities with a powerful text-to-image diffusion model. To narrow the style domain gap between the images synthesized by the text-to-image diffusion model and shape renderings used to train the image-to-shape generator, we further propose to jointly optimize a learnable text prompt and fine-tune the text-to-image diffusion model for rendering-style image generation. Our method,", + "bbox": [ + 75, + 542, + 472, + 861 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Dream3D, is capable of generating imaginative 3D content with superior visual quality and shape accuracy compared to state-of-the-art methods. Our project page is at https://bluestyle97.github.io/dream3d/.", + "bbox": [ + 500, + 529, + 892, + 589 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 618, + 632, + 633 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Text-to-3D synthesis endeavors to create 3D content that is coherent with an input text, which has the potential to benefit a wide range of applications such as animations, games, and virtual reality. Recently developed zero-shot text-to-image models [34,44,45,48,50] have made remarkable progress and can generate diverse, high-fidelity, and imaginative images from various text prompts. However, extending this success to the text-to-3D synthesis task is challenging because it is not practically feasible to collect a comprehensive paired text-3D dataset.", + "bbox": [ + 496, + 643, + 892, + 794 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Zero-shot text-to-3D synthesis [19, 22, 24, 40, 51], which eliminates the need for paired data, is an attractive approach that typically relies on powerful vision-language models such as CLIP [58]. There are two main categories of this approach. 1) CLIP-based generative models, such as CLIP-Forge [51]. They utilize images as an intermediate bridge and train a mapper from the CLIP image embeddings of", + "bbox": [ + 496, + 795, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Work done during an internship at ARC Lab, Tencent PCG.", + "bbox": [ + 94, + 875, + 415, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding Author.", + "bbox": [ + 96, + 887, + 225, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "20908", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ShapeNet renderings to the shape embeddings of a 3D shape generator, then switch to the CLIP text embedding as the input at test time. 2) CLIP-guided 3D optimization methods, such as DreamFields [19] and PureCLIPNeRF [24]. They continuously optimize the CLIP similarity loss between a text prompt and rendered images of a 3D scene representation, such as neural radiance fields [1,26,32,41]. While the first category heavily relies on 3D shape generators trained on limited 3D shapes and seldom has the capacity to adjust its shape structures, the second category has more creative freedom with the \"dreaming ability\" to generate diverse shape structures and textures.", + "bbox": [ + 75, + 90, + 472, + 272 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We develop our method building upon CLIP-guided 3D optimization methods. Although these methods can produce remarkable outcomes, they typically fail to create precise and accurate 3D structures that conform to the input text (Fig. 1, $2^{\\mathrm{nd}}$ row). Due to the scratch training and random initialization without any prior knowledge, these methods tend to generate highly-unconstrained \"adversarial contents\" that have high CLIP scores but low visual quality. To address this issue and synthesize more faithful 3D contents, we suggest generating a high-quality 3D shape from the input text first and then using it as an explicit \"3D shape prior\" in the CLIP-guided 3D optimization process. In the text-to-shape* stage, we begin by synthesizing a 3D shape without textures of the main common object in the text prompt. We then use it as the initialization of a voxel-based neural radiance field and optimize it with the full prompt.", + "bbox": [ + 75, + 273, + 472, + 516 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The text-to-shape generation itself is a challenging task. Previous methods [19, 51] are often trained on images and tested with texts, and use CLIP to bridge the two modalities. However, this approach leads to a mismatching problem due to the gap between the CLIP text and image embedding spaces. Additionally, existing methods cannot produce high-quality 3D shapes. In this work, we propose to directly bridge the text and image modalities with a powerful text-to-image diffusion model, i.e., Stable Diffusion [48]. We use the text-to-image diffusion model to synthesize an image from the input text and then feed the image into an image-to-shape generator to produce high-quality 3D shapes. Since we use the same procedure in both training and testing, the mismatching problem is largely reduced. However, there is still a style domain gap between the images synthesized by Stable Diffusion and the shape renderings used to train the image-to-shape generator. Inspired by recent work on controllable text-to-image synthesis [11,49], we propose to jointly optimize a learnable text prompt and fine-tune the Stable Diffusion to address this domain gap. The fine-tuned Stable Diffusion can reliably synthesize images in the style of shape renderings used to train the image", + "bbox": [ + 75, + 517, + 472, + 849 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "to-shape module without suffering from the domain gap.", + "bbox": [ + 500, + 90, + 872, + 106 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To summarize, 1) We make the first attempt to introduce the explicit 3D shape prior into CLIP-guided 3D optimization methods. The proposed method can generate more accurate and high-quality 3D shapes conforming to the corresponding text, while still enjoying the \"dreaming\" ability of generating diverse shape structures and textures (Fig. 1, $1^{\\mathrm{st}}$ row). Therefore, we name our method \"Dream3D\" as it has both strengths. 2) Regarding text-to-shape generation, we present a straightforward yet effective approach that directly connects the text and image modalities using a powerful text-to-image diffusion model. To narrow the style domain gap between the synthesized images and shape renderings, we further propose to jointly optimize a learnable text prompt and fine-tune the text-to-image diffusion model for rendering-style image generation. 3) Our Dream3D can generate imaginative 3D content with better visual quality and shape accuracy than state-of-the-art methods. Additionally, our text-to-shape pipeline can produce 3D shapes of higher quality than previous work.", + "bbox": [ + 496, + 107, + 893, + 393 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 407, + 640, + 422 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3D Shape Generation. Generative models for 3D shapes have been extensively studied in recent years. It is more challenging than 2D image generation due to the expensive 3D data collection and the complexity of 3D shapes. Various 3D generators employ different shape representations, e.g., voxel grids [3, 25, 56], point clouds [2, 61, 63, 65, 68], meshes [13, 14, 16, 33], and implicit fields [8, 29, 59, 60, 67]. These generators are trained to model the distribution of shape geometry (and optionally, texture) from a collection of 3D shapes. Some methods [4, 5, 12, 36, 38, 39, 53] attempt to learn a 3D generator using only 2D image supervision. These methods incorporate explicit 3D representations, such as meshes [12, 38, 39] and neural radiance fields [4, 5, 36, 53], along with surface or volume-based differentiable rendering techniques [20, 21, 32, 35], to enable the learning of 3D awareness from images.", + "bbox": [ + 496, + 431, + 893, + 674 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Text-to-Image. Previous studies in text-to-image synthesis [42, 46, 62, 66] have focused mainly on domain-specific datasets and utilized GANs [15]. However, recent advances in scalable generative architectures and large-scale text-image datasets [52] have enabled unprecedented performance in zero-shot text-to-image synthesis. DALL-E [45] and GLIDE [34], as pioneering works, employ autoregressive model [10] and diffusion model [18, 54] as their architectures, respectively. DALL-E 2 [44] utilizes a diffusion prior network to translate CLIP text embeddings to CLIP image embeddings, and an unCLIP module to synthesize images from CLIP image embeddings. In Imagen [50] and Stable Diffusion [48], a large pre-trained text encoder is employed to guide the sampling process of a diffusion model in pixel space and latent space, respectively.", + "bbox": [ + 496, + 674, + 895, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_footnote", + "text": "*Throughout this paper, we use the term \"shape\" to refer to 3D geometric models without textures, while some works [7,28] also use this term for textured 3D models.", + "bbox": [ + 75, + 862, + 470, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "20909", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/524d40fe14bb7a3fa580077ad1d342e62b2c0cafd62fb9a5fdba20036a88726c.jpg", + "image_caption": [ + "Figure 2. Overview of our text-to-3D synthesis framework. (a) In the first text-to-shape stage, a fine-tuned Stable Diffusion $G_{I}$ is employed to synthesize a rendering-style image $I_{r}$ from the input text prompt $y$ . This image is then used to generate a latent shape embedding $e_{S}$ with the assistance of a shape embedding generation network $G_{M}$ . Finally, the high-quality 3D shape generator $G_{S}$ leverages $e_{S}$ to produce a 3D shape $S$ , which is used as an explicit 3D shape prior. (b) In the second optimization stage, the 3D shape prior $S$ is utilized to initialize a neural radiance field, which is further optimized with CLIP guidance to synthesize 3D content that is consistent with the input text prompt $y$ ." + ], + "image_footnote": [], + "bbox": [ + 84, + 107, + 885, + 284 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Zero-Shot Text-to-3D. Zero-shot text-to-3D generation techniques [19,22,24,31,40,51] exploit the joint text-image modeling capability of pre-trained vision-language models such as CLIP [43] to obviate the need for paired text-3D data. CLIP-Forge [51] trains a normalizing flow [9, 47] model to convert CLIP image embeddings to VAE [23] shape embeddings, and switches the input to CLIP text embeddings at the inference time. ISS [27] trains a mapper to map the CLIP image embedding into the latent shape code of a pre-trained single-view reconstruction (SVR) network [35], which is then fine-tuned by taking the CLIP text embedding as input. DreamFields [19] and CLIP-Mesh [22] are pioneering works that explore zero-shot 3D content creation using only CLIP guidance. The former optimizes a randomly-initialized NeRF, while the latter optimizes a spherical template mesh as well as random texture and normal maps. PureCLIPNeRF [24] enhances DreamFields with grid-based representation [55] and more diverse image augmentations. Recently, DreamFusion [40] has gained popularity in the research community due to its impressive results. Powered by a strong text-to-image model, ImageGen [50], it can generate high-fidelity 3D objects using the score distillation loss.", + "bbox": [ + 75, + 387, + 472, + 734 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 752, + 169, + 768 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our objective is to generate 3D content that aligns with the given input text prompt $y$ . As illustrated in Fig. 2, our framework for text-guided 3D synthesis comprises two stages. In the first stage (Sec. 3.2), we obtain an explicit 3D shape prior $S$ using a text-guided 3D shape generation process. The text-guided shape generation process involves a text-to-image phase that employs a fine-tuned Stable Diffusion model [48] $G_{I}$ (Sec. 3.3), and an image-to-shape phase", + "bbox": [ + 75, + 779, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "that employs a shape embedding generation network $G_{M}$ and a high-quality 3D shape generator $G_{S}$ . In the second stage (Sec. 3.1), we utilize the 3D prior $S$ to initialize a neural radiance field [32], and optimize it with CLIP [43] guidance to generate the 3D content. Our framework only requires a collection of textureless 3D shapes without any text labels to train the 3D generator $G_{S}$ , and the fine-tuning process of $G_{I}$ converges rapidly.", + "bbox": [ + 496, + 387, + 893, + 508 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. CLIP-Guided 3D Optimization with explicit 3D Shape Prior", + "text_level": 1, + "bbox": [ + 498, + 517, + 893, + 550 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Background: 3D Optimization with CLIP Guidance. CLIP [43] is a powerful vision-language model that comprises a text encoder $E_{T}$ , and an image encoder $E_{I}$ . By maximizing the cosine similarity between the text embedding and the image embedding encoded by $E_{T}$ and $E_{I}$ respectively on a large-scale paired text-image dataset, CLIP aligns the text and image modalities in a shared latent embedding space.", + "bbox": [ + 496, + 556, + 890, + 676 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Prior research [19, 22, 24] leverages the capability of CLIP [43] to generate 3D contents from text. Starting from a randomly-initialized 3D representation parameterized by $\\theta$ , they render images from multiple viewpoints and optimize $\\theta$ by minimizing the CLIP similarity loss between the rendered image $\\mathcal{R}(\\boldsymbol{v}_i; \\theta)$ and the text prompt $y$ :", + "bbox": [ + 496, + 678, + 893, + 768 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {C L I P}} = - E _ {I} \\left(\\mathcal {R} \\left(\\theta ; \\boldsymbol {v} _ {i}\\right)\\right) ^ {T} E _ {T} (y), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 583, + 779, + 890, + 799 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathcal{R}$ denotes the rendering process, and $\\pmb{v}_i$ denotes the rendering viewpoint at the $i$ -th optimization step. Specifically, DreamFields [19] and PureCLIPNeRF [24] employ neural radiance fields [32] (NeRF) as the 3D representation $\\theta$ , while CLIP-Mesh [22] uses a spherical template mesh with associated texture and normal maps.", + "bbox": [ + 496, + 809, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "header", + "text": "\"A park bench overgrown with vines\"", + "bbox": [ + 339, + 90, + 581, + 106 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "20910", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Observations and Motivations. Though these CLIP-guided optimization methods can generate impressive results, we observe that they often fall short in producing precise and detailed 3D structures that accurately match the text description. As depicted in Fig. 1, we employ these methods to create 3D content featuring common objects, but the outcomes exhibited distortion artifacts and appeared unusual, adversely affecting their visual quality and hindering their use in real-world applications.", + "bbox": [ + 75, + 90, + 468, + 226 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We attribute the failure of previous works to generate accurate and realistic objects to two main factors: (i) The optimization process begins with a randomly-initialized 3D representation lacking any explicit 3D shape prior, making it very challenging for the models to conjure up the scene from scratch. (ii) The CLIP loss in Eq. (1) prioritizes global consistency between the rendered image and the text prompt, rather than offering robust and precise guidance on the synthesized 3D structure. As a result, the optimization output is significantly unconstrained.", + "bbox": [ + 75, + 227, + 470, + 377 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Optimization with 3D Shape Prior as Initialization. To address the aforementioned issue and generate more faithful 3D content, we propose to use a text-to-shape generation process to create a high-quality 3D shape $S$ from the input text prompt $y$ . Subsequently, we use it as an explicit \"3D shape prior\" to initialize the CLIP-guided 3D optimization process. As illustrated in Fig. 2, for the text prompt \"a park bench overgrown with vines\", we first synthesize \"a park bench\" without textures in the text-to-shape stage. We then use it as the initialization of a neural radiance field and optimize it with the full prompt, following previous works.", + "bbox": [ + 75, + 378, + 468, + 542 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our optimization process utilizes DVGO [55], an efficient NeRF variant that represents NeRF using a density voxel grid $V_{\\mathrm{density}} \\in \\mathbb{R}^{N_x \\times N_y \\times N_z}$ and a shallow color MLP $f_{\\mathrm{rgb}}$ . We start by taking a 3D shape $S$ generated by the text-to-shape process, represented as an SDF grid $\\tilde{V}_{\\mathrm{sdf}} \\in \\mathbb{R}^{N_x \\times N_y \\times N_z}$ , and transform it into the density voxel grid $V_{\\mathrm{density}}$ using the following equations [37,55,64]:", + "bbox": [ + 76, + 544, + 470, + 650 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\Sigma} = \\frac {1}{\\beta} \\text {s i g m o i d} \\left(- \\frac {\\tilde {\\boldsymbol {V}} _ {\\mathrm {s d f}}}{\\beta}\\right), \\tag {2a}\n$$\n", + "text_format": "latex", + "bbox": [ + 191, + 660, + 468, + 700 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {V} _ {\\text {d e n s i t y}} = \\max (0, \\text {s o f t p l u s} ^ {- 1} (\\boldsymbol {\\Sigma})) \\tag {2b}\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 703, + 468, + 722 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here, $\\operatorname{sigmoid}(x) = 1 / (1 + e^{-x})$ and $\\operatorname{softplus}^{-1}(x) = \\log(e^x - 1)$ . Eq. (2a) converts SDF values to density for volume rendering, where $\\beta > 0$ is a hyper-parameter controlling the sharpness of the shape boundary (smaller $\\beta$ leads to sharper shape boundary, $\\beta = 0.05$ in our experiments). Eq. (2b) transforms the density into pre-activated density. To ensure that the distribution of the accumulated transmittance is the same as DVGO, we clamp the minimum value of the density outside the shape prior as 0.", + "bbox": [ + 75, + 733, + 468, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "With the density grid $V_{\\mathrm{density}}$ initialized by the 3D shape $S$ and the color MLP $f_{\\mathrm{rgb}}$ initialized randomly, we render", + "bbox": [ + 76, + 869, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "image $\\mathcal{R}(\\boldsymbol{V}_{\\mathrm{density}}, f_{\\mathrm{rgb}}; \\boldsymbol{v}_i)$ from viewpoint $\\boldsymbol{v}_i$ and optimize $\\theta = (V_{\\mathrm{density}}, f_{\\mathrm{rgb}})$ with the CLIP loss in Eq. (1). Following DreamFields [19] and PureCLIPNeRF [24], we perform background augmentations for the rendered images and leverage the transmittance loss introduced by [19] to reduce noise and spurious density. Besides, since CLIP loss cannot provide accurate geometrical supervision, the 3D shape prior may be gradually disturbed and \"forgotten\", thus we also adopt a shape-prior-preserving loss to preserve the global structure of the 3D shape prior:", + "bbox": [ + 496, + 90, + 890, + 242 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {p r i o r}} = - \\sum_ {(x, y, z)} \\mathbb {1} (\\tilde {\\boldsymbol {V}} _ {\\mathrm {s d f}} < 0) \\cdot \\operatorname {a l p h a} (\\boldsymbol {V} _ {\\text {d e n s i t y}}), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 251, + 890, + 286 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbb{1}(\\cdot)$ is the indicator function, and $\\mathrm{alpha}(\\cdot)$ transforms the density into the opacity representing the probability of termination at each position in volume rendering.", + "bbox": [ + 496, + 294, + 890, + 339 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "By initializing NeRF with an explicit 3D shape prior, we give extra knowledge on how the 3D content should look like and prevent the model from imagining from scratch and generating \"adversarial contents\" that have high CLIP scores but low visual quality. Based on the initialization, the CLIP-guided optimization further provides flexibility and is able to synthesize more diverse structures and textures.", + "bbox": [ + 496, + 340, + 890, + 445 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Stable-Diffusion-Assisted Text-to-Shape Generation as 3D Shape Prior", + "text_level": 1, + "bbox": [ + 498, + 454, + 890, + 486 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To obtain the 3D shape prior, a text-guided shape generation scheme is required, which is a challenging task due to the lack of paired text-shape datasets. Previous approaches [27, 51] typically first train an image-to-shape model using rendered images, and then bridge the text and image modalities using the CLIP embedding space.", + "bbox": [ + 496, + 493, + 890, + 583 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "CLIP-Forge [51] trains a normalizing flow network to map CLIP image embeddings of shape renderings to latent embeddings of a volumetric shape auto-encoder, and at test time, it switches to CLIP text embeddings as input. However, the shape auto-encoder has difficulty in generating high-quality and diverse 3D shapes, and directly feeding CLIP text embeddings to the flow network trained on CLIP image embeddings suffers from the gap between the CLIP text and image embedding spaces. ISS [27] trains a mapper network to map CLIP image embeddings of shape renderings to the latent space of a pre-trained single-view reconstruction (SVR) model, and fine-tunes the mapper at test time by maximizing the CLIP similarity between the text prompt and the images rendered from synthesized shapes. While the test-time fine-tuning alleviates the gap between the CLIP text and image embeddings, it is cumbersome to fine-tune the mapper for each text prompt.", + "bbox": [ + 496, + 583, + 890, + 839 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In contrast to the aforementioned methods that connect the text and image modalities in the CLIP embedding space, we use a powerful text-to-image diffusion model to directly bridge the two modalities. Specifically, we first synthesize", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "20911", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "an image from the input text and then feed it into an image-to-shape module to generate a high-quality 3D shape. This pipeline is more concise and naturally eliminates the gap between CLIP text and image embeddings. However, it introduces a new domain gap between the images generated by the text-to-image diffusion model and the shape renderings used to train the image-to-shape module. We will introduce a novel technique to alleviate this gap in Sec. 3.3.", + "bbox": [ + 75, + 90, + 472, + 210 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Text-to-Image Diffusion Model. Diffusion models [18,54] are generative models trained to reverse a diffusion process. The diffusion process begins with a sample from the data distribution, $\\pmb{x}_0 \\sim q(\\pmb{x}_0)$ , which is gradually corrupted by Gaussian noise over $T$ timesteps: $\\pmb{x}_t = \\sqrt{\\alpha_t} \\pmb{x}_{t-1} + \\sqrt{1 - \\alpha_t} \\pmb{\\epsilon}_{t-1}, t = 1, 2, \\dots, T$ , where $\\alpha_t$ defines the noise level and $\\pmb{\\epsilon}_{t-1}$ denotes the noise added at timestep $t-1$ . To reverse this process, a denoising network $\\epsilon_\\theta$ is trained to estimate the added noise at each timestep. During inference, samples can be generated by iteratively denoising pure Gaussian noise. Text-to-image diffusion models further condition the denoising process on texts. Given a text prompt $y$ and a text encoder $c_\\theta$ , the training objective is:", + "bbox": [ + 75, + 212, + 472, + 409 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {d i f f u s i o n}} = \\mathbb {E} _ {\\boldsymbol {x} _ {0}, t, \\boldsymbol {\\epsilon} _ {t}, y} \\| \\boldsymbol {\\epsilon} _ {t} - \\epsilon_ {\\theta} (\\boldsymbol {x} _ {t}, t, c _ {\\theta} (y)) \\| _ {2} ^ {2} \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 120, + 412, + 468, + 433 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this work, we use Stable Diffusion $^{\\dagger}$ [48], an open-source text-to-image diffusion model, which employs a CLIP ViT-L/14 text encoder as $c_{\\theta}$ and is trained on the large-scale LAION-5B dataset [52]. Stable Diffusion is known for its ability to generate diverse and imaginative images in various styles from heterogeneous text prompts.", + "bbox": [ + 75, + 438, + 468, + 529 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "High-quality 3D generator. To provide a more precise initialization for optimization, high-quality 3D shapes are highly desirable. In this work, we utilize the SDF-StyleGAN [67], a state-of-the-art 3D generative model, to generate high-quality 3D priors. SDF-StyleGAN is a StyleGAN2-like architecture that maps a random noise $z \\sim \\mathcal{N}(0, I)$ to a latent shape embedding $e_S \\in \\mathcal{W}$ and synthesizes a 3D feature volume $F_V$ , which is an implicit shape representation. We can query the SDF value at arbitrary position $x$ by feeding the interpolated feature from $F_V$ at $x$ into a jointly trained MLP. We improve upon the original SDF-StyleGAN, which trains one network for each shape category, by training a single 3D shape generator $G_S$ on the 13 categories of ShapeNet [6]. This modification provides greater flexibility in the text-to-shape process.", + "bbox": [ + 75, + 529, + 472, + 755 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Shape Embedding Mapping Network. To bridge the image and shape modalities, we further train a shape embedding mapping network $G_{M}$ . Firstly, we utilize $G_{S}$ to generate a large set of 3D shapes $\\{S^i\\}_{i=1}^N$ and shape embeddings $\\{e_S^i\\}_{i=1}^N$ . Then, we render $S^i$ from $K$ viewpoints to obtain shape renderings $\\{I_r^j\\}_{j=1}^{NK}$ and the corresponding image embeddings $\\{e_I^j\\}_{j=1}^{NK}$ with the CLIP image encoder $E_I$ , forming a paired image-shape embedding dataset", + "bbox": [ + 75, + 756, + 472, + 881 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/b4e0ed76e7fdb1233075066571549772dbbfbeaa1f538d708ac8cb7cfcc13f12.jpg", + "image_caption": [ + "Figure 3. Fine-tuning Stable Diffusion into a stylized generator. (a) We fine-tune the text embedding $\\mathbf{v}_{*}$ of a placeholder token $*$ and the weights of Stable Diffusion using a dataset $D_{S}$ that contains ShapeNet renderings and text descriptions in the format of \"a CLS in the style of *\". Additionally, we use another dataset $D_{reg}$ , which contains images synthesized by the original Stable Diffusion with text prompts in the format of \"a CLS\", for regularization purposes. (b) With the fine-tuned Stable Diffusion, we can synthesize images that match the style of ShapeNet renderings by appending the postfix \"in the style of *\" to the text prompt." + ], + "image_footnote": [], + "bbox": [ + 501, + 88, + 689, + 210 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/b473cec8fefa12e558e25cb8efd0fc31db8c2f7fdaca5e3a0b37616baeda3173.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 717, + 89, + 890, + 210 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$\\{(e_I^j,e_S^j)\\}_{j = 1}^{NK}$ . Finally, we use this dataset to train a conditional diffusion model $G_{M}$ which can synthesize shape embeddings from image embeddings of shape renderings.", + "bbox": [ + 496, + 373, + 890, + 421 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To prepare the dataset for training $G_{M}$ , we generate $N = 64000$ shapes using $G_{S}$ and render $K = 24$ views for each shape. The ranges of azimuth and elevation angles of the rendered views are $[-90^{\\circ}, 90^{\\circ}]$ and $[20^{\\circ}, 30^{\\circ}]$ , respectively. We employ an SDF renderer [20] since we represent the synthesized shapes with SDF grids.", + "bbox": [ + 496, + 421, + 890, + 512 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Fine-tuning Stable Diffusion for Rendering-Style Image Generation", + "text_level": 1, + "bbox": [ + 498, + 525, + 890, + 556 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As stated in Sec. 3.2, we use Stable Diffusion to directly bridge the text and image modalities for text-to-shape generation. Nonetheless, the image-to-shape module is trained on shape renderings, which exhibit a significant style domain gap from the images produced by Stable Diffusion. Previous research [27, 51] has attempted to combine a text-to-image model with an image-to-shape model for text-to-shape generation. However, this approach is plagued by the aforementioned style domain gap, leading to flawed geometric structures and diminished performance.", + "bbox": [ + 496, + 565, + 890, + 715 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Inspired by recent work on controllable text-to-image generation such as textual inversion [11] and Dream-Booth [49], we propose a method for addressing the domain gap problem by fine-tuning Stable Diffusion into a stylized generator. Our core idea is to enable Stable Diffusion to replicate the style of shape renderings used to train the image-to-shape module outlined in Sec. 3.2. This allows us to seamlessly input the generated stylized images into the image-to-shape module without being affected by the domain gap.", + "bbox": [ + 496, + 718, + 890, + 869 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Fine-tuning Process. The fine-tuning process is illustrated in Fig. 3. To fine-tune Stable Diffusion, we need a dataset", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "$\\dagger$ https://github.com/CompVis/stable-diffusion", + "bbox": [ + 94, + 886, + 442, + 898 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "20912", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/9102a5eabaa95608c6ad339ba28bc1078507425bba8f87134796b39775262e94.jpg", + "image_caption": [ + "Figure 4. Qualitative comparison on text-guided 3D synthesis. The 3D shape prior used to initialize the CLIP-guided optimization process for each of our results (the last row) is also visualized below." + ], + "image_footnote": [], + "bbox": [ + 78, + 88, + 888, + 378 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "that consists of shape renderings and related stylized text prompts. For each shape $S$ in the ShapeNet dataset, we generate a set of shape renderings $\\{I_S^j\\}_{j=1}^{N_S}$ . Subsequently, each rendering $I_S^j$ is linked with a stylized text prompt $y_S^j$ in the format of \"a CLS in the style of *\", where CLS denotes the shape category name and * represents a placeholder token that requires optimization for its text embedding. For instance, if the image is rendered from a chair shape, then the associated text prompt will be \"a chair in the style of *\". The paired dataset $D_S = (I_S^j, y_S^j)_{j=1}^{N_S}$ is then utilized to fine-tune Stable Diffusion by minimizing $\\mathcal{L}_{\\text{diffusion}}$ presented in Eq. (4).", + "bbox": [ + 75, + 424, + 472, + 611 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "During fine-tuning, we freeze the CLIP text encoder of Stable Diffusion, and optimize two objectives: (i) the text embedding of the placeholder token *, denoted as $v_{*}$ , and (ii) the parameters $\\theta$ of the diffusion model $\\epsilon_{\\theta}$ . Optimizing the text embedding $v_{*}$ aims to learn a virtual word that captures the style of the rendered images best, even though it is not present in the vocabulary of the text encoder. Fine-tuning the parameters $\\theta$ of the diffusion model further enhances the ability to capture the style precisely since it is hard to control the synthesis of Stable Diffusion solely on the language level. Our experiments demonstrate stable convergence of the fine-tuning process in approximately 2000 optimization steps, requiring only 40 minutes on a single Tesla A100 GPU. We show some synthesized results using the fine-tuned model in Fig. 3.", + "bbox": [ + 75, + 613, + 472, + 839 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Dataset Scale and Background Augmentation. We have identified two essential techniques empirically that enable the fine-tuned model to synthesize stylized images in a stable manner. Firstly, unlike textual inversion [11] or Dream-", + "bbox": [ + 75, + 839, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Booth [49] which utilize only 3-5 images, fine-tuning with a larger set of shape renderings containing thousands of images helps the model capture the style more precisely. Secondly, fine-tuning Stable Diffusion using shape renderings with a pure-white background results in a chaotic and uncontrollable background during inference. However, augmenting the shape renderings with random solid-color backgrounds allows the fine-tuned model to synthesize images with solid-color backgrounds stably, making it easy to remove the background if necessary. Further details can be found in the supplementary material.", + "bbox": [ + 496, + 424, + 893, + 592 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 603, + 633, + 619 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we evaluate the efficacy of our proposed text-to-3D synthesis framework. Initially, we compare our results with state-of-the-art techniques (Sec. 4.1). Subsequently, we demonstrate the effectiveness of our Stable-Diffusion-assisted approach for text-to-shape generation (Sec. 4.2). Furthermore, we conduct ablation studies to assess the effectiveness of critical components of our framework (Sec. 4.3).", + "bbox": [ + 496, + 628, + 890, + 748 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Dataset. Our framework requires only a set of textured 3D shapes for training the 3D shape generator $G_{S}$ . Specifically, we employ 13 categories from ShapeNet [6] and utilize the data preprocessing procedure of Zheng et al. [67] to generate $128^{3}$ SDF grids from the original meshes. During the fine-tuning of Stable Diffusion, we employ the SDF renderer [20] to produce a shape rendering dataset.", + "bbox": [ + 496, + 750, + 892, + 854 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation details. The 3D generator $G_{S}$ utilizes the SDF-StyleGAN architecture. The diffusion-model-based shape embedding mapping network $G_{M}$ is based on an", + "bbox": [ + 496, + 854, + 893, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "20913", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/5c3558c05f9899d283a11020170badc5d3dfc2c8604b06f50d362bda9afbdf25.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodCLIP R-Precision ↑
ViT-B/32ViT-B/16
DreamFields [19]63.2492.65
CLIP-Mesh [22]75.0091.18
PureCLIPNeRF [24]73.5388.24
Ours w/o 3D prior75.4794.34
Ours85.2998.53
", + "bbox": [ + 112, + 88, + 434, + 183 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "open-source DALL-E 2 implementation. We train $G_{M}$ by extracting image embeddings from shape renderings using the CLIP ViT-B/32 image encoder. The stylized text-to-image generator $G_{I}$ is fine-tuned from Stable Diffusion v1.4. In the optimization stage, we set the learning rates for the density grid $V_{\\mathrm{density}}$ and color MLP $f_{\\mathrm{rgb}}$ to $5 \\times 10^{-1}$ and $5 \\times 10^{-3}$ respectively, and we adopt the CLIP ViT-B/16 encoder as the guidance model. For each text prompt, we optimize for 5000 steps, while previous NeRF-based text-to-3D methods [19, 24] typically require 10000 steps or more.", + "bbox": [ + 75, + 263, + 468, + 414 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Evaluation Metrics. Regarding the primary results of our framework, i.e., text-guided 3D content synthesis, we report the CLIP retrieval precision on a manually created dataset of diverse text prompts and objects. For specifics regarding the dataset, please refer to the supplementary material. This metric quantifies the percentage of generated images that the CLIP encoder associates with the correct text prompt used for generation. We utilize Fréchet Inception Distance (FID) [17] to evaluate the shape generation quality for the initial text-to-shape generation stage.", + "bbox": [ + 75, + 415, + 468, + 566 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.1. Text-Guided 3D Synthesis", + "text_level": 1, + "bbox": [ + 76, + 578, + 313, + 594 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We compare our method with three state-of-the-art baseline methods on the task of text-guided 3D synthesis, i.e., DreamFields [19], CLIP-Mesh [22], and PureCLIPN-erF [24]. We conduct tests using the default settings and official implementations for all baseline methods. In particular, we utilize the medium-quality configuration of DreamFields and the implicit architecture variant of PureCLIPN-erF owing to its superior performance.", + "bbox": [ + 75, + 601, + 468, + 722 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Time cost. Thanks to the shape prior initialization, our CLIP-guided optimization process exhibits significantly improved efficiency compared to previous NeRF-based methods. Dream3D optimizes for only 5000 steps within 25 minutes, while DreamFields and PureCLIPNeRF require more than 10000 steps, taking over an hour (measured on 1 A100 GPU). Training the 3D shape generator $G_{S}$ takes 7 days on 4 A100 GPUs and training the shape embedding generation network $G_{M}$ takes 1 day on 1 A100 GPU. It is worth noting that these models are only trained once and their inference", + "bbox": [ + 75, + 723, + 468, + 875 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a5943730caa4e1f0d957ba4fe953225ef3fa2671eab2c8ff5a0e696a0fd9bbe3.jpg", + "image_caption": [ + "Figure 5. Text-guided 3D shape generation results. All the visualized meshes are extracted at the resolution of $64^{3}$ . We can observe that our method can generate significantly more plausible 3D shapes benefitting from the high-quality 3D shape generator." + ], + "image_footnote": [], + "bbox": [ + 506, + 88, + 890, + 318 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/6f5e614799fd13df9d0a4ba595ae7b782e7c2ab4ae49f1bee659947cfcb67fc1.jpg", + "table_caption": [ + "Table 1. Quantitative comparison on Text-guided 3D synthesis. All methods employ CLIP ViT/16 as the guiding model for optimization, while two distinct CLIP models are utilized to compute the CLIP retrieval precision." + ], + "table_footnote": [], + "table_body": "
MethodFID ↓
CLIP-Forge [51]112.38
Ours w/o text-to-image58.36
Ours w/o fine-tuning SD61.88
Ours40.83
", + "bbox": [ + 591, + 388, + 797, + 460 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Quantitative comparison on text-to-shape generation and ablation studies on the efficacy of fine-tuning Stable Diffusion.", + "bbox": [ + 498, + 465, + 890, + 494 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "time can be neglected compared to the optimization cost.", + "bbox": [ + 498, + 507, + 874, + 522 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Quantitative Results. We report the CLIP retrieval precision metrics in Tab. 1. It is noteworthy that both the baseline methods and our approach utilize the CLIP ViT-B/16 encoder for optimization, and both the CLIP ViT-B/16 and CLIP ViT-B/32 encoders are employed as retrieval models. As Table Tab. 1 shows, our method achieves the highest CLIP R-Precision with both retrieval models. Moreover, our framework exhibits a significantly smaller performance gap between the two retrieval models compared to the baseline methods. By leveraging the 3D shape prior, our method initiates the optimization from a superior starting point, thereby mitigating the adversarial generation problem that prioritizes obtaining high CLIP scores while neglecting the visual quality. Consequently, our method demonstrates more robust performance across different CLIP models.", + "bbox": [ + 496, + 523, + 890, + 748 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Qualitative Results. The qualitative comparison is presented in Fig. 4, indicating that the baseline methods [19, 22, 24] encounter challenges in generating precise and realistic 3D objects, resulting in distorted and unrealistic visuals. DreamFields' results are frequently blurry and diffuse, while PureCLIPNeRF tends to synthesize symmetric objects. CLIP-Mesh experiences difficulties in generating intricate visual effects due to its explicit mesh representation. In contrast, our method effectively generates higher-quality 3D structures by incorporating explicit 3D shape priors.", + "bbox": [ + 496, + 750, + 890, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_footnote", + "text": "https://github.com/lucidrains/DALLE2-pytorch", + "bbox": [ + 93, + 886, + 450, + 898 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "20914", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Text-to-Shape Generation", + "text_level": 1, + "bbox": [ + 76, + 90, + 312, + 107 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The research on zero-shot text-to-shape generation is limited, and we compare our approach with CLIP-Forge [51] and measure the quality of shape generation using the Fréchet Inception Distance (FID). Specifically, we synthesize 3 shapes for each prompt from a dataset of 233 text prompts provided by CLIP-Forge. Then, we render 5 images for each synthesized shape and compare them to a set of ground truth ShapeNet renderings to compute the FID. The ground truth images are obtained by randomly choosing 200 shapes from the test set of each ShapeNet category and rendering 5 views for each shape.", + "bbox": [ + 75, + 113, + 468, + 280 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "As shown in Tab. 2, our approach achieves a lower FID than CLIP-Forge. CLIP-Forge employs a volumetric shape auto-encoder to generate 3D shapes. However, the qualitative results in Fig. 5 indicate poor shape generation capability, making it difficult to generate plausible 3D shapes. A high-quality 3D shape prior is also advantageous for the optimization process as an excellent initialization.", + "bbox": [ + 75, + 279, + 468, + 386 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Ablation Studies", + "text_level": 1, + "bbox": [ + 76, + 393, + 241, + 409 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effectiveness of Fine-tuning Stable Diffusion. Our approach employs a fine-tuned Stable Diffusion to establish a connection between the text and image modalities. To evaluate its efficacy, we employ the original Stable Diffusion model to produce images from the text prompts of CLIP-Forge [51]. Subsequently, we employ these images to generate 3D shapes using the image-to-shape module. The results in the $3^{\\mathrm{rd}}$ row of Tab. 2 indicate a decline in FID performance, suggesting that this approach would negatively impact the shape generation process. Furthermore, we directly test using text embedding to generate shape embeddings with $G_{M}$ , which also leads to a decline in performance as seen in the $2^{\\mathrm{nd}}$ row of Tab. 2.", + "bbox": [ + 75, + 417, + 468, + 613 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effectiveness of 3D Shape Prior. To validate the efficacy of the 3D shape prior, we eliminate the first stage of our framework and optimize from scratch using the same text prompts as presented in Sec. 4.1. Subsequently, we evaluate the CLIP retrieval precision. The outcomes presented in Tab. 1 indicate that optimizing without 3D shape prior results in a considerable decline in performance, thereby demonstrating its effectiveness.", + "bbox": [ + 75, + 613, + 468, + 733 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effectiveness of $\\mathcal{L}_{\\mathrm{prior}}$ . The 3D prior preserving loss $\\mathcal{L}_{\\mathrm{prior}}$ shown in Eq. (3) aims to reinforce the 3D prior during the optimization process in case that the prior is gradually disturbed and discarded. To demonstrate its effectiveness, we synthesized \"a park bench\" as a prior for the prompt \"A park bench overgrown with vines\", and then optimize with and without $\\mathcal{L}_{\\mathrm{prior}}$ and compared the results, which are visualized in Fig. 6. The results indicate that using $\\mathcal{L}_{\\mathrm{prior}}$ during optimization helps maintain the structure of the 3D prior shape, while discarding it causes distortion and discontinuity artifacts, thereby disturbing the initial shape.", + "bbox": [ + 75, + 734, + 468, + 902 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e6c19593b239dc0ba9829ca87158caa7282160a0180f412d18a801588eec06f7.jpg", + "image_caption": [ + "\"A park bench overgrown with vines\"", + "Figure 6. The effect of the 3D prior preserving loss $\\mathcal{L}_{prior}$ ." + ], + "image_footnote": [], + "bbox": [ + 506, + 106, + 883, + 244 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Limitations and Future Work", + "text_level": 1, + "bbox": [ + 498, + 277, + 772, + 292 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Our framework relies on a fine-tuned Stable Diffusion to generate rendering-style images. Despite its strong generation capability, Stable Diffusion may produce shape images that fall outside the distribution of the training data of the image-to-shape module. This is due to the fact that Stable Diffusion is trained on an internet-scale text-image dataset, whereas the 3D shape generator is trained on ShapeNet. Furthermore, the quality of text-to-shape synthesis in our framework is heavily reliant on the generation capability of the 3D generator. Our future work will explore incorporating stronger 3D priors into our framework to enable it to work with a wider range of object categories.", + "bbox": [ + 496, + 303, + 890, + 484 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Additionally, our framework is indeed orthogonal to score distillation-based text-to-3D methods [30, 40, 57], as we can also utilize the score distillation sampling objective for optimization. We believe that incorporating 3D shape priors can enhance the quality and diversity of the generation results, as DreamFusion [40] acknowledged.", + "bbox": [ + 496, + 484, + 890, + 575 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 588, + 617, + 604 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper introduces Dream3D, a text-to-3D synthesis framework that can generate diverse and imaginative 3D content from text prompts. Our approach incorporates explicit 3D shape priors into the CLIP-guided optimization process to generate more plausible 3D structures. To address the text-to-shape generation, we propose a straightforward yet effective method that utilizes a fine-tuned text-to-image diffusion model to bridge the text and image modalities. Our method is shown to generate 3D content with superior visual quality and shape accuracy compared to previous work, as demonstrated by extensive experiments.", + "bbox": [ + 496, + 613, + 890, + 779 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. The work was supported by National Key R&D Program of China (2018AAA0100704), NSFC #61932020, #62172279, Science and Technology Commission of Shanghai Municipality (Grant No. 20ZR1436000), Program of Shanghai Academic Research Leader, and \"Shuguang Program\" supported by Shanghai Education Development Foundation and Shanghai Municipal Education Commission.", + "bbox": [ + 496, + 779, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "20915", + "bbox": [ + 478, + 944, + 517, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Jonathan T. Barron, Ben Mildenhall, Dor Verbin, Pratul P. Srinivasan, and Peter Hedman. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), pages 5826-5835, October 2021. 2" + ], + "bbox": [ + 501, + 92, + 893, + 416 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "20918", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Dream3D_ Zero-Shot Text-to-3D Synthesis Using 3D Shape Prior and Text-to-Image Diffusion Models/5d7485a5-1935-43d5-ba5e-14f7126fbb06_model.json b/2023/Dream3D_ Zero-Shot Text-to-3D Synthesis Using 3D Shape Prior and Text-to-Image Diffusion Models/5d7485a5-1935-43d5-ba5e-14f7126fbb06_model.json new file mode 100644 index 0000000000000000000000000000000000000000..c2ebf352334e57eba468ffab610394fcefd66c66 --- /dev/null +++ b/2023/Dream3D_ Zero-Shot Text-to-3D Synthesis Using 3D Shape Prior and Text-to-Image Diffusion Models/5d7485a5-1935-43d5-ba5e-14f7126fbb06_model.json @@ -0,0 +1,2246 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.137, + 0.13, + 0.834, + 0.176 + ], + "angle": 0, + "content": "Dream3D: Zero-Shot Text-to-3D Synthesis Using 3D Shape Prior and Text-to-Image Diffusion Models" + }, + { + "type": "text", + "bbox": [ + 0.235, + 0.203, + 0.734, + 0.222 + ], + "angle": 0, + "content": "Jiale \\(\\mathbf{X}\\mathbf{u}^{1,3*}\\) Xintao Wang\\(^{1\\dagger}\\) Weihao Cheng\\(^{1}\\) Yan-Pei Cao\\(^{1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.295, + 0.222, + 0.682, + 0.239 + ], + "angle": 0, + "content": "Ying Shan\\(^{1}\\) Xiaohu Qie\\(^{2}\\) Shenghua Gao\\(^{3,4,5\\dagger}\\)" + }, + { + "type": "text", + "bbox": [ + 0.269, + 0.239, + 0.703, + 0.257 + ], + "angle": 0, + "content": "\\(^{1}\\)ARC Lab, \\(^{2}\\)Tencent PCG \\(^{3}\\)ShanghaiTech University" + }, + { + "type": "text", + "bbox": [ + 0.192, + 0.257, + 0.777, + 0.275 + ], + "angle": 0, + "content": "\\(^{4}\\)Shanghai Engineering Research Center of Intelligent Vision and Imaging" + }, + { + "type": "text", + "bbox": [ + 0.176, + 0.275, + 0.796, + 0.293 + ], + "angle": 0, + "content": "5Shanghai Engineering Research Center of Energy Efficient and Custom AI IC" + }, + { + "type": "image", + "bbox": [ + 0.085, + 0.305, + 0.874, + 0.47 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.484, + 0.893, + 0.514 + ], + "angle": 0, + "content": "Figure 1. By utilizing 3D shape priors and powerful text-to-image diffusion models, our Dream3D can generate 3D content that exhibits superior visual quality and shape accuracy in accordance with the text prompt when compared to PureCLIPNeRF [24]." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.528, + 0.314, + 0.544 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.544, + 0.473, + 0.862 + ], + "angle": 0, + "content": "Recent CLIP-guided 3D optimization methods, such as DreamFields [19] and PureCLIPNeRF [24], have achieved impressive results in zero-shot text-to-3D synthesis. However, due to scratch training and random initialization without prior knowledge, these methods often fail to generate accurate and faithful 3D structures that conform to the input text. In this paper, we make the first attempt to introduce explicit 3D shape priors into the CLIP-guided 3D optimization process. Specifically, we first generate a high-quality 3D shape from the input text in the text-to-shape stage as a 3D shape prior. We then use it as the initialization of a neural radiance field and optimize it with the full prompt. To address the challenging text-to-shape generation task, we present a simple yet effective approach that directly bridges the text and image modalities with a powerful text-to-image diffusion model. To narrow the style domain gap between the images synthesized by the text-to-image diffusion model and shape renderings used to train the image-to-shape generator, we further propose to jointly optimize a learnable text prompt and fine-tune the text-to-image diffusion model for rendering-style image generation. Our method," + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.53, + 0.893, + 0.59 + ], + "angle": 0, + "content": "Dream3D, is capable of generating imaginative 3D content with superior visual quality and shape accuracy compared to state-of-the-art methods. Our project page is at https://bluestyle97.github.io/dream3d/." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.619, + 0.633, + 0.635 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.893, + 0.795 + ], + "angle": 0, + "content": "Text-to-3D synthesis endeavors to create 3D content that is coherent with an input text, which has the potential to benefit a wide range of applications such as animations, games, and virtual reality. Recently developed zero-shot text-to-image models [34,44,45,48,50] have made remarkable progress and can generate diverse, high-fidelity, and imaginative images from various text prompts. However, extending this success to the text-to-3D synthesis task is challenging because it is not practically feasible to collect a comprehensive paired text-3D dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Zero-shot text-to-3D synthesis [19, 22, 24, 40, 51], which eliminates the need for paired data, is an attractive approach that typically relies on powerful vision-language models such as CLIP [58]. There are two main categories of this approach. 1) CLIP-based generative models, such as CLIP-Forge [51]. They utilize images as an intermediate bridge and train a mapper from the CLIP image embeddings of" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.875, + 0.416, + 0.888 + ], + "angle": 0, + "content": "*Work done during an internship at ARC Lab, Tencent PCG." + }, + { + "type": "page_footnote", + "bbox": [ + 0.098, + 0.888, + 0.227, + 0.9 + ], + "angle": 0, + "content": "† Corresponding Author." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.875, + 0.416, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20908" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.273 + ], + "angle": 0, + "content": "ShapeNet renderings to the shape embeddings of a 3D shape generator, then switch to the CLIP text embedding as the input at test time. 2) CLIP-guided 3D optimization methods, such as DreamFields [19] and PureCLIPNeRF [24]. They continuously optimize the CLIP similarity loss between a text prompt and rendered images of a 3D scene representation, such as neural radiance fields [1,26,32,41]. While the first category heavily relies on 3D shape generators trained on limited 3D shapes and seldom has the capacity to adjust its shape structures, the second category has more creative freedom with the \"dreaming ability\" to generate diverse shape structures and textures." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.274, + 0.473, + 0.517 + ], + "angle": 0, + "content": "We develop our method building upon CLIP-guided 3D optimization methods. Although these methods can produce remarkable outcomes, they typically fail to create precise and accurate 3D structures that conform to the input text (Fig. 1, \\(2^{\\mathrm{nd}}\\) row). Due to the scratch training and random initialization without any prior knowledge, these methods tend to generate highly-unconstrained \"adversarial contents\" that have high CLIP scores but low visual quality. To address this issue and synthesize more faithful 3D contents, we suggest generating a high-quality 3D shape from the input text first and then using it as an explicit \"3D shape prior\" in the CLIP-guided 3D optimization process. In the text-to-shape* stage, we begin by synthesizing a 3D shape without textures of the main common object in the text prompt. We then use it as the initialization of a voxel-based neural radiance field and optimize it with the full prompt." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.518, + 0.473, + 0.851 + ], + "angle": 0, + "content": "The text-to-shape generation itself is a challenging task. Previous methods [19, 51] are often trained on images and tested with texts, and use CLIP to bridge the two modalities. However, this approach leads to a mismatching problem due to the gap between the CLIP text and image embedding spaces. Additionally, existing methods cannot produce high-quality 3D shapes. In this work, we propose to directly bridge the text and image modalities with a powerful text-to-image diffusion model, i.e., Stable Diffusion [48]. We use the text-to-image diffusion model to synthesize an image from the input text and then feed the image into an image-to-shape generator to produce high-quality 3D shapes. Since we use the same procedure in both training and testing, the mismatching problem is largely reduced. However, there is still a style domain gap between the images synthesized by Stable Diffusion and the shape renderings used to train the image-to-shape generator. Inspired by recent work on controllable text-to-image synthesis [11,49], we propose to jointly optimize a learnable text prompt and fine-tune the Stable Diffusion to address this domain gap. The fine-tuned Stable Diffusion can reliably synthesize images in the style of shape renderings used to train the image" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.874, + 0.107 + ], + "angle": 0, + "content": "to-shape module without suffering from the domain gap." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.108, + 0.895, + 0.395 + ], + "angle": 0, + "content": "To summarize, 1) We make the first attempt to introduce the explicit 3D shape prior into CLIP-guided 3D optimization methods. The proposed method can generate more accurate and high-quality 3D shapes conforming to the corresponding text, while still enjoying the \"dreaming\" ability of generating diverse shape structures and textures (Fig. 1, \\(1^{\\mathrm{st}}\\) row). Therefore, we name our method \"Dream3D\" as it has both strengths. 2) Regarding text-to-shape generation, we present a straightforward yet effective approach that directly connects the text and image modalities using a powerful text-to-image diffusion model. To narrow the style domain gap between the synthesized images and shape renderings, we further propose to jointly optimize a learnable text prompt and fine-tune the text-to-image diffusion model for rendering-style image generation. 3) Our Dream3D can generate imaginative 3D content with better visual quality and shape accuracy than state-of-the-art methods. Additionally, our text-to-shape pipeline can produce 3D shapes of higher quality than previous work." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.408, + 0.642, + 0.423 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.433, + 0.895, + 0.675 + ], + "angle": 0, + "content": "3D Shape Generation. Generative models for 3D shapes have been extensively studied in recent years. It is more challenging than 2D image generation due to the expensive 3D data collection and the complexity of 3D shapes. Various 3D generators employ different shape representations, e.g., voxel grids [3, 25, 56], point clouds [2, 61, 63, 65, 68], meshes [13, 14, 16, 33], and implicit fields [8, 29, 59, 60, 67]. These generators are trained to model the distribution of shape geometry (and optionally, texture) from a collection of 3D shapes. Some methods [4, 5, 12, 36, 38, 39, 53] attempt to learn a 3D generator using only 2D image supervision. These methods incorporate explicit 3D representations, such as meshes [12, 38, 39] and neural radiance fields [4, 5, 36, 53], along with surface or volume-based differentiable rendering techniques [20, 21, 32, 35], to enable the learning of 3D awareness from images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.896, + 0.903 + ], + "angle": 0, + "content": "Text-to-Image. Previous studies in text-to-image synthesis [42, 46, 62, 66] have focused mainly on domain-specific datasets and utilized GANs [15]. However, recent advances in scalable generative architectures and large-scale text-image datasets [52] have enabled unprecedented performance in zero-shot text-to-image synthesis. DALL-E [45] and GLIDE [34], as pioneering works, employ autoregressive model [10] and diffusion model [18, 54] as their architectures, respectively. DALL-E 2 [44] utilizes a diffusion prior network to translate CLIP text embeddings to CLIP image embeddings, and an unCLIP module to synthesize images from CLIP image embeddings. In Imagen [50] and Stable Diffusion [48], a large pre-trained text encoder is employed to guide the sampling process of a diffusion model in pixel space and latent space, respectively." + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.863, + 0.472, + 0.901 + ], + "angle": 0, + "content": "*Throughout this paper, we use the term \"shape\" to refer to 3D geometric models without textures, while some works [7,28] also use this term for textured 3D models." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20909" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.34, + 0.092, + 0.582, + 0.107 + ], + "angle": 0, + "content": "\"A park bench overgrown with vines\"" + }, + { + "type": "image", + "bbox": [ + 0.086, + 0.108, + 0.887, + 0.285 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.292, + 0.896, + 0.378 + ], + "angle": 0, + "content": "Figure 2. Overview of our text-to-3D synthesis framework. (a) In the first text-to-shape stage, a fine-tuned Stable Diffusion \\( G_{I} \\) is employed to synthesize a rendering-style image \\( I_{r} \\) from the input text prompt \\( y \\). This image is then used to generate a latent shape embedding \\( e_{S} \\) with the assistance of a shape embedding generation network \\( G_{M} \\). Finally, the high-quality 3D shape generator \\( G_{S} \\) leverages \\( e_{S} \\) to produce a 3D shape \\( S \\), which is used as an explicit 3D shape prior. (b) In the second optimization stage, the 3D shape prior \\( S \\) is utilized to initialize a neural radiance field, which is further optimized with CLIP guidance to synthesize 3D content that is consistent with the input text prompt \\( y \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.388, + 0.473, + 0.735 + ], + "angle": 0, + "content": "Zero-Shot Text-to-3D. Zero-shot text-to-3D generation techniques [19,22,24,31,40,51] exploit the joint text-image modeling capability of pre-trained vision-language models such as CLIP [43] to obviate the need for paired text-3D data. CLIP-Forge [51] trains a normalizing flow [9, 47] model to convert CLIP image embeddings to VAE [23] shape embeddings, and switches the input to CLIP text embeddings at the inference time. ISS [27] trains a mapper to map the CLIP image embedding into the latent shape code of a pre-trained single-view reconstruction (SVR) network [35], which is then fine-tuned by taking the CLIP text embedding as input. DreamFields [19] and CLIP-Mesh [22] are pioneering works that explore zero-shot 3D content creation using only CLIP guidance. The former optimizes a randomly-initialized NeRF, while the latter optimizes a spherical template mesh as well as random texture and normal maps. PureCLIPNeRF [24] enhances DreamFields with grid-based representation [55] and more diverse image augmentations. Recently, DreamFusion [40] has gained popularity in the research community due to its impressive results. Powered by a strong text-to-image model, ImageGen [50], it can generate high-fidelity 3D objects using the score distillation loss." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.753, + 0.17, + 0.77 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Our objective is to generate 3D content that aligns with the given input text prompt \\( y \\). As illustrated in Fig. 2, our framework for text-guided 3D synthesis comprises two stages. In the first stage (Sec. 3.2), we obtain an explicit 3D shape prior \\( S \\) using a text-guided 3D shape generation process. The text-guided shape generation process involves a text-to-image phase that employs a fine-tuned Stable Diffusion model [48] \\( G_{I} \\) (Sec. 3.3), and an image-to-shape phase" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.388, + 0.895, + 0.51 + ], + "angle": 0, + "content": "that employs a shape embedding generation network \\( G_{M} \\) and a high-quality 3D shape generator \\( G_{S} \\). In the second stage (Sec. 3.1), we utilize the 3D prior \\( S \\) to initialize a neural radiance field [32], and optimize it with CLIP [43] guidance to generate the 3D content. Our framework only requires a collection of textureless 3D shapes without any text labels to train the 3D generator \\( G_{S} \\), and the fine-tuning process of \\( G_{I} \\) converges rapidly." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.518, + 0.895, + 0.551 + ], + "angle": 0, + "content": "3.1. CLIP-Guided 3D Optimization with explicit 3D Shape Prior" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.558, + 0.892, + 0.678 + ], + "angle": 0, + "content": "Background: 3D Optimization with CLIP Guidance. CLIP [43] is a powerful vision-language model that comprises a text encoder \\( E_{T} \\), and an image encoder \\( E_{I} \\). By maximizing the cosine similarity between the text embedding and the image embedding encoded by \\( E_{T} \\) and \\( E_{I} \\) respectively on a large-scale paired text-image dataset, CLIP aligns the text and image modalities in a shared latent embedding space." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.679, + 0.895, + 0.77 + ], + "angle": 0, + "content": "Prior research [19, 22, 24] leverages the capability of CLIP [43] to generate 3D contents from text. Starting from a randomly-initialized 3D representation parameterized by \\(\\theta\\), they render images from multiple viewpoints and optimize \\(\\theta\\) by minimizing the CLIP similarity loss between the rendered image \\(\\mathcal{R}(\\boldsymbol{v}_i; \\theta)\\) and the text prompt \\(y\\):" + }, + { + "type": "equation", + "bbox": [ + 0.584, + 0.78, + 0.892, + 0.8 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {C L I P}} = - E _ {I} \\left(\\mathcal {R} \\left(\\theta ; \\boldsymbol {v} _ {i}\\right)\\right) ^ {T} E _ {T} (y), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.895, + 0.903 + ], + "angle": 0, + "content": "where \\(\\mathcal{R}\\) denotes the rendering process, and \\(\\pmb{v}_i\\) denotes the rendering viewpoint at the \\(i\\)-th optimization step. Specifically, DreamFields [19] and PureCLIPNeRF [24] employ neural radiance fields [32] (NeRF) as the 3D representation \\(\\theta\\), while CLIP-Mesh [22] uses a spherical template mesh with associated texture and normal maps." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20910" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.227 + ], + "angle": 0, + "content": "Observations and Motivations. Though these CLIP-guided optimization methods can generate impressive results, we observe that they often fall short in producing precise and detailed 3D structures that accurately match the text description. As depicted in Fig. 1, we employ these methods to create 3D content featuring common objects, but the outcomes exhibited distortion artifacts and appeared unusual, adversely affecting their visual quality and hindering their use in real-world applications." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.228, + 0.471, + 0.378 + ], + "angle": 0, + "content": "We attribute the failure of previous works to generate accurate and realistic objects to two main factors: (i) The optimization process begins with a randomly-initialized 3D representation lacking any explicit 3D shape prior, making it very challenging for the models to conjure up the scene from scratch. (ii) The CLIP loss in Eq. (1) prioritizes global consistency between the rendered image and the text prompt, rather than offering robust and precise guidance on the synthesized 3D structure. As a result, the optimization output is significantly unconstrained." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.379, + 0.47, + 0.544 + ], + "angle": 0, + "content": "Optimization with 3D Shape Prior as Initialization. To address the aforementioned issue and generate more faithful 3D content, we propose to use a text-to-shape generation process to create a high-quality 3D shape \\( S \\) from the input text prompt \\( y \\). Subsequently, we use it as an explicit \"3D shape prior\" to initialize the CLIP-guided 3D optimization process. As illustrated in Fig. 2, for the text prompt \"a park bench overgrown with vines\", we first synthesize \"a park bench\" without textures in the text-to-shape stage. We then use it as the initialization of a neural radiance field and optimize it with the full prompt, following previous works." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.545, + 0.471, + 0.651 + ], + "angle": 0, + "content": "Our optimization process utilizes DVGO [55], an efficient NeRF variant that represents NeRF using a density voxel grid \\(V_{\\mathrm{density}} \\in \\mathbb{R}^{N_x \\times N_y \\times N_z}\\) and a shallow color MLP \\(f_{\\mathrm{rgb}}\\). We start by taking a 3D shape \\(S\\) generated by the text-to-shape process, represented as an SDF grid \\(\\tilde{V}_{\\mathrm{sdf}} \\in \\mathbb{R}^{N_x \\times N_y \\times N_z}\\), and transform it into the density voxel grid \\(V_{\\mathrm{density}}\\) using the following equations [37,55,64]:" + }, + { + "type": "equation", + "bbox": [ + 0.192, + 0.661, + 0.469, + 0.702 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\Sigma} = \\frac {1}{\\beta} \\text {s i g m o i d} \\left(- \\frac {\\tilde {\\boldsymbol {V}} _ {\\mathrm {s d f}}}{\\beta}\\right), \\tag {2a}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.158, + 0.704, + 0.469, + 0.723 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {V} _ {\\text {d e n s i t y}} = \\max (0, \\text {s o f t p l u s} ^ {- 1} (\\boldsymbol {\\Sigma})) \\tag {2b}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.734, + 0.469, + 0.87 + ], + "angle": 0, + "content": "Here, \\( \\operatorname{sigmoid}(x) = 1 / (1 + e^{-x}) \\) and \\( \\operatorname{softplus}^{-1}(x) = \\log(e^x - 1) \\). Eq. (2a) converts SDF values to density for volume rendering, where \\( \\beta > 0 \\) is a hyper-parameter controlling the sharpness of the shape boundary (smaller \\( \\beta \\) leads to sharper shape boundary, \\( \\beta = 0.05 \\) in our experiments). Eq. (2b) transforms the density into pre-activated density. To ensure that the distribution of the accumulated transmittance is the same as DVGO, we clamp the minimum value of the density outside the shape prior as 0." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.902 + ], + "angle": 0, + "content": "With the density grid \\(V_{\\mathrm{density}}\\) initialized by the 3D shape \\(S\\) and the color MLP \\(f_{\\mathrm{rgb}}\\) initialized randomly, we render" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.243 + ], + "angle": 0, + "content": "image \\(\\mathcal{R}(\\boldsymbol{V}_{\\mathrm{density}}, f_{\\mathrm{rgb}}; \\boldsymbol{v}_i)\\) from viewpoint \\(\\boldsymbol{v}_i\\) and optimize \\(\\theta = (V_{\\mathrm{density}}, f_{\\mathrm{rgb}})\\) with the CLIP loss in Eq. (1). Following DreamFields [19] and PureCLIPNeRF [24], we perform background augmentations for the rendered images and leverage the transmittance loss introduced by [19] to reduce noise and spurious density. Besides, since CLIP loss cannot provide accurate geometrical supervision, the 3D shape prior may be gradually disturbed and \"forgotten\", thus we also adopt a shape-prior-preserving loss to preserve the global structure of the 3D shape prior:" + }, + { + "type": "equation", + "bbox": [ + 0.526, + 0.252, + 0.892, + 0.287 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {p r i o r}} = - \\sum_ {(x, y, z)} \\mathbb {1} (\\tilde {\\boldsymbol {V}} _ {\\mathrm {s d f}} < 0) \\cdot \\operatorname {a l p h a} (\\boldsymbol {V} _ {\\text {d e n s i t y}}), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.295, + 0.892, + 0.34 + ], + "angle": 0, + "content": "where \\(\\mathbb{1}(\\cdot)\\) is the indicator function, and \\(\\mathrm{alpha}(\\cdot)\\) transforms the density into the opacity representing the probability of termination at each position in volume rendering." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.341, + 0.892, + 0.446 + ], + "angle": 0, + "content": "By initializing NeRF with an explicit 3D shape prior, we give extra knowledge on how the 3D content should look like and prevent the model from imagining from scratch and generating \"adversarial contents\" that have high CLIP scores but low visual quality. Based on the initialization, the CLIP-guided optimization further provides flexibility and is able to synthesize more diverse structures and textures." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.455, + 0.892, + 0.487 + ], + "angle": 0, + "content": "3.2. Stable-Diffusion-Assisted Text-to-Shape Generation as 3D Shape Prior" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.494, + 0.892, + 0.584 + ], + "angle": 0, + "content": "To obtain the 3D shape prior, a text-guided shape generation scheme is required, which is a challenging task due to the lack of paired text-shape datasets. Previous approaches [27, 51] typically first train an image-to-shape model using rendered images, and then bridge the text and image modalities using the CLIP embedding space." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.892, + 0.84 + ], + "angle": 0, + "content": "CLIP-Forge [51] trains a normalizing flow network to map CLIP image embeddings of shape renderings to latent embeddings of a volumetric shape auto-encoder, and at test time, it switches to CLIP text embeddings as input. However, the shape auto-encoder has difficulty in generating high-quality and diverse 3D shapes, and directly feeding CLIP text embeddings to the flow network trained on CLIP image embeddings suffers from the gap between the CLIP text and image embedding spaces. ISS [27] trains a mapper network to map CLIP image embeddings of shape renderings to the latent space of a pre-trained single-view reconstruction (SVR) model, and fine-tunes the mapper at test time by maximizing the CLIP similarity between the text prompt and the images rendered from synthesized shapes. While the test-time fine-tuning alleviates the gap between the CLIP text and image embeddings, it is cumbersome to fine-tune the mapper for each text prompt." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In contrast to the aforementioned methods that connect the text and image modalities in the CLIP embedding space, we use a powerful text-to-image diffusion model to directly bridge the two modalities. Specifically, we first synthesize" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "20911" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.212 + ], + "angle": 0, + "content": "an image from the input text and then feed it into an image-to-shape module to generate a high-quality 3D shape. This pipeline is more concise and naturally eliminates the gap between CLIP text and image embeddings. However, it introduces a new domain gap between the images generated by the text-to-image diffusion model and the shape renderings used to train the image-to-shape module. We will introduce a novel technique to alleviate this gap in Sec. 3.3." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.213, + 0.473, + 0.41 + ], + "angle": 0, + "content": "Text-to-Image Diffusion Model. Diffusion models [18,54] are generative models trained to reverse a diffusion process. The diffusion process begins with a sample from the data distribution, \\( \\pmb{x}_0 \\sim q(\\pmb{x}_0) \\), which is gradually corrupted by Gaussian noise over \\( T \\) timesteps: \\( \\pmb{x}_t = \\sqrt{\\alpha_t} \\pmb{x}_{t-1} + \\sqrt{1 - \\alpha_t} \\pmb{\\epsilon}_{t-1}, t = 1, 2, \\dots, T \\), where \\( \\alpha_t \\) defines the noise level and \\( \\pmb{\\epsilon}_{t-1} \\) denotes the noise added at timestep \\( t-1 \\). To reverse this process, a denoising network \\( \\epsilon_\\theta \\) is trained to estimate the added noise at each timestep. During inference, samples can be generated by iteratively denoising pure Gaussian noise. Text-to-image diffusion models further condition the denoising process on texts. Given a text prompt \\( y \\) and a text encoder \\( c_\\theta \\), the training objective is:" + }, + { + "type": "equation", + "bbox": [ + 0.121, + 0.414, + 0.47, + 0.434 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {d i f f u s i o n}} = \\mathbb {E} _ {\\boldsymbol {x} _ {0}, t, \\boldsymbol {\\epsilon} _ {t}, y} \\| \\boldsymbol {\\epsilon} _ {t} - \\epsilon_ {\\theta} (\\boldsymbol {x} _ {t}, t, c _ {\\theta} (y)) \\| _ {2} ^ {2} \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.439, + 0.47, + 0.53 + ], + "angle": 0, + "content": "In this work, we use Stable Diffusion\\(^{\\dagger}\\) [48], an open-source text-to-image diffusion model, which employs a CLIP ViT-L/14 text encoder as \\( c_{\\theta} \\) and is trained on the large-scale LAION-5B dataset [52]. Stable Diffusion is known for its ability to generate diverse and imaginative images in various styles from heterogeneous text prompts." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.53, + 0.473, + 0.756 + ], + "angle": 0, + "content": "High-quality 3D generator. To provide a more precise initialization for optimization, high-quality 3D shapes are highly desirable. In this work, we utilize the SDF-StyleGAN [67], a state-of-the-art 3D generative model, to generate high-quality 3D priors. SDF-StyleGAN is a StyleGAN2-like architecture that maps a random noise \\( z \\sim \\mathcal{N}(0, I) \\) to a latent shape embedding \\( e_S \\in \\mathcal{W} \\) and synthesizes a 3D feature volume \\( F_V \\), which is an implicit shape representation. We can query the SDF value at arbitrary position \\( x \\) by feeding the interpolated feature from \\( F_V \\) at \\( x \\) into a jointly trained MLP. We improve upon the original SDF-StyleGAN, which trains one network for each shape category, by training a single 3D shape generator \\( G_S \\) on the 13 categories of ShapeNet [6]. This modification provides greater flexibility in the text-to-shape process." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.757, + 0.473, + 0.882 + ], + "angle": 0, + "content": "Shape Embedding Mapping Network. To bridge the image and shape modalities, we further train a shape embedding mapping network \\( G_{M} \\). Firstly, we utilize \\( G_{S} \\) to generate a large set of 3D shapes \\( \\{S^i\\}_{i=1}^N \\) and shape embeddings \\( \\{e_S^i\\}_{i=1}^N \\). Then, we render \\( S^i \\) from \\( K \\) viewpoints to obtain shape renderings \\( \\{I_r^j\\}_{j=1}^{NK} \\) and the corresponding image embeddings \\( \\{e_I^j\\}_{j=1}^{NK} \\) with the CLIP image encoder \\( E_I \\), forming a paired image-shape embedding dataset" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.089, + 0.691, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.718, + 0.09, + 0.891, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.222, + 0.895, + 0.362 + ], + "angle": 0, + "content": "Figure 3. Fine-tuning Stable Diffusion into a stylized generator. (a) We fine-tune the text embedding \\(\\mathbf{v}_{*}\\) of a placeholder token \\(*\\) and the weights of Stable Diffusion using a dataset \\(D_{S}\\) that contains ShapeNet renderings and text descriptions in the format of \"a CLS in the style of *\". Additionally, we use another dataset \\(D_{reg}\\), which contains images synthesized by the original Stable Diffusion with text prompts in the format of \"a CLS\", for regularization purposes. (b) With the fine-tuned Stable Diffusion, we can synthesize images that match the style of ShapeNet renderings by appending the postfix \"in the style of *\" to the text prompt." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.374, + 0.892, + 0.422 + ], + "angle": 0, + "content": "\\(\\{(e_I^j,e_S^j)\\}_{j = 1}^{NK}\\). Finally, we use this dataset to train a conditional diffusion model \\(G_{M}\\) which can synthesize shape embeddings from image embeddings of shape renderings." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.422, + 0.892, + 0.513 + ], + "angle": 0, + "content": "To prepare the dataset for training \\( G_{M} \\), we generate \\( N = 64000 \\) shapes using \\( G_{S} \\) and render \\( K = 24 \\) views for each shape. The ranges of azimuth and elevation angles of the rendered views are \\( [-90^{\\circ}, 90^{\\circ}] \\) and \\( [20^{\\circ}, 30^{\\circ}] \\), respectively. We employ an SDF renderer [20] since we represent the synthesized shapes with SDF grids." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.526, + 0.892, + 0.558 + ], + "angle": 0, + "content": "3.3. Fine-tuning Stable Diffusion for Rendering-Style Image Generation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.566, + 0.892, + 0.717 + ], + "angle": 0, + "content": "As stated in Sec. 3.2, we use Stable Diffusion to directly bridge the text and image modalities for text-to-shape generation. Nonetheless, the image-to-shape module is trained on shape renderings, which exhibit a significant style domain gap from the images produced by Stable Diffusion. Previous research [27, 51] has attempted to combine a text-to-image model with an image-to-shape model for text-to-shape generation. However, this approach is plagued by the aforementioned style domain gap, leading to flawed geometric structures and diminished performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.719, + 0.892, + 0.87 + ], + "angle": 0, + "content": "Inspired by recent work on controllable text-to-image generation such as textual inversion [11] and Dream-Booth [49], we propose a method for addressing the domain gap problem by fine-tuning Stable Diffusion into a stylized generator. Our core idea is to enable Stable Diffusion to replicate the style of shape renderings used to train the image-to-shape module outlined in Sec. 3.2. This allows us to seamlessly input the generated stylized images into the image-to-shape module without being affected by the domain gap." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Fine-tuning Process. The fine-tuning process is illustrated in Fig. 3. To fine-tune Stable Diffusion, we need a dataset" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.444, + 0.9 + ], + "angle": 0, + "content": "\\(\\dagger\\)https://github.com/CompVis/stable-diffusion" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "20912" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.089, + 0.889, + 0.379 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.385, + 0.893, + 0.414 + ], + "angle": 0, + "content": "Figure 4. Qualitative comparison on text-guided 3D synthesis. The 3D shape prior used to initialize the CLIP-guided optimization process for each of our results (the last row) is also visualized below." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.425, + 0.473, + 0.612 + ], + "angle": 0, + "content": "that consists of shape renderings and related stylized text prompts. For each shape \\(S\\) in the ShapeNet dataset, we generate a set of shape renderings \\(\\{I_S^j\\}_{j=1}^{N_S}\\). Subsequently, each rendering \\(I_S^j\\) is linked with a stylized text prompt \\(y_S^j\\) in the format of \"a CLS in the style of *\", where CLS denotes the shape category name and * represents a placeholder token that requires optimization for its text embedding. For instance, if the image is rendered from a chair shape, then the associated text prompt will be \"a chair in the style of *\". The paired dataset \\(D_S = (I_S^j, y_S^j)_{j=1}^{N_S}\\) is then utilized to fine-tune Stable Diffusion by minimizing \\(\\mathcal{L}_{\\text{diffusion}}\\) presented in Eq. (4)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.614, + 0.473, + 0.84 + ], + "angle": 0, + "content": "During fine-tuning, we freeze the CLIP text encoder of Stable Diffusion, and optimize two objectives: (i) the text embedding of the placeholder token *, denoted as \\( v_{*} \\), and (ii) the parameters \\( \\theta \\) of the diffusion model \\( \\epsilon_{\\theta} \\). Optimizing the text embedding \\( v_{*} \\) aims to learn a virtual word that captures the style of the rendered images best, even though it is not present in the vocabulary of the text encoder. Fine-tuning the parameters \\( \\theta \\) of the diffusion model further enhances the ability to capture the style precisely since it is hard to control the synthesis of Stable Diffusion solely on the language level. Our experiments demonstrate stable convergence of the fine-tuning process in approximately 2000 optimization steps, requiring only 40 minutes on a single Tesla A100 GPU. We show some synthesized results using the fine-tuned model in Fig. 3." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.472, + 0.903 + ], + "angle": 0, + "content": "Dataset Scale and Background Augmentation. We have identified two essential techniques empirically that enable the fine-tuned model to synthesize stylized images in a stable manner. Firstly, unlike textual inversion [11] or Dream-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.425, + 0.895, + 0.593 + ], + "angle": 0, + "content": "Booth [49] which utilize only 3-5 images, fine-tuning with a larger set of shape renderings containing thousands of images helps the model capture the style more precisely. Secondly, fine-tuning Stable Diffusion using shape renderings with a pure-white background results in a chaotic and uncontrollable background during inference. However, augmenting the shape renderings with random solid-color backgrounds allows the fine-tuned model to synthesize images with solid-color backgrounds stably, making it easy to remove the background if necessary. Further details can be found in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.604, + 0.634, + 0.621 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.892, + 0.749 + ], + "angle": 0, + "content": "In this section, we evaluate the efficacy of our proposed text-to-3D synthesis framework. Initially, we compare our results with state-of-the-art techniques (Sec. 4.1). Subsequently, we demonstrate the effectiveness of our Stable-Diffusion-assisted approach for text-to-shape generation (Sec. 4.2). Furthermore, we conduct ablation studies to assess the effectiveness of critical components of our framework (Sec. 4.3)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.893, + 0.856 + ], + "angle": 0, + "content": "Dataset. Our framework requires only a set of textured 3D shapes for training the 3D shape generator \\( G_{S} \\). Specifically, we employ 13 categories from ShapeNet [6] and utilize the data preprocessing procedure of Zheng et al. [67] to generate \\( 128^{3} \\) SDF grids from the original meshes. During the fine-tuning of Stable Diffusion, we employ the SDF renderer [20] to produce a shape rendering dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.894, + 0.902 + ], + "angle": 0, + "content": "Implementation details. The 3D generator \\( G_{S} \\) utilizes the SDF-StyleGAN architecture. The diffusion-model-based shape embedding mapping network \\( G_{M} \\) is based on an" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20913" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.113, + 0.089, + 0.435, + 0.184 + ], + "angle": 0, + "content": "
MethodCLIP R-Precision ↑
ViT-B/32ViT-B/16
DreamFields [19]63.2492.65
CLIP-Mesh [22]75.0091.18
PureCLIPNeRF [24]73.5388.24
Ours w/o 3D prior75.4794.34
Ours85.2998.53
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.194, + 0.47, + 0.25 + ], + "angle": 0, + "content": "Table 1. Quantitative comparison on Text-guided 3D synthesis. All methods employ CLIP ViT/16 as the guiding model for optimization, while two distinct CLIP models are utilized to compute the CLIP retrieval precision." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.264, + 0.469, + 0.415 + ], + "angle": 0, + "content": "open-source DALL-E 2 implementation. We train \\( G_{M} \\) by extracting image embeddings from shape renderings using the CLIP ViT-B/32 image encoder. The stylized text-to-image generator \\( G_{I} \\) is fine-tuned from Stable Diffusion v1.4. In the optimization stage, we set the learning rates for the density grid \\( V_{\\mathrm{density}} \\) and color MLP \\( f_{\\mathrm{rgb}} \\) to \\( 5 \\times 10^{-1} \\) and \\( 5 \\times 10^{-3} \\) respectively, and we adopt the CLIP ViT-B/16 encoder as the guidance model. For each text prompt, we optimize for 5000 steps, while previous NeRF-based text-to-3D methods [19, 24] typically require 10000 steps or more." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.416, + 0.47, + 0.568 + ], + "angle": 0, + "content": "Evaluation Metrics. Regarding the primary results of our framework, i.e., text-guided 3D content synthesis, we report the CLIP retrieval precision on a manually created dataset of diverse text prompts and objects. For specifics regarding the dataset, please refer to the supplementary material. This metric quantifies the percentage of generated images that the CLIP encoder associates with the correct text prompt used for generation. We utilize Fréchet Inception Distance (FID) [17] to evaluate the shape generation quality for the initial text-to-shape generation stage." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.579, + 0.314, + 0.595 + ], + "angle": 0, + "content": "4.1. Text-Guided 3D Synthesis" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.602, + 0.469, + 0.723 + ], + "angle": 0, + "content": "We compare our method with three state-of-the-art baseline methods on the task of text-guided 3D synthesis, i.e., DreamFields [19], CLIP-Mesh [22], and PureCLIPN-erF [24]. We conduct tests using the default settings and official implementations for all baseline methods. In particular, we utilize the medium-quality configuration of DreamFields and the implicit architecture variant of PureCLIPN-erF owing to its superior performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.724, + 0.469, + 0.875 + ], + "angle": 0, + "content": "Time cost. Thanks to the shape prior initialization, our CLIP-guided optimization process exhibits significantly improved efficiency compared to previous NeRF-based methods. Dream3D optimizes for only 5000 steps within 25 minutes, while DreamFields and PureCLIPNeRF require more than 10000 steps, taking over an hour (measured on 1 A100 GPU). Training the 3D shape generator \\( G_{S} \\) takes 7 days on 4 A100 GPUs and training the shape embedding generation network \\( G_{M} \\) takes 1 day on 1 A100 GPU. It is worth noting that these models are only trained once and their inference" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.089, + 0.891, + 0.319 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.326, + 0.892, + 0.382 + ], + "angle": 0, + "content": "Figure 5. Text-guided 3D shape generation results. All the visualized meshes are extracted at the resolution of \\(64^{3}\\). We can observe that our method can generate significantly more plausible 3D shapes benefitting from the high-quality 3D shape generator." + }, + { + "type": "table", + "bbox": [ + 0.593, + 0.389, + 0.799, + 0.461 + ], + "angle": 0, + "content": "
MethodFID ↓
CLIP-Forge [51]112.38
Ours w/o text-to-image58.36
Ours w/o fine-tuning SD61.88
Ours40.83
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.467, + 0.892, + 0.495 + ], + "angle": 0, + "content": "Table 2. Quantitative comparison on text-to-shape generation and ablation studies on the efficacy of fine-tuning Stable Diffusion." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.508, + 0.875, + 0.523 + ], + "angle": 0, + "content": "time can be neglected compared to the optimization cost." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.524, + 0.892, + 0.749 + ], + "angle": 0, + "content": "Quantitative Results. We report the CLIP retrieval precision metrics in Tab. 1. It is noteworthy that both the baseline methods and our approach utilize the CLIP ViT-B/16 encoder for optimization, and both the CLIP ViT-B/16 and CLIP ViT-B/32 encoders are employed as retrieval models. As Table Tab. 1 shows, our method achieves the highest CLIP R-Precision with both retrieval models. Moreover, our framework exhibits a significantly smaller performance gap between the two retrieval models compared to the baseline methods. By leveraging the 3D shape prior, our method initiates the optimization from a superior starting point, thereby mitigating the adversarial generation problem that prioritizes obtaining high CLIP scores while neglecting the visual quality. Consequently, our method demonstrates more robust performance across different CLIP models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Qualitative Results. The qualitative comparison is presented in Fig. 4, indicating that the baseline methods [19, 22, 24] encounter challenges in generating precise and realistic 3D objects, resulting in distorted and unrealistic visuals. DreamFields' results are frequently blurry and diffuse, while PureCLIPNeRF tends to synthesize symmetric objects. CLIP-Mesh experiences difficulties in generating intricate visual effects due to its explicit mesh representation. In contrast, our method effectively generates higher-quality 3D structures by incorporating explicit 3D shape priors." + }, + { + "type": "page_footnote", + "bbox": [ + 0.094, + 0.887, + 0.451, + 0.9 + ], + "angle": 0, + "content": "https://github.com/lucidrains/DALLE2-pytorch" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20914" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.077, + 0.091, + 0.313, + 0.108 + ], + "angle": 0, + "content": "4.2. Text-to-Shape Generation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.114, + 0.47, + 0.281 + ], + "angle": 0, + "content": "The research on zero-shot text-to-shape generation is limited, and we compare our approach with CLIP-Forge [51] and measure the quality of shape generation using the Fréchet Inception Distance (FID). Specifically, we synthesize 3 shapes for each prompt from a dataset of 233 text prompts provided by CLIP-Forge. Then, we render 5 images for each synthesized shape and compare them to a set of ground truth ShapeNet renderings to compute the FID. The ground truth images are obtained by randomly choosing 200 shapes from the test set of each ShapeNet category and rendering 5 views for each shape." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.28, + 0.47, + 0.387 + ], + "angle": 0, + "content": "As shown in Tab. 2, our approach achieves a lower FID than CLIP-Forge. CLIP-Forge employs a volumetric shape auto-encoder to generate 3D shapes. However, the qualitative results in Fig. 5 indicate poor shape generation capability, making it difficult to generate plausible 3D shapes. A high-quality 3D shape prior is also advantageous for the optimization process as an excellent initialization." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.395, + 0.243, + 0.41 + ], + "angle": 0, + "content": "4.3. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.418, + 0.47, + 0.614 + ], + "angle": 0, + "content": "Effectiveness of Fine-tuning Stable Diffusion. Our approach employs a fine-tuned Stable Diffusion to establish a connection between the text and image modalities. To evaluate its efficacy, we employ the original Stable Diffusion model to produce images from the text prompts of CLIP-Forge [51]. Subsequently, we employ these images to generate 3D shapes using the image-to-shape module. The results in the \\(3^{\\mathrm{rd}}\\) row of Tab. 2 indicate a decline in FID performance, suggesting that this approach would negatively impact the shape generation process. Furthermore, we directly test using text embedding to generate shape embeddings with \\(G_{M}\\), which also leads to a decline in performance as seen in the \\(2^{\\mathrm{nd}}\\) row of Tab. 2." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.614, + 0.47, + 0.734 + ], + "angle": 0, + "content": "Effectiveness of 3D Shape Prior. To validate the efficacy of the 3D shape prior, we eliminate the first stage of our framework and optimize from scratch using the same text prompts as presented in Sec. 4.1. Subsequently, we evaluate the CLIP retrieval precision. The outcomes presented in Tab. 1 indicate that optimizing without 3D shape prior results in a considerable decline in performance, thereby demonstrating its effectiveness." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Effectiveness of \\(\\mathcal{L}_{\\mathrm{prior}}\\). The 3D prior preserving loss \\(\\mathcal{L}_{\\mathrm{prior}}\\) shown in Eq. (3) aims to reinforce the 3D prior during the optimization process in case that the prior is gradually disturbed and discarded. To demonstrate its effectiveness, we synthesized \"a park bench\" as a prior for the prompt \"A park bench overgrown with vines\", and then optimize with and without \\(\\mathcal{L}_{\\mathrm{prior}}\\) and compared the results, which are visualized in Fig. 6. The results indicate that using \\(\\mathcal{L}_{\\mathrm{prior}}\\) during optimization helps maintain the structure of the 3D prior shape, while discarding it causes distortion and discontinuity artifacts, thereby disturbing the initial shape." + }, + { + "type": "image_caption", + "bbox": [ + 0.658, + 0.093, + 0.85, + 0.105 + ], + "angle": 0, + "content": "\"A park bench overgrown with vines\"" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.107, + 0.885, + 0.245 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.518, + 0.253, + 0.872, + 0.268 + ], + "angle": 0, + "content": "Figure 6. The effect of the 3D prior preserving loss \\(\\mathcal{L}_{prior}\\)." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.278, + 0.774, + 0.294 + ], + "angle": 0, + "content": "5. Limitations and Future Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.304, + 0.892, + 0.485 + ], + "angle": 0, + "content": "Our framework relies on a fine-tuned Stable Diffusion to generate rendering-style images. Despite its strong generation capability, Stable Diffusion may produce shape images that fall outside the distribution of the training data of the image-to-shape module. This is due to the fact that Stable Diffusion is trained on an internet-scale text-image dataset, whereas the 3D shape generator is trained on ShapeNet. Furthermore, the quality of text-to-shape synthesis in our framework is heavily reliant on the generation capability of the 3D generator. Our future work will explore incorporating stronger 3D priors into our framework to enable it to work with a wider range of object categories." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.485, + 0.892, + 0.576 + ], + "angle": 0, + "content": "Additionally, our framework is indeed orthogonal to score distillation-based text-to-3D methods [30, 40, 57], as we can also utilize the score distillation sampling objective for optimization. We believe that incorporating 3D shape priors can enhance the quality and diversity of the generation results, as DreamFusion [40] acknowledged." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.589, + 0.619, + 0.605 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.892, + 0.78 + ], + "angle": 0, + "content": "This paper introduces Dream3D, a text-to-3D synthesis framework that can generate diverse and imaginative 3D content from text prompts. Our approach incorporates explicit 3D shape priors into the CLIP-guided optimization process to generate more plausible 3D structures. To address the text-to-shape generation, we propose a straightforward yet effective method that utilizes a fine-tuned text-to-image diffusion model to bridge the text and image modalities. Our method is shown to generate 3D content with superior visual quality and shape accuracy compared to previous work, as demonstrated by extensive experiments." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Acknowledgements. The work was supported by National Key R&D Program of China (2018AAA0100704), NSFC #61932020, #62172279, Science and Technology Commission of Shanghai Municipality (Grant No. 20ZR1436000), Program of Shanghai Academic Research Leader, and \"Shuguang Program\" supported by Shanghai Education Development Foundation and Shanghai Municipal Education Commission." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.958 + ], + "angle": 0, + "content": "20915" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.184 + ], + "angle": 0, + "content": "[1] Jonathan T. Barron, Ben Mildenhall, Dor Verbin, Pratul P. Srinivasan, and Peter Hedman. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), pages 5826-5835, October 2021. 2" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.894, + 0.417 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "20918" + } + ] +] \ No newline at end of file diff --git a/2023/Dream3D_ Zero-Shot Text-to-3D Synthesis Using 3D Shape Prior and Text-to-Image Diffusion Models/5d7485a5-1935-43d5-ba5e-14f7126fbb06_origin.pdf b/2023/Dream3D_ Zero-Shot Text-to-3D Synthesis Using 3D Shape Prior and Text-to-Image Diffusion Models/5d7485a5-1935-43d5-ba5e-14f7126fbb06_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..b05f229c8aaadc8a856ef302414851d99cbd32fc --- /dev/null +++ b/2023/Dream3D_ Zero-Shot Text-to-3D Synthesis Using 3D Shape Prior and Text-to-Image Diffusion Models/5d7485a5-1935-43d5-ba5e-14f7126fbb06_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:908b3be2a45ff038d915aeecb2d13e0b245e074fa12193adf2d1d8edd3b35e06 +size 3698289 diff --git a/2023/Dream3D_ Zero-Shot Text-to-3D Synthesis Using 3D Shape Prior and Text-to-Image Diffusion Models/full.md b/2023/Dream3D_ Zero-Shot Text-to-3D Synthesis Using 3D Shape Prior and Text-to-Image Diffusion Models/full.md new file mode 100644 index 0000000000000000000000000000000000000000..e98a9a5829aaa9f05aa0454d9b5d4bd8e71a1b28 --- /dev/null +++ b/2023/Dream3D_ Zero-Shot Text-to-3D Synthesis Using 3D Shape Prior and Text-to-Image Diffusion Models/full.md @@ -0,0 +1,289 @@ +# Dream3D: Zero-Shot Text-to-3D Synthesis Using 3D Shape Prior and Text-to-Image Diffusion Models + +Jiale $\mathbf{X}\mathbf{u}^{1,3*}$ Xintao Wang $^{1\dagger}$ Weihao Cheng $^{1}$ Yan-Pei Cao $^{1}$ + +Ying Shan $^{1}$ Xiaohu Qie $^{2}$ Shenghua Gao $^{3,4,5\dagger}$ + +$^{1}$ ARC Lab, $^{2}$ Tencent PCG $^{3}$ ShanghaiTech University + +$^{4}$ Shanghai Engineering Research Center of Intelligent Vision and Imaging + +5Shanghai Engineering Research Center of Energy Efficient and Custom AI IC + +![](images/27b6d39b54de98af975a92b7b93107819d362439da52df667d3939bdd301c62f.jpg) +Figure 1. By utilizing 3D shape priors and powerful text-to-image diffusion models, our Dream3D can generate 3D content that exhibits superior visual quality and shape accuracy in accordance with the text prompt when compared to PureCLIPNeRF [24]. + +# Abstract + +Recent CLIP-guided 3D optimization methods, such as DreamFields [19] and PureCLIPNeRF [24], have achieved impressive results in zero-shot text-to-3D synthesis. However, due to scratch training and random initialization without prior knowledge, these methods often fail to generate accurate and faithful 3D structures that conform to the input text. In this paper, we make the first attempt to introduce explicit 3D shape priors into the CLIP-guided 3D optimization process. Specifically, we first generate a high-quality 3D shape from the input text in the text-to-shape stage as a 3D shape prior. We then use it as the initialization of a neural radiance field and optimize it with the full prompt. To address the challenging text-to-shape generation task, we present a simple yet effective approach that directly bridges the text and image modalities with a powerful text-to-image diffusion model. To narrow the style domain gap between the images synthesized by the text-to-image diffusion model and shape renderings used to train the image-to-shape generator, we further propose to jointly optimize a learnable text prompt and fine-tune the text-to-image diffusion model for rendering-style image generation. Our method, + +Dream3D, is capable of generating imaginative 3D content with superior visual quality and shape accuracy compared to state-of-the-art methods. Our project page is at https://bluestyle97.github.io/dream3d/. + +# 1. Introduction + +Text-to-3D synthesis endeavors to create 3D content that is coherent with an input text, which has the potential to benefit a wide range of applications such as animations, games, and virtual reality. Recently developed zero-shot text-to-image models [34,44,45,48,50] have made remarkable progress and can generate diverse, high-fidelity, and imaginative images from various text prompts. However, extending this success to the text-to-3D synthesis task is challenging because it is not practically feasible to collect a comprehensive paired text-3D dataset. + +Zero-shot text-to-3D synthesis [19, 22, 24, 40, 51], which eliminates the need for paired data, is an attractive approach that typically relies on powerful vision-language models such as CLIP [58]. There are two main categories of this approach. 1) CLIP-based generative models, such as CLIP-Forge [51]. They utilize images as an intermediate bridge and train a mapper from the CLIP image embeddings of + +ShapeNet renderings to the shape embeddings of a 3D shape generator, then switch to the CLIP text embedding as the input at test time. 2) CLIP-guided 3D optimization methods, such as DreamFields [19] and PureCLIPNeRF [24]. They continuously optimize the CLIP similarity loss between a text prompt and rendered images of a 3D scene representation, such as neural radiance fields [1,26,32,41]. While the first category heavily relies on 3D shape generators trained on limited 3D shapes and seldom has the capacity to adjust its shape structures, the second category has more creative freedom with the "dreaming ability" to generate diverse shape structures and textures. + +We develop our method building upon CLIP-guided 3D optimization methods. Although these methods can produce remarkable outcomes, they typically fail to create precise and accurate 3D structures that conform to the input text (Fig. 1, $2^{\mathrm{nd}}$ row). Due to the scratch training and random initialization without any prior knowledge, these methods tend to generate highly-unconstrained "adversarial contents" that have high CLIP scores but low visual quality. To address this issue and synthesize more faithful 3D contents, we suggest generating a high-quality 3D shape from the input text first and then using it as an explicit "3D shape prior" in the CLIP-guided 3D optimization process. In the text-to-shape* stage, we begin by synthesizing a 3D shape without textures of the main common object in the text prompt. We then use it as the initialization of a voxel-based neural radiance field and optimize it with the full prompt. + +The text-to-shape generation itself is a challenging task. Previous methods [19, 51] are often trained on images and tested with texts, and use CLIP to bridge the two modalities. However, this approach leads to a mismatching problem due to the gap between the CLIP text and image embedding spaces. Additionally, existing methods cannot produce high-quality 3D shapes. In this work, we propose to directly bridge the text and image modalities with a powerful text-to-image diffusion model, i.e., Stable Diffusion [48]. We use the text-to-image diffusion model to synthesize an image from the input text and then feed the image into an image-to-shape generator to produce high-quality 3D shapes. Since we use the same procedure in both training and testing, the mismatching problem is largely reduced. However, there is still a style domain gap between the images synthesized by Stable Diffusion and the shape renderings used to train the image-to-shape generator. Inspired by recent work on controllable text-to-image synthesis [11,49], we propose to jointly optimize a learnable text prompt and fine-tune the Stable Diffusion to address this domain gap. The fine-tuned Stable Diffusion can reliably synthesize images in the style of shape renderings used to train the image + +to-shape module without suffering from the domain gap. + +To summarize, 1) We make the first attempt to introduce the explicit 3D shape prior into CLIP-guided 3D optimization methods. The proposed method can generate more accurate and high-quality 3D shapes conforming to the corresponding text, while still enjoying the "dreaming" ability of generating diverse shape structures and textures (Fig. 1, $1^{\mathrm{st}}$ row). Therefore, we name our method "Dream3D" as it has both strengths. 2) Regarding text-to-shape generation, we present a straightforward yet effective approach that directly connects the text and image modalities using a powerful text-to-image diffusion model. To narrow the style domain gap between the synthesized images and shape renderings, we further propose to jointly optimize a learnable text prompt and fine-tune the text-to-image diffusion model for rendering-style image generation. 3) Our Dream3D can generate imaginative 3D content with better visual quality and shape accuracy than state-of-the-art methods. Additionally, our text-to-shape pipeline can produce 3D shapes of higher quality than previous work. + +# 2. Related Work + +3D Shape Generation. Generative models for 3D shapes have been extensively studied in recent years. It is more challenging than 2D image generation due to the expensive 3D data collection and the complexity of 3D shapes. Various 3D generators employ different shape representations, e.g., voxel grids [3, 25, 56], point clouds [2, 61, 63, 65, 68], meshes [13, 14, 16, 33], and implicit fields [8, 29, 59, 60, 67]. These generators are trained to model the distribution of shape geometry (and optionally, texture) from a collection of 3D shapes. Some methods [4, 5, 12, 36, 38, 39, 53] attempt to learn a 3D generator using only 2D image supervision. These methods incorporate explicit 3D representations, such as meshes [12, 38, 39] and neural radiance fields [4, 5, 36, 53], along with surface or volume-based differentiable rendering techniques [20, 21, 32, 35], to enable the learning of 3D awareness from images. + +Text-to-Image. Previous studies in text-to-image synthesis [42, 46, 62, 66] have focused mainly on domain-specific datasets and utilized GANs [15]. However, recent advances in scalable generative architectures and large-scale text-image datasets [52] have enabled unprecedented performance in zero-shot text-to-image synthesis. DALL-E [45] and GLIDE [34], as pioneering works, employ autoregressive model [10] and diffusion model [18, 54] as their architectures, respectively. DALL-E 2 [44] utilizes a diffusion prior network to translate CLIP text embeddings to CLIP image embeddings, and an unCLIP module to synthesize images from CLIP image embeddings. In Imagen [50] and Stable Diffusion [48], a large pre-trained text encoder is employed to guide the sampling process of a diffusion model in pixel space and latent space, respectively. + +![](images/524d40fe14bb7a3fa580077ad1d342e62b2c0cafd62fb9a5fdba20036a88726c.jpg) +Figure 2. Overview of our text-to-3D synthesis framework. (a) In the first text-to-shape stage, a fine-tuned Stable Diffusion $G_{I}$ is employed to synthesize a rendering-style image $I_{r}$ from the input text prompt $y$ . This image is then used to generate a latent shape embedding $e_{S}$ with the assistance of a shape embedding generation network $G_{M}$ . Finally, the high-quality 3D shape generator $G_{S}$ leverages $e_{S}$ to produce a 3D shape $S$ , which is used as an explicit 3D shape prior. (b) In the second optimization stage, the 3D shape prior $S$ is utilized to initialize a neural radiance field, which is further optimized with CLIP guidance to synthesize 3D content that is consistent with the input text prompt $y$ . + +Zero-Shot Text-to-3D. Zero-shot text-to-3D generation techniques [19,22,24,31,40,51] exploit the joint text-image modeling capability of pre-trained vision-language models such as CLIP [43] to obviate the need for paired text-3D data. CLIP-Forge [51] trains a normalizing flow [9, 47] model to convert CLIP image embeddings to VAE [23] shape embeddings, and switches the input to CLIP text embeddings at the inference time. ISS [27] trains a mapper to map the CLIP image embedding into the latent shape code of a pre-trained single-view reconstruction (SVR) network [35], which is then fine-tuned by taking the CLIP text embedding as input. DreamFields [19] and CLIP-Mesh [22] are pioneering works that explore zero-shot 3D content creation using only CLIP guidance. The former optimizes a randomly-initialized NeRF, while the latter optimizes a spherical template mesh as well as random texture and normal maps. PureCLIPNeRF [24] enhances DreamFields with grid-based representation [55] and more diverse image augmentations. Recently, DreamFusion [40] has gained popularity in the research community due to its impressive results. Powered by a strong text-to-image model, ImageGen [50], it can generate high-fidelity 3D objects using the score distillation loss. + +# 3. Method + +Our objective is to generate 3D content that aligns with the given input text prompt $y$ . As illustrated in Fig. 2, our framework for text-guided 3D synthesis comprises two stages. In the first stage (Sec. 3.2), we obtain an explicit 3D shape prior $S$ using a text-guided 3D shape generation process. The text-guided shape generation process involves a text-to-image phase that employs a fine-tuned Stable Diffusion model [48] $G_{I}$ (Sec. 3.3), and an image-to-shape phase + +that employs a shape embedding generation network $G_{M}$ and a high-quality 3D shape generator $G_{S}$ . In the second stage (Sec. 3.1), we utilize the 3D prior $S$ to initialize a neural radiance field [32], and optimize it with CLIP [43] guidance to generate the 3D content. Our framework only requires a collection of textureless 3D shapes without any text labels to train the 3D generator $G_{S}$ , and the fine-tuning process of $G_{I}$ converges rapidly. + +# 3.1. CLIP-Guided 3D Optimization with explicit 3D Shape Prior + +Background: 3D Optimization with CLIP Guidance. CLIP [43] is a powerful vision-language model that comprises a text encoder $E_{T}$ , and an image encoder $E_{I}$ . By maximizing the cosine similarity between the text embedding and the image embedding encoded by $E_{T}$ and $E_{I}$ respectively on a large-scale paired text-image dataset, CLIP aligns the text and image modalities in a shared latent embedding space. + +Prior research [19, 22, 24] leverages the capability of CLIP [43] to generate 3D contents from text. Starting from a randomly-initialized 3D representation parameterized by $\theta$ , they render images from multiple viewpoints and optimize $\theta$ by minimizing the CLIP similarity loss between the rendered image $\mathcal{R}(\boldsymbol{v}_i; \theta)$ and the text prompt $y$ : + +$$ +\mathcal {L} _ {\mathrm {C L I P}} = - E _ {I} \left(\mathcal {R} \left(\theta ; \boldsymbol {v} _ {i}\right)\right) ^ {T} E _ {T} (y), \tag {1} +$$ + +where $\mathcal{R}$ denotes the rendering process, and $\pmb{v}_i$ denotes the rendering viewpoint at the $i$ -th optimization step. Specifically, DreamFields [19] and PureCLIPNeRF [24] employ neural radiance fields [32] (NeRF) as the 3D representation $\theta$ , while CLIP-Mesh [22] uses a spherical template mesh with associated texture and normal maps. + +Observations and Motivations. Though these CLIP-guided optimization methods can generate impressive results, we observe that they often fall short in producing precise and detailed 3D structures that accurately match the text description. As depicted in Fig. 1, we employ these methods to create 3D content featuring common objects, but the outcomes exhibited distortion artifacts and appeared unusual, adversely affecting their visual quality and hindering their use in real-world applications. + +We attribute the failure of previous works to generate accurate and realistic objects to two main factors: (i) The optimization process begins with a randomly-initialized 3D representation lacking any explicit 3D shape prior, making it very challenging for the models to conjure up the scene from scratch. (ii) The CLIP loss in Eq. (1) prioritizes global consistency between the rendered image and the text prompt, rather than offering robust and precise guidance on the synthesized 3D structure. As a result, the optimization output is significantly unconstrained. + +Optimization with 3D Shape Prior as Initialization. To address the aforementioned issue and generate more faithful 3D content, we propose to use a text-to-shape generation process to create a high-quality 3D shape $S$ from the input text prompt $y$ . Subsequently, we use it as an explicit "3D shape prior" to initialize the CLIP-guided 3D optimization process. As illustrated in Fig. 2, for the text prompt "a park bench overgrown with vines", we first synthesize "a park bench" without textures in the text-to-shape stage. We then use it as the initialization of a neural radiance field and optimize it with the full prompt, following previous works. + +Our optimization process utilizes DVGO [55], an efficient NeRF variant that represents NeRF using a density voxel grid $V_{\mathrm{density}} \in \mathbb{R}^{N_x \times N_y \times N_z}$ and a shallow color MLP $f_{\mathrm{rgb}}$ . We start by taking a 3D shape $S$ generated by the text-to-shape process, represented as an SDF grid $\tilde{V}_{\mathrm{sdf}} \in \mathbb{R}^{N_x \times N_y \times N_z}$ , and transform it into the density voxel grid $V_{\mathrm{density}}$ using the following equations [37,55,64]: + +$$ +\boldsymbol {\Sigma} = \frac {1}{\beta} \text {s i g m o i d} \left(- \frac {\tilde {\boldsymbol {V}} _ {\mathrm {s d f}}}{\beta}\right), \tag {2a} +$$ + +$$ +\boldsymbol {V} _ {\text {d e n s i t y}} = \max (0, \text {s o f t p l u s} ^ {- 1} (\boldsymbol {\Sigma})) \tag {2b} +$$ + +Here, $\operatorname{sigmoid}(x) = 1 / (1 + e^{-x})$ and $\operatorname{softplus}^{-1}(x) = \log(e^x - 1)$ . Eq. (2a) converts SDF values to density for volume rendering, where $\beta > 0$ is a hyper-parameter controlling the sharpness of the shape boundary (smaller $\beta$ leads to sharper shape boundary, $\beta = 0.05$ in our experiments). Eq. (2b) transforms the density into pre-activated density. To ensure that the distribution of the accumulated transmittance is the same as DVGO, we clamp the minimum value of the density outside the shape prior as 0. + +With the density grid $V_{\mathrm{density}}$ initialized by the 3D shape $S$ and the color MLP $f_{\mathrm{rgb}}$ initialized randomly, we render + +image $\mathcal{R}(\boldsymbol{V}_{\mathrm{density}}, f_{\mathrm{rgb}}; \boldsymbol{v}_i)$ from viewpoint $\boldsymbol{v}_i$ and optimize $\theta = (V_{\mathrm{density}}, f_{\mathrm{rgb}})$ with the CLIP loss in Eq. (1). Following DreamFields [19] and PureCLIPNeRF [24], we perform background augmentations for the rendered images and leverage the transmittance loss introduced by [19] to reduce noise and spurious density. Besides, since CLIP loss cannot provide accurate geometrical supervision, the 3D shape prior may be gradually disturbed and "forgotten", thus we also adopt a shape-prior-preserving loss to preserve the global structure of the 3D shape prior: + +$$ +\mathcal {L} _ {\text {p r i o r}} = - \sum_ {(x, y, z)} \mathbb {1} (\tilde {\boldsymbol {V}} _ {\mathrm {s d f}} < 0) \cdot \operatorname {a l p h a} (\boldsymbol {V} _ {\text {d e n s i t y}}), \tag {3} +$$ + +where $\mathbb{1}(\cdot)$ is the indicator function, and $\mathrm{alpha}(\cdot)$ transforms the density into the opacity representing the probability of termination at each position in volume rendering. + +By initializing NeRF with an explicit 3D shape prior, we give extra knowledge on how the 3D content should look like and prevent the model from imagining from scratch and generating "adversarial contents" that have high CLIP scores but low visual quality. Based on the initialization, the CLIP-guided optimization further provides flexibility and is able to synthesize more diverse structures and textures. + +# 3.2. Stable-Diffusion-Assisted Text-to-Shape Generation as 3D Shape Prior + +To obtain the 3D shape prior, a text-guided shape generation scheme is required, which is a challenging task due to the lack of paired text-shape datasets. Previous approaches [27, 51] typically first train an image-to-shape model using rendered images, and then bridge the text and image modalities using the CLIP embedding space. + +CLIP-Forge [51] trains a normalizing flow network to map CLIP image embeddings of shape renderings to latent embeddings of a volumetric shape auto-encoder, and at test time, it switches to CLIP text embeddings as input. However, the shape auto-encoder has difficulty in generating high-quality and diverse 3D shapes, and directly feeding CLIP text embeddings to the flow network trained on CLIP image embeddings suffers from the gap between the CLIP text and image embedding spaces. ISS [27] trains a mapper network to map CLIP image embeddings of shape renderings to the latent space of a pre-trained single-view reconstruction (SVR) model, and fine-tunes the mapper at test time by maximizing the CLIP similarity between the text prompt and the images rendered from synthesized shapes. While the test-time fine-tuning alleviates the gap between the CLIP text and image embeddings, it is cumbersome to fine-tune the mapper for each text prompt. + +In contrast to the aforementioned methods that connect the text and image modalities in the CLIP embedding space, we use a powerful text-to-image diffusion model to directly bridge the two modalities. Specifically, we first synthesize + +an image from the input text and then feed it into an image-to-shape module to generate a high-quality 3D shape. This pipeline is more concise and naturally eliminates the gap between CLIP text and image embeddings. However, it introduces a new domain gap between the images generated by the text-to-image diffusion model and the shape renderings used to train the image-to-shape module. We will introduce a novel technique to alleviate this gap in Sec. 3.3. + +Text-to-Image Diffusion Model. Diffusion models [18,54] are generative models trained to reverse a diffusion process. The diffusion process begins with a sample from the data distribution, $\pmb{x}_0 \sim q(\pmb{x}_0)$ , which is gradually corrupted by Gaussian noise over $T$ timesteps: $\pmb{x}_t = \sqrt{\alpha_t} \pmb{x}_{t-1} + \sqrt{1 - \alpha_t} \pmb{\epsilon}_{t-1}, t = 1, 2, \dots, T$ , where $\alpha_t$ defines the noise level and $\pmb{\epsilon}_{t-1}$ denotes the noise added at timestep $t-1$ . To reverse this process, a denoising network $\epsilon_\theta$ is trained to estimate the added noise at each timestep. During inference, samples can be generated by iteratively denoising pure Gaussian noise. Text-to-image diffusion models further condition the denoising process on texts. Given a text prompt $y$ and a text encoder $c_\theta$ , the training objective is: + +$$ +\mathcal {L} _ {\text {d i f f u s i o n}} = \mathbb {E} _ {\boldsymbol {x} _ {0}, t, \boldsymbol {\epsilon} _ {t}, y} \| \boldsymbol {\epsilon} _ {t} - \epsilon_ {\theta} (\boldsymbol {x} _ {t}, t, c _ {\theta} (y)) \| _ {2} ^ {2} \tag {4} +$$ + +In this work, we use Stable Diffusion $^{\dagger}$ [48], an open-source text-to-image diffusion model, which employs a CLIP ViT-L/14 text encoder as $c_{\theta}$ and is trained on the large-scale LAION-5B dataset [52]. Stable Diffusion is known for its ability to generate diverse and imaginative images in various styles from heterogeneous text prompts. + +High-quality 3D generator. To provide a more precise initialization for optimization, high-quality 3D shapes are highly desirable. In this work, we utilize the SDF-StyleGAN [67], a state-of-the-art 3D generative model, to generate high-quality 3D priors. SDF-StyleGAN is a StyleGAN2-like architecture that maps a random noise $z \sim \mathcal{N}(0, I)$ to a latent shape embedding $e_S \in \mathcal{W}$ and synthesizes a 3D feature volume $F_V$ , which is an implicit shape representation. We can query the SDF value at arbitrary position $x$ by feeding the interpolated feature from $F_V$ at $x$ into a jointly trained MLP. We improve upon the original SDF-StyleGAN, which trains one network for each shape category, by training a single 3D shape generator $G_S$ on the 13 categories of ShapeNet [6]. This modification provides greater flexibility in the text-to-shape process. + +Shape Embedding Mapping Network. To bridge the image and shape modalities, we further train a shape embedding mapping network $G_{M}$ . Firstly, we utilize $G_{S}$ to generate a large set of 3D shapes $\{S^i\}_{i=1}^N$ and shape embeddings $\{e_S^i\}_{i=1}^N$ . Then, we render $S^i$ from $K$ viewpoints to obtain shape renderings $\{I_r^j\}_{j=1}^{NK}$ and the corresponding image embeddings $\{e_I^j\}_{j=1}^{NK}$ with the CLIP image encoder $E_I$ , forming a paired image-shape embedding dataset + +![](images/b4e0ed76e7fdb1233075066571549772dbbfbeaa1f538d708ac8cb7cfcc13f12.jpg) +Figure 3. Fine-tuning Stable Diffusion into a stylized generator. (a) We fine-tune the text embedding $\mathbf{v}_{*}$ of a placeholder token $*$ and the weights of Stable Diffusion using a dataset $D_{S}$ that contains ShapeNet renderings and text descriptions in the format of "a CLS in the style of *". Additionally, we use another dataset $D_{reg}$ , which contains images synthesized by the original Stable Diffusion with text prompts in the format of "a CLS", for regularization purposes. (b) With the fine-tuned Stable Diffusion, we can synthesize images that match the style of ShapeNet renderings by appending the postfix "in the style of *" to the text prompt. + +![](images/b473cec8fefa12e558e25cb8efd0fc31db8c2f7fdaca5e3a0b37616baeda3173.jpg) + +$\{(e_I^j,e_S^j)\}_{j = 1}^{NK}$ . Finally, we use this dataset to train a conditional diffusion model $G_{M}$ which can synthesize shape embeddings from image embeddings of shape renderings. + +To prepare the dataset for training $G_{M}$ , we generate $N = 64000$ shapes using $G_{S}$ and render $K = 24$ views for each shape. The ranges of azimuth and elevation angles of the rendered views are $[-90^{\circ}, 90^{\circ}]$ and $[20^{\circ}, 30^{\circ}]$ , respectively. We employ an SDF renderer [20] since we represent the synthesized shapes with SDF grids. + +# 3.3. Fine-tuning Stable Diffusion for Rendering-Style Image Generation + +As stated in Sec. 3.2, we use Stable Diffusion to directly bridge the text and image modalities for text-to-shape generation. Nonetheless, the image-to-shape module is trained on shape renderings, which exhibit a significant style domain gap from the images produced by Stable Diffusion. Previous research [27, 51] has attempted to combine a text-to-image model with an image-to-shape model for text-to-shape generation. However, this approach is plagued by the aforementioned style domain gap, leading to flawed geometric structures and diminished performance. + +Inspired by recent work on controllable text-to-image generation such as textual inversion [11] and Dream-Booth [49], we propose a method for addressing the domain gap problem by fine-tuning Stable Diffusion into a stylized generator. Our core idea is to enable Stable Diffusion to replicate the style of shape renderings used to train the image-to-shape module outlined in Sec. 3.2. This allows us to seamlessly input the generated stylized images into the image-to-shape module without being affected by the domain gap. + +Fine-tuning Process. The fine-tuning process is illustrated in Fig. 3. To fine-tune Stable Diffusion, we need a dataset + +![](images/9102a5eabaa95608c6ad339ba28bc1078507425bba8f87134796b39775262e94.jpg) +Figure 4. Qualitative comparison on text-guided 3D synthesis. The 3D shape prior used to initialize the CLIP-guided optimization process for each of our results (the last row) is also visualized below. + +that consists of shape renderings and related stylized text prompts. For each shape $S$ in the ShapeNet dataset, we generate a set of shape renderings $\{I_S^j\}_{j=1}^{N_S}$ . Subsequently, each rendering $I_S^j$ is linked with a stylized text prompt $y_S^j$ in the format of "a CLS in the style of *", where CLS denotes the shape category name and * represents a placeholder token that requires optimization for its text embedding. For instance, if the image is rendered from a chair shape, then the associated text prompt will be "a chair in the style of *". The paired dataset $D_S = (I_S^j, y_S^j)_{j=1}^{N_S}$ is then utilized to fine-tune Stable Diffusion by minimizing $\mathcal{L}_{\text{diffusion}}$ presented in Eq. (4). + +During fine-tuning, we freeze the CLIP text encoder of Stable Diffusion, and optimize two objectives: (i) the text embedding of the placeholder token *, denoted as $v_{*}$ , and (ii) the parameters $\theta$ of the diffusion model $\epsilon_{\theta}$ . Optimizing the text embedding $v_{*}$ aims to learn a virtual word that captures the style of the rendered images best, even though it is not present in the vocabulary of the text encoder. Fine-tuning the parameters $\theta$ of the diffusion model further enhances the ability to capture the style precisely since it is hard to control the synthesis of Stable Diffusion solely on the language level. Our experiments demonstrate stable convergence of the fine-tuning process in approximately 2000 optimization steps, requiring only 40 minutes on a single Tesla A100 GPU. We show some synthesized results using the fine-tuned model in Fig. 3. + +Dataset Scale and Background Augmentation. We have identified two essential techniques empirically that enable the fine-tuned model to synthesize stylized images in a stable manner. Firstly, unlike textual inversion [11] or Dream- + +Booth [49] which utilize only 3-5 images, fine-tuning with a larger set of shape renderings containing thousands of images helps the model capture the style more precisely. Secondly, fine-tuning Stable Diffusion using shape renderings with a pure-white background results in a chaotic and uncontrollable background during inference. However, augmenting the shape renderings with random solid-color backgrounds allows the fine-tuned model to synthesize images with solid-color backgrounds stably, making it easy to remove the background if necessary. Further details can be found in the supplementary material. + +# 4. Experiments + +In this section, we evaluate the efficacy of our proposed text-to-3D synthesis framework. Initially, we compare our results with state-of-the-art techniques (Sec. 4.1). Subsequently, we demonstrate the effectiveness of our Stable-Diffusion-assisted approach for text-to-shape generation (Sec. 4.2). Furthermore, we conduct ablation studies to assess the effectiveness of critical components of our framework (Sec. 4.3). + +Dataset. Our framework requires only a set of textured 3D shapes for training the 3D shape generator $G_{S}$ . Specifically, we employ 13 categories from ShapeNet [6] and utilize the data preprocessing procedure of Zheng et al. [67] to generate $128^{3}$ SDF grids from the original meshes. During the fine-tuning of Stable Diffusion, we employ the SDF renderer [20] to produce a shape rendering dataset. + +Implementation details. The 3D generator $G_{S}$ utilizes the SDF-StyleGAN architecture. The diffusion-model-based shape embedding mapping network $G_{M}$ is based on an + +
MethodCLIP R-Precision ↑
ViT-B/32ViT-B/16
DreamFields [19]63.2492.65
CLIP-Mesh [22]75.0091.18
PureCLIPNeRF [24]73.5388.24
Ours w/o 3D prior75.4794.34
Ours85.2998.53
+ +open-source DALL-E 2 implementation. We train $G_{M}$ by extracting image embeddings from shape renderings using the CLIP ViT-B/32 image encoder. The stylized text-to-image generator $G_{I}$ is fine-tuned from Stable Diffusion v1.4. In the optimization stage, we set the learning rates for the density grid $V_{\mathrm{density}}$ and color MLP $f_{\mathrm{rgb}}$ to $5 \times 10^{-1}$ and $5 \times 10^{-3}$ respectively, and we adopt the CLIP ViT-B/16 encoder as the guidance model. For each text prompt, we optimize for 5000 steps, while previous NeRF-based text-to-3D methods [19, 24] typically require 10000 steps or more. + +Evaluation Metrics. Regarding the primary results of our framework, i.e., text-guided 3D content synthesis, we report the CLIP retrieval precision on a manually created dataset of diverse text prompts and objects. For specifics regarding the dataset, please refer to the supplementary material. This metric quantifies the percentage of generated images that the CLIP encoder associates with the correct text prompt used for generation. We utilize Fréchet Inception Distance (FID) [17] to evaluate the shape generation quality for the initial text-to-shape generation stage. + +# 4.1. Text-Guided 3D Synthesis + +We compare our method with three state-of-the-art baseline methods on the task of text-guided 3D synthesis, i.e., DreamFields [19], CLIP-Mesh [22], and PureCLIPN-erF [24]. We conduct tests using the default settings and official implementations for all baseline methods. In particular, we utilize the medium-quality configuration of DreamFields and the implicit architecture variant of PureCLIPN-erF owing to its superior performance. + +Time cost. Thanks to the shape prior initialization, our CLIP-guided optimization process exhibits significantly improved efficiency compared to previous NeRF-based methods. Dream3D optimizes for only 5000 steps within 25 minutes, while DreamFields and PureCLIPNeRF require more than 10000 steps, taking over an hour (measured on 1 A100 GPU). Training the 3D shape generator $G_{S}$ takes 7 days on 4 A100 GPUs and training the shape embedding generation network $G_{M}$ takes 1 day on 1 A100 GPU. It is worth noting that these models are only trained once and their inference + +![](images/a5943730caa4e1f0d957ba4fe953225ef3fa2671eab2c8ff5a0e696a0fd9bbe3.jpg) +Figure 5. Text-guided 3D shape generation results. All the visualized meshes are extracted at the resolution of $64^{3}$ . We can observe that our method can generate significantly more plausible 3D shapes benefitting from the high-quality 3D shape generator. + +Table 1. Quantitative comparison on Text-guided 3D synthesis. All methods employ CLIP ViT/16 as the guiding model for optimization, while two distinct CLIP models are utilized to compute the CLIP retrieval precision. + +
MethodFID ↓
CLIP-Forge [51]112.38
Ours w/o text-to-image58.36
Ours w/o fine-tuning SD61.88
Ours40.83
+ +Table 2. Quantitative comparison on text-to-shape generation and ablation studies on the efficacy of fine-tuning Stable Diffusion. + +time can be neglected compared to the optimization cost. + +Quantitative Results. We report the CLIP retrieval precision metrics in Tab. 1. It is noteworthy that both the baseline methods and our approach utilize the CLIP ViT-B/16 encoder for optimization, and both the CLIP ViT-B/16 and CLIP ViT-B/32 encoders are employed as retrieval models. As Table Tab. 1 shows, our method achieves the highest CLIP R-Precision with both retrieval models. Moreover, our framework exhibits a significantly smaller performance gap between the two retrieval models compared to the baseline methods. By leveraging the 3D shape prior, our method initiates the optimization from a superior starting point, thereby mitigating the adversarial generation problem that prioritizes obtaining high CLIP scores while neglecting the visual quality. Consequently, our method demonstrates more robust performance across different CLIP models. + +Qualitative Results. The qualitative comparison is presented in Fig. 4, indicating that the baseline methods [19, 22, 24] encounter challenges in generating precise and realistic 3D objects, resulting in distorted and unrealistic visuals. DreamFields' results are frequently blurry and diffuse, while PureCLIPNeRF tends to synthesize symmetric objects. CLIP-Mesh experiences difficulties in generating intricate visual effects due to its explicit mesh representation. In contrast, our method effectively generates higher-quality 3D structures by incorporating explicit 3D shape priors. + +# 4.2. Text-to-Shape Generation + +The research on zero-shot text-to-shape generation is limited, and we compare our approach with CLIP-Forge [51] and measure the quality of shape generation using the Fréchet Inception Distance (FID). Specifically, we synthesize 3 shapes for each prompt from a dataset of 233 text prompts provided by CLIP-Forge. Then, we render 5 images for each synthesized shape and compare them to a set of ground truth ShapeNet renderings to compute the FID. The ground truth images are obtained by randomly choosing 200 shapes from the test set of each ShapeNet category and rendering 5 views for each shape. + +As shown in Tab. 2, our approach achieves a lower FID than CLIP-Forge. CLIP-Forge employs a volumetric shape auto-encoder to generate 3D shapes. However, the qualitative results in Fig. 5 indicate poor shape generation capability, making it difficult to generate plausible 3D shapes. A high-quality 3D shape prior is also advantageous for the optimization process as an excellent initialization. + +# 4.3. Ablation Studies + +Effectiveness of Fine-tuning Stable Diffusion. Our approach employs a fine-tuned Stable Diffusion to establish a connection between the text and image modalities. To evaluate its efficacy, we employ the original Stable Diffusion model to produce images from the text prompts of CLIP-Forge [51]. Subsequently, we employ these images to generate 3D shapes using the image-to-shape module. The results in the $3^{\mathrm{rd}}$ row of Tab. 2 indicate a decline in FID performance, suggesting that this approach would negatively impact the shape generation process. Furthermore, we directly test using text embedding to generate shape embeddings with $G_{M}$ , which also leads to a decline in performance as seen in the $2^{\mathrm{nd}}$ row of Tab. 2. + +Effectiveness of 3D Shape Prior. To validate the efficacy of the 3D shape prior, we eliminate the first stage of our framework and optimize from scratch using the same text prompts as presented in Sec. 4.1. Subsequently, we evaluate the CLIP retrieval precision. The outcomes presented in Tab. 1 indicate that optimizing without 3D shape prior results in a considerable decline in performance, thereby demonstrating its effectiveness. + +Effectiveness of $\mathcal{L}_{\mathrm{prior}}$ . The 3D prior preserving loss $\mathcal{L}_{\mathrm{prior}}$ shown in Eq. (3) aims to reinforce the 3D prior during the optimization process in case that the prior is gradually disturbed and discarded. To demonstrate its effectiveness, we synthesized "a park bench" as a prior for the prompt "A park bench overgrown with vines", and then optimize with and without $\mathcal{L}_{\mathrm{prior}}$ and compared the results, which are visualized in Fig. 6. The results indicate that using $\mathcal{L}_{\mathrm{prior}}$ during optimization helps maintain the structure of the 3D prior shape, while discarding it causes distortion and discontinuity artifacts, thereby disturbing the initial shape. + +![](images/e6c19593b239dc0ba9829ca87158caa7282160a0180f412d18a801588eec06f7.jpg) +"A park bench overgrown with vines" +Figure 6. The effect of the 3D prior preserving loss $\mathcal{L}_{prior}$ . + +# 5. Limitations and Future Work + +Our framework relies on a fine-tuned Stable Diffusion to generate rendering-style images. Despite its strong generation capability, Stable Diffusion may produce shape images that fall outside the distribution of the training data of the image-to-shape module. This is due to the fact that Stable Diffusion is trained on an internet-scale text-image dataset, whereas the 3D shape generator is trained on ShapeNet. Furthermore, the quality of text-to-shape synthesis in our framework is heavily reliant on the generation capability of the 3D generator. Our future work will explore incorporating stronger 3D priors into our framework to enable it to work with a wider range of object categories. + +Additionally, our framework is indeed orthogonal to score distillation-based text-to-3D methods [30, 40, 57], as we can also utilize the score distillation sampling objective for optimization. We believe that incorporating 3D shape priors can enhance the quality and diversity of the generation results, as DreamFusion [40] acknowledged. + +# 6. Conclusion + +This paper introduces Dream3D, a text-to-3D synthesis framework that can generate diverse and imaginative 3D content from text prompts. Our approach incorporates explicit 3D shape priors into the CLIP-guided optimization process to generate more plausible 3D structures. To address the text-to-shape generation, we propose a straightforward yet effective method that utilizes a fine-tuned text-to-image diffusion model to bridge the text and image modalities. Our method is shown to generate 3D content with superior visual quality and shape accuracy compared to previous work, as demonstrated by extensive experiments. + +Acknowledgements. The work was supported by National Key R&D Program of China (2018AAA0100704), NSFC #61932020, #62172279, Science and Technology Commission of Shanghai Municipality (Grant No. 20ZR1436000), Program of Shanghai Academic Research Leader, and "Shuguang Program" supported by Shanghai Education Development Foundation and Shanghai Municipal Education Commission. + +# References + +[1] Jonathan T. Barron, Ben Mildenhall, Dor Verbin, Pratul P. Srinivasan, and Peter Hedman. 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By utilizing 3D shape priors and powerful text-to-image diffusion models, our Dream3D can generate 3D content that exhibits superior visual quality and shape accuracy in accordance with the text prompt when compared to PureCLIPNeRF [24]." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 143, + 418, + 192, + 430 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 418, + 192, + 430 + ], + "spans": [ + { + "bbox": [ + 143, + 418, + 192, + 430 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 430, + 289, + 682 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 430, + 289, + 682 + ], + "spans": [ + { + "bbox": [ + 46, + 430, + 289, + 682 + ], + "type": "text", + "content": "Recent CLIP-guided 3D optimization methods, such as DreamFields [19] and PureCLIPNeRF [24], have achieved impressive results in zero-shot text-to-3D synthesis. However, due to scratch training and random initialization without prior knowledge, these methods often fail to generate accurate and faithful 3D structures that conform to the input text. In this paper, we make the first attempt to introduce explicit 3D shape priors into the CLIP-guided 3D optimization process. Specifically, we first generate a high-quality 3D shape from the input text in the text-to-shape stage as a 3D shape prior. We then use it as the initialization of a neural radiance field and optimize it with the full prompt. To address the challenging text-to-shape generation task, we present a simple yet effective approach that directly bridges the text and image modalities with a powerful text-to-image diffusion model. To narrow the style domain gap between the images synthesized by the text-to-image diffusion model and shape renderings used to train the image-to-shape generator, we further propose to jointly optimize a learnable text prompt and fine-tune the text-to-image diffusion model for rendering-style image generation. Our method," + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 419, + 546, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 419, + 546, + 467 + ], + "spans": [ + { + "bbox": [ + 306, + 419, + 546, + 467 + ], + "type": "text", + "content": "Dream3D, is capable of generating imaginative 3D content with superior visual quality and shape accuracy compared to state-of-the-art methods. Our project page is at https://bluestyle97.github.io/dream3d/." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 490, + 387, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 490, + 387, + 502 + ], + "spans": [ + { + "bbox": [ + 306, + 490, + 387, + 502 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 510, + 546, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 546, + 629 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 546, + 629 + ], + "type": "text", + "content": "Text-to-3D synthesis endeavors to create 3D content that is coherent with an input text, which has the potential to benefit a wide range of applications such as animations, games, and virtual reality. Recently developed zero-shot text-to-image models [34,44,45,48,50] have made remarkable progress and can generate diverse, high-fidelity, and imaginative images from various text prompts. However, extending this success to the text-to-3D synthesis task is challenging because it is not practically feasible to collect a comprehensive paired text-3D dataset." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "type": "text", + "content": "Zero-shot text-to-3D synthesis [19, 22, 24, 40, 51], which eliminates the need for paired data, is an attractive approach that typically relies on powerful vision-language models such as CLIP [58]. There are two main categories of this approach. 1) CLIP-based generative models, such as CLIP-Forge [51]. They utilize images as an intermediate bridge and train a mapper from the CLIP image embeddings of" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 693, + 254, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 693, + 254, + 703 + ], + "spans": [ + { + "bbox": [ + 58, + 693, + 254, + 703 + ], + "type": "text", + "content": "*Work done during an internship at ARC Lab, Tencent PCG." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 59, + 703, + 138, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 703, + 138, + 712 + ], + "spans": [ + { + "bbox": [ + 59, + 703, + 138, + 712 + ], + "type": "text", + "content": "† Corresponding Author." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20908" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "content": "ShapeNet renderings to the shape embeddings of a 3D shape generator, then switch to the CLIP text embedding as the input at test time. 2) CLIP-guided 3D optimization methods, such as DreamFields [19] and PureCLIPNeRF [24]. They continuously optimize the CLIP similarity loss between a text prompt and rendered images of a 3D scene representation, such as neural radiance fields [1,26,32,41]. While the first category heavily relies on 3D shape generators trained on limited 3D shapes and seldom has the capacity to adjust its shape structures, the second category has more creative freedom with the \"dreaming ability\" to generate diverse shape structures and textures." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 217, + 289, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 217, + 289, + 409 + ], + "spans": [ + { + "bbox": [ + 46, + 217, + 289, + 409 + ], + "type": "text", + "content": "We develop our method building upon CLIP-guided 3D optimization methods. Although these methods can produce remarkable outcomes, they typically fail to create precise and accurate 3D structures that conform to the input text (Fig. 1, " + }, + { + "bbox": [ + 46, + 217, + 289, + 409 + ], + "type": "inline_equation", + "content": "2^{\\mathrm{nd}}" + }, + { + "bbox": [ + 46, + 217, + 289, + 409 + ], + "type": "text", + "content": " row). Due to the scratch training and random initialization without any prior knowledge, these methods tend to generate highly-unconstrained \"adversarial contents\" that have high CLIP scores but low visual quality. To address this issue and synthesize more faithful 3D contents, we suggest generating a high-quality 3D shape from the input text first and then using it as an explicit \"3D shape prior\" in the CLIP-guided 3D optimization process. In the text-to-shape* stage, we begin by synthesizing a 3D shape without textures of the main common object in the text prompt. We then use it as the initialization of a voxel-based neural radiance field and optimize it with the full prompt." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 410, + 289, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 410, + 289, + 673 + ], + "spans": [ + { + "bbox": [ + 46, + 410, + 289, + 673 + ], + "type": "text", + "content": "The text-to-shape generation itself is a challenging task. Previous methods [19, 51] are often trained on images and tested with texts, and use CLIP to bridge the two modalities. However, this approach leads to a mismatching problem due to the gap between the CLIP text and image embedding spaces. Additionally, existing methods cannot produce high-quality 3D shapes. In this work, we propose to directly bridge the text and image modalities with a powerful text-to-image diffusion model, i.e., Stable Diffusion [48]. We use the text-to-image diffusion model to synthesize an image from the input text and then feed the image into an image-to-shape generator to produce high-quality 3D shapes. Since we use the same procedure in both training and testing, the mismatching problem is largely reduced. However, there is still a style domain gap between the images synthesized by Stable Diffusion and the shape renderings used to train the image-to-shape generator. Inspired by recent work on controllable text-to-image synthesis [11,49], we propose to jointly optimize a learnable text prompt and fine-tune the Stable Diffusion to address this domain gap. The fine-tuned Stable Diffusion can reliably synthesize images in the style of shape renderings used to train the image" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 306, + 72, + 534, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 534, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 534, + 84 + ], + "type": "text", + "content": "to-shape module without suffering from the domain gap." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 85, + 547, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 85, + 547, + 312 + ], + "spans": [ + { + "bbox": [ + 304, + 85, + 547, + 312 + ], + "type": "text", + "content": "To summarize, 1) We make the first attempt to introduce the explicit 3D shape prior into CLIP-guided 3D optimization methods. The proposed method can generate more accurate and high-quality 3D shapes conforming to the corresponding text, while still enjoying the \"dreaming\" ability of generating diverse shape structures and textures (Fig. 1, " + }, + { + "bbox": [ + 304, + 85, + 547, + 312 + ], + "type": "inline_equation", + "content": "1^{\\mathrm{st}}" + }, + { + "bbox": [ + 304, + 85, + 547, + 312 + ], + "type": "text", + "content": " row). Therefore, we name our method \"Dream3D\" as it has both strengths. 2) Regarding text-to-shape generation, we present a straightforward yet effective approach that directly connects the text and image modalities using a powerful text-to-image diffusion model. To narrow the style domain gap between the synthesized images and shape renderings, we further propose to jointly optimize a learnable text prompt and fine-tune the text-to-image diffusion model for rendering-style image generation. 3) Our Dream3D can generate imaginative 3D content with better visual quality and shape accuracy than state-of-the-art methods. Additionally, our text-to-shape pipeline can produce 3D shapes of higher quality than previous work." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 323, + 392, + 335 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 323, + 392, + 335 + ], + "spans": [ + { + "bbox": [ + 306, + 323, + 392, + 335 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 342, + 547, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 342, + 547, + 534 + ], + "spans": [ + { + "bbox": [ + 304, + 342, + 547, + 534 + ], + "type": "text", + "content": "3D Shape Generation. Generative models for 3D shapes have been extensively studied in recent years. It is more challenging than 2D image generation due to the expensive 3D data collection and the complexity of 3D shapes. Various 3D generators employ different shape representations, e.g., voxel grids [3, 25, 56], point clouds [2, 61, 63, 65, 68], meshes [13, 14, 16, 33], and implicit fields [8, 29, 59, 60, 67]. These generators are trained to model the distribution of shape geometry (and optionally, texture) from a collection of 3D shapes. Some methods [4, 5, 12, 36, 38, 39, 53] attempt to learn a 3D generator using only 2D image supervision. These methods incorporate explicit 3D representations, such as meshes [12, 38, 39] and neural radiance fields [4, 5, 36, 53], along with surface or volume-based differentiable rendering techniques [20, 21, 32, 35], to enable the learning of 3D awareness from images." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 534, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 548, + 715 + ], + "type": "text", + "content": "Text-to-Image. Previous studies in text-to-image synthesis [42, 46, 62, 66] have focused mainly on domain-specific datasets and utilized GANs [15]. However, recent advances in scalable generative architectures and large-scale text-image datasets [52] have enabled unprecedented performance in zero-shot text-to-image synthesis. DALL-E [45] and GLIDE [34], as pioneering works, employ autoregressive model [10] and diffusion model [18, 54] as their architectures, respectively. DALL-E 2 [44] utilizes a diffusion prior network to translate CLIP text embeddings to CLIP image embeddings, and an unCLIP module to synthesize images from CLIP image embeddings. In Imagen [50] and Stable Diffusion [48], a large pre-trained text encoder is employed to guide the sampling process of a diffusion model in pixel space and latent space, respectively." + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 46, + 683, + 288, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 683, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 683, + 288, + 713 + ], + "type": "text", + "content": "*Throughout this paper, we use the term \"shape\" to refer to 3D geometric models without textures, while some works [7,28] also use this term for textured 3D models." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20909" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 85, + 542, + 225 + ], + "blocks": [ + { + "bbox": [ + 52, + 85, + 542, + 225 + ], + "lines": [ + { + "bbox": [ + 52, + 85, + 542, + 225 + ], + "spans": [ + { + "bbox": [ + 52, + 85, + 542, + 225 + ], + "type": "image", + "image_path": "524d40fe14bb7a3fa580077ad1d342e62b2c0cafd62fb9a5fdba20036a88726c.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 231, + 548, + 299 + ], + "lines": [ + { + "bbox": [ + 46, + 231, + 548, + 299 + ], + "spans": [ + { + "bbox": [ + 46, + 231, + 548, + 299 + ], + "type": "text", + "content": "Figure 2. Overview of our text-to-3D synthesis framework. (a) In the first text-to-shape stage, a fine-tuned Stable Diffusion " + }, + { + "bbox": [ + 46, + 231, + 548, + 299 + ], + "type": "inline_equation", + "content": "G_{I}" + }, + { + "bbox": [ + 46, + 231, + 548, + 299 + ], + "type": "text", + "content": " is employed to synthesize a rendering-style image " + }, + { + "bbox": [ + 46, + 231, + 548, + 299 + ], + "type": "inline_equation", + "content": "I_{r}" + }, + { + "bbox": [ + 46, + 231, + 548, + 299 + ], + "type": "text", + "content": " from the input text prompt " + }, + { + "bbox": [ + 46, + 231, + 548, + 299 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 231, + 548, + 299 + ], + "type": "text", + "content": ". This image is then used to generate a latent shape embedding " + }, + { + "bbox": [ + 46, + 231, + 548, + 299 + ], + "type": "inline_equation", + "content": "e_{S}" + }, + { + "bbox": [ + 46, + 231, + 548, + 299 + ], + "type": "text", + "content": " with the assistance of a shape embedding generation network " + }, + { + "bbox": [ + 46, + 231, + 548, + 299 + ], + "type": "inline_equation", + "content": "G_{M}" + }, + { + "bbox": [ + 46, + 231, + 548, + 299 + ], + "type": "text", + "content": ". Finally, the high-quality 3D shape generator " + }, + { + "bbox": [ + 46, + 231, + 548, + 299 + ], + "type": "inline_equation", + "content": "G_{S}" + }, + { + "bbox": [ + 46, + 231, + 548, + 299 + ], + "type": "text", + "content": " leverages " + }, + { + "bbox": [ + 46, + 231, + 548, + 299 + ], + "type": "inline_equation", + "content": "e_{S}" + }, + { + "bbox": [ + 46, + 231, + 548, + 299 + ], + "type": "text", + "content": " to produce a 3D shape " + }, + { + "bbox": [ + 46, + 231, + 548, + 299 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 231, + 548, + 299 + ], + "type": "text", + "content": ", which is used as an explicit 3D shape prior. (b) In the second optimization stage, the 3D shape prior " + }, + { + "bbox": [ + 46, + 231, + 548, + 299 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 231, + 548, + 299 + ], + "type": "text", + "content": " is utilized to initialize a neural radiance field, which is further optimized with CLIP guidance to synthesize 3D content that is consistent with the input text prompt " + }, + { + "bbox": [ + 46, + 231, + 548, + 299 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 231, + 548, + 299 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 307, + 289, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 307, + 289, + 582 + ], + "spans": [ + { + "bbox": [ + 46, + 307, + 289, + 582 + ], + "type": "text", + "content": "Zero-Shot Text-to-3D. Zero-shot text-to-3D generation techniques [19,22,24,31,40,51] exploit the joint text-image modeling capability of pre-trained vision-language models such as CLIP [43] to obviate the need for paired text-3D data. CLIP-Forge [51] trains a normalizing flow [9, 47] model to convert CLIP image embeddings to VAE [23] shape embeddings, and switches the input to CLIP text embeddings at the inference time. ISS [27] trains a mapper to map the CLIP image embedding into the latent shape code of a pre-trained single-view reconstruction (SVR) network [35], which is then fine-tuned by taking the CLIP text embedding as input. DreamFields [19] and CLIP-Mesh [22] are pioneering works that explore zero-shot 3D content creation using only CLIP guidance. The former optimizes a randomly-initialized NeRF, while the latter optimizes a spherical template mesh as well as random texture and normal maps. PureCLIPNeRF [24] enhances DreamFields with grid-based representation [55] and more diverse image augmentations. Recently, DreamFusion [40] has gained popularity in the research community due to its impressive results. Powered by a strong text-to-image model, ImageGen [50], it can generate high-fidelity 3D objects using the score distillation loss." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 596, + 104, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 596, + 104, + 609 + ], + "spans": [ + { + "bbox": [ + 47, + 596, + 104, + 609 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "text", + "content": "Our objective is to generate 3D content that aligns with the given input text prompt " + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "text", + "content": ". As illustrated in Fig. 2, our framework for text-guided 3D synthesis comprises two stages. In the first stage (Sec. 3.2), we obtain an explicit 3D shape prior " + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "text", + "content": " using a text-guided 3D shape generation process. The text-guided shape generation process involves a text-to-image phase that employs a fine-tuned Stable Diffusion model [48] " + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "inline_equation", + "content": "G_{I}" + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "text", + "content": " (Sec. 3.3), and an image-to-shape phase" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 307, + 547, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 307, + 547, + 403 + ], + "spans": [ + { + "bbox": [ + 304, + 307, + 547, + 403 + ], + "type": "text", + "content": "that employs a shape embedding generation network " + }, + { + "bbox": [ + 304, + 307, + 547, + 403 + ], + "type": "inline_equation", + "content": "G_{M}" + }, + { + "bbox": [ + 304, + 307, + 547, + 403 + ], + "type": "text", + "content": " and a high-quality 3D shape generator " + }, + { + "bbox": [ + 304, + 307, + 547, + 403 + ], + "type": "inline_equation", + "content": "G_{S}" + }, + { + "bbox": [ + 304, + 307, + 547, + 403 + ], + "type": "text", + "content": ". In the second stage (Sec. 3.1), we utilize the 3D prior " + }, + { + "bbox": [ + 304, + 307, + 547, + 403 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 307, + 547, + 403 + ], + "type": "text", + "content": " to initialize a neural radiance field [32], and optimize it with CLIP [43] guidance to generate the 3D content. Our framework only requires a collection of textureless 3D shapes without any text labels to train the 3D generator " + }, + { + "bbox": [ + 304, + 307, + 547, + 403 + ], + "type": "inline_equation", + "content": "G_{S}" + }, + { + "bbox": [ + 304, + 307, + 547, + 403 + ], + "type": "text", + "content": ", and the fine-tuning process of " + }, + { + "bbox": [ + 304, + 307, + 547, + 403 + ], + "type": "inline_equation", + "content": "G_{I}" + }, + { + "bbox": [ + 304, + 307, + 547, + 403 + ], + "type": "text", + "content": " converges rapidly." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 410, + 547, + 436 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 410, + 547, + 436 + ], + "spans": [ + { + "bbox": [ + 305, + 410, + 547, + 436 + ], + "type": "text", + "content": "3.1. CLIP-Guided 3D Optimization with explicit 3D Shape Prior" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 441, + 545, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 441, + 545, + 536 + ], + "spans": [ + { + "bbox": [ + 304, + 441, + 545, + 536 + ], + "type": "text", + "content": "Background: 3D Optimization with CLIP Guidance. CLIP [43] is a powerful vision-language model that comprises a text encoder " + }, + { + "bbox": [ + 304, + 441, + 545, + 536 + ], + "type": "inline_equation", + "content": "E_{T}" + }, + { + "bbox": [ + 304, + 441, + 545, + 536 + ], + "type": "text", + "content": ", and an image encoder " + }, + { + "bbox": [ + 304, + 441, + 545, + 536 + ], + "type": "inline_equation", + "content": "E_{I}" + }, + { + "bbox": [ + 304, + 441, + 545, + 536 + ], + "type": "text", + "content": ". By maximizing the cosine similarity between the text embedding and the image embedding encoded by " + }, + { + "bbox": [ + 304, + 441, + 545, + 536 + ], + "type": "inline_equation", + "content": "E_{T}" + }, + { + "bbox": [ + 304, + 441, + 545, + 536 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 441, + 545, + 536 + ], + "type": "inline_equation", + "content": "E_{I}" + }, + { + "bbox": [ + 304, + 441, + 545, + 536 + ], + "type": "text", + "content": " respectively on a large-scale paired text-image dataset, CLIP aligns the text and image modalities in a shared latent embedding space." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 537, + 547, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 537, + 547, + 609 + ], + "spans": [ + { + "bbox": [ + 304, + 537, + 547, + 609 + ], + "type": "text", + "content": "Prior research [19, 22, 24] leverages the capability of CLIP [43] to generate 3D contents from text. Starting from a randomly-initialized 3D representation parameterized by " + }, + { + "bbox": [ + 304, + 537, + 547, + 609 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 537, + 547, + 609 + ], + "type": "text", + "content": ", they render images from multiple viewpoints and optimize " + }, + { + "bbox": [ + 304, + 537, + 547, + 609 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 537, + 547, + 609 + ], + "type": "text", + "content": " by minimizing the CLIP similarity loss between the rendered image " + }, + { + "bbox": [ + 304, + 537, + 547, + 609 + ], + "type": "inline_equation", + "content": "\\mathcal{R}(\\boldsymbol{v}_i; \\theta)" + }, + { + "bbox": [ + 304, + 537, + 547, + 609 + ], + "type": "text", + "content": " and the text prompt " + }, + { + "bbox": [ + 304, + 537, + 547, + 609 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 537, + 547, + 609 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 357, + 617, + 545, + 633 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 357, + 617, + 545, + 633 + ], + "spans": [ + { + "bbox": [ + 357, + 617, + 545, + 633 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {C L I P}} = - E _ {I} \\left(\\mathcal {R} \\left(\\theta ; \\boldsymbol {v} _ {i}\\right)\\right) ^ {T} E _ {T} (y), \\tag {1}", + "image_path": "85f95cbd7f1909808bc20a49d893380db111dde25dfa502a30b3defedef1684b.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": " denotes the rendering process, and " + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\pmb{v}_i" + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": " denotes the rendering viewpoint at the " + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": "-th optimization step. Specifically, DreamFields [19] and PureCLIPNeRF [24] employ neural radiance fields [32] (NeRF) as the 3D representation " + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": ", while CLIP-Mesh [22] uses a spherical template mesh with associated texture and normal maps." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 208, + 72, + 356, + 84 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 208, + 72, + 356, + 84 + ], + "spans": [ + { + "bbox": [ + 208, + 72, + 356, + 84 + ], + "type": "text", + "content": "\"A park bench overgrown with vines\"" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20910" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "text", + "content": "Observations and Motivations. Though these CLIP-guided optimization methods can generate impressive results, we observe that they often fall short in producing precise and detailed 3D structures that accurately match the text description. As depicted in Fig. 1, we employ these methods to create 3D content featuring common objects, but the outcomes exhibited distortion artifacts and appeared unusual, adversely affecting their visual quality and hindering their use in real-world applications." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 180, + 288, + 299 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 180, + 288, + 299 + ], + "spans": [ + { + "bbox": [ + 46, + 180, + 288, + 299 + ], + "type": "text", + "content": "We attribute the failure of previous works to generate accurate and realistic objects to two main factors: (i) The optimization process begins with a randomly-initialized 3D representation lacking any explicit 3D shape prior, making it very challenging for the models to conjure up the scene from scratch. (ii) The CLIP loss in Eq. (1) prioritizes global consistency between the rendered image and the text prompt, rather than offering robust and precise guidance on the synthesized 3D structure. As a result, the optimization output is significantly unconstrained." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 300, + 287, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 300, + 287, + 430 + ], + "spans": [ + { + "bbox": [ + 46, + 300, + 287, + 430 + ], + "type": "text", + "content": "Optimization with 3D Shape Prior as Initialization. To address the aforementioned issue and generate more faithful 3D content, we propose to use a text-to-shape generation process to create a high-quality 3D shape " + }, + { + "bbox": [ + 46, + 300, + 287, + 430 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 300, + 287, + 430 + ], + "type": "text", + "content": " from the input text prompt " + }, + { + "bbox": [ + 46, + 300, + 287, + 430 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 300, + 287, + 430 + ], + "type": "text", + "content": ". Subsequently, we use it as an explicit \"3D shape prior\" to initialize the CLIP-guided 3D optimization process. As illustrated in Fig. 2, for the text prompt \"a park bench overgrown with vines\", we first synthesize \"a park bench\" without textures in the text-to-shape stage. We then use it as the initialization of a neural radiance field and optimize it with the full prompt, following previous works." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 431, + 288, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 431, + 288, + 515 + ], + "spans": [ + { + "bbox": [ + 47, + 431, + 288, + 515 + ], + "type": "text", + "content": "Our optimization process utilizes DVGO [55], an efficient NeRF variant that represents NeRF using a density voxel grid " + }, + { + "bbox": [ + 47, + 431, + 288, + 515 + ], + "type": "inline_equation", + "content": "V_{\\mathrm{density}} \\in \\mathbb{R}^{N_x \\times N_y \\times N_z}" + }, + { + "bbox": [ + 47, + 431, + 288, + 515 + ], + "type": "text", + "content": " and a shallow color MLP " + }, + { + "bbox": [ + 47, + 431, + 288, + 515 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{rgb}}" + }, + { + "bbox": [ + 47, + 431, + 288, + 515 + ], + "type": "text", + "content": ". We start by taking a 3D shape " + }, + { + "bbox": [ + 47, + 431, + 288, + 515 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 47, + 431, + 288, + 515 + ], + "type": "text", + "content": " generated by the text-to-shape process, represented as an SDF grid " + }, + { + "bbox": [ + 47, + 431, + 288, + 515 + ], + "type": "inline_equation", + "content": "\\tilde{V}_{\\mathrm{sdf}} \\in \\mathbb{R}^{N_x \\times N_y \\times N_z}" + }, + { + "bbox": [ + 47, + 431, + 288, + 515 + ], + "type": "text", + "content": ", and transform it into the density voxel grid " + }, + { + "bbox": [ + 47, + 431, + 288, + 515 + ], + "type": "inline_equation", + "content": "V_{\\mathrm{density}}" + }, + { + "bbox": [ + 47, + 431, + 288, + 515 + ], + "type": "text", + "content": " using the following equations [37,55,64]:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 117, + 523, + 287, + 555 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 117, + 523, + 287, + 555 + ], + "spans": [ + { + "bbox": [ + 117, + 523, + 287, + 555 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\Sigma} = \\frac {1}{\\beta} \\text {s i g m o i d} \\left(- \\frac {\\tilde {\\boldsymbol {V}} _ {\\mathrm {s d f}}}{\\beta}\\right), \\tag {2a}", + "image_path": "fcffb0b651c77734d8a764701330bd862f72e50f6749651c61da83bc9528e89f.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 96, + 557, + 287, + 572 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 557, + 287, + 572 + ], + "spans": [ + { + "bbox": [ + 96, + 557, + 287, + 572 + ], + "type": "interline_equation", + "content": "\\boldsymbol {V} _ {\\text {d e n s i t y}} = \\max (0, \\text {s o f t p l u s} ^ {- 1} (\\boldsymbol {\\Sigma})) \\tag {2b}", + "image_path": "dfcf7c841f32846af414b5bedb1f775ee391bed40c6ba3ff068f0ed535d10a4a.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 581, + 287, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 581, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 581, + 287, + 689 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 46, + 581, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\operatorname{sigmoid}(x) = 1 / (1 + e^{-x})" + }, + { + "bbox": [ + 46, + 581, + 287, + 689 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 581, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\operatorname{softplus}^{-1}(x) = \\log(e^x - 1)" + }, + { + "bbox": [ + 46, + 581, + 287, + 689 + ], + "type": "text", + "content": ". Eq. (2a) converts SDF values to density for volume rendering, where " + }, + { + "bbox": [ + 46, + 581, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\beta > 0" + }, + { + "bbox": [ + 46, + 581, + 287, + 689 + ], + "type": "text", + "content": " is a hyper-parameter controlling the sharpness of the shape boundary (smaller " + }, + { + "bbox": [ + 46, + 581, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 581, + 287, + 689 + ], + "type": "text", + "content": " leads to sharper shape boundary, " + }, + { + "bbox": [ + 46, + 581, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\beta = 0.05" + }, + { + "bbox": [ + 46, + 581, + 287, + 689 + ], + "type": "text", + "content": " in our experiments). Eq. (2b) transforms the density into pre-activated density. To ensure that the distribution of the accumulated transmittance is the same as DVGO, we clamp the minimum value of the density outside the shape prior as 0." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "With the density grid " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "V_{\\mathrm{density}}" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": " initialized by the 3D shape " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": " and the color MLP " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{rgb}}" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": " initialized randomly, we render" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 545, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 192 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 192 + ], + "type": "text", + "content": "image " + }, + { + "bbox": [ + 304, + 72, + 545, + 192 + ], + "type": "inline_equation", + "content": "\\mathcal{R}(\\boldsymbol{V}_{\\mathrm{density}}, f_{\\mathrm{rgb}}; \\boldsymbol{v}_i)" + }, + { + "bbox": [ + 304, + 72, + 545, + 192 + ], + "type": "text", + "content": " from viewpoint " + }, + { + "bbox": [ + 304, + 72, + 545, + 192 + ], + "type": "inline_equation", + "content": "\\boldsymbol{v}_i" + }, + { + "bbox": [ + 304, + 72, + 545, + 192 + ], + "type": "text", + "content": " and optimize " + }, + { + "bbox": [ + 304, + 72, + 545, + 192 + ], + "type": "inline_equation", + "content": "\\theta = (V_{\\mathrm{density}}, f_{\\mathrm{rgb}})" + }, + { + "bbox": [ + 304, + 72, + 545, + 192 + ], + "type": "text", + "content": " with the CLIP loss in Eq. (1). Following DreamFields [19] and PureCLIPNeRF [24], we perform background augmentations for the rendered images and leverage the transmittance loss introduced by [19] to reduce noise and spurious density. Besides, since CLIP loss cannot provide accurate geometrical supervision, the 3D shape prior may be gradually disturbed and \"forgotten\", thus we also adopt a shape-prior-preserving loss to preserve the global structure of the 3D shape prior:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 321, + 199, + 545, + 227 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 199, + 545, + 227 + ], + "spans": [ + { + "bbox": [ + 321, + 199, + 545, + 227 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {p r i o r}} = - \\sum_ {(x, y, z)} \\mathbb {1} (\\tilde {\\boldsymbol {V}} _ {\\mathrm {s d f}} < 0) \\cdot \\operatorname {a l p h a} (\\boldsymbol {V} _ {\\text {d e n s i t y}}), \\tag {3}", + "image_path": "f075546a7ad8186275d87398fa04ebadc3d625a89037f4a82f75f4564961bb86.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 233, + 545, + 269 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 233, + 545, + 269 + ], + "spans": [ + { + "bbox": [ + 304, + 233, + 545, + 269 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 233, + 545, + 269 + ], + "type": "inline_equation", + "content": "\\mathbb{1}(\\cdot)" + }, + { + "bbox": [ + 304, + 233, + 545, + 269 + ], + "type": "text", + "content": " is the indicator function, and " + }, + { + "bbox": [ + 304, + 233, + 545, + 269 + ], + "type": "inline_equation", + "content": "\\mathrm{alpha}(\\cdot)" + }, + { + "bbox": [ + 304, + 233, + 545, + 269 + ], + "type": "text", + "content": " transforms the density into the opacity representing the probability of termination at each position in volume rendering." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 270, + 545, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 270, + 545, + 353 + ], + "spans": [ + { + "bbox": [ + 304, + 270, + 545, + 353 + ], + "type": "text", + "content": "By initializing NeRF with an explicit 3D shape prior, we give extra knowledge on how the 3D content should look like and prevent the model from imagining from scratch and generating \"adversarial contents\" that have high CLIP scores but low visual quality. Based on the initialization, the CLIP-guided optimization further provides flexibility and is able to synthesize more diverse structures and textures." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 360, + 545, + 385 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 360, + 545, + 385 + ], + "spans": [ + { + "bbox": [ + 305, + 360, + 545, + 385 + ], + "type": "text", + "content": "3.2. Stable-Diffusion-Assisted Text-to-Shape Generation as 3D Shape Prior" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 391, + 545, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 391, + 545, + 462 + ], + "spans": [ + { + "bbox": [ + 304, + 391, + 545, + 462 + ], + "type": "text", + "content": "To obtain the 3D shape prior, a text-guided shape generation scheme is required, which is a challenging task due to the lack of paired text-shape datasets. Previous approaches [27, 51] typically first train an image-to-shape model using rendered images, and then bridge the text and image modalities using the CLIP embedding space." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 462, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 545, + 665 + ], + "type": "text", + "content": "CLIP-Forge [51] trains a normalizing flow network to map CLIP image embeddings of shape renderings to latent embeddings of a volumetric shape auto-encoder, and at test time, it switches to CLIP text embeddings as input. However, the shape auto-encoder has difficulty in generating high-quality and diverse 3D shapes, and directly feeding CLIP text embeddings to the flow network trained on CLIP image embeddings suffers from the gap between the CLIP text and image embedding spaces. ISS [27] trains a mapper network to map CLIP image embeddings of shape renderings to the latent space of a pre-trained single-view reconstruction (SVR) model, and fine-tunes the mapper at test time by maximizing the CLIP similarity between the text prompt and the images rendered from synthesized shapes. While the test-time fine-tuning alleviates the gap between the CLIP text and image embeddings, it is cumbersome to fine-tune the mapper for each text prompt." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "In contrast to the aforementioned methods that connect the text and image modalities in the CLIP embedding space, we use a powerful text-to-image diffusion model to directly bridge the two modalities. Specifically, we first synthesize" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20911" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "content": "an image from the input text and then feed it into an image-to-shape module to generate a high-quality 3D shape. This pipeline is more concise and naturally eliminates the gap between CLIP text and image embeddings. However, it introduces a new domain gap between the images generated by the text-to-image diffusion model and the shape renderings used to train the image-to-shape module. We will introduce a novel technique to alleviate this gap in Sec. 3.3." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 168, + 289, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 168, + 289, + 324 + ], + "spans": [ + { + "bbox": [ + 46, + 168, + 289, + 324 + ], + "type": "text", + "content": "Text-to-Image Diffusion Model. Diffusion models [18,54] are generative models trained to reverse a diffusion process. The diffusion process begins with a sample from the data distribution, " + }, + { + "bbox": [ + 46, + 168, + 289, + 324 + ], + "type": "inline_equation", + "content": "\\pmb{x}_0 \\sim q(\\pmb{x}_0)" + }, + { + "bbox": [ + 46, + 168, + 289, + 324 + ], + "type": "text", + "content": ", which is gradually corrupted by Gaussian noise over " + }, + { + "bbox": [ + 46, + 168, + 289, + 324 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 168, + 289, + 324 + ], + "type": "text", + "content": " timesteps: " + }, + { + "bbox": [ + 46, + 168, + 289, + 324 + ], + "type": "inline_equation", + "content": "\\pmb{x}_t = \\sqrt{\\alpha_t} \\pmb{x}_{t-1} + \\sqrt{1 - \\alpha_t} \\pmb{\\epsilon}_{t-1}, t = 1, 2, \\dots, T" + }, + { + "bbox": [ + 46, + 168, + 289, + 324 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 168, + 289, + 324 + ], + "type": "inline_equation", + "content": "\\alpha_t" + }, + { + "bbox": [ + 46, + 168, + 289, + 324 + ], + "type": "text", + "content": " defines the noise level and " + }, + { + "bbox": [ + 46, + 168, + 289, + 324 + ], + "type": "inline_equation", + "content": "\\pmb{\\epsilon}_{t-1}" + }, + { + "bbox": [ + 46, + 168, + 289, + 324 + ], + "type": "text", + "content": " denotes the noise added at timestep " + }, + { + "bbox": [ + 46, + 168, + 289, + 324 + ], + "type": "inline_equation", + "content": "t-1" + }, + { + "bbox": [ + 46, + 168, + 289, + 324 + ], + "type": "text", + "content": ". To reverse this process, a denoising network " + }, + { + "bbox": [ + 46, + 168, + 289, + 324 + ], + "type": "inline_equation", + "content": "\\epsilon_\\theta" + }, + { + "bbox": [ + 46, + 168, + 289, + 324 + ], + "type": "text", + "content": " is trained to estimate the added noise at each timestep. During inference, samples can be generated by iteratively denoising pure Gaussian noise. Text-to-image diffusion models further condition the denoising process on texts. Given a text prompt " + }, + { + "bbox": [ + 46, + 168, + 289, + 324 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 168, + 289, + 324 + ], + "type": "text", + "content": " and a text encoder " + }, + { + "bbox": [ + 46, + 168, + 289, + 324 + ], + "type": "inline_equation", + "content": "c_\\theta" + }, + { + "bbox": [ + 46, + 168, + 289, + 324 + ], + "type": "text", + "content": ", the training objective is:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 74, + 327, + 287, + 343 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 74, + 327, + 287, + 343 + ], + "spans": [ + { + "bbox": [ + 74, + 327, + 287, + 343 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {d i f f u s i o n}} = \\mathbb {E} _ {\\boldsymbol {x} _ {0}, t, \\boldsymbol {\\epsilon} _ {t}, y} \\| \\boldsymbol {\\epsilon} _ {t} - \\epsilon_ {\\theta} (\\boldsymbol {x} _ {t}, t, c _ {\\theta} (y)) \\| _ {2} ^ {2} \\tag {4}", + "image_path": "185ebe3262ea230b517c8f235021414ce2def37c8443151080d91b25a16caa51.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 347, + 287, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 347, + 287, + 419 + ], + "spans": [ + { + "bbox": [ + 46, + 347, + 287, + 419 + ], + "type": "text", + "content": "In this work, we use Stable Diffusion" + }, + { + "bbox": [ + 46, + 347, + 287, + 419 + ], + "type": "inline_equation", + "content": "^{\\dagger}" + }, + { + "bbox": [ + 46, + 347, + 287, + 419 + ], + "type": "text", + "content": " [48], an open-source text-to-image diffusion model, which employs a CLIP ViT-L/14 text encoder as " + }, + { + "bbox": [ + 46, + 347, + 287, + 419 + ], + "type": "inline_equation", + "content": "c_{\\theta}" + }, + { + "bbox": [ + 46, + 347, + 287, + 419 + ], + "type": "text", + "content": " and is trained on the large-scale LAION-5B dataset [52]. Stable Diffusion is known for its ability to generate diverse and imaginative images in various styles from heterogeneous text prompts." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 419, + 289, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 419, + 289, + 598 + ], + "spans": [ + { + "bbox": [ + 46, + 419, + 289, + 598 + ], + "type": "text", + "content": "High-quality 3D generator. To provide a more precise initialization for optimization, high-quality 3D shapes are highly desirable. In this work, we utilize the SDF-StyleGAN [67], a state-of-the-art 3D generative model, to generate high-quality 3D priors. SDF-StyleGAN is a StyleGAN2-like architecture that maps a random noise " + }, + { + "bbox": [ + 46, + 419, + 289, + 598 + ], + "type": "inline_equation", + "content": "z \\sim \\mathcal{N}(0, I)" + }, + { + "bbox": [ + 46, + 419, + 289, + 598 + ], + "type": "text", + "content": " to a latent shape embedding " + }, + { + "bbox": [ + 46, + 419, + 289, + 598 + ], + "type": "inline_equation", + "content": "e_S \\in \\mathcal{W}" + }, + { + "bbox": [ + 46, + 419, + 289, + 598 + ], + "type": "text", + "content": " and synthesizes a 3D feature volume " + }, + { + "bbox": [ + 46, + 419, + 289, + 598 + ], + "type": "inline_equation", + "content": "F_V" + }, + { + "bbox": [ + 46, + 419, + 289, + 598 + ], + "type": "text", + "content": ", which is an implicit shape representation. We can query the SDF value at arbitrary position " + }, + { + "bbox": [ + 46, + 419, + 289, + 598 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 419, + 289, + 598 + ], + "type": "text", + "content": " by feeding the interpolated feature from " + }, + { + "bbox": [ + 46, + 419, + 289, + 598 + ], + "type": "inline_equation", + "content": "F_V" + }, + { + "bbox": [ + 46, + 419, + 289, + 598 + ], + "type": "text", + "content": " at " + }, + { + "bbox": [ + 46, + 419, + 289, + 598 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 419, + 289, + 598 + ], + "type": "text", + "content": " into a jointly trained MLP. We improve upon the original SDF-StyleGAN, which trains one network for each shape category, by training a single 3D shape generator " + }, + { + "bbox": [ + 46, + 419, + 289, + 598 + ], + "type": "inline_equation", + "content": "G_S" + }, + { + "bbox": [ + 46, + 419, + 289, + 598 + ], + "type": "text", + "content": " on the 13 categories of ShapeNet [6]. This modification provides greater flexibility in the text-to-shape process." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 599, + 289, + 698 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 599, + 289, + 698 + ], + "spans": [ + { + "bbox": [ + 46, + 599, + 289, + 698 + ], + "type": "text", + "content": "Shape Embedding Mapping Network. To bridge the image and shape modalities, we further train a shape embedding mapping network " + }, + { + "bbox": [ + 46, + 599, + 289, + 698 + ], + "type": "inline_equation", + "content": "G_{M}" + }, + { + "bbox": [ + 46, + 599, + 289, + 698 + ], + "type": "text", + "content": ". Firstly, we utilize " + }, + { + "bbox": [ + 46, + 599, + 289, + 698 + ], + "type": "inline_equation", + "content": "G_{S}" + }, + { + "bbox": [ + 46, + 599, + 289, + 698 + ], + "type": "text", + "content": " to generate a large set of 3D shapes " + }, + { + "bbox": [ + 46, + 599, + 289, + 698 + ], + "type": "inline_equation", + "content": "\\{S^i\\}_{i=1}^N" + }, + { + "bbox": [ + 46, + 599, + 289, + 698 + ], + "type": "text", + "content": " and shape embeddings " + }, + { + "bbox": [ + 46, + 599, + 289, + 698 + ], + "type": "inline_equation", + "content": "\\{e_S^i\\}_{i=1}^N" + }, + { + "bbox": [ + 46, + 599, + 289, + 698 + ], + "type": "text", + "content": ". Then, we render " + }, + { + "bbox": [ + 46, + 599, + 289, + 698 + ], + "type": "inline_equation", + "content": "S^i" + }, + { + "bbox": [ + 46, + 599, + 289, + 698 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 46, + 599, + 289, + 698 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 599, + 289, + 698 + ], + "type": "text", + "content": " viewpoints to obtain shape renderings " + }, + { + "bbox": [ + 46, + 599, + 289, + 698 + ], + "type": "inline_equation", + "content": "\\{I_r^j\\}_{j=1}^{NK}" + }, + { + "bbox": [ + 46, + 599, + 289, + 698 + ], + "type": "text", + "content": " and the corresponding image embeddings " + }, + { + "bbox": [ + 46, + 599, + 289, + 698 + ], + "type": "inline_equation", + "content": "\\{e_I^j\\}_{j=1}^{NK}" + }, + { + "bbox": [ + 46, + 599, + 289, + 698 + ], + "type": "text", + "content": " with the CLIP image encoder " + }, + { + "bbox": [ + 46, + 599, + 289, + 698 + ], + "type": "inline_equation", + "content": "E_I" + }, + { + "bbox": [ + 46, + 599, + 289, + 698 + ], + "type": "text", + "content": ", forming a paired image-shape embedding dataset" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 307, + 70, + 422, + 167 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 422, + 167 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 422, + 167 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 422, + 167 + ], + "type": "image", + "image_path": "b4e0ed76e7fdb1233075066571549772dbbfbeaa1f538d708ac8cb7cfcc13f12.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 175, + 547, + 286 + ], + "lines": [ + { + "bbox": [ + 304, + 175, + 547, + 286 + ], + "spans": [ + { + "bbox": [ + 304, + 175, + 547, + 286 + ], + "type": "text", + "content": "Figure 3. Fine-tuning Stable Diffusion into a stylized generator. (a) We fine-tune the text embedding " + }, + { + "bbox": [ + 304, + 175, + 547, + 286 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_{*}" + }, + { + "bbox": [ + 304, + 175, + 547, + 286 + ], + "type": "text", + "content": " of a placeholder token " + }, + { + "bbox": [ + 304, + 175, + 547, + 286 + ], + "type": "inline_equation", + "content": "*" + }, + { + "bbox": [ + 304, + 175, + 547, + 286 + ], + "type": "text", + "content": " and the weights of Stable Diffusion using a dataset " + }, + { + "bbox": [ + 304, + 175, + 547, + 286 + ], + "type": "inline_equation", + "content": "D_{S}" + }, + { + "bbox": [ + 304, + 175, + 547, + 286 + ], + "type": "text", + "content": " that contains ShapeNet renderings and text descriptions in the format of \"a CLS in the style of *\". Additionally, we use another dataset " + }, + { + "bbox": [ + 304, + 175, + 547, + 286 + ], + "type": "inline_equation", + "content": "D_{reg}" + }, + { + "bbox": [ + 304, + 175, + 547, + 286 + ], + "type": "text", + "content": ", which contains images synthesized by the original Stable Diffusion with text prompts in the format of \"a CLS\", for regularization purposes. (b) With the fine-tuned Stable Diffusion, we can synthesize images that match the style of ShapeNet renderings by appending the postfix \"in the style of *\" to the text prompt." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 439, + 71, + 545, + 167 + ], + "blocks": [ + { + "bbox": [ + 439, + 71, + 545, + 167 + ], + "lines": [ + { + "bbox": [ + 439, + 71, + 545, + 167 + ], + "spans": [ + { + "bbox": [ + 439, + 71, + 545, + 167 + ], + "type": "image", + "image_path": "b473cec8fefa12e558e25cb8efd0fc31db8c2f7fdaca5e3a0b37616baeda3173.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 296, + 545, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 296, + 545, + 334 + ], + "spans": [ + { + "bbox": [ + 304, + 296, + 545, + 334 + ], + "type": "inline_equation", + "content": "\\{(e_I^j,e_S^j)\\}_{j = 1}^{NK}" + }, + { + "bbox": [ + 304, + 296, + 545, + 334 + ], + "type": "text", + "content": ". Finally, we use this dataset to train a conditional diffusion model " + }, + { + "bbox": [ + 304, + 296, + 545, + 334 + ], + "type": "inline_equation", + "content": "G_{M}" + }, + { + "bbox": [ + 304, + 296, + 545, + 334 + ], + "type": "text", + "content": " which can synthesize shape embeddings from image embeddings of shape renderings." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 334, + 545, + 406 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 334, + 545, + 406 + ], + "spans": [ + { + "bbox": [ + 304, + 334, + 545, + 406 + ], + "type": "text", + "content": "To prepare the dataset for training " + }, + { + "bbox": [ + 304, + 334, + 545, + 406 + ], + "type": "inline_equation", + "content": "G_{M}" + }, + { + "bbox": [ + 304, + 334, + 545, + 406 + ], + "type": "text", + "content": ", we generate " + }, + { + "bbox": [ + 304, + 334, + 545, + 406 + ], + "type": "inline_equation", + "content": "N = 64000" + }, + { + "bbox": [ + 304, + 334, + 545, + 406 + ], + "type": "text", + "content": " shapes using " + }, + { + "bbox": [ + 304, + 334, + 545, + 406 + ], + "type": "inline_equation", + "content": "G_{S}" + }, + { + "bbox": [ + 304, + 334, + 545, + 406 + ], + "type": "text", + "content": " and render " + }, + { + "bbox": [ + 304, + 334, + 545, + 406 + ], + "type": "inline_equation", + "content": "K = 24" + }, + { + "bbox": [ + 304, + 334, + 545, + 406 + ], + "type": "text", + "content": " views for each shape. The ranges of azimuth and elevation angles of the rendered views are " + }, + { + "bbox": [ + 304, + 334, + 545, + 406 + ], + "type": "inline_equation", + "content": "[-90^{\\circ}, 90^{\\circ}]" + }, + { + "bbox": [ + 304, + 334, + 545, + 406 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 334, + 545, + 406 + ], + "type": "inline_equation", + "content": "[20^{\\circ}, 30^{\\circ}]" + }, + { + "bbox": [ + 304, + 334, + 545, + 406 + ], + "type": "text", + "content": ", respectively. We employ an SDF renderer [20] since we represent the synthesized shapes with SDF grids." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 416, + 545, + 441 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 416, + 545, + 441 + ], + "spans": [ + { + "bbox": [ + 305, + 416, + 545, + 441 + ], + "type": "text", + "content": "3.3. Fine-tuning Stable Diffusion for Rendering-Style Image Generation" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 448, + 545, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 448, + 545, + 567 + ], + "spans": [ + { + "bbox": [ + 304, + 448, + 545, + 567 + ], + "type": "text", + "content": "As stated in Sec. 3.2, we use Stable Diffusion to directly bridge the text and image modalities for text-to-shape generation. Nonetheless, the image-to-shape module is trained on shape renderings, which exhibit a significant style domain gap from the images produced by Stable Diffusion. Previous research [27, 51] has attempted to combine a text-to-image model with an image-to-shape model for text-to-shape generation. However, this approach is plagued by the aforementioned style domain gap, leading to flawed geometric structures and diminished performance." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 569, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 569, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 569, + 545, + 689 + ], + "type": "text", + "content": "Inspired by recent work on controllable text-to-image generation such as textual inversion [11] and Dream-Booth [49], we propose a method for addressing the domain gap problem by fine-tuning Stable Diffusion into a stylized generator. Our core idea is to enable Stable Diffusion to replicate the style of shape renderings used to train the image-to-shape module outlined in Sec. 3.2. This allows us to seamlessly input the generated stylized images into the image-to-shape module without being affected by the domain gap." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "Fine-tuning Process. The fine-tuning process is illustrated in Fig. 3. To fine-tune Stable Diffusion, we need a dataset" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 58, + 702, + 271, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 271, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 271, + 712 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 58, + 702, + 271, + 712 + ], + "type": "text", + "content": "https://github.com/CompVis/stable-diffusion" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "20912" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 70, + 544, + 300 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 544, + 300 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 544, + 300 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 544, + 300 + ], + "type": "image", + "image_path": "9102a5eabaa95608c6ad339ba28bc1078507425bba8f87134796b39775262e94.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 304, + 546, + 327 + ], + "lines": [ + { + "bbox": [ + 46, + 304, + 546, + 327 + ], + "spans": [ + { + "bbox": [ + 46, + 304, + 546, + 327 + ], + "type": "text", + "content": "Figure 4. Qualitative comparison on text-guided 3D synthesis. The 3D shape prior used to initialize the CLIP-guided optimization process for each of our results (the last row) is also visualized below." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 336, + 289, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 336, + 289, + 484 + ], + "spans": [ + { + "bbox": [ + 46, + 336, + 289, + 484 + ], + "type": "text", + "content": "that consists of shape renderings and related stylized text prompts. For each shape " + }, + { + "bbox": [ + 46, + 336, + 289, + 484 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 336, + 289, + 484 + ], + "type": "text", + "content": " in the ShapeNet dataset, we generate a set of shape renderings " + }, + { + "bbox": [ + 46, + 336, + 289, + 484 + ], + "type": "inline_equation", + "content": "\\{I_S^j\\}_{j=1}^{N_S}" + }, + { + "bbox": [ + 46, + 336, + 289, + 484 + ], + "type": "text", + "content": ". Subsequently, each rendering " + }, + { + "bbox": [ + 46, + 336, + 289, + 484 + ], + "type": "inline_equation", + "content": "I_S^j" + }, + { + "bbox": [ + 46, + 336, + 289, + 484 + ], + "type": "text", + "content": " is linked with a stylized text prompt " + }, + { + "bbox": [ + 46, + 336, + 289, + 484 + ], + "type": "inline_equation", + "content": "y_S^j" + }, + { + "bbox": [ + 46, + 336, + 289, + 484 + ], + "type": "text", + "content": " in the format of \"a CLS in the style of *\", where CLS denotes the shape category name and * represents a placeholder token that requires optimization for its text embedding. For instance, if the image is rendered from a chair shape, then the associated text prompt will be \"a chair in the style of *\". The paired dataset " + }, + { + "bbox": [ + 46, + 336, + 289, + 484 + ], + "type": "inline_equation", + "content": "D_S = (I_S^j, y_S^j)_{j=1}^{N_S}" + }, + { + "bbox": [ + 46, + 336, + 289, + 484 + ], + "type": "text", + "content": " is then utilized to fine-tune Stable Diffusion by minimizing " + }, + { + "bbox": [ + 46, + 336, + 289, + 484 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{diffusion}}" + }, + { + "bbox": [ + 46, + 336, + 289, + 484 + ], + "type": "text", + "content": " presented in Eq. (4)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 486, + 289, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 486, + 289, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 486, + 289, + 665 + ], + "type": "text", + "content": "During fine-tuning, we freeze the CLIP text encoder of Stable Diffusion, and optimize two objectives: (i) the text embedding of the placeholder token *, denoted as " + }, + { + "bbox": [ + 46, + 486, + 289, + 665 + ], + "type": "inline_equation", + "content": "v_{*}" + }, + { + "bbox": [ + 46, + 486, + 289, + 665 + ], + "type": "text", + "content": ", and (ii) the parameters " + }, + { + "bbox": [ + 46, + 486, + 289, + 665 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 486, + 289, + 665 + ], + "type": "text", + "content": " of the diffusion model " + }, + { + "bbox": [ + 46, + 486, + 289, + 665 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 46, + 486, + 289, + 665 + ], + "type": "text", + "content": ". Optimizing the text embedding " + }, + { + "bbox": [ + 46, + 486, + 289, + 665 + ], + "type": "inline_equation", + "content": "v_{*}" + }, + { + "bbox": [ + 46, + 486, + 289, + 665 + ], + "type": "text", + "content": " aims to learn a virtual word that captures the style of the rendered images best, even though it is not present in the vocabulary of the text encoder. Fine-tuning the parameters " + }, + { + "bbox": [ + 46, + 486, + 289, + 665 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 486, + 289, + 665 + ], + "type": "text", + "content": " of the diffusion model further enhances the ability to capture the style precisely since it is hard to control the synthesis of Stable Diffusion solely on the language level. Our experiments demonstrate stable convergence of the fine-tuning process in approximately 2000 optimization steps, requiring only 40 minutes on a single Tesla A100 GPU. We show some synthesized results using the fine-tuned model in Fig. 3." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": "Dataset Scale and Background Augmentation. We have identified two essential techniques empirically that enable the fine-tuned model to synthesize stylized images in a stable manner. Firstly, unlike textual inversion [11] or Dream-" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 336, + 547, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 336, + 547, + 469 + ], + "spans": [ + { + "bbox": [ + 304, + 336, + 547, + 469 + ], + "type": "text", + "content": "Booth [49] which utilize only 3-5 images, fine-tuning with a larger set of shape renderings containing thousands of images helps the model capture the style more precisely. Secondly, fine-tuning Stable Diffusion using shape renderings with a pure-white background results in a chaotic and uncontrollable background during inference. However, augmenting the shape renderings with random solid-color backgrounds allows the fine-tuned model to synthesize images with solid-color backgrounds stably, making it easy to remove the background if necessary. Further details can be found in the supplementary material." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 478, + 388, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 478, + 388, + 491 + ], + "spans": [ + { + "bbox": [ + 306, + 478, + 388, + 491 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 498, + 545, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 593 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 593 + ], + "type": "text", + "content": "In this section, we evaluate the efficacy of our proposed text-to-3D synthesis framework. Initially, we compare our results with state-of-the-art techniques (Sec. 4.1). Subsequently, we demonstrate the effectiveness of our Stable-Diffusion-assisted approach for text-to-shape generation (Sec. 4.2). Furthermore, we conduct ablation studies to assess the effectiveness of critical components of our framework (Sec. 4.3)." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 594, + 546, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 546, + 677 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 546, + 677 + ], + "type": "text", + "content": "Dataset. Our framework requires only a set of textured 3D shapes for training the 3D shape generator " + }, + { + "bbox": [ + 304, + 594, + 546, + 677 + ], + "type": "inline_equation", + "content": "G_{S}" + }, + { + "bbox": [ + 304, + 594, + 546, + 677 + ], + "type": "text", + "content": ". Specifically, we employ 13 categories from ShapeNet [6] and utilize the data preprocessing procedure of Zheng et al. [67] to generate " + }, + { + "bbox": [ + 304, + 594, + 546, + 677 + ], + "type": "inline_equation", + "content": "128^{3}" + }, + { + "bbox": [ + 304, + 594, + 546, + 677 + ], + "type": "text", + "content": " SDF grids from the original meshes. During the fine-tuning of Stable Diffusion, we employ the SDF renderer [20] to produce a shape rendering dataset." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 677, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 714 + ], + "type": "text", + "content": "Implementation details. The 3D generator " + }, + { + "bbox": [ + 304, + 677, + 547, + 714 + ], + "type": "inline_equation", + "content": "G_{S}" + }, + { + "bbox": [ + 304, + 677, + 547, + 714 + ], + "type": "text", + "content": " utilizes the SDF-StyleGAN architecture. The diffusion-model-based shape embedding mapping network " + }, + { + "bbox": [ + 304, + 677, + 547, + 714 + ], + "type": "inline_equation", + "content": "G_{M}" + }, + { + "bbox": [ + 304, + 677, + 547, + 714 + ], + "type": "text", + "content": " is based on an" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20913" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 69, + 70, + 266, + 145 + ], + "blocks": [ + { + "bbox": [ + 69, + 70, + 266, + 145 + ], + "lines": [ + { + "bbox": [ + 69, + 70, + 266, + 145 + ], + "spans": [ + { + "bbox": [ + 69, + 70, + 266, + 145 + ], + "type": "table", + "html": "
MethodCLIP R-Precision ↑
ViT-B/32ViT-B/16
DreamFields [19]63.2492.65
CLIP-Mesh [22]75.0091.18
PureCLIPNeRF [24]73.5388.24
Ours w/o 3D prior75.4794.34
Ours85.2998.53
", + "image_path": "5c3558c05f9899d283a11020170badc5d3dfc2c8604b06f50d362bda9afbdf25.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 209, + 287, + 328 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 209, + 287, + 328 + ], + "spans": [ + { + "bbox": [ + 46, + 209, + 287, + 328 + ], + "type": "text", + "content": "open-source DALL-E 2 implementation. We train " + }, + { + "bbox": [ + 46, + 209, + 287, + 328 + ], + "type": "inline_equation", + "content": "G_{M}" + }, + { + "bbox": [ + 46, + 209, + 287, + 328 + ], + "type": "text", + "content": " by extracting image embeddings from shape renderings using the CLIP ViT-B/32 image encoder. The stylized text-to-image generator " + }, + { + "bbox": [ + 46, + 209, + 287, + 328 + ], + "type": "inline_equation", + "content": "G_{I}" + }, + { + "bbox": [ + 46, + 209, + 287, + 328 + ], + "type": "text", + "content": " is fine-tuned from Stable Diffusion v1.4. In the optimization stage, we set the learning rates for the density grid " + }, + { + "bbox": [ + 46, + 209, + 287, + 328 + ], + "type": "inline_equation", + "content": "V_{\\mathrm{density}}" + }, + { + "bbox": [ + 46, + 209, + 287, + 328 + ], + "type": "text", + "content": " and color MLP " + }, + { + "bbox": [ + 46, + 209, + 287, + 328 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{rgb}}" + }, + { + "bbox": [ + 46, + 209, + 287, + 328 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 209, + 287, + 328 + ], + "type": "inline_equation", + "content": "5 \\times 10^{-1}" + }, + { + "bbox": [ + 46, + 209, + 287, + 328 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 209, + 287, + 328 + ], + "type": "inline_equation", + "content": "5 \\times 10^{-3}" + }, + { + "bbox": [ + 46, + 209, + 287, + 328 + ], + "type": "text", + "content": " respectively, and we adopt the CLIP ViT-B/16 encoder as the guidance model. For each text prompt, we optimize for 5000 steps, while previous NeRF-based text-to-3D methods [19, 24] typically require 10000 steps or more." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 329, + 287, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 329, + 287, + 449 + ], + "spans": [ + { + "bbox": [ + 46, + 329, + 287, + 449 + ], + "type": "text", + "content": "Evaluation Metrics. Regarding the primary results of our framework, i.e., text-guided 3D content synthesis, we report the CLIP retrieval precision on a manually created dataset of diverse text prompts and objects. For specifics regarding the dataset, please refer to the supplementary material. This metric quantifies the percentage of generated images that the CLIP encoder associates with the correct text prompt used for generation. We utilize Fréchet Inception Distance (FID) [17] to evaluate the shape generation quality for the initial text-to-shape generation stage." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 458, + 192, + 471 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 458, + 192, + 471 + ], + "spans": [ + { + "bbox": [ + 47, + 458, + 192, + 471 + ], + "type": "text", + "content": "4.1. Text-Guided 3D Synthesis" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 476, + 287, + 572 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 476, + 287, + 572 + ], + "spans": [ + { + "bbox": [ + 46, + 476, + 287, + 572 + ], + "type": "text", + "content": "We compare our method with three state-of-the-art baseline methods on the task of text-guided 3D synthesis, i.e., DreamFields [19], CLIP-Mesh [22], and PureCLIPN-erF [24]. We conduct tests using the default settings and official implementations for all baseline methods. In particular, we utilize the medium-quality configuration of DreamFields and the implicit architecture variant of PureCLIPN-erF owing to its superior performance." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 573, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 573, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 573, + 287, + 693 + ], + "type": "text", + "content": "Time cost. Thanks to the shape prior initialization, our CLIP-guided optimization process exhibits significantly improved efficiency compared to previous NeRF-based methods. Dream3D optimizes for only 5000 steps within 25 minutes, while DreamFields and PureCLIPNeRF require more than 10000 steps, taking over an hour (measured on 1 A100 GPU). Training the 3D shape generator " + }, + { + "bbox": [ + 46, + 573, + 287, + 693 + ], + "type": "inline_equation", + "content": "G_{S}" + }, + { + "bbox": [ + 46, + 573, + 287, + 693 + ], + "type": "text", + "content": " takes 7 days on 4 A100 GPUs and training the shape embedding generation network " + }, + { + "bbox": [ + 46, + 573, + 287, + 693 + ], + "type": "inline_equation", + "content": "G_{M}" + }, + { + "bbox": [ + 46, + 573, + 287, + 693 + ], + "type": "text", + "content": " takes 1 day on 1 A100 GPU. It is worth noting that these models are only trained once and their inference" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 310, + 70, + 545, + 252 + ], + "blocks": [ + { + "bbox": [ + 310, + 70, + 545, + 252 + ], + "lines": [ + { + "bbox": [ + 310, + 70, + 545, + 252 + ], + "spans": [ + { + "bbox": [ + 310, + 70, + 545, + 252 + ], + "type": "image", + "image_path": "a5943730caa4e1f0d957ba4fe953225ef3fa2671eab2c8ff5a0e696a0fd9bbe3.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 258, + 545, + 302 + ], + "lines": [ + { + "bbox": [ + 305, + 258, + 545, + 302 + ], + "spans": [ + { + "bbox": [ + 305, + 258, + 545, + 302 + ], + "type": "text", + "content": "Figure 5. Text-guided 3D shape generation results. All the visualized meshes are extracted at the resolution of " + }, + { + "bbox": [ + 305, + 258, + 545, + 302 + ], + "type": "inline_equation", + "content": "64^{3}" + }, + { + "bbox": [ + 305, + 258, + 545, + 302 + ], + "type": "text", + "content": ". We can observe that our method can generate significantly more plausible 3D shapes benefitting from the high-quality 3D shape generator." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 362, + 308, + 488, + 365 + ], + "blocks": [ + { + "bbox": [ + 46, + 153, + 287, + 198 + ], + "lines": [ + { + "bbox": [ + 46, + 153, + 287, + 198 + ], + "spans": [ + { + "bbox": [ + 46, + 153, + 287, + 198 + ], + "type": "text", + "content": "Table 1. Quantitative comparison on Text-guided 3D synthesis. All methods employ CLIP ViT/16 as the guiding model for optimization, while two distinct CLIP models are utilized to compute the CLIP retrieval precision." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 362, + 308, + 488, + 365 + ], + "lines": [ + { + "bbox": [ + 362, + 308, + 488, + 365 + ], + "spans": [ + { + "bbox": [ + 362, + 308, + 488, + 365 + ], + "type": "table", + "html": "
MethodFID ↓
CLIP-Forge [51]112.38
Ours w/o text-to-image58.36
Ours w/o fine-tuning SD61.88
Ours40.83
", + "image_path": "6f5e614799fd13df9d0a4ba595ae7b782e7c2ab4ae49f1bee659947cfcb67fc1.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 369, + 545, + 392 + ], + "lines": [ + { + "bbox": [ + 305, + 369, + 545, + 392 + ], + "spans": [ + { + "bbox": [ + 305, + 369, + 545, + 392 + ], + "type": "text", + "content": "Table 2. Quantitative comparison on text-to-shape generation and ablation studies on the efficacy of fine-tuning Stable Diffusion." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 402, + 535, + 414 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 402, + 535, + 414 + ], + "spans": [ + { + "bbox": [ + 305, + 402, + 535, + 414 + ], + "type": "text", + "content": "time can be neglected compared to the optimization cost." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 415, + 545, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 415, + 545, + 593 + ], + "spans": [ + { + "bbox": [ + 304, + 415, + 545, + 593 + ], + "type": "text", + "content": "Quantitative Results. We report the CLIP retrieval precision metrics in Tab. 1. It is noteworthy that both the baseline methods and our approach utilize the CLIP ViT-B/16 encoder for optimization, and both the CLIP ViT-B/16 and CLIP ViT-B/32 encoders are employed as retrieval models. As Table Tab. 1 shows, our method achieves the highest CLIP R-Precision with both retrieval models. Moreover, our framework exhibits a significantly smaller performance gap between the two retrieval models compared to the baseline methods. By leveraging the 3D shape prior, our method initiates the optimization from a superior starting point, thereby mitigating the adversarial generation problem that prioritizes obtaining high CLIP scores while neglecting the visual quality. Consequently, our method demonstrates more robust performance across different CLIP models." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 594, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 714 + ], + "type": "text", + "content": "Qualitative Results. The qualitative comparison is presented in Fig. 4, indicating that the baseline methods [19, 22, 24] encounter challenges in generating precise and realistic 3D objects, resulting in distorted and unrealistic visuals. DreamFields' results are frequently blurry and diffuse, while PureCLIPNeRF tends to synthesize symmetric objects. CLIP-Mesh experiences difficulties in generating intricate visual effects due to its explicit mesh representation. In contrast, our method effectively generates higher-quality 3D structures by incorporating explicit 3D shape priors." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 57, + 702, + 276, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 702, + 276, + 712 + ], + "spans": [ + { + "bbox": [ + 57, + 702, + 276, + 712 + ], + "type": "text", + "content": "https://github.com/lucidrains/DALLE2-pytorch" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20914" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 191, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 191, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 191, + 85 + ], + "type": "text", + "content": "4.2. Text-to-Shape Generation" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 90, + 287, + 222 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 90, + 287, + 222 + ], + "spans": [ + { + "bbox": [ + 46, + 90, + 287, + 222 + ], + "type": "text", + "content": "The research on zero-shot text-to-shape generation is limited, and we compare our approach with CLIP-Forge [51] and measure the quality of shape generation using the Fréchet Inception Distance (FID). Specifically, we synthesize 3 shapes for each prompt from a dataset of 233 text prompts provided by CLIP-Forge. Then, we render 5 images for each synthesized shape and compare them to a set of ground truth ShapeNet renderings to compute the FID. The ground truth images are obtained by randomly choosing 200 shapes from the test set of each ShapeNet category and rendering 5 views for each shape." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 221, + 287, + 306 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 221, + 287, + 306 + ], + "spans": [ + { + "bbox": [ + 46, + 221, + 287, + 306 + ], + "type": "text", + "content": "As shown in Tab. 2, our approach achieves a lower FID than CLIP-Forge. CLIP-Forge employs a volumetric shape auto-encoder to generate 3D shapes. However, the qualitative results in Fig. 5 indicate poor shape generation capability, making it difficult to generate plausible 3D shapes. A high-quality 3D shape prior is also advantageous for the optimization process as an excellent initialization." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 312, + 148, + 324 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 312, + 148, + 324 + ], + "spans": [ + { + "bbox": [ + 47, + 312, + 148, + 324 + ], + "type": "text", + "content": "4.3. Ablation Studies" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 331, + 287, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 331, + 287, + 486 + ], + "spans": [ + { + "bbox": [ + 46, + 331, + 287, + 486 + ], + "type": "text", + "content": "Effectiveness of Fine-tuning Stable Diffusion. Our approach employs a fine-tuned Stable Diffusion to establish a connection between the text and image modalities. To evaluate its efficacy, we employ the original Stable Diffusion model to produce images from the text prompts of CLIP-Forge [51]. Subsequently, we employ these images to generate 3D shapes using the image-to-shape module. The results in the " + }, + { + "bbox": [ + 46, + 331, + 287, + 486 + ], + "type": "inline_equation", + "content": "3^{\\mathrm{rd}}" + }, + { + "bbox": [ + 46, + 331, + 287, + 486 + ], + "type": "text", + "content": " row of Tab. 2 indicate a decline in FID performance, suggesting that this approach would negatively impact the shape generation process. Furthermore, we directly test using text embedding to generate shape embeddings with " + }, + { + "bbox": [ + 46, + 331, + 287, + 486 + ], + "type": "inline_equation", + "content": "G_{M}" + }, + { + "bbox": [ + 46, + 331, + 287, + 486 + ], + "type": "text", + "content": ", which also leads to a decline in performance as seen in the " + }, + { + "bbox": [ + 46, + 331, + 287, + 486 + ], + "type": "inline_equation", + "content": "2^{\\mathrm{nd}}" + }, + { + "bbox": [ + 46, + 331, + 287, + 486 + ], + "type": "text", + "content": " row of Tab. 2." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 486, + 287, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 486, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 486, + 287, + 581 + ], + "type": "text", + "content": "Effectiveness of 3D Shape Prior. To validate the efficacy of the 3D shape prior, we eliminate the first stage of our framework and optimize from scratch using the same text prompts as presented in Sec. 4.1. Subsequently, we evaluate the CLIP retrieval precision. The outcomes presented in Tab. 1 indicate that optimizing without 3D shape prior results in a considerable decline in performance, thereby demonstrating its effectiveness." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "type": "text", + "content": "Effectiveness of " + }, + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{prior}}" + }, + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "type": "text", + "content": ". The 3D prior preserving loss " + }, + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{prior}}" + }, + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "type": "text", + "content": " shown in Eq. (3) aims to reinforce the 3D prior during the optimization process in case that the prior is gradually disturbed and discarded. To demonstrate its effectiveness, we synthesized \"a park bench\" as a prior for the prompt \"A park bench overgrown with vines\", and then optimize with and without " + }, + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{prior}}" + }, + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "type": "text", + "content": " and compared the results, which are visualized in Fig. 6. The results indicate that using " + }, + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{prior}}" + }, + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "type": "text", + "content": " during optimization helps maintain the structure of the 3D prior shape, while discarding it causes distortion and discontinuity artifacts, thereby disturbing the initial shape." + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 310, + 84, + 541, + 194 + ], + "blocks": [ + { + "bbox": [ + 402, + 73, + 520, + 83 + ], + "lines": [ + { + "bbox": [ + 402, + 73, + 520, + 83 + ], + "spans": [ + { + "bbox": [ + 402, + 73, + 520, + 83 + ], + "type": "text", + "content": "\"A park bench overgrown with vines\"" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 310, + 84, + 541, + 194 + ], + "lines": [ + { + "bbox": [ + 310, + 84, + 541, + 194 + ], + "spans": [ + { + "bbox": [ + 310, + 84, + 541, + 194 + ], + "type": "image", + "image_path": "e6c19593b239dc0ba9829ca87158caa7282160a0180f412d18a801588eec06f7.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 317, + 200, + 533, + 212 + ], + "lines": [ + { + "bbox": [ + 317, + 200, + 533, + 212 + ], + "spans": [ + { + "bbox": [ + 317, + 200, + 533, + 212 + ], + "type": "text", + "content": "Figure 6. The effect of the 3D prior preserving loss " + }, + { + "bbox": [ + 317, + 200, + 533, + 212 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{prior}" + }, + { + "bbox": [ + 317, + 200, + 533, + 212 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 220, + 473, + 232 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 220, + 473, + 232 + ], + "spans": [ + { + "bbox": [ + 305, + 220, + 473, + 232 + ], + "type": "text", + "content": "5. Limitations and Future Work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 240, + 545, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 240, + 545, + 384 + ], + "spans": [ + { + "bbox": [ + 304, + 240, + 545, + 384 + ], + "type": "text", + "content": "Our framework relies on a fine-tuned Stable Diffusion to generate rendering-style images. Despite its strong generation capability, Stable Diffusion may produce shape images that fall outside the distribution of the training data of the image-to-shape module. This is due to the fact that Stable Diffusion is trained on an internet-scale text-image dataset, whereas the 3D shape generator is trained on ShapeNet. Furthermore, the quality of text-to-shape synthesis in our framework is heavily reliant on the generation capability of the 3D generator. Our future work will explore incorporating stronger 3D priors into our framework to enable it to work with a wider range of object categories." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 384, + 545, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 384, + 545, + 456 + ], + "spans": [ + { + "bbox": [ + 304, + 384, + 545, + 456 + ], + "type": "text", + "content": "Additionally, our framework is indeed orthogonal to score distillation-based text-to-3D methods [30, 40, 57], as we can also utilize the score distillation sampling objective for optimization. We believe that incorporating 3D shape priors can enhance the quality and diversity of the generation results, as DreamFusion [40] acknowledged." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 466, + 378, + 479 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 466, + 378, + 479 + ], + "spans": [ + { + "bbox": [ + 306, + 466, + 378, + 479 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 486, + 545, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 545, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 545, + 617 + ], + "type": "text", + "content": "This paper introduces Dream3D, a text-to-3D synthesis framework that can generate diverse and imaginative 3D content from text prompts. Our approach incorporates explicit 3D shape priors into the CLIP-guided optimization process to generate more plausible 3D structures. To address the text-to-shape generation, we propose a straightforward yet effective method that utilizes a fine-tuned text-to-image diffusion model to bridge the text and image modalities. Our method is shown to generate 3D content with superior visual quality and shape accuracy compared to previous work, as demonstrated by extensive experiments." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 617, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 712 + ], + "type": "text", + "content": "Acknowledgements. The work was supported by National Key R&D Program of China (2018AAA0100704), NSFC #61932020, #62172279, Science and Technology Commission of Shanghai Municipality (Grant No. 20ZR1436000), Program of Shanghai Academic Research Leader, and \"Shuguang Program\" supported by Shanghai Education Development Foundation and Shanghai Municipal Education Commission." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "text", + "content": "20915" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "text", + "content": "[1] Jonathan T. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), pages 5826-5835, October 2021. 2" + } + ] + } + ], + "index": 19 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "20918" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/DreamBooth_ Fine Tuning Text-to-Image Diffusion Models for Subject-Driven Generation/88ef8e93-ceab-4a73-b104-1d6bfb6b0d91_content_list.json b/2023/DreamBooth_ Fine Tuning Text-to-Image Diffusion Models for Subject-Driven Generation/88ef8e93-ceab-4a73-b104-1d6bfb6b0d91_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..ed1c51152158abead8700ab60fee6867b8daaa48 --- /dev/null +++ b/2023/DreamBooth_ Fine Tuning Text-to-Image Diffusion Models for Subject-Driven Generation/88ef8e93-ceab-4a73-b104-1d6bfb6b0d91_content_list.json @@ -0,0 +1,1754 @@ +[ + { + "type": "text", + "text": "DreamBooth: Fine Tuning Text-to-Image Diffusion Models for Subject-Driven Generation", + "text_level": 1, + "bbox": [ + 187, + 107, + 782, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Nataniel Ruiz*,1,2 \nYael Pritch1", + "bbox": [ + 217, + 170, + 359, + 205 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yuanzhen Li1 \nMichael Rubinstein1", + "bbox": [ + 408, + 171, + 575, + 205 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Varun Jampani1 \nKfir Aberman1", + "bbox": [ + 622, + 171, + 750, + 205 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ Google Research $^{2}$ Boston University", + "bbox": [ + 321, + 205, + 648, + 224 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3442321aa9916391c47fc2cce204ded31b170d3b100a8c35bfd12ba7f58ba7d3.jpg", + "image_caption": [ + "Figure 1. With just a few images (typically 3-5) of a subject (left), *DreamBooth*—our AI-powered photo booth—can generate a myriad of images of the subject in different contexts (right), using the guidance of a text prompt. The results exhibit natural interactions with the environment, as well as novel articulations and variation in lighting conditions, all while maintaining high fidelity to the key visual features of the subject." + ], + "image_footnote": [], + "bbox": [ + 76, + 234, + 290, + 401 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/db94b4d58a34be658b4ffe1c46cf34d352cae9b7c985e53f66e083f3e19a108a.jpg", + "image_caption": [ + "in the Acropolis" + ], + "image_footnote": [], + "bbox": [ + 312, + 233, + 508, + 385 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c65e4b281aa64ea8777307936bec71f48063252d993246ee2eb990078adc2aba.jpg", + "image_caption": [ + "swimming" + ], + "image_footnote": [], + "bbox": [ + 511, + 233, + 599, + 303 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/771025a37b86c8c8a269c7b54575ab411ae18603601774881799581345a9f6b5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 509, + 315, + 601, + 401 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/68665b973ec6e05b150713e0602a32e2dd568c13e004243e2d8fa34a3c557a7c.jpg", + "image_caption": [ + "sleeping" + ], + "image_footnote": [], + "bbox": [ + 602, + 233, + 692, + 303 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4bc62c2fddc3e157f16cab6b44280a2bb833c24bbc44805b4f8ee3bd994dbccf.jpg", + "image_caption": [ + "in a bucket" + ], + "image_footnote": [], + "bbox": [ + 602, + 315, + 692, + 386 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/54b6954ef2d190902a0500691749d74ca5e964f4bc0a0dcebd5cb3de32b5d3d1.jpg", + "image_caption": [ + "getting a haircut" + ], + "image_footnote": [], + "bbox": [ + 694, + 233, + 890, + 385 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 479, + 313, + 494 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Large text-to-image models achieved a remarkable leap in the evolution of AI, enabling high-quality and diverse synthesis of images from a given text prompt. However, these models lack the ability to mimic the appearance of subjects in a given reference set and synthesize novel renditions of them in different contexts. In this work, we present a new approach for \"personalization\" of text-to-image diffusion models. Given as input just a few images of a subject, we fine-tune a pretrained text-to-image model such that it learns to bind a unique identifier with that specific subject. Once the subject is embedded in the output domain of the model, the unique identifier can be used to synthesize novel photorealistic images of the subject contextualized in different scenes. By leveraging the semantic prior embedded in the model with a new autogenous class-specific prior preservation loss, our technique enables synthesizing the subject in diverse scenes, poses, views and lighting conditions that do not appear in the reference images. We apply our technique to several previously-unassailable tasks, including subject recontextualization, text-guided view synthesis, and artistic rendering, all while preserving the subject's key features. We also provide a new dataset and evaluation protocol for this new task of subject-driven generation. Project page: https://dreambooth.github.io/", + "bbox": [ + 73, + 510, + 473, + 875 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 501, + 523, + 630, + 539 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Can you imagine your own dog traveling around the world, or your favorite bag displayed in the most exclusive showroom in Paris? What about your parrot being the main character of an illustrated storybook? Rendering such imaginary scenes is a challenging task that requires synthesizing instances of specific subjects (e.g., objects, animals) in new contexts such that they naturally and seamlessly blend into the scene.", + "bbox": [ + 496, + 549, + 890, + 667 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently developed large text-to-image models have shown unprecedented capabilities, by enabling high-quality and diverse synthesis of images based on a text prompt written in natural language [51,58]. One of the main advantages of such models is the strong semantic prior learned from a large collection of image-caption pairs. Such a prior learns, for instance, to bind the word \"dog\" with various instances of dogs that can appear in different poses and contexts in an image. While the synthesis capabilities of these models are unprecedented, they lack the ability to mimic the appearance of subjects in a given reference set, and synthesize novel renditions of the same subjects in different contexts. The main reason is that the expressiveness of their output domain is limited; even the most detailed textual description of an object may yield instances with different appearances.", + "bbox": [ + 496, + 670, + 892, + 897 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*This research was performed while Nataniel Ruiz was at Google.", + "bbox": [ + 106, + 886, + 457, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "22500", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Furthermore, even models whose text embedding lies in a shared language-vision space [50] cannot accurately reconstruct the appearance of given subjects but only create variations of the image content (Figure 2).", + "bbox": [ + 75, + 90, + 468, + 151 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we present a new approach for \"personalization\" of text-to-image diffusion models (adapting them to user-specific image generation needs). Our goal is to expand the language-vision dictionary of the model such that it binds new words with specific subjects the user wants to generate. Once the new dictionary is embedded in the model, it can use these words to synthesize novel photorealistic images of the subject, contextualized in different scenes, while preserving their key identifying features. The effect is akin to a \"magic photo booth\"—once a few images of the subject are taken, the booth generates photos of the subject in different conditions and scenes, as guided by simple and intuitive text prompts (Figure 1).", + "bbox": [ + 75, + 152, + 470, + 347 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "More formally, given a few images of a subject ( $\\sim 3-5$ ), our objective is to implant the subject into the output domain of the model such that it can be synthesized with a unique identifier. To that end, we propose a technique to represent a given subject with rare token identifiers and fine-tune a pre-trained, diffusion-based text-to-image framework.", + "bbox": [ + 75, + 347, + 468, + 450 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We fine-tune the text-to-image model with the input images and text prompts containing a unique identifier followed by the class name of the subject (e.g., \"A [V] dog\"). The latter enables the model to use its prior knowledge on the subject class while the class-specific instance is bound with the unique identifier. In order to prevent language drift [32, 38] that causes the model to associate the class name (e.g., \"dog\") with the specific instance, we propose an autogenous, class-specific prior preservation loss, which leverages the semantic prior on the class that is embedded in the model, and encourages it to generate diverse instances of the same class as our subject.", + "bbox": [ + 75, + 453, + 468, + 633 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We apply our approach to a myriad of text-based image generation applications including recontextualization of subjects, modification of their properties, original art renditions, and more, paving the way to a new stream of previously unassailable tasks. We highlight the contribution of each component in our method via ablation studies, and compare with alternative baselines and related work. We also conduct a user study to evaluate subject and prompt fidelity in our synthesized images, compared to alternative approaches.", + "bbox": [ + 75, + 633, + 468, + 785 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To the best of our knowledge, ours is the first technique that tackles this new challenging problem of subject-driven generation, allowing users, from just a few casually captured images of a subject, synthesize novel renditions of the subject in different contexts while maintaining its distinctive features.", + "bbox": [ + 75, + 785, + 468, + 875 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To evaluate this new task, we also construct a new dataset", + "bbox": [ + 96, + 876, + 468, + 891 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/c3c53d6f4cd1fba09cbf2caaa7c804cc71abc99fa0e4518b52a7fe09ab265c45.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 521, + 90, + 676, + 167 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/4f53552b3939b88c44a0919c428583283856e60d524e02f3bd19eb6a4a09f13f.jpg", + "image_caption": [ + "Input Images" + ], + "image_footnote": [], + "bbox": [ + 532, + 169, + 676, + 224 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/130b008d17545087bb94eb3e6d76948c9f35c35f12bb2fecc8387d3bbbb67a77.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 692, + 90, + 763, + 160 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/5731f5f93b4025c60645f4d8077768cfd21ff3d45731f041b3738e86f26866d7.jpg", + "image_caption": [ + "Image-guided, DALL-E2" + ], + "image_footnote": [], + "bbox": [ + 707, + 160, + 815, + 224 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/94bea41ded2188391e42ca3530a2c314b39985ee3e69c61d7752d71e27025485.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 844, + 107, + 864, + 133 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/379e3d99f0e9e7f2003d45b828ba516c2219ba93b61f5ee89739bb5f0c07bbf4.jpg", + "image_caption": [ + "Text-guided, Imagen", + "Figure 2. Subject-driven generation. Given a particular clock (left), it is hard to generate it while maintaining high fidelity to its key visual features (second and third columns showing DALL-E2 [51] image-guided generation andImagen [58] text-guided generation; text prompt used forImagen: \"retro style yellow alarm clock with a white clock face and a yellow number three on the right part of the clock face in the jungle\"). Our approach (right) can synthesize the clock with high fidelity and in new contexts (text prompt: \"a $[V]$ clock in the jungle\")." + ], + "image_footnote": [], + "bbox": [ + 519, + 247, + 694, + 382 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/0bbf76bf092e8ddcf7fac6b8ad3c166e239d6e4ddcc8ca4339003f64d9a67ad1.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 697, + 247, + 869, + 382 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "that contains various subjects captured in different contexts, and propose a new evaluation protocol that measures the subject fidelity and prompt fidelity of the generated results. We make our dataset and evaluation protocol publicly available on the project webpage", + "bbox": [ + 498, + 542, + 890, + 619 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 500, + 632, + 635, + 647 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Image Composition. Image composition techniques [13, 36, 67] aim to clone a given subject into a new background such that the subject melds into the scene. To consider composition in novel poses, one may apply 3D reconstruction techniques [6, 8, 39, 47, 65] which usually works on rigid objects and require a larger number of views. Some drawbacks include scene integration (lighting, shadows, contact) and the inability to generate novel scenes. In contrast, our approach enables generation of subjects in novel poses and new contexts.", + "bbox": [ + 498, + 657, + 890, + 808 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Text-to-Image Editing and Synthesis. Text-driven image manipulation has recently achieved significant progress using GANs [9, 22, 27-29] combined with image-text representations such as CLIP [50], yielding realistic manipulations using text [2, 7, 21, 41, 46, 68]. These methods work well on structured scenarios (e.g. human face edit", + "bbox": [ + 498, + 809, + 890, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "22501", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ing) and can struggle over diverse datasets where subjects are varied. Crowson et al. [14] use VQ-GAN [18] and train over more diverse data to alleviate this concern. Other works [4, 30] exploit the recent diffusion models [25, 25, 43, 55, 57, 59–63], which achieve state-of-the-art generation quality over highly diverse datasets, often surpassing GANs [15]. While most works that require only text are limited to global editing [14, 31], Bar-Tal et al. [5] proposed a text-based localized editing technique without using masks, showing impressive results. While most of these editing approaches allow modification of global properties or local editing of a given image, none enables generating novel renditions of a given subject in new contexts.", + "bbox": [ + 75, + 90, + 472, + 287 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "There also exists work on text-to-image synthesis [14, 16, 19, 24, 26, 33, 34, 48, 49, 52, 55, 64, 71]. Recent large text-to-image models such asImagen [58], DALL-E2 [51], Parti [69], CogView2 [17] and Stable Diffusion [55] demonstrated unprecedented semantic generation. These models do not provide fine-grained control over a generated image and use text guidance only. Specifically, it is challenging or impossible to preserve the identity of a subject consistently across synthesized images.", + "bbox": [ + 75, + 287, + 472, + 422 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Controllable Generative Models. There are various approaches to control generative models, where some of them might prove to be viable directions for subject-driven prompt-guided image synthesis. Liu et al. [37] propose a diffusion-based technique allowing for image variations guided by reference image or text. To overcome subject modification, several works [3, 42] assume a user-provided mask to restrict the modified area. Inversion [12, 15, 51] can be used to preserve a subject while modifying context. Prompt-to-prompt [23] allows for local and global editing without an input mask. These methods fall short of identity-preserving novel sample generation of a subject.", + "bbox": [ + 75, + 422, + 472, + 604 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the context of GANs, Pivotal Tuning [54] allows for real image editing by finetuning the model with an inverted latent code anchor, and Nitzan et al. [44] extended this work to GAN finetuning on faces to train a personalized prior, which requires around 100 images and are limited to the face domain. Casanova et al. [11] propose an instance conditioned GAN that can generate variations of an instance, although it can struggle with unique subjects and does not preserve all subject details.", + "bbox": [ + 75, + 604, + 472, + 739 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Finally, the concurrent work of Gal et al. [20] proposes a method to represent visual concepts, like an object or a style, through new tokens in the embedding space of a frozen text-to-image model, resulting in small personalized token embeddings. While this method is limited by the expressiveness of the frozen diffusion model, our fine-tuning approach enables us to embed the subject within the model's output domain, resulting in the generation of novel images of the subject which preserve its key visual features.", + "bbox": [ + 75, + 739, + 472, + 877 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 498, + 89, + 591, + 106 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given only a few (typically 3-5) casually captured images of a specific subject, without any textual description, our objective is to generate new images of the subject with high detail fidelity and with variations guided by text prompts. Example variations include changing the subject location, changing subject properties such as color or shape, modifying the subject's pose, viewpoint, and other semantic modifications. We do not impose any restrictions on input image capture settings and the subject image can have varying contexts. We next provide some background on text-to-image diffusion models (Sec. 3.1), then present our finetuning technique to bind a unique identifier with a subject described in a few images (Sec. 3.2), and finally propose a class-specific prior-preservation loss that enables us to overcome language drift in our fine-tuned model (Sec. 3.3).", + "bbox": [ + 496, + 114, + 893, + 343 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Text-to-Image Diffusion Models", + "text_level": 1, + "bbox": [ + 498, + 349, + 782, + 367 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Diffusion models are probabilistic generative models that are trained to learn a data distribution by the gradual denoising of a variable sampled from a Gaussian distribution. Specifically, we are interested in a pre-trained text-to-image diffusion model $\\hat{\\mathbf{x}}_{\\theta}$ that, given an initial noise map $\\epsilon \\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})$ and a conditioning vector $\\mathbf{c} = \\Gamma (\\mathbf{P})$ generated using a text encoder $\\Gamma$ and a text prompt $\\mathbf{P}$ , generates an image $\\mathbf{x}_{\\mathrm{gen}} = \\hat{\\mathbf{x}}_{\\theta}(\\epsilon ,\\mathbf{c})$ . They are trained using a squared error loss to denoise a variably-noised image or latent code $\\mathbf{z}_t\\coloneqq \\alpha_t\\mathbf{x} + \\sigma_t\\boldsymbol {\\epsilon}$ as follows:", + "bbox": [ + 496, + 375, + 893, + 526 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbb {E} _ {\\mathbf {x}, \\mathbf {c}, \\boldsymbol {\\epsilon}, t} \\left[ w _ {t} \\| \\hat {\\mathbf {x}} _ {\\theta} \\left(\\alpha_ {t} \\mathbf {x} + \\sigma_ {t} \\boldsymbol {\\epsilon}, \\mathbf {c}\\right) - \\mathbf {x} \\| _ {2} ^ {2} \\right] \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 536, + 890, + 556 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{x}$ is the ground-truth image, $\\mathbf{c}$ is a conditioning vector (e.g., obtained from a text prompt), and $\\alpha_{t},\\sigma_{t},w_{t}$ are terms that control the noise schedule and sample quality, and are functions of the diffusion process time $t\\sim$ $\\mathcal{U}([0,1])$ . A more detailed description is given in the supplementary material.", + "bbox": [ + 496, + 565, + 893, + 656 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Personalization of Text-to-Image Models", + "text_level": 1, + "bbox": [ + 498, + 665, + 848, + 681 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our first task is to implant the subject instance into the output domain of the model such that we can query the model for varied novel images of the subject. One natural idea is to fine-tune the model using the few-shot dataset of the subject. Careful care had to be taken when fine-tuning generative models such as GANs in a few-shot scenario as it can cause overfitting and mode-collapse - as well as not capturing the target distribution sufficiently well. There has been research on techniques to avoid these pitfalls [35,40,45,53,66], although, in contrast to our work, this line of work primarily seeks to generate images that resemble the target distribution but has no requirement of subject preservation. With regards to these pitfalls, we observe the peculiar finding that, given a careful fine-tuning setup", + "bbox": [ + 496, + 688, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "22502", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/c7cbf436cc0d1aa70e98add5bfad489037acca707374c036cea8b4ac6f10c08f.jpg", + "image_caption": [ + "Figure 3. Fine-tuning. Given $\\sim 3 - 5$ images of a subject we fine-tune a text-to-image diffusion model with the input images paired with a text prompt containing a unique identifier and the name of the class the subject belongs to (e.g., \"A [V] dog\"), in parallel, we apply a class-specific prior preservation loss, which leverages the semantic prior that the model has on the class and encourages it to generate diverse instances belong to the subject's class using the class name in a text prompt (e.g., \"A dog\")." + ], + "image_footnote": [], + "bbox": [ + 86, + 89, + 460, + 324 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "using the diffusion loss from Eq 1, large text-to-image diffusion models seem to excel at integrating new information into their domain without forgetting the prior or overfitting to a small set of training images.", + "bbox": [ + 75, + 455, + 468, + 517 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Designing Prompts for Few-Shot Personalization Our goal is to \"implant\" a new (unique identifier, subject) pair into the diffusion model's \"dictionary\". In order to bypass the overhead of writing detailed image descriptions for a given image set we opt for a simpler approach and label all input images of the subject \"a [identifier] [class noun]\", where [identifier] is a unique identifier linked to the subject and [class noun] is a coarse class descriptor of the subject (e.g. cat, dog, watch, etc.). The class descriptor can be provided by the user or obtained using a classifier. We use a class descriptor in the sentence in order to tether the prior of the class to our unique subject and find that using a wrong class descriptor, or no class descriptor increases training time and language drift while decreasing performance. In essence, we seek to leverage the model's prior of the specific class and entangle it with the embedding of our subject's unique identifier so we can leverage the visual prior to generate new poses and articulations of the subject in different contexts.", + "bbox": [ + 75, + 534, + 468, + 821 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Rare-token Identifiers We generally find existing English words (e.g. \"unique\", \"special\") suboptimal since the model has to learn to disentangle them from their original meaning and to re-entangle them to reference our subject.", + "bbox": [ + 75, + 839, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This motivates the need for an identifier that has a weak prior in both the language model and the diffusion model. A hazardous way of doing this is to select random characters in the English language and concatenate them to generate a rare identifier (e.g. \"xxy5syt00\"). In reality, the tokenizer might tokenize each letter separately, and the prior for the diffusion model is strong for these letters. We often find that these tokens incur the similar weaknesses as using common English words. Our approach is to find rare tokens in the vocabulary, and then invert these tokens into text space, in order to minimize the probability of the identifier having a strong prior. We perform a rare-token lookup in the vocabulary and obtain a sequence of rare token identifiers $f(\\hat{\\mathbf{V}})$ , where $f$ is a tokenizer; a function that maps character sequences to tokens and $\\hat{\\mathbf{V}}$ is the decoded text stemming from the tokens $f(\\hat{\\mathbf{V}})$ . The sequence can be of variable length $k$ , and find that relatively short sequences of $k = \\{1, \\dots, 3\\}$ work well. Then, by inverting the vocabulary using the tokenizer on $f(\\hat{\\mathbf{V}})$ we obtain a sequence of characters that define our unique identifier $\\hat{\\mathbf{V}}$ . For Imagen, we find that using uniform random sampling of tokens that correspond to 3 or fewer Unicode characters (without spaces) and using tokens in the T5-XXL tokenizer range of $\\{5000, \\dots, 10000\\}$ works well.", + "bbox": [ + 496, + 90, + 893, + 455 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Class-specific Prior Preservation Loss", + "text_level": 1, + "bbox": [ + 500, + 464, + 825, + 479 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In our experience, the best results for maximum subject fidelity are achieved by fine-tuning all layers of the model. This includes fine-tuning layers that are conditioned on the text embeddings, which gives rise to the problem of language drift. Language drift has been an observed problem in language models [32, 38], where a model that is pre-trained on a large text corpus and later fine-tuned for a specific task progressively loses syntactic and semantic knowledge of the language. To the best of our knowledge, we are the first to find a similar phenomenon affecting diffusion models, where to model slowly forgets how to generate subjects of the same class as the target subject.", + "bbox": [ + 496, + 487, + 890, + 667 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Another problem is the possibility of reduced output diversity. Text-to-image diffusion models naturally possess high amounts of output diversity. When fine-tuning on a small set of images we would like to be able to generate the subject in novel viewpoints, poses and articulations. Yet, there is a risk of reducing the amount of variability in the output poses and views of the subject (e.g. snapping to the few-shot views). We observe that this is often the case, especially when the model is trained for too long.", + "bbox": [ + 496, + 667, + 890, + 804 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To mitigate the two aforementioned issues, we propose an autogenous class-specific prior preservation loss that encourages diversity and counters language drift. In essence, our method is to supervise the model with its own generated samples, in order for it to retain the prior once the few-shot fine-tuning begins. This allows it to generate di", + "bbox": [ + 496, + 805, + 890, + 896 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "22503", + "bbox": [ + 478, + 944, + 517, + 957 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "verse images of the class prior, as well as retain knowledge about the class prior that it can use in conjunction with knowledge about the subject instance. Specifically, we generate data $\\mathbf{x}_{\\mathrm{pr}} = \\hat{\\mathbf{x}} (\\mathbf{z}_{t_1},\\mathbf{c}_{\\mathrm{pr}})$ by using the ancestral sampler on the frozen pre-trained diffusion model with random initial noise $\\mathbf{z}_{t_1}\\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})$ and conditioning vector $\\mathbf{c}_{\\mathrm{pr}}\\coloneqq \\Gamma (f(\"a[class~noun]^\")$ ). The loss becomes:", + "bbox": [ + 75, + 90, + 472, + 198 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathbb {E} _ {\\mathbf {x}, \\mathbf {c}, \\epsilon , \\epsilon^ {\\prime}, t} [ w _ {t} \\| \\hat {\\mathbf {x}} _ {\\theta} (\\alpha_ {t} \\mathbf {x} + \\sigma_ {t} \\epsilon , \\mathbf {c}) - \\mathbf {x} \\| _ {2} ^ {2} + \\\\ \\lambda w _ {t ^ {\\prime}} \\| \\hat {\\mathbf {x}} _ {\\theta} \\left(\\alpha_ {t ^ {\\prime}} \\mathbf {x} _ {\\mathrm {p r}} + \\sigma_ {t ^ {\\prime}} \\boldsymbol {\\epsilon} ^ {\\prime}, \\mathbf {c} _ {\\mathrm {p r}}\\right) - \\mathbf {x} _ {\\mathrm {p r}} \\| _ {2} ^ {2} ], \\tag {2} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 209, + 468, + 248 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where the second term is the prior-preservation term that supervises the model with its own generated images, and $\\lambda$ controls for the relative weight of this term. Figure 3 illustrates the model fine-tuning with the class-generated samples and prior-preservation loss. Despite being simple, we find this prior-preservation loss is effective in encouraging output diversity and in overcoming language-drift. We also find that we can train the model for more iterations without risking overfitting. We find that $\\sim 1000$ iterations with $\\lambda = 1$ and learning rate $10^{-5}$ for Imagen [58] and $5 \\times 10^{-6}$ for Stable Diffusion [56], and with a subject dataset size of 3-5 images is enough to achieve good results. During this process, $\\sim 1000$ \"a [class noun]\" samples are generated - but less can be used. The training process takes about 5 minutes on one TPUv4 for Imagen, and 5 minutes on a NVIDIA A100 for Stable Diffusion.", + "bbox": [ + 75, + 256, + 472, + 498 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 511, + 209, + 527 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we show experiments and applications. Our method enables a large expanse of text-guided semantic modifications of our subject instances, including recontextualization, modification of subject properties such as material and species, art rendition, and viewpoint modification. Importantly, across all of these modifications, we are able to preserve the unique visual features that give the subject its identity and essence. If the task is recontextualization, then the subject features are unmodified, but appearance (e.g., pose) may change. If the task is a stronger semantic modification, such as crossing between our subject and another species/object, then the key features of the subject are preserved after modification. In this section, we reference the subject's unique identifier using [V]. We include specific Imagen and Stable Diffusion implementation details in the supp. material.", + "bbox": [ + 75, + 536, + 472, + 779 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Dataset and Evaluation", + "text_level": 1, + "bbox": [ + 76, + 786, + 294, + 801 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Dataset We collected a dataset of 30 subjects, including unique objects and pets such as backpacks, stuffed animals, dogs, cats, sunglasses, cartoons, etc. Images for this dataset were collected by the authors or sourced from Unsplash [1]. We also collected 25 prompts: 20 recontextualization prompts and 5 property modification prompts for", + "bbox": [ + 75, + 809, + 470, + 902 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/aee47dcdbc8578c305dc5eef0fd1db433b1e948bace2ee720a996d17b7989565.jpg", + "image_caption": [ + "Figure 4. Comparisons with Textual Inversion [20] Given 4 input images (top row), we compare: DreamBooth Imagen (2nd row), DreamBooth Stable Diffusion (3rd row), Textual Inversion (bottom row). Output images were created with the following prompts (left to right): \"a [V] vase in the snow\", \"a [V] vase on the beach\", \"a [V] vase in the jungle\", \"a [V] vase with the Eiffel Tower in the background\". DreamBooth is stronger in both subject and prompt fidelity." + ], + "image_footnote": [], + "bbox": [ + 498, + 90, + 893, + 449 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/9bd692d75b87c6322067639d9ebc38daea7d23fec65d1259171d928787646d2f.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodDINO ↑CLIP-I ↑CLIP-T ↑
Real Images0.7740.885N/A
DreamBooth (Imagen)0.6960.8120.306
DreamBooth (Stable Diffusion)0.6680.8030.305
Textual Inversion (Stable Diffusion)0.5690.7800.255
", + "bbox": [ + 503, + 583, + 890, + 657 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/b0834702315f42c42c1cb7107c7deb977068e1badc19e2cf61a5cb2559046a6e.jpg", + "table_caption": [ + "Table 1. Subject fidelity (DINO, CLIP-I) and prompt fidelity (CLIP-T, CLIP-T-L) quantitative metric comparison." + ], + "table_footnote": [], + "table_body": "
MethodSubject Fidelity ↑Prompt Fidelity ↑
DreamBooth (Stable Diffusion)68%81%
Textual Inversion (Stable Diffusion)22%12%
Undecided10%7%
", + "bbox": [ + 503, + 708, + 890, + 767 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 2. Subject fidelity and prompt fidelity user preference.", + "bbox": [ + 511, + 776, + 872, + 791 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "objects; 10 recontextualization, 10 accessorization, and 5 property modification prompts for live subjects/pets. The full list of images and prompts can be found in the supplementary material.", + "bbox": [ + 496, + 804, + 890, + 864 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For the evaluation suite we generate four images per subject and per prompt, totaling 3,000 images. This allows us", + "bbox": [ + 496, + 864, + 890, + 896 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "22504", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/28aff1ddc51eaa78fd4f9fb02089d0ffc1b9468019c019d73ef36bf019786bc6.jpg", + "image_caption": [ + "Input images" + ], + "image_footnote": [], + "bbox": [ + 83, + 104, + 462, + 178 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/07f9b84995d19538c736a6d37bbf5651126517d6612c658c810995d118884b96.jpg", + "image_caption": [ + "w/o prior-preservation loss" + ], + "image_footnote": [], + "bbox": [ + 83, + 196, + 462, + 268 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2f20582f418d00e378dd860aa844384e8bb48376219093cb58f51b3d88201c95.jpg", + "image_caption": [ + "with prior-preservation loss", + "Figure 5. Encouraging diversity with prior-preservation loss. Naive fine-tuning can result in overfitting to input image context and subject appearance (e.g. pose). PPL acts as a regularizer that alleviates overfitting and encourages diversity, allowing for more pose variability and appearance diversity." + ], + "image_footnote": [], + "bbox": [ + 83, + 287, + 462, + 359 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "to robustly measure performances and generalization capabilities of a method. We make our dataset and evaluation protocol publicly available on the project webpage for future use in evaluating subject-driven generation.", + "bbox": [ + 75, + 455, + 468, + 515 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation Metrics One important aspect to evaluate is subject fidelity: the preservation of subject details in generated images. For this, we compute two metrics: CLIP-I and DINO [10]. CLIP-I is the average pairwise cosine similarity between CLIP [50] embeddings of generated and real images. Although this metric has been used in other work [20], it is not constructed to distinguish between different subjects that could have highly similar text descriptions (e.g. two different yellow clocks). Our proposed DINO metric is the average pairwise cosine similarity between the ViT-S/16 DINO embeddings of generated and real images. This is our preferred metric, since, by construction and in contrast to supervised networks, DINO is not trained to ignore differences between subjects of the same class. Instead, the self-supervised training objective encourages distinction of unique features of a subject or image. The second important aspect to evaluate is prompt fidelity, measured as the average cosine similarity between prompt and image CLIP embeddings. We denote this as CLIP-T.", + "bbox": [ + 75, + 534, + 468, + 820 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Comparisons", + "text_level": 1, + "bbox": [ + 76, + 830, + 215, + 845 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare our results with Textual Inversion, the recent concurrent work of Gal et al. [20], using the hyperparameters provided in their work. We find that this work is", + "bbox": [ + 75, + 853, + 468, + 897 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "the only comparable work in the literature that is subject-driven, text-guided and generates novel images. We generate images for DreamBooth using Imagen, DreamBooth using Stable Diffusion and Textual Inversion using Stable Diffusion. We compute DINO and CLIP-I subject fidelity metrics and the CLIP-T prompt fidelity metric. In Table 1 we show sizeable gaps in both subject and prompt fidelity metrics for DreamBooth over Textual Inversion. We find that DreamBooth (Imagen) achieves higher scores for both subject and prompt fidelity than DreamBooth (Stable Diffusion), approaching the upper-bound of subject fidelity for real images. We believe that this is due to the larger expressive power and higher output quality of Imagen.", + "bbox": [ + 496, + 90, + 890, + 286 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Further, we compare Textual Inversion (Stable Diffusion) and DreamBooth (Stable Diffusion) by conducting a user study. For subject fidelity, we asked 72 users to answer questionnaires of 25 comparative questions (3 users per questionnaire), totaling 1800 answers. Samples are randomly selected from a large pool. Each question shows the set of real images for a subject, and one generated image of that subject by each method (with a random prompt). Users are asked to answer the question: \"Which of the two images best reproduces the identity (e.g. item type and details) of the reference item?\", and we include a \"Cannot Determine / Both Equally\" option. Similarly for prompt fidelity, we ask \"Which of the two images is best described by the reference text?\". We average results using majority voting and present them in Table 2. We find an overwhelming preference for DreamBooth for both subject fidelity and prompt fidelity. This shines a light on results in Table 1, where DINO differences of around 0.1 and CLIP-T differences of 0.05 are significant in terms of user preference. Finally, we show qualitative comparisons in Figure 4. We observe that DreamBooth better preserves subject identity, and is more faithful to prompts. We show samples of the user study in the supp. material.", + "bbox": [ + 496, + 287, + 892, + 633 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Ablation Studies", + "text_level": 1, + "bbox": [ + 500, + 643, + 663, + 657 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Prior Preservation Loss Ablation We fine-tune Imagen on 15 subjects from our dataset, with and without our proposed prior preservation loss (PPL). The prior preservation loss seeks to combat language drift and preserve the prior. We compute a prior preservation metric (PRES) by computing the average pairwise DINO embeddings between generated images of random subjects of the prior class and real images of our specific subject. The higher this metric, the more similar random subjects of the class are to our specific subject, indicating collapse of the prior. We report results in Table 3 and observe that PPL substantially counteracts language drift and helps retain the ability to generate diverse images of the prior class. Additionally, we compute a diversity metric (DIV) using the average LPIPS [70] cosine similarity between generated images of same subject with", + "bbox": [ + 496, + 667, + 890, + 893 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "22505", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/902a65ada13ea4e80f72741a1a6edc2b76124b42e5e6c30da35e229d945a52ae.jpg", + "image_caption": [ + "Input images" + ], + "image_footnote": [], + "bbox": [ + 76, + 95, + 233, + 215 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/47b34d7771a57259b777df8a2791913fd0a23663824dd0f892ea3bcd2e714600.jpg", + "image_caption": [ + "A [V] backpack in the Grand Canyon" + ], + "image_footnote": [], + "bbox": [ + 246, + 95, + 406, + 215 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/bd605973e071ac6ab47b404ffe26539de65d48bfb54af04cd42122b5394f6c59.jpg", + "image_caption": [ + "A wet [V] backpack in water" + ], + "image_footnote": [], + "bbox": [ + 408, + 95, + 566, + 217 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f98da00597c135ed579552b0cd08735a5526e95fd39394aa8c812d3c4d15b04a.jpg", + "image_caption": [ + "A [V] backpack in Boston" + ], + "image_footnote": [], + "bbox": [ + 570, + 95, + 725, + 217 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4ff637ebbb0e5affcbe4f1bc39afae2e09993711ceb5d478d0ed6854fa2ee812.jpg", + "image_caption": [ + "A [V] backpack with the night sky" + ], + "image_footnote": [], + "bbox": [ + 730, + 95, + 885, + 217 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2bb0c349ac60d94a375a342173e96ef3daea128399eaed43d23f31d5aa8cadfb.jpg", + "image_caption": [ + "Input images" + ], + "image_footnote": [], + "bbox": [ + 76, + 244, + 233, + 364 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/59752e2bc7139db6ad6226c3e9cf6f84ec57b6783eddb1f89746f9668e542227.jpg", + "image_caption": [ + "A [V] teapot floating in milk" + ], + "image_footnote": [], + "bbox": [ + 248, + 244, + 406, + 366 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/62c33ac8c97ae3822790092b16e4b24f0871e9cd3a4d5f4918706e0cc30f5ed2.jpg", + "image_caption": [ + "A transparent [V] teapot with milk inside" + ], + "image_footnote": [], + "bbox": [ + 410, + 244, + 566, + 366 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a8e847849a70957febeaee0ea23ac6edaa4a22ca110c7404481b8ba8e662feea.jpg", + "image_caption": [ + "A [V] teapot pouring tea" + ], + "image_footnote": [], + "bbox": [ + 570, + 244, + 725, + 364 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/35d2250ce44be635e3ca43866f470d433e5c8be908eea4236fe1b6f31383b058.jpg", + "image_caption": [ + "A [V] teapot floating in the sea", + "Figure 6. Recontextualization. We generate images of the subjects in different environments, with high preservation of subject details and realistic scene-subject interactions. We show the prompts below each image." + ], + "image_footnote": [], + "bbox": [ + 730, + 244, + 885, + 366 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/5031f4e67780663af0f5ca27612c3374a0da99fb45ba3e4345c8222a47743d7e.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodPRES ↓DIV ↑DINO ↑CLIP-I ↑CLIP-T ↑
DreamBooth (Imagen) w/ PPL0.4930.3910.6840.8150.308
DreamBooth (Imagen)0.6640.3710.7120.8280.306
", + "bbox": [ + 78, + 445, + 467, + 487 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/6155da281f7776c774237553169bea4aad5e2d7deddeaf22e14ce8c4909d2192.jpg", + "table_caption": [ + "Table 3. Prior preservation loss (PPL) ablation displaying a prior preservation (PRES) metric, diversity metric (DIV) and subject and prompt fidelity metrics." + ], + "table_footnote": [], + "table_body": "
MethodDINO ↑CLIP-I ↑
Correct Class0.7440.853
No Class0.3030.607
Wrong Class0.4540.728
", + "bbox": [ + 176, + 553, + 369, + 611 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4. Class name ablation with subject fidelity metrics.", + "bbox": [ + 94, + 622, + 439, + 636 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "same prompt. We observe that our model trained with PPL achieves higher diversity (with slightly diminished subject fidelity), which can also be observed qualitatively in Figure 5, where our model trained with PPL overfits less to the environment of the reference images and can generate the dog in more diverse poses and articulations.", + "bbox": [ + 75, + 647, + 468, + 738 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Class-Prior Ablation We finetune Imagen on a subset of our dataset subjects (5 subjects) with no class noun, a randomly sampled incorrect class noun, and the correct class noun. With the correct class noun for our subject, we are able to faithfully fit to the subject, take advantage of the class prior, allowing us to generate our subject in various contexts. When an incorrect class noun (e.g. \"can\" for a backpack) is used, we run into contention between our subject and and the class prior - sometimes obtaining cylindri", + "bbox": [ + 75, + 757, + 470, + 893 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "cal backpacks, or otherwise misshapen subjects. If we train with no class noun, the model does not leverage the class prior, has difficulty learning the subject and converging, and can generate erroneous samples. Subject fidelity results are shown in Table 4, with substantially higher subject fidelity for our proposed approach.", + "bbox": [ + 496, + 448, + 890, + 539 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Applications", + "text_level": 1, + "bbox": [ + 500, + 547, + 633, + 565 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Recontextualization We can generate novel images for a specific subject in different contexts (Figure 6) with descriptive prompts (\"a [V] [class noun] [context description)\"). Importantly, we are able to generate the subject in new poses and articulations, with previously unseen scene structure and realistic integration of the subject in the scene (e.g. contact, shadows, reflections).", + "bbox": [ + 496, + 571, + 890, + 676 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Art Renditions Given a prompt “a painting of a [V] [class noun] in the style of [famous painter]” or “a statue of a [V] [class noun] in the style of [famous sculptor]” we are able to generate artistic renditions of our subject. Unlike style transfer, where the source structure is preserved and only the style is transferred, we are able to generate meaningful, novel variations depending on the artistic style, while preserving subject identity. E.g., as shown in Figure 7, “Michelangelo”, we generated a pose that is novel and not seen in the input images.", + "bbox": [ + 496, + 688, + 890, + 839 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Novel View Synthesis We are able to render the subject under novel viewpoints. In Figure 7, we generate new images of the input cat (with consistent complex fur patterns)", + "bbox": [ + 496, + 849, + 890, + 897 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "22506", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/67bfe2a7a9c50225b443313d746c869c05fe41ebb3b449a98b294d7596fa5707.jpg", + "image_caption": [ + "Figure 7. Novel view synthesis, art renditions, and property modifications. We are able to generate novel and meaningful images while faithfully preserving subject identity and essence. More applications and examples in the supplementary material." + ], + "image_footnote": [], + "bbox": [ + 78, + 89, + 468, + 409 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4ce3f54196e57db34a5f47f3f46e3a830fb3bdf5acf1ed5c6941d07f0bf74f8c.jpg", + "image_caption": [ + "(b) Context-appearance entanglement" + ], + "image_footnote": [], + "bbox": [ + 81, + 494, + 202, + 611 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/271595383f4c5e363a3d72b1ef87efd0f3f1483cff4fe679aaf6afcc3af595c1.jpg", + "image_caption": [ + "(a) Incorrect context synthesis", + "in the ISS" + ], + "image_footnote": [], + "bbox": [ + 225, + 513, + 344, + 604 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/256d62bdb1b058df2ee43fdb453451f721e697b97b8163c6cf56ff850953699b.jpg", + "image_caption": [ + "on the moon" + ], + "image_footnote": [], + "bbox": [ + 346, + 515, + 460, + 604 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a12117a968f8a68ae26b5d5cf5c58528a76ef0dce90b5a9ea8c820722702ffd1.jpg", + "image_caption": [ + "in the Bolivian salt flats", + "on top of a blue fabric", + "Figure 8. Failure modes. Given a rare prompted context the model might fail at generating the correct environment (a). It is possible for context and subject appearance to become entangled (b). Finally, it is possible for the model to overfit and generate images similar to the training set, especially if prompts reflect the original environment of the training set (c)." + ], + "image_footnote": [], + "bbox": [ + 88, + 651, + 323, + 743 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "", + "bbox": [ + 210, + 651, + 323, + 741 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/33010a76d4fe29e907525b3b3f8e4ba6b26b69d7d0edf6e610643b97f6920a95.jpg", + "image_caption": [ + "(c) Overfitting", + "in the forest" + ], + "image_footnote": [], + "bbox": [ + 346, + 651, + 462, + 741 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "under new viewpoints. We highlight that the model has not seen this specific cat from behind, below, or above - yet it is able to extrapolate knowledge from the class prior to generate these novel views given only 4 frontal images of the subject.", + "bbox": [ + 496, + 90, + 890, + 167 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Property Modification We are able to modify subject properties. For example, we show crosses between a specific Chow Chow dog and different animal species in the bottom row of Figure 7. We prompt the model with sentences of the following structure: \"a cross of a [V] dog and a [target species]\". In particular, we can see in this example that the identity of the dog is well preserved even when the species changes - the face of the dog has certain unique features that are well preserved and melded with the target species. Other property modifications are possible, such as material modification (e.g. \"a transparent [V] teapot\" in Figure 6). Some are harder than others and depend on the prior of the base generation model.", + "bbox": [ + 496, + 183, + 890, + 380 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Limitations", + "text_level": 1, + "bbox": [ + 500, + 387, + 625, + 402 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We illustrate some failure models of our method in Figure 8. The first is related to not being able to accurately generate the prompted context. Possible reasons are a weak prior for these contexts, or difficulty in generating both the subject and specified concept together due to low probability of co-occurrence in the training set. The second is context-appearance entanglement, where the appearance of the subject changes due to the prompted context, exemplified in Figure 8 with color changes of the backpack. Third, we also observe overfitting to the real images that happen when the prompt is similar to the original setting in which the subject was seen.", + "bbox": [ + 496, + 410, + 890, + 590 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Other limitations are that some subjects are easier to learn than others (e.g. dogs and cats). Occasionally, with subjects that are rarer, the model is unable to support as many subject variations. Finally, there is also variability in the fidelity of the subject and some generated images might contain hallucinated subject features, depending on the strength of the model prior, and the complexity of the semantic modification.", + "bbox": [ + 496, + 592, + 890, + 712 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusions", + "text_level": 1, + "bbox": [ + 500, + 724, + 625, + 739 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We presented an approach for synthesizing novel renditions of a subject using a few images of the subject and the guidance of a text prompt. Our key idea is to embed a given subject instance in the output domain of a text-to-image diffusion model by binding the subject to a unique identifier. Remarkably - this fine-tuning process can work given only 3-5 subject images, making the technique particularly accessible. We demonstrated a variety of applications with animals and objects in generated photorealistic scenes, in most cases indistinguishable from real images.", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "22507", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Unsplash. https://unsplash.com/.", + "[2] Rameen Abdal, Peihao Zhu, John Femiani, Niloy J Mitra, and Peter Wonka. Clip2stylegan: Unsupervised extraction of stylegan edit directions. arXiv preprint arXiv:2112.05219, 2021.", + "[3] Omri Avrahami, Ohad Fried, and Dani Lischinski. Blended latent diffusion. arXiv preprint arXiv:2206.02779, 2022.", + "[4] Omri Avrahami, Dani Lischinski, and Ohad Fried. Blended diffusion for text-driven editing of natural images. 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In Proceedings of the IEEE conference on" + ], + "bbox": [ + 78, + 90, + 468, + 897 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "computer vision and pattern recognition, pages 6199-6208, 2018.", + "bbox": [ + 532, + 90, + 890, + 119 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "22510", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/DreamBooth_ Fine Tuning Text-to-Image Diffusion Models for Subject-Driven Generation/88ef8e93-ceab-4a73-b104-1d6bfb6b0d91_model.json b/2023/DreamBooth_ Fine Tuning Text-to-Image Diffusion Models for Subject-Driven Generation/88ef8e93-ceab-4a73-b104-1d6bfb6b0d91_model.json new file mode 100644 index 0000000000000000000000000000000000000000..1336509d9f5a8ca17e616bd1c924fca566c84c43 --- /dev/null +++ b/2023/DreamBooth_ Fine Tuning Text-to-Image Diffusion Models for Subject-Driven Generation/88ef8e93-ceab-4a73-b104-1d6bfb6b0d91_model.json @@ -0,0 +1,2763 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.189, + 0.108, + 0.784, + 0.154 + ], + "angle": 0, + "content": "DreamBooth: Fine Tuning Text-to-Image Diffusion Models for Subject-Driven Generation" + }, + { + "type": "text", + "bbox": [ + 0.218, + 0.171, + 0.36, + 0.206 + ], + "angle": 0, + "content": "Nataniel Ruiz*,1,2 \nYael Pritch1" + }, + { + "type": "text", + "bbox": [ + 0.41, + 0.172, + 0.576, + 0.206 + ], + "angle": 0, + "content": "Yuanzhen Li1 \nMichael Rubinstein1" + }, + { + "type": "text", + "bbox": [ + 0.624, + 0.172, + 0.751, + 0.206 + ], + "angle": 0, + "content": "Varun Jampani1 \nKfir Aberman1" + }, + { + "type": "text", + "bbox": [ + 0.323, + 0.207, + 0.65, + 0.226 + ], + "angle": 0, + "content": "\\(^{1}\\) Google Research \\(^{2}\\) Boston University" + }, + { + "type": "image", + "bbox": [ + 0.078, + 0.235, + 0.291, + 0.402 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.313, + 0.234, + 0.509, + 0.386 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.357, + 0.387, + 0.466, + 0.402 + ], + "angle": 0, + "content": "in the Acropolis" + }, + { + "type": "image", + "bbox": [ + 0.512, + 0.234, + 0.601, + 0.304 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.524, + 0.304, + 0.588, + 0.315 + ], + "angle": 0, + "content": "swimming" + }, + { + "type": "image", + "bbox": [ + 0.511, + 0.316, + 0.602, + 0.402 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.603, + 0.234, + 0.693, + 0.304 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.627, + 0.304, + 0.681, + 0.316 + ], + "angle": 0, + "content": "sleeping" + }, + { + "type": "image", + "bbox": [ + 0.604, + 0.316, + 0.693, + 0.387 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.617, + 0.388, + 0.691, + 0.401 + ], + "angle": 0, + "content": "in a bucket" + }, + { + "type": "image", + "bbox": [ + 0.696, + 0.234, + 0.892, + 0.386 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.735, + 0.388, + 0.852, + 0.402 + ], + "angle": 0, + "content": "getting a haircut" + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.411, + 0.894, + 0.467 + ], + "angle": 0, + "content": "Figure 1. With just a few images (typically 3-5) of a subject (left), *DreamBooth*—our AI-powered photo booth—can generate a myriad of images of the subject in different contexts (right), using the guidance of a text prompt. The results exhibit natural interactions with the environment, as well as novel articulations and variation in lighting conditions, all while maintaining high fidelity to the key visual features of the subject." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.48, + 0.314, + 0.495 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.511, + 0.474, + 0.875 + ], + "angle": 0, + "content": "Large text-to-image models achieved a remarkable leap in the evolution of AI, enabling high-quality and diverse synthesis of images from a given text prompt. However, these models lack the ability to mimic the appearance of subjects in a given reference set and synthesize novel renditions of them in different contexts. In this work, we present a new approach for \"personalization\" of text-to-image diffusion models. Given as input just a few images of a subject, we fine-tune a pretrained text-to-image model such that it learns to bind a unique identifier with that specific subject. Once the subject is embedded in the output domain of the model, the unique identifier can be used to synthesize novel photorealistic images of the subject contextualized in different scenes. By leveraging the semantic prior embedded in the model with a new autogenous class-specific prior preservation loss, our technique enables synthesizing the subject in diverse scenes, poses, views and lighting conditions that do not appear in the reference images. We apply our technique to several previously-unassailable tasks, including subject recontextualization, text-guided view synthesis, and artistic rendering, all while preserving the subject's key features. We also provide a new dataset and evaluation protocol for this new task of subject-driven generation. Project page: https://dreambooth.github.io/" + }, + { + "type": "page_footnote", + "bbox": [ + 0.107, + 0.887, + 0.458, + 0.901 + ], + "angle": 0, + "content": "*This research was performed while Nataniel Ruiz was at Google." + }, + { + "type": "title", + "bbox": [ + 0.502, + 0.524, + 0.631, + 0.54 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.55, + 0.892, + 0.669 + ], + "angle": 0, + "content": "Can you imagine your own dog traveling around the world, or your favorite bag displayed in the most exclusive showroom in Paris? What about your parrot being the main character of an illustrated storybook? Rendering such imaginary scenes is a challenging task that requires synthesizing instances of specific subjects (e.g., objects, animals) in new contexts such that they naturally and seamlessly blend into the scene." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.671, + 0.893, + 0.898 + ], + "angle": 0, + "content": "Recently developed large text-to-image models have shown unprecedented capabilities, by enabling high-quality and diverse synthesis of images based on a text prompt written in natural language [51,58]. One of the main advantages of such models is the strong semantic prior learned from a large collection of image-caption pairs. Such a prior learns, for instance, to bind the word \"dog\" with various instances of dogs that can appear in different poses and contexts in an image. While the synthesis capabilities of these models are unprecedented, they lack the ability to mimic the appearance of subjects in a given reference set, and synthesize novel renditions of the same subjects in different contexts. The main reason is that the expressiveness of their output domain is limited; even the most detailed textual description of an object may yield instances with different appearances." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "22500" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.152 + ], + "angle": 0, + "content": "Furthermore, even models whose text embedding lies in a shared language-vision space [50] cannot accurately reconstruct the appearance of given subjects but only create variations of the image content (Figure 2)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.153, + 0.471, + 0.348 + ], + "angle": 0, + "content": "In this work, we present a new approach for \"personalization\" of text-to-image diffusion models (adapting them to user-specific image generation needs). Our goal is to expand the language-vision dictionary of the model such that it binds new words with specific subjects the user wants to generate. Once the new dictionary is embedded in the model, it can use these words to synthesize novel photorealistic images of the subject, contextualized in different scenes, while preserving their key identifying features. The effect is akin to a \"magic photo booth\"—once a few images of the subject are taken, the booth generates photos of the subject in different conditions and scenes, as guided by simple and intuitive text prompts (Figure 1)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.348, + 0.47, + 0.452 + ], + "angle": 0, + "content": "More formally, given a few images of a subject (\\(\\sim 3-5\\)), our objective is to implant the subject into the output domain of the model such that it can be synthesized with a unique identifier. To that end, we propose a technique to represent a given subject with rare token identifiers and fine-tune a pre-trained, diffusion-based text-to-image framework." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.454, + 0.47, + 0.635 + ], + "angle": 0, + "content": "We fine-tune the text-to-image model with the input images and text prompts containing a unique identifier followed by the class name of the subject (e.g., \"A [V] dog\"). The latter enables the model to use its prior knowledge on the subject class while the class-specific instance is bound with the unique identifier. In order to prevent language drift [32, 38] that causes the model to associate the class name (e.g., \"dog\") with the specific instance, we propose an autogenous, class-specific prior preservation loss, which leverages the semantic prior on the class that is embedded in the model, and encourages it to generate diverse instances of the same class as our subject." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.635, + 0.47, + 0.786 + ], + "angle": 0, + "content": "We apply our approach to a myriad of text-based image generation applications including recontextualization of subjects, modification of their properties, original art renditions, and more, paving the way to a new stream of previously unassailable tasks. We highlight the contribution of each component in our method via ablation studies, and compare with alternative baselines and related work. We also conduct a user study to evaluate subject and prompt fidelity in our synthesized images, compared to alternative approaches." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.786, + 0.47, + 0.876 + ], + "angle": 0, + "content": "To the best of our knowledge, ours is the first technique that tackles this new challenging problem of subject-driven generation, allowing users, from just a few casually captured images of a subject, synthesize novel renditions of the subject in different contexts while maintaining its distinctive features." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.877, + 0.47, + 0.892 + ], + "angle": 0, + "content": "To evaluate this new task, we also construct a new dataset" + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.091, + 0.677, + 0.169 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.533, + 0.17, + 0.677, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.578, + 0.228, + 0.646, + 0.24 + ], + "angle": 0, + "content": "Input Images" + }, + { + "type": "image", + "bbox": [ + 0.693, + 0.091, + 0.764, + 0.161 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.709, + 0.161, + 0.816, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.726, + 0.228, + 0.855, + 0.239 + ], + "angle": 0, + "content": "Image-guided, DALL-E2" + }, + { + "type": "image", + "bbox": [ + 0.845, + 0.108, + 0.865, + 0.134 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.521, + 0.248, + 0.695, + 0.383 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.561, + 0.385, + 0.665, + 0.396 + ], + "angle": 0, + "content": "Text-guided, Imagen" + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.248, + 0.87, + 0.383 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.775, + 0.386, + 0.801, + 0.395 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.409, + 0.892, + 0.534 + ], + "angle": 0, + "content": "Figure 2. Subject-driven generation. Given a particular clock (left), it is hard to generate it while maintaining high fidelity to its key visual features (second and third columns showing DALL-E2 [51] image-guided generation andImagen [58] text-guided generation; text prompt used forImagen: \"retro style yellow alarm clock with a white clock face and a yellow number three on the right part of the clock face in the jungle\"). Our approach (right) can synthesize the clock with high fidelity and in new contexts (text prompt: \"a \\([V]\\) clock in the jungle\")." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.544, + 0.892, + 0.62 + ], + "angle": 0, + "content": "that contains various subjects captured in different contexts, and propose a new evaluation protocol that measures the subject fidelity and prompt fidelity of the generated results. We make our dataset and evaluation protocol publicly available on the project webpage" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.633, + 0.637, + 0.648 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.658, + 0.892, + 0.809 + ], + "angle": 0, + "content": "Image Composition. Image composition techniques [13, 36, 67] aim to clone a given subject into a new background such that the subject melds into the scene. To consider composition in novel poses, one may apply 3D reconstruction techniques [6, 8, 39, 47, 65] which usually works on rigid objects and require a larger number of views. Some drawbacks include scene integration (lighting, shadows, contact) and the inability to generate novel scenes. In contrast, our approach enables generation of subjects in novel poses and new contexts." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.81, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Text-to-Image Editing and Synthesis. Text-driven image manipulation has recently achieved significant progress using GANs [9, 22, 27-29] combined with image-text representations such as CLIP [50], yielding realistic manipulations using text [2, 7, 21, 41, 46, 68]. These methods work well on structured scenarios (e.g. human face edit" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "22501" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.288 + ], + "angle": 0, + "content": "ing) and can struggle over diverse datasets where subjects are varied. Crowson et al. [14] use VQ-GAN [18] and train over more diverse data to alleviate this concern. Other works [4, 30] exploit the recent diffusion models [25, 25, 43, 55, 57, 59–63], which achieve state-of-the-art generation quality over highly diverse datasets, often surpassing GANs [15]. While most works that require only text are limited to global editing [14, 31], Bar-Tal et al. [5] proposed a text-based localized editing technique without using masks, showing impressive results. While most of these editing approaches allow modification of global properties or local editing of a given image, none enables generating novel renditions of a given subject in new contexts." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.288, + 0.473, + 0.424 + ], + "angle": 0, + "content": "There also exists work on text-to-image synthesis [14, 16, 19, 24, 26, 33, 34, 48, 49, 52, 55, 64, 71]. Recent large text-to-image models such asImagen [58], DALL-E2 [51], Parti [69], CogView2 [17] and Stable Diffusion [55] demonstrated unprecedented semantic generation. These models do not provide fine-grained control over a generated image and use text guidance only. Specifically, it is challenging or impossible to preserve the identity of a subject consistently across synthesized images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.424, + 0.473, + 0.606 + ], + "angle": 0, + "content": "Controllable Generative Models. There are various approaches to control generative models, where some of them might prove to be viable directions for subject-driven prompt-guided image synthesis. Liu et al. [37] propose a diffusion-based technique allowing for image variations guided by reference image or text. To overcome subject modification, several works [3, 42] assume a user-provided mask to restrict the modified area. Inversion [12, 15, 51] can be used to preserve a subject while modifying context. Prompt-to-prompt [23] allows for local and global editing without an input mask. These methods fall short of identity-preserving novel sample generation of a subject." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.606, + 0.473, + 0.741 + ], + "angle": 0, + "content": "In the context of GANs, Pivotal Tuning [54] allows for real image editing by finetuning the model with an inverted latent code anchor, and Nitzan et al. [44] extended this work to GAN finetuning on faces to train a personalized prior, which requires around 100 images and are limited to the face domain. Casanova et al. [11] propose an instance conditioned GAN that can generate variations of an instance, although it can struggle with unique subjects and does not preserve all subject details." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.741, + 0.473, + 0.878 + ], + "angle": 0, + "content": "Finally, the concurrent work of Gal et al. [20] proposes a method to represent visual concepts, like an object or a style, through new tokens in the embedding space of a frozen text-to-image model, resulting in small personalized token embeddings. While this method is limited by the expressiveness of the frozen diffusion model, our fine-tuning approach enables us to embed the subject within the model's output domain, resulting in the generation of novel images of the subject which preserve its key visual features." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.09, + 0.593, + 0.107 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.115, + 0.895, + 0.344 + ], + "angle": 0, + "content": "Given only a few (typically 3-5) casually captured images of a specific subject, without any textual description, our objective is to generate new images of the subject with high detail fidelity and with variations guided by text prompts. Example variations include changing the subject location, changing subject properties such as color or shape, modifying the subject's pose, viewpoint, and other semantic modifications. We do not impose any restrictions on input image capture settings and the subject image can have varying contexts. We next provide some background on text-to-image diffusion models (Sec. 3.1), then present our finetuning technique to bind a unique identifier with a subject described in a few images (Sec. 3.2), and finally propose a class-specific prior-preservation loss that enables us to overcome language drift in our fine-tuned model (Sec. 3.3)." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.351, + 0.783, + 0.368 + ], + "angle": 0, + "content": "3.1. Text-to-Image Diffusion Models" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.375, + 0.895, + 0.527 + ], + "angle": 0, + "content": "Diffusion models are probabilistic generative models that are trained to learn a data distribution by the gradual denoising of a variable sampled from a Gaussian distribution. Specifically, we are interested in a pre-trained text-to-image diffusion model \\(\\hat{\\mathbf{x}}_{\\theta}\\) that, given an initial noise map \\(\\epsilon \\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})\\) and a conditioning vector \\(\\mathbf{c} = \\Gamma (\\mathbf{P})\\) generated using a text encoder \\(\\Gamma\\) and a text prompt \\(\\mathbf{P}\\), generates an image \\(\\mathbf{x}_{\\mathrm{gen}} = \\hat{\\mathbf{x}}_{\\theta}(\\epsilon ,\\mathbf{c})\\). They are trained using a squared error loss to denoise a variably-noised image or latent code \\(\\mathbf{z}_t\\coloneqq \\alpha_t\\mathbf{x} + \\sigma_t\\boldsymbol {\\epsilon}\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.568, + 0.537, + 0.892, + 0.557 + ], + "angle": 0, + "content": "\\[\n\\mathbb {E} _ {\\mathbf {x}, \\mathbf {c}, \\boldsymbol {\\epsilon}, t} \\left[ w _ {t} \\| \\hat {\\mathbf {x}} _ {\\theta} \\left(\\alpha_ {t} \\mathbf {x} + \\sigma_ {t} \\boldsymbol {\\epsilon}, \\mathbf {c}\\right) - \\mathbf {x} \\| _ {2} ^ {2} \\right] \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.566, + 0.895, + 0.657 + ], + "angle": 0, + "content": "where \\(\\mathbf{x}\\) is the ground-truth image, \\(\\mathbf{c}\\) is a conditioning vector (e.g., obtained from a text prompt), and \\(\\alpha_{t},\\sigma_{t},w_{t}\\) are terms that control the noise schedule and sample quality, and are functions of the diffusion process time \\(t\\sim\\) \\(\\mathcal{U}([0,1])\\). A more detailed description is given in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.666, + 0.849, + 0.683 + ], + "angle": 0, + "content": "3.2. Personalization of Text-to-Image Models" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Our first task is to implant the subject instance into the output domain of the model such that we can query the model for varied novel images of the subject. One natural idea is to fine-tune the model using the few-shot dataset of the subject. Careful care had to be taken when fine-tuning generative models such as GANs in a few-shot scenario as it can cause overfitting and mode-collapse - as well as not capturing the target distribution sufficiently well. There has been research on techniques to avoid these pitfalls [35,40,45,53,66], although, in contrast to our work, this line of work primarily seeks to generate images that resemble the target distribution but has no requirement of subject preservation. With regards to these pitfalls, we observe the peculiar finding that, given a careful fine-tuning setup" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "22502" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.09, + 0.462, + 0.325 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.332, + 0.472, + 0.446 + ], + "angle": 0, + "content": "Figure 3. Fine-tuning. Given \\(\\sim 3 - 5\\) images of a subject we fine-tune a text-to-image diffusion model with the input images paired with a text prompt containing a unique identifier and the name of the class the subject belongs to (e.g., \"A [V] dog\"), in parallel, we apply a class-specific prior preservation loss, which leverages the semantic prior that the model has on the class and encourages it to generate diverse instances belong to the subject's class using the class name in a text prompt (e.g., \"A dog\")." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.457, + 0.47, + 0.518 + ], + "angle": 0, + "content": "using the diffusion loss from Eq 1, large text-to-image diffusion models seem to excel at integrating new information into their domain without forgetting the prior or overfitting to a small set of training images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.535, + 0.47, + 0.822 + ], + "angle": 0, + "content": "Designing Prompts for Few-Shot Personalization Our goal is to \"implant\" a new (unique identifier, subject) pair into the diffusion model's \"dictionary\". In order to bypass the overhead of writing detailed image descriptions for a given image set we opt for a simpler approach and label all input images of the subject \"a [identifier] [class noun]\", where [identifier] is a unique identifier linked to the subject and [class noun] is a coarse class descriptor of the subject (e.g. cat, dog, watch, etc.). The class descriptor can be provided by the user or obtained using a classifier. We use a class descriptor in the sentence in order to tether the prior of the class to our unique subject and find that using a wrong class descriptor, or no class descriptor increases training time and language drift while decreasing performance. In essence, we seek to leverage the model's prior of the specific class and entangle it with the embedding of our subject's unique identifier so we can leverage the visual prior to generate new poses and articulations of the subject in different contexts." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Rare-token Identifiers We generally find existing English words (e.g. \"unique\", \"special\") suboptimal since the model has to learn to disentangle them from their original meaning and to re-entangle them to reference our subject." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.456 + ], + "angle": 0, + "content": "This motivates the need for an identifier that has a weak prior in both the language model and the diffusion model. A hazardous way of doing this is to select random characters in the English language and concatenate them to generate a rare identifier (e.g. \"xxy5syt00\"). In reality, the tokenizer might tokenize each letter separately, and the prior for the diffusion model is strong for these letters. We often find that these tokens incur the similar weaknesses as using common English words. Our approach is to find rare tokens in the vocabulary, and then invert these tokens into text space, in order to minimize the probability of the identifier having a strong prior. We perform a rare-token lookup in the vocabulary and obtain a sequence of rare token identifiers \\( f(\\hat{\\mathbf{V}}) \\), where \\( f \\) is a tokenizer; a function that maps character sequences to tokens and \\( \\hat{\\mathbf{V}} \\) is the decoded text stemming from the tokens \\( f(\\hat{\\mathbf{V}}) \\). The sequence can be of variable length \\( k \\), and find that relatively short sequences of \\( k = \\{1, \\dots, 3\\} \\) work well. Then, by inverting the vocabulary using the tokenizer on \\( f(\\hat{\\mathbf{V}}) \\) we obtain a sequence of characters that define our unique identifier \\( \\hat{\\mathbf{V}} \\). For Imagen, we find that using uniform random sampling of tokens that correspond to 3 or fewer Unicode characters (without spaces) and using tokens in the T5-XXL tokenizer range of \\( \\{5000, \\dots, 10000\\} \\) works well." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.465, + 0.826, + 0.481 + ], + "angle": 0, + "content": "3.3. Class-specific Prior Preservation Loss" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.488, + 0.892, + 0.669 + ], + "angle": 0, + "content": "In our experience, the best results for maximum subject fidelity are achieved by fine-tuning all layers of the model. This includes fine-tuning layers that are conditioned on the text embeddings, which gives rise to the problem of language drift. Language drift has been an observed problem in language models [32, 38], where a model that is pre-trained on a large text corpus and later fine-tuned for a specific task progressively loses syntactic and semantic knowledge of the language. To the best of our knowledge, we are the first to find a similar phenomenon affecting diffusion models, where to model slowly forgets how to generate subjects of the same class as the target subject." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.669, + 0.892, + 0.805 + ], + "angle": 0, + "content": "Another problem is the possibility of reduced output diversity. Text-to-image diffusion models naturally possess high amounts of output diversity. When fine-tuning on a small set of images we would like to be able to generate the subject in novel viewpoints, poses and articulations. Yet, there is a risk of reducing the amount of variability in the output poses and views of the subject (e.g. snapping to the few-shot views). We observe that this is often the case, especially when the model is trained for too long." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.806, + 0.892, + 0.897 + ], + "angle": 0, + "content": "To mitigate the two aforementioned issues, we propose an autogenous class-specific prior preservation loss that encourages diversity and counters language drift. In essence, our method is to supervise the model with its own generated samples, in order for it to retain the prior once the few-shot fine-tuning begins. This allows it to generate di" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.958 + ], + "angle": 0, + "content": "22503" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.199 + ], + "angle": 0, + "content": "verse images of the class prior, as well as retain knowledge about the class prior that it can use in conjunction with knowledge about the subject instance. Specifically, we generate data \\(\\mathbf{x}_{\\mathrm{pr}} = \\hat{\\mathbf{x}} (\\mathbf{z}_{t_1},\\mathbf{c}_{\\mathrm{pr}})\\) by using the ancestral sampler on the frozen pre-trained diffusion model with random initial noise \\(\\mathbf{z}_{t_1}\\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})\\) and conditioning vector \\(\\mathbf{c}_{\\mathrm{pr}}\\coloneqq \\Gamma (f(\"a[class~noun]^\")\\)). The loss becomes:" + }, + { + "type": "equation", + "bbox": [ + 0.093, + 0.21, + 0.469, + 0.249 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathbb {E} _ {\\mathbf {x}, \\mathbf {c}, \\epsilon , \\epsilon^ {\\prime}, t} [ w _ {t} \\| \\hat {\\mathbf {x}} _ {\\theta} (\\alpha_ {t} \\mathbf {x} + \\sigma_ {t} \\epsilon , \\mathbf {c}) - \\mathbf {x} \\| _ {2} ^ {2} + \\\\ \\lambda w _ {t ^ {\\prime}} \\| \\hat {\\mathbf {x}} _ {\\theta} \\left(\\alpha_ {t ^ {\\prime}} \\mathbf {x} _ {\\mathrm {p r}} + \\sigma_ {t ^ {\\prime}} \\boldsymbol {\\epsilon} ^ {\\prime}, \\mathbf {c} _ {\\mathrm {p r}}\\right) - \\mathbf {x} _ {\\mathrm {p r}} \\| _ {2} ^ {2} ], \\tag {2} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.257, + 0.473, + 0.499 + ], + "angle": 0, + "content": "where the second term is the prior-preservation term that supervises the model with its own generated images, and \\(\\lambda\\) controls for the relative weight of this term. Figure 3 illustrates the model fine-tuning with the class-generated samples and prior-preservation loss. Despite being simple, we find this prior-preservation loss is effective in encouraging output diversity and in overcoming language-drift. We also find that we can train the model for more iterations without risking overfitting. We find that \\(\\sim 1000\\) iterations with \\(\\lambda = 1\\) and learning rate \\(10^{-5}\\) for Imagen [58] and \\(5 \\times 10^{-6}\\) for Stable Diffusion [56], and with a subject dataset size of 3-5 images is enough to achieve good results. During this process, \\(\\sim 1000\\) \"a [class noun]\" samples are generated - but less can be used. The training process takes about 5 minutes on one TPUv4 for Imagen, and 5 minutes on a NVIDIA A100 for Stable Diffusion." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.512, + 0.21, + 0.529 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.537, + 0.473, + 0.78 + ], + "angle": 0, + "content": "In this section, we show experiments and applications. Our method enables a large expanse of text-guided semantic modifications of our subject instances, including recontextualization, modification of subject properties such as material and species, art rendition, and viewpoint modification. Importantly, across all of these modifications, we are able to preserve the unique visual features that give the subject its identity and essence. If the task is recontextualization, then the subject features are unmodified, but appearance (e.g., pose) may change. If the task is a stronger semantic modification, such as crossing between our subject and another species/object, then the key features of the subject are preserved after modification. In this section, we reference the subject's unique identifier using [V]. We include specific Imagen and Stable Diffusion implementation details in the supp. material." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.787, + 0.295, + 0.803 + ], + "angle": 0, + "content": "4.1. Dataset and Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.472, + 0.903 + ], + "angle": 0, + "content": "Dataset We collected a dataset of 30 subjects, including unique objects and pets such as backpacks, stuffed animals, dogs, cats, sunglasses, cartoons, etc. Images for this dataset were collected by the authors or sourced from Unsplash [1]. We also collected 25 prompts: 20 recontextualization prompts and 5 property modification prompts for" + }, + { + "type": "image", + "bbox": [ + 0.499, + 0.091, + 0.895, + 0.45 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.459, + 0.895, + 0.571 + ], + "angle": 0, + "content": "Figure 4. Comparisons with Textual Inversion [20] Given 4 input images (top row), we compare: DreamBooth Imagen (2nd row), DreamBooth Stable Diffusion (3rd row), Textual Inversion (bottom row). Output images were created with the following prompts (left to right): \"a [V] vase in the snow\", \"a [V] vase on the beach\", \"a [V] vase in the jungle\", \"a [V] vase with the Eiffel Tower in the background\". DreamBooth is stronger in both subject and prompt fidelity." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.584, + 0.891, + 0.658 + ], + "angle": 0, + "content": "
MethodDINO ↑CLIP-I ↑CLIP-T ↑
Real Images0.7740.885N/A
DreamBooth (Imagen)0.6960.8120.306
DreamBooth (Stable Diffusion)0.6680.8030.305
Textual Inversion (Stable Diffusion)0.5690.7800.255
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.667, + 0.892, + 0.697 + ], + "angle": 0, + "content": "Table 1. Subject fidelity (DINO, CLIP-I) and prompt fidelity (CLIP-T, CLIP-T-L) quantitative metric comparison." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.709, + 0.891, + 0.768 + ], + "angle": 0, + "content": "
MethodSubject Fidelity ↑Prompt Fidelity ↑
DreamBooth (Stable Diffusion)68%81%
Textual Inversion (Stable Diffusion)22%12%
Undecided10%7%
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.777, + 0.874, + 0.792 + ], + "angle": 0, + "content": "Table 2. Subject fidelity and prompt fidelity user preference." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.805, + 0.892, + 0.866 + ], + "angle": 0, + "content": "objects; 10 recontextualization, 10 accessorization, and 5 property modification prompts for live subjects/pets. The full list of images and prompts can be found in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.866, + 0.892, + 0.897 + ], + "angle": 0, + "content": "For the evaluation suite we generate four images per subject and per prompt, totaling 3,000 images. This allows us" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "22504" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.238, + 0.092, + 0.314, + 0.104 + ], + "angle": 0, + "content": "Input images" + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.106, + 0.464, + 0.179 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.198, + 0.183, + 0.351, + 0.196 + ], + "angle": 0, + "content": "w/o prior-preservation loss" + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.197, + 0.464, + 0.27 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.197, + 0.274, + 0.353, + 0.286 + ], + "angle": 0, + "content": "with prior-preservation loss" + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.288, + 0.464, + 0.36 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.372, + 0.469, + 0.442 + ], + "angle": 0, + "content": "Figure 5. Encouraging diversity with prior-preservation loss. Naive fine-tuning can result in overfitting to input image context and subject appearance (e.g. pose). PPL acts as a regularizer that alleviates overfitting and encourages diversity, allowing for more pose variability and appearance diversity." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.456, + 0.469, + 0.516 + ], + "angle": 0, + "content": "to robustly measure performances and generalization capabilities of a method. We make our dataset and evaluation protocol publicly available on the project webpage for future use in evaluating subject-driven generation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.535, + 0.469, + 0.821 + ], + "angle": 0, + "content": "Evaluation Metrics One important aspect to evaluate is subject fidelity: the preservation of subject details in generated images. For this, we compute two metrics: CLIP-I and DINO [10]. CLIP-I is the average pairwise cosine similarity between CLIP [50] embeddings of generated and real images. Although this metric has been used in other work [20], it is not constructed to distinguish between different subjects that could have highly similar text descriptions (e.g. two different yellow clocks). Our proposed DINO metric is the average pairwise cosine similarity between the ViT-S/16 DINO embeddings of generated and real images. This is our preferred metric, since, by construction and in contrast to supervised networks, DINO is not trained to ignore differences between subjects of the same class. Instead, the self-supervised training objective encourages distinction of unique features of a subject or image. The second important aspect to evaluate is prompt fidelity, measured as the average cosine similarity between prompt and image CLIP embeddings. We denote this as CLIP-T." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.831, + 0.216, + 0.847 + ], + "angle": 0, + "content": "4.2. Comparisons" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.854, + 0.469, + 0.898 + ], + "angle": 0, + "content": "We compare our results with Textual Inversion, the recent concurrent work of Gal et al. [20], using the hyperparameters provided in their work. We find that this work is" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.287 + ], + "angle": 0, + "content": "the only comparable work in the literature that is subject-driven, text-guided and generates novel images. We generate images for DreamBooth using Imagen, DreamBooth using Stable Diffusion and Textual Inversion using Stable Diffusion. We compute DINO and CLIP-I subject fidelity metrics and the CLIP-T prompt fidelity metric. In Table 1 we show sizeable gaps in both subject and prompt fidelity metrics for DreamBooth over Textual Inversion. We find that DreamBooth (Imagen) achieves higher scores for both subject and prompt fidelity than DreamBooth (Stable Diffusion), approaching the upper-bound of subject fidelity for real images. We believe that this is due to the larger expressive power and higher output quality of Imagen." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.288, + 0.893, + 0.635 + ], + "angle": 0, + "content": "Further, we compare Textual Inversion (Stable Diffusion) and DreamBooth (Stable Diffusion) by conducting a user study. For subject fidelity, we asked 72 users to answer questionnaires of 25 comparative questions (3 users per questionnaire), totaling 1800 answers. Samples are randomly selected from a large pool. Each question shows the set of real images for a subject, and one generated image of that subject by each method (with a random prompt). Users are asked to answer the question: \"Which of the two images best reproduces the identity (e.g. item type and details) of the reference item?\", and we include a \"Cannot Determine / Both Equally\" option. Similarly for prompt fidelity, we ask \"Which of the two images is best described by the reference text?\". We average results using majority voting and present them in Table 2. We find an overwhelming preference for DreamBooth for both subject fidelity and prompt fidelity. This shines a light on results in Table 1, where DINO differences of around 0.1 and CLIP-T differences of 0.05 are significant in terms of user preference. Finally, we show qualitative comparisons in Figure 4. We observe that DreamBooth better preserves subject identity, and is more faithful to prompts. We show samples of the user study in the supp. material." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.644, + 0.665, + 0.659 + ], + "angle": 0, + "content": "4.3. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.668, + 0.892, + 0.895 + ], + "angle": 0, + "content": "Prior Preservation Loss Ablation We fine-tune Imagen on 15 subjects from our dataset, with and without our proposed prior preservation loss (PPL). The prior preservation loss seeks to combat language drift and preserve the prior. We compute a prior preservation metric (PRES) by computing the average pairwise DINO embeddings between generated images of random subjects of the prior class and real images of our specific subject. The higher this metric, the more similar random subjects of the class are to our specific subject, indicating collapse of the prior. We report results in Table 3 and observe that PPL substantially counteracts language drift and helps retain the ability to generate diverse images of the prior class. Additionally, we compute a diversity metric (DIV) using the average LPIPS [70] cosine similarity between generated images of same subject with" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "22505" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.096, + 0.235, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.118, + 0.218, + 0.194, + 0.231 + ], + "angle": 0, + "content": "Input images" + }, + { + "type": "image", + "bbox": [ + 0.248, + 0.096, + 0.407, + 0.217 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.262, + 0.218, + 0.388, + 0.243 + ], + "angle": 0, + "content": "A [V] backpack in the Grand Canyon" + }, + { + "type": "image", + "bbox": [ + 0.41, + 0.096, + 0.567, + 0.218 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.432, + 0.218, + 0.546, + 0.242 + ], + "angle": 0, + "content": "A wet [V] backpack in water" + }, + { + "type": "image", + "bbox": [ + 0.571, + 0.096, + 0.727, + 0.218 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.575, + 0.218, + 0.722, + 0.231 + ], + "angle": 0, + "content": "A [V] backpack in Boston" + }, + { + "type": "image", + "bbox": [ + 0.731, + 0.096, + 0.887, + 0.218 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.743, + 0.218, + 0.882, + 0.243 + ], + "angle": 0, + "content": "A [V] backpack with the night sky" + }, + { + "type": "image", + "bbox": [ + 0.078, + 0.245, + 0.234, + 0.365 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.118, + 0.368, + 0.194, + 0.381 + ], + "angle": 0, + "content": "Input images" + }, + { + "type": "image", + "bbox": [ + 0.249, + 0.245, + 0.407, + 0.367 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.265, + 0.367, + 0.383, + 0.391 + ], + "angle": 0, + "content": "A [V] teapot floating in milk" + }, + { + "type": "image", + "bbox": [ + 0.411, + 0.245, + 0.567, + 0.367 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.419, + 0.368, + 0.558, + 0.392 + ], + "angle": 0, + "content": "A transparent [V] teapot with milk inside" + }, + { + "type": "image", + "bbox": [ + 0.571, + 0.245, + 0.727, + 0.366 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.619, + 0.367, + 0.691, + 0.393 + ], + "angle": 0, + "content": "A [V] teapot pouring tea" + }, + { + "type": "image", + "bbox": [ + 0.731, + 0.245, + 0.887, + 0.367 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.75, + 0.367, + 0.868, + 0.391 + ], + "angle": 0, + "content": "A [V] teapot floating in the sea" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.407, + 0.892, + 0.435 + ], + "angle": 0, + "content": "Figure 6. Recontextualization. We generate images of the subjects in different environments, with high preservation of subject details and realistic scene-subject interactions. We show the prompts below each image." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.446, + 0.468, + 0.488 + ], + "angle": 0, + "content": "
MethodPRES ↓DIV ↑DINO ↑CLIP-I ↑CLIP-T ↑
DreamBooth (Imagen) w/ PPL0.4930.3910.6840.8150.308
DreamBooth (Imagen)0.6640.3710.7120.8280.306
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.499, + 0.47, + 0.54 + ], + "angle": 0, + "content": "Table 3. Prior preservation loss (PPL) ablation displaying a prior preservation (PRES) metric, diversity metric (DIV) and subject and prompt fidelity metrics." + }, + { + "type": "table", + "bbox": [ + 0.178, + 0.554, + 0.37, + 0.612 + ], + "angle": 0, + "content": "
MethodDINO ↑CLIP-I ↑
Correct Class0.7440.853
No Class0.3030.607
Wrong Class0.4540.728
" + }, + { + "type": "table_caption", + "bbox": [ + 0.096, + 0.623, + 0.441, + 0.637 + ], + "angle": 0, + "content": "Table 4. Class name ablation with subject fidelity metrics." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.648, + 0.47, + 0.739 + ], + "angle": 0, + "content": "same prompt. We observe that our model trained with PPL achieves higher diversity (with slightly diminished subject fidelity), which can also be observed qualitatively in Figure 5, where our model trained with PPL overfits less to the environment of the reference images and can generate the dog in more diverse poses and articulations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.758, + 0.471, + 0.894 + ], + "angle": 0, + "content": "Class-Prior Ablation We finetune Imagen on a subset of our dataset subjects (5 subjects) with no class noun, a randomly sampled incorrect class noun, and the correct class noun. With the correct class noun for our subject, we are able to faithfully fit to the subject, take advantage of the class prior, allowing us to generate our subject in various contexts. When an incorrect class noun (e.g. \"can\" for a backpack) is used, we run into contention between our subject and and the class prior - sometimes obtaining cylindri" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.449, + 0.892, + 0.54 + ], + "angle": 0, + "content": "cal backpacks, or otherwise misshapen subjects. If we train with no class noun, the model does not leverage the class prior, has difficulty learning the subject and converging, and can generate erroneous samples. Subject fidelity results are shown in Table 4, with substantially higher subject fidelity for our proposed approach." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.549, + 0.634, + 0.566 + ], + "angle": 0, + "content": "4.4. Applications" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.572, + 0.892, + 0.678 + ], + "angle": 0, + "content": "Recontextualization We can generate novel images for a specific subject in different contexts (Figure 6) with descriptive prompts (\"a [V] [class noun] [context description)\"). Importantly, we are able to generate the subject in new poses and articulations, with previously unseen scene structure and realistic integration of the subject in the scene (e.g. contact, shadows, reflections)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.892, + 0.84 + ], + "angle": 0, + "content": "Art Renditions Given a prompt “a painting of a [V] [class noun] in the style of [famous painter]” or “a statue of a [V] [class noun] in the style of [famous sculptor]” we are able to generate artistic renditions of our subject. Unlike style transfer, where the source structure is preserved and only the style is transferred, we are able to generate meaningful, novel variations depending on the artistic style, while preserving subject identity. E.g., as shown in Figure 7, “Michelangelo”, we generated a pose that is novel and not seen in the input images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.851, + 0.892, + 0.898 + ], + "angle": 0, + "content": "Novel View Synthesis We are able to render the subject under novel viewpoints. In Figure 7, we generate new images of the input cat (with consistent complex fur patterns)" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22506" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.09, + 0.47, + 0.41 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.423, + 0.47, + 0.478 + ], + "angle": 0, + "content": "Figure 7. Novel view synthesis, art renditions, and property modifications. We are able to generate novel and meaningful images while faithfully preserving subject identity and essence. More applications and examples in the supplementary material." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.495, + 0.203, + 0.612 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.229, + 0.495, + 0.436, + 0.509 + ], + "angle": 0, + "content": "(a) Incorrect context synthesis" + }, + { + "type": "image", + "bbox": [ + 0.227, + 0.515, + 0.345, + 0.606 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.347, + 0.516, + 0.462, + 0.606 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.254, + 0.61, + 0.304, + 0.62 + ], + "angle": 0, + "content": "in the ISS" + }, + { + "type": "image_caption", + "bbox": [ + 0.373, + 0.61, + 0.434, + 0.62 + ], + "angle": 0, + "content": "on the moon" + }, + { + "type": "image_caption", + "bbox": [ + 0.097, + 0.631, + 0.319, + 0.645 + ], + "angle": 0, + "content": "(b) Context-appearance entanglement" + }, + { + "type": "image", + "bbox": [ + 0.089, + 0.652, + 0.325, + 0.744 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.746, + 0.205, + 0.757 + ], + "angle": 0, + "content": "in the Bolivian salt flats" + }, + { + "type": "image", + "bbox": [ + 0.212, + 0.652, + 0.324, + 0.742 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.214, + 0.746, + 0.321, + 0.757 + ], + "angle": 0, + "content": "on top of a blue fabric" + }, + { + "type": "image_caption", + "bbox": [ + 0.36, + 0.631, + 0.446, + 0.645 + ], + "angle": 0, + "content": "(c) Overfitting" + }, + { + "type": "image", + "bbox": [ + 0.347, + 0.652, + 0.464, + 0.742 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.373, + 0.746, + 0.432, + 0.756 + ], + "angle": 0, + "content": "in the forest" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.767, + 0.47, + 0.852 + ], + "angle": 0, + "content": "Figure 8. Failure modes. Given a rare prompted context the model might fail at generating the correct environment (a). It is possible for context and subject appearance to become entangled (b). Finally, it is possible for the model to overfit and generate images similar to the training set, especially if prompts reflect the original environment of the training set (c)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.168 + ], + "angle": 0, + "content": "under new viewpoints. We highlight that the model has not seen this specific cat from behind, below, or above - yet it is able to extrapolate knowledge from the class prior to generate these novel views given only 4 frontal images of the subject." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.184, + 0.892, + 0.381 + ], + "angle": 0, + "content": "Property Modification We are able to modify subject properties. For example, we show crosses between a specific Chow Chow dog and different animal species in the bottom row of Figure 7. We prompt the model with sentences of the following structure: \"a cross of a [V] dog and a [target species]\". In particular, we can see in this example that the identity of the dog is well preserved even when the species changes - the face of the dog has certain unique features that are well preserved and melded with the target species. Other property modifications are possible, such as material modification (e.g. \"a transparent [V] teapot\" in Figure 6). Some are harder than others and depend on the prior of the base generation model." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.388, + 0.627, + 0.403 + ], + "angle": 0, + "content": "4.5. Limitations" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.411, + 0.892, + 0.591 + ], + "angle": 0, + "content": "We illustrate some failure models of our method in Figure 8. The first is related to not being able to accurately generate the prompted context. Possible reasons are a weak prior for these contexts, or difficulty in generating both the subject and specified concept together due to low probability of co-occurrence in the training set. The second is context-appearance entanglement, where the appearance of the subject changes due to the prompted context, exemplified in Figure 8 with color changes of the backpack. Third, we also observe overfitting to the real images that happen when the prompt is similar to the original setting in which the subject was seen." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.593, + 0.892, + 0.713 + ], + "angle": 0, + "content": "Other limitations are that some subjects are easier to learn than others (e.g. dogs and cats). Occasionally, with subjects that are rarer, the model is unable to support as many subject variations. Finally, there is also variability in the fidelity of the subject and some generated images might contain hallucinated subject features, depending on the strength of the model prior, and the complexity of the semantic modification." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.725, + 0.627, + 0.74 + ], + "angle": 0, + "content": "5. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We presented an approach for synthesizing novel renditions of a subject using a few images of the subject and the guidance of a text prompt. Our key idea is to embed a given subject instance in the output domain of a text-to-image diffusion model by binding the subject to a unique identifier. Remarkably - this fine-tuning process can work given only 3-5 subject images, making the technique particularly accessible. 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With just a few images (typically 3-5) of a subject (left), *DreamBooth*—our AI-powered photo booth—can generate a myriad of images of the subject in different contexts (right), using the guidance of a text prompt. The results exhibit natural interactions with the environment, as well as novel articulations and variation in lighting conditions, all while maintaining high fidelity to the key visual features of the subject. + +![](images/db94b4d58a34be658b4ffe1c46cf34d352cae9b7c985e53f66e083f3e19a108a.jpg) +in the Acropolis + +![](images/c65e4b281aa64ea8777307936bec71f48063252d993246ee2eb990078adc2aba.jpg) +swimming + +![](images/771025a37b86c8c8a269c7b54575ab411ae18603601774881799581345a9f6b5.jpg) + +![](images/68665b973ec6e05b150713e0602a32e2dd568c13e004243e2d8fa34a3c557a7c.jpg) +sleeping + +![](images/4bc62c2fddc3e157f16cab6b44280a2bb833c24bbc44805b4f8ee3bd994dbccf.jpg) +in a bucket + +![](images/54b6954ef2d190902a0500691749d74ca5e964f4bc0a0dcebd5cb3de32b5d3d1.jpg) +getting a haircut + +# Abstract + +Large text-to-image models achieved a remarkable leap in the evolution of AI, enabling high-quality and diverse synthesis of images from a given text prompt. However, these models lack the ability to mimic the appearance of subjects in a given reference set and synthesize novel renditions of them in different contexts. In this work, we present a new approach for "personalization" of text-to-image diffusion models. Given as input just a few images of a subject, we fine-tune a pretrained text-to-image model such that it learns to bind a unique identifier with that specific subject. Once the subject is embedded in the output domain of the model, the unique identifier can be used to synthesize novel photorealistic images of the subject contextualized in different scenes. By leveraging the semantic prior embedded in the model with a new autogenous class-specific prior preservation loss, our technique enables synthesizing the subject in diverse scenes, poses, views and lighting conditions that do not appear in the reference images. We apply our technique to several previously-unassailable tasks, including subject recontextualization, text-guided view synthesis, and artistic rendering, all while preserving the subject's key features. We also provide a new dataset and evaluation protocol for this new task of subject-driven generation. Project page: https://dreambooth.github.io/ + +# 1. Introduction + +Can you imagine your own dog traveling around the world, or your favorite bag displayed in the most exclusive showroom in Paris? What about your parrot being the main character of an illustrated storybook? Rendering such imaginary scenes is a challenging task that requires synthesizing instances of specific subjects (e.g., objects, animals) in new contexts such that they naturally and seamlessly blend into the scene. + +Recently developed large text-to-image models have shown unprecedented capabilities, by enabling high-quality and diverse synthesis of images based on a text prompt written in natural language [51,58]. One of the main advantages of such models is the strong semantic prior learned from a large collection of image-caption pairs. Such a prior learns, for instance, to bind the word "dog" with various instances of dogs that can appear in different poses and contexts in an image. While the synthesis capabilities of these models are unprecedented, they lack the ability to mimic the appearance of subjects in a given reference set, and synthesize novel renditions of the same subjects in different contexts. The main reason is that the expressiveness of their output domain is limited; even the most detailed textual description of an object may yield instances with different appearances. + +Furthermore, even models whose text embedding lies in a shared language-vision space [50] cannot accurately reconstruct the appearance of given subjects but only create variations of the image content (Figure 2). + +In this work, we present a new approach for "personalization" of text-to-image diffusion models (adapting them to user-specific image generation needs). Our goal is to expand the language-vision dictionary of the model such that it binds new words with specific subjects the user wants to generate. Once the new dictionary is embedded in the model, it can use these words to synthesize novel photorealistic images of the subject, contextualized in different scenes, while preserving their key identifying features. The effect is akin to a "magic photo booth"—once a few images of the subject are taken, the booth generates photos of the subject in different conditions and scenes, as guided by simple and intuitive text prompts (Figure 1). + +More formally, given a few images of a subject ( $\sim 3-5$ ), our objective is to implant the subject into the output domain of the model such that it can be synthesized with a unique identifier. To that end, we propose a technique to represent a given subject with rare token identifiers and fine-tune a pre-trained, diffusion-based text-to-image framework. + +We fine-tune the text-to-image model with the input images and text prompts containing a unique identifier followed by the class name of the subject (e.g., "A [V] dog"). The latter enables the model to use its prior knowledge on the subject class while the class-specific instance is bound with the unique identifier. In order to prevent language drift [32, 38] that causes the model to associate the class name (e.g., "dog") with the specific instance, we propose an autogenous, class-specific prior preservation loss, which leverages the semantic prior on the class that is embedded in the model, and encourages it to generate diverse instances of the same class as our subject. + +We apply our approach to a myriad of text-based image generation applications including recontextualization of subjects, modification of their properties, original art renditions, and more, paving the way to a new stream of previously unassailable tasks. We highlight the contribution of each component in our method via ablation studies, and compare with alternative baselines and related work. We also conduct a user study to evaluate subject and prompt fidelity in our synthesized images, compared to alternative approaches. + +To the best of our knowledge, ours is the first technique that tackles this new challenging problem of subject-driven generation, allowing users, from just a few casually captured images of a subject, synthesize novel renditions of the subject in different contexts while maintaining its distinctive features. + +To evaluate this new task, we also construct a new dataset + +![](images/c3c53d6f4cd1fba09cbf2caaa7c804cc71abc99fa0e4518b52a7fe09ab265c45.jpg) + +![](images/4f53552b3939b88c44a0919c428583283856e60d524e02f3bd19eb6a4a09f13f.jpg) +Input Images + +![](images/130b008d17545087bb94eb3e6d76948c9f35c35f12bb2fecc8387d3bbbb67a77.jpg) + +![](images/5731f5f93b4025c60645f4d8077768cfd21ff3d45731f041b3738e86f26866d7.jpg) +Image-guided, DALL-E2 + +![](images/94bea41ded2188391e42ca3530a2c314b39985ee3e69c61d7752d71e27025485.jpg) + +![](images/379e3d99f0e9e7f2003d45b828ba516c2219ba93b61f5ee89739bb5f0c07bbf4.jpg) +Text-guided, Imagen +Figure 2. Subject-driven generation. Given a particular clock (left), it is hard to generate it while maintaining high fidelity to its key visual features (second and third columns showing DALL-E2 [51] image-guided generation andImagen [58] text-guided generation; text prompt used forImagen: "retro style yellow alarm clock with a white clock face and a yellow number three on the right part of the clock face in the jungle"). Our approach (right) can synthesize the clock with high fidelity and in new contexts (text prompt: "a $[V]$ clock in the jungle"). + +![](images/0bbf76bf092e8ddcf7fac6b8ad3c166e239d6e4ddcc8ca4339003f64d9a67ad1.jpg) +Ours + +that contains various subjects captured in different contexts, and propose a new evaluation protocol that measures the subject fidelity and prompt fidelity of the generated results. We make our dataset and evaluation protocol publicly available on the project webpage + +# 2. Related work + +Image Composition. Image composition techniques [13, 36, 67] aim to clone a given subject into a new background such that the subject melds into the scene. To consider composition in novel poses, one may apply 3D reconstruction techniques [6, 8, 39, 47, 65] which usually works on rigid objects and require a larger number of views. Some drawbacks include scene integration (lighting, shadows, contact) and the inability to generate novel scenes. In contrast, our approach enables generation of subjects in novel poses and new contexts. + +Text-to-Image Editing and Synthesis. Text-driven image manipulation has recently achieved significant progress using GANs [9, 22, 27-29] combined with image-text representations such as CLIP [50], yielding realistic manipulations using text [2, 7, 21, 41, 46, 68]. These methods work well on structured scenarios (e.g. human face edit + +ing) and can struggle over diverse datasets where subjects are varied. Crowson et al. [14] use VQ-GAN [18] and train over more diverse data to alleviate this concern. Other works [4, 30] exploit the recent diffusion models [25, 25, 43, 55, 57, 59–63], which achieve state-of-the-art generation quality over highly diverse datasets, often surpassing GANs [15]. While most works that require only text are limited to global editing [14, 31], Bar-Tal et al. [5] proposed a text-based localized editing technique without using masks, showing impressive results. While most of these editing approaches allow modification of global properties or local editing of a given image, none enables generating novel renditions of a given subject in new contexts. + +There also exists work on text-to-image synthesis [14, 16, 19, 24, 26, 33, 34, 48, 49, 52, 55, 64, 71]. Recent large text-to-image models such asImagen [58], DALL-E2 [51], Parti [69], CogView2 [17] and Stable Diffusion [55] demonstrated unprecedented semantic generation. These models do not provide fine-grained control over a generated image and use text guidance only. Specifically, it is challenging or impossible to preserve the identity of a subject consistently across synthesized images. + +Controllable Generative Models. There are various approaches to control generative models, where some of them might prove to be viable directions for subject-driven prompt-guided image synthesis. Liu et al. [37] propose a diffusion-based technique allowing for image variations guided by reference image or text. To overcome subject modification, several works [3, 42] assume a user-provided mask to restrict the modified area. Inversion [12, 15, 51] can be used to preserve a subject while modifying context. Prompt-to-prompt [23] allows for local and global editing without an input mask. These methods fall short of identity-preserving novel sample generation of a subject. + +In the context of GANs, Pivotal Tuning [54] allows for real image editing by finetuning the model with an inverted latent code anchor, and Nitzan et al. [44] extended this work to GAN finetuning on faces to train a personalized prior, which requires around 100 images and are limited to the face domain. Casanova et al. [11] propose an instance conditioned GAN that can generate variations of an instance, although it can struggle with unique subjects and does not preserve all subject details. + +Finally, the concurrent work of Gal et al. [20] proposes a method to represent visual concepts, like an object or a style, through new tokens in the embedding space of a frozen text-to-image model, resulting in small personalized token embeddings. While this method is limited by the expressiveness of the frozen diffusion model, our fine-tuning approach enables us to embed the subject within the model's output domain, resulting in the generation of novel images of the subject which preserve its key visual features. + +# 3. Method + +Given only a few (typically 3-5) casually captured images of a specific subject, without any textual description, our objective is to generate new images of the subject with high detail fidelity and with variations guided by text prompts. Example variations include changing the subject location, changing subject properties such as color or shape, modifying the subject's pose, viewpoint, and other semantic modifications. We do not impose any restrictions on input image capture settings and the subject image can have varying contexts. We next provide some background on text-to-image diffusion models (Sec. 3.1), then present our finetuning technique to bind a unique identifier with a subject described in a few images (Sec. 3.2), and finally propose a class-specific prior-preservation loss that enables us to overcome language drift in our fine-tuned model (Sec. 3.3). + +# 3.1. Text-to-Image Diffusion Models + +Diffusion models are probabilistic generative models that are trained to learn a data distribution by the gradual denoising of a variable sampled from a Gaussian distribution. Specifically, we are interested in a pre-trained text-to-image diffusion model $\hat{\mathbf{x}}_{\theta}$ that, given an initial noise map $\epsilon \sim \mathcal{N}(\mathbf{0},\mathbf{I})$ and a conditioning vector $\mathbf{c} = \Gamma (\mathbf{P})$ generated using a text encoder $\Gamma$ and a text prompt $\mathbf{P}$ , generates an image $\mathbf{x}_{\mathrm{gen}} = \hat{\mathbf{x}}_{\theta}(\epsilon ,\mathbf{c})$ . They are trained using a squared error loss to denoise a variably-noised image or latent code $\mathbf{z}_t\coloneqq \alpha_t\mathbf{x} + \sigma_t\boldsymbol {\epsilon}$ as follows: + +$$ +\mathbb {E} _ {\mathbf {x}, \mathbf {c}, \boldsymbol {\epsilon}, t} \left[ w _ {t} \| \hat {\mathbf {x}} _ {\theta} \left(\alpha_ {t} \mathbf {x} + \sigma_ {t} \boldsymbol {\epsilon}, \mathbf {c}\right) - \mathbf {x} \| _ {2} ^ {2} \right] \tag {1} +$$ + +where $\mathbf{x}$ is the ground-truth image, $\mathbf{c}$ is a conditioning vector (e.g., obtained from a text prompt), and $\alpha_{t},\sigma_{t},w_{t}$ are terms that control the noise schedule and sample quality, and are functions of the diffusion process time $t\sim$ $\mathcal{U}([0,1])$ . A more detailed description is given in the supplementary material. + +# 3.2. Personalization of Text-to-Image Models + +Our first task is to implant the subject instance into the output domain of the model such that we can query the model for varied novel images of the subject. One natural idea is to fine-tune the model using the few-shot dataset of the subject. Careful care had to be taken when fine-tuning generative models such as GANs in a few-shot scenario as it can cause overfitting and mode-collapse - as well as not capturing the target distribution sufficiently well. There has been research on techniques to avoid these pitfalls [35,40,45,53,66], although, in contrast to our work, this line of work primarily seeks to generate images that resemble the target distribution but has no requirement of subject preservation. With regards to these pitfalls, we observe the peculiar finding that, given a careful fine-tuning setup + +![](images/c7cbf436cc0d1aa70e98add5bfad489037acca707374c036cea8b4ac6f10c08f.jpg) +Figure 3. Fine-tuning. Given $\sim 3 - 5$ images of a subject we fine-tune a text-to-image diffusion model with the input images paired with a text prompt containing a unique identifier and the name of the class the subject belongs to (e.g., "A [V] dog"), in parallel, we apply a class-specific prior preservation loss, which leverages the semantic prior that the model has on the class and encourages it to generate diverse instances belong to the subject's class using the class name in a text prompt (e.g., "A dog"). + +using the diffusion loss from Eq 1, large text-to-image diffusion models seem to excel at integrating new information into their domain without forgetting the prior or overfitting to a small set of training images. + +Designing Prompts for Few-Shot Personalization Our goal is to "implant" a new (unique identifier, subject) pair into the diffusion model's "dictionary". In order to bypass the overhead of writing detailed image descriptions for a given image set we opt for a simpler approach and label all input images of the subject "a [identifier] [class noun]", where [identifier] is a unique identifier linked to the subject and [class noun] is a coarse class descriptor of the subject (e.g. cat, dog, watch, etc.). The class descriptor can be provided by the user or obtained using a classifier. We use a class descriptor in the sentence in order to tether the prior of the class to our unique subject and find that using a wrong class descriptor, or no class descriptor increases training time and language drift while decreasing performance. In essence, we seek to leverage the model's prior of the specific class and entangle it with the embedding of our subject's unique identifier so we can leverage the visual prior to generate new poses and articulations of the subject in different contexts. + +Rare-token Identifiers We generally find existing English words (e.g. "unique", "special") suboptimal since the model has to learn to disentangle them from their original meaning and to re-entangle them to reference our subject. + +This motivates the need for an identifier that has a weak prior in both the language model and the diffusion model. A hazardous way of doing this is to select random characters in the English language and concatenate them to generate a rare identifier (e.g. "xxy5syt00"). In reality, the tokenizer might tokenize each letter separately, and the prior for the diffusion model is strong for these letters. We often find that these tokens incur the similar weaknesses as using common English words. Our approach is to find rare tokens in the vocabulary, and then invert these tokens into text space, in order to minimize the probability of the identifier having a strong prior. We perform a rare-token lookup in the vocabulary and obtain a sequence of rare token identifiers $f(\hat{\mathbf{V}})$ , where $f$ is a tokenizer; a function that maps character sequences to tokens and $\hat{\mathbf{V}}$ is the decoded text stemming from the tokens $f(\hat{\mathbf{V}})$ . The sequence can be of variable length $k$ , and find that relatively short sequences of $k = \{1, \dots, 3\}$ work well. Then, by inverting the vocabulary using the tokenizer on $f(\hat{\mathbf{V}})$ we obtain a sequence of characters that define our unique identifier $\hat{\mathbf{V}}$ . For Imagen, we find that using uniform random sampling of tokens that correspond to 3 or fewer Unicode characters (without spaces) and using tokens in the T5-XXL tokenizer range of $\{5000, \dots, 10000\}$ works well. + +# 3.3. Class-specific Prior Preservation Loss + +In our experience, the best results for maximum subject fidelity are achieved by fine-tuning all layers of the model. This includes fine-tuning layers that are conditioned on the text embeddings, which gives rise to the problem of language drift. Language drift has been an observed problem in language models [32, 38], where a model that is pre-trained on a large text corpus and later fine-tuned for a specific task progressively loses syntactic and semantic knowledge of the language. To the best of our knowledge, we are the first to find a similar phenomenon affecting diffusion models, where to model slowly forgets how to generate subjects of the same class as the target subject. + +Another problem is the possibility of reduced output diversity. Text-to-image diffusion models naturally possess high amounts of output diversity. When fine-tuning on a small set of images we would like to be able to generate the subject in novel viewpoints, poses and articulations. Yet, there is a risk of reducing the amount of variability in the output poses and views of the subject (e.g. snapping to the few-shot views). We observe that this is often the case, especially when the model is trained for too long. + +To mitigate the two aforementioned issues, we propose an autogenous class-specific prior preservation loss that encourages diversity and counters language drift. In essence, our method is to supervise the model with its own generated samples, in order for it to retain the prior once the few-shot fine-tuning begins. This allows it to generate di + +verse images of the class prior, as well as retain knowledge about the class prior that it can use in conjunction with knowledge about the subject instance. Specifically, we generate data $\mathbf{x}_{\mathrm{pr}} = \hat{\mathbf{x}} (\mathbf{z}_{t_1},\mathbf{c}_{\mathrm{pr}})$ by using the ancestral sampler on the frozen pre-trained diffusion model with random initial noise $\mathbf{z}_{t_1}\sim \mathcal{N}(\mathbf{0},\mathbf{I})$ and conditioning vector $\mathbf{c}_{\mathrm{pr}}\coloneqq \Gamma (f("a[class~noun]^")$ ). The loss becomes: + +$$ +\begin{array}{l} \mathbb {E} _ {\mathbf {x}, \mathbf {c}, \epsilon , \epsilon^ {\prime}, t} [ w _ {t} \| \hat {\mathbf {x}} _ {\theta} (\alpha_ {t} \mathbf {x} + \sigma_ {t} \epsilon , \mathbf {c}) - \mathbf {x} \| _ {2} ^ {2} + \\ \lambda w _ {t ^ {\prime}} \| \hat {\mathbf {x}} _ {\theta} \left(\alpha_ {t ^ {\prime}} \mathbf {x} _ {\mathrm {p r}} + \sigma_ {t ^ {\prime}} \boldsymbol {\epsilon} ^ {\prime}, \mathbf {c} _ {\mathrm {p r}}\right) - \mathbf {x} _ {\mathrm {p r}} \| _ {2} ^ {2} ], \tag {2} \\ \end{array} +$$ + +where the second term is the prior-preservation term that supervises the model with its own generated images, and $\lambda$ controls for the relative weight of this term. Figure 3 illustrates the model fine-tuning with the class-generated samples and prior-preservation loss. Despite being simple, we find this prior-preservation loss is effective in encouraging output diversity and in overcoming language-drift. We also find that we can train the model for more iterations without risking overfitting. We find that $\sim 1000$ iterations with $\lambda = 1$ and learning rate $10^{-5}$ for Imagen [58] and $5 \times 10^{-6}$ for Stable Diffusion [56], and with a subject dataset size of 3-5 images is enough to achieve good results. During this process, $\sim 1000$ "a [class noun]" samples are generated - but less can be used. The training process takes about 5 minutes on one TPUv4 for Imagen, and 5 minutes on a NVIDIA A100 for Stable Diffusion. + +# 4. Experiments + +In this section, we show experiments and applications. Our method enables a large expanse of text-guided semantic modifications of our subject instances, including recontextualization, modification of subject properties such as material and species, art rendition, and viewpoint modification. Importantly, across all of these modifications, we are able to preserve the unique visual features that give the subject its identity and essence. If the task is recontextualization, then the subject features are unmodified, but appearance (e.g., pose) may change. If the task is a stronger semantic modification, such as crossing between our subject and another species/object, then the key features of the subject are preserved after modification. In this section, we reference the subject's unique identifier using [V]. We include specific Imagen and Stable Diffusion implementation details in the supp. material. + +# 4.1. Dataset and Evaluation + +Dataset We collected a dataset of 30 subjects, including unique objects and pets such as backpacks, stuffed animals, dogs, cats, sunglasses, cartoons, etc. Images for this dataset were collected by the authors or sourced from Unsplash [1]. We also collected 25 prompts: 20 recontextualization prompts and 5 property modification prompts for + +![](images/aee47dcdbc8578c305dc5eef0fd1db433b1e948bace2ee720a996d17b7989565.jpg) +Figure 4. Comparisons with Textual Inversion [20] Given 4 input images (top row), we compare: DreamBooth Imagen (2nd row), DreamBooth Stable Diffusion (3rd row), Textual Inversion (bottom row). Output images were created with the following prompts (left to right): "a [V] vase in the snow", "a [V] vase on the beach", "a [V] vase in the jungle", "a [V] vase with the Eiffel Tower in the background". DreamBooth is stronger in both subject and prompt fidelity. + +
MethodDINO ↑CLIP-I ↑CLIP-T ↑
Real Images0.7740.885N/A
DreamBooth (Imagen)0.6960.8120.306
DreamBooth (Stable Diffusion)0.6680.8030.305
Textual Inversion (Stable Diffusion)0.5690.7800.255
+ +Table 1. Subject fidelity (DINO, CLIP-I) and prompt fidelity (CLIP-T, CLIP-T-L) quantitative metric comparison. + +
MethodSubject Fidelity ↑Prompt Fidelity ↑
DreamBooth (Stable Diffusion)68%81%
Textual Inversion (Stable Diffusion)22%12%
Undecided10%7%
+ +Table 2. Subject fidelity and prompt fidelity user preference. + +objects; 10 recontextualization, 10 accessorization, and 5 property modification prompts for live subjects/pets. The full list of images and prompts can be found in the supplementary material. + +For the evaluation suite we generate four images per subject and per prompt, totaling 3,000 images. This allows us + +![](images/28aff1ddc51eaa78fd4f9fb02089d0ffc1b9468019c019d73ef36bf019786bc6.jpg) +Input images + +![](images/07f9b84995d19538c736a6d37bbf5651126517d6612c658c810995d118884b96.jpg) +w/o prior-preservation loss + +![](images/2f20582f418d00e378dd860aa844384e8bb48376219093cb58f51b3d88201c95.jpg) +with prior-preservation loss +Figure 5. Encouraging diversity with prior-preservation loss. Naive fine-tuning can result in overfitting to input image context and subject appearance (e.g. pose). PPL acts as a regularizer that alleviates overfitting and encourages diversity, allowing for more pose variability and appearance diversity. + +to robustly measure performances and generalization capabilities of a method. We make our dataset and evaluation protocol publicly available on the project webpage for future use in evaluating subject-driven generation. + +Evaluation Metrics One important aspect to evaluate is subject fidelity: the preservation of subject details in generated images. For this, we compute two metrics: CLIP-I and DINO [10]. CLIP-I is the average pairwise cosine similarity between CLIP [50] embeddings of generated and real images. Although this metric has been used in other work [20], it is not constructed to distinguish between different subjects that could have highly similar text descriptions (e.g. two different yellow clocks). Our proposed DINO metric is the average pairwise cosine similarity between the ViT-S/16 DINO embeddings of generated and real images. This is our preferred metric, since, by construction and in contrast to supervised networks, DINO is not trained to ignore differences between subjects of the same class. Instead, the self-supervised training objective encourages distinction of unique features of a subject or image. The second important aspect to evaluate is prompt fidelity, measured as the average cosine similarity between prompt and image CLIP embeddings. We denote this as CLIP-T. + +# 4.2. Comparisons + +We compare our results with Textual Inversion, the recent concurrent work of Gal et al. [20], using the hyperparameters provided in their work. We find that this work is + +the only comparable work in the literature that is subject-driven, text-guided and generates novel images. We generate images for DreamBooth using Imagen, DreamBooth using Stable Diffusion and Textual Inversion using Stable Diffusion. We compute DINO and CLIP-I subject fidelity metrics and the CLIP-T prompt fidelity metric. In Table 1 we show sizeable gaps in both subject and prompt fidelity metrics for DreamBooth over Textual Inversion. We find that DreamBooth (Imagen) achieves higher scores for both subject and prompt fidelity than DreamBooth (Stable Diffusion), approaching the upper-bound of subject fidelity for real images. We believe that this is due to the larger expressive power and higher output quality of Imagen. + +Further, we compare Textual Inversion (Stable Diffusion) and DreamBooth (Stable Diffusion) by conducting a user study. For subject fidelity, we asked 72 users to answer questionnaires of 25 comparative questions (3 users per questionnaire), totaling 1800 answers. Samples are randomly selected from a large pool. Each question shows the set of real images for a subject, and one generated image of that subject by each method (with a random prompt). Users are asked to answer the question: "Which of the two images best reproduces the identity (e.g. item type and details) of the reference item?", and we include a "Cannot Determine / Both Equally" option. Similarly for prompt fidelity, we ask "Which of the two images is best described by the reference text?". We average results using majority voting and present them in Table 2. We find an overwhelming preference for DreamBooth for both subject fidelity and prompt fidelity. This shines a light on results in Table 1, where DINO differences of around 0.1 and CLIP-T differences of 0.05 are significant in terms of user preference. Finally, we show qualitative comparisons in Figure 4. We observe that DreamBooth better preserves subject identity, and is more faithful to prompts. We show samples of the user study in the supp. material. + +# 4.3. Ablation Studies + +Prior Preservation Loss Ablation We fine-tune Imagen on 15 subjects from our dataset, with and without our proposed prior preservation loss (PPL). The prior preservation loss seeks to combat language drift and preserve the prior. We compute a prior preservation metric (PRES) by computing the average pairwise DINO embeddings between generated images of random subjects of the prior class and real images of our specific subject. The higher this metric, the more similar random subjects of the class are to our specific subject, indicating collapse of the prior. We report results in Table 3 and observe that PPL substantially counteracts language drift and helps retain the ability to generate diverse images of the prior class. Additionally, we compute a diversity metric (DIV) using the average LPIPS [70] cosine similarity between generated images of same subject with + +![](images/902a65ada13ea4e80f72741a1a6edc2b76124b42e5e6c30da35e229d945a52ae.jpg) +Input images + +![](images/47b34d7771a57259b777df8a2791913fd0a23663824dd0f892ea3bcd2e714600.jpg) +A [V] backpack in the Grand Canyon + +![](images/bd605973e071ac6ab47b404ffe26539de65d48bfb54af04cd42122b5394f6c59.jpg) +A wet [V] backpack in water + +![](images/f98da00597c135ed579552b0cd08735a5526e95fd39394aa8c812d3c4d15b04a.jpg) +A [V] backpack in Boston + +![](images/4ff637ebbb0e5affcbe4f1bc39afae2e09993711ceb5d478d0ed6854fa2ee812.jpg) +A [V] backpack with the night sky + +![](images/2bb0c349ac60d94a375a342173e96ef3daea128399eaed43d23f31d5aa8cadfb.jpg) +Input images + +![](images/59752e2bc7139db6ad6226c3e9cf6f84ec57b6783eddb1f89746f9668e542227.jpg) +A [V] teapot floating in milk + +![](images/62c33ac8c97ae3822790092b16e4b24f0871e9cd3a4d5f4918706e0cc30f5ed2.jpg) +A transparent [V] teapot with milk inside + +![](images/a8e847849a70957febeaee0ea23ac6edaa4a22ca110c7404481b8ba8e662feea.jpg) +A [V] teapot pouring tea + +![](images/35d2250ce44be635e3ca43866f470d433e5c8be908eea4236fe1b6f31383b058.jpg) +A [V] teapot floating in the sea +Figure 6. Recontextualization. We generate images of the subjects in different environments, with high preservation of subject details and realistic scene-subject interactions. We show the prompts below each image. + +
MethodPRES ↓DIV ↑DINO ↑CLIP-I ↑CLIP-T ↑
DreamBooth (Imagen) w/ PPL0.4930.3910.6840.8150.308
DreamBooth (Imagen)0.6640.3710.7120.8280.306
+ +Table 3. Prior preservation loss (PPL) ablation displaying a prior preservation (PRES) metric, diversity metric (DIV) and subject and prompt fidelity metrics. + +
MethodDINO ↑CLIP-I ↑
Correct Class0.7440.853
No Class0.3030.607
Wrong Class0.4540.728
+ +Table 4. Class name ablation with subject fidelity metrics. + +same prompt. We observe that our model trained with PPL achieves higher diversity (with slightly diminished subject fidelity), which can also be observed qualitatively in Figure 5, where our model trained with PPL overfits less to the environment of the reference images and can generate the dog in more diverse poses and articulations. + +Class-Prior Ablation We finetune Imagen on a subset of our dataset subjects (5 subjects) with no class noun, a randomly sampled incorrect class noun, and the correct class noun. With the correct class noun for our subject, we are able to faithfully fit to the subject, take advantage of the class prior, allowing us to generate our subject in various contexts. When an incorrect class noun (e.g. "can" for a backpack) is used, we run into contention between our subject and and the class prior - sometimes obtaining cylindri + +cal backpacks, or otherwise misshapen subjects. If we train with no class noun, the model does not leverage the class prior, has difficulty learning the subject and converging, and can generate erroneous samples. Subject fidelity results are shown in Table 4, with substantially higher subject fidelity for our proposed approach. + +# 4.4. Applications + +Recontextualization We can generate novel images for a specific subject in different contexts (Figure 6) with descriptive prompts ("a [V] [class noun] [context description)"). Importantly, we are able to generate the subject in new poses and articulations, with previously unseen scene structure and realistic integration of the subject in the scene (e.g. contact, shadows, reflections). + +Art Renditions Given a prompt “a painting of a [V] [class noun] in the style of [famous painter]” or “a statue of a [V] [class noun] in the style of [famous sculptor]” we are able to generate artistic renditions of our subject. Unlike style transfer, where the source structure is preserved and only the style is transferred, we are able to generate meaningful, novel variations depending on the artistic style, while preserving subject identity. E.g., as shown in Figure 7, “Michelangelo”, we generated a pose that is novel and not seen in the input images. + +Novel View Synthesis We are able to render the subject under novel viewpoints. In Figure 7, we generate new images of the input cat (with consistent complex fur patterns) + +![](images/67bfe2a7a9c50225b443313d746c869c05fe41ebb3b449a98b294d7596fa5707.jpg) +Figure 7. Novel view synthesis, art renditions, and property modifications. We are able to generate novel and meaningful images while faithfully preserving subject identity and essence. More applications and examples in the supplementary material. + +![](images/4ce3f54196e57db34a5f47f3f46e3a830fb3bdf5acf1ed5c6941d07f0bf74f8c.jpg) +(b) Context-appearance entanglement + +![](images/271595383f4c5e363a3d72b1ef87efd0f3f1483cff4fe679aaf6afcc3af595c1.jpg) +(a) Incorrect context synthesis +in the ISS + +![](images/256d62bdb1b058df2ee43fdb453451f721e697b97b8163c6cf56ff850953699b.jpg) +on the moon + +![](images/a12117a968f8a68ae26b5d5cf5c58528a76ef0dce90b5a9ea8c820722702ffd1.jpg) +in the Bolivian salt flats +on top of a blue fabric +Figure 8. Failure modes. Given a rare prompted context the model might fail at generating the correct environment (a). It is possible for context and subject appearance to become entangled (b). Finally, it is possible for the model to overfit and generate images similar to the training set, especially if prompts reflect the original environment of the training set (c). + +![](images/33010a76d4fe29e907525b3b3f8e4ba6b26b69d7d0edf6e610643b97f6920a95.jpg) +(c) Overfitting +in the forest + +under new viewpoints. We highlight that the model has not seen this specific cat from behind, below, or above - yet it is able to extrapolate knowledge from the class prior to generate these novel views given only 4 frontal images of the subject. + +Property Modification We are able to modify subject properties. For example, we show crosses between a specific Chow Chow dog and different animal species in the bottom row of Figure 7. We prompt the model with sentences of the following structure: "a cross of a [V] dog and a [target species]". In particular, we can see in this example that the identity of the dog is well preserved even when the species changes - the face of the dog has certain unique features that are well preserved and melded with the target species. Other property modifications are possible, such as material modification (e.g. "a transparent [V] teapot" in Figure 6). Some are harder than others and depend on the prior of the base generation model. + +# 4.5. Limitations + +We illustrate some failure models of our method in Figure 8. The first is related to not being able to accurately generate the prompted context. Possible reasons are a weak prior for these contexts, or difficulty in generating both the subject and specified concept together due to low probability of co-occurrence in the training set. The second is context-appearance entanglement, where the appearance of the subject changes due to the prompted context, exemplified in Figure 8 with color changes of the backpack. Third, we also observe overfitting to the real images that happen when the prompt is similar to the original setting in which the subject was seen. + +Other limitations are that some subjects are easier to learn than others (e.g. dogs and cats). Occasionally, with subjects that are rarer, the model is unable to support as many subject variations. Finally, there is also variability in the fidelity of the subject and some generated images might contain hallucinated subject features, depending on the strength of the model prior, and the complexity of the semantic modification. + +# 5. Conclusions + +We presented an approach for synthesizing novel renditions of a subject using a few images of the subject and the guidance of a text prompt. Our key idea is to embed a given subject instance in the output domain of a text-to-image diffusion model by binding the subject to a unique identifier. 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"text", + "content": "Large text-to-image models achieved a remarkable leap in the evolution of AI, enabling high-quality and diverse synthesis of images from a given text prompt. However, these models lack the ability to mimic the appearance of subjects in a given reference set and synthesize novel renditions of them in different contexts. In this work, we present a new approach for \"personalization\" of text-to-image diffusion models. Given as input just a few images of a subject, we fine-tune a pretrained text-to-image model such that it learns to bind a unique identifier with that specific subject. Once the subject is embedded in the output domain of the model, the unique identifier can be used to synthesize novel photorealistic images of the subject contextualized in different scenes. By leveraging the semantic prior embedded in the model with a new autogenous class-specific prior preservation loss, our technique enables synthesizing the subject in diverse scenes, poses, views and lighting conditions that do not appear in the reference images. We apply our technique to several previously-unassailable tasks, including subject recontextualization, text-guided view synthesis, and artistic rendering, all while preserving the subject's key features. We also provide a new dataset and evaluation protocol for this new task of subject-driven generation. Project page: https://dreambooth.github.io/" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 307, + 415, + 386, + 427 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 415, + 386, + 427 + ], + "spans": [ + { + "bbox": [ + 307, + 415, + 386, + 427 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 435, + 545, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 435, + 545, + 529 + ], + "spans": [ + { + "bbox": [ + 304, + 435, + 545, + 529 + ], + "type": "text", + "content": "Can you imagine your own dog traveling around the world, or your favorite bag displayed in the most exclusive showroom in Paris? What about your parrot being the main character of an illustrated storybook? Rendering such imaginary scenes is a challenging task that requires synthesizing instances of specific subjects (e.g., objects, animals) in new contexts such that they naturally and seamlessly blend into the scene." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 531, + 546, + 711 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 531, + 546, + 711 + ], + "spans": [ + { + "bbox": [ + 304, + 531, + 546, + 711 + ], + "type": "text", + "content": "Recently developed large text-to-image models have shown unprecedented capabilities, by enabling high-quality and diverse synthesis of images based on a text prompt written in natural language [51,58]. One of the main advantages of such models is the strong semantic prior learned from a large collection of image-caption pairs. Such a prior learns, for instance, to bind the word \"dog\" with various instances of dogs that can appear in different poses and contexts in an image. While the synthesis capabilities of these models are unprecedented, they lack the ability to mimic the appearance of subjects in a given reference set, and synthesize novel renditions of the same subjects in different contexts. The main reason is that the expressiveness of their output domain is limited; even the most detailed textual description of an object may yield instances with different appearances." + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 65, + 702, + 280, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 702, + 280, + 713 + ], + "spans": [ + { + "bbox": [ + 65, + 702, + 280, + 713 + ], + "type": "text", + "content": "*This research was performed while Nataniel Ruiz was at Google." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "22500" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": "Furthermore, even models whose text embedding lies in a shared language-vision space [50] cannot accurately reconstruct the appearance of given subjects but only create variations of the image content (Figure 2)." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 121, + 288, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 121, + 288, + 275 + ], + "spans": [ + { + "bbox": [ + 46, + 121, + 288, + 275 + ], + "type": "text", + "content": "In this work, we present a new approach for \"personalization\" of text-to-image diffusion models (adapting them to user-specific image generation needs). Our goal is to expand the language-vision dictionary of the model such that it binds new words with specific subjects the user wants to generate. Once the new dictionary is embedded in the model, it can use these words to synthesize novel photorealistic images of the subject, contextualized in different scenes, while preserving their key identifying features. The effect is akin to a \"magic photo booth\"—once a few images of the subject are taken, the booth generates photos of the subject in different conditions and scenes, as guided by simple and intuitive text prompts (Figure 1)." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 275, + 287, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 275, + 287, + 357 + ], + "spans": [ + { + "bbox": [ + 46, + 275, + 287, + 357 + ], + "type": "text", + "content": "More formally, given a few images of a subject (" + }, + { + "bbox": [ + 46, + 275, + 287, + 357 + ], + "type": "inline_equation", + "content": "\\sim 3-5" + }, + { + "bbox": [ + 46, + 275, + 287, + 357 + ], + "type": "text", + "content": "), our objective is to implant the subject into the output domain of the model such that it can be synthesized with a unique identifier. To that end, we propose a technique to represent a given subject with rare token identifiers and fine-tune a pre-trained, diffusion-based text-to-image framework." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 359, + 287, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 359, + 287, + 502 + ], + "spans": [ + { + "bbox": [ + 46, + 359, + 287, + 502 + ], + "type": "text", + "content": "We fine-tune the text-to-image model with the input images and text prompts containing a unique identifier followed by the class name of the subject (e.g., \"A [V] dog\"). The latter enables the model to use its prior knowledge on the subject class while the class-specific instance is bound with the unique identifier. In order to prevent language drift [32, 38] that causes the model to associate the class name (e.g., \"dog\") with the specific instance, we propose an autogenous, class-specific prior preservation loss, which leverages the semantic prior on the class that is embedded in the model, and encourages it to generate diverse instances of the same class as our subject." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 502, + 287, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 502, + 287, + 622 + ], + "spans": [ + { + "bbox": [ + 46, + 502, + 287, + 622 + ], + "type": "text", + "content": "We apply our approach to a myriad of text-based image generation applications including recontextualization of subjects, modification of their properties, original art renditions, and more, paving the way to a new stream of previously unassailable tasks. We highlight the contribution of each component in our method via ablation studies, and compare with alternative baselines and related work. We also conduct a user study to evaluate subject and prompt fidelity in our synthesized images, compared to alternative approaches." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 622, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 622, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 622, + 287, + 693 + ], + "type": "text", + "content": "To the best of our knowledge, ours is the first technique that tackles this new challenging problem of subject-driven generation, allowing users, from just a few casually captured images of a subject, synthesize novel renditions of the subject in different contexts while maintaining its distinctive features." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 59, + 694, + 287, + 706 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 694, + 287, + 706 + ], + "spans": [ + { + "bbox": [ + 59, + 694, + 287, + 706 + ], + "type": "text", + "content": "To evaluate this new task, we also construct a new dataset" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 319, + 72, + 414, + 133 + ], + "blocks": [ + { + "bbox": [ + 319, + 72, + 414, + 133 + ], + "lines": [ + { + "bbox": [ + 319, + 72, + 414, + 133 + ], + "spans": [ + { + "bbox": [ + 319, + 72, + 414, + 133 + ], + "type": "image", + "image_path": "c3c53d6f4cd1fba09cbf2caaa7c804cc71abc99fa0e4518b52a7fe09ab265c45.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 326, + 134, + 414, + 178 + ], + "blocks": [ + { + "bbox": [ + 326, + 134, + 414, + 178 + ], + "lines": [ + { + "bbox": [ + 326, + 134, + 414, + 178 + ], + "spans": [ + { + "bbox": [ + 326, + 134, + 414, + 178 + ], + "type": "image", + "image_path": "4f53552b3939b88c44a0919c428583283856e60d524e02f3bd19eb6a4a09f13f.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 353, + 180, + 395, + 190 + ], + "lines": [ + { + "bbox": [ + 353, + 180, + 395, + 190 + ], + "spans": [ + { + "bbox": [ + 353, + 180, + 395, + 190 + ], + "type": "text", + "content": "Input Images" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 424, + 72, + 467, + 127 + ], + "blocks": [ + { + "bbox": [ + 424, + 72, + 467, + 127 + ], + "lines": [ + { + "bbox": [ + 424, + 72, + 467, + 127 + ], + "spans": [ + { + "bbox": [ + 424, + 72, + 467, + 127 + ], + "type": "image", + "image_path": "130b008d17545087bb94eb3e6d76948c9f35c35f12bb2fecc8387d3bbbb67a77.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 433, + 127, + 499, + 178 + ], + "blocks": [ + { + "bbox": [ + 433, + 127, + 499, + 178 + ], + "lines": [ + { + "bbox": [ + 433, + 127, + 499, + 178 + ], + "spans": [ + { + "bbox": [ + 433, + 127, + 499, + 178 + ], + "type": "image", + "image_path": "5731f5f93b4025c60645f4d8077768cfd21ff3d45731f041b3738e86f26866d7.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 444, + 180, + 523, + 189 + ], + "lines": [ + { + "bbox": [ + 444, + 180, + 523, + 189 + ], + "spans": [ + { + "bbox": [ + 444, + 180, + 523, + 189 + ], + "type": "text", + "content": "Image-guided, DALL-E2" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 517, + 85, + 529, + 106 + ], + "blocks": [ + { + "bbox": [ + 517, + 85, + 529, + 106 + ], + "lines": [ + { + "bbox": [ + 517, + 85, + 529, + 106 + ], + "spans": [ + { + "bbox": [ + 517, + 85, + 529, + 106 + ], + "type": "image", + "image_path": "94bea41ded2188391e42ca3530a2c314b39985ee3e69c61d7752d71e27025485.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 318, + 196, + 425, + 303 + ], + "blocks": [ + { + "bbox": [ + 318, + 196, + 425, + 303 + ], + "lines": [ + { + "bbox": [ + 318, + 196, + 425, + 303 + ], + "spans": [ + { + "bbox": [ + 318, + 196, + 425, + 303 + ], + "type": "image", + "image_path": "379e3d99f0e9e7f2003d45b828ba516c2219ba93b61f5ee89739bb5f0c07bbf4.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 343, + 304, + 406, + 313 + ], + "lines": [ + { + "bbox": [ + 343, + 304, + 406, + 313 + ], + "spans": [ + { + "bbox": [ + 343, + 304, + 406, + 313 + ], + "type": "text", + "content": "Text-guided, Imagen" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 323, + 545, + 422 + ], + "lines": [ + { + "bbox": [ + 305, + 323, + 545, + 422 + ], + "spans": [ + { + "bbox": [ + 305, + 323, + 545, + 422 + ], + "type": "text", + "content": "Figure 2. Subject-driven generation. Given a particular clock (left), it is hard to generate it while maintaining high fidelity to its key visual features (second and third columns showing DALL-E2 [51] image-guided generation andImagen [58] text-guided generation; text prompt used forImagen: \"retro style yellow alarm clock with a white clock face and a yellow number three on the right part of the clock face in the jungle\"). Our approach (right) can synthesize the clock with high fidelity and in new contexts (text prompt: \"a " + }, + { + "bbox": [ + 305, + 323, + 545, + 422 + ], + "type": "inline_equation", + "content": "[V]" + }, + { + "bbox": [ + 305, + 323, + 545, + 422 + ], + "type": "text", + "content": " clock in the jungle\")." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 427, + 196, + 532, + 303 + ], + "blocks": [ + { + "bbox": [ + 427, + 196, + 532, + 303 + ], + "lines": [ + { + "bbox": [ + 427, + 196, + 532, + 303 + ], + "spans": [ + { + "bbox": [ + 427, + 196, + 532, + 303 + ], + "type": "image", + "image_path": "0bbf76bf092e8ddcf7fac6b8ad3c166e239d6e4ddcc8ca4339003f64d9a67ad1.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 474, + 305, + 490, + 312 + ], + "lines": [ + { + "bbox": [ + 474, + 305, + 490, + 312 + ], + "spans": [ + { + "bbox": [ + 474, + 305, + 490, + 312 + ], + "type": "text", + "content": "Ours" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 430, + 545, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 430, + 545, + 491 + ], + "spans": [ + { + "bbox": [ + 305, + 430, + 545, + 491 + ], + "type": "text", + "content": "that contains various subjects captured in different contexts, and propose a new evaluation protocol that measures the subject fidelity and prompt fidelity of the generated results. We make our dataset and evaluation protocol publicly available on the project webpage" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 501, + 389, + 513 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 501, + 389, + 513 + ], + "spans": [ + { + "bbox": [ + 306, + 501, + 389, + 513 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 521, + 545, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 521, + 545, + 640 + ], + "spans": [ + { + "bbox": [ + 305, + 521, + 545, + 640 + ], + "type": "text", + "content": "Image Composition. Image composition techniques [13, 36, 67] aim to clone a given subject into a new background such that the subject melds into the scene. To consider composition in novel poses, one may apply 3D reconstruction techniques [6, 8, 39, 47, 65] which usually works on rigid objects and require a larger number of views. Some drawbacks include scene integration (lighting, shadows, contact) and the inability to generate novel scenes. In contrast, our approach enables generation of subjects in novel poses and new contexts." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 641, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 641, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 305, + 641, + 545, + 712 + ], + "type": "text", + "content": "Text-to-Image Editing and Synthesis. Text-driven image manipulation has recently achieved significant progress using GANs [9, 22, 27-29] combined with image-text representations such as CLIP [50], yielding realistic manipulations using text [2, 7, 21, 41, 46, 68]. These methods work well on structured scenarios (e.g. human face edit" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22501" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": "ing) and can struggle over diverse datasets where subjects are varied. Crowson et al. [14] use VQ-GAN [18] and train over more diverse data to alleviate this concern. Other works [4, 30] exploit the recent diffusion models [25, 25, 43, 55, 57, 59–63], which achieve state-of-the-art generation quality over highly diverse datasets, often surpassing GANs [15]. While most works that require only text are limited to global editing [14, 31], Bar-Tal et al. [5] proposed a text-based localized editing technique without using masks, showing impressive results. While most of these editing approaches allow modification of global properties or local editing of a given image, none enables generating novel renditions of a given subject in new contexts." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 228, + 289, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 228, + 289, + 335 + ], + "spans": [ + { + "bbox": [ + 46, + 228, + 289, + 335 + ], + "type": "text", + "content": "There also exists work on text-to-image synthesis [14, 16, 19, 24, 26, 33, 34, 48, 49, 52, 55, 64, 71]. Recent large text-to-image models such asImagen [58], DALL-E2 [51], Parti [69], CogView2 [17] and Stable Diffusion [55] demonstrated unprecedented semantic generation. These models do not provide fine-grained control over a generated image and use text guidance only. Specifically, it is challenging or impossible to preserve the identity of a subject consistently across synthesized images." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 335, + 289, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 335, + 289, + 479 + ], + "spans": [ + { + "bbox": [ + 46, + 335, + 289, + 479 + ], + "type": "text", + "content": "Controllable Generative Models. There are various approaches to control generative models, where some of them might prove to be viable directions for subject-driven prompt-guided image synthesis. Liu et al. [37] propose a diffusion-based technique allowing for image variations guided by reference image or text. To overcome subject modification, several works [3, 42] assume a user-provided mask to restrict the modified area. Inversion [12, 15, 51] can be used to preserve a subject while modifying context. Prompt-to-prompt [23] allows for local and global editing without an input mask. These methods fall short of identity-preserving novel sample generation of a subject." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 479, + 289, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 479, + 289, + 586 + ], + "spans": [ + { + "bbox": [ + 46, + 479, + 289, + 586 + ], + "type": "text", + "content": "In the context of GANs, Pivotal Tuning [54] allows for real image editing by finetuning the model with an inverted latent code anchor, and Nitzan et al. [44] extended this work to GAN finetuning on faces to train a personalized prior, which requires around 100 images and are limited to the face domain. Casanova et al. [11] propose an instance conditioned GAN that can generate variations of an instance, although it can struggle with unique subjects and does not preserve all subject details." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 586, + 289, + 695 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 586, + 289, + 695 + ], + "spans": [ + { + "bbox": [ + 46, + 586, + 289, + 695 + ], + "type": "text", + "content": "Finally, the concurrent work of Gal et al. [20] proposes a method to represent visual concepts, like an object or a style, through new tokens in the embedding space of a frozen text-to-image model, resulting in small personalized token embeddings. While this method is limited by the expressiveness of the frozen diffusion model, our fine-tuning approach enables us to embed the subject within the model's output domain, resulting in the generation of novel images of the subject which preserve its key visual features." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 71, + 362, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 71, + 362, + 84 + ], + "spans": [ + { + "bbox": [ + 305, + 71, + 362, + 84 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 91, + 547, + 272 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 91, + 547, + 272 + ], + "spans": [ + { + "bbox": [ + 304, + 91, + 547, + 272 + ], + "type": "text", + "content": "Given only a few (typically 3-5) casually captured images of a specific subject, without any textual description, our objective is to generate new images of the subject with high detail fidelity and with variations guided by text prompts. Example variations include changing the subject location, changing subject properties such as color or shape, modifying the subject's pose, viewpoint, and other semantic modifications. We do not impose any restrictions on input image capture settings and the subject image can have varying contexts. We next provide some background on text-to-image diffusion models (Sec. 3.1), then present our finetuning technique to bind a unique identifier with a subject described in a few images (Sec. 3.2), and finally propose a class-specific prior-preservation loss that enables us to overcome language drift in our fine-tuned model (Sec. 3.3)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 277, + 479, + 291 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 277, + 479, + 291 + ], + "spans": [ + { + "bbox": [ + 305, + 277, + 479, + 291 + ], + "type": "text", + "content": "3.1. Text-to-Image Diffusion Models" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 297, + 547, + 417 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 297, + 547, + 417 + ], + "spans": [ + { + "bbox": [ + 304, + 297, + 547, + 417 + ], + "type": "text", + "content": "Diffusion models are probabilistic generative models that are trained to learn a data distribution by the gradual denoising of a variable sampled from a Gaussian distribution. Specifically, we are interested in a pre-trained text-to-image diffusion model " + }, + { + "bbox": [ + 304, + 297, + 547, + 417 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{x}}_{\\theta}" + }, + { + "bbox": [ + 304, + 297, + 547, + 417 + ], + "type": "text", + "content": " that, given an initial noise map " + }, + { + "bbox": [ + 304, + 297, + 547, + 417 + ], + "type": "inline_equation", + "content": "\\epsilon \\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})" + }, + { + "bbox": [ + 304, + 297, + 547, + 417 + ], + "type": "text", + "content": " and a conditioning vector " + }, + { + "bbox": [ + 304, + 297, + 547, + 417 + ], + "type": "inline_equation", + "content": "\\mathbf{c} = \\Gamma (\\mathbf{P})" + }, + { + "bbox": [ + 304, + 297, + 547, + 417 + ], + "type": "text", + "content": " generated using a text encoder " + }, + { + "bbox": [ + 304, + 297, + 547, + 417 + ], + "type": "inline_equation", + "content": "\\Gamma" + }, + { + "bbox": [ + 304, + 297, + 547, + 417 + ], + "type": "text", + "content": " and a text prompt " + }, + { + "bbox": [ + 304, + 297, + 547, + 417 + ], + "type": "inline_equation", + "content": "\\mathbf{P}" + }, + { + "bbox": [ + 304, + 297, + 547, + 417 + ], + "type": "text", + "content": ", generates an image " + }, + { + "bbox": [ + 304, + 297, + 547, + 417 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{\\mathrm{gen}} = \\hat{\\mathbf{x}}_{\\theta}(\\epsilon ,\\mathbf{c})" + }, + { + "bbox": [ + 304, + 297, + 547, + 417 + ], + "type": "text", + "content": ". They are trained using a squared error loss to denoise a variably-noised image or latent code " + }, + { + "bbox": [ + 304, + 297, + 547, + 417 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_t\\coloneqq \\alpha_t\\mathbf{x} + \\sigma_t\\boldsymbol {\\epsilon}" + }, + { + "bbox": [ + 304, + 297, + 547, + 417 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 347, + 425, + 545, + 441 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 425, + 545, + 441 + ], + "spans": [ + { + "bbox": [ + 347, + 425, + 545, + 441 + ], + "type": "interline_equation", + "content": "\\mathbb {E} _ {\\mathbf {x}, \\mathbf {c}, \\boldsymbol {\\epsilon}, t} \\left[ w _ {t} \\| \\hat {\\mathbf {x}} _ {\\theta} \\left(\\alpha_ {t} \\mathbf {x} + \\sigma_ {t} \\boldsymbol {\\epsilon}, \\mathbf {c}\\right) - \\mathbf {x} \\| _ {2} ^ {2} \\right] \\tag {1}", + "image_path": "29520dd521a11e9ad2c040f4f2a55117c6cd3af6e7bf752a7e33d1d6ebad85f6.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 448, + 547, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 448, + 547, + 520 + ], + "spans": [ + { + "bbox": [ + 304, + 448, + 547, + 520 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 448, + 547, + 520 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 448, + 547, + 520 + ], + "type": "text", + "content": " is the ground-truth image, " + }, + { + "bbox": [ + 304, + 448, + 547, + 520 + ], + "type": "inline_equation", + "content": "\\mathbf{c}" + }, + { + "bbox": [ + 304, + 448, + 547, + 520 + ], + "type": "text", + "content": " is a conditioning vector (e.g., obtained from a text prompt), and " + }, + { + "bbox": [ + 304, + 448, + 547, + 520 + ], + "type": "inline_equation", + "content": "\\alpha_{t},\\sigma_{t},w_{t}" + }, + { + "bbox": [ + 304, + 448, + 547, + 520 + ], + "type": "text", + "content": " are terms that control the noise schedule and sample quality, and are functions of the diffusion process time " + }, + { + "bbox": [ + 304, + 448, + 547, + 520 + ], + "type": "inline_equation", + "content": "t\\sim" + }, + { + "bbox": [ + 304, + 448, + 547, + 520 + ], + "type": "inline_equation", + "content": "\\mathcal{U}([0,1])" + }, + { + "bbox": [ + 304, + 448, + 547, + 520 + ], + "type": "text", + "content": ". A more detailed description is given in the supplementary material." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 527, + 519, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 527, + 519, + 540 + ], + "spans": [ + { + "bbox": [ + 305, + 527, + 519, + 540 + ], + "type": "text", + "content": "3.2. Personalization of Text-to-Image Models" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "type": "text", + "content": "Our first task is to implant the subject instance into the output domain of the model such that we can query the model for varied novel images of the subject. One natural idea is to fine-tune the model using the few-shot dataset of the subject. Careful care had to be taken when fine-tuning generative models such as GANs in a few-shot scenario as it can cause overfitting and mode-collapse - as well as not capturing the target distribution sufficiently well. There has been research on techniques to avoid these pitfalls [35,40,45,53,66], although, in contrast to our work, this line of work primarily seeks to generate images that resemble the target distribution but has no requirement of subject preservation. With regards to these pitfalls, we observe the peculiar finding that, given a careful fine-tuning setup" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "22502" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 71, + 282, + 257 + ], + "blocks": [ + { + "bbox": [ + 53, + 71, + 282, + 257 + ], + "lines": [ + { + "bbox": [ + 53, + 71, + 282, + 257 + ], + "spans": [ + { + "bbox": [ + 53, + 71, + 282, + 257 + ], + "type": "image", + "image_path": "c7cbf436cc0d1aa70e98add5bfad489037acca707374c036cea8b4ac6f10c08f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 262, + 288, + 353 + ], + "lines": [ + { + "bbox": [ + 46, + 262, + 288, + 353 + ], + "spans": [ + { + "bbox": [ + 46, + 262, + 288, + 353 + ], + "type": "text", + "content": "Figure 3. Fine-tuning. Given " + }, + { + "bbox": [ + 46, + 262, + 288, + 353 + ], + "type": "inline_equation", + "content": "\\sim 3 - 5" + }, + { + "bbox": [ + 46, + 262, + 288, + 353 + ], + "type": "text", + "content": " images of a subject we fine-tune a text-to-image diffusion model with the input images paired with a text prompt containing a unique identifier and the name of the class the subject belongs to (e.g., \"A [V] dog\"), in parallel, we apply a class-specific prior preservation loss, which leverages the semantic prior that the model has on the class and encourages it to generate diverse instances belong to the subject's class using the class name in a text prompt (e.g., \"A dog\")." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 361, + 287, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 361, + 287, + 410 + ], + "spans": [ + { + "bbox": [ + 46, + 361, + 287, + 410 + ], + "type": "text", + "content": "using the diffusion loss from Eq 1, large text-to-image diffusion models seem to excel at integrating new information into their domain without forgetting the prior or overfitting to a small set of training images." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 423, + 287, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 423, + 287, + 651 + ], + "spans": [ + { + "bbox": [ + 46, + 423, + 287, + 651 + ], + "type": "text", + "content": "Designing Prompts for Few-Shot Personalization Our goal is to \"implant\" a new (unique identifier, subject) pair into the diffusion model's \"dictionary\". In order to bypass the overhead of writing detailed image descriptions for a given image set we opt for a simpler approach and label all input images of the subject \"a [identifier] [class noun]\", where [identifier] is a unique identifier linked to the subject and [class noun] is a coarse class descriptor of the subject (e.g. cat, dog, watch, etc.). The class descriptor can be provided by the user or obtained using a classifier. We use a class descriptor in the sentence in order to tether the prior of the class to our unique subject and find that using a wrong class descriptor, or no class descriptor increases training time and language drift while decreasing performance. In essence, we seek to leverage the model's prior of the specific class and entangle it with the embedding of our subject's unique identifier so we can leverage the visual prior to generate new poses and articulations of the subject in different contexts." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "type": "text", + "content": "Rare-token Identifiers We generally find existing English words (e.g. \"unique\", \"special\") suboptimal since the model has to learn to disentangle them from their original meaning and to re-entangle them to reference our subject." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 547, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 361 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 361 + ], + "type": "text", + "content": "This motivates the need for an identifier that has a weak prior in both the language model and the diffusion model. A hazardous way of doing this is to select random characters in the English language and concatenate them to generate a rare identifier (e.g. \"xxy5syt00\"). In reality, the tokenizer might tokenize each letter separately, and the prior for the diffusion model is strong for these letters. We often find that these tokens incur the similar weaknesses as using common English words. Our approach is to find rare tokens in the vocabulary, and then invert these tokens into text space, in order to minimize the probability of the identifier having a strong prior. We perform a rare-token lookup in the vocabulary and obtain a sequence of rare token identifiers " + }, + { + "bbox": [ + 304, + 72, + 547, + 361 + ], + "type": "inline_equation", + "content": "f(\\hat{\\mathbf{V}})" + }, + { + "bbox": [ + 304, + 72, + 547, + 361 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 72, + 547, + 361 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 72, + 547, + 361 + ], + "type": "text", + "content": " is a tokenizer; a function that maps character sequences to tokens and " + }, + { + "bbox": [ + 304, + 72, + 547, + 361 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{V}}" + }, + { + "bbox": [ + 304, + 72, + 547, + 361 + ], + "type": "text", + "content": " is the decoded text stemming from the tokens " + }, + { + "bbox": [ + 304, + 72, + 547, + 361 + ], + "type": "inline_equation", + "content": "f(\\hat{\\mathbf{V}})" + }, + { + "bbox": [ + 304, + 72, + 547, + 361 + ], + "type": "text", + "content": ". The sequence can be of variable length " + }, + { + "bbox": [ + 304, + 72, + 547, + 361 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 72, + 547, + 361 + ], + "type": "text", + "content": ", and find that relatively short sequences of " + }, + { + "bbox": [ + 304, + 72, + 547, + 361 + ], + "type": "inline_equation", + "content": "k = \\{1, \\dots, 3\\}" + }, + { + "bbox": [ + 304, + 72, + 547, + 361 + ], + "type": "text", + "content": " work well. Then, by inverting the vocabulary using the tokenizer on " + }, + { + "bbox": [ + 304, + 72, + 547, + 361 + ], + "type": "inline_equation", + "content": "f(\\hat{\\mathbf{V}})" + }, + { + "bbox": [ + 304, + 72, + 547, + 361 + ], + "type": "text", + "content": " we obtain a sequence of characters that define our unique identifier " + }, + { + "bbox": [ + 304, + 72, + 547, + 361 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{V}}" + }, + { + "bbox": [ + 304, + 72, + 547, + 361 + ], + "type": "text", + "content": ". For Imagen, we find that using uniform random sampling of tokens that correspond to 3 or fewer Unicode characters (without spaces) and using tokens in the T5-XXL tokenizer range of " + }, + { + "bbox": [ + 304, + 72, + 547, + 361 + ], + "type": "inline_equation", + "content": "\\{5000, \\dots, 10000\\}" + }, + { + "bbox": [ + 304, + 72, + 547, + 361 + ], + "type": "text", + "content": " works well." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 368, + 505, + 380 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 368, + 505, + 380 + ], + "spans": [ + { + "bbox": [ + 306, + 368, + 505, + 380 + ], + "type": "text", + "content": "3.3. Class-specific Prior Preservation Loss" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 386, + 545, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 386, + 545, + 529 + ], + "spans": [ + { + "bbox": [ + 304, + 386, + 545, + 529 + ], + "type": "text", + "content": "In our experience, the best results for maximum subject fidelity are achieved by fine-tuning all layers of the model. This includes fine-tuning layers that are conditioned on the text embeddings, which gives rise to the problem of language drift. Language drift has been an observed problem in language models [32, 38], where a model that is pre-trained on a large text corpus and later fine-tuned for a specific task progressively loses syntactic and semantic knowledge of the language. To the best of our knowledge, we are the first to find a similar phenomenon affecting diffusion models, where to model slowly forgets how to generate subjects of the same class as the target subject." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 529, + 545, + 637 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 529, + 545, + 637 + ], + "spans": [ + { + "bbox": [ + 304, + 529, + 545, + 637 + ], + "type": "text", + "content": "Another problem is the possibility of reduced output diversity. Text-to-image diffusion models naturally possess high amounts of output diversity. When fine-tuning on a small set of images we would like to be able to generate the subject in novel viewpoints, poses and articulations. Yet, there is a risk of reducing the amount of variability in the output poses and views of the subject (e.g. snapping to the few-shot views). We observe that this is often the case, especially when the model is trained for too long." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 638, + 545, + 710 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 638, + 545, + 710 + ], + "spans": [ + { + "bbox": [ + 304, + 638, + 545, + 710 + ], + "type": "text", + "content": "To mitigate the two aforementioned issues, we propose an autogenous class-specific prior preservation loss that encourages diversity and counters language drift. In essence, our method is to supervise the model with its own generated samples, in order for it to retain the prior once the few-shot fine-tuning begins. This allows it to generate di" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "text", + "content": "22503" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 157 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 157 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 157 + ], + "type": "text", + "content": "verse images of the class prior, as well as retain knowledge about the class prior that it can use in conjunction with knowledge about the subject instance. Specifically, we generate data " + }, + { + "bbox": [ + 46, + 72, + 289, + 157 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{\\mathrm{pr}} = \\hat{\\mathbf{x}} (\\mathbf{z}_{t_1},\\mathbf{c}_{\\mathrm{pr}})" + }, + { + "bbox": [ + 46, + 72, + 289, + 157 + ], + "type": "text", + "content": " by using the ancestral sampler on the frozen pre-trained diffusion model with random initial noise " + }, + { + "bbox": [ + 46, + 72, + 289, + 157 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{t_1}\\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})" + }, + { + "bbox": [ + 46, + 72, + 289, + 157 + ], + "type": "text", + "content": " and conditioning vector " + }, + { + "bbox": [ + 46, + 72, + 289, + 157 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_{\\mathrm{pr}}\\coloneqq \\Gamma (f(\"a[class~noun]^\")" + }, + { + "bbox": [ + 46, + 72, + 289, + 157 + ], + "type": "text", + "content": "). The loss becomes:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 166, + 287, + 197 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 166, + 287, + 197 + ], + "spans": [ + { + "bbox": [ + 56, + 166, + 287, + 197 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathbb {E} _ {\\mathbf {x}, \\mathbf {c}, \\epsilon , \\epsilon^ {\\prime}, t} [ w _ {t} \\| \\hat {\\mathbf {x}} _ {\\theta} (\\alpha_ {t} \\mathbf {x} + \\sigma_ {t} \\epsilon , \\mathbf {c}) - \\mathbf {x} \\| _ {2} ^ {2} + \\\\ \\lambda w _ {t ^ {\\prime}} \\| \\hat {\\mathbf {x}} _ {\\theta} \\left(\\alpha_ {t ^ {\\prime}} \\mathbf {x} _ {\\mathrm {p r}} + \\sigma_ {t ^ {\\prime}} \\boldsymbol {\\epsilon} ^ {\\prime}, \\mathbf {c} _ {\\mathrm {p r}}\\right) - \\mathbf {x} _ {\\mathrm {p r}} \\| _ {2} ^ {2} ], \\tag {2} \\\\ \\end{array}", + "image_path": "5d684a6ebbef562304d25aa713ec48c418d6fbefd187fe101960a3d21133b4fa.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 203, + 289, + 395 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 203, + 289, + 395 + ], + "spans": [ + { + "bbox": [ + 46, + 203, + 289, + 395 + ], + "type": "text", + "content": "where the second term is the prior-preservation term that supervises the model with its own generated images, and " + }, + { + "bbox": [ + 46, + 203, + 289, + 395 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 203, + 289, + 395 + ], + "type": "text", + "content": " controls for the relative weight of this term. Figure 3 illustrates the model fine-tuning with the class-generated samples and prior-preservation loss. Despite being simple, we find this prior-preservation loss is effective in encouraging output diversity and in overcoming language-drift. We also find that we can train the model for more iterations without risking overfitting. We find that " + }, + { + "bbox": [ + 46, + 203, + 289, + 395 + ], + "type": "inline_equation", + "content": "\\sim 1000" + }, + { + "bbox": [ + 46, + 203, + 289, + 395 + ], + "type": "text", + "content": " iterations with " + }, + { + "bbox": [ + 46, + 203, + 289, + 395 + ], + "type": "inline_equation", + "content": "\\lambda = 1" + }, + { + "bbox": [ + 46, + 203, + 289, + 395 + ], + "type": "text", + "content": " and learning rate " + }, + { + "bbox": [ + 46, + 203, + 289, + 395 + ], + "type": "inline_equation", + "content": "10^{-5}" + }, + { + "bbox": [ + 46, + 203, + 289, + 395 + ], + "type": "text", + "content": " for Imagen [58] and " + }, + { + "bbox": [ + 46, + 203, + 289, + 395 + ], + "type": "inline_equation", + "content": "5 \\times 10^{-6}" + }, + { + "bbox": [ + 46, + 203, + 289, + 395 + ], + "type": "text", + "content": " for Stable Diffusion [56], and with a subject dataset size of 3-5 images is enough to achieve good results. During this process, " + }, + { + "bbox": [ + 46, + 203, + 289, + 395 + ], + "type": "inline_equation", + "content": "\\sim 1000" + }, + { + "bbox": [ + 46, + 203, + 289, + 395 + ], + "type": "text", + "content": " \"a [class noun]\" samples are generated - but less can be used. The training process takes about 5 minutes on one TPUv4 for Imagen, and 5 minutes on a NVIDIA A100 for Stable Diffusion." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 405, + 128, + 418 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 405, + 128, + 418 + ], + "spans": [ + { + "bbox": [ + 47, + 405, + 128, + 418 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 425, + 289, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 425, + 289, + 617 + ], + "spans": [ + { + "bbox": [ + 46, + 425, + 289, + 617 + ], + "type": "text", + "content": "In this section, we show experiments and applications. Our method enables a large expanse of text-guided semantic modifications of our subject instances, including recontextualization, modification of subject properties such as material and species, art rendition, and viewpoint modification. Importantly, across all of these modifications, we are able to preserve the unique visual features that give the subject its identity and essence. If the task is recontextualization, then the subject features are unmodified, but appearance (e.g., pose) may change. If the task is a stronger semantic modification, such as crossing between our subject and another species/object, then the key features of the subject are preserved after modification. In this section, we reference the subject's unique identifier using [V]. We include specific Imagen and Stable Diffusion implementation details in the supp. material." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 623, + 180, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 623, + 180, + 635 + ], + "spans": [ + { + "bbox": [ + 47, + 623, + 180, + 635 + ], + "type": "text", + "content": "4.1. Dataset and Evaluation" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "text", + "content": "Dataset We collected a dataset of 30 subjects, including unique objects and pets such as backpacks, stuffed animals, dogs, cats, sunglasses, cartoons, etc. Images for this dataset were collected by the authors or sourced from Unsplash [1]. We also collected 25 prompts: 20 recontextualization prompts and 5 property modification prompts for" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 305, + 72, + 547, + 356 + ], + "blocks": [ + { + "bbox": [ + 305, + 72, + 547, + 356 + ], + "lines": [ + { + "bbox": [ + 305, + 72, + 547, + 356 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 547, + 356 + ], + "type": "image", + "image_path": "aee47dcdbc8578c305dc5eef0fd1db433b1e948bace2ee720a996d17b7989565.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 363, + 547, + 452 + ], + "lines": [ + { + "bbox": [ + 304, + 363, + 547, + 452 + ], + "spans": [ + { + "bbox": [ + 304, + 363, + 547, + 452 + ], + "type": "text", + "content": "Figure 4. Comparisons with Textual Inversion [20] Given 4 input images (top row), we compare: DreamBooth Imagen (2nd row), DreamBooth Stable Diffusion (3rd row), Textual Inversion (bottom row). Output images were created with the following prompts (left to right): \"a [V] vase in the snow\", \"a [V] vase on the beach\", \"a [V] vase in the jungle\", \"a [V] vase with the Eiffel Tower in the background\". DreamBooth is stronger in both subject and prompt fidelity." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 308, + 462, + 545, + 521 + ], + "blocks": [ + { + "bbox": [ + 308, + 462, + 545, + 521 + ], + "lines": [ + { + "bbox": [ + 308, + 462, + 545, + 521 + ], + "spans": [ + { + "bbox": [ + 308, + 462, + 545, + 521 + ], + "type": "table", + "html": "
MethodDINO ↑CLIP-I ↑CLIP-T ↑
Real Images0.7740.885N/A
DreamBooth (Imagen)0.6960.8120.306
DreamBooth (Stable Diffusion)0.6680.8030.305
Textual Inversion (Stable Diffusion)0.5690.7800.255
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MethodSubject Fidelity ↑Prompt Fidelity ↑
DreamBooth (Stable Diffusion)68%81%
Textual Inversion (Stable Diffusion)22%12%
Undecided10%7%
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The full list of images and prompts can be found in the supplementary material." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 685, + 545, + 710 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 685, + 545, + 710 + ], + "spans": [ + { + "bbox": [ + 304, + 685, + 545, + 710 + ], + "type": "text", + "content": "For the evaluation suite we generate four images per subject and per prompt, totaling 3,000 images. This allows us" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "22504" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 83, + 283, + 141 + ], + "blocks": [ + { + "bbox": [ + 145, + 72, + 192, + 82 + ], + "lines": [ + { + "bbox": [ + 145, + 72, + 192, + 82 + ], + "spans": [ + { + "bbox": [ + 145, + 72, + 192, + 82 + ], + "type": "text", + "content": "Input images" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 51, + 83, + 283, + 141 + ], + "lines": [ + { + "bbox": [ + 51, + 83, + 283, + 141 + ], + "spans": [ + { + "bbox": [ + 51, + 83, + 283, + 141 + ], + "type": "image", + "image_path": "28aff1ddc51eaa78fd4f9fb02089d0ffc1b9468019c019d73ef36bf019786bc6.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 51, + 156, + 283, + 213 + ], + "blocks": [ + { + "bbox": [ + 121, + 144, + 214, + 155 + ], + "lines": [ + { + "bbox": [ + 121, + 144, + 214, + 155 + ], + "spans": [ + { + "bbox": [ + 121, + 144, + 214, + 155 + ], + "type": "text", + "content": "w/o prior-preservation loss" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 51, + 156, + 283, + 213 + ], + "lines": [ + { + "bbox": [ + 51, + 156, + 283, + 213 + ], + "spans": [ + { + "bbox": [ + 51, + 156, + 283, + 213 + ], + "type": "image", + "image_path": "07f9b84995d19538c736a6d37bbf5651126517d6612c658c810995d118884b96.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 51, + 228, + 283, + 285 + ], + "blocks": [ + { + "bbox": [ + 120, + 217, + 216, + 226 + ], + "lines": [ + { + "bbox": [ + 120, + 217, + 216, + 226 + ], + "spans": [ + { + "bbox": [ + 120, + 217, + 216, + 226 + ], + "type": "text", + "content": "with prior-preservation loss" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 51, + 228, + 283, + 285 + ], + "lines": [ + { + "bbox": [ + 51, + 228, + 283, + 285 + ], + "spans": [ + { + "bbox": [ + 51, + 228, + 283, + 285 + ], + "type": "image", + "image_path": "2f20582f418d00e378dd860aa844384e8bb48376219093cb58f51b3d88201c95.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 294, + 287, + 350 + ], + "lines": [ + { + "bbox": [ + 46, + 294, + 287, + 350 + ], + "spans": [ + { + "bbox": [ + 46, + 294, + 287, + 350 + ], + "type": "text", + "content": "Figure 5. Encouraging diversity with prior-preservation loss. Naive fine-tuning can result in overfitting to input image context and subject appearance (e.g. pose). PPL acts as a regularizer that alleviates overfitting and encourages diversity, allowing for more pose variability and appearance diversity." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 361, + 287, + 408 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 361, + 287, + 408 + ], + "spans": [ + { + "bbox": [ + 46, + 361, + 287, + 408 + ], + "type": "text", + "content": "to robustly measure performances and generalization capabilities of a method. We make our dataset and evaluation protocol publicly available on the project webpage for future use in evaluating subject-driven generation." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 423, + 287, + 650 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 423, + 287, + 650 + ], + "spans": [ + { + "bbox": [ + 46, + 423, + 287, + 650 + ], + "type": "text", + "content": "Evaluation Metrics One important aspect to evaluate is subject fidelity: the preservation of subject details in generated images. For this, we compute two metrics: CLIP-I and DINO [10]. CLIP-I is the average pairwise cosine similarity between CLIP [50] embeddings of generated and real images. Although this metric has been used in other work [20], it is not constructed to distinguish between different subjects that could have highly similar text descriptions (e.g. two different yellow clocks). Our proposed DINO metric is the average pairwise cosine similarity between the ViT-S/16 DINO embeddings of generated and real images. This is our preferred metric, since, by construction and in contrast to supervised networks, DINO is not trained to ignore differences between subjects of the same class. Instead, the self-supervised training objective encourages distinction of unique features of a subject or image. The second important aspect to evaluate is prompt fidelity, measured as the average cosine similarity between prompt and image CLIP embeddings. We denote this as CLIP-T." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 658, + 132, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 132, + 670 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 132, + 670 + ], + "type": "text", + "content": "4.2. Comparisons" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 676, + 287, + 711 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 676, + 287, + 711 + ], + "spans": [ + { + "bbox": [ + 46, + 676, + 287, + 711 + ], + "type": "text", + "content": "We compare our results with Textual Inversion, the recent concurrent work of Gal et al. [20], using the hyperparameters provided in their work. We find that this work is" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 72, + 545, + 227 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 227 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 227 + ], + "type": "text", + "content": "the only comparable work in the literature that is subject-driven, text-guided and generates novel images. We generate images for DreamBooth using Imagen, DreamBooth using Stable Diffusion and Textual Inversion using Stable Diffusion. We compute DINO and CLIP-I subject fidelity metrics and the CLIP-T prompt fidelity metric. In Table 1 we show sizeable gaps in both subject and prompt fidelity metrics for DreamBooth over Textual Inversion. We find that DreamBooth (Imagen) achieves higher scores for both subject and prompt fidelity than DreamBooth (Stable Diffusion), approaching the upper-bound of subject fidelity for real images. We believe that this is due to the larger expressive power and higher output quality of Imagen." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 228, + 546, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 228, + 546, + 502 + ], + "spans": [ + { + "bbox": [ + 304, + 228, + 546, + 502 + ], + "type": "text", + "content": "Further, we compare Textual Inversion (Stable Diffusion) and DreamBooth (Stable Diffusion) by conducting a user study. For subject fidelity, we asked 72 users to answer questionnaires of 25 comparative questions (3 users per questionnaire), totaling 1800 answers. Samples are randomly selected from a large pool. Each question shows the set of real images for a subject, and one generated image of that subject by each method (with a random prompt). Users are asked to answer the question: \"Which of the two images best reproduces the identity (e.g. item type and details) of the reference item?\", and we include a \"Cannot Determine / Both Equally\" option. Similarly for prompt fidelity, we ask \"Which of the two images is best described by the reference text?\". We average results using majority voting and present them in Table 2. We find an overwhelming preference for DreamBooth for both subject fidelity and prompt fidelity. This shines a light on results in Table 1, where DINO differences of around 0.1 and CLIP-T differences of 0.05 are significant in terms of user preference. Finally, we show qualitative comparisons in Figure 4. We observe that DreamBooth better preserves subject identity, and is more faithful to prompts. We show samples of the user study in the supp. material." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 510, + 406, + 521 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 510, + 406, + 521 + ], + "spans": [ + { + "bbox": [ + 306, + 510, + 406, + 521 + ], + "type": "text", + "content": "4.3. Ablation Studies" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 529, + 545, + 708 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 529, + 545, + 708 + ], + "spans": [ + { + "bbox": [ + 304, + 529, + 545, + 708 + ], + "type": "text", + "content": "Prior Preservation Loss Ablation We fine-tune Imagen on 15 subjects from our dataset, with and without our proposed prior preservation loss (PPL). The prior preservation loss seeks to combat language drift and preserve the prior. We compute a prior preservation metric (PRES) by computing the average pairwise DINO embeddings between generated images of random subjects of the prior class and real images of our specific subject. The higher this metric, the more similar random subjects of the class are to our specific subject, indicating collapse of the prior. We report results in Table 3 and observe that PPL substantially counteracts language drift and helps retain the ability to generate diverse images of the prior class. 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"text", + "content": "A [V] teapot floating in the sea" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 322, + 545, + 344 + ], + "lines": [ + { + "bbox": [ + 46, + 322, + 545, + 344 + ], + "spans": [ + { + "bbox": [ + 46, + 322, + 545, + 344 + ], + "type": "text", + "content": "Figure 6. Recontextualization. We generate images of the subjects in different environments, with high preservation of subject details and realistic scene-subject interactions. We show the prompts below each image." + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "type": "table", + "bbox": [ + 48, + 353, + 286, + 386 + ], + "blocks": [ + { + "bbox": [ + 48, + 353, + 286, + 386 + ], + "lines": [ + { + "bbox": [ + 48, + 353, + 286, + 386 + ], + "spans": [ + { + "bbox": [ + 48, + 353, + 286, + 386 + ], + "type": "table", + "html": "
MethodPRES ↓DIV ↑DINO ↑CLIP-I ↑CLIP-T ↑
DreamBooth (Imagen) w/ PPL0.4930.3910.6840.8150.308
DreamBooth (Imagen)0.6640.3710.7120.8280.306
", + "image_path": "5031f4e67780663af0f5ca27612c3374a0da99fb45ba3e4345c8222a47743d7e.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "table_body" + } + ], + "index": 21 + }, + { + "type": "table", + "bbox": [ + 108, + 438, + 226, + 484 + ], + "blocks": [ + { + "bbox": [ + 46, + 395, + 287, + 427 + ], + "lines": [ + { + "bbox": [ + 46, + 395, + 287, + 427 + ], + "spans": [ + { + "bbox": [ + 46, + 395, + 287, + 427 + ], + "type": "text", + "content": "Table 3. Prior preservation loss (PPL) ablation displaying a prior preservation (PRES) metric, diversity metric (DIV) and subject and prompt fidelity metrics." + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 108, + 438, + 226, + 484 + ], + "lines": [ + { + "bbox": [ + 108, + 438, + 226, + 484 + ], + "spans": [ + { + "bbox": [ + 108, + 438, + 226, + 484 + ], + "type": "table", + "html": "
MethodDINO ↑CLIP-I ↑
Correct Class0.7440.853
No Class0.3030.607
Wrong Class0.4540.728
", + "image_path": "6155da281f7776c774237553169bea4aad5e2d7deddeaf22e14ce8c4909d2192.jpg" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "table_body" + } + ], + "index": 23 + }, + { + "bbox": [ + 58, + 493, + 269, + 504 + ], + "lines": [ + { + "bbox": [ + 58, + 493, + 269, + 504 + ], + "spans": [ + { + "bbox": [ + 58, + 493, + 269, + 504 + ], + "type": "text", + "content": "Table 4. Class name ablation with subject fidelity metrics." + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 513, + 287, + 585 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 513, + 287, + 585 + ], + "spans": [ + { + "bbox": [ + 46, + 513, + 287, + 585 + ], + "type": "text", + "content": "same prompt. We observe that our model trained with PPL achieves higher diversity (with slightly diminished subject fidelity), which can also be observed qualitatively in Figure 5, where our model trained with PPL overfits less to the environment of the reference images and can generate the dog in more diverse poses and articulations." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 46, + 600, + 288, + 708 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 600, + 288, + 708 + ], + "spans": [ + { + "bbox": [ + 46, + 600, + 288, + 708 + ], + "type": "text", + "content": "Class-Prior Ablation We finetune Imagen on a subset of our dataset subjects (5 subjects) with no class noun, a randomly sampled incorrect class noun, and the correct class noun. With the correct class noun for our subject, we are able to faithfully fit to the subject, take advantage of the class prior, allowing us to generate our subject in various contexts. When an incorrect class noun (e.g. \"can\" for a backpack) is used, we run into contention between our subject and and the class prior - sometimes obtaining cylindri" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 355, + 545, + 427 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 355, + 545, + 427 + ], + "spans": [ + { + "bbox": [ + 304, + 355, + 545, + 427 + ], + "type": "text", + "content": "cal backpacks, or otherwise misshapen subjects. If we train with no class noun, the model does not leverage the class prior, has difficulty learning the subject and converging, and can generate erroneous samples. Subject fidelity results are shown in Table 4, with substantially higher subject fidelity for our proposed approach." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 306, + 434, + 388, + 448 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 434, + 388, + 448 + ], + "spans": [ + { + "bbox": [ + 306, + 434, + 388, + 448 + ], + "type": "text", + "content": "4.4. Applications" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 304, + 453, + 545, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 453, + 545, + 536 + ], + "spans": [ + { + "bbox": [ + 304, + 453, + 545, + 536 + ], + "type": "text", + "content": "Recontextualization We can generate novel images for a specific subject in different contexts (Figure 6) with descriptive prompts (\"a [V] [class noun] [context description)\"). Importantly, we are able to generate the subject in new poses and articulations, with previously unseen scene structure and realistic integration of the subject in the scene (e.g. contact, shadows, reflections)." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 304, + 545, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 545, + 665 + ], + "type": "text", + "content": "Art Renditions Given a prompt “a painting of a [V] [class noun] in the style of [famous painter]” or “a statue of a [V] [class noun] in the style of [famous sculptor]” we are able to generate artistic renditions of our subject. Unlike style transfer, where the source structure is preserved and only the style is transferred, we are able to generate meaningful, novel variations depending on the artistic style, while preserving subject identity. E.g., as shown in Figure 7, “Michelangelo”, we generated a pose that is novel and not seen in the input images." + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 304, + 673, + 545, + 711 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 673, + 545, + 711 + ], + "spans": [ + { + "bbox": [ + 304, + 673, + 545, + 711 + ], + "type": "text", + "content": "Novel View Synthesis We are able to render the subject under novel viewpoints. In Figure 7, we generate new images of the input cat (with consistent complex fur patterns)" + } + ] + } + ], + "index": 31 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22506" + } + ] + } + ], + "index": 32 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 71, + 287, + 324 + ], + "blocks": [ + { + "bbox": [ + 48, + 71, + 287, + 324 + ], + "lines": [ + { + "bbox": [ + 48, + 71, + 287, + 324 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 287, + 324 + ], + "type": "image", + "image_path": "67bfe2a7a9c50225b443313d746c869c05fe41ebb3b449a98b294d7596fa5707.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 335, + 287, + 378 + ], + "lines": [ + { + "bbox": [ + 46, + 335, + 287, + 378 + ], + "spans": [ + { + "bbox": [ + 46, + 335, + 287, + 378 + ], + "type": "text", + "content": "Figure 7. Novel view synthesis, art renditions, and property modifications. We are able to generate novel and meaningful images while faithfully preserving subject identity and essence. More applications and examples in the supplementary material." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 50, + 392, + 124, + 484 + ], + "blocks": [ + { + "bbox": [ + 50, + 392, + 124, + 484 + ], + "lines": [ + { + "bbox": [ + 50, + 392, + 124, + 484 + ], + "spans": [ + { + "bbox": [ + 50, + 392, + 124, + 484 + ], + "type": "image", + "image_path": "4ce3f54196e57db34a5f47f3f46e3a830fb3bdf5acf1ed5c6941d07f0bf74f8c.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 59, + 499, + 195, + 510 + ], + "lines": [ + { + "bbox": [ + 59, + 499, + 195, + 510 + ], + "spans": [ + { + "bbox": [ + 59, + 499, + 195, + 510 + ], + "type": "text", + "content": "(b) Context-appearance entanglement" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 138, + 407, + 211, + 479 + ], + "blocks": [ + { + "bbox": [ + 140, + 392, + 266, + 403 + ], + "lines": [ + { + "bbox": [ + 140, + 392, + 266, + 403 + ], + "spans": [ + { + "bbox": [ + 140, + 392, + 266, + 403 + ], + "type": "text", + "content": "(a) Incorrect context synthesis" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 138, + 407, + 211, + 479 + ], + "lines": [ + { + "bbox": [ + 138, + 407, + 211, + 479 + ], + "spans": [ + { + "bbox": [ + 138, + 407, + 211, + 479 + ], + "type": "image", + "image_path": "271595383f4c5e363a3d72b1ef87efd0f3f1483cff4fe679aaf6afcc3af595c1.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 155, + 483, + 186, + 491 + ], + "lines": [ + { + "bbox": [ + 155, + 483, + 186, + 491 + ], + "spans": [ + { + "bbox": [ + 155, + 483, + 186, + 491 + ], + "type": "text", + "content": "in the ISS" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 212, + 408, + 282, + 479 + ], + "blocks": [ + { + "bbox": [ + 212, + 408, + 282, + 479 + ], + "lines": [ + { + "bbox": [ + 212, + 408, + 282, + 479 + ], + "spans": [ + { + "bbox": [ + 212, + 408, + 282, + 479 + ], + "type": "image", + "image_path": "256d62bdb1b058df2ee43fdb453451f721e697b97b8163c6cf56ff850953699b.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 228, + 483, + 265, + 491 + ], + "lines": [ + { + "bbox": [ + 228, + 483, + 265, + 491 + ], + "spans": [ + { + "bbox": [ + 228, + 483, + 265, + 491 + ], + "type": "text", + "content": "on the moon" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 54, + 516, + 198, + 589 + ], + "blocks": [ + { + "bbox": [ + 54, + 516, + 198, + 589 + ], + "lines": [ + { + "bbox": [ + 54, + 516, + 198, + 589 + ], + "spans": [ + { + "bbox": [ + 54, + 516, + 198, + 589 + ], + "type": "image", + "image_path": "a12117a968f8a68ae26b5d5cf5c58528a76ef0dce90b5a9ea8c820722702ffd1.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 590, + 125, + 599 + ], + "lines": [ + { + "bbox": [ + 54, + 590, + 125, + 599 + ], + "spans": [ + { + "bbox": [ + 54, + 590, + 125, + 599 + ], + "type": "text", + "content": "in the Bolivian salt flats" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 130, + 590, + 196, + 599 + ], + "lines": [ + { + "bbox": [ + 130, + 590, + 196, + 599 + ], + "spans": [ + { + "bbox": [ + 130, + 590, + 196, + 599 + ], + "type": "text", + "content": "on top of a blue fabric" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 607, + 287, + 674 + ], + "lines": [ + { + "bbox": [ + 46, + 607, + 287, + 674 + ], + "spans": [ + { + "bbox": [ + 46, + 607, + 287, + 674 + ], + "type": "text", + "content": "Figure 8. Failure modes. Given a rare prompted context the model might fail at generating the correct environment (a). It is possible for context and subject appearance to become entangled (b). Finally, it is possible for the model to overfit and generate images similar to the training set, especially if prompts reflect the original environment of the training set (c)." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 129, + 516, + 198, + 587 + ], + "angle": 0, + "lines": [ + { + "bbox": [ + 129, + 516, + 198, + 587 + ], + "spans": [ + { + "bbox": [ + 129, + 516, + 198, + 587 + ], + "type": "image", + "image_path": "311b91116ef8e7fe0264e995949d5f6f8052a8583ae5330ed12db913894025c7.jpg" + } + ] + } + ], + "index": 11, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 212, + 516, + 283, + 587 + ], + "blocks": [ + { + "bbox": [ + 220, + 499, + 272, + 510 + ], + "lines": [ + { + "bbox": [ + 220, + 499, + 272, + 510 + ], + "spans": [ + { + "bbox": [ + 220, + 499, + 272, + 510 + ], + "type": "text", + "content": "(c) Overfitting" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 212, + 516, + 283, + 587 + ], + "lines": [ + { + "bbox": [ + 212, + 516, + 283, + 587 + ], + "spans": [ + { + "bbox": [ + 212, + 516, + 283, + 587 + ], + "type": "image", + "image_path": "33010a76d4fe29e907525b3b3f8e4ba6b26b69d7d0edf6e610643b97f6920a95.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 228, + 590, + 264, + 598 + ], + "lines": [ + { + "bbox": [ + 228, + 590, + 264, + 598 + ], + "spans": [ + { + "bbox": [ + 228, + 590, + 264, + 598 + ], + "type": "text", + "content": "in the forest" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": "under new viewpoints. We highlight that the model has not seen this specific cat from behind, below, or above - yet it is able to extrapolate knowledge from the class prior to generate these novel views given only 4 frontal images of the subject." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 145, + 545, + 301 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 145, + 545, + 301 + ], + "spans": [ + { + "bbox": [ + 304, + 145, + 545, + 301 + ], + "type": "text", + "content": "Property Modification We are able to modify subject properties. For example, we show crosses between a specific Chow Chow dog and different animal species in the bottom row of Figure 7. We prompt the model with sentences of the following structure: \"a cross of a [V] dog and a [target species]\". In particular, we can see in this example that the identity of the dog is well preserved even when the species changes - the face of the dog has certain unique features that are well preserved and melded with the target species. Other property modifications are possible, such as material modification (e.g. \"a transparent [V] teapot\" in Figure 6). Some are harder than others and depend on the prior of the base generation model." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 307, + 383, + 319 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 307, + 383, + 319 + ], + "spans": [ + { + "bbox": [ + 306, + 307, + 383, + 319 + ], + "type": "text", + "content": "4.5. Limitations" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 325, + 545, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 325, + 545, + 468 + ], + "spans": [ + { + "bbox": [ + 304, + 325, + 545, + 468 + ], + "type": "text", + "content": "We illustrate some failure models of our method in Figure 8. The first is related to not being able to accurately generate the prompted context. Possible reasons are a weak prior for these contexts, or difficulty in generating both the subject and specified concept together due to low probability of co-occurrence in the training set. The second is context-appearance entanglement, where the appearance of the subject changes due to the prompted context, exemplified in Figure 8 with color changes of the backpack. Third, we also observe overfitting to the real images that happen when the prompt is similar to the original setting in which the subject was seen." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 469, + 545, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 469, + 545, + 564 + ], + "spans": [ + { + "bbox": [ + 304, + 469, + 545, + 564 + ], + "type": "text", + "content": "Other limitations are that some subjects are easier to learn than others (e.g. dogs and cats). Occasionally, with subjects that are rarer, the model is unable to support as many subject variations. Finally, there is also variability in the fidelity of the subject and some generated images might contain hallucinated subject features, depending on the strength of the model prior, and the complexity of the semantic modification." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 574, + 383, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 574, + 383, + 586 + ], + "spans": [ + { + "bbox": [ + 306, + 574, + 383, + 586 + ], + "type": "text", + "content": "5. Conclusions" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "We presented an approach for synthesizing novel renditions of a subject using a few images of the subject and the guidance of a text prompt. Our key idea is to embed a given subject instance in the output domain of a text-to-image diffusion model by binding the subject to a unique identifier. Remarkably - this fine-tuning process can work given only 3-5 subject images, making the technique particularly accessible. 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In particular, we conduct researches on three core questions: First, what to drop in self-attention layers? Different from dropping attention weights in literature, we propose to move dropout operations forward ahead of attention matrix calculation and set the Key as the dropout unit, yielding a novel dropout-before-softmax scheme. We theoretically verify that this scheme helps keep both regularization and probability features of attention weights, alleviating the overfittings problem to specific patterns and enhancing the model to globally capture vital information; Second, how to schedule the drop ratio in consecutive layers? In contrast to exploit a constant drop ratio for all layers, we present a new decreasing schedule that gradually decreases the drop ratio along the stack of self-attention layers. We experimentally validate the proposed schedule can avoid overfittings in low-level features and missing in high-level semantics, thus improving the robustness and stableness of model training; Third, whether need to perform structured dropout operation as CNN? We attempt patch-based block-version of dropout operation and find that this useful trick for CNN is not essential for ViT. Given exploration on the above three questions, we present the novel DropKey method that regards Key as the drop unit and exploits decreasing schedule for drop ratio, improving ViTs in a general way. Comprehensive experiments demonstrate the effectiveness of DropKey for various ViT architectures, e.g. T2T, VOLO, CeiT and DeiT, as well as for various vision", + "bbox": [ + 75, + 407, + 472, + 861 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tasks, e.g., image classification, object detection, human-object interaction detection and human body shape recovery.", + "bbox": [ + 500, + 377, + 890, + 422 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 501, + 431, + 630, + 446 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Vision Transformer (ViT) [6] has achieved great success for various vision tasks, e.g., image recognition [7, 12, 20, 34, 35], object detection [1], human body shape estimation [18], etc. Prior works mainly focus on researches of patch division, architecture design and task extension. However, the dropout technique for self-attention layer, which plays the essential role to achieve good generalizability, is surprisingly ignored by the community.", + "bbox": [ + 496, + 458, + 890, + 580 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Different from the counterpart for Convolutional Neural Networks (CNNs), the dropout in ViT directly utilizes the one in original Transformer designed for Natural Language Processing, which sets attention weights as the manipulation unit with a constant dropout ratio for all layers. Despite of its simplicity, this vanilla design faces three major problems. First, it breaks the probability distribution of attention weights due to the averaging operation on non-dropout units after softmax normalization. Although this regularizes the attention weights, it still overfits specific patterns locally due to the failure on penalizing score peaks, as shown in Fig. 1 (a) and (b); Second, the vanilla design is sensitive to the constant dropout ratio, since high ratio occurs missing of semantic information in high-level representations while low ratios overfitting in low-level features, resulting in the unstable training process; Third, it ignores the structured characteristic of input patch grid to ViT, which plays an effective role to improve performance with blockwise dropout in CNNs. These three problems degrade the performance and limit the generalizability of ViTs.", + "bbox": [ + 496, + 580, + 892, + 883 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Motivated by this, we propose to analyze and improve", + "bbox": [ + 519, + 885, + 890, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal contribution", + "bbox": [ + 94, + 875, + 202, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding author", + "bbox": [ + 96, + 887, + 218, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "22700", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "the dropout technique in self-attention layer, further pushing forward the frontier of ViTs for vision tasks in a general way. Specifically, we focus on three core aspects:", + "bbox": [ + 76, + 90, + 468, + 136 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "What to drop in self-attention layer Different from dropping attention weights as in the vanilla design, we propose to set the Key as the dropout unit, which is essential input of self-attention layer and significantly affects the output. This moves the dropout operation forward before calculating the attention matrix as shown in Fig. 1 (c) and yields a novel dropout-before-softmax scheme. This scheme regularizes attention weights and keeps their probability distribution at the same time, which intuitively helps penalize weight peaks and lift weight foots. We theoretically verify this property via implicitly introducing an adaptive smoothing coefficient for the attention operator from the perspective of gradient optimization by formulating a Lagrange function. With the dropout-before-softmax scheme, self-attention layers can capture vital information in a global manner, thus overcoming the overfittings problem to specific patterns occurred in the vanilla dropout and enhancing the model generalizability as visualization of feature map in Fig. 1 (c). For the training phase, this scheme can be simply implemented by swapping the operation order of softmax and dropout in vanilla design, which provides a general way to effectively enhance ViTs. For inference phase, we conduct an additional finetune phase to align the expectations to training phase, further improving the performance.", + "bbox": [ + 76, + 138, + 472, + 501 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "How to schedule the drop ratio In contrast to exploiting a constant drop ratio for all layers, we present a new linear decreasing schedule that gradually decreases the drop ratio along the stack of self-attention layers. This schedule leads to a high drop ratio in shallow layers while the low one in deep layers, thus avoiding over fittings to low-level features and preserving sufficient high-level semantics. We experimentally verify the effectiveness of the proposed decreasing schedule for drop ratio to stable the training phase and improve the robustness.", + "bbox": [ + 76, + 505, + 472, + 655 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Whether need to perform structured drop Inspired by the DropBlock [10] method for CNNs, we implement two structured versions of the dropout operation for ViTs: the block-version dropout that drops keys corresponding to contiguous patches in images or feature maps; the crossversion dropout that drops keys corresponding to patches in horizontal and vertical stripes. We conduct thorough experiments to validate their efficacy and find that the structure trick useful for CNN is not essential for ViT, due to the powerful capability of ViT to grasp contextual information in full image range.", + "bbox": [ + 76, + 657, + 472, + 824 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Given exploration on the above three aspects, we present a novel DropKey method that utilizes Key as the drop unit and decreasing schedule for drop ratio. In particular, DropKey overcomes drawbacks of the vanilla dropout technique for ViTs, improving performance in a general and effective", + "bbox": [ + 76, + 825, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "way. Comprehensive experiments on different ViT architectures and vision tasks demonstrate the efficacy of DropKey. Our contributions are in three folds: First, to our best knowledge, we are the first to theoretically and experimentally analyze dropout technique for self-attention layers in ViT from three core aspects: drop unit, drop schedule and structured necessity; Second, according to our analysis, we present a novel DropKey method to effectively improve the dropout technique in ViT. Third, with DropKey, we improve multiple ViT architectures to achieve new SOTAs on various vision tasks.", + "bbox": [ + 496, + 90, + 893, + 257 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 262, + 640, + 277 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Vision Transformers Inspired by the Transformer architectures in NLP, some works introduce attention block to replace convolution layers to model long-range dependencies [6, 11, 17, 29, 30, 31, 37]. ViT[6] is the pioneering work which splits an image to non-overlapping patches and then these patches are fed to a transformer to evaluate attention scores. Prior works mainly focus on patch division, architecture design and tasks extension. For example, CvT[31] proposes a hybrid architecture to mix convolutional with attention layers to introduce local inductive bias. [3, 7, 20] proposes to reduce the computation cost. Despite the progress, previous works ignore the dropout technique in self-attention layer, which play an important role to keep good generalizability.", + "bbox": [ + 496, + 287, + 893, + 500 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Dropout Dropout is a common technique for improving the generalizability of neural networks, e.g., CNNs [16], RNNs [21] and GNNs [24]. For CNNs, [10] points out the lack of success of dropout for convolutional layers is due to dense information flowing and then proposes a form of structured Dropout. DropConnect [28] randomly masks a subset of weights within the model. For RNNs, the first prominent research on dropout is presented in [8], which is equipped with a learnable dropout rate.", + "bbox": [ + 496, + 503, + 893, + 638 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "For GNNs, to alleviate over-fitting and over-smoothing issues, DropEdge [23] randomly removes part of edges in the input stage at each training epoch and theoretically demonstrates the effect of the proposed method. For ViTs, most original publicly code of multiple popular vision transformer simply intuitively apply dropout operation on attention matrix.", + "bbox": [ + 496, + 640, + 893, + 744 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "DropAttention [36] presents a novel way for transformer in NLPs. It refers to perform randomly drop on the attention matrix. There are two two main forms of applying DropAttention for the transformer training, DropAttention-unit and DropAttention-elements. Similar to the standard Dropout [25], DropAttention-unit randomly drops the unit, that is, these dropped token will not be used as attend patches for each query patch. As the general form of DropAttention-unit, DropAttention-elements randomly drops elements in attention weights matrix which", + "bbox": [ + 496, + 750, + 895, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "22701", + "bbox": [ + 478, + 944, + 517, + 957 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/71ca9e25de2d60876fb0c5c4a0f812693a8980d1cb656c8f30f17289497c6566.jpg", + "image_caption": [ + "Input Image" + ], + "image_footnote": [], + "bbox": [ + 76, + 85, + 436, + 244 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/6efa2f8668f852025f41a74d14bc0b85e2ab408653f5271ff42c9e46e79d9206.jpg", + "image_caption": [ + "(b) Attention w/ Dropout", + "Figure 1. Comparison between the proposed DropKey and existing vanilla dropout techniques in self-attention layers for ViTs. (a) Self-attention without dropout, which suffers overfitting problems to local patch; (b) Self-attention with vanilla dropout, which regularizes the attention weights but still overfits specific patterns; (c) Self-attention with our DropKey, which overcomes prior problems and improves the model to capture vital information in a global manner. Best viewed in color." + ], + "image_footnote": [], + "bbox": [ + 433, + 87, + 663, + 247 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/13a34b72c80da52b51e9e29e7a11d7ca0501806630d06e306efbe33358ad0b33.jpg", + "image_caption": [ + "(c) Attention w/ DropKey" + ], + "image_footnote": [], + "bbox": [ + 663, + 88, + 893, + 246 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "is similar to DropConnect [28]. Different from standard Dropout [25], DropAttention introduce re-normalize to guarantee the sum of attention weights to 1 and help training process to be more steady. However, there is no further discussion and theoretical analysis on this phenomenon.", + "bbox": [ + 75, + 328, + 470, + 404 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 405, + 166, + 420 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our generic DropKey is inspired by DropAttention and proposed for self-attention operator in vision transformer. The main idea of DropKey is to adaptively adjust attention weight to obtain a smoother attention vector. In this section, we start by introducing the theoretical explanation of DropKey, then the implementation will be explained in detail.", + "bbox": [ + 75, + 430, + 468, + 520 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Methodology", + "text_level": 1, + "bbox": [ + 76, + 520, + 212, + 534 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As discussed in the above section, transformer-based model tends to rely on local features rather than general global information. To alleviate this issue, we propose to reduce local-bias by encouraging models to learn a smoother attention weight for each patch. To this end, we attempt to reduce the attention weight of the patch which has a large attention weight, and vice versa. Nevertheless, it is tedious and difficult to achieve this by explicitly setting rules. In this work, we found DropKey achieves the above implicitly by normalizing the attention vector that has performed the dropout operation. Specifically, by given an image $I \\in \\mathbb{R}^{H \\times W \\times C}$ , where $H$ denotes height, $W$ denotes width and $C$ denotes channels, Vision Transformer architecture starts by dicing it into $n_h \\times n_w$ patches $x \\in \\mathbb{R}^{n_c}$ . Then, $x$ is used as input of self-attention layer and the output $o$ can be computed as follows", + "bbox": [ + 73, + 534, + 470, + 775 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\no = \\sum_ {j = 1} ^ {n _ {h} n _ {w}} \\left(\\frac {d _ {j} p _ {j}}{\\sum_ {j = 1} ^ {n _ {h} n _ {w}} d _ {j} p _ {j}}\\right) v _ {j} \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 781, + 468, + 821 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\np _ {j} = \\frac {\\exp \\left(\\frac {q k _ {j} ^ {T}}{\\text {s c a l e}}\\right)}{\\sum_ {j = 1} ^ {n _ {h} n _ {w}} \\exp \\left(\\frac {q k _ {j} ^ {T}}{\\text {s c a l e}}\\right)} \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 187, + 821, + 468, + 867 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $q = \\mathcal{F}_q(x), k = \\mathcal{F}_k(x), v = \\mathcal{F}_v(x)$ , and $q_i, k_j, v_j$ denote query of $i^{th}$ patch, key of $j^{th}$ patch, value of $j^{th}$ patch and $o$", + "bbox": [ + 75, + 869, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "denotes the output of one patch. $\\mathcal{F}_q(\\cdot),\\mathcal{F}_k(\\cdot),\\mathcal{F}_v(\\cdot)$ denote projection layers with weights of dimensions $n_c\\times n_c$ . scale denotes scaling factor and is set to $\\sqrt{n_c}$ $d$ denotes drop ratio and $d_{j}\\sim Bernoulli(1 - d)$ . Here, for convenience, we focus on one head and omit the index of patch. By performing re-normalize, DropKey has the ability to adaptively adjust attention weight to smoother. Next, we provide theoretical analysis of our method to demonstrate its effectiveness.", + "bbox": [ + 496, + 328, + 890, + 462 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Here, we formulate the expectation output of model via introducing DropKey in training stage as:", + "bbox": [ + 498, + 465, + 890, + 496 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathbb {E} _ {d _ {j}, 1 \\leq j \\leq n _ {h} n _ {w}} [ o ] = \\mathbb {E} _ {d _ {j}, 1 \\leq j \\leq n _ {h} n _ {w}} [ \\sum_ {j = 1} ^ {n _ {h} n _ {w}} (\\frac {d _ {j} p _ {j}}{\\sum_ {j = 1} ^ {n _ {h} n _ {w}} d _ {j} p _ {j}}) v _ {j} ] \\tag {3} \\\\ = \\sum_ {j = 1} ^ {n _ {h} n _ {w}} \\mathbb {E} _ {d _ {j}, 1 \\leq j \\leq n _ {h} n _ {w}} [ \\frac {d _ {j}}{\\sum_ {j = 1} ^ {n _ {h} n _ {w}} d _ {j} p _ {j}} ] p _ {j} v _ {j} = \\sum_ {j = 1} ^ {n _ {h} n _ {w}} c _ {j} p _ {j} v _ {j} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 506, + 502, + 890, + 575 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $c_{j} = \\mathbb{E}_{d_{j},1\\leq j\\leq n_{h}n_{w}}\\left[\\frac{d_{j}}{\\sum_{j = 1}^{n_{h}n_{w}}d_{j}p_{j}}\\right] > 0$ is a smoothing coefficient which is related to $d_{j}$ and $p_j$ .", + "bbox": [ + 498, + 583, + 890, + 619 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Note that $c$ in Equ (3) can be considered to add an additional smoothing prior to distribution $p$ , i.e., $c_{s} < c_{t}$ when $p_{s} > p_{t}, 1 \\leq s, t \\leq n_{h}n_{w}$ . The specific proof is as follows:", + "bbox": [ + 498, + 619, + 890, + 659 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} c _ {s} - c _ {t} = \\mathbb {E} _ {d _ {j}, 1 \\leq j \\leq n _ {h} n _ {w}} [ \\frac {d _ {s}}{\\sum_ {j = 1} ^ {n _ {h} n _ {w}} d _ {j} p _ {j}} ] - \\mathbb {E} _ {d _ {j}, 1 \\leq j \\leq n _ {h} n _ {w}} [ \\frac {d _ {t}}{\\sum_ {j = 1} ^ {n _ {h} n _ {w}} d _ {j} p _ {j}} ] \\\\ = d (1 - d) \\mathbb {E} _ {d _ {j}, 1} \\leq j \\leq n _ {h} n _ {w} \\left[ \\frac {1}{\\sum_ {j \\neq s , t} ^ {n _ {h} n _ {w}} d _ {j} p _ {j} + p _ {s}} - \\frac {1}{\\sum_ {j \\neq s , t} ^ {n _ {h} n _ {w}} d _ {j} p _ {j} + p _ {t}} \\right] < 0 \\tag {4} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 674, + 890, + 732 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "It is natural to find $c$ serves as a factor to implicitly encourage the model properly to reduce the consideration of the patch with large $p$ and improve the effectiveness of the patch with small attention weight. Meanwhile, $c$ can be adjusted adaptively according to the distribution of samples in the training stage without any manual design. Nevertheless, a noteworthy problem is that since we removed DropKey in the inference phase, the output expectations in training and inference stage are inconsistent, which will decrease the performance. In Section 3.2, we propose two methods to alleviate this problem.", + "bbox": [ + 496, + 734, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "22702", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Having explored the implicit regularization effects of DropKey, we also demonstrate it from the perspective of gradient optimization. For simplicity, we start by considering a simple but universal optimization objective as follows:", + "bbox": [ + 76, + 90, + 472, + 151 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {p _ {j}, v _ {j}} \\frac {1}{2} \\| \\sum_ {j = 1} ^ {N} p _ {j} v _ {j} - y \\| ^ {2} \\text {s . t .} p _ {j} > 0, \\sum_ {j = 1} p _ {j} = 1, 1 \\leq j \\leq N \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 169, + 468, + 205 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $p_j \\in \\mathbb{R}$ , $v_j \\in \\mathbb{R}^r$ denotes learnable parameters and $y \\in \\mathbb{R}^r$ denotes target. This simple problem captures the essential part of the training of a single self-attention layer, especially when the neural networks are large, and it may shed light on the training of deep models. Here, $p_j$ and $v_j$ can be considered as attention weight and value in attention mechanism. Naturally, $v_j$ can be decomposed into two directions, which are the same direction as $y$ and the direction perpendicular to $y$ :", + "bbox": [ + 76, + 209, + 472, + 347 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nv _ {j} = \\beta_ {j} e + \\alpha_ {j} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 220, + 358, + 468, + 376 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\beta$ is a scalar, $e\\in \\mathbb{R}^r$ is the unit vector of $y$ and $\\alpha_{j}$ is the component perpendicular to $y$ . Similarly, we can rewrite $y$ to $Me$ where $M = ||y||$ . Then, the Lagrange function of Equ (5) can be formulated as follows:", + "bbox": [ + 76, + 383, + 472, + 445 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL \\left(p _ {j}, v _ {j}, \\lambda\\right) = \\frac {1}{2} | | \\sum_ {j = 1} ^ {N} p _ {j} v _ {j} - y | | ^ {2} - \\lambda \\left(\\sum_ {j = 1} ^ {N} p _ {j} - 1\\right) \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 124, + 449, + 468, + 487 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In order to analysis the gradient, we take the partial derivatives of $p_j$ and $v_j$ :", + "bbox": [ + 76, + 489, + 468, + 523 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {\\partial L}{\\partial p _ {j}} = (v - y) ^ {T} v _ {j} - \\lambda = \\left(\\sum_ {j = 1} ^ {N} p _ {j} \\beta_ {j} - M\\right) \\beta_ {j} + \\left(\\sum_ {j = 1} ^ {N} p _ {j} \\alpha_ {j}\\right) ^ {T} \\alpha_ {j} - \\lambda \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 527, + 468, + 574 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {\\partial L}{\\partial v _ {j}} = p _ {j} (v - y) = p _ {j} \\left(\\sum_ {j = 1} ^ {N} p _ {j} \\beta_ {j} - M\\right) e + p _ {j} \\left(\\sum_ {j = 1} ^ {N} p _ {j} \\alpha_ {j}\\right) \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 109, + 590, + 468, + 628 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here, for simplicity, we note $v = \\sum_{j=1}^{N} p_j v_j = (\\sum_{j=1}^{N} p_j \\beta_j) e + \\sum_{j=1}^{N} p_j \\alpha_j$ . From the chain rule of backpropagation, we also have:", + "bbox": [ + 76, + 635, + 468, + 686 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {\\partial L}{\\partial \\beta_ {j}} = p _ {j} \\left(\\sum_ {j = 1} ^ {N} p _ {j} \\beta_ {j} - M\\right) \\quad \\frac {\\partial L}{\\partial \\alpha_ {j}} = p _ {j} \\left(\\sum_ {j = 1} ^ {N} p _ {j} \\alpha_ {j}\\right) \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 120, + 691, + 468, + 727 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Equ (10) indicates that the gradient $\\frac{\\partial L}{\\partial \\beta_s} < \\frac{\\partial L}{\\partial \\beta_t}$ when $p_s > p_t$ and this backward propagation properties would lead $\\frac{\\partial L}{\\partial p_s} < \\frac{\\partial L}{\\partial p_t}$ . By subtracting $\\frac{\\partial L}{\\partial p_s}$ and $\\frac{\\partial L}{\\partial p_t}$ , we will have:", + "bbox": [ + 76, + 733, + 468, + 785 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {\\partial L}{\\partial p _ {s}} - \\frac {\\partial L}{\\partial p _ {t}} = \\left(\\sum_ {j = 1} ^ {N} p _ {j} \\beta_ {j} - M\\right) \\left(\\beta_ {s} - \\beta_ {t}\\right) + \\left(\\sum_ {j = 1} ^ {N} p _ {j} \\alpha_ {j}\\right) ^ {T} \\left(\\alpha_ {s} - \\alpha_ {t}\\right) \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 797, + 468, + 834 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Since all parameters are randomly initialized, it can be assumed that the initial solution is far from the optimal solution, that is, $p_1^{(0)} = p_2^{(0)} = \\dots = p_N^{(0)} = \\frac{1}{N}$ , $|\\beta_j^{(0)}| \\ll M$ , $1 \\leq j \\leq N$ . Consequently, the first additive term plays", + "bbox": [ + 76, + 838, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the leading role in Equ (11). Due to $\\frac{\\partial L}{\\partial\\beta_s} < \\frac{\\partial L}{\\partial\\beta_t}$ , the update speed of $\\beta_{s}$ is faster than $\\beta_{t}$ and then lead $\\beta_{s} > \\beta_{t}$ , $\\frac{\\partial L}{\\partial p_s} < \\frac{\\partial L}{\\partial p_t}$ . Based on the above analysis, it can be concluded that a larger $p$ would promote $\\beta$ larger, while a larger $\\beta$ would further promote $p$ larger. Finally, the output of model would be controlled by a few sparse blocks. Conversely, DropKey avoids suffering local-bias by introducing the parameter $c$ to enforce distribution $p$ to be smoother.", + "bbox": [ + 496, + 89, + 890, + 212 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Implementation", + "text_level": 1, + "bbox": [ + 498, + 214, + 660, + 229 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "What to drop? Different from DropAttention, we integrate Dropout and re-normalize into one stage by dropping key rather than weight. At each training iteration, DropKey masks a certain rate of keys of the input key map by random. It is worth noting that we generate masked key map for each query, instead of sharing the same masked key map for all query vectors. Specifically, given the query $Q \\in \\mathbb{R}^{n_h n_w \\times n_c}$ , key $K \\in \\mathbb{R}^{n_h n_w \\times n_c}$ and value $V \\in \\mathbb{R}^{n_h n_w \\times n_c}$ of a feature map, it first computes the dot products of the query with all keys and divide each by scaling factor $scale = \\sqrt{n_c}$ . Subsequently, we randomly generate a mask matrix $D \\in \\mathbb{R}^{1 \\times (n_h n_w \\times n_h n_w)}$ with drop ratio $d$ to enforce some elements of the similarity matrix to be -inf. The formulation of $D$ as follows:", + "bbox": [ + 496, + 231, + 890, + 443 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nd _ {j} = \\left\\{ \\begin{array}{c c} 0 & \\text {w i t h p r o b a b i l i t y} 1 - d \\\\ - \\infty & \\text {w i t h p r o b a b i l i t y} d \\end{array} \\right. \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 449, + 890, + 477 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Finally, the attention weight matrix is computed by given masked similarity matrix as input. Formally, we compute the outputs of a patch as:", + "bbox": [ + 496, + 484, + 890, + 531 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\no = \\sum_ {j = 1} ^ {n _ {h} n _ {w}} p _ {j} v _ {j} \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 648, + 539, + 890, + 573 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np _ {j} = \\frac {\\exp \\left(d _ {j} + \\frac {q k _ {j} ^ {T}}{\\text {s c a l e}}\\right)}{\\sum_ {j = 1} ^ {n _ {h} n _ {w}} \\exp \\left(d _ {j} + \\frac {q k _ {j} ^ {T}}{\\text {s c a l e}}\\right)} \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 602, + 574, + 890, + 618 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $q_{i}, k_{j}, v_{j}$ denote query of $i^{th}$ patch, key of $j^{th}$ patch, value of $j^{th}$ patch. It is not difficult to find that Equ (13) and Equ (14) is the same equivalent form of Equ (1) and Equ (2). In particular, as shown in Algorithm 1, we only need to add two lines of code to pure attention to implement DropKey. Obviously, compared with Dropout, DropKey only changes the position of introducing mask.", + "bbox": [ + 496, + 621, + 890, + 728 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Scheduled Drop Ratio Vision transformer always consists of few self-attention blocks to gradually learn high-dimensional features. Generally, early layers operates low-level visual features and deeper layers aim to model spatially coarse but complex information. Hence, we attempt to set smaller drop ratio for deeper layers to avoid missing important objects-relevant information. Specifically, instead of stochastically dropping with some fixed probability in Dropout, we gradually decrease number of dropped keys over the layers during training stage. We find that this scheduled drop ratio not only work well for DropKey, but also significantly improves the performance of Dropout.", + "bbox": [ + 496, + 734, + 890, + 916 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "22703", + "bbox": [ + 478, + 944, + 517, + 957 + ], + "page_idx": 3 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1 Attention with DropKey code" + ], + "code_body": "N: token number, D: token dim\n# Q: query (N, D), K: key (N, D), V: value (N, D)\n# use_DropKey: whether use DropKey\n# mask_ratio: ratio to mask\ndef Attention(Q, K, V, use_DropKey, mask_ratio)\n attn = (Q * (Q.shape[1] ** -0.5)) @ K.transpose(-2, -1)\n # use DropKey as regularizer\n if use_DropKey == True:\n m_r = torch.ones_like(attn) * mask_ratio\n attn = attn + torchBernoulli(m_r) * -1e12\n attn = attn softmax(dim=-1)\n x = attn @ V\n return x", + "bbox": [ + 112, + 130, + 486, + 263 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/04e29115b96e251ad71d1fcb331528b0c3c249cd019044fef878d7449be8aeb7.jpg", + "image_caption": [ + "Figure 2. Mask sampling in DropKey, DropKey-Block and DropKey-Cross. The yellow patches are used as attend key to interact with a query and blue patches are dropped. Red symbol denotes the valid seed and the window size of DropKey-Block and DropKey-Cross is 3 and 1, respectively." + ], + "image_footnote": [], + "bbox": [ + 544, + 97, + 643, + 181 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/5026f1478ccf11a203bf6e0edd3c4ada679b32bbbac072a416323326e9eddbaf.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 656, + 97, + 756, + 184 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/b5a915e33b9c77cc39d6fedf59d62501c0b500fd571d9053c4ed886cdb22268e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 769, + 97, + 870, + 184 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Structured DropKey Although structured drop has been dally explored in convolution network, there is no work to study the impact of structured drop on vision transformer. In this section, we implement two structured forms of DropKey which are named DropKey-Block and DropKey-Cross (see Figure 2). For DropKey-Block, inspired by DropBlock [10], we drop contiguous patches in a square-shape window of feature maps. Actually, we re-set drop ratio $d_{block}$ for each patch as: $d_{block} = \\frac{d}{s^2}\\frac{n_h n_w}{(n_h - s + 1)(n_w - s + 1)}$ where $d$ denotes the probability of dropping a patch in DropKey. The valid seed region is $(n_h - s + 1)(n_w - s + 1)$ where $s$ denotes the size of window and $n_h, n_w$ denotes height, weight of feature map.", + "bbox": [ + 75, + 286, + 472, + 484 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The cross-shape window attention is proved to achieve strong modeling capability [5] which also indicates the information in this structure is correlated. For DropKeyCross, we discard features in a cross window to prevent information flow through self-attention. In our implementation, we drop the rows and columns of valid seed and re-set the drop ratio $d_{cross}$ for each patch as: $d_{cross} = \\frac{d}{s(n_h + n_w - s)}\\frac{n_hn_w}{(n_h - s + 1)(n_w - s + 1)}$ . Note that the formulations for block- and cross-version are only the approximation, because there will be some overlapped when perform drop.", + "bbox": [ + 75, + 484, + 468, + 637 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Align Expectation As mentioned in Section 3.1, the misaligned expectations have a certain negative impact on the model, so we attempt to use two methods to align the expectation. The first one is to use Monte Carlo method to estimate $c$ . We perform multiple random drop and calculate the attention weight matrix after each drop operation. Finally, the average of calculated multiple weight matrices is applied as the input for the next step. For the second one, we take the inspiration from [9] and propose to finetune the model without DropKey, as an extra stage after DropKey training. We experimentally verify that the second strategy performs better with experiment in Section 4.1.1.", + "bbox": [ + 75, + 642, + 468, + 824 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 829, + 209, + 845 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We conduct experiments on three tasks, image classification, object detection, human-object interaction detection and human mesh recovery, to show the efficacy and gener", + "bbox": [ + 75, + 854, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "alizability of our DropKey for improving ViTs.", + "bbox": [ + 498, + 286, + 812, + 301 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Image Classification", + "text_level": 1, + "bbox": [ + 500, + 301, + 691, + 316 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets We conduct the following experiments with T2T [34], VOLO [35], CeiT [33] and DeiT [27] for image classification on CIFAR10 [13], CIFAR100 [15] and ImageNet [4]. a) We conduct the ablation study to demonstrate the effects of introducing modified DropAttention to three T2T and three VOLO backbone architectures on CIFAR10 and CIFAR100. b) We validate the modified DropAttention by training T2T and VOLO from scratch on ImageNet.", + "bbox": [ + 496, + 318, + 890, + 439 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training By default, models are trained with random initialization on all datasets. Due to the missing training setting for T2T [34] and VOLO [35], we conduct grid search on learning rate and epoch number to make the vanilla backbones achieve the best performance. All implementation specifics can be seen in Appendix. For ImageNet, our training recipe follows [34, 35]. Specifically, we set 50 epochs and keep learning rate as $10^{-5}$ for finetune stage for all datasets.", + "bbox": [ + 496, + 441, + 890, + 577 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1.1 Ablations on CIFAR10 and CIFAR100", + "text_level": 1, + "bbox": [ + 498, + 580, + 821, + 594 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Does DropKey boost generalization? T2T [34] and VOLO [35] are the widely used vision transformer architecture for image recognition. However, the DropAttention applied in these architectures does not apply re-normalize operation. In the following experiments, we plug in the DropKey to the family of T2T/VOLO and compare results with the version that use Dropout. The results in Figure 3 indicate DropKey can consistently increase the performance of various architectures on CIFAR10 and CIFAR100. On CIFAR100 with T2T19, for example, DropKey gains $1.7\\%$ improvement for the adaptive coefficient yields further improvement. Additionally, we found that drop ratio is also an essential factor affecting performance. Take T2T14 with DropKey as an example, the accuracy initially increases with increasing drop ratio until it achieves its peak accuracy of $79.2\\%$ at drop ratio $= 0.3$ and it declines upon further increase of the drop ratio. These suggest that the introduction of DropKey would be beneficial to the network for avoiding suffering overfits. However, a larger drop ratio can lead to an inability to capture valid information about the object.", + "bbox": [ + 496, + 598, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "aside_text", + "text": "10 98 65432-", + "bbox": [ + 52, + 130, + 68, + 263 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "22704", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/4390224b4a38e64389d33ef70d386fcf2af52057faffc7bdf012468f13febc0a.jpg", + "image_caption": [ + "Figure 3. Comparison of models with Dropout or DropKey on CIFAR10 and CIFAR100." + ], + "image_footnote": [], + "bbox": [ + 76, + 85, + 277, + 224 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f3ca36e684c55adcdd188f20bbea94c29c397e605edfb0abce6db98f9a5f6b25.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 282, + 85, + 482, + 224 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/312dada1f8b5286e0b902490b866ca0c921360795b393104e9bba906c2d5f84e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 488, + 85, + 687, + 224 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/ae50168f0aa9b51bc460ca4b02a7deda2ceae1dd4cf06ba591b8440b9393a452.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 694, + 85, + 893, + 224 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Similar to DropKey, the performance of Dropout is also related to drop ratio.", + "bbox": [ + 75, + 252, + 468, + 282 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "How does the choice of scheduled strategy of drop ratio impact accuracy? The ablation in Table 1 analyzes the accuracy of DropKey by adjusting the strategy of setting drop ratio. Specifically, we validate three strategy as follows: a) Constant: drop ratio is constant over self attention layers. b) Scheduled $\\uparrow$ : drop ratio is linearly increased over self attention layers. c) Scheduled $\\downarrow$ : drop ratio is linearly decreased over self attention layers. Firstly, we find that Scheduled $\\downarrow$ outperform Constant whether using re-normalize or not. Secondly, introducing drop ratio with Scheduled $\\uparrow$ would seriously affect the performance of the model and even perform worse than the pure vision transformer. This phenomenon is in line with our expectation, since deeper layers often contain high-level semantic information which is essential to perform classification. A large drop ratio in deep layer will increase the risk of losing important features which would make model difficult to converge to a generalized solution. Hence, we set drop ratio with Scheduled $\\downarrow$ in all following experiments.", + "bbox": [ + 75, + 287, + 472, + 575 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Is Dropkey helpful to capture global information? The contribution of DropKey is to generate a smoother attention weight matrix to encourage models to focus on global features. Class token has been proved to be effective in aggregating the information of the whole image, so we measure the smoothness of the attention distribution by calculating the entropy of its attention weight vector. Specifically, we define the entropy of the attention vector of class token as follows $E_{i} = -\\sum_{j}p_{j}^{i}\\log p_{j}^{i}$ where $p_j^i$ denotes the attention weight of $j^{th}$ attending patch in $i^{th}$ head.", + "bbox": [ + 75, + 580, + 468, + 733 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Note that a small entropy denotes that this head focuses on sparse patches. For convenience, the mean of entropy of multi-head as $E$ is reported in Figure 4. Clearly, it reads that while both Dropout and DropKey are able to improve the value of entropy, the improvement by DropKey is more significant. Meanwhile, when the drop rate increases, the entropy increase accordingly. In addition, to further verify the necessity of the adaptive coefficient for capturing general global information, we visualize the attention map (Figure 5) from class token in the last transformer layer. Obviously, the model with DropKey smoothly assigns attention", + "bbox": [ + 75, + 734, + 470, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "weight to the area related to the instance. Finally, we further verify that our method can alleviate local-bias via the fact that transformers with DropKey perform robustly in occluded scenarios.", + "bbox": [ + 496, + 252, + 890, + 311 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Is structured drop is useful to vision transformer? In this section, we analyze whether structured masking is useful for vision transformer via DropKey-Block and DropKey-Cross. Specifically, we swept over window size from 3 to 5 for DropKey-Block and from 1 to 3 for DropKey-Cross. Compared with the DropKey, the structured drop degrade the performance of the model in all case and classification accuracy will decrease with the further increase of the window size. One possible reason for this phenomenon is that a larger drop ratio in shallow transformer layer results in losing vital information of object. However, a larger drop ratio is the key to avoid overfit to low-level feature. Therefore, we encourage set a larger drop ratio rather than the introduction of structured drop.", + "bbox": [ + 496, + 316, + 892, + 527 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "How does align expectations impact accuracy? As discussed above, the mismatched expectations problem arises when directly use trained model with DropKey to test. Herein, to address above issue, we explore the impact of two methods, Monte Carlo and finetune, on the performance of network. The results in Table 3 indicates that accuracy can be improved regardless of the expectation alignment operation. Additionally, the accuracy of Monte Carlo increases with increasing sampling iterations. However, huge sampling iterations will lead to unacceptable computational cost. To fairly compare with Dropout, we also finetune it with the same training hyper-parameters as DropKey and then note that finetune only brings insignificant performance improvement or even over-fitting. In conclusion, alignment expectation of training and inference stage indeed can further improve the accuracy of the model.", + "bbox": [ + 496, + 532, + 893, + 773 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1.2 DropKey vs Dropout on ImageNet", + "text_level": 1, + "bbox": [ + 498, + 777, + 792, + 792 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We provide the accuracy under other different drop ratio for each backbone with DropKey on ImageNet, and contrast them with existing State of the Arts (SOTA) equipped with Dropout, including T2T, VOLO, CeiT and DeiT in Table 4. We have these findings: (1) Clearly, our DropKey obtains significant enhancement against pure backbone. Meanwhile, We note that Dropout can only bring a little boost", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "22705", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/d1b555ff08608db23690e6bcc78a1ae7c43618413ea20db739033245bff8cde3.jpg", + "table_caption": [ + "Table 1. Comparison of models with Dropout or DropKey on CIFAR10 and CIFAR100 when introducing different scheduled strategy of drop ratio. The drop ratio is set as 0.3 for all models." + ], + "table_footnote": [], + "table_body": "
ModelCIFAR10CIFAR100
Scheduled↑ConstantScheduled↓Scheduled↑ConstantScheduled↓
T2T14 [34] + Dropout96.796.997.277.077.878.4
T2T14 [34] + DropKey97.097.497.677.278.679.2
T2T19 [34] + Dropout96.697.197.477.378.178.5
T2T19 [34] + DropKey97.197.297.978.078.480.1
T2T24 [34] + Dropout96.497.097.576.777.378.2
T2T24 [34] + DropKey96.697.297.776.978.379.3
VOLOd1 [35] + Dropout95.896.496.677.378.279.0
VOLOd1 [35] + DropKey96.296.797.178.178.679.6
VOLOd2 [35] + Dropout95.696.196.477.078.479.0
VOLOd2 [35] + DropKey95.796.697.077.779.079.9
VOLOd3 [35] + Dropout96.096.396.677.177.978.5
VOLOd3 [35] + DropKey96.296.496.977.478.178.7
", + "bbox": [ + 176, + 117, + 785, + 311 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f0ed617387f35bd25e49f0fef5a07d4b870cc4320c6b5a40a8ca1b8dadede16f.jpg", + "image_caption": [ + "Figure 4. The histogram of entropy on CIFAR100. dr denotes drop ratio." + ], + "image_footnote": [], + "bbox": [ + 120, + 315, + 405, + 452 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/ac0765edfb26589582004ecd6965a731c72eced219bd00003c1280feee798f94.jpg", + "table_caption": [ + "Table 2. Comparison of different structured drop on CIFAR100. $s$ denotes window size and drop ratio is set as 0.3 for all models." + ], + "table_footnote": [], + "table_body": "
ModelRandomBlockCross
s=3s=5s=1s=3
T2T14 [34] + Dropout78.478.177.177.976.8
T2T14 [34] + DropKey79.278.777.578.677.4
VOLOd1 [35] + Dropout78.678.076.777.676.4
VOLOd1 [35] + DropKey79.278.577.578.377.1
", + "bbox": [ + 93, + 530, + 450, + 612 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/8848e54970b536436476913988fc617479fb2f3c154701272cf2b1f0e804514f.jpg", + "table_caption": [ + "Table 3. Comparison of models w/ or w/o Align Expectations on CIFAR100. Pure denotes the model without align expectation and drop ratio is set as 0.3 for all models." + ], + "table_footnote": [], + "table_body": "
ModelPurew/ Monte Carlow/ Finetune
20006000
T2T14 [34] + Dropout78.4--78.4
T2T14 [34] + DropKey78.878.979.179.2
T2T19 [34] + Dropout78.5--78.6
T2T19 [34] + DropKey79.379.580.280.1
", + "bbox": [ + 102, + 659, + 439, + 742 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "to backbones and it even would degrade the performance of the model in some cases (eg. T2T14, CeiT-T and DeiT-B). This indicates that the adaptive smoothing operator is more helpful to encourage the model to capture general information in large-scale datasets. (2) Compare to lightweight models, heavyweight often need the larger drop ratio to achieve a remarkable boost. For T2T14 and VOLOd1, the best accuracy is obtained under the dr=0.05. Instead, T2T19 and VOLOd2 achieve the best accuracy when dr=0.1, which suggests heavyweight models adopt a larger drop ratio to", + "bbox": [ + 75, + 750, + 472, + 902 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/dc7f74540448bd734f045d228aab8399d04e23103719791404df2be8c315270e.jpg", + "image_caption": [ + "Figure 5. Visualization on CIFAR100." + ], + "image_footnote": [], + "bbox": [ + 464, + 314, + 859, + 467 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "prevent overfitting.", + "bbox": [ + 500, + 503, + 627, + 517 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Object Detection in COCO", + "text_level": 1, + "bbox": [ + 500, + 517, + 743, + 532 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we verify the generalizability and effectiveness of DropKey for object detection on COCO dataset [19]. We apply DETR [1] framework for the experiments. Specifically, DETR is composed of the backbone, encoder and decoder. We followed the model architecture, anchor definition and training recipe in [1] to build DETR+Dropout and DETR+DropKey. In Table 5, we report the results of DETR [1] with Dropout or DropKey in terms of AP. It can be seen that, our DropKey significantly outperforms existing Dropout. In detail, DropKey achieve $+0.7$ , $+1.1$ , $+0.4$ , $+0.3$ , $+0.8$ and $+0.7$ higher AP than the Dropout, which is regarded as a remarkable boost considering the challenge on this benchmark. Another observation is that large objects benefit more from DropKey than small objects. These results suggest that DropKey has the advantage over Dropout.", + "bbox": [ + 496, + 534, + 890, + 775 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Human-Object Interaction Detection in HICODET", + "text_level": 1, + "bbox": [ + 500, + 777, + 890, + 808 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Since the task of scene graph and relation understanding is quite sensitive to global context learning, so we also verify the effectiveness of DropKey in QPIC [26] for Human-Object Interaction Detection in HICO-DET [2]. QPIC is a transformer-based feature extractor that can effectively aggregate contextually important information. We respec", + "bbox": [ + 496, + 810, + 890, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "22706", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/8f6ba0c75afaff7c272600c4b510f00e9ff702c2d71fa1ad15bc9ffad4a08457.jpg", + "table_caption": [ + "Table 4. Comparisons on backbones with Dropout or DropKey on ImageNet. dr denotes drop ratio." + ], + "table_footnote": [], + "table_body": "
ModelTop-1ModelTop-1
T2T14 [34]81.76 ± 0.05VOLOd1 [35]84.27 ± 0.12
T2T14 [34] + Dropout(dr=0.05)81.65 ± 0.04VOLOd1 [35] + Dropout(dr=0.05)84.35 ± 0.11
T2T14 [34] + Dropout(dr=0.1)81.53 ± 0.08VOLOd1 [35] + Dropout(dr=0.1)84.31 ± 0.04
T2T14 [34] + DropKey(dr=0.05)82.04 ± 0.14VOLOd1 [35] + DropKey(dr=0.05)84.53 ± 0.03
T2T14 [34] + DropKey(dr=0.1)81.93 ± 0.09VOLOd1 [35] + DropKey(dr=0.1)84.39 ± 0.02
T2T19 [34]82.56 ± 0.09VOLOd2 [35]85.24 ± 0.05
T2T19[34] + Dropout(dr=0.05)82.63 ± 0.05VOLOd2 [35] + Dropout(dr=0.05)85.22 ± 0.08
T2T19[34] + Dropout(dr=0.1)82.68 ± 0.04VOLOd2 [35] + Dropout(dr=0.1)85.21 ± 0.03
T2T19[34] + DropKey(dr=0.05)82.71 ± 0.02VOLOd2 [35] + DropKey(dr=0.05)85.33 ± 0.12
T2T19 [34] + DropKey(dr=0.1)82.94 ± 0.04VOLOd2 [35] + DropKey(dr=0.1)85.38 ± 0.06
CeiT-T [33]81.92 ± 0.06DeiT-B [27]81.94 ± 0.02
CeiT-T [33] + Dropout(dr=0.05)81.90 ± 0.03DeiT-B [27] + Dropout(dr=0.05)81.91 ± 0.04
CeiT-T [33] + Dropout(dr=0.1)81.83 ± 0.06DeiT-B [27] + Dropout(dr=0.1)81.87 ± 0.05
CeiT-T [33] + DropKey(dr=0.05)82.14 ± 0.05DeiT-B [27] + DropKey(dr=0.05)82.23 ± 0.01
CeiT-T [33] + DropKey(dr=0.1)82.27 ± 0.06DeiT-B [27] + DropKey(dr=0.1)82.25 ± 0.08
", + "bbox": [ + 192, + 104, + 774, + 323 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/7a99004a56f0fca6e95073ed15b888624f2c12edbf5cf8ea812c2853989bcd97.jpg", + "table_caption": [ + "Table 5. Comparison of DETR with Dropout and DropKey on COCO validation set. Table 6. Comparison of METRO with Dropout and Dropout key on HUMBI." + ], + "table_footnote": [], + "table_body": "
ModelAP\\( AP_{50} \\)\\( AP_{75} \\)\\( AP_S \\)\\( AP_M \\)\\( AP_L \\)
DETR [1]41.962.144.220.645.760.7
DETR [1] + Dropout42.262.344.320.845.961.1
DETR [1] + DropKey42.963.444.721.146.761.8
", + "bbox": [ + 122, + 366, + 509, + 422 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/fb2cf462eaca421e51e3a11210ee61667d2f7fca52eb3a50f8212a44042d0fad.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelmPVE↓mPJPE↓PA-mPJPE↓
METRO [18]57.851.539.9
METRO [18] + Dropout57.951.639.7
METRO [18] + DropKey57.151.039.5
", + "bbox": [ + 549, + 367, + 879, + 422 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/ac0a208d3cbe4ff84e99f6ca00ca1d6ede45eeeda4a5341aeec1eddb0f688536.jpg", + "table_caption": [ + "Table 7. Comparison of QPIC with Dropout and DropKey on HICO-DET." + ], + "table_footnote": [], + "table_body": "
Modelfull (Default)rare (Default)non-rare (Default)full (Known object)rare (Known object)non-rare (Known object)
QPIC-ResNet101 [26] + Dropout (dr=0.1)29.9624.0331.6332.4226.0134.31
QPIC-ResNet101 [26] + Dropout (dr=0.3)30.0224.1731.7232.4926.1334.41
QPIC-ResNet101 [26] + DropKey (dr=0.3)30.8724.6332.2433.2126.6634.94
", + "bbox": [ + 106, + 448, + 857, + 523 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "tively introduce Dropout and DropKey to both encoder and decoder in QPIC and train these models with the same training recipe as [26]. The model named \"QPIC-ResNet101 + Dropout (dr=0.1)\" is the result of our reproduction of QPIC with Schedued $\\downarrow$ drop ratio (Official realization is equipped with Constant drop ratio). The experimental results in Table 7 suggest DropKey has higher performance gain on the different evaluating indicators which are consistent with our expectations.", + "bbox": [ + 75, + 534, + 468, + 669 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Human Body Mesh Recovery in HUMBI", + "text_level": 1, + "bbox": [ + 76, + 671, + 424, + 686 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We verify the efficacy of DropKey for human body mesh task on HUMBI [32]. We follow conventions to train with 294 subjects from scratch and test with 120 subjects. We use Mean Per Vetex Error (MPVE) [22], Mean Per Joint Position Error (MPJPE) [14] and Procrustes Analysis MPJPE (PA-MPJPE) [38] as metrics. We use public METRO [18] as the baseline to apply DropKey to self-attention layer and Table 6 summaries the results. we can see that DropKey consistently improves the performance for all standard metrics. Specifically, DropKey brings about 0.7, 0.5 and 0.4 on mPVE, mPJPE and PA-mPJPE, respectively, while Dropout only boosts 0.2 performance on one metric. These results further verify the generalizability of DropKey as well as its superiority over vanilla dropout.", + "bbox": [ + 75, + 688, + 470, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 532, + 617, + 547 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we explore the drop unit, drop schedule and structured necessity of the dropout technique in ViT. Specifically, we propose to set Key as the drop unit, which yields a novel dropout-before-softmax scheme. We theoretically and experimentally verify that this scheme can regularize attention weights and meanwhile and keep them as a probability distribution simultaneously, helping capture vital patterns in a global manner and overcome local-bias problems that occurred to vanilla dropout. In addition, we present a new decreasing schedule for drop ratio, which stabilizes the training phase by avoiding overfittings in low-level features and maintaining sufficient high-level features. Moreover, we also experimentally show that structured dropout is not necessary for ViT. We distill the above analysis as a novel DropKey method, which plays as an improved version of dropout for ViT. Comprehensive experiments with different architectures on various vision tasks demonstrate the effectiveness of the proposed DropKey for enhancing ViTs.", + "bbox": [ + 496, + 547, + 890, + 819 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements", + "text_level": 1, + "bbox": [ + 500, + 821, + 666, + 838 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper is supported by the National key research and development program of China (2021YFA1000403), and the National Natural Science Foundation of China (Nos. U19B2040, 11991022).", + "bbox": [ + 496, + 839, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "22707", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 106 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Nicolas Carion, Francisco Massa, Gabriel Synnaeve, Nicolas Usunier, Alexander Kirillov, and Sergey Zagoruyko. End-to-end object detection with transformers. arXiv preprint arXiv:2005.12872, 2020. 1, 7, 8", + "[2] Yu-Wei Chao, Yunfan Liu, Xieyang Liu, Huayi Zeng, and Jia Deng. Learning to detect human-object interactions. In WACV, pages 381–389, 2018. 7", + "[3] Xiangxiang Chu, Zhi Tian, Yuqing Wang, Bo Zhang, Haibing Ren, Xiaolin Wei, Huaxia Xia, and Chunhua Shen. Twins: Revisiting the design of spatial attention in vision transformers. 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IEEE transactions on pattern analysis and machine intelligence, 41(4):901-914. 8" + ], + "bbox": [ + 78, + 90, + 467, + 512 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "22709", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/DropKey for Vision Transformer/539b4cee-3610-4b35-8990-86b8994c51f3_model.json b/2023/DropKey for Vision Transformer/539b4cee-3610-4b35-8990-86b8994c51f3_model.json new file mode 100644 index 0000000000000000000000000000000000000000..e7218ebd92d95dc4323a84c15fcd7dc71f34d43d --- /dev/null +++ b/2023/DropKey for Vision Transformer/539b4cee-3610-4b35-8990-86b8994c51f3_model.json @@ -0,0 +1,2123 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.318, + 0.131, + 0.655, + 0.154 + ], + "angle": 0, + "content": "DropKey for Vision Transformer" + }, + { + "type": "text", + "bbox": [ + 0.245, + 0.192, + 0.725, + 0.23 + ], + "angle": 0, + "content": "Bonan \\(\\mathrm{Li}^{*1}\\), Yinhan \\(\\mathrm{Hu}^{*1}\\), Xuecheng \\(\\mathrm{Nie}^2\\), Congying \\(\\mathrm{Han}^{\\dagger 1}\\), Xiangjian Jiang\\(^3\\), Tiande Guo\\(^1\\), Luoqi Liu\\(^2\\)" + }, + { + "type": "text", + "bbox": [ + 0.307, + 0.241, + 0.664, + 0.259 + ], + "angle": 0, + "content": "1University of Chinese Academy of Sciences" + }, + { + "type": "text", + "bbox": [ + 0.402, + 0.26, + 0.568, + 0.276 + ], + "angle": 0, + "content": "\\(^{2}\\)MT Lab, Meitu Inc." + }, + { + "type": "text", + "bbox": [ + 0.383, + 0.277, + 0.588, + 0.295 + ], + "angle": 0, + "content": "\\(^{3}\\)University of Cambridge" + }, + { + "type": "text", + "bbox": [ + 0.217, + 0.295, + 0.756, + 0.312 + ], + "angle": 0, + "content": "{libonan, hancy, tdguo}@ucas.ac.cn, huhinhan16@mails.ucas.ac.cn" + }, + { + "type": "text", + "bbox": [ + 0.312, + 0.313, + 0.66, + 0.331 + ], + "angle": 0, + "content": "{nxc,llq5} \\(@\\) meitu.com,xj265@cam.ac.uk" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.376, + 0.314, + 0.391 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.409, + 0.473, + 0.862 + ], + "angle": 0, + "content": "In this paper, we focus on analyzing and improving the dropout technique for self-attention layers of Vision Transformer, which is important while surprisingly ignored by prior works. In particular, we conduct researches on three core questions: First, what to drop in self-attention layers? Different from dropping attention weights in literature, we propose to move dropout operations forward ahead of attention matrix calculation and set the Key as the dropout unit, yielding a novel dropout-before-softmax scheme. We theoretically verify that this scheme helps keep both regularization and probability features of attention weights, alleviating the overfittings problem to specific patterns and enhancing the model to globally capture vital information; Second, how to schedule the drop ratio in consecutive layers? In contrast to exploit a constant drop ratio for all layers, we present a new decreasing schedule that gradually decreases the drop ratio along the stack of self-attention layers. We experimentally validate the proposed schedule can avoid overfittings in low-level features and missing in high-level semantics, thus improving the robustness and stableness of model training; Third, whether need to perform structured dropout operation as CNN? We attempt patch-based block-version of dropout operation and find that this useful trick for CNN is not essential for ViT. Given exploration on the above three questions, we present the novel DropKey method that regards Key as the drop unit and exploits decreasing schedule for drop ratio, improving ViTs in a general way. Comprehensive experiments demonstrate the effectiveness of DropKey for various ViT architectures, e.g. T2T, VOLO, CeiT and DeiT, as well as for various vision" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.378, + 0.892, + 0.424 + ], + "angle": 0, + "content": "tasks, e.g., image classification, object detection, human-object interaction detection and human body shape recovery." + }, + { + "type": "title", + "bbox": [ + 0.502, + 0.432, + 0.632, + 0.448 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.459, + 0.892, + 0.581 + ], + "angle": 0, + "content": "Vision Transformer (ViT) [6] has achieved great success for various vision tasks, e.g., image recognition [7, 12, 20, 34, 35], object detection [1], human body shape estimation [18], etc. Prior works mainly focus on researches of patch division, architecture design and task extension. However, the dropout technique for self-attention layer, which plays the essential role to achieve good generalizability, is surprisingly ignored by the community." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.582, + 0.893, + 0.884 + ], + "angle": 0, + "content": "Different from the counterpart for Convolutional Neural Networks (CNNs), the dropout in ViT directly utilizes the one in original Transformer designed for Natural Language Processing, which sets attention weights as the manipulation unit with a constant dropout ratio for all layers. Despite of its simplicity, this vanilla design faces three major problems. First, it breaks the probability distribution of attention weights due to the averaging operation on non-dropout units after softmax normalization. Although this regularizes the attention weights, it still overfits specific patterns locally due to the failure on penalizing score peaks, as shown in Fig. 1 (a) and (b); Second, the vanilla design is sensitive to the constant dropout ratio, since high ratio occurs missing of semantic information in high-level representations while low ratios overfitting in low-level features, resulting in the unstable training process; Third, it ignores the structured characteristic of input patch grid to ViT, which plays an effective role to improve performance with blockwise dropout in CNNs. These three problems degrade the performance and limit the generalizability of ViTs." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Motivated by this, we propose to analyze and improve" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.875, + 0.204, + 0.888 + ], + "angle": 0, + "content": "*Equal contribution" + }, + { + "type": "page_footnote", + "bbox": [ + 0.098, + 0.888, + 0.22, + 0.9 + ], + "angle": 0, + "content": "† Corresponding author" + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.875, + 0.22, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "22700" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.137 + ], + "angle": 0, + "content": "the dropout technique in self-attention layer, further pushing forward the frontier of ViTs for vision tasks in a general way. Specifically, we focus on three core aspects:" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.14, + 0.473, + 0.502 + ], + "angle": 0, + "content": "What to drop in self-attention layer Different from dropping attention weights as in the vanilla design, we propose to set the Key as the dropout unit, which is essential input of self-attention layer and significantly affects the output. This moves the dropout operation forward before calculating the attention matrix as shown in Fig. 1 (c) and yields a novel dropout-before-softmax scheme. This scheme regularizes attention weights and keeps their probability distribution at the same time, which intuitively helps penalize weight peaks and lift weight foots. We theoretically verify this property via implicitly introducing an adaptive smoothing coefficient for the attention operator from the perspective of gradient optimization by formulating a Lagrange function. With the dropout-before-softmax scheme, self-attention layers can capture vital information in a global manner, thus overcoming the overfittings problem to specific patterns occurred in the vanilla dropout and enhancing the model generalizability as visualization of feature map in Fig. 1 (c). For the training phase, this scheme can be simply implemented by swapping the operation order of softmax and dropout in vanilla design, which provides a general way to effectively enhance ViTs. For inference phase, we conduct an additional finetune phase to align the expectations to training phase, further improving the performance." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.506, + 0.473, + 0.656 + ], + "angle": 0, + "content": "How to schedule the drop ratio In contrast to exploiting a constant drop ratio for all layers, we present a new linear decreasing schedule that gradually decreases the drop ratio along the stack of self-attention layers. This schedule leads to a high drop ratio in shallow layers while the low one in deep layers, thus avoiding over fittings to low-level features and preserving sufficient high-level semantics. We experimentally verify the effectiveness of the proposed decreasing schedule for drop ratio to stable the training phase and improve the robustness." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.659, + 0.473, + 0.825 + ], + "angle": 0, + "content": "Whether need to perform structured drop Inspired by the DropBlock [10] method for CNNs, we implement two structured versions of the dropout operation for ViTs: the block-version dropout that drops keys corresponding to contiguous patches in images or feature maps; the crossversion dropout that drops keys corresponding to patches in horizontal and vertical stripes. We conduct thorough experiments to validate their efficacy and find that the structure trick useful for CNN is not essential for ViT, due to the powerful capability of ViT to grasp contextual information in full image range." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.826, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Given exploration on the above three aspects, we present a novel DropKey method that utilizes Key as the drop unit and decreasing schedule for drop ratio. In particular, DropKey overcomes drawbacks of the vanilla dropout technique for ViTs, improving performance in a general and effective" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.258 + ], + "angle": 0, + "content": "way. Comprehensive experiments on different ViT architectures and vision tasks demonstrate the efficacy of DropKey. Our contributions are in three folds: First, to our best knowledge, we are the first to theoretically and experimentally analyze dropout technique for self-attention layers in ViT from three core aspects: drop unit, drop schedule and structured necessity; Second, according to our analysis, we present a novel DropKey method to effectively improve the dropout technique in ViT. Third, with DropKey, we improve multiple ViT architectures to achieve new SOTAs on various vision tasks." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.263, + 0.642, + 0.279 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.289, + 0.895, + 0.501 + ], + "angle": 0, + "content": "Vision Transformers Inspired by the Transformer architectures in NLP, some works introduce attention block to replace convolution layers to model long-range dependencies [6, 11, 17, 29, 30, 31, 37]. ViT[6] is the pioneering work which splits an image to non-overlapping patches and then these patches are fed to a transformer to evaluate attention scores. Prior works mainly focus on patch division, architecture design and tasks extension. For example, CvT[31] proposes a hybrid architecture to mix convolutional with attention layers to introduce local inductive bias. [3, 7, 20] proposes to reduce the computation cost. Despite the progress, previous works ignore the dropout technique in self-attention layer, which play an important role to keep good generalizability." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.504, + 0.895, + 0.64 + ], + "angle": 0, + "content": "Dropout Dropout is a common technique for improving the generalizability of neural networks, e.g., CNNs [16], RNNs [21] and GNNs [24]. For CNNs, [10] points out the lack of success of dropout for convolutional layers is due to dense information flowing and then proposes a form of structured Dropout. DropConnect [28] randomly masks a subset of weights within the model. For RNNs, the first prominent research on dropout is presented in [8], which is equipped with a learnable dropout rate." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.641, + 0.895, + 0.746 + ], + "angle": 0, + "content": "For GNNs, to alleviate over-fitting and over-smoothing issues, DropEdge [23] randomly removes part of edges in the input stage at each training epoch and theoretically demonstrates the effect of the proposed method. For ViTs, most original publicly code of multiple popular vision transformer simply intuitively apply dropout operation on attention matrix." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.897, + 0.903 + ], + "angle": 0, + "content": "DropAttention [36] presents a novel way for transformer in NLPs. It refers to perform randomly drop on the attention matrix. There are two two main forms of applying DropAttention for the transformer training, DropAttention-unit and DropAttention-elements. Similar to the standard Dropout [25], DropAttention-unit randomly drops the unit, that is, these dropped token will not be used as attend patches for each query patch. As the general form of DropAttention-unit, DropAttention-elements randomly drops elements in attention weights matrix which" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.958 + ], + "angle": 0, + "content": "22701" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.087, + 0.437, + 0.246 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.098, + 0.252, + 0.174, + 0.266 + ], + "angle": 0, + "content": "Input Image" + }, + { + "type": "image", + "bbox": [ + 0.434, + 0.088, + 0.664, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.462, + 0.252, + 0.61, + 0.266 + ], + "angle": 0, + "content": "(b) Attention w/ Dropout" + }, + { + "type": "image", + "bbox": [ + 0.665, + 0.089, + 0.895, + 0.247 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.695, + 0.252, + 0.842, + 0.266 + ], + "angle": 0, + "content": "(c) Attention w/ DropKey" + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.272, + 0.894, + 0.327 + ], + "angle": 0, + "content": "Figure 1. Comparison between the proposed DropKey and existing vanilla dropout techniques in self-attention layers for ViTs. (a) Self-attention without dropout, which suffers overfitting problems to local patch; (b) Self-attention with vanilla dropout, which regularizes the attention weights but still overfits specific patterns; (c) Self-attention with our DropKey, which overcomes prior problems and improves the model to capture vital information in a global manner. Best viewed in color." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.329, + 0.471, + 0.405 + ], + "angle": 0, + "content": "is similar to DropConnect [28]. Different from standard Dropout [25], DropAttention introduce re-normalize to guarantee the sum of attention weights to 1 and help training process to be more steady. However, there is no further discussion and theoretical analysis on this phenomenon." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.406, + 0.168, + 0.421 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.431, + 0.47, + 0.521 + ], + "angle": 0, + "content": "Our generic DropKey is inspired by DropAttention and proposed for self-attention operator in vision transformer. The main idea of DropKey is to adaptively adjust attention weight to obtain a smoother attention vector. In this section, we start by introducing the theoretical explanation of DropKey, then the implementation will be explained in detail." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.521, + 0.214, + 0.535 + ], + "angle": 0, + "content": "3.1. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.535, + 0.471, + 0.776 + ], + "angle": 0, + "content": "As discussed in the above section, transformer-based model tends to rely on local features rather than general global information. To alleviate this issue, we propose to reduce local-bias by encouraging models to learn a smoother attention weight for each patch. To this end, we attempt to reduce the attention weight of the patch which has a large attention weight, and vice versa. Nevertheless, it is tedious and difficult to achieve this by explicitly setting rules. In this work, we found DropKey achieves the above implicitly by normalizing the attention vector that has performed the dropout operation. Specifically, by given an image \\(I \\in \\mathbb{R}^{H \\times W \\times C}\\), where \\(H\\) denotes height, \\(W\\) denotes width and \\(C\\) denotes channels, Vision Transformer architecture starts by dicing it into \\(n_h \\times n_w\\) patches \\(x \\in \\mathbb{R}^{n_c}\\). Then, \\(x\\) is used as input of self-attention layer and the output \\(o\\) can be computed as follows" + }, + { + "type": "equation", + "bbox": [ + 0.18, + 0.782, + 0.47, + 0.822 + ], + "angle": 0, + "content": "\\[\no = \\sum_ {j = 1} ^ {n _ {h} n _ {w}} \\left(\\frac {d _ {j} p _ {j}}{\\sum_ {j = 1} ^ {n _ {h} n _ {w}} d _ {j} p _ {j}}\\right) v _ {j} \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.188, + 0.822, + 0.469, + 0.868 + ], + "angle": 0, + "content": "\\[\np _ {j} = \\frac {\\exp \\left(\\frac {q k _ {j} ^ {T}}{\\text {s c a l e}}\\right)}{\\sum_ {j = 1} ^ {n _ {h} n _ {w}} \\exp \\left(\\frac {q k _ {j} ^ {T}}{\\text {s c a l e}}\\right)} \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.471, + 0.902 + ], + "angle": 0, + "content": "where \\(q = \\mathcal{F}_q(x), k = \\mathcal{F}_k(x), v = \\mathcal{F}_v(x)\\), and \\(q_i, k_j, v_j\\) denote query of \\(i^{th}\\) patch, key of \\(j^{th}\\) patch, value of \\(j^{th}\\) patch and \\(o\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.329, + 0.892, + 0.463 + ], + "angle": 0, + "content": "denotes the output of one patch. \\(\\mathcal{F}_q(\\cdot),\\mathcal{F}_k(\\cdot),\\mathcal{F}_v(\\cdot)\\) denote projection layers with weights of dimensions \\(n_c\\times n_c\\) . scale denotes scaling factor and is set to \\(\\sqrt{n_c}\\) \\(d\\) denotes drop ratio and \\(d_{j}\\sim Bernoulli(1 - d)\\) . Here, for convenience, we focus on one head and omit the index of patch. By performing re-normalize, DropKey has the ability to adaptively adjust attention weight to smoother. Next, we provide theoretical analysis of our method to demonstrate its effectiveness." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.466, + 0.892, + 0.497 + ], + "angle": 0, + "content": "Here, we formulate the expectation output of model via introducing DropKey in training stage as:" + }, + { + "type": "equation", + "bbox": [ + 0.508, + 0.503, + 0.892, + 0.576 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathbb {E} _ {d _ {j}, 1 \\leq j \\leq n _ {h} n _ {w}} [ o ] = \\mathbb {E} _ {d _ {j}, 1 \\leq j \\leq n _ {h} n _ {w}} [ \\sum_ {j = 1} ^ {n _ {h} n _ {w}} (\\frac {d _ {j} p _ {j}}{\\sum_ {j = 1} ^ {n _ {h} n _ {w}} d _ {j} p _ {j}}) v _ {j} ] \\tag {3} \\\\ = \\sum_ {j = 1} ^ {n _ {h} n _ {w}} \\mathbb {E} _ {d _ {j}, 1 \\leq j \\leq n _ {h} n _ {w}} [ \\frac {d _ {j}}{\\sum_ {j = 1} ^ {n _ {h} n _ {w}} d _ {j} p _ {j}} ] p _ {j} v _ {j} = \\sum_ {j = 1} ^ {n _ {h} n _ {w}} c _ {j} p _ {j} v _ {j} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.584, + 0.891, + 0.621 + ], + "angle": 0, + "content": "where \\( c_{j} = \\mathbb{E}_{d_{j},1\\leq j\\leq n_{h}n_{w}}\\left[\\frac{d_{j}}{\\sum_{j = 1}^{n_{h}n_{w}}d_{j}p_{j}}\\right] > 0 \\) is a smoothing coefficient which is related to \\( d_{j} \\) and \\( p_j \\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.621, + 0.892, + 0.66 + ], + "angle": 0, + "content": "Note that \\(c\\) in Equ (3) can be considered to add an additional smoothing prior to distribution \\(p\\), i.e., \\(c_{s} < c_{t}\\) when \\(p_{s} > p_{t}, 1 \\leq s, t \\leq n_{h}n_{w}\\). The specific proof is as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.675, + 0.892, + 0.733 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} c _ {s} - c _ {t} = \\mathbb {E} _ {d _ {j}, 1 \\leq j \\leq n _ {h} n _ {w}} [ \\frac {d _ {s}}{\\sum_ {j = 1} ^ {n _ {h} n _ {w}} d _ {j} p _ {j}} ] - \\mathbb {E} _ {d _ {j}, 1 \\leq j \\leq n _ {h} n _ {w}} [ \\frac {d _ {t}}{\\sum_ {j = 1} ^ {n _ {h} n _ {w}} d _ {j} p _ {j}} ] \\\\ = d (1 - d) \\mathbb {E} _ {d _ {j}, 1} \\leq j \\leq n _ {h} n _ {w} \\left[ \\frac {1}{\\sum_ {j \\neq s , t} ^ {n _ {h} n _ {w}} d _ {j} p _ {j} + p _ {s}} - \\frac {1}{\\sum_ {j \\neq s , t} ^ {n _ {h} n _ {w}} d _ {j} p _ {j} + p _ {t}} \\right] < 0 \\tag {4} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "It is natural to find \\( c \\) serves as a factor to implicitly encourage the model properly to reduce the consideration of the patch with large \\( p \\) and improve the effectiveness of the patch with small attention weight. Meanwhile, \\( c \\) can be adjusted adaptively according to the distribution of samples in the training stage without any manual design. Nevertheless, a noteworthy problem is that since we removed DropKey in the inference phase, the output expectations in training and inference stage are inconsistent, which will decrease the performance. In Section 3.2, we propose two methods to alleviate this problem." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22702" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.152 + ], + "angle": 0, + "content": "Having explored the implicit regularization effects of DropKey, we also demonstrate it from the perspective of gradient optimization. For simplicity, we start by considering a simple but universal optimization objective as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.092, + 0.17, + 0.47, + 0.207 + ], + "angle": 0, + "content": "\\[\n\\min _ {p _ {j}, v _ {j}} \\frac {1}{2} \\| \\sum_ {j = 1} ^ {N} p _ {j} v _ {j} - y \\| ^ {2} \\text {s . t .} p _ {j} > 0, \\sum_ {j = 1} p _ {j} = 1, 1 \\leq j \\leq N \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.21, + 0.473, + 0.348 + ], + "angle": 0, + "content": "where \\( p_j \\in \\mathbb{R} \\), \\( v_j \\in \\mathbb{R}^r \\) denotes learnable parameters and \\( y \\in \\mathbb{R}^r \\) denotes target. This simple problem captures the essential part of the training of a single self-attention layer, especially when the neural networks are large, and it may shed light on the training of deep models. Here, \\( p_j \\) and \\( v_j \\) can be considered as attention weight and value in attention mechanism. Naturally, \\( v_j \\) can be decomposed into two directions, which are the same direction as \\( y \\) and the direction perpendicular to \\( y \\):" + }, + { + "type": "equation", + "bbox": [ + 0.221, + 0.359, + 0.47, + 0.377 + ], + "angle": 0, + "content": "\\[\nv _ {j} = \\beta_ {j} e + \\alpha_ {j} \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.385, + 0.473, + 0.446 + ], + "angle": 0, + "content": "where \\(\\beta\\) is a scalar, \\(e\\in \\mathbb{R}^r\\) is the unit vector of \\(y\\) and \\(\\alpha_{j}\\) is the component perpendicular to \\(y\\). Similarly, we can rewrite \\(y\\) to \\(Me\\) where \\(M = ||y||\\). Then, the Lagrange function of Equ (5) can be formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.125, + 0.45, + 0.47, + 0.488 + ], + "angle": 0, + "content": "\\[\nL \\left(p _ {j}, v _ {j}, \\lambda\\right) = \\frac {1}{2} | | \\sum_ {j = 1} ^ {N} p _ {j} v _ {j} - y | | ^ {2} - \\lambda \\left(\\sum_ {j = 1} ^ {N} p _ {j} - 1\\right) \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.491, + 0.47, + 0.524 + ], + "angle": 0, + "content": "In order to analysis the gradient, we take the partial derivatives of \\( p_j \\) and \\( v_j \\):" + }, + { + "type": "equation", + "bbox": [ + 0.078, + 0.528, + 0.47, + 0.575 + ], + "angle": 0, + "content": "\\[\n\\frac {\\partial L}{\\partial p _ {j}} = (v - y) ^ {T} v _ {j} - \\lambda = \\left(\\sum_ {j = 1} ^ {N} p _ {j} \\beta_ {j} - M\\right) \\beta_ {j} + \\left(\\sum_ {j = 1} ^ {N} p _ {j} \\alpha_ {j}\\right) ^ {T} \\alpha_ {j} - \\lambda \\tag {8}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.11, + 0.592, + 0.47, + 0.629 + ], + "angle": 0, + "content": "\\[\n\\frac {\\partial L}{\\partial v _ {j}} = p _ {j} (v - y) = p _ {j} \\left(\\sum_ {j = 1} ^ {N} p _ {j} \\beta_ {j} - M\\right) e + p _ {j} \\left(\\sum_ {j = 1} ^ {N} p _ {j} \\alpha_ {j}\\right) \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.636, + 0.469, + 0.687 + ], + "angle": 0, + "content": "Here, for simplicity, we note \\( v = \\sum_{j=1}^{N} p_j v_j = (\\sum_{j=1}^{N} p_j \\beta_j) e + \\sum_{j=1}^{N} p_j \\alpha_j \\). From the chain rule of backpropagation, we also have:" + }, + { + "type": "equation", + "bbox": [ + 0.122, + 0.692, + 0.47, + 0.728 + ], + "angle": 0, + "content": "\\[\n\\frac {\\partial L}{\\partial \\beta_ {j}} = p _ {j} \\left(\\sum_ {j = 1} ^ {N} p _ {j} \\beta_ {j} - M\\right) \\quad \\frac {\\partial L}{\\partial \\alpha_ {j}} = p _ {j} \\left(\\sum_ {j = 1} ^ {N} p _ {j} \\alpha_ {j}\\right) \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.734, + 0.47, + 0.786 + ], + "angle": 0, + "content": "Equ (10) indicates that the gradient \\(\\frac{\\partial L}{\\partial \\beta_s} < \\frac{\\partial L}{\\partial \\beta_t}\\) when \\(p_s > p_t\\) and this backward propagation properties would lead \\(\\frac{\\partial L}{\\partial p_s} < \\frac{\\partial L}{\\partial p_t}\\). By subtracting \\(\\frac{\\partial L}{\\partial p_s}\\) and \\(\\frac{\\partial L}{\\partial p_t}\\), we will have:" + }, + { + "type": "equation", + "bbox": [ + 0.085, + 0.798, + 0.47, + 0.835 + ], + "angle": 0, + "content": "\\[\n\\frac {\\partial L}{\\partial p _ {s}} - \\frac {\\partial L}{\\partial p _ {t}} = \\left(\\sum_ {j = 1} ^ {N} p _ {j} \\beta_ {j} - M\\right) \\left(\\beta_ {s} - \\beta_ {t}\\right) + \\left(\\sum_ {j = 1} ^ {N} p _ {j} \\alpha_ {j}\\right) ^ {T} \\left(\\alpha_ {s} - \\alpha_ {t}\\right) \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.839, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Since all parameters are randomly initialized, it can be assumed that the initial solution is far from the optimal solution, that is, \\( p_1^{(0)} = p_2^{(0)} = \\dots = p_N^{(0)} = \\frac{1}{N} \\), \\( |\\beta_j^{(0)}| \\ll M \\), \\( 1 \\leq j \\leq N \\). Consequently, the first additive term plays" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.09, + 0.892, + 0.213 + ], + "angle": 0, + "content": "the leading role in Equ (11). Due to \\(\\frac{\\partial L}{\\partial\\beta_s} < \\frac{\\partial L}{\\partial\\beta_t}\\), the update speed of \\(\\beta_{s}\\) is faster than \\(\\beta_{t}\\) and then lead \\(\\beta_{s} > \\beta_{t}\\), \\(\\frac{\\partial L}{\\partial p_s} < \\frac{\\partial L}{\\partial p_t}\\). Based on the above analysis, it can be concluded that a larger \\(p\\) would promote \\(\\beta\\) larger, while a larger \\(\\beta\\) would further promote \\(p\\) larger. Finally, the output of model would be controlled by a few sparse blocks. Conversely, DropKey avoids suffering local-bias by introducing the parameter \\(c\\) to enforce distribution \\(p\\) to be smoother." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.215, + 0.661, + 0.23 + ], + "angle": 0, + "content": "3.2. Implementation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.232, + 0.892, + 0.444 + ], + "angle": 0, + "content": "What to drop? Different from DropAttention, we integrate Dropout and re-normalize into one stage by dropping key rather than weight. At each training iteration, DropKey masks a certain rate of keys of the input key map by random. It is worth noting that we generate masked key map for each query, instead of sharing the same masked key map for all query vectors. Specifically, given the query \\( Q \\in \\mathbb{R}^{n_h n_w \\times n_c} \\), key \\( K \\in \\mathbb{R}^{n_h n_w \\times n_c} \\) and value \\( V \\in \\mathbb{R}^{n_h n_w \\times n_c} \\) of a feature map, it first computes the dot products of the query with all keys and divide each by scaling factor \\( scale = \\sqrt{n_c} \\). Subsequently, we randomly generate a mask matrix \\( D \\in \\mathbb{R}^{1 \\times (n_h n_w \\times n_h n_w)} \\) with drop ratio \\( d \\) to enforce some elements of the similarity matrix to be -inf. The formulation of \\( D \\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.568, + 0.45, + 0.892, + 0.478 + ], + "angle": 0, + "content": "\\[\nd _ {j} = \\left\\{ \\begin{array}{c c} 0 & \\text {w i t h p r o b a b i l i t y} 1 - d \\\\ - \\infty & \\text {w i t h p r o b a b i l i t y} d \\end{array} \\right. \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.486, + 0.892, + 0.532 + ], + "angle": 0, + "content": "Finally, the attention weight matrix is computed by given masked similarity matrix as input. Formally, we compute the outputs of a patch as:" + }, + { + "type": "equation", + "bbox": [ + 0.649, + 0.54, + 0.892, + 0.574 + ], + "angle": 0, + "content": "\\[\no = \\sum_ {j = 1} ^ {n _ {h} n _ {w}} p _ {j} v _ {j} \\tag {13}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.604, + 0.575, + 0.892, + 0.619 + ], + "angle": 0, + "content": "\\[\np _ {j} = \\frac {\\exp \\left(d _ {j} + \\frac {q k _ {j} ^ {T}}{\\text {s c a l e}}\\right)}{\\sum_ {j = 1} ^ {n _ {h} n _ {w}} \\exp \\left(d _ {j} + \\frac {q k _ {j} ^ {T}}{\\text {s c a l e}}\\right)} \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.622, + 0.892, + 0.729 + ], + "angle": 0, + "content": "where \\( q_{i}, k_{j}, v_{j} \\) denote query of \\( i^{th} \\) patch, key of \\( j^{th} \\) patch, value of \\( j^{th} \\) patch. It is not difficult to find that Equ (13) and Equ (14) is the same equivalent form of Equ (1) and Equ (2). In particular, as shown in Algorithm 1, we only need to add two lines of code to pure attention to implement DropKey. Obviously, compared with Dropout, DropKey only changes the position of introducing mask." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.917 + ], + "angle": 0, + "content": "Scheduled Drop Ratio Vision transformer always consists of few self-attention blocks to gradually learn high-dimensional features. Generally, early layers operates low-level visual features and deeper layers aim to model spatially coarse but complex information. Hence, we attempt to set smaller drop ratio for deeper layers to avoid missing important objects-relevant information. Specifically, instead of stochastically dropping with some fixed probability in Dropout, we gradually decrease number of dropped keys over the layers during training stage. We find that this scheduled drop ratio not only work well for DropKey, but also significantly improves the performance of Dropout." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.958 + ], + "angle": 0, + "content": "22703" + } + ], + [ + { + "type": "aside_text", + "bbox": [ + 0.053, + 0.131, + 0.069, + 0.264 + ], + "angle": 270, + "content": "10 98 65432-" + }, + { + "type": "code_caption", + "bbox": [ + 0.079, + 0.106, + 0.365, + 0.122 + ], + "angle": 0, + "content": "Algorithm 1 Attention with DropKey code" + }, + { + "type": "algorithm", + "bbox": [ + 0.114, + 0.131, + 0.488, + 0.265 + ], + "angle": 0, + "content": "N: token number, D: token dim\n# Q: query (N, D), K: key (N, D), V: value (N, D)\n# use_DropKey: whether use DropKey\n# mask_ratio: ratio to mask\ndef Attention(Q, K, V, use_DropKey, mask_ratio)\n attn = (Q * (Q.shape[1] ** -0.5)) @ K.transpose(-2, -1)\n # use DropKey as regularizer\n if use_DropKey == True:\n m_r = torch.ones_like(attn) * mask_ratio\n attn = attn + torchBernoulli(m_r) * -1e12\n attn = attn softmax(dim=-1)\n x = attn @ V\n return x" + }, + { + "type": "image", + "bbox": [ + 0.545, + 0.098, + 0.645, + 0.183 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.658, + 0.098, + 0.758, + 0.185 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.771, + 0.098, + 0.871, + 0.185 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.525, + 0.195, + 0.89, + 0.266 + ], + "angle": 0, + "content": "Figure 2. Mask sampling in DropKey, DropKey-Block and DropKey-Cross. The yellow patches are used as attend key to interact with a query and blue patches are dropped. Red symbol denotes the valid seed and the window size of DropKey-Block and DropKey-Cross is 3 and 1, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.287, + 0.473, + 0.485 + ], + "angle": 0, + "content": "Structured DropKey Although structured drop has been dally explored in convolution network, there is no work to study the impact of structured drop on vision transformer. In this section, we implement two structured forms of DropKey which are named DropKey-Block and DropKey-Cross (see Figure 2). For DropKey-Block, inspired by DropBlock [10], we drop contiguous patches in a square-shape window of feature maps. Actually, we re-set drop ratio \\(d_{block}\\) for each patch as: \\(d_{block} = \\frac{d}{s^2}\\frac{n_h n_w}{(n_h - s + 1)(n_w - s + 1)}\\) where \\(d\\) denotes the probability of dropping a patch in DropKey. The valid seed region is \\((n_h - s + 1)(n_w - s + 1)\\) where \\(s\\) denotes the size of window and \\(n_h, n_w\\) denotes height, weight of feature map." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.486, + 0.47, + 0.638 + ], + "angle": 0, + "content": "The cross-shape window attention is proved to achieve strong modeling capability [5] which also indicates the information in this structure is correlated. For DropKeyCross, we discard features in a cross window to prevent information flow through self-attention. In our implementation, we drop the rows and columns of valid seed and re-set the drop ratio \\( d_{cross} \\) for each patch as: \\( d_{cross} = \\frac{d}{s(n_h + n_w - s)}\\frac{n_hn_w}{(n_h - s + 1)(n_w - s + 1)} \\). Note that the formulations for block- and cross-version are only the approximation, because there will be some overlapped when perform drop." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.643, + 0.47, + 0.825 + ], + "angle": 0, + "content": "Align Expectation As mentioned in Section 3.1, the misaligned expectations have a certain negative impact on the model, so we attempt to use two methods to align the expectation. The first one is to use Monte Carlo method to estimate \\( c \\). We perform multiple random drop and calculate the attention weight matrix after each drop operation. Finally, the average of calculated multiple weight matrices is applied as the input for the next step. For the second one, we take the inspiration from [9] and propose to finetune the model without DropKey, as an extra stage after DropKey training. We experimentally verify that the second strategy performs better with experiment in Section 4.1.1." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.83, + 0.21, + 0.847 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.902 + ], + "angle": 0, + "content": "We conduct experiments on three tasks, image classification, object detection, human-object interaction detection and human mesh recovery, to show the efficacy and gener" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.287, + 0.813, + 0.302 + ], + "angle": 0, + "content": "alizability of our DropKey for improving ViTs." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.303, + 0.692, + 0.318 + ], + "angle": 0, + "content": "4.1. Image Classification" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.319, + 0.892, + 0.44 + ], + "angle": 0, + "content": "Datasets We conduct the following experiments with T2T [34], VOLO [35], CeiT [33] and DeiT [27] for image classification on CIFAR10 [13], CIFAR100 [15] and ImageNet [4]. a) We conduct the ablation study to demonstrate the effects of introducing modified DropAttention to three T2T and three VOLO backbone architectures on CIFAR10 and CIFAR100. b) We validate the modified DropAttention by training T2T and VOLO from scratch on ImageNet." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.443, + 0.892, + 0.578 + ], + "angle": 0, + "content": "Training By default, models are trained with random initialization on all datasets. Due to the missing training setting for T2T [34] and VOLO [35], we conduct grid search on learning rate and epoch number to make the vanilla backbones achieve the best performance. All implementation specifics can be seen in Appendix. For ImageNet, our training recipe follows [34, 35]. Specifically, we set 50 epochs and keep learning rate as \\(10^{-5}\\) for finetune stage for all datasets." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.582, + 0.822, + 0.595 + ], + "angle": 0, + "content": "4.1.1 Ablations on CIFAR10 and CIFAR100" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Does DropKey boost generalization? T2T [34] and VOLO [35] are the widely used vision transformer architecture for image recognition. However, the DropAttention applied in these architectures does not apply re-normalize operation. In the following experiments, we plug in the DropKey to the family of T2T/VOLO and compare results with the version that use Dropout. The results in Figure 3 indicate DropKey can consistently increase the performance of various architectures on CIFAR10 and CIFAR100. On CIFAR100 with T2T19, for example, DropKey gains \\(1.7\\%\\) improvement for the adaptive coefficient yields further improvement. Additionally, we found that drop ratio is also an essential factor affecting performance. Take T2T14 with DropKey as an example, the accuracy initially increases with increasing drop ratio until it achieves its peak accuracy of \\(79.2\\%\\) at drop ratio \\(= 0.3\\) and it declines upon further increase of the drop ratio. These suggest that the introduction of DropKey would be beneficial to the network for avoiding suffering overfits. However, a larger drop ratio can lead to an inability to capture valid information about the object." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22704" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.087, + 0.278, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.284, + 0.087, + 0.483, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.49, + 0.087, + 0.688, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.695, + 0.087, + 0.895, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.219, + 0.237, + 0.747, + 0.251 + ], + "angle": 0, + "content": "Figure 3. Comparison of models with Dropout or DropKey on CIFAR10 and CIFAR100." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.253, + 0.47, + 0.283 + ], + "angle": 0, + "content": "Similar to DropKey, the performance of Dropout is also related to drop ratio." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.288, + 0.473, + 0.576 + ], + "angle": 0, + "content": "How does the choice of scheduled strategy of drop ratio impact accuracy? The ablation in Table 1 analyzes the accuracy of DropKey by adjusting the strategy of setting drop ratio. Specifically, we validate three strategy as follows: a) Constant: drop ratio is constant over self attention layers. b) Scheduled\\(\\uparrow\\): drop ratio is linearly increased over self attention layers. c) Scheduled\\(\\downarrow\\): drop ratio is linearly decreased over self attention layers. Firstly, we find that Scheduled\\(\\downarrow\\) outperform Constant whether using re-normalize or not. Secondly, introducing drop ratio with Scheduled\\(\\uparrow\\) would seriously affect the performance of the model and even perform worse than the pure vision transformer. This phenomenon is in line with our expectation, since deeper layers often contain high-level semantic information which is essential to perform classification. A large drop ratio in deep layer will increase the risk of losing important features which would make model difficult to converge to a generalized solution. Hence, we set drop ratio with Scheduled\\(\\downarrow\\) in all following experiments." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.581, + 0.47, + 0.734 + ], + "angle": 0, + "content": "Is Dropkey helpful to capture global information? The contribution of DropKey is to generate a smoother attention weight matrix to encourage models to focus on global features. Class token has been proved to be effective in aggregating the information of the whole image, so we measure the smoothness of the attention distribution by calculating the entropy of its attention weight vector. Specifically, we define the entropy of the attention vector of class token as follows \\( E_{i} = -\\sum_{j}p_{j}^{i}\\log p_{j}^{i} \\) where \\( p_j^i \\) denotes the attention weight of \\( j^{th} \\) attending patch in \\( i^{th} \\) head." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Note that a small entropy denotes that this head focuses on sparse patches. For convenience, the mean of entropy of multi-head as \\( E \\) is reported in Figure 4. Clearly, it reads that while both Dropout and DropKey are able to improve the value of entropy, the improvement by DropKey is more significant. Meanwhile, when the drop rate increases, the entropy increase accordingly. In addition, to further verify the necessity of the adaptive coefficient for capturing general global information, we visualize the attention map (Figure 5) from class token in the last transformer layer. Obviously, the model with DropKey smoothly assigns attention" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.253, + 0.892, + 0.312 + ], + "angle": 0, + "content": "weight to the area related to the instance. Finally, we further verify that our method can alleviate local-bias via the fact that transformers with DropKey perform robustly in occluded scenarios." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.317, + 0.893, + 0.529 + ], + "angle": 0, + "content": "Is structured drop is useful to vision transformer? In this section, we analyze whether structured masking is useful for vision transformer via DropKey-Block and DropKey-Cross. Specifically, we swept over window size from 3 to 5 for DropKey-Block and from 1 to 3 for DropKey-Cross. Compared with the DropKey, the structured drop degrade the performance of the model in all case and classification accuracy will decrease with the further increase of the window size. One possible reason for this phenomenon is that a larger drop ratio in shallow transformer layer results in losing vital information of object. However, a larger drop ratio is the key to avoid overfit to low-level feature. Therefore, we encourage set a larger drop ratio rather than the introduction of structured drop." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.533, + 0.895, + 0.775 + ], + "angle": 0, + "content": "How does align expectations impact accuracy? As discussed above, the mismatched expectations problem arises when directly use trained model with DropKey to test. Herein, to address above issue, we explore the impact of two methods, Monte Carlo and finetune, on the performance of network. The results in Table 3 indicates that accuracy can be improved regardless of the expectation alignment operation. Additionally, the accuracy of Monte Carlo increases with increasing sampling iterations. However, huge sampling iterations will lead to unacceptable computational cost. To fairly compare with Dropout, we also finetune it with the same training hyper-parameters as DropKey and then note that finetune only brings insignificant performance improvement or even over-fitting. In conclusion, alignment expectation of training and inference stage indeed can further improve the accuracy of the model." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.778, + 0.794, + 0.793 + ], + "angle": 0, + "content": "4.1.2 DropKey vs Dropout on ImageNet" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We provide the accuracy under other different drop ratio for each backbone with DropKey on ImageNet, and contrast them with existing State of the Arts (SOTA) equipped with Dropout, including T2T, VOLO, CeiT and DeiT in Table 4. We have these findings: (1) Clearly, our DropKey obtains significant enhancement against pure backbone. Meanwhile, We note that Dropout can only bring a little boost" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22705" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.117 + ], + "angle": 0, + "content": "Table 1. Comparison of models with Dropout or DropKey on CIFAR10 and CIFAR100 when introducing different scheduled strategy of drop ratio. The drop ratio is set as 0.3 for all models." + }, + { + "type": "table", + "bbox": [ + 0.177, + 0.118, + 0.787, + 0.313 + ], + "angle": 0, + "content": "
ModelCIFAR10CIFAR100
Scheduled↑ConstantScheduled↓Scheduled↑ConstantScheduled↓
T2T14 [34] + Dropout96.796.997.277.077.878.4
T2T14 [34] + DropKey97.097.497.677.278.679.2
T2T19 [34] + Dropout96.697.197.477.378.178.5
T2T19 [34] + DropKey97.197.297.978.078.480.1
T2T24 [34] + Dropout96.497.097.576.777.378.2
T2T24 [34] + DropKey96.697.297.776.978.379.3
VOLOd1 [35] + Dropout95.896.496.677.378.279.0
VOLOd1 [35] + DropKey96.296.797.178.178.679.6
VOLOd2 [35] + Dropout95.696.196.477.078.479.0
VOLOd2 [35] + DropKey95.796.697.077.779.079.9
VOLOd3 [35] + Dropout96.096.396.677.177.978.5
VOLOd3 [35] + DropKey96.296.496.977.478.178.7
" + }, + { + "type": "image", + "bbox": [ + 0.122, + 0.316, + 0.406, + 0.453 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.08, + 0.466, + 0.443, + 0.495 + ], + "angle": 0, + "content": "Figure 4. The histogram of entropy on CIFAR100. dr denotes drop ratio." + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.501, + 0.468, + 0.529 + ], + "angle": 0, + "content": "Table 2. Comparison of different structured drop on CIFAR100. \\( s \\) denotes window size and drop ratio is set as 0.3 for all models." + }, + { + "type": "table", + "bbox": [ + 0.094, + 0.531, + 0.451, + 0.613 + ], + "angle": 0, + "content": "
ModelRandomBlockCross
s=3s=5s=1s=3
T2T14 [34] + Dropout78.478.177.177.976.8
T2T14 [34] + DropKey79.278.777.578.677.4
VOLOd1 [35] + Dropout78.678.076.777.676.4
VOLOd1 [35] + DropKey79.278.577.578.377.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.618, + 0.47, + 0.659 + ], + "angle": 0, + "content": "Table 3. Comparison of models w/ or w/o Align Expectations on CIFAR100. Pure denotes the model without align expectation and drop ratio is set as 0.3 for all models." + }, + { + "type": "table", + "bbox": [ + 0.104, + 0.66, + 0.441, + 0.743 + ], + "angle": 0, + "content": "
ModelPurew/ Monte Carlow/ Finetune
20006000
T2T14 [34] + Dropout78.4--78.4
T2T14 [34] + DropKey78.878.979.179.2
T2T19 [34] + Dropout78.5--78.6
T2T19 [34] + DropKey79.379.580.280.1
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.473, + 0.904 + ], + "angle": 0, + "content": "to backbones and it even would degrade the performance of the model in some cases (eg. T2T14, CeiT-T and DeiT-B). This indicates that the adaptive smoothing operator is more helpful to encourage the model to capture general information in large-scale datasets. (2) Compare to lightweight models, heavyweight often need the larger drop ratio to achieve a remarkable boost. For T2T14 and VOLOd1, the best accuracy is obtained under the dr=0.05. Instead, T2T19 and VOLOd2 achieve the best accuracy when dr=0.1, which suggests heavyweight models adopt a larger drop ratio to" + }, + { + "type": "image", + "bbox": [ + 0.465, + 0.315, + 0.861, + 0.468 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.547, + 0.479, + 0.778, + 0.493 + ], + "angle": 0, + "content": "Figure 5. Visualization on CIFAR100." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.505, + 0.628, + 0.518 + ], + "angle": 0, + "content": "prevent overfitting." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.518, + 0.744, + 0.534 + ], + "angle": 0, + "content": "4.2. Object Detection in COCO" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.535, + 0.892, + 0.776 + ], + "angle": 0, + "content": "In this section, we verify the generalizability and effectiveness of DropKey for object detection on COCO dataset [19]. We apply DETR [1] framework for the experiments. Specifically, DETR is composed of the backbone, encoder and decoder. We followed the model architecture, anchor definition and training recipe in [1] to build DETR+Dropout and DETR+DropKey. In Table 5, we report the results of DETR [1] with Dropout or DropKey in terms of AP. It can be seen that, our DropKey significantly outperforms existing Dropout. In detail, DropKey achieve \\(+0.7\\), \\(+1.1\\), \\(+0.4\\), \\(+0.3\\), \\(+0.8\\) and \\(+0.7\\) higher AP than the Dropout, which is regarded as a remarkable boost considering the challenge on this benchmark. Another observation is that large objects benefit more from DropKey than small objects. These results suggest that DropKey has the advantage over Dropout." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.779, + 0.891, + 0.809 + ], + "angle": 0, + "content": "4.3. Human-Object Interaction Detection in HICODET" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Since the task of scene graph and relation understanding is quite sensitive to global context learning, so we also verify the effectiveness of DropKey in QPIC [26] for Human-Object Interaction Detection in HICO-DET [2]. QPIC is a transformer-based feature extractor that can effectively aggregate contextually important information. We respec" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "22706" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.192, + 0.09, + 0.776, + 0.104 + ], + "angle": 0, + "content": "Table 4. Comparisons on backbones with Dropout or DropKey on ImageNet. dr denotes drop ratio." + }, + { + "type": "table", + "bbox": [ + 0.194, + 0.106, + 0.775, + 0.324 + ], + "angle": 0, + "content": "
ModelTop-1ModelTop-1
T2T14 [34]81.76 ± 0.05VOLOd1 [35]84.27 ± 0.12
T2T14 [34] + Dropout(dr=0.05)81.65 ± 0.04VOLOd1 [35] + Dropout(dr=0.05)84.35 ± 0.11
T2T14 [34] + Dropout(dr=0.1)81.53 ± 0.08VOLOd1 [35] + Dropout(dr=0.1)84.31 ± 0.04
T2T14 [34] + DropKey(dr=0.05)82.04 ± 0.14VOLOd1 [35] + DropKey(dr=0.05)84.53 ± 0.03
T2T14 [34] + DropKey(dr=0.1)81.93 ± 0.09VOLOd1 [35] + DropKey(dr=0.1)84.39 ± 0.02
T2T19 [34]82.56 ± 0.09VOLOd2 [35]85.24 ± 0.05
T2T19[34] + Dropout(dr=0.05)82.63 ± 0.05VOLOd2 [35] + Dropout(dr=0.05)85.22 ± 0.08
T2T19[34] + Dropout(dr=0.1)82.68 ± 0.04VOLOd2 [35] + Dropout(dr=0.1)85.21 ± 0.03
T2T19[34] + DropKey(dr=0.05)82.71 ± 0.02VOLOd2 [35] + DropKey(dr=0.05)85.33 ± 0.12
T2T19 [34] + DropKey(dr=0.1)82.94 ± 0.04VOLOd2 [35] + DropKey(dr=0.1)85.38 ± 0.06
CeiT-T [33]81.92 ± 0.06DeiT-B [27]81.94 ± 0.02
CeiT-T [33] + Dropout(dr=0.05)81.90 ± 0.03DeiT-B [27] + Dropout(dr=0.05)81.91 ± 0.04
CeiT-T [33] + Dropout(dr=0.1)81.83 ± 0.06DeiT-B [27] + Dropout(dr=0.1)81.87 ± 0.05
CeiT-T [33] + DropKey(dr=0.05)82.14 ± 0.05DeiT-B [27] + DropKey(dr=0.05)82.23 ± 0.01
CeiT-T [33] + DropKey(dr=0.1)82.27 ± 0.06DeiT-B [27] + DropKey(dr=0.1)82.25 ± 0.08
" + }, + { + "type": "table_caption", + "bbox": [ + 0.086, + 0.328, + 0.877, + 0.355 + ], + "angle": 0, + "content": "Table 5. Comparison of DETR with Dropout and DropKey on COCO validation set. Table 6. Comparison of METRO with Dropout and Dropout key on HUMBI." + }, + { + "type": "table", + "bbox": [ + 0.124, + 0.367, + 0.51, + 0.424 + ], + "angle": 0, + "content": "
ModelAP\\( AP_{50} \\)\\( AP_{75} \\)\\( AP_S \\)\\( AP_M \\)\\( AP_L \\)
DETR [1]41.962.144.220.645.760.7
DETR [1] + Dropout42.262.344.320.845.961.1
DETR [1] + DropKey42.963.444.721.146.761.8
" + }, + { + "type": "table", + "bbox": [ + 0.55, + 0.368, + 0.88, + 0.424 + ], + "angle": 0, + "content": "
ModelmPVE↓mPJPE↓PA-mPJPE↓
METRO [18]57.851.539.9
METRO [18] + Dropout57.951.639.7
METRO [18] + DropKey57.151.039.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.265, + 0.433, + 0.704, + 0.447 + ], + "angle": 0, + "content": "Table 7. Comparison of QPIC with Dropout and DropKey on HICO-DET." + }, + { + "type": "table", + "bbox": [ + 0.107, + 0.449, + 0.859, + 0.524 + ], + "angle": 0, + "content": "
Modelfull (Default)rare (Default)non-rare (Default)full (Known object)rare (Known object)non-rare (Known object)
QPIC-ResNet101 [26] + Dropout (dr=0.1)29.9624.0331.6332.4226.0134.31
QPIC-ResNet101 [26] + Dropout (dr=0.3)30.0224.1731.7232.4926.1334.41
QPIC-ResNet101 [26] + DropKey (dr=0.3)30.8724.6332.2433.2126.6634.94
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.535, + 0.47, + 0.67 + ], + "angle": 0, + "content": "tively introduce Dropout and DropKey to both encoder and decoder in QPIC and train these models with the same training recipe as [26]. The model named \"QPIC-ResNet101 + Dropout (dr=0.1)\" is the result of our reproduction of QPIC with Schedued \\(\\downarrow\\) drop ratio (Official realization is equipped with Constant drop ratio). The experimental results in Table 7 suggest DropKey has higher performance gain on the different evaluating indicators which are consistent with our expectations." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.672, + 0.426, + 0.688 + ], + "angle": 0, + "content": "4.4. Human Body Mesh Recovery in HUMBI" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.471, + 0.901 + ], + "angle": 0, + "content": "We verify the efficacy of DropKey for human body mesh task on HUMBI [32]. We follow conventions to train with 294 subjects from scratch and test with 120 subjects. We use Mean Per Vetex Error (MPVE) [22], Mean Per Joint Position Error (MPJPE) [14] and Procrustes Analysis MPJPE (PA-MPJPE) [38] as metrics. We use public METRO [18] as the baseline to apply DropKey to self-attention layer and Table 6 summaries the results. we can see that DropKey consistently improves the performance for all standard metrics. Specifically, DropKey brings about 0.7, 0.5 and 0.4 on mPVE, mPJPE and PA-mPJPE, respectively, while Dropout only boosts 0.2 performance on one metric. These results further verify the generalizability of DropKey as well as its superiority over vanilla dropout." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.534, + 0.619, + 0.548 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.549, + 0.892, + 0.82 + ], + "angle": 0, + "content": "In this paper, we explore the drop unit, drop schedule and structured necessity of the dropout technique in ViT. Specifically, we propose to set Key as the drop unit, which yields a novel dropout-before-softmax scheme. We theoretically and experimentally verify that this scheme can regularize attention weights and meanwhile and keep them as a probability distribution simultaneously, helping capture vital patterns in a global manner and overcome local-bias problems that occurred to vanilla dropout. In addition, we present a new decreasing schedule for drop ratio, which stabilizes the training phase by avoiding overfittings in low-level features and maintaining sufficient high-level features. Moreover, we also experimentally show that structured dropout is not necessary for ViT. We distill the above analysis as a novel DropKey method, which plays as an improved version of dropout for ViT. Comprehensive experiments with different architectures on various vision tasks demonstrate the effectiveness of the proposed DropKey for enhancing ViTs." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.823, + 0.668, + 0.839 + ], + "angle": 0, + "content": "Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.9 + ], + "angle": 0, + "content": "This paper is supported by the National key research and development program of China (2021YFA1000403), and the National Natural Science Foundation of China (Nos. U19B2040, 11991022)." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "22707" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.09, + 0.176, + 0.107 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.169 + ], + "angle": 0, + "content": "[1] Nicolas Carion, Francisco Massa, Gabriel Synnaeve, Nicolas Usunier, Alexander Kirillov, and Sergey Zagoruyko. End-to-end object detection with transformers. arXiv preprint arXiv:2005.12872, 2020. 1, 7, 8" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.17, + 0.47, + 0.21 + ], + "angle": 0, + "content": "[2] Yu-Wei Chao, Yunfan Liu, Xieyang Liu, Huayi Zeng, and Jia Deng. Learning to detect human-object interactions. 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IEEE transactions on pattern analysis and machine intelligence, 41(4):901-914. 8" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.468, + 0.513 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22709" + } + ] +] \ No newline at end of file diff --git a/2023/DropKey for Vision Transformer/539b4cee-3610-4b35-8990-86b8994c51f3_origin.pdf b/2023/DropKey for Vision Transformer/539b4cee-3610-4b35-8990-86b8994c51f3_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..823c62dcaed20f3423112f38befbbf80806a4d2e --- /dev/null +++ b/2023/DropKey for Vision Transformer/539b4cee-3610-4b35-8990-86b8994c51f3_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:f7fd9cf22d6920fb71ce7b3d4b58e6c03b443ccb4e2a3cdb8b156b870925a5da +size 5383951 diff --git a/2023/DropKey for Vision Transformer/full.md b/2023/DropKey for Vision Transformer/full.md new file mode 100644 index 0000000000000000000000000000000000000000..c41860df3df641e9ba46e1e417c9369817763d09 --- /dev/null +++ b/2023/DropKey for Vision Transformer/full.md @@ -0,0 +1,337 @@ +# DropKey for Vision Transformer + +Bonan $\mathrm{Li}^{*1}$ , Yinhan $\mathrm{Hu}^{*1}$ , Xuecheng $\mathrm{Nie}^2$ , Congying $\mathrm{Han}^{\dagger 1}$ , Xiangjian Jiang $^3$ , Tiande Guo $^1$ , Luoqi Liu $^2$ + +1University of Chinese Academy of Sciences + +$^{2}$ MT Lab, Meitu Inc. + +$^{3}$ University of Cambridge + +{libonan, hancy, tdguo}@ucas.ac.cn, huhinhan16@mails.ucas.ac.cn + +{nxc,llq5} $@$ meitu.com,xj265@cam.ac.uk + +# Abstract + +In this paper, we focus on analyzing and improving the dropout technique for self-attention layers of Vision Transformer, which is important while surprisingly ignored by prior works. In particular, we conduct researches on three core questions: First, what to drop in self-attention layers? Different from dropping attention weights in literature, we propose to move dropout operations forward ahead of attention matrix calculation and set the Key as the dropout unit, yielding a novel dropout-before-softmax scheme. We theoretically verify that this scheme helps keep both regularization and probability features of attention weights, alleviating the overfittings problem to specific patterns and enhancing the model to globally capture vital information; Second, how to schedule the drop ratio in consecutive layers? In contrast to exploit a constant drop ratio for all layers, we present a new decreasing schedule that gradually decreases the drop ratio along the stack of self-attention layers. We experimentally validate the proposed schedule can avoid overfittings in low-level features and missing in high-level semantics, thus improving the robustness and stableness of model training; Third, whether need to perform structured dropout operation as CNN? We attempt patch-based block-version of dropout operation and find that this useful trick for CNN is not essential for ViT. Given exploration on the above three questions, we present the novel DropKey method that regards Key as the drop unit and exploits decreasing schedule for drop ratio, improving ViTs in a general way. Comprehensive experiments demonstrate the effectiveness of DropKey for various ViT architectures, e.g. T2T, VOLO, CeiT and DeiT, as well as for various vision + +tasks, e.g., image classification, object detection, human-object interaction detection and human body shape recovery. + +# 1. Introduction + +Vision Transformer (ViT) [6] has achieved great success for various vision tasks, e.g., image recognition [7, 12, 20, 34, 35], object detection [1], human body shape estimation [18], etc. Prior works mainly focus on researches of patch division, architecture design and task extension. However, the dropout technique for self-attention layer, which plays the essential role to achieve good generalizability, is surprisingly ignored by the community. + +Different from the counterpart for Convolutional Neural Networks (CNNs), the dropout in ViT directly utilizes the one in original Transformer designed for Natural Language Processing, which sets attention weights as the manipulation unit with a constant dropout ratio for all layers. Despite of its simplicity, this vanilla design faces three major problems. First, it breaks the probability distribution of attention weights due to the averaging operation on non-dropout units after softmax normalization. Although this regularizes the attention weights, it still overfits specific patterns locally due to the failure on penalizing score peaks, as shown in Fig. 1 (a) and (b); Second, the vanilla design is sensitive to the constant dropout ratio, since high ratio occurs missing of semantic information in high-level representations while low ratios overfitting in low-level features, resulting in the unstable training process; Third, it ignores the structured characteristic of input patch grid to ViT, which plays an effective role to improve performance with blockwise dropout in CNNs. These three problems degrade the performance and limit the generalizability of ViTs. + +Motivated by this, we propose to analyze and improve + +the dropout technique in self-attention layer, further pushing forward the frontier of ViTs for vision tasks in a general way. Specifically, we focus on three core aspects: + +What to drop in self-attention layer Different from dropping attention weights as in the vanilla design, we propose to set the Key as the dropout unit, which is essential input of self-attention layer and significantly affects the output. This moves the dropout operation forward before calculating the attention matrix as shown in Fig. 1 (c) and yields a novel dropout-before-softmax scheme. This scheme regularizes attention weights and keeps their probability distribution at the same time, which intuitively helps penalize weight peaks and lift weight foots. We theoretically verify this property via implicitly introducing an adaptive smoothing coefficient for the attention operator from the perspective of gradient optimization by formulating a Lagrange function. With the dropout-before-softmax scheme, self-attention layers can capture vital information in a global manner, thus overcoming the overfittings problem to specific patterns occurred in the vanilla dropout and enhancing the model generalizability as visualization of feature map in Fig. 1 (c). For the training phase, this scheme can be simply implemented by swapping the operation order of softmax and dropout in vanilla design, which provides a general way to effectively enhance ViTs. For inference phase, we conduct an additional finetune phase to align the expectations to training phase, further improving the performance. + +How to schedule the drop ratio In contrast to exploiting a constant drop ratio for all layers, we present a new linear decreasing schedule that gradually decreases the drop ratio along the stack of self-attention layers. This schedule leads to a high drop ratio in shallow layers while the low one in deep layers, thus avoiding over fittings to low-level features and preserving sufficient high-level semantics. We experimentally verify the effectiveness of the proposed decreasing schedule for drop ratio to stable the training phase and improve the robustness. + +Whether need to perform structured drop Inspired by the DropBlock [10] method for CNNs, we implement two structured versions of the dropout operation for ViTs: the block-version dropout that drops keys corresponding to contiguous patches in images or feature maps; the crossversion dropout that drops keys corresponding to patches in horizontal and vertical stripes. We conduct thorough experiments to validate their efficacy and find that the structure trick useful for CNN is not essential for ViT, due to the powerful capability of ViT to grasp contextual information in full image range. + +Given exploration on the above three aspects, we present a novel DropKey method that utilizes Key as the drop unit and decreasing schedule for drop ratio. In particular, DropKey overcomes drawbacks of the vanilla dropout technique for ViTs, improving performance in a general and effective + +way. Comprehensive experiments on different ViT architectures and vision tasks demonstrate the efficacy of DropKey. Our contributions are in three folds: First, to our best knowledge, we are the first to theoretically and experimentally analyze dropout technique for self-attention layers in ViT from three core aspects: drop unit, drop schedule and structured necessity; Second, according to our analysis, we present a novel DropKey method to effectively improve the dropout technique in ViT. Third, with DropKey, we improve multiple ViT architectures to achieve new SOTAs on various vision tasks. + +# 2. Related Work + +Vision Transformers Inspired by the Transformer architectures in NLP, some works introduce attention block to replace convolution layers to model long-range dependencies [6, 11, 17, 29, 30, 31, 37]. ViT[6] is the pioneering work which splits an image to non-overlapping patches and then these patches are fed to a transformer to evaluate attention scores. Prior works mainly focus on patch division, architecture design and tasks extension. For example, CvT[31] proposes a hybrid architecture to mix convolutional with attention layers to introduce local inductive bias. [3, 7, 20] proposes to reduce the computation cost. Despite the progress, previous works ignore the dropout technique in self-attention layer, which play an important role to keep good generalizability. + +Dropout Dropout is a common technique for improving the generalizability of neural networks, e.g., CNNs [16], RNNs [21] and GNNs [24]. For CNNs, [10] points out the lack of success of dropout for convolutional layers is due to dense information flowing and then proposes a form of structured Dropout. DropConnect [28] randomly masks a subset of weights within the model. For RNNs, the first prominent research on dropout is presented in [8], which is equipped with a learnable dropout rate. + +For GNNs, to alleviate over-fitting and over-smoothing issues, DropEdge [23] randomly removes part of edges in the input stage at each training epoch and theoretically demonstrates the effect of the proposed method. For ViTs, most original publicly code of multiple popular vision transformer simply intuitively apply dropout operation on attention matrix. + +DropAttention [36] presents a novel way for transformer in NLPs. It refers to perform randomly drop on the attention matrix. There are two two main forms of applying DropAttention for the transformer training, DropAttention-unit and DropAttention-elements. Similar to the standard Dropout [25], DropAttention-unit randomly drops the unit, that is, these dropped token will not be used as attend patches for each query patch. As the general form of DropAttention-unit, DropAttention-elements randomly drops elements in attention weights matrix which + +![](images/71ca9e25de2d60876fb0c5c4a0f812693a8980d1cb656c8f30f17289497c6566.jpg) +Input Image + +![](images/6efa2f8668f852025f41a74d14bc0b85e2ab408653f5271ff42c9e46e79d9206.jpg) +(b) Attention w/ Dropout +Figure 1. Comparison between the proposed DropKey and existing vanilla dropout techniques in self-attention layers for ViTs. (a) Self-attention without dropout, which suffers overfitting problems to local patch; (b) Self-attention with vanilla dropout, which regularizes the attention weights but still overfits specific patterns; (c) Self-attention with our DropKey, which overcomes prior problems and improves the model to capture vital information in a global manner. Best viewed in color. + +![](images/13a34b72c80da52b51e9e29e7a11d7ca0501806630d06e306efbe33358ad0b33.jpg) +(c) Attention w/ DropKey + +is similar to DropConnect [28]. Different from standard Dropout [25], DropAttention introduce re-normalize to guarantee the sum of attention weights to 1 and help training process to be more steady. However, there is no further discussion and theoretical analysis on this phenomenon. + +# 3. Method + +Our generic DropKey is inspired by DropAttention and proposed for self-attention operator in vision transformer. The main idea of DropKey is to adaptively adjust attention weight to obtain a smoother attention vector. In this section, we start by introducing the theoretical explanation of DropKey, then the implementation will be explained in detail. + +# 3.1. Methodology + +As discussed in the above section, transformer-based model tends to rely on local features rather than general global information. To alleviate this issue, we propose to reduce local-bias by encouraging models to learn a smoother attention weight for each patch. To this end, we attempt to reduce the attention weight of the patch which has a large attention weight, and vice versa. Nevertheless, it is tedious and difficult to achieve this by explicitly setting rules. In this work, we found DropKey achieves the above implicitly by normalizing the attention vector that has performed the dropout operation. Specifically, by given an image $I \in \mathbb{R}^{H \times W \times C}$ , where $H$ denotes height, $W$ denotes width and $C$ denotes channels, Vision Transformer architecture starts by dicing it into $n_h \times n_w$ patches $x \in \mathbb{R}^{n_c}$ . Then, $x$ is used as input of self-attention layer and the output $o$ can be computed as follows + +$$ +o = \sum_ {j = 1} ^ {n _ {h} n _ {w}} \left(\frac {d _ {j} p _ {j}}{\sum_ {j = 1} ^ {n _ {h} n _ {w}} d _ {j} p _ {j}}\right) v _ {j} \tag {1} +$$ + +$$ +p _ {j} = \frac {\exp \left(\frac {q k _ {j} ^ {T}}{\text {s c a l e}}\right)}{\sum_ {j = 1} ^ {n _ {h} n _ {w}} \exp \left(\frac {q k _ {j} ^ {T}}{\text {s c a l e}}\right)} \tag {2} +$$ + +where $q = \mathcal{F}_q(x), k = \mathcal{F}_k(x), v = \mathcal{F}_v(x)$ , and $q_i, k_j, v_j$ denote query of $i^{th}$ patch, key of $j^{th}$ patch, value of $j^{th}$ patch and $o$ + +denotes the output of one patch. $\mathcal{F}_q(\cdot),\mathcal{F}_k(\cdot),\mathcal{F}_v(\cdot)$ denote projection layers with weights of dimensions $n_c\times n_c$ . scale denotes scaling factor and is set to $\sqrt{n_c}$ $d$ denotes drop ratio and $d_{j}\sim Bernoulli(1 - d)$ . Here, for convenience, we focus on one head and omit the index of patch. By performing re-normalize, DropKey has the ability to adaptively adjust attention weight to smoother. Next, we provide theoretical analysis of our method to demonstrate its effectiveness. + +Here, we formulate the expectation output of model via introducing DropKey in training stage as: + +$$ +\begin{array}{l} \mathbb {E} _ {d _ {j}, 1 \leq j \leq n _ {h} n _ {w}} [ o ] = \mathbb {E} _ {d _ {j}, 1 \leq j \leq n _ {h} n _ {w}} [ \sum_ {j = 1} ^ {n _ {h} n _ {w}} (\frac {d _ {j} p _ {j}}{\sum_ {j = 1} ^ {n _ {h} n _ {w}} d _ {j} p _ {j}}) v _ {j} ] \tag {3} \\ = \sum_ {j = 1} ^ {n _ {h} n _ {w}} \mathbb {E} _ {d _ {j}, 1 \leq j \leq n _ {h} n _ {w}} [ \frac {d _ {j}}{\sum_ {j = 1} ^ {n _ {h} n _ {w}} d _ {j} p _ {j}} ] p _ {j} v _ {j} = \sum_ {j = 1} ^ {n _ {h} n _ {w}} c _ {j} p _ {j} v _ {j} \\ \end{array} +$$ + +where $c_{j} = \mathbb{E}_{d_{j},1\leq j\leq n_{h}n_{w}}\left[\frac{d_{j}}{\sum_{j = 1}^{n_{h}n_{w}}d_{j}p_{j}}\right] > 0$ is a smoothing coefficient which is related to $d_{j}$ and $p_j$ . + +Note that $c$ in Equ (3) can be considered to add an additional smoothing prior to distribution $p$ , i.e., $c_{s} < c_{t}$ when $p_{s} > p_{t}, 1 \leq s, t \leq n_{h}n_{w}$ . The specific proof is as follows: + +$$ +\begin{array}{l} c _ {s} - c _ {t} = \mathbb {E} _ {d _ {j}, 1 \leq j \leq n _ {h} n _ {w}} [ \frac {d _ {s}}{\sum_ {j = 1} ^ {n _ {h} n _ {w}} d _ {j} p _ {j}} ] - \mathbb {E} _ {d _ {j}, 1 \leq j \leq n _ {h} n _ {w}} [ \frac {d _ {t}}{\sum_ {j = 1} ^ {n _ {h} n _ {w}} d _ {j} p _ {j}} ] \\ = d (1 - d) \mathbb {E} _ {d _ {j}, 1} \leq j \leq n _ {h} n _ {w} \left[ \frac {1}{\sum_ {j \neq s , t} ^ {n _ {h} n _ {w}} d _ {j} p _ {j} + p _ {s}} - \frac {1}{\sum_ {j \neq s , t} ^ {n _ {h} n _ {w}} d _ {j} p _ {j} + p _ {t}} \right] < 0 \tag {4} \\ \end{array} +$$ + +It is natural to find $c$ serves as a factor to implicitly encourage the model properly to reduce the consideration of the patch with large $p$ and improve the effectiveness of the patch with small attention weight. Meanwhile, $c$ can be adjusted adaptively according to the distribution of samples in the training stage without any manual design. Nevertheless, a noteworthy problem is that since we removed DropKey in the inference phase, the output expectations in training and inference stage are inconsistent, which will decrease the performance. In Section 3.2, we propose two methods to alleviate this problem. + +Having explored the implicit regularization effects of DropKey, we also demonstrate it from the perspective of gradient optimization. For simplicity, we start by considering a simple but universal optimization objective as follows: + +$$ +\min _ {p _ {j}, v _ {j}} \frac {1}{2} \| \sum_ {j = 1} ^ {N} p _ {j} v _ {j} - y \| ^ {2} \text {s . t .} p _ {j} > 0, \sum_ {j = 1} p _ {j} = 1, 1 \leq j \leq N \tag {5} +$$ + +where $p_j \in \mathbb{R}$ , $v_j \in \mathbb{R}^r$ denotes learnable parameters and $y \in \mathbb{R}^r$ denotes target. This simple problem captures the essential part of the training of a single self-attention layer, especially when the neural networks are large, and it may shed light on the training of deep models. Here, $p_j$ and $v_j$ can be considered as attention weight and value in attention mechanism. Naturally, $v_j$ can be decomposed into two directions, which are the same direction as $y$ and the direction perpendicular to $y$ : + +$$ +v _ {j} = \beta_ {j} e + \alpha_ {j} \tag {6} +$$ + +where $\beta$ is a scalar, $e\in \mathbb{R}^r$ is the unit vector of $y$ and $\alpha_{j}$ is the component perpendicular to $y$ . Similarly, we can rewrite $y$ to $Me$ where $M = ||y||$ . Then, the Lagrange function of Equ (5) can be formulated as follows: + +$$ +L \left(p _ {j}, v _ {j}, \lambda\right) = \frac {1}{2} | | \sum_ {j = 1} ^ {N} p _ {j} v _ {j} - y | | ^ {2} - \lambda \left(\sum_ {j = 1} ^ {N} p _ {j} - 1\right) \tag {7} +$$ + +In order to analysis the gradient, we take the partial derivatives of $p_j$ and $v_j$ : + +$$ +\frac {\partial L}{\partial p _ {j}} = (v - y) ^ {T} v _ {j} - \lambda = \left(\sum_ {j = 1} ^ {N} p _ {j} \beta_ {j} - M\right) \beta_ {j} + \left(\sum_ {j = 1} ^ {N} p _ {j} \alpha_ {j}\right) ^ {T} \alpha_ {j} - \lambda \tag {8} +$$ + +$$ +\frac {\partial L}{\partial v _ {j}} = p _ {j} (v - y) = p _ {j} \left(\sum_ {j = 1} ^ {N} p _ {j} \beta_ {j} - M\right) e + p _ {j} \left(\sum_ {j = 1} ^ {N} p _ {j} \alpha_ {j}\right) \tag {9} +$$ + +Here, for simplicity, we note $v = \sum_{j=1}^{N} p_j v_j = (\sum_{j=1}^{N} p_j \beta_j) e + \sum_{j=1}^{N} p_j \alpha_j$ . From the chain rule of backpropagation, we also have: + +$$ +\frac {\partial L}{\partial \beta_ {j}} = p _ {j} \left(\sum_ {j = 1} ^ {N} p _ {j} \beta_ {j} - M\right) \quad \frac {\partial L}{\partial \alpha_ {j}} = p _ {j} \left(\sum_ {j = 1} ^ {N} p _ {j} \alpha_ {j}\right) \tag {10} +$$ + +Equ (10) indicates that the gradient $\frac{\partial L}{\partial \beta_s} < \frac{\partial L}{\partial \beta_t}$ when $p_s > p_t$ and this backward propagation properties would lead $\frac{\partial L}{\partial p_s} < \frac{\partial L}{\partial p_t}$ . By subtracting $\frac{\partial L}{\partial p_s}$ and $\frac{\partial L}{\partial p_t}$ , we will have: + +$$ +\frac {\partial L}{\partial p _ {s}} - \frac {\partial L}{\partial p _ {t}} = \left(\sum_ {j = 1} ^ {N} p _ {j} \beta_ {j} - M\right) \left(\beta_ {s} - \beta_ {t}\right) + \left(\sum_ {j = 1} ^ {N} p _ {j} \alpha_ {j}\right) ^ {T} \left(\alpha_ {s} - \alpha_ {t}\right) \tag {11} +$$ + +Since all parameters are randomly initialized, it can be assumed that the initial solution is far from the optimal solution, that is, $p_1^{(0)} = p_2^{(0)} = \dots = p_N^{(0)} = \frac{1}{N}$ , $|\beta_j^{(0)}| \ll M$ , $1 \leq j \leq N$ . Consequently, the first additive term plays + +the leading role in Equ (11). Due to $\frac{\partial L}{\partial\beta_s} < \frac{\partial L}{\partial\beta_t}$ , the update speed of $\beta_{s}$ is faster than $\beta_{t}$ and then lead $\beta_{s} > \beta_{t}$ , $\frac{\partial L}{\partial p_s} < \frac{\partial L}{\partial p_t}$ . Based on the above analysis, it can be concluded that a larger $p$ would promote $\beta$ larger, while a larger $\beta$ would further promote $p$ larger. Finally, the output of model would be controlled by a few sparse blocks. Conversely, DropKey avoids suffering local-bias by introducing the parameter $c$ to enforce distribution $p$ to be smoother. + +# 3.2. Implementation + +What to drop? Different from DropAttention, we integrate Dropout and re-normalize into one stage by dropping key rather than weight. At each training iteration, DropKey masks a certain rate of keys of the input key map by random. It is worth noting that we generate masked key map for each query, instead of sharing the same masked key map for all query vectors. Specifically, given the query $Q \in \mathbb{R}^{n_h n_w \times n_c}$ , key $K \in \mathbb{R}^{n_h n_w \times n_c}$ and value $V \in \mathbb{R}^{n_h n_w \times n_c}$ of a feature map, it first computes the dot products of the query with all keys and divide each by scaling factor $scale = \sqrt{n_c}$ . Subsequently, we randomly generate a mask matrix $D \in \mathbb{R}^{1 \times (n_h n_w \times n_h n_w)}$ with drop ratio $d$ to enforce some elements of the similarity matrix to be -inf. The formulation of $D$ as follows: + +$$ +d _ {j} = \left\{ \begin{array}{c c} 0 & \text {w i t h p r o b a b i l i t y} 1 - d \\ - \infty & \text {w i t h p r o b a b i l i t y} d \end{array} \right. \tag {12} +$$ + +Finally, the attention weight matrix is computed by given masked similarity matrix as input. Formally, we compute the outputs of a patch as: + +$$ +o = \sum_ {j = 1} ^ {n _ {h} n _ {w}} p _ {j} v _ {j} \tag {13} +$$ + +$$ +p _ {j} = \frac {\exp \left(d _ {j} + \frac {q k _ {j} ^ {T}}{\text {s c a l e}}\right)}{\sum_ {j = 1} ^ {n _ {h} n _ {w}} \exp \left(d _ {j} + \frac {q k _ {j} ^ {T}}{\text {s c a l e}}\right)} \tag {14} +$$ + +where $q_{i}, k_{j}, v_{j}$ denote query of $i^{th}$ patch, key of $j^{th}$ patch, value of $j^{th}$ patch. It is not difficult to find that Equ (13) and Equ (14) is the same equivalent form of Equ (1) and Equ (2). In particular, as shown in Algorithm 1, we only need to add two lines of code to pure attention to implement DropKey. Obviously, compared with Dropout, DropKey only changes the position of introducing mask. + +Scheduled Drop Ratio Vision transformer always consists of few self-attention blocks to gradually learn high-dimensional features. Generally, early layers operates low-level visual features and deeper layers aim to model spatially coarse but complex information. Hence, we attempt to set smaller drop ratio for deeper layers to avoid missing important objects-relevant information. Specifically, instead of stochastically dropping with some fixed probability in Dropout, we gradually decrease number of dropped keys over the layers during training stage. We find that this scheduled drop ratio not only work well for DropKey, but also significantly improves the performance of Dropout. + +Algorithm 1 Attention with DropKey code +N: token number, D: token dim +# Q: query (N, D), K: key (N, D), V: value (N, D) +# use_DropKey: whether use DropKey +# mask_ratio: ratio to mask +def Attention(Q, K, V, use_DropKey, mask_ratio) + attn = (Q * (Q.shape[1] ** -0.5)) @ K.transpose(-2, -1) + # use DropKey as regularizer + if use_DropKey == True: + m_r = torch.ones_like(attn) * mask_ratio + attn = attn + torchBernoulli(m_r) * -1e12 + attn = attn softmax(dim=-1) + x = attn @ V + return x + +![](images/04e29115b96e251ad71d1fcb331528b0c3c249cd019044fef878d7449be8aeb7.jpg) +Figure 2. Mask sampling in DropKey, DropKey-Block and DropKey-Cross. The yellow patches are used as attend key to interact with a query and blue patches are dropped. Red symbol denotes the valid seed and the window size of DropKey-Block and DropKey-Cross is 3 and 1, respectively. + +![](images/5026f1478ccf11a203bf6e0edd3c4ada679b32bbbac072a416323326e9eddbaf.jpg) + +![](images/b5a915e33b9c77cc39d6fedf59d62501c0b500fd571d9053c4ed886cdb22268e.jpg) + +Structured DropKey Although structured drop has been dally explored in convolution network, there is no work to study the impact of structured drop on vision transformer. In this section, we implement two structured forms of DropKey which are named DropKey-Block and DropKey-Cross (see Figure 2). For DropKey-Block, inspired by DropBlock [10], we drop contiguous patches in a square-shape window of feature maps. Actually, we re-set drop ratio $d_{block}$ for each patch as: $d_{block} = \frac{d}{s^2}\frac{n_h n_w}{(n_h - s + 1)(n_w - s + 1)}$ where $d$ denotes the probability of dropping a patch in DropKey. The valid seed region is $(n_h - s + 1)(n_w - s + 1)$ where $s$ denotes the size of window and $n_h, n_w$ denotes height, weight of feature map. + +The cross-shape window attention is proved to achieve strong modeling capability [5] which also indicates the information in this structure is correlated. For DropKeyCross, we discard features in a cross window to prevent information flow through self-attention. In our implementation, we drop the rows and columns of valid seed and re-set the drop ratio $d_{cross}$ for each patch as: $d_{cross} = \frac{d}{s(n_h + n_w - s)}\frac{n_hn_w}{(n_h - s + 1)(n_w - s + 1)}$ . Note that the formulations for block- and cross-version are only the approximation, because there will be some overlapped when perform drop. + +Align Expectation As mentioned in Section 3.1, the misaligned expectations have a certain negative impact on the model, so we attempt to use two methods to align the expectation. The first one is to use Monte Carlo method to estimate $c$ . We perform multiple random drop and calculate the attention weight matrix after each drop operation. Finally, the average of calculated multiple weight matrices is applied as the input for the next step. For the second one, we take the inspiration from [9] and propose to finetune the model without DropKey, as an extra stage after DropKey training. We experimentally verify that the second strategy performs better with experiment in Section 4.1.1. + +# 4. Experiments + +We conduct experiments on three tasks, image classification, object detection, human-object interaction detection and human mesh recovery, to show the efficacy and gener + +alizability of our DropKey for improving ViTs. + +# 4.1. Image Classification + +Datasets We conduct the following experiments with T2T [34], VOLO [35], CeiT [33] and DeiT [27] for image classification on CIFAR10 [13], CIFAR100 [15] and ImageNet [4]. a) We conduct the ablation study to demonstrate the effects of introducing modified DropAttention to three T2T and three VOLO backbone architectures on CIFAR10 and CIFAR100. b) We validate the modified DropAttention by training T2T and VOLO from scratch on ImageNet. + +Training By default, models are trained with random initialization on all datasets. Due to the missing training setting for T2T [34] and VOLO [35], we conduct grid search on learning rate and epoch number to make the vanilla backbones achieve the best performance. All implementation specifics can be seen in Appendix. For ImageNet, our training recipe follows [34, 35]. Specifically, we set 50 epochs and keep learning rate as $10^{-5}$ for finetune stage for all datasets. + +# 4.1.1 Ablations on CIFAR10 and CIFAR100 + +Does DropKey boost generalization? T2T [34] and VOLO [35] are the widely used vision transformer architecture for image recognition. However, the DropAttention applied in these architectures does not apply re-normalize operation. In the following experiments, we plug in the DropKey to the family of T2T/VOLO and compare results with the version that use Dropout. The results in Figure 3 indicate DropKey can consistently increase the performance of various architectures on CIFAR10 and CIFAR100. On CIFAR100 with T2T19, for example, DropKey gains $1.7\%$ improvement for the adaptive coefficient yields further improvement. Additionally, we found that drop ratio is also an essential factor affecting performance. Take T2T14 with DropKey as an example, the accuracy initially increases with increasing drop ratio until it achieves its peak accuracy of $79.2\%$ at drop ratio $= 0.3$ and it declines upon further increase of the drop ratio. These suggest that the introduction of DropKey would be beneficial to the network for avoiding suffering overfits. However, a larger drop ratio can lead to an inability to capture valid information about the object. + +![](images/4390224b4a38e64389d33ef70d386fcf2af52057faffc7bdf012468f13febc0a.jpg) +Figure 3. Comparison of models with Dropout or DropKey on CIFAR10 and CIFAR100. + +![](images/f3ca36e684c55adcdd188f20bbea94c29c397e605edfb0abce6db98f9a5f6b25.jpg) + +![](images/312dada1f8b5286e0b902490b866ca0c921360795b393104e9bba906c2d5f84e.jpg) + +![](images/ae50168f0aa9b51bc460ca4b02a7deda2ceae1dd4cf06ba591b8440b9393a452.jpg) + +Similar to DropKey, the performance of Dropout is also related to drop ratio. + +How does the choice of scheduled strategy of drop ratio impact accuracy? The ablation in Table 1 analyzes the accuracy of DropKey by adjusting the strategy of setting drop ratio. Specifically, we validate three strategy as follows: a) Constant: drop ratio is constant over self attention layers. b) Scheduled $\uparrow$ : drop ratio is linearly increased over self attention layers. c) Scheduled $\downarrow$ : drop ratio is linearly decreased over self attention layers. Firstly, we find that Scheduled $\downarrow$ outperform Constant whether using re-normalize or not. Secondly, introducing drop ratio with Scheduled $\uparrow$ would seriously affect the performance of the model and even perform worse than the pure vision transformer. This phenomenon is in line with our expectation, since deeper layers often contain high-level semantic information which is essential to perform classification. A large drop ratio in deep layer will increase the risk of losing important features which would make model difficult to converge to a generalized solution. Hence, we set drop ratio with Scheduled $\downarrow$ in all following experiments. + +Is Dropkey helpful to capture global information? The contribution of DropKey is to generate a smoother attention weight matrix to encourage models to focus on global features. Class token has been proved to be effective in aggregating the information of the whole image, so we measure the smoothness of the attention distribution by calculating the entropy of its attention weight vector. Specifically, we define the entropy of the attention vector of class token as follows $E_{i} = -\sum_{j}p_{j}^{i}\log p_{j}^{i}$ where $p_j^i$ denotes the attention weight of $j^{th}$ attending patch in $i^{th}$ head. + +Note that a small entropy denotes that this head focuses on sparse patches. For convenience, the mean of entropy of multi-head as $E$ is reported in Figure 4. Clearly, it reads that while both Dropout and DropKey are able to improve the value of entropy, the improvement by DropKey is more significant. Meanwhile, when the drop rate increases, the entropy increase accordingly. In addition, to further verify the necessity of the adaptive coefficient for capturing general global information, we visualize the attention map (Figure 5) from class token in the last transformer layer. Obviously, the model with DropKey smoothly assigns attention + +weight to the area related to the instance. Finally, we further verify that our method can alleviate local-bias via the fact that transformers with DropKey perform robustly in occluded scenarios. + +Is structured drop is useful to vision transformer? In this section, we analyze whether structured masking is useful for vision transformer via DropKey-Block and DropKey-Cross. Specifically, we swept over window size from 3 to 5 for DropKey-Block and from 1 to 3 for DropKey-Cross. Compared with the DropKey, the structured drop degrade the performance of the model in all case and classification accuracy will decrease with the further increase of the window size. One possible reason for this phenomenon is that a larger drop ratio in shallow transformer layer results in losing vital information of object. However, a larger drop ratio is the key to avoid overfit to low-level feature. Therefore, we encourage set a larger drop ratio rather than the introduction of structured drop. + +How does align expectations impact accuracy? As discussed above, the mismatched expectations problem arises when directly use trained model with DropKey to test. Herein, to address above issue, we explore the impact of two methods, Monte Carlo and finetune, on the performance of network. The results in Table 3 indicates that accuracy can be improved regardless of the expectation alignment operation. Additionally, the accuracy of Monte Carlo increases with increasing sampling iterations. However, huge sampling iterations will lead to unacceptable computational cost. To fairly compare with Dropout, we also finetune it with the same training hyper-parameters as DropKey and then note that finetune only brings insignificant performance improvement or even over-fitting. In conclusion, alignment expectation of training and inference stage indeed can further improve the accuracy of the model. + +# 4.1.2 DropKey vs Dropout on ImageNet + +We provide the accuracy under other different drop ratio for each backbone with DropKey on ImageNet, and contrast them with existing State of the Arts (SOTA) equipped with Dropout, including T2T, VOLO, CeiT and DeiT in Table 4. We have these findings: (1) Clearly, our DropKey obtains significant enhancement against pure backbone. Meanwhile, We note that Dropout can only bring a little boost + +Table 1. Comparison of models with Dropout or DropKey on CIFAR10 and CIFAR100 when introducing different scheduled strategy of drop ratio. The drop ratio is set as 0.3 for all models. + +
ModelCIFAR10CIFAR100
Scheduled↑ConstantScheduled↓Scheduled↑ConstantScheduled↓
T2T14 [34] + Dropout96.796.997.277.077.878.4
T2T14 [34] + DropKey97.097.497.677.278.679.2
T2T19 [34] + Dropout96.697.197.477.378.178.5
T2T19 [34] + DropKey97.197.297.978.078.480.1
T2T24 [34] + Dropout96.497.097.576.777.378.2
T2T24 [34] + DropKey96.697.297.776.978.379.3
VOLOd1 [35] + Dropout95.896.496.677.378.279.0
VOLOd1 [35] + DropKey96.296.797.178.178.679.6
VOLOd2 [35] + Dropout95.696.196.477.078.479.0
VOLOd2 [35] + DropKey95.796.697.077.779.079.9
VOLOd3 [35] + Dropout96.096.396.677.177.978.5
VOLOd3 [35] + DropKey96.296.496.977.478.178.7
+ +![](images/f0ed617387f35bd25e49f0fef5a07d4b870cc4320c6b5a40a8ca1b8dadede16f.jpg) +Figure 4. The histogram of entropy on CIFAR100. dr denotes drop ratio. + +Table 2. Comparison of different structured drop on CIFAR100. $s$ denotes window size and drop ratio is set as 0.3 for all models. + +
ModelRandomBlockCross
s=3s=5s=1s=3
T2T14 [34] + Dropout78.478.177.177.976.8
T2T14 [34] + DropKey79.278.777.578.677.4
VOLOd1 [35] + Dropout78.678.076.777.676.4
VOLOd1 [35] + DropKey79.278.577.578.377.1
+ +Table 3. Comparison of models w/ or w/o Align Expectations on CIFAR100. Pure denotes the model without align expectation and drop ratio is set as 0.3 for all models. + +
ModelPurew/ Monte Carlow/ Finetune
20006000
T2T14 [34] + Dropout78.4--78.4
T2T14 [34] + DropKey78.878.979.179.2
T2T19 [34] + Dropout78.5--78.6
T2T19 [34] + DropKey79.379.580.280.1
+ +to backbones and it even would degrade the performance of the model in some cases (eg. T2T14, CeiT-T and DeiT-B). This indicates that the adaptive smoothing operator is more helpful to encourage the model to capture general information in large-scale datasets. (2) Compare to lightweight models, heavyweight often need the larger drop ratio to achieve a remarkable boost. For T2T14 and VOLOd1, the best accuracy is obtained under the dr=0.05. Instead, T2T19 and VOLOd2 achieve the best accuracy when dr=0.1, which suggests heavyweight models adopt a larger drop ratio to + +![](images/dc7f74540448bd734f045d228aab8399d04e23103719791404df2be8c315270e.jpg) +Figure 5. Visualization on CIFAR100. + +prevent overfitting. + +# 4.2. Object Detection in COCO + +In this section, we verify the generalizability and effectiveness of DropKey for object detection on COCO dataset [19]. We apply DETR [1] framework for the experiments. Specifically, DETR is composed of the backbone, encoder and decoder. We followed the model architecture, anchor definition and training recipe in [1] to build DETR+Dropout and DETR+DropKey. In Table 5, we report the results of DETR [1] with Dropout or DropKey in terms of AP. It can be seen that, our DropKey significantly outperforms existing Dropout. In detail, DropKey achieve $+0.7$ , $+1.1$ , $+0.4$ , $+0.3$ , $+0.8$ and $+0.7$ higher AP than the Dropout, which is regarded as a remarkable boost considering the challenge on this benchmark. Another observation is that large objects benefit more from DropKey than small objects. These results suggest that DropKey has the advantage over Dropout. + +# 4.3. Human-Object Interaction Detection in HICODET + +Since the task of scene graph and relation understanding is quite sensitive to global context learning, so we also verify the effectiveness of DropKey in QPIC [26] for Human-Object Interaction Detection in HICO-DET [2]. QPIC is a transformer-based feature extractor that can effectively aggregate contextually important information. We respec + +Table 4. Comparisons on backbones with Dropout or DropKey on ImageNet. dr denotes drop ratio. + +
ModelTop-1ModelTop-1
T2T14 [34]81.76 ± 0.05VOLOd1 [35]84.27 ± 0.12
T2T14 [34] + Dropout(dr=0.05)81.65 ± 0.04VOLOd1 [35] + Dropout(dr=0.05)84.35 ± 0.11
T2T14 [34] + Dropout(dr=0.1)81.53 ± 0.08VOLOd1 [35] + Dropout(dr=0.1)84.31 ± 0.04
T2T14 [34] + DropKey(dr=0.05)82.04 ± 0.14VOLOd1 [35] + DropKey(dr=0.05)84.53 ± 0.03
T2T14 [34] + DropKey(dr=0.1)81.93 ± 0.09VOLOd1 [35] + DropKey(dr=0.1)84.39 ± 0.02
T2T19 [34]82.56 ± 0.09VOLOd2 [35]85.24 ± 0.05
T2T19[34] + Dropout(dr=0.05)82.63 ± 0.05VOLOd2 [35] + Dropout(dr=0.05)85.22 ± 0.08
T2T19[34] + Dropout(dr=0.1)82.68 ± 0.04VOLOd2 [35] + Dropout(dr=0.1)85.21 ± 0.03
T2T19[34] + DropKey(dr=0.05)82.71 ± 0.02VOLOd2 [35] + DropKey(dr=0.05)85.33 ± 0.12
T2T19 [34] + DropKey(dr=0.1)82.94 ± 0.04VOLOd2 [35] + DropKey(dr=0.1)85.38 ± 0.06
CeiT-T [33]81.92 ± 0.06DeiT-B [27]81.94 ± 0.02
CeiT-T [33] + Dropout(dr=0.05)81.90 ± 0.03DeiT-B [27] + Dropout(dr=0.05)81.91 ± 0.04
CeiT-T [33] + Dropout(dr=0.1)81.83 ± 0.06DeiT-B [27] + Dropout(dr=0.1)81.87 ± 0.05
CeiT-T [33] + DropKey(dr=0.05)82.14 ± 0.05DeiT-B [27] + DropKey(dr=0.05)82.23 ± 0.01
CeiT-T [33] + DropKey(dr=0.1)82.27 ± 0.06DeiT-B [27] + DropKey(dr=0.1)82.25 ± 0.08
+ +Table 5. Comparison of DETR with Dropout and DropKey on COCO validation set. Table 6. Comparison of METRO with Dropout and Dropout key on HUMBI. + +
ModelAP\( AP_{50} \)\( AP_{75} \)\( AP_S \)\( AP_M \)\( AP_L \)
DETR [1]41.962.144.220.645.760.7
DETR [1] + Dropout42.262.344.320.845.961.1
DETR [1] + DropKey42.963.444.721.146.761.8
+ +
ModelmPVE↓mPJPE↓PA-mPJPE↓
METRO [18]57.851.539.9
METRO [18] + Dropout57.951.639.7
METRO [18] + DropKey57.151.039.5
+ +Table 7. Comparison of QPIC with Dropout and DropKey on HICO-DET. + +
Modelfull (Default)rare (Default)non-rare (Default)full (Known object)rare (Known object)non-rare (Known object)
QPIC-ResNet101 [26] + Dropout (dr=0.1)29.9624.0331.6332.4226.0134.31
QPIC-ResNet101 [26] + Dropout (dr=0.3)30.0224.1731.7232.4926.1334.41
QPIC-ResNet101 [26] + DropKey (dr=0.3)30.8724.6332.2433.2126.6634.94
+ +tively introduce Dropout and DropKey to both encoder and decoder in QPIC and train these models with the same training recipe as [26]. The model named "QPIC-ResNet101 + Dropout (dr=0.1)" is the result of our reproduction of QPIC with Schedued $\downarrow$ drop ratio (Official realization is equipped with Constant drop ratio). The experimental results in Table 7 suggest DropKey has higher performance gain on the different evaluating indicators which are consistent with our expectations. + +# 4.4. Human Body Mesh Recovery in HUMBI + +We verify the efficacy of DropKey for human body mesh task on HUMBI [32]. We follow conventions to train with 294 subjects from scratch and test with 120 subjects. We use Mean Per Vetex Error (MPVE) [22], Mean Per Joint Position Error (MPJPE) [14] and Procrustes Analysis MPJPE (PA-MPJPE) [38] as metrics. We use public METRO [18] as the baseline to apply DropKey to self-attention layer and Table 6 summaries the results. we can see that DropKey consistently improves the performance for all standard metrics. Specifically, DropKey brings about 0.7, 0.5 and 0.4 on mPVE, mPJPE and PA-mPJPE, respectively, while Dropout only boosts 0.2 performance on one metric. These results further verify the generalizability of DropKey as well as its superiority over vanilla dropout. + +# 5. Conclusion + +In this paper, we explore the drop unit, drop schedule and structured necessity of the dropout technique in ViT. Specifically, we propose to set Key as the drop unit, which yields a novel dropout-before-softmax scheme. We theoretically and experimentally verify that this scheme can regularize attention weights and meanwhile and keep them as a probability distribution simultaneously, helping capture vital patterns in a global manner and overcome local-bias problems that occurred to vanilla dropout. In addition, we present a new decreasing schedule for drop ratio, which stabilizes the training phase by avoiding overfittings in low-level features and maintaining sufficient high-level features. Moreover, we also experimentally show that structured dropout is not necessary for ViT. We distill the above analysis as a novel DropKey method, which plays as an improved version of dropout for ViT. Comprehensive experiments with different architectures on various vision tasks demonstrate the effectiveness of the proposed DropKey for enhancing ViTs. + +# Acknowledgements + +This paper is supported by the National key research and development program of China (2021YFA1000403), and the National Natural Science Foundation of China (Nos. U19B2040, 11991022). + +# References + +[1] Nicolas Carion, Francisco Massa, Gabriel Synnaeve, Nicolas Usunier, Alexander Kirillov, and Sergey Zagoruyko. 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"content": "Abstract" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 323, + 289, + 682 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 323, + 289, + 682 + ], + "spans": [ + { + "bbox": [ + 46, + 323, + 289, + 682 + ], + "type": "text", + "content": "In this paper, we focus on analyzing and improving the dropout technique for self-attention layers of Vision Transformer, which is important while surprisingly ignored by prior works. In particular, we conduct researches on three core questions: First, what to drop in self-attention layers? Different from dropping attention weights in literature, we propose to move dropout operations forward ahead of attention matrix calculation and set the Key as the dropout unit, yielding a novel dropout-before-softmax scheme. We theoretically verify that this scheme helps keep both regularization and probability features of attention weights, alleviating the overfittings problem to specific patterns and enhancing the model to globally capture vital information; Second, how to schedule the drop ratio in consecutive layers? In contrast to exploit a constant drop ratio for all layers, we present a new decreasing schedule that gradually decreases the drop ratio along the stack of self-attention layers. We experimentally validate the proposed schedule can avoid overfittings in low-level features and missing in high-level semantics, thus improving the robustness and stableness of model training; Third, whether need to perform structured dropout operation as CNN? We attempt patch-based block-version of dropout operation and find that this useful trick for CNN is not essential for ViT. Given exploration on the above three questions, we present the novel DropKey method that regards Key as the drop unit and exploits decreasing schedule for drop ratio, improving ViTs in a general way. Comprehensive experiments demonstrate the effectiveness of DropKey for various ViT architectures, e.g. T2T, VOLO, CeiT and DeiT, as well as for various vision" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 299, + 545, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 299, + 545, + 335 + ], + "spans": [ + { + "bbox": [ + 306, + 299, + 545, + 335 + ], + "type": "text", + "content": "tasks, e.g., image classification, object detection, human-object interaction detection and human body shape recovery." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 307, + 342, + 386, + 354 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 342, + 386, + 354 + ], + "spans": [ + { + "bbox": [ + 307, + 342, + 386, + 354 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 363, + 545, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 363, + 545, + 460 + ], + "spans": [ + { + "bbox": [ + 304, + 363, + 545, + 460 + ], + "type": "text", + "content": "Vision Transformer (ViT) [6] has achieved great success for various vision tasks, e.g., image recognition [7, 12, 20, 34, 35], object detection [1], human body shape estimation [18], etc. Prior works mainly focus on researches of patch division, architecture design and task extension. However, the dropout technique for self-attention layer, which plays the essential role to achieve good generalizability, is surprisingly ignored by the community." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 460, + 546, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 460, + 546, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 460, + 546, + 700 + ], + "type": "text", + "content": "Different from the counterpart for Convolutional Neural Networks (CNNs), the dropout in ViT directly utilizes the one in original Transformer designed for Natural Language Processing, which sets attention weights as the manipulation unit with a constant dropout ratio for all layers. Despite of its simplicity, this vanilla design faces three major problems. First, it breaks the probability distribution of attention weights due to the averaging operation on non-dropout units after softmax normalization. Although this regularizes the attention weights, it still overfits specific patterns locally due to the failure on penalizing score peaks, as shown in Fig. 1 (a) and (b); Second, the vanilla design is sensitive to the constant dropout ratio, since high ratio occurs missing of semantic information in high-level representations while low ratios overfitting in low-level features, resulting in the unstable training process; Third, it ignores the structured characteristic of input patch grid to ViT, which plays an effective role to improve performance with blockwise dropout in CNNs. These three problems degrade the performance and limit the generalizability of ViTs." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 318, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 318, + 701, + 545, + 714 + ], + "type": "text", + "content": "Motivated by this, we propose to analyze and improve" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 693, + 124, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 693, + 124, + 703 + ], + "spans": [ + { + "bbox": [ + 58, + 693, + 124, + 703 + ], + "type": "text", + "content": "*Equal contribution" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 59, + 703, + 134, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 703, + 134, + 712 + ], + "spans": [ + { + "bbox": [ + 59, + 703, + 134, + 712 + ], + "type": "text", + "content": "† Corresponding author" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "22700" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 108 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 108 + ], + "type": "text", + "content": "the dropout technique in self-attention layer, further pushing forward the frontier of ViTs for vision tasks in a general way. Specifically, we focus on three core aspects:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 110, + 289, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 110, + 289, + 397 + ], + "spans": [ + { + "bbox": [ + 47, + 110, + 289, + 397 + ], + "type": "text", + "content": "What to drop in self-attention layer Different from dropping attention weights as in the vanilla design, we propose to set the Key as the dropout unit, which is essential input of self-attention layer and significantly affects the output. This moves the dropout operation forward before calculating the attention matrix as shown in Fig. 1 (c) and yields a novel dropout-before-softmax scheme. This scheme regularizes attention weights and keeps their probability distribution at the same time, which intuitively helps penalize weight peaks and lift weight foots. We theoretically verify this property via implicitly introducing an adaptive smoothing coefficient for the attention operator from the perspective of gradient optimization by formulating a Lagrange function. With the dropout-before-softmax scheme, self-attention layers can capture vital information in a global manner, thus overcoming the overfittings problem to specific patterns occurred in the vanilla dropout and enhancing the model generalizability as visualization of feature map in Fig. 1 (c). For the training phase, this scheme can be simply implemented by swapping the operation order of softmax and dropout in vanilla design, which provides a general way to effectively enhance ViTs. For inference phase, we conduct an additional finetune phase to align the expectations to training phase, further improving the performance." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 400, + 289, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 400, + 289, + 519 + ], + "spans": [ + { + "bbox": [ + 47, + 400, + 289, + 519 + ], + "type": "text", + "content": "How to schedule the drop ratio In contrast to exploiting a constant drop ratio for all layers, we present a new linear decreasing schedule that gradually decreases the drop ratio along the stack of self-attention layers. This schedule leads to a high drop ratio in shallow layers while the low one in deep layers, thus avoiding over fittings to low-level features and preserving sufficient high-level semantics. We experimentally verify the effectiveness of the proposed decreasing schedule for drop ratio to stable the training phase and improve the robustness." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 521, + 289, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 521, + 289, + 653 + ], + "spans": [ + { + "bbox": [ + 47, + 521, + 289, + 653 + ], + "type": "text", + "content": "Whether need to perform structured drop Inspired by the DropBlock [10] method for CNNs, we implement two structured versions of the dropout operation for ViTs: the block-version dropout that drops keys corresponding to contiguous patches in images or feature maps; the crossversion dropout that drops keys corresponding to patches in horizontal and vertical stripes. We conduct thorough experiments to validate their efficacy and find that the structure trick useful for CNN is not essential for ViT, due to the powerful capability of ViT to grasp contextual information in full image range." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 654, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 654, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 654, + 289, + 715 + ], + "type": "text", + "content": "Given exploration on the above three aspects, we present a novel DropKey method that utilizes Key as the drop unit and decreasing schedule for drop ratio. In particular, DropKey overcomes drawbacks of the vanilla dropout technique for ViTs, improving performance in a general and effective" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 547, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 204 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 204 + ], + "type": "text", + "content": "way. Comprehensive experiments on different ViT architectures and vision tasks demonstrate the efficacy of DropKey. Our contributions are in three folds: First, to our best knowledge, we are the first to theoretically and experimentally analyze dropout technique for self-attention layers in ViT from three core aspects: drop unit, drop schedule and structured necessity; Second, according to our analysis, we present a novel DropKey method to effectively improve the dropout technique in ViT. Third, with DropKey, we improve multiple ViT architectures to achieve new SOTAs on various vision tasks." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 208, + 392, + 220 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 208, + 392, + 220 + ], + "spans": [ + { + "bbox": [ + 306, + 208, + 392, + 220 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 228, + 547, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 228, + 547, + 396 + ], + "spans": [ + { + "bbox": [ + 304, + 228, + 547, + 396 + ], + "type": "text", + "content": "Vision Transformers Inspired by the Transformer architectures in NLP, some works introduce attention block to replace convolution layers to model long-range dependencies [6, 11, 17, 29, 30, 31, 37]. ViT[6] is the pioneering work which splits an image to non-overlapping patches and then these patches are fed to a transformer to evaluate attention scores. Prior works mainly focus on patch division, architecture design and tasks extension. For example, CvT[31] proposes a hybrid architecture to mix convolutional with attention layers to introduce local inductive bias. [3, 7, 20] proposes to reduce the computation cost. Despite the progress, previous works ignore the dropout technique in self-attention layer, which play an important role to keep good generalizability." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 399, + 547, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 399, + 547, + 506 + ], + "spans": [ + { + "bbox": [ + 304, + 399, + 547, + 506 + ], + "type": "text", + "content": "Dropout Dropout is a common technique for improving the generalizability of neural networks, e.g., CNNs [16], RNNs [21] and GNNs [24]. For CNNs, [10] points out the lack of success of dropout for convolutional layers is due to dense information flowing and then proposes a form of structured Dropout. DropConnect [28] randomly masks a subset of weights within the model. For RNNs, the first prominent research on dropout is presented in [8], which is equipped with a learnable dropout rate." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 507, + 547, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 507, + 547, + 590 + ], + "spans": [ + { + "bbox": [ + 304, + 507, + 547, + 590 + ], + "type": "text", + "content": "For GNNs, to alleviate over-fitting and over-smoothing issues, DropEdge [23] randomly removes part of edges in the input stage at each training epoch and theoretically demonstrates the effect of the proposed method. For ViTs, most original publicly code of multiple popular vision transformer simply intuitively apply dropout operation on attention matrix." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 594, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 548, + 715 + ], + "type": "text", + "content": "DropAttention [36] presents a novel way for transformer in NLPs. It refers to perform randomly drop on the attention matrix. There are two two main forms of applying DropAttention for the transformer training, DropAttention-unit and DropAttention-elements. Similar to the standard Dropout [25], DropAttention-unit randomly drops the unit, that is, these dropped token will not be used as attend patches for each query patch. As the general form of DropAttention-unit, DropAttention-elements randomly drops elements in attention weights matrix which" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "text", + "content": "22701" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 68, + 267, + 194 + ], + "blocks": [ + { + "bbox": [ + 47, + 68, + 267, + 194 + ], + "lines": [ + { + "bbox": [ + 47, + 68, + 267, + 194 + ], + "spans": [ + { + "bbox": [ + 47, + 68, + 267, + 194 + ], + "type": "image", + "image_path": "71ca9e25de2d60876fb0c5c4a0f812693a8980d1cb656c8f30f17289497c6566.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 59, + 199, + 106, + 210 + ], + "lines": [ + { + "bbox": [ + 59, + 199, + 106, + 210 + ], + "spans": [ + { + "bbox": [ + 59, + 199, + 106, + 210 + ], + "type": "text", + "content": "Input Image" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 265, + 69, + 406, + 196 + ], + "blocks": [ + { + "bbox": [ + 265, + 69, + 406, + 196 + ], + "lines": [ + { + "bbox": [ + 265, + 69, + 406, + 196 + ], + "spans": [ + { + "bbox": [ + 265, + 69, + 406, + 196 + ], + "type": "image", + "image_path": "6efa2f8668f852025f41a74d14bc0b85e2ab408653f5271ff42c9e46e79d9206.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 282, + 199, + 373, + 210 + ], + "lines": [ + { + "bbox": [ + 282, + 199, + 373, + 210 + ], + "spans": [ + { + "bbox": [ + 282, + 199, + 373, + 210 + ], + "type": "text", + "content": "(b) Attention w/ Dropout" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 45, + 215, + 547, + 258 + ], + "lines": [ + { + "bbox": [ + 45, + 215, + 547, + 258 + ], + "spans": [ + { + "bbox": [ + 45, + 215, + 547, + 258 + ], + "type": "text", + "content": "Figure 1. Comparison between the proposed DropKey and existing vanilla dropout techniques in self-attention layers for ViTs. (a) Self-attention without dropout, which suffers overfitting problems to local patch; (b) Self-attention with vanilla dropout, which regularizes the attention weights but still overfits specific patterns; (c) Self-attention with our DropKey, which overcomes prior problems and improves the model to capture vital information in a global manner. Best viewed in color." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 406, + 70, + 547, + 195 + ], + "blocks": [ + { + "bbox": [ + 406, + 70, + 547, + 195 + ], + "lines": [ + { + "bbox": [ + 406, + 70, + 547, + 195 + ], + "spans": [ + { + "bbox": [ + 406, + 70, + 547, + 195 + ], + "type": "image", + "image_path": "13a34b72c80da52b51e9e29e7a11d7ca0501806630d06e306efbe33358ad0b33.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 425, + 199, + 515, + 210 + ], + "lines": [ + { + "bbox": [ + 425, + 199, + 515, + 210 + ], + "spans": [ + { + "bbox": [ + 425, + 199, + 515, + 210 + ], + "type": "text", + "content": "(c) Attention w/ DropKey" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 260, + 288, + 320 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 260, + 288, + 320 + ], + "spans": [ + { + "bbox": [ + 46, + 260, + 288, + 320 + ], + "type": "text", + "content": "is similar to DropConnect [28]. Different from standard Dropout [25], DropAttention introduce re-normalize to guarantee the sum of attention weights to 1 and help training process to be more steady. However, there is no further discussion and theoretical analysis on this phenomenon." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 321, + 102, + 333 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 321, + 102, + 333 + ], + "spans": [ + { + "bbox": [ + 47, + 321, + 102, + 333 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 341, + 287, + 412 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 341, + 287, + 412 + ], + "spans": [ + { + "bbox": [ + 46, + 341, + 287, + 412 + ], + "type": "text", + "content": "Our generic DropKey is inspired by DropAttention and proposed for self-attention operator in vision transformer. The main idea of DropKey is to adaptively adjust attention weight to obtain a smoother attention vector. In this section, we start by introducing the theoretical explanation of DropKey, then the implementation will be explained in detail." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 412, + 130, + 423 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 412, + 130, + 423 + ], + "spans": [ + { + "bbox": [ + 47, + 412, + 130, + 423 + ], + "type": "text", + "content": "3.1. Methodology" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 45, + 423, + 288, + 614 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 423, + 288, + 614 + ], + "spans": [ + { + "bbox": [ + 45, + 423, + 288, + 614 + ], + "type": "text", + "content": "As discussed in the above section, transformer-based model tends to rely on local features rather than general global information. To alleviate this issue, we propose to reduce local-bias by encouraging models to learn a smoother attention weight for each patch. To this end, we attempt to reduce the attention weight of the patch which has a large attention weight, and vice versa. Nevertheless, it is tedious and difficult to achieve this by explicitly setting rules. In this work, we found DropKey achieves the above implicitly by normalizing the attention vector that has performed the dropout operation. Specifically, by given an image " + }, + { + "bbox": [ + 45, + 423, + 288, + 614 + ], + "type": "inline_equation", + "content": "I \\in \\mathbb{R}^{H \\times W \\times C}" + }, + { + "bbox": [ + 45, + 423, + 288, + 614 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 45, + 423, + 288, + 614 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 45, + 423, + 288, + 614 + ], + "type": "text", + "content": " denotes height, " + }, + { + "bbox": [ + 45, + 423, + 288, + 614 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 45, + 423, + 288, + 614 + ], + "type": "text", + "content": " denotes width and " + }, + { + "bbox": [ + 45, + 423, + 288, + 614 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 45, + 423, + 288, + 614 + ], + "type": "text", + "content": " denotes channels, Vision Transformer architecture starts by dicing it into " + }, + { + "bbox": [ + 45, + 423, + 288, + 614 + ], + "type": "inline_equation", + "content": "n_h \\times n_w" + }, + { + "bbox": [ + 45, + 423, + 288, + 614 + ], + "type": "text", + "content": " patches " + }, + { + "bbox": [ + 45, + 423, + 288, + 614 + ], + "type": "inline_equation", + "content": "x \\in \\mathbb{R}^{n_c}" + }, + { + "bbox": [ + 45, + 423, + 288, + 614 + ], + "type": "text", + "content": ". Then, " + }, + { + "bbox": [ + 45, + 423, + 288, + 614 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 45, + 423, + 288, + 614 + ], + "type": "text", + "content": " is used as input of self-attention layer and the output " + }, + { + "bbox": [ + 45, + 423, + 288, + 614 + ], + "type": "inline_equation", + "content": "o" + }, + { + "bbox": [ + 45, + 423, + 288, + 614 + ], + "type": "text", + "content": " can be computed as follows" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 110, + 619, + 287, + 651 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 619, + 287, + 651 + ], + "spans": [ + { + "bbox": [ + 110, + 619, + 287, + 651 + ], + "type": "interline_equation", + "content": "o = \\sum_ {j = 1} ^ {n _ {h} n _ {w}} \\left(\\frac {d _ {j} p _ {j}}{\\sum_ {j = 1} ^ {n _ {h} n _ {w}} d _ {j} p _ {j}}\\right) v _ {j} \\tag {1}", + "image_path": "42e54393dff0ba61acecbb0588a953679af8451457ad110bfb67fd2146910750.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 115, + 651, + 287, + 687 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 651, + 287, + 687 + ], + "spans": [ + { + "bbox": [ + 115, + 651, + 287, + 687 + ], + "type": "interline_equation", + "content": "p _ {j} = \\frac {\\exp \\left(\\frac {q k _ {j} ^ {T}}{\\text {s c a l e}}\\right)}{\\sum_ {j = 1} ^ {n _ {h} n _ {w}} \\exp \\left(\\frac {q k _ {j} ^ {T}}{\\text {s c a l e}}\\right)} \\tag {2}", + "image_path": "d3981c39827e095ce7c2d86376b8dcb83a910421b44f2cb38fb84b04647c2c98.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 689, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 288, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 689, + 288, + 714 + ], + "type": "inline_equation", + "content": "q = \\mathcal{F}_q(x), k = \\mathcal{F}_k(x), v = \\mathcal{F}_v(x)" + }, + { + "bbox": [ + 46, + 689, + 288, + 714 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 689, + 288, + 714 + ], + "type": "inline_equation", + "content": "q_i, k_j, v_j" + }, + { + "bbox": [ + 46, + 689, + 288, + 714 + ], + "type": "text", + "content": " denote query of " + }, + { + "bbox": [ + 46, + 689, + 288, + 714 + ], + "type": "inline_equation", + "content": "i^{th}" + }, + { + "bbox": [ + 46, + 689, + 288, + 714 + ], + "type": "text", + "content": " patch, key of " + }, + { + "bbox": [ + 46, + 689, + 288, + 714 + ], + "type": "inline_equation", + "content": "j^{th}" + }, + { + "bbox": [ + 46, + 689, + 288, + 714 + ], + "type": "text", + "content": " patch, value of " + }, + { + "bbox": [ + 46, + 689, + 288, + 714 + ], + "type": "inline_equation", + "content": "j^{th}" + }, + { + "bbox": [ + 46, + 689, + 288, + 714 + ], + "type": "text", + "content": " patch and " + }, + { + "bbox": [ + 46, + 689, + 288, + 714 + ], + "type": "inline_equation", + "content": "o" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 260, + 545, + 366 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 260, + 545, + 366 + ], + "spans": [ + { + "bbox": [ + 304, + 260, + 545, + 366 + ], + "type": "text", + "content": "denotes the output of one patch. " + }, + { + "bbox": [ + 304, + 260, + 545, + 366 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_q(\\cdot),\\mathcal{F}_k(\\cdot),\\mathcal{F}_v(\\cdot)" + }, + { + "bbox": [ + 304, + 260, + 545, + 366 + ], + "type": "text", + "content": " denote projection layers with weights of dimensions " + }, + { + "bbox": [ + 304, + 260, + 545, + 366 + ], + "type": "inline_equation", + "content": "n_c\\times n_c" + }, + { + "bbox": [ + 304, + 260, + 545, + 366 + ], + "type": "text", + "content": " . scale denotes scaling factor and is set to " + }, + { + "bbox": [ + 304, + 260, + 545, + 366 + ], + "type": "inline_equation", + "content": "\\sqrt{n_c}" + }, + { + "bbox": [ + 304, + 260, + 545, + 366 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 260, + 545, + 366 + ], + "type": "text", + "content": " denotes drop ratio and " + }, + { + "bbox": [ + 304, + 260, + 545, + 366 + ], + "type": "inline_equation", + "content": "d_{j}\\sim Bernoulli(1 - d)" + }, + { + "bbox": [ + 304, + 260, + 545, + 366 + ], + "type": "text", + "content": " . Here, for convenience, we focus on one head and omit the index of patch. By performing re-normalize, DropKey has the ability to adaptively adjust attention weight to smoother. Next, we provide theoretical analysis of our method to demonstrate its effectiveness." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 369, + 545, + 393 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 369, + 545, + 393 + ], + "spans": [ + { + "bbox": [ + 305, + 369, + 545, + 393 + ], + "type": "text", + "content": "Here, we formulate the expectation output of model via introducing DropKey in training stage as:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 310, + 398, + 545, + 456 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 398, + 545, + 456 + ], + "spans": [ + { + "bbox": [ + 310, + 398, + 545, + 456 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathbb {E} _ {d _ {j}, 1 \\leq j \\leq n _ {h} n _ {w}} [ o ] = \\mathbb {E} _ {d _ {j}, 1 \\leq j \\leq n _ {h} n _ {w}} [ \\sum_ {j = 1} ^ {n _ {h} n _ {w}} (\\frac {d _ {j} p _ {j}}{\\sum_ {j = 1} ^ {n _ {h} n _ {w}} d _ {j} p _ {j}}) v _ {j} ] \\tag {3} \\\\ = \\sum_ {j = 1} ^ {n _ {h} n _ {w}} \\mathbb {E} _ {d _ {j}, 1 \\leq j \\leq n _ {h} n _ {w}} [ \\frac {d _ {j}}{\\sum_ {j = 1} ^ {n _ {h} n _ {w}} d _ {j} p _ {j}} ] p _ {j} v _ {j} = \\sum_ {j = 1} ^ {n _ {h} n _ {w}} c _ {j} p _ {j} v _ {j} \\\\ \\end{array}", + "image_path": "b0c791fc82488a262a46c6848b6abd7bf5b21855ff279a700d10b4bf935c5fd3.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 462, + 545, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 462, + 545, + 491 + ], + "spans": [ + { + "bbox": [ + 305, + 462, + 545, + 491 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 462, + 545, + 491 + ], + "type": "inline_equation", + "content": "c_{j} = \\mathbb{E}_{d_{j},1\\leq j\\leq n_{h}n_{w}}\\left[\\frac{d_{j}}{\\sum_{j = 1}^{n_{h}n_{w}}d_{j}p_{j}}\\right] > 0" + }, + { + "bbox": [ + 305, + 462, + 545, + 491 + ], + "type": "text", + "content": " is a smoothing coefficient which is related to " + }, + { + "bbox": [ + 305, + 462, + 545, + 491 + ], + "type": "inline_equation", + "content": "d_{j}" + }, + { + "bbox": [ + 305, + 462, + 545, + 491 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 462, + 545, + 491 + ], + "type": "inline_equation", + "content": "p_j" + }, + { + "bbox": [ + 305, + 462, + 545, + 491 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 491, + 545, + 522 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 491, + 545, + 522 + ], + "spans": [ + { + "bbox": [ + 305, + 491, + 545, + 522 + ], + "type": "text", + "content": "Note that " + }, + { + "bbox": [ + 305, + 491, + 545, + 522 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 305, + 491, + 545, + 522 + ], + "type": "text", + "content": " in Equ (3) can be considered to add an additional smoothing prior to distribution " + }, + { + "bbox": [ + 305, + 491, + 545, + 522 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 305, + 491, + 545, + 522 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 305, + 491, + 545, + 522 + ], + "type": "inline_equation", + "content": "c_{s} < c_{t}" + }, + { + "bbox": [ + 305, + 491, + 545, + 522 + ], + "type": "text", + "content": " when " + }, + { + "bbox": [ + 305, + 491, + 545, + 522 + ], + "type": "inline_equation", + "content": "p_{s} > p_{t}, 1 \\leq s, t \\leq n_{h}n_{w}" + }, + { + "bbox": [ + 305, + 491, + 545, + 522 + ], + "type": "text", + "content": ". The specific proof is as follows:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 534, + 545, + 580 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 534, + 545, + 580 + ], + "spans": [ + { + "bbox": [ + 306, + 534, + 545, + 580 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} c _ {s} - c _ {t} = \\mathbb {E} _ {d _ {j}, 1 \\leq j \\leq n _ {h} n _ {w}} [ \\frac {d _ {s}}{\\sum_ {j = 1} ^ {n _ {h} n _ {w}} d _ {j} p _ {j}} ] - \\mathbb {E} _ {d _ {j}, 1 \\leq j \\leq n _ {h} n _ {w}} [ \\frac {d _ {t}}{\\sum_ {j = 1} ^ {n _ {h} n _ {w}} d _ {j} p _ {j}} ] \\\\ = d (1 - d) \\mathbb {E} _ {d _ {j}, 1} \\leq j \\leq n _ {h} n _ {w} \\left[ \\frac {1}{\\sum_ {j \\neq s , t} ^ {n _ {h} n _ {w}} d _ {j} p _ {j} + p _ {s}} - \\frac {1}{\\sum_ {j \\neq s , t} ^ {n _ {h} n _ {w}} d _ {j} p _ {j} + p _ {t}} \\right] < 0 \\tag {4} \\\\ \\end{array}", + "image_path": "d6b186192e895aa0d445e59abb202ef3ce819a0a6b40b95a5dac4d1c72cfe260.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "It is natural to find " + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": " serves as a factor to implicitly encourage the model properly to reduce the consideration of the patch with large " + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": " and improve the effectiveness of the patch with small attention weight. Meanwhile, " + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": " can be adjusted adaptively according to the distribution of samples in the training stage without any manual design. Nevertheless, a noteworthy problem is that since we removed DropKey in the inference phase, the output expectations in training and inference stage are inconsistent, which will decrease the performance. In Section 3.2, we propose two methods to alleviate this problem." + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22702" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 120 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 120 + ], + "type": "text", + "content": "Having explored the implicit regularization effects of DropKey, we also demonstrate it from the perspective of gradient optimization. For simplicity, we start by considering a simple but universal optimization objective as follows:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 134, + 287, + 163 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 134, + 287, + 163 + ], + "spans": [ + { + "bbox": [ + 56, + 134, + 287, + 163 + ], + "type": "interline_equation", + "content": "\\min _ {p _ {j}, v _ {j}} \\frac {1}{2} \\| \\sum_ {j = 1} ^ {N} p _ {j} v _ {j} - y \\| ^ {2} \\text {s . t .} p _ {j} > 0, \\sum_ {j = 1} p _ {j} = 1, 1 \\leq j \\leq N \\tag {5}", + "image_path": "84aa0fc002653d39d931233c441a4c244b38e56ab2b9dca5a5b22c3a064b629a.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 166, + 289, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 166, + 289, + 275 + ], + "spans": [ + { + "bbox": [ + 47, + 166, + 289, + 275 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 166, + 289, + 275 + ], + "type": "inline_equation", + "content": "p_j \\in \\mathbb{R}" + }, + { + "bbox": [ + 47, + 166, + 289, + 275 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 166, + 289, + 275 + ], + "type": "inline_equation", + "content": "v_j \\in \\mathbb{R}^r" + }, + { + "bbox": [ + 47, + 166, + 289, + 275 + ], + "type": "text", + "content": " denotes learnable parameters and " + }, + { + "bbox": [ + 47, + 166, + 289, + 275 + ], + "type": "inline_equation", + "content": "y \\in \\mathbb{R}^r" + }, + { + "bbox": [ + 47, + 166, + 289, + 275 + ], + "type": "text", + "content": " denotes target. This simple problem captures the essential part of the training of a single self-attention layer, especially when the neural networks are large, and it may shed light on the training of deep models. Here, " + }, + { + "bbox": [ + 47, + 166, + 289, + 275 + ], + "type": "inline_equation", + "content": "p_j" + }, + { + "bbox": [ + 47, + 166, + 289, + 275 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 166, + 289, + 275 + ], + "type": "inline_equation", + "content": "v_j" + }, + { + "bbox": [ + 47, + 166, + 289, + 275 + ], + "type": "text", + "content": " can be considered as attention weight and value in attention mechanism. Naturally, " + }, + { + "bbox": [ + 47, + 166, + 289, + 275 + ], + "type": "inline_equation", + "content": "v_j" + }, + { + "bbox": [ + 47, + 166, + 289, + 275 + ], + "type": "text", + "content": " can be decomposed into two directions, which are the same direction as " + }, + { + "bbox": [ + 47, + 166, + 289, + 275 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 47, + 166, + 289, + 275 + ], + "type": "text", + "content": " and the direction perpendicular to " + }, + { + "bbox": [ + 47, + 166, + 289, + 275 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 47, + 166, + 289, + 275 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 135, + 284, + 287, + 298 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 135, + 284, + 287, + 298 + ], + "spans": [ + { + "bbox": [ + 135, + 284, + 287, + 298 + ], + "type": "interline_equation", + "content": "v _ {j} = \\beta_ {j} e + \\alpha_ {j} \\tag {6}", + "image_path": "f603b37a013cb180c3d347100da048fc99696148c1dde88f2e1df3039845e52b.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 304, + 289, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 304, + 289, + 353 + ], + "spans": [ + { + "bbox": [ + 47, + 304, + 289, + 353 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 304, + 289, + 353 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 47, + 304, + 289, + 353 + ], + "type": "text", + "content": " is a scalar, " + }, + { + "bbox": [ + 47, + 304, + 289, + 353 + ], + "type": "inline_equation", + "content": "e\\in \\mathbb{R}^r" + }, + { + "bbox": [ + 47, + 304, + 289, + 353 + ], + "type": "text", + "content": " is the unit vector of " + }, + { + "bbox": [ + 47, + 304, + 289, + 353 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 47, + 304, + 289, + 353 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 304, + 289, + 353 + ], + "type": "inline_equation", + "content": "\\alpha_{j}" + }, + { + "bbox": [ + 47, + 304, + 289, + 353 + ], + "type": "text", + "content": " is the component perpendicular to " + }, + { + "bbox": [ + 47, + 304, + 289, + 353 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 47, + 304, + 289, + 353 + ], + "type": "text", + "content": ". Similarly, we can rewrite " + }, + { + "bbox": [ + 47, + 304, + 289, + 353 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 47, + 304, + 289, + 353 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 47, + 304, + 289, + 353 + ], + "type": "inline_equation", + "content": "Me" + }, + { + "bbox": [ + 47, + 304, + 289, + 353 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 47, + 304, + 289, + 353 + ], + "type": "inline_equation", + "content": "M = ||y||" + }, + { + "bbox": [ + 47, + 304, + 289, + 353 + ], + "type": "text", + "content": ". Then, the Lagrange function of Equ (5) can be formulated as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 76, + 356, + 287, + 386 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 76, + 356, + 287, + 386 + ], + "spans": [ + { + "bbox": [ + 76, + 356, + 287, + 386 + ], + "type": "interline_equation", + "content": "L \\left(p _ {j}, v _ {j}, \\lambda\\right) = \\frac {1}{2} | | \\sum_ {j = 1} ^ {N} p _ {j} v _ {j} - y | | ^ {2} - \\lambda \\left(\\sum_ {j = 1} ^ {N} p _ {j} - 1\\right) \\tag {7}", + "image_path": "d0c05c4b8c813a1dcc97bb9935ec8d721d9bc7a47feee4848b68b881cf048943.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 388, + 287, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 388, + 287, + 415 + ], + "spans": [ + { + "bbox": [ + 47, + 388, + 287, + 415 + ], + "type": "text", + "content": "In order to analysis the gradient, we take the partial derivatives of " + }, + { + "bbox": [ + 47, + 388, + 287, + 415 + ], + "type": "inline_equation", + "content": "p_j" + }, + { + "bbox": [ + 47, + 388, + 287, + 415 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 388, + 287, + 415 + ], + "type": "inline_equation", + "content": "v_j" + }, + { + "bbox": [ + 47, + 388, + 287, + 415 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 418, + 287, + 455 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 418, + 287, + 455 + ], + "spans": [ + { + "bbox": [ + 47, + 418, + 287, + 455 + ], + "type": "interline_equation", + "content": "\\frac {\\partial L}{\\partial p _ {j}} = (v - y) ^ {T} v _ {j} - \\lambda = \\left(\\sum_ {j = 1} ^ {N} p _ {j} \\beta_ {j} - M\\right) \\beta_ {j} + \\left(\\sum_ {j = 1} ^ {N} p _ {j} \\alpha_ {j}\\right) ^ {T} \\alpha_ {j} - \\lambda \\tag {8}", + "image_path": "9a3716faaff239321ab4d19deab07573fc0ad45bee27d3faebd9ed218a1aee37.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 67, + 468, + 287, + 498 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 468, + 287, + 498 + ], + "spans": [ + { + "bbox": [ + 67, + 468, + 287, + 498 + ], + "type": "interline_equation", + "content": "\\frac {\\partial L}{\\partial v _ {j}} = p _ {j} (v - y) = p _ {j} \\left(\\sum_ {j = 1} ^ {N} p _ {j} \\beta_ {j} - M\\right) e + p _ {j} \\left(\\sum_ {j = 1} ^ {N} p _ {j} \\alpha_ {j}\\right) \\tag {9}", + "image_path": "a705d5179d800a7820f1a15ac665f31b040b0c6d339efd22c7b24a70ded7dd09.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 503, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 503, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 47, + 503, + 287, + 544 + ], + "type": "text", + "content": "Here, for simplicity, we note " + }, + { + "bbox": [ + 47, + 503, + 287, + 544 + ], + "type": "inline_equation", + "content": "v = \\sum_{j=1}^{N} p_j v_j = (\\sum_{j=1}^{N} p_j \\beta_j) e + \\sum_{j=1}^{N} p_j \\alpha_j" + }, + { + "bbox": [ + 47, + 503, + 287, + 544 + ], + "type": "text", + "content": ". From the chain rule of backpropagation, we also have:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 74, + 548, + 287, + 576 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 74, + 548, + 287, + 576 + ], + "spans": [ + { + "bbox": [ + 74, + 548, + 287, + 576 + ], + "type": "interline_equation", + "content": "\\frac {\\partial L}{\\partial \\beta_ {j}} = p _ {j} \\left(\\sum_ {j = 1} ^ {N} p _ {j} \\beta_ {j} - M\\right) \\quad \\frac {\\partial L}{\\partial \\alpha_ {j}} = p _ {j} \\left(\\sum_ {j = 1} ^ {N} p _ {j} \\alpha_ {j}\\right) \\tag {10}", + "image_path": "fbbf35df4777cb73746cbb4ddc8dbfeae70153d6dab8e72c1bda46dd28a8365a.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 581, + 287, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 581, + 287, + 622 + ], + "spans": [ + { + "bbox": [ + 47, + 581, + 287, + 622 + ], + "type": "text", + "content": "Equ (10) indicates that the gradient " + }, + { + "bbox": [ + 47, + 581, + 287, + 622 + ], + "type": "inline_equation", + "content": "\\frac{\\partial L}{\\partial \\beta_s} < \\frac{\\partial L}{\\partial \\beta_t}" + }, + { + "bbox": [ + 47, + 581, + 287, + 622 + ], + "type": "text", + "content": " when " + }, + { + "bbox": [ + 47, + 581, + 287, + 622 + ], + "type": "inline_equation", + "content": "p_s > p_t" + }, + { + "bbox": [ + 47, + 581, + 287, + 622 + ], + "type": "text", + "content": " and this backward propagation properties would lead " + }, + { + "bbox": [ + 47, + 581, + 287, + 622 + ], + "type": "inline_equation", + "content": "\\frac{\\partial L}{\\partial p_s} < \\frac{\\partial L}{\\partial p_t}" + }, + { + "bbox": [ + 47, + 581, + 287, + 622 + ], + "type": "text", + "content": ". By subtracting " + }, + { + "bbox": [ + 47, + 581, + 287, + 622 + ], + "type": "inline_equation", + "content": "\\frac{\\partial L}{\\partial p_s}" + }, + { + "bbox": [ + 47, + 581, + 287, + 622 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 581, + 287, + 622 + ], + "type": "inline_equation", + "content": "\\frac{\\partial L}{\\partial p_t}" + }, + { + "bbox": [ + 47, + 581, + 287, + 622 + ], + "type": "text", + "content": ", we will have:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 52, + 632, + 287, + 661 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 632, + 287, + 661 + ], + "spans": [ + { + "bbox": [ + 52, + 632, + 287, + 661 + ], + "type": "interline_equation", + "content": "\\frac {\\partial L}{\\partial p _ {s}} - \\frac {\\partial L}{\\partial p _ {t}} = \\left(\\sum_ {j = 1} ^ {N} p _ {j} \\beta_ {j} - M\\right) \\left(\\beta_ {s} - \\beta_ {t}\\right) + \\left(\\sum_ {j = 1} ^ {N} p _ {j} \\alpha_ {j}\\right) ^ {T} \\left(\\alpha_ {s} - \\alpha_ {t}\\right) \\tag {11}", + "image_path": "b75adf23e10a5f76acb72c8dd307ee28c0646060b5bc196359c9631ec86d3aca.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 664, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 664, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 664, + 287, + 715 + ], + "type": "text", + "content": "Since all parameters are randomly initialized, it can be assumed that the initial solution is far from the optimal solution, that is, " + }, + { + "bbox": [ + 47, + 664, + 287, + 715 + ], + "type": "inline_equation", + "content": "p_1^{(0)} = p_2^{(0)} = \\dots = p_N^{(0)} = \\frac{1}{N}" + }, + { + "bbox": [ + 47, + 664, + 287, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 664, + 287, + 715 + ], + "type": "inline_equation", + "content": "|\\beta_j^{(0)}| \\ll M" + }, + { + "bbox": [ + 47, + 664, + 287, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 664, + 287, + 715 + ], + "type": "inline_equation", + "content": "1 \\leq j \\leq N" + }, + { + "bbox": [ + 47, + 664, + 287, + 715 + ], + "type": "text", + "content": ". Consequently, the first additive term plays" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 71, + 545, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 71, + 545, + 168 + ], + "spans": [ + { + "bbox": [ + 304, + 71, + 545, + 168 + ], + "type": "text", + "content": "the leading role in Equ (11). Due to " + }, + { + "bbox": [ + 304, + 71, + 545, + 168 + ], + "type": "inline_equation", + "content": "\\frac{\\partial L}{\\partial\\beta_s} < \\frac{\\partial L}{\\partial\\beta_t}" + }, + { + "bbox": [ + 304, + 71, + 545, + 168 + ], + "type": "text", + "content": ", the update speed of " + }, + { + "bbox": [ + 304, + 71, + 545, + 168 + ], + "type": "inline_equation", + "content": "\\beta_{s}" + }, + { + "bbox": [ + 304, + 71, + 545, + 168 + ], + "type": "text", + "content": " is faster than " + }, + { + "bbox": [ + 304, + 71, + 545, + 168 + ], + "type": "inline_equation", + "content": "\\beta_{t}" + }, + { + "bbox": [ + 304, + 71, + 545, + 168 + ], + "type": "text", + "content": " and then lead " + }, + { + "bbox": [ + 304, + 71, + 545, + 168 + ], + "type": "inline_equation", + "content": "\\beta_{s} > \\beta_{t}" + }, + { + "bbox": [ + 304, + 71, + 545, + 168 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 71, + 545, + 168 + ], + "type": "inline_equation", + "content": "\\frac{\\partial L}{\\partial p_s} < \\frac{\\partial L}{\\partial p_t}" + }, + { + "bbox": [ + 304, + 71, + 545, + 168 + ], + "type": "text", + "content": ". Based on the above analysis, it can be concluded that a larger " + }, + { + "bbox": [ + 304, + 71, + 545, + 168 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 304, + 71, + 545, + 168 + ], + "type": "text", + "content": " would promote " + }, + { + "bbox": [ + 304, + 71, + 545, + 168 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 71, + 545, + 168 + ], + "type": "text", + "content": " larger, while a larger " + }, + { + "bbox": [ + 304, + 71, + 545, + 168 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 71, + 545, + 168 + ], + "type": "text", + "content": " would further promote " + }, + { + "bbox": [ + 304, + 71, + 545, + 168 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 304, + 71, + 545, + 168 + ], + "type": "text", + "content": " larger. Finally, the output of model would be controlled by a few sparse blocks. Conversely, DropKey avoids suffering local-bias by introducing the parameter " + }, + { + "bbox": [ + 304, + 71, + 545, + 168 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 71, + 545, + 168 + ], + "type": "text", + "content": " to enforce distribution " + }, + { + "bbox": [ + 304, + 71, + 545, + 168 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 304, + 71, + 545, + 168 + ], + "type": "text", + "content": " to be smoother." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 170, + 404, + 182 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 170, + 404, + 182 + ], + "spans": [ + { + "bbox": [ + 305, + 170, + 404, + 182 + ], + "type": "text", + "content": "3.2. Implementation" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 183, + 545, + 351 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 183, + 545, + 351 + ], + "spans": [ + { + "bbox": [ + 304, + 183, + 545, + 351 + ], + "type": "text", + "content": "What to drop? Different from DropAttention, we integrate Dropout and re-normalize into one stage by dropping key rather than weight. At each training iteration, DropKey masks a certain rate of keys of the input key map by random. It is worth noting that we generate masked key map for each query, instead of sharing the same masked key map for all query vectors. Specifically, given the query " + }, + { + "bbox": [ + 304, + 183, + 545, + 351 + ], + "type": "inline_equation", + "content": "Q \\in \\mathbb{R}^{n_h n_w \\times n_c}" + }, + { + "bbox": [ + 304, + 183, + 545, + 351 + ], + "type": "text", + "content": ", key " + }, + { + "bbox": [ + 304, + 183, + 545, + 351 + ], + "type": "inline_equation", + "content": "K \\in \\mathbb{R}^{n_h n_w \\times n_c}" + }, + { + "bbox": [ + 304, + 183, + 545, + 351 + ], + "type": "text", + "content": " and value " + }, + { + "bbox": [ + 304, + 183, + 545, + 351 + ], + "type": "inline_equation", + "content": "V \\in \\mathbb{R}^{n_h n_w \\times n_c}" + }, + { + "bbox": [ + 304, + 183, + 545, + 351 + ], + "type": "text", + "content": " of a feature map, it first computes the dot products of the query with all keys and divide each by scaling factor " + }, + { + "bbox": [ + 304, + 183, + 545, + 351 + ], + "type": "inline_equation", + "content": "scale = \\sqrt{n_c}" + }, + { + "bbox": [ + 304, + 183, + 545, + 351 + ], + "type": "text", + "content": ". Subsequently, we randomly generate a mask matrix " + }, + { + "bbox": [ + 304, + 183, + 545, + 351 + ], + "type": "inline_equation", + "content": "D \\in \\mathbb{R}^{1 \\times (n_h n_w \\times n_h n_w)}" + }, + { + "bbox": [ + 304, + 183, + 545, + 351 + ], + "type": "text", + "content": " with drop ratio " + }, + { + "bbox": [ + 304, + 183, + 545, + 351 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 183, + 545, + 351 + ], + "type": "text", + "content": " to enforce some elements of the similarity matrix to be -inf. The formulation of " + }, + { + "bbox": [ + 304, + 183, + 545, + 351 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 183, + 545, + 351 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 347, + 356, + 545, + 378 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 356, + 545, + 378 + ], + "spans": [ + { + "bbox": [ + 347, + 356, + 545, + 378 + ], + "type": "interline_equation", + "content": "d _ {j} = \\left\\{ \\begin{array}{c c} 0 & \\text {w i t h p r o b a b i l i t y} 1 - d \\\\ - \\infty & \\text {w i t h p r o b a b i l i t y} d \\end{array} \\right. \\tag {12}", + "image_path": "c953f9c23939c7618b1c1ac2915a6bc7e4380e9e58206d51f86d0f200e31777f.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 384, + 545, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 384, + 545, + 421 + ], + "spans": [ + { + "bbox": [ + 304, + 384, + 545, + 421 + ], + "type": "text", + "content": "Finally, the attention weight matrix is computed by given masked similarity matrix as input. Formally, we compute the outputs of a patch as:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 397, + 427, + 545, + 454 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 397, + 427, + 545, + 454 + ], + "spans": [ + { + "bbox": [ + 397, + 427, + 545, + 454 + ], + "type": "interline_equation", + "content": "o = \\sum_ {j = 1} ^ {n _ {h} n _ {w}} p _ {j} v _ {j} \\tag {13}", + "image_path": "4be012225e0ed380d8a82291b5296ab0dbdd6db59059579fea3067b24266d5a3.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 369, + 455, + 545, + 490 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 369, + 455, + 545, + 490 + ], + "spans": [ + { + "bbox": [ + 369, + 455, + 545, + 490 + ], + "type": "interline_equation", + "content": "p _ {j} = \\frac {\\exp \\left(d _ {j} + \\frac {q k _ {j} ^ {T}}{\\text {s c a l e}}\\right)}{\\sum_ {j = 1} ^ {n _ {h} n _ {w}} \\exp \\left(d _ {j} + \\frac {q k _ {j} ^ {T}}{\\text {s c a l e}}\\right)} \\tag {14}", + "image_path": "8bf5105acbdc4ddfedffe933e6d6efc25d0b9ad512869e5c36c5585badfae2c9.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 492, + 545, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 492, + 545, + 577 + ], + "spans": [ + { + "bbox": [ + 304, + 492, + 545, + 577 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 492, + 545, + 577 + ], + "type": "inline_equation", + "content": "q_{i}, k_{j}, v_{j}" + }, + { + "bbox": [ + 304, + 492, + 545, + 577 + ], + "type": "text", + "content": " denote query of " + }, + { + "bbox": [ + 304, + 492, + 545, + 577 + ], + "type": "inline_equation", + "content": "i^{th}" + }, + { + "bbox": [ + 304, + 492, + 545, + 577 + ], + "type": "text", + "content": " patch, key of " + }, + { + "bbox": [ + 304, + 492, + 545, + 577 + ], + "type": "inline_equation", + "content": "j^{th}" + }, + { + "bbox": [ + 304, + 492, + 545, + 577 + ], + "type": "text", + "content": " patch, value of " + }, + { + "bbox": [ + 304, + 492, + 545, + 577 + ], + "type": "inline_equation", + "content": "j^{th}" + }, + { + "bbox": [ + 304, + 492, + 545, + 577 + ], + "type": "text", + "content": " patch. It is not difficult to find that Equ (13) and Equ (14) is the same equivalent form of Equ (1) and Equ (2). In particular, as shown in Algorithm 1, we only need to add two lines of code to pure attention to implement DropKey. Obviously, compared with Dropout, DropKey only changes the position of introducing mask." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 582, + 545, + 726 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 726 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 726 + ], + "type": "text", + "content": "Scheduled Drop Ratio Vision transformer always consists of few self-attention blocks to gradually learn high-dimensional features. Generally, early layers operates low-level visual features and deeper layers aim to model spatially coarse but complex information. Hence, we attempt to set smaller drop ratio for deeper layers to avoid missing important objects-relevant information. Specifically, instead of stochastically dropping with some fixed probability in Dropout, we gradually decrease number of dropped keys over the layers during training stage. We find that this scheduled drop ratio not only work well for DropKey, but also significantly improves the performance of Dropout." + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "text", + "content": "22703" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "code", + "bbox": [ + 69, + 103, + 298, + 209 + ], + "blocks": [ + { + "bbox": [ + 48, + 83, + 223, + 96 + ], + "lines": [ + { + "bbox": [ + 48, + 83, + 223, + 96 + ], + "spans": [ + { + "bbox": [ + 48, + 83, + 223, + 96 + ], + "type": "text", + "content": "Algorithm 1 Attention with DropKey code" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 69, + 103, + 298, + 209 + ], + "lines": [ + { + "bbox": [ + 69, + 103, + 298, + 209 + ], + "spans": [ + { + "bbox": [ + 69, + 103, + 298, + 209 + ], + "type": "text", + "content": "N: token number, D: token dim\n# Q: query (N, D), K: key (N, D), V: value (N, D)\n# use_DropKey: whether use DropKey\n# mask_ratio: ratio to mask\ndef Attention(Q, K, V, use_DropKey, mask_ratio)\n attn = (Q * (Q.shape[1] ** -0.5)) @ K.transpose(-2, -1)\n # use DropKey as regularizer\n if use_DropKey == True:\n m_r = torch.ones_like(attn) * mask_ratio\n attn = attn + torchBernoulli(m_r) * -1e12\n attn = attn softmax(dim=-1)\n x = attn @ V\n return x" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "code_body" + } + ], + "index": 2, + "sub_type": "algorithm" + }, + { + "type": "image", + "bbox": [ + 333, + 77, + 394, + 144 + ], + "blocks": [ + { + "bbox": [ + 333, + 77, + 394, + 144 + ], + "lines": [ + { + "bbox": [ + 333, + 77, + 394, + 144 + ], + "spans": [ + { + "bbox": [ + 333, + 77, + 394, + 144 + ], + "type": "image", + "image_path": "04e29115b96e251ad71d1fcb331528b0c3c249cd019044fef878d7449be8aeb7.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 321, + 154, + 544, + 210 + ], + "lines": [ + { + "bbox": [ + 321, + 154, + 544, + 210 + ], + "spans": [ + { + "bbox": [ + 321, + 154, + 544, + 210 + ], + "type": "text", + "content": "Figure 2. Mask sampling in DropKey, DropKey-Block and DropKey-Cross. The yellow patches are used as attend key to interact with a query and blue patches are dropped. Red symbol denotes the valid seed and the window size of DropKey-Block and DropKey-Cross is 3 and 1, respectively." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 402, + 77, + 463, + 146 + ], + "blocks": [ + { + "bbox": [ + 402, + 77, + 463, + 146 + ], + "lines": [ + { + "bbox": [ + 402, + 77, + 463, + 146 + ], + "spans": [ + { + "bbox": [ + 402, + 77, + 463, + 146 + ], + "type": "image", + "image_path": "5026f1478ccf11a203bf6e0edd3c4ada679b32bbbac072a416323326e9eddbaf.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 471, + 77, + 533, + 146 + ], + "blocks": [ + { + "bbox": [ + 471, + 77, + 533, + 146 + ], + "lines": [ + { + "bbox": [ + 471, + 77, + 533, + 146 + ], + "spans": [ + { + "bbox": [ + 471, + 77, + 533, + 146 + ], + "type": "image", + "image_path": "b5a915e33b9c77cc39d6fedf59d62501c0b500fd571d9053c4ed886cdb22268e.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 227, + 289, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 227, + 289, + 384 + ], + "spans": [ + { + "bbox": [ + 46, + 227, + 289, + 384 + ], + "type": "text", + "content": "Structured DropKey Although structured drop has been dally explored in convolution network, there is no work to study the impact of structured drop on vision transformer. In this section, we implement two structured forms of DropKey which are named DropKey-Block and DropKey-Cross (see Figure 2). For DropKey-Block, inspired by DropBlock [10], we drop contiguous patches in a square-shape window of feature maps. Actually, we re-set drop ratio " + }, + { + "bbox": [ + 46, + 227, + 289, + 384 + ], + "type": "inline_equation", + "content": "d_{block}" + }, + { + "bbox": [ + 46, + 227, + 289, + 384 + ], + "type": "text", + "content": " for each patch as: " + }, + { + "bbox": [ + 46, + 227, + 289, + 384 + ], + "type": "inline_equation", + "content": "d_{block} = \\frac{d}{s^2}\\frac{n_h n_w}{(n_h - s + 1)(n_w - s + 1)}" + }, + { + "bbox": [ + 46, + 227, + 289, + 384 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 46, + 227, + 289, + 384 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 227, + 289, + 384 + ], + "type": "text", + "content": " denotes the probability of dropping a patch in DropKey. The valid seed region is " + }, + { + "bbox": [ + 46, + 227, + 289, + 384 + ], + "type": "inline_equation", + "content": "(n_h - s + 1)(n_w - s + 1)" + }, + { + "bbox": [ + 46, + 227, + 289, + 384 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 46, + 227, + 289, + 384 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 227, + 289, + 384 + ], + "type": "text", + "content": " denotes the size of window and " + }, + { + "bbox": [ + 46, + 227, + 289, + 384 + ], + "type": "inline_equation", + "content": "n_h, n_w" + }, + { + "bbox": [ + 46, + 227, + 289, + 384 + ], + "type": "text", + "content": " denotes height, weight of feature map." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 384, + 287, + 505 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 384, + 287, + 505 + ], + "spans": [ + { + "bbox": [ + 46, + 384, + 287, + 505 + ], + "type": "text", + "content": "The cross-shape window attention is proved to achieve strong modeling capability [5] which also indicates the information in this structure is correlated. For DropKeyCross, we discard features in a cross window to prevent information flow through self-attention. In our implementation, we drop the rows and columns of valid seed and re-set the drop ratio " + }, + { + "bbox": [ + 46, + 384, + 287, + 505 + ], + "type": "inline_equation", + "content": "d_{cross}" + }, + { + "bbox": [ + 46, + 384, + 287, + 505 + ], + "type": "text", + "content": " for each patch as: " + }, + { + "bbox": [ + 46, + 384, + 287, + 505 + ], + "type": "inline_equation", + "content": "d_{cross} = \\frac{d}{s(n_h + n_w - s)}\\frac{n_hn_w}{(n_h - s + 1)(n_w - s + 1)}" + }, + { + "bbox": [ + 46, + 384, + 287, + 505 + ], + "type": "text", + "content": ". Note that the formulations for block- and cross-version are only the approximation, because there will be some overlapped when perform drop." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 509, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 509, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 509, + 287, + 653 + ], + "type": "text", + "content": "Align Expectation As mentioned in Section 3.1, the misaligned expectations have a certain negative impact on the model, so we attempt to use two methods to align the expectation. The first one is to use Monte Carlo method to estimate " + }, + { + "bbox": [ + 46, + 509, + 287, + 653 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 509, + 287, + 653 + ], + "type": "text", + "content": ". We perform multiple random drop and calculate the attention weight matrix after each drop operation. Finally, the average of calculated multiple weight matrices is applied as the input for the next step. For the second one, we take the inspiration from [9] and propose to finetune the model without DropKey, as an extra stage after DropKey training. We experimentally verify that the second strategy performs better with experiment in Section 4.1.1." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 657, + 128, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 657, + 128, + 670 + ], + "spans": [ + { + "bbox": [ + 47, + 657, + 128, + 670 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "content": "We conduct experiments on three tasks, image classification, object detection, human-object interaction detection and human mesh recovery, to show the efficacy and gener" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 227, + 497, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 227, + 497, + 239 + ], + "spans": [ + { + "bbox": [ + 305, + 227, + 497, + 239 + ], + "type": "text", + "content": "alizability of our DropKey for improving ViTs." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 239, + 423, + 251 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 239, + 423, + 251 + ], + "spans": [ + { + "bbox": [ + 306, + 239, + 423, + 251 + ], + "type": "text", + "content": "4.1. Image Classification" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 252, + 545, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 252, + 545, + 348 + ], + "spans": [ + { + "bbox": [ + 304, + 252, + 545, + 348 + ], + "type": "text", + "content": "Datasets We conduct the following experiments with T2T [34], VOLO [35], CeiT [33] and DeiT [27] for image classification on CIFAR10 [13], CIFAR100 [15] and ImageNet [4]. a) We conduct the ablation study to demonstrate the effects of introducing modified DropAttention to three T2T and three VOLO backbone architectures on CIFAR10 and CIFAR100. b) We validate the modified DropAttention by training T2T and VOLO from scratch on ImageNet." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 350, + 545, + 457 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 350, + 545, + 457 + ], + "spans": [ + { + "bbox": [ + 304, + 350, + 545, + 457 + ], + "type": "text", + "content": "Training By default, models are trained with random initialization on all datasets. Due to the missing training setting for T2T [34] and VOLO [35], we conduct grid search on learning rate and epoch number to make the vanilla backbones achieve the best performance. All implementation specifics can be seen in Appendix. For ImageNet, our training recipe follows [34, 35]. Specifically, we set 50 epochs and keep learning rate as " + }, + { + "bbox": [ + 304, + 350, + 545, + 457 + ], + "type": "inline_equation", + "content": "10^{-5}" + }, + { + "bbox": [ + 304, + 350, + 545, + 457 + ], + "type": "text", + "content": " for finetune stage for all datasets." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 460, + 503, + 471 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 460, + 503, + 471 + ], + "spans": [ + { + "bbox": [ + 305, + 460, + 503, + 471 + ], + "type": "text", + "content": "4.1.1 Ablations on CIFAR10 and CIFAR100" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 474, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 545, + 713 + ], + "type": "text", + "content": "Does DropKey boost generalization? T2T [34] and VOLO [35] are the widely used vision transformer architecture for image recognition. However, the DropAttention applied in these architectures does not apply re-normalize operation. In the following experiments, we plug in the DropKey to the family of T2T/VOLO and compare results with the version that use Dropout. The results in Figure 3 indicate DropKey can consistently increase the performance of various architectures on CIFAR10 and CIFAR100. On CIFAR100 with T2T19, for example, DropKey gains " + }, + { + "bbox": [ + 304, + 474, + 545, + 713 + ], + "type": "inline_equation", + "content": "1.7\\%" + }, + { + "bbox": [ + 304, + 474, + 545, + 713 + ], + "type": "text", + "content": " improvement for the adaptive coefficient yields further improvement. Additionally, we found that drop ratio is also an essential factor affecting performance. Take T2T14 with DropKey as an example, the accuracy initially increases with increasing drop ratio until it achieves its peak accuracy of " + }, + { + "bbox": [ + 304, + 474, + 545, + 713 + ], + "type": "inline_equation", + "content": "79.2\\%" + }, + { + "bbox": [ + 304, + 474, + 545, + 713 + ], + "type": "text", + "content": " at drop ratio " + }, + { + "bbox": [ + 304, + 474, + 545, + 713 + ], + "type": "inline_equation", + "content": "= 0.3" + }, + { + "bbox": [ + 304, + 474, + 545, + 713 + ], + "type": "text", + "content": " and it declines upon further increase of the drop ratio. These suggest that the introduction of DropKey would be beneficial to the network for avoiding suffering overfits. However, a larger drop ratio can lead to an inability to capture valid information about the object." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 32, + 103, + 42, + 209 + ], + "type": "aside_text", + "angle": 270, + "lines": [ + { + "bbox": [ + 32, + 103, + 42, + 209 + ], + "spans": [ + { + "bbox": [ + 32, + 103, + 42, + 209 + ], + "type": "text", + "content": "10 98 65432-" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22704" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 68, + 170, + 178 + ], + "blocks": [ + { + "bbox": [ + 47, + 68, + 170, + 178 + ], + "lines": [ + { + "bbox": [ + 47, + 68, + 170, + 178 + ], + "spans": [ + { + "bbox": [ + 47, + 68, + 170, + 178 + ], + "type": "image", + "image_path": "4390224b4a38e64389d33ef70d386fcf2af52057faffc7bdf012468f13febc0a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 134, + 187, + 457, + 198 + ], + "lines": [ + { + "bbox": [ + 134, + 187, + 457, + 198 + ], + "spans": [ + { + "bbox": [ + 134, + 187, + 457, + 198 + ], + "type": "text", + "content": "Figure 3. Comparison of models with Dropout or DropKey on CIFAR10 and CIFAR100." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 173, + 68, + 295, + 178 + ], + "blocks": [ + { + "bbox": [ + 173, + 68, + 295, + 178 + ], + "lines": [ + { + "bbox": [ + 173, + 68, + 295, + 178 + ], + "spans": [ + { + "bbox": [ + 173, + 68, + 295, + 178 + ], + "type": "image", + "image_path": "f3ca36e684c55adcdd188f20bbea94c29c397e605edfb0abce6db98f9a5f6b25.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 299, + 68, + 421, + 178 + ], + "blocks": [ + { + "bbox": [ + 299, + 68, + 421, + 178 + ], + "lines": [ + { + "bbox": [ + 299, + 68, + 421, + 178 + ], + "spans": [ + { + "bbox": [ + 299, + 68, + 421, + 178 + ], + "type": "image", + "image_path": "312dada1f8b5286e0b902490b866ca0c921360795b393104e9bba906c2d5f84e.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 425, + 68, + 547, + 178 + ], + "blocks": [ + { + "bbox": [ + 425, + 68, + 547, + 178 + ], + "lines": [ + { + "bbox": [ + 425, + 68, + 547, + 178 + ], + "spans": [ + { + "bbox": [ + 425, + 68, + 547, + 178 + ], + "type": "image", + "image_path": "ae50168f0aa9b51bc460ca4b02a7deda2ceae1dd4cf06ba591b8440b9393a452.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 200, + 287, + 224 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 200, + 287, + 224 + ], + "spans": [ + { + "bbox": [ + 46, + 200, + 287, + 224 + ], + "type": "text", + "content": "Similar to DropKey, the performance of Dropout is also related to drop ratio." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 228, + 289, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 228, + 289, + 456 + ], + "spans": [ + { + "bbox": [ + 46, + 228, + 289, + 456 + ], + "type": "text", + "content": "How does the choice of scheduled strategy of drop ratio impact accuracy? The ablation in Table 1 analyzes the accuracy of DropKey by adjusting the strategy of setting drop ratio. Specifically, we validate three strategy as follows: a) Constant: drop ratio is constant over self attention layers. b) Scheduled" + }, + { + "bbox": [ + 46, + 228, + 289, + 456 + ], + "type": "inline_equation", + "content": "\\uparrow" + }, + { + "bbox": [ + 46, + 228, + 289, + 456 + ], + "type": "text", + "content": ": drop ratio is linearly increased over self attention layers. c) Scheduled" + }, + { + "bbox": [ + 46, + 228, + 289, + 456 + ], + "type": "inline_equation", + "content": "\\downarrow" + }, + { + "bbox": [ + 46, + 228, + 289, + 456 + ], + "type": "text", + "content": ": drop ratio is linearly decreased over self attention layers. Firstly, we find that Scheduled" + }, + { + "bbox": [ + 46, + 228, + 289, + 456 + ], + "type": "inline_equation", + "content": "\\downarrow" + }, + { + "bbox": [ + 46, + 228, + 289, + 456 + ], + "type": "text", + "content": " outperform Constant whether using re-normalize or not. Secondly, introducing drop ratio with Scheduled" + }, + { + "bbox": [ + 46, + 228, + 289, + 456 + ], + "type": "inline_equation", + "content": "\\uparrow" + }, + { + "bbox": [ + 46, + 228, + 289, + 456 + ], + "type": "text", + "content": " would seriously affect the performance of the model and even perform worse than the pure vision transformer. This phenomenon is in line with our expectation, since deeper layers often contain high-level semantic information which is essential to perform classification. A large drop ratio in deep layer will increase the risk of losing important features which would make model difficult to converge to a generalized solution. Hence, we set drop ratio with Scheduled" + }, + { + "bbox": [ + 46, + 228, + 289, + 456 + ], + "type": "inline_equation", + "content": "\\downarrow" + }, + { + "bbox": [ + 46, + 228, + 289, + 456 + ], + "type": "text", + "content": " in all following experiments." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 460, + 287, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 460, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 460, + 287, + 581 + ], + "type": "text", + "content": "Is Dropkey helpful to capture global information? The contribution of DropKey is to generate a smoother attention weight matrix to encourage models to focus on global features. Class token has been proved to be effective in aggregating the information of the whole image, so we measure the smoothness of the attention distribution by calculating the entropy of its attention weight vector. Specifically, we define the entropy of the attention vector of class token as follows " + }, + { + "bbox": [ + 46, + 460, + 287, + 581 + ], + "type": "inline_equation", + "content": "E_{i} = -\\sum_{j}p_{j}^{i}\\log p_{j}^{i}" + }, + { + "bbox": [ + 46, + 460, + 287, + 581 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 46, + 460, + 287, + 581 + ], + "type": "inline_equation", + "content": "p_j^i" + }, + { + "bbox": [ + 46, + 460, + 287, + 581 + ], + "type": "text", + "content": " denotes the attention weight of " + }, + { + "bbox": [ + 46, + 460, + 287, + 581 + ], + "type": "inline_equation", + "content": "j^{th}" + }, + { + "bbox": [ + 46, + 460, + 287, + 581 + ], + "type": "text", + "content": " attending patch in " + }, + { + "bbox": [ + 46, + 460, + 287, + 581 + ], + "type": "inline_equation", + "content": "i^{th}" + }, + { + "bbox": [ + 46, + 460, + 287, + 581 + ], + "type": "text", + "content": " head." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "content": "Note that a small entropy denotes that this head focuses on sparse patches. For convenience, the mean of entropy of multi-head as " + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "content": " is reported in Figure 4. Clearly, it reads that while both Dropout and DropKey are able to improve the value of entropy, the improvement by DropKey is more significant. Meanwhile, when the drop rate increases, the entropy increase accordingly. In addition, to further verify the necessity of the adaptive coefficient for capturing general global information, we visualize the attention map (Figure 5) from class token in the last transformer layer. Obviously, the model with DropKey smoothly assigns attention" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 200, + 545, + 247 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 200, + 545, + 247 + ], + "spans": [ + { + "bbox": [ + 304, + 200, + 545, + 247 + ], + "type": "text", + "content": "weight to the area related to the instance. Finally, we further verify that our method can alleviate local-bias via the fact that transformers with DropKey perform robustly in occluded scenarios." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 251, + 546, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 251, + 546, + 418 + ], + "spans": [ + { + "bbox": [ + 304, + 251, + 546, + 418 + ], + "type": "text", + "content": "Is structured drop is useful to vision transformer? In this section, we analyze whether structured masking is useful for vision transformer via DropKey-Block and DropKey-Cross. Specifically, we swept over window size from 3 to 5 for DropKey-Block and from 1 to 3 for DropKey-Cross. Compared with the DropKey, the structured drop degrade the performance of the model in all case and classification accuracy will decrease with the further increase of the window size. One possible reason for this phenomenon is that a larger drop ratio in shallow transformer layer results in losing vital information of object. However, a larger drop ratio is the key to avoid overfit to low-level feature. Therefore, we encourage set a larger drop ratio rather than the introduction of structured drop." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 422, + 547, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 422, + 547, + 613 + ], + "spans": [ + { + "bbox": [ + 304, + 422, + 547, + 613 + ], + "type": "text", + "content": "How does align expectations impact accuracy? As discussed above, the mismatched expectations problem arises when directly use trained model with DropKey to test. Herein, to address above issue, we explore the impact of two methods, Monte Carlo and finetune, on the performance of network. The results in Table 3 indicates that accuracy can be improved regardless of the expectation alignment operation. Additionally, the accuracy of Monte Carlo increases with increasing sampling iterations. However, huge sampling iterations will lead to unacceptable computational cost. To fairly compare with Dropout, we also finetune it with the same training hyper-parameters as DropKey and then note that finetune only brings insignificant performance improvement or even over-fitting. In conclusion, alignment expectation of training and inference stage indeed can further improve the accuracy of the model." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 616, + 485, + 628 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 616, + 485, + 628 + ], + "spans": [ + { + "bbox": [ + 305, + 616, + 485, + 628 + ], + "type": "text", + "content": "4.1.2 DropKey vs Dropout on ImageNet" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "We provide the accuracy under other different drop ratio for each backbone with DropKey on ImageNet, and contrast them with existing State of the Arts (SOTA) equipped with Dropout, including T2T, VOLO, CeiT and DeiT in Table 4. We have these findings: (1) Clearly, our DropKey obtains significant enhancement against pure backbone. Meanwhile, We note that Dropout can only bring a little boost" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22705" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 108, + 93, + 481, + 247 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 92 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 92 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 92 + ], + "type": "text", + "content": "Table 1. Comparison of models with Dropout or DropKey on CIFAR10 and CIFAR100 when introducing different scheduled strategy of drop ratio. The drop ratio is set as 0.3 for all models." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 108, + 93, + 481, + 247 + ], + "lines": [ + { + "bbox": [ + 108, + 93, + 481, + 247 + ], + "spans": [ + { + "bbox": [ + 108, + 93, + 481, + 247 + ], + "type": "table", + "html": "
ModelCIFAR10CIFAR100
Scheduled↑ConstantScheduled↓Scheduled↑ConstantScheduled↓
T2T14 [34] + Dropout96.796.997.277.077.878.4
T2T14 [34] + DropKey97.097.497.677.278.679.2
T2T19 [34] + Dropout96.697.197.477.378.178.5
T2T19 [34] + DropKey97.197.297.978.078.480.1
T2T24 [34] + Dropout96.497.097.576.777.378.2
T2T24 [34] + DropKey96.697.297.776.978.379.3
VOLOd1 [35] + Dropout95.896.496.677.378.279.0
VOLOd1 [35] + DropKey96.296.797.178.178.679.6
VOLOd2 [35] + Dropout95.696.196.477.078.479.0
VOLOd2 [35] + DropKey95.796.697.077.779.079.9
VOLOd3 [35] + Dropout96.096.396.677.177.978.5
VOLOd3 [35] + DropKey96.296.496.977.478.178.7
", + "image_path": "d1b555ff08608db23690e6bcc78a1ae7c43618413ea20db739033245bff8cde3.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 74, + 250, + 248, + 358 + ], + "blocks": [ + { + "bbox": [ + 74, + 250, + 248, + 358 + ], + "lines": [ + { + "bbox": [ + 74, + 250, + 248, + 358 + ], + "spans": [ + { + "bbox": [ + 74, + 250, + 248, + 358 + ], + "type": "image", + "image_path": "f0ed617387f35bd25e49f0fef5a07d4b870cc4320c6b5a40a8ca1b8dadede16f.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 48, + 369, + 271, + 392 + ], + "lines": [ + { + "bbox": [ + 48, + 369, + 271, + 392 + ], + "spans": [ + { + "bbox": [ + 48, + 369, + 271, + 392 + ], + "type": "text", + "content": "Figure 4. The histogram of entropy on CIFAR100. dr denotes drop ratio." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 57, + 420, + 276, + 485 + ], + "blocks": [ + { + "bbox": [ + 47, + 396, + 286, + 418 + ], + "lines": [ + { + "bbox": [ + 47, + 396, + 286, + 418 + ], + "spans": [ + { + "bbox": [ + 47, + 396, + 286, + 418 + ], + "type": "text", + "content": "Table 2. Comparison of different structured drop on CIFAR100. " + }, + { + "bbox": [ + 47, + 396, + 286, + 418 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 47, + 396, + 286, + 418 + ], + "type": "text", + "content": " denotes window size and drop ratio is set as 0.3 for all models." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 57, + 420, + 276, + 485 + ], + "lines": [ + { + "bbox": [ + 57, + 420, + 276, + 485 + ], + "spans": [ + { + "bbox": [ + 57, + 420, + 276, + 485 + ], + "type": "table", + "html": "
ModelRandomBlockCross
s=3s=5s=1s=3
T2T14 [34] + Dropout78.478.177.177.976.8
T2T14 [34] + DropKey79.278.777.578.677.4
VOLOd1 [35] + Dropout78.678.076.777.676.4
VOLOd1 [35] + DropKey79.278.577.578.377.1
", + "image_path": "ac0765edfb26589582004ecd6965a731c72eced219bd00003c1280feee798f94.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 63, + 522, + 269, + 588 + ], + "blocks": [ + { + "bbox": [ + 46, + 489, + 287, + 521 + ], + "lines": [ + { + "bbox": [ + 46, + 489, + 287, + 521 + ], + "spans": [ + { + "bbox": [ + 46, + 489, + 287, + 521 + ], + "type": "text", + "content": "Table 3. Comparison of models w/ or w/o Align Expectations on CIFAR100. Pure denotes the model without align expectation and drop ratio is set as 0.3 for all models." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 63, + 522, + 269, + 588 + ], + "lines": [ + { + "bbox": [ + 63, + 522, + 269, + 588 + ], + "spans": [ + { + "bbox": [ + 63, + 522, + 269, + 588 + ], + "type": "table", + "html": "
ModelPurew/ Monte Carlow/ Finetune
20006000
T2T14 [34] + Dropout78.4--78.4
T2T14 [34] + DropKey78.878.979.179.2
T2T19 [34] + Dropout78.5--78.6
T2T19 [34] + DropKey79.379.580.280.1
", + "image_path": "8848e54970b536436476913988fc617479fb2f3c154701272cf2b1f0e804514f.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": "to backbones and it even would degrade the performance of the model in some cases (eg. T2T14, CeiT-T and DeiT-B). This indicates that the adaptive smoothing operator is more helpful to encourage the model to capture general information in large-scale datasets. (2) Compare to lightweight models, heavyweight often need the larger drop ratio to achieve a remarkable boost. For T2T14 and VOLOd1, the best accuracy is obtained under the dr=0.05. Instead, T2T19 and VOLOd2 achieve the best accuracy when dr=0.1, which suggests heavyweight models adopt a larger drop ratio to" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 284, + 249, + 526, + 370 + ], + "blocks": [ + { + "bbox": [ + 284, + 249, + 526, + 370 + ], + "lines": [ + { + "bbox": [ + 284, + 249, + 526, + 370 + ], + "spans": [ + { + "bbox": [ + 284, + 249, + 526, + 370 + ], + "type": "image", + "image_path": "dc7f74540448bd734f045d228aab8399d04e23103719791404df2be8c315270e.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 334, + 379, + 476, + 390 + ], + "lines": [ + { + "bbox": [ + 334, + 379, + 476, + 390 + ], + "spans": [ + { + "bbox": [ + 334, + 379, + 476, + 390 + ], + "type": "text", + "content": "Figure 5. Visualization on CIFAR100." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 399, + 384, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 399, + 384, + 410 + ], + "spans": [ + { + "bbox": [ + 306, + 399, + 384, + 410 + ], + "type": "text", + "content": "prevent overfitting." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 410, + 455, + 422 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 410, + 455, + 422 + ], + "spans": [ + { + "bbox": [ + 306, + 410, + 455, + 422 + ], + "type": "text", + "content": "4.2. Object Detection in COCO" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 423, + 545, + 614 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 423, + 545, + 614 + ], + "spans": [ + { + "bbox": [ + 304, + 423, + 545, + 614 + ], + "type": "text", + "content": "In this section, we verify the generalizability and effectiveness of DropKey for object detection on COCO dataset [19]. We apply DETR [1] framework for the experiments. Specifically, DETR is composed of the backbone, encoder and decoder. We followed the model architecture, anchor definition and training recipe in [1] to build DETR+Dropout and DETR+DropKey. In Table 5, we report the results of DETR [1] with Dropout or DropKey in terms of AP. It can be seen that, our DropKey significantly outperforms existing Dropout. In detail, DropKey achieve " + }, + { + "bbox": [ + 304, + 423, + 545, + 614 + ], + "type": "inline_equation", + "content": "+0.7" + }, + { + "bbox": [ + 304, + 423, + 545, + 614 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 423, + 545, + 614 + ], + "type": "inline_equation", + "content": "+1.1" + }, + { + "bbox": [ + 304, + 423, + 545, + 614 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 423, + 545, + 614 + ], + "type": "inline_equation", + "content": "+0.4" + }, + { + "bbox": [ + 304, + 423, + 545, + 614 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 423, + 545, + 614 + ], + "type": "inline_equation", + "content": "+0.3" + }, + { + "bbox": [ + 304, + 423, + 545, + 614 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 423, + 545, + 614 + ], + "type": "inline_equation", + "content": "+0.8" + }, + { + "bbox": [ + 304, + 423, + 545, + 614 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 423, + 545, + 614 + ], + "type": "inline_equation", + "content": "+0.7" + }, + { + "bbox": [ + 304, + 423, + 545, + 614 + ], + "type": "text", + "content": " higher AP than the Dropout, which is regarded as a remarkable boost considering the challenge on this benchmark. Another observation is that large objects benefit more from DropKey than small objects. These results suggest that DropKey has the advantage over Dropout." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 616, + 545, + 640 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 616, + 545, + 640 + ], + "spans": [ + { + "bbox": [ + 306, + 616, + 545, + 640 + ], + "type": "text", + "content": "4.3. Human-Object Interaction Detection in HICODET" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 642, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 715 + ], + "type": "text", + "content": "Since the task of scene graph and relation understanding is quite sensitive to global context learning, so we also verify the effectiveness of DropKey in QPIC [26] for Human-Object Interaction Detection in HICO-DET [2]. QPIC is a transformer-based feature extractor that can effectively aggregate contextually important information. We respec" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "22706" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 118, + 83, + 474, + 256 + ], + "blocks": [ + { + "bbox": [ + 117, + 71, + 474, + 82 + ], + "lines": [ + { + "bbox": [ + 117, + 71, + 474, + 82 + ], + "spans": [ + { + "bbox": [ + 117, + 71, + 474, + 82 + ], + "type": "text", + "content": "Table 4. Comparisons on backbones with Dropout or DropKey on ImageNet. dr denotes drop ratio." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 118, + 83, + 474, + 256 + ], + "lines": [ + { + "bbox": [ + 118, + 83, + 474, + 256 + ], + "spans": [ + { + "bbox": [ + 118, + 83, + 474, + 256 + ], + "type": "table", + "html": "
ModelTop-1ModelTop-1
T2T14 [34]81.76 ± 0.05VOLOd1 [35]84.27 ± 0.12
T2T14 [34] + Dropout(dr=0.05)81.65 ± 0.04VOLOd1 [35] + Dropout(dr=0.05)84.35 ± 0.11
T2T14 [34] + Dropout(dr=0.1)81.53 ± 0.08VOLOd1 [35] + Dropout(dr=0.1)84.31 ± 0.04
T2T14 [34] + DropKey(dr=0.05)82.04 ± 0.14VOLOd1 [35] + DropKey(dr=0.05)84.53 ± 0.03
T2T14 [34] + DropKey(dr=0.1)81.93 ± 0.09VOLOd1 [35] + DropKey(dr=0.1)84.39 ± 0.02
T2T19 [34]82.56 ± 0.09VOLOd2 [35]85.24 ± 0.05
T2T19[34] + Dropout(dr=0.05)82.63 ± 0.05VOLOd2 [35] + Dropout(dr=0.05)85.22 ± 0.08
T2T19[34] + Dropout(dr=0.1)82.68 ± 0.04VOLOd2 [35] + Dropout(dr=0.1)85.21 ± 0.03
T2T19[34] + DropKey(dr=0.05)82.71 ± 0.02VOLOd2 [35] + DropKey(dr=0.05)85.33 ± 0.12
T2T19 [34] + DropKey(dr=0.1)82.94 ± 0.04VOLOd2 [35] + DropKey(dr=0.1)85.38 ± 0.06
CeiT-T [33]81.92 ± 0.06DeiT-B [27]81.94 ± 0.02
CeiT-T [33] + Dropout(dr=0.05)81.90 ± 0.03DeiT-B [27] + Dropout(dr=0.05)81.91 ± 0.04
CeiT-T [33] + Dropout(dr=0.1)81.83 ± 0.06DeiT-B [27] + Dropout(dr=0.1)81.87 ± 0.05
CeiT-T [33] + DropKey(dr=0.05)82.14 ± 0.05DeiT-B [27] + DropKey(dr=0.05)82.23 ± 0.01
CeiT-T [33] + DropKey(dr=0.1)82.27 ± 0.06DeiT-B [27] + DropKey(dr=0.1)82.25 ± 0.08
", + "image_path": "8f6ba0c75afaff7c272600c4b510f00e9ff702c2d71fa1ad15bc9ffad4a08457.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 75, + 290, + 312, + 335 + ], + "blocks": [ + { + "bbox": [ + 52, + 259, + 536, + 281 + ], + "lines": [ + { + "bbox": [ + 52, + 259, + 536, + 281 + ], + "spans": [ + { + "bbox": [ + 52, + 259, + 536, + 281 + ], + "type": "text", + "content": "Table 5. Comparison of DETR with Dropout and DropKey on COCO validation set. Table 6. Comparison of METRO with Dropout and Dropout key on HUMBI." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 75, + 290, + 312, + 335 + ], + "lines": [ + { + "bbox": [ + 75, + 290, + 312, + 335 + ], + "spans": [ + { + "bbox": [ + 75, + 290, + 312, + 335 + ], + "type": "table", + "html": "
ModelAP\\( AP_{50} \\)\\( AP_{75} \\)\\( AP_S \\)\\( AP_M \\)\\( AP_L \\)
DETR [1]41.962.144.220.645.760.7
DETR [1] + Dropout42.262.344.320.845.961.1
DETR [1] + DropKey42.963.444.721.146.761.8
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ModelmPVE↓mPJPE↓PA-mPJPE↓
METRO [18]57.851.539.9
METRO [18] + Dropout57.951.639.7
METRO [18] + DropKey57.151.039.5
", + "image_path": "fb2cf462eaca421e51e3a11210ee61667d2f7fca52eb3a50f8212a44042d0fad.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 65, + 355, + 525, + 415 + ], + "blocks": [ + { + "bbox": [ + 162, + 342, + 430, + 354 + ], + "lines": [ + { + "bbox": [ + 162, + 342, + 430, + 354 + ], + "spans": [ + { + "bbox": [ + 162, + 342, + 430, + 354 + ], + "type": "text", + "content": "Table 7. Comparison of QPIC with Dropout and DropKey on HICO-DET." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 65, + 355, + 525, + 415 + ], + "lines": [ + { + "bbox": [ + 65, + 355, + 525, + 415 + ], + "spans": [ + { + "bbox": [ + 65, + 355, + 525, + 415 + ], + "type": "table", + "html": "
Modelfull (Default)rare (Default)non-rare (Default)full (Known object)rare (Known object)non-rare (Known object)
QPIC-ResNet101 [26] + Dropout (dr=0.1)29.9624.0331.6332.4226.0134.31
QPIC-ResNet101 [26] + Dropout (dr=0.3)30.0224.1731.7232.4926.1334.41
QPIC-ResNet101 [26] + DropKey (dr=0.3)30.8724.6332.2433.2126.6634.94
", + "image_path": "ac0a208d3cbe4ff84e99f6ca00ca1d6ede45eeeda4a5341aeec1eddb0f688536.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 423, + 287, + 530 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 423, + 287, + 530 + ], + "spans": [ + { + "bbox": [ + 46, + 423, + 287, + 530 + ], + "type": "text", + "content": "tively introduce Dropout and DropKey to both encoder and decoder in QPIC and train these models with the same training recipe as [26]. The model named \"QPIC-ResNet101 + Dropout (dr=0.1)\" is the result of our reproduction of QPIC with Schedued " + }, + { + "bbox": [ + 46, + 423, + 287, + 530 + ], + "type": "inline_equation", + "content": "\\downarrow" + }, + { + "bbox": [ + 46, + 423, + 287, + 530 + ], + "type": "text", + "content": " drop ratio (Official realization is equipped with Constant drop ratio). The experimental results in Table 7 suggest DropKey has higher performance gain on the different evaluating indicators which are consistent with our expectations." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 532, + 260, + 544 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 532, + 260, + 544 + ], + "spans": [ + { + "bbox": [ + 47, + 532, + 260, + 544 + ], + "type": "text", + "content": "4.4. Human Body Mesh Recovery in HUMBI" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "text", + "content": "We verify the efficacy of DropKey for human body mesh task on HUMBI [32]. We follow conventions to train with 294 subjects from scratch and test with 120 subjects. We use Mean Per Vetex Error (MPVE) [22], Mean Per Joint Position Error (MPJPE) [14] and Procrustes Analysis MPJPE (PA-MPJPE) [38] as metrics. We use public METRO [18] as the baseline to apply DropKey to self-attention layer and Table 6 summaries the results. we can see that DropKey consistently improves the performance for all standard metrics. Specifically, DropKey brings about 0.7, 0.5 and 0.4 on mPVE, mPJPE and PA-mPJPE, respectively, while Dropout only boosts 0.2 performance on one metric. These results further verify the generalizability of DropKey as well as its superiority over vanilla dropout." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 422, + 378, + 434 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 422, + 378, + 434 + ], + "spans": [ + { + "bbox": [ + 306, + 422, + 378, + 434 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 434, + 545, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 434, + 545, + 649 + ], + "spans": [ + { + "bbox": [ + 304, + 434, + 545, + 649 + ], + "type": "text", + "content": "In this paper, we explore the drop unit, drop schedule and structured necessity of the dropout technique in ViT. Specifically, we propose to set Key as the drop unit, which yields a novel dropout-before-softmax scheme. We theoretically and experimentally verify that this scheme can regularize attention weights and meanwhile and keep them as a probability distribution simultaneously, helping capture vital patterns in a global manner and overcome local-bias problems that occurred to vanilla dropout. In addition, we present a new decreasing schedule for drop ratio, which stabilizes the training phase by avoiding overfittings in low-level features and maintaining sufficient high-level features. Moreover, we also experimentally show that structured dropout is not necessary for ViT. We distill the above analysis as a novel DropKey method, which plays as an improved version of dropout for ViT. Comprehensive experiments with different architectures on various vision tasks demonstrate the effectiveness of the proposed DropKey for enhancing ViTs." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 651, + 408, + 664 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 651, + 408, + 664 + ], + "spans": [ + { + "bbox": [ + 306, + 651, + 408, + 664 + ], + "type": "text", + "content": "Acknowledgements" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 665, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 712 + ], + "type": "text", + "content": "This paper is supported by the National key research and development program of China (2021YFA1000403), and the National Natural Science Foundation of China (Nos. 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IEEE transactions on pattern analysis and machine intelligence, 41(4):901-914. 8" + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "22709" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/DropMAE_ Masked Autoencoders With Spatial-Attention Dropout for Tracking Tasks/63a61ae0-513f-436f-959c-a8f318e90bde_content_list.json b/2023/DropMAE_ Masked Autoencoders With Spatial-Attention Dropout for Tracking Tasks/63a61ae0-513f-436f-959c-a8f318e90bde_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..fb21792129109689b4c965a403b02b9eacdfd371 --- /dev/null +++ b/2023/DropMAE_ Masked Autoencoders With Spatial-Attention Dropout for Tracking Tasks/63a61ae0-513f-436f-959c-a8f318e90bde_content_list.json @@ -0,0 +1,1739 @@ +[ + { + "type": "text", + "text": "DropMAE: Masked Autoencoders with Spatial-Attention Dropout for Tracking Tasks", + "text_level": 1, + "bbox": [ + 133, + 128, + 836, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Qiangqiang Wu $^{1}$ Tianyu Yang $^{2*}$ Ziquan Liu $^{1}$ Baoyuan Wu $^{4}$ Ying Shan $^{3}$ Antoni B. Chan $^{1}$ $^{1}$ Department of Computer Science, City University of Hong Kong \n $^{2}$ International Digital Economy Academy \n $^{3}$ Tencent AI Lab \n $^{4}$ School of Data Science, The Chinese University of Hong Kong, Shenzhen", + "bbox": [ + 89, + 202, + 877, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{qiangqwu2-c, ziquanliu2-c}@my.cityu.edu.hk, tianyu-yang@outlook.com wubaoyuan@cuhk.edu.cn, yingsshan@tencent.com, abchan@cityu.edu.hk", + "bbox": [ + 184, + 276, + 785, + 309 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 344, + 313, + 359 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we study masked autoencoder (MAE) pretraining on videos for matching-based downstream tasks, including visual object tracking (VOT) and video object segmentation (VOS). A simple extension of MAE is to randomly mask out frame patches in videos and reconstruct the frame pixels. However, we find that this simple baseline heavily relies on spatial cues while ignoring temporal relations for frame reconstruction, thus leading to sub-optimal temporal matching representations for VOT and VOS. To alleviate this problem, we propose DropMAE, which adaptively performs spatial-attention dropout in the frame reconstruction to facilitate temporal correspondence learning in videos. We show that our DropMAE is a strong and efficient temporal matching learner, which achieves better fin-tuning results on matching-based tasks than the ImageNet-based MAE with $2 \\times$ faster pre-training speed. Moreover, we also find that motion diversity in pre-training videos is more important than scene diversity for improving the performance on VOT and VOS. Our pre-trained DropMAE model can be directly loaded in existing ViT-based trackers for fine-tuning without further modifications. Notably, DropMAE sets new state-of-the-art performance on 8 out of 9 highly competitive video tracking and segmentation datasets. Our code and pre-trained models are available at https://github.com/jimmy-dq/DropMAE.git.", + "bbox": [ + 75, + 376, + 473, + 753 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 773, + 209, + 790 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, transformers have achieved enormous success in many research areas, such as natural language processing (NLP) [6, 22], computer vision [97] and audio generation [43, 73]. In NLP, masked autoencoding is commonly used to train large-scale generalizable NLP transformers contain-", + "bbox": [ + 75, + 800, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e7d6e014764de89d35928317174cc4c910bea04284f0e58182ea59f5a2ddc3b2.jpg", + "image_caption": [ + "Figure 1. State-of-the-art comparison on GOT-10k [39] following the one-shot protocol. Our DropTrack with the proposed DropMAE pre-training achieves state-of-the-art performance without using complicated pipelines such as online updating." + ], + "image_footnote": [], + "bbox": [ + 522, + 344, + 870, + 513 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ing billions of parameters. Inspired by the great success of self-supervised learning in NLP, recent advances [36, 89] in computer vision suggest that training large-scale vision transformers may undertake a similar trajectory with NLP. The seminal work MAE [36] reconstructs the input image from a small portion of patches. The learned representation in this masked autoencoder has been demonstrated to be effective in many computer vision tasks, such as image classification, object detection and semantic segmentation.", + "bbox": [ + 496, + 594, + 893, + 731 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In video object tracking (VOT), recently two works, SimTrack [10] and OSTrack [97], explore using an MAE pre-trained ViT model as the tracking backbone. Notably, these two trackers achieve state-of-the-art performance on existing tracking benchmarks without using complicated tracking pipelines. The key to their success is the robust pre-training weights learned by MAE on ImageNet [68]. In addition, [10, 97] also demonstrate that, for VOT, MAE unsupervised pre-training on ImageNet is more effective than supervised pre-training using class labels – this is mainly because MAE pre-training learns more fine-grained local", + "bbox": [ + 496, + 734, + 895, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding Author", + "bbox": [ + 94, + 886, + 223, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "14561", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/6530ce119ca61be6f977a4dbc61cb893fe139c97b44268ddbd165eeb23fc1924.jpg", + "image_caption": [ + "TwinMAE (Layer-6)" + ], + "image_footnote": [], + "bbox": [ + 102, + 90, + 263, + 154 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/405a66ef12c21545d00e72c09b400aa6f600b37b6b92e387998bd2c6922b47d9.jpg", + "image_caption": [ + "TwinMAE (Layer-8)" + ], + "image_footnote": [], + "bbox": [ + 264, + 90, + 421, + 154 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/60b6a096c2fc3930ccbf0ff72a45b7d1ffa1e3bb0fd00108eccd6c71e3424d8f.jpg", + "image_caption": [ + "DropMAE (Layer-6)" + ], + "image_footnote": [], + "bbox": [ + 101, + 167, + 263, + 229 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/8a1bfd9080640ba61dcd1127f2babe6185cba5793a9c23c62d4e4392c929d139.jpg", + "image_caption": [ + "DropMAE (Layer-8)", + "Figure 2. Visualization of the attention maps of the TwinMAE baseline and our DropMAE in the reconstruction of a random masked patch, which is denoted as a red bounding box in the left input frame. TwinMAE leverages the spatial cues (within the same frame) more than temporal cues (between frames) for reconstruction. Our proposed DropMAE improves the baseline by effectively alleviating co-adaptation between spatial cues in the reconstruction, focusing more on temporal cues, thus achieving better learning of temporal correspondences for VOT and VOS." + ], + "image_footnote": [], + "bbox": [ + 264, + 167, + 421, + 229 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "structures that are useful for accurate target localization required for VOT, whereas supervised training learns high-level class-related features that are invariant over appearance changes. Despite the promising performance achieved by [10,97], the MAE pre-training on ImageNet could still be sub-optimal for the tracking task due to the natural gap between images and videos, i.e., no prior temporal correspondence information can be learned in static images. However, previous tracking methods [3,42,83] have shown that temporal correspondence learning is the key in developing a robust and discriminative tracker. Thus there is an opportunity to further develop the MAE framework specifically for matching-base video tasks, such as VOT and VOS.", + "bbox": [ + 75, + 395, + 467, + 592 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "One simple way to extend MAE to videos is to randomly mask out frame patches in a video clip (i.e., video frame pairs) and then reconstruct the video clip. We denote this simple baseline as twin MAE (TwinMAE). Given a masked patch query, as illustrated in Figs. 2 & 4, we find that TwinMAE heavily relies on the spatially neighbouring patches within the same frame to reconstruct the masked patch, which implies a heavy co-adaptation of spatial cues (within-frame tokens) for reconstruction and may cause learning of sub-optimal temporal representations for matching-based downstream tasks like video object tracking and segmentation.", + "bbox": [ + 75, + 595, + 467, + 775 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address this issue with the TwinMAE baseline, we propose DropMAE specifically designed for pre-training a masked autoencoder for matching-based video downstream tasks (e.g., VOT and VOS). Our DropMAE adaptively performs spatial-attention dropout to break up co-adaptation between spatial cues (within-frame tokens) during the frame reconstruction, thus encouraging more temporal interactions and facilitating temporal correspondence learning in", + "bbox": [ + 75, + 779, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "the pre-training stage. Interestingly, we obtain several important findings with DropMAE: 1) DropMAE is an effective and efficient temporal correspondence learner, which achieves better fine-tuning results on matching-based tasks than the ImageNet-based MAE with $2 \\times$ faster pre-training speed. 2) Motion diversity in pre-training videos is more important than scene diversity for improving the performance on VOT and VOS.", + "bbox": [ + 496, + 90, + 890, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We conduct downstream task evaluation on 9 competitive VOT and VOS benchmarks, achieving state-of-the-art performance on these benchmarks. In particular, our trackers with DropMAE pre-training obtain $75.9\\%$ AO on GOT-10k, $52.7\\%$ AUC on $\\mathrm{LaSOT}_{ext}$ , $56.9\\%$ AUC on TNL2K and $92.1\\% /83.0\\%$ $\\mathcal{J}\\& \\mathcal{F}$ scores on DAVIS-16/17, w/o using complicated online updating or memory mechanisms.", + "bbox": [ + 496, + 212, + 890, + 316 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, the main contributions of our work are:", + "bbox": [ + 517, + 318, + 864, + 330 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- To the best of our knowledge, we are the first to investigate masked autoencoder video pre-training for temporal matching-based downstream tasks. Specifically, we explore various video data sources for pre-training and build a TwinMAE baseline to study its effectiveness on temporal matching tasks. Since none exists, we further build a ViT-based VOS baseline for fine-tuning.", + "- We propose DropMAE, which adaptively performs spatial-attention dropout in the frame reconstruction to facilitate effective temporal correspondence learning in videos.", + "- Our trackers with DropMAE pre-training sets new state-of-the-art performance on 8 out of 9 highly competitive video tracking and segmentation benchmarks without complicated tracking pipelines." + ], + "bbox": [ + 517, + 332, + 890, + 559 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 573, + 638, + 588 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Visual object tracking and segmentation. Given an annotated bounding box in the first frame of a test video, visual object tracking (VOT) aims to accurately predict the target's bounding boxes in the following frames. Similarly, for visual object segmentation (VOS), given an annotated binary mask in the first frame, VOS aims to predict dense target masks in the remaining frames. In the early development of VOT, correlation filter-based approaches [19, 21, 31, 37, 46, 47, 51, 53, 82, 84] are dominant trackers due to their favorable ability in modeling target appearance variation. With the development of deep learning, deep Siamese networks [70, 78] are introduced to VOT. The representative work SiamFC [3] takes template and search images as input for target localization. Based on SiamFC, many improvements have been made, e.g., scale regression [41, 42, 94], online template updating [34, 93, 99], multilevel feature fusion [29], loss design [23] and backbone design [10, 41, 97, 103]. For VOS, matching-based approaches, e.g., STM [60], AOT [96] and STCN [15], achieve promising results on existing VOS benchmarks. Recent improve", + "bbox": [ + 496, + 598, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "14562", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ments [14, 50] on online memory design further improve the previous SOTA results in VOS. Recent studies including SimTrack [10] and OSTrack [97] show that the ViT backbone [24] with MAE pre-training on ImageNet is effective for object tracking.", + "bbox": [ + 75, + 90, + 468, + 166 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Despite the great success of ViT with MAE pre-training on tracking, this static ImageNet-based pre-training still lacks temporal correspondence learning. Moreover, the developments of VOT and VOS show that learning strong temporal matching ability is essential for video tracking tasks. To the best of our best knowledge, we are the first to investigate masked autoencoder self-supervised video pretraining for tracking tasks. Our proposed DropMAE can learn reliable temporal correspondences, which we demonstrate are effective for downstream tracking tasks.", + "bbox": [ + 75, + 167, + 467, + 316 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Self-supervised Learning. Self-supervised learning has received significant interest in the past few decades. There are many manually-designed pretext tasks for pre-training, such as image colorization [100], jigsaw puzzle solving [59], future frame prediction [69, 75] and rotation prediction [33]. Contrastive learning approaches [7, 11, 25, 35, 86, 88] are the mainstream self-supervised methods in recent years. However, these methods are sensitive to the type and strength of applied data augmentation, which makes them hard to train. Inspired by masked language modeling [6, 22], masked image modeling (MIM) approaches are proposed for learning unsupervised image [36, 89] or video representations [30, 71], which have been shown to be effective for many downstream tasks including image classification, object detection and video action recognition. However, there is no specifically designed pre-training approaches for temporal matching-based task, such as VOT and VOS. In this work, we propose DropMAE to explore this direction.", + "bbox": [ + 75, + 316, + 467, + 589 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 602, + 166, + 617 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We propose a self-supervised video pre-training method to learn robust representations for temporal matching-based downstream tasks, including VOT and VOS tasks. We firstly introduce a simple extension of MAE to temporal matching representation learning from video, (TwinMAE). We then illustrate the limitations of the TwinMAE baseline and propose a spatial-attention dropout strategy to facilitate temporal correspondence learning, denoted as DropMAE. The overall pipeline of both DropMAE and TwinMAE is shown in Fig. 3. Finally, we introduce the VOT and VOS methods used for fine-tuning the downstream tasks.", + "bbox": [ + 75, + 627, + 467, + 792 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Temporal Masked Autoencoder (TwinMAE)", + "text_level": 1, + "bbox": [ + 76, + 801, + 450, + 816 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The masked autoencoder (MAE) model [36] consists of an encoder and a decoder. Its basic idea is to randomly mask out a large portion (e.g., $75\\%$ ) of patches in an image and then reconstruct the image pixels. Specifically, the encoder only takes visible patches as input for feature", + "bbox": [ + 75, + 824, + 467, + 900 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/3293ae28c6284e5210978380adb58fd2e22443cb556269346e8033a5c2f4e92d.jpg", + "image_caption": [ + "Figure 3. An illustration of our DropMAE. The proposed adaptive spatial-attention dropout (ASAD) facilitates temporal correspondence learning for temporal matching tasks. TwinMAE follows the same pipeline except that the ASAD module is not used." + ], + "image_footnote": [], + "bbox": [ + 504, + 80, + 888, + 195 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "learning, and then the decoder is input with both visible and masked patches to produce the image reconstruction. In order to adapt to downstream video matching-based tasks, one naive extension is to directly apply MAE on concatenated video frames, hoping to learn temporal matching representations from video frame pairs, which we denote as TwinMAE.", + "bbox": [ + 496, + 263, + 890, + 368 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "It should be noted that existing works [30,71] that extend MAE to video representation learning are mainly designed for the downstream task of video action recognition, where a long video clip (e.g., 16 frames) is used for reconstruction-based pre-training. To keep consistent with our downstream tasks of VOT/VOS, we follow the general training settings used in object tracking [3,97], where two frames are sampled from one video as input to TwinMAE for pre-training. This adaptation significantly reduces the computational and memory cost compared to existing video pre-training approaches [30, 71], due to the quadratic complexity of ViTs.", + "bbox": [ + 496, + 369, + 890, + 536 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Patch embedding. Firstly, we randomly sample 2 frames within a video with a predefined maximal frame gap. For each frame, we follow the vanilla ViT to divide it into non-overlapping patches. The patches extracted from the two frames are then concatenated together to form the overall patch sequence. We then randomly mask out patches in the patch sequence until a predefined mask ratio is reached. Note that we use the same mask ratio (i.e., $75\\%$ ) with the original MAE, since the information redundancy of two frames should be similar to a single image. The visible patches are embedded by linear projection [24], and the masked patches are embedded using a shared learnable mask token. All the embedded patches are added with positional embeddings [24].", + "bbox": [ + 496, + 537, + 890, + 747 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Frame identity embedding. To distinguish between the masked tokens in the same spatial location of the two frames, we use two learnable frame identity embeddings to indicate the two input frames. The corresponding frame identity embedding is added to each embedded patch.", + "bbox": [ + 496, + 750, + 890, + 824 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Autoencoder and Training. Following the autoencoding pipeline in the original MAE [36], the encoder only takes visible embedded patches as input, and the decoder is input with all the embedded patches for masked patch reconstruction. We use the same normalized pixel loss from MAE for", + "bbox": [ + 496, + 825, + 890, + 898 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "14563", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/0b86d533f9b1810228924c7f3db5c4e248b6c4922ea43cf8536348b0c01e4311.jpg", + "image_caption": [ + "Figure 4. The average within-frame and between-frame attention scores obtained by TwinMAE and DropMAE in different decoder layers. The attention score is calculated on 20 randomly sampled K400 validation videos, and is averaged on all heads and locations." + ], + "image_footnote": [], + "bbox": [ + 127, + 80, + 421, + 196 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "training the whole network architecture.", + "bbox": [ + 76, + 263, + 341, + 277 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Limitation of TwinMAE Baseline", + "text_level": 1, + "bbox": [ + 76, + 289, + 367, + 304 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The visualization of the reconstruction for our TwinMAE baseline is shown in Fig. 2. We also quantitatively compare the average within-frame and between-frame attentions during the reconstruction in Fig. 4. Interestingly, we find the TwinMAE reconstruction heavily relies on within-frame patches or spatial cues, which may lead to sub-optimal temporal representations for matching-based video tasks.", + "bbox": [ + 75, + 311, + 468, + 431 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "When only using within-frame spatial cues, the decoder will perform the reconstruction using only context information in the neighboring patches, and thus the learned encoder representations will embed context information. In contrast, when using between-frame cues, the decoder will learn to perform matching of patches between frames so as to recover the corresponding target patch in the other frame. Thus, decoding with between-frame cues will make the encoder learn representations that support temporal matching between frames. Previous works in object tracking [3, 83] also suggest that temporal correspondence learning plays a key role in developing a robust and discriminative tracker. Since TwinMAE relies more on context information, it is still suboptimal for downstream tracking tasks.", + "bbox": [ + 75, + 433, + 468, + 643 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Adaptive Spatial-Attention Dropout", + "text_level": 1, + "bbox": [ + 76, + 650, + 387, + 667 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To address issue of TwinMAE discussed in Sec. 3.2, we propose a Adaptive Spatial-Attention Dropout (ASAD) to facilitate the temporal correspondence learning in the temporal MAE. Given a query token, our basic idea is to adaptively drop a portion of its within-frame cues in order to facilitate the model to learn more reliable temporal correspondence, i.e., between-frame cues. That is, we restrict the interactions between the query token and tokens in the same frame, and encourage more interactions with tokens in the other frame, through manipulation of the computed spatial-attention in the transformer. Therefore, to minimize the reconstruction loss, the model is facilitated to learn a better temporal matching ability, which is essential in matching-based video tasks.", + "bbox": [ + 75, + 672, + 468, + 883 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Before introducing the proposed ASAD, we firstly revisit", + "bbox": [ + 96, + 885, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/62cca43fd372487f30c55ac9e42300f13a96114d6e210ccca736660ae16c2b6f.jpg", + "image_caption": [ + "Figure 5. Visualization of the temporal matching function $f_{tem}$ on an example frame pair. A large value of $f_{tem}(i)$ indicates that the $i$ -th pixel matches well to a pixel in the other frame." + ], + "image_footnote": [], + "bbox": [ + 506, + 90, + 890, + 176 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the multi-head self-attention in ViT [24]. Let $\\mathbf{z} \\in \\mathbb{R}^{N \\times D}$ be the input sequence of the two concatenated input frames, $N$ denotes the total patch number in the two frames and $D$ is the feature dimension. The standard multi-head self-attention [24] can be formulated as:", + "bbox": [ + 498, + 242, + 890, + 318 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n[ \\mathbf {q}, \\mathbf {k}, \\mathbf {v} ] = \\mathbf {z} \\mathbf {U} _ {q k v}, \\quad \\mathrm {S A} (\\mathbf {z}) = \\operatorname {s o f t m a x} \\left(\\frac {1}{\\sqrt {D _ {k}}} \\mathbf {q} \\mathbf {k} ^ {T}\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 325, + 890, + 347 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {M S A} (\\mathbf {z}) = \\left[ \\operatorname {S A} _ {1} (\\mathbf {z}); \\operatorname {S A} _ {2} (\\mathbf {z}); \\dots ; \\operatorname {S A} _ {k} (\\mathbf {z}) \\right] \\mathbf {U} _ {m}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 511, + 349, + 890, + 367 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{U}_{qkv} \\in \\mathbb{R}^{D \\times 3D_k}$ and $\\mathbf{U}_m \\in \\mathbb{R}^{k \\cdot D_k \\times D}$ . Let $A = \\frac{\\mathbf{q}\\mathbf{k}^T}{\\sqrt{D_k}} \\in \\mathbb{R}^{N \\times N}$ denote the attention matrix. Our ASAD performs spatial-attention dropout on $A$ so as to remove some within-frame interactions.", + "bbox": [ + 498, + 375, + 890, + 439 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Temporal matching probability. We first need to consider the best tokens on which to apply ASAD. Intuitively, a query token that has a strong match in the other frame should be a good candidate, since, in the absence of within-frame cues, it can still be reconstructed well using the temporal cues in the other frame. Here, we define a temporal matching function $f_{tem}(\\cdot)$ to measure the temporal matching probability of the $i$ -th query token:", + "bbox": [ + 498, + 441, + 890, + 561 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nf _ {t e m} (i) = \\max _ {j \\in \\Omega_ {t} (i)} \\left(\\hat {A} _ {i, j}\\right), \\quad \\hat {A} = \\operatorname {s o f t m a x} _ {\\text {r o w}} (A), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 570, + 890, + 595 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the softmax function is applied on each row of $A$ , $f_{tem}(i) \\in [0,1]$ , and $\\Omega_t(i)$ denotes the temporal index set of the $i$ -th query token, which contains all the token indices of the other frame. A larger value of $f_{tem}(i)$ indicates a larger probability that the $i$ -th query token is well-matched in the other frame, and thus a good candidate for ASAD. A visualization of $f_{tem}(\\cdot)$ is shown in Fig. 5.", + "bbox": [ + 498, + 603, + 890, + 709 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Overall dropout probability measurement. The overall spatial-attention dropout probability at location $(i,j)$ is measured by using both the temporal matching probability and the normalized spatial importance:", + "bbox": [ + 498, + 709, + 890, + 768 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nW _ {i, j} = f _ {\\text {t e m}} (i) \\frac {\\hat {A} _ {i , j}}{\\sum_ {j \\in \\Omega_ {s} (i)} \\hat {A} _ {i , j}}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 589, + 777, + 890, + 816 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\Omega_s(i)$ is the spatial index set that contains all the other token indices (i.e., excluding the query index itself) in the same frame as the $i$ -th query. When $W_{i,j}$ is large, the $i$ -th query token has a good between-frame match, and meanwhile the $j$ -th within-frame token is important for the $i$ -th", + "bbox": [ + 498, + 824, + 890, + 898 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "14564", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "query. In this case, dropping the attention element $(i,j)$ in $A$ facilitates the model to use between-frame (temporally-matched) tokens for token learning or reconstruction. Finally, we set the dropout probability for self-attention and temporal-self-attention to be 0, i.e., $W_{i,i} = W_{i,i + N / 2} = 0$ .", + "bbox": [ + 75, + 90, + 467, + 167 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Note that there are $N(N / 2 - 1)$ (i.e., excluding self-attention elements) spatial-attention elements in total, and only these spatial-attention elements are considered for dropout. With a pre-defined dropout ratio $P$ , we globally drop a total of $N_{d} = PN(N / 2 - 1)$ attention elements from $A$ .", + "bbox": [ + 75, + 167, + 467, + 257 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Sampling for Dropout. We draw $N_{d}$ elements from a multinomial distribution based on the dropout probability matrix $W$ . Then we drop the elements in $A$ with the corresponding indices by setting their values to $-\\infty$ . After applying the softmax function in (1), the corresponding spatial-attention weights are removed. The other operations are the same with the original multi-head self attention mechanisms used in ViT. The PyTorch-like pseudocode is presented in the Supplemental.", + "bbox": [ + 75, + 260, + 467, + 396 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our ASAD method has negligible additional time cost compared with TwinMAE, due to the efficient matrix operation in GPUs. We apply ASAD to each layer in the decoder during the pre-training stage, so as to learn encoder representations that support temporal matching. In the next section, we introduce downstream task fine-tuning based on the well pre-trained ViT model.", + "bbox": [ + 75, + 397, + 467, + 502 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Downstream Temporal Matching Tasks", + "text_level": 1, + "bbox": [ + 76, + 517, + 415, + 534 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After obtaining the pre-trained DropMAE model, we fine-tune the well-learned encoder (i.e., the ViT model) on downstream temporal matching tasks, i.e., VOT and VOS.", + "bbox": [ + 75, + 542, + 467, + 587 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4.1 Video Object Tracking", + "text_level": 1, + "bbox": [ + 76, + 607, + 290, + 622 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Recently, the MAE ViT models pre-trained on ImageNet are applied to VOT and show impressive results. We use the state-of-the-art tracker OSTrack [97] as our baseline tracker for fine-tuning. In OSTrack, the cropped template and search images are firstly serialized into sequences and concatenated together. Then the overall sequence is added with the positional embeddings and input to the ViT backbone for joint feature extraction and interaction. Finally, the updated search features are input to a prediction head to predict the target bounding box.", + "bbox": [ + 75, + 633, + 467, + 784 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "During the fine-tuning stage, we use our pre-trained DropMAE encoder weights to initialize the ViT backbone used in OSTrack. Meanwhile, two frame identity embeddings are respectively added to template and search embeddings, in order to keep consistency with the pre-training stage. We use the same training losses of the original OSTrack. The detailed training parameters are shown in Supplementary for reference.", + "bbox": [ + 75, + 786, + 467, + 906 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4.2 Video Object Segmentation", + "text_level": 1, + "bbox": [ + 500, + 90, + 743, + 106 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For VOS, there are currently no methods based on ViT. Thus, we build a simple VOS baseline with a ViT backbone.", + "bbox": [ + 496, + 114, + 890, + 143 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Input serialization. Given a template frame with a binary mask, VOS aims to segment the object-of-interest in each frame of a video. Similar to the pre-training stage, the binary mask map, template and search frames are firstly converted to patch sequences, and then linearly projected and added with positional embeddings. Two frame identity embeddings are added to the template and search embeddings, and the mask embeddings are added to the template embeddings for mask encoding.", + "bbox": [ + 496, + 145, + 890, + 280 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Joint feature extraction and interaction. The template and search embeddings are concatenated together and input to the ViT backbone for joint feature extraction and matching. We use the updated search features extracted from the last layer of ViT for mask prediction.", + "bbox": [ + 496, + 281, + 890, + 354 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Mask prediction. The existing VOS approaches [14, 15, 60, 96] employ multi-resolution features for mask prediction. However, the updated search features are single-resolution. We follow [45] to upsample the search features to $2 \\times$ and $4 \\times$ sizes via two deconvolutional modules. Finally, we use the same decoder used in [15, 60] for mask prediction.", + "bbox": [ + 496, + 356, + 890, + 446 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training loss. We use the commonly-used cross entropy loss [15, 60] to train the whole network architecture.", + "bbox": [ + 496, + 446, + 890, + 476 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Online inference. During the online inference, we use the first frame with the mask annotation as the memory frame for online target matching in the search frame.", + "bbox": [ + 496, + 477, + 890, + 521 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The pipeline figure and more implementation details can be found in Supplementary.", + "bbox": [ + 496, + 522, + 890, + 551 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 498, + 565, + 630, + 582 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Implementation Details", + "text_level": 1, + "bbox": [ + 500, + 590, + 715, + 606 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. In the pre-training stage, we explore various large-scale video data sources to pre-train our DropMAE model, including Kinetics-400 [40] (K400), Kinetics-600 [8] (K600), Kinetics-700 [9] (K700), Moments in Time [56] (MiT) and WebVid-2M [1]. The detailed performance comparison using different pre-training datasets is shown in the ablation study. For fine-tuning on VOT, we follow the training settings used in our baseline OSTrack [97]. We use the training splits of LaSOT [28], COCO [49], TrackingNet [57] and GOT-10k [39] for training. For the GOT-10k evaluation, we follow the one-shot evaluation and only fine-tune the model on the training split of GOT-10k. For VOS finetuning, we use Youtube-VOS [90] and Davis [64] datasets for fine-tuning following the standard convention [15, 60].", + "bbox": [ + 496, + 613, + 890, + 824 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Pre-training and fine-tuning. For DropMAE pre-training, the default input is two frames with a spatial size of $224 \\times 224$ pixels. The frames are randomly sampled from each video within a maximum frame gap of 50. During the pretraining, one epoch is counted when all videos are sampled", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "14565", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/77b9c59593663d9e7b155bcaf307d18503290e2aed743e56026c75ab44673aab.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsPre-training DataEpochsPre-train. Time (h)GOT-10k (VOT)DAVIS-17 (VOS)
AOSR0.5SR0.75J&FJF
No Pre-training---62.772.853.769.566.972.2
Supervised IN1k [72]IN1K300-69.779.065.678.074.881.1
Supervised IN21k [66]IN21K80-70.280.765.478.575.481.7
CLIP [65]IN1K32-67.476.860.073.670.576.7
MOCO-v3 [12]IN1K300-70.180.165.378.475.481.5
BeiT [2]IN1K800103.167.476.860.076.172.779.4
MAE [36]IN1K16008473.783.270.881.778.584.9
TwinMAEK40040020.772.283.265.979.376.482.3
TwinMAEK40080041.372.983.668.580.777.983.6
TwinMAEK400160082.774.284.969.481.278.184.2
DropMAEK40040021.173.283.967.581.378.584.0
DropMAEK40080042.274.885.470.582.779.785.6
DropMAEK400160084.475.886.472.083.180.286.0
DropMAEK70080092.475.986.872.083.080.285.7
", + "bbox": [ + 122, + 79, + 843, + 275 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/fb8a2b611551a99cecd9761edc9c9e557901dfee1d37027f2cf70b744eec4359.jpg", + "table_caption": [ + "Table 1. Comparison of pre-training methods on downstream VOT and VOS tasks on GOT-10k [39] and DAVIS-17 [64]. All methods adopt the ViT-B/16 model [24] with $224\\times 224$ input images for pre-training. The pre-training time is measured on 64 NVIDIA V100 GPUs. The best two results are shown in red and blue." + ], + "table_footnote": [], + "table_body": "
MethodSourceGOT-10k [39]TNL2K [79]LaSOText [27]LaSOT [28]
AOSR0.5SR0.75AUCPAUCPNormPAUCPNormP
SiamFC [3]ECCVW1634.835.39.829.528.623.031.126.933.642.033.9
MDNet [58]CVPR1629.930.39.9--27.934.931.839.746.037.3
ECO [19]ICCV1731.630.911.132.631.722.025.224.032.433.830.1
SiamPRN++ [41]CVPR1951.761.632.541.341.234.041.639.649.656.949.1
DiMP [4]ICCV1961.171.749.244.743.439.247.645.156.965.056.7
SiamR-CNN [74]CVPR2064.972.859.752.352.8---64.872.2-
LTMU [18]CVPR20---48.547.341.449.947.357.2-57.2
Ocean [104]ECCV2061.172.147.338.437.7---56.065.156.6
TrDiMP [76]CVPR2167.177.758.3-----63.9-61.4
TransT [13]CVPR2167.176.860.950.751.7---64.973.869.0
AutoMatch [102]ICCV2165.276.654.347.243.537.6-43.058.3-59.9
STARK [92]ICCV2168.878.164.1-----67.177.0-
KeepTrack [55]ICCV21-----48.2--67.177.270.2
MixFormer-L [17]CVPR2270.780.067.8-----70.179.976.3
SBT [87]CVPR2270.480.864.7-----66.7-71.1
UAST [98]ICML2263.574.151.4-----57.1-58.7
SwinTrack-384 [48]NeurIPS2272.480.567.855.957.149.1-55.671.3-76.5
AiATrack [32]ECCV2269.680.063.2--46.854.454.249.656.949.1
CIA50 [63]ECCV2267.979.060.350.957.6---66.2-69.6
SimTrack-L [10]ECCV2269.878.866.055.655.7---70.579.7-
OSTrack-384 [97]ECCV2273.783.270.855.956.750.561.357.671.181.177.6
DropTrackOurs75.986.872.056.957.952.763.960.271.881.878.1
", + "bbox": [ + 107, + 334, + 859, + 626 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Comparison with state-of-the-art VOT approaches on four large-scale challenging datasets. The best two results are shown in red and blue. For GOT-10k evaluation, all the methods follow the one-shot protocol, training only on the training set in GOT-10k.", + "bbox": [ + 75, + 628, + 892, + 659 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "once. For fair comparison, we use the same mask ratio (i.e., $75\\%$ ) and training hyper-parameters of MAE [36] to pretrain the TwinMAE and DropMAE models. Following [14, 15], we use a bootstrapped cross entropy loss for training. The detailed pre-training and fine-tuning hyper-parameters are in the Supplementary.", + "bbox": [ + 75, + 684, + 468, + 776 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Comparison with Pre-Training Methods", + "text_level": 1, + "bbox": [ + 75, + 792, + 421, + 808 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In Table 1, we compare our DropMAE with existing pre-training methods on the downstream tasks of VOT and VOS. DropMAE and TwinMAE are pre-trained using videos (K400, K700), while MAE and other methods are pre-trained on ImageNet 1k or 21k (IN1K, IN21K). The VOT and VOS baselines illustrated in Sec. 3.4 use the", + "bbox": [ + 75, + 810, + 470, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "official pre-trained VIT-B/16 models provided by existing pre-training approaches (see Table 1) for fine-tuning. TwinMAE with 800-epoch training performs favorably against MAE on VOT, but achieves inferior results on VOS. There are two main reasons: 1) TwinMAE is not effective enough at learning temporal matches; 2) The number of object classes in K400 is limited, and meanwhile the object classes in DAVIS-17 are included in ImageNet. Thus MAE generalizes well to VOS. Our DropMAE, which is a stronger temporal matching learner, outperforms MAE on both the VOT and VOS tasks with 800-epoch training (i.e., 42.2 hours $^{1}$ )", + "bbox": [ + 496, + 684, + 893, + 851 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "In our implementation, we perform video decoding and extract the video frames on the fly in each training iteration, which could be further sped up using some tricks like repeated sampling [30].", + "bbox": [ + 498, + 862, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "14566", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/afa95419d66b7761ab29ea32c37c21e99abd8ff434fc821bc5b3043223cbe34d.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodOTB100AUCITBAUCTrackingNet
AUCPNorm
SiamFC [3]58.344.157.166.3
Ocean [104]68.447.7--
ATOM [20]68.347.270.377.1
DiMP [4]53.733974.080.1
TransT [13]69.554.781.486.7
STARK [92]68.157.682.086.9
OSTrack [97]-64.883.988.5
DropTrack69.665.084.188.9
", + "bbox": [ + 114, + 77, + 431, + 200 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "by using the K400 dataset. This indicates that our DropMAE is $2\\times$ faster than MAE.", + "bbox": [ + 75, + 262, + 468, + 292 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5. State-of-the-art Comparison", + "text_level": 1, + "bbox": [ + 76, + 308, + 339, + 327 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we compare our fine-tuned VOT and VOS models, denoted as DropTrack and DropSeg, with state-of-the-art approaches on VOT and VOS benchmarks. We use DropMAE trained on K700 with 800 epochs as the pretraining model for both VOT and VOS fine-tuning.", + "bbox": [ + 75, + 334, + 468, + 411 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.1. Video Object Tracking", + "text_level": 1, + "bbox": [ + 76, + 421, + 290, + 438 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To demonstrate the effectiveness of the proposed DropMAE for VOT, we compare our DropTrack with state-of-the-art trackers on 7 challenging tracking benchmarks. GOT-10k. GOT-10k [39] is a challenging dataset that follows the one-shot evaluation protocol, where the trackers are required to be trained on its training split, and the test object classes have no overlap with the objects in the training split. As shown in Table 2, our DropTrack achieves state-of-the-art results on this dataset, outperforming OSTrack by $2.2\\%$ and $3.6\\%$ in terms of AO and $\\mathrm{SR}_{0.5}$ . This implies that the temporal correspondence learning in the pretraining is beneficial for the downstream tracking task. Although there exists a domain gap between the pre-training data and the test data (i.e., a large portion of test objects in GOT-10k are animals, vehicles and object parts, whereas K700 only consists of human-centric action videos), the temporal matching ability learned by DropMAE can still be transferred to the downstream tracking task, improving the tracking performance.", + "bbox": [ + 75, + 445, + 468, + 733 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "LaSOT. LaSOT consists of 280 long test sequences, and our results are presented in Table 2. Our DropTrack sets a new record on this dataset with $71.8\\%$ AUC, $81.8\\%$ $\\mathrm{P}_{\\text {Norm }}$ and $78.1\\%$ P, which shows the great potential of our DropTrack in robust long-term visual tracking.", + "bbox": [ + 75, + 733, + 468, + 809 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "$\\mathbf{LaSOT}_{ext}$ . $\\mathbf{LaSOT}_{ext}$ is an extension of LaSOT with more challenging video sequences for testing - similar to GOT-10k, the test split has a large gap with the training split, and sequences with novel object classes (i.e., not appeared in ImageNet) are used for evaluation. Our DropMAE outperforms the other trackers by large margins. This demon", + "bbox": [ + 75, + 809, + 468, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/d2dfe40de76e5cc59da93e286f84a59553f025a87a076c5ce0c62d246d452c32.jpg", + "table_caption": [ + "Table 3. Comparison with state-of-the-art VOT approaches on OTB100 [85], ITB [44] and TrackingNet [57]. The best two results are shown in red and blue." + ], + "table_footnote": [], + "table_body": "
MethodSourceOLMSDAVIS-2016 [62]DAVIS-2017 [64]
J&FJFJ&FJF
RANet [80]ICCV19✓85.585.585.465.763.268.2
STM [60]ICCV19✓✓89.388.789.981.879.284.3
FRTM [67]CVPR20✓✓83.583.683.476.773.979.6
TVOS [101]CVPR20✓---72.369.974.7
LWL [5]ECCV20✓✓---81.679.184.1
CFBI [95]ECCV20✓89.488.390.581.979.184.6
UniTrack [81]NeurIPS21✓----58.4-
STCN- [15]NeurIPS21✓---82.579.385.7
SSTVOS [26]CVPR21✓---82.579.985.1
SWEM- [50]CVPR22✓89.5--81.9--
RTS [61]ECCV22✓✓---80.277.982.6
OSMN [54]TPAMI1873.574.072.954.852.557.1
FAVOS [16]CVPR1881.082.479.558.254.661.8
VideoMatch [38]ECCV18-81.0-56.5--
SiamMask [77]CVPR1969.871.767.856.454.358.5
D3S [52]CVPR2074.075.472.660.857.863.8
Siam R-CNN [52]CVPR20---70.666.175.0
Unicorn [91]ECCV2287.486.588.269.265.273.2
DropSegOurs92.190.993.383.080.285.7
", + "bbox": [ + 504, + 77, + 893, + 271 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4. Comparison with state-of-the-art VOS approaches on the validation sets of DAVIS-2016 [62] and DAVIS-2017 [64]. OL, M and S indicate Online Learning, using Memory mechanism, and using Synthetic videos for pre-training.", + "bbox": [ + 498, + 276, + 890, + 330 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ed83c71d96fd8d2644c89bf60bedded699817a2a6a3e61e3a075d5f0bc17fdef.jpg", + "image_caption": [ + "Figure 6. Ablation study of the dropout ratio $P$ on the GOT-10k (VOT) and DAVIS-17 (VOS) datasets." + ], + "image_footnote": [], + "bbox": [ + 521, + 330, + 870, + 444 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "strates that a tracker with DropMAE pre-training generalizes well to unseen objects in generic visual object tracking. TNL2K. TNL2K is a large-scale evaluation dataset that consists of 700 test videos with various challenges, such as significant appearance variation and manually added adversarial samples. As illustrated in Table 2, our DropMAE significantly outperforms the other trackers on this dataset. ITB, TrackingNet and OTB100. In Table 3, we evaluate our DropTrack on ITB [44], OTB100 [85] and TrackingNet [57], achieving state-of-the-art performance on each one. DropTrack is slightly better than OSTrack on ITB and TrackingNet. We believe the main reason is the fully overlapped training and test object classes in these two datasets, which reduces the effect of pre-training. A competitive tracker on these two datasets can be learned even using supervised ImageNet weights, which has been shown in [97].", + "bbox": [ + 496, + 489, + 890, + 731 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "On all 7 VOT datasets, our DropTrack outperforms the baseline OSTrack, which demonstrates that our DropMAE pre-training on videos learns better temporal-matching representations than the MAE model trained on ImageNet, resulting in more a robust tracker that generalizes well to both unseen and seen objects.", + "bbox": [ + 496, + 731, + 890, + 821 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Video Object Segmentation", + "text_level": 1, + "bbox": [ + 500, + 830, + 746, + 848 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In Table 4, we compare our DropSeg with existing VOS approaches on the DAVIS-16/17 [62,64].", + "bbox": [ + 498, + 854, + 890, + 883 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "DAVIS-16. DAVIS-16 is composed of 20 manually anno", + "bbox": [ + 500, + 885, + 890, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "14567", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/4f5b895ed60699257569ab5af6122c94c907704b9ad66a436c7c03a48ca6db48.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DatasetsNo. \nVideosNo. \nActionsVOTVOS
AOSR0.5SR0.75J&F
K400 [40]240,00040073.283.967.582.7
K600 [8]390,00060074.585.569.582.8
K700 [9]526,76870075.686.271.483.0
MiT [56]802,24433975.185.570.682.8
WebVid [1]240,000-72.883.467.381.5
WebVid [1]960,000-73.485.069.582.9
", + "bbox": [ + 81, + 88, + 462, + 186 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "tated test sequences. As shown in Table 4, our one-shot DropSeg approach, without using any online learning and complicated memory mechanisms, achieves the best $\\mathcal{J}\\&\\mathcal{F}$ score of $92.1\\%$ , which significantly outperforms the other compared one-shot approaches and is even better than the approaches with complicated pipelines (i.e., OL, M and S). This implies that the pixel-wise correspondence learned during the pre-training is effective for capturing long-range dependencies between various frames in VOS.", + "bbox": [ + 75, + 246, + 467, + 381 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "DAVIS-17. DAVIS-17 is an extension of DAVIS-16, comprising more challenging videos and supports multi-object segmentation. In Table 4, our DropSeg achieves competitive results of $83.0\\%$ $\\mathcal{I}\\& \\mathcal{F}$ , $80.2\\%$ $\\mathcal{I}$ and $85.7\\%$ $\\mathcal{F}$ , which shows its superiority in handling more challenging videos.", + "bbox": [ + 75, + 382, + 467, + 458 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "More VOS results and comparisons are included in the supplementary.", + "bbox": [ + 76, + 458, + 467, + 488 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Ablation Studies", + "text_level": 1, + "bbox": [ + 76, + 497, + 240, + 512 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this section, we conduct ablation studies to provide more detailed analysis of our method. We use DropMAE with 400-epoch pre-training for the ablation study.", + "bbox": [ + 75, + 522, + 467, + 568 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The effect of dropout ratio $P$ . We study the effect of dropout rate $P$ in Fig. 6. A relatively small dropout ratio of $P = 0.1$ works well on both VOT and VOS tasks. Meanwhile, dropping too many spatial cues (e.g., $P = 0.2$ ) degrades the downstream tasks, which is mainly because the spatial cues are also useful for accurate localization and segmentation. $P = 0.1$ is the optimal setting, and thus we adopt it in the following experiments.", + "bbox": [ + 75, + 568, + 467, + 688 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Pre-training video sources. Since we are the first to explore masked autoencoder pre-training for temporal matching tasks, it is not clear which video dataset is the optimal choice for pre-training. Here, we use five popular video datasets for pre-training, including K400 [40], K600 [8], K700 [9], MiT [56] and WebVid-2M [1]. For WebVid-2M, we randomly sample 240k and 960k videos for fair comparison and faster validation. The downstream tracking results are reported in Table 5. Performance is not favorable even using 960,000 videos in WebVid for pre-training. This indicates that WebViD is not a good choice for tracking pre-training, which is mainly because it is a video caption dataset that focuses on scene diversity and lacks rich object motion. From the experiments on the K400/600/700 and", + "bbox": [ + 75, + 688, + 467, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/74bb59102c31ae66761cb1a9b7196928686025aa37b58bd574db32e798541d38.jpg", + "table_caption": [ + "Table 5. The downstream VOT and VOS performance on GOT-10k and DAVIS-17 obtained by using our DropMAE pre-trained on various video datasets. VOS uses 800 epochs pre-training." + ], + "table_footnote": [], + "table_body": "
SettingsGOT-10k
DropTrack-K400-400E73.2/67.5
w/ ASAP in Encoder73.1/68.1
w/ domain specific data73.4/68.8
w/o frame identity embed72.9/67.4
", + "bbox": [ + 581, + 88, + 807, + 151 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 6. The tracking performance of $\\mathrm{{AO}}/{\\mathrm{{SR}}}_{0.75}$ on GOT10-k reported by variants with different settings.", + "bbox": [ + 498, + 152, + 890, + 180 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "MiT, tracking benefits from pre-training with from rich action classes (i.e., 700 action classes of K700), from which the model can learn stronger temporal matching ability.", + "bbox": [ + 498, + 191, + 890, + 237 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Applying ASAD to the encoder. Here we test applying ASAD to all layers including both encoder and decoder of masked autoencoder. As shown in Table 6, this variant gains improvements (0.6% in $\\mathrm{SR}_{0.75}$ ) over the original baseline. Considering its additional cost and limited performance improvement, we only apply ASAD to the decoder.", + "bbox": [ + 498, + 238, + 890, + 327 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Domain specific data. We also add the tracking training data (without using box annotations), including TrackingNet, LaSOT, and GOT-10k, into K400 for pre-training. The downstream tracking performance by using the larger pre-training set is 73.4/68.8, which is better than the baseline. It shows that the domain-specific data is helpful to bridge the domain gap, which can be considered as future work to extend Kinetic datasets with more tracking videos.", + "bbox": [ + 498, + 329, + 890, + 449 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Frame identity embedding. During pre-training, the frame identity embedding is used to identify masked patches in the same 2D location of the two frames. From Table 6, we can find that downstream fine-tuning without the frame identity embedding performs worse than with it, since not using it is inconsistent with the pre-training stage.", + "bbox": [ + 498, + 450, + 890, + 540 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 546, + 617, + 561 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper investigated masked autoencoding pretraining for temporal matching-based downstream tasks. Specifically, an adaptive spatial-attention dropout method is proposed to facilitate temporal correspondence learning in self-supervised pre-training on videos. We show that our proposed pre-training method DropMAE can achieve better downstream performance on VOT and VOS than the image-based MAE, while using $50\\%$ less pre-training time. In addition, as the first work investigating this problem, we show the guidelines of selecting video sources for pre-training, i.e., selecting videos with rich motion information is more beneficial for temporal matching-based downstream tasks. The experimental results on VOT and VOS show that our DropMAE sets new state-of-the-art results on 8 out of 9 tracking benchmarks. We expect our DropMAE to serve as a strong pre-trained backbone in future work.", + "bbox": [ + 498, + 571, + 890, + 814 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "8. Acknowledgment", + "text_level": 1, + "bbox": [ + 500, + 829, + 669, + 845 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CityU 11215820).", + "bbox": [ + 498, + 854, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "14568", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Max Bain, Arsha Nagrani, Gül Varol, and Andrew Zisserman. Frozen in time: A joint video and image encoder for end-to-end retrieval. In ICCV, 2021. 5, 8", + "[2] H. Bao, L. Dong, and F. Wei. Beit: Bert pre-training of image transformers. In arXiv:2106.08254, 2021. 6", + "[3] L. Bertinetto, J. Valmadre, J.F. Henriques, A. 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In ECCV, 2020. 6, 7" + ], + "bbox": [ + 503, + 90, + 890, + 577 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "14571", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/DropMAE_ Masked Autoencoders With Spatial-Attention Dropout for Tracking Tasks/63a61ae0-513f-436f-959c-a8f318e90bde_model.json b/2023/DropMAE_ Masked Autoencoders With Spatial-Attention Dropout for Tracking Tasks/63a61ae0-513f-436f-959c-a8f318e90bde_model.json new file mode 100644 index 0000000000000000000000000000000000000000..b8d446dcc90842e13807465a46ac4332aefeb5ad --- /dev/null +++ b/2023/DropMAE_ Masked Autoencoders With Spatial-Attention Dropout for Tracking Tasks/63a61ae0-513f-436f-959c-a8f318e90bde_model.json @@ -0,0 +1,2884 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.135, + 0.13, + 0.838, + 0.177 + ], + "angle": 0, + "content": "DropMAE: Masked Autoencoders with Spatial-Attention Dropout for Tracking Tasks" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.203, + 0.878, + 0.275 + ], + "angle": 0, + "content": "Qiangqiang Wu\\(^{1}\\) Tianyu Yang\\(^{2*}\\) Ziquan Liu\\(^{1}\\) Baoyuan Wu\\(^{4}\\) Ying Shan\\(^{3}\\) Antoni B. Chan\\(^{1}\\) \n\\(^{1}\\)Department of Computer Science, City University of Hong Kong \n\\(^{2}\\)International Digital Economy Academy \n\\(^{3}\\)Tencent AI Lab \n\\(^{4}\\)School of Data Science, The Chinese University of Hong Kong, Shenzhen" + }, + { + "type": "text", + "bbox": [ + 0.185, + 0.277, + 0.786, + 0.31 + ], + "angle": 0, + "content": "{qiangqwu2-c, ziquanliu2-c}@my.cityu.edu.hk, tianyu-yang@outlook.com wubaoyuan@cuhk.edu.cn, yingsshan@tencent.com, abchan@cityu.edu.hk" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.345, + 0.314, + 0.361 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.377, + 0.474, + 0.755 + ], + "angle": 0, + "content": "In this paper, we study masked autoencoder (MAE) pretraining on videos for matching-based downstream tasks, including visual object tracking (VOT) and video object segmentation (VOS). A simple extension of MAE is to randomly mask out frame patches in videos and reconstruct the frame pixels. However, we find that this simple baseline heavily relies on spatial cues while ignoring temporal relations for frame reconstruction, thus leading to sub-optimal temporal matching representations for VOT and VOS. To alleviate this problem, we propose DropMAE, which adaptively performs spatial-attention dropout in the frame reconstruction to facilitate temporal correspondence learning in videos. We show that our DropMAE is a strong and efficient temporal matching learner, which achieves better fin-tuning results on matching-based tasks than the ImageNet-based MAE with \\(2 \\times\\) faster pre-training speed. Moreover, we also find that motion diversity in pre-training videos is more important than scene diversity for improving the performance on VOT and VOS. Our pre-trained DropMAE model can be directly loaded in existing ViT-based trackers for fine-tuning without further modifications. Notably, DropMAE sets new state-of-the-art performance on 8 out of 9 highly competitive video tracking and segmentation datasets. Our code and pre-trained models are available at https://github.com/jimmy-dq/DropMAE.git." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.775, + 0.21, + 0.791 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.801, + 0.47, + 0.879 + ], + "angle": 0, + "content": "Recently, transformers have achieved enormous success in many research areas, such as natural language processing (NLP) [6, 22], computer vision [97] and audio generation [43, 73]. In NLP, masked autoencoding is commonly used to train large-scale generalizable NLP transformers contain-" + }, + { + "type": "image", + "bbox": [ + 0.523, + 0.345, + 0.871, + 0.515 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.518, + 0.895, + 0.575 + ], + "angle": 0, + "content": "Figure 1. State-of-the-art comparison on GOT-10k [39] following the one-shot protocol. Our DropTrack with the proposed DropMAE pre-training achieves state-of-the-art performance without using complicated pipelines such as online updating." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.595, + 0.895, + 0.732 + ], + "angle": 0, + "content": "ing billions of parameters. Inspired by the great success of self-supervised learning in NLP, recent advances [36, 89] in computer vision suggest that training large-scale vision transformers may undertake a similar trajectory with NLP. The seminal work MAE [36] reconstructs the input image from a small portion of patches. The learned representation in this masked autoencoder has been demonstrated to be effective in many computer vision tasks, such as image classification, object detection and semantic segmentation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.896, + 0.903 + ], + "angle": 0, + "content": "In video object tracking (VOT), recently two works, SimTrack [10] and OSTrack [97], explore using an MAE pre-trained ViT model as the tracking backbone. Notably, these two trackers achieve state-of-the-art performance on existing tracking benchmarks without using complicated tracking pipelines. The key to their success is the robust pre-training weights learned by MAE on ImageNet [68]. In addition, [10, 97] also demonstrate that, for VOT, MAE unsupervised pre-training on ImageNet is more effective than supervised pre-training using class labels – this is mainly because MAE pre-training learns more fine-grained local" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.225, + 0.9 + ], + "angle": 0, + "content": "*Corresponding Author" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "14561" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.104, + 0.092, + 0.264, + 0.155 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.146, + 0.156, + 0.236, + 0.166 + ], + "angle": 0, + "content": "TwinMAE (Layer-6)" + }, + { + "type": "image", + "bbox": [ + 0.266, + 0.092, + 0.422, + 0.155 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.307, + 0.156, + 0.398, + 0.166 + ], + "angle": 0, + "content": "TwinMAE (Layer-8)" + }, + { + "type": "image", + "bbox": [ + 0.102, + 0.168, + 0.264, + 0.231 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.147, + 0.232, + 0.241, + 0.242 + ], + "angle": 0, + "content": "DropMAE (Layer-6)" + }, + { + "type": "image", + "bbox": [ + 0.266, + 0.168, + 0.423, + 0.231 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.308, + 0.232, + 0.402, + 0.242 + ], + "angle": 0, + "content": "DropMAE (Layer-8)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.252, + 0.47, + 0.376 + ], + "angle": 0, + "content": "Figure 2. Visualization of the attention maps of the TwinMAE baseline and our DropMAE in the reconstruction of a random masked patch, which is denoted as a red bounding box in the left input frame. TwinMAE leverages the spatial cues (within the same frame) more than temporal cues (between frames) for reconstruction. Our proposed DropMAE improves the baseline by effectively alleviating co-adaptation between spatial cues in the reconstruction, focusing more on temporal cues, thus achieving better learning of temporal correspondences for VOT and VOS." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.396, + 0.468, + 0.593 + ], + "angle": 0, + "content": "structures that are useful for accurate target localization required for VOT, whereas supervised training learns high-level class-related features that are invariant over appearance changes. Despite the promising performance achieved by [10,97], the MAE pre-training on ImageNet could still be sub-optimal for the tracking task due to the natural gap between images and videos, i.e., no prior temporal correspondence information can be learned in static images. However, previous tracking methods [3,42,83] have shown that temporal correspondence learning is the key in developing a robust and discriminative tracker. Thus there is an opportunity to further develop the MAE framework specifically for matching-base video tasks, such as VOT and VOS." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.596, + 0.468, + 0.776 + ], + "angle": 0, + "content": "One simple way to extend MAE to videos is to randomly mask out frame patches in a video clip (i.e., video frame pairs) and then reconstruct the video clip. We denote this simple baseline as twin MAE (TwinMAE). Given a masked patch query, as illustrated in Figs. 2 & 4, we find that TwinMAE heavily relies on the spatially neighbouring patches within the same frame to reconstruct the masked patch, which implies a heavy co-adaptation of spatial cues (within-frame tokens) for reconstruction and may cause learning of sub-optimal temporal representations for matching-based downstream tasks like video object tracking and segmentation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.468, + 0.901 + ], + "angle": 0, + "content": "To address this issue with the TwinMAE baseline, we propose DropMAE specifically designed for pre-training a masked autoencoder for matching-based video downstream tasks (e.g., VOT and VOS). Our DropMAE adaptively performs spatial-attention dropout to break up co-adaptation between spatial cues (within-frame tokens) during the frame reconstruction, thus encouraging more temporal interactions and facilitating temporal correspondence learning in" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.212 + ], + "angle": 0, + "content": "the pre-training stage. Interestingly, we obtain several important findings with DropMAE: 1) DropMAE is an effective and efficient temporal correspondence learner, which achieves better fine-tuning results on matching-based tasks than the ImageNet-based MAE with \\(2 \\times\\) faster pre-training speed. 2) Motion diversity in pre-training videos is more important than scene diversity for improving the performance on VOT and VOS." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.213, + 0.892, + 0.318 + ], + "angle": 0, + "content": "We conduct downstream task evaluation on 9 competitive VOT and VOS benchmarks, achieving state-of-the-art performance on these benchmarks. In particular, our trackers with DropMAE pre-training obtain \\(75.9\\%\\) AO on GOT-10k, \\(52.7\\%\\) AUC on \\(\\mathrm{LaSOT}_{ext}\\), \\(56.9\\%\\) AUC on TNL2K and \\(92.1\\% /83.0\\%\\) \\(\\mathcal{J}\\& \\mathcal{F}\\) scores on DAVIS-16/17, w/o using complicated online updating or memory mechanisms." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.319, + 0.866, + 0.332 + ], + "angle": 0, + "content": "In summary, the main contributions of our work are:" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.333, + 0.892, + 0.438 + ], + "angle": 0, + "content": "- To the best of our knowledge, we are the first to investigate masked autoencoder video pre-training for temporal matching-based downstream tasks. Specifically, we explore various video data sources for pre-training and build a TwinMAE baseline to study its effectiveness on temporal matching tasks. Since none exists, we further build a ViT-based VOS baseline for fine-tuning." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.44, + 0.892, + 0.498 + ], + "angle": 0, + "content": "- We propose DropMAE, which adaptively performs spatial-attention dropout in the frame reconstruction to facilitate effective temporal correspondence learning in videos." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.5, + 0.891, + 0.56 + ], + "angle": 0, + "content": "- Our trackers with DropMAE pre-training sets new state-of-the-art performance on 8 out of 9 highly competitive video tracking and segmentation benchmarks without complicated tracking pipelines." + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.333, + 0.892, + 0.56 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.574, + 0.64, + 0.589 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Visual object tracking and segmentation. Given an annotated bounding box in the first frame of a test video, visual object tracking (VOT) aims to accurately predict the target's bounding boxes in the following frames. Similarly, for visual object segmentation (VOS), given an annotated binary mask in the first frame, VOS aims to predict dense target masks in the remaining frames. In the early development of VOT, correlation filter-based approaches [19, 21, 31, 37, 46, 47, 51, 53, 82, 84] are dominant trackers due to their favorable ability in modeling target appearance variation. With the development of deep learning, deep Siamese networks [70, 78] are introduced to VOT. The representative work SiamFC [3] takes template and search images as input for target localization. Based on SiamFC, many improvements have been made, e.g., scale regression [41, 42, 94], online template updating [34, 93, 99], multilevel feature fusion [29], loss design [23] and backbone design [10, 41, 97, 103]. For VOS, matching-based approaches, e.g., STM [60], AOT [96] and STCN [15], achieve promising results on existing VOS benchmarks. Recent improve" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14562" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.167 + ], + "angle": 0, + "content": "ments [14, 50] on online memory design further improve the previous SOTA results in VOS. Recent studies including SimTrack [10] and OSTrack [97] show that the ViT backbone [24] with MAE pre-training on ImageNet is effective for object tracking." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.168, + 0.468, + 0.317 + ], + "angle": 0, + "content": "Despite the great success of ViT with MAE pre-training on tracking, this static ImageNet-based pre-training still lacks temporal correspondence learning. Moreover, the developments of VOT and VOS show that learning strong temporal matching ability is essential for video tracking tasks. To the best of our best knowledge, we are the first to investigate masked autoencoder self-supervised video pretraining for tracking tasks. Our proposed DropMAE can learn reliable temporal correspondences, which we demonstrate are effective for downstream tracking tasks." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.318, + 0.468, + 0.59 + ], + "angle": 0, + "content": "Self-supervised Learning. Self-supervised learning has received significant interest in the past few decades. There are many manually-designed pretext tasks for pre-training, such as image colorization [100], jigsaw puzzle solving [59], future frame prediction [69, 75] and rotation prediction [33]. Contrastive learning approaches [7, 11, 25, 35, 86, 88] are the mainstream self-supervised methods in recent years. However, these methods are sensitive to the type and strength of applied data augmentation, which makes them hard to train. Inspired by masked language modeling [6, 22], masked image modeling (MIM) approaches are proposed for learning unsupervised image [36, 89] or video representations [30, 71], which have been shown to be effective for many downstream tasks including image classification, object detection and video action recognition. However, there is no specifically designed pre-training approaches for temporal matching-based task, such as VOT and VOS. In this work, we propose DropMAE to explore this direction." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.603, + 0.168, + 0.618 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.628, + 0.468, + 0.793 + ], + "angle": 0, + "content": "We propose a self-supervised video pre-training method to learn robust representations for temporal matching-based downstream tasks, including VOT and VOS tasks. We firstly introduce a simple extension of MAE to temporal matching representation learning from video, (TwinMAE). We then illustrate the limitations of the TwinMAE baseline and propose a spatial-attention dropout strategy to facilitate temporal correspondence learning, denoted as DropMAE. The overall pipeline of both DropMAE and TwinMAE is shown in Fig. 3. Finally, we introduce the VOT and VOS methods used for fine-tuning the downstream tasks." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.802, + 0.452, + 0.818 + ], + "angle": 0, + "content": "3.1. Temporal Masked Autoencoder (TwinMAE)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.468, + 0.901 + ], + "angle": 0, + "content": "The masked autoencoder (MAE) model [36] consists of an encoder and a decoder. Its basic idea is to randomly mask out a large portion (e.g., \\(75\\%\\)) of patches in an image and then reconstruct the image pixels. Specifically, the encoder only takes visible patches as input for feature" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.081, + 0.889, + 0.196 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.199, + 0.892, + 0.255 + ], + "angle": 0, + "content": "Figure 3. An illustration of our DropMAE. The proposed adaptive spatial-attention dropout (ASAD) facilitates temporal correspondence learning for temporal matching tasks. TwinMAE follows the same pipeline except that the ASAD module is not used." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.265, + 0.892, + 0.369 + ], + "angle": 0, + "content": "learning, and then the decoder is input with both visible and masked patches to produce the image reconstruction. In order to adapt to downstream video matching-based tasks, one naive extension is to directly apply MAE on concatenated video frames, hoping to learn temporal matching representations from video frame pairs, which we denote as TwinMAE." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.371, + 0.892, + 0.537 + ], + "angle": 0, + "content": "It should be noted that existing works [30,71] that extend MAE to video representation learning are mainly designed for the downstream task of video action recognition, where a long video clip (e.g., 16 frames) is used for reconstruction-based pre-training. To keep consistent with our downstream tasks of VOT/VOS, we follow the general training settings used in object tracking [3,97], where two frames are sampled from one video as input to TwinMAE for pre-training. This adaptation significantly reduces the computational and memory cost compared to existing video pre-training approaches [30, 71], due to the quadratic complexity of ViTs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.538, + 0.892, + 0.748 + ], + "angle": 0, + "content": "Patch embedding. Firstly, we randomly sample 2 frames within a video with a predefined maximal frame gap. For each frame, we follow the vanilla ViT to divide it into non-overlapping patches. The patches extracted from the two frames are then concatenated together to form the overall patch sequence. We then randomly mask out patches in the patch sequence until a predefined mask ratio is reached. Note that we use the same mask ratio (i.e., \\(75\\%\\)) with the original MAE, since the information redundancy of two frames should be similar to a single image. The visible patches are embedded by linear projection [24], and the masked patches are embedded using a shared learnable mask token. All the embedded patches are added with positional embeddings [24]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.825 + ], + "angle": 0, + "content": "Frame identity embedding. To distinguish between the masked tokens in the same spatial location of the two frames, we use two learnable frame identity embeddings to indicate the two input frames. The corresponding frame identity embedding is added to each embedded patch." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Autoencoder and Training. Following the autoencoding pipeline in the original MAE [36], the encoder only takes visible embedded patches as input, and the decoder is input with all the embedded patches for masked patch reconstruction. We use the same normalized pixel loss from MAE for" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "14563" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.129, + 0.081, + 0.422, + 0.197 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.2, + 0.47, + 0.254 + ], + "angle": 0, + "content": "Figure 4. The average within-frame and between-frame attention scores obtained by TwinMAE and DropMAE in different decoder layers. The attention score is calculated on 20 randomly sampled K400 validation videos, and is averaged on all heads and locations." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.265, + 0.343, + 0.279 + ], + "angle": 0, + "content": "training the whole network architecture." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.29, + 0.368, + 0.305 + ], + "angle": 0, + "content": "3.2. Limitation of TwinMAE Baseline" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.313, + 0.469, + 0.432 + ], + "angle": 0, + "content": "The visualization of the reconstruction for our TwinMAE baseline is shown in Fig. 2. We also quantitatively compare the average within-frame and between-frame attentions during the reconstruction in Fig. 4. Interestingly, we find the TwinMAE reconstruction heavily relies on within-frame patches or spatial cues, which may lead to sub-optimal temporal representations for matching-based video tasks." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.434, + 0.47, + 0.645 + ], + "angle": 0, + "content": "When only using within-frame spatial cues, the decoder will perform the reconstruction using only context information in the neighboring patches, and thus the learned encoder representations will embed context information. In contrast, when using between-frame cues, the decoder will learn to perform matching of patches between frames so as to recover the corresponding target patch in the other frame. Thus, decoding with between-frame cues will make the encoder learn representations that support temporal matching between frames. Previous works in object tracking [3, 83] also suggest that temporal correspondence learning plays a key role in developing a robust and discriminative tracker. Since TwinMAE relies more on context information, it is still suboptimal for downstream tracking tasks." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.651, + 0.388, + 0.668 + ], + "angle": 0, + "content": "3.3. Adaptive Spatial-Attention Dropout" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.674, + 0.469, + 0.884 + ], + "angle": 0, + "content": "To address issue of TwinMAE discussed in Sec. 3.2, we propose a Adaptive Spatial-Attention Dropout (ASAD) to facilitate the temporal correspondence learning in the temporal MAE. Given a query token, our basic idea is to adaptively drop a portion of its within-frame cues in order to facilitate the model to learn more reliable temporal correspondence, i.e., between-frame cues. That is, we restrict the interactions between the query token and tokens in the same frame, and encourage more interactions with tokens in the other frame, through manipulation of the computed spatial-attention in the transformer. Therefore, to minimize the reconstruction loss, the model is facilitated to learn a better temporal matching ability, which is essential in matching-based video tasks." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Before introducing the proposed ASAD, we firstly revisit" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.091, + 0.891, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.179, + 0.892, + 0.22 + ], + "angle": 0, + "content": "Figure 5. Visualization of the temporal matching function \\( f_{tem} \\) on an example frame pair. A large value of \\( f_{tem}(i) \\) indicates that the \\( i \\)-th pixel matches well to a pixel in the other frame." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.243, + 0.892, + 0.319 + ], + "angle": 0, + "content": "the multi-head self-attention in ViT [24]. Let \\(\\mathbf{z} \\in \\mathbb{R}^{N \\times D}\\) be the input sequence of the two concatenated input frames, \\(N\\) denotes the total patch number in the two frames and \\(D\\) is the feature dimension. The standard multi-head self-attention [24] can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.327, + 0.891, + 0.348 + ], + "angle": 0, + "content": "\\[\n[ \\mathbf {q}, \\mathbf {k}, \\mathbf {v} ] = \\mathbf {z} \\mathbf {U} _ {q k v}, \\quad \\mathrm {S A} (\\mathbf {z}) = \\operatorname {s o f t m a x} \\left(\\frac {1}{\\sqrt {D _ {k}}} \\mathbf {q} \\mathbf {k} ^ {T}\\right), \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.513, + 0.351, + 0.891, + 0.368 + ], + "angle": 0, + "content": "\\[\n\\operatorname {M S A} (\\mathbf {z}) = \\left[ \\operatorname {S A} _ {1} (\\mathbf {z}); \\operatorname {S A} _ {2} (\\mathbf {z}); \\dots ; \\operatorname {S A} _ {k} (\\mathbf {z}) \\right] \\mathbf {U} _ {m}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.376, + 0.892, + 0.44 + ], + "angle": 0, + "content": "where \\(\\mathbf{U}_{qkv} \\in \\mathbb{R}^{D \\times 3D_k}\\) and \\(\\mathbf{U}_m \\in \\mathbb{R}^{k \\cdot D_k \\times D}\\). Let \\(A = \\frac{\\mathbf{q}\\mathbf{k}^T}{\\sqrt{D_k}} \\in \\mathbb{R}^{N \\times N}\\) denote the attention matrix. Our ASAD performs spatial-attention dropout on \\(A\\) so as to remove some within-frame interactions." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.443, + 0.892, + 0.563 + ], + "angle": 0, + "content": "Temporal matching probability. We first need to consider the best tokens on which to apply ASAD. Intuitively, a query token that has a strong match in the other frame should be a good candidate, since, in the absence of within-frame cues, it can still be reconstructed well using the temporal cues in the other frame. Here, we define a temporal matching function \\( f_{tem}(\\cdot) \\) to measure the temporal matching probability of the \\( i \\)-th query token:" + }, + { + "type": "equation", + "bbox": [ + 0.526, + 0.571, + 0.891, + 0.597 + ], + "angle": 0, + "content": "\\[\nf _ {t e m} (i) = \\max _ {j \\in \\Omega_ {t} (i)} \\left(\\hat {A} _ {i, j}\\right), \\quad \\hat {A} = \\operatorname {s o f t m a x} _ {\\text {r o w}} (A), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.604, + 0.892, + 0.71 + ], + "angle": 0, + "content": "where the softmax function is applied on each row of \\( A \\), \\( f_{tem}(i) \\in [0,1] \\), and \\( \\Omega_t(i) \\) denotes the temporal index set of the \\( i \\)-th query token, which contains all the token indices of the other frame. A larger value of \\( f_{tem}(i) \\) indicates a larger probability that the \\( i \\)-th query token is well-matched in the other frame, and thus a good candidate for ASAD. A visualization of \\( f_{tem}(\\cdot) \\) is shown in Fig. 5." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.71, + 0.891, + 0.77 + ], + "angle": 0, + "content": "Overall dropout probability measurement. The overall spatial-attention dropout probability at location \\((i,j)\\) is measured by using both the temporal matching probability and the normalized spatial importance:" + }, + { + "type": "equation", + "bbox": [ + 0.591, + 0.778, + 0.891, + 0.818 + ], + "angle": 0, + "content": "\\[\nW _ {i, j} = f _ {\\text {t e m}} (i) \\frac {\\hat {A} _ {i , j}}{\\sum_ {j \\in \\Omega_ {s} (i)} \\hat {A} _ {i , j}}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.825, + 0.892, + 0.9 + ], + "angle": 0, + "content": "where \\(\\Omega_s(i)\\) is the spatial index set that contains all the other token indices (i.e., excluding the query index itself) in the same frame as the \\(i\\)-th query. When \\(W_{i,j}\\) is large, the \\(i\\)-th query token has a good between-frame match, and meanwhile the \\(j\\)-th within-frame token is important for the \\(i\\)-th" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14564" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.468, + 0.168 + ], + "angle": 0, + "content": "query. In this case, dropping the attention element \\((i,j)\\) in \\(A\\) facilitates the model to use between-frame (temporally-matched) tokens for token learning or reconstruction. Finally, we set the dropout probability for self-attention and temporal-self-attention to be 0, i.e., \\(W_{i,i} = W_{i,i + N / 2} = 0\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.169, + 0.468, + 0.258 + ], + "angle": 0, + "content": "Note that there are \\( N(N / 2 - 1) \\) (i.e., excluding self-attention elements) spatial-attention elements in total, and only these spatial-attention elements are considered for dropout. With a pre-defined dropout ratio \\( P \\), we globally drop a total of \\( N_{d} = PN(N / 2 - 1) \\) attention elements from \\( A \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.261, + 0.468, + 0.397 + ], + "angle": 0, + "content": "Sampling for Dropout. We draw \\( N_{d} \\) elements from a multinomial distribution based on the dropout probability matrix \\( W \\). Then we drop the elements in \\( A \\) with the corresponding indices by setting their values to \\( -\\infty \\). After applying the softmax function in (1), the corresponding spatial-attention weights are removed. The other operations are the same with the original multi-head self attention mechanisms used in ViT. The PyTorch-like pseudocode is presented in the Supplemental." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.398, + 0.468, + 0.503 + ], + "angle": 0, + "content": "Our ASAD method has negligible additional time cost compared with TwinMAE, due to the efficient matrix operation in GPUs. We apply ASAD to each layer in the decoder during the pre-training stage, so as to learn encoder representations that support temporal matching. In the next section, we introduce downstream task fine-tuning based on the well pre-trained ViT model." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.518, + 0.416, + 0.535 + ], + "angle": 0, + "content": "3.4. Downstream Temporal Matching Tasks" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.543, + 0.468, + 0.588 + ], + "angle": 0, + "content": "After obtaining the pre-trained DropMAE model, we fine-tune the well-learned encoder (i.e., the ViT model) on downstream temporal matching tasks, i.e., VOT and VOS." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.608, + 0.291, + 0.623 + ], + "angle": 0, + "content": "3.4.1 Video Object Tracking" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.634, + 0.468, + 0.785 + ], + "angle": 0, + "content": "Recently, the MAE ViT models pre-trained on ImageNet are applied to VOT and show impressive results. We use the state-of-the-art tracker OSTrack [97] as our baseline tracker for fine-tuning. In OSTrack, the cropped template and search images are firstly serialized into sequences and concatenated together. Then the overall sequence is added with the positional embeddings and input to the ViT backbone for joint feature extraction and interaction. Finally, the updated search features are input to a prediction head to predict the target bounding box." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.787, + 0.468, + 0.907 + ], + "angle": 0, + "content": "During the fine-tuning stage, we use our pre-trained DropMAE encoder weights to initialize the ViT backbone used in OSTrack. Meanwhile, two frame identity embeddings are respectively added to template and search embeddings, in order to keep consistency with the pre-training stage. We use the same training losses of the original OSTrack. The detailed training parameters are shown in Supplementary for reference." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.092, + 0.744, + 0.107 + ], + "angle": 0, + "content": "3.4.2 Video Object Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.115, + 0.892, + 0.145 + ], + "angle": 0, + "content": "For VOS, there are currently no methods based on ViT. Thus, we build a simple VOS baseline with a ViT backbone." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.146, + 0.892, + 0.281 + ], + "angle": 0, + "content": "Input serialization. Given a template frame with a binary mask, VOS aims to segment the object-of-interest in each frame of a video. Similar to the pre-training stage, the binary mask map, template and search frames are firstly converted to patch sequences, and then linearly projected and added with positional embeddings. Two frame identity embeddings are added to the template and search embeddings, and the mask embeddings are added to the template embeddings for mask encoding." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.282, + 0.892, + 0.356 + ], + "angle": 0, + "content": "Joint feature extraction and interaction. The template and search embeddings are concatenated together and input to the ViT backbone for joint feature extraction and matching. We use the updated search features extracted from the last layer of ViT for mask prediction." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.357, + 0.892, + 0.447 + ], + "angle": 0, + "content": "Mask prediction. The existing VOS approaches [14, 15, 60, 96] employ multi-resolution features for mask prediction. However, the updated search features are single-resolution. We follow [45] to upsample the search features to \\(2 \\times\\) and \\(4 \\times\\) sizes via two deconvolutional modules. Finally, we use the same decoder used in [15, 60] for mask prediction." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.448, + 0.892, + 0.477 + ], + "angle": 0, + "content": "Training loss. We use the commonly-used cross entropy loss [15, 60] to train the whole network architecture." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.478, + 0.892, + 0.522 + ], + "angle": 0, + "content": "Online inference. During the online inference, we use the first frame with the mask annotation as the memory frame for online target matching in the search frame." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.523, + 0.892, + 0.553 + ], + "angle": 0, + "content": "The pipeline figure and more implementation details can be found in Supplementary." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.566, + 0.632, + 0.583 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.591, + 0.716, + 0.607 + ], + "angle": 0, + "content": "4.1. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.892, + 0.825 + ], + "angle": 0, + "content": "Datasets. In the pre-training stage, we explore various large-scale video data sources to pre-train our DropMAE model, including Kinetics-400 [40] (K400), Kinetics-600 [8] (K600), Kinetics-700 [9] (K700), Moments in Time [56] (MiT) and WebVid-2M [1]. The detailed performance comparison using different pre-training datasets is shown in the ablation study. For fine-tuning on VOT, we follow the training settings used in our baseline OSTrack [97]. We use the training splits of LaSOT [28], COCO [49], TrackingNet [57] and GOT-10k [39] for training. For the GOT-10k evaluation, we follow the one-shot evaluation and only fine-tune the model on the training split of GOT-10k. For VOS finetuning, we use Youtube-VOS [90] and Davis [64] datasets for fine-tuning following the standard convention [15, 60]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Pre-training and fine-tuning. For DropMAE pre-training, the default input is two frames with a spatial size of \\(224 \\times 224\\) pixels. The frames are randomly sampled from each video within a maximum frame gap of 50. During the pretraining, one epoch is counted when all videos are sampled" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14565" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.124, + 0.08, + 0.844, + 0.276 + ], + "angle": 0, + "content": "
MethodsPre-training DataEpochsPre-train. Time (h)GOT-10k (VOT)DAVIS-17 (VOS)
AOSR0.5SR0.75J&FJF
No Pre-training---62.772.853.769.566.972.2
Supervised IN1k [72]IN1K300-69.779.065.678.074.881.1
Supervised IN21k [66]IN21K80-70.280.765.478.575.481.7
CLIP [65]IN1K32-67.476.860.073.670.576.7
MOCO-v3 [12]IN1K300-70.180.165.378.475.481.5
BeiT [2]IN1K800103.167.476.860.076.172.779.4
MAE [36]IN1K16008473.783.270.881.778.584.9
TwinMAEK40040020.772.283.265.979.376.482.3
TwinMAEK40080041.372.983.668.580.777.983.6
TwinMAEK400160082.774.284.969.481.278.184.2
DropMAEK40040021.173.283.967.581.378.584.0
DropMAEK40080042.274.885.470.582.779.785.6
DropMAEK400160084.475.886.472.083.180.286.0
DropMAEK70080092.475.986.872.083.080.285.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.28, + 0.893, + 0.322 + ], + "angle": 0, + "content": "Table 1. Comparison of pre-training methods on downstream VOT and VOS tasks on GOT-10k [39] and DAVIS-17 [64]. All methods adopt the ViT-B/16 model [24] with \\(224\\times 224\\) input images for pre-training. The pre-training time is measured on 64 NVIDIA V100 GPUs. The best two results are shown in red and blue." + }, + { + "type": "table", + "bbox": [ + 0.108, + 0.335, + 0.861, + 0.627 + ], + "angle": 0, + "content": "
MethodSourceGOT-10k [39]TNL2K [79]LaSOText [27]LaSOT [28]
AOSR0.5SR0.75AUCPAUCPNormPAUCPNormP
SiamFC [3]ECCVW1634.835.39.829.528.623.031.126.933.642.033.9
MDNet [58]CVPR1629.930.39.9--27.934.931.839.746.037.3
ECO [19]ICCV1731.630.911.132.631.722.025.224.032.433.830.1
SiamPRN++ [41]CVPR1951.761.632.541.341.234.041.639.649.656.949.1
DiMP [4]ICCV1961.171.749.244.743.439.247.645.156.965.056.7
SiamR-CNN [74]CVPR2064.972.859.752.352.8---64.872.2-
LTMU [18]CVPR20---48.547.341.449.947.357.2-57.2
Ocean [104]ECCV2061.172.147.338.437.7---56.065.156.6
TrDiMP [76]CVPR2167.177.758.3-----63.9-61.4
TransT [13]CVPR2167.176.860.950.751.7---64.973.869.0
AutoMatch [102]ICCV2165.276.654.347.243.537.6-43.058.3-59.9
STARK [92]ICCV2168.878.164.1-----67.177.0-
KeepTrack [55]ICCV21-----48.2--67.177.270.2
MixFormer-L [17]CVPR2270.780.067.8-----70.179.976.3
SBT [87]CVPR2270.480.864.7-----66.7-71.1
UAST [98]ICML2263.574.151.4-----57.1-58.7
SwinTrack-384 [48]NeurIPS2272.480.567.855.957.149.1-55.671.3-76.5
AiATrack [32]ECCV2269.680.063.2--46.854.454.249.656.949.1
CIA50 [63]ECCV2267.979.060.350.957.6---66.2-69.6
SimTrack-L [10]ECCV2269.878.866.055.655.7---70.579.7-
OSTrack-384 [97]ECCV2273.783.270.855.956.750.561.357.671.181.177.6
DropTrackOurs75.986.872.056.957.952.763.960.271.881.878.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.63, + 0.893, + 0.66 + ], + "angle": 0, + "content": "Table 2. Comparison with state-of-the-art VOT approaches on four large-scale challenging datasets. The best two results are shown in red and blue. For GOT-10k evaluation, all the methods follow the one-shot protocol, training only on the training set in GOT-10k." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.685, + 0.47, + 0.777 + ], + "angle": 0, + "content": "once. For fair comparison, we use the same mask ratio (i.e., \\(75\\%\\)) and training hyper-parameters of MAE [36] to pretrain the TwinMAE and DropMAE models. Following [14, 15], we use a bootstrapped cross entropy loss for training. The detailed pre-training and fine-tuning hyper-parameters are in the Supplementary." + }, + { + "type": "title", + "bbox": [ + 0.076, + 0.793, + 0.423, + 0.809 + ], + "angle": 0, + "content": "4.2. Comparison with Pre-Training Methods" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.471, + 0.901 + ], + "angle": 0, + "content": "In Table 1, we compare our DropMAE with existing pre-training methods on the downstream tasks of VOT and VOS. DropMAE and TwinMAE are pre-trained using videos (K400, K700), while MAE and other methods are pre-trained on ImageNet 1k or 21k (IN1K, IN21K). The VOT and VOS baselines illustrated in Sec. 3.4 use the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.685, + 0.895, + 0.852 + ], + "angle": 0, + "content": "official pre-trained VIT-B/16 models provided by existing pre-training approaches (see Table 1) for fine-tuning. TwinMAE with 800-epoch training performs favorably against MAE on VOT, but achieves inferior results on VOS. There are two main reasons: 1) TwinMAE is not effective enough at learning temporal matches; 2) The number of object classes in K400 is limited, and meanwhile the object classes in DAVIS-17 are included in ImageNet. Thus MAE generalizes well to VOS. Our DropMAE, which is a stronger temporal matching learner, outperforms MAE on both the VOT and VOS tasks with 800-epoch training (i.e., 42.2 hours\\(^{1}\\))" + }, + { + "type": "page_footnote", + "bbox": [ + 0.499, + 0.863, + 0.895, + 0.903 + ], + "angle": 0, + "content": "In our implementation, we perform video decoding and extract the video frames on the fly in each training iteration, which could be further sped up using some tricks like repeated sampling [30]." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "14566" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.115, + 0.078, + 0.432, + 0.201 + ], + "angle": 0, + "content": "
MethodOTB100AUCITBAUCTrackingNet
AUCPNorm
SiamFC [3]58.344.157.166.3
Ocean [104]68.447.7--
ATOM [20]68.347.270.377.1
DiMP [4]53.733974.080.1
TransT [13]69.554.781.486.7
STARK [92]68.157.682.086.9
OSTrack [97]-64.883.988.5
DropTrack69.665.084.188.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.206, + 0.47, + 0.248 + ], + "angle": 0, + "content": "Table 3. Comparison with state-of-the-art VOT approaches on OTB100 [85], ITB [44] and TrackingNet [57]. The best two results are shown in red and blue." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.263, + 0.47, + 0.293 + ], + "angle": 0, + "content": "by using the K400 dataset. This indicates that our DropMAE is \\(2\\times\\) faster than MAE." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.309, + 0.34, + 0.328 + ], + "angle": 0, + "content": "5. State-of-the-art Comparison" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.335, + 0.47, + 0.412 + ], + "angle": 0, + "content": "In this section, we compare our fine-tuned VOT and VOS models, denoted as DropTrack and DropSeg, with state-of-the-art approaches on VOT and VOS benchmarks. We use DropMAE trained on K700 with 800 epochs as the pretraining model for both VOT and VOS fine-tuning." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.422, + 0.291, + 0.439 + ], + "angle": 0, + "content": "5.1. Video Object Tracking" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.446, + 0.47, + 0.734 + ], + "angle": 0, + "content": "To demonstrate the effectiveness of the proposed DropMAE for VOT, we compare our DropTrack with state-of-the-art trackers on 7 challenging tracking benchmarks. GOT-10k. GOT-10k [39] is a challenging dataset that follows the one-shot evaluation protocol, where the trackers are required to be trained on its training split, and the test object classes have no overlap with the objects in the training split. As shown in Table 2, our DropTrack achieves state-of-the-art results on this dataset, outperforming OSTrack by \\(2.2\\%\\) and \\(3.6\\%\\) in terms of AO and \\(\\mathrm{SR}_{0.5}\\). This implies that the temporal correspondence learning in the pretraining is beneficial for the downstream tracking task. Although there exists a domain gap between the pre-training data and the test data (i.e., a large portion of test objects in GOT-10k are animals, vehicles and object parts, whereas K700 only consists of human-centric action videos), the temporal matching ability learned by DropMAE can still be transferred to the downstream tracking task, improving the tracking performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.734, + 0.47, + 0.81 + ], + "angle": 0, + "content": "LaSOT. LaSOT consists of 280 long test sequences, and our results are presented in Table 2. Our DropTrack sets a new record on this dataset with \\(71.8\\%\\) AUC, \\(81.8\\%\\) \\(\\mathrm{P}_{\\text {Norm }}\\) and \\(78.1\\%\\) P, which shows the great potential of our DropTrack in robust long-term visual tracking." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.47, + 0.902 + ], + "angle": 0, + "content": "\\(\\mathbf{LaSOT}_{ext}\\). \\(\\mathbf{LaSOT}_{ext}\\) is an extension of LaSOT with more challenging video sequences for testing - similar to GOT-10k, the test split has a large gap with the training split, and sequences with novel object classes (i.e., not appeared in ImageNet) are used for evaluation. Our DropMAE outperforms the other trackers by large margins. This demon" + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.078, + 0.895, + 0.272 + ], + "angle": 0, + "content": "
MethodSourceOLMSDAVIS-2016 [62]DAVIS-2017 [64]
J&FJFJ&FJF
RANet [80]ICCV19✓85.585.585.465.763.268.2
STM [60]ICCV19✓✓89.388.789.981.879.284.3
FRTM [67]CVPR20✓✓83.583.683.476.773.979.6
TVOS [101]CVPR20✓---72.369.974.7
LWL [5]ECCV20✓✓---81.679.184.1
CFBI [95]ECCV20✓89.488.390.581.979.184.6
UniTrack [81]NeurIPS21✓----58.4-
STCN- [15]NeurIPS21✓---82.579.385.7
SSTVOS [26]CVPR21✓---82.579.985.1
SWEM- [50]CVPR22✓89.5--81.9--
RTS [61]ECCV22✓✓---80.277.982.6
OSMN [54]TPAMI1873.574.072.954.852.557.1
FAVOS [16]CVPR1881.082.479.558.254.661.8
VideoMatch [38]ECCV18-81.0-56.5--
SiamMask [77]CVPR1969.871.767.856.454.358.5
D3S [52]CVPR2074.075.472.660.857.863.8
Siam R-CNN [52]CVPR20---70.666.175.0
Unicorn [91]ECCV2287.486.588.269.265.273.2
DropSegOurs92.190.993.383.080.285.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.277, + 0.892, + 0.332 + ], + "angle": 0, + "content": "Table 4. Comparison with state-of-the-art VOS approaches on the validation sets of DAVIS-2016 [62] and DAVIS-2017 [64]. OL, M and S indicate Online Learning, using Memory mechanism, and using Synthetic videos for pre-training." + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.332, + 0.872, + 0.445 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.446, + 0.892, + 0.473 + ], + "angle": 0, + "content": "Figure 6. Ablation study of the dropout ratio \\( P \\) on the GOT-10k (VOT) and DAVIS-17 (VOS) datasets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.49, + 0.892, + 0.732 + ], + "angle": 0, + "content": "strates that a tracker with DropMAE pre-training generalizes well to unseen objects in generic visual object tracking. TNL2K. TNL2K is a large-scale evaluation dataset that consists of 700 test videos with various challenges, such as significant appearance variation and manually added adversarial samples. As illustrated in Table 2, our DropMAE significantly outperforms the other trackers on this dataset. ITB, TrackingNet and OTB100. In Table 3, we evaluate our DropTrack on ITB [44], OTB100 [85] and TrackingNet [57], achieving state-of-the-art performance on each one. DropTrack is slightly better than OSTrack on ITB and TrackingNet. We believe the main reason is the fully overlapped training and test object classes in these two datasets, which reduces the effect of pre-training. A competitive tracker on these two datasets can be learned even using supervised ImageNet weights, which has been shown in [97]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.732, + 0.892, + 0.822 + ], + "angle": 0, + "content": "On all 7 VOT datasets, our DropTrack outperforms the baseline OSTrack, which demonstrates that our DropMAE pre-training on videos learns better temporal-matching representations than the MAE model trained on ImageNet, resulting in more a robust tracker that generalizes well to both unseen and seen objects." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.832, + 0.747, + 0.849 + ], + "angle": 0, + "content": "5.2. Video Object Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.855, + 0.891, + 0.885 + ], + "angle": 0, + "content": "In Table 4, we compare our DropSeg with existing VOS approaches on the DAVIS-16/17 [62,64]." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.886, + 0.891, + 0.902 + ], + "angle": 0, + "content": "DAVIS-16. DAVIS-16 is composed of 20 manually anno" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14567" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.464, + 0.187 + ], + "angle": 0, + "content": "
DatasetsNo. \nVideosNo. \nActionsVOTVOS
AOSR0.5SR0.75J&F
K400 [40]240,00040073.283.967.582.7
K600 [8]390,00060074.585.569.582.8
K700 [9]526,76870075.686.271.483.0
MiT [56]802,24433975.185.570.682.8
WebVid [1]240,000-72.883.467.381.5
WebVid [1]960,000-73.485.069.582.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.189, + 0.468, + 0.231 + ], + "angle": 0, + "content": "Table 5. The downstream VOT and VOS performance on GOT-10k and DAVIS-17 obtained by using our DropMAE pre-trained on various video datasets. VOS uses 800 epochs pre-training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.247, + 0.468, + 0.382 + ], + "angle": 0, + "content": "tated test sequences. As shown in Table 4, our one-shot DropSeg approach, without using any online learning and complicated memory mechanisms, achieves the best \\(\\mathcal{J}\\&\\mathcal{F}\\) score of \\(92.1\\%\\), which significantly outperforms the other compared one-shot approaches and is even better than the approaches with complicated pipelines (i.e., OL, M and S). This implies that the pixel-wise correspondence learned during the pre-training is effective for capturing long-range dependencies between various frames in VOS." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.383, + 0.468, + 0.459 + ], + "angle": 0, + "content": "DAVIS-17. DAVIS-17 is an extension of DAVIS-16, comprising more challenging videos and supports multi-object segmentation. In Table 4, our DropSeg achieves competitive results of \\(83.0\\%\\) \\(\\mathcal{I}\\& \\mathcal{F}\\), \\(80.2\\%\\) \\(\\mathcal{I}\\) and \\(85.7\\%\\) \\(\\mathcal{F}\\), which shows its superiority in handling more challenging videos." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.459, + 0.468, + 0.489 + ], + "angle": 0, + "content": "More VOS results and comparisons are included in the supplementary." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.498, + 0.241, + 0.513 + ], + "angle": 0, + "content": "6. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.523, + 0.468, + 0.569 + ], + "angle": 0, + "content": "In this section, we conduct ablation studies to provide more detailed analysis of our method. We use DropMAE with 400-epoch pre-training for the ablation study." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.569, + 0.468, + 0.689 + ], + "angle": 0, + "content": "The effect of dropout ratio \\( P \\). We study the effect of dropout rate \\( P \\) in Fig. 6. A relatively small dropout ratio of \\( P = 0.1 \\) works well on both VOT and VOS tasks. Meanwhile, dropping too many spatial cues (e.g., \\( P = 0.2 \\)) degrades the downstream tasks, which is mainly because the spatial cues are also useful for accurate localization and segmentation. \\( P = 0.1 \\) is the optimal setting, and thus we adopt it in the following experiments." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Pre-training video sources. Since we are the first to explore masked autoencoder pre-training for temporal matching tasks, it is not clear which video dataset is the optimal choice for pre-training. Here, we use five popular video datasets for pre-training, including K400 [40], K600 [8], K700 [9], MiT [56] and WebVid-2M [1]. For WebVid-2M, we randomly sample 240k and 960k videos for fair comparison and faster validation. The downstream tracking results are reported in Table 5. Performance is not favorable even using 960,000 videos in WebVid for pre-training. This indicates that WebViD is not a good choice for tracking pre-training, which is mainly because it is a video caption dataset that focuses on scene diversity and lacks rich object motion. From the experiments on the K400/600/700 and" + }, + { + "type": "table", + "bbox": [ + 0.582, + 0.089, + 0.808, + 0.152 + ], + "angle": 0, + "content": "
SettingsGOT-10k
DropTrack-K400-400E73.2/67.5
w/ ASAP in Encoder73.1/68.1
w/ domain specific data73.4/68.8
w/o frame identity embed72.9/67.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.153, + 0.892, + 0.181 + ], + "angle": 0, + "content": "Table 6. The tracking performance of \\( \\mathrm{{AO}}/{\\mathrm{{SR}}}_{0.75} \\) on GOT10-k reported by variants with different settings." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.192, + 0.892, + 0.238 + ], + "angle": 0, + "content": "MiT, tracking benefits from pre-training with from rich action classes (i.e., 700 action classes of K700), from which the model can learn stronger temporal matching ability." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.239, + 0.892, + 0.328 + ], + "angle": 0, + "content": "Applying ASAD to the encoder. Here we test applying ASAD to all layers including both encoder and decoder of masked autoencoder. As shown in Table 6, this variant gains improvements (0.6% in \\(\\mathrm{SR}_{0.75}\\)) over the original baseline. Considering its additional cost and limited performance improvement, we only apply ASAD to the decoder." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.33, + 0.892, + 0.45 + ], + "angle": 0, + "content": "Domain specific data. We also add the tracking training data (without using box annotations), including TrackingNet, LaSOT, and GOT-10k, into K400 for pre-training. The downstream tracking performance by using the larger pre-training set is 73.4/68.8, which is better than the baseline. It shows that the domain-specific data is helpful to bridge the domain gap, which can be considered as future work to extend Kinetic datasets with more tracking videos." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.451, + 0.892, + 0.541 + ], + "angle": 0, + "content": "Frame identity embedding. During pre-training, the frame identity embedding is used to identify masked patches in the same 2D location of the two frames. From Table 6, we can find that downstream fine-tuning without the frame identity embedding performs worse than with it, since not using it is inconsistent with the pre-training stage." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.547, + 0.619, + 0.563 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.573, + 0.892, + 0.815 + ], + "angle": 0, + "content": "This paper investigated masked autoencoding pretraining for temporal matching-based downstream tasks. Specifically, an adaptive spatial-attention dropout method is proposed to facilitate temporal correspondence learning in self-supervised pre-training on videos. We show that our proposed pre-training method DropMAE can achieve better downstream performance on VOT and VOS than the image-based MAE, while using \\(50\\%\\) less pre-training time. In addition, as the first work investigating this problem, we show the guidelines of selecting video sources for pre-training, i.e., selecting videos with rich motion information is more beneficial for temporal matching-based downstream tasks. The experimental results on VOT and VOS show that our DropMAE sets new state-of-the-art results on 8 out of 9 tracking benchmarks. We expect our DropMAE to serve as a strong pre-trained backbone in future work." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.83, + 0.671, + 0.847 + ], + "angle": 0, + "content": "8. Acknowledgment" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "This work was supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CityU 11215820)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14568" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.096, + 0.116, + 0.47, + 0.157 + ], + "angle": 0, + "content": "[1] Max Bain, Arsha Nagrani, Gül Varol, and Andrew Zisserman. Frozen in time: A joint video and image encoder for end-to-end retrieval. In ICCV, 2021. 5, 8" + }, + { + "type": "ref_text", + "bbox": [ + 0.095, + 0.159, + 0.471, + 0.186 + ], + "angle": 0, + "content": "[2] H. Bao, L. Dong, and F. Wei. Beit: Bert pre-training of image transformers. 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Chan $^{1}$ $^{1}$ Department of Computer Science, City University of Hong Kong + $^{2}$ International Digital Economy Academy + $^{3}$ Tencent AI Lab + $^{4}$ School of Data Science, The Chinese University of Hong Kong, Shenzhen + +{qiangqwu2-c, ziquanliu2-c}@my.cityu.edu.hk, tianyu-yang@outlook.com wubaoyuan@cuhk.edu.cn, yingsshan@tencent.com, abchan@cityu.edu.hk + +# Abstract + +In this paper, we study masked autoencoder (MAE) pretraining on videos for matching-based downstream tasks, including visual object tracking (VOT) and video object segmentation (VOS). A simple extension of MAE is to randomly mask out frame patches in videos and reconstruct the frame pixels. However, we find that this simple baseline heavily relies on spatial cues while ignoring temporal relations for frame reconstruction, thus leading to sub-optimal temporal matching representations for VOT and VOS. To alleviate this problem, we propose DropMAE, which adaptively performs spatial-attention dropout in the frame reconstruction to facilitate temporal correspondence learning in videos. We show that our DropMAE is a strong and efficient temporal matching learner, which achieves better fin-tuning results on matching-based tasks than the ImageNet-based MAE with $2 \times$ faster pre-training speed. Moreover, we also find that motion diversity in pre-training videos is more important than scene diversity for improving the performance on VOT and VOS. Our pre-trained DropMAE model can be directly loaded in existing ViT-based trackers for fine-tuning without further modifications. Notably, DropMAE sets new state-of-the-art performance on 8 out of 9 highly competitive video tracking and segmentation datasets. Our code and pre-trained models are available at https://github.com/jimmy-dq/DropMAE.git. + +# 1. Introduction + +Recently, transformers have achieved enormous success in many research areas, such as natural language processing (NLP) [6, 22], computer vision [97] and audio generation [43, 73]. In NLP, masked autoencoding is commonly used to train large-scale generalizable NLP transformers contain- + +![](images/e7d6e014764de89d35928317174cc4c910bea04284f0e58182ea59f5a2ddc3b2.jpg) +Figure 1. State-of-the-art comparison on GOT-10k [39] following the one-shot protocol. Our DropTrack with the proposed DropMAE pre-training achieves state-of-the-art performance without using complicated pipelines such as online updating. + +ing billions of parameters. Inspired by the great success of self-supervised learning in NLP, recent advances [36, 89] in computer vision suggest that training large-scale vision transformers may undertake a similar trajectory with NLP. The seminal work MAE [36] reconstructs the input image from a small portion of patches. The learned representation in this masked autoencoder has been demonstrated to be effective in many computer vision tasks, such as image classification, object detection and semantic segmentation. + +In video object tracking (VOT), recently two works, SimTrack [10] and OSTrack [97], explore using an MAE pre-trained ViT model as the tracking backbone. Notably, these two trackers achieve state-of-the-art performance on existing tracking benchmarks without using complicated tracking pipelines. The key to their success is the robust pre-training weights learned by MAE on ImageNet [68]. In addition, [10, 97] also demonstrate that, for VOT, MAE unsupervised pre-training on ImageNet is more effective than supervised pre-training using class labels – this is mainly because MAE pre-training learns more fine-grained local + +![](images/6530ce119ca61be6f977a4dbc61cb893fe139c97b44268ddbd165eeb23fc1924.jpg) +TwinMAE (Layer-6) + +![](images/405a66ef12c21545d00e72c09b400aa6f600b37b6b92e387998bd2c6922b47d9.jpg) +TwinMAE (Layer-8) + +![](images/60b6a096c2fc3930ccbf0ff72a45b7d1ffa1e3bb0fd00108eccd6c71e3424d8f.jpg) +DropMAE (Layer-6) + +![](images/8a1bfd9080640ba61dcd1127f2babe6185cba5793a9c23c62d4e4392c929d139.jpg) +DropMAE (Layer-8) +Figure 2. Visualization of the attention maps of the TwinMAE baseline and our DropMAE in the reconstruction of a random masked patch, which is denoted as a red bounding box in the left input frame. TwinMAE leverages the spatial cues (within the same frame) more than temporal cues (between frames) for reconstruction. Our proposed DropMAE improves the baseline by effectively alleviating co-adaptation between spatial cues in the reconstruction, focusing more on temporal cues, thus achieving better learning of temporal correspondences for VOT and VOS. + +structures that are useful for accurate target localization required for VOT, whereas supervised training learns high-level class-related features that are invariant over appearance changes. Despite the promising performance achieved by [10,97], the MAE pre-training on ImageNet could still be sub-optimal for the tracking task due to the natural gap between images and videos, i.e., no prior temporal correspondence information can be learned in static images. However, previous tracking methods [3,42,83] have shown that temporal correspondence learning is the key in developing a robust and discriminative tracker. Thus there is an opportunity to further develop the MAE framework specifically for matching-base video tasks, such as VOT and VOS. + +One simple way to extend MAE to videos is to randomly mask out frame patches in a video clip (i.e., video frame pairs) and then reconstruct the video clip. We denote this simple baseline as twin MAE (TwinMAE). Given a masked patch query, as illustrated in Figs. 2 & 4, we find that TwinMAE heavily relies on the spatially neighbouring patches within the same frame to reconstruct the masked patch, which implies a heavy co-adaptation of spatial cues (within-frame tokens) for reconstruction and may cause learning of sub-optimal temporal representations for matching-based downstream tasks like video object tracking and segmentation. + +To address this issue with the TwinMAE baseline, we propose DropMAE specifically designed for pre-training a masked autoencoder for matching-based video downstream tasks (e.g., VOT and VOS). Our DropMAE adaptively performs spatial-attention dropout to break up co-adaptation between spatial cues (within-frame tokens) during the frame reconstruction, thus encouraging more temporal interactions and facilitating temporal correspondence learning in + +the pre-training stage. Interestingly, we obtain several important findings with DropMAE: 1) DropMAE is an effective and efficient temporal correspondence learner, which achieves better fine-tuning results on matching-based tasks than the ImageNet-based MAE with $2 \times$ faster pre-training speed. 2) Motion diversity in pre-training videos is more important than scene diversity for improving the performance on VOT and VOS. + +We conduct downstream task evaluation on 9 competitive VOT and VOS benchmarks, achieving state-of-the-art performance on these benchmarks. In particular, our trackers with DropMAE pre-training obtain $75.9\%$ AO on GOT-10k, $52.7\%$ AUC on $\mathrm{LaSOT}_{ext}$ , $56.9\%$ AUC on TNL2K and $92.1\% /83.0\%$ $\mathcal{J}\& \mathcal{F}$ scores on DAVIS-16/17, w/o using complicated online updating or memory mechanisms. + +In summary, the main contributions of our work are: + +- To the best of our knowledge, we are the first to investigate masked autoencoder video pre-training for temporal matching-based downstream tasks. Specifically, we explore various video data sources for pre-training and build a TwinMAE baseline to study its effectiveness on temporal matching tasks. Since none exists, we further build a ViT-based VOS baseline for fine-tuning. +- We propose DropMAE, which adaptively performs spatial-attention dropout in the frame reconstruction to facilitate effective temporal correspondence learning in videos. +- Our trackers with DropMAE pre-training sets new state-of-the-art performance on 8 out of 9 highly competitive video tracking and segmentation benchmarks without complicated tracking pipelines. + +# 2. Related Work + +Visual object tracking and segmentation. Given an annotated bounding box in the first frame of a test video, visual object tracking (VOT) aims to accurately predict the target's bounding boxes in the following frames. Similarly, for visual object segmentation (VOS), given an annotated binary mask in the first frame, VOS aims to predict dense target masks in the remaining frames. In the early development of VOT, correlation filter-based approaches [19, 21, 31, 37, 46, 47, 51, 53, 82, 84] are dominant trackers due to their favorable ability in modeling target appearance variation. With the development of deep learning, deep Siamese networks [70, 78] are introduced to VOT. The representative work SiamFC [3] takes template and search images as input for target localization. Based on SiamFC, many improvements have been made, e.g., scale regression [41, 42, 94], online template updating [34, 93, 99], multilevel feature fusion [29], loss design [23] and backbone design [10, 41, 97, 103]. For VOS, matching-based approaches, e.g., STM [60], AOT [96] and STCN [15], achieve promising results on existing VOS benchmarks. Recent improve + +ments [14, 50] on online memory design further improve the previous SOTA results in VOS. Recent studies including SimTrack [10] and OSTrack [97] show that the ViT backbone [24] with MAE pre-training on ImageNet is effective for object tracking. + +Despite the great success of ViT with MAE pre-training on tracking, this static ImageNet-based pre-training still lacks temporal correspondence learning. Moreover, the developments of VOT and VOS show that learning strong temporal matching ability is essential for video tracking tasks. To the best of our best knowledge, we are the first to investigate masked autoencoder self-supervised video pretraining for tracking tasks. Our proposed DropMAE can learn reliable temporal correspondences, which we demonstrate are effective for downstream tracking tasks. + +Self-supervised Learning. Self-supervised learning has received significant interest in the past few decades. There are many manually-designed pretext tasks for pre-training, such as image colorization [100], jigsaw puzzle solving [59], future frame prediction [69, 75] and rotation prediction [33]. Contrastive learning approaches [7, 11, 25, 35, 86, 88] are the mainstream self-supervised methods in recent years. However, these methods are sensitive to the type and strength of applied data augmentation, which makes them hard to train. Inspired by masked language modeling [6, 22], masked image modeling (MIM) approaches are proposed for learning unsupervised image [36, 89] or video representations [30, 71], which have been shown to be effective for many downstream tasks including image classification, object detection and video action recognition. However, there is no specifically designed pre-training approaches for temporal matching-based task, such as VOT and VOS. In this work, we propose DropMAE to explore this direction. + +# 3. Method + +We propose a self-supervised video pre-training method to learn robust representations for temporal matching-based downstream tasks, including VOT and VOS tasks. We firstly introduce a simple extension of MAE to temporal matching representation learning from video, (TwinMAE). We then illustrate the limitations of the TwinMAE baseline and propose a spatial-attention dropout strategy to facilitate temporal correspondence learning, denoted as DropMAE. The overall pipeline of both DropMAE and TwinMAE is shown in Fig. 3. Finally, we introduce the VOT and VOS methods used for fine-tuning the downstream tasks. + +# 3.1. Temporal Masked Autoencoder (TwinMAE) + +The masked autoencoder (MAE) model [36] consists of an encoder and a decoder. Its basic idea is to randomly mask out a large portion (e.g., $75\%$ ) of patches in an image and then reconstruct the image pixels. Specifically, the encoder only takes visible patches as input for feature + +![](images/3293ae28c6284e5210978380adb58fd2e22443cb556269346e8033a5c2f4e92d.jpg) +Figure 3. An illustration of our DropMAE. The proposed adaptive spatial-attention dropout (ASAD) facilitates temporal correspondence learning for temporal matching tasks. TwinMAE follows the same pipeline except that the ASAD module is not used. + +learning, and then the decoder is input with both visible and masked patches to produce the image reconstruction. In order to adapt to downstream video matching-based tasks, one naive extension is to directly apply MAE on concatenated video frames, hoping to learn temporal matching representations from video frame pairs, which we denote as TwinMAE. + +It should be noted that existing works [30,71] that extend MAE to video representation learning are mainly designed for the downstream task of video action recognition, where a long video clip (e.g., 16 frames) is used for reconstruction-based pre-training. To keep consistent with our downstream tasks of VOT/VOS, we follow the general training settings used in object tracking [3,97], where two frames are sampled from one video as input to TwinMAE for pre-training. This adaptation significantly reduces the computational and memory cost compared to existing video pre-training approaches [30, 71], due to the quadratic complexity of ViTs. + +Patch embedding. Firstly, we randomly sample 2 frames within a video with a predefined maximal frame gap. For each frame, we follow the vanilla ViT to divide it into non-overlapping patches. The patches extracted from the two frames are then concatenated together to form the overall patch sequence. We then randomly mask out patches in the patch sequence until a predefined mask ratio is reached. Note that we use the same mask ratio (i.e., $75\%$ ) with the original MAE, since the information redundancy of two frames should be similar to a single image. The visible patches are embedded by linear projection [24], and the masked patches are embedded using a shared learnable mask token. All the embedded patches are added with positional embeddings [24]. + +Frame identity embedding. To distinguish between the masked tokens in the same spatial location of the two frames, we use two learnable frame identity embeddings to indicate the two input frames. The corresponding frame identity embedding is added to each embedded patch. + +Autoencoder and Training. Following the autoencoding pipeline in the original MAE [36], the encoder only takes visible embedded patches as input, and the decoder is input with all the embedded patches for masked patch reconstruction. We use the same normalized pixel loss from MAE for + +![](images/0b86d533f9b1810228924c7f3db5c4e248b6c4922ea43cf8536348b0c01e4311.jpg) +Figure 4. The average within-frame and between-frame attention scores obtained by TwinMAE and DropMAE in different decoder layers. The attention score is calculated on 20 randomly sampled K400 validation videos, and is averaged on all heads and locations. + +training the whole network architecture. + +# 3.2. Limitation of TwinMAE Baseline + +The visualization of the reconstruction for our TwinMAE baseline is shown in Fig. 2. We also quantitatively compare the average within-frame and between-frame attentions during the reconstruction in Fig. 4. Interestingly, we find the TwinMAE reconstruction heavily relies on within-frame patches or spatial cues, which may lead to sub-optimal temporal representations for matching-based video tasks. + +When only using within-frame spatial cues, the decoder will perform the reconstruction using only context information in the neighboring patches, and thus the learned encoder representations will embed context information. In contrast, when using between-frame cues, the decoder will learn to perform matching of patches between frames so as to recover the corresponding target patch in the other frame. Thus, decoding with between-frame cues will make the encoder learn representations that support temporal matching between frames. Previous works in object tracking [3, 83] also suggest that temporal correspondence learning plays a key role in developing a robust and discriminative tracker. Since TwinMAE relies more on context information, it is still suboptimal for downstream tracking tasks. + +# 3.3. Adaptive Spatial-Attention Dropout + +To address issue of TwinMAE discussed in Sec. 3.2, we propose a Adaptive Spatial-Attention Dropout (ASAD) to facilitate the temporal correspondence learning in the temporal MAE. Given a query token, our basic idea is to adaptively drop a portion of its within-frame cues in order to facilitate the model to learn more reliable temporal correspondence, i.e., between-frame cues. That is, we restrict the interactions between the query token and tokens in the same frame, and encourage more interactions with tokens in the other frame, through manipulation of the computed spatial-attention in the transformer. Therefore, to minimize the reconstruction loss, the model is facilitated to learn a better temporal matching ability, which is essential in matching-based video tasks. + +Before introducing the proposed ASAD, we firstly revisit + +![](images/62cca43fd372487f30c55ac9e42300f13a96114d6e210ccca736660ae16c2b6f.jpg) +Figure 5. Visualization of the temporal matching function $f_{tem}$ on an example frame pair. A large value of $f_{tem}(i)$ indicates that the $i$ -th pixel matches well to a pixel in the other frame. + +the multi-head self-attention in ViT [24]. Let $\mathbf{z} \in \mathbb{R}^{N \times D}$ be the input sequence of the two concatenated input frames, $N$ denotes the total patch number in the two frames and $D$ is the feature dimension. The standard multi-head self-attention [24] can be formulated as: + +$$ +[ \mathbf {q}, \mathbf {k}, \mathbf {v} ] = \mathbf {z} \mathbf {U} _ {q k v}, \quad \mathrm {S A} (\mathbf {z}) = \operatorname {s o f t m a x} \left(\frac {1}{\sqrt {D _ {k}}} \mathbf {q} \mathbf {k} ^ {T}\right), \tag {1} +$$ + +$$ +\operatorname {M S A} (\mathbf {z}) = \left[ \operatorname {S A} _ {1} (\mathbf {z}); \operatorname {S A} _ {2} (\mathbf {z}); \dots ; \operatorname {S A} _ {k} (\mathbf {z}) \right] \mathbf {U} _ {m}, \tag {2} +$$ + +where $\mathbf{U}_{qkv} \in \mathbb{R}^{D \times 3D_k}$ and $\mathbf{U}_m \in \mathbb{R}^{k \cdot D_k \times D}$ . Let $A = \frac{\mathbf{q}\mathbf{k}^T}{\sqrt{D_k}} \in \mathbb{R}^{N \times N}$ denote the attention matrix. Our ASAD performs spatial-attention dropout on $A$ so as to remove some within-frame interactions. + +Temporal matching probability. We first need to consider the best tokens on which to apply ASAD. Intuitively, a query token that has a strong match in the other frame should be a good candidate, since, in the absence of within-frame cues, it can still be reconstructed well using the temporal cues in the other frame. Here, we define a temporal matching function $f_{tem}(\cdot)$ to measure the temporal matching probability of the $i$ -th query token: + +$$ +f _ {t e m} (i) = \max _ {j \in \Omega_ {t} (i)} \left(\hat {A} _ {i, j}\right), \quad \hat {A} = \operatorname {s o f t m a x} _ {\text {r o w}} (A), \tag {3} +$$ + +where the softmax function is applied on each row of $A$ , $f_{tem}(i) \in [0,1]$ , and $\Omega_t(i)$ denotes the temporal index set of the $i$ -th query token, which contains all the token indices of the other frame. A larger value of $f_{tem}(i)$ indicates a larger probability that the $i$ -th query token is well-matched in the other frame, and thus a good candidate for ASAD. A visualization of $f_{tem}(\cdot)$ is shown in Fig. 5. + +Overall dropout probability measurement. The overall spatial-attention dropout probability at location $(i,j)$ is measured by using both the temporal matching probability and the normalized spatial importance: + +$$ +W _ {i, j} = f _ {\text {t e m}} (i) \frac {\hat {A} _ {i , j}}{\sum_ {j \in \Omega_ {s} (i)} \hat {A} _ {i , j}}, \tag {4} +$$ + +where $\Omega_s(i)$ is the spatial index set that contains all the other token indices (i.e., excluding the query index itself) in the same frame as the $i$ -th query. When $W_{i,j}$ is large, the $i$ -th query token has a good between-frame match, and meanwhile the $j$ -th within-frame token is important for the $i$ -th + +query. In this case, dropping the attention element $(i,j)$ in $A$ facilitates the model to use between-frame (temporally-matched) tokens for token learning or reconstruction. Finally, we set the dropout probability for self-attention and temporal-self-attention to be 0, i.e., $W_{i,i} = W_{i,i + N / 2} = 0$ . + +Note that there are $N(N / 2 - 1)$ (i.e., excluding self-attention elements) spatial-attention elements in total, and only these spatial-attention elements are considered for dropout. With a pre-defined dropout ratio $P$ , we globally drop a total of $N_{d} = PN(N / 2 - 1)$ attention elements from $A$ . + +Sampling for Dropout. We draw $N_{d}$ elements from a multinomial distribution based on the dropout probability matrix $W$ . Then we drop the elements in $A$ with the corresponding indices by setting their values to $-\infty$ . After applying the softmax function in (1), the corresponding spatial-attention weights are removed. The other operations are the same with the original multi-head self attention mechanisms used in ViT. The PyTorch-like pseudocode is presented in the Supplemental. + +Our ASAD method has negligible additional time cost compared with TwinMAE, due to the efficient matrix operation in GPUs. We apply ASAD to each layer in the decoder during the pre-training stage, so as to learn encoder representations that support temporal matching. In the next section, we introduce downstream task fine-tuning based on the well pre-trained ViT model. + +# 3.4. Downstream Temporal Matching Tasks + +After obtaining the pre-trained DropMAE model, we fine-tune the well-learned encoder (i.e., the ViT model) on downstream temporal matching tasks, i.e., VOT and VOS. + +# 3.4.1 Video Object Tracking + +Recently, the MAE ViT models pre-trained on ImageNet are applied to VOT and show impressive results. We use the state-of-the-art tracker OSTrack [97] as our baseline tracker for fine-tuning. In OSTrack, the cropped template and search images are firstly serialized into sequences and concatenated together. Then the overall sequence is added with the positional embeddings and input to the ViT backbone for joint feature extraction and interaction. Finally, the updated search features are input to a prediction head to predict the target bounding box. + +During the fine-tuning stage, we use our pre-trained DropMAE encoder weights to initialize the ViT backbone used in OSTrack. Meanwhile, two frame identity embeddings are respectively added to template and search embeddings, in order to keep consistency with the pre-training stage. We use the same training losses of the original OSTrack. The detailed training parameters are shown in Supplementary for reference. + +# 3.4.2 Video Object Segmentation + +For VOS, there are currently no methods based on ViT. Thus, we build a simple VOS baseline with a ViT backbone. + +Input serialization. Given a template frame with a binary mask, VOS aims to segment the object-of-interest in each frame of a video. Similar to the pre-training stage, the binary mask map, template and search frames are firstly converted to patch sequences, and then linearly projected and added with positional embeddings. Two frame identity embeddings are added to the template and search embeddings, and the mask embeddings are added to the template embeddings for mask encoding. + +Joint feature extraction and interaction. The template and search embeddings are concatenated together and input to the ViT backbone for joint feature extraction and matching. We use the updated search features extracted from the last layer of ViT for mask prediction. + +Mask prediction. The existing VOS approaches [14, 15, 60, 96] employ multi-resolution features for mask prediction. However, the updated search features are single-resolution. We follow [45] to upsample the search features to $2 \times$ and $4 \times$ sizes via two deconvolutional modules. Finally, we use the same decoder used in [15, 60] for mask prediction. + +Training loss. We use the commonly-used cross entropy loss [15, 60] to train the whole network architecture. + +Online inference. During the online inference, we use the first frame with the mask annotation as the memory frame for online target matching in the search frame. + +The pipeline figure and more implementation details can be found in Supplementary. + +# 4. Experiments + +# 4.1. Implementation Details + +Datasets. In the pre-training stage, we explore various large-scale video data sources to pre-train our DropMAE model, including Kinetics-400 [40] (K400), Kinetics-600 [8] (K600), Kinetics-700 [9] (K700), Moments in Time [56] (MiT) and WebVid-2M [1]. The detailed performance comparison using different pre-training datasets is shown in the ablation study. For fine-tuning on VOT, we follow the training settings used in our baseline OSTrack [97]. We use the training splits of LaSOT [28], COCO [49], TrackingNet [57] and GOT-10k [39] for training. For the GOT-10k evaluation, we follow the one-shot evaluation and only fine-tune the model on the training split of GOT-10k. For VOS finetuning, we use Youtube-VOS [90] and Davis [64] datasets for fine-tuning following the standard convention [15, 60]. + +Pre-training and fine-tuning. For DropMAE pre-training, the default input is two frames with a spatial size of $224 \times 224$ pixels. The frames are randomly sampled from each video within a maximum frame gap of 50. During the pretraining, one epoch is counted when all videos are sampled + +
MethodsPre-training DataEpochsPre-train. Time (h)GOT-10k (VOT)DAVIS-17 (VOS)
AOSR0.5SR0.75J&FJF
No Pre-training---62.772.853.769.566.972.2
Supervised IN1k [72]IN1K300-69.779.065.678.074.881.1
Supervised IN21k [66]IN21K80-70.280.765.478.575.481.7
CLIP [65]IN1K32-67.476.860.073.670.576.7
MOCO-v3 [12]IN1K300-70.180.165.378.475.481.5
BeiT [2]IN1K800103.167.476.860.076.172.779.4
MAE [36]IN1K16008473.783.270.881.778.584.9
TwinMAEK40040020.772.283.265.979.376.482.3
TwinMAEK40080041.372.983.668.580.777.983.6
TwinMAEK400160082.774.284.969.481.278.184.2
DropMAEK40040021.173.283.967.581.378.584.0
DropMAEK40080042.274.885.470.582.779.785.6
DropMAEK400160084.475.886.472.083.180.286.0
DropMAEK70080092.475.986.872.083.080.285.7
+ +Table 1. Comparison of pre-training methods on downstream VOT and VOS tasks on GOT-10k [39] and DAVIS-17 [64]. All methods adopt the ViT-B/16 model [24] with $224\times 224$ input images for pre-training. The pre-training time is measured on 64 NVIDIA V100 GPUs. The best two results are shown in red and blue. + +
MethodSourceGOT-10k [39]TNL2K [79]LaSOText [27]LaSOT [28]
AOSR0.5SR0.75AUCPAUCPNormPAUCPNormP
SiamFC [3]ECCVW1634.835.39.829.528.623.031.126.933.642.033.9
MDNet [58]CVPR1629.930.39.9--27.934.931.839.746.037.3
ECO [19]ICCV1731.630.911.132.631.722.025.224.032.433.830.1
SiamPRN++ [41]CVPR1951.761.632.541.341.234.041.639.649.656.949.1
DiMP [4]ICCV1961.171.749.244.743.439.247.645.156.965.056.7
SiamR-CNN [74]CVPR2064.972.859.752.352.8---64.872.2-
LTMU [18]CVPR20---48.547.341.449.947.357.2-57.2
Ocean [104]ECCV2061.172.147.338.437.7---56.065.156.6
TrDiMP [76]CVPR2167.177.758.3-----63.9-61.4
TransT [13]CVPR2167.176.860.950.751.7---64.973.869.0
AutoMatch [102]ICCV2165.276.654.347.243.537.6-43.058.3-59.9
STARK [92]ICCV2168.878.164.1-----67.177.0-
KeepTrack [55]ICCV21-----48.2--67.177.270.2
MixFormer-L [17]CVPR2270.780.067.8-----70.179.976.3
SBT [87]CVPR2270.480.864.7-----66.7-71.1
UAST [98]ICML2263.574.151.4-----57.1-58.7
SwinTrack-384 [48]NeurIPS2272.480.567.855.957.149.1-55.671.3-76.5
AiATrack [32]ECCV2269.680.063.2--46.854.454.249.656.949.1
CIA50 [63]ECCV2267.979.060.350.957.6---66.2-69.6
SimTrack-L [10]ECCV2269.878.866.055.655.7---70.579.7-
OSTrack-384 [97]ECCV2273.783.270.855.956.750.561.357.671.181.177.6
DropTrackOurs75.986.872.056.957.952.763.960.271.881.878.1
+ +Table 2. Comparison with state-of-the-art VOT approaches on four large-scale challenging datasets. The best two results are shown in red and blue. For GOT-10k evaluation, all the methods follow the one-shot protocol, training only on the training set in GOT-10k. + +once. For fair comparison, we use the same mask ratio (i.e., $75\%$ ) and training hyper-parameters of MAE [36] to pretrain the TwinMAE and DropMAE models. Following [14, 15], we use a bootstrapped cross entropy loss for training. The detailed pre-training and fine-tuning hyper-parameters are in the Supplementary. + +# 4.2. Comparison with Pre-Training Methods + +In Table 1, we compare our DropMAE with existing pre-training methods on the downstream tasks of VOT and VOS. DropMAE and TwinMAE are pre-trained using videos (K400, K700), while MAE and other methods are pre-trained on ImageNet 1k or 21k (IN1K, IN21K). The VOT and VOS baselines illustrated in Sec. 3.4 use the + +official pre-trained VIT-B/16 models provided by existing pre-training approaches (see Table 1) for fine-tuning. TwinMAE with 800-epoch training performs favorably against MAE on VOT, but achieves inferior results on VOS. There are two main reasons: 1) TwinMAE is not effective enough at learning temporal matches; 2) The number of object classes in K400 is limited, and meanwhile the object classes in DAVIS-17 are included in ImageNet. Thus MAE generalizes well to VOS. Our DropMAE, which is a stronger temporal matching learner, outperforms MAE on both the VOT and VOS tasks with 800-epoch training (i.e., 42.2 hours $^{1}$ ) + +
MethodOTB100AUCITBAUCTrackingNet
AUCPNorm
SiamFC [3]58.344.157.166.3
Ocean [104]68.447.7--
ATOM [20]68.347.270.377.1
DiMP [4]53.733974.080.1
TransT [13]69.554.781.486.7
STARK [92]68.157.682.086.9
OSTrack [97]-64.883.988.5
DropTrack69.665.084.188.9
+ +by using the K400 dataset. This indicates that our DropMAE is $2\times$ faster than MAE. + +# 5. State-of-the-art Comparison + +In this section, we compare our fine-tuned VOT and VOS models, denoted as DropTrack and DropSeg, with state-of-the-art approaches on VOT and VOS benchmarks. We use DropMAE trained on K700 with 800 epochs as the pretraining model for both VOT and VOS fine-tuning. + +# 5.1. Video Object Tracking + +To demonstrate the effectiveness of the proposed DropMAE for VOT, we compare our DropTrack with state-of-the-art trackers on 7 challenging tracking benchmarks. GOT-10k. GOT-10k [39] is a challenging dataset that follows the one-shot evaluation protocol, where the trackers are required to be trained on its training split, and the test object classes have no overlap with the objects in the training split. As shown in Table 2, our DropTrack achieves state-of-the-art results on this dataset, outperforming OSTrack by $2.2\%$ and $3.6\%$ in terms of AO and $\mathrm{SR}_{0.5}$ . This implies that the temporal correspondence learning in the pretraining is beneficial for the downstream tracking task. Although there exists a domain gap between the pre-training data and the test data (i.e., a large portion of test objects in GOT-10k are animals, vehicles and object parts, whereas K700 only consists of human-centric action videos), the temporal matching ability learned by DropMAE can still be transferred to the downstream tracking task, improving the tracking performance. + +LaSOT. LaSOT consists of 280 long test sequences, and our results are presented in Table 2. Our DropTrack sets a new record on this dataset with $71.8\%$ AUC, $81.8\%$ $\mathrm{P}_{\text {Norm }}$ and $78.1\%$ P, which shows the great potential of our DropTrack in robust long-term visual tracking. + +$\mathbf{LaSOT}_{ext}$ . $\mathbf{LaSOT}_{ext}$ is an extension of LaSOT with more challenging video sequences for testing - similar to GOT-10k, the test split has a large gap with the training split, and sequences with novel object classes (i.e., not appeared in ImageNet) are used for evaluation. Our DropMAE outperforms the other trackers by large margins. This demon + +Table 3. Comparison with state-of-the-art VOT approaches on OTB100 [85], ITB [44] and TrackingNet [57]. The best two results are shown in red and blue. + +
MethodSourceOLMSDAVIS-2016 [62]DAVIS-2017 [64]
J&FJFJ&FJF
RANet [80]ICCV19✓85.585.585.465.763.268.2
STM [60]ICCV19✓✓89.388.789.981.879.284.3
FRTM [67]CVPR20✓✓83.583.683.476.773.979.6
TVOS [101]CVPR20✓---72.369.974.7
LWL [5]ECCV20✓✓---81.679.184.1
CFBI [95]ECCV20✓89.488.390.581.979.184.6
UniTrack [81]NeurIPS21✓----58.4-
STCN- [15]NeurIPS21✓---82.579.385.7
SSTVOS [26]CVPR21✓---82.579.985.1
SWEM- [50]CVPR22✓89.5--81.9--
RTS [61]ECCV22✓✓---80.277.982.6
OSMN [54]TPAMI1873.574.072.954.852.557.1
FAVOS [16]CVPR1881.082.479.558.254.661.8
VideoMatch [38]ECCV18-81.0-56.5--
SiamMask [77]CVPR1969.871.767.856.454.358.5
D3S [52]CVPR2074.075.472.660.857.863.8
Siam R-CNN [52]CVPR20---70.666.175.0
Unicorn [91]ECCV2287.486.588.269.265.273.2
DropSegOurs92.190.993.383.080.285.7
+ +Table 4. Comparison with state-of-the-art VOS approaches on the validation sets of DAVIS-2016 [62] and DAVIS-2017 [64]. OL, M and S indicate Online Learning, using Memory mechanism, and using Synthetic videos for pre-training. + +![](images/ed83c71d96fd8d2644c89bf60bedded699817a2a6a3e61e3a075d5f0bc17fdef.jpg) +Figure 6. Ablation study of the dropout ratio $P$ on the GOT-10k (VOT) and DAVIS-17 (VOS) datasets. + +strates that a tracker with DropMAE pre-training generalizes well to unseen objects in generic visual object tracking. TNL2K. TNL2K is a large-scale evaluation dataset that consists of 700 test videos with various challenges, such as significant appearance variation and manually added adversarial samples. As illustrated in Table 2, our DropMAE significantly outperforms the other trackers on this dataset. ITB, TrackingNet and OTB100. In Table 3, we evaluate our DropTrack on ITB [44], OTB100 [85] and TrackingNet [57], achieving state-of-the-art performance on each one. DropTrack is slightly better than OSTrack on ITB and TrackingNet. We believe the main reason is the fully overlapped training and test object classes in these two datasets, which reduces the effect of pre-training. A competitive tracker on these two datasets can be learned even using supervised ImageNet weights, which has been shown in [97]. + +On all 7 VOT datasets, our DropTrack outperforms the baseline OSTrack, which demonstrates that our DropMAE pre-training on videos learns better temporal-matching representations than the MAE model trained on ImageNet, resulting in more a robust tracker that generalizes well to both unseen and seen objects. + +# 5.2. Video Object Segmentation + +In Table 4, we compare our DropSeg with existing VOS approaches on the DAVIS-16/17 [62,64]. + +DAVIS-16. DAVIS-16 is composed of 20 manually anno + +
DatasetsNo. +VideosNo. +ActionsVOTVOS
AOSR0.5SR0.75J&F
K400 [40]240,00040073.283.967.582.7
K600 [8]390,00060074.585.569.582.8
K700 [9]526,76870075.686.271.483.0
MiT [56]802,24433975.185.570.682.8
WebVid [1]240,000-72.883.467.381.5
WebVid [1]960,000-73.485.069.582.9
+ +tated test sequences. As shown in Table 4, our one-shot DropSeg approach, without using any online learning and complicated memory mechanisms, achieves the best $\mathcal{J}\&\mathcal{F}$ score of $92.1\%$ , which significantly outperforms the other compared one-shot approaches and is even better than the approaches with complicated pipelines (i.e., OL, M and S). This implies that the pixel-wise correspondence learned during the pre-training is effective for capturing long-range dependencies between various frames in VOS. + +DAVIS-17. DAVIS-17 is an extension of DAVIS-16, comprising more challenging videos and supports multi-object segmentation. In Table 4, our DropSeg achieves competitive results of $83.0\%$ $\mathcal{I}\& \mathcal{F}$ , $80.2\%$ $\mathcal{I}$ and $85.7\%$ $\mathcal{F}$ , which shows its superiority in handling more challenging videos. + +More VOS results and comparisons are included in the supplementary. + +# 6. Ablation Studies + +In this section, we conduct ablation studies to provide more detailed analysis of our method. We use DropMAE with 400-epoch pre-training for the ablation study. + +The effect of dropout ratio $P$ . We study the effect of dropout rate $P$ in Fig. 6. A relatively small dropout ratio of $P = 0.1$ works well on both VOT and VOS tasks. Meanwhile, dropping too many spatial cues (e.g., $P = 0.2$ ) degrades the downstream tasks, which is mainly because the spatial cues are also useful for accurate localization and segmentation. $P = 0.1$ is the optimal setting, and thus we adopt it in the following experiments. + +Pre-training video sources. Since we are the first to explore masked autoencoder pre-training for temporal matching tasks, it is not clear which video dataset is the optimal choice for pre-training. Here, we use five popular video datasets for pre-training, including K400 [40], K600 [8], K700 [9], MiT [56] and WebVid-2M [1]. For WebVid-2M, we randomly sample 240k and 960k videos for fair comparison and faster validation. The downstream tracking results are reported in Table 5. Performance is not favorable even using 960,000 videos in WebVid for pre-training. This indicates that WebViD is not a good choice for tracking pre-training, which is mainly because it is a video caption dataset that focuses on scene diversity and lacks rich object motion. From the experiments on the K400/600/700 and + +Table 5. The downstream VOT and VOS performance on GOT-10k and DAVIS-17 obtained by using our DropMAE pre-trained on various video datasets. VOS uses 800 epochs pre-training. + +
SettingsGOT-10k
DropTrack-K400-400E73.2/67.5
w/ ASAP in Encoder73.1/68.1
w/ domain specific data73.4/68.8
w/o frame identity embed72.9/67.4
+ +Table 6. The tracking performance of $\mathrm{{AO}}/{\mathrm{{SR}}}_{0.75}$ on GOT10-k reported by variants with different settings. + +MiT, tracking benefits from pre-training with from rich action classes (i.e., 700 action classes of K700), from which the model can learn stronger temporal matching ability. + +Applying ASAD to the encoder. Here we test applying ASAD to all layers including both encoder and decoder of masked autoencoder. As shown in Table 6, this variant gains improvements (0.6% in $\mathrm{SR}_{0.75}$ ) over the original baseline. Considering its additional cost and limited performance improvement, we only apply ASAD to the decoder. + +Domain specific data. We also add the tracking training data (without using box annotations), including TrackingNet, LaSOT, and GOT-10k, into K400 for pre-training. The downstream tracking performance by using the larger pre-training set is 73.4/68.8, which is better than the baseline. It shows that the domain-specific data is helpful to bridge the domain gap, which can be considered as future work to extend Kinetic datasets with more tracking videos. + +Frame identity embedding. During pre-training, the frame identity embedding is used to identify masked patches in the same 2D location of the two frames. From Table 6, we can find that downstream fine-tuning without the frame identity embedding performs worse than with it, since not using it is inconsistent with the pre-training stage. + +# 7. Conclusion + +This paper investigated masked autoencoding pretraining for temporal matching-based downstream tasks. Specifically, an adaptive spatial-attention dropout method is proposed to facilitate temporal correspondence learning in self-supervised pre-training on videos. We show that our proposed pre-training method DropMAE can achieve better downstream performance on VOT and VOS than the image-based MAE, while using $50\%$ less pre-training time. 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A simple extension of MAE is to randomly mask out frame patches in videos and reconstruct the frame pixels. However, we find that this simple baseline heavily relies on spatial cues while ignoring temporal relations for frame reconstruction, thus leading to sub-optimal temporal matching representations for VOT and VOS. To alleviate this problem, we propose DropMAE, which adaptively performs spatial-attention dropout in the frame reconstruction to facilitate temporal correspondence learning in videos. We show that our DropMAE is a strong and efficient temporal matching learner, which achieves better fin-tuning results on matching-based tasks than the ImageNet-based MAE with " + }, + { + "bbox": [ + 46, + 298, + 290, + 597 + ], + "type": "inline_equation", + "content": "2 \\times" + }, + { + "bbox": [ + 46, + 298, + 290, + 597 + ], + "type": "text", + "content": " faster pre-training speed. Moreover, we also find that motion diversity in pre-training videos is more important than scene diversity for improving the performance on VOT and VOS. Our pre-trained DropMAE model can be directly loaded in existing ViT-based trackers for fine-tuning without further modifications. Notably, DropMAE sets new state-of-the-art performance on 8 out of 9 highly competitive video tracking and segmentation datasets. Our code and pre-trained models are available at https://github.com/jimmy-dq/DropMAE.git." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 613, + 128, + 626 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 613, + 128, + 626 + ], + "spans": [ + { + "bbox": [ + 47, + 613, + 128, + 626 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 634, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 634, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 634, + 287, + 696 + ], + "type": "text", + "content": "Recently, transformers have achieved enormous success in many research areas, such as natural language processing (NLP) [6, 22], computer vision [97] and audio generation [43, 73]. In NLP, masked autoencoding is commonly used to train large-scale generalizable NLP transformers contain-" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 320, + 273, + 533, + 407 + ], + "blocks": [ + { + "bbox": [ + 320, + 273, + 533, + 407 + ], + "lines": [ + { + "bbox": [ + 320, + 273, + 533, + 407 + ], + "spans": [ + { + "bbox": [ + 320, + 273, + 533, + 407 + ], + "type": "image", + "image_path": "e7d6e014764de89d35928317174cc4c910bea04284f0e58182ea59f5a2ddc3b2.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 410, + 547, + 455 + ], + "lines": [ + { + "bbox": [ + 305, + 410, + 547, + 455 + ], + "spans": [ + { + "bbox": [ + 305, + 410, + 547, + 455 + ], + "type": "text", + "content": "Figure 1. State-of-the-art comparison on GOT-10k [39] following the one-shot protocol. Our DropTrack with the proposed DropMAE pre-training achieves state-of-the-art performance without using complicated pipelines such as online updating." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 471, + 547, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 471, + 547, + 579 + ], + "spans": [ + { + "bbox": [ + 304, + 471, + 547, + 579 + ], + "type": "text", + "content": "ing billions of parameters. Inspired by the great success of self-supervised learning in NLP, recent advances [36, 89] in computer vision suggest that training large-scale vision transformers may undertake a similar trajectory with NLP. The seminal work MAE [36] reconstructs the input image from a small portion of patches. The learned representation in this masked autoencoder has been demonstrated to be effective in many computer vision tasks, such as image classification, object detection and semantic segmentation." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "type": "text", + "content": "In video object tracking (VOT), recently two works, SimTrack [10] and OSTrack [97], explore using an MAE pre-trained ViT model as the tracking backbone. Notably, these two trackers achieve state-of-the-art performance on existing tracking benchmarks without using complicated tracking pipelines. The key to their success is the robust pre-training weights learned by MAE on ImageNet [68]. In addition, [10, 97] also demonstrate that, for VOT, MAE unsupervised pre-training on ImageNet is more effective than supervised pre-training using class labels – this is mainly because MAE pre-training learns more fine-grained local" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 137, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 137, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 137, + 712 + ], + "type": "text", + "content": "*Corresponding Author" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14561" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 63, + 72, + 161, + 122 + ], + "blocks": [ + { + "bbox": [ + 63, + 72, + 161, + 122 + ], + "lines": [ + { + "bbox": [ + 63, + 72, + 161, + 122 + ], + "spans": [ + { + "bbox": [ + 63, + 72, + 161, + 122 + ], + "type": "image", + "image_path": "6530ce119ca61be6f977a4dbc61cb893fe139c97b44268ddbd165eeb23fc1924.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 89, + 123, + 144, + 131 + ], + "lines": [ + { + "bbox": [ + 89, + 123, + 144, + 131 + ], + "spans": [ + { + "bbox": [ + 89, + 123, + 144, + 131 + ], + "type": "text", + "content": "TwinMAE (Layer-6)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 162, + 72, + 258, + 122 + ], + "blocks": [ + { + "bbox": [ + 162, + 72, + 258, + 122 + ], + "lines": [ + { + "bbox": [ + 162, + 72, + 258, + 122 + ], + "spans": [ + { + "bbox": [ + 162, + 72, + 258, + 122 + ], + "type": "image", + "image_path": "405a66ef12c21545d00e72c09b400aa6f600b37b6b92e387998bd2c6922b47d9.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 187, + 123, + 243, + 131 + ], + "lines": [ + { + "bbox": [ + 187, + 123, + 243, + 131 + ], + "spans": [ + { + "bbox": [ + 187, + 123, + 243, + 131 + ], + "type": "text", + "content": "TwinMAE (Layer-8)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 62, + 133, + 161, + 182 + ], + "blocks": [ + { + "bbox": [ + 62, + 133, + 161, + 182 + ], + "lines": [ + { + "bbox": [ + 62, + 133, + 161, + 182 + ], + "spans": [ + { + "bbox": [ + 62, + 133, + 161, + 182 + ], + "type": "image", + "image_path": "60b6a096c2fc3930ccbf0ff72a45b7d1ffa1e3bb0fd00108eccd6c71e3424d8f.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 89, + 183, + 147, + 191 + ], + "lines": [ + { + "bbox": [ + 89, + 183, + 147, + 191 + ], + "spans": [ + { + "bbox": [ + 89, + 183, + 147, + 191 + ], + "type": "text", + "content": "DropMAE (Layer-6)" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 162, + 133, + 258, + 182 + ], + "blocks": [ + { + "bbox": [ + 162, + 133, + 258, + 182 + ], + "lines": [ + { + "bbox": [ + 162, + 133, + 258, + 182 + ], + "spans": [ + { + "bbox": [ + 162, + 133, + 258, + 182 + ], + "type": "image", + "image_path": "8a1bfd9080640ba61dcd1127f2babe6185cba5793a9c23c62d4e4392c929d139.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 188, + 183, + 246, + 191 + ], + "lines": [ + { + "bbox": [ + 188, + 183, + 246, + 191 + ], + "spans": [ + { + "bbox": [ + 188, + 183, + 246, + 191 + ], + "type": "text", + "content": "DropMAE (Layer-8)" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 199, + 287, + 297 + ], + "lines": [ + { + "bbox": [ + 46, + 199, + 287, + 297 + ], + "spans": [ + { + "bbox": [ + 46, + 199, + 287, + 297 + ], + "type": "text", + "content": "Figure 2. Visualization of the attention maps of the TwinMAE baseline and our DropMAE in the reconstruction of a random masked patch, which is denoted as a red bounding box in the left input frame. TwinMAE leverages the spatial cues (within the same frame) more than temporal cues (between frames) for reconstruction. Our proposed DropMAE improves the baseline by effectively alleviating co-adaptation between spatial cues in the reconstruction, focusing more on temporal cues, thus achieving better learning of temporal correspondences for VOT and VOS." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 313, + 286, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 313, + 286, + 469 + ], + "spans": [ + { + "bbox": [ + 46, + 313, + 286, + 469 + ], + "type": "text", + "content": "structures that are useful for accurate target localization required for VOT, whereas supervised training learns high-level class-related features that are invariant over appearance changes. Despite the promising performance achieved by [10,97], the MAE pre-training on ImageNet could still be sub-optimal for the tracking task due to the natural gap between images and videos, i.e., no prior temporal correspondence information can be learned in static images. However, previous tracking methods [3,42,83] have shown that temporal correspondence learning is the key in developing a robust and discriminative tracker. Thus there is an opportunity to further develop the MAE framework specifically for matching-base video tasks, such as VOT and VOS." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 472, + 286, + 614 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 472, + 286, + 614 + ], + "spans": [ + { + "bbox": [ + 46, + 472, + 286, + 614 + ], + "type": "text", + "content": "One simple way to extend MAE to videos is to randomly mask out frame patches in a video clip (i.e., video frame pairs) and then reconstruct the video clip. We denote this simple baseline as twin MAE (TwinMAE). Given a masked patch query, as illustrated in Figs. 2 & 4, we find that TwinMAE heavily relies on the spatially neighbouring patches within the same frame to reconstruct the masked patch, which implies a heavy co-adaptation of spatial cues (within-frame tokens) for reconstruction and may cause learning of sub-optimal temporal representations for matching-based downstream tasks like video object tracking and segmentation." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "type": "text", + "content": "To address this issue with the TwinMAE baseline, we propose DropMAE specifically designed for pre-training a masked autoencoder for matching-based video downstream tasks (e.g., VOT and VOS). Our DropMAE adaptively performs spatial-attention dropout to break up co-adaptation between spatial cues (within-frame tokens) during the frame reconstruction, thus encouraging more temporal interactions and facilitating temporal correspondence learning in" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "content": "the pre-training stage. Interestingly, we obtain several important findings with DropMAE: 1) DropMAE is an effective and efficient temporal correspondence learner, which achieves better fine-tuning results on matching-based tasks than the ImageNet-based MAE with " + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "inline_equation", + "content": "2 \\times" + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "content": " faster pre-training speed. 2) Motion diversity in pre-training videos is more important than scene diversity for improving the performance on VOT and VOS." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 168, + 545, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 168, + 545, + 251 + ], + "spans": [ + { + "bbox": [ + 304, + 168, + 545, + 251 + ], + "type": "text", + "content": "We conduct downstream task evaluation on 9 competitive VOT and VOS benchmarks, achieving state-of-the-art performance on these benchmarks. In particular, our trackers with DropMAE pre-training obtain " + }, + { + "bbox": [ + 304, + 168, + 545, + 251 + ], + "type": "inline_equation", + "content": "75.9\\%" + }, + { + "bbox": [ + 304, + 168, + 545, + 251 + ], + "type": "text", + "content": " AO on GOT-10k, " + }, + { + "bbox": [ + 304, + 168, + 545, + 251 + ], + "type": "inline_equation", + "content": "52.7\\%" + }, + { + "bbox": [ + 304, + 168, + 545, + 251 + ], + "type": "text", + "content": " AUC on " + }, + { + "bbox": [ + 304, + 168, + 545, + 251 + ], + "type": "inline_equation", + "content": "\\mathrm{LaSOT}_{ext}" + }, + { + "bbox": [ + 304, + 168, + 545, + 251 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 168, + 545, + 251 + ], + "type": "inline_equation", + "content": "56.9\\%" + }, + { + "bbox": [ + 304, + 168, + 545, + 251 + ], + "type": "text", + "content": " AUC on TNL2K and " + }, + { + "bbox": [ + 304, + 168, + 545, + 251 + ], + "type": "inline_equation", + "content": "92.1\\% /83.0\\%" + }, + { + "bbox": [ + 304, + 168, + 545, + 251 + ], + "type": "inline_equation", + "content": "\\mathcal{J}\\& \\mathcal{F}" + }, + { + "bbox": [ + 304, + 168, + 545, + 251 + ], + "type": "text", + "content": " scores on DAVIS-16/17, w/o using complicated online updating or memory mechanisms." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 317, + 252, + 529, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 252, + 529, + 262 + ], + "spans": [ + { + "bbox": [ + 317, + 252, + 529, + 262 + ], + "type": "text", + "content": "In summary, the main contributions of our work are:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 317, + 263, + 545, + 443 + ], + "type": "list", + "angle": 0, + "index": 18, + "blocks": [ + { + "bbox": [ + 317, + 263, + 545, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 263, + 545, + 346 + ], + "spans": [ + { + "bbox": [ + 317, + 263, + 545, + 346 + ], + "type": "text", + "content": "- To the best of our knowledge, we are the first to investigate masked autoencoder video pre-training for temporal matching-based downstream tasks. Specifically, we explore various video data sources for pre-training and build a TwinMAE baseline to study its effectiveness on temporal matching tasks. Since none exists, we further build a ViT-based VOS baseline for fine-tuning." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 317, + 348, + 545, + 394 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 348, + 545, + 394 + ], + "spans": [ + { + "bbox": [ + 317, + 348, + 545, + 394 + ], + "type": "text", + "content": "- We propose DropMAE, which adaptively performs spatial-attention dropout in the frame reconstruction to facilitate effective temporal correspondence learning in videos." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 317, + 396, + 545, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 396, + 545, + 443 + ], + "spans": [ + { + "bbox": [ + 317, + 396, + 545, + 443 + ], + "type": "text", + "content": "- Our trackers with DropMAE pre-training sets new state-of-the-art performance on 8 out of 9 highly competitive video tracking and segmentation benchmarks without complicated tracking pipelines." + } + ] + } + ], + "index": 17 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 454, + 391, + 466 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 454, + 391, + 466 + ], + "spans": [ + { + "bbox": [ + 306, + 454, + 391, + 466 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 474, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 545, + 713 + ], + "type": "text", + "content": "Visual object tracking and segmentation. Given an annotated bounding box in the first frame of a test video, visual object tracking (VOT) aims to accurately predict the target's bounding boxes in the following frames. Similarly, for visual object segmentation (VOS), given an annotated binary mask in the first frame, VOS aims to predict dense target masks in the remaining frames. In the early development of VOT, correlation filter-based approaches [19, 21, 31, 37, 46, 47, 51, 53, 82, 84] are dominant trackers due to their favorable ability in modeling target appearance variation. With the development of deep learning, deep Siamese networks [70, 78] are introduced to VOT. The representative work SiamFC [3] takes template and search images as input for target localization. Based on SiamFC, many improvements have been made, e.g., scale regression [41, 42, 94], online template updating [34, 93, 99], multilevel feature fusion [29], loss design [23] and backbone design [10, 41, 97, 103]. For VOS, matching-based approaches, e.g., STM [60], AOT [96] and STCN [15], achieve promising results on existing VOS benchmarks. Recent improve" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14562" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "type": "text", + "content": "ments [14, 50] on online memory design further improve the previous SOTA results in VOS. Recent studies including SimTrack [10] and OSTrack [97] show that the ViT backbone [24] with MAE pre-training on ImageNet is effective for object tracking." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 133, + 286, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 133, + 286, + 251 + ], + "spans": [ + { + "bbox": [ + 46, + 133, + 286, + 251 + ], + "type": "text", + "content": "Despite the great success of ViT with MAE pre-training on tracking, this static ImageNet-based pre-training still lacks temporal correspondence learning. Moreover, the developments of VOT and VOS show that learning strong temporal matching ability is essential for video tracking tasks. To the best of our best knowledge, we are the first to investigate masked autoencoder self-supervised video pretraining for tracking tasks. Our proposed DropMAE can learn reliable temporal correspondences, which we demonstrate are effective for downstream tracking tasks." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 251, + 286, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 251, + 286, + 467 + ], + "spans": [ + { + "bbox": [ + 46, + 251, + 286, + 467 + ], + "type": "text", + "content": "Self-supervised Learning. Self-supervised learning has received significant interest in the past few decades. There are many manually-designed pretext tasks for pre-training, such as image colorization [100], jigsaw puzzle solving [59], future frame prediction [69, 75] and rotation prediction [33]. Contrastive learning approaches [7, 11, 25, 35, 86, 88] are the mainstream self-supervised methods in recent years. However, these methods are sensitive to the type and strength of applied data augmentation, which makes them hard to train. Inspired by masked language modeling [6, 22], masked image modeling (MIM) approaches are proposed for learning unsupervised image [36, 89] or video representations [30, 71], which have been shown to be effective for many downstream tasks including image classification, object detection and video action recognition. However, there is no specifically designed pre-training approaches for temporal matching-based task, such as VOT and VOS. In this work, we propose DropMAE to explore this direction." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 477, + 102, + 489 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 477, + 102, + 489 + ], + "spans": [ + { + "bbox": [ + 47, + 477, + 102, + 489 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 497, + 286, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 497, + 286, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 497, + 286, + 628 + ], + "type": "text", + "content": "We propose a self-supervised video pre-training method to learn robust representations for temporal matching-based downstream tasks, including VOT and VOS tasks. We firstly introduce a simple extension of MAE to temporal matching representation learning from video, (TwinMAE). We then illustrate the limitations of the TwinMAE baseline and propose a spatial-attention dropout strategy to facilitate temporal correspondence learning, denoted as DropMAE. The overall pipeline of both DropMAE and TwinMAE is shown in Fig. 3. Finally, we introduce the VOT and VOS methods used for fine-tuning the downstream tasks." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 635, + 276, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 635, + 276, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 635, + 276, + 647 + ], + "type": "text", + "content": "3.1. Temporal Masked Autoencoder (TwinMAE)" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 653, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 286, + 713 + ], + "type": "text", + "content": "The masked autoencoder (MAE) model [36] consists of an encoder and a decoder. Its basic idea is to randomly mask out a large portion (e.g., " + }, + { + "bbox": [ + 46, + 653, + 286, + 713 + ], + "type": "inline_equation", + "content": "75\\%" + }, + { + "bbox": [ + 46, + 653, + 286, + 713 + ], + "type": "text", + "content": ") of patches in an image and then reconstruct the image pixels. Specifically, the encoder only takes visible patches as input for feature" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 309, + 64, + 544, + 155 + ], + "blocks": [ + { + "bbox": [ + 309, + 64, + 544, + 155 + ], + "lines": [ + { + "bbox": [ + 309, + 64, + 544, + 155 + ], + "spans": [ + { + "bbox": [ + 309, + 64, + 544, + 155 + ], + "type": "image", + "image_path": "3293ae28c6284e5210978380adb58fd2e22443cb556269346e8033a5c2f4e92d.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 157, + 545, + 201 + ], + "lines": [ + { + "bbox": [ + 305, + 157, + 545, + 201 + ], + "spans": [ + { + "bbox": [ + 305, + 157, + 545, + 201 + ], + "type": "text", + "content": "Figure 3. An illustration of our DropMAE. The proposed adaptive spatial-attention dropout (ASAD) facilitates temporal correspondence learning for temporal matching tasks. TwinMAE follows the same pipeline except that the ASAD module is not used." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 209, + 545, + 292 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 209, + 545, + 292 + ], + "spans": [ + { + "bbox": [ + 304, + 209, + 545, + 292 + ], + "type": "text", + "content": "learning, and then the decoder is input with both visible and masked patches to produce the image reconstruction. In order to adapt to downstream video matching-based tasks, one naive extension is to directly apply MAE on concatenated video frames, hoping to learn temporal matching representations from video frame pairs, which we denote as TwinMAE." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 293, + 545, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 293, + 545, + 425 + ], + "spans": [ + { + "bbox": [ + 304, + 293, + 545, + 425 + ], + "type": "text", + "content": "It should be noted that existing works [30,71] that extend MAE to video representation learning are mainly designed for the downstream task of video action recognition, where a long video clip (e.g., 16 frames) is used for reconstruction-based pre-training. To keep consistent with our downstream tasks of VOT/VOS, we follow the general training settings used in object tracking [3,97], where two frames are sampled from one video as input to TwinMAE for pre-training. This adaptation significantly reduces the computational and memory cost compared to existing video pre-training approaches [30, 71], due to the quadratic complexity of ViTs." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 426, + 545, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 545, + 592 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 545, + 592 + ], + "type": "text", + "content": "Patch embedding. Firstly, we randomly sample 2 frames within a video with a predefined maximal frame gap. For each frame, we follow the vanilla ViT to divide it into non-overlapping patches. The patches extracted from the two frames are then concatenated together to form the overall patch sequence. We then randomly mask out patches in the patch sequence until a predefined mask ratio is reached. Note that we use the same mask ratio (i.e., " + }, + { + "bbox": [ + 304, + 426, + 545, + 592 + ], + "type": "inline_equation", + "content": "75\\%" + }, + { + "bbox": [ + 304, + 426, + 545, + 592 + ], + "type": "text", + "content": ") with the original MAE, since the information redundancy of two frames should be similar to a single image. The visible patches are embedded by linear projection [24], and the masked patches are embedded using a shared learnable mask token. All the embedded patches are added with positional embeddings [24]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 594, + 545, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 653 + ], + "type": "text", + "content": "Frame identity embedding. To distinguish between the masked tokens in the same spatial location of the two frames, we use two learnable frame identity embeddings to indicate the two input frames. The corresponding frame identity embedding is added to each embedded patch." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 654, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 712 + ], + "type": "text", + "content": "Autoencoder and Training. Following the autoencoding pipeline in the original MAE [36], the encoder only takes visible embedded patches as input, and the decoder is input with all the embedded patches for masked patch reconstruction. We use the same normalized pixel loss from MAE for" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14563" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 78, + 64, + 258, + 156 + ], + "blocks": [ + { + "bbox": [ + 78, + 64, + 258, + 156 + ], + "lines": [ + { + "bbox": [ + 78, + 64, + 258, + 156 + ], + "spans": [ + { + "bbox": [ + 78, + 64, + 258, + 156 + ], + "type": "image", + "image_path": "0b86d533f9b1810228924c7f3db5c4e248b6c4922ea43cf8536348b0c01e4311.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 158, + 287, + 201 + ], + "lines": [ + { + "bbox": [ + 47, + 158, + 287, + 201 + ], + "spans": [ + { + "bbox": [ + 47, + 158, + 287, + 201 + ], + "type": "text", + "content": "Figure 4. The average within-frame and between-frame attention scores obtained by TwinMAE and DropMAE in different decoder layers. The attention score is calculated on 20 randomly sampled K400 validation videos, and is averaged on all heads and locations." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 209, + 209, + 220 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 209, + 209, + 220 + ], + "spans": [ + { + "bbox": [ + 47, + 209, + 209, + 220 + ], + "type": "text", + "content": "training the whole network architecture." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 229, + 225, + 241 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 229, + 225, + 241 + ], + "spans": [ + { + "bbox": [ + 47, + 229, + 225, + 241 + ], + "type": "text", + "content": "3.2. Limitation of TwinMAE Baseline" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 247, + 287, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 247, + 287, + 342 + ], + "spans": [ + { + "bbox": [ + 46, + 247, + 287, + 342 + ], + "type": "text", + "content": "The visualization of the reconstruction for our TwinMAE baseline is shown in Fig. 2. We also quantitatively compare the average within-frame and between-frame attentions during the reconstruction in Fig. 4. Interestingly, we find the TwinMAE reconstruction heavily relies on within-frame patches or spatial cues, which may lead to sub-optimal temporal representations for matching-based video tasks." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 343, + 287, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 343, + 287, + 510 + ], + "spans": [ + { + "bbox": [ + 46, + 343, + 287, + 510 + ], + "type": "text", + "content": "When only using within-frame spatial cues, the decoder will perform the reconstruction using only context information in the neighboring patches, and thus the learned encoder representations will embed context information. In contrast, when using between-frame cues, the decoder will learn to perform matching of patches between frames so as to recover the corresponding target patch in the other frame. Thus, decoding with between-frame cues will make the encoder learn representations that support temporal matching between frames. Previous works in object tracking [3, 83] also suggest that temporal correspondence learning plays a key role in developing a robust and discriminative tracker. Since TwinMAE relies more on context information, it is still suboptimal for downstream tracking tasks." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 515, + 237, + 529 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 515, + 237, + 529 + ], + "spans": [ + { + "bbox": [ + 47, + 515, + 237, + 529 + ], + "type": "text", + "content": "3.3. Adaptive Spatial-Attention Dropout" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 533, + 287, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 287, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 287, + 700 + ], + "type": "text", + "content": "To address issue of TwinMAE discussed in Sec. 3.2, we propose a Adaptive Spatial-Attention Dropout (ASAD) to facilitate the temporal correspondence learning in the temporal MAE. Given a query token, our basic idea is to adaptively drop a portion of its within-frame cues in order to facilitate the model to learn more reliable temporal correspondence, i.e., between-frame cues. That is, we restrict the interactions between the query token and tokens in the same frame, and encourage more interactions with tokens in the other frame, through manipulation of the computed spatial-attention in the transformer. Therefore, to minimize the reconstruction loss, the model is facilitated to learn a better temporal matching ability, which is essential in matching-based video tasks." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "type": "text", + "content": "Before introducing the proposed ASAD, we firstly revisit" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 310, + 72, + 545, + 140 + ], + "blocks": [ + { + "bbox": [ + 310, + 72, + 545, + 140 + ], + "lines": [ + { + "bbox": [ + 310, + 72, + 545, + 140 + ], + "spans": [ + { + "bbox": [ + 310, + 72, + 545, + 140 + ], + "type": "image", + "image_path": "62cca43fd372487f30c55ac9e42300f13a96114d6e210ccca736660ae16c2b6f.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 141, + 545, + 174 + ], + "lines": [ + { + "bbox": [ + 305, + 141, + 545, + 174 + ], + "spans": [ + { + "bbox": [ + 305, + 141, + 545, + 174 + ], + "type": "text", + "content": "Figure 5. Visualization of the temporal matching function " + }, + { + "bbox": [ + 305, + 141, + 545, + 174 + ], + "type": "inline_equation", + "content": "f_{tem}" + }, + { + "bbox": [ + 305, + 141, + 545, + 174 + ], + "type": "text", + "content": " on an example frame pair. A large value of " + }, + { + "bbox": [ + 305, + 141, + 545, + 174 + ], + "type": "inline_equation", + "content": "f_{tem}(i)" + }, + { + "bbox": [ + 305, + 141, + 545, + 174 + ], + "type": "text", + "content": " indicates that the " + }, + { + "bbox": [ + 305, + 141, + 545, + 174 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 305, + 141, + 545, + 174 + ], + "type": "text", + "content": "-th pixel matches well to a pixel in the other frame." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 192, + 545, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 192, + 545, + 252 + ], + "spans": [ + { + "bbox": [ + 305, + 192, + 545, + 252 + ], + "type": "text", + "content": "the multi-head self-attention in ViT [24]. Let " + }, + { + "bbox": [ + 305, + 192, + 545, + 252 + ], + "type": "inline_equation", + "content": "\\mathbf{z} \\in \\mathbb{R}^{N \\times D}" + }, + { + "bbox": [ + 305, + 192, + 545, + 252 + ], + "type": "text", + "content": " be the input sequence of the two concatenated input frames, " + }, + { + "bbox": [ + 305, + 192, + 545, + 252 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 305, + 192, + 545, + 252 + ], + "type": "text", + "content": " denotes the total patch number in the two frames and " + }, + { + "bbox": [ + 305, + 192, + 545, + 252 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 305, + 192, + 545, + 252 + ], + "type": "text", + "content": " is the feature dimension. The standard multi-head self-attention [24] can be formulated as:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 315, + 258, + 545, + 275 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 258, + 545, + 275 + ], + "spans": [ + { + "bbox": [ + 315, + 258, + 545, + 275 + ], + "type": "interline_equation", + "content": "[ \\mathbf {q}, \\mathbf {k}, \\mathbf {v} ] = \\mathbf {z} \\mathbf {U} _ {q k v}, \\quad \\mathrm {S A} (\\mathbf {z}) = \\operatorname {s o f t m a x} \\left(\\frac {1}{\\sqrt {D _ {k}}} \\mathbf {q} \\mathbf {k} ^ {T}\\right), \\tag {1}", + "image_path": "b31994305c5cdd63b3a9fea86cde27019804c4d1190079ce4cf44ce918886274.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 277, + 545, + 291 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 277, + 545, + 291 + ], + "spans": [ + { + "bbox": [ + 313, + 277, + 545, + 291 + ], + "type": "interline_equation", + "content": "\\operatorname {M S A} (\\mathbf {z}) = \\left[ \\operatorname {S A} _ {1} (\\mathbf {z}); \\operatorname {S A} _ {2} (\\mathbf {z}); \\dots ; \\operatorname {S A} _ {k} (\\mathbf {z}) \\right] \\mathbf {U} _ {m}, \\tag {2}", + "image_path": "d62c3ce4dc1de64a206b120422e5c1a27d3d49b1e81064e64bff8c5823f4deef.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 297, + 545, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 297, + 545, + 348 + ], + "spans": [ + { + "bbox": [ + 305, + 297, + 545, + 348 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 297, + 545, + 348 + ], + "type": "inline_equation", + "content": "\\mathbf{U}_{qkv} \\in \\mathbb{R}^{D \\times 3D_k}" + }, + { + "bbox": [ + 305, + 297, + 545, + 348 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 297, + 545, + 348 + ], + "type": "inline_equation", + "content": "\\mathbf{U}_m \\in \\mathbb{R}^{k \\cdot D_k \\times D}" + }, + { + "bbox": [ + 305, + 297, + 545, + 348 + ], + "type": "text", + "content": ". Let " + }, + { + "bbox": [ + 305, + 297, + 545, + 348 + ], + "type": "inline_equation", + "content": "A = \\frac{\\mathbf{q}\\mathbf{k}^T}{\\sqrt{D_k}} \\in \\mathbb{R}^{N \\times N}" + }, + { + "bbox": [ + 305, + 297, + 545, + 348 + ], + "type": "text", + "content": " denote the attention matrix. Our ASAD performs spatial-attention dropout on " + }, + { + "bbox": [ + 305, + 297, + 545, + 348 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 305, + 297, + 545, + 348 + ], + "type": "text", + "content": " so as to remove some within-frame interactions." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 350, + 545, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 350, + 545, + 445 + ], + "spans": [ + { + "bbox": [ + 305, + 350, + 545, + 445 + ], + "type": "text", + "content": "Temporal matching probability. We first need to consider the best tokens on which to apply ASAD. Intuitively, a query token that has a strong match in the other frame should be a good candidate, since, in the absence of within-frame cues, it can still be reconstructed well using the temporal cues in the other frame. Here, we define a temporal matching function " + }, + { + "bbox": [ + 305, + 350, + 545, + 445 + ], + "type": "inline_equation", + "content": "f_{tem}(\\cdot)" + }, + { + "bbox": [ + 305, + 350, + 545, + 445 + ], + "type": "text", + "content": " to measure the temporal matching probability of the " + }, + { + "bbox": [ + 305, + 350, + 545, + 445 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 305, + 350, + 545, + 445 + ], + "type": "text", + "content": "-th query token:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 321, + 452, + 545, + 472 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 452, + 545, + 472 + ], + "spans": [ + { + "bbox": [ + 321, + 452, + 545, + 472 + ], + "type": "interline_equation", + "content": "f _ {t e m} (i) = \\max _ {j \\in \\Omega_ {t} (i)} \\left(\\hat {A} _ {i, j}\\right), \\quad \\hat {A} = \\operatorname {s o f t m a x} _ {\\text {r o w}} (A), \\tag {3}", + "image_path": "f388d98fb68bc121037dbda27cf2c69e707ee905167c13a0382c6c7eae5bbb58.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 478, + 545, + 562 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 478, + 545, + 562 + ], + "spans": [ + { + "bbox": [ + 305, + 478, + 545, + 562 + ], + "type": "text", + "content": "where the softmax function is applied on each row of " + }, + { + "bbox": [ + 305, + 478, + 545, + 562 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 305, + 478, + 545, + 562 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 478, + 545, + 562 + ], + "type": "inline_equation", + "content": "f_{tem}(i) \\in [0,1]" + }, + { + "bbox": [ + 305, + 478, + 545, + 562 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 478, + 545, + 562 + ], + "type": "inline_equation", + "content": "\\Omega_t(i)" + }, + { + "bbox": [ + 305, + 478, + 545, + 562 + ], + "type": "text", + "content": " denotes the temporal index set of the " + }, + { + "bbox": [ + 305, + 478, + 545, + 562 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 305, + 478, + 545, + 562 + ], + "type": "text", + "content": "-th query token, which contains all the token indices of the other frame. A larger value of " + }, + { + "bbox": [ + 305, + 478, + 545, + 562 + ], + "type": "inline_equation", + "content": "f_{tem}(i)" + }, + { + "bbox": [ + 305, + 478, + 545, + 562 + ], + "type": "text", + "content": " indicates a larger probability that the " + }, + { + "bbox": [ + 305, + 478, + 545, + 562 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 305, + 478, + 545, + 562 + ], + "type": "text", + "content": "-th query token is well-matched in the other frame, and thus a good candidate for ASAD. A visualization of " + }, + { + "bbox": [ + 305, + 478, + 545, + 562 + ], + "type": "inline_equation", + "content": "f_{tem}(\\cdot)" + }, + { + "bbox": [ + 305, + 478, + 545, + 562 + ], + "type": "text", + "content": " is shown in Fig. 5." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 562, + 545, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 562, + 545, + 609 + ], + "spans": [ + { + "bbox": [ + 305, + 562, + 545, + 609 + ], + "type": "text", + "content": "Overall dropout probability measurement. The overall spatial-attention dropout probability at location " + }, + { + "bbox": [ + 305, + 562, + 545, + 609 + ], + "type": "inline_equation", + "content": "(i,j)" + }, + { + "bbox": [ + 305, + 562, + 545, + 609 + ], + "type": "text", + "content": " is measured by using both the temporal matching probability and the normalized spatial importance:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 361, + 616, + 545, + 647 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 361, + 616, + 545, + 647 + ], + "spans": [ + { + "bbox": [ + 361, + 616, + 545, + 647 + ], + "type": "interline_equation", + "content": "W _ {i, j} = f _ {\\text {t e m}} (i) \\frac {\\hat {A} _ {i , j}}{\\sum_ {j \\in \\Omega_ {s} (i)} \\hat {A} _ {i , j}}, \\tag {4}", + "image_path": "1f9878e42fc607c85a16bd649ac19482d90f4df50dab48f8f24fa0d64c3f3e68.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 653, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 653, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 305, + 653, + 545, + 712 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 653, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\Omega_s(i)" + }, + { + "bbox": [ + 305, + 653, + 545, + 712 + ], + "type": "text", + "content": " is the spatial index set that contains all the other token indices (i.e., excluding the query index itself) in the same frame as the " + }, + { + "bbox": [ + 305, + 653, + 545, + 712 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 305, + 653, + 545, + 712 + ], + "type": "text", + "content": "-th query. When " + }, + { + "bbox": [ + 305, + 653, + 545, + 712 + ], + "type": "inline_equation", + "content": "W_{i,j}" + }, + { + "bbox": [ + 305, + 653, + 545, + 712 + ], + "type": "text", + "content": " is large, the " + }, + { + "bbox": [ + 305, + 653, + 545, + 712 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 305, + 653, + 545, + 712 + ], + "type": "text", + "content": "-th query token has a good between-frame match, and meanwhile the " + }, + { + "bbox": [ + 305, + 653, + 545, + 712 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 305, + 653, + 545, + 712 + ], + "type": "text", + "content": "-th within-frame token is important for the " + }, + { + "bbox": [ + 305, + 653, + 545, + 712 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 305, + 653, + 545, + 712 + ], + "type": "text", + "content": "-th" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14564" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 286, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 286, + 133 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 286, + 133 + ], + "type": "text", + "content": "query. In this case, dropping the attention element " + }, + { + "bbox": [ + 46, + 72, + 286, + 133 + ], + "type": "inline_equation", + "content": "(i,j)" + }, + { + "bbox": [ + 46, + 72, + 286, + 133 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 46, + 72, + 286, + 133 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 72, + 286, + 133 + ], + "type": "text", + "content": " facilitates the model to use between-frame (temporally-matched) tokens for token learning or reconstruction. Finally, we set the dropout probability for self-attention and temporal-self-attention to be 0, i.e., " + }, + { + "bbox": [ + 46, + 72, + 286, + 133 + ], + "type": "inline_equation", + "content": "W_{i,i} = W_{i,i + N / 2} = 0" + }, + { + "bbox": [ + 46, + 72, + 286, + 133 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 133, + 286, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 133, + 286, + 204 + ], + "spans": [ + { + "bbox": [ + 46, + 133, + 286, + 204 + ], + "type": "text", + "content": "Note that there are " + }, + { + "bbox": [ + 46, + 133, + 286, + 204 + ], + "type": "inline_equation", + "content": "N(N / 2 - 1)" + }, + { + "bbox": [ + 46, + 133, + 286, + 204 + ], + "type": "text", + "content": " (i.e., excluding self-attention elements) spatial-attention elements in total, and only these spatial-attention elements are considered for dropout. With a pre-defined dropout ratio " + }, + { + "bbox": [ + 46, + 133, + 286, + 204 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 133, + 286, + 204 + ], + "type": "text", + "content": ", we globally drop a total of " + }, + { + "bbox": [ + 46, + 133, + 286, + 204 + ], + "type": "inline_equation", + "content": "N_{d} = PN(N / 2 - 1)" + }, + { + "bbox": [ + 46, + 133, + 286, + 204 + ], + "type": "text", + "content": " attention elements from " + }, + { + "bbox": [ + 46, + 133, + 286, + 204 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 133, + 286, + 204 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 206, + 286, + 314 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 206, + 286, + 314 + ], + "spans": [ + { + "bbox": [ + 46, + 206, + 286, + 314 + ], + "type": "text", + "content": "Sampling for Dropout. We draw " + }, + { + "bbox": [ + 46, + 206, + 286, + 314 + ], + "type": "inline_equation", + "content": "N_{d}" + }, + { + "bbox": [ + 46, + 206, + 286, + 314 + ], + "type": "text", + "content": " elements from a multinomial distribution based on the dropout probability matrix " + }, + { + "bbox": [ + 46, + 206, + 286, + 314 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 46, + 206, + 286, + 314 + ], + "type": "text", + "content": ". Then we drop the elements in " + }, + { + "bbox": [ + 46, + 206, + 286, + 314 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 206, + 286, + 314 + ], + "type": "text", + "content": " with the corresponding indices by setting their values to " + }, + { + "bbox": [ + 46, + 206, + 286, + 314 + ], + "type": "inline_equation", + "content": "-\\infty" + }, + { + "bbox": [ + 46, + 206, + 286, + 314 + ], + "type": "text", + "content": ". After applying the softmax function in (1), the corresponding spatial-attention weights are removed. The other operations are the same with the original multi-head self attention mechanisms used in ViT. The PyTorch-like pseudocode is presented in the Supplemental." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 315, + 286, + 398 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 315, + 286, + 398 + ], + "spans": [ + { + "bbox": [ + 46, + 315, + 286, + 398 + ], + "type": "text", + "content": "Our ASAD method has negligible additional time cost compared with TwinMAE, due to the efficient matrix operation in GPUs. We apply ASAD to each layer in the decoder during the pre-training stage, so as to learn encoder representations that support temporal matching. In the next section, we introduce downstream task fine-tuning based on the well pre-trained ViT model." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 410, + 254, + 423 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 410, + 254, + 423 + ], + "spans": [ + { + "bbox": [ + 47, + 410, + 254, + 423 + ], + "type": "text", + "content": "3.4. Downstream Temporal Matching Tasks" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 430, + 286, + 465 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 430, + 286, + 465 + ], + "spans": [ + { + "bbox": [ + 46, + 430, + 286, + 465 + ], + "type": "text", + "content": "After obtaining the pre-trained DropMAE model, we fine-tune the well-learned encoder (i.e., the ViT model) on downstream temporal matching tasks, i.e., VOT and VOS." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 481, + 178, + 493 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 481, + 178, + 493 + ], + "spans": [ + { + "bbox": [ + 47, + 481, + 178, + 493 + ], + "type": "text", + "content": "3.4.1 Video Object Tracking" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 502, + 286, + 621 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 502, + 286, + 621 + ], + "spans": [ + { + "bbox": [ + 46, + 502, + 286, + 621 + ], + "type": "text", + "content": "Recently, the MAE ViT models pre-trained on ImageNet are applied to VOT and show impressive results. We use the state-of-the-art tracker OSTrack [97] as our baseline tracker for fine-tuning. In OSTrack, the cropped template and search images are firstly serialized into sequences and concatenated together. Then the overall sequence is added with the positional embeddings and input to the ViT backbone for joint feature extraction and interaction. Finally, the updated search features are input to a prediction head to predict the target bounding box." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 623, + 286, + 718 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 623, + 286, + 718 + ], + "spans": [ + { + "bbox": [ + 46, + 623, + 286, + 718 + ], + "type": "text", + "content": "During the fine-tuning stage, we use our pre-trained DropMAE encoder weights to initialize the ViT backbone used in OSTrack. Meanwhile, two frame identity embeddings are respectively added to template and search embeddings, in order to keep consistency with the pre-training stage. We use the same training losses of the original OSTrack. The detailed training parameters are shown in Supplementary for reference." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 72, + 455, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 455, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 455, + 84 + ], + "type": "text", + "content": "3.4.2 Video Object Segmentation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 91, + 545, + 114 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 91, + 545, + 114 + ], + "spans": [ + { + "bbox": [ + 304, + 91, + 545, + 114 + ], + "type": "text", + "content": "For VOS, there are currently no methods based on ViT. Thus, we build a simple VOS baseline with a ViT backbone." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 115, + 545, + 222 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 115, + 545, + 222 + ], + "spans": [ + { + "bbox": [ + 304, + 115, + 545, + 222 + ], + "type": "text", + "content": "Input serialization. Given a template frame with a binary mask, VOS aims to segment the object-of-interest in each frame of a video. Similar to the pre-training stage, the binary mask map, template and search frames are firstly converted to patch sequences, and then linearly projected and added with positional embeddings. Two frame identity embeddings are added to the template and search embeddings, and the mask embeddings are added to the template embeddings for mask encoding." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 223, + 545, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 223, + 545, + 281 + ], + "spans": [ + { + "bbox": [ + 304, + 223, + 545, + 281 + ], + "type": "text", + "content": "Joint feature extraction and interaction. The template and search embeddings are concatenated together and input to the ViT backbone for joint feature extraction and matching. We use the updated search features extracted from the last layer of ViT for mask prediction." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 282, + 545, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 282, + 545, + 354 + ], + "spans": [ + { + "bbox": [ + 304, + 282, + 545, + 354 + ], + "type": "text", + "content": "Mask prediction. The existing VOS approaches [14, 15, 60, 96] employ multi-resolution features for mask prediction. However, the updated search features are single-resolution. We follow [45] to upsample the search features to " + }, + { + "bbox": [ + 304, + 282, + 545, + 354 + ], + "type": "inline_equation", + "content": "2 \\times" + }, + { + "bbox": [ + 304, + 282, + 545, + 354 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 282, + 545, + 354 + ], + "type": "inline_equation", + "content": "4 \\times" + }, + { + "bbox": [ + 304, + 282, + 545, + 354 + ], + "type": "text", + "content": " sizes via two deconvolutional modules. Finally, we use the same decoder used in [15, 60] for mask prediction." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 354, + 545, + 377 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 354, + 545, + 377 + ], + "spans": [ + { + "bbox": [ + 304, + 354, + 545, + 377 + ], + "type": "text", + "content": "Training loss. We use the commonly-used cross entropy loss [15, 60] to train the whole network architecture." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 378, + 545, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 378, + 545, + 413 + ], + "spans": [ + { + "bbox": [ + 304, + 378, + 545, + 413 + ], + "type": "text", + "content": "Online inference. During the online inference, we use the first frame with the mask annotation as the memory frame for online target matching in the search frame." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 414, + 545, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 414, + 545, + 437 + ], + "spans": [ + { + "bbox": [ + 304, + 414, + 545, + 437 + ], + "type": "text", + "content": "The pipeline figure and more implementation details can be found in Supplementary." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 448, + 386, + 461 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 448, + 386, + 461 + ], + "spans": [ + { + "bbox": [ + 305, + 448, + 386, + 461 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 468, + 438, + 480 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 468, + 438, + 480 + ], + "spans": [ + { + "bbox": [ + 306, + 468, + 438, + 480 + ], + "type": "text", + "content": "4.1. Implementation Details" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 486, + 545, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 545, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 545, + 653 + ], + "type": "text", + "content": "Datasets. In the pre-training stage, we explore various large-scale video data sources to pre-train our DropMAE model, including Kinetics-400 [40] (K400), Kinetics-600 [8] (K600), Kinetics-700 [9] (K700), Moments in Time [56] (MiT) and WebVid-2M [1]. The detailed performance comparison using different pre-training datasets is shown in the ablation study. For fine-tuning on VOT, we follow the training settings used in our baseline OSTrack [97]. We use the training splits of LaSOT [28], COCO [49], TrackingNet [57] and GOT-10k [39] for training. For the GOT-10k evaluation, we follow the one-shot evaluation and only fine-tune the model on the training split of GOT-10k. For VOS finetuning, we use Youtube-VOS [90] and Davis [64] datasets for fine-tuning following the standard convention [15, 60]." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "Pre-training and fine-tuning. For DropMAE pre-training, the default input is two frames with a spatial size of " + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": " pixels. The frames are randomly sampled from each video within a maximum frame gap of 50. During the pretraining, one epoch is counted when all videos are sampled" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14565" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 75, + 63, + 516, + 218 + ], + "blocks": [ + { + "bbox": [ + 75, + 63, + 516, + 218 + ], + "lines": [ + { + "bbox": [ + 75, + 63, + 516, + 218 + ], + "spans": [ + { + "bbox": [ + 75, + 63, + 516, + 218 + ], + "type": "table", + "html": "
MethodsPre-training DataEpochsPre-train. Time (h)GOT-10k (VOT)DAVIS-17 (VOS)
AOSR0.5SR0.75J&FJF
No Pre-training---62.772.853.769.566.972.2
Supervised IN1k [72]IN1K300-69.779.065.678.074.881.1
Supervised IN21k [66]IN21K80-70.280.765.478.575.481.7
CLIP [65]IN1K32-67.476.860.073.670.576.7
MOCO-v3 [12]IN1K300-70.180.165.378.475.481.5
BeiT [2]IN1K800103.167.476.860.076.172.779.4
MAE [36]IN1K16008473.783.270.881.778.584.9
TwinMAEK40040020.772.283.265.979.376.482.3
TwinMAEK40080041.372.983.668.580.777.983.6
TwinMAEK400160082.774.284.969.481.278.184.2
DropMAEK40040021.173.283.967.581.378.584.0
DropMAEK40080042.274.885.470.582.779.785.6
DropMAEK400160084.475.886.472.083.180.286.0
DropMAEK70080092.475.986.872.083.080.285.7
", + "image_path": "77b9c59593663d9e7b155bcaf307d18503290e2aed743e56026c75ab44673aab.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 66, + 265, + 526, + 496 + ], + "blocks": [ + { + "bbox": [ + 46, + 221, + 546, + 255 + ], + "lines": [ + { + "bbox": [ + 46, + 221, + 546, + 255 + ], + "spans": [ + { + "bbox": [ + 46, + 221, + 546, + 255 + ], + "type": "text", + "content": "Table 1. Comparison of pre-training methods on downstream VOT and VOS tasks on GOT-10k [39] and DAVIS-17 [64]. All methods adopt the ViT-B/16 model [24] with " + }, + { + "bbox": [ + 46, + 221, + 546, + 255 + ], + "type": "inline_equation", + "content": "224\\times 224" + }, + { + "bbox": [ + 46, + 221, + 546, + 255 + ], + "type": "text", + "content": " input images for pre-training. The pre-training time is measured on 64 NVIDIA V100 GPUs. The best two results are shown in red and blue." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 66, + 265, + 526, + 496 + ], + "lines": [ + { + "bbox": [ + 66, + 265, + 526, + 496 + ], + "spans": [ + { + "bbox": [ + 66, + 265, + 526, + 496 + ], + "type": "table", + "html": "
MethodSourceGOT-10k [39]TNL2K [79]LaSOText [27]LaSOT [28]
AOSR0.5SR0.75AUCPAUCPNormPAUCPNormP
SiamFC [3]ECCVW1634.835.39.829.528.623.031.126.933.642.033.9
MDNet [58]CVPR1629.930.39.9--27.934.931.839.746.037.3
ECO [19]ICCV1731.630.911.132.631.722.025.224.032.433.830.1
SiamPRN++ [41]CVPR1951.761.632.541.341.234.041.639.649.656.949.1
DiMP [4]ICCV1961.171.749.244.743.439.247.645.156.965.056.7
SiamR-CNN [74]CVPR2064.972.859.752.352.8---64.872.2-
LTMU [18]CVPR20---48.547.341.449.947.357.2-57.2
Ocean [104]ECCV2061.172.147.338.437.7---56.065.156.6
TrDiMP [76]CVPR2167.177.758.3-----63.9-61.4
TransT [13]CVPR2167.176.860.950.751.7---64.973.869.0
AutoMatch [102]ICCV2165.276.654.347.243.537.6-43.058.3-59.9
STARK [92]ICCV2168.878.164.1-----67.177.0-
KeepTrack [55]ICCV21-----48.2--67.177.270.2
MixFormer-L [17]CVPR2270.780.067.8-----70.179.976.3
SBT [87]CVPR2270.480.864.7-----66.7-71.1
UAST [98]ICML2263.574.151.4-----57.1-58.7
SwinTrack-384 [48]NeurIPS2272.480.567.855.957.149.1-55.671.3-76.5
AiATrack [32]ECCV2269.680.063.2--46.854.454.249.656.949.1
CIA50 [63]ECCV2267.979.060.350.957.6---66.2-69.6
SimTrack-L [10]ECCV2269.878.866.055.655.7---70.579.7-
OSTrack-384 [97]ECCV2273.783.270.855.956.750.561.357.671.181.177.6
DropTrackOurs75.986.872.056.957.952.763.960.271.881.878.1
", + "image_path": "fb8a2b611551a99cecd9761edc9c9e557901dfee1d37027f2cf70b744eec4359.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 498, + 546, + 522 + ], + "lines": [ + { + "bbox": [ + 46, + 498, + 546, + 522 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 546, + 522 + ], + "type": "text", + "content": "Table 2. Comparison with state-of-the-art VOT approaches on four large-scale challenging datasets. The best two results are shown in red and blue. For GOT-10k evaluation, all the methods follow the one-shot protocol, training only on the training set in GOT-10k." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 542, + 287, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 542, + 287, + 615 + ], + "spans": [ + { + "bbox": [ + 46, + 542, + 287, + 615 + ], + "type": "text", + "content": "once. For fair comparison, we use the same mask ratio (i.e., " + }, + { + "bbox": [ + 46, + 542, + 287, + 615 + ], + "type": "inline_equation", + "content": "75\\%" + }, + { + "bbox": [ + 46, + 542, + 287, + 615 + ], + "type": "text", + "content": ") and training hyper-parameters of MAE [36] to pretrain the TwinMAE and DropMAE models. Following [14, 15], we use a bootstrapped cross entropy loss for training. The detailed pre-training and fine-tuning hyper-parameters are in the Supplementary." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 628, + 258, + 640 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 628, + 258, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 628, + 258, + 640 + ], + "type": "text", + "content": "4.2. Comparison with Pre-Training Methods" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 642, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 288, + 713 + ], + "type": "text", + "content": "In Table 1, we compare our DropMAE with existing pre-training methods on the downstream tasks of VOT and VOS. DropMAE and TwinMAE are pre-trained using videos (K400, K700), while MAE and other methods are pre-trained on ImageNet 1k or 21k (IN1K, IN21K). The VOT and VOS baselines illustrated in Sec. 3.4 use the" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 542, + 547, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 542, + 547, + 674 + ], + "spans": [ + { + "bbox": [ + 304, + 542, + 547, + 674 + ], + "type": "text", + "content": "official pre-trained VIT-B/16 models provided by existing pre-training approaches (see Table 1) for fine-tuning. TwinMAE with 800-epoch training performs favorably against MAE on VOT, but achieves inferior results on VOS. There are two main reasons: 1) TwinMAE is not effective enough at learning temporal matches; 2) The number of object classes in K400 is limited, and meanwhile the object classes in DAVIS-17 are included in ImageNet. Thus MAE generalizes well to VOS. Our DropMAE, which is a stronger temporal matching learner, outperforms MAE on both the VOT and VOS tasks with 800-epoch training (i.e., 42.2 hours" + }, + { + "bbox": [ + 304, + 542, + 547, + 674 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 304, + 542, + 547, + 674 + ], + "type": "text", + "content": ")" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 305, + 683, + 547, + 715 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 683, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 683, + 547, + 715 + ], + "type": "text", + "content": "In our implementation, we perform video decoding and extract the video frames on the fly in each training iteration, which could be further sped up using some tricks like repeated sampling [30]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "14566" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 70, + 61, + 264, + 159 + ], + "blocks": [ + { + "bbox": [ + 70, + 61, + 264, + 159 + ], + "lines": [ + { + "bbox": [ + 70, + 61, + 264, + 159 + ], + "spans": [ + { + "bbox": [ + 70, + 61, + 264, + 159 + ], + "type": "table", + "html": "
MethodOTB100AUCITBAUCTrackingNet
AUCPNorm
SiamFC [3]58.344.157.166.3
Ocean [104]68.447.7--
ATOM [20]68.347.270.377.1
DiMP [4]53.733974.080.1
TransT [13]69.554.781.486.7
STARK [92]68.157.682.086.9
OSTrack [97]-64.883.988.5
DropTrack69.665.084.188.9
", + "image_path": "afa95419d66b7761ab29ea32c37c21e99abd8ff434fc821bc5b3043223cbe34d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 208, + 287, + 232 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 208, + 287, + 232 + ], + "spans": [ + { + "bbox": [ + 46, + 208, + 287, + 232 + ], + "type": "text", + "content": "by using the K400 dataset. This indicates that our DropMAE is " + }, + { + "bbox": [ + 46, + 208, + 287, + 232 + ], + "type": "inline_equation", + "content": "2\\times" + }, + { + "bbox": [ + 46, + 208, + 287, + 232 + ], + "type": "text", + "content": " faster than MAE." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 244, + 208, + 259 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 244, + 208, + 259 + ], + "spans": [ + { + "bbox": [ + 47, + 244, + 208, + 259 + ], + "type": "text", + "content": "5. State-of-the-art Comparison" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 265, + 287, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 265, + 287, + 326 + ], + "spans": [ + { + "bbox": [ + 46, + 265, + 287, + 326 + ], + "type": "text", + "content": "In this section, we compare our fine-tuned VOT and VOS models, denoted as DropTrack and DropSeg, with state-of-the-art approaches on VOT and VOS benchmarks. We use DropMAE trained on K700 with 800 epochs as the pretraining model for both VOT and VOS fine-tuning." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 334, + 178, + 347 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 334, + 178, + 347 + ], + "spans": [ + { + "bbox": [ + 47, + 334, + 178, + 347 + ], + "type": "text", + "content": "5.1. Video Object Tracking" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 353, + 287, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 353, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 353, + 287, + 581 + ], + "type": "text", + "content": "To demonstrate the effectiveness of the proposed DropMAE for VOT, we compare our DropTrack with state-of-the-art trackers on 7 challenging tracking benchmarks. GOT-10k. GOT-10k [39] is a challenging dataset that follows the one-shot evaluation protocol, where the trackers are required to be trained on its training split, and the test object classes have no overlap with the objects in the training split. As shown in Table 2, our DropTrack achieves state-of-the-art results on this dataset, outperforming OSTrack by " + }, + { + "bbox": [ + 46, + 353, + 287, + 581 + ], + "type": "inline_equation", + "content": "2.2\\%" + }, + { + "bbox": [ + 46, + 353, + 287, + 581 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 353, + 287, + 581 + ], + "type": "inline_equation", + "content": "3.6\\%" + }, + { + "bbox": [ + 46, + 353, + 287, + 581 + ], + "type": "text", + "content": " in terms of AO and " + }, + { + "bbox": [ + 46, + 353, + 287, + 581 + ], + "type": "inline_equation", + "content": "\\mathrm{SR}_{0.5}" + }, + { + "bbox": [ + 46, + 353, + 287, + 581 + ], + "type": "text", + "content": ". This implies that the temporal correspondence learning in the pretraining is beneficial for the downstream tracking task. Although there exists a domain gap between the pre-training data and the test data (i.e., a large portion of test objects in GOT-10k are animals, vehicles and object parts, whereas K700 only consists of human-centric action videos), the temporal matching ability learned by DropMAE can still be transferred to the downstream tracking task, improving the tracking performance." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 581, + 287, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 581, + 287, + 641 + ], + "spans": [ + { + "bbox": [ + 46, + 581, + 287, + 641 + ], + "type": "text", + "content": "LaSOT. LaSOT consists of 280 long test sequences, and our results are presented in Table 2. Our DropTrack sets a new record on this dataset with " + }, + { + "bbox": [ + 46, + 581, + 287, + 641 + ], + "type": "inline_equation", + "content": "71.8\\%" + }, + { + "bbox": [ + 46, + 581, + 287, + 641 + ], + "type": "text", + "content": " AUC, " + }, + { + "bbox": [ + 46, + 581, + 287, + 641 + ], + "type": "inline_equation", + "content": "81.8\\%" + }, + { + "bbox": [ + 46, + 581, + 287, + 641 + ], + "type": "inline_equation", + "content": "\\mathrm{P}_{\\text {Norm }}" + }, + { + "bbox": [ + 46, + 581, + 287, + 641 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 581, + 287, + 641 + ], + "type": "inline_equation", + "content": "78.1\\%" + }, + { + "bbox": [ + 46, + 581, + 287, + 641 + ], + "type": "text", + "content": " P, which shows the great potential of our DropTrack in robust long-term visual tracking." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{LaSOT}_{ext}" + }, + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{LaSOT}_{ext}" + }, + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "type": "text", + "content": " is an extension of LaSOT with more challenging video sequences for testing - similar to GOT-10k, the test split has a large gap with the training split, and sequences with novel object classes (i.e., not appeared in ImageNet) are used for evaluation. Our DropMAE outperforms the other trackers by large margins. This demon" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 309, + 61, + 547, + 215 + ], + "blocks": [ + { + "bbox": [ + 46, + 163, + 287, + 196 + ], + "lines": [ + { + "bbox": [ + 46, + 163, + 287, + 196 + ], + "spans": [ + { + "bbox": [ + 46, + 163, + 287, + 196 + ], + "type": "text", + "content": "Table 3. Comparison with state-of-the-art VOT approaches on OTB100 [85], ITB [44] and TrackingNet [57]. The best two results are shown in red and blue." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 61, + 547, + 215 + ], + "lines": [ + { + "bbox": [ + 309, + 61, + 547, + 215 + ], + "spans": [ + { + "bbox": [ + 309, + 61, + 547, + 215 + ], + "type": "table", + "html": "
MethodSourceOLMSDAVIS-2016 [62]DAVIS-2017 [64]
J&FJFJ&FJF
RANet [80]ICCV19✓85.585.585.465.763.268.2
STM [60]ICCV19✓✓89.388.789.981.879.284.3
FRTM [67]CVPR20✓✓83.583.683.476.773.979.6
TVOS [101]CVPR20✓---72.369.974.7
LWL [5]ECCV20✓✓---81.679.184.1
CFBI [95]ECCV20✓89.488.390.581.979.184.6
UniTrack [81]NeurIPS21✓----58.4-
STCN- [15]NeurIPS21✓---82.579.385.7
SSTVOS [26]CVPR21✓---82.579.985.1
SWEM- [50]CVPR22✓89.5--81.9--
RTS [61]ECCV22✓✓---80.277.982.6
OSMN [54]TPAMI1873.574.072.954.852.557.1
FAVOS [16]CVPR1881.082.479.558.254.661.8
VideoMatch [38]ECCV18-81.0-56.5--
SiamMask [77]CVPR1969.871.767.856.454.358.5
D3S [52]CVPR2074.075.472.660.857.863.8
Siam R-CNN [52]CVPR20---70.666.175.0
Unicorn [91]ECCV2287.486.588.269.265.273.2
DropSegOurs92.190.993.383.080.285.7
", + "image_path": "d2dfe40de76e5cc59da93e286f84a59553f025a87a076c5ce0c62d246d452c32.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 219, + 545, + 262 + ], + "lines": [ + { + "bbox": [ + 305, + 219, + 545, + 262 + ], + "spans": [ + { + "bbox": [ + 305, + 219, + 545, + 262 + ], + "type": "text", + "content": "Table 4. Comparison with state-of-the-art VOS approaches on the validation sets of DAVIS-2016 [62] and DAVIS-2017 [64]. OL, M and S indicate Online Learning, using Memory mechanism, and using Synthetic videos for pre-training." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 319, + 262, + 533, + 352 + ], + "blocks": [ + { + "bbox": [ + 319, + 262, + 533, + 352 + ], + "lines": [ + { + "bbox": [ + 319, + 262, + 533, + 352 + ], + "spans": [ + { + "bbox": [ + 319, + 262, + 533, + 352 + ], + "type": "image", + "image_path": "ed83c71d96fd8d2644c89bf60bedded699817a2a6a3e61e3a075d5f0bc17fdef.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 353, + 545, + 374 + ], + "lines": [ + { + "bbox": [ + 306, + 353, + 545, + 374 + ], + "spans": [ + { + "bbox": [ + 306, + 353, + 545, + 374 + ], + "type": "text", + "content": "Figure 6. Ablation study of the dropout ratio " + }, + { + "bbox": [ + 306, + 353, + 545, + 374 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 306, + 353, + 545, + 374 + ], + "type": "text", + "content": " on the GOT-10k (VOT) and DAVIS-17 (VOS) datasets." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 388, + 545, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 388, + 545, + 579 + ], + "spans": [ + { + "bbox": [ + 304, + 388, + 545, + 579 + ], + "type": "text", + "content": "strates that a tracker with DropMAE pre-training generalizes well to unseen objects in generic visual object tracking. TNL2K. TNL2K is a large-scale evaluation dataset that consists of 700 test videos with various challenges, such as significant appearance variation and manually added adversarial samples. As illustrated in Table 2, our DropMAE significantly outperforms the other trackers on this dataset. ITB, TrackingNet and OTB100. In Table 3, we evaluate our DropTrack on ITB [44], OTB100 [85] and TrackingNet [57], achieving state-of-the-art performance on each one. DropTrack is slightly better than OSTrack on ITB and TrackingNet. We believe the main reason is the fully overlapped training and test object classes in these two datasets, which reduces the effect of pre-training. A competitive tracker on these two datasets can be learned even using supervised ImageNet weights, which has been shown in [97]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 579, + 545, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 579, + 545, + 651 + ], + "spans": [ + { + "bbox": [ + 304, + 579, + 545, + 651 + ], + "type": "text", + "content": "On all 7 VOT datasets, our DropTrack outperforms the baseline OSTrack, which demonstrates that our DropMAE pre-training on videos learns better temporal-matching representations than the MAE model trained on ImageNet, resulting in more a robust tracker that generalizes well to both unseen and seen objects." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 658, + 457, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 658, + 457, + 672 + ], + "spans": [ + { + "bbox": [ + 306, + 658, + 457, + 672 + ], + "type": "text", + "content": "5.2. Video Object Segmentation" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 677, + 545, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 700 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 700 + ], + "type": "text", + "content": "In Table 4, we compare our DropSeg with existing VOS approaches on the DAVIS-16/17 [62,64]." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "type": "text", + "content": "DAVIS-16. DAVIS-16 is composed of 20 manually anno" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14567" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 283, + 148 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 283, + 148 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 283, + 148 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 283, + 148 + ], + "type": "table", + "html": "
DatasetsNo. \nVideosNo. \nActionsVOTVOS
AOSR0.5SR0.75J&F
K400 [40]240,00040073.283.967.582.7
K600 [8]390,00060074.585.569.582.8
K700 [9]526,76870075.686.271.483.0
MiT [56]802,24433975.185.570.682.8
WebVid [1]240,000-72.883.467.381.5
WebVid [1]960,000-73.485.069.582.9
", + "image_path": "4f5b895ed60699257569ab5af6122c94c907704b9ad66a436c7c03a48ca6db48.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 195, + 286, + 302 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 195, + 286, + 302 + ], + "spans": [ + { + "bbox": [ + 46, + 195, + 286, + 302 + ], + "type": "text", + "content": "tated test sequences. As shown in Table 4, our one-shot DropSeg approach, without using any online learning and complicated memory mechanisms, achieves the best " + }, + { + "bbox": [ + 46, + 195, + 286, + 302 + ], + "type": "inline_equation", + "content": "\\mathcal{J}\\&\\mathcal{F}" + }, + { + "bbox": [ + 46, + 195, + 286, + 302 + ], + "type": "text", + "content": " score of " + }, + { + "bbox": [ + 46, + 195, + 286, + 302 + ], + "type": "inline_equation", + "content": "92.1\\%" + }, + { + "bbox": [ + 46, + 195, + 286, + 302 + ], + "type": "text", + "content": ", which significantly outperforms the other compared one-shot approaches and is even better than the approaches with complicated pipelines (i.e., OL, M and S). This implies that the pixel-wise correspondence learned during the pre-training is effective for capturing long-range dependencies between various frames in VOS." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 303, + 286, + 363 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 303, + 286, + 363 + ], + "spans": [ + { + "bbox": [ + 46, + 303, + 286, + 363 + ], + "type": "text", + "content": "DAVIS-17. DAVIS-17 is an extension of DAVIS-16, comprising more challenging videos and supports multi-object segmentation. In Table 4, our DropSeg achieves competitive results of " + }, + { + "bbox": [ + 46, + 303, + 286, + 363 + ], + "type": "inline_equation", + "content": "83.0\\%" + }, + { + "bbox": [ + 46, + 303, + 286, + 363 + ], + "type": "inline_equation", + "content": "\\mathcal{I}\\& \\mathcal{F}" + }, + { + "bbox": [ + 46, + 303, + 286, + 363 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 303, + 286, + 363 + ], + "type": "inline_equation", + "content": "80.2\\%" + }, + { + "bbox": [ + 46, + 303, + 286, + 363 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 46, + 303, + 286, + 363 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 303, + 286, + 363 + ], + "type": "inline_equation", + "content": "85.7\\%" + }, + { + "bbox": [ + 46, + 303, + 286, + 363 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 46, + 303, + 286, + 363 + ], + "type": "text", + "content": ", which shows its superiority in handling more challenging videos." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 363, + 286, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 363, + 286, + 387 + ], + "spans": [ + { + "bbox": [ + 47, + 363, + 286, + 387 + ], + "type": "text", + "content": "More VOS results and comparisons are included in the supplementary." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 394, + 147, + 406 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 394, + 147, + 406 + ], + "spans": [ + { + "bbox": [ + 47, + 394, + 147, + 406 + ], + "type": "text", + "content": "6. Ablation Studies" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 414, + 286, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 414, + 286, + 450 + ], + "spans": [ + { + "bbox": [ + 46, + 414, + 286, + 450 + ], + "type": "text", + "content": "In this section, we conduct ablation studies to provide more detailed analysis of our method. We use DropMAE with 400-epoch pre-training for the ablation study." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 450, + 286, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 450, + 286, + 545 + ], + "spans": [ + { + "bbox": [ + 46, + 450, + 286, + 545 + ], + "type": "text", + "content": "The effect of dropout ratio " + }, + { + "bbox": [ + 46, + 450, + 286, + 545 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 450, + 286, + 545 + ], + "type": "text", + "content": ". We study the effect of dropout rate " + }, + { + "bbox": [ + 46, + 450, + 286, + 545 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 450, + 286, + 545 + ], + "type": "text", + "content": " in Fig. 6. A relatively small dropout ratio of " + }, + { + "bbox": [ + 46, + 450, + 286, + 545 + ], + "type": "inline_equation", + "content": "P = 0.1" + }, + { + "bbox": [ + 46, + 450, + 286, + 545 + ], + "type": "text", + "content": " works well on both VOT and VOS tasks. Meanwhile, dropping too many spatial cues (e.g., " + }, + { + "bbox": [ + 46, + 450, + 286, + 545 + ], + "type": "inline_equation", + "content": "P = 0.2" + }, + { + "bbox": [ + 46, + 450, + 286, + 545 + ], + "type": "text", + "content": ") degrades the downstream tasks, which is mainly because the spatial cues are also useful for accurate localization and segmentation. " + }, + { + "bbox": [ + 46, + 450, + 286, + 545 + ], + "type": "inline_equation", + "content": "P = 0.1" + }, + { + "bbox": [ + 46, + 450, + 286, + 545 + ], + "type": "text", + "content": " is the optimal setting, and thus we adopt it in the following experiments." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 545, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 286, + 713 + ], + "type": "text", + "content": "Pre-training video sources. Since we are the first to explore masked autoencoder pre-training for temporal matching tasks, it is not clear which video dataset is the optimal choice for pre-training. Here, we use five popular video datasets for pre-training, including K400 [40], K600 [8], K700 [9], MiT [56] and WebVid-2M [1]. For WebVid-2M, we randomly sample 240k and 960k videos for fair comparison and faster validation. The downstream tracking results are reported in Table 5. Performance is not favorable even using 960,000 videos in WebVid for pre-training. This indicates that WebViD is not a good choice for tracking pre-training, which is mainly because it is a video caption dataset that focuses on scene diversity and lacks rich object motion. From the experiments on the K400/600/700 and" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 356, + 70, + 494, + 120 + ], + "blocks": [ + { + "bbox": [ + 47, + 149, + 286, + 182 + ], + "lines": [ + { + "bbox": [ + 47, + 149, + 286, + 182 + ], + "spans": [ + { + "bbox": [ + 47, + 149, + 286, + 182 + ], + "type": "text", + "content": "Table 5. The downstream VOT and VOS performance on GOT-10k and DAVIS-17 obtained by using our DropMAE pre-trained on various video datasets. VOS uses 800 epochs pre-training." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 356, + 70, + 494, + 120 + ], + "lines": [ + { + "bbox": [ + 356, + 70, + 494, + 120 + ], + "spans": [ + { + "bbox": [ + 356, + 70, + 494, + 120 + ], + "type": "table", + "html": "
SettingsGOT-10k
DropTrack-K400-400E73.2/67.5
w/ ASAP in Encoder73.1/68.1
w/ domain specific data73.4/68.8
w/o frame identity embed72.9/67.4
", + "image_path": "74bb59102c31ae66761cb1a9b7196928686025aa37b58bd574db32e798541d38.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 121, + 545, + 143 + ], + "lines": [ + { + "bbox": [ + 305, + 121, + 545, + 143 + ], + "spans": [ + { + "bbox": [ + 305, + 121, + 545, + 143 + ], + "type": "text", + "content": "Table 6. The tracking performance of " + }, + { + "bbox": [ + 305, + 121, + 545, + 143 + ], + "type": "inline_equation", + "content": "\\mathrm{{AO}}/{\\mathrm{{SR}}}_{0.75}" + }, + { + "bbox": [ + 305, + 121, + 545, + 143 + ], + "type": "text", + "content": " on GOT10-k reported by variants with different settings." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 152, + 545, + 188 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 152, + 545, + 188 + ], + "spans": [ + { + "bbox": [ + 305, + 152, + 545, + 188 + ], + "type": "text", + "content": "MiT, tracking benefits from pre-training with from rich action classes (i.e., 700 action classes of K700), from which the model can learn stronger temporal matching ability." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 189, + 545, + 259 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 189, + 545, + 259 + ], + "spans": [ + { + "bbox": [ + 305, + 189, + 545, + 259 + ], + "type": "text", + "content": "Applying ASAD to the encoder. Here we test applying ASAD to all layers including both encoder and decoder of masked autoencoder. As shown in Table 6, this variant gains improvements (0.6% in " + }, + { + "bbox": [ + 305, + 189, + 545, + 259 + ], + "type": "inline_equation", + "content": "\\mathrm{SR}_{0.75}" + }, + { + "bbox": [ + 305, + 189, + 545, + 259 + ], + "type": "text", + "content": ") over the original baseline. Considering its additional cost and limited performance improvement, we only apply ASAD to the decoder." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 261, + 545, + 356 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 261, + 545, + 356 + ], + "spans": [ + { + "bbox": [ + 305, + 261, + 545, + 356 + ], + "type": "text", + "content": "Domain specific data. We also add the tracking training data (without using box annotations), including TrackingNet, LaSOT, and GOT-10k, into K400 for pre-training. The downstream tracking performance by using the larger pre-training set is 73.4/68.8, which is better than the baseline. It shows that the domain-specific data is helpful to bridge the domain gap, which can be considered as future work to extend Kinetic datasets with more tracking videos." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 357, + 545, + 428 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 357, + 545, + 428 + ], + "spans": [ + { + "bbox": [ + 305, + 357, + 545, + 428 + ], + "type": "text", + "content": "Frame identity embedding. During pre-training, the frame identity embedding is used to identify masked patches in the same 2D location of the two frames. From Table 6, we can find that downstream fine-tuning without the frame identity embedding performs worse than with it, since not using it is inconsistent with the pre-training stage." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 433, + 378, + 445 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 433, + 378, + 445 + ], + "spans": [ + { + "bbox": [ + 306, + 433, + 378, + 445 + ], + "type": "text", + "content": "7. Conclusion" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 453, + 545, + 645 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 453, + 545, + 645 + ], + "spans": [ + { + "bbox": [ + 305, + 453, + 545, + 645 + ], + "type": "text", + "content": "This paper investigated masked autoencoding pretraining for temporal matching-based downstream tasks. Specifically, an adaptive spatial-attention dropout method is proposed to facilitate temporal correspondence learning in self-supervised pre-training on videos. We show that our proposed pre-training method DropMAE can achieve better downstream performance on VOT and VOS than the image-based MAE, while using " + }, + { + "bbox": [ + 305, + 453, + 545, + 645 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 305, + 453, + 545, + 645 + ], + "type": "text", + "content": " less pre-training time. In addition, as the first work investigating this problem, we show the guidelines of selecting video sources for pre-training, i.e., selecting videos with rich motion information is more beneficial for temporal matching-based downstream tasks. The experimental results on VOT and VOS show that our DropMAE sets new state-of-the-art results on 8 out of 9 tracking benchmarks. We expect our DropMAE to serve as a strong pre-trained backbone in future work." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 657, + 410, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 657, + 410, + 670 + ], + "spans": [ + { + "bbox": [ + 306, + 657, + 410, + 670 + ], + "type": "text", + "content": "8. Acknowledgment" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": "This work was supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CityU 11215820)." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14568" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 53, + 91, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 19, + "blocks": [ + { + "bbox": [ + 58, + 91, + 287, + 124 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 91, + 287, + 124 + ], + "spans": [ + { + "bbox": [ + 58, + 91, + 287, + 124 + ], + "type": "text", + "content": "[1] Max Bain, Arsha Nagrani, Gül Varol, and Andrew Zisserman. 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In ECCV, 2020. 6, 7" + } + ] + } + ], + "index": 32 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14571" + } + ] + } + ], + "index": 34 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Dual Alignment Unsupervised Domain Adaptation for Video-Text Retrieval/8b3047df-13e0-4f30-a21d-3acd07314d19_content_list.json b/2023/Dual Alignment Unsupervised Domain Adaptation for Video-Text Retrieval/8b3047df-13e0-4f30-a21d-3acd07314d19_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..10def37eec0b0b5a377d981bd32b717a9beffd75 --- /dev/null +++ b/2023/Dual Alignment Unsupervised Domain Adaptation for Video-Text Retrieval/8b3047df-13e0-4f30-a21d-3acd07314d19_content_list.json @@ -0,0 +1,1629 @@ +[ + { + "type": "text", + "text": "Dual Alignment Unsupervised Domain Adaptation for Video-Text Retrieval", + "text_level": 1, + "bbox": [ + 104, + 130, + 866, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Xiaoshuai Hao $^{1,2}$ , Wanqian Zhang $^{1*}$ , Dayan Wu $^{1}$ , Fei Zhu $^{1,2}$ , Bo Li $^{1,2}$", + "bbox": [ + 210, + 179, + 759, + 198 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ Institute of Information Engineering, Chinese Academy of Sciences", + "bbox": [ + 210, + 198, + 756, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ School of Cyber Security, University of Chinese Academy of Sciences", + "bbox": [ + 204, + 215, + 766, + 234 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{haoxiaoshuai, zhangwanqian, wudayan, zhufei, libo}@ie.ac.cn", + "bbox": [ + 228, + 236, + 733, + 251 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 286, + 313, + 301 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Video-text retrieval is an emerging stream in both computer vision and natural language processing communities, which aims to find relevant videos given text queries. In this paper, we study the notoriously challenging task, i.e., Unsupervised Domain Adaptation Video-text Retrieval (UDAVR), wherein training and testing data come from different distributions. Previous works merely alleviate the domain shift, which however overlook the pairwise misalignment issue in target domain, i.e., there exist no semantic relationships between target videos and texts. To tackle this, we propose a novel method named Dual Alignment Domain Adaptation (DADA). Specifically, we first introduce the cross-modal semantic embedding to generate discriminative source features in a joint embedding space. Besides, we utilize the video and text domain adaptations to smoothly balance the minimization of the domain shifts. To tackle the pairwise misalignment in target domain, we propose the Dual Alignment Consistency (DAC) to fully exploit the semantic information of both modalities in target domain. The proposed DAC adaptively aligns the videotext pairs which are more likely to be relevant in target domain, enabling that positive pairs are increasing progressively and the noisy ones will potentially be aligned in the later stages. To that end, our method can generate more truly aligned target pairs and ensure the discriminability of target features. Compared with the state-of-the-art methods, DADA achieves $20.18\\%$ and $18.61\\%$ relative improvements on $R@1$ under the setting of TGIF $\\rightarrow$ MSR-VTT and TGIF $\\rightarrow$ MSVD respectively, demonstrating the superiority of our method.", + "bbox": [ + 75, + 318, + 473, + 773 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 803, + 209, + 819 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Video-text retrieval enables users to search videos with a simple and natural language description. The de facto paradigm is to learn high-level visual-textual embeddings", + "bbox": [ + 76, + 829, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/79b3fe71cfcd097fc48f9ba1a070663a6372f9fc7e1275fa8c2a01bb21d181c2.jpg", + "image_caption": [ + "Figure 1. Illustration of the proposed method. Previous methods simply bring source and target features closer (blue and red ovals are overlapping each other), whereas inevitably mixing target videos (red circles) and texts (red triangles) together, ignoring whether they are semantically relevant or not. Instead, our method exploits the semantic structures in target domain to adaptively generate truly aligned video-text pairs (dotted circles) and ensure the discriminability of target data. Best viewed in color." + ], + "image_footnote": [], + "bbox": [ + 511, + 284, + 671, + 452 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0287bf1d7ba016a1ca9a5358ff98d9a6f667916ce0d2283ff6dfdd822560e09a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 686, + 285, + 890, + 452 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "by off-the-shelf feature extractors, and to measure semantic similarities in a joint embedding space [13, 42, 46, 63]. Despite their thrilling success, the primary assumption is that training and testing data come from the same distribution, which whereas may not hold in real scenarios.", + "bbox": [ + 496, + 594, + 890, + 669 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To alleviate the domain shift problem, Unsupervised Domain Adaptation (UDA) has gained a lot of attention due to its efficient training without the need of supervision in target domain. UDA transfers knowledge from a labeled source domain to an unlabeled target domain [15, 33, 40, 41, 53], which has made remarkable progress in many fields, such as image classification [33, 56], autonomous driving [54, 55], medical image processing [35, 36], and video-based action recognition [50, 52]. However, these methods are originally designed for classification tasks, which might not be suitable for the video-text retrieval.", + "bbox": [ + 496, + 671, + 892, + 837 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Note that in UDA Video-text Retrieval (UDAVR), there exists no identical label set for source and target domains. The only supervision is the semantic relationship in source dataset, which is also the general setting for UDA", + "bbox": [ + 496, + 839, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author.", + "bbox": [ + 94, + 886, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "18962", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "cross-modal tasks [4, 11, 62, 64]. To that end, some approaches have been recently proposed [9, 17, 39], such as directly minimizing the distribution discrepancy [17], distilling knowledge from the source domain [9], or introducing pre-defined prototype assignments [39]. However, they overlook the pairwise misalignment issue in target domain, i.e., there exist no semantic relationships between target videos and texts. Merely alleviating the video and text domain shifts is a sub-optimal solution, which fails to fully explore the semantic structures of target data, i.e., whether the video-text pair is semantically relevant or not. As illustrated in Fig. 1, previous methods bring the learned source and target features close together, which whereas inevitably mixes up target videos and texts, ignoring whether they are a truly relevant pair or not. This will further induce less discriminative target features, and thus becomes the motivation of our work.", + "bbox": [ + 75, + 90, + 472, + 345 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we propose a novel method named Dual Alignment Domain Adaptation (DADA) to tackle the pairwise misalignment issue in target domain. We first introduce the cross-modal semantic embedding to generate discriminative source features in a joint embedding space, where semantically relevant pairs should lie close together and vice versa. To alleviate the domain shift, we further utilize a smooth adaptation procedure to balance the minimization of distribution shifts between source and target domains. Last but not least, to tackle the pairwise misalignment in target domain, we propose a simple yet effective Dual Alignment Consistency (DAC), which fully exploits the semantic information of both modalities in target domain. The proposed DAC adaptively aligns the video-text pairs which are more likely to be relevant in target domain, enabling that (1) positive pairs are increasing progressively, (2) the noisy ones will potentially be aligned in the later stages and (3) the discriminability of target features. Extensive experiments on several benchmarks demonstrate the superiority of our method.", + "bbox": [ + 75, + 347, + 472, + 648 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The contributions of this paper are mainly threefold:", + "bbox": [ + 96, + 648, + 442, + 664 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- To tackle the pairwise misalignment problem in UDAVR task, we develop a novel method named Dual Alignment Domain Adaptation (DADA) which fully exploits the semantic structures of target data.", + "- The proposed Dual Alignment Consistency (DAC) mechanism adaptively aligns the most similar videos and texts in target domain, ensure that the positive pairs are increasing progressively and the noisy ones are potentially aligned in later stages.", + "- Compared with the state-of-the-art methods, DADA achieves $20.18\\%$ and $18.61\\%$ relative improvements on R@1 under the setting of TGIF $\\rightarrow$ MSRVTT and TGIF $\\rightarrow$ MSVD respectively, demonstrating the superiority of our method." + ], + "bbox": [ + 96, + 671, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 89, + 640, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Video-Text Retrieval. In recent years, cross-modal embedding-based approaches [2, 10, 20, 26, 27, 37, 47, 58] have emerged as a dominant paradigm for video-text retrieval. [48] proposes the JEMC framework using action, object, text and audio features by a simple concatenation fusion strategy. CE [37] adopts video features extracted from all modalities to encode a video. T2VLAD [59] automatically learns text-and-video semantic topics and reemphasizes the importance of local semantic alignment between texts and videos. HGR [10] proposes a Hierarchical Graph Reasoning (HGR) model, which decomposes video-text pairs into global-to-local levels. GPO [5] learns to automatically adapt itself to the best pooling strategy for different baselines. Recently, the Contrastive Language-Image Pretraining (CLIP) [3] model is widely used in video-text retrieval [24, 31, 38, 45]. CLIP4Clip [43] investigates three mechanisms of similarity calculation based on the pretrained CLIP. Similarly, CLIP2video [18] focuses on the spatial semantics captured by the CLIP model. Different from them, we explore the video-text retrieval task through the lens of unsupervised domain adaptation.", + "bbox": [ + 496, + 114, + 890, + 431 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Unsupervised Domain Adaptation. UDA transfers predictive models from a fully-labeled source domain to an unlabeled target domain. Existing classification-based UDA methods seek to alleviate the domain shift between source and target domains [15, 22, 33, 40, 41, 56, 60]. Besides, UDA methods have been extended to various video-based tasks, like video action recognition [6, 12, 49], video segmentation [7, 8] and video localisation [1]. Recently, some cross-modal tasks also resort to UDA and try to utilize the unpaired data in target domain, such as image captioning [11, 62, 64] and VQA [4]. The similar work to ours is DCKT [29] which focuses on UDA image-text retrieval and transfers knowledge from a large dataset to promote the model performance on small dataset. However, DCKT needs labeled target image-text pairs during the training procedure, which fails to work well for UDAVR task.", + "bbox": [ + 496, + 431, + 890, + 672 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Unsupervised Domain Adaptation for Video-Text Retrieval. To the best of our knowledge, there are only a few explorations of the UDAVR task [9, 17, 39]. MAN [17] proposes three alignments to alleviate different gaps in UDAVR task. CAPQ [9] comprises a concept preservation regulariser to enhance the transferability of the learned embeddings. ACP [39] focuses on minimizing both uni-modal and cross-modal distribution shift across the source and target domains. Compared to these methods, our approach differs in three aspects. (1) MAN tries to directly alleviate three different gaps in a classification-based manner, which is not suitable for cross-modal retrieval task. (2) CAPQ and ACP maximize the mutual information or minimize the KL-divergence between the prototype assignments of source and target videos, which however ignores the domain shift", + "bbox": [ + 496, + 674, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "18963", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/a47805a002ce6ec0e783d86a017d88284003bc20cb05c08c11f897b27fb3e9ab.jpg", + "image_caption": [ + "Figure 2. The overall framework of DADA. Video/text features are first fed into video/text encoders to generate high-level representations. The video and text domain adaptation modules simultaneously alleviate the distribution shifts across domains in both modalities ( $\\mathcal{L}_{\\mathcal{D}}^{video}$ and $\\mathcal{L}_{\\mathcal{D}}^{text}$ ). Source video and text features are expected to be discriminative by the cross-modal semantic embedding ( $\\mathcal{L}_{\\mathcal{S}}$ ). Besides, the proposed Dual Alignment Consistency (DAC) adaptively aligns the target video-text pairs which are more likely to be relevant and progressively generates dual aligned video-text pairs $(v_{i}^{p}, t_{i}^{p})_{i=1}^{n_{p}}$ in target domain( $\\mathcal{L}_{\\mathcal{P}}$ ). Best viewed in color." + ], + "image_footnote": [], + "bbox": [ + 81, + 92, + 867, + 367 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "in text modality. (3) The semantic relationships of videos and texts in target domain have not been fully exploited by previous methods, leading to the pairwise misalignment issue, which is the primary concern of this paper.", + "bbox": [ + 75, + 467, + 468, + 529 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 76, + 542, + 210, + 559 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminaries", + "text_level": 1, + "bbox": [ + 76, + 566, + 217, + 580 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For notational clarity, we first introduce some symbols and definitions used throughout this paper. Formally, assume that we have a set of samples in source domain $\\left\\{(\\mathcal{V}^s,\\mathcal{T}^s) = (v_i^s,t_i^s)_{i = 1}^{n_s}\\right\\}$ , where $n_{s}$ indicates the number of video-text pairs. Similarly, we also have a set of samples in target domain $\\left\\{\\mathcal{V}^t = \\{v_i^t\\}_{i = 1}^{n_t},\\mathcal{T}^t = \\{t_j^t\\}_{j = 1}^{n_t}\\right\\}$ with two collections of $n_t$ videos $\\mathcal{V}^t$ and texts $\\mathcal{T}^t$ , respectively. Note that the target videos and texts are unpaired, which means the supervised information, i.e., whether one target video-text pair is semantically relevant or not, is not available in target domain. The Unsupervised Domain Adaptation Video-text Retrieval (UDAVR) aims at improving the model's generalization performance on target domain with the utilization of source domain. The overall framework of our method is illustrated in Fig. 2.", + "bbox": [ + 75, + 590, + 468, + 824 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given one video-text pair, following the state-of-the-art baseline in video-text retrieval [5], we utilize a video encoder $\\varphi (\\cdot)$ and a text encoder $\\psi (\\cdot)$ to map each video sample $v$ and text description $t$ into a joint embedding space. The visual embedding $\\varphi (v)\\in \\mathbb{R}^{M}$ and text embedding", + "bbox": [ + 75, + 825, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$\\psi (t)\\in \\mathbb{R}^{M}$ are semantically relevant if the text describes the video, where $M$ denotes the dimension in the common space. In the source domain, we utilize the video-text contrastive loss to guide the semantic alignment learning. Following [30, 32, 51], the contrastive loss considers matched pairs as positive and all others pairs that can be formed in a batch as negatives. For each input video-text pair $(v_{i},t_{i})$ , the video-text contrastive loss consists of two symmetric terms, one for video-to-text classification:", + "bbox": [ + 496, + 467, + 890, + 603 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} ^ {v 2 t} = - \\log \\frac {\\exp \\left(s \\left(v _ {i} , t _ {i}\\right) / \\tau\\right)}{\\sum_ {j} ^ {B} \\exp \\left(s \\left(v _ {i} , t _ {j}\\right) / \\tau\\right)}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 608, + 890, + 646 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "and the other for text-to-video classification:", + "bbox": [ + 500, + 648, + 794, + 662 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} ^ {t 2 v} = - \\log \\frac {\\exp (s (t _ {i} , v _ {i}) / \\tau)}{\\sum_ {j} ^ {B} \\exp (s (t _ {i} , v _ {j}) / \\tau)}. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 666, + 890, + 704 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$\\tau$ is the temperature parameter and $B$ is the batch size. We calculate similarity scores with the cosine similarity, which is a widely-used similarity metric and has been proved effective [10, 16]:", + "bbox": [ + 496, + 708, + 890, + 768 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\ns \\left(v _ {i}, t _ {j}\\right) = \\frac {\\varphi \\left(v _ {i}\\right) \\cdot \\psi \\left(t _ {j}\\right)}{\\| \\varphi \\left(v _ {i}\\right) \\| \\| \\psi \\left(t _ {j}\\right) \\|}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 581, + 772, + 890, + 806 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\varphi(v_{i})$ and $\\psi(t_{j})$ are the corresponding mapped features, and $\\|\\cdot\\|$ denotes the $l_{2}$ norm of vectors and the Frobenius norm of matrices. Formally, the contrastive loss for the video-text pairs is as follows:", + "bbox": [ + 496, + 810, + 890, + 869 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathcal {S}} = \\frac {1}{2} \\left(\\mathcal {L} ^ {v 2 t} + \\mathcal {L} ^ {t 2 v}\\right). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 599, + 875, + 890, + 905 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "18964", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/976ef896aa61316564b31a85631689d2c23659e144d925e7690c54c61baf4332.jpg", + "image_caption": [ + "Figure 3. Illustration of the performance decrease when training data and testing data are sampled from different distributions. Mt, Md and Tf denote the dataset MSR-VTT, MSVD and TGIF, respectively. For instance, $\\mathrm{Mt} \\rightarrow \\mathrm{Md}$ denotes training on MSR-VTT and testing on MSVD." + ], + "image_footnote": [], + "bbox": [ + 83, + 90, + 205, + 218 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/00b146e88b8acde9b038ccc463e31a2ba2a7d01923fbafde4caba206b66e23e9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 210, + 90, + 334, + 217 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/5fbf0c1592dc7ce2546fea735070df63e402bd665512cd30eb7a562da11b932f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 341, + 90, + 462, + 217 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Domain Adaptation in UDAVR", + "text_level": 1, + "bbox": [ + 76, + 325, + 349, + 343 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Different datasets usually have inconsistent data distributions and representations, thus leading to the domain shift problem. To verify this, we show the performance comparisons in Fig. 3, where training data and testing data come from different distributions. As can be seen, when both training and testing data come from MSR-VTT dataset, i.e., $\\mathrm{Mt} \\rightarrow \\mathrm{Mt}$ , the R@10 result is $34.30\\%$ . In the contrast, when training on MSVD and testing on MSR-VTT, i.e., $\\mathrm{Md} \\rightarrow \\mathrm{Mt}$ , the R@10 result decreases to $13.27\\%$ , indicating a relative $21.03\\%$ performance drop. The significant performance degeneration identifies the domain shift problem in UDAVR.", + "bbox": [ + 75, + 349, + 468, + 516 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To alleviate this, we resort to recently proposed DA method [14], which generates intermediate domain representations on-the-fly to gradually bridge the source and target domains. By utilizing the appropriate intermediate domain to bridge the source and target, the source knowledge can be better transferred to the target domain. Specifically, we denote distributions of source, target and intermediate domain as $P_{s}$ , $P_{t}$ and $P_{i}$ respectively, and use $D(\\cdot)$ to represent the Euclidean distance. Besides, we also introduce the domain factor $\\alpha$ for the source and target domains respectively. The domain factor can be seen as the relevance of the intermediate domain to the other two extreme domains. Thus, in the video stream, the distance relationship (contrary to the relevance relationship) between $P_{i}$ and other two domains, i.e., $P_{s}$ and $P_{t}$ , can be formulated as:", + "bbox": [ + 75, + 517, + 468, + 743 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {D \\left(P _ {s} ^ {v} , P _ {i} ^ {v}\\right)}{D \\left(P _ {t} ^ {v} , P _ {i} ^ {v}\\right)} = \\frac {\\alpha}{1 - \\alpha}. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 753, + 468, + 787 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Formally, the domain shift problem can be converted into minimizing the intermediate domain loss as:", + "bbox": [ + 76, + 797, + 468, + 827 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathcal {D}} ^ {\\text {v i d e o}} = \\alpha D \\left(P _ {s} ^ {v}, P _ {i} ^ {v}\\right) + (1 - \\alpha) D \\left(P _ {t} ^ {v}, P _ {i} ^ {v}\\right). \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 120, + 839, + 468, + 859 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The loss in Eq. 6 aims at guiding the distribution of appropriate intermediate domain to keep the right distance to", + "bbox": [ + 76, + 869, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/b2ee174c12326d491d47ff40d91cbd31b5ffdc84376b1761d1f5fac169349234.jpg", + "image_caption": [ + "Figure 4. Illustration of Dual Alignment Consistency (DAC). If $v_{i*}^{t}$ and $t_{j*}^{t}$ are the reciprocal nearest neighbor of each other, then they can be considered as a truly aligned pair in target domain." + ], + "image_footnote": [], + "bbox": [ + 501, + 88, + 880, + 252 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the source and target domains. Similarly, in the text stream, the intermediate domain loss can be computed as:", + "bbox": [ + 498, + 320, + 888, + 349 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathcal {D}} ^ {t e x t} = \\alpha D \\left(P _ {s} ^ {t}, P _ {i} ^ {t}\\right) + (1 - \\alpha) D \\left(P _ {t} ^ {t}, P _ {i} ^ {t}\\right). \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 550, + 363, + 890, + 381 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To sum up, the domain adaptation loss can be defined as:", + "bbox": [ + 519, + 397, + 890, + 411 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathcal {D}} = \\mathcal {L} _ {\\mathcal {D}} ^ {\\text {v i d e o}} + \\mathcal {L} _ {\\mathcal {D}} ^ {\\text {t e x t}}. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 619, + 429, + 890, + 446 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Dual Alignment Consistency", + "text_level": 1, + "bbox": [ + 500, + 470, + 754, + 486 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Despite the efficiency of the cross-modal semantic embedding and domain adaptations, we argue that the desired discriminability in target domain still can not be ensured. Note that in UDA cross-modal tasks, there exists no identical label set for source and target domains, and the only supervision available is the semantic relationship in the source dataset [4, 11, 62, 64]. Merely alleviating the domain shift will inevitably mix up target videos and texts, ignoring whether they are a relevant pair or not. This thus leads to the pairwise misalignment issue in target domain. In other words, the target videos and texts are unpaired, which means the pairwise information is not available in target domain.", + "bbox": [ + 496, + 494, + 890, + 689 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To alleviate this, we propose a simple yet effective Dual Alignment Consistency (DAC). The DAC tries to utilize the truly aligned target video-text pairs which are more likely to be semantically relevant, and to avoid including the noisy ones which tend to be irrelevant. Specifically, given the target set $\\left\\{\\mathcal{V}^t = \\{v_i^t\\}_{i=1}^{n_t}, \\mathcal{T}^t = \\{t_j^t\\}_{j=1}^{n_t}\\right\\}$ , we try to find if there exist truly positive video-text pairs. $(v_i^t, t_j^t)$ can be considered as a truly positive pair if and only if $v_i^t$ and $t_j^t$ are mutually the most similar to each other, indicating a dual aligned pair. For a target video $v_i^t$ , we calculate the similarities of $v_i^t$ and all the target texts, which can be defined as:", + "bbox": [ + 496, + 691, + 892, + 867 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {S} _ {v _ {i} ^ {t}} ^ {\\mathcal {V} \\rightarrow \\mathcal {T}} = \\left[ S _ {v _ {i} ^ {t} t _ {1} ^ {t}}, S _ {v _ {i} ^ {t} t _ {2} ^ {t}}, \\dots , S _ {v _ {i} ^ {t} t _ {j} ^ {t}}, \\dots , S _ {v _ {i} ^ {t} t _ {n t} ^ {t}} \\right]. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 540, + 881, + 890, + 904 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "18965", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/324d12e966c9bc015816b584289220727f71249db9676e1912b1ca0a50668210.jpg", + "table_caption": [ + "Table 1. Comparison of three datasets, i.e., MSR-VTT, MSVD and TGIF in the UDAVR task." + ], + "table_footnote": [], + "table_body": "
Dataset#Videos#caps.Video Len.Query Len.#Train#Val# TestSceneText Src.Video Src.Semantics
MSR-VTT10,000200k20s9.346,5134972,990OpenAMTYouTubeCategory
MSVD1,97086k10s7.031,200100670OpenAMTYouTubeMulti. Lang.
TGIF101,412120k3s8.6779,45110,65111,310Anim. GIFCrowdsourcingTumblrNone
", + "bbox": [ + 81, + 106, + 883, + 172 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Then, we nominate the selected text for target video $v_{i}^{t}$ with the maximum similarity as the candidate matching text:", + "bbox": [ + 76, + 196, + 468, + 227 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nj ^ {*} = \\arg \\max _ {j \\in \\{1, 2, \\dots , n _ {t} \\}} S _ {v _ {i} ^ {t} t _ {j} ^ {t}}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 169, + 237, + 468, + 261 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $j^{*}$ is the index of the candidate matching text $t_{j^*}^t$ . Similarly, the candidate matching text $t_{j^*}^t$ is further calculated back to video set in a similar way, and the corresponding candidate matching video $v_{i^*}^t$ can be nominated according to $\\mathbf{S}_{t_j}^{\\mathcal{T}\\to \\mathcal{V}}$ . As in Fig. 4, this dual mapping and matching operation between $\\mathcal{V}^t$ and $\\mathcal{T}^t$ determines the dual alignment consistency as:", + "bbox": [ + 76, + 268, + 468, + 378 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{ \\begin{array}{l l} \\left(v _ {i ^ {*}} ^ {t}, t _ {j ^ {*}} ^ {t}\\right) \\text {i s a n a l i g n e d p a i r ,} & \\text {i f} v _ {i ^ {*}} ^ {t} = v _ {i} ^ {t}, \\\\ \\left(v _ {i ^ {*}} ^ {t}, t _ {j ^ {*}} ^ {t}\\right) \\text {i s a m i s a l i g n e d p a i r ,} & \\text {i f} v _ {i ^ {*}} ^ {t} \\neq v _ {i} ^ {t}. \\end{array} \\right. \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 387, + 468, + 428 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The dual alignment consistency requires $v_{i*}^t$ and $t_{j*}^t$ to be the reciprocal nearest neighbor of each other, indicating a truly aligned (or positive) pair. To that end, we can obtain $n_p$ positive pairs in one batch from target dataset, denoted as $\\{(V^p, T^p) = (v_i^p, t_i^p)_{i=1}^{n_p}\\}$ , where $(v_i^p, t_i^p) = (v_{i*}^t, t_{j*}^t)$ .", + "bbox": [ + 76, + 436, + 468, + 513 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To further boost the accuracy of aligned pairs, we introduce $T$ as the threshold to sort the similarities of all pairs in one batch with descending order and choose the $T$ -th value, implying to select top $T$ similar pairs. The intuition is that a truly positive video-text pair should not only be the most similar to each other, but also have a relatively high similarity score compared with all the misaligned pairs. We also conduct some vanilla aligning mechanisms and ablations on threshold $T$ , which are reported in Sec. 4 (Tab. 3 and Fig. 5).", + "bbox": [ + 75, + 513, + 468, + 648 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "With these self-discovered matching pairs, we can treat the pairwise misalignment issue as a fully supervised problem to benefit the model training. Similar to $\\mathcal{L}_S$ in source domain, the dual alignment consistency loss can be defined as:", + "bbox": [ + 75, + 648, + 468, + 720 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\mathcal {P}} = - \\frac {1}{2} \\left(\\log \\frac {\\exp \\left(s \\left(v _ {i} ^ {p} , t _ {i} ^ {p}\\right) / \\tau\\right)}{\\sum_ {j} ^ {n _ {p}} \\exp \\left(s \\left(v _ {i} ^ {p} , t _ {j} ^ {p}\\right) / \\tau\\right)} \\right. \\tag {12} \\\\ + \\log \\frac {\\exp \\left(s \\left(t _ {i} ^ {p} , v _ {i} ^ {p}\\right) / \\tau\\right)}{\\sum_ {j} ^ {n _ {p}} \\exp \\left(s \\left(t _ {i} ^ {p} , v _ {j} ^ {p}\\right) / \\tau\\right)} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 135, + 729, + 468, + 803 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "During the training process, the positive pairs are increasing progressively and the noisy ones will potentially be aligned in the later stages (empirical results can be found in Fig. 5). To this end, more target samples are truly aligned as relevant video-text pairs, generating discriminative features in target domain.", + "bbox": [ + 75, + 810, + 468, + 898 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Overall Training", + "text_level": 1, + "bbox": [ + 500, + 196, + 666, + 214 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In a nutshell, we minimize the sum of the above losses, including the semantic embedding loss $\\mathcal{L}_S$ in source domain, the domain adaptation loss $\\mathcal{L}_{\\mathcal{D}}$ for alleviating domain shift, and the dual alignment consistency loss $\\mathcal{L}_{\\mathcal{P}}$ for aligning positive pairs in target domain. Combining these loss terms together, the overall objective function can be formulated as:", + "bbox": [ + 496, + 224, + 890, + 328 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {\\mathcal {S}} + \\lambda_ {1} \\mathcal {L} _ {\\mathcal {D}} + \\lambda_ {2} \\mathcal {L} _ {\\mathcal {P}}, \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 596, + 340, + 890, + 357 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\lambda_{1}$ and $\\lambda_{2}$ are hyper parameters for balancing these terms. The parameters of the whole network can readily be updated by the stochastic gradient descent (SGD) algorithm and the chain rules.", + "bbox": [ + 496, + 375, + 890, + 434 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 460, + 630, + 477 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental Setting", + "text_level": 1, + "bbox": [ + 500, + 488, + 697, + 505 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. In this paper, we take advantage of existing datasets across three domains to explore the UDAVR task. To be specific, we construct a comprehensive evaluation benchmark which is the combination of three widely used datasets, i.e., MSR-VTT (Mt) [61], MSVD (Md) [23] and TGIF (Tf) [34]. An overview of three datasets is given in Tab. 1. The diversities of different datasets, e.g., lengths, numbers and video scenes, contribute to the domain shift in UDAVR task.", + "bbox": [ + 496, + 515, + 890, + 650 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation Metrics. We adopt standard retrieval metrics (following [10, 25, 28]) to evaluate the performance of video-text retrieval. We measure rank-based performance by R@K (higher is better) and also report Median Rank, i.e., MR, (lower is better).", + "bbox": [ + 496, + 655, + 890, + 729 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation Details. For fair comparison, we utilize the same architecture of the video and text encoders as in GPO [5], which is the state-of-the-art baseline for videotext retrieval. Note that our method is orthogonal to the visual and textual encoder, allowing us to flexibly embrace state-of-the-art visual and textual encoders, of which the details are discussed in ablation studies. The length of shared embedding $M$ is set to 1024. Moreover, we adopt the Adam optimizer for all our experiments, set $\\lambda_1 = \\lambda_2 = 0.1$ . We set the mini-batch size to 64, and utilize a step-decayed learning rate with initialization value 0.0001.", + "bbox": [ + 496, + 734, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "18966", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/4122094afd49c384baa56c654fa73e48474cc90d7413898e81c2a83ab11ec065.jpg", + "table_caption": [ + "Table 2. Effect of ${\\mathcal{L}}_{\\mathcal{P}}$ and ${\\mathcal{L}}_{\\mathcal{D}}$ ." + ], + "table_footnote": [], + "table_body": "
MethodTf→MtTf→Md
R1↑R10↑MR↓R1↑R10↑MR↓
DADA(w/o Lp)2.9815.939710.2639.1818
DADA(w/o LD)4.1220.297511.4741.9017
DADA5.3024.545014.3448.7711
", + "bbox": [ + 83, + 104, + 460, + 189 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/fda0d60f9712b4825d66508862052b3f21ca577d57fd261577893c9c82d7018c.jpg", + "table_caption": [ + "Table 3. Comparison of different alignment mechanisms." + ], + "table_footnote": [], + "table_body": "
MethodTf→MtTf→Md
R1↑R10↑MR↓R1↑R10↑MR↓
DADA(w/ text)3.5217.2911113.1645.6713
DADA(w/ video)3.2615.6114613.0446.3113
DADA(w/o T)4.8422.476713.5344.7715
DADA5.3024.545014.3448.7711
", + "bbox": [ + 81, + 220, + 460, + 320 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Ablation Studies", + "text_level": 1, + "bbox": [ + 76, + 345, + 240, + 361 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Effect of $\\mathcal{L}_{\\mathcal{P}}$ and $\\mathcal{L}_{\\mathcal{D}}$ . To evaluate the contribution of $\\mathcal{L}_{\\mathcal{P}}$ and $\\mathcal{L}_{\\mathcal{D}}$ , we train the model by removing each component solely and present the results in Tab. 2. The results of DADA(w/o $\\mathcal{L}_{\\mathcal{D}}$ ) and DADA(w/o $\\mathcal{L}_{\\mathcal{P}}$ ) are inferior to the full DADA method, verifying the effectiveness of both components. Besides, DADA(w/o $\\mathcal{L}_{\\mathcal{P}}$ ) achieves worse performance than DADA(w/o $\\mathcal{L}_{\\mathcal{D}}$ ), further indicating that the dual alignment consistency is more important than simply alleviating the domain shift.", + "bbox": [ + 75, + 369, + 468, + 505 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Effect of Dual Alignment Consistency. To explore the effectiveness of Dual Alignment Consistency (DAC), we comprehensively investigate several alignment mechanisms and show the results in Tab. 3. Specifically, DADA (w/ text) selects the unique text with the highest similarity for each target video. Similarly, DADA (w/ video) selects the unique video with the highest similarity for each target text. DADA (w/o $T$ ) removes the threshold $T$ of DAC. The results of DADA (w/ text) and DADA (w/ video) are worse than the full DADA method, demonstrating that the dual alignment mechanism is superior to aligning from only one modality stream. Meanwhile, the result of DADA (w/o $T$ ) is also inferior, which proves that the constraint on high similarities of truly aligned pairs is effective.", + "bbox": [ + 75, + 507, + 468, + 717 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Furthermore, Fig. 5 shows the effect of threshold $T$ in dual alignment consistency within one batch during the training procedure. We can find that in Fig. 5(a), the number of dual aligned pairs (w/ $T$ ) is relatively smaller than that of w/o $T$ . This is acceptable since the threshold $T$ constrains that aligned pairs should also have relatively high similarities compared to all pairs. As in Fig. 5(b), however, the accuracy of truly aligned pairs (w/ $T$ ) is evidently higher than that of w/o $T$ , indicating that considering the threshold $T$ of DAC ensures the number of truly aligned pairs. As the training proceeds, the number of truly aligned pairs increases adaptively, which justifies the intuition that positive", + "bbox": [ + 75, + 719, + 470, + 901 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f618b1be8555bae8ecc8b2e1a9392be52da843596c22ef885796ac277dfe1997.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 509, + 90, + 686, + 205 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e88875ba0bb8ffa7584f7dfe3354d4d650e86c4eeb7133cd5c7d826cb103bb5d.jpg", + "image_caption": [ + "(b)", + "Figure 5. Analysis on threshold $T$ of dual alignment consistency. As training epochs proceeds, (a) numbers of dual aligned pairs and (b) accuracy of truly aligned pairs in one batch." + ], + "image_footnote": [], + "bbox": [ + 705, + 90, + 882, + 205 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/226a1f078836f0466420f7a306b69cecce8b4652eb296efb88130b3d09a03254.jpg", + "table_caption": [ + "Table 4. Impact of different source datasets scales. Split-1/2/3 denotes 7,945/39,726/79,451 training data in source domain, respectively. Split-1 is adopted as the baseline." + ], + "table_footnote": [], + "table_body": "
SplitsTf→MtTf→Md
R1↑R10↑MR↓R1↑R10↑MR↓
split-15.3024.545014.3448.7711
split-27.8231.383319.1054.028
split-39.0835.792420.5857.407
", + "bbox": [ + 537, + 330, + 846, + 414 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "pairs are increasing and noisy ones are diminished.", + "bbox": [ + 500, + 429, + 836, + 443 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Impact of source datasets scales. To assess the impact of source datasets scales on the UDAVR task, we randomly split the TGIF dataset into three splits: Split-1/2/3 denotes 7,945/39,726/79,451 training data in source domain, respectively. The results are shown in Tab. 4. We observe that on one hand, increasing the number of training data in source dataset brings a trend of performance gain (split-1 to split-2). This is reasonable since large-scale source dataset usually provide more knowledge when transferring to the target domain. On the other hand, when the number goes to a relatively large value (split-2 to split-3), the performance gain is mostly marginal when transferring from TGIF to MSVD. We argue that the pairwise misalignment issue in UDAVR task can not be solved by simply increasing the number of source training data. Considering the data volume of MSR-VTT and MSVD, we adopt split-1 as the baseline for TGIF dataset.", + "bbox": [ + 496, + 445, + 890, + 700 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Generalization to different video-text retrieval methods. As shown in Tab. 5, we implement several state-of-the-art video-text retrieval methods and the corresponding combinations with our DADA. Clearly, our method consistently improves the performances on target domain when combined with original baselines. Surprisingly, when combined with CLIP based methods, our DADA can still contribute to a remarkable performance gain. This verifies that the pairwise misalignment issue can't be diminished by merely adopting more powerful cross-modal retrieval methods, justifying the efficacy of our method.", + "bbox": [ + 496, + 703, + 890, + 868 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Sensitivity of Hyper-parameters. We conduct experiments under the setting of $\\mathrm{Tf}\\rightarrow \\mathrm{Mt}$ and $\\mathrm{Tf}\\rightarrow \\mathrm{Md}$ , and present", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "18967", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e26ddef27b8d8be1f38ba5906f6a0659809037be8d0ae6c9bb7966323bc83b70.jpg", + "image_caption": [ + "(a) Source Only" + ], + "image_footnote": [], + "bbox": [ + 140, + 103, + 305, + 215 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/68ab1b328bbf4f35ca1d27f5ca9c827e78a529f2a8a40d453869e242b0a14b20.jpg", + "image_caption": [ + "(b) MMD [40]", + "Figure 6. The t-SNE visualizations of (a) Source Only, (b) MMD, (c) ACP and (d) Our method. Blue/red denotes source/target domain, while circles/triangles denote videos/texts. Our method progressively generates truly aligned video-text pairs in target domain, i.e., red circles and triangles are close together if they are semantically relevant (best viewed in color)." + ], + "image_footnote": [], + "bbox": [ + 321, + 103, + 488, + 218 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/974c25b586687b929a959f1dc2fb91740ca56e29172fe78e3decbccc5490554f.jpg", + "image_caption": [ + "(c) ACP [39]" + ], + "image_footnote": [], + "bbox": [ + 504, + 103, + 671, + 218 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/84c19c36784c98e1860244db92d9e799b28cf713b1fecfded721207f3038c22a.jpg", + "image_caption": [ + "(d) Our method" + ], + "image_footnote": [], + "bbox": [ + 686, + 103, + 854, + 218 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/e6c3435853137534454c0ceec536b290bfad7b487b1a1160b146d570a3a45d88.jpg", + "table_caption": [ + "Table 5. Generalization to different video-text retrieval methods: (a) Single feature based methods (b) Multi-feature based methods and (c) CLIP based methods." + ], + "table_footnote": [], + "table_body": "
BackboneTf→MtTf→Md
R1↑R10↑MR↓R1↑R10↑MR↓
(a)HGR [10]2.2011.981549.2537.7321
HGR + DADA3.8218.759610.9739.1620
GPO [5]2.6913.631449.3937.7720
GPO + DADA5.3024.545014.3448.7711
(b)CE [37]2.9314.712210.339.218
CE + DADA5.6725.304715.2049.8711
MMT [21]4.2022.307812.4546.5318
MMT + DADA6.2327.313817.3050.3410
(c)CLIP4CLIP [44]7.2028.503519.2350.238
CLIP4CLIP + DADA8.6233.122821.3058.906
CLIP2Video [19]7.8031.503120.2351.208
CLIP2Video + DADA8.9036.502523.1063.65
", + "bbox": [ + 81, + 364, + 467, + 565 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ea2ba4db78a36c44e8731484fda6e52efd7e444c6fa2e49cf59d400bb54f3c82.jpg", + "image_caption": [ + "Figure 7. Sensitivity of hyper-parameters." + ], + "image_footnote": [], + "bbox": [ + 86, + 585, + 263, + 699 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ec4e7faa404804109d3770e63ce6686f10304810d322922481cf2f6d50c07141.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 284, + 585, + 459, + 699 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "the sensitivity of hyper-parameters $\\alpha$ and $T$ in Fig. 7. Within a wide range of $\\alpha$ in [0.1, 0.9], the performance only varies in a small range, indicating the robustness to different choices of $\\alpha$ . Similarly, when progressively increasing threshold $T$ in DAC from 16 to 1,024, our method consistently performs well and achieves the best when $T = 128$ . Thus, we set $\\alpha$ to 0.7 and $T$ to 128 under all settings.", + "bbox": [ + 75, + 746, + 468, + 852 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Feature Visualisations. We randomly choose 100 pairs in source and target domain respectively, and show the t-SNE [57] visualizations of Source Only, MMD, ACP and", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "our method in Fig. 6. As can be seen, (a) Source Only shows that blue and red features are clearly separated, indicating the video and text domain shifts. (b) MMD and (c) ACP alleviate the domain shift, whereas inevitably mix up target videos and texts, ignoring whether they are a relevant pair or not. Obviously, our method not only diminishes the domain shift, i.e., blue and red features are mixed up, but also generates aligned pairs in target domain, i.e., red circles and triangles are close together if relevant.", + "bbox": [ + 496, + 321, + 893, + 459 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Comparison with the State-of-the-arts", + "text_level": 1, + "bbox": [ + 498, + 478, + 828, + 493 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We compare our method with several state-of-the-art baselines across three categories, i.e., Source Only, DA methods and UDAVR methods. As a lower bound, we include the non-adapted Source Only results, which directly applies the model trained on the source domain to the target domain. We also implement five classification-based (i.e. typical) DA methods and modify them for the UDAVR task, including MMD [40], CORAL [53], DANN [22], IDM [14] and SCDA [33]. Moreover, we compare to three recently proposed UDAVR methods, i.e., MAN [17], CAPQ [9] and ACP [39]. For fairness, all methods adopt the same features and the backbone network as [5].", + "bbox": [ + 496, + 503, + 890, + 685 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Tab. 6 shows that: (1) As the lower bound, Source Only achieves the worst performance, which identifies the existed domain shift problem. (2) Traditional DA methods in setting (a) are ineffective for the challenging UDAVR task, which can only slightly outperform the Source Only baseline. We owe this to that there exists no identical label set in UDAVR, which is the key difference of classification tasks. (3) Our method consistently outperforms other UDAVR methods in setting (b) on all adaptation directions across the three datasets, which demonstrates the effectiveness of dual alignment consistency. Compared with the SOTA method ACP, DADA achieves $20.18\\%$ and $18.61\\%$ relative improvements on $\\mathrm{R@1}$ under the setting of Tf $\\rightarrow$ Mt and Tf $\\rightarrow$ Md respectively.", + "bbox": [ + 496, + 689, + 892, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "18968", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/10a3e1cf01ea2c45d39144a0942fdb5f921f56fcae47a4b6fbeac8d095627f2e.jpg", + "table_caption": [ + "Table 6. Comparison with different baselines. We denote Tf the TGIF, Mt the MSR-VTT and Md the MSVD dataset." + ], + "table_footnote": [], + "table_body": "
MethodTf→MtMt→TfTf→MdMd→TfMt→MdMd→Mt
R1↑R10↑MR↓R1↑R10↑MR↓R1↑R10↑MR↓R1↑R10↑MR↓R1↑R10↑MR↓R1↑R10↑MR↓
Source Only2.6913.631446.3025.43609.3937.77203.8016.9910215.0246.96122.5013.27136
(a)MMD [40]2.6813.591356.7727.11549.1136.11233.5016.2811915.3147.65122.6213.18136
CORAL [53]2.7414.071286.5626.49529.4437.87213.6517.3410815.6549.43112.6513.34138
DANN [22]2.7613.941276.8627.17489.2738.00203.7416.7210315.6748.67112.6213.17134
IDM [14]2.5913.111497.1225.35608.0535.51233.2415.7812013.9647.77122.5412.39165
SCDA [33]2.7914.221306.9226.70539.8437.11223.3017.0210815.6448.65112.5512.98138
(b)MAN [17]2.5312.981446.4225.96638.8437.06213.0616.3111915.0548.51112.4012.00174
CAPQ [9]3.4617.021107.3325.64629.3037.97213.9717.7511315.6649.08113.3515.47158
ACP [39]4.4121.72647.8326.725012.0941.38185.1221.468217.8754.3485.9025.6854
OursDADA5.3024.54508.2128.974514.3448.77116.0322.527818.9757.9376.4027.6142
", + "bbox": [ + 107, + 104, + 857, + 323 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6ea72e219c71c836f0f1c3b4414d2533f88220dc6ce51d1834b77d0ded20040f.jpg", + "image_caption": [ + "Figure 8. Qualitative results of query texts and corresponding videos along with the changes in rank A←B←C, where A denotes the rank of DADA, B the ACP method and C the Source Only." + ], + "image_footnote": [], + "bbox": [ + 187, + 338, + 795, + 599 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Qualitative Results", + "text_level": 1, + "bbox": [ + 76, + 659, + 261, + 674 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "As in Fig. 8, given a query text, we present how the rank of the relevant video changes with different methods. Obviously, our method results in higher ranks of relevant videos compared with Source Only and ACP. Interestingly, our method performs worse given the query 'A fox is diving into the snow', which might be owed to the confusion of the white fox and the background.", + "bbox": [ + 75, + 681, + 470, + 789 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 800, + 194, + 814 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we focus on the notoriously challenging task, i.e., UDA Video-text Retrieval (UDAVR), and develop the simple yet effective Dual Alignment Domain Adaptation (DADA) method. We introduce the cross-modal semantic embedding and domain adaptation to simultane", + "bbox": [ + 75, + 825, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ously generate discriminative source features and alleviate the video and text domain shifts. To tackle the pairwise alignment issue, we propose the Dual Alignment Consistency (DAC), which progressively generates truly aligned target pairs and ensures the discriminability of target features. Extensive experiments justify our superiority.", + "bbox": [ + 496, + 660, + 890, + 751 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Acknowledgement", + "text_level": 1, + "bbox": [ + 500, + 768, + 679, + 786 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported by the National Key R&D Program of China under Grant 2022YFB3103500, the National Natural Science Foundation of China under Grants 62106258, 62006242 and 62202459, and the China Postdoctoral Science Foundation under Grant 2022M713348 and 2022TQ0363, and Young Elite Scientists Sponsorship Program by BAST (NO.BYESS2023304).", + "bbox": [ + 496, + 794, + 890, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "18969", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Nakul Agarwal, Yi-Ting Chen, Behzad Dariush, and Ming-Hsuan Yang. 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IEEE Transactions on Image Processing, 30:1180-1192, 2020. 2, 4", + "bbox": [ + 501, + 90, + 893, + 147 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "18972", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Dual Alignment Unsupervised Domain Adaptation for Video-Text Retrieval/8b3047df-13e0-4f30-a21d-3acd07314d19_model.json b/2023/Dual Alignment Unsupervised Domain Adaptation for Video-Text Retrieval/8b3047df-13e0-4f30-a21d-3acd07314d19_model.json new file mode 100644 index 0000000000000000000000000000000000000000..c7ff33026e7719146211c8b84c380111992f096a --- /dev/null +++ b/2023/Dual Alignment Unsupervised Domain Adaptation for Video-Text Retrieval/8b3047df-13e0-4f30-a21d-3acd07314d19_model.json @@ -0,0 +1,2411 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.105, + 0.131, + 0.867, + 0.154 + ], + "angle": 0, + "content": "Dual Alignment Unsupervised Domain Adaptation for Video-Text Retrieval" + }, + { + "type": "text", + "bbox": [ + 0.211, + 0.18, + 0.761, + 0.199 + ], + "angle": 0, + "content": "Xiaoshuai Hao\\(^{1,2}\\), Wanqian Zhang\\(^{1*}\\), Dayan Wu\\(^{1}\\), Fei Zhu\\(^{1,2}\\), Bo Li\\(^{1,2}\\)" + }, + { + "type": "text", + "bbox": [ + 0.211, + 0.199, + 0.757, + 0.217 + ], + "angle": 0, + "content": "\\(^{1}\\)Institute of Information Engineering, Chinese Academy of Sciences" + }, + { + "type": "text", + "bbox": [ + 0.205, + 0.217, + 0.767, + 0.235 + ], + "angle": 0, + "content": "\\(^{2}\\)School of Cyber Security, University of Chinese Academy of Sciences" + }, + { + "type": "text", + "bbox": [ + 0.23, + 0.237, + 0.735, + 0.252 + ], + "angle": 0, + "content": "{haoxiaoshuai, zhangwanqian, wudayan, zhufei, libo}@ie.ac.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.287, + 0.314, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.319, + 0.474, + 0.775 + ], + "angle": 0, + "content": "Video-text retrieval is an emerging stream in both computer vision and natural language processing communities, which aims to find relevant videos given text queries. In this paper, we study the notoriously challenging task, i.e., Unsupervised Domain Adaptation Video-text Retrieval (UDAVR), wherein training and testing data come from different distributions. Previous works merely alleviate the domain shift, which however overlook the pairwise misalignment issue in target domain, i.e., there exist no semantic relationships between target videos and texts. To tackle this, we propose a novel method named Dual Alignment Domain Adaptation (DADA). Specifically, we first introduce the cross-modal semantic embedding to generate discriminative source features in a joint embedding space. Besides, we utilize the video and text domain adaptations to smoothly balance the minimization of the domain shifts. To tackle the pairwise misalignment in target domain, we propose the Dual Alignment Consistency (DAC) to fully exploit the semantic information of both modalities in target domain. The proposed DAC adaptively aligns the videotext pairs which are more likely to be relevant in target domain, enabling that positive pairs are increasing progressively and the noisy ones will potentially be aligned in the later stages. To that end, our method can generate more truly aligned target pairs and ensure the discriminability of target features. Compared with the state-of-the-art methods, DADA achieves \\(20.18\\%\\) and \\(18.61\\%\\) relative improvements on \\(R@1\\) under the setting of TGIF \\(\\rightarrow\\) MSR-VTT and TGIF \\(\\rightarrow\\) MSVD respectively, demonstrating the superiority of our method." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.804, + 0.21, + 0.82 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.83, + 0.47, + 0.876 + ], + "angle": 0, + "content": "Video-text retrieval enables users to search videos with a simple and natural language description. The de facto paradigm is to learn high-level visual-textual embeddings" + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.285, + 0.673, + 0.453 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.687, + 0.286, + 0.892, + 0.453 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.458, + 0.895, + 0.57 + ], + "angle": 0, + "content": "Figure 1. Illustration of the proposed method. Previous methods simply bring source and target features closer (blue and red ovals are overlapping each other), whereas inevitably mixing target videos (red circles) and texts (red triangles) together, ignoring whether they are semantically relevant or not. Instead, our method exploits the semantic structures in target domain to adaptively generate truly aligned video-text pairs (dotted circles) and ensure the discriminability of target data. Best viewed in color." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.595, + 0.892, + 0.67 + ], + "angle": 0, + "content": "by off-the-shelf feature extractors, and to measure semantic similarities in a joint embedding space [13, 42, 46, 63]. Despite their thrilling success, the primary assumption is that training and testing data come from the same distribution, which whereas may not hold in real scenarios." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.672, + 0.893, + 0.838 + ], + "angle": 0, + "content": "To alleviate the domain shift problem, Unsupervised Domain Adaptation (UDA) has gained a lot of attention due to its efficient training without the need of supervision in target domain. UDA transfers knowledge from a labeled source domain to an unlabeled target domain [15, 33, 40, 41, 53], which has made remarkable progress in many fields, such as image classification [33, 56], autonomous driving [54, 55], medical image processing [35, 36], and video-based action recognition [50, 52]. However, these methods are originally designed for classification tasks, which might not be suitable for the video-text retrieval." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Note that in UDA Video-text Retrieval (UDAVR), there exists no identical label set for source and target domains. The only supervision is the semantic relationship in source dataset, which is also the general setting for UDA" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.222, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "18962" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.346 + ], + "angle": 0, + "content": "cross-modal tasks [4, 11, 62, 64]. To that end, some approaches have been recently proposed [9, 17, 39], such as directly minimizing the distribution discrepancy [17], distilling knowledge from the source domain [9], or introducing pre-defined prototype assignments [39]. However, they overlook the pairwise misalignment issue in target domain, i.e., there exist no semantic relationships between target videos and texts. Merely alleviating the video and text domain shifts is a sub-optimal solution, which fails to fully explore the semantic structures of target data, i.e., whether the video-text pair is semantically relevant or not. As illustrated in Fig. 1, previous methods bring the learned source and target features close together, which whereas inevitably mixes up target videos and texts, ignoring whether they are a truly relevant pair or not. This will further induce less discriminative target features, and thus becomes the motivation of our work." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.348, + 0.473, + 0.65 + ], + "angle": 0, + "content": "In this paper, we propose a novel method named Dual Alignment Domain Adaptation (DADA) to tackle the pairwise misalignment issue in target domain. We first introduce the cross-modal semantic embedding to generate discriminative source features in a joint embedding space, where semantically relevant pairs should lie close together and vice versa. To alleviate the domain shift, we further utilize a smooth adaptation procedure to balance the minimization of distribution shifts between source and target domains. Last but not least, to tackle the pairwise misalignment in target domain, we propose a simple yet effective Dual Alignment Consistency (DAC), which fully exploits the semantic information of both modalities in target domain. The proposed DAC adaptively aligns the video-text pairs which are more likely to be relevant in target domain, enabling that (1) positive pairs are increasing progressively, (2) the noisy ones will potentially be aligned in the later stages and (3) the discriminability of target features. Extensive experiments on several benchmarks demonstrate the superiority of our method." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.65, + 0.443, + 0.665 + ], + "angle": 0, + "content": "The contributions of this paper are mainly threefold:" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.672, + 0.468, + 0.733 + ], + "angle": 0, + "content": "- To tackle the pairwise misalignment problem in UDAVR task, we develop a novel method named Dual Alignment Domain Adaptation (DADA) which fully exploits the semantic structures of target data." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.741, + 0.468, + 0.817 + ], + "angle": 0, + "content": "- The proposed Dual Alignment Consistency (DAC) mechanism adaptively aligns the most similar videos and texts in target domain, ensure that the positive pairs are increasing progressively and the noisy ones are potentially aligned in later stages." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.825, + 0.468, + 0.901 + ], + "angle": 0, + "content": "- Compared with the state-of-the-art methods, DADA achieves \\(20.18\\%\\) and \\(18.61\\%\\) relative improvements on R@1 under the setting of TGIF \\(\\rightarrow\\) MSRVTT and TGIF \\(\\rightarrow\\) MSVD respectively, demonstrating the superiority of our method." + }, + { + "type": "list", + "bbox": [ + 0.097, + 0.672, + 0.468, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.09, + 0.642, + 0.106 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.115, + 0.892, + 0.432 + ], + "angle": 0, + "content": "Video-Text Retrieval. In recent years, cross-modal embedding-based approaches [2, 10, 20, 26, 27, 37, 47, 58] have emerged as a dominant paradigm for video-text retrieval. [48] proposes the JEMC framework using action, object, text and audio features by a simple concatenation fusion strategy. CE [37] adopts video features extracted from all modalities to encode a video. T2VLAD [59] automatically learns text-and-video semantic topics and reemphasizes the importance of local semantic alignment between texts and videos. HGR [10] proposes a Hierarchical Graph Reasoning (HGR) model, which decomposes video-text pairs into global-to-local levels. GPO [5] learns to automatically adapt itself to the best pooling strategy for different baselines. Recently, the Contrastive Language-Image Pretraining (CLIP) [3] model is widely used in video-text retrieval [24, 31, 38, 45]. CLIP4Clip [43] investigates three mechanisms of similarity calculation based on the pretrained CLIP. Similarly, CLIP2video [18] focuses on the spatial semantics captured by the CLIP model. Different from them, we explore the video-text retrieval task through the lens of unsupervised domain adaptation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.433, + 0.892, + 0.674 + ], + "angle": 0, + "content": "Unsupervised Domain Adaptation. UDA transfers predictive models from a fully-labeled source domain to an unlabeled target domain. Existing classification-based UDA methods seek to alleviate the domain shift between source and target domains [15, 22, 33, 40, 41, 56, 60]. Besides, UDA methods have been extended to various video-based tasks, like video action recognition [6, 12, 49], video segmentation [7, 8] and video localisation [1]. Recently, some cross-modal tasks also resort to UDA and try to utilize the unpaired data in target domain, such as image captioning [11, 62, 64] and VQA [4]. The similar work to ours is DCKT [29] which focuses on UDA image-text retrieval and transfers knowledge from a large dataset to promote the model performance on small dataset. However, DCKT needs labeled target image-text pairs during the training procedure, which fails to work well for UDAVR task." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Unsupervised Domain Adaptation for Video-Text Retrieval. To the best of our knowledge, there are only a few explorations of the UDAVR task [9, 17, 39]. MAN [17] proposes three alignments to alleviate different gaps in UDAVR task. CAPQ [9] comprises a concept preservation regulariser to enhance the transferability of the learned embeddings. ACP [39] focuses on minimizing both uni-modal and cross-modal distribution shift across the source and target domains. Compared to these methods, our approach differs in three aspects. (1) MAN tries to directly alleviate three different gaps in a classification-based manner, which is not suitable for cross-modal retrieval task. (2) CAPQ and ACP maximize the mutual information or minimize the KL-divergence between the prototype assignments of source and target videos, which however ignores the domain shift" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18963" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.093, + 0.868, + 0.368 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.385, + 0.892, + 0.456 + ], + "angle": 0, + "content": "Figure 2. The overall framework of DADA. Video/text features are first fed into video/text encoders to generate high-level representations. The video and text domain adaptation modules simultaneously alleviate the distribution shifts across domains in both modalities (\\(\\mathcal{L}_{\\mathcal{D}}^{video}\\) and \\(\\mathcal{L}_{\\mathcal{D}}^{text}\\)). Source video and text features are expected to be discriminative by the cross-modal semantic embedding (\\(\\mathcal{L}_{\\mathcal{S}}\\)). Besides, the proposed Dual Alignment Consistency (DAC) adaptively aligns the target video-text pairs which are more likely to be relevant and progressively generates dual aligned video-text pairs \\((v_{i}^{p}, t_{i}^{p})_{i=1}^{n_{p}}\\) in target domain(\\(\\mathcal{L}_{\\mathcal{P}}\\)). Best viewed in color." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.468, + 0.47, + 0.53 + ], + "angle": 0, + "content": "in text modality. (3) The semantic relationships of videos and texts in target domain have not been fully exploited by previous methods, leading to the pairwise misalignment issue, which is the primary concern of this paper." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.543, + 0.212, + 0.56 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.568, + 0.218, + 0.582 + ], + "angle": 0, + "content": "3.1. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.592, + 0.47, + 0.825 + ], + "angle": 0, + "content": "For notational clarity, we first introduce some symbols and definitions used throughout this paper. Formally, assume that we have a set of samples in source domain \\(\\left\\{(\\mathcal{V}^s,\\mathcal{T}^s) = (v_i^s,t_i^s)_{i = 1}^{n_s}\\right\\}\\), where \\(n_{s}\\) indicates the number of video-text pairs. Similarly, we also have a set of samples in target domain \\(\\left\\{\\mathcal{V}^t = \\{v_i^t\\}_{i = 1}^{n_t},\\mathcal{T}^t = \\{t_j^t\\}_{j = 1}^{n_t}\\right\\}\\) with two collections of \\(n_t\\) videos \\(\\mathcal{V}^t\\) and texts \\(\\mathcal{T}^t\\), respectively. Note that the target videos and texts are unpaired, which means the supervised information, i.e., whether one target video-text pair is semantically relevant or not, is not available in target domain. The Unsupervised Domain Adaptation Video-text Retrieval (UDAVR) aims at improving the model's generalization performance on target domain with the utilization of source domain. The overall framework of our method is illustrated in Fig. 2." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Given one video-text pair, following the state-of-the-art baseline in video-text retrieval [5], we utilize a video encoder \\(\\varphi (\\cdot)\\) and a text encoder \\(\\psi (\\cdot)\\) to map each video sample \\(v\\) and text description \\(t\\) into a joint embedding space. The visual embedding \\(\\varphi (v)\\in \\mathbb{R}^{M}\\) and text embedding" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.468, + 0.892, + 0.604 + ], + "angle": 0, + "content": "\\(\\psi (t)\\in \\mathbb{R}^{M}\\) are semantically relevant if the text describes the video, where \\(M\\) denotes the dimension in the common space. In the source domain, we utilize the video-text contrastive loss to guide the semantic alignment learning. Following [30, 32, 51], the contrastive loss considers matched pairs as positive and all others pairs that can be formed in a batch as negatives. For each input video-text pair \\((v_{i},t_{i})\\), the video-text contrastive loss consists of two symmetric terms, one for video-to-text classification:" + }, + { + "type": "equation", + "bbox": [ + 0.568, + 0.609, + 0.892, + 0.647 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} ^ {v 2 t} = - \\log \\frac {\\exp \\left(s \\left(v _ {i} , t _ {i}\\right) / \\tau\\right)}{\\sum_ {j} ^ {B} \\exp \\left(s \\left(v _ {i} , t _ {j}\\right) / \\tau\\right)}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.65, + 0.795, + 0.664 + ], + "angle": 0, + "content": "and the other for text-to-video classification:" + }, + { + "type": "equation", + "bbox": [ + 0.568, + 0.667, + 0.892, + 0.705 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} ^ {t 2 v} = - \\log \\frac {\\exp (s (t _ {i} , v _ {i}) / \\tau)}{\\sum_ {j} ^ {B} \\exp (s (t _ {i} , v _ {j}) / \\tau)}. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.709, + 0.892, + 0.769 + ], + "angle": 0, + "content": "\\(\\tau\\) is the temperature parameter and \\(B\\) is the batch size. We calculate similarity scores with the cosine similarity, which is a widely-used similarity metric and has been proved effective [10, 16]:" + }, + { + "type": "equation", + "bbox": [ + 0.582, + 0.773, + 0.892, + 0.807 + ], + "angle": 0, + "content": "\\[\ns \\left(v _ {i}, t _ {j}\\right) = \\frac {\\varphi \\left(v _ {i}\\right) \\cdot \\psi \\left(t _ {j}\\right)}{\\| \\varphi \\left(v _ {i}\\right) \\| \\| \\psi \\left(t _ {j}\\right) \\|}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.871 + ], + "angle": 0, + "content": "where \\(\\varphi(v_{i})\\) and \\(\\psi(t_{j})\\) are the corresponding mapped features, and \\(\\|\\cdot\\|\\) denotes the \\(l_{2}\\) norm of vectors and the Frobenius norm of matrices. Formally, the contrastive loss for the video-text pairs is as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.6, + 0.876, + 0.892, + 0.906 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathcal {S}} = \\frac {1}{2} \\left(\\mathcal {L} ^ {v 2 t} + \\mathcal {L} ^ {t 2 v}\\right). \\tag {4}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18964" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.092, + 0.207, + 0.219 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.212, + 0.092, + 0.335, + 0.218 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.342, + 0.092, + 0.464, + 0.218 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.231, + 0.47, + 0.301 + ], + "angle": 0, + "content": "Figure 3. Illustration of the performance decrease when training data and testing data are sampled from different distributions. Mt, Md and Tf denote the dataset MSR-VTT, MSVD and TGIF, respectively. For instance, \\(\\mathrm{Mt} \\rightarrow \\mathrm{Md}\\) denotes training on MSR-VTT and testing on MSVD." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.327, + 0.351, + 0.344 + ], + "angle": 0, + "content": "3.2. Domain Adaptation in UDAVR" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.351, + 0.469, + 0.517 + ], + "angle": 0, + "content": "Different datasets usually have inconsistent data distributions and representations, thus leading to the domain shift problem. To verify this, we show the performance comparisons in Fig. 3, where training data and testing data come from different distributions. As can be seen, when both training and testing data come from MSR-VTT dataset, i.e., \\(\\mathrm{Mt} \\rightarrow \\mathrm{Mt}\\), the R@10 result is \\(34.30\\%\\). In the contrast, when training on MSVD and testing on MSR-VTT, i.e., \\(\\mathrm{Md} \\rightarrow \\mathrm{Mt}\\), the R@10 result decreases to \\(13.27\\%\\), indicating a relative \\(21.03\\%\\) performance drop. The significant performance degeneration identifies the domain shift problem in UDAVR." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.518, + 0.47, + 0.744 + ], + "angle": 0, + "content": "To alleviate this, we resort to recently proposed DA method [14], which generates intermediate domain representations on-the-fly to gradually bridge the source and target domains. By utilizing the appropriate intermediate domain to bridge the source and target, the source knowledge can be better transferred to the target domain. Specifically, we denote distributions of source, target and intermediate domain as \\( P_{s} \\), \\( P_{t} \\) and \\( P_{i} \\) respectively, and use \\( D(\\cdot) \\) to represent the Euclidean distance. Besides, we also introduce the domain factor \\( \\alpha \\) for the source and target domains respectively. The domain factor can be seen as the relevance of the intermediate domain to the other two extreme domains. Thus, in the video stream, the distance relationship (contrary to the relevance relationship) between \\( P_{i} \\) and other two domains, i.e., \\( P_{s} \\) and \\( P_{t} \\), can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.19, + 0.754, + 0.469, + 0.789 + ], + "angle": 0, + "content": "\\[\n\\frac {D \\left(P _ {s} ^ {v} , P _ {i} ^ {v}\\right)}{D \\left(P _ {t} ^ {v} , P _ {i} ^ {v}\\right)} = \\frac {\\alpha}{1 - \\alpha}. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.799, + 0.469, + 0.828 + ], + "angle": 0, + "content": "Formally, the domain shift problem can be converted into minimizing the intermediate domain loss as:" + }, + { + "type": "equation", + "bbox": [ + 0.121, + 0.84, + 0.469, + 0.86 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathcal {D}} ^ {\\text {v i d e o}} = \\alpha D \\left(P _ {s} ^ {v}, P _ {i} ^ {v}\\right) + (1 - \\alpha) D \\left(P _ {t} ^ {v}, P _ {i} ^ {v}\\right). \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.902 + ], + "angle": 0, + "content": "The loss in Eq. 6 aims at guiding the distribution of appropriate intermediate domain to keep the right distance to" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.089, + 0.882, + 0.253 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.262, + 0.892, + 0.304 + ], + "angle": 0, + "content": "Figure 4. Illustration of Dual Alignment Consistency (DAC). If \\( v_{i*}^{t} \\) and \\( t_{j*}^{t} \\) are the reciprocal nearest neighbor of each other, then they can be considered as a truly aligned pair in target domain." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.321, + 0.89, + 0.351 + ], + "angle": 0, + "content": "the source and target domains. Similarly, in the text stream, the intermediate domain loss can be computed as:" + }, + { + "type": "equation", + "bbox": [ + 0.551, + 0.364, + 0.892, + 0.382 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathcal {D}} ^ {t e x t} = \\alpha D \\left(P _ {s} ^ {t}, P _ {i} ^ {t}\\right) + (1 - \\alpha) D \\left(P _ {t} ^ {t}, P _ {i} ^ {t}\\right). \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.398, + 0.891, + 0.412 + ], + "angle": 0, + "content": "To sum up, the domain adaptation loss can be defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.62, + 0.43, + 0.891, + 0.448 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathcal {D}} = \\mathcal {L} _ {\\mathcal {D}} ^ {\\text {v i d e o}} + \\mathcal {L} _ {\\mathcal {D}} ^ {\\text {t e x t}}. \\tag {8}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.471, + 0.755, + 0.487 + ], + "angle": 0, + "content": "3.3. Dual Alignment Consistency" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.496, + 0.892, + 0.69 + ], + "angle": 0, + "content": "Despite the efficiency of the cross-modal semantic embedding and domain adaptations, we argue that the desired discriminability in target domain still can not be ensured. Note that in UDA cross-modal tasks, there exists no identical label set for source and target domains, and the only supervision available is the semantic relationship in the source dataset [4, 11, 62, 64]. Merely alleviating the domain shift will inevitably mix up target videos and texts, ignoring whether they are a relevant pair or not. This thus leads to the pairwise misalignment issue in target domain. In other words, the target videos and texts are unpaired, which means the pairwise information is not available in target domain." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.693, + 0.893, + 0.868 + ], + "angle": 0, + "content": "To alleviate this, we propose a simple yet effective Dual Alignment Consistency (DAC). The DAC tries to utilize the truly aligned target video-text pairs which are more likely to be semantically relevant, and to avoid including the noisy ones which tend to be irrelevant. Specifically, given the target set \\(\\left\\{\\mathcal{V}^t = \\{v_i^t\\}_{i=1}^{n_t}, \\mathcal{T}^t = \\{t_j^t\\}_{j=1}^{n_t}\\right\\}\\), we try to find if there exist truly positive video-text pairs. \\((v_i^t, t_j^t)\\) can be considered as a truly positive pair if and only if \\(v_i^t\\) and \\(t_j^t\\) are mutually the most similar to each other, indicating a dual aligned pair. For a target video \\(v_i^t\\), we calculate the similarities of \\(v_i^t\\) and all the target texts, which can be defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.541, + 0.882, + 0.891, + 0.905 + ], + "angle": 0, + "content": "\\[\n\\mathbf {S} _ {v _ {i} ^ {t}} ^ {\\mathcal {V} \\rightarrow \\mathcal {T}} = \\left[ S _ {v _ {i} ^ {t} t _ {1} ^ {t}}, S _ {v _ {i} ^ {t} t _ {2} ^ {t}}, \\dots , S _ {v _ {i} ^ {t} t _ {j} ^ {t}}, \\dots , S _ {v _ {i} ^ {t} t _ {n t} ^ {t}} \\right]. \\tag {9}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "18965" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.207, + 0.089, + 0.761, + 0.103 + ], + "angle": 0, + "content": "Table 1. Comparison of three datasets, i.e., MSR-VTT, MSVD and TGIF in the UDAVR task." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.107, + 0.885, + 0.174 + ], + "angle": 0, + "content": "
Dataset#Videos#caps.Video Len.Query Len.#Train#Val# TestSceneText Src.Video Src.Semantics
MSR-VTT10,000200k20s9.346,5134972,990OpenAMTYouTubeCategory
MSVD1,97086k10s7.031,200100670OpenAMTYouTubeMulti. Lang.
TGIF101,412120k3s8.6779,45110,65111,310Anim. GIFCrowdsourcingTumblrNone
" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.198, + 0.469, + 0.228 + ], + "angle": 0, + "content": "Then, we nominate the selected text for target video \\( v_{i}^{t} \\) with the maximum similarity as the candidate matching text:" + }, + { + "type": "equation", + "bbox": [ + 0.17, + 0.238, + 0.469, + 0.262 + ], + "angle": 0, + "content": "\\[\nj ^ {*} = \\arg \\max _ {j \\in \\{1, 2, \\dots , n _ {t} \\}} S _ {v _ {i} ^ {t} t _ {j} ^ {t}}, \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.27, + 0.469, + 0.38 + ], + "angle": 0, + "content": "where \\(j^{*}\\) is the index of the candidate matching text \\(t_{j^*}^t\\). Similarly, the candidate matching text \\(t_{j^*}^t\\) is further calculated back to video set in a similar way, and the corresponding candidate matching video \\(v_{i^*}^t\\) can be nominated according to \\(\\mathbf{S}_{t_j}^{\\mathcal{T}\\to \\mathcal{V}}\\). As in Fig. 4, this dual mapping and matching operation between \\(\\mathcal{V}^t\\) and \\(\\mathcal{T}^t\\) determines the dual alignment consistency as:" + }, + { + "type": "equation", + "bbox": [ + 0.1, + 0.388, + 0.469, + 0.429 + ], + "angle": 0, + "content": "\\[\n\\left\\{ \\begin{array}{l l} \\left(v _ {i ^ {*}} ^ {t}, t _ {j ^ {*}} ^ {t}\\right) \\text {i s a n a l i g n e d p a i r ,} & \\text {i f} v _ {i ^ {*}} ^ {t} = v _ {i} ^ {t}, \\\\ \\left(v _ {i ^ {*}} ^ {t}, t _ {j ^ {*}} ^ {t}\\right) \\text {i s a m i s a l i g n e d p a i r ,} & \\text {i f} v _ {i ^ {*}} ^ {t} \\neq v _ {i} ^ {t}. \\end{array} \\right. \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.437, + 0.469, + 0.514 + ], + "angle": 0, + "content": "The dual alignment consistency requires \\( v_{i*}^t \\) and \\( t_{j*}^t \\) to be the reciprocal nearest neighbor of each other, indicating a truly aligned (or positive) pair. To that end, we can obtain \\( n_p \\) positive pairs in one batch from target dataset, denoted as \\( \\{(V^p, T^p) = (v_i^p, t_i^p)_{i=1}^{n_p}\\} \\), where \\( (v_i^p, t_i^p) = (v_{i*}^t, t_{j*}^t) \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.514, + 0.469, + 0.649 + ], + "angle": 0, + "content": "To further boost the accuracy of aligned pairs, we introduce \\( T \\) as the threshold to sort the similarities of all pairs in one batch with descending order and choose the \\( T \\)-th value, implying to select top \\( T \\) similar pairs. The intuition is that a truly positive video-text pair should not only be the most similar to each other, but also have a relatively high similarity score compared with all the misaligned pairs. We also conduct some vanilla aligning mechanisms and ablations on threshold \\( T \\), which are reported in Sec. 4 (Tab. 3 and Fig. 5)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.649, + 0.469, + 0.722 + ], + "angle": 0, + "content": "With these self-discovered matching pairs, we can treat the pairwise misalignment issue as a fully supervised problem to benefit the model training. Similar to \\(\\mathcal{L}_S\\) in source domain, the dual alignment consistency loss can be defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.136, + 0.73, + 0.469, + 0.804 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\mathcal {P}} = - \\frac {1}{2} \\left(\\log \\frac {\\exp \\left(s \\left(v _ {i} ^ {p} , t _ {i} ^ {p}\\right) / \\tau\\right)}{\\sum_ {j} ^ {n _ {p}} \\exp \\left(s \\left(v _ {i} ^ {p} , t _ {j} ^ {p}\\right) / \\tau\\right)} \\right. \\tag {12} \\\\ + \\log \\frac {\\exp \\left(s \\left(t _ {i} ^ {p} , v _ {i} ^ {p}\\right) / \\tau\\right)}{\\sum_ {j} ^ {n _ {p}} \\exp \\left(s \\left(t _ {i} ^ {p} , v _ {j} ^ {p}\\right) / \\tau\\right)} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.469, + 0.9 + ], + "angle": 0, + "content": "During the training process, the positive pairs are increasing progressively and the noisy ones will potentially be aligned in the later stages (empirical results can be found in Fig. 5). To this end, more target samples are truly aligned as relevant video-text pairs, generating discriminative features in target domain." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.198, + 0.667, + 0.215 + ], + "angle": 0, + "content": "3.4. Overall Training" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.225, + 0.892, + 0.329 + ], + "angle": 0, + "content": "In a nutshell, we minimize the sum of the above losses, including the semantic embedding loss \\(\\mathcal{L}_S\\) in source domain, the domain adaptation loss \\(\\mathcal{L}_{\\mathcal{D}}\\) for alleviating domain shift, and the dual alignment consistency loss \\(\\mathcal{L}_{\\mathcal{P}}\\) for aligning positive pairs in target domain. Combining these loss terms together, the overall objective function can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.598, + 0.342, + 0.891, + 0.358 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {\\mathcal {S}} + \\lambda_ {1} \\mathcal {L} _ {\\mathcal {D}} + \\lambda_ {2} \\mathcal {L} _ {\\mathcal {P}}, \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.375, + 0.892, + 0.435 + ], + "angle": 0, + "content": "where \\(\\lambda_{1}\\) and \\(\\lambda_{2}\\) are hyper parameters for balancing these terms. The parameters of the whole network can readily be updated by the stochastic gradient descent (SGD) algorithm and the chain rules." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.461, + 0.632, + 0.478 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.489, + 0.699, + 0.506 + ], + "angle": 0, + "content": "4.1. Experimental Setting" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.516, + 0.892, + 0.651 + ], + "angle": 0, + "content": "Datasets. In this paper, we take advantage of existing datasets across three domains to explore the UDAVR task. To be specific, we construct a comprehensive evaluation benchmark which is the combination of three widely used datasets, i.e., MSR-VTT (Mt) [61], MSVD (Md) [23] and TGIF (Tf) [34]. An overview of three datasets is given in Tab. 1. The diversities of different datasets, e.g., lengths, numbers and video scenes, contribute to the domain shift in UDAVR task." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.656, + 0.892, + 0.731 + ], + "angle": 0, + "content": "Evaluation Metrics. We adopt standard retrieval metrics (following [10, 25, 28]) to evaluate the performance of video-text retrieval. We measure rank-based performance by R@K (higher is better) and also report Median Rank, i.e., MR, (lower is better)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Implementation Details. For fair comparison, we utilize the same architecture of the video and text encoders as in GPO [5], which is the state-of-the-art baseline for videotext retrieval. Note that our method is orthogonal to the visual and textual encoder, allowing us to flexibly embrace state-of-the-art visual and textual encoders, of which the details are discussed in ablation studies. The length of shared embedding \\( M \\) is set to 1024. Moreover, we adopt the Adam optimizer for all our experiments, set \\( \\lambda_1 = \\lambda_2 = 0.1 \\). We set the mini-batch size to 64, and utilize a step-decayed learning rate with initialization value 0.0001." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18966" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.182, + 0.09, + 0.366, + 0.103 + ], + "angle": 0, + "content": "Table 2. Effect of \\( {\\mathcal{L}}_{\\mathcal{P}} \\) and \\( {\\mathcal{L}}_{\\mathcal{D}} \\) ." + }, + { + "type": "table", + "bbox": [ + 0.084, + 0.106, + 0.462, + 0.19 + ], + "angle": 0, + "content": "
MethodTf→MtTf→Md
R1↑R10↑MR↓R1↑R10↑MR↓
DADA(w/o Lp)2.9815.939710.2639.1818
DADA(w/o LD)4.1220.297511.4741.9017
DADA5.3024.545014.3448.7711
" + }, + { + "type": "table_caption", + "bbox": [ + 0.104, + 0.206, + 0.442, + 0.219 + ], + "angle": 0, + "content": "Table 3. Comparison of different alignment mechanisms." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.222, + 0.462, + 0.321 + ], + "angle": 0, + "content": "
MethodTf→MtTf→Md
R1↑R10↑MR↓R1↑R10↑MR↓
DADA(w/ text)3.5217.2911113.1645.6713
DADA(w/ video)3.2615.6114613.0446.3113
DADA(w/o T)4.8422.476713.5344.7715
DADA5.3024.545014.3448.7711
" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.347, + 0.241, + 0.362 + ], + "angle": 0, + "content": "4.2. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.371, + 0.47, + 0.506 + ], + "angle": 0, + "content": "Effect of \\(\\mathcal{L}_{\\mathcal{P}}\\) and \\(\\mathcal{L}_{\\mathcal{D}}\\). To evaluate the contribution of \\(\\mathcal{L}_{\\mathcal{P}}\\) and \\(\\mathcal{L}_{\\mathcal{D}}\\), we train the model by removing each component solely and present the results in Tab. 2. The results of DADA(w/o \\(\\mathcal{L}_{\\mathcal{D}}\\)) and DADA(w/o \\(\\mathcal{L}_{\\mathcal{P}}\\)) are inferior to the full DADA method, verifying the effectiveness of both components. Besides, DADA(w/o \\(\\mathcal{L}_{\\mathcal{P}}\\)) achieves worse performance than DADA(w/o \\(\\mathcal{L}_{\\mathcal{D}}\\)), further indicating that the dual alignment consistency is more important than simply alleviating the domain shift." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.508, + 0.47, + 0.718 + ], + "angle": 0, + "content": "Effect of Dual Alignment Consistency. To explore the effectiveness of Dual Alignment Consistency (DAC), we comprehensively investigate several alignment mechanisms and show the results in Tab. 3. Specifically, DADA (w/ text) selects the unique text with the highest similarity for each target video. Similarly, DADA (w/ video) selects the unique video with the highest similarity for each target text. DADA (w/o \\( T \\)) removes the threshold \\( T \\) of DAC. The results of DADA (w/ text) and DADA (w/ video) are worse than the full DADA method, demonstrating that the dual alignment mechanism is superior to aligning from only one modality stream. Meanwhile, the result of DADA (w/o \\( T \\)) is also inferior, which proves that the constraint on high similarities of truly aligned pairs is effective." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Furthermore, Fig. 5 shows the effect of threshold \\( T \\) in dual alignment consistency within one batch during the training procedure. We can find that in Fig. 5(a), the number of dual aligned pairs (w/ \\( T \\)) is relatively smaller than that of w/o \\( T \\). This is acceptable since the threshold \\( T \\) constrains that aligned pairs should also have relatively high similarities compared to all pairs. As in Fig. 5(b), however, the accuracy of truly aligned pairs (w/ \\( T \\)) is evidently higher than that of w/o \\( T \\), indicating that considering the threshold \\( T \\) of DAC ensures the number of truly aligned pairs. As the training proceeds, the number of truly aligned pairs increases adaptively, which justifies the intuition that positive" + }, + { + "type": "image", + "bbox": [ + 0.511, + 0.091, + 0.687, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.589, + 0.214, + 0.609, + 0.227 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.706, + 0.091, + 0.883, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.785, + 0.213, + 0.806, + 0.226 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.228, + 0.892, + 0.271 + ], + "angle": 0, + "content": "Figure 5. Analysis on threshold \\( T \\) of dual alignment consistency. As training epochs proceeds, (a) numbers of dual aligned pairs and (b) accuracy of truly aligned pairs in one batch." + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.287, + 0.892, + 0.33 + ], + "angle": 0, + "content": "Table 4. Impact of different source datasets scales. Split-1/2/3 denotes 7,945/39,726/79,451 training data in source domain, respectively. Split-1 is adopted as the baseline." + }, + { + "type": "table", + "bbox": [ + 0.539, + 0.332, + 0.848, + 0.415 + ], + "angle": 0, + "content": "
SplitsTf→MtTf→Md
R1↑R10↑MR↓R1↑R10↑MR↓
split-15.3024.545014.3448.7711
split-27.8231.383319.1054.028
split-39.0835.792420.5857.407
" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.43, + 0.837, + 0.444 + ], + "angle": 0, + "content": "pairs are increasing and noisy ones are diminished." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.446, + 0.892, + 0.701 + ], + "angle": 0, + "content": "Impact of source datasets scales. To assess the impact of source datasets scales on the UDAVR task, we randomly split the TGIF dataset into three splits: Split-1/2/3 denotes 7,945/39,726/79,451 training data in source domain, respectively. The results are shown in Tab. 4. We observe that on one hand, increasing the number of training data in source dataset brings a trend of performance gain (split-1 to split-2). This is reasonable since large-scale source dataset usually provide more knowledge when transferring to the target domain. On the other hand, when the number goes to a relatively large value (split-2 to split-3), the performance gain is mostly marginal when transferring from TGIF to MSVD. We argue that the pairwise misalignment issue in UDAVR task can not be solved by simply increasing the number of source training data. Considering the data volume of MSR-VTT and MSVD, we adopt split-1 as the baseline for TGIF dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.892, + 0.869 + ], + "angle": 0, + "content": "Generalization to different video-text retrieval methods. As shown in Tab. 5, we implement several state-of-the-art video-text retrieval methods and the corresponding combinations with our DADA. Clearly, our method consistently improves the performances on target domain when combined with original baselines. Surprisingly, when combined with CLIP based methods, our DADA can still contribute to a remarkable performance gain. This verifies that the pairwise misalignment issue can't be diminished by merely adopting more powerful cross-modal retrieval methods, justifying the efficacy of our method." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Sensitivity of Hyper-parameters. We conduct experiments under the setting of \\(\\mathrm{Tf}\\rightarrow \\mathrm{Mt}\\) and \\(\\mathrm{Tf}\\rightarrow \\mathrm{Md}\\), and present" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18967" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.141, + 0.104, + 0.307, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.169, + 0.23, + 0.255, + 0.242 + ], + "angle": 0, + "content": "(a) Source Only" + }, + { + "type": "image", + "bbox": [ + 0.323, + 0.104, + 0.49, + 0.219 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.355, + 0.23, + 0.434, + 0.242 + ], + "angle": 0, + "content": "(b) MMD [40]" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.104, + 0.672, + 0.219 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.541, + 0.23, + 0.612, + 0.242 + ], + "angle": 0, + "content": "(c) ACP [39]" + }, + { + "type": "image", + "bbox": [ + 0.687, + 0.104, + 0.855, + 0.219 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.717, + 0.23, + 0.802, + 0.242 + ], + "angle": 0, + "content": "(d) Our method" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.255, + 0.895, + 0.296 + ], + "angle": 0, + "content": "Figure 6. The t-SNE visualizations of (a) Source Only, (b) MMD, (c) ACP and (d) Our method. Blue/red denotes source/target domain, while circles/triangles denote videos/texts. Our method progressively generates truly aligned video-text pairs in target domain, i.e., red circles and triangles are close together if they are semantically relevant (best viewed in color)." + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.321, + 0.47, + 0.362 + ], + "angle": 0, + "content": "Table 5. Generalization to different video-text retrieval methods: (a) Single feature based methods (b) Multi-feature based methods and (c) CLIP based methods." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.365, + 0.468, + 0.566 + ], + "angle": 0, + "content": "
BackboneTf→MtTf→Md
R1↑R10↑MR↓R1↑R10↑MR↓
(a)HGR [10]2.2011.981549.2537.7321
HGR + DADA3.8218.759610.9739.1620
GPO [5]2.6913.631449.3937.7720
GPO + DADA5.3024.545014.3448.7711
(b)CE [37]2.9314.712210.339.218
CE + DADA5.6725.304715.2049.8711
MMT [21]4.2022.307812.4546.5318
MMT + DADA6.2327.313817.3050.3410
(c)CLIP4CLIP [44]7.2028.503519.2350.238
CLIP4CLIP + DADA8.6233.122821.3058.906
CLIP2Video [19]7.8031.503120.2351.208
CLIP2Video + DADA8.9036.502523.1063.65
" + }, + { + "type": "image", + "bbox": [ + 0.087, + 0.586, + 0.264, + 0.7 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.285, + 0.586, + 0.46, + 0.7 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.148, + 0.707, + 0.398, + 0.721 + ], + "angle": 0, + "content": "Figure 7. Sensitivity of hyper-parameters." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.747, + 0.47, + 0.853 + ], + "angle": 0, + "content": "the sensitivity of hyper-parameters \\(\\alpha\\) and \\(T\\) in Fig. 7. Within a wide range of \\(\\alpha\\) in [0.1, 0.9], the performance only varies in a small range, indicating the robustness to different choices of \\(\\alpha\\). Similarly, when progressively increasing threshold \\(T\\) in DAC from 16 to 1,024, our method consistently performs well and achieves the best when \\(T = 128\\). Thus, we set \\(\\alpha\\) to 0.7 and \\(T\\) to 128 under all settings." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Feature Visualisations. We randomly choose 100 pairs in source and target domain respectively, and show the t-SNE [57] visualizations of Source Only, MMD, ACP and" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.323, + 0.895, + 0.46 + ], + "angle": 0, + "content": "our method in Fig. 6. As can be seen, (a) Source Only shows that blue and red features are clearly separated, indicating the video and text domain shifts. (b) MMD and (c) ACP alleviate the domain shift, whereas inevitably mix up target videos and texts, ignoring whether they are a relevant pair or not. Obviously, our method not only diminishes the domain shift, i.e., blue and red features are mixed up, but also generates aligned pairs in target domain, i.e., red circles and triangles are close together if relevant." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.479, + 0.829, + 0.494 + ], + "angle": 0, + "content": "4.3. Comparison with the State-of-the-arts" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.505, + 0.892, + 0.686 + ], + "angle": 0, + "content": "We compare our method with several state-of-the-art baselines across three categories, i.e., Source Only, DA methods and UDAVR methods. As a lower bound, we include the non-adapted Source Only results, which directly applies the model trained on the source domain to the target domain. We also implement five classification-based (i.e. typical) DA methods and modify them for the UDAVR task, including MMD [40], CORAL [53], DANN [22], IDM [14] and SCDA [33]. Moreover, we compare to three recently proposed UDAVR methods, i.e., MAN [17], CAPQ [9] and ACP [39]. For fairness, all methods adopt the same features and the backbone network as [5]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.69, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Tab. 6 shows that: (1) As the lower bound, Source Only achieves the worst performance, which identifies the existed domain shift problem. (2) Traditional DA methods in setting (a) are ineffective for the challenging UDAVR task, which can only slightly outperform the Source Only baseline. We owe this to that there exists no identical label set in UDAVR, which is the key difference of classification tasks. (3) Our method consistently outperforms other UDAVR methods in setting (b) on all adaptation directions across the three datasets, which demonstrates the effectiveness of dual alignment consistency. Compared with the SOTA method ACP, DADA achieves \\(20.18\\%\\) and \\(18.61\\%\\) relative improvements on \\(\\mathrm{R@1}\\) under the setting of Tf \\(\\rightarrow\\) Mt and Tf \\(\\rightarrow\\) Md respectively." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.956 + ], + "angle": 0, + "content": "18968" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.139, + 0.089, + 0.832, + 0.103 + ], + "angle": 0, + "content": "Table 6. Comparison with different baselines. We denote Tf the TGIF, Mt the MSR-VTT and Md the MSVD dataset." + }, + { + "type": "table", + "bbox": [ + 0.109, + 0.106, + 0.859, + 0.324 + ], + "angle": 0, + "content": "
MethodTf→MtMt→TfTf→MdMd→TfMt→MdMd→Mt
R1↑R10↑MR↓R1↑R10↑MR↓R1↑R10↑MR↓R1↑R10↑MR↓R1↑R10↑MR↓R1↑R10↑MR↓
Source Only2.6913.631446.3025.43609.3937.77203.8016.9910215.0246.96122.5013.27136
(a)MMD [40]2.6813.591356.7727.11549.1136.11233.5016.2811915.3147.65122.6213.18136
CORAL [53]2.7414.071286.5626.49529.4437.87213.6517.3410815.6549.43112.6513.34138
DANN [22]2.7613.941276.8627.17489.2738.00203.7416.7210315.6748.67112.6213.17134
IDM [14]2.5913.111497.1225.35608.0535.51233.2415.7812013.9647.77122.5412.39165
SCDA [33]2.7914.221306.9226.70539.8437.11223.3017.0210815.6448.65112.5512.98138
(b)MAN [17]2.5312.981446.4225.96638.8437.06213.0616.3111915.0548.51112.4012.00174
CAPQ [9]3.4617.021107.3325.64629.3037.97213.9717.7511315.6649.08113.3515.47158
ACP [39]4.4121.72647.8326.725012.0941.38185.1221.468217.8754.3485.9025.6854
OursDADA5.3024.54508.2128.974514.3448.77116.0322.527818.9757.9376.4027.6142
" + }, + { + "type": "image", + "bbox": [ + 0.189, + 0.339, + 0.797, + 0.601 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.618, + 0.895, + 0.648 + ], + "angle": 0, + "content": "Figure 8. Qualitative results of query texts and corresponding videos along with the changes in rank A←B←C, where A denotes the rank of DADA, B the ACP method and C the Source Only." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.66, + 0.262, + 0.675 + ], + "angle": 0, + "content": "4.4. Qualitative Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.683, + 0.471, + 0.79 + ], + "angle": 0, + "content": "As in Fig. 8, given a query text, we present how the rank of the relevant video changes with different methods. Obviously, our method results in higher ranks of relevant videos compared with Source Only and ACP. Interestingly, our method performs worse given the query 'A fox is diving into the snow', which might be owed to the confusion of the white fox and the background." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.801, + 0.196, + 0.815 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.471, + 0.903 + ], + "angle": 0, + "content": "In this paper, we focus on the notoriously challenging task, i.e., UDA Video-text Retrieval (UDAVR), and develop the simple yet effective Dual Alignment Domain Adaptation (DADA) method. We introduce the cross-modal semantic embedding and domain adaptation to simultane" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.661, + 0.892, + 0.752 + ], + "angle": 0, + "content": "ously generate discriminative source features and alleviate the video and text domain shifts. To tackle the pairwise alignment issue, we propose the Dual Alignment Consistency (DAC), which progressively generates truly aligned target pairs and ensures the discriminability of target features. Extensive experiments justify our superiority." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.769, + 0.681, + 0.787 + ], + "angle": 0, + "content": "6. Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.903 + ], + "angle": 0, + "content": "This work was supported by the National Key R&D Program of China under Grant 2022YFB3103500, the National Natural Science Foundation of China under Grants 62106258, 62006242 and 62202459, and the China Postdoctoral Science Foundation under Grant 2022M713348 and 2022TQ0363, and Young Elite Scientists Sponsorship Program by BAST (NO.BYESS2023304)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18969" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.17 + ], + "angle": 0, + "content": "[1] Nakul Agarwal, Yi-Ting Chen, Behzad Dariush, and Ming-Hsuan Yang. Unsupervised domain adaptation for spatiotemporal action localization. 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In this paper, we study the notoriously challenging task, i.e., Unsupervised Domain Adaptation Video-text Retrieval (UDAVR), wherein training and testing data come from different distributions. Previous works merely alleviate the domain shift, which however overlook the pairwise misalignment issue in target domain, i.e., there exist no semantic relationships between target videos and texts. To tackle this, we propose a novel method named Dual Alignment Domain Adaptation (DADA). Specifically, we first introduce the cross-modal semantic embedding to generate discriminative source features in a joint embedding space. Besides, we utilize the video and text domain adaptations to smoothly balance the minimization of the domain shifts. To tackle the pairwise misalignment in target domain, we propose the Dual Alignment Consistency (DAC) to fully exploit the semantic information of both modalities in target domain. The proposed DAC adaptively aligns the videotext pairs which are more likely to be relevant in target domain, enabling that positive pairs are increasing progressively and the noisy ones will potentially be aligned in the later stages. To that end, our method can generate more truly aligned target pairs and ensure the discriminability of target features. Compared with the state-of-the-art methods, DADA achieves $20.18\%$ and $18.61\%$ relative improvements on $R@1$ under the setting of TGIF $\rightarrow$ MSR-VTT and TGIF $\rightarrow$ MSVD respectively, demonstrating the superiority of our method. + +# 1. Introduction + +Video-text retrieval enables users to search videos with a simple and natural language description. The de facto paradigm is to learn high-level visual-textual embeddings + +![](images/79b3fe71cfcd097fc48f9ba1a070663a6372f9fc7e1275fa8c2a01bb21d181c2.jpg) +Figure 1. Illustration of the proposed method. Previous methods simply bring source and target features closer (blue and red ovals are overlapping each other), whereas inevitably mixing target videos (red circles) and texts (red triangles) together, ignoring whether they are semantically relevant or not. Instead, our method exploits the semantic structures in target domain to adaptively generate truly aligned video-text pairs (dotted circles) and ensure the discriminability of target data. Best viewed in color. + +![](images/0287bf1d7ba016a1ca9a5358ff98d9a6f667916ce0d2283ff6dfdd822560e09a.jpg) + +by off-the-shelf feature extractors, and to measure semantic similarities in a joint embedding space [13, 42, 46, 63]. Despite their thrilling success, the primary assumption is that training and testing data come from the same distribution, which whereas may not hold in real scenarios. + +To alleviate the domain shift problem, Unsupervised Domain Adaptation (UDA) has gained a lot of attention due to its efficient training without the need of supervision in target domain. UDA transfers knowledge from a labeled source domain to an unlabeled target domain [15, 33, 40, 41, 53], which has made remarkable progress in many fields, such as image classification [33, 56], autonomous driving [54, 55], medical image processing [35, 36], and video-based action recognition [50, 52]. However, these methods are originally designed for classification tasks, which might not be suitable for the video-text retrieval. + +Note that in UDA Video-text Retrieval (UDAVR), there exists no identical label set for source and target domains. The only supervision is the semantic relationship in source dataset, which is also the general setting for UDA + +cross-modal tasks [4, 11, 62, 64]. To that end, some approaches have been recently proposed [9, 17, 39], such as directly minimizing the distribution discrepancy [17], distilling knowledge from the source domain [9], or introducing pre-defined prototype assignments [39]. However, they overlook the pairwise misalignment issue in target domain, i.e., there exist no semantic relationships between target videos and texts. Merely alleviating the video and text domain shifts is a sub-optimal solution, which fails to fully explore the semantic structures of target data, i.e., whether the video-text pair is semantically relevant or not. As illustrated in Fig. 1, previous methods bring the learned source and target features close together, which whereas inevitably mixes up target videos and texts, ignoring whether they are a truly relevant pair or not. This will further induce less discriminative target features, and thus becomes the motivation of our work. + +In this paper, we propose a novel method named Dual Alignment Domain Adaptation (DADA) to tackle the pairwise misalignment issue in target domain. We first introduce the cross-modal semantic embedding to generate discriminative source features in a joint embedding space, where semantically relevant pairs should lie close together and vice versa. To alleviate the domain shift, we further utilize a smooth adaptation procedure to balance the minimization of distribution shifts between source and target domains. Last but not least, to tackle the pairwise misalignment in target domain, we propose a simple yet effective Dual Alignment Consistency (DAC), which fully exploits the semantic information of both modalities in target domain. The proposed DAC adaptively aligns the video-text pairs which are more likely to be relevant in target domain, enabling that (1) positive pairs are increasing progressively, (2) the noisy ones will potentially be aligned in the later stages and (3) the discriminability of target features. Extensive experiments on several benchmarks demonstrate the superiority of our method. + +The contributions of this paper are mainly threefold: + +- To tackle the pairwise misalignment problem in UDAVR task, we develop a novel method named Dual Alignment Domain Adaptation (DADA) which fully exploits the semantic structures of target data. +- The proposed Dual Alignment Consistency (DAC) mechanism adaptively aligns the most similar videos and texts in target domain, ensure that the positive pairs are increasing progressively and the noisy ones are potentially aligned in later stages. +- Compared with the state-of-the-art methods, DADA achieves $20.18\%$ and $18.61\%$ relative improvements on R@1 under the setting of TGIF $\rightarrow$ MSRVTT and TGIF $\rightarrow$ MSVD respectively, demonstrating the superiority of our method. + +# 2. Related Work + +Video-Text Retrieval. In recent years, cross-modal embedding-based approaches [2, 10, 20, 26, 27, 37, 47, 58] have emerged as a dominant paradigm for video-text retrieval. [48] proposes the JEMC framework using action, object, text and audio features by a simple concatenation fusion strategy. CE [37] adopts video features extracted from all modalities to encode a video. T2VLAD [59] automatically learns text-and-video semantic topics and reemphasizes the importance of local semantic alignment between texts and videos. HGR [10] proposes a Hierarchical Graph Reasoning (HGR) model, which decomposes video-text pairs into global-to-local levels. GPO [5] learns to automatically adapt itself to the best pooling strategy for different baselines. Recently, the Contrastive Language-Image Pretraining (CLIP) [3] model is widely used in video-text retrieval [24, 31, 38, 45]. CLIP4Clip [43] investigates three mechanisms of similarity calculation based on the pretrained CLIP. Similarly, CLIP2video [18] focuses on the spatial semantics captured by the CLIP model. Different from them, we explore the video-text retrieval task through the lens of unsupervised domain adaptation. + +Unsupervised Domain Adaptation. UDA transfers predictive models from a fully-labeled source domain to an unlabeled target domain. Existing classification-based UDA methods seek to alleviate the domain shift between source and target domains [15, 22, 33, 40, 41, 56, 60]. Besides, UDA methods have been extended to various video-based tasks, like video action recognition [6, 12, 49], video segmentation [7, 8] and video localisation [1]. Recently, some cross-modal tasks also resort to UDA and try to utilize the unpaired data in target domain, such as image captioning [11, 62, 64] and VQA [4]. The similar work to ours is DCKT [29] which focuses on UDA image-text retrieval and transfers knowledge from a large dataset to promote the model performance on small dataset. However, DCKT needs labeled target image-text pairs during the training procedure, which fails to work well for UDAVR task. + +Unsupervised Domain Adaptation for Video-Text Retrieval. To the best of our knowledge, there are only a few explorations of the UDAVR task [9, 17, 39]. MAN [17] proposes three alignments to alleviate different gaps in UDAVR task. CAPQ [9] comprises a concept preservation regulariser to enhance the transferability of the learned embeddings. ACP [39] focuses on minimizing both uni-modal and cross-modal distribution shift across the source and target domains. Compared to these methods, our approach differs in three aspects. (1) MAN tries to directly alleviate three different gaps in a classification-based manner, which is not suitable for cross-modal retrieval task. (2) CAPQ and ACP maximize the mutual information or minimize the KL-divergence between the prototype assignments of source and target videos, which however ignores the domain shift + +![](images/a47805a002ce6ec0e783d86a017d88284003bc20cb05c08c11f897b27fb3e9ab.jpg) +Figure 2. The overall framework of DADA. Video/text features are first fed into video/text encoders to generate high-level representations. The video and text domain adaptation modules simultaneously alleviate the distribution shifts across domains in both modalities ( $\mathcal{L}_{\mathcal{D}}^{video}$ and $\mathcal{L}_{\mathcal{D}}^{text}$ ). Source video and text features are expected to be discriminative by the cross-modal semantic embedding ( $\mathcal{L}_{\mathcal{S}}$ ). Besides, the proposed Dual Alignment Consistency (DAC) adaptively aligns the target video-text pairs which are more likely to be relevant and progressively generates dual aligned video-text pairs $(v_{i}^{p}, t_{i}^{p})_{i=1}^{n_{p}}$ in target domain( $\mathcal{L}_{\mathcal{P}}$ ). Best viewed in color. + +in text modality. (3) The semantic relationships of videos and texts in target domain have not been fully exploited by previous methods, leading to the pairwise misalignment issue, which is the primary concern of this paper. + +# 3. Methodology + +# 3.1. Preliminaries + +For notational clarity, we first introduce some symbols and definitions used throughout this paper. Formally, assume that we have a set of samples in source domain $\left\{(\mathcal{V}^s,\mathcal{T}^s) = (v_i^s,t_i^s)_{i = 1}^{n_s}\right\}$ , where $n_{s}$ indicates the number of video-text pairs. Similarly, we also have a set of samples in target domain $\left\{\mathcal{V}^t = \{v_i^t\}_{i = 1}^{n_t},\mathcal{T}^t = \{t_j^t\}_{j = 1}^{n_t}\right\}$ with two collections of $n_t$ videos $\mathcal{V}^t$ and texts $\mathcal{T}^t$ , respectively. Note that the target videos and texts are unpaired, which means the supervised information, i.e., whether one target video-text pair is semantically relevant or not, is not available in target domain. The Unsupervised Domain Adaptation Video-text Retrieval (UDAVR) aims at improving the model's generalization performance on target domain with the utilization of source domain. The overall framework of our method is illustrated in Fig. 2. + +Given one video-text pair, following the state-of-the-art baseline in video-text retrieval [5], we utilize a video encoder $\varphi (\cdot)$ and a text encoder $\psi (\cdot)$ to map each video sample $v$ and text description $t$ into a joint embedding space. The visual embedding $\varphi (v)\in \mathbb{R}^{M}$ and text embedding + +$\psi (t)\in \mathbb{R}^{M}$ are semantically relevant if the text describes the video, where $M$ denotes the dimension in the common space. In the source domain, we utilize the video-text contrastive loss to guide the semantic alignment learning. Following [30, 32, 51], the contrastive loss considers matched pairs as positive and all others pairs that can be formed in a batch as negatives. For each input video-text pair $(v_{i},t_{i})$ , the video-text contrastive loss consists of two symmetric terms, one for video-to-text classification: + +$$ +\mathcal {L} ^ {v 2 t} = - \log \frac {\exp \left(s \left(v _ {i} , t _ {i}\right) / \tau\right)}{\sum_ {j} ^ {B} \exp \left(s \left(v _ {i} , t _ {j}\right) / \tau\right)}, \tag {1} +$$ + +and the other for text-to-video classification: + +$$ +\mathcal {L} ^ {t 2 v} = - \log \frac {\exp (s (t _ {i} , v _ {i}) / \tau)}{\sum_ {j} ^ {B} \exp (s (t _ {i} , v _ {j}) / \tau)}. \tag {2} +$$ + +$\tau$ is the temperature parameter and $B$ is the batch size. We calculate similarity scores with the cosine similarity, which is a widely-used similarity metric and has been proved effective [10, 16]: + +$$ +s \left(v _ {i}, t _ {j}\right) = \frac {\varphi \left(v _ {i}\right) \cdot \psi \left(t _ {j}\right)}{\| \varphi \left(v _ {i}\right) \| \| \psi \left(t _ {j}\right) \|}, \tag {3} +$$ + +where $\varphi(v_{i})$ and $\psi(t_{j})$ are the corresponding mapped features, and $\|\cdot\|$ denotes the $l_{2}$ norm of vectors and the Frobenius norm of matrices. Formally, the contrastive loss for the video-text pairs is as follows: + +$$ +\mathcal {L} _ {\mathcal {S}} = \frac {1}{2} \left(\mathcal {L} ^ {v 2 t} + \mathcal {L} ^ {t 2 v}\right). \tag {4} +$$ + +![](images/976ef896aa61316564b31a85631689d2c23659e144d925e7690c54c61baf4332.jpg) +Figure 3. Illustration of the performance decrease when training data and testing data are sampled from different distributions. Mt, Md and Tf denote the dataset MSR-VTT, MSVD and TGIF, respectively. For instance, $\mathrm{Mt} \rightarrow \mathrm{Md}$ denotes training on MSR-VTT and testing on MSVD. + +![](images/00b146e88b8acde9b038ccc463e31a2ba2a7d01923fbafde4caba206b66e23e9.jpg) + +![](images/5fbf0c1592dc7ce2546fea735070df63e402bd665512cd30eb7a562da11b932f.jpg) + +# 3.2. Domain Adaptation in UDAVR + +Different datasets usually have inconsistent data distributions and representations, thus leading to the domain shift problem. To verify this, we show the performance comparisons in Fig. 3, where training data and testing data come from different distributions. As can be seen, when both training and testing data come from MSR-VTT dataset, i.e., $\mathrm{Mt} \rightarrow \mathrm{Mt}$ , the R@10 result is $34.30\%$ . In the contrast, when training on MSVD and testing on MSR-VTT, i.e., $\mathrm{Md} \rightarrow \mathrm{Mt}$ , the R@10 result decreases to $13.27\%$ , indicating a relative $21.03\%$ performance drop. The significant performance degeneration identifies the domain shift problem in UDAVR. + +To alleviate this, we resort to recently proposed DA method [14], which generates intermediate domain representations on-the-fly to gradually bridge the source and target domains. By utilizing the appropriate intermediate domain to bridge the source and target, the source knowledge can be better transferred to the target domain. Specifically, we denote distributions of source, target and intermediate domain as $P_{s}$ , $P_{t}$ and $P_{i}$ respectively, and use $D(\cdot)$ to represent the Euclidean distance. Besides, we also introduce the domain factor $\alpha$ for the source and target domains respectively. The domain factor can be seen as the relevance of the intermediate domain to the other two extreme domains. Thus, in the video stream, the distance relationship (contrary to the relevance relationship) between $P_{i}$ and other two domains, i.e., $P_{s}$ and $P_{t}$ , can be formulated as: + +$$ +\frac {D \left(P _ {s} ^ {v} , P _ {i} ^ {v}\right)}{D \left(P _ {t} ^ {v} , P _ {i} ^ {v}\right)} = \frac {\alpha}{1 - \alpha}. \tag {5} +$$ + +Formally, the domain shift problem can be converted into minimizing the intermediate domain loss as: + +$$ +\mathcal {L} _ {\mathcal {D}} ^ {\text {v i d e o}} = \alpha D \left(P _ {s} ^ {v}, P _ {i} ^ {v}\right) + (1 - \alpha) D \left(P _ {t} ^ {v}, P _ {i} ^ {v}\right). \tag {6} +$$ + +The loss in Eq. 6 aims at guiding the distribution of appropriate intermediate domain to keep the right distance to + +![](images/b2ee174c12326d491d47ff40d91cbd31b5ffdc84376b1761d1f5fac169349234.jpg) +Figure 4. Illustration of Dual Alignment Consistency (DAC). If $v_{i*}^{t}$ and $t_{j*}^{t}$ are the reciprocal nearest neighbor of each other, then they can be considered as a truly aligned pair in target domain. + +the source and target domains. Similarly, in the text stream, the intermediate domain loss can be computed as: + +$$ +\mathcal {L} _ {\mathcal {D}} ^ {t e x t} = \alpha D \left(P _ {s} ^ {t}, P _ {i} ^ {t}\right) + (1 - \alpha) D \left(P _ {t} ^ {t}, P _ {i} ^ {t}\right). \tag {7} +$$ + +To sum up, the domain adaptation loss can be defined as: + +$$ +\mathcal {L} _ {\mathcal {D}} = \mathcal {L} _ {\mathcal {D}} ^ {\text {v i d e o}} + \mathcal {L} _ {\mathcal {D}} ^ {\text {t e x t}}. \tag {8} +$$ + +# 3.3. Dual Alignment Consistency + +Despite the efficiency of the cross-modal semantic embedding and domain adaptations, we argue that the desired discriminability in target domain still can not be ensured. Note that in UDA cross-modal tasks, there exists no identical label set for source and target domains, and the only supervision available is the semantic relationship in the source dataset [4, 11, 62, 64]. Merely alleviating the domain shift will inevitably mix up target videos and texts, ignoring whether they are a relevant pair or not. This thus leads to the pairwise misalignment issue in target domain. In other words, the target videos and texts are unpaired, which means the pairwise information is not available in target domain. + +To alleviate this, we propose a simple yet effective Dual Alignment Consistency (DAC). The DAC tries to utilize the truly aligned target video-text pairs which are more likely to be semantically relevant, and to avoid including the noisy ones which tend to be irrelevant. Specifically, given the target set $\left\{\mathcal{V}^t = \{v_i^t\}_{i=1}^{n_t}, \mathcal{T}^t = \{t_j^t\}_{j=1}^{n_t}\right\}$ , we try to find if there exist truly positive video-text pairs. $(v_i^t, t_j^t)$ can be considered as a truly positive pair if and only if $v_i^t$ and $t_j^t$ are mutually the most similar to each other, indicating a dual aligned pair. For a target video $v_i^t$ , we calculate the similarities of $v_i^t$ and all the target texts, which can be defined as: + +$$ +\mathbf {S} _ {v _ {i} ^ {t}} ^ {\mathcal {V} \rightarrow \mathcal {T}} = \left[ S _ {v _ {i} ^ {t} t _ {1} ^ {t}}, S _ {v _ {i} ^ {t} t _ {2} ^ {t}}, \dots , S _ {v _ {i} ^ {t} t _ {j} ^ {t}}, \dots , S _ {v _ {i} ^ {t} t _ {n t} ^ {t}} \right]. \tag {9} +$$ + +Table 1. Comparison of three datasets, i.e., MSR-VTT, MSVD and TGIF in the UDAVR task. + +
Dataset#Videos#caps.Video Len.Query Len.#Train#Val# TestSceneText Src.Video Src.Semantics
MSR-VTT10,000200k20s9.346,5134972,990OpenAMTYouTubeCategory
MSVD1,97086k10s7.031,200100670OpenAMTYouTubeMulti. Lang.
TGIF101,412120k3s8.6779,45110,65111,310Anim. GIFCrowdsourcingTumblrNone
+ +Then, we nominate the selected text for target video $v_{i}^{t}$ with the maximum similarity as the candidate matching text: + +$$ +j ^ {*} = \arg \max _ {j \in \{1, 2, \dots , n _ {t} \}} S _ {v _ {i} ^ {t} t _ {j} ^ {t}}, \tag {10} +$$ + +where $j^{*}$ is the index of the candidate matching text $t_{j^*}^t$ . Similarly, the candidate matching text $t_{j^*}^t$ is further calculated back to video set in a similar way, and the corresponding candidate matching video $v_{i^*}^t$ can be nominated according to $\mathbf{S}_{t_j}^{\mathcal{T}\to \mathcal{V}}$ . As in Fig. 4, this dual mapping and matching operation between $\mathcal{V}^t$ and $\mathcal{T}^t$ determines the dual alignment consistency as: + +$$ +\left\{ \begin{array}{l l} \left(v _ {i ^ {*}} ^ {t}, t _ {j ^ {*}} ^ {t}\right) \text {i s a n a l i g n e d p a i r ,} & \text {i f} v _ {i ^ {*}} ^ {t} = v _ {i} ^ {t}, \\ \left(v _ {i ^ {*}} ^ {t}, t _ {j ^ {*}} ^ {t}\right) \text {i s a m i s a l i g n e d p a i r ,} & \text {i f} v _ {i ^ {*}} ^ {t} \neq v _ {i} ^ {t}. \end{array} \right. \tag {11} +$$ + +The dual alignment consistency requires $v_{i*}^t$ and $t_{j*}^t$ to be the reciprocal nearest neighbor of each other, indicating a truly aligned (or positive) pair. To that end, we can obtain $n_p$ positive pairs in one batch from target dataset, denoted as $\{(V^p, T^p) = (v_i^p, t_i^p)_{i=1}^{n_p}\}$ , where $(v_i^p, t_i^p) = (v_{i*}^t, t_{j*}^t)$ . + +To further boost the accuracy of aligned pairs, we introduce $T$ as the threshold to sort the similarities of all pairs in one batch with descending order and choose the $T$ -th value, implying to select top $T$ similar pairs. The intuition is that a truly positive video-text pair should not only be the most similar to each other, but also have a relatively high similarity score compared with all the misaligned pairs. We also conduct some vanilla aligning mechanisms and ablations on threshold $T$ , which are reported in Sec. 4 (Tab. 3 and Fig. 5). + +With these self-discovered matching pairs, we can treat the pairwise misalignment issue as a fully supervised problem to benefit the model training. Similar to $\mathcal{L}_S$ in source domain, the dual alignment consistency loss can be defined as: + +$$ +\begin{array}{l} \mathcal {L} _ {\mathcal {P}} = - \frac {1}{2} \left(\log \frac {\exp \left(s \left(v _ {i} ^ {p} , t _ {i} ^ {p}\right) / \tau\right)}{\sum_ {j} ^ {n _ {p}} \exp \left(s \left(v _ {i} ^ {p} , t _ {j} ^ {p}\right) / \tau\right)} \right. \tag {12} \\ + \log \frac {\exp \left(s \left(t _ {i} ^ {p} , v _ {i} ^ {p}\right) / \tau\right)}{\sum_ {j} ^ {n _ {p}} \exp \left(s \left(t _ {i} ^ {p} , v _ {j} ^ {p}\right) / \tau\right)} \\ \end{array} +$$ + +During the training process, the positive pairs are increasing progressively and the noisy ones will potentially be aligned in the later stages (empirical results can be found in Fig. 5). To this end, more target samples are truly aligned as relevant video-text pairs, generating discriminative features in target domain. + +# 3.4. Overall Training + +In a nutshell, we minimize the sum of the above losses, including the semantic embedding loss $\mathcal{L}_S$ in source domain, the domain adaptation loss $\mathcal{L}_{\mathcal{D}}$ for alleviating domain shift, and the dual alignment consistency loss $\mathcal{L}_{\mathcal{P}}$ for aligning positive pairs in target domain. Combining these loss terms together, the overall objective function can be formulated as: + +$$ +\mathcal {L} = \mathcal {L} _ {\mathcal {S}} + \lambda_ {1} \mathcal {L} _ {\mathcal {D}} + \lambda_ {2} \mathcal {L} _ {\mathcal {P}}, \tag {13} +$$ + +where $\lambda_{1}$ and $\lambda_{2}$ are hyper parameters for balancing these terms. The parameters of the whole network can readily be updated by the stochastic gradient descent (SGD) algorithm and the chain rules. + +# 4. Experiments + +# 4.1. Experimental Setting + +Datasets. In this paper, we take advantage of existing datasets across three domains to explore the UDAVR task. To be specific, we construct a comprehensive evaluation benchmark which is the combination of three widely used datasets, i.e., MSR-VTT (Mt) [61], MSVD (Md) [23] and TGIF (Tf) [34]. An overview of three datasets is given in Tab. 1. The diversities of different datasets, e.g., lengths, numbers and video scenes, contribute to the domain shift in UDAVR task. + +Evaluation Metrics. We adopt standard retrieval metrics (following [10, 25, 28]) to evaluate the performance of video-text retrieval. We measure rank-based performance by R@K (higher is better) and also report Median Rank, i.e., MR, (lower is better). + +Implementation Details. For fair comparison, we utilize the same architecture of the video and text encoders as in GPO [5], which is the state-of-the-art baseline for videotext retrieval. Note that our method is orthogonal to the visual and textual encoder, allowing us to flexibly embrace state-of-the-art visual and textual encoders, of which the details are discussed in ablation studies. The length of shared embedding $M$ is set to 1024. Moreover, we adopt the Adam optimizer for all our experiments, set $\lambda_1 = \lambda_2 = 0.1$ . We set the mini-batch size to 64, and utilize a step-decayed learning rate with initialization value 0.0001. + +Table 2. Effect of ${\mathcal{L}}_{\mathcal{P}}$ and ${\mathcal{L}}_{\mathcal{D}}$ . + +
MethodTf→MtTf→Md
R1↑R10↑MR↓R1↑R10↑MR↓
DADA(w/o Lp)2.9815.939710.2639.1818
DADA(w/o LD)4.1220.297511.4741.9017
DADA5.3024.545014.3448.7711
+ +Table 3. Comparison of different alignment mechanisms. + +
MethodTf→MtTf→Md
R1↑R10↑MR↓R1↑R10↑MR↓
DADA(w/ text)3.5217.2911113.1645.6713
DADA(w/ video)3.2615.6114613.0446.3113
DADA(w/o T)4.8422.476713.5344.7715
DADA5.3024.545014.3448.7711
+ +# 4.2. Ablation Studies + +Effect of $\mathcal{L}_{\mathcal{P}}$ and $\mathcal{L}_{\mathcal{D}}$ . To evaluate the contribution of $\mathcal{L}_{\mathcal{P}}$ and $\mathcal{L}_{\mathcal{D}}$ , we train the model by removing each component solely and present the results in Tab. 2. The results of DADA(w/o $\mathcal{L}_{\mathcal{D}}$ ) and DADA(w/o $\mathcal{L}_{\mathcal{P}}$ ) are inferior to the full DADA method, verifying the effectiveness of both components. Besides, DADA(w/o $\mathcal{L}_{\mathcal{P}}$ ) achieves worse performance than DADA(w/o $\mathcal{L}_{\mathcal{D}}$ ), further indicating that the dual alignment consistency is more important than simply alleviating the domain shift. + +Effect of Dual Alignment Consistency. To explore the effectiveness of Dual Alignment Consistency (DAC), we comprehensively investigate several alignment mechanisms and show the results in Tab. 3. Specifically, DADA (w/ text) selects the unique text with the highest similarity for each target video. Similarly, DADA (w/ video) selects the unique video with the highest similarity for each target text. DADA (w/o $T$ ) removes the threshold $T$ of DAC. The results of DADA (w/ text) and DADA (w/ video) are worse than the full DADA method, demonstrating that the dual alignment mechanism is superior to aligning from only one modality stream. Meanwhile, the result of DADA (w/o $T$ ) is also inferior, which proves that the constraint on high similarities of truly aligned pairs is effective. + +Furthermore, Fig. 5 shows the effect of threshold $T$ in dual alignment consistency within one batch during the training procedure. We can find that in Fig. 5(a), the number of dual aligned pairs (w/ $T$ ) is relatively smaller than that of w/o $T$ . This is acceptable since the threshold $T$ constrains that aligned pairs should also have relatively high similarities compared to all pairs. As in Fig. 5(b), however, the accuracy of truly aligned pairs (w/ $T$ ) is evidently higher than that of w/o $T$ , indicating that considering the threshold $T$ of DAC ensures the number of truly aligned pairs. As the training proceeds, the number of truly aligned pairs increases adaptively, which justifies the intuition that positive + +![](images/f618b1be8555bae8ecc8b2e1a9392be52da843596c22ef885796ac277dfe1997.jpg) +(a) + +![](images/e88875ba0bb8ffa7584f7dfe3354d4d650e86c4eeb7133cd5c7d826cb103bb5d.jpg) +(b) +Figure 5. Analysis on threshold $T$ of dual alignment consistency. As training epochs proceeds, (a) numbers of dual aligned pairs and (b) accuracy of truly aligned pairs in one batch. + +Table 4. Impact of different source datasets scales. Split-1/2/3 denotes 7,945/39,726/79,451 training data in source domain, respectively. Split-1 is adopted as the baseline. + +
SplitsTf→MtTf→Md
R1↑R10↑MR↓R1↑R10↑MR↓
split-15.3024.545014.3448.7711
split-27.8231.383319.1054.028
split-39.0835.792420.5857.407
+ +pairs are increasing and noisy ones are diminished. + +Impact of source datasets scales. To assess the impact of source datasets scales on the UDAVR task, we randomly split the TGIF dataset into three splits: Split-1/2/3 denotes 7,945/39,726/79,451 training data in source domain, respectively. The results are shown in Tab. 4. We observe that on one hand, increasing the number of training data in source dataset brings a trend of performance gain (split-1 to split-2). This is reasonable since large-scale source dataset usually provide more knowledge when transferring to the target domain. On the other hand, when the number goes to a relatively large value (split-2 to split-3), the performance gain is mostly marginal when transferring from TGIF to MSVD. We argue that the pairwise misalignment issue in UDAVR task can not be solved by simply increasing the number of source training data. Considering the data volume of MSR-VTT and MSVD, we adopt split-1 as the baseline for TGIF dataset. + +Generalization to different video-text retrieval methods. As shown in Tab. 5, we implement several state-of-the-art video-text retrieval methods and the corresponding combinations with our DADA. Clearly, our method consistently improves the performances on target domain when combined with original baselines. Surprisingly, when combined with CLIP based methods, our DADA can still contribute to a remarkable performance gain. This verifies that the pairwise misalignment issue can't be diminished by merely adopting more powerful cross-modal retrieval methods, justifying the efficacy of our method. + +Sensitivity of Hyper-parameters. We conduct experiments under the setting of $\mathrm{Tf}\rightarrow \mathrm{Mt}$ and $\mathrm{Tf}\rightarrow \mathrm{Md}$ , and present + +![](images/e26ddef27b8d8be1f38ba5906f6a0659809037be8d0ae6c9bb7966323bc83b70.jpg) +(a) Source Only + +![](images/68ab1b328bbf4f35ca1d27f5ca9c827e78a529f2a8a40d453869e242b0a14b20.jpg) +(b) MMD [40] +Figure 6. The t-SNE visualizations of (a) Source Only, (b) MMD, (c) ACP and (d) Our method. Blue/red denotes source/target domain, while circles/triangles denote videos/texts. Our method progressively generates truly aligned video-text pairs in target domain, i.e., red circles and triangles are close together if they are semantically relevant (best viewed in color). + +![](images/974c25b586687b929a959f1dc2fb91740ca56e29172fe78e3decbccc5490554f.jpg) +(c) ACP [39] + +![](images/84c19c36784c98e1860244db92d9e799b28cf713b1fecfded721207f3038c22a.jpg) +(d) Our method + +Table 5. Generalization to different video-text retrieval methods: (a) Single feature based methods (b) Multi-feature based methods and (c) CLIP based methods. + +
BackboneTf→MtTf→Md
R1↑R10↑MR↓R1↑R10↑MR↓
(a)HGR [10]2.2011.981549.2537.7321
HGR + DADA3.8218.759610.9739.1620
GPO [5]2.6913.631449.3937.7720
GPO + DADA5.3024.545014.3448.7711
(b)CE [37]2.9314.712210.339.218
CE + DADA5.6725.304715.2049.8711
MMT [21]4.2022.307812.4546.5318
MMT + DADA6.2327.313817.3050.3410
(c)CLIP4CLIP [44]7.2028.503519.2350.238
CLIP4CLIP + DADA8.6233.122821.3058.906
CLIP2Video [19]7.8031.503120.2351.208
CLIP2Video + DADA8.9036.502523.1063.65
+ +![](images/ea2ba4db78a36c44e8731484fda6e52efd7e444c6fa2e49cf59d400bb54f3c82.jpg) +Figure 7. Sensitivity of hyper-parameters. + +![](images/ec4e7faa404804109d3770e63ce6686f10304810d322922481cf2f6d50c07141.jpg) + +the sensitivity of hyper-parameters $\alpha$ and $T$ in Fig. 7. Within a wide range of $\alpha$ in [0.1, 0.9], the performance only varies in a small range, indicating the robustness to different choices of $\alpha$ . Similarly, when progressively increasing threshold $T$ in DAC from 16 to 1,024, our method consistently performs well and achieves the best when $T = 128$ . Thus, we set $\alpha$ to 0.7 and $T$ to 128 under all settings. + +Feature Visualisations. We randomly choose 100 pairs in source and target domain respectively, and show the t-SNE [57] visualizations of Source Only, MMD, ACP and + +our method in Fig. 6. As can be seen, (a) Source Only shows that blue and red features are clearly separated, indicating the video and text domain shifts. (b) MMD and (c) ACP alleviate the domain shift, whereas inevitably mix up target videos and texts, ignoring whether they are a relevant pair or not. Obviously, our method not only diminishes the domain shift, i.e., blue and red features are mixed up, but also generates aligned pairs in target domain, i.e., red circles and triangles are close together if relevant. + +# 4.3. Comparison with the State-of-the-arts + +We compare our method with several state-of-the-art baselines across three categories, i.e., Source Only, DA methods and UDAVR methods. As a lower bound, we include the non-adapted Source Only results, which directly applies the model trained on the source domain to the target domain. We also implement five classification-based (i.e. typical) DA methods and modify them for the UDAVR task, including MMD [40], CORAL [53], DANN [22], IDM [14] and SCDA [33]. Moreover, we compare to three recently proposed UDAVR methods, i.e., MAN [17], CAPQ [9] and ACP [39]. For fairness, all methods adopt the same features and the backbone network as [5]. + +Tab. 6 shows that: (1) As the lower bound, Source Only achieves the worst performance, which identifies the existed domain shift problem. (2) Traditional DA methods in setting (a) are ineffective for the challenging UDAVR task, which can only slightly outperform the Source Only baseline. We owe this to that there exists no identical label set in UDAVR, which is the key difference of classification tasks. (3) Our method consistently outperforms other UDAVR methods in setting (b) on all adaptation directions across the three datasets, which demonstrates the effectiveness of dual alignment consistency. Compared with the SOTA method ACP, DADA achieves $20.18\%$ and $18.61\%$ relative improvements on $\mathrm{R@1}$ under the setting of Tf $\rightarrow$ Mt and Tf $\rightarrow$ Md respectively. + +Table 6. Comparison with different baselines. We denote Tf the TGIF, Mt the MSR-VTT and Md the MSVD dataset. + +
MethodTf→MtMt→TfTf→MdMd→TfMt→MdMd→Mt
R1↑R10↑MR↓R1↑R10↑MR↓R1↑R10↑MR↓R1↑R10↑MR↓R1↑R10↑MR↓R1↑R10↑MR↓
Source Only2.6913.631446.3025.43609.3937.77203.8016.9910215.0246.96122.5013.27136
(a)MMD [40]2.6813.591356.7727.11549.1136.11233.5016.2811915.3147.65122.6213.18136
CORAL [53]2.7414.071286.5626.49529.4437.87213.6517.3410815.6549.43112.6513.34138
DANN [22]2.7613.941276.8627.17489.2738.00203.7416.7210315.6748.67112.6213.17134
IDM [14]2.5913.111497.1225.35608.0535.51233.2415.7812013.9647.77122.5412.39165
SCDA [33]2.7914.221306.9226.70539.8437.11223.3017.0210815.6448.65112.5512.98138
(b)MAN [17]2.5312.981446.4225.96638.8437.06213.0616.3111915.0548.51112.4012.00174
CAPQ [9]3.4617.021107.3325.64629.3037.97213.9717.7511315.6649.08113.3515.47158
ACP [39]4.4121.72647.8326.725012.0941.38185.1221.468217.8754.3485.9025.6854
OursDADA5.3024.54508.2128.974514.3448.77116.0322.527818.9757.9376.4027.6142
+ +![](images/6ea72e219c71c836f0f1c3b4414d2533f88220dc6ce51d1834b77d0ded20040f.jpg) +Figure 8. Qualitative results of query texts and corresponding videos along with the changes in rank A←B←C, where A denotes the rank of DADA, B the ACP method and C the Source Only. + +# 4.4. Qualitative Results + +As in Fig. 8, given a query text, we present how the rank of the relevant video changes with different methods. Obviously, our method results in higher ranks of relevant videos compared with Source Only and ACP. Interestingly, our method performs worse given the query 'A fox is diving into the snow', which might be owed to the confusion of the white fox and the background. + +# 5. Conclusion + +In this paper, we focus on the notoriously challenging task, i.e., UDA Video-text Retrieval (UDAVR), and develop the simple yet effective Dual Alignment Domain Adaptation (DADA) method. We introduce the cross-modal semantic embedding and domain adaptation to simultane + +ously generate discriminative source features and alleviate the video and text domain shifts. To tackle the pairwise alignment issue, we propose the Dual Alignment Consistency (DAC), which progressively generates truly aligned target pairs and ensures the discriminability of target features. Extensive experiments justify our superiority. + +# 6. Acknowledgement + +This work was supported by the National Key R&D Program of China under Grant 2022YFB3103500, the National Natural Science Foundation of China under Grants 62106258, 62006242 and 62202459, and the China Postdoctoral Science Foundation under Grant 2022M713348 and 2022TQ0363, and Young Elite Scientists Sponsorship Program by BAST (NO.BYESS2023304). + +# References + +[1] Nakul Agarwal, Yi-Ting Chen, Behzad Dariush, and Ming-Hsuan Yang. Unsupervised domain adaptation for spatiotemporal action localization. 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In this paper, we study the notoriously challenging task, i.e., Unsupervised Domain Adaptation Video-text Retrieval (UDAVR), wherein training and testing data come from different distributions. Previous works merely alleviate the domain shift, which however overlook the pairwise misalignment issue in target domain, i.e., there exist no semantic relationships between target videos and texts. To tackle this, we propose a novel method named Dual Alignment Domain Adaptation (DADA). Specifically, we first introduce the cross-modal semantic embedding to generate discriminative source features in a joint embedding space. Besides, we utilize the video and text domain adaptations to smoothly balance the minimization of the domain shifts. To tackle the pairwise misalignment in target domain, we propose the Dual Alignment Consistency (DAC) to fully exploit the semantic information of both modalities in target domain. The proposed DAC adaptively aligns the videotext pairs which are more likely to be relevant in target domain, enabling that positive pairs are increasing progressively and the noisy ones will potentially be aligned in the later stages. To that end, our method can generate more truly aligned target pairs and ensure the discriminability of target features. Compared with the state-of-the-art methods, DADA achieves " + }, + { + "bbox": [ + 46, + 252, + 290, + 613 + ], + "type": "inline_equation", + "content": "20.18\\%" + }, + { + "bbox": [ + 46, + 252, + 290, + 613 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 252, + 290, + 613 + ], + "type": "inline_equation", + "content": "18.61\\%" + }, + { + "bbox": [ + 46, + 252, + 290, + 613 + ], + "type": "text", + "content": " relative improvements on " + }, + { + "bbox": [ + 46, + 252, + 290, + 613 + ], + "type": "inline_equation", + "content": "R@1" + }, + { + "bbox": [ + 46, + 252, + 290, + 613 + ], + "type": "text", + "content": " under the setting of TGIF " + }, + { + "bbox": [ + 46, + 252, + 290, + 613 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 46, + 252, + 290, + 613 + ], + "type": "text", + "content": " MSR-VTT and TGIF " + }, + { + "bbox": [ + 46, + 252, + 290, + 613 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 46, + 252, + 290, + 613 + ], + "type": "text", + "content": " MSVD respectively, demonstrating the superiority of our method." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 636, + 128, + 649 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 636, + 128, + 649 + ], + "spans": [ + { + "bbox": [ + 47, + 636, + 128, + 649 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 657, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 657, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 47, + 657, + 287, + 693 + ], + "type": "text", + "content": "Video-text retrieval enables users to search videos with a simple and natural language description. The de facto paradigm is to learn high-level visual-textual embeddings" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 313, + 225, + 411, + 358 + ], + "blocks": [ + { + "bbox": [ + 313, + 225, + 411, + 358 + ], + "lines": [ + { + "bbox": [ + 313, + 225, + 411, + 358 + ], + "spans": [ + { + "bbox": [ + 313, + 225, + 411, + 358 + ], + "type": "image", + "image_path": "79b3fe71cfcd097fc48f9ba1a070663a6372f9fc7e1275fa8c2a01bb21d181c2.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 362, + 547, + 451 + ], + "lines": [ + { + "bbox": [ + 304, + 362, + 547, + 451 + ], + "spans": [ + { + "bbox": [ + 304, + 362, + 547, + 451 + ], + "type": "text", + "content": "Figure 1. Illustration of the proposed method. Previous methods simply bring source and target features closer (blue and red ovals are overlapping each other), whereas inevitably mixing target videos (red circles) and texts (red triangles) together, ignoring whether they are semantically relevant or not. Instead, our method exploits the semantic structures in target domain to adaptively generate truly aligned video-text pairs (dotted circles) and ensure the discriminability of target data. Best viewed in color." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 420, + 226, + 545, + 358 + ], + "blocks": [ + { + "bbox": [ + 420, + 226, + 545, + 358 + ], + "lines": [ + { + "bbox": [ + 420, + 226, + 545, + 358 + ], + "spans": [ + { + "bbox": [ + 420, + 226, + 545, + 358 + ], + "type": "image", + "image_path": "0287bf1d7ba016a1ca9a5358ff98d9a6f667916ce0d2283ff6dfdd822560e09a.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 471, + 545, + 530 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 471, + 545, + 530 + ], + "spans": [ + { + "bbox": [ + 304, + 471, + 545, + 530 + ], + "type": "text", + "content": "by off-the-shelf feature extractors, and to measure semantic similarities in a joint embedding space [13, 42, 46, 63]. Despite their thrilling success, the primary assumption is that training and testing data come from the same distribution, which whereas may not hold in real scenarios." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 532, + 546, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 532, + 546, + 663 + ], + "spans": [ + { + "bbox": [ + 304, + 532, + 546, + 663 + ], + "type": "text", + "content": "To alleviate the domain shift problem, Unsupervised Domain Adaptation (UDA) has gained a lot of attention due to its efficient training without the need of supervision in target domain. UDA transfers knowledge from a labeled source domain to an unlabeled target domain [15, 33, 40, 41, 53], which has made remarkable progress in many fields, such as image classification [33, 56], autonomous driving [54, 55], medical image processing [35, 36], and video-based action recognition [50, 52]. However, these methods are originally designed for classification tasks, which might not be suitable for the video-text retrieval." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "content": "Note that in UDA Video-text Retrieval (UDAVR), there exists no identical label set for source and target domains. The only supervision is the semantic relationship in source dataset, which is also the general setting for UDA" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "type": "text", + "content": "*Corresponding author." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "18962" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 274 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 274 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 274 + ], + "type": "text", + "content": "cross-modal tasks [4, 11, 62, 64]. To that end, some approaches have been recently proposed [9, 17, 39], such as directly minimizing the distribution discrepancy [17], distilling knowledge from the source domain [9], or introducing pre-defined prototype assignments [39]. However, they overlook the pairwise misalignment issue in target domain, i.e., there exist no semantic relationships between target videos and texts. Merely alleviating the video and text domain shifts is a sub-optimal solution, which fails to fully explore the semantic structures of target data, i.e., whether the video-text pair is semantically relevant or not. As illustrated in Fig. 1, previous methods bring the learned source and target features close together, which whereas inevitably mixes up target videos and texts, ignoring whether they are a truly relevant pair or not. This will further induce less discriminative target features, and thus becomes the motivation of our work." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 275, + 289, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 275, + 289, + 514 + ], + "spans": [ + { + "bbox": [ + 46, + 275, + 289, + 514 + ], + "type": "text", + "content": "In this paper, we propose a novel method named Dual Alignment Domain Adaptation (DADA) to tackle the pairwise misalignment issue in target domain. We first introduce the cross-modal semantic embedding to generate discriminative source features in a joint embedding space, where semantically relevant pairs should lie close together and vice versa. To alleviate the domain shift, we further utilize a smooth adaptation procedure to balance the minimization of distribution shifts between source and target domains. Last but not least, to tackle the pairwise misalignment in target domain, we propose a simple yet effective Dual Alignment Consistency (DAC), which fully exploits the semantic information of both modalities in target domain. The proposed DAC adaptively aligns the video-text pairs which are more likely to be relevant in target domain, enabling that (1) positive pairs are increasing progressively, (2) the noisy ones will potentially be aligned in the later stages and (3) the discriminability of target features. Extensive experiments on several benchmarks demonstrate the superiority of our method." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 59, + 514, + 271, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 514, + 271, + 526 + ], + "spans": [ + { + "bbox": [ + 59, + 514, + 271, + 526 + ], + "type": "text", + "content": "The contributions of this paper are mainly threefold:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 532, + 286, + 713 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 59, + 532, + 286, + 580 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 532, + 286, + 580 + ], + "spans": [ + { + "bbox": [ + 59, + 532, + 286, + 580 + ], + "type": "text", + "content": "- To tackle the pairwise misalignment problem in UDAVR task, we develop a novel method named Dual Alignment Domain Adaptation (DADA) which fully exploits the semantic structures of target data." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 59, + 586, + 286, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 586, + 286, + 647 + ], + "spans": [ + { + "bbox": [ + 59, + 586, + 286, + 647 + ], + "type": "text", + "content": "- The proposed Dual Alignment Consistency (DAC) mechanism adaptively aligns the most similar videos and texts in target domain, ensure that the positive pairs are increasing progressively and the noisy ones are potentially aligned in later stages." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 59, + 653, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 653, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 59, + 653, + 286, + 713 + ], + "type": "text", + "content": "- Compared with the state-of-the-art methods, DADA achieves " + }, + { + "bbox": [ + 59, + 653, + 286, + 713 + ], + "type": "inline_equation", + "content": "20.18\\%" + }, + { + "bbox": [ + 59, + 653, + 286, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 59, + 653, + 286, + 713 + ], + "type": "inline_equation", + "content": "18.61\\%" + }, + { + "bbox": [ + 59, + 653, + 286, + 713 + ], + "type": "text", + "content": " relative improvements on R@1 under the setting of TGIF " + }, + { + "bbox": [ + 59, + 653, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 59, + 653, + 286, + 713 + ], + "type": "text", + "content": " MSRVTT and TGIF " + }, + { + "bbox": [ + 59, + 653, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 59, + 653, + 286, + 713 + ], + "type": "text", + "content": " MSVD respectively, demonstrating the superiority of our method." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 71, + 392, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 71, + 392, + 83 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 392, + 83 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 91, + 545, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 91, + 545, + 342 + ], + "spans": [ + { + "bbox": [ + 304, + 91, + 545, + 342 + ], + "type": "text", + "content": "Video-Text Retrieval. In recent years, cross-modal embedding-based approaches [2, 10, 20, 26, 27, 37, 47, 58] have emerged as a dominant paradigm for video-text retrieval. [48] proposes the JEMC framework using action, object, text and audio features by a simple concatenation fusion strategy. CE [37] adopts video features extracted from all modalities to encode a video. T2VLAD [59] automatically learns text-and-video semantic topics and reemphasizes the importance of local semantic alignment between texts and videos. HGR [10] proposes a Hierarchical Graph Reasoning (HGR) model, which decomposes video-text pairs into global-to-local levels. GPO [5] learns to automatically adapt itself to the best pooling strategy for different baselines. Recently, the Contrastive Language-Image Pretraining (CLIP) [3] model is widely used in video-text retrieval [24, 31, 38, 45]. CLIP4Clip [43] investigates three mechanisms of similarity calculation based on the pretrained CLIP. Similarly, CLIP2video [18] focuses on the spatial semantics captured by the CLIP model. Different from them, we explore the video-text retrieval task through the lens of unsupervised domain adaptation." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 342, + 545, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 342, + 545, + 533 + ], + "spans": [ + { + "bbox": [ + 304, + 342, + 545, + 533 + ], + "type": "text", + "content": "Unsupervised Domain Adaptation. UDA transfers predictive models from a fully-labeled source domain to an unlabeled target domain. Existing classification-based UDA methods seek to alleviate the domain shift between source and target domains [15, 22, 33, 40, 41, 56, 60]. Besides, UDA methods have been extended to various video-based tasks, like video action recognition [6, 12, 49], video segmentation [7, 8] and video localisation [1]. Recently, some cross-modal tasks also resort to UDA and try to utilize the unpaired data in target domain, such as image captioning [11, 62, 64] and VQA [4]. The similar work to ours is DCKT [29] which focuses on UDA image-text retrieval and transfers knowledge from a large dataset to promote the model performance on small dataset. However, DCKT needs labeled target image-text pairs during the training procedure, which fails to work well for UDAVR task." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": "Unsupervised Domain Adaptation for Video-Text Retrieval. To the best of our knowledge, there are only a few explorations of the UDAVR task [9, 17, 39]. MAN [17] proposes three alignments to alleviate different gaps in UDAVR task. CAPQ [9] comprises a concept preservation regulariser to enhance the transferability of the learned embeddings. ACP [39] focuses on minimizing both uni-modal and cross-modal distribution shift across the source and target domains. Compared to these methods, our approach differs in three aspects. (1) MAN tries to directly alleviate three different gaps in a classification-based manner, which is not suitable for cross-modal retrieval task. (2) CAPQ and ACP maximize the mutual information or minimize the KL-divergence between the prototype assignments of source and target videos, which however ignores the domain shift" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18963" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 73, + 531, + 291 + ], + "blocks": [ + { + "bbox": [ + 50, + 73, + 531, + 291 + ], + "lines": [ + { + "bbox": [ + 50, + 73, + 531, + 291 + ], + "spans": [ + { + "bbox": [ + 50, + 73, + 531, + 291 + ], + "type": "image", + "image_path": "a47805a002ce6ec0e783d86a017d88284003bc20cb05c08c11f897b27fb3e9ab.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 304, + 545, + 361 + ], + "lines": [ + { + "bbox": [ + 46, + 304, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 46, + 304, + 545, + 361 + ], + "type": "text", + "content": "Figure 2. The overall framework of DADA. Video/text features are first fed into video/text encoders to generate high-level representations. The video and text domain adaptation modules simultaneously alleviate the distribution shifts across domains in both modalities (" + }, + { + "bbox": [ + 46, + 304, + 545, + 361 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathcal{D}}^{video}" + }, + { + "bbox": [ + 46, + 304, + 545, + 361 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 304, + 545, + 361 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathcal{D}}^{text}" + }, + { + "bbox": [ + 46, + 304, + 545, + 361 + ], + "type": "text", + "content": "). Source video and text features are expected to be discriminative by the cross-modal semantic embedding (" + }, + { + "bbox": [ + 46, + 304, + 545, + 361 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathcal{S}}" + }, + { + "bbox": [ + 46, + 304, + 545, + 361 + ], + "type": "text", + "content": "). Besides, the proposed Dual Alignment Consistency (DAC) adaptively aligns the target video-text pairs which are more likely to be relevant and progressively generates dual aligned video-text pairs " + }, + { + "bbox": [ + 46, + 304, + 545, + 361 + ], + "type": "inline_equation", + "content": "(v_{i}^{p}, t_{i}^{p})_{i=1}^{n_{p}}" + }, + { + "bbox": [ + 46, + 304, + 545, + 361 + ], + "type": "text", + "content": " in target domain(" + }, + { + "bbox": [ + 46, + 304, + 545, + 361 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathcal{P}}" + }, + { + "bbox": [ + 46, + 304, + 545, + 361 + ], + "type": "text", + "content": "). Best viewed in color." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 370, + 287, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 370, + 287, + 419 + ], + "spans": [ + { + "bbox": [ + 46, + 370, + 287, + 419 + ], + "type": "text", + "content": "in text modality. (3) The semantic relationships of videos and texts in target domain have not been fully exploited by previous methods, leading to the pairwise misalignment issue, which is the primary concern of this paper." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 430, + 129, + 443 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 430, + 129, + 443 + ], + "spans": [ + { + "bbox": [ + 47, + 430, + 129, + 443 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 449, + 133, + 460 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 449, + 133, + 460 + ], + "spans": [ + { + "bbox": [ + 47, + 449, + 133, + 460 + ], + "type": "text", + "content": "3.1. Preliminaries" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 468, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 468, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 468, + 287, + 653 + ], + "type": "text", + "content": "For notational clarity, we first introduce some symbols and definitions used throughout this paper. Formally, assume that we have a set of samples in source domain " + }, + { + "bbox": [ + 46, + 468, + 287, + 653 + ], + "type": "inline_equation", + "content": "\\left\\{(\\mathcal{V}^s,\\mathcal{T}^s) = (v_i^s,t_i^s)_{i = 1}^{n_s}\\right\\}" + }, + { + "bbox": [ + 46, + 468, + 287, + 653 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 468, + 287, + 653 + ], + "type": "inline_equation", + "content": "n_{s}" + }, + { + "bbox": [ + 46, + 468, + 287, + 653 + ], + "type": "text", + "content": " indicates the number of video-text pairs. Similarly, we also have a set of samples in target domain " + }, + { + "bbox": [ + 46, + 468, + 287, + 653 + ], + "type": "inline_equation", + "content": "\\left\\{\\mathcal{V}^t = \\{v_i^t\\}_{i = 1}^{n_t},\\mathcal{T}^t = \\{t_j^t\\}_{j = 1}^{n_t}\\right\\}" + }, + { + "bbox": [ + 46, + 468, + 287, + 653 + ], + "type": "text", + "content": " with two collections of " + }, + { + "bbox": [ + 46, + 468, + 287, + 653 + ], + "type": "inline_equation", + "content": "n_t" + }, + { + "bbox": [ + 46, + 468, + 287, + 653 + ], + "type": "text", + "content": " videos " + }, + { + "bbox": [ + 46, + 468, + 287, + 653 + ], + "type": "inline_equation", + "content": "\\mathcal{V}^t" + }, + { + "bbox": [ + 46, + 468, + 287, + 653 + ], + "type": "text", + "content": " and texts " + }, + { + "bbox": [ + 46, + 468, + 287, + 653 + ], + "type": "inline_equation", + "content": "\\mathcal{T}^t" + }, + { + "bbox": [ + 46, + 468, + 287, + 653 + ], + "type": "text", + "content": ", respectively. Note that the target videos and texts are unpaired, which means the supervised information, i.e., whether one target video-text pair is semantically relevant or not, is not available in target domain. The Unsupervised Domain Adaptation Video-text Retrieval (UDAVR) aims at improving the model's generalization performance on target domain with the utilization of source domain. The overall framework of our method is illustrated in Fig. 2." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "text", + "content": "Given one video-text pair, following the state-of-the-art baseline in video-text retrieval [5], we utilize a video encoder " + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\varphi (\\cdot)" + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "text", + "content": " and a text encoder " + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\psi (\\cdot)" + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "text", + "content": " to map each video sample " + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "text", + "content": " and text description " + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "text", + "content": " into a joint embedding space. The visual embedding " + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\varphi (v)\\in \\mathbb{R}^{M}" + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "text", + "content": " and text embedding" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 370, + 545, + 478 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 370, + 545, + 478 + ], + "spans": [ + { + "bbox": [ + 304, + 370, + 545, + 478 + ], + "type": "inline_equation", + "content": "\\psi (t)\\in \\mathbb{R}^{M}" + }, + { + "bbox": [ + 304, + 370, + 545, + 478 + ], + "type": "text", + "content": " are semantically relevant if the text describes the video, where " + }, + { + "bbox": [ + 304, + 370, + 545, + 478 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 370, + 545, + 478 + ], + "type": "text", + "content": " denotes the dimension in the common space. In the source domain, we utilize the video-text contrastive loss to guide the semantic alignment learning. Following [30, 32, 51], the contrastive loss considers matched pairs as positive and all others pairs that can be formed in a batch as negatives. For each input video-text pair " + }, + { + "bbox": [ + 304, + 370, + 545, + 478 + ], + "type": "inline_equation", + "content": "(v_{i},t_{i})" + }, + { + "bbox": [ + 304, + 370, + 545, + 478 + ], + "type": "text", + "content": ", the video-text contrastive loss consists of two symmetric terms, one for video-to-text classification:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 347, + 482, + 545, + 512 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 482, + 545, + 512 + ], + "spans": [ + { + "bbox": [ + 347, + 482, + 545, + 512 + ], + "type": "interline_equation", + "content": "\\mathcal {L} ^ {v 2 t} = - \\log \\frac {\\exp \\left(s \\left(v _ {i} , t _ {i}\\right) / \\tau\\right)}{\\sum_ {j} ^ {B} \\exp \\left(s \\left(v _ {i} , t _ {j}\\right) / \\tau\\right)}, \\tag {1}", + "image_path": "d5fe9c28ef362a183fb03ca329f4d57b5146c2446ca769aaf53294217b5c71f8.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 514, + 486, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 514, + 486, + 525 + ], + "spans": [ + { + "bbox": [ + 306, + 514, + 486, + 525 + ], + "type": "text", + "content": "and the other for text-to-video classification:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 347, + 528, + 545, + 558 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 528, + 545, + 558 + ], + "spans": [ + { + "bbox": [ + 347, + 528, + 545, + 558 + ], + "type": "interline_equation", + "content": "\\mathcal {L} ^ {t 2 v} = - \\log \\frac {\\exp (s (t _ {i} , v _ {i}) / \\tau)}{\\sum_ {j} ^ {B} \\exp (s (t _ {i} , v _ {j}) / \\tau)}. \\tag {2}", + "image_path": "fc1d034d6e7c9ef053f7ef1bb8d82c042ade216217c8136f89d88a96722504bc.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 561, + 545, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 561, + 545, + 609 + ], + "spans": [ + { + "bbox": [ + 304, + 561, + 545, + 609 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 561, + 545, + 609 + ], + "type": "text", + "content": " is the temperature parameter and " + }, + { + "bbox": [ + 304, + 561, + 545, + 609 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 304, + 561, + 545, + 609 + ], + "type": "text", + "content": " is the batch size. We calculate similarity scores with the cosine similarity, which is a widely-used similarity metric and has been proved effective [10, 16]:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 356, + 612, + 545, + 639 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 356, + 612, + 545, + 639 + ], + "spans": [ + { + "bbox": [ + 356, + 612, + 545, + 639 + ], + "type": "interline_equation", + "content": "s \\left(v _ {i}, t _ {j}\\right) = \\frac {\\varphi \\left(v _ {i}\\right) \\cdot \\psi \\left(t _ {j}\\right)}{\\| \\varphi \\left(v _ {i}\\right) \\| \\| \\psi \\left(t _ {j}\\right) \\|}, \\tag {3}", + "image_path": "60fcf01b8d470a56aee36d7497003c20a1bd93d96a497d7f345dd3e44444bcc7.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 642, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 689 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 642, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\varphi(v_{i})" + }, + { + "bbox": [ + 304, + 642, + 545, + 689 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 642, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\psi(t_{j})" + }, + { + "bbox": [ + 304, + 642, + 545, + 689 + ], + "type": "text", + "content": " are the corresponding mapped features, and " + }, + { + "bbox": [ + 304, + 642, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\|\\cdot\\|" + }, + { + "bbox": [ + 304, + 642, + 545, + 689 + ], + "type": "text", + "content": " denotes the " + }, + { + "bbox": [ + 304, + 642, + 545, + 689 + ], + "type": "inline_equation", + "content": "l_{2}" + }, + { + "bbox": [ + 304, + 642, + 545, + 689 + ], + "type": "text", + "content": " norm of vectors and the Frobenius norm of matrices. Formally, the contrastive loss for the video-text pairs is as follows:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 367, + 693, + 545, + 717 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 367, + 693, + 545, + 717 + ], + "spans": [ + { + "bbox": [ + 367, + 693, + 545, + 717 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathcal {S}} = \\frac {1}{2} \\left(\\mathcal {L} ^ {v 2 t} + \\mathcal {L} ^ {t 2 v}\\right). \\tag {4}", + "image_path": "9b7dd8dcb0da6776d1b9b0600f28671ba8a592d1ad13febe56c1f16158af5e77.jpg" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18964" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 72, + 126, + 173 + ], + "blocks": [ + { + "bbox": [ + 51, + 72, + 126, + 173 + ], + "lines": [ + { + "bbox": [ + 51, + 72, + 126, + 173 + ], + "spans": [ + { + "bbox": [ + 51, + 72, + 126, + 173 + ], + "type": "image", + "image_path": "976ef896aa61316564b31a85631689d2c23659e144d925e7690c54c61baf4332.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 182, + 287, + 238 + ], + "lines": [ + { + "bbox": [ + 46, + 182, + 287, + 238 + ], + "spans": [ + { + "bbox": [ + 46, + 182, + 287, + 238 + ], + "type": "text", + "content": "Figure 3. Illustration of the performance decrease when training data and testing data are sampled from different distributions. Mt, Md and Tf denote the dataset MSR-VTT, MSVD and TGIF, respectively. For instance, " + }, + { + "bbox": [ + 46, + 182, + 287, + 238 + ], + "type": "inline_equation", + "content": "\\mathrm{Mt} \\rightarrow \\mathrm{Md}" + }, + { + "bbox": [ + 46, + 182, + 287, + 238 + ], + "type": "text", + "content": " denotes training on MSR-VTT and testing on MSVD." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 129, + 72, + 205, + 172 + ], + "blocks": [ + { + "bbox": [ + 129, + 72, + 205, + 172 + ], + "lines": [ + { + "bbox": [ + 129, + 72, + 205, + 172 + ], + "spans": [ + { + "bbox": [ + 129, + 72, + 205, + 172 + ], + "type": "image", + "image_path": "00b146e88b8acde9b038ccc463e31a2ba2a7d01923fbafde4caba206b66e23e9.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 209, + 72, + 283, + 172 + ], + "blocks": [ + { + "bbox": [ + 209, + 72, + 283, + 172 + ], + "lines": [ + { + "bbox": [ + 209, + 72, + 283, + 172 + ], + "spans": [ + { + "bbox": [ + 209, + 72, + 283, + 172 + ], + "type": "image", + "image_path": "5fbf0c1592dc7ce2546fea735070df63e402bd665512cd30eb7a562da11b932f.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 258, + 214, + 272 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 258, + 214, + 272 + ], + "spans": [ + { + "bbox": [ + 47, + 258, + 214, + 272 + ], + "type": "text", + "content": "3.2. Domain Adaptation in UDAVR" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 277, + 287, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 277, + 287, + 409 + ], + "spans": [ + { + "bbox": [ + 46, + 277, + 287, + 409 + ], + "type": "text", + "content": "Different datasets usually have inconsistent data distributions and representations, thus leading to the domain shift problem. To verify this, we show the performance comparisons in Fig. 3, where training data and testing data come from different distributions. As can be seen, when both training and testing data come from MSR-VTT dataset, i.e., " + }, + { + "bbox": [ + 46, + 277, + 287, + 409 + ], + "type": "inline_equation", + "content": "\\mathrm{Mt} \\rightarrow \\mathrm{Mt}" + }, + { + "bbox": [ + 46, + 277, + 287, + 409 + ], + "type": "text", + "content": ", the R@10 result is " + }, + { + "bbox": [ + 46, + 277, + 287, + 409 + ], + "type": "inline_equation", + "content": "34.30\\%" + }, + { + "bbox": [ + 46, + 277, + 287, + 409 + ], + "type": "text", + "content": ". In the contrast, when training on MSVD and testing on MSR-VTT, i.e., " + }, + { + "bbox": [ + 46, + 277, + 287, + 409 + ], + "type": "inline_equation", + "content": "\\mathrm{Md} \\rightarrow \\mathrm{Mt}" + }, + { + "bbox": [ + 46, + 277, + 287, + 409 + ], + "type": "text", + "content": ", the R@10 result decreases to " + }, + { + "bbox": [ + 46, + 277, + 287, + 409 + ], + "type": "inline_equation", + "content": "13.27\\%" + }, + { + "bbox": [ + 46, + 277, + 287, + 409 + ], + "type": "text", + "content": ", indicating a relative " + }, + { + "bbox": [ + 46, + 277, + 287, + 409 + ], + "type": "inline_equation", + "content": "21.03\\%" + }, + { + "bbox": [ + 46, + 277, + 287, + 409 + ], + "type": "text", + "content": " performance drop. The significant performance degeneration identifies the domain shift problem in UDAVR." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 410, + 287, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 410, + 287, + 589 + ], + "spans": [ + { + "bbox": [ + 46, + 410, + 287, + 589 + ], + "type": "text", + "content": "To alleviate this, we resort to recently proposed DA method [14], which generates intermediate domain representations on-the-fly to gradually bridge the source and target domains. By utilizing the appropriate intermediate domain to bridge the source and target, the source knowledge can be better transferred to the target domain. Specifically, we denote distributions of source, target and intermediate domain as " + }, + { + "bbox": [ + 46, + 410, + 287, + 589 + ], + "type": "inline_equation", + "content": "P_{s}" + }, + { + "bbox": [ + 46, + 410, + 287, + 589 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 410, + 287, + 589 + ], + "type": "inline_equation", + "content": "P_{t}" + }, + { + "bbox": [ + 46, + 410, + 287, + 589 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 410, + 287, + 589 + ], + "type": "inline_equation", + "content": "P_{i}" + }, + { + "bbox": [ + 46, + 410, + 287, + 589 + ], + "type": "text", + "content": " respectively, and use " + }, + { + "bbox": [ + 46, + 410, + 287, + 589 + ], + "type": "inline_equation", + "content": "D(\\cdot)" + }, + { + "bbox": [ + 46, + 410, + 287, + 589 + ], + "type": "text", + "content": " to represent the Euclidean distance. Besides, we also introduce the domain factor " + }, + { + "bbox": [ + 46, + 410, + 287, + 589 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 410, + 287, + 589 + ], + "type": "text", + "content": " for the source and target domains respectively. The domain factor can be seen as the relevance of the intermediate domain to the other two extreme domains. Thus, in the video stream, the distance relationship (contrary to the relevance relationship) between " + }, + { + "bbox": [ + 46, + 410, + 287, + 589 + ], + "type": "inline_equation", + "content": "P_{i}" + }, + { + "bbox": [ + 46, + 410, + 287, + 589 + ], + "type": "text", + "content": " and other two domains, i.e., " + }, + { + "bbox": [ + 46, + 410, + 287, + 589 + ], + "type": "inline_equation", + "content": "P_{s}" + }, + { + "bbox": [ + 46, + 410, + 287, + 589 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 410, + 287, + 589 + ], + "type": "inline_equation", + "content": "P_{t}" + }, + { + "bbox": [ + 46, + 410, + 287, + 589 + ], + "type": "text", + "content": ", can be formulated as:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 116, + 597, + 287, + 624 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 597, + 287, + 624 + ], + "spans": [ + { + "bbox": [ + 116, + 597, + 287, + 624 + ], + "type": "interline_equation", + "content": "\\frac {D \\left(P _ {s} ^ {v} , P _ {i} ^ {v}\\right)}{D \\left(P _ {t} ^ {v} , P _ {i} ^ {v}\\right)} = \\frac {\\alpha}{1 - \\alpha}. \\tag {5}", + "image_path": "bc5a9914d07713577468fa1b3c99d6b06c3b9088aede572e5e658c9ad54644eb.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 632, + 287, + 655 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 632, + 287, + 655 + ], + "spans": [ + { + "bbox": [ + 47, + 632, + 287, + 655 + ], + "type": "text", + "content": "Formally, the domain shift problem can be converted into minimizing the intermediate domain loss as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 74, + 665, + 287, + 681 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 74, + 665, + 287, + 681 + ], + "spans": [ + { + "bbox": [ + 74, + 665, + 287, + 681 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathcal {D}} ^ {\\text {v i d e o}} = \\alpha D \\left(P _ {s} ^ {v}, P _ {i} ^ {v}\\right) + (1 - \\alpha) D \\left(P _ {t} ^ {v}, P _ {i} ^ {v}\\right). \\tag {6}", + "image_path": "2f5bf1dffbdb81fb4eae9d43afae7fb9d98f943ffe536aa2a23bd8a9d45651fe.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "The loss in Eq. 6 aims at guiding the distribution of appropriate intermediate domain to keep the right distance to" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 307, + 70, + 539, + 200 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 539, + 200 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 539, + 200 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 539, + 200 + ], + "type": "image", + "image_path": "b2ee174c12326d491d47ff40d91cbd31b5ffdc84376b1761d1f5fac169349234.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 207, + 545, + 240 + ], + "lines": [ + { + "bbox": [ + 305, + 207, + 545, + 240 + ], + "spans": [ + { + "bbox": [ + 305, + 207, + 545, + 240 + ], + "type": "text", + "content": "Figure 4. Illustration of Dual Alignment Consistency (DAC). If " + }, + { + "bbox": [ + 305, + 207, + 545, + 240 + ], + "type": "inline_equation", + "content": "v_{i*}^{t}" + }, + { + "bbox": [ + 305, + 207, + 545, + 240 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 207, + 545, + 240 + ], + "type": "inline_equation", + "content": "t_{j*}^{t}" + }, + { + "bbox": [ + 305, + 207, + 545, + 240 + ], + "type": "text", + "content": " are the reciprocal nearest neighbor of each other, then they can be considered as a truly aligned pair in target domain." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 254, + 544, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 254, + 544, + 277 + ], + "spans": [ + { + "bbox": [ + 305, + 254, + 544, + 277 + ], + "type": "text", + "content": "the source and target domains. Similarly, in the text stream, the intermediate domain loss can be computed as:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 337, + 288, + 545, + 302 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 337, + 288, + 545, + 302 + ], + "spans": [ + { + "bbox": [ + 337, + 288, + 545, + 302 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathcal {D}} ^ {t e x t} = \\alpha D \\left(P _ {s} ^ {t}, P _ {i} ^ {t}\\right) + (1 - \\alpha) D \\left(P _ {t} ^ {t}, P _ {i} ^ {t}\\right). \\tag {7}", + "image_path": "1bb23f5031da874710b5da6483b0c706968b82018671257d4e5d1cfe4d377f5b.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 318, + 315, + 545, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 315, + 545, + 326 + ], + "spans": [ + { + "bbox": [ + 318, + 315, + 545, + 326 + ], + "type": "text", + "content": "To sum up, the domain adaptation loss can be defined as:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 379, + 340, + 545, + 354 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 379, + 340, + 545, + 354 + ], + "spans": [ + { + "bbox": [ + 379, + 340, + 545, + 354 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathcal {D}} = \\mathcal {L} _ {\\mathcal {D}} ^ {\\text {v i d e o}} + \\mathcal {L} _ {\\mathcal {D}} ^ {\\text {t e x t}}. \\tag {8}", + "image_path": "0df9544eaf98874babc461dae0c48d1c6f925ccbdcd6d326daec14a5d2fb67e9.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 373, + 462, + 385 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 373, + 462, + 385 + ], + "spans": [ + { + "bbox": [ + 306, + 373, + 462, + 385 + ], + "type": "text", + "content": "3.3. Dual Alignment Consistency" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 392, + 545, + 546 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 392, + 545, + 546 + ], + "spans": [ + { + "bbox": [ + 304, + 392, + 545, + 546 + ], + "type": "text", + "content": "Despite the efficiency of the cross-modal semantic embedding and domain adaptations, we argue that the desired discriminability in target domain still can not be ensured. Note that in UDA cross-modal tasks, there exists no identical label set for source and target domains, and the only supervision available is the semantic relationship in the source dataset [4, 11, 62, 64]. Merely alleviating the domain shift will inevitably mix up target videos and texts, ignoring whether they are a relevant pair or not. This thus leads to the pairwise misalignment issue in target domain. In other words, the target videos and texts are unpaired, which means the pairwise information is not available in target domain." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 548, + 546, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 548, + 546, + 687 + ], + "spans": [ + { + "bbox": [ + 304, + 548, + 546, + 687 + ], + "type": "text", + "content": "To alleviate this, we propose a simple yet effective Dual Alignment Consistency (DAC). The DAC tries to utilize the truly aligned target video-text pairs which are more likely to be semantically relevant, and to avoid including the noisy ones which tend to be irrelevant. Specifically, given the target set " + }, + { + "bbox": [ + 304, + 548, + 546, + 687 + ], + "type": "inline_equation", + "content": "\\left\\{\\mathcal{V}^t = \\{v_i^t\\}_{i=1}^{n_t}, \\mathcal{T}^t = \\{t_j^t\\}_{j=1}^{n_t}\\right\\}" + }, + { + "bbox": [ + 304, + 548, + 546, + 687 + ], + "type": "text", + "content": ", we try to find if there exist truly positive video-text pairs. " + }, + { + "bbox": [ + 304, + 548, + 546, + 687 + ], + "type": "inline_equation", + "content": "(v_i^t, t_j^t)" + }, + { + "bbox": [ + 304, + 548, + 546, + 687 + ], + "type": "text", + "content": " can be considered as a truly positive pair if and only if " + }, + { + "bbox": [ + 304, + 548, + 546, + 687 + ], + "type": "inline_equation", + "content": "v_i^t" + }, + { + "bbox": [ + 304, + 548, + 546, + 687 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 548, + 546, + 687 + ], + "type": "inline_equation", + "content": "t_j^t" + }, + { + "bbox": [ + 304, + 548, + 546, + 687 + ], + "type": "text", + "content": " are mutually the most similar to each other, indicating a dual aligned pair. For a target video " + }, + { + "bbox": [ + 304, + 548, + 546, + 687 + ], + "type": "inline_equation", + "content": "v_i^t" + }, + { + "bbox": [ + 304, + 548, + 546, + 687 + ], + "type": "text", + "content": ", we calculate the similarities of " + }, + { + "bbox": [ + 304, + 548, + 546, + 687 + ], + "type": "inline_equation", + "content": "v_i^t" + }, + { + "bbox": [ + 304, + 548, + 546, + 687 + ], + "type": "text", + "content": " and all the target texts, which can be defined as:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 331, + 698, + 545, + 716 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 331, + 698, + 545, + 716 + ], + "spans": [ + { + "bbox": [ + 331, + 698, + 545, + 716 + ], + "type": "interline_equation", + "content": "\\mathbf {S} _ {v _ {i} ^ {t}} ^ {\\mathcal {V} \\rightarrow \\mathcal {T}} = \\left[ S _ {v _ {i} ^ {t} t _ {1} ^ {t}}, S _ {v _ {i} ^ {t} t _ {2} ^ {t}}, \\dots , S _ {v _ {i} ^ {t} t _ {j} ^ {t}}, \\dots , S _ {v _ {i} ^ {t} t _ {n t} ^ {t}} \\right]. \\tag {9}", + "image_path": "1c828b92191b286104556c46a5545e560fb7e1e1997d2fcf3c5bcf0129c21d80.jpg" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18965" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 84, + 541, + 137 + ], + "blocks": [ + { + "bbox": [ + 126, + 70, + 465, + 81 + ], + "lines": [ + { + "bbox": [ + 126, + 70, + 465, + 81 + ], + "spans": [ + { + "bbox": [ + 126, + 70, + 465, + 81 + ], + "type": "text", + "content": "Table 1. Comparison of three datasets, i.e., MSR-VTT, MSVD and TGIF in the UDAVR task." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 84, + 541, + 137 + ], + "lines": [ + { + "bbox": [ + 50, + 84, + 541, + 137 + ], + "spans": [ + { + "bbox": [ + 50, + 84, + 541, + 137 + ], + "type": "table", + "html": "
Dataset#Videos#caps.Video Len.Query Len.#Train#Val# TestSceneText Src.Video Src.Semantics
MSR-VTT10,000200k20s9.346,5134972,990OpenAMTYouTubeCategory
MSVD1,97086k10s7.031,200100670OpenAMTYouTubeMulti. Lang.
TGIF101,412120k3s8.6779,45110,65111,310Anim. GIFCrowdsourcingTumblrNone
", + "image_path": "324d12e966c9bc015816b584289220727f71249db9676e1912b1ca0a50668210.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 156, + 287, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 156, + 287, + 180 + ], + "spans": [ + { + "bbox": [ + 47, + 156, + 287, + 180 + ], + "type": "text", + "content": "Then, we nominate the selected text for target video " + }, + { + "bbox": [ + 47, + 156, + 287, + 180 + ], + "type": "inline_equation", + "content": "v_{i}^{t}" + }, + { + "bbox": [ + 47, + 156, + 287, + 180 + ], + "type": "text", + "content": " with the maximum similarity as the candidate matching text:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 104, + 188, + 287, + 207 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 188, + 287, + 207 + ], + "spans": [ + { + "bbox": [ + 104, + 188, + 287, + 207 + ], + "type": "interline_equation", + "content": "j ^ {*} = \\arg \\max _ {j \\in \\{1, 2, \\dots , n _ {t} \\}} S _ {v _ {i} ^ {t} t _ {j} ^ {t}}, \\tag {10}", + "image_path": "075ccebe93784e1992afd9fc937ea9e6969bd4a12fa59dd26540c7fd1fceb6a2.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 213, + 287, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 213, + 287, + 300 + ], + "spans": [ + { + "bbox": [ + 47, + 213, + 287, + 300 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 213, + 287, + 300 + ], + "type": "inline_equation", + "content": "j^{*}" + }, + { + "bbox": [ + 47, + 213, + 287, + 300 + ], + "type": "text", + "content": " is the index of the candidate matching text " + }, + { + "bbox": [ + 47, + 213, + 287, + 300 + ], + "type": "inline_equation", + "content": "t_{j^*}^t" + }, + { + "bbox": [ + 47, + 213, + 287, + 300 + ], + "type": "text", + "content": ". Similarly, the candidate matching text " + }, + { + "bbox": [ + 47, + 213, + 287, + 300 + ], + "type": "inline_equation", + "content": "t_{j^*}^t" + }, + { + "bbox": [ + 47, + 213, + 287, + 300 + ], + "type": "text", + "content": " is further calculated back to video set in a similar way, and the corresponding candidate matching video " + }, + { + "bbox": [ + 47, + 213, + 287, + 300 + ], + "type": "inline_equation", + "content": "v_{i^*}^t" + }, + { + "bbox": [ + 47, + 213, + 287, + 300 + ], + "type": "text", + "content": " can be nominated according to " + }, + { + "bbox": [ + 47, + 213, + 287, + 300 + ], + "type": "inline_equation", + "content": "\\mathbf{S}_{t_j}^{\\mathcal{T}\\to \\mathcal{V}}" + }, + { + "bbox": [ + 47, + 213, + 287, + 300 + ], + "type": "text", + "content": ". As in Fig. 4, this dual mapping and matching operation between " + }, + { + "bbox": [ + 47, + 213, + 287, + 300 + ], + "type": "inline_equation", + "content": "\\mathcal{V}^t" + }, + { + "bbox": [ + 47, + 213, + 287, + 300 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 213, + 287, + 300 + ], + "type": "inline_equation", + "content": "\\mathcal{T}^t" + }, + { + "bbox": [ + 47, + 213, + 287, + 300 + ], + "type": "text", + "content": " determines the dual alignment consistency as:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 61, + 307, + 287, + 339 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 307, + 287, + 339 + ], + "spans": [ + { + "bbox": [ + 61, + 307, + 287, + 339 + ], + "type": "interline_equation", + "content": "\\left\\{ \\begin{array}{l l} \\left(v _ {i ^ {*}} ^ {t}, t _ {j ^ {*}} ^ {t}\\right) \\text {i s a n a l i g n e d p a i r ,} & \\text {i f} v _ {i ^ {*}} ^ {t} = v _ {i} ^ {t}, \\\\ \\left(v _ {i ^ {*}} ^ {t}, t _ {j ^ {*}} ^ {t}\\right) \\text {i s a m i s a l i g n e d p a i r ,} & \\text {i f} v _ {i ^ {*}} ^ {t} \\neq v _ {i} ^ {t}. \\end{array} \\right. \\tag {11}", + "image_path": "c65352e26dbda8a4ff5bdbbaee4514a6140838aad0633c6bbfe21b504f49e2d7.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 346, + 287, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 346, + 287, + 407 + ], + "spans": [ + { + "bbox": [ + 47, + 346, + 287, + 407 + ], + "type": "text", + "content": "The dual alignment consistency requires " + }, + { + "bbox": [ + 47, + 346, + 287, + 407 + ], + "type": "inline_equation", + "content": "v_{i*}^t" + }, + { + "bbox": [ + 47, + 346, + 287, + 407 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 346, + 287, + 407 + ], + "type": "inline_equation", + "content": "t_{j*}^t" + }, + { + "bbox": [ + 47, + 346, + 287, + 407 + ], + "type": "text", + "content": " to be the reciprocal nearest neighbor of each other, indicating a truly aligned (or positive) pair. To that end, we can obtain " + }, + { + "bbox": [ + 47, + 346, + 287, + 407 + ], + "type": "inline_equation", + "content": "n_p" + }, + { + "bbox": [ + 47, + 346, + 287, + 407 + ], + "type": "text", + "content": " positive pairs in one batch from target dataset, denoted as " + }, + { + "bbox": [ + 47, + 346, + 287, + 407 + ], + "type": "inline_equation", + "content": "\\{(V^p, T^p) = (v_i^p, t_i^p)_{i=1}^{n_p}\\}" + }, + { + "bbox": [ + 47, + 346, + 287, + 407 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 346, + 287, + 407 + ], + "type": "inline_equation", + "content": "(v_i^p, t_i^p) = (v_{i*}^t, t_{j*}^t)" + }, + { + "bbox": [ + 47, + 346, + 287, + 407 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 407, + 287, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 407, + 287, + 514 + ], + "spans": [ + { + "bbox": [ + 46, + 407, + 287, + 514 + ], + "type": "text", + "content": "To further boost the accuracy of aligned pairs, we introduce " + }, + { + "bbox": [ + 46, + 407, + 287, + 514 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 407, + 287, + 514 + ], + "type": "text", + "content": " as the threshold to sort the similarities of all pairs in one batch with descending order and choose the " + }, + { + "bbox": [ + 46, + 407, + 287, + 514 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 407, + 287, + 514 + ], + "type": "text", + "content": "-th value, implying to select top " + }, + { + "bbox": [ + 46, + 407, + 287, + 514 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 407, + 287, + 514 + ], + "type": "text", + "content": " similar pairs. The intuition is that a truly positive video-text pair should not only be the most similar to each other, but also have a relatively high similarity score compared with all the misaligned pairs. We also conduct some vanilla aligning mechanisms and ablations on threshold " + }, + { + "bbox": [ + 46, + 407, + 287, + 514 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 407, + 287, + 514 + ], + "type": "text", + "content": ", which are reported in Sec. 4 (Tab. 3 and Fig. 5)." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 514, + 287, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 514, + 287, + 571 + ], + "spans": [ + { + "bbox": [ + 46, + 514, + 287, + 571 + ], + "type": "text", + "content": "With these self-discovered matching pairs, we can treat the pairwise misalignment issue as a fully supervised problem to benefit the model training. Similar to " + }, + { + "bbox": [ + 46, + 514, + 287, + 571 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_S" + }, + { + "bbox": [ + 46, + 514, + 287, + 571 + ], + "type": "text", + "content": " in source domain, the dual alignment consistency loss can be defined as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 83, + 578, + 287, + 636 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 578, + 287, + 636 + ], + "spans": [ + { + "bbox": [ + 83, + 578, + 287, + 636 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\mathcal {P}} = - \\frac {1}{2} \\left(\\log \\frac {\\exp \\left(s \\left(v _ {i} ^ {p} , t _ {i} ^ {p}\\right) / \\tau\\right)}{\\sum_ {j} ^ {n _ {p}} \\exp \\left(s \\left(v _ {i} ^ {p} , t _ {j} ^ {p}\\right) / \\tau\\right)} \\right. \\tag {12} \\\\ + \\log \\frac {\\exp \\left(s \\left(t _ {i} ^ {p} , v _ {i} ^ {p}\\right) / \\tau\\right)}{\\sum_ {j} ^ {n _ {p}} \\exp \\left(s \\left(t _ {i} ^ {p} , v _ {j} ^ {p}\\right) / \\tau\\right)} \\\\ \\end{array}", + "image_path": "9642f4832e705ff8ad35c8bac01cd97410fb6fa542d5a713da7d31fe7d903b99.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 642, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 287, + 712 + ], + "type": "text", + "content": "During the training process, the positive pairs are increasing progressively and the noisy ones will potentially be aligned in the later stages (empirical results can be found in Fig. 5). To this end, more target samples are truly aligned as relevant video-text pairs, generating discriminative features in target domain." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 156, + 408, + 170 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 156, + 408, + 170 + ], + "spans": [ + { + "bbox": [ + 306, + 156, + 408, + 170 + ], + "type": "text", + "content": "3.4. Overall Training" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 178, + 545, + 260 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 178, + 545, + 260 + ], + "spans": [ + { + "bbox": [ + 304, + 178, + 545, + 260 + ], + "type": "text", + "content": "In a nutshell, we minimize the sum of the above losses, including the semantic embedding loss " + }, + { + "bbox": [ + 304, + 178, + 545, + 260 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_S" + }, + { + "bbox": [ + 304, + 178, + 545, + 260 + ], + "type": "text", + "content": " in source domain, the domain adaptation loss " + }, + { + "bbox": [ + 304, + 178, + 545, + 260 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathcal{D}}" + }, + { + "bbox": [ + 304, + 178, + 545, + 260 + ], + "type": "text", + "content": " for alleviating domain shift, and the dual alignment consistency loss " + }, + { + "bbox": [ + 304, + 178, + 545, + 260 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathcal{P}}" + }, + { + "bbox": [ + 304, + 178, + 545, + 260 + ], + "type": "text", + "content": " for aligning positive pairs in target domain. Combining these loss terms together, the overall objective function can be formulated as:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 365, + 270, + 545, + 283 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 270, + 545, + 283 + ], + "spans": [ + { + "bbox": [ + 365, + 270, + 545, + 283 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {\\mathcal {S}} + \\lambda_ {1} \\mathcal {L} _ {\\mathcal {D}} + \\lambda_ {2} \\mathcal {L} _ {\\mathcal {P}}, \\tag {13}", + "image_path": "e48a04dbc6fec3147025c5c5b8b339a0cf3855fe9a31c51efa5d4dfa53284b90.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 297, + 545, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 297, + 545, + 344 + ], + "spans": [ + { + "bbox": [ + 304, + 297, + 545, + 344 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 297, + 545, + 344 + ], + "type": "inline_equation", + "content": "\\lambda_{1}" + }, + { + "bbox": [ + 304, + 297, + 545, + 344 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 297, + 545, + 344 + ], + "type": "inline_equation", + "content": "\\lambda_{2}" + }, + { + "bbox": [ + 304, + 297, + 545, + 344 + ], + "type": "text", + "content": " are hyper parameters for balancing these terms. The parameters of the whole network can readily be updated by the stochastic gradient descent (SGD) algorithm and the chain rules." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 365, + 386, + 378 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 365, + 386, + 378 + ], + "spans": [ + { + "bbox": [ + 306, + 365, + 386, + 378 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 387, + 427, + 400 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 387, + 427, + 400 + ], + "spans": [ + { + "bbox": [ + 306, + 387, + 427, + 400 + ], + "type": "text", + "content": "4.1. Experimental Setting" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 408, + 545, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 408, + 545, + 515 + ], + "spans": [ + { + "bbox": [ + 304, + 408, + 545, + 515 + ], + "type": "text", + "content": "Datasets. In this paper, we take advantage of existing datasets across three domains to explore the UDAVR task. To be specific, we construct a comprehensive evaluation benchmark which is the combination of three widely used datasets, i.e., MSR-VTT (Mt) [61], MSVD (Md) [23] and TGIF (Tf) [34]. An overview of three datasets is given in Tab. 1. The diversities of different datasets, e.g., lengths, numbers and video scenes, contribute to the domain shift in UDAVR task." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 519, + 545, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 519, + 545, + 578 + ], + "spans": [ + { + "bbox": [ + 304, + 519, + 545, + 578 + ], + "type": "text", + "content": "Evaluation Metrics. We adopt standard retrieval metrics (following [10, 25, 28]) to evaluate the performance of video-text retrieval. We measure rank-based performance by R@K (higher is better) and also report Median Rank, i.e., MR, (lower is better)." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "Implementation Details. For fair comparison, we utilize the same architecture of the video and text encoders as in GPO [5], which is the state-of-the-art baseline for videotext retrieval. Note that our method is orthogonal to the visual and textual encoder, allowing us to flexibly embrace state-of-the-art visual and textual encoders, of which the details are discussed in ablation studies. The length of shared embedding " + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": " is set to 1024. Moreover, we adopt the Adam optimizer for all our experiments, set " + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\lambda_1 = \\lambda_2 = 0.1" + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": ". We set the mini-batch size to 64, and utilize a step-decayed learning rate with initialization value 0.0001." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18966" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 51, + 83, + 282, + 150 + ], + "blocks": [ + { + "bbox": [ + 111, + 71, + 223, + 81 + ], + "lines": [ + { + "bbox": [ + 111, + 71, + 223, + 81 + ], + "spans": [ + { + "bbox": [ + 111, + 71, + 223, + 81 + ], + "type": "text", + "content": "Table 2. Effect of " + }, + { + "bbox": [ + 111, + 71, + 223, + 81 + ], + "type": "inline_equation", + "content": "{\\mathcal{L}}_{\\mathcal{P}}" + }, + { + "bbox": [ + 111, + 71, + 223, + 81 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 111, + 71, + 223, + 81 + ], + "type": "inline_equation", + "content": "{\\mathcal{L}}_{\\mathcal{D}}" + }, + { + "bbox": [ + 111, + 71, + 223, + 81 + ], + "type": "text", + "content": " ." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 51, + 83, + 282, + 150 + ], + "lines": [ + { + "bbox": [ + 51, + 83, + 282, + 150 + ], + "spans": [ + { + "bbox": [ + 51, + 83, + 282, + 150 + ], + "type": "table", + "html": "
MethodTf→MtTf→Md
R1↑R10↑MR↓R1↑R10↑MR↓
DADA(w/o Lp)2.9815.939710.2639.1818
DADA(w/o LD)4.1220.297511.4741.9017
DADA5.3024.545014.3448.7711
", + "image_path": "4122094afd49c384baa56c654fa73e48474cc90d7413898e81c2a83ab11ec065.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 50, + 175, + 282, + 254 + ], + "blocks": [ + { + "bbox": [ + 63, + 163, + 270, + 173 + ], + "lines": [ + { + "bbox": [ + 63, + 163, + 270, + 173 + ], + "spans": [ + { + "bbox": [ + 63, + 163, + 270, + 173 + ], + "type": "text", + "content": "Table 3. Comparison of different alignment mechanisms." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 175, + 282, + 254 + ], + "lines": [ + { + "bbox": [ + 50, + 175, + 282, + 254 + ], + "spans": [ + { + "bbox": [ + 50, + 175, + 282, + 254 + ], + "type": "table", + "html": "
MethodTf→MtTf→Md
R1↑R10↑MR↓R1↑R10↑MR↓
DADA(w/ text)3.5217.2911113.1645.6713
DADA(w/ video)3.2615.6114613.0446.3113
DADA(w/o T)4.8422.476713.5344.7715
DADA5.3024.545014.3448.7711
", + "image_path": "fda0d60f9712b4825d66508862052b3f21ca577d57fd261577893c9c82d7018c.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 274, + 147, + 286 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 274, + 147, + 286 + ], + "spans": [ + { + "bbox": [ + 47, + 274, + 147, + 286 + ], + "type": "text", + "content": "4.2. Ablation Studies" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 293, + 287, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 293, + 287, + 400 + ], + "spans": [ + { + "bbox": [ + 46, + 293, + 287, + 400 + ], + "type": "text", + "content": "Effect of " + }, + { + "bbox": [ + 46, + 293, + 287, + 400 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathcal{P}}" + }, + { + "bbox": [ + 46, + 293, + 287, + 400 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 293, + 287, + 400 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathcal{D}}" + }, + { + "bbox": [ + 46, + 293, + 287, + 400 + ], + "type": "text", + "content": ". To evaluate the contribution of " + }, + { + "bbox": [ + 46, + 293, + 287, + 400 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathcal{P}}" + }, + { + "bbox": [ + 46, + 293, + 287, + 400 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 293, + 287, + 400 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathcal{D}}" + }, + { + "bbox": [ + 46, + 293, + 287, + 400 + ], + "type": "text", + "content": ", we train the model by removing each component solely and present the results in Tab. 2. The results of DADA(w/o " + }, + { + "bbox": [ + 46, + 293, + 287, + 400 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathcal{D}}" + }, + { + "bbox": [ + 46, + 293, + 287, + 400 + ], + "type": "text", + "content": ") and DADA(w/o " + }, + { + "bbox": [ + 46, + 293, + 287, + 400 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathcal{P}}" + }, + { + "bbox": [ + 46, + 293, + 287, + 400 + ], + "type": "text", + "content": ") are inferior to the full DADA method, verifying the effectiveness of both components. Besides, DADA(w/o " + }, + { + "bbox": [ + 46, + 293, + 287, + 400 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathcal{P}}" + }, + { + "bbox": [ + 46, + 293, + 287, + 400 + ], + "type": "text", + "content": ") achieves worse performance than DADA(w/o " + }, + { + "bbox": [ + 46, + 293, + 287, + 400 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathcal{D}}" + }, + { + "bbox": [ + 46, + 293, + 287, + 400 + ], + "type": "text", + "content": "), further indicating that the dual alignment consistency is more important than simply alleviating the domain shift." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 402, + 287, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 402, + 287, + 568 + ], + "spans": [ + { + "bbox": [ + 46, + 402, + 287, + 568 + ], + "type": "text", + "content": "Effect of Dual Alignment Consistency. To explore the effectiveness of Dual Alignment Consistency (DAC), we comprehensively investigate several alignment mechanisms and show the results in Tab. 3. Specifically, DADA (w/ text) selects the unique text with the highest similarity for each target video. Similarly, DADA (w/ video) selects the unique video with the highest similarity for each target text. DADA (w/o " + }, + { + "bbox": [ + 46, + 402, + 287, + 568 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 402, + 287, + 568 + ], + "type": "text", + "content": ") removes the threshold " + }, + { + "bbox": [ + 46, + 402, + 287, + 568 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 402, + 287, + 568 + ], + "type": "text", + "content": " of DAC. The results of DADA (w/ text) and DADA (w/ video) are worse than the full DADA method, demonstrating that the dual alignment mechanism is superior to aligning from only one modality stream. Meanwhile, the result of DADA (w/o " + }, + { + "bbox": [ + 46, + 402, + 287, + 568 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 402, + 287, + 568 + ], + "type": "text", + "content": ") is also inferior, which proves that the constraint on high similarities of truly aligned pairs is effective." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": "Furthermore, Fig. 5 shows the effect of threshold " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": " in dual alignment consistency within one batch during the training procedure. We can find that in Fig. 5(a), the number of dual aligned pairs (w/ " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": ") is relatively smaller than that of w/o " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": ". This is acceptable since the threshold " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": " constrains that aligned pairs should also have relatively high similarities compared to all pairs. As in Fig. 5(b), however, the accuracy of truly aligned pairs (w/ " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": ") is evidently higher than that of w/o " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": ", indicating that considering the threshold " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": " of DAC ensures the number of truly aligned pairs. As the training proceeds, the number of truly aligned pairs increases adaptively, which justifies the intuition that positive" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 312, + 72, + 420, + 163 + ], + "blocks": [ + { + "bbox": [ + 312, + 72, + 420, + 163 + ], + "lines": [ + { + "bbox": [ + 312, + 72, + 420, + 163 + ], + "spans": [ + { + "bbox": [ + 312, + 72, + 420, + 163 + ], + "type": "image", + "image_path": "f618b1be8555bae8ecc8b2e1a9392be52da843596c22ef885796ac277dfe1997.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 360, + 169, + 372, + 179 + ], + "lines": [ + { + "bbox": [ + 360, + 169, + 372, + 179 + ], + "spans": [ + { + "bbox": [ + 360, + 169, + 372, + 179 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 432, + 72, + 540, + 163 + ], + "blocks": [ + { + "bbox": [ + 432, + 72, + 540, + 163 + ], + "lines": [ + { + "bbox": [ + 432, + 72, + 540, + 163 + ], + "spans": [ + { + "bbox": [ + 432, + 72, + 540, + 163 + ], + "type": "image", + "image_path": "e88875ba0bb8ffa7584f7dfe3354d4d650e86c4eeb7133cd5c7d826cb103bb5d.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 480, + 168, + 493, + 178 + ], + "lines": [ + { + "bbox": [ + 480, + 168, + 493, + 178 + ], + "spans": [ + { + "bbox": [ + 480, + 168, + 493, + 178 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 180, + 545, + 214 + ], + "lines": [ + { + "bbox": [ + 305, + 180, + 545, + 214 + ], + "spans": [ + { + "bbox": [ + 305, + 180, + 545, + 214 + ], + "type": "text", + "content": "Figure 5. Analysis on threshold " + }, + { + "bbox": [ + 305, + 180, + 545, + 214 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 305, + 180, + 545, + 214 + ], + "type": "text", + "content": " of dual alignment consistency. As training epochs proceeds, (a) numbers of dual aligned pairs and (b) accuracy of truly aligned pairs in one batch." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 329, + 262, + 518, + 328 + ], + "blocks": [ + { + "bbox": [ + 305, + 227, + 545, + 261 + ], + "lines": [ + { + "bbox": [ + 305, + 227, + 545, + 261 + ], + "spans": [ + { + "bbox": [ + 305, + 227, + 545, + 261 + ], + "type": "text", + "content": "Table 4. Impact of different source datasets scales. Split-1/2/3 denotes 7,945/39,726/79,451 training data in source domain, respectively. Split-1 is adopted as the baseline." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 329, + 262, + 518, + 328 + ], + "lines": [ + { + "bbox": [ + 329, + 262, + 518, + 328 + ], + "spans": [ + { + "bbox": [ + 329, + 262, + 518, + 328 + ], + "type": "table", + "html": "
SplitsTf→MtTf→Md
R1↑R10↑MR↓R1↑R10↑MR↓
split-15.3024.545014.3448.7711
split-27.8231.383319.1054.028
split-39.0835.792420.5857.407
", + "image_path": "226a1f078836f0466420f7a306b69cecce8b4652eb296efb88130b3d09a03254.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_body" + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 340, + 512, + 351 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 340, + 512, + 351 + ], + "spans": [ + { + "bbox": [ + 306, + 340, + 512, + 351 + ], + "type": "text", + "content": "pairs are increasing and noisy ones are diminished." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 353, + 545, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 353, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 353, + 545, + 555 + ], + "type": "text", + "content": "Impact of source datasets scales. To assess the impact of source datasets scales on the UDAVR task, we randomly split the TGIF dataset into three splits: Split-1/2/3 denotes 7,945/39,726/79,451 training data in source domain, respectively. The results are shown in Tab. 4. We observe that on one hand, increasing the number of training data in source dataset brings a trend of performance gain (split-1 to split-2). This is reasonable since large-scale source dataset usually provide more knowledge when transferring to the target domain. On the other hand, when the number goes to a relatively large value (split-2 to split-3), the performance gain is mostly marginal when transferring from TGIF to MSVD. We argue that the pairwise misalignment issue in UDAVR task can not be solved by simply increasing the number of source training data. Considering the data volume of MSR-VTT and MSVD, we adopt split-1 as the baseline for TGIF dataset." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 557, + 545, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 545, + 688 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 545, + 688 + ], + "type": "text", + "content": "Generalization to different video-text retrieval methods. As shown in Tab. 5, we implement several state-of-the-art video-text retrieval methods and the corresponding combinations with our DADA. Clearly, our method consistently improves the performances on target domain when combined with original baselines. Surprisingly, when combined with CLIP based methods, our DADA can still contribute to a remarkable performance gain. This verifies that the pairwise misalignment issue can't be diminished by merely adopting more powerful cross-modal retrieval methods, justifying the efficacy of our method." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "Sensitivity of Hyper-parameters. We conduct experiments under the setting of " + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{Tf}\\rightarrow \\mathrm{Mt}" + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{Tf}\\rightarrow \\mathrm{Md}" + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": ", and present" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18967" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 86, + 82, + 187, + 171 + ], + "blocks": [ + { + "bbox": [ + 86, + 82, + 187, + 171 + ], + "lines": [ + { + "bbox": [ + 86, + 82, + 187, + 171 + ], + "spans": [ + { + "bbox": [ + 86, + 82, + 187, + 171 + ], + "type": "image", + "image_path": "e26ddef27b8d8be1f38ba5906f6a0659809037be8d0ae6c9bb7966323bc83b70.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 103, + 182, + 156, + 191 + ], + "lines": [ + { + "bbox": [ + 103, + 182, + 156, + 191 + ], + "spans": [ + { + "bbox": [ + 103, + 182, + 156, + 191 + ], + "type": "text", + "content": "(a) Source Only" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 197, + 82, + 299, + 173 + ], + "blocks": [ + { + "bbox": [ + 197, + 82, + 299, + 173 + ], + "lines": [ + { + "bbox": [ + 197, + 82, + 299, + 173 + ], + "spans": [ + { + "bbox": [ + 197, + 82, + 299, + 173 + ], + "type": "image", + "image_path": "68ab1b328bbf4f35ca1d27f5ca9c827e78a529f2a8a40d453869e242b0a14b20.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 217, + 182, + 265, + 191 + ], + "lines": [ + { + "bbox": [ + 217, + 182, + 265, + 191 + ], + "spans": [ + { + "bbox": [ + 217, + 182, + 265, + 191 + ], + "type": "text", + "content": "(b) MMD [40]" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 201, + 547, + 234 + ], + "lines": [ + { + "bbox": [ + 46, + 201, + 547, + 234 + ], + "spans": [ + { + "bbox": [ + 46, + 201, + 547, + 234 + ], + "type": "text", + "content": "Figure 6. The t-SNE visualizations of (a) Source Only, (b) MMD, (c) ACP and (d) Our method. Blue/red denotes source/target domain, while circles/triangles denote videos/texts. Our method progressively generates truly aligned video-text pairs in target domain, i.e., red circles and triangles are close together if they are semantically relevant (best viewed in color)." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 309, + 82, + 411, + 173 + ], + "blocks": [ + { + "bbox": [ + 309, + 82, + 411, + 173 + ], + "lines": [ + { + "bbox": [ + 309, + 82, + 411, + 173 + ], + "spans": [ + { + "bbox": [ + 309, + 82, + 411, + 173 + ], + "type": "image", + "image_path": "974c25b586687b929a959f1dc2fb91740ca56e29172fe78e3decbccc5490554f.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 331, + 182, + 374, + 191 + ], + "lines": [ + { + "bbox": [ + 331, + 182, + 374, + 191 + ], + "spans": [ + { + "bbox": [ + 331, + 182, + 374, + 191 + ], + "type": "text", + "content": "(c) ACP [39]" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 420, + 82, + 523, + 173 + ], + "blocks": [ + { + "bbox": [ + 420, + 82, + 523, + 173 + ], + "lines": [ + { + "bbox": [ + 420, + 82, + 523, + 173 + ], + "spans": [ + { + "bbox": [ + 420, + 82, + 523, + 173 + ], + "type": "image", + "image_path": "84c19c36784c98e1860244db92d9e799b28cf713b1fecfded721207f3038c22a.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 438, + 182, + 490, + 191 + ], + "lines": [ + { + "bbox": [ + 438, + 182, + 490, + 191 + ], + "spans": [ + { + "bbox": [ + 438, + 182, + 490, + 191 + ], + "type": "text", + "content": "(d) Our method" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 50, + 289, + 286, + 448 + ], + "blocks": [ + { + "bbox": [ + 47, + 254, + 287, + 286 + ], + "lines": [ + { + "bbox": [ + 47, + 254, + 287, + 286 + ], + "spans": [ + { + "bbox": [ + 47, + 254, + 287, + 286 + ], + "type": "text", + "content": "Table 5. Generalization to different video-text retrieval methods: (a) Single feature based methods (b) Multi-feature based methods and (c) CLIP based methods." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 289, + 286, + 448 + ], + "lines": [ + { + "bbox": [ + 50, + 289, + 286, + 448 + ], + "spans": [ + { + "bbox": [ + 50, + 289, + 286, + 448 + ], + "type": "table", + "html": "
BackboneTf→MtTf→Md
R1↑R10↑MR↓R1↑R10↑MR↓
(a)HGR [10]2.2011.981549.2537.7321
HGR + DADA3.8218.759610.9739.1620
GPO [5]2.6913.631449.3937.7720
GPO + DADA5.3024.545014.3448.7711
(b)CE [37]2.9314.712210.339.218
CE + DADA5.6725.304715.2049.8711
MMT [21]4.2022.307812.4546.5318
MMT + DADA6.2327.313817.3050.3410
(c)CLIP4CLIP [44]7.2028.503519.2350.238
CLIP4CLIP + DADA8.6233.122821.3058.906
CLIP2Video [19]7.8031.503120.2351.208
CLIP2Video + DADA8.9036.502523.1063.65
", + "image_path": "e6c3435853137534454c0ceec536b290bfad7b487b1a1160b146d570a3a45d88.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 53, + 464, + 161, + 554 + ], + "blocks": [ + { + "bbox": [ + 53, + 464, + 161, + 554 + ], + "lines": [ + { + "bbox": [ + 53, + 464, + 161, + 554 + ], + "spans": [ + { + "bbox": [ + 53, + 464, + 161, + 554 + ], + "type": "image", + "image_path": "ea2ba4db78a36c44e8731484fda6e52efd7e444c6fa2e49cf59d400bb54f3c82.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 90, + 559, + 243, + 571 + ], + "lines": [ + { + "bbox": [ + 90, + 559, + 243, + 571 + ], + "spans": [ + { + "bbox": [ + 90, + 559, + 243, + 571 + ], + "type": "text", + "content": "Figure 7. Sensitivity of hyper-parameters." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 174, + 464, + 281, + 554 + ], + "blocks": [ + { + "bbox": [ + 174, + 464, + 281, + 554 + ], + "lines": [ + { + "bbox": [ + 174, + 464, + 281, + 554 + ], + "spans": [ + { + "bbox": [ + 174, + 464, + 281, + 554 + ], + "type": "image", + "image_path": "ec4e7faa404804109d3770e63ce6686f10304810d322922481cf2f6d50c07141.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 591, + 287, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 591, + 287, + 675 + ], + "spans": [ + { + "bbox": [ + 46, + 591, + 287, + 675 + ], + "type": "text", + "content": "the sensitivity of hyper-parameters " + }, + { + "bbox": [ + 46, + 591, + 287, + 675 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 591, + 287, + 675 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 591, + 287, + 675 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 591, + 287, + 675 + ], + "type": "text", + "content": " in Fig. 7. Within a wide range of " + }, + { + "bbox": [ + 46, + 591, + 287, + 675 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 591, + 287, + 675 + ], + "type": "text", + "content": " in [0.1, 0.9], the performance only varies in a small range, indicating the robustness to different choices of " + }, + { + "bbox": [ + 46, + 591, + 287, + 675 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 591, + 287, + 675 + ], + "type": "text", + "content": ". Similarly, when progressively increasing threshold " + }, + { + "bbox": [ + 46, + 591, + 287, + 675 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 591, + 287, + 675 + ], + "type": "text", + "content": " in DAC from 16 to 1,024, our method consistently performs well and achieves the best when " + }, + { + "bbox": [ + 46, + 591, + 287, + 675 + ], + "type": "inline_equation", + "content": "T = 128" + }, + { + "bbox": [ + 46, + 591, + 287, + 675 + ], + "type": "text", + "content": ". Thus, we set " + }, + { + "bbox": [ + 46, + 591, + 287, + 675 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 591, + 287, + 675 + ], + "type": "text", + "content": " to 0.7 and " + }, + { + "bbox": [ + 46, + 591, + 287, + 675 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 591, + 287, + 675 + ], + "type": "text", + "content": " to 128 under all settings." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "Feature Visualisations. We randomly choose 100 pairs in source and target domain respectively, and show the t-SNE [57] visualizations of Source Only, MMD, ACP and" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 255, + 547, + 364 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 255, + 547, + 364 + ], + "spans": [ + { + "bbox": [ + 304, + 255, + 547, + 364 + ], + "type": "text", + "content": "our method in Fig. 6. As can be seen, (a) Source Only shows that blue and red features are clearly separated, indicating the video and text domain shifts. (b) MMD and (c) ACP alleviate the domain shift, whereas inevitably mix up target videos and texts, ignoring whether they are a relevant pair or not. Obviously, our method not only diminishes the domain shift, i.e., blue and red features are mixed up, but also generates aligned pairs in target domain, i.e., red circles and triangles are close together if relevant." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 379, + 507, + 391 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 379, + 507, + 391 + ], + "spans": [ + { + "bbox": [ + 305, + 379, + 507, + 391 + ], + "type": "text", + "content": "4.3. Comparison with the State-of-the-arts" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 399, + 545, + 543 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 399, + 545, + 543 + ], + "spans": [ + { + "bbox": [ + 304, + 399, + 545, + 543 + ], + "type": "text", + "content": "We compare our method with several state-of-the-art baselines across three categories, i.e., Source Only, DA methods and UDAVR methods. As a lower bound, we include the non-adapted Source Only results, which directly applies the model trained on the source domain to the target domain. We also implement five classification-based (i.e. typical) DA methods and modify them for the UDAVR task, including MMD [40], CORAL [53], DANN [22], IDM [14] and SCDA [33]. Moreover, we compare to three recently proposed UDAVR methods, i.e., MAN [17], CAPQ [9] and ACP [39]. For fairness, all methods adopt the same features and the backbone network as [5]." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "text", + "content": "Tab. 6 shows that: (1) As the lower bound, Source Only achieves the worst performance, which identifies the existed domain shift problem. (2) Traditional DA methods in setting (a) are ineffective for the challenging UDAVR task, which can only slightly outperform the Source Only baseline. We owe this to that there exists no identical label set in UDAVR, which is the key difference of classification tasks. (3) Our method consistently outperforms other UDAVR methods in setting (b) on all adaptation directions across the three datasets, which demonstrates the effectiveness of dual alignment consistency. Compared with the SOTA method ACP, DADA achieves " + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "inline_equation", + "content": "20.18\\%" + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "inline_equation", + "content": "18.61\\%" + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "text", + "content": " relative improvements on " + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{R@1}" + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "text", + "content": " under the setting of Tf " + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "text", + "content": " Mt and Tf " + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "text", + "content": " Md respectively." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18968" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 66, + 83, + 525, + 256 + ], + "blocks": [ + { + "bbox": [ + 85, + 70, + 509, + 81 + ], + "lines": [ + { + "bbox": [ + 85, + 70, + 509, + 81 + ], + "spans": [ + { + "bbox": [ + 85, + 70, + 509, + 81 + ], + "type": "text", + "content": "Table 6. Comparison with different baselines. We denote Tf the TGIF, Mt the MSR-VTT and Md the MSVD dataset." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 66, + 83, + 525, + 256 + ], + "lines": [ + { + "bbox": [ + 66, + 83, + 525, + 256 + ], + "spans": [ + { + "bbox": [ + 66, + 83, + 525, + 256 + ], + "type": "table", + "html": "
MethodTf→MtMt→TfTf→MdMd→TfMt→MdMd→Mt
R1↑R10↑MR↓R1↑R10↑MR↓R1↑R10↑MR↓R1↑R10↑MR↓R1↑R10↑MR↓R1↑R10↑MR↓
Source Only2.6913.631446.3025.43609.3937.77203.8016.9910215.0246.96122.5013.27136
(a)MMD [40]2.6813.591356.7727.11549.1136.11233.5016.2811915.3147.65122.6213.18136
CORAL [53]2.7414.071286.5626.49529.4437.87213.6517.3410815.6549.43112.6513.34138
DANN [22]2.7613.941276.8627.17489.2738.00203.7416.7210315.6748.67112.6213.17134
IDM [14]2.5913.111497.1225.35608.0535.51233.2415.7812013.9647.77122.5412.39165
SCDA [33]2.7914.221306.9226.70539.8437.11223.3017.0210815.6448.65112.5512.98138
(b)MAN [17]2.5312.981446.4225.96638.8437.06213.0616.3111915.0548.51112.4012.00174
CAPQ [9]3.4617.021107.3325.64629.3037.97213.9717.7511315.6649.08113.3515.47158
ACP [39]4.4121.72647.8326.725012.0941.38185.1221.468217.8754.3485.9025.6854
OursDADA5.3024.54508.2128.974514.3448.77116.0322.527818.9757.9376.4027.6142
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Qualitative results of query texts and corresponding videos along with the changes in rank A←B←C, where A denotes the rank of DADA, B the ACP method and C the Source Only." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 522, + 160, + 534 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 522, + 160, + 534 + ], + "spans": [ + { + "bbox": [ + 47, + 522, + 160, + 534 + ], + "type": "text", + "content": "4.4. Qualitative Results" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 540, + 288, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 540, + 288, + 625 + ], + "spans": [ + { + "bbox": [ + 46, + 540, + 288, + 625 + ], + "type": "text", + "content": "As in Fig. 8, given a query text, we present how the rank of the relevant video changes with different methods. Obviously, our method results in higher ranks of relevant videos compared with Source Only and ACP. Interestingly, our method performs worse given the query 'A fox is diving into the snow', which might be owed to the confusion of the white fox and the background." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 634, + 119, + 645 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 634, + 119, + 645 + ], + "spans": [ + { + "bbox": [ + 47, + 634, + 119, + 645 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "type": "text", + "content": "In this paper, we focus on the notoriously challenging task, i.e., UDA Video-text Retrieval (UDAVR), and develop the simple yet effective Dual Alignment Domain Adaptation (DADA) method. We introduce the cross-modal semantic embedding and domain adaptation to simultane" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 523, + 545, + 595 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 523, + 545, + 595 + ], + "spans": [ + { + "bbox": [ + 304, + 523, + 545, + 595 + ], + "type": "text", + "content": "ously generate discriminative source features and alleviate the video and text domain shifts. To tackle the pairwise alignment issue, we propose the Dual Alignment Consistency (DAC), which progressively generates truly aligned target pairs and ensures the discriminability of target features. Extensive experiments justify our superiority." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 609, + 416, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 609, + 416, + 623 + ], + "spans": [ + { + "bbox": [ + 306, + 609, + 416, + 623 + ], + "type": "text", + "content": "6. Acknowledgement" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 629, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 715 + ], + "type": "text", + "content": "This work was supported by the National Key R&D Program of China under Grant 2022YFB3103500, the National Natural Science Foundation of China under Grants 62106258, 62006242 and 62202459, and the China Postdoctoral Science Foundation under Grant 2022M713348 and 2022TQ0363, and Young Elite Scientists Sponsorship Program by BAST (NO.BYESS2023304)." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18969" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "text", + "content": "[1] Nakul Agarwal, Yi-Ting Chen, Behzad Dariush, and Ming-Hsuan Yang. 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IEEE Transactions on Image Processing, 30:1180-1192, 2020. 2, 4" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "text", + "content": "18972" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Dual-Bridging With Adversarial Noise Generation for Domain Adaptive rPPG Estimation/d848ec4a-af95-428f-9e60-c6e80b3b4e6b_content_list.json b/2023/Dual-Bridging With Adversarial Noise Generation for Domain Adaptive rPPG Estimation/d848ec4a-af95-428f-9e60-c6e80b3b4e6b_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..82f67780e283ec5283e5009f1d35bbe04e58f47b --- /dev/null +++ b/2023/Dual-Bridging With Adversarial Noise Generation for Domain Adaptive rPPG Estimation/d848ec4a-af95-428f-9e60-c6e80b3b4e6b_content_list.json @@ -0,0 +1,1516 @@ +[ + { + "type": "text", + "text": "Dual-bridging with Adversarial Noise Generation for Domain Adaptive rPPG Estimation", + "text_level": 1, + "bbox": [ + 94, + 128, + 875, + 174 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Jingda Du*, Si-Qi Liu*, Bochao Zhang, Pong C. Yuen \nDepartment of Computer Science, Hong Kong Baptist University, Hong Kong \ncsjddu, siqiliu, csbczhang, pcyuen @comp.hkbu.edu.hk", + "bbox": [ + 176, + 203, + 792, + 256 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 291, + 313, + 306 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The remote photoplethysmography (rPPG) technique can estimate pulse-related metrics (e.g. heart rate and respiratory rate) from facial videos and has a high potential for health monitoring. The latest deep rPPG methods can model in-distribution noise due to head motion, video compression, etc., and estimate high-quality rPPG signals under similar scenarios. However, deep rPPG models may not generalize well to the target test domain with unseen noise and distortions. In this paper, to improve the generalization ability of rPPG models, we propose a dual-bridging network to reduce the domain discrepancy by aligning intermediate domains and synthesizing the target noise in the source domain for better noise reduction. To comprehensively explore the target domain noise, we propose a novel adversarial noise generation in which the noise generator indirectly competes with the noise reducer. To further improve the robustness of the noise reducer, we propose hard noise pattern mining to encourage the generator to learn hard noise patterns contained in the target domain features. We evaluated the proposed method on three public datasets with different types of interferences. Under different cross-domain scenarios, the comprehensive results show the effectiveness of our method.", + "bbox": [ + 75, + 323, + 473, + 672 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 700, + 209, + 715 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "With the development of rPPG technology, physiological metrics such as heart rate [27], heart rate variability [34], respiratory rate [21] can also be estimated from facial videos. Deep learning-based rPPG methods overcome non-physiological intensity variations [30, 49] and model noise in training samples [24, 28]. Despite the high accuracy under intra-dataset evaluations, the deep rPPG models may not be able to generalize well to unseen interferences in the test domain. The domain gap is mainly from unseen non-physiological interferences such as lighting conditions,", + "bbox": [ + 75, + 724, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/69a4b7f67cc20dde76cff892cc346fc36b4c52c233514d9d1b08c08abff9b352.jpg", + "image_caption": [ + "(a) GAN-based Noise Modeling" + ], + "image_footnote": [], + "bbox": [ + 509, + 287, + 676, + 349 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/52d17f5e609f0464fe54aa68ab7fec9d8437622d9032f3f5a67608612b140eb8.jpg", + "image_caption": [ + "(b) Intuitive UDA Solution", + "Figure 1. The comparison between (a) typical intra-dataset adversarial rPPG noise modeling, (b) an intuitive UDA framework for rPPG feature alignment, and (c) our proposed dual-bridging network with adversarial noise modeling and hard noise pattern mining $(HM)$ . Here SYN denotes synthetic data, DT is for the denoised target domain, $G$ , $D$ , and $NR$ denotes the generator, domain classifier, and noise reducer, respectively." + ], + "image_footnote": [], + "bbox": [ + 509, + 378, + 683, + 441 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/6260a258ce919b07f23efdd9ce72255d5aa70b4ec89876708b6fac498dd91923.jpg", + "image_caption": [ + "(c) Dual-bridging with Adversarial Noise Generation (Ours)" + ], + "image_footnote": [], + "bbox": [ + 699, + 287, + 883, + 436 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "camera sensors, video compression algorithms, facial expressions, etc. They can induce distortions in estimated rPPG signals and reduce both the accuracy and the reliability of pulse-related metrics estimation. Considering it is hard to cover all interferences during the training stage, to improve the usability of rPPG in realistic applications, one main challenge is how to boost the generalizability of rPPG models to unseen scenarios.", + "bbox": [ + 496, + 598, + 893, + 717 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In recent research of rPPG, both deep learning-based frameworks and mechanisms [45, 46, 49] are proposed to overcome the non-physiological intensity variations. GAN-based disentanglement learning has also been adopted to reduce the noise from pseudo [28] or synthesized [24] noisy features. We summarize this approach in Figure 1 (a) where a discriminator is employed to distinguish the generated feature (SYN in figure) from the original one. These methods can perform well under intra-dataset evaluation settings since the in-distribution noise patterns are thoroughly investigated with a large number of adversarial learning iterations. However, they may fail when encountering unseen", + "bbox": [ + 496, + 719, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* Equal contribution", + "bbox": [ + 94, + 886, + 207, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "10355", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "domains in real application scenarios since noise patterns may be different from the ones of training data.", + "bbox": [ + 76, + 90, + 468, + 121 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Intuitively, the unsupervised domain adaptation (UDA) technique can help in bridging the gap between source and target domain [7, 14, 17, 44]. As shown in Figure 1 (b), a noise reducer module $NR$ that aims to obtain noise-free domain-invariant representations can be learned by fighting against the domain classifier $D$ . However, this intuitive solution may not work well since the domain classification may not be able to give sufficient information for $NR$ to identify whether the feature components are noise or physiological information. Directly aligning the rPPG features from different domains may end up distorting the physiological information since they are from different subjects. The ground-truth PPG (GT-PPG) signal with detailed waveform information helps preserve the physiological information and can provide much more informative guidance with the regression task. However, GT-PPG is available in the source domain but not the target domain. How to leverage the source domain GT-PPG to train $NR$ to be robust to the noise from the target domain is the key issue to be solved in this work. To achieve it we propose the dual bridging noise modeling network as shown in Figure 1 (c). The first bridging works as high-level guidance where the denoised target domain feature is adversarially pulled to the source domain feature (as Figure 1 (b)). On top of it, the second bridging aims to help synthesize the target domain noise and inject it into the source domain denoised feature so that the GT-PPG regression can help finetune the $NR$ for better robustness in the target domain. An adversarial noise generation module $(G|NR)$ is designed where the generator is conditioned on the $NR$ so that it keeps on overcoming the complex noise pattern that can hardly be solved in the first bridging. With the high-level guidance (first bridging) and detailed signal regression (second bridging), the $NR$ can handle the target domain noise better and therefore improve the accuracy of rPPG estimation in the target domain. To further discover the remaining noise vestige, we build a hard noise pattern mining mechanism to squeeze the unsolved local noise pattern from the denoised target feature so that $G|NR$ can thoroughly synthesize it.", + "bbox": [ + 76, + 125, + 472, + 715 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In sum, the contributions of this work are: (1) A dual-bridging noise modeling network that adapts target domain noise in a coarse-to-fine manner. (2) An adversarial noise generation mechanism to progressively synthesize and inject the hard target domain noisy features into the source domain while keeping the physiological information. (3) A hard noise pattern mining mechanism to further explore the target domain noise patterns with larger variations. We evaluated the proposed method on three public datasets with various types of interferences including facial motion and expression, video compression, skin tone, and heartbeat ranges. Under different cross-domain scenarios, the com", + "bbox": [ + 75, + 719, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The prehensive results show the effectiveness of our method.", + "bbox": [ + 498, + 90, + 870, + 107 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 121, + 640, + 137 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Remote physiological estimation", + "text_level": 1, + "bbox": [ + 500, + 147, + 782, + 162 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Traditional rPPG methods [5, 16, 32, 39, 40, 41] estimate pulse signal from facial videos by extracting and modeling the detailed heartbeat-caused skin color variation. To estimate pulse-induced intensity variations with more details from facial videos, deep learning-based networks and mechanisms have been proposed. With facial video input, various spatial-temporal neural networks have been developed [4, 20, 22, 23, 37, 48, 49]. To evaluate the effectiveness, rPPG datasets with various interferences including head motion [36], facial expression [15, 39], video compression [9], and skin color [42] are constructed. In addition, rPPG estimation can be conducted from pre-processed representations like normalized difference [3, 18, 21, 30], spatial-temporal map [24, 28]. To further improve robustness, self-adaptive [3, 21] and background-guided [19, 30] attention mechanisms have been proposed to emphasize important facial regions in physiological representation. Furthermore, [28] proposed the cross-verified strategy to disentangle noise and physiological representation and [24] proposed to model in-distribution noise for learning noise-resistant physiological representation. [25, 26] proposed to synthesize diverse facial videos for rPPG estimation. Unsupervised learning-based methods [8, 37] are also proposed to learn rPPG estimation from unlabeled facial videos. However, the previously proposed methods are prone to experience performance drops in cross-dataset evaluation, where the target domain may contain unseen noise. This is due to unseen noise patterns that may not be fully overcome, and the physiological representation may be polluted and cause distortions in the rPPG signals.", + "bbox": [ + 496, + 170, + 893, + 625 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Unsupervised domain adaptation methods", + "text_level": 1, + "bbox": [ + 500, + 635, + 859, + 651 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In recent research on computer vision, many unsupervised domain adaptation methods have been proposed to learn domain-invariant representation. [7] proposed to suppress domain-invariant information with domain label guided adversarial training. [33] proposed a bi-directional generation framework that can map target domain samples to the source domain and preserve semantic information for classification. [14] proposed to use adversarial domain training and distributional feature alignment guided by maximum density divergence to achieve adaptation. [43] considered that domain adversarial training may not be coordinated with the main task and proposed using meta-learning to improve the effectiveness of feature alignment. Unlike common computer vision tasks, feature alignment in the rPPG estimation requires more detailed information which cannot be fully provided by domain labels. There", + "bbox": [ + 496, + 659, + 893, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "10356", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/9d2bf40e180d984b60d5b1068046ab31a1684675c4a88cacb499c8eeab28b5c1.jpg", + "image_caption": [ + "Figure 2. Framework of the dual-bridging noise modeling network. The dual-bridging can reduce the domain discrepancy in the feature space by training the noise reducer with both high-level guidance from domain classification and detailed waveform guidance from synthetic features regression. The adversarial noise generation forces the generator $G$ to compete with the noise reducer $NR$ and synthesize noisy features with unsolved noise in the target domain. The hard noise pattern mining removes high-quality temporal features and encourages the generator to further explore hard noise patterns in the target domain." + ], + "image_footnote": [], + "bbox": [ + 109, + 88, + 851, + 385 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "fore, we propose the dual-bridging noise modeling network to take advantage of both domain labels and the source domain ground truth to guide the rPPG feature alignment.", + "bbox": [ + 75, + 489, + 470, + 537 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Proposed Method", + "text_level": 1, + "bbox": [ + 76, + 556, + 250, + 573 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The overview of the proposed dual-bridging noise modeling network is shown in Figure 2. Given the input face video from the source and target domain, we construct the STMap (details are in section 4.2) as the input of the feature extractor and then perform dual-bridging noise modeling on the middle representation. The first bridging provides high-level guidance where the source feature $f_{j}^{s}$ and the denoised target feature $f_{i}^{t}$ are pulled together with the domain classifier. The synthesized target domain feature $f_{j}^{s}$ is obtained from the $f_{i}^{t}$ through the adversarial noise generation module. The second bridge aims to pull $f_{j}^{s}$ to $f_{i}^{t}$ so that the target domain noise can be overcome by $NR$ with the guidance of PPG $y_{s}$ (regression) The generator in the adversarial noise generation module is conditioned on the $NR$ so that it keeps on overcoming the complex noise pattern that can hardly be solved in the first bridging. With the dual-bridging noise modeling that contains both high-level (first bridge) and detailed waveform guidance (second bridge), the $NR$ can handle the target domain noise better. Finally, $NR$ works with the feature extractor and rPPG estimator to do the rPPG estimation in the target domain.", + "bbox": [ + 75, + 583, + 470, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Dual-bridging", + "text_level": 1, + "bbox": [ + 500, + 489, + 645, + 506 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "With respect to the feature extractor $\\Theta$ , we define source domain features as $F_{s} = \\{f_{j}^{s}\\}_{j = 1}^{M}$ and target domain features as $F_{t} = \\{f_{i}^{t}\\}_{i = 1}^{N}$ , where $f_{j}^{s} = \\Theta (x_{j}^{s})$ and $f_{i}^{t} = \\Theta (x_{i}^{t})$ . Since the rPPG patterns are similar between different participants, the pre-trained feature extractor can preserve enough physiological information in $F_{t}$ and noise modeling is the key to noise reduction of the target domain features. Detailed information for guidance is necessary to overcome the complex noise in the target domain features.", + "bbox": [ + 496, + 513, + 890, + 650 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To reduce the noise contained in $F_{t}$ , we propose the adaptive noise reduction bridging to reduce the noise contained in target domain features supervised by the domain classifier. In this bridging, we design the noise reducer with the noise estimation function $\\Phi$ in a residual way as follows:", + "bbox": [ + 496, + 651, + 890, + 726 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {f} _ {i} ^ {t} = f _ {i} ^ {t} - \\Phi \\left(f _ {i} ^ {t}\\right) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 635, + 739, + 890, + 757 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\hat{f}_i^t$ is a denoised physiological feature and we define $\\hat{F}_t = \\{\\hat{f}_i^t\\}_{i=1}^N$ as the denoised target domain. The direct estimation of high-quality physiological features could be hard, and we choose to estimate the noise and use the residual structure to reduce the noise in the target domain features. We build an adversarial training between the noise reducer $\\Phi$ and the domain classifier $D$ as follows:", + "bbox": [ + 496, + 763, + 890, + 869 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\max _ {D} \\min _ {\\Phi} L _ {N R} = \\mathbb {E} [ \\| 1 - D \\left(f _ {j} ^ {s}\\right) \\| _ {2} ] + \\mathbb {E} [ \\| D \\left(\\hat {f} _ {i} ^ {t}\\right) \\| _ {2} ] \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 509, + 880, + 890, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "10357", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "With high-level guidance from domain classification, some simple noise patterns can be overcome, and less noisy features can be aligned. However, high-level guidance may not overcome complex noise patterns without detailed waveform information for guidance. And the brute-force feature alignment may even change the physiological information of rPPG features when complex noise patterns are encountered. The phenomenon can be reflected by our ablation study in section 4.3.", + "bbox": [ + 75, + 90, + 468, + 226 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To involve detailed information for supervision, we propose the complex noise generation bridging to generate target domain noise and synthesize noisy features to guide the noise reducer. From the source domain direction, we estimate the noise patterns in the target domain by generating noise and synthesizing noisy features as follows:", + "bbox": [ + 75, + 227, + 468, + 316 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\bar {f} _ {j} ^ {s} = f _ {j} ^ {s} + \\Psi (n _ {k}) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 210, + 325, + 468, + 347 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\overline{f}_j^s$ is a raw noisy feature, $n_k$ is random noise, and $\\Psi$ is the generator. And we define the synthetic feature domain $\\hat{F}_s = \\{\\hat{f}_j^s\\}_{j=1}^M$ as follows:", + "bbox": [ + 76, + 357, + 468, + 405 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {f} _ {j} ^ {s} = \\bar {f} _ {j} ^ {s} - \\Phi \\left(\\bar {f} _ {j} ^ {s}\\right) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 212, + 415, + 468, + 436 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To control the range of noise generation, we build the adversarial training between the noise generator and the domain classifier with respect to the denoised target domain as follows:", + "bbox": [ + 75, + 445, + 468, + 503 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\underset {D} {\\max} \\underset {\\Psi} {\\min} L _ {G} = \\mathbb {E} [ \\| 1 - D (f _ {j} ^ {s}) \\| _ {2} ] + \\mathbb {E} [ \\| D (\\overline {{f}} _ {j} ^ {s}) \\| _ {2} ] \\\\ + \\mathbb {E} [ \\| D (\\hat {f} _ {i} ^ {t}) \\| _ {2} ] \\quad (5) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 94, + 518, + 468, + 564 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this bridging, the domain classifier can guide the generator to learn target domain noise patterns and synthesize noisy features with preserved physiological information. Thus, the source domain PPG signals $y_{j}^{s}$ can be utilized to guide the noise reducer to overcome generated complex noise patterns as follows:", + "bbox": [ + 75, + 573, + 468, + 662 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {S Y N} = 1 - r \\left(E \\left(\\hat {f} _ {j} ^ {s}\\right), y _ {j} ^ {s}\\right) \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 672, + 468, + 693 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$E$ is the rPPG estimator, and $r$ is the Pearson correlation function. With this bridging, the physiological information can be preserved in the noise reduction and the other bridging can align more target domain features under large domain discrepancy.", + "bbox": [ + 75, + 702, + 468, + 777 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Adversarial noise generation", + "text_level": 1, + "bbox": [ + 76, + 786, + 333, + 801 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "With the guidance from the domain classifier, part of the target domain noise patterns can be generated. However, in the adversarial training process, the generator may not fully explore target domain noise patterns. To comprehensively explore the target domain noise for rPPG feature alignment, we propose a novel adversarial noise generation. As shown", + "bbox": [ + 75, + 809, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/bbd318603034ac46a71b923721f314f8c178fd598942fc7bacc0adb3b6c1f37e.jpg", + "image_caption": [ + "Figure 3. Illustration of hard noise pattern mining." + ], + "image_footnote": [], + "bbox": [ + 522, + 87, + 874, + 148 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "in Figure 2, the generator is conditioned on the noise reducer and forced to explore the unsolved noise contained in the target domain features. The noise reducer is trained with the synthetic features and corresponding PPG signals to overcome the generated noise. The adversarial correlation between the generator and the noise reducer is shown as follows:", + "bbox": [ + 496, + 203, + 890, + 306 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\max _ {\\Psi} \\min _ {\\Phi} L _ {A N G} = \\mathbb {E} [ \\| 1 - D (\\hat {f} _ {j} ^ {s}) \\| _ {2} ] + \\mathbb {E} [ 1 - r (E (\\hat {f} _ {j} ^ {s}), y _ {j} ^ {s}) ] \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 319, + 890, + 354 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This adversarial training is based on two different optimization functions, but not the gradient reverse layer. Therefore, the novel noise patterns are not generated based on adversarial attacks but are searched from unsolved noise patterns in the target domain. With our adversarial noise generation, the dual-bridging structure can progressively generate target domain noise patterns, and the noise reduction ability can be significantly improved.", + "bbox": [ + 496, + 356, + 890, + 477 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Hard noise pattern mining", + "text_level": 1, + "bbox": [ + 500, + 487, + 740, + 503 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To further improve the robustness of the noise reducer, we propose the hard noise pattern mining as illustrated in Figure 3. Considering the redundancy of rPPG estimation, features with one or several high-quality temporal features can contribute to accurate estimation. Thus, the noise reducer may just learn to overcome relatively simple noise patterns and some hard noise patterns may not be learned. To further explore the hard noise patterns, we need to reduce the shortcuts for noise reduction and generate hard noise patterns for training. In our hard noise pattern mining module, we identify high-quality temporal features with respect to the morphology consistency $M$ which is defined as follows:", + "bbox": [ + 496, + 510, + 890, + 705 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nM = \\max _ {t = 1} ^ {n} r \\left(g _ {0: T}, g _ {t: t + T}\\right) \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 607, + 705, + 890, + 729 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$r$ is the Pearson correlation, $g$ is a temporal feature, $t$ is the sliding start point, and $T$ is the time length of morphology consistency evaluation. With respect to the morphology consistency, we define temporal features with significant periodicity as high-quality features. After identifying high-quality temporal features, we can remove the corresponding feature slice and preserve hard slices for noise generation. Correspondingly, more hard noise patterns will be generated and the noise reduction ability can be further improved for rPPG feature alignment.", + "bbox": [ + 496, + 734, + 890, + 883 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The detailed optimization process of our proposed", + "bbox": [ + 517, + 885, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "10358", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Algorithm 1 The optimization process for our dual-bridging algorithm.", + "bbox": [ + 76, + 90, + 467, + 119 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Input: Noise generator $\\Psi$ , noise reducer $\\Phi$ and domain classifier $D$ , total epochs $L$ , mini-batch $B$ , source domain samples $x_{j}^{s}$ , source domain labels $y_{j}^{s}$ , target domain samples $x_{i}^{t}$ .", + "bbox": [ + 76, + 122, + 467, + 183 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "for $l = 1$ to $L$ do", + "bbox": [ + 94, + 186, + 210, + 199 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "for $b = 1$ to $B$ do", + "bbox": [ + 117, + 200, + 238, + 213 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Obtain $f_{j}^{s}$ and $f_{i}^{t}$ with pre-trained feature extractor from $x_{j}^{s}$ and $x_{i}^{t}$", + "bbox": [ + 94, + 215, + 467, + 246 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Obtain $\\hat{f}_i^t$ with noise reducer", + "bbox": [ + 143, + 248, + 334, + 263 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Update noise reducer $\\Phi$ and domain classifier $D$ with $L_{DE}$", + "bbox": [ + 94, + 265, + 467, + 292 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Generate $\\overline{f}_j^s$ and $\\hat{f}_j^s$ with updated noise reducer and noise generator", + "bbox": [ + 94, + 292, + 467, + 324 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Update noise generator $\\Psi$ with $L_{G}$ and $L_{R}$", + "bbox": [ + 143, + 325, + 429, + 340 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Update noise reducer $\\Phi$ with $L_{SYN}$", + "bbox": [ + 143, + 340, + 383, + 354 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "end for", + "bbox": [ + 119, + 356, + 171, + 368 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "end forOutput: Learned noise reducer $\\Phi$", + "bbox": [ + 94, + 369, + 372, + 385 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "method is shown in Algorithm 1. After training the dual-bridging algorithm, we can estimate rPPG signals in the target domain as follows:", + "bbox": [ + 75, + 414, + 467, + 459 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {y} _ {i} ^ {t} = E \\left(\\Theta \\left(x _ {i} ^ {t}\\right) - \\Phi \\left(\\Theta \\left(x _ {i} ^ {t}\\right)\\right)\\right) \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 469, + 467, + 487 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$\\hat{y}_i^t$ is the estimated rPPG signal.", + "bbox": [ + 76, + 496, + 287, + 513 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 525, + 209, + 541 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We conduct experiments on three publicly available datasets with different types of interference to evaluate the accuracy and generalization ability of our dual-bridging noise modeling network. Three protocols that simulate the typical domain discrepancies in real application scenarios are adopted, i.e., 1) task-independent evaluation, 2) participant-independent evaluation, and 3) cross-dataset evaluation. Mean absolute error (MAE), root mean square error (RMSE), and Pearson correlation coefficient (r) are adopted to evaluate the performance of average heart rate based on the estimated rPPG signal. The unit for MAE and RMSE is beats per minute (bpm).", + "bbox": [ + 75, + 542, + 467, + 724 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Datasets and Baselines", + "text_level": 1, + "bbox": [ + 76, + 733, + 287, + 748 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We evaluate the proposed method on the following datasets, which cover different types/levels of head motion, facial expression, compression artifacts, skin color, and also heartbeat ranges.", + "bbox": [ + 75, + 750, + 467, + 809 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "PURE [36] dataset contains facial videos of 10 Caucasian participants (8 men, 2 women) in six different behavior modes with head motion and facial expression. The videos are uncompressed and captured at 30fps in $640 \\times 480$ . Synchronized GT-PPG signals are captured at $60\\mathrm{Hz}$ using pulse oximeter pulox CMS50E.", + "bbox": [ + 75, + 810, + 467, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "MMSE-HR [39] datasets contains 102 facial videos captured from 40 participants of different ethnicities with different emotions. The emotion-related spontaneous facial expressions can also induce facial intensity variations. The video frames are captured at 25fps in $1040 \\times 1392$ and compressed in JPG format, and their frame rate is $25\\mathrm{Hz}$ . GT blood volume signals are captured by the Biopac MP150.", + "bbox": [ + 496, + 90, + 890, + 196 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "UBFC-rPPG [1] dataset contains 42 facial videos captured under a human-computer interaction scene which causes head motions and larger heart rate range (63-145 bpm). Videos are recorded by the Logitech C920 Webcam at 30fps in $640 \\times 480$ . Synchronized GT-PPG signals are captured by CMS50E.", + "bbox": [ + 496, + 196, + 890, + 287 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Baselines We compared the proposed method with traditional rPPG methods [5, 16, 32, 39, 40, 41] and the latest deep rPPG models [3, 4, 13, 21, 22, 23, 24, 27, 28, 29, 34, 37, 45, 47, 49] to show the generalization ability. We also compared the proposed method with popular UDA methods [7, 17] to show the effectiveness of rPPG feature alignment.", + "bbox": [ + 496, + 287, + 890, + 378 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Implementation details", + "text_level": 1, + "bbox": [ + 500, + 388, + 712, + 402 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our method is implemented with PyTorch and trained on an NVIDIA Tesla V100. We align the facial regions with four landmarks using the perspective transformation and generate the STmap [27] as input. We resample all STmaps and the corresponding labels at $30\\mathrm{Hz}$ . The frame number for each STmap is 300 and adjacent STmaps have 270 overlapped frames. In experiments, we pre-train the 2D CNN model on the source domain for rPPG estimation. The threshold of morphology consistency for hard noise pattern mining is 0.82. In the domain adaptation training stage, we set the batch size to 64 and adopt the Adam optimizer [11] for training. The learning rate for the noise pattern generator and noise reducer is 1e-4. And the learning rate for the domain classifier is 3e-5. The weight decay is 1e-4 for all optimizers. We train our domain adaptation algorithm for 200 epochs in the task-independent and PURE to MMSE-HR evaluations, and 2000 epochs in the MMSE-HR to PURE evaluation. We select the weights of the noise reducer for the test according to the estimation loss of synthesized samples. Under certain domain discrepancies, the details of the rPPG signals may not be preserved.", + "bbox": [ + 496, + 405, + 890, + 723 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Task-independent evaluation", + "text_level": 1, + "bbox": [ + 500, + 733, + 756, + 748 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We first evaluate the proposed method in the task-independent scenario, which has a smaller domain discrepancy. The MMSE-HR collected facial videos under different activities and we regard each activity as a task. Within MMSE-HR, the unseen non-physiological intensity variations are mainly induced by different head motion and facial expression changes. In this evaluation, we set one task as the target domain and the other tasks as the source domain. From the experimental results in Table 1, we can find that even under the intra-dataset scenario, the domain", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "10359", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/304b68c2e8a3d912bcc519647e25165f039717bc128856328533df15236d275e.jpg", + "table_caption": [ + "Table 1. Experimental results for task-independent evaluation on MMSE-HR." + ], + "table_footnote": [ + "* Trained on VIPL-HR datasets due to the large model-scale" + ], + "table_body": "
MethodMAERMSEr
Li2014 [16]-19.950.38
CHROM [5]-13.970.55
Tulyakov2016 [39]-11.370.71
ST-Attention* [29]-10.100.64
RhythmNet [27]-5.030.86
CVD* [28]-6.040.84
PhysNet [47]-13.250.44
DeepPhys [3]4.439.980.80
TS-CAN [21]3.857.210.86
AutoHR [45]-5.870.89
BVPNet [4]-7.470.79
Federated2022 [23]2.992.420.79
EfficientPhys-C [22]2.915.430.92
EfficientPhys-T1 [22]3.487.210.86
PhysFormer* [49]2.845.360.92
ERM [12]1.302.580.99
DANN [7]1.242.710.99
CST [17]1.202.420.99
Ours0.852.050.99
", + "bbox": [ + 119, + 128, + 426, + 433 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/de3f50186752e284bf7a0937aec4f1bc72a5e60150d552d8ada5aa97ae7dbf41.jpg", + "table_caption": [ + "Table 2. Experimental results for participant-independent evaluation on UBFC-rPPG dataset." + ], + "table_footnote": [], + "table_body": "
MethodMAERMSEr
GREEN [40]4.4711.60.842
ICA [32]3.518.640.908
CHROM [5]3.444.610.968
POS [41]2.446.610.936
CK [35]2.293.800.981
Frédéric [2]5.458.64-
HeartTrack [31]2.413.370.983
ETA-rPPGNet [10]1.463.970.93
DAE [34]1.482.490.97
PulseGAN [34]1.192.100.98
Meta-rPPG [13]5.977.420.53
CVD [28]2.193.120.99
Gideon2021 [8]3.64.60.95
Federated2022 [23]2.004.380.93
Dual-GAN [24]0.440.670.99
ContrastPhys [37]0.641.000.99
ERM [12]0.751.840.99
DANN [7]0.581.190.99
CST [17]0.411.040.99
Ours0.160.570.99
", + "bbox": [ + 122, + 505, + 424, + 825 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "discrepancy can decrease the performance of deep rPPG models. And under small domain discrepancies, common UDA methods are effective and can overcome certain noise", + "bbox": [ + 76, + 854, + 468, + 898 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "patterns in the target domain. Our method can effectively reduce the unseen non-physiological intensity variations in feature space through noise reduction of rPPG features and achieves state-of-the-art performance.", + "bbox": [ + 496, + 90, + 890, + 151 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. Participant-independent evaluation.", + "text_level": 1, + "bbox": [ + 498, + 162, + 810, + 178 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The domain discrepancy can also come from differences between participants like head motions under human-computer interaction scenarios. Caucasian and Asian participants are included and we evaluate this participant-independent setting with the UBFC-rPPG dataset. We follow the protocol in [24,34] to select 30 participants for training and use the rest 12 participants for testing. As the experimental results shown in Table 2, the domain discrepancy is small with respect to deep rPPG models and pre-trained rPPG models also have low error. Compared to common UDA methods, our proposed method can provide more detailed information for noise reduction supervision and more noise patterns can be overcome in the feature alignment.", + "bbox": [ + 496, + 185, + 890, + 382 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.5. Cross-dataset evaluation", + "text_level": 1, + "bbox": [ + 498, + 393, + 723, + 407 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our method is also evaluated in the cross-dataset setting with MMSE-HR and PURE. The selected datasets have differences in aspects such as head motion, From the view of the rPPG estimation, the MMSE-HR dataset contains more challenging scenarios (video compression, facial expression changes) than the PURE dataset. A challenging source domain could be beneficial to generalization ability and reduce the difficulty of the adaptation process. We provide details of the cross-dataset evaluations in the following paragraphs.", + "bbox": [ + 496, + 416, + 890, + 551 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "From MMSE-HR to PURE. In this experiment, we select the MMSE-HR dataset as the source domain and the PURE dataset as the target domain. Since the source domain is more challenging than the target domain, the adaptation process could be relatively easy. The experimental results are shown in Table 3. We can find that DANN cannot improve the generalization ability of rPPG models and only high-level guidance cannot align noisy features to high-quality features. While the cycle self-training strategy can provide certain details of the rPPG waveform and is more effective in reducing the domain discrepancy in rPPG estimation. Our method can progressively generate noise patterns in the target domain and synthesize noisy samples to provide detailed information from the source domain labels. Our method achieves state-of-the-art performance in this UDA scenario, and the low RMSE shows that our method is effective in reducing strong outliers. We provide some examples in Figure 3 (a) in which the noise reduction process can remove fake peaks in one period. After removing fake peaks, the periodicity of rPPG signal can be improved and the heart rate estimation can be more accurate.", + "bbox": [ + 496, + 551, + 890, + 868 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "From PURE to MMSE-HR. In this experiment, we select the PURE dataset that has fewer facial videos with mild", + "bbox": [ + 498, + 869, + 890, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "10360", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/7fafbef7af63f1f926f09b66ff389d79cc91433718445247d8f631147c45d5ca.jpg", + "table_caption": [ + "Table 3. Experimental results for cross-dataset evaluation between PURE and MMSE-HR datasets." + ], + "table_footnote": [], + "table_body": "
MethodMMSE-HR → PUREPURE → MMSE-HR
MAERMSErMAERMSEr
CHROM [5]3.2512.920.845.7212.690.58
POS [41]2.8312.490.854.9813.110.53
CVD [28]2.753.980.984.087.030.84
ERM [12]2.498.480.932.595.440.96
DANN [7]2.696.970.952.847.650.93
CST [17]1.272.960.992.325.970.96
EfficientT1 [22]---3.045.910.92
PhysFormer [49]---2.845.360.92
Synthetic [25]---2.263.700.97
Ours1.101.670.991.713.720.98
", + "bbox": [ + 80, + 128, + 468, + 327 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/fb4cf00516a5e11f4fe2530e0db31c483c477f82b055e229120dab9a34fc538a.jpg", + "table_caption": [ + "Table 4. Experimental results for cross-dataset evaluation from PURE to UBFC-rPPG." + ], + "table_footnote": [], + "table_body": "
MethodPURE → UBFC-rPPG
MAERMSEr
CHROM [5]3.106.840.93
POS [41]3.526.840.90
DAE [34]2.705.170.96
PulseGAN [34]2.094.420.97
Siamese-rPPG [38]1.298.73-
Dual-GAN [24]0.741.020.99
ERM [12]1.503.360.96
DANN [7]3.246.130.96
CST [17]2.244.730.97
Ours0.581.110.99
", + "bbox": [ + 125, + 382, + 421, + 584 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "interferences (like slow head rotation, translation) as the source Compared to the MMSE $\\rightarrow$ PURE setting, the domain gap in PURE $\\rightarrow$ MMSE is harder to overcome since the noise patterns in the target domain are more challenging. In this experiment, our method is also compared with two rPPG methods [22, 49] which are pre-trained in the VIPL-HR dataset with more facial videos and scenarios. We also compare with [25] which uses synthetic facial videos and the AFRL dataset [6] for training. As shown in Table 3, in this challenging setting, we find that all baseline methods have lower performance compared with the other cross-dataset settings. Under this challenging setting, our dual-bridging with adversarial noise generation algorithm can effectively explore the specific noise patterns from the target domain. Additionally, by synthesizing noisy features similar to target domain features, the noise reduction ability can be dramatically improved to reduce the domain discrepancy. And our method can achieve state-of-the-art performance under this cross-dataset validation. We also provide some", + "bbox": [ + 75, + 613, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "examples in Figure 3 (b) and find that noise reduction can improve the quality of rPPG signals. Especially some noisy rPPG signals show low periodicity, after the noise reduction, clear peaks can be observed. In this case, the intuitive UDA solution DANN also may not be able to learn domain-invariant representation with domain labels only for supervision. The cycle self-training strategy can only adaptively overcome a part of the domain discrepancy. Whereas, the EfficientT1, PhysFormer, and Synthetic methods pretrained on larger datasets show better robustness.", + "bbox": [ + 496, + 90, + 890, + 242 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "From PURE to UBFC-rPPG. In this experiment, we select the PURE dataset with head motion as the source domain and the UBFC-rPPG dataset with compression and a wider range of heart rate as the target domain. The experimental results are shown in Table 4. The compression enlarges the domain discrepancy for rPPG estimation because some information is lost during compression and facial intensities are changed. Our proposed method can simulate the compression-induced noise and provide detailed information to effectively align rPPG features. In this setting, the pre-trained rPPG models in [34, 38] cannot handle the relatively larger domain gap (caused by the video compression) well. For common UDA methods, the high-level guidance from domain classification cannot fully guide the rPPG feature alignment and noise is still preserved in rPPG features.", + "bbox": [ + 496, + 244, + 890, + 472 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this cross-dataset evaluation, we show the domain adaptation process in rPPG estimation under various domain discrepancies. Experimental results show that adapting deep rPPG models to less challenging scenarios, common UDA methods are effective. However, to adapt deep rPPG models to more challenging scenarios, more detailed information about the rPPG waveform is desired to reduce the domain discrepancy. And our method can provide both noise patterns and waveform information with the synthesized samples for noise reduction training. We can find that the domain discrepancy has been reduced after noise reduction, as shown in Figure 4, especially for the harder cases PURE $\\rightarrow$ MMSE-HR. Compared to collecting large-scale dataset to improve the generalization ability of deep rPPG models, our dual-bridging noise modeling network is effective and convenient.", + "bbox": [ + 496, + 474, + 890, + 715 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ablation study. We conduct ablation study with cross-dataset settings to show the effectiveness of each bridge in our method as shown in Table 5. We first show the experimental result of the pre-train model. The $\\mathrm{NR} \\leftrightarrow \\mathrm{D}$ represents that a noise reducer and a domain classifier are adversarially trained to reduce the domain discrepancy. Denoised target domain features are used to estimate rPPG signals. The noise reducer can adaptively overcome some noise patterns under a small domain discrepancy. When the domain discrepancy is large, the domain labels may not provide enough detailed information for training the noise reducer. To prevent the noise reducer from generating random phys", + "bbox": [ + 496, + 719, + 890, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "10361", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/160a6cf8b34f704d0cb4f22704a1e6b4d98bd5bb32d9e0ae04d516036ce13f32.jpg", + "table_caption": [ + "Table 5. Experimental results for ablation study." + ], + "table_footnote": [], + "table_body": "
MethodMMSE-HR → PUREPURE → MMSE-HR
MAERMSErMAERMSEr
Pre-trained rPPG model2.969.570.912.093.920.98
+ NR ↔ D2.137.140.9520.2726.340.58
+ NR ↔ D + G ↔ D1.663.660.981.883.850.98
+ NR ↔ D + G ↔ D + G|NR ↔ D1.131.710.991.713.720.98
+ NR ↔ D + G ↔ D + G|NR ↔ D + HM1.101.670.991.884.160.98
", + "bbox": [ + 191, + 114, + 777, + 234 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c25b9db073f3494126013c1a3aa9745938f12ea648f409acf290b634e88feb85.jpg", + "image_caption": [ + "Figure 4. Visualization of rPPG estimation before (orange) and after (green) noise reduction compared with GT-PPG (blue). (a) contains examples of MMSE-HR $\\rightarrow$ PURE evaluation and (b) is of PURE $\\rightarrow$ MMSE-HR." + ], + "image_footnote": [], + "bbox": [ + 86, + 257, + 459, + 390 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "iological features under adversarial training, the strong regression supervision from rPPG waveform is necessary. For $\\mathrm{NR} \\leftrightarrow \\mathrm{D} + \\mathrm{G} \\leftrightarrow \\mathrm{D}$ , the noise generator is not conditioned on the noise reducer and can also synthesize noisy samples to train the noise reducer. The synthesized noisy samples prevent the noise reducer from generating random physiological features with detailed guidance from PPG signals. For $\\mathrm{NR} \\leftrightarrow \\mathrm{D} + \\mathrm{G} \\leftrightarrow \\mathrm{D} + \\mathrm{G}|\\mathrm{NR} \\leftrightarrow \\mathrm{D}$ , i.e., dual-bridging with adversarial noise generation, the noise patterns in the target domain can be progressively generated to improve the denoising ability. The hard noise pattern mining can improve the robustness of the noise reducer when there is less interference in the target domain. However, with strong interference in the target domain, too many hard noise patterns may distract the noise reducer from overcoming originally generated noise patterns and we saw a decrease of performance in the PURE $\\rightarrow$ MMSE-HR.", + "bbox": [ + 75, + 488, + 468, + 744 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.6. Discussion", + "text_level": 1, + "bbox": [ + 76, + 758, + 194, + 773 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The generalization problem is a key challenge in applying rPPG techniques to real-world health monitoring applications. Especially for deep learning-based rPPG methods, the training data contain certain biases that may prevent rPPG models from learning domain-invariant physiological representations. Results show that generating noise patterns in the target domain and synthesizing samples for noise reduction can effectively reduce the domain discrepancy.", + "bbox": [ + 75, + 779, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ancy thereby improving the quality of rPPG signals.", + "bbox": [ + 500, + 258, + 841, + 273 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We also found the effectiveness of using domain labels to help domain-invariant physiological representation learning when domain discrepancy is small. However, when domain discrepancy increases, the gain of feature alignment in such adversarial training tends to be smaller. Without target domain labels for noise reduction, generating noise patterns similar to the target domain is easier than directly denoising target domain features under a large domain discrepancy. In the noise generation procedure, some out-of-distribution noise patterns can also be generated and can further improve the generalization ability for unseen interferences.", + "bbox": [ + 496, + 275, + 890, + 440 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Although our dual-bridging adaptation can work on most cases and achieve state-of-the-art, we still have limitations on handling hard cases with very large domain discrepancies (e.g., large head motion + facial expression + video compression in Table 4). Such rarely happened combined artifacts and can be regarded as a long-tailed distribution (of artifacts) problem. How to pay more attention to those rare but hard cases could be a key to solve it in the future.", + "bbox": [ + 496, + 441, + 890, + 561 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 579, + 617, + 594 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Recent deep learning-based rPPG methods can learn to overcome non-physiological intensity variations from data, but may also involve bias induced by data and hinder the generalization ability. In this paper, we proposed a novel dual-bridging noise modeling network to reduce the domain discrepancy in rPPG estimation. With the proposed tri-adversarial optimization, the noise generator can progressively explore the noise patterns in the target domain and the coarse-to-fine guidance can effectively improve the noise reduction ability. In addition, comprehensive evaluations of different domain discrepancies show the effectiveness of our method. In future work, we may consider using unlabeled and synthesised [42] facial videos from multiple domains with various external interferences to learn domain-invariant physiological representations.", + "bbox": [ + 496, + 601, + 890, + 829 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Acknowledgement", + "text_level": 1, + "bbox": [ + 500, + 844, + 679, + 859 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This project is partially supported by Hong Kong RGC General Research Fund RGC/HKBU12200820.", + "bbox": [ + 500, + 869, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "10362", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Serge Bobbia, Richard Macwan, Yannick Benezeth, Alamin Mansouri, and Julien Dubois. 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In CVPR, pages 4186-4196, 2022. 1, 2, 5, 6, 7" + ], + "bbox": [ + 501, + 92, + 890, + 484 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "10364", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Dual-Bridging With Adversarial Noise Generation for Domain Adaptive rPPG Estimation/d848ec4a-af95-428f-9e60-c6e80b3b4e6b_model.json b/2023/Dual-Bridging With Adversarial Noise Generation for Domain Adaptive rPPG Estimation/d848ec4a-af95-428f-9e60-c6e80b3b4e6b_model.json new file mode 100644 index 0000000000000000000000000000000000000000..7ddf38d303395dea16c44b65474f2bd3223f93e6 --- /dev/null +++ b/2023/Dual-Bridging With Adversarial Noise Generation for Domain Adaptive rPPG Estimation/d848ec4a-af95-428f-9e60-c6e80b3b4e6b_model.json @@ -0,0 +1,2090 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.096, + 0.13, + 0.877, + 0.175 + ], + "angle": 0, + "content": "Dual-bridging with Adversarial Noise Generation for Domain Adaptive rPPG Estimation" + }, + { + "type": "text", + "bbox": [ + 0.178, + 0.204, + 0.793, + 0.257 + ], + "angle": 0, + "content": "Jingda Du*, Si-Qi Liu*, Bochao Zhang, Pong C. Yuen \nDepartment of Computer Science, Hong Kong Baptist University, Hong Kong \ncsjddu, siqiliu, csbczhang, pcyuen @comp.hkbu.edu.hk" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.292, + 0.314, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.324, + 0.474, + 0.673 + ], + "angle": 0, + "content": "The remote photoplethysmography (rPPG) technique can estimate pulse-related metrics (e.g. heart rate and respiratory rate) from facial videos and has a high potential for health monitoring. The latest deep rPPG methods can model in-distribution noise due to head motion, video compression, etc., and estimate high-quality rPPG signals under similar scenarios. However, deep rPPG models may not generalize well to the target test domain with unseen noise and distortions. In this paper, to improve the generalization ability of rPPG models, we propose a dual-bridging network to reduce the domain discrepancy by aligning intermediate domains and synthesizing the target noise in the source domain for better noise reduction. To comprehensively explore the target domain noise, we propose a novel adversarial noise generation in which the noise generator indirectly competes with the noise reducer. To further improve the robustness of the noise reducer, we propose hard noise pattern mining to encourage the generator to learn hard noise patterns contained in the target domain features. We evaluated the proposed method on three public datasets with different types of interferences. Under different cross-domain scenarios, the comprehensive results show the effectiveness of our method." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.701, + 0.21, + 0.716 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.726, + 0.47, + 0.879 + ], + "angle": 0, + "content": "With the development of rPPG technology, physiological metrics such as heart rate [27], heart rate variability [34], respiratory rate [21] can also be estimated from facial videos. Deep learning-based rPPG methods overcome non-physiological intensity variations [30, 49] and model noise in training samples [24, 28]. Despite the high accuracy under intra-dataset evaluations, the deep rPPG models may not be able to generalize well to unseen interferences in the test domain. The domain gap is mainly from unseen non-physiological interferences such as lighting conditions," + }, + { + "type": "image", + "bbox": [ + 0.511, + 0.289, + 0.677, + 0.351 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.356, + 0.663, + 0.367 + ], + "angle": 0, + "content": "(a) GAN-based Noise Modeling" + }, + { + "type": "image", + "bbox": [ + 0.511, + 0.38, + 0.684, + 0.442 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.527, + 0.447, + 0.648, + 0.458 + ], + "angle": 0, + "content": "(b) Intuitive UDA Solution" + }, + { + "type": "image", + "bbox": [ + 0.7, + 0.289, + 0.885, + 0.438 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.717, + 0.44, + 0.875, + 0.461 + ], + "angle": 0, + "content": "(c) Dual-bridging with Adversarial Noise Generation (Ours)" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.473, + 0.895, + 0.572 + ], + "angle": 0, + "content": "Figure 1. The comparison between (a) typical intra-dataset adversarial rPPG noise modeling, (b) an intuitive UDA framework for rPPG feature alignment, and (c) our proposed dual-bridging network with adversarial noise modeling and hard noise pattern mining \\((HM)\\). Here SYN denotes synthetic data, DT is for the denoised target domain, \\(G\\), \\(D\\), and \\(NR\\) denotes the generator, domain classifier, and noise reducer, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.894, + 0.718 + ], + "angle": 0, + "content": "camera sensors, video compression algorithms, facial expressions, etc. They can induce distortions in estimated rPPG signals and reduce both the accuracy and the reliability of pulse-related metrics estimation. Considering it is hard to cover all interferences during the training stage, to improve the usability of rPPG in realistic applications, one main challenge is how to boost the generalizability of rPPG models to unseen scenarios." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.903 + ], + "angle": 0, + "content": "In recent research of rPPG, both deep learning-based frameworks and mechanisms [45, 46, 49] are proposed to overcome the non-physiological intensity variations. GAN-based disentanglement learning has also been adopted to reduce the noise from pseudo [28] or synthesized [24] noisy features. We summarize this approach in Figure 1 (a) where a discriminator is employed to distinguish the generated feature (SYN in figure) from the original one. These methods can perform well under intra-dataset evaluation settings since the in-distribution noise patterns are thoroughly investigated with a large number of adversarial learning iterations. However, they may fail when encountering unseen" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.208, + 0.9 + ], + "angle": 0, + "content": "* Equal contribution" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10355" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.122 + ], + "angle": 0, + "content": "domains in real application scenarios since noise patterns may be different from the ones of training data." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.126, + 0.473, + 0.716 + ], + "angle": 0, + "content": "Intuitively, the unsupervised domain adaptation (UDA) technique can help in bridging the gap between source and target domain [7, 14, 17, 44]. As shown in Figure 1 (b), a noise reducer module \\( NR \\) that aims to obtain noise-free domain-invariant representations can be learned by fighting against the domain classifier \\( D \\). However, this intuitive solution may not work well since the domain classification may not be able to give sufficient information for \\( NR \\) to identify whether the feature components are noise or physiological information. Directly aligning the rPPG features from different domains may end up distorting the physiological information since they are from different subjects. The ground-truth PPG (GT-PPG) signal with detailed waveform information helps preserve the physiological information and can provide much more informative guidance with the regression task. However, GT-PPG is available in the source domain but not the target domain. How to leverage the source domain GT-PPG to train \\( NR \\) to be robust to the noise from the target domain is the key issue to be solved in this work. To achieve it we propose the dual bridging noise modeling network as shown in Figure 1 (c). The first bridging works as high-level guidance where the denoised target domain feature is adversarially pulled to the source domain feature (as Figure 1 (b)). On top of it, the second bridging aims to help synthesize the target domain noise and inject it into the source domain denoised feature so that the GT-PPG regression can help finetune the \\( NR \\) for better robustness in the target domain. An adversarial noise generation module \\( (G|NR) \\) is designed where the generator is conditioned on the \\( NR \\) so that it keeps on overcoming the complex noise pattern that can hardly be solved in the first bridging. With the high-level guidance (first bridging) and detailed signal regression (second bridging), the \\( NR \\) can handle the target domain noise better and therefore improve the accuracy of rPPG estimation in the target domain. To further discover the remaining noise vestige, we build a hard noise pattern mining mechanism to squeeze the unsolved local noise pattern from the denoised target feature so that \\( G|NR \\) can thoroughly synthesize it." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.472, + 0.902 + ], + "angle": 0, + "content": "In sum, the contributions of this work are: (1) A dual-bridging noise modeling network that adapts target domain noise in a coarse-to-fine manner. (2) An adversarial noise generation mechanism to progressively synthesize and inject the hard target domain noisy features into the source domain while keeping the physiological information. (3) A hard noise pattern mining mechanism to further explore the target domain noise patterns with larger variations. We evaluated the proposed method on three public datasets with various types of interferences including facial motion and expression, video compression, skin tone, and heartbeat ranges. Under different cross-domain scenarios, the com" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.872, + 0.108 + ], + "angle": 0, + "content": "The prehensive results show the effectiveness of our method." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.122, + 0.642, + 0.138 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.148, + 0.783, + 0.164 + ], + "angle": 0, + "content": "2.1. Remote physiological estimation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.171, + 0.895, + 0.626 + ], + "angle": 0, + "content": "Traditional rPPG methods [5, 16, 32, 39, 40, 41] estimate pulse signal from facial videos by extracting and modeling the detailed heartbeat-caused skin color variation. To estimate pulse-induced intensity variations with more details from facial videos, deep learning-based networks and mechanisms have been proposed. With facial video input, various spatial-temporal neural networks have been developed [4, 20, 22, 23, 37, 48, 49]. To evaluate the effectiveness, rPPG datasets with various interferences including head motion [36], facial expression [15, 39], video compression [9], and skin color [42] are constructed. In addition, rPPG estimation can be conducted from pre-processed representations like normalized difference [3, 18, 21, 30], spatial-temporal map [24, 28]. To further improve robustness, self-adaptive [3, 21] and background-guided [19, 30] attention mechanisms have been proposed to emphasize important facial regions in physiological representation. Furthermore, [28] proposed the cross-verified strategy to disentangle noise and physiological representation and [24] proposed to model in-distribution noise for learning noise-resistant physiological representation. [25, 26] proposed to synthesize diverse facial videos for rPPG estimation. Unsupervised learning-based methods [8, 37] are also proposed to learn rPPG estimation from unlabeled facial videos. However, the previously proposed methods are prone to experience performance drops in cross-dataset evaluation, where the target domain may contain unseen noise. This is due to unseen noise patterns that may not be fully overcome, and the physiological representation may be polluted and cause distortions in the rPPG signals." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.636, + 0.86, + 0.652 + ], + "angle": 0, + "content": "2.2. Unsupervised domain adaptation methods" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.895, + 0.901 + ], + "angle": 0, + "content": "In recent research on computer vision, many unsupervised domain adaptation methods have been proposed to learn domain-invariant representation. [7] proposed to suppress domain-invariant information with domain label guided adversarial training. [33] proposed a bi-directional generation framework that can map target domain samples to the source domain and preserve semantic information for classification. [14] proposed to use adversarial domain training and distributional feature alignment guided by maximum density divergence to achieve adaptation. [43] considered that domain adversarial training may not be coordinated with the main task and proposed using meta-learning to improve the effectiveness of feature alignment. Unlike common computer vision tasks, feature alignment in the rPPG estimation requires more detailed information which cannot be fully provided by domain labels. There" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "10356" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.11, + 0.089, + 0.852, + 0.386 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.395, + 0.895, + 0.466 + ], + "angle": 0, + "content": "Figure 2. Framework of the dual-bridging noise modeling network. The dual-bridging can reduce the domain discrepancy in the feature space by training the noise reducer with both high-level guidance from domain classification and detailed waveform guidance from synthetic features regression. The adversarial noise generation forces the generator \\( G \\) to compete with the noise reducer \\( NR \\) and synthesize noisy features with unsolved noise in the target domain. The hard noise pattern mining removes high-quality temporal features and encourages the generator to further explore hard noise patterns in the target domain." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.491, + 0.471, + 0.538 + ], + "angle": 0, + "content": "fore, we propose the dual-bridging noise modeling network to take advantage of both domain labels and the source domain ground truth to guide the rPPG feature alignment." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.557, + 0.251, + 0.574 + ], + "angle": 0, + "content": "3. Proposed Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.584, + 0.471, + 0.901 + ], + "angle": 0, + "content": "The overview of the proposed dual-bridging noise modeling network is shown in Figure 2. Given the input face video from the source and target domain, we construct the STMap (details are in section 4.2) as the input of the feature extractor and then perform dual-bridging noise modeling on the middle representation. The first bridging provides high-level guidance where the source feature \\( f_{j}^{s} \\) and the denoised target feature \\( f_{i}^{t} \\) are pulled together with the domain classifier. The synthesized target domain feature \\( f_{j}^{s} \\) is obtained from the \\( f_{i}^{t} \\) through the adversarial noise generation module. The second bridge aims to pull \\( f_{j}^{s} \\) to \\( f_{i}^{t} \\) so that the target domain noise can be overcome by \\( NR \\) with the guidance of PPG \\( y_{s} \\) (regression) The generator in the adversarial noise generation module is conditioned on the \\( NR \\) so that it keeps on overcoming the complex noise pattern that can hardly be solved in the first bridging. With the dual-bridging noise modeling that contains both high-level (first bridge) and detailed waveform guidance (second bridge), the \\( NR \\) can handle the target domain noise better. Finally, \\( NR \\) works with the feature extractor and rPPG estimator to do the rPPG estimation in the target domain." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.491, + 0.646, + 0.507 + ], + "angle": 0, + "content": "3.1. Dual-bridging" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.514, + 0.892, + 0.651 + ], + "angle": 0, + "content": "With respect to the feature extractor \\(\\Theta\\), we define source domain features as \\(F_{s} = \\{f_{j}^{s}\\}_{j = 1}^{M}\\) and target domain features as \\(F_{t} = \\{f_{i}^{t}\\}_{i = 1}^{N}\\), where \\(f_{j}^{s} = \\Theta (x_{j}^{s})\\) and \\(f_{i}^{t} = \\Theta (x_{i}^{t})\\). Since the rPPG patterns are similar between different participants, the pre-trained feature extractor can preserve enough physiological information in \\(F_{t}\\) and noise modeling is the key to noise reduction of the target domain features. Detailed information for guidance is necessary to overcome the complex noise in the target domain features." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.652, + 0.892, + 0.727 + ], + "angle": 0, + "content": "To reduce the noise contained in \\( F_{t} \\), we propose the adaptive noise reduction bridging to reduce the noise contained in target domain features supervised by the domain classifier. In this bridging, we design the noise reducer with the noise estimation function \\( \\Phi \\) in a residual way as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.637, + 0.74, + 0.892, + 0.758 + ], + "angle": 0, + "content": "\\[\n\\hat {f} _ {i} ^ {t} = f _ {i} ^ {t} - \\Phi \\left(f _ {i} ^ {t}\\right) \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.764, + 0.892, + 0.871 + ], + "angle": 0, + "content": "where \\(\\hat{f}_i^t\\) is a denoised physiological feature and we define \\(\\hat{F}_t = \\{\\hat{f}_i^t\\}_{i=1}^N\\) as the denoised target domain. The direct estimation of high-quality physiological features could be hard, and we choose to estimate the noise and use the residual structure to reduce the noise in the target domain features. We build an adversarial training between the noise reducer \\(\\Phi\\) and the domain classifier \\(D\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.511, + 0.881, + 0.892, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\max _ {D} \\min _ {\\Phi} L _ {N R} = \\mathbb {E} [ \\| 1 - D \\left(f _ {j} ^ {s}\\right) \\| _ {2} ] + \\mathbb {E} [ \\| D \\left(\\hat {f} _ {i} ^ {t}\\right) \\| _ {2} ] \\tag {2}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10357" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.227 + ], + "angle": 0, + "content": "With high-level guidance from domain classification, some simple noise patterns can be overcome, and less noisy features can be aligned. However, high-level guidance may not overcome complex noise patterns without detailed waveform information for guidance. And the brute-force feature alignment may even change the physiological information of rPPG features when complex noise patterns are encountered. The phenomenon can be reflected by our ablation study in section 4.3." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.228, + 0.469, + 0.318 + ], + "angle": 0, + "content": "To involve detailed information for supervision, we propose the complex noise generation bridging to generate target domain noise and synthesize noisy features to guide the noise reducer. From the source domain direction, we estimate the noise patterns in the target domain by generating noise and synthesizing noisy features as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.211, + 0.327, + 0.47, + 0.348 + ], + "angle": 0, + "content": "\\[\n\\bar {f} _ {j} ^ {s} = f _ {j} ^ {s} + \\Psi (n _ {k}) \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.358, + 0.469, + 0.406 + ], + "angle": 0, + "content": "where \\(\\overline{f}_j^s\\) is a raw noisy feature, \\(n_k\\) is random noise, and \\(\\Psi\\) is the generator. And we define the synthetic feature domain \\(\\hat{F}_s = \\{\\hat{f}_j^s\\}_{j=1}^M\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.213, + 0.416, + 0.469, + 0.437 + ], + "angle": 0, + "content": "\\[\n\\hat {f} _ {j} ^ {s} = \\bar {f} _ {j} ^ {s} - \\Phi \\left(\\bar {f} _ {j} ^ {s}\\right) \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.446, + 0.469, + 0.505 + ], + "angle": 0, + "content": "To control the range of noise generation, we build the adversarial training between the noise generator and the domain classifier with respect to the denoised target domain as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.096, + 0.519, + 0.469, + 0.565 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\underset {D} {\\max} \\underset {\\Psi} {\\min} L _ {G} = \\mathbb {E} [ \\| 1 - D (f _ {j} ^ {s}) \\| _ {2} ] + \\mathbb {E} [ \\| D (\\overline {{f}} _ {j} ^ {s}) \\| _ {2} ] \\\\ + \\mathbb {E} [ \\| D (\\hat {f} _ {i} ^ {t}) \\| _ {2} ] \\quad (5) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.574, + 0.469, + 0.664 + ], + "angle": 0, + "content": "In this bridging, the domain classifier can guide the generator to learn target domain noise patterns and synthesize noisy features with preserved physiological information. Thus, the source domain PPG signals \\( y_{j}^{s} \\) can be utilized to guide the noise reducer to overcome generated complex noise patterns as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.182, + 0.674, + 0.469, + 0.694 + ], + "angle": 0, + "content": "\\[\nL _ {S Y N} = 1 - r \\left(E \\left(\\hat {f} _ {j} ^ {s}\\right), y _ {j} ^ {s}\\right) \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.703, + 0.469, + 0.779 + ], + "angle": 0, + "content": "\\(E\\) is the rPPG estimator, and \\(r\\) is the Pearson correlation function. With this bridging, the physiological information can be preserved in the noise reduction and the other bridging can align more target domain features under large domain discrepancy." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.787, + 0.334, + 0.803 + ], + "angle": 0, + "content": "3.2. Adversarial noise generation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.469, + 0.901 + ], + "angle": 0, + "content": "With the guidance from the domain classifier, part of the target domain noise patterns can be generated. However, in the adversarial training process, the generator may not fully explore target domain noise patterns. To comprehensively explore the target domain noise for rPPG feature alignment, we propose a novel adversarial noise generation. As shown" + }, + { + "type": "image", + "bbox": [ + 0.524, + 0.088, + 0.875, + 0.15 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.545, + 0.163, + 0.845, + 0.178 + ], + "angle": 0, + "content": "Figure 3. Illustration of hard noise pattern mining." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.204, + 0.892, + 0.308 + ], + "angle": 0, + "content": "in Figure 2, the generator is conditioned on the noise reducer and forced to explore the unsolved noise contained in the target domain features. The noise reducer is trained with the synthetic features and corresponding PPG signals to overcome the generated noise. The adversarial correlation between the generator and the noise reducer is shown as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.32, + 0.891, + 0.356 + ], + "angle": 0, + "content": "\\[\n\\max _ {\\Psi} \\min _ {\\Phi} L _ {A N G} = \\mathbb {E} [ \\| 1 - D (\\hat {f} _ {j} ^ {s}) \\| _ {2} ] + \\mathbb {E} [ 1 - r (E (\\hat {f} _ {j} ^ {s}), y _ {j} ^ {s}) ] \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.357, + 0.892, + 0.478 + ], + "angle": 0, + "content": "This adversarial training is based on two different optimization functions, but not the gradient reverse layer. Therefore, the novel noise patterns are not generated based on adversarial attacks but are searched from unsolved noise patterns in the target domain. With our adversarial noise generation, the dual-bridging structure can progressively generate target domain noise patterns, and the noise reduction ability can be significantly improved." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.488, + 0.741, + 0.504 + ], + "angle": 0, + "content": "3.3. Hard noise pattern mining" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.511, + 0.892, + 0.706 + ], + "angle": 0, + "content": "To further improve the robustness of the noise reducer, we propose the hard noise pattern mining as illustrated in Figure 3. Considering the redundancy of rPPG estimation, features with one or several high-quality temporal features can contribute to accurate estimation. Thus, the noise reducer may just learn to overcome relatively simple noise patterns and some hard noise patterns may not be learned. To further explore the hard noise patterns, we need to reduce the shortcuts for noise reduction and generate hard noise patterns for training. In our hard noise pattern mining module, we identify high-quality temporal features with respect to the morphology consistency \\(M\\) which is defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.608, + 0.706, + 0.891, + 0.73 + ], + "angle": 0, + "content": "\\[\nM = \\max _ {t = 1} ^ {n} r \\left(g _ {0: T}, g _ {t: t + T}\\right) \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.885 + ], + "angle": 0, + "content": "\\(r\\) is the Pearson correlation, \\(g\\) is a temporal feature, \\(t\\) is the sliding start point, and \\(T\\) is the time length of morphology consistency evaluation. With respect to the morphology consistency, we define temporal features with significant periodicity as high-quality features. After identifying high-quality temporal features, we can remove the corresponding feature slice and preserve hard slices for noise generation. Correspondingly, more hard noise patterns will be generated and the noise reduction ability can be further improved for rPPG feature alignment." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "The detailed optimization process of our proposed" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10358" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.078, + 0.091, + 0.468, + 0.12 + ], + "angle": 0, + "content": "Algorithm 1 The optimization process for our dual-bridging algorithm." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.123, + 0.468, + 0.184 + ], + "angle": 0, + "content": "Input: Noise generator \\(\\Psi\\), noise reducer \\(\\Phi\\) and domain classifier \\(D\\), total epochs \\(L\\), mini-batch \\(B\\), source domain samples \\(x_{j}^{s}\\), source domain labels \\(y_{j}^{s}\\), target domain samples \\(x_{i}^{t}\\)." + }, + { + "type": "text", + "bbox": [ + 0.095, + 0.187, + 0.212, + 0.2 + ], + "angle": 0, + "content": "for \\(l = 1\\) to \\(L\\) do" + }, + { + "type": "text", + "bbox": [ + 0.119, + 0.202, + 0.24, + 0.214 + ], + "angle": 0, + "content": "for \\(b = 1\\) to \\(B\\) do" + }, + { + "type": "text", + "bbox": [ + 0.095, + 0.216, + 0.468, + 0.247 + ], + "angle": 0, + "content": "Obtain \\( f_{j}^{s} \\) and \\( f_{i}^{t} \\) with pre-trained feature extractor from \\( x_{j}^{s} \\) and \\( x_{i}^{t} \\)" + }, + { + "type": "text", + "bbox": [ + 0.144, + 0.249, + 0.336, + 0.265 + ], + "angle": 0, + "content": "Obtain \\(\\hat{f}_i^t\\) with noise reducer" + }, + { + "type": "text", + "bbox": [ + 0.095, + 0.266, + 0.468, + 0.294 + ], + "angle": 0, + "content": "Update noise reducer \\(\\Phi\\) and domain classifier \\(D\\) with \\(L_{DE}\\)" + }, + { + "type": "text", + "bbox": [ + 0.095, + 0.294, + 0.468, + 0.325 + ], + "angle": 0, + "content": "Generate \\(\\overline{f}_j^s\\) and \\(\\hat{f}_j^s\\) with updated noise reducer and noise generator" + }, + { + "type": "text", + "bbox": [ + 0.144, + 0.326, + 0.431, + 0.341 + ], + "angle": 0, + "content": "Update noise generator \\(\\Psi\\) with \\(L_{G}\\) and \\(L_{R}\\)" + }, + { + "type": "text", + "bbox": [ + 0.144, + 0.342, + 0.384, + 0.356 + ], + "angle": 0, + "content": "Update noise reducer \\(\\Phi\\) with \\(L_{SYN}\\)" + }, + { + "type": "text", + "bbox": [ + 0.12, + 0.357, + 0.173, + 0.369 + ], + "angle": 0, + "content": "end for" + }, + { + "type": "text", + "bbox": [ + 0.095, + 0.371, + 0.373, + 0.386 + ], + "angle": 0, + "content": "end forOutput: Learned noise reducer \\(\\Phi\\)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.415, + 0.468, + 0.46 + ], + "angle": 0, + "content": "method is shown in Algorithm 1. After training the dual-bridging algorithm, we can estimate rPPG signals in the target domain as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.176, + 0.47, + 0.468, + 0.488 + ], + "angle": 0, + "content": "\\[\n\\hat {y} _ {i} ^ {t} = E \\left(\\Theta \\left(x _ {i} ^ {t}\\right) - \\Phi \\left(\\Theta \\left(x _ {i} ^ {t}\\right)\\right)\\right) \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.497, + 0.288, + 0.514 + ], + "angle": 0, + "content": "\\(\\hat{y}_i^t\\) is the estimated rPPG signal." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.526, + 0.21, + 0.542 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.544, + 0.468, + 0.725 + ], + "angle": 0, + "content": "We conduct experiments on three publicly available datasets with different types of interference to evaluate the accuracy and generalization ability of our dual-bridging noise modeling network. Three protocols that simulate the typical domain discrepancies in real application scenarios are adopted, i.e., 1) task-independent evaluation, 2) participant-independent evaluation, and 3) cross-dataset evaluation. Mean absolute error (MAE), root mean square error (RMSE), and Pearson correlation coefficient (r) are adopted to evaluate the performance of average heart rate based on the estimated rPPG signal. The unit for MAE and RMSE is beats per minute (bpm)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.734, + 0.288, + 0.749 + ], + "angle": 0, + "content": "4.1. Datasets and Baselines" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.468, + 0.81 + ], + "angle": 0, + "content": "We evaluate the proposed method on the following datasets, which cover different types/levels of head motion, facial expression, compression artifacts, skin color, and also heartbeat ranges." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.468, + 0.901 + ], + "angle": 0, + "content": "PURE [36] dataset contains facial videos of 10 Caucasian participants (8 men, 2 women) in six different behavior modes with head motion and facial expression. The videos are uncompressed and captured at 30fps in \\(640 \\times 480\\). Synchronized GT-PPG signals are captured at \\(60\\mathrm{Hz}\\) using pulse oximeter pulox CMS50E." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.091, + 0.892, + 0.198 + ], + "angle": 0, + "content": "MMSE-HR [39] datasets contains 102 facial videos captured from 40 participants of different ethnicities with different emotions. The emotion-related spontaneous facial expressions can also induce facial intensity variations. The video frames are captured at 25fps in \\(1040 \\times 1392\\) and compressed in JPG format, and their frame rate is \\(25\\mathrm{Hz}\\). GT blood volume signals are captured by the Biopac MP150." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.198, + 0.892, + 0.288 + ], + "angle": 0, + "content": "UBFC-rPPG [1] dataset contains 42 facial videos captured under a human-computer interaction scene which causes head motions and larger heart rate range (63-145 bpm). Videos are recorded by the Logitech C920 Webcam at 30fps in \\(640 \\times 480\\). Synchronized GT-PPG signals are captured by CMS50E." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.289, + 0.892, + 0.38 + ], + "angle": 0, + "content": "Baselines We compared the proposed method with traditional rPPG methods [5, 16, 32, 39, 40, 41] and the latest deep rPPG models [3, 4, 13, 21, 22, 23, 24, 27, 28, 29, 34, 37, 45, 47, 49] to show the generalization ability. We also compared the proposed method with popular UDA methods [7, 17] to show the effectiveness of rPPG feature alignment." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.39, + 0.714, + 0.404 + ], + "angle": 0, + "content": "4.2. Implementation details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.406, + 0.892, + 0.724 + ], + "angle": 0, + "content": "Our method is implemented with PyTorch and trained on an NVIDIA Tesla V100. We align the facial regions with four landmarks using the perspective transformation and generate the STmap [27] as input. We resample all STmaps and the corresponding labels at \\(30\\mathrm{Hz}\\). The frame number for each STmap is 300 and adjacent STmaps have 270 overlapped frames. In experiments, we pre-train the 2D CNN model on the source domain for rPPG estimation. The threshold of morphology consistency for hard noise pattern mining is 0.82. In the domain adaptation training stage, we set the batch size to 64 and adopt the Adam optimizer [11] for training. The learning rate for the noise pattern generator and noise reducer is 1e-4. And the learning rate for the domain classifier is 3e-5. The weight decay is 1e-4 for all optimizers. We train our domain adaptation algorithm for 200 epochs in the task-independent and PURE to MMSE-HR evaluations, and 2000 epochs in the MMSE-HR to PURE evaluation. We select the weights of the noise reducer for the test according to the estimation loss of synthesized samples. Under certain domain discrepancies, the details of the rPPG signals may not be preserved." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.734, + 0.757, + 0.749 + ], + "angle": 0, + "content": "4.3. Task-independent evaluation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We first evaluate the proposed method in the task-independent scenario, which has a smaller domain discrepancy. The MMSE-HR collected facial videos under different activities and we regard each activity as a task. Within MMSE-HR, the unseen non-physiological intensity variations are mainly induced by different head motion and facial expression changes. In this evaluation, we set one task as the target domain and the other tasks as the source domain. From the experimental results in Table 1, we can find that even under the intra-dataset scenario, the domain" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10359" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.09, + 0.47, + 0.117 + ], + "angle": 0, + "content": "Table 1. Experimental results for task-independent evaluation on MMSE-HR." + }, + { + "type": "table", + "bbox": [ + 0.12, + 0.129, + 0.428, + 0.434 + ], + "angle": 0, + "content": "
MethodMAERMSEr
Li2014 [16]-19.950.38
CHROM [5]-13.970.55
Tulyakov2016 [39]-11.370.71
ST-Attention* [29]-10.100.64
RhythmNet [27]-5.030.86
CVD* [28]-6.040.84
PhysNet [47]-13.250.44
DeepPhys [3]4.439.980.80
TS-CAN [21]3.857.210.86
AutoHR [45]-5.870.89
BVPNet [4]-7.470.79
Federated2022 [23]2.992.420.79
EfficientPhys-C [22]2.915.430.92
EfficientPhys-T1 [22]3.487.210.86
PhysFormer* [49]2.845.360.92
ERM [12]1.302.580.99
DANN [7]1.242.710.99
CST [17]1.202.420.99
Ours0.852.050.99
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.123, + 0.436, + 0.4, + 0.448 + ], + "angle": 0, + "content": "* Trained on VIPL-HR datasets due to the large model-scale" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.467, + 0.468, + 0.494 + ], + "angle": 0, + "content": "Table 2. Experimental results for participant-independent evaluation on UBFC-rPPG dataset." + }, + { + "type": "table", + "bbox": [ + 0.123, + 0.506, + 0.426, + 0.826 + ], + "angle": 0, + "content": "
MethodMAERMSEr
GREEN [40]4.4711.60.842
ICA [32]3.518.640.908
CHROM [5]3.444.610.968
POS [41]2.446.610.936
CK [35]2.293.800.981
Frédéric [2]5.458.64-
HeartTrack [31]2.413.370.983
ETA-rPPGNet [10]1.463.970.93
DAE [34]1.482.490.97
PulseGAN [34]1.192.100.98
Meta-rPPG [13]5.977.420.53
CVD [28]2.193.120.99
Gideon2021 [8]3.64.60.95
Federated2022 [23]2.004.380.93
Dual-GAN [24]0.440.670.99
ContrastPhys [37]0.641.000.99
ERM [12]0.751.840.99
DANN [7]0.581.190.99
CST [17]0.411.040.99
Ours0.160.570.99
" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.47, + 0.9 + ], + "angle": 0, + "content": "discrepancy can decrease the performance of deep rPPG models. And under small domain discrepancies, common UDA methods are effective and can overcome certain noise" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.152 + ], + "angle": 0, + "content": "patterns in the target domain. Our method can effectively reduce the unseen non-physiological intensity variations in feature space through noise reduction of rPPG features and achieves state-of-the-art performance." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.163, + 0.812, + 0.179 + ], + "angle": 0, + "content": "4.4. Participant-independent evaluation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.186, + 0.892, + 0.383 + ], + "angle": 0, + "content": "The domain discrepancy can also come from differences between participants like head motions under human-computer interaction scenarios. Caucasian and Asian participants are included and we evaluate this participant-independent setting with the UBFC-rPPG dataset. We follow the protocol in [24,34] to select 30 participants for training and use the rest 12 participants for testing. As the experimental results shown in Table 2, the domain discrepancy is small with respect to deep rPPG models and pre-trained rPPG models also have low error. Compared to common UDA methods, our proposed method can provide more detailed information for noise reduction supervision and more noise patterns can be overcome in the feature alignment." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.394, + 0.725, + 0.408 + ], + "angle": 0, + "content": "4.5. Cross-dataset evaluation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.417, + 0.892, + 0.552 + ], + "angle": 0, + "content": "Our method is also evaluated in the cross-dataset setting with MMSE-HR and PURE. The selected datasets have differences in aspects such as head motion, From the view of the rPPG estimation, the MMSE-HR dataset contains more challenging scenarios (video compression, facial expression changes) than the PURE dataset. A challenging source domain could be beneficial to generalization ability and reduce the difficulty of the adaptation process. We provide details of the cross-dataset evaluations in the following paragraphs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.553, + 0.892, + 0.869 + ], + "angle": 0, + "content": "From MMSE-HR to PURE. In this experiment, we select the MMSE-HR dataset as the source domain and the PURE dataset as the target domain. Since the source domain is more challenging than the target domain, the adaptation process could be relatively easy. The experimental results are shown in Table 3. We can find that DANN cannot improve the generalization ability of rPPG models and only high-level guidance cannot align noisy features to high-quality features. While the cycle self-training strategy can provide certain details of the rPPG waveform and is more effective in reducing the domain discrepancy in rPPG estimation. Our method can progressively generate noise patterns in the target domain and synthesize noisy samples to provide detailed information from the source domain labels. Our method achieves state-of-the-art performance in this UDA scenario, and the low RMSE shows that our method is effective in reducing strong outliers. We provide some examples in Figure 3 (a) in which the noise reduction process can remove fake peaks in one period. After removing fake peaks, the periodicity of rPPG signal can be improved and the heart rate estimation can be more accurate." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.9 + ], + "angle": 0, + "content": "From PURE to MMSE-HR. In this experiment, we select the PURE dataset that has fewer facial videos with mild" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10360" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.09, + 0.47, + 0.119 + ], + "angle": 0, + "content": "Table 3. Experimental results for cross-dataset evaluation between PURE and MMSE-HR datasets." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.129, + 0.47, + 0.328 + ], + "angle": 0, + "content": "
MethodMMSE-HR → PUREPURE → MMSE-HR
MAERMSErMAERMSEr
CHROM [5]3.2512.920.845.7212.690.58
POS [41]2.8312.490.854.9813.110.53
CVD [28]2.753.980.984.087.030.84
ERM [12]2.498.480.932.595.440.96
DANN [7]2.696.970.952.847.650.93
CST [17]1.272.960.992.325.970.96
EfficientT1 [22]---3.045.910.92
PhysFormer [49]---2.845.360.92
Synthetic [25]---2.263.700.97
Ours1.101.670.991.713.720.98
" + }, + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.344, + 0.47, + 0.372 + ], + "angle": 0, + "content": "Table 4. Experimental results for cross-dataset evaluation from PURE to UBFC-rPPG." + }, + { + "type": "table", + "bbox": [ + 0.127, + 0.383, + 0.422, + 0.585 + ], + "angle": 0, + "content": "
MethodPURE → UBFC-rPPG
MAERMSEr
CHROM [5]3.106.840.93
POS [41]3.526.840.90
DAE [34]2.705.170.96
PulseGAN [34]2.094.420.97
Siamese-rPPG [38]1.298.73-
Dual-GAN [24]0.741.020.99
ERM [12]1.503.360.96
DANN [7]3.246.130.96
CST [17]2.244.730.97
Ours0.581.110.99
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.614, + 0.471, + 0.902 + ], + "angle": 0, + "content": "interferences (like slow head rotation, translation) as the source Compared to the MMSE \\(\\rightarrow\\) PURE setting, the domain gap in PURE \\(\\rightarrow\\)MMSE is harder to overcome since the noise patterns in the target domain are more challenging. In this experiment, our method is also compared with two rPPG methods [22, 49] which are pre-trained in the VIPL-HR dataset with more facial videos and scenarios. We also compare with [25] which uses synthetic facial videos and the AFRL dataset [6] for training. As shown in Table 3, in this challenging setting, we find that all baseline methods have lower performance compared with the other cross-dataset settings. Under this challenging setting, our dual-bridging with adversarial noise generation algorithm can effectively explore the specific noise patterns from the target domain. Additionally, by synthesizing noisy features similar to target domain features, the noise reduction ability can be dramatically improved to reduce the domain discrepancy. And our method can achieve state-of-the-art performance under this cross-dataset validation. We also provide some" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.243 + ], + "angle": 0, + "content": "examples in Figure 3 (b) and find that noise reduction can improve the quality of rPPG signals. Especially some noisy rPPG signals show low periodicity, after the noise reduction, clear peaks can be observed. In this case, the intuitive UDA solution DANN also may not be able to learn domain-invariant representation with domain labels only for supervision. The cycle self-training strategy can only adaptively overcome a part of the domain discrepancy. Whereas, the EfficientT1, PhysFormer, and Synthetic methods pretrained on larger datasets show better robustness." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.245, + 0.892, + 0.473 + ], + "angle": 0, + "content": "From PURE to UBFC-rPPG. In this experiment, we select the PURE dataset with head motion as the source domain and the UBFC-rPPG dataset with compression and a wider range of heart rate as the target domain. The experimental results are shown in Table 4. The compression enlarges the domain discrepancy for rPPG estimation because some information is lost during compression and facial intensities are changed. Our proposed method can simulate the compression-induced noise and provide detailed information to effectively align rPPG features. In this setting, the pre-trained rPPG models in [34, 38] cannot handle the relatively larger domain gap (caused by the video compression) well. For common UDA methods, the high-level guidance from domain classification cannot fully guide the rPPG feature alignment and noise is still preserved in rPPG features." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.476, + 0.892, + 0.717 + ], + "angle": 0, + "content": "In this cross-dataset evaluation, we show the domain adaptation process in rPPG estimation under various domain discrepancies. Experimental results show that adapting deep rPPG models to less challenging scenarios, common UDA methods are effective. However, to adapt deep rPPG models to more challenging scenarios, more detailed information about the rPPG waveform is desired to reduce the domain discrepancy. And our method can provide both noise patterns and waveform information with the synthesized samples for noise reduction training. We can find that the domain discrepancy has been reduced after noise reduction, as shown in Figure 4, especially for the harder cases PURE \\(\\rightarrow\\) MMSE-HR. Compared to collecting large-scale dataset to improve the generalization ability of deep rPPG models, our dual-bridging noise modeling network is effective and convenient." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Ablation study. We conduct ablation study with cross-dataset settings to show the effectiveness of each bridge in our method as shown in Table 5. We first show the experimental result of the pre-train model. The \\(\\mathrm{NR} \\leftrightarrow \\mathrm{D}\\) represents that a noise reducer and a domain classifier are adversarially trained to reduce the domain discrepancy. Denoised target domain features are used to estimate rPPG signals. The noise reducer can adaptively overcome some noise patterns under a small domain discrepancy. When the domain discrepancy is large, the domain labels may not provide enough detailed information for training the noise reducer. To prevent the noise reducer from generating random phys" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "10361" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.342, + 0.09, + 0.629, + 0.105 + ], + "angle": 0, + "content": "Table 5. Experimental results for ablation study." + }, + { + "type": "table", + "bbox": [ + 0.192, + 0.115, + 0.778, + 0.235 + ], + "angle": 0, + "content": "
MethodMMSE-HR → PUREPURE → MMSE-HR
MAERMSErMAERMSEr
Pre-trained rPPG model2.969.570.912.093.920.98
+ NR ↔ D2.137.140.9520.2726.340.58
+ NR ↔ D + G ↔ D1.663.660.981.883.850.98
+ NR ↔ D + G ↔ D + G|NR ↔ D1.131.710.991.713.720.98
+ NR ↔ D + G ↔ D + G|NR ↔ D + HM1.101.670.991.884.160.98
" + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.258, + 0.46, + 0.391 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.403, + 0.471, + 0.459 + ], + "angle": 0, + "content": "Figure 4. Visualization of rPPG estimation before (orange) and after (green) noise reduction compared with GT-PPG (blue). (a) contains examples of MMSE-HR \\(\\rightarrow\\) PURE evaluation and (b) is of PURE \\(\\rightarrow\\)MMSE-HR." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.489, + 0.47, + 0.745 + ], + "angle": 0, + "content": "iological features under adversarial training, the strong regression supervision from rPPG waveform is necessary. For \\(\\mathrm{NR} \\leftrightarrow \\mathrm{D} + \\mathrm{G} \\leftrightarrow \\mathrm{D}\\), the noise generator is not conditioned on the noise reducer and can also synthesize noisy samples to train the noise reducer. The synthesized noisy samples prevent the noise reducer from generating random physiological features with detailed guidance from PPG signals. For \\(\\mathrm{NR} \\leftrightarrow \\mathrm{D} + \\mathrm{G} \\leftrightarrow \\mathrm{D} + \\mathrm{G}|\\mathrm{NR} \\leftrightarrow \\mathrm{D}\\), i.e., dual-bridging with adversarial noise generation, the noise patterns in the target domain can be progressively generated to improve the denoising ability. The hard noise pattern mining can improve the robustness of the noise reducer when there is less interference in the target domain. However, with strong interference in the target domain, too many hard noise patterns may distract the noise reducer from overcoming originally generated noise patterns and we saw a decrease of performance in the PURE \\(\\rightarrow\\) MMSE-HR." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.759, + 0.195, + 0.774 + ], + "angle": 0, + "content": "4.6. Discussion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.469, + 0.901 + ], + "angle": 0, + "content": "The generalization problem is a key challenge in applying rPPG techniques to real-world health monitoring applications. Especially for deep learning-based rPPG methods, the training data contain certain biases that may prevent rPPG models from learning domain-invariant physiological representations. Results show that generating noise patterns in the target domain and synthesizing samples for noise reduction can effectively reduce the domain discrepancy." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.26, + 0.843, + 0.275 + ], + "angle": 0, + "content": "ancy thereby improving the quality of rPPG signals." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.276, + 0.892, + 0.441 + ], + "angle": 0, + "content": "We also found the effectiveness of using domain labels to help domain-invariant physiological representation learning when domain discrepancy is small. However, when domain discrepancy increases, the gain of feature alignment in such adversarial training tends to be smaller. Without target domain labels for noise reduction, generating noise patterns similar to the target domain is easier than directly denoising target domain features under a large domain discrepancy. In the noise generation procedure, some out-of-distribution noise patterns can also be generated and can further improve the generalization ability for unseen interferences." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.443, + 0.892, + 0.563 + ], + "angle": 0, + "content": "Although our dual-bridging adaptation can work on most cases and achieve state-of-the-art, we still have limitations on handling hard cases with very large domain discrepancies (e.g., large head motion + facial expression + video compression in Table 4). Such rarely happened combined artifacts and can be regarded as a long-tailed distribution (of artifacts) problem. How to pay more attention to those rare but hard cases could be a key to solve it in the future." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.58, + 0.619, + 0.595 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.602, + 0.892, + 0.83 + ], + "angle": 0, + "content": "Recent deep learning-based rPPG methods can learn to overcome non-physiological intensity variations from data, but may also involve bias induced by data and hinder the generalization ability. In this paper, we proposed a novel dual-bridging noise modeling network to reduce the domain discrepancy in rPPG estimation. With the proposed tri-adversarial optimization, the noise generator can progressively explore the noise patterns in the target domain and the coarse-to-fine guidance can effectively improve the noise reduction ability. In addition, comprehensive evaluations of different domain discrepancies show the effectiveness of our method. In future work, we may consider using unlabeled and synthesised [42] facial videos from multiple domains with various external interferences to learn domain-invariant physiological representations." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.845, + 0.681, + 0.861 + ], + "angle": 0, + "content": "6. Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.9 + ], + "angle": 0, + "content": "This project is partially supported by Hong Kong RGC General Research Fund RGC/HKBU12200820." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10362" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.17 + ], + "angle": 0, + "content": "[1] Serge Bobbia, Richard Macwan, Yannick Benezeth, Alamin Mansouri, and Julien Dubois. 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Yuen +Department of Computer Science, Hong Kong Baptist University, Hong Kong +csjddu, siqiliu, csbczhang, pcyuen @comp.hkbu.edu.hk + +# Abstract + +The remote photoplethysmography (rPPG) technique can estimate pulse-related metrics (e.g. heart rate and respiratory rate) from facial videos and has a high potential for health monitoring. The latest deep rPPG methods can model in-distribution noise due to head motion, video compression, etc., and estimate high-quality rPPG signals under similar scenarios. However, deep rPPG models may not generalize well to the target test domain with unseen noise and distortions. In this paper, to improve the generalization ability of rPPG models, we propose a dual-bridging network to reduce the domain discrepancy by aligning intermediate domains and synthesizing the target noise in the source domain for better noise reduction. To comprehensively explore the target domain noise, we propose a novel adversarial noise generation in which the noise generator indirectly competes with the noise reducer. To further improve the robustness of the noise reducer, we propose hard noise pattern mining to encourage the generator to learn hard noise patterns contained in the target domain features. We evaluated the proposed method on three public datasets with different types of interferences. Under different cross-domain scenarios, the comprehensive results show the effectiveness of our method. + +# 1. Introduction + +With the development of rPPG technology, physiological metrics such as heart rate [27], heart rate variability [34], respiratory rate [21] can also be estimated from facial videos. Deep learning-based rPPG methods overcome non-physiological intensity variations [30, 49] and model noise in training samples [24, 28]. Despite the high accuracy under intra-dataset evaluations, the deep rPPG models may not be able to generalize well to unseen interferences in the test domain. The domain gap is mainly from unseen non-physiological interferences such as lighting conditions, + +![](images/69a4b7f67cc20dde76cff892cc346fc36b4c52c233514d9d1b08c08abff9b352.jpg) +(a) GAN-based Noise Modeling + +![](images/52d17f5e609f0464fe54aa68ab7fec9d8437622d9032f3f5a67608612b140eb8.jpg) +(b) Intuitive UDA Solution +Figure 1. The comparison between (a) typical intra-dataset adversarial rPPG noise modeling, (b) an intuitive UDA framework for rPPG feature alignment, and (c) our proposed dual-bridging network with adversarial noise modeling and hard noise pattern mining $(HM)$ . Here SYN denotes synthetic data, DT is for the denoised target domain, $G$ , $D$ , and $NR$ denotes the generator, domain classifier, and noise reducer, respectively. + +![](images/6260a258ce919b07f23efdd9ce72255d5aa70b4ec89876708b6fac498dd91923.jpg) +(c) Dual-bridging with Adversarial Noise Generation (Ours) + +camera sensors, video compression algorithms, facial expressions, etc. They can induce distortions in estimated rPPG signals and reduce both the accuracy and the reliability of pulse-related metrics estimation. Considering it is hard to cover all interferences during the training stage, to improve the usability of rPPG in realistic applications, one main challenge is how to boost the generalizability of rPPG models to unseen scenarios. + +In recent research of rPPG, both deep learning-based frameworks and mechanisms [45, 46, 49] are proposed to overcome the non-physiological intensity variations. GAN-based disentanglement learning has also been adopted to reduce the noise from pseudo [28] or synthesized [24] noisy features. We summarize this approach in Figure 1 (a) where a discriminator is employed to distinguish the generated feature (SYN in figure) from the original one. These methods can perform well under intra-dataset evaluation settings since the in-distribution noise patterns are thoroughly investigated with a large number of adversarial learning iterations. However, they may fail when encountering unseen + +domains in real application scenarios since noise patterns may be different from the ones of training data. + +Intuitively, the unsupervised domain adaptation (UDA) technique can help in bridging the gap between source and target domain [7, 14, 17, 44]. As shown in Figure 1 (b), a noise reducer module $NR$ that aims to obtain noise-free domain-invariant representations can be learned by fighting against the domain classifier $D$ . However, this intuitive solution may not work well since the domain classification may not be able to give sufficient information for $NR$ to identify whether the feature components are noise or physiological information. Directly aligning the rPPG features from different domains may end up distorting the physiological information since they are from different subjects. The ground-truth PPG (GT-PPG) signal with detailed waveform information helps preserve the physiological information and can provide much more informative guidance with the regression task. However, GT-PPG is available in the source domain but not the target domain. How to leverage the source domain GT-PPG to train $NR$ to be robust to the noise from the target domain is the key issue to be solved in this work. To achieve it we propose the dual bridging noise modeling network as shown in Figure 1 (c). The first bridging works as high-level guidance where the denoised target domain feature is adversarially pulled to the source domain feature (as Figure 1 (b)). On top of it, the second bridging aims to help synthesize the target domain noise and inject it into the source domain denoised feature so that the GT-PPG regression can help finetune the $NR$ for better robustness in the target domain. An adversarial noise generation module $(G|NR)$ is designed where the generator is conditioned on the $NR$ so that it keeps on overcoming the complex noise pattern that can hardly be solved in the first bridging. With the high-level guidance (first bridging) and detailed signal regression (second bridging), the $NR$ can handle the target domain noise better and therefore improve the accuracy of rPPG estimation in the target domain. To further discover the remaining noise vestige, we build a hard noise pattern mining mechanism to squeeze the unsolved local noise pattern from the denoised target feature so that $G|NR$ can thoroughly synthesize it. + +In sum, the contributions of this work are: (1) A dual-bridging noise modeling network that adapts target domain noise in a coarse-to-fine manner. (2) An adversarial noise generation mechanism to progressively synthesize and inject the hard target domain noisy features into the source domain while keeping the physiological information. (3) A hard noise pattern mining mechanism to further explore the target domain noise patterns with larger variations. We evaluated the proposed method on three public datasets with various types of interferences including facial motion and expression, video compression, skin tone, and heartbeat ranges. Under different cross-domain scenarios, the com + +The prehensive results show the effectiveness of our method. + +# 2. Related Work + +# 2.1. Remote physiological estimation + +Traditional rPPG methods [5, 16, 32, 39, 40, 41] estimate pulse signal from facial videos by extracting and modeling the detailed heartbeat-caused skin color variation. To estimate pulse-induced intensity variations with more details from facial videos, deep learning-based networks and mechanisms have been proposed. With facial video input, various spatial-temporal neural networks have been developed [4, 20, 22, 23, 37, 48, 49]. To evaluate the effectiveness, rPPG datasets with various interferences including head motion [36], facial expression [15, 39], video compression [9], and skin color [42] are constructed. In addition, rPPG estimation can be conducted from pre-processed representations like normalized difference [3, 18, 21, 30], spatial-temporal map [24, 28]. To further improve robustness, self-adaptive [3, 21] and background-guided [19, 30] attention mechanisms have been proposed to emphasize important facial regions in physiological representation. Furthermore, [28] proposed the cross-verified strategy to disentangle noise and physiological representation and [24] proposed to model in-distribution noise for learning noise-resistant physiological representation. [25, 26] proposed to synthesize diverse facial videos for rPPG estimation. Unsupervised learning-based methods [8, 37] are also proposed to learn rPPG estimation from unlabeled facial videos. However, the previously proposed methods are prone to experience performance drops in cross-dataset evaluation, where the target domain may contain unseen noise. This is due to unseen noise patterns that may not be fully overcome, and the physiological representation may be polluted and cause distortions in the rPPG signals. + +# 2.2. Unsupervised domain adaptation methods + +In recent research on computer vision, many unsupervised domain adaptation methods have been proposed to learn domain-invariant representation. [7] proposed to suppress domain-invariant information with domain label guided adversarial training. [33] proposed a bi-directional generation framework that can map target domain samples to the source domain and preserve semantic information for classification. [14] proposed to use adversarial domain training and distributional feature alignment guided by maximum density divergence to achieve adaptation. [43] considered that domain adversarial training may not be coordinated with the main task and proposed using meta-learning to improve the effectiveness of feature alignment. Unlike common computer vision tasks, feature alignment in the rPPG estimation requires more detailed information which cannot be fully provided by domain labels. There + +![](images/9d2bf40e180d984b60d5b1068046ab31a1684675c4a88cacb499c8eeab28b5c1.jpg) +Figure 2. Framework of the dual-bridging noise modeling network. The dual-bridging can reduce the domain discrepancy in the feature space by training the noise reducer with both high-level guidance from domain classification and detailed waveform guidance from synthetic features regression. The adversarial noise generation forces the generator $G$ to compete with the noise reducer $NR$ and synthesize noisy features with unsolved noise in the target domain. The hard noise pattern mining removes high-quality temporal features and encourages the generator to further explore hard noise patterns in the target domain. + +fore, we propose the dual-bridging noise modeling network to take advantage of both domain labels and the source domain ground truth to guide the rPPG feature alignment. + +# 3. Proposed Method + +The overview of the proposed dual-bridging noise modeling network is shown in Figure 2. Given the input face video from the source and target domain, we construct the STMap (details are in section 4.2) as the input of the feature extractor and then perform dual-bridging noise modeling on the middle representation. The first bridging provides high-level guidance where the source feature $f_{j}^{s}$ and the denoised target feature $f_{i}^{t}$ are pulled together with the domain classifier. The synthesized target domain feature $f_{j}^{s}$ is obtained from the $f_{i}^{t}$ through the adversarial noise generation module. The second bridge aims to pull $f_{j}^{s}$ to $f_{i}^{t}$ so that the target domain noise can be overcome by $NR$ with the guidance of PPG $y_{s}$ (regression) The generator in the adversarial noise generation module is conditioned on the $NR$ so that it keeps on overcoming the complex noise pattern that can hardly be solved in the first bridging. With the dual-bridging noise modeling that contains both high-level (first bridge) and detailed waveform guidance (second bridge), the $NR$ can handle the target domain noise better. Finally, $NR$ works with the feature extractor and rPPG estimator to do the rPPG estimation in the target domain. + +# 3.1. Dual-bridging + +With respect to the feature extractor $\Theta$ , we define source domain features as $F_{s} = \{f_{j}^{s}\}_{j = 1}^{M}$ and target domain features as $F_{t} = \{f_{i}^{t}\}_{i = 1}^{N}$ , where $f_{j}^{s} = \Theta (x_{j}^{s})$ and $f_{i}^{t} = \Theta (x_{i}^{t})$ . Since the rPPG patterns are similar between different participants, the pre-trained feature extractor can preserve enough physiological information in $F_{t}$ and noise modeling is the key to noise reduction of the target domain features. Detailed information for guidance is necessary to overcome the complex noise in the target domain features. + +To reduce the noise contained in $F_{t}$ , we propose the adaptive noise reduction bridging to reduce the noise contained in target domain features supervised by the domain classifier. In this bridging, we design the noise reducer with the noise estimation function $\Phi$ in a residual way as follows: + +$$ +\hat {f} _ {i} ^ {t} = f _ {i} ^ {t} - \Phi \left(f _ {i} ^ {t}\right) \tag {1} +$$ + +where $\hat{f}_i^t$ is a denoised physiological feature and we define $\hat{F}_t = \{\hat{f}_i^t\}_{i=1}^N$ as the denoised target domain. The direct estimation of high-quality physiological features could be hard, and we choose to estimate the noise and use the residual structure to reduce the noise in the target domain features. We build an adversarial training between the noise reducer $\Phi$ and the domain classifier $D$ as follows: + +$$ +\max _ {D} \min _ {\Phi} L _ {N R} = \mathbb {E} [ \| 1 - D \left(f _ {j} ^ {s}\right) \| _ {2} ] + \mathbb {E} [ \| D \left(\hat {f} _ {i} ^ {t}\right) \| _ {2} ] \tag {2} +$$ + +With high-level guidance from domain classification, some simple noise patterns can be overcome, and less noisy features can be aligned. However, high-level guidance may not overcome complex noise patterns without detailed waveform information for guidance. And the brute-force feature alignment may even change the physiological information of rPPG features when complex noise patterns are encountered. The phenomenon can be reflected by our ablation study in section 4.3. + +To involve detailed information for supervision, we propose the complex noise generation bridging to generate target domain noise and synthesize noisy features to guide the noise reducer. From the source domain direction, we estimate the noise patterns in the target domain by generating noise and synthesizing noisy features as follows: + +$$ +\bar {f} _ {j} ^ {s} = f _ {j} ^ {s} + \Psi (n _ {k}) \tag {3} +$$ + +where $\overline{f}_j^s$ is a raw noisy feature, $n_k$ is random noise, and $\Psi$ is the generator. And we define the synthetic feature domain $\hat{F}_s = \{\hat{f}_j^s\}_{j=1}^M$ as follows: + +$$ +\hat {f} _ {j} ^ {s} = \bar {f} _ {j} ^ {s} - \Phi \left(\bar {f} _ {j} ^ {s}\right) \tag {4} +$$ + +To control the range of noise generation, we build the adversarial training between the noise generator and the domain classifier with respect to the denoised target domain as follows: + +$$ +\begin{array}{l} \underset {D} {\max} \underset {\Psi} {\min} L _ {G} = \mathbb {E} [ \| 1 - D (f _ {j} ^ {s}) \| _ {2} ] + \mathbb {E} [ \| D (\overline {{f}} _ {j} ^ {s}) \| _ {2} ] \\ + \mathbb {E} [ \| D (\hat {f} _ {i} ^ {t}) \| _ {2} ] \quad (5) \\ \end{array} +$$ + +In this bridging, the domain classifier can guide the generator to learn target domain noise patterns and synthesize noisy features with preserved physiological information. Thus, the source domain PPG signals $y_{j}^{s}$ can be utilized to guide the noise reducer to overcome generated complex noise patterns as follows: + +$$ +L _ {S Y N} = 1 - r \left(E \left(\hat {f} _ {j} ^ {s}\right), y _ {j} ^ {s}\right) \tag {6} +$$ + +$E$ is the rPPG estimator, and $r$ is the Pearson correlation function. With this bridging, the physiological information can be preserved in the noise reduction and the other bridging can align more target domain features under large domain discrepancy. + +# 3.2. Adversarial noise generation + +With the guidance from the domain classifier, part of the target domain noise patterns can be generated. However, in the adversarial training process, the generator may not fully explore target domain noise patterns. To comprehensively explore the target domain noise for rPPG feature alignment, we propose a novel adversarial noise generation. As shown + +![](images/bbd318603034ac46a71b923721f314f8c178fd598942fc7bacc0adb3b6c1f37e.jpg) +Figure 3. Illustration of hard noise pattern mining. + +in Figure 2, the generator is conditioned on the noise reducer and forced to explore the unsolved noise contained in the target domain features. The noise reducer is trained with the synthetic features and corresponding PPG signals to overcome the generated noise. The adversarial correlation between the generator and the noise reducer is shown as follows: + +$$ +\max _ {\Psi} \min _ {\Phi} L _ {A N G} = \mathbb {E} [ \| 1 - D (\hat {f} _ {j} ^ {s}) \| _ {2} ] + \mathbb {E} [ 1 - r (E (\hat {f} _ {j} ^ {s}), y _ {j} ^ {s}) ] \tag {7} +$$ + +This adversarial training is based on two different optimization functions, but not the gradient reverse layer. Therefore, the novel noise patterns are not generated based on adversarial attacks but are searched from unsolved noise patterns in the target domain. With our adversarial noise generation, the dual-bridging structure can progressively generate target domain noise patterns, and the noise reduction ability can be significantly improved. + +# 3.3. Hard noise pattern mining + +To further improve the robustness of the noise reducer, we propose the hard noise pattern mining as illustrated in Figure 3. Considering the redundancy of rPPG estimation, features with one or several high-quality temporal features can contribute to accurate estimation. Thus, the noise reducer may just learn to overcome relatively simple noise patterns and some hard noise patterns may not be learned. To further explore the hard noise patterns, we need to reduce the shortcuts for noise reduction and generate hard noise patterns for training. In our hard noise pattern mining module, we identify high-quality temporal features with respect to the morphology consistency $M$ which is defined as follows: + +$$ +M = \max _ {t = 1} ^ {n} r \left(g _ {0: T}, g _ {t: t + T}\right) \tag {8} +$$ + +$r$ is the Pearson correlation, $g$ is a temporal feature, $t$ is the sliding start point, and $T$ is the time length of morphology consistency evaluation. With respect to the morphology consistency, we define temporal features with significant periodicity as high-quality features. After identifying high-quality temporal features, we can remove the corresponding feature slice and preserve hard slices for noise generation. Correspondingly, more hard noise patterns will be generated and the noise reduction ability can be further improved for rPPG feature alignment. + +The detailed optimization process of our proposed + +Algorithm 1 The optimization process for our dual-bridging algorithm. + +Input: Noise generator $\Psi$ , noise reducer $\Phi$ and domain classifier $D$ , total epochs $L$ , mini-batch $B$ , source domain samples $x_{j}^{s}$ , source domain labels $y_{j}^{s}$ , target domain samples $x_{i}^{t}$ . + +for $l = 1$ to $L$ do + +for $b = 1$ to $B$ do + +Obtain $f_{j}^{s}$ and $f_{i}^{t}$ with pre-trained feature extractor from $x_{j}^{s}$ and $x_{i}^{t}$ + +Obtain $\hat{f}_i^t$ with noise reducer + +Update noise reducer $\Phi$ and domain classifier $D$ with $L_{DE}$ + +Generate $\overline{f}_j^s$ and $\hat{f}_j^s$ with updated noise reducer and noise generator + +Update noise generator $\Psi$ with $L_{G}$ and $L_{R}$ + +Update noise reducer $\Phi$ with $L_{SYN}$ + +end for + +end forOutput: Learned noise reducer $\Phi$ + +method is shown in Algorithm 1. After training the dual-bridging algorithm, we can estimate rPPG signals in the target domain as follows: + +$$ +\hat {y} _ {i} ^ {t} = E \left(\Theta \left(x _ {i} ^ {t}\right) - \Phi \left(\Theta \left(x _ {i} ^ {t}\right)\right)\right) \tag {9} +$$ + +$\hat{y}_i^t$ is the estimated rPPG signal. + +# 4. Experiments + +We conduct experiments on three publicly available datasets with different types of interference to evaluate the accuracy and generalization ability of our dual-bridging noise modeling network. Three protocols that simulate the typical domain discrepancies in real application scenarios are adopted, i.e., 1) task-independent evaluation, 2) participant-independent evaluation, and 3) cross-dataset evaluation. Mean absolute error (MAE), root mean square error (RMSE), and Pearson correlation coefficient (r) are adopted to evaluate the performance of average heart rate based on the estimated rPPG signal. The unit for MAE and RMSE is beats per minute (bpm). + +# 4.1. Datasets and Baselines + +We evaluate the proposed method on the following datasets, which cover different types/levels of head motion, facial expression, compression artifacts, skin color, and also heartbeat ranges. + +PURE [36] dataset contains facial videos of 10 Caucasian participants (8 men, 2 women) in six different behavior modes with head motion and facial expression. The videos are uncompressed and captured at 30fps in $640 \times 480$ . Synchronized GT-PPG signals are captured at $60\mathrm{Hz}$ using pulse oximeter pulox CMS50E. + +MMSE-HR [39] datasets contains 102 facial videos captured from 40 participants of different ethnicities with different emotions. The emotion-related spontaneous facial expressions can also induce facial intensity variations. The video frames are captured at 25fps in $1040 \times 1392$ and compressed in JPG format, and their frame rate is $25\mathrm{Hz}$ . GT blood volume signals are captured by the Biopac MP150. + +UBFC-rPPG [1] dataset contains 42 facial videos captured under a human-computer interaction scene which causes head motions and larger heart rate range (63-145 bpm). Videos are recorded by the Logitech C920 Webcam at 30fps in $640 \times 480$ . Synchronized GT-PPG signals are captured by CMS50E. + +Baselines We compared the proposed method with traditional rPPG methods [5, 16, 32, 39, 40, 41] and the latest deep rPPG models [3, 4, 13, 21, 22, 23, 24, 27, 28, 29, 34, 37, 45, 47, 49] to show the generalization ability. We also compared the proposed method with popular UDA methods [7, 17] to show the effectiveness of rPPG feature alignment. + +# 4.2. Implementation details + +Our method is implemented with PyTorch and trained on an NVIDIA Tesla V100. We align the facial regions with four landmarks using the perspective transformation and generate the STmap [27] as input. We resample all STmaps and the corresponding labels at $30\mathrm{Hz}$ . The frame number for each STmap is 300 and adjacent STmaps have 270 overlapped frames. In experiments, we pre-train the 2D CNN model on the source domain for rPPG estimation. The threshold of morphology consistency for hard noise pattern mining is 0.82. In the domain adaptation training stage, we set the batch size to 64 and adopt the Adam optimizer [11] for training. The learning rate for the noise pattern generator and noise reducer is 1e-4. And the learning rate for the domain classifier is 3e-5. The weight decay is 1e-4 for all optimizers. We train our domain adaptation algorithm for 200 epochs in the task-independent and PURE to MMSE-HR evaluations, and 2000 epochs in the MMSE-HR to PURE evaluation. We select the weights of the noise reducer for the test according to the estimation loss of synthesized samples. Under certain domain discrepancies, the details of the rPPG signals may not be preserved. + +# 4.3. Task-independent evaluation + +We first evaluate the proposed method in the task-independent scenario, which has a smaller domain discrepancy. The MMSE-HR collected facial videos under different activities and we regard each activity as a task. Within MMSE-HR, the unseen non-physiological intensity variations are mainly induced by different head motion and facial expression changes. In this evaluation, we set one task as the target domain and the other tasks as the source domain. From the experimental results in Table 1, we can find that even under the intra-dataset scenario, the domain + +Table 1. Experimental results for task-independent evaluation on MMSE-HR. + +
MethodMAERMSEr
Li2014 [16]-19.950.38
CHROM [5]-13.970.55
Tulyakov2016 [39]-11.370.71
ST-Attention* [29]-10.100.64
RhythmNet [27]-5.030.86
CVD* [28]-6.040.84
PhysNet [47]-13.250.44
DeepPhys [3]4.439.980.80
TS-CAN [21]3.857.210.86
AutoHR [45]-5.870.89
BVPNet [4]-7.470.79
Federated2022 [23]2.992.420.79
EfficientPhys-C [22]2.915.430.92
EfficientPhys-T1 [22]3.487.210.86
PhysFormer* [49]2.845.360.92
ERM [12]1.302.580.99
DANN [7]1.242.710.99
CST [17]1.202.420.99
Ours0.852.050.99
+ +* Trained on VIPL-HR datasets due to the large model-scale + +Table 2. Experimental results for participant-independent evaluation on UBFC-rPPG dataset. + +
MethodMAERMSEr
GREEN [40]4.4711.60.842
ICA [32]3.518.640.908
CHROM [5]3.444.610.968
POS [41]2.446.610.936
CK [35]2.293.800.981
Frédéric [2]5.458.64-
HeartTrack [31]2.413.370.983
ETA-rPPGNet [10]1.463.970.93
DAE [34]1.482.490.97
PulseGAN [34]1.192.100.98
Meta-rPPG [13]5.977.420.53
CVD [28]2.193.120.99
Gideon2021 [8]3.64.60.95
Federated2022 [23]2.004.380.93
Dual-GAN [24]0.440.670.99
ContrastPhys [37]0.641.000.99
ERM [12]0.751.840.99
DANN [7]0.581.190.99
CST [17]0.411.040.99
Ours0.160.570.99
+ +discrepancy can decrease the performance of deep rPPG models. And under small domain discrepancies, common UDA methods are effective and can overcome certain noise + +patterns in the target domain. Our method can effectively reduce the unseen non-physiological intensity variations in feature space through noise reduction of rPPG features and achieves state-of-the-art performance. + +# 4.4. Participant-independent evaluation. + +The domain discrepancy can also come from differences between participants like head motions under human-computer interaction scenarios. Caucasian and Asian participants are included and we evaluate this participant-independent setting with the UBFC-rPPG dataset. We follow the protocol in [24,34] to select 30 participants for training and use the rest 12 participants for testing. As the experimental results shown in Table 2, the domain discrepancy is small with respect to deep rPPG models and pre-trained rPPG models also have low error. Compared to common UDA methods, our proposed method can provide more detailed information for noise reduction supervision and more noise patterns can be overcome in the feature alignment. + +# 4.5. Cross-dataset evaluation + +Our method is also evaluated in the cross-dataset setting with MMSE-HR and PURE. The selected datasets have differences in aspects such as head motion, From the view of the rPPG estimation, the MMSE-HR dataset contains more challenging scenarios (video compression, facial expression changes) than the PURE dataset. A challenging source domain could be beneficial to generalization ability and reduce the difficulty of the adaptation process. We provide details of the cross-dataset evaluations in the following paragraphs. + +From MMSE-HR to PURE. In this experiment, we select the MMSE-HR dataset as the source domain and the PURE dataset as the target domain. Since the source domain is more challenging than the target domain, the adaptation process could be relatively easy. The experimental results are shown in Table 3. We can find that DANN cannot improve the generalization ability of rPPG models and only high-level guidance cannot align noisy features to high-quality features. While the cycle self-training strategy can provide certain details of the rPPG waveform and is more effective in reducing the domain discrepancy in rPPG estimation. Our method can progressively generate noise patterns in the target domain and synthesize noisy samples to provide detailed information from the source domain labels. Our method achieves state-of-the-art performance in this UDA scenario, and the low RMSE shows that our method is effective in reducing strong outliers. We provide some examples in Figure 3 (a) in which the noise reduction process can remove fake peaks in one period. After removing fake peaks, the periodicity of rPPG signal can be improved and the heart rate estimation can be more accurate. + +From PURE to MMSE-HR. In this experiment, we select the PURE dataset that has fewer facial videos with mild + +Table 3. Experimental results for cross-dataset evaluation between PURE and MMSE-HR datasets. + +
MethodMMSE-HR → PUREPURE → MMSE-HR
MAERMSErMAERMSEr
CHROM [5]3.2512.920.845.7212.690.58
POS [41]2.8312.490.854.9813.110.53
CVD [28]2.753.980.984.087.030.84
ERM [12]2.498.480.932.595.440.96
DANN [7]2.696.970.952.847.650.93
CST [17]1.272.960.992.325.970.96
EfficientT1 [22]---3.045.910.92
PhysFormer [49]---2.845.360.92
Synthetic [25]---2.263.700.97
Ours1.101.670.991.713.720.98
+ +Table 4. Experimental results for cross-dataset evaluation from PURE to UBFC-rPPG. + +
MethodPURE → UBFC-rPPG
MAERMSEr
CHROM [5]3.106.840.93
POS [41]3.526.840.90
DAE [34]2.705.170.96
PulseGAN [34]2.094.420.97
Siamese-rPPG [38]1.298.73-
Dual-GAN [24]0.741.020.99
ERM [12]1.503.360.96
DANN [7]3.246.130.96
CST [17]2.244.730.97
Ours0.581.110.99
+ +interferences (like slow head rotation, translation) as the source Compared to the MMSE $\rightarrow$ PURE setting, the domain gap in PURE $\rightarrow$ MMSE is harder to overcome since the noise patterns in the target domain are more challenging. In this experiment, our method is also compared with two rPPG methods [22, 49] which are pre-trained in the VIPL-HR dataset with more facial videos and scenarios. We also compare with [25] which uses synthetic facial videos and the AFRL dataset [6] for training. As shown in Table 3, in this challenging setting, we find that all baseline methods have lower performance compared with the other cross-dataset settings. Under this challenging setting, our dual-bridging with adversarial noise generation algorithm can effectively explore the specific noise patterns from the target domain. Additionally, by synthesizing noisy features similar to target domain features, the noise reduction ability can be dramatically improved to reduce the domain discrepancy. And our method can achieve state-of-the-art performance under this cross-dataset validation. We also provide some + +examples in Figure 3 (b) and find that noise reduction can improve the quality of rPPG signals. Especially some noisy rPPG signals show low periodicity, after the noise reduction, clear peaks can be observed. In this case, the intuitive UDA solution DANN also may not be able to learn domain-invariant representation with domain labels only for supervision. The cycle self-training strategy can only adaptively overcome a part of the domain discrepancy. Whereas, the EfficientT1, PhysFormer, and Synthetic methods pretrained on larger datasets show better robustness. + +From PURE to UBFC-rPPG. In this experiment, we select the PURE dataset with head motion as the source domain and the UBFC-rPPG dataset with compression and a wider range of heart rate as the target domain. The experimental results are shown in Table 4. The compression enlarges the domain discrepancy for rPPG estimation because some information is lost during compression and facial intensities are changed. Our proposed method can simulate the compression-induced noise and provide detailed information to effectively align rPPG features. In this setting, the pre-trained rPPG models in [34, 38] cannot handle the relatively larger domain gap (caused by the video compression) well. For common UDA methods, the high-level guidance from domain classification cannot fully guide the rPPG feature alignment and noise is still preserved in rPPG features. + +In this cross-dataset evaluation, we show the domain adaptation process in rPPG estimation under various domain discrepancies. Experimental results show that adapting deep rPPG models to less challenging scenarios, common UDA methods are effective. However, to adapt deep rPPG models to more challenging scenarios, more detailed information about the rPPG waveform is desired to reduce the domain discrepancy. And our method can provide both noise patterns and waveform information with the synthesized samples for noise reduction training. We can find that the domain discrepancy has been reduced after noise reduction, as shown in Figure 4, especially for the harder cases PURE $\rightarrow$ MMSE-HR. Compared to collecting large-scale dataset to improve the generalization ability of deep rPPG models, our dual-bridging noise modeling network is effective and convenient. + +Ablation study. We conduct ablation study with cross-dataset settings to show the effectiveness of each bridge in our method as shown in Table 5. We first show the experimental result of the pre-train model. The $\mathrm{NR} \leftrightarrow \mathrm{D}$ represents that a noise reducer and a domain classifier are adversarially trained to reduce the domain discrepancy. Denoised target domain features are used to estimate rPPG signals. The noise reducer can adaptively overcome some noise patterns under a small domain discrepancy. When the domain discrepancy is large, the domain labels may not provide enough detailed information for training the noise reducer. To prevent the noise reducer from generating random phys + +Table 5. Experimental results for ablation study. + +
MethodMMSE-HR → PUREPURE → MMSE-HR
MAERMSErMAERMSEr
Pre-trained rPPG model2.969.570.912.093.920.98
+ NR ↔ D2.137.140.9520.2726.340.58
+ NR ↔ D + G ↔ D1.663.660.981.883.850.98
+ NR ↔ D + G ↔ D + G|NR ↔ D1.131.710.991.713.720.98
+ NR ↔ D + G ↔ D + G|NR ↔ D + HM1.101.670.991.884.160.98
+ +![](images/c25b9db073f3494126013c1a3aa9745938f12ea648f409acf290b634e88feb85.jpg) +Figure 4. Visualization of rPPG estimation before (orange) and after (green) noise reduction compared with GT-PPG (blue). (a) contains examples of MMSE-HR $\rightarrow$ PURE evaluation and (b) is of PURE $\rightarrow$ MMSE-HR. + +iological features under adversarial training, the strong regression supervision from rPPG waveform is necessary. For $\mathrm{NR} \leftrightarrow \mathrm{D} + \mathrm{G} \leftrightarrow \mathrm{D}$ , the noise generator is not conditioned on the noise reducer and can also synthesize noisy samples to train the noise reducer. The synthesized noisy samples prevent the noise reducer from generating random physiological features with detailed guidance from PPG signals. For $\mathrm{NR} \leftrightarrow \mathrm{D} + \mathrm{G} \leftrightarrow \mathrm{D} + \mathrm{G}|\mathrm{NR} \leftrightarrow \mathrm{D}$ , i.e., dual-bridging with adversarial noise generation, the noise patterns in the target domain can be progressively generated to improve the denoising ability. The hard noise pattern mining can improve the robustness of the noise reducer when there is less interference in the target domain. However, with strong interference in the target domain, too many hard noise patterns may distract the noise reducer from overcoming originally generated noise patterns and we saw a decrease of performance in the PURE $\rightarrow$ MMSE-HR. + +# 4.6. Discussion + +The generalization problem is a key challenge in applying rPPG techniques to real-world health monitoring applications. Especially for deep learning-based rPPG methods, the training data contain certain biases that may prevent rPPG models from learning domain-invariant physiological representations. Results show that generating noise patterns in the target domain and synthesizing samples for noise reduction can effectively reduce the domain discrepancy. + +ancy thereby improving the quality of rPPG signals. + +We also found the effectiveness of using domain labels to help domain-invariant physiological representation learning when domain discrepancy is small. However, when domain discrepancy increases, the gain of feature alignment in such adversarial training tends to be smaller. Without target domain labels for noise reduction, generating noise patterns similar to the target domain is easier than directly denoising target domain features under a large domain discrepancy. In the noise generation procedure, some out-of-distribution noise patterns can also be generated and can further improve the generalization ability for unseen interferences. + +Although our dual-bridging adaptation can work on most cases and achieve state-of-the-art, we still have limitations on handling hard cases with very large domain discrepancies (e.g., large head motion + facial expression + video compression in Table 4). Such rarely happened combined artifacts and can be regarded as a long-tailed distribution (of artifacts) problem. How to pay more attention to those rare but hard cases could be a key to solve it in the future. + +# 5. Conclusion + +Recent deep learning-based rPPG methods can learn to overcome non-physiological intensity variations from data, but may also involve bias induced by data and hinder the generalization ability. In this paper, we proposed a novel dual-bridging noise modeling network to reduce the domain discrepancy in rPPG estimation. With the proposed tri-adversarial optimization, the noise generator can progressively explore the noise patterns in the target domain and the coarse-to-fine guidance can effectively improve the noise reduction ability. In addition, comprehensive evaluations of different domain discrepancies show the effectiveness of our method. In future work, we may consider using unlabeled and synthesised [42] facial videos from multiple domains with various external interferences to learn domain-invariant physiological representations. + +# 6. Acknowledgement + +This project is partially supported by Hong Kong RGC General Research Fund RGC/HKBU12200820. + +# References + +[1] Serge Bobbia, Richard Macwan, Yannick Benezeth, Alamin Mansouri, and Julien Dubois. Unsupervised skin tissue segmentation for remote photoplethysmography. 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In CVPR, pages 4186-4196, 2022. 1, 2, 5, 6, 7 \ No newline at end of file diff --git a/2023/Dual-Bridging With Adversarial Noise Generation for Domain Adaptive rPPG Estimation/images.zip b/2023/Dual-Bridging With Adversarial Noise Generation for Domain Adaptive rPPG Estimation/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..07918be0e010eda7e0a0baab29163abce19d0715 --- /dev/null +++ b/2023/Dual-Bridging With Adversarial Noise Generation for Domain Adaptive rPPG Estimation/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:a23069a50c542e5885860c9962538692d0d34d9564ea8100429ab39a1e014da5 +size 479331 diff --git a/2023/Dual-Bridging With Adversarial Noise Generation for Domain Adaptive rPPG Estimation/layout.json b/2023/Dual-Bridging With Adversarial Noise Generation for Domain Adaptive rPPG Estimation/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..d3bf23e8c000df6e2c5953ee90d9ea7b8b5406ba --- /dev/null +++ b/2023/Dual-Bridging With Adversarial Noise Generation for Domain Adaptive rPPG Estimation/layout.json @@ -0,0 +1,8190 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 58, + 102, + 536, + 138 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 102, + 536, + 138 + ], + "spans": [ + { + "bbox": [ + 58, + 102, + 536, + 138 + ], + "type": "text", + "content": "Dual-bridging with Adversarial Noise Generation for Domain Adaptive rPPG Estimation" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 108, + 161, + 485, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 161, + 485, + 203 + ], + "spans": [ + { + "bbox": [ + 108, + 161, + 485, + 203 + ], + "type": "text", + "content": "Jingda Du*, Si-Qi Liu*, Bochao Zhang, Pong C. Yuen \nDepartment of Computer Science, Hong Kong Baptist University, Hong Kong \ncsjddu, siqiliu, csbczhang, pcyuen @comp.hkbu.edu.hk" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "spans": [ + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 256, + 290, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 256, + 290, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 256, + 290, + 533 + ], + "type": "text", + "content": "The remote photoplethysmography (rPPG) technique can estimate pulse-related metrics (e.g. heart rate and respiratory rate) from facial videos and has a high potential for health monitoring. The latest deep rPPG methods can model in-distribution noise due to head motion, video compression, etc., and estimate high-quality rPPG signals under similar scenarios. However, deep rPPG models may not generalize well to the target test domain with unseen noise and distortions. In this paper, to improve the generalization ability of rPPG models, we propose a dual-bridging network to reduce the domain discrepancy by aligning intermediate domains and synthesizing the target noise in the source domain for better noise reduction. To comprehensively explore the target domain noise, we propose a novel adversarial noise generation in which the noise generator indirectly competes with the noise reducer. To further improve the robustness of the noise reducer, we propose hard noise pattern mining to encourage the generator to learn hard noise patterns contained in the target domain features. We evaluated the proposed method on three public datasets with different types of interferences. Under different cross-domain scenarios, the comprehensive results show the effectiveness of our method." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 555, + 128, + 567 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 555, + 128, + 567 + ], + "spans": [ + { + "bbox": [ + 47, + 555, + 128, + 567 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 574, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 574, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 574, + 287, + 696 + ], + "type": "text", + "content": "With the development of rPPG technology, physiological metrics such as heart rate [27], heart rate variability [34], respiratory rate [21] can also be estimated from facial videos. Deep learning-based rPPG methods overcome non-physiological intensity variations [30, 49] and model noise in training samples [24, 28]. Despite the high accuracy under intra-dataset evaluations, the deep rPPG models may not be able to generalize well to unseen interferences in the test domain. 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Here SYN denotes synthetic data, DT is for the denoised target domain, " + }, + { + "bbox": [ + 304, + 374, + 547, + 453 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 374, + 547, + 453 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 374, + 547, + 453 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 374, + 547, + 453 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 374, + 547, + 453 + ], + "type": "inline_equation", + "content": "NR" + }, + { + "bbox": [ + 304, + 374, + 547, + 453 + ], + "type": "text", + "content": " denotes the generator, domain classifier, and noise reducer, respectively." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 428, + 228, + 541, + 346 + ], + "blocks": [ + { + "bbox": [ + 428, + 228, + 541, + 346 + ], + "lines": [ + { + "bbox": [ + 428, + 228, + 541, + 346 + ], + "spans": [ + { + "bbox": [ + 428, + 228, + 541, + 346 + ], + "type": "image", + "image_path": "6260a258ce919b07f23efdd9ce72255d5aa70b4ec89876708b6fac498dd91923.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 438, + 348, + 535, + 365 + ], + "lines": [ + { + "bbox": [ + 438, + 348, + 535, + 365 + ], + "spans": [ + { + "bbox": [ + 438, + 348, + 535, + 365 + ], + "type": "text", + "content": "(c) Dual-bridging with Adversarial Noise Generation (Ours)" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 474, + 547, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 547, + 568 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 547, + 568 + ], + "type": "text", + "content": "camera sensors, video compression algorithms, facial expressions, etc. They can induce distortions in estimated rPPG signals and reduce both the accuracy and the reliability of pulse-related metrics estimation. Considering it is hard to cover all interferences during the training stage, to improve the usability of rPPG in realistic applications, one main challenge is how to boost the generalizability of rPPG models to unseen scenarios." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": "In recent research of rPPG, both deep learning-based frameworks and mechanisms [45, 46, 49] are proposed to overcome the non-physiological intensity variations. GAN-based disentanglement learning has also been adopted to reduce the noise from pseudo [28] or synthesized [24] noisy features. We summarize this approach in Figure 1 (a) where a discriminator is employed to distinguish the generated feature (SYN in figure) from the original one. These methods can perform well under intra-dataset evaluation settings since the in-distribution noise patterns are thoroughly investigated with a large number of adversarial learning iterations. However, they may fail when encountering unseen" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 127, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 127, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 127, + 712 + ], + "type": "text", + "content": "* Equal contribution" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10355" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": "domains in real application scenarios since noise patterns may be different from the ones of training data." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 99, + 289, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 99, + 289, + 567 + ], + "spans": [ + { + "bbox": [ + 47, + 99, + 289, + 567 + ], + "type": "text", + "content": "Intuitively, the unsupervised domain adaptation (UDA) technique can help in bridging the gap between source and target domain [7, 14, 17, 44]. As shown in Figure 1 (b), a noise reducer module " + }, + { + "bbox": [ + 47, + 99, + 289, + 567 + ], + "type": "inline_equation", + "content": "NR" + }, + { + "bbox": [ + 47, + 99, + 289, + 567 + ], + "type": "text", + "content": " that aims to obtain noise-free domain-invariant representations can be learned by fighting against the domain classifier " + }, + { + "bbox": [ + 47, + 99, + 289, + 567 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 47, + 99, + 289, + 567 + ], + "type": "text", + "content": ". However, this intuitive solution may not work well since the domain classification may not be able to give sufficient information for " + }, + { + "bbox": [ + 47, + 99, + 289, + 567 + ], + "type": "inline_equation", + "content": "NR" + }, + { + "bbox": [ + 47, + 99, + 289, + 567 + ], + "type": "text", + "content": " to identify whether the feature components are noise or physiological information. Directly aligning the rPPG features from different domains may end up distorting the physiological information since they are from different subjects. The ground-truth PPG (GT-PPG) signal with detailed waveform information helps preserve the physiological information and can provide much more informative guidance with the regression task. However, GT-PPG is available in the source domain but not the target domain. How to leverage the source domain GT-PPG to train " + }, + { + "bbox": [ + 47, + 99, + 289, + 567 + ], + "type": "inline_equation", + "content": "NR" + }, + { + "bbox": [ + 47, + 99, + 289, + 567 + ], + "type": "text", + "content": " to be robust to the noise from the target domain is the key issue to be solved in this work. To achieve it we propose the dual bridging noise modeling network as shown in Figure 1 (c). The first bridging works as high-level guidance where the denoised target domain feature is adversarially pulled to the source domain feature (as Figure 1 (b)). On top of it, the second bridging aims to help synthesize the target domain noise and inject it into the source domain denoised feature so that the GT-PPG regression can help finetune the " + }, + { + "bbox": [ + 47, + 99, + 289, + 567 + ], + "type": "inline_equation", + "content": "NR" + }, + { + "bbox": [ + 47, + 99, + 289, + 567 + ], + "type": "text", + "content": " for better robustness in the target domain. An adversarial noise generation module " + }, + { + "bbox": [ + 47, + 99, + 289, + 567 + ], + "type": "inline_equation", + "content": "(G|NR)" + }, + { + "bbox": [ + 47, + 99, + 289, + 567 + ], + "type": "text", + "content": " is designed where the generator is conditioned on the " + }, + { + "bbox": [ + 47, + 99, + 289, + 567 + ], + "type": "inline_equation", + "content": "NR" + }, + { + "bbox": [ + 47, + 99, + 289, + 567 + ], + "type": "text", + "content": " so that it keeps on overcoming the complex noise pattern that can hardly be solved in the first bridging. With the high-level guidance (first bridging) and detailed signal regression (second bridging), the " + }, + { + "bbox": [ + 47, + 99, + 289, + 567 + ], + "type": "inline_equation", + "content": "NR" + }, + { + "bbox": [ + 47, + 99, + 289, + 567 + ], + "type": "text", + "content": " can handle the target domain noise better and therefore improve the accuracy of rPPG estimation in the target domain. To further discover the remaining noise vestige, we build a hard noise pattern mining mechanism to squeeze the unsolved local noise pattern from the denoised target feature so that " + }, + { + "bbox": [ + 47, + 99, + 289, + 567 + ], + "type": "inline_equation", + "content": "G|NR" + }, + { + "bbox": [ + 47, + 99, + 289, + 567 + ], + "type": "text", + "content": " can thoroughly synthesize it." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": "In sum, the contributions of this work are: (1) A dual-bridging noise modeling network that adapts target domain noise in a coarse-to-fine manner. (2) An adversarial noise generation mechanism to progressively synthesize and inject the hard target domain noisy features into the source domain while keeping the physiological information. (3) A hard noise pattern mining mechanism to further explore the target domain noise patterns with larger variations. We evaluated the proposed method on three public datasets with various types of interferences including facial motion and expression, video compression, skin tone, and heartbeat ranges. Under different cross-domain scenarios, the com" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 305, + 72, + 533, + 85 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 533, + 85 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 533, + 85 + ], + "type": "text", + "content": "The prehensive results show the effectiveness of our method." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 306, + 96, + 392, + 109 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 96, + 392, + 109 + ], + "spans": [ + { + "bbox": [ + 306, + 96, + 392, + 109 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 117, + 479, + 129 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 117, + 479, + 129 + ], + "spans": [ + { + "bbox": [ + 306, + 117, + 479, + 129 + ], + "type": "text", + "content": "2.1. Remote physiological estimation" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 135, + 547, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 135, + 547, + 495 + ], + "spans": [ + { + "bbox": [ + 304, + 135, + 547, + 495 + ], + "type": "text", + "content": "Traditional rPPG methods [5, 16, 32, 39, 40, 41] estimate pulse signal from facial videos by extracting and modeling the detailed heartbeat-caused skin color variation. To estimate pulse-induced intensity variations with more details from facial videos, deep learning-based networks and mechanisms have been proposed. With facial video input, various spatial-temporal neural networks have been developed [4, 20, 22, 23, 37, 48, 49]. To evaluate the effectiveness, rPPG datasets with various interferences including head motion [36], facial expression [15, 39], video compression [9], and skin color [42] are constructed. In addition, rPPG estimation can be conducted from pre-processed representations like normalized difference [3, 18, 21, 30], spatial-temporal map [24, 28]. To further improve robustness, self-adaptive [3, 21] and background-guided [19, 30] attention mechanisms have been proposed to emphasize important facial regions in physiological representation. Furthermore, [28] proposed the cross-verified strategy to disentangle noise and physiological representation and [24] proposed to model in-distribution noise for learning noise-resistant physiological representation. [25, 26] proposed to synthesize diverse facial videos for rPPG estimation. Unsupervised learning-based methods [8, 37] are also proposed to learn rPPG estimation from unlabeled facial videos. However, the previously proposed methods are prone to experience performance drops in cross-dataset evaluation, where the target domain may contain unseen noise. This is due to unseen noise patterns that may not be fully overcome, and the physiological representation may be polluted and cause distortions in the rPPG signals." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 503, + 526, + 516 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 503, + 526, + 516 + ], + "spans": [ + { + "bbox": [ + 306, + 503, + 526, + 516 + ], + "type": "text", + "content": "2.2. Unsupervised domain adaptation methods" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 522, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 547, + 713 + ], + "type": "text", + "content": "In recent research on computer vision, many unsupervised domain adaptation methods have been proposed to learn domain-invariant representation. [7] proposed to suppress domain-invariant information with domain label guided adversarial training. [33] proposed a bi-directional generation framework that can map target domain samples to the source domain and preserve semantic information for classification. [14] proposed to use adversarial domain training and distributional feature alignment guided by maximum density divergence to achieve adaptation. [43] considered that domain adversarial training may not be coordinated with the main task and proposed using meta-learning to improve the effectiveness of feature alignment. Unlike common computer vision tasks, feature alignment in the rPPG estimation requires more detailed information which cannot be fully provided by domain labels. There" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "10356" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 67, + 70, + 521, + 305 + ], + "blocks": [ + { + "bbox": [ + 67, + 70, + 521, + 305 + ], + "lines": [ + { + "bbox": [ + 67, + 70, + 521, + 305 + ], + "spans": [ + { + "bbox": [ + 67, + 70, + 521, + 305 + ], + "type": "image", + "image_path": "9d2bf40e180d984b60d5b1068046ab31a1684675c4a88cacb499c8eeab28b5c1.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 312, + 547, + 369 + ], + "lines": [ + { + "bbox": [ + 46, + 312, + 547, + 369 + ], + "spans": [ + { + "bbox": [ + 46, + 312, + 547, + 369 + ], + "type": "text", + "content": "Figure 2. Framework of the dual-bridging noise modeling network. The dual-bridging can reduce the domain discrepancy in the feature space by training the noise reducer with both high-level guidance from domain classification and detailed waveform guidance from synthetic features regression. The adversarial noise generation forces the generator " + }, + { + "bbox": [ + 46, + 312, + 547, + 369 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 312, + 547, + 369 + ], + "type": "text", + "content": " to compete with the noise reducer " + }, + { + "bbox": [ + 46, + 312, + 547, + 369 + ], + "type": "inline_equation", + "content": "NR" + }, + { + "bbox": [ + 46, + 312, + 547, + 369 + ], + "type": "text", + "content": " and synthesize noisy features with unsolved noise in the target domain. The hard noise pattern mining removes high-quality temporal features and encourages the generator to further explore hard noise patterns in the target domain." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 388, + 288, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 388, + 288, + 426 + ], + "spans": [ + { + "bbox": [ + 46, + 388, + 288, + 426 + ], + "type": "text", + "content": "fore, we propose the dual-bridging noise modeling network to take advantage of both domain labels and the source domain ground truth to guide the rPPG feature alignment." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 441, + 153, + 454 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 441, + 153, + 454 + ], + "spans": [ + { + "bbox": [ + 47, + 441, + 153, + 454 + ], + "type": "text", + "content": "3. Proposed Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 462, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 462, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 462, + 288, + 713 + ], + "type": "text", + "content": "The overview of the proposed dual-bridging noise modeling network is shown in Figure 2. Given the input face video from the source and target domain, we construct the STMap (details are in section 4.2) as the input of the feature extractor and then perform dual-bridging noise modeling on the middle representation. The first bridging provides high-level guidance where the source feature " + }, + { + "bbox": [ + 46, + 462, + 288, + 713 + ], + "type": "inline_equation", + "content": "f_{j}^{s}" + }, + { + "bbox": [ + 46, + 462, + 288, + 713 + ], + "type": "text", + "content": " and the denoised target feature " + }, + { + "bbox": [ + 46, + 462, + 288, + 713 + ], + "type": "inline_equation", + "content": "f_{i}^{t}" + }, + { + "bbox": [ + 46, + 462, + 288, + 713 + ], + "type": "text", + "content": " are pulled together with the domain classifier. The synthesized target domain feature " + }, + { + "bbox": [ + 46, + 462, + 288, + 713 + ], + "type": "inline_equation", + "content": "f_{j}^{s}" + }, + { + "bbox": [ + 46, + 462, + 288, + 713 + ], + "type": "text", + "content": " is obtained from the " + }, + { + "bbox": [ + 46, + 462, + 288, + 713 + ], + "type": "inline_equation", + "content": "f_{i}^{t}" + }, + { + "bbox": [ + 46, + 462, + 288, + 713 + ], + "type": "text", + "content": " through the adversarial noise generation module. The second bridge aims to pull " + }, + { + "bbox": [ + 46, + 462, + 288, + 713 + ], + "type": "inline_equation", + "content": "f_{j}^{s}" + }, + { + "bbox": [ + 46, + 462, + 288, + 713 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 462, + 288, + 713 + ], + "type": "inline_equation", + "content": "f_{i}^{t}" + }, + { + "bbox": [ + 46, + 462, + 288, + 713 + ], + "type": "text", + "content": " so that the target domain noise can be overcome by " + }, + { + "bbox": [ + 46, + 462, + 288, + 713 + ], + "type": "inline_equation", + "content": "NR" + }, + { + "bbox": [ + 46, + 462, + 288, + 713 + ], + "type": "text", + "content": " with the guidance of PPG " + }, + { + "bbox": [ + 46, + 462, + 288, + 713 + ], + "type": "inline_equation", + "content": "y_{s}" + }, + { + "bbox": [ + 46, + 462, + 288, + 713 + ], + "type": "text", + "content": " (regression) The generator in the adversarial noise generation module is conditioned on the " + }, + { + "bbox": [ + 46, + 462, + 288, + 713 + ], + "type": "inline_equation", + "content": "NR" + }, + { + "bbox": [ + 46, + 462, + 288, + 713 + ], + "type": "text", + "content": " so that it keeps on overcoming the complex noise pattern that can hardly be solved in the first bridging. With the dual-bridging noise modeling that contains both high-level (first bridge) and detailed waveform guidance (second bridge), the " + }, + { + "bbox": [ + 46, + 462, + 288, + 713 + ], + "type": "inline_equation", + "content": "NR" + }, + { + "bbox": [ + 46, + 462, + 288, + 713 + ], + "type": "text", + "content": " can handle the target domain noise better. Finally, " + }, + { + "bbox": [ + 46, + 462, + 288, + 713 + ], + "type": "inline_equation", + "content": "NR" + }, + { + "bbox": [ + 46, + 462, + 288, + 713 + ], + "type": "text", + "content": " works with the feature extractor and rPPG estimator to do the rPPG estimation in the target domain." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 388, + 395, + 401 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 388, + 395, + 401 + ], + "spans": [ + { + "bbox": [ + 306, + 388, + 395, + 401 + ], + "type": "text", + "content": "3.1. Dual-bridging" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 407, + 545, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 407, + 545, + 515 + ], + "spans": [ + { + "bbox": [ + 304, + 407, + 545, + 515 + ], + "type": "text", + "content": "With respect to the feature extractor " + }, + { + "bbox": [ + 304, + 407, + 545, + 515 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 304, + 407, + 545, + 515 + ], + "type": "text", + "content": ", we define source domain features as " + }, + { + "bbox": [ + 304, + 407, + 545, + 515 + ], + "type": "inline_equation", + "content": "F_{s} = \\{f_{j}^{s}\\}_{j = 1}^{M}" + }, + { + "bbox": [ + 304, + 407, + 545, + 515 + ], + "type": "text", + "content": " and target domain features as " + }, + { + "bbox": [ + 304, + 407, + 545, + 515 + ], + "type": "inline_equation", + "content": "F_{t} = \\{f_{i}^{t}\\}_{i = 1}^{N}" + }, + { + "bbox": [ + 304, + 407, + 545, + 515 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 407, + 545, + 515 + ], + "type": "inline_equation", + "content": "f_{j}^{s} = \\Theta (x_{j}^{s})" + }, + { + "bbox": [ + 304, + 407, + 545, + 515 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 407, + 545, + 515 + ], + "type": "inline_equation", + "content": "f_{i}^{t} = \\Theta (x_{i}^{t})" + }, + { + "bbox": [ + 304, + 407, + 545, + 515 + ], + "type": "text", + "content": ". Since the rPPG patterns are similar between different participants, the pre-trained feature extractor can preserve enough physiological information in " + }, + { + "bbox": [ + 304, + 407, + 545, + 515 + ], + "type": "inline_equation", + "content": "F_{t}" + }, + { + "bbox": [ + 304, + 407, + 545, + 515 + ], + "type": "text", + "content": " and noise modeling is the key to noise reduction of the target domain features. Detailed information for guidance is necessary to overcome the complex noise in the target domain features." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 516, + 545, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 516, + 545, + 575 + ], + "spans": [ + { + "bbox": [ + 304, + 516, + 545, + 575 + ], + "type": "text", + "content": "To reduce the noise contained in " + }, + { + "bbox": [ + 304, + 516, + 545, + 575 + ], + "type": "inline_equation", + "content": "F_{t}" + }, + { + "bbox": [ + 304, + 516, + 545, + 575 + ], + "type": "text", + "content": ", we propose the adaptive noise reduction bridging to reduce the noise contained in target domain features supervised by the domain classifier. In this bridging, we design the noise reducer with the noise estimation function " + }, + { + "bbox": [ + 304, + 516, + 545, + 575 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 304, + 516, + 545, + 575 + ], + "type": "text", + "content": " in a residual way as follows:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 389, + 586, + 545, + 600 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 389, + 586, + 545, + 600 + ], + "spans": [ + { + "bbox": [ + 389, + 586, + 545, + 600 + ], + "type": "interline_equation", + "content": "\\hat {f} _ {i} ^ {t} = f _ {i} ^ {t} - \\Phi \\left(f _ {i} ^ {t}\\right) \\tag {1}", + "image_path": "ea28f01ba34bee6a61d553a297d3fc05dbc8efcc7dd5a89c33840028cadf759b.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\hat{f}_i^t" + }, + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "type": "text", + "content": " is a denoised physiological feature and we define " + }, + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\hat{F}_t = \\{\\hat{f}_i^t\\}_{i=1}^N" + }, + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "type": "text", + "content": " as the denoised target domain. The direct estimation of high-quality physiological features could be hard, and we choose to estimate the noise and use the residual structure to reduce the noise in the target domain features. We build an adversarial training between the noise reducer " + }, + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "type": "text", + "content": " and the domain classifier " + }, + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 312, + 697, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 697, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 312, + 697, + 545, + 715 + ], + "type": "interline_equation", + "content": "\\max _ {D} \\min _ {\\Phi} L _ {N R} = \\mathbb {E} [ \\| 1 - D \\left(f _ {j} ^ {s}\\right) \\| _ {2} ] + \\mathbb {E} [ \\| D \\left(\\hat {f} _ {i} ^ {t}\\right) \\| _ {2} ] \\tag {2}", + "image_path": "4e63e9bca645bfb085d44ad8d42e5456c9d9873de0f3d2d794d7a3f22e279c57.jpg" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10357" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "text", + "content": "With high-level guidance from domain classification, some simple noise patterns can be overcome, and less noisy features can be aligned. However, high-level guidance may not overcome complex noise patterns without detailed waveform information for guidance. And the brute-force feature alignment may even change the physiological information of rPPG features when complex noise patterns are encountered. The phenomenon can be reflected by our ablation study in section 4.3." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 180, + 287, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 180, + 287, + 251 + ], + "spans": [ + { + "bbox": [ + 46, + 180, + 287, + 251 + ], + "type": "text", + "content": "To involve detailed information for supervision, we propose the complex noise generation bridging to generate target domain noise and synthesize noisy features to guide the noise reducer. From the source domain direction, we estimate the noise patterns in the target domain by generating noise and synthesizing noisy features as follows:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 129, + 258, + 287, + 275 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 129, + 258, + 287, + 275 + ], + "spans": [ + { + "bbox": [ + 129, + 258, + 287, + 275 + ], + "type": "interline_equation", + "content": "\\bar {f} _ {j} ^ {s} = f _ {j} ^ {s} + \\Psi (n _ {k}) \\tag {3}", + "image_path": "71f399168d2521ffb49c072c3c086b39e134117b0cff2848d7b31f3688677432.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 283, + 287, + 321 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 283, + 287, + 321 + ], + "spans": [ + { + "bbox": [ + 47, + 283, + 287, + 321 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 283, + 287, + 321 + ], + "type": "inline_equation", + "content": "\\overline{f}_j^s" + }, + { + "bbox": [ + 47, + 283, + 287, + 321 + ], + "type": "text", + "content": " is a raw noisy feature, " + }, + { + "bbox": [ + 47, + 283, + 287, + 321 + ], + "type": "inline_equation", + "content": "n_k" + }, + { + "bbox": [ + 47, + 283, + 287, + 321 + ], + "type": "text", + "content": " is random noise, and " + }, + { + "bbox": [ + 47, + 283, + 287, + 321 + ], + "type": "inline_equation", + "content": "\\Psi" + }, + { + "bbox": [ + 47, + 283, + 287, + 321 + ], + "type": "text", + "content": " is the generator. And we define the synthetic feature domain " + }, + { + "bbox": [ + 47, + 283, + 287, + 321 + ], + "type": "inline_equation", + "content": "\\hat{F}_s = \\{\\hat{f}_j^s\\}_{j=1}^M" + }, + { + "bbox": [ + 47, + 283, + 287, + 321 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 130, + 329, + 287, + 346 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 130, + 329, + 287, + 346 + ], + "spans": [ + { + "bbox": [ + 130, + 329, + 287, + 346 + ], + "type": "interline_equation", + "content": "\\hat {f} _ {j} ^ {s} = \\bar {f} _ {j} ^ {s} - \\Phi \\left(\\bar {f} _ {j} ^ {s}\\right) \\tag {4}", + "image_path": "1d21ef2d01c1acab818d65eb817763cef4856d8687faab97a3731fa64ae4a469.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 353, + 287, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 353, + 287, + 399 + ], + "spans": [ + { + "bbox": [ + 46, + 353, + 287, + 399 + ], + "type": "text", + "content": "To control the range of noise generation, we build the adversarial training between the noise generator and the domain classifier with respect to the denoised target domain as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 58, + 411, + 287, + 447 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 411, + 287, + 447 + ], + "spans": [ + { + "bbox": [ + 58, + 411, + 287, + 447 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\underset {D} {\\max} \\underset {\\Psi} {\\min} L _ {G} = \\mathbb {E} [ \\| 1 - D (f _ {j} ^ {s}) \\| _ {2} ] + \\mathbb {E} [ \\| D (\\overline {{f}} _ {j} ^ {s}) \\| _ {2} ] \\\\ + \\mathbb {E} [ \\| D (\\hat {f} _ {i} ^ {t}) \\| _ {2} ] \\quad (5) \\\\ \\end{array}", + "image_path": "5eec5da7f22a91e54af48960882cf7e8c3ba59bcbe4955c79f3fd6cd1d55579d.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 454, + 287, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 454, + 287, + 525 + ], + "spans": [ + { + "bbox": [ + 46, + 454, + 287, + 525 + ], + "type": "text", + "content": "In this bridging, the domain classifier can guide the generator to learn target domain noise patterns and synthesize noisy features with preserved physiological information. Thus, the source domain PPG signals " + }, + { + "bbox": [ + 46, + 454, + 287, + 525 + ], + "type": "inline_equation", + "content": "y_{j}^{s}" + }, + { + "bbox": [ + 46, + 454, + 287, + 525 + ], + "type": "text", + "content": " can be utilized to guide the noise reducer to overcome generated complex noise patterns as follows:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 111, + 533, + 287, + 549 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 533, + 287, + 549 + ], + "spans": [ + { + "bbox": [ + 111, + 533, + 287, + 549 + ], + "type": "interline_equation", + "content": "L _ {S Y N} = 1 - r \\left(E \\left(\\hat {f} _ {j} ^ {s}\\right), y _ {j} ^ {s}\\right) \\tag {6}", + "image_path": "492686f81c01399f1b9fc4c7428dc27738eda5dff5812314b9276c7bbbfe43ff.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 556, + 287, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 556, + 287, + 616 + ], + "spans": [ + { + "bbox": [ + 46, + 556, + 287, + 616 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 46, + 556, + 287, + 616 + ], + "type": "text", + "content": " is the rPPG estimator, and " + }, + { + "bbox": [ + 46, + 556, + 287, + 616 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 556, + 287, + 616 + ], + "type": "text", + "content": " is the Pearson correlation function. With this bridging, the physiological information can be preserved in the noise reduction and the other bridging can align more target domain features under large domain discrepancy." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 623, + 204, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 623, + 204, + 635 + ], + "spans": [ + { + "bbox": [ + 47, + 623, + 204, + 635 + ], + "type": "text", + "content": "3.2. Adversarial noise generation" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "text", + "content": "With the guidance from the domain classifier, part of the target domain noise patterns can be generated. However, in the adversarial training process, the generator may not fully explore target domain noise patterns. To comprehensively explore the target domain noise for rPPG feature alignment, we propose a novel adversarial noise generation. As shown" + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 320, + 69, + 535, + 118 + ], + "blocks": [ + { + "bbox": [ + 320, + 69, + 535, + 118 + ], + "lines": [ + { + "bbox": [ + 320, + 69, + 535, + 118 + ], + "spans": [ + { + "bbox": [ + 320, + 69, + 535, + 118 + ], + "type": "image", + "image_path": "bbd318603034ac46a71b923721f314f8c178fd598942fc7bacc0adb3b6c1f37e.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 333, + 129, + 517, + 140 + ], + "lines": [ + { + "bbox": [ + 333, + 129, + 517, + 140 + ], + "spans": [ + { + "bbox": [ + 333, + 129, + 517, + 140 + ], + "type": "text", + "content": "Figure 3. Illustration of hard noise pattern mining." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 161, + 545, + 243 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 161, + 545, + 243 + ], + "spans": [ + { + "bbox": [ + 304, + 161, + 545, + 243 + ], + "type": "text", + "content": "in Figure 2, the generator is conditioned on the noise reducer and forced to explore the unsolved noise contained in the target domain features. The noise reducer is trained with the synthetic features and corresponding PPG signals to overcome the generated noise. The adversarial correlation between the generator and the noise reducer is shown as follows:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 253, + 545, + 281 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 253, + 545, + 281 + ], + "spans": [ + { + "bbox": [ + 306, + 253, + 545, + 281 + ], + "type": "interline_equation", + "content": "\\max _ {\\Psi} \\min _ {\\Phi} L _ {A N G} = \\mathbb {E} [ \\| 1 - D (\\hat {f} _ {j} ^ {s}) \\| _ {2} ] + \\mathbb {E} [ 1 - r (E (\\hat {f} _ {j} ^ {s}), y _ {j} ^ {s}) ] \\tag {7}", + "image_path": "4379c1173c697abf3b45ee11950e4f6a0a03706407ad98e909c0479baffe609f.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 282, + 545, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 282, + 545, + 378 + ], + "spans": [ + { + "bbox": [ + 304, + 282, + 545, + 378 + ], + "type": "text", + "content": "This adversarial training is based on two different optimization functions, but not the gradient reverse layer. Therefore, the novel noise patterns are not generated based on adversarial attacks but are searched from unsolved noise patterns in the target domain. With our adversarial noise generation, the dual-bridging structure can progressively generate target domain noise patterns, and the noise reduction ability can be significantly improved." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 386, + 453, + 399 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 386, + 453, + 399 + ], + "spans": [ + { + "bbox": [ + 306, + 386, + 453, + 399 + ], + "type": "text", + "content": "3.3. Hard noise pattern mining" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 404, + 545, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 404, + 545, + 559 + ], + "spans": [ + { + "bbox": [ + 304, + 404, + 545, + 559 + ], + "type": "text", + "content": "To further improve the robustness of the noise reducer, we propose the hard noise pattern mining as illustrated in Figure 3. Considering the redundancy of rPPG estimation, features with one or several high-quality temporal features can contribute to accurate estimation. Thus, the noise reducer may just learn to overcome relatively simple noise patterns and some hard noise patterns may not be learned. To further explore the hard noise patterns, we need to reduce the shortcuts for noise reduction and generate hard noise patterns for training. In our hard noise pattern mining module, we identify high-quality temporal features with respect to the morphology consistency " + }, + { + "bbox": [ + 304, + 404, + 545, + 559 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 404, + 545, + 559 + ], + "type": "text", + "content": " which is defined as follows:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 372, + 559, + 545, + 578 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 372, + 559, + 545, + 578 + ], + "spans": [ + { + "bbox": [ + 372, + 559, + 545, + 578 + ], + "type": "interline_equation", + "content": "M = \\max _ {t = 1} ^ {n} r \\left(g _ {0: T}, g _ {t: t + T}\\right) \\tag {8}", + "image_path": "c53418d29570f9216df1f9d3194e98d8380a2ee90ae62a1970310ac624dfd765.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 582, + 545, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 700 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 304, + 582, + 545, + 700 + ], + "type": "text", + "content": " is the Pearson correlation, " + }, + { + "bbox": [ + 304, + 582, + 545, + 700 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 304, + 582, + 545, + 700 + ], + "type": "text", + "content": " is a temporal feature, " + }, + { + "bbox": [ + 304, + 582, + 545, + 700 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 582, + 545, + 700 + ], + "type": "text", + "content": " is the sliding start point, and " + }, + { + "bbox": [ + 304, + 582, + 545, + 700 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 582, + 545, + 700 + ], + "type": "text", + "content": " is the time length of morphology consistency evaluation. With respect to the morphology consistency, we define temporal features with significant periodicity as high-quality features. After identifying high-quality temporal features, we can remove the corresponding feature slice and preserve hard slices for noise generation. Correspondingly, more hard noise patterns will be generated and the noise reduction ability can be further improved for rPPG feature alignment." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "text", + "content": "The detailed optimization process of our proposed" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10358" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 286, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 286, + 95 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 286, + 95 + ], + "type": "text", + "content": "Algorithm 1 The optimization process for our dual-bridging algorithm." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 97, + 286, + 145 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 97, + 286, + 145 + ], + "spans": [ + { + "bbox": [ + 47, + 97, + 286, + 145 + ], + "type": "text", + "content": "Input: Noise generator " + }, + { + "bbox": [ + 47, + 97, + 286, + 145 + ], + "type": "inline_equation", + "content": "\\Psi" + }, + { + "bbox": [ + 47, + 97, + 286, + 145 + ], + "type": "text", + "content": ", noise reducer " + }, + { + "bbox": [ + 47, + 97, + 286, + 145 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 47, + 97, + 286, + 145 + ], + "type": "text", + "content": " and domain classifier " + }, + { + "bbox": [ + 47, + 97, + 286, + 145 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 47, + 97, + 286, + 145 + ], + "type": "text", + "content": ", total epochs " + }, + { + "bbox": [ + 47, + 97, + 286, + 145 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 47, + 97, + 286, + 145 + ], + "type": "text", + "content": ", mini-batch " + }, + { + "bbox": [ + 47, + 97, + 286, + 145 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 47, + 97, + 286, + 145 + ], + "type": "text", + "content": ", source domain samples " + }, + { + "bbox": [ + 47, + 97, + 286, + 145 + ], + "type": "inline_equation", + "content": "x_{j}^{s}" + }, + { + "bbox": [ + 47, + 97, + 286, + 145 + ], + "type": "text", + "content": ", source domain labels " + }, + { + "bbox": [ + 47, + 97, + 286, + 145 + ], + "type": "inline_equation", + "content": "y_{j}^{s}" + }, + { + "bbox": [ + 47, + 97, + 286, + 145 + ], + "type": "text", + "content": ", target domain samples " + }, + { + "bbox": [ + 47, + 97, + 286, + 145 + ], + "type": "inline_equation", + 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After training the dual-bridging algorithm, we can estimate rPPG signals in the target domain as follows:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 107, + 372, + 286, + 386 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 372, + 286, + 386 + ], + "spans": [ + { + "bbox": [ + 107, + 372, + 286, + 386 + ], + "type": "interline_equation", + "content": "\\hat {y} _ {i} ^ {t} = E \\left(\\Theta \\left(x _ {i} ^ {t}\\right) - \\Phi \\left(\\Theta \\left(x _ {i} ^ {t}\\right)\\right)\\right) \\tag {9}", + "image_path": "fe035baacb043cd8ae8d5c08fcb7cca489b22dcd01cd6fd3ef300945c80329dd.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 393, + 176, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 393, + 176, + 407 + ], + "spans": [ + { + "bbox": [ + 47, + 393, + 176, + 407 + ], + "type": "inline_equation", + "content": "\\hat{y}_i^t" + }, + { + "bbox": [ + 47, + 393, + 176, + 407 + ], + "type": "text", + "content": " is the estimated rPPG signal." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 47, + 416, + 128, + 429 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 416, + 128, + 429 + ], + "spans": [ + { + "bbox": [ + 47, + 416, + 128, + 429 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 430, + 286, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 430, + 286, + 574 + ], + "spans": [ + { + "bbox": [ + 46, + 430, + 286, + 574 + ], + "type": "text", + "content": "We conduct experiments on three publicly available datasets with different types of interference to evaluate the accuracy and generalization ability of our dual-bridging noise modeling network. Three protocols that simulate the typical domain discrepancies in real application scenarios are adopted, i.e., 1) task-independent evaluation, 2) participant-independent evaluation, and 3) cross-dataset evaluation. Mean absolute error (MAE), root mean square error (RMSE), and Pearson correlation coefficient (r) are adopted to evaluate the performance of average heart rate based on the estimated rPPG signal. The unit for MAE and RMSE is beats per minute (bpm)." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 47, + 581, + 176, + 593 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 581, + 176, + 593 + ], + "spans": [ + { + "bbox": [ + 47, + 581, + 176, + 593 + ], + "type": "text", + "content": "4.1. Datasets and Baselines" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 46, + 594, + 286, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 286, + 641 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 286, + 641 + ], + "type": "text", + "content": "We evaluate the proposed method on the following datasets, which cover different types/levels of head motion, facial expression, compression artifacts, skin color, and also heartbeat ranges." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 46, + 642, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 286, + 713 + ], + "type": "text", + "content": "PURE [36] dataset contains facial videos of 10 Caucasian participants (8 men, 2 women) in six different behavior modes with head motion and facial expression. The videos are uncompressed and captured at 30fps in " + }, + { + "bbox": [ + 46, + 642, + 286, + 713 + ], + "type": "inline_equation", + "content": "640 \\times 480" + }, + { + "bbox": [ + 46, + 642, + 286, + 713 + ], + "type": "text", + "content": ". Synchronized GT-PPG signals are captured at " + }, + { + "bbox": [ + 46, + 642, + 286, + 713 + ], + "type": "inline_equation", + "content": "60\\mathrm{Hz}" + }, + { + "bbox": [ + 46, + 642, + 286, + 713 + ], + "type": "text", + "content": " using pulse oximeter pulox CMS50E." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": "MMSE-HR [39] datasets contains 102 facial videos captured from 40 participants of different ethnicities with different emotions. The emotion-related spontaneous facial expressions can also induce facial intensity variations. The video frames are captured at 25fps in " + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "1040 \\times 1392" + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": " and compressed in JPG format, and their frame rate is " + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "25\\mathrm{Hz}" + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": ". GT blood volume signals are captured by the Biopac MP150." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 156, + 545, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 156, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 304, + 156, + 545, + 228 + ], + "type": "text", + "content": "UBFC-rPPG [1] dataset contains 42 facial videos captured under a human-computer interaction scene which causes head motions and larger heart rate range (63-145 bpm). Videos are recorded by the Logitech C920 Webcam at 30fps in " + }, + { + "bbox": [ + 304, + 156, + 545, + 228 + ], + "type": "inline_equation", + "content": "640 \\times 480" + }, + { + "bbox": [ + 304, + 156, + 545, + 228 + ], + "type": "text", + "content": ". Synchronized GT-PPG signals are captured by CMS50E." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 228, + 545, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 228, + 545, + 300 + ], + "spans": [ + { + "bbox": [ + 304, + 228, + 545, + 300 + ], + "type": "text", + "content": "Baselines We compared the proposed method with traditional rPPG methods [5, 16, 32, 39, 40, 41] and the latest deep rPPG models [3, 4, 13, 21, 22, 23, 24, 27, 28, 29, 34, 37, 45, 47, 49] to show the generalization ability. We also compared the proposed method with popular UDA methods [7, 17] to show the effectiveness of rPPG feature alignment." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 308, + 436, + 319 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 308, + 436, + 319 + ], + "spans": [ + { + "bbox": [ + 306, + 308, + 436, + 319 + ], + "type": "text", + "content": "4.2. Implementation details" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 321, + 545, + 573 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 321, + 545, + 573 + ], + "spans": [ + { + "bbox": [ + 304, + 321, + 545, + 573 + ], + "type": "text", + "content": "Our method is implemented with PyTorch and trained on an NVIDIA Tesla V100. We align the facial regions with four landmarks using the perspective transformation and generate the STmap [27] as input. We resample all STmaps and the corresponding labels at " + }, + { + "bbox": [ + 304, + 321, + 545, + 573 + ], + "type": "inline_equation", + "content": "30\\mathrm{Hz}" + }, + { + "bbox": [ + 304, + 321, + 545, + 573 + ], + "type": "text", + "content": ". The frame number for each STmap is 300 and adjacent STmaps have 270 overlapped frames. In experiments, we pre-train the 2D CNN model on the source domain for rPPG estimation. The threshold of morphology consistency for hard noise pattern mining is 0.82. In the domain adaptation training stage, we set the batch size to 64 and adopt the Adam optimizer [11] for training. The learning rate for the noise pattern generator and noise reducer is 1e-4. And the learning rate for the domain classifier is 3e-5. The weight decay is 1e-4 for all optimizers. We train our domain adaptation algorithm for 200 epochs in the task-independent and PURE to MMSE-HR evaluations, and 2000 epochs in the MMSE-HR to PURE evaluation. We select the weights of the noise reducer for the test according to the estimation loss of synthesized samples. Under certain domain discrepancies, the details of the rPPG signals may not be preserved." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 306, + 581, + 463, + 593 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 581, + 463, + 593 + ], + "spans": [ + { + "bbox": [ + 306, + 581, + 463, + 593 + ], + "type": "text", + "content": "4.3. Task-independent evaluation" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "We first evaluate the proposed method in the task-independent scenario, which has a smaller domain discrepancy. The MMSE-HR collected facial videos under different activities and we regard each activity as a task. Within MMSE-HR, the unseen non-physiological intensity variations are mainly induced by different head motion and facial expression changes. In this evaluation, we set one task as the target domain and the other tasks as the source domain. From the experimental results in Table 1, we can find that even under the intra-dataset scenario, the domain" + } + ] + } + ], + "index": 26 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10359" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 73, + 102, + 261, + 343 + ], + "blocks": [ + { + "bbox": [ + 47, + 71, + 287, + 92 + ], + "lines": [ + { + "bbox": [ + 47, + 71, + 287, + 92 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 287, + 92 + ], + "type": "text", + "content": "Table 1. Experimental results for task-independent evaluation on MMSE-HR." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 73, + 102, + 261, + 343 + ], + "lines": [ + { + "bbox": [ + 73, + 102, + 261, + 343 + ], + "spans": [ + { + "bbox": [ + 73, + 102, + 261, + 343 + ], + "type": "table", + "html": "
MethodMAERMSEr
Li2014 [16]-19.950.38
CHROM [5]-13.970.55
Tulyakov2016 [39]-11.370.71
ST-Attention* [29]-10.100.64
RhythmNet [27]-5.030.86
CVD* [28]-6.040.84
PhysNet [47]-13.250.44
DeepPhys [3]4.439.980.80
TS-CAN [21]3.857.210.86
AutoHR [45]-5.870.89
BVPNet [4]-7.470.79
Federated2022 [23]2.992.420.79
EfficientPhys-C [22]2.915.430.92
EfficientPhys-T1 [22]3.487.210.86
PhysFormer* [49]2.845.360.92
ERM [12]1.302.580.99
DANN [7]1.242.710.99
CST [17]1.202.420.99
Ours0.852.050.99
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MethodMAERMSEr
GREEN [40]4.4711.60.842
ICA [32]3.518.640.908
CHROM [5]3.444.610.968
POS [41]2.446.610.936
CK [35]2.293.800.981
Frédéric [2]5.458.64-
HeartTrack [31]2.413.370.983
ETA-rPPGNet [10]1.463.970.93
DAE [34]1.482.490.97
PulseGAN [34]1.192.100.98
Meta-rPPG [13]5.977.420.53
CVD [28]2.193.120.99
Gideon2021 [8]3.64.60.95
Federated2022 [23]2.004.380.93
Dual-GAN [24]0.440.670.99
ContrastPhys [37]0.641.000.99
ERM [12]0.751.840.99
DANN [7]0.581.190.99
CST [17]0.411.040.99
Ours0.160.570.99
", + "image_path": "de3f50186752e284bf7a0937aec4f1bc72a5e60150d552d8ada5aa97ae7dbf41.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 677, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 712 + ], + "type": "text", + "content": "discrepancy can decrease the performance of deep rPPG models. And under small domain discrepancies, common UDA methods are effective and can overcome certain noise" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": "patterns in the target domain. Our method can effectively reduce the unseen non-physiological intensity variations in feature space through noise reduction of rPPG features and achieves state-of-the-art performance." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 129, + 496, + 141 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 129, + 496, + 141 + ], + "spans": [ + { + "bbox": [ + 305, + 129, + 496, + 141 + ], + "type": "text", + "content": "4.4. Participant-independent evaluation." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 147, + 545, + 303 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 147, + 545, + 303 + ], + "spans": [ + { + "bbox": [ + 304, + 147, + 545, + 303 + ], + "type": "text", + "content": "The domain discrepancy can also come from differences between participants like head motions under human-computer interaction scenarios. Caucasian and Asian participants are included and we evaluate this participant-independent setting with the UBFC-rPPG dataset. We follow the protocol in [24,34] to select 30 participants for training and use the rest 12 participants for testing. As the experimental results shown in Table 2, the domain discrepancy is small with respect to deep rPPG models and pre-trained rPPG models also have low error. Compared to common UDA methods, our proposed method can provide more detailed information for noise reduction supervision and more noise patterns can be overcome in the feature alignment." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 312, + 443, + 323 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 312, + 443, + 323 + ], + "spans": [ + { + "bbox": [ + 305, + 312, + 443, + 323 + ], + "type": "text", + "content": "4.5. Cross-dataset evaluation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 330, + 545, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 330, + 545, + 437 + ], + "spans": [ + { + "bbox": [ + 304, + 330, + 545, + 437 + ], + "type": "text", + "content": "Our method is also evaluated in the cross-dataset setting with MMSE-HR and PURE. The selected datasets have differences in aspects such as head motion, From the view of the rPPG estimation, the MMSE-HR dataset contains more challenging scenarios (video compression, facial expression changes) than the PURE dataset. A challenging source domain could be beneficial to generalization ability and reduce the difficulty of the adaptation process. We provide details of the cross-dataset evaluations in the following paragraphs." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 437, + 545, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 545, + 688 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 545, + 688 + ], + "type": "text", + "content": "From MMSE-HR to PURE. In this experiment, we select the MMSE-HR dataset as the source domain and the PURE dataset as the target domain. Since the source domain is more challenging than the target domain, the adaptation process could be relatively easy. The experimental results are shown in Table 3. We can find that DANN cannot improve the generalization ability of rPPG models and only high-level guidance cannot align noisy features to high-quality features. While the cycle self-training strategy can provide certain details of the rPPG waveform and is more effective in reducing the domain discrepancy in rPPG estimation. Our method can progressively generate noise patterns in the target domain and synthesize noisy samples to provide detailed information from the source domain labels. Our method achieves state-of-the-art performance in this UDA scenario, and the low RMSE shows that our method is effective in reducing strong outliers. We provide some examples in Figure 3 (a) in which the noise reduction process can remove fake peaks in one period. After removing fake peaks, the periodicity of rPPG signal can be improved and the heart rate estimation can be more accurate." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 689, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 712 + ], + "type": "text", + "content": "From PURE to MMSE-HR. In this experiment, we select the PURE dataset that has fewer facial videos with mild" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10360" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 102, + 287, + 259 + ], + "blocks": [ + { + "bbox": [ + 47, + 71, + 287, + 94 + ], + "lines": [ + { + "bbox": [ + 47, + 71, + 287, + 94 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 287, + 94 + ], + "type": "text", + "content": "Table 3. Experimental results for cross-dataset evaluation between PURE and MMSE-HR datasets." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 102, + 287, + 259 + ], + "lines": [ + { + "bbox": [ + 49, + 102, + 287, + 259 + ], + "spans": [ + { + "bbox": [ + 49, + 102, + 287, + 259 + ], + "type": "table", + "html": "
MethodMMSE-HR → PUREPURE → MMSE-HR
MAERMSErMAERMSEr
CHROM [5]3.2512.920.845.7212.690.58
POS [41]2.8312.490.854.9813.110.53
CVD [28]2.753.980.984.087.030.84
ERM [12]2.498.480.932.595.440.96
DANN [7]2.696.970.952.847.650.93
CST [17]1.272.960.992.325.970.96
EfficientT1 [22]---3.045.910.92
PhysFormer [49]---2.845.360.92
Synthetic [25]---2.263.700.97
Ours1.101.670.991.713.720.98
", + "image_path": "7fafbef7af63f1f926f09b66ff389d79cc91433718445247d8f631147c45d5ca.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 77, + 303, + 258, + 463 + ], + "blocks": [ + { + "bbox": [ + 47, + 272, + 287, + 294 + ], + "lines": [ + { + "bbox": [ + 47, + 272, + 287, + 294 + ], + "spans": [ + { + "bbox": [ + 47, + 272, + 287, + 294 + ], + "type": "text", + "content": "Table 4. Experimental results for cross-dataset evaluation from PURE to UBFC-rPPG." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 77, + 303, + 258, + 463 + ], + "lines": [ + { + "bbox": [ + 77, + 303, + 258, + 463 + ], + "spans": [ + { + "bbox": [ + 77, + 303, + 258, + 463 + ], + "type": "table", + "html": "
MethodPURE → UBFC-rPPG
MAERMSEr
CHROM [5]3.106.840.93
POS [41]3.526.840.90
DAE [34]2.705.170.96
PulseGAN [34]2.094.420.97
Siamese-rPPG [38]1.298.73-
Dual-GAN [24]0.741.020.99
ERM [12]1.503.360.96
DANN [7]3.246.130.96
CST [17]2.244.730.97
Ours0.581.110.99
", + "image_path": "fb4cf00516a5e11f4fe2530e0db31c483c477f82b055e229120dab9a34fc538a.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 486, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 486, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 486, + 288, + 714 + ], + "type": "text", + "content": "interferences (like slow head rotation, translation) as the source Compared to the MMSE " + }, + { + "bbox": [ + 46, + 486, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 46, + 486, + 288, + 714 + ], + "type": "text", + "content": " PURE setting, the domain gap in PURE " + }, + { + "bbox": [ + 46, + 486, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 46, + 486, + 288, + 714 + ], + "type": "text", + "content": "MMSE is harder to overcome since the noise patterns in the target domain are more challenging. In this experiment, our method is also compared with two rPPG methods [22, 49] which are pre-trained in the VIPL-HR dataset with more facial videos and scenarios. We also compare with [25] which uses synthetic facial videos and the AFRL dataset [6] for training. As shown in Table 3, in this challenging setting, we find that all baseline methods have lower performance compared with the other cross-dataset settings. Under this challenging setting, our dual-bridging with adversarial noise generation algorithm can effectively explore the specific noise patterns from the target domain. Additionally, by synthesizing noisy features similar to target domain features, the noise reduction ability can be dramatically improved to reduce the domain discrepancy. And our method can achieve state-of-the-art performance under this cross-dataset validation. We also provide some" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 545, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 192 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 192 + ], + "type": "text", + "content": "examples in Figure 3 (b) and find that noise reduction can improve the quality of rPPG signals. Especially some noisy rPPG signals show low periodicity, after the noise reduction, clear peaks can be observed. In this case, the intuitive UDA solution DANN also may not be able to learn domain-invariant representation with domain labels only for supervision. The cycle self-training strategy can only adaptively overcome a part of the domain discrepancy. Whereas, the EfficientT1, PhysFormer, and Synthetic methods pretrained on larger datasets show better robustness." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 194, + 545, + 374 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 194, + 545, + 374 + ], + "spans": [ + { + "bbox": [ + 304, + 194, + 545, + 374 + ], + "type": "text", + "content": "From PURE to UBFC-rPPG. In this experiment, we select the PURE dataset with head motion as the source domain and the UBFC-rPPG dataset with compression and a wider range of heart rate as the target domain. The experimental results are shown in Table 4. The compression enlarges the domain discrepancy for rPPG estimation because some information is lost during compression and facial intensities are changed. Our proposed method can simulate the compression-induced noise and provide detailed information to effectively align rPPG features. In this setting, the pre-trained rPPG models in [34, 38] cannot handle the relatively larger domain gap (caused by the video compression) well. For common UDA methods, the high-level guidance from domain classification cannot fully guide the rPPG feature alignment and noise is still preserved in rPPG features." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 376, + 545, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 376, + 545, + 567 + ], + "spans": [ + { + "bbox": [ + 304, + 376, + 545, + 567 + ], + "type": "text", + "content": "In this cross-dataset evaluation, we show the domain adaptation process in rPPG estimation under various domain discrepancies. Experimental results show that adapting deep rPPG models to less challenging scenarios, common UDA methods are effective. However, to adapt deep rPPG models to more challenging scenarios, more detailed information about the rPPG waveform is desired to reduce the domain discrepancy. And our method can provide both noise patterns and waveform information with the synthesized samples for noise reduction training. We can find that the domain discrepancy has been reduced after noise reduction, as shown in Figure 4, especially for the harder cases PURE " + }, + { + "bbox": [ + 304, + 376, + 545, + 567 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 304, + 376, + 545, + 567 + ], + "type": "text", + "content": " MMSE-HR. Compared to collecting large-scale dataset to improve the generalization ability of deep rPPG models, our dual-bridging noise modeling network is effective and convenient." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 570, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 714 + ], + "type": "text", + "content": "Ablation study. We conduct ablation study with cross-dataset settings to show the effectiveness of each bridge in our method as shown in Table 5. We first show the experimental result of the pre-train model. The " + }, + { + "bbox": [ + 304, + 570, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{NR} \\leftrightarrow \\mathrm{D}" + }, + { + "bbox": [ + 304, + 570, + 545, + 714 + ], + "type": "text", + "content": " represents that a noise reducer and a domain classifier are adversarially trained to reduce the domain discrepancy. Denoised target domain features are used to estimate rPPG signals. The noise reducer can adaptively overcome some noise patterns under a small domain discrepancy. When the domain discrepancy is large, the domain labels may not provide enough detailed information for training the noise reducer. To prevent the noise reducer from generating random phys" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10361" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 117, + 91, + 476, + 186 + ], + "blocks": [ + { + "bbox": [ + 209, + 71, + 384, + 83 + ], + "lines": [ + { + "bbox": [ + 209, + 71, + 384, + 83 + ], + "spans": [ + { + "bbox": [ + 209, + 71, + 384, + 83 + ], + "type": "text", + "content": "Table 5. Experimental results for ablation study." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 117, + 91, + 476, + 186 + ], + "lines": [ + { + "bbox": [ + 117, + 91, + 476, + 186 + ], + "spans": [ + { + "bbox": [ + 117, + 91, + 476, + 186 + ], + "type": "table", + "html": "
MethodMMSE-HR → PUREPURE → MMSE-HR
MAERMSErMAERMSEr
Pre-trained rPPG model2.969.570.912.093.920.98
+ NR ↔ D2.137.140.9520.2726.340.58
+ NR ↔ D + G ↔ D1.663.660.981.883.850.98
+ NR ↔ D + G ↔ D + G|NR ↔ D1.131.710.991.713.720.98
+ NR ↔ D + G ↔ D + G|NR ↔ D + HM1.101.670.991.884.160.98
", + "image_path": "160a6cf8b34f704d0cb4f22704a1e6b4d98bd5bb32d9e0ae04d516036ce13f32.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 53, + 204, + 281, + 309 + ], + "blocks": [ + { + "bbox": [ + 53, + 204, + 281, + 309 + ], + "lines": [ + { + "bbox": [ + 53, + 204, + 281, + 309 + ], + "spans": [ + { + "bbox": [ + 53, + 204, + 281, + 309 + ], + "type": "image", + "image_path": "c25b9db073f3494126013c1a3aa9745938f12ea648f409acf290b634e88feb85.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 319, + 288, + 363 + ], + "lines": [ + { + "bbox": [ + 46, + 319, + 288, + 363 + ], + "spans": [ + { + "bbox": [ + 46, + 319, + 288, + 363 + ], + "type": "text", + "content": "Figure 4. Visualization of rPPG estimation before (orange) and after (green) noise reduction compared with GT-PPG (blue). (a) contains examples of MMSE-HR " + }, + { + "bbox": [ + 46, + 319, + 288, + 363 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 46, + 319, + 288, + 363 + ], + "type": "text", + "content": " PURE evaluation and (b) is of PURE " + }, + { + "bbox": [ + 46, + 319, + 288, + 363 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 46, + 319, + 288, + 363 + ], + "type": "text", + "content": "MMSE-HR." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 387, + 287, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 387, + 287, + 590 + ], + "spans": [ + { + "bbox": [ + 46, + 387, + 287, + 590 + ], + "type": "text", + "content": "iological features under adversarial training, the strong regression supervision from rPPG waveform is necessary. For " + }, + { + "bbox": [ + 46, + 387, + 287, + 590 + ], + "type": "inline_equation", + "content": "\\mathrm{NR} \\leftrightarrow \\mathrm{D} + \\mathrm{G} \\leftrightarrow \\mathrm{D}" + }, + { + "bbox": [ + 46, + 387, + 287, + 590 + ], + "type": "text", + "content": ", the noise generator is not conditioned on the noise reducer and can also synthesize noisy samples to train the noise reducer. The synthesized noisy samples prevent the noise reducer from generating random physiological features with detailed guidance from PPG signals. For " + }, + { + "bbox": [ + 46, + 387, + 287, + 590 + ], + "type": "inline_equation", + "content": "\\mathrm{NR} \\leftrightarrow \\mathrm{D} + \\mathrm{G} \\leftrightarrow \\mathrm{D} + \\mathrm{G}|\\mathrm{NR} \\leftrightarrow \\mathrm{D}" + }, + { + "bbox": [ + 46, + 387, + 287, + 590 + ], + "type": "text", + "content": ", i.e., dual-bridging with adversarial noise generation, the noise patterns in the target domain can be progressively generated to improve the denoising ability. The hard noise pattern mining can improve the robustness of the noise reducer when there is less interference in the target domain. However, with strong interference in the target domain, too many hard noise patterns may distract the noise reducer from overcoming originally generated noise patterns and we saw a decrease of performance in the PURE " + }, + { + "bbox": [ + 46, + 387, + 287, + 590 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 46, + 387, + 287, + 590 + ], + "type": "text", + "content": " MMSE-HR." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 601, + 119, + 613 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 601, + 119, + 613 + ], + "spans": [ + { + "bbox": [ + 47, + 601, + 119, + 613 + ], + "type": "text", + "content": "4.6. Discussion" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": "The generalization problem is a key challenge in applying rPPG techniques to real-world health monitoring applications. Especially for deep learning-based rPPG methods, the training data contain certain biases that may prevent rPPG models from learning domain-invariant physiological representations. Results show that generating noise patterns in the target domain and synthesizing samples for noise reduction can effectively reduce the domain discrepancy." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 205, + 515, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 205, + 515, + 217 + ], + "spans": [ + { + "bbox": [ + 306, + 205, + 515, + 217 + ], + "type": "text", + "content": "ancy thereby improving the quality of rPPG signals." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 218, + 545, + 349 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 218, + 545, + 349 + ], + "spans": [ + { + "bbox": [ + 304, + 218, + 545, + 349 + ], + "type": "text", + "content": "We also found the effectiveness of using domain labels to help domain-invariant physiological representation learning when domain discrepancy is small. However, when domain discrepancy increases, the gain of feature alignment in such adversarial training tends to be smaller. Without target domain labels for noise reduction, generating noise patterns similar to the target domain is easier than directly denoising target domain features under a large domain discrepancy. In the noise generation procedure, some out-of-distribution noise patterns can also be generated and can further improve the generalization ability for unseen interferences." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 350, + 545, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 350, + 545, + 445 + ], + "spans": [ + { + "bbox": [ + 304, + 350, + 545, + 445 + ], + "type": "text", + "content": "Although our dual-bridging adaptation can work on most cases and achieve state-of-the-art, we still have limitations on handling hard cases with very large domain discrepancies (e.g., large head motion + facial expression + video compression in Table 4). Such rarely happened combined artifacts and can be regarded as a long-tailed distribution (of artifacts) problem. How to pay more attention to those rare but hard cases could be a key to solve it in the future." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 459, + 378, + 471 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 459, + 378, + 471 + ], + "spans": [ + { + "bbox": [ + 306, + 459, + 378, + 471 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 476, + 545, + 657 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 476, + 545, + 657 + ], + "spans": [ + { + "bbox": [ + 304, + 476, + 545, + 657 + ], + "type": "text", + "content": "Recent deep learning-based rPPG methods can learn to overcome non-physiological intensity variations from data, but may also involve bias induced by data and hinder the generalization ability. In this paper, we proposed a novel dual-bridging noise modeling network to reduce the domain discrepancy in rPPG estimation. With the proposed tri-adversarial optimization, the noise generator can progressively explore the noise patterns in the target domain and the coarse-to-fine guidance can effectively improve the noise reduction ability. In addition, comprehensive evaluations of different domain discrepancies show the effectiveness of our method. In future work, we may consider using unlabeled and synthesised [42] facial videos from multiple domains with various external interferences to learn domain-invariant physiological representations." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 669, + 416, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 669, + 416, + 681 + ], + "spans": [ + { + "bbox": [ + 306, + 669, + 416, + 681 + ], + "type": "text", + "content": "6. Acknowledgement" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 689, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 712 + ], + "type": "text", + "content": "This project is partially supported by Hong Kong RGC General Research Fund RGC/HKBU12200820." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10362" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "text", + "content": "[1] Serge Bobbia, Richard Macwan, Yannick Benezeth, Alamin Mansouri, and Julien Dubois. 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In CVPR, pages 4186-4196, 2022. 1, 2, 5, 6, 7" + } + ] + } + ], + "index": 20 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "10364" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Dual-Path Adaptation From Image to Video Transformers/58cf23aa-7524-4b95-9291-20d982a61012_content_list.json b/2023/Dual-Path Adaptation From Image to Video Transformers/58cf23aa-7524-4b95-9291-20d982a61012_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..dcced62827357092ceb6441564301ace64985a85 --- /dev/null +++ b/2023/Dual-Path Adaptation From Image to Video Transformers/58cf23aa-7524-4b95-9291-20d982a61012_content_list.json @@ -0,0 +1,1770 @@ +[ + { + "type": "text", + "text": "Dual-path Adaptation from Image to Video Transformers", + "text_level": 1, + "bbox": [ + 200, + 122, + 796, + 143 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Jungin Park1*", + "bbox": [ + 228, + 168, + 347, + 187 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Jiyoung Lee $^{2*}$", + "bbox": [ + 406, + 168, + 524, + 187 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Kwanghoon Sohn $^{1,3\\dagger}$", + "bbox": [ + 586, + 168, + 759, + 187 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ Yonsei University", + "bbox": [ + 100, + 191, + 257, + 210 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ NAVER AI Lab", + "bbox": [ + 295, + 191, + 438, + 208 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{3}$ Korea Institute of Science and Technology (KIST)", + "bbox": [ + 478, + 191, + 895, + 210 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{newrun, khsohn}@yonsei.ac.kr", + "bbox": [ + 247, + 215, + 510, + 229 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "lee.j@navercorp.com", + "bbox": [ + 571, + 215, + 749, + 229 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 240, + 262, + 319, + 277 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we efficiently transfer the surpassing representation power of the vision foundation models, such as ViT and Swin, for video understanding with only a few trainable parameters. Previous adaptation methods have simultaneously considered spatial and temporal modeling with a unified learnable module but still suffered from fully leveraging the representative capabilities of image transformers. We argue that the popular dual-path (two-stream) architecture in video models can mitigate this problem. We propose a novel DUALPATH adaptation separated into spatial and temporal adaptation paths, where a lightweight bottleneck adapter is employed in each transformer block. Especially for temporal dynamic modeling, we incorporate consecutive frames into a grid-like frameset to precisely imitate vision transformers' capability that extrapolates relationships between tokens. In addition, we extensively investigate the multiple baselines from a unified perspective in video understanding and compare them with DUALPATH. Experimental results on four action recognition benchmarks prove that pretrained image transformers with DUALPATH can be effectively generalized beyond the data domain.", + "bbox": [ + 78, + 292, + 484, + 592 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 78, + 606, + 213, + 620 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recognizing when, where, and what happened is a fundamental capability in the human cognition system to understand our natural world. The research for video understanding inspires such capability for machine intelligence to comprehend scenes over time flow. Over the last decade, the development of deep neural networks [10,33,66,73] has contributed towards advances in video understanding.", + "bbox": [ + 78, + 623, + 482, + 722 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Vision Transformer (ViT) [17] has recently emerged, making an upheaval in the research field of computer vision. ViT and its variants [16, 46, 72, 78] have demonstrated remarkable generalizability and transferability of their repre", + "bbox": [ + 78, + 722, + 482, + 781 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/cc6811a31128b3756b96466320126e9df1cf714a41b65756cf31c0817a9bc225.jpg", + "image_caption": [ + "Figure 1. Performance comparison on the Kinetics-400 [38] dataset. We depict the action recognition performance (vertical axis, $\\%$ ) with respect to the number of trainable parameters (horizontal axis). The size of circles indicates GFLOPs for inference." + ], + "image_footnote": [], + "bbox": [ + 515, + 260, + 915, + 450 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "sentations with scaled-up foundation models [34, 53, 63, 69, 77, 79] and large-scale web-collected image data (e.g. JFT-3B [79], LAION-5B [58]). To capitalize on well-trained visual foundation models, finetuning entire parameters of the pretrained models with task-specific objectives has been the most popular transfer technique. However, it requires high-quality training data and plenty of computational resources to update the whole parameters for each downstream task, making overwhelming efforts for training. While partial finetuning [28], which trains additional multilayer perceptron (MLP) layers to the top of the model, has also been widely used for affordable training costs, unsatisfactory performance has been pointed out as a problem.", + "bbox": [ + 510, + 519, + 917, + 705 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Most recently, parameter-efficient transfer learning (PETL) methods [25, 26, 31, 32, 41, 61] have been proposed as an alternative to finetuning in the natural language processing area to adapt the large-scale language model, such as GPT series [8, 54, 55] and T5 [56], for each task. They have successfully attained comparable or even surpassing performance to full-tuning parameters by learning a small number of extra trainable parameters only while keeping the original parameters of the pretrained model frozen. Thanks to their effectiveness and simplicity, they have been ex", + "bbox": [ + 510, + 705, + 917, + 848 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 95, + 8, + 169, + 46 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation.", + "bbox": [ + 228, + 5, + 818, + 21 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "Except for this watermark, it is identical to the accepted version;", + "bbox": [ + 317, + 21, + 731, + 33 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 287, + 34, + 761, + 48 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* Equal contributions. † Corresponding author.", + "bbox": [ + 78, + 789, + 349, + 801 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "Official code: https://github.com/park-jungin/DualPath", + "bbox": [ + 78, + 801, + 473, + 812 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "This research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF2021R1A2C2006703).", + "bbox": [ + 78, + 812, + 480, + 846 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "2203", + "bbox": [ + 468, + 877, + 500, + 888 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tended to vision models by applying prompt-based methods [3, 35] and adapter-based methods [11, 49, 64]. They have efficiently adapted pretrained models to downstream tasks with significantly reduced tuning parameters, but most of these works mainly focus on transferring image models to image tasks [3, 11, 35, 49] and vision-language models to vision-language tasks [64]. Inspired by the advances of the prior arts, we raise two conceivable questions: (1) Is it possible to transfer the parameters of the image foundation model to another video domain? (2) Is it also possible the transferred model performs comparably to the carefully designed video models that take the spatiotemporal nature of the video into account?", + "bbox": [ + 80, + 85, + 480, + 268 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "While image models have demonstrated strong spatial context modeling capabilities [34, 53, 63, 79], video transformer models [1, 47, 57, 76] require a more complex architecture (e.g. 539 vs 48912 GFLOPs [57]) with a large number of parameters (e.g. 84M vs 876M parameters [76]) than ViT for temporal context reasoning. Therefore, the challenge in transferring image models for video understanding is to encode the temporal context of videos while leveraging the discriminative spatial context of the pretrained image models. A naive solution is to finetune image models on a video dataset by directly applying previous prompt/adapter-based approaches [3, 11, 35, 49]. However, these approaches inevitably ignore the temporal context in videos because they bridge only the spatial contexts between image and video data.", + "bbox": [ + 80, + 274, + 480, + 486 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we propose a novel adapter-based dualpath parameter efficient tuning method for video understanding, namely DUALPATH, which consists of two distinct paths (spatial path and temporal path). For both paths, we freeze the pretrained image model and train only additional bottleneck adapters for tuning. The spatial path is designed to encode the spatial contexts that can be inferred from the appearance of individual frames with the minimum tuning of the pretrained image model. To reduce the computation burden, we sparsely use the frames with a low frame rate in the spatial path. The temporal path corresponds to the temporal context that should be encoded by grasping the dynamic relationship over several frames sampled with a high frame rate. Especially for two reasons, we construct a grid-like frameset that consists of consecutive low-resolution frames as an input of the temporal path: (i) preventing computational efficiency loss caused by calculating multiple frames simultaneously; (ii) precisely imitating the ViT's ability for extrapolating global dependencies between input tokens. To compare our DUALPATH with existing methods broadly, we implement several baselines with a unified perspective on recent domain-specific PETL approaches [11, 35, 49]. Extensive experiments on several action recognition benchmarks [23, 38, 39, 42] demonstrate the effectiveness and", + "bbox": [ + 80, + 492, + 480, + 845 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "high efficiency of our DUALPATH, achieving comparable and even better performance than the baselines and prior video models [1, 7, 18, 22, 40, 43, 47, 57, 68, 76]. We achieve these results with extremely low computational costs for both training and inference, as demonstrated in Fig. 1.", + "bbox": [ + 515, + 85, + 915, + 156 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 515, + 172, + 657, + 186 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Pretraining vision models. To address the burdens of collecting large-scale labeled datasets for supervised learning [15, 63, 79], self-supervised learning methods [12, 13, 24,27,28,74] have been introduced to learn general-purpose visual representations from unlabeled data. Similarly, self-supervised learning methods for videos have also been proposed with large-scale unlabeled video/video-language data [20,51,52,62,65,68,75]. However, collecting even unlabeled video-language pairs is still quite costly compared to image-language pairs. In addition, pretraining video models require more computational power than images. We thus take advantage of the powerful pretrained image-based models for efficient video understanding.", + "bbox": [ + 515, + 191, + 915, + 375 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Video action recognition. Action recognition is one of the most fundamental research topics for video understanding. Early works have been built upon convolution neural networks (CNNs) [10, 21, 44, 66, 73] to effectively infer the spatiotemporal context for action recognition. Since Vision Transformer (ViT) [17] has become a new paradigm in computer vision, transformers for video understanding have been actively studied by extending pretrained image models. The pretrained image transformers have been used to initialize the part of the video transformers [1, 7, 76, 80] or inflated to the video transformers [47]. While transformers have demonstrated superior performance on video action recognition, they require full finetuning on video datasets, making the training inefficient.", + "bbox": [ + 515, + 376, + 915, + 575 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Parameter-efficient transfer learning (PETL). To address the memory and parameter inefficiency of full/partial-finetuning, PETL has first introduced in natural language processing (NLP) [6,25,26,31,32,41,61]. The main objective of PETL is to attain comparable or surpassing performance on downstream tasks by finetuning with only a small number of trainable parameters. Although PETL approaches [3, 11, 11, 35, 36, 49, 64] have recently been studied in computer vision, they are 'blind' to other modalities such that image models are used for image tasks, and so are the other modalities. In contrast, we share the same objective as recent works for image-to-video transfer learning [37, 45, 48, 50], demonstrating the pretrained image models can be good video learners. However, they have several limitations in terms of parameter and computational efficiency. For example, [45] learned an extra decoder that contains 3D convolution layers and cross-frame attention, and [50] inserted additional depth-wise 3D convolution layers between the down-/up-projection layers of the adapter to", + "bbox": [ + 515, + 577, + 915, + 845 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "2204", + "bbox": [ + 468, + 878, + 500, + 888 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "perform temporal reasoning, inducing computational inefficiency. The most recent works [37,48] require an additional text encoder branch as a classifier. Moreover, they have computational efficiency proportional to the temporal resolution. Our DUALPATH accomplishes more efficient spatiotemporal modeling while achieving higher performance.", + "bbox": [ + 78, + 85, + 480, + 172 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Preliminaries and Baselines", + "text_level": 1, + "bbox": [ + 78, + 183, + 344, + 199 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Vision transformers for video", + "text_level": 1, + "bbox": [ + 78, + 203, + 349, + 216 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We briefly describe how to apply vision transformers for video understanding below. Following [67], given a set of $T$ frames in a video, we split each frame into $N$ patches of size $(P \\times P)$ and tokenize them using a linear projection, such that", + "bbox": [ + 78, + 219, + 484, + 288 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {X} _ {t} = \\left[ \\mathbf {x} _ {t} \\left\\{\\left[ \\mathrm {C L S} \\right] \\right\\}, \\mathbf {x} _ {t} ^ {1}, \\mathbf {x} _ {t} ^ {2}, \\dots , \\mathbf {x} _ {t} ^ {N} \\right] + \\mathbf {p}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 134, + 300, + 480, + 318 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{X}_t$ is a set of tokens for the $t$ -th frame, and $\\mathbf{x}_t\\{\\mathrm{CLS}\\}$ and $\\mathbf{p}$ denote a learnable class token and a learned positional embedding respectively. We feed $(N + 1)$ tokens of each frame to a sequence of $L$ transformer blocks, and the output of the $l$ -th block $\\mathbf{h}_{l,t}$ can be derived by the following equations:", + "bbox": [ + 78, + 326, + 482, + 413 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {z} _ {l, t} = \\mathbf {h} _ {l - 1, t} + \\mathrm {M H A} (\\mathrm {L N} (\\mathbf {h} _ {l - 1, t})), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 159, + 423, + 480, + 445 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {h} _ {l, t} = \\mathbf {z} _ {l, t} + \\operatorname {M L P} (\\ln (\\mathbf {z} _ {l, t})),\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 442, + 379, + 457 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where LN, MHA, and MLP denote a layer normalization [2], multi-head attention [67], and a multilayer perceptron operation, respectively. We apply layer normalization to the learned $T$ class tokens from the final transformer block and treat them as a set of frame representations.", + "bbox": [ + 78, + 466, + 482, + 537 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To take minimal temporal modeling into account the following baselines [11, 35, 49], we employ a temporal transformer block followed by a full-connected (FC) layer as a classifier for video action recognition, similar to [37]. We add learnable temporal positional embeddings $\\mathbf{p}_{\\mathrm{temp}}$ to the frame representations (i.e., $\\mathbf{x}_t\\{\\mathrm{cl}\\mathbf{s}\\} \\gets \\mathbf{x}_t\\{\\mathrm{cl}\\mathbf{s}\\} + \\mathbf{p}_{\\mathrm{temp}}$ ) and feed them into the transformer classifier. For the ST-adapter [50], we use a single FC layer as a classifier.", + "bbox": [ + 78, + 538, + 482, + 652 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Baselines", + "text_level": 1, + "bbox": [ + 78, + 659, + 191, + 673 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The objective of our work is to transfer the superiority of vision transformers pretrained on large-scale image datasets to the video domain through efficient finetuning with a small number of learnable parameters, while freezing the pretrained parameters. To compare with other methods, we generalize four recent PETL methods to the video domain only with the least possible transformation; (1) VPT [35] (2) AdaptFormer [11] (3) Pro-tuning [49] (4) ST-adapter [50]. The most of works have been originally proposed to adapt pretrained image models to downstream image tasks [11, 35, 49] and video models to video tasks [11], by learning visual prompt tokens [35], adapter", + "bbox": [ + 78, + 676, + 482, + 848 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/0d130e43d9de9b4053b68b241a10d58c585112f48271fa2fdba61c2f7f347e8d.jpg", + "image_caption": [ + "(a) VPT [35]" + ], + "image_footnote": [], + "bbox": [ + 537, + 84, + 710, + 168 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/2c82839b12d43b96cb61f9a21a18c3a24eb6c6f79b4b7211beb574d6c48deef2.jpg", + "image_caption": [ + "(b) Parallel Adapter [11]" + ], + "image_footnote": [], + "bbox": [ + 719, + 82, + 895, + 168 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/56e58334dc2d8ad711272a19cde900f16f2eecbceb80c423b39e597ebb695fdb.jpg", + "image_caption": [ + "(c) Serial Adapter [11]" + ], + "image_footnote": [], + "bbox": [ + 537, + 183, + 631, + 294 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/42bb65e6c745943f00cffb8e5bfe5e81e85600312af0e361ef28df3bca31dbf5.jpg", + "image_caption": [ + "(d) Prompt Block [49]" + ], + "image_footnote": [], + "bbox": [ + 663, + 183, + 763, + 294 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/9cc0dd574dab336362cc723c490150acfe5ddc409dc703846c4703ea1e3ec888.jpg", + "image_caption": [ + "(e) ST-Adapter [50]", + "Figure 2. Baselines for image-to-video transfer learning. (a) Visual Prompt Tuning [35]; (b) Parallel adapter and (c) serial adapter [11]; (d) Pro-Tuning [49]; and (e) ST-Adapter [50]." + ], + "image_footnote": [], + "bbox": [ + 798, + 187, + 895, + 294 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "blocks [11] and prompt prediction blocks [49]. Only the ST-adapter [50] has proposed image-to-video transfer learning. In this section, we describe baselines for image-to-video transfer learning in detail. For brevity, we leave out the subscripts in Eq. 2 and arouse them as needed. In addition, we represent the learnable and frozen parameters in red and blue colors, respectively.", + "bbox": [ + 512, + 368, + 917, + 467 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Visual prompt tuning (VPT) [35] prepends $K$ trainable prompt tokens to the input space of every transformer block1 while keeping pretrained parameters frozen. The input tokens for each transformer block can be written as:", + "bbox": [ + 512, + 468, + 917, + 525 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {\\mathbf {h}} = [ \\mathbf {e}; \\mathbf {h} ], \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 672, + 533, + 917, + 552 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{e} \\in \\mathbb{R}^{K \\times d}$ is a set of trainable visual prompt tokens and $d$ is a channel dimension of the original token.", + "bbox": [ + 512, + 560, + 915, + 589 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "AdaptFormer [11] learns a trainable bottleneck module [26, 31]. The intermediate feature $\\mathbf{z}$ in Eq. 2 of each transformer block is fed into the AdapterMLP that consists of the original MLP layers and a bottleneck structure (parallel adapter in Fig. 2b). The output of the AdaptFormer block can be formulated by:", + "bbox": [ + 512, + 589, + 917, + 674 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {\\mathbf {z}} = \\sigma (\\underset {\\sim} {\\mathrm {L N}} (\\mathbf {z}) \\cdot \\mathbf {W} _ {\\text {d o w n}}) \\cdot \\mathbf {W} _ {\\text {u p}}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 601, + 683, + 915, + 708 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {h} = \\mathbf {z} + \\operatorname {M L P} (\\operatorname {L N} (\\mathbf {z})) + s \\cdot \\tilde {\\mathbf {z}},\n$$\n", + "text_format": "latex", + "bbox": [ + 603, + 703, + 818, + 720 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{W}_{\\mathrm{down}}$ , $\\mathbf{W}_{\\mathrm{up}}$ are trainable down- and up-projection matrices, $\\sigma(\\cdot)$ is an activation function, and $s$ is a scaling factor.", + "bbox": [ + 512, + 731, + 917, + 772 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Pro-tuning [49] predicts task-specific vision prompts $\\mathbf{v}$ from the output of each transformer block using consecu", + "bbox": [ + 512, + 775, + 917, + 803 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "1While the original work also presented a shallow version (VPT-Shallow) that inserts prompt tokens to the first layer, we explore a deep version (VPT-Deep) only.", + "bbox": [ + 512, + 810, + 917, + 846 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "2205", + "bbox": [ + 468, + 878, + 500, + 888 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/ece0194475dd68a2c943119364e9ee270bed0a86e9773dd04f6ef0063104074d.jpg", + "image_caption": [ + "Figure 3. Overall architecture of DUALPATH. The pretrained image transformer takes a grid-like frameset and $T_{s}$ frames as inputs. We learn the temporal and spatial contexts separately through two distinct paths. During training, we only update newly introduced adapters and the classifier while freezing the pretrained layers." + ], + "image_footnote": [], + "bbox": [ + 82, + 84, + 675, + 292 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/089ae6f20f80879fbcb7d6e8cd3ad8fcd95a2af7e7d446706ba3be347d7fe3fe.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 684, + 89, + 915, + 291 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "tive 2D convolution layers. The output of each block is reshaped as $\\mathbb{R}^{P\\times P\\times C}$ to apply 2D convolutions and the final representation is derived by adding $\\mathbf{v}$ and $\\mathbf{h}$ :", + "bbox": [ + 78, + 350, + 480, + 394 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {v} = \\operatorname {R e s h a p e} \\left(\\sigma (\\underset {\\sim} {\\operatorname {C o n v 2 d}} (\\operatorname {R e s h a p e} (\\mathbf {h})))\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 117, + 400, + 480, + 425 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {\\mathbf {h}} = \\mathbf {h} + \\mathbf {v},\n$$\n", + "text_format": "latex", + "bbox": [ + 236, + 420, + 319, + 435 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where Conv2D consists of $1 \\times 1$ convolution layer followed by $5 \\times 5$ depth-wise convolution [14] and $1 \\times 1$ convolution. ST-adapter [50] inserts a depth-wise 3D convolution layer between the down-projection layer and the activation function of the adapter. Different from the conventional adapters (e.g. AdaptFormer [11]), the ST-adapter takes tokens for all frames to enable the model to capture temporality in videos. The output of the ST-adapter can be represented as:", + "bbox": [ + 78, + 445, + 482, + 558 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\bar {\\mathbf {z}} _ {t} = \\overline {{\\mathrm {L N}}} (\\mathbf {z} _ {t}),\n$$\n", + "text_format": "latex", + "bbox": [ + 205, + 565, + 307, + 583 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\hat {\\mathbf {z}} = \\sigma (\\text {D - C o n v 3 d} ([ \\tilde {\\mathbf {z}} _ {1} \\cdot \\mathbf {W} _ {\\text {d o w n}}, \\dots , \\tilde {\\mathbf {z}} _ {T} \\cdot \\mathbf {W} _ {\\text {d o w n}} ])) \\cdot \\mathbf {W} _ {\\text {u p}}, \\\\ \\mathbf {h} _ {t} = \\mathbf {z} _ {t} + \\underline {{\\mathrm {M L P}}} (\\tilde {\\mathbf {z}} _ {t}) + s \\cdot \\hat {\\mathbf {z}} _ {t}, \\tag {6} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 80, + 583, + 480, + 632 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where D-Conv3d denotes the depth-wise 3D convolution layer. Note that the same down-projection matrix $\\mathbf{W}_{\\mathrm{down}}$ is applied to all tokens regardless of the frame index $t$ .", + "bbox": [ + 78, + 633, + 480, + 675 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We emphasize that most of the baselines [11,35,49] have not concerned with temporal modeling. Even though ST-Adapter [50] has employed depth-wise 3D convolution layers between linear projections, it results in high computational cost. To entirely leverage a simple and efficient architecture of the adapter [11], we incorporate the dual-path design into the pretrained image transformers.", + "bbox": [ + 78, + 675, + 482, + 776 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Method", + "text_level": 1, + "bbox": [ + 78, + 785, + 171, + 800 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The dual-path design (also called two-stream) is well-known architecture in CNN-based models for video recognition [10, 21, 60]. They have commonly used an optical", + "bbox": [ + 78, + 804, + 482, + 847 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "flow [10, 60] or multiple frames with a high temporal resolution [21] to capture rapidly changing motion. Despite the effectiveness of dual-path architecture, it has yet to be explored with the transformer due to high computational costs. In this work, we propose a novel PETL method, called DUALPATH, comprised of spatial and temporal path adaptation. To the best of our knowledge, our DUALPATH is the first attempt to explicitly build the two-stream architecture upon the transformer while maintaining the computational cost similar to the single-stream architecture. The overall framework is depicted in Fig. 3.", + "bbox": [ + 510, + 350, + 917, + 507 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Spatial adaptation", + "text_level": 1, + "bbox": [ + 512, + 511, + 695, + 526 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Since the image foundation models have been trained on large amounts of web datasets, we can intuitively speculate that they might be powerful to encode the spatial context even in videos. In order to make the outstanding ability of spatial modeling to be more suitable for video understanding with a slight parameter tuning, we adopt two parallel adapters for MHA and MLP in each transformer block. The parallel adapters allow the model to learn the spatial context for action recognition from the appearance of target video data while maintaining the original contexts for object recognition.", + "bbox": [ + 510, + 527, + 917, + 684 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Specifically, we sample $T_{S}$ frames from a video and tokenize each frame. Similar to Eq. 1, the set of spatial tokens $\\mathbf{X}_t^{\\mathrm{SP}}$ includes the learnable positional encodings $\\mathbf{p}^{\\mathrm{SP}}$ and the spatial class token $\\mathbf{x}_t^{\\mathrm{SP}}\\{[\\mathrm{CLS}]\\}$ . The spatial adaptation in the $l$ -th transformer block can be formulated by the following equations:", + "bbox": [ + 512, + 684, + 917, + 776 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathbf {z} _ {l} ^ {\\mathrm {S P}} = \\mathbf {h} _ {l - 1} ^ {\\mathrm {S P}} + \\mathrm {M H A} (\\mathrm {L N} (\\mathbf {h} _ {l - 1} ^ {\\mathrm {S P}})) + \\text {A d a p t e r} (\\mathrm {L N} (\\mathbf {h} _ {l - 1} ^ {\\mathrm {S P}})), \\\\ \\mathbf {h} _ {l} ^ {\\mathrm {S P}} = \\mathbf {z} _ {l} ^ {\\mathrm {S P}} + \\underline {{\\operatorname {M L P}}} (\\underline {{\\operatorname {L N}}} (\\mathbf {z} _ {l} ^ {\\mathrm {S P}})) + \\underline {{\\operatorname {A d p a t e r}}} (\\underline {{\\operatorname {L N}}} (\\mathbf {z} _ {l} ^ {\\mathrm {S P}})), \\tag {7} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 526, + 784, + 915, + 831 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{h}_0^{\\mathrm{SP}} = [\\mathbf{x}_t^{\\mathrm{SP}}\\{\\mathrm{[CLS]}\\} ,\\mathbf{X}_t^{\\mathrm{SP}}] + \\mathbf{p}^{\\mathrm{SP}}$ .We average", + "bbox": [ + 512, + 831, + 915, + 848 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "2206", + "bbox": [ + 468, + 877, + 500, + 888 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the set of the spatial [CLS] tokens from the final transformer block to obtain a global spatial representation $\\mathbf{y}^{\\mathrm{SP}}$ , such that,", + "bbox": [ + 78, + 85, + 485, + 129 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {y} ^ {\\mathrm {S P}} = \\frac {1}{T _ {S}} \\sum_ {t = 1} ^ {T _ {S}} \\mathbf {x} _ {t} ^ {\\mathrm {S P}} \\left\\{\\left[ \\mathrm {C L S} \\right] \\right\\}. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 178, + 136, + 482, + 174 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Recent methods have discussed that a high frame rate only increases the computation volume and is unnecessary to understand the semantics of appearance [9, 21]. We thus sparsely sample $T_{S}$ frames with a low frame rate (e.g. 8 frames per clip).", + "bbox": [ + 78, + 183, + 484, + 255 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Temporal adaptation", + "text_level": 1, + "bbox": [ + 78, + 262, + 284, + 277 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "While spatial adaptation enables the models to take the spatial contexts in video data, the image models are still incapable of modeling the temporal dynamics. The key component that allows video transformers to model the solid temporal context is to learn relationships between local patches across frames in the video [1, 7]. To make image models capable of effectively establishing this component, we suggest a novel grid-like frameset transform technique that aggregates multiple frames into a unified grid-like frameset. Our grid-like frameset design is inspired by recent visual prompting research [4, 5]. It is simple yet surprisingly effective in imitating temporal modeling as spatial modeling and certainly reduces the computation. In each transformer block, we adopt two additional serial adapters for MHA and MLP, respectively.", + "bbox": [ + 77, + 278, + 484, + 491 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "More concretely, we sample $T$ frames from a video and scale them with factors of $w$ and $h$ , such that the scaled frame size is $[W / w \\times H / h \\times 3]$ . We stack $w \\times h$ scaled frames according to temporal ordering and reshape a stacked frame to construct a set of frames in a grid form of the same size as the original frame (i.e., $[W \\times H \\times 3]$ ). Note that the total number of grid-like framesets is $T_{G} = T / wh$ . The set of temporal tokens $\\mathbf{X}_{g}^{\\mathrm{TP}}$ for the $g$ -th frameset is obtained in the same way in Eq. 1 and combined with the learnable temporal class token $\\mathbf{x}_{g}^{\\mathrm{TP}}\\left\\{\\left[\\mathrm{CLS}\\right]\\right\\}$ . Unlike the spatial adaptation, we use fixed 3D positional encodings [70], $\\mathbf{p}^{\\mathrm{TP}}$ , to the tokens to take the absolute temporal order and spatial positions of patches into account. The input transformation allows transformers to observe multiple frames at the same level. In experiments, we mainly construct a grid-like frameset from 16 original frames (i.e., scaling factors $w = h = 4$ ) to take the computational efficiency and promising performance.", + "bbox": [ + 77, + 491, + 482, + 750 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Whereas the parallel adapter is used in the spatial path, we sequentially append adapters to the top of MHA and MLP layers in each transformer block. Formally, temporal adaptation in the $l$ -th block can be described as:", + "bbox": [ + 78, + 750, + 484, + 806 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathbf {z} _ {l} ^ {\\mathrm {T P}} = \\mathbf {h} _ {l - 1} ^ {\\mathrm {T P}} + \\text {A d a p t e r} (\\underset {\\leftarrow} {\\mathrm {M H A}} (\\underset {\\leftarrow} {\\mathrm {L N}} (\\mathbf {h} _ {l - 1} ^ {\\mathrm {T P}}))), \\tag {9} \\\\ \\mathbf {h} _ {l} ^ {\\mathrm {T P}} = \\mathbf {z} _ {l} ^ {\\mathrm {T P}} + \\text {A d p a t e r} (\\operatorname {M L P} (\\operatorname {L N} (\\mathbf {z} _ {l} ^ {\\mathrm {T P}}))), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 119, + 812, + 482, + 850 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/903993652c334d6437281a7d27c13c59eff87e58efdcfba736578e3e0212a7ea.jpg", + "image_caption": [ + "(a) DUALPATH w/o TA", + "Figure 4. Visualization of attention maps (a) without temporal adaptation (TA) and (b) with temporal adaptation for the action 'Spinning [something] that quickly stops spinning' in SSv2 [23]." + ], + "image_footnote": [], + "bbox": [ + 526, + 83, + 710, + 212 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/4ea058028768dba022c0198589b5fbbfaec44a6cb273f5a1ab51662417053759.jpg", + "image_caption": [ + "(b) DUALPATH w/ TA" + ], + "image_footnote": [], + "bbox": [ + 721, + 82, + 905, + 212 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{h}_0^{\\mathrm{TP}} = [\\mathbf{x}_g^{\\mathrm{TP}}\\{\\mathrm{[CLS]}\\} ,\\mathbf{X}_g^{\\mathrm{TP}}] + \\mathbf{p}^{\\mathrm{TP}}$ . Similar to spatial adaptation, a global temporal representation $\\mathbf{y}^{\\mathrm{TP}}$ can be derived by averaging the set of the temporal [CLS] tokens from the final transformer block, i.e.,", + "bbox": [ + 512, + 287, + 917, + 350 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {y} ^ {\\mathrm {T P}} = \\frac {1}{T _ {G}} \\sum_ {g = 1} ^ {T _ {G}} \\mathbf {x} _ {g} ^ {\\mathrm {T P}} \\{[ \\mathrm {C L S} ] \\}. \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 611, + 361, + 917, + 401 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For the final prediction, we concatenate the global spatial and temporal representations and feed them into the classifier with GeLU activation [29] between two FC layers.", + "bbox": [ + 512, + 414, + 917, + 456 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Does a grid-like frameset really help to encode temporal context?", + "text_level": 1, + "bbox": [ + 512, + 468, + 917, + 495 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This work presents a new standpoint to perform video action recognition with the pretrained image transformer by transforming multiple frames into a unified grid-like frame-set. However, it is still questionable whether the temporal path of DUALPATH can really capture the temporal context of videos. In this section, we provide some qualitative examples of the attention map. To validate the ability of precise temporal modeling, we sample videos from the SSv2 [23] dataset. Following [50], we depict the attention map of $\\mathbf{x}_g^{\\mathrm{TP}}\\{[\\mathrm{CLS}]\\}$ from the final transformer block of the temporal path. As shown in Fig. 4, the model with the temporal adaptation (TA) of DUALPATH tends to concentrate on action-related regions, contrary to the model without TA that focuses on the irrelevant background. This result suggests that the temporal adaptation of DUALPATH strengthens the temporal modeling ability of the image model. More examples are shown in Fig. A1 of Appendix.", + "bbox": [ + 510, + 499, + 917, + 741 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experiment", + "text_level": 1, + "bbox": [ + 512, + 756, + 640, + 772 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Evaluation setup", + "text_level": 1, + "bbox": [ + 512, + 776, + 685, + 791 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. We evaluate the proposed method on four standard action recognition datasets, including the Kinetics-400 (K400) [38], HMDB51 [39], Something-something-v2 (SSv2) [23], and Diving-48 [42].", + "bbox": [ + 512, + 793, + 917, + 851 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "2207", + "bbox": [ + 468, + 877, + 500, + 888 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/38bbd82649b5ca95ba0136f7aa1ca208126f7c458b69a7bfb187fa8f6b1b53ac.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Method & Arch.PretrainModel # ParamsTrainable # ParamsGFLOPsR@1R@5Views
Full-tuning
SlowFast+NL [21]-60M60M702079.893.916×3×10
MViT-B [18]-37M37M409581.295.164×3×3
UniFormer-B [40]IN-1K50M50M310883.095.432×4×3
TimeSformer-L [7]IN-21K121M121M714080.794.764×1×3
ViViT-L/16×2 FE [1]IN-1K311M311M398080.692.732×1×1
VideoSwin-L [47]IN-21K197M197M724883.195.932×4×3
MViTv2-L [43]IN-21K218M218M4242086.197.032×3×5
MTV-L [76]JFT876M876M1805084.396.332×4×3
TokenLearner-L/10 [57]JFT450M450M4891285.496.364×4×3
ActionCLIP [68]CLIP142M142M1689083.897.132×10×3
X-CLIP-L/14 [48]CLIP420M420M789087.197.68×4×3
Parameter Efficient Tuning
EVL [45] w/ ViT-L/14CLIP368M59M808887.3-32×3×1
ST-Adapter [50] w/ ViT-B/16CLIP93M7M182182.796.232×3×1
DUALPATH w/ ViT-B/16CLIP96M10M71085.497.132×3×1
DUALPATH w/ ViT-L/14CLIP330M27M186887.797.832×3×1
", + "bbox": [ + 144, + 82, + 853, + 351 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Performance comparisons for action recognition on the Kinetics-400 [38] dataset. Note that Views = #frames × #clips × #spatial.", + "bbox": [ + 78, + 356, + 915, + 369 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Kinetics-400 (K400) contains about 240K training videos and 20K validation videos for 400 human action categories. Each video is trimmed to have a length of 10 seconds. While the K400 dataset provides a wide range of categories, they are known to be highly biased in spatial appearance [59].", + "- Somthing-something-v2 (SSv2) is a more challenging dataset since they require strong temporal modeling [59]. They contain about 168.9K training videos and 24.7K validation videos for 174 classes.", + "- HMDB51 is a small dataset that provides about 7K videos of 51 action categories. We use all three splits, each split of which consists of 3570 and 1530 videos for training and evaluation, respectively. We report the average accuracy for three splits.", + "- Diving-48 is a fine-grained diving action dataset. We use train-test split v2 that contains about 15K training videos and 2K validation videos of 48 diving actions. Since the action can not be determined by only the static representations (e.g. objects or background), stronger temporal modeling is required for this dataset." + ], + "bbox": [ + 99, + 387, + 480, + 705 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Pretrained image backbone. We employ CLIP pretrained ViT-B/16 and ViT-L/14 as backbones. The results with Swin-B [46] are provided in Tab. A2 of the Appendix.", + "bbox": [ + 78, + 709, + 480, + 753 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- ViT-B/16 [17] consists of 12 transformer blocks with 86M parameters and takes patches of size $16 \\times 16$ as inputs.", + "- ViT-L/14 [17], a larger model than ViT-B/16, contains 24 transformer blocks with 303M parameters. It takes $14 \\times 14$ patches as inputs." + ], + "bbox": [ + 99, + 758, + 480, + 850 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation details. For the K400, HMDB51, and Diving-48 datasets, we uniformly sample 8 frames (i.e., $T_{s} = 8$ ) with the sampling interval 8 in the spatial path. In the temporal path, we uniformly sample 16, 32, and 48 frames with the sampling intervals 4, 2, and 1 to construct 1, 2, and 3 grid-like framesets (i.e., $T_{g} = 1,2,3$ ), respectively. For the SSv2 dataset, we sample the same number of frames as in other datasets, but with a dynamic sampling interval to cover the whole video. Note that the frames for the spatial path are the subset of the temporal path frames. Please refer to more implementation details in Appendix A.", + "bbox": [ + 512, + 387, + 917, + 544 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Comparison with state-of-the-art", + "text_level": 1, + "bbox": [ + 512, + 557, + 811, + 571 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we compare the proposed method with baselines [11, 35, 49, 50] in Sec. 3 and state-of-the-art video transformers [1, 7, 18, 40, 43, 45, 47, 48, 57, 68, 76] to demonstrate the effectiveness of the proposed method on four video action recognition datasets. Note that the number of frames of the spatial adaptation path of DUALPATH is fixed to 8 for all experiments, i.e., $T_{S} = 8$ .", + "bbox": [ + 512, + 575, + 917, + 675 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results on Kinetics-400. We report the results evaluated on K400 [38] in Tab. 1. We first compare the proposed method with state-of-the-art video models that are pretrained on the large-scale image dataset and fully finetuned on K400. In terms of memory and computational efficiency, video models require a huge number of parameters ( $\\sim$ 450M [57]) and computations ( $\\sim$ 48912 GFLOPs [57]). On the other hand, we require only 10M trainable parameters which are newly stored, and 710 GFLOPs for inference using 32 frames with ViT-B/16 [17] backbone. Compared to X-CLIP-L/14 [48] which leverages the additional text branch, our DUALPATH achieves state-of-the-art performance with ViT-L/14 back", + "bbox": [ + 512, + 677, + 917, + 847 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "2208", + "bbox": [ + 468, + 878, + 500, + 888 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/2e6e2bddad645435d7d954fe18cdf5b0de5ccd6d1c5f0f8101dbe07a5c86dfea.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Method & Arch.PretrainModel\n#ParamsTrainable\n#ParamsGFLOPsR@1R@5Views
Full-tuning
Full-tuning ViT-B/16 [17]CLIP86M86M41944.077.08×1×3
Full-tuning ViT-L/14 [17]CLIP303M303M194148.777.58×1×3
TimeSformer-L [7]IN-21K121M121M714062.4-64×1×3
MTV-B [76]IN-21K310M310M479067.690.432×4×3
MViT-B [18]K40037M37M51067.190.832×1×3
MViTv2-B [43]K40051M51M67570.592.740×1×3
ViViT-L/16×2 [1]IN-21K/K400311M311M1189265.489.816×4×3
VideoSwin-B [47]IN-21K/K40089M89M96369.692.732×1×1
Omnivore [22]IN-21K/K400---71.493.532×1×3
MViTv2-B [43]IN-21K/K400213M213M848473.394.132×1×3
UniFormer-B [40]IN-21K/K60050M50M77771.292.832×1×3
Parameter Efficient Tuning
VideoPrompt* [37] w/ ViT-B/16CLIP92M6M53731.060.38×1×3
VPT [35] w/ ViT-B/16CLIP92M6M53736.261.18×1×3
AdaptFormer [11] w/ ViT-B/16CLIP94M8M54451.370.68×1×3
Pro-tuning [49] w/ ViT-B/16CLIP95M9M53850.869.98×1×3
EVL [45] w/ ViT-L/14CLIP484M175M964166.7-32×1×3
ST-Adapter [50] w/ ViT-B/16CLIP97M11M195569.592.632×3×1
DUALPATH w/ ViT-B/16CLIP99M13M64269.692.516×1×3
DUALPATH w/ ViT-B/16CLIP99M13M71670.392.932×1×3
DUALPATH w/ ViT-B/16CLIP99M13M79171.293.248×1×3
DUALPATH w/ ViT-L/14CLIP336M33M171370.292.716×1×3
DUALPATH w/ ViT-L/14CLIP336M33M193271.493.432×1×3
DUALPATH w/ ViT-L/14CLIP336M33M215172.293.748×1×3
", + "bbox": [ + 122, + 83, + 873, + 455 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "bone. The comparisons with parameter-efficient tuning methods [45, 50] show that our DUALPATH achieves higher performance while requiring much lower burdens in computations under the same conditions.", + "bbox": [ + 78, + 504, + 480, + 560 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results on Something-Something-v2. We present the performance comparisons on SSv2 [23] in Tab. 2. The results show that our DUALPATH with ViT-B/16 achieves comparable or better performance than the prior supervised video models [1,7,18,76], requiring a much smaller number of trainable parameters and GFLOPs. Our DUALPATH with ViT-L/14 shows more competitive performance, outperforming most prior works [22, 40, 43]. The baselines [11, 35, 37, 49], which have relatively weak temporal modeling ability, show significantly poor performance, implying that strong temporal modeling is mandatory for the SSv2 dataset. The comparisons to the CLIP pretrained PET approaches [45, 50] with ViT-B/16 demonstrate the effectiveness and efficiency of DUALPATH, achieving higher performance (70.3 vs 69.5 [50]) with significantly low computations (716 vs 9641 [45] GFLOPs) using 32 frames. Thanks to the extreme computational efficiency, our DUALPATH comprises more competitive performance using 48 frames ( $T_{G} = 3$ ) with low computation requirements.", + "bbox": [ + 78, + 562, + 482, + 831 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results on HMDB51. In Tab. 3, we compare the re", + "bbox": [ + 78, + 832, + 480, + 846 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/d3038be6237e83c67f4bbc12698b6988d4d82935cc32956ce52e9d2cce4f42f9.jpg", + "table_caption": [ + "Table 2. Performance comparisons for action recognition on the SSv2 [23] dataset. Note that we reproduce VideoPrompt [37] without the additional text branch for fair comparison (denoting with *)." + ], + "table_footnote": [], + "table_body": "
Method & Arch.ClassifierParamsHMDB51
Full-tuning w/ ViT-B/16 [17]Lin.86M59.4
Linear w/ ViT-B/16Lin.0.1M61.2
VPT [35] w/ ViT-B/16Trans.7M62.4
AdaptFormer [11] w/ ViT-B/16Trans.8M63.7
Pro-tuning [49] w/ ViT-B/16Trans.9M63.3
VideoPrompt [37] w/ ViT-B/16Trans.6M66.4
ST-Adapter* [50] w/ ViT-B/16Lin.7M65.9
DUALPATH w/ ViT-B/16MLPs.10M75.6
", + "bbox": [ + 515, + 502, + 922, + 633 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Performance comparisons for action recognition on the HMDB51 [39] dataset with the CLIP pretrained ViT-B/16 [53]. We report the type of classifier and the number of learnable parameters for baselines and ours. Lin. and Trans. denote the linear classifier and temporal transformer, respectively. Our DUALPATH uses two MLP layers as the classifier. Note that we reproduce ST-Adapter [50] for fair comparison in terms of the pretrained dataset (denoting with $*$ ).", + "bbox": [ + 512, + 636, + 917, + 741 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "sults with baselines [11, 35, 37, 49, 50] on HMDB51 [39] that dominantly requires strong spatial modeling for action recognition. Surprisingly, our DUALPATH significantly outperforms baselines by large margins. This result demonstrates DUALPATH fully capitalizes on the exceptional spatial modeling ability of the pretrained image model for ac", + "bbox": [ + 510, + 760, + 917, + 847 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "2209", + "bbox": [ + 468, + 877, + 500, + 888 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/79531bd1c8052868c81646355374af9e02e7993661d455035077abf0cce0cd7b.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Method & Arch.PretrainParamsDiving48
Supervised
TimeSformer-L [7]IN-21K121M81.0
VideoSwin-B [47]IN-21K88M81.9
SIFAR-B-14 [19]IN-21K87M87.3
ORViT [30]IN-21K160M88.0
Parameter Efficient Tuning
DUALPATH w/ ViT-B/16CLIP10M88.7
", + "bbox": [ + 99, + 82, + 460, + 208 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "tion recognition. The comparison with VideoPrompt [37] that uses the additional text branch demonstrates the effectiveness of DUALPATH, improving $9.2\\%$ performance improvement.", + "bbox": [ + 78, + 268, + 480, + 324 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Results on Diving-48. Tab. 4 shows performance comparisons on Diving-48 [42] that requires fine-grained action recognition. Our DUALPATH consistently outperforms all video models with only 10M trainable parameters. Particularly, we obtain a better performance than ORViT [30] which utilizes the additional tracking model. It indicates the utility of DUALPATH in fine-grained action recognition and the superiority of temporal modeling of DUALPATH.", + "bbox": [ + 78, + 324, + 480, + 439 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.3. Components analysis", + "text_level": 1, + "bbox": [ + 78, + 447, + 282, + 462 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Impact of dual-path. In the top panel of Tab. 5, we train the model by ablating each path and evaluate the performance on SSv2. Without the temporal path (DUALPATH w/o TA), the performance is significantly degraded despite using a larger number of frames ( $T_{S} = 16$ vs 8). Without the spatial path (DUALPATH w/o SA), we can obtain slightly better performance than the result without the temporal adaptation. Since the SSv2 requires strong temporal modeling, we speculate that two ablation studies show comparison results. However, it still shows a substantial performance gap compared to the full model of DUALPATH, demonstrating the effectiveness of the dual-path design.", + "bbox": [ + 78, + 463, + 480, + 633 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Frame rates in spatial path. In the middle panel of Tab. 5, we analyze the effect according to the number of frames used in the spatial path. The temporal path identically uses 16 frames to construct a grid-like frameset, and frames used in the spatial path are sampled from such 16 frames. A large number of $T_{S}$ slightly improves performance, however, requires more computational costs. Considering the performance improvement compared to the computation increase, we mainly set $T_{S}$ to 8.", + "bbox": [ + 78, + 633, + 480, + 760 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Number of frames in grid. We scale down original frames with scaling factors $w$ and $h$ to construct grid-like framesets. These factors thus determine the number of frames the model observes within one grid-like frameset. While a large value of factors increases the temporal resolution, the information of each frame is inevitably reduced. For exam-", + "bbox": [ + 78, + 760, + 480, + 847 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/e201c4e06857f9ba57ed80e4d9b0bc35e3ea3f64ad65109437110cfd309d1d04.jpg", + "table_caption": [ + "Table 4. Performance comparisons for action recognition on the Diving-48 [42] dataset. We report the pretrained dataset, the number of learnable parameters (M) for each method, and the accuracy." + ], + "table_footnote": [], + "table_body": "
MethodParamsGFLOPsSSv2Views
Effectiveness of Each Path
DUALPATH w/o TA5M101653.716×3×1
DUALPATH w/o SA8M13455.116×3×1
Effectiveness of TS
TS=813M64269.316×3×1
TS=1213M89669.616×3×1
TS=1613M115069.816×3×1
Effectiveness of scaling factors
w=h=2 (TG=16)13M175266.464×3×1
w=h=4 (TG=4)13M86471.864×3×1
w=h=8 (TG=1)13M64261.564×3×1
DUALPATH13M64269.316×3×1
", + "bbox": [ + 526, + 82, + 904, + 284 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5. Performance with respect to variants of the components.", + "bbox": [ + 515, + 287, + 912, + 300 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ple, the original frame is scaled down to the size of $28 \\times 28$ with $w = h = 8$ . Meanwhile, a small value of factors retains richer information from the original frame, however, makes the temporal resolution small. As shown in the bottom panel of Tab. 5, we attain the best performance with $w = h = 4$ .", + "bbox": [ + 512, + 323, + 915, + 395 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion and Future Work", + "text_level": 1, + "bbox": [ + 512, + 409, + 789, + 424 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we have introduced the novel image-to-video transfer learning approach, DUALPATH. By incorporating a dual-path design into image transformers, DUALPATH adapts image models to the video task (i.e., action recognition) with a small number of trainable parameters. The spatial path adaptation strengthens the inherent spatial context modeling of the pretrained image transformers for video data. The temporal path adaptation transforms multiple frames into a unified grid-like frameset, enabling the image model to capture relationships between frames. We appropriately employ the bottlenecked adapters in each path to adapt the pretrained features to target video data. In addition, we present several baselines transforming recent PETL approaches [11, 35, 49] for image-to-video adaptation. Experimental results demonstrated the superiority of the dualpath design and the grid-like frameset prompting, outperforming several baselines and supervised video models.", + "bbox": [ + 512, + 430, + 915, + 671 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "There are many possible directions for future work, encompassing cross-domain transfer learning. While we have explored image-to-video transfer learning, large foundation vision-language models are available. It would also be interesting to expand the superior pretrained 2D knowledge to 3D spatial modeling [71]. We hope our study will foster research and provide a foundation for cross-domain transfer learning.", + "bbox": [ + 510, + 673, + 915, + 788 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement. This research was supported by the Yonsei Signature Research Cluster Program of 2022 (2022-22-0002) and the KIST Institutional Program (Project No.2E32283-23-064).", + "bbox": [ + 512, + 790, + 915, + 847 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "2210", + "bbox": [ + 468, + 877, + 500, + 888 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 80, + 84, + 178, + 98 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Anurag Arnab, Mostafa Dehghani, Georg Heigold, Chen Sun, Mario Lučić, and Cordelia Schmid. Vivit: A video vision transformer. In ICCV, 2021. 2, 5, 6, 7", + "[2] Jimmy Lei Ba, Jamie Ryan Kiros, and Geoffrey E. Hinton. Layer normalization. arXiv preprint: arXiv:1607.06450, 2016.3", + "[3] Hyojin Bahng, Ali Jahanian, Swami Sankaranarayanan, and Phillip Isola. 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In ICCV, 2021. 2" + ], + "bbox": [ + 517, + 87, + 915, + 284 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "2213", + "bbox": [ + 468, + 878, + 500, + 888 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Dual-Path Adaptation From Image to Video Transformers/58cf23aa-7524-4b95-9291-20d982a61012_model.json b/2023/Dual-Path Adaptation From Image to Video Transformers/58cf23aa-7524-4b95-9291-20d982a61012_model.json new file mode 100644 index 0000000000000000000000000000000000000000..fe54e93961917f87196061946ce353637d292af6 --- /dev/null +++ b/2023/Dual-Path Adaptation From Image to Video Transformers/58cf23aa-7524-4b95-9291-20d982a61012_model.json @@ -0,0 +1,2730 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.096, + 0.009, + 0.171, + 0.047 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.23, + 0.006, + 0.819, + 0.022 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation." + }, + { + "type": "header", + "bbox": [ + 0.318, + 0.022, + 0.732, + 0.034 + ], + "angle": 0, + "content": "Except for this watermark, it is identical to the accepted version;" + }, + { + "type": "header", + "bbox": [ + 0.288, + 0.035, + 0.762, + 0.049 + ], + "angle": 0, + "content": "the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.2, + 0.123, + 0.798, + 0.144 + ], + "angle": 0, + "content": "Dual-path Adaptation from Image to Video Transformers" + }, + { + "type": "text", + "bbox": [ + 0.23, + 0.17, + 0.348, + 0.188 + ], + "angle": 0, + "content": "Jungin Park1*" + }, + { + "type": "text", + "bbox": [ + 0.407, + 0.17, + 0.525, + 0.188 + ], + "angle": 0, + "content": "Jiyoung Lee\\(^{2*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.587, + 0.17, + 0.76, + 0.188 + ], + "angle": 0, + "content": "Kwanghoon Sohn\\(^{1,3\\dagger}\\)" + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.192, + 0.258, + 0.211 + ], + "angle": 0, + "content": "\\(^{1}\\)Yonsei University" + }, + { + "type": "text", + "bbox": [ + 0.297, + 0.192, + 0.439, + 0.209 + ], + "angle": 0, + "content": "\\(^{2}\\)NAVER AI Lab" + }, + { + "type": "text", + "bbox": [ + 0.479, + 0.192, + 0.896, + 0.211 + ], + "angle": 0, + "content": "\\(^{3}\\)Korea Institute of Science and Technology (KIST)" + }, + { + "type": "text", + "bbox": [ + 0.248, + 0.216, + 0.512, + 0.23 + ], + "angle": 0, + "content": "{newrun, khsohn}@yonsei.ac.kr" + }, + { + "type": "text", + "bbox": [ + 0.573, + 0.216, + 0.751, + 0.23 + ], + "angle": 0, + "content": "lee.j@navercorp.com" + }, + { + "type": "title", + "bbox": [ + 0.242, + 0.263, + 0.321, + 0.278 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.293, + 0.485, + 0.593 + ], + "angle": 0, + "content": "In this paper, we efficiently transfer the surpassing representation power of the vision foundation models, such as ViT and Swin, for video understanding with only a few trainable parameters. Previous adaptation methods have simultaneously considered spatial and temporal modeling with a unified learnable module but still suffered from fully leveraging the representative capabilities of image transformers. We argue that the popular dual-path (two-stream) architecture in video models can mitigate this problem. We propose a novel DUALPATH adaptation separated into spatial and temporal adaptation paths, where a lightweight bottleneck adapter is employed in each transformer block. Especially for temporal dynamic modeling, we incorporate consecutive frames into a grid-like frameset to precisely imitate vision transformers' capability that extrapolates relationships between tokens. In addition, we extensively investigate the multiple baselines from a unified perspective in video understanding and compare them with DUALPATH. Experimental results on four action recognition benchmarks prove that pretrained image transformers with DUALPATH can be effectively generalized beyond the data domain." + }, + { + "type": "title", + "bbox": [ + 0.08, + 0.607, + 0.215, + 0.621 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.624, + 0.483, + 0.724 + ], + "angle": 0, + "content": "Recognizing when, where, and what happened is a fundamental capability in the human cognition system to understand our natural world. The research for video understanding inspires such capability for machine intelligence to comprehend scenes over time flow. Over the last decade, the development of deep neural networks [10,33,66,73] has contributed towards advances in video understanding." + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.724, + 0.483, + 0.782 + ], + "angle": 0, + "content": "Vision Transformer (ViT) [17] has recently emerged, making an upheaval in the research field of computer vision. ViT and its variants [16, 46, 72, 78] have demonstrated remarkable generalizability and transferability of their repre" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.261, + 0.916, + 0.451 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.452, + 0.918, + 0.505 + ], + "angle": 0, + "content": "Figure 1. Performance comparison on the Kinetics-400 [38] dataset. We depict the action recognition performance (vertical axis, \\(\\%\\) ) with respect to the number of trainable parameters (horizontal axis). The size of circles indicates GFLOPs for inference." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.52, + 0.918, + 0.706 + ], + "angle": 0, + "content": "sentations with scaled-up foundation models [34, 53, 63, 69, 77, 79] and large-scale web-collected image data (e.g. JFT-3B [79], LAION-5B [58]). To capitalize on well-trained visual foundation models, finetuning entire parameters of the pretrained models with task-specific objectives has been the most popular transfer technique. However, it requires high-quality training data and plenty of computational resources to update the whole parameters for each downstream task, making overwhelming efforts for training. While partial finetuning [28], which trains additional multilayer perceptron (MLP) layers to the top of the model, has also been widely used for affordable training costs, unsatisfactory performance has been pointed out as a problem." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.706, + 0.919, + 0.849 + ], + "angle": 0, + "content": "Most recently, parameter-efficient transfer learning (PETL) methods [25, 26, 31, 32, 41, 61] have been proposed as an alternative to finetuning in the natural language processing area to adapt the large-scale language model, such as GPT series [8, 54, 55] and T5 [56], for each task. They have successfully attained comparable or even surpassing performance to full-tuning parameters by learning a small number of extra trainable parameters only while keeping the original parameters of the pretrained model frozen. Thanks to their effectiveness and simplicity, they have been ex" + }, + { + "type": "page_footnote", + "bbox": [ + 0.08, + 0.79, + 0.35, + 0.802 + ], + "angle": 0, + "content": "* Equal contributions. † Corresponding author." + }, + { + "type": "page_footnote", + "bbox": [ + 0.08, + 0.802, + 0.475, + 0.813 + ], + "angle": 0, + "content": "Official code: https://github.com/park-jungin/DualPath" + }, + { + "type": "page_footnote", + "bbox": [ + 0.08, + 0.813, + 0.482, + 0.847 + ], + "angle": 0, + "content": "This research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF2021R1A2C2006703)." + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.79, + 0.482, + 0.847 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.878, + 0.501, + 0.889 + ], + "angle": 0, + "content": "2203" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.081, + 0.086, + 0.482, + 0.269 + ], + "angle": 0, + "content": "tended to vision models by applying prompt-based methods [3, 35] and adapter-based methods [11, 49, 64]. They have efficiently adapted pretrained models to downstream tasks with significantly reduced tuning parameters, but most of these works mainly focus on transferring image models to image tasks [3, 11, 35, 49] and vision-language models to vision-language tasks [64]. Inspired by the advances of the prior arts, we raise two conceivable questions: (1) Is it possible to transfer the parameters of the image foundation model to another video domain? (2) Is it also possible the transferred model performs comparably to the carefully designed video models that take the spatiotemporal nature of the video into account?" + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.275, + 0.482, + 0.487 + ], + "angle": 0, + "content": "While image models have demonstrated strong spatial context modeling capabilities [34, 53, 63, 79], video transformer models [1, 47, 57, 76] require a more complex architecture (e.g. 539 vs 48912 GFLOPs [57]) with a large number of parameters (e.g. 84M vs 876M parameters [76]) than ViT for temporal context reasoning. Therefore, the challenge in transferring image models for video understanding is to encode the temporal context of videos while leveraging the discriminative spatial context of the pretrained image models. A naive solution is to finetune image models on a video dataset by directly applying previous prompt/adapter-based approaches [3, 11, 35, 49]. However, these approaches inevitably ignore the temporal context in videos because they bridge only the spatial contexts between image and video data." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.493, + 0.482, + 0.846 + ], + "angle": 0, + "content": "In this paper, we propose a novel adapter-based dualpath parameter efficient tuning method for video understanding, namely DUALPATH, which consists of two distinct paths (spatial path and temporal path). For both paths, we freeze the pretrained image model and train only additional bottleneck adapters for tuning. The spatial path is designed to encode the spatial contexts that can be inferred from the appearance of individual frames with the minimum tuning of the pretrained image model. To reduce the computation burden, we sparsely use the frames with a low frame rate in the spatial path. The temporal path corresponds to the temporal context that should be encoded by grasping the dynamic relationship over several frames sampled with a high frame rate. Especially for two reasons, we construct a grid-like frameset that consists of consecutive low-resolution frames as an input of the temporal path: (i) preventing computational efficiency loss caused by calculating multiple frames simultaneously; (ii) precisely imitating the ViT's ability for extrapolating global dependencies between input tokens. To compare our DUALPATH with existing methods broadly, we implement several baselines with a unified perspective on recent domain-specific PETL approaches [11, 35, 49]. Extensive experiments on several action recognition benchmarks [23, 38, 39, 42] demonstrate the effectiveness and" + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.086, + 0.916, + 0.157 + ], + "angle": 0, + "content": "high efficiency of our DUALPATH, achieving comparable and even better performance than the baselines and prior video models [1, 7, 18, 22, 40, 43, 47, 57, 68, 76]. We achieve these results with extremely low computational costs for both training and inference, as demonstrated in Fig. 1." + }, + { + "type": "title", + "bbox": [ + 0.517, + 0.173, + 0.658, + 0.187 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.192, + 0.916, + 0.376 + ], + "angle": 0, + "content": "Pretraining vision models. To address the burdens of collecting large-scale labeled datasets for supervised learning [15, 63, 79], self-supervised learning methods [12, 13, 24,27,28,74] have been introduced to learn general-purpose visual representations from unlabeled data. Similarly, self-supervised learning methods for videos have also been proposed with large-scale unlabeled video/video-language data [20,51,52,62,65,68,75]. However, collecting even unlabeled video-language pairs is still quite costly compared to image-language pairs. In addition, pretraining video models require more computational power than images. We thus take advantage of the powerful pretrained image-based models for efficient video understanding." + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.378, + 0.916, + 0.576 + ], + "angle": 0, + "content": "Video action recognition. Action recognition is one of the most fundamental research topics for video understanding. Early works have been built upon convolution neural networks (CNNs) [10, 21, 44, 66, 73] to effectively infer the spatiotemporal context for action recognition. Since Vision Transformer (ViT) [17] has become a new paradigm in computer vision, transformers for video understanding have been actively studied by extending pretrained image models. The pretrained image transformers have been used to initialize the part of the video transformers [1, 7, 76, 80] or inflated to the video transformers [47]. While transformers have demonstrated superior performance on video action recognition, they require full finetuning on video datasets, making the training inefficient." + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.578, + 0.916, + 0.846 + ], + "angle": 0, + "content": "Parameter-efficient transfer learning (PETL). To address the memory and parameter inefficiency of full/partial-finetuning, PETL has first introduced in natural language processing (NLP) [6,25,26,31,32,41,61]. The main objective of PETL is to attain comparable or surpassing performance on downstream tasks by finetuning with only a small number of trainable parameters. Although PETL approaches [3, 11, 11, 35, 36, 49, 64] have recently been studied in computer vision, they are 'blind' to other modalities such that image models are used for image tasks, and so are the other modalities. In contrast, we share the same objective as recent works for image-to-video transfer learning [37, 45, 48, 50], demonstrating the pretrained image models can be good video learners. However, they have several limitations in terms of parameter and computational efficiency. For example, [45] learned an extra decoder that contains 3D convolution layers and cross-frame attention, and [50] inserted additional depth-wise 3D convolution layers between the down-/up-projection layers of the adapter to" + }, + { + "type": "page_number", + "bbox": [ + 0.47, + 0.879, + 0.501, + 0.889 + ], + "angle": 0, + "content": "2204" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.079, + 0.086, + 0.482, + 0.173 + ], + "angle": 0, + "content": "perform temporal reasoning, inducing computational inefficiency. The most recent works [37,48] require an additional text encoder branch as a classifier. Moreover, they have computational efficiency proportional to the temporal resolution. Our DUALPATH accomplishes more efficient spatiotemporal modeling while achieving higher performance." + }, + { + "type": "title", + "bbox": [ + 0.08, + 0.184, + 0.345, + 0.2 + ], + "angle": 0, + "content": "3. Preliminaries and Baselines" + }, + { + "type": "title", + "bbox": [ + 0.08, + 0.204, + 0.35, + 0.217 + ], + "angle": 0, + "content": "3.1. Vision transformers for video" + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.22, + 0.485, + 0.29 + ], + "angle": 0, + "content": "We briefly describe how to apply vision transformers for video understanding below. Following [67], given a set of \\( T \\) frames in a video, we split each frame into \\( N \\) patches of size \\( (P \\times P) \\) and tokenize them using a linear projection, such that" + }, + { + "type": "equation", + "bbox": [ + 0.136, + 0.301, + 0.482, + 0.319 + ], + "angle": 0, + "content": "\\[\n\\mathbf {X} _ {t} = \\left[ \\mathbf {x} _ {t} \\left\\{\\left[ \\mathrm {C L S} \\right] \\right\\}, \\mathbf {x} _ {t} ^ {1}, \\mathbf {x} _ {t} ^ {2}, \\dots , \\mathbf {x} _ {t} ^ {N} \\right] + \\mathbf {p}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.328, + 0.484, + 0.414 + ], + "angle": 0, + "content": "where \\(\\mathbf{X}_t\\) is a set of tokens for the \\(t\\)-th frame, and \\(\\mathbf{x}_t\\{\\mathrm{CLS}\\}\\) and \\(\\mathbf{p}\\) denote a learnable class token and a learned positional embedding respectively. We feed \\((N + 1)\\) tokens of each frame to a sequence of \\(L\\) transformer blocks, and the output of the \\(l\\)-th block \\(\\mathbf{h}_{l,t}\\) can be derived by the following equations:" + }, + { + "type": "equation", + "bbox": [ + 0.161, + 0.424, + 0.482, + 0.447 + ], + "angle": 0, + "content": "\\[\n\\mathbf {z} _ {l, t} = \\mathbf {h} _ {l - 1, t} + \\mathrm {M H A} (\\mathrm {L N} (\\mathbf {h} _ {l - 1, t})), \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.18, + 0.443, + 0.381, + 0.458 + ], + "angle": 0, + "content": "\\[\n\\mathbf {h} _ {l, t} = \\mathbf {z} _ {l, t} + \\operatorname {M L P} (\\ln (\\mathbf {z} _ {l, t})),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.467, + 0.483, + 0.538 + ], + "angle": 0, + "content": "where LN, MHA, and MLP denote a layer normalization [2], multi-head attention [67], and a multilayer perceptron operation, respectively. We apply layer normalization to the learned \\(T\\) class tokens from the final transformer block and treat them as a set of frame representations." + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.539, + 0.483, + 0.653 + ], + "angle": 0, + "content": "To take minimal temporal modeling into account the following baselines [11, 35, 49], we employ a temporal transformer block followed by a full-connected (FC) layer as a classifier for video action recognition, similar to [37]. We add learnable temporal positional embeddings \\(\\mathbf{p}_{\\mathrm{temp}}\\) to the frame representations (i.e., \\(\\mathbf{x}_t\\{\\mathrm{cl}\\mathbf{s}\\} \\gets \\mathbf{x}_t\\{\\mathrm{cl}\\mathbf{s}\\} + \\mathbf{p}_{\\mathrm{temp}}\\)) and feed them into the transformer classifier. For the ST-adapter [50], we use a single FC layer as a classifier." + }, + { + "type": "title", + "bbox": [ + 0.08, + 0.661, + 0.192, + 0.674 + ], + "angle": 0, + "content": "3.2. Baselines" + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.677, + 0.483, + 0.849 + ], + "angle": 0, + "content": "The objective of our work is to transfer the superiority of vision transformers pretrained on large-scale image datasets to the video domain through efficient finetuning with a small number of learnable parameters, while freezing the pretrained parameters. To compare with other methods, we generalize four recent PETL methods to the video domain only with the least possible transformation; (1) VPT [35] (2) AdaptFormer [11] (3) Pro-tuning [49] (4) ST-adapter [50]. The most of works have been originally proposed to adapt pretrained image models to downstream image tasks [11, 35, 49] and video models to video tasks [11], by learning visual prompt tokens [35], adapter" + }, + { + "type": "image", + "bbox": [ + 0.539, + 0.085, + 0.712, + 0.17 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.589, + 0.171, + 0.662, + 0.183 + ], + "angle": 0, + "content": "(a) VPT [35]" + }, + { + "type": "image", + "bbox": [ + 0.721, + 0.083, + 0.896, + 0.169 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.741, + 0.171, + 0.875, + 0.183 + ], + "angle": 0, + "content": "(b) Parallel Adapter [11]" + }, + { + "type": "image", + "bbox": [ + 0.539, + 0.184, + 0.633, + 0.296 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.523, + 0.297, + 0.648, + 0.31 + ], + "angle": 0, + "content": "(c) Serial Adapter [11]" + }, + { + "type": "image", + "bbox": [ + 0.665, + 0.184, + 0.764, + 0.296 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.656, + 0.297, + 0.778, + 0.31 + ], + "angle": 0, + "content": "(d) Prompt Block [49]" + }, + { + "type": "image", + "bbox": [ + 0.799, + 0.189, + 0.896, + 0.295 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.794, + 0.297, + 0.902, + 0.31 + ], + "angle": 0, + "content": "(e) ST-Adapter [50]" + }, + { + "type": "image_caption", + "bbox": [ + 0.514, + 0.311, + 0.918, + 0.352 + ], + "angle": 0, + "content": "Figure 2. Baselines for image-to-video transfer learning. (a) Visual Prompt Tuning [35]; (b) Parallel adapter and (c) serial adapter [11]; (d) Pro-Tuning [49]; and (e) ST-Adapter [50]." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.369, + 0.918, + 0.468 + ], + "angle": 0, + "content": "blocks [11] and prompt prediction blocks [49]. Only the ST-adapter [50] has proposed image-to-video transfer learning. In this section, we describe baselines for image-to-video transfer learning in detail. For brevity, we leave out the subscripts in Eq. 2 and arouse them as needed. In addition, we represent the learnable and frozen parameters in red and blue colors, respectively." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.469, + 0.918, + 0.526 + ], + "angle": 0, + "content": "Visual prompt tuning (VPT) [35] prepends \\( K \\) trainable prompt tokens to the input space of every transformer block1 while keeping pretrained parameters frozen. The input tokens for each transformer block can be written as:" + }, + { + "type": "equation", + "bbox": [ + 0.673, + 0.534, + 0.918, + 0.553 + ], + "angle": 0, + "content": "\\[\n\\tilde {\\mathbf {h}} = [ \\mathbf {e}; \\mathbf {h} ], \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.561, + 0.916, + 0.59 + ], + "angle": 0, + "content": "where \\(\\mathbf{e} \\in \\mathbb{R}^{K \\times d}\\) is a set of trainable visual prompt tokens and \\(d\\) is a channel dimension of the original token." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.59, + 0.918, + 0.675 + ], + "angle": 0, + "content": "AdaptFormer [11] learns a trainable bottleneck module [26, 31]. The intermediate feature \\(\\mathbf{z}\\) in Eq. 2 of each transformer block is fed into the AdapterMLP that consists of the original MLP layers and a bottleneck structure (parallel adapter in Fig. 2b). The output of the AdaptFormer block can be formulated by:" + }, + { + "type": "equation", + "bbox": [ + 0.602, + 0.684, + 0.917, + 0.709 + ], + "angle": 0, + "content": "\\[\n\\tilde {\\mathbf {z}} = \\sigma (\\underset {\\sim} {\\mathrm {L N}} (\\mathbf {z}) \\cdot \\mathbf {W} _ {\\text {d o w n}}) \\cdot \\mathbf {W} _ {\\text {u p}}, \\tag {4}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.604, + 0.705, + 0.82, + 0.721 + ], + "angle": 0, + "content": "\\[\n\\mathbf {h} = \\mathbf {z} + \\operatorname {M L P} (\\operatorname {L N} (\\mathbf {z})) + s \\cdot \\tilde {\\mathbf {z}},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.732, + 0.918, + 0.773 + ], + "angle": 0, + "content": "where \\(\\mathbf{W}_{\\mathrm{down}}\\), \\(\\mathbf{W}_{\\mathrm{up}}\\) are trainable down- and up-projection matrices, \\(\\sigma(\\cdot)\\) is an activation function, and \\(s\\) is a scaling factor." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.776, + 0.918, + 0.804 + ], + "angle": 0, + "content": "Pro-tuning [49] predicts task-specific vision prompts \\(\\mathbf{v}\\) from the output of each transformer block using consecu" + }, + { + "type": "page_footnote", + "bbox": [ + 0.513, + 0.812, + 0.918, + 0.847 + ], + "angle": 0, + "content": "1While the original work also presented a shallow version (VPT-Shallow) that inserts prompt tokens to the first layer, we explore a deep version (VPT-Deep) only." + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.879, + 0.501, + 0.889 + ], + "angle": 0, + "content": "2205" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.085, + 0.677, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.685, + 0.09, + 0.917, + 0.292 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.078, + 0.294, + 0.919, + 0.334 + ], + "angle": 0, + "content": "Figure 3. Overall architecture of DUALPATH. The pretrained image transformer takes a grid-like frameset and \\( T_{s} \\) frames as inputs. We learn the temporal and spatial contexts separately through two distinct paths. During training, we only update newly introduced adapters and the classifier while freezing the pretrained layers." + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.351, + 0.482, + 0.395 + ], + "angle": 0, + "content": "tive 2D convolution layers. The output of each block is reshaped as \\(\\mathbb{R}^{P\\times P\\times C}\\) to apply 2D convolutions and the final representation is derived by adding \\(\\mathbf{v}\\) and \\(\\mathbf{h}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.119, + 0.401, + 0.482, + 0.426 + ], + "angle": 0, + "content": "\\[\n\\mathbf {v} = \\operatorname {R e s h a p e} \\left(\\sigma (\\underset {\\sim} {\\operatorname {C o n v 2 d}} (\\operatorname {R e s h a p e} (\\mathbf {h})))\\right), \\tag {5}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.237, + 0.422, + 0.32, + 0.436 + ], + "angle": 0, + "content": "\\[\n\\tilde {\\mathbf {h}} = \\mathbf {h} + \\mathbf {v},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.446, + 0.483, + 0.56 + ], + "angle": 0, + "content": "where Conv2D consists of \\(1 \\times 1\\) convolution layer followed by \\(5 \\times 5\\) depth-wise convolution [14] and \\(1 \\times 1\\) convolution. ST-adapter [50] inserts a depth-wise 3D convolution layer between the down-projection layer and the activation function of the adapter. Different from the conventional adapters (e.g. AdaptFormer [11]), the ST-adapter takes tokens for all frames to enable the model to capture temporality in videos. The output of the ST-adapter can be represented as:" + }, + { + "type": "equation", + "bbox": [ + 0.206, + 0.567, + 0.308, + 0.584 + ], + "angle": 0, + "content": "\\[\n\\bar {\\mathbf {z}} _ {t} = \\overline {{\\mathrm {L N}}} (\\mathbf {z} _ {t}),\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.081, + 0.585, + 0.482, + 0.633 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\hat {\\mathbf {z}} = \\sigma (\\text {D - C o n v 3 d} ([ \\tilde {\\mathbf {z}} _ {1} \\cdot \\mathbf {W} _ {\\text {d o w n}}, \\dots , \\tilde {\\mathbf {z}} _ {T} \\cdot \\mathbf {W} _ {\\text {d o w n}} ])) \\cdot \\mathbf {W} _ {\\text {u p}}, \\\\ \\mathbf {h} _ {t} = \\mathbf {z} _ {t} + \\underline {{\\mathrm {M L P}}} (\\tilde {\\mathbf {z}} _ {t}) + s \\cdot \\hat {\\mathbf {z}} _ {t}, \\tag {6} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.634, + 0.482, + 0.676 + ], + "angle": 0, + "content": "where D-Conv3d denotes the depth-wise 3D convolution layer. Note that the same down-projection matrix \\(\\mathbf{W}_{\\mathrm{down}}\\) is applied to all tokens regardless of the frame index \\(t\\)." + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.676, + 0.483, + 0.777 + ], + "angle": 0, + "content": "We emphasize that most of the baselines [11,35,49] have not concerned with temporal modeling. Even though ST-Adapter [50] has employed depth-wise 3D convolution layers between linear projections, it results in high computational cost. To entirely leverage a simple and efficient architecture of the adapter [11], we incorporate the dual-path design into the pretrained image transformers." + }, + { + "type": "title", + "bbox": [ + 0.08, + 0.787, + 0.173, + 0.801 + ], + "angle": 0, + "content": "4. Method" + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.805, + 0.483, + 0.848 + ], + "angle": 0, + "content": "The dual-path design (also called two-stream) is well-known architecture in CNN-based models for video recognition [10, 21, 60]. They have commonly used an optical" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.351, + 0.918, + 0.508 + ], + "angle": 0, + "content": "flow [10, 60] or multiple frames with a high temporal resolution [21] to capture rapidly changing motion. Despite the effectiveness of dual-path architecture, it has yet to be explored with the transformer due to high computational costs. In this work, we propose a novel PETL method, called DUALPATH, comprised of spatial and temporal path adaptation. To the best of our knowledge, our DUALPATH is the first attempt to explicitly build the two-stream architecture upon the transformer while maintaining the computational cost similar to the single-stream architecture. The overall framework is depicted in Fig. 3." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.512, + 0.697, + 0.527 + ], + "angle": 0, + "content": "4.1. Spatial adaptation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.529, + 0.918, + 0.685 + ], + "angle": 0, + "content": "Since the image foundation models have been trained on large amounts of web datasets, we can intuitively speculate that they might be powerful to encode the spatial context even in videos. In order to make the outstanding ability of spatial modeling to be more suitable for video understanding with a slight parameter tuning, we adopt two parallel adapters for MHA and MLP in each transformer block. The parallel adapters allow the model to learn the spatial context for action recognition from the appearance of target video data while maintaining the original contexts for object recognition." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.686, + 0.918, + 0.777 + ], + "angle": 0, + "content": "Specifically, we sample \\( T_{S} \\) frames from a video and tokenize each frame. Similar to Eq. 1, the set of spatial tokens \\( \\mathbf{X}_t^{\\mathrm{SP}} \\) includes the learnable positional encodings \\( \\mathbf{p}^{\\mathrm{SP}} \\) and the spatial class token \\( \\mathbf{x}_t^{\\mathrm{SP}}\\{[\\mathrm{CLS}]\\} \\). The spatial adaptation in the \\( l \\)-th transformer block can be formulated by the following equations:" + }, + { + "type": "equation", + "bbox": [ + 0.527, + 0.785, + 0.916, + 0.832 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathbf {z} _ {l} ^ {\\mathrm {S P}} = \\mathbf {h} _ {l - 1} ^ {\\mathrm {S P}} + \\mathrm {M H A} (\\mathrm {L N} (\\mathbf {h} _ {l - 1} ^ {\\mathrm {S P}})) + \\text {A d a p t e r} (\\mathrm {L N} (\\mathbf {h} _ {l - 1} ^ {\\mathrm {S P}})), \\\\ \\mathbf {h} _ {l} ^ {\\mathrm {S P}} = \\mathbf {z} _ {l} ^ {\\mathrm {S P}} + \\underline {{\\operatorname {M L P}}} (\\underline {{\\operatorname {L N}}} (\\mathbf {z} _ {l} ^ {\\mathrm {S P}})) + \\underline {{\\operatorname {A d p a t e r}}} (\\underline {{\\operatorname {L N}}} (\\mathbf {z} _ {l} ^ {\\mathrm {S P}})), \\tag {7} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.832, + 0.917, + 0.85 + ], + "angle": 0, + "content": "where \\(\\mathbf{h}_0^{\\mathrm{SP}} = [\\mathbf{x}_t^{\\mathrm{SP}}\\{\\mathrm{[CLS]}\\} ,\\mathbf{X}_t^{\\mathrm{SP}}] + \\mathbf{p}^{\\mathrm{SP}}\\) .We average" + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.878, + 0.502, + 0.889 + ], + "angle": 0, + "content": "2206" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.079, + 0.086, + 0.487, + 0.13 + ], + "angle": 0, + "content": "the set of the spatial [CLS] tokens from the final transformer block to obtain a global spatial representation \\(\\mathbf{y}^{\\mathrm{SP}}\\), such that," + }, + { + "type": "equation", + "bbox": [ + 0.179, + 0.137, + 0.483, + 0.175 + ], + "angle": 0, + "content": "\\[\n\\mathbf {y} ^ {\\mathrm {S P}} = \\frac {1}{T _ {S}} \\sum_ {t = 1} ^ {T _ {S}} \\mathbf {x} _ {t} ^ {\\mathrm {S P}} \\left\\{\\left[ \\mathrm {C L S} \\right] \\right\\}. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.184, + 0.485, + 0.256 + ], + "angle": 0, + "content": "Recent methods have discussed that a high frame rate only increases the computation volume and is unnecessary to understand the semantics of appearance [9, 21]. We thus sparsely sample \\( T_{S} \\) frames with a low frame rate (e.g. 8 frames per clip)." + }, + { + "type": "title", + "bbox": [ + 0.079, + 0.263, + 0.285, + 0.278 + ], + "angle": 0, + "content": "4.2. Temporal adaptation" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.279, + 0.485, + 0.492 + ], + "angle": 0, + "content": "While spatial adaptation enables the models to take the spatial contexts in video data, the image models are still incapable of modeling the temporal dynamics. The key component that allows video transformers to model the solid temporal context is to learn relationships between local patches across frames in the video [1, 7]. To make image models capable of effectively establishing this component, we suggest a novel grid-like frameset transform technique that aggregates multiple frames into a unified grid-like frameset. Our grid-like frameset design is inspired by recent visual prompting research [4, 5]. It is simple yet surprisingly effective in imitating temporal modeling as spatial modeling and certainly reduces the computation. In each transformer block, we adopt two additional serial adapters for MHA and MLP, respectively." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.492, + 0.484, + 0.751 + ], + "angle": 0, + "content": "More concretely, we sample \\( T \\) frames from a video and scale them with factors of \\( w \\) and \\( h \\), such that the scaled frame size is \\( [W / w \\times H / h \\times 3] \\). We stack \\( w \\times h \\) scaled frames according to temporal ordering and reshape a stacked frame to construct a set of frames in a grid form of the same size as the original frame (i.e., \\( [W \\times H \\times 3] \\)). Note that the total number of grid-like framesets is \\( T_{G} = T / wh \\). The set of temporal tokens \\( \\mathbf{X}_{g}^{\\mathrm{TP}} \\) for the \\( g \\)-th frameset is obtained in the same way in Eq. 1 and combined with the learnable temporal class token \\( \\mathbf{x}_{g}^{\\mathrm{TP}}\\left\\{\\left[\\mathrm{CLS}\\right]\\right\\} \\). Unlike the spatial adaptation, we use fixed 3D positional encodings [70], \\( \\mathbf{p}^{\\mathrm{TP}} \\), to the tokens to take the absolute temporal order and spatial positions of patches into account. The input transformation allows transformers to observe multiple frames at the same level. In experiments, we mainly construct a grid-like frameset from 16 original frames (i.e., scaling factors \\( w = h = 4 \\)) to take the computational efficiency and promising performance." + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.751, + 0.485, + 0.807 + ], + "angle": 0, + "content": "Whereas the parallel adapter is used in the spatial path, we sequentially append adapters to the top of MHA and MLP layers in each transformer block. Formally, temporal adaptation in the \\(l\\)-th block can be described as:" + }, + { + "type": "equation", + "bbox": [ + 0.12, + 0.813, + 0.483, + 0.851 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathbf {z} _ {l} ^ {\\mathrm {T P}} = \\mathbf {h} _ {l - 1} ^ {\\mathrm {T P}} + \\text {A d a p t e r} (\\underset {\\leftarrow} {\\mathrm {M H A}} (\\underset {\\leftarrow} {\\mathrm {L N}} (\\mathbf {h} _ {l - 1} ^ {\\mathrm {T P}}))), \\tag {9} \\\\ \\mathbf {h} _ {l} ^ {\\mathrm {T P}} = \\mathbf {z} _ {l} ^ {\\mathrm {T P}} + \\text {A d p a t e r} (\\operatorname {M L P} (\\operatorname {L N} (\\mathbf {z} _ {l} ^ {\\mathrm {T P}}))), \\\\ \\end{array}\n\\]" + }, + { + "type": "image", + "bbox": [ + 0.527, + 0.084, + 0.712, + 0.214 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.555, + 0.216, + 0.684, + 0.227 + ], + "angle": 0, + "content": "(a) DUALPATH w/o TA" + }, + { + "type": "image", + "bbox": [ + 0.722, + 0.083, + 0.907, + 0.214 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.753, + 0.215, + 0.875, + 0.227 + ], + "angle": 0, + "content": "(b) DUALPATH w/ TA" + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.231, + 0.918, + 0.271 + ], + "angle": 0, + "content": "Figure 4. Visualization of attention maps (a) without temporal adaptation (TA) and (b) with temporal adaptation for the action 'Spinning [something] that quickly stops spinning' in SSv2 [23]." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.288, + 0.918, + 0.351 + ], + "angle": 0, + "content": "where \\(\\mathbf{h}_0^{\\mathrm{TP}} = [\\mathbf{x}_g^{\\mathrm{TP}}\\{\\mathrm{[CLS]}\\} ,\\mathbf{X}_g^{\\mathrm{TP}}] + \\mathbf{p}^{\\mathrm{TP}}\\) . Similar to spatial adaptation, a global temporal representation \\(\\mathbf{y}^{\\mathrm{TP}}\\) can be derived by averaging the set of the temporal [CLS] tokens from the final transformer block, i.e.," + }, + { + "type": "equation", + "bbox": [ + 0.612, + 0.362, + 0.918, + 0.402 + ], + "angle": 0, + "content": "\\[\n\\mathbf {y} ^ {\\mathrm {T P}} = \\frac {1}{T _ {G}} \\sum_ {g = 1} ^ {T _ {G}} \\mathbf {x} _ {g} ^ {\\mathrm {T P}} \\{[ \\mathrm {C L S} ] \\}. \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.415, + 0.918, + 0.457 + ], + "angle": 0, + "content": "For the final prediction, we concatenate the global spatial and temporal representations and feed them into the classifier with GeLU activation [29] between two FC layers." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.469, + 0.918, + 0.497 + ], + "angle": 0, + "content": "4.3. Does a grid-like frameset really help to encode temporal context?" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.5, + 0.919, + 0.742 + ], + "angle": 0, + "content": "This work presents a new standpoint to perform video action recognition with the pretrained image transformer by transforming multiple frames into a unified grid-like frame-set. However, it is still questionable whether the temporal path of DUALPATH can really capture the temporal context of videos. In this section, we provide some qualitative examples of the attention map. To validate the ability of precise temporal modeling, we sample videos from the SSv2 [23] dataset. Following [50], we depict the attention map of \\(\\mathbf{x}_g^{\\mathrm{TP}}\\{[\\mathrm{CLS}]\\}\\) from the final transformer block of the temporal path. As shown in Fig. 4, the model with the temporal adaptation (TA) of DUALPATH tends to concentrate on action-related regions, contrary to the model without TA that focuses on the irrelevant background. This result suggests that the temporal adaptation of DUALPATH strengthens the temporal modeling ability of the image model. More examples are shown in Fig. A1 of Appendix." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.757, + 0.642, + 0.773 + ], + "angle": 0, + "content": "5. Experiment" + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.777, + 0.686, + 0.792 + ], + "angle": 0, + "content": "5.1. Evaluation setup" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.794, + 0.918, + 0.852 + ], + "angle": 0, + "content": "Datasets. We evaluate the proposed method on four standard action recognition datasets, including the Kinetics-400 (K400) [38], HMDB51 [39], Something-something-v2 (SSv2) [23], and Diving-48 [42]." + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.878, + 0.502, + 0.889 + ], + "angle": 0, + "content": "2207" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.145, + 0.083, + 0.855, + 0.352 + ], + "angle": 0, + "content": "
Method & Arch.PretrainModel # ParamsTrainable # ParamsGFLOPsR@1R@5Views
Full-tuning
SlowFast+NL [21]-60M60M702079.893.916×3×10
MViT-B [18]-37M37M409581.295.164×3×3
UniFormer-B [40]IN-1K50M50M310883.095.432×4×3
TimeSformer-L [7]IN-21K121M121M714080.794.764×1×3
ViViT-L/16×2 FE [1]IN-1K311M311M398080.692.732×1×1
VideoSwin-L [47]IN-21K197M197M724883.195.932×4×3
MViTv2-L [43]IN-21K218M218M4242086.197.032×3×5
MTV-L [76]JFT876M876M1805084.396.332×4×3
TokenLearner-L/10 [57]JFT450M450M4891285.496.364×4×3
ActionCLIP [68]CLIP142M142M1689083.897.132×10×3
X-CLIP-L/14 [48]CLIP420M420M789087.197.68×4×3
Parameter Efficient Tuning
EVL [45] w/ ViT-L/14CLIP368M59M808887.3-32×3×1
ST-Adapter [50] w/ ViT-B/16CLIP93M7M182182.796.232×3×1
DUALPATH w/ ViT-B/16CLIP96M10M71085.497.132×3×1
DUALPATH w/ ViT-L/14CLIP330M27M186887.797.832×3×1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.08, + 0.357, + 0.916, + 0.37 + ], + "angle": 0, + "content": "Table 1. Performance comparisons for action recognition on the Kinetics-400 [38] dataset. Note that Views = #frames × #clips × #spatial." + }, + { + "type": "text", + "bbox": [ + 0.1, + 0.388, + 0.482, + 0.474 + ], + "angle": 0, + "content": "- Kinetics-400 (K400) contains about 240K training videos and 20K validation videos for 400 human action categories. Each video is trimmed to have a length of 10 seconds. While the K400 dataset provides a wide range of categories, they are known to be highly biased in spatial appearance [59]." + }, + { + "type": "text", + "bbox": [ + 0.1, + 0.48, + 0.482, + 0.536 + ], + "angle": 0, + "content": "- Somthing-something-v2 (SSv2) is a more challenging dataset since they require strong temporal modeling [59]. They contain about 168.9K training videos and 24.7K validation videos for 174 classes." + }, + { + "type": "text", + "bbox": [ + 0.1, + 0.543, + 0.482, + 0.613 + ], + "angle": 0, + "content": "- HMDB51 is a small dataset that provides about 7K videos of 51 action categories. We use all three splits, each split of which consists of 3570 and 1530 videos for training and evaluation, respectively. We report the average accuracy for three splits." + }, + { + "type": "text", + "bbox": [ + 0.1, + 0.62, + 0.482, + 0.706 + ], + "angle": 0, + "content": "- Diving-48 is a fine-grained diving action dataset. We use train-test split v2 that contains about 15K training videos and 2K validation videos of 48 diving actions. Since the action can not be determined by only the static representations (e.g. objects or background), stronger temporal modeling is required for this dataset." + }, + { + "type": "list", + "bbox": [ + 0.1, + 0.388, + 0.482, + 0.706 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.08, + 0.711, + 0.482, + 0.755 + ], + "angle": 0, + "content": "Pretrained image backbone. We employ CLIP pretrained ViT-B/16 and ViT-L/14 as backbones. The results with Swin-B [46] are provided in Tab. A2 of the Appendix." + }, + { + "type": "text", + "bbox": [ + 0.1, + 0.759, + 0.482, + 0.802 + ], + "angle": 0, + "content": "- ViT-B/16 [17] consists of 12 transformer blocks with 86M parameters and takes patches of size \\(16 \\times 16\\) as inputs." + }, + { + "type": "text", + "bbox": [ + 0.1, + 0.808, + 0.482, + 0.851 + ], + "angle": 0, + "content": "- ViT-L/14 [17], a larger model than ViT-B/16, contains 24 transformer blocks with 303M parameters. It takes \\(14 \\times 14\\) patches as inputs." + }, + { + "type": "list", + "bbox": [ + 0.1, + 0.759, + 0.482, + 0.851 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.388, + 0.918, + 0.545 + ], + "angle": 0, + "content": "Implementation details. For the K400, HMDB51, and Diving-48 datasets, we uniformly sample 8 frames (i.e., \\( T_{s} = 8 \\)) with the sampling interval 8 in the spatial path. In the temporal path, we uniformly sample 16, 32, and 48 frames with the sampling intervals 4, 2, and 1 to construct 1, 2, and 3 grid-like framesets (i.e., \\( T_{g} = 1,2,3 \\)), respectively. For the SSv2 dataset, we sample the same number of frames as in other datasets, but with a dynamic sampling interval to cover the whole video. Note that the frames for the spatial path are the subset of the temporal path frames. Please refer to more implementation details in Appendix A." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.558, + 0.813, + 0.573 + ], + "angle": 0, + "content": "5.2. Comparison with state-of-the-art" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.576, + 0.918, + 0.676 + ], + "angle": 0, + "content": "In this section, we compare the proposed method with baselines [11, 35, 49, 50] in Sec. 3 and state-of-the-art video transformers [1, 7, 18, 40, 43, 45, 47, 48, 57, 68, 76] to demonstrate the effectiveness of the proposed method on four video action recognition datasets. Note that the number of frames of the spatial adaptation path of DUALPATH is fixed to 8 for all experiments, i.e., \\( T_{S} = 8 \\)." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.678, + 0.918, + 0.848 + ], + "angle": 0, + "content": "Results on Kinetics-400. We report the results evaluated on K400 [38] in Tab. 1. We first compare the proposed method with state-of-the-art video models that are pretrained on the large-scale image dataset and fully finetuned on K400. In terms of memory and computational efficiency, video models require a huge number of parameters (\\(\\sim\\)450M [57]) and computations (\\(\\sim\\)48912 GFLOPs [57]). On the other hand, we require only 10M trainable parameters which are newly stored, and 710 GFLOPs for inference using 32 frames with ViT-B/16 [17] backbone. Compared to X-CLIP-L/14 [48] which leverages the additional text branch, our DUALPATH achieves state-of-the-art performance with ViT-L/14 back" + }, + { + "type": "page_number", + "bbox": [ + 0.47, + 0.879, + 0.502, + 0.889 + ], + "angle": 0, + "content": "2208" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.123, + 0.084, + 0.875, + 0.456 + ], + "angle": 0, + "content": "
Method & Arch.PretrainModel\n#ParamsTrainable\n#ParamsGFLOPsR@1R@5Views
Full-tuning
Full-tuning ViT-B/16 [17]CLIP86M86M41944.077.08×1×3
Full-tuning ViT-L/14 [17]CLIP303M303M194148.777.58×1×3
TimeSformer-L [7]IN-21K121M121M714062.4-64×1×3
MTV-B [76]IN-21K310M310M479067.690.432×4×3
MViT-B [18]K40037M37M51067.190.832×1×3
MViTv2-B [43]K40051M51M67570.592.740×1×3
ViViT-L/16×2 [1]IN-21K/K400311M311M1189265.489.816×4×3
VideoSwin-B [47]IN-21K/K40089M89M96369.692.732×1×1
Omnivore [22]IN-21K/K400---71.493.532×1×3
MViTv2-B [43]IN-21K/K400213M213M848473.394.132×1×3
UniFormer-B [40]IN-21K/K60050M50M77771.292.832×1×3
Parameter Efficient Tuning
VideoPrompt* [37] w/ ViT-B/16CLIP92M6M53731.060.38×1×3
VPT [35] w/ ViT-B/16CLIP92M6M53736.261.18×1×3
AdaptFormer [11] w/ ViT-B/16CLIP94M8M54451.370.68×1×3
Pro-tuning [49] w/ ViT-B/16CLIP95M9M53850.869.98×1×3
EVL [45] w/ ViT-L/14CLIP484M175M964166.7-32×1×3
ST-Adapter [50] w/ ViT-B/16CLIP97M11M195569.592.632×3×1
DUALPATH w/ ViT-B/16CLIP99M13M64269.692.516×1×3
DUALPATH w/ ViT-B/16CLIP99M13M71670.392.932×1×3
DUALPATH w/ ViT-B/16CLIP99M13M79171.293.248×1×3
DUALPATH w/ ViT-L/14CLIP336M33M171370.292.716×1×3
DUALPATH w/ ViT-L/14CLIP336M33M193271.493.432×1×3
DUALPATH w/ ViT-L/14CLIP336M33M215172.293.748×1×3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.079, + 0.461, + 0.916, + 0.487 + ], + "angle": 0, + "content": "Table 2. Performance comparisons for action recognition on the SSv2 [23] dataset. Note that we reproduce VideoPrompt [37] without the additional text branch for fair comparison (denoting with *)." + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.505, + 0.482, + 0.561 + ], + "angle": 0, + "content": "bone. The comparisons with parameter-efficient tuning methods [45, 50] show that our DUALPATH achieves higher performance while requiring much lower burdens in computations under the same conditions." + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.563, + 0.483, + 0.832 + ], + "angle": 0, + "content": "Results on Something-Something-v2. We present the performance comparisons on SSv2 [23] in Tab. 2. The results show that our DUALPATH with ViT-B/16 achieves comparable or better performance than the prior supervised video models [1,7,18,76], requiring a much smaller number of trainable parameters and GFLOPs. Our DUALPATH with ViT-L/14 shows more competitive performance, outperforming most prior works [22, 40, 43]. The baselines [11, 35, 37, 49], which have relatively weak temporal modeling ability, show significantly poor performance, implying that strong temporal modeling is mandatory for the SSv2 dataset. The comparisons to the CLIP pretrained PET approaches [45, 50] with ViT-B/16 demonstrate the effectiveness and efficiency of DUALPATH, achieving higher performance (70.3 vs 69.5 [50]) with significantly low computations (716 vs 9641 [45] GFLOPs) using 32 frames. Thanks to the extreme computational efficiency, our DUALPATH comprises more competitive performance using 48 frames (\\( T_{G} = 3 \\)) with low computation requirements." + }, + { + "type": "text", + "bbox": [ + 0.08, + 0.833, + 0.482, + 0.847 + ], + "angle": 0, + "content": "Results on HMDB51. In Tab. 3, we compare the re" + }, + { + "type": "table", + "bbox": [ + 0.516, + 0.503, + 0.924, + 0.634 + ], + "angle": 0, + "content": "
Method & Arch.ClassifierParamsHMDB51
Full-tuning w/ ViT-B/16 [17]Lin.86M59.4
Linear w/ ViT-B/16Lin.0.1M61.2
VPT [35] w/ ViT-B/16Trans.7M62.4
AdaptFormer [11] w/ ViT-B/16Trans.8M63.7
Pro-tuning [49] w/ ViT-B/16Trans.9M63.3
VideoPrompt [37] w/ ViT-B/16Trans.6M66.4
ST-Adapter* [50] w/ ViT-B/16Lin.7M65.9
DUALPATH w/ ViT-B/16MLPs.10M75.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.637, + 0.918, + 0.742 + ], + "angle": 0, + "content": "Table 3. Performance comparisons for action recognition on the HMDB51 [39] dataset with the CLIP pretrained ViT-B/16 [53]. We report the type of classifier and the number of learnable parameters for baselines and ours. Lin. and Trans. denote the linear classifier and temporal transformer, respectively. Our DUALPATH uses two MLP layers as the classifier. Note that we reproduce ST-Adapter [50] for fair comparison in terms of the pretrained dataset (denoting with \\(*\\))." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.762, + 0.918, + 0.848 + ], + "angle": 0, + "content": "sults with baselines [11, 35, 37, 49, 50] on HMDB51 [39] that dominantly requires strong spatial modeling for action recognition. Surprisingly, our DUALPATH significantly outperforms baselines by large margins. This result demonstrates DUALPATH fully capitalizes on the exceptional spatial modeling ability of the pretrained image model for ac" + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.878, + 0.502, + 0.889 + ], + "angle": 0, + "content": "2209" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.1, + 0.083, + 0.462, + 0.209 + ], + "angle": 0, + "content": "
Method & Arch.PretrainParamsDiving48
Supervised
TimeSformer-L [7]IN-21K121M81.0
VideoSwin-B [47]IN-21K88M81.9
SIFAR-B-14 [19]IN-21K87M87.3
ORViT [30]IN-21K160M88.0
Parameter Efficient Tuning
DUALPATH w/ ViT-B/16CLIP10M88.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.079, + 0.211, + 0.482, + 0.251 + ], + "angle": 0, + "content": "Table 4. Performance comparisons for action recognition on the Diving-48 [42] dataset. We report the pretrained dataset, the number of learnable parameters (M) for each method, and the accuracy." + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.269, + 0.482, + 0.325 + ], + "angle": 0, + "content": "tion recognition. The comparison with VideoPrompt [37] that uses the additional text branch demonstrates the effectiveness of DUALPATH, improving \\(9.2\\%\\) performance improvement." + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.325, + 0.482, + 0.44 + ], + "angle": 0, + "content": "Results on Diving-48. Tab. 4 shows performance comparisons on Diving-48 [42] that requires fine-grained action recognition. Our DUALPATH consistently outperforms all video models with only 10M trainable parameters. Particularly, we obtain a better performance than ORViT [30] which utilizes the additional tracking model. It indicates the utility of DUALPATH in fine-grained action recognition and the superiority of temporal modeling of DUALPATH." + }, + { + "type": "title", + "bbox": [ + 0.08, + 0.448, + 0.284, + 0.463 + ], + "angle": 0, + "content": "5.3. Components analysis" + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.464, + 0.482, + 0.634 + ], + "angle": 0, + "content": "Impact of dual-path. In the top panel of Tab. 5, we train the model by ablating each path and evaluate the performance on SSv2. Without the temporal path (DUALPATH w/o TA), the performance is significantly degraded despite using a larger number of frames (\\( T_{S} = 16 \\) vs 8). Without the spatial path (DUALPATH w/o SA), we can obtain slightly better performance than the result without the temporal adaptation. Since the SSv2 requires strong temporal modeling, we speculate that two ablation studies show comparison results. However, it still shows a substantial performance gap compared to the full model of DUALPATH, demonstrating the effectiveness of the dual-path design." + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.634, + 0.482, + 0.762 + ], + "angle": 0, + "content": "Frame rates in spatial path. In the middle panel of Tab. 5, we analyze the effect according to the number of frames used in the spatial path. The temporal path identically uses 16 frames to construct a grid-like frameset, and frames used in the spatial path are sampled from such 16 frames. A large number of \\( T_{S} \\) slightly improves performance, however, requires more computational costs. Considering the performance improvement compared to the computation increase, we mainly set \\( T_{S} \\) to 8." + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.762, + 0.482, + 0.848 + ], + "angle": 0, + "content": "Number of frames in grid. We scale down original frames with scaling factors \\( w \\) and \\( h \\) to construct grid-like framesets. These factors thus determine the number of frames the model observes within one grid-like frameset. While a large value of factors increases the temporal resolution, the information of each frame is inevitably reduced. For exam-" + }, + { + "type": "table", + "bbox": [ + 0.527, + 0.083, + 0.905, + 0.285 + ], + "angle": 0, + "content": "
MethodParamsGFLOPsSSv2Views
Effectiveness of Each Path
DUALPATH w/o TA5M101653.716×3×1
DUALPATH w/o SA8M13455.116×3×1
Effectiveness of TS
TS=813M64269.316×3×1
TS=1213M89669.616×3×1
TS=1613M115069.816×3×1
Effectiveness of scaling factors
w=h=2 (TG=16)13M175266.464×3×1
w=h=4 (TG=4)13M86471.864×3×1
w=h=8 (TG=1)13M64261.564×3×1
DUALPATH13M64269.316×3×1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.516, + 0.288, + 0.913, + 0.302 + ], + "angle": 0, + "content": "Table 5. Performance with respect to variants of the components." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.324, + 0.916, + 0.396 + ], + "angle": 0, + "content": "ple, the original frame is scaled down to the size of \\(28 \\times 28\\) with \\(w = h = 8\\). Meanwhile, a small value of factors retains richer information from the original frame, however, makes the temporal resolution small. As shown in the bottom panel of Tab. 5, we attain the best performance with \\(w = h = 4\\)." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.41, + 0.791, + 0.425 + ], + "angle": 0, + "content": "6. Conclusion and Future Work" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.431, + 0.917, + 0.673 + ], + "angle": 0, + "content": "In this paper, we have introduced the novel image-to-video transfer learning approach, DUALPATH. By incorporating a dual-path design into image transformers, DUALPATH adapts image models to the video task (i.e., action recognition) with a small number of trainable parameters. The spatial path adaptation strengthens the inherent spatial context modeling of the pretrained image transformers for video data. The temporal path adaptation transforms multiple frames into a unified grid-like frameset, enabling the image model to capture relationships between frames. We appropriately employ the bottlenecked adapters in each path to adapt the pretrained features to target video data. In addition, we present several baselines transforming recent PETL approaches [11, 35, 49] for image-to-video adaptation. Experimental results demonstrated the superiority of the dualpath design and the grid-like frameset prompting, outperforming several baselines and supervised video models." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.674, + 0.917, + 0.789 + ], + "angle": 0, + "content": "There are many possible directions for future work, encompassing cross-domain transfer learning. While we have explored image-to-video transfer learning, large foundation vision-language models are available. It would also be interesting to expand the superior pretrained 2D knowledge to 3D spatial modeling [71]. We hope our study will foster research and provide a foundation for cross-domain transfer learning." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.791, + 0.917, + 0.848 + ], + "angle": 0, + "content": "Acknowledgement. This research was supported by the Yonsei Signature Research Cluster Program of 2022 (2022-22-0002) and the KIST Institutional Program (Project No.2E32283-23-064)." + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.878, + 0.502, + 0.889 + ], + "angle": 0, + "content": "2210" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.082, + 0.085, + 0.179, + 0.099 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.089, + 0.109, + 0.482, + 0.147 + ], + "angle": 0, + "content": "[1] Anurag Arnab, Mostafa Dehghani, Georg Heigold, Chen Sun, Mario Lučić, and Cordelia Schmid. Vivit: A video vision transformer. In ICCV, 2021. 2, 5, 6, 7" + }, + { + "type": "ref_text", + "bbox": [ + 0.09, + 0.149, + 0.483, + 0.187 + ], + "angle": 0, + "content": "[2] Jimmy Lei Ba, Jamie Ryan Kiros, and Geoffrey E. Hinton. 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In ICCV, 2021. 2" + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.088, + 0.916, + 0.285 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.879, + 0.501, + 0.889 + ], + "angle": 0, + "content": "2213" + } + ] +] \ No newline at end of file diff --git a/2023/Dual-Path Adaptation From Image to Video Transformers/58cf23aa-7524-4b95-9291-20d982a61012_origin.pdf b/2023/Dual-Path Adaptation From Image to Video Transformers/58cf23aa-7524-4b95-9291-20d982a61012_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..fa7704b01074c9b610fc4724563d5a40f54a7e58 --- /dev/null +++ b/2023/Dual-Path Adaptation From Image to Video Transformers/58cf23aa-7524-4b95-9291-20d982a61012_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:af76a5dfdbe562a49d1b7bd4ebcc2a179d64180c9006966a51da20dc592d53e4 +size 2627621 diff --git a/2023/Dual-Path Adaptation From Image to Video Transformers/full.md b/2023/Dual-Path Adaptation From Image to Video Transformers/full.md new file mode 100644 index 0000000000000000000000000000000000000000..b5eac60eec9839a814d436870eceb89d4966ffcc --- /dev/null +++ b/2023/Dual-Path Adaptation From Image to Video Transformers/full.md @@ -0,0 +1,373 @@ +# Dual-path Adaptation from Image to Video Transformers + +Jungin Park1* + +Jiyoung Lee $^{2*}$ + +Kwanghoon Sohn $^{1,3\dagger}$ + +$^{1}$ Yonsei University + +$^{2}$ NAVER AI Lab + +$^{3}$ Korea Institute of Science and Technology (KIST) + +{newrun, khsohn}@yonsei.ac.kr + +lee.j@navercorp.com + +# Abstract + +In this paper, we efficiently transfer the surpassing representation power of the vision foundation models, such as ViT and Swin, for video understanding with only a few trainable parameters. Previous adaptation methods have simultaneously considered spatial and temporal modeling with a unified learnable module but still suffered from fully leveraging the representative capabilities of image transformers. We argue that the popular dual-path (two-stream) architecture in video models can mitigate this problem. We propose a novel DUALPATH adaptation separated into spatial and temporal adaptation paths, where a lightweight bottleneck adapter is employed in each transformer block. Especially for temporal dynamic modeling, we incorporate consecutive frames into a grid-like frameset to precisely imitate vision transformers' capability that extrapolates relationships between tokens. In addition, we extensively investigate the multiple baselines from a unified perspective in video understanding and compare them with DUALPATH. Experimental results on four action recognition benchmarks prove that pretrained image transformers with DUALPATH can be effectively generalized beyond the data domain. + +# 1. Introduction + +Recognizing when, where, and what happened is a fundamental capability in the human cognition system to understand our natural world. The research for video understanding inspires such capability for machine intelligence to comprehend scenes over time flow. Over the last decade, the development of deep neural networks [10,33,66,73] has contributed towards advances in video understanding. + +Vision Transformer (ViT) [17] has recently emerged, making an upheaval in the research field of computer vision. ViT and its variants [16, 46, 72, 78] have demonstrated remarkable generalizability and transferability of their repre + +![](images/cc6811a31128b3756b96466320126e9df1cf714a41b65756cf31c0817a9bc225.jpg) +Figure 1. Performance comparison on the Kinetics-400 [38] dataset. We depict the action recognition performance (vertical axis, $\%$ ) with respect to the number of trainable parameters (horizontal axis). The size of circles indicates GFLOPs for inference. + +sentations with scaled-up foundation models [34, 53, 63, 69, 77, 79] and large-scale web-collected image data (e.g. JFT-3B [79], LAION-5B [58]). To capitalize on well-trained visual foundation models, finetuning entire parameters of the pretrained models with task-specific objectives has been the most popular transfer technique. However, it requires high-quality training data and plenty of computational resources to update the whole parameters for each downstream task, making overwhelming efforts for training. While partial finetuning [28], which trains additional multilayer perceptron (MLP) layers to the top of the model, has also been widely used for affordable training costs, unsatisfactory performance has been pointed out as a problem. + +Most recently, parameter-efficient transfer learning (PETL) methods [25, 26, 31, 32, 41, 61] have been proposed as an alternative to finetuning in the natural language processing area to adapt the large-scale language model, such as GPT series [8, 54, 55] and T5 [56], for each task. They have successfully attained comparable or even surpassing performance to full-tuning parameters by learning a small number of extra trainable parameters only while keeping the original parameters of the pretrained model frozen. Thanks to their effectiveness and simplicity, they have been ex + +tended to vision models by applying prompt-based methods [3, 35] and adapter-based methods [11, 49, 64]. They have efficiently adapted pretrained models to downstream tasks with significantly reduced tuning parameters, but most of these works mainly focus on transferring image models to image tasks [3, 11, 35, 49] and vision-language models to vision-language tasks [64]. Inspired by the advances of the prior arts, we raise two conceivable questions: (1) Is it possible to transfer the parameters of the image foundation model to another video domain? (2) Is it also possible the transferred model performs comparably to the carefully designed video models that take the spatiotemporal nature of the video into account? + +While image models have demonstrated strong spatial context modeling capabilities [34, 53, 63, 79], video transformer models [1, 47, 57, 76] require a more complex architecture (e.g. 539 vs 48912 GFLOPs [57]) with a large number of parameters (e.g. 84M vs 876M parameters [76]) than ViT for temporal context reasoning. Therefore, the challenge in transferring image models for video understanding is to encode the temporal context of videos while leveraging the discriminative spatial context of the pretrained image models. A naive solution is to finetune image models on a video dataset by directly applying previous prompt/adapter-based approaches [3, 11, 35, 49]. However, these approaches inevitably ignore the temporal context in videos because they bridge only the spatial contexts between image and video data. + +In this paper, we propose a novel adapter-based dualpath parameter efficient tuning method for video understanding, namely DUALPATH, which consists of two distinct paths (spatial path and temporal path). For both paths, we freeze the pretrained image model and train only additional bottleneck adapters for tuning. The spatial path is designed to encode the spatial contexts that can be inferred from the appearance of individual frames with the minimum tuning of the pretrained image model. To reduce the computation burden, we sparsely use the frames with a low frame rate in the spatial path. The temporal path corresponds to the temporal context that should be encoded by grasping the dynamic relationship over several frames sampled with a high frame rate. Especially for two reasons, we construct a grid-like frameset that consists of consecutive low-resolution frames as an input of the temporal path: (i) preventing computational efficiency loss caused by calculating multiple frames simultaneously; (ii) precisely imitating the ViT's ability for extrapolating global dependencies between input tokens. To compare our DUALPATH with existing methods broadly, we implement several baselines with a unified perspective on recent domain-specific PETL approaches [11, 35, 49]. Extensive experiments on several action recognition benchmarks [23, 38, 39, 42] demonstrate the effectiveness and + +high efficiency of our DUALPATH, achieving comparable and even better performance than the baselines and prior video models [1, 7, 18, 22, 40, 43, 47, 57, 68, 76]. We achieve these results with extremely low computational costs for both training and inference, as demonstrated in Fig. 1. + +# 2. Related Work + +Pretraining vision models. To address the burdens of collecting large-scale labeled datasets for supervised learning [15, 63, 79], self-supervised learning methods [12, 13, 24,27,28,74] have been introduced to learn general-purpose visual representations from unlabeled data. Similarly, self-supervised learning methods for videos have also been proposed with large-scale unlabeled video/video-language data [20,51,52,62,65,68,75]. However, collecting even unlabeled video-language pairs is still quite costly compared to image-language pairs. In addition, pretraining video models require more computational power than images. We thus take advantage of the powerful pretrained image-based models for efficient video understanding. + +Video action recognition. Action recognition is one of the most fundamental research topics for video understanding. Early works have been built upon convolution neural networks (CNNs) [10, 21, 44, 66, 73] to effectively infer the spatiotemporal context for action recognition. Since Vision Transformer (ViT) [17] has become a new paradigm in computer vision, transformers for video understanding have been actively studied by extending pretrained image models. The pretrained image transformers have been used to initialize the part of the video transformers [1, 7, 76, 80] or inflated to the video transformers [47]. While transformers have demonstrated superior performance on video action recognition, they require full finetuning on video datasets, making the training inefficient. + +Parameter-efficient transfer learning (PETL). To address the memory and parameter inefficiency of full/partial-finetuning, PETL has first introduced in natural language processing (NLP) [6,25,26,31,32,41,61]. The main objective of PETL is to attain comparable or surpassing performance on downstream tasks by finetuning with only a small number of trainable parameters. Although PETL approaches [3, 11, 11, 35, 36, 49, 64] have recently been studied in computer vision, they are 'blind' to other modalities such that image models are used for image tasks, and so are the other modalities. In contrast, we share the same objective as recent works for image-to-video transfer learning [37, 45, 48, 50], demonstrating the pretrained image models can be good video learners. However, they have several limitations in terms of parameter and computational efficiency. For example, [45] learned an extra decoder that contains 3D convolution layers and cross-frame attention, and [50] inserted additional depth-wise 3D convolution layers between the down-/up-projection layers of the adapter to + +perform temporal reasoning, inducing computational inefficiency. The most recent works [37,48] require an additional text encoder branch as a classifier. Moreover, they have computational efficiency proportional to the temporal resolution. Our DUALPATH accomplishes more efficient spatiotemporal modeling while achieving higher performance. + +# 3. Preliminaries and Baselines + +# 3.1. Vision transformers for video + +We briefly describe how to apply vision transformers for video understanding below. Following [67], given a set of $T$ frames in a video, we split each frame into $N$ patches of size $(P \times P)$ and tokenize them using a linear projection, such that + +$$ +\mathbf {X} _ {t} = \left[ \mathbf {x} _ {t} \left\{\left[ \mathrm {C L S} \right] \right\}, \mathbf {x} _ {t} ^ {1}, \mathbf {x} _ {t} ^ {2}, \dots , \mathbf {x} _ {t} ^ {N} \right] + \mathbf {p}, \tag {1} +$$ + +where $\mathbf{X}_t$ is a set of tokens for the $t$ -th frame, and $\mathbf{x}_t\{\mathrm{CLS}\}$ and $\mathbf{p}$ denote a learnable class token and a learned positional embedding respectively. We feed $(N + 1)$ tokens of each frame to a sequence of $L$ transformer blocks, and the output of the $l$ -th block $\mathbf{h}_{l,t}$ can be derived by the following equations: + +$$ +\mathbf {z} _ {l, t} = \mathbf {h} _ {l - 1, t} + \mathrm {M H A} (\mathrm {L N} (\mathbf {h} _ {l - 1, t})), \tag {2} +$$ + +$$ +\mathbf {h} _ {l, t} = \mathbf {z} _ {l, t} + \operatorname {M L P} (\ln (\mathbf {z} _ {l, t})), +$$ + +where LN, MHA, and MLP denote a layer normalization [2], multi-head attention [67], and a multilayer perceptron operation, respectively. We apply layer normalization to the learned $T$ class tokens from the final transformer block and treat them as a set of frame representations. + +To take minimal temporal modeling into account the following baselines [11, 35, 49], we employ a temporal transformer block followed by a full-connected (FC) layer as a classifier for video action recognition, similar to [37]. We add learnable temporal positional embeddings $\mathbf{p}_{\mathrm{temp}}$ to the frame representations (i.e., $\mathbf{x}_t\{\mathrm{cl}\mathbf{s}\} \gets \mathbf{x}_t\{\mathrm{cl}\mathbf{s}\} + \mathbf{p}_{\mathrm{temp}}$ ) and feed them into the transformer classifier. For the ST-adapter [50], we use a single FC layer as a classifier. + +# 3.2. Baselines + +The objective of our work is to transfer the superiority of vision transformers pretrained on large-scale image datasets to the video domain through efficient finetuning with a small number of learnable parameters, while freezing the pretrained parameters. To compare with other methods, we generalize four recent PETL methods to the video domain only with the least possible transformation; (1) VPT [35] (2) AdaptFormer [11] (3) Pro-tuning [49] (4) ST-adapter [50]. The most of works have been originally proposed to adapt pretrained image models to downstream image tasks [11, 35, 49] and video models to video tasks [11], by learning visual prompt tokens [35], adapter + +![](images/0d130e43d9de9b4053b68b241a10d58c585112f48271fa2fdba61c2f7f347e8d.jpg) +(a) VPT [35] + +![](images/2c82839b12d43b96cb61f9a21a18c3a24eb6c6f79b4b7211beb574d6c48deef2.jpg) +(b) Parallel Adapter [11] + +![](images/56e58334dc2d8ad711272a19cde900f16f2eecbceb80c423b39e597ebb695fdb.jpg) +(c) Serial Adapter [11] + +![](images/42bb65e6c745943f00cffb8e5bfe5e81e85600312af0e361ef28df3bca31dbf5.jpg) +(d) Prompt Block [49] + +![](images/9cc0dd574dab336362cc723c490150acfe5ddc409dc703846c4703ea1e3ec888.jpg) +(e) ST-Adapter [50] +Figure 2. Baselines for image-to-video transfer learning. (a) Visual Prompt Tuning [35]; (b) Parallel adapter and (c) serial adapter [11]; (d) Pro-Tuning [49]; and (e) ST-Adapter [50]. + +blocks [11] and prompt prediction blocks [49]. Only the ST-adapter [50] has proposed image-to-video transfer learning. In this section, we describe baselines for image-to-video transfer learning in detail. For brevity, we leave out the subscripts in Eq. 2 and arouse them as needed. In addition, we represent the learnable and frozen parameters in red and blue colors, respectively. + +Visual prompt tuning (VPT) [35] prepends $K$ trainable prompt tokens to the input space of every transformer block1 while keeping pretrained parameters frozen. The input tokens for each transformer block can be written as: + +$$ +\tilde {\mathbf {h}} = [ \mathbf {e}; \mathbf {h} ], \tag {3} +$$ + +where $\mathbf{e} \in \mathbb{R}^{K \times d}$ is a set of trainable visual prompt tokens and $d$ is a channel dimension of the original token. + +AdaptFormer [11] learns a trainable bottleneck module [26, 31]. The intermediate feature $\mathbf{z}$ in Eq. 2 of each transformer block is fed into the AdapterMLP that consists of the original MLP layers and a bottleneck structure (parallel adapter in Fig. 2b). The output of the AdaptFormer block can be formulated by: + +$$ +\tilde {\mathbf {z}} = \sigma (\underset {\sim} {\mathrm {L N}} (\mathbf {z}) \cdot \mathbf {W} _ {\text {d o w n}}) \cdot \mathbf {W} _ {\text {u p}}, \tag {4} +$$ + +$$ +\mathbf {h} = \mathbf {z} + \operatorname {M L P} (\operatorname {L N} (\mathbf {z})) + s \cdot \tilde {\mathbf {z}}, +$$ + +where $\mathbf{W}_{\mathrm{down}}$ , $\mathbf{W}_{\mathrm{up}}$ are trainable down- and up-projection matrices, $\sigma(\cdot)$ is an activation function, and $s$ is a scaling factor. + +Pro-tuning [49] predicts task-specific vision prompts $\mathbf{v}$ from the output of each transformer block using consecu + +![](images/ece0194475dd68a2c943119364e9ee270bed0a86e9773dd04f6ef0063104074d.jpg) +Figure 3. Overall architecture of DUALPATH. The pretrained image transformer takes a grid-like frameset and $T_{s}$ frames as inputs. We learn the temporal and spatial contexts separately through two distinct paths. During training, we only update newly introduced adapters and the classifier while freezing the pretrained layers. + +![](images/089ae6f20f80879fbcb7d6e8cd3ad8fcd95a2af7e7d446706ba3be347d7fe3fe.jpg) + +tive 2D convolution layers. The output of each block is reshaped as $\mathbb{R}^{P\times P\times C}$ to apply 2D convolutions and the final representation is derived by adding $\mathbf{v}$ and $\mathbf{h}$ : + +$$ +\mathbf {v} = \operatorname {R e s h a p e} \left(\sigma (\underset {\sim} {\operatorname {C o n v 2 d}} (\operatorname {R e s h a p e} (\mathbf {h})))\right), \tag {5} +$$ + +$$ +\tilde {\mathbf {h}} = \mathbf {h} + \mathbf {v}, +$$ + +where Conv2D consists of $1 \times 1$ convolution layer followed by $5 \times 5$ depth-wise convolution [14] and $1 \times 1$ convolution. ST-adapter [50] inserts a depth-wise 3D convolution layer between the down-projection layer and the activation function of the adapter. Different from the conventional adapters (e.g. AdaptFormer [11]), the ST-adapter takes tokens for all frames to enable the model to capture temporality in videos. The output of the ST-adapter can be represented as: + +$$ +\bar {\mathbf {z}} _ {t} = \overline {{\mathrm {L N}}} (\mathbf {z} _ {t}), +$$ + +$$ +\begin{array}{l} \hat {\mathbf {z}} = \sigma (\text {D - C o n v 3 d} ([ \tilde {\mathbf {z}} _ {1} \cdot \mathbf {W} _ {\text {d o w n}}, \dots , \tilde {\mathbf {z}} _ {T} \cdot \mathbf {W} _ {\text {d o w n}} ])) \cdot \mathbf {W} _ {\text {u p}}, \\ \mathbf {h} _ {t} = \mathbf {z} _ {t} + \underline {{\mathrm {M L P}}} (\tilde {\mathbf {z}} _ {t}) + s \cdot \hat {\mathbf {z}} _ {t}, \tag {6} \\ \end{array} +$$ + +where D-Conv3d denotes the depth-wise 3D convolution layer. Note that the same down-projection matrix $\mathbf{W}_{\mathrm{down}}$ is applied to all tokens regardless of the frame index $t$ . + +We emphasize that most of the baselines [11,35,49] have not concerned with temporal modeling. Even though ST-Adapter [50] has employed depth-wise 3D convolution layers between linear projections, it results in high computational cost. To entirely leverage a simple and efficient architecture of the adapter [11], we incorporate the dual-path design into the pretrained image transformers. + +# 4. Method + +The dual-path design (also called two-stream) is well-known architecture in CNN-based models for video recognition [10, 21, 60]. They have commonly used an optical + +flow [10, 60] or multiple frames with a high temporal resolution [21] to capture rapidly changing motion. Despite the effectiveness of dual-path architecture, it has yet to be explored with the transformer due to high computational costs. In this work, we propose a novel PETL method, called DUALPATH, comprised of spatial and temporal path adaptation. To the best of our knowledge, our DUALPATH is the first attempt to explicitly build the two-stream architecture upon the transformer while maintaining the computational cost similar to the single-stream architecture. The overall framework is depicted in Fig. 3. + +# 4.1. Spatial adaptation + +Since the image foundation models have been trained on large amounts of web datasets, we can intuitively speculate that they might be powerful to encode the spatial context even in videos. In order to make the outstanding ability of spatial modeling to be more suitable for video understanding with a slight parameter tuning, we adopt two parallel adapters for MHA and MLP in each transformer block. The parallel adapters allow the model to learn the spatial context for action recognition from the appearance of target video data while maintaining the original contexts for object recognition. + +Specifically, we sample $T_{S}$ frames from a video and tokenize each frame. Similar to Eq. 1, the set of spatial tokens $\mathbf{X}_t^{\mathrm{SP}}$ includes the learnable positional encodings $\mathbf{p}^{\mathrm{SP}}$ and the spatial class token $\mathbf{x}_t^{\mathrm{SP}}\{[\mathrm{CLS}]\}$ . The spatial adaptation in the $l$ -th transformer block can be formulated by the following equations: + +$$ +\begin{array}{l} \mathbf {z} _ {l} ^ {\mathrm {S P}} = \mathbf {h} _ {l - 1} ^ {\mathrm {S P}} + \mathrm {M H A} (\mathrm {L N} (\mathbf {h} _ {l - 1} ^ {\mathrm {S P}})) + \text {A d a p t e r} (\mathrm {L N} (\mathbf {h} _ {l - 1} ^ {\mathrm {S P}})), \\ \mathbf {h} _ {l} ^ {\mathrm {S P}} = \mathbf {z} _ {l} ^ {\mathrm {S P}} + \underline {{\operatorname {M L P}}} (\underline {{\operatorname {L N}}} (\mathbf {z} _ {l} ^ {\mathrm {S P}})) + \underline {{\operatorname {A d p a t e r}}} (\underline {{\operatorname {L N}}} (\mathbf {z} _ {l} ^ {\mathrm {S P}})), \tag {7} \\ \end{array} +$$ + +where $\mathbf{h}_0^{\mathrm{SP}} = [\mathbf{x}_t^{\mathrm{SP}}\{\mathrm{[CLS]}\} ,\mathbf{X}_t^{\mathrm{SP}}] + \mathbf{p}^{\mathrm{SP}}$ .We average + +the set of the spatial [CLS] tokens from the final transformer block to obtain a global spatial representation $\mathbf{y}^{\mathrm{SP}}$ , such that, + +$$ +\mathbf {y} ^ {\mathrm {S P}} = \frac {1}{T _ {S}} \sum_ {t = 1} ^ {T _ {S}} \mathbf {x} _ {t} ^ {\mathrm {S P}} \left\{\left[ \mathrm {C L S} \right] \right\}. \tag {8} +$$ + +Recent methods have discussed that a high frame rate only increases the computation volume and is unnecessary to understand the semantics of appearance [9, 21]. We thus sparsely sample $T_{S}$ frames with a low frame rate (e.g. 8 frames per clip). + +# 4.2. Temporal adaptation + +While spatial adaptation enables the models to take the spatial contexts in video data, the image models are still incapable of modeling the temporal dynamics. The key component that allows video transformers to model the solid temporal context is to learn relationships between local patches across frames in the video [1, 7]. To make image models capable of effectively establishing this component, we suggest a novel grid-like frameset transform technique that aggregates multiple frames into a unified grid-like frameset. Our grid-like frameset design is inspired by recent visual prompting research [4, 5]. It is simple yet surprisingly effective in imitating temporal modeling as spatial modeling and certainly reduces the computation. In each transformer block, we adopt two additional serial adapters for MHA and MLP, respectively. + +More concretely, we sample $T$ frames from a video and scale them with factors of $w$ and $h$ , such that the scaled frame size is $[W / w \times H / h \times 3]$ . We stack $w \times h$ scaled frames according to temporal ordering and reshape a stacked frame to construct a set of frames in a grid form of the same size as the original frame (i.e., $[W \times H \times 3]$ ). Note that the total number of grid-like framesets is $T_{G} = T / wh$ . The set of temporal tokens $\mathbf{X}_{g}^{\mathrm{TP}}$ for the $g$ -th frameset is obtained in the same way in Eq. 1 and combined with the learnable temporal class token $\mathbf{x}_{g}^{\mathrm{TP}}\left\{\left[\mathrm{CLS}\right]\right\}$ . Unlike the spatial adaptation, we use fixed 3D positional encodings [70], $\mathbf{p}^{\mathrm{TP}}$ , to the tokens to take the absolute temporal order and spatial positions of patches into account. The input transformation allows transformers to observe multiple frames at the same level. In experiments, we mainly construct a grid-like frameset from 16 original frames (i.e., scaling factors $w = h = 4$ ) to take the computational efficiency and promising performance. + +Whereas the parallel adapter is used in the spatial path, we sequentially append adapters to the top of MHA and MLP layers in each transformer block. Formally, temporal adaptation in the $l$ -th block can be described as: + +$$ +\begin{array}{l} \mathbf {z} _ {l} ^ {\mathrm {T P}} = \mathbf {h} _ {l - 1} ^ {\mathrm {T P}} + \text {A d a p t e r} (\underset {\leftarrow} {\mathrm {M H A}} (\underset {\leftarrow} {\mathrm {L N}} (\mathbf {h} _ {l - 1} ^ {\mathrm {T P}}))), \tag {9} \\ \mathbf {h} _ {l} ^ {\mathrm {T P}} = \mathbf {z} _ {l} ^ {\mathrm {T P}} + \text {A d p a t e r} (\operatorname {M L P} (\operatorname {L N} (\mathbf {z} _ {l} ^ {\mathrm {T P}}))), \\ \end{array} +$$ + +![](images/903993652c334d6437281a7d27c13c59eff87e58efdcfba736578e3e0212a7ea.jpg) +(a) DUALPATH w/o TA +Figure 4. Visualization of attention maps (a) without temporal adaptation (TA) and (b) with temporal adaptation for the action 'Spinning [something] that quickly stops spinning' in SSv2 [23]. + +![](images/4ea058028768dba022c0198589b5fbbfaec44a6cb273f5a1ab51662417053759.jpg) +(b) DUALPATH w/ TA + +where $\mathbf{h}_0^{\mathrm{TP}} = [\mathbf{x}_g^{\mathrm{TP}}\{\mathrm{[CLS]}\} ,\mathbf{X}_g^{\mathrm{TP}}] + \mathbf{p}^{\mathrm{TP}}$ . Similar to spatial adaptation, a global temporal representation $\mathbf{y}^{\mathrm{TP}}$ can be derived by averaging the set of the temporal [CLS] tokens from the final transformer block, i.e., + +$$ +\mathbf {y} ^ {\mathrm {T P}} = \frac {1}{T _ {G}} \sum_ {g = 1} ^ {T _ {G}} \mathbf {x} _ {g} ^ {\mathrm {T P}} \{[ \mathrm {C L S} ] \}. \tag {10} +$$ + +For the final prediction, we concatenate the global spatial and temporal representations and feed them into the classifier with GeLU activation [29] between two FC layers. + +# 4.3. Does a grid-like frameset really help to encode temporal context? + +This work presents a new standpoint to perform video action recognition with the pretrained image transformer by transforming multiple frames into a unified grid-like frame-set. However, it is still questionable whether the temporal path of DUALPATH can really capture the temporal context of videos. In this section, we provide some qualitative examples of the attention map. To validate the ability of precise temporal modeling, we sample videos from the SSv2 [23] dataset. Following [50], we depict the attention map of $\mathbf{x}_g^{\mathrm{TP}}\{[\mathrm{CLS}]\}$ from the final transformer block of the temporal path. As shown in Fig. 4, the model with the temporal adaptation (TA) of DUALPATH tends to concentrate on action-related regions, contrary to the model without TA that focuses on the irrelevant background. This result suggests that the temporal adaptation of DUALPATH strengthens the temporal modeling ability of the image model. More examples are shown in Fig. A1 of Appendix. + +# 5. Experiment + +# 5.1. Evaluation setup + +Datasets. We evaluate the proposed method on four standard action recognition datasets, including the Kinetics-400 (K400) [38], HMDB51 [39], Something-something-v2 (SSv2) [23], and Diving-48 [42]. + +
Method & Arch.PretrainModel # ParamsTrainable # ParamsGFLOPsR@1R@5Views
Full-tuning
SlowFast+NL [21]-60M60M702079.893.916×3×10
MViT-B [18]-37M37M409581.295.164×3×3
UniFormer-B [40]IN-1K50M50M310883.095.432×4×3
TimeSformer-L [7]IN-21K121M121M714080.794.764×1×3
ViViT-L/16×2 FE [1]IN-1K311M311M398080.692.732×1×1
VideoSwin-L [47]IN-21K197M197M724883.195.932×4×3
MViTv2-L [43]IN-21K218M218M4242086.197.032×3×5
MTV-L [76]JFT876M876M1805084.396.332×4×3
TokenLearner-L/10 [57]JFT450M450M4891285.496.364×4×3
ActionCLIP [68]CLIP142M142M1689083.897.132×10×3
X-CLIP-L/14 [48]CLIP420M420M789087.197.68×4×3
Parameter Efficient Tuning
EVL [45] w/ ViT-L/14CLIP368M59M808887.3-32×3×1
ST-Adapter [50] w/ ViT-B/16CLIP93M7M182182.796.232×3×1
DUALPATH w/ ViT-B/16CLIP96M10M71085.497.132×3×1
DUALPATH w/ ViT-L/14CLIP330M27M186887.797.832×3×1
+ +Table 1. Performance comparisons for action recognition on the Kinetics-400 [38] dataset. Note that Views = #frames × #clips × #spatial. + +- Kinetics-400 (K400) contains about 240K training videos and 20K validation videos for 400 human action categories. Each video is trimmed to have a length of 10 seconds. While the K400 dataset provides a wide range of categories, they are known to be highly biased in spatial appearance [59]. +- Somthing-something-v2 (SSv2) is a more challenging dataset since they require strong temporal modeling [59]. They contain about 168.9K training videos and 24.7K validation videos for 174 classes. +- HMDB51 is a small dataset that provides about 7K videos of 51 action categories. We use all three splits, each split of which consists of 3570 and 1530 videos for training and evaluation, respectively. We report the average accuracy for three splits. +- Diving-48 is a fine-grained diving action dataset. We use train-test split v2 that contains about 15K training videos and 2K validation videos of 48 diving actions. Since the action can not be determined by only the static representations (e.g. objects or background), stronger temporal modeling is required for this dataset. + +Pretrained image backbone. We employ CLIP pretrained ViT-B/16 and ViT-L/14 as backbones. The results with Swin-B [46] are provided in Tab. A2 of the Appendix. + +- ViT-B/16 [17] consists of 12 transformer blocks with 86M parameters and takes patches of size $16 \times 16$ as inputs. +- ViT-L/14 [17], a larger model than ViT-B/16, contains 24 transformer blocks with 303M parameters. It takes $14 \times 14$ patches as inputs. + +Implementation details. For the K400, HMDB51, and Diving-48 datasets, we uniformly sample 8 frames (i.e., $T_{s} = 8$ ) with the sampling interval 8 in the spatial path. In the temporal path, we uniformly sample 16, 32, and 48 frames with the sampling intervals 4, 2, and 1 to construct 1, 2, and 3 grid-like framesets (i.e., $T_{g} = 1,2,3$ ), respectively. For the SSv2 dataset, we sample the same number of frames as in other datasets, but with a dynamic sampling interval to cover the whole video. Note that the frames for the spatial path are the subset of the temporal path frames. Please refer to more implementation details in Appendix A. + +# 5.2. Comparison with state-of-the-art + +In this section, we compare the proposed method with baselines [11, 35, 49, 50] in Sec. 3 and state-of-the-art video transformers [1, 7, 18, 40, 43, 45, 47, 48, 57, 68, 76] to demonstrate the effectiveness of the proposed method on four video action recognition datasets. Note that the number of frames of the spatial adaptation path of DUALPATH is fixed to 8 for all experiments, i.e., $T_{S} = 8$ . + +Results on Kinetics-400. We report the results evaluated on K400 [38] in Tab. 1. We first compare the proposed method with state-of-the-art video models that are pretrained on the large-scale image dataset and fully finetuned on K400. In terms of memory and computational efficiency, video models require a huge number of parameters ( $\sim$ 450M [57]) and computations ( $\sim$ 48912 GFLOPs [57]). On the other hand, we require only 10M trainable parameters which are newly stored, and 710 GFLOPs for inference using 32 frames with ViT-B/16 [17] backbone. Compared to X-CLIP-L/14 [48] which leverages the additional text branch, our DUALPATH achieves state-of-the-art performance with ViT-L/14 back + +
Method & Arch.PretrainModel +#ParamsTrainable +#ParamsGFLOPsR@1R@5Views
Full-tuning
Full-tuning ViT-B/16 [17]CLIP86M86M41944.077.08×1×3
Full-tuning ViT-L/14 [17]CLIP303M303M194148.777.58×1×3
TimeSformer-L [7]IN-21K121M121M714062.4-64×1×3
MTV-B [76]IN-21K310M310M479067.690.432×4×3
MViT-B [18]K40037M37M51067.190.832×1×3
MViTv2-B [43]K40051M51M67570.592.740×1×3
ViViT-L/16×2 [1]IN-21K/K400311M311M1189265.489.816×4×3
VideoSwin-B [47]IN-21K/K40089M89M96369.692.732×1×1
Omnivore [22]IN-21K/K400---71.493.532×1×3
MViTv2-B [43]IN-21K/K400213M213M848473.394.132×1×3
UniFormer-B [40]IN-21K/K60050M50M77771.292.832×1×3
Parameter Efficient Tuning
VideoPrompt* [37] w/ ViT-B/16CLIP92M6M53731.060.38×1×3
VPT [35] w/ ViT-B/16CLIP92M6M53736.261.18×1×3
AdaptFormer [11] w/ ViT-B/16CLIP94M8M54451.370.68×1×3
Pro-tuning [49] w/ ViT-B/16CLIP95M9M53850.869.98×1×3
EVL [45] w/ ViT-L/14CLIP484M175M964166.7-32×1×3
ST-Adapter [50] w/ ViT-B/16CLIP97M11M195569.592.632×3×1
DUALPATH w/ ViT-B/16CLIP99M13M64269.692.516×1×3
DUALPATH w/ ViT-B/16CLIP99M13M71670.392.932×1×3
DUALPATH w/ ViT-B/16CLIP99M13M79171.293.248×1×3
DUALPATH w/ ViT-L/14CLIP336M33M171370.292.716×1×3
DUALPATH w/ ViT-L/14CLIP336M33M193271.493.432×1×3
DUALPATH w/ ViT-L/14CLIP336M33M215172.293.748×1×3
+ +bone. The comparisons with parameter-efficient tuning methods [45, 50] show that our DUALPATH achieves higher performance while requiring much lower burdens in computations under the same conditions. + +Results on Something-Something-v2. We present the performance comparisons on SSv2 [23] in Tab. 2. The results show that our DUALPATH with ViT-B/16 achieves comparable or better performance than the prior supervised video models [1,7,18,76], requiring a much smaller number of trainable parameters and GFLOPs. Our DUALPATH with ViT-L/14 shows more competitive performance, outperforming most prior works [22, 40, 43]. The baselines [11, 35, 37, 49], which have relatively weak temporal modeling ability, show significantly poor performance, implying that strong temporal modeling is mandatory for the SSv2 dataset. The comparisons to the CLIP pretrained PET approaches [45, 50] with ViT-B/16 demonstrate the effectiveness and efficiency of DUALPATH, achieving higher performance (70.3 vs 69.5 [50]) with significantly low computations (716 vs 9641 [45] GFLOPs) using 32 frames. Thanks to the extreme computational efficiency, our DUALPATH comprises more competitive performance using 48 frames ( $T_{G} = 3$ ) with low computation requirements. + +Results on HMDB51. In Tab. 3, we compare the re + +Table 2. Performance comparisons for action recognition on the SSv2 [23] dataset. Note that we reproduce VideoPrompt [37] without the additional text branch for fair comparison (denoting with *). + +
Method & Arch.ClassifierParamsHMDB51
Full-tuning w/ ViT-B/16 [17]Lin.86M59.4
Linear w/ ViT-B/16Lin.0.1M61.2
VPT [35] w/ ViT-B/16Trans.7M62.4
AdaptFormer [11] w/ ViT-B/16Trans.8M63.7
Pro-tuning [49] w/ ViT-B/16Trans.9M63.3
VideoPrompt [37] w/ ViT-B/16Trans.6M66.4
ST-Adapter* [50] w/ ViT-B/16Lin.7M65.9
DUALPATH w/ ViT-B/16MLPs.10M75.6
+ +Table 3. Performance comparisons for action recognition on the HMDB51 [39] dataset with the CLIP pretrained ViT-B/16 [53]. We report the type of classifier and the number of learnable parameters for baselines and ours. Lin. and Trans. denote the linear classifier and temporal transformer, respectively. Our DUALPATH uses two MLP layers as the classifier. Note that we reproduce ST-Adapter [50] for fair comparison in terms of the pretrained dataset (denoting with $*$ ). + +sults with baselines [11, 35, 37, 49, 50] on HMDB51 [39] that dominantly requires strong spatial modeling for action recognition. Surprisingly, our DUALPATH significantly outperforms baselines by large margins. This result demonstrates DUALPATH fully capitalizes on the exceptional spatial modeling ability of the pretrained image model for ac + +
Method & Arch.PretrainParamsDiving48
Supervised
TimeSformer-L [7]IN-21K121M81.0
VideoSwin-B [47]IN-21K88M81.9
SIFAR-B-14 [19]IN-21K87M87.3
ORViT [30]IN-21K160M88.0
Parameter Efficient Tuning
DUALPATH w/ ViT-B/16CLIP10M88.7
+ +tion recognition. The comparison with VideoPrompt [37] that uses the additional text branch demonstrates the effectiveness of DUALPATH, improving $9.2\%$ performance improvement. + +Results on Diving-48. Tab. 4 shows performance comparisons on Diving-48 [42] that requires fine-grained action recognition. Our DUALPATH consistently outperforms all video models with only 10M trainable parameters. Particularly, we obtain a better performance than ORViT [30] which utilizes the additional tracking model. It indicates the utility of DUALPATH in fine-grained action recognition and the superiority of temporal modeling of DUALPATH. + +# 5.3. Components analysis + +Impact of dual-path. In the top panel of Tab. 5, we train the model by ablating each path and evaluate the performance on SSv2. Without the temporal path (DUALPATH w/o TA), the performance is significantly degraded despite using a larger number of frames ( $T_{S} = 16$ vs 8). Without the spatial path (DUALPATH w/o SA), we can obtain slightly better performance than the result without the temporal adaptation. Since the SSv2 requires strong temporal modeling, we speculate that two ablation studies show comparison results. However, it still shows a substantial performance gap compared to the full model of DUALPATH, demonstrating the effectiveness of the dual-path design. + +Frame rates in spatial path. In the middle panel of Tab. 5, we analyze the effect according to the number of frames used in the spatial path. The temporal path identically uses 16 frames to construct a grid-like frameset, and frames used in the spatial path are sampled from such 16 frames. A large number of $T_{S}$ slightly improves performance, however, requires more computational costs. Considering the performance improvement compared to the computation increase, we mainly set $T_{S}$ to 8. + +Number of frames in grid. We scale down original frames with scaling factors $w$ and $h$ to construct grid-like framesets. These factors thus determine the number of frames the model observes within one grid-like frameset. While a large value of factors increases the temporal resolution, the information of each frame is inevitably reduced. For exam- + +Table 4. Performance comparisons for action recognition on the Diving-48 [42] dataset. We report the pretrained dataset, the number of learnable parameters (M) for each method, and the accuracy. + +
MethodParamsGFLOPsSSv2Views
Effectiveness of Each Path
DUALPATH w/o TA5M101653.716×3×1
DUALPATH w/o SA8M13455.116×3×1
Effectiveness of TS
TS=813M64269.316×3×1
TS=1213M89669.616×3×1
TS=1613M115069.816×3×1
Effectiveness of scaling factors
w=h=2 (TG=16)13M175266.464×3×1
w=h=4 (TG=4)13M86471.864×3×1
w=h=8 (TG=1)13M64261.564×3×1
DUALPATH13M64269.316×3×1
+ +Table 5. Performance with respect to variants of the components. + +ple, the original frame is scaled down to the size of $28 \times 28$ with $w = h = 8$ . Meanwhile, a small value of factors retains richer information from the original frame, however, makes the temporal resolution small. As shown in the bottom panel of Tab. 5, we attain the best performance with $w = h = 4$ . + +# 6. Conclusion and Future Work + +In this paper, we have introduced the novel image-to-video transfer learning approach, DUALPATH. By incorporating a dual-path design into image transformers, DUALPATH adapts image models to the video task (i.e., action recognition) with a small number of trainable parameters. The spatial path adaptation strengthens the inherent spatial context modeling of the pretrained image transformers for video data. The temporal path adaptation transforms multiple frames into a unified grid-like frameset, enabling the image model to capture relationships between frames. We appropriately employ the bottlenecked adapters in each path to adapt the pretrained features to target video data. In addition, we present several baselines transforming recent PETL approaches [11, 35, 49] for image-to-video adaptation. Experimental results demonstrated the superiority of the dualpath design and the grid-like frameset prompting, outperforming several baselines and supervised video models. + +There are many possible directions for future work, encompassing cross-domain transfer learning. While we have explored image-to-video transfer learning, large foundation vision-language models are available. It would also be interesting to expand the superior pretrained 2D knowledge to 3D spatial modeling [71]. We hope our study will foster research and provide a foundation for cross-domain transfer learning. + +Acknowledgement. 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Previous adaptation methods have simultaneously considered spatial and temporal modeling with a unified learnable module but still suffered from fully leveraging the representative capabilities of image transformers. We argue that the popular dual-path (two-stream) architecture in video models can mitigate this problem. We propose a novel DUALPATH adaptation separated into spatial and temporal adaptation paths, where a lightweight bottleneck adapter is employed in each transformer block. Especially for temporal dynamic modeling, we incorporate consecutive frames into a grid-like frameset to precisely imitate vision transformers' capability that extrapolates relationships between tokens. In addition, we extensively investigate the multiple baselines from a unified perspective in video understanding and compare them with DUALPATH. Experimental results on four action recognition benchmarks prove that pretrained image transformers with DUALPATH can be effectively generalized beyond the data domain." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 47, + 510, + 127, + 522 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 510, + 127, + 522 + ], + "spans": [ + { + "bbox": [ + 47, + 510, + 127, + 522 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 47, + 524, + 287, + 608 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 524, + 287, + 608 + ], + "spans": [ + { + "bbox": [ + 47, + 524, + 287, + 608 + ], + "type": "text", + "content": "Recognizing when, where, and what happened is a fundamental capability in the human cognition system to understand our natural world. The research for video understanding inspires such capability for machine intelligence to comprehend scenes over time flow. Over the last decade, the development of deep neural networks [10,33,66,73] has contributed towards advances in video understanding." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 47, + 608, + 287, + 657 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 608, + 287, + 657 + ], + "spans": [ + { + "bbox": [ + 47, + 608, + 287, + 657 + ], + "type": "text", + "content": "Vision Transformer (ViT) [17] has recently emerged, making an upheaval in the research field of computer vision. ViT and its variants [16, 46, 72, 78] have demonstrated remarkable generalizability and transferability of their repre" + } + ] + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 307, + 219, + 545, + 379 + ], + "blocks": [ + { + "bbox": [ + 307, + 219, + 545, + 379 + ], + "lines": [ + { + "bbox": [ + 307, + 219, + 545, + 379 + ], + "spans": [ + { + "bbox": [ + 307, + 219, + 545, + 379 + ], + "type": "image", + "image_path": "cc6811a31128b3756b96466320126e9df1cf714a41b65756cf31c0817a9bc225.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 380, + 546, + 424 + ], + "lines": [ + { + "bbox": [ + 305, + 380, + 546, + 424 + ], + "spans": [ + { + "bbox": [ + 305, + 380, + 546, + 424 + ], + "type": "text", + "content": "Figure 1. Performance comparison on the Kinetics-400 [38] dataset. We depict the action recognition performance (vertical axis, " + }, + { + "bbox": [ + 305, + 380, + 546, + 424 + ], + "type": "inline_equation", + "content": "\\%" + }, + { + "bbox": [ + 305, + 380, + 546, + 424 + ], + "type": "text", + "content": " ) with respect to the number of trainable parameters (horizontal axis). The size of circles indicates GFLOPs for inference." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 437, + 546, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 546, + 593 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 546, + 593 + ], + "type": "text", + "content": "sentations with scaled-up foundation models [34, 53, 63, 69, 77, 79] and large-scale web-collected image data (e.g. JFT-3B [79], LAION-5B [58]). To capitalize on well-trained visual foundation models, finetuning entire parameters of the pretrained models with task-specific objectives has been the most popular transfer technique. However, it requires high-quality training data and plenty of computational resources to update the whole parameters for each downstream task, making overwhelming efforts for training. While partial finetuning [28], which trains additional multilayer perceptron (MLP) layers to the top of the model, has also been widely used for affordable training costs, unsatisfactory performance has been pointed out as a problem." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 593, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 593, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 593, + 546, + 714 + ], + "type": "text", + "content": "Most recently, parameter-efficient transfer learning (PETL) methods [25, 26, 31, 32, 41, 61] have been proposed as an alternative to finetuning in the natural language processing area to adapt the large-scale language model, such as GPT series [8, 54, 55] and T5 [56], for each task. They have successfully attained comparable or even surpassing performance to full-tuning parameters by learning a small number of extra trainable parameters only while keeping the original parameters of the pretrained model frozen. Thanks to their effectiveness and simplicity, they have been ex" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 57, + 7, + 101, + 39 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 7, + 101, + 39 + ], + "spans": [ + { + "bbox": [ + 57, + 7, + 101, + 39 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 136, + 5, + 487, + 18 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 136, + 5, + 487, + 18 + ], + "spans": [ + { + "bbox": [ + 136, + 5, + 487, + 18 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 189, + 18, + 435, + 28 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 189, + 18, + 435, + 28 + ], + "spans": [ + { + "bbox": [ + 189, + 18, + 435, + 28 + ], + "type": "text", + "content": "Except for this watermark, it is identical to the accepted version;" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 171, + 29, + 453, + 41 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 171, + 29, + 453, + 41 + ], + "spans": [ + { + "bbox": [ + 171, + 29, + 453, + 41 + ], + "type": "text", + "content": "the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 664, + 208, + 674 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 664, + 208, + 674 + ], + "spans": [ + { + "bbox": [ + 47, + 664, + 208, + 674 + ], + "type": "text", + "content": "* Equal contributions. † Corresponding author." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 47, + 674, + 282, + 683 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 674, + 282, + 683 + ], + "spans": [ + { + "bbox": [ + 47, + 674, + 282, + 683 + ], + "type": "text", + "content": "Official code: https://github.com/park-jungin/DualPath" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 47, + 683, + 286, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 683, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 683, + 286, + 712 + ], + "type": "text", + "content": "This research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF2021R1A2C2006703)." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 279, + 738, + 298, + 747 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 738, + 298, + 747 + ], + "spans": [ + { + "bbox": [ + 279, + 738, + 298, + 747 + ], + "type": "text", + "content": "2203" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 595, + 841 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 72, + 286, + 226 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 72, + 286, + 226 + ], + "spans": [ + { + "bbox": [ + 48, + 72, + 286, + 226 + ], + "type": "text", + "content": "tended to vision models by applying prompt-based methods [3, 35] and adapter-based methods [11, 49, 64]. They have efficiently adapted pretrained models to downstream tasks with significantly reduced tuning parameters, but most of these works mainly focus on transferring image models to image tasks [3, 11, 35, 49] and vision-language models to vision-language tasks [64]. Inspired by the advances of the prior arts, we raise two conceivable questions: (1) Is it possible to transfer the parameters of the image foundation model to another video domain? (2) Is it also possible the transferred model performs comparably to the carefully designed video models that take the spatiotemporal nature of the video into account?" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 231, + 286, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 231, + 286, + 409 + ], + "spans": [ + { + "bbox": [ + 48, + 231, + 286, + 409 + ], + "type": "text", + "content": "While image models have demonstrated strong spatial context modeling capabilities [34, 53, 63, 79], video transformer models [1, 47, 57, 76] require a more complex architecture (e.g. 539 vs 48912 GFLOPs [57]) with a large number of parameters (e.g. 84M vs 876M parameters [76]) than ViT for temporal context reasoning. Therefore, the challenge in transferring image models for video understanding is to encode the temporal context of videos while leveraging the discriminative spatial context of the pretrained image models. A naive solution is to finetune image models on a video dataset by directly applying previous prompt/adapter-based approaches [3, 11, 35, 49]. However, these approaches inevitably ignore the temporal context in videos because they bridge only the spatial contexts between image and video data." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 48, + 414, + 286, + 711 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 414, + 286, + 711 + ], + "spans": [ + { + "bbox": [ + 48, + 414, + 286, + 711 + ], + "type": "text", + "content": "In this paper, we propose a novel adapter-based dualpath parameter efficient tuning method for video understanding, namely DUALPATH, which consists of two distinct paths (spatial path and temporal path). For both paths, we freeze the pretrained image model and train only additional bottleneck adapters for tuning. The spatial path is designed to encode the spatial contexts that can be inferred from the appearance of individual frames with the minimum tuning of the pretrained image model. To reduce the computation burden, we sparsely use the frames with a low frame rate in the spatial path. The temporal path corresponds to the temporal context that should be encoded by grasping the dynamic relationship over several frames sampled with a high frame rate. Especially for two reasons, we construct a grid-like frameset that consists of consecutive low-resolution frames as an input of the temporal path: (i) preventing computational efficiency loss caused by calculating multiple frames simultaneously; (ii) precisely imitating the ViT's ability for extrapolating global dependencies between input tokens. To compare our DUALPATH with existing methods broadly, we implement several baselines with a unified perspective on recent domain-specific PETL approaches [11, 35, 49]. Extensive experiments on several action recognition benchmarks [23, 38, 39, 42] demonstrate the effectiveness and" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 307, + 72, + 545, + 132 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 72, + 545, + 132 + ], + "spans": [ + { + "bbox": [ + 307, + 72, + 545, + 132 + ], + "type": "text", + "content": "high efficiency of our DUALPATH, achieving comparable and even better performance than the baselines and prior video models [1, 7, 18, 22, 40, 43, 47, 57, 68, 76]. We achieve these results with extremely low computational costs for both training and inference, as demonstrated in Fig. 1." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 307, + 145, + 391, + 157 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 145, + 391, + 157 + ], + "spans": [ + { + "bbox": [ + 307, + 145, + 391, + 157 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 307, + 161, + 545, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 161, + 545, + 316 + ], + "spans": [ + { + "bbox": [ + 307, + 161, + 545, + 316 + ], + "type": "text", + "content": "Pretraining vision models. To address the burdens of collecting large-scale labeled datasets for supervised learning [15, 63, 79], self-supervised learning methods [12, 13, 24,27,28,74] have been introduced to learn general-purpose visual representations from unlabeled data. Similarly, self-supervised learning methods for videos have also been proposed with large-scale unlabeled video/video-language data [20,51,52,62,65,68,75]. However, collecting even unlabeled video-language pairs is still quite costly compared to image-language pairs. In addition, pretraining video models require more computational power than images. We thus take advantage of the powerful pretrained image-based models for efficient video understanding." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 307, + 317, + 545, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 317, + 545, + 484 + ], + "spans": [ + { + "bbox": [ + 307, + 317, + 545, + 484 + ], + "type": "text", + "content": "Video action recognition. Action recognition is one of the most fundamental research topics for video understanding. Early works have been built upon convolution neural networks (CNNs) [10, 21, 44, 66, 73] to effectively infer the spatiotemporal context for action recognition. Since Vision Transformer (ViT) [17] has become a new paradigm in computer vision, transformers for video understanding have been actively studied by extending pretrained image models. The pretrained image transformers have been used to initialize the part of the video transformers [1, 7, 76, 80] or inflated to the video transformers [47]. While transformers have demonstrated superior performance on video action recognition, they require full finetuning on video datasets, making the training inefficient." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 307, + 486, + 545, + 711 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 486, + 545, + 711 + ], + "spans": [ + { + "bbox": [ + 307, + 486, + 545, + 711 + ], + "type": "text", + "content": "Parameter-efficient transfer learning (PETL). To address the memory and parameter inefficiency of full/partial-finetuning, PETL has first introduced in natural language processing (NLP) [6,25,26,31,32,41,61]. The main objective of PETL is to attain comparable or surpassing performance on downstream tasks by finetuning with only a small number of trainable parameters. Although PETL approaches [3, 11, 11, 35, 36, 49, 64] have recently been studied in computer vision, they are 'blind' to other modalities such that image models are used for image tasks, and so are the other modalities. In contrast, we share the same objective as recent works for image-to-video transfer learning [37, 45, 48, 50], demonstrating the pretrained image models can be good video learners. However, they have several limitations in terms of parameter and computational efficiency. For example, [45] learned an extra decoder that contains 3D convolution layers and cross-frame attention, and [50] inserted additional depth-wise 3D convolution layers between the down-/up-projection layers of the adapter to" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 739, + 298, + 747 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 739, + 298, + 747 + ], + "spans": [ + { + "bbox": [ + 279, + 739, + 298, + 747 + ], + "type": "text", + "content": "2204" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 595, + 841 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 286, + 145 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 286, + 145 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 286, + 145 + ], + "type": "text", + "content": "perform temporal reasoning, inducing computational inefficiency. The most recent works [37,48] require an additional text encoder branch as a classifier. Moreover, they have computational efficiency proportional to the temporal resolution. Our DUALPATH accomplishes more efficient spatiotemporal modeling while achieving higher performance." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 154, + 205, + 168 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 154, + 205, + 168 + ], + "spans": [ + { + "bbox": [ + 47, + 154, + 205, + 168 + ], + "type": "text", + "content": "3. Preliminaries and Baselines" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 171, + 208, + 182 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 171, + 208, + 182 + ], + "spans": [ + { + "bbox": [ + 47, + 171, + 208, + 182 + ], + "type": "text", + "content": "3.1. Vision transformers for video" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 185, + 288, + 243 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 185, + 288, + 243 + ], + "spans": [ + { + "bbox": [ + 47, + 185, + 288, + 243 + ], + "type": "text", + "content": "We briefly describe how to apply vision transformers for video understanding below. Following [67], given a set of " + }, + { + "bbox": [ + 47, + 185, + 288, + 243 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 47, + 185, + 288, + 243 + ], + "type": "text", + "content": " frames in a video, we split each frame into " + }, + { + "bbox": [ + 47, + 185, + 288, + 243 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 47, + 185, + 288, + 243 + ], + "type": "text", + "content": " patches of size " + }, + { + "bbox": [ + 47, + 185, + 288, + 243 + ], + "type": "inline_equation", + "content": "(P \\times P)" + }, + { + "bbox": [ + 47, + 185, + 288, + 243 + ], + "type": "text", + "content": " and tokenize them using a linear projection, such that" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 80, + 253, + 286, + 268 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 253, + 286, + 268 + ], + "spans": [ + { + "bbox": [ + 80, + 253, + 286, + 268 + ], + "type": "interline_equation", + "content": "\\mathbf {X} _ {t} = \\left[ \\mathbf {x} _ {t} \\left\\{\\left[ \\mathrm {C L S} \\right] \\right\\}, \\mathbf {x} _ {t} ^ {1}, \\mathbf {x} _ {t} ^ {2}, \\dots , \\mathbf {x} _ {t} ^ {N} \\right] + \\mathbf {p}, \\tag {1}", + "image_path": "edae0c8c59086ca02ae1e143ddd6d167884ea1a93a44568daa3e7c9ee2d949e5.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 275, + 287, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 275, + 287, + 348 + ], + "spans": [ + { + "bbox": [ + 47, + 275, + 287, + 348 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 275, + 287, + 348 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_t" + }, + { + "bbox": [ + 47, + 275, + 287, + 348 + ], + "type": "text", + "content": " is a set of tokens for the " + }, + { + "bbox": [ + 47, + 275, + 287, + 348 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 275, + 287, + 348 + ], + "type": "text", + "content": "-th frame, and " + }, + { + "bbox": [ + 47, + 275, + 287, + 348 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t\\{\\mathrm{CLS}\\}" + }, + { + "bbox": [ + 47, + 275, + 287, + 348 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 275, + 287, + 348 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 47, + 275, + 287, + 348 + ], + "type": "text", + "content": " denote a learnable class token and a learned positional embedding respectively. We feed " + }, + { + "bbox": [ + 47, + 275, + 287, + 348 + ], + "type": "inline_equation", + "content": "(N + 1)" + }, + { + "bbox": [ + 47, + 275, + 287, + 348 + ], + "type": "text", + "content": " tokens of each frame to a sequence of " + }, + { + "bbox": [ + 47, + 275, + 287, + 348 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 47, + 275, + 287, + 348 + ], + "type": "text", + "content": " transformer blocks, and the output of the " + }, + { + "bbox": [ + 47, + 275, + 287, + 348 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 47, + 275, + 287, + 348 + ], + "type": "text", + "content": "-th block " + }, + { + "bbox": [ + 47, + 275, + 287, + 348 + ], + "type": "inline_equation", + "content": "\\mathbf{h}_{l,t}" + }, + { + "bbox": [ + 47, + 275, + 287, + 348 + ], + "type": "text", + "content": " can be derived by the following equations:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 95, + 356, + 286, + 375 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 95, + 356, + 286, + 375 + ], + "spans": [ + { + "bbox": [ + 95, + 356, + 286, + 375 + ], + "type": "interline_equation", + "content": "\\mathbf {z} _ {l, t} = \\mathbf {h} _ {l - 1, t} + \\mathrm {M H A} (\\mathrm {L N} (\\mathbf {h} _ {l - 1, t})), \\tag {2}", + "image_path": "e4c7d9351b2ad4ea31d2341c241f1c2e1b431a25c60f894d2bef2da4722f584b.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 107, + 372, + 226, + 385 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 372, + 226, + 385 + ], + "spans": [ + { + "bbox": [ + 107, + 372, + 226, + 385 + ], + "type": "interline_equation", + "content": "\\mathbf {h} _ {l, t} = \\mathbf {z} _ {l, t} + \\operatorname {M L P} (\\ln (\\mathbf {z} _ {l, t})),", + "image_path": "1a46ff06c9b800da6fc2be267f677e14a4ebd1168fe18a2247a9669e0fb7a2d5.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 392, + 287, + 452 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 392, + 287, + 452 + ], + "spans": [ + { + "bbox": [ + 47, + 392, + 287, + 452 + ], + "type": "text", + "content": "where LN, MHA, and MLP denote a layer normalization [2], multi-head attention [67], and a multilayer perceptron operation, respectively. We apply layer normalization to the learned " + }, + { + "bbox": [ + 47, + 392, + 287, + 452 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 47, + 392, + 287, + 452 + ], + "type": "text", + "content": " class tokens from the final transformer block and treat them as a set of frame representations." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 453, + 287, + 549 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 453, + 287, + 549 + ], + "spans": [ + { + "bbox": [ + 47, + 453, + 287, + 549 + ], + "type": "text", + "content": "To take minimal temporal modeling into account the following baselines [11, 35, 49], we employ a temporal transformer block followed by a full-connected (FC) layer as a classifier for video action recognition, similar to [37]. We add learnable temporal positional embeddings " + }, + { + "bbox": [ + 47, + 453, + 287, + 549 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_{\\mathrm{temp}}" + }, + { + "bbox": [ + 47, + 453, + 287, + 549 + ], + "type": "text", + "content": " to the frame representations (i.e., " + }, + { + "bbox": [ + 47, + 453, + 287, + 549 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t\\{\\mathrm{cl}\\mathbf{s}\\} \\gets \\mathbf{x}_t\\{\\mathrm{cl}\\mathbf{s}\\} + \\mathbf{p}_{\\mathrm{temp}}" + }, + { + "bbox": [ + 47, + 453, + 287, + 549 + ], + "type": "text", + "content": ") and feed them into the transformer classifier. For the ST-adapter [50], we use a single FC layer as a classifier." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 555, + 114, + 566 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 555, + 114, + 566 + ], + "spans": [ + { + "bbox": [ + 47, + 555, + 114, + 566 + ], + "type": "text", + "content": "3.2. Baselines" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 569, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 569, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 569, + 287, + 714 + ], + "type": "text", + "content": "The objective of our work is to transfer the superiority of vision transformers pretrained on large-scale image datasets to the video domain through efficient finetuning with a small number of learnable parameters, while freezing the pretrained parameters. To compare with other methods, we generalize four recent PETL methods to the video domain only with the least possible transformation; (1) VPT [35] (2) AdaptFormer [11] (3) Pro-tuning [49] (4) ST-adapter [50]. The most of works have been originally proposed to adapt pretrained image models to downstream image tasks [11, 35, 49] and video models to video tasks [11], by learning visual prompt tokens [35], adapter" + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 320, + 71, + 423, + 142 + ], + "blocks": [ + { + "bbox": [ + 320, + 71, + 423, + 142 + ], + "lines": [ + { + "bbox": [ + 320, + 71, + 423, + 142 + ], + "spans": [ + { + "bbox": [ + 320, + 71, + 423, + 142 + ], + "type": "image", + "image_path": "0d130e43d9de9b4053b68b241a10d58c585112f48271fa2fdba61c2f7f347e8d.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 350, + 143, + 393, + 153 + ], + "lines": [ + { + "bbox": [ + 350, + 143, + 393, + 153 + ], + "spans": [ + { + "bbox": [ + 350, + 143, + 393, + 153 + ], + "type": "text", + "content": "(a) VPT [35]" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 428, + 69, + 533, + 142 + ], + "blocks": [ + { + "bbox": [ + 428, + 69, + 533, + 142 + ], + "lines": [ + { + "bbox": [ + 428, + 69, + 533, + 142 + ], + "spans": [ + { + "bbox": [ + 428, + 69, + 533, + 142 + ], + "type": "image", + "image_path": "2c82839b12d43b96cb61f9a21a18c3a24eb6c6f79b4b7211beb574d6c48deef2.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 440, + 143, + 520, + 153 + ], + "lines": [ + { + "bbox": [ + 440, + 143, + 520, + 153 + ], + "spans": [ + { + "bbox": [ + 440, + 143, + 520, + 153 + ], + "type": "text", + "content": "(b) Parallel Adapter [11]" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 320, + 154, + 376, + 248 + ], + "blocks": [ + { + "bbox": [ + 320, + 154, + 376, + 248 + ], + "lines": [ + { + "bbox": [ + 320, + 154, + 376, + 248 + ], + "spans": [ + { + "bbox": [ + 320, + 154, + 376, + 248 + ], + "type": "image", + "image_path": "56e58334dc2d8ad711272a19cde900f16f2eecbceb80c423b39e597ebb695fdb.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 311, + 249, + 385, + 260 + ], + "lines": [ + { + "bbox": [ + 311, + 249, + 385, + 260 + ], + "spans": [ + { + "bbox": [ + 311, + 249, + 385, + 260 + ], + "type": "text", + "content": "(c) Serial Adapter [11]" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 395, + 154, + 454, + 248 + ], + "blocks": [ + { + "bbox": [ + 395, + 154, + 454, + 248 + ], + "lines": [ + { + "bbox": [ + 395, + 154, + 454, + 248 + ], + "spans": [ + { + "bbox": [ + 395, + 154, + 454, + 248 + ], + "type": "image", + "image_path": "42bb65e6c745943f00cffb8e5bfe5e81e85600312af0e361ef28df3bca31dbf5.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 390, + 249, + 462, + 260 + ], + "lines": [ + { + "bbox": [ + 390, + 249, + 462, + 260 + ], + "spans": [ + { + "bbox": [ + 390, + 249, + 462, + 260 + ], + "type": "text", + "content": "(d) Prompt Block [49]" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "type": "image", + "bbox": [ + 475, + 158, + 533, + 248 + ], + "blocks": [ + { + "bbox": [ + 475, + 158, + 533, + 248 + ], + "lines": [ + { + "bbox": [ + 475, + 158, + 533, + 248 + ], + "spans": [ + { + "bbox": [ + 475, + 158, + 533, + 248 + ], + "type": "image", + "image_path": "9cc0dd574dab336362cc723c490150acfe5ddc409dc703846c4703ea1e3ec888.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 472, + 249, + 536, + 260 + ], + "lines": [ + { + "bbox": [ + 472, + 249, + 536, + 260 + ], + "spans": [ + { + "bbox": [ + 472, + 249, + 536, + 260 + ], + "type": "text", + "content": "(e) ST-Adapter [50]" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 261, + 546, + 296 + ], + "lines": [ + { + "bbox": [ + 305, + 261, + 546, + 296 + ], + "spans": [ + { + "bbox": [ + 305, + 261, + 546, + 296 + ], + "type": "text", + "content": "Figure 2. Baselines for image-to-video transfer learning. (a) Visual Prompt Tuning [35]; (b) Parallel adapter and (c) serial adapter [11]; (d) Pro-Tuning [49]; and (e) ST-Adapter [50]." + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 310, + 546, + 393 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 310, + 546, + 393 + ], + "spans": [ + { + "bbox": [ + 305, + 310, + 546, + 393 + ], + "type": "text", + "content": "blocks [11] and prompt prediction blocks [49]. Only the ST-adapter [50] has proposed image-to-video transfer learning. In this section, we describe baselines for image-to-video transfer learning in detail. For brevity, we leave out the subscripts in Eq. 2 and arouse them as needed. In addition, we represent the learnable and frozen parameters in red and blue colors, respectively." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 305, + 394, + 546, + 442 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 394, + 546, + 442 + ], + "spans": [ + { + "bbox": [ + 305, + 394, + 546, + 442 + ], + "type": "text", + "content": "Visual prompt tuning (VPT) [35] prepends " + }, + { + "bbox": [ + 305, + 394, + 546, + 442 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 305, + 394, + 546, + 442 + ], + "type": "text", + "content": " trainable prompt tokens to the input space of every transformer block1 while keeping pretrained parameters frozen. The input tokens for each transformer block can be written as:" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 400, + 449, + 546, + 465 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 400, + 449, + 546, + 465 + ], + "spans": [ + { + "bbox": [ + 400, + 449, + 546, + 465 + ], + "type": "interline_equation", + "content": "\\tilde {\\mathbf {h}} = [ \\mathbf {e}; \\mathbf {h} ], \\tag {3}", + "image_path": "d98aa2d27d7d40886c55d600a0bcf80cde4f75f8495701f90f6880db549bd9d7.jpg" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 305, + 471, + 545, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 471, + 545, + 496 + ], + "spans": [ + { + "bbox": [ + 305, + 471, + 545, + 496 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 471, + 545, + 496 + ], + "type": "inline_equation", + "content": "\\mathbf{e} \\in \\mathbb{R}^{K \\times d}" + }, + { + "bbox": [ + 305, + 471, + 545, + 496 + ], + "type": "text", + "content": " is a set of trainable visual prompt tokens and " + }, + { + "bbox": [ + 305, + 471, + 545, + 496 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 305, + 471, + 545, + 496 + ], + "type": "text", + "content": " is a channel dimension of the original token." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 305, + 496, + 546, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 496, + 546, + 567 + ], + "spans": [ + { + "bbox": [ + 305, + 496, + 546, + 567 + ], + "type": "text", + "content": "AdaptFormer [11] learns a trainable bottleneck module [26, 31]. The intermediate feature " + }, + { + "bbox": [ + 305, + 496, + 546, + 567 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 305, + 496, + 546, + 567 + ], + "type": "text", + "content": " in Eq. 2 of each transformer block is fed into the AdapterMLP that consists of the original MLP layers and a bottleneck structure (parallel adapter in Fig. 2b). The output of the AdaptFormer block can be formulated by:" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 358, + 575, + 545, + 596 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 575, + 545, + 596 + ], + "spans": [ + { + "bbox": [ + 358, + 575, + 545, + 596 + ], + "type": "interline_equation", + "content": "\\tilde {\\mathbf {z}} = \\sigma (\\underset {\\sim} {\\mathrm {L N}} (\\mathbf {z}) \\cdot \\mathbf {W} _ {\\text {d o w n}}) \\cdot \\mathbf {W} _ {\\text {u p}}, \\tag {4}", + "image_path": "4b524b7e292d78c3629dec0705962dcd57959c2a586dcc5cc12850e31f53c575.jpg" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 359, + 592, + 487, + 606 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 592, + 487, + 606 + ], + "spans": [ + { + "bbox": [ + 359, + 592, + 487, + 606 + ], + "type": "interline_equation", + "content": "\\mathbf {h} = \\mathbf {z} + \\operatorname {M L P} (\\operatorname {L N} (\\mathbf {z})) + s \\cdot \\tilde {\\mathbf {z}},", + "image_path": "8dc839d8d26b0fa1d827189140155175ecbaaa4cd87e78e3b4231dfe5bf8fcaa.jpg" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 305, + 615, + 546, + 650 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 615, + 546, + 650 + ], + "spans": [ + { + "bbox": [ + 305, + 615, + 546, + 650 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 615, + 546, + 650 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_{\\mathrm{down}}" + }, + { + "bbox": [ + 305, + 615, + 546, + 650 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 615, + 546, + 650 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_{\\mathrm{up}}" + }, + { + "bbox": [ + 305, + 615, + 546, + 650 + ], + "type": "text", + "content": " are trainable down- and up-projection matrices, " + }, + { + "bbox": [ + 305, + 615, + 546, + 650 + ], + "type": "inline_equation", + "content": "\\sigma(\\cdot)" + }, + { + "bbox": [ + 305, + 615, + 546, + 650 + ], + "type": "text", + "content": " is an activation function, and " + }, + { + "bbox": [ + 305, + 615, + 546, + 650 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 305, + 615, + 546, + 650 + ], + "type": "text", + "content": " is a scaling factor." + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 305, + 652, + 546, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 652, + 546, + 676 + ], + "spans": [ + { + "bbox": [ + 305, + 652, + 546, + 676 + ], + "type": "text", + "content": "Pro-tuning [49] predicts task-specific vision prompts " + }, + { + "bbox": [ + 305, + 652, + 546, + 676 + ], + "type": "inline_equation", + "content": "\\mathbf{v}" + }, + { + "bbox": [ + 305, + 652, + 546, + 676 + ], + "type": "text", + "content": " from the output of each transformer block using consecu" + } + ] + } + ], + "index": 31 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 305, + 682, + 546, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 682, + 546, + 712 + ], + "spans": [ + { + "bbox": [ + 305, + 682, + 546, + 712 + ], + "type": "text", + "content": "1While the original work also presented a shallow version (VPT-Shallow) that inserts prompt tokens to the first layer, we explore a deep version (VPT-Deep) only." + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 279, + 739, + 298, + 747 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 739, + 298, + 747 + ], + "spans": [ + { + "bbox": [ + 279, + 739, + 298, + 747 + ], + "type": "text", + "content": "2205" + } + ] + } + ], + "index": 33 + } + ], + "page_size": [ + 595, + 841 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 71, + 402, + 246 + ], + "blocks": [ + { + "bbox": [ + 49, + 71, + 402, + 246 + ], + "lines": [ + { + "bbox": [ + 49, + 71, + 402, + 246 + ], + "spans": [ + { + "bbox": [ + 49, + 71, + 402, + 246 + ], + "type": "image", + "image_path": "ece0194475dd68a2c943119364e9ee270bed0a86e9773dd04f6ef0063104074d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 247, + 546, + 280 + ], + "lines": [ + { + "bbox": [ + 46, + 247, + 546, + 280 + ], + "spans": [ + { + "bbox": [ + 46, + 247, + 546, + 280 + ], + "type": "text", + "content": "Figure 3. Overall architecture of DUALPATH. The pretrained image transformer takes a grid-like frameset and " + }, + { + "bbox": [ + 46, + 247, + 546, + 280 + ], + "type": "inline_equation", + "content": "T_{s}" + }, + { + "bbox": [ + 46, + 247, + 546, + 280 + ], + "type": "text", + "content": " frames as inputs. We learn the temporal and spatial contexts separately through two distinct paths. During training, we only update newly introduced adapters and the classifier while freezing the pretrained layers." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 407, + 75, + 545, + 245 + ], + "blocks": [ + { + "bbox": [ + 407, + 75, + 545, + 245 + ], + "lines": [ + { + "bbox": [ + 407, + 75, + 545, + 245 + ], + "spans": [ + { + "bbox": [ + 407, + 75, + 545, + 245 + ], + "type": "image", + "image_path": "089ae6f20f80879fbcb7d6e8cd3ad8fcd95a2af7e7d446706ba3be347d7fe3fe.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 295, + 286, + 332 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 295, + 286, + 332 + ], + "spans": [ + { + "bbox": [ + 47, + 295, + 286, + 332 + ], + "type": "text", + "content": "tive 2D convolution layers. The output of each block is reshaped as " + }, + { + "bbox": [ + 47, + 295, + 286, + 332 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{P\\times P\\times C}" + }, + { + "bbox": [ + 47, + 295, + 286, + 332 + ], + "type": "text", + "content": " to apply 2D convolutions and the final representation is derived by adding " + }, + { + "bbox": [ + 47, + 295, + 286, + 332 + ], + "type": "inline_equation", + "content": "\\mathbf{v}" + }, + { + "bbox": [ + 47, + 295, + 286, + 332 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 295, + 286, + 332 + ], + "type": "inline_equation", + "content": "\\mathbf{h}" + }, + { + "bbox": [ + 47, + 295, + 286, + 332 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 70, + 337, + 286, + 358 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 337, + 286, + 358 + ], + "spans": [ + { + "bbox": [ + 70, + 337, + 286, + 358 + ], + "type": "interline_equation", + "content": "\\mathbf {v} = \\operatorname {R e s h a p e} \\left(\\sigma (\\underset {\\sim} {\\operatorname {C o n v 2 d}} (\\operatorname {R e s h a p e} (\\mathbf {h})))\\right), \\tag {5}", + "image_path": "dc964e84db3fbe085e4c0b82fbbca81fa38dc07ea13800974a7df9510f05bdf5.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 141, + 354, + 190, + 366 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 354, + 190, + 366 + ], + "spans": [ + { + "bbox": [ + 141, + 354, + 190, + 366 + ], + "type": "interline_equation", + "content": "\\tilde {\\mathbf {h}} = \\mathbf {h} + \\mathbf {v},", + "image_path": "467646f43a69155a24880f88dcadf49f3c634573390b22c87225953874f5ae78.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 375, + 287, + 470 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 375, + 287, + 470 + ], + "spans": [ + { + "bbox": [ + 47, + 375, + 287, + 470 + ], + "type": "text", + "content": "where Conv2D consists of " + }, + { + "bbox": [ + 47, + 375, + 287, + 470 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 47, + 375, + 287, + 470 + ], + "type": "text", + "content": " convolution layer followed by " + }, + { + "bbox": [ + 47, + 375, + 287, + 470 + ], + "type": "inline_equation", + "content": "5 \\times 5" + }, + { + "bbox": [ + 47, + 375, + 287, + 470 + ], + "type": "text", + "content": " depth-wise convolution [14] and " + }, + { + "bbox": [ + 47, + 375, + 287, + 470 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 47, + 375, + 287, + 470 + ], + "type": "text", + "content": " convolution. ST-adapter [50] inserts a depth-wise 3D convolution layer between the down-projection layer and the activation function of the adapter. Different from the conventional adapters (e.g. AdaptFormer [11]), the ST-adapter takes tokens for all frames to enable the model to capture temporality in videos. The output of the ST-adapter can be represented as:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 122, + 476, + 183, + 491 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 122, + 476, + 183, + 491 + ], + "spans": [ + { + "bbox": [ + 122, + 476, + 183, + 491 + ], + "type": "interline_equation", + "content": "\\bar {\\mathbf {z}} _ {t} = \\overline {{\\mathrm {L N}}} (\\mathbf {z} _ {t}),", + "image_path": "3cb7186a014d3b42a5282c20bb87a15545cbdb3f09a63199c456a1f2f166af91.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 48, + 491, + 286, + 532 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 491, + 286, + 532 + ], + "spans": [ + { + "bbox": [ + 48, + 491, + 286, + 532 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\hat {\\mathbf {z}} = \\sigma (\\text {D - C o n v 3 d} ([ \\tilde {\\mathbf {z}} _ {1} \\cdot \\mathbf {W} _ {\\text {d o w n}}, \\dots , \\tilde {\\mathbf {z}} _ {T} \\cdot \\mathbf {W} _ {\\text {d o w n}} ])) \\cdot \\mathbf {W} _ {\\text {u p}}, \\\\ \\mathbf {h} _ {t} = \\mathbf {z} _ {t} + \\underline {{\\mathrm {M L P}}} (\\tilde {\\mathbf {z}} _ {t}) + s \\cdot \\hat {\\mathbf {z}} _ {t}, \\tag {6} \\\\ \\end{array}", + "image_path": "221c34a7efe4113d15ea03c826f6d91deebc4db0125dc980a5d172f0b5e8a2d8.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 533, + 286, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 533, + 286, + 568 + ], + "spans": [ + { + "bbox": [ + 47, + 533, + 286, + 568 + ], + "type": "text", + "content": "where D-Conv3d denotes the depth-wise 3D convolution layer. Note that the same down-projection matrix " + }, + { + "bbox": [ + 47, + 533, + 286, + 568 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_{\\mathrm{down}}" + }, + { + "bbox": [ + 47, + 533, + 286, + 568 + ], + "type": "text", + "content": " is applied to all tokens regardless of the frame index " + }, + { + "bbox": [ + 47, + 533, + 286, + 568 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 533, + 286, + 568 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 568, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 568, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 47, + 568, + 287, + 653 + ], + "type": "text", + "content": "We emphasize that most of the baselines [11,35,49] have not concerned with temporal modeling. Even though ST-Adapter [50] has employed depth-wise 3D convolution layers between linear projections, it results in high computational cost. To entirely leverage a simple and efficient architecture of the adapter [11], we incorporate the dual-path design into the pretrained image transformers." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 661, + 102, + 673 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 661, + 102, + 673 + ], + "spans": [ + { + "bbox": [ + 47, + 661, + 102, + 673 + ], + "type": "text", + "content": "4. Method" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": "The dual-path design (also called two-stream) is well-known architecture in CNN-based models for video recognition [10, 21, 60]. They have commonly used an optical" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 295, + 546, + 427 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 295, + 546, + 427 + ], + "spans": [ + { + "bbox": [ + 304, + 295, + 546, + 427 + ], + "type": "text", + "content": "flow [10, 60] or multiple frames with a high temporal resolution [21] to capture rapidly changing motion. Despite the effectiveness of dual-path architecture, it has yet to be explored with the transformer due to high computational costs. In this work, we propose a novel PETL method, called DUALPATH, comprised of spatial and temporal path adaptation. To the best of our knowledge, our DUALPATH is the first attempt to explicitly build the two-stream architecture upon the transformer while maintaining the computational cost similar to the single-stream architecture. The overall framework is depicted in Fig. 3." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 430, + 414, + 443 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 430, + 414, + 443 + ], + "spans": [ + { + "bbox": [ + 305, + 430, + 414, + 443 + ], + "type": "text", + "content": "4.1. Spatial adaptation" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 444, + 546, + 576 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 444, + 546, + 576 + ], + "spans": [ + { + "bbox": [ + 304, + 444, + 546, + 576 + ], + "type": "text", + "content": "Since the image foundation models have been trained on large amounts of web datasets, we can intuitively speculate that they might be powerful to encode the spatial context even in videos. In order to make the outstanding ability of spatial modeling to be more suitable for video understanding with a slight parameter tuning, we adopt two parallel adapters for MHA and MLP in each transformer block. The parallel adapters allow the model to learn the spatial context for action recognition from the appearance of target video data while maintaining the original contexts for object recognition." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 576, + 546, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 576, + 546, + 653 + ], + "spans": [ + { + "bbox": [ + 305, + 576, + 546, + 653 + ], + "type": "text", + "content": "Specifically, we sample " + }, + { + "bbox": [ + 305, + 576, + 546, + 653 + ], + "type": "inline_equation", + "content": "T_{S}" + }, + { + "bbox": [ + 305, + 576, + 546, + 653 + ], + "type": "text", + "content": " frames from a video and tokenize each frame. Similar to Eq. 1, the set of spatial tokens " + }, + { + "bbox": [ + 305, + 576, + 546, + 653 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_t^{\\mathrm{SP}}" + }, + { + "bbox": [ + 305, + 576, + 546, + 653 + ], + "type": "text", + "content": " includes the learnable positional encodings " + }, + { + "bbox": [ + 305, + 576, + 546, + 653 + ], + "type": "inline_equation", + "content": "\\mathbf{p}^{\\mathrm{SP}}" + }, + { + "bbox": [ + 305, + 576, + 546, + 653 + ], + "type": "text", + "content": " and the spatial class token " + }, + { + "bbox": [ + 305, + 576, + 546, + 653 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t^{\\mathrm{SP}}\\{[\\mathrm{CLS}]\\}" + }, + { + "bbox": [ + 305, + 576, + 546, + 653 + ], + "type": "text", + "content": ". The spatial adaptation in the " + }, + { + "bbox": [ + 305, + 576, + 546, + 653 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 305, + 576, + 546, + 653 + ], + "type": "text", + "content": "-th transformer block can be formulated by the following equations:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 660, + 545, + 699 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 660, + 545, + 699 + ], + "spans": [ + { + "bbox": [ + 313, + 660, + 545, + 699 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathbf {z} _ {l} ^ {\\mathrm {S P}} = \\mathbf {h} _ {l - 1} ^ {\\mathrm {S P}} + \\mathrm {M H A} (\\mathrm {L N} (\\mathbf {h} _ {l - 1} ^ {\\mathrm {S P}})) + \\text {A d a p t e r} (\\mathrm {L N} (\\mathbf {h} _ {l - 1} ^ {\\mathrm {S P}})), \\\\ \\mathbf {h} _ {l} ^ {\\mathrm {S P}} = \\mathbf {z} _ {l} ^ {\\mathrm {S P}} + \\underline {{\\operatorname {M L P}}} (\\underline {{\\operatorname {L N}}} (\\mathbf {z} _ {l} ^ {\\mathrm {S P}})) + \\underline {{\\operatorname {A d p a t e r}}} (\\underline {{\\operatorname {L N}}} (\\mathbf {z} _ {l} ^ {\\mathrm {S P}})), \\tag {7} \\\\ \\end{array}", + "image_path": "b52d10fe687dfd5bc2b2c0bd9f3c9c8b69262b2b91f7ba7f16f8bceea3535cf0.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 699, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 699, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 699, + 545, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 699, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{h}_0^{\\mathrm{SP}} = [\\mathbf{x}_t^{\\mathrm{SP}}\\{\\mathrm{[CLS]}\\} ,\\mathbf{X}_t^{\\mathrm{SP}}] + \\mathbf{p}^{\\mathrm{SP}}" + }, + { + "bbox": [ + 305, + 699, + 545, + 714 + ], + "type": "text", + "content": " .We average" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 738, + 298, + 747 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 738, + 298, + 747 + ], + "spans": [ + { + "bbox": [ + 279, + 738, + 298, + 747 + ], + "type": "text", + "content": "2206" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 595, + 841 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 109 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 109 + ], + "type": "text", + "content": "the set of the spatial [CLS] tokens from the final transformer block to obtain a global spatial representation " + }, + { + "bbox": [ + 47, + 72, + 289, + 109 + ], + "type": "inline_equation", + "content": "\\mathbf{y}^{\\mathrm{SP}}" + }, + { + "bbox": [ + 47, + 72, + 289, + 109 + ], + "type": "text", + "content": ", such that," + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 115, + 287, + 147 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 115, + 287, + 147 + ], + "spans": [ + { + "bbox": [ + 106, + 115, + 287, + 147 + ], + "type": "interline_equation", + "content": "\\mathbf {y} ^ {\\mathrm {S P}} = \\frac {1}{T _ {S}} \\sum_ {t = 1} ^ {T _ {S}} \\mathbf {x} _ {t} ^ {\\mathrm {S P}} \\left\\{\\left[ \\mathrm {C L S} \\right] \\right\\}. \\tag {8}", + "image_path": "7b0154c0e355f3fcbaaf5a9b08774f729b368a050413bd6e20a7e8717bfbdd9b.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 154, + 288, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 154, + 288, + 215 + ], + "spans": [ + { + "bbox": [ + 47, + 154, + 288, + 215 + ], + "type": "text", + "content": "Recent methods have discussed that a high frame rate only increases the computation volume and is unnecessary to understand the semantics of appearance [9, 21]. We thus sparsely sample " + }, + { + "bbox": [ + 47, + 154, + 288, + 215 + ], + "type": "inline_equation", + "content": "T_{S}" + }, + { + "bbox": [ + 47, + 154, + 288, + 215 + ], + "type": "text", + "content": " frames with a low frame rate (e.g. 8 frames per clip)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 221, + 169, + 233 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 221, + 169, + 233 + ], + "spans": [ + { + "bbox": [ + 47, + 221, + 169, + 233 + ], + "type": "text", + "content": "4.2. Temporal adaptation" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 234, + 288, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 234, + 288, + 413 + ], + "spans": [ + { + "bbox": [ + 46, + 234, + 288, + 413 + ], + "type": "text", + "content": "While spatial adaptation enables the models to take the spatial contexts in video data, the image models are still incapable of modeling the temporal dynamics. The key component that allows video transformers to model the solid temporal context is to learn relationships between local patches across frames in the video [1, 7]. To make image models capable of effectively establishing this component, we suggest a novel grid-like frameset transform technique that aggregates multiple frames into a unified grid-like frameset. Our grid-like frameset design is inspired by recent visual prompting research [4, 5]. It is simple yet surprisingly effective in imitating temporal modeling as spatial modeling and certainly reduces the computation. In each transformer block, we adopt two additional serial adapters for MHA and MLP, respectively." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 413, + 287, + 631 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 413, + 287, + 631 + ], + "spans": [ + { + "bbox": [ + 46, + 413, + 287, + 631 + ], + "type": "text", + "content": "More concretely, we sample " + }, + { + "bbox": [ + 46, + 413, + 287, + 631 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 413, + 287, + 631 + ], + "type": "text", + "content": " frames from a video and scale them with factors of " + }, + { + "bbox": [ + 46, + 413, + 287, + 631 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 46, + 413, + 287, + 631 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 413, + 287, + 631 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 46, + 413, + 287, + 631 + ], + "type": "text", + "content": ", such that the scaled frame size is " + }, + { + "bbox": [ + 46, + 413, + 287, + 631 + ], + "type": "inline_equation", + "content": "[W / w \\times H / h \\times 3]" + }, + { + "bbox": [ + 46, + 413, + 287, + 631 + ], + "type": "text", + "content": ". We stack " + }, + { + "bbox": [ + 46, + 413, + 287, + 631 + ], + "type": "inline_equation", + "content": "w \\times h" + }, + { + "bbox": [ + 46, + 413, + 287, + 631 + ], + "type": "text", + "content": " scaled frames according to temporal ordering and reshape a stacked frame to construct a set of frames in a grid form of the same size as the original frame (i.e., " + }, + { + "bbox": [ + 46, + 413, + 287, + 631 + ], + "type": "inline_equation", + "content": "[W \\times H \\times 3]" + }, + { + "bbox": [ + 46, + 413, + 287, + 631 + ], + "type": "text", + "content": "). Note that the total number of grid-like framesets is " + }, + { + "bbox": [ + 46, + 413, + 287, + 631 + ], + "type": "inline_equation", + "content": "T_{G} = T / wh" + }, + { + "bbox": [ + 46, + 413, + 287, + 631 + ], + "type": "text", + "content": ". The set of temporal tokens " + }, + { + "bbox": [ + 46, + 413, + 287, + 631 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_{g}^{\\mathrm{TP}}" + }, + { + "bbox": [ + 46, + 413, + 287, + 631 + ], + "type": "text", + "content": " for the " + }, + { + "bbox": [ + 46, + 413, + 287, + 631 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 46, + 413, + 287, + 631 + ], + "type": "text", + "content": "-th frameset is obtained in the same way in Eq. 1 and combined with the learnable temporal class token " + }, + { + "bbox": [ + 46, + 413, + 287, + 631 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{g}^{\\mathrm{TP}}\\left\\{\\left[\\mathrm{CLS}\\right]\\right\\}" + }, + { + "bbox": [ + 46, + 413, + 287, + 631 + ], + "type": "text", + "content": ". Unlike the spatial adaptation, we use fixed 3D positional encodings [70], " + }, + { + "bbox": [ + 46, + 413, + 287, + 631 + ], + "type": "inline_equation", + "content": "\\mathbf{p}^{\\mathrm{TP}}" + }, + { + "bbox": [ + 46, + 413, + 287, + 631 + ], + "type": "text", + "content": ", to the tokens to take the absolute temporal order and spatial positions of patches into account. The input transformation allows transformers to observe multiple frames at the same level. In experiments, we mainly construct a grid-like frameset from 16 original frames (i.e., scaling factors " + }, + { + "bbox": [ + 46, + 413, + 287, + 631 + ], + "type": "inline_equation", + "content": "w = h = 4" + }, + { + "bbox": [ + 46, + 413, + 287, + 631 + ], + "type": "text", + "content": ") to take the computational efficiency and promising performance." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 631, + 288, + 678 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 631, + 288, + 678 + ], + "spans": [ + { + "bbox": [ + 47, + 631, + 288, + 678 + ], + "type": "text", + "content": "Whereas the parallel adapter is used in the spatial path, we sequentially append adapters to the top of MHA and MLP layers in each transformer block. Formally, temporal adaptation in the " + }, + { + "bbox": [ + 47, + 631, + 288, + 678 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 47, + 631, + 288, + 678 + ], + "type": "text", + "content": "-th block can be described as:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 71, + 683, + 287, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 71, + 683, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 71, + 683, + 287, + 715 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathbf {z} _ {l} ^ {\\mathrm {T P}} = \\mathbf {h} _ {l - 1} ^ {\\mathrm {T P}} + \\text {A d a p t e r} (\\underset {\\leftarrow} {\\mathrm {M H A}} (\\underset {\\leftarrow} {\\mathrm {L N}} (\\mathbf {h} _ {l - 1} ^ {\\mathrm {T P}}))), \\tag {9} \\\\ \\mathbf {h} _ {l} ^ {\\mathrm {T P}} = \\mathbf {z} _ {l} ^ {\\mathrm {T P}} + \\text {A d p a t e r} (\\operatorname {M L P} (\\operatorname {L N} (\\mathbf {z} _ {l} ^ {\\mathrm {T P}}))), \\\\ \\end{array}", + "image_path": "2c057cb7d7e971f0c96f977d9326278a13906d8a29021601f272fa2178fe1721.jpg" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 313, + 70, + 423, + 179 + ], + "blocks": [ + { + "bbox": [ + 313, + 70, + 423, + 179 + ], + "lines": [ + { + "bbox": [ + 313, + 70, + 423, + 179 + ], + "spans": [ + { + "bbox": [ + 313, + 70, + 423, + 179 + ], + "type": "image", + "image_path": "903993652c334d6437281a7d27c13c59eff87e58efdcfba736578e3e0212a7ea.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 330, + 181, + 406, + 190 + ], + "lines": [ + { + "bbox": [ + 330, + 181, + 406, + 190 + ], + "spans": [ + { + "bbox": [ + 330, + 181, + 406, + 190 + ], + "type": "text", + "content": "(a) DUALPATH w/o TA" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 194, + 546, + 227 + ], + "lines": [ + { + "bbox": [ + 305, + 194, + 546, + 227 + ], + "spans": [ + { + "bbox": [ + 305, + 194, + 546, + 227 + ], + "type": "text", + "content": "Figure 4. Visualization of attention maps (a) without temporal adaptation (TA) and (b) with temporal adaptation for the action 'Spinning [something] that quickly stops spinning' in SSv2 [23]." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 429, + 69, + 539, + 179 + ], + "blocks": [ + { + "bbox": [ + 429, + 69, + 539, + 179 + ], + "lines": [ + { + "bbox": [ + 429, + 69, + 539, + 179 + ], + "spans": [ + { + "bbox": [ + 429, + 69, + 539, + 179 + ], + "type": "image", + "image_path": "4ea058028768dba022c0198589b5fbbfaec44a6cb273f5a1ab51662417053759.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 448, + 180, + 520, + 190 + ], + "lines": [ + { + "bbox": [ + 448, + 180, + 520, + 190 + ], + "spans": [ + { + "bbox": [ + 448, + 180, + 520, + 190 + ], + "type": "text", + "content": "(b) DUALPATH w/ TA" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 242, + 546, + 295 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 242, + 546, + 295 + ], + "spans": [ + { + "bbox": [ + 305, + 242, + 546, + 295 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 242, + 546, + 295 + ], + "type": "inline_equation", + "content": "\\mathbf{h}_0^{\\mathrm{TP}} = [\\mathbf{x}_g^{\\mathrm{TP}}\\{\\mathrm{[CLS]}\\} ,\\mathbf{X}_g^{\\mathrm{TP}}] + \\mathbf{p}^{\\mathrm{TP}}" + }, + { + "bbox": [ + 305, + 242, + 546, + 295 + ], + "type": "text", + "content": " . Similar to spatial adaptation, a global temporal representation " + }, + { + "bbox": [ + 305, + 242, + 546, + 295 + ], + "type": "inline_equation", + "content": "\\mathbf{y}^{\\mathrm{TP}}" + }, + { + "bbox": [ + 305, + 242, + 546, + 295 + ], + "type": "text", + "content": " can be derived by averaging the set of the temporal [CLS] tokens from the final transformer block, i.e.," + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 364, + 304, + 546, + 338 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 304, + 546, + 338 + ], + "spans": [ + { + "bbox": [ + 364, + 304, + 546, + 338 + ], + "type": "interline_equation", + "content": "\\mathbf {y} ^ {\\mathrm {T P}} = \\frac {1}{T _ {G}} \\sum_ {g = 1} ^ {T _ {G}} \\mathbf {x} _ {g} ^ {\\mathrm {T P}} \\{[ \\mathrm {C L S} ] \\}. \\tag {10}", + "image_path": "c6e4dafbd700deb99c42a0946c5ab745caaf8022317e6c12383069f49b5f7dd2.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 349, + 546, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 349, + 546, + 384 + ], + "spans": [ + { + "bbox": [ + 305, + 349, + 546, + 384 + ], + "type": "text", + "content": "For the final prediction, we concatenate the global spatial and temporal representations and feed them into the classifier with GeLU activation [29] between two FC layers." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 394, + 546, + 417 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 394, + 546, + 417 + ], + "spans": [ + { + "bbox": [ + 305, + 394, + 546, + 417 + ], + "type": "text", + "content": "4.3. Does a grid-like frameset really help to encode temporal context?" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 420, + 546, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 420, + 546, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 420, + 546, + 624 + ], + "type": "text", + "content": "This work presents a new standpoint to perform video action recognition with the pretrained image transformer by transforming multiple frames into a unified grid-like frame-set. However, it is still questionable whether the temporal path of DUALPATH can really capture the temporal context of videos. In this section, we provide some qualitative examples of the attention map. To validate the ability of precise temporal modeling, we sample videos from the SSv2 [23] dataset. Following [50], we depict the attention map of " + }, + { + "bbox": [ + 304, + 420, + 546, + 624 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_g^{\\mathrm{TP}}\\{[\\mathrm{CLS}]\\}" + }, + { + "bbox": [ + 304, + 420, + 546, + 624 + ], + "type": "text", + "content": " from the final transformer block of the temporal path. As shown in Fig. 4, the model with the temporal adaptation (TA) of DUALPATH tends to concentrate on action-related regions, contrary to the model without TA that focuses on the irrelevant background. This result suggests that the temporal adaptation of DUALPATH strengthens the temporal modeling ability of the image model. More examples are shown in Fig. A1 of Appendix." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 636, + 381, + 650 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 636, + 381, + 650 + ], + "spans": [ + { + "bbox": [ + 305, + 636, + 381, + 650 + ], + "type": "text", + "content": "5. Experiment" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 653, + 408, + 666 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 653, + 408, + 666 + ], + "spans": [ + { + "bbox": [ + 305, + 653, + 408, + 666 + ], + "type": "text", + "content": "5.1. Evaluation setup" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 667, + 546, + 716 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 667, + 546, + 716 + ], + "spans": [ + { + "bbox": [ + 305, + 667, + 546, + 716 + ], + "type": "text", + "content": "Datasets. We evaluate the proposed method on four standard action recognition datasets, including the Kinetics-400 (K400) [38], HMDB51 [39], Something-something-v2 (SSv2) [23], and Diving-48 [42]." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 738, + 298, + 747 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 738, + 298, + 747 + ], + "spans": [ + { + "bbox": [ + 279, + 738, + 298, + 747 + ], + "type": "text", + "content": "2207" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 595, + 841 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 86, + 69, + 508, + 296 + ], + "blocks": [ + { + "bbox": [ + 86, + 69, + 508, + 296 + ], + "lines": [ + { + "bbox": [ + 86, + 69, + 508, + 296 + ], + "spans": [ + { + "bbox": [ + 86, + 69, + 508, + 296 + ], + "type": "table", + "html": "
Method & Arch.PretrainModel # ParamsTrainable # ParamsGFLOPsR@1R@5Views
Full-tuning
SlowFast+NL [21]-60M60M702079.893.916×3×10
MViT-B [18]-37M37M409581.295.164×3×3
UniFormer-B [40]IN-1K50M50M310883.095.432×4×3
TimeSformer-L [7]IN-21K121M121M714080.794.764×1×3
ViViT-L/16×2 FE [1]IN-1K311M311M398080.692.732×1×1
VideoSwin-L [47]IN-21K197M197M724883.195.932×4×3
MViTv2-L [43]IN-21K218M218M4242086.197.032×3×5
MTV-L [76]JFT876M876M1805084.396.332×4×3
TokenLearner-L/10 [57]JFT450M450M4891285.496.364×4×3
ActionCLIP [68]CLIP142M142M1689083.897.132×10×3
X-CLIP-L/14 [48]CLIP420M420M789087.197.68×4×3
Parameter Efficient Tuning
EVL [45] w/ ViT-L/14CLIP368M59M808887.3-32×3×1
ST-Adapter [50] w/ ViT-B/16CLIP93M7M182182.796.232×3×1
DUALPATH w/ ViT-B/16CLIP96M10M71085.497.132×3×1
DUALPATH w/ ViT-L/14CLIP330M27M186887.797.832×3×1
", + "image_path": "38bbd82649b5ca95ba0136f7aa1ca208126f7c458b69a7bfb187fa8f6b1b53ac.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 300, + 545, + 311 + ], + "lines": [ + { + "bbox": [ + 47, + 300, + 545, + 311 + ], + "spans": [ + { + "bbox": [ + 47, + 300, + 545, + 311 + ], + "type": "text", + "content": "Table 1. Performance comparisons for action recognition on the Kinetics-400 [38] dataset. Note that Views = #frames × #clips × #spatial." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 59, + 326, + 286, + 593 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 59, + 326, + 286, + 398 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 326, + 286, + 398 + ], + "spans": [ + { + "bbox": [ + 59, + 326, + 286, + 398 + ], + "type": "text", + "content": "- Kinetics-400 (K400) contains about 240K training videos and 20K validation videos for 400 human action categories. Each video is trimmed to have a length of 10 seconds. While the K400 dataset provides a wide range of categories, they are known to be highly biased in spatial appearance [59]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 403, + 286, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 403, + 286, + 450 + ], + "spans": [ + { + "bbox": [ + 59, + 403, + 286, + 450 + ], + "type": "text", + "content": "- Somthing-something-v2 (SSv2) is a more challenging dataset since they require strong temporal modeling [59]. They contain about 168.9K training videos and 24.7K validation videos for 174 classes." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 59, + 456, + 286, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 456, + 286, + 515 + ], + "spans": [ + { + "bbox": [ + 59, + 456, + 286, + 515 + ], + "type": "text", + "content": "- HMDB51 is a small dataset that provides about 7K videos of 51 action categories. We use all three splits, each split of which consists of 3570 and 1530 videos for training and evaluation, respectively. We report the average accuracy for three splits." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 59, + 521, + 286, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 521, + 286, + 593 + ], + "spans": [ + { + "bbox": [ + 59, + 521, + 286, + 593 + ], + "type": "text", + "content": "- Diving-48 is a fine-grained diving action dataset. We use train-test split v2 that contains about 15K training videos and 2K validation videos of 48 diving actions. Since the action can not be determined by only the static representations (e.g. objects or background), stronger temporal modeling is required for this dataset." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 597, + 286, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 597, + 286, + 634 + ], + "spans": [ + { + "bbox": [ + 47, + 597, + 286, + 634 + ], + "type": "text", + "content": "Pretrained image backbone. We employ CLIP pretrained ViT-B/16 and ViT-L/14 as backbones. The results with Swin-B [46] are provided in Tab. A2 of the Appendix." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 59, + 638, + 286, + 715 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 59, + 638, + 286, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 638, + 286, + 674 + ], + "spans": [ + { + "bbox": [ + 59, + 638, + 286, + 674 + ], + "type": "text", + "content": "- ViT-B/16 [17] consists of 12 transformer blocks with 86M parameters and takes patches of size " + }, + { + "bbox": [ + 59, + 638, + 286, + 674 + ], + "type": "inline_equation", + "content": "16 \\times 16" + }, + { + "bbox": [ + 59, + 638, + 286, + 674 + ], + "type": "text", + "content": " as inputs." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 59, + 679, + 286, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 679, + 286, + 715 + ], + "spans": [ + { + "bbox": [ + 59, + 679, + 286, + 715 + ], + "type": "text", + "content": "- ViT-L/14 [17], a larger model than ViT-B/16, contains 24 transformer blocks with 303M parameters. It takes " + }, + { + "bbox": [ + 59, + 679, + 286, + 715 + ], + "type": "inline_equation", + "content": "14 \\times 14" + }, + { + "bbox": [ + 59, + 679, + 286, + 715 + ], + "type": "text", + "content": " patches as inputs." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 305, + 326, + 546, + 458 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 326, + 546, + 458 + ], + "spans": [ + { + "bbox": [ + 305, + 326, + 546, + 458 + ], + "type": "text", + "content": "Implementation details. For the K400, HMDB51, and Diving-48 datasets, we uniformly sample 8 frames (i.e., " + }, + { + "bbox": [ + 305, + 326, + 546, + 458 + ], + "type": "inline_equation", + "content": "T_{s} = 8" + }, + { + "bbox": [ + 305, + 326, + 546, + 458 + ], + "type": "text", + "content": ") with the sampling interval 8 in the spatial path. In the temporal path, we uniformly sample 16, 32, and 48 frames with the sampling intervals 4, 2, and 1 to construct 1, 2, and 3 grid-like framesets (i.e., " + }, + { + "bbox": [ + 305, + 326, + 546, + 458 + ], + "type": "inline_equation", + "content": "T_{g} = 1,2,3" + }, + { + "bbox": [ + 305, + 326, + 546, + 458 + ], + "type": "text", + "content": "), respectively. For the SSv2 dataset, we sample the same number of frames as in other datasets, but with a dynamic sampling interval to cover the whole video. Note that the frames for the spatial path are the subset of the temporal path frames. Please refer to more implementation details in Appendix A." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 469, + 483, + 481 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 469, + 483, + 481 + ], + "spans": [ + { + "bbox": [ + 305, + 469, + 483, + 481 + ], + "type": "text", + "content": "5.2. Comparison with state-of-the-art" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 484, + 546, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 484, + 546, + 568 + ], + "spans": [ + { + "bbox": [ + 305, + 484, + 546, + 568 + ], + "type": "text", + "content": "In this section, we compare the proposed method with baselines [11, 35, 49, 50] in Sec. 3 and state-of-the-art video transformers [1, 7, 18, 40, 43, 45, 47, 48, 57, 68, 76] to demonstrate the effectiveness of the proposed method on four video action recognition datasets. Note that the number of frames of the spatial adaptation path of DUALPATH is fixed to 8 for all experiments, i.e., " + }, + { + "bbox": [ + 305, + 484, + 546, + 568 + ], + "type": "inline_equation", + "content": "T_{S} = 8" + }, + { + "bbox": [ + 305, + 484, + 546, + 568 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 570, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 570, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 570, + 546, + 713 + ], + "type": "text", + "content": "Results on Kinetics-400. We report the results evaluated on K400 [38] in Tab. 1. We first compare the proposed method with state-of-the-art video models that are pretrained on the large-scale image dataset and fully finetuned on K400. In terms of memory and computational efficiency, video models require a huge number of parameters (" + }, + { + "bbox": [ + 305, + 570, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\sim" + }, + { + "bbox": [ + 305, + 570, + 546, + 713 + ], + "type": "text", + "content": "450M [57]) and computations (" + }, + { + "bbox": [ + 305, + 570, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\sim" + }, + { + "bbox": [ + 305, + 570, + 546, + 713 + ], + "type": "text", + "content": "48912 GFLOPs [57]). On the other hand, we require only 10M trainable parameters which are newly stored, and 710 GFLOPs for inference using 32 frames with ViT-B/16 [17] backbone. Compared to X-CLIP-L/14 [48] which leverages the additional text branch, our DUALPATH achieves state-of-the-art performance with ViT-L/14 back" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 739, + 298, + 747 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 739, + 298, + 747 + ], + "spans": [ + { + "bbox": [ + 279, + 739, + 298, + 747 + ], + "type": "text", + "content": "2208" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 595, + 841 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 73, + 70, + 520, + 383 + ], + "blocks": [ + { + "bbox": [ + 73, + 70, + 520, + 383 + ], + "lines": [ + { + "bbox": [ + 73, + 70, + 520, + 383 + ], + "spans": [ + { + "bbox": [ + 73, + 70, + 520, + 383 + ], + "type": "table", + "html": "
Method & Arch.PretrainModel\n#ParamsTrainable\n#ParamsGFLOPsR@1R@5Views
Full-tuning
Full-tuning ViT-B/16 [17]CLIP86M86M41944.077.08×1×3
Full-tuning ViT-L/14 [17]CLIP303M303M194148.777.58×1×3
TimeSformer-L [7]IN-21K121M121M714062.4-64×1×3
MTV-B [76]IN-21K310M310M479067.690.432×4×3
MViT-B [18]K40037M37M51067.190.832×1×3
MViTv2-B [43]K40051M51M67570.592.740×1×3
ViViT-L/16×2 [1]IN-21K/K400311M311M1189265.489.816×4×3
VideoSwin-B [47]IN-21K/K40089M89M96369.692.732×1×1
Omnivore [22]IN-21K/K400---71.493.532×1×3
MViTv2-B [43]IN-21K/K400213M213M848473.394.132×1×3
UniFormer-B [40]IN-21K/K60050M50M77771.292.832×1×3
Parameter Efficient Tuning
VideoPrompt* [37] w/ ViT-B/16CLIP92M6M53731.060.38×1×3
VPT [35] w/ ViT-B/16CLIP92M6M53736.261.18×1×3
AdaptFormer [11] w/ ViT-B/16CLIP94M8M54451.370.68×1×3
Pro-tuning [49] w/ ViT-B/16CLIP95M9M53850.869.98×1×3
EVL [45] w/ ViT-L/14CLIP484M175M964166.7-32×1×3
ST-Adapter [50] w/ ViT-B/16CLIP97M11M195569.592.632×3×1
DUALPATH w/ ViT-B/16CLIP99M13M64269.692.516×1×3
DUALPATH w/ ViT-B/16CLIP99M13M71670.392.932×1×3
DUALPATH w/ ViT-B/16CLIP99M13M79171.293.248×1×3
DUALPATH w/ ViT-L/14CLIP336M33M171370.292.716×1×3
DUALPATH w/ ViT-L/14CLIP336M33M193271.493.432×1×3
DUALPATH w/ ViT-L/14CLIP336M33M215172.293.748×1×3
", + "image_path": "2e6e2bddad645435d7d954fe18cdf5b0de5ccd6d1c5f0f8101dbe07a5c86dfea.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 424, + 286, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 424, + 286, + 471 + ], + "spans": [ + { + "bbox": [ + 47, + 424, + 286, + 471 + ], + "type": "text", + "content": "bone. The comparisons with parameter-efficient tuning methods [45, 50] show that our DUALPATH achieves higher performance while requiring much lower burdens in computations under the same conditions." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 473, + 287, + 699 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 473, + 287, + 699 + ], + "spans": [ + { + "bbox": [ + 47, + 473, + 287, + 699 + ], + "type": "text", + "content": "Results on Something-Something-v2. We present the performance comparisons on SSv2 [23] in Tab. 2. The results show that our DUALPATH with ViT-B/16 achieves comparable or better performance than the prior supervised video models [1,7,18,76], requiring a much smaller number of trainable parameters and GFLOPs. Our DUALPATH with ViT-L/14 shows more competitive performance, outperforming most prior works [22, 40, 43]. The baselines [11, 35, 37, 49], which have relatively weak temporal modeling ability, show significantly poor performance, implying that strong temporal modeling is mandatory for the SSv2 dataset. The comparisons to the CLIP pretrained PET approaches [45, 50] with ViT-B/16 demonstrate the effectiveness and efficiency of DUALPATH, achieving higher performance (70.3 vs 69.5 [50]) with significantly low computations (716 vs 9641 [45] GFLOPs) using 32 frames. Thanks to the extreme computational efficiency, our DUALPATH comprises more competitive performance using 48 frames (" + }, + { + "bbox": [ + 47, + 473, + 287, + 699 + ], + "type": "inline_equation", + "content": "T_{G} = 3" + }, + { + "bbox": [ + 47, + 473, + 287, + 699 + ], + "type": "text", + "content": ") with low computation requirements." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 700, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 700, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 700, + 286, + 712 + ], + "type": "text", + "content": "Results on HMDB51. In Tab. 3, we compare the re" + } + ] + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 307, + 423, + 549, + 533 + ], + "blocks": [ + { + "bbox": [ + 47, + 387, + 545, + 409 + ], + "lines": [ + { + "bbox": [ + 47, + 387, + 545, + 409 + ], + "spans": [ + { + "bbox": [ + 47, + 387, + 545, + 409 + ], + "type": "text", + "content": "Table 2. Performance comparisons for action recognition on the SSv2 [23] dataset. Note that we reproduce VideoPrompt [37] without the additional text branch for fair comparison (denoting with *)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 423, + 549, + 533 + ], + "lines": [ + { + "bbox": [ + 307, + 423, + 549, + 533 + ], + "spans": [ + { + "bbox": [ + 307, + 423, + 549, + 533 + ], + "type": "table", + "html": "
Method & Arch.ClassifierParamsHMDB51
Full-tuning w/ ViT-B/16 [17]Lin.86M59.4
Linear w/ ViT-B/16Lin.0.1M61.2
VPT [35] w/ ViT-B/16Trans.7M62.4
AdaptFormer [11] w/ ViT-B/16Trans.8M63.7
Pro-tuning [49] w/ ViT-B/16Trans.9M63.3
VideoPrompt [37] w/ ViT-B/16Trans.6M66.4
ST-Adapter* [50] w/ ViT-B/16Lin.7M65.9
DUALPATH w/ ViT-B/16MLPs.10M75.6
", + "image_path": "d3038be6237e83c67f4bbc12698b6988d4d82935cc32956ce52e9d2cce4f42f9.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 535, + 546, + 624 + ], + "lines": [ + { + "bbox": [ + 305, + 535, + 546, + 624 + ], + "spans": [ + { + "bbox": [ + 305, + 535, + 546, + 624 + ], + "type": "text", + "content": "Table 3. Performance comparisons for action recognition on the HMDB51 [39] dataset with the CLIP pretrained ViT-B/16 [53]. We report the type of classifier and the number of learnable parameters for baselines and ours. Lin. and Trans. denote the linear classifier and temporal transformer, respectively. Our DUALPATH uses two MLP layers as the classifier. Note that we reproduce ST-Adapter [50] for fair comparison in terms of the pretrained dataset (denoting with " + }, + { + "bbox": [ + 305, + 535, + 546, + 624 + ], + "type": "inline_equation", + "content": "*" + }, + { + "bbox": [ + 305, + 535, + 546, + 624 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 640, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 640, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 640, + 546, + 713 + ], + "type": "text", + "content": "sults with baselines [11, 35, 37, 49, 50] on HMDB51 [39] that dominantly requires strong spatial modeling for action recognition. Surprisingly, our DUALPATH significantly outperforms baselines by large margins. This result demonstrates DUALPATH fully capitalizes on the exceptional spatial modeling ability of the pretrained image model for ac" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 738, + 298, + 747 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 738, + 298, + 747 + ], + "spans": [ + { + "bbox": [ + 279, + 738, + 298, + 747 + ], + "type": "text", + "content": "2209" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 595, + 841 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 59, + 69, + 274, + 175 + ], + "blocks": [ + { + "bbox": [ + 59, + 69, + 274, + 175 + ], + "lines": [ + { + "bbox": [ + 59, + 69, + 274, + 175 + ], + "spans": [ + { + "bbox": [ + 59, + 69, + 274, + 175 + ], + "type": "table", + "html": "
Method & Arch.PretrainParamsDiving48
Supervised
TimeSformer-L [7]IN-21K121M81.0
VideoSwin-B [47]IN-21K88M81.9
SIFAR-B-14 [19]IN-21K87M87.3
ORViT [30]IN-21K160M88.0
Parameter Efficient Tuning
DUALPATH w/ ViT-B/16CLIP10M88.7
", + "image_path": "79531bd1c8052868c81646355374af9e02e7993661d455035077abf0cce0cd7b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 226, + 286, + 273 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 226, + 286, + 273 + ], + "spans": [ + { + "bbox": [ + 47, + 226, + 286, + 273 + ], + "type": "text", + "content": "tion recognition. The comparison with VideoPrompt [37] that uses the additional text branch demonstrates the effectiveness of DUALPATH, improving " + }, + { + "bbox": [ + 47, + 226, + 286, + 273 + ], + "type": "inline_equation", + "content": "9.2\\%" + }, + { + "bbox": [ + 47, + 226, + 286, + 273 + ], + "type": "text", + "content": " performance improvement." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 273, + 286, + 370 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 273, + 286, + 370 + ], + "spans": [ + { + "bbox": [ + 47, + 273, + 286, + 370 + ], + "type": "text", + "content": "Results on Diving-48. Tab. 4 shows performance comparisons on Diving-48 [42] that requires fine-grained action recognition. Our DUALPATH consistently outperforms all video models with only 10M trainable parameters. Particularly, we obtain a better performance than ORViT [30] which utilizes the additional tracking model. It indicates the utility of DUALPATH in fine-grained action recognition and the superiority of temporal modeling of DUALPATH." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 376, + 168, + 389 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 376, + 168, + 389 + ], + "spans": [ + { + "bbox": [ + 47, + 376, + 168, + 389 + ], + "type": "text", + "content": "5.3. Components analysis" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 390, + 286, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 390, + 286, + 533 + ], + "spans": [ + { + "bbox": [ + 47, + 390, + 286, + 533 + ], + "type": "text", + "content": "Impact of dual-path. In the top panel of Tab. 5, we train the model by ablating each path and evaluate the performance on SSv2. Without the temporal path (DUALPATH w/o TA), the performance is significantly degraded despite using a larger number of frames (" + }, + { + "bbox": [ + 47, + 390, + 286, + 533 + ], + "type": "inline_equation", + "content": "T_{S} = 16" + }, + { + "bbox": [ + 47, + 390, + 286, + 533 + ], + "type": "text", + "content": " vs 8). Without the spatial path (DUALPATH w/o SA), we can obtain slightly better performance than the result without the temporal adaptation. Since the SSv2 requires strong temporal modeling, we speculate that two ablation studies show comparison results. However, it still shows a substantial performance gap compared to the full model of DUALPATH, demonstrating the effectiveness of the dual-path design." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 533, + 286, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 533, + 286, + 640 + ], + "spans": [ + { + "bbox": [ + 47, + 533, + 286, + 640 + ], + "type": "text", + "content": "Frame rates in spatial path. In the middle panel of Tab. 5, we analyze the effect according to the number of frames used in the spatial path. The temporal path identically uses 16 frames to construct a grid-like frameset, and frames used in the spatial path are sampled from such 16 frames. A large number of " + }, + { + "bbox": [ + 47, + 533, + 286, + 640 + ], + "type": "inline_equation", + "content": "T_{S}" + }, + { + "bbox": [ + 47, + 533, + 286, + 640 + ], + "type": "text", + "content": " slightly improves performance, however, requires more computational costs. Considering the performance improvement compared to the computation increase, we mainly set " + }, + { + "bbox": [ + 47, + 533, + 286, + 640 + ], + "type": "inline_equation", + "content": "T_{S}" + }, + { + "bbox": [ + 47, + 533, + 286, + 640 + ], + "type": "text", + "content": " to 8." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 640, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 640, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 640, + 286, + 713 + ], + "type": "text", + "content": "Number of frames in grid. We scale down original frames with scaling factors " + }, + { + "bbox": [ + 47, + 640, + 286, + 713 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 47, + 640, + 286, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 640, + 286, + 713 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 47, + 640, + 286, + 713 + ], + "type": "text", + "content": " to construct grid-like framesets. These factors thus determine the number of frames the model observes within one grid-like frameset. While a large value of factors increases the temporal resolution, the information of each frame is inevitably reduced. For exam-" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 313, + 69, + 538, + 239 + ], + "blocks": [ + { + "bbox": [ + 47, + 177, + 286, + 211 + ], + "lines": [ + { + "bbox": [ + 47, + 177, + 286, + 211 + ], + "spans": [ + { + "bbox": [ + 47, + 177, + 286, + 211 + ], + "type": "text", + "content": "Table 4. Performance comparisons for action recognition on the Diving-48 [42] dataset. We report the pretrained dataset, the number of learnable parameters (M) for each method, and the accuracy." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 313, + 69, + 538, + 239 + ], + "lines": [ + { + "bbox": [ + 313, + 69, + 538, + 239 + ], + "spans": [ + { + "bbox": [ + 313, + 69, + 538, + 239 + ], + "type": "table", + "html": "
MethodParamsGFLOPsSSv2Views
Effectiveness of Each Path
DUALPATH w/o TA5M101653.716×3×1
DUALPATH w/o SA8M13455.116×3×1
Effectiveness of TS
TS=813M64269.316×3×1
TS=1213M89669.616×3×1
TS=1613M115069.816×3×1
Effectiveness of scaling factors
w=h=2 (TG=16)13M175266.464×3×1
w=h=4 (TG=4)13M86471.864×3×1
w=h=8 (TG=1)13M64261.564×3×1
DUALPATH13M64269.316×3×1
", + "image_path": "e201c4e06857f9ba57ed80e4d9b0bc35e3ea3f64ad65109437110cfd309d1d04.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 307, + 242, + 543, + 253 + ], + "lines": [ + { + "bbox": [ + 307, + 242, + 543, + 253 + ], + "spans": [ + { + "bbox": [ + 307, + 242, + 543, + 253 + ], + "type": "text", + "content": "Table 5. Performance with respect to variants of the components." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 272, + 545, + 333 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 272, + 545, + 333 + ], + "spans": [ + { + "bbox": [ + 305, + 272, + 545, + 333 + ], + "type": "text", + "content": "ple, the original frame is scaled down to the size of " + }, + { + "bbox": [ + 305, + 272, + 545, + 333 + ], + "type": "inline_equation", + "content": "28 \\times 28" + }, + { + "bbox": [ + 305, + 272, + 545, + 333 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 305, + 272, + 545, + 333 + ], + "type": "inline_equation", + "content": "w = h = 8" + }, + { + "bbox": [ + 305, + 272, + 545, + 333 + ], + "type": "text", + "content": ". Meanwhile, a small value of factors retains richer information from the original frame, however, makes the temporal resolution small. As shown in the bottom panel of Tab. 5, we attain the best performance with " + }, + { + "bbox": [ + 305, + 272, + 545, + 333 + ], + "type": "inline_equation", + "content": "w = h = 4" + }, + { + "bbox": [ + 305, + 272, + 545, + 333 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 344, + 470, + 357 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 344, + 470, + 357 + ], + "spans": [ + { + "bbox": [ + 305, + 344, + 470, + 357 + ], + "type": "text", + "content": "6. Conclusion and Future Work" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 362, + 545, + 565 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 362, + 545, + 565 + ], + "spans": [ + { + "bbox": [ + 305, + 362, + 545, + 565 + ], + "type": "text", + "content": "In this paper, we have introduced the novel image-to-video transfer learning approach, DUALPATH. By incorporating a dual-path design into image transformers, DUALPATH adapts image models to the video task (i.e., action recognition) with a small number of trainable parameters. The spatial path adaptation strengthens the inherent spatial context modeling of the pretrained image transformers for video data. The temporal path adaptation transforms multiple frames into a unified grid-like frameset, enabling the image model to capture relationships between frames. We appropriately employ the bottlenecked adapters in each path to adapt the pretrained features to target video data. In addition, we present several baselines transforming recent PETL approaches [11, 35, 49] for image-to-video adaptation. Experimental results demonstrated the superiority of the dualpath design and the grid-like frameset prompting, outperforming several baselines and supervised video models." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 566, + 545, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 566, + 545, + 663 + ], + "spans": [ + { + "bbox": [ + 304, + 566, + 545, + 663 + ], + "type": "text", + "content": "There are many possible directions for future work, encompassing cross-domain transfer learning. While we have explored image-to-video transfer learning, large foundation vision-language models are available. It would also be interesting to expand the superior pretrained 2D knowledge to 3D spatial modeling [71]. We hope our study will foster research and provide a foundation for cross-domain transfer learning." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgement. This research was supported by the Yonsei Signature Research Cluster Program of 2022 (2022-22-0002) and the KIST Institutional Program (Project No.2E32283-23-064)." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 738, + 298, + 747 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 738, + 298, + 747 + ], + "spans": [ + { + "bbox": [ + 279, + 738, + 298, + 747 + ], + "type": "text", + "content": "2210" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 595, + 841 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 52, + 91, + 286, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 91, + 286, + 123 + ], + "spans": [ + { + "bbox": [ + 52, + 91, + 286, + 123 + ], + "type": "text", + "content": "[1] Anurag Arnab, Mostafa Dehghani, Georg Heigold, Chen Sun, Mario Lučić, and Cordelia Schmid. 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These pixel-correspondence candidates are computed based on the relative pose estimates between the frames. Accurate pose predictions are essential for precise matching cost computation as they influence the epipolar geometry. Furthermore, improved depth estimates can, in turn, be used to align pose estimates.", + "bbox": [ + 75, + 342, + 470, + 478 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Inspired by traditional structure-from-motion (SfM) principles, we propose the DualRefine model, which tightly couples depth and pose estimation through a feedback loop. Our novel update pipeline uses a deep equilibrium model framework to iteratively refine depth estimates and a hidden state of feature maps by computing local matching costs based on epipolar geometry. Importantly, we used the refined depth estimates and feature maps to compute pose updates at each step. This update in the pose estimates slowly alters the epipolar geometry during the refinement process. Experimental results on the KITTI dataset demonstrate competitive depth prediction and odometry prediction performance surpassing published self-supervised baselines1.", + "bbox": [ + 75, + 479, + 473, + 676 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 709, + 209, + 724 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The optimization of the coordinates of observed 3D points and camera poses forms the basis of structure-from-motion (SfM). Estimation of both lays the foundation for robotics [34, 35, 75], autonomous driving [20], or AR/VR applications [60]. Traditionally, however, SfM techniques are susceptible to errors in scenes with texture-less regions, dynamic objects, etc. This has motivated the development of deep learning models that can learn to predict depth from monocular images [14, 15, 18, 48, 50]. These models can", + "bbox": [ + 75, + 734, + 470, + 872 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/51d9d2420784a8180a9c6d411068c2941a66e1b94957758097e6f74b21a543d5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 598, + 309, + 799, + 409 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/94d061c2aebb73a8d075d885cea015514d7cf9b7a7f47cbcb8cb237e196e7e5f.jpg", + "image_caption": [ + "Figure 1. (a) The estimated pose of a camera affects the epipolar geometry. (b) The epipolar line in the source image, calculated from yellow points in the target image, for the PoseNet-based [43] initial pose regression (red) and our refined pose (green). The yellow point in the source image is calculated based on our final depth and pose estimates." + ], + "image_footnote": [], + "bbox": [ + 594, + 412, + 799, + 556 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "accurately predict depth based solely on image cues, without requiring geometric information.", + "bbox": [ + 496, + 652, + 893, + 683 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In recent years, self-supervised training of depth and pose models has become an attractive method, as it alleviates the need for ground truth while demonstrating precision comparable to those of supervised counterparts [7, 19, 22, 23, 26, 28, 30, 61, 70, 74, 83, 87, 98, 106, 108]. Such an approach uses depth and pose predictions to synthesize neighboring images in a video sequence and enforce consistency between them. As the image sequence is also available at test time, recent self-supervised methods also study the use of multiple frames during inference [91]. These typically involve the construction of cost volumes from multiple views to compute pixel correspondences, bearing similarities to (multi-view) stereo models [4, 44, 77]. By incorporating multi-frame data, geometric information is integrated to make depth predic", + "bbox": [ + 496, + 689, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "", + "bbox": [ + 76, + 886, + 401, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "726", + "bbox": [ + 485, + 945, + 511, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tions, improving the performance as well as the robustness. In such a multi-frame matching-based model, the accuracy of matching costs computation is essential. Recent work in DepthFormer [29] demonstrates its importance, as they designed a Transformer [84]-based module to improve matching costs and achieve state-of-the-art (SoTA) depth accuracy. However, their approach came with a large memory cost.", + "bbox": [ + 75, + 90, + 470, + 196 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Unlike stereo tasks, the aforementioned self-supervised multi-frame models do not assume known camera poses and use estimates learned by a teacher network, typically a PoseNet [43]-based model. This network takes two images as input and regresses a 6-DoF pose prediction. As the estimated pose affects the computation of epipolar geometry (Fig. 1(a)), the accuracy of the pose estimates is crucial to obtain accurate correspondence matches between multiple frames. However, as noted in recent studies [72], pure learning-based pose regression generally still lags behind its traditional counterpart, due to the lack of geometric reasoning. By refining the pose estimates, we can improve the accuracy of the matching costs, potentially leading to better depth estimates as well. In Fig. 1(b), we show that the epipolar lines calculated from the regressed poses do not align with our refined estimates. Conversely, a better depth prediction may lead to a better pose prediction. Thus, instead of building the cost volume once using regressed poses, we choose to perform refinements of both depth and pose in parallel and sample updated local cost volumes at each iteration. This approach is fundamentally inspired by traditional SfM optimization and is closely aligned with feedback-based models that directly couple depth and pose predictions [27].", + "bbox": [ + 75, + 200, + 473, + 549 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we propose a depth and pose refinement model that drives both towards an equilibrium, trained in a self-supervised framework. We accomplish this by making the following contributions: First, We introduce an iterative update module that is based on epipolar geometry and direct alignment. We sample candidate matches along the epipolar line that evolves based on the current pose estimates. Then the sampled matching costs are used to infer per-pixel confidences that are used to compute depth refinements. The updated depth estimates are then used in direct feature-metric alignments to refine the pose updates towards convergence. As a result, our model can perform geometrically consistent depth and pose updates. Second, These updates refine the initial estimates made by the single-frame model. By doing so, we do not rely on full cost volume construction and base our updates only on local cost volumes, making it simpler, more memory efficient, and more robust. Lastly, we design our method within a deep equilibrium (DEQ) framework [3] to implicitly drive the predictions towards a fixed point. Importantly, DEQ allows for efficient training with low training memory, improving upon the huge memory consumption of previous work. With our proposed novel design, we show improved depth estimates through experiments that are com", + "bbox": [ + 75, + 553, + 473, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "petitive with the SoTA models. Furthermore, our model demonstrates improved global consistency of visual odometry results, outperforming other learning-based models.", + "bbox": [ + 498, + 90, + 893, + 137 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 151, + 640, + 167 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Depth from a single image", + "text_level": 1, + "bbox": [ + 500, + 176, + 736, + 193 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The depth prediction problem for a single image is ill-posed due to the possibility of different 3D scenes projecting onto the same 2D image [32]. Nonetheless, humans can predict depth from a single image through experience. Motivated by this, numerous supervised neural network models were proposed to solve the monocular depth estimation task, starting with Eigen et al.'s paper [15]. Subsequently, performance was improved by modifying the model architecture [14,48,64,94], training on large dataset [13,53,95,100], designing robust loss functions [49,103], and transforming the problem into a classification task [52]. However, supervisory depth estimation requires ground-truth depth maps, which are difficult to collect in large quantities and of high quality. This challenge is one of the main reasons why researchers are exploring semi-supervised training, where the model expects weak supervision, such as providing relative depth [12], camera poses [101], or utilizing synthetic data for training [1,47,62].", + "bbox": [ + 496, + 200, + 895, + 472 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The need for weak supervision still presents limitations in generalizability and scalability, among other aspects. To address these constraints, research on self-supervised training techniques is gaining momentum. These techniques involve using geometry in stereo matching [19, 22] or with a sequence of single-camera images, as initially proposed by [106]. Monodepth2 [23] refined the idea of exploiting image sequences for training by using auto-masking and minimum reprojection losses to address occlusion and egomotion issues. Further improvements were made by defining the problem as a classification task [25, 42], modifying the architecture [28], feature-based loss for regions with low texture [74, 101], or reducing artifacts from moving objects [11, 46, 80].", + "bbox": [ + 496, + 473, + 895, + 683 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our work is based on self-supervised monocular depth and employs them as a teacher and initial estimate.", + "bbox": [ + 500, + 684, + 893, + 714 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Depth from multiple frames", + "text_level": 1, + "bbox": [ + 500, + 724, + 751, + 742 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Relying on single frames at test-time requires the model to make several assumptions about the scene's geometrical details. In contrast, multi-frame approaches, which leverage available temporal information and incorporate multi-view geometry, reduce the need for such assumptions.", + "bbox": [ + 496, + 750, + 893, + 824 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Multi-frame depth prediction is closely related to stereo depth estimation, where neural networks convert input stereo images into depth maps, as demonstrated by [54, 63, 82]. Kendall et al. [44] achieved a significant improvement by constructing a plane-sweep stereo cost volume. Generally,", + "bbox": [ + 496, + 825, + 895, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "727", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "multi-view stereo (MVS) research is more relevant to our work, as it utilizes an unstructured collection of scene images, meaning that the pose between different images is not fixed. In studies like [36, 38, 58, 90, 97], it was common to combine the previously mentioned cost volumes with ground truth depth and camera poses for guidance. Consequently, these works require camera poses during inference [56, 92]. Although some research managed to relax the pose requirement during inference, training still necessitates this supervision [77, 82].", + "bbox": [ + 75, + 90, + 472, + 241 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The methods discussed above, along with advances in other domains such as scale domain adaptation [31, 69, 104], view synthesis [23, 93], and other supervisory techniques [26, 30], have significantly impacted the performance of self-supervised approaches. ManyDepth [91], which is similar to our work, focuses on the drawbacks of using a single image during inference and proposes a flexible model that takes advantage of multiple frames at test time, if available. ManyDepth reduces artifacts from moving objects and temporarily stationary cameras by using a single-frame model as a teacher, resulting in improved depth map accuracy. More recently, DepthFormer [29] achieved substantial accuracy improvements by using Transformers [84] to obtain improved pixel matching costs.", + "bbox": [ + 75, + 243, + 473, + 455 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Inspired by traditional bundle adjustments, we design a model that simultaneously solves for both depth and pose while incorporating many of the advancements mentioned earlier. Our approach is most similar to DRO [27]. However, compared to their approach, our model tightly integrates multi-view geometry into the iterative updates formulation and bases our refinements on the local epipolar geometry.", + "bbox": [ + 75, + 455, + 470, + 561 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Iterative refinements", + "text_level": 1, + "bbox": [ + 76, + 573, + 272, + 588 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Iterative refinement has been employed to improve prediction quality in various learning tasks, including object detection [6, 24], optical flow estimation [37, 78], semantic segmentation [68, 102], and others [40, 71]. Some recent research has attempted to iterate the refinement process using deep convolutional networks [9, 21, 55, 57]. Other works train the same network repeatedly by utilizing the results of the previous iteration [99, 102]. In particular, RAFT [78] found success with its iterative refinement procedure for flow estimation. DEQ-flow [2] employed a deep equilibrium (DEQ) [3] framework to reduce the memory consumption of RAFT during training while maintaining accuracy.", + "bbox": [ + 75, + 597, + 472, + 779 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "A key component of our model is inspired by the iterative updates of RAFT and DEQ-flow. Instead of optical flow, our model refines depth and pose estimates in parallel. We design our refinement module to tightly couple the two predictions, considering the epipolar geometry of adjacent frames. With every update, the epipolar geometry is refined, which also results in a more accurate matching costs computation of pixel correspondences.", + "bbox": [ + 75, + 780, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.4. Pose estimation", + "text_level": 1, + "bbox": [ + 500, + 90, + 656, + 104 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Pose estimation is a crucial component in self-supervised monocular depth models. In many works, PoseNet-based models [43] take a pair of adjacent image frames and output a 6 DoF pose estimation. This class of models is straightforward, but often less accurate than their traditional counterparts [16, 17, 65] due to the absence of geometry constraints. Recent work in deep learning-based localization has adopted differentiable geometrically inspired designs within their models by using direct alignments [72, 85, 86] or geometric alignments based on optical flow [79]. These models demonstrate better generalization properties and accuracy. The use of self-supervised monocular depth has also been used to improve traditional odometry [8, 96]. However, our interest lies in learning to refine both depth and pose in the self-supervision pipeline. To improve the accuracy of pose estimation, we integrate direct alignment within the recurrent module, ensuring geometrically consistent prediction between depth and pose.", + "bbox": [ + 496, + 112, + 895, + 387 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 397, + 591, + 412 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our model comprises two primary sub-modules. The first is a single frame self-supervised depth and pose estimator, building upon previous frameworks [23, 105], which we revisit in Sec. 3.1. This network serves as both a teacher and an initializer for the second sub-module, our proposed multi-frame network, presented in detail in Sec. 3.2.", + "bbox": [ + 496, + 422, + 893, + 513 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Self-supervised depth and pose", + "text_level": 1, + "bbox": [ + 500, + 521, + 774, + 537 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We begin by describing the canonical self-supervised monocular depth estimation pipeline [23], which serves as the foundation for our approach. This depth training method assumes that a monocular camera with an intrinsic parameter $K$ captures an image sequence of a scene. In this process, two networks are trained in parallel to estimate the per-pixel depth map of the images $D$ and the relative poses between adjacent image frames. By warping neighboring images towards a shared target frame using these two predictions, self-supervised training can be performed by enforcing photometric consistency between the frames.", + "bbox": [ + 496, + 544, + 893, + 710 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given the depth map $D$ of a target image and its relative pose with a source image $T_{t\\rightarrow s}$ , we can calculate the projection of each pixel $u = (x,y)$ of the target image onto the source image as follows:", + "bbox": [ + 496, + 710, + 893, + 771 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nz ^ {\\prime} u ^ {\\prime} = z ^ {\\prime} \\left[\\begin{array}{l}x ^ {\\prime}\\\\y ^ {\\prime}\\\\1\\end{array}\\right] = K T _ {t \\rightarrow s} \\left(D [ u ] K ^ {- 1} \\left[\\begin{array}{l}x\\\\y\\\\1\\end{array}\\right]\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 557, + 776, + 893, + 825 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "using the estimated depth at that pixel $D[u]$ . The source images can then be warped towards the target frame by sampling the pixel values at the calculated projection", + "bbox": [ + 496, + 830, + 893, + 878 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nI _ {s \\rightarrow t} [ u ] = I _ {s} \\langle u ^ {\\prime} \\rangle , \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 640, + 883, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "728", + "bbox": [ + 485, + 945, + 511, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/75a2a72803f499eb42d709327ef11302dff73ceedc98f3083e705e386b494917.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 83, + 85, + 519, + 276 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/208b987c812c8a5409c3061d15e025593878273f80ac26912fc279dfe572e9f4.jpg", + "image_caption": [ + "DEQ updates", + "Figure 2. (a) The overall pipeline of the model. Given a pair of source and target images, the teacher model predicts an initial depth $D_0$ and pose $T_0$ , as well as initial hidden states that will be updated. DEQ-based alignments are then performed to find the fixed point and output the final predictions. (b) Each iteration in the update step takes the current depth and pose estimates. Matching costs are sampled along the current epipolar lines that evolves based on the pose estimates. The updates are computed by Conv-GRU. Then feature-metric alignment is used to obtain a geometrically consistent pose update." + ], + "image_footnote": [], + "bbox": [ + 527, + 89, + 883, + 281 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\langle \\cdot \\rangle$ indicates bilinear interpolation, implemented using the spatial transformer network (STN) [39].", + "bbox": [ + 75, + 371, + 468, + 401 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The self-supervised loss is calculated as a combination of the photometric error and the edge-aware smoothness loss:", + "bbox": [ + 76, + 402, + 470, + 433 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {s e l f - s u p} = \\lambda_ {p} \\mathcal {L} _ {p} + \\lambda_ {s} \\mathcal {L} _ {s}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 184, + 446, + 468, + 464 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the photometric error between the warped source image and the target image is calculated using the structural similarity loss, and the minimum error is taken between multiple warped images to account for occlusions. Interested readers can refer to [23]. The self-supervised loss is typically computed at multiple scales to stabilize the training.", + "bbox": [ + 75, + 476, + 468, + 566 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this paper, we train a monocular depth estimator and a pose estimation network using this pipeline, serving two purposes. First, following ManyDepth [91], we use these models as a teacher to constrain the multi-frame predictions in the presence of dynamic objects. Additionally, we employ them as an initializer for the multi-frame alignment network.", + "bbox": [ + 75, + 566, + 470, + 657 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1.1 Monocular model", + "text_level": 1, + "bbox": [ + 76, + 679, + 254, + 694 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We build our monocular depth estimation model based on DIFFNet [105], a SoTA self-supervised single-frame estimator. We extract feature maps at multiple scales $s$ from the target image using the HRNet architecture [88]. In accordance with DIFFNet, feature maps from multiple stages are accumulated in $F^{(1/2^s)}$ . Then, we employ disparity decoders to make disparity predictions at scales $s = \\{2,3\\}$ . The pose estimation network follows the canonical PoseNet [43] architecture, taking two input images and outputting 6-DoF values, with a ResNet18 [33] backbone. The predicted disparity and pose estimation from these networks are used as a teacher to train our alignment sub-module, as was done in ManyDepth [91].", + "bbox": [ + 75, + 703, + 472, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Deep equilibrium alignments", + "text_level": 1, + "bbox": [ + 500, + 371, + 759, + 387 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In our alignment sub-module, we assume that additional input from source image(s) is available, which can be used to refine the depth and pose estimates. In this work, we focus on using the image from the previous frame in the image sequence as our source image.", + "bbox": [ + 496, + 393, + 890, + 469 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our alignment module is formulated as a deep equilibrium model [3] that updates the hidden states, depth, and pose estimates to a fixed point. Specifically, at the fixed point $z^{*}$ ,", + "bbox": [ + 496, + 469, + 893, + 531 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left(h ^ {*}, D ^ {*}, T ^ {*}\\right) = z ^ {*} = \\mathrm {U} \\left(z ^ {*}, x\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 599, + 541, + 890, + 558 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $z$ is composed of a hidden state $h$ , the depth prediction $D$ , and the pose prediction $T$ . U represents our update function, refining the depth and pose alternatively. $x$ is an input to the update module, obtained based on the epipolar geometry at each step, which we discuss in the next subsection. We perform these iterative updates at scale $s = 2$ .", + "bbox": [ + 496, + 569, + 893, + 659 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "From the feature extraction output, we compute an initial hidden state for our recurrent updates $h^{[0]} = \\tanh(\\mathrm{H}(F^{(1/4)}))$ and a context feature $q = \\mathrm{Q}(F^{(1/4)})$ . Both H and Q are composed of a single residual block [33] followed by a convolutional layer.", + "bbox": [ + 496, + 660, + 893, + 736 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.1 Depth updates around local neighborhood", + "text_level": 1, + "bbox": [ + 500, + 753, + 846, + 768 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Local epipolar sampling. As discussed previously, our refinement is based on the pixel matching between the target image and the source image. We use the first two blocks of the HRNet feature extractor to extract unary features from the source image $m_{s}^{(1/4)}$ and the target image $m_{t}^{(1/4)}$ , which we will use to calculate the matching costs.", + "bbox": [ + 496, + 777, + 890, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Similarly to RAFT [78], our aim is to compute the matching values for candidate correspondences around the current", + "bbox": [ + 498, + 869, + 893, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "729", + "bbox": [ + 485, + 945, + 509, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/395494b452023615536bb36e9426be5caa26a3526da0de3999e145f47cccb7ed.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 83, + 90, + 285, + 154 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/b0b7b842fe4be54e5b4f264f024c7f623e1f8bb4605c437c20aba26ff56d3076.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 285, + 90, + 486, + 152 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/bc48dfe32f0688ffaba94ba9ce01b0b115b90789c4a59cd9475f9c88f6bb0af2.jpg", + "image_caption": [ + "$D_0$" + ], + "image_footnote": [], + "bbox": [ + 486, + 90, + 687, + 152 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/3c224035a5e518ec80a30e2cf8111b50d71f5087ee6c3c8fc591f5b19ea4653a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 687, + 90, + 888, + 152 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/3aeada78b38f30e3f7dea33e8843aaed5c3bb3856192839afe27d7a13c4c9d27.jpg", + "image_caption": [ + "Wq" + ], + "image_footnote": [], + "bbox": [ + 84, + 171, + 287, + 220 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/93efbceecf60ca0a61d2eff73c5ccb294c6a774fd3965e0f2baf3ec330584d69.jpg", + "image_caption": [ + "$W_{h,5}$" + ], + "image_footnote": [], + "bbox": [ + 287, + 171, + 488, + 220 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/db798ff483221e90da4af122aa6f089ca9df34963021818882608b299d04e882.jpg", + "image_caption": [ + "$D_{5}$" + ], + "image_footnote": [], + "bbox": [ + 488, + 171, + 687, + 220 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/db68dbffda1634fd61545eb5aad5d18865835b6cfeec7b1fdb54fb806ed2a175.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 687, + 171, + 887, + 220 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/ab64af8451a8d5b7e0d0301d6a8eb0b86bf2e68f88727c2b3014d59a939d2c0b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 83, + 224, + 285, + 285 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/ffaa0c62d72b627cd074ac682a6016ee064416dd206d5a44e6cc5c7715430bcf.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 285, + 224, + 488, + 285 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/e141bda6c6e77c30a01f0c33b7bf979a52c44bd3bdb8b1e8726fe729274f3511.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 488, + 224, + 687, + 285 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/5e50c44b7d8252803ef5f30fc4f03148d865f05f5ded74d53ca421292bda8adc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 687, + 224, + 888, + 285 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/5c1259e985fcb7fdb84035569910e440a7e1fc3f1bc93931a0fbe2cf825f1526.jpg", + "image_caption": [ + "Wq", + "Figure 3. Qualitative results on KITTI data. $I_{s}$ : input image; $W_{q}$ , $W_{h,0}$ , and $W_{h,5}$ : confidence weights; $D_{0}$ , $D_{5}$ : disparity estimates; The Abs Rel error for the depth estimates." + ], + "image_footnote": [], + "bbox": [ + 83, + 304, + 287, + 352 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/8dda74a09b391eb5ca265cba9015dd08e6c0306282aef4e7b20c53d2851cbe45.jpg", + "image_caption": [ + "$W_{h,5}$" + ], + "image_footnote": [], + "bbox": [ + 285, + 304, + 488, + 352 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/38636b52cf916573f7ec926f68ae2667f5ed6e93e794586d30cf7775b26a356f.jpg", + "image_caption": [ + "$D_{5}$" + ], + "image_footnote": [], + "bbox": [ + 488, + 304, + 687, + 352 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/cf844cc748508cfb657673d0296076f7664b675c102f0d777bda2adea94f80ae.jpg", + "image_caption": [ + "AbsRel5" + ], + "image_footnote": [], + "bbox": [ + 687, + 304, + 888, + 352 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "prediction and use them as input to our update module at the update step $k$ . Unlike RAFT, however, we perform matching along an epipolar line based on the pose estimate $T_{k}$ . This is done by computing the projected coordinates $u_{k}^{\\prime}$ in the source image obtained from (1) at the depths of interest. The depth candidates are computed to be the neighborhood of the current prediction. Instead of computing the all-pair correlation as was done in RAFT, we compute feature matching on the fly.", + "bbox": [ + 75, + 407, + 468, + 542 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "At each pixel $u$ , we compute the local depth candidates as $D[u]_k \\pm (i \\times c \\times n)$ , with $i \\in \\mathbb{Z}$ and $i \\leq r$ . We set the sampling radius hyperparameter $r = 8$ in our experiments. In depth estimation, the error typically grows with distance. To account for this, we define $c = D[u] / C$ as a function of depth to make the sampling range dependent on the depth, where we set $C$ as a trainable parameter. Following RAFT, to collect the matching information from a larger neighborhood, we sampled at multiple levels $n = \\{1,2,3\\}$ . At each level, we bilinearly resize the matching feature map of the source image $m_s^{(1/4)}$ with a scale of $1/2^n$ . Then, the matching features are sampled at the calculated corresponding set of coordinates $u_k'$ , and the absolute differences with the target feature", + "bbox": [ + 75, + 544, + 470, + 744 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {C} _ {k} [ u ] = \\left| m _ {t} [ u ] - m _ {s} \\langle u _ {k} ^ {\\prime} \\rangle \\right| \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 753, + 468, + 770 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "are calculated and gathered. This provides us with a map $\\mathbf{C}_k$ that contains $n \\times (2 \\times r + 1)$ matching cost values at the corresponding depth candidates. We then encode these matching costs along with the depth using a two-layer convolutional neural network (CNN) to compute the input for the update module", + "bbox": [ + 75, + 779, + 470, + 869 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nx _ {k} = \\left[ \\operatorname {C N N} _ {\\mathbf {C}} \\left(\\mathbf {C} _ {k}\\right), \\operatorname {C N N} _ {D _ {x}} \\left(D _ {k}\\right), q \\right], \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 882, + 468, + 898 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $[\\cdot ,\\cdot ]$ represents the concatenation.", + "bbox": [ + 500, + 407, + 764, + 422 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Depth update. The update function calculates an updated hidden state $h_{k+1}$ using the Conv-GRU block [5,41,78]. $h_{k+1}$ is used to compute the depth updates. To stabilize training, we use the activation function $\\tanh(\\cdot)$ to bound the absolute update values for the depths to be within $r \\cdot c$ :", + "bbox": [ + 498, + 433, + 892, + 508 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nD _ {k + 1} = D _ {k} + r \\cdot c \\cdot \\tanh \\left(\\mathrm {C N N} _ {D _ {\\mathrm {U}}} \\left(h _ {k + 1}\\right)\\right). \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 560, + 520, + 892, + 537 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "These updates are performed in an alternating fashion with the pose updates to reach the fixed point $D^{*}$ . Using $h^{*}$ , we compute a convex upsampling to obtain the final depth estimate at the input resolution.", + "bbox": [ + 498, + 546, + 892, + 607 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2.2 Feature-metric pose alignments", + "text_level": 1, + "bbox": [ + 500, + 625, + 772, + 641 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In (1), the accuracy of pose estimation affects the calculation of the coordinates of pixels. Hence, a refined pose estimate would also improve the reliability of the matching costs. To refine the pose while being geometrically consistent, we perform our pose updates based on direct feature alignments [16, 17, 87]. These updates $\\delta_{k}$ can be calculated by solving $H_{k}\\delta_{k} = b_{k}$ , where", + "bbox": [ + 496, + 648, + 893, + 755 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nH _ {k} = \\mathcal {J} _ {k} ^ {T} \\operatorname {d i a g} \\left(W _ {k}\\right) \\mathcal {J} _ {k} \\text {a n d} b _ {k} = - \\mathcal {J} _ {k} ^ {T} \\operatorname {d i a g} \\left(W _ {k}\\right) r _ {k} \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 535, + 763, + 890, + 787 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nr _ {k} [ u ] = m _ {s} \\left\\langle u _ {k} ^ {\\prime} \\right\\rangle - m _ {t} [ u ],\n$$\n", + "text_format": "latex", + "bbox": [ + 702, + 785, + 852, + 800 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "and $\\mathcal{J}$ is the Jacobian with respect to the pose.", + "bbox": [ + 500, + 810, + 808, + 825 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To compute this pose update, one could assign uniform confidence to every pixel in the image. However, in Eq. (8), additional confidence weights per pixel $W$ can also be integrated. This is done for two reasons. First, the solution for the pose updates can be affected by dynamic objects", + "bbox": [ + 496, + 825, + 893, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "730", + "bbox": [ + 485, + 944, + 511, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "as well as inaccurate feature alignments that may occur in region with repeated textures. To account for this, the confidence weighting of the input context feature map $W_{q}$ can be computed [72]. Specifically, we computed a confidence map $W_{t,s} = 1 / (1 + \\mathrm{ReLU}(\\mathrm{CNN}_{W_q}(F_{t,s}))$ for both target and source images. The source confidence is warped towards the target frame using Eqs. (1) and (2). Finally, the confidence is computed as $W_{q} = W_{t}\\cdot W_{s,\\text{warped}}$ . This confidence weight is only computed once to assign per-pixel confidence for the input images.", + "bbox": [ + 75, + 90, + 472, + 241 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Second, the accuracy of pose updates would depend on the accuracy of the depth estimates. To obtain more accurate pose updates, we would like to assign more alignment confidence to the region with higher depth accuracy. We use a neural network to infer this confidence from the matching costs. Since the hidden states $h$ have a history of these matching costs, another confidence weights $W_{h,k} = \\mathrm{CNN}_{W_h}(h_k)$ can be computed. Unlike the previous confidence map, this one is computed and evolves at every update step. By doing so, the network can use the depth predictions to guide the pose estimates towards convergence using the depth information. In our experiments, we investigate the use of each confidence weighting and combination of both $W_{k} = W_{q}W_{h,k}$ .", + "bbox": [ + 75, + 243, + 472, + 440 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Finally, we can compute the updated pose as $T_{k + 1} = \\exp (\\delta_k^{\\wedge})T_k$ . These operations are designed to be differentiable to enable end-to-end training.", + "bbox": [ + 76, + 440, + 472, + 486 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.2.3 DEQ training", + "text_level": 1, + "bbox": [ + 76, + 510, + 227, + 526 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We adopt a DEQ framework, wherein the above steps are repeated until the depth and pose values reach a fixed point, at which the update value is minimal. In our implementation, the fixed points of depth and pose are chosen separately, and it is possible for both to be selected from different update steps. Finally, the training gradient is computed using the chosen depth and pose fixed points. Operations prior to the fixed point do not require saving gradients in memory, which allows memory-efficient training.", + "bbox": [ + 75, + 535, + 468, + 671 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As noted in Eqs. (1) to (3), the self-supervision losses can be computed given a depth and pose prediction. At the fixed point, we compute two additional self-supervision losses. The first performs source-to-target image warping through the pairing of the final depth $D^{*}$ and the initial pose $T_{0}$ , where we detach $T_{0}$ from the computational graph to act as a teacher. This loss is used so that the output of the teacher and refinement modules shares the same scaling. The second performs the warping with the pairing of $D^{*}$ and $T^{*}$ . This loss helps drive refined estimation of both depth and pose towards the optimal value. Detailed experiments for this choice of loss pairings are provided in the supplementary.", + "bbox": [ + 75, + 672, + 468, + 854 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In both losses, we also apply the consistency loss between $D_0$ and $D^*$ , similar to ManyDepth [91], to account for dynamic objects or occluded regions. Specifically, we extract", + "bbox": [ + 76, + 854, + 472, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "coarse depth predictions from the raw feature matchings and mask regions where large disagreements occur, and enforce consistency with the teacher depth. Unlike ManyDepth, however, our method does not explicitly construct a cost volume. To obtain the coarse depth, we search for the lowest matching cost around the neighborhood of the teacher depth, similar to Sec. 3.2.1, but with a larger neighborhood range. This approach offers an additional advantage compared to the cost volume-based method, as we do not need to rely on an estimated minimum and maximum depth or know the scale of the estimates. Moreover, since the computation of coarse depth depends on the accuracy of feature matching costs, it can be improved with more accurate pose estimates (Tab. 2).", + "bbox": [ + 496, + 90, + 893, + 303 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 316, + 633, + 334 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Dataset and metrics", + "text_level": 1, + "bbox": [ + 500, + 343, + 689, + 357 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For depth estimation experiments, we use the Eigen train/test split [15] from the KITTI dataset [20]. To evaluate the estimated depths, we scale them by a scalar to match the scale of the ground truth. We employ standard depth evaluation metrics [14, 15], including absolute and squared relative error (Abs Rel, Sq Rel), root mean square error (RMSE, RMSE log), and accuracy under threshold $(\\delta_{1}, \\delta_{2}$ , and $\\delta_{3})$ with a maximum depth set at $80m$ . Lower values are better for the first four metrics, while higher values are better for the remaining three.", + "bbox": [ + 496, + 366, + 893, + 518 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For the visual odometry experiments, we use the KITTI odometry dataset and follow the same training and evaluation sequences (Seq. 00-08 for training and Seq. 09-10 for evaluation) as in previous work [106]. Since our estimation relies on a monocular camera, the estimated trajectories are aligned with the ground truth using the 7 DoF Umyama alignment [81]. We use standard odometry evaluation metrics such as translation $(t_{err})$ and rotation $(r_{err})$ error [20], and absolute trajectory error (ATE) [76].", + "bbox": [ + 496, + 518, + 893, + 655 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Implementation details", + "text_level": 1, + "bbox": [ + 500, + 664, + 714, + 681 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We conduct our experiments using PyTorch [66] on an RTX 3090 GPU with a batch size of 12. Following [23], we apply color and flip augmentations and resize input images to a resolution of $640 \\times 192$ . For our high resolution experiments, we resize the images to $960 \\times 288$ . We train the entire network for 15 epochs with a learning rate of $10^{-3}$ , at which point we freeze the teacher depth and pose models. We then continue to train the network with a learning rate of $10^{-4}$ . Adam optimizer [45] is employed with $\\beta_{1} = 0.9$ and $\\beta_{2} = 0.999$ .", + "bbox": [ + 496, + 688, + 893, + 839 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As mentioned earlier, the depth backbone is based on the HRNet architecture [88]. For the teacher pose model, we adhere to the standard design, using the first five layers of a ResNet18 initialized with ImageNet pre-trained weights as", + "bbox": [ + 496, + 839, + 893, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "731", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/ef01027e808834ca59bd1b8de364e6154a29b3b41c1b9a94cbc39cc2f87815a5.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodTest framesSemanticsW × HAbs Rel ↓Sq Rel ↓RMSE ↓RMSE log ↓δ1 ↑δ2 ↑δ3 ↑
Low & mid resRanjan et al. [70]1832 × 2560.1481.1495.4640.2260.8150.9350.973
EPC++ [59]1832 × 2560.1411.0295.3500.2160.8160.9410.976
Struct2depth (M) [10]1●416 × 1280.1411.0265.2910.2150.8160.9450.979
Videos in the wild [26]1●416 × 1280.1280.9595.2300.2120.8450.9470.976
Guizilini et al. [30]1●640 × 1920.1020.6984.3810.1780.8960.9640.984
Johnston et al. [42]1640 × 1920.1060.8614.6990.1850.8890.9620.982
Monodepth2 [23]1640 × 1920.1150.9034.8630.1930.8770.9590.981
Packnet-SFM [28]1640 × 1920.1110.7854.6010.1890.8780.9600.982
Li et al. [51]1416 × 1280.1300.9505.1380.2090.8430.9480.978
DIFFNet [105]1640 × 1920.1020.7644.4830.1800.8960.9650.983
DualRefine-initial (D0)1640 × 1920.1030.7214.4760.1800.8910.9650.984
Patil et al. [67]N†640 × 1920.1110.8214.6500.1870.8830.9610.982
Wang et al. [89]2 (-1, 0)640 × 1920.1060.7994.6620.1870.8890.9610.982
ManyDepth (MR) [91]2 (-1, 0)640 × 1920.0980.7704.4590.1760.9000.9650.983
DepthFormer [29]2 (-1, 0)640 × 1920.0900.6614.1490.1750.9050.9670.984
DualRefine-refined (D*)2 (-1, 0)640 × 1920.0900.6584.2370.1710.9120.9670.984
High resDRO [27]2 (-1, 0)960 × 3200.0880.7974.4640.2120.8990.9590.980
Wang et al. [89]2 (-1, 0)1024 × 3200.1060.7734.4910.1850.8900.9620.982
ManyDepth (HR ResNet50) [91]2 (-1, 0)1024 × 3200.0910.6944.2450.1710.9110.9680.983
DualRefine-refined (HR) (D*)2 (-1, 0)960 × 2880.0890.7544.2730.1700.9170.9680.983
", + "bbox": [ + 78, + 90, + 893, + 335 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/4b551e64506ff816f584adb7be0309b65729f78c91daff439c4bb1a0b2e341e4.jpg", + "table_caption": [ + "Table 1. Results and comparison with other state-of-the-arts models on the KITTI [20] Eigen split. Bold: Best, Underscore: Second best. † : evaluated on whole sequences" + ], + "table_footnote": [], + "table_body": "
Pose UpdatesConsistency maskAbs RelSq RelRMSEδ1δ2
no updateT00.0970.7134.4620.8980.964
no weightsT00.0900.6584.2370.9120.967
no Wh,kT00.0900.6454.2730.9080.966
no WqT00.0910.7134.2950.9100.967
Wq and Wh,kT00.0890.6524.2820.9090.967
no weightsT*0.0910.6454.2010.9100.968
", + "bbox": [ + 78, + 391, + 470, + 489 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "an encoder, followed by a decoder that outputs 6-DoF pose estimates. At test time, depth estimates are made using the current frame and the previous frame when available. When the previous frame is unavailable, we skip the refinement module and simply use the initial estimates.", + "bbox": [ + 75, + 547, + 468, + 625 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation", + "text_level": 1, + "bbox": [ + 76, + 633, + 181, + 648 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Pose updates. We analyze the effect of pose refinement toward depth and present the findings in Table 2. Our model that does not perform pose updates has the worst accuracy.", + "bbox": [ + 75, + 657, + 468, + 702 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "**Evolving confidence weighting.** We also show the impact of confidence weightings. Interestingly, similar performance can be observed for all models that perform pose updates, even when no confidence weighting is used to guide the pose computation.", + "bbox": [ + 75, + 703, + 468, + 777 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "DEQ iteration. In addition to studying the effect of pose refinements, we also investigate aspects of DEQ iterative updates and present the findings when we vary the number of iterations during training and at test time in Table 3. The results suggest that 6 iterations is sufficient for the model to find the fixed point. We speculate that the initial estimate provides a reliable starting point and hence the fast convergence. On our machine, the 6 update iterations increase the", + "bbox": [ + 75, + 779, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/d24ddb1b179e296e478d2e18969d50925166e2547b0c6063fd0b359900c42783.jpg", + "table_caption": [ + "Table 2. Ablation experiment for the effect of pose updates on the KITTI [20] Eigen split. Bold: Best." + ], + "table_footnote": [], + "table_body": "
DEQ # itersAbs RelSq RelRMSEδ1Time (ms)
3→30.0970.7774.4310.90653
6→30.0980.6954.3180.90553
6→60.0900.6584.2370.91268
12→30.1020.7324.4280.90053
12→60.0950.7084.3360.90768
12→120.0920.7074.3160.90999
", + "bbox": [ + 535, + 388, + 859, + 491 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Ablation experiment for the DEQ iterations on the KITTI [20] Eigen split. $a \\rightarrow b$ represents $a : \\#$ iters at training and $b : \\#$ iters at test time. Bold: Best.", + "bbox": [ + 498, + 500, + 893, + 537 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "baseline model's inference time from $37.90\\mathrm{ms}$ by $\\sim 31$ ms to a total of $68.49~\\mathrm{ms}$ , running at almost 15 fps. However, we only use PyTorch basic functions in our implementation, and further optimization of the code could be made.", + "bbox": [ + 498, + 560, + 893, + 621 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Depth results", + "text_level": 1, + "bbox": [ + 500, + 633, + 638, + 648 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 1 shows the comparison of our depth estimation with SoTA self-supervised models. We compare with models that train on monocular video. Our model outperforms most previous models and is competitive with the Transformer [84]-based DepthFormer [29] model. Specifically, our model shows a significant improvement in $\\delta_{1}$ , suggesting highly accurate inliers. Furthermore, compared to DepthFormer that requires 16GB training memory per batch, ours only consumes 24GB of memory for 12 batches, around $1/8 \\times$ the memory requirement. This is mainly because our method refines 2D hidden states based on local sampling, while [29] refines 2D feature maps and a 3D feature volume using self/cross-attention along every depth bin.", + "bbox": [ + 496, + 657, + 893, + 853 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Fig. 3 displays qualitative outputs for the disparity and error map of our model. We can observe an improvement to the error map of the refined depth. We also additionally dis", + "bbox": [ + 498, + 854, + 893, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "732", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/fbdbef79bfa320622b7f2138ffc2e544a3a98170db936ca984623f5f4e7f249d.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsSeq 9Seq 10
\\(t_{err}(\\%) \\downarrow\\)\\(r_{err}(\\circ/100m) \\downarrow\\)ATE (m) ↓\\(t_{err}(\\%) \\downarrow\\)\\(r_{err}(\\circ/100m) \\downarrow\\)ATE (m) ↓
ORB-SLAM2 [65] (w/o LC)9.670.344.104.040.36.43
ORB-SLAM2 [65]3.220.48.844.250.38.51
SfMLearner [106]19.156.8277.7940.4017.6967.34
GeoNet [98]28.729.8158.4523.909.043.04
DeepMatchVO [73]9.913.827.0812.185.924.44
Monodepth2 [23]17.173.8576.2211.685.3120.35
DW [26]-Learned--20.91--17.88
DW [26]-Corrected--19.01--14.85
SC-Depth [7]7.313.0523.567.794.9012.00
Zou et al. [107]3.491.0011.305.811.811.80
P-RGBD SLAM [8]5.081.0513.404.322.347.99
DualRefine-initial (T0)9.062.5939.319.454.0515.13
DualRefine-refined (T*)3.431.045.186.801.1310.85
", + "bbox": [ + 122, + 88, + 854, + 287 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4. Results on Seq. 09 and Seq. 10 of the KITTI odometry data. We provide a comparison with other state-of-the-art self-supervised depth and odometry methods. ORB-SLAM2 is included as a representative non-learning based method. Bold: Best, Underscore: Second best.", + "bbox": [ + 75, + 295, + 892, + 321 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/04295fabd8eb446cf2c99475ac6ac114f378c3750eaae67cd49a61c42233d14b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 181, + 349, + 377, + 537 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b71cdbab517d4d36a67999a9adaa375601d81b64b97d765abb46eab84ee4ec09.jpg", + "image_caption": [ + "Figure 4. Estimated trajectory by the initial pose estimator and the refined trajectory using our pose refinement module on (a) Seq. 09 and (b) Seq. 10 of KITTI odometry data. The refined pose estimate improves the global trajectory, even without explicitly training for global consistency." + ], + "image_footnote": [], + "bbox": [ + 122, + 555, + 433, + 655 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "play confidence weight outputs obtained by the model that computes them. We observe that the confidence $W_{q}$ , which is calculated once, assigns the high confidence sparsely. Interestingly, the confidence weights that evolve with each iteration initially assign high confidence to far-away points and moves towards closer points with increasing iterations.", + "bbox": [ + 75, + 748, + 468, + 838 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitation: we note an increase in error for the moving vehicle in the lower image set. The worse RMSE of our model compared to DepthFormer also indicates higher outlier predictions. This could be due to repeated operation of", + "bbox": [ + 75, + 839, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "our iterative updates, which further exacerbate the outlier problem. Even with consistency masking, the model we propose displays limitations with dynamic objects. However, the results of the last row of Tab. 2 show that using the refined pose to extract the consistency mask for training slightly improves Sq Rel, RMSE, and $\\delta_{2}$ . We leave further the discussion of this issue for future study.", + "bbox": [ + 496, + 340, + 893, + 448 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Odometry results", + "text_level": 1, + "bbox": [ + 498, + 458, + 669, + 474 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We present the results for visual odometry of the teacher model and the refinement model in Table 4. We also present the results of previous models that were trained on monocular videos. Our refinement module drastically improves the initial odometry results, as shown in Fig. 4. Although the goal of our study was to improve the estimation of local poses for accurate matching, we outperformed most of the other models in all metrics. Even without explicit training to ensure scale consistency, as in [7,8], our refined output demonstrates a globally consistent odometry prediction. Additionally, unlike Zou et al. [107] which infers pose from long-term geometry, this result is achieved with only two input frames to infer pose estimates. Our model also achieves an ATE that is on par with the traditional ORB-SLAM2, which performs global geometric optimization, although our results in $r_{err}$ still lag behind.", + "bbox": [ + 496, + 482, + 893, + 724 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusions", + "text_level": 1, + "bbox": [ + 500, + 739, + 627, + 753 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we introduced a self-supervised pipeline for multi-frame depth and pose estimation and refinement. By leveraging the combined power of neural network representation and geometric constraints to refine both depth and pose, our approach achieved state-of-the-art performance in both tasks. Our method also demonstrates greater efficiency than competing methods, with potential for further improvement. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 9788-9798, 2019. 3", + "[105] Hang Zhou, David Greenwood, and Sarah Taylor. Self-supervised monocular depth estimation with internal feature fusion. arXiv preprint arXiv:2110.09482, 2021. 3, 4, 7", + "[106] Tinghui Zhou, Matthew Brown, Noah Snavely, and David G Lowe. Unsupervised learning of depth and ego-motion from video. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 1851-1858, 2017. 1, 2, 6, 8", + "[107] Yuliang Zou, Pan Ji, Quoc-Huy Tran, Jia-Bin Huang, and Manmohan Chandraker. Learning monocular visual odometry via self-supervised long-term modeling. In European Conference on Computer Vision, pages 710-727. Springer, 2020. 8", + "[108] Yuliang Zou, Zelun Luo, and Jia-Bin Huang. Df-net: Unsupervised joint learning of depth and flow using cross-task consistency. In Proceedings of the European conference on computer vision (ECCV), pages 36-53, 2018. 1" + ], + "bbox": [ + 78, + 90, + 468, + 501 + ], + "page_idx": 12 + }, + { + "type": "page_number", + "text": "738", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 12 + } +] \ No newline at end of file diff --git a/2023/DualRefine_ Self-Supervised Depth and Pose Estimation Through Iterative Epipolar Sampling and Refinement Toward Equilibrium/afa982aa-a8cf-442d-886c-70412ae83518_model.json b/2023/DualRefine_ Self-Supervised Depth and Pose Estimation Through Iterative Epipolar Sampling and Refinement Toward Equilibrium/afa982aa-a8cf-442d-886c-70412ae83518_model.json new file mode 100644 index 0000000000000000000000000000000000000000..ab5be200c0c8fdada200eb03dd2aa46b22faa0ae --- /dev/null +++ b/2023/DualRefine_ Self-Supervised Depth and Pose Estimation Through Iterative Epipolar Sampling and Refinement Toward Equilibrium/afa982aa-a8cf-442d-886c-70412ae83518_model.json @@ -0,0 +1,3119 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.107, + 0.131, + 0.865, + 0.177 + ], + "angle": 0, + "content": "DualRefine: Self-Supervised Depth and Pose Estimation Through Iterative Epipolar Sampling and Refinement Toward Equilibrium" + }, + { + "type": "text", + "bbox": [ + 0.241, + 0.203, + 0.726, + 0.221 + ], + "angle": 0, + "content": "Antyanta Bangunharcana1, Ahmed Magd2, Kyung-Soo Kim1" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.222, + 0.856, + 0.258 + ], + "angle": 0, + "content": "\\(^{1}\\)Mechatronics, Systems, and Control Laboratory, \\(^{2}\\)Vehicular Systems Design and Control Lab Korea Advanced Institute of Science and Technology (KAIST), Republic of Korea" + }, + { + "type": "text", + "bbox": [ + 0.297, + 0.26, + 0.668, + 0.275 + ], + "angle": 0, + "content": "{antabangun，a.magd，kyungsoo}@kaist.ac.kr" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.31, + 0.314, + 0.327 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.343, + 0.471, + 0.479 + ], + "angle": 0, + "content": "Self-supervised multi-frame depth estimation achieves high accuracy by computing matching costs of pixel correspondences between adjacent frames, injecting geometric information into the network. These pixel-correspondence candidates are computed based on the relative pose estimates between the frames. Accurate pose predictions are essential for precise matching cost computation as they influence the epipolar geometry. Furthermore, improved depth estimates can, in turn, be used to align pose estimates." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.481, + 0.474, + 0.678 + ], + "angle": 0, + "content": "Inspired by traditional structure-from-motion (SfM) principles, we propose the DualRefine model, which tightly couples depth and pose estimation through a feedback loop. Our novel update pipeline uses a deep equilibrium model framework to iteratively refine depth estimates and a hidden state of feature maps by computing local matching costs based on epipolar geometry. Importantly, we used the refined depth estimates and feature maps to compute pose updates at each step. This update in the pose estimates slowly alters the epipolar geometry during the refinement process. Experimental results on the KITTI dataset demonstrate competitive depth prediction and odometry prediction performance surpassing published self-supervised baselines1." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.71, + 0.21, + 0.725 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.736, + 0.471, + 0.873 + ], + "angle": 0, + "content": "The optimization of the coordinates of observed 3D points and camera poses forms the basis of structure-from-motion (SfM). Estimation of both lays the foundation for robotics [34, 35, 75], autonomous driving [20], or AR/VR applications [60]. Traditionally, however, SfM techniques are susceptible to errors in scenes with texture-less regions, dynamic objects, etc. This has motivated the development of deep learning models that can learn to predict depth from monocular images [14, 15, 18, 48, 50]. These models can" + }, + { + "type": "image", + "bbox": [ + 0.599, + 0.31, + 0.8, + 0.41 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.596, + 0.414, + 0.8, + 0.558 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.57, + 0.895, + 0.631 + ], + "angle": 0, + "content": "Figure 1. (a) The estimated pose of a camera affects the epipolar geometry. (b) The epipolar line in the source image, calculated from yellow points in the target image, for the PoseNet-based [43] initial pose regression (red) and our refined pose (green). The yellow point in the source image is calculated based on our final depth and pose estimates." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.654, + 0.894, + 0.684 + ], + "angle": 0, + "content": "accurately predict depth based solely on image cues, without requiring geometric information." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.69, + 0.895, + 0.901 + ], + "angle": 0, + "content": "In recent years, self-supervised training of depth and pose models has become an attractive method, as it alleviates the need for ground truth while demonstrating precision comparable to those of supervised counterparts [7, 19, 22, 23, 26, 28, 30, 61, 70, 74, 83, 87, 98, 106, 108]. Such an approach uses depth and pose predictions to synthesize neighboring images in a video sequence and enforce consistency between them. As the image sequence is also available at test time, recent self-supervised methods also study the use of multiple frames during inference [91]. These typically involve the construction of cost volumes from multiple views to compute pixel correspondences, bearing similarities to (multi-view) stereo models [4, 44, 77]. By incorporating multi-frame data, geometric information is integrated to make depth predic" + }, + { + "type": "page_footnote", + "bbox": [ + 0.078, + 0.887, + 0.402, + 0.9 + ], + "angle": 0, + "content": "" + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.512, + 0.957 + ], + "angle": 0, + "content": "726" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.198 + ], + "angle": 0, + "content": "tions, improving the performance as well as the robustness. In such a multi-frame matching-based model, the accuracy of matching costs computation is essential. Recent work in DepthFormer [29] demonstrates its importance, as they designed a Transformer [84]-based module to improve matching costs and achieve state-of-the-art (SoTA) depth accuracy. However, their approach came with a large memory cost." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.202, + 0.474, + 0.55 + ], + "angle": 0, + "content": "Unlike stereo tasks, the aforementioned self-supervised multi-frame models do not assume known camera poses and use estimates learned by a teacher network, typically a PoseNet [43]-based model. This network takes two images as input and regresses a 6-DoF pose prediction. As the estimated pose affects the computation of epipolar geometry (Fig. 1(a)), the accuracy of the pose estimates is crucial to obtain accurate correspondence matches between multiple frames. However, as noted in recent studies [72], pure learning-based pose regression generally still lags behind its traditional counterpart, due to the lack of geometric reasoning. By refining the pose estimates, we can improve the accuracy of the matching costs, potentially leading to better depth estimates as well. In Fig. 1(b), we show that the epipolar lines calculated from the regressed poses do not align with our refined estimates. Conversely, a better depth prediction may lead to a better pose prediction. Thus, instead of building the cost volume once using regressed poses, we choose to perform refinements of both depth and pose in parallel and sample updated local cost volumes at each iteration. This approach is fundamentally inspired by traditional SfM optimization and is closely aligned with feedback-based models that directly couple depth and pose predictions [27]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.554, + 0.474, + 0.903 + ], + "angle": 0, + "content": "In this work, we propose a depth and pose refinement model that drives both towards an equilibrium, trained in a self-supervised framework. We accomplish this by making the following contributions: First, We introduce an iterative update module that is based on epipolar geometry and direct alignment. We sample candidate matches along the epipolar line that evolves based on the current pose estimates. Then the sampled matching costs are used to infer per-pixel confidences that are used to compute depth refinements. The updated depth estimates are then used in direct feature-metric alignments to refine the pose updates towards convergence. As a result, our model can perform geometrically consistent depth and pose updates. Second, These updates refine the initial estimates made by the single-frame model. By doing so, we do not rely on full cost volume construction and base our updates only on local cost volumes, making it simpler, more memory efficient, and more robust. Lastly, we design our method within a deep equilibrium (DEQ) framework [3] to implicitly drive the predictions towards a fixed point. Importantly, DEQ allows for efficient training with low training memory, improving upon the huge memory consumption of previous work. With our proposed novel design, we show improved depth estimates through experiments that are com" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.895, + 0.138 + ], + "angle": 0, + "content": "petitive with the SoTA models. Furthermore, our model demonstrates improved global consistency of visual odometry results, outperforming other learning-based models." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.152, + 0.642, + 0.168 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.177, + 0.738, + 0.194 + ], + "angle": 0, + "content": "2.1. Depth from a single image" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.201, + 0.896, + 0.473 + ], + "angle": 0, + "content": "The depth prediction problem for a single image is ill-posed due to the possibility of different 3D scenes projecting onto the same 2D image [32]. Nonetheless, humans can predict depth from a single image through experience. Motivated by this, numerous supervised neural network models were proposed to solve the monocular depth estimation task, starting with Eigen et al.'s paper [15]. Subsequently, performance was improved by modifying the model architecture [14,48,64,94], training on large dataset [13,53,95,100], designing robust loss functions [49,103], and transforming the problem into a classification task [52]. However, supervisory depth estimation requires ground-truth depth maps, which are difficult to collect in large quantities and of high quality. This challenge is one of the main reasons why researchers are exploring semi-supervised training, where the model expects weak supervision, such as providing relative depth [12], camera poses [101], or utilizing synthetic data for training [1,47,62]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.474, + 0.897, + 0.684 + ], + "angle": 0, + "content": "The need for weak supervision still presents limitations in generalizability and scalability, among other aspects. To address these constraints, research on self-supervised training techniques is gaining momentum. These techniques involve using geometry in stereo matching [19, 22] or with a sequence of single-camera images, as initially proposed by [106]. Monodepth2 [23] refined the idea of exploiting image sequences for training by using auto-masking and minimum reprojection losses to address occlusion and egomotion issues. Further improvements were made by defining the problem as a classification task [25, 42], modifying the architecture [28], feature-based loss for regions with low texture [74, 101], or reducing artifacts from moving objects [11, 46, 80]." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.685, + 0.894, + 0.715 + ], + "angle": 0, + "content": "Our work is based on self-supervised monocular depth and employs them as a teacher and initial estimate." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.726, + 0.753, + 0.743 + ], + "angle": 0, + "content": "2.2. Depth from multiple frames" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.895, + 0.825 + ], + "angle": 0, + "content": "Relying on single frames at test-time requires the model to make several assumptions about the scene's geometrical details. In contrast, multi-frame approaches, which leverage available temporal information and incorporate multi-view geometry, reduce the need for such assumptions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.896, + 0.903 + ], + "angle": 0, + "content": "Multi-frame depth prediction is closely related to stereo depth estimation, where neural networks convert input stereo images into depth maps, as demonstrated by [54, 63, 82]. Kendall et al. [44] achieved a significant improvement by constructing a plane-sweep stereo cost volume. Generally," + }, + { + "type": "page_number", + "bbox": [ + 0.487, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "727" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.242 + ], + "angle": 0, + "content": "multi-view stereo (MVS) research is more relevant to our work, as it utilizes an unstructured collection of scene images, meaning that the pose between different images is not fixed. In studies like [36, 38, 58, 90, 97], it was common to combine the previously mentioned cost volumes with ground truth depth and camera poses for guidance. Consequently, these works require camera poses during inference [56, 92]. Although some research managed to relax the pose requirement during inference, training still necessitates this supervision [77, 82]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.244, + 0.474, + 0.456 + ], + "angle": 0, + "content": "The methods discussed above, along with advances in other domains such as scale domain adaptation [31, 69, 104], view synthesis [23, 93], and other supervisory techniques [26, 30], have significantly impacted the performance of self-supervised approaches. ManyDepth [91], which is similar to our work, focuses on the drawbacks of using a single image during inference and proposes a flexible model that takes advantage of multiple frames at test time, if available. ManyDepth reduces artifacts from moving objects and temporarily stationary cameras by using a single-frame model as a teacher, resulting in improved depth map accuracy. More recently, DepthFormer [29] achieved substantial accuracy improvements by using Transformers [84] to obtain improved pixel matching costs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.456, + 0.472, + 0.562 + ], + "angle": 0, + "content": "Inspired by traditional bundle adjustments, we design a model that simultaneously solves for both depth and pose while incorporating many of the advancements mentioned earlier. Our approach is most similar to DRO [27]. However, compared to their approach, our model tightly integrates multi-view geometry into the iterative updates formulation and bases our refinements on the local epipolar geometry." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.574, + 0.274, + 0.589 + ], + "angle": 0, + "content": "2.3. Iterative refinements" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.598, + 0.473, + 0.78 + ], + "angle": 0, + "content": "Iterative refinement has been employed to improve prediction quality in various learning tasks, including object detection [6, 24], optical flow estimation [37, 78], semantic segmentation [68, 102], and others [40, 71]. Some recent research has attempted to iterate the refinement process using deep convolutional networks [9, 21, 55, 57]. Other works train the same network repeatedly by utilizing the results of the previous iteration [99, 102]. In particular, RAFT [78] found success with its iterative refinement procedure for flow estimation. DEQ-flow [2] employed a deep equilibrium (DEQ) [3] framework to reduce the memory consumption of RAFT during training while maintaining accuracy." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.473, + 0.903 + ], + "angle": 0, + "content": "A key component of our model is inspired by the iterative updates of RAFT and DEQ-flow. Instead of optical flow, our model refines depth and pose estimates in parallel. We design our refinement module to tightly couple the two predictions, considering the epipolar geometry of adjacent frames. With every update, the epipolar geometry is refined, which also results in a more accurate matching costs computation of pixel correspondences." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.091, + 0.658, + 0.106 + ], + "angle": 0, + "content": "2.4. Pose estimation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.113, + 0.896, + 0.388 + ], + "angle": 0, + "content": "Pose estimation is a crucial component in self-supervised monocular depth models. In many works, PoseNet-based models [43] take a pair of adjacent image frames and output a 6 DoF pose estimation. This class of models is straightforward, but often less accurate than their traditional counterparts [16, 17, 65] due to the absence of geometry constraints. Recent work in deep learning-based localization has adopted differentiable geometrically inspired designs within their models by using direct alignments [72, 85, 86] or geometric alignments based on optical flow [79]. These models demonstrate better generalization properties and accuracy. The use of self-supervised monocular depth has also been used to improve traditional odometry [8, 96]. However, our interest lies in learning to refine both depth and pose in the self-supervision pipeline. To improve the accuracy of pose estimation, we integrate direct alignment within the recurrent module, ensuring geometrically consistent prediction between depth and pose." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.398, + 0.593, + 0.414 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.423, + 0.895, + 0.514 + ], + "angle": 0, + "content": "Our model comprises two primary sub-modules. The first is a single frame self-supervised depth and pose estimator, building upon previous frameworks [23, 105], which we revisit in Sec. 3.1. This network serves as both a teacher and an initializer for the second sub-module, our proposed multi-frame network, presented in detail in Sec. 3.2." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.522, + 0.776, + 0.538 + ], + "angle": 0, + "content": "3.1. Self-supervised depth and pose" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.545, + 0.895, + 0.711 + ], + "angle": 0, + "content": "We begin by describing the canonical self-supervised monocular depth estimation pipeline [23], which serves as the foundation for our approach. This depth training method assumes that a monocular camera with an intrinsic parameter \\( K \\) captures an image sequence of a scene. In this process, two networks are trained in parallel to estimate the per-pixel depth map of the images \\( D \\) and the relative poses between adjacent image frames. By warping neighboring images towards a shared target frame using these two predictions, self-supervised training can be performed by enforcing photometric consistency between the frames." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.711, + 0.895, + 0.772 + ], + "angle": 0, + "content": "Given the depth map \\(D\\) of a target image and its relative pose with a source image \\(T_{t\\rightarrow s}\\), we can calculate the projection of each pixel \\(u = (x,y)\\) of the target image onto the source image as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.558, + 0.777, + 0.895, + 0.827 + ], + "angle": 0, + "content": "\\[\nz ^ {\\prime} u ^ {\\prime} = z ^ {\\prime} \\left[\\begin{array}{l}x ^ {\\prime}\\\\y ^ {\\prime}\\\\1\\end{array}\\right] = K T _ {t \\rightarrow s} \\left(D [ u ] K ^ {- 1} \\left[\\begin{array}{l}x\\\\y\\\\1\\end{array}\\right]\\right), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.832, + 0.895, + 0.879 + ], + "angle": 0, + "content": "using the estimated depth at that pixel \\( D[u] \\). The source images can then be warped towards the target frame by sampling the pixel values at the calculated projection" + }, + { + "type": "equation", + "bbox": [ + 0.641, + 0.885, + 0.895, + 0.903 + ], + "angle": 0, + "content": "\\[\nI _ {s \\rightarrow t} [ u ] = I _ {s} \\langle u ^ {\\prime} \\rangle , \\tag {2}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.512, + 0.957 + ], + "angle": 0, + "content": "728" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.087, + 0.52, + 0.277 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.528, + 0.09, + 0.885, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.534, + 0.284, + 0.645, + 0.299 + ], + "angle": 0, + "content": "DEQ updates" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.309, + 0.895, + 0.361 + ], + "angle": 0, + "content": "Figure 2. (a) The overall pipeline of the model. Given a pair of source and target images, the teacher model predicts an initial depth \\( D_0 \\) and pose \\( T_0 \\), as well as initial hidden states that will be updated. DEQ-based alignments are then performed to find the fixed point and output the final predictions. (b) Each iteration in the update step takes the current depth and pose estimates. Matching costs are sampled along the current epipolar lines that evolves based on the pose estimates. The updates are computed by Conv-GRU. Then feature-metric alignment is used to obtain a geometrically consistent pose update." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.372, + 0.47, + 0.402 + ], + "angle": 0, + "content": "where \\(\\langle \\cdot \\rangle\\) indicates bilinear interpolation, implemented using the spatial transformer network (STN) [39]." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.403, + 0.471, + 0.434 + ], + "angle": 0, + "content": "The self-supervised loss is calculated as a combination of the photometric error and the edge-aware smoothness loss:" + }, + { + "type": "equation", + "bbox": [ + 0.186, + 0.447, + 0.47, + 0.465 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {s e l f - s u p} = \\lambda_ {p} \\mathcal {L} _ {p} + \\lambda_ {s} \\mathcal {L} _ {s}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.477, + 0.47, + 0.568 + ], + "angle": 0, + "content": "where the photometric error between the warped source image and the target image is calculated using the structural similarity loss, and the minimum error is taken between multiple warped images to account for occlusions. Interested readers can refer to [23]. The self-supervised loss is typically computed at multiple scales to stabilize the training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.568, + 0.471, + 0.659 + ], + "angle": 0, + "content": "In this paper, we train a monocular depth estimator and a pose estimation network using this pipeline, serving two purposes. First, following ManyDepth [91], we use these models as a teacher to constrain the multi-frame predictions in the presence of dynamic objects. Additionally, we employ them as an initializer for the multi-frame alignment network." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.68, + 0.255, + 0.695 + ], + "angle": 0, + "content": "3.1.1 Monocular model" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.473, + 0.903 + ], + "angle": 0, + "content": "We build our monocular depth estimation model based on DIFFNet [105], a SoTA self-supervised single-frame estimator. We extract feature maps at multiple scales \\( s \\) from the target image using the HRNet architecture [88]. In accordance with DIFFNet, feature maps from multiple stages are accumulated in \\( F^{(1/2^s)} \\). Then, we employ disparity decoders to make disparity predictions at scales \\( s = \\{2,3\\} \\). The pose estimation network follows the canonical PoseNet [43] architecture, taking two input images and outputting 6-DoF values, with a ResNet18 [33] backbone. The predicted disparity and pose estimation from these networks are used as a teacher to train our alignment sub-module, as was done in ManyDepth [91]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.372, + 0.76, + 0.388 + ], + "angle": 0, + "content": "3.2. Deep equilibrium alignments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.395, + 0.892, + 0.47 + ], + "angle": 0, + "content": "In our alignment sub-module, we assume that additional input from source image(s) is available, which can be used to refine the depth and pose estimates. In this work, we focus on using the image from the previous frame in the image sequence as our source image." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.47, + 0.894, + 0.532 + ], + "angle": 0, + "content": "Our alignment module is formulated as a deep equilibrium model [3] that updates the hidden states, depth, and pose estimates to a fixed point. Specifically, at the fixed point \\( z^{*} \\)," + }, + { + "type": "equation", + "bbox": [ + 0.601, + 0.542, + 0.892, + 0.559 + ], + "angle": 0, + "content": "\\[\n\\left(h ^ {*}, D ^ {*}, T ^ {*}\\right) = z ^ {*} = \\mathrm {U} \\left(z ^ {*}, x\\right), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.57, + 0.895, + 0.66 + ], + "angle": 0, + "content": "where \\( z \\) is composed of a hidden state \\( h \\), the depth prediction \\( D \\), and the pose prediction \\( T \\). U represents our update function, refining the depth and pose alternatively. \\( x \\) is an input to the update module, obtained based on the epipolar geometry at each step, which we discuss in the next subsection. We perform these iterative updates at scale \\( s = 2 \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.661, + 0.894, + 0.737 + ], + "angle": 0, + "content": "From the feature extraction output, we compute an initial hidden state for our recurrent updates \\( h^{[0]} = \\tanh(\\mathrm{H}(F^{(1/4)})) \\) and a context feature \\( q = \\mathrm{Q}(F^{(1/4)}) \\). Both H and Q are composed of a single residual block [33] followed by a convolutional layer." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.754, + 0.848, + 0.77 + ], + "angle": 0, + "content": "3.2.1 Depth updates around local neighborhood" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.778, + 0.892, + 0.871 + ], + "angle": 0, + "content": "Local epipolar sampling. As discussed previously, our refinement is based on the pixel matching between the target image and the source image. We use the first two blocks of the HRNet feature extractor to extract unary features from the source image \\( m_{s}^{(1/4)} \\) and the target image \\( m_{t}^{(1/4)} \\), which we will use to calculate the matching costs." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Similarly to RAFT [78], our aim is to compute the matching values for candidate correspondences around the current" + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "729" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.092, + 0.287, + 0.155 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.176, + 0.159, + 0.196, + 0.173 + ], + "angle": 0, + "content": "Wq" + }, + { + "type": "image", + "bbox": [ + 0.287, + 0.092, + 0.488, + 0.153 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.373, + 0.159, + 0.403, + 0.172 + ], + "angle": 0, + "content": "\\(W_{h,5}\\)" + }, + { + "type": "image", + "bbox": [ + 0.488, + 0.092, + 0.688, + 0.153 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.58, + 0.094, + 0.597, + 0.106 + ], + "angle": 0, + "content": "\\(D_0\\)" + }, + { + "type": "image", + "bbox": [ + 0.689, + 0.092, + 0.889, + 0.153 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.58, + 0.159, + 0.597, + 0.172 + ], + "angle": 0, + "content": "\\(D_{5}\\)" + }, + { + "type": "image", + "bbox": [ + 0.086, + 0.172, + 0.288, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.288, + 0.172, + 0.489, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.49, + 0.172, + 0.688, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.689, + 0.172, + 0.888, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.226, + 0.287, + 0.286 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.177, + 0.292, + 0.196, + 0.305 + ], + "angle": 0, + "content": "Wq" + }, + { + "type": "image", + "bbox": [ + 0.287, + 0.226, + 0.489, + 0.286 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.375, + 0.292, + 0.403, + 0.305 + ], + "angle": 0, + "content": "\\(W_{h,5}\\)" + }, + { + "type": "image", + "bbox": [ + 0.489, + 0.226, + 0.688, + 0.286 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.58, + 0.293, + 0.597, + 0.305 + ], + "angle": 0, + "content": "\\(D_{5}\\)" + }, + { + "type": "image", + "bbox": [ + 0.689, + 0.226, + 0.889, + 0.286 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.763, + 0.292, + 0.815, + 0.305 + ], + "angle": 0, + "content": "AbsRel5" + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.305, + 0.288, + 0.353 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.287, + 0.305, + 0.489, + 0.353 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.49, + 0.305, + 0.688, + 0.353 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.689, + 0.305, + 0.889, + 0.353 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.369, + 0.893, + 0.395 + ], + "angle": 0, + "content": "Figure 3. Qualitative results on KITTI data. \\( I_{s} \\): input image; \\( W_{q} \\), \\( W_{h,0} \\), and \\( W_{h,5} \\): confidence weights; \\( D_{0} \\), \\( D_{5} \\): disparity estimates; The Abs Rel error for the depth estimates." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.409, + 0.47, + 0.544 + ], + "angle": 0, + "content": "prediction and use them as input to our update module at the update step \\( k \\). Unlike RAFT, however, we perform matching along an epipolar line based on the pose estimate \\( T_{k} \\). This is done by computing the projected coordinates \\( u_{k}^{\\prime} \\) in the source image obtained from (1) at the depths of interest. The depth candidates are computed to be the neighborhood of the current prediction. Instead of computing the all-pair correlation as was done in RAFT, we compute feature matching on the fly." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.545, + 0.471, + 0.745 + ], + "angle": 0, + "content": "At each pixel \\( u \\), we compute the local depth candidates as \\( D[u]_k \\pm (i \\times c \\times n) \\), with \\( i \\in \\mathbb{Z} \\) and \\( i \\leq r \\). We set the sampling radius hyperparameter \\( r = 8 \\) in our experiments. In depth estimation, the error typically grows with distance. To account for this, we define \\( c = D[u] / C \\) as a function of depth to make the sampling range dependent on the depth, where we set \\( C \\) as a trainable parameter. Following RAFT, to collect the matching information from a larger neighborhood, we sampled at multiple levels \\( n = \\{1,2,3\\} \\). At each level, we bilinearly resize the matching feature map of the source image \\( m_s^{(1/4)} \\) with a scale of \\( 1/2^n \\). Then, the matching features are sampled at the calculated corresponding set of coordinates \\( u_k' \\), and the absolute differences with the target feature" + }, + { + "type": "equation", + "bbox": [ + 0.191, + 0.754, + 0.47, + 0.771 + ], + "angle": 0, + "content": "\\[\n\\mathbf {C} _ {k} [ u ] = \\left| m _ {t} [ u ] - m _ {s} \\langle u _ {k} ^ {\\prime} \\rangle \\right| \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.471, + 0.87 + ], + "angle": 0, + "content": "are calculated and gathered. This provides us with a map \\(\\mathbf{C}_k\\) that contains \\(n \\times (2 \\times r + 1)\\) matching cost values at the corresponding depth candidates. We then encode these matching costs along with the depth using a two-layer convolutional neural network (CNN) to compute the input for the update module" + }, + { + "type": "equation", + "bbox": [ + 0.158, + 0.883, + 0.47, + 0.9 + ], + "angle": 0, + "content": "\\[\nx _ {k} = \\left[ \\operatorname {C N N} _ {\\mathbf {C}} \\left(\\mathbf {C} _ {k}\\right), \\operatorname {C N N} _ {D _ {x}} \\left(D _ {k}\\right), q \\right], \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.409, + 0.766, + 0.424 + ], + "angle": 0, + "content": "where \\([\\cdot ,\\cdot ]\\) represents the concatenation." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.434, + 0.893, + 0.51 + ], + "angle": 0, + "content": "Depth update. The update function calculates an updated hidden state \\( h_{k+1} \\) using the Conv-GRU block [5,41,78]. \\( h_{k+1} \\) is used to compute the depth updates. To stabilize training, we use the activation function \\( \\tanh(\\cdot) \\) to bound the absolute update values for the depths to be within \\( r \\cdot c \\):" + }, + { + "type": "equation", + "bbox": [ + 0.562, + 0.521, + 0.893, + 0.538 + ], + "angle": 0, + "content": "\\[\nD _ {k + 1} = D _ {k} + r \\cdot c \\cdot \\tanh \\left(\\mathrm {C N N} _ {D _ {\\mathrm {U}}} \\left(h _ {k + 1}\\right)\\right). \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.547, + 0.893, + 0.608 + ], + "angle": 0, + "content": "These updates are performed in an alternating fashion with the pose updates to reach the fixed point \\( D^{*} \\). Using \\( h^{*} \\), we compute a convex upsampling to obtain the final depth estimate at the input resolution." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.626, + 0.774, + 0.642 + ], + "angle": 0, + "content": "3.2.2 Feature-metric pose alignments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.649, + 0.894, + 0.756 + ], + "angle": 0, + "content": "In (1), the accuracy of pose estimation affects the calculation of the coordinates of pixels. Hence, a refined pose estimate would also improve the reliability of the matching costs. To refine the pose while being geometrically consistent, we perform our pose updates based on direct feature alignments [16, 17, 87]. These updates \\(\\delta_{k}\\) can be calculated by solving \\(H_{k}\\delta_{k} = b_{k}\\), where" + }, + { + "type": "equation", + "bbox": [ + 0.536, + 0.764, + 0.892, + 0.788 + ], + "angle": 0, + "content": "\\[\nH _ {k} = \\mathcal {J} _ {k} ^ {T} \\operatorname {d i a g} \\left(W _ {k}\\right) \\mathcal {J} _ {k} \\text {a n d} b _ {k} = - \\mathcal {J} _ {k} ^ {T} \\operatorname {d i a g} \\left(W _ {k}\\right) r _ {k} \\tag {8}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.704, + 0.786, + 0.854, + 0.801 + ], + "angle": 0, + "content": "\\[\nr _ {k} [ u ] = m _ {s} \\left\\langle u _ {k} ^ {\\prime} \\right\\rangle - m _ {t} [ u ],\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.811, + 0.809, + 0.826 + ], + "angle": 0, + "content": "and \\(\\mathcal{J}\\) is the Jacobian with respect to the pose." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.894, + 0.901 + ], + "angle": 0, + "content": "To compute this pose update, one could assign uniform confidence to every pixel in the image. However, in Eq. (8), additional confidence weights per pixel \\( W \\) can also be integrated. This is done for two reasons. First, the solution for the pose updates can be affected by dynamic objects" + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.945, + 0.512, + 0.957 + ], + "angle": 0, + "content": "730" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.242 + ], + "angle": 0, + "content": "as well as inaccurate feature alignments that may occur in region with repeated textures. To account for this, the confidence weighting of the input context feature map \\( W_{q} \\) can be computed [72]. Specifically, we computed a confidence map \\( W_{t,s} = 1 / (1 + \\mathrm{ReLU}(\\mathrm{CNN}_{W_q}(F_{t,s})) \\) for both target and source images. The source confidence is warped towards the target frame using Eqs. (1) and (2). Finally, the confidence is computed as \\( W_{q} = W_{t}\\cdot W_{s,\\text{warped}} \\). This confidence weight is only computed once to assign per-pixel confidence for the input images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.244, + 0.473, + 0.441 + ], + "angle": 0, + "content": "Second, the accuracy of pose updates would depend on the accuracy of the depth estimates. To obtain more accurate pose updates, we would like to assign more alignment confidence to the region with higher depth accuracy. We use a neural network to infer this confidence from the matching costs. Since the hidden states \\( h \\) have a history of these matching costs, another confidence weights \\( W_{h,k} = \\mathrm{CNN}_{W_h}(h_k) \\) can be computed. Unlike the previous confidence map, this one is computed and evolves at every update step. By doing so, the network can use the depth predictions to guide the pose estimates towards convergence using the depth information. In our experiments, we investigate the use of each confidence weighting and combination of both \\( W_{k} = W_{q}W_{h,k} \\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.441, + 0.473, + 0.487 + ], + "angle": 0, + "content": "Finally, we can compute the updated pose as \\( T_{k + 1} = \\exp (\\delta_k^{\\wedge})T_k \\). These operations are designed to be differentiable to enable end-to-end training." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.511, + 0.228, + 0.527 + ], + "angle": 0, + "content": "3.2.3 DEQ training" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.536, + 0.47, + 0.672 + ], + "angle": 0, + "content": "We adopt a DEQ framework, wherein the above steps are repeated until the depth and pose values reach a fixed point, at which the update value is minimal. In our implementation, the fixed points of depth and pose are chosen separately, and it is possible for both to be selected from different update steps. Finally, the training gradient is computed using the chosen depth and pose fixed points. Operations prior to the fixed point do not require saving gradients in memory, which allows memory-efficient training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.673, + 0.47, + 0.856 + ], + "angle": 0, + "content": "As noted in Eqs. (1) to (3), the self-supervision losses can be computed given a depth and pose prediction. At the fixed point, we compute two additional self-supervision losses. The first performs source-to-target image warping through the pairing of the final depth \\( D^{*} \\) and the initial pose \\( T_{0} \\), where we detach \\( T_{0} \\) from the computational graph to act as a teacher. This loss is used so that the output of the teacher and refinement modules shares the same scaling. The second performs the warping with the pairing of \\( D^{*} \\) and \\( T^{*} \\). This loss helps drive refined estimation of both depth and pose towards the optimal value. Detailed experiments for this choice of loss pairings are provided in the supplementary." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.473, + 0.902 + ], + "angle": 0, + "content": "In both losses, we also apply the consistency loss between \\( D_0 \\) and \\( D^* \\), similar to ManyDepth [91], to account for dynamic objects or occluded regions. Specifically, we extract" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.304 + ], + "angle": 0, + "content": "coarse depth predictions from the raw feature matchings and mask regions where large disagreements occur, and enforce consistency with the teacher depth. Unlike ManyDepth, however, our method does not explicitly construct a cost volume. To obtain the coarse depth, we search for the lowest matching cost around the neighborhood of the teacher depth, similar to Sec. 3.2.1, but with a larger neighborhood range. This approach offers an additional advantage compared to the cost volume-based method, as we do not need to rely on an estimated minimum and maximum depth or know the scale of the estimates. Moreover, since the computation of coarse depth depends on the accuracy of feature matching costs, it can be improved with more accurate pose estimates (Tab. 2)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.318, + 0.634, + 0.335 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.344, + 0.691, + 0.358 + ], + "angle": 0, + "content": "4.1. Dataset and metrics" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.367, + 0.895, + 0.519 + ], + "angle": 0, + "content": "For depth estimation experiments, we use the Eigen train/test split [15] from the KITTI dataset [20]. To evaluate the estimated depths, we scale them by a scalar to match the scale of the ground truth. We employ standard depth evaluation metrics [14, 15], including absolute and squared relative error (Abs Rel, Sq Rel), root mean square error (RMSE, RMSE log), and accuracy under threshold \\((\\delta_{1}, \\delta_{2}\\), and \\(\\delta_{3})\\) with a maximum depth set at \\(80m\\). Lower values are better for the first four metrics, while higher values are better for the remaining three." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.519, + 0.895, + 0.656 + ], + "angle": 0, + "content": "For the visual odometry experiments, we use the KITTI odometry dataset and follow the same training and evaluation sequences (Seq. 00-08 for training and Seq. 09-10 for evaluation) as in previous work [106]. Since our estimation relies on a monocular camera, the estimated trajectories are aligned with the ground truth using the 7 DoF Umyama alignment [81]. We use standard odometry evaluation metrics such as translation \\((t_{err})\\) and rotation \\((r_{err})\\) error [20], and absolute trajectory error (ATE) [76]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.665, + 0.715, + 0.682 + ], + "angle": 0, + "content": "4.2. Implementation details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.895, + 0.84 + ], + "angle": 0, + "content": "We conduct our experiments using PyTorch [66] on an RTX 3090 GPU with a batch size of 12. Following [23], we apply color and flip augmentations and resize input images to a resolution of \\(640 \\times 192\\). For our high resolution experiments, we resize the images to \\(960 \\times 288\\). We train the entire network for 15 epochs with a learning rate of \\(10^{-3}\\), at which point we freeze the teacher depth and pose models. We then continue to train the network with a learning rate of \\(10^{-4}\\). Adam optimizer [45] is employed with \\(\\beta_{1} = 0.9\\) and \\(\\beta_{2} = 0.999\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.902 + ], + "angle": 0, + "content": "As mentioned earlier, the depth backbone is based on the HRNet architecture [88]. For the teacher pose model, we adhere to the standard design, using the first five layers of a ResNet18 initialized with ImageNet pre-trained weights as" + }, + { + "type": "page_number", + "bbox": [ + 0.487, + 0.946, + 0.51, + 0.957 + ], + "angle": 0, + "content": "731" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.08, + 0.091, + 0.894, + 0.336 + ], + "angle": 0, + "content": "
MethodTest framesSemanticsW × HAbs Rel ↓Sq Rel ↓RMSE ↓RMSE log ↓δ1 ↑δ2 ↑δ3 ↑
Low & mid resRanjan et al. [70]1832 × 2560.1481.1495.4640.2260.8150.9350.973
EPC++ [59]1832 × 2560.1411.0295.3500.2160.8160.9410.976
Struct2depth (M) [10]1●416 × 1280.1411.0265.2910.2150.8160.9450.979
Videos in the wild [26]1●416 × 1280.1280.9595.2300.2120.8450.9470.976
Guizilini et al. [30]1●640 × 1920.1020.6984.3810.1780.8960.9640.984
Johnston et al. [42]1640 × 1920.1060.8614.6990.1850.8890.9620.982
Monodepth2 [23]1640 × 1920.1150.9034.8630.1930.8770.9590.981
Packnet-SFM [28]1640 × 1920.1110.7854.6010.1890.8780.9600.982
Li et al. [51]1416 × 1280.1300.9505.1380.2090.8430.9480.978
DIFFNet [105]1640 × 1920.1020.7644.4830.1800.8960.9650.983
DualRefine-initial (D0)1640 × 1920.1030.7214.4760.1800.8910.9650.984
Patil et al. [67]N†640 × 1920.1110.8214.6500.1870.8830.9610.982
Wang et al. [89]2 (-1, 0)640 × 1920.1060.7994.6620.1870.8890.9610.982
ManyDepth (MR) [91]2 (-1, 0)640 × 1920.0980.7704.4590.1760.9000.9650.983
DepthFormer [29]2 (-1, 0)640 × 1920.0900.6614.1490.1750.9050.9670.984
DualRefine-refined (D*)2 (-1, 0)640 × 1920.0900.6584.2370.1710.9120.9670.984
High resDRO [27]2 (-1, 0)960 × 3200.0880.7974.4640.2120.8990.9590.980
Wang et al. [89]2 (-1, 0)1024 × 3200.1060.7734.4910.1850.8900.9620.982
ManyDepth (HR ResNet50) [91]2 (-1, 0)1024 × 3200.0910.6944.2450.1710.9110.9680.983
DualRefine-refined (HR) (D*)2 (-1, 0)960 × 2880.0890.7544.2730.1700.9170.9680.983
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.347, + 0.893, + 0.375 + ], + "angle": 0, + "content": "Table 1. Results and comparison with other state-of-the-arts models on the KITTI [20] Eigen split. Bold: Best, Underscore: Second best. † : evaluated on whole sequences" + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.392, + 0.472, + 0.491 + ], + "angle": 0, + "content": "
Pose UpdatesConsistency maskAbs RelSq RelRMSEδ1δ2
no updateT00.0970.7134.4620.8980.964
no weightsT00.0900.6584.2370.9120.967
no Wh,kT00.0900.6454.2730.9080.966
no WqT00.0910.7134.2950.9100.967
Wq and Wh,kT00.0890.6524.2820.9090.967
no weightsT*0.0910.6454.2010.9100.968
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.501, + 0.47, + 0.527 + ], + "angle": 0, + "content": "Table 2. Ablation experiment for the effect of pose updates on the KITTI [20] Eigen split. Bold: Best." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.549, + 0.47, + 0.625 + ], + "angle": 0, + "content": "an encoder, followed by a decoder that outputs 6-DoF pose estimates. At test time, depth estimates are made using the current frame and the previous frame when available. When the previous frame is unavailable, we skip the refinement module and simply use the initial estimates." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.635, + 0.182, + 0.649 + ], + "angle": 0, + "content": "4.3. Ablation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.659, + 0.47, + 0.703 + ], + "angle": 0, + "content": "Pose updates. We analyze the effect of pose refinement toward depth and present the findings in Table 2. Our model that does not perform pose updates has the worst accuracy." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.47, + 0.779 + ], + "angle": 0, + "content": "**Evolving confidence weighting.** We also show the impact of confidence weightings. Interestingly, similar performance can be observed for all models that perform pose updates, even when no confidence weighting is used to guide the pose computation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.471, + 0.902 + ], + "angle": 0, + "content": "DEQ iteration. In addition to studying the effect of pose refinements, we also investigate aspects of DEQ iterative updates and present the findings when we vary the number of iterations during training and at test time in Table 3. The results suggest that 6 iterations is sufficient for the model to find the fixed point. We speculate that the initial estimate provides a reliable starting point and hence the fast convergence. On our machine, the 6 update iterations increase the" + }, + { + "type": "table", + "bbox": [ + 0.536, + 0.39, + 0.861, + 0.492 + ], + "angle": 0, + "content": "
DEQ # itersAbs RelSq RelRMSEδ1Time (ms)
3→30.0970.7774.4310.90653
6→30.0980.6954.3180.90553
6→60.0900.6584.2370.91268
12→30.1020.7324.4280.90053
12→60.0950.7084.3360.90768
12→120.0920.7074.3160.90999
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.501, + 0.895, + 0.538 + ], + "angle": 0, + "content": "Table 3. Ablation experiment for the DEQ iterations on the KITTI [20] Eigen split. \\( a \\rightarrow b \\) represents \\( a : \\# \\) iters at training and \\( b : \\# \\) iters at test time. Bold: Best." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.561, + 0.895, + 0.622 + ], + "angle": 0, + "content": "baseline model's inference time from \\(37.90\\mathrm{ms}\\) by \\(\\sim 31\\) ms to a total of \\(68.49~\\mathrm{ms}\\), running at almost 15 fps. However, we only use PyTorch basic functions in our implementation, and further optimization of the code could be made." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.634, + 0.64, + 0.65 + ], + "angle": 0, + "content": "4.4. Depth results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.895, + 0.854 + ], + "angle": 0, + "content": "Table 1 shows the comparison of our depth estimation with SoTA self-supervised models. We compare with models that train on monocular video. Our model outperforms most previous models and is competitive with the Transformer [84]-based DepthFormer [29] model. Specifically, our model shows a significant improvement in \\(\\delta_{1}\\), suggesting highly accurate inliers. Furthermore, compared to DepthFormer that requires 16GB training memory per batch, ours only consumes 24GB of memory for 12 batches, around \\(1/8 \\times\\) the memory requirement. This is mainly because our method refines 2D hidden states based on local sampling, while [29] refines 2D feature maps and a 3D feature volume using self/cross-attention along every depth bin." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Fig. 3 displays qualitative outputs for the disparity and error map of our model. We can observe an improvement to the error map of the refined depth. We also additionally dis" + }, + { + "type": "page_number", + "bbox": [ + 0.487, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "732" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.123, + 0.089, + 0.855, + 0.288 + ], + "angle": 0, + "content": "
MethodsSeq 9Seq 10
\\(t_{err}(\\%) \\downarrow\\)\\(r_{err}(\\circ/100m) \\downarrow\\)ATE (m) ↓\\(t_{err}(\\%) \\downarrow\\)\\(r_{err}(\\circ/100m) \\downarrow\\)ATE (m) ↓
ORB-SLAM2 [65] (w/o LC)9.670.344.104.040.36.43
ORB-SLAM2 [65]3.220.48.844.250.38.51
SfMLearner [106]19.156.8277.7940.4017.6967.34
GeoNet [98]28.729.8158.4523.909.043.04
DeepMatchVO [73]9.913.827.0812.185.924.44
Monodepth2 [23]17.173.8576.2211.685.3120.35
DW [26]-Learned--20.91--17.88
DW [26]-Corrected--19.01--14.85
SC-Depth [7]7.313.0523.567.794.9012.00
Zou et al. [107]3.491.0011.305.811.811.80
P-RGBD SLAM [8]5.081.0513.404.322.347.99
DualRefine-initial (T0)9.062.5939.319.454.0515.13
DualRefine-refined (T*)3.431.045.186.801.1310.85
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.296, + 0.893, + 0.322 + ], + "angle": 0, + "content": "Table 4. Results on Seq. 09 and Seq. 10 of the KITTI odometry data. We provide a comparison with other state-of-the-art self-supervised depth and odometry methods. ORB-SLAM2 is included as a representative non-learning based method. Bold: Best, Underscore: Second best." + }, + { + "type": "image", + "bbox": [ + 0.182, + 0.351, + 0.379, + 0.539 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.123, + 0.556, + 0.434, + 0.656 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.675, + 0.472, + 0.725 + ], + "angle": 0, + "content": "Figure 4. Estimated trajectory by the initial pose estimator and the refined trajectory using our pose refinement module on (a) Seq. 09 and (b) Seq. 10 of KITTI odometry data. The refined pose estimate improves the global trajectory, even without explicitly training for global consistency." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.749, + 0.47, + 0.839 + ], + "angle": 0, + "content": "play confidence weight outputs obtained by the model that computes them. We observe that the confidence \\( W_{q} \\), which is calculated once, assigns the high confidence sparsely. Interestingly, the confidence weights that evolve with each iteration initially assign high confidence to far-away points and moves towards closer points with increasing iterations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Limitation: we note an increase in error for the moving vehicle in the lower image set. The worse RMSE of our model compared to DepthFormer also indicates higher outlier predictions. This could be due to repeated operation of" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.342, + 0.895, + 0.449 + ], + "angle": 0, + "content": "our iterative updates, which further exacerbate the outlier problem. Even with consistency masking, the model we propose displays limitations with dynamic objects. However, the results of the last row of Tab. 2 show that using the refined pose to extract the consistency mask for training slightly improves Sq Rel, RMSE, and \\(\\delta_{2}\\). We leave further the discussion of this issue for future study." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.459, + 0.671, + 0.475 + ], + "angle": 0, + "content": "4.5. Odometry results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.483, + 0.895, + 0.725 + ], + "angle": 0, + "content": "We present the results for visual odometry of the teacher model and the refinement model in Table 4. We also present the results of previous models that were trained on monocular videos. Our refinement module drastically improves the initial odometry results, as shown in Fig. 4. Although the goal of our study was to improve the estimation of local poses for accurate matching, we outperformed most of the other models in all metrics. Even without explicit training to ensure scale consistency, as in [7,8], our refined output demonstrates a globally consistent odometry prediction. Additionally, unlike Zou et al. [107] which infers pose from long-term geometry, this result is achieved with only two input frames to infer pose estimates. Our model also achieves an ATE that is on par with the traditional ORB-SLAM2, which performs global geometric optimization, although our results in \\( r_{err} \\) still lag behind." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.74, + 0.628, + 0.755 + ], + "angle": 0, + "content": "5. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.895, + 0.901 + ], + "angle": 0, + "content": "In this paper, we introduced a self-supervised pipeline for multi-frame depth and pose estimation and refinement. By leveraging the combined power of neural network representation and geometric constraints to refine both depth and pose, our approach achieved state-of-the-art performance in both tasks. Our method also demonstrates greater efficiency than competing methods, with potential for further improvement. Nevertheless, we still observed poorer depth accuracy in dynamic scenes." + }, + { + "type": "page_number", + "bbox": [ + 0.487, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "733" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.096, + 0.117, + 0.472, + 0.186 + ], + "angle": 0, + "content": "[1] Amir Atapour-Abarghouei and Toby P Breckon. Real-time monocular depth estimation using synthetic data with domain adaptation via image style transfer. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 2800–2810, 2018. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.095, + 0.187, + 0.472, + 0.243 + ], + "angle": 0, + "content": "[2] Shaojie Bai, Zhengyang Geng, Yash Savani, and J Zico Kolter. Deep equilibrium optical flow estimation. 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In Proceedings of the European conference on computer vision (ECCV), pages 36-53, 2018. 1" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.469, + 0.502 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.487, + 0.946, + 0.511, + 0.956 + ], + "angle": 0, + "content": "738" + } + ] +] \ No newline at end of file diff --git a/2023/DualRefine_ Self-Supervised Depth and Pose Estimation Through Iterative Epipolar Sampling and Refinement Toward Equilibrium/afa982aa-a8cf-442d-886c-70412ae83518_origin.pdf b/2023/DualRefine_ Self-Supervised Depth and Pose Estimation Through Iterative Epipolar Sampling and Refinement Toward Equilibrium/afa982aa-a8cf-442d-886c-70412ae83518_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..ff76354151717e9ec381aad71c8d6a8fdae93683 --- /dev/null +++ b/2023/DualRefine_ Self-Supervised Depth and Pose Estimation Through Iterative Epipolar Sampling and Refinement Toward Equilibrium/afa982aa-a8cf-442d-886c-70412ae83518_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:39f6a884164c9a77c14c0907b3dae4a6bc9864dd9b7d2e6aa94d67150e00d486 +size 3251237 diff --git a/2023/DualRefine_ Self-Supervised Depth and Pose Estimation Through Iterative Epipolar Sampling and Refinement Toward Equilibrium/full.md b/2023/DualRefine_ Self-Supervised Depth and Pose Estimation Through Iterative Epipolar Sampling and Refinement Toward Equilibrium/full.md new file mode 100644 index 0000000000000000000000000000000000000000..0c53929ff8e2993d8b79e3003d8aa833d7949268 --- /dev/null +++ b/2023/DualRefine_ Self-Supervised Depth and Pose Estimation Through Iterative Epipolar Sampling and Refinement Toward Equilibrium/full.md @@ -0,0 +1,414 @@ +# DualRefine: Self-Supervised Depth and Pose Estimation Through Iterative Epipolar Sampling and Refinement Toward Equilibrium + +Antyanta Bangunharcana1, Ahmed Magd2, Kyung-Soo Kim1 + +$^{1}$ Mechatronics, Systems, and Control Laboratory, $^{2}$ Vehicular Systems Design and Control Lab Korea Advanced Institute of Science and Technology (KAIST), Republic of Korea + +{antabangun，a.magd，kyungsoo}@kaist.ac.kr + +# Abstract + +Self-supervised multi-frame depth estimation achieves high accuracy by computing matching costs of pixel correspondences between adjacent frames, injecting geometric information into the network. These pixel-correspondence candidates are computed based on the relative pose estimates between the frames. Accurate pose predictions are essential for precise matching cost computation as they influence the epipolar geometry. Furthermore, improved depth estimates can, in turn, be used to align pose estimates. + +Inspired by traditional structure-from-motion (SfM) principles, we propose the DualRefine model, which tightly couples depth and pose estimation through a feedback loop. Our novel update pipeline uses a deep equilibrium model framework to iteratively refine depth estimates and a hidden state of feature maps by computing local matching costs based on epipolar geometry. Importantly, we used the refined depth estimates and feature maps to compute pose updates at each step. This update in the pose estimates slowly alters the epipolar geometry during the refinement process. Experimental results on the KITTI dataset demonstrate competitive depth prediction and odometry prediction performance surpassing published self-supervised baselines1. + +# 1. Introduction + +The optimization of the coordinates of observed 3D points and camera poses forms the basis of structure-from-motion (SfM). Estimation of both lays the foundation for robotics [34, 35, 75], autonomous driving [20], or AR/VR applications [60]. Traditionally, however, SfM techniques are susceptible to errors in scenes with texture-less regions, dynamic objects, etc. This has motivated the development of deep learning models that can learn to predict depth from monocular images [14, 15, 18, 48, 50]. These models can + +![](images/51d9d2420784a8180a9c6d411068c2941a66e1b94957758097e6f74b21a543d5.jpg) + +![](images/94d061c2aebb73a8d075d885cea015514d7cf9b7a7f47cbcb8cb237e196e7e5f.jpg) +Figure 1. (a) The estimated pose of a camera affects the epipolar geometry. (b) The epipolar line in the source image, calculated from yellow points in the target image, for the PoseNet-based [43] initial pose regression (red) and our refined pose (green). The yellow point in the source image is calculated based on our final depth and pose estimates. + +accurately predict depth based solely on image cues, without requiring geometric information. + +In recent years, self-supervised training of depth and pose models has become an attractive method, as it alleviates the need for ground truth while demonstrating precision comparable to those of supervised counterparts [7, 19, 22, 23, 26, 28, 30, 61, 70, 74, 83, 87, 98, 106, 108]. Such an approach uses depth and pose predictions to synthesize neighboring images in a video sequence and enforce consistency between them. As the image sequence is also available at test time, recent self-supervised methods also study the use of multiple frames during inference [91]. These typically involve the construction of cost volumes from multiple views to compute pixel correspondences, bearing similarities to (multi-view) stereo models [4, 44, 77]. By incorporating multi-frame data, geometric information is integrated to make depth predic + +tions, improving the performance as well as the robustness. In such a multi-frame matching-based model, the accuracy of matching costs computation is essential. Recent work in DepthFormer [29] demonstrates its importance, as they designed a Transformer [84]-based module to improve matching costs and achieve state-of-the-art (SoTA) depth accuracy. However, their approach came with a large memory cost. + +Unlike stereo tasks, the aforementioned self-supervised multi-frame models do not assume known camera poses and use estimates learned by a teacher network, typically a PoseNet [43]-based model. This network takes two images as input and regresses a 6-DoF pose prediction. As the estimated pose affects the computation of epipolar geometry (Fig. 1(a)), the accuracy of the pose estimates is crucial to obtain accurate correspondence matches between multiple frames. However, as noted in recent studies [72], pure learning-based pose regression generally still lags behind its traditional counterpart, due to the lack of geometric reasoning. By refining the pose estimates, we can improve the accuracy of the matching costs, potentially leading to better depth estimates as well. In Fig. 1(b), we show that the epipolar lines calculated from the regressed poses do not align with our refined estimates. Conversely, a better depth prediction may lead to a better pose prediction. Thus, instead of building the cost volume once using regressed poses, we choose to perform refinements of both depth and pose in parallel and sample updated local cost volumes at each iteration. This approach is fundamentally inspired by traditional SfM optimization and is closely aligned with feedback-based models that directly couple depth and pose predictions [27]. + +In this work, we propose a depth and pose refinement model that drives both towards an equilibrium, trained in a self-supervised framework. We accomplish this by making the following contributions: First, We introduce an iterative update module that is based on epipolar geometry and direct alignment. We sample candidate matches along the epipolar line that evolves based on the current pose estimates. Then the sampled matching costs are used to infer per-pixel confidences that are used to compute depth refinements. The updated depth estimates are then used in direct feature-metric alignments to refine the pose updates towards convergence. As a result, our model can perform geometrically consistent depth and pose updates. Second, These updates refine the initial estimates made by the single-frame model. By doing so, we do not rely on full cost volume construction and base our updates only on local cost volumes, making it simpler, more memory efficient, and more robust. Lastly, we design our method within a deep equilibrium (DEQ) framework [3] to implicitly drive the predictions towards a fixed point. Importantly, DEQ allows for efficient training with low training memory, improving upon the huge memory consumption of previous work. With our proposed novel design, we show improved depth estimates through experiments that are com + +petitive with the SoTA models. Furthermore, our model demonstrates improved global consistency of visual odometry results, outperforming other learning-based models. + +# 2. Related Work + +# 2.1. Depth from a single image + +The depth prediction problem for a single image is ill-posed due to the possibility of different 3D scenes projecting onto the same 2D image [32]. Nonetheless, humans can predict depth from a single image through experience. Motivated by this, numerous supervised neural network models were proposed to solve the monocular depth estimation task, starting with Eigen et al.'s paper [15]. Subsequently, performance was improved by modifying the model architecture [14,48,64,94], training on large dataset [13,53,95,100], designing robust loss functions [49,103], and transforming the problem into a classification task [52]. However, supervisory depth estimation requires ground-truth depth maps, which are difficult to collect in large quantities and of high quality. This challenge is one of the main reasons why researchers are exploring semi-supervised training, where the model expects weak supervision, such as providing relative depth [12], camera poses [101], or utilizing synthetic data for training [1,47,62]. + +The need for weak supervision still presents limitations in generalizability and scalability, among other aspects. To address these constraints, research on self-supervised training techniques is gaining momentum. These techniques involve using geometry in stereo matching [19, 22] or with a sequence of single-camera images, as initially proposed by [106]. Monodepth2 [23] refined the idea of exploiting image sequences for training by using auto-masking and minimum reprojection losses to address occlusion and egomotion issues. Further improvements were made by defining the problem as a classification task [25, 42], modifying the architecture [28], feature-based loss for regions with low texture [74, 101], or reducing artifacts from moving objects [11, 46, 80]. + +Our work is based on self-supervised monocular depth and employs them as a teacher and initial estimate. + +# 2.2. Depth from multiple frames + +Relying on single frames at test-time requires the model to make several assumptions about the scene's geometrical details. In contrast, multi-frame approaches, which leverage available temporal information and incorporate multi-view geometry, reduce the need for such assumptions. + +Multi-frame depth prediction is closely related to stereo depth estimation, where neural networks convert input stereo images into depth maps, as demonstrated by [54, 63, 82]. Kendall et al. [44] achieved a significant improvement by constructing a plane-sweep stereo cost volume. Generally, + +multi-view stereo (MVS) research is more relevant to our work, as it utilizes an unstructured collection of scene images, meaning that the pose between different images is not fixed. In studies like [36, 38, 58, 90, 97], it was common to combine the previously mentioned cost volumes with ground truth depth and camera poses for guidance. Consequently, these works require camera poses during inference [56, 92]. Although some research managed to relax the pose requirement during inference, training still necessitates this supervision [77, 82]. + +The methods discussed above, along with advances in other domains such as scale domain adaptation [31, 69, 104], view synthesis [23, 93], and other supervisory techniques [26, 30], have significantly impacted the performance of self-supervised approaches. ManyDepth [91], which is similar to our work, focuses on the drawbacks of using a single image during inference and proposes a flexible model that takes advantage of multiple frames at test time, if available. ManyDepth reduces artifacts from moving objects and temporarily stationary cameras by using a single-frame model as a teacher, resulting in improved depth map accuracy. More recently, DepthFormer [29] achieved substantial accuracy improvements by using Transformers [84] to obtain improved pixel matching costs. + +Inspired by traditional bundle adjustments, we design a model that simultaneously solves for both depth and pose while incorporating many of the advancements mentioned earlier. Our approach is most similar to DRO [27]. However, compared to their approach, our model tightly integrates multi-view geometry into the iterative updates formulation and bases our refinements on the local epipolar geometry. + +# 2.3. Iterative refinements + +Iterative refinement has been employed to improve prediction quality in various learning tasks, including object detection [6, 24], optical flow estimation [37, 78], semantic segmentation [68, 102], and others [40, 71]. Some recent research has attempted to iterate the refinement process using deep convolutional networks [9, 21, 55, 57]. Other works train the same network repeatedly by utilizing the results of the previous iteration [99, 102]. In particular, RAFT [78] found success with its iterative refinement procedure for flow estimation. DEQ-flow [2] employed a deep equilibrium (DEQ) [3] framework to reduce the memory consumption of RAFT during training while maintaining accuracy. + +A key component of our model is inspired by the iterative updates of RAFT and DEQ-flow. Instead of optical flow, our model refines depth and pose estimates in parallel. We design our refinement module to tightly couple the two predictions, considering the epipolar geometry of adjacent frames. With every update, the epipolar geometry is refined, which also results in a more accurate matching costs computation of pixel correspondences. + +# 2.4. Pose estimation + +Pose estimation is a crucial component in self-supervised monocular depth models. In many works, PoseNet-based models [43] take a pair of adjacent image frames and output a 6 DoF pose estimation. This class of models is straightforward, but often less accurate than their traditional counterparts [16, 17, 65] due to the absence of geometry constraints. Recent work in deep learning-based localization has adopted differentiable geometrically inspired designs within their models by using direct alignments [72, 85, 86] or geometric alignments based on optical flow [79]. These models demonstrate better generalization properties and accuracy. The use of self-supervised monocular depth has also been used to improve traditional odometry [8, 96]. However, our interest lies in learning to refine both depth and pose in the self-supervision pipeline. To improve the accuracy of pose estimation, we integrate direct alignment within the recurrent module, ensuring geometrically consistent prediction between depth and pose. + +# 3. Method + +Our model comprises two primary sub-modules. The first is a single frame self-supervised depth and pose estimator, building upon previous frameworks [23, 105], which we revisit in Sec. 3.1. This network serves as both a teacher and an initializer for the second sub-module, our proposed multi-frame network, presented in detail in Sec. 3.2. + +# 3.1. Self-supervised depth and pose + +We begin by describing the canonical self-supervised monocular depth estimation pipeline [23], which serves as the foundation for our approach. This depth training method assumes that a monocular camera with an intrinsic parameter $K$ captures an image sequence of a scene. In this process, two networks are trained in parallel to estimate the per-pixel depth map of the images $D$ and the relative poses between adjacent image frames. By warping neighboring images towards a shared target frame using these two predictions, self-supervised training can be performed by enforcing photometric consistency between the frames. + +Given the depth map $D$ of a target image and its relative pose with a source image $T_{t\rightarrow s}$ , we can calculate the projection of each pixel $u = (x,y)$ of the target image onto the source image as follows: + +$$ +z ^ {\prime} u ^ {\prime} = z ^ {\prime} \left[\begin{array}{l}x ^ {\prime}\\y ^ {\prime}\\1\end{array}\right] = K T _ {t \rightarrow s} \left(D [ u ] K ^ {- 1} \left[\begin{array}{l}x\\y\\1\end{array}\right]\right), \tag {1} +$$ + +using the estimated depth at that pixel $D[u]$ . The source images can then be warped towards the target frame by sampling the pixel values at the calculated projection + +$$ +I _ {s \rightarrow t} [ u ] = I _ {s} \langle u ^ {\prime} \rangle , \tag {2} +$$ + +![](images/75a2a72803f499eb42d709327ef11302dff73ceedc98f3083e705e386b494917.jpg) + +![](images/208b987c812c8a5409c3061d15e025593878273f80ac26912fc279dfe572e9f4.jpg) +DEQ updates +Figure 2. (a) The overall pipeline of the model. Given a pair of source and target images, the teacher model predicts an initial depth $D_0$ and pose $T_0$ , as well as initial hidden states that will be updated. DEQ-based alignments are then performed to find the fixed point and output the final predictions. (b) Each iteration in the update step takes the current depth and pose estimates. Matching costs are sampled along the current epipolar lines that evolves based on the pose estimates. The updates are computed by Conv-GRU. Then feature-metric alignment is used to obtain a geometrically consistent pose update. + +where $\langle \cdot \rangle$ indicates bilinear interpolation, implemented using the spatial transformer network (STN) [39]. + +The self-supervised loss is calculated as a combination of the photometric error and the edge-aware smoothness loss: + +$$ +\mathcal {L} _ {s e l f - s u p} = \lambda_ {p} \mathcal {L} _ {p} + \lambda_ {s} \mathcal {L} _ {s}, \tag {3} +$$ + +where the photometric error between the warped source image and the target image is calculated using the structural similarity loss, and the minimum error is taken between multiple warped images to account for occlusions. Interested readers can refer to [23]. The self-supervised loss is typically computed at multiple scales to stabilize the training. + +In this paper, we train a monocular depth estimator and a pose estimation network using this pipeline, serving two purposes. First, following ManyDepth [91], we use these models as a teacher to constrain the multi-frame predictions in the presence of dynamic objects. Additionally, we employ them as an initializer for the multi-frame alignment network. + +# 3.1.1 Monocular model + +We build our monocular depth estimation model based on DIFFNet [105], a SoTA self-supervised single-frame estimator. We extract feature maps at multiple scales $s$ from the target image using the HRNet architecture [88]. In accordance with DIFFNet, feature maps from multiple stages are accumulated in $F^{(1/2^s)}$ . Then, we employ disparity decoders to make disparity predictions at scales $s = \{2,3\}$ . The pose estimation network follows the canonical PoseNet [43] architecture, taking two input images and outputting 6-DoF values, with a ResNet18 [33] backbone. The predicted disparity and pose estimation from these networks are used as a teacher to train our alignment sub-module, as was done in ManyDepth [91]. + +# 3.2. Deep equilibrium alignments + +In our alignment sub-module, we assume that additional input from source image(s) is available, which can be used to refine the depth and pose estimates. In this work, we focus on using the image from the previous frame in the image sequence as our source image. + +Our alignment module is formulated as a deep equilibrium model [3] that updates the hidden states, depth, and pose estimates to a fixed point. Specifically, at the fixed point $z^{*}$ , + +$$ +\left(h ^ {*}, D ^ {*}, T ^ {*}\right) = z ^ {*} = \mathrm {U} \left(z ^ {*}, x\right), \tag {4} +$$ + +where $z$ is composed of a hidden state $h$ , the depth prediction $D$ , and the pose prediction $T$ . U represents our update function, refining the depth and pose alternatively. $x$ is an input to the update module, obtained based on the epipolar geometry at each step, which we discuss in the next subsection. We perform these iterative updates at scale $s = 2$ . + +From the feature extraction output, we compute an initial hidden state for our recurrent updates $h^{[0]} = \tanh(\mathrm{H}(F^{(1/4)}))$ and a context feature $q = \mathrm{Q}(F^{(1/4)})$ . Both H and Q are composed of a single residual block [33] followed by a convolutional layer. + +# 3.2.1 Depth updates around local neighborhood + +Local epipolar sampling. As discussed previously, our refinement is based on the pixel matching between the target image and the source image. We use the first two blocks of the HRNet feature extractor to extract unary features from the source image $m_{s}^{(1/4)}$ and the target image $m_{t}^{(1/4)}$ , which we will use to calculate the matching costs. + +Similarly to RAFT [78], our aim is to compute the matching values for candidate correspondences around the current + +![](images/395494b452023615536bb36e9426be5caa26a3526da0de3999e145f47cccb7ed.jpg) + +![](images/b0b7b842fe4be54e5b4f264f024c7f623e1f8bb4605c437c20aba26ff56d3076.jpg) + +![](images/bc48dfe32f0688ffaba94ba9ce01b0b115b90789c4a59cd9475f9c88f6bb0af2.jpg) +$D_0$ + +![](images/3c224035a5e518ec80a30e2cf8111b50d71f5087ee6c3c8fc591f5b19ea4653a.jpg) + +![](images/3aeada78b38f30e3f7dea33e8843aaed5c3bb3856192839afe27d7a13c4c9d27.jpg) +Wq + +![](images/93efbceecf60ca0a61d2eff73c5ccb294c6a774fd3965e0f2baf3ec330584d69.jpg) +$W_{h,5}$ + +![](images/db798ff483221e90da4af122aa6f089ca9df34963021818882608b299d04e882.jpg) +$D_{5}$ + +![](images/db68dbffda1634fd61545eb5aad5d18865835b6cfeec7b1fdb54fb806ed2a175.jpg) + +![](images/ab64af8451a8d5b7e0d0301d6a8eb0b86bf2e68f88727c2b3014d59a939d2c0b.jpg) + +![](images/ffaa0c62d72b627cd074ac682a6016ee064416dd206d5a44e6cc5c7715430bcf.jpg) + +![](images/e141bda6c6e77c30a01f0c33b7bf979a52c44bd3bdb8b1e8726fe729274f3511.jpg) + +![](images/5e50c44b7d8252803ef5f30fc4f03148d865f05f5ded74d53ca421292bda8adc.jpg) + +![](images/5c1259e985fcb7fdb84035569910e440a7e1fc3f1bc93931a0fbe2cf825f1526.jpg) +Wq +Figure 3. Qualitative results on KITTI data. $I_{s}$ : input image; $W_{q}$ , $W_{h,0}$ , and $W_{h,5}$ : confidence weights; $D_{0}$ , $D_{5}$ : disparity estimates; The Abs Rel error for the depth estimates. + +![](images/8dda74a09b391eb5ca265cba9015dd08e6c0306282aef4e7b20c53d2851cbe45.jpg) +$W_{h,5}$ + +![](images/38636b52cf916573f7ec926f68ae2667f5ed6e93e794586d30cf7775b26a356f.jpg) +$D_{5}$ + +![](images/cf844cc748508cfb657673d0296076f7664b675c102f0d777bda2adea94f80ae.jpg) +AbsRel5 + +prediction and use them as input to our update module at the update step $k$ . Unlike RAFT, however, we perform matching along an epipolar line based on the pose estimate $T_{k}$ . This is done by computing the projected coordinates $u_{k}^{\prime}$ in the source image obtained from (1) at the depths of interest. The depth candidates are computed to be the neighborhood of the current prediction. Instead of computing the all-pair correlation as was done in RAFT, we compute feature matching on the fly. + +At each pixel $u$ , we compute the local depth candidates as $D[u]_k \pm (i \times c \times n)$ , with $i \in \mathbb{Z}$ and $i \leq r$ . We set the sampling radius hyperparameter $r = 8$ in our experiments. In depth estimation, the error typically grows with distance. To account for this, we define $c = D[u] / C$ as a function of depth to make the sampling range dependent on the depth, where we set $C$ as a trainable parameter. Following RAFT, to collect the matching information from a larger neighborhood, we sampled at multiple levels $n = \{1,2,3\}$ . At each level, we bilinearly resize the matching feature map of the source image $m_s^{(1/4)}$ with a scale of $1/2^n$ . Then, the matching features are sampled at the calculated corresponding set of coordinates $u_k'$ , and the absolute differences with the target feature + +$$ +\mathbf {C} _ {k} [ u ] = \left| m _ {t} [ u ] - m _ {s} \langle u _ {k} ^ {\prime} \rangle \right| \tag {5} +$$ + +are calculated and gathered. This provides us with a map $\mathbf{C}_k$ that contains $n \times (2 \times r + 1)$ matching cost values at the corresponding depth candidates. We then encode these matching costs along with the depth using a two-layer convolutional neural network (CNN) to compute the input for the update module + +$$ +x _ {k} = \left[ \operatorname {C N N} _ {\mathbf {C}} \left(\mathbf {C} _ {k}\right), \operatorname {C N N} _ {D _ {x}} \left(D _ {k}\right), q \right], \tag {6} +$$ + +where $[\cdot ,\cdot ]$ represents the concatenation. + +Depth update. The update function calculates an updated hidden state $h_{k+1}$ using the Conv-GRU block [5,41,78]. $h_{k+1}$ is used to compute the depth updates. To stabilize training, we use the activation function $\tanh(\cdot)$ to bound the absolute update values for the depths to be within $r \cdot c$ : + +$$ +D _ {k + 1} = D _ {k} + r \cdot c \cdot \tanh \left(\mathrm {C N N} _ {D _ {\mathrm {U}}} \left(h _ {k + 1}\right)\right). \tag {7} +$$ + +These updates are performed in an alternating fashion with the pose updates to reach the fixed point $D^{*}$ . Using $h^{*}$ , we compute a convex upsampling to obtain the final depth estimate at the input resolution. + +# 3.2.2 Feature-metric pose alignments + +In (1), the accuracy of pose estimation affects the calculation of the coordinates of pixels. Hence, a refined pose estimate would also improve the reliability of the matching costs. To refine the pose while being geometrically consistent, we perform our pose updates based on direct feature alignments [16, 17, 87]. These updates $\delta_{k}$ can be calculated by solving $H_{k}\delta_{k} = b_{k}$ , where + +$$ +H _ {k} = \mathcal {J} _ {k} ^ {T} \operatorname {d i a g} \left(W _ {k}\right) \mathcal {J} _ {k} \text {a n d} b _ {k} = - \mathcal {J} _ {k} ^ {T} \operatorname {d i a g} \left(W _ {k}\right) r _ {k} \tag {8} +$$ + +$$ +r _ {k} [ u ] = m _ {s} \left\langle u _ {k} ^ {\prime} \right\rangle - m _ {t} [ u ], +$$ + +and $\mathcal{J}$ is the Jacobian with respect to the pose. + +To compute this pose update, one could assign uniform confidence to every pixel in the image. However, in Eq. (8), additional confidence weights per pixel $W$ can also be integrated. This is done for two reasons. First, the solution for the pose updates can be affected by dynamic objects + +as well as inaccurate feature alignments that may occur in region with repeated textures. To account for this, the confidence weighting of the input context feature map $W_{q}$ can be computed [72]. Specifically, we computed a confidence map $W_{t,s} = 1 / (1 + \mathrm{ReLU}(\mathrm{CNN}_{W_q}(F_{t,s}))$ for both target and source images. The source confidence is warped towards the target frame using Eqs. (1) and (2). Finally, the confidence is computed as $W_{q} = W_{t}\cdot W_{s,\text{warped}}$ . This confidence weight is only computed once to assign per-pixel confidence for the input images. + +Second, the accuracy of pose updates would depend on the accuracy of the depth estimates. To obtain more accurate pose updates, we would like to assign more alignment confidence to the region with higher depth accuracy. We use a neural network to infer this confidence from the matching costs. Since the hidden states $h$ have a history of these matching costs, another confidence weights $W_{h,k} = \mathrm{CNN}_{W_h}(h_k)$ can be computed. Unlike the previous confidence map, this one is computed and evolves at every update step. By doing so, the network can use the depth predictions to guide the pose estimates towards convergence using the depth information. In our experiments, we investigate the use of each confidence weighting and combination of both $W_{k} = W_{q}W_{h,k}$ . + +Finally, we can compute the updated pose as $T_{k + 1} = \exp (\delta_k^{\wedge})T_k$ . These operations are designed to be differentiable to enable end-to-end training. + +# 3.2.3 DEQ training + +We adopt a DEQ framework, wherein the above steps are repeated until the depth and pose values reach a fixed point, at which the update value is minimal. In our implementation, the fixed points of depth and pose are chosen separately, and it is possible for both to be selected from different update steps. Finally, the training gradient is computed using the chosen depth and pose fixed points. Operations prior to the fixed point do not require saving gradients in memory, which allows memory-efficient training. + +As noted in Eqs. (1) to (3), the self-supervision losses can be computed given a depth and pose prediction. At the fixed point, we compute two additional self-supervision losses. The first performs source-to-target image warping through the pairing of the final depth $D^{*}$ and the initial pose $T_{0}$ , where we detach $T_{0}$ from the computational graph to act as a teacher. This loss is used so that the output of the teacher and refinement modules shares the same scaling. The second performs the warping with the pairing of $D^{*}$ and $T^{*}$ . This loss helps drive refined estimation of both depth and pose towards the optimal value. Detailed experiments for this choice of loss pairings are provided in the supplementary. + +In both losses, we also apply the consistency loss between $D_0$ and $D^*$ , similar to ManyDepth [91], to account for dynamic objects or occluded regions. Specifically, we extract + +coarse depth predictions from the raw feature matchings and mask regions where large disagreements occur, and enforce consistency with the teacher depth. Unlike ManyDepth, however, our method does not explicitly construct a cost volume. To obtain the coarse depth, we search for the lowest matching cost around the neighborhood of the teacher depth, similar to Sec. 3.2.1, but with a larger neighborhood range. This approach offers an additional advantage compared to the cost volume-based method, as we do not need to rely on an estimated minimum and maximum depth or know the scale of the estimates. Moreover, since the computation of coarse depth depends on the accuracy of feature matching costs, it can be improved with more accurate pose estimates (Tab. 2). + +# 4. Experiments + +# 4.1. Dataset and metrics + +For depth estimation experiments, we use the Eigen train/test split [15] from the KITTI dataset [20]. To evaluate the estimated depths, we scale them by a scalar to match the scale of the ground truth. We employ standard depth evaluation metrics [14, 15], including absolute and squared relative error (Abs Rel, Sq Rel), root mean square error (RMSE, RMSE log), and accuracy under threshold $(\delta_{1}, \delta_{2}$ , and $\delta_{3})$ with a maximum depth set at $80m$ . Lower values are better for the first four metrics, while higher values are better for the remaining three. + +For the visual odometry experiments, we use the KITTI odometry dataset and follow the same training and evaluation sequences (Seq. 00-08 for training and Seq. 09-10 for evaluation) as in previous work [106]. Since our estimation relies on a monocular camera, the estimated trajectories are aligned with the ground truth using the 7 DoF Umyama alignment [81]. We use standard odometry evaluation metrics such as translation $(t_{err})$ and rotation $(r_{err})$ error [20], and absolute trajectory error (ATE) [76]. + +# 4.2. Implementation details + +We conduct our experiments using PyTorch [66] on an RTX 3090 GPU with a batch size of 12. Following [23], we apply color and flip augmentations and resize input images to a resolution of $640 \times 192$ . For our high resolution experiments, we resize the images to $960 \times 288$ . We train the entire network for 15 epochs with a learning rate of $10^{-3}$ , at which point we freeze the teacher depth and pose models. We then continue to train the network with a learning rate of $10^{-4}$ . Adam optimizer [45] is employed with $\beta_{1} = 0.9$ and $\beta_{2} = 0.999$ . + +As mentioned earlier, the depth backbone is based on the HRNet architecture [88]. For the teacher pose model, we adhere to the standard design, using the first five layers of a ResNet18 initialized with ImageNet pre-trained weights as + +
MethodTest framesSemanticsW × HAbs Rel ↓Sq Rel ↓RMSE ↓RMSE log ↓δ1 ↑δ2 ↑δ3 ↑
Low & mid resRanjan et al. [70]1832 × 2560.1481.1495.4640.2260.8150.9350.973
EPC++ [59]1832 × 2560.1411.0295.3500.2160.8160.9410.976
Struct2depth (M) [10]1●416 × 1280.1411.0265.2910.2150.8160.9450.979
Videos in the wild [26]1●416 × 1280.1280.9595.2300.2120.8450.9470.976
Guizilini et al. [30]1●640 × 1920.1020.6984.3810.1780.8960.9640.984
Johnston et al. [42]1640 × 1920.1060.8614.6990.1850.8890.9620.982
Monodepth2 [23]1640 × 1920.1150.9034.8630.1930.8770.9590.981
Packnet-SFM [28]1640 × 1920.1110.7854.6010.1890.8780.9600.982
Li et al. [51]1416 × 1280.1300.9505.1380.2090.8430.9480.978
DIFFNet [105]1640 × 1920.1020.7644.4830.1800.8960.9650.983
DualRefine-initial (D0)1640 × 1920.1030.7214.4760.1800.8910.9650.984
Patil et al. [67]N†640 × 1920.1110.8214.6500.1870.8830.9610.982
Wang et al. [89]2 (-1, 0)640 × 1920.1060.7994.6620.1870.8890.9610.982
ManyDepth (MR) [91]2 (-1, 0)640 × 1920.0980.7704.4590.1760.9000.9650.983
DepthFormer [29]2 (-1, 0)640 × 1920.0900.6614.1490.1750.9050.9670.984
DualRefine-refined (D*)2 (-1, 0)640 × 1920.0900.6584.2370.1710.9120.9670.984
High resDRO [27]2 (-1, 0)960 × 3200.0880.7974.4640.2120.8990.9590.980
Wang et al. [89]2 (-1, 0)1024 × 3200.1060.7734.4910.1850.8900.9620.982
ManyDepth (HR ResNet50) [91]2 (-1, 0)1024 × 3200.0910.6944.2450.1710.9110.9680.983
DualRefine-refined (HR) (D*)2 (-1, 0)960 × 2880.0890.7544.2730.1700.9170.9680.983
+ +Table 1. Results and comparison with other state-of-the-arts models on the KITTI [20] Eigen split. Bold: Best, Underscore: Second best. † : evaluated on whole sequences + +
Pose UpdatesConsistency maskAbs RelSq RelRMSEδ1δ2
no updateT00.0970.7134.4620.8980.964
no weightsT00.0900.6584.2370.9120.967
no Wh,kT00.0900.6454.2730.9080.966
no WqT00.0910.7134.2950.9100.967
Wq and Wh,kT00.0890.6524.2820.9090.967
no weightsT*0.0910.6454.2010.9100.968
+ +an encoder, followed by a decoder that outputs 6-DoF pose estimates. At test time, depth estimates are made using the current frame and the previous frame when available. When the previous frame is unavailable, we skip the refinement module and simply use the initial estimates. + +# 4.3. Ablation + +Pose updates. We analyze the effect of pose refinement toward depth and present the findings in Table 2. Our model that does not perform pose updates has the worst accuracy. + +**Evolving confidence weighting.** We also show the impact of confidence weightings. Interestingly, similar performance can be observed for all models that perform pose updates, even when no confidence weighting is used to guide the pose computation. + +DEQ iteration. In addition to studying the effect of pose refinements, we also investigate aspects of DEQ iterative updates and present the findings when we vary the number of iterations during training and at test time in Table 3. The results suggest that 6 iterations is sufficient for the model to find the fixed point. We speculate that the initial estimate provides a reliable starting point and hence the fast convergence. On our machine, the 6 update iterations increase the + +Table 2. Ablation experiment for the effect of pose updates on the KITTI [20] Eigen split. Bold: Best. + +
DEQ # itersAbs RelSq RelRMSEδ1Time (ms)
3→30.0970.7774.4310.90653
6→30.0980.6954.3180.90553
6→60.0900.6584.2370.91268
12→30.1020.7324.4280.90053
12→60.0950.7084.3360.90768
12→120.0920.7074.3160.90999
+ +Table 3. Ablation experiment for the DEQ iterations on the KITTI [20] Eigen split. $a \rightarrow b$ represents $a : \#$ iters at training and $b : \#$ iters at test time. Bold: Best. + +baseline model's inference time from $37.90\mathrm{ms}$ by $\sim 31$ ms to a total of $68.49~\mathrm{ms}$ , running at almost 15 fps. However, we only use PyTorch basic functions in our implementation, and further optimization of the code could be made. + +# 4.4. Depth results + +Table 1 shows the comparison of our depth estimation with SoTA self-supervised models. We compare with models that train on monocular video. Our model outperforms most previous models and is competitive with the Transformer [84]-based DepthFormer [29] model. Specifically, our model shows a significant improvement in $\delta_{1}$ , suggesting highly accurate inliers. Furthermore, compared to DepthFormer that requires 16GB training memory per batch, ours only consumes 24GB of memory for 12 batches, around $1/8 \times$ the memory requirement. This is mainly because our method refines 2D hidden states based on local sampling, while [29] refines 2D feature maps and a 3D feature volume using self/cross-attention along every depth bin. + +Fig. 3 displays qualitative outputs for the disparity and error map of our model. We can observe an improvement to the error map of the refined depth. We also additionally dis + +
MethodsSeq 9Seq 10
\(t_{err}(\%) \downarrow\)\(r_{err}(\circ/100m) \downarrow\)ATE (m) ↓\(t_{err}(\%) \downarrow\)\(r_{err}(\circ/100m) \downarrow\)ATE (m) ↓
ORB-SLAM2 [65] (w/o LC)9.670.344.104.040.36.43
ORB-SLAM2 [65]3.220.48.844.250.38.51
SfMLearner [106]19.156.8277.7940.4017.6967.34
GeoNet [98]28.729.8158.4523.909.043.04
DeepMatchVO [73]9.913.827.0812.185.924.44
Monodepth2 [23]17.173.8576.2211.685.3120.35
DW [26]-Learned--20.91--17.88
DW [26]-Corrected--19.01--14.85
SC-Depth [7]7.313.0523.567.794.9012.00
Zou et al. [107]3.491.0011.305.811.811.80
P-RGBD SLAM [8]5.081.0513.404.322.347.99
DualRefine-initial (T0)9.062.5939.319.454.0515.13
DualRefine-refined (T*)3.431.045.186.801.1310.85
+ +Table 4. Results on Seq. 09 and Seq. 10 of the KITTI odometry data. We provide a comparison with other state-of-the-art self-supervised depth and odometry methods. ORB-SLAM2 is included as a representative non-learning based method. Bold: Best, Underscore: Second best. + +![](images/04295fabd8eb446cf2c99475ac6ac114f378c3750eaae67cd49a61c42233d14b.jpg) + +![](images/b71cdbab517d4d36a67999a9adaa375601d81b64b97d765abb46eab84ee4ec09.jpg) +Figure 4. Estimated trajectory by the initial pose estimator and the refined trajectory using our pose refinement module on (a) Seq. 09 and (b) Seq. 10 of KITTI odometry data. The refined pose estimate improves the global trajectory, even without explicitly training for global consistency. + +play confidence weight outputs obtained by the model that computes them. We observe that the confidence $W_{q}$ , which is calculated once, assigns the high confidence sparsely. Interestingly, the confidence weights that evolve with each iteration initially assign high confidence to far-away points and moves towards closer points with increasing iterations. + +Limitation: we note an increase in error for the moving vehicle in the lower image set. The worse RMSE of our model compared to DepthFormer also indicates higher outlier predictions. This could be due to repeated operation of + +our iterative updates, which further exacerbate the outlier problem. Even with consistency masking, the model we propose displays limitations with dynamic objects. However, the results of the last row of Tab. 2 show that using the refined pose to extract the consistency mask for training slightly improves Sq Rel, RMSE, and $\delta_{2}$ . We leave further the discussion of this issue for future study. + +# 4.5. Odometry results + +We present the results for visual odometry of the teacher model and the refinement model in Table 4. We also present the results of previous models that were trained on monocular videos. Our refinement module drastically improves the initial odometry results, as shown in Fig. 4. Although the goal of our study was to improve the estimation of local poses for accurate matching, we outperformed most of the other models in all metrics. Even without explicit training to ensure scale consistency, as in [7,8], our refined output demonstrates a globally consistent odometry prediction. Additionally, unlike Zou et al. [107] which infers pose from long-term geometry, this result is achieved with only two input frames to infer pose estimates. Our model also achieves an ATE that is on par with the traditional ORB-SLAM2, which performs global geometric optimization, although our results in $r_{err}$ still lag behind. + +# 5. Conclusions + +In this paper, we introduced a self-supervised pipeline for multi-frame depth and pose estimation and refinement. 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Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 582, + 288, + 691 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 288, + 691 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 288, + 691 + ], + "type": "text", + "content": "The optimization of the coordinates of observed 3D points and camera poses forms the basis of structure-from-motion (SfM). Estimation of both lays the foundation for robotics [34, 35, 75], autonomous driving [20], or AR/VR applications [60]. Traditionally, however, SfM techniques are susceptible to errors in scenes with texture-less regions, dynamic objects, etc. This has motivated the development of deep learning models that can learn to predict depth from monocular images [14, 15, 18, 48, 50]. 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(a) The estimated pose of a camera affects the epipolar geometry. (b) The epipolar line in the source image, calculated from yellow points in the target image, for the PoseNet-based [43] initial pose regression (red) and our refined pose (green). The yellow point in the source image is calculated based on our final depth and pose estimates." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 517, + 547, + 541 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 517, + 547, + 541 + ], + "spans": [ + { + "bbox": [ + 304, + 517, + 547, + 541 + ], + "type": "text", + "content": "accurately predict depth based solely on image cues, without requiring geometric information." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "type": "text", + "content": "In recent years, self-supervised training of depth and pose models has become an attractive method, as it alleviates the need for ground truth while demonstrating precision comparable to those of supervised counterparts [7, 19, 22, 23, 26, 28, 30, 61, 70, 74, 83, 87, 98, 106, 108]. Such an approach uses depth and pose predictions to synthesize neighboring images in a video sequence and enforce consistency between them. As the image sequence is also available at test time, recent self-supervised methods also study the use of multiple frames during inference [91]. These typically involve the construction of cost volumes from multiple views to compute pixel correspondences, bearing similarities to (multi-view) stereo models [4, 44, 77]. By incorporating multi-frame data, geometric information is integrated to make depth predic" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 702, + 246, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 702, + 246, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 702, + 246, + 712 + ], + "type": "text", + "content": "" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "type": "text", + "content": "726" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 156 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 156 + ], + "type": "text", + "content": "tions, improving the performance as well as the robustness. In such a multi-frame matching-based model, the accuracy of matching costs computation is essential. Recent work in DepthFormer [29] demonstrates its importance, as they designed a Transformer [84]-based module to improve matching costs and achieve state-of-the-art (SoTA) depth accuracy. However, their approach came with a large memory cost." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 159, + 290, + 435 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 159, + 290, + 435 + ], + "spans": [ + { + "bbox": [ + 46, + 159, + 290, + 435 + ], + "type": "text", + "content": "Unlike stereo tasks, the aforementioned self-supervised multi-frame models do not assume known camera poses and use estimates learned by a teacher network, typically a PoseNet [43]-based model. This network takes two images as input and regresses a 6-DoF pose prediction. As the estimated pose affects the computation of epipolar geometry (Fig. 1(a)), the accuracy of the pose estimates is crucial to obtain accurate correspondence matches between multiple frames. However, as noted in recent studies [72], pure learning-based pose regression generally still lags behind its traditional counterpart, due to the lack of geometric reasoning. By refining the pose estimates, we can improve the accuracy of the matching costs, potentially leading to better depth estimates as well. In Fig. 1(b), we show that the epipolar lines calculated from the regressed poses do not align with our refined estimates. Conversely, a better depth prediction may lead to a better pose prediction. Thus, instead of building the cost volume once using regressed poses, we choose to perform refinements of both depth and pose in parallel and sample updated local cost volumes at each iteration. This approach is fundamentally inspired by traditional SfM optimization and is closely aligned with feedback-based models that directly couple depth and pose predictions [27]." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 438, + 290, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 438, + 290, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 438, + 290, + 715 + ], + "type": "text", + "content": "In this work, we propose a depth and pose refinement model that drives both towards an equilibrium, trained in a self-supervised framework. We accomplish this by making the following contributions: First, We introduce an iterative update module that is based on epipolar geometry and direct alignment. We sample candidate matches along the epipolar line that evolves based on the current pose estimates. Then the sampled matching costs are used to infer per-pixel confidences that are used to compute depth refinements. The updated depth estimates are then used in direct feature-metric alignments to refine the pose updates towards convergence. As a result, our model can perform geometrically consistent depth and pose updates. Second, These updates refine the initial estimates made by the single-frame model. By doing so, we do not rely on full cost volume construction and base our updates only on local cost volumes, making it simpler, more memory efficient, and more robust. Lastly, we design our method within a deep equilibrium (DEQ) framework [3] to implicitly drive the predictions towards a fixed point. Importantly, DEQ allows for efficient training with low training memory, improving upon the huge memory consumption of previous work. With our proposed novel design, we show improved depth estimates through experiments that are com" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 305, + 72, + 547, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 547, + 109 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 547, + 109 + ], + "type": "text", + "content": "petitive with the SoTA models. Furthermore, our model demonstrates improved global consistency of visual odometry results, outperforming other learning-based models." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 306, + 120, + 392, + 133 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 120, + 392, + 133 + ], + "spans": [ + { + "bbox": [ + 306, + 120, + 392, + 133 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 140, + 451, + 153 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 140, + 451, + 153 + ], + "spans": [ + { + "bbox": [ + 306, + 140, + 451, + 153 + ], + "type": "text", + "content": "2.1. Depth from a single image" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 159, + 548, + 374 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 159, + 548, + 374 + ], + "spans": [ + { + "bbox": [ + 304, + 159, + 548, + 374 + ], + "type": "text", + "content": "The depth prediction problem for a single image is ill-posed due to the possibility of different 3D scenes projecting onto the same 2D image [32]. Nonetheless, humans can predict depth from a single image through experience. Motivated by this, numerous supervised neural network models were proposed to solve the monocular depth estimation task, starting with Eigen et al.'s paper [15]. Subsequently, performance was improved by modifying the model architecture [14,48,64,94], training on large dataset [13,53,95,100], designing robust loss functions [49,103], and transforming the problem into a classification task [52]. However, supervisory depth estimation requires ground-truth depth maps, which are difficult to collect in large quantities and of high quality. This challenge is one of the main reasons why researchers are exploring semi-supervised training, where the model expects weak supervision, such as providing relative depth [12], camera poses [101], or utilizing synthetic data for training [1,47,62]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 375, + 548, + 541 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 375, + 548, + 541 + ], + "spans": [ + { + "bbox": [ + 304, + 375, + 548, + 541 + ], + "type": "text", + "content": "The need for weak supervision still presents limitations in generalizability and scalability, among other aspects. To address these constraints, research on self-supervised training techniques is gaining momentum. These techniques involve using geometry in stereo matching [19, 22] or with a sequence of single-camera images, as initially proposed by [106]. Monodepth2 [23] refined the idea of exploiting image sequences for training by using auto-masking and minimum reprojection losses to address occlusion and egomotion issues. Further improvements were made by defining the problem as a classification task [25, 42], modifying the architecture [28], feature-based loss for regions with low texture [74, 101], or reducing artifacts from moving objects [11, 46, 80]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 542, + 547, + 566 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 542, + 547, + 566 + ], + "spans": [ + { + "bbox": [ + 306, + 542, + 547, + 566 + ], + "type": "text", + "content": "Our work is based on self-supervised monocular depth and employs them as a teacher and initial estimate." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 574, + 460, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 574, + 460, + 588 + ], + "spans": [ + { + "bbox": [ + 306, + 574, + 460, + 588 + ], + "type": "text", + "content": "2.2. Depth from multiple frames" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 594, + 547, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 653 + ], + "type": "text", + "content": "Relying on single frames at test-time requires the model to make several assumptions about the scene's geometrical details. In contrast, multi-frame approaches, which leverage available temporal information and incorporate multi-view geometry, reduce the need for such assumptions." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 654, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 548, + 715 + ], + "type": "text", + "content": "Multi-frame depth prediction is closely related to stereo depth estimation, where neural networks convert input stereo images into depth maps, as demonstrated by [54, 63, 82]. Kendall et al. [44] achieved a significant improvement by constructing a plane-sweep stereo cost volume. Generally," + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "727" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "content": "multi-view stereo (MVS) research is more relevant to our work, as it utilizes an unstructured collection of scene images, meaning that the pose between different images is not fixed. In studies like [36, 38, 58, 90, 97], it was common to combine the previously mentioned cost volumes with ground truth depth and camera poses for guidance. Consequently, these works require camera poses during inference [56, 92]. Although some research managed to relax the pose requirement during inference, training still necessitates this supervision [77, 82]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 193, + 290, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 193, + 290, + 361 + ], + "spans": [ + { + "bbox": [ + 46, + 193, + 290, + 361 + ], + "type": "text", + "content": "The methods discussed above, along with advances in other domains such as scale domain adaptation [31, 69, 104], view synthesis [23, 93], and other supervisory techniques [26, 30], have significantly impacted the performance of self-supervised approaches. ManyDepth [91], which is similar to our work, focuses on the drawbacks of using a single image during inference and proposes a flexible model that takes advantage of multiple frames at test time, if available. ManyDepth reduces artifacts from moving objects and temporarily stationary cameras by using a single-frame model as a teacher, resulting in improved depth map accuracy. More recently, DepthFormer [29] achieved substantial accuracy improvements by using Transformers [84] to obtain improved pixel matching costs." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 361, + 288, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 361, + 288, + 445 + ], + "spans": [ + { + "bbox": [ + 46, + 361, + 288, + 445 + ], + "type": "text", + "content": "Inspired by traditional bundle adjustments, we design a model that simultaneously solves for both depth and pose while incorporating many of the advancements mentioned earlier. Our approach is most similar to DRO [27]. However, compared to their approach, our model tightly integrates multi-view geometry into the iterative updates formulation and bases our refinements on the local epipolar geometry." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 454, + 167, + 466 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 454, + 167, + 466 + ], + "spans": [ + { + "bbox": [ + 47, + 454, + 167, + 466 + ], + "type": "text", + "content": "2.3. Iterative refinements" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 473, + 289, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 473, + 289, + 617 + ], + "spans": [ + { + "bbox": [ + 46, + 473, + 289, + 617 + ], + "type": "text", + "content": "Iterative refinement has been employed to improve prediction quality in various learning tasks, including object detection [6, 24], optical flow estimation [37, 78], semantic segmentation [68, 102], and others [40, 71]. Some recent research has attempted to iterate the refinement process using deep convolutional networks [9, 21, 55, 57]. Other works train the same network repeatedly by utilizing the results of the previous iteration [99, 102]. In particular, RAFT [78] found success with its iterative refinement procedure for flow estimation. DEQ-flow [2] employed a deep equilibrium (DEQ) [3] framework to reduce the memory consumption of RAFT during training while maintaining accuracy." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 618, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 289, + 715 + ], + "type": "text", + "content": "A key component of our model is inspired by the iterative updates of RAFT and DEQ-flow. Instead of optical flow, our model refines depth and pose estimates in parallel. We design our refinement module to tightly couple the two predictions, considering the epipolar geometry of adjacent frames. With every update, the epipolar geometry is refined, which also results in a more accurate matching costs computation of pixel correspondences." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 72, + 402, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 402, + 83 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 402, + 83 + ], + "type": "text", + "content": "2.4. Pose estimation" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 89, + 548, + 307 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 89, + 548, + 307 + ], + "spans": [ + { + "bbox": [ + 304, + 89, + 548, + 307 + ], + "type": "text", + "content": "Pose estimation is a crucial component in self-supervised monocular depth models. In many works, PoseNet-based models [43] take a pair of adjacent image frames and output a 6 DoF pose estimation. This class of models is straightforward, but often less accurate than their traditional counterparts [16, 17, 65] due to the absence of geometry constraints. Recent work in deep learning-based localization has adopted differentiable geometrically inspired designs within their models by using direct alignments [72, 85, 86] or geometric alignments based on optical flow [79]. These models demonstrate better generalization properties and accuracy. The use of self-supervised monocular depth has also been used to improve traditional odometry [8, 96]. However, our interest lies in learning to refine both depth and pose in the self-supervision pipeline. To improve the accuracy of pose estimation, we integrate direct alignment within the recurrent module, ensuring geometrically consistent prediction between depth and pose." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 315, + 362, + 327 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 315, + 362, + 327 + ], + "spans": [ + { + "bbox": [ + 306, + 315, + 362, + 327 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 335, + 547, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 335, + 547, + 407 + ], + "spans": [ + { + "bbox": [ + 304, + 335, + 547, + 407 + ], + "type": "text", + "content": "Our model comprises two primary sub-modules. The first is a single frame self-supervised depth and pose estimator, building upon previous frameworks [23, 105], which we revisit in Sec. 3.1. This network serves as both a teacher and an initializer for the second sub-module, our proposed multi-frame network, presented in detail in Sec. 3.2." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 413, + 474, + 426 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 413, + 474, + 426 + ], + "spans": [ + { + "bbox": [ + 306, + 413, + 474, + 426 + ], + "type": "text", + "content": "3.1. Self-supervised depth and pose" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 431, + 547, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 431, + 547, + 563 + ], + "spans": [ + { + "bbox": [ + 304, + 431, + 547, + 563 + ], + "type": "text", + "content": "We begin by describing the canonical self-supervised monocular depth estimation pipeline [23], which serves as the foundation for our approach. This depth training method assumes that a monocular camera with an intrinsic parameter " + }, + { + "bbox": [ + 304, + 431, + 547, + 563 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 431, + 547, + 563 + ], + "type": "text", + "content": " captures an image sequence of a scene. In this process, two networks are trained in parallel to estimate the per-pixel depth map of the images " + }, + { + "bbox": [ + 304, + 431, + 547, + 563 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 431, + 547, + 563 + ], + "type": "text", + "content": " and the relative poses between adjacent image frames. By warping neighboring images towards a shared target frame using these two predictions, self-supervised training can be performed by enforcing photometric consistency between the frames." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 563, + 547, + 611 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 563, + 547, + 611 + ], + "spans": [ + { + "bbox": [ + 304, + 563, + 547, + 611 + ], + "type": "text", + "content": "Given the depth map " + }, + { + "bbox": [ + 304, + 563, + 547, + 611 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 563, + 547, + 611 + ], + "type": "text", + "content": " of a target image and its relative pose with a source image " + }, + { + "bbox": [ + 304, + 563, + 547, + 611 + ], + "type": "inline_equation", + "content": "T_{t\\rightarrow s}" + }, + { + "bbox": [ + 304, + 563, + 547, + 611 + ], + "type": "text", + "content": ", we can calculate the projection of each pixel " + }, + { + "bbox": [ + 304, + 563, + 547, + 611 + ], + "type": "inline_equation", + "content": "u = (x,y)" + }, + { + "bbox": [ + 304, + 563, + 547, + 611 + ], + "type": "text", + "content": " of the target image onto the source image as follows:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 341, + 615, + 547, + 654 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 341, + 615, + 547, + 654 + ], + "spans": [ + { + "bbox": [ + 341, + 615, + 547, + 654 + ], + "type": "interline_equation", + "content": "z ^ {\\prime} u ^ {\\prime} = z ^ {\\prime} \\left[\\begin{array}{l}x ^ {\\prime}\\\\y ^ {\\prime}\\\\1\\end{array}\\right] = K T _ {t \\rightarrow s} \\left(D [ u ] K ^ {- 1} \\left[\\begin{array}{l}x\\\\y\\\\1\\end{array}\\right]\\right), \\tag {1}", + "image_path": "cbd29a29a08f8d2d15b47dfb5c5293f450c5e4bff88cfb9a274a3a1708b36158.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 658, + 547, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 658, + 547, + 696 + ], + "spans": [ + { + "bbox": [ + 304, + 658, + 547, + 696 + ], + "type": "text", + "content": "using the estimated depth at that pixel " + }, + { + "bbox": [ + 304, + 658, + 547, + 696 + ], + "type": "inline_equation", + "content": "D[u]" + }, + { + "bbox": [ + 304, + 658, + 547, + 696 + ], + "type": "text", + "content": ". The source images can then be warped towards the target frame by sampling the pixel values at the calculated projection" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 392, + 700, + 547, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 392, + 700, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 392, + 700, + 547, + 715 + ], + "type": "interline_equation", + "content": "I _ {s \\rightarrow t} [ u ] = I _ {s} \\langle u ^ {\\prime} \\rangle , \\tag {2}", + "image_path": "cab4ac194d5f41eb44bf57116b414baa8abd64b316aabb5ba40b50d2686a6f4e.jpg" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "type": "text", + "content": "728" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 68, + 318, + 219 + ], + "blocks": [ + { + "bbox": [ + 51, + 68, + 318, + 219 + ], + "lines": [ + { + "bbox": [ + 51, + 68, + 318, + 219 + ], + "spans": [ + { + "bbox": [ + 51, + 68, + 318, + 219 + ], + "type": "image", + "image_path": "75a2a72803f499eb42d709327ef11302dff73ceedc98f3083e705e386b494917.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 323, + 71, + 541, + 223 + ], + "blocks": [ + { + "bbox": [ + 323, + 71, + 541, + 223 + ], + "lines": [ + { + "bbox": [ + 323, + 71, + 541, + 223 + ], + "spans": [ + { + "bbox": [ + 323, + 71, + 541, + 223 + ], + "type": "image", + "image_path": "208b987c812c8a5409c3061d15e025593878273f80ac26912fc279dfe572e9f4.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 326, + 224, + 394, + 236 + ], + "lines": [ + { + "bbox": [ + 326, + 224, + 394, + 236 + ], + "spans": [ + { + "bbox": [ + 326, + 224, + 394, + 236 + ], + "type": "text", + "content": "DEQ updates" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 244, + 547, + 285 + ], + "lines": [ + { + "bbox": [ + 46, + 244, + 547, + 285 + ], + "spans": [ + { + "bbox": [ + 46, + 244, + 547, + 285 + ], + "type": "text", + "content": "Figure 2. (a) The overall pipeline of the model. Given a pair of source and target images, the teacher model predicts an initial depth " + }, + { + "bbox": [ + 46, + 244, + 547, + 285 + ], + "type": "inline_equation", + "content": "D_0" + }, + { + "bbox": [ + 46, + 244, + 547, + 285 + ], + "type": "text", + "content": " and pose " + }, + { + "bbox": [ + 46, + 244, + 547, + 285 + ], + "type": "inline_equation", + "content": "T_0" + }, + { + "bbox": [ + 46, + 244, + 547, + 285 + ], + "type": "text", + "content": ", as well as initial hidden states that will be updated. DEQ-based alignments are then performed to find the fixed point and output the final predictions. (b) Each iteration in the update step takes the current depth and pose estimates. Matching costs are sampled along the current epipolar lines that evolves based on the pose estimates. The updates are computed by Conv-GRU. Then feature-metric alignment is used to obtain a geometrically consistent pose update." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 294, + 287, + 318 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 294, + 287, + 318 + ], + "spans": [ + { + "bbox": [ + 46, + 294, + 287, + 318 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 294, + 287, + 318 + ], + "type": "inline_equation", + "content": "\\langle \\cdot \\rangle" + }, + { + "bbox": [ + 46, + 294, + 287, + 318 + ], + "type": "text", + "content": " indicates bilinear interpolation, implemented using the spatial transformer network (STN) [39]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 319, + 288, + 343 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 319, + 288, + 343 + ], + "spans": [ + { + "bbox": [ + 47, + 319, + 288, + 343 + ], + "type": "text", + "content": "The self-supervised loss is calculated as a combination of the photometric error and the edge-aware smoothness loss:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 113, + 354, + 287, + 368 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 354, + 287, + 368 + ], + "spans": [ + { + "bbox": [ + 113, + 354, + 287, + 368 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {s e l f - s u p} = \\lambda_ {p} \\mathcal {L} _ {p} + \\lambda_ {s} \\mathcal {L} _ {s}, \\tag {3}", + "image_path": "baddde2634f3de2dd932803d627907165980cab11b52ff6986c7cae0f1d14d13.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 377, + 287, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 377, + 287, + 449 + ], + "spans": [ + { + "bbox": [ + 46, + 377, + 287, + 449 + ], + "type": "text", + "content": "where the photometric error between the warped source image and the target image is calculated using the structural similarity loss, and the minimum error is taken between multiple warped images to account for occlusions. Interested readers can refer to [23]. The self-supervised loss is typically computed at multiple scales to stabilize the training." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 449, + 288, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 288, + 521 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 288, + 521 + ], + "type": "text", + "content": "In this paper, we train a monocular depth estimator and a pose estimation network using this pipeline, serving two purposes. First, following ManyDepth [91], we use these models as a teacher to constrain the multi-frame predictions in the presence of dynamic objects. Additionally, we employ them as an initializer for the multi-frame alignment network." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 538, + 156, + 550 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 538, + 156, + 550 + ], + "spans": [ + { + "bbox": [ + 47, + 538, + 156, + 550 + ], + "type": "text", + "content": "3.1.1 Monocular model" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 557, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 289, + 715 + ], + "type": "text", + "content": "We build our monocular depth estimation model based on DIFFNet [105], a SoTA self-supervised single-frame estimator. We extract feature maps at multiple scales " + }, + { + "bbox": [ + 46, + 557, + 289, + 715 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 557, + 289, + 715 + ], + "type": "text", + "content": " from the target image using the HRNet architecture [88]. In accordance with DIFFNet, feature maps from multiple stages are accumulated in " + }, + { + "bbox": [ + 46, + 557, + 289, + 715 + ], + "type": "inline_equation", + "content": "F^{(1/2^s)}" + }, + { + "bbox": [ + 46, + 557, + 289, + 715 + ], + "type": "text", + "content": ". Then, we employ disparity decoders to make disparity predictions at scales " + }, + { + "bbox": [ + 46, + 557, + 289, + 715 + ], + "type": "inline_equation", + "content": "s = \\{2,3\\}" + }, + { + "bbox": [ + 46, + 557, + 289, + 715 + ], + "type": "text", + "content": ". The pose estimation network follows the canonical PoseNet [43] architecture, taking two input images and outputting 6-DoF values, with a ResNet18 [33] backbone. The predicted disparity and pose estimation from these networks are used as a teacher to train our alignment sub-module, as was done in ManyDepth [91]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 294, + 465, + 307 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 294, + 465, + 307 + ], + "spans": [ + { + "bbox": [ + 306, + 294, + 465, + 307 + ], + "type": "text", + "content": "3.2. Deep equilibrium alignments" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 312, + 545, + 372 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 312, + 545, + 372 + ], + "spans": [ + { + "bbox": [ + 304, + 312, + 545, + 372 + ], + "type": "text", + "content": "In our alignment sub-module, we assume that additional input from source image(s) is available, which can be used to refine the depth and pose estimates. In this work, we focus on using the image from the previous frame in the image sequence as our source image." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 372, + 547, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 372, + 547, + 421 + ], + "spans": [ + { + "bbox": [ + 304, + 372, + 547, + 421 + ], + "type": "text", + "content": "Our alignment module is formulated as a deep equilibrium model [3] that updates the hidden states, depth, and pose estimates to a fixed point. Specifically, at the fixed point " + }, + { + "bbox": [ + 304, + 372, + 547, + 421 + ], + "type": "inline_equation", + "content": "z^{*}" + }, + { + "bbox": [ + 304, + 372, + 547, + 421 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 367, + 429, + 545, + 442 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 367, + 429, + 545, + 442 + ], + "spans": [ + { + "bbox": [ + 367, + 429, + 545, + 442 + ], + "type": "interline_equation", + "content": "\\left(h ^ {*}, D ^ {*}, T ^ {*}\\right) = z ^ {*} = \\mathrm {U} \\left(z ^ {*}, x\\right), \\tag {4}", + "image_path": "8f52e81f80fdcbbb563795c83fffd14173b27345bcd71b25d474b9c8679d5758.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 451, + 547, + 522 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 451, + 547, + 522 + ], + "spans": [ + { + "bbox": [ + 304, + 451, + 547, + 522 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 451, + 547, + 522 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 304, + 451, + 547, + 522 + ], + "type": "text", + "content": " is composed of a hidden state " + }, + { + "bbox": [ + 304, + 451, + 547, + 522 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 304, + 451, + 547, + 522 + ], + "type": "text", + "content": ", the depth prediction " + }, + { + "bbox": [ + 304, + 451, + 547, + 522 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 451, + 547, + 522 + ], + "type": "text", + "content": ", and the pose prediction " + }, + { + "bbox": [ + 304, + 451, + 547, + 522 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 451, + 547, + 522 + ], + "type": "text", + "content": ". U represents our update function, refining the depth and pose alternatively. " + }, + { + "bbox": [ + 304, + 451, + 547, + 522 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 451, + 547, + 522 + ], + "type": "text", + "content": " is an input to the update module, obtained based on the epipolar geometry at each step, which we discuss in the next subsection. We perform these iterative updates at scale " + }, + { + "bbox": [ + 304, + 451, + 547, + 522 + ], + "type": "inline_equation", + "content": "s = 2" + }, + { + "bbox": [ + 304, + 451, + 547, + 522 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 523, + 547, + 583 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 523, + 547, + 583 + ], + "spans": [ + { + "bbox": [ + 304, + 523, + 547, + 583 + ], + "type": "text", + "content": "From the feature extraction output, we compute an initial hidden state for our recurrent updates " + }, + { + "bbox": [ + 304, + 523, + 547, + 583 + ], + "type": "inline_equation", + "content": "h^{[0]} = \\tanh(\\mathrm{H}(F^{(1/4)}))" + }, + { + "bbox": [ + 304, + 523, + 547, + 583 + ], + "type": "text", + "content": " and a context feature " + }, + { + "bbox": [ + 304, + 523, + 547, + 583 + ], + "type": "inline_equation", + "content": "q = \\mathrm{Q}(F^{(1/4)})" + }, + { + "bbox": [ + 304, + 523, + 547, + 583 + ], + "type": "text", + "content": ". Both H and Q are composed of a single residual block [33] followed by a convolutional layer." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 597, + 518, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 597, + 518, + 609 + ], + "spans": [ + { + "bbox": [ + 306, + 597, + 518, + 609 + ], + "type": "text", + "content": "3.2.1 Depth updates around local neighborhood" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 616, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 616, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 616, + 545, + 689 + ], + "type": "text", + "content": "Local epipolar sampling. As discussed previously, our refinement is based on the pixel matching between the target image and the source image. 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" + }, + { + "bbox": [ + 46, + 292, + 546, + 312 + ], + "type": "inline_equation", + "content": "I_{s}" + }, + { + "bbox": [ + 46, + 292, + 546, + 312 + ], + "type": "text", + "content": ": input image; " + }, + { + "bbox": [ + 46, + 292, + 546, + 312 + ], + "type": "inline_equation", + "content": "W_{q}" + }, + { + "bbox": [ + 46, + 292, + 546, + 312 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 292, + 546, + 312 + ], + "type": "inline_equation", + "content": "W_{h,0}" + }, + { + "bbox": [ + 46, + 292, + 546, + 312 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 292, + 546, + 312 + ], + "type": "inline_equation", + "content": "W_{h,5}" + }, + { + "bbox": [ + 46, + 292, + 546, + 312 + ], + "type": "text", + "content": ": confidence weights; " + }, + { + "bbox": [ + 46, + 292, + 546, + 312 + ], + "type": "inline_equation", + "content": "D_{0}" + }, + { + "bbox": [ + 46, + 292, + 546, + 312 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 292, + 546, + 312 + ], + "type": "inline_equation", + "content": "D_{5}" + }, + { + "bbox": [ + 46, + 292, + 546, + 312 + ], + "type": "text", + "content": ": disparity estimates; The Abs Rel error for the depth estimates." + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_caption" + } + ], + "index": 20 + }, + { + "type": "image", + "bbox": [ + 175, + 241, + 299, + 279 + ], + "blocks": [ + { + "bbox": [ + 229, + 231, + 246, + 241 + ], + "lines": [ + { + "bbox": [ + 229, + 231, + 246, + 241 + ], + "spans": [ + { + "bbox": [ + 229, + 231, + 246, + 241 + ], + "type": "inline_equation", + "content": "W_{h,5}" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 175, + 241, + 299, + 279 + ], + "lines": [ + { + "bbox": [ + 175, + 241, + 299, + 279 + ], + "spans": [ + { + "bbox": [ + 175, + 241, + 299, + 279 + ], + "type": "image", + "image_path": "8dda74a09b391eb5ca265cba9015dd08e6c0306282aef4e7b20c53d2851cbe45.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + } + ], + "index": 21 + }, + { + "type": "image", + "bbox": [ + 299, + 241, + 421, + 279 + ], + "blocks": [ + { + "bbox": [ + 354, + 232, + 365, + 241 + ], + "lines": [ + { + "bbox": [ + 354, + 232, + 365, + 241 + ], + "spans": [ + { + "bbox": [ + 354, + 232, + 365, + 241 + ], + "type": "inline_equation", + "content": "D_{5}" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 299, + 241, + 421, + 279 + ], + "lines": [ + { + "bbox": [ + 299, + 241, + 421, + 279 + ], + "spans": [ + { + "bbox": [ + 299, + 241, + 421, + 279 + ], + "type": "image", + "image_path": "38636b52cf916573f7ec926f68ae2667f5ed6e93e794586d30cf7775b26a356f.jpg" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_body" + } + ], + "index": 22 + }, + { + "type": "image", + "bbox": [ + 421, + 241, + 544, + 279 + ], + "blocks": [ + { + "bbox": [ + 466, + 231, + 498, + 241 + ], + "lines": [ + { + "bbox": [ + 466, + 231, + 498, + 241 + ], + "spans": [ + { + "bbox": [ + 466, + 231, + 498, + 241 + ], + "type": "text", + "content": "AbsRel5" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 421, + 241, + 544, + 279 + ], + "lines": [ + { + "bbox": [ + 421, + 241, + 544, + 279 + ], + "spans": [ + { + "bbox": [ + 421, + 241, + 544, + 279 + ], + "type": "image", + "image_path": "cf844cc748508cfb657673d0296076f7664b675c102f0d777bda2adea94f80ae.jpg" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_body" + } + ], + "index": 23 + }, + { + "bbox": [ + 46, + 323, + 287, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 323, + 287, + 430 + ], + "spans": [ + { + "bbox": [ + 46, + 323, + 287, + 430 + ], + "type": "text", + "content": "prediction and use them as input to our update module at the update step " + }, + { + "bbox": [ + 46, + 323, + 287, + 430 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 323, + 287, + 430 + ], + "type": "text", + "content": ". Unlike RAFT, however, we perform matching along an epipolar line based on the pose estimate " + }, + { + "bbox": [ + 46, + 323, + 287, + 430 + ], + "type": "inline_equation", + "content": "T_{k}" + }, + { + "bbox": [ + 46, + 323, + 287, + 430 + ], + "type": "text", + "content": ". This is done by computing the projected coordinates " + }, + { + "bbox": [ + 46, + 323, + 287, + 430 + ], + "type": "inline_equation", + "content": "u_{k}^{\\prime}" + }, + { + "bbox": [ + 46, + 323, + 287, + 430 + ], + "type": "text", + "content": " in the source image obtained from (1) at the depths of interest. The depth candidates are computed to be the neighborhood of the current prediction. Instead of computing the all-pair correlation as was done in RAFT, we compute feature matching on the fly." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 46, + 431, + 288, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 431, + 288, + 590 + ], + "spans": [ + { + "bbox": [ + 46, + 431, + 288, + 590 + ], + "type": "text", + "content": "At each pixel " + }, + { + "bbox": [ + 46, + 431, + 288, + 590 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 46, + 431, + 288, + 590 + ], + "type": "text", + "content": ", we compute the local depth candidates as " + }, + { + "bbox": [ + 46, + 431, + 288, + 590 + ], + "type": "inline_equation", + "content": "D[u]_k \\pm (i \\times c \\times n)" + }, + { + "bbox": [ + 46, + 431, + 288, + 590 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 46, + 431, + 288, + 590 + ], + "type": "inline_equation", + "content": "i \\in \\mathbb{Z}" + }, + { + "bbox": [ + 46, + 431, + 288, + 590 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 431, + 288, + 590 + ], + "type": "inline_equation", + "content": "i \\leq r" + }, + { + "bbox": [ + 46, + 431, + 288, + 590 + ], + "type": "text", + "content": ". We set the sampling radius hyperparameter " + }, + { + "bbox": [ + 46, + 431, + 288, + 590 + ], + "type": "inline_equation", + "content": "r = 8" + }, + { + "bbox": [ + 46, + 431, + 288, + 590 + ], + "type": "text", + "content": " in our experiments. In depth estimation, the error typically grows with distance. To account for this, we define " + }, + { + "bbox": [ + 46, + 431, + 288, + 590 + ], + "type": "inline_equation", + "content": "c = D[u] / C" + }, + { + "bbox": [ + 46, + 431, + 288, + 590 + ], + "type": "text", + "content": " as a function of depth to make the sampling range dependent on the depth, where we set " + }, + { + "bbox": [ + 46, + 431, + 288, + 590 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 431, + 288, + 590 + ], + "type": "text", + "content": " as a trainable parameter. Following RAFT, to collect the matching information from a larger neighborhood, we sampled at multiple levels " + }, + { + "bbox": [ + 46, + 431, + 288, + 590 + ], + "type": "inline_equation", + "content": "n = \\{1,2,3\\}" + }, + { + "bbox": [ + 46, + 431, + 288, + 590 + ], + "type": "text", + "content": ". At each level, we bilinearly resize the matching feature map of the source image " + }, + { + "bbox": [ + 46, + 431, + 288, + 590 + ], + "type": "inline_equation", + "content": "m_s^{(1/4)}" + }, + { + "bbox": [ + 46, + 431, + 288, + 590 + ], + "type": "text", + "content": " with a scale of " + }, + { + "bbox": [ + 46, + 431, + 288, + 590 + ], + "type": "inline_equation", + "content": "1/2^n" + }, + { + "bbox": [ + 46, + 431, + 288, + 590 + ], + "type": "text", + "content": ". Then, the matching features are sampled at the calculated corresponding set of coordinates " + }, + { + "bbox": [ + 46, + 431, + 288, + 590 + ], + "type": "inline_equation", + "content": "u_k'" + }, + { + "bbox": [ + 46, + 431, + 288, + 590 + ], + "type": "text", + "content": ", and the absolute differences with the target feature" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 116, + 597, + 287, + 610 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 597, + 287, + 610 + ], + "spans": [ + { + "bbox": [ + 116, + 597, + 287, + 610 + ], + "type": "interline_equation", + "content": "\\mathbf {C} _ {k} [ u ] = \\left| m _ {t} [ u ] - m _ {s} \\langle u _ {k} ^ {\\prime} \\rangle \\right| \\tag {5}", + "image_path": "9b174a1ef753ac4262fbe46c28b1c569d0412c513c2ddfa3eccbef457091b059.jpg" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 46, + 617, + 288, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 288, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 288, + 689 + ], + "type": "text", + "content": "are calculated and gathered. This provides us with a map " + }, + { + "bbox": [ + 46, + 617, + 288, + 689 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_k" + }, + { + "bbox": [ + 46, + 617, + 288, + 689 + ], + "type": "text", + "content": " that contains " + }, + { + "bbox": [ + 46, + 617, + 288, + 689 + ], + "type": "inline_equation", + "content": "n \\times (2 \\times r + 1)" + }, + { + "bbox": [ + 46, + 617, + 288, + 689 + ], + "type": "text", + "content": " matching cost values at the corresponding depth candidates. We then encode these matching costs along with the depth using a two-layer convolutional neural network (CNN) to compute the input for the update module" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 96, + 699, + 287, + 712 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 699, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 96, + 699, + 287, + 712 + ], + "type": "interline_equation", + "content": "x _ {k} = \\left[ \\operatorname {C N N} _ {\\mathbf {C}} \\left(\\mathbf {C} _ {k}\\right), \\operatorname {C N N} _ {D _ {x}} \\left(D _ {k}\\right), q \\right], \\tag {6}", + "image_path": "698aacff77d1abc62364aee044a17d6d8acd7c4c105513de97ae4f07971f61fa.jpg" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 306, + 323, + 468, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 323, + 468, + 335 + ], + "spans": [ + { + "bbox": [ + 306, + 323, + 468, + 335 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 323, + 468, + 335 + ], + "type": "inline_equation", + "content": "[\\cdot ,\\cdot ]" + }, + { + "bbox": [ + 306, + 323, + 468, + 335 + ], + "type": "text", + "content": " represents the concatenation." + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 305, + 343, + 546, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 343, + 546, + 403 + ], + "spans": [ + { + "bbox": [ + 305, + 343, + 546, + 403 + ], + "type": "text", + "content": "Depth update. The update function calculates an updated hidden state " + }, + { + "bbox": [ + 305, + 343, + 546, + 403 + ], + "type": "inline_equation", + "content": "h_{k+1}" + }, + { + "bbox": [ + 305, + 343, + 546, + 403 + ], + "type": "text", + "content": " using the Conv-GRU block [5,41,78]. " + }, + { + "bbox": [ + 305, + 343, + 546, + 403 + ], + "type": "inline_equation", + "content": "h_{k+1}" + }, + { + "bbox": [ + 305, + 343, + 546, + 403 + ], + "type": "text", + "content": " is used to compute the depth updates. To stabilize training, we use the activation function " + }, + { + "bbox": [ + 305, + 343, + 546, + 403 + ], + "type": "inline_equation", + "content": "\\tanh(\\cdot)" + }, + { + "bbox": [ + 305, + 343, + 546, + 403 + ], + "type": "text", + "content": " to bound the absolute update values for the depths to be within " + }, + { + "bbox": [ + 305, + 343, + 546, + 403 + ], + "type": "inline_equation", + "content": "r \\cdot c" + }, + { + "bbox": [ + 305, + 343, + 546, + 403 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 343, + 412, + 546, + 426 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 343, + 412, + 546, + 426 + ], + "spans": [ + { + "bbox": [ + 343, + 412, + 546, + 426 + ], + "type": "interline_equation", + "content": "D _ {k + 1} = D _ {k} + r \\cdot c \\cdot \\tanh \\left(\\mathrm {C N N} _ {D _ {\\mathrm {U}}} \\left(h _ {k + 1}\\right)\\right). \\tag {7}", + "image_path": "dba60cfc5c6208f71e78671398487f7fc37ef47a10ae654de86216a1abf7a8ad.jpg" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 305, + 433, + 546, + 481 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 433, + 546, + 481 + ], + "spans": [ + { + "bbox": [ + 305, + 433, + 546, + 481 + ], + "type": "text", + "content": "These updates are performed in an alternating fashion with the pose updates to reach the fixed point " + }, + { + "bbox": [ + 305, + 433, + 546, + 481 + ], + "type": "inline_equation", + "content": "D^{*}" + }, + { + "bbox": [ + 305, + 433, + 546, + 481 + ], + "type": "text", + "content": ". Using " + }, + { + "bbox": [ + 305, + 433, + 546, + 481 + ], + "type": "inline_equation", + "content": "h^{*}" + }, + { + "bbox": [ + 305, + 433, + 546, + 481 + ], + "type": "text", + "content": ", we compute a convex upsampling to obtain the final depth estimate at the input resolution." + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 306, + 495, + 473, + 508 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 495, + 473, + 508 + ], + "spans": [ + { + "bbox": [ + 306, + 495, + 473, + 508 + ], + "type": "text", + "content": "3.2.2 Feature-metric pose alignments" + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 304, + 514, + 547, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 514, + 547, + 598 + ], + "spans": [ + { + "bbox": [ + 304, + 514, + 547, + 598 + ], + "type": "text", + "content": "In (1), the accuracy of pose estimation affects the calculation of the coordinates of pixels. Hence, a refined pose estimate would also improve the reliability of the matching costs. To refine the pose while being geometrically consistent, we perform our pose updates based on direct feature alignments [16, 17, 87]. These updates " + }, + { + "bbox": [ + 304, + 514, + 547, + 598 + ], + "type": "inline_equation", + "content": "\\delta_{k}" + }, + { + "bbox": [ + 304, + 514, + 547, + 598 + ], + "type": "text", + "content": " can be calculated by solving " + }, + { + "bbox": [ + 304, + 514, + 547, + 598 + ], + "type": "inline_equation", + "content": "H_{k}\\delta_{k} = b_{k}" + }, + { + "bbox": [ + 304, + 514, + 547, + 598 + ], + "type": "text", + "content": ", where" + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 328, + 605, + 545, + 624 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 328, + 605, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 328, + 605, + 545, + 624 + ], + "type": "interline_equation", + "content": "H _ {k} = \\mathcal {J} _ {k} ^ {T} \\operatorname {d i a g} \\left(W _ {k}\\right) \\mathcal {J} _ {k} \\text {a n d} b _ {k} = - \\mathcal {J} _ {k} ^ {T} \\operatorname {d i a g} \\left(W _ {k}\\right) r _ {k} \\tag {8}", + "image_path": "bdd359a681bdd67fd9924b81fd40934565723153a23317d390e81f68711f131b.jpg" + } + ] + } + ], + "index": 36 + }, + { + "bbox": [ + 430, + 622, + 522, + 634 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 430, + 622, + 522, + 634 + ], + "spans": [ + { + "bbox": [ + 430, + 622, + 522, + 634 + ], + "type": "interline_equation", + "content": "r _ {k} [ u ] = m _ {s} \\left\\langle u _ {k} ^ {\\prime} \\right\\rangle - m _ {t} [ u ],", + "image_path": "b0c157bd9bf4162adf43713add74e9edb58e2766da4afcb3e080f625123a25c3.jpg" + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 306, + 642, + 495, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 642, + 495, + 654 + ], + "spans": [ + { + "bbox": [ + 306, + 642, + 495, + 654 + ], + "type": "text", + "content": "and " + }, + { + "bbox": [ + 306, + 642, + 495, + 654 + ], + "type": "inline_equation", + "content": "\\mathcal{J}" + }, + { + "bbox": [ + 306, + 642, + 495, + 654 + ], + "type": "text", + "content": " is the Jacobian with respect to the pose." + } + ] + } + ], + "index": 38 + }, + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "type": "text", + "content": "To compute this pose update, one could assign uniform confidence to every pixel in the image. However, in Eq. (8), additional confidence weights per pixel " + }, + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "type": "text", + "content": " can also be integrated. This is done for two reasons. First, the solution for the pose updates can be affected by dynamic objects" + } + ] + } + ], + "index": 39 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 297, + 748, + 313, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 748, + 313, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 748, + 313, + 757 + ], + "type": "text", + "content": "730" + } + ] + } + ], + "index": 40 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "content": "as well as inaccurate feature alignments that may occur in region with repeated textures. To account for this, the confidence weighting of the input context feature map " + }, + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "inline_equation", + "content": "W_{q}" + }, + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "content": " can be computed [72]. Specifically, we computed a confidence map " + }, + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "inline_equation", + "content": "W_{t,s} = 1 / (1 + \\mathrm{ReLU}(\\mathrm{CNN}_{W_q}(F_{t,s}))" + }, + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "content": " for both target and source images. The source confidence is warped towards the target frame using Eqs. (1) and (2). Finally, the confidence is computed as " + }, + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "inline_equation", + "content": "W_{q} = W_{t}\\cdot W_{s,\\text{warped}}" + }, + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "content": ". This confidence weight is only computed once to assign per-pixel confidence for the input images." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 193, + 289, + 349 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 193, + 289, + 349 + ], + "spans": [ + { + "bbox": [ + 46, + 193, + 289, + 349 + ], + "type": "text", + "content": "Second, the accuracy of pose updates would depend on the accuracy of the depth estimates. To obtain more accurate pose updates, we would like to assign more alignment confidence to the region with higher depth accuracy. We use a neural network to infer this confidence from the matching costs. Since the hidden states " + }, + { + "bbox": [ + 46, + 193, + 289, + 349 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 46, + 193, + 289, + 349 + ], + "type": "text", + "content": " have a history of these matching costs, another confidence weights " + }, + { + "bbox": [ + 46, + 193, + 289, + 349 + ], + "type": "inline_equation", + "content": "W_{h,k} = \\mathrm{CNN}_{W_h}(h_k)" + }, + { + "bbox": [ + 46, + 193, + 289, + 349 + ], + "type": "text", + "content": " can be computed. Unlike the previous confidence map, this one is computed and evolves at every update step. By doing so, the network can use the depth predictions to guide the pose estimates towards convergence using the depth information. In our experiments, we investigate the use of each confidence weighting and combination of both " + }, + { + "bbox": [ + 46, + 193, + 289, + 349 + ], + "type": "inline_equation", + "content": "W_{k} = W_{q}W_{h,k}" + }, + { + "bbox": [ + 46, + 193, + 289, + 349 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 349, + 289, + 385 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 349, + 289, + 385 + ], + "spans": [ + { + "bbox": [ + 47, + 349, + 289, + 385 + ], + "type": "text", + "content": "Finally, we can compute the updated pose as " + }, + { + "bbox": [ + 47, + 349, + 289, + 385 + ], + "type": "inline_equation", + "content": "T_{k + 1} = \\exp (\\delta_k^{\\wedge})T_k" + }, + { + "bbox": [ + 47, + 349, + 289, + 385 + ], + "type": "text", + "content": ". These operations are designed to be differentiable to enable end-to-end training." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 404, + 139, + 417 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 404, + 139, + 417 + ], + "spans": [ + { + "bbox": [ + 47, + 404, + 139, + 417 + ], + "type": "text", + "content": "3.2.3 DEQ training" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 424, + 287, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 424, + 287, + 532 + ], + "spans": [ + { + "bbox": [ + 46, + 424, + 287, + 532 + ], + "type": "text", + "content": "We adopt a DEQ framework, wherein the above steps are repeated until the depth and pose values reach a fixed point, at which the update value is minimal. In our implementation, the fixed points of depth and pose are chosen separately, and it is possible for both to be selected from different update steps. Finally, the training gradient is computed using the chosen depth and pose fixed points. Operations prior to the fixed point do not require saving gradients in memory, which allows memory-efficient training." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 533, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 287, + 677 + ], + "type": "text", + "content": "As noted in Eqs. (1) to (3), the self-supervision losses can be computed given a depth and pose prediction. At the fixed point, we compute two additional self-supervision losses. The first performs source-to-target image warping through the pairing of the final depth " + }, + { + "bbox": [ + 46, + 533, + 287, + 677 + ], + "type": "inline_equation", + "content": "D^{*}" + }, + { + "bbox": [ + 46, + 533, + 287, + 677 + ], + "type": "text", + "content": " and the initial pose " + }, + { + "bbox": [ + 46, + 533, + 287, + 677 + ], + "type": "inline_equation", + "content": "T_{0}" + }, + { + "bbox": [ + 46, + 533, + 287, + 677 + ], + "type": "text", + "content": ", where we detach " + }, + { + "bbox": [ + 46, + 533, + 287, + 677 + ], + "type": "inline_equation", + "content": "T_{0}" + }, + { + "bbox": [ + 46, + 533, + 287, + 677 + ], + "type": "text", + "content": " from the computational graph to act as a teacher. This loss is used so that the output of the teacher and refinement modules shares the same scaling. The second performs the warping with the pairing of " + }, + { + "bbox": [ + 46, + 533, + 287, + 677 + ], + "type": "inline_equation", + "content": "D^{*}" + }, + { + "bbox": [ + 46, + 533, + 287, + 677 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 533, + 287, + 677 + ], + "type": "inline_equation", + "content": "T^{*}" + }, + { + "bbox": [ + 46, + 533, + 287, + 677 + ], + "type": "text", + "content": ". This loss helps drive refined estimation of both depth and pose towards the optimal value. Detailed experiments for this choice of loss pairings are provided in the supplementary." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 677, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 289, + 714 + ], + "type": "text", + "content": "In both losses, we also apply the consistency loss between " + }, + { + "bbox": [ + 47, + 677, + 289, + 714 + ], + "type": "inline_equation", + "content": "D_0" + }, + { + "bbox": [ + 47, + 677, + 289, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 677, + 289, + 714 + ], + "type": "inline_equation", + "content": "D^*" + }, + { + "bbox": [ + 47, + 677, + 289, + 714 + ], + "type": "text", + "content": ", similar to ManyDepth [91], to account for dynamic objects or occluded regions. Specifically, we extract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "text", + "content": "coarse depth predictions from the raw feature matchings and mask regions where large disagreements occur, and enforce consistency with the teacher depth. Unlike ManyDepth, however, our method does not explicitly construct a cost volume. To obtain the coarse depth, we search for the lowest matching cost around the neighborhood of the teacher depth, similar to Sec. 3.2.1, but with a larger neighborhood range. This approach offers an additional advantage compared to the cost volume-based method, as we do not need to rely on an estimated minimum and maximum depth or know the scale of the estimates. Moreover, since the computation of coarse depth depends on the accuracy of feature matching costs, it can be improved with more accurate pose estimates (Tab. 2)." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 251, + 388, + 265 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 251, + 388, + 265 + ], + "spans": [ + { + "bbox": [ + 306, + 251, + 388, + 265 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 272, + 422, + 283 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 272, + 422, + 283 + ], + "spans": [ + { + "bbox": [ + 306, + 272, + 422, + 283 + ], + "type": "text", + "content": "4.1. Dataset and metrics" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 290, + 547, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 290, + 547, + 411 + ], + "spans": [ + { + "bbox": [ + 304, + 290, + 547, + 411 + ], + "type": "text", + "content": "For depth estimation experiments, we use the Eigen train/test split [15] from the KITTI dataset [20]. To evaluate the estimated depths, we scale them by a scalar to match the scale of the ground truth. We employ standard depth evaluation metrics [14, 15], including absolute and squared relative error (Abs Rel, Sq Rel), root mean square error (RMSE, RMSE log), and accuracy under threshold " + }, + { + "bbox": [ + 304, + 290, + 547, + 411 + ], + "type": "inline_equation", + "content": "(\\delta_{1}, \\delta_{2}" + }, + { + "bbox": [ + 304, + 290, + 547, + 411 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 290, + 547, + 411 + ], + "type": "inline_equation", + "content": "\\delta_{3})" + }, + { + "bbox": [ + 304, + 290, + 547, + 411 + ], + "type": "text", + "content": " with a maximum depth set at " + }, + { + "bbox": [ + 304, + 290, + 547, + 411 + ], + "type": "inline_equation", + "content": "80m" + }, + { + "bbox": [ + 304, + 290, + 547, + 411 + ], + "type": "text", + "content": ". Lower values are better for the first four metrics, while higher values are better for the remaining three." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 411, + 547, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 411, + 547, + 519 + ], + "spans": [ + { + "bbox": [ + 304, + 411, + 547, + 519 + ], + "type": "text", + "content": "For the visual odometry experiments, we use the KITTI odometry dataset and follow the same training and evaluation sequences (Seq. 00-08 for training and Seq. 09-10 for evaluation) as in previous work [106]. Since our estimation relies on a monocular camera, the estimated trajectories are aligned with the ground truth using the 7 DoF Umyama alignment [81]. We use standard odometry evaluation metrics such as translation " + }, + { + "bbox": [ + 304, + 411, + 547, + 519 + ], + "type": "inline_equation", + "content": "(t_{err})" + }, + { + "bbox": [ + 304, + 411, + 547, + 519 + ], + "type": "text", + "content": " and rotation " + }, + { + "bbox": [ + 304, + 411, + 547, + 519 + ], + "type": "inline_equation", + "content": "(r_{err})" + }, + { + "bbox": [ + 304, + 411, + 547, + 519 + ], + "type": "text", + "content": " error [20], and absolute trajectory error (ATE) [76]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 526, + 437, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 526, + 437, + 540 + ], + "spans": [ + { + "bbox": [ + 306, + 526, + 437, + 540 + ], + "type": "text", + "content": "4.2. Implementation details" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 545, + 547, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 547, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 547, + 665 + ], + "type": "text", + "content": "We conduct our experiments using PyTorch [66] on an RTX 3090 GPU with a batch size of 12. Following [23], we apply color and flip augmentations and resize input images to a resolution of " + }, + { + "bbox": [ + 304, + 545, + 547, + 665 + ], + "type": "inline_equation", + "content": "640 \\times 192" + }, + { + "bbox": [ + 304, + 545, + 547, + 665 + ], + "type": "text", + "content": ". For our high resolution experiments, we resize the images to " + }, + { + "bbox": [ + 304, + 545, + 547, + 665 + ], + "type": "inline_equation", + "content": "960 \\times 288" + }, + { + "bbox": [ + 304, + 545, + 547, + 665 + ], + "type": "text", + "content": ". We train the entire network for 15 epochs with a learning rate of " + }, + { + "bbox": [ + 304, + 545, + 547, + 665 + ], + "type": "inline_equation", + "content": "10^{-3}" + }, + { + "bbox": [ + 304, + 545, + 547, + 665 + ], + "type": "text", + "content": ", at which point we freeze the teacher depth and pose models. We then continue to train the network with a learning rate of " + }, + { + "bbox": [ + 304, + 545, + 547, + 665 + ], + "type": "inline_equation", + "content": "10^{-4}" + }, + { + "bbox": [ + 304, + 545, + 547, + 665 + ], + "type": "text", + "content": ". Adam optimizer [45] is employed with " + }, + { + "bbox": [ + 304, + 545, + 547, + 665 + ], + "type": "inline_equation", + "content": "\\beta_{1} = 0.9" + }, + { + "bbox": [ + 304, + 545, + 547, + 665 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 545, + 547, + 665 + ], + "type": "inline_equation", + "content": "\\beta_{2} = 0.999" + }, + { + "bbox": [ + 304, + 545, + 547, + 665 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "type": "text", + "content": "As mentioned earlier, the depth backbone is based on the HRNet architecture [88]. For the teacher pose model, we adhere to the standard design, using the first five layers of a ResNet18 initialized with ImageNet pre-trained weights as" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "731" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 72, + 547, + 266 + ], + "blocks": [ + { + "bbox": [ + 48, + 72, + 547, + 266 + ], + "lines": [ + { + "bbox": [ + 48, + 72, + 547, + 266 + ], + "spans": [ + { + "bbox": [ + 48, + 72, + 547, + 266 + ], + "type": "table", + "html": "
MethodTest framesSemanticsW × HAbs Rel ↓Sq Rel ↓RMSE ↓RMSE log ↓δ1 ↑δ2 ↑δ3 ↑
Low & mid resRanjan et al. [70]1832 × 2560.1481.1495.4640.2260.8150.9350.973
EPC++ [59]1832 × 2560.1411.0295.3500.2160.8160.9410.976
Struct2depth (M) [10]1●416 × 1280.1411.0265.2910.2150.8160.9450.979
Videos in the wild [26]1●416 × 1280.1280.9595.2300.2120.8450.9470.976
Guizilini et al. [30]1●640 × 1920.1020.6984.3810.1780.8960.9640.984
Johnston et al. [42]1640 × 1920.1060.8614.6990.1850.8890.9620.982
Monodepth2 [23]1640 × 1920.1150.9034.8630.1930.8770.9590.981
Packnet-SFM [28]1640 × 1920.1110.7854.6010.1890.8780.9600.982
Li et al. [51]1416 × 1280.1300.9505.1380.2090.8430.9480.978
DIFFNet [105]1640 × 1920.1020.7644.4830.1800.8960.9650.983
DualRefine-initial (D0)1640 × 1920.1030.7214.4760.1800.8910.9650.984
Patil et al. [67]N†640 × 1920.1110.8214.6500.1870.8830.9610.982
Wang et al. [89]2 (-1, 0)640 × 1920.1060.7994.6620.1870.8890.9610.982
ManyDepth (MR) [91]2 (-1, 0)640 × 1920.0980.7704.4590.1760.9000.9650.983
DepthFormer [29]2 (-1, 0)640 × 1920.0900.6614.1490.1750.9050.9670.984
DualRefine-refined (D*)2 (-1, 0)640 × 1920.0900.6584.2370.1710.9120.9670.984
High resDRO [27]2 (-1, 0)960 × 3200.0880.7974.4640.2120.8990.9590.980
Wang et al. [89]2 (-1, 0)1024 × 3200.1060.7734.4910.1850.8900.9620.982
ManyDepth (HR ResNet50) [91]2 (-1, 0)1024 × 3200.0910.6944.2450.1710.9110.9680.983
DualRefine-refined (HR) (D*)2 (-1, 0)960 × 2880.0890.7544.2730.1700.9170.9680.983
", + "image_path": "ef01027e808834ca59bd1b8de364e6154a29b3b41c1b9a94cbc39cc2f87815a5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 48, + 310, + 288, + 388 + ], + "blocks": [ + { + "bbox": [ + 47, + 274, + 546, + 297 + ], + "lines": [ + { + "bbox": [ + 47, + 274, + 546, + 297 + ], + "spans": [ + { + "bbox": [ + 47, + 274, + 546, + 297 + ], + "type": "text", + "content": "Table 1. Results and comparison with other state-of-the-arts models on the KITTI [20] Eigen split. Bold: Best, Underscore: Second best. † : evaluated on whole sequences" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 310, + 288, + 388 + ], + "lines": [ + { + "bbox": [ + 48, + 310, + 288, + 388 + ], + "spans": [ + { + "bbox": [ + 48, + 310, + 288, + 388 + ], + "type": "table", + "html": "
Pose UpdatesConsistency maskAbs RelSq RelRMSEδ1δ2
no updateT00.0970.7134.4620.8980.964
no weightsT00.0900.6584.2370.9120.967
no Wh,kT00.0900.6454.2730.9080.966
no WqT00.0910.7134.2950.9100.967
Wq and Wh,kT00.0890.6524.2820.9090.967
no weightsT*0.0910.6454.2010.9100.968
", + "image_path": "4b551e64506ff816f584adb7be0309b65729f78c91daff439c4bb1a0b2e341e4.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 434, + 287, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 434, + 287, + 495 + ], + "spans": [ + { + "bbox": [ + 46, + 434, + 287, + 495 + ], + "type": "text", + "content": "an encoder, followed by a decoder that outputs 6-DoF pose estimates. At test time, depth estimates are made using the current frame and the previous frame when available. When the previous frame is unavailable, we skip the refinement module and simply use the initial estimates." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 502, + 111, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 502, + 111, + 514 + ], + "spans": [ + { + "bbox": [ + 47, + 502, + 111, + 514 + ], + "type": "text", + "content": "4.3. Ablation" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 521, + 287, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 556 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 556 + ], + "type": "text", + "content": "Pose updates. We analyze the effect of pose refinement toward depth and present the findings in Table 2. Our model that does not perform pose updates has the worst accuracy." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 557, + 287, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 287, + 616 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 287, + 616 + ], + "type": "text", + "content": "**Evolving confidence weighting.** We also show the impact of confidence weightings. Interestingly, similar performance can be observed for all models that perform pose updates, even when no confidence weighting is used to guide the pose computation." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "content": "DEQ iteration. In addition to studying the effect of pose refinements, we also investigate aspects of DEQ iterative updates and present the findings when we vary the number of iterations during training and at test time in Table 3. The results suggest that 6 iterations is sufficient for the model to find the fixed point. We speculate that the initial estimate provides a reliable starting point and hence the fast convergence. On our machine, the 6 update iterations increase the" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 328, + 308, + 526, + 389 + ], + "blocks": [ + { + "bbox": [ + 47, + 396, + 287, + 417 + ], + "lines": [ + { + "bbox": [ + 47, + 396, + 287, + 417 + ], + "spans": [ + { + "bbox": [ + 47, + 396, + 287, + 417 + ], + "type": "text", + "content": "Table 2. Ablation experiment for the effect of pose updates on the KITTI [20] Eigen split. Bold: Best." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 328, + 308, + 526, + 389 + ], + "lines": [ + { + "bbox": [ + 328, + 308, + 526, + 389 + ], + "spans": [ + { + "bbox": [ + 328, + 308, + 526, + 389 + ], + "type": "table", + "html": "
DEQ # itersAbs RelSq RelRMSEδ1Time (ms)
3→30.0970.7774.4310.90653
6→30.0980.6954.3180.90553
6→60.0900.6584.2370.91268
12→30.1020.7324.4280.90053
12→60.0950.7084.3360.90768
12→120.0920.7074.3160.90999
", + "image_path": "d24ddb1b179e296e478d2e18969d50925166e2547b0c6063fd0b359900c42783.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 396, + 547, + 426 + ], + "lines": [ + { + "bbox": [ + 305, + 396, + 547, + 426 + ], + "spans": [ + { + "bbox": [ + 305, + 396, + 547, + 426 + ], + "type": "text", + "content": "Table 3. Ablation experiment for the DEQ iterations on the KITTI [20] Eigen split. " + }, + { + "bbox": [ + 305, + 396, + 547, + 426 + ], + "type": "inline_equation", + "content": "a \\rightarrow b" + }, + { + "bbox": [ + 305, + 396, + 547, + 426 + ], + "type": "text", + "content": " represents " + }, + { + "bbox": [ + 305, + 396, + 547, + 426 + ], + "type": "inline_equation", + "content": "a : \\#" + }, + { + "bbox": [ + 305, + 396, + 547, + 426 + ], + "type": "text", + "content": " iters at training and " + }, + { + "bbox": [ + 305, + 396, + 547, + 426 + ], + "type": "inline_equation", + "content": "b : \\#" + }, + { + "bbox": [ + 305, + 396, + 547, + 426 + ], + "type": "text", + "content": " iters at test time. Bold: Best." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 444, + 547, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 444, + 547, + 492 + ], + "spans": [ + { + "bbox": [ + 305, + 444, + 547, + 492 + ], + "type": "text", + "content": "baseline model's inference time from " + }, + { + "bbox": [ + 305, + 444, + 547, + 492 + ], + "type": "inline_equation", + "content": "37.90\\mathrm{ms}" + }, + { + "bbox": [ + 305, + 444, + 547, + 492 + ], + "type": "text", + "content": " by " + }, + { + "bbox": [ + 305, + 444, + 547, + 492 + ], + "type": "inline_equation", + "content": "\\sim 31" + }, + { + "bbox": [ + 305, + 444, + 547, + 492 + ], + "type": "text", + "content": " ms to a total of " + }, + { + "bbox": [ + 305, + 444, + 547, + 492 + ], + "type": "inline_equation", + "content": "68.49~\\mathrm{ms}" + }, + { + "bbox": [ + 305, + 444, + 547, + 492 + ], + "type": "text", + "content": ", running at almost 15 fps. However, we only use PyTorch basic functions in our implementation, and further optimization of the code could be made." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 502, + 391, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 502, + 391, + 514 + ], + "spans": [ + { + "bbox": [ + 306, + 502, + 391, + 514 + ], + "type": "text", + "content": "4.4. Depth results" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 521, + 547, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 547, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 547, + 676 + ], + "type": "text", + "content": "Table 1 shows the comparison of our depth estimation with SoTA self-supervised models. We compare with models that train on monocular video. Our model outperforms most previous models and is competitive with the Transformer [84]-based DepthFormer [29] model. Specifically, our model shows a significant improvement in " + }, + { + "bbox": [ + 304, + 521, + 547, + 676 + ], + "type": "inline_equation", + "content": "\\delta_{1}" + }, + { + "bbox": [ + 304, + 521, + 547, + 676 + ], + "type": "text", + "content": ", suggesting highly accurate inliers. Furthermore, compared to DepthFormer that requires 16GB training memory per batch, ours only consumes 24GB of memory for 12 batches, around " + }, + { + "bbox": [ + 304, + 521, + 547, + 676 + ], + "type": "inline_equation", + "content": "1/8 \\times" + }, + { + "bbox": [ + 304, + 521, + 547, + 676 + ], + "type": "text", + "content": " the memory requirement. This is mainly because our method refines 2D hidden states based on local sampling, while [29] refines 2D feature maps and a 3D feature volume using self/cross-attention along every depth bin." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "text", + "content": "Fig. 3 displays qualitative outputs for the disparity and error map of our model. We can observe an improvement to the error map of the refined depth. We also additionally dis" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "732" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 75, + 70, + 523, + 228 + ], + "blocks": [ + { + "bbox": [ + 75, + 70, + 523, + 228 + ], + "lines": [ + { + "bbox": [ + 75, + 70, + 523, + 228 + ], + "spans": [ + { + "bbox": [ + 75, + 70, + 523, + 228 + ], + "type": "table", + "html": "
MethodsSeq 9Seq 10
\\(t_{err}(\\%) \\downarrow\\)\\(r_{err}(\\circ/100m) \\downarrow\\)ATE (m) ↓\\(t_{err}(\\%) \\downarrow\\)\\(r_{err}(\\circ/100m) \\downarrow\\)ATE (m) ↓
ORB-SLAM2 [65] (w/o LC)9.670.344.104.040.36.43
ORB-SLAM2 [65]3.220.48.844.250.38.51
SfMLearner [106]19.156.8277.7940.4017.6967.34
GeoNet [98]28.729.8158.4523.909.043.04
DeepMatchVO [73]9.913.827.0812.185.924.44
Monodepth2 [23]17.173.8576.2211.685.3120.35
DW [26]-Learned--20.91--17.88
DW [26]-Corrected--19.01--14.85
SC-Depth [7]7.313.0523.567.794.9012.00
Zou et al. [107]3.491.0011.305.811.811.80
P-RGBD SLAM [8]5.081.0513.404.322.347.99
DualRefine-initial (T0)9.062.5939.319.454.0515.13
DualRefine-refined (T*)3.431.045.186.801.1310.85
", + "image_path": "fbdbef79bfa320622b7f2138ffc2e544a3a98170db936ca984623f5f4e7f249d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 234, + 546, + 255 + ], + "lines": [ + { + "bbox": [ + 46, + 234, + 546, + 255 + ], + "spans": [ + { + "bbox": [ + 46, + 234, + 546, + 255 + ], + "type": "text", + "content": "Table 4. Results on Seq. 09 and Seq. 10 of the KITTI odometry data. We provide a comparison with other state-of-the-art self-supervised depth and odometry methods. ORB-SLAM2 is included as a representative non-learning based method. Bold: Best, Underscore: Second best." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 111, + 277, + 231, + 426 + ], + "blocks": [ + { + "bbox": [ + 111, + 277, + 231, + 426 + ], + "lines": [ + { + "bbox": [ + 111, + 277, + 231, + 426 + ], + "spans": [ + { + "bbox": [ + 111, + 277, + 231, + 426 + ], + "type": "image", + "image_path": "04295fabd8eb446cf2c99475ac6ac114f378c3750eaae67cd49a61c42233d14b.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 75, + 440, + 265, + 519 + ], + "blocks": [ + { + "bbox": [ + 75, + 440, + 265, + 519 + ], + "lines": [ + { + "bbox": [ + 75, + 440, + 265, + 519 + ], + "spans": [ + { + "bbox": [ + 75, + 440, + 265, + 519 + ], + "type": "image", + "image_path": "b71cdbab517d4d36a67999a9adaa375601d81b64b97d765abb46eab84ee4ec09.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 534, + 288, + 574 + ], + "lines": [ + { + "bbox": [ + 46, + 534, + 288, + 574 + ], + "spans": [ + { + "bbox": [ + 46, + 534, + 288, + 574 + ], + "type": "text", + "content": "Figure 4. Estimated trajectory by the initial pose estimator and the refined trajectory using our pose refinement module on (a) Seq. 09 and (b) Seq. 10 of KITTI odometry data. The refined pose estimate improves the global trajectory, even without explicitly training for global consistency." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 593, + 287, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 593, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 593, + 287, + 664 + ], + "type": "text", + "content": "play confidence weight outputs obtained by the model that computes them. We observe that the confidence " + }, + { + "bbox": [ + 46, + 593, + 287, + 664 + ], + "type": "inline_equation", + "content": "W_{q}" + }, + { + "bbox": [ + 46, + 593, + 287, + 664 + ], + "type": "text", + "content": ", which is calculated once, assigns the high confidence sparsely. Interestingly, the confidence weights that evolve with each iteration initially assign high confidence to far-away points and moves towards closer points with increasing iterations." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": "Limitation: we note an increase in error for the moving vehicle in the lower image set. The worse RMSE of our model compared to DepthFormer also indicates higher outlier predictions. This could be due to repeated operation of" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 270, + 547, + 355 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 270, + 547, + 355 + ], + "spans": [ + { + "bbox": [ + 304, + 270, + 547, + 355 + ], + "type": "text", + "content": "our iterative updates, which further exacerbate the outlier problem. Even with consistency masking, the model we propose displays limitations with dynamic objects. However, the results of the last row of Tab. 2 show that using the refined pose to extract the consistency mask for training slightly improves Sq Rel, RMSE, and " + }, + { + "bbox": [ + 304, + 270, + 547, + 355 + ], + "type": "inline_equation", + "content": "\\delta_{2}" + }, + { + "bbox": [ + 304, + 270, + 547, + 355 + ], + "type": "text", + "content": ". We leave further the discussion of this issue for future study." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 363, + 410, + 376 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 363, + 410, + 376 + ], + "spans": [ + { + "bbox": [ + 305, + 363, + 410, + 376 + ], + "type": "text", + "content": "4.5. Odometry results" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 382, + 547, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 382, + 547, + 574 + ], + "spans": [ + { + "bbox": [ + 304, + 382, + 547, + 574 + ], + "type": "text", + "content": "We present the results for visual odometry of the teacher model and the refinement model in Table 4. We also present the results of previous models that were trained on monocular videos. Our refinement module drastically improves the initial odometry results, as shown in Fig. 4. Although the goal of our study was to improve the estimation of local poses for accurate matching, we outperformed most of the other models in all metrics. Even without explicit training to ensure scale consistency, as in [7,8], our refined output demonstrates a globally consistent odometry prediction. Additionally, unlike Zou et al. [107] which infers pose from long-term geometry, this result is achieved with only two input frames to infer pose estimates. Our model also achieves an ATE that is on par with the traditional ORB-SLAM2, which performs global geometric optimization, although our results in " + }, + { + "bbox": [ + 304, + 382, + 547, + 574 + ], + "type": "inline_equation", + "content": "r_{err}" + }, + { + "bbox": [ + 304, + 382, + 547, + 574 + ], + "type": "text", + "content": " still lag behind." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 586, + 384, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 586, + 384, + 597 + ], + "spans": [ + { + "bbox": [ + 306, + 586, + 384, + 597 + ], + "type": "text", + "content": "5. Conclusions" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "type": "text", + "content": "In this paper, we introduced a self-supervised pipeline for multi-frame depth and pose estimation and refinement. By leveraging the combined power of neural network representation and geometric constraints to refine both depth and pose, our approach achieved state-of-the-art performance in both tasks. Our method also demonstrates greater efficiency than competing methods, with potential for further improvement. Nevertheless, we still observed poorer depth accuracy in dynamic scenes." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "733" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 53, + 92, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 58, + 92, + 288, + 147 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 92, + 288, + 147 + ], + "spans": [ + { + "bbox": [ + 58, + 92, + 288, + 147 + ], + "type": "text", + "content": "[1] Amir Atapour-Abarghouei and Toby P Breckon. 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In Proceedings of the European conference on computer vision (ECCV), pages 36-53, 2018. 1" + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "738" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 12 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/DualRel_ Semi-Supervised Mitochondria Segmentation From a Prototype Perspective/ffadc065-1edc-42b2-a626-096c78b5c896_content_list.json b/2023/DualRel_ Semi-Supervised Mitochondria Segmentation From a Prototype Perspective/ffadc065-1edc-42b2-a626-096c78b5c896_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..4b014cedd583e93eda202b0952cc8ebd6a38a58e --- /dev/null +++ b/2023/DualRel_ Semi-Supervised Mitochondria Segmentation From a Prototype Perspective/ffadc065-1edc-42b2-a626-096c78b5c896_content_list.json @@ -0,0 +1,2184 @@ +[ + { + "type": "text", + "text": "DualRel: Semi-Supervised Mitochondria Segmentation from A Prototype Perspective", + "text_level": 1, + "bbox": [ + 179, + 85, + 790, + 132 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Huayu Mai $^{1*}$ Rui Sun $^{1*}$ Tianzhu Zhang $^{1,2,3\\dagger}$ Zhiwei Xiong $^{1,2}$ Feng Wu $^{1,2}$ $^{1}$ University of Science and Technology of China \n $^{2}$ Institute of Artificial Intelligence, Hefei Comprehensive National Science Center \n $^{3}$ Deep Space Exploration Lab", + "bbox": [ + 119, + 143, + 843, + 219 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{mai556, issunrui}@mail.ustc.edu.cn, {tzzhang, zwxiong, fengwu}@ustc.edu.cn", + "bbox": [ + 151, + 219, + 810, + 234 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 268, + 313, + 286 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Automatic mitochondria segmentation enjoys great popularity with the development of deep learning. However, existing methods rely heavily on the labor-intensive manual gathering by experienced domain experts. And naively applying semi-supervised segmentation methods in the natural image field to mitigate the labeling cost is undesirable. In this work, we analyze the gap between mitochondrial images and natural images and rethink how to achieve effective semi-supervised mitochondria segmentation, from the perspective of reliable prototype-level supervision. We propose a novel end-to-end dual-reliable (DualRel) network, including a reliable pixel aggregation module and a reliable prototype selection module. The proposed DualRel enjoys several merits. First, to learn the prototypes well without any explicit supervision, we carefully design the referential correlation to rectify the direct pairwise correlation. Second, the reliable prototype selection module is responsible for further evaluating the reliability of prototypes in constructing prototype-level consistency regularization. Extensive experimental results on three challenging benchmarks demonstrate that our method performs favorably against state-of-the-art semi-supervised segmentation methods. Importantly, with extremely few samples used for training, DualRel is also on par with current state-of-the-art fully supervised methods.", + "bbox": [ + 75, + 301, + 473, + 680 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 705, + 209, + 722 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Mitochondria, as one of the crucial organelles, are the primary energy providers for cell activities and are essential for metabolism. Quantification of mitochondrial morphology can not only promote basic scientific research (e.g., cellular physiology [1, 5]), but also provide new insight for clinical diagnosis (e.g., neurodegenerative diseases [20] and diabetes [24]). Recently, with the development of deep learning, semantic segmentation [2, 14, 18, 27, 30, 33] enables in-depth exploration of mitochondrial morphology", + "bbox": [ + 75, + 729, + 468, + 867 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/45b09b3daf7ea3290afe19195ce7769ec3a47266366437e5cc4bc4d490e8f139.jpg", + "image_caption": [ + "Confusion Density: 0.06" + ], + "image_footnote": [], + "bbox": [ + 504, + 268, + 589, + 319 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3963f0a779532bac1f67f83ba06a122b596337b40aa6093aa1a4f8d9b8f0c569.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 594, + 268, + 679, + 319 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/73ad7898f2ef553d2aef638b61369d92e4a6237d5aa8f9f6eae5925d7e187d91.jpg", + "image_caption": [ + "Confusion Density: 0.21" + ], + "image_footnote": [], + "bbox": [ + 712, + 268, + 797, + 319 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c9415103f7464f5306d9c21e2b73e08c5bd70625dcb85bfb89fb288c6e72b496.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 803, + 268, + 887, + 319 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/6f36ae1a85d70f0761680d30d78d05f71c4653cc9962bb483fede33d51bcb126.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 504, + 337, + 586, + 383 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/31bfcf0361c575d53a0b6b40eaffedee4f53b83652fc0705f62674e611e2ad8b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 594, + 337, + 676, + 383 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/748b7391b7d0c6c2e950c6254647ba6c7e6ac6e386ddcd25f3dbc87641023760.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 681, + 338, + 705, + 383 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/86f8ac02f91686a95ab9aae681fc8affc3ce0bafb8d756f89e98f30400bfbd36.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 506, + 383, + 576, + 452 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/2a6197659e7623841564f21a8218cd10cccd5233c90bd03dd6909ed8b524479d.jpg", + "image_caption": [ + "(c)", + "Background pixel" + ], + "image_footnote": [], + "bbox": [ + 594, + 383, + 676, + 452 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4afa57124bd0a6d941b1594938bc785e96aa0b91a3a51f00b48b546089dbdc34.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 692, + 338, + 767, + 375 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/659478dc8489f1621011877ee557940d9858adc5142786b7884cf0d9f0b59bab.jpg", + "image_caption": [ + "□ Foreground protocol", + "Pixel-Prototype Correlation", + "Fixtive Reference Correlation" + ], + "image_footnote": [], + "bbox": [ + 687, + 377, + 774, + 416 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/2eb6dfdc0e6606c95b3c50b1a198a3c5945f4aebf6bd977b58fcdcca17c720b6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 797, + 338, + 883, + 375 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/63a72b5c6817f46e1debbe1ce76cb7c899968d431c7d7f8a44c5c17121c5ec50.jpg", + "image_caption": [ + "Figure 1. Illustration of our motivation. (a) shows the confusion map and density (i.e., the expected inverse confidence per pixel) of mitochondrial and natural images. (b) shows the unreliability caused by direct pairwise prototype-pixel correlation that is conditioned only on visual similarity. (c) shows how to construct pixel-reference correlation to rectify the direct pairwise correlation in a referential correlation manner." + ], + "image_footnote": [], + "bbox": [ + 795, + 377, + 880, + 416 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "from high-resolution electron microscopy (EM) images and make conspicuous achievements. However, their flexibility and scalability are limited in the actual deployment because the numerous cluttered irrelevant organelles that require labor-intensive manual discrimination and gathering by experienced domain experts [10, 21]. Therefore, we begin to turn attention to semi-supervised segmentation with the assumption that enormous unlabeled data is accessible, aiming to alleviate the data-hungry issue.", + "bbox": [ + 496, + 597, + 892, + 733 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Semi-supervised segmentation enjoys great popularity in the field of natural images, and representative works such as CPS [3], which imposes pixel-level consistency regularization and establishes state-of-the-art performance. It naturally comes into mind to directly apply a CPS-like method to semi-supervised mitochondria segmentation. However, there exist a large gap between mitochondrial and natural images. As shown in Fig. 1 (a), we observe that the confusion density (i.e., the expected inverse confidence per pixel) in mitochondrial images significantly surpasses counterpart in natural images, implying that directly employing", + "bbox": [ + 496, + 734, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal contribution", + "bbox": [ + 94, + 875, + 202, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding author", + "bbox": [ + 96, + 887, + 218, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "19617", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "pixel-level consistency regularization as supervision signals on mitochondrial images will inevitably increase the risk of unreliability. The most intuitive example is that there exist considerable boundary regions in mitochondrial images, and the segmentation network is naturally equivocal for these regions, as proven in [15]. In this case, some relatively small mitochondria are easily overwhelmed by this ambiguity, leading to sub-optimal results.", + "bbox": [ + 75, + 90, + 470, + 212 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In order to seek more reliable supervision signals to alleviate the undependable problem caused by pixel-level supervision, we draw inspiration from the inbuilt resistance to noisy pixels of prototypes and construct more robust and reliable prototype-level supervision. To achieve this goal, two issues need to be considered. (1) Unreliable pixels. Considering the cluttered background caused by under/overexposure and out-of-focus problems during EM imaging, the prototype inevitably absorbs unreliable pixels (i.e., heterogeneous semantic clues) during the interaction of corresponding pixels with a suitable pattern. We argue that directly forcing pairwise prototype-pixel correlation is primarily at blame. As shown in Fig. 1 (b), due to the foreground-background ambiguity, the foreground prototype $f_{1}$ is erroneously closer to $p_{2}$ located in the background than counterpart point $p_{1}$ with similar pattern situated in the foreground. Therefore, it is highly desirable to suppress the unreliable pixels caused by the direct pairwise prototype-pixel correlation that is only conditioned on visual similarity during prototype learning process. (2) Unreliable prototypes. Intuitively, not all prototypes are equivalent for building prototype-level consistency regularization. For example, for a prototype that focuses on mitochondrial boundary patterns, the inherent unreliability of the pixels belonging to these patterns, as discussed above, will also taint the purity of this prototype with equivocality. Therefore, the prototype-level supervision signals should be further optimized to guarantee that the true reliable prototypes enjoy higher weights.", + "bbox": [ + 75, + 215, + 470, + 654 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To mitigate the above issues, we rethink how to achieve effective consistency regularization for semi-supervised mitochondria segmentation, from the perspective of reliable prototype-level supervision. We propose a Dual-Reliable (DualRel) network including a reliable pixel aggregation module and a reliable prototype selection module. In the reliable pixel aggregation module (RPIA), to learn the prototypes well without any explicit supervision, we carefully design the referential correlation to rectify the direct pairwise correlation, enabling the prototype absorb counterpart reliable pixels with the same semantic pattern during the interaction with the pixels. The main idea is, for each pixel/prototype, we can obtain the referential correlation (i.e., a likelihood vector) by comparing this pixel/prototype with a set of reliable reference points. In essence, the referential correlation reflects the consensus among reliable ref", + "bbox": [ + 75, + 659, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ference points with a broader receptive field and thus it encodes the relative semantic comparability of the reference points that can be relied upon, which is from a different perspective than the absolute pairwise prototype-pixel correlation. Intuitively, each pair of true prototype-pixel correlation (e.g., the $f_{1} - p_{1}$ pair in Fig. 1 (c) derived from the prototypes and mitochondria images should be not only visually similar to each other (i.e., high direct pairwise prototype-pixel correlation), but also similar to any other reference point (i.e., similar referential correlation pair). Moreover, we assemble referential correlation into the cross-attention mechanism with the ability to capture long-range dependencies. In this case, the relatively equivocal pixels (e.g., the $f_{1} - p_{2}$ pair in Fig. 1 (c) will be suppressed while the reliable ones are highlighted to reduce the correspondence noise. In the reliable prototype selection module (RPrS), in order to further evaluate the reliability of prototypes in constructing prototype-level consistency regularization, we draw inspiration from bayesian deep learning [12] and devise a reliability-aware consistency loss to pursue implicitly learn the reliability about each prototype in a data-driven way. In this way, the equivocal prototypes will be suppressed while the reliable ones are highlighted in the supervision signals.", + "bbox": [ + 496, + 90, + 890, + 438 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, our contributions can be concluded as follows: (1) To the best of our knowledge, this is the first work to rethink how to achieve effective consistency regularization for semi-supervised mitochondria segmentation, from the perspective of reliable prototype-level supervision. We analyze the gap between mitochondrial images and natural images, hoping our work will provide some insight for researchers in this field. (2) We propose a dual-reliable (DualRel) network in a unified framework. Specifically, we design the reliable pixel aggregation module to rectify the direct pairwise correlation, the reliable prototype selection module to further evaluate the reliability of prototypes in constructing prototype-level consistency regularization. (3) Extensive experimental results on three challenging benchmarks demonstrate that our method performs favorably against state-of-the-art semi-supervised segmentation methods. Importantly, with extremely few samples used for training, DualRel is also on par with current state-of-the-art fully supervised methods.", + "bbox": [ + 496, + 439, + 890, + 727 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 743, + 640, + 758 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Mitochondria Segmentation", + "text_level": 1, + "bbox": [ + 500, + 770, + 751, + 786 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Segmenting mitochondria in EM images is vital for researchers to explore cellular functions and subcellular activities. Rather than traditional methods utilizing hand-crafted features [14, 18, 27], DL-based networks have shown significant performance improvement on mitochondria segmentation. The pioneering work Lucchi et al. [19] design a deep neural network based on supervoxels to model shapes of mi", + "bbox": [ + 496, + 794, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "19618", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "tochondria. Oztel et al. [26] propose a deep convolutional neural network with a sliding window strategy and post-processing steps to boost the performance. Wei et al. [35] introduce a 3D U-Net based network and release a new challenging dataset containing mitochondria images with higher resolution. However, all previous methods only focus on the fully-supervised training, which require a large amount of labeled data. In this work, we introduce semi-supervised learning into mitochondria segmentation, aiming to alleviate the data-hungry issue.", + "bbox": [ + 75, + 90, + 472, + 243 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Semi-supervised Semantic Segmentation", + "text_level": 1, + "bbox": [ + 76, + 250, + 421, + 266 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "With the development of semi-supervised learning, various kinds of semi-supervised semantic segmentation algorithms have been proposed. GAN-based methods [9,22,29] try to synthesize additional training data or generate the pseudo labels for unlabeled data by using adversarial loss. Recently, the consistency regularization [6,23,34] has been intensely studied in semi-supervised semantic segmentation. The main idea of this type of approach is that the intermediate features or predictions should maintain consistency across different semantic-preserving transformations on the input or different network initialization [36, 37]. MT [31] is a representative work that first adopts the teacher network to guide the learning of the student network in semi-supervised semantic segmentation. Alternatively, CCT [25] introduces dual independent models to supervise each other with the soft probability output, while CPS [3] is supervised with hard pseudo segmentation maps. GCT [11] employs two segmentation networks with the same structure but different weight initialization and enforces the consistency between the predictions. However, the above pixel-level supervision-based methods perform poorly on semi-supervised mitochondria tasks.", + "bbox": [ + 75, + 273, + 472, + 604 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 617, + 168, + 633 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we first formulate the semi-supervised mitochondria segmentation task and present the overview of the proposed DualRel. Then we describe the details of the reliable pixel aggregation module (RPiA) and reliable prototype selection module (RPrs) of DualRel. Finally, the training and inference procedure are discussed.", + "bbox": [ + 75, + 642, + 468, + 734 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Overview", + "text_level": 1, + "bbox": [ + 76, + 741, + 187, + 755 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In semi-supervised mitochondria segmentation task, we wish to train a segmentation network with training data $D^{L}\\cup D^{U}$ . In the labeled set $D^{L} = \\{\\mathbf{I}_{i}^{L},\\mathbf{Y}_{i}\\}_{i = 0}^{N}$ , each image is associated with a ground truth label $\\mathbf{Y}\\in \\{0,1\\}^{H\\times W}$ where 1 denotes foreground while 0 denotes background. In the unlabeled set $D^{U} = \\{\\mathbf{I}_{j}^{U}\\}_{j = 0}^{M}$ , $M$ images are provided without ground truth. Given an EM image $\\mathbf{I}$ (for brevity, we omit the superscript $L / U$ and subscript $i / j$ ), let $\\mathbf{X}\\in \\mathbb{R}^{h\\times w\\times D}$ denotes the feature map extracted from", + "bbox": [ + 75, + 763, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "feature extractor (e.g., ResNet50 [8]), where $h$ , $w$ and $D$ denote the height, width and channel number of the feature map, respectively. Subsequently, the feature map $\\mathbf{X}$ is fed into the upsampling module (e.g., U-Net [28]) which outputs pixel embedding $\\mathbf{E} \\in \\mathbb{R}^{H \\times W \\times C}$ with the same spatial scale as original input image. As illustrated in Fig. 2, the proposed DualRel includes two branches of feature extractor and upsampling module, which are of the same structure but different weight initialization. Such a two-branch structure is devised to construct consistency supervision signals for unlabeled data, which is a popular paradigm in semi-supervised learning. Besides, a reliable pixel aggregation module and a reliable prototype selection module are introduced to construct prototype-level consistency regularization for semi-supervised mitochondria segmentation.", + "bbox": [ + 496, + 90, + 890, + 318 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Reliable Pixel Aggregation", + "text_level": 1, + "bbox": [ + 498, + 325, + 741, + 340 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To construct prototype-level supervision, we prepend a set of learnable embeddings $\\mathbf{F} = \\{\\mathbf{f}_k\\}_{k=1}^K$ (referred to as mito filters). Each filter $\\mathbf{f}_k$ is represented as a $C$ -dimension vector to interact with the feature map $\\mathbf{X}$ and absorb counterpart reliable pixels with the same semantic pattern. Then, we adopt a cross-attention mechanism [32] to realize the interaction and obtain mito features $\\widetilde{\\mathbf{F}} = \\{\\widetilde{\\mathbf{f}}_k\\}_{k=1}^K$ .", + "bbox": [ + 496, + 348, + 890, + 455 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Since the cross-attention requires a 1D sequence as the input, we first utilize a $1\\times 1$ convolution kernel to reduce the channel number of the feature map $\\mathbf{X}$ from $D$ to $C$ , and then flatten the spatial dimensions to produce the feature sequence $\\widetilde{\\mathbf{X}} = \\{\\widetilde{\\mathbf{x}}_i\\}_{i = 1}^{hw}\\in \\mathbb{R}^{hw\\times C}$ . Specifically, we denote mito filters $\\{\\mathbf{f}_k\\}_{k = 1}^K$ as queries, the feature map $\\widetilde{\\mathbf{X}}$ as keys and values. Formally,", + "bbox": [ + 496, + 455, + 890, + 563 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {q} _ {k} = \\mathbf {f} _ {k} \\mathbf {W} ^ {Q}, \\mathbf {k} _ {i} = \\widetilde {\\mathbf {x}} _ {i} \\mathbf {W} ^ {K}, \\mathbf {v} _ {i} = \\widetilde {\\mathbf {x}} _ {i} \\mathbf {W} ^ {V}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 555, + 569, + 890, + 588 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{W}^Q, \\mathbf{W}^K, \\mathbf{W}^V \\in \\mathbb{R}^{C \\times C}$ are linear projections, $k = 1, 2, \\ldots, K$ and $i = 1, 2, \\ldots, hw$ . Then the pairwise correlation $s_{k,i}$ between each query $\\mathbf{q}_k$ and the $i^{th}$ key $\\mathbf{k}_i$ is given as", + "bbox": [ + 496, + 593, + 890, + 655 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\ns _ {k, i} = \\frac {\\exp \\left(\\beta_ {k , i}\\right)}{\\sum_ {j = 1} ^ {h w} \\exp \\left(\\beta_ {k , j}\\right)}, \\beta_ {k, i} = \\frac {\\mathbf {q} _ {k} \\mathbf {k} _ {i} ^ {\\top}}{\\sqrt {C}}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 563, + 662, + 890, + 700 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\sqrt{C}$ is a scaling factor to stabilize training and $T$ refers to the transpose operation.", + "bbox": [ + 496, + 709, + 890, + 739 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Due to the susceptibility of pairwise filter-pixel correlation, the mito filter inevitably absorbs unreliable pixels during the interaction. We carefully design the referential correlation assembled in cross-attention to mitigate such issue. Specifically, we define $N$ reference points $\\widetilde{\\mathbf{X}}^R = \\{\\widetilde{\\mathbf{x}}_n^R\\}_{n=1}^N \\in \\mathbb{R}^{N \\times C}$ (detailed in the supplementary material). Respectively calculating the filter-reference correlation and the pixel-reference correlation as same as Eq. (2):", + "bbox": [ + 496, + 741, + 890, + 862 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {S} _ {k} ^ {F R} = \\operatorname {s o f t m a x} (\\frac {\\left(\\mathbf {f} _ {k} \\mathbf {W} ^ {Q}\\right) \\left(\\widetilde {\\mathbf {X}} ^ {R} \\mathbf {W} ^ {K}\\right) ^ {\\intercal}}{\\sqrt {C}}), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 558, + 868, + 890, + 905 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "19619", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/748fea748352817b86ef22f93b993611704d6d1b3994c83598ddcae6b0830ab6.jpg", + "image_caption": [ + "Figure 2. Illustration of the proposed DualRel. DualRel is mainly composed of a reliable pixel aggregation module to rectify the direct pairwise correlation, and a reliable prototype selection module responsible for further evaluating the reliability of prototypes in constructing prototype-level consistency regularization. \"GAP\" represents a global average pooling layer [16] and \"Merge\" is described in Sec. 3.4." + ], + "image_footnote": [], + "bbox": [ + 122, + 89, + 851, + 335 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {S} _ {i} ^ {P R} = \\operatorname {s o f t m a x} \\left(\\frac {\\left(\\widetilde {\\mathbf {x}} _ {i} \\mathbf {W} ^ {Q}\\right) \\left(\\widetilde {\\mathbf {X}} ^ {R} \\mathbf {W} ^ {K}\\right) ^ {\\top}}{\\sqrt {C}}\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 135, + 412, + 468, + 448 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{S}_k^{FR} \\in \\mathbb{R}^{1 \\times N}$ and $\\mathbf{S}_i^{PR} \\in \\mathbb{R}^{1 \\times N}$ are regarded as the referential correlation. And then, we get the similarity between the referential correlations by:", + "bbox": [ + 76, + 450, + 468, + 498 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nc _ {k, i} = \\mathbf {S} _ {k} ^ {F R} \\left(\\mathbf {S} _ {i} ^ {P R}\\right) ^ {\\top}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 202, + 505, + 468, + 525 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "which is used to rectify the direct pairwise correlation.", + "bbox": [ + 76, + 532, + 437, + 547 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Then, the mito features $\\{\\widetilde{\\mathbf{f}}_k\\}_{k = 1}^K$ can be got by blending values with the rectified correlations:", + "bbox": [ + 76, + 547, + 468, + 578 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\widetilde {\\mathbf {f}} _ {k} = \\sum_ {i} ^ {h w} c _ {k, i} \\cdot s _ {k, i} \\cdot \\mathbf {v} _ {i}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 191, + 585, + 468, + 626 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Reliable Prototype Selection", + "text_level": 1, + "bbox": [ + 76, + 633, + 331, + 648 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Before describing the reliable prototype selection mechanism, we first formulate the process of obtaining the mito prototypes $\\mathbf{P} = \\{\\mathbf{p}_k\\}_{k=1}^K$ . First, calculating the activation maps $\\mathbf{A} = \\{\\mathbf{A}_k\\}_{k=1}^K \\in \\mathbb{R}^{K \\times H \\times W}$ by:", + "bbox": [ + 76, + 657, + 468, + 718 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {A} _ {k} = \\operatorname {s i g m o i d} \\left(\\mathbf {f} _ {k} \\mathbf {E} ^ {\\top}\\right), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 194, + 724, + 468, + 742 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{A}_k$ denotes the activation map of the $k^{th}$ mito feature on pixel embedding $\\mathbf{E}$ . Then, based on the activation maps $\\mathbf{A}$ , we generate mito prototypes $\\{\\mathbf{p}_k\\}_{k=1}^K$ by global average pooling (GAP):", + "bbox": [ + 76, + 751, + 468, + 811 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {p} _ {k} = \\frac {1}{H W} \\sum_ {i = 1} ^ {H} \\sum_ {j = 1} ^ {W} \\mathbf {A} _ {k, i, j} \\cdot \\mathbf {E} _ {i, j}. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 160, + 819, + 468, + 862 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Intuitively, not all prototypes are equivalent for building prototype-level consistency regularization. In order to", + "bbox": [ + 76, + 869, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "further evaluate the reliability of prototypes in constructing prototype-level consistency regularization, we devise a reliability-aware consistency loss to pursue implicitly learn the reliability about each prototype in a data-driven way. Firstly, we estimate the reliability $\\mathbf{R} = \\{r_k\\}_{k=1}^K$ for each prototype. In specific, we concatenate the mito features $\\widetilde{\\mathbf{f}}_k^1$ and $\\widetilde{\\mathbf{f}}_k^2$ (the superscript denotes which baranch the mito features from) in channel dimension and feed them into a two layers MLP followed by the sigmoid function, as in Eq. (9):", + "bbox": [ + 496, + 415, + 890, + 556 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nr _ {k} = \\operatorname {s i g m o i d} \\left(\\operatorname {M L P} \\left(\\operatorname {c o n c a t} \\left(\\widetilde {\\mathbf {f}} _ {k} ^ {1}, \\widetilde {\\mathbf {f}} _ {k} ^ {2}\\right)\\right). \\right. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 568, + 565, + 890, + 585 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In order to guarantee that the true reliable prototypes enjoy higher weights and the equivocal ones are suppressed, we regard the $\\mathbf{R}$ as a attenuation factor and get the reliable prototype consistency loss as:", + "bbox": [ + 496, + 594, + 890, + 655 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {r p c} = \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\left(e ^ {1 - \\frac {1}{r _ {k}}} \\times L _ {2} \\left(\\mathbf {p} _ {k} ^ {1}, \\mathbf {p} _ {k} ^ {2}\\right) - \\lambda \\times r _ {k}\\right), \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 662, + 890, + 705 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $L_{2}(\\cdot)$ denotes L2 distance and the $\\lambda$ is the weight for the regularization term preventing the estimated reliability from zero.", + "bbox": [ + 496, + 714, + 890, + 758 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Training and inference", + "text_level": 1, + "bbox": [ + 500, + 768, + 710, + 785 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For the follow-up training and inference, we need to merge the activation maps $\\mathbf{A}$ into foreground-background probability map $\\widetilde{\\mathbf{Y}}\\in \\mathbb{R}^{2\\times H\\times W}$ . In our implementation, we simply treat the summation of the first half of the activation maps as foreground probability (corresponding the summation of the $1^{st}$ to the $\\frac{K}{2}^{th}$ activation maps), and the summation of the other half as background probability.", + "bbox": [ + 496, + 791, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "19620", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Besides, considering the large size and shape variation of the mitochondria, the mito prototype learning may focus on the same (e.g., the entire foreground), making the reliable prototype selection module degeneration. Therefore, we impose a diversity loss to expand the discrepancy among mito features. Formally,", + "bbox": [ + 75, + 90, + 472, + 183 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {d i v} = \\sum_ {i = 1} ^ {K} \\sum_ {j = 1, i \\neq j} ^ {K} \\left(\\frac {\\langle \\widetilde {\\mathbf {f}} _ {i} , \\widetilde {\\mathbf {f}} _ {j} \\rangle}{\\| \\widetilde {\\mathbf {f}} _ {i} \\| _ {2} \\| \\widetilde {\\mathbf {f}} _ {j} \\| _ {2}}\\right). \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 160, + 191, + 468, + 234 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The intuition behind this loss is trivial. If the $i^{th}$ and $j^{th}$ features give a high attention to the same region, the $\\mathcal{L}_{div}$ will be large and prompt these features to adjust themselves adaptively.", + "bbox": [ + 75, + 243, + 468, + 305 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "During Training, we calculate the supervise loss for the output prediction of two branch with labeled data by", + "bbox": [ + 76, + 305, + 468, + 338 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {s u p} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\left(\\operatorname {C E} \\left(\\widetilde {\\mathbf {Y}} ^ {\\mathbf {1}}, \\mathbf {Y}\\right) + \\operatorname {C E} \\left(\\widetilde {\\mathbf {Y}} ^ {\\mathbf {2}}, \\mathbf {Y}\\right)\\right), \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 107, + 345, + 468, + 386 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathrm{CE}(\\cdot)$ denotes the standard cross entropy loss. As a result, our DualRel is trained by minimizing the overall objective as follows:", + "bbox": [ + 75, + 395, + 472, + 443 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {\\sup } + \\mathcal {L} _ {r p c} + \\lambda_ {d i v} \\times \\mathcal {L} _ {d i v}, \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 158, + 455, + 468, + 472 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\lambda_{div}$ is the trade-off weight.", + "bbox": [ + 76, + 477, + 307, + 491 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "During inference, we get the predicted mask $\\widehat{\\mathbf{Y}}$ by apply argmax operation on probability map $\\widetilde{\\mathbf{Y}}$ from one branch, without extra computation cost.", + "bbox": [ + 75, + 491, + 468, + 539 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 550, + 209, + 566 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Datasets and Evaluation Metrics", + "text_level": 1, + "bbox": [ + 76, + 575, + 364, + 590 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We conduct experiments on the most popular benchmarks including Lucchi [19], Lucchi++ [2], MitoEM dataset [35]. Lucchi [19] contains two sub-volumes, acquired from the CA1 hippocampus region of the mouse brain for training and testing. Each sub-volume consists of $165 \\times 1024 \\times 768$ EM images provided with manual mitochondria segmentation mask. And Lucchi++ [2] is reannotated by three neuroscience and biology experts, and has the same size as Lucchi with more accurate mitochondria segmentation mask. MitoEM dataset [35] contains two volumes attained from rat and human cortex, dubbed mito-R and mito-H respectively. Each volume consists of 400 training images, 100 validation images and 500 test images with a resolution of $4096 \\times 4096$ . Among them, the ground-truth labels are publicly available for the training set and the validation set. In our experiments, we train on training set and evaluate on validation set.", + "bbox": [ + 75, + 598, + 472, + 854 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation Metrics. We adopt Dice similarity coefficient (DSC) and Jaccard-index coefficient (JAC) to evaluate the accuracy of segmentation in our experiments.", + "bbox": [ + 75, + 854, + 472, + 902 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/514743f13c251938c5dd071c3f72e7aab12e083a53420b71cfed790de724a799.jpg", + "table_caption": [ + "Table 1. Comparison with state-of-the-art re-implemented methods on Lucchi [19] and Lucchi++ [2] dataset under different partition protocols. Partition protocols denote the ratio of labeled data used for training, followed by the actual number of mitochondrial images." + ], + "table_footnote": [], + "table_body": "
1/32 (5)1/16 (10)1/8 (20)1/2 (82)
MethodJACDSCJACDSCJACDSCJACDSC
Lucchi
MT[NIPS17] [31]71.8582.5372.4882.8375.4984.7278.6086.73
CCT[CVPR20] [25]84.7591.6285.4891.7385.8491.9486.6092.73
GCT[ECCV20] [11]83.5190.9384.6492.0285.8691.7286.2092.41
CPS[CVPR21] [3]84.5591.5784.6191.1885.1691.5785.5192.03
DualRel85.6392.2486.3592.4287.2193.1687.6293.31
Lucchi++
MT[NIPS17] [31]79.5187.1182.8990.1786.9192.3387.2493.42
CCT[CVPR20] [25]87.3692.6387.8493.2288.5493.7489.3694.19
GCT[ECCV20] [11]86.6092.1686.9592.0587.8693.1288.6993.79
CPS[CVPR21] [3]86.3692.4287.2293.0787.8793.3688.3093.52
DualRel87.8193.4288.2293.7489.9194.6390.5495.52
", + "bbox": [ + 503, + 169, + 903, + 349 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Implementation Details", + "text_level": 1, + "bbox": [ + 500, + 375, + 718, + 390 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In the semi-supervised setting, we sample a certain ratio from the training set as labeled set $D^{L}$ , and the rest are treat as unlabeled set $D^{U}$ . For a fair comparison, we follow the following guidelines in training and inference stage for all re-implemented methods. We adopt ResNet50 [8] as backbone network for feature extraction by removing the global average pooling (GAP) layer and fully connected layer, and utilize U-Net structure [28] for upsampling. During training, we feed the network with $512 \\times 512$ images randomly cropped from original EM images with random mirror, random rotate and elastic transform augmentation. Extra color jitter is adopted to reduce overfitting. We use mini-batch SGD to train our model with momentum set to 0.9 and weight decay fixed as 0.0005. We initialize the learning rate with $5 \\times 10^{-3}$ with batch size of 4, and halve the learning rate at the $50\\%$ , $70\\%$ and $90\\%$ of the overall training epoch. During inference, We adopt a sliding window of size $512 \\times 512$ and step 256.", + "bbox": [ + 496, + 397, + 893, + 671 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Comparison with State-of-the-art Methods", + "text_level": 1, + "bbox": [ + 498, + 680, + 864, + 696 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We reproduce the most representative and competitive methods [3,11,25,31] in the semi-supervised natural image semantic segmentation task, and report their performance on Lucchi derivatives (i.e., Lucchi and Lucchi++) and Mi-toEM dataset, establishing a semi-supervised mitochondria segmentation benchmark.", + "bbox": [ + 496, + 704, + 890, + 794 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Lucchi derivatives. Tab. 1 shows the comparison of our method with the state-of-the-art re-implemented methods on Lucchi and Lucchi++ dataset. We consistently observe that our DualRel outperforms all other methods under all partition protocols, which strongly proves the effectiveness of our method. Specifically, our approach achieves $89.9\\%$ JAC, $94.6\\%$ DSC on Lucchi++ and $87.2\\%$ JAC, $93.1\\%$ DSC", + "bbox": [ + 496, + 795, + 893, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "19621", + "bbox": [ + 480, + 944, + 517, + 957 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/724e5d374e2a85a593ca77ddbd89bb08c314e2f8a34b97a43a46d44e123dc1e6.jpg", + "table_caption": [ + "Table 2. Comparison with state-of-the-art re-implemented methods on MitoEM [35] dataset under different partition protocols." + ], + "table_footnote": [], + "table_body": "
1/32 (12)1/16 (25)1/8 (50)1/2 (200)
MethodJACDSCJACDSCJACDSCJACDSC
mito-R
\\(MT_{[NIPS17]}\\)(31)81.1187.5284.6490.6184.9190.8286.9992.41
\\(CCT_{[CVPR20]}\\)(25)88.9193.2289.4893.8889.7194.0389.7494.12
\\(GCT_{[ECCV20]}\\)(11)88.2292.8188.6192.7389.0393.4189.1193.72
\\(CPS_{[CVPR21]}\\)(3)88.7193.7189.6294.4189.7194.5290.0294.72
DualRel89.6194.5290.3194.9390.7295.1190.9195.23
mito-H
\\(MT_{[NIPS17]}\\)(31)81.9089.3282.7189.6283.5790.3684.6391.14
\\(CCT_{[CVPR20]}\\)(25)83.4290.6184.1890.7584.8791.2485.0791.37
\\(GCT_{[ECCV20]}\\)(11)82.1289.8183.3290.9184.6291.0284.8191.06
\\(CPS_{[CVPR21]}\\)(3)84.2291.8184.2991.4785.4292.1286.3192.65
DualRel85.6192.2285.9392.4486.2192.4386.5392.72
", + "bbox": [ + 80, + 128, + 478, + 306 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "on Lucchi under 1/8 partition protocol (only 20 labeled images). This means that even if we only label a small proportion of images, we can train a satisfactory segmentation model in an appropriate way. Compared to the best method CPS [3] in the field of natural image, our DualRel achieves a large margin of $2.05\\% / 1.59\\%$ in JAC/DSC under 1/8 partition protocol, which favorably manifests the benefits of prototype-level consistency regularization.", + "bbox": [ + 75, + 333, + 468, + 455 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "MitoEM dataset. In Tab. 2 we report the performance on MitoEM dataset, which is much more complex than Lucchi and Lucchi++, with larger image size, more messy background and more diverse mitochondrial morphology. DualRel also achieves convincing performance even when the labeled data is scarce. Under 1/32 partition protocol, i.e., training the network with solely 12 labeled images and 388 unlabeled images, we obtain $89.6\\%$ JAC, $94.5\\%$ DSC on mito-R and $85\\%$ JAC, $91.9\\%$ DSC on mito-H. This demonstrates the stability of our method, which can model the reliability of the prototype for a more robust prototype-level supervision, even in the face of more complex scene.", + "bbox": [ + 75, + 455, + 468, + 636 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparison with fully supervised methods. Tab. 3 tabulates the quantitative results compared with fully supervised methods. We observe that with only 5 annotated images, DualRel even surpasses fully supervised methods that utilize all annotated samples, such as 2D U-Net [28], by $0.7\\% / 1.2\\%$ in JAC/DSC. When the number of available labeled samples increases (e.g., half the total images), our method is on par with state-of-the-art fully supervised methods (e.g., Casser [2]) without any post-processing. This sheds light on the great promise of semi-supervised mitochondria segmentation tasks, where light labeling cost can yield competitive performance.", + "bbox": [ + 75, + 637, + 468, + 819 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. Ablation Study and Analysis", + "text_level": 1, + "bbox": [ + 76, + 830, + 333, + 847 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To look deeper into our method, we perform a series of ablation studies on Lucchi dataset with ResNet50 as backbone under 1/8 partition protocol to analyze each compo", + "bbox": [ + 75, + 854, + 468, + 902 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/c83bddab32bd70b57fd572532840e046b682811fb538c35474e4cc4791d91817.jpg", + "table_caption": [ + "Table 3. Comparison with state-of-the-art fully supervised methods on Lucchi dataset [19]. \"Post-Processing\" stands for whether to use post-processing such as Z-Filtering." + ], + "table_footnote": [], + "table_body": "
MethodPost-ProcessinglabelsJACDSC
Lucchi [18]X16575.586.0
Peng and Yuan [27]X16583.390.9
2D U-Net [28]X16584.491.5
Cheng (2D) [4]X16586.592.8
Liu [17]✓16586.492.6
Khadangi [13]X16586.592.7
Casser [2]✓16588.493.8
DualRel (1/32)X585.692.2
DualRel (1/2)X8287.693.3
", + "bbox": [ + 521, + 142, + 867, + 292 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/99914347224ee38a36f23a0513a7babddc089892b376aee11a5fe85073502b26.jpg", + "table_caption": [ + "Table 4. Evaluation of the effectiveness of different components on Lucchi dataset." + ], + "table_footnote": [], + "table_body": "
Pixel-level
ThresholdJACDSC
CPS [3]085.1691.57
0.585.2091.62
0.784.0791.48
0.983.9390.89
Prototype-level
RPIARPrSJACDSC
w/o ref.w/ ref.
✓85.9791.94
✓86.5792.72
✓✓87.2193.16
", + "bbox": [ + 557, + 344, + 831, + 539 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ment of our DualRel, including the reliable pixel aggregation module (RPIA), and the reliable prototype selection module (RPrS). Note that we remove all modules except the two branches of feature extractor and upsampling module and a separate cross-attention mechanism, to directly construct prototype-level consistency regularization as our baseline.", + "bbox": [ + 496, + 566, + 890, + 657 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Analysis of the Pixel-level Consistency Regularization. In Sec. 1, we intuitively demonstrate that there exists gap between natural images and mitochondrial images, and directly employing pixel-level consistency regularization on mitochondrial images will inevitably increase the risk of unreliability. Naively, we can select high-confidence pixels based on a pre-defined threshold to attempt to alleviate the unreliability. The upper part of Tab. 4 tabulates the impact of different thresholds on the semi-supervised model based on pixel-level supervision. We observe that selecting high confidence points brings negligible improvement and even impairs model performance when the threshold is set too high. Then, we further quantitatively analyze the reasons for this case from the perspective of expected calibration error (ECE) [7], which measures the discrepancy between the confidence and accuracy of the network output,", + "bbox": [ + 496, + 659, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "19622", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 5. Comparison with state-of-the-art methods in model calibration and study on different network configurations.", + "bbox": [ + 76, + 88, + 468, + 117 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/269d561cdc4579d6ccac2ba7e9f59d1ae22a64a9d4e91ab7843dec250f5a405e.jpg", + "table_caption": [ + "(a) Quantification of expected calibration error (ECE)." + ], + "table_footnote": [], + "table_body": "
MethodECE (↓) (%)
MT15.2
CCT12.5
GCT10.2
CPS8.3
DualRel1.8
", + "bbox": [ + 109, + 151, + 230, + 277 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/3e884c8c3c22fc836e24c30fd0582cc65231bcf37fe720f06c551e9705405645.jpg", + "table_caption": [ + "(b) Ablation on different architecture." + ], + "table_footnote": [], + "table_body": "
JACDSC
CNN86.9992.65
Transformer87.2193.16
", + "bbox": [ + 251, + 142, + 434, + 195 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/e0d107ab9060cdda5e699f4353e4094d7dd51606679d3d6b1a2b406b344f44f6.jpg", + "table_caption": [ + "(c) Performance comparison with and without diversity loss." + ], + "table_footnote": [], + "table_body": "
JACDSC
w/o div.86.5792.87
w/ div.87.2193.16
", + "bbox": [ + 251, + 223, + 434, + 275 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "as known as calibration, has been explored. Poorer network calibration, weaker the correlation between the confidence and accuracy of the network output. In other words, even if the network predicts with high confidence, there is a high probability that it will be unreliable. Tab. 5a shows the calibration of different methods, the larger the value, the poorer the calibration. Therefore, it is impracticable to select reliable points only conditioned on confidence.", + "bbox": [ + 75, + 305, + 467, + 425 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Analysis of the Prototype-level Consistency Regularization. As shown in Tab. 4, the baseline that utilizes prototype-level supervision achieves a clear lead, compared to methods based on pixel-level consistency regularization. Moreover, Tab. 5a shows our DualRel achieves better calibration benefiting from RPiA and RPrS module, which is in line with the design idea of prototype-level supervision.", + "bbox": [ + 75, + 426, + 467, + 532 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of the Reliable Pixel Aggregation Module. As shown in Tab. 4, the introduction of the referential correlation (ref.) in RPiA achieves a certain performance lift compared with the baseline (i.e., a separate cross-attention mechanism without ref.), that is, $91.94\\%$ vs. $92.72\\%$ in DSC. The improvement can be mainly ascribed to the strong ability of the RPiA to rectify the direct pairwise correlation, enabling the prototype absorbs counterpart reliable pixels with the same semantic pattern during the interaction with the pixels.", + "bbox": [ + 75, + 535, + 467, + 685 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of the Reliable Prototype Selection Module. The addition of RPrS also contributes to a remarkable performance (86.57% vs. 87.21%). This proves the necessity of suppressing the equivocal prototypes, our RPrS can further evaluate the reliability of prototypes in constructing prototype-level consistency regularization.", + "bbox": [ + 75, + 686, + 467, + 777 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of Transformer-based Cross-attention Mechanism. We perform the ablation study that replaces the Transformer-like cross-attention by using convolutional networks with similar parameters in Tab. 5b. In detail, We use the convolutional layers followed by a softmax function to change the channel size of the feature map to obtain $K$ mito features when replacing cross attention. The feedforward network (FFN) is replaced by the convolutional lay", + "bbox": [ + 75, + 779, + 467, + 900 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/59bd003b535271412411b51308841248c6868fa1e19ed3691457bdf4a3efc68c.jpg", + "image_caption": [ + "Figure 3. Evaluation of the number of prototypes $K$ , and the hyperparameters $\\lambda_{div}$ ." + ], + "image_footnote": [], + "bbox": [ + 501, + 88, + 687, + 189 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5c35a0b361de060d46d57128e59e3923e761904ef24f1fc45b08585e7ddee768.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 697, + 89, + 885, + 190 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ers, and the rest of the model remains the same. We observe that cross-attention achieves better performance thanks to the long-range modeling capabilities of the transformer.", + "bbox": [ + 496, + 250, + 890, + 294 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of Diversity Loss. As shown in Tab. 5c, with the utilization of diversity loss, further improvements can be observed. Diversity loss prevents the prototypes from focusing on similar local semantic clues. And diverse prototypes can capture mitochondria variations and achieve more precise segmentation.", + "bbox": [ + 496, + 294, + 890, + 383 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Hyperparameter Evaluations. As shown in Fig. 3, we evaluate how $K$ and $\\lambda_{div}$ affects our model learning. We can observe that the performance continues to grow until $K = 12$ , which means it is sufficient to mine 12 semantic patterns of mitochondria. And $\\lambda_{div}$ controls the relative importance of the diversity loss, our model achieves much better performance when $\\lambda_{div} = 0.05$ .", + "bbox": [ + 496, + 383, + 890, + 489 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Vasualization", + "text_level": 1, + "bbox": [ + 500, + 500, + 638, + 513 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Visualization of Predictions. To further analyze and understand the proposed method, we visualize a series of segmentation results and prototype activation areas. As shown in Fig. 4, it can be noticed that other methods tend to incorrectly segment the non-target region (dyed in blue) or are unable to activate all the mitochondria (dyed in red). We deem the main reason is that numerous ambiguous pixels inherent in EM images severely confuse the models designed for natural images. With the assistance of the RPiA, the negative effects of unreliable pixels are mostly eliminated. Besides, the RPrS assigns larger weights to the more reliable prototypes to obtain robust prototype-level supervision. Our DualRel generates more accurate prediction masks compared with other methods, which demonstrates the effectiveness of the cooperation of the above two modules.", + "bbox": [ + 496, + 523, + 890, + 762 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Visualization of Correlation Weights. To more intuitively demonstrate the unreliable pixels suppression ability endowed by RPiA, we conduct qualitative visualization on the correlation maps between the mito filters and the image features. As shown in Fig. 6, we find that in the absence of RPiA, pixel features that with distinct semantics sometimes share high similarity with specific prototypes as shown in the parts marked by the red box. We claim that this is detrimental because aggregating features that not align to the", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "19623", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b43dc6aeacb1c34229c010edd9089fd2b7671b16b20ebb989eab9d2f83170356.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 119, + 90, + 218, + 148 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6c7202ecdfe3cbc154af02f45e8ac8281a548106d32d2b0390c40a75156f7a59.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 225, + 90, + 323, + 148 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5296b6424e7bfdd2aeaa5f5465a1355f7359eff62a1115e6dbbfafffc673d928.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 330, + 90, + 428, + 148 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": 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"image_caption": [], + "image_footnote": [], + "bbox": [ + 746, + 218, + 844, + 275 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7203274d09ee01b0b728c020b838af2c8c3e4a543f382f267fd9b37b824d5a94.jpg", + "image_caption": [ + "EM Image" + ], + "image_footnote": [], + "bbox": [ + 120, + 281, + 218, + 339 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/31c3b1885834c6f807caeb6daaa828448fb5a1839e01b0a9ea7910311738f393.jpg", + "image_caption": [ + "Ground Truth" + ], + "image_footnote": [], + "bbox": [ + 225, + 281, + 323, + 339 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a785f18a70d1468ea06da3a5cbebd1f57fd485d529d6709811019f396ef9bf24.jpg", + "image_caption": [ + "MT" + ], + "image_footnote": [], + "bbox": [ + 331, + 281, + 428, + 339 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/cc6c31c7aefcf099ff1229924ea21c1b5ca020f2236b1daab68ec6285e19795a.jpg", + "image_caption": [ + "CCT", + "Figure 4. Qualitative results of the proposed DualRel and other methods under 1/8 ratio on Lucchi." + ], + "image_footnote": [], + "bbox": [ + 436, + 281, + 532, + 339 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e142374309f2c5c34cd1452c8694476428bafb859692df88f7af995beee31352.jpg", + "image_caption": [ + "GCT" + ], + "image_footnote": [], + "bbox": [ + 539, + 281, + 635, + 339 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/aa996a14a3c5acd63510ef671fbe6bc82770055149fe3f5383a6d7f071a0f510.jpg", + "image_caption": [ + "CPS" + ], + "image_footnote": [], + "bbox": [ + 643, + 281, + 740, + 339 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/65c7ca94e4b04131dc0f73f42889a0cd264d1231f24eab5be053bca2006195fd.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 746, + 281, + 844, + 339 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/25967433531ebf64aabfbf4afac8a33ba00614866f5cf019bd4db178a95717bc.jpg", + "image_caption": [ + "EM Image", + "Figure 5. The visualization of the reliability of prototypes and its corresponding activation maps." + ], + "image_footnote": [], + "bbox": [ + 119, + 406, + 233, + 473 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/26ec4cfc77d2138c8cd6ccd5f64e8b372f8959f864cc9a60433cf12d98e8ece8.jpg", + "image_caption": [ + "Ground Truth" + ], + "image_footnote": [], + "bbox": [ + 241, + 407, + 356, + 473 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d34fc3a86493b3689ad8cfc85ad4fe4676b431d65cfd9c99db7b585578bc2bae.jpg", + "image_caption": [ + "Reliability=0.53" + ], + "image_footnote": [], + "bbox": [ + 364, + 407, + 478, + 473 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b14c20ff71b0d54153efd44a35086ffa3790f3506f449ecd1d55f7c652a93474.jpg", + "image_caption": [ + "Reliability=0.91" + ], + "image_footnote": [], + "bbox": [ + 486, + 407, + 601, + 473 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/71d745b71873dc00c62c12c6948cb4061859dab35f2c38230dbb664f4b644ced.jpg", + "image_caption": [ + "Background Prototypes", + "Reliability=0.84" + ], + "image_footnote": [], + "bbox": [ + 609, + 407, + 723, + 473 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7298b05df8bd9a696d615902d15602fed9ffe5f5fe83a20b5410d3e186ee3600.jpg", + "image_caption": [ + "Reliability=0.32" + ], + "image_footnote": [], + "bbox": [ + 730, + 407, + 844, + 473 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3b86f9dbc1c46116bb0d59fd11380d47768cd9374ab2f50def3d6c6ea330f33d.jpg", + "image_caption": [ + "Figure 6. Visualization of the pixel-prototype correlation weights." + ], + "image_footnote": [], + "bbox": [ + 99, + 531, + 272, + 690 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5881450b17a6269f37771fb2e961c9d299373422c0939bbef373cee64e7c4813.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 282, + 531, + 447, + 690 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "prototypes with large weights will lead to confusion. The second row presents the results with RPiA, we observe a significant reduction in false activation, demonstrating the effectiveness of RPiA in suppressing false matches.", + "bbox": [ + 75, + 744, + 468, + 806 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Visualization of Reliability and Activation Maps. To vividly present the working mechanism of reliable prototype selection module (RPrS), we visualize the reliability of prototypes and its corresponding activation maps. As shown in Fig. 5, some prototypes with clear foreground or background semantic clues occupy larger weights (i.e.,", + "bbox": [ + 75, + 809, + 468, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "$4^{th}$ and $5^{th}$ columns), while some prototypes focusing on mitochondrial boundary patterns are assigned with smaller weights (i.e., $3^{rd}$ and $6^{th}$ columns). This is in line with the design idea of RPrS, that is, pursuing implicitly learning the reliability of each prototype in a data-driven way. In this case, the equivocal prototypes will be suppressed while the reliable ones are highlighted in the supervision signals.", + "bbox": [ + 498, + 531, + 890, + 638 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 659, + 617, + 674 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we rethink how to achieve effective semi-supervised mitochondria segmentation. We propose a novel end-to-end dual-reliable (DualRel) network, including a reliable pixel aggregation module and a reliable prototype selection module. Extensive experimental results demonstrate the effectiveness. This work is expected to open a new venue for future research in this field.", + "bbox": [ + 498, + 686, + 890, + 790 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Acknowledgments", + "text_level": 1, + "bbox": [ + 500, + 811, + 678, + 830 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was partially supported by the National Nature Science Foundation of China (Grant 62022078, 62021001), National Defense Basic Scientific Research Program (Grant JCKY2022911B002).", + "bbox": [ + 498, + 839, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "19624", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Silvia Campello and Luca Scorrano. Mitochondrial shape changes: orchestrating cell pathophysiology. EMBO reports, 11(9):678-684, 2010. 1", + "[2] Vincent Casser, Kai Kang, Hanspeter Pfister, and Daniel Haehn. Fast mitochondria detection for connectomics. 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In Proceedings of the IEEE/CVF international conference on computer vision, pages 6023-6032, 2019. 3", + "[37] Hongyi Zhang, Moustapha Cisse, Yann N Dauphin, and David Lopez-Paz. mixup: Beyond empirical risk minimization. arXiv preprint arXiv:1710.09412, 2017. 3" + ], + "bbox": [ + 78, + 90, + 468, + 739 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "19626", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/DualRel_ Semi-Supervised Mitochondria Segmentation From a Prototype Perspective/ffadc065-1edc-42b2-a626-096c78b5c896_model.json b/2023/DualRel_ Semi-Supervised Mitochondria Segmentation From a Prototype Perspective/ffadc065-1edc-42b2-a626-096c78b5c896_model.json new file mode 100644 index 0000000000000000000000000000000000000000..0a1359f1a7a9f4f005fd1b79a5d048ef6d24000b --- /dev/null +++ b/2023/DualRel_ Semi-Supervised Mitochondria Segmentation From a Prototype Perspective/ffadc065-1edc-42b2-a626-096c78b5c896_model.json @@ -0,0 +1,2761 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.18, + 0.087, + 0.791, + 0.133 + ], + "angle": 0, + "content": "DualRel: Semi-Supervised Mitochondria Segmentation from A Prototype Perspective" + }, + { + "type": "text", + "bbox": [ + 0.12, + 0.145, + 0.844, + 0.22 + ], + "angle": 0, + "content": "Huayu Mai\\(^{1*}\\) Rui Sun\\(^{1*}\\) Tianzhu Zhang\\(^{1,2,3\\dagger}\\) Zhiwei Xiong\\(^{1,2}\\) Feng Wu\\(^{1,2}\\) \n\\(^{1}\\)University of Science and Technology of China \n\\(^{2}\\)Institute of Artificial Intelligence, Hefei Comprehensive National Science Center \n\\(^{3}\\)Deep Space Exploration Lab" + }, + { + "type": "text", + "bbox": [ + 0.153, + 0.22, + 0.812, + 0.235 + ], + "angle": 0, + "content": "{mai556, issunrui}@mail.ustc.edu.cn, {tzzhang, zwxiong, fengwu}@ustc.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.27, + 0.314, + 0.287 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.302, + 0.474, + 0.681 + ], + "angle": 0, + "content": "Automatic mitochondria segmentation enjoys great popularity with the development of deep learning. However, existing methods rely heavily on the labor-intensive manual gathering by experienced domain experts. And naively applying semi-supervised segmentation methods in the natural image field to mitigate the labeling cost is undesirable. In this work, we analyze the gap between mitochondrial images and natural images and rethink how to achieve effective semi-supervised mitochondria segmentation, from the perspective of reliable prototype-level supervision. We propose a novel end-to-end dual-reliable (DualRel) network, including a reliable pixel aggregation module and a reliable prototype selection module. The proposed DualRel enjoys several merits. First, to learn the prototypes well without any explicit supervision, we carefully design the referential correlation to rectify the direct pairwise correlation. Second, the reliable prototype selection module is responsible for further evaluating the reliability of prototypes in constructing prototype-level consistency regularization. Extensive experimental results on three challenging benchmarks demonstrate that our method performs favorably against state-of-the-art semi-supervised segmentation methods. Importantly, with extremely few samples used for training, DualRel is also on par with current state-of-the-art fully supervised methods." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.706, + 0.21, + 0.723 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.731, + 0.47, + 0.868 + ], + "angle": 0, + "content": "Mitochondria, as one of the crucial organelles, are the primary energy providers for cell activities and are essential for metabolism. Quantification of mitochondrial morphology can not only promote basic scientific research (e.g., cellular physiology [1, 5]), but also provide new insight for clinical diagnosis (e.g., neurodegenerative diseases [20] and diabetes [24]). Recently, with the development of deep learning, semantic segmentation [2, 14, 18, 27, 30, 33] enables in-depth exploration of mitochondrial morphology" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.269, + 0.59, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.564, + 0.323, + 0.627, + 0.331 + ], + "angle": 0, + "content": "Confusion Density: 0.06" + }, + { + "type": "image", + "bbox": [ + 0.595, + 0.27, + 0.681, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.713, + 0.27, + 0.798, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.769, + 0.323, + 0.832, + 0.331 + ], + "angle": 0, + "content": "Confusion Density: 0.21" + }, + { + "type": "image", + "bbox": [ + 0.804, + 0.27, + 0.888, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.691, + 0.33, + 0.703, + 0.337 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.338, + 0.587, + 0.385 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.595, + 0.338, + 0.678, + 0.385 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.683, + 0.339, + 0.706, + 0.385 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.385, + 0.577, + 0.453 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.538, + 0.454, + 0.551, + 0.462 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.595, + 0.385, + 0.678, + 0.453 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.637, + 0.454, + 0.646, + 0.461 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image", + "bbox": [ + 0.693, + 0.339, + 0.768, + 0.375 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.689, + 0.378, + 0.776, + 0.417 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.799, + 0.339, + 0.884, + 0.375 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.797, + 0.378, + 0.882, + 0.417 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.693, + 0.431, + 0.753, + 0.44 + ], + "angle": 0, + "content": "□ Foreground protocol" + }, + { + "type": "image_caption", + "bbox": [ + 0.693, + 0.442, + 0.756, + 0.452 + ], + "angle": 0, + "content": "Background pixel" + }, + { + "type": "image_caption", + "bbox": [ + 0.776, + 0.431, + 0.872, + 0.44 + ], + "angle": 0, + "content": "Pixel-Prototype Correlation" + }, + { + "type": "image_caption", + "bbox": [ + 0.776, + 0.442, + 0.887, + 0.452 + ], + "angle": 0, + "content": "Fixtive Reference Correlation" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.474, + 0.893, + 0.571 + ], + "angle": 0, + "content": "Figure 1. Illustration of our motivation. (a) shows the confusion map and density (i.e., the expected inverse confidence per pixel) of mitochondrial and natural images. (b) shows the unreliability caused by direct pairwise prototype-pixel correlation that is conditioned only on visual similarity. (c) shows how to construct pixel-reference correlation to rectify the direct pairwise correlation in a referential correlation manner." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.598, + 0.893, + 0.734 + ], + "angle": 0, + "content": "from high-resolution electron microscopy (EM) images and make conspicuous achievements. However, their flexibility and scalability are limited in the actual deployment because the numerous cluttered irrelevant organelles that require labor-intensive manual discrimination and gathering by experienced domain experts [10, 21]. Therefore, we begin to turn attention to semi-supervised segmentation with the assumption that enormous unlabeled data is accessible, aiming to alleviate the data-hungry issue." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Semi-supervised segmentation enjoys great popularity in the field of natural images, and representative works such as CPS [3], which imposes pixel-level consistency regularization and establishes state-of-the-art performance. It naturally comes into mind to directly apply a CPS-like method to semi-supervised mitochondria segmentation. However, there exist a large gap between mitochondrial and natural images. As shown in Fig. 1 (a), we observe that the confusion density (i.e., the expected inverse confidence per pixel) in mitochondrial images significantly surpasses counterpart in natural images, implying that directly employing" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.875, + 0.204, + 0.888 + ], + "angle": 0, + "content": "*Equal contribution" + }, + { + "type": "page_footnote", + "bbox": [ + 0.098, + 0.888, + 0.22, + 0.9 + ], + "angle": 0, + "content": "† Corresponding author" + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.875, + 0.22, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19617" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.213 + ], + "angle": 0, + "content": "pixel-level consistency regularization as supervision signals on mitochondrial images will inevitably increase the risk of unreliability. The most intuitive example is that there exist considerable boundary regions in mitochondrial images, and the segmentation network is naturally equivocal for these regions, as proven in [15]. In this case, some relatively small mitochondria are easily overwhelmed by this ambiguity, leading to sub-optimal results." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.217, + 0.471, + 0.655 + ], + "angle": 0, + "content": "In order to seek more reliable supervision signals to alleviate the undependable problem caused by pixel-level supervision, we draw inspiration from the inbuilt resistance to noisy pixels of prototypes and construct more robust and reliable prototype-level supervision. To achieve this goal, two issues need to be considered. (1) Unreliable pixels. Considering the cluttered background caused by under/overexposure and out-of-focus problems during EM imaging, the prototype inevitably absorbs unreliable pixels (i.e., heterogeneous semantic clues) during the interaction of corresponding pixels with a suitable pattern. We argue that directly forcing pairwise prototype-pixel correlation is primarily at blame. As shown in Fig. 1 (b), due to the foreground-background ambiguity, the foreground prototype \\( f_{1} \\) is erroneously closer to \\( p_{2} \\) located in the background than counterpart point \\( p_{1} \\) with similar pattern situated in the foreground. Therefore, it is highly desirable to suppress the unreliable pixels caused by the direct pairwise prototype-pixel correlation that is only conditioned on visual similarity during prototype learning process. (2) Unreliable prototypes. Intuitively, not all prototypes are equivalent for building prototype-level consistency regularization. For example, for a prototype that focuses on mitochondrial boundary patterns, the inherent unreliability of the pixels belonging to these patterns, as discussed above, will also taint the purity of this prototype with equivocality. Therefore, the prototype-level supervision signals should be further optimized to guarantee that the true reliable prototypes enjoy higher weights." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.66, + 0.47, + 0.901 + ], + "angle": 0, + "content": "To mitigate the above issues, we rethink how to achieve effective consistency regularization for semi-supervised mitochondria segmentation, from the perspective of reliable prototype-level supervision. We propose a Dual-Reliable (DualRel) network including a reliable pixel aggregation module and a reliable prototype selection module. In the reliable pixel aggregation module (RPIA), to learn the prototypes well without any explicit supervision, we carefully design the referential correlation to rectify the direct pairwise correlation, enabling the prototype absorb counterpart reliable pixels with the same semantic pattern during the interaction with the pixels. The main idea is, for each pixel/prototype, we can obtain the referential correlation (i.e., a likelihood vector) by comparing this pixel/prototype with a set of reliable reference points. In essence, the referential correlation reflects the consensus among reliable ref" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.439 + ], + "angle": 0, + "content": "ference points with a broader receptive field and thus it encodes the relative semantic comparability of the reference points that can be relied upon, which is from a different perspective than the absolute pairwise prototype-pixel correlation. Intuitively, each pair of true prototype-pixel correlation (e.g., the \\( f_{1} - p_{1} \\) pair in Fig. 1 (c) derived from the prototypes and mitochondria images should be not only visually similar to each other (i.e., high direct pairwise prototype-pixel correlation), but also similar to any other reference point (i.e., similar referential correlation pair). Moreover, we assemble referential correlation into the cross-attention mechanism with the ability to capture long-range dependencies. In this case, the relatively equivocal pixels (e.g., the \\( f_{1} - p_{2} \\) pair in Fig. 1 (c) will be suppressed while the reliable ones are highlighted to reduce the correspondence noise. In the reliable prototype selection module (RPrS), in order to further evaluate the reliability of prototypes in constructing prototype-level consistency regularization, we draw inspiration from bayesian deep learning [12] and devise a reliability-aware consistency loss to pursue implicitly learn the reliability about each prototype in a data-driven way. In this way, the equivocal prototypes will be suppressed while the reliable ones are highlighted in the supervision signals." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.44, + 0.892, + 0.728 + ], + "angle": 0, + "content": "In this work, our contributions can be concluded as follows: (1) To the best of our knowledge, this is the first work to rethink how to achieve effective consistency regularization for semi-supervised mitochondria segmentation, from the perspective of reliable prototype-level supervision. We analyze the gap between mitochondrial images and natural images, hoping our work will provide some insight for researchers in this field. (2) We propose a dual-reliable (DualRel) network in a unified framework. Specifically, we design the reliable pixel aggregation module to rectify the direct pairwise correlation, the reliable prototype selection module to further evaluate the reliability of prototypes in constructing prototype-level consistency regularization. (3) Extensive experimental results on three challenging benchmarks demonstrate that our method performs favorably against state-of-the-art semi-supervised segmentation methods. Importantly, with extremely few samples used for training, DualRel is also on par with current state-of-the-art fully supervised methods." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.744, + 0.642, + 0.76 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.771, + 0.753, + 0.787 + ], + "angle": 0, + "content": "2.1. Mitochondria Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Segmenting mitochondria in EM images is vital for researchers to explore cellular functions and subcellular activities. Rather than traditional methods utilizing hand-crafted features [14, 18, 27], DL-based networks have shown significant performance improvement on mitochondria segmentation. The pioneering work Lucchi et al. [19] design a deep neural network based on supervoxels to model shapes of mi" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "19618" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.244 + ], + "angle": 0, + "content": "tochondria. Oztel et al. [26] propose a deep convolutional neural network with a sliding window strategy and post-processing steps to boost the performance. Wei et al. [35] introduce a 3D U-Net based network and release a new challenging dataset containing mitochondria images with higher resolution. However, all previous methods only focus on the fully-supervised training, which require a large amount of labeled data. In this work, we introduce semi-supervised learning into mitochondria segmentation, aiming to alleviate the data-hungry issue." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.251, + 0.423, + 0.267 + ], + "angle": 0, + "content": "2.2. Semi-supervised Semantic Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.274, + 0.473, + 0.606 + ], + "angle": 0, + "content": "With the development of semi-supervised learning, various kinds of semi-supervised semantic segmentation algorithms have been proposed. GAN-based methods [9,22,29] try to synthesize additional training data or generate the pseudo labels for unlabeled data by using adversarial loss. Recently, the consistency regularization [6,23,34] has been intensely studied in semi-supervised semantic segmentation. The main idea of this type of approach is that the intermediate features or predictions should maintain consistency across different semantic-preserving transformations on the input or different network initialization [36, 37]. MT [31] is a representative work that first adopts the teacher network to guide the learning of the student network in semi-supervised semantic segmentation. Alternatively, CCT [25] introduces dual independent models to supervise each other with the soft probability output, while CPS [3] is supervised with hard pseudo segmentation maps. GCT [11] employs two segmentation networks with the same structure but different weight initialization and enforces the consistency between the predictions. However, the above pixel-level supervision-based methods perform poorly on semi-supervised mitochondria tasks." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.618, + 0.169, + 0.634 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.643, + 0.47, + 0.735 + ], + "angle": 0, + "content": "In this section, we first formulate the semi-supervised mitochondria segmentation task and present the overview of the proposed DualRel. Then we describe the details of the reliable pixel aggregation module (RPiA) and reliable prototype selection module (RPrs) of DualRel. Finally, the training and inference procedure are discussed." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.742, + 0.188, + 0.756 + ], + "angle": 0, + "content": "3.1. Overview" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.47, + 0.902 + ], + "angle": 0, + "content": "In semi-supervised mitochondria segmentation task, we wish to train a segmentation network with training data \\(D^{L}\\cup D^{U}\\). In the labeled set \\(D^{L} = \\{\\mathbf{I}_{i}^{L},\\mathbf{Y}_{i}\\}_{i = 0}^{N}\\), each image is associated with a ground truth label \\(\\mathbf{Y}\\in \\{0,1\\}^{H\\times W}\\) where 1 denotes foreground while 0 denotes background. In the unlabeled set \\(D^{U} = \\{\\mathbf{I}_{j}^{U}\\}_{j = 0}^{M}\\), \\(M\\) images are provided without ground truth. Given an EM image \\(\\mathbf{I}\\) (for brevity, we omit the superscript \\(L / U\\) and subscript \\(i / j\\)), let \\(\\mathbf{X}\\in \\mathbb{R}^{h\\times w\\times D}\\) denotes the feature map extracted from" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.319 + ], + "angle": 0, + "content": "feature extractor (e.g., ResNet50 [8]), where \\( h \\), \\( w \\) and \\( D \\) denote the height, width and channel number of the feature map, respectively. Subsequently, the feature map \\( \\mathbf{X} \\) is fed into the upsampling module (e.g., U-Net [28]) which outputs pixel embedding \\( \\mathbf{E} \\in \\mathbb{R}^{H \\times W \\times C} \\) with the same spatial scale as original input image. As illustrated in Fig. 2, the proposed DualRel includes two branches of feature extractor and upsampling module, which are of the same structure but different weight initialization. Such a two-branch structure is devised to construct consistency supervision signals for unlabeled data, which is a popular paradigm in semi-supervised learning. Besides, a reliable pixel aggregation module and a reliable prototype selection module are introduced to construct prototype-level consistency regularization for semi-supervised mitochondria segmentation." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.326, + 0.742, + 0.342 + ], + "angle": 0, + "content": "3.2. Reliable Pixel Aggregation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.349, + 0.892, + 0.457 + ], + "angle": 0, + "content": "To construct prototype-level supervision, we prepend a set of learnable embeddings \\(\\mathbf{F} = \\{\\mathbf{f}_k\\}_{k=1}^K\\) (referred to as mito filters). Each filter \\(\\mathbf{f}_k\\) is represented as a \\(C\\)-dimension vector to interact with the feature map \\(\\mathbf{X}\\) and absorb counterpart reliable pixels with the same semantic pattern. Then, we adopt a cross-attention mechanism [32] to realize the interaction and obtain mito features \\(\\widetilde{\\mathbf{F}} = \\{\\widetilde{\\mathbf{f}}_k\\}_{k=1}^K\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.457, + 0.892, + 0.564 + ], + "angle": 0, + "content": "Since the cross-attention requires a 1D sequence as the input, we first utilize a \\(1\\times 1\\) convolution kernel to reduce the channel number of the feature map \\(\\mathbf{X}\\) from \\(D\\) to \\(C\\), and then flatten the spatial dimensions to produce the feature sequence \\(\\widetilde{\\mathbf{X}} = \\{\\widetilde{\\mathbf{x}}_i\\}_{i = 1}^{hw}\\in \\mathbb{R}^{hw\\times C}\\). Specifically, we denote mito filters \\(\\{\\mathbf{f}_k\\}_{k = 1}^K\\) as queries, the feature map \\(\\widetilde{\\mathbf{X}}\\) as keys and values. Formally," + }, + { + "type": "equation", + "bbox": [ + 0.557, + 0.57, + 0.891, + 0.589 + ], + "angle": 0, + "content": "\\[\n\\mathbf {q} _ {k} = \\mathbf {f} _ {k} \\mathbf {W} ^ {Q}, \\mathbf {k} _ {i} = \\widetilde {\\mathbf {x}} _ {i} \\mathbf {W} ^ {K}, \\mathbf {v} _ {i} = \\widetilde {\\mathbf {x}} _ {i} \\mathbf {W} ^ {V}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.594, + 0.891, + 0.656 + ], + "angle": 0, + "content": "where \\(\\mathbf{W}^Q, \\mathbf{W}^K, \\mathbf{W}^V \\in \\mathbb{R}^{C \\times C}\\) are linear projections, \\(k = 1, 2, \\ldots, K\\) and \\(i = 1, 2, \\ldots, hw\\). Then the pairwise correlation \\(s_{k,i}\\) between each query \\(\\mathbf{q}_k\\) and the \\(i^{th}\\) key \\(\\mathbf{k}_i\\) is given as" + }, + { + "type": "equation", + "bbox": [ + 0.564, + 0.663, + 0.892, + 0.702 + ], + "angle": 0, + "content": "\\[\ns _ {k, i} = \\frac {\\exp \\left(\\beta_ {k , i}\\right)}{\\sum_ {j = 1} ^ {h w} \\exp \\left(\\beta_ {k , j}\\right)}, \\beta_ {k, i} = \\frac {\\mathbf {q} _ {k} \\mathbf {k} _ {i} ^ {\\top}}{\\sqrt {C}}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.71, + 0.891, + 0.741 + ], + "angle": 0, + "content": "where \\(\\sqrt{C}\\) is a scaling factor to stabilize training and \\(T\\) refers to the transpose operation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.742, + 0.892, + 0.863 + ], + "angle": 0, + "content": "Due to the susceptibility of pairwise filter-pixel correlation, the mito filter inevitably absorbs unreliable pixels during the interaction. We carefully design the referential correlation assembled in cross-attention to mitigate such issue. Specifically, we define \\(N\\) reference points \\(\\widetilde{\\mathbf{X}}^R = \\{\\widetilde{\\mathbf{x}}_n^R\\}_{n=1}^N \\in \\mathbb{R}^{N \\times C}\\) (detailed in the supplementary material). Respectively calculating the filter-reference correlation and the pixel-reference correlation as same as Eq. (2):" + }, + { + "type": "equation", + "bbox": [ + 0.559, + 0.869, + 0.892, + 0.906 + ], + "angle": 0, + "content": "\\[\n\\mathbf {S} _ {k} ^ {F R} = \\operatorname {s o f t m a x} (\\frac {\\left(\\mathbf {f} _ {k} \\mathbf {W} ^ {Q}\\right) \\left(\\widetilde {\\mathbf {X}} ^ {R} \\mathbf {W} ^ {K}\\right) ^ {\\intercal}}{\\sqrt {C}}), \\tag {3}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19619" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.123, + 0.09, + 0.852, + 0.337 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.348, + 0.895, + 0.391 + ], + "angle": 0, + "content": "Figure 2. Illustration of the proposed DualRel. DualRel is mainly composed of a reliable pixel aggregation module to rectify the direct pairwise correlation, and a reliable prototype selection module responsible for further evaluating the reliability of prototypes in constructing prototype-level consistency regularization. \"GAP\" represents a global average pooling layer [16] and \"Merge\" is described in Sec. 3.4." + }, + { + "type": "equation", + "bbox": [ + 0.136, + 0.413, + 0.47, + 0.449 + ], + "angle": 0, + "content": "\\[\n\\mathbf {S} _ {i} ^ {P R} = \\operatorname {s o f t m a x} \\left(\\frac {\\left(\\widetilde {\\mathbf {x}} _ {i} \\mathbf {W} ^ {Q}\\right) \\left(\\widetilde {\\mathbf {X}} ^ {R} \\mathbf {W} ^ {K}\\right) ^ {\\top}}{\\sqrt {C}}\\right), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.452, + 0.47, + 0.499 + ], + "angle": 0, + "content": "where \\(\\mathbf{S}_k^{FR} \\in \\mathbb{R}^{1 \\times N}\\) and \\(\\mathbf{S}_i^{PR} \\in \\mathbb{R}^{1 \\times N}\\) are regarded as the referential correlation. And then, we get the similarity between the referential correlations by:" + }, + { + "type": "equation", + "bbox": [ + 0.203, + 0.506, + 0.47, + 0.526 + ], + "angle": 0, + "content": "\\[\nc _ {k, i} = \\mathbf {S} _ {k} ^ {F R} \\left(\\mathbf {S} _ {i} ^ {P R}\\right) ^ {\\top}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.534, + 0.438, + 0.548 + ], + "angle": 0, + "content": "which is used to rectify the direct pairwise correlation." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.549, + 0.469, + 0.579 + ], + "angle": 0, + "content": "Then, the mito features \\(\\{\\widetilde{\\mathbf{f}}_k\\}_{k = 1}^K\\) can be got by blending values with the rectified correlations:" + }, + { + "type": "equation", + "bbox": [ + 0.192, + 0.586, + 0.47, + 0.627 + ], + "angle": 0, + "content": "\\[\n\\widetilde {\\mathbf {f}} _ {k} = \\sum_ {i} ^ {h w} c _ {k, i} \\cdot s _ {k, i} \\cdot \\mathbf {v} _ {i}, \\tag {6}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.635, + 0.332, + 0.65 + ], + "angle": 0, + "content": "3.3. Reliable Prototype Selection" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.658, + 0.469, + 0.719 + ], + "angle": 0, + "content": "Before describing the reliable prototype selection mechanism, we first formulate the process of obtaining the mito prototypes \\(\\mathbf{P} = \\{\\mathbf{p}_k\\}_{k=1}^K\\). First, calculating the activation maps \\(\\mathbf{A} = \\{\\mathbf{A}_k\\}_{k=1}^K \\in \\mathbb{R}^{K \\times H \\times W}\\) by:" + }, + { + "type": "equation", + "bbox": [ + 0.196, + 0.726, + 0.469, + 0.743 + ], + "angle": 0, + "content": "\\[\n\\mathbf {A} _ {k} = \\operatorname {s i g m o i d} \\left(\\mathbf {f} _ {k} \\mathbf {E} ^ {\\top}\\right), \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.752, + 0.469, + 0.813 + ], + "angle": 0, + "content": "where \\(\\mathbf{A}_k\\) denotes the activation map of the \\(k^{th}\\) mito feature on pixel embedding \\(\\mathbf{E}\\). Then, based on the activation maps \\(\\mathbf{A}\\), we generate mito prototypes \\(\\{\\mathbf{p}_k\\}_{k=1}^K\\) by global average pooling (GAP):" + }, + { + "type": "equation", + "bbox": [ + 0.161, + 0.82, + 0.469, + 0.863 + ], + "angle": 0, + "content": "\\[\n\\mathbf {p} _ {k} = \\frac {1}{H W} \\sum_ {i = 1} ^ {H} \\sum_ {j = 1} ^ {W} \\mathbf {A} _ {k, i, j} \\cdot \\mathbf {E} _ {i, j}. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Intuitively, not all prototypes are equivalent for building prototype-level consistency regularization. In order to" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.416, + 0.892, + 0.557 + ], + "angle": 0, + "content": "further evaluate the reliability of prototypes in constructing prototype-level consistency regularization, we devise a reliability-aware consistency loss to pursue implicitly learn the reliability about each prototype in a data-driven way. Firstly, we estimate the reliability \\(\\mathbf{R} = \\{r_k\\}_{k=1}^K\\) for each prototype. In specific, we concatenate the mito features \\(\\widetilde{\\mathbf{f}}_k^1\\) and \\(\\widetilde{\\mathbf{f}}_k^2\\) (the superscript denotes which baranch the mito features from) in channel dimension and feed them into a two layers MLP followed by the sigmoid function, as in Eq. (9):" + }, + { + "type": "equation", + "bbox": [ + 0.569, + 0.566, + 0.892, + 0.587 + ], + "angle": 0, + "content": "\\[\nr _ {k} = \\operatorname {s i g m o i d} \\left(\\operatorname {M L P} \\left(\\operatorname {c o n c a t} \\left(\\widetilde {\\mathbf {f}} _ {k} ^ {1}, \\widetilde {\\mathbf {f}} _ {k} ^ {2}\\right)\\right). \\right. \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.595, + 0.892, + 0.656 + ], + "angle": 0, + "content": "In order to guarantee that the true reliable prototypes enjoy higher weights and the equivocal ones are suppressed, we regard the \\(\\mathbf{R}\\) as a attenuation factor and get the reliable prototype consistency loss as:" + }, + { + "type": "equation", + "bbox": [ + 0.521, + 0.664, + 0.892, + 0.706 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {r p c} = \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\left(e ^ {1 - \\frac {1}{r _ {k}}} \\times L _ {2} \\left(\\mathbf {p} _ {k} ^ {1}, \\mathbf {p} _ {k} ^ {2}\\right) - \\lambda \\times r _ {k}\\right), \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.715, + 0.892, + 0.76 + ], + "angle": 0, + "content": "where \\( L_{2}(\\cdot) \\) denotes L2 distance and the \\( \\lambda \\) is the weight for the regularization term preventing the estimated reliability from zero." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.769, + 0.712, + 0.786 + ], + "angle": 0, + "content": "3.4. Training and inference" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.792, + 0.892, + 0.901 + ], + "angle": 0, + "content": "For the follow-up training and inference, we need to merge the activation maps \\(\\mathbf{A}\\) into foreground-background probability map \\(\\widetilde{\\mathbf{Y}}\\in \\mathbb{R}^{2\\times H\\times W}\\). In our implementation, we simply treat the summation of the first half of the activation maps as foreground probability (corresponding the summation of the \\(1^{st}\\) to the \\(\\frac{K}{2}^{th}\\) activation maps), and the summation of the other half as background probability." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19620" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.184 + ], + "angle": 0, + "content": "Besides, considering the large size and shape variation of the mitochondria, the mito prototype learning may focus on the same (e.g., the entire foreground), making the reliable prototype selection module degeneration. Therefore, we impose a diversity loss to expand the discrepancy among mito features. Formally," + }, + { + "type": "equation", + "bbox": [ + 0.161, + 0.192, + 0.47, + 0.235 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {d i v} = \\sum_ {i = 1} ^ {K} \\sum_ {j = 1, i \\neq j} ^ {K} \\left(\\frac {\\langle \\widetilde {\\mathbf {f}} _ {i} , \\widetilde {\\mathbf {f}} _ {j} \\rangle}{\\| \\widetilde {\\mathbf {f}} _ {i} \\| _ {2} \\| \\widetilde {\\mathbf {f}} _ {j} \\| _ {2}}\\right). \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.244, + 0.47, + 0.306 + ], + "angle": 0, + "content": "The intuition behind this loss is trivial. If the \\(i^{th}\\) and \\(j^{th}\\) features give a high attention to the same region, the \\(\\mathcal{L}_{div}\\) will be large and prompt these features to adjust themselves adaptively." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.306, + 0.47, + 0.339 + ], + "angle": 0, + "content": "During Training, we calculate the supervise loss for the output prediction of two branch with labeled data by" + }, + { + "type": "equation", + "bbox": [ + 0.108, + 0.346, + 0.47, + 0.387 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {s u p} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\left(\\operatorname {C E} \\left(\\widetilde {\\mathbf {Y}} ^ {\\mathbf {1}}, \\mathbf {Y}\\right) + \\operatorname {C E} \\left(\\widetilde {\\mathbf {Y}} ^ {\\mathbf {2}}, \\mathbf {Y}\\right)\\right), \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.396, + 0.473, + 0.444 + ], + "angle": 0, + "content": "where \\(\\mathrm{CE}(\\cdot)\\) denotes the standard cross entropy loss. As a result, our DualRel is trained by minimizing the overall objective as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.16, + 0.456, + 0.47, + 0.473 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {\\sup } + \\mathcal {L} _ {r p c} + \\lambda_ {d i v} \\times \\mathcal {L} _ {d i v}, \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.478, + 0.308, + 0.492 + ], + "angle": 0, + "content": "where \\(\\lambda_{div}\\) is the trade-off weight." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.492, + 0.469, + 0.54 + ], + "angle": 0, + "content": "During inference, we get the predicted mask \\(\\widehat{\\mathbf{Y}}\\) by apply argmax operation on probability map \\(\\widetilde{\\mathbf{Y}}\\) from one branch, without extra computation cost." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.551, + 0.21, + 0.568 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.576, + 0.365, + 0.591 + ], + "angle": 0, + "content": "4.1. Datasets and Evaluation Metrics" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.473, + 0.856 + ], + "angle": 0, + "content": "We conduct experiments on the most popular benchmarks including Lucchi [19], Lucchi++ [2], MitoEM dataset [35]. Lucchi [19] contains two sub-volumes, acquired from the CA1 hippocampus region of the mouse brain for training and testing. Each sub-volume consists of \\(165 \\times 1024 \\times 768\\) EM images provided with manual mitochondria segmentation mask. And Lucchi++ [2] is reannotated by three neuroscience and biology experts, and has the same size as Lucchi with more accurate mitochondria segmentation mask. MitoEM dataset [35] contains two volumes attained from rat and human cortex, dubbed mito-R and mito-H respectively. Each volume consists of 400 training images, 100 validation images and 500 test images with a resolution of \\(4096 \\times 4096\\). Among them, the ground-truth labels are publicly available for the training set and the validation set. In our experiments, we train on training set and evaluate on validation set." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Evaluation Metrics. We adopt Dice similarity coefficient (DSC) and Jaccard-index coefficient (JAC) to evaluate the accuracy of segmentation in our experiments." + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.09, + 0.895, + 0.16 + ], + "angle": 0, + "content": "Table 1. Comparison with state-of-the-art re-implemented methods on Lucchi [19] and Lucchi++ [2] dataset under different partition protocols. Partition protocols denote the ratio of labeled data used for training, followed by the actual number of mitochondrial images." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.17, + 0.905, + 0.35 + ], + "angle": 0, + "content": "
1/32 (5)1/16 (10)1/8 (20)1/2 (82)
MethodJACDSCJACDSCJACDSCJACDSC
Lucchi
MT[NIPS17] [31]71.8582.5372.4882.8375.4984.7278.6086.73
CCT[CVPR20] [25]84.7591.6285.4891.7385.8491.9486.6092.73
GCT[ECCV20] [11]83.5190.9384.6492.0285.8691.7286.2092.41
CPS[CVPR21] [3]84.5591.5784.6191.1885.1691.5785.5192.03
DualRel85.6392.2486.3592.4287.2193.1687.6293.31
Lucchi++
MT[NIPS17] [31]79.5187.1182.8990.1786.9192.3387.2493.42
CCT[CVPR20] [25]87.3692.6387.8493.2288.5493.7489.3694.19
GCT[ECCV20] [11]86.6092.1686.9592.0587.8693.1288.6993.79
CPS[CVPR21] [3]86.3692.4287.2293.0787.8793.3688.3093.52
DualRel87.8193.4288.2293.7489.9194.6390.5495.52
" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.375, + 0.719, + 0.391 + ], + "angle": 0, + "content": "4.2. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.398, + 0.895, + 0.672 + ], + "angle": 0, + "content": "In the semi-supervised setting, we sample a certain ratio from the training set as labeled set \\( D^{L} \\), and the rest are treat as unlabeled set \\( D^{U} \\). For a fair comparison, we follow the following guidelines in training and inference stage for all re-implemented methods. We adopt ResNet50 [8] as backbone network for feature extraction by removing the global average pooling (GAP) layer and fully connected layer, and utilize U-Net structure [28] for upsampling. During training, we feed the network with \\( 512 \\times 512 \\) images randomly cropped from original EM images with random mirror, random rotate and elastic transform augmentation. Extra color jitter is adopted to reduce overfitting. We use mini-batch SGD to train our model with momentum set to 0.9 and weight decay fixed as 0.0005. We initialize the learning rate with \\( 5 \\times 10^{-3} \\) with batch size of 4, and halve the learning rate at the \\( 50\\% \\), \\( 70\\% \\) and \\( 90\\% \\) of the overall training epoch. During inference, We adopt a sliding window of size \\( 512 \\times 512 \\) and step 256." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.681, + 0.866, + 0.697 + ], + "angle": 0, + "content": "4.3. Comparison with State-of-the-art Methods" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.892, + 0.795 + ], + "angle": 0, + "content": "We reproduce the most representative and competitive methods [3,11,25,31] in the semi-supervised natural image semantic segmentation task, and report their performance on Lucchi derivatives (i.e., Lucchi and Lucchi++) and Mi-toEM dataset, establishing a semi-supervised mitochondria segmentation benchmark." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Lucchi derivatives. Tab. 1 shows the comparison of our method with the state-of-the-art re-implemented methods on Lucchi and Lucchi++ dataset. We consistently observe that our DualRel outperforms all other methods under all partition protocols, which strongly proves the effectiveness of our method. Specifically, our approach achieves \\(89.9\\%\\) JAC, \\(94.6\\%\\) DSC on Lucchi++ and \\(87.2\\%\\) JAC, \\(93.1\\%\\) DSC" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.958 + ], + "angle": 0, + "content": "19621" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.47, + 0.118 + ], + "angle": 0, + "content": "Table 2. Comparison with state-of-the-art re-implemented methods on MitoEM [35] dataset under different partition protocols." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.129, + 0.48, + 0.307 + ], + "angle": 0, + "content": "
1/32 (12)1/16 (25)1/8 (50)1/2 (200)
MethodJACDSCJACDSCJACDSCJACDSC
mito-R
\\(MT_{[NIPS17]}\\)(31)81.1187.5284.6490.6184.9190.8286.9992.41
\\(CCT_{[CVPR20]}\\)(25)88.9193.2289.4893.8889.7194.0389.7494.12
\\(GCT_{[ECCV20]}\\)(11)88.2292.8188.6192.7389.0393.4189.1193.72
\\(CPS_{[CVPR21]}\\)(3)88.7193.7189.6294.4189.7194.5290.0294.72
DualRel89.6194.5290.3194.9390.7295.1190.9195.23
mito-H
\\(MT_{[NIPS17]}\\)(31)81.9089.3282.7189.6283.5790.3684.6391.14
\\(CCT_{[CVPR20]}\\)(25)83.4290.6184.1890.7584.8791.2485.0791.37
\\(GCT_{[ECCV20]}\\)(11)82.1289.8183.3290.9184.6291.0284.8191.06
\\(CPS_{[CVPR21]}\\)(3)84.2291.8184.2991.4785.4292.1286.3192.65
DualRel85.6192.2285.9392.4486.2192.4386.5392.72
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.334, + 0.47, + 0.456 + ], + "angle": 0, + "content": "on Lucchi under 1/8 partition protocol (only 20 labeled images). This means that even if we only label a small proportion of images, we can train a satisfactory segmentation model in an appropriate way. Compared to the best method CPS [3] in the field of natural image, our DualRel achieves a large margin of \\(2.05\\% / 1.59\\%\\) in JAC/DSC under 1/8 partition protocol, which favorably manifests the benefits of prototype-level consistency regularization." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.457, + 0.47, + 0.637 + ], + "angle": 0, + "content": "MitoEM dataset. In Tab. 2 we report the performance on MitoEM dataset, which is much more complex than Lucchi and Lucchi++, with larger image size, more messy background and more diverse mitochondrial morphology. DualRel also achieves convincing performance even when the labeled data is scarce. Under 1/32 partition protocol, i.e., training the network with solely 12 labeled images and 388 unlabeled images, we obtain \\(89.6\\%\\) JAC, \\(94.5\\%\\) DSC on mito-R and \\(85\\%\\) JAC, \\(91.9\\%\\) DSC on mito-H. This demonstrates the stability of our method, which can model the reliability of the prototype for a more robust prototype-level supervision, even in the face of more complex scene." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.638, + 0.47, + 0.82 + ], + "angle": 0, + "content": "Comparison with fully supervised methods. Tab. 3 tabulates the quantitative results compared with fully supervised methods. We observe that with only 5 annotated images, DualRel even surpasses fully supervised methods that utilize all annotated samples, such as 2D U-Net [28], by \\(0.7\\% / 1.2\\%\\) in JAC/DSC. When the number of available labeled samples increases (e.g., half the total images), our method is on par with state-of-the-art fully supervised methods (e.g., Casser [2]) without any post-processing. This sheds light on the great promise of semi-supervised mitochondria segmentation tasks, where light labeling cost can yield competitive performance." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.832, + 0.334, + 0.848 + ], + "angle": 0, + "content": "4.4. Ablation Study and Analysis" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.903 + ], + "angle": 0, + "content": "To look deeper into our method, we perform a series of ablation studies on Lucchi dataset with ResNet50 as backbone under 1/8 partition protocol to analyze each compo" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.089, + 0.892, + 0.133 + ], + "angle": 0, + "content": "Table 3. Comparison with state-of-the-art fully supervised methods on Lucchi dataset [19]. \"Post-Processing\" stands for whether to use post-processing such as Z-Filtering." + }, + { + "type": "table", + "bbox": [ + 0.522, + 0.143, + 0.868, + 0.293 + ], + "angle": 0, + "content": "
MethodPost-ProcessinglabelsJACDSC
Lucchi [18]X16575.586.0
Peng and Yuan [27]X16583.390.9
2D U-Net [28]X16584.491.5
Cheng (2D) [4]X16586.592.8
Liu [17]✓16586.492.6
Khadangi [13]X16586.592.7
Casser [2]✓16588.493.8
DualRel (1/32)X585.692.2
DualRel (1/2)X8287.693.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.306, + 0.892, + 0.334 + ], + "angle": 0, + "content": "Table 4. Evaluation of the effectiveness of different components on Lucchi dataset." + }, + { + "type": "table", + "bbox": [ + 0.558, + 0.345, + 0.832, + 0.54 + ], + "angle": 0, + "content": "
Pixel-level
ThresholdJACDSC
CPS [3]085.1691.57
0.585.2091.62
0.784.0791.48
0.983.9390.89
Prototype-level
RPIARPrSJACDSC
w/o ref.w/ ref.
✓85.9791.94
✓86.5792.72
✓✓87.2193.16
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.568, + 0.892, + 0.659 + ], + "angle": 0, + "content": "ment of our DualRel, including the reliable pixel aggregation module (RPIA), and the reliable prototype selection module (RPrS). Note that we remove all modules except the two branches of feature extractor and upsampling module and a separate cross-attention mechanism, to directly construct prototype-level consistency regularization as our baseline." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Analysis of the Pixel-level Consistency Regularization. In Sec. 1, we intuitively demonstrate that there exists gap between natural images and mitochondrial images, and directly employing pixel-level consistency regularization on mitochondrial images will inevitably increase the risk of unreliability. Naively, we can select high-confidence pixels based on a pre-defined threshold to attempt to alleviate the unreliability. The upper part of Tab. 4 tabulates the impact of different thresholds on the semi-supervised model based on pixel-level supervision. We observe that selecting high confidence points brings negligible improvement and even impairs model performance when the threshold is set too high. Then, we further quantitatively analyze the reasons for this case from the perspective of expected calibration error (ECE) [7], which measures the discrepancy between the confidence and accuracy of the network output," + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19622" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.47, + 0.118 + ], + "angle": 0, + "content": "Table 5. Comparison with state-of-the-art methods in model calibration and study on different network configurations." + }, + { + "type": "table_caption", + "bbox": [ + 0.106, + 0.13, + 0.248, + 0.15 + ], + "angle": 0, + "content": "(a) Quantification of expected calibration error (ECE)." + }, + { + "type": "table", + "bbox": [ + 0.11, + 0.152, + 0.232, + 0.279 + ], + "angle": 0, + "content": "
MethodECE (↓) (%)
MT15.2
CCT12.5
GCT10.2
CPS8.3
DualRel1.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.255, + 0.131, + 0.428, + 0.141 + ], + "angle": 0, + "content": "(b) Ablation on different architecture." + }, + { + "type": "table", + "bbox": [ + 0.253, + 0.143, + 0.436, + 0.196 + ], + "angle": 0, + "content": "
JACDSC
CNN86.9992.65
Transformer87.2193.16
" + }, + { + "type": "table_caption", + "bbox": [ + 0.25, + 0.2, + 0.435, + 0.221 + ], + "angle": 0, + "content": "(c) Performance comparison with and without diversity loss." + }, + { + "type": "table", + "bbox": [ + 0.253, + 0.224, + 0.436, + 0.276 + ], + "angle": 0, + "content": "
JACDSC
w/o div.86.5792.87
w/ div.87.2193.16
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.306, + 0.468, + 0.426 + ], + "angle": 0, + "content": "as known as calibration, has been explored. Poorer network calibration, weaker the correlation between the confidence and accuracy of the network output. In other words, even if the network predicts with high confidence, there is a high probability that it will be unreliable. Tab. 5a shows the calibration of different methods, the larger the value, the poorer the calibration. Therefore, it is impracticable to select reliable points only conditioned on confidence." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.428, + 0.468, + 0.534 + ], + "angle": 0, + "content": "Analysis of the Prototype-level Consistency Regularization. As shown in Tab. 4, the baseline that utilizes prototype-level supervision achieves a clear lead, compared to methods based on pixel-level consistency regularization. Moreover, Tab. 5a shows our DualRel achieves better calibration benefiting from RPiA and RPrS module, which is in line with the design idea of prototype-level supervision." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.536, + 0.468, + 0.686 + ], + "angle": 0, + "content": "Effectiveness of the Reliable Pixel Aggregation Module. As shown in Tab. 4, the introduction of the referential correlation (ref.) in RPiA achieves a certain performance lift compared with the baseline (i.e., a separate cross-attention mechanism without ref.), that is, \\(91.94\\%\\) vs. \\(92.72\\%\\) in DSC. The improvement can be mainly ascribed to the strong ability of the RPiA to rectify the direct pairwise correlation, enabling the prototype absorbs counterpart reliable pixels with the same semantic pattern during the interaction with the pixels." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.688, + 0.468, + 0.779 + ], + "angle": 0, + "content": "Effectiveness of the Reliable Prototype Selection Module. The addition of RPrS also contributes to a remarkable performance (86.57% vs. 87.21%). This proves the necessity of suppressing the equivocal prototypes, our RPrS can further evaluate the reliability of prototypes in constructing prototype-level consistency regularization." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Effectiveness of Transformer-based Cross-attention Mechanism. We perform the ablation study that replaces the Transformer-like cross-attention by using convolutional networks with similar parameters in Tab. 5b. In detail, We use the convolutional layers followed by a softmax function to change the channel size of the feature map to obtain \\(K\\) mito features when replacing cross attention. The feedforward network (FFN) is replaced by the convolutional lay" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.089, + 0.689, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.09, + 0.886, + 0.191 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.196, + 0.89, + 0.224 + ], + "angle": 0, + "content": "Figure 3. Evaluation of the number of prototypes \\( K \\), and the hyperparameters \\( \\lambda_{div} \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.25, + 0.892, + 0.295 + ], + "angle": 0, + "content": "ers, and the rest of the model remains the same. We observe that cross-attention achieves better performance thanks to the long-range modeling capabilities of the transformer." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.295, + 0.892, + 0.385 + ], + "angle": 0, + "content": "Effectiveness of Diversity Loss. As shown in Tab. 5c, with the utilization of diversity loss, further improvements can be observed. Diversity loss prevents the prototypes from focusing on similar local semantic clues. And diverse prototypes can capture mitochondria variations and achieve more precise segmentation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.385, + 0.892, + 0.491 + ], + "angle": 0, + "content": "Hyperparameter Evaluations. As shown in Fig. 3, we evaluate how \\( K \\) and \\( \\lambda_{div} \\) affects our model learning. We can observe that the performance continues to grow until \\( K = 12 \\), which means it is sufficient to mine 12 semantic patterns of mitochondria. And \\( \\lambda_{div} \\) controls the relative importance of the diversity loss, our model achieves much better performance when \\( \\lambda_{div} = 0.05 \\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.5, + 0.64, + 0.515 + ], + "angle": 0, + "content": "4.5. Vasualization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.524, + 0.892, + 0.763 + ], + "angle": 0, + "content": "Visualization of Predictions. To further analyze and understand the proposed method, we visualize a series of segmentation results and prototype activation areas. As shown in Fig. 4, it can be noticed that other methods tend to incorrectly segment the non-target region (dyed in blue) or are unable to activate all the mitochondria (dyed in red). We deem the main reason is that numerous ambiguous pixels inherent in EM images severely confuse the models designed for natural images. With the assistance of the RPiA, the negative effects of unreliable pixels are mostly eliminated. Besides, the RPrS assigns larger weights to the more reliable prototypes to obtain robust prototype-level supervision. Our DualRel generates more accurate prediction masks compared with other methods, which demonstrates the effectiveness of the cooperation of the above two modules." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Visualization of Correlation Weights. To more intuitively demonstrate the unreliable pixels suppression ability endowed by RPiA, we conduct qualitative visualization on the correlation maps between the mito filters and the image features. As shown in Fig. 6, we find that in the absence of RPiA, pixel features that with distinct semantics sometimes share high similarity with specific prototypes as shown in the parts marked by the red box. We claim that this is detrimental because aggregating features that not align to the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19623" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.12, + 0.091, + 0.22, + 0.15 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.226, + 0.092, + 0.325, + 0.15 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.331, + 0.092, + 0.429, + 0.15 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.437, + 0.092, + 0.535, + 0.15 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.54, + 0.092, + 0.637, + 0.15 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.644, + 0.092, + 0.741, + 0.15 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.748, + 0.092, + 0.845, + 0.15 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.122, + 0.155, + 0.219, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.227, + 0.155, + 0.324, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.332, + 0.155, + 0.429, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.437, + 0.155, + 0.534, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.54, + 0.155, + 0.636, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.644, + 0.155, + 0.741, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.748, + 0.155, + 0.844, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.122, + 0.219, + 0.219, + 0.276 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.227, + 0.219, + 0.324, + 0.276 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.333, + 0.219, + 0.429, + 0.276 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.437, + 0.219, + 0.534, + 0.276 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.54, + 0.219, + 0.636, + 0.276 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.644, + 0.219, + 0.741, + 0.276 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.748, + 0.219, + 0.845, + 0.276 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.122, + 0.282, + 0.219, + 0.34 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.14, + 0.345, + 0.2, + 0.357 + ], + "angle": 0, + "content": "EM Image" + }, + { + "type": "image", + "bbox": [ + 0.227, + 0.282, + 0.325, + 0.34 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.238, + 0.345, + 0.314, + 0.356 + ], + "angle": 0, + "content": "Ground Truth" + }, + { + "type": "image", + "bbox": [ + 0.333, + 0.282, + 0.429, + 0.34 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.37, + 0.345, + 0.392, + 0.356 + ], + "angle": 0, + "content": "MT" + }, + { + "type": "image", + "bbox": [ + 0.437, + 0.282, + 0.534, + 0.34 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.47, + 0.345, + 0.5, + 0.356 + ], + "angle": 0, + "content": "CCT" + }, + { + "type": "image", + "bbox": [ + 0.54, + 0.282, + 0.636, + 0.34 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.574, + 0.345, + 0.603, + 0.356 + ], + "angle": 0, + "content": "GCT" + }, + { + "type": "image", + "bbox": [ + 0.644, + 0.282, + 0.741, + 0.34 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.679, + 0.345, + 0.706, + 0.356 + ], + "angle": 0, + "content": "CPS" + }, + { + "type": "image", + "bbox": [ + 0.748, + 0.282, + 0.845, + 0.34 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.783, + 0.345, + 0.812, + 0.356 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.192, + 0.361, + 0.777, + 0.375 + ], + "angle": 0, + "content": "Figure 4. Qualitative results of the proposed DualRel and other methods under 1/8 ratio on Lucchi." + }, + { + "type": "image", + "bbox": [ + 0.12, + 0.407, + 0.235, + 0.474 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.148, + 0.476, + 0.208, + 0.487 + ], + "angle": 0, + "content": "EM Image" + }, + { + "type": "image", + "bbox": [ + 0.243, + 0.408, + 0.357, + 0.474 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.262, + 0.476, + 0.339, + 0.487 + ], + "angle": 0, + "content": "Ground Truth" + }, + { + "type": "image", + "bbox": [ + 0.366, + 0.408, + 0.479, + 0.474 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.377, + 0.475, + 0.468, + 0.487 + ], + "angle": 0, + "content": "Reliability=0.53" + }, + { + "type": "image", + "bbox": [ + 0.488, + 0.408, + 0.602, + 0.474 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.501, + 0.475, + 0.59, + 0.487 + ], + "angle": 0, + "content": "Reliability=0.91" + }, + { + "type": "image_caption", + "bbox": [ + 0.663, + 0.391, + 0.794, + 0.404 + ], + "angle": 0, + "content": "Background Prototypes" + }, + { + "type": "image", + "bbox": [ + 0.61, + 0.408, + 0.724, + 0.474 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.623, + 0.475, + 0.714, + 0.487 + ], + "angle": 0, + "content": "Reliability=0.84" + }, + { + "type": "image", + "bbox": [ + 0.732, + 0.408, + 0.846, + 0.474 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.743, + 0.475, + 0.835, + 0.488 + ], + "angle": 0, + "content": "Reliability=0.32" + }, + { + "type": "image_caption", + "bbox": [ + 0.198, + 0.492, + 0.771, + 0.507 + ], + "angle": 0, + "content": "Figure 5. The visualization of the reliability of prototypes and its corresponding activation maps." + }, + { + "type": "image", + "bbox": [ + 0.101, + 0.532, + 0.274, + 0.691 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.283, + 0.532, + 0.449, + 0.691 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.697, + 0.468, + 0.711 + ], + "angle": 0, + "content": "Figure 6. Visualization of the pixel-prototype correlation weights." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.746, + 0.469, + 0.807 + ], + "angle": 0, + "content": "prototypes with large weights will lead to confusion. The second row presents the results with RPiA, we observe a significant reduction in false activation, demonstrating the effectiveness of RPiA in suppressing false matches." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.469, + 0.902 + ], + "angle": 0, + "content": "Visualization of Reliability and Activation Maps. To vividly present the working mechanism of reliable prototype selection module (RPrS), we visualize the reliability of prototypes and its corresponding activation maps. As shown in Fig. 5, some prototypes with clear foreground or background semantic clues occupy larger weights (i.e.," + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.532, + 0.892, + 0.64 + ], + "angle": 0, + "content": "\\(4^{th}\\) and \\(5^{th}\\) columns), while some prototypes focusing on mitochondrial boundary patterns are assigned with smaller weights (i.e., \\(3^{rd}\\) and \\(6^{th}\\) columns). This is in line with the design idea of RPrS, that is, pursuing implicitly learning the reliability of each prototype in a data-driven way. In this case, the equivocal prototypes will be suppressed while the reliable ones are highlighted in the supervision signals." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.66, + 0.619, + 0.675 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.687, + 0.892, + 0.791 + ], + "angle": 0, + "content": "In this paper, we rethink how to achieve effective semi-supervised mitochondria segmentation. We propose a novel end-to-end dual-reliable (DualRel) network, including a reliable pixel aggregation module and a reliable prototype selection module. Extensive experimental results demonstrate the effectiveness. This work is expected to open a new venue for future research in this field." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.813, + 0.679, + 0.831 + ], + "angle": 0, + "content": "6. Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "This work was partially supported by the National Nature Science Foundation of China (Grant 62022078, 62021001), National Defense Basic Scientific Research Program (Grant JCKY2022911B002)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19624" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.468, + 0.156 + ], + "angle": 0, + "content": "[1] Silvia Campello and Luca Scorrano. Mitochondrial shape changes: orchestrating cell pathophysiology. EMBO reports, 11(9):678-684, 2010. 1" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.159, + 0.468, + 0.212 + ], + "angle": 0, + "content": "[2] Vincent Casser, Kai Kang, Hanspeter Pfister, and Daniel Haehn. 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However, existing methods rely heavily on the labor-intensive manual gathering by experienced domain experts. And naively applying semi-supervised segmentation methods in the natural image field to mitigate the labeling cost is undesirable. In this work, we analyze the gap between mitochondrial images and natural images and rethink how to achieve effective semi-supervised mitochondria segmentation, from the perspective of reliable prototype-level supervision. We propose a novel end-to-end dual-reliable (DualRel) network, including a reliable pixel aggregation module and a reliable prototype selection module. The proposed DualRel enjoys several merits. First, to learn the prototypes well without any explicit supervision, we carefully design the referential correlation to rectify the direct pairwise correlation. Second, the reliable prototype selection module is responsible for further evaluating the reliability of prototypes in constructing prototype-level consistency regularization. Extensive experimental results on three challenging benchmarks demonstrate that our method performs favorably against state-of-the-art semi-supervised segmentation methods. Importantly, with extremely few samples used for training, DualRel is also on par with current state-of-the-art fully supervised methods. + +# 1. Introduction + +Mitochondria, as one of the crucial organelles, are the primary energy providers for cell activities and are essential for metabolism. Quantification of mitochondrial morphology can not only promote basic scientific research (e.g., cellular physiology [1, 5]), but also provide new insight for clinical diagnosis (e.g., neurodegenerative diseases [20] and diabetes [24]). Recently, with the development of deep learning, semantic segmentation [2, 14, 18, 27, 30, 33] enables in-depth exploration of mitochondrial morphology + +![](images/45b09b3daf7ea3290afe19195ce7769ec3a47266366437e5cc4bc4d490e8f139.jpg) +Confusion Density: 0.06 + +![](images/3963f0a779532bac1f67f83ba06a122b596337b40aa6093aa1a4f8d9b8f0c569.jpg) + +![](images/73ad7898f2ef553d2aef638b61369d92e4a6237d5aa8f9f6eae5925d7e187d91.jpg) +Confusion Density: 0.21 + +![](images/c9415103f7464f5306d9c21e2b73e08c5bd70625dcb85bfb89fb288c6e72b496.jpg) + +![](images/6f36ae1a85d70f0761680d30d78d05f71c4653cc9962bb483fede33d51bcb126.jpg) + +![](images/31bfcf0361c575d53a0b6b40eaffedee4f53b83652fc0705f62674e611e2ad8b.jpg) + +![](images/748b7391b7d0c6c2e950c6254647ba6c7e6ac6e386ddcd25f3dbc87641023760.jpg) +(a) + +![](images/86f8ac02f91686a95ab9aae681fc8affc3ce0bafb8d756f89e98f30400bfbd36.jpg) +(b) + +![](images/2a6197659e7623841564f21a8218cd10cccd5233c90bd03dd6909ed8b524479d.jpg) +(c) +Background pixel + +![](images/4afa57124bd0a6d941b1594938bc785e96aa0b91a3a51f00b48b546089dbdc34.jpg) + +![](images/659478dc8489f1621011877ee557940d9858adc5142786b7884cf0d9f0b59bab.jpg) +□ Foreground protocol +Pixel-Prototype Correlation +Fixtive Reference Correlation + +![](images/2eb6dfdc0e6606c95b3c50b1a198a3c5945f4aebf6bd977b58fcdcca17c720b6.jpg) + +![](images/63a72b5c6817f46e1debbe1ce76cb7c899968d431c7d7f8a44c5c17121c5ec50.jpg) +Figure 1. Illustration of our motivation. (a) shows the confusion map and density (i.e., the expected inverse confidence per pixel) of mitochondrial and natural images. (b) shows the unreliability caused by direct pairwise prototype-pixel correlation that is conditioned only on visual similarity. (c) shows how to construct pixel-reference correlation to rectify the direct pairwise correlation in a referential correlation manner. + +from high-resolution electron microscopy (EM) images and make conspicuous achievements. However, their flexibility and scalability are limited in the actual deployment because the numerous cluttered irrelevant organelles that require labor-intensive manual discrimination and gathering by experienced domain experts [10, 21]. Therefore, we begin to turn attention to semi-supervised segmentation with the assumption that enormous unlabeled data is accessible, aiming to alleviate the data-hungry issue. + +Semi-supervised segmentation enjoys great popularity in the field of natural images, and representative works such as CPS [3], which imposes pixel-level consistency regularization and establishes state-of-the-art performance. It naturally comes into mind to directly apply a CPS-like method to semi-supervised mitochondria segmentation. However, there exist a large gap between mitochondrial and natural images. As shown in Fig. 1 (a), we observe that the confusion density (i.e., the expected inverse confidence per pixel) in mitochondrial images significantly surpasses counterpart in natural images, implying that directly employing + +pixel-level consistency regularization as supervision signals on mitochondrial images will inevitably increase the risk of unreliability. The most intuitive example is that there exist considerable boundary regions in mitochondrial images, and the segmentation network is naturally equivocal for these regions, as proven in [15]. In this case, some relatively small mitochondria are easily overwhelmed by this ambiguity, leading to sub-optimal results. + +In order to seek more reliable supervision signals to alleviate the undependable problem caused by pixel-level supervision, we draw inspiration from the inbuilt resistance to noisy pixels of prototypes and construct more robust and reliable prototype-level supervision. To achieve this goal, two issues need to be considered. (1) Unreliable pixels. Considering the cluttered background caused by under/overexposure and out-of-focus problems during EM imaging, the prototype inevitably absorbs unreliable pixels (i.e., heterogeneous semantic clues) during the interaction of corresponding pixels with a suitable pattern. We argue that directly forcing pairwise prototype-pixel correlation is primarily at blame. As shown in Fig. 1 (b), due to the foreground-background ambiguity, the foreground prototype $f_{1}$ is erroneously closer to $p_{2}$ located in the background than counterpart point $p_{1}$ with similar pattern situated in the foreground. Therefore, it is highly desirable to suppress the unreliable pixels caused by the direct pairwise prototype-pixel correlation that is only conditioned on visual similarity during prototype learning process. (2) Unreliable prototypes. Intuitively, not all prototypes are equivalent for building prototype-level consistency regularization. For example, for a prototype that focuses on mitochondrial boundary patterns, the inherent unreliability of the pixels belonging to these patterns, as discussed above, will also taint the purity of this prototype with equivocality. Therefore, the prototype-level supervision signals should be further optimized to guarantee that the true reliable prototypes enjoy higher weights. + +To mitigate the above issues, we rethink how to achieve effective consistency regularization for semi-supervised mitochondria segmentation, from the perspective of reliable prototype-level supervision. We propose a Dual-Reliable (DualRel) network including a reliable pixel aggregation module and a reliable prototype selection module. In the reliable pixel aggregation module (RPIA), to learn the prototypes well without any explicit supervision, we carefully design the referential correlation to rectify the direct pairwise correlation, enabling the prototype absorb counterpart reliable pixels with the same semantic pattern during the interaction with the pixels. The main idea is, for each pixel/prototype, we can obtain the referential correlation (i.e., a likelihood vector) by comparing this pixel/prototype with a set of reliable reference points. In essence, the referential correlation reflects the consensus among reliable ref + +ference points with a broader receptive field and thus it encodes the relative semantic comparability of the reference points that can be relied upon, which is from a different perspective than the absolute pairwise prototype-pixel correlation. Intuitively, each pair of true prototype-pixel correlation (e.g., the $f_{1} - p_{1}$ pair in Fig. 1 (c) derived from the prototypes and mitochondria images should be not only visually similar to each other (i.e., high direct pairwise prototype-pixel correlation), but also similar to any other reference point (i.e., similar referential correlation pair). Moreover, we assemble referential correlation into the cross-attention mechanism with the ability to capture long-range dependencies. In this case, the relatively equivocal pixels (e.g., the $f_{1} - p_{2}$ pair in Fig. 1 (c) will be suppressed while the reliable ones are highlighted to reduce the correspondence noise. In the reliable prototype selection module (RPrS), in order to further evaluate the reliability of prototypes in constructing prototype-level consistency regularization, we draw inspiration from bayesian deep learning [12] and devise a reliability-aware consistency loss to pursue implicitly learn the reliability about each prototype in a data-driven way. In this way, the equivocal prototypes will be suppressed while the reliable ones are highlighted in the supervision signals. + +In this work, our contributions can be concluded as follows: (1) To the best of our knowledge, this is the first work to rethink how to achieve effective consistency regularization for semi-supervised mitochondria segmentation, from the perspective of reliable prototype-level supervision. We analyze the gap between mitochondrial images and natural images, hoping our work will provide some insight for researchers in this field. (2) We propose a dual-reliable (DualRel) network in a unified framework. Specifically, we design the reliable pixel aggregation module to rectify the direct pairwise correlation, the reliable prototype selection module to further evaluate the reliability of prototypes in constructing prototype-level consistency regularization. (3) Extensive experimental results on three challenging benchmarks demonstrate that our method performs favorably against state-of-the-art semi-supervised segmentation methods. Importantly, with extremely few samples used for training, DualRel is also on par with current state-of-the-art fully supervised methods. + +# 2. Related Work + +# 2.1. Mitochondria Segmentation + +Segmenting mitochondria in EM images is vital for researchers to explore cellular functions and subcellular activities. Rather than traditional methods utilizing hand-crafted features [14, 18, 27], DL-based networks have shown significant performance improvement on mitochondria segmentation. The pioneering work Lucchi et al. [19] design a deep neural network based on supervoxels to model shapes of mi + +tochondria. Oztel et al. [26] propose a deep convolutional neural network with a sliding window strategy and post-processing steps to boost the performance. Wei et al. [35] introduce a 3D U-Net based network and release a new challenging dataset containing mitochondria images with higher resolution. However, all previous methods only focus on the fully-supervised training, which require a large amount of labeled data. In this work, we introduce semi-supervised learning into mitochondria segmentation, aiming to alleviate the data-hungry issue. + +# 2.2. Semi-supervised Semantic Segmentation + +With the development of semi-supervised learning, various kinds of semi-supervised semantic segmentation algorithms have been proposed. GAN-based methods [9,22,29] try to synthesize additional training data or generate the pseudo labels for unlabeled data by using adversarial loss. Recently, the consistency regularization [6,23,34] has been intensely studied in semi-supervised semantic segmentation. The main idea of this type of approach is that the intermediate features or predictions should maintain consistency across different semantic-preserving transformations on the input or different network initialization [36, 37]. MT [31] is a representative work that first adopts the teacher network to guide the learning of the student network in semi-supervised semantic segmentation. Alternatively, CCT [25] introduces dual independent models to supervise each other with the soft probability output, while CPS [3] is supervised with hard pseudo segmentation maps. GCT [11] employs two segmentation networks with the same structure but different weight initialization and enforces the consistency between the predictions. However, the above pixel-level supervision-based methods perform poorly on semi-supervised mitochondria tasks. + +# 3. Method + +In this section, we first formulate the semi-supervised mitochondria segmentation task and present the overview of the proposed DualRel. Then we describe the details of the reliable pixel aggregation module (RPiA) and reliable prototype selection module (RPrs) of DualRel. Finally, the training and inference procedure are discussed. + +# 3.1. Overview + +In semi-supervised mitochondria segmentation task, we wish to train a segmentation network with training data $D^{L}\cup D^{U}$ . In the labeled set $D^{L} = \{\mathbf{I}_{i}^{L},\mathbf{Y}_{i}\}_{i = 0}^{N}$ , each image is associated with a ground truth label $\mathbf{Y}\in \{0,1\}^{H\times W}$ where 1 denotes foreground while 0 denotes background. In the unlabeled set $D^{U} = \{\mathbf{I}_{j}^{U}\}_{j = 0}^{M}$ , $M$ images are provided without ground truth. Given an EM image $\mathbf{I}$ (for brevity, we omit the superscript $L / U$ and subscript $i / j$ ), let $\mathbf{X}\in \mathbb{R}^{h\times w\times D}$ denotes the feature map extracted from + +feature extractor (e.g., ResNet50 [8]), where $h$ , $w$ and $D$ denote the height, width and channel number of the feature map, respectively. Subsequently, the feature map $\mathbf{X}$ is fed into the upsampling module (e.g., U-Net [28]) which outputs pixel embedding $\mathbf{E} \in \mathbb{R}^{H \times W \times C}$ with the same spatial scale as original input image. As illustrated in Fig. 2, the proposed DualRel includes two branches of feature extractor and upsampling module, which are of the same structure but different weight initialization. Such a two-branch structure is devised to construct consistency supervision signals for unlabeled data, which is a popular paradigm in semi-supervised learning. Besides, a reliable pixel aggregation module and a reliable prototype selection module are introduced to construct prototype-level consistency regularization for semi-supervised mitochondria segmentation. + +# 3.2. Reliable Pixel Aggregation + +To construct prototype-level supervision, we prepend a set of learnable embeddings $\mathbf{F} = \{\mathbf{f}_k\}_{k=1}^K$ (referred to as mito filters). Each filter $\mathbf{f}_k$ is represented as a $C$ -dimension vector to interact with the feature map $\mathbf{X}$ and absorb counterpart reliable pixels with the same semantic pattern. Then, we adopt a cross-attention mechanism [32] to realize the interaction and obtain mito features $\widetilde{\mathbf{F}} = \{\widetilde{\mathbf{f}}_k\}_{k=1}^K$ . + +Since the cross-attention requires a 1D sequence as the input, we first utilize a $1\times 1$ convolution kernel to reduce the channel number of the feature map $\mathbf{X}$ from $D$ to $C$ , and then flatten the spatial dimensions to produce the feature sequence $\widetilde{\mathbf{X}} = \{\widetilde{\mathbf{x}}_i\}_{i = 1}^{hw}\in \mathbb{R}^{hw\times C}$ . Specifically, we denote mito filters $\{\mathbf{f}_k\}_{k = 1}^K$ as queries, the feature map $\widetilde{\mathbf{X}}$ as keys and values. Formally, + +$$ +\mathbf {q} _ {k} = \mathbf {f} _ {k} \mathbf {W} ^ {Q}, \mathbf {k} _ {i} = \widetilde {\mathbf {x}} _ {i} \mathbf {W} ^ {K}, \mathbf {v} _ {i} = \widetilde {\mathbf {x}} _ {i} \mathbf {W} ^ {V}, \tag {1} +$$ + +where $\mathbf{W}^Q, \mathbf{W}^K, \mathbf{W}^V \in \mathbb{R}^{C \times C}$ are linear projections, $k = 1, 2, \ldots, K$ and $i = 1, 2, \ldots, hw$ . Then the pairwise correlation $s_{k,i}$ between each query $\mathbf{q}_k$ and the $i^{th}$ key $\mathbf{k}_i$ is given as + +$$ +s _ {k, i} = \frac {\exp \left(\beta_ {k , i}\right)}{\sum_ {j = 1} ^ {h w} \exp \left(\beta_ {k , j}\right)}, \beta_ {k, i} = \frac {\mathbf {q} _ {k} \mathbf {k} _ {i} ^ {\top}}{\sqrt {C}}, \tag {2} +$$ + +where $\sqrt{C}$ is a scaling factor to stabilize training and $T$ refers to the transpose operation. + +Due to the susceptibility of pairwise filter-pixel correlation, the mito filter inevitably absorbs unreliable pixels during the interaction. We carefully design the referential correlation assembled in cross-attention to mitigate such issue. Specifically, we define $N$ reference points $\widetilde{\mathbf{X}}^R = \{\widetilde{\mathbf{x}}_n^R\}_{n=1}^N \in \mathbb{R}^{N \times C}$ (detailed in the supplementary material). Respectively calculating the filter-reference correlation and the pixel-reference correlation as same as Eq. (2): + +$$ +\mathbf {S} _ {k} ^ {F R} = \operatorname {s o f t m a x} (\frac {\left(\mathbf {f} _ {k} \mathbf {W} ^ {Q}\right) \left(\widetilde {\mathbf {X}} ^ {R} \mathbf {W} ^ {K}\right) ^ {\intercal}}{\sqrt {C}}), \tag {3} +$$ + +![](images/748fea748352817b86ef22f93b993611704d6d1b3994c83598ddcae6b0830ab6.jpg) +Figure 2. Illustration of the proposed DualRel. DualRel is mainly composed of a reliable pixel aggregation module to rectify the direct pairwise correlation, and a reliable prototype selection module responsible for further evaluating the reliability of prototypes in constructing prototype-level consistency regularization. "GAP" represents a global average pooling layer [16] and "Merge" is described in Sec. 3.4. + +$$ +\mathbf {S} _ {i} ^ {P R} = \operatorname {s o f t m a x} \left(\frac {\left(\widetilde {\mathbf {x}} _ {i} \mathbf {W} ^ {Q}\right) \left(\widetilde {\mathbf {X}} ^ {R} \mathbf {W} ^ {K}\right) ^ {\top}}{\sqrt {C}}\right), \tag {4} +$$ + +where $\mathbf{S}_k^{FR} \in \mathbb{R}^{1 \times N}$ and $\mathbf{S}_i^{PR} \in \mathbb{R}^{1 \times N}$ are regarded as the referential correlation. And then, we get the similarity between the referential correlations by: + +$$ +c _ {k, i} = \mathbf {S} _ {k} ^ {F R} \left(\mathbf {S} _ {i} ^ {P R}\right) ^ {\top}, \tag {5} +$$ + +which is used to rectify the direct pairwise correlation. + +Then, the mito features $\{\widetilde{\mathbf{f}}_k\}_{k = 1}^K$ can be got by blending values with the rectified correlations: + +$$ +\widetilde {\mathbf {f}} _ {k} = \sum_ {i} ^ {h w} c _ {k, i} \cdot s _ {k, i} \cdot \mathbf {v} _ {i}, \tag {6} +$$ + +# 3.3. Reliable Prototype Selection + +Before describing the reliable prototype selection mechanism, we first formulate the process of obtaining the mito prototypes $\mathbf{P} = \{\mathbf{p}_k\}_{k=1}^K$ . First, calculating the activation maps $\mathbf{A} = \{\mathbf{A}_k\}_{k=1}^K \in \mathbb{R}^{K \times H \times W}$ by: + +$$ +\mathbf {A} _ {k} = \operatorname {s i g m o i d} \left(\mathbf {f} _ {k} \mathbf {E} ^ {\top}\right), \tag {7} +$$ + +where $\mathbf{A}_k$ denotes the activation map of the $k^{th}$ mito feature on pixel embedding $\mathbf{E}$ . Then, based on the activation maps $\mathbf{A}$ , we generate mito prototypes $\{\mathbf{p}_k\}_{k=1}^K$ by global average pooling (GAP): + +$$ +\mathbf {p} _ {k} = \frac {1}{H W} \sum_ {i = 1} ^ {H} \sum_ {j = 1} ^ {W} \mathbf {A} _ {k, i, j} \cdot \mathbf {E} _ {i, j}. \tag {8} +$$ + +Intuitively, not all prototypes are equivalent for building prototype-level consistency regularization. In order to + +further evaluate the reliability of prototypes in constructing prototype-level consistency regularization, we devise a reliability-aware consistency loss to pursue implicitly learn the reliability about each prototype in a data-driven way. Firstly, we estimate the reliability $\mathbf{R} = \{r_k\}_{k=1}^K$ for each prototype. In specific, we concatenate the mito features $\widetilde{\mathbf{f}}_k^1$ and $\widetilde{\mathbf{f}}_k^2$ (the superscript denotes which baranch the mito features from) in channel dimension and feed them into a two layers MLP followed by the sigmoid function, as in Eq. (9): + +$$ +r _ {k} = \operatorname {s i g m o i d} \left(\operatorname {M L P} \left(\operatorname {c o n c a t} \left(\widetilde {\mathbf {f}} _ {k} ^ {1}, \widetilde {\mathbf {f}} _ {k} ^ {2}\right)\right). \right. \tag {9} +$$ + +In order to guarantee that the true reliable prototypes enjoy higher weights and the equivocal ones are suppressed, we regard the $\mathbf{R}$ as a attenuation factor and get the reliable prototype consistency loss as: + +$$ +\mathcal {L} _ {r p c} = \frac {1}{K} \sum_ {k = 1} ^ {K} \left(e ^ {1 - \frac {1}{r _ {k}}} \times L _ {2} \left(\mathbf {p} _ {k} ^ {1}, \mathbf {p} _ {k} ^ {2}\right) - \lambda \times r _ {k}\right), \tag {10} +$$ + +where $L_{2}(\cdot)$ denotes L2 distance and the $\lambda$ is the weight for the regularization term preventing the estimated reliability from zero. + +# 3.4. Training and inference + +For the follow-up training and inference, we need to merge the activation maps $\mathbf{A}$ into foreground-background probability map $\widetilde{\mathbf{Y}}\in \mathbb{R}^{2\times H\times W}$ . In our implementation, we simply treat the summation of the first half of the activation maps as foreground probability (corresponding the summation of the $1^{st}$ to the $\frac{K}{2}^{th}$ activation maps), and the summation of the other half as background probability. + +Besides, considering the large size and shape variation of the mitochondria, the mito prototype learning may focus on the same (e.g., the entire foreground), making the reliable prototype selection module degeneration. Therefore, we impose a diversity loss to expand the discrepancy among mito features. Formally, + +$$ +\mathcal {L} _ {d i v} = \sum_ {i = 1} ^ {K} \sum_ {j = 1, i \neq j} ^ {K} \left(\frac {\langle \widetilde {\mathbf {f}} _ {i} , \widetilde {\mathbf {f}} _ {j} \rangle}{\| \widetilde {\mathbf {f}} _ {i} \| _ {2} \| \widetilde {\mathbf {f}} _ {j} \| _ {2}}\right). \tag {11} +$$ + +The intuition behind this loss is trivial. If the $i^{th}$ and $j^{th}$ features give a high attention to the same region, the $\mathcal{L}_{div}$ will be large and prompt these features to adjust themselves adaptively. + +During Training, we calculate the supervise loss for the output prediction of two branch with labeled data by + +$$ +\mathcal {L} _ {s u p} = \frac {1}{N} \sum_ {i = 1} ^ {N} \left(\operatorname {C E} \left(\widetilde {\mathbf {Y}} ^ {\mathbf {1}}, \mathbf {Y}\right) + \operatorname {C E} \left(\widetilde {\mathbf {Y}} ^ {\mathbf {2}}, \mathbf {Y}\right)\right), \tag {12} +$$ + +where $\mathrm{CE}(\cdot)$ denotes the standard cross entropy loss. As a result, our DualRel is trained by minimizing the overall objective as follows: + +$$ +\mathcal {L} = \mathcal {L} _ {\sup } + \mathcal {L} _ {r p c} + \lambda_ {d i v} \times \mathcal {L} _ {d i v}, \tag {13} +$$ + +where $\lambda_{div}$ is the trade-off weight. + +During inference, we get the predicted mask $\widehat{\mathbf{Y}}$ by apply argmax operation on probability map $\widetilde{\mathbf{Y}}$ from one branch, without extra computation cost. + +# 4. Experiments + +# 4.1. Datasets and Evaluation Metrics + +We conduct experiments on the most popular benchmarks including Lucchi [19], Lucchi++ [2], MitoEM dataset [35]. Lucchi [19] contains two sub-volumes, acquired from the CA1 hippocampus region of the mouse brain for training and testing. Each sub-volume consists of $165 \times 1024 \times 768$ EM images provided with manual mitochondria segmentation mask. And Lucchi++ [2] is reannotated by three neuroscience and biology experts, and has the same size as Lucchi with more accurate mitochondria segmentation mask. MitoEM dataset [35] contains two volumes attained from rat and human cortex, dubbed mito-R and mito-H respectively. Each volume consists of 400 training images, 100 validation images and 500 test images with a resolution of $4096 \times 4096$ . Among them, the ground-truth labels are publicly available for the training set and the validation set. In our experiments, we train on training set and evaluate on validation set. + +Evaluation Metrics. We adopt Dice similarity coefficient (DSC) and Jaccard-index coefficient (JAC) to evaluate the accuracy of segmentation in our experiments. + +Table 1. Comparison with state-of-the-art re-implemented methods on Lucchi [19] and Lucchi++ [2] dataset under different partition protocols. Partition protocols denote the ratio of labeled data used for training, followed by the actual number of mitochondrial images. + +
1/32 (5)1/16 (10)1/8 (20)1/2 (82)
MethodJACDSCJACDSCJACDSCJACDSC
Lucchi
MT[NIPS17] [31]71.8582.5372.4882.8375.4984.7278.6086.73
CCT[CVPR20] [25]84.7591.6285.4891.7385.8491.9486.6092.73
GCT[ECCV20] [11]83.5190.9384.6492.0285.8691.7286.2092.41
CPS[CVPR21] [3]84.5591.5784.6191.1885.1691.5785.5192.03
DualRel85.6392.2486.3592.4287.2193.1687.6293.31
Lucchi++
MT[NIPS17] [31]79.5187.1182.8990.1786.9192.3387.2493.42
CCT[CVPR20] [25]87.3692.6387.8493.2288.5493.7489.3694.19
GCT[ECCV20] [11]86.6092.1686.9592.0587.8693.1288.6993.79
CPS[CVPR21] [3]86.3692.4287.2293.0787.8793.3688.3093.52
DualRel87.8193.4288.2293.7489.9194.6390.5495.52
+ +# 4.2. Implementation Details + +In the semi-supervised setting, we sample a certain ratio from the training set as labeled set $D^{L}$ , and the rest are treat as unlabeled set $D^{U}$ . For a fair comparison, we follow the following guidelines in training and inference stage for all re-implemented methods. We adopt ResNet50 [8] as backbone network for feature extraction by removing the global average pooling (GAP) layer and fully connected layer, and utilize U-Net structure [28] for upsampling. During training, we feed the network with $512 \times 512$ images randomly cropped from original EM images with random mirror, random rotate and elastic transform augmentation. Extra color jitter is adopted to reduce overfitting. We use mini-batch SGD to train our model with momentum set to 0.9 and weight decay fixed as 0.0005. We initialize the learning rate with $5 \times 10^{-3}$ with batch size of 4, and halve the learning rate at the $50\%$ , $70\%$ and $90\%$ of the overall training epoch. During inference, We adopt a sliding window of size $512 \times 512$ and step 256. + +# 4.3. Comparison with State-of-the-art Methods + +We reproduce the most representative and competitive methods [3,11,25,31] in the semi-supervised natural image semantic segmentation task, and report their performance on Lucchi derivatives (i.e., Lucchi and Lucchi++) and Mi-toEM dataset, establishing a semi-supervised mitochondria segmentation benchmark. + +Lucchi derivatives. Tab. 1 shows the comparison of our method with the state-of-the-art re-implemented methods on Lucchi and Lucchi++ dataset. We consistently observe that our DualRel outperforms all other methods under all partition protocols, which strongly proves the effectiveness of our method. Specifically, our approach achieves $89.9\%$ JAC, $94.6\%$ DSC on Lucchi++ and $87.2\%$ JAC, $93.1\%$ DSC + +Table 2. Comparison with state-of-the-art re-implemented methods on MitoEM [35] dataset under different partition protocols. + +
1/32 (12)1/16 (25)1/8 (50)1/2 (200)
MethodJACDSCJACDSCJACDSCJACDSC
mito-R
\(MT_{[NIPS17]}\)(31)81.1187.5284.6490.6184.9190.8286.9992.41
\(CCT_{[CVPR20]}\)(25)88.9193.2289.4893.8889.7194.0389.7494.12
\(GCT_{[ECCV20]}\)(11)88.2292.8188.6192.7389.0393.4189.1193.72
\(CPS_{[CVPR21]}\)(3)88.7193.7189.6294.4189.7194.5290.0294.72
DualRel89.6194.5290.3194.9390.7295.1190.9195.23
mito-H
\(MT_{[NIPS17]}\)(31)81.9089.3282.7189.6283.5790.3684.6391.14
\(CCT_{[CVPR20]}\)(25)83.4290.6184.1890.7584.8791.2485.0791.37
\(GCT_{[ECCV20]}\)(11)82.1289.8183.3290.9184.6291.0284.8191.06
\(CPS_{[CVPR21]}\)(3)84.2291.8184.2991.4785.4292.1286.3192.65
DualRel85.6192.2285.9392.4486.2192.4386.5392.72
+ +on Lucchi under 1/8 partition protocol (only 20 labeled images). This means that even if we only label a small proportion of images, we can train a satisfactory segmentation model in an appropriate way. Compared to the best method CPS [3] in the field of natural image, our DualRel achieves a large margin of $2.05\% / 1.59\%$ in JAC/DSC under 1/8 partition protocol, which favorably manifests the benefits of prototype-level consistency regularization. + +MitoEM dataset. In Tab. 2 we report the performance on MitoEM dataset, which is much more complex than Lucchi and Lucchi++, with larger image size, more messy background and more diverse mitochondrial morphology. DualRel also achieves convincing performance even when the labeled data is scarce. Under 1/32 partition protocol, i.e., training the network with solely 12 labeled images and 388 unlabeled images, we obtain $89.6\%$ JAC, $94.5\%$ DSC on mito-R and $85\%$ JAC, $91.9\%$ DSC on mito-H. This demonstrates the stability of our method, which can model the reliability of the prototype for a more robust prototype-level supervision, even in the face of more complex scene. + +Comparison with fully supervised methods. Tab. 3 tabulates the quantitative results compared with fully supervised methods. We observe that with only 5 annotated images, DualRel even surpasses fully supervised methods that utilize all annotated samples, such as 2D U-Net [28], by $0.7\% / 1.2\%$ in JAC/DSC. When the number of available labeled samples increases (e.g., half the total images), our method is on par with state-of-the-art fully supervised methods (e.g., Casser [2]) without any post-processing. This sheds light on the great promise of semi-supervised mitochondria segmentation tasks, where light labeling cost can yield competitive performance. + +# 4.4. Ablation Study and Analysis + +To look deeper into our method, we perform a series of ablation studies on Lucchi dataset with ResNet50 as backbone under 1/8 partition protocol to analyze each compo + +Table 3. Comparison with state-of-the-art fully supervised methods on Lucchi dataset [19]. "Post-Processing" stands for whether to use post-processing such as Z-Filtering. + +
MethodPost-ProcessinglabelsJACDSC
Lucchi [18]X16575.586.0
Peng and Yuan [27]X16583.390.9
2D U-Net [28]X16584.491.5
Cheng (2D) [4]X16586.592.8
Liu [17]✓16586.492.6
Khadangi [13]X16586.592.7
Casser [2]✓16588.493.8
DualRel (1/32)X585.692.2
DualRel (1/2)X8287.693.3
+ +Table 4. Evaluation of the effectiveness of different components on Lucchi dataset. + +
Pixel-level
ThresholdJACDSC
CPS [3]085.1691.57
0.585.2091.62
0.784.0791.48
0.983.9390.89
Prototype-level
RPIARPrSJACDSC
w/o ref.w/ ref.
✓85.9791.94
✓86.5792.72
✓✓87.2193.16
+ +ment of our DualRel, including the reliable pixel aggregation module (RPIA), and the reliable prototype selection module (RPrS). Note that we remove all modules except the two branches of feature extractor and upsampling module and a separate cross-attention mechanism, to directly construct prototype-level consistency regularization as our baseline. + +Analysis of the Pixel-level Consistency Regularization. In Sec. 1, we intuitively demonstrate that there exists gap between natural images and mitochondrial images, and directly employing pixel-level consistency regularization on mitochondrial images will inevitably increase the risk of unreliability. Naively, we can select high-confidence pixels based on a pre-defined threshold to attempt to alleviate the unreliability. The upper part of Tab. 4 tabulates the impact of different thresholds on the semi-supervised model based on pixel-level supervision. We observe that selecting high confidence points brings negligible improvement and even impairs model performance when the threshold is set too high. Then, we further quantitatively analyze the reasons for this case from the perspective of expected calibration error (ECE) [7], which measures the discrepancy between the confidence and accuracy of the network output, + +Table 5. Comparison with state-of-the-art methods in model calibration and study on different network configurations. + +(a) Quantification of expected calibration error (ECE). + +
MethodECE (↓) (%)
MT15.2
CCT12.5
GCT10.2
CPS8.3
DualRel1.8
+ +(b) Ablation on different architecture. + +
JACDSC
CNN86.9992.65
Transformer87.2193.16
+ +(c) Performance comparison with and without diversity loss. + +
JACDSC
w/o div.86.5792.87
w/ div.87.2193.16
+ +as known as calibration, has been explored. Poorer network calibration, weaker the correlation between the confidence and accuracy of the network output. In other words, even if the network predicts with high confidence, there is a high probability that it will be unreliable. Tab. 5a shows the calibration of different methods, the larger the value, the poorer the calibration. Therefore, it is impracticable to select reliable points only conditioned on confidence. + +Analysis of the Prototype-level Consistency Regularization. As shown in Tab. 4, the baseline that utilizes prototype-level supervision achieves a clear lead, compared to methods based on pixel-level consistency regularization. Moreover, Tab. 5a shows our DualRel achieves better calibration benefiting from RPiA and RPrS module, which is in line with the design idea of prototype-level supervision. + +Effectiveness of the Reliable Pixel Aggregation Module. As shown in Tab. 4, the introduction of the referential correlation (ref.) in RPiA achieves a certain performance lift compared with the baseline (i.e., a separate cross-attention mechanism without ref.), that is, $91.94\%$ vs. $92.72\%$ in DSC. The improvement can be mainly ascribed to the strong ability of the RPiA to rectify the direct pairwise correlation, enabling the prototype absorbs counterpart reliable pixels with the same semantic pattern during the interaction with the pixels. + +Effectiveness of the Reliable Prototype Selection Module. The addition of RPrS also contributes to a remarkable performance (86.57% vs. 87.21%). This proves the necessity of suppressing the equivocal prototypes, our RPrS can further evaluate the reliability of prototypes in constructing prototype-level consistency regularization. + +Effectiveness of Transformer-based Cross-attention Mechanism. We perform the ablation study that replaces the Transformer-like cross-attention by using convolutional networks with similar parameters in Tab. 5b. In detail, We use the convolutional layers followed by a softmax function to change the channel size of the feature map to obtain $K$ mito features when replacing cross attention. The feedforward network (FFN) is replaced by the convolutional lay + +![](images/59bd003b535271412411b51308841248c6868fa1e19ed3691457bdf4a3efc68c.jpg) +Figure 3. Evaluation of the number of prototypes $K$ , and the hyperparameters $\lambda_{div}$ . + +![](images/5c35a0b361de060d46d57128e59e3923e761904ef24f1fc45b08585e7ddee768.jpg) + +ers, and the rest of the model remains the same. We observe that cross-attention achieves better performance thanks to the long-range modeling capabilities of the transformer. + +Effectiveness of Diversity Loss. As shown in Tab. 5c, with the utilization of diversity loss, further improvements can be observed. Diversity loss prevents the prototypes from focusing on similar local semantic clues. And diverse prototypes can capture mitochondria variations and achieve more precise segmentation. + +Hyperparameter Evaluations. As shown in Fig. 3, we evaluate how $K$ and $\lambda_{div}$ affects our model learning. We can observe that the performance continues to grow until $K = 12$ , which means it is sufficient to mine 12 semantic patterns of mitochondria. And $\lambda_{div}$ controls the relative importance of the diversity loss, our model achieves much better performance when $\lambda_{div} = 0.05$ . + +# 4.5. Vasualization + +Visualization of Predictions. To further analyze and understand the proposed method, we visualize a series of segmentation results and prototype activation areas. As shown in Fig. 4, it can be noticed that other methods tend to incorrectly segment the non-target region (dyed in blue) or are unable to activate all the mitochondria (dyed in red). We deem the main reason is that numerous ambiguous pixels inherent in EM images severely confuse the models designed for natural images. With the assistance of the RPiA, the negative effects of unreliable pixels are mostly eliminated. Besides, the RPrS assigns larger weights to the more reliable prototypes to obtain robust prototype-level supervision. Our DualRel generates more accurate prediction masks compared with other methods, which demonstrates the effectiveness of the cooperation of the above two modules. + +Visualization of Correlation Weights. To more intuitively demonstrate the unreliable pixels suppression ability endowed by RPiA, we conduct qualitative visualization on the correlation maps between the mito filters and the image features. As shown in Fig. 6, we find that in the absence of RPiA, pixel features that with distinct semantics sometimes share high similarity with specific prototypes as shown in the parts marked by the red box. We claim that this is detrimental because aggregating features that not align to the + +![](images/b43dc6aeacb1c34229c010edd9089fd2b7671b16b20ebb989eab9d2f83170356.jpg) + +![](images/6c7202ecdfe3cbc154af02f45e8ac8281a548106d32d2b0390c40a75156f7a59.jpg) + +![](images/5296b6424e7bfdd2aeaa5f5465a1355f7359eff62a1115e6dbbfafffc673d928.jpg) + +![](images/be6d04bd81b107cda4701982197eda5c3001f946631fce1aa03d2390edd61f72.jpg) + +![](images/1c166d5fe26271da0aa241b4a40ec4e427f1067ef9a5d02c114fa4c8cda92030.jpg) + +![](images/5454f6b37d16b8a7e493a70b4a948ae7781d6f2080bdbcfc83487209f5902312.jpg) + +![](images/f71fdf1812df3ec3d64c24efd699517c9225bce4c4a3a4433e24c5aad500ebbd.jpg) + +![](images/1b15e17d238abf61ff5da10a26240bbc8cf0c287b9fd15474344f1a145c0fe6b.jpg) + +![](images/1960a717a72eef3413cb7f2f8b4a6f909c77ea69c15cdb714061a4c3894db26e.jpg) + +![](images/94be2eb9f44ae25e32c5a2bc5d29d6da70ddd450e532472fe6d9cbc2beed2ff9.jpg) + +![](images/c4e805771a2cfcad670a6ce8fbaee5d731696eb29a1ef2dbf7f71b5e25e7ca00.jpg) + +![](images/fb124bc4d7da521890fd63a9eaa45b81ee6028e4386c0e1caed973377060c0a6.jpg) + +![](images/d837ee219f2fa3c23b36005c4eec1c111805363f30ab008bccaf52bcea4dadfe.jpg) + +![](images/4575864ca79b59fd1c57a1f83ad524fe181fb4a90a12eeec42f20eb4caff3c60.jpg) + +![](images/17b4045fa8e0fe49b7ca557297abc61d4a3db97f395d3cd47a24151d20ae7559.jpg) + +![](images/624f7811ae270c6955ffd93cea6ced9d6e221e793c4333c01649773959546e2e.jpg) + +![](images/8dd858b459e1d162ce09f64f3d0f563661433f09a3472cbf722017d735659e31.jpg) + +![](images/b3a0fb29e076499c1fe10e1c20b6f2572741bf0c137d0489afb8b0f4c674e321.jpg) + +![](images/ecfda17e63c8c18a7ebaa324bc460add5c4b65a6cef470c264910417088906d1.jpg) + +![](images/b3ecac303542e3a9b2eb6fde425297494566a71ace01deaaab108f303868acde.jpg) + +![](images/7e266bd369162387b9aaf4013f7999017b0cd4e33ff3640d02bc0371308d12ae.jpg) + +![](images/7203274d09ee01b0b728c020b838af2c8c3e4a543f382f267fd9b37b824d5a94.jpg) +EM Image + +![](images/31c3b1885834c6f807caeb6daaa828448fb5a1839e01b0a9ea7910311738f393.jpg) +Ground Truth + +![](images/a785f18a70d1468ea06da3a5cbebd1f57fd485d529d6709811019f396ef9bf24.jpg) +MT + +![](images/cc6c31c7aefcf099ff1229924ea21c1b5ca020f2236b1daab68ec6285e19795a.jpg) +CCT +Figure 4. Qualitative results of the proposed DualRel and other methods under 1/8 ratio on Lucchi. + +![](images/e142374309f2c5c34cd1452c8694476428bafb859692df88f7af995beee31352.jpg) +GCT + +![](images/aa996a14a3c5acd63510ef671fbe6bc82770055149fe3f5383a6d7f071a0f510.jpg) +CPS + +![](images/65c7ca94e4b04131dc0f73f42889a0cd264d1231f24eab5be053bca2006195fd.jpg) +Ours + +![](images/25967433531ebf64aabfbf4afac8a33ba00614866f5cf019bd4db178a95717bc.jpg) +EM Image +Figure 5. The visualization of the reliability of prototypes and its corresponding activation maps. + +![](images/26ec4cfc77d2138c8cd6ccd5f64e8b372f8959f864cc9a60433cf12d98e8ece8.jpg) +Ground Truth + +![](images/d34fc3a86493b3689ad8cfc85ad4fe4676b431d65cfd9c99db7b585578bc2bae.jpg) +Reliability=0.53 + +![](images/b14c20ff71b0d54153efd44a35086ffa3790f3506f449ecd1d55f7c652a93474.jpg) +Reliability=0.91 + +![](images/71d745b71873dc00c62c12c6948cb4061859dab35f2c38230dbb664f4b644ced.jpg) +Background Prototypes +Reliability=0.84 + +![](images/7298b05df8bd9a696d615902d15602fed9ffe5f5fe83a20b5410d3e186ee3600.jpg) +Reliability=0.32 + +![](images/3b86f9dbc1c46116bb0d59fd11380d47768cd9374ab2f50def3d6c6ea330f33d.jpg) +Figure 6. Visualization of the pixel-prototype correlation weights. + +![](images/5881450b17a6269f37771fb2e961c9d299373422c0939bbef373cee64e7c4813.jpg) + +prototypes with large weights will lead to confusion. The second row presents the results with RPiA, we observe a significant reduction in false activation, demonstrating the effectiveness of RPiA in suppressing false matches. + +Visualization of Reliability and Activation Maps. To vividly present the working mechanism of reliable prototype selection module (RPrS), we visualize the reliability of prototypes and its corresponding activation maps. As shown in Fig. 5, some prototypes with clear foreground or background semantic clues occupy larger weights (i.e., + +$4^{th}$ and $5^{th}$ columns), while some prototypes focusing on mitochondrial boundary patterns are assigned with smaller weights (i.e., $3^{rd}$ and $6^{th}$ columns). This is in line with the design idea of RPrS, that is, pursuing implicitly learning the reliability of each prototype in a data-driven way. In this case, the equivocal prototypes will be suppressed while the reliable ones are highlighted in the supervision signals. + +# 5. Conclusion + +In this paper, we rethink how to achieve effective semi-supervised mitochondria segmentation. We propose a novel end-to-end dual-reliable (DualRel) network, including a reliable pixel aggregation module and a reliable prototype selection module. Extensive experimental results demonstrate the effectiveness. This work is expected to open a new venue for future research in this field. + +# 6. Acknowledgments + +This work was partially supported by the National Nature Science Foundation of China (Grant 62022078, 62021001), National Defense Basic Scientific Research Program (Grant JCKY2022911B002). + +# References + +[1] Silvia Campello and Luca Scorrano. Mitochondrial shape changes: orchestrating cell pathophysiology. EMBO reports, 11(9):678-684, 2010. 1 +[2] Vincent Casser, Kai Kang, Hanspeter Pfister, and Daniel Haehn. Fast mitochondria detection for connectomics. In Medical Imaging with Deep Learning, pages 111-120. 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In Proceedings of the IEEE/CVF international conference on computer vision, pages 6023-6032, 2019. 3 +[37] Hongyi Zhang, Moustapha Cisse, Yann N Dauphin, and David Lopez-Paz. mixup: Beyond empirical risk minimization. arXiv preprint arXiv:1710.09412, 2017. 3 \ No newline at end of file diff --git a/2023/DualRel_ Semi-Supervised Mitochondria Segmentation From a Prototype Perspective/images.zip b/2023/DualRel_ Semi-Supervised Mitochondria Segmentation From a Prototype Perspective/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..9f435bcadbf023cf296a3ceef0db20e1373f3a22 --- /dev/null +++ b/2023/DualRel_ Semi-Supervised Mitochondria Segmentation From a Prototype Perspective/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:f59d30e219707b23332680939e317ac8f9f7d5457c6f7832d2e349baaa4716cf +size 571438 diff --git a/2023/DualRel_ Semi-Supervised Mitochondria Segmentation From a Prototype Perspective/layout.json b/2023/DualRel_ Semi-Supervised Mitochondria Segmentation From a Prototype Perspective/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..28ee5ffd857f51b65431b13b0086f43d9fe944a1 --- /dev/null +++ b/2023/DualRel_ Semi-Supervised Mitochondria Segmentation From a Prototype Perspective/layout.json @@ -0,0 +1,11171 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 110, + 68, + 484, + 105 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 68, + 484, + 105 + ], + "spans": [ + { + "bbox": [ + 110, + 68, + 484, + 105 + ], + "type": "text", + "content": "DualRel: Semi-Supervised Mitochondria Segmentation from A Prototype Perspective" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 73, + 114, + 516, + 174 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 73, + 114, + 516, + 174 + ], + "spans": [ + { + "bbox": [ + 73, + 114, + 516, + 174 + ], + "type": "text", + "content": "Huayu Mai" + }, + { + "bbox": [ + 73, + 114, + 516, + 174 + ], + "type": "inline_equation", + "content": "^{1*}" + }, + { + "bbox": [ + 73, + 114, + 516, + 174 + ], + "type": "text", + "content": " Rui Sun" + }, + { + "bbox": [ + 73, + 114, + 516, + 174 + ], + "type": "inline_equation", + "content": "^{1*}" + }, + { + "bbox": [ + 73, + 114, + 516, + 174 + ], + "type": "text", + "content": " Tianzhu Zhang" + }, + { + "bbox": [ + 73, + 114, + 516, + 174 + ], + "type": "inline_equation", + "content": "^{1,2,3\\dagger}" + }, + { + "bbox": [ + 73, + 114, + 516, + 174 + ], + "type": "text", + "content": " Zhiwei Xiong" + }, + { + "bbox": [ + 73, + 114, + 516, + 174 + ], + "type": "inline_equation", + "content": "^{1,2}" + }, + { + "bbox": [ + 73, + 114, + 516, + 174 + ], + "type": "text", + "content": " Feng Wu" + }, + { + "bbox": [ + 73, + 114, + 516, + 174 + ], + "type": "inline_equation", + "content": "^{1,2}" + }, + { + "bbox": [ + 73, + 114, + 516, + 174 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 73, + 114, + 516, + 174 + ], + "type": "text", + "content": "University of Science and Technology of China \n" + }, + { + "bbox": [ + 73, + 114, + 516, + 174 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 73, + 114, + 516, + 174 + ], + "type": "text", + "content": "Institute of Artificial Intelligence, Hefei Comprehensive National Science Center \n" + }, + { + "bbox": [ + 73, + 114, + 516, + 174 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 73, + 114, + 516, + 174 + ], + "type": "text", + "content": "Deep Space Exploration Lab" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 93, + 174, + 496, + 186 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 174, + 496, + 186 + ], + "spans": [ + { + "bbox": [ + 93, + 174, + 496, + 186 + ], + "type": "text", + "content": "{mai556, issunrui}@mail.ustc.edu.cn, {tzzhang, zwxiong, fengwu}@ustc.edu.cn" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 213, + 192, + 227 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 213, + 192, + 227 + ], + "spans": [ + { + "bbox": [ + 143, + 213, + 192, + 227 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 239, + 290, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 239, + 290, + 539 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 290, + 539 + ], + "type": "text", + "content": "Automatic mitochondria segmentation enjoys great popularity with the development of deep learning. 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Illustration of our motivation. (a) shows the confusion map and density (i.e., the expected inverse confidence per pixel) of mitochondrial and natural images. (b) shows the unreliability caused by direct pairwise prototype-pixel correlation that is conditioned only on visual similarity. (c) shows how to construct pixel-reference correlation to rectify the direct pairwise correlation in a referential correlation manner." + } + ] + } + ], + "index": 31, + "angle": 0, + "type": "image_caption" + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 473, + 546, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 473, + 546, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 473, + 546, + 581 + ], + "type": "text", + "content": "from high-resolution electron microscopy (EM) images and make conspicuous achievements. However, their flexibility and scalability are limited in the actual deployment because the numerous cluttered irrelevant organelles that require labor-intensive manual discrimination and gathering by experienced domain experts [10, 21]. Therefore, we begin to turn attention to semi-supervised segmentation with the assumption that enormous unlabeled data is accessible, aiming to alleviate the data-hungry issue." + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "content": "Semi-supervised segmentation enjoys great popularity in the field of natural images, and representative works such as CPS [3], which imposes pixel-level consistency regularization and establishes state-of-the-art performance. It naturally comes into mind to directly apply a CPS-like method to semi-supervised mitochondria segmentation. However, there exist a large gap between mitochondrial and natural images. As shown in Fig. 1 (a), we observe that the confusion density (i.e., the expected inverse confidence per pixel) in mitochondrial images significantly surpasses counterpart in natural images, implying that directly employing" + } + ] + } + ], + "index": 33 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 693, + 124, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 693, + 124, + 703 + ], + "spans": [ + { + "bbox": [ + 58, + 693, + 124, + 703 + ], + "type": "text", + "content": "*Equal contribution" + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 59, + 703, + 134, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 703, + 134, + 712 + ], + "spans": [ + { + "bbox": [ + 59, + 703, + 134, + 712 + ], + "type": "text", + "content": "† Corresponding author" + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19617" + } + ] + } + ], + "index": 37 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 168 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 168 + ], + "type": "text", + "content": "pixel-level consistency regularization as supervision signals on mitochondrial images will inevitably increase the risk of unreliability. The most intuitive example is that there exist considerable boundary regions in mitochondrial images, and the segmentation network is naturally equivocal for these regions, as proven in [15]. In this case, some relatively small mitochondria are easily overwhelmed by this ambiguity, leading to sub-optimal results." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 171, + 288, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 171, + 288, + 518 + ], + "spans": [ + { + "bbox": [ + 46, + 171, + 288, + 518 + ], + "type": "text", + "content": "In order to seek more reliable supervision signals to alleviate the undependable problem caused by pixel-level supervision, we draw inspiration from the inbuilt resistance to noisy pixels of prototypes and construct more robust and reliable prototype-level supervision. To achieve this goal, two issues need to be considered. (1) Unreliable pixels. Considering the cluttered background caused by under/overexposure and out-of-focus problems during EM imaging, the prototype inevitably absorbs unreliable pixels (i.e., heterogeneous semantic clues) during the interaction of corresponding pixels with a suitable pattern. We argue that directly forcing pairwise prototype-pixel correlation is primarily at blame. As shown in Fig. 1 (b), due to the foreground-background ambiguity, the foreground prototype " + }, + { + "bbox": [ + 46, + 171, + 288, + 518 + ], + "type": "inline_equation", + "content": "f_{1}" + }, + { + "bbox": [ + 46, + 171, + 288, + 518 + ], + "type": "text", + "content": " is erroneously closer to " + }, + { + "bbox": [ + 46, + 171, + 288, + 518 + ], + "type": "inline_equation", + "content": "p_{2}" + }, + { + "bbox": [ + 46, + 171, + 288, + 518 + ], + "type": "text", + "content": " located in the background than counterpart point " + }, + { + "bbox": [ + 46, + 171, + 288, + 518 + ], + "type": "inline_equation", + "content": "p_{1}" + }, + { + "bbox": [ + 46, + 171, + 288, + 518 + ], + "type": "text", + "content": " with similar pattern situated in the foreground. Therefore, it is highly desirable to suppress the unreliable pixels caused by the direct pairwise prototype-pixel correlation that is only conditioned on visual similarity during prototype learning process. (2) Unreliable prototypes. Intuitively, not all prototypes are equivalent for building prototype-level consistency regularization. For example, for a prototype that focuses on mitochondrial boundary patterns, the inherent unreliability of the pixels belonging to these patterns, as discussed above, will also taint the purity of this prototype with equivocality. Therefore, the prototype-level supervision signals should be further optimized to guarantee that the true reliable prototypes enjoy higher weights." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "text", + "content": "To mitigate the above issues, we rethink how to achieve effective consistency regularization for semi-supervised mitochondria segmentation, from the perspective of reliable prototype-level supervision. We propose a Dual-Reliable (DualRel) network including a reliable pixel aggregation module and a reliable prototype selection module. In the reliable pixel aggregation module (RPIA), to learn the prototypes well without any explicit supervision, we carefully design the referential correlation to rectify the direct pairwise correlation, enabling the prototype absorb counterpart reliable pixels with the same semantic pattern during the interaction with the pixels. The main idea is, for each pixel/prototype, we can obtain the referential correlation (i.e., a likelihood vector) by comparing this pixel/prototype with a set of reliable reference points. In essence, the referential correlation reflects the consensus among reliable ref" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 304, + 72, + 545, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 347 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 347 + ], + "type": "text", + "content": "ference points with a broader receptive field and thus it encodes the relative semantic comparability of the reference points that can be relied upon, which is from a different perspective than the absolute pairwise prototype-pixel correlation. Intuitively, each pair of true prototype-pixel correlation (e.g., the " + }, + { + "bbox": [ + 304, + 72, + 545, + 347 + ], + "type": "inline_equation", + "content": "f_{1} - p_{1}" + }, + { + "bbox": [ + 304, + 72, + 545, + 347 + ], + "type": "text", + "content": " pair in Fig. 1 (c) derived from the prototypes and mitochondria images should be not only visually similar to each other (i.e., high direct pairwise prototype-pixel correlation), but also similar to any other reference point (i.e., similar referential correlation pair). Moreover, we assemble referential correlation into the cross-attention mechanism with the ability to capture long-range dependencies. In this case, the relatively equivocal pixels (e.g., the " + }, + { + "bbox": [ + 304, + 72, + 545, + 347 + ], + "type": "inline_equation", + "content": "f_{1} - p_{2}" + }, + { + "bbox": [ + 304, + 72, + 545, + 347 + ], + "type": "text", + "content": " pair in Fig. 1 (c) will be suppressed while the reliable ones are highlighted to reduce the correspondence noise. In the reliable prototype selection module (RPrS), in order to further evaluate the reliability of prototypes in constructing prototype-level consistency regularization, we draw inspiration from bayesian deep learning [12] and devise a reliability-aware consistency loss to pursue implicitly learn the reliability about each prototype in a data-driven way. In this way, the equivocal prototypes will be suppressed while the reliable ones are highlighted in the supervision signals." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 348, + 545, + 576 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 348, + 545, + 576 + ], + "spans": [ + { + "bbox": [ + 304, + 348, + 545, + 576 + ], + "type": "text", + "content": "In this work, our contributions can be concluded as follows: (1) To the best of our knowledge, this is the first work to rethink how to achieve effective consistency regularization for semi-supervised mitochondria segmentation, from the perspective of reliable prototype-level supervision. We analyze the gap between mitochondrial images and natural images, hoping our work will provide some insight for researchers in this field. (2) We propose a dual-reliable (DualRel) network in a unified framework. Specifically, we design the reliable pixel aggregation module to rectify the direct pairwise correlation, the reliable prototype selection module to further evaluate the reliability of prototypes in constructing prototype-level consistency regularization. (3) Extensive experimental results on three challenging benchmarks demonstrate that our method performs favorably against state-of-the-art semi-supervised segmentation methods. Importantly, with extremely few samples used for training, DualRel is also on par with current state-of-the-art fully supervised methods." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 589, + 392, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 589, + 392, + 601 + ], + "spans": [ + { + "bbox": [ + 306, + 589, + 392, + 601 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 610, + 460, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 610, + 460, + 623 + ], + "spans": [ + { + "bbox": [ + 306, + 610, + 460, + 623 + ], + "type": "text", + "content": "2.1. Mitochondria Segmentation" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": "Segmenting mitochondria in EM images is vital for researchers to explore cellular functions and subcellular activities. Rather than traditional methods utilizing hand-crafted features [14, 18, 27], DL-based networks have shown significant performance improvement on mitochondria segmentation. The pioneering work Lucchi et al. [19] design a deep neural network based on supervoxels to model shapes of mi" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "19618" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": "tochondria. Oztel et al. [26] propose a deep convolutional neural network with a sliding window strategy and post-processing steps to boost the performance. Wei et al. [35] introduce a 3D U-Net based network and release a new challenging dataset containing mitochondria images with higher resolution. However, all previous methods only focus on the fully-supervised training, which require a large amount of labeled data. In this work, we introduce semi-supervised learning into mitochondria segmentation, aiming to alleviate the data-hungry issue." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 198, + 258, + 211 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 198, + 258, + 211 + ], + "spans": [ + { + "bbox": [ + 47, + 198, + 258, + 211 + ], + "type": "text", + "content": "2.2. Semi-supervised Semantic Segmentation" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 217, + 289, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 217, + 289, + 479 + ], + "spans": [ + { + "bbox": [ + 46, + 217, + 289, + 479 + ], + "type": "text", + "content": "With the development of semi-supervised learning, various kinds of semi-supervised semantic segmentation algorithms have been proposed. GAN-based methods [9,22,29] try to synthesize additional training data or generate the pseudo labels for unlabeled data by using adversarial loss. Recently, the consistency regularization [6,23,34] has been intensely studied in semi-supervised semantic segmentation. The main idea of this type of approach is that the intermediate features or predictions should maintain consistency across different semantic-preserving transformations on the input or different network initialization [36, 37]. MT [31] is a representative work that first adopts the teacher network to guide the learning of the student network in semi-supervised semantic segmentation. Alternatively, CCT [25] introduces dual independent models to supervise each other with the soft probability output, while CPS [3] is supervised with hard pseudo segmentation maps. GCT [11] employs two segmentation networks with the same structure but different weight initialization and enforces the consistency between the predictions. However, the above pixel-level supervision-based methods perform poorly on semi-supervised mitochondria tasks." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 489, + 103, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 489, + 103, + 502 + ], + "spans": [ + { + "bbox": [ + 47, + 489, + 103, + 502 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 509, + 287, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 509, + 287, + 582 + ], + "spans": [ + { + "bbox": [ + 46, + 509, + 287, + 582 + ], + "type": "text", + "content": "In this section, we first formulate the semi-supervised mitochondria segmentation task and present the overview of the proposed DualRel. Then we describe the details of the reliable pixel aggregation module (RPiA) and reliable prototype selection module (RPrs) of DualRel. Finally, the training and inference procedure are discussed." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 587, + 115, + 598 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 587, + 115, + 598 + ], + "spans": [ + { + "bbox": [ + 47, + 587, + 115, + 598 + ], + "type": "text", + "content": "3.1. Overview" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": "In semi-supervised mitochondria segmentation task, we wish to train a segmentation network with training data " + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "inline_equation", + "content": "D^{L}\\cup D^{U}" + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": ". In the labeled set " + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "inline_equation", + "content": "D^{L} = \\{\\mathbf{I}_{i}^{L},\\mathbf{Y}_{i}\\}_{i = 0}^{N}" + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": ", each image is associated with a ground truth label " + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}\\in \\{0,1\\}^{H\\times W}" + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": " where 1 denotes foreground while 0 denotes background. In the unlabeled set " + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "inline_equation", + "content": "D^{U} = \\{\\mathbf{I}_{j}^{U}\\}_{j = 0}^{M}" + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": " images are provided without ground truth. Given an EM image " + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{I}" + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": " (for brevity, we omit the superscript " + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "inline_equation", + "content": "L / U" + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": " and subscript " + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "inline_equation", + "content": "i / j" + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": "), let " + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{X}\\in \\mathbb{R}^{h\\times w\\times D}" + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": " denotes the feature map extracted from" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 545, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 252 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 252 + ], + "type": "text", + "content": "feature extractor (e.g., ResNet50 [8]), where " + }, + { + "bbox": [ + 304, + 72, + 545, + 252 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 304, + 72, + 545, + 252 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 72, + 545, + 252 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 72, + 545, + 252 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 545, + 252 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 72, + 545, + 252 + ], + "type": "text", + "content": " denote the height, width and channel number of the feature map, respectively. Subsequently, the feature map " + }, + { + "bbox": [ + 304, + 72, + 545, + 252 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 304, + 72, + 545, + 252 + ], + "type": "text", + "content": " is fed into the upsampling module (e.g., U-Net [28]) which outputs pixel embedding " + }, + { + "bbox": [ + 304, + 72, + 545, + 252 + ], + "type": "inline_equation", + "content": "\\mathbf{E} \\in \\mathbb{R}^{H \\times W \\times C}" + }, + { + "bbox": [ + 304, + 72, + 545, + 252 + ], + "type": "text", + "content": " with the same spatial scale as original input image. As illustrated in Fig. 2, the proposed DualRel includes two branches of feature extractor and upsampling module, which are of the same structure but different weight initialization. Such a two-branch structure is devised to construct consistency supervision signals for unlabeled data, which is a popular paradigm in semi-supervised learning. Besides, a reliable pixel aggregation module and a reliable prototype selection module are introduced to construct prototype-level consistency regularization for semi-supervised mitochondria segmentation." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 258, + 454, + 270 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 258, + 454, + 270 + ], + "spans": [ + { + "bbox": [ + 305, + 258, + 454, + 270 + ], + "type": "text", + "content": "3.2. Reliable Pixel Aggregation" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 276, + 545, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 276, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 304, + 276, + 545, + 361 + ], + "type": "text", + "content": "To construct prototype-level supervision, we prepend a set of learnable embeddings " + }, + { + "bbox": [ + 304, + 276, + 545, + 361 + ], + "type": "inline_equation", + "content": "\\mathbf{F} = \\{\\mathbf{f}_k\\}_{k=1}^K" + }, + { + "bbox": [ + 304, + 276, + 545, + 361 + ], + "type": "text", + "content": " (referred to as mito filters). Each filter " + }, + { + "bbox": [ + 304, + 276, + 545, + 361 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_k" + }, + { + "bbox": [ + 304, + 276, + 545, + 361 + ], + "type": "text", + "content": " is represented as a " + }, + { + "bbox": [ + 304, + 276, + 545, + 361 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 276, + 545, + 361 + ], + "type": "text", + "content": "-dimension vector to interact with the feature map " + }, + { + "bbox": [ + 304, + 276, + 545, + 361 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 304, + 276, + 545, + 361 + ], + "type": "text", + "content": " and absorb counterpart reliable pixels with the same semantic pattern. Then, we adopt a cross-attention mechanism [32] to realize the interaction and obtain mito features " + }, + { + "bbox": [ + 304, + 276, + 545, + 361 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathbf{F}} = \\{\\widetilde{\\mathbf{f}}_k\\}_{k=1}^K" + }, + { + "bbox": [ + 304, + 276, + 545, + 361 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 361, + 545, + 446 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 361, + 545, + 446 + ], + "spans": [ + { + "bbox": [ + 304, + 361, + 545, + 446 + ], + "type": "text", + "content": "Since the cross-attention requires a 1D sequence as the input, we first utilize a " + }, + { + "bbox": [ + 304, + 361, + 545, + 446 + ], + "type": "inline_equation", + "content": "1\\times 1" + }, + { + "bbox": [ + 304, + 361, + 545, + 446 + ], + "type": "text", + "content": " convolution kernel to reduce the channel number of the feature map " + }, + { + "bbox": [ + 304, + 361, + 545, + 446 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 304, + 361, + 545, + 446 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 304, + 361, + 545, + 446 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 361, + 545, + 446 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 361, + 545, + 446 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 361, + 545, + 446 + ], + "type": "text", + "content": ", and then flatten the spatial dimensions to produce the feature sequence " + }, + { + "bbox": [ + 304, + 361, + 545, + 446 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathbf{X}} = \\{\\widetilde{\\mathbf{x}}_i\\}_{i = 1}^{hw}\\in \\mathbb{R}^{hw\\times C}" + }, + { + "bbox": [ + 304, + 361, + 545, + 446 + ], + "type": "text", + "content": ". Specifically, we denote mito filters " + }, + { + "bbox": [ + 304, + 361, + 545, + 446 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{f}_k\\}_{k = 1}^K" + }, + { + "bbox": [ + 304, + 361, + 545, + 446 + ], + "type": "text", + "content": " as queries, the feature map " + }, + { + "bbox": [ + 304, + 361, + 545, + 446 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathbf{X}}" + }, + { + "bbox": [ + 304, + 361, + 545, + 446 + ], + "type": "text", + "content": " as keys and values. Formally," + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 340, + 451, + 545, + 466 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 340, + 451, + 545, + 466 + ], + "spans": [ + { + "bbox": [ + 340, + 451, + 545, + 466 + ], + "type": "interline_equation", + "content": "\\mathbf {q} _ {k} = \\mathbf {f} _ {k} \\mathbf {W} ^ {Q}, \\mathbf {k} _ {i} = \\widetilde {\\mathbf {x}} _ {i} \\mathbf {W} ^ {K}, \\mathbf {v} _ {i} = \\widetilde {\\mathbf {x}} _ {i} \\mathbf {W} ^ {V}, \\tag {1}", + "image_path": "d31610adfe58cbbcee71e657a57298f4c45efa70e507b53e845c8db72a47dc41.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 470, + 545, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 470, + 545, + 519 + ], + "spans": [ + { + "bbox": [ + 304, + 470, + 545, + 519 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 470, + 545, + 519 + ], + "type": "inline_equation", + "content": "\\mathbf{W}^Q, \\mathbf{W}^K, \\mathbf{W}^V \\in \\mathbb{R}^{C \\times C}" + }, + { + "bbox": [ + 304, + 470, + 545, + 519 + ], + "type": "text", + "content": " are linear projections, " + }, + { + "bbox": [ + 304, + 470, + 545, + 519 + ], + "type": "inline_equation", + "content": "k = 1, 2, \\ldots, K" + }, + { + "bbox": [ + 304, + 470, + 545, + 519 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 470, + 545, + 519 + ], + "type": "inline_equation", + "content": "i = 1, 2, \\ldots, hw" + }, + { + "bbox": [ + 304, + 470, + 545, + 519 + ], + "type": "text", + "content": ". Then the pairwise correlation " + }, + { + "bbox": [ + 304, + 470, + 545, + 519 + ], + "type": "inline_equation", + "content": "s_{k,i}" + }, + { + "bbox": [ + 304, + 470, + 545, + 519 + ], + "type": "text", + "content": " between each query " + }, + { + "bbox": [ + 304, + 470, + 545, + 519 + ], + "type": "inline_equation", + "content": "\\mathbf{q}_k" + }, + { + "bbox": [ + 304, + 470, + 545, + 519 + ], + "type": "text", + "content": " and the " + }, + { + "bbox": [ + 304, + 470, + 545, + 519 + ], + "type": "inline_equation", + "content": "i^{th}" + }, + { + "bbox": [ + 304, + 470, + 545, + 519 + ], + "type": "text", + "content": " key " + }, + { + "bbox": [ + 304, + 470, + 545, + 519 + ], + "type": "inline_equation", + "content": "\\mathbf{k}_i" + }, + { + "bbox": [ + 304, + 470, + 545, + 519 + ], + "type": "text", + "content": " is given as" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 345, + 525, + 545, + 555 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 525, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 345, + 525, + 545, + 555 + ], + "type": "interline_equation", + "content": "s _ {k, i} = \\frac {\\exp \\left(\\beta_ {k , i}\\right)}{\\sum_ {j = 1} ^ {h w} \\exp \\left(\\beta_ {k , j}\\right)}, \\beta_ {k, i} = \\frac {\\mathbf {q} _ {k} \\mathbf {k} _ {i} ^ {\\top}}{\\sqrt {C}}, \\tag {2}", + "image_path": "f86247d8458fcbc167c975d0d612d8acd3ad7af67395b7e0d9dc829ca6870919.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 562, + 545, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 562, + 545, + 586 + ], + "spans": [ + { + "bbox": [ + 304, + 562, + 545, + 586 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 562, + 545, + 586 + ], + "type": "inline_equation", + "content": "\\sqrt{C}" + }, + { + "bbox": [ + 304, + 562, + 545, + 586 + ], + "type": "text", + "content": " is a scaling factor to stabilize training and " + }, + { + "bbox": [ + 304, + 562, + 545, + 586 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 562, + 545, + 586 + ], + "type": "text", + "content": " refers to the transpose operation." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 587, + 545, + 683 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 587, + 545, + 683 + ], + "spans": [ + { + "bbox": [ + 304, + 587, + 545, + 683 + ], + "type": "text", + "content": "Due to the susceptibility of pairwise filter-pixel correlation, the mito filter inevitably absorbs unreliable pixels during the interaction. We carefully design the referential correlation assembled in cross-attention to mitigate such issue. Specifically, we define " + }, + { + "bbox": [ + 304, + 587, + 545, + 683 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 587, + 545, + 683 + ], + "type": "text", + "content": " reference points " + }, + { + "bbox": [ + 304, + 587, + 545, + 683 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathbf{X}}^R = \\{\\widetilde{\\mathbf{x}}_n^R\\}_{n=1}^N \\in \\mathbb{R}^{N \\times C}" + }, + { + "bbox": [ + 304, + 587, + 545, + 683 + ], + "type": "text", + "content": " (detailed in the supplementary material). Respectively calculating the filter-reference correlation and the pixel-reference correlation as same as Eq. (2):" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 342, + 688, + 545, + 717 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 342, + 688, + 545, + 717 + ], + "spans": [ + { + "bbox": [ + 342, + 688, + 545, + 717 + ], + "type": "interline_equation", + "content": "\\mathbf {S} _ {k} ^ {F R} = \\operatorname {s o f t m a x} (\\frac {\\left(\\mathbf {f} _ {k} \\mathbf {W} ^ {Q}\\right) \\left(\\widetilde {\\mathbf {X}} ^ {R} \\mathbf {W} ^ {K}\\right) ^ {\\intercal}}{\\sqrt {C}}), \\tag {3}", + "image_path": "1b70278aeb2c24ed539f7ab136a95e00c203d5a6a66fb89018a37038a36cc9d3.jpg" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19619" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 75, + 71, + 521, + 266 + ], + "blocks": [ + { + "bbox": [ + 75, + 71, + 521, + 266 + ], + "lines": [ + { + "bbox": [ + 75, + 71, + 521, + 266 + ], + "spans": [ + { + "bbox": [ + 75, + 71, + 521, + 266 + ], + "type": "image", + "image_path": "748fea748352817b86ef22f93b993611704d6d1b3994c83598ddcae6b0830ab6.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 275, + 547, + 309 + ], + "lines": [ + { + "bbox": [ + 46, + 275, + 547, + 309 + ], + "spans": [ + { + "bbox": [ + 46, + 275, + 547, + 309 + ], + "type": "text", + "content": "Figure 2. Illustration of the proposed DualRel. DualRel is mainly composed of a reliable pixel aggregation module to rectify the direct pairwise correlation, and a reliable prototype selection module responsible for further evaluating the reliability of prototypes in constructing prototype-level consistency regularization. \"GAP\" represents a global average pooling layer [16] and \"Merge\" is described in Sec. 3.4." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 83, + 327, + 287, + 355 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 327, + 287, + 355 + ], + "spans": [ + { + "bbox": [ + 83, + 327, + 287, + 355 + ], + "type": "interline_equation", + "content": "\\mathbf {S} _ {i} ^ {P R} = \\operatorname {s o f t m a x} \\left(\\frac {\\left(\\widetilde {\\mathbf {x}} _ {i} \\mathbf {W} ^ {Q}\\right) \\left(\\widetilde {\\mathbf {X}} ^ {R} \\mathbf {W} ^ {K}\\right) ^ {\\top}}{\\sqrt {C}}\\right), \\tag {4}", + "image_path": "a15cb70f2f4ec195a53dcdb0a0d38d892b62e2fe43efca3388b98ee06d67b693.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 357, + 287, + 395 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 357, + 287, + 395 + ], + "spans": [ + { + "bbox": [ + 47, + 357, + 287, + 395 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 357, + 287, + 395 + ], + "type": "inline_equation", + "content": "\\mathbf{S}_k^{FR} \\in \\mathbb{R}^{1 \\times N}" + }, + { + "bbox": [ + 47, + 357, + 287, + 395 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 357, + 287, + 395 + ], + "type": "inline_equation", + "content": "\\mathbf{S}_i^{PR} \\in \\mathbb{R}^{1 \\times N}" + }, + { + "bbox": [ + 47, + 357, + 287, + 395 + ], + "type": "text", + "content": " are regarded as the referential correlation. And then, we get the similarity between the referential correlations by:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 124, + 400, + 287, + 416 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 124, + 400, + 287, + 416 + ], + "spans": [ + { + "bbox": [ + 124, + 400, + 287, + 416 + ], + "type": "interline_equation", + "content": "c _ {k, i} = \\mathbf {S} _ {k} ^ {F R} \\left(\\mathbf {S} _ {i} ^ {P R}\\right) ^ {\\top}, \\tag {5}", + "image_path": "5df113444d878864ede57db4b430d974dd5d79f22bf791c741823f0dd0e922ae.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 422, + 268, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 422, + 268, + 434 + ], + "spans": [ + { + "bbox": [ + 47, + 422, + 268, + 434 + ], + "type": "text", + "content": "which is used to rectify the direct pairwise correlation." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 434, + 287, + 458 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 434, + 287, + 458 + ], + "spans": [ + { + "bbox": [ + 47, + 434, + 287, + 458 + ], + "type": "text", + "content": "Then, the mito features " + }, + { + "bbox": [ + 47, + 434, + 287, + 458 + ], + "type": "inline_equation", + "content": "\\{\\widetilde{\\mathbf{f}}_k\\}_{k = 1}^K" + }, + { + "bbox": [ + 47, + 434, + 287, + 458 + ], + "type": "text", + "content": " can be got by blending values with the rectified correlations:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 117, + 464, + 287, + 496 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 117, + 464, + 287, + 496 + ], + "spans": [ + { + "bbox": [ + 117, + 464, + 287, + 496 + ], + "type": "interline_equation", + "content": "\\widetilde {\\mathbf {f}} _ {k} = \\sum_ {i} ^ {h w} c _ {k, i} \\cdot s _ {k, i} \\cdot \\mathbf {v} _ {i}, \\tag {6}", + "image_path": "f1e980b11c120049375fe3d157d1ff8ce555d395997b8175c538cba6511e66e2.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 502, + 203, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 502, + 203, + 514 + ], + "spans": [ + { + "bbox": [ + 47, + 502, + 203, + 514 + ], + "type": "text", + "content": "3.3. Reliable Prototype Selection" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 521, + 287, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 521, + 287, + 569 + ], + "spans": [ + { + "bbox": [ + 47, + 521, + 287, + 569 + ], + "type": "text", + "content": "Before describing the reliable prototype selection mechanism, we first formulate the process of obtaining the mito prototypes " + }, + { + "bbox": [ + 47, + 521, + 287, + 569 + ], + "type": "inline_equation", + "content": "\\mathbf{P} = \\{\\mathbf{p}_k\\}_{k=1}^K" + }, + { + "bbox": [ + 47, + 521, + 287, + 569 + ], + "type": "text", + "content": ". First, calculating the activation maps " + }, + { + "bbox": [ + 47, + 521, + 287, + 569 + ], + "type": "inline_equation", + "content": "\\mathbf{A} = \\{\\mathbf{A}_k\\}_{k=1}^K \\in \\mathbb{R}^{K \\times H \\times W}" + }, + { + "bbox": [ + 47, + 521, + 287, + 569 + ], + "type": "text", + "content": " by:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 119, + 574, + 287, + 588 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 119, + 574, + 287, + 588 + ], + "spans": [ + { + "bbox": [ + 119, + 574, + 287, + 588 + ], + "type": "interline_equation", + "content": "\\mathbf {A} _ {k} = \\operatorname {s i g m o i d} \\left(\\mathbf {f} _ {k} \\mathbf {E} ^ {\\top}\\right), \\tag {7}", + "image_path": "8519afa87c6d5042fbdce3568616e7a99b8eecd4879fec33af6dfdf2938e7e98.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 595, + 287, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 595, + 287, + 643 + ], + "spans": [ + { + "bbox": [ + 47, + 595, + 287, + 643 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 595, + 287, + 643 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_k" + }, + { + "bbox": [ + 47, + 595, + 287, + 643 + ], + "type": "text", + "content": " denotes the activation map of the " + }, + { + "bbox": [ + 47, + 595, + 287, + 643 + ], + "type": "inline_equation", + "content": "k^{th}" + }, + { + "bbox": [ + 47, + 595, + 287, + 643 + ], + "type": "text", + "content": " mito feature on pixel embedding " + }, + { + "bbox": [ + 47, + 595, + 287, + 643 + ], + "type": "inline_equation", + "content": "\\mathbf{E}" + }, + { + "bbox": [ + 47, + 595, + 287, + 643 + ], + "type": "text", + "content": ". Then, based on the activation maps " + }, + { + "bbox": [ + 47, + 595, + 287, + 643 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 47, + 595, + 287, + 643 + ], + "type": "text", + "content": ", we generate mito prototypes " + }, + { + "bbox": [ + 47, + 595, + 287, + 643 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{p}_k\\}_{k=1}^K" + }, + { + "bbox": [ + 47, + 595, + 287, + 643 + ], + "type": "text", + "content": " by global average pooling (GAP):" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 98, + 649, + 287, + 683 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 98, + 649, + 287, + 683 + ], + "spans": [ + { + "bbox": [ + 98, + 649, + 287, + 683 + ], + "type": "interline_equation", + "content": "\\mathbf {p} _ {k} = \\frac {1}{H W} \\sum_ {i = 1} ^ {H} \\sum_ {j = 1} ^ {W} \\mathbf {A} _ {k, i, j} \\cdot \\mathbf {E} _ {i, j}. \\tag {8}", + "image_path": "634861a4b5e2a84c5771de7f4c52135d4c33b94d3fca9ebcf9007cfae1ed5638.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "Intuitively, not all prototypes are equivalent for building prototype-level consistency regularization. In order to" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 329, + 545, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 329, + 545, + 441 + ], + "spans": [ + { + "bbox": [ + 304, + 329, + 545, + 441 + ], + "type": "text", + "content": "further evaluate the reliability of prototypes in constructing prototype-level consistency regularization, we devise a reliability-aware consistency loss to pursue implicitly learn the reliability about each prototype in a data-driven way. Firstly, we estimate the reliability " + }, + { + "bbox": [ + 304, + 329, + 545, + 441 + ], + "type": "inline_equation", + "content": "\\mathbf{R} = \\{r_k\\}_{k=1}^K" + }, + { + "bbox": [ + 304, + 329, + 545, + 441 + ], + "type": "text", + "content": " for each prototype. In specific, we concatenate the mito features " + }, + { + "bbox": [ + 304, + 329, + 545, + 441 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathbf{f}}_k^1" + }, + { + "bbox": [ + 304, + 329, + 545, + 441 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 329, + 545, + 441 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathbf{f}}_k^2" + }, + { + "bbox": [ + 304, + 329, + 545, + 441 + ], + "type": "text", + "content": " (the superscript denotes which baranch the mito features from) in channel dimension and feed them into a two layers MLP followed by the sigmoid function, as in Eq. (9):" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 348, + 448, + 545, + 464 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 448, + 545, + 464 + ], + "spans": [ + { + "bbox": [ + 348, + 448, + 545, + 464 + ], + "type": "interline_equation", + "content": "r _ {k} = \\operatorname {s i g m o i d} \\left(\\operatorname {M L P} \\left(\\operatorname {c o n c a t} \\left(\\widetilde {\\mathbf {f}} _ {k} ^ {1}, \\widetilde {\\mathbf {f}} _ {k} ^ {2}\\right)\\right). \\right. \\tag {9}", + "image_path": "fa0f9acfea8d8ef2bd2ef23962f0ee65b1211eb261144ede79c7a5c9e4f41c1d.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 471, + 545, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 471, + 545, + 519 + ], + "spans": [ + { + "bbox": [ + 304, + 471, + 545, + 519 + ], + "type": "text", + "content": "In order to guarantee that the true reliable prototypes enjoy higher weights and the equivocal ones are suppressed, we regard the " + }, + { + "bbox": [ + 304, + 471, + 545, + 519 + ], + "type": "inline_equation", + "content": "\\mathbf{R}" + }, + { + "bbox": [ + 304, + 471, + 545, + 519 + ], + "type": "text", + "content": " as a attenuation factor and get the reliable prototype consistency loss as:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 318, + 525, + 545, + 559 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 525, + 545, + 559 + ], + "spans": [ + { + "bbox": [ + 318, + 525, + 545, + 559 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {r p c} = \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\left(e ^ {1 - \\frac {1}{r _ {k}}} \\times L _ {2} \\left(\\mathbf {p} _ {k} ^ {1}, \\mathbf {p} _ {k} ^ {2}\\right) - \\lambda \\times r _ {k}\\right), \\tag {10}", + "image_path": "f2ef015181a9c7d0bb85f588ab87eb9c887835eeaba4fc8ff214548060ccd3a8.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 566, + 545, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 566, + 545, + 601 + ], + "spans": [ + { + "bbox": [ + 304, + 566, + 545, + 601 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 566, + 545, + 601 + ], + "type": "inline_equation", + "content": "L_{2}(\\cdot)" + }, + { + "bbox": [ + 304, + 566, + 545, + 601 + ], + "type": "text", + "content": " denotes L2 distance and the " + }, + { + "bbox": [ + 304, + 566, + 545, + 601 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 566, + 545, + 601 + ], + "type": "text", + "content": " is the weight for the regularization term preventing the estimated reliability from zero." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 609, + 435, + 622 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 609, + 435, + 622 + ], + "spans": [ + { + "bbox": [ + 306, + 609, + 435, + 622 + ], + "type": "text", + "content": "3.4. Training and inference" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 627, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 627, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 627, + 545, + 713 + ], + "type": "text", + "content": "For the follow-up training and inference, we need to merge the activation maps " + }, + { + "bbox": [ + 304, + 627, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 304, + 627, + 545, + 713 + ], + "type": "text", + "content": " into foreground-background probability map " + }, + { + "bbox": [ + 304, + 627, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathbf{Y}}\\in \\mathbb{R}^{2\\times H\\times W}" + }, + { + "bbox": [ + 304, + 627, + 545, + 713 + ], + "type": "text", + "content": ". In our implementation, we simply treat the summation of the first half of the activation maps as foreground probability (corresponding the summation of the " + }, + { + "bbox": [ + 304, + 627, + 545, + 713 + ], + "type": "inline_equation", + "content": "1^{st}" + }, + { + "bbox": [ + 304, + 627, + 545, + 713 + ], + "type": "text", + "content": " to the " + }, + { + "bbox": [ + 304, + 627, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\frac{K}{2}^{th}" + }, + { + "bbox": [ + 304, + 627, + 545, + 713 + ], + "type": "text", + "content": " activation maps), and the summation of the other half as background probability." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19620" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "text", + "content": "Besides, considering the large size and shape variation of the mitochondria, the mito prototype learning may focus on the same (e.g., the entire foreground), making the reliable prototype selection module degeneration. Therefore, we impose a diversity loss to expand the discrepancy among mito features. Formally," + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 98, + 152, + 287, + 186 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 98, + 152, + 287, + 186 + ], + "spans": [ + { + "bbox": [ + 98, + 152, + 287, + 186 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {d i v} = \\sum_ {i = 1} ^ {K} \\sum_ {j = 1, i \\neq j} ^ {K} \\left(\\frac {\\langle \\widetilde {\\mathbf {f}} _ {i} , \\widetilde {\\mathbf {f}} _ {j} \\rangle}{\\| \\widetilde {\\mathbf {f}} _ {i} \\| _ {2} \\| \\widetilde {\\mathbf {f}} _ {j} \\| _ {2}}\\right). \\tag {11}", + "image_path": "23b45a3acf46070289e92b6cff5b8b5d21c3bcd0c30153b3885a913c58f0c2da.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 193, + 287, + 242 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 193, + 287, + 242 + ], + "spans": [ + { + "bbox": [ + 46, + 193, + 287, + 242 + ], + "type": "text", + "content": "The intuition behind this loss is trivial. If the " + }, + { + "bbox": [ + 46, + 193, + 287, + 242 + ], + "type": "inline_equation", + "content": "i^{th}" + }, + { + "bbox": [ + 46, + 193, + 287, + 242 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 193, + 287, + 242 + ], + "type": "inline_equation", + "content": "j^{th}" + }, + { + "bbox": [ + 46, + 193, + 287, + 242 + ], + "type": "text", + "content": " features give a high attention to the same region, the " + }, + { + "bbox": [ + 46, + 193, + 287, + 242 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{div}" + }, + { + "bbox": [ + 46, + 193, + 287, + 242 + ], + "type": "text", + "content": " will be large and prompt these features to adjust themselves adaptively." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 242, + 287, + 268 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 242, + 287, + 268 + ], + "spans": [ + { + "bbox": [ + 47, + 242, + 287, + 268 + ], + "type": "text", + "content": "During Training, we calculate the supervise loss for the output prediction of two branch with labeled data by" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 66, + 274, + 287, + 306 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 274, + 287, + 306 + ], + "spans": [ + { + "bbox": [ + 66, + 274, + 287, + 306 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {s u p} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\left(\\operatorname {C E} \\left(\\widetilde {\\mathbf {Y}} ^ {\\mathbf {1}}, \\mathbf {Y}\\right) + \\operatorname {C E} \\left(\\widetilde {\\mathbf {Y}} ^ {\\mathbf {2}}, \\mathbf {Y}\\right)\\right), \\tag {12}", + "image_path": "f089ad137dba240fa8e07cc0ca2a01ab0fbb7c02cc232423abd89e920884d763.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 313, + 289, + 351 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 313, + 289, + 351 + ], + "spans": [ + { + "bbox": [ + 46, + 313, + 289, + 351 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 313, + 289, + 351 + ], + "type": "inline_equation", + "content": "\\mathrm{CE}(\\cdot)" + }, + { + "bbox": [ + 46, + 313, + 289, + 351 + ], + "type": "text", + "content": " denotes the standard cross entropy loss. As a result, our DualRel is trained by minimizing the overall objective as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 97, + 361, + 287, + 374 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 361, + 287, + 374 + ], + "spans": [ + { + "bbox": [ + 97, + 361, + 287, + 374 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {\\sup } + \\mathcal {L} _ {r p c} + \\lambda_ {d i v} \\times \\mathcal {L} _ {d i v}, \\tag {13}", + "image_path": "7157017b8054e08e6997ed09f3abca1bbde1a3b83449a305803935eea7444d7b.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 378, + 188, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 378, + 188, + 389 + ], + "spans": [ + { + "bbox": [ + 47, + 378, + 188, + 389 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 378, + 188, + 389 + ], + "type": "inline_equation", + "content": "\\lambda_{div}" + }, + { + "bbox": [ + 47, + 378, + 188, + 389 + ], + "type": "text", + "content": " is the trade-off weight." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 389, + 287, + 427 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 389, + 287, + 427 + ], + "spans": [ + { + "bbox": [ + 46, + 389, + 287, + 427 + ], + "type": "text", + "content": "During inference, we get the predicted mask " + }, + { + "bbox": [ + 46, + 389, + 287, + 427 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathbf{Y}}" + }, + { + "bbox": [ + 46, + 389, + 287, + 427 + ], + "type": "text", + "content": " by apply argmax operation on probability map " + }, + { + "bbox": [ + 46, + 389, + 287, + 427 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathbf{Y}}" + }, + { + "bbox": [ + 46, + 389, + 287, + 427 + ], + "type": "text", + "content": " from one branch, without extra computation cost." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 436, + 128, + 449 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 436, + 128, + 449 + ], + "spans": [ + { + "bbox": [ + 47, + 436, + 128, + 449 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 456, + 223, + 468 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 456, + 223, + 468 + ], + "spans": [ + { + "bbox": [ + 47, + 456, + 223, + 468 + ], + "type": "text", + "content": "4.1. Datasets and Evaluation Metrics" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 474, + 289, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 289, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 289, + 677 + ], + "type": "text", + "content": "We conduct experiments on the most popular benchmarks including Lucchi [19], Lucchi++ [2], MitoEM dataset [35]. Lucchi [19] contains two sub-volumes, acquired from the CA1 hippocampus region of the mouse brain for training and testing. Each sub-volume consists of " + }, + { + "bbox": [ + 46, + 474, + 289, + 677 + ], + "type": "inline_equation", + "content": "165 \\times 1024 \\times 768" + }, + { + "bbox": [ + 46, + 474, + 289, + 677 + ], + "type": "text", + "content": " EM images provided with manual mitochondria segmentation mask. And Lucchi++ [2] is reannotated by three neuroscience and biology experts, and has the same size as Lucchi with more accurate mitochondria segmentation mask. MitoEM dataset [35] contains two volumes attained from rat and human cortex, dubbed mito-R and mito-H respectively. Each volume consists of 400 training images, 100 validation images and 500 test images with a resolution of " + }, + { + "bbox": [ + 46, + 474, + 289, + 677 + ], + "type": "inline_equation", + "content": "4096 \\times 4096" + }, + { + "bbox": [ + 46, + 474, + 289, + 677 + ], + "type": "text", + "content": ". Among them, the ground-truth labels are publicly available for the training set and the validation set. In our experiments, we train on training set and evaluate on validation set." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "type": "text", + "content": "Evaluation Metrics. We adopt Dice similarity coefficient (DSC) and Jaccard-index coefficient (JAC) to evaluate the accuracy of segmentation in our experiments." + } + ] + } + ], + "index": 12 + }, + { + "type": "table", + "bbox": [ + 308, + 134, + 553, + 277 + ], + "blocks": [ + { + "bbox": [ + 305, + 71, + 547, + 126 + ], + "lines": [ + { + "bbox": [ + 305, + 71, + 547, + 126 + ], + "spans": [ + { + "bbox": [ + 305, + 71, + 547, + 126 + ], + "type": "text", + "content": "Table 1. Comparison with state-of-the-art re-implemented methods on Lucchi [19] and Lucchi++ [2] dataset under different partition protocols. Partition protocols denote the ratio of labeled data used for training, followed by the actual number of mitochondrial images." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 134, + 553, + 277 + ], + "lines": [ + { + "bbox": [ + 308, + 134, + 553, + 277 + ], + "spans": [ + { + "bbox": [ + 308, + 134, + 553, + 277 + ], + "type": "table", + "html": "
1/32 (5)1/16 (10)1/8 (20)1/2 (82)
MethodJACDSCJACDSCJACDSCJACDSC
Lucchi
MT[NIPS17] [31]71.8582.5372.4882.8375.4984.7278.6086.73
CCT[CVPR20] [25]84.7591.6285.4891.7385.8491.9486.6092.73
GCT[ECCV20] [11]83.5190.9384.6492.0285.8691.7286.2092.41
CPS[CVPR21] [3]84.5591.5784.6191.1885.1691.5785.5192.03
DualRel85.6392.2486.3592.4287.2193.1687.6293.31
Lucchi++
MT[NIPS17] [31]79.5187.1182.8990.1786.9192.3387.2493.42
CCT[CVPR20] [25]87.3692.6387.8493.2288.5493.7489.3694.19
GCT[ECCV20] [11]86.6092.1686.9592.0587.8693.1288.6993.79
CPS[CVPR21] [3]86.3692.4287.2293.0787.8793.3688.3093.52
DualRel87.8193.4288.2293.7489.9194.6390.5495.52
", + "image_path": "514743f13c251938c5dd071c3f72e7aab12e083a53420b71cfed790de724a799.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_body" + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 297, + 440, + 309 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 297, + 440, + 309 + ], + "spans": [ + { + "bbox": [ + 306, + 297, + 440, + 309 + ], + "type": "text", + "content": "4.2. Implementation Details" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 315, + 547, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 315, + 547, + 532 + ], + "spans": [ + { + "bbox": [ + 304, + 315, + 547, + 532 + ], + "type": "text", + "content": "In the semi-supervised setting, we sample a certain ratio from the training set as labeled set " + }, + { + "bbox": [ + 304, + 315, + 547, + 532 + ], + "type": "inline_equation", + "content": "D^{L}" + }, + { + "bbox": [ + 304, + 315, + 547, + 532 + ], + "type": "text", + "content": ", and the rest are treat as unlabeled set " + }, + { + "bbox": [ + 304, + 315, + 547, + 532 + ], + "type": "inline_equation", + "content": "D^{U}" + }, + { + "bbox": [ + 304, + 315, + 547, + 532 + ], + "type": "text", + "content": ". For a fair comparison, we follow the following guidelines in training and inference stage for all re-implemented methods. We adopt ResNet50 [8] as backbone network for feature extraction by removing the global average pooling (GAP) layer and fully connected layer, and utilize U-Net structure [28] for upsampling. During training, we feed the network with " + }, + { + "bbox": [ + 304, + 315, + 547, + 532 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 304, + 315, + 547, + 532 + ], + "type": "text", + "content": " images randomly cropped from original EM images with random mirror, random rotate and elastic transform augmentation. Extra color jitter is adopted to reduce overfitting. We use mini-batch SGD to train our model with momentum set to 0.9 and weight decay fixed as 0.0005. We initialize the learning rate with " + }, + { + "bbox": [ + 304, + 315, + 547, + 532 + ], + "type": "inline_equation", + "content": "5 \\times 10^{-3}" + }, + { + "bbox": [ + 304, + 315, + 547, + 532 + ], + "type": "text", + "content": " with batch size of 4, and halve the learning rate at the " + }, + { + "bbox": [ + 304, + 315, + 547, + 532 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 304, + 315, + 547, + 532 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 315, + 547, + 532 + ], + "type": "inline_equation", + "content": "70\\%" + }, + { + "bbox": [ + 304, + 315, + 547, + 532 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 315, + 547, + 532 + ], + "type": "inline_equation", + "content": "90\\%" + }, + { + "bbox": [ + 304, + 315, + 547, + 532 + ], + "type": "text", + "content": " of the overall training epoch. During inference, We adopt a sliding window of size " + }, + { + "bbox": [ + 304, + 315, + 547, + 532 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 304, + 315, + 547, + 532 + ], + "type": "text", + "content": " and step 256." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 539, + 529, + 552 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 539, + 529, + 552 + ], + "spans": [ + { + "bbox": [ + 305, + 539, + 529, + 552 + ], + "type": "text", + "content": "4.3. Comparison with State-of-the-art Methods" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 558, + 545, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 545, + 629 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 545, + 629 + ], + "type": "text", + "content": "We reproduce the most representative and competitive methods [3,11,25,31] in the semi-supervised natural image semantic segmentation task, and report their performance on Lucchi derivatives (i.e., Lucchi and Lucchi++) and Mi-toEM dataset, establishing a semi-supervised mitochondria segmentation benchmark." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "type": "text", + "content": "Lucchi derivatives. Tab. 1 shows the comparison of our method with the state-of-the-art re-implemented methods on Lucchi and Lucchi++ dataset. We consistently observe that our DualRel outperforms all other methods under all partition protocols, which strongly proves the effectiveness of our method. Specifically, our approach achieves " + }, + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "type": "inline_equation", + "content": "89.9\\%" + }, + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "type": "text", + "content": " JAC, " + }, + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "type": "inline_equation", + "content": "94.6\\%" + }, + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "type": "text", + "content": " DSC on Lucchi++ and " + }, + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "type": "inline_equation", + "content": "87.2\\%" + }, + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "type": "text", + "content": " JAC, " + }, + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "type": "inline_equation", + "content": "93.1\\%" + }, + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "type": "text", + "content": " DSC" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 758 + ], + "type": "text", + "content": "19621" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 102, + 293, + 243 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "type": "text", + "content": "Table 2. Comparison with state-of-the-art re-implemented methods on MitoEM [35] dataset under different partition protocols." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 102, + 293, + 243 + ], + "lines": [ + { + "bbox": [ + 49, + 102, + 293, + 243 + ], + "spans": [ + { + "bbox": [ + 49, + 102, + 293, + 243 + ], + "type": "table", + "html": "
1/32 (12)1/16 (25)1/8 (50)1/2 (200)
MethodJACDSCJACDSCJACDSCJACDSC
mito-R
\\(MT_{[NIPS17]}\\)(31)81.1187.5284.6490.6184.9190.8286.9992.41
\\(CCT_{[CVPR20]}\\)(25)88.9193.2289.4893.8889.7194.0389.7494.12
\\(GCT_{[ECCV20]}\\)(11)88.2292.8188.6192.7389.0393.4189.1193.72
\\(CPS_{[CVPR21]}\\)(3)88.7193.7189.6294.4189.7194.5290.0294.72
DualRel89.6194.5290.3194.9390.7295.1190.9195.23
mito-H
\\(MT_{[NIPS17]}\\)(31)81.9089.3282.7189.6283.5790.3684.6391.14
\\(CCT_{[CVPR20]}\\)(25)83.4290.6184.1890.7584.8791.2485.0791.37
\\(GCT_{[ECCV20]}\\)(11)82.1289.8183.3290.9184.6291.0284.8191.06
\\(CPS_{[CVPR21]}\\)(3)84.2291.8184.2991.4785.4292.1286.3192.65
DualRel85.6192.2285.9392.4486.2192.4386.5392.72
", + "image_path": "724e5d374e2a85a593ca77ddbd89bb08c314e2f8a34b97a43a46d44e123dc1e6.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 264, + 287, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 264, + 287, + 361 + ], + "spans": [ + { + "bbox": [ + 46, + 264, + 287, + 361 + ], + "type": "text", + "content": "on Lucchi under 1/8 partition protocol (only 20 labeled images). This means that even if we only label a small proportion of images, we can train a satisfactory segmentation model in an appropriate way. Compared to the best method CPS [3] in the field of natural image, our DualRel achieves a large margin of " + }, + { + "bbox": [ + 46, + 264, + 287, + 361 + ], + "type": "inline_equation", + "content": "2.05\\% / 1.59\\%" + }, + { + "bbox": [ + 46, + 264, + 287, + 361 + ], + "type": "text", + "content": " in JAC/DSC under 1/8 partition protocol, which favorably manifests the benefits of prototype-level consistency regularization." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 361, + 287, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 361, + 287, + 504 + ], + "spans": [ + { + "bbox": [ + 46, + 361, + 287, + 504 + ], + "type": "text", + "content": "MitoEM dataset. In Tab. 2 we report the performance on MitoEM dataset, which is much more complex than Lucchi and Lucchi++, with larger image size, more messy background and more diverse mitochondrial morphology. DualRel also achieves convincing performance even when the labeled data is scarce. Under 1/32 partition protocol, i.e., training the network with solely 12 labeled images and 388 unlabeled images, we obtain " + }, + { + "bbox": [ + 46, + 361, + 287, + 504 + ], + "type": "inline_equation", + "content": "89.6\\%" + }, + { + "bbox": [ + 46, + 361, + 287, + 504 + ], + "type": "text", + "content": " JAC, " + }, + { + "bbox": [ + 46, + 361, + 287, + 504 + ], + "type": "inline_equation", + "content": "94.5\\%" + }, + { + "bbox": [ + 46, + 361, + 287, + 504 + ], + "type": "text", + "content": " DSC on mito-R and " + }, + { + "bbox": [ + 46, + 361, + 287, + 504 + ], + "type": "inline_equation", + "content": "85\\%" + }, + { + "bbox": [ + 46, + 361, + 287, + 504 + ], + "type": "text", + "content": " JAC, " + }, + { + "bbox": [ + 46, + 361, + 287, + 504 + ], + "type": "inline_equation", + "content": "91.9\\%" + }, + { + "bbox": [ + 46, + 361, + 287, + 504 + ], + "type": "text", + "content": " DSC on mito-H. This demonstrates the stability of our method, which can model the reliability of the prototype for a more robust prototype-level supervision, even in the face of more complex scene." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 505, + 287, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 505, + 287, + 649 + ], + "spans": [ + { + "bbox": [ + 46, + 505, + 287, + 649 + ], + "type": "text", + "content": "Comparison with fully supervised methods. Tab. 3 tabulates the quantitative results compared with fully supervised methods. We observe that with only 5 annotated images, DualRel even surpasses fully supervised methods that utilize all annotated samples, such as 2D U-Net [28], by " + }, + { + "bbox": [ + 46, + 505, + 287, + 649 + ], + "type": "inline_equation", + "content": "0.7\\% / 1.2\\%" + }, + { + "bbox": [ + 46, + 505, + 287, + 649 + ], + "type": "text", + "content": " in JAC/DSC. When the number of available labeled samples increases (e.g., half the total images), our method is on par with state-of-the-art fully supervised methods (e.g., Casser [2]) without any post-processing. This sheds light on the great promise of semi-supervised mitochondria segmentation tasks, where light labeling cost can yield competitive performance." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 658, + 204, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 204, + 671 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 204, + 671 + ], + "type": "text", + "content": "4.4. Ablation Study and Analysis" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "text", + "content": "To look deeper into our method, we perform a series of ablation studies on Lucchi dataset with ResNet50 as backbone under 1/8 partition protocol to analyze each compo" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 319, + 113, + 531, + 232 + ], + "blocks": [ + { + "bbox": [ + 305, + 70, + 545, + 105 + ], + "lines": [ + { + "bbox": [ + 305, + 70, + 545, + 105 + ], + "spans": [ + { + "bbox": [ + 305, + 70, + 545, + 105 + ], + "type": "text", + "content": "Table 3. Comparison with state-of-the-art fully supervised methods on Lucchi dataset [19]. \"Post-Processing\" stands for whether to use post-processing such as Z-Filtering." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 319, + 113, + 531, + 232 + ], + "lines": [ + { + "bbox": [ + 319, + 113, + 531, + 232 + ], + "spans": [ + { + "bbox": [ + 319, + 113, + 531, + 232 + ], + "type": "table", + "html": "
MethodPost-ProcessinglabelsJACDSC
Lucchi [18]X16575.586.0
Peng and Yuan [27]X16583.390.9
2D U-Net [28]X16584.491.5
Cheng (2D) [4]X16586.592.8
Liu [17]✓16586.492.6
Khadangi [13]X16586.592.7
Casser [2]✓16588.493.8
DualRel (1/32)X585.692.2
DualRel (1/2)X8287.693.3
", + "image_path": "c83bddab32bd70b57fd572532840e046b682811fb538c35474e4cc4791d91817.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 341, + 273, + 509, + 427 + ], + "blocks": [ + { + "bbox": [ + 305, + 242, + 545, + 264 + ], + "lines": [ + { + "bbox": [ + 305, + 242, + 545, + 264 + ], + "spans": [ + { + "bbox": [ + 305, + 242, + 545, + 264 + ], + "type": "text", + "content": "Table 4. Evaluation of the effectiveness of different components on Lucchi dataset." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 341, + 273, + 509, + 427 + ], + "lines": [ + { + "bbox": [ + 341, + 273, + 509, + 427 + ], + "spans": [ + { + "bbox": [ + 341, + 273, + 509, + 427 + ], + "type": "table", + "html": "
Pixel-level
ThresholdJACDSC
CPS [3]085.1691.57
0.585.2091.62
0.784.0791.48
0.983.9390.89
Prototype-level
RPIARPrSJACDSC
w/o ref.w/ ref.
✓85.9791.94
✓86.5792.72
✓✓87.2193.16
", + "image_path": "99914347224ee38a36f23a0513a7babddc089892b376aee11a5fe85073502b26.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 449, + 545, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 545, + 521 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 545, + 521 + ], + "type": "text", + "content": "ment of our DualRel, including the reliable pixel aggregation module (RPIA), and the reliable prototype selection module (RPrS). Note that we remove all modules except the two branches of feature extractor and upsampling module and a separate cross-attention mechanism, to directly construct prototype-level consistency regularization as our baseline." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "content": "Analysis of the Pixel-level Consistency Regularization. In Sec. 1, we intuitively demonstrate that there exists gap between natural images and mitochondrial images, and directly employing pixel-level consistency regularization on mitochondrial images will inevitably increase the risk of unreliability. Naively, we can select high-confidence pixels based on a pre-defined threshold to attempt to alleviate the unreliability. The upper part of Tab. 4 tabulates the impact of different thresholds on the semi-supervised model based on pixel-level supervision. We observe that selecting high confidence points brings negligible improvement and even impairs model performance when the threshold is set too high. Then, we further quantitatively analyze the reasons for this case from the perspective of expected calibration error (ECE) [7], which measures the discrepancy between the confidence and accuracy of the network output," + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19622" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "type": "text", + "content": "Table 5. Comparison with state-of-the-art methods in model calibration and study on different network configurations." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "text" + }, + { + "type": "table", + "bbox": [ + 67, + 120, + 141, + 220 + ], + "blocks": [ + { + "bbox": [ + 64, + 102, + 151, + 118 + ], + "lines": [ + { + "bbox": [ + 64, + 102, + 151, + 118 + ], + "spans": [ + { + "bbox": [ + 64, + 102, + 151, + 118 + ], + "type": "text", + "content": "(a) Quantification of expected calibration error (ECE)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 67, + 120, + 141, + 220 + ], + "lines": [ + { + "bbox": [ + 67, + 120, + 141, + 220 + ], + "spans": [ + { + "bbox": [ + 67, + 120, + 141, + 220 + ], + "type": "table", + "html": "
MethodECE (↓) (%)
MT15.2
CCT12.5
GCT10.2
CPS8.3
DualRel1.8
", + "image_path": "269d561cdc4579d6ccac2ba7e9f59d1ae22a64a9d4e91ab7843dec250f5a405e.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 154, + 113, + 266, + 155 + ], + "blocks": [ + { + "bbox": [ + 156, + 103, + 261, + 111 + ], + "lines": [ + { + "bbox": [ + 156, + 103, + 261, + 111 + ], + "spans": [ + { + "bbox": [ + 156, + 103, + 261, + 111 + ], + "type": "text", + "content": "(b) Ablation on different architecture." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 154, + 113, + 266, + 155 + ], + "lines": [ + { + "bbox": [ + 154, + 113, + 266, + 155 + ], + "spans": [ + { + "bbox": [ + 154, + 113, + 266, + 155 + ], + "type": "table", + "html": "
JACDSC
CNN86.9992.65
Transformer87.2193.16
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JACDSC
w/o div.86.5792.87
w/ div.87.2193.16
", + "image_path": "e0d107ab9060cdda5e699f4353e4094d7dd51606679d3d6b1a2b406b344f44f6.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 242, + 286, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 242, + 286, + 337 + ], + "spans": [ + { + "bbox": [ + 46, + 242, + 286, + 337 + ], + "type": "text", + "content": "as known as calibration, has been explored. Poorer network calibration, weaker the correlation between the confidence and accuracy of the network output. In other words, even if the network predicts with high confidence, there is a high probability that it will be unreliable. Tab. 5a shows the calibration of different methods, the larger the value, the poorer the calibration. Therefore, it is impracticable to select reliable points only conditioned on confidence." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 338, + 286, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 338, + 286, + 422 + ], + "spans": [ + { + "bbox": [ + 46, + 338, + 286, + 422 + ], + "type": "text", + "content": "Analysis of the Prototype-level Consistency Regularization. As shown in Tab. 4, the baseline that utilizes prototype-level supervision achieves a clear lead, compared to methods based on pixel-level consistency regularization. Moreover, Tab. 5a shows our DualRel achieves better calibration benefiting from RPiA and RPrS module, which is in line with the design idea of prototype-level supervision." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 424, + 286, + 543 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 424, + 286, + 543 + ], + "spans": [ + { + "bbox": [ + 46, + 424, + 286, + 543 + ], + "type": "text", + "content": "Effectiveness of the Reliable Pixel Aggregation Module. As shown in Tab. 4, the introduction of the referential correlation (ref.) in RPiA achieves a certain performance lift compared with the baseline (i.e., a separate cross-attention mechanism without ref.), that is, " + }, + { + "bbox": [ + 46, + 424, + 286, + 543 + ], + "type": "inline_equation", + "content": "91.94\\%" + }, + { + "bbox": [ + 46, + 424, + 286, + 543 + ], + "type": "text", + "content": " vs. " + }, + { + "bbox": [ + 46, + 424, + 286, + 543 + ], + "type": "inline_equation", + "content": "92.72\\%" + }, + { + "bbox": [ + 46, + 424, + 286, + 543 + ], + "type": "text", + "content": " in DSC. The improvement can be mainly ascribed to the strong ability of the RPiA to rectify the direct pairwise correlation, enabling the prototype absorbs counterpart reliable pixels with the same semantic pattern during the interaction with the pixels." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 544, + 286, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 544, + 286, + 616 + ], + "spans": [ + { + "bbox": [ + 46, + 544, + 286, + 616 + ], + "type": "text", + "content": "Effectiveness of the Reliable Prototype Selection Module. The addition of RPrS also contributes to a remarkable performance (86.57% vs. 87.21%). This proves the necessity of suppressing the equivocal prototypes, our RPrS can further evaluate the reliability of prototypes in constructing prototype-level consistency regularization." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "type": "text", + "content": "Effectiveness of Transformer-based Cross-attention Mechanism. We perform the ablation study that replaces the Transformer-like cross-attention by using convolutional networks with similar parameters in Tab. 5b. In detail, We use the convolutional layers followed by a softmax function to change the channel size of the feature map to obtain " + }, + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "type": "text", + "content": " mito features when replacing cross attention. The feedforward network (FFN) is replaced by the convolutional lay" + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 307, + 70, + 421, + 150 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 421, + 150 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 421, + 150 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 421, + 150 + ], + "type": "image", + "image_path": "59bd003b535271412411b51308841248c6868fa1e19ed3691457bdf4a3efc68c.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 155, + 544, + 177 + ], + "lines": [ + { + "bbox": [ + 305, + 155, + 544, + 177 + ], + "spans": [ + { + "bbox": [ + 305, + 155, + 544, + 177 + ], + "type": "text", + "content": "Figure 3. Evaluation of the number of prototypes " + }, + { + "bbox": [ + 305, + 155, + 544, + 177 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 305, + 155, + 544, + 177 + ], + "type": "text", + "content": ", and the hyperparameters " + }, + { + "bbox": [ + 305, + 155, + 544, + 177 + ], + "type": "inline_equation", + "content": "\\lambda_{div}" + }, + { + "bbox": [ + 305, + 155, + 544, + 177 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 427, + 71, + 542, + 151 + ], + "blocks": [ + { + "bbox": [ + 427, + 71, + 542, + 151 + ], + "lines": [ + { + "bbox": [ + 427, + 71, + 542, + 151 + ], + "spans": [ + { + "bbox": [ + 427, + 71, + 542, + 151 + ], + "type": "image", + "image_path": "5c35a0b361de060d46d57128e59e3923e761904ef24f1fc45b08585e7ddee768.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 198, + 545, + 233 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 198, + 545, + 233 + ], + "spans": [ + { + "bbox": [ + 304, + 198, + 545, + 233 + ], + "type": "text", + "content": "ers, and the rest of the model remains the same. We observe that cross-attention achieves better performance thanks to the long-range modeling capabilities of the transformer." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 233, + 545, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 233, + 545, + 304 + ], + "spans": [ + { + "bbox": [ + 304, + 233, + 545, + 304 + ], + "type": "text", + "content": "Effectiveness of Diversity Loss. As shown in Tab. 5c, with the utilization of diversity loss, further improvements can be observed. Diversity loss prevents the prototypes from focusing on similar local semantic clues. And diverse prototypes can capture mitochondria variations and achieve more precise segmentation." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 304, + 545, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 304, + 545, + 388 + ], + "spans": [ + { + "bbox": [ + 304, + 304, + 545, + 388 + ], + "type": "text", + "content": "Hyperparameter Evaluations. As shown in Fig. 3, we evaluate how " + }, + { + "bbox": [ + 304, + 304, + 545, + 388 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 304, + 545, + 388 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 304, + 545, + 388 + ], + "type": "inline_equation", + "content": "\\lambda_{div}" + }, + { + "bbox": [ + 304, + 304, + 545, + 388 + ], + "type": "text", + "content": " affects our model learning. We can observe that the performance continues to grow until " + }, + { + "bbox": [ + 304, + 304, + 545, + 388 + ], + "type": "inline_equation", + "content": "K = 12" + }, + { + "bbox": [ + 304, + 304, + 545, + 388 + ], + "type": "text", + "content": ", which means it is sufficient to mine 12 semantic patterns of mitochondria. And " + }, + { + "bbox": [ + 304, + 304, + 545, + 388 + ], + "type": "inline_equation", + "content": "\\lambda_{div}" + }, + { + "bbox": [ + 304, + 304, + 545, + 388 + ], + "type": "text", + "content": " controls the relative importance of the diversity loss, our model achieves much better performance when " + }, + { + "bbox": [ + 304, + 304, + 545, + 388 + ], + "type": "inline_equation", + "content": "\\lambda_{div} = 0.05" + }, + { + "bbox": [ + 304, + 304, + 545, + 388 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 396, + 391, + 407 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 396, + 391, + 407 + ], + "spans": [ + { + "bbox": [ + 306, + 396, + 391, + 407 + ], + "type": "text", + "content": "4.5. Vasualization" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 415, + 545, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 415, + 545, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 415, + 545, + 604 + ], + "type": "text", + "content": "Visualization of Predictions. To further analyze and understand the proposed method, we visualize a series of segmentation results and prototype activation areas. As shown in Fig. 4, it can be noticed that other methods tend to incorrectly segment the non-target region (dyed in blue) or are unable to activate all the mitochondria (dyed in red). We deem the main reason is that numerous ambiguous pixels inherent in EM images severely confuse the models designed for natural images. With the assistance of the RPiA, the negative effects of unreliable pixels are mostly eliminated. Besides, the RPrS assigns larger weights to the more reliable prototypes to obtain robust prototype-level supervision. Our DualRel generates more accurate prediction masks compared with other methods, which demonstrates the effectiveness of the cooperation of the above two modules." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "Visualization of Correlation Weights. To more intuitively demonstrate the unreliable pixels suppression ability endowed by RPiA, we conduct qualitative visualization on the correlation maps between the mito filters and the image features. As shown in Fig. 6, we find that in the absence of RPiA, pixel features that with distinct semantics sometimes share high similarity with specific prototypes as shown in the parts marked by the red box. 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Visualization of the pixel-prototype correlation weights." + } + ] + } + ], + "index": 52, + "angle": 0, + "type": "image_caption" + } + ], + "index": 50 + }, + { + "type": "image", + "bbox": [ + 173, + 421, + 274, + 547 + ], + "blocks": [ + { + "bbox": [ + 173, + 421, + 274, + 547 + ], + "lines": [ + { + "bbox": [ + 173, + 421, + 274, + 547 + ], + "spans": [ + { + "bbox": [ + 173, + 421, + 274, + 547 + ], + "type": "image", + "image_path": "5881450b17a6269f37771fb2e961c9d299373422c0939bbef373cee64e7c4813.jpg" + } + ] + } + ], + "index": 51, + "angle": 0, + "type": "image_body" + } + ], + "index": 51 + }, + { + "bbox": [ + 46, + 590, + 287, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 590, + 287, + 639 + ], + "spans": [ + { + "bbox": [ + 46, + 590, + 287, + 639 + ], + "type": "text", + "content": "prototypes with large weights will lead to confusion. The second row presents the results with RPiA, we observe a significant reduction in false activation, demonstrating the effectiveness of RPiA in suppressing false matches." + } + ] + } + ], + "index": 53 + }, + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "type": "text", + "content": "Visualization of Reliability and Activation Maps. To vividly present the working mechanism of reliable prototype selection module (RPrS), we visualize the reliability of prototypes and its corresponding activation maps. As shown in Fig. 5, some prototypes with clear foreground or background semantic clues occupy larger weights (i.e.," + } + ] + } + ], + "index": 54 + }, + { + "bbox": [ + 305, + 421, + 545, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 421, + 545, + 506 + ], + "spans": [ + { + "bbox": [ + 305, + 421, + 545, + 506 + ], + "type": "inline_equation", + "content": "4^{th}" + }, + { + "bbox": [ + 305, + 421, + 545, + 506 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 421, + 545, + 506 + ], + "type": "inline_equation", + "content": "5^{th}" + }, + { + "bbox": [ + 305, + 421, + 545, + 506 + ], + "type": "text", + "content": " columns), while some prototypes focusing on mitochondrial boundary patterns are assigned with smaller weights (i.e., " + }, + { + "bbox": [ + 305, + 421, + 545, + 506 + ], + "type": "inline_equation", + "content": "3^{rd}" + }, + { + "bbox": [ + 305, + 421, + 545, + 506 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 421, + 545, + 506 + ], + "type": "inline_equation", + "content": "6^{th}" + }, + { + "bbox": [ + 305, + 421, + 545, + 506 + ], + "type": "text", + "content": " columns). This is in line with the design idea of RPrS, that is, pursuing implicitly learning the reliability of each prototype in a data-driven way. In this case, the equivocal prototypes will be suppressed while the reliable ones are highlighted in the supervision signals." + } + ] + } + ], + "index": 55 + }, + { + "bbox": [ + 306, + 522, + 378, + 534 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 522, + 378, + 534 + ], + "spans": [ + { + "bbox": [ + 306, + 522, + 378, + 534 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 56 + }, + { + "bbox": [ + 305, + 544, + 545, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 544, + 545, + 626 + ], + "spans": [ + { + "bbox": [ + 305, + 544, + 545, + 626 + ], + "type": "text", + "content": "In this paper, we rethink how to achieve effective semi-supervised mitochondria segmentation. We propose a novel end-to-end dual-reliable (DualRel) network, including a reliable pixel aggregation module and a reliable prototype selection module. Extensive experimental results demonstrate the effectiveness. This work is expected to open a new venue for future research in this field." + } + ] + } + ], + "index": 57 + }, + { + "bbox": [ + 306, + 643, + 415, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 643, + 415, + 658 + ], + "spans": [ + { + "bbox": [ + 306, + 643, + 415, + 658 + ], + "type": "text", + "content": "6. Acknowledgments" + } + ] + } + ], + "index": 58 + }, + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "text", + "content": "This work was partially supported by the National Nature Science Foundation of China (Grant 62022078, 62021001), National Defense Basic Scientific Research Program (Grant JCKY2022911B002)." + } + ] + } + ], + "index": 59 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19624" + } + ] + } + ], + "index": 60 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 286, + 712 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 53, + 91, + 286, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 286, + 123 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 286, + 123 + ], + "type": "text", + "content": "[1] Silvia Campello and Luca Scorrano. 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High-quality vector fonts (copyable on electronic devices) synthesized by DualVector (left), with smoothly-interpolated styles (right). Both sentences are pangrams. Please zoom in for details." + ], + "image_footnote": [], + "bbox": [ + 89, + 277, + 405, + 388 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3d892fddaf1a7d8161fd4fa3e7f1a425e23cb59ac0335818baa4d8f547718224.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 431, + 280, + 869, + 388 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 438, + 313, + 453 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Automatic generation of fonts can be an important aid to typeface design. Many current approaches regard glyphs as pixelated images, which present artifacts when scaling and inevitable quality losses after vectorization. On the other hand, existing vector font synthesis methods either fail to represent the shape concisely or require vector supervision during training. To push the quality of vector font synthesis to the next level, we propose a novel dual-part representation for vector glyphs, where each glyph is modeled as a collection of closed \"positive\" and \"negative\" path pairs. The glyph contour is then obtained by boolean operations on these paths. We first learn such a representation only from glyph images and devise a subsequent contour refinement step to align the contour with an image representation to further enhance details. Our method, named DualVector, outperforms state-of-the-art methods in vector font synthesis both quantitatively and qualitatively. Our synthesized vector fonts can be easily converted to common digital font formats like TrueType Font for practical use. The code is released at https://github.com/thuliu-yt16/dualvector.", + "bbox": [ + 73, + 470, + 473, + 773 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 803, + 209, + 819 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Fonts with various styles play an important role in content display and distribution. Excellent font design is time-consuming and labor-intensive. Recent machine learning", + "bbox": [ + 75, + 829, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "innovations have made font generation possible, but how to automatically generate high-quality vector fonts remains a task of practical importance in the artistic and computer graphics and vision communities.", + "bbox": [ + 500, + 438, + 892, + 500 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Benefiting from the development of image generation techniques, mainstream font synthesis methods [2, 12, 24, 41, 42] could generate pixelated glyph images. Despite the promising quality, images of glyphs incur aliasing artifacts on edges when discretely sampled, and thus are not competent for high-quality rendering or printing at arbitrary resolutions. To alleviate this problem, some methods [7, 34] adopt coordinate-based neural networks to model a glyph as a contiguous neural field, which have also shown great potential in modeling 3D geometry and scenes [7, 30, 32]. Although glyphs represented by the implicit field can be rendered at arbitrary resolutions, it is hard to preserve details in high-frequency regions such as edges and corners, not to mention the high computational costs as the network needs to be evaluated for every pixel. Researchers have made much effort to directly synthesize vector fonts [4, 27, 33, 39] in recent years, with the main difficulty lying in finding a representation of vector graphics that can be encoded or decoded effectively in a deep learning framework. One typical approach represents a vector shape as a sequence of drawing commands and adopts sequence modeling techniques such as recurrent networks and transformers. The drawbacks are twofold: (1) Modeling command sequences can be much harder than images. There are infinitely many command sequences that correspond to the same-looking shape, which brings ambiguities in learning and makes it hard to construct", + "bbox": [ + 496, + 508, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author", + "bbox": [ + 101, + 887, + 227, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "14193", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "an effective manifold for valid glyph shapes. (2) Ground-truth drawing commands are often required to provide sufficient supervision for high-quality modeling and synthesis.", + "bbox": [ + 76, + 90, + 468, + 137 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To overcome these challenges, we first propose a dual-part vector font representation, where each glyph shape is the union of a fixed number of dual parts. Each dual part is formed by the subtraction of a \"positive\" and a \"negative\" geometric primitive. While there are many choices for the geometric primitives [6, 8, 25], we adopt closed Bezier paths for their great representational ability. They are also widely supported in digital font formats which makes it easy to convert our representation to these formats for practical use. We reduce the problem of predicting complicated drawing command sequences to predicting multiple basic primitives. From this perspective, both manifold learning and latent space interpolation become more feasible.", + "bbox": [ + 75, + 138, + 470, + 335 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Based on the dual-part representation, we introduce DualVector, a method to learn such a representation for high-quality font modeling and synthesis from only glyph images without any vector supervision. A straightforward way to achieve this is to directly optimize the parameters of the Bezier curves with differentiable rendering techniques for vector graphics [22]. However, this approach easily gets stuck in the local minima as valuable gradients are only defined at shape intersections. Taking inspiration from implicit field training for 2D and 3D shapes [6, 25, 32], we supervise the occupancy value derived from the analytical expression of the Bezier curves and adopt an initialization strategy based on unsigned distance field (UDF) to provide dense gradients across the entire pixel space. For local detail fidelity, we also train a glyph image generation model and devise a subsequent contour refinement step to align the contour of the vector shape with that of the image by differentiable rendering [22]. We compare our approach with state-of-the-art methods in font modeling and generation and demonstrate the superior quality of our vector font outputs. Our main contributions are:", + "bbox": [ + 75, + 339, + 470, + 657 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- A new dual-part font representation based on boolean operations of Bezier paths, which enables efficient shape modeling and unsupervised manifold learning.", + "- A method named DualVector that models both the dual-part and pixelated representation, and introduces a contour refinement step to obtain vector fonts with richer details as well as a UDF initialization strategy for better convergence.", + "- DualVector achieves state-of-the-art quality in font modeling and generation, with outputs that can be easily converted to common digital font formats." + ], + "bbox": [ + 96, + 684, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 89, + 640, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Glyph Image Generation", + "text_level": 1, + "bbox": [ + 500, + 114, + 728, + 131 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Benefiting from the development of image generation [10, 14, 16], either black-white [12, 15, 37, 40] or artistic glyph image generation [2, 23, 41, 42] is well explored in the past decade. MC-GAN [2] synthesized ornamented glyphs for capital letters in an end-to-end manner from a small subset of the same style. Attr2Font [38] generated visually pleasing results according to style attributes and content references. Most of these methods follow the disentanglement of style and content codes, and so does the image generation branch in DualVector. But these glyph image generation efforts do not step outside the 2D pixelated representation which sets an upper bound for rendering quality, efficiency, and practicality.", + "bbox": [ + 496, + 138, + 890, + 335 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Image Rasterization and Vectorization", + "text_level": 1, + "bbox": [ + 500, + 344, + 830, + 359 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Rasterization and vectorization are dual problems in image processing. Previous efforts on rasterization have typically focused on anti-aliasing [9, 11, 31] and high-performance rendering on modern graphics hardware [3, 17, 21, 26]. Traditional image vectorization approaches rely on region segmentation, line extraction, and contour tracing for gray-scale images [35], pixel arts [18], animations [44] and general images [1, 5, 19, 36, 45, 46]. Recently, researchers have turned to bridging the raster and vector domains [22, 29], enabling existing well-established algorithms for raster images to be also applied to vector representations. DiffVG [22] is a differentiable rendering technique for vector graphics enabling the optimization of vector primitive parameters based on raster criteria. In our work, it is employed to align the vector and pixel representation in the contour refinement step.", + "bbox": [ + 496, + 368, + 890, + 609 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.3. Vector Font Generation", + "text_level": 1, + "bbox": [ + 500, + 619, + 718, + 635 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "SVG-VAE [27] was the first attempt to build a sequential generative model on SVG fonts. DeepSVG [4] developed a hierarchical transformer-based generative model for complex SVG icons generation and interpolation. Exploiting implicit neural representation, multi-implicit [34] modeled fonts with a permutation-invariant set of learned implicit functions which can preserve font features, such as smooth edges and sharp corners, and generate good interpolation results. Liu et al. [25] proposed a primitive-based representation, which views glyph shapes as the combination of primitives enclosed by implicit curves. Implicit representation-based methods can convert the zero-level set of their output fields to contour representation with the 2D marching cube [28] algorithm, although it produces multiple segmented lines and lacks accuracy and efficiency in rendering and editing. Im2Vec [33] can synthesize complex vector graphics with varying topologies without vector super", + "bbox": [ + 496, + 643, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "14194", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/df4217b94fc36294faf9377ed7b37181bda1a365f3f5d6367ccd3db5e1f17b4e.jpg", + "image_caption": [ + "Figure 2. DualVector contains the following components: (a) a vector branch that maps the latent code $z$ to several closed Bézier paths which are further gathered to form a global shape of the glyph; (b) an image branch that generates pixelated images with faithful details; (c) a contour refinement step that obtains the contour via boolean operations on dual-parts and optimizes it with the image guidance at inference time. Both the vector and the image branch are trained using the glyph images. Dual parts are distinguished by their colors." + ], + "image_footnote": [], + "bbox": [ + 133, + 97, + 834, + 364 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "vision. It rendered layered Bézier paths predicted from image features using DiffVG [22] and trains the system in an auto-encoding manner. DeepVecFont [39] adopted a dual-modality learning framework that utilizes both sequence and image features for high-quality vector font synthesis. But the results it produces may have the wrong topology, including self-intersection or invalid paths. In contrast to these methods, our approach does not require vector supervision and is very efficient in vector representation, with high quality glyph generation.", + "bbox": [ + 75, + 436, + 472, + 588 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. DualVector", + "text_level": 1, + "bbox": [ + 76, + 601, + 197, + 617 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we first illustrate the proposed dual-part representation for fonts (Sec. 3.1) and then introduce the components of DualVector for training this representation from glyph images (Secs. 3.2 to 3.4) and how the model can be used for font reconstruction and generation (Sec. 3.5). In DualVector, we adopt a joint representation of vector and image for fonts, as shown in Fig. 2. The latent space is shared by both modalities, and we associate each glyph with a latent code $z \\in \\mathbf{R}^d$ produced by the task-specific encoding process. The latent code $z$ is fed into the two decoding branches to obtain a dual-part representation and an image representation respectively. The output of the vector branch is further processed by a contour refinement step to generate the final contour representation under the image guidance.", + "bbox": [ + 75, + 626, + 468, + 839 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Dual-Part Representation", + "text_level": 1, + "bbox": [ + 76, + 847, + 312, + 863 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In our dual-part representation, we consider the closed parametric Bézier paths as our basic primitives for several", + "bbox": [ + 76, + 869, + 468, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "reasons: (1) Bézier paths are powerful enough to approximate various shapes; (2) The contour of a closed shape produced by boolean operations on Bézier paths is still a set of Bézier paths, i.e., the closure property; (3) Bézier paths are widely used in modern font design, making the learned representation highly applicable. For convenience, we use a triplet of control points $(\\pmb{a},\\pmb{b},\\pmb{c})$ to denote a quadratic Bézier curve $B(\\cdot ;\\pmb {a},\\pmb {b},\\pmb {c})$ determined by the control points: $B(t;\\pmb {a},\\pmb {b},\\pmb {c}) = (1 - t)^{2}\\pmb {a} + (1 - t)t\\pmb {b} + t^{2}\\pmb {c}t\\in [0,1]$ 1 Since a glyph often consists of a number of strokes with similar appearances, we propose to represent each glyph $g$ with $N$ closed Bézier paths $\\{P_i\\}_{i = 1}^N$ . Each path $P_{i}$ is defined by $M$ end-to-end connected quadratic Bézier curves $\\{B_{i,j}(\\pmb{x}_{i,2j - 1},\\pmb{x}_{i,2j},\\pmb{x}_{i,2j + 1})\\}_{j = 1}^{M}(\\pmb{x}_{i,2M + 1} = \\pmb{x}_{i,1})$ .We introduce the occupancy field of a closed path $P_{i}$ as", + "bbox": [ + 496, + 436, + 890, + 665 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {O} _ {P _ {i}} (\\boldsymbol {x}) = \\left\\{ \\begin{array}{l l} 1, & \\boldsymbol {x} \\in P _ {i} \\\\ 0, & \\boldsymbol {x} \\notin P _ {i} \\end{array} \\right. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 602, + 666, + 890, + 696 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The entire glyph shape $g$ could simply be denoted as the union of all the paths $\\cup_{i} P_{i}$ . We normalize the coordinate range of the glyph to $[-1, 1]^{2}$ . Thus given any point $x$ on the canvas $[-1, 1]^{2}$ , we can determine whether it is inside the represented glyph shape by a maximum operation, leading to the occupancy field of $g$ :", + "bbox": [ + 496, + 696, + 890, + 787 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {O} (\\boldsymbol {x}) = \\max _ {i} \\mathcal {O} _ {P _ {i}} (\\boldsymbol {x}) = \\left\\{ \\begin{array}{l l} 1, & \\boldsymbol {x} \\in \\cup_ {i} P _ {i} \\\\ 0, & \\boldsymbol {x} \\notin \\cup_ {i} P _ {i} \\end{array} \\right. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 547, + 787, + 890, + 820 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "However, we find that the above representation can model fonts with convex curves on the contour but struggles to reconstruct shapes with holes. Therefore, in practice, we pair each path $P_{i}$ with a negative path $Q_{i}$ , and term this pair $(P_{i}, Q_{i})$ as a \"dual part\". In this way, $g$ is represented as", + "bbox": [ + 496, + 825, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "14195", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$\\cup_{i}(P_{i} - Q_{i})$ . The occupancy field $\\mathcal{O}$ is then derived as:", + "bbox": [ + 75, + 90, + 444, + 104 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {O} (\\boldsymbol {x}) = \\max _ {i} [ \\min \\left(\\mathcal {O} _ {P _ {i}} (\\boldsymbol {x}), 1 - \\mathcal {O} _ {Q _ {i}} (\\boldsymbol {x})\\right) ] = \\left\\{ \\begin{array}{l l} 1, & \\boldsymbol {x} \\in g \\\\ 0, & \\boldsymbol {x} \\notin g \\end{array} \\right. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 107, + 468, + 151 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Even though $\\mathcal{O}$ is the analytical occupancy field of $g$ , it is not differentiable w.r.t. the parameters of the paths. Therefore, in order to apply gradient descent to learn such a representation, we calculate the approximate occupancy field $\\hat{\\mathcal{O}}$ from the signed distance field (SDF) of $g$ . Since the distance $d(p;B)$ from any point $p$ to a Bézier curve $B$ can be derived analytically, the SDF of a path can be calculated differentiably w.r.t. its control points as follows:", + "bbox": [ + 75, + 152, + 468, + 273 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ns _ {P _ {i}} (\\boldsymbol {x}) = \\left[ 2 \\mathcal {O} _ {P _ {i}} (\\boldsymbol {x}) - 1 \\right] \\min _ {j} d (\\boldsymbol {x}; B _ {i, j}) \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 275, + 468, + 297 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Following previous vector graphics rasterization techniques [22, 31, 34], we approximate $\\mathcal{O}$ by analytical pixel prefiltering with a parabolic kernel $\\alpha$ :", + "bbox": [ + 75, + 297, + 468, + 340 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathcal {O}} _ {P _ {i}} (\\boldsymbol {x}) = \\alpha \\left(s _ {P _ {i}} (\\boldsymbol {x})\\right)\n$$\n", + "text_format": "latex", + "bbox": [ + 166, + 343, + 313, + 359 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathcal {O}} = \\max _ {i} [ \\min (\\hat {\\mathcal {O}} _ {P _ {i}}, 1 - \\hat {\\mathcal {O}} _ {Q _ {i}}) ] \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 166, + 359, + 468, + 386 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Vector Branch", + "text_level": 1, + "bbox": [ + 76, + 398, + 225, + 414 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The vector branch takes a latent code $z$ and outputs a set of dual-parts that represent a vector glyph. The path decoder $\\mathcal{D}_P$ directly predicts the control points of the positive paths $\\{P_i\\}_{i=1}^N$ and the negative ones $\\{Q_i\\}_{i=1}^N$ from $z$ :", + "bbox": [ + 76, + 424, + 468, + 484 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{\\boldsymbol {x} _ {i, j} \\right\\} = \\mathcal {D} _ {P} (z), 1 \\leq i \\leq 2 N, 1 \\leq j \\leq 2 M \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 127, + 484, + 468, + 501 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\{\\pmb{x}_{i,j}\\}_{i = 1}^{N}$ are control points for $\\{P_i\\}_{i = 1}^N$ and $\\{\\pmb{x}_{i,j}\\}_{i = N + 1}^{2N}$ are control points for $\\{Q_i\\}_{i = 1}^N$", + "bbox": [ + 76, + 501, + 468, + 534 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Image Branch", + "text_level": 1, + "bbox": [ + 76, + 545, + 222, + 561 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To combine with the advantages of image generation approaches, we train an auxiliary image branch that maps $z$ to a pixelated image $\\mathcal{I}$ of the glyph it represents. Here we adopt a CNN-based decoder $\\mathcal{D}_I$ :", + "bbox": [ + 75, + 570, + 468, + 630 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {I} = \\mathcal {D} _ {I} (z) \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 233, + 632, + 468, + 647 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{I}$ is a gray-scale image in shape $H\\times W$ . It provides detailed shape guidance to refine the vector shape contour.", + "bbox": [ + 75, + 648, + 468, + 678 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Contour Refinement", + "text_level": 1, + "bbox": [ + 76, + 691, + 271, + 705 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Although the dual-part representation produced by the vector branch can already be rendered, there still exists a gap between it and modern contour representations for fonts. Therefore, we first convert it to the contour of the glyph $\\partial \\mathcal{O}$ with an off-the-shelf tool Paper.js [20] which can perform arbitrary boolean operations on SVG paths. Here the contour $\\partial \\mathcal{O}$ is a set of K closed Bézier paths.", + "bbox": [ + 75, + 715, + 468, + 821 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\partial \\mathcal {O} = \\left\\{C _ {1}, C _ {2}, \\dots , C _ {K} \\right\\} \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 823, + 467, + 839 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $K$ denotes the number of independent paths. Each individual part or hole increases $K$ by 1. $C_i$ is a closed Bezier path composed of $l_i$ quadratic Bezier segments $\\{\\hat{B}_{i,j}(\\hat{\\pmb{x}}_{i,2j - 1},\\hat{\\pmb{x}}_{i,2j},\\hat{\\pmb{x}}_{i,2j + 1})\\}_{j = 1}^{l_i}$", + "bbox": [ + 75, + 839, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "After this conversion, we exploit the image generation results to further refine $\\partial \\mathcal{O}$ with differentiable rendering techniques [22]. $\\mathcal{I}$ could naturally serve as a pixelated version of the occupancy field $\\mathcal{O}$ . During the refinement, we devise several strategies to improve the quality and efficiency of our representation:", + "bbox": [ + 496, + 90, + 890, + 181 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Subdivision To improve the representational ability, we split long Bézier curves (with a length greater than $10\\%$ of the canvas width) at their midpoints.", + "bbox": [ + 496, + 203, + 890, + 250 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Simplification To improve the efficiency of the contour representation, we replace the Bézier curves with a line segment connecting its two endpoints if they are close enough. For a Bézier curve $(a, b, c)$ , we simply define how faithfully the segment $ac$ could represent the curve by the angle between $\\vec{ba}$ and $\\vec{bc}$ . Also, we examine if there exist two adjacent Bézier segments that could be combined as a single one. Since all quadratic Bézier curves are parts of a parabola curve, we derive the parameters of the corresponding parabola curves from the control points and combine the two curves if their parameters are close enough. We also aggregate the endpoints of lines and curves that are too short.", + "bbox": [ + 496, + 271, + 890, + 452 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Pruning Prior to refinement, some Bezier paths on the contour may enclose extremely small regions which will confuse the refinement process and produce redundant curves that eventually converge to a single point. We trim those closed paths $C_i$ with areas under a certain threshold.", + "bbox": [ + 496, + 474, + 890, + 549 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "More implementation details of these strategies can be found in the supplemental material.", + "bbox": [ + 496, + 551, + 890, + 580 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.5. Implementation and Training", + "text_level": 1, + "bbox": [ + 500, + 592, + 764, + 608 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this subsection, we will dive into how we utilize the proposed representation in both the font reconstruction and generation tasks.", + "bbox": [ + 496, + 616, + 890, + 661 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.5.1 Optimization Objectives", + "text_level": 1, + "bbox": [ + 500, + 684, + 723, + 699 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Optimization objectives can be divided into those at training time and those at inference time. The training-time objectives are task-related.", + "bbox": [ + 496, + 708, + 890, + 753 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Font reconstruction. For the font reconstruction task, the input to our system is a gray-scale image of a glyph and the output is the corresponding vector representation. The pixelated image $\\mathcal{I}_g$ of the glyph $g$ is first passed through an image encoder $\\mathcal{E}$ to obtain the latent code $z$ :", + "bbox": [ + 496, + 776, + 890, + 849 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nz = \\mathcal {E} \\left(\\mathcal {I} _ {g}\\right) \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 658, + 852, + 890, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The latent code is then decoded by our vector branch and image branch into dual-parts $\\{(P_i,Q_i)\\}_{i = 1}^N$ and a pixelated", + "bbox": [ + 496, + 869, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "14196", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "output $\\mathcal{I}$ . We optimize the trainable modules $\\mathcal{E},\\mathcal{D}_I$ and $\\mathcal{D}_P$ simultaneously with the following loss functions:", + "bbox": [ + 76, + 90, + 467, + 119 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\lambda_ {P} \\mathcal {L} _ {P} + \\lambda_ {I} \\mathcal {L} _ {I} \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 205, + 123, + 467, + 137 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where we adopt an extra perceptual loss [43]:", + "bbox": [ + 76, + 138, + 379, + 152 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {P} = \\mathbb {E} _ {\\boldsymbol {x} \\sim [ - 1, 1 ] ^ {2}} \\left[ \\left\\| \\hat {\\mathcal {O}} (\\boldsymbol {x}) - \\mathcal {I} _ {g} (\\boldsymbol {x}) \\right\\| _ {1} \\right] \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 155, + 467, + 176 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {I} = \\left| \\left| \\mathcal {I} - \\mathcal {I} _ {g} \\right| \\right| _ {2} + \\operatorname {L P I P S} (\\mathcal {I}, \\mathcal {I} _ {g})\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 175, + 375, + 191 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Font generation. The input to the font generation task is multiple style reference images $\\{R_i\\}_{i=1}^{N_R}$ along with the corresponding character label $T$ . The number of references $N_R$ may vary during training to allow the model to accept a variable number of references during inference. The style references are first mapped to their features $\\{f_i\\}_{i=1}^{N_R}$ with an image encoder $\\mathcal{E}_f$ . We then apply stacked self-attention layers (SA) to aggregate these features to a style latent code $z_{style}$ with a variational loss to enable font sampling. Character labels are mapped to vector representations by a learnable label embedding layer and then fused with $z_{style}$ to yield the latent code $z_T$ of the target glyph. Then $z_T$ is fed to the decoders to generate the glyph, the same as the reconstruction task. The whole process can be described as follows:", + "bbox": [ + 76, + 196, + 467, + 407 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nf _ {i} = \\mathcal {E} _ {f} (R _ {i})\n$$\n", + "text_format": "latex", + "bbox": [ + 200, + 419, + 284, + 436 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mu , \\sigma = \\operatorname {S A} \\left(f _ {1}, f _ {2}, \\dots , f _ {N _ {R}}\\right) \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 184, + 438, + 467, + 460 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nz _ {s t y l e} = \\mu + \\epsilon \\sigma , \\epsilon \\sim \\mathcal {N} (0, 1) \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 176, + 457, + 467, + 473 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nz _ {T} = \\operatorname {F F N} ([ z _ {\\text {s t y l e}}, T ])\n$$\n", + "text_format": "latex", + "bbox": [ + 196, + 476, + 343, + 492 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To ease training, we use the pre-trained $\\mathcal{E}$ from the reconstruction task to encode ground truth output $g_{T}$ and train the encoder with the following guidance:", + "bbox": [ + 76, + 497, + 467, + 542 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {l a t e n t}} = \\left\\| z _ {T} - \\mathcal {E} \\left(g _ {T}\\right) \\right\\| _ {2} \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 184, + 542, + 467, + 559 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To enable font sampling, we adopt a Kullback-Leibler divergence loss [16]:", + "bbox": [ + 76, + 561, + 467, + 589 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {k l} = \\mathrm {K L} \\left(\\mathcal {N} \\left(\\mu , \\sigma^ {2}\\right) | | \\mathcal {N} (0, 1)\\right) \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 169, + 590, + 467, + 607 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Next, the encoder is fine-tuned along with the pre-trained $\\mathcal{D}_I$ and $\\mathcal{D}_P$ from the reconstruction task using the loss in 11 with $\\mathcal{L}_{kl}$ .", + "bbox": [ + 76, + 609, + 467, + 652 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Refinement Both the reconstruction and generation tasks share the same contour refinement process. Given $\\partial \\mathcal{O}$ and $\\mathcal{I}$ , the refinement process produces the optimized glyph contour in SVG format by inference-time optimization. In the optimization, we utilize DiffVG [22], denoted as DR, to render the contour in a differentiable manner. The control points of $\\mathcal{O}$ are refined to minimize the following loss function:", + "bbox": [ + 76, + 657, + 467, + 775 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {r e f i n e}} = \\mathcal {L} _ {\\text {r a s}} + \\lambda_ {\\text {r e g}} \\mathcal {L} _ {\\text {r e g}} \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 178, + 777, + 467, + 794 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{\\text{render}}$ is the photometric loss between the rasterized image and the image branch output.", + "bbox": [ + 76, + 800, + 467, + 828 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {r a s} = \\left| \\left| \\mathrm {D R} (\\partial \\mathcal {O}) - \\mathcal {I} \\right| \\right| _ {1} \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 187, + 830, + 467, + 845 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The regularization term limits the overall length of $\\mathcal{O}$ .", + "bbox": [ + 76, + 847, + 431, + 861 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {r e g} = \\sum_ {i = 1} ^ {K} \\operatorname {l e n} \\left(C _ {i}\\right) \\tag {18}\n$$\n", + "text_format": "latex", + "bbox": [ + 205, + 863, + 467, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5.2 Unsigned Distance Field Warm-up", + "text_level": 1, + "bbox": [ + 500, + 90, + 794, + 106 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Although the vector branch is end-to-end trainable, the gradients only appear near the boundaries. Therefore, to overcome the vanishing gradient problem, we add an extra loss based on the unsigned distance field (UDF) of the vector parts to warm up the system training.", + "bbox": [ + 496, + 116, + 890, + 191 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In general, for two closed curves $c_{1}, c_{2}$ , we cannot obtain the exact SDF of the shape after arbitrary boolean operations on the curves by point-wise operations on their respective SDFs. For the union of two SDFs, as an approximation, we have", + "bbox": [ + 496, + 191, + 890, + 265 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\ns _ {c _ {1} \\cup c _ {2}} (\\boldsymbol {x}) \\left\\{ \\begin{array}{l l} = \\min \\left(s _ {c _ {1}} (\\boldsymbol {x}), s _ {c _ {2}} (\\boldsymbol {x})\\right), & \\boldsymbol {x} \\notin c _ {1} \\cup c _ {2} \\\\ \\leq \\min \\left(s _ {c _ {1}} (\\boldsymbol {x}), s _ {c _ {2}} (\\boldsymbol {x})\\right), & \\boldsymbol {x} \\in c _ {1} \\cup c _ {2} \\end{array} \\right. \\tag {19}\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 266, + 890, + 310 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The $\\min(\\cdot)$ operation gives a correct SDF outside the shape but an inaccurate SDF inside the shape. Similarly, the $\\max(\\cdot)$ gives a correct SDF inside and an inaccurate SDF outside for the intersection of two SDFs. Therefore, it is hard to calculate the accurate SDF $s_{\\mathcal{O}}$ for the glyph. Fortunately, we only aim to provide a coarse initialization for the dual parts, preventing the optimization process from falling into local minima early in the training. We find that using an approximate unsigned distance field works well to achieve this goal. Here we define the UDF $u$ as", + "bbox": [ + 496, + 311, + 890, + 460 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nu (\\boldsymbol {x}) = \\max (0, s (\\boldsymbol {x})) \\tag {20}\n$$\n", + "text_format": "latex", + "bbox": [ + 620, + 463, + 890, + 478 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\min (\\cdot)$ gives a correct global UDF for unions of shapes. The approximate UDF $\\hat{u}_q$ is computed as", + "bbox": [ + 496, + 479, + 890, + 508 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {u} _ {g} = \\min _ {i} \\left[ \\max \\left(u _ {P _ {i}}, u _ {Q _ {i}}\\right) \\right] \\tag {21}\n$$\n", + "text_format": "latex", + "bbox": [ + 606, + 510, + 890, + 530 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where", + "bbox": [ + 500, + 531, + 544, + 542 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nu _ {P _ {i}} (\\boldsymbol {x}) = \\max \\left(s _ {P _ {i}} (\\boldsymbol {x}), 0\\right)\n$$\n", + "text_format": "latex", + "bbox": [ + 599, + 545, + 776, + 561 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} u _ {Q _ {i}} (\\boldsymbol {x}) = \\max (- s _ {Q _ {i}} (\\boldsymbol {x}), 0) \\end{array} \\tag {22}\n$$\n", + "text_format": "latex", + "bbox": [ + 599, + 556, + 888, + 580 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We apply the following losses to warm up the training process for the font reconstruction task:", + "bbox": [ + 496, + 585, + 888, + 613 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\lambda_ {P} \\mathcal {L} _ {P} + \\lambda_ {I} \\mathcal {L} _ {I} + \\lambda_ {u} \\mathcal {L} _ {u}\n$$\n", + "text_format": "latex", + "bbox": [ + 578, + 614, + 769, + 628 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {u} = \\mathbb {E} _ {\\boldsymbol {x} \\sim [ - 1, 1 ] ^ {2}} \\left[ \\left| \\left| \\hat {u} _ {g} (\\boldsymbol {x}) - u _ {g} (\\boldsymbol {x}) \\right| \\right| _ {1} \\right] \\tag {23}\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 625, + 888, + 648 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where the ground truth UDF $u_{g}$ is derived from the pixel image $g$ .", + "bbox": [ + 496, + 648, + 888, + 678 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 694, + 630, + 710 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Dataset", + "text_level": 1, + "bbox": [ + 500, + 720, + 593, + 733 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We use the SVG-Fonts dataset from SVG-VAE [27] for all the experiments. Following DeepVecFont [39], we sample a subset of the dataset with 8035 fonts for training and 1425 fonts for evaluation. The resolution of input glyph images is set to $128 \\times 128$ . Please refer to the supplementary material for implementation details.", + "bbox": [ + 496, + 743, + 890, + 834 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Font Reconstruction", + "text_level": 1, + "bbox": [ + 500, + 845, + 692, + 859 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this experiment, we investigate how faithfully different methods can reconstruct the input glyph images with", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "14197", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/a1fe2572a50a84efd3196dcfc6c9d15a7514b58a04c7cb3ffb2ce93aa21d0b1a.jpg", + "image_caption": [ + "Figure 3. Comparison of font reconstruction quality. We show the input glyph image row by row, our reconstructed image $\\mathcal{I}$ from the image branch, dual-parts $\\mathcal{O}$ from the vector branch, and our final result after contour refinement, as well as vector outputs from alternative methods." + ], + "image_footnote": [], + "bbox": [ + 83, + 89, + 467, + 308 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "vector outputs, which can also be regarded as font vectorization. Im2Vec [33] and our method directly produce vector representations from glyph images, while for Multi-Implicits [34], we adopt the 2D marching cube algorithm and extract the contours. As can be seen from a qualitative comparison in Fig. 3, our representation could faithfully reconstruct global shapes as well as local details from the pixelated input. Im2Vec [33] could only preserve coarse shapes and suffers from wrong topologies as shown in the \"A\" example as it is easy to fall into local optimum without the global gradient. Multi-Implicits [34] results in finer details than Im2Vec [33] but still exhibit unsmooth edges and rounded corners. To quantitatively evaluate how accurate the vector outputs are, we calculate three metrics, namely SSIM, L1, and s-IoU, between the rendered images and the ground truth images under different resolutions. Tab. 1 shows that our method surpasses the two alternatives by a clear margin on all metrics. Using parametric curves as primitives, our method, along with Im2Vec [33], maintains a stable L1 error across all resolutions for the smooth edges, while for Multi-Implicits [34] the L1 error gets larger as the resolution increases, resulting from the high-frequency noises at the extracted boundaries.", + "bbox": [ + 75, + 393, + 468, + 739 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Font Generation", + "text_level": 1, + "bbox": [ + 76, + 753, + 240, + 768 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To evaluate the generation ability of our method, we adopt the few-shot font generation setting, where a subset of glyphs with the same style is given and models are trained to produce a complete set of glyphs that are consistent with the input glyphs in style. This task is also dubbed \"font complement\" or \"font style transfer\" in other works. We compare our method with several popular methods in font generation: DeepVecFont [39], Multi-Implicits [34],", + "bbox": [ + 75, + 779, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/75e8b75ee9657237fa6cc3513f96959580bde2dccf3a5d952d6abeb86e9822c8.jpg", + "table_caption": [ + "Table 1. Quantitative comparison with Im2Vec [33] and Multi-Implicits [34] on three image-level metrics at different resolutions for the font reconstruction task. The gray scale is normalized to [0,1]. s-IoU, from [34], measures the overlap." + ], + "table_footnote": [], + "table_body": "
MethodResolutionSSIM↑L1↓s-IoU↑
Ours12820.94360.01370.8879
25620.94830.01360.9068
51220.95790.01360.9135
Multi-Implicits12820.92310.01830.8709
25620.92620.02080.8721
51220.94190.02130.8739
Im2Vec12820.78000.05040.6832
25620.85660.05040.6847
51220.89570.05040.6851
", + "bbox": [ + 501, + 152, + 911, + 333 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Im2Vec [33] and Attr2Font [38]. For a fair comparison, we use the same four characters, 'A', 'B', 'a', and 'b' as style references for each font and evaluate image-level metrics on the generated characters. Since Im2Vec [33] is an image vectorization method, we apply it to the images generated by Attr2Font [38]. Multi-Implicits [34] follows an auto-decoder architecture, so we freeze the decoder and find the optimal latent vector for a font by minimizing the losses between the given style references and the predicted ones using gradient descent.", + "bbox": [ + 496, + 340, + 892, + 492 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As illustrated in Fig. 4, DeepVecFont [39] may generate characters with wrong topologies due to the incorrect initial contour prediction, such as 'A', 'L', and 'Z'. The fixed topology in the optimization process makes it difficult to produce the necessary details, which are particularly symbolic in serif fonts. In addition, unconstrained contour generation may also produce self-intersections, like the 'g' and 'r', which are not easy to fix in subsequent processing. Im2Vec [33] tends to produce rounded corners and is only able to produce the coarse style, lacking details. Multi-Implicits [34] generates vector results from implicit signed distance fields (SDF) through a 2D Marching cube algorithm, leading to free-form contours. Therefore the edges are not smooth enough and have unpleasing noises, such as the 'g' and 'x' in the figure. Attr2Font [38] can generate generally satisfactory font images, but it cannot maintain high-quality rendering when scaling.", + "bbox": [ + 496, + 492, + 892, + 750 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Compared with the above methods, our method is capable of not only grasping the overall style of the input references but also generating new glyphs with clear boundaries and sharp edges, achieving optimal visual quality. The efficient dual-part representation along with the differentiable occupancy supervision establishes a link between pixelated images and vector graphics, allowing the unsupervised synthesis of vector fonts with aligned shapes and correct topologies. The refinement step allows the composition of the contour to be freely changed and thus ensures", + "bbox": [ + 496, + 750, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "14198", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/5de01a1d0d9c18081a2b7831b8e1fb61bbc976138deaeb67a5c0d0125b7503f7.jpg", + "image_caption": [ + "Figure 4. Font generation results of Attr2Font, Im2Vec, Multi-Implicits, DeepVecFont, and DualVector. The input style references are marked with red boxes. We trace the zero-level sets of SDFs in a piece-wise linear way to get SVGs from Multi-Implicits [34]. Typical failure cases are marked in blue dashed boxes. Some details are zoomed-in in the leftmost column." + ], + "image_footnote": [], + "bbox": [ + 83, + 90, + 890, + 404 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/b292ead284b4123d5f7eb22ab7c0d0414c2db325a626e3ea0f092ef891655be3.jpg", + "table_caption": [ + "Table 2. Quantitative comparison of image-level metrics of Attr2Font [38], Im2Vec [33], Multi-Implicits [34], DeepVecFont [39] and DualVector in the font complement experiment." + ], + "table_footnote": [ + "[38] synthesizes pixelated images only." + ], + "table_body": "
MethodResolutionSSIM↑L1↓s-IoU↑
Ours12820.82880.04610.7395
25620.87270.04600.7453
51220.90750.04600.7469
DeepVecFont12820.81650.05060.7125
25620.86400.05060.7171
51220.90110.05060.7182
Multi-Implicits12820.80250.05780.6857
25620.85330.06030.6814
51220.89140.06080.6811
Im2Vec12820.75760.07330.5731
25620.82700.07340.5751
51220.87390.07340.5756
Attr2Fonta12820.78410.05120.6393
", + "bbox": [ + 78, + 505, + 486, + 753 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "that our synthesized glyphs have high-fidelity details under the guidance of high-resolution glyph images. Quantitative results on three image-level metrics at different resolutions are shown in Tab. 2. For methods producing vector shapes, we also count the average number of commands used for each synthesized vector character, with smaller numbers indicating more compact outputs. The results are shown in Tab. 3. Multi-Implicits [34] uses a large number of short", + "bbox": [ + 75, + 779, + 472, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/a54c9bb74d7bf541a51456ae01b53ac237be88e36f2d731f9ba097371e87a6e4.jpg", + "table_caption": [ + "Table 3. The average number of commands used per glyph for different methods in the font generation task. M, L, Q, and C denote move, straight line, quadratic Bezier curve, and cubic Bezier curve respectively." + ], + "table_footnote": [], + "table_body": "
CommandMLQCTotal↓
Ours1.428.2111.06020.69
DeepVecFont [39]1.378.2309.6819.28
Multi-Implicits [34]6.161446.53001452.69
Im2Vec [33]4008084
Human-Designed1.389.1708.5119.06
", + "bbox": [ + 504, + 518, + 913, + 623 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "line segments to represent the boundary due to the marching cube algorithm. Im2Vec [33] represents a shape with 4 parts each enclosed by 20 cubic Bezier curves, lacking flexibility and details. Our method performs boolean operations on the quadratic Bezier curves from dual parts, achieving comparable compactness with human-designed fonts and outputs from methods with vector supervision [39].", + "bbox": [ + 496, + 638, + 893, + 744 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Ablation Studies", + "text_level": 1, + "bbox": [ + 500, + 755, + 665, + 770 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To demonstrate the effectiveness of several key design choices in our method, we conduct ablation studies on the font reconstruction task. We investigate the following degraded variants: (a) replace the union of dual parts with the union of all the paths; (b) train without the UDF warm-up process; and (c) remove the refining strategy during refinement. We show the comparison results of a representative case in Fig. 5. Without the dual-part representation, variant", + "bbox": [ + 496, + 779, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "14199", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6581d532c982eec0a674319624eee9aeeed566969e9c6c0dfbaefbda9dc20821.jpg", + "image_caption": [ + "Figure 5. The contours of an \"M\" reconstructed by our method, compared with three degraded variants." + ], + "image_footnote": [], + "bbox": [ + 94, + 74, + 462, + 200 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/8d608d58308fea82086583ca3828dc0d263fa94096587671b0cfbf17811007cd.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
L1↓#Lines↓# Curves↓
(a) w/o dual parts0.014312.2314.06
(b) w/o warm-up0.014611.1913.12
(c) w/o refining strategy0.0148-22.07
Full Model0.01368.9711.81
", + "bbox": [ + 78, + 285, + 493, + 385 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "(a) cannot reconstruct concave regions very well, as they can be hard to represent by the union of simply closed paths. Without UDF initialization, variant (b) produces contours with useless curves that are hard to be eliminated during optimization. Without the refining strategy, variant (c) may generate inaccurate edges with zigzags. Quantitative results in Tab. 4 also verify the quality improvements brought by the three design choices.", + "bbox": [ + 75, + 401, + 467, + 521 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We also experimentally investigate the effect of different $(N,M)$ s on the representation capacity. We choose several settings of $(N,M)$ and train only the vector branch (i.e. no contour refinement) with the same number of epochs to reconstruct the input. Tab. 5 shows that $M = 4$ is optimal and the reconstruction accuracy of the vector branch increases as $N$ increases. The accuracy does not gain too much changing $N$ from 6 to 8. So considering the time cost for training and inference, we select $(N,M) = (6,4)$ in the above experiments.", + "bbox": [ + 75, + 521, + 467, + 672 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/55919d547d1caabadd9a4835ca7f459c8792fdd1986452ac55a1bbfa20dbbb07.jpg", + "table_caption": [ + "Table 5. Different reconstruction settings and metrics. The image-based metrics use a resolution of $512 \\times 512$ ." + ], + "table_footnote": [], + "table_body": "
NMSSIM↑L1↓s-IOU↑
240.92620.02820.8338
440.92920.02590.8464
640.93030.02500.8512
840.93060.02470.8525
630.92930.02560.8480
650.93000.02520.8498
", + "bbox": [ + 135, + 708, + 410, + 832 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Font Sampling and Interpolation", + "text_level": 1, + "bbox": [ + 76, + 845, + 366, + 863 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In the font generation task, the style latent code $z_{style}$ is trained with a variational loss $\\mathcal{L}_{kl}$ , enabling generating", + "bbox": [ + 75, + 869, + 467, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "fonts of new styles by sampling $z_{style}$ from $\\mathcal{N}(0,1)$ . We show in Fig. 1 (left) and Fig. 6 multiple styles of fonts sampled. Please refer to our supplementary material for more examples. Also, benefiting from our dual-part representation, we can perform smooth interpolation between arbitrary font styles as demonstrated in Fig. 1 (right).", + "bbox": [ + 496, + 90, + 890, + 181 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0bc638233b068125a099ec9c73b9f7b8e4ac1d4384e8b99eeecb135d8ed4fc57.jpg", + "image_caption": [ + "Table 4. Quantitative results of reconstruction accuracy for different model variants in ablation studies. All the output vector glyphs are rendered at $512 \\times 512$ to compute the L1 error.", + "Figure 6. New fonts with style codes sampled in $\\mathcal{N}(0,1)$ ." + ], + "image_footnote": [], + "bbox": [ + 501, + 185, + 890, + 311 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Limitations", + "text_level": 1, + "bbox": [ + 500, + 349, + 622, + 364 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The contour refinement step requires gradient descent during inference and therefore imposes a large time overhead, similar to DeepVecFont [39]. The process could potentially be accomplished by forwarding inferences of some generation models, such as the diffusion models [13]. Another limitation is that DualVector only focuses on the synthesis of glyphs on a fixed-size canvas, without considering the kerning between them, making the spacing between characters less natural. This may be solved by post-processing the SVG with some automatic kerning methods or by learning through a data-driven approach.", + "bbox": [ + 496, + 375, + 890, + 541 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 556, + 617, + 571 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We present DualVector as a new representation and generation method for vector fonts. DualVector models a glyph as dual parts and introduces a contour refinement step to add pleasing details to the contours of the dual parts. Our method is able to generate vector fonts without vector supervision, which can be directly converted to common digital font formats for content presentation and distribution. Comparisons with different methods of font reconstruction and generation tasks demonstrate that our approach produces fonts with the best quality among all the alternatives. In the future, more plausible initialization and supervision could be exploited to generalize this representation to more complex fonts (e.g. Chinese fonts). We hope this research contributes to the typeface design industry and provide inspiration for broader works on the understanding and generation of 2D man-made content such as cartoon characters and icons.", + "bbox": [ + 496, + 582, + 890, + 838 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement This work was supported by the Natural Science Foundation of China (Project Number 61832016), and Tsinghua-Tencent Joint Laboratory for Internet Innovation Technology.", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "14200", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Adobe Inc. 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Graph., 41(3):34:1-34:17, 2022. 2" + ], + "bbox": [ + 501, + 92, + 890, + 443 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "14202", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/DualVector_ Unsupervised Vector Font Synthesis With Dual-Part Representation/64299b13-1bde-4ab7-949f-d03cb4326255_model.json b/2023/DualVector_ Unsupervised Vector Font Synthesis With Dual-Part Representation/64299b13-1bde-4ab7-949f-d03cb4326255_model.json new file mode 100644 index 0000000000000000000000000000000000000000..83ee25d618651a7d31beb2164257357d21766642 --- /dev/null +++ b/2023/DualVector_ Unsupervised Vector Font Synthesis With Dual-Part Representation/64299b13-1bde-4ab7-949f-d03cb4326255_model.json @@ -0,0 +1,2376 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.082, + 0.131, + 0.89, + 0.155 + ], + "angle": 0, + "content": "DualVector: Unsupervised Vector Font Synthesis with Dual-Part Representation" + }, + { + "type": "text", + "bbox": [ + 0.208, + 0.18, + 0.766, + 0.218 + ], + "angle": 0, + "content": "Ying-Tian Liu1 Zhifei Zhang2 Yuan-Chen Guo1 Matthew Fisher2 Zhaowen Wang2 Song-Hai Zhang1*" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.216, + 0.885, + 0.27 + ], + "angle": 0, + "content": "\\(^{1}\\)BNRist, Department of Computer Science and Technology, Tsinghua University \\(^{2}\\) Adobe Research \\(\\{\\text { liuyingt20@mails.,guocyl9@mails.,shz@} \\}\\)tsinghua.edu.cn \\(\\{\\text { zzhang, matfishe, zhawang}\\} @\\)adobe.com" + }, + { + "type": "image", + "bbox": [ + 0.09, + 0.279, + 0.406, + 0.39 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.432, + 0.281, + 0.87, + 0.389 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.397, + 0.893, + 0.426 + ], + "angle": 0, + "content": "Figure 1. High-quality vector fonts (copyable on electronic devices) synthesized by DualVector (left), with smoothly-interpolated styles (right). Both sentences are pangrams. Please zoom in for details." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.439, + 0.314, + 0.454 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.471, + 0.474, + 0.775 + ], + "angle": 0, + "content": "Automatic generation of fonts can be an important aid to typeface design. Many current approaches regard glyphs as pixelated images, which present artifacts when scaling and inevitable quality losses after vectorization. On the other hand, existing vector font synthesis methods either fail to represent the shape concisely or require vector supervision during training. To push the quality of vector font synthesis to the next level, we propose a novel dual-part representation for vector glyphs, where each glyph is modeled as a collection of closed \"positive\" and \"negative\" path pairs. The glyph contour is then obtained by boolean operations on these paths. We first learn such a representation only from glyph images and devise a subsequent contour refinement step to align the contour with an image representation to further enhance details. Our method, named DualVector, outperforms state-of-the-art methods in vector font synthesis both quantitatively and qualitatively. Our synthesized vector fonts can be easily converted to common digital font formats like TrueType Font for practical use. The code is released at https://github.com/thuliu-yt16/dualvector." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.804, + 0.21, + 0.82 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.83, + 0.47, + 0.876 + ], + "angle": 0, + "content": "Fonts with various styles play an important role in content display and distribution. Excellent font design is time-consuming and labor-intensive. Recent machine learning" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.439, + 0.893, + 0.501 + ], + "angle": 0, + "content": "innovations have made font generation possible, but how to automatically generate high-quality vector fonts remains a task of practical importance in the artistic and computer graphics and vision communities." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.509, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Benefiting from the development of image generation techniques, mainstream font synthesis methods [2, 12, 24, 41, 42] could generate pixelated glyph images. Despite the promising quality, images of glyphs incur aliasing artifacts on edges when discretely sampled, and thus are not competent for high-quality rendering or printing at arbitrary resolutions. To alleviate this problem, some methods [7, 34] adopt coordinate-based neural networks to model a glyph as a contiguous neural field, which have also shown great potential in modeling 3D geometry and scenes [7, 30, 32]. Although glyphs represented by the implicit field can be rendered at arbitrary resolutions, it is hard to preserve details in high-frequency regions such as edges and corners, not to mention the high computational costs as the network needs to be evaluated for every pixel. Researchers have made much effort to directly synthesize vector fonts [4, 27, 33, 39] in recent years, with the main difficulty lying in finding a representation of vector graphics that can be encoded or decoded effectively in a deep learning framework. One typical approach represents a vector shape as a sequence of drawing commands and adopts sequence modeling techniques such as recurrent networks and transformers. The drawbacks are twofold: (1) Modeling command sequences can be much harder than images. There are infinitely many command sequences that correspond to the same-looking shape, which brings ambiguities in learning and makes it hard to construct" + }, + { + "type": "page_footnote", + "bbox": [ + 0.102, + 0.888, + 0.228, + 0.901 + ], + "angle": 0, + "content": "*Corresponding author" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14193" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.138 + ], + "angle": 0, + "content": "an effective manifold for valid glyph shapes. (2) Ground-truth drawing commands are often required to provide sufficient supervision for high-quality modeling and synthesis." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.14, + 0.471, + 0.337 + ], + "angle": 0, + "content": "To overcome these challenges, we first propose a dual-part vector font representation, where each glyph shape is the union of a fixed number of dual parts. Each dual part is formed by the subtraction of a \"positive\" and a \"negative\" geometric primitive. While there are many choices for the geometric primitives [6, 8, 25], we adopt closed Bezier paths for their great representational ability. They are also widely supported in digital font formats which makes it easy to convert our representation to these formats for practical use. We reduce the problem of predicting complicated drawing command sequences to predicting multiple basic primitives. From this perspective, both manifold learning and latent space interpolation become more feasible." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.34, + 0.471, + 0.658 + ], + "angle": 0, + "content": "Based on the dual-part representation, we introduce DualVector, a method to learn such a representation for high-quality font modeling and synthesis from only glyph images without any vector supervision. A straightforward way to achieve this is to directly optimize the parameters of the Bezier curves with differentiable rendering techniques for vector graphics [22]. However, this approach easily gets stuck in the local minima as valuable gradients are only defined at shape intersections. Taking inspiration from implicit field training for 2D and 3D shapes [6, 25, 32], we supervise the occupancy value derived from the analytical expression of the Bezier curves and adopt an initialization strategy based on unsigned distance field (UDF) to provide dense gradients across the entire pixel space. For local detail fidelity, we also train a glyph image generation model and devise a subsequent contour refinement step to align the contour of the vector shape with that of the image by differentiable rendering [22]. We compare our approach with state-of-the-art methods in font modeling and generation and demonstrate the superior quality of our vector font outputs. Our main contributions are:" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.685, + 0.469, + 0.732 + ], + "angle": 0, + "content": "- A new dual-part font representation based on boolean operations of Bezier paths, which enables efficient shape modeling and unsupervised manifold learning." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.755, + 0.469, + 0.831 + ], + "angle": 0, + "content": "- A method named DualVector that models both the dual-part and pixelated representation, and introduces a contour refinement step to obtain vector fonts with richer details as well as a UDF initialization strategy for better convergence." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.856, + 0.469, + 0.901 + ], + "angle": 0, + "content": "- DualVector achieves state-of-the-art quality in font modeling and generation, with outputs that can be easily converted to common digital font formats." + }, + { + "type": "list", + "bbox": [ + 0.097, + 0.685, + 0.469, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.09, + 0.642, + 0.105 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.115, + 0.729, + 0.132 + ], + "angle": 0, + "content": "2.1. Glyph Image Generation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.139, + 0.892, + 0.336 + ], + "angle": 0, + "content": "Benefiting from the development of image generation [10, 14, 16], either black-white [12, 15, 37, 40] or artistic glyph image generation [2, 23, 41, 42] is well explored in the past decade. MC-GAN [2] synthesized ornamented glyphs for capital letters in an end-to-end manner from a small subset of the same style. Attr2Font [38] generated visually pleasing results according to style attributes and content references. Most of these methods follow the disentanglement of style and content codes, and so does the image generation branch in DualVector. But these glyph image generation efforts do not step outside the 2D pixelated representation which sets an upper bound for rendering quality, efficiency, and practicality." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.345, + 0.831, + 0.361 + ], + "angle": 0, + "content": "2.2. Image Rasterization and Vectorization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.369, + 0.892, + 0.611 + ], + "angle": 0, + "content": "Rasterization and vectorization are dual problems in image processing. Previous efforts on rasterization have typically focused on anti-aliasing [9, 11, 31] and high-performance rendering on modern graphics hardware [3, 17, 21, 26]. Traditional image vectorization approaches rely on region segmentation, line extraction, and contour tracing for gray-scale images [35], pixel arts [18], animations [44] and general images [1, 5, 19, 36, 45, 46]. Recently, researchers have turned to bridging the raster and vector domains [22, 29], enabling existing well-established algorithms for raster images to be also applied to vector representations. DiffVG [22] is a differentiable rendering technique for vector graphics enabling the optimization of vector primitive parameters based on raster criteria. In our work, it is employed to align the vector and pixel representation in the contour refinement step." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.621, + 0.719, + 0.636 + ], + "angle": 0, + "content": "2.3. Vector Font Generation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.892, + 0.901 + ], + "angle": 0, + "content": "SVG-VAE [27] was the first attempt to build a sequential generative model on SVG fonts. DeepSVG [4] developed a hierarchical transformer-based generative model for complex SVG icons generation and interpolation. Exploiting implicit neural representation, multi-implicit [34] modeled fonts with a permutation-invariant set of learned implicit functions which can preserve font features, such as smooth edges and sharp corners, and generate good interpolation results. Liu et al. [25] proposed a primitive-based representation, which views glyph shapes as the combination of primitives enclosed by implicit curves. Implicit representation-based methods can convert the zero-level set of their output fields to contour representation with the 2D marching cube [28] algorithm, although it produces multiple segmented lines and lacks accuracy and efficiency in rendering and editing. Im2Vec [33] can synthesize complex vector graphics with varying topologies without vector super" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "14194" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.134, + 0.098, + 0.836, + 0.366 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.369, + 0.895, + 0.427 + ], + "angle": 0, + "content": "Figure 2. DualVector contains the following components: (a) a vector branch that maps the latent code \\( z \\) to several closed Bézier paths which are further gathered to form a global shape of the glyph; (b) an image branch that generates pixelated images with faithful details; (c) a contour refinement step that obtains the contour via boolean operations on dual-parts and optimizes it with the image guidance at inference time. Both the vector and the image branch are trained using the glyph images. Dual parts are distinguished by their colors." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.437, + 0.473, + 0.589 + ], + "angle": 0, + "content": "vision. It rendered layered Bézier paths predicted from image features using DiffVG [22] and trains the system in an auto-encoding manner. DeepVecFont [39] adopted a dual-modality learning framework that utilizes both sequence and image features for high-quality vector font synthesis. But the results it produces may have the wrong topology, including self-intersection or invalid paths. In contrast to these methods, our approach does not require vector supervision and is very efficient in vector representation, with high quality glyph generation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.602, + 0.199, + 0.618 + ], + "angle": 0, + "content": "3. DualVector" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.627, + 0.47, + 0.84 + ], + "angle": 0, + "content": "In this section, we first illustrate the proposed dual-part representation for fonts (Sec. 3.1) and then introduce the components of DualVector for training this representation from glyph images (Secs. 3.2 to 3.4) and how the model can be used for font reconstruction and generation (Sec. 3.5). In DualVector, we adopt a joint representation of vector and image for fonts, as shown in Fig. 2. The latent space is shared by both modalities, and we associate each glyph with a latent code \\( z \\in \\mathbf{R}^d \\) produced by the task-specific encoding process. The latent code \\( z \\) is fed into the two decoding branches to obtain a dual-part representation and an image representation respectively. The output of the vector branch is further processed by a contour refinement step to generate the final contour representation under the image guidance." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.848, + 0.313, + 0.864 + ], + "angle": 0, + "content": "3.1. Dual-Part Representation" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.903 + ], + "angle": 0, + "content": "In our dual-part representation, we consider the closed parametric Bézier paths as our basic primitives for several" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.437, + 0.892, + 0.666 + ], + "angle": 0, + "content": "reasons: (1) Bézier paths are powerful enough to approximate various shapes; (2) The contour of a closed shape produced by boolean operations on Bézier paths is still a set of Bézier paths, i.e., the closure property; (3) Bézier paths are widely used in modern font design, making the learned representation highly applicable. For convenience, we use a triplet of control points \\((\\pmb{a},\\pmb{b},\\pmb{c})\\) to denote a quadratic Bézier curve \\(B(\\cdot ;\\pmb {a},\\pmb {b},\\pmb {c})\\) determined by the control points: \\(B(t;\\pmb {a},\\pmb {b},\\pmb {c}) = (1 - t)^{2}\\pmb {a} + (1 - t)t\\pmb {b} + t^{2}\\pmb {c}t\\in [0,1]\\) 1 Since a glyph often consists of a number of strokes with similar appearances, we propose to represent each glyph \\(g\\) with \\(N\\) closed Bézier paths \\(\\{P_i\\}_{i = 1}^N\\) . Each path \\(P_{i}\\) is defined by \\(M\\) end-to-end connected quadratic Bézier curves \\(\\{B_{i,j}(\\pmb{x}_{i,2j - 1},\\pmb{x}_{i,2j},\\pmb{x}_{i,2j + 1})\\}_{j = 1}^{M}(\\pmb{x}_{i,2M + 1} = \\pmb{x}_{i,1})\\) .We introduce the occupancy field of a closed path \\(P_{i}\\) as" + }, + { + "type": "equation", + "bbox": [ + 0.604, + 0.667, + 0.891, + 0.697 + ], + "angle": 0, + "content": "\\[\n\\mathcal {O} _ {P _ {i}} (\\boldsymbol {x}) = \\left\\{ \\begin{array}{l l} 1, & \\boldsymbol {x} \\in P _ {i} \\\\ 0, & \\boldsymbol {x} \\notin P _ {i} \\end{array} \\right. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.698, + 0.892, + 0.789 + ], + "angle": 0, + "content": "The entire glyph shape \\( g \\) could simply be denoted as the union of all the paths \\( \\cup_{i} P_{i} \\). We normalize the coordinate range of the glyph to \\( [-1, 1]^{2} \\). Thus given any point \\( x \\) on the canvas \\( [-1, 1]^{2} \\), we can determine whether it is inside the represented glyph shape by a maximum operation, leading to the occupancy field of \\( g \\):" + }, + { + "type": "equation", + "bbox": [ + 0.549, + 0.789, + 0.891, + 0.821 + ], + "angle": 0, + "content": "\\[\n\\mathcal {O} (\\boldsymbol {x}) = \\max _ {i} \\mathcal {O} _ {P _ {i}} (\\boldsymbol {x}) = \\left\\{ \\begin{array}{l l} 1, & \\boldsymbol {x} \\in \\cup_ {i} P _ {i} \\\\ 0, & \\boldsymbol {x} \\notin \\cup_ {i} P _ {i} \\end{array} \\right. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.895, + 0.903 + ], + "angle": 0, + "content": "However, we find that the above representation can model fonts with convex curves on the contour but struggles to reconstruct shapes with holes. Therefore, in practice, we pair each path \\( P_{i} \\) with a negative path \\( Q_{i} \\), and term this pair \\( (P_{i}, Q_{i}) \\) as a \"dual part\". In this way, \\( g \\) is represented as" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14195" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.445, + 0.106 + ], + "angle": 0, + "content": "\\(\\cup_{i}(P_{i} - Q_{i})\\) . The occupancy field \\(\\mathcal{O}\\) is then derived as:" + }, + { + "type": "equation", + "bbox": [ + 0.078, + 0.108, + 0.469, + 0.152 + ], + "angle": 0, + "content": "\\[\n\\mathcal {O} (\\boldsymbol {x}) = \\max _ {i} [ \\min \\left(\\mathcal {O} _ {P _ {i}} (\\boldsymbol {x}), 1 - \\mathcal {O} _ {Q _ {i}} (\\boldsymbol {x})\\right) ] = \\left\\{ \\begin{array}{l l} 1, & \\boldsymbol {x} \\in g \\\\ 0, & \\boldsymbol {x} \\notin g \\end{array} \\right. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.154, + 0.469, + 0.274 + ], + "angle": 0, + "content": "Even though \\(\\mathcal{O}\\) is the analytical occupancy field of \\(g\\), it is not differentiable w.r.t. the parameters of the paths. Therefore, in order to apply gradient descent to learn such a representation, we calculate the approximate occupancy field \\(\\hat{\\mathcal{O}}\\) from the signed distance field (SDF) of \\(g\\). Since the distance \\(d(p;B)\\) from any point \\(p\\) to a Bézier curve \\(B\\) can be derived analytically, the SDF of a path can be calculated differentiably w.r.t. its control points as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.14, + 0.276, + 0.469, + 0.298 + ], + "angle": 0, + "content": "\\[\ns _ {P _ {i}} (\\boldsymbol {x}) = \\left[ 2 \\mathcal {O} _ {P _ {i}} (\\boldsymbol {x}) - 1 \\right] \\min _ {j} d (\\boldsymbol {x}; B _ {i, j}) \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.298, + 0.469, + 0.342 + ], + "angle": 0, + "content": "Following previous vector graphics rasterization techniques [22, 31, 34], we approximate \\(\\mathcal{O}\\) by analytical pixel prefiltering with a parabolic kernel \\(\\alpha\\):" + }, + { + "type": "equation", + "bbox": [ + 0.168, + 0.344, + 0.314, + 0.361 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathcal {O}} _ {P _ {i}} (\\boldsymbol {x}) = \\alpha \\left(s _ {P _ {i}} (\\boldsymbol {x})\\right)\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.168, + 0.361, + 0.469, + 0.387 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathcal {O}} = \\max _ {i} [ \\min (\\hat {\\mathcal {O}} _ {P _ {i}}, 1 - \\hat {\\mathcal {O}} _ {Q _ {i}}) ] \\tag {6}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.399, + 0.226, + 0.415 + ], + "angle": 0, + "content": "3.2. Vector Branch" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.425, + 0.469, + 0.485 + ], + "angle": 0, + "content": "The vector branch takes a latent code \\(z\\) and outputs a set of dual-parts that represent a vector glyph. The path decoder \\(\\mathcal{D}_P\\) directly predicts the control points of the positive paths \\(\\{P_i\\}_{i=1}^N\\) and the negative ones \\(\\{Q_i\\}_{i=1}^N\\) from \\(z\\):" + }, + { + "type": "equation", + "bbox": [ + 0.129, + 0.486, + 0.469, + 0.502 + ], + "angle": 0, + "content": "\\[\n\\left\\{\\boldsymbol {x} _ {i, j} \\right\\} = \\mathcal {D} _ {P} (z), 1 \\leq i \\leq 2 N, 1 \\leq j \\leq 2 M \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.502, + 0.469, + 0.535 + ], + "angle": 0, + "content": "where \\(\\{\\pmb{x}_{i,j}\\}_{i = 1}^{N}\\) are control points for \\(\\{P_i\\}_{i = 1}^N\\) and \\(\\{\\pmb{x}_{i,j}\\}_{i = N + 1}^{2N}\\) are control points for \\(\\{Q_i\\}_{i = 1}^N\\)" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.546, + 0.223, + 0.562 + ], + "angle": 0, + "content": "3.3. Image Branch" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.571, + 0.469, + 0.631 + ], + "angle": 0, + "content": "To combine with the advantages of image generation approaches, we train an auxiliary image branch that maps \\( z \\) to a pixelated image \\( \\mathcal{I} \\) of the glyph it represents. Here we adopt a CNN-based decoder \\( \\mathcal{D}_I \\):" + }, + { + "type": "equation", + "bbox": [ + 0.234, + 0.633, + 0.469, + 0.648 + ], + "angle": 0, + "content": "\\[\n\\mathcal {I} = \\mathcal {D} _ {I} (z) \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.649, + 0.469, + 0.679 + ], + "angle": 0, + "content": "where \\(\\mathcal{I}\\) is a gray-scale image in shape \\(H\\times W\\). It provides detailed shape guidance to refine the vector shape contour." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.692, + 0.272, + 0.707 + ], + "angle": 0, + "content": "3.4. Contour Refinement" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.717, + 0.469, + 0.822 + ], + "angle": 0, + "content": "Although the dual-part representation produced by the vector branch can already be rendered, there still exists a gap between it and modern contour representations for fonts. Therefore, we first convert it to the contour of the glyph \\(\\partial \\mathcal{O}\\) with an off-the-shelf tool Paper.js [20] which can perform arbitrary boolean operations on SVG paths. Here the contour \\(\\partial \\mathcal{O}\\) is a set of K closed Bézier paths." + }, + { + "type": "equation", + "bbox": [ + 0.191, + 0.824, + 0.468, + 0.84 + ], + "angle": 0, + "content": "\\[\n\\partial \\mathcal {O} = \\left\\{C _ {1}, C _ {2}, \\dots , C _ {K} \\right\\} \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.469, + 0.904 + ], + "angle": 0, + "content": "where \\(K\\) denotes the number of independent paths. Each individual part or hole increases \\(K\\) by 1. \\(C_i\\) is a closed Bezier path composed of \\(l_i\\) quadratic Bezier segments \\(\\{\\hat{B}_{i,j}(\\hat{\\pmb{x}}_{i,2j - 1},\\hat{\\pmb{x}}_{i,2j},\\hat{\\pmb{x}}_{i,2j + 1})\\}_{j = 1}^{l_i}\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.182 + ], + "angle": 0, + "content": "After this conversion, we exploit the image generation results to further refine \\(\\partial \\mathcal{O}\\) with differentiable rendering techniques [22]. \\(\\mathcal{I}\\) could naturally serve as a pixelated version of the occupancy field \\(\\mathcal{O}\\). During the refinement, we devise several strategies to improve the quality and efficiency of our representation:" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.204, + 0.892, + 0.25 + ], + "angle": 0, + "content": "Subdivision To improve the representational ability, we split long Bézier curves (with a length greater than \\(10\\%\\) of the canvas width) at their midpoints." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.272, + 0.892, + 0.453 + ], + "angle": 0, + "content": "Simplification To improve the efficiency of the contour representation, we replace the Bézier curves with a line segment connecting its two endpoints if they are close enough. For a Bézier curve \\((a, b, c)\\), we simply define how faithfully the segment \\(ac\\) could represent the curve by the angle between \\(\\vec{ba}\\) and \\(\\vec{bc}\\). Also, we examine if there exist two adjacent Bézier segments that could be combined as a single one. Since all quadratic Bézier curves are parts of a parabola curve, we derive the parameters of the corresponding parabola curves from the control points and combine the two curves if their parameters are close enough. We also aggregate the endpoints of lines and curves that are too short." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.476, + 0.892, + 0.55 + ], + "angle": 0, + "content": "Pruning Prior to refinement, some Bezier paths on the contour may enclose extremely small regions which will confuse the refinement process and produce redundant curves that eventually converge to a single point. We trim those closed paths \\( C_i \\) with areas under a certain threshold." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.552, + 0.892, + 0.581 + ], + "angle": 0, + "content": "More implementation details of these strategies can be found in the supplemental material." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.593, + 0.765, + 0.609 + ], + "angle": 0, + "content": "3.5. Implementation and Training" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.617, + 0.892, + 0.662 + ], + "angle": 0, + "content": "In this subsection, we will dive into how we utilize the proposed representation in both the font reconstruction and generation tasks." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.685, + 0.724, + 0.7 + ], + "angle": 0, + "content": "3.5.1 Optimization Objectives" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.709, + 0.892, + 0.754 + ], + "angle": 0, + "content": "Optimization objectives can be divided into those at training time and those at inference time. The training-time objectives are task-related." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.777, + 0.892, + 0.851 + ], + "angle": 0, + "content": "Font reconstruction. For the font reconstruction task, the input to our system is a gray-scale image of a glyph and the output is the corresponding vector representation. The pixelated image \\(\\mathcal{I}_g\\) of the glyph \\(g\\) is first passed through an image encoder \\(\\mathcal{E}\\) to obtain the latent code \\(z\\):" + }, + { + "type": "equation", + "bbox": [ + 0.66, + 0.853, + 0.891, + 0.87 + ], + "angle": 0, + "content": "\\[\nz = \\mathcal {E} \\left(\\mathcal {I} _ {g}\\right) \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "The latent code is then decoded by our vector branch and image branch into dual-parts \\(\\{(P_i,Q_i)\\}_{i = 1}^N\\) and a pixelated" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "14196" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.468, + 0.121 + ], + "angle": 0, + "content": "output \\(\\mathcal{I}\\). We optimize the trainable modules \\(\\mathcal{E},\\mathcal{D}_I\\) and \\(\\mathcal{D}_P\\) simultaneously with the following loss functions:" + }, + { + "type": "equation", + "bbox": [ + 0.206, + 0.124, + 0.468, + 0.138 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\lambda_ {P} \\mathcal {L} _ {P} + \\lambda_ {I} \\mathcal {L} _ {I} \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.14, + 0.38, + 0.154 + ], + "angle": 0, + "content": "where we adopt an extra perceptual loss [43]:" + }, + { + "type": "equation", + "bbox": [ + 0.149, + 0.156, + 0.468, + 0.178 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {P} = \\mathbb {E} _ {\\boldsymbol {x} \\sim [ - 1, 1 ] ^ {2}} \\left[ \\left\\| \\hat {\\mathcal {O}} (\\boldsymbol {x}) - \\mathcal {I} _ {g} (\\boldsymbol {x}) \\right\\| _ {1} \\right] \\tag {12}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.153, + 0.176, + 0.376, + 0.192 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {I} = \\left| \\left| \\mathcal {I} - \\mathcal {I} _ {g} \\right| \\right| _ {2} + \\operatorname {L P I P S} (\\mathcal {I}, \\mathcal {I} _ {g})\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.197, + 0.468, + 0.408 + ], + "angle": 0, + "content": "Font generation. The input to the font generation task is multiple style reference images \\(\\{R_i\\}_{i=1}^{N_R}\\) along with the corresponding character label \\(T\\). The number of references \\(N_R\\) may vary during training to allow the model to accept a variable number of references during inference. The style references are first mapped to their features \\(\\{f_i\\}_{i=1}^{N_R}\\) with an image encoder \\(\\mathcal{E}_f\\). We then apply stacked self-attention layers (SA) to aggregate these features to a style latent code \\(z_{style}\\) with a variational loss to enable font sampling. Character labels are mapped to vector representations by a learnable label embedding layer and then fused with \\(z_{style}\\) to yield the latent code \\(z_T\\) of the target glyph. Then \\(z_T\\) is fed to the decoders to generate the glyph, the same as the reconstruction task. The whole process can be described as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.201, + 0.42, + 0.285, + 0.437 + ], + "angle": 0, + "content": "\\[\nf _ {i} = \\mathcal {E} _ {f} (R _ {i})\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.186, + 0.439, + 0.468, + 0.462 + ], + "angle": 0, + "content": "\\[\n\\mu , \\sigma = \\operatorname {S A} \\left(f _ {1}, f _ {2}, \\dots , f _ {N _ {R}}\\right) \\tag {13}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.177, + 0.458, + 0.468, + 0.474 + ], + "angle": 0, + "content": "\\[\nz _ {s t y l e} = \\mu + \\epsilon \\sigma , \\epsilon \\sim \\mathcal {N} (0, 1) \\tag {15}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.197, + 0.477, + 0.344, + 0.493 + ], + "angle": 0, + "content": "\\[\nz _ {T} = \\operatorname {F F N} ([ z _ {\\text {s t y l e}}, T ])\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.498, + 0.468, + 0.543 + ], + "angle": 0, + "content": "To ease training, we use the pre-trained \\(\\mathcal{E}\\) from the reconstruction task to encode ground truth output \\(g_{T}\\) and train the encoder with the following guidance:" + }, + { + "type": "equation", + "bbox": [ + 0.185, + 0.544, + 0.468, + 0.56 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {l a t e n t}} = \\left\\| z _ {T} - \\mathcal {E} \\left(g _ {T}\\right) \\right\\| _ {2} \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.562, + 0.468, + 0.59 + ], + "angle": 0, + "content": "To enable font sampling, we adopt a Kullback-Leibler divergence loss [16]:" + }, + { + "type": "equation", + "bbox": [ + 0.17, + 0.591, + 0.468, + 0.608 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {k l} = \\mathrm {K L} \\left(\\mathcal {N} \\left(\\mu , \\sigma^ {2}\\right) | | \\mathcal {N} (0, 1)\\right) \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.61, + 0.468, + 0.653 + ], + "angle": 0, + "content": "Next, the encoder is fine-tuned along with the pre-trained \\(\\mathcal{D}_I\\) and \\(\\mathcal{D}_P\\) from the reconstruction task using the loss in 11 with \\(\\mathcal{L}_{kl}\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.658, + 0.468, + 0.776 + ], + "angle": 0, + "content": "Refinement Both the reconstruction and generation tasks share the same contour refinement process. Given \\(\\partial \\mathcal{O}\\) and \\(\\mathcal{I}\\), the refinement process produces the optimized glyph contour in SVG format by inference-time optimization. In the optimization, we utilize DiffVG [22], denoted as DR, to render the contour in a differentiable manner. The control points of \\(\\mathcal{O}\\) are refined to minimize the following loss function:" + }, + { + "type": "equation", + "bbox": [ + 0.179, + 0.779, + 0.468, + 0.795 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {r e f i n e}} = \\mathcal {L} _ {\\text {r a s}} + \\lambda_ {\\text {r e g}} \\mathcal {L} _ {\\text {r e g}} \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.801, + 0.468, + 0.829 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{\\text{render}}\\) is the photometric loss between the rasterized image and the image branch output." + }, + { + "type": "equation", + "bbox": [ + 0.188, + 0.831, + 0.468, + 0.847 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {r a s} = \\left| \\left| \\mathrm {D R} (\\partial \\mathcal {O}) - \\mathcal {I} \\right| \\right| _ {1} \\tag {17}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.848, + 0.433, + 0.862 + ], + "angle": 0, + "content": "The regularization term limits the overall length of \\(\\mathcal{O}\\)." + }, + { + "type": "equation", + "bbox": [ + 0.206, + 0.864, + 0.468, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {r e g} = \\sum_ {i = 1} ^ {K} \\operatorname {l e n} \\left(C _ {i}\\right) \\tag {18}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.092, + 0.795, + 0.107 + ], + "angle": 0, + "content": "3.5.2 Unsigned Distance Field Warm-up" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.117, + 0.892, + 0.193 + ], + "angle": 0, + "content": "Although the vector branch is end-to-end trainable, the gradients only appear near the boundaries. Therefore, to overcome the vanishing gradient problem, we add an extra loss based on the unsigned distance field (UDF) of the vector parts to warm up the system training." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.193, + 0.892, + 0.266 + ], + "angle": 0, + "content": "In general, for two closed curves \\( c_{1}, c_{2} \\), we cannot obtain the exact SDF of the shape after arbitrary boolean operations on the curves by point-wise operations on their respective SDFs. For the union of two SDFs, as an approximation, we have" + }, + { + "type": "equation", + "bbox": [ + 0.519, + 0.267, + 0.892, + 0.311 + ], + "angle": 0, + "content": "\\[\ns _ {c _ {1} \\cup c _ {2}} (\\boldsymbol {x}) \\left\\{ \\begin{array}{l l} = \\min \\left(s _ {c _ {1}} (\\boldsymbol {x}), s _ {c _ {2}} (\\boldsymbol {x})\\right), & \\boldsymbol {x} \\notin c _ {1} \\cup c _ {2} \\\\ \\leq \\min \\left(s _ {c _ {1}} (\\boldsymbol {x}), s _ {c _ {2}} (\\boldsymbol {x})\\right), & \\boldsymbol {x} \\in c _ {1} \\cup c _ {2} \\end{array} \\right. \\tag {19}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.312, + 0.892, + 0.462 + ], + "angle": 0, + "content": "The \\(\\min(\\cdot)\\) operation gives a correct SDF outside the shape but an inaccurate SDF inside the shape. Similarly, the \\(\\max(\\cdot)\\) gives a correct SDF inside and an inaccurate SDF outside for the intersection of two SDFs. Therefore, it is hard to calculate the accurate SDF \\(s_{\\mathcal{O}}\\) for the glyph. Fortunately, we only aim to provide a coarse initialization for the dual parts, preventing the optimization process from falling into local minima early in the training. We find that using an approximate unsigned distance field works well to achieve this goal. Here we define the UDF \\(u\\) as" + }, + { + "type": "equation", + "bbox": [ + 0.621, + 0.464, + 0.891, + 0.479 + ], + "angle": 0, + "content": "\\[\nu (\\boldsymbol {x}) = \\max (0, s (\\boldsymbol {x})) \\tag {20}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.48, + 0.892, + 0.51 + ], + "angle": 0, + "content": "where \\(\\min (\\cdot)\\) gives a correct global UDF for unions of shapes. The approximate UDF \\(\\hat{u}_q\\) is computed as" + }, + { + "type": "equation", + "bbox": [ + 0.607, + 0.511, + 0.891, + 0.531 + ], + "angle": 0, + "content": "\\[\n\\hat {u} _ {g} = \\min _ {i} \\left[ \\max \\left(u _ {P _ {i}}, u _ {Q _ {i}}\\right) \\right] \\tag {21}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.532, + 0.545, + 0.544 + ], + "angle": 0, + "content": "where" + }, + { + "type": "equation", + "bbox": [ + 0.601, + 0.546, + 0.777, + 0.562 + ], + "angle": 0, + "content": "\\[\nu _ {P _ {i}} (\\boldsymbol {x}) = \\max \\left(s _ {P _ {i}} (\\boldsymbol {x}), 0\\right)\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.601, + 0.557, + 0.89, + 0.581 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} u _ {Q _ {i}} (\\boldsymbol {x}) = \\max (- s _ {Q _ {i}} (\\boldsymbol {x}), 0) \\end{array} \\tag {22}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.586, + 0.89, + 0.614 + ], + "angle": 0, + "content": "We apply the following losses to warm up the training process for the font reconstruction task:" + }, + { + "type": "equation", + "bbox": [ + 0.579, + 0.615, + 0.771, + 0.629 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\lambda_ {P} \\mathcal {L} _ {P} + \\lambda_ {I} \\mathcal {L} _ {I} + \\lambda_ {u} \\mathcal {L} _ {u}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.572, + 0.625, + 0.89, + 0.649 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {u} = \\mathbb {E} _ {\\boldsymbol {x} \\sim [ - 1, 1 ] ^ {2}} \\left[ \\left| \\left| \\hat {u} _ {g} (\\boldsymbol {x}) - u _ {g} (\\boldsymbol {x}) \\right| \\right| _ {1} \\right] \\tag {23}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.649, + 0.89, + 0.679 + ], + "angle": 0, + "content": "where the ground truth UDF \\( u_{g} \\) is derived from the pixel image \\( g \\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.695, + 0.632, + 0.711 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.721, + 0.594, + 0.734 + ], + "angle": 0, + "content": "4.1. Dataset" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.744, + 0.892, + 0.835 + ], + "angle": 0, + "content": "We use the SVG-Fonts dataset from SVG-VAE [27] for all the experiments. Following DeepVecFont [39], we sample a subset of the dataset with 8035 fonts for training and 1425 fonts for evaluation. The resolution of input glyph images is set to \\(128 \\times 128\\). Please refer to the supplementary material for implementation details." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.847, + 0.693, + 0.861 + ], + "angle": 0, + "content": "4.2. Font Reconstruction" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In this experiment, we investigate how faithfully different methods can reconstruct the input glyph images with" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14197" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.09, + 0.468, + 0.309 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.319, + 0.471, + 0.388 + ], + "angle": 0, + "content": "Figure 3. Comparison of font reconstruction quality. We show the input glyph image row by row, our reconstructed image \\(\\mathcal{I}\\) from the image branch, dual-parts \\(\\mathcal{O}\\) from the vector branch, and our final result after contour refinement, as well as vector outputs from alternative methods." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.394, + 0.47, + 0.741 + ], + "angle": 0, + "content": "vector outputs, which can also be regarded as font vectorization. Im2Vec [33] and our method directly produce vector representations from glyph images, while for Multi-Implicits [34], we adopt the 2D marching cube algorithm and extract the contours. As can be seen from a qualitative comparison in Fig. 3, our representation could faithfully reconstruct global shapes as well as local details from the pixelated input. Im2Vec [33] could only preserve coarse shapes and suffers from wrong topologies as shown in the \"A\" example as it is easy to fall into local optimum without the global gradient. Multi-Implicits [34] results in finer details than Im2Vec [33] but still exhibit unsmooth edges and rounded corners. To quantitatively evaluate how accurate the vector outputs are, we calculate three metrics, namely SSIM, L1, and s-IoU, between the rendered images and the ground truth images under different resolutions. Tab. 1 shows that our method surpasses the two alternatives by a clear margin on all metrics. Using parametric curves as primitives, our method, along with Im2Vec [33], maintains a stable L1 error across all resolutions for the smooth edges, while for Multi-Implicits [34] the L1 error gets larger as the resolution increases, resulting from the high-frequency noises at the extracted boundaries." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.755, + 0.241, + 0.77 + ], + "angle": 0, + "content": "4.3. Font Generation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.471, + 0.903 + ], + "angle": 0, + "content": "To evaluate the generation ability of our method, we adopt the few-shot font generation setting, where a subset of glyphs with the same style is given and models are trained to produce a complete set of glyphs that are consistent with the input glyphs in style. This task is also dubbed \"font complement\" or \"font style transfer\" in other works. We compare our method with several popular methods in font generation: DeepVecFont [39], Multi-Implicits [34]," + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.089, + 0.893, + 0.146 + ], + "angle": 0, + "content": "Table 1. Quantitative comparison with Im2Vec [33] and Multi-Implicits [34] on three image-level metrics at different resolutions for the font reconstruction task. The gray scale is normalized to [0,1]. s-IoU, from [34], measures the overlap." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.154, + 0.912, + 0.334 + ], + "angle": 0, + "content": "
MethodResolutionSSIM↑L1↓s-IoU↑
Ours12820.94360.01370.8879
25620.94830.01360.9068
51220.95790.01360.9135
Multi-Implicits12820.92310.01830.8709
25620.92620.02080.8721
51220.94190.02130.8739
Im2Vec12820.78000.05040.6832
25620.85660.05040.6847
51220.89570.05040.6851
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.342, + 0.893, + 0.493 + ], + "angle": 0, + "content": "Im2Vec [33] and Attr2Font [38]. For a fair comparison, we use the same four characters, 'A', 'B', 'a', and 'b' as style references for each font and evaluate image-level metrics on the generated characters. Since Im2Vec [33] is an image vectorization method, we apply it to the images generated by Attr2Font [38]. Multi-Implicits [34] follows an auto-decoder architecture, so we freeze the decoder and find the optimal latent vector for a font by minimizing the losses between the given style references and the predicted ones using gradient descent." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.493, + 0.893, + 0.75 + ], + "angle": 0, + "content": "As illustrated in Fig. 4, DeepVecFont [39] may generate characters with wrong topologies due to the incorrect initial contour prediction, such as 'A', 'L', and 'Z'. The fixed topology in the optimization process makes it difficult to produce the necessary details, which are particularly symbolic in serif fonts. In addition, unconstrained contour generation may also produce self-intersections, like the 'g' and 'r', which are not easy to fix in subsequent processing. Im2Vec [33] tends to produce rounded corners and is only able to produce the coarse style, lacking details. Multi-Implicits [34] generates vector results from implicit signed distance fields (SDF) through a 2D Marching cube algorithm, leading to free-form contours. Therefore the edges are not smooth enough and have unpleasing noises, such as the 'g' and 'x' in the figure. Attr2Font [38] can generate generally satisfactory font images, but it cannot maintain high-quality rendering when scaling." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Compared with the above methods, our method is capable of not only grasping the overall style of the input references but also generating new glyphs with clear boundaries and sharp edges, achieving optimal visual quality. The efficient dual-part representation along with the differentiable occupancy supervision establishes a link between pixelated images and vector graphics, allowing the unsupervised synthesis of vector fonts with aligned shapes and correct topologies. The refinement step allows the composition of the contour to be freely changed and thus ensures" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14198" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.092, + 0.892, + 0.405 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.405, + 0.895, + 0.448 + ], + "angle": 0, + "content": "Figure 4. Font generation results of Attr2Font, Im2Vec, Multi-Implicits, DeepVecFont, and DualVector. The input style references are marked with red boxes. We trace the zero-level sets of SDFs in a piece-wise linear way to get SVGs from Multi-Implicits [34]. Typical failure cases are marked in blue dashed boxes. Some details are zoomed-in in the leftmost column." + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.453, + 0.475, + 0.496 + ], + "angle": 0, + "content": "Table 2. Quantitative comparison of image-level metrics of Attr2Font [38], Im2Vec [33], Multi-Implicits [34], DeepVecFont [39] and DualVector in the font complement experiment." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.506, + 0.487, + 0.755 + ], + "angle": 0, + "content": "
MethodResolutionSSIM↑L1↓s-IoU↑
Ours12820.82880.04610.7395
25620.87270.04600.7453
51220.90750.04600.7469
DeepVecFont12820.81650.05060.7125
25620.86400.05060.7171
51220.90110.05060.7182
Multi-Implicits12820.80250.05780.6857
25620.85330.06030.6814
51220.89140.06080.6811
Im2Vec12820.75760.07330.5731
25620.82700.07340.5751
51220.87390.07340.5756
Attr2Fonta12820.78410.05120.6393
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.096, + 0.763, + 0.314, + 0.777 + ], + "angle": 0, + "content": "[38] synthesizes pixelated images only." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.473, + 0.902 + ], + "angle": 0, + "content": "that our synthesized glyphs have high-fidelity details under the guidance of high-resolution glyph images. Quantitative results on three image-level metrics at different resolutions are shown in Tab. 2. For methods producing vector shapes, we also count the average number of commands used for each synthesized vector character, with smaller numbers indicating more compact outputs. The results are shown in Tab. 3. Multi-Implicits [34] uses a large number of short" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.453, + 0.895, + 0.509 + ], + "angle": 0, + "content": "Table 3. The average number of commands used per glyph for different methods in the font generation task. M, L, Q, and C denote move, straight line, quadratic Bezier curve, and cubic Bezier curve respectively." + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.52, + 0.915, + 0.624 + ], + "angle": 0, + "content": "
CommandMLQCTotal↓
Ours1.428.2111.06020.69
DeepVecFont [39]1.378.2309.6819.28
Multi-Implicits [34]6.161446.53001452.69
Im2Vec [33]4008084
Human-Designed1.389.1708.5119.06
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.639, + 0.895, + 0.746 + ], + "angle": 0, + "content": "line segments to represent the boundary due to the marching cube algorithm. Im2Vec [33] represents a shape with 4 parts each enclosed by 20 cubic Bezier curves, lacking flexibility and details. Our method performs boolean operations on the quadratic Bezier curves from dual parts, achieving comparable compactness with human-designed fonts and outputs from methods with vector supervision [39]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.756, + 0.666, + 0.771 + ], + "angle": 0, + "content": "4.4. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.895, + 0.903 + ], + "angle": 0, + "content": "To demonstrate the effectiveness of several key design choices in our method, we conduct ablation studies on the font reconstruction task. We investigate the following degraded variants: (a) replace the union of dual parts with the union of all the paths; (b) train without the UDF warm-up process; and (c) remove the refining strategy during refinement. We show the comparison results of a representative case in Fig. 5. Without the dual-part representation, variant" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "14199" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.095, + 0.075, + 0.464, + 0.201 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.202, + 0.468, + 0.23 + ], + "angle": 0, + "content": "Figure 5. The contours of an \"M\" reconstructed by our method, compared with three degraded variants." + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.233, + 0.468, + 0.275 + ], + "angle": 0, + "content": "Table 4. Quantitative results of reconstruction accuracy for different model variants in ablation studies. All the output vector glyphs are rendered at \\(512 \\times 512\\) to compute the L1 error." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.286, + 0.495, + 0.386 + ], + "angle": 0, + "content": "
L1↓#Lines↓# Curves↓
(a) w/o dual parts0.014312.2314.06
(b) w/o warm-up0.014611.1913.12
(c) w/o refining strategy0.0148-22.07
Full Model0.01368.9711.81
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.402, + 0.468, + 0.522 + ], + "angle": 0, + "content": "(a) cannot reconstruct concave regions very well, as they can be hard to represent by the union of simply closed paths. Without UDF initialization, variant (b) produces contours with useless curves that are hard to be eliminated during optimization. Without the refining strategy, variant (c) may generate inaccurate edges with zigzags. Quantitative results in Tab. 4 also verify the quality improvements brought by the three design choices." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.522, + 0.468, + 0.674 + ], + "angle": 0, + "content": "We also experimentally investigate the effect of different \\((N,M)\\) s on the representation capacity. We choose several settings of \\((N,M)\\) and train only the vector branch (i.e. no contour refinement) with the same number of epochs to reconstruct the input. Tab. 5 shows that \\(M = 4\\) is optimal and the reconstruction accuracy of the vector branch increases as \\(N\\) increases. The accuracy does not gain too much changing \\(N\\) from 6 to 8. So considering the time cost for training and inference, we select \\((N,M) = (6,4)\\) in the above experiments." + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.677, + 0.468, + 0.704 + ], + "angle": 0, + "content": "Table 5. Different reconstruction settings and metrics. The image-based metrics use a resolution of \\(512 \\times 512\\)." + }, + { + "type": "table", + "bbox": [ + 0.136, + 0.709, + 0.411, + 0.833 + ], + "angle": 0, + "content": "
NMSSIM↑L1↓s-IOU↑
240.92620.02820.8338
440.92920.02590.8464
640.93030.02500.8512
840.93060.02470.8525
630.92930.02560.8480
650.93000.02520.8498
" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.847, + 0.367, + 0.864 + ], + "angle": 0, + "content": "4.5. Font Sampling and Interpolation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.468, + 0.902 + ], + "angle": 0, + "content": "In the font generation task, the style latent code \\( z_{style} \\) is trained with a variational loss \\( \\mathcal{L}_{kl} \\), enabling generating" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.183 + ], + "angle": 0, + "content": "fonts of new styles by sampling \\( z_{style} \\) from \\( \\mathcal{N}(0,1) \\). We show in Fig. 1 (left) and Fig. 6 multiple styles of fonts sampled. Please refer to our supplementary material for more examples. Also, benefiting from our dual-part representation, we can perform smooth interpolation between arbitrary font styles as demonstrated in Fig. 1 (right)." + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.186, + 0.892, + 0.312 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.524, + 0.321, + 0.868, + 0.337 + ], + "angle": 0, + "content": "Figure 6. New fonts with style codes sampled in \\(\\mathcal{N}(0,1)\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.35, + 0.623, + 0.366 + ], + "angle": 0, + "content": "5. Limitations" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.376, + 0.892, + 0.542 + ], + "angle": 0, + "content": "The contour refinement step requires gradient descent during inference and therefore imposes a large time overhead, similar to DeepVecFont [39]. The process could potentially be accomplished by forwarding inferences of some generation models, such as the diffusion models [13]. Another limitation is that DualVector only focuses on the synthesis of glyphs on a fixed-size canvas, without considering the kerning between them, making the spacing between characters less natural. This may be solved by post-processing the SVG with some automatic kerning methods or by learning through a data-driven approach." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.558, + 0.619, + 0.573 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.583, + 0.892, + 0.839 + ], + "angle": 0, + "content": "We present DualVector as a new representation and generation method for vector fonts. DualVector models a glyph as dual parts and introduces a contour refinement step to add pleasing details to the contours of the dual parts. Our method is able to generate vector fonts without vector supervision, which can be directly converted to common digital font formats for content presentation and distribution. Comparisons with different methods of font reconstruction and generation tasks demonstrate that our approach produces fonts with the best quality among all the alternatives. In the future, more plausible initialization and supervision could be exploited to generalize this representation to more complex fonts (e.g. Chinese fonts). We hope this research contributes to the typeface design industry and provide inspiration for broader works on the understanding and generation of 2D man-made content such as cartoon characters and icons." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgement This work was supported by the Natural Science Foundation of China (Project Number 61832016), and Tsinghua-Tencent Joint Laboratory for Internet Innovation Technology." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14200" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.303, + 0.13 + ], + "angle": 0, + "content": "[1] Adobe Inc. 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High-quality vector fonts (copyable on electronic devices) synthesized by DualVector (left), with smoothly-interpolated styles (right). Both sentences are pangrams. Please zoom in for details. + +![](images/3d892fddaf1a7d8161fd4fa3e7f1a425e23cb59ac0335818baa4d8f547718224.jpg) + +# Abstract + +Automatic generation of fonts can be an important aid to typeface design. Many current approaches regard glyphs as pixelated images, which present artifacts when scaling and inevitable quality losses after vectorization. On the other hand, existing vector font synthesis methods either fail to represent the shape concisely or require vector supervision during training. To push the quality of vector font synthesis to the next level, we propose a novel dual-part representation for vector glyphs, where each glyph is modeled as a collection of closed "positive" and "negative" path pairs. The glyph contour is then obtained by boolean operations on these paths. We first learn such a representation only from glyph images and devise a subsequent contour refinement step to align the contour with an image representation to further enhance details. Our method, named DualVector, outperforms state-of-the-art methods in vector font synthesis both quantitatively and qualitatively. Our synthesized vector fonts can be easily converted to common digital font formats like TrueType Font for practical use. The code is released at https://github.com/thuliu-yt16/dualvector. + +# 1. Introduction + +Fonts with various styles play an important role in content display and distribution. Excellent font design is time-consuming and labor-intensive. Recent machine learning + +innovations have made font generation possible, but how to automatically generate high-quality vector fonts remains a task of practical importance in the artistic and computer graphics and vision communities. + +Benefiting from the development of image generation techniques, mainstream font synthesis methods [2, 12, 24, 41, 42] could generate pixelated glyph images. Despite the promising quality, images of glyphs incur aliasing artifacts on edges when discretely sampled, and thus are not competent for high-quality rendering or printing at arbitrary resolutions. To alleviate this problem, some methods [7, 34] adopt coordinate-based neural networks to model a glyph as a contiguous neural field, which have also shown great potential in modeling 3D geometry and scenes [7, 30, 32]. Although glyphs represented by the implicit field can be rendered at arbitrary resolutions, it is hard to preserve details in high-frequency regions such as edges and corners, not to mention the high computational costs as the network needs to be evaluated for every pixel. Researchers have made much effort to directly synthesize vector fonts [4, 27, 33, 39] in recent years, with the main difficulty lying in finding a representation of vector graphics that can be encoded or decoded effectively in a deep learning framework. One typical approach represents a vector shape as a sequence of drawing commands and adopts sequence modeling techniques such as recurrent networks and transformers. The drawbacks are twofold: (1) Modeling command sequences can be much harder than images. There are infinitely many command sequences that correspond to the same-looking shape, which brings ambiguities in learning and makes it hard to construct + +an effective manifold for valid glyph shapes. (2) Ground-truth drawing commands are often required to provide sufficient supervision for high-quality modeling and synthesis. + +To overcome these challenges, we first propose a dual-part vector font representation, where each glyph shape is the union of a fixed number of dual parts. Each dual part is formed by the subtraction of a "positive" and a "negative" geometric primitive. While there are many choices for the geometric primitives [6, 8, 25], we adopt closed Bezier paths for their great representational ability. They are also widely supported in digital font formats which makes it easy to convert our representation to these formats for practical use. We reduce the problem of predicting complicated drawing command sequences to predicting multiple basic primitives. From this perspective, both manifold learning and latent space interpolation become more feasible. + +Based on the dual-part representation, we introduce DualVector, a method to learn such a representation for high-quality font modeling and synthesis from only glyph images without any vector supervision. A straightforward way to achieve this is to directly optimize the parameters of the Bezier curves with differentiable rendering techniques for vector graphics [22]. However, this approach easily gets stuck in the local minima as valuable gradients are only defined at shape intersections. Taking inspiration from implicit field training for 2D and 3D shapes [6, 25, 32], we supervise the occupancy value derived from the analytical expression of the Bezier curves and adopt an initialization strategy based on unsigned distance field (UDF) to provide dense gradients across the entire pixel space. For local detail fidelity, we also train a glyph image generation model and devise a subsequent contour refinement step to align the contour of the vector shape with that of the image by differentiable rendering [22]. We compare our approach with state-of-the-art methods in font modeling and generation and demonstrate the superior quality of our vector font outputs. Our main contributions are: + +- A new dual-part font representation based on boolean operations of Bezier paths, which enables efficient shape modeling and unsupervised manifold learning. +- A method named DualVector that models both the dual-part and pixelated representation, and introduces a contour refinement step to obtain vector fonts with richer details as well as a UDF initialization strategy for better convergence. +- DualVector achieves state-of-the-art quality in font modeling and generation, with outputs that can be easily converted to common digital font formats. + +# 2. Related Work + +# 2.1. Glyph Image Generation + +Benefiting from the development of image generation [10, 14, 16], either black-white [12, 15, 37, 40] or artistic glyph image generation [2, 23, 41, 42] is well explored in the past decade. MC-GAN [2] synthesized ornamented glyphs for capital letters in an end-to-end manner from a small subset of the same style. Attr2Font [38] generated visually pleasing results according to style attributes and content references. Most of these methods follow the disentanglement of style and content codes, and so does the image generation branch in DualVector. But these glyph image generation efforts do not step outside the 2D pixelated representation which sets an upper bound for rendering quality, efficiency, and practicality. + +# 2.2. Image Rasterization and Vectorization + +Rasterization and vectorization are dual problems in image processing. Previous efforts on rasterization have typically focused on anti-aliasing [9, 11, 31] and high-performance rendering on modern graphics hardware [3, 17, 21, 26]. Traditional image vectorization approaches rely on region segmentation, line extraction, and contour tracing for gray-scale images [35], pixel arts [18], animations [44] and general images [1, 5, 19, 36, 45, 46]. Recently, researchers have turned to bridging the raster and vector domains [22, 29], enabling existing well-established algorithms for raster images to be also applied to vector representations. DiffVG [22] is a differentiable rendering technique for vector graphics enabling the optimization of vector primitive parameters based on raster criteria. In our work, it is employed to align the vector and pixel representation in the contour refinement step. + +# 2.3. Vector Font Generation + +SVG-VAE [27] was the first attempt to build a sequential generative model on SVG fonts. DeepSVG [4] developed a hierarchical transformer-based generative model for complex SVG icons generation and interpolation. Exploiting implicit neural representation, multi-implicit [34] modeled fonts with a permutation-invariant set of learned implicit functions which can preserve font features, such as smooth edges and sharp corners, and generate good interpolation results. Liu et al. [25] proposed a primitive-based representation, which views glyph shapes as the combination of primitives enclosed by implicit curves. Implicit representation-based methods can convert the zero-level set of their output fields to contour representation with the 2D marching cube [28] algorithm, although it produces multiple segmented lines and lacks accuracy and efficiency in rendering and editing. Im2Vec [33] can synthesize complex vector graphics with varying topologies without vector super + +![](images/df4217b94fc36294faf9377ed7b37181bda1a365f3f5d6367ccd3db5e1f17b4e.jpg) +Figure 2. DualVector contains the following components: (a) a vector branch that maps the latent code $z$ to several closed Bézier paths which are further gathered to form a global shape of the glyph; (b) an image branch that generates pixelated images with faithful details; (c) a contour refinement step that obtains the contour via boolean operations on dual-parts and optimizes it with the image guidance at inference time. Both the vector and the image branch are trained using the glyph images. Dual parts are distinguished by their colors. + +vision. It rendered layered Bézier paths predicted from image features using DiffVG [22] and trains the system in an auto-encoding manner. DeepVecFont [39] adopted a dual-modality learning framework that utilizes both sequence and image features for high-quality vector font synthesis. But the results it produces may have the wrong topology, including self-intersection or invalid paths. In contrast to these methods, our approach does not require vector supervision and is very efficient in vector representation, with high quality glyph generation. + +# 3. DualVector + +In this section, we first illustrate the proposed dual-part representation for fonts (Sec. 3.1) and then introduce the components of DualVector for training this representation from glyph images (Secs. 3.2 to 3.4) and how the model can be used for font reconstruction and generation (Sec. 3.5). In DualVector, we adopt a joint representation of vector and image for fonts, as shown in Fig. 2. The latent space is shared by both modalities, and we associate each glyph with a latent code $z \in \mathbf{R}^d$ produced by the task-specific encoding process. The latent code $z$ is fed into the two decoding branches to obtain a dual-part representation and an image representation respectively. The output of the vector branch is further processed by a contour refinement step to generate the final contour representation under the image guidance. + +# 3.1. Dual-Part Representation + +In our dual-part representation, we consider the closed parametric Bézier paths as our basic primitives for several + +reasons: (1) Bézier paths are powerful enough to approximate various shapes; (2) The contour of a closed shape produced by boolean operations on Bézier paths is still a set of Bézier paths, i.e., the closure property; (3) Bézier paths are widely used in modern font design, making the learned representation highly applicable. For convenience, we use a triplet of control points $(\pmb{a},\pmb{b},\pmb{c})$ to denote a quadratic Bézier curve $B(\cdot ;\pmb {a},\pmb {b},\pmb {c})$ determined by the control points: $B(t;\pmb {a},\pmb {b},\pmb {c}) = (1 - t)^{2}\pmb {a} + (1 - t)t\pmb {b} + t^{2}\pmb {c}t\in [0,1]$ 1 Since a glyph often consists of a number of strokes with similar appearances, we propose to represent each glyph $g$ with $N$ closed Bézier paths $\{P_i\}_{i = 1}^N$ . Each path $P_{i}$ is defined by $M$ end-to-end connected quadratic Bézier curves $\{B_{i,j}(\pmb{x}_{i,2j - 1},\pmb{x}_{i,2j},\pmb{x}_{i,2j + 1})\}_{j = 1}^{M}(\pmb{x}_{i,2M + 1} = \pmb{x}_{i,1})$ .We introduce the occupancy field of a closed path $P_{i}$ as + +$$ +\mathcal {O} _ {P _ {i}} (\boldsymbol {x}) = \left\{ \begin{array}{l l} 1, & \boldsymbol {x} \in P _ {i} \\ 0, & \boldsymbol {x} \notin P _ {i} \end{array} \right. \tag {2} +$$ + +The entire glyph shape $g$ could simply be denoted as the union of all the paths $\cup_{i} P_{i}$ . We normalize the coordinate range of the glyph to $[-1, 1]^{2}$ . Thus given any point $x$ on the canvas $[-1, 1]^{2}$ , we can determine whether it is inside the represented glyph shape by a maximum operation, leading to the occupancy field of $g$ : + +$$ +\mathcal {O} (\boldsymbol {x}) = \max _ {i} \mathcal {O} _ {P _ {i}} (\boldsymbol {x}) = \left\{ \begin{array}{l l} 1, & \boldsymbol {x} \in \cup_ {i} P _ {i} \\ 0, & \boldsymbol {x} \notin \cup_ {i} P _ {i} \end{array} \right. \tag {3} +$$ + +However, we find that the above representation can model fonts with convex curves on the contour but struggles to reconstruct shapes with holes. Therefore, in practice, we pair each path $P_{i}$ with a negative path $Q_{i}$ , and term this pair $(P_{i}, Q_{i})$ as a "dual part". In this way, $g$ is represented as + +$\cup_{i}(P_{i} - Q_{i})$ . The occupancy field $\mathcal{O}$ is then derived as: + +$$ +\mathcal {O} (\boldsymbol {x}) = \max _ {i} [ \min \left(\mathcal {O} _ {P _ {i}} (\boldsymbol {x}), 1 - \mathcal {O} _ {Q _ {i}} (\boldsymbol {x})\right) ] = \left\{ \begin{array}{l l} 1, & \boldsymbol {x} \in g \\ 0, & \boldsymbol {x} \notin g \end{array} \right. \tag {4} +$$ + +Even though $\mathcal{O}$ is the analytical occupancy field of $g$ , it is not differentiable w.r.t. the parameters of the paths. Therefore, in order to apply gradient descent to learn such a representation, we calculate the approximate occupancy field $\hat{\mathcal{O}}$ from the signed distance field (SDF) of $g$ . Since the distance $d(p;B)$ from any point $p$ to a Bézier curve $B$ can be derived analytically, the SDF of a path can be calculated differentiably w.r.t. its control points as follows: + +$$ +s _ {P _ {i}} (\boldsymbol {x}) = \left[ 2 \mathcal {O} _ {P _ {i}} (\boldsymbol {x}) - 1 \right] \min _ {j} d (\boldsymbol {x}; B _ {i, j}) \tag {5} +$$ + +Following previous vector graphics rasterization techniques [22, 31, 34], we approximate $\mathcal{O}$ by analytical pixel prefiltering with a parabolic kernel $\alpha$ : + +$$ +\hat {\mathcal {O}} _ {P _ {i}} (\boldsymbol {x}) = \alpha \left(s _ {P _ {i}} (\boldsymbol {x})\right) +$$ + +$$ +\hat {\mathcal {O}} = \max _ {i} [ \min (\hat {\mathcal {O}} _ {P _ {i}}, 1 - \hat {\mathcal {O}} _ {Q _ {i}}) ] \tag {6} +$$ + +# 3.2. Vector Branch + +The vector branch takes a latent code $z$ and outputs a set of dual-parts that represent a vector glyph. The path decoder $\mathcal{D}_P$ directly predicts the control points of the positive paths $\{P_i\}_{i=1}^N$ and the negative ones $\{Q_i\}_{i=1}^N$ from $z$ : + +$$ +\left\{\boldsymbol {x} _ {i, j} \right\} = \mathcal {D} _ {P} (z), 1 \leq i \leq 2 N, 1 \leq j \leq 2 M \tag {7} +$$ + +where $\{\pmb{x}_{i,j}\}_{i = 1}^{N}$ are control points for $\{P_i\}_{i = 1}^N$ and $\{\pmb{x}_{i,j}\}_{i = N + 1}^{2N}$ are control points for $\{Q_i\}_{i = 1}^N$ + +# 3.3. Image Branch + +To combine with the advantages of image generation approaches, we train an auxiliary image branch that maps $z$ to a pixelated image $\mathcal{I}$ of the glyph it represents. Here we adopt a CNN-based decoder $\mathcal{D}_I$ : + +$$ +\mathcal {I} = \mathcal {D} _ {I} (z) \tag {8} +$$ + +where $\mathcal{I}$ is a gray-scale image in shape $H\times W$ . It provides detailed shape guidance to refine the vector shape contour. + +# 3.4. Contour Refinement + +Although the dual-part representation produced by the vector branch can already be rendered, there still exists a gap between it and modern contour representations for fonts. Therefore, we first convert it to the contour of the glyph $\partial \mathcal{O}$ with an off-the-shelf tool Paper.js [20] which can perform arbitrary boolean operations on SVG paths. Here the contour $\partial \mathcal{O}$ is a set of K closed Bézier paths. + +$$ +\partial \mathcal {O} = \left\{C _ {1}, C _ {2}, \dots , C _ {K} \right\} \tag {9} +$$ + +where $K$ denotes the number of independent paths. Each individual part or hole increases $K$ by 1. $C_i$ is a closed Bezier path composed of $l_i$ quadratic Bezier segments $\{\hat{B}_{i,j}(\hat{\pmb{x}}_{i,2j - 1},\hat{\pmb{x}}_{i,2j},\hat{\pmb{x}}_{i,2j + 1})\}_{j = 1}^{l_i}$ + +After this conversion, we exploit the image generation results to further refine $\partial \mathcal{O}$ with differentiable rendering techniques [22]. $\mathcal{I}$ could naturally serve as a pixelated version of the occupancy field $\mathcal{O}$ . During the refinement, we devise several strategies to improve the quality and efficiency of our representation: + +Subdivision To improve the representational ability, we split long Bézier curves (with a length greater than $10\%$ of the canvas width) at their midpoints. + +Simplification To improve the efficiency of the contour representation, we replace the Bézier curves with a line segment connecting its two endpoints if they are close enough. For a Bézier curve $(a, b, c)$ , we simply define how faithfully the segment $ac$ could represent the curve by the angle between $\vec{ba}$ and $\vec{bc}$ . Also, we examine if there exist two adjacent Bézier segments that could be combined as a single one. Since all quadratic Bézier curves are parts of a parabola curve, we derive the parameters of the corresponding parabola curves from the control points and combine the two curves if their parameters are close enough. We also aggregate the endpoints of lines and curves that are too short. + +Pruning Prior to refinement, some Bezier paths on the contour may enclose extremely small regions which will confuse the refinement process and produce redundant curves that eventually converge to a single point. We trim those closed paths $C_i$ with areas under a certain threshold. + +More implementation details of these strategies can be found in the supplemental material. + +# 3.5. Implementation and Training + +In this subsection, we will dive into how we utilize the proposed representation in both the font reconstruction and generation tasks. + +# 3.5.1 Optimization Objectives + +Optimization objectives can be divided into those at training time and those at inference time. The training-time objectives are task-related. + +Font reconstruction. For the font reconstruction task, the input to our system is a gray-scale image of a glyph and the output is the corresponding vector representation. The pixelated image $\mathcal{I}_g$ of the glyph $g$ is first passed through an image encoder $\mathcal{E}$ to obtain the latent code $z$ : + +$$ +z = \mathcal {E} \left(\mathcal {I} _ {g}\right) \tag {10} +$$ + +The latent code is then decoded by our vector branch and image branch into dual-parts $\{(P_i,Q_i)\}_{i = 1}^N$ and a pixelated + +output $\mathcal{I}$ . We optimize the trainable modules $\mathcal{E},\mathcal{D}_I$ and $\mathcal{D}_P$ simultaneously with the following loss functions: + +$$ +\mathcal {L} = \lambda_ {P} \mathcal {L} _ {P} + \lambda_ {I} \mathcal {L} _ {I} \tag {11} +$$ + +where we adopt an extra perceptual loss [43]: + +$$ +\mathcal {L} _ {P} = \mathbb {E} _ {\boldsymbol {x} \sim [ - 1, 1 ] ^ {2}} \left[ \left\| \hat {\mathcal {O}} (\boldsymbol {x}) - \mathcal {I} _ {g} (\boldsymbol {x}) \right\| _ {1} \right] \tag {12} +$$ + +$$ +\mathcal {L} _ {I} = \left| \left| \mathcal {I} - \mathcal {I} _ {g} \right| \right| _ {2} + \operatorname {L P I P S} (\mathcal {I}, \mathcal {I} _ {g}) +$$ + +Font generation. The input to the font generation task is multiple style reference images $\{R_i\}_{i=1}^{N_R}$ along with the corresponding character label $T$ . The number of references $N_R$ may vary during training to allow the model to accept a variable number of references during inference. The style references are first mapped to their features $\{f_i\}_{i=1}^{N_R}$ with an image encoder $\mathcal{E}_f$ . We then apply stacked self-attention layers (SA) to aggregate these features to a style latent code $z_{style}$ with a variational loss to enable font sampling. Character labels are mapped to vector representations by a learnable label embedding layer and then fused with $z_{style}$ to yield the latent code $z_T$ of the target glyph. Then $z_T$ is fed to the decoders to generate the glyph, the same as the reconstruction task. The whole process can be described as follows: + +$$ +f _ {i} = \mathcal {E} _ {f} (R _ {i}) +$$ + +$$ +\mu , \sigma = \operatorname {S A} \left(f _ {1}, f _ {2}, \dots , f _ {N _ {R}}\right) \tag {13} +$$ + +$$ +z _ {s t y l e} = \mu + \epsilon \sigma , \epsilon \sim \mathcal {N} (0, 1) \tag {15} +$$ + +$$ +z _ {T} = \operatorname {F F N} ([ z _ {\text {s t y l e}}, T ]) +$$ + +To ease training, we use the pre-trained $\mathcal{E}$ from the reconstruction task to encode ground truth output $g_{T}$ and train the encoder with the following guidance: + +$$ +\mathcal {L} _ {\text {l a t e n t}} = \left\| z _ {T} - \mathcal {E} \left(g _ {T}\right) \right\| _ {2} \tag {14} +$$ + +To enable font sampling, we adopt a Kullback-Leibler divergence loss [16]: + +$$ +\mathcal {L} _ {k l} = \mathrm {K L} \left(\mathcal {N} \left(\mu , \sigma^ {2}\right) | | \mathcal {N} (0, 1)\right) \tag {15} +$$ + +Next, the encoder is fine-tuned along with the pre-trained $\mathcal{D}_I$ and $\mathcal{D}_P$ from the reconstruction task using the loss in 11 with $\mathcal{L}_{kl}$ . + +Refinement Both the reconstruction and generation tasks share the same contour refinement process. Given $\partial \mathcal{O}$ and $\mathcal{I}$ , the refinement process produces the optimized glyph contour in SVG format by inference-time optimization. In the optimization, we utilize DiffVG [22], denoted as DR, to render the contour in a differentiable manner. The control points of $\mathcal{O}$ are refined to minimize the following loss function: + +$$ +\mathcal {L} _ {\text {r e f i n e}} = \mathcal {L} _ {\text {r a s}} + \lambda_ {\text {r e g}} \mathcal {L} _ {\text {r e g}} \tag {16} +$$ + +where $\mathcal{L}_{\text{render}}$ is the photometric loss between the rasterized image and the image branch output. + +$$ +\mathcal {L} _ {r a s} = \left| \left| \mathrm {D R} (\partial \mathcal {O}) - \mathcal {I} \right| \right| _ {1} \tag {17} +$$ + +The regularization term limits the overall length of $\mathcal{O}$ . + +$$ +\mathcal {L} _ {r e g} = \sum_ {i = 1} ^ {K} \operatorname {l e n} \left(C _ {i}\right) \tag {18} +$$ + +# 3.5.2 Unsigned Distance Field Warm-up + +Although the vector branch is end-to-end trainable, the gradients only appear near the boundaries. Therefore, to overcome the vanishing gradient problem, we add an extra loss based on the unsigned distance field (UDF) of the vector parts to warm up the system training. + +In general, for two closed curves $c_{1}, c_{2}$ , we cannot obtain the exact SDF of the shape after arbitrary boolean operations on the curves by point-wise operations on their respective SDFs. For the union of two SDFs, as an approximation, we have + +$$ +s _ {c _ {1} \cup c _ {2}} (\boldsymbol {x}) \left\{ \begin{array}{l l} = \min \left(s _ {c _ {1}} (\boldsymbol {x}), s _ {c _ {2}} (\boldsymbol {x})\right), & \boldsymbol {x} \notin c _ {1} \cup c _ {2} \\ \leq \min \left(s _ {c _ {1}} (\boldsymbol {x}), s _ {c _ {2}} (\boldsymbol {x})\right), & \boldsymbol {x} \in c _ {1} \cup c _ {2} \end{array} \right. \tag {19} +$$ + +The $\min(\cdot)$ operation gives a correct SDF outside the shape but an inaccurate SDF inside the shape. Similarly, the $\max(\cdot)$ gives a correct SDF inside and an inaccurate SDF outside for the intersection of two SDFs. Therefore, it is hard to calculate the accurate SDF $s_{\mathcal{O}}$ for the glyph. Fortunately, we only aim to provide a coarse initialization for the dual parts, preventing the optimization process from falling into local minima early in the training. We find that using an approximate unsigned distance field works well to achieve this goal. Here we define the UDF $u$ as + +$$ +u (\boldsymbol {x}) = \max (0, s (\boldsymbol {x})) \tag {20} +$$ + +where $\min (\cdot)$ gives a correct global UDF for unions of shapes. The approximate UDF $\hat{u}_q$ is computed as + +$$ +\hat {u} _ {g} = \min _ {i} \left[ \max \left(u _ {P _ {i}}, u _ {Q _ {i}}\right) \right] \tag {21} +$$ + +where + +$$ +u _ {P _ {i}} (\boldsymbol {x}) = \max \left(s _ {P _ {i}} (\boldsymbol {x}), 0\right) +$$ + +$$ +\begin{array}{l} u _ {Q _ {i}} (\boldsymbol {x}) = \max (- s _ {Q _ {i}} (\boldsymbol {x}), 0) \end{array} \tag {22} +$$ + +We apply the following losses to warm up the training process for the font reconstruction task: + +$$ +\mathcal {L} = \lambda_ {P} \mathcal {L} _ {P} + \lambda_ {I} \mathcal {L} _ {I} + \lambda_ {u} \mathcal {L} _ {u} +$$ + +$$ +\mathcal {L} _ {u} = \mathbb {E} _ {\boldsymbol {x} \sim [ - 1, 1 ] ^ {2}} \left[ \left| \left| \hat {u} _ {g} (\boldsymbol {x}) - u _ {g} (\boldsymbol {x}) \right| \right| _ {1} \right] \tag {23} +$$ + +where the ground truth UDF $u_{g}$ is derived from the pixel image $g$ . + +# 4. Experiments + +# 4.1. Dataset + +We use the SVG-Fonts dataset from SVG-VAE [27] for all the experiments. Following DeepVecFont [39], we sample a subset of the dataset with 8035 fonts for training and 1425 fonts for evaluation. The resolution of input glyph images is set to $128 \times 128$ . Please refer to the supplementary material for implementation details. + +# 4.2. Font Reconstruction + +In this experiment, we investigate how faithfully different methods can reconstruct the input glyph images with + +![](images/a1fe2572a50a84efd3196dcfc6c9d15a7514b58a04c7cb3ffb2ce93aa21d0b1a.jpg) +Figure 3. Comparison of font reconstruction quality. We show the input glyph image row by row, our reconstructed image $\mathcal{I}$ from the image branch, dual-parts $\mathcal{O}$ from the vector branch, and our final result after contour refinement, as well as vector outputs from alternative methods. + +vector outputs, which can also be regarded as font vectorization. Im2Vec [33] and our method directly produce vector representations from glyph images, while for Multi-Implicits [34], we adopt the 2D marching cube algorithm and extract the contours. As can be seen from a qualitative comparison in Fig. 3, our representation could faithfully reconstruct global shapes as well as local details from the pixelated input. Im2Vec [33] could only preserve coarse shapes and suffers from wrong topologies as shown in the "A" example as it is easy to fall into local optimum without the global gradient. Multi-Implicits [34] results in finer details than Im2Vec [33] but still exhibit unsmooth edges and rounded corners. To quantitatively evaluate how accurate the vector outputs are, we calculate three metrics, namely SSIM, L1, and s-IoU, between the rendered images and the ground truth images under different resolutions. Tab. 1 shows that our method surpasses the two alternatives by a clear margin on all metrics. Using parametric curves as primitives, our method, along with Im2Vec [33], maintains a stable L1 error across all resolutions for the smooth edges, while for Multi-Implicits [34] the L1 error gets larger as the resolution increases, resulting from the high-frequency noises at the extracted boundaries. + +# 4.3. Font Generation + +To evaluate the generation ability of our method, we adopt the few-shot font generation setting, where a subset of glyphs with the same style is given and models are trained to produce a complete set of glyphs that are consistent with the input glyphs in style. This task is also dubbed "font complement" or "font style transfer" in other works. We compare our method with several popular methods in font generation: DeepVecFont [39], Multi-Implicits [34], + +Table 1. Quantitative comparison with Im2Vec [33] and Multi-Implicits [34] on three image-level metrics at different resolutions for the font reconstruction task. The gray scale is normalized to [0,1]. s-IoU, from [34], measures the overlap. + +
MethodResolutionSSIM↑L1↓s-IoU↑
Ours12820.94360.01370.8879
25620.94830.01360.9068
51220.95790.01360.9135
Multi-Implicits12820.92310.01830.8709
25620.92620.02080.8721
51220.94190.02130.8739
Im2Vec12820.78000.05040.6832
25620.85660.05040.6847
51220.89570.05040.6851
+ +Im2Vec [33] and Attr2Font [38]. For a fair comparison, we use the same four characters, 'A', 'B', 'a', and 'b' as style references for each font and evaluate image-level metrics on the generated characters. Since Im2Vec [33] is an image vectorization method, we apply it to the images generated by Attr2Font [38]. Multi-Implicits [34] follows an auto-decoder architecture, so we freeze the decoder and find the optimal latent vector for a font by minimizing the losses between the given style references and the predicted ones using gradient descent. + +As illustrated in Fig. 4, DeepVecFont [39] may generate characters with wrong topologies due to the incorrect initial contour prediction, such as 'A', 'L', and 'Z'. The fixed topology in the optimization process makes it difficult to produce the necessary details, which are particularly symbolic in serif fonts. In addition, unconstrained contour generation may also produce self-intersections, like the 'g' and 'r', which are not easy to fix in subsequent processing. Im2Vec [33] tends to produce rounded corners and is only able to produce the coarse style, lacking details. Multi-Implicits [34] generates vector results from implicit signed distance fields (SDF) through a 2D Marching cube algorithm, leading to free-form contours. Therefore the edges are not smooth enough and have unpleasing noises, such as the 'g' and 'x' in the figure. Attr2Font [38] can generate generally satisfactory font images, but it cannot maintain high-quality rendering when scaling. + +Compared with the above methods, our method is capable of not only grasping the overall style of the input references but also generating new glyphs with clear boundaries and sharp edges, achieving optimal visual quality. The efficient dual-part representation along with the differentiable occupancy supervision establishes a link between pixelated images and vector graphics, allowing the unsupervised synthesis of vector fonts with aligned shapes and correct topologies. The refinement step allows the composition of the contour to be freely changed and thus ensures + +![](images/5de01a1d0d9c18081a2b7831b8e1fb61bbc976138deaeb67a5c0d0125b7503f7.jpg) +Figure 4. Font generation results of Attr2Font, Im2Vec, Multi-Implicits, DeepVecFont, and DualVector. The input style references are marked with red boxes. We trace the zero-level sets of SDFs in a piece-wise linear way to get SVGs from Multi-Implicits [34]. Typical failure cases are marked in blue dashed boxes. Some details are zoomed-in in the leftmost column. + +Table 2. Quantitative comparison of image-level metrics of Attr2Font [38], Im2Vec [33], Multi-Implicits [34], DeepVecFont [39] and DualVector in the font complement experiment. + +
MethodResolutionSSIM↑L1↓s-IoU↑
Ours12820.82880.04610.7395
25620.87270.04600.7453
51220.90750.04600.7469
DeepVecFont12820.81650.05060.7125
25620.86400.05060.7171
51220.90110.05060.7182
Multi-Implicits12820.80250.05780.6857
25620.85330.06030.6814
51220.89140.06080.6811
Im2Vec12820.75760.07330.5731
25620.82700.07340.5751
51220.87390.07340.5756
Attr2Fonta12820.78410.05120.6393
+ +[38] synthesizes pixelated images only. + +that our synthesized glyphs have high-fidelity details under the guidance of high-resolution glyph images. Quantitative results on three image-level metrics at different resolutions are shown in Tab. 2. For methods producing vector shapes, we also count the average number of commands used for each synthesized vector character, with smaller numbers indicating more compact outputs. The results are shown in Tab. 3. Multi-Implicits [34] uses a large number of short + +Table 3. The average number of commands used per glyph for different methods in the font generation task. M, L, Q, and C denote move, straight line, quadratic Bezier curve, and cubic Bezier curve respectively. + +
CommandMLQCTotal↓
Ours1.428.2111.06020.69
DeepVecFont [39]1.378.2309.6819.28
Multi-Implicits [34]6.161446.53001452.69
Im2Vec [33]4008084
Human-Designed1.389.1708.5119.06
+ +line segments to represent the boundary due to the marching cube algorithm. Im2Vec [33] represents a shape with 4 parts each enclosed by 20 cubic Bezier curves, lacking flexibility and details. Our method performs boolean operations on the quadratic Bezier curves from dual parts, achieving comparable compactness with human-designed fonts and outputs from methods with vector supervision [39]. + +# 4.4. Ablation Studies + +To demonstrate the effectiveness of several key design choices in our method, we conduct ablation studies on the font reconstruction task. We investigate the following degraded variants: (a) replace the union of dual parts with the union of all the paths; (b) train without the UDF warm-up process; and (c) remove the refining strategy during refinement. We show the comparison results of a representative case in Fig. 5. Without the dual-part representation, variant + +![](images/6581d532c982eec0a674319624eee9aeeed566969e9c6c0dfbaefbda9dc20821.jpg) +Figure 5. The contours of an "M" reconstructed by our method, compared with three degraded variants. + +
L1↓#Lines↓# Curves↓
(a) w/o dual parts0.014312.2314.06
(b) w/o warm-up0.014611.1913.12
(c) w/o refining strategy0.0148-22.07
Full Model0.01368.9711.81
+ +(a) cannot reconstruct concave regions very well, as they can be hard to represent by the union of simply closed paths. Without UDF initialization, variant (b) produces contours with useless curves that are hard to be eliminated during optimization. Without the refining strategy, variant (c) may generate inaccurate edges with zigzags. Quantitative results in Tab. 4 also verify the quality improvements brought by the three design choices. + +We also experimentally investigate the effect of different $(N,M)$ s on the representation capacity. We choose several settings of $(N,M)$ and train only the vector branch (i.e. no contour refinement) with the same number of epochs to reconstruct the input. Tab. 5 shows that $M = 4$ is optimal and the reconstruction accuracy of the vector branch increases as $N$ increases. The accuracy does not gain too much changing $N$ from 6 to 8. So considering the time cost for training and inference, we select $(N,M) = (6,4)$ in the above experiments. + +Table 5. Different reconstruction settings and metrics. The image-based metrics use a resolution of $512 \times 512$ . + +
NMSSIM↑L1↓s-IOU↑
240.92620.02820.8338
440.92920.02590.8464
640.93030.02500.8512
840.93060.02470.8525
630.92930.02560.8480
650.93000.02520.8498
+ +# 4.5. Font Sampling and Interpolation + +In the font generation task, the style latent code $z_{style}$ is trained with a variational loss $\mathcal{L}_{kl}$ , enabling generating + +fonts of new styles by sampling $z_{style}$ from $\mathcal{N}(0,1)$ . We show in Fig. 1 (left) and Fig. 6 multiple styles of fonts sampled. Please refer to our supplementary material for more examples. Also, benefiting from our dual-part representation, we can perform smooth interpolation between arbitrary font styles as demonstrated in Fig. 1 (right). + +![](images/0bc638233b068125a099ec9c73b9f7b8e4ac1d4384e8b99eeecb135d8ed4fc57.jpg) +Table 4. Quantitative results of reconstruction accuracy for different model variants in ablation studies. All the output vector glyphs are rendered at $512 \times 512$ to compute the L1 error. +Figure 6. New fonts with style codes sampled in $\mathcal{N}(0,1)$ . + +# 5. Limitations + +The contour refinement step requires gradient descent during inference and therefore imposes a large time overhead, similar to DeepVecFont [39]. The process could potentially be accomplished by forwarding inferences of some generation models, such as the diffusion models [13]. Another limitation is that DualVector only focuses on the synthesis of glyphs on a fixed-size canvas, without considering the kerning between them, making the spacing between characters less natural. This may be solved by post-processing the SVG with some automatic kerning methods or by learning through a data-driven approach. + +# 6. Conclusion + +We present DualVector as a new representation and generation method for vector fonts. DualVector models a glyph as dual parts and introduces a contour refinement step to add pleasing details to the contours of the dual parts. Our method is able to generate vector fonts without vector supervision, which can be directly converted to common digital font formats for content presentation and distribution. Comparisons with different methods of font reconstruction and generation tasks demonstrate that our approach produces fonts with the best quality among all the alternatives. In the future, more plausible initialization and supervision could be exploited to generalize this representation to more complex fonts (e.g. Chinese fonts). We hope this research contributes to the typeface design industry and provide inspiration for broader works on the understanding and generation of 2D man-made content such as cartoon characters and icons. + +Acknowledgement This work was supported by the Natural Science Foundation of China (Project Number 61832016), and Tsinghua-Tencent Joint Laboratory for Internet Innovation Technology. + +# References + +[1] Adobe Inc. 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High-quality vector fonts (copyable on electronic devices) synthesized by DualVector (left), with smoothly-interpolated styles (right). Both sentences are pangrams. Please zoom in for details." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 264, + 222, + 532, + 308 + ], + "blocks": [ + { + "bbox": [ + 264, + 222, + 532, + 308 + ], + "lines": [ + { + "bbox": [ + 264, + 222, + 532, + 308 + ], + "spans": [ + { + "bbox": [ + 264, + 222, + 532, + 308 + ], + "type": "image", + "image_path": "3d892fddaf1a7d8161fd4fa3e7f1a425e23cb59ac0335818baa4d8f547718224.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 143, + 347, + 192, + 359 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 347, + 192, + 359 + ], + "spans": [ + { + "bbox": [ + 143, + 347, + 192, + 359 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 45, + 373, + 290, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 373, + 290, + 613 + ], + "spans": [ + { + "bbox": [ + 45, + 373, + 290, + 613 + ], + "type": "text", + "content": "Automatic generation of fonts can be an important aid to typeface design. Many current approaches regard glyphs as pixelated images, which present artifacts when scaling and inevitable quality losses after vectorization. On the other hand, existing vector font synthesis methods either fail to represent the shape concisely or require vector supervision during training. To push the quality of vector font synthesis to the next level, we propose a novel dual-part representation for vector glyphs, where each glyph is modeled as a collection of closed \"positive\" and \"negative\" path pairs. The glyph contour is then obtained by boolean operations on these paths. We first learn such a representation only from glyph images and devise a subsequent contour refinement step to align the contour with an image representation to further enhance details. Our method, named DualVector, outperforms state-of-the-art methods in vector font synthesis both quantitatively and qualitatively. Our synthesized vector fonts can be easily converted to common digital font formats like TrueType Font for practical use. The code is released at https://github.com/thuliu-yt16/dualvector." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 636, + 128, + 649 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 636, + 128, + 649 + ], + "spans": [ + { + "bbox": [ + 47, + 636, + 128, + 649 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 657, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 657, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 657, + 287, + 693 + ], + "type": "text", + "content": "Fonts with various styles play an important role in content display and distribution. Excellent font design is time-consuming and labor-intensive. Recent machine learning" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 347, + 546, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 347, + 546, + 396 + ], + "spans": [ + { + "bbox": [ + 306, + 347, + 546, + 396 + ], + "type": "text", + "content": "innovations have made font generation possible, but how to automatically generate high-quality vector fonts remains a task of practical importance in the artistic and computer graphics and vision communities." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 403, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 403, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 403, + 547, + 715 + ], + "type": "text", + "content": "Benefiting from the development of image generation techniques, mainstream font synthesis methods [2, 12, 24, 41, 42] could generate pixelated glyph images. Despite the promising quality, images of glyphs incur aliasing artifacts on edges when discretely sampled, and thus are not competent for high-quality rendering or printing at arbitrary resolutions. To alleviate this problem, some methods [7, 34] adopt coordinate-based neural networks to model a glyph as a contiguous neural field, which have also shown great potential in modeling 3D geometry and scenes [7, 30, 32]. Although glyphs represented by the implicit field can be rendered at arbitrary resolutions, it is hard to preserve details in high-frequency regions such as edges and corners, not to mention the high computational costs as the network needs to be evaluated for every pixel. Researchers have made much effort to directly synthesize vector fonts [4, 27, 33, 39] in recent years, with the main difficulty lying in finding a representation of vector graphics that can be encoded or decoded effectively in a deep learning framework. One typical approach represents a vector shape as a sequence of drawing commands and adopts sequence modeling techniques such as recurrent networks and transformers. The drawbacks are twofold: (1) Modeling command sequences can be much harder than images. There are infinitely many command sequences that correspond to the same-looking shape, which brings ambiguities in learning and makes it hard to construct" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 62, + 703, + 139, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 703, + 139, + 713 + ], + "spans": [ + { + "bbox": [ + 62, + 703, + 139, + 713 + ], + "type": "text", + "content": "*Corresponding author" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14193" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "text", + "content": "an effective manifold for valid glyph shapes. (2) Ground-truth drawing commands are often required to provide sufficient supervision for high-quality modeling and synthesis." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 110, + 288, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 110, + 288, + 266 + ], + "spans": [ + { + "bbox": [ + 46, + 110, + 288, + 266 + ], + "type": "text", + "content": "To overcome these challenges, we first propose a dual-part vector font representation, where each glyph shape is the union of a fixed number of dual parts. Each dual part is formed by the subtraction of a \"positive\" and a \"negative\" geometric primitive. While there are many choices for the geometric primitives [6, 8, 25], we adopt closed Bezier paths for their great representational ability. They are also widely supported in digital font formats which makes it easy to convert our representation to these formats for practical use. We reduce the problem of predicting complicated drawing command sequences to predicting multiple basic primitives. From this perspective, both manifold learning and latent space interpolation become more feasible." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 269, + 288, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 269, + 288, + 521 + ], + "spans": [ + { + "bbox": [ + 46, + 269, + 288, + 521 + ], + "type": "text", + "content": "Based on the dual-part representation, we introduce DualVector, a method to learn such a representation for high-quality font modeling and synthesis from only glyph images without any vector supervision. A straightforward way to achieve this is to directly optimize the parameters of the Bezier curves with differentiable rendering techniques for vector graphics [22]. However, this approach easily gets stuck in the local minima as valuable gradients are only defined at shape intersections. Taking inspiration from implicit field training for 2D and 3D shapes [6, 25, 32], we supervise the occupancy value derived from the analytical expression of the Bezier curves and adopt an initialization strategy based on unsigned distance field (UDF) to provide dense gradients across the entire pixel space. For local detail fidelity, we also train a glyph image generation model and devise a subsequent contour refinement step to align the contour of the vector shape with that of the image by differentiable rendering [22]. We compare our approach with state-of-the-art methods in font modeling and generation and demonstrate the superior quality of our vector font outputs. Our main contributions are:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 542, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 59, + 542, + 287, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 542, + 287, + 579 + ], + "spans": [ + { + "bbox": [ + 59, + 542, + 287, + 579 + ], + "type": "text", + "content": "- A new dual-part font representation based on boolean operations of Bezier paths, which enables efficient shape modeling and unsupervised manifold learning." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 59, + 597, + 287, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 597, + 287, + 658 + ], + "spans": [ + { + "bbox": [ + 59, + 597, + 287, + 658 + ], + "type": "text", + "content": "- A method named DualVector that models both the dual-part and pixelated representation, and introduces a contour refinement step to obtain vector fonts with richer details as well as a UDF initialization strategy for better convergence." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 59, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 59, + 677, + 287, + 713 + ], + "type": "text", + "content": "- DualVector achieves state-of-the-art quality in font modeling and generation, with outputs that can be easily converted to common digital font formats." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 71, + 392, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 71, + 392, + 83 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 392, + 83 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 91, + 446, + 104 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 91, + 446, + 104 + ], + "spans": [ + { + "bbox": [ + 306, + 91, + 446, + 104 + ], + "type": "text", + "content": "2.1. Glyph Image Generation" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 110, + 545, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 110, + 545, + 266 + ], + "spans": [ + { + "bbox": [ + 304, + 110, + 545, + 266 + ], + "type": "text", + "content": "Benefiting from the development of image generation [10, 14, 16], either black-white [12, 15, 37, 40] or artistic glyph image generation [2, 23, 41, 42] is well explored in the past decade. MC-GAN [2] synthesized ornamented glyphs for capital letters in an end-to-end manner from a small subset of the same style. Attr2Font [38] generated visually pleasing results according to style attributes and content references. Most of these methods follow the disentanglement of style and content codes, and so does the image generation branch in DualVector. But these glyph image generation efforts do not step outside the 2D pixelated representation which sets an upper bound for rendering quality, efficiency, and practicality." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 273, + 508, + 285 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 273, + 508, + 285 + ], + "spans": [ + { + "bbox": [ + 306, + 273, + 508, + 285 + ], + "type": "text", + "content": "2.2. Image Rasterization and Vectorization" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 292, + 545, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 292, + 545, + 483 + ], + "spans": [ + { + "bbox": [ + 304, + 292, + 545, + 483 + ], + "type": "text", + "content": "Rasterization and vectorization are dual problems in image processing. Previous efforts on rasterization have typically focused on anti-aliasing [9, 11, 31] and high-performance rendering on modern graphics hardware [3, 17, 21, 26]. Traditional image vectorization approaches rely on region segmentation, line extraction, and contour tracing for gray-scale images [35], pixel arts [18], animations [44] and general images [1, 5, 19, 36, 45, 46]. Recently, researchers have turned to bridging the raster and vector domains [22, 29], enabling existing well-established algorithms for raster images to be also applied to vector representations. DiffVG [22] is a differentiable rendering technique for vector graphics enabling the optimization of vector primitive parameters based on raster criteria. In our work, it is employed to align the vector and pixel representation in the contour refinement step." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 491, + 440, + 503 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 491, + 440, + 503 + ], + "spans": [ + { + "bbox": [ + 306, + 491, + 440, + 503 + ], + "type": "text", + "content": "2.3. Vector Font Generation" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": "SVG-VAE [27] was the first attempt to build a sequential generative model on SVG fonts. DeepSVG [4] developed a hierarchical transformer-based generative model for complex SVG icons generation and interpolation. Exploiting implicit neural representation, multi-implicit [34] modeled fonts with a permutation-invariant set of learned implicit functions which can preserve font features, such as smooth edges and sharp corners, and generate good interpolation results. Liu et al. [25] proposed a primitive-based representation, which views glyph shapes as the combination of primitives enclosed by implicit curves. Implicit representation-based methods can convert the zero-level set of their output fields to contour representation with the 2D marching cube [28] algorithm, although it produces multiple segmented lines and lacks accuracy and efficiency in rendering and editing. Im2Vec [33] can synthesize complex vector graphics with varying topologies without vector super" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "14194" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 82, + 77, + 511, + 289 + ], + "blocks": [ + { + "bbox": [ + 82, + 77, + 511, + 289 + ], + "lines": [ + { + "bbox": [ + 82, + 77, + 511, + 289 + ], + "spans": [ + { + "bbox": [ + 82, + 77, + 511, + 289 + ], + "type": "image", + "image_path": "df4217b94fc36294faf9377ed7b37181bda1a365f3f5d6367ccd3db5e1f17b4e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 292, + 547, + 338 + ], + "lines": [ + { + "bbox": [ + 46, + 292, + 547, + 338 + ], + "spans": [ + { + "bbox": [ + 46, + 292, + 547, + 338 + ], + "type": "text", + "content": "Figure 2. DualVector contains the following components: (a) a vector branch that maps the latent code " + }, + { + "bbox": [ + 46, + 292, + 547, + 338 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 292, + 547, + 338 + ], + "type": "text", + "content": " to several closed Bézier paths which are further gathered to form a global shape of the glyph; (b) an image branch that generates pixelated images with faithful details; (c) a contour refinement step that obtains the contour via boolean operations on dual-parts and optimizes it with the image guidance at inference time. Both the vector and the image branch are trained using the glyph images. Dual parts are distinguished by their colors." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 346, + 289, + 466 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 346, + 289, + 466 + ], + "spans": [ + { + "bbox": [ + 46, + 346, + 289, + 466 + ], + "type": "text", + "content": "vision. It rendered layered Bézier paths predicted from image features using DiffVG [22] and trains the system in an auto-encoding manner. DeepVecFont [39] adopted a dual-modality learning framework that utilizes both sequence and image features for high-quality vector font synthesis. But the results it produces may have the wrong topology, including self-intersection or invalid paths. In contrast to these methods, our approach does not require vector supervision and is very efficient in vector representation, with high quality glyph generation." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 476, + 121, + 489 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 476, + 121, + 489 + ], + "spans": [ + { + "bbox": [ + 47, + 476, + 121, + 489 + ], + "type": "text", + "content": "3. DualVector" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 496, + 287, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 496, + 287, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 496, + 287, + 665 + ], + "type": "text", + "content": "In this section, we first illustrate the proposed dual-part representation for fonts (Sec. 3.1) and then introduce the components of DualVector for training this representation from glyph images (Secs. 3.2 to 3.4) and how the model can be used for font reconstruction and generation (Sec. 3.5). In DualVector, we adopt a joint representation of vector and image for fonts, as shown in Fig. 2. The latent space is shared by both modalities, and we associate each glyph with a latent code " + }, + { + "bbox": [ + 46, + 496, + 287, + 665 + ], + "type": "inline_equation", + "content": "z \\in \\mathbf{R}^d" + }, + { + "bbox": [ + 46, + 496, + 287, + 665 + ], + "type": "text", + "content": " produced by the task-specific encoding process. The latent code " + }, + { + "bbox": [ + 46, + 496, + 287, + 665 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 496, + 287, + 665 + ], + "type": "text", + "content": " is fed into the two decoding branches to obtain a dual-part representation and an image representation respectively. The output of the vector branch is further processed by a contour refinement step to generate the final contour representation under the image guidance." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 671, + 191, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 191, + 684 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 191, + 684 + ], + "type": "text", + "content": "3.1. Dual-Part Representation" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "content": "In our dual-part representation, we consider the closed parametric Bézier paths as our basic primitives for several" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 346, + 545, + 527 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 346, + 545, + 527 + ], + "spans": [ + { + "bbox": [ + 304, + 346, + 545, + 527 + ], + "type": "text", + "content": "reasons: (1) Bézier paths are powerful enough to approximate various shapes; (2) The contour of a closed shape produced by boolean operations on Bézier paths is still a set of Bézier paths, i.e., the closure property; (3) Bézier paths are widely used in modern font design, making the learned representation highly applicable. For convenience, we use a triplet of control points " + }, + { + "bbox": [ + 304, + 346, + 545, + 527 + ], + "type": "inline_equation", + "content": "(\\pmb{a},\\pmb{b},\\pmb{c})" + }, + { + "bbox": [ + 304, + 346, + 545, + 527 + ], + "type": "text", + "content": " to denote a quadratic Bézier curve " + }, + { + "bbox": [ + 304, + 346, + 545, + 527 + ], + "type": "inline_equation", + "content": "B(\\cdot ;\\pmb {a},\\pmb {b},\\pmb {c})" + }, + { + "bbox": [ + 304, + 346, + 545, + 527 + ], + "type": "text", + "content": " determined by the control points: " + }, + { + "bbox": [ + 304, + 346, + 545, + 527 + ], + "type": "inline_equation", + "content": "B(t;\\pmb {a},\\pmb {b},\\pmb {c}) = (1 - t)^{2}\\pmb {a} + (1 - t)t\\pmb {b} + t^{2}\\pmb {c}t\\in [0,1]" + }, + { + "bbox": [ + 304, + 346, + 545, + 527 + ], + "type": "text", + "content": " 1 Since a glyph often consists of a number of strokes with similar appearances, we propose to represent each glyph " + }, + { + "bbox": [ + 304, + 346, + 545, + 527 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 304, + 346, + 545, + 527 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 346, + 545, + 527 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 346, + 545, + 527 + ], + "type": "text", + "content": " closed Bézier paths " + }, + { + "bbox": [ + 304, + 346, + 545, + 527 + ], + "type": "inline_equation", + "content": "\\{P_i\\}_{i = 1}^N" + }, + { + "bbox": [ + 304, + 346, + 545, + 527 + ], + "type": "text", + "content": " . Each path " + }, + { + "bbox": [ + 304, + 346, + 545, + 527 + ], + "type": "inline_equation", + "content": "P_{i}" + }, + { + "bbox": [ + 304, + 346, + 545, + 527 + ], + "type": "text", + "content": " is defined by " + }, + { + "bbox": [ + 304, + 346, + 545, + 527 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 346, + 545, + 527 + ], + "type": "text", + "content": " end-to-end connected quadratic Bézier curves " + }, + { + "bbox": [ + 304, + 346, + 545, + 527 + ], + "type": "inline_equation", + "content": "\\{B_{i,j}(\\pmb{x}_{i,2j - 1},\\pmb{x}_{i,2j},\\pmb{x}_{i,2j + 1})\\}_{j = 1}^{M}(\\pmb{x}_{i,2M + 1} = \\pmb{x}_{i,1})" + }, + { + "bbox": [ + 304, + 346, + 545, + 527 + ], + "type": "text", + "content": " .We introduce the occupancy field of a closed path " + }, + { + "bbox": [ + 304, + 346, + 545, + 527 + ], + "type": "inline_equation", + "content": "P_{i}" + }, + { + "bbox": [ + 304, + 346, + 545, + 527 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 369, + 528, + 545, + 552 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 369, + 528, + 545, + 552 + ], + "spans": [ + { + "bbox": [ + 369, + 528, + 545, + 552 + ], + "type": "interline_equation", + "content": "\\mathcal {O} _ {P _ {i}} (\\boldsymbol {x}) = \\left\\{ \\begin{array}{l l} 1, & \\boldsymbol {x} \\in P _ {i} \\\\ 0, & \\boldsymbol {x} \\notin P _ {i} \\end{array} \\right. \\tag {2}", + "image_path": "ddfca4e603a7844deaad9d1051da2c304bd686c4a9837f67faf3e331154f3d72.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 552, + 545, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 552, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 552, + 545, + 624 + ], + "type": "text", + "content": "The entire glyph shape " + }, + { + "bbox": [ + 304, + 552, + 545, + 624 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 304, + 552, + 545, + 624 + ], + "type": "text", + "content": " could simply be denoted as the union of all the paths " + }, + { + "bbox": [ + 304, + 552, + 545, + 624 + ], + "type": "inline_equation", + "content": "\\cup_{i} P_{i}" + }, + { + "bbox": [ + 304, + 552, + 545, + 624 + ], + "type": "text", + "content": ". We normalize the coordinate range of the glyph to " + }, + { + "bbox": [ + 304, + 552, + 545, + 624 + ], + "type": "inline_equation", + "content": "[-1, 1]^{2}" + }, + { + "bbox": [ + 304, + 552, + 545, + 624 + ], + "type": "text", + "content": ". Thus given any point " + }, + { + "bbox": [ + 304, + 552, + 545, + 624 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 552, + 545, + 624 + ], + "type": "text", + "content": " on the canvas " + }, + { + "bbox": [ + 304, + 552, + 545, + 624 + ], + "type": "inline_equation", + "content": "[-1, 1]^{2}" + }, + { + "bbox": [ + 304, + 552, + 545, + 624 + ], + "type": "text", + "content": ", we can determine whether it is inside the represented glyph shape by a maximum operation, leading to the occupancy field of " + }, + { + "bbox": [ + 304, + 552, + 545, + 624 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 304, + 552, + 545, + 624 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 335, + 624, + 545, + 650 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 335, + 624, + 545, + 650 + ], + "spans": [ + { + "bbox": [ + 335, + 624, + 545, + 650 + ], + "type": "interline_equation", + "content": "\\mathcal {O} (\\boldsymbol {x}) = \\max _ {i} \\mathcal {O} _ {P _ {i}} (\\boldsymbol {x}) = \\left\\{ \\begin{array}{l l} 1, & \\boldsymbol {x} \\in \\cup_ {i} P _ {i} \\\\ 0, & \\boldsymbol {x} \\notin \\cup_ {i} P _ {i} \\end{array} \\right. \\tag {3}", + "image_path": "06b0f06ada1d54176923e4d8299a6fddb54936c4e9baa76ceab851b26c95dca9.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "content": "However, we find that the above representation can model fonts with convex curves on the contour but struggles to reconstruct shapes with holes. Therefore, in practice, we pair each path " + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "inline_equation", + "content": "P_{i}" + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "content": " with a negative path " + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "inline_equation", + "content": "Q_{i}" + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "content": ", and term this pair " + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "inline_equation", + "content": "(P_{i}, Q_{i})" + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "content": " as a \"dual part\". In this way, " + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "content": " is represented as" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14195" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 272, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 272, + 83 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 272, + 83 + ], + "type": "inline_equation", + "content": "\\cup_{i}(P_{i} - Q_{i})" + }, + { + "bbox": [ + 46, + 72, + 272, + 83 + ], + "type": "text", + "content": " . The occupancy field " + }, + { + "bbox": [ + 46, + 72, + 272, + 83 + ], + "type": "inline_equation", + "content": "\\mathcal{O}" + }, + { + "bbox": [ + 46, + 72, + 272, + 83 + ], + "type": "text", + "content": " is then derived as:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 85, + 287, + 120 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 85, + 287, + 120 + ], + "spans": [ + { + "bbox": [ + 47, + 85, + 287, + 120 + ], + "type": "interline_equation", + "content": "\\mathcal {O} (\\boldsymbol {x}) = \\max _ {i} [ \\min \\left(\\mathcal {O} _ {P _ {i}} (\\boldsymbol {x}), 1 - \\mathcal {O} _ {Q _ {i}} (\\boldsymbol {x})\\right) ] = \\left\\{ \\begin{array}{l l} 1, & \\boldsymbol {x} \\in g \\\\ 0, & \\boldsymbol {x} \\notin g \\end{array} \\right. \\tag {4}", + "image_path": "f8f78284642b60778548ee94a7781b83a48b872389cd7c673df64363eecd05b9.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 121, + 287, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 121, + 287, + 217 + ], + "spans": [ + { + "bbox": [ + 46, + 121, + 287, + 217 + ], + "type": "text", + "content": "Even though " + }, + { + "bbox": [ + 46, + 121, + 287, + 217 + ], + "type": "inline_equation", + "content": "\\mathcal{O}" + }, + { + "bbox": [ + 46, + 121, + 287, + 217 + ], + "type": "text", + "content": " is the analytical occupancy field of " + }, + { + "bbox": [ + 46, + 121, + 287, + 217 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 46, + 121, + 287, + 217 + ], + "type": "text", + "content": ", it is not differentiable w.r.t. the parameters of the paths. Therefore, in order to apply gradient descent to learn such a representation, we calculate the approximate occupancy field " + }, + { + "bbox": [ + 46, + 121, + 287, + 217 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{O}}" + }, + { + "bbox": [ + 46, + 121, + 287, + 217 + ], + "type": "text", + "content": " from the signed distance field (SDF) of " + }, + { + "bbox": [ + 46, + 121, + 287, + 217 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 46, + 121, + 287, + 217 + ], + "type": "text", + "content": ". Since the distance " + }, + { + "bbox": [ + 46, + 121, + 287, + 217 + ], + "type": "inline_equation", + "content": "d(p;B)" + }, + { + "bbox": [ + 46, + 121, + 287, + 217 + ], + "type": "text", + "content": " from any point " + }, + { + "bbox": [ + 46, + 121, + 287, + 217 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 121, + 287, + 217 + ], + "type": "text", + "content": " to a Bézier curve " + }, + { + "bbox": [ + 46, + 121, + 287, + 217 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 46, + 121, + 287, + 217 + ], + "type": "text", + "content": " can be derived analytically, the SDF of a path can be calculated differentiably w.r.t. its control points as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 85, + 218, + 287, + 236 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 218, + 287, + 236 + ], + "spans": [ + { + "bbox": [ + 85, + 218, + 287, + 236 + ], + "type": "interline_equation", + "content": "s _ {P _ {i}} (\\boldsymbol {x}) = \\left[ 2 \\mathcal {O} _ {P _ {i}} (\\boldsymbol {x}) - 1 \\right] \\min _ {j} d (\\boldsymbol {x}; B _ {i, j}) \\tag {5}", + "image_path": "e2ea91065d154d1d54af7bbb42f8ed45dc2a98a19edc6d86823af23fddca846f.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 236, + 287, + 270 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 236, + 287, + 270 + ], + "spans": [ + { + "bbox": [ + 46, + 236, + 287, + 270 + ], + "type": "text", + "content": "Following previous vector graphics rasterization techniques [22, 31, 34], we approximate " + }, + { + "bbox": [ + 46, + 236, + 287, + 270 + ], + "type": "inline_equation", + "content": "\\mathcal{O}" + }, + { + "bbox": [ + 46, + 236, + 287, + 270 + ], + "type": "text", + "content": " by analytical pixel prefiltering with a parabolic kernel " + }, + { + "bbox": [ + 46, + 236, + 287, + 270 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 236, + 287, + 270 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 102, + 272, + 192, + 285 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 272, + 192, + 285 + ], + "spans": [ + { + "bbox": [ + 102, + 272, + 192, + 285 + ], + "type": "interline_equation", + "content": "\\hat {\\mathcal {O}} _ {P _ {i}} (\\boldsymbol {x}) = \\alpha \\left(s _ {P _ {i}} (\\boldsymbol {x})\\right)", + "image_path": "8e98e4bc8e91105f7af048d72c5003ce5ca8b68b611e3841fadfac4ac82193b0.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 102, + 285, + 287, + 306 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 285, + 287, + 306 + ], + "spans": [ + { + "bbox": [ + 102, + 285, + 287, + 306 + ], + "type": "interline_equation", + "content": "\\hat {\\mathcal {O}} = \\max _ {i} [ \\min (\\hat {\\mathcal {O}} _ {P _ {i}}, 1 - \\hat {\\mathcal {O}} _ {Q _ {i}}) ] \\tag {6}", + "image_path": "6067508efbbdbec47e6002e3d1306826dfa7139066443c5750078c2d4a017352.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 316, + 138, + 328 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 316, + 138, + 328 + ], + "spans": [ + { + "bbox": [ + 47, + 316, + 138, + 328 + ], + "type": "text", + "content": "3.2. Vector Branch" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 336, + 287, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 336, + 287, + 384 + ], + "spans": [ + { + "bbox": [ + 47, + 336, + 287, + 384 + ], + "type": "text", + "content": "The vector branch takes a latent code " + }, + { + "bbox": [ + 47, + 336, + 287, + 384 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 47, + 336, + 287, + 384 + ], + "type": "text", + "content": " and outputs a set of dual-parts that represent a vector glyph. The path decoder " + }, + { + "bbox": [ + 47, + 336, + 287, + 384 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_P" + }, + { + "bbox": [ + 47, + 336, + 287, + 384 + ], + "type": "text", + "content": " directly predicts the control points of the positive paths " + }, + { + "bbox": [ + 47, + 336, + 287, + 384 + ], + "type": "inline_equation", + "content": "\\{P_i\\}_{i=1}^N" + }, + { + "bbox": [ + 47, + 336, + 287, + 384 + ], + "type": "text", + "content": " and the negative ones " + }, + { + "bbox": [ + 47, + 336, + 287, + 384 + ], + "type": "inline_equation", + "content": "\\{Q_i\\}_{i=1}^N" + }, + { + "bbox": [ + 47, + 336, + 287, + 384 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 47, + 336, + 287, + 384 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 47, + 336, + 287, + 384 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 78, + 384, + 287, + 397 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 384, + 287, + 397 + ], + "spans": [ + { + "bbox": [ + 78, + 384, + 287, + 397 + ], + "type": "interline_equation", + "content": "\\left\\{\\boldsymbol {x} _ {i, j} \\right\\} = \\mathcal {D} _ {P} (z), 1 \\leq i \\leq 2 N, 1 \\leq j \\leq 2 M \\tag {7}", + "image_path": "7f40c4d26c0ecaf993ae6c6bd12bc59337ca0360ace984ba032817e9fe3bc4bb.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 397, + 287, + 423 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 397, + 287, + 423 + ], + "spans": [ + { + "bbox": [ + 47, + 397, + 287, + 423 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 397, + 287, + 423 + ], + "type": "inline_equation", + "content": "\\{\\pmb{x}_{i,j}\\}_{i = 1}^{N}" + }, + { + "bbox": [ + 47, + 397, + 287, + 423 + ], + "type": "text", + "content": " are control points for " + }, + { + "bbox": [ + 47, + 397, + 287, + 423 + ], + "type": "inline_equation", + "content": "\\{P_i\\}_{i = 1}^N" + }, + { + "bbox": [ + 47, + 397, + 287, + 423 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 397, + 287, + 423 + ], + "type": "inline_equation", + "content": "\\{\\pmb{x}_{i,j}\\}_{i = N + 1}^{2N}" + }, + { + "bbox": [ + 47, + 397, + 287, + 423 + ], + "type": "text", + "content": " are control points for " + }, + { + "bbox": [ + 47, + 397, + 287, + 423 + ], + "type": "inline_equation", + "content": "\\{Q_i\\}_{i = 1}^N" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 432, + 136, + 445 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 432, + 136, + 445 + ], + "spans": [ + { + "bbox": [ + 47, + 432, + 136, + 445 + ], + "type": "text", + "content": "3.3. Image Branch" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 452, + 287, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 452, + 287, + 499 + ], + "spans": [ + { + "bbox": [ + 46, + 452, + 287, + 499 + ], + "type": "text", + "content": "To combine with the advantages of image generation approaches, we train an auxiliary image branch that maps " + }, + { + "bbox": [ + 46, + 452, + 287, + 499 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 452, + 287, + 499 + ], + "type": "text", + "content": " to a pixelated image " + }, + { + "bbox": [ + 46, + 452, + 287, + 499 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 46, + 452, + 287, + 499 + ], + "type": "text", + "content": " of the glyph it represents. Here we adopt a CNN-based decoder " + }, + { + "bbox": [ + 46, + 452, + 287, + 499 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_I" + }, + { + "bbox": [ + 46, + 452, + 287, + 499 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 143, + 501, + 287, + 513 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 501, + 287, + 513 + ], + "spans": [ + { + "bbox": [ + 143, + 501, + 287, + 513 + ], + "type": "interline_equation", + "content": "\\mathcal {I} = \\mathcal {D} _ {I} (z) \\tag {8}", + "image_path": "be78fa4f737d88354dc9100ef8b8606147b117bd914f331a50fcfbb0ef0660b1.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 514, + 287, + 537 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 514, + 287, + 537 + ], + "spans": [ + { + "bbox": [ + 46, + 514, + 287, + 537 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 514, + 287, + 537 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 46, + 514, + 287, + 537 + ], + "type": "text", + "content": " is a gray-scale image in shape " + }, + { + "bbox": [ + 46, + 514, + 287, + 537 + ], + "type": "inline_equation", + "content": "H\\times W" + }, + { + "bbox": [ + 46, + 514, + 287, + 537 + ], + "type": "text", + "content": ". It provides detailed shape guidance to refine the vector shape contour." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 47, + 548, + 166, + 559 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 548, + 166, + 559 + ], + "spans": [ + { + "bbox": [ + 47, + 548, + 166, + 559 + ], + "type": "text", + "content": "3.4. Contour Refinement" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 567, + 287, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 567, + 287, + 651 + ], + "spans": [ + { + "bbox": [ + 46, + 567, + 287, + 651 + ], + "type": "text", + "content": "Although the dual-part representation produced by the vector branch can already be rendered, there still exists a gap between it and modern contour representations for fonts. Therefore, we first convert it to the contour of the glyph " + }, + { + "bbox": [ + 46, + 567, + 287, + 651 + ], + "type": "inline_equation", + "content": "\\partial \\mathcal{O}" + }, + { + "bbox": [ + 46, + 567, + 287, + 651 + ], + "type": "text", + "content": " with an off-the-shelf tool Paper.js [20] which can perform arbitrary boolean operations on SVG paths. Here the contour " + }, + { + "bbox": [ + 46, + 567, + 287, + 651 + ], + "type": "inline_equation", + "content": "\\partial \\mathcal{O}" + }, + { + "bbox": [ + 46, + 567, + 287, + 651 + ], + "type": "text", + "content": " is a set of K closed Bézier paths." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 116, + 652, + 286, + 665 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 652, + 286, + 665 + ], + "spans": [ + { + "bbox": [ + 116, + 652, + 286, + 665 + ], + "type": "interline_equation", + "content": "\\partial \\mathcal {O} = \\left\\{C _ {1}, C _ {2}, \\dots , C _ {K} \\right\\} \\tag {9}", + "image_path": "2e6e759f0b6a7d34b0039491a4e9fc6d798663ffd844433c7dc2996b8c2e1e72.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "type": "text", + "content": " denotes the number of independent paths. Each individual part or hole increases " + }, + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "type": "text", + "content": " by 1. " + }, + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "type": "inline_equation", + "content": "C_i" + }, + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "type": "text", + "content": " is a closed Bezier path composed of " + }, + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "type": "inline_equation", + "content": "l_i" + }, + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "type": "text", + "content": " quadratic Bezier segments " + }, + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\{\\hat{B}_{i,j}(\\hat{\\pmb{x}}_{i,2j - 1},\\hat{\\pmb{x}}_{i,2j},\\hat{\\pmb{x}}_{i,2j + 1})\\}_{j = 1}^{l_i}" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": "After this conversion, we exploit the image generation results to further refine " + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "\\partial \\mathcal{O}" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": " with differentiable rendering techniques [22]. " + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": " could naturally serve as a pixelated version of the occupancy field " + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "\\mathcal{O}" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": ". During the refinement, we devise several strategies to improve the quality and efficiency of our representation:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 161, + 545, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 161, + 545, + 198 + ], + "spans": [ + { + "bbox": [ + 304, + 161, + 545, + 198 + ], + "type": "text", + "content": "Subdivision To improve the representational ability, we split long Bézier curves (with a length greater than " + }, + { + "bbox": [ + 304, + 161, + 545, + 198 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 304, + 161, + 545, + 198 + ], + "type": "text", + "content": " of the canvas width) at their midpoints." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 215, + 545, + 358 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 215, + 545, + 358 + ], + "spans": [ + { + "bbox": [ + 304, + 215, + 545, + 358 + ], + "type": "text", + "content": "Simplification To improve the efficiency of the contour representation, we replace the Bézier curves with a line segment connecting its two endpoints if they are close enough. For a Bézier curve " + }, + { + "bbox": [ + 304, + 215, + 545, + 358 + ], + "type": "inline_equation", + "content": "(a, b, c)" + }, + { + "bbox": [ + 304, + 215, + 545, + 358 + ], + "type": "text", + "content": ", we simply define how faithfully the segment " + }, + { + "bbox": [ + 304, + 215, + 545, + 358 + ], + "type": "inline_equation", + "content": "ac" + }, + { + "bbox": [ + 304, + 215, + 545, + 358 + ], + "type": "text", + "content": " could represent the curve by the angle between " + }, + { + "bbox": [ + 304, + 215, + 545, + 358 + ], + "type": "inline_equation", + "content": "\\vec{ba}" + }, + { + "bbox": [ + 304, + 215, + 545, + 358 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 215, + 545, + 358 + ], + "type": "inline_equation", + "content": "\\vec{bc}" + }, + { + "bbox": [ + 304, + 215, + 545, + 358 + ], + "type": "text", + "content": ". Also, we examine if there exist two adjacent Bézier segments that could be combined as a single one. Since all quadratic Bézier curves are parts of a parabola curve, we derive the parameters of the corresponding parabola curves from the control points and combine the two curves if their parameters are close enough. We also aggregate the endpoints of lines and curves that are too short." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 376, + 545, + 435 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 376, + 545, + 435 + ], + "spans": [ + { + "bbox": [ + 304, + 376, + 545, + 435 + ], + "type": "text", + "content": "Pruning Prior to refinement, some Bezier paths on the contour may enclose extremely small regions which will confuse the refinement process and produce redundant curves that eventually converge to a single point. We trim those closed paths " + }, + { + "bbox": [ + 304, + 376, + 545, + 435 + ], + "type": "inline_equation", + "content": "C_i" + }, + { + "bbox": [ + 304, + 376, + 545, + 435 + ], + "type": "text", + "content": " with areas under a certain threshold." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 437, + 545, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 545, + 460 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 545, + 460 + ], + "type": "text", + "content": "More implementation details of these strategies can be found in the supplemental material." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 469, + 468, + 482 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 469, + 468, + 482 + ], + "spans": [ + { + "bbox": [ + 306, + 469, + 468, + 482 + ], + "type": "text", + "content": "3.5. Implementation and Training" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 488, + 545, + 524 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 488, + 545, + 524 + ], + "spans": [ + { + "bbox": [ + 304, + 488, + 545, + 524 + ], + "type": "text", + "content": "In this subsection, we will dive into how we utilize the proposed representation in both the font reconstruction and generation tasks." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 306, + 542, + 443, + 554 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 542, + 443, + 554 + ], + "spans": [ + { + "bbox": [ + 306, + 542, + 443, + 554 + ], + "type": "text", + "content": "3.5.1 Optimization Objectives" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 561, + 545, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 561, + 545, + 597 + ], + "spans": [ + { + "bbox": [ + 304, + 561, + 545, + 597 + ], + "type": "text", + "content": "Optimization objectives can be divided into those at training time and those at inference time. The training-time objectives are task-related." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 304, + 615, + 545, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 615, + 545, + 673 + ], + "spans": [ + { + "bbox": [ + 304, + 615, + 545, + 673 + ], + "type": "text", + "content": "Font reconstruction. For the font reconstruction task, the input to our system is a gray-scale image of a glyph and the output is the corresponding vector representation. The pixelated image " + }, + { + "bbox": [ + 304, + 615, + 545, + 673 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_g" + }, + { + "bbox": [ + 304, + 615, + 545, + 673 + ], + "type": "text", + "content": " of the glyph " + }, + { + "bbox": [ + 304, + 615, + 545, + 673 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 304, + 615, + 545, + 673 + ], + "type": "text", + "content": " is first passed through an image encoder " + }, + { + "bbox": [ + 304, + 615, + 545, + 673 + ], + "type": "inline_equation", + "content": "\\mathcal{E}" + }, + { + "bbox": [ + 304, + 615, + 545, + 673 + ], + "type": "text", + "content": " to obtain the latent code " + }, + { + "bbox": [ + 304, + 615, + 545, + 673 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 304, + 615, + 545, + 673 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 403, + 675, + 545, + 689 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 403, + 675, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 403, + 675, + 545, + 689 + ], + "type": "interline_equation", + "content": "z = \\mathcal {E} \\left(\\mathcal {I} _ {g}\\right) \\tag {10}", + "image_path": "446462b9929a377d68d2d9efa339f3ed8d6bb2fea30313a79bace5a290225e1e.jpg" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "content": "The latent code is then decoded by our vector branch and image branch into dual-parts " + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\{(P_i,Q_i)\\}_{i = 1}^N" + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "content": " and a pixelated" + } + ] + } + ], + "index": 30 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "14196" + } + ] + } + ], + "index": 31 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 286, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 286, + 95 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 286, + 95 + ], + "type": "text", + "content": "output " + }, + { + "bbox": [ + 47, + 72, + 286, + 95 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 47, + 72, + 286, + 95 + ], + "type": "text", + "content": ". We optimize the trainable modules " + }, + { + "bbox": [ + 47, + 72, + 286, + 95 + ], + "type": "inline_equation", + "content": "\\mathcal{E},\\mathcal{D}_I" + }, + { + "bbox": [ + 47, + 72, + 286, + 95 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 72, + 286, + 95 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_P" + }, + { + "bbox": [ + 47, + 72, + 286, + 95 + ], + "type": "text", + "content": " simultaneously with the following loss functions:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 126, + 98, + 286, + 109 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 126, + 98, + 286, + 109 + ], + "spans": [ + { + "bbox": [ + 126, + 98, + 286, + 109 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\lambda_ {P} \\mathcal {L} _ {P} + \\lambda_ {I} \\mathcal {L} _ {I} \\tag {11}", + "image_path": "bba6d7f78f1dafa9c92b366f0bedd63009a07cee7b43df342a90888fc404217e.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 110, + 232, + 121 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 110, + 232, + 121 + ], + "spans": [ + { + "bbox": [ + 47, + 110, + 232, + 121 + ], + "type": "text", + "content": "where we adopt an extra perceptual loss [43]:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 91, + 123, + 286, + 140 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 123, + 286, + 140 + ], + "spans": [ + { + "bbox": [ + 91, + 123, + 286, + 140 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {P} = \\mathbb {E} _ {\\boldsymbol {x} \\sim [ - 1, 1 ] ^ {2}} \\left[ \\left\\| \\hat {\\mathcal {O}} (\\boldsymbol {x}) - \\mathcal {I} _ {g} (\\boldsymbol {x}) \\right\\| _ {1} \\right] \\tag {12}", + "image_path": "4e0fa53569c284d10dffff20e9fc0b9aa3e5596107f560a05bb13c03bbc0c154.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 93, + 139, + 230, + 152 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 139, + 230, + 152 + ], + "spans": [ + { + "bbox": [ + 93, + 139, + 230, + 152 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {I} = \\left| \\left| \\mathcal {I} - \\mathcal {I} _ {g} \\right| \\right| _ {2} + \\operatorname {L P I P S} (\\mathcal {I}, \\mathcal {I} _ {g})", + "image_path": "0ce4cefb1d4de6f1b9bb351c68077388db2e8c972bccbb3c54d5adfa34fa8f8c.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 156, + 286, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 156, + 286, + 323 + ], + "spans": [ + { + "bbox": [ + 47, + 156, + 286, + 323 + ], + "type": "text", + "content": "Font generation. The input to the font generation task is multiple style reference images " + }, + { + "bbox": [ + 47, + 156, + 286, + 323 + ], + "type": "inline_equation", + "content": "\\{R_i\\}_{i=1}^{N_R}" + }, + { + "bbox": [ + 47, + 156, + 286, + 323 + ], + "type": "text", + "content": " along with the corresponding character label " + }, + { + "bbox": [ + 47, + 156, + 286, + 323 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 47, + 156, + 286, + 323 + ], + "type": "text", + "content": ". The number of references " + }, + { + "bbox": [ + 47, + 156, + 286, + 323 + ], + "type": "inline_equation", + "content": "N_R" + }, + { + "bbox": [ + 47, + 156, + 286, + 323 + ], + "type": "text", + "content": " may vary during training to allow the model to accept a variable number of references during inference. The style references are first mapped to their features " + }, + { + "bbox": [ + 47, + 156, + 286, + 323 + ], + "type": "inline_equation", + "content": "\\{f_i\\}_{i=1}^{N_R}" + }, + { + "bbox": [ + 47, + 156, + 286, + 323 + ], + "type": "text", + "content": " with an image encoder " + }, + { + "bbox": [ + 47, + 156, + 286, + 323 + ], + "type": "inline_equation", + "content": "\\mathcal{E}_f" + }, + { + "bbox": [ + 47, + 156, + 286, + 323 + ], + "type": "text", + "content": ". We then apply stacked self-attention layers (SA) to aggregate these features to a style latent code " + }, + { + "bbox": [ + 47, + 156, + 286, + 323 + ], + "type": "inline_equation", + "content": "z_{style}" + }, + { + "bbox": [ + 47, + 156, + 286, + 323 + ], + "type": "text", + "content": " with a variational loss to enable font sampling. Character labels are mapped to vector representations by a learnable label embedding layer and then fused with " + }, + { + "bbox": [ + 47, + 156, + 286, + 323 + ], + "type": "inline_equation", + "content": "z_{style}" + }, + { + "bbox": [ + 47, + 156, + 286, + 323 + ], + "type": "text", + "content": " to yield the latent code " + }, + { + "bbox": [ + 47, + 156, + 286, + 323 + ], + "type": "inline_equation", + "content": "z_T" + }, + { + "bbox": [ + 47, + 156, + 286, + 323 + ], + "type": "text", + "content": " of the target glyph. Then " + }, + { + "bbox": [ + 47, + 156, + 286, + 323 + ], + "type": "inline_equation", + "content": "z_T" + }, + { + "bbox": [ + 47, + 156, + 286, + 323 + ], + "type": "text", + "content": " is fed to the decoders to generate the glyph, the same as the reconstruction task. The whole process can be described as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 123, + 332, + 174, + 346 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 332, + 174, + 346 + ], + "spans": [ + { + "bbox": [ + 123, + 332, + 174, + 346 + ], + "type": "interline_equation", + "content": "f _ {i} = \\mathcal {E} _ {f} (R _ {i})", + "image_path": "8c72fe19a4f3b3ae09928cdb508019216c4729a0e431f117eeb38f73ade06f98.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 113, + 347, + 286, + 365 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 347, + 286, + 365 + ], + "spans": [ + { + "bbox": [ + 113, + 347, + 286, + 365 + ], + "type": "interline_equation", + "content": "\\mu , \\sigma = \\operatorname {S A} \\left(f _ {1}, f _ {2}, \\dots , f _ {N _ {R}}\\right) \\tag {13}", + "image_path": "782ec961bb59f5f685ccc08811997fb9656aa190416e34293ec87d5c07d7702e.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 108, + 362, + 286, + 375 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 362, + 286, + 375 + ], + "spans": [ + { + "bbox": [ + 108, + 362, + 286, + 375 + ], + "type": "interline_equation", + "content": "z _ {s t y l e} = \\mu + \\epsilon \\sigma , \\epsilon \\sim \\mathcal {N} (0, 1) \\tag {15}", + "image_path": "894194b0c8381df86dd6b6cb24204a05e67dcc3a87add53549e5c33401988e90.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 120, + 377, + 210, + 390 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 120, + 377, + 210, + 390 + ], + "spans": [ + { + "bbox": [ + 120, + 377, + 210, + 390 + ], + "type": "interline_equation", + "content": "z _ {T} = \\operatorname {F F N} ([ z _ {\\text {s t y l e}}, T ])", + "image_path": "2017baea766173c77a1906c3d9bd915bd22f6b01546aff97fef9179df5010fb8.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 394, + 286, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 394, + 286, + 430 + ], + "spans": [ + { + "bbox": [ + 47, + 394, + 286, + 430 + ], + "type": "text", + "content": "To ease training, we use the pre-trained " + }, + { + "bbox": [ + 47, + 394, + 286, + 430 + ], + "type": "inline_equation", + "content": "\\mathcal{E}" + }, + { + "bbox": [ + 47, + 394, + 286, + 430 + ], + "type": "text", + "content": " from the reconstruction task to encode ground truth output " + }, + { + "bbox": [ + 47, + 394, + 286, + 430 + ], + "type": "inline_equation", + "content": "g_{T}" + }, + { + "bbox": [ + 47, + 394, + 286, + 430 + ], + "type": "text", + "content": " and train the encoder with the following guidance:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 113, + 430, + 286, + 443 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 430, + 286, + 443 + ], + "spans": [ + { + "bbox": [ + 113, + 430, + 286, + 443 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {l a t e n t}} = \\left\\| z _ {T} - \\mathcal {E} \\left(g _ {T}\\right) \\right\\| _ {2} \\tag {14}", + "image_path": "edf19b86014fd2f47909a1ca5aabb604edb4211e5924fd93578129db7a30eced.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 445, + 286, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 445, + 286, + 467 + ], + "spans": [ + { + "bbox": [ + 47, + 445, + 286, + 467 + ], + "type": "text", + "content": "To enable font sampling, we adopt a Kullback-Leibler divergence loss [16]:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 104, + 468, + 286, + 481 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 468, + 286, + 481 + ], + "spans": [ + { + "bbox": [ + 104, + 468, + 286, + 481 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {k l} = \\mathrm {K L} \\left(\\mathcal {N} \\left(\\mu , \\sigma^ {2}\\right) | | \\mathcal {N} (0, 1)\\right) \\tag {15}", + "image_path": "db71e904ed0a0b7b42b549da44d8a8baa9579f26907c0e410eb9d54a0d508bd6.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 483, + 286, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 483, + 286, + 517 + ], + "spans": [ + { + "bbox": [ + 47, + 483, + 286, + 517 + ], + "type": "text", + "content": "Next, the encoder is fine-tuned along with the pre-trained " + }, + { + "bbox": [ + 47, + 483, + 286, + 517 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_I" + }, + { + "bbox": [ + 47, + 483, + 286, + 517 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 483, + 286, + 517 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_P" + }, + { + "bbox": [ + 47, + 483, + 286, + 517 + ], + "type": "text", + "content": " from the reconstruction task using the loss in 11 with " + }, + { + "bbox": [ + 47, + 483, + 286, + 517 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{kl}" + }, + { + "bbox": [ + 47, + 483, + 286, + 517 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 47, + 521, + 286, + 614 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 521, + 286, + 614 + ], + "spans": [ + { + "bbox": [ + 47, + 521, + 286, + 614 + ], + "type": "text", + "content": "Refinement Both the reconstruction and generation tasks share the same contour refinement process. Given " + }, + { + "bbox": [ + 47, + 521, + 286, + 614 + ], + "type": "inline_equation", + "content": "\\partial \\mathcal{O}" + }, + { + "bbox": [ + 47, + 521, + 286, + 614 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 521, + 286, + 614 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 47, + 521, + 286, + 614 + ], + "type": "text", + "content": ", the refinement process produces the optimized glyph contour in SVG format by inference-time optimization. In the optimization, we utilize DiffVG [22], denoted as DR, to render the contour in a differentiable manner. The control points of " + }, + { + "bbox": [ + 47, + 521, + 286, + 614 + ], + "type": "inline_equation", + "content": "\\mathcal{O}" + }, + { + "bbox": [ + 47, + 521, + 286, + 614 + ], + "type": "text", + "content": " are refined to minimize the following loss function:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 109, + 616, + 286, + 629 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 109, + 616, + 286, + 629 + ], + "spans": [ + { + "bbox": [ + 109, + 616, + 286, + 629 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {r e f i n e}} = \\mathcal {L} _ {\\text {r a s}} + \\lambda_ {\\text {r e g}} \\mathcal {L} _ {\\text {r e g}} \\tag {16}", + "image_path": "d8e30574332b18f12f4bb749166f8e47ada414f65fdffb48e28252177ff6b9f9.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 47, + 634, + 286, + 656 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 634, + 286, + 656 + ], + "spans": [ + { + "bbox": [ + 47, + 634, + 286, + 656 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 634, + 286, + 656 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{render}}" + }, + { + "bbox": [ + 47, + 634, + 286, + 656 + ], + "type": "text", + "content": " is the photometric loss between the rasterized image and the image branch output." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 115, + 658, + 286, + 670 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 658, + 286, + 670 + ], + "spans": [ + { + "bbox": [ + 115, + 658, + 286, + 670 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {r a s} = \\left| \\left| \\mathrm {D R} (\\partial \\mathcal {O}) - \\mathcal {I} \\right| \\right| _ {1} \\tag {17}", + "image_path": "b1fb8ae63e5527b932a64b42b107592f7eeadbccc8448bb2bded6e957441dcf9.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 47, + 671, + 264, + 682 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 264, + 682 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 264, + 682 + ], + "type": "text", + "content": "The regularization term limits the overall length of " + }, + { + "bbox": [ + 47, + 671, + 264, + 682 + ], + "type": "inline_equation", + "content": "\\mathcal{O}" + }, + { + "bbox": [ + 47, + 671, + 264, + 682 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 126, + 684, + 286, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 126, + 684, + 286, + 715 + ], + "spans": [ + { + "bbox": [ + 126, + 684, + 286, + 715 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {r e g} = \\sum_ {i = 1} ^ {K} \\operatorname {l e n} \\left(C _ {i}\\right) \\tag {18}", + "image_path": "92aaa09d200573e76dbf7445577af2aabfb28c7ae0b1c94b0435fde0eb2bb17e.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 72, + 486, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 486, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 486, + 84 + ], + "type": "text", + "content": "3.5.2 Unsigned Distance Field Warm-up" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 92, + 545, + 152 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 92, + 545, + 152 + ], + "spans": [ + { + "bbox": [ + 304, + 92, + 545, + 152 + ], + "type": "text", + "content": "Although the vector branch is end-to-end trainable, the gradients only appear near the boundaries. Therefore, to overcome the vanishing gradient problem, we add an extra loss based on the unsigned distance field (UDF) of the vector parts to warm up the system training." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 152, + 545, + 210 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 152, + 545, + 210 + ], + "spans": [ + { + "bbox": [ + 304, + 152, + 545, + 210 + ], + "type": "text", + "content": "In general, for two closed curves " + }, + { + "bbox": [ + 304, + 152, + 545, + 210 + ], + "type": "inline_equation", + "content": "c_{1}, c_{2}" + }, + { + "bbox": [ + 304, + 152, + 545, + 210 + ], + "type": "text", + "content": ", we cannot obtain the exact SDF of the shape after arbitrary boolean operations on the curves by point-wise operations on their respective SDFs. For the union of two SDFs, as an approximation, we have" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 317, + 211, + 545, + 246 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 211, + 545, + 246 + ], + "spans": [ + { + "bbox": [ + 317, + 211, + 545, + 246 + ], + "type": "interline_equation", + "content": "s _ {c _ {1} \\cup c _ {2}} (\\boldsymbol {x}) \\left\\{ \\begin{array}{l l} = \\min \\left(s _ {c _ {1}} (\\boldsymbol {x}), s _ {c _ {2}} (\\boldsymbol {x})\\right), & \\boldsymbol {x} \\notin c _ {1} \\cup c _ {2} \\\\ \\leq \\min \\left(s _ {c _ {1}} (\\boldsymbol {x}), s _ {c _ {2}} (\\boldsymbol {x})\\right), & \\boldsymbol {x} \\in c _ {1} \\cup c _ {2} \\end{array} \\right. \\tag {19}", + "image_path": "43ca86b3183a558f4962e56c5cf75d00c281891233a15b1cd97a3b6a37380c5e.jpg" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 247, + 545, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 247, + 545, + 365 + ], + "spans": [ + { + "bbox": [ + 304, + 247, + 545, + 365 + ], + "type": "text", + "content": "The " + }, + { + "bbox": [ + 304, + 247, + 545, + 365 + ], + "type": "inline_equation", + "content": "\\min(\\cdot)" + }, + { + "bbox": [ + 304, + 247, + 545, + 365 + ], + "type": "text", + "content": " operation gives a correct SDF outside the shape but an inaccurate SDF inside the shape. Similarly, the " + }, + { + "bbox": [ + 304, + 247, + 545, + 365 + ], + "type": "inline_equation", + "content": "\\max(\\cdot)" + }, + { + "bbox": [ + 304, + 247, + 545, + 365 + ], + "type": "text", + "content": " gives a correct SDF inside and an inaccurate SDF outside for the intersection of two SDFs. Therefore, it is hard to calculate the accurate SDF " + }, + { + "bbox": [ + 304, + 247, + 545, + 365 + ], + "type": "inline_equation", + "content": "s_{\\mathcal{O}}" + }, + { + "bbox": [ + 304, + 247, + 545, + 365 + ], + "type": "text", + "content": " for the glyph. Fortunately, we only aim to provide a coarse initialization for the dual parts, preventing the optimization process from falling into local minima early in the training. We find that using an approximate unsigned distance field works well to achieve this goal. Here we define the UDF " + }, + { + "bbox": [ + 304, + 247, + 545, + 365 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 304, + 247, + 545, + 365 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 380, + 367, + 545, + 379 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 380, + 367, + 545, + 379 + ], + "spans": [ + { + "bbox": [ + 380, + 367, + 545, + 379 + ], + "type": "interline_equation", + "content": "u (\\boldsymbol {x}) = \\max (0, s (\\boldsymbol {x})) \\tag {20}", + "image_path": "14752506254fe412b760af5866fcfa2769739eb2cfcb904b88eada6908a57a53.jpg" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 380, + 545, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 380, + 545, + 403 + ], + "spans": [ + { + "bbox": [ + 304, + 380, + 545, + 403 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 380, + 545, + 403 + ], + "type": "inline_equation", + "content": "\\min (\\cdot)" + }, + { + "bbox": [ + 304, + 380, + 545, + 403 + ], + "type": "text", + "content": " gives a correct global UDF for unions of shapes. The approximate UDF " + }, + { + "bbox": [ + 304, + 380, + 545, + 403 + ], + "type": "inline_equation", + "content": "\\hat{u}_q" + }, + { + "bbox": [ + 304, + 380, + 545, + 403 + ], + "type": "text", + "content": " is computed as" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 371, + 404, + 545, + 420 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 371, + 404, + 545, + 420 + ], + "spans": [ + { + "bbox": [ + 371, + 404, + 545, + 420 + ], + "type": "interline_equation", + "content": "\\hat {u} _ {g} = \\min _ {i} \\left[ \\max \\left(u _ {P _ {i}}, u _ {Q _ {i}}\\right) \\right] \\tag {21}", + "image_path": "3cdb97adb930a9993d5b292765d5cc0f97aef998fb7c2ef5bf08b7d4740018de.jpg" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 306, + 421, + 333, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 421, + 333, + 430 + ], + "spans": [ + { + "bbox": [ + 306, + 421, + 333, + 430 + ], + "type": "text", + "content": "where" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 367, + 432, + 475, + 445 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 367, + 432, + 475, + 445 + ], + "spans": [ + { + "bbox": [ + 367, + 432, + 475, + 445 + ], + "type": "interline_equation", + "content": "u _ {P _ {i}} (\\boldsymbol {x}) = \\max \\left(s _ {P _ {i}} (\\boldsymbol {x}), 0\\right)", + "image_path": "b40e993b2b2476f9788f2f707cde507faf18e7801d12ec818cb1a404ea93f0b4.jpg" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 367, + 441, + 544, + 460 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 367, + 441, + 544, + 460 + ], + "spans": [ + { + "bbox": [ + 367, + 441, + 544, + 460 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} u _ {Q _ {i}} (\\boldsymbol {x}) = \\max (- s _ {Q _ {i}} (\\boldsymbol {x}), 0) \\end{array} \\tag {22}", + "image_path": "64eb392415ecb44c705d3fa72e0be751c2ca99a9460c406a216629a2774dec00.jpg" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 304, + 464, + 544, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 464, + 544, + 486 + ], + "spans": [ + { + "bbox": [ + 304, + 464, + 544, + 486 + ], + "type": "text", + "content": "We apply the following losses to warm up the training process for the font reconstruction task:" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 354, + 487, + 471, + 498 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 354, + 487, + 471, + 498 + ], + "spans": [ + { + "bbox": [ + 354, + 487, + 471, + 498 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\lambda_ {P} \\mathcal {L} _ {P} + \\lambda_ {I} \\mathcal {L} _ {I} + \\lambda_ {u} \\mathcal {L} _ {u}", + "image_path": "1efe534fd8b7001f0d3ca75b4307041a7fc12aae2562574443512cd7aba0e764.jpg" + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 350, + 495, + 544, + 514 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 350, + 495, + 544, + 514 + ], + "spans": [ + { + "bbox": [ + 350, + 495, + 544, + 514 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {u} = \\mathbb {E} _ {\\boldsymbol {x} \\sim [ - 1, 1 ] ^ {2}} \\left[ \\left| \\left| \\hat {u} _ {g} (\\boldsymbol {x}) - u _ {g} (\\boldsymbol {x}) \\right| \\right| _ {1} \\right] \\tag {23}", + "image_path": "c7806c10345563da707d5b5011a3f93dae016c788489e5d6a219af9730c6651a.jpg" + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 304, + 514, + 544, + 537 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 514, + 544, + 537 + ], + "spans": [ + { + "bbox": [ + 304, + 514, + 544, + 537 + ], + "type": "text", + "content": "where the ground truth UDF " + }, + { + "bbox": [ + 304, + 514, + 544, + 537 + ], + "type": "inline_equation", + "content": "u_{g}" + }, + { + "bbox": [ + 304, + 514, + 544, + 537 + ], + "type": "text", + "content": " is derived from the pixel image " + }, + { + "bbox": [ + 304, + 514, + 544, + 537 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 304, + 514, + 544, + 537 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 306, + 550, + 386, + 563 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 550, + 386, + 563 + ], + "spans": [ + { + "bbox": [ + 306, + 550, + 386, + 563 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 36 + }, + { + "bbox": [ + 306, + 571, + 363, + 581 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 571, + 363, + 581 + ], + "spans": [ + { + "bbox": [ + 306, + 571, + 363, + 581 + ], + "type": "text", + "content": "4.1. Dataset" + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 304, + 589, + 545, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 589, + 545, + 661 + ], + "spans": [ + { + "bbox": [ + 304, + 589, + 545, + 661 + ], + "type": "text", + "content": "We use the SVG-Fonts dataset from SVG-VAE [27] for all the experiments. Following DeepVecFont [39], we sample a subset of the dataset with 8035 fonts for training and 1425 fonts for evaluation. The resolution of input glyph images is set to " + }, + { + "bbox": [ + 304, + 589, + 545, + 661 + ], + "type": "inline_equation", + "content": "128 \\times 128" + }, + { + "bbox": [ + 304, + 589, + 545, + 661 + ], + "type": "text", + "content": ". Please refer to the supplementary material for implementation details." + } + ] + } + ], + "index": 38 + }, + { + "bbox": [ + 306, + 670, + 424, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 670, + 424, + 681 + ], + "spans": [ + { + "bbox": [ + 306, + 670, + 424, + 681 + ], + "type": "text", + "content": "4.2. Font Reconstruction" + } + ] + } + ], + "index": 39 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "In this experiment, we investigate how faithfully different methods can reconstruct the input glyph images with" + } + ] + } + ], + "index": 40 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14197" + } + ] + } + ], + "index": 41 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 71, + 286, + 244 + ], + "blocks": [ + { + "bbox": [ + 51, + 71, + 286, + 244 + ], + "lines": [ + { + "bbox": [ + 51, + 71, + 286, + 244 + ], + "spans": [ + { + "bbox": [ + 51, + 71, + 286, + 244 + ], + "type": "image", + "image_path": "a1fe2572a50a84efd3196dcfc6c9d15a7514b58a04c7cb3ffb2ce93aa21d0b1a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 252, + 288, + 307 + ], + "lines": [ + { + "bbox": [ + 46, + 252, + 288, + 307 + ], + "spans": [ + { + "bbox": [ + 46, + 252, + 288, + 307 + ], + "type": "text", + "content": "Figure 3. Comparison of font reconstruction quality. We show the input glyph image row by row, our reconstructed image " + }, + { + "bbox": [ + 46, + 252, + 288, + 307 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 46, + 252, + 288, + 307 + ], + "type": "text", + "content": " from the image branch, dual-parts " + }, + { + "bbox": [ + 46, + 252, + 288, + 307 + ], + "type": "inline_equation", + "content": "\\mathcal{O}" + }, + { + "bbox": [ + 46, + 252, + 288, + 307 + ], + "type": "text", + "content": " from the vector branch, and our final result after contour refinement, as well as vector outputs from alternative methods." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 312, + 287, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 312, + 287, + 586 + ], + "spans": [ + { + "bbox": [ + 46, + 312, + 287, + 586 + ], + "type": "text", + "content": "vector outputs, which can also be regarded as font vectorization. Im2Vec [33] and our method directly produce vector representations from glyph images, while for Multi-Implicits [34], we adopt the 2D marching cube algorithm and extract the contours. As can be seen from a qualitative comparison in Fig. 3, our representation could faithfully reconstruct global shapes as well as local details from the pixelated input. Im2Vec [33] could only preserve coarse shapes and suffers from wrong topologies as shown in the \"A\" example as it is easy to fall into local optimum without the global gradient. Multi-Implicits [34] results in finer details than Im2Vec [33] but still exhibit unsmooth edges and rounded corners. To quantitatively evaluate how accurate the vector outputs are, we calculate three metrics, namely SSIM, L1, and s-IoU, between the rendered images and the ground truth images under different resolutions. Tab. 1 shows that our method surpasses the two alternatives by a clear margin on all metrics. Using parametric curves as primitives, our method, along with Im2Vec [33], maintains a stable L1 error across all resolutions for the smooth edges, while for Multi-Implicits [34] the L1 error gets larger as the resolution increases, resulting from the high-frequency noises at the extracted boundaries." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 597, + 147, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 597, + 147, + 609 + ], + "spans": [ + { + "bbox": [ + 47, + 597, + 147, + 609 + ], + "type": "text", + "content": "4.3. Font Generation" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "text", + "content": "To evaluate the generation ability of our method, we adopt the few-shot font generation setting, where a subset of glyphs with the same style is given and models are trained to produce a complete set of glyphs that are consistent with the input glyphs in style. This task is also dubbed \"font complement\" or \"font style transfer\" in other works. We compare our method with several popular methods in font generation: DeepVecFont [39], Multi-Implicits [34]," + } + ] + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 307, + 121, + 558, + 264 + ], + "blocks": [ + { + "bbox": [ + 305, + 70, + 546, + 115 + ], + "lines": [ + { + "bbox": [ + 305, + 70, + 546, + 115 + ], + "spans": [ + { + "bbox": [ + 305, + 70, + 546, + 115 + ], + "type": "text", + "content": "Table 1. Quantitative comparison with Im2Vec [33] and Multi-Implicits [34] on three image-level metrics at different resolutions for the font reconstruction task. The gray scale is normalized to [0,1]. s-IoU, from [34], measures the overlap." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 121, + 558, + 264 + ], + "lines": [ + { + "bbox": [ + 307, + 121, + 558, + 264 + ], + "spans": [ + { + "bbox": [ + 307, + 121, + 558, + 264 + ], + "type": "table", + "html": "
MethodResolutionSSIM↑L1↓s-IoU↑
Ours12820.94360.01370.8879
25620.94830.01360.9068
51220.95790.01360.9135
Multi-Implicits12820.92310.01830.8709
25620.92620.02080.8721
51220.94190.02130.8739
Im2Vec12820.78000.05040.6832
25620.85660.05040.6847
51220.89570.05040.6851
", + "image_path": "75e8b75ee9657237fa6cc3513f96959580bde2dccf3a5d952d6abeb86e9822c8.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 270, + 546, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 270, + 546, + 390 + ], + "spans": [ + { + "bbox": [ + 304, + 270, + 546, + 390 + ], + "type": "text", + "content": "Im2Vec [33] and Attr2Font [38]. For a fair comparison, we use the same four characters, 'A', 'B', 'a', and 'b' as style references for each font and evaluate image-level metrics on the generated characters. Since Im2Vec [33] is an image vectorization method, we apply it to the images generated by Attr2Font [38]. Multi-Implicits [34] follows an auto-decoder architecture, so we freeze the decoder and find the optimal latent vector for a font by minimizing the losses between the given style references and the predicted ones using gradient descent." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 390, + 546, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 390, + 546, + 594 + ], + "spans": [ + { + "bbox": [ + 304, + 390, + 546, + 594 + ], + "type": "text", + "content": "As illustrated in Fig. 4, DeepVecFont [39] may generate characters with wrong topologies due to the incorrect initial contour prediction, such as 'A', 'L', and 'Z'. The fixed topology in the optimization process makes it difficult to produce the necessary details, which are particularly symbolic in serif fonts. In addition, unconstrained contour generation may also produce self-intersections, like the 'g' and 'r', which are not easy to fix in subsequent processing. Im2Vec [33] tends to produce rounded corners and is only able to produce the coarse style, lacking details. Multi-Implicits [34] generates vector results from implicit signed distance fields (SDF) through a 2D Marching cube algorithm, leading to free-form contours. Therefore the edges are not smooth enough and have unpleasing noises, such as the 'g' and 'x' in the figure. Attr2Font [38] can generate generally satisfactory font images, but it cannot maintain high-quality rendering when scaling." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "text", + "content": "Compared with the above methods, our method is capable of not only grasping the overall style of the input references but also generating new glyphs with clear boundaries and sharp edges, achieving optimal visual quality. The efficient dual-part representation along with the differentiable occupancy supervision establishes a link between pixelated images and vector graphics, allowing the unsupervised synthesis of vector fonts with aligned shapes and correct topologies. The refinement step allows the composition of the contour to be freely changed and thus ensures" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14198" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 72, + 545, + 320 + ], + "blocks": [ + { + "bbox": [ + 51, + 72, + 545, + 320 + ], + "lines": [ + { + "bbox": [ + 51, + 72, + 545, + 320 + ], + "spans": [ + { + "bbox": [ + 51, + 72, + 545, + 320 + ], + "type": "image", + "image_path": "5de01a1d0d9c18081a2b7831b8e1fb61bbc976138deaeb67a5c0d0125b7503f7.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 320, + 547, + 354 + ], + "lines": [ + { + "bbox": [ + 46, + 320, + 547, + 354 + ], + "spans": [ + { + "bbox": [ + 46, + 320, + 547, + 354 + ], + "type": "text", + "content": "Figure 4. Font generation results of Attr2Font, Im2Vec, Multi-Implicits, DeepVecFont, and DualVector. The input style references are marked with red boxes. We trace the zero-level sets of SDFs in a piece-wise linear way to get SVGs from Multi-Implicits [34]. Typical failure cases are marked in blue dashed boxes. Some details are zoomed-in in the leftmost column." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 48, + 400, + 298, + 597 + ], + "blocks": [ + { + "bbox": [ + 47, + 358, + 290, + 392 + ], + "lines": [ + { + "bbox": [ + 47, + 358, + 290, + 392 + ], + "spans": [ + { + "bbox": [ + 47, + 358, + 290, + 392 + ], + "type": "text", + "content": "Table 2. Quantitative comparison of image-level metrics of Attr2Font [38], Im2Vec [33], Multi-Implicits [34], DeepVecFont [39] and DualVector in the font complement experiment." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 400, + 298, + 597 + ], + "lines": [ + { + "bbox": [ + 48, + 400, + 298, + 597 + ], + "spans": [ + { + "bbox": [ + 48, + 400, + 298, + 597 + ], + "type": "table", + "html": "
MethodResolutionSSIM↑L1↓s-IoU↑
Ours12820.82880.04610.7395
25620.87270.04600.7453
51220.90750.04600.7469
DeepVecFont12820.81650.05060.7125
25620.86400.05060.7171
51220.90110.05060.7182
Multi-Implicits12820.80250.05780.6857
25620.85330.06030.6814
51220.89140.06080.6811
Im2Vec12820.75760.07330.5731
25620.82700.07340.5751
51220.87390.07340.5756
Attr2Fonta12820.78410.05120.6393
", + "image_path": "b292ead284b4123d5f7eb22ab7c0d0414c2db325a626e3ea0f092ef891655be3.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 58, + 604, + 192, + 615 + ], + "lines": [ + { + "bbox": [ + 58, + 604, + 192, + 615 + ], + "spans": [ + { + "bbox": [ + 58, + 604, + 192, + 615 + ], + "type": "text", + "content": "[38] synthesizes pixelated images only." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 617, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 289, + 714 + ], + "type": "text", + "content": "that our synthesized glyphs have high-fidelity details under the guidance of high-resolution glyph images. Quantitative results on three image-level metrics at different resolutions are shown in Tab. 2. For methods producing vector shapes, we also count the average number of commands used for each synthesized vector character, with smaller numbers indicating more compact outputs. The results are shown in Tab. 3. Multi-Implicits [34] uses a large number of short" + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 309, + 411, + 559, + 494 + ], + "blocks": [ + { + "bbox": [ + 305, + 358, + 547, + 403 + ], + "lines": [ + { + "bbox": [ + 305, + 358, + 547, + 403 + ], + "spans": [ + { + "bbox": [ + 305, + 358, + 547, + 403 + ], + "type": "text", + "content": "Table 3. The average number of commands used per glyph for different methods in the font generation task. M, L, Q, and C denote move, straight line, quadratic Bezier curve, and cubic Bezier curve respectively." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 411, + 559, + 494 + ], + "lines": [ + { + "bbox": [ + 309, + 411, + 559, + 494 + ], + "spans": [ + { + "bbox": [ + 309, + 411, + 559, + 494 + ], + "type": "table", + "html": "
CommandMLQCTotal↓
Ours1.428.2111.06020.69
DeepVecFont [39]1.378.2309.6819.28
Multi-Implicits [34]6.161446.53001452.69
Im2Vec [33]4008084
Human-Designed1.389.1708.5119.06
", + "image_path": "a54c9bb74d7bf541a51456ae01b53ac237be88e36f2d731f9ba097371e87a6e4.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 506, + 547, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 506, + 547, + 590 + ], + "spans": [ + { + "bbox": [ + 304, + 506, + 547, + 590 + ], + "type": "text", + "content": "line segments to represent the boundary due to the marching cube algorithm. Im2Vec [33] represents a shape with 4 parts each enclosed by 20 cubic Bezier curves, lacking flexibility and details. Our method performs boolean operations on the quadratic Bezier curves from dual parts, achieving comparable compactness with human-designed fonts and outputs from methods with vector supervision [39]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 598, + 407, + 610 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 598, + 407, + 610 + ], + "spans": [ + { + "bbox": [ + 306, + 598, + 407, + 610 + ], + "type": "text", + "content": "4.4. Ablation Studies" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "type": "text", + "content": "To demonstrate the effectiveness of several key design choices in our method, we conduct ablation studies on the font reconstruction task. We investigate the following degraded variants: (a) replace the union of dual parts with the union of all the paths; (b) train without the UDF warm-up process; and (c) remove the refining strategy during refinement. We show the comparison results of a representative case in Fig. 5. Without the dual-part representation, variant" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "14199" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 58, + 59, + 283, + 159 + ], + "blocks": [ + { + "bbox": [ + 58, + 59, + 283, + 159 + ], + "lines": [ + { + "bbox": [ + 58, + 59, + 283, + 159 + ], + "spans": [ + { + "bbox": [ + 58, + 59, + 283, + 159 + ], + "type": "image", + "image_path": "6581d532c982eec0a674319624eee9aeeed566969e9c6c0dfbaefbda9dc20821.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 159, + 286, + 182 + ], + "lines": [ + { + "bbox": [ + 46, + 159, + 286, + 182 + ], + "spans": [ + { + "bbox": [ + 46, + 159, + 286, + 182 + ], + "type": "text", + "content": "Figure 5. The contours of an \"M\" reconstructed by our method, compared with three degraded variants." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 48, + 226, + 302, + 305 + ], + "blocks": [ + { + "bbox": [ + 48, + 226, + 302, + 305 + ], + "lines": [ + { + "bbox": [ + 48, + 226, + 302, + 305 + ], + "spans": [ + { + "bbox": [ + 48, + 226, + 302, + 305 + ], + "type": "table", + "html": "
L1↓#Lines↓# Curves↓
(a) w/o dual parts0.014312.2314.06
(b) w/o warm-up0.014611.1913.12
(c) w/o refining strategy0.0148-22.07
Full Model0.01368.9711.81
", + "image_path": "8d608d58308fea82086583ca3828dc0d263fa94096587671b0cfbf17811007cd.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 318, + 286, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 318, + 286, + 413 + ], + "spans": [ + { + "bbox": [ + 46, + 318, + 286, + 413 + ], + "type": "text", + "content": "(a) cannot reconstruct concave regions very well, as they can be hard to represent by the union of simply closed paths. Without UDF initialization, variant (b) produces contours with useless curves that are hard to be eliminated during optimization. Without the refining strategy, variant (c) may generate inaccurate edges with zigzags. Quantitative results in Tab. 4 also verify the quality improvements brought by the three design choices." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 413, + 286, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 413, + 286, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 413, + 286, + 533 + ], + "type": "text", + "content": "We also experimentally investigate the effect of different " + }, + { + "bbox": [ + 46, + 413, + 286, + 533 + ], + "type": "inline_equation", + "content": "(N,M)" + }, + { + "bbox": [ + 46, + 413, + 286, + 533 + ], + "type": "text", + "content": " s on the representation capacity. We choose several settings of " + }, + { + "bbox": [ + 46, + 413, + 286, + 533 + ], + "type": "inline_equation", + "content": "(N,M)" + }, + { + "bbox": [ + 46, + 413, + 286, + 533 + ], + "type": "text", + "content": " and train only the vector branch (i.e. no contour refinement) with the same number of epochs to reconstruct the input. Tab. 5 shows that " + }, + { + "bbox": [ + 46, + 413, + 286, + 533 + ], + "type": "inline_equation", + "content": "M = 4" + }, + { + "bbox": [ + 46, + 413, + 286, + 533 + ], + "type": "text", + "content": " is optimal and the reconstruction accuracy of the vector branch increases as " + }, + { + "bbox": [ + 46, + 413, + 286, + 533 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 413, + 286, + 533 + ], + "type": "text", + "content": " increases. The accuracy does not gain too much changing " + }, + { + "bbox": [ + 46, + 413, + 286, + 533 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 413, + 286, + 533 + ], + "type": "text", + "content": " from 6 to 8. So considering the time cost for training and inference, we select " + }, + { + "bbox": [ + 46, + 413, + 286, + 533 + ], + "type": "inline_equation", + "content": "(N,M) = (6,4)" + }, + { + "bbox": [ + 46, + 413, + 286, + 533 + ], + "type": "text", + "content": " in the above experiments." + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 83, + 561, + 251, + 659 + ], + "blocks": [ + { + "bbox": [ + 46, + 536, + 286, + 557 + ], + "lines": [ + { + "bbox": [ + 46, + 536, + 286, + 557 + ], + "spans": [ + { + "bbox": [ + 46, + 536, + 286, + 557 + ], + "type": "text", + "content": "Table 5. Different reconstruction settings and metrics. The image-based metrics use a resolution of " + }, + { + "bbox": [ + 46, + 536, + 286, + 557 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 46, + 536, + 286, + 557 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 83, + 561, + 251, + 659 + ], + "lines": [ + { + "bbox": [ + 83, + 561, + 251, + 659 + ], + "spans": [ + { + "bbox": [ + 83, + 561, + 251, + 659 + ], + "type": "table", + "html": "
NMSSIM↑L1↓s-IOU↑
240.92620.02820.8338
440.92920.02590.8464
640.93030.02500.8512
840.93060.02470.8525
630.92930.02560.8480
650.93000.02520.8498
", + "image_path": "55919d547d1caabadd9a4835ca7f459c8792fdd1986452ac55a1bbfa20dbbb07.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 670, + 224, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 670, + 224, + 684 + ], + "spans": [ + { + "bbox": [ + 47, + 670, + 224, + 684 + ], + "type": "text", + "content": "4.5. Font Sampling and Interpolation" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 689, + 286, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 286, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 286, + 714 + ], + "type": "text", + "content": "In the font generation task, the style latent code " + }, + { + "bbox": [ + 46, + 689, + 286, + 714 + ], + "type": "inline_equation", + "content": "z_{style}" + }, + { + "bbox": [ + 46, + 689, + 286, + 714 + ], + "type": "text", + "content": " is trained with a variational loss " + }, + { + "bbox": [ + 46, + 689, + 286, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{kl}" + }, + { + "bbox": [ + 46, + 689, + 286, + 714 + ], + "type": "text", + "content": ", enabling generating" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": "fonts of new styles by sampling " + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "z_{style}" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(0,1)" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": ". We show in Fig. 1 (left) and Fig. 6 multiple styles of fonts sampled. Please refer to our supplementary material for more examples. Also, benefiting from our dual-part representation, we can perform smooth interpolation between arbitrary font styles as demonstrated in Fig. 1 (right)." + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 307, + 147, + 545, + 247 + ], + "blocks": [ + { + "bbox": [ + 46, + 184, + 286, + 217 + ], + "lines": [ + { + "bbox": [ + 46, + 184, + 286, + 217 + ], + "spans": [ + { + "bbox": [ + 46, + 184, + 286, + 217 + ], + "type": "text", + "content": "Table 4. Quantitative results of reconstruction accuracy for different model variants in ablation studies. All the output vector glyphs are rendered at " + }, + { + "bbox": [ + 46, + 184, + 286, + 217 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 46, + 184, + 286, + 217 + ], + "type": "text", + "content": " to compute the L1 error." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 307, + 147, + 545, + 247 + ], + "lines": [ + { + "bbox": [ + 307, + 147, + 545, + 247 + ], + "spans": [ + { + "bbox": [ + 307, + 147, + 545, + 247 + ], + "type": "image", + "image_path": "0bc638233b068125a099ec9c73b9f7b8e4ac1d4384e8b99eeecb135d8ed4fc57.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 320, + 254, + 531, + 266 + ], + "lines": [ + { + "bbox": [ + 320, + 254, + 531, + 266 + ], + "spans": [ + { + "bbox": [ + 320, + 254, + 531, + 266 + ], + "type": "text", + "content": "Figure 6. New fonts with style codes sampled in " + }, + { + "bbox": [ + 320, + 254, + 531, + 266 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(0,1)" + }, + { + "bbox": [ + 320, + 254, + 531, + 266 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 277, + 381, + 289 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 277, + 381, + 289 + ], + "spans": [ + { + "bbox": [ + 306, + 277, + 381, + 289 + ], + "type": "text", + "content": "5. Limitations" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 297, + 545, + 429 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 297, + 545, + 429 + ], + "spans": [ + { + "bbox": [ + 304, + 297, + 545, + 429 + ], + "type": "text", + "content": "The contour refinement step requires gradient descent during inference and therefore imposes a large time overhead, similar to DeepVecFont [39]. The process could potentially be accomplished by forwarding inferences of some generation models, such as the diffusion models [13]. Another limitation is that DualVector only focuses on the synthesis of glyphs on a fixed-size canvas, without considering the kerning between them, making the spacing between characters less natural. This may be solved by post-processing the SVG with some automatic kerning methods or by learning through a data-driven approach." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 441, + 378, + 453 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 441, + 378, + 453 + ], + "spans": [ + { + "bbox": [ + 306, + 441, + 378, + 453 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 461, + 545, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 461, + 545, + 664 + ], + "spans": [ + { + "bbox": [ + 304, + 461, + 545, + 664 + ], + "type": "text", + "content": "We present DualVector as a new representation and generation method for vector fonts. DualVector models a glyph as dual parts and introduces a contour refinement step to add pleasing details to the contours of the dual parts. Our method is able to generate vector fonts without vector supervision, which can be directly converted to common digital font formats for content presentation and distribution. Comparisons with different methods of font reconstruction and generation tasks demonstrate that our approach produces fonts with the best quality among all the alternatives. In the future, more plausible initialization and supervision could be exploited to generalize this representation to more complex fonts (e.g. Chinese fonts). We hope this research contributes to the typeface design industry and provide inspiration for broader works on the understanding and generation of 2D man-made content such as cartoon characters and icons." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgement This work was supported by the Natural Science Foundation of China (Project Number 61832016), and Tsinghua-Tencent Joint Laboratory for Internet Innovation Technology." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14200" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 712 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 91, + 185, + 102 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 185, + 102 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 185, + 102 + ], + "type": "text", + "content": "[1] Adobe Inc. 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Graph., 41(3):34:1-34:17, 2022. 2" + } + ] + } + ], + "index": 20 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "14202" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/DyLiN_ Making Light Field Networks Dynamic/52436ab0-0f6f-44ce-bee8-32ea0aeba3bb_content_list.json b/2023/DyLiN_ Making Light Field Networks Dynamic/52436ab0-0f6f-44ce-bee8-32ea0aeba3bb_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..5b0c526dbe18fa3aa8c1e3336c912b4e0ddca44c --- /dev/null +++ b/2023/DyLiN_ Making Light Field Networks Dynamic/52436ab0-0f6f-44ce-bee8-32ea0aeba3bb_content_list.json @@ -0,0 +1,2187 @@ +[ + { + "type": "text", + "text": "DyLiN: Making Light Field Networks Dynamic", + "text_level": 1, + "bbox": [ + 243, + 130, + 725, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Heng Yu $^{1}$ Joel Julin $^{1}$ Zoltán Á. Milacski $^{1}$ Koichiro Niinuma $^{2}$ László A. Jeni $^{1}$", + "bbox": [ + 138, + 179, + 821, + 199 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ Robotics Institute, Carnegie Mellon University $^{2}$ Fujitsu Research of America", + "bbox": [ + 166, + 203, + 803, + 222 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{hengyu, jjulin, zmilacsk}@andrew.cmu.edu kniinuma@fujitsu.com laszlojeni@cmu.edu", + "bbox": [ + 112, + 224, + 857, + 239 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/77421cff7e6b340c742fea16a2a3c10e52f9a2edc3ac6a78f41c136c7c86ed57.jpg", + "image_caption": [ + "Ground Truth Video" + ], + "image_footnote": [], + "bbox": [ + 119, + 252, + 243, + 353 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f7c9031bbf98eec2226aecccbe5b960fcf54eabf8e4e2770f8f50ff7f0fd4040.jpg", + "image_caption": [ + "HyperNeRF [28] \nRender time: 3 s" + ], + "image_footnote": [], + "bbox": [ + 245, + 253, + 370, + 354 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/2da5fb9899fc9b58d3f0b0f6ef8043efd602b9abd36dfa0ff8d9e2135cd38f10.jpg", + "image_caption": [ + "TiNeuVox [8] Render time: 7s" + ], + "image_footnote": [], + "bbox": [ + 372, + 253, + 493, + 354 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/506cb6e69f4b76c3fbffedff1410d301732965ee2dbede6a0dd61cbf374775cb.jpg", + "image_caption": [ + "Ours Render time: 0.1s" + ], + "image_footnote": [], + "bbox": [ + 496, + 252, + 620, + 354 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/7a050fccc2ab54ee2110db3c3a1fe022b66826f80e1ddf9f0d82bba0fb3adb00.jpg", + "image_caption": [ + "Figure 1. Our proposed DyLiN for dynamic 3D scene rendering achieves higher quality than its HyperNeRF teacher model and the state-of-the-art TiNeuVox model, while being an order of magnitude faster. Right: DyLiN is of moderate storage size (shown by dot radii). For each method, the relative improvement in Peak Signal-to-Noise Ratio over NeRF ( $\\Delta$ PSNR) is measured for the best-performing scene." + ], + "image_footnote": [], + "bbox": [ + 624, + 252, + 846, + 369 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 453, + 313, + 469 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Light Field Networks, the re-formulations of radiance fields to oriented rays, are magnitudes faster than their coordinate network counterparts, and provide higher fidelity with respect to representing 3D structures from 2D observations. They would be well suited for generic scene representation and manipulation, but suffer from one problem: they are limited to holistic and static scenes. In this paper, we propose the Dynamic Light Field Network (DyLiN) method that can handle non-rigid deformations, including topological changes. We learn a deformation field from input rays to canonical rays, and lift them into a higher dimensional space to handle discontinuities. We further introduce CoDyLiN, which augments DyLiN with controllable attribute inputs. We train both models via knowledge distillation from pretrained dynamic radiance fields. We evaluated DyLiN using both synthetic and real world datasets that include various non-rigid deformations. DyLiN qualitatively outperformed and quantitatively matched state-of-the-art methods in terms of visual fidelity, while being $25 - 71 \\times$ computationally faster. We also tested CoDyLiN on attribute annotated data and it surpassed its teacher model. Project page: https://dylin2023.github.io.", + "bbox": [ + 75, + 484, + 472, + 818 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 845, + 207, + 859 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Machine vision has made tremendous progress with respect to reasoning about 3D structure using 2D observa", + "bbox": [ + 75, + 869, + 470, + 902 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tions. Much of this progress can be attributed to the emergence of coordinate networks [6,21,26], such as Neural Radiance Fields (NeRF) [23] and its variants [2, 20, 22, 39]. They provide an object agnostic representation for 3D scenes and can be used for high-fidelity synthesis for unseen views. While NeRFs mainly focus on static scenes, a series of works [10,27,29,34] extend the idea to dynamic cases via additional components that map the observed deformations to a canonical space, supporting moving and shape-evolving objects. It was further shown that by lifting this canonical space to higher dimensions the method can handle changes in scene topology as well [28].", + "bbox": [ + 496, + 454, + 890, + 636 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, the applicability of NeRF models is considerably limited by their computational complexities. From each pixel, one typically casts a ray from that pixel, and numerically integrates the radiance and color densities computed by a Multi-Layer Perceptron (MLP) across the ray, approximating the pixel color. Specifically, the numerical integration involves sampling hundreds of points across the ray, and evaluating the MLP at all of those locations. Several works have been proposed for speeding up static NeRFs. These include employing a compact 3D representation structure [9, 18, 43], breaking up the MLP into multiple smaller networks [30, 31], leveraging depth information [7, 24], and using fewer sampling points [17, 24, 42]. Yet, these methods still rely on integration and suffer from sampling many points, making them prohibitively slow for real-time applications. Recently, Light Field Networks (LFNs) [32] proposed replacing integration with a direct ray-to", + "bbox": [ + 496, + 643, + 892, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "12397", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "color regressor, trained using the same sparse set of images, requiring only a single forward pass. R2L [36] extended LFNs to use a very deep residual architecture, trained by distillation from a NeRF teacher model to avoid overfitting. In contrast to static NeRF acceleration, speeding up dynamic NeRFs is a much less discussed problem in the literature. This is potentially due to the much increased difficulty of the task, as one also has to deal with the high variability of motion. In this direction, [8, 38] greatly reduce the training time by using well-designed data structures, but their solutions still rely on integration. LFNs are clearly better suited for acceleration, yet, to the best of our knowledge, no works have attempted extending LFNs to the dynamic scenario.", + "bbox": [ + 75, + 90, + 472, + 303 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we propose 2 schemes extending LFNs to dynamic scene deformations, topological changes and controllability. First, we introduce DyLiN, by incorporating a deformation field and a hyperspace representation to deal with non-rigid transformations, while distilling knowledge from a pretrained dynamic NeRF. Afterwards, we also propose CoDyLiN, via adding controllable input attributes, trained with synthetic training data generated by a pretrained Controllable NeRF (CoNeRF) [13] teacher model. To test the efficiencies of our proposed schemes, we perform empirical experiments on both synthetic and real datasets. We show that our DyLiN achieves better image quality and an order of magnitude faster rendering speed than its original dynamic NeRF teacher model and the state-of-the-art TiNeuVox [8] method. Similarly, we also show that CoDyLiN outperforms its CoNeRF teacher. We further execute ablation studies to verify the individual effectiveness of different components of our model. Our methods can be also understood as accelerated versions of their respective teacher models, and we are not aware of any prior works that attempt speeding up CoNeRF.", + "bbox": [ + 75, + 306, + 472, + 625 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions can be summarized as follows:", + "bbox": [ + 76, + 625, + 403, + 638 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose DyLiN, an extension of LFNs that can handle dynamic scenes with topological changes. DyLiN achieves this through non-bending ray deformations, hyperspace lifting for whole rays, and knowledge distillation from dynamic NeRFs.", + "- We show that DyLiN achieves state-of-the-art results on both synthetic and real-world scenes, while being an order of magnitude faster than the competition. We also include an ablation study to analyze the contributions of our model components.", + "- We introduce CoDyLiN, further extending our DyLiN to handle controllable input attributes." + ], + "bbox": [ + 94, + 662, + 468, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 500, + 89, + 650, + 106 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Dynamic NeRFs. NeRFs have demonstrated impressive performances in novel view synthesis for static scenes. Extending these results to dynamic (deformable) domains has sparked considerable research interest [10, 27-29, 34]. Among these works, the ones that most closely resemble ours are D-NeRF [29] and HyperNeRF [28]. D-NeRF uses a translational deformation field with temporal positional encoding. HyperNeRF introduces a hyperspace representation, allowing topological variations to be effectively captured. Our work expands upon these works, as we propose DyLiN, a similar method for LFNs. We use the above dynamic NeRFs as pretrained teacher models for DyLiN, achieving better fidelity with orders of magnitude shorter rendering times.", + "bbox": [ + 496, + 114, + 893, + 327 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Accelerated NeRFs. The high computational complexity of NeRFs has motivated several follow-up works on speeding up the numerical integration process. The following first set of works are restricted to static scenarios. NSVF [18] represents the scene with a set of voxel-bounded MLPs organized in a sparse voxel octree, allowing voxels without relevant content to be skipped. KiloNeRF [31] divides the scene into a grid and trains a tiny MLP network for each cell within the grid, saving on pointwise evaluations. AutoInt [17] reduces the number of point samples for each ray using learned partial integrals. In contrast to the above procedures, speeding up dynamic NeRFs is much less discussed in the literature, as there are only 2 papers published on this subject. Wang et al. [38] proposed a method based on Fourier plenoctrees for real-time dynamic rendering, however, the technique requires an expensive rigid scene capturing setup. TiNeuVox [8] reduces training time by augmenting the MLP with time-aware voxel features and a tiny deformation network, while using a multi-distance interpolation method to model temporal variations. Interestingly, all of the aforementioned methods suffer from sampling hundreds of points during numerical integration, and none of them support changes in topology, whereas our proposed DyLiN excels from both perspectives.", + "bbox": [ + 496, + 349, + 893, + 712 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Light Field Networks (LFNs). As opposed to the aforementioned techniques that accelerate numerical integration within NeRFs, some works have attempted completely replacing numerical integration with direct per-ray color MLP regressors called Light Field Networks (LFNs). Since these approaches accept rays as inputs, they rely heavily on the ray representation. Several such representations exist in the literature. Plenoptic functions [1,3] encode 3D rays with 5D representations, i.e., a 3D point on a ray and 2 axis-angle ray directions. Light fields [11,15] use 4D ray codes most commonly through two-plane parameterization: given 2 parallel", + "bbox": [ + 496, + 734, + 895, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "12398", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "planes, rays are encoded by the 2D coordinates of the 2 ray-plane intersection points. Sadly, these representations are either discontinuous or cannot represent the full set of rays. Recently, Sitzmann et al. [32] advocate for the usage of the 6D Plücker coordinate representation, i.e., a 3D point on a ray coupled with its cross product with a 3D direction. They argue that this representation covers the whole set of rays and is continuous. Consequently, they feed it as input to an LFN, and additionally apply Meta-Learning across scenes to learn a multi-view consistency prior. However, they have not considered alternative ray representations, MLP architectures or training procedures, and only tested their method on toy datasets. R2L [36] employs an even more effective ray encoding by concatenating few points sampled from it, and proposes a very deep (88 layers) residual MLP network for LFNs. They resolve the proneness to overfitting by training the MLP with an abundance of synthetic images generated by a pretrained NeRF having a shallow MLP. Interestingly, they find that the student LFN model produces significantly better rendering quality than its teacher NeRF model, while being about 30 times faster. Our work extends LFNs to dynamic deformations, topological changes and controllability, achieving similar gains over the pretrained dynamic NeRF teacher models.", + "bbox": [ + 76, + 90, + 472, + 454 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Knowledge Distillation. The process of training a student model with synthetic data generated by a teacher model is called Knowledge Distillation (KD) [4], and it has been widely used in the vision and language domains [5, 15, 35, 37] as a form of data augmentation. Like R2L [36], we also use KD for training, however, our teacher and student models are both dynamic and more complex than their R2L counterparts.", + "bbox": [ + 76, + 470, + 470, + 594 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methods", + "text_level": 1, + "bbox": [ + 76, + 607, + 174, + 622 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we present our two solutions for extending LFNs. First, in Sec. 3.1, we propose DyLiN, supporting dynamic deformations and hyperspace representations via two respective MLPs. We use KD to train DyLiN with synthetic data generated by a pretrained dynamic NeRF teacher model. Second, in Sec. 3.2, we introduce CoDyLiN, which further augments DyLiN with controllability, via lifting attribute inputs to hyperspace with MLPs, and masking their hyperspace codes for disentanglement. In this case, we also train via KD, but the teacher model is a pretrained controllable NeRF.", + "bbox": [ + 75, + 632, + 468, + 797 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. DyLiN", + "text_level": 1, + "bbox": [ + 76, + 806, + 166, + 823 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1.1 Network Architecture", + "text_level": 1, + "bbox": [ + 76, + 830, + 284, + 845 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our overall DyLiN architecture $G_{\\phi}$ is summarized in Fig. 2. It processes rays instead of the widely adopted 3D point inputs as follows.", + "bbox": [ + 76, + 854, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/eb611fc11c9f351ec87e652c6b80c33ca2e3fb5f408b8349017a25244215e366.jpg", + "image_caption": [ + "Figure 2. Schematic diagram of our proposed DyLiN architecture. We take a ray $r = (o, d)$ and time $t$ as input. We deform $r$ into $r' = (o', d')$ , and sample few points $x_k, k = 1, \\ldots, K$ along $r'$ to encode it (blue). In parallel, we also lift $r$ and $t$ to the hyperspace code $w$ (green), and concatenate it with each $x_k$ . We use the concatenation to regress the RGB color of $r$ at $t$ directly (red)." + ], + "image_footnote": [], + "bbox": [ + 506, + 90, + 890, + 193 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Specifically, our deformation MLP $T_{\\omega}$ maps an input ray $r = (o,d)$ to canonical space ray $r' = (o',d')$ :", + "bbox": [ + 498, + 315, + 890, + 347 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\left(o ^ {\\prime}, d ^ {\\prime}\\right) = T _ {\\omega} (o, d, t). \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 624, + 356, + 890, + 375 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Unlike the pointwise deformation MLP proposed in Nerfies [27], which bends rays by offsetting their points independently, our MLP outputs rays explicitly, hence no ray bending occurs. Furthermore, after obtaining $r'$ , we encode it by sampling and concatenating $K$ points along it.", + "bbox": [ + 498, + 383, + 890, + 459 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our hyperspace $\\mathrm{MLP}H_{\\psi}$ is similar to $T_{\\omega}$ , except it outputs a hyperspace representation $w$ :", + "bbox": [ + 498, + 460, + 890, + 489 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nw = H _ {\\psi} (o, d, t). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 637, + 501, + 890, + 517 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In contrast to HyperNeRF [28], which predicts a hyperspace code $w$ for each 3D point, we use rays and compute a single $w$ for each ray.", + "bbox": [ + 498, + 529, + 890, + 573 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Both MLPs further take the index $t$ as input to encode temporal deformations.", + "bbox": [ + 498, + 574, + 890, + 603 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Once the $K$ points and $w$ are obtained, we concatenate them and feed the result into our LFN $R_{\\pi}$ , which is a deep residual color MLP regressor. Overall, we can collect the model parameters as $\\phi = [\\omega, \\psi, \\pi]$ .", + "bbox": [ + 498, + 604, + 890, + 662 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Note that without our two MLPs $T_{\\omega}$ and $H_{\\psi}$ , our DyLiN falls back to the vanilla LFN.", + "bbox": [ + 498, + 664, + 890, + 694 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1.2 Training Procedure", + "text_level": 1, + "bbox": [ + 500, + 713, + 691, + 728 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our training procedure is composed of 3 phases.", + "bbox": [ + 500, + 736, + 818, + 751 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "First, we pretrain a dynamic NeRF model $F_{\\theta}$ (e.g., D-NeRF [29] or HyperNeRF [28]) by randomly sampling time $t$ and input ray $r$ , and minimizing the Mean Squared Error (MSE) against the corresponding RGB color of monocular target video $I$ :", + "bbox": [ + 498, + 752, + 890, + 827 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\theta} \\mathbb {E} _ {t, r = (o, d)} \\left[ \\| F _ {\\theta} (o, d, t) - I (o, d, t) \\| _ {2} ^ {2} \\right]. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 547, + 837, + 890, + 859 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Recall, that $F_{\\theta}$ is slow, as it performs numerical integration across the ray $r = (o,d)$ .", + "bbox": [ + 498, + 869, + 890, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "12399", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Second, we employ the newly obtained $F_{\\theta^{*}}$ as the teacher model for our DyLiN student model $G_{\\phi}$ via KD. Specifically, we minimize the MSE loss against the respective pseudo ground truth ray color generated by $F_{\\theta^{*}}$ across $S$ ray samples:", + "bbox": [ + 76, + 90, + 468, + 167 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\phi} \\mathbb {E} _ {t, r = (o, d)} \\left[ \\| G _ {\\phi} (o, d, t) - F _ {\\theta^ {*}} (o, d, t) \\| _ {2} ^ {2} \\right], \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 114, + 175, + 468, + 199 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "yielding $G_{\\tilde{\\phi}}$ . Note how this is considerably different from R2L [36], which uses a static LFN that is distilled from a static NeRF.", + "bbox": [ + 76, + 208, + 468, + 252 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Finally, we initialize our student model $G_{\\phi}$ with parameters $\\tilde{\\phi}$ and fine-tune it using the original real video data:", + "bbox": [ + 76, + 253, + 468, + 285 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\phi , \\phi_ {0} = \\tilde {\\phi}} \\mathbb {E} _ {t, r = (o, d)} \\left[ \\| G _ {\\phi} (o, d, t) - I (o, d, t) \\| _ {2} ^ {2} \\right], \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 104, + 294, + 468, + 321 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "obtaining $\\phi^{*}$", + "bbox": [ + 76, + 330, + 169, + 344 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. CoDyLiN", + "text_level": 1, + "bbox": [ + 76, + 352, + 186, + 368 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.1 Network Architecture", + "text_level": 1, + "bbox": [ + 76, + 376, + 282, + 390 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We further demonstrate that our DyLiN architecture from Sec. 3.1.1 can be extended to the controllable scenario using attribute inputs with hyperspace MLPs and attention masks. Our proposed CoDyLiN network $Q_{\\tau}$ is depicted in Fig. 3.", + "bbox": [ + 76, + 400, + 468, + 460 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/00a15c60d3686dad6e085f5e9986fb9cef9b3c4b3a263cdd33a8ed42397c2300.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 81, + 472, + 460, + 637 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/1bbd2f1c55b5855d780110e51b22b80a808040ebb10f7c56dbb4d5c1fc481640.jpg", + "image_caption": [ + "Figure 3. Schematic diagram of our proposed CoDyLiN architecture. We augment our DyLiN (blue, green, red) by introducing scalar attribute inputs $\\alpha_{i} \\in [-1,1]$ , $i = 1,\\dots,n$ and lifting them to their respective hyperspace codes $w_{i}$ (orange,..., pink MLPs). Next, $M_{i}$ disentangles $w_{i}$ from $w_{j}$ , $j \\neq i$ by masking it into $w_{i}'$ (orange,..., pink boxes and bottom insets). We concatenate the sampled points $x_{k}$ , $k = 1,\\ldots,K$ with the $w_{i}'$ , $i = 1,\\ldots,n$ and predict the RGB color corresponding to the inputs (red). Arrows from $(o',d')$ and $w_{0}$ to $M_{i}$ are omitted from the top figure for simplicity. Compare this with Fig. 2." + ], + "image_footnote": [], + "bbox": [ + 84, + 648, + 220, + 703 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/904facdb90e9b7df016ce03052b76f0cf3057663380db0553a2cde1b8192840f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 230, + 650, + 341, + 703 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/a733914acca885ad9f04f58f090af783ad9a5eccb0f6edbd90cd1949ccc33eca.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 352, + 654, + 468, + 694 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Specifically, we start from DyLiN $G_{\\phi}$ and add scalar inputs $\\alpha_{i} \\in [-1,1]$ , $i = 1, \\dots, n$ next to $o, d, t$ . Intuitively,", + "bbox": [ + 76, + 869, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "these are given strength values for specific local attributes, which can be interpolated continuously. $n$ is the total number of attributes.", + "bbox": [ + 498, + 90, + 890, + 133 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Each $\\alpha_{i}$ is then processed independently with its own hyperspace MLP $H_{i,\\psi_i}$ to yield the hyperspace code $w_{i}$ :", + "bbox": [ + 498, + 136, + 890, + 167 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nw _ {i} = H _ {i, \\psi_ {i}} (o, d, t). \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 627, + 172, + 890, + 189 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Next, we include mask MLP regressors $M_{i,\\rho_i}$ to generate scalar attention masks $\\hat{m}_i \\in [0,1]$ for each $w_i$ (including $w_0 = w$ ):", + "bbox": [ + 498, + 195, + 890, + 239 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {m} _ {i} = M _ {i, \\rho_ {i}} (w _ {i}, w, o, d),\n$$\n", + "text_format": "latex", + "bbox": [ + 593, + 244, + 761, + 262 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {m} _ {0} = 1 - \\sum_ {i = 1} ^ {n} \\hat {m} _ {i}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 591, + 265, + 890, + 304 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nw _ {i} ^ {\\prime} = \\hat {m} _ {i} \\cdot w _ {i}, \\quad i = 0, \\dots , n,\n$$\n", + "text_format": "latex", + "bbox": [ + 596, + 308, + 797, + 323 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This helps the architecture to spatially disentangle (i.e., localize) the effects of attributes $\\alpha_{i}$ , while $\\hat{m}_0$ can be understood as the space not affected by any attributes.", + "bbox": [ + 500, + 329, + 890, + 375 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Finally, we sample $K$ points on the ray similarly to Sec. 3.1.1, concatenate those with the $w_{i}^{\\prime}$ vectors, and process the result further with LFN $R_{\\pi}$ . Again, we can use a shorthand for the parameters: $\\tau = [\\omega, \\psi, \\psi_1, \\ldots, \\psi_n, \\rho_1, \\ldots, \\rho_n, \\pi]$ .", + "bbox": [ + 498, + 375, + 890, + 450 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Observe that without our MLPs $H_{i,\\psi_i}$ , $M_{i,\\rho_i}$ , $i = 1, \\dots, n$ , our CoDyLiN reverts to our simpler DyLiN. Different from CoNeRF [13], we process rays instead of points, and use the $\\alpha_i$ as inputs instead of targets.", + "bbox": [ + 498, + 450, + 890, + 510 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.2 Training Procedure", + "text_level": 1, + "bbox": [ + 500, + 527, + 689, + 542 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Akin to Sec. 3.1.2, we split training into pretraining and distillation steps, but omit fine-tuning.", + "bbox": [ + 498, + 551, + 890, + 580 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "First, we pretrain a CoNeRF model $E_{\\nu}$ [13] by randomly sampling $(t,r,i)$ , against 3 ground truths: ray color, attribute values $\\alpha_{i}$ and 2D per-attribute masks $m_{2D,i}$ . This yields us $E_{\\nu^{*}}$ . For brevity, we omit the details of this step, and kindly forward the reader to Section 3 in [13].", + "bbox": [ + 498, + 582, + 890, + 656 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Second, we distill from our teacher CoNeRF model $E_{\\nu^{*}}$ into our student CoDyLiN $Q_{\\tau}$ by randomly sampling $t,r,\\alpha_{1},\\ldots ,\\alpha_{n}$ , and minimizing the MSE against 2 pseudo ground truths, i.e., ray colors and 2D masks $\\bar{m}_{2D,i}$ :", + "bbox": [ + 498, + 657, + 890, + 717 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\min _ {\\tau} \\mathbb {E} _ {t, r = (o, d)} \\left[ \\| Q _ {\\tau} (o, d, t, \\alpha_ {1: n}) - \\bar {E} _ {\\nu^ {*}} (o, d, t, \\alpha_ {1: n}) \\| _ {2} ^ {2} \\right. \\\\ \\left. + \\lambda_ {m} \\cdot \\sum_ {i = 0} ^ {n} \\| \\hat {m} _ {i} (o, d, t, \\alpha_ {i}) - \\bar {m} _ {2 D} (o, d, t, \\alpha_ {1: n}) _ {i} \\| _ {2} ^ {2} \\right], \\tag {8} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 727, + 890, + 816 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\bar{E}_{\\nu}$ is identical to $E_{\\nu}$ except for taking $\\alpha_{1:n} = [\\alpha_1,\\dots ,\\alpha_n]$ as input and outputting the masks $\\bar{m}_{2D,i},i = 0,\\ldots ,n$ . We denote the result of the optimization as $Q_{\\tau^{*}}$", + "bbox": [ + 498, + 824, + 890, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We highlight that our teacher and student models are both controllable in this setup.", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "12400", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Experimental Setup", + "text_level": 1, + "bbox": [ + 76, + 89, + 269, + 107 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Datasets", + "text_level": 1, + "bbox": [ + 76, + 114, + 179, + 128 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To test our hypotheses, we performed experiments on three types of dynamic scenes: synthetic, real and real controllable.", + "bbox": [ + 75, + 138, + 468, + 183 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Synthetic Scenes. We utilized the synthetic $360^{\\circ}$ dynamic dataset introduced by [29], which contains 8 animated objects with complicated geometry and realistic non-Lambertian materials. Each dynamic scene consists of 50 to 200 training images and 20 testing images. We used $400 \\times 400$ image resolution. We applied D-NeRF [29] as our teacher model with the publicly available pretrained weights.", + "bbox": [ + 75, + 184, + 468, + 304 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Real Scenes. We collected real dynamic data from 2 sources. First, we utilized 5 topologically varying scenes provided by [28] (Broom, 3D Printer, Chicken, Americano and Banana), which were captured by a rig encompassing a pole with two Google Pixel 3 phones rigidly attached roughly $16\\mathrm{cm}$ apart. Second, we collected human facial videos using an iPhone 13 Pro camera. We rendered both sets at $960 \\times 540$ image resolution. We pretrained a HyperNeRF [28] teacher model from scratch for each scene.", + "bbox": [ + 75, + 305, + 468, + 439 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Real Controllable Scenes. We borrowed 2 real controllable scenes from [13] (closing/opening eyes/mouth, and transformer), which are captured either with a Google Pixel 3a or an Apple iPhone 13 Pro, and contain annotations over various attributes. We applied image resolution of $480 \\times 270$ pixels. We pretrained a CoNeRF [13] teacher model from scratch per scene.", + "bbox": [ + 75, + 441, + 468, + 546 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Settings", + "text_level": 1, + "bbox": [ + 76, + 558, + 174, + 574 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Throughout our experiments, we use the settings listed below, many of which follow [36].", + "bbox": [ + 75, + 582, + 468, + 612 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In order to retain efficiency, we define $T_{\\omega}$ and $H_{\\psi}$ to be small MLPs, with $T_{\\omega}$ consisting of 7 layers of 128 units with $r' \\in \\mathbb{R}^6$ , and $H_{\\psi}$ having 6 layers of 64 units with $w \\in \\mathbb{R}^8$ . Then, we use $K = 16$ sampled points to represent rays, where sampling is done randomly during training and evenly spaced during inference.", + "bbox": [ + 75, + 613, + 468, + 703 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Contrary to $T_{\\omega}$ and $H_{\\psi}$ , our LFN $R_{\\pi}$ is a very deep residual color MLP regressor, containing 88 layers with 256 units per layer, in order to have enough capacity to learn the video generation process.", + "bbox": [ + 75, + 704, + 468, + 763 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We generate rays within Eqs. (3) to (5) and (8) by sampling ray origins $o = (x_o, y_o, z_o)$ and normalized directions $d = (x_d, y_d, z_d)$ randomly from the uniform distribution $U$ as follows:", + "bbox": [ + 75, + 765, + 468, + 824 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nx _ {o} \\sim U \\left(x _ {o} ^ {\\min }, x _ {o} ^ {\\max }\\right), \\quad x _ {d} \\sim U \\left(x _ {d} ^ {\\min }, x _ {d} ^ {\\max }\\right), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 101, + 838, + 468, + 854 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\ny _ {o} \\sim U \\left(y _ {o} ^ {\\min }, y _ {o} ^ {\\max }\\right), \\quad y _ {d} \\sim U \\left(y _ {d} ^ {\\min }, y _ {d} ^ {\\max }\\right), \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 859, + 468, + 876 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nz _ {o} \\sim U \\left(z _ {o} ^ {\\min }, z _ {o} ^ {\\max }\\right), \\quad z _ {d} \\sim U \\left(z _ {d} ^ {\\min }, z _ {d} ^ {\\max }\\right), \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 104, + 880, + 468, + 897 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where the min, max bounds of the 6 intervals are inferred from the original training video. In addition to uniform sampling, we also apply the hard example mining strategy suggested in [36] to focus on fine-grained details. We used $S = 10,000$ training samples during KD in (4).", + "bbox": [ + 498, + 90, + 890, + 166 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Subsequently, we also randomly sample time step $t$ uniformly from the unit interval: $t \\sim U(0,1)$ .", + "bbox": [ + 498, + 167, + 890, + 196 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Optionally, for our CoDyLiN experiments, we define each $H_{i,\\psi_i}$ to be a small MLP having 5 layers of 128 units with $w_{i} \\in \\mathbb{R}^{8}$ . During training, we uniformly sample attributes within $[-1,1]$ : $\\alpha_{i} \\sim U(-1,1)$ , and let $\\lambda_{m} = 0.1$ .", + "bbox": [ + 496, + 196, + 890, + 257 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "During training, we used Adam [14] with learning rate $5 \\times 10^{-4}$ and batch size 4,096.", + "bbox": [ + 498, + 258, + 890, + 286 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We performed all experiments on single NVIDIA A100 GPUs.", + "bbox": [ + 498, + 287, + 890, + 316 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Baseline Models", + "text_level": 1, + "bbox": [ + 500, + 327, + 661, + 342 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For testing our methods, we compared quality and speed against several baseline models, including NeRF [23], NV [19], NSFF [16], Nerfies [27], HyperNeRF [28], two variants of TiNeuVox [8], DirectVoxGo [33], Plenoxels [9], T-NeRF and D-NeRF [29], as well as CoNeRF [13].", + "bbox": [ + 498, + 351, + 890, + 426 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/03c51ac6ec9028fe761670820cc6eb88cbec11fcb0e7d5d9ab74ab83190189e3.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 516, + 438, + 879, + 526 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/3e8cc66a72439b1327a9ca8e7899c8107dba8831b9e0653a607bb93a493d447f.jpg", + "image_caption": [ + "(b)", + "Figure 4. Our two ablated baseline models, omitting components of our DyLiN. (a) Without our two proposed MLPs. (b) Pointwise deformation MLP only, predicting offsets jointly." + ], + "image_footnote": [], + "bbox": [ + 516, + 541, + 879, + 662 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In addition, we performed an ablation study by comparing against 2 simplified versions of our DyLiN architecture. First, we omitted both of our deformation and hyperspace MLPs and simply concatenated the time step $t$ to the sampled ray points (essentially resulting in a dynamic R2L). This method is illustrated in Fig. 4a. Second, we employed a pointwise deformation MLP (5 layers of 256 units) inspired by [29], which deforms points along a ray by predicting their offsets jointly, i.e., it can bend rays. This is contrast to our DyLiN, which deforms rays explicitly without", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "12401", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "bending and also applies a hyperspace MLP. This scheme is depicted in Fig. 4b. In both baselines, the deep residual color MLP regressors were kept intact. Next, we also tested the effects of our fine-tuning procedure from (5) by training all of our models both with and without it. Lastly, we assessed the dependences on the number of sampled points along rays $K$ and on the number of training samples $S$ during KD in (4).", + "bbox": [ + 75, + 90, + 472, + 212 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. Evaluation Metrics", + "text_level": 1, + "bbox": [ + 76, + 222, + 261, + 238 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For quantitatively evaluating the quality of generated images, we calculated the Peak Signal-to-Noise Ratio (PSNR) [12] in decibels (dB), the Structural Similarity Index (SSIM) [25,40], the Multi-Scale SSIM (MS-SSIM) [41] and the Learned Perceptual Image Patch Similarity (LPIPS) [44] metrics. Intuitively, PSNR is a pixelwise score, while SSIM and MS-SSIM also take pixel correlations and multiple scales into account, respectively, yet all of these tend to favor blurred images. LPIPS compares deep neural representations of images and is much closer to human perception, promoting semantically better and sharper images.", + "bbox": [ + 75, + 246, + 468, + 412 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Furthermore, for testing space and time complexity, we computed the storage size of parameters in megabytes (MB) and measured the wall-clock time in milliseconds (ms) while rendering the synthetic Lego scene with each model.", + "bbox": [ + 75, + 412, + 468, + 474 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Results", + "text_level": 1, + "bbox": [ + 76, + 488, + 163, + 503 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Quantitative Results", + "text_level": 1, + "bbox": [ + 76, + 513, + 271, + 529 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Tab. 1 and Tab. 2 contain our quantitative results for reconstruction quality on synthetic and real dynamic scenes, accordingly. We found that among prior works, TiNeuVox-B performed the best on synthetic scenes with respect to each metric. On real scenes, however, NSFF took the lead. Despite having strong metrics, NSFF is qualitatively poor and slow. Surprisingly, during ablation, even our most basic model (DyLiN without the two MLPs from Fig. 4a) could generate perceptually better looking images than TiNeuVox-B, thanks to the increased training dataset size via KD. Incorporating the MLPs $T_{\\omega}$ and $H_{\\psi}$ into the model each improved results slightly. Interestingly, fine-tuning on real data as in (5) gave a substantial boost. In addition, our relative PSNR improvement over the teacher model (Tab. 1=+1.93 dB, up to +3.16 dB per scene; Tab. 2=+2.7 dB, up to +13.14 dB) is better than that of R2L [36] (+1.4 dB, up to +2.8 dB).", + "bbox": [ + 75, + 537, + 468, + 792 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Tab. 3 shows quantitative results for space and time complexity on the synthetic Lego scene. We found that there is a trade-off between the two metrics, as prior works are typically optimized for just one of those. In contrast, all of our proposed DyLiN variants settle at the golden mean between the two extremes. When compared to the strongest baseline TiNeuVox-B, our method requires 3 times as much", + "bbox": [ + 75, + 795, + 470, + 901 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/bbcf623efc63c17fa3498ec641651ea96103dd0aa444273c53c23499179dc33c.jpg", + "table_caption": [ + "Table 1. Quantitative results on synthetic dynamic scenes. Notations: Multi-Layer Perceptron (MLP), PD (pointwise deformation), FT (fine-tuning). We utilized D-NeRF as the teacher model for our DyLiNs. The winning numbers are highlighted in bold." + ], + "table_footnote": [], + "table_body": "
MethodPSNR↑SSIM↑LPIPS↓
NeRF [23]19.000.87000.1825
DirectVoxGo [33]18.610.85380.1688
Plenoxels [9]20.240.86880.1600
T-NeRF [29]29.510.95130.0788
D-NeRF [29]30.500.95250.0663
TiNeuVox-S [8]30.750.95500.0663
TiNeuVox-B [8]32.670.97250.0425
DyLiN, w/o two MLPs, w/o FT (ours)31.160.99310.0281
DyLiN, w/o two MLPs (ours)32.070.99370.0196
DyLiN, PD MLP only, w/o FT (ours)31.260.99320.0279
DyLiN, PD MLP only (ours)31.240.99400.0189
DyLiN, w/o FT (ours)31.370.99330.0275
DyLiN (ours)32.430.99430.0184
", + "bbox": [ + 501, + 155, + 893, + 348 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/0092b6c96208b1db58a1da0c596e8000ce9ebfa235d84726c0548571352cb8c4.jpg", + "table_caption": [ + "Table 2. Quantitative results on real dynamic scenes. Notations: Multi-Layer Perceptron (MLP), PD (pointwise deformation), FT (fine-tuning). We utilized HyperNeRF as the teacher model for our DyLiNs. The winning numbers are highlighted in bold." + ], + "table_footnote": [], + "table_body": "
MethodPSNR↑MS-SSIM↑
NeRF [23]20.10.745
NV [19]16.90.571
NSFF [16]26.30.916
Nerfies [27]22.20.803
HyperNeRF [28]22.40.814
TiNeuVox-S [8]23.40.813
TiNeuVox-B [8]24.30.837
DyLiN, w/o two MLPs, w/o FT (ours)23.80.882
DyLiN, w/o two MLPs (ours)24.20.894
DyLiN, PD MLP only, w/o FT (ours)23.90.885
DyLiN, PD MLP only (ours)24.60.903
DyLiN, w/o FT (ours)24.00.886
DyLiN (ours)25.10.910
", + "bbox": [ + 501, + 431, + 890, + 643 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "storage but is nearly 2 orders of magnitude faster. Plenoxels and NV, the only methods that require less computation than ours, perform much worse in quality.", + "bbox": [ + 496, + 672, + 890, + 718 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Fig. 5 reports quantitative ablation results for dependencies on the number of sampled points per ray $K$ and on the number of training samples during KD $S$ , performed on the synthetic Standup scene. For dependence on $K$ (Fig. 5a), we found that there were no significant differences between test set PNSR scores for $K \\in \\{4,8,16,32\\}$ , while we encountered overfitting for $K \\in \\{64,128\\}$ . This justified our choice of $K = 16$ for the rest of our experiments. Regarding the effect of $S$ (Fig. 5b), overfitting occurred for smaller sample sizes including $S \\in \\{100;500;1,000;5,000\\}$ . The test and training set PSNR scores were much closer for $S = 10,000$ , validating our general setting.", + "bbox": [ + 496, + 719, + 893, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "12402", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/3a8f237825752d8c526f026308bb37af724dd4d4568eae6f284666fff9b93253.jpg", + "table_caption": [ + "Table 3. Quantitative results for space and time complexity on the synthetic Lego scene. Notations: Multi-Layer Perceptron (MLP), PD (pointwise deformation), FT (fine-tuning)." + ], + "table_footnote": [], + "table_body": "
MethodStorage (MB)Wall-clock time (ms)
NeRF [23]5.002,950.0
DirectVoxGo [33]205.001,090.0
Plenoxels [9]717.0050.0
NV [19]439.0074.9
D-NeRF [29]4.008,150.0
NSFF [16]14.175,450.0
HyperNeRF [28]15.362,900.0
TiNeuVox-S [8]23.703,280.0
TiNeuVox-B [8]23.706,920.0
DyLiN, w/o two MLPs, w/o FT (ours)68.04115.4
DyLiN, w/o two MLPs (ours)68.04115.4
DyLiN, PD MLP only, w/o FT (ours)72.60115.7
DyLiN, PD MLP only (ours)72.60115.7
DyLiN, w/o FT (ours)70.11116.0
DyLiN (ours)70.11116.0
", + "bbox": [ + 76, + 142, + 470, + 395 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3a589bdc785b0810b64439fb8489a7fc69f0ffb95dea2912bdaf86d0a0b6d3a3.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 94, + 414, + 447, + 568 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/619835508c0103e5a24dd60fe777f8717547f5875baf0dcf33b80718d1d519a2.jpg", + "image_caption": [ + "(b)", + "Figure 5. Quantitative results for ablation on the synthetic Standup scene. (a) Dependence on the number of sampled points $K$ across ray $r'$ . (b) Dependence on the number of training samples $S$ during Knowledge Distillation (KD)." + ], + "image_footnote": [], + "bbox": [ + 94, + 585, + 447, + 739 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Our controllable numerical results are collected in Tab. 4. In short, our CoDyLiN was able to considerably outperform CoNeRF with respect to MS-SSIM and speed.", + "bbox": [ + 75, + 854, + 468, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/b83646819a5e053b5d66a069bab09cd907313f0268998e2334b9af1d09a98cdb.jpg", + "table_caption": [ + "Table 4. Quantitative results on real controllable scenes. We utilized CoNeRF as the teacher model for our CoDyLiN. The winning numbers are highlighted in bold." + ], + "table_footnote": [], + "table_body": "
MethodEyes/MouthTransformer
PSNR†MS-SSIM†Wall-clock time (ms)PSNR†MS-SSIM†Wall-clock time (ms)
CoNeRF [13]21.46580.74586230.023.03190.88784360.0
CoDyLiN (ours)21.46550.9510116.323.58820.9779116.0
", + "bbox": [ + 500, + 142, + 890, + 203 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Qualitative Results", + "text_level": 1, + "bbox": [ + 500, + 229, + 683, + 244 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Fig. 6 and Fig. 7 depict qualitative results for reconstruction quality on synthetic and real dynamic scenes, respectively. Both show that our full DyLiN model generated the sharpest, most detailed images, as it was able to capture cloth wrinkles (Fig. 6j) and the eye of the chicken (Fig. 7e). The competing methods tended to oversmooth these features. We also ablated the effect of omitting fine-tuning (Fig. 6i, Fig. 7d), and results declined considerably.", + "bbox": [ + 496, + 253, + 890, + 375 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For the sake of completeness, Fig. 8 illustrates qualitative ablation results for our model components on real dynamic scenes. We found that sequentially adding our two proposed MLPs $T_{\\omega}$ and $H_{\\psi}$ improves the reconstruction, e.g., the gum between the teeth (Fig. 8e) and the fingers (Fig. 8j) become more and more apparent. Without the MLPs, these parts were heavily blurred (Fig. 8c, Fig. 8h).", + "bbox": [ + 496, + 375, + 890, + 479 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We kindly ask readers to refer to the supplementary material for CoDyLiN's qualitative results.", + "bbox": [ + 498, + 481, + 890, + 512 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 526, + 617, + 542 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We proposed two architectures for extending LFNs to dynamic scenes. Specifically, we introduced DyLiN, which models ray deformations without bending and lifts whole rays into a hyperspace, and CoDyLiN, which allows for controllable attribute inputs. We trained both techniques via knowledge distillation from various dynamic NeRF teacher models. We found that DyLiN produces state-of-the-art quality even without ray bending and CoDyLiN outperforms its teacher model, while both are nearly 2 orders of magnitude faster than their strongest baselines.", + "bbox": [ + 496, + 551, + 890, + 703 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Our methods do not come without limitations, however. Most importantly, they focus on speeding up inference, as they require pretrained teacher models, which can be expensive to obtain. In some experiments, our solutions were outperformed in terms of the PSNR score. Using the winners as teacher models could improve performance. Additionally, distillation from multiple teacher models or joint training of the teacher and student models are also yet to be explored. Moreover, we currently represent rays implicitly by sampling $K$ points along them, but increasing this number can lead to overfitting. An explicit ray representation may be more effective. Finally, voxelizing and quantizing our models could improve efficiency.", + "bbox": [ + 496, + 704, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "12403", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9578a25ec48c190fd52604412f4b9daa5510905c0581f068df992c493af42486.jpg", + "image_caption": [ + "Hook" + ], + "image_footnote": [], + "bbox": [ + 137, + 106, + 200, + 170 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/48f4c374207810d67be2bf020ae3b4267f1df1d613adf2bc819deb9b4dc93362.jpg", + "image_caption": [ + "(a) Ground Truth" + ], + "image_footnote": [], + "bbox": [ + 254, + 111, + 361, + 195 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4489c0de780caa6e3b2942483105bd1082d6fd9abe1f33a2a523c4f14d4fd067.jpg", + "image_caption": [ + "(b) D-NeRF [29]" + ], + "image_footnote": [], + "bbox": [ + 379, + 111, + 486, + 196 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/808de1b043234fe5894873f3afc346eac9d354d4f65a42f93c95398e51019587.jpg", + "image_caption": [ + "(c) TiNeuVox [8]" + ], + "image_footnote": [], + "bbox": [ + 506, + 111, + 612, + 196 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9cdc5bb332c116c596bc740685f6c2f1681a37cb767f6d7ff7dd5e22aba8fc13.jpg", + "image_caption": [ + "(d) Ours-1" + ], + "image_footnote": [], + "bbox": [ + 630, + 111, + 736, + 196 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9617dd849e6544ac9df602759ad6d4e15ee2b99d7c83e2f64ab26689a72083af.jpg", + "image_caption": [ + "(e) Ours-2" + ], + "image_footnote": [], + "bbox": [ + 756, + 111, + 864, + 196 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3ebc925e407086a30f8076cb84dc99a6661361d7ae383e051055a16d9f596326.jpg", + "image_caption": [ + "Jumping Jacks" + ], + "image_footnote": [], + "bbox": [ + 130, + 220, + 210, + 305 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d1b2205db9b8b4d453cbefba32bcf88e7ff69c089951e1d099257f2adef5c3f4.jpg", + "image_caption": [ + "(f) Ground Truth" + ], + "image_footnote": [], + "bbox": [ + 238, + 234, + 359, + 319 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6aa2cd67ebe324823299fbf7035ad432d02ad94f523055ef4abe23d635a8a4f5.jpg", + "image_caption": [ + "(g) D-NeRF [29]" + ], + "image_footnote": [], + "bbox": [ + 364, + 234, + 485, + 319 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/528f46bf89b956a917703617f9488439b729f814fc6e8a859112d719423ddf8c.jpg", + "image_caption": [ + "(h) TiNeuVox [8]" + ], + "image_footnote": [], + "bbox": [ + 490, + 233, + 609, + 319 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/071ea108bd0b1de78975371a653201c569b2b39b973fceeb6bacc752293e67b5.jpg", + "image_caption": [ + "(i) Ours-1" + ], + "image_footnote": [], + "bbox": [ + 614, + 234, + 735, + 319 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/19bda05b92f597c50378ad717bd88d55374464976f0671042659b5c7fcf26c3d.jpg", + "image_caption": [ + "(j) Ours-2" + ], + "image_footnote": [], + "bbox": [ + 740, + 234, + 861, + 319 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ba8af6b89c9b6dea068705de846b92082a936d89d089fbd492e8bba18b7a7352.jpg", + "image_caption": [ + "Figure 6. Qualitative results on synthetic dynamic scenes. We compare our DyLiN (Ours-1, Ours-2) with the ground truth, the D-NeRF teacher model and TiNeuVox. Ours-1 and Ours-2 were trained without and with fine-tuning on the original data, respectively.", + "Chicken" + ], + "image_footnote": [], + "bbox": [ + 138, + 386, + 200, + 463 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4287ab10e0c93d42055f130a69deaf210737f8d0c2f1d6a554074f6a671d655b.jpg", + "image_caption": [ + "(a) Ground Truth" + ], + "image_footnote": [], + "bbox": [ + 236, + 386, + 359, + 463 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/15c15daa0cba666e52c3084ad4f6a1af238817b4a3cc1f1bdae3e770eec102f1.jpg", + "image_caption": [ + "(b) HyperNeRF [28]" + ], + "image_footnote": [], + "bbox": [ + 362, + 386, + 486, + 462 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6b303054b14892dcef8727d9428a8ddce1d53639783f5d3e7bfc66f6af0b86af.jpg", + "image_caption": [ + "(c) TiNeuVox [8]" + ], + "image_footnote": [], + "bbox": [ + 486, + 386, + 612, + 462 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/56ae82ba6bb685bac5e668928de5e84237f01eea6a6dedb8675eb27021e76110.jpg", + "image_caption": [ + "(d) Ours-1" + ], + "image_footnote": [], + "bbox": [ + 614, + 386, + 735, + 462 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/bff2e78c69aeb61239d7afcc30595a0b1d32a0adf1b0814931f8b05261040f13.jpg", + "image_caption": [ + "(e) Ours-2" + ], + "image_footnote": [], + "bbox": [ + 736, + 386, + 861, + 462 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/928db10c9328026da447202d13112ee1654832b67dc46ed104d518e94654af08.jpg", + "image_caption": [ + "Figure 7. Qualitative results on a real dynamic scene. We compare our DyLiN (Ours-1, Ours-2) with the ground truth, the HyperNeRF teacher model and TiNeuVox. Ours-1 and Ours-2 were trained without and with fine-tuning on the original data, respectively." + ], + "image_footnote": [], + "bbox": [ + 138, + 531, + 200, + 612 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4999f67d4c8f94f5e95f4db731b4a529d8c50556a8f2a5783b02f994a720c73e.jpg", + "image_caption": [ + "Expression", + "Peel Banana", + "Figure 8. Qualitative results for ablation on real dynamic scenes. We compare our DyLiN (Ours-1, Ours-2, Ours-3) with the ground truth and the HyperNeRF teacher model. Ours-1 was trained without our two MLPs. Ours-2 was trained with pointwise deformation MLP only. Ours-3 is our full model with both of our proposed two MLPs." + ], + "image_footnote": [], + "bbox": [ + 137, + 625, + 205, + 715 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/dfc6a0b2dbe30527f69200ae8543e5a8cc52f2fd6b574ebbcea22b69aeb86d59.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 236, + 531, + 359, + 611 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/45f194ab4bbe01ae096e8bc0e5b753aec6c02927901ef69ad249de3f79cf19cb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 362, + 531, + 486, + 611 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/41aa19a3cf6dcb375286445665b3036b274529462fdd551494297a2c17c2235c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 486, + 531, + 609, + 611 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e08bd673768e108be682274a886ba6a6142f51cddd992031d41020c84184d226.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 612, + 531, + 735, + 611 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b2ac217ce2fca53eeef11522cd08160d228161ba6cf4172f76236498e5b258ed.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 736, + 531, + 862, + 611 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0860322012e35936b7ab288f5faa8c5daa0c4260111f49ff26d17db0ed98e1d0.jpg", + "image_caption": [ + "(a) Ground Truth", + "(f) Ground Truth" + ], + "image_footnote": [], + "bbox": [ + 235, + 625, + 359, + 715 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7f5b9904fb1d4bb4cef233194ff5e90fe56397e8f9a593031083102c42fbd142.jpg", + "image_caption": [ + "(b) HyperNeRF [28]", + "(g) HyperNeRF [28]" + ], + "image_footnote": [], + "bbox": [ + 362, + 625, + 483, + 715 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/72f368ab2bd6e4dea265641e3d49e6528da9c1693050153e8235a90521bcdeff.jpg", + "image_caption": [ + "(c) Ours-1", + "(h) Ours-1" + ], + "image_footnote": [], + "bbox": [ + 486, + 625, + 607, + 715 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9ae192b24a4126555365d98ca09a49267c97841bf6453b4131573a424cb948b1.jpg", + "image_caption": [ + "(d) Ours-2", + "(i) Ours-2" + ], + "image_footnote": [], + "bbox": [ + 612, + 625, + 735, + 715 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2302cc80473dfff4ac9835e36533deb4ba36b12e3c386c7ec0346a42c0081d29.jpg", + "image_caption": [ + "(e) Ours-3", + "(j) Ours-3" + ], + "image_footnote": [], + "bbox": [ + 736, + 625, + 859, + 715 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Our results are encouraging steps towards achieving real-time volumetric rendering and animation, and we hope that our work will contribute to the progress in these areas.", + "bbox": [ + 75, + 811, + 468, + 856 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements", + "text_level": 1, + "bbox": [ + 500, + 810, + 666, + 827 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This research was supported partially by Fujitsu. We thank Chaoyang Wang from Carnegie Mellon University for the helpful discussion.", + "bbox": [ + 498, + 854, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "12404", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] E.H. Adelson and J.Y.A. Wang. Single Lens Stereo with a Plenoptic Camera. IEEE Trans. Pattern Anal. Mach. Intell., 14(2):99-106, 1992. 2", + "[2] Jonathan T Barron, Ben Mildenhall, Matthew Tancik, Peter Hedman, Ricardo Martin-Brualla, et al. Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields. In Proc. IEEE/CVF ICCV, pages 5855–5864, 2021. 1", + "[3] James R Bergen and Edward H Adelson. The Plenoptic Function and the Elements of Early Vision. Comput. Model. Vis. 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IEEE/CVF CVPR, pages 586-595, 2018. 6" + ], + "bbox": [ + 78, + 90, + 468, + 854 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "12406", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/DyLiN_ Making Light Field Networks Dynamic/52436ab0-0f6f-44ce-bee8-32ea0aeba3bb_model.json b/2023/DyLiN_ Making Light Field Networks Dynamic/52436ab0-0f6f-44ce-bee8-32ea0aeba3bb_model.json new file mode 100644 index 0000000000000000000000000000000000000000..5475be1cdf13936bef7be7c1f34ed00cb4ff39d5 --- /dev/null +++ b/2023/DyLiN_ Making Light Field Networks Dynamic/52436ab0-0f6f-44ce-bee8-32ea0aeba3bb_model.json @@ -0,0 +1,3014 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.245, + 0.131, + 0.726, + 0.154 + ], + "angle": 0, + "content": "DyLiN: Making Light Field Networks Dynamic" + }, + { + "type": "text", + "bbox": [ + 0.14, + 0.18, + 0.823, + 0.2 + ], + "angle": 0, + "content": "Heng Yu\\(^{1}\\) Joel Julin\\(^{1}\\) Zoltán Á. Milacski\\(^{1}\\) Koichiro Niinuma\\(^{2}\\) László A. Jeni\\(^{1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.168, + 0.204, + 0.804, + 0.223 + ], + "angle": 0, + "content": "\\(^{1}\\)Robotics Institute, Carnegie Mellon University \\(^{2}\\)Fujitsu Research of America" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.225, + 0.858, + 0.24 + ], + "angle": 0, + "content": "{hengyu, jjulin, zmilacsk}@andrew.cmu.edu kniinuma@fujitsu.com laszlojeni@cmu.edu" + }, + { + "type": "image", + "bbox": [ + 0.12, + 0.253, + 0.245, + 0.354 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.135, + 0.358, + 0.228, + 0.386 + ], + "angle": 0, + "content": "Ground Truth Video" + }, + { + "type": "image", + "bbox": [ + 0.246, + 0.254, + 0.371, + 0.355 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.252, + 0.357, + 0.364, + 0.386 + ], + "angle": 0, + "content": "HyperNeRF [28] \nRender time: 3 s" + }, + { + "type": "image", + "bbox": [ + 0.373, + 0.254, + 0.495, + 0.355 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.379, + 0.357, + 0.489, + 0.386 + ], + "angle": 0, + "content": "TiNeuVox [8] Render time: 7s" + }, + { + "type": "image", + "bbox": [ + 0.497, + 0.253, + 0.621, + 0.355 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.357, + 0.62, + 0.386 + ], + "angle": 0, + "content": "Ours Render time: 0.1s" + }, + { + "type": "image", + "bbox": [ + 0.625, + 0.253, + 0.848, + 0.37 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.399, + 0.895, + 0.442 + ], + "angle": 0, + "content": "Figure 1. Our proposed DyLiN for dynamic 3D scene rendering achieves higher quality than its HyperNeRF teacher model and the state-of-the-art TiNeuVox model, while being an order of magnitude faster. Right: DyLiN is of moderate storage size (shown by dot radii). For each method, the relative improvement in Peak Signal-to-Noise Ratio over NeRF (\\(\\Delta\\)PSNR) is measured for the best-performing scene." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.454, + 0.314, + 0.47 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.486, + 0.473, + 0.819 + ], + "angle": 0, + "content": "Light Field Networks, the re-formulations of radiance fields to oriented rays, are magnitudes faster than their coordinate network counterparts, and provide higher fidelity with respect to representing 3D structures from 2D observations. They would be well suited for generic scene representation and manipulation, but suffer from one problem: they are limited to holistic and static scenes. In this paper, we propose the Dynamic Light Field Network (DyLiN) method that can handle non-rigid deformations, including topological changes. We learn a deformation field from input rays to canonical rays, and lift them into a higher dimensional space to handle discontinuities. We further introduce CoDyLiN, which augments DyLiN with controllable attribute inputs. We train both models via knowledge distillation from pretrained dynamic radiance fields. We evaluated DyLiN using both synthetic and real world datasets that include various non-rigid deformations. DyLiN qualitatively outperformed and quantitatively matched state-of-the-art methods in terms of visual fidelity, while being \\(25 - 71 \\times\\) computationally faster. We also tested CoDyLiN on attribute annotated data and it surpassed its teacher model. Project page: https://dylin2023.github.io." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.846, + 0.208, + 0.861 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Machine vision has made tremendous progress with respect to reasoning about 3D structure using 2D observa" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.455, + 0.892, + 0.637 + ], + "angle": 0, + "content": "tions. Much of this progress can be attributed to the emergence of coordinate networks [6,21,26], such as Neural Radiance Fields (NeRF) [23] and its variants [2, 20, 22, 39]. They provide an object agnostic representation for 3D scenes and can be used for high-fidelity synthesis for unseen views. While NeRFs mainly focus on static scenes, a series of works [10,27,29,34] extend the idea to dynamic cases via additional components that map the observed deformations to a canonical space, supporting moving and shape-evolving objects. It was further shown that by lifting this canonical space to higher dimensions the method can handle changes in scene topology as well [28]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.893, + 0.902 + ], + "angle": 0, + "content": "However, the applicability of NeRF models is considerably limited by their computational complexities. From each pixel, one typically casts a ray from that pixel, and numerically integrates the radiance and color densities computed by a Multi-Layer Perceptron (MLP) across the ray, approximating the pixel color. Specifically, the numerical integration involves sampling hundreds of points across the ray, and evaluating the MLP at all of those locations. Several works have been proposed for speeding up static NeRFs. These include employing a compact 3D representation structure [9, 18, 43], breaking up the MLP into multiple smaller networks [30, 31], leveraging depth information [7, 24], and using fewer sampling points [17, 24, 42]. Yet, these methods still rely on integration and suffer from sampling many points, making them prohibitively slow for real-time applications. Recently, Light Field Networks (LFNs) [32] proposed replacing integration with a direct ray-to" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12397" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.304 + ], + "angle": 0, + "content": "color regressor, trained using the same sparse set of images, requiring only a single forward pass. R2L [36] extended LFNs to use a very deep residual architecture, trained by distillation from a NeRF teacher model to avoid overfitting. In contrast to static NeRF acceleration, speeding up dynamic NeRFs is a much less discussed problem in the literature. This is potentially due to the much increased difficulty of the task, as one also has to deal with the high variability of motion. In this direction, [8, 38] greatly reduce the training time by using well-designed data structures, but their solutions still rely on integration. LFNs are clearly better suited for acceleration, yet, to the best of our knowledge, no works have attempted extending LFNs to the dynamic scenario." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.308, + 0.473, + 0.625 + ], + "angle": 0, + "content": "In this paper, we propose 2 schemes extending LFNs to dynamic scene deformations, topological changes and controllability. First, we introduce DyLiN, by incorporating a deformation field and a hyperspace representation to deal with non-rigid transformations, while distilling knowledge from a pretrained dynamic NeRF. Afterwards, we also propose CoDyLiN, via adding controllable input attributes, trained with synthetic training data generated by a pretrained Controllable NeRF (CoNeRF) [13] teacher model. To test the efficiencies of our proposed schemes, we perform empirical experiments on both synthetic and real datasets. We show that our DyLiN achieves better image quality and an order of magnitude faster rendering speed than its original dynamic NeRF teacher model and the state-of-the-art TiNeuVox [8] method. Similarly, we also show that CoDyLiN outperforms its CoNeRF teacher. We further execute ablation studies to verify the individual effectiveness of different components of our model. Our methods can be also understood as accelerated versions of their respective teacher models, and we are not aware of any prior works that attempt speeding up CoNeRF." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.625, + 0.405, + 0.64 + ], + "angle": 0, + "content": "Our contributions can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.663, + 0.47, + 0.74 + ], + "angle": 0, + "content": "- We propose DyLiN, an extension of LFNs that can handle dynamic scenes with topological changes. DyLiN achieves this through non-bending ray deformations, hyperspace lifting for whole rays, and knowledge distillation from dynamic NeRFs." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.767, + 0.47, + 0.843 + ], + "angle": 0, + "content": "- We show that DyLiN achieves state-of-the-art results on both synthetic and real-world scenes, while being an order of magnitude faster than the competition. We also include an ablation study to analyze the contributions of our model components." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.871, + 0.47, + 0.902 + ], + "angle": 0, + "content": "- We introduce CoDyLiN, further extending our DyLiN to handle controllable input attributes." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.663, + 0.47, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.09, + 0.651, + 0.107 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.116, + 0.895, + 0.328 + ], + "angle": 0, + "content": "Dynamic NeRFs. NeRFs have demonstrated impressive performances in novel view synthesis for static scenes. Extending these results to dynamic (deformable) domains has sparked considerable research interest [10, 27-29, 34]. Among these works, the ones that most closely resemble ours are D-NeRF [29] and HyperNeRF [28]. D-NeRF uses a translational deformation field with temporal positional encoding. HyperNeRF introduces a hyperspace representation, allowing topological variations to be effectively captured. Our work expands upon these works, as we propose DyLiN, a similar method for LFNs. We use the above dynamic NeRFs as pretrained teacher models for DyLiN, achieving better fidelity with orders of magnitude shorter rendering times." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.35, + 0.895, + 0.713 + ], + "angle": 0, + "content": "Accelerated NeRFs. The high computational complexity of NeRFs has motivated several follow-up works on speeding up the numerical integration process. The following first set of works are restricted to static scenarios. NSVF [18] represents the scene with a set of voxel-bounded MLPs organized in a sparse voxel octree, allowing voxels without relevant content to be skipped. KiloNeRF [31] divides the scene into a grid and trains a tiny MLP network for each cell within the grid, saving on pointwise evaluations. AutoInt [17] reduces the number of point samples for each ray using learned partial integrals. In contrast to the above procedures, speeding up dynamic NeRFs is much less discussed in the literature, as there are only 2 papers published on this subject. Wang et al. [38] proposed a method based on Fourier plenoctrees for real-time dynamic rendering, however, the technique requires an expensive rigid scene capturing setup. TiNeuVox [8] reduces training time by augmenting the MLP with time-aware voxel features and a tiny deformation network, while using a multi-distance interpolation method to model temporal variations. Interestingly, all of the aforementioned methods suffer from sampling hundreds of points during numerical integration, and none of them support changes in topology, whereas our proposed DyLiN excels from both perspectives." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.897, + 0.903 + ], + "angle": 0, + "content": "Light Field Networks (LFNs). As opposed to the aforementioned techniques that accelerate numerical integration within NeRFs, some works have attempted completely replacing numerical integration with direct per-ray color MLP regressors called Light Field Networks (LFNs). Since these approaches accept rays as inputs, they rely heavily on the ray representation. Several such representations exist in the literature. Plenoptic functions [1,3] encode 3D rays with 5D representations, i.e., a 3D point on a ray and 2 axis-angle ray directions. Light fields [11,15] use 4D ray codes most commonly through two-plane parameterization: given 2 parallel" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "12398" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.455 + ], + "angle": 0, + "content": "planes, rays are encoded by the 2D coordinates of the 2 ray-plane intersection points. Sadly, these representations are either discontinuous or cannot represent the full set of rays. Recently, Sitzmann et al. [32] advocate for the usage of the 6D Plücker coordinate representation, i.e., a 3D point on a ray coupled with its cross product with a 3D direction. They argue that this representation covers the whole set of rays and is continuous. Consequently, they feed it as input to an LFN, and additionally apply Meta-Learning across scenes to learn a multi-view consistency prior. However, they have not considered alternative ray representations, MLP architectures or training procedures, and only tested their method on toy datasets. R2L [36] employs an even more effective ray encoding by concatenating few points sampled from it, and proposes a very deep (88 layers) residual MLP network for LFNs. They resolve the proneness to overfitting by training the MLP with an abundance of synthetic images generated by a pretrained NeRF having a shallow MLP. Interestingly, they find that the student LFN model produces significantly better rendering quality than its teacher NeRF model, while being about 30 times faster. Our work extends LFNs to dynamic deformations, topological changes and controllability, achieving similar gains over the pretrained dynamic NeRF teacher models." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.472, + 0.472, + 0.595 + ], + "angle": 0, + "content": "Knowledge Distillation. The process of training a student model with synthetic data generated by a teacher model is called Knowledge Distillation (KD) [4], and it has been widely used in the vision and language domains [5, 15, 35, 37] as a form of data augmentation. Like R2L [36], we also use KD for training, however, our teacher and student models are both dynamic and more complex than their R2L counterparts." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.608, + 0.176, + 0.623 + ], + "angle": 0, + "content": "3. Methods" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.633, + 0.47, + 0.799 + ], + "angle": 0, + "content": "In this section, we present our two solutions for extending LFNs. First, in Sec. 3.1, we propose DyLiN, supporting dynamic deformations and hyperspace representations via two respective MLPs. We use KD to train DyLiN with synthetic data generated by a pretrained dynamic NeRF teacher model. Second, in Sec. 3.2, we introduce CoDyLiN, which further augments DyLiN with controllability, via lifting attribute inputs to hyperspace with MLPs, and masking their hyperspace codes for disentanglement. In this case, we also train via KD, but the teacher model is a pretrained controllable NeRF." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.808, + 0.168, + 0.824 + ], + "angle": 0, + "content": "3.1. DyLiN" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.832, + 0.285, + 0.846 + ], + "angle": 0, + "content": "3.1.1 Network Architecture" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.469, + 0.902 + ], + "angle": 0, + "content": "Our overall DyLiN architecture \\( G_{\\phi} \\) is summarized in Fig. 2. It processes rays instead of the widely adopted 3D point inputs as follows." + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.091, + 0.891, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.206, + 0.894, + 0.292 + ], + "angle": 0, + "content": "Figure 2. Schematic diagram of our proposed DyLiN architecture. We take a ray \\( r = (o, d) \\) and time \\( t \\) as input. We deform \\( r \\) into \\( r' = (o', d') \\), and sample few points \\( x_k, k = 1, \\ldots, K \\) along \\( r' \\) to encode it (blue). In parallel, we also lift \\( r \\) and \\( t \\) to the hyperspace code \\( w \\) (green), and concatenate it with each \\( x_k \\). We use the concatenation to regress the RGB color of \\( r \\) at \\( t \\) directly (red)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.316, + 0.892, + 0.348 + ], + "angle": 0, + "content": "Specifically, our deformation MLP \\( T_{\\omega} \\) maps an input ray \\( r = (o,d) \\) to canonical space ray \\( r' = (o',d') \\):" + }, + { + "type": "equation", + "bbox": [ + 0.625, + 0.357, + 0.892, + 0.375 + ], + "angle": 0, + "content": "\\[\n\\left(o ^ {\\prime}, d ^ {\\prime}\\right) = T _ {\\omega} (o, d, t). \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.385, + 0.892, + 0.46 + ], + "angle": 0, + "content": "Unlike the pointwise deformation MLP proposed in Nerfies [27], which bends rays by offsetting their points independently, our MLP outputs rays explicitly, hence no ray bending occurs. Furthermore, after obtaining \\( r' \\), we encode it by sampling and concatenating \\( K \\) points along it." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.461, + 0.892, + 0.491 + ], + "angle": 0, + "content": "Our hyperspace \\(\\mathrm{MLP}H_{\\psi}\\) is similar to \\(T_{\\omega}\\), except it outputs a hyperspace representation \\(w\\):" + }, + { + "type": "equation", + "bbox": [ + 0.638, + 0.502, + 0.891, + 0.518 + ], + "angle": 0, + "content": "\\[\nw = H _ {\\psi} (o, d, t). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.53, + 0.892, + 0.574 + ], + "angle": 0, + "content": "In contrast to HyperNeRF [28], which predicts a hyperspace code \\( w \\) for each 3D point, we use rays and compute a single \\( w \\) for each ray." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.575, + 0.892, + 0.604 + ], + "angle": 0, + "content": "Both MLPs further take the index \\( t \\) as input to encode temporal deformations." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.606, + 0.892, + 0.664 + ], + "angle": 0, + "content": "Once the \\(K\\) points and \\(w\\) are obtained, we concatenate them and feed the result into our LFN \\(R_{\\pi}\\), which is a deep residual color MLP regressor. Overall, we can collect the model parameters as \\(\\phi = [\\omega, \\psi, \\pi]\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.665, + 0.892, + 0.695 + ], + "angle": 0, + "content": "Note that without our two MLPs \\( T_{\\omega} \\) and \\( H_{\\psi} \\), our DyLiN falls back to the vanilla LFN." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.714, + 0.692, + 0.729 + ], + "angle": 0, + "content": "3.1.2 Training Procedure" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.737, + 0.82, + 0.752 + ], + "angle": 0, + "content": "Our training procedure is composed of 3 phases." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.753, + 0.892, + 0.828 + ], + "angle": 0, + "content": "First, we pretrain a dynamic NeRF model \\( F_{\\theta} \\) (e.g., D-NeRF [29] or HyperNeRF [28]) by randomly sampling time \\( t \\) and input ray \\( r \\), and minimizing the Mean Squared Error (MSE) against the corresponding RGB color of monocular target video \\( I \\):" + }, + { + "type": "equation", + "bbox": [ + 0.548, + 0.838, + 0.892, + 0.861 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\theta} \\mathbb {E} _ {t, r = (o, d)} \\left[ \\| F _ {\\theta} (o, d, t) - I (o, d, t) \\| _ {2} ^ {2} \\right]. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Recall, that \\(F_{\\theta}\\) is slow, as it performs numerical integration across the ray \\(r = (o,d)\\)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12399" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.168 + ], + "angle": 0, + "content": "Second, we employ the newly obtained \\(F_{\\theta^{*}}\\) as the teacher model for our DyLiN student model \\(G_{\\phi}\\) via KD. Specifically, we minimize the MSE loss against the respective pseudo ground truth ray color generated by \\(F_{\\theta^{*}}\\) across \\(S\\) ray samples:" + }, + { + "type": "equation", + "bbox": [ + 0.116, + 0.176, + 0.469, + 0.2 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\phi} \\mathbb {E} _ {t, r = (o, d)} \\left[ \\| G _ {\\phi} (o, d, t) - F _ {\\theta^ {*}} (o, d, t) \\| _ {2} ^ {2} \\right], \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.209, + 0.469, + 0.253 + ], + "angle": 0, + "content": "yielding \\( G_{\\tilde{\\phi}} \\). Note how this is considerably different from R2L [36], which uses a static LFN that is distilled from a static NeRF." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.255, + 0.469, + 0.286 + ], + "angle": 0, + "content": "Finally, we initialize our student model \\( G_{\\phi} \\) with parameters \\( \\tilde{\\phi} \\) and fine-tune it using the original real video data:" + }, + { + "type": "equation", + "bbox": [ + 0.106, + 0.295, + 0.469, + 0.322 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\phi , \\phi_ {0} = \\tilde {\\phi}} \\mathbb {E} _ {t, r = (o, d)} \\left[ \\| G _ {\\phi} (o, d, t) - I (o, d, t) \\| _ {2} ^ {2} \\right], \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.331, + 0.17, + 0.345 + ], + "angle": 0, + "content": "obtaining \\(\\phi^{*}\\)" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.353, + 0.187, + 0.369 + ], + "angle": 0, + "content": "3.2. CoDyLiN" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.377, + 0.284, + 0.391 + ], + "angle": 0, + "content": "3.2.1 Network Architecture" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.401, + 0.469, + 0.462 + ], + "angle": 0, + "content": "We further demonstrate that our DyLiN architecture from Sec. 3.1.1 can be extended to the controllable scenario using attribute inputs with hyperspace MLPs and attention masks. Our proposed CoDyLiN network \\( Q_{\\tau} \\) is depicted in Fig. 3." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.473, + 0.462, + 0.638 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.085, + 0.649, + 0.221, + 0.704 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.231, + 0.651, + 0.343, + 0.704 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.353, + 0.655, + 0.47, + 0.695 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.716, + 0.47, + 0.856 + ], + "angle": 0, + "content": "Figure 3. Schematic diagram of our proposed CoDyLiN architecture. We augment our DyLiN (blue, green, red) by introducing scalar attribute inputs \\(\\alpha_{i} \\in [-1,1]\\), \\(i = 1,\\dots,n\\) and lifting them to their respective hyperspace codes \\(w_{i}\\) (orange,..., pink MLPs). Next, \\(M_{i}\\) disentangles \\(w_{i}\\) from \\(w_{j}\\), \\(j \\neq i\\) by masking it into \\(w_{i}'\\) (orange,..., pink boxes and bottom insets). We concatenate the sampled points \\(x_{k}\\), \\(k = 1,\\ldots,K\\) with the \\(w_{i}'\\), \\(i = 1,\\ldots,n\\) and predict the RGB color corresponding to the inputs (red). Arrows from \\((o',d')\\) and \\(w_{0}\\) to \\(M_{i}\\) are omitted from the top figure for simplicity. Compare this with Fig. 2." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.902 + ], + "angle": 0, + "content": "Specifically, we start from DyLiN \\( G_{\\phi} \\) and add scalar inputs \\( \\alpha_{i} \\in [-1,1] \\), \\( i = 1, \\dots, n \\) next to \\( o, d, t \\). Intuitively," + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.891, + 0.135 + ], + "angle": 0, + "content": "these are given strength values for specific local attributes, which can be interpolated continuously. \\( n \\) is the total number of attributes." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.137, + 0.891, + 0.168 + ], + "angle": 0, + "content": "Each \\(\\alpha_{i}\\) is then processed independently with its own hyperspace MLP \\(H_{i,\\psi_i}\\) to yield the hyperspace code \\(w_{i}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.628, + 0.174, + 0.891, + 0.19 + ], + "angle": 0, + "content": "\\[\nw _ {i} = H _ {i, \\psi_ {i}} (o, d, t). \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.196, + 0.891, + 0.24 + ], + "angle": 0, + "content": "Next, we include mask MLP regressors \\( M_{i,\\rho_i} \\) to generate scalar attention masks \\( \\hat{m}_i \\in [0,1] \\) for each \\( w_i \\) (including \\( w_0 = w \\)):" + }, + { + "type": "equation", + "bbox": [ + 0.594, + 0.246, + 0.762, + 0.263 + ], + "angle": 0, + "content": "\\[\n\\hat {m} _ {i} = M _ {i, \\rho_ {i}} (w _ {i}, w, o, d),\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.592, + 0.266, + 0.891, + 0.305 + ], + "angle": 0, + "content": "\\[\n\\hat {m} _ {0} = 1 - \\sum_ {i = 1} ^ {n} \\hat {m} _ {i}, \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.598, + 0.309, + 0.798, + 0.324 + ], + "angle": 0, + "content": "\\[\nw _ {i} ^ {\\prime} = \\hat {m} _ {i} \\cdot w _ {i}, \\quad i = 0, \\dots , n,\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.33, + 0.891, + 0.375 + ], + "angle": 0, + "content": "This helps the architecture to spatially disentangle (i.e., localize) the effects of attributes \\(\\alpha_{i}\\), while \\(\\hat{m}_0\\) can be understood as the space not affected by any attributes." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.376, + 0.891, + 0.451 + ], + "angle": 0, + "content": "Finally, we sample \\(K\\) points on the ray similarly to Sec. 3.1.1, concatenate those with the \\(w_{i}^{\\prime}\\) vectors, and process the result further with LFN \\(R_{\\pi}\\). Again, we can use a shorthand for the parameters: \\(\\tau = [\\omega, \\psi, \\psi_1, \\ldots, \\psi_n, \\rho_1, \\ldots, \\rho_n, \\pi]\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.452, + 0.891, + 0.511 + ], + "angle": 0, + "content": "Observe that without our MLPs \\(H_{i,\\psi_i}\\), \\(M_{i,\\rho_i}\\), \\(i = 1, \\dots, n\\), our CoDyLiN reverts to our simpler DyLiN. Different from CoNeRF [13], we process rays instead of points, and use the \\(\\alpha_i\\) as inputs instead of targets." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.529, + 0.691, + 0.543 + ], + "angle": 0, + "content": "3.2.2 Training Procedure" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.552, + 0.891, + 0.582 + ], + "angle": 0, + "content": "Akin to Sec. 3.1.2, we split training into pretraining and distillation steps, but omit fine-tuning." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.583, + 0.891, + 0.657 + ], + "angle": 0, + "content": "First, we pretrain a CoNeRF model \\( E_{\\nu} \\) [13] by randomly sampling \\( (t,r,i) \\), against 3 ground truths: ray color, attribute values \\( \\alpha_{i} \\) and 2D per-attribute masks \\( m_{2D,i} \\). This yields us \\( E_{\\nu^{*}} \\). For brevity, we omit the details of this step, and kindly forward the reader to Section 3 in [13]." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.658, + 0.891, + 0.718 + ], + "angle": 0, + "content": "Second, we distill from our teacher CoNeRF model \\(E_{\\nu^{*}}\\) into our student CoDyLiN \\(Q_{\\tau}\\) by randomly sampling \\(t,r,\\alpha_{1},\\ldots ,\\alpha_{n}\\), and minimizing the MSE against 2 pseudo ground truths, i.e., ray colors and 2D masks \\(\\bar{m}_{2D,i}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.518, + 0.728, + 0.891, + 0.817 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\min _ {\\tau} \\mathbb {E} _ {t, r = (o, d)} \\left[ \\| Q _ {\\tau} (o, d, t, \\alpha_ {1: n}) - \\bar {E} _ {\\nu^ {*}} (o, d, t, \\alpha_ {1: n}) \\| _ {2} ^ {2} \\right. \\\\ \\left. + \\lambda_ {m} \\cdot \\sum_ {i = 0} ^ {n} \\| \\hat {m} _ {i} (o, d, t, \\alpha_ {i}) - \\bar {m} _ {2 D} (o, d, t, \\alpha_ {1: n}) _ {i} \\| _ {2} ^ {2} \\right], \\tag {8} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.825, + 0.891, + 0.87 + ], + "angle": 0, + "content": "where \\(\\bar{E}_{\\nu}\\) is identical to \\(E_{\\nu}\\) except for taking \\(\\alpha_{1:n} = [\\alpha_1,\\dots ,\\alpha_n]\\) as input and outputting the masks \\(\\bar{m}_{2D,i},i = 0,\\ldots ,n\\) . We denote the result of the optimization as \\(Q_{\\tau^{*}}\\)" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.891, + 0.901 + ], + "angle": 0, + "content": "We highlight that our teacher and student models are both controllable in this setup." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12400" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.077, + 0.09, + 0.27, + 0.108 + ], + "angle": 0, + "content": "4. Experimental Setup" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.116, + 0.181, + 0.13 + ], + "angle": 0, + "content": "4.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.14, + 0.47, + 0.184 + ], + "angle": 0, + "content": "To test our hypotheses, we performed experiments on three types of dynamic scenes: synthetic, real and real controllable." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.185, + 0.469, + 0.305 + ], + "angle": 0, + "content": "Synthetic Scenes. We utilized the synthetic \\(360^{\\circ}\\) dynamic dataset introduced by [29], which contains 8 animated objects with complicated geometry and realistic non-Lambertian materials. Each dynamic scene consists of 50 to 200 training images and 20 testing images. We used \\(400 \\times 400\\) image resolution. We applied D-NeRF [29] as our teacher model with the publicly available pretrained weights." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.306, + 0.469, + 0.44 + ], + "angle": 0, + "content": "Real Scenes. We collected real dynamic data from 2 sources. First, we utilized 5 topologically varying scenes provided by [28] (Broom, 3D Printer, Chicken, Americano and Banana), which were captured by a rig encompassing a pole with two Google Pixel 3 phones rigidly attached roughly \\(16\\mathrm{cm}\\) apart. Second, we collected human facial videos using an iPhone 13 Pro camera. We rendered both sets at \\(960 \\times 540\\) image resolution. We pretrained a HyperNeRF [28] teacher model from scratch for each scene." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.442, + 0.469, + 0.547 + ], + "angle": 0, + "content": "Real Controllable Scenes. We borrowed 2 real controllable scenes from [13] (closing/opening eyes/mouth, and transformer), which are captured either with a Google Pixel 3a or an Apple iPhone 13 Pro, and contain annotations over various attributes. We applied image resolution of \\(480 \\times 270\\) pixels. We pretrained a CoNeRF [13] teacher model from scratch per scene." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.559, + 0.176, + 0.575 + ], + "angle": 0, + "content": "4.2. Settings" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.583, + 0.469, + 0.613 + ], + "angle": 0, + "content": "Throughout our experiments, we use the settings listed below, many of which follow [36]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.614, + 0.469, + 0.704 + ], + "angle": 0, + "content": "In order to retain efficiency, we define \\( T_{\\omega} \\) and \\( H_{\\psi} \\) to be small MLPs, with \\( T_{\\omega} \\) consisting of 7 layers of 128 units with \\( r' \\in \\mathbb{R}^6 \\), and \\( H_{\\psi} \\) having 6 layers of 64 units with \\( w \\in \\mathbb{R}^8 \\). Then, we use \\( K = 16 \\) sampled points to represent rays, where sampling is done randomly during training and evenly spaced during inference." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.469, + 0.765 + ], + "angle": 0, + "content": "Contrary to \\( T_{\\omega} \\) and \\( H_{\\psi} \\), our LFN \\( R_{\\pi} \\) is a very deep residual color MLP regressor, containing 88 layers with 256 units per layer, in order to have enough capacity to learn the video generation process." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.766, + 0.469, + 0.825 + ], + "angle": 0, + "content": "We generate rays within Eqs. (3) to (5) and (8) by sampling ray origins \\(o = (x_o, y_o, z_o)\\) and normalized directions \\(d = (x_d, y_d, z_d)\\) randomly from the uniform distribution \\(U\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.102, + 0.839, + 0.469, + 0.856 + ], + "angle": 0, + "content": "\\[\nx _ {o} \\sim U \\left(x _ {o} ^ {\\min }, x _ {o} ^ {\\max }\\right), \\quad x _ {d} \\sim U \\left(x _ {d} ^ {\\min }, x _ {d} ^ {\\max }\\right), \\tag {9}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.104, + 0.86, + 0.469, + 0.877 + ], + "angle": 0, + "content": "\\[\ny _ {o} \\sim U \\left(y _ {o} ^ {\\min }, y _ {o} ^ {\\max }\\right), \\quad y _ {d} \\sim U \\left(y _ {d} ^ {\\min }, y _ {d} ^ {\\max }\\right), \\tag {10}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.106, + 0.881, + 0.469, + 0.898 + ], + "angle": 0, + "content": "\\[\nz _ {o} \\sim U \\left(z _ {o} ^ {\\min }, z _ {o} ^ {\\max }\\right), \\quad z _ {d} \\sim U \\left(z _ {d} ^ {\\min }, z _ {d} ^ {\\max }\\right), \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.167 + ], + "angle": 0, + "content": "where the min, max bounds of the 6 intervals are inferred from the original training video. In addition to uniform sampling, we also apply the hard example mining strategy suggested in [36] to focus on fine-grained details. We used \\( S = 10,000 \\) training samples during KD in (4)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.168, + 0.892, + 0.197 + ], + "angle": 0, + "content": "Subsequently, we also randomly sample time step \\(t\\) uniformly from the unit interval: \\(t \\sim U(0,1)\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.198, + 0.892, + 0.258 + ], + "angle": 0, + "content": "Optionally, for our CoDyLiN experiments, we define each \\(H_{i,\\psi_i}\\) to be a small MLP having 5 layers of 128 units with \\(w_{i} \\in \\mathbb{R}^{8}\\). During training, we uniformly sample attributes within \\([-1,1]\\): \\(\\alpha_{i} \\sim U(-1,1)\\), and let \\(\\lambda_{m} = 0.1\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.259, + 0.892, + 0.287 + ], + "angle": 0, + "content": "During training, we used Adam [14] with learning rate \\(5 \\times 10^{-4}\\) and batch size 4,096." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.289, + 0.892, + 0.317 + ], + "angle": 0, + "content": "We performed all experiments on single NVIDIA A100 GPUs." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.328, + 0.662, + 0.343 + ], + "angle": 0, + "content": "4.3. Baseline Models" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.352, + 0.892, + 0.428 + ], + "angle": 0, + "content": "For testing our methods, we compared quality and speed against several baseline models, including NeRF [23], NV [19], NSFF [16], Nerfies [27], HyperNeRF [28], two variants of TiNeuVox [8], DirectVoxGo [33], Plenoxels [9], T-NeRF and D-NeRF [29], as well as CoNeRF [13]." + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.439, + 0.88, + 0.527 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.688, + 0.53, + 0.705, + 0.541 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.542, + 0.88, + 0.663 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.688, + 0.667, + 0.705, + 0.678 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.69, + 0.892, + 0.733 + ], + "angle": 0, + "content": "Figure 4. Our two ablated baseline models, omitting components of our DyLiN. (a) Without our two proposed MLPs. (b) Pointwise deformation MLP only, predicting offsets jointly." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In addition, we performed an ablation study by comparing against 2 simplified versions of our DyLiN architecture. First, we omitted both of our deformation and hyperspace MLPs and simply concatenated the time step \\(t\\) to the sampled ray points (essentially resulting in a dynamic R2L). This method is illustrated in Fig. 4a. Second, we employed a pointwise deformation MLP (5 layers of 256 units) inspired by [29], which deforms points along a ray by predicting their offsets jointly, i.e., it can bend rays. This is contrast to our DyLiN, which deforms rays explicitly without" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "12401" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.473, + 0.213 + ], + "angle": 0, + "content": "bending and also applies a hyperspace MLP. This scheme is depicted in Fig. 4b. In both baselines, the deep residual color MLP regressors were kept intact. Next, we also tested the effects of our fine-tuning procedure from (5) by training all of our models both with and without it. Lastly, we assessed the dependences on the number of sampled points along rays \\( K \\) and on the number of training samples \\( S \\) during KD in (4)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.223, + 0.263, + 0.239 + ], + "angle": 0, + "content": "4.4. Evaluation Metrics" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.247, + 0.47, + 0.413 + ], + "angle": 0, + "content": "For quantitatively evaluating the quality of generated images, we calculated the Peak Signal-to-Noise Ratio (PSNR) [12] in decibels (dB), the Structural Similarity Index (SSIM) [25,40], the Multi-Scale SSIM (MS-SSIM) [41] and the Learned Perceptual Image Patch Similarity (LPIPS) [44] metrics. Intuitively, PSNR is a pixelwise score, while SSIM and MS-SSIM also take pixel correlations and multiple scales into account, respectively, yet all of these tend to favor blurred images. LPIPS compares deep neural representations of images and is much closer to human perception, promoting semantically better and sharper images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.414, + 0.47, + 0.475 + ], + "angle": 0, + "content": "Furthermore, for testing space and time complexity, we computed the storage size of parameters in megabytes (MB) and measured the wall-clock time in milliseconds (ms) while rendering the synthetic Lego scene with each model." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.489, + 0.165, + 0.505 + ], + "angle": 0, + "content": "5. Results" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.514, + 0.272, + 0.53 + ], + "angle": 0, + "content": "5.1. Quantitative Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.538, + 0.47, + 0.794 + ], + "angle": 0, + "content": "Tab. 1 and Tab. 2 contain our quantitative results for reconstruction quality on synthetic and real dynamic scenes, accordingly. We found that among prior works, TiNeuVox-B performed the best on synthetic scenes with respect to each metric. On real scenes, however, NSFF took the lead. Despite having strong metrics, NSFF is qualitatively poor and slow. Surprisingly, during ablation, even our most basic model (DyLiN without the two MLPs from Fig. 4a) could generate perceptually better looking images than TiNeuVox-B, thanks to the increased training dataset size via KD. Incorporating the MLPs \\( T_{\\omega} \\) and \\( H_{\\psi} \\) into the model each improved results slightly. Interestingly, fine-tuning on real data as in (5) gave a substantial boost. In addition, our relative PSNR improvement over the teacher model (Tab. 1=+1.93 dB, up to +3.16 dB per scene; Tab. 2=+2.7 dB, up to +13.14 dB) is better than that of R2L [36] (+1.4 dB, up to +2.8 dB)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Tab. 3 shows quantitative results for space and time complexity on the synthetic Lego scene. We found that there is a trade-off between the two metrics, as prior works are typically optimized for just one of those. In contrast, all of our proposed DyLiN variants settle at the golden mean between the two extremes. When compared to the strongest baseline TiNeuVox-B, our method requires 3 times as much" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.089, + 0.894, + 0.147 + ], + "angle": 0, + "content": "Table 1. Quantitative results on synthetic dynamic scenes. Notations: Multi-Layer Perceptron (MLP), PD (pointwise deformation), FT (fine-tuning). We utilized D-NeRF as the teacher model for our DyLiNs. The winning numbers are highlighted in bold." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.156, + 0.894, + 0.349 + ], + "angle": 0, + "content": "
MethodPSNR↑SSIM↑LPIPS↓
NeRF [23]19.000.87000.1825
DirectVoxGo [33]18.610.85380.1688
Plenoxels [9]20.240.86880.1600
T-NeRF [29]29.510.95130.0788
D-NeRF [29]30.500.95250.0663
TiNeuVox-S [8]30.750.95500.0663
TiNeuVox-B [8]32.670.97250.0425
DyLiN, w/o two MLPs, w/o FT (ours)31.160.99310.0281
DyLiN, w/o two MLPs (ours)32.070.99370.0196
DyLiN, PD MLP only, w/o FT (ours)31.260.99320.0279
DyLiN, PD MLP only (ours)31.240.99400.0189
DyLiN, w/o FT (ours)31.370.99330.0275
DyLiN (ours)32.430.99430.0184
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.366, + 0.894, + 0.423 + ], + "angle": 0, + "content": "Table 2. Quantitative results on real dynamic scenes. Notations: Multi-Layer Perceptron (MLP), PD (pointwise deformation), FT (fine-tuning). We utilized HyperNeRF as the teacher model for our DyLiNs. The winning numbers are highlighted in bold." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.433, + 0.892, + 0.644 + ], + "angle": 0, + "content": "
MethodPSNR↑MS-SSIM↑
NeRF [23]20.10.745
NV [19]16.90.571
NSFF [16]26.30.916
Nerfies [27]22.20.803
HyperNeRF [28]22.40.814
TiNeuVox-S [8]23.40.813
TiNeuVox-B [8]24.30.837
DyLiN, w/o two MLPs, w/o FT (ours)23.80.882
DyLiN, w/o two MLPs (ours)24.20.894
DyLiN, PD MLP only, w/o FT (ours)23.90.885
DyLiN, PD MLP only (ours)24.60.903
DyLiN, w/o FT (ours)24.00.886
DyLiN (ours)25.10.910
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.673, + 0.892, + 0.719 + ], + "angle": 0, + "content": "storage but is nearly 2 orders of magnitude faster. Plenoxels and NV, the only methods that require less computation than ours, perform much worse in quality." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Fig. 5 reports quantitative ablation results for dependencies on the number of sampled points per ray \\( K \\) and on the number of training samples during KD \\( S \\), performed on the synthetic Standup scene. For dependence on \\( K \\) (Fig. 5a), we found that there were no significant differences between test set PNSR scores for \\( K \\in \\{4,8,16,32\\} \\), while we encountered overfitting for \\( K \\in \\{64,128\\} \\). This justified our choice of \\( K = 16 \\) for the rest of our experiments. Regarding the effect of \\( S \\) (Fig. 5b), overfitting occurred for smaller sample sizes including \\( S \\in \\{100;500;1,000;5,000\\} \\). The test and training set PSNR scores were much closer for \\( S = 10,000 \\), validating our general setting." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "12402" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.472, + 0.132 + ], + "angle": 0, + "content": "Table 3. Quantitative results for space and time complexity on the synthetic Lego scene. Notations: Multi-Layer Perceptron (MLP), PD (pointwise deformation), FT (fine-tuning)." + }, + { + "type": "table", + "bbox": [ + 0.078, + 0.143, + 0.472, + 0.396 + ], + "angle": 0, + "content": "
MethodStorage (MB)Wall-clock time (ms)
NeRF [23]5.002,950.0
DirectVoxGo [33]205.001,090.0
Plenoxels [9]717.0050.0
NV [19]439.0074.9
D-NeRF [29]4.008,150.0
NSFF [16]14.175,450.0
HyperNeRF [28]15.362,900.0
TiNeuVox-S [8]23.703,280.0
TiNeuVox-B [8]23.706,920.0
DyLiN, w/o two MLPs, w/o FT (ours)68.04115.4
DyLiN, w/o two MLPs (ours)68.04115.4
DyLiN, PD MLP only, w/o FT (ours)72.60115.7
DyLiN, PD MLP only (ours)72.60115.7
DyLiN, w/o FT (ours)70.11116.0
DyLiN (ours)70.11116.0
" + }, + { + "type": "image", + "bbox": [ + 0.096, + 0.415, + 0.449, + 0.569 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.266, + 0.574, + 0.283, + 0.584 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.095, + 0.587, + 0.449, + 0.74 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.265, + 0.745, + 0.283, + 0.756 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.769, + 0.47, + 0.825 + ], + "angle": 0, + "content": "Figure 5. Quantitative results for ablation on the synthetic Standup scene. (a) Dependence on the number of sampled points \\( K \\) across ray \\( r' \\). (b) Dependence on the number of training samples \\( S \\) during Knowledge Distillation (KD)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Our controllable numerical results are collected in Tab. 4. In short, our CoDyLiN was able to considerably outperform CoNeRF with respect to MS-SSIM and speed." + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.089, + 0.892, + 0.132 + ], + "angle": 0, + "content": "Table 4. Quantitative results on real controllable scenes. We utilized CoNeRF as the teacher model for our CoDyLiN. The winning numbers are highlighted in bold." + }, + { + "type": "table", + "bbox": [ + 0.501, + 0.143, + 0.892, + 0.204 + ], + "angle": 0, + "content": "
MethodEyes/MouthTransformer
PSNR†MS-SSIM†Wall-clock time (ms)PSNR†MS-SSIM†Wall-clock time (ms)
CoNeRF [13]21.46580.74586230.023.03190.88784360.0
CoDyLiN (ours)21.46550.9510116.323.58820.9779116.0
" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.23, + 0.684, + 0.246 + ], + "angle": 0, + "content": "5.2. Qualitative Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.254, + 0.892, + 0.375 + ], + "angle": 0, + "content": "Fig. 6 and Fig. 7 depict qualitative results for reconstruction quality on synthetic and real dynamic scenes, respectively. Both show that our full DyLiN model generated the sharpest, most detailed images, as it was able to capture cloth wrinkles (Fig. 6j) and the eye of the chicken (Fig. 7e). The competing methods tended to oversmooth these features. We also ablated the effect of omitting fine-tuning (Fig. 6i, Fig. 7d), and results declined considerably." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.375, + 0.892, + 0.481 + ], + "angle": 0, + "content": "For the sake of completeness, Fig. 8 illustrates qualitative ablation results for our model components on real dynamic scenes. We found that sequentially adding our two proposed MLPs \\( T_{\\omega} \\) and \\( H_{\\psi} \\) improves the reconstruction, e.g., the gum between the teeth (Fig. 8e) and the fingers (Fig. 8j) become more and more apparent. Without the MLPs, these parts were heavily blurred (Fig. 8c, Fig. 8h)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.482, + 0.892, + 0.513 + ], + "angle": 0, + "content": "We kindly ask readers to refer to the supplementary material for CoDyLiN's qualitative results." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.527, + 0.619, + 0.543 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.553, + 0.892, + 0.704 + ], + "angle": 0, + "content": "We proposed two architectures for extending LFNs to dynamic scenes. Specifically, we introduced DyLiN, which models ray deformations without bending and lifts whole rays into a hyperspace, and CoDyLiN, which allows for controllable attribute inputs. We trained both techniques via knowledge distillation from various dynamic NeRF teacher models. We found that DyLiN produces state-of-the-art quality even without ray bending and CoDyLiN outperforms its teacher model, while both are nearly 2 orders of magnitude faster than their strongest baselines." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Our methods do not come without limitations, however. Most importantly, they focus on speeding up inference, as they require pretrained teacher models, which can be expensive to obtain. In some experiments, our solutions were outperformed in terms of the PSNR score. Using the winners as teacher models could improve performance. Additionally, distillation from multiple teacher models or joint training of the teacher and student models are also yet to be explored. Moreover, we currently represent rays implicitly by sampling \\( K \\) points along them, but increasing this number can lead to overfitting. An explicit ray representation may be more effective. Finally, voxelizing and quantizing our models could improve efficiency." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12403" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.138, + 0.107, + 0.201, + 0.171 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.153, + 0.198, + 0.187, + 0.21 + ], + "angle": 0, + "content": "Hook" + }, + { + "type": "image", + "bbox": [ + 0.255, + 0.112, + 0.362, + 0.196 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.254, + 0.199, + 0.345, + 0.21 + ], + "angle": 0, + "content": "(a) Ground Truth" + }, + { + "type": "image", + "bbox": [ + 0.38, + 0.112, + 0.487, + 0.197 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.379, + 0.199, + 0.47, + 0.211 + ], + "angle": 0, + "content": "(b) D-NeRF [29]" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.112, + 0.613, + 0.197 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.505, + 0.199, + 0.596, + 0.211 + ], + "angle": 0, + "content": "(c) TiNeuVox [8]" + }, + { + "type": "image", + "bbox": [ + 0.632, + 0.112, + 0.738, + 0.197 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.648, + 0.199, + 0.702, + 0.21 + ], + "angle": 0, + "content": "(d) Ours-1" + }, + { + "type": "image", + "bbox": [ + 0.757, + 0.112, + 0.865, + 0.197 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.773, + 0.199, + 0.829, + 0.21 + ], + "angle": 0, + "content": "(e) Ours-2" + }, + { + "type": "image", + "bbox": [ + 0.131, + 0.222, + 0.212, + 0.306 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.129, + 0.321, + 0.215, + 0.333 + ], + "angle": 0, + "content": "Jumping Jacks" + }, + { + "type": "image", + "bbox": [ + 0.24, + 0.236, + 0.361, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.253, + 0.322, + 0.342, + 0.333 + ], + "angle": 0, + "content": "(f) Ground Truth" + }, + { + "type": "image", + "bbox": [ + 0.366, + 0.236, + 0.486, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.378, + 0.322, + 0.468, + 0.334 + ], + "angle": 0, + "content": "(g) D-NeRF [29]" + }, + { + "type": "image", + "bbox": [ + 0.491, + 0.234, + 0.611, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.502, + 0.322, + 0.594, + 0.334 + ], + "angle": 0, + "content": "(h) TiNeuVox [8]" + }, + { + "type": "image", + "bbox": [ + 0.616, + 0.236, + 0.736, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.647, + 0.322, + 0.699, + 0.333 + ], + "angle": 0, + "content": "(i) Ours-1" + }, + { + "type": "image", + "bbox": [ + 0.741, + 0.236, + 0.862, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.772, + 0.322, + 0.826, + 0.333 + ], + "angle": 0, + "content": "(j) Ours-2" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.345, + 0.894, + 0.374 + ], + "angle": 0, + "content": "Figure 6. Qualitative results on synthetic dynamic scenes. We compare our DyLiN (Ours-1, Ours-2) with the ground truth, the D-NeRF teacher model and TiNeuVox. Ours-1 and Ours-2 were trained without and with fine-tuning on the original data, respectively." + }, + { + "type": "image", + "bbox": [ + 0.14, + 0.387, + 0.201, + 0.464 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.146, + 0.465, + 0.194, + 0.476 + ], + "angle": 0, + "content": "Chicken" + }, + { + "type": "image", + "bbox": [ + 0.237, + 0.387, + 0.361, + 0.464 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.254, + 0.465, + 0.345, + 0.476 + ], + "angle": 0, + "content": "(a) Ground Truth" + }, + { + "type": "image", + "bbox": [ + 0.363, + 0.387, + 0.487, + 0.463 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.371, + 0.465, + 0.479, + 0.477 + ], + "angle": 0, + "content": "(b) HyperNeRF [28]" + }, + { + "type": "image", + "bbox": [ + 0.488, + 0.387, + 0.613, + 0.463 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.505, + 0.465, + 0.596, + 0.477 + ], + "angle": 0, + "content": "(c) TiNeuVox [8]" + }, + { + "type": "image", + "bbox": [ + 0.615, + 0.387, + 0.736, + 0.463 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.648, + 0.465, + 0.703, + 0.476 + ], + "angle": 0, + "content": "(d) Ours-1" + }, + { + "type": "image", + "bbox": [ + 0.738, + 0.387, + 0.862, + 0.463 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.773, + 0.465, + 0.829, + 0.476 + ], + "angle": 0, + "content": "(e) Ours-2" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.489, + 0.893, + 0.518 + ], + "angle": 0, + "content": "Figure 7. Qualitative results on a real dynamic scene. We compare our DyLiN (Ours-1, Ours-2) with the ground truth, the HyperNeRF teacher model and TiNeuVox. Ours-1 and Ours-2 were trained without and with fine-tuning on the original data, respectively." + }, + { + "type": "image", + "bbox": [ + 0.139, + 0.532, + 0.201, + 0.613 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.138, + 0.614, + 0.201, + 0.625 + ], + "angle": 0, + "content": "Expression" + }, + { + "type": "image", + "bbox": [ + 0.138, + 0.626, + 0.207, + 0.717 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.136, + 0.719, + 0.208, + 0.73 + ], + "angle": 0, + "content": "Peel Banana" + }, + { + "type": "image", + "bbox": [ + 0.237, + 0.532, + 0.361, + 0.612 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.254, + 0.614, + 0.345, + 0.624 + ], + "angle": 0, + "content": "(a) Ground Truth" + }, + { + "type": "image", + "bbox": [ + 0.363, + 0.532, + 0.487, + 0.612 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.37, + 0.614, + 0.479, + 0.625 + ], + "angle": 0, + "content": "(b) HyperNeRF [28]" + }, + { + "type": "image", + "bbox": [ + 0.488, + 0.532, + 0.611, + 0.612 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.523, + 0.614, + 0.577, + 0.624 + ], + "angle": 0, + "content": "(c) Ours-1" + }, + { + "type": "image", + "bbox": [ + 0.614, + 0.532, + 0.736, + 0.612 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.648, + 0.614, + 0.704, + 0.624 + ], + "angle": 0, + "content": "(d) Ours-2" + }, + { + "type": "image", + "bbox": [ + 0.738, + 0.532, + 0.863, + 0.612 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.773, + 0.614, + 0.829, + 0.624 + ], + "angle": 0, + "content": "(e) Ours-3" + }, + { + "type": "image", + "bbox": [ + 0.236, + 0.626, + 0.36, + 0.717 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.253, + 0.719, + 0.342, + 0.73 + ], + "angle": 0, + "content": "(f) Ground Truth" + }, + { + "type": "image", + "bbox": [ + 0.363, + 0.626, + 0.485, + 0.717 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.368, + 0.719, + 0.477, + 0.731 + ], + "angle": 0, + "content": "(g) HyperNeRF [28]" + }, + { + "type": "image", + "bbox": [ + 0.487, + 0.626, + 0.609, + 0.717 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.52, + 0.719, + 0.576, + 0.73 + ], + "angle": 0, + "content": "(h) Ours-1" + }, + { + "type": "image", + "bbox": [ + 0.614, + 0.626, + 0.736, + 0.717 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.647, + 0.719, + 0.7, + 0.73 + ], + "angle": 0, + "content": "(i) Ours-2" + }, + { + "type": "image", + "bbox": [ + 0.738, + 0.626, + 0.86, + 0.717 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.773, + 0.719, + 0.826, + 0.73 + ], + "angle": 0, + "content": "(j) Ours-3" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.744, + 0.894, + 0.786 + ], + "angle": 0, + "content": "Figure 8. Qualitative results for ablation on real dynamic scenes. We compare our DyLiN (Ours-1, Ours-2, Ours-3) with the ground truth and the HyperNeRF teacher model. Ours-1 was trained without our two MLPs. Ours-2 was trained with pointwise deformation MLP only. Ours-3 is our full model with both of our proposed two MLPs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.812, + 0.469, + 0.857 + ], + "angle": 0, + "content": "Our results are encouraging steps towards achieving real-time volumetric rendering and animation, and we hope that our work will contribute to the progress in these areas." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.811, + 0.667, + 0.828 + ], + "angle": 0, + "content": "Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "This research was supported partially by Fujitsu. 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IEEE/CVF CVPR, pages 586-595, 2018. 6" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.47, + 0.856 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "12406" + } + ] +] \ No newline at end of file diff --git a/2023/DyLiN_ Making Light Field Networks Dynamic/52436ab0-0f6f-44ce-bee8-32ea0aeba3bb_origin.pdf b/2023/DyLiN_ Making Light Field Networks Dynamic/52436ab0-0f6f-44ce-bee8-32ea0aeba3bb_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..74260350df111956d6466e4c827ebfceaef7a473 --- /dev/null +++ b/2023/DyLiN_ Making Light Field Networks Dynamic/52436ab0-0f6f-44ce-bee8-32ea0aeba3bb_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:8efa457252c380b99c44bce54cfdaebfff0bdd68e9c098a2e7d7fdf9cdb2a73f +size 6769879 diff --git a/2023/DyLiN_ Making Light Field Networks Dynamic/full.md b/2023/DyLiN_ Making Light Field Networks Dynamic/full.md new file mode 100644 index 0000000000000000000000000000000000000000..90fc1541c32f222060a6bb55b6f0b9330a087eeb --- /dev/null +++ b/2023/DyLiN_ Making Light Field Networks Dynamic/full.md @@ -0,0 +1,447 @@ +# DyLiN: Making Light Field Networks Dynamic + +Heng Yu $^{1}$ Joel Julin $^{1}$ Zoltán Á. Milacski $^{1}$ Koichiro Niinuma $^{2}$ László A. Jeni $^{1}$ + +$^{1}$ Robotics Institute, Carnegie Mellon University $^{2}$ Fujitsu Research of America + +{hengyu, jjulin, zmilacsk}@andrew.cmu.edu kniinuma@fujitsu.com laszlojeni@cmu.edu + +![](images/77421cff7e6b340c742fea16a2a3c10e52f9a2edc3ac6a78f41c136c7c86ed57.jpg) +Ground Truth Video + +![](images/f7c9031bbf98eec2226aecccbe5b960fcf54eabf8e4e2770f8f50ff7f0fd4040.jpg) +HyperNeRF [28] +Render time: 3 s + +![](images/2da5fb9899fc9b58d3f0b0f6ef8043efd602b9abd36dfa0ff8d9e2135cd38f10.jpg) +TiNeuVox [8] Render time: 7s + +![](images/506cb6e69f4b76c3fbffedff1410d301732965ee2dbede6a0dd61cbf374775cb.jpg) +Ours Render time: 0.1s + +![](images/7a050fccc2ab54ee2110db3c3a1fe022b66826f80e1ddf9f0d82bba0fb3adb00.jpg) +Figure 1. Our proposed DyLiN for dynamic 3D scene rendering achieves higher quality than its HyperNeRF teacher model and the state-of-the-art TiNeuVox model, while being an order of magnitude faster. Right: DyLiN is of moderate storage size (shown by dot radii). For each method, the relative improvement in Peak Signal-to-Noise Ratio over NeRF ( $\Delta$ PSNR) is measured for the best-performing scene. + +# Abstract + +Light Field Networks, the re-formulations of radiance fields to oriented rays, are magnitudes faster than their coordinate network counterparts, and provide higher fidelity with respect to representing 3D structures from 2D observations. They would be well suited for generic scene representation and manipulation, but suffer from one problem: they are limited to holistic and static scenes. In this paper, we propose the Dynamic Light Field Network (DyLiN) method that can handle non-rigid deformations, including topological changes. We learn a deformation field from input rays to canonical rays, and lift them into a higher dimensional space to handle discontinuities. We further introduce CoDyLiN, which augments DyLiN with controllable attribute inputs. We train both models via knowledge distillation from pretrained dynamic radiance fields. We evaluated DyLiN using both synthetic and real world datasets that include various non-rigid deformations. DyLiN qualitatively outperformed and quantitatively matched state-of-the-art methods in terms of visual fidelity, while being $25 - 71 \times$ computationally faster. We also tested CoDyLiN on attribute annotated data and it surpassed its teacher model. Project page: https://dylin2023.github.io. + +# 1. Introduction + +Machine vision has made tremendous progress with respect to reasoning about 3D structure using 2D observa + +tions. Much of this progress can be attributed to the emergence of coordinate networks [6,21,26], such as Neural Radiance Fields (NeRF) [23] and its variants [2, 20, 22, 39]. They provide an object agnostic representation for 3D scenes and can be used for high-fidelity synthesis for unseen views. While NeRFs mainly focus on static scenes, a series of works [10,27,29,34] extend the idea to dynamic cases via additional components that map the observed deformations to a canonical space, supporting moving and shape-evolving objects. It was further shown that by lifting this canonical space to higher dimensions the method can handle changes in scene topology as well [28]. + +However, the applicability of NeRF models is considerably limited by their computational complexities. From each pixel, one typically casts a ray from that pixel, and numerically integrates the radiance and color densities computed by a Multi-Layer Perceptron (MLP) across the ray, approximating the pixel color. Specifically, the numerical integration involves sampling hundreds of points across the ray, and evaluating the MLP at all of those locations. Several works have been proposed for speeding up static NeRFs. These include employing a compact 3D representation structure [9, 18, 43], breaking up the MLP into multiple smaller networks [30, 31], leveraging depth information [7, 24], and using fewer sampling points [17, 24, 42]. Yet, these methods still rely on integration and suffer from sampling many points, making them prohibitively slow for real-time applications. Recently, Light Field Networks (LFNs) [32] proposed replacing integration with a direct ray-to + +color regressor, trained using the same sparse set of images, requiring only a single forward pass. R2L [36] extended LFNs to use a very deep residual architecture, trained by distillation from a NeRF teacher model to avoid overfitting. In contrast to static NeRF acceleration, speeding up dynamic NeRFs is a much less discussed problem in the literature. This is potentially due to the much increased difficulty of the task, as one also has to deal with the high variability of motion. In this direction, [8, 38] greatly reduce the training time by using well-designed data structures, but their solutions still rely on integration. LFNs are clearly better suited for acceleration, yet, to the best of our knowledge, no works have attempted extending LFNs to the dynamic scenario. + +In this paper, we propose 2 schemes extending LFNs to dynamic scene deformations, topological changes and controllability. First, we introduce DyLiN, by incorporating a deformation field and a hyperspace representation to deal with non-rigid transformations, while distilling knowledge from a pretrained dynamic NeRF. Afterwards, we also propose CoDyLiN, via adding controllable input attributes, trained with synthetic training data generated by a pretrained Controllable NeRF (CoNeRF) [13] teacher model. To test the efficiencies of our proposed schemes, we perform empirical experiments on both synthetic and real datasets. We show that our DyLiN achieves better image quality and an order of magnitude faster rendering speed than its original dynamic NeRF teacher model and the state-of-the-art TiNeuVox [8] method. Similarly, we also show that CoDyLiN outperforms its CoNeRF teacher. We further execute ablation studies to verify the individual effectiveness of different components of our model. Our methods can be also understood as accelerated versions of their respective teacher models, and we are not aware of any prior works that attempt speeding up CoNeRF. + +Our contributions can be summarized as follows: + +- We propose DyLiN, an extension of LFNs that can handle dynamic scenes with topological changes. DyLiN achieves this through non-bending ray deformations, hyperspace lifting for whole rays, and knowledge distillation from dynamic NeRFs. +- We show that DyLiN achieves state-of-the-art results on both synthetic and real-world scenes, while being an order of magnitude faster than the competition. We also include an ablation study to analyze the contributions of our model components. +- We introduce CoDyLiN, further extending our DyLiN to handle controllable input attributes. + +# 2. Related Works + +Dynamic NeRFs. NeRFs have demonstrated impressive performances in novel view synthesis for static scenes. Extending these results to dynamic (deformable) domains has sparked considerable research interest [10, 27-29, 34]. Among these works, the ones that most closely resemble ours are D-NeRF [29] and HyperNeRF [28]. D-NeRF uses a translational deformation field with temporal positional encoding. HyperNeRF introduces a hyperspace representation, allowing topological variations to be effectively captured. Our work expands upon these works, as we propose DyLiN, a similar method for LFNs. We use the above dynamic NeRFs as pretrained teacher models for DyLiN, achieving better fidelity with orders of magnitude shorter rendering times. + +Accelerated NeRFs. The high computational complexity of NeRFs has motivated several follow-up works on speeding up the numerical integration process. The following first set of works are restricted to static scenarios. NSVF [18] represents the scene with a set of voxel-bounded MLPs organized in a sparse voxel octree, allowing voxels without relevant content to be skipped. KiloNeRF [31] divides the scene into a grid and trains a tiny MLP network for each cell within the grid, saving on pointwise evaluations. AutoInt [17] reduces the number of point samples for each ray using learned partial integrals. In contrast to the above procedures, speeding up dynamic NeRFs is much less discussed in the literature, as there are only 2 papers published on this subject. Wang et al. [38] proposed a method based on Fourier plenoctrees for real-time dynamic rendering, however, the technique requires an expensive rigid scene capturing setup. TiNeuVox [8] reduces training time by augmenting the MLP with time-aware voxel features and a tiny deformation network, while using a multi-distance interpolation method to model temporal variations. Interestingly, all of the aforementioned methods suffer from sampling hundreds of points during numerical integration, and none of them support changes in topology, whereas our proposed DyLiN excels from both perspectives. + +Light Field Networks (LFNs). As opposed to the aforementioned techniques that accelerate numerical integration within NeRFs, some works have attempted completely replacing numerical integration with direct per-ray color MLP regressors called Light Field Networks (LFNs). Since these approaches accept rays as inputs, they rely heavily on the ray representation. Several such representations exist in the literature. Plenoptic functions [1,3] encode 3D rays with 5D representations, i.e., a 3D point on a ray and 2 axis-angle ray directions. Light fields [11,15] use 4D ray codes most commonly through two-plane parameterization: given 2 parallel + +planes, rays are encoded by the 2D coordinates of the 2 ray-plane intersection points. Sadly, these representations are either discontinuous or cannot represent the full set of rays. Recently, Sitzmann et al. [32] advocate for the usage of the 6D Plücker coordinate representation, i.e., a 3D point on a ray coupled with its cross product with a 3D direction. They argue that this representation covers the whole set of rays and is continuous. Consequently, they feed it as input to an LFN, and additionally apply Meta-Learning across scenes to learn a multi-view consistency prior. However, they have not considered alternative ray representations, MLP architectures or training procedures, and only tested their method on toy datasets. R2L [36] employs an even more effective ray encoding by concatenating few points sampled from it, and proposes a very deep (88 layers) residual MLP network for LFNs. They resolve the proneness to overfitting by training the MLP with an abundance of synthetic images generated by a pretrained NeRF having a shallow MLP. Interestingly, they find that the student LFN model produces significantly better rendering quality than its teacher NeRF model, while being about 30 times faster. Our work extends LFNs to dynamic deformations, topological changes and controllability, achieving similar gains over the pretrained dynamic NeRF teacher models. + +Knowledge Distillation. The process of training a student model with synthetic data generated by a teacher model is called Knowledge Distillation (KD) [4], and it has been widely used in the vision and language domains [5, 15, 35, 37] as a form of data augmentation. Like R2L [36], we also use KD for training, however, our teacher and student models are both dynamic and more complex than their R2L counterparts. + +# 3. Methods + +In this section, we present our two solutions for extending LFNs. First, in Sec. 3.1, we propose DyLiN, supporting dynamic deformations and hyperspace representations via two respective MLPs. We use KD to train DyLiN with synthetic data generated by a pretrained dynamic NeRF teacher model. Second, in Sec. 3.2, we introduce CoDyLiN, which further augments DyLiN with controllability, via lifting attribute inputs to hyperspace with MLPs, and masking their hyperspace codes for disentanglement. In this case, we also train via KD, but the teacher model is a pretrained controllable NeRF. + +# 3.1. DyLiN + +# 3.1.1 Network Architecture + +Our overall DyLiN architecture $G_{\phi}$ is summarized in Fig. 2. It processes rays instead of the widely adopted 3D point inputs as follows. + +![](images/eb611fc11c9f351ec87e652c6b80c33ca2e3fb5f408b8349017a25244215e366.jpg) +Figure 2. Schematic diagram of our proposed DyLiN architecture. We take a ray $r = (o, d)$ and time $t$ as input. We deform $r$ into $r' = (o', d')$ , and sample few points $x_k, k = 1, \ldots, K$ along $r'$ to encode it (blue). In parallel, we also lift $r$ and $t$ to the hyperspace code $w$ (green), and concatenate it with each $x_k$ . We use the concatenation to regress the RGB color of $r$ at $t$ directly (red). + +Specifically, our deformation MLP $T_{\omega}$ maps an input ray $r = (o,d)$ to canonical space ray $r' = (o',d')$ : + +$$ +\left(o ^ {\prime}, d ^ {\prime}\right) = T _ {\omega} (o, d, t). \tag {1} +$$ + +Unlike the pointwise deformation MLP proposed in Nerfies [27], which bends rays by offsetting their points independently, our MLP outputs rays explicitly, hence no ray bending occurs. Furthermore, after obtaining $r'$ , we encode it by sampling and concatenating $K$ points along it. + +Our hyperspace $\mathrm{MLP}H_{\psi}$ is similar to $T_{\omega}$ , except it outputs a hyperspace representation $w$ : + +$$ +w = H _ {\psi} (o, d, t). \tag {2} +$$ + +In contrast to HyperNeRF [28], which predicts a hyperspace code $w$ for each 3D point, we use rays and compute a single $w$ for each ray. + +Both MLPs further take the index $t$ as input to encode temporal deformations. + +Once the $K$ points and $w$ are obtained, we concatenate them and feed the result into our LFN $R_{\pi}$ , which is a deep residual color MLP regressor. Overall, we can collect the model parameters as $\phi = [\omega, \psi, \pi]$ . + +Note that without our two MLPs $T_{\omega}$ and $H_{\psi}$ , our DyLiN falls back to the vanilla LFN. + +# 3.1.2 Training Procedure + +Our training procedure is composed of 3 phases. + +First, we pretrain a dynamic NeRF model $F_{\theta}$ (e.g., D-NeRF [29] or HyperNeRF [28]) by randomly sampling time $t$ and input ray $r$ , and minimizing the Mean Squared Error (MSE) against the corresponding RGB color of monocular target video $I$ : + +$$ +\min _ {\theta} \mathbb {E} _ {t, r = (o, d)} \left[ \| F _ {\theta} (o, d, t) - I (o, d, t) \| _ {2} ^ {2} \right]. \tag {3} +$$ + +Recall, that $F_{\theta}$ is slow, as it performs numerical integration across the ray $r = (o,d)$ . + +Second, we employ the newly obtained $F_{\theta^{*}}$ as the teacher model for our DyLiN student model $G_{\phi}$ via KD. Specifically, we minimize the MSE loss against the respective pseudo ground truth ray color generated by $F_{\theta^{*}}$ across $S$ ray samples: + +$$ +\min _ {\phi} \mathbb {E} _ {t, r = (o, d)} \left[ \| G _ {\phi} (o, d, t) - F _ {\theta^ {*}} (o, d, t) \| _ {2} ^ {2} \right], \tag {4} +$$ + +yielding $G_{\tilde{\phi}}$ . Note how this is considerably different from R2L [36], which uses a static LFN that is distilled from a static NeRF. + +Finally, we initialize our student model $G_{\phi}$ with parameters $\tilde{\phi}$ and fine-tune it using the original real video data: + +$$ +\min _ {\phi , \phi_ {0} = \tilde {\phi}} \mathbb {E} _ {t, r = (o, d)} \left[ \| G _ {\phi} (o, d, t) - I (o, d, t) \| _ {2} ^ {2} \right], \tag {5} +$$ + +obtaining $\phi^{*}$ + +# 3.2. CoDyLiN + +# 3.2.1 Network Architecture + +We further demonstrate that our DyLiN architecture from Sec. 3.1.1 can be extended to the controllable scenario using attribute inputs with hyperspace MLPs and attention masks. Our proposed CoDyLiN network $Q_{\tau}$ is depicted in Fig. 3. + +![](images/00a15c60d3686dad6e085f5e9986fb9cef9b3c4b3a263cdd33a8ed42397c2300.jpg) + +![](images/1bbd2f1c55b5855d780110e51b22b80a808040ebb10f7c56dbb4d5c1fc481640.jpg) +Figure 3. Schematic diagram of our proposed CoDyLiN architecture. We augment our DyLiN (blue, green, red) by introducing scalar attribute inputs $\alpha_{i} \in [-1,1]$ , $i = 1,\dots,n$ and lifting them to their respective hyperspace codes $w_{i}$ (orange,..., pink MLPs). Next, $M_{i}$ disentangles $w_{i}$ from $w_{j}$ , $j \neq i$ by masking it into $w_{i}'$ (orange,..., pink boxes and bottom insets). We concatenate the sampled points $x_{k}$ , $k = 1,\ldots,K$ with the $w_{i}'$ , $i = 1,\ldots,n$ and predict the RGB color corresponding to the inputs (red). Arrows from $(o',d')$ and $w_{0}$ to $M_{i}$ are omitted from the top figure for simplicity. Compare this with Fig. 2. + +![](images/904facdb90e9b7df016ce03052b76f0cf3057663380db0553a2cde1b8192840f.jpg) + +![](images/a733914acca885ad9f04f58f090af783ad9a5eccb0f6edbd90cd1949ccc33eca.jpg) + +Specifically, we start from DyLiN $G_{\phi}$ and add scalar inputs $\alpha_{i} \in [-1,1]$ , $i = 1, \dots, n$ next to $o, d, t$ . Intuitively, + +these are given strength values for specific local attributes, which can be interpolated continuously. $n$ is the total number of attributes. + +Each $\alpha_{i}$ is then processed independently with its own hyperspace MLP $H_{i,\psi_i}$ to yield the hyperspace code $w_{i}$ : + +$$ +w _ {i} = H _ {i, \psi_ {i}} (o, d, t). \tag {6} +$$ + +Next, we include mask MLP regressors $M_{i,\rho_i}$ to generate scalar attention masks $\hat{m}_i \in [0,1]$ for each $w_i$ (including $w_0 = w$ ): + +$$ +\hat {m} _ {i} = M _ {i, \rho_ {i}} (w _ {i}, w, o, d), +$$ + +$$ +\hat {m} _ {0} = 1 - \sum_ {i = 1} ^ {n} \hat {m} _ {i}, \tag {7} +$$ + +$$ +w _ {i} ^ {\prime} = \hat {m} _ {i} \cdot w _ {i}, \quad i = 0, \dots , n, +$$ + +This helps the architecture to spatially disentangle (i.e., localize) the effects of attributes $\alpha_{i}$ , while $\hat{m}_0$ can be understood as the space not affected by any attributes. + +Finally, we sample $K$ points on the ray similarly to Sec. 3.1.1, concatenate those with the $w_{i}^{\prime}$ vectors, and process the result further with LFN $R_{\pi}$ . Again, we can use a shorthand for the parameters: $\tau = [\omega, \psi, \psi_1, \ldots, \psi_n, \rho_1, \ldots, \rho_n, \pi]$ . + +Observe that without our MLPs $H_{i,\psi_i}$ , $M_{i,\rho_i}$ , $i = 1, \dots, n$ , our CoDyLiN reverts to our simpler DyLiN. Different from CoNeRF [13], we process rays instead of points, and use the $\alpha_i$ as inputs instead of targets. + +# 3.2.2 Training Procedure + +Akin to Sec. 3.1.2, we split training into pretraining and distillation steps, but omit fine-tuning. + +First, we pretrain a CoNeRF model $E_{\nu}$ [13] by randomly sampling $(t,r,i)$ , against 3 ground truths: ray color, attribute values $\alpha_{i}$ and 2D per-attribute masks $m_{2D,i}$ . This yields us $E_{\nu^{*}}$ . For brevity, we omit the details of this step, and kindly forward the reader to Section 3 in [13]. + +Second, we distill from our teacher CoNeRF model $E_{\nu^{*}}$ into our student CoDyLiN $Q_{\tau}$ by randomly sampling $t,r,\alpha_{1},\ldots ,\alpha_{n}$ , and minimizing the MSE against 2 pseudo ground truths, i.e., ray colors and 2D masks $\bar{m}_{2D,i}$ : + +$$ +\begin{array}{l} \min _ {\tau} \mathbb {E} _ {t, r = (o, d)} \left[ \| Q _ {\tau} (o, d, t, \alpha_ {1: n}) - \bar {E} _ {\nu^ {*}} (o, d, t, \alpha_ {1: n}) \| _ {2} ^ {2} \right. \\ \left. + \lambda_ {m} \cdot \sum_ {i = 0} ^ {n} \| \hat {m} _ {i} (o, d, t, \alpha_ {i}) - \bar {m} _ {2 D} (o, d, t, \alpha_ {1: n}) _ {i} \| _ {2} ^ {2} \right], \tag {8} \\ \end{array} +$$ + +where $\bar{E}_{\nu}$ is identical to $E_{\nu}$ except for taking $\alpha_{1:n} = [\alpha_1,\dots ,\alpha_n]$ as input and outputting the masks $\bar{m}_{2D,i},i = 0,\ldots ,n$ . We denote the result of the optimization as $Q_{\tau^{*}}$ + +We highlight that our teacher and student models are both controllable in this setup. + +# 4. Experimental Setup + +# 4.1. Datasets + +To test our hypotheses, we performed experiments on three types of dynamic scenes: synthetic, real and real controllable. + +Synthetic Scenes. We utilized the synthetic $360^{\circ}$ dynamic dataset introduced by [29], which contains 8 animated objects with complicated geometry and realistic non-Lambertian materials. Each dynamic scene consists of 50 to 200 training images and 20 testing images. We used $400 \times 400$ image resolution. We applied D-NeRF [29] as our teacher model with the publicly available pretrained weights. + +Real Scenes. We collected real dynamic data from 2 sources. First, we utilized 5 topologically varying scenes provided by [28] (Broom, 3D Printer, Chicken, Americano and Banana), which were captured by a rig encompassing a pole with two Google Pixel 3 phones rigidly attached roughly $16\mathrm{cm}$ apart. Second, we collected human facial videos using an iPhone 13 Pro camera. We rendered both sets at $960 \times 540$ image resolution. We pretrained a HyperNeRF [28] teacher model from scratch for each scene. + +Real Controllable Scenes. We borrowed 2 real controllable scenes from [13] (closing/opening eyes/mouth, and transformer), which are captured either with a Google Pixel 3a or an Apple iPhone 13 Pro, and contain annotations over various attributes. We applied image resolution of $480 \times 270$ pixels. We pretrained a CoNeRF [13] teacher model from scratch per scene. + +# 4.2. Settings + +Throughout our experiments, we use the settings listed below, many of which follow [36]. + +In order to retain efficiency, we define $T_{\omega}$ and $H_{\psi}$ to be small MLPs, with $T_{\omega}$ consisting of 7 layers of 128 units with $r' \in \mathbb{R}^6$ , and $H_{\psi}$ having 6 layers of 64 units with $w \in \mathbb{R}^8$ . Then, we use $K = 16$ sampled points to represent rays, where sampling is done randomly during training and evenly spaced during inference. + +Contrary to $T_{\omega}$ and $H_{\psi}$ , our LFN $R_{\pi}$ is a very deep residual color MLP regressor, containing 88 layers with 256 units per layer, in order to have enough capacity to learn the video generation process. + +We generate rays within Eqs. (3) to (5) and (8) by sampling ray origins $o = (x_o, y_o, z_o)$ and normalized directions $d = (x_d, y_d, z_d)$ randomly from the uniform distribution $U$ as follows: + +$$ +x _ {o} \sim U \left(x _ {o} ^ {\min }, x _ {o} ^ {\max }\right), \quad x _ {d} \sim U \left(x _ {d} ^ {\min }, x _ {d} ^ {\max }\right), \tag {9} +$$ + +$$ +y _ {o} \sim U \left(y _ {o} ^ {\min }, y _ {o} ^ {\max }\right), \quad y _ {d} \sim U \left(y _ {d} ^ {\min }, y _ {d} ^ {\max }\right), \tag {10} +$$ + +$$ +z _ {o} \sim U \left(z _ {o} ^ {\min }, z _ {o} ^ {\max }\right), \quad z _ {d} \sim U \left(z _ {d} ^ {\min }, z _ {d} ^ {\max }\right), \tag {11} +$$ + +where the min, max bounds of the 6 intervals are inferred from the original training video. In addition to uniform sampling, we also apply the hard example mining strategy suggested in [36] to focus on fine-grained details. We used $S = 10,000$ training samples during KD in (4). + +Subsequently, we also randomly sample time step $t$ uniformly from the unit interval: $t \sim U(0,1)$ . + +Optionally, for our CoDyLiN experiments, we define each $H_{i,\psi_i}$ to be a small MLP having 5 layers of 128 units with $w_{i} \in \mathbb{R}^{8}$ . During training, we uniformly sample attributes within $[-1,1]$ : $\alpha_{i} \sim U(-1,1)$ , and let $\lambda_{m} = 0.1$ . + +During training, we used Adam [14] with learning rate $5 \times 10^{-4}$ and batch size 4,096. + +We performed all experiments on single NVIDIA A100 GPUs. + +# 4.3. Baseline Models + +For testing our methods, we compared quality and speed against several baseline models, including NeRF [23], NV [19], NSFF [16], Nerfies [27], HyperNeRF [28], two variants of TiNeuVox [8], DirectVoxGo [33], Plenoxels [9], T-NeRF and D-NeRF [29], as well as CoNeRF [13]. + +![](images/03c51ac6ec9028fe761670820cc6eb88cbec11fcb0e7d5d9ab74ab83190189e3.jpg) +(a) + +![](images/3e8cc66a72439b1327a9ca8e7899c8107dba8831b9e0653a607bb93a493d447f.jpg) +(b) +Figure 4. Our two ablated baseline models, omitting components of our DyLiN. (a) Without our two proposed MLPs. (b) Pointwise deformation MLP only, predicting offsets jointly. + +In addition, we performed an ablation study by comparing against 2 simplified versions of our DyLiN architecture. First, we omitted both of our deformation and hyperspace MLPs and simply concatenated the time step $t$ to the sampled ray points (essentially resulting in a dynamic R2L). This method is illustrated in Fig. 4a. Second, we employed a pointwise deformation MLP (5 layers of 256 units) inspired by [29], which deforms points along a ray by predicting their offsets jointly, i.e., it can bend rays. This is contrast to our DyLiN, which deforms rays explicitly without + +bending and also applies a hyperspace MLP. This scheme is depicted in Fig. 4b. In both baselines, the deep residual color MLP regressors were kept intact. Next, we also tested the effects of our fine-tuning procedure from (5) by training all of our models both with and without it. Lastly, we assessed the dependences on the number of sampled points along rays $K$ and on the number of training samples $S$ during KD in (4). + +# 4.4. Evaluation Metrics + +For quantitatively evaluating the quality of generated images, we calculated the Peak Signal-to-Noise Ratio (PSNR) [12] in decibels (dB), the Structural Similarity Index (SSIM) [25,40], the Multi-Scale SSIM (MS-SSIM) [41] and the Learned Perceptual Image Patch Similarity (LPIPS) [44] metrics. Intuitively, PSNR is a pixelwise score, while SSIM and MS-SSIM also take pixel correlations and multiple scales into account, respectively, yet all of these tend to favor blurred images. LPIPS compares deep neural representations of images and is much closer to human perception, promoting semantically better and sharper images. + +Furthermore, for testing space and time complexity, we computed the storage size of parameters in megabytes (MB) and measured the wall-clock time in milliseconds (ms) while rendering the synthetic Lego scene with each model. + +# 5. Results + +# 5.1. Quantitative Results + +Tab. 1 and Tab. 2 contain our quantitative results for reconstruction quality on synthetic and real dynamic scenes, accordingly. We found that among prior works, TiNeuVox-B performed the best on synthetic scenes with respect to each metric. On real scenes, however, NSFF took the lead. Despite having strong metrics, NSFF is qualitatively poor and slow. Surprisingly, during ablation, even our most basic model (DyLiN without the two MLPs from Fig. 4a) could generate perceptually better looking images than TiNeuVox-B, thanks to the increased training dataset size via KD. Incorporating the MLPs $T_{\omega}$ and $H_{\psi}$ into the model each improved results slightly. Interestingly, fine-tuning on real data as in (5) gave a substantial boost. In addition, our relative PSNR improvement over the teacher model (Tab. 1=+1.93 dB, up to +3.16 dB per scene; Tab. 2=+2.7 dB, up to +13.14 dB) is better than that of R2L [36] (+1.4 dB, up to +2.8 dB). + +Tab. 3 shows quantitative results for space and time complexity on the synthetic Lego scene. We found that there is a trade-off between the two metrics, as prior works are typically optimized for just one of those. In contrast, all of our proposed DyLiN variants settle at the golden mean between the two extremes. When compared to the strongest baseline TiNeuVox-B, our method requires 3 times as much + +Table 1. Quantitative results on synthetic dynamic scenes. Notations: Multi-Layer Perceptron (MLP), PD (pointwise deformation), FT (fine-tuning). We utilized D-NeRF as the teacher model for our DyLiNs. The winning numbers are highlighted in bold. + +
MethodPSNR↑SSIM↑LPIPS↓
NeRF [23]19.000.87000.1825
DirectVoxGo [33]18.610.85380.1688
Plenoxels [9]20.240.86880.1600
T-NeRF [29]29.510.95130.0788
D-NeRF [29]30.500.95250.0663
TiNeuVox-S [8]30.750.95500.0663
TiNeuVox-B [8]32.670.97250.0425
DyLiN, w/o two MLPs, w/o FT (ours)31.160.99310.0281
DyLiN, w/o two MLPs (ours)32.070.99370.0196
DyLiN, PD MLP only, w/o FT (ours)31.260.99320.0279
DyLiN, PD MLP only (ours)31.240.99400.0189
DyLiN, w/o FT (ours)31.370.99330.0275
DyLiN (ours)32.430.99430.0184
+ +Table 2. Quantitative results on real dynamic scenes. Notations: Multi-Layer Perceptron (MLP), PD (pointwise deformation), FT (fine-tuning). We utilized HyperNeRF as the teacher model for our DyLiNs. The winning numbers are highlighted in bold. + +
MethodPSNR↑MS-SSIM↑
NeRF [23]20.10.745
NV [19]16.90.571
NSFF [16]26.30.916
Nerfies [27]22.20.803
HyperNeRF [28]22.40.814
TiNeuVox-S [8]23.40.813
TiNeuVox-B [8]24.30.837
DyLiN, w/o two MLPs, w/o FT (ours)23.80.882
DyLiN, w/o two MLPs (ours)24.20.894
DyLiN, PD MLP only, w/o FT (ours)23.90.885
DyLiN, PD MLP only (ours)24.60.903
DyLiN, w/o FT (ours)24.00.886
DyLiN (ours)25.10.910
+ +storage but is nearly 2 orders of magnitude faster. Plenoxels and NV, the only methods that require less computation than ours, perform much worse in quality. + +Fig. 5 reports quantitative ablation results for dependencies on the number of sampled points per ray $K$ and on the number of training samples during KD $S$ , performed on the synthetic Standup scene. For dependence on $K$ (Fig. 5a), we found that there were no significant differences between test set PNSR scores for $K \in \{4,8,16,32\}$ , while we encountered overfitting for $K \in \{64,128\}$ . This justified our choice of $K = 16$ for the rest of our experiments. Regarding the effect of $S$ (Fig. 5b), overfitting occurred for smaller sample sizes including $S \in \{100;500;1,000;5,000\}$ . The test and training set PSNR scores were much closer for $S = 10,000$ , validating our general setting. + +Table 3. Quantitative results for space and time complexity on the synthetic Lego scene. Notations: Multi-Layer Perceptron (MLP), PD (pointwise deformation), FT (fine-tuning). + +
MethodStorage (MB)Wall-clock time (ms)
NeRF [23]5.002,950.0
DirectVoxGo [33]205.001,090.0
Plenoxels [9]717.0050.0
NV [19]439.0074.9
D-NeRF [29]4.008,150.0
NSFF [16]14.175,450.0
HyperNeRF [28]15.362,900.0
TiNeuVox-S [8]23.703,280.0
TiNeuVox-B [8]23.706,920.0
DyLiN, w/o two MLPs, w/o FT (ours)68.04115.4
DyLiN, w/o two MLPs (ours)68.04115.4
DyLiN, PD MLP only, w/o FT (ours)72.60115.7
DyLiN, PD MLP only (ours)72.60115.7
DyLiN, w/o FT (ours)70.11116.0
DyLiN (ours)70.11116.0
+ +![](images/3a589bdc785b0810b64439fb8489a7fc69f0ffb95dea2912bdaf86d0a0b6d3a3.jpg) +(a) + +![](images/619835508c0103e5a24dd60fe777f8717547f5875baf0dcf33b80718d1d519a2.jpg) +(b) +Figure 5. Quantitative results for ablation on the synthetic Standup scene. (a) Dependence on the number of sampled points $K$ across ray $r'$ . (b) Dependence on the number of training samples $S$ during Knowledge Distillation (KD). + +Our controllable numerical results are collected in Tab. 4. In short, our CoDyLiN was able to considerably outperform CoNeRF with respect to MS-SSIM and speed. + +Table 4. Quantitative results on real controllable scenes. We utilized CoNeRF as the teacher model for our CoDyLiN. The winning numbers are highlighted in bold. + +
MethodEyes/MouthTransformer
PSNR†MS-SSIM†Wall-clock time (ms)PSNR†MS-SSIM†Wall-clock time (ms)
CoNeRF [13]21.46580.74586230.023.03190.88784360.0
CoDyLiN (ours)21.46550.9510116.323.58820.9779116.0
+ +# 5.2. Qualitative Results + +Fig. 6 and Fig. 7 depict qualitative results for reconstruction quality on synthetic and real dynamic scenes, respectively. Both show that our full DyLiN model generated the sharpest, most detailed images, as it was able to capture cloth wrinkles (Fig. 6j) and the eye of the chicken (Fig. 7e). The competing methods tended to oversmooth these features. We also ablated the effect of omitting fine-tuning (Fig. 6i, Fig. 7d), and results declined considerably. + +For the sake of completeness, Fig. 8 illustrates qualitative ablation results for our model components on real dynamic scenes. We found that sequentially adding our two proposed MLPs $T_{\omega}$ and $H_{\psi}$ improves the reconstruction, e.g., the gum between the teeth (Fig. 8e) and the fingers (Fig. 8j) become more and more apparent. Without the MLPs, these parts were heavily blurred (Fig. 8c, Fig. 8h). + +We kindly ask readers to refer to the supplementary material for CoDyLiN's qualitative results. + +# 6. Conclusion + +We proposed two architectures for extending LFNs to dynamic scenes. Specifically, we introduced DyLiN, which models ray deformations without bending and lifts whole rays into a hyperspace, and CoDyLiN, which allows for controllable attribute inputs. We trained both techniques via knowledge distillation from various dynamic NeRF teacher models. We found that DyLiN produces state-of-the-art quality even without ray bending and CoDyLiN outperforms its teacher model, while both are nearly 2 orders of magnitude faster than their strongest baselines. + +Our methods do not come without limitations, however. Most importantly, they focus on speeding up inference, as they require pretrained teacher models, which can be expensive to obtain. In some experiments, our solutions were outperformed in terms of the PSNR score. Using the winners as teacher models could improve performance. Additionally, distillation from multiple teacher models or joint training of the teacher and student models are also yet to be explored. Moreover, we currently represent rays implicitly by sampling $K$ points along them, but increasing this number can lead to overfitting. An explicit ray representation may be more effective. Finally, voxelizing and quantizing our models could improve efficiency. + +![](images/9578a25ec48c190fd52604412f4b9daa5510905c0581f068df992c493af42486.jpg) +Hook + +![](images/48f4c374207810d67be2bf020ae3b4267f1df1d613adf2bc819deb9b4dc93362.jpg) +(a) Ground Truth + +![](images/4489c0de780caa6e3b2942483105bd1082d6fd9abe1f33a2a523c4f14d4fd067.jpg) +(b) D-NeRF [29] + +![](images/808de1b043234fe5894873f3afc346eac9d354d4f65a42f93c95398e51019587.jpg) +(c) TiNeuVox [8] + +![](images/9cdc5bb332c116c596bc740685f6c2f1681a37cb767f6d7ff7dd5e22aba8fc13.jpg) +(d) Ours-1 + +![](images/9617dd849e6544ac9df602759ad6d4e15ee2b99d7c83e2f64ab26689a72083af.jpg) +(e) Ours-2 + +![](images/3ebc925e407086a30f8076cb84dc99a6661361d7ae383e051055a16d9f596326.jpg) +Jumping Jacks + +![](images/d1b2205db9b8b4d453cbefba32bcf88e7ff69c089951e1d099257f2adef5c3f4.jpg) +(f) Ground Truth + +![](images/6aa2cd67ebe324823299fbf7035ad432d02ad94f523055ef4abe23d635a8a4f5.jpg) +(g) D-NeRF [29] + +![](images/528f46bf89b956a917703617f9488439b729f814fc6e8a859112d719423ddf8c.jpg) +(h) TiNeuVox [8] + +![](images/071ea108bd0b1de78975371a653201c569b2b39b973fceeb6bacc752293e67b5.jpg) +(i) Ours-1 + +![](images/19bda05b92f597c50378ad717bd88d55374464976f0671042659b5c7fcf26c3d.jpg) +(j) Ours-2 + +![](images/ba8af6b89c9b6dea068705de846b92082a936d89d089fbd492e8bba18b7a7352.jpg) +Figure 6. Qualitative results on synthetic dynamic scenes. We compare our DyLiN (Ours-1, Ours-2) with the ground truth, the D-NeRF teacher model and TiNeuVox. Ours-1 and Ours-2 were trained without and with fine-tuning on the original data, respectively. +Chicken + +![](images/4287ab10e0c93d42055f130a69deaf210737f8d0c2f1d6a554074f6a671d655b.jpg) +(a) Ground Truth + +![](images/15c15daa0cba666e52c3084ad4f6a1af238817b4a3cc1f1bdae3e770eec102f1.jpg) +(b) HyperNeRF [28] + +![](images/6b303054b14892dcef8727d9428a8ddce1d53639783f5d3e7bfc66f6af0b86af.jpg) +(c) TiNeuVox [8] + +![](images/56ae82ba6bb685bac5e668928de5e84237f01eea6a6dedb8675eb27021e76110.jpg) +(d) Ours-1 + +![](images/bff2e78c69aeb61239d7afcc30595a0b1d32a0adf1b0814931f8b05261040f13.jpg) +(e) Ours-2 + +![](images/928db10c9328026da447202d13112ee1654832b67dc46ed104d518e94654af08.jpg) +Figure 7. Qualitative results on a real dynamic scene. We compare our DyLiN (Ours-1, Ours-2) with the ground truth, the HyperNeRF teacher model and TiNeuVox. Ours-1 and Ours-2 were trained without and with fine-tuning on the original data, respectively. + +![](images/4999f67d4c8f94f5e95f4db731b4a529d8c50556a8f2a5783b02f994a720c73e.jpg) +Expression +Peel Banana +Figure 8. Qualitative results for ablation on real dynamic scenes. We compare our DyLiN (Ours-1, Ours-2, Ours-3) with the ground truth and the HyperNeRF teacher model. Ours-1 was trained without our two MLPs. Ours-2 was trained with pointwise deformation MLP only. Ours-3 is our full model with both of our proposed two MLPs. + +![](images/dfc6a0b2dbe30527f69200ae8543e5a8cc52f2fd6b574ebbcea22b69aeb86d59.jpg) + +![](images/45f194ab4bbe01ae096e8bc0e5b753aec6c02927901ef69ad249de3f79cf19cb.jpg) + +![](images/41aa19a3cf6dcb375286445665b3036b274529462fdd551494297a2c17c2235c.jpg) + +![](images/e08bd673768e108be682274a886ba6a6142f51cddd992031d41020c84184d226.jpg) + +![](images/b2ac217ce2fca53eeef11522cd08160d228161ba6cf4172f76236498e5b258ed.jpg) + +![](images/0860322012e35936b7ab288f5faa8c5daa0c4260111f49ff26d17db0ed98e1d0.jpg) +(a) Ground Truth +(f) Ground Truth + +![](images/7f5b9904fb1d4bb4cef233194ff5e90fe56397e8f9a593031083102c42fbd142.jpg) +(b) HyperNeRF [28] +(g) HyperNeRF [28] + +![](images/72f368ab2bd6e4dea265641e3d49e6528da9c1693050153e8235a90521bcdeff.jpg) +(c) Ours-1 +(h) Ours-1 + +![](images/9ae192b24a4126555365d98ca09a49267c97841bf6453b4131573a424cb948b1.jpg) +(d) Ours-2 +(i) Ours-2 + +![](images/2302cc80473dfff4ac9835e36533deb4ba36b12e3c386c7ec0346a42c0081d29.jpg) +(e) Ours-3 +(j) Ours-3 + +Our results are encouraging steps towards achieving real-time volumetric rendering and animation, and we hope that our work will contribute to the progress in these areas. + +# Acknowledgements + +This research was supported partially by Fujitsu. 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Multiscale structural similarity for image quality assessment. In The 37th Asilomar SSC, volume 2, pages 1398-1402. IEEE, 2003. 6 +[42] Qiangeng Xu, Zexiang Xu, Julien Philip, Sai Bi, Zhixin Shu, et al. Point-NeRF: Point-based Neural Radiance Fields. In Proc. IEEE/CVF CVPR, pages 5438–5448, 2022. 1 +[43] Alex Yu, Ruilong Li, Matthew Tancik, Hao Li, Ren Ng, et al. PlenOctrees for Real-time Rendering of Neural Radiance Fields. In Proc. IEEE/CVF ICCV, pages 5752-5761, 2021. 1 +[44] Richard Zhang, Phillip Isola, Alexei A Efros, Eli Shechtman, and Oliver Wang. The Unreasonable Effectiveness of Deep Features as a Perceptual Metric. In Proc. 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Our proposed DyLiN for dynamic 3D scene rendering achieves higher quality than its HyperNeRF teacher model and the state-of-the-art TiNeuVox model, while being an order of magnitude faster. Right: DyLiN is of moderate storage size (shown by dot radii). For each method, the relative improvement in Peak Signal-to-Noise Ratio over NeRF (" + }, + { + "bbox": [ + 46, + 316, + 547, + 350 + ], + "type": "inline_equation", + "content": "\\Delta" + }, + { + "bbox": [ + 46, + 316, + 547, + 350 + ], + "type": "text", + "content": "PSNR) is measured for the best-performing scene." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 143, + 359, + 192, + 372 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 359, + 192, + 372 + ], + "spans": [ + { + "bbox": [ + 143, + 359, + 192, + 372 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 46, + 384, + 289, + 648 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 384, + 289, + 648 + ], + "spans": [ + { + "bbox": [ + 46, + 384, + 289, + 648 + ], + "type": "text", + "content": "Light Field Networks, the re-formulations of radiance fields to oriented rays, are magnitudes faster than their coordinate network counterparts, and provide higher fidelity with respect to representing 3D structures from 2D observations. They would be well suited for generic scene representation and manipulation, but suffer from one problem: they are limited to holistic and static scenes. In this paper, we propose the Dynamic Light Field Network (DyLiN) method that can handle non-rigid deformations, including topological changes. We learn a deformation field from input rays to canonical rays, and lift them into a higher dimensional space to handle discontinuities. We further introduce CoDyLiN, which augments DyLiN with controllable attribute inputs. We train both models via knowledge distillation from pretrained dynamic radiance fields. We evaluated DyLiN using both synthetic and real world datasets that include various non-rigid deformations. DyLiN qualitatively outperformed and quantitatively matched state-of-the-art methods in terms of visual fidelity, while being " + }, + { + "bbox": [ + 46, + 384, + 289, + 648 + ], + "type": "inline_equation", + "content": "25 - 71 \\times" + }, + { + "bbox": [ + 46, + 384, + 289, + 648 + ], + "type": "text", + "content": " computationally faster. We also tested CoDyLiN on attribute annotated data and it surpassed its teacher model. Project page: https://dylin2023.github.io." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 47, + 670, + 127, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 670, + 127, + 681 + ], + "spans": [ + { + "bbox": [ + 47, + 670, + 127, + 681 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "text", + "content": "Machine vision has made tremendous progress with respect to reasoning about 3D structure using 2D observa" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 360, + 545, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 360, + 545, + 504 + ], + "spans": [ + { + "bbox": [ + 304, + 360, + 545, + 504 + ], + "type": "text", + "content": "tions. Much of this progress can be attributed to the emergence of coordinate networks [6,21,26], such as Neural Radiance Fields (NeRF) [23] and its variants [2, 20, 22, 39]. They provide an object agnostic representation for 3D scenes and can be used for high-fidelity synthesis for unseen views. While NeRFs mainly focus on static scenes, a series of works [10,27,29,34] extend the idea to dynamic cases via additional components that map the observed deformations to a canonical space, supporting moving and shape-evolving objects. It was further shown that by lifting this canonical space to higher dimensions the method can handle changes in scene topology as well [28]." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 510, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 546, + 714 + ], + "type": "text", + "content": "However, the applicability of NeRF models is considerably limited by their computational complexities. From each pixel, one typically casts a ray from that pixel, and numerically integrates the radiance and color densities computed by a Multi-Layer Perceptron (MLP) across the ray, approximating the pixel color. Specifically, the numerical integration involves sampling hundreds of points across the ray, and evaluating the MLP at all of those locations. Several works have been proposed for speeding up static NeRFs. These include employing a compact 3D representation structure [9, 18, 43], breaking up the MLP into multiple smaller networks [30, 31], leveraging depth information [7, 24], and using fewer sampling points [17, 24, 42]. Yet, these methods still rely on integration and suffer from sampling many points, making them prohibitively slow for real-time applications. Recently, Light Field Networks (LFNs) [32] proposed replacing integration with a direct ray-to" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12397" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "content": "color regressor, trained using the same sparse set of images, requiring only a single forward pass. R2L [36] extended LFNs to use a very deep residual architecture, trained by distillation from a NeRF teacher model to avoid overfitting. In contrast to static NeRF acceleration, speeding up dynamic NeRFs is a much less discussed problem in the literature. This is potentially due to the much increased difficulty of the task, as one also has to deal with the high variability of motion. In this direction, [8, 38] greatly reduce the training time by using well-designed data structures, but their solutions still rely on integration. LFNs are clearly better suited for acceleration, yet, to the best of our knowledge, no works have attempted extending LFNs to the dynamic scenario." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 243, + 289, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 243, + 289, + 495 + ], + "spans": [ + { + "bbox": [ + 46, + 243, + 289, + 495 + ], + "type": "text", + "content": "In this paper, we propose 2 schemes extending LFNs to dynamic scene deformations, topological changes and controllability. First, we introduce DyLiN, by incorporating a deformation field and a hyperspace representation to deal with non-rigid transformations, while distilling knowledge from a pretrained dynamic NeRF. Afterwards, we also propose CoDyLiN, via adding controllable input attributes, trained with synthetic training data generated by a pretrained Controllable NeRF (CoNeRF) [13] teacher model. To test the efficiencies of our proposed schemes, we perform empirical experiments on both synthetic and real datasets. We show that our DyLiN achieves better image quality and an order of magnitude faster rendering speed than its original dynamic NeRF teacher model and the state-of-the-art TiNeuVox [8] method. Similarly, we also show that CoDyLiN outperforms its CoNeRF teacher. We further execute ablation studies to verify the individual effectiveness of different components of our model. Our methods can be also understood as accelerated versions of their respective teacher models, and we are not aware of any prior works that attempt speeding up CoNeRF." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 495, + 247, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 495, + 247, + 506 + ], + "spans": [ + { + "bbox": [ + 47, + 495, + 247, + 506 + ], + "type": "text", + "content": "Our contributions can be summarized as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 58, + 525, + 287, + 714 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 58, + 525, + 287, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 525, + 287, + 586 + ], + "spans": [ + { + "bbox": [ + 58, + 525, + 287, + 586 + ], + "type": "text", + "content": "- We propose DyLiN, an extension of LFNs that can handle dynamic scenes with topological changes. DyLiN achieves this through non-bending ray deformations, hyperspace lifting for whole rays, and knowledge distillation from dynamic NeRFs." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 607, + 287, + 667 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 607, + 287, + 667 + ], + "spans": [ + { + "bbox": [ + 58, + 607, + 287, + 667 + ], + "type": "text", + "content": "- We show that DyLiN achieves state-of-the-art results on both synthetic and real-world scenes, while being an order of magnitude faster than the competition. We also include an ablation study to analyze the contributions of our model components." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 58, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 58, + 689, + 287, + 714 + ], + "type": "text", + "content": "- We introduce CoDyLiN, further extending our DyLiN to handle controllable input attributes." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 71, + 398, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 71, + 398, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 398, + 84 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 91, + 547, + 259 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 91, + 547, + 259 + ], + "spans": [ + { + "bbox": [ + 304, + 91, + 547, + 259 + ], + "type": "text", + "content": "Dynamic NeRFs. NeRFs have demonstrated impressive performances in novel view synthesis for static scenes. Extending these results to dynamic (deformable) domains has sparked considerable research interest [10, 27-29, 34]. Among these works, the ones that most closely resemble ours are D-NeRF [29] and HyperNeRF [28]. D-NeRF uses a translational deformation field with temporal positional encoding. HyperNeRF introduces a hyperspace representation, allowing topological variations to be effectively captured. Our work expands upon these works, as we propose DyLiN, a similar method for LFNs. We use the above dynamic NeRFs as pretrained teacher models for DyLiN, achieving better fidelity with orders of magnitude shorter rendering times." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 277, + 547, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 277, + 547, + 564 + ], + "spans": [ + { + "bbox": [ + 304, + 277, + 547, + 564 + ], + "type": "text", + "content": "Accelerated NeRFs. The high computational complexity of NeRFs has motivated several follow-up works on speeding up the numerical integration process. The following first set of works are restricted to static scenarios. NSVF [18] represents the scene with a set of voxel-bounded MLPs organized in a sparse voxel octree, allowing voxels without relevant content to be skipped. KiloNeRF [31] divides the scene into a grid and trains a tiny MLP network for each cell within the grid, saving on pointwise evaluations. AutoInt [17] reduces the number of point samples for each ray using learned partial integrals. In contrast to the above procedures, speeding up dynamic NeRFs is much less discussed in the literature, as there are only 2 papers published on this subject. Wang et al. [38] proposed a method based on Fourier plenoctrees for real-time dynamic rendering, however, the technique requires an expensive rigid scene capturing setup. TiNeuVox [8] reduces training time by augmenting the MLP with time-aware voxel features and a tiny deformation network, while using a multi-distance interpolation method to model temporal variations. Interestingly, all of the aforementioned methods suffer from sampling hundreds of points during numerical integration, and none of them support changes in topology, whereas our proposed DyLiN excels from both perspectives." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "type": "text", + "content": "Light Field Networks (LFNs). As opposed to the aforementioned techniques that accelerate numerical integration within NeRFs, some works have attempted completely replacing numerical integration with direct per-ray color MLP regressors called Light Field Networks (LFNs). Since these approaches accept rays as inputs, they rely heavily on the ray representation. Several such representations exist in the literature. Plenoptic functions [1,3] encode 3D rays with 5D representations, i.e., a 3D point on a ray and 2 axis-angle ray directions. Light fields [11,15] use 4D ray codes most commonly through two-plane parameterization: given 2 parallel" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "12398" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 360 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 360 + ], + "type": "text", + "content": "planes, rays are encoded by the 2D coordinates of the 2 ray-plane intersection points. Sadly, these representations are either discontinuous or cannot represent the full set of rays. Recently, Sitzmann et al. [32] advocate for the usage of the 6D Plücker coordinate representation, i.e., a 3D point on a ray coupled with its cross product with a 3D direction. They argue that this representation covers the whole set of rays and is continuous. Consequently, they feed it as input to an LFN, and additionally apply Meta-Learning across scenes to learn a multi-view consistency prior. However, they have not considered alternative ray representations, MLP architectures or training procedures, and only tested their method on toy datasets. R2L [36] employs an even more effective ray encoding by concatenating few points sampled from it, and proposes a very deep (88 layers) residual MLP network for LFNs. They resolve the proneness to overfitting by training the MLP with an abundance of synthetic images generated by a pretrained NeRF having a shallow MLP. Interestingly, they find that the student LFN model produces significantly better rendering quality than its teacher NeRF model, while being about 30 times faster. Our work extends LFNs to dynamic deformations, topological changes and controllability, achieving similar gains over the pretrained dynamic NeRF teacher models." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 373, + 288, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 373, + 288, + 471 + ], + "spans": [ + { + "bbox": [ + 47, + 373, + 288, + 471 + ], + "type": "text", + "content": "Knowledge Distillation. The process of training a student model with synthetic data generated by a teacher model is called Knowledge Distillation (KD) [4], and it has been widely used in the vision and language domains [5, 15, 35, 37] as a form of data augmentation. Like R2L [36], we also use KD for training, however, our teacher and student models are both dynamic and more complex than their R2L counterparts." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 481, + 107, + 493 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 481, + 107, + 493 + ], + "spans": [ + { + "bbox": [ + 47, + 481, + 107, + 493 + ], + "type": "text", + "content": "3. Methods" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 501, + 287, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 501, + 287, + 632 + ], + "spans": [ + { + "bbox": [ + 46, + 501, + 287, + 632 + ], + "type": "text", + "content": "In this section, we present our two solutions for extending LFNs. First, in Sec. 3.1, we propose DyLiN, supporting dynamic deformations and hyperspace representations via two respective MLPs. We use KD to train DyLiN with synthetic data generated by a pretrained dynamic NeRF teacher model. Second, in Sec. 3.2, we introduce CoDyLiN, which further augments DyLiN with controllability, via lifting attribute inputs to hyperspace with MLPs, and masking their hyperspace codes for disentanglement. In this case, we also train via KD, but the teacher model is a pretrained controllable NeRF." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 639, + 102, + 652 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 639, + 102, + 652 + ], + "spans": [ + { + "bbox": [ + 47, + 639, + 102, + 652 + ], + "type": "text", + "content": "3.1. DyLiN" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 658, + 174, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 174, + 670 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 174, + 670 + ], + "type": "text", + "content": "3.1.1 Network Architecture" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "text", + "content": "Our overall DyLiN architecture " + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "inline_equation", + "content": "G_{\\phi}" + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "text", + "content": " is summarized in Fig. 2. It processes rays instead of the widely adopted 3D point inputs as follows." + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 310, + 72, + 545, + 153 + ], + "blocks": [ + { + "bbox": [ + 310, + 72, + 545, + 153 + ], + "lines": [ + { + "bbox": [ + 310, + 72, + 545, + 153 + ], + "spans": [ + { + "bbox": [ + 310, + 72, + 545, + 153 + ], + "type": "image", + "image_path": "eb611fc11c9f351ec87e652c6b80c33ca2e3fb5f408b8349017a25244215e366.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 163, + 547, + 231 + ], + "lines": [ + { + "bbox": [ + 305, + 163, + 547, + 231 + ], + "spans": [ + { + "bbox": [ + 305, + 163, + 547, + 231 + ], + "type": "text", + "content": "Figure 2. Schematic diagram of our proposed DyLiN architecture. We take a ray " + }, + { + "bbox": [ + 305, + 163, + 547, + 231 + ], + "type": "inline_equation", + "content": "r = (o, d)" + }, + { + "bbox": [ + 305, + 163, + 547, + 231 + ], + "type": "text", + "content": " and time " + }, + { + "bbox": [ + 305, + 163, + 547, + 231 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 305, + 163, + 547, + 231 + ], + "type": "text", + "content": " as input. We deform " + }, + { + "bbox": [ + 305, + 163, + 547, + 231 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 305, + 163, + 547, + 231 + ], + "type": "text", + "content": " into " + }, + { + "bbox": [ + 305, + 163, + 547, + 231 + ], + "type": "inline_equation", + "content": "r' = (o', d')" + }, + { + "bbox": [ + 305, + 163, + 547, + 231 + ], + "type": "text", + "content": ", and sample few points " + }, + { + "bbox": [ + 305, + 163, + 547, + 231 + ], + "type": "inline_equation", + "content": "x_k, k = 1, \\ldots, K" + }, + { + "bbox": [ + 305, + 163, + 547, + 231 + ], + "type": "text", + "content": " along " + }, + { + "bbox": [ + 305, + 163, + 547, + 231 + ], + "type": "inline_equation", + "content": "r'" + }, + { + "bbox": [ + 305, + 163, + 547, + 231 + ], + "type": "text", + "content": " to encode it (blue). In parallel, we also lift " + }, + { + "bbox": [ + 305, + 163, + 547, + 231 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 305, + 163, + 547, + 231 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 163, + 547, + 231 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 305, + 163, + 547, + 231 + ], + "type": "text", + "content": " to the hyperspace code " + }, + { + "bbox": [ + 305, + 163, + 547, + 231 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 305, + 163, + 547, + 231 + ], + "type": "text", + "content": " (green), and concatenate it with each " + }, + { + "bbox": [ + 305, + 163, + 547, + 231 + ], + "type": "inline_equation", + "content": "x_k" + }, + { + "bbox": [ + 305, + 163, + 547, + 231 + ], + "type": "text", + "content": ". We use the concatenation to regress the RGB color of " + }, + { + "bbox": [ + 305, + 163, + 547, + 231 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 305, + 163, + 547, + 231 + ], + "type": "text", + "content": " at " + }, + { + "bbox": [ + 305, + 163, + 547, + 231 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 305, + 163, + 547, + 231 + ], + "type": "text", + "content": " directly (red)." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 250, + 545, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 250, + 545, + 275 + ], + "spans": [ + { + "bbox": [ + 305, + 250, + 545, + 275 + ], + "type": "text", + "content": "Specifically, our deformation MLP " + }, + { + "bbox": [ + 305, + 250, + 545, + 275 + ], + "type": "inline_equation", + "content": "T_{\\omega}" + }, + { + "bbox": [ + 305, + 250, + 545, + 275 + ], + "type": "text", + "content": " maps an input ray " + }, + { + "bbox": [ + 305, + 250, + 545, + 275 + ], + "type": "inline_equation", + "content": "r = (o,d)" + }, + { + "bbox": [ + 305, + 250, + 545, + 275 + ], + "type": "text", + "content": " to canonical space ray " + }, + { + "bbox": [ + 305, + 250, + 545, + 275 + ], + "type": "inline_equation", + "content": "r' = (o',d')" + }, + { + "bbox": [ + 305, + 250, + 545, + 275 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 382, + 282, + 545, + 297 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 382, + 282, + 545, + 297 + ], + "spans": [ + { + "bbox": [ + 382, + 282, + 545, + 297 + ], + "type": "interline_equation", + "content": "\\left(o ^ {\\prime}, d ^ {\\prime}\\right) = T _ {\\omega} (o, d, t). \\tag {1}", + "image_path": "7b303e4d429c8a3cc682b302bf21908c39405d3dd62972b40b333dbbaff39d19.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 304, + 545, + 364 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 304, + 545, + 364 + ], + "spans": [ + { + "bbox": [ + 305, + 304, + 545, + 364 + ], + "type": "text", + "content": "Unlike the pointwise deformation MLP proposed in Nerfies [27], which bends rays by offsetting their points independently, our MLP outputs rays explicitly, hence no ray bending occurs. Furthermore, after obtaining " + }, + { + "bbox": [ + 305, + 304, + 545, + 364 + ], + "type": "inline_equation", + "content": "r'" + }, + { + "bbox": [ + 305, + 304, + 545, + 364 + ], + "type": "text", + "content": ", we encode it by sampling and concatenating " + }, + { + "bbox": [ + 305, + 304, + 545, + 364 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 305, + 304, + 545, + 364 + ], + "type": "text", + "content": " points along it." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 365, + 545, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 365, + 545, + 388 + ], + "spans": [ + { + "bbox": [ + 305, + 365, + 545, + 388 + ], + "type": "text", + "content": "Our hyperspace " + }, + { + "bbox": [ + 305, + 365, + 545, + 388 + ], + "type": "inline_equation", + "content": "\\mathrm{MLP}H_{\\psi}" + }, + { + "bbox": [ + 305, + 365, + 545, + 388 + ], + "type": "text", + "content": " is similar to " + }, + { + "bbox": [ + 305, + 365, + 545, + 388 + ], + "type": "inline_equation", + "content": "T_{\\omega}" + }, + { + "bbox": [ + 305, + 365, + 545, + 388 + ], + "type": "text", + "content": ", except it outputs a hyperspace representation " + }, + { + "bbox": [ + 305, + 365, + 545, + 388 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 305, + 365, + 545, + 388 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 390, + 397, + 545, + 410 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 390, + 397, + 545, + 410 + ], + "spans": [ + { + "bbox": [ + 390, + 397, + 545, + 410 + ], + "type": "interline_equation", + "content": "w = H _ {\\psi} (o, d, t). \\tag {2}", + "image_path": "b4e3f5e48f03d105f6851f665cf35acfc080964602b2f0303f2e3e99d79b9fd9.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 419, + 545, + 454 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 419, + 545, + 454 + ], + "spans": [ + { + "bbox": [ + 305, + 419, + 545, + 454 + ], + "type": "text", + "content": "In contrast to HyperNeRF [28], which predicts a hyperspace code " + }, + { + "bbox": [ + 305, + 419, + 545, + 454 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 305, + 419, + 545, + 454 + ], + "type": "text", + "content": " for each 3D point, we use rays and compute a single " + }, + { + "bbox": [ + 305, + 419, + 545, + 454 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 305, + 419, + 545, + 454 + ], + "type": "text", + "content": " for each ray." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 455, + 545, + 478 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 455, + 545, + 478 + ], + "spans": [ + { + "bbox": [ + 305, + 455, + 545, + 478 + ], + "type": "text", + "content": "Both MLPs further take the index " + }, + { + "bbox": [ + 305, + 455, + 545, + 478 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 305, + 455, + 545, + 478 + ], + "type": "text", + "content": " as input to encode temporal deformations." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 479, + 545, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 479, + 545, + 525 + ], + "spans": [ + { + "bbox": [ + 305, + 479, + 545, + 525 + ], + "type": "text", + "content": "Once the " + }, + { + "bbox": [ + 305, + 479, + 545, + 525 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 305, + 479, + 545, + 525 + ], + "type": "text", + "content": " points and " + }, + { + "bbox": [ + 305, + 479, + 545, + 525 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 305, + 479, + 545, + 525 + ], + "type": "text", + "content": " are obtained, we concatenate them and feed the result into our LFN " + }, + { + "bbox": [ + 305, + 479, + 545, + 525 + ], + "type": "inline_equation", + "content": "R_{\\pi}" + }, + { + "bbox": [ + 305, + 479, + 545, + 525 + ], + "type": "text", + "content": ", which is a deep residual color MLP regressor. Overall, we can collect the model parameters as " + }, + { + "bbox": [ + 305, + 479, + 545, + 525 + ], + "type": "inline_equation", + "content": "\\phi = [\\omega, \\psi, \\pi]" + }, + { + "bbox": [ + 305, + 479, + 545, + 525 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 526, + 545, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 526, + 545, + 550 + ], + "spans": [ + { + "bbox": [ + 305, + 526, + 545, + 550 + ], + "type": "text", + "content": "Note that without our two MLPs " + }, + { + "bbox": [ + 305, + 526, + 545, + 550 + ], + "type": "inline_equation", + "content": "T_{\\omega}" + }, + { + "bbox": [ + 305, + 526, + 545, + 550 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 526, + 545, + 550 + ], + "type": "inline_equation", + "content": "H_{\\psi}" + }, + { + "bbox": [ + 305, + 526, + 545, + 550 + ], + "type": "text", + "content": ", our DyLiN falls back to the vanilla LFN." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 565, + 423, + 577 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 565, + 423, + 577 + ], + "spans": [ + { + "bbox": [ + 306, + 565, + 423, + 577 + ], + "type": "text", + "content": "3.1.2 Training Procedure" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 583, + 501, + 595 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 583, + 501, + 595 + ], + "spans": [ + { + "bbox": [ + 306, + 583, + 501, + 595 + ], + "type": "text", + "content": "Our training procedure is composed of 3 phases." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 596, + 545, + 655 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 596, + 545, + 655 + ], + "spans": [ + { + "bbox": [ + 305, + 596, + 545, + 655 + ], + "type": "text", + "content": "First, we pretrain a dynamic NeRF model " + }, + { + "bbox": [ + 305, + 596, + 545, + 655 + ], + "type": "inline_equation", + "content": "F_{\\theta}" + }, + { + "bbox": [ + 305, + 596, + 545, + 655 + ], + "type": "text", + "content": " (e.g., D-NeRF [29] or HyperNeRF [28]) by randomly sampling time " + }, + { + "bbox": [ + 305, + 596, + 545, + 655 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 305, + 596, + 545, + 655 + ], + "type": "text", + "content": " and input ray " + }, + { + "bbox": [ + 305, + 596, + 545, + 655 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 305, + 596, + 545, + 655 + ], + "type": "text", + "content": ", and minimizing the Mean Squared Error (MSE) against the corresponding RGB color of monocular target video " + }, + { + "bbox": [ + 305, + 596, + 545, + 655 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 305, + 596, + 545, + 655 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 335, + 663, + 545, + 681 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 335, + 663, + 545, + 681 + ], + "spans": [ + { + "bbox": [ + 335, + 663, + 545, + 681 + ], + "type": "interline_equation", + "content": "\\min _ {\\theta} \\mathbb {E} _ {t, r = (o, d)} \\left[ \\| F _ {\\theta} (o, d, t) - I (o, d, t) \\| _ {2} ^ {2} \\right]. \\tag {3}", + "image_path": "bfd7c7a9f9c8abcb3d7eed41025e56eefeef7ad2e3ebb4500a00d3520dd8da27.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": "Recall, that " + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "F_{\\theta}" + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": " is slow, as it performs numerical integration across the ray " + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "r = (o,d)" + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12399" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "text", + "content": "Second, we employ the newly obtained " + }, + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "inline_equation", + "content": "F_{\\theta^{*}}" + }, + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "text", + "content": " as the teacher model for our DyLiN student model " + }, + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "inline_equation", + "content": "G_{\\phi}" + }, + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "text", + "content": " via KD. Specifically, we minimize the MSE loss against the respective pseudo ground truth ray color generated by " + }, + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "inline_equation", + "content": "F_{\\theta^{*}}" + }, + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "text", + "content": " across " + }, + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "text", + "content": " ray samples:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 70, + 139, + 287, + 158 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 139, + 287, + 158 + ], + "spans": [ + { + "bbox": [ + 70, + 139, + 287, + 158 + ], + "type": "interline_equation", + "content": "\\min _ {\\phi} \\mathbb {E} _ {t, r = (o, d)} \\left[ \\| G _ {\\phi} (o, d, t) - F _ {\\theta^ {*}} (o, d, t) \\| _ {2} ^ {2} \\right], \\tag {4}", + "image_path": "81b0f2ee1a97aaced3477dbf08c767a1bec7194cd02cd8eee02e75ba6e55453a.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 165, + 287, + 200 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 165, + 287, + 200 + ], + "spans": [ + { + "bbox": [ + 47, + 165, + 287, + 200 + ], + "type": "text", + "content": "yielding " + }, + { + "bbox": [ + 47, + 165, + 287, + 200 + ], + "type": "inline_equation", + "content": "G_{\\tilde{\\phi}}" + }, + { + "bbox": [ + 47, + 165, + 287, + 200 + ], + "type": "text", + "content": ". Note how this is considerably different from R2L [36], which uses a static LFN that is distilled from a static NeRF." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 201, + 287, + 226 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 201, + 287, + 226 + ], + "spans": [ + { + "bbox": [ + 47, + 201, + 287, + 226 + ], + "type": "text", + "content": "Finally, we initialize our student model " + }, + { + "bbox": [ + 47, + 201, + 287, + 226 + ], + "type": "inline_equation", + "content": "G_{\\phi}" + }, + { + "bbox": [ + 47, + 201, + 287, + 226 + ], + "type": "text", + "content": " with parameters " + }, + { + "bbox": [ + 47, + 201, + 287, + 226 + ], + "type": "inline_equation", + "content": "\\tilde{\\phi}" + }, + { + "bbox": [ + 47, + 201, + 287, + 226 + ], + "type": "text", + "content": " and fine-tune it using the original real video data:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 64, + 233, + 287, + 255 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 233, + 287, + 255 + ], + "spans": [ + { + "bbox": [ + 64, + 233, + 287, + 255 + ], + "type": "interline_equation", + "content": "\\min _ {\\phi , \\phi_ {0} = \\tilde {\\phi}} \\mathbb {E} _ {t, r = (o, d)} \\left[ \\| G _ {\\phi} (o, d, t) - I (o, d, t) \\| _ {2} ^ {2} \\right], \\tag {5}", + "image_path": "318aa7abc0c2396b091c0a9b3d2abf2f746e98ccc55de85f2faa235086b14d94.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 262, + 104, + 273 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 262, + 104, + 273 + ], + "spans": [ + { + "bbox": [ + 47, + 262, + 104, + 273 + ], + "type": "text", + "content": "obtaining " + }, + { + "bbox": [ + 47, + 262, + 104, + 273 + ], + "type": "inline_equation", + "content": "\\phi^{*}" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 279, + 114, + 292 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 279, + 114, + 292 + ], + "spans": [ + { + "bbox": [ + 47, + 279, + 114, + 292 + ], + "type": "text", + "content": "3.2. CoDyLiN" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 298, + 173, + 309 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 298, + 173, + 309 + ], + "spans": [ + { + "bbox": [ + 47, + 298, + 173, + 309 + ], + "type": "text", + "content": "3.2.1 Network Architecture" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 317, + 287, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 317, + 287, + 365 + ], + "spans": [ + { + "bbox": [ + 47, + 317, + 287, + 365 + ], + "type": "text", + "content": "We further demonstrate that our DyLiN architecture from Sec. 3.1.1 can be extended to the controllable scenario using attribute inputs with hyperspace MLPs and attention masks. Our proposed CoDyLiN network " + }, + { + "bbox": [ + 47, + 317, + 287, + 365 + ], + "type": "inline_equation", + "content": "Q_{\\tau}" + }, + { + "bbox": [ + 47, + 317, + 287, + 365 + ], + "type": "text", + "content": " is depicted in Fig. 3." + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 50, + 374, + 282, + 505 + ], + "blocks": [ + { + "bbox": [ + 50, + 374, + 282, + 505 + ], + "lines": [ + { + "bbox": [ + 50, + 374, + 282, + 505 + ], + "spans": [ + { + "bbox": [ + 50, + 374, + 282, + 505 + ], + "type": "image", + "image_path": "00a15c60d3686dad6e085f5e9986fb9cef9b3c4b3a263cdd33a8ed42397c2300.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 52, + 514, + 135, + 557 + ], + "blocks": [ + { + "bbox": [ + 52, + 514, + 135, + 557 + ], + "lines": [ + { + "bbox": [ + 52, + 514, + 135, + 557 + ], + "spans": [ + { + "bbox": [ + 52, + 514, + 135, + 557 + ], + "type": "image", + "image_path": "1bbd2f1c55b5855d780110e51b22b80a808040ebb10f7c56dbb4d5c1fc481640.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 567, + 287, + 677 + ], + "lines": [ + { + "bbox": [ + 46, + 567, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 567, + 287, + 677 + ], + "type": "text", + "content": "Figure 3. Schematic diagram of our proposed CoDyLiN architecture. We augment our DyLiN (blue, green, red) by introducing scalar attribute inputs " + }, + { + "bbox": [ + 46, + 567, + 287, + 677 + ], + "type": "inline_equation", + "content": "\\alpha_{i} \\in [-1,1]" + }, + { + "bbox": [ + 46, + 567, + 287, + 677 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 567, + 287, + 677 + ], + "type": "inline_equation", + "content": "i = 1,\\dots,n" + }, + { + "bbox": [ + 46, + 567, + 287, + 677 + ], + "type": "text", + "content": " and lifting them to their respective hyperspace codes " + }, + { + "bbox": [ + 46, + 567, + 287, + 677 + ], + "type": "inline_equation", + "content": "w_{i}" + }, + { + "bbox": [ + 46, + 567, + 287, + 677 + ], + "type": "text", + "content": " (orange,..., pink MLPs). Next, " + }, + { + "bbox": [ + 46, + 567, + 287, + 677 + ], + "type": "inline_equation", + "content": "M_{i}" + }, + { + "bbox": [ + 46, + 567, + 287, + 677 + ], + "type": "text", + "content": " disentangles " + }, + { + "bbox": [ + 46, + 567, + 287, + 677 + ], + "type": "inline_equation", + "content": "w_{i}" + }, + { + "bbox": [ + 46, + 567, + 287, + 677 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 46, + 567, + 287, + 677 + ], + "type": "inline_equation", + "content": "w_{j}" + }, + { + "bbox": [ + 46, + 567, + 287, + 677 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 567, + 287, + 677 + ], + "type": "inline_equation", + "content": "j \\neq i" + }, + { + "bbox": [ + 46, + 567, + 287, + 677 + ], + "type": "text", + "content": " by masking it into " + }, + { + "bbox": [ + 46, + 567, + 287, + 677 + ], + "type": "inline_equation", + "content": "w_{i}'" + }, + { + "bbox": [ + 46, + 567, + 287, + 677 + ], + "type": "text", + "content": " (orange,..., pink boxes and bottom insets). We concatenate the sampled points " + }, + { + "bbox": [ + 46, + 567, + 287, + 677 + ], + "type": "inline_equation", + "content": "x_{k}" + }, + { + "bbox": [ + 46, + 567, + 287, + 677 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 567, + 287, + 677 + ], + "type": "inline_equation", + "content": "k = 1,\\ldots,K" + }, + { + "bbox": [ + 46, + 567, + 287, + 677 + ], + "type": "text", + "content": " with the " + }, + { + "bbox": [ + 46, + 567, + 287, + 677 + ], + "type": "inline_equation", + "content": "w_{i}'" + }, + { + "bbox": [ + 46, + 567, + 287, + 677 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 567, + 287, + 677 + ], + "type": "inline_equation", + "content": "i = 1,\\ldots,n" + }, + { + "bbox": [ + 46, + 567, + 287, + 677 + ], + "type": "text", + "content": " and predict the RGB color corresponding to the inputs (red). Arrows from " + }, + { + "bbox": [ + 46, + 567, + 287, + 677 + ], + "type": "inline_equation", + "content": "(o',d')" + }, + { + "bbox": [ + 46, + 567, + 287, + 677 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 567, + 287, + 677 + ], + "type": "inline_equation", + "content": "w_{0}" + }, + { + "bbox": [ + 46, + 567, + 287, + 677 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 567, + 287, + 677 + ], + "type": "inline_equation", + "content": "M_{i}" + }, + { + "bbox": [ + 46, + 567, + 287, + 677 + ], + "type": "text", + "content": " are omitted from the top figure for simplicity. Compare this with Fig. 2." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 141, + 515, + 209, + 557 + ], + "blocks": [ + { + "bbox": [ + 141, + 515, + 209, + 557 + ], + "lines": [ + { + "bbox": [ + 141, + 515, + 209, + 557 + ], + "spans": [ + { + "bbox": [ + 141, + 515, + 209, + 557 + ], + "type": "image", + "image_path": "904facdb90e9b7df016ce03052b76f0cf3057663380db0553a2cde1b8192840f.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 216, + 518, + 287, + 550 + ], + "blocks": [ + { + "bbox": [ + 216, + 518, + 287, + 550 + ], + "lines": [ + { + "bbox": [ + 216, + 518, + 287, + 550 + ], + "spans": [ + { + "bbox": [ + 216, + 518, + 287, + 550 + ], + "type": "image", + "image_path": "a733914acca885ad9f04f58f090af783ad9a5eccb0f6edbd90cd1949ccc33eca.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "Specifically, we start from DyLiN " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "G_{\\phi}" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": " and add scalar inputs " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\alpha_{i} \\in [-1,1]" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "i = 1, \\dots, n" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": " next to " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "o, d, t" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": ". Intuitively," + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 72, + 545, + 106 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 106 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 106 + ], + "type": "text", + "content": "these are given strength values for specific local attributes, which can be interpolated continuously. " + }, + { + "bbox": [ + 305, + 72, + 545, + 106 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 305, + 72, + 545, + 106 + ], + "type": "text", + "content": " is the total number of attributes." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 108, + 545, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 108, + 545, + 133 + ], + "spans": [ + { + "bbox": [ + 305, + 108, + 545, + 133 + ], + "type": "text", + "content": "Each " + }, + { + "bbox": [ + 305, + 108, + 545, + 133 + ], + "type": "inline_equation", + "content": "\\alpha_{i}" + }, + { + "bbox": [ + 305, + 108, + 545, + 133 + ], + "type": "text", + "content": " is then processed independently with its own hyperspace MLP " + }, + { + "bbox": [ + 305, + 108, + 545, + 133 + ], + "type": "inline_equation", + "content": "H_{i,\\psi_i}" + }, + { + "bbox": [ + 305, + 108, + 545, + 133 + ], + "type": "text", + "content": " to yield the hyperspace code " + }, + { + "bbox": [ + 305, + 108, + 545, + 133 + ], + "type": "inline_equation", + "content": "w_{i}" + }, + { + "bbox": [ + 305, + 108, + 545, + 133 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 384, + 137, + 545, + 150 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 384, + 137, + 545, + 150 + ], + "spans": [ + { + "bbox": [ + 384, + 137, + 545, + 150 + ], + "type": "interline_equation", + "content": "w _ {i} = H _ {i, \\psi_ {i}} (o, d, t). \\tag {6}", + "image_path": "a310cc629bf8d3feb84a20ad23963b0771f4c89f059e5a92223b5ecd359d8e58.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 155, + 545, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 155, + 545, + 190 + ], + "spans": [ + { + "bbox": [ + 305, + 155, + 545, + 190 + ], + "type": "text", + "content": "Next, we include mask MLP regressors " + }, + { + "bbox": [ + 305, + 155, + 545, + 190 + ], + "type": "inline_equation", + "content": "M_{i,\\rho_i}" + }, + { + "bbox": [ + 305, + 155, + 545, + 190 + ], + "type": "text", + "content": " to generate scalar attention masks " + }, + { + "bbox": [ + 305, + 155, + 545, + 190 + ], + "type": "inline_equation", + "content": "\\hat{m}_i \\in [0,1]" + }, + { + "bbox": [ + 305, + 155, + 545, + 190 + ], + "type": "text", + "content": " for each " + }, + { + "bbox": [ + 305, + 155, + 545, + 190 + ], + "type": "inline_equation", + "content": "w_i" + }, + { + "bbox": [ + 305, + 155, + 545, + 190 + ], + "type": "text", + "content": " (including " + }, + { + "bbox": [ + 305, + 155, + 545, + 190 + ], + "type": "inline_equation", + "content": "w_0 = w" + }, + { + "bbox": [ + 305, + 155, + 545, + 190 + ], + "type": "text", + "content": "):" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 363, + 194, + 466, + 208 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 363, + 194, + 466, + 208 + ], + "spans": [ + { + "bbox": [ + 363, + 194, + 466, + 208 + ], + "type": "interline_equation", + "content": "\\hat {m} _ {i} = M _ {i, \\rho_ {i}} (w _ {i}, w, o, d),", + "image_path": "361b87a2623a4e98c330254bd47dd61e047e9a9774838dd37bddd2c5a9784fdc.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 362, + 210, + 545, + 241 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 362, + 210, + 545, + 241 + ], + "spans": [ + { + "bbox": [ + 362, + 210, + 545, + 241 + ], + "type": "interline_equation", + "content": "\\hat {m} _ {0} = 1 - \\sum_ {i = 1} ^ {n} \\hat {m} _ {i}, \\tag {7}", + "image_path": "6ce2b0317c80f5739f2ad71b9260aa38c24a41bc8caba56f98dff8a7f964c767.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 365, + 244, + 488, + 256 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 244, + 488, + 256 + ], + "spans": [ + { + "bbox": [ + 365, + 244, + 488, + 256 + ], + "type": "interline_equation", + "content": "w _ {i} ^ {\\prime} = \\hat {m} _ {i} \\cdot w _ {i}, \\quad i = 0, \\dots , n,", + "image_path": "3d71ad393ca2fe12e261afe377f5e61145aae98db927255e200ca11b478fbf58.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 261, + 545, + 297 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 261, + 545, + 297 + ], + "spans": [ + { + "bbox": [ + 306, + 261, + 545, + 297 + ], + "type": "text", + "content": "This helps the architecture to spatially disentangle (i.e., localize) the effects of attributes " + }, + { + "bbox": [ + 306, + 261, + 545, + 297 + ], + "type": "inline_equation", + "content": "\\alpha_{i}" + }, + { + "bbox": [ + 306, + 261, + 545, + 297 + ], + "type": "text", + "content": ", while " + }, + { + "bbox": [ + 306, + 261, + 545, + 297 + ], + "type": "inline_equation", + "content": "\\hat{m}_0" + }, + { + "bbox": [ + 306, + 261, + 545, + 297 + ], + "type": "text", + "content": " can be understood as the space not affected by any attributes." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 305, + 297, + 545, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 297, + 545, + 357 + ], + "spans": [ + { + "bbox": [ + 305, + 297, + 545, + 357 + ], + "type": "text", + "content": "Finally, we sample " + }, + { + "bbox": [ + 305, + 297, + 545, + 357 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 305, + 297, + 545, + 357 + ], + "type": "text", + "content": " points on the ray similarly to Sec. 3.1.1, concatenate those with the " + }, + { + "bbox": [ + 305, + 297, + 545, + 357 + ], + "type": "inline_equation", + "content": "w_{i}^{\\prime}" + }, + { + "bbox": [ + 305, + 297, + 545, + 357 + ], + "type": "text", + "content": " vectors, and process the result further with LFN " + }, + { + "bbox": [ + 305, + 297, + 545, + 357 + ], + "type": "inline_equation", + "content": "R_{\\pi}" + }, + { + "bbox": [ + 305, + 297, + 545, + 357 + ], + "type": "text", + "content": ". Again, we can use a shorthand for the parameters: " + }, + { + "bbox": [ + 305, + 297, + 545, + 357 + ], + "type": "inline_equation", + "content": "\\tau = [\\omega, \\psi, \\psi_1, \\ldots, \\psi_n, \\rho_1, \\ldots, \\rho_n, \\pi]" + }, + { + "bbox": [ + 305, + 297, + 545, + 357 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 305, + 357, + 545, + 404 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 357, + 545, + 404 + ], + "spans": [ + { + "bbox": [ + 305, + 357, + 545, + 404 + ], + "type": "text", + "content": "Observe that without our MLPs " + }, + { + "bbox": [ + 305, + 357, + 545, + 404 + ], + "type": "inline_equation", + "content": "H_{i,\\psi_i}" + }, + { + "bbox": [ + 305, + 357, + 545, + 404 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 357, + 545, + 404 + ], + "type": "inline_equation", + "content": "M_{i,\\rho_i}" + }, + { + "bbox": [ + 305, + 357, + 545, + 404 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 357, + 545, + 404 + ], + "type": "inline_equation", + "content": "i = 1, \\dots, n" + }, + { + "bbox": [ + 305, + 357, + 545, + 404 + ], + "type": "text", + "content": ", our CoDyLiN reverts to our simpler DyLiN. Different from CoNeRF [13], we process rays instead of points, and use the " + }, + { + "bbox": [ + 305, + 357, + 545, + 404 + ], + "type": "inline_equation", + "content": "\\alpha_i" + }, + { + "bbox": [ + 305, + 357, + 545, + 404 + ], + "type": "text", + "content": " as inputs instead of targets." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 306, + 418, + 422, + 430 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 418, + 422, + 430 + ], + "spans": [ + { + "bbox": [ + 306, + 418, + 422, + 430 + ], + "type": "text", + "content": "3.2.2 Training Procedure" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 305, + 437, + 545, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 437, + 545, + 460 + ], + "spans": [ + { + "bbox": [ + 305, + 437, + 545, + 460 + ], + "type": "text", + "content": "Akin to Sec. 3.1.2, we split training into pretraining and distillation steps, but omit fine-tuning." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 305, + 461, + 545, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 461, + 545, + 520 + ], + "spans": [ + { + "bbox": [ + 305, + 461, + 545, + 520 + ], + "type": "text", + "content": "First, we pretrain a CoNeRF model " + }, + { + "bbox": [ + 305, + 461, + 545, + 520 + ], + "type": "inline_equation", + "content": "E_{\\nu}" + }, + { + "bbox": [ + 305, + 461, + 545, + 520 + ], + "type": "text", + "content": " [13] by randomly sampling " + }, + { + "bbox": [ + 305, + 461, + 545, + 520 + ], + "type": "inline_equation", + "content": "(t,r,i)" + }, + { + "bbox": [ + 305, + 461, + 545, + 520 + ], + "type": "text", + "content": ", against 3 ground truths: ray color, attribute values " + }, + { + "bbox": [ + 305, + 461, + 545, + 520 + ], + "type": "inline_equation", + "content": "\\alpha_{i}" + }, + { + "bbox": [ + 305, + 461, + 545, + 520 + ], + "type": "text", + "content": " and 2D per-attribute masks " + }, + { + "bbox": [ + 305, + 461, + 545, + 520 + ], + "type": "inline_equation", + "content": "m_{2D,i}" + }, + { + "bbox": [ + 305, + 461, + 545, + 520 + ], + "type": "text", + "content": ". This yields us " + }, + { + "bbox": [ + 305, + 461, + 545, + 520 + ], + "type": "inline_equation", + "content": "E_{\\nu^{*}}" + }, + { + "bbox": [ + 305, + 461, + 545, + 520 + ], + "type": "text", + "content": ". For brevity, we omit the details of this step, and kindly forward the reader to Section 3 in [13]." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 305, + 521, + 545, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 521, + 545, + 568 + ], + "spans": [ + { + "bbox": [ + 305, + 521, + 545, + 568 + ], + "type": "text", + "content": "Second, we distill from our teacher CoNeRF model " + }, + { + "bbox": [ + 305, + 521, + 545, + 568 + ], + "type": "inline_equation", + "content": "E_{\\nu^{*}}" + }, + { + "bbox": [ + 305, + 521, + 545, + 568 + ], + "type": "text", + "content": " into our student CoDyLiN " + }, + { + "bbox": [ + 305, + 521, + 545, + 568 + ], + "type": "inline_equation", + "content": "Q_{\\tau}" + }, + { + "bbox": [ + 305, + 521, + 545, + 568 + ], + "type": "text", + "content": " by randomly sampling " + }, + { + "bbox": [ + 305, + 521, + 545, + 568 + ], + "type": "inline_equation", + "content": "t,r,\\alpha_{1},\\ldots ,\\alpha_{n}" + }, + { + "bbox": [ + 305, + 521, + 545, + 568 + ], + "type": "text", + "content": ", and minimizing the MSE against 2 pseudo ground truths, i.e., ray colors and 2D masks " + }, + { + "bbox": [ + 305, + 521, + 545, + 568 + ], + "type": "inline_equation", + "content": "\\bar{m}_{2D,i}" + }, + { + "bbox": [ + 305, + 521, + 545, + 568 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 317, + 576, + 545, + 647 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 576, + 545, + 647 + ], + "spans": [ + { + "bbox": [ + 317, + 576, + 545, + 647 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\min _ {\\tau} \\mathbb {E} _ {t, r = (o, d)} \\left[ \\| Q _ {\\tau} (o, d, t, \\alpha_ {1: n}) - \\bar {E} _ {\\nu^ {*}} (o, d, t, \\alpha_ {1: n}) \\| _ {2} ^ {2} \\right. \\\\ \\left. + \\lambda_ {m} \\cdot \\sum_ {i = 0} ^ {n} \\| \\hat {m} _ {i} (o, d, t, \\alpha_ {i}) - \\bar {m} _ {2 D} (o, d, t, \\alpha_ {1: n}) _ {i} \\| _ {2} ^ {2} \\right], \\tag {8} \\\\ \\end{array}", + "image_path": "1fbb67acb3a13cd3f4fd16a02c15f1c7b483698dba21ae503040f9149f82572f.jpg" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 305, + 653, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 653, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 305, + 653, + 545, + 689 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 653, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\bar{E}_{\\nu}" + }, + { + "bbox": [ + 305, + 653, + 545, + 689 + ], + "type": "text", + "content": " is identical to " + }, + { + "bbox": [ + 305, + 653, + 545, + 689 + ], + "type": "inline_equation", + "content": "E_{\\nu}" + }, + { + "bbox": [ + 305, + 653, + 545, + 689 + ], + "type": "text", + "content": " except for taking " + }, + { + "bbox": [ + 305, + 653, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\alpha_{1:n} = [\\alpha_1,\\dots ,\\alpha_n]" + }, + { + "bbox": [ + 305, + 653, + 545, + 689 + ], + "type": "text", + "content": " as input and outputting the masks " + }, + { + "bbox": [ + 305, + 653, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\bar{m}_{2D,i},i = 0,\\ldots ,n" + }, + { + "bbox": [ + 305, + 653, + 545, + 689 + ], + "type": "text", + "content": " . We denote the result of the optimization as " + }, + { + "bbox": [ + 305, + 653, + 545, + 689 + ], + "type": "inline_equation", + "content": "Q_{\\tau^{*}}" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "We highlight that our teacher and student models are both controllable in this setup." + } + ] + } + ], + "index": 31 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12400" + } + ] + } + ], + "index": 32 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 71, + 165, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 71, + 165, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 165, + 85 + ], + "type": "text", + "content": "4. Experimental Setup" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 91, + 110, + 102 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 91, + 110, + 102 + ], + "spans": [ + { + "bbox": [ + 47, + 91, + 110, + 102 + ], + "type": "text", + "content": "4.1. Datasets" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 110, + 287, + 145 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 110, + 287, + 145 + ], + "spans": [ + { + "bbox": [ + 46, + 110, + 287, + 145 + ], + "type": "text", + "content": "To test our hypotheses, we performed experiments on three types of dynamic scenes: synthetic, real and real controllable." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 146, + 287, + 241 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 146, + 287, + 241 + ], + "spans": [ + { + "bbox": [ + 46, + 146, + 287, + 241 + ], + "type": "text", + "content": "Synthetic Scenes. We utilized the synthetic " + }, + { + "bbox": [ + 46, + 146, + 287, + 241 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 46, + 146, + 287, + 241 + ], + "type": "text", + "content": " dynamic dataset introduced by [29], which contains 8 animated objects with complicated geometry and realistic non-Lambertian materials. Each dynamic scene consists of 50 to 200 training images and 20 testing images. We used " + }, + { + "bbox": [ + 46, + 146, + 287, + 241 + ], + "type": "inline_equation", + "content": "400 \\times 400" + }, + { + "bbox": [ + 46, + 146, + 287, + 241 + ], + "type": "text", + "content": " image resolution. We applied D-NeRF [29] as our teacher model with the publicly available pretrained weights." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 242, + 287, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 242, + 287, + 348 + ], + "spans": [ + { + "bbox": [ + 46, + 242, + 287, + 348 + ], + "type": "text", + "content": "Real Scenes. We collected real dynamic data from 2 sources. First, we utilized 5 topologically varying scenes provided by [28] (Broom, 3D Printer, Chicken, Americano and Banana), which were captured by a rig encompassing a pole with two Google Pixel 3 phones rigidly attached roughly " + }, + { + "bbox": [ + 46, + 242, + 287, + 348 + ], + "type": "inline_equation", + "content": "16\\mathrm{cm}" + }, + { + "bbox": [ + 46, + 242, + 287, + 348 + ], + "type": "text", + "content": " apart. Second, we collected human facial videos using an iPhone 13 Pro camera. We rendered both sets at " + }, + { + "bbox": [ + 46, + 242, + 287, + 348 + ], + "type": "inline_equation", + "content": "960 \\times 540" + }, + { + "bbox": [ + 46, + 242, + 287, + 348 + ], + "type": "text", + "content": " image resolution. We pretrained a HyperNeRF [28] teacher model from scratch for each scene." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 350, + 287, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 350, + 287, + 433 + ], + "spans": [ + { + "bbox": [ + 46, + 350, + 287, + 433 + ], + "type": "text", + "content": "Real Controllable Scenes. We borrowed 2 real controllable scenes from [13] (closing/opening eyes/mouth, and transformer), which are captured either with a Google Pixel 3a or an Apple iPhone 13 Pro, and contain annotations over various attributes. We applied image resolution of " + }, + { + "bbox": [ + 46, + 350, + 287, + 433 + ], + "type": "inline_equation", + "content": "480 \\times 270" + }, + { + "bbox": [ + 46, + 350, + 287, + 433 + ], + "type": "text", + "content": " pixels. We pretrained a CoNeRF [13] teacher model from scratch per scene." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 442, + 107, + 455 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 442, + 107, + 455 + ], + "spans": [ + { + "bbox": [ + 47, + 442, + 107, + 455 + ], + "type": "text", + "content": "4.2. Settings" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 461, + 287, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 461, + 287, + 485 + ], + "spans": [ + { + "bbox": [ + 46, + 461, + 287, + 485 + ], + "type": "text", + "content": "Throughout our experiments, we use the settings listed below, many of which follow [36]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 486, + 287, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 486, + 287, + 557 + ], + "spans": [ + { + "bbox": [ + 46, + 486, + 287, + 557 + ], + "type": "text", + "content": "In order to retain efficiency, we define " + }, + { + "bbox": [ + 46, + 486, + 287, + 557 + ], + "type": "inline_equation", + "content": "T_{\\omega}" + }, + { + "bbox": [ + 46, + 486, + 287, + 557 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 486, + 287, + 557 + ], + "type": "inline_equation", + "content": "H_{\\psi}" + }, + { + "bbox": [ + 46, + 486, + 287, + 557 + ], + "type": "text", + "content": " to be small MLPs, with " + }, + { + "bbox": [ + 46, + 486, + 287, + 557 + ], + "type": "inline_equation", + "content": "T_{\\omega}" + }, + { + "bbox": [ + 46, + 486, + 287, + 557 + ], + "type": "text", + "content": " consisting of 7 layers of 128 units with " + }, + { + "bbox": [ + 46, + 486, + 287, + 557 + ], + "type": "inline_equation", + "content": "r' \\in \\mathbb{R}^6" + }, + { + "bbox": [ + 46, + 486, + 287, + 557 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 486, + 287, + 557 + ], + "type": "inline_equation", + "content": "H_{\\psi}" + }, + { + "bbox": [ + 46, + 486, + 287, + 557 + ], + "type": "text", + "content": " having 6 layers of 64 units with " + }, + { + "bbox": [ + 46, + 486, + 287, + 557 + ], + "type": "inline_equation", + "content": "w \\in \\mathbb{R}^8" + }, + { + "bbox": [ + 46, + 486, + 287, + 557 + ], + "type": "text", + "content": ". Then, we use " + }, + { + "bbox": [ + 46, + 486, + 287, + 557 + ], + "type": "inline_equation", + "content": "K = 16" + }, + { + "bbox": [ + 46, + 486, + 287, + 557 + ], + "type": "text", + "content": " sampled points to represent rays, where sampling is done randomly during training and evenly spaced during inference." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 558, + 287, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 287, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 287, + 605 + ], + "type": "text", + "content": "Contrary to " + }, + { + "bbox": [ + 46, + 558, + 287, + 605 + ], + "type": "inline_equation", + "content": "T_{\\omega}" + }, + { + "bbox": [ + 46, + 558, + 287, + 605 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 558, + 287, + 605 + ], + "type": "inline_equation", + "content": "H_{\\psi}" + }, + { + "bbox": [ + 46, + 558, + 287, + 605 + ], + "type": "text", + "content": ", our LFN " + }, + { + "bbox": [ + 46, + 558, + 287, + 605 + ], + "type": "inline_equation", + "content": "R_{\\pi}" + }, + { + "bbox": [ + 46, + 558, + 287, + 605 + ], + "type": "text", + "content": " is a very deep residual color MLP regressor, containing 88 layers with 256 units per layer, in order to have enough capacity to learn the video generation process." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 606, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 606, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 606, + 287, + 653 + ], + "type": "text", + "content": "We generate rays within Eqs. (3) to (5) and (8) by sampling ray origins " + }, + { + "bbox": [ + 46, + 606, + 287, + 653 + ], + "type": "inline_equation", + "content": "o = (x_o, y_o, z_o)" + }, + { + "bbox": [ + 46, + 606, + 287, + 653 + ], + "type": "text", + "content": " and normalized directions " + }, + { + "bbox": [ + 46, + 606, + 287, + 653 + ], + "type": "inline_equation", + "content": "d = (x_d, y_d, z_d)" + }, + { + "bbox": [ + 46, + 606, + 287, + 653 + ], + "type": "text", + "content": " randomly from the uniform distribution " + }, + { + "bbox": [ + 46, + 606, + 287, + 653 + ], + "type": "inline_equation", + "content": "U" + }, + { + "bbox": [ + 46, + 606, + 287, + 653 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 62, + 664, + 287, + 677 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 664, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 62, + 664, + 287, + 677 + ], + "type": "interline_equation", + "content": "x _ {o} \\sim U \\left(x _ {o} ^ {\\min }, x _ {o} ^ {\\max }\\right), \\quad x _ {d} \\sim U \\left(x _ {d} ^ {\\min }, x _ {d} ^ {\\max }\\right), \\tag {9}", + "image_path": "ca63e0f3524f54207ea14909d01b1ca5b3de5550c8ad65cef861955dc98b2774.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 63, + 681, + 287, + 694 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 681, + 287, + 694 + ], + "spans": [ + { + "bbox": [ + 63, + 681, + 287, + 694 + ], + "type": "interline_equation", + "content": "y _ {o} \\sim U \\left(y _ {o} ^ {\\min }, y _ {o} ^ {\\max }\\right), \\quad y _ {d} \\sim U \\left(y _ {d} ^ {\\min }, y _ {d} ^ {\\max }\\right), \\tag {10}", + "image_path": "eced79ace363db8497a414fde9ae1e55d88aaa961ba895f30b3464367fe13908.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 64, + 697, + 287, + 711 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 697, + 287, + 711 + ], + "spans": [ + { + "bbox": [ + 64, + 697, + 287, + 711 + ], + "type": "interline_equation", + "content": "z _ {o} \\sim U \\left(z _ {o} ^ {\\min }, z _ {o} ^ {\\max }\\right), \\quad z _ {d} \\sim U \\left(z _ {d} ^ {\\min }, z _ {d} ^ {\\max }\\right), \\tag {11}", + "image_path": "f3bb0ff14707d1c31f70e965bf00d91f4c6c1624731bd02fa186e2e8043af0ef.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 72, + 545, + 132 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 132 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 132 + ], + "type": "text", + "content": "where the min, max bounds of the 6 intervals are inferred from the original training video. In addition to uniform sampling, we also apply the hard example mining strategy suggested in [36] to focus on fine-grained details. We used " + }, + { + "bbox": [ + 305, + 72, + 545, + 132 + ], + "type": "inline_equation", + "content": "S = 10,000" + }, + { + "bbox": [ + 305, + 72, + 545, + 132 + ], + "type": "text", + "content": " training samples during KD in (4)." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 133, + 545, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 133, + 545, + 156 + ], + "spans": [ + { + "bbox": [ + 305, + 133, + 545, + 156 + ], + "type": "text", + "content": "Subsequently, we also randomly sample time step " + }, + { + "bbox": [ + 305, + 133, + 545, + 156 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 305, + 133, + 545, + 156 + ], + "type": "text", + "content": " uniformly from the unit interval: " + }, + { + "bbox": [ + 305, + 133, + 545, + 156 + ], + "type": "inline_equation", + "content": "t \\sim U(0,1)" + }, + { + "bbox": [ + 305, + 133, + 545, + 156 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 156, + 545, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 156, + 545, + 204 + ], + "spans": [ + { + "bbox": [ + 304, + 156, + 545, + 204 + ], + "type": "text", + "content": "Optionally, for our CoDyLiN experiments, we define each " + }, + { + "bbox": [ + 304, + 156, + 545, + 204 + ], + "type": "inline_equation", + "content": "H_{i,\\psi_i}" + }, + { + "bbox": [ + 304, + 156, + 545, + 204 + ], + "type": "text", + "content": " to be a small MLP having 5 layers of 128 units with " + }, + { + "bbox": [ + 304, + 156, + 545, + 204 + ], + "type": "inline_equation", + "content": "w_{i} \\in \\mathbb{R}^{8}" + }, + { + "bbox": [ + 304, + 156, + 545, + 204 + ], + "type": "text", + "content": ". During training, we uniformly sample attributes within " + }, + { + "bbox": [ + 304, + 156, + 545, + 204 + ], + "type": "inline_equation", + "content": "[-1,1]" + }, + { + "bbox": [ + 304, + 156, + 545, + 204 + ], + "type": "text", + "content": ": " + }, + { + "bbox": [ + 304, + 156, + 545, + 204 + ], + "type": "inline_equation", + "content": "\\alpha_{i} \\sim U(-1,1)" + }, + { + "bbox": [ + 304, + 156, + 545, + 204 + ], + "type": "text", + "content": ", and let " + }, + { + "bbox": [ + 304, + 156, + 545, + 204 + ], + "type": "inline_equation", + "content": "\\lambda_{m} = 0.1" + }, + { + "bbox": [ + 304, + 156, + 545, + 204 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 205, + 545, + 227 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 205, + 545, + 227 + ], + "spans": [ + { + "bbox": [ + 305, + 205, + 545, + 227 + ], + "type": "text", + "content": "During training, we used Adam [14] with learning rate " + }, + { + "bbox": [ + 305, + 205, + 545, + 227 + ], + "type": "inline_equation", + "content": "5 \\times 10^{-4}" + }, + { + "bbox": [ + 305, + 205, + 545, + 227 + ], + "type": "text", + "content": " and batch size 4,096." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 228, + 545, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 228, + 545, + 251 + ], + "spans": [ + { + "bbox": [ + 305, + 228, + 545, + 251 + ], + "type": "text", + "content": "We performed all experiments on single NVIDIA A100 GPUs." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 259, + 405, + 271 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 259, + 405, + 271 + ], + "spans": [ + { + "bbox": [ + 306, + 259, + 405, + 271 + ], + "type": "text", + "content": "4.3. Baseline Models" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 278, + 545, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 278, + 545, + 338 + ], + "spans": [ + { + "bbox": [ + 305, + 278, + 545, + 338 + ], + "type": "text", + "content": "For testing our methods, we compared quality and speed against several baseline models, including NeRF [23], NV [19], NSFF [16], Nerfies [27], HyperNeRF [28], two variants of TiNeuVox [8], DirectVoxGo [33], Plenoxels [9], T-NeRF and D-NeRF [29], as well as CoNeRF [13]." + } + ] + } + ], + "index": 20 + }, + { + "type": "image", + "bbox": [ + 316, + 347, + 538, + 417 + ], + "blocks": [ + { + "bbox": [ + 316, + 347, + 538, + 417 + ], + "lines": [ + { + "bbox": [ + 316, + 347, + 538, + 417 + ], + "spans": [ + { + "bbox": [ + 316, + 347, + 538, + 417 + ], + "type": "image", + "image_path": "03c51ac6ec9028fe761670820cc6eb88cbec11fcb0e7d5d9ab74ab83190189e3.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 421, + 419, + 431, + 428 + ], + "lines": [ + { + "bbox": [ + 421, + 419, + 431, + 428 + ], + "spans": [ + { + "bbox": [ + 421, + 419, + 431, + 428 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + } + ], + "index": 21 + }, + { + "type": "image", + "bbox": [ + 316, + 429, + 538, + 525 + ], + "blocks": [ + { + "bbox": [ + 316, + 429, + 538, + 525 + ], + "lines": [ + { + "bbox": [ + 316, + 429, + 538, + 525 + ], + "spans": [ + { + "bbox": [ + 316, + 429, + 538, + 525 + ], + "type": "image", + "image_path": "3e8cc66a72439b1327a9ca8e7899c8107dba8831b9e0653a607bb93a493d447f.jpg" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 421, + 528, + 431, + 536 + ], + "lines": [ + { + "bbox": [ + 421, + 528, + 431, + 536 + ], + "spans": [ + { + "bbox": [ + 421, + 528, + 431, + 536 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 546, + 545, + 580 + ], + "lines": [ + { + "bbox": [ + 305, + 546, + 545, + 580 + ], + "spans": [ + { + "bbox": [ + 305, + 546, + 545, + 580 + ], + "type": "text", + "content": "Figure 4. Our two ablated baseline models, omitting components of our DyLiN. (a) Without our two proposed MLPs. (b) Pointwise deformation MLP only, predicting offsets jointly." + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_caption" + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "In addition, we performed an ablation study by comparing against 2 simplified versions of our DyLiN architecture. First, we omitted both of our deformation and hyperspace MLPs and simply concatenated the time step " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": " to the sampled ray points (essentially resulting in a dynamic R2L). This method is illustrated in Fig. 4a. Second, we employed a pointwise deformation MLP (5 layers of 256 units) inspired by [29], which deforms points along a ray by predicting their offsets jointly, i.e., it can bend rays. This is contrast to our DyLiN, which deforms rays explicitly without" + } + ] + } + ], + "index": 26 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12401" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": "bending and also applies a hyperspace MLP. This scheme is depicted in Fig. 4b. In both baselines, the deep residual color MLP regressors were kept intact. Next, we also tested the effects of our fine-tuning procedure from (5) by training all of our models both with and without it. Lastly, we assessed the dependences on the number of sampled points along rays " + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": " and on the number of training samples " + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": " during KD in (4)." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 176, + 160, + 189 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 176, + 160, + 189 + ], + "spans": [ + { + "bbox": [ + 47, + 176, + 160, + 189 + ], + "type": "text", + "content": "4.4. Evaluation Metrics" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 195, + 287, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 195, + 287, + 327 + ], + "spans": [ + { + "bbox": [ + 46, + 195, + 287, + 327 + ], + "type": "text", + "content": "For quantitatively evaluating the quality of generated images, we calculated the Peak Signal-to-Noise Ratio (PSNR) [12] in decibels (dB), the Structural Similarity Index (SSIM) [25,40], the Multi-Scale SSIM (MS-SSIM) [41] and the Learned Perceptual Image Patch Similarity (LPIPS) [44] metrics. Intuitively, PSNR is a pixelwise score, while SSIM and MS-SSIM also take pixel correlations and multiple scales into account, respectively, yet all of these tend to favor blurred images. LPIPS compares deep neural representations of images and is much closer to human perception, promoting semantically better and sharper images." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 327, + 287, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 327, + 287, + 376 + ], + "spans": [ + { + "bbox": [ + 46, + 327, + 287, + 376 + ], + "type": "text", + "content": "Furthermore, for testing space and time complexity, we computed the storage size of parameters in megabytes (MB) and measured the wall-clock time in milliseconds (ms) while rendering the synthetic Lego scene with each model." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 387, + 100, + 399 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 387, + 100, + 399 + ], + "spans": [ + { + "bbox": [ + 47, + 387, + 100, + 399 + ], + "type": "text", + "content": "5. Results" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 407, + 166, + 419 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 407, + 166, + 419 + ], + "spans": [ + { + "bbox": [ + 47, + 407, + 166, + 419 + ], + "type": "text", + "content": "5.1. Quantitative Results" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 426, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 426, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 287, + 628 + ], + "type": "text", + "content": "Tab. 1 and Tab. 2 contain our quantitative results for reconstruction quality on synthetic and real dynamic scenes, accordingly. We found that among prior works, TiNeuVox-B performed the best on synthetic scenes with respect to each metric. On real scenes, however, NSFF took the lead. Despite having strong metrics, NSFF is qualitatively poor and slow. Surprisingly, during ablation, even our most basic model (DyLiN without the two MLPs from Fig. 4a) could generate perceptually better looking images than TiNeuVox-B, thanks to the increased training dataset size via KD. Incorporating the MLPs " + }, + { + "bbox": [ + 46, + 426, + 287, + 628 + ], + "type": "inline_equation", + "content": "T_{\\omega}" + }, + { + "bbox": [ + 46, + 426, + 287, + 628 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 426, + 287, + 628 + ], + "type": "inline_equation", + "content": "H_{\\psi}" + }, + { + "bbox": [ + 46, + 426, + 287, + 628 + ], + "type": "text", + "content": " into the model each improved results slightly. Interestingly, fine-tuning on real data as in (5) gave a substantial boost. In addition, our relative PSNR improvement over the teacher model (Tab. 1=+1.93 dB, up to +3.16 dB per scene; Tab. 2=+2.7 dB, up to +13.14 dB) is better than that of R2L [36] (+1.4 dB, up to +2.8 dB)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "content": "Tab. 3 shows quantitative results for space and time complexity on the synthetic Lego scene. We found that there is a trade-off between the two metrics, as prior works are typically optimized for just one of those. In contrast, all of our proposed DyLiN variants settle at the golden mean between the two extremes. When compared to the strongest baseline TiNeuVox-B, our method requires 3 times as much" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 307, + 123, + 547, + 276 + ], + "blocks": [ + { + "bbox": [ + 304, + 70, + 547, + 116 + ], + "lines": [ + { + "bbox": [ + 304, + 70, + 547, + 116 + ], + "spans": [ + { + "bbox": [ + 304, + 70, + 547, + 116 + ], + "type": "text", + "content": "Table 1. Quantitative results on synthetic dynamic scenes. Notations: Multi-Layer Perceptron (MLP), PD (pointwise deformation), FT (fine-tuning). We utilized D-NeRF as the teacher model for our DyLiNs. The winning numbers are highlighted in bold." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 123, + 547, + 276 + ], + "lines": [ + { + "bbox": [ + 307, + 123, + 547, + 276 + ], + "spans": [ + { + "bbox": [ + 307, + 123, + 547, + 276 + ], + "type": "table", + "html": "
MethodPSNR↑SSIM↑LPIPS↓
NeRF [23]19.000.87000.1825
DirectVoxGo [33]18.610.85380.1688
Plenoxels [9]20.240.86880.1600
T-NeRF [29]29.510.95130.0788
D-NeRF [29]30.500.95250.0663
TiNeuVox-S [8]30.750.95500.0663
TiNeuVox-B [8]32.670.97250.0425
DyLiN, w/o two MLPs, w/o FT (ours)31.160.99310.0281
DyLiN, w/o two MLPs (ours)32.070.99370.0196
DyLiN, PD MLP only, w/o FT (ours)31.260.99320.0279
DyLiN, PD MLP only (ours)31.240.99400.0189
DyLiN, w/o FT (ours)31.370.99330.0275
DyLiN (ours)32.430.99430.0184
", + "image_path": "bbcf623efc63c17fa3498ec641651ea96103dd0aa444273c53c23499179dc33c.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 307, + 342, + 545, + 510 + ], + "blocks": [ + { + "bbox": [ + 304, + 289, + 547, + 335 + ], + "lines": [ + { + "bbox": [ + 304, + 289, + 547, + 335 + ], + "spans": [ + { + "bbox": [ + 304, + 289, + 547, + 335 + ], + "type": "text", + "content": "Table 2. Quantitative results on real dynamic scenes. Notations: Multi-Layer Perceptron (MLP), PD (pointwise deformation), FT (fine-tuning). We utilized HyperNeRF as the teacher model for our DyLiNs. The winning numbers are highlighted in bold." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 342, + 545, + 510 + ], + "lines": [ + { + "bbox": [ + 307, + 342, + 545, + 510 + ], + "spans": [ + { + "bbox": [ + 307, + 342, + 545, + 510 + ], + "type": "table", + "html": "
MethodPSNR↑MS-SSIM↑
NeRF [23]20.10.745
NV [19]16.90.571
NSFF [16]26.30.916
Nerfies [27]22.20.803
HyperNeRF [28]22.40.814
TiNeuVox-S [8]23.40.813
TiNeuVox-B [8]24.30.837
DyLiN, w/o two MLPs, w/o FT (ours)23.80.882
DyLiN, w/o two MLPs (ours)24.20.894
DyLiN, PD MLP only, w/o FT (ours)23.90.885
DyLiN, PD MLP only (ours)24.60.903
DyLiN, w/o FT (ours)24.00.886
DyLiN (ours)25.10.910
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MethodStorage (MB)Wall-clock time (ms)
NeRF [23]5.002,950.0
DirectVoxGo [33]205.001,090.0
Plenoxels [9]717.0050.0
NV [19]439.0074.9
D-NeRF [29]4.008,150.0
NSFF [16]14.175,450.0
HyperNeRF [28]15.362,900.0
TiNeuVox-S [8]23.703,280.0
TiNeuVox-B [8]23.706,920.0
DyLiN, w/o two MLPs, w/o FT (ours)68.04115.4
DyLiN, w/o two MLPs (ours)68.04115.4
DyLiN, PD MLP only, w/o FT (ours)72.60115.7
DyLiN, PD MLP only (ours)72.60115.7
DyLiN, w/o FT (ours)70.11116.0
DyLiN (ours)70.11116.0
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MethodEyes/MouthTransformer
PSNR†MS-SSIM†Wall-clock time (ms)PSNR†MS-SSIM†Wall-clock time (ms)
CoNeRF [13]21.46580.74586230.023.03190.88784360.0
CoDyLiN (ours)21.46550.9510116.323.58820.9779116.0
", + "image_path": "b83646819a5e053b5d66a069bab09cd907313f0268998e2334b9af1d09a98cdb.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 182, + 418, + 194 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 182, + 418, + 194 + ], + "spans": [ + { + "bbox": [ + 306, + 182, + 418, + 194 + ], + "type": "text", + "content": "5.2. Qualitative Results" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 201, + 545, + 297 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 201, + 545, + 297 + ], + "spans": [ + { + "bbox": [ + 304, + 201, + 545, + 297 + ], + "type": "text", + "content": "Fig. 6 and Fig. 7 depict qualitative results for reconstruction quality on synthetic and real dynamic scenes, respectively. Both show that our full DyLiN model generated the sharpest, most detailed images, as it was able to capture cloth wrinkles (Fig. 6j) and the eye of the chicken (Fig. 7e). The competing methods tended to oversmooth these features. We also ablated the effect of omitting fine-tuning (Fig. 6i, Fig. 7d), and results declined considerably." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 297, + 545, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 297, + 545, + 380 + ], + "spans": [ + { + "bbox": [ + 304, + 297, + 545, + 380 + ], + "type": "text", + "content": "For the sake of completeness, Fig. 8 illustrates qualitative ablation results for our model components on real dynamic scenes. We found that sequentially adding our two proposed MLPs " + }, + { + "bbox": [ + 304, + 297, + 545, + 380 + ], + "type": "inline_equation", + "content": "T_{\\omega}" + }, + { + "bbox": [ + 304, + 297, + 545, + 380 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 297, + 545, + 380 + ], + "type": "inline_equation", + "content": "H_{\\psi}" + }, + { + "bbox": [ + 304, + 297, + 545, + 380 + ], + "type": "text", + "content": " improves the reconstruction, e.g., the gum between the teeth (Fig. 8e) and the fingers (Fig. 8j) become more and more apparent. Without the MLPs, these parts were heavily blurred (Fig. 8c, Fig. 8h)." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 381, + 545, + 406 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 381, + 545, + 406 + ], + "spans": [ + { + "bbox": [ + 305, + 381, + 545, + 406 + ], + "type": "text", + "content": "We kindly ask readers to refer to the supplementary material for CoDyLiN's qualitative results." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 417, + 378, + 430 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 417, + 378, + 430 + ], + "spans": [ + { + "bbox": [ + 306, + 417, + 378, + 430 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 437, + 545, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 545, + 557 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 545, + 557 + ], + "type": "text", + "content": "We proposed two architectures for extending LFNs to dynamic scenes. Specifically, we introduced DyLiN, which models ray deformations without bending and lifts whole rays into a hyperspace, and CoDyLiN, which allows for controllable attribute inputs. We trained both techniques via knowledge distillation from various dynamic NeRF teacher models. We found that DyLiN produces state-of-the-art quality even without ray bending and CoDyLiN outperforms its teacher model, while both are nearly 2 orders of magnitude faster than their strongest baselines." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": "Our methods do not come without limitations, however. Most importantly, they focus on speeding up inference, as they require pretrained teacher models, which can be expensive to obtain. In some experiments, our solutions were outperformed in terms of the PSNR score. Using the winners as teacher models could improve performance. Additionally, distillation from multiple teacher models or joint training of the teacher and student models are also yet to be explored. Moreover, we currently represent rays implicitly by sampling " + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": " points along them, but increasing this number can lead to overfitting. An explicit ray representation may be more effective. 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Qualitative results on synthetic dynamic scenes. We compare our DyLiN (Ours-1, Ours-2) with the ground truth, the D-NeRF teacher model and TiNeuVox. 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Qualitative results on a real dynamic scene. We compare our DyLiN (Ours-1, Ours-2) with the ground truth, the HyperNeRF teacher model and TiNeuVox. 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Qualitative results for ablation on real dynamic scenes. We compare our DyLiN (Ours-1, Ours-2, Ours-3) with the ground truth and the HyperNeRF teacher model. Ours-1 was trained without our two MLPs. Ours-2 was trained with pointwise deformation MLP only. 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work will contribute to the progress in these areas." + } + ] + } + ], + "index": 63 + }, + { + "bbox": [ + 306, + 642, + 408, + 655 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 642, + 408, + 655 + ], + "spans": [ + { + "bbox": [ + 306, + 642, + 408, + 655 + ], + "type": "text", + "content": "Acknowledgements" + } + ] + } + ], + "index": 64 + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": "This research was supported partially by Fujitsu. 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Our DyNCA model can synthesize infinitely-long realistic dynamic texture videos with arbitrary size in real time. Target Appearance: DyNCA learns a desired texture pattern from a given target appearance image. Target Dynamics: DyNCA can learn motion from different target sources. We allow the users to define the desired motion either by a hand-crafted optical-flow image or a dynamic texture video. Synthesized Result: DyNCA synthesizes realistic dynamic texture videos. Each synthesized video frame resembles the target appearance, while the concatenation of frames induces the motion of the target dynamics. See our real-time interactive demo at2." + ], + "image_footnote": [], + "bbox": [ + 96, + 419, + 227, + 518 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ddc83b4c7923f45f5a1bc6275de9de18dbc128f4d8c92e68871d2c5aec013ced.jpg", + "image_caption": [ + "Video" + ], + "image_footnote": [], + "bbox": [ + 267, + 330, + 362, + 404 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/45966c4f191bf4ee5cae3661d48656f9ecc7390ba437df922badffacbbfb806a.jpg", + "image_caption": [ + "OF" + ], + "image_footnote": [], + "bbox": [ + 248, + 417, + 380, + 518 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/cf584ffedc425327d7c16ce5c4f1804a8f119e965c3e9e2118db998e6837cc6e.jpg", + "image_caption": [ + "Target Dynamics (Motion)", + "Optical Flow" + ], + "image_footnote": [], + "bbox": [ + 421, + 320, + 542, + 412 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e44f2e8b7f51fa18aa7a6b3eb2056c57b808477ef5d0fc1988b76213b6c524ec.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 416, + 417, + 547, + 518 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a5d2576970e5fa41a44c4e0d00d756a4d0ae1d2b6a8ccff5f5da0be5135f68d8.jpg", + "image_caption": [ + "Synthesized Result", + "Video" + ], + "image_footnote": [], + "bbox": [ + 571, + 316, + 705, + 417 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/2d54df8eaf53063dc028df219ec433daa115ea3eab1e410da941694e1910cf72.jpg", + "image_caption": [ + "Optical Flow", + "OF" + ], + "image_footnote": [], + "bbox": [ + 740, + 316, + 870, + 417 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b4dc052941b12160862469599aadd4b4d451994f88b4b776fe568006e4373952.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 571, + 417, + 704, + 518 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/fdf93e113c0338d9c70e4978bdd53ae17fd7c2d4c84ee2fc721e60b785b8da0a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 740, + 420, + 870, + 518 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 611, + 312, + 626 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Current Dynamic Texture Synthesis (DyTS) models can synthesize realistic videos. However, they require a slow iterative optimization process to synthesize a single fixed-size short video, and they do not offer any post-training control over the synthesis process. We propose Dynamic Neural Cellular Automata (DyNCA), a framework for real-time and controllable dynamic texture synthesis. Our method is built upon the recently introduced NCA models and can synthesize infinitely long and arbitrary-sized realistic video textures in real time. We quantitatively and qualitatively evaluate our model and show that our synthesized videos appear more realistic than the existing results. We improve the SOTA DyTS performance by $2 \\sim 4$ orders of magnitude. Moreover, our model offers several real-time video controls including motion speed, motion direction, and an editing brush tool. We exhibit our trained models in an online interactive demo that runs on local hardware and is accessible on personal computers and smartphones.", + "bbox": [ + 75, + 642, + 472, + 914 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 501, + 611, + 630, + 626 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Textures are everywhere. We perceive them as spatially repetitive patterns. Dynamic Textures are textures that change over time and induce a sense of motion. Flames, sea waves, and fluttering branches are everyday examples. Understanding and computationally modeling dynamic textures is an intriguing problem, as these patterns are observed in most natural scenes.", + "bbox": [ + 496, + 635, + 890, + 739 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The goal of Dynamic Texture Synthesis (DyTS) [5-8, 10, 12, 23, 24, 27, 29, 32] is to generate perceptually-equivalent samples of an exemplar video texture3. Applications of DyTS include the creation of special effects for backdrops and video games [21], dynamic style transfer [24], and creating cinematographs [12].", + "bbox": [ + 496, + 741, + 890, + 832 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The state-of-the-art (SOTA) dynamic texture synthesis", + "bbox": [ + 517, + 833, + 890, + 849 + ], + "page_idx": 0 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "1We use the same flow visualization as Baker et al. [2].", + "2Link to the demo: https://dynca.github.io", + "3We use \"video texture\" and \"dynamic texture\" interchangeably." + ], + "bbox": [ + 517, + 862, + 857, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "20742", + "bbox": [ + 478, + 950, + 517, + 962 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0e567009c008855a90037bf37ec3cdf2519799aac14fc532476247cfb1f6c9c2.jpg", + "image_caption": [ + "Figure 2. Overview of DyNCA. Starting from a seed state, DyNCA iteratively updates it, generating an image sequence. We extract images from this sequence and compare them with an appearance target as well as a motion target to obtain the DyNCA training objectives. After training, DyNCA can adapt to seeds of different heights and widths, and synthesize videos with arbitrary lengths. Sequentially applying DyNCA updates on the seed synthesizes dynamic texture videos in real time." + ], + "image_footnote": [], + "bbox": [ + 78, + 88, + 472, + 207 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "methods [8,24,27,29,32] follow the same trend. They aim to find better optimization strategies to iteratively update a randomly initialized video until the synthesized video resembles the exemplar dynamic texture. Although the SOTA methods are able to synthesize acceptable quality videos, their optimization process is very slow and requires several hours to generate a single fixed-resolution short video on a high-end GPU. Moreover, these methods do not offer any post-training control over the synthesized video.", + "bbox": [ + 75, + 338, + 468, + 474 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper we propose Dynamic Neural Cellular Automata (DyNCA), a model for dynamic texture synthesis that is fast to train, and once trained, can synthesize infinitely-long, arbitrary-resolution dynamic texture videos in real time on a low-end GPU. Moreover, our method enables several real-time video editing controls, including motion direction and motion speed. Through quantitative and qualitative analysis we demonstrate that our synthesized videos achieve better quality and realism than the previous results in the literature.", + "bbox": [ + 75, + 476, + 468, + 626 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our model builds upon the recently introduced Neural Cellular Automata (NCA) model [18, 19]. While Niklasson et al. [19] train the NCA with the goal of synthesizing static textures only, the NCA model is able to spontaneously generate randomly moving patterns. As an inherent property of NCA, these spontaneous motions are, however, unstructured and uncontrolled. We modify the architecture and the training scheme of NCA so that it can learn to synthesize video textures that have the desired motion and appearance.", + "bbox": [ + 75, + 627, + 468, + 763 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In short, our DyNCA model acts as a stochastic Partial Differential Equation (PDE), parameterized by a small neural network. DyNCA starts from a constant initial state called seed, and then iteratively evolves the state according to its trainable PDE update rule to generate a sequence of images. This image sequence is then evaluated against the appearance exemplar and the motion target to calculate the loss functions for the optimization of DyNCA, as illustrated in Figure 2. We allow the user to specify the desired", + "bbox": [ + 75, + 763, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "motion either by a motion vector field or an exemplar dynamic texture video. Moreover, by using a different target for the appearance and the motion, our model can perform dynamic style transfer, as shown in Figure 1. Our contributions summarized are:", + "bbox": [ + 496, + 90, + 890, + 167 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Our DyNCA model, once trained, can synthesize dynamic texture videos in real time.", + "- Our synthesized videos are on-par with or even better than the existing results in terms of realism and quality.", + "- After training, our DyNCA model can synthesize infinitely-long videos with arbitrary frame sizes.", + "- Our DyNCA framework enables several real-time interactive video editing controls including speed, direction, a brush tool, and local coordinate transformation.", + "- We can perform real-time dynamic style transfer by learning appearance and motion from distinct sources." + ], + "bbox": [ + 517, + 174, + 890, + 378 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 500, + 390, + 650, + 406 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In the following section, we discuss the existing DyTS methods. For comparison, Table 1 summarizes the strengths (✓) and shortcomings (X) of these methods.", + "bbox": [ + 498, + 415, + 890, + 460 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Dynamic Texture Synthesis", + "text_level": 1, + "bbox": [ + 498, + 469, + 745, + 486 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In the literature, there are two dominant techniques to synthesize dynamic texture videos. Recent approaches follow the seminal work of Gatys et al. [9] for texture synthesis. The authors propose an optimization-based method that relies on the features extracted by a deep neural network trained for image classification. Gatys et al. [9] show that the Gram matrices of features extracted by the VGG network [22] capture the perceptual qualities of texture images. Funke et al. [8] extend Gatys's idea to dynamic texture synthesis, and use a cross-frame Gram matrix of VGG features to capture the temporal characteristics of dynamic textures. Tesfaldet et al. [24] and Zhang et al. [32] use a pre-trained optical flow network for extracting the motion features, which allows them to disentangle the appearance and motion aspects of video textures. Xie et al. [27] use an energy-based model characterized by a spatio-temporal 3D ConvNet and synthesize textures by sampling using Langevin dynamics.", + "bbox": [ + 496, + 492, + 890, + 763 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "These methods utilize the expressivity of neural networks to produce realistic high-quality dynamic texture videos. However, they require a long training time to synthesize a single short video. Moreover, none of these methods provide any post-training controls over motion speed, frame size, and motion direction. These shortcomings make these methods unsuitable for real-time applications.", + "bbox": [ + 496, + 763, + 890, + 869 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Earlier DyTS methods that can potentially enable real-time synthesis utilized PDEs to model dynamic textures", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "20743", + "bbox": [ + 478, + 950, + 517, + 963 + ], + "page_idx": 1 + }, + { + "type": "table", + "img_path": "images/7b36c04db6feb878ead0594f71b5a014fef269e81a8cec56cb304525071a274a.jpg", + "table_caption": [], + "table_footnote": [ + "Table 1. Comparison of DyTS methods. (A) Can synthesize videos with arbitrary frame size after training. (B) Can synthesize arbitrarily long videos. (C) Can synthesize new video samples without re-training. (D) Allows real-time video editing (speed, direction, and a brush tool). (E) Does not rely on pre-trained models to extract motion or texture information. (F) Has disentangled appearance and motion. (G) Can learn motion from vector fields." + ], + "table_body": "
MethodABCDEFG
Costantini et al. [5]X✓✓X✓XX
Doretto et al. [6]X✓✓X✓XX
Funke et al. [8]X✓XXXXX
Tesfaldet et al. [24]X✓XXX✓✓
Xie et al. [27]XXXX✓XX
Zhang et al. [32]X✓XXX✓✓
DyNCA (Ours)✓✓✓✓X✓✓
", + "bbox": [ + 78, + 88, + 467, + 237 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "[5, 6, 10, 30, 31]. To synthesize video textures, Doretto et al. [6] propose to use a linear dynamical system (LDS) in which each frame of the video is controlled by a latent variable whose evolution through time is driven by random noise. The latent variable is obtained via projection of the target texture image into a lower dimensional space by singular value decomposition (SVD). Costantini et al. [5] propose to use higher-order SVD to improve the expressivity of LDS-based models. Yuan et al. [31] introduce feedback into the LDS to improve the stability of the dynamical system. All these methods can synthesize new video textures without re-training, and potentially in real time. However, the synthesized videos are of low quality and contain artifacts.", + "bbox": [ + 75, + 348, + 468, + 545 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our DyNCA method benefits from the best of both approaches by combining the expressivity of neural networks with PDEs. Having $2 \\sim 4$ orders of magnitude fewer parameters than the SOTA models, our model can synthesize realistic dynamic texture videos in real time.", + "bbox": [ + 75, + 545, + 468, + 621 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. NCA for Texture Synthesis", + "text_level": 1, + "bbox": [ + 76, + 633, + 318, + 648 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Gilpin [11] shows that Cellular Automata models can be represented using Convolutional Neural Networks. Extending [11], Mordvinstev et al. [18] propose the Neural Cellular Automata model and show its potential in creating various self-organizing systems [17-20]. NCA is inspired by Turing's seminal work [25] on pattern generation, and the observation that many natural patterns stem from local interactions between tiny particles, cells, or molecules [19].", + "bbox": [ + 75, + 657, + 468, + 777 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Niklasson et al. [17, 19] were the first to train NCA models to synthesize textures. While the NCA training signal originates from a static exemplar texture image, the model is able to spontaneously generate stable but randomly moving textures. We modify the architecture and training scheme of NCA to enable synthesizing structured motion. First, our DyNCA model receives supervision from a pre-trained optical-flow network, which enables it to synthesize a video", + "bbox": [ + 75, + 779, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "texture with structured motion. Moreover, we incorporate multi-scale perception and positional encoding into the DyNCA architecture. The proposed architectural changes increase the communication range of the cells and allow the cells to be aware of global information, respectively.", + "bbox": [ + 496, + 90, + 890, + 167 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. DyNCA Architecture", + "text_level": 1, + "bbox": [ + 500, + 174, + 702, + 191 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the following sections, we first review the NCA model and then present the architecture of our DyNCA.", + "bbox": [ + 500, + 196, + 890, + 229 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Neural Cellular Automata (NCA)", + "text_level": 1, + "bbox": [ + 500, + 234, + 792, + 250 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The idea of NCA stems from cellular automata, in which cells live on a grid, and each cell communicates with its neighbors to determine the cell's next state. In NCA, cell states at time $t$ are represented by $\\mathbf{S}^t \\in \\mathbb{R}^{H \\times W \\times C}$ where $H \\times W$ is the grid size. The $C$ dimensional vector $s_{ij}^t$ encodes the state of the cell at location $i, j$ , where the first three dimensions define the RGB color of the cell.", + "bbox": [ + 496, + 255, + 890, + 359 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The NCA starts from a constant zero-filled initial state called seed and evolves this state over time according to its trainable PDE. The update rule of this PDE consists of two parts, Perception and Stochastic Update. At the perception stage, each cell gathers information from its surrounding neighbors, forming the perception vector $z_{ij} \\in \\mathbb{R}^{4C}$ , illustrated in the green box in Figure 3.", + "bbox": [ + 496, + 361, + 890, + 469 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nz _ {i j} = \\operatorname {C o n c a t} \\left(s _ {i j}, \\nabla_ {\\mathrm {x}} \\mathbf {S} | _ {i j}, \\nabla_ {\\mathrm {y}} \\mathbf {S} | _ {i j}, \\nabla^ {2} \\mathbf {S} | _ {i j}\\right) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 549, + 476, + 890, + 494 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Note that the convolution kernels in the perception stage are frozen during training. In the stochastic update stage, the new state of each cell is determined based on its perception vector. The update stage of NCA can be viewed as a stochastic discrete-time, discrete-space PDE:", + "bbox": [ + 496, + 500, + 890, + 575 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathbf {S} ^ {t + 1} = \\mathcal {F} (\\mathbf {S} ^ {t}) = \\mathbf {S} ^ {t} + \\frac {\\partial \\mathbf {S}}{\\partial t} \\Delta t \\tag {2} \\\\ \\frac {\\partial s _ {i j}}{\\partial t} = \\operatorname {M L P} \\left(z _ {i j}\\right) \\odot M \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 593, + 579, + 890, + 640 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where MLP is a Multi Layered Perceptron with two layers and a ReLU activation function. The residual update values produced by the MLP are multiplied by a binary random variable $M$ to introduce stochasticity into the model. This ensures that the cells can work asynchronously, and also enables synthesizing new texture samples. The stochastic update stage is illustrated in the blue box in Figure 3.", + "bbox": [ + 496, + 643, + 890, + 750 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To facilitate long-range cell communication and to allow the cells to be aware of global information, we introduce multi-scale perception and positional encoding into the vanilla NCA architecture, respectively. Our experiments in section 5 demonstrate their necessity for DyTS. The overall architecture of our DyNCA model is illustrated in Figure 3. To the best of our knowledge, we are the first to incorporate these two architectural changes in conjunction with NCA models. In the following sections, we elaborate on the proposed architectural modifications.", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "20744", + "bbox": [ + 478, + 950, + 517, + 963 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/11bba1529c422dfab78a28e8ccdaddb3b6c543e448075db2466bf50e159c7883.jpg", + "image_caption": [ + "Figure 3. Illustration of a single DyNCA step. Given an input state $\\mathbf{S}^t\\in R^{H\\times W\\times C}$ at time step $t$ , each cell first perceives its neighbors on various scales with the same perception layer. The perception tensor of each scale is then upsampled and summed up, and is concatenated with the positional encoding tensor $\\mathbf{P}_{xy}$ . Each cell then applies the same update rule, parameterized by a small MLP. Finally, all cells perform a stochastic residual update to determine the state of the cells in time $t + \\Delta t$ . We use $\\Delta t = 1$ in our model." + ], + "image_footnote": [], + "bbox": [ + 83, + 89, + 506, + 366 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/4079eea13ba9b4f96674a7860867462d0a91816c64c1ea81c5454c0731822e58.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 509, + 89, + 893, + 366 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Multi-scale Perception", + "text_level": 1, + "bbox": [ + 76, + 438, + 285, + 454 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the perception stage of vanilla NCA, each cell only receives information from its eight surrounding cells. Therefore, many timesteps are needed for far-apart cells to perceive and communicate with each other. This problem becomes more pronounced when we increase the grid size $H \\times W$ , since the $3 \\times 3$ perception kernels become smaller in proportion to the image size. One straightforward solution is to increase the number of NCA steps during training to facilitate long-range cell communication. However, this simple solution increases memory usage, slows down the training, and makes the training more unstable.", + "bbox": [ + 75, + 462, + 470, + 628 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To solve this problem, we propose Multi-Scale Perception (MSP). The idea of using multi-scale analysis predates deep learning and has shown its effectiveness in many computer vision tasks [1, 3, 14, 15]. We build a pyramid of cell states via bilinear downsampling and apply the same perception kernels at different scales. To combine the information from all scales, we upsample and sum up the perception vectors, as shown in the red box in Figure 3. Multi-scale perception increases the communication range of the cells and allows messages to pass between faraway cells in fewer steps. It also improves the stability of DyNCA and makes the training less sensitive to hyperparameters. We perform an ablation study of multi-scale perception in section 5.4 and show its importance in preserving appearance fidelity.", + "bbox": [ + 75, + 628, + 468, + 840 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Positional Encoding", + "text_level": 1, + "bbox": [ + 76, + 847, + 267, + 864 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In order to apply the $3 \\times 3$ depth-wise convolutions in the perception stage, one needs to adopt a padding strat", + "bbox": [ + 76, + 869, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "egy to retain the spatial dimensions. Niklasson et al. [19] use circular padding to make the cells homogeneous and to reduce spatial inductive bias. While cell homogeneity is a good assumption for generating static textures, it is not suitable for synthesizing structured motion. Our intuition is that, in physical systems, motion not only arises from local interactions between tiny particles and cells, but also from global external forces such as gravity. Hence, we allow the cells to be aware of their position and propose to use replicate padding and Cartesian Positional Encoding (CPE), which is known to provide a more consistent spatial inductive bias than zero-padding [28]. As illustrated in the purple box in Figure 3, we concatenate the output of the multi-scale perception stage with a two-channel tensor $\\mathbf{P}_{\\mathrm{xy}}$ , where $\\mathbf{P}_{ij} = \\left[ \\begin{array}{c}2i + 1.0\\\\ \\frac{W}{2j + 1.0}\\\\ H \\end{array} \\right] - 1.0$ . Our ablation study in section 5.4 shows that employing CPE drastically improves motion consistency and accuracy in the synthesized videos.", + "bbox": [ + 496, + 439, + 893, + 712 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. DyNCA Training", + "text_level": 1, + "bbox": [ + 500, + 724, + 669, + 743 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our DyNCA model acts as a PDE and generates a sequence of images $\\mathcal{I}^g = \\{\\mathcal{I}_1^g,\\mathcal{I}_2^g,\\ldots \\}$ . We sample the synthesized video frames $\\mathcal{V}^g = \\{\\mathcal{V}_1^g,\\mathcal{V}_2^g,\\ldots \\}$ from this image sequence by mapping $T$ DyNCA steps to one frame, i.e. $\\mathcal{V}_k^g = \\mathcal{I}_{kT}^g$ . The synthesized video is then evaluated against the target appearance and the target motion to compute the appearance loss $\\mathcal{L}_{appr}$ and the motion loss $\\mathcal{L}_{motion}$ , respectively. This process is shown in Figure 2. Our final loss is $\\mathcal{L}_{\\mathrm{DyNCA}} = \\mathcal{L}_{appr} + \\lambda \\mathcal{L}_{motion}$ . The overall scheme of the proposed loss functions is illustrated in Figure 4.", + "bbox": [ + 496, + 750, + 890, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "20745", + "bbox": [ + 478, + 950, + 517, + 963 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/c893b5e96e0d53b59cebc21d2d02456e24b20dc48cf433a0f555196b05c7db4e.jpg", + "image_caption": [ + "Figure 4. Overview of our loss functions. Appearance loss $(\\mathcal{L}_{appr})$ : DyNCA learns the target appearance from a static image via minimizing an optimal-transport-based style matching loss [13] between deep features extracted from the VGG16 network [22]. Motion Loss $(\\mathcal{L}_{mvec})$ : We guide DyNCA to synthesize a video having an optical flow similar to the target vector field. Motion Loss $(\\mathcal{L}_{mvec})$ : DyNCA fits the target video motion by minimizing an optimal-transport-based style matching loss between deep features of a pre-trained optical-flow prediction network." + ], + "image_footnote": [], + "bbox": [ + 80, + 88, + 468, + 478 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Appearance Loss", + "text_level": 1, + "bbox": [ + 76, + 633, + 245, + 650 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We follow the texture fitting scheme proposed by Niklasson et al. [19], where the statistics of deep features of the NCA-generated images are forced to match the ones of the target texture. We use a pre-trained VGG16 network [22] to extract the deep features from the images. We denote VGG as $\\mathcal{F}_{VGG}$ and the feature map extracted from layer $l$ as $\\mathcal{F}_{VGG}^l$ . Niklasson et al. [19] use the Gram matrix to define the training objective of the NCA. However, using Gram matrices can cause unstable training [26], and can result in textures with wrong colors [16, 19]. Hence, we use the style loss proposed by Kolkin et al. [13], which has shown to produce better results. This loss is composed of a structure-matching term and a moment-matching term. Given a feature map of size $C\\times H\\times W$ , the algorithm first creates a set of deep features with $n = H\\times W$ elements by flattening the feature map along the spatial dimensions. Let $X$ and $Y$", + "bbox": [ + 75, + 659, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "be the deep feature set of a synthesized image and target appearance image, respectively. Then the structure-matching term $\\mathcal{L}_s$ and the moment-matching term $\\mathcal{L}_m$ are defined as:", + "bbox": [ + 498, + 90, + 890, + 137 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nD (A, B) = \\frac {1}{| A |} \\sum_ {i} \\min _ {j} \\left(1 - \\frac {A _ {i} \\cdot B _ {j}}{| | A _ {i} | | _ {2} | | B _ {j} | | _ {2}}\\right) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 527, + 146, + 890, + 184 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {s} (X, Y) = \\max \\left\\{D (X, Y), D (Y, X) \\right\\},\n$$\n", + "text_format": "latex", + "bbox": [ + 547, + 186, + 825, + 204 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {m} (X, Y) = \\frac {1}{C} \\| \\boldsymbol {\\mu} _ {X} - \\boldsymbol {\\mu} _ {Y} \\| _ {1} + \\frac {1}{C ^ {2}} \\| \\boldsymbol {\\Sigma} _ {X} - \\boldsymbol {\\Sigma} _ {Y} \\| _ {1}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 508, + 207, + 890, + 237 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $D$ measures the distance between two deep feature sets, and $\\pmb{\\mu},\\pmb{\\Sigma}$ are the mean and covariance matrix of their corresponding set, respectively. Let $X_{k}^{l}$ and $Y^{l}$ be deep VGG features extracted by $\\mathcal{F}_{VGG}^{\\text{conv } l-1}$ , where $l$ and $k$ indicate the VGG block index and the synthesized image index, respectively. Our final appearance loss is then defined as:", + "bbox": [ + 498, + 238, + 890, + 329 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {a p p r}} = \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\sum_ {l = 1} ^ {5} \\left(\\mathcal {L} _ {s} \\left(X _ {k} ^ {l}, Y ^ {l}\\right) + \\mathcal {L} _ {m} \\left(X _ {k} ^ {l}, Y ^ {l}\\right)\\right) \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 334, + 890, + 377 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Motion Loss", + "text_level": 1, + "bbox": [ + 500, + 381, + 632, + 396 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The motion loss guides the DyNCA to produce the desired motion. We use the pre-trained Optical-Flow Prediction Network from [24] to quantify the motion information between two frames. We denote this network as $\\mathcal{F}_{OF}$ , and the feature map extracted from layer $l$ as $\\mathcal{F}_{OF}^l$ . For different types of target motion sources, namely vector fields and videos, our motion loss takes two different forms, $\\mathcal{L}_{mvec}$ and $\\mathcal{L}_{mvid}$ , respectively. These terms are discussed below.", + "bbox": [ + 498, + 402, + 890, + 523 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2.1 Motion from Vector Field", + "text_level": 1, + "bbox": [ + 500, + 534, + 732, + 547 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Let $U^t \\in \\mathbb{R}^{H \\times W \\times 2}$ be the target motion vector field. Let $U^g = \\mathcal{F}_{OF}(\\mathcal{I}_{t_1}^g, \\mathcal{I}_{t_2}^g)$ be the optical-flow prediction on two synthesized images, where $t_1, t_2$ are two random indices such that $t_2 > t_1$ . We propose two losses, $\\mathcal{L}_{dir}$ for matching the motion direction, defined as:", + "bbox": [ + 498, + 556, + 890, + 633 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {d i r} = \\frac {1}{H W} \\sum_ {i, j} \\left(1 - \\frac {U _ {i j} ^ {g} \\cdot U _ {i j} ^ {t}}{\\left\\| U _ {i j} ^ {g} \\right\\| _ {2} \\left\\| U _ {i j} ^ {t} \\right\\| _ {2}}\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 552, + 638, + 890, + 681 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "and $\\mathcal{L}_{norm}$ for matching the motion magnitude, defined as:", + "bbox": [ + 500, + 686, + 888, + 702 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {n o r m}} = \\frac {1}{H W} \\sum_ {i, j} \\left| \\frac {T}{t _ {2} - t _ {1}} \\left\\| U _ {i j} ^ {g} \\right\\| _ {2} - \\left\\| U _ {i j} ^ {t} \\right\\| _ {2} \\right|. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 522, + 705, + 890, + 744 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Since $t_1, t_2$ are selected randomly, we scale the norm of the $U^g$ by $\\frac{T}{t_2 - t_1}$ before comparing it against the target motion vector field. We define our final loss $\\mathcal{L}_{mvec}$ as:", + "bbox": [ + 500, + 750, + 890, + 796 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {m v e c} = (1. 0 - \\min \\{1. 0, \\mathcal {L} _ {d i r} \\}) \\mathcal {L} _ {\\text {n o r m}} + \\gamma \\mathcal {L} _ {d i r}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 516, + 801, + 890, + 819 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\gamma$ is a constant coefficient. We set the norm-matching loss weight to $(1.0 - \\min\\{1.0, \\mathcal{L}_{dir}\\})$ to guide the training process to first focus on producing motion with the correct direction before trying to match the norm of the synthesized motion with the target vector field.", + "bbox": [ + 498, + 825, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "20746", + "bbox": [ + 478, + 950, + 517, + 963 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2.2 Motion from Video", + "text_level": 1, + "bbox": [ + 76, + 90, + 266, + 104 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For training DyNCA to learn the motion from a target video, we aim to match the motion between successive frames of the synthesized and target videos. We synthesize a video $\\mathcal{V}^g$ with $K$ frames, and randomly pick the same number of consecutive frames from the target video, forming $\\mathcal{V}^t$ . Inspired by Tesfaldet et al. [24], we feed successive video frames to a pre-trained optical-flow network and extract deep features from the concatenation layer of the network, denoted as $\\mathcal{F}_{OF}^{concat}$ . To compare the deep optical flow features of the target and the synthesized videos, we use the same structure-matching and moment-matching terms defined in Section 4.1. We denote the extracted deep optical-flow features as $X_{k}$ for the synthesized video, and $Y_{k}$ for the target video, where $k$ indicates the frame index. Notice that there are $K - 1$ successive frame pairs in total. We define the objective for learning motion from video textures as:", + "bbox": [ + 75, + 109, + 472, + 352 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {m v i d} = \\frac {1}{K - 1} \\sum_ {k = 1} ^ {K - 1} \\left(\\mathcal {L} _ {s} \\left(X _ {k}, Y _ {k}\\right) + \\mathcal {L} _ {m} \\left(X _ {k}, Y _ {k}\\right)\\right) \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 356, + 468, + 397 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 76, + 404, + 209, + 421 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We conduct experiments on the critical parameters of DyNCA, including $N_{C}, N_{H}, N_{W}, N_{FC}$ , where $N_{C}, N_{H}, N_{W}$ are the size of the DyNCA seed state and $N_{FC}$ is the output dimensionality of the first layer of MLP in DyNCA. Concretely, we set $N_{C} = 12$ , $N_{FC} = 96$ for DyNCA-S and $N_{C} = 16$ , $N_{FC} = 128$ for DyNCA-L. Although DyNCA can adapt to arbitrary seed sizes after training, the seed resolution used during training affects the texture details. We experiment with both $128^{2}$ and $256^{2}$ spatial resolutions for the seed. We use Positional Encoding for all of the DyNCA configurations, and enable Multi-Scale Perception only when training with the $256 \\times 256$ seed size. Table 2 summarizes the DyNCA configurations. We perform our experiments on an Nvidia-A100 GPU, and use Adam optimizer with an initial learning rate of 0.001. We refer the reader to the supplementary for further training details.", + "bbox": [ + 75, + 422, + 472, + 666 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Dynamic Texture Synthesis", + "text_level": 1, + "bbox": [ + 76, + 669, + 321, + 686 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We present the results of synthesizing dynamic textures using DyNCA, where the target motion is either a vector field or a video, and the target appearance is a static image.", + "bbox": [ + 75, + 689, + 468, + 734 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Motion from Vector Field: We manually design 12 target vector fields, and for each target motion, we train both DyNCA-S and DyNCA-L configurations on 45 different target appearances. We provide the resulting 1080 trained models in our real-time interactive demo. We set seed size to $128 \\times 128$ and $T = 24$ , assuming that 24 steps of DyNCA update equals one frame of the synthesized video. Figure 6 shows the optical flow of the DyNCA-S synthesized videos and the corresponding target vector fields used for training.", + "bbox": [ + 75, + 734, + 468, + 869 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Motion from Video. We train DyNCA to match the target motion from videos. For the target appearance image,", + "bbox": [ + 76, + 869, + 468, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "we use one of the video frames or a stylistic image, to perform dynamic texture synthesis and dynamic style transfer, respectively. We train both DyNCA-S and DyNCA-L on 59 target dynamic texture videos provided in [24], setting seed size to $256 \\times 256$ and $T = 64$ . Figure 5 provides some visual results. More results are provided in our demo and supplementary. In Table 2, we compare our DyNCA and the previous SOTA models [24,27] in terms of the computational costs, namely performance and the number of parameters. Note that our DyNCA model is orders of magnitude more efficient in both training and synthesis time as well as the number of parameters. We refer the reader to the supplementary material for the detailed experimental setup.", + "bbox": [ + 496, + 90, + 890, + 287 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Real-time Video Editing", + "text_level": 1, + "bbox": [ + 498, + 291, + 723, + 308 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "DyNCA can also perform real-time video editing by utilizing the post-training NCA controls introduced in [19]. These edits include direction control, speed control, a brush tool, and local coordinate transformations. We refer the reader to our online demo at https://dynca.github.io for real-time and interactive visualization and experimentation.", + "bbox": [ + 496, + 311, + 890, + 402 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Direction Control: By rotating the Sobel convolution kernels $\\nabla_{\\mathrm{x}}$ and $\\nabla_{\\mathrm{y}}$ in the perception stage, we can control the direction of the motion in the synthesized video. This is done by replacing $\\nabla_{\\mathrm{x}}$ and $\\nabla_{\\mathrm{y}}$ with $\\nabla_{\\mathrm{u}}$ and $\\nabla_{\\mathrm{v}}$ , where $\\binom{\\mathrm{u}}{\\mathrm{v}} = \\mathrm{R}_{\\theta}\\binom{\\mathrm{x}}{\\mathrm{y}}$ and $\\mathbf{R}_{\\theta}$ is the rotation matrix with angle $\\theta$ . We also rotate $\\mathbf{P}_{\\mathrm{xy}}$ by angle $\\theta$ so that the position-dependent part of the motion magnitude also rotates accordingly.", + "bbox": [ + 496, + 402, + 890, + 507 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Speed Control: We control the speed of the synthesized video by increasing/decreasing $T$ , which determines how many DyNCA steps are used to synthesize one video frame. Brush Tool: The brush tool allows the users to delete pixels from the video. Since our DyNCA model exhibits the self-organization property of the original NCA [19], the model can reorganize itself and continue synthesizing realistic videos by naturally filling the deleted pixels.", + "bbox": [ + 496, + 507, + 890, + 627 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Local Coordinate Transformation: DyNCA can create complex motion transformations by allowing each cell to use a different rotation angle $\\theta(i,j)$ for transforming its Sobel convolution kernels. For example, setting the rotation angle for the cell at location $(i,j)$ to $\\arctan\\left(\\frac{i - \\frac{W}{2}}{j - \\frac{H}{2}}\\right)$ will transform a rightward motion into a circular motion.", + "bbox": [ + 496, + 628, + 890, + 726 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.3. User Study", + "text_level": 1, + "bbox": [ + 500, + 729, + 620, + 746 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Although it is tempting to use a metric, e.g. the Gram matrix difference [9], to compare the quality of the videos synthesized by different methods, the variety of training objectives used in the existing methods makes such comparisons biased and unfair. Therefore, we conduct a similar user study as Tesfaldet et al. [24] to quantitatively evaluate and compare the realism of the videos. We show a pair of videos to the participants and ask them to choose the video that appears more realistic. We compare the videos synthesized by (DyNCA, [24], [27]) with each other and also", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "20747", + "bbox": [ + 478, + 950, + 519, + 963 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0a050e8d64d35c4866191f49ad2919f305fa8b82139ba07bbecb7e9843a0ca75.jpg", + "image_caption": [ + "Figure 5. Results of dynamic texture synthesis and dynamic style transfer with DyNCA-L-256². Dynamic Texture Synthesis: DyNCA faithfully reproduces the target appearance and target dynamics. Dynamic Style Transfer: DyNCA can learn appearance and motion from different sources. Note that DyNCA does not simply copy the target dynamics from the video, but learns the style of the given motion and naturally adapts it to the target appearance, as shown by the optical-flow images. See our real-time interactive demo https://dynca.github.io" + ], + "image_footnote": [], + "bbox": [ + 76, + 85, + 875, + 529 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/46baa5983c256e2719cca253920839b75aa07198a00821218820d8961f291c65.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodRes.Training Time (s)Synthesis Time (s)# Parameters
A [24]2562#frames × 5005.0 × 102#frames × 0.2M
B [27]2242#frames × 4004.0 × 10281M
C [27]1002#frames × 8.58.5 × 1002.8M
DyNCA-S128223203.3 × 10-20.006M
DyNCA-S256239805.7 × 10-20.006M
DyNCA-L128223703.5 × 10-20.010M
DyNCA-L256243805.7 × 10-20.010M
", + "bbox": [ + 78, + 597, + 467, + 698 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Comparison of training time, synthesis time per frame, and number of trainable parameters of different DyTS methods. (A) Tesfaldet et al. [24]; (B) Xie et al. [27] FC config; (C) Xie et al. [27] ST config. For (B) and (C), training and synthesis happen simultaneously, and the video is synthesized once the training is finished. All methods are evaluated on a single A100 40GB GPU.", + "bbox": [ + 75, + 700, + 468, + 785 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "with real videos using the same 59 dynamic texture videos as Tesfaldet et al. [24]. Table 3 shows the results of our user study. Each entry shows the percentage of times that the video from the corresponding column was chosen over the video from the corresponding row. Our method outperforms the other DyTS method in realism. We refer the reader to our supplementary for more details on the user study.", + "bbox": [ + 75, + 797, + 470, + 905 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a45fcb4faaedbb3aa9a4d3ffb77be7e765725db8810a36e21476476ef6e78fbe.jpg", + "image_caption": [ + "Figure 6. Results of DyNCA trained on various target vector fields as the motion target. First and second row: Symbolic and colored optical-flow representations of the target vector fields. Third row: Snapshot of the optical-flow estimations of the videos synthesized by DyNCA-S-128 $^2$ . The target appearance used for training the model is fibrous_0145 texture from the DTD dataset [4]." + ], + "image_footnote": [], + "bbox": [ + 501, + 597, + 890, + 685 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.4. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 787, + 653, + 804 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Positional Encoding: We ablate the Cartesian Positional Encoding (CPE) and train DyNCA-S-128² with different padding strategies for comparison. In Table 4, we report the average of $\\mathcal{L}_{dir}$ and $\\mathcal{L}_{norm}$ losses on 4 target vector fields (Diverge, Converge, Circular, and Hyperbolic shown in the last 4 columns of Figure 6) and 10 different target", + "bbox": [ + 496, + 809, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "20748", + "bbox": [ + 478, + 950, + 519, + 963 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8c8d3f742d707ec980ba1acce2387a8efdcf0eb7468e55cd9fbac59da95a61f7.jpg", + "image_caption": [ + "Table 3. Top: Comparison of real and synthesized video frames from different methods: (A) Tesfaldet et al. [24]; (B) Xie et al. [27] FC config; (C) Xie et al. [27] ST config. Bottom: Pair-wise comparison results from our user study. The participants see two videos one after another in random order and are asked to choose the video that appears more realistic. Our DyNCA achieves an on-par \"fooling\" rate when compared with real videos. Yet, our synthesized videos look more realistic when compared to existing DyTS methods (60%, 54%, 80%). All error margins are $\\leq 2\\%$ ." + ], + "image_footnote": [], + "bbox": [ + 81, + 89, + 472, + 343 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "appearances. The results demonstrate that CPE is a necessary component for DyNCA to learn the motion from a structured target vector field, in which the motion direction and magnitude are position-dependent. We show the importance of CPE for video motion fitting in the supplementary.", + "bbox": [ + 75, + 486, + 468, + 561 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Multi-Scale Perception:. MSP is key to enable training DyNCA with larger seed sizes. We train DyNCA-L-256² both with and without multi-scale perception and evaluate the results qualitatively and quantitatively. Figure 8 shows the corresponding synthesized video frames, qualitatively demonstrating that single-scale perception causes artifacts to appear in the synthesized frames. We also perform a quantitative evaluation in the supplementary, showing that training with multi-scale perception improves both the appearance $\\mathcal{L}_{\\text {appr }}$ and the video motion $\\mathcal{L}_{\\text {mvid }}$ losses.", + "bbox": [ + 75, + 564, + 470, + 717 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Limitations", + "text_level": 1, + "bbox": [ + 76, + 724, + 200, + 742 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "DyNCA has certain limitations. In the case of vector field motion, it cannot generate a correct motion when the target appearance and the target motion are not compatible. For example, DyNCA fails to move a 45-degree oblique pattern in a circular manner. For video motion, we find it difficult to automatically set the motion loss weight $\\lambda$ . Moreover, DyNCA cannot generate diverse motion when the target videos are violating the underlying assumption of dynamic textures, i.e. when they are not temporally homogeneous. In these cases, DyNCA suffers from overfitting to", + "bbox": [ + 75, + 750, + 472, + 902 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/38e301f20932046dc65e7b8c018a89d67a679032a4c95c5c250e3c8308018ac2.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Seed SizeLossCircularZeroReplicateCPE
128 × 128Ldir0.9890.1620.3180.062
Lnorm0.6400.2960.3640.235
256 × 256Ldir0.9930.4110.4780.054
Lnorm0.6780.3310.3970.218
", + "bbox": [ + 504, + 88, + 888, + 176 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4. Comparison of motion loss for DyNCA trained with different padding strategies. Using Cartesian Positional Encoding (CPE) improves the motion fidelity, and allows the DyNCA to synthesize the correct motion regardless of the seed size.", + "bbox": [ + 498, + 180, + 893, + 236 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/284cd135bc054349cf1545540163df165acfcf31c2c252f9a29b291ca3ddea1e.jpg", + "image_caption": [ + "Figure 8. Comparison between training DyNCA with and without multi-scale perception. The first row shows the target appearance texture. The results without multi-scale perception (second row) contain artifacts and are of lower quality." + ], + "image_footnote": [], + "bbox": [ + 509, + 239, + 893, + 458 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "the dominant direction of the motion in the target videos We refer to our supplementary material for more details.", + "bbox": [ + 498, + 527, + 890, + 560 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 564, + 619, + 579 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We propose DyNCA, a model that can, in real time, synthesize dynamic texture videos with arbitrary frame size and infinite length. Exploiting multi-scale perception and positional encoding, the cells in DyNCA can readily perform long-range communication and obtain global information. This ensures improved performance both in terms of visual quality and computational expressivity as compared to the vanilla NCA model, as we show with both qualitative and quantitative experiments. DyNCA can learn motion either from a hand-crafted vector field or a video, thus allowing for broader synthesis options. DyNCA produces more realistic video textures than the current DyTS methods, as demonstrated through a user study. DyNCA is also $2 \\sim 4$ orders of magnitude faster than the SOTA methods in synthesis time and has much fewer trainable parameters, thus facilitating real-world deployment. Lastly, DyNCA allows for several real-time and interactive video control tools that let the users control DyNCA without re-training.", + "bbox": [ + 496, + 587, + 890, + 858 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement. This work was supported in part by the Swiss National Science Foundation via the Sinergia grant CRSII5-180359.", + "bbox": [ + 498, + 859, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "20749", + "bbox": [ + 478, + 950, + 519, + 963 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Edward H Adelson, Charles H Anderson, James R Bergen, Peter J Burt, and Joan M Ogden. Pyramid methods in image processing. RCA engineer, 29(6):33-41, 1984. 4", + "[2] Simon Baker, Daniel Scharstein, JP Lewis, Stefan Roth, Michael J Black, and Richard Szeliski. A database and evaluation methodology for optical flow. International Journal of Computer Vision, 92(1):1-31, 2011. 1", + "[3] Peter J Burt and Edward H Adelson. The laplacian pyramid as a compact image code. 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In Yoshua Bengio and Yann LeCun, editors, 3rd International Conference on Learning Representations, ICLR 2015, San Diego, CA, USA, May 7-9, 2015, Conference Track Proceedings, 2015. 2, 5", + "[23] Stefano Soatto, Gianfranco Doretto, and Ying Nian Wu. Dynamic textures. In Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001, volume 2, pages 439-446. IEEE, 2001. 1", + "[24] Matthew Tesfaldet, Marcus A Brubaker, and Konstantinos G Derpanis. Two-stream convolutional networks for dynamic texture synthesis. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 6703-6712, 2018. 1, 2, 3, 5, 6, 7, 8", + "[25] Alan Mathison Turing. The chemical basis of morphogenesis. Bulletin of Mathematical Biology, 52(1):153-197, 1990. 3", + "[26] Pierre Wilmot, Eric Risser, and Connelly Barnes. Stable and controllable neural texture synthesis and style transfer using histogram losses. CoRR, abs/1701.08893, 2017. 5", + "[27] Jianwen Xie, Song-Chun Zhu, and Ying Nian Wu. Synthesizing dynamic patterns by spatial-temporal generative convnet. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 7093-7101, 2017. 1, 2, 3, 6, 7, 8", + "[28] Rui Xu, Xintao Wang, Kai Chen, Bolei Zhou, and Chen Change Loy. Positional encoding as spatial inductive bias in gans. In *arxiv*, December 2020. 4", + "[29] Feng Yang, Gui-Song Xia, Liangpei Zhang, and Xin Huang. Stationary dynamic texture synthesis using convolutional neural networks. In 2016 IEEE 13th International Conference on Signal Processing (ICSP), pages 1135-1139. IEEE, 2016. 1, 2", + "[30] Xinge You, Weigang Guo, Shujian Yu, Kan Li, José C Principe, and Dacheng Tao. Kernel learning for dynamic texture synthesis. IEEE Transactions on Image Processing, 25(10):4782-4795, 2016. 3" + ], + "bbox": [ + 501, + 92, + 890, + 898 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "20750", + "bbox": [ + 478, + 950, + 517, + 963 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[31] Lu Yuan, Fang Wen, Ce Liu, and Heung-Yeung Shum. Synthesizing dynamic texture with closed-loop linear dynamic system. In European Conference on Computer Vision, pages 603-616. Springer, 2004. 3", + "[32] Kaitai Zhang, Bin Wang, Hong-Shuo Chen, Xuejing Lei, Ye Wang, and C-C Jay Kuo. Dynamic texture synthesis by incorporating long-range spatial and temporal correlations. In 2021 International Symposium on Signals, Circuits and Systems (ISSCS), pages 1-4. IEEE, 2021. 1, 2, 3" + ], + "bbox": [ + 78, + 90, + 468, + 218 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "20751", + "bbox": [ + 478, + 950, + 517, + 962 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/DyNCA_ Real-Time Dynamic Texture Synthesis Using Neural Cellular Automata/786b41ed-e991-424e-9c74-c623b61a6162_model.json b/2023/DyNCA_ Real-Time Dynamic Texture Synthesis Using Neural Cellular Automata/786b41ed-e991-424e-9c74-c623b61a6162_model.json new file mode 100644 index 0000000000000000000000000000000000000000..2b76ca564ab249984dcfbe06c900fa481b4b85e8 --- /dev/null +++ b/2023/DyNCA_ Real-Time Dynamic Texture Synthesis Using Neural Cellular Automata/786b41ed-e991-424e-9c74-c623b61a6162_model.json @@ -0,0 +1,2101 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.248, + 0.131, + 0.723, + 0.175 + ], + "angle": 0, + "content": "DyNCA: Real-time Dynamic Texture Synthesis Using Neural Cellular Automata" + }, + { + "type": "text", + "bbox": [ + 0.204, + 0.204, + 0.766, + 0.24 + ], + "angle": 0, + "content": "Ehsan Pajouheshgar*, Yitao Xu*, Tong Zhang, Sabine Süsstrunk \nSchool of Computer and Communication Sciences, EPFL, Switzerland" + }, + { + "type": "text", + "bbox": [ + 0.174, + 0.242, + 0.792, + 0.258 + ], + "angle": 0, + "content": "{ ehsan.pajouheshgar, yitao.xu, tong.zhang, sabine.susstrunk }@epfl.ch" + }, + { + "type": "image_caption", + "bbox": [ + 0.094, + 0.289, + 0.236, + 0.304 + ], + "angle": 0, + "content": "Target Appearance" + }, + { + "type": "image", + "bbox": [ + 0.097, + 0.317, + 0.229, + 0.418 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.098, + 0.42, + 0.228, + 0.52 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.296, + 0.28, + 0.489, + 0.295 + ], + "angle": 0, + "content": "Target Dynamics (Motion)" + }, + { + "type": "image_caption", + "bbox": [ + 0.295, + 0.296, + 0.337, + 0.31 + ], + "angle": 0, + "content": "Video" + }, + { + "type": "image_caption", + "bbox": [ + 0.437, + 0.296, + 0.528, + 0.311 + ], + "angle": 0, + "content": "Optical Flow" + }, + { + "type": "image", + "bbox": [ + 0.269, + 0.331, + 0.364, + 0.405 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.249, + 0.419, + 0.382, + 0.52 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.385, + 0.462, + 0.413, + 0.478 + ], + "angle": 0, + "content": "OF" + }, + { + "type": "image", + "bbox": [ + 0.423, + 0.321, + 0.543, + 0.414 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.417, + 0.419, + 0.548, + 0.52 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.649, + 0.28, + 0.788, + 0.295 + ], + "angle": 0, + "content": "Synthesized Result" + }, + { + "type": "image_caption", + "bbox": [ + 0.617, + 0.296, + 0.66, + 0.31 + ], + "angle": 0, + "content": "Video" + }, + { + "type": "image_caption", + "bbox": [ + 0.761, + 0.296, + 0.851, + 0.311 + ], + "angle": 0, + "content": "Optical Flow" + }, + { + "type": "image", + "bbox": [ + 0.573, + 0.317, + 0.706, + 0.418 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.713, + 0.359, + 0.736, + 0.375 + ], + "angle": 0, + "content": "OF" + }, + { + "type": "image", + "bbox": [ + 0.741, + 0.317, + 0.872, + 0.419 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.573, + 0.419, + 0.705, + 0.52 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.741, + 0.421, + 0.872, + 0.52 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.527, + 0.894, + 0.596 + ], + "angle": 0, + "content": "Figure 1. Our DyNCA model can synthesize infinitely-long realistic dynamic texture videos with arbitrary size in real time. Target Appearance: DyNCA learns a desired texture pattern from a given target appearance image. Target Dynamics: DyNCA can learn motion from different target sources. We allow the users to define the desired motion either by a hand-crafted optical-flow image or a dynamic texture video. Synthesized Result: DyNCA synthesizes realistic dynamic texture videos. Each synthesized video frame resembles the target appearance, while the concatenation of frames induces the motion of the target dynamics. See our real-time interactive demo at2." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.612, + 0.313, + 0.627 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.643, + 0.473, + 0.915 + ], + "angle": 0, + "content": "Current Dynamic Texture Synthesis (DyTS) models can synthesize realistic videos. However, they require a slow iterative optimization process to synthesize a single fixed-size short video, and they do not offer any post-training control over the synthesis process. We propose Dynamic Neural Cellular Automata (DyNCA), a framework for real-time and controllable dynamic texture synthesis. Our method is built upon the recently introduced NCA models and can synthesize infinitely long and arbitrary-sized realistic video textures in real time. We quantitatively and qualitatively evaluate our model and show that our synthesized videos appear more realistic than the existing results. We improve the SOTA DyTS performance by \\(2 \\sim 4\\) orders of magnitude. Moreover, our model offers several real-time video controls including motion speed, motion direction, and an editing brush tool. We exhibit our trained models in an online interactive demo that runs on local hardware and is accessible on personal computers and smartphones." + }, + { + "type": "title", + "bbox": [ + 0.502, + 0.612, + 0.631, + 0.627 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.636, + 0.892, + 0.74 + ], + "angle": 0, + "content": "Textures are everywhere. We perceive them as spatially repetitive patterns. Dynamic Textures are textures that change over time and induce a sense of motion. Flames, sea waves, and fluttering branches are everyday examples. Understanding and computationally modeling dynamic textures is an intriguing problem, as these patterns are observed in most natural scenes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.742, + 0.892, + 0.833 + ], + "angle": 0, + "content": "The goal of Dynamic Texture Synthesis (DyTS) [5-8, 10, 12, 23, 24, 27, 29, 32] is to generate perceptually-equivalent samples of an exemplar video texture3. Applications of DyTS include the creation of special effects for backdrops and video games [21], dynamic style transfer [24], and creating cinematographs [12]." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.834, + 0.892, + 0.85 + ], + "angle": 0, + "content": "The state-of-the-art (SOTA) dynamic texture synthesis" + }, + { + "type": "ref_text", + "bbox": [ + 0.518, + 0.863, + 0.81, + 0.876 + ], + "angle": 0, + "content": "1We use the same flow visualization as Baker et al. [2]." + }, + { + "type": "ref_text", + "bbox": [ + 0.519, + 0.876, + 0.743, + 0.888 + ], + "angle": 0, + "content": "2Link to the demo: https://dynca.github.io" + }, + { + "type": "ref_text", + "bbox": [ + 0.519, + 0.888, + 0.859, + 0.901 + ], + "angle": 0, + "content": "3We use \"video texture\" and \"dynamic texture\" interchangeably." + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.863, + 0.859, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.952, + 0.519, + 0.963 + ], + "angle": 0, + "content": "20742" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.089, + 0.473, + 0.208 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.218, + 0.473, + 0.33 + ], + "angle": 0, + "content": "Figure 2. Overview of DyNCA. Starting from a seed state, DyNCA iteratively updates it, generating an image sequence. We extract images from this sequence and compare them with an appearance target as well as a motion target to obtain the DyNCA training objectives. After training, DyNCA can adapt to seeds of different heights and widths, and synthesize videos with arbitrary lengths. Sequentially applying DyNCA updates on the seed synthesizes dynamic texture videos in real time." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.339, + 0.47, + 0.476 + ], + "angle": 0, + "content": "methods [8,24,27,29,32] follow the same trend. They aim to find better optimization strategies to iteratively update a randomly initialized video until the synthesized video resembles the exemplar dynamic texture. Although the SOTA methods are able to synthesize acceptable quality videos, their optimization process is very slow and requires several hours to generate a single fixed-resolution short video on a high-end GPU. Moreover, these methods do not offer any post-training control over the synthesized video." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.477, + 0.47, + 0.627 + ], + "angle": 0, + "content": "In this paper we propose Dynamic Neural Cellular Automata (DyNCA), a model for dynamic texture synthesis that is fast to train, and once trained, can synthesize infinitely-long, arbitrary-resolution dynamic texture videos in real time on a low-end GPU. Moreover, our method enables several real-time video editing controls, including motion direction and motion speed. Through quantitative and qualitative analysis we demonstrate that our synthesized videos achieve better quality and realism than the previous results in the literature." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.628, + 0.47, + 0.765 + ], + "angle": 0, + "content": "Our model builds upon the recently introduced Neural Cellular Automata (NCA) model [18, 19]. While Niklasson et al. [19] train the NCA with the goal of synthesizing static textures only, the NCA model is able to spontaneously generate randomly moving patterns. As an inherent property of NCA, these spontaneous motions are, however, unstructured and uncontrolled. We modify the architecture and the training scheme of NCA so that it can learn to synthesize video textures that have the desired motion and appearance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.471, + 0.902 + ], + "angle": 0, + "content": "In short, our DyNCA model acts as a stochastic Partial Differential Equation (PDE), parameterized by a small neural network. DyNCA starts from a constant initial state called seed, and then iteratively evolves the state according to its trainable PDE update rule to generate a sequence of images. This image sequence is then evaluated against the appearance exemplar and the motion target to calculate the loss functions for the optimization of DyNCA, as illustrated in Figure 2. We allow the user to specify the desired" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.168 + ], + "angle": 0, + "content": "motion either by a motion vector field or an exemplar dynamic texture video. Moreover, by using a different target for the appearance and the motion, our model can perform dynamic style transfer, as shown in Figure 1. Our contributions summarized are:" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.175, + 0.892, + 0.206 + ], + "angle": 0, + "content": "- Our DyNCA model, once trained, can synthesize dynamic texture videos in real time." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.215, + 0.892, + 0.247 + ], + "angle": 0, + "content": "- Our synthesized videos are on-par with or even better than the existing results in terms of realism and quality." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.254, + 0.892, + 0.285 + ], + "angle": 0, + "content": "- After training, our DyNCA model can synthesize infinitely-long videos with arbitrary frame sizes." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.293, + 0.892, + 0.339 + ], + "angle": 0, + "content": "- Our DyNCA framework enables several real-time interactive video editing controls including speed, direction, a brush tool, and local coordinate transformation." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.348, + 0.892, + 0.379 + ], + "angle": 0, + "content": "- We can perform real-time dynamic style transfer by learning appearance and motion from distinct sources." + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.175, + 0.892, + 0.379 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.391, + 0.651, + 0.407 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.416, + 0.892, + 0.462 + ], + "angle": 0, + "content": "In the following section, we discuss the existing DyTS methods. For comparison, Table 1 summarizes the strengths (✓) and shortcomings (X) of these methods." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.47, + 0.746, + 0.487 + ], + "angle": 0, + "content": "2.1. Dynamic Texture Synthesis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.493, + 0.892, + 0.765 + ], + "angle": 0, + "content": "In the literature, there are two dominant techniques to synthesize dynamic texture videos. Recent approaches follow the seminal work of Gatys et al. [9] for texture synthesis. The authors propose an optimization-based method that relies on the features extracted by a deep neural network trained for image classification. Gatys et al. [9] show that the Gram matrices of features extracted by the VGG network [22] capture the perceptual qualities of texture images. Funke et al. [8] extend Gatys's idea to dynamic texture synthesis, and use a cross-frame Gram matrix of VGG features to capture the temporal characteristics of dynamic textures. Tesfaldet et al. [24] and Zhang et al. [32] use a pre-trained optical flow network for extracting the motion features, which allows them to disentangle the appearance and motion aspects of video textures. Xie et al. [27] use an energy-based model characterized by a spatio-temporal 3D ConvNet and synthesize textures by sampling using Langevin dynamics." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.871 + ], + "angle": 0, + "content": "These methods utilize the expressivity of neural networks to produce realistic high-quality dynamic texture videos. However, they require a long training time to synthesize a single short video. Moreover, none of these methods provide any post-training controls over motion speed, frame size, and motion direction. These shortcomings make these methods unsuitable for real-time applications." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Earlier DyTS methods that can potentially enable real-time synthesis utilized PDEs to model dynamic textures" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.952, + 0.519, + 0.964 + ], + "angle": 0, + "content": "20743" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.08, + 0.089, + 0.468, + 0.238 + ], + "angle": 0, + "content": "
MethodABCDEFG
Costantini et al. [5]X✓✓X✓XX
Doretto et al. [6]X✓✓X✓XX
Funke et al. [8]X✓XXXXX
Tesfaldet et al. [24]X✓XXX✓✓
Xie et al. [27]XXXX✓XX
Zhang et al. [32]X✓XXX✓✓
DyNCA (Ours)✓✓✓✓X✓✓
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.076, + 0.24, + 0.47, + 0.337 + ], + "angle": 0, + "content": "Table 1. Comparison of DyTS methods. (A) Can synthesize videos with arbitrary frame size after training. (B) Can synthesize arbitrarily long videos. (C) Can synthesize new video samples without re-training. (D) Allows real-time video editing (speed, direction, and a brush tool). (E) Does not rely on pre-trained models to extract motion or texture information. (F) Has disentangled appearance and motion. (G) Can learn motion from vector fields." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.349, + 0.47, + 0.546 + ], + "angle": 0, + "content": "[5, 6, 10, 30, 31]. To synthesize video textures, Doretto et al. [6] propose to use a linear dynamical system (LDS) in which each frame of the video is controlled by a latent variable whose evolution through time is driven by random noise. The latent variable is obtained via projection of the target texture image into a lower dimensional space by singular value decomposition (SVD). Costantini et al. [5] propose to use higher-order SVD to improve the expressivity of LDS-based models. Yuan et al. [31] introduce feedback into the LDS to improve the stability of the dynamical system. All these methods can synthesize new video textures without re-training, and potentially in real time. However, the synthesized videos are of low quality and contain artifacts." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.546, + 0.469, + 0.622 + ], + "angle": 0, + "content": "Our DyNCA method benefits from the best of both approaches by combining the expressivity of neural networks with PDEs. Having \\(2 \\sim 4\\) orders of magnitude fewer parameters than the SOTA models, our model can synthesize realistic dynamic texture videos in real time." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.634, + 0.32, + 0.65 + ], + "angle": 0, + "content": "2.2. NCA for Texture Synthesis" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.658, + 0.469, + 0.779 + ], + "angle": 0, + "content": "Gilpin [11] shows that Cellular Automata models can be represented using Convolutional Neural Networks. Extending [11], Mordvinstev et al. [18] propose the Neural Cellular Automata model and show its potential in creating various self-organizing systems [17-20]. NCA is inspired by Turing's seminal work [25] on pattern generation, and the observation that many natural patterns stem from local interactions between tiny particles, cells, or molecules [19]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Niklasson et al. [17, 19] were the first to train NCA models to synthesize textures. While the NCA training signal originates from a static exemplar texture image, the model is able to spontaneously generate stable but randomly moving textures. We modify the architecture and training scheme of NCA to enable synthesizing structured motion. First, our DyNCA model receives supervision from a pre-trained optical-flow network, which enables it to synthesize a video" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.168 + ], + "angle": 0, + "content": "texture with structured motion. Moreover, we incorporate multi-scale perception and positional encoding into the DyNCA architecture. The proposed architectural changes increase the communication range of the cells and allow the cells to be aware of global information, respectively." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.175, + 0.704, + 0.192 + ], + "angle": 0, + "content": "3. DyNCA Architecture" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.198, + 0.892, + 0.23 + ], + "angle": 0, + "content": "In the following sections, we first review the NCA model and then present the architecture of our DyNCA." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.235, + 0.794, + 0.25 + ], + "angle": 0, + "content": "3.1. Neural Cellular Automata (NCA)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.256, + 0.892, + 0.361 + ], + "angle": 0, + "content": "The idea of NCA stems from cellular automata, in which cells live on a grid, and each cell communicates with its neighbors to determine the cell's next state. In NCA, cell states at time \\( t \\) are represented by \\( \\mathbf{S}^t \\in \\mathbb{R}^{H \\times W \\times C} \\) where \\( H \\times W \\) is the grid size. The \\( C \\) dimensional vector \\( s_{ij}^t \\) encodes the state of the cell at location \\( i, j \\), where the first three dimensions define the RGB color of the cell." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.362, + 0.892, + 0.47 + ], + "angle": 0, + "content": "The NCA starts from a constant zero-filled initial state called seed and evolves this state over time according to its trainable PDE. The update rule of this PDE consists of two parts, Perception and Stochastic Update. At the perception stage, each cell gathers information from its surrounding neighbors, forming the perception vector \\( z_{ij} \\in \\mathbb{R}^{4C} \\), illustrated in the green box in Figure 3." + }, + { + "type": "equation", + "bbox": [ + 0.55, + 0.477, + 0.891, + 0.496 + ], + "angle": 0, + "content": "\\[\nz _ {i j} = \\operatorname {C o n c a t} \\left(s _ {i j}, \\nabla_ {\\mathrm {x}} \\mathbf {S} | _ {i j}, \\nabla_ {\\mathrm {y}} \\mathbf {S} | _ {i j}, \\nabla^ {2} \\mathbf {S} | _ {i j}\\right) \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.5, + 0.892, + 0.576 + ], + "angle": 0, + "content": "Note that the convolution kernels in the perception stage are frozen during training. In the stochastic update stage, the new state of each cell is determined based on its perception vector. The update stage of NCA can be viewed as a stochastic discrete-time, discrete-space PDE:" + }, + { + "type": "equation", + "bbox": [ + 0.594, + 0.58, + 0.891, + 0.641 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathbf {S} ^ {t + 1} = \\mathcal {F} (\\mathbf {S} ^ {t}) = \\mathbf {S} ^ {t} + \\frac {\\partial \\mathbf {S}}{\\partial t} \\Delta t \\tag {2} \\\\ \\frac {\\partial s _ {i j}}{\\partial t} = \\operatorname {M L P} \\left(z _ {i j}\\right) \\odot M \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.892, + 0.75 + ], + "angle": 0, + "content": "where MLP is a Multi Layered Perceptron with two layers and a ReLU activation function. The residual update values produced by the MLP are multiplied by a binary random variable \\(M\\) to introduce stochasticity into the model. This ensures that the cells can work asynchronously, and also enables synthesizing new texture samples. The stochastic update stage is illustrated in the blue box in Figure 3." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "To facilitate long-range cell communication and to allow the cells to be aware of global information, we introduce multi-scale perception and positional encoding into the vanilla NCA architecture, respectively. Our experiments in section 5 demonstrate their necessity for DyTS. The overall architecture of our DyNCA model is illustrated in Figure 3. To the best of our knowledge, we are the first to incorporate these two architectural changes in conjunction with NCA models. In the following sections, we elaborate on the proposed architectural modifications." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.952, + 0.519, + 0.964 + ], + "angle": 0, + "content": "20744" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.09, + 0.508, + 0.367 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.51, + 0.09, + 0.895, + 0.367 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.372, + 0.895, + 0.43 + ], + "angle": 0, + "content": "Figure 3. Illustration of a single DyNCA step. Given an input state \\(\\mathbf{S}^t\\in R^{H\\times W\\times C}\\) at time step \\(t\\), each cell first perceives its neighbors on various scales with the same perception layer. The perception tensor of each scale is then upsampled and summed up, and is concatenated with the positional encoding tensor \\(\\mathbf{P}_{xy}\\). Each cell then applies the same update rule, parameterized by a small MLP. Finally, all cells perform a stochastic residual update to determine the state of the cells in time \\(t + \\Delta t\\). We use \\(\\Delta t = 1\\) in our model." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.439, + 0.286, + 0.455 + ], + "angle": 0, + "content": "3.2. Multi-scale Perception" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.463, + 0.471, + 0.629 + ], + "angle": 0, + "content": "In the perception stage of vanilla NCA, each cell only receives information from its eight surrounding cells. Therefore, many timesteps are needed for far-apart cells to perceive and communicate with each other. This problem becomes more pronounced when we increase the grid size \\( H \\times W \\), since the \\( 3 \\times 3 \\) perception kernels become smaller in proportion to the image size. One straightforward solution is to increase the number of NCA steps during training to facilitate long-range cell communication. However, this simple solution increases memory usage, slows down the training, and makes the training more unstable." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.63, + 0.47, + 0.841 + ], + "angle": 0, + "content": "To solve this problem, we propose Multi-Scale Perception (MSP). The idea of using multi-scale analysis predates deep learning and has shown its effectiveness in many computer vision tasks [1, 3, 14, 15]. We build a pyramid of cell states via bilinear downsampling and apply the same perception kernels at different scales. To combine the information from all scales, we upsample and sum up the perception vectors, as shown in the red box in Figure 3. Multi-scale perception increases the communication range of the cells and allows messages to pass between faraway cells in fewer steps. It also improves the stability of DyNCA and makes the training less sensitive to hyperparameters. We perform an ablation study of multi-scale perception in section 5.4 and show its importance in preserving appearance fidelity." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.848, + 0.268, + 0.865 + ], + "angle": 0, + "content": "3.3. Positional Encoding" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.902 + ], + "angle": 0, + "content": "In order to apply the \\(3 \\times 3\\) depth-wise convolutions in the perception stage, one needs to adopt a padding strat" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.44, + 0.895, + 0.713 + ], + "angle": 0, + "content": "egy to retain the spatial dimensions. Niklasson et al. [19] use circular padding to make the cells homogeneous and to reduce spatial inductive bias. While cell homogeneity is a good assumption for generating static textures, it is not suitable for synthesizing structured motion. Our intuition is that, in physical systems, motion not only arises from local interactions between tiny particles and cells, but also from global external forces such as gravity. Hence, we allow the cells to be aware of their position and propose to use replicate padding and Cartesian Positional Encoding (CPE), which is known to provide a more consistent spatial inductive bias than zero-padding [28]. As illustrated in the purple box in Figure 3, we concatenate the output of the multi-scale perception stage with a two-channel tensor \\(\\mathbf{P}_{\\mathrm{xy}}\\), where \\(\\mathbf{P}_{ij} = \\left[ \\begin{array}{c}2i + 1.0\\\\ \\frac{W}{2j + 1.0}\\\\ H \\end{array} \\right] - 1.0\\). Our ablation study in section 5.4 shows that employing CPE drastically improves motion consistency and accuracy in the synthesized videos." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.726, + 0.67, + 0.744 + ], + "angle": 0, + "content": "4. DyNCA Training" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.751, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Our DyNCA model acts as a PDE and generates a sequence of images \\(\\mathcal{I}^g = \\{\\mathcal{I}_1^g,\\mathcal{I}_2^g,\\ldots \\}\\). We sample the synthesized video frames \\(\\mathcal{V}^g = \\{\\mathcal{V}_1^g,\\mathcal{V}_2^g,\\ldots \\}\\) from this image sequence by mapping \\(T\\) DyNCA steps to one frame, i.e. \\(\\mathcal{V}_k^g = \\mathcal{I}_{kT}^g\\). The synthesized video is then evaluated against the target appearance and the target motion to compute the appearance loss \\(\\mathcal{L}_{appr}\\) and the motion loss \\(\\mathcal{L}_{motion}\\), respectively. This process is shown in Figure 2. Our final loss is \\(\\mathcal{L}_{\\mathrm{DyNCA}} = \\mathcal{L}_{appr} + \\lambda \\mathcal{L}_{motion}\\). The overall scheme of the proposed loss functions is illustrated in Figure 4." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.952, + 0.518, + 0.964 + ], + "angle": 0, + "content": "20745" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.47, + 0.479 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.493, + 0.47, + 0.618 + ], + "angle": 0, + "content": "Figure 4. Overview of our loss functions. Appearance loss \\((\\mathcal{L}_{appr})\\): DyNCA learns the target appearance from a static image via minimizing an optimal-transport-based style matching loss [13] between deep features extracted from the VGG16 network [22]. Motion Loss \\((\\mathcal{L}_{mvec})\\): We guide DyNCA to synthesize a video having an optical flow similar to the target vector field. Motion Loss \\((\\mathcal{L}_{mvec})\\): DyNCA fits the target video motion by minimizing an optimal-transport-based style matching loss between deep features of a pre-trained optical-flow prediction network." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.635, + 0.246, + 0.651 + ], + "angle": 0, + "content": "4.1. Appearance Loss" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.66, + 0.47, + 0.901 + ], + "angle": 0, + "content": "We follow the texture fitting scheme proposed by Niklasson et al. [19], where the statistics of deep features of the NCA-generated images are forced to match the ones of the target texture. We use a pre-trained VGG16 network [22] to extract the deep features from the images. We denote VGG as \\(\\mathcal{F}_{VGG}\\) and the feature map extracted from layer \\(l\\) as \\(\\mathcal{F}_{VGG}^l\\). Niklasson et al. [19] use the Gram matrix to define the training objective of the NCA. However, using Gram matrices can cause unstable training [26], and can result in textures with wrong colors [16, 19]. Hence, we use the style loss proposed by Kolkin et al. [13], which has shown to produce better results. This loss is composed of a structure-matching term and a moment-matching term. Given a feature map of size \\(C\\times H\\times W\\), the algorithm first creates a set of deep features with \\(n = H\\times W\\) elements by flattening the feature map along the spatial dimensions. Let \\(X\\) and \\(Y\\)" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.138 + ], + "angle": 0, + "content": "be the deep feature set of a synthesized image and target appearance image, respectively. Then the structure-matching term \\(\\mathcal{L}_s\\) and the moment-matching term \\(\\mathcal{L}_m\\) are defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.528, + 0.147, + 0.892, + 0.185 + ], + "angle": 0, + "content": "\\[\nD (A, B) = \\frac {1}{| A |} \\sum_ {i} \\min _ {j} \\left(1 - \\frac {A _ {i} \\cdot B _ {j}}{| | A _ {i} | | _ {2} | | B _ {j} | | _ {2}}\\right) \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.549, + 0.187, + 0.826, + 0.205 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {s} (X, Y) = \\max \\left\\{D (X, Y), D (Y, X) \\right\\},\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.509, + 0.208, + 0.892, + 0.238 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {m} (X, Y) = \\frac {1}{C} \\| \\boldsymbol {\\mu} _ {X} - \\boldsymbol {\\mu} _ {Y} \\| _ {1} + \\frac {1}{C ^ {2}} \\| \\boldsymbol {\\Sigma} _ {X} - \\boldsymbol {\\Sigma} _ {Y} \\| _ {1}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.239, + 0.892, + 0.33 + ], + "angle": 0, + "content": "where \\(D\\) measures the distance between two deep feature sets, and \\(\\pmb{\\mu},\\pmb{\\Sigma}\\) are the mean and covariance matrix of their corresponding set, respectively. Let \\(X_{k}^{l}\\) and \\(Y^{l}\\) be deep VGG features extracted by \\(\\mathcal{F}_{VGG}^{\\text{conv } l-1}\\), where \\(l\\) and \\(k\\) indicate the VGG block index and the synthesized image index, respectively. Our final appearance loss is then defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.518, + 0.335, + 0.892, + 0.378 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {a p p r}} = \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\sum_ {l = 1} ^ {5} \\left(\\mathcal {L} _ {s} \\left(X _ {k} ^ {l}, Y ^ {l}\\right) + \\mathcal {L} _ {m} \\left(X _ {k} ^ {l}, Y ^ {l}\\right)\\right) \\tag {5}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.382, + 0.633, + 0.397 + ], + "angle": 0, + "content": "4.2. Motion Loss" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.403, + 0.892, + 0.524 + ], + "angle": 0, + "content": "The motion loss guides the DyNCA to produce the desired motion. We use the pre-trained Optical-Flow Prediction Network from [24] to quantify the motion information between two frames. We denote this network as \\(\\mathcal{F}_{OF}\\), and the feature map extracted from layer \\(l\\) as \\(\\mathcal{F}_{OF}^l\\). For different types of target motion sources, namely vector fields and videos, our motion loss takes two different forms, \\(\\mathcal{L}_{mvec}\\) and \\(\\mathcal{L}_{mvid}\\), respectively. These terms are discussed below." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.535, + 0.733, + 0.548 + ], + "angle": 0, + "content": "4.2.1 Motion from Vector Field" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.557, + 0.892, + 0.634 + ], + "angle": 0, + "content": "Let \\( U^t \\in \\mathbb{R}^{H \\times W \\times 2} \\) be the target motion vector field. Let \\( U^g = \\mathcal{F}_{OF}(\\mathcal{I}_{t_1}^g, \\mathcal{I}_{t_2}^g) \\) be the optical-flow prediction on two synthesized images, where \\( t_1, t_2 \\) are two random indices such that \\( t_2 > t_1 \\). We propose two losses, \\( \\mathcal{L}_{dir} \\) for matching the motion direction, defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.553, + 0.639, + 0.892, + 0.682 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {d i r} = \\frac {1}{H W} \\sum_ {i, j} \\left(1 - \\frac {U _ {i j} ^ {g} \\cdot U _ {i j} ^ {t}}{\\left\\| U _ {i j} ^ {g} \\right\\| _ {2} \\left\\| U _ {i j} ^ {t} \\right\\| _ {2}}\\right), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.687, + 0.89, + 0.703 + ], + "angle": 0, + "content": "and \\(\\mathcal{L}_{norm}\\) for matching the motion magnitude, defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.524, + 0.707, + 0.892, + 0.746 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {n o r m}} = \\frac {1}{H W} \\sum_ {i, j} \\left| \\frac {T}{t _ {2} - t _ {1}} \\left\\| U _ {i j} ^ {g} \\right\\| _ {2} - \\left\\| U _ {i j} ^ {t} \\right\\| _ {2} \\right|. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.751, + 0.892, + 0.797 + ], + "angle": 0, + "content": "Since \\( t_1, t_2 \\) are selected randomly, we scale the norm of the \\( U^g \\) by \\( \\frac{T}{t_2 - t_1} \\) before comparing it against the target motion vector field. We define our final loss \\( \\mathcal{L}_{mvec} \\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.517, + 0.803, + 0.892, + 0.82 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {m v e c} = (1. 0 - \\min \\{1. 0, \\mathcal {L} _ {d i r} \\}) \\mathcal {L} _ {\\text {n o r m}} + \\gamma \\mathcal {L} _ {d i r}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "where \\(\\gamma\\) is a constant coefficient. We set the norm-matching loss weight to \\((1.0 - \\min\\{1.0, \\mathcal{L}_{dir}\\})\\) to guide the training process to first focus on producing motion with the correct direction before trying to match the norm of the synthesized motion with the target vector field." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.952, + 0.519, + 0.964 + ], + "angle": 0, + "content": "20746" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.077, + 0.092, + 0.267, + 0.106 + ], + "angle": 0, + "content": "4.2.2 Motion from Video" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.111, + 0.473, + 0.353 + ], + "angle": 0, + "content": "For training DyNCA to learn the motion from a target video, we aim to match the motion between successive frames of the synthesized and target videos. We synthesize a video \\(\\mathcal{V}^g\\) with \\(K\\) frames, and randomly pick the same number of consecutive frames from the target video, forming \\(\\mathcal{V}^t\\). Inspired by Tesfaldet et al. [24], we feed successive video frames to a pre-trained optical-flow network and extract deep features from the concatenation layer of the network, denoted as \\(\\mathcal{F}_{OF}^{concat}\\). To compare the deep optical flow features of the target and the synthesized videos, we use the same structure-matching and moment-matching terms defined in Section 4.1. We denote the extracted deep optical-flow features as \\(X_{k}\\) for the synthesized video, and \\(Y_{k}\\) for the target video, where \\(k\\) indicates the frame index. Notice that there are \\(K - 1\\) successive frame pairs in total. We define the objective for learning motion from video textures as:" + }, + { + "type": "equation", + "bbox": [ + 0.092, + 0.357, + 0.47, + 0.398 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {m v i d} = \\frac {1}{K - 1} \\sum_ {k = 1} ^ {K - 1} \\left(\\mathcal {L} _ {s} \\left(X _ {k}, Y _ {k}\\right) + \\mathcal {L} _ {m} \\left(X _ {k}, Y _ {k}\\right)\\right) \\tag {9}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.405, + 0.21, + 0.422 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.424, + 0.473, + 0.667 + ], + "angle": 0, + "content": "We conduct experiments on the critical parameters of DyNCA, including \\( N_{C}, N_{H}, N_{W}, N_{FC} \\), where \\( N_{C}, N_{H}, N_{W} \\) are the size of the DyNCA seed state and \\( N_{FC} \\) is the output dimensionality of the first layer of MLP in DyNCA. Concretely, we set \\( N_{C} = 12 \\), \\( N_{FC} = 96 \\) for DyNCA-S and \\( N_{C} = 16 \\), \\( N_{FC} = 128 \\) for DyNCA-L. Although DyNCA can adapt to arbitrary seed sizes after training, the seed resolution used during training affects the texture details. We experiment with both \\( 128^{2} \\) and \\( 256^{2} \\) spatial resolutions for the seed. We use Positional Encoding for all of the DyNCA configurations, and enable Multi-Scale Perception only when training with the \\( 256 \\times 256 \\) seed size. Table 2 summarizes the DyNCA configurations. We perform our experiments on an Nvidia-A100 GPU, and use Adam optimizer with an initial learning rate of 0.001. We refer the reader to the supplementary for further training details." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.67, + 0.323, + 0.687 + ], + "angle": 0, + "content": "5.1. Dynamic Texture Synthesis" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.69, + 0.47, + 0.735 + ], + "angle": 0, + "content": "We present the results of synthesizing dynamic textures using DyNCA, where the target motion is either a vector field or a video, and the target appearance is a static image." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.469, + 0.87 + ], + "angle": 0, + "content": "Motion from Vector Field: We manually design 12 target vector fields, and for each target motion, we train both DyNCA-S and DyNCA-L configurations on 45 different target appearances. We provide the resulting 1080 trained models in our real-time interactive demo. We set seed size to \\(128 \\times 128\\) and \\(T = 24\\), assuming that 24 steps of DyNCA update equals one frame of the synthesized video. Figure 6 shows the optical flow of the DyNCA-S synthesized videos and the corresponding target vector fields used for training." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.902 + ], + "angle": 0, + "content": "Motion from Video. We train DyNCA to match the target motion from videos. For the target appearance image," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.289 + ], + "angle": 0, + "content": "we use one of the video frames or a stylistic image, to perform dynamic texture synthesis and dynamic style transfer, respectively. We train both DyNCA-S and DyNCA-L on 59 target dynamic texture videos provided in [24], setting seed size to \\(256 \\times 256\\) and \\(T = 64\\). Figure 5 provides some visual results. More results are provided in our demo and supplementary. In Table 2, we compare our DyNCA and the previous SOTA models [24,27] in terms of the computational costs, namely performance and the number of parameters. Note that our DyNCA model is orders of magnitude more efficient in both training and synthesis time as well as the number of parameters. We refer the reader to the supplementary material for the detailed experimental setup." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.292, + 0.724, + 0.309 + ], + "angle": 0, + "content": "5.2. Real-time Video Editing" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.312, + 0.892, + 0.403 + ], + "angle": 0, + "content": "DyNCA can also perform real-time video editing by utilizing the post-training NCA controls introduced in [19]. These edits include direction control, speed control, a brush tool, and local coordinate transformations. We refer the reader to our online demo at https://dynca.github.io for real-time and interactive visualization and experimentation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.403, + 0.892, + 0.508 + ], + "angle": 0, + "content": "Direction Control: By rotating the Sobel convolution kernels \\(\\nabla_{\\mathrm{x}}\\) and \\(\\nabla_{\\mathrm{y}}\\) in the perception stage, we can control the direction of the motion in the synthesized video. This is done by replacing \\(\\nabla_{\\mathrm{x}}\\) and \\(\\nabla_{\\mathrm{y}}\\) with \\(\\nabla_{\\mathrm{u}}\\) and \\(\\nabla_{\\mathrm{v}}\\), where \\(\\binom{\\mathrm{u}}{\\mathrm{v}} = \\mathrm{R}_{\\theta}\\binom{\\mathrm{x}}{\\mathrm{y}}\\) and \\(\\mathbf{R}_{\\theta}\\) is the rotation matrix with angle \\(\\theta\\). We also rotate \\(\\mathbf{P}_{\\mathrm{xy}}\\) by angle \\(\\theta\\) so that the position-dependent part of the motion magnitude also rotates accordingly." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.508, + 0.892, + 0.628 + ], + "angle": 0, + "content": "Speed Control: We control the speed of the synthesized video by increasing/decreasing \\( T \\), which determines how many DyNCA steps are used to synthesize one video frame. Brush Tool: The brush tool allows the users to delete pixels from the video. Since our DyNCA model exhibits the self-organization property of the original NCA [19], the model can reorganize itself and continue synthesizing realistic videos by naturally filling the deleted pixels." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.892, + 0.727 + ], + "angle": 0, + "content": "Local Coordinate Transformation: DyNCA can create complex motion transformations by allowing each cell to use a different rotation angle \\(\\theta(i,j)\\) for transforming its Sobel convolution kernels. For example, setting the rotation angle for the cell at location \\((i,j)\\) to \\(\\arctan\\left(\\frac{i - \\frac{W}{2}}{j - \\frac{H}{2}}\\right)\\) will transform a rightward motion into a circular motion." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.731, + 0.622, + 0.747 + ], + "angle": 0, + "content": "5.3. User Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Although it is tempting to use a metric, e.g. the Gram matrix difference [9], to compare the quality of the videos synthesized by different methods, the variety of training objectives used in the existing methods makes such comparisons biased and unfair. Therefore, we conduct a similar user study as Tesfaldet et al. [24] to quantitatively evaluate and compare the realism of the videos. We show a pair of videos to the participants and ask them to choose the video that appears more realistic. We compare the videos synthesized by (DyNCA, [24], [27]) with each other and also" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.951, + 0.521, + 0.964 + ], + "angle": 0, + "content": "20747" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.087, + 0.877, + 0.53 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.534, + 0.895, + 0.592 + ], + "angle": 0, + "content": "Figure 5. Results of dynamic texture synthesis and dynamic style transfer with DyNCA-L-256². Dynamic Texture Synthesis: DyNCA faithfully reproduces the target appearance and target dynamics. Dynamic Style Transfer: DyNCA can learn appearance and motion from different sources. Note that DyNCA does not simply copy the target dynamics from the video, but learns the style of the given motion and naturally adapts it to the target appearance, as shown by the optical-flow images. See our real-time interactive demo https://dynca.github.io" + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.598, + 0.468, + 0.699 + ], + "angle": 0, + "content": "
MethodRes.Training Time (s)Synthesis Time (s)# Parameters
A [24]2562#frames × 5005.0 × 102#frames × 0.2M
B [27]2242#frames × 4004.0 × 10281M
C [27]1002#frames × 8.58.5 × 1002.8M
DyNCA-S128223203.3 × 10-20.006M
DyNCA-S256239805.7 × 10-20.006M
DyNCA-L128223703.5 × 10-20.010M
DyNCA-L256243805.7 × 10-20.010M
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.702, + 0.47, + 0.786 + ], + "angle": 0, + "content": "Table 2. Comparison of training time, synthesis time per frame, and number of trainable parameters of different DyTS methods. (A) Tesfaldet et al. [24]; (B) Xie et al. [27] FC config; (C) Xie et al. [27] ST config. For (B) and (C), training and synthesis happen simultaneously, and the video is synthesized once the training is finished. All methods are evaluated on a single A100 40GB GPU." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.799, + 0.471, + 0.906 + ], + "angle": 0, + "content": "with real videos using the same 59 dynamic texture videos as Tesfaldet et al. [24]. Table 3 shows the results of our user study. Each entry shows the percentage of times that the video from the corresponding column was chosen over the video from the corresponding row. Our method outperforms the other DyTS method in realism. We refer the reader to our supplementary for more details on the user study." + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.598, + 0.892, + 0.686 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.688, + 0.895, + 0.773 + ], + "angle": 0, + "content": "Figure 6. Results of DyNCA trained on various target vector fields as the motion target. First and second row: Symbolic and colored optical-flow representations of the target vector fields. Third row: Snapshot of the optical-flow estimations of the videos synthesized by DyNCA-S-128\\(^2\\). The target appearance used for training the model is fibrous_0145 texture from the DTD dataset [4]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.788, + 0.655, + 0.805 + ], + "angle": 0, + "content": "5.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Positional Encoding: We ablate the Cartesian Positional Encoding (CPE) and train DyNCA-S-128² with different padding strategies for comparison. In Table 4, we report the average of \\(\\mathcal{L}_{dir}\\) and \\(\\mathcal{L}_{norm}\\) losses on 4 target vector fields (Diverge, Converge, Circular, and Hyperbolic shown in the last 4 columns of Figure 6) and 10 different target" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.952, + 0.52, + 0.964 + ], + "angle": 0, + "content": "20748" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.09, + 0.473, + 0.344 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.347, + 0.473, + 0.472 + ], + "angle": 0, + "content": "Table 3. Top: Comparison of real and synthesized video frames from different methods: (A) Tesfaldet et al. [24]; (B) Xie et al. [27] FC config; (C) Xie et al. [27] ST config. Bottom: Pair-wise comparison results from our user study. The participants see two videos one after another in random order and are asked to choose the video that appears more realistic. Our DyNCA achieves an on-par \"fooling\" rate when compared with real videos. Yet, our synthesized videos look more realistic when compared to existing DyTS methods (60%, 54%, 80%). All error margins are \\(\\leq 2\\%\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.487, + 0.47, + 0.563 + ], + "angle": 0, + "content": "appearances. The results demonstrate that CPE is a necessary component for DyNCA to learn the motion from a structured target vector field, in which the motion direction and magnitude are position-dependent. We show the importance of CPE for video motion fitting in the supplementary." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.565, + 0.471, + 0.718 + ], + "angle": 0, + "content": "Multi-Scale Perception:. MSP is key to enable training DyNCA with larger seed sizes. We train DyNCA-L-256² both with and without multi-scale perception and evaluate the results qualitatively and quantitatively. Figure 8 shows the corresponding synthesized video frames, qualitatively demonstrating that single-scale perception causes artifacts to appear in the synthesized frames. We also perform a quantitative evaluation in the supplementary, showing that training with multi-scale perception improves both the appearance \\(\\mathcal{L}_{\\text {appr }}\\) and the video motion \\(\\mathcal{L}_{\\text {mvid }}\\) losses." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.726, + 0.201, + 0.743 + ], + "angle": 0, + "content": "6. Limitations" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.473, + 0.904 + ], + "angle": 0, + "content": "DyNCA has certain limitations. In the case of vector field motion, it cannot generate a correct motion when the target appearance and the target motion are not compatible. For example, DyNCA fails to move a 45-degree oblique pattern in a circular manner. For video motion, we find it difficult to automatically set the motion loss weight \\(\\lambda\\). Moreover, DyNCA cannot generate diverse motion when the target videos are violating the underlying assumption of dynamic textures, i.e. when they are not temporally homogeneous. In these cases, DyNCA suffers from overfitting to" + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.089, + 0.89, + 0.178 + ], + "angle": 0, + "content": "
Seed SizeLossCircularZeroReplicateCPE
128 × 128Ldir0.9890.1620.3180.062
Lnorm0.6400.2960.3640.235
256 × 256Ldir0.9930.4110.4780.054
Lnorm0.6780.3310.3970.218
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.181, + 0.895, + 0.237 + ], + "angle": 0, + "content": "Table 4. Comparison of motion loss for DyNCA trained with different padding strategies. Using Cartesian Positional Encoding (CPE) improves the motion fidelity, and allows the DyNCA to synthesize the correct motion regardless of the seed size." + }, + { + "type": "image", + "bbox": [ + 0.511, + 0.24, + 0.895, + 0.459 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.46, + 0.895, + 0.517 + ], + "angle": 0, + "content": "Figure 8. Comparison between training DyNCA with and without multi-scale perception. The first row shows the target appearance texture. The results without multi-scale perception (second row) contain artifacts and are of lower quality." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.529, + 0.892, + 0.561 + ], + "angle": 0, + "content": "the dominant direction of the motion in the target videos We refer to our supplementary material for more details." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.565, + 0.62, + 0.58 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.588, + 0.892, + 0.859 + ], + "angle": 0, + "content": "We propose DyNCA, a model that can, in real time, synthesize dynamic texture videos with arbitrary frame size and infinite length. Exploiting multi-scale perception and positional encoding, the cells in DyNCA can readily perform long-range communication and obtain global information. This ensures improved performance both in terms of visual quality and computational expressivity as compared to the vanilla NCA model, as we show with both qualitative and quantitative experiments. DyNCA can learn motion either from a hand-crafted vector field or a video, thus allowing for broader synthesis options. DyNCA produces more realistic video textures than the current DyTS methods, as demonstrated through a user study. DyNCA is also \\(2 \\sim 4\\) orders of magnitude faster than the SOTA methods in synthesis time and has much fewer trainable parameters, thus facilitating real-world deployment. Lastly, DyNCA allows for several real-time and interactive video control tools that let the users control DyNCA without re-training." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.86, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Acknowledgement. This work was supported in part by the Swiss National Science Foundation via the Sinergia grant CRSII5-180359." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.952, + 0.52, + 0.964 + ], + "angle": 0, + "content": "20749" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.469, + 0.157 + ], + "angle": 0, + "content": "[1] Edward H Adelson, Charles H Anderson, James R Bergen, Peter J Burt, and Joan M Ogden. Pyramid methods in image processing. RCA engineer, 29(6):33-41, 1984. 4" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.157, + 0.469, + 0.213 + ], + "angle": 0, + "content": "[2] Simon Baker, Daniel Scharstein, JP Lewis, Stefan Roth, Michael J Black, and Richard Szeliski. A database and evaluation methodology for optical flow. 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IEEE, 2021. 1, 2, 3" + }, + { + "type": "list", + "bbox": [ + 0.079, + 0.092, + 0.47, + 0.219 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.952, + 0.518, + 0.963 + ], + "angle": 0, + "content": "20751" + } + ] +] \ No newline at end of file diff --git a/2023/DyNCA_ Real-Time Dynamic Texture Synthesis Using Neural Cellular Automata/786b41ed-e991-424e-9c74-c623b61a6162_origin.pdf b/2023/DyNCA_ Real-Time Dynamic Texture Synthesis Using Neural Cellular Automata/786b41ed-e991-424e-9c74-c623b61a6162_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..e95c4c75658928a9d2b98c43810a78031efa6f79 --- /dev/null +++ b/2023/DyNCA_ Real-Time Dynamic Texture Synthesis Using Neural Cellular Automata/786b41ed-e991-424e-9c74-c623b61a6162_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:78b63c1a2c63087e6dfedfafc4dcb90c04a5a9f199782d525ca809b7a81d507d +size 5424779 diff --git a/2023/DyNCA_ Real-Time Dynamic Texture Synthesis Using Neural Cellular Automata/full.md b/2023/DyNCA_ Real-Time Dynamic Texture Synthesis Using Neural Cellular Automata/full.md new file mode 100644 index 0000000000000000000000000000000000000000..ce3a1d507158ec0c211942cdfbed2797448d4ada --- /dev/null +++ b/2023/DyNCA_ Real-Time Dynamic Texture Synthesis Using Neural Cellular Automata/full.md @@ -0,0 +1,312 @@ +# DyNCA: Real-time Dynamic Texture Synthesis Using Neural Cellular Automata + +Ehsan Pajouheshgar*, Yitao Xu*, Tong Zhang, Sabine Süsstrunk +School of Computer and Communication Sciences, EPFL, Switzerland + +{ ehsan.pajouheshgar, yitao.xu, tong.zhang, sabine.susstrunk }@epfl.ch + +![](images/b435ab578847b00e2757207c25fee773f8299d36a9bf29df7a14325f72c3a271.jpg) +Target Appearance + +![](images/aaf33f80691ab6763250c0deb82e4ff67d053072d1b5a5dde5525451387c474f.jpg) +Figure 1. Our DyNCA model can synthesize infinitely-long realistic dynamic texture videos with arbitrary size in real time. Target Appearance: DyNCA learns a desired texture pattern from a given target appearance image. Target Dynamics: DyNCA can learn motion from different target sources. We allow the users to define the desired motion either by a hand-crafted optical-flow image or a dynamic texture video. Synthesized Result: DyNCA synthesizes realistic dynamic texture videos. Each synthesized video frame resembles the target appearance, while the concatenation of frames induces the motion of the target dynamics. See our real-time interactive demo at2. + +![](images/ddc83b4c7923f45f5a1bc6275de9de18dbc128f4d8c92e68871d2c5aec013ced.jpg) +Video + +![](images/45966c4f191bf4ee5cae3661d48656f9ecc7390ba437df922badffacbbfb806a.jpg) +OF + +![](images/cf584ffedc425327d7c16ce5c4f1804a8f119e965c3e9e2118db998e6837cc6e.jpg) +Target Dynamics (Motion) +Optical Flow + +![](images/e44f2e8b7f51fa18aa7a6b3eb2056c57b808477ef5d0fc1988b76213b6c524ec.jpg) + +![](images/a5d2576970e5fa41a44c4e0d00d756a4d0ae1d2b6a8ccff5f5da0be5135f68d8.jpg) +Synthesized Result +Video + +![](images/2d54df8eaf53063dc028df219ec433daa115ea3eab1e410da941694e1910cf72.jpg) +Optical Flow +OF + +![](images/b4dc052941b12160862469599aadd4b4d451994f88b4b776fe568006e4373952.jpg) + +![](images/fdf93e113c0338d9c70e4978bdd53ae17fd7c2d4c84ee2fc721e60b785b8da0a.jpg) + +# Abstract + +Current Dynamic Texture Synthesis (DyTS) models can synthesize realistic videos. However, they require a slow iterative optimization process to synthesize a single fixed-size short video, and they do not offer any post-training control over the synthesis process. We propose Dynamic Neural Cellular Automata (DyNCA), a framework for real-time and controllable dynamic texture synthesis. Our method is built upon the recently introduced NCA models and can synthesize infinitely long and arbitrary-sized realistic video textures in real time. We quantitatively and qualitatively evaluate our model and show that our synthesized videos appear more realistic than the existing results. We improve the SOTA DyTS performance by $2 \sim 4$ orders of magnitude. Moreover, our model offers several real-time video controls including motion speed, motion direction, and an editing brush tool. We exhibit our trained models in an online interactive demo that runs on local hardware and is accessible on personal computers and smartphones. + +# 1. Introduction + +Textures are everywhere. We perceive them as spatially repetitive patterns. Dynamic Textures are textures that change over time and induce a sense of motion. Flames, sea waves, and fluttering branches are everyday examples. Understanding and computationally modeling dynamic textures is an intriguing problem, as these patterns are observed in most natural scenes. + +The goal of Dynamic Texture Synthesis (DyTS) [5-8, 10, 12, 23, 24, 27, 29, 32] is to generate perceptually-equivalent samples of an exemplar video texture3. Applications of DyTS include the creation of special effects for backdrops and video games [21], dynamic style transfer [24], and creating cinematographs [12]. + +The state-of-the-art (SOTA) dynamic texture synthesis + +1We use the same flow visualization as Baker et al. [2]. +2Link to the demo: https://dynca.github.io +3We use "video texture" and "dynamic texture" interchangeably. + +![](images/0e567009c008855a90037bf37ec3cdf2519799aac14fc532476247cfb1f6c9c2.jpg) +Figure 2. Overview of DyNCA. Starting from a seed state, DyNCA iteratively updates it, generating an image sequence. We extract images from this sequence and compare them with an appearance target as well as a motion target to obtain the DyNCA training objectives. After training, DyNCA can adapt to seeds of different heights and widths, and synthesize videos with arbitrary lengths. Sequentially applying DyNCA updates on the seed synthesizes dynamic texture videos in real time. + +methods [8,24,27,29,32] follow the same trend. They aim to find better optimization strategies to iteratively update a randomly initialized video until the synthesized video resembles the exemplar dynamic texture. Although the SOTA methods are able to synthesize acceptable quality videos, their optimization process is very slow and requires several hours to generate a single fixed-resolution short video on a high-end GPU. Moreover, these methods do not offer any post-training control over the synthesized video. + +In this paper we propose Dynamic Neural Cellular Automata (DyNCA), a model for dynamic texture synthesis that is fast to train, and once trained, can synthesize infinitely-long, arbitrary-resolution dynamic texture videos in real time on a low-end GPU. Moreover, our method enables several real-time video editing controls, including motion direction and motion speed. Through quantitative and qualitative analysis we demonstrate that our synthesized videos achieve better quality and realism than the previous results in the literature. + +Our model builds upon the recently introduced Neural Cellular Automata (NCA) model [18, 19]. While Niklasson et al. [19] train the NCA with the goal of synthesizing static textures only, the NCA model is able to spontaneously generate randomly moving patterns. As an inherent property of NCA, these spontaneous motions are, however, unstructured and uncontrolled. We modify the architecture and the training scheme of NCA so that it can learn to synthesize video textures that have the desired motion and appearance. + +In short, our DyNCA model acts as a stochastic Partial Differential Equation (PDE), parameterized by a small neural network. DyNCA starts from a constant initial state called seed, and then iteratively evolves the state according to its trainable PDE update rule to generate a sequence of images. This image sequence is then evaluated against the appearance exemplar and the motion target to calculate the loss functions for the optimization of DyNCA, as illustrated in Figure 2. We allow the user to specify the desired + +motion either by a motion vector field or an exemplar dynamic texture video. Moreover, by using a different target for the appearance and the motion, our model can perform dynamic style transfer, as shown in Figure 1. Our contributions summarized are: + +- Our DyNCA model, once trained, can synthesize dynamic texture videos in real time. +- Our synthesized videos are on-par with or even better than the existing results in terms of realism and quality. +- After training, our DyNCA model can synthesize infinitely-long videos with arbitrary frame sizes. +- Our DyNCA framework enables several real-time interactive video editing controls including speed, direction, a brush tool, and local coordinate transformation. +- We can perform real-time dynamic style transfer by learning appearance and motion from distinct sources. + +# 2. Related Works + +In the following section, we discuss the existing DyTS methods. For comparison, Table 1 summarizes the strengths (✓) and shortcomings (X) of these methods. + +# 2.1. Dynamic Texture Synthesis + +In the literature, there are two dominant techniques to synthesize dynamic texture videos. Recent approaches follow the seminal work of Gatys et al. [9] for texture synthesis. The authors propose an optimization-based method that relies on the features extracted by a deep neural network trained for image classification. Gatys et al. [9] show that the Gram matrices of features extracted by the VGG network [22] capture the perceptual qualities of texture images. Funke et al. [8] extend Gatys's idea to dynamic texture synthesis, and use a cross-frame Gram matrix of VGG features to capture the temporal characteristics of dynamic textures. Tesfaldet et al. [24] and Zhang et al. [32] use a pre-trained optical flow network for extracting the motion features, which allows them to disentangle the appearance and motion aspects of video textures. Xie et al. [27] use an energy-based model characterized by a spatio-temporal 3D ConvNet and synthesize textures by sampling using Langevin dynamics. + +These methods utilize the expressivity of neural networks to produce realistic high-quality dynamic texture videos. However, they require a long training time to synthesize a single short video. Moreover, none of these methods provide any post-training controls over motion speed, frame size, and motion direction. These shortcomings make these methods unsuitable for real-time applications. + +Earlier DyTS methods that can potentially enable real-time synthesis utilized PDEs to model dynamic textures + +
MethodABCDEFG
Costantini et al. [5]X✓✓X✓XX
Doretto et al. [6]X✓✓X✓XX
Funke et al. [8]X✓XXXXX
Tesfaldet et al. [24]X✓XXX✓✓
Xie et al. [27]XXXX✓XX
Zhang et al. [32]X✓XXX✓✓
DyNCA (Ours)✓✓✓✓X✓✓
+ +Table 1. Comparison of DyTS methods. (A) Can synthesize videos with arbitrary frame size after training. (B) Can synthesize arbitrarily long videos. (C) Can synthesize new video samples without re-training. (D) Allows real-time video editing (speed, direction, and a brush tool). (E) Does not rely on pre-trained models to extract motion or texture information. (F) Has disentangled appearance and motion. (G) Can learn motion from vector fields. + +[5, 6, 10, 30, 31]. To synthesize video textures, Doretto et al. [6] propose to use a linear dynamical system (LDS) in which each frame of the video is controlled by a latent variable whose evolution through time is driven by random noise. The latent variable is obtained via projection of the target texture image into a lower dimensional space by singular value decomposition (SVD). Costantini et al. [5] propose to use higher-order SVD to improve the expressivity of LDS-based models. Yuan et al. [31] introduce feedback into the LDS to improve the stability of the dynamical system. All these methods can synthesize new video textures without re-training, and potentially in real time. However, the synthesized videos are of low quality and contain artifacts. + +Our DyNCA method benefits from the best of both approaches by combining the expressivity of neural networks with PDEs. Having $2 \sim 4$ orders of magnitude fewer parameters than the SOTA models, our model can synthesize realistic dynamic texture videos in real time. + +# 2.2. NCA for Texture Synthesis + +Gilpin [11] shows that Cellular Automata models can be represented using Convolutional Neural Networks. Extending [11], Mordvinstev et al. [18] propose the Neural Cellular Automata model and show its potential in creating various self-organizing systems [17-20]. NCA is inspired by Turing's seminal work [25] on pattern generation, and the observation that many natural patterns stem from local interactions between tiny particles, cells, or molecules [19]. + +Niklasson et al. [17, 19] were the first to train NCA models to synthesize textures. While the NCA training signal originates from a static exemplar texture image, the model is able to spontaneously generate stable but randomly moving textures. We modify the architecture and training scheme of NCA to enable synthesizing structured motion. First, our DyNCA model receives supervision from a pre-trained optical-flow network, which enables it to synthesize a video + +texture with structured motion. Moreover, we incorporate multi-scale perception and positional encoding into the DyNCA architecture. The proposed architectural changes increase the communication range of the cells and allow the cells to be aware of global information, respectively. + +# 3. DyNCA Architecture + +In the following sections, we first review the NCA model and then present the architecture of our DyNCA. + +# 3.1. Neural Cellular Automata (NCA) + +The idea of NCA stems from cellular automata, in which cells live on a grid, and each cell communicates with its neighbors to determine the cell's next state. In NCA, cell states at time $t$ are represented by $\mathbf{S}^t \in \mathbb{R}^{H \times W \times C}$ where $H \times W$ is the grid size. The $C$ dimensional vector $s_{ij}^t$ encodes the state of the cell at location $i, j$ , where the first three dimensions define the RGB color of the cell. + +The NCA starts from a constant zero-filled initial state called seed and evolves this state over time according to its trainable PDE. The update rule of this PDE consists of two parts, Perception and Stochastic Update. At the perception stage, each cell gathers information from its surrounding neighbors, forming the perception vector $z_{ij} \in \mathbb{R}^{4C}$ , illustrated in the green box in Figure 3. + +$$ +z _ {i j} = \operatorname {C o n c a t} \left(s _ {i j}, \nabla_ {\mathrm {x}} \mathbf {S} | _ {i j}, \nabla_ {\mathrm {y}} \mathbf {S} | _ {i j}, \nabla^ {2} \mathbf {S} | _ {i j}\right) \tag {1} +$$ + +Note that the convolution kernels in the perception stage are frozen during training. In the stochastic update stage, the new state of each cell is determined based on its perception vector. The update stage of NCA can be viewed as a stochastic discrete-time, discrete-space PDE: + +$$ +\begin{array}{l} \mathbf {S} ^ {t + 1} = \mathcal {F} (\mathbf {S} ^ {t}) = \mathbf {S} ^ {t} + \frac {\partial \mathbf {S}}{\partial t} \Delta t \tag {2} \\ \frac {\partial s _ {i j}}{\partial t} = \operatorname {M L P} \left(z _ {i j}\right) \odot M \\ \end{array} +$$ + +where MLP is a Multi Layered Perceptron with two layers and a ReLU activation function. The residual update values produced by the MLP are multiplied by a binary random variable $M$ to introduce stochasticity into the model. This ensures that the cells can work asynchronously, and also enables synthesizing new texture samples. The stochastic update stage is illustrated in the blue box in Figure 3. + +To facilitate long-range cell communication and to allow the cells to be aware of global information, we introduce multi-scale perception and positional encoding into the vanilla NCA architecture, respectively. Our experiments in section 5 demonstrate their necessity for DyTS. The overall architecture of our DyNCA model is illustrated in Figure 3. To the best of our knowledge, we are the first to incorporate these two architectural changes in conjunction with NCA models. In the following sections, we elaborate on the proposed architectural modifications. + +![](images/11bba1529c422dfab78a28e8ccdaddb3b6c543e448075db2466bf50e159c7883.jpg) +Figure 3. Illustration of a single DyNCA step. Given an input state $\mathbf{S}^t\in R^{H\times W\times C}$ at time step $t$ , each cell first perceives its neighbors on various scales with the same perception layer. The perception tensor of each scale is then upsampled and summed up, and is concatenated with the positional encoding tensor $\mathbf{P}_{xy}$ . Each cell then applies the same update rule, parameterized by a small MLP. Finally, all cells perform a stochastic residual update to determine the state of the cells in time $t + \Delta t$ . We use $\Delta t = 1$ in our model. + +![](images/4079eea13ba9b4f96674a7860867462d0a91816c64c1ea81c5454c0731822e58.jpg) + +# 3.2. Multi-scale Perception + +In the perception stage of vanilla NCA, each cell only receives information from its eight surrounding cells. Therefore, many timesteps are needed for far-apart cells to perceive and communicate with each other. This problem becomes more pronounced when we increase the grid size $H \times W$ , since the $3 \times 3$ perception kernels become smaller in proportion to the image size. One straightforward solution is to increase the number of NCA steps during training to facilitate long-range cell communication. However, this simple solution increases memory usage, slows down the training, and makes the training more unstable. + +To solve this problem, we propose Multi-Scale Perception (MSP). The idea of using multi-scale analysis predates deep learning and has shown its effectiveness in many computer vision tasks [1, 3, 14, 15]. We build a pyramid of cell states via bilinear downsampling and apply the same perception kernels at different scales. To combine the information from all scales, we upsample and sum up the perception vectors, as shown in the red box in Figure 3. Multi-scale perception increases the communication range of the cells and allows messages to pass between faraway cells in fewer steps. It also improves the stability of DyNCA and makes the training less sensitive to hyperparameters. We perform an ablation study of multi-scale perception in section 5.4 and show its importance in preserving appearance fidelity. + +# 3.3. Positional Encoding + +In order to apply the $3 \times 3$ depth-wise convolutions in the perception stage, one needs to adopt a padding strat + +egy to retain the spatial dimensions. Niklasson et al. [19] use circular padding to make the cells homogeneous and to reduce spatial inductive bias. While cell homogeneity is a good assumption for generating static textures, it is not suitable for synthesizing structured motion. Our intuition is that, in physical systems, motion not only arises from local interactions between tiny particles and cells, but also from global external forces such as gravity. Hence, we allow the cells to be aware of their position and propose to use replicate padding and Cartesian Positional Encoding (CPE), which is known to provide a more consistent spatial inductive bias than zero-padding [28]. As illustrated in the purple box in Figure 3, we concatenate the output of the multi-scale perception stage with a two-channel tensor $\mathbf{P}_{\mathrm{xy}}$ , where $\mathbf{P}_{ij} = \left[ \begin{array}{c}2i + 1.0\\ \frac{W}{2j + 1.0}\\ H \end{array} \right] - 1.0$ . Our ablation study in section 5.4 shows that employing CPE drastically improves motion consistency and accuracy in the synthesized videos. + +# 4. DyNCA Training + +Our DyNCA model acts as a PDE and generates a sequence of images $\mathcal{I}^g = \{\mathcal{I}_1^g,\mathcal{I}_2^g,\ldots \}$ . We sample the synthesized video frames $\mathcal{V}^g = \{\mathcal{V}_1^g,\mathcal{V}_2^g,\ldots \}$ from this image sequence by mapping $T$ DyNCA steps to one frame, i.e. $\mathcal{V}_k^g = \mathcal{I}_{kT}^g$ . The synthesized video is then evaluated against the target appearance and the target motion to compute the appearance loss $\mathcal{L}_{appr}$ and the motion loss $\mathcal{L}_{motion}$ , respectively. This process is shown in Figure 2. Our final loss is $\mathcal{L}_{\mathrm{DyNCA}} = \mathcal{L}_{appr} + \lambda \mathcal{L}_{motion}$ . The overall scheme of the proposed loss functions is illustrated in Figure 4. + +![](images/c893b5e96e0d53b59cebc21d2d02456e24b20dc48cf433a0f555196b05c7db4e.jpg) +Figure 4. Overview of our loss functions. Appearance loss $(\mathcal{L}_{appr})$ : DyNCA learns the target appearance from a static image via minimizing an optimal-transport-based style matching loss [13] between deep features extracted from the VGG16 network [22]. Motion Loss $(\mathcal{L}_{mvec})$ : We guide DyNCA to synthesize a video having an optical flow similar to the target vector field. Motion Loss $(\mathcal{L}_{mvec})$ : DyNCA fits the target video motion by minimizing an optimal-transport-based style matching loss between deep features of a pre-trained optical-flow prediction network. + +# 4.1. Appearance Loss + +We follow the texture fitting scheme proposed by Niklasson et al. [19], where the statistics of deep features of the NCA-generated images are forced to match the ones of the target texture. We use a pre-trained VGG16 network [22] to extract the deep features from the images. We denote VGG as $\mathcal{F}_{VGG}$ and the feature map extracted from layer $l$ as $\mathcal{F}_{VGG}^l$ . Niklasson et al. [19] use the Gram matrix to define the training objective of the NCA. However, using Gram matrices can cause unstable training [26], and can result in textures with wrong colors [16, 19]. Hence, we use the style loss proposed by Kolkin et al. [13], which has shown to produce better results. This loss is composed of a structure-matching term and a moment-matching term. Given a feature map of size $C\times H\times W$ , the algorithm first creates a set of deep features with $n = H\times W$ elements by flattening the feature map along the spatial dimensions. Let $X$ and $Y$ + +be the deep feature set of a synthesized image and target appearance image, respectively. Then the structure-matching term $\mathcal{L}_s$ and the moment-matching term $\mathcal{L}_m$ are defined as: + +$$ +D (A, B) = \frac {1}{| A |} \sum_ {i} \min _ {j} \left(1 - \frac {A _ {i} \cdot B _ {j}}{| | A _ {i} | | _ {2} | | B _ {j} | | _ {2}}\right) \tag {3} +$$ + +$$ +\mathcal {L} _ {s} (X, Y) = \max \left\{D (X, Y), D (Y, X) \right\}, +$$ + +$$ +\mathcal {L} _ {m} (X, Y) = \frac {1}{C} \| \boldsymbol {\mu} _ {X} - \boldsymbol {\mu} _ {Y} \| _ {1} + \frac {1}{C ^ {2}} \| \boldsymbol {\Sigma} _ {X} - \boldsymbol {\Sigma} _ {Y} \| _ {1}, \tag {4} +$$ + +where $D$ measures the distance between two deep feature sets, and $\pmb{\mu},\pmb{\Sigma}$ are the mean and covariance matrix of their corresponding set, respectively. Let $X_{k}^{l}$ and $Y^{l}$ be deep VGG features extracted by $\mathcal{F}_{VGG}^{\text{conv } l-1}$ , where $l$ and $k$ indicate the VGG block index and the synthesized image index, respectively. Our final appearance loss is then defined as: + +$$ +\mathcal {L} _ {\text {a p p r}} = \frac {1}{K} \sum_ {k = 1} ^ {K} \sum_ {l = 1} ^ {5} \left(\mathcal {L} _ {s} \left(X _ {k} ^ {l}, Y ^ {l}\right) + \mathcal {L} _ {m} \left(X _ {k} ^ {l}, Y ^ {l}\right)\right) \tag {5} +$$ + +# 4.2. Motion Loss + +The motion loss guides the DyNCA to produce the desired motion. We use the pre-trained Optical-Flow Prediction Network from [24] to quantify the motion information between two frames. We denote this network as $\mathcal{F}_{OF}$ , and the feature map extracted from layer $l$ as $\mathcal{F}_{OF}^l$ . For different types of target motion sources, namely vector fields and videos, our motion loss takes two different forms, $\mathcal{L}_{mvec}$ and $\mathcal{L}_{mvid}$ , respectively. These terms are discussed below. + +# 4.2.1 Motion from Vector Field + +Let $U^t \in \mathbb{R}^{H \times W \times 2}$ be the target motion vector field. Let $U^g = \mathcal{F}_{OF}(\mathcal{I}_{t_1}^g, \mathcal{I}_{t_2}^g)$ be the optical-flow prediction on two synthesized images, where $t_1, t_2$ are two random indices such that $t_2 > t_1$ . We propose two losses, $\mathcal{L}_{dir}$ for matching the motion direction, defined as: + +$$ +\mathcal {L} _ {d i r} = \frac {1}{H W} \sum_ {i, j} \left(1 - \frac {U _ {i j} ^ {g} \cdot U _ {i j} ^ {t}}{\left\| U _ {i j} ^ {g} \right\| _ {2} \left\| U _ {i j} ^ {t} \right\| _ {2}}\right), \tag {6} +$$ + +and $\mathcal{L}_{norm}$ for matching the motion magnitude, defined as: + +$$ +\mathcal {L} _ {\text {n o r m}} = \frac {1}{H W} \sum_ {i, j} \left| \frac {T}{t _ {2} - t _ {1}} \left\| U _ {i j} ^ {g} \right\| _ {2} - \left\| U _ {i j} ^ {t} \right\| _ {2} \right|. \tag {7} +$$ + +Since $t_1, t_2$ are selected randomly, we scale the norm of the $U^g$ by $\frac{T}{t_2 - t_1}$ before comparing it against the target motion vector field. We define our final loss $\mathcal{L}_{mvec}$ as: + +$$ +\mathcal {L} _ {m v e c} = (1. 0 - \min \{1. 0, \mathcal {L} _ {d i r} \}) \mathcal {L} _ {\text {n o r m}} + \gamma \mathcal {L} _ {d i r}, \tag {8} +$$ + +where $\gamma$ is a constant coefficient. We set the norm-matching loss weight to $(1.0 - \min\{1.0, \mathcal{L}_{dir}\})$ to guide the training process to first focus on producing motion with the correct direction before trying to match the norm of the synthesized motion with the target vector field. + +# 4.2.2 Motion from Video + +For training DyNCA to learn the motion from a target video, we aim to match the motion between successive frames of the synthesized and target videos. We synthesize a video $\mathcal{V}^g$ with $K$ frames, and randomly pick the same number of consecutive frames from the target video, forming $\mathcal{V}^t$ . Inspired by Tesfaldet et al. [24], we feed successive video frames to a pre-trained optical-flow network and extract deep features from the concatenation layer of the network, denoted as $\mathcal{F}_{OF}^{concat}$ . To compare the deep optical flow features of the target and the synthesized videos, we use the same structure-matching and moment-matching terms defined in Section 4.1. We denote the extracted deep optical-flow features as $X_{k}$ for the synthesized video, and $Y_{k}$ for the target video, where $k$ indicates the frame index. Notice that there are $K - 1$ successive frame pairs in total. We define the objective for learning motion from video textures as: + +$$ +\mathcal {L} _ {m v i d} = \frac {1}{K - 1} \sum_ {k = 1} ^ {K - 1} \left(\mathcal {L} _ {s} \left(X _ {k}, Y _ {k}\right) + \mathcal {L} _ {m} \left(X _ {k}, Y _ {k}\right)\right) \tag {9} +$$ + +# 5. Experiments + +We conduct experiments on the critical parameters of DyNCA, including $N_{C}, N_{H}, N_{W}, N_{FC}$ , where $N_{C}, N_{H}, N_{W}$ are the size of the DyNCA seed state and $N_{FC}$ is the output dimensionality of the first layer of MLP in DyNCA. Concretely, we set $N_{C} = 12$ , $N_{FC} = 96$ for DyNCA-S and $N_{C} = 16$ , $N_{FC} = 128$ for DyNCA-L. Although DyNCA can adapt to arbitrary seed sizes after training, the seed resolution used during training affects the texture details. We experiment with both $128^{2}$ and $256^{2}$ spatial resolutions for the seed. We use Positional Encoding for all of the DyNCA configurations, and enable Multi-Scale Perception only when training with the $256 \times 256$ seed size. Table 2 summarizes the DyNCA configurations. We perform our experiments on an Nvidia-A100 GPU, and use Adam optimizer with an initial learning rate of 0.001. We refer the reader to the supplementary for further training details. + +# 5.1. Dynamic Texture Synthesis + +We present the results of synthesizing dynamic textures using DyNCA, where the target motion is either a vector field or a video, and the target appearance is a static image. + +Motion from Vector Field: We manually design 12 target vector fields, and for each target motion, we train both DyNCA-S and DyNCA-L configurations on 45 different target appearances. We provide the resulting 1080 trained models in our real-time interactive demo. We set seed size to $128 \times 128$ and $T = 24$ , assuming that 24 steps of DyNCA update equals one frame of the synthesized video. Figure 6 shows the optical flow of the DyNCA-S synthesized videos and the corresponding target vector fields used for training. + +Motion from Video. We train DyNCA to match the target motion from videos. For the target appearance image, + +we use one of the video frames or a stylistic image, to perform dynamic texture synthesis and dynamic style transfer, respectively. We train both DyNCA-S and DyNCA-L on 59 target dynamic texture videos provided in [24], setting seed size to $256 \times 256$ and $T = 64$ . Figure 5 provides some visual results. More results are provided in our demo and supplementary. In Table 2, we compare our DyNCA and the previous SOTA models [24,27] in terms of the computational costs, namely performance and the number of parameters. Note that our DyNCA model is orders of magnitude more efficient in both training and synthesis time as well as the number of parameters. We refer the reader to the supplementary material for the detailed experimental setup. + +# 5.2. Real-time Video Editing + +DyNCA can also perform real-time video editing by utilizing the post-training NCA controls introduced in [19]. These edits include direction control, speed control, a brush tool, and local coordinate transformations. We refer the reader to our online demo at https://dynca.github.io for real-time and interactive visualization and experimentation. + +Direction Control: By rotating the Sobel convolution kernels $\nabla_{\mathrm{x}}$ and $\nabla_{\mathrm{y}}$ in the perception stage, we can control the direction of the motion in the synthesized video. This is done by replacing $\nabla_{\mathrm{x}}$ and $\nabla_{\mathrm{y}}$ with $\nabla_{\mathrm{u}}$ and $\nabla_{\mathrm{v}}$ , where $\binom{\mathrm{u}}{\mathrm{v}} = \mathrm{R}_{\theta}\binom{\mathrm{x}}{\mathrm{y}}$ and $\mathbf{R}_{\theta}$ is the rotation matrix with angle $\theta$ . We also rotate $\mathbf{P}_{\mathrm{xy}}$ by angle $\theta$ so that the position-dependent part of the motion magnitude also rotates accordingly. + +Speed Control: We control the speed of the synthesized video by increasing/decreasing $T$ , which determines how many DyNCA steps are used to synthesize one video frame. Brush Tool: The brush tool allows the users to delete pixels from the video. Since our DyNCA model exhibits the self-organization property of the original NCA [19], the model can reorganize itself and continue synthesizing realistic videos by naturally filling the deleted pixels. + +Local Coordinate Transformation: DyNCA can create complex motion transformations by allowing each cell to use a different rotation angle $\theta(i,j)$ for transforming its Sobel convolution kernels. For example, setting the rotation angle for the cell at location $(i,j)$ to $\arctan\left(\frac{i - \frac{W}{2}}{j - \frac{H}{2}}\right)$ will transform a rightward motion into a circular motion. + +# 5.3. User Study + +Although it is tempting to use a metric, e.g. the Gram matrix difference [9], to compare the quality of the videos synthesized by different methods, the variety of training objectives used in the existing methods makes such comparisons biased and unfair. Therefore, we conduct a similar user study as Tesfaldet et al. [24] to quantitatively evaluate and compare the realism of the videos. We show a pair of videos to the participants and ask them to choose the video that appears more realistic. We compare the videos synthesized by (DyNCA, [24], [27]) with each other and also + +![](images/0a050e8d64d35c4866191f49ad2919f305fa8b82139ba07bbecb7e9843a0ca75.jpg) +Figure 5. Results of dynamic texture synthesis and dynamic style transfer with DyNCA-L-256². Dynamic Texture Synthesis: DyNCA faithfully reproduces the target appearance and target dynamics. Dynamic Style Transfer: DyNCA can learn appearance and motion from different sources. Note that DyNCA does not simply copy the target dynamics from the video, but learns the style of the given motion and naturally adapts it to the target appearance, as shown by the optical-flow images. See our real-time interactive demo https://dynca.github.io + +
MethodRes.Training Time (s)Synthesis Time (s)# Parameters
A [24]2562#frames × 5005.0 × 102#frames × 0.2M
B [27]2242#frames × 4004.0 × 10281M
C [27]1002#frames × 8.58.5 × 1002.8M
DyNCA-S128223203.3 × 10-20.006M
DyNCA-S256239805.7 × 10-20.006M
DyNCA-L128223703.5 × 10-20.010M
DyNCA-L256243805.7 × 10-20.010M
+ +Table 2. Comparison of training time, synthesis time per frame, and number of trainable parameters of different DyTS methods. (A) Tesfaldet et al. [24]; (B) Xie et al. [27] FC config; (C) Xie et al. [27] ST config. For (B) and (C), training and synthesis happen simultaneously, and the video is synthesized once the training is finished. All methods are evaluated on a single A100 40GB GPU. + +with real videos using the same 59 dynamic texture videos as Tesfaldet et al. [24]. Table 3 shows the results of our user study. Each entry shows the percentage of times that the video from the corresponding column was chosen over the video from the corresponding row. Our method outperforms the other DyTS method in realism. We refer the reader to our supplementary for more details on the user study. + +![](images/a45fcb4faaedbb3aa9a4d3ffb77be7e765725db8810a36e21476476ef6e78fbe.jpg) +Figure 6. Results of DyNCA trained on various target vector fields as the motion target. First and second row: Symbolic and colored optical-flow representations of the target vector fields. Third row: Snapshot of the optical-flow estimations of the videos synthesized by DyNCA-S-128 $^2$ . The target appearance used for training the model is fibrous_0145 texture from the DTD dataset [4]. + +# 5.4. Ablation Study + +Positional Encoding: We ablate the Cartesian Positional Encoding (CPE) and train DyNCA-S-128² with different padding strategies for comparison. In Table 4, we report the average of $\mathcal{L}_{dir}$ and $\mathcal{L}_{norm}$ losses on 4 target vector fields (Diverge, Converge, Circular, and Hyperbolic shown in the last 4 columns of Figure 6) and 10 different target + +![](images/8c8d3f742d707ec980ba1acce2387a8efdcf0eb7468e55cd9fbac59da95a61f7.jpg) +Table 3. Top: Comparison of real and synthesized video frames from different methods: (A) Tesfaldet et al. [24]; (B) Xie et al. [27] FC config; (C) Xie et al. [27] ST config. Bottom: Pair-wise comparison results from our user study. The participants see two videos one after another in random order and are asked to choose the video that appears more realistic. Our DyNCA achieves an on-par "fooling" rate when compared with real videos. Yet, our synthesized videos look more realistic when compared to existing DyTS methods (60%, 54%, 80%). All error margins are $\leq 2\%$ . + +appearances. The results demonstrate that CPE is a necessary component for DyNCA to learn the motion from a structured target vector field, in which the motion direction and magnitude are position-dependent. We show the importance of CPE for video motion fitting in the supplementary. + +Multi-Scale Perception:. MSP is key to enable training DyNCA with larger seed sizes. We train DyNCA-L-256² both with and without multi-scale perception and evaluate the results qualitatively and quantitatively. Figure 8 shows the corresponding synthesized video frames, qualitatively demonstrating that single-scale perception causes artifacts to appear in the synthesized frames. We also perform a quantitative evaluation in the supplementary, showing that training with multi-scale perception improves both the appearance $\mathcal{L}_{\text {appr }}$ and the video motion $\mathcal{L}_{\text {mvid }}$ losses. + +# 6. Limitations + +DyNCA has certain limitations. In the case of vector field motion, it cannot generate a correct motion when the target appearance and the target motion are not compatible. For example, DyNCA fails to move a 45-degree oblique pattern in a circular manner. For video motion, we find it difficult to automatically set the motion loss weight $\lambda$ . Moreover, DyNCA cannot generate diverse motion when the target videos are violating the underlying assumption of dynamic textures, i.e. when they are not temporally homogeneous. In these cases, DyNCA suffers from overfitting to + +
Seed SizeLossCircularZeroReplicateCPE
128 × 128Ldir0.9890.1620.3180.062
Lnorm0.6400.2960.3640.235
256 × 256Ldir0.9930.4110.4780.054
Lnorm0.6780.3310.3970.218
+ +Table 4. Comparison of motion loss for DyNCA trained with different padding strategies. Using Cartesian Positional Encoding (CPE) improves the motion fidelity, and allows the DyNCA to synthesize the correct motion regardless of the seed size. + +![](images/284cd135bc054349cf1545540163df165acfcf31c2c252f9a29b291ca3ddea1e.jpg) +Figure 8. Comparison between training DyNCA with and without multi-scale perception. The first row shows the target appearance texture. The results without multi-scale perception (second row) contain artifacts and are of lower quality. + +the dominant direction of the motion in the target videos We refer to our supplementary material for more details. + +# 7. Conclusion + +We propose DyNCA, a model that can, in real time, synthesize dynamic texture videos with arbitrary frame size and infinite length. Exploiting multi-scale perception and positional encoding, the cells in DyNCA can readily perform long-range communication and obtain global information. This ensures improved performance both in terms of visual quality and computational expressivity as compared to the vanilla NCA model, as we show with both qualitative and quantitative experiments. DyNCA can learn motion either from a hand-crafted vector field or a video, thus allowing for broader synthesis options. DyNCA produces more realistic video textures than the current DyTS methods, as demonstrated through a user study. DyNCA is also $2 \sim 4$ orders of magnitude faster than the SOTA methods in synthesis time and has much fewer trainable parameters, thus facilitating real-world deployment. Lastly, DyNCA allows for several real-time and interactive video control tools that let the users control DyNCA without re-training. + +Acknowledgement. This work was supported in part by the Swiss National Science Foundation via the Sinergia grant CRSII5-180359. + +# References + +[1] Edward H Adelson, Charles H Anderson, James R Bergen, Peter J Burt, and Joan M Ogden. 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However, they require a slow iterative optimization process to synthesize a single fixed-size short video, and they do not offer any post-training control over the synthesis process. We propose Dynamic Neural Cellular Automata (DyNCA), a framework for real-time and controllable dynamic texture synthesis. Our method is built upon the recently introduced NCA models and can synthesize infinitely long and arbitrary-sized realistic video textures in real time. We quantitatively and qualitatively evaluate our model and show that our synthesized videos appear more realistic than the existing results. We improve the SOTA DyTS performance by " + }, + { + "bbox": [ + 46, + 509, + 289, + 724 + ], + "type": "inline_equation", + "content": "2 \\sim 4" + }, + { + "bbox": [ + 46, + 509, + 289, + 724 + ], + "type": "text", + "content": " orders of magnitude. Moreover, our model offers several real-time video controls including motion speed, motion direction, and an editing brush tool. We exhibit our trained models in an online interactive demo that runs on local hardware and is accessible on personal computers and smartphones." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 307, + 484, + 386, + 496 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 484, + 386, + 496 + ], + "spans": [ + { + "bbox": [ + 307, + 484, + 386, + 496 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 304, + 503, + 545, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 503, + 545, + 586 + ], + "spans": [ + { + "bbox": [ + 304, + 503, + 545, + 586 + ], + "type": "text", + "content": "Textures are everywhere. We perceive them as spatially repetitive patterns. Dynamic Textures are textures that change over time and induce a sense of motion. Flames, sea waves, and fluttering branches are everyday examples. Understanding and computationally modeling dynamic textures is an intriguing problem, as these patterns are observed in most natural scenes." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 304, + 587, + 545, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 587, + 545, + 659 + ], + "spans": [ + { + "bbox": [ + 304, + 587, + 545, + 659 + ], + "type": "text", + "content": "The goal of Dynamic Texture Synthesis (DyTS) [5-8, 10, 12, 23, 24, 27, 29, 32] is to generate perceptually-equivalent samples of an exemplar video texture3. Applications of DyTS include the creation of special effects for backdrops and video games [21], dynamic style transfer [24], and creating cinematographs [12]." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 317, + 660, + 545, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 660, + 545, + 673 + ], + "spans": [ + { + "bbox": [ + 317, + 660, + 545, + 673 + ], + "type": "text", + "content": "The state-of-the-art (SOTA) dynamic texture synthesis" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 317, + 683, + 525, + 713 + ], + "type": "list", + "angle": 0, + "index": 34, + "blocks": [ + { + "bbox": [ + 317, + 683, + 495, + 693 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 683, + 495, + 693 + ], + "spans": [ + { + "bbox": [ + 317, + 683, + 495, + 693 + ], + "type": "text", + "content": "1We use the same flow visualization as Baker et al. [2]." + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 317, + 693, + 454, + 703 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 693, + 454, + 703 + ], + "spans": [ + { + "bbox": [ + 317, + 693, + 454, + 703 + ], + "type": "text", + "content": "2Link to the demo: https://dynca.github.io" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 317, + 703, + 525, + 713 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 703, + 525, + 713 + ], + "spans": [ + { + "bbox": [ + 317, + 703, + 525, + 713 + ], + "type": "text", + "content": "3We use \"video texture\" and \"dynamic texture\" interchangeably." + } + ] + } + ], + "index": 33 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 753, + 317, + 762 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 753, + 317, + 762 + ], + "spans": [ + { + "bbox": [ + 293, + 753, + 317, + 762 + ], + "type": "text", + "content": "20742" + } + ] + } + ], + "index": 35 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 70, + 289, + 164 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 289, + 164 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 289, + 164 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 289, + 164 + ], + "type": "image", + "image_path": "0e567009c008855a90037bf37ec3cdf2519799aac14fc532476247cfb1f6c9c2.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 172, + 289, + 261 + ], + "lines": [ + { + "bbox": [ + 46, + 172, + 289, + 261 + ], + "spans": [ + { + "bbox": [ + 46, + 172, + 289, + 261 + ], + "type": "text", + "content": "Figure 2. Overview of DyNCA. Starting from a seed state, DyNCA iteratively updates it, generating an image sequence. We extract images from this sequence and compare them with an appearance target as well as a motion target to obtain the DyNCA training objectives. After training, DyNCA can adapt to seeds of different heights and widths, and synthesize videos with arbitrary lengths. Sequentially applying DyNCA updates on the seed synthesizes dynamic texture videos in real time." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 268, + 287, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 268, + 287, + 376 + ], + "spans": [ + { + "bbox": [ + 46, + 268, + 287, + 376 + ], + "type": "text", + "content": "methods [8,24,27,29,32] follow the same trend. They aim to find better optimization strategies to iteratively update a randomly initialized video until the synthesized video resembles the exemplar dynamic texture. Although the SOTA methods are able to synthesize acceptable quality videos, their optimization process is very slow and requires several hours to generate a single fixed-resolution short video on a high-end GPU. Moreover, these methods do not offer any post-training control over the synthesized video." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 377, + 287, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 377, + 287, + 496 + ], + "spans": [ + { + "bbox": [ + 46, + 377, + 287, + 496 + ], + "type": "text", + "content": "In this paper we propose Dynamic Neural Cellular Automata (DyNCA), a model for dynamic texture synthesis that is fast to train, and once trained, can synthesize infinitely-long, arbitrary-resolution dynamic texture videos in real time on a low-end GPU. Moreover, our method enables several real-time video editing controls, including motion direction and motion speed. Through quantitative and qualitative analysis we demonstrate that our synthesized videos achieve better quality and realism than the previous results in the literature." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 497, + 287, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 497, + 287, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 497, + 287, + 605 + ], + "type": "text", + "content": "Our model builds upon the recently introduced Neural Cellular Automata (NCA) model [18, 19]. While Niklasson et al. [19] train the NCA with the goal of synthesizing static textures only, the NCA model is able to spontaneously generate randomly moving patterns. As an inherent property of NCA, these spontaneous motions are, however, unstructured and uncontrolled. We modify the architecture and the training scheme of NCA so that it can learn to synthesize video textures that have the desired motion and appearance." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "text", + "content": "In short, our DyNCA model acts as a stochastic Partial Differential Equation (PDE), parameterized by a small neural network. DyNCA starts from a constant initial state called seed, and then iteratively evolves the state according to its trainable PDE update rule to generate a sequence of images. This image sequence is then evaluated against the appearance exemplar and the motion target to calculate the loss functions for the optimization of DyNCA, as illustrated in Figure 2. We allow the user to specify the desired" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": "motion either by a motion vector field or an exemplar dynamic texture video. Moreover, by using a different target for the appearance and the motion, our model can perform dynamic style transfer, as shown in Figure 1. Our contributions summarized are:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 138, + 545, + 300 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 317, + 138, + 545, + 163 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 138, + 545, + 163 + ], + "spans": [ + { + "bbox": [ + 317, + 138, + 545, + 163 + ], + "type": "text", + "content": "- Our DyNCA model, once trained, can synthesize dynamic texture videos in real time." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 317, + 170, + 545, + 195 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 170, + 545, + 195 + ], + "spans": [ + { + "bbox": [ + 317, + 170, + 545, + 195 + ], + "type": "text", + "content": "- Our synthesized videos are on-par with or even better than the existing results in terms of realism and quality." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 317, + 201, + 545, + 225 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 201, + 545, + 225 + ], + "spans": [ + { + "bbox": [ + 317, + 201, + 545, + 225 + ], + "type": "text", + "content": "- After training, our DyNCA model can synthesize infinitely-long videos with arbitrary frame sizes." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 317, + 232, + 545, + 268 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 232, + 545, + 268 + ], + "spans": [ + { + "bbox": [ + 317, + 232, + 545, + 268 + ], + "type": "text", + "content": "- Our DyNCA framework enables several real-time interactive video editing controls including speed, direction, a brush tool, and local coordinate transformation." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 317, + 275, + 545, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 275, + 545, + 300 + ], + "spans": [ + { + "bbox": [ + 317, + 275, + 545, + 300 + ], + "type": "text", + "content": "- We can perform real-time dynamic style transfer by learning appearance and motion from distinct sources." + } + ] + } + ], + "index": 11 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 309, + 398, + 322 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 309, + 398, + 322 + ], + "spans": [ + { + "bbox": [ + 306, + 309, + 398, + 322 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 329, + 545, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 329, + 545, + 365 + ], + "spans": [ + { + "bbox": [ + 305, + 329, + 545, + 365 + ], + "type": "text", + "content": "In the following section, we discuss the existing DyTS methods. For comparison, Table 1 summarizes the strengths (✓) and shortcomings (X) of these methods." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 372, + 456, + 385 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 372, + 456, + 385 + ], + "spans": [ + { + "bbox": [ + 305, + 372, + 456, + 385 + ], + "type": "text", + "content": "2.1. Dynamic Texture Synthesis" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 390, + 545, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 390, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 390, + 545, + 605 + ], + "type": "text", + "content": "In the literature, there are two dominant techniques to synthesize dynamic texture videos. Recent approaches follow the seminal work of Gatys et al. [9] for texture synthesis. The authors propose an optimization-based method that relies on the features extracted by a deep neural network trained for image classification. Gatys et al. [9] show that the Gram matrices of features extracted by the VGG network [22] capture the perceptual qualities of texture images. Funke et al. [8] extend Gatys's idea to dynamic texture synthesis, and use a cross-frame Gram matrix of VGG features to capture the temporal characteristics of dynamic textures. Tesfaldet et al. [24] and Zhang et al. [32] use a pre-trained optical flow network for extracting the motion features, which allows them to disentangle the appearance and motion aspects of video textures. Xie et al. [27] use an energy-based model characterized by a spatio-temporal 3D ConvNet and synthesize textures by sampling using Langevin dynamics." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "type": "text", + "content": "These methods utilize the expressivity of neural networks to produce realistic high-quality dynamic texture videos. However, they require a long training time to synthesize a single short video. Moreover, none of these methods provide any post-training controls over motion speed, frame size, and motion direction. These shortcomings make these methods unsuitable for real-time applications." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "Earlier DyTS methods that can potentially enable real-time synthesis utilized PDEs to model dynamic textures" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 753, + 317, + 763 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 753, + 317, + 763 + ], + "spans": [ + { + "bbox": [ + 293, + 753, + 317, + 763 + ], + "type": "text", + "content": "20743" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 70, + 286, + 188 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 286, + 188 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 286, + 188 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 286, + 188 + ], + "type": "table", + "html": "
MethodABCDEFG
Costantini et al. [5]X✓✓X✓XX
Doretto et al. [6]X✓✓X✓XX
Funke et al. [8]X✓XXXXX
Tesfaldet et al. [24]X✓XXX✓✓
Xie et al. [27]XXXX✓XX
Zhang et al. [32]X✓XXX✓✓
DyNCA (Ours)✓✓✓✓X✓✓
", + "image_path": "7b36c04db6feb878ead0594f71b5a014fef269e81a8cec56cb304525071a274a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 46, + 190, + 287, + 266 + ], + "lines": [ + { + "bbox": [ + 46, + 190, + 287, + 266 + ], + "spans": [ + { + "bbox": [ + 46, + 190, + 287, + 266 + ], + "type": "text", + "content": "Table 1. Comparison of DyTS methods. (A) Can synthesize videos with arbitrary frame size after training. (B) Can synthesize arbitrarily long videos. (C) Can synthesize new video samples without re-training. (D) Allows real-time video editing (speed, direction, and a brush tool). (E) Does not rely on pre-trained models to extract motion or texture information. (F) Has disentangled appearance and motion. (G) Can learn motion from vector fields." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 276, + 287, + 432 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 276, + 287, + 432 + ], + "spans": [ + { + "bbox": [ + 46, + 276, + 287, + 432 + ], + "type": "text", + "content": "[5, 6, 10, 30, 31]. To synthesize video textures, Doretto et al. [6] propose to use a linear dynamical system (LDS) in which each frame of the video is controlled by a latent variable whose evolution through time is driven by random noise. The latent variable is obtained via projection of the target texture image into a lower dimensional space by singular value decomposition (SVD). Costantini et al. [5] propose to use higher-order SVD to improve the expressivity of LDS-based models. Yuan et al. [31] introduce feedback into the LDS to improve the stability of the dynamical system. All these methods can synthesize new video textures without re-training, and potentially in real time. However, the synthesized videos are of low quality and contain artifacts." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 432, + 287, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 432, + 287, + 492 + ], + "spans": [ + { + "bbox": [ + 46, + 432, + 287, + 492 + ], + "type": "text", + "content": "Our DyNCA method benefits from the best of both approaches by combining the expressivity of neural networks with PDEs. Having " + }, + { + "bbox": [ + 46, + 432, + 287, + 492 + ], + "type": "inline_equation", + "content": "2 \\sim 4" + }, + { + "bbox": [ + 46, + 432, + 287, + 492 + ], + "type": "text", + "content": " orders of magnitude fewer parameters than the SOTA models, our model can synthesize realistic dynamic texture videos in real time." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 502, + 195, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 502, + 195, + 514 + ], + "spans": [ + { + "bbox": [ + 47, + 502, + 195, + 514 + ], + "type": "text", + "content": "2.2. NCA for Texture Synthesis" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 521, + 287, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 616 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 616 + ], + "type": "text", + "content": "Gilpin [11] shows that Cellular Automata models can be represented using Convolutional Neural Networks. Extending [11], Mordvinstev et al. [18] propose the Neural Cellular Automata model and show its potential in creating various self-organizing systems [17-20]. NCA is inspired by Turing's seminal work [25] on pattern generation, and the observation that many natural patterns stem from local interactions between tiny particles, cells, or molecules [19]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": "Niklasson et al. [17, 19] were the first to train NCA models to synthesize textures. While the NCA training signal originates from a static exemplar texture image, the model is able to spontaneously generate stable but randomly moving textures. We modify the architecture and training scheme of NCA to enable synthesizing structured motion. First, our DyNCA model receives supervision from a pre-trained optical-flow network, which enables it to synthesize a video" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": "texture with structured motion. Moreover, we incorporate multi-scale perception and positional encoding into the DyNCA architecture. The proposed architectural changes increase the communication range of the cells and allow the cells to be aware of global information, respectively." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 138, + 430, + 152 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 138, + 430, + 152 + ], + "spans": [ + { + "bbox": [ + 306, + 138, + 430, + 152 + ], + "type": "text", + "content": "3. DyNCA Architecture" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 156, + 545, + 182 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 156, + 545, + 182 + ], + "spans": [ + { + "bbox": [ + 306, + 156, + 545, + 182 + ], + "type": "text", + "content": "In the following sections, we first review the NCA model and then present the architecture of our DyNCA." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 186, + 485, + 198 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 186, + 485, + 198 + ], + "spans": [ + { + "bbox": [ + 306, + 186, + 485, + 198 + ], + "type": "text", + "content": "3.1. Neural Cellular Automata (NCA)" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 202, + 545, + 285 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 202, + 545, + 285 + ], + "spans": [ + { + "bbox": [ + 304, + 202, + 545, + 285 + ], + "type": "text", + "content": "The idea of NCA stems from cellular automata, in which cells live on a grid, and each cell communicates with its neighbors to determine the cell's next state. In NCA, cell states at time " + }, + { + "bbox": [ + 304, + 202, + 545, + 285 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 202, + 545, + 285 + ], + "type": "text", + "content": " are represented by " + }, + { + "bbox": [ + 304, + 202, + 545, + 285 + ], + "type": "inline_equation", + "content": "\\mathbf{S}^t \\in \\mathbb{R}^{H \\times W \\times C}" + }, + { + "bbox": [ + 304, + 202, + 545, + 285 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 202, + 545, + 285 + ], + "type": "inline_equation", + "content": "H \\times W" + }, + { + "bbox": [ + 304, + 202, + 545, + 285 + ], + "type": "text", + "content": " is the grid size. The " + }, + { + "bbox": [ + 304, + 202, + 545, + 285 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 202, + 545, + 285 + ], + "type": "text", + "content": " dimensional vector " + }, + { + "bbox": [ + 304, + 202, + 545, + 285 + ], + "type": "inline_equation", + "content": "s_{ij}^t" + }, + { + "bbox": [ + 304, + 202, + 545, + 285 + ], + "type": "text", + "content": " encodes the state of the cell at location " + }, + { + "bbox": [ + 304, + 202, + 545, + 285 + ], + "type": "inline_equation", + "content": "i, j" + }, + { + "bbox": [ + 304, + 202, + 545, + 285 + ], + "type": "text", + "content": ", where the first three dimensions define the RGB color of the cell." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 286, + 545, + 372 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 286, + 545, + 372 + ], + "spans": [ + { + "bbox": [ + 304, + 286, + 545, + 372 + ], + "type": "text", + "content": "The NCA starts from a constant zero-filled initial state called seed and evolves this state over time according to its trainable PDE. The update rule of this PDE consists of two parts, Perception and Stochastic Update. At the perception stage, each cell gathers information from its surrounding neighbors, forming the perception vector " + }, + { + "bbox": [ + 304, + 286, + 545, + 372 + ], + "type": "inline_equation", + "content": "z_{ij} \\in \\mathbb{R}^{4C}" + }, + { + "bbox": [ + 304, + 286, + 545, + 372 + ], + "type": "text", + "content": ", illustrated in the green box in Figure 3." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 336, + 377, + 545, + 392 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 336, + 377, + 545, + 392 + ], + "spans": [ + { + "bbox": [ + 336, + 377, + 545, + 392 + ], + "type": "interline_equation", + "content": "z _ {i j} = \\operatorname {C o n c a t} \\left(s _ {i j}, \\nabla_ {\\mathrm {x}} \\mathbf {S} | _ {i j}, \\nabla_ {\\mathrm {y}} \\mathbf {S} | _ {i j}, \\nabla^ {2} \\mathbf {S} | _ {i j}\\right) \\tag {1}", + "image_path": "ef4af006696371743130594abb752d7432b40d61bd99864013f7f7aaaa3a51ec.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 396, + 545, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 396, + 545, + 456 + ], + "spans": [ + { + "bbox": [ + 304, + 396, + 545, + 456 + ], + "type": "text", + "content": "Note that the convolution kernels in the perception stage are frozen during training. In the stochastic update stage, the new state of each cell is determined based on its perception vector. The update stage of NCA can be viewed as a stochastic discrete-time, discrete-space PDE:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 363, + 459, + 545, + 507 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 363, + 459, + 545, + 507 + ], + "spans": [ + { + "bbox": [ + 363, + 459, + 545, + 507 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathbf {S} ^ {t + 1} = \\mathcal {F} (\\mathbf {S} ^ {t}) = \\mathbf {S} ^ {t} + \\frac {\\partial \\mathbf {S}}{\\partial t} \\Delta t \\tag {2} \\\\ \\frac {\\partial s _ {i j}}{\\partial t} = \\operatorname {M L P} \\left(z _ {i j}\\right) \\odot M \\\\ \\end{array}", + "image_path": "38982eece75d8e38cdd2dc8f0a82f35d5b9e840a423161469a00044c43dd331b.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 510, + 545, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 545, + 594 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 545, + 594 + ], + "type": "text", + "content": "where MLP is a Multi Layered Perceptron with two layers and a ReLU activation function. The residual update values produced by the MLP are multiplied by a binary random variable " + }, + { + "bbox": [ + 304, + 510, + 545, + 594 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 510, + 545, + 594 + ], + "type": "text", + "content": " to introduce stochasticity into the model. This ensures that the cells can work asynchronously, and also enables synthesizing new texture samples. The stochastic update stage is illustrated in the blue box in Figure 3." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "To facilitate long-range cell communication and to allow the cells to be aware of global information, we introduce multi-scale perception and positional encoding into the vanilla NCA architecture, respectively. Our experiments in section 5 demonstrate their necessity for DyTS. The overall architecture of our DyNCA model is illustrated in Figure 3. To the best of our knowledge, we are the first to incorporate these two architectural changes in conjunction with NCA models. In the following sections, we elaborate on the proposed architectural modifications." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 753, + 317, + 763 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 753, + 317, + 763 + ], + "spans": [ + { + "bbox": [ + 293, + 753, + 317, + 763 + ], + "type": "text", + "content": "20744" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 71, + 310, + 290 + ], + "blocks": [ + { + "bbox": [ + 51, + 71, + 310, + 290 + ], + "lines": [ + { + "bbox": [ + 51, + 71, + 310, + 290 + ], + "spans": [ + { + "bbox": [ + 51, + 71, + 310, + 290 + ], + "type": "image", + "image_path": "11bba1529c422dfab78a28e8ccdaddb3b6c543e448075db2466bf50e159c7883.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 294, + 547, + 340 + ], + "lines": [ + { + "bbox": [ + 46, + 294, + 547, + 340 + ], + "spans": [ + { + "bbox": [ + 46, + 294, + 547, + 340 + ], + "type": "text", + "content": "Figure 3. Illustration of a single DyNCA step. Given an input state " + }, + { + "bbox": [ + 46, + 294, + 547, + 340 + ], + "type": "inline_equation", + "content": "\\mathbf{S}^t\\in R^{H\\times W\\times C}" + }, + { + "bbox": [ + 46, + 294, + 547, + 340 + ], + "type": "text", + "content": " at time step " + }, + { + "bbox": [ + 46, + 294, + 547, + 340 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 294, + 547, + 340 + ], + "type": "text", + "content": ", each cell first perceives its neighbors on various scales with the same perception layer. The perception tensor of each scale is then upsampled and summed up, and is concatenated with the positional encoding tensor " + }, + { + "bbox": [ + 46, + 294, + 547, + 340 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_{xy}" + }, + { + "bbox": [ + 46, + 294, + 547, + 340 + ], + "type": "text", + "content": ". Each cell then applies the same update rule, parameterized by a small MLP. Finally, all cells perform a stochastic residual update to determine the state of the cells in time " + }, + { + "bbox": [ + 46, + 294, + 547, + 340 + ], + "type": "inline_equation", + "content": "t + \\Delta t" + }, + { + "bbox": [ + 46, + 294, + 547, + 340 + ], + "type": "text", + "content": ". We use " + }, + { + "bbox": [ + 46, + 294, + 547, + 340 + ], + "type": "inline_equation", + "content": "\\Delta t = 1" + }, + { + "bbox": [ + 46, + 294, + 547, + 340 + ], + "type": "text", + "content": " in our model." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 312, + 71, + 547, + 290 + ], + "blocks": [ + { + "bbox": [ + 312, + 71, + 547, + 290 + ], + "lines": [ + { + "bbox": [ + 312, + 71, + 547, + 290 + ], + "spans": [ + { + "bbox": [ + 312, + 71, + 547, + 290 + ], + "type": "image", + "image_path": "4079eea13ba9b4f96674a7860867462d0a91816c64c1ea81c5454c0731822e58.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 347, + 175, + 360 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 347, + 175, + 360 + ], + "spans": [ + { + "bbox": [ + 47, + 347, + 175, + 360 + ], + "type": "text", + "content": "3.2. Multi-scale Perception" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 366, + 288, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 366, + 288, + 498 + ], + "spans": [ + { + "bbox": [ + 46, + 366, + 288, + 498 + ], + "type": "text", + "content": "In the perception stage of vanilla NCA, each cell only receives information from its eight surrounding cells. Therefore, many timesteps are needed for far-apart cells to perceive and communicate with each other. This problem becomes more pronounced when we increase the grid size " + }, + { + "bbox": [ + 46, + 366, + 288, + 498 + ], + "type": "inline_equation", + "content": "H \\times W" + }, + { + "bbox": [ + 46, + 366, + 288, + 498 + ], + "type": "text", + "content": ", since the " + }, + { + "bbox": [ + 46, + 366, + 288, + 498 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 46, + 366, + 288, + 498 + ], + "type": "text", + "content": " perception kernels become smaller in proportion to the image size. One straightforward solution is to increase the number of NCA steps during training to facilitate long-range cell communication. However, this simple solution increases memory usage, slows down the training, and makes the training more unstable." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 498, + 287, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 287, + 666 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 287, + 666 + ], + "type": "text", + "content": "To solve this problem, we propose Multi-Scale Perception (MSP). The idea of using multi-scale analysis predates deep learning and has shown its effectiveness in many computer vision tasks [1, 3, 14, 15]. We build a pyramid of cell states via bilinear downsampling and apply the same perception kernels at different scales. To combine the information from all scales, we upsample and sum up the perception vectors, as shown in the red box in Figure 3. Multi-scale perception increases the communication range of the cells and allows messages to pass between faraway cells in fewer steps. It also improves the stability of DyNCA and makes the training less sensitive to hyperparameters. We perform an ablation study of multi-scale perception in section 5.4 and show its importance in preserving appearance fidelity." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 671, + 164, + 685 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 164, + 685 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 164, + 685 + ], + "type": "text", + "content": "3.3. Positional Encoding" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "In order to apply the " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": " depth-wise convolutions in the perception stage, one needs to adopt a padding strat" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 348, + 547, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 348, + 547, + 564 + ], + "spans": [ + { + "bbox": [ + 304, + 348, + 547, + 564 + ], + "type": "text", + "content": "egy to retain the spatial dimensions. Niklasson et al. [19] use circular padding to make the cells homogeneous and to reduce spatial inductive bias. While cell homogeneity is a good assumption for generating static textures, it is not suitable for synthesizing structured motion. Our intuition is that, in physical systems, motion not only arises from local interactions between tiny particles and cells, but also from global external forces such as gravity. Hence, we allow the cells to be aware of their position and propose to use replicate padding and Cartesian Positional Encoding (CPE), which is known to provide a more consistent spatial inductive bias than zero-padding [28]. As illustrated in the purple box in Figure 3, we concatenate the output of the multi-scale perception stage with a two-channel tensor " + }, + { + "bbox": [ + 304, + 348, + 547, + 564 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_{\\mathrm{xy}}" + }, + { + "bbox": [ + 304, + 348, + 547, + 564 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 348, + 547, + 564 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_{ij} = \\left[ \\begin{array}{c}2i + 1.0\\\\ \\frac{W}{2j + 1.0}\\\\ H \\end{array} \\right] - 1.0" + }, + { + "bbox": [ + 304, + 348, + 547, + 564 + ], + "type": "text", + "content": ". Our ablation study in section 5.4 shows that employing CPE drastically improves motion consistency and accuracy in the synthesized videos." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 574, + 410, + 589 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 574, + 410, + 589 + ], + "spans": [ + { + "bbox": [ + 306, + 574, + 410, + 589 + ], + "type": "text", + "content": "4. DyNCA Training" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 594, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 715 + ], + "type": "text", + "content": "Our DyNCA model acts as a PDE and generates a sequence of images " + }, + { + "bbox": [ + 304, + 594, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{I}^g = \\{\\mathcal{I}_1^g,\\mathcal{I}_2^g,\\ldots \\}" + }, + { + "bbox": [ + 304, + 594, + 545, + 715 + ], + "type": "text", + "content": ". We sample the synthesized video frames " + }, + { + "bbox": [ + 304, + 594, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{V}^g = \\{\\mathcal{V}_1^g,\\mathcal{V}_2^g,\\ldots \\}" + }, + { + "bbox": [ + 304, + 594, + 545, + 715 + ], + "type": "text", + "content": " from this image sequence by mapping " + }, + { + "bbox": [ + 304, + 594, + 545, + 715 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 594, + 545, + 715 + ], + "type": "text", + "content": " DyNCA steps to one frame, i.e. " + }, + { + "bbox": [ + 304, + 594, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_k^g = \\mathcal{I}_{kT}^g" + }, + { + "bbox": [ + 304, + 594, + 545, + 715 + ], + "type": "text", + "content": ". The synthesized video is then evaluated against the target appearance and the target motion to compute the appearance loss " + }, + { + "bbox": [ + 304, + 594, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{appr}" + }, + { + "bbox": [ + 304, + 594, + 545, + 715 + ], + "type": "text", + "content": " and the motion loss " + }, + { + "bbox": [ + 304, + 594, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{motion}" + }, + { + "bbox": [ + 304, + 594, + 545, + 715 + ], + "type": "text", + "content": ", respectively. This process is shown in Figure 2. Our final loss is " + }, + { + "bbox": [ + 304, + 594, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{DyNCA}} = \\mathcal{L}_{appr} + \\lambda \\mathcal{L}_{motion}" + }, + { + "bbox": [ + 304, + 594, + 545, + 715 + ], + "type": "text", + "content": ". The overall scheme of the proposed loss functions is illustrated in Figure 4." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 753, + 317, + 763 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 753, + 317, + 763 + ], + "spans": [ + { + "bbox": [ + 293, + 753, + 317, + 763 + ], + "type": "text", + "content": "20745" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 287, + 379 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 287, + 379 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 287, + 379 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 287, + 379 + ], + "type": "image", + "image_path": "c893b5e96e0d53b59cebc21d2d02456e24b20dc48cf433a0f555196b05c7db4e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 390, + 287, + 489 + ], + "lines": [ + { + "bbox": [ + 46, + 390, + 287, + 489 + ], + "spans": [ + { + "bbox": [ + 46, + 390, + 287, + 489 + ], + "type": "text", + "content": "Figure 4. Overview of our loss functions. Appearance loss " + }, + { + "bbox": [ + 46, + 390, + 287, + 489 + ], + "type": "inline_equation", + "content": "(\\mathcal{L}_{appr})" + }, + { + "bbox": [ + 46, + 390, + 287, + 489 + ], + "type": "text", + "content": ": DyNCA learns the target appearance from a static image via minimizing an optimal-transport-based style matching loss [13] between deep features extracted from the VGG16 network [22]. Motion Loss " + }, + { + "bbox": [ + 46, + 390, + 287, + 489 + ], + "type": "inline_equation", + "content": "(\\mathcal{L}_{mvec})" + }, + { + "bbox": [ + 46, + 390, + 287, + 489 + ], + "type": "text", + "content": ": We guide DyNCA to synthesize a video having an optical flow similar to the target vector field. Motion Loss " + }, + { + "bbox": [ + 46, + 390, + 287, + 489 + ], + "type": "inline_equation", + "content": "(\\mathcal{L}_{mvec})" + }, + { + "bbox": [ + 46, + 390, + 287, + 489 + ], + "type": "text", + "content": ": DyNCA fits the target video motion by minimizing an optimal-transport-based style matching loss between deep features of a pre-trained optical-flow prediction network." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 502, + 150, + 515 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 502, + 150, + 515 + ], + "spans": [ + { + "bbox": [ + 47, + 502, + 150, + 515 + ], + "type": "text", + "content": "4.1. Appearance Loss" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "text", + "content": "We follow the texture fitting scheme proposed by Niklasson et al. [19], where the statistics of deep features of the NCA-generated images are forced to match the ones of the target texture. We use a pre-trained VGG16 network [22] to extract the deep features from the images. We denote VGG as " + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{VGG}" + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "text", + "content": " and the feature map extracted from layer " + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{VGG}^l" + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "text", + "content": ". Niklasson et al. [19] use the Gram matrix to define the training objective of the NCA. However, using Gram matrices can cause unstable training [26], and can result in textures with wrong colors [16, 19]. Hence, we use the style loss proposed by Kolkin et al. [13], which has shown to produce better results. This loss is composed of a structure-matching term and a moment-matching term. Given a feature map of size " + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "inline_equation", + "content": "C\\times H\\times W" + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "text", + "content": ", the algorithm first creates a set of deep features with " + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "inline_equation", + "content": "n = H\\times W" + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "text", + "content": " elements by flattening the feature map along the spatial dimensions. Let " + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "inline_equation", + "content": "Y" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": "be the deep feature set of a synthesized image and target appearance image, respectively. Then the structure-matching term " + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_s" + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": " and the moment-matching term " + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_m" + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": " are defined as:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 323, + 116, + 545, + 146 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 116, + 545, + 146 + ], + "spans": [ + { + "bbox": [ + 323, + 116, + 545, + 146 + ], + "type": "interline_equation", + "content": "D (A, B) = \\frac {1}{| A |} \\sum_ {i} \\min _ {j} \\left(1 - \\frac {A _ {i} \\cdot B _ {j}}{| | A _ {i} | | _ {2} | | B _ {j} | | _ {2}}\\right) \\tag {3}", + "image_path": "9cba8f578a2ad9369a28d05ad5c3b39f24b62c6a086918187ec4bf91d05be56d.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 335, + 148, + 505, + 162 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 335, + 148, + 505, + 162 + ], + "spans": [ + { + "bbox": [ + 335, + 148, + 505, + 162 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {s} (X, Y) = \\max \\left\\{D (X, Y), D (Y, X) \\right\\},", + "image_path": "c1d45225c7ac6a98e3695d46b1272d2122cec139e3a5b1dc04670648879ac8b3.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 311, + 164, + 545, + 188 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 164, + 545, + 188 + ], + "spans": [ + { + "bbox": [ + 311, + 164, + 545, + 188 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {m} (X, Y) = \\frac {1}{C} \\| \\boldsymbol {\\mu} _ {X} - \\boldsymbol {\\mu} _ {Y} \\| _ {1} + \\frac {1}{C ^ {2}} \\| \\boldsymbol {\\Sigma} _ {X} - \\boldsymbol {\\Sigma} _ {Y} \\| _ {1}, \\tag {4}", + "image_path": "059dbdb76d03599859e5643c33e56b2821483eafe691a3d76f99adceecfe07c1.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 189, + 545, + 261 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 189, + 545, + 261 + ], + "spans": [ + { + "bbox": [ + 305, + 189, + 545, + 261 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 189, + 545, + 261 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 305, + 189, + 545, + 261 + ], + "type": "text", + "content": " measures the distance between two deep feature sets, and " + }, + { + "bbox": [ + 305, + 189, + 545, + 261 + ], + "type": "inline_equation", + "content": "\\pmb{\\mu},\\pmb{\\Sigma}" + }, + { + "bbox": [ + 305, + 189, + 545, + 261 + ], + "type": "text", + "content": " are the mean and covariance matrix of their corresponding set, respectively. Let " + }, + { + "bbox": [ + 305, + 189, + 545, + 261 + ], + "type": "inline_equation", + "content": "X_{k}^{l}" + }, + { + "bbox": [ + 305, + 189, + 545, + 261 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 189, + 545, + 261 + ], + "type": "inline_equation", + "content": "Y^{l}" + }, + { + "bbox": [ + 305, + 189, + 545, + 261 + ], + "type": "text", + "content": " be deep VGG features extracted by " + }, + { + "bbox": [ + 305, + 189, + 545, + 261 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{VGG}^{\\text{conv } l-1}" + }, + { + "bbox": [ + 305, + 189, + 545, + 261 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 305, + 189, + 545, + 261 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 305, + 189, + 545, + 261 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 189, + 545, + 261 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 189, + 545, + 261 + ], + "type": "text", + "content": " indicate the VGG block index and the synthesized image index, respectively. Our final appearance loss is then defined as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 317, + 265, + 545, + 299 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 265, + 545, + 299 + ], + "spans": [ + { + "bbox": [ + 317, + 265, + 545, + 299 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {a p p r}} = \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\sum_ {l = 1} ^ {5} \\left(\\mathcal {L} _ {s} \\left(X _ {k} ^ {l}, Y ^ {l}\\right) + \\mathcal {L} _ {m} \\left(X _ {k} ^ {l}, Y ^ {l}\\right)\\right) \\tag {5}", + "image_path": "fe30f9068c31facb1c1fb6569add482846ab3b72f474bcba6a5e4c57473075ba.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 302, + 387, + 314 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 302, + 387, + 314 + ], + "spans": [ + { + "bbox": [ + 306, + 302, + 387, + 314 + ], + "type": "text", + "content": "4.2. Motion Loss" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 319, + 545, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 319, + 545, + 415 + ], + "spans": [ + { + "bbox": [ + 305, + 319, + 545, + 415 + ], + "type": "text", + "content": "The motion loss guides the DyNCA to produce the desired motion. We use the pre-trained Optical-Flow Prediction Network from [24] to quantify the motion information between two frames. We denote this network as " + }, + { + "bbox": [ + 305, + 319, + 545, + 415 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{OF}" + }, + { + "bbox": [ + 305, + 319, + 545, + 415 + ], + "type": "text", + "content": ", and the feature map extracted from layer " + }, + { + "bbox": [ + 305, + 319, + 545, + 415 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 305, + 319, + 545, + 415 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 305, + 319, + 545, + 415 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{OF}^l" + }, + { + "bbox": [ + 305, + 319, + 545, + 415 + ], + "type": "text", + "content": ". For different types of target motion sources, namely vector fields and videos, our motion loss takes two different forms, " + }, + { + "bbox": [ + 305, + 319, + 545, + 415 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{mvec}" + }, + { + "bbox": [ + 305, + 319, + 545, + 415 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 319, + 545, + 415 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{mvid}" + }, + { + "bbox": [ + 305, + 319, + 545, + 415 + ], + "type": "text", + "content": ", respectively. These terms are discussed below." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 423, + 448, + 434 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 423, + 448, + 434 + ], + "spans": [ + { + "bbox": [ + 306, + 423, + 448, + 434 + ], + "type": "text", + "content": "4.2.1 Motion from Vector Field" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 441, + 545, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 441, + 545, + 502 + ], + "spans": [ + { + "bbox": [ + 305, + 441, + 545, + 502 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 305, + 441, + 545, + 502 + ], + "type": "inline_equation", + "content": "U^t \\in \\mathbb{R}^{H \\times W \\times 2}" + }, + { + "bbox": [ + 305, + 441, + 545, + 502 + ], + "type": "text", + "content": " be the target motion vector field. Let " + }, + { + "bbox": [ + 305, + 441, + 545, + 502 + ], + "type": "inline_equation", + "content": "U^g = \\mathcal{F}_{OF}(\\mathcal{I}_{t_1}^g, \\mathcal{I}_{t_2}^g)" + }, + { + "bbox": [ + 305, + 441, + 545, + 502 + ], + "type": "text", + "content": " be the optical-flow prediction on two synthesized images, where " + }, + { + "bbox": [ + 305, + 441, + 545, + 502 + ], + "type": "inline_equation", + "content": "t_1, t_2" + }, + { + "bbox": [ + 305, + 441, + 545, + 502 + ], + "type": "text", + "content": " are two random indices such that " + }, + { + "bbox": [ + 305, + 441, + 545, + 502 + ], + "type": "inline_equation", + "content": "t_2 > t_1" + }, + { + "bbox": [ + 305, + 441, + 545, + 502 + ], + "type": "text", + "content": ". We propose two losses, " + }, + { + "bbox": [ + 305, + 441, + 545, + 502 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{dir}" + }, + { + "bbox": [ + 305, + 441, + 545, + 502 + ], + "type": "text", + "content": " for matching the motion direction, defined as:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 338, + 506, + 545, + 540 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 338, + 506, + 545, + 540 + ], + "spans": [ + { + "bbox": [ + 338, + 506, + 545, + 540 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {d i r} = \\frac {1}{H W} \\sum_ {i, j} \\left(1 - \\frac {U _ {i j} ^ {g} \\cdot U _ {i j} ^ {t}}{\\left\\| U _ {i j} ^ {g} \\right\\| _ {2} \\left\\| U _ {i j} ^ {t} \\right\\| _ {2}}\\right), \\tag {6}", + "image_path": "6a666b8db5f4f590dae77e2b0097538207b825b2fb2a5736493a7856a4d01119.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 544, + 544, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 544, + 544, + 556 + ], + "spans": [ + { + "bbox": [ + 306, + 544, + 544, + 556 + ], + "type": "text", + "content": "and " + }, + { + "bbox": [ + 306, + 544, + 544, + 556 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{norm}" + }, + { + "bbox": [ + 306, + 544, + 544, + 556 + ], + "type": "text", + "content": " for matching the motion magnitude, defined as:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 320, + 559, + 545, + 590 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 559, + 545, + 590 + ], + "spans": [ + { + "bbox": [ + 320, + 559, + 545, + 590 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {n o r m}} = \\frac {1}{H W} \\sum_ {i, j} \\left| \\frac {T}{t _ {2} - t _ {1}} \\left\\| U _ {i j} ^ {g} \\right\\| _ {2} - \\left\\| U _ {i j} ^ {t} \\right\\| _ {2} \\right|. \\tag {7}", + "image_path": "716b0aa772e4a7b62fde47b312dc34c3772f368811ad1f87203920317e422321.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 594, + 545, + 631 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 594, + 545, + 631 + ], + "spans": [ + { + "bbox": [ + 306, + 594, + 545, + 631 + ], + "type": "text", + "content": "Since " + }, + { + "bbox": [ + 306, + 594, + 545, + 631 + ], + "type": "inline_equation", + "content": "t_1, t_2" + }, + { + "bbox": [ + 306, + 594, + 545, + 631 + ], + "type": "text", + "content": " are selected randomly, we scale the norm of the " + }, + { + "bbox": [ + 306, + 594, + 545, + 631 + ], + "type": "inline_equation", + "content": "U^g" + }, + { + "bbox": [ + 306, + 594, + 545, + 631 + ], + "type": "text", + "content": " by " + }, + { + "bbox": [ + 306, + 594, + 545, + 631 + ], + "type": "inline_equation", + "content": "\\frac{T}{t_2 - t_1}" + }, + { + "bbox": [ + 306, + 594, + 545, + 631 + ], + "type": "text", + "content": " before comparing it against the target motion vector field. We define our final loss " + }, + { + "bbox": [ + 306, + 594, + 545, + 631 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{mvec}" + }, + { + "bbox": [ + 306, + 594, + 545, + 631 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 316, + 635, + 545, + 649 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 635, + 545, + 649 + ], + "spans": [ + { + "bbox": [ + 316, + 635, + 545, + 649 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {m v e c} = (1. 0 - \\min \\{1. 0, \\mathcal {L} _ {d i r} \\}) \\mathcal {L} _ {\\text {n o r m}} + \\gamma \\mathcal {L} _ {d i r}, \\tag {8}", + "image_path": "93421be988ac2465077b8481cc37bd0d07d8dcd90850c14a9d0520f1b586db6f.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 654, + 545, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 654, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 305, + 654, + 545, + 713 + ], + "type": "text", + "content": " is a constant coefficient. We set the norm-matching loss weight to " + }, + { + "bbox": [ + 305, + 654, + 545, + 713 + ], + "type": "inline_equation", + "content": "(1.0 - \\min\\{1.0, \\mathcal{L}_{dir}\\})" + }, + { + "bbox": [ + 305, + 654, + 545, + 713 + ], + "type": "text", + "content": " to guide the training process to first focus on producing motion with the correct direction before trying to match the norm of the synthesized motion with the target vector field." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 753, + 317, + 763 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 753, + 317, + 763 + ], + "spans": [ + { + "bbox": [ + 293, + 753, + 317, + 763 + ], + "type": "text", + "content": "20746" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 163, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 163, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 163, + 83 + ], + "type": "text", + "content": "4.2.2 Motion from Video" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 87, + 289, + 279 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 87, + 289, + 279 + ], + "spans": [ + { + "bbox": [ + 46, + 87, + 289, + 279 + ], + "type": "text", + "content": "For training DyNCA to learn the motion from a target video, we aim to match the motion between successive frames of the synthesized and target videos. We synthesize a video " + }, + { + "bbox": [ + 46, + 87, + 289, + 279 + ], + "type": "inline_equation", + "content": "\\mathcal{V}^g" + }, + { + "bbox": [ + 46, + 87, + 289, + 279 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 46, + 87, + 289, + 279 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 87, + 289, + 279 + ], + "type": "text", + "content": " frames, and randomly pick the same number of consecutive frames from the target video, forming " + }, + { + "bbox": [ + 46, + 87, + 289, + 279 + ], + "type": "inline_equation", + "content": "\\mathcal{V}^t" + }, + { + "bbox": [ + 46, + 87, + 289, + 279 + ], + "type": "text", + "content": ". Inspired by Tesfaldet et al. [24], we feed successive video frames to a pre-trained optical-flow network and extract deep features from the concatenation layer of the network, denoted as " + }, + { + "bbox": [ + 46, + 87, + 289, + 279 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{OF}^{concat}" + }, + { + "bbox": [ + 46, + 87, + 289, + 279 + ], + "type": "text", + "content": ". To compare the deep optical flow features of the target and the synthesized videos, we use the same structure-matching and moment-matching terms defined in Section 4.1. We denote the extracted deep optical-flow features as " + }, + { + "bbox": [ + 46, + 87, + 289, + 279 + ], + "type": "inline_equation", + "content": "X_{k}" + }, + { + "bbox": [ + 46, + 87, + 289, + 279 + ], + "type": "text", + "content": " for the synthesized video, and " + }, + { + "bbox": [ + 46, + 87, + 289, + 279 + ], + "type": "inline_equation", + "content": "Y_{k}" + }, + { + "bbox": [ + 46, + 87, + 289, + 279 + ], + "type": "text", + "content": " for the target video, where " + }, + { + "bbox": [ + 46, + 87, + 289, + 279 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 87, + 289, + 279 + ], + "type": "text", + "content": " indicates the frame index. Notice that there are " + }, + { + "bbox": [ + 46, + 87, + 289, + 279 + ], + "type": "inline_equation", + "content": "K - 1" + }, + { + "bbox": [ + 46, + 87, + 289, + 279 + ], + "type": "text", + "content": " successive frame pairs in total. We define the objective for learning motion from video textures as:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 282, + 287, + 315 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 282, + 287, + 315 + ], + "spans": [ + { + "bbox": [ + 56, + 282, + 287, + 315 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {m v i d} = \\frac {1}{K - 1} \\sum_ {k = 1} ^ {K - 1} \\left(\\mathcal {L} _ {s} \\left(X _ {k}, Y _ {k}\\right) + \\mathcal {L} _ {m} \\left(X _ {k}, Y _ {k}\\right)\\right) \\tag {9}", + "image_path": "da7d1a16a73a7556dc1649f4ba17c035248af9b77d70da4a1e85ab8a56e0cc7c.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 320, + 128, + 334 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 320, + 128, + 334 + ], + "spans": [ + { + "bbox": [ + 47, + 320, + 128, + 334 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 335, + 289, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 335, + 289, + 528 + ], + "spans": [ + { + "bbox": [ + 46, + 335, + 289, + 528 + ], + "type": "text", + "content": "We conduct experiments on the critical parameters of DyNCA, including " + }, + { + "bbox": [ + 46, + 335, + 289, + 528 + ], + "type": "inline_equation", + "content": "N_{C}, N_{H}, N_{W}, N_{FC}" + }, + { + "bbox": [ + 46, + 335, + 289, + 528 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 335, + 289, + 528 + ], + "type": "inline_equation", + "content": "N_{C}, N_{H}, N_{W}" + }, + { + "bbox": [ + 46, + 335, + 289, + 528 + ], + "type": "text", + "content": " are the size of the DyNCA seed state and " + }, + { + "bbox": [ + 46, + 335, + 289, + 528 + ], + "type": "inline_equation", + "content": "N_{FC}" + }, + { + "bbox": [ + 46, + 335, + 289, + 528 + ], + "type": "text", + "content": " is the output dimensionality of the first layer of MLP in DyNCA. Concretely, we set " + }, + { + "bbox": [ + 46, + 335, + 289, + 528 + ], + "type": "inline_equation", + "content": "N_{C} = 12" + }, + { + "bbox": [ + 46, + 335, + 289, + 528 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 335, + 289, + 528 + ], + "type": "inline_equation", + "content": "N_{FC} = 96" + }, + { + "bbox": [ + 46, + 335, + 289, + 528 + ], + "type": "text", + "content": " for DyNCA-S and " + }, + { + "bbox": [ + 46, + 335, + 289, + 528 + ], + "type": "inline_equation", + "content": "N_{C} = 16" + }, + { + "bbox": [ + 46, + 335, + 289, + 528 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 335, + 289, + 528 + ], + "type": "inline_equation", + "content": "N_{FC} = 128" + }, + { + "bbox": [ + 46, + 335, + 289, + 528 + ], + "type": "text", + "content": " for DyNCA-L. Although DyNCA can adapt to arbitrary seed sizes after training, the seed resolution used during training affects the texture details. We experiment with both " + }, + { + "bbox": [ + 46, + 335, + 289, + 528 + ], + "type": "inline_equation", + "content": "128^{2}" + }, + { + "bbox": [ + 46, + 335, + 289, + 528 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 335, + 289, + 528 + ], + "type": "inline_equation", + "content": "256^{2}" + }, + { + "bbox": [ + 46, + 335, + 289, + 528 + ], + "type": "text", + "content": " spatial resolutions for the seed. We use Positional Encoding for all of the DyNCA configurations, and enable Multi-Scale Perception only when training with the " + }, + { + "bbox": [ + 46, + 335, + 289, + 528 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 46, + 335, + 289, + 528 + ], + "type": "text", + "content": " seed size. Table 2 summarizes the DyNCA configurations. We perform our experiments on an Nvidia-A100 GPU, and use Adam optimizer with an initial learning rate of 0.001. We refer the reader to the supplementary for further training details." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 530, + 197, + 544 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 530, + 197, + 544 + ], + "spans": [ + { + "bbox": [ + 47, + 530, + 197, + 544 + ], + "type": "text", + "content": "5.1. Dynamic Texture Synthesis" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 546, + 287, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 546, + 287, + 582 + ], + "spans": [ + { + "bbox": [ + 46, + 546, + 287, + 582 + ], + "type": "text", + "content": "We present the results of synthesizing dynamic textures using DyNCA, where the target motion is either a vector field or a video, and the target appearance is a static image." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 582, + 287, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 689 + ], + "type": "text", + "content": "Motion from Vector Field: We manually design 12 target vector fields, and for each target motion, we train both DyNCA-S and DyNCA-L configurations on 45 different target appearances. We provide the resulting 1080 trained models in our real-time interactive demo. We set seed size to " + }, + { + "bbox": [ + 46, + 582, + 287, + 689 + ], + "type": "inline_equation", + "content": "128 \\times 128" + }, + { + "bbox": [ + 46, + 582, + 287, + 689 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 582, + 287, + 689 + ], + "type": "inline_equation", + "content": "T = 24" + }, + { + "bbox": [ + 46, + 582, + 287, + 689 + ], + "type": "text", + "content": ", assuming that 24 steps of DyNCA update equals one frame of the synthesized video. Figure 6 shows the optical flow of the DyNCA-S synthesized videos and the corresponding target vector fields used for training." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "Motion from Video. We train DyNCA to match the target motion from videos. For the target appearance image," + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "content": "we use one of the video frames or a stylistic image, to perform dynamic texture synthesis and dynamic style transfer, respectively. We train both DyNCA-S and DyNCA-L on 59 target dynamic texture videos provided in [24], setting seed size to " + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "inline_equation", + "content": "T = 64" + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "content": ". Figure 5 provides some visual results. More results are provided in our demo and supplementary. In Table 2, we compare our DyNCA and the previous SOTA models [24,27] in terms of the computational costs, namely performance and the number of parameters. Note that our DyNCA model is orders of magnitude more efficient in both training and synthesis time as well as the number of parameters. We refer the reader to the supplementary material for the detailed experimental setup." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 231, + 443, + 244 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 231, + 443, + 244 + ], + "spans": [ + { + "bbox": [ + 305, + 231, + 443, + 244 + ], + "type": "text", + "content": "5.2. Real-time Video Editing" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 247, + 545, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 247, + 545, + 319 + ], + "spans": [ + { + "bbox": [ + 304, + 247, + 545, + 319 + ], + "type": "text", + "content": "DyNCA can also perform real-time video editing by utilizing the post-training NCA controls introduced in [19]. These edits include direction control, speed control, a brush tool, and local coordinate transformations. We refer the reader to our online demo at https://dynca.github.io for real-time and interactive visualization and experimentation." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 319, + 545, + 402 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 319, + 545, + 402 + ], + "spans": [ + { + "bbox": [ + 304, + 319, + 545, + 402 + ], + "type": "text", + "content": "Direction Control: By rotating the Sobel convolution kernels " + }, + { + "bbox": [ + 304, + 319, + 545, + 402 + ], + "type": "inline_equation", + "content": "\\nabla_{\\mathrm{x}}" + }, + { + "bbox": [ + 304, + 319, + 545, + 402 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 319, + 545, + 402 + ], + "type": "inline_equation", + "content": "\\nabla_{\\mathrm{y}}" + }, + { + "bbox": [ + 304, + 319, + 545, + 402 + ], + "type": "text", + "content": " in the perception stage, we can control the direction of the motion in the synthesized video. This is done by replacing " + }, + { + "bbox": [ + 304, + 319, + 545, + 402 + ], + "type": "inline_equation", + "content": "\\nabla_{\\mathrm{x}}" + }, + { + "bbox": [ + 304, + 319, + 545, + 402 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 319, + 545, + 402 + ], + "type": "inline_equation", + "content": "\\nabla_{\\mathrm{y}}" + }, + { + "bbox": [ + 304, + 319, + 545, + 402 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 319, + 545, + 402 + ], + "type": "inline_equation", + "content": "\\nabla_{\\mathrm{u}}" + }, + { + "bbox": [ + 304, + 319, + 545, + 402 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 319, + 545, + 402 + ], + "type": "inline_equation", + "content": "\\nabla_{\\mathrm{v}}" + }, + { + "bbox": [ + 304, + 319, + 545, + 402 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 319, + 545, + 402 + ], + "type": "inline_equation", + "content": "\\binom{\\mathrm{u}}{\\mathrm{v}} = \\mathrm{R}_{\\theta}\\binom{\\mathrm{x}}{\\mathrm{y}}" + }, + { + "bbox": [ + 304, + 319, + 545, + 402 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 319, + 545, + 402 + ], + "type": "inline_equation", + "content": "\\mathbf{R}_{\\theta}" + }, + { + "bbox": [ + 304, + 319, + 545, + 402 + ], + "type": "text", + "content": " is the rotation matrix with angle " + }, + { + "bbox": [ + 304, + 319, + 545, + 402 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 319, + 545, + 402 + ], + "type": "text", + "content": ". We also rotate " + }, + { + "bbox": [ + 304, + 319, + 545, + 402 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_{\\mathrm{xy}}" + }, + { + "bbox": [ + 304, + 319, + 545, + 402 + ], + "type": "text", + "content": " by angle " + }, + { + "bbox": [ + 304, + 319, + 545, + 402 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 319, + 545, + 402 + ], + "type": "text", + "content": " so that the position-dependent part of the motion magnitude also rotates accordingly." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 402, + 545, + 497 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 402, + 545, + 497 + ], + "spans": [ + { + "bbox": [ + 304, + 402, + 545, + 497 + ], + "type": "text", + "content": "Speed Control: We control the speed of the synthesized video by increasing/decreasing " + }, + { + "bbox": [ + 304, + 402, + 545, + 497 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 402, + 545, + 497 + ], + "type": "text", + "content": ", which determines how many DyNCA steps are used to synthesize one video frame. Brush Tool: The brush tool allows the users to delete pixels from the video. Since our DyNCA model exhibits the self-organization property of the original NCA [19], the model can reorganize itself and continue synthesizing realistic videos by naturally filling the deleted pixels." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 498, + 545, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 575 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 575 + ], + "type": "text", + "content": "Local Coordinate Transformation: DyNCA can create complex motion transformations by allowing each cell to use a different rotation angle " + }, + { + "bbox": [ + 304, + 498, + 545, + 575 + ], + "type": "inline_equation", + "content": "\\theta(i,j)" + }, + { + "bbox": [ + 304, + 498, + 545, + 575 + ], + "type": "text", + "content": " for transforming its Sobel convolution kernels. For example, setting the rotation angle for the cell at location " + }, + { + "bbox": [ + 304, + 498, + 545, + 575 + ], + "type": "inline_equation", + "content": "(i,j)" + }, + { + "bbox": [ + 304, + 498, + 545, + 575 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 498, + 545, + 575 + ], + "type": "inline_equation", + "content": "\\arctan\\left(\\frac{i - \\frac{W}{2}}{j - \\frac{H}{2}}\\right)" + }, + { + "bbox": [ + 304, + 498, + 545, + 575 + ], + "type": "text", + "content": " will transform a rightward motion into a circular motion." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 578, + 380, + 591 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 578, + 380, + 591 + ], + "spans": [ + { + "bbox": [ + 306, + 578, + 380, + 591 + ], + "type": "text", + "content": "5.3. User Study" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "Although it is tempting to use a metric, e.g. the Gram matrix difference [9], to compare the quality of the videos synthesized by different methods, the variety of training objectives used in the existing methods makes such comparisons biased and unfair. Therefore, we conduct a similar user study as Tesfaldet et al. [24] to quantitatively evaluate and compare the realism of the videos. We show a pair of videos to the participants and ask them to choose the video that appears more realistic. We compare the videos synthesized by (DyNCA, [24], [27]) with each other and also" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 753, + 318, + 763 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 753, + 318, + 763 + ], + "spans": [ + { + "bbox": [ + 293, + 753, + 318, + 763 + ], + "type": "text", + "content": "20747" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 68, + 536, + 419 + ], + "blocks": [ + { + "bbox": [ + 47, + 68, + 536, + 419 + ], + "lines": [ + { + "bbox": [ + 47, + 68, + 536, + 419 + ], + "spans": [ + { + "bbox": [ + 47, + 68, + 536, + 419 + ], + "type": "image", + "image_path": "0a050e8d64d35c4866191f49ad2919f305fa8b82139ba07bbecb7e9843a0ca75.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 422, + 547, + 468 + ], + "lines": [ + { + "bbox": [ + 46, + 422, + 547, + 468 + ], + "spans": [ + { + "bbox": [ + 46, + 422, + 547, + 468 + ], + "type": "text", + "content": "Figure 5. Results of dynamic texture synthesis and dynamic style transfer with DyNCA-L-256². Dynamic Texture Synthesis: DyNCA faithfully reproduces the target appearance and target dynamics. Dynamic Style Transfer: DyNCA can learn appearance and motion from different sources. Note that DyNCA does not simply copy the target dynamics from the video, but learns the style of the given motion and naturally adapts it to the target appearance, as shown by the optical-flow images. See our real-time interactive demo https://dynca.github.io" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 48, + 473, + 286, + 553 + ], + "blocks": [ + { + "bbox": [ + 48, + 473, + 286, + 553 + ], + "lines": [ + { + "bbox": [ + 48, + 473, + 286, + 553 + ], + "spans": [ + { + "bbox": [ + 48, + 473, + 286, + 553 + ], + "type": "table", + "html": "
MethodRes.Training Time (s)Synthesis Time (s)# Parameters
A [24]2562#frames × 5005.0 × 102#frames × 0.2M
B [27]2242#frames × 4004.0 × 10281M
C [27]1002#frames × 8.58.5 × 1002.8M
DyNCA-S128223203.3 × 10-20.006M
DyNCA-S256239805.7 × 10-20.006M
DyNCA-L128223703.5 × 10-20.010M
DyNCA-L256243805.7 × 10-20.010M
", + "image_path": "46baa5983c256e2719cca253920839b75aa07198a00821218820d8961f291c65.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 555, + 287, + 622 + ], + "lines": [ + { + "bbox": [ + 46, + 555, + 287, + 622 + ], + "spans": [ + { + "bbox": [ + 46, + 555, + 287, + 622 + ], + "type": "text", + "content": "Table 2. Comparison of training time, synthesis time per frame, and number of trainable parameters of different DyTS methods. (A) Tesfaldet et al. [24]; (B) Xie et al. [27] FC config; (C) Xie et al. [27] ST config. For (B) and (C), training and synthesis happen simultaneously, and the video is synthesized once the training is finished. All methods are evaluated on a single A100 40GB GPU." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 632, + 288, + 717 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 632, + 288, + 717 + ], + "spans": [ + { + "bbox": [ + 46, + 632, + 288, + 717 + ], + "type": "text", + "content": "with real videos using the same 59 dynamic texture videos as Tesfaldet et al. [24]. Table 3 shows the results of our user study. Each entry shows the percentage of times that the video from the corresponding column was chosen over the video from the corresponding row. Our method outperforms the other DyTS method in realism. We refer the reader to our supplementary for more details on the user study." + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 307, + 473, + 545, + 543 + ], + "blocks": [ + { + "bbox": [ + 307, + 473, + 545, + 543 + ], + "lines": [ + { + "bbox": [ + 307, + 473, + 545, + 543 + ], + "spans": [ + { + "bbox": [ + 307, + 473, + 545, + 543 + ], + "type": "image", + "image_path": "a45fcb4faaedbb3aa9a4d3ffb77be7e765725db8810a36e21476476ef6e78fbe.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 544, + 547, + 612 + ], + "lines": [ + { + "bbox": [ + 304, + 544, + 547, + 612 + ], + "spans": [ + { + "bbox": [ + 304, + 544, + 547, + 612 + ], + "type": "text", + "content": "Figure 6. Results of DyNCA trained on various target vector fields as the motion target. First and second row: Symbolic and colored optical-flow representations of the target vector fields. Third row: Snapshot of the optical-flow estimations of the videos synthesized by DyNCA-S-128" + }, + { + "bbox": [ + 304, + 544, + 547, + 612 + ], + "type": "inline_equation", + "content": "^2" + }, + { + "bbox": [ + 304, + 544, + 547, + 612 + ], + "type": "text", + "content": ". The target appearance used for training the model is fibrous_0145 texture from the DTD dataset [4]." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 624, + 400, + 637 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 624, + 400, + 637 + ], + "spans": [ + { + "bbox": [ + 306, + 624, + 400, + 637 + ], + "type": "text", + "content": "5.4. Ablation Study" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": "Positional Encoding: We ablate the Cartesian Positional Encoding (CPE) and train DyNCA-S-128² with different padding strategies for comparison. In Table 4, we report the average of " + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{dir}" + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{norm}" + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": " losses on 4 target vector fields (Diverge, Converge, Circular, and Hyperbolic shown in the last 4 columns of Figure 6) and 10 different target" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 753, + 318, + 763 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 753, + 318, + 763 + ], + "spans": [ + { + "bbox": [ + 293, + 753, + 318, + 763 + ], + "type": "text", + "content": "20748" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 71, + 289, + 272 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 289, + 272 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 289, + 272 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 289, + 272 + ], + "type": "image", + "image_path": "8c8d3f742d707ec980ba1acce2387a8efdcf0eb7468e55cd9fbac59da95a61f7.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 274, + 289, + 373 + ], + "lines": [ + { + "bbox": [ + 46, + 274, + 289, + 373 + ], + "spans": [ + { + "bbox": [ + 46, + 274, + 289, + 373 + ], + "type": "text", + "content": "Table 3. Top: Comparison of real and synthesized video frames from different methods: (A) Tesfaldet et al. [24]; (B) Xie et al. [27] FC config; (C) Xie et al. [27] ST config. Bottom: Pair-wise comparison results from our user study. The participants see two videos one after another in random order and are asked to choose the video that appears more realistic. Our DyNCA achieves an on-par \"fooling\" rate when compared with real videos. Yet, our synthesized videos look more realistic when compared to existing DyTS methods (60%, 54%, 80%). All error margins are " + }, + { + "bbox": [ + 46, + 274, + 289, + 373 + ], + "type": "inline_equation", + "content": "\\leq 2\\%" + }, + { + "bbox": [ + 46, + 274, + 289, + 373 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 385, + 287, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 385, + 287, + 445 + ], + "spans": [ + { + "bbox": [ + 46, + 385, + 287, + 445 + ], + "type": "text", + "content": "appearances. The results demonstrate that CPE is a necessary component for DyNCA to learn the motion from a structured target vector field, in which the motion direction and magnitude are position-dependent. We show the importance of CPE for video motion fitting in the supplementary." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 447, + 288, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 447, + 288, + 568 + ], + "spans": [ + { + "bbox": [ + 46, + 447, + 288, + 568 + ], + "type": "text", + "content": "Multi-Scale Perception:. MSP is key to enable training DyNCA with larger seed sizes. We train DyNCA-L-256² both with and without multi-scale perception and evaluate the results qualitatively and quantitatively. Figure 8 shows the corresponding synthesized video frames, qualitatively demonstrating that single-scale perception causes artifacts to appear in the synthesized frames. We also perform a quantitative evaluation in the supplementary, showing that training with multi-scale perception improves both the appearance " + }, + { + "bbox": [ + 46, + 447, + 288, + 568 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text {appr }}" + }, + { + "bbox": [ + 46, + 447, + 288, + 568 + ], + "type": "text", + "content": " and the video motion " + }, + { + "bbox": [ + 46, + 447, + 288, + 568 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text {mvid }}" + }, + { + "bbox": [ + 46, + 447, + 288, + 568 + ], + "type": "text", + "content": " losses." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 574, + 123, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 574, + 123, + 588 + ], + "spans": [ + { + "bbox": [ + 47, + 574, + 123, + 588 + ], + "type": "text", + "content": "6. Limitations" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": "DyNCA has certain limitations. In the case of vector field motion, it cannot generate a correct motion when the target appearance and the target motion are not compatible. For example, DyNCA fails to move a 45-degree oblique pattern in a circular manner. For video motion, we find it difficult to automatically set the motion loss weight " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": ". Moreover, DyNCA cannot generate diverse motion when the target videos are violating the underlying assumption of dynamic textures, i.e. when they are not temporally homogeneous. In these cases, DyNCA suffers from overfitting to" + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 309, + 70, + 544, + 140 + ], + "blocks": [ + { + "bbox": [ + 309, + 70, + 544, + 140 + ], + "lines": [ + { + "bbox": [ + 309, + 70, + 544, + 140 + ], + "spans": [ + { + "bbox": [ + 309, + 70, + 544, + 140 + ], + "type": "table", + "html": "
Seed SizeLossCircularZeroReplicateCPE
128 × 128Ldir0.9890.1620.3180.062
Lnorm0.6400.2960.3640.235
256 × 256Ldir0.9930.4110.4780.054
Lnorm0.6780.3310.3970.218
", + "image_path": "38e301f20932046dc65e7b8c018a89d67a679032a4c95c5c250e3c8308018ac2.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 143, + 547, + 187 + ], + "lines": [ + { + "bbox": [ + 305, + 143, + 547, + 187 + ], + "spans": [ + { + "bbox": [ + 305, + 143, + 547, + 187 + ], + "type": "text", + "content": "Table 4. Comparison of motion loss for DyNCA trained with different padding strategies. Using Cartesian Positional Encoding (CPE) improves the motion fidelity, and allows the DyNCA to synthesize the correct motion regardless of the seed size." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 312, + 190, + 547, + 363 + ], + "blocks": [ + { + "bbox": [ + 312, + 190, + 547, + 363 + ], + "lines": [ + { + "bbox": [ + 312, + 190, + 547, + 363 + ], + "spans": [ + { + "bbox": [ + 312, + 190, + 547, + 363 + ], + "type": "image", + "image_path": "284cd135bc054349cf1545540163df165acfcf31c2c252f9a29b291ca3ddea1e.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 364, + 547, + 409 + ], + "lines": [ + { + "bbox": [ + 305, + 364, + 547, + 409 + ], + "spans": [ + { + "bbox": [ + 305, + 364, + 547, + 409 + ], + "type": "text", + "content": "Figure 8. Comparison between training DyNCA with and without multi-scale perception. The first row shows the target appearance texture. The results without multi-scale perception (second row) contain artifacts and are of lower quality." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 418, + 545, + 444 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 418, + 545, + 444 + ], + "spans": [ + { + "bbox": [ + 305, + 418, + 545, + 444 + ], + "type": "text", + "content": "the dominant direction of the motion in the target videos We refer to our supplementary material for more details." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 447, + 379, + 459 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 447, + 379, + 459 + ], + "spans": [ + { + "bbox": [ + 306, + 447, + 379, + 459 + ], + "type": "text", + "content": "7. Conclusion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 465, + 545, + 680 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 465, + 545, + 680 + ], + "spans": [ + { + "bbox": [ + 304, + 465, + 545, + 680 + ], + "type": "text", + "content": "We propose DyNCA, a model that can, in real time, synthesize dynamic texture videos with arbitrary frame size and infinite length. Exploiting multi-scale perception and positional encoding, the cells in DyNCA can readily perform long-range communication and obtain global information. This ensures improved performance both in terms of visual quality and computational expressivity as compared to the vanilla NCA model, as we show with both qualitative and quantitative experiments. DyNCA can learn motion either from a hand-crafted vector field or a video, thus allowing for broader synthesis options. DyNCA produces more realistic video textures than the current DyTS methods, as demonstrated through a user study. DyNCA is also " + }, + { + "bbox": [ + 304, + 465, + 545, + 680 + ], + "type": "inline_equation", + "content": "2 \\sim 4" + }, + { + "bbox": [ + 304, + 465, + 545, + 680 + ], + "type": "text", + "content": " orders of magnitude faster than the SOTA methods in synthesis time and has much fewer trainable parameters, thus facilitating real-world deployment. Lastly, DyNCA allows for several real-time and interactive video control tools that let the users control DyNCA without re-training." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 681, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 681, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 305, + 681, + 545, + 712 + ], + "type": "text", + "content": "Acknowledgement. This work was supported in part by the Swiss National Science Foundation via the Sinergia grant CRSII5-180359." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 753, + 318, + 763 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 753, + 318, + 763 + ], + "spans": [ + { + "bbox": [ + 293, + 753, + 318, + 763 + ], + "type": "text", + "content": "20749" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "text", + "content": "[1] Edward H Adelson, Charles H Anderson, James R Bergen, Peter J Burt, and Joan M Ogden. 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IEEE, 2021. 1, 2, 3" + } + ] + } + ], + "index": 1 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 753, + 317, + 762 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 753, + 317, + 762 + ], + "spans": [ + { + "bbox": [ + 293, + 753, + 317, + 762 + ], + "type": "text", + "content": "20751" + } + ] + } + ], + "index": 3 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/DynIBaR_ Neural Dynamic Image-Based Rendering/b5d1340a-3f6f-462f-9df3-03c14583f216_content_list.json b/2023/DynIBaR_ Neural Dynamic Image-Based Rendering/b5d1340a-3f6f-462f-9df3-03c14583f216_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..9ab77bf6073c59975caf8dd706d29a0493cefe89 --- /dev/null +++ b/2023/DynIBaR_ Neural Dynamic Image-Based Rendering/b5d1340a-3f6f-462f-9df3-03c14583f216_content_list.json @@ -0,0 +1,1958 @@ +[ + { + "type": "text", + "text": "DynIBaR: Neural Dynamic Image-Based Rendering", + "text_level": 1, + "bbox": [ + 220, + 130, + 750, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Zhengqi Li $^{1}$ , Qianqian Wang $^{1,2}$ , Forrester Cole $^{1}$ , Richard Tucker $^{1}$ , Noah Snavely $^{1}$ $^{1}$ Google Research Cornell Tech", + "bbox": [ + 160, + 179, + 807, + 224 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d3cb349a4e5ceca88db79495c2df84267210e7979e1893564eccf9f4573a674e.jpg", + "image_caption": [ + "Figure 1. Recent methods for synthesizing novel views from monocular videos of dynamic scenes-like HyperNeRF [50] and NSFF [35]–struggle to render high-quality views from long videos featuring complex camera and scene motion. We present a new approach that addresses these limitations, illustrated above via an application to 6DoF video stabilization, where we apply our approach and prior methods on a 30-second, shaky video clip, and compare novel views rendered along a smoothed camera path (left). On a dynamic scenes dataset (right) [75], our approach significantly improves rendering fidelity, as indicated by synthesized images and LPIPS errors computed on pixels corresponding to moving objects (yellow numbers). Please see the supplementary video for full results." + ], + "image_footnote": [], + "bbox": [ + 81, + 276, + 666, + 481 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0f605202fa0409d18adf9ef3673301e5e09a28d5f1dc1758e9d78287c3b365b3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 678, + 276, + 888, + 479 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 588, + 313, + 603 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We address the problem of synthesizing novel views from a monocular video depicting a complex dynamic scene. State-of-the-art methods based on temporally varying Neural Radiance Fields (aka dynamic NeRFs) have shown impressive results on this task. However, for long videos with complex object motions and uncontrolled camera trajectories, these methods can produce blurry or inaccurate renderings, hampering their use in real-world applications. Instead of encoding the entire dynamic scene within the weights of MLPs, we present a new approach that addresses these limitations by adopting a volumetric image-based rendering framework that synthesizes new viewpoints by aggregating features from nearby views in a scene motion-aware manner. Our system retains the advantages of prior methods in its ability to model complex scenes and view-dependent effects, but also enables synthesizing photo-realistic novel views from long videos featuring complex scene dynamics with unconstrained camera trajectories. We demonstrate signifi", + "bbox": [ + 73, + 628, + 473, + 902 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "cant improvements over state-of-the-art methods on dynamic scene datasets, and also apply our approach to in-the-wild videos with challenging camera and object motion, where prior methods fail to produce high-quality renderings.", + "bbox": [ + 498, + 589, + 893, + 650 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 679, + 632, + 695 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Computer vision methods can now produce free-viewpoint renderings of static 3D scenes with spectacular quality. What about moving scenes, like those featuring people or pets? Novel view synthesis from a monocular video of a dynamic scene is a much more challenging dynamic scene reconstruction problem. Recent work has made progress towards synthesizing novel views in both space and time, thanks to new time-varying neural volumetric representations like HyperNeRF [50] and Neural Scene Flow Fields (NSFF) [35], which encode spatiotemporally varying scene content volumetrically within a coordinate-based multi-layer perceptron (MLP).", + "bbox": [ + 496, + 705, + 895, + 886 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, these dynamic NeRF methods have limitations", + "bbox": [ + 517, + 887, + 890, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "4273", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "that prevent their application to casual, in-the-wild videos. Local scene flow-based methods like NSFF struggle to scale to longer input videos captured with unconstrained camera motions: the NSFF paper only claims good performance for 1-second, forward-facing videos [35]. Methods like HyperNeRF that construct a canonical model are mostly constrained to object-centric scenes with controlled camera paths, and can fail on scenes with complex object motion.", + "bbox": [ + 75, + 90, + 472, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we present a new approach that is scalable to dynamic videos captured with 1) long time duration, 2) unbounded scenes, 3) uncontrolled camera trajectories, and 4) fast and complex object motion. Our approach retains the advantages of volumetric scene representations that can model intricate scene geometry with view-dependent effects, while significantly improving rendering fidelity for both static and dynamic scene content compared to recent methods [35, 50], as illustrated in Fig. 1.", + "bbox": [ + 75, + 212, + 472, + 347 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We take inspiration from recent methods for rendering static scenes that synthesize novel images by aggregating local image features from nearby views along epipolar lines [39, 64, 70]. However, scenes that are in motion violate the epipolar constraints assumed by those methods. We instead propose to aggregate multi-view image features in scene motion-adjusted ray space, which allows us to correctly reason about spatio-temporally varying geometry and appearance.", + "bbox": [ + 75, + 347, + 472, + 482 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We also encountered many efficiency and robustness challenges in scaling up aggregation-based methods to dynamic scenes. To efficiently model scene motion across multiple views, we model this motion using motion trajectory fields that span multiple frames, represented with learned basis functions. Furthermore, to achieve temporal coherence in our dynamic scene reconstruction, we introduce a new temporal photometric loss that operates in motion-adjusted ray space. Finally, to improve the quality of novel views, we propose to factor the scene into static and dynamic components through a new IBR-based motion segmentation technique within a Bayesian learning framework.", + "bbox": [ + 75, + 484, + 472, + 665 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "On two dynamic scene benchmarks, we show that our approach can render highly detailed scene content and significantly improves upon the state-of-the-art, leading to an average reduction in LPIPS errors by over $50\\%$ both across entire scenes, as well as on regions corresponding to dynamic objects. We also show that our method can be applied to inthe-wild videos with long duration, complex scene motion, and uncontrolled camera trajectories, where prior state-ofthe-art methods fail to produce high quality renderings. We hope that our work advances the applicability of dynamic view synthesis methods to real-world videos.", + "bbox": [ + 75, + 665, + 472, + 830 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 844, + 218, + 859 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Novel view synthesis. Classic image-based rendering (IBR) methods synthesize novel views by integrating pixel", + "bbox": [ + 75, + 869, + 470, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "information from input images [58], and can be categorized according to their dependence on explicit geometry. Light field or lumigraph rendering methods [9, 21, 26, 32] generate new views by filtering and interpolating sampled rays, without use of explicit geometric models. To handle sparser input views, many approaches [7, 14, 18, 23, 24, 26, 30, 52, 54, 55] leverage pre-computed proxy geometry such as depth maps or meshes to render novel views.", + "bbox": [ + 496, + 90, + 893, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recently, neural representations have demonstrated high-quality novel view synthesis [12, 17, 38, 40, 46, 48, 59-62, 72, 81]. In particular, Neural Radiance Fields (NeRF) [46] achieves an unprecedented level of fidelity by encoding continuous scene radiance fields within multi-layer perceptrons (MLPs). Among all methods building on NeRF, IBRNet [70] is the most relevant to our work. IBRNet combines classical IBR techniques with volume rendering to produce a generalized IBR module that can render high-quality views without per-scene optimization. Our work extends this kind of volumetric IBR framework designed for static scenes [11, 64, 70] to more challenging dynamic scenes. Note that our focus is on synthesizing higher-quality novel views for long videos with complex camera and object motion, rather than on generalization across scenes.", + "bbox": [ + 496, + 212, + 895, + 439 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Dynamic scene view synthesis. Our work is related to geometric reconstruction of dynamic scenes from RGBD [5, 15, 25, 47, 68, 83] or monocular videos [31, 44, 78, 80]. However, depth- or mesh-based representations struggle to model complex geometry and view-dependent effects.", + "bbox": [ + 496, + 446, + 893, + 521 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Most prior work on novel view synthesis for dynamic scenes requires multiple synchronized input videos [1, 3, 6, 27, 33, 63, 69, 76, 82], limiting their real-world applicability. Some methods [8, 13, 22, 51, 71] use domain knowledge such as template models to achieve high-quality results, but are restricted to specific categories [41, 56]. More recently, many works propose to synthesize novel views of dynamic scenes from a single camera. Yoon et al. [75] render novel views through explicit warping using depth maps obtained via single-view depth and multi-view stereo. However, this method fails to model complex scene geometry and to fill in realistic and consistent content at disocclusions. With advances in neural rendering, NeRF-based dynamic view synthesis methods have shown state-of-the-art results [16, 35, 53, 66, 74]. Some approaches, such as Nerfies [49] and HyperNeRF [50], represent scenes using a deformation field mapping each local observation to a canonical scene representation. These deformations are conditioned on time [53] or a per-frame latent code [49, 50, 66], and are parameterized as translations [53, 66] or rigid body motion fields [49, 50]. These methods can handle long videos, but are mostly limited to object-centric scenes with relatively small object motion and controlled camera paths. Other methods represent scenes as time-varying NeRFs [19, 20, 35, 67, 74]. In particular, NSFF uses neural scene flow fields that can", + "bbox": [ + 496, + 523, + 895, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "4274", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/87c90d518b08baa1383f2d6cf463dadae9fce64a13fea8dd9ce1256a36366b0b.jpg", + "image_caption": [ + "Figure 2. Rendering via motion-adjusted multi-view feature aggregation. Given a sampled location $\\mathbf{x}$ at time $i$ along a target ray $\\mathbf{r}$ , we estimate its motion trajectory, which determines the 3D correspondence of $\\mathbf{x}$ at nearby time $j \\in \\mathcal{N}(i)$ , denoted $\\mathbf{x}_{i \\rightarrow j}$ . Each warped point is then projected into its corresponding source view. Image features $\\mathbf{f}_j$ extracted along the projected curves are aggregated and fed to the ray transformer with time embedding $\\gamma(i)$ , producing per-sample color and density $(\\mathbf{c}_i, \\sigma_i)$ . The final pixel color $\\hat{\\mathbf{C}}_i$ is then synthesized by volume rendering $(\\mathbf{c}_i, \\sigma_i)$ along $\\mathbf{r}$ ." + ], + "image_footnote": [], + "bbox": [ + 78, + 89, + 467, + 214 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "capture fast and complex 3D scene motion for in-the-wild videos [35]. However, this method only works well for short (1-2 second), forward-facing videos.", + "bbox": [ + 75, + 375, + 470, + 421 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Dynamic Image-Based Rendering", + "text_level": 1, + "bbox": [ + 76, + 434, + 383, + 452 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a monocular video of a dynamic scene with frames $(I_1, I_2, \\ldots, I_N)$ and known camera parameters $(\\mathbf{P}_1, \\mathbf{P}_2, \\ldots, \\mathbf{P}_N)$ , our goal is to synthesize a novel viewpoint at any desired time within the video. Like many other approaches, we train per-video, first optimizing a model to reconstruct the input frames, then using this model to render novel views.", + "bbox": [ + 75, + 459, + 470, + 563 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Rather than encoding 3D color and density directly in the weights of an MLP as in recent dynamic NeRF methods, we integrate classical IBR ideas into a volumetric rendering framework. Compared to explicit surfaces, volumetric representations can more readily model complex scene geometry with view-dependent effects.", + "bbox": [ + 75, + 565, + 468, + 655 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The following sections introduce our methods for scene-motion-adjusted multi-view feature aggregation (Sec. 3.1), and enforcing temporal consistency via cross-time rendering in motion-adjusted ray space (Sec. 3.2). Our full system combines a static model and a dynamic model to produce a color at each pixel. Accurate scene factorization is achieved via segmentation masks derived from a separately trained motion segmentation module within a Bayesian learning framework (Sec. 3.3).", + "bbox": [ + 75, + 656, + 470, + 791 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Motion-adjusted feature aggregation", + "text_level": 1, + "bbox": [ + 76, + 801, + 395, + 818 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We synthesize new views by aggregating features extracted from temporally nearby source views. To render an image at time $i$ , we first identify source views $I_{j}$ within a temporal radius $r$ frames of $i$ , $j \\in \\mathcal{N}(i) = [i - r, i + r]$ . For each source view, we extract a 2D feature map $F_{i}$ through a", + "bbox": [ + 75, + 825, + 470, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "shared convolutional encoder network to form an input tuple $\\{I_j,\\mathbf{P}_j,F_j\\}$", + "bbox": [ + 500, + 90, + 890, + 122 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To predict the color and density of each point sampled along a target ray $\\mathbf{r}$ , we must aggregate source view features while accounting for scene motion. For a static scene, points along a target ray will lie along a corresponding epipolar line in a neighboring source view, hence we can aggregate potential correspondences by simply sampling along neighboring epipolar lines [64, 70]. However, moving scene elements violate epipolar constraints, leading to inconsistent feature aggregation if motion is not accounted for. Hence, we perform motion-adjusted feature aggregation, as shown in Fig. 3. To determine correspondence in dynamic scenes, one straightforward idea is to estimate a scene flow field via an MLP [35] to determine a given point's motion-adjusted 3D location at a nearby time. However, this strategy is computational infeasible in a volumetric IBR framework due to recursive unrolling of the MLPs.", + "bbox": [ + 496, + 122, + 893, + 363 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Motion trajectory fields. Instead, we represent scene motion using motion trajectory fields described in terms of learned basis functions. For a given 3D point $\\mathbf{x}$ along target ray $\\mathbf{r}$ at time $i$ , we encode its trajectory coefficients with an MLP $G_{\\mathrm{MT}}$ :", + "bbox": [ + 496, + 369, + 893, + 445 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{\\phi_ {i} ^ {l} (\\mathbf {x}) \\right\\} _ {l = 1} ^ {L} = G _ {\\mathrm {M T}} (\\gamma (\\mathbf {x}), \\gamma (i)), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 452, + 890, + 470 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\phi_i^l\\in \\mathcal{R}^3$ are basis coefficients (with separate coefficients for $x,y,$ and $z$ using the motion basis described below) and $\\gamma$ denotes positional encoding. We choose $L = 6$ bases and 16 linearly increasing frequencies for the encoding $\\gamma$ , based on the assumption that scene motion tends to be low frequency [80].", + "bbox": [ + 496, + 476, + 893, + 566 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We also introduce a global learnable motion basis $\\{h_i^l\\}_{l = 1}^L,h_i^l\\in \\mathcal{R}$ , spanning every time step $i$ of the input video, which is optimized jointly with the MLP. The motion trajectory of $\\mathbf{x}$ is then defined as $\\Gamma_{\\mathbf{x},i}(j) = \\sum_{l = 1}^{L}h_{j}^{l}\\phi_{i}^{l}(\\mathbf{x})$ and thus, the relative displacement between $\\mathbf{x}$ and its 3D correspondence $\\mathbf{x}_{i\\rightarrow j}$ at time $j$ is computed as", + "bbox": [ + 496, + 566, + 893, + 657 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\Delta_ {\\mathbf {x}, i} (j) = \\Gamma_ {\\mathbf {x}, i} (j) - \\Gamma_ {\\mathbf {x}, i} (i). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 598, + 666, + 890, + 683 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "With this motion trajectory representation, finding 3D correspondences for a query point $\\mathbf{x}$ in neighboring views requires just a single MLP query, allowing efficient multi-view feature aggregation within our volume rendering framework. We initialize the basis $\\{h_i^l\\}_{l = 1}^L$ with the DCT basis as proposed by Wang et al. [67], but fine-tune it along with other components during optimization, since we observe that a fixed DCT basis can fail to model a wide range of real-world motions (see third column of Fig. 4).", + "bbox": [ + 496, + 688, + 893, + 824 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Using the estimated motion trajectory of $\\mathbf{x}$ at time $i$ , we denote $\\mathbf{x}$ 's corresponding 3D point at time $j$ as $\\mathbf{x}_{i\\rightarrow j} = \\mathbf{x} + \\Delta_{\\mathbf{x},i}(j)$ . We project each warped point $\\mathbf{x}_{i\\rightarrow j}$ into its source view $I_{j}$ using camera parameters $\\mathbf{P}_j$ , and extract color and feature vector $\\mathbf{f}_j$ at the projected 2D pixel location.", + "bbox": [ + 496, + 825, + 893, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "4275", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/8b9233be694e197a6021b471b2f2d1c3667ff80d110475c573bc5c9a6e2b9575.jpg", + "image_caption": [ + "Figure 3. Temporal consistency via cross-time rendering. To enforce temporal consistency in a dynamic reconstruction, we render each frame $I_{i}$ using the scene model from a nearby time $j$ , which we call cross-time rendering. A ray $\\mathbf{r}$ from image $i$ is instead rendered using a curved ray $\\mathbf{r}_{i\\rightarrow j}$ , i.e., $\\mathbf{r}$ warped to time $j$ . That is, having computed the motion-adjusted point $\\mathbf{x}_{i\\rightarrow j} = \\mathbf{x} + \\Delta_{\\mathbf{x},i}(j)$ at nearby time $j$ from every sampled location along $\\mathbf{r}$ , we query $\\mathbf{x}_{i\\rightarrow j}$ and time $j$ via the MLP to predict its motion trajectory $\\Gamma_{\\mathbf{x}_{i\\rightarrow j},j}$ , along which we aggregate image features $\\mathbf{f}_k$ extracted from source views within time $k\\in \\mathcal{N}(j)$ . The aggregated features along $\\mathbf{r}_{i\\rightarrow j}$ are fed to the ray transformer with time embedding $\\gamma (j)$ to produce per-sample color and density $(\\mathbf{c}_j,\\sigma_j)$ at time $j$ . A pixel color $\\hat{\\mathbf{C}}_{j\\rightarrow i}$ is computed by volume rendering $(\\mathbf{c}_j,\\sigma_j)$ , and then compared to the ground truth color $\\mathbf{C}_i$ to form a reconstruction loss $\\mathcal{L}_{\\mathrm{pho}}$ ." + ], + "image_footnote": [], + "bbox": [ + 81, + 89, + 467, + 234 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The resulting set of source features across neighbor views $j$ is fed to a shared MLP whose output features are aggregated through weighted average pooling [70] to produce a single feature vector at each 3D sample point along ray $\\mathbf{r}$ . A ray transformer network with time embedding $\\gamma(i)$ then processes the sequence of aggregated features along the ray to predict per-sample colors and densities $(\\mathbf{c}_i, \\sigma_i)$ (see Fig. 2). We then use standard NeRF volume rendering [4] to obtain a final pixel color $\\hat{\\mathbf{C}}_i(\\mathbf{r})$ for the ray from this sequence of colors and densities.", + "bbox": [ + 75, + 467, + 470, + 618 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Cross-time rendering for temporal consistency", + "text_level": 1, + "bbox": [ + 76, + 632, + 468, + 648 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "If we optimize our dynamic scene representation by comparing $\\hat{\\mathbf{C}}_i$ with $\\mathbf{C}_i$ alone, the representation might overfit to the input images: it might perfectly reconstruct those views, but fail to render correct novel views. This can happen because the representation has the capacity to reconstruct completely separate models for each time instance, without utilizing or accurately reconstructing scene motion. Therefore, to recover a consistent scene with physically plausible motion, we enforce temporal coherence of the scene representation. One way to define temporal coherence in this context is that the scene at two neighboring times $i$ and $j$ should be consistent when taking scene motion into account [19, 35, 67].", + "bbox": [ + 75, + 657, + 472, + 853 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In particular, we enforce temporal photometric consistency in our optimized representation via cross-time rendering in motion-adjusted ray space, as shown in Fig. 3. The", + "bbox": [ + 75, + 854, + 472, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "idea is to render a view at time $i$ but via some nearby time $j$ , which we refer to as cross-time rendering. For each nearby time $j \\in \\mathcal{N}(i)$ , rather than directly using points $\\mathbf{x}$ along ray $\\mathbf{r}$ , we consider the points $\\mathbf{x}_{i \\to j}$ along motion-adjusted ray $\\mathbf{r}_{i \\to j}$ and treat them as if they lie along a ray at time $j$ .", + "bbox": [ + 496, + 90, + 893, + 167 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Specifically, having computed the motion-adjusted points $\\mathbf{x}_{i\\rightarrow j}$ , we query the MLP to predict the coefficients of new trajectories $\\{\\phi_j^l (\\mathbf{x}_{i\\rightarrow j})_{l = 1}^L = G_{\\mathrm{MT}}(\\mathbf{x}_{i\\rightarrow j},\\gamma (j))$ , and use these to compute corresponding 3D points $(\\mathbf{x}_{i\\rightarrow j})_{j\\rightarrow k}$ for images $k$ in the temporal window $\\mathcal{N}(j)$ , using Eq. 2. These new 3D correspondences are then used to render a pixel color exactly as described for a \"straight\" ray $\\mathbf{r}_i$ in Sec. 3.1, except now along the curved, motion-adjusted ray $\\mathbf{r}_{i\\rightarrow j}$ . That is, each point $(\\mathbf{x}_{i\\rightarrow j})_{j\\rightarrow k}$ is projected into its source view $I_{k}$ and feature maps $F_{k}$ with camera parameters $\\mathbf{P}_k$ to extract an RGB color and image feature $\\mathbf{f}_k$ , and then these features are aggregated and input to the ray transformer with the time embedding $\\gamma (j)$ . The result is a sequence of colors and densities $(\\mathbf{c}_j,\\sigma_j)$ along $\\mathbf{r}_{i\\rightarrow j}$ at time $j$ , which can be composited through volume rendering to form a color $\\hat{\\mathbf{C}}_{j\\rightarrow i}$ .", + "bbox": [ + 496, + 167, + 893, + 393 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We can then compare $\\hat{\\mathbf{C}}_{j\\rightarrow i}(\\mathbf{r})$ with the target pixel $\\mathbf{C}_i(\\mathbf{r})$ via a motion-disocclusion-aware RGB reconstruction loss:", + "bbox": [ + 498, + 396, + 893, + 426 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {p h o}} = \\sum_ {\\mathbf {r}} \\sum_ {j \\in \\mathcal {N} (i)} \\hat {\\mathbf {W}} _ {j \\rightarrow i} (\\mathbf {r}) \\rho \\left(\\mathbf {C} _ {i} (\\mathbf {r}), \\hat {\\mathbf {C}} _ {j \\rightarrow i} (\\mathbf {r})\\right). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 431, + 890, + 465 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We use a generalized Charbonnier loss [10] for the RGB loss $\\rho$ . $\\hat{\\mathbf{W}}_{j\\rightarrow i}(\\mathbf{r})$ is a motion disocclusion weight computed by the difference of accumulated alpha weights between time $i$ and $j$ to address the motion disocclusion ambiguity described by NSFF [35] (see supplement for more details). Note that when $j = i$ , there is no scene motion-induced displacement, meaning $\\hat{\\mathbf{C}}_{j\\rightarrow i} = \\hat{\\mathbf{C}}_i$ and no disocclusion weights are involved ( $\\hat{\\mathbf{W}}_{j\\rightarrow i} = 1$ ). We show a comparison between our method with and without enforcing temporal consistency in the first column of Fig. 4.", + "bbox": [ + 496, + 472, + 893, + 625 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Combining static and dynamic models", + "text_level": 1, + "bbox": [ + 498, + 635, + 831, + 651 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As observed in NSFF, synthesizing novel views using a small temporal window is insufficient to recover complete and high-quality content for static scene regions, since the contents may only be observed in spatially distant frames due to uncontrolled camera paths. Therefore, we follow the ideas of NSFF [35], and model the entire scene using two separate representations. Dynamic content $(\\mathbf{c}_i,\\sigma_i)$ is represented with a time-varying model as above (used for cross-time rendering during optimization). Static content $(\\mathbf{c},\\sigma)$ is represented with a time-invariant model, which renders in the same way as the time-varying model, but aggregates multiview features without scene motion adjustment (i.e., along epipolar lines).", + "bbox": [ + 496, + 657, + 893, + 853 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The dynamic and static predictions are combined and rendered to a single output color $\\hat{\\mathbf{C}}_i^{\\mathrm{full}}$ (or $\\hat{\\mathbf{C}}_{j\\rightarrow i}^{\\mathrm{full}}$ during cross-time rendering) using the method for combining static and", + "bbox": [ + 498, + 854, + 893, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "4276", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/f00d932c889262daa8dee0efa234b05c984ee7804d3d5125c49942bab306af35.jpg", + "image_caption": [ + "(a) w/o TC" + ], + "image_footnote": [], + "bbox": [ + 80, + 88, + 173, + 232 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/109b70af9de32f69344a60a0164ac61035f3413b4851684825b4783a82590249.jpg", + "image_caption": [ + "(b) w/ SF" + ], + "image_footnote": [], + "bbox": [ + 178, + 88, + 272, + 231 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/9e788bb74bcafb3ba480a5e947ce50928ed63bb4ec66b9e5e303ed13eddbac35.jpg", + "image_caption": [ + "(c) w/ DCT basis" + ], + "image_footnote": [], + "bbox": [ + 274, + 88, + 370, + 231 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/dfd9e1a19fc0d530fe3ed4be67f11feca56c044d853878d5203c92aa72742768.jpg", + "image_caption": [ + "(d) Ours", + "Figure 4. Qualitative ablations. From left to right, we show rendered novel views (top) and depths (bottom) from our system (a) without enforcing temporal consistency, (b) aggregating image features with scene flow fields instead of motion trajectories, (c) representing motion trajectory with a fixed DCT basis instead of a learned one, and (d) with full configuration. Simpler configurations significantly degrade rendering quality as indicated by PSNR calculated over the regions of moving objects." + ], + "image_footnote": [], + "bbox": [ + 372, + 88, + 468, + 231 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "transient models of NeRF-W [45]. Each model's color and density estimates can also be rendered separately, giving color $\\hat{\\mathbf{C}}^{\\mathrm{st}}$ for static content and $\\hat{\\mathbf{C}}_i^{\\mathrm{dy}}$ for dynamic content.", + "bbox": [ + 75, + 388, + 468, + 436 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "When combining the two representations, we rewrite the photometric consistency term in Eq. 3 as a loss comparing $\\hat{\\mathbf{C}}_{j\\rightarrow i}^{\\mathrm{full}}(\\mathbf{r})$ with target pixel $\\mathbf{C}_i(\\mathbf{r})$ :", + "bbox": [ + 76, + 436, + 468, + 483 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {p h o}} = \\sum_ {\\mathbf {r}} \\sum_ {j \\in \\mathcal {N} (i)} \\hat {\\mathbf {W}} _ {j \\rightarrow i} (\\mathbf {r}) \\rho \\left(\\mathbf {C} _ {i} (\\mathbf {r}), \\hat {\\mathbf {C}} _ {j \\rightarrow i} ^ {\\text {f u l l}} (\\mathbf {r})\\right) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 104, + 493, + 468, + 527 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Image-based motion segmentation. In our framework, we observed that without any initialization, scene factorization tends to be dominated by either the time-invariant or the time-varying representation, a phenomena also observed in recent methods [28, 42]. To facilitate factorization, Gao et al. [19] initialize their system using masks from semantic segmentation, relying on the assumption that all moving objects are captured by a set of candidate semantic segmentation labels, and segmentation masks are temporally accurate. However, these assumptions do not hold in many real-world scenarios, as observed by Zhang et al. [79]. Instead, we propose a new motion segmentation module that produces segmentation masks for supervising our main two-component scene representation. Our idea is inspired by the Bayesian learning techniques proposed in recent work [45, 79], but integrated into a volumetric IBR representation for dynamic videos.", + "bbox": [ + 75, + 537, + 472, + 792 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In particular, before training our main two-component scene representation, we jointly train two lightweight models to obtain a motion segmentation mask $M_{i}$ for each input frame $I_{i}$ . We model static scene content with an IBR-Net [70] that renders a pixel color $\\hat{\\mathbf{B}}^{\\mathrm{st}}$ using volume rendering along each ray via feature aggregation along epipolar lines from nearby source views without considering scene", + "bbox": [ + 75, + 795, + 472, + 901 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/4293e6e7f9e288c64fae755d71a7b6b757cfd16360545161584a7bf417145905.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 88, + 601, + 130 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/bd50b74c6baddecfcc2d12220e3e1018435063ce76898d035cf950fbf944d4c5.jpg", + "image_caption": [ + "Figure 5. Motion segmentation. We show full rendering $\\hat{\\mathbf{B}}_i^{\\mathrm{full}}$ (top) and motion segmentation overlaid with rendered dynamic content $\\alpha_i^{\\mathrm{dy}}\\odot \\hat{\\mathbf{B}}_i^{\\mathrm{dy}}$ (bottom). Our approach segments challenging dynamic elements such as the moving shadow, swing, and swaying bushes." + ], + "image_footnote": [], + "bbox": [ + 506, + 131, + 601, + 172 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/8b3b5c0611f6cb555a3f49eb3a63568b2dfc46ab9a257ba177719b17518de73b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 602, + 88, + 696, + 130 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/2d5474edfc09460de47b49677a3ae598b08daed948249eb68f2f9e4594a6c004.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 602, + 131, + 696, + 172 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/2c5c5fc3033adf98524a590aa412bc396df3a23e3814ef563b46501a626c3ed0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 697, + 88, + 787, + 130 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/ab65b0e5894ded0bcd7dc2bd4b29652abd673ab3ea3583c80cd24a42a1617bf5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 789, + 88, + 885, + 130 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "motion; we model dynamic scene content with a 2D convolutional encoder-decoder network $D$ , which predicts a 2D opacity map $\\alpha_{i}^{\\mathrm{dy}}$ , confidence map $\\beta_{i}^{\\mathrm{dy}}$ , and RGB image $\\hat{\\mathbf{B}}_{i}^{\\mathrm{dy}}$ from an input frame:", + "bbox": [ + 496, + 262, + 893, + 321 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {B}} _ {i} ^ {\\mathrm {d y}}, \\boldsymbol {\\alpha} _ {i} ^ {\\mathrm {d y}}, \\boldsymbol {\\beta} _ {i} ^ {\\mathrm {d y}} = D (I _ {i}). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 614, + 323, + 890, + 343 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The full reconstructed image is then composited pixelwise from the outputs of the two models:", + "bbox": [ + 496, + 345, + 890, + 375 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {B}} _ {i} ^ {\\text {f u l l}} (\\mathbf {r}) = \\boldsymbol {\\alpha} _ {i} ^ {\\mathrm {d y}} (\\mathbf {r}) \\hat {\\mathbf {B}} _ {i} ^ {\\mathrm {d y}} (\\mathbf {r}) + (1 - \\boldsymbol {\\alpha} _ {i} ^ {\\mathrm {d y}} (\\mathbf {r})) \\hat {\\mathbf {B}} ^ {\\mathrm {s t}} (\\mathbf {r}). \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 378, + 890, + 398 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To segment moving objects, we assume the observed pixel color is uncertain in a heteroscedastic aleatoric manner, and model the observations in the video with a Cauchy distribution with time dependent confidence $\\beta_{i}^{\\mathrm{dy}}$ . By taking the negative log-likelihood of the observations, our segmentation loss is written as a weighted reconstruction loss:", + "bbox": [ + 496, + 400, + 893, + 491 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {s e g}} = \\sum_ {\\mathbf {r}} \\log \\left(\\beta_ {i} ^ {\\mathrm {d y}} (\\mathbf {r}) + \\frac {\\left| \\left| \\hat {\\mathbf {B}} _ {i} ^ {\\text {f u l l}} (\\mathbf {r}) - \\mathbf {C} _ {i} (\\mathbf {r}) \\right| \\right| ^ {2}}{\\beta_ {i} ^ {\\mathrm {d y}} (\\mathbf {r})}\\right). \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 493, + 890, + 535 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "By optimizing the two models using Eq. 7, we obtain a motion segmentation mask $M_{i}$ by thresholding $\\alpha_{i}^{\\mathrm{dy}}$ at 0.5. We do not require an alpha regularization loss as in NeRF-W [45] to avoid degeneracies, since we naturally include such an inductive basis by excluding skip connections from network $D$ , which leads $D$ to converge more slowly than the static IBR model. We show our estimated motion segmentation masks overlaid on input images in Fig. 5.", + "bbox": [ + 496, + 537, + 893, + 657 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Supervision with segmentation masks. We initialize our main time-varying and time-invariant models with masks $M_{i}$ as in Omnimatte [43], by applying a reconstruction loss to renderings from the time-varying model in dynamic regions, and to renderings from the time-invariant model in static regions:", + "bbox": [ + 496, + 662, + 893, + 755 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\text {m a s k}} = \\sum_ {\\mathbf {r}} (1 - M _ {i}) (\\mathbf {r}) \\rho \\left(\\hat {\\mathbf {C}} ^ {\\mathrm {s t}} (\\mathbf {r}), \\mathbf {C} _ {i} (\\mathbf {r})\\right) \\\\ + \\sum_ {\\mathbf {r}} M _ {i} (\\mathbf {r}) \\rho \\left(\\hat {\\mathbf {C}} _ {i} ^ {\\mathrm {d y}} (\\mathbf {r}), \\mathbf {C} _ {i} (\\mathbf {r})\\right) \\tag {8} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 555, + 757, + 890, + 821 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We perform morphological erosion and dilation on $M_{i}$ to obtain masks of dynamic and static regions respectively in order to turn off the loss near mask boundaries. We supervise the system with $\\mathcal{L}_{\\mathrm{mask}}$ and decay the weights by a factor of 5 for dynamic regions every 50K optimization steps.", + "bbox": [ + 496, + 825, + 893, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "4277", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Regularization", + "text_level": 1, + "bbox": [ + 76, + 90, + 227, + 107 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As noted in prior work, monocular reconstruction of complex dynamic scenes is highly ill-posed, and using photometric consistency alone is insufficient to avoid bad local minima during optimization [19, 35]. Therefore, we adopt regularization schemes used in prior work [2, 35, 73, 75], which consist of three main parts $\\mathcal{L}_{\\mathrm{reg}} = \\mathcal{L}_{\\mathrm{data}} + \\mathcal{L}_{\\mathrm{MT}} + \\mathcal{L}_{\\mathrm{cpt}}$ . $\\mathcal{L}_{\\mathrm{data}}$ is a data-driven term consisting of $\\ell_{1}$ monocular depth and optical flow consistency priors using the estimates from Zhang et al. [80] and RAFT [65]. $\\mathcal{L}_{\\mathrm{MT}}$ is a motion trajectory regularization term that encourages estimated trajectory fields to be cycle-consistent and spatial-temporally smooth. $\\mathcal{L}_{\\mathrm{cpt}}$ is a compactness prior that encourages the scene decomposition to be binary via an entropy loss, and mitigates floaters through distortion losses [2]. We refer readers to the supplement for more details.", + "bbox": [ + 75, + 113, + 472, + 339 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In summary, the final combined loss used to optimize our main representation for space-time view synthesis is:", + "bbox": [ + 76, + 340, + 470, + 371 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {\\text {p h o}} + \\mathcal {L} _ {\\text {m a s k}} + \\mathcal {L} _ {\\text {r e g}}. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 184, + 377, + 468, + 393 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Implementation details", + "text_level": 1, + "bbox": [ + 76, + 404, + 295, + 422 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Data. We conduct numerical evaluations on the Nvidia Dynamic Scene Dataset [75] and UCSD Dynamic Scenes Dataset [37]. Each dataset consists of eight forward-facing dynamic scenes recorded by synchronized multi-view cameras. We follow prior work [35] to derive a monocular video from each sequence, where each video contains $100\\sim 250$ frames. We removed frames that lack large regions of moving objects. We follow the protocol from prior work [35] that uses held-out images per time instance for evaluation. We also tested the methods on in-the-wild monocular videos, which feature more challenging camera and object motions [20].", + "bbox": [ + 75, + 430, + 472, + 611 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "View selection. For the time-varying, dynamic model we use a frame window radius of $r = 3$ for all experiments. For the time-invariant model representing static scene content, we use separate strategies for the dynamic scenes benchmarks and for in-the-wild videos. For the benchmarks, where camera viewpoints are located at discrete camera rig locations, we choose all nearby distinct viewpoints whose timestep is within 12 frames of the target time. For in-the-wild videos, naively choosing the nearest source views can lead to poor reconstruction due to insufficient camera baseline. Thus, to ensure that for any rendered pixel we have sufficient source views for computing its color, we select source views from distant frames. If we wish to select $N^{\\mathrm{vs}}$ source views for the time-invariant model, we sub-sample every $\\frac{2r_{\\mathrm{max}}}{N^{\\mathrm{vs}}}$ frames from the input video to build a candidate pool, where for a given target time $i$ , we only search source views within $[i - r_{\\mathrm{max}}, i + r_{\\mathrm{max}}]$ frames. We estimate $r_{\\mathrm{max}}^{\\mathrm{max}}$ using the method of Li et al. [34] based on SfM point可视ibility and camera relative baseline. We then construct a", + "bbox": [ + 75, + 613, + 472, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/d9ac34a35ea1d612ab91ffdb128ef06c12af5339b6ab8164fcd04ad8dda25d24.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsFullDynamic Only
SSIM↑PSNR↑LPIPS↓SSIM↑PSNR↑LPIPS↓
Nerfies [49]0.60920.640.2040.45517.350.258
HyperNeRF [50]0.65420.900.1820.44617.560.242
DVS [19]0.92127.440.0700.77822.630.144
NSFF [35]0.92728.900.0620.78323.080.159
Ours0.95730.910.0270.82624.310.062
", + "bbox": [ + 501, + 88, + 890, + 186 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Quantitative evaluation on the Nvidia dataset [75].", + "bbox": [ + 508, + 190, + 880, + 205 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "final set of source views for the model by choosing the top $N^{\\mathrm{vs}}$ frames in the candidate pool that are the closest to the target view in terms of camera baseline. We set $N^{\\mathrm{vs}} = 16$ .", + "bbox": [ + 498, + 231, + 890, + 277 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Global spatial coordinate embedding With local image feature aggregation alone, it is hard to determine density accurately on non-surface or occluded surface points due to inconsistent features from different source views, as described in NeuRay [39]. Therefore, to improve global reasoning for density prediction, we append a global spatial coordinate embedding as an input to the ray transformer, in addition to the time embedding, similar to the ideas from [64]. Please see supplement for more details.", + "bbox": [ + 496, + 281, + 893, + 417 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Handling degeneracy through virtual views. Prior work [35] observed that optimization can converge to bad local minimal if camera and object motions are close to colinear, or object motions are too fast to track. Inspired by [36], we synthesize images at eight randomly sampled nearby viewpoints for every input via depths estimated by [80]. During rendering, we randomly sample a virtual view as additional source image. We only apply this technique to in-the-wild videos since it improves optimization stability and rendering quality for such inputs, whereas we don't observe improvement on the benchmarks due to disentangled camera-object motions as described by [20].", + "bbox": [ + 496, + 422, + 893, + 604 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Time interpolation. Our approach also allows for time interpolation by performing scene motion-based splatting, as introduced by NSFF [35]. To render at a specified target fractional time, we predict the volumetric density and color at two nearby input times by aggregating local image features from their corresponding set of source views. The predicted color and density are then splatted and linearly blended via the scene flow derived from our motion trajectories, and weighted according to the target fractional time index.", + "bbox": [ + 496, + 608, + 893, + 744 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Setup. We estimate camera poses using COLMAP [57]. For each ray, we use a coarse-to-fine sampling strategy with 128 per-ray samples as in Wang et al. [70]. A separate model is trained from scratch for each scene using the Adam optimizer [29]. The network architecture for two main representations is a variant of that of IBRNet [70]. We reconstruct the entire scene in Euclidean space without special scene parameterization. Optimizing a full system on a 10 second video takes around two days using 8 Nvidia A100s, and rendering takes roughly 20 seconds for a $768 \\times 432$ frame. We", + "bbox": [ + 496, + 750, + 895, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "4278", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/3d776eba96f1803c797b21b2807ece60d3cf77bfe48be57fefc53ddb3c199c6c.jpg", + "image_caption": [ + "Our rendered views" + ], + "image_footnote": [], + "bbox": [ + 80, + 88, + 176, + 220 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/593df20c052cd13a6a061df9745ee2bc9de0aec5ad036c67c24a13158ee22e02.jpg", + "image_caption": [ + "DVS" + ], + "image_footnote": [], + "bbox": [ + 179, + 88, + 235, + 220 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/54a68978a082babcb7b4bc5f0e0d03de32db745cee26c9f52c0db53b5ae981de.jpg", + "image_caption": [ + "HyperNeRF" + ], + "image_footnote": [], + "bbox": [ + 236, + 88, + 292, + 220 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e4f452290da38fe2bd13ef41f4b52b39e01e91e0fe13b0bcaa08498db18a67d1.jpg", + "image_caption": [ + "NSFF", + "Figure 6. Qualitative comparisons on the Nvidia dataset [75]." + ], + "image_footnote": [], + "bbox": [ + 295, + 88, + 351, + 220 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/74b19900d2dc88d78b363e564d081f2f8156bde25b05538f4ed7598a238abc1a.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 352, + 88, + 408, + 220 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/de37927ee5ffbf2bc82eb0f52b89928096d6b978f9b584b394debc7922cff216.jpg", + "image_caption": [ + "GT" + ], + "image_footnote": [], + "bbox": [ + 411, + 88, + 467, + 220 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/5860b7a9703bd64fcf57c8c05526ae470d7d49debeb07d7b8bffa4ad968a96eb.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsFullDynamic Only
SSIM↑PSNR↑LPIPS↓SSIM↑PSNR↑LPIPS↓
Nerfies [49]0.82324.320.0960.59518.450.234
HyperNeRF [50]0.85925.100.0950.61819.260.212
DVS [19]0.94330.640.0750.86626.570.096
NSFF [35]0.95231.750.0340.85125.830.115
Ours0.98336.470.0140.90928.010.042
", + "bbox": [ + 78, + 268, + 465, + 364 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Quantitative evaluation on the UCSD dataset [37].", + "bbox": [ + 86, + 371, + 455, + 385 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "refer readers to the supplemental material for network architectures, hyper-parameters setting, and additional details.", + "bbox": [ + 75, + 411, + 470, + 441 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5. Evaluation", + "text_level": 1, + "bbox": [ + 76, + 455, + 192, + 470 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.1. Baselines and error metrics", + "text_level": 1, + "bbox": [ + 76, + 479, + 323, + 494 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We compare our approach to state-of-the-art monocular view synthesis methods. Specifically, we compare to three recent canonical space-based methods, Nerfies [49], and HyperNeRF [50], and to two scene flow-based methods, NSFF [35] and Dynamic View Synthesis (DVS) from Gao et al. [19]. For fair comparisons, we use the same depth, optical flow and motion segmentation masks used for our approach as inputs to other methods.", + "bbox": [ + 75, + 503, + 470, + 625 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Following prior work [35], we report the rendering quality of each method with three standard error metrics: peak signal-to-noise ratio (PSNR), structural similarity (SSIM), and perceptual similarity via LPIPS [77], and calculate errors both over the entire scene (Full) and restricted to moving regions (Dynamic Only).", + "bbox": [ + 75, + 625, + 468, + 715 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2.Quantitative evaluation", + "text_level": 1, + "bbox": [ + 76, + 726, + 294, + 742 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Quantitative results on the two benchmark datasets are shown in Table 1 and Table 2. Our approach significantly improves over prior state-of-the-art methods in terms of all error metrics. Notably, our approach improves PSNR over entire scene upon the second best methods by 2dB and 4dB on each of the two datasets. Our approach also reduces LPIPS error, a major indicator of perceptual quality compared with real images [77], by over $50\\%$ . These results suggest that our framework is much more effective at recovering highly detailed scene contents.", + "bbox": [ + 75, + 750, + 470, + 898 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8d010bf52c01f35cffb791746740e39432e449402f60ccf0046c930b35030ab5.jpg", + "image_caption": [ + "Our rendered views", + "Figure 7. Qualitative comparisons on the UCSD dataset [37]." + ], + "image_footnote": [], + "bbox": [ + 501, + 88, + 599, + 220 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ff59b50d98d0184f5cfaf8254f4af5d228b4334a205379fc820f084edcadc8c7.jpg", + "image_caption": [ + "DVS" + ], + "image_footnote": [], + "bbox": [ + 602, + 88, + 658, + 220 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/47a517a517e98b78db2e93800f0b63091e03287affb5961ff81e39c77ed3c474.jpg", + "image_caption": [ + "HyperNeRF" + ], + "image_footnote": [], + "bbox": [ + 658, + 88, + 715, + 220 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b3e8e6718a46b39ee11be7b34b1c4ab8c9d9135b313b4657310c49ad0cb7b52b.jpg", + "image_caption": [ + "NSFF" + ], + "image_footnote": [], + "bbox": [ + 718, + 88, + 772, + 220 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c2a9e6be3f8b2b9cc71ed547d21fce4985d230e5e47b35bf13908a9b680a6947.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 776, + 88, + 831, + 220 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6cd332f745c2acb1d1fe83a06d43fac2e4360e72710b07280bb8776d884f5d89.jpg", + "image_caption": [ + "GT" + ], + "image_footnote": [], + "bbox": [ + 834, + 88, + 890, + 220 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ablation study. We conduct an ablation study on the Nvidia Dynamic Scene Dataset to validate the effectiveness of our various proposed system components. We show comparisons between our full system and variants in Tab. 3: A) baseline IBRNet [70] with extra time embedding; B) without enforcing temporal consistency via cross-time rendering; C) using scene flow fields to aggregate image features within one time step; D) predicting multiple 3D scene flow vectors pointing to $2r$ nearby times at each sample; E) without using a time-invariant static scene model; F) without masked reconstruction loss via estimated motion segmentation masks; and G) without regularization loss. For this ablation study, we train each model with 64 samples per ray. Without our motion trajectory representation and temporal consistency, view synthesis quality degrades significantly as shown in the first three rows of Tab. 3. Integrating a global spatial coordinate embedding further improves rendering quality. Combining static and dynamic models improves quality for static elements, as seen in metrics over full scenes. Finally, removing supervision from motion segmentation or regularization reduces overall rendering quality, demonstrating the value of proposed losses for avoiding bad local minimal during optimization.", + "bbox": [ + 496, + 282, + 893, + 631 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Qualitative evaluation", + "text_level": 1, + "bbox": [ + 500, + 642, + 705, + 659 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Dynamic scenes dataset. We provide qualitative comparisons between our approach and three prior state-of-the-art methods [19, 35, 50] on the test views from two datasets in Fig. 6 and Fig.7. Prior dynamic-NeRF methods have difficulty rendering details of moving objects, as seen in the excessively blurred dynamic content including the texture of balloons, human faces, and clothing. In contrast, our approach synthesizes photo-realistic novel views of both static and dynamic scene content and which are closest to the ground truth images.", + "bbox": [ + 496, + 667, + 893, + 818 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In-the-wild videos. We show qualitative comparisons on in-the-wild footage of complex dynamic scenes. We show comparisons with Dynamic-NeRF based methods in Fig. 8, and Fig. 9 shows comparisons with point cloud rendering using depths [80]. Our approach synthesizes photo-realistic", + "bbox": [ + 496, + 824, + 893, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "4279", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8a0d628d664b461106331167aadfcb36ee07d14e56a2cf0c0c367f7706e61548.jpg", + "image_caption": [ + "Input" + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 171, + 243 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3748e0049fa3f60d3ab0b2c29fe467a2f394770486f57710639cd0b87f926f1d.jpg", + "image_caption": [ + "DVS" + ], + "image_footnote": [], + "bbox": [ + 171, + 88, + 346, + 244 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/666f28fc07ce48329332469e73a6faea3d937de83d9d5b33de8957fcd1ca4246.jpg", + "image_caption": [ + "HyperNeRF", + "Figure 8. Qualitative comparisons on in-the-wild videos. We show results on 10-second videos of complex dynamic scenes. The leftmost column shows the start and end frames of each video; on the right we show novel views at intermediate times rendered from our approach and prior state-of-the-art methods [19,35,50]." + ], + "image_footnote": [], + "bbox": [ + 348, + 88, + 527, + 244 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/49d02da58f0182bf12b36344f6f16551cad415c7f173e9e219634a1e5c0b8bda.jpg", + "image_caption": [ + "NSFF" + ], + "image_footnote": [], + "bbox": [ + 529, + 88, + 707, + 244 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/92cd4c156cccb001e58694bba8a13f0e09c4b08f54e11c1b677636931cf41b07.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 709, + 88, + 890, + 244 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2df62ad10ade8370b6c816267cbfa910ac8450c9626d29c0edf41fcbd6103e12.jpg", + "image_caption": [ + "Figure 9. From left to right, We show inputs and corresponding novel views rendered from explicit depth warping with Zhang et al. [80], and from our approach." + ], + "image_footnote": [], + "bbox": [ + 78, + 330, + 467, + 445 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/f15eae0c6ff895243afe07c4b9edd8f8c8828863d7706e6844e38097361611c2.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsFullDynamic Only
SSIM↑PSNR↑LPIPS↓SSIM↑PSNR↑LPIPS↓
A) [70]+time0.90525.330.0810.68320.090.122
B) w/o TC0.91127.570.0740.75122.160.104
C) w/ SF0.93529.420.0350.79722.410.095
D) w/ M-SF0.94729.590.0330.81422.970.084
E) w/o static rep.0.91928.190.0470.84024.010.071
F) w/o Lmask0.93029.950.0360.83524.300.063
G) w/o Lreg0.92129.460.0420.79522.190.080
Full0.95730.770.0280.83724.270.066
", + "bbox": [ + 78, + 505, + 467, + 635 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 3. Ablation study on the Nvidia Dataset. See Sec. 5.2 for detailed descriptions of each configuration.", + "bbox": [ + 75, + 640, + 470, + 670 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "novel views, whereas prior dynamic-Nerf methods fail to recover high-quality details of both static and moving scene contents, such as the shirt wrinkles and the dog's fur in Fig. 8. On the other hand, explicit depth warping produces holes at regions near disocculusions and out of field of view. We refer readers to the supplementary video for full comparisons.", + "bbox": [ + 75, + 694, + 470, + 787 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Discussion and conclusion", + "text_level": 1, + "bbox": [ + 76, + 799, + 318, + 815 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations. Our method is limited to relatively small viewpoint changes compared with methods designed for static or quasi-static scene; Our method is not able to handle small fast moving object due to incorrect initial depth and optical flow estimates (left, Fig. 10). In addition, compared to", + "bbox": [ + 75, + 824, + 472, + 902 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6a5c70a4cb23179dda7b619599307285d93c36e7fbeea198f7d704415474d980.jpg", + "image_caption": [ + "Figure 10. Limitations. Our method might fail to model moving thin objects such as moving leash (left). Our method can fail to render dynamic contents only visible in distant frames (middle). The rendered static content can be unrealistic or blank if insufficient source views feature are aggregated for a given pixel (right)." + ], + "image_footnote": [], + "bbox": [ + 500, + 330, + 630, + 388 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d0c2038055b9eff8213e504c62f7355a1bc1ab38dba4f3bfdca32c65cc95a6b2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 630, + 330, + 759, + 388 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f2b4401b5ab9b67c28a5e317844551354d6ac3de52a8e0cd9f5e2e21635b0a54.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 761, + 330, + 890, + 388 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "prior dynamic NeRF methods, the synthesized views are not strictly multi-view consistent, and rendering quality of static content depends on which source views are selected (middle, Fig. 10). Our approach is also sensitive to degenerate motion patterns from in-the-wild videos, in which object and camera motion is mostly colinear, but we show heuristics to handle such cases in the supplemental. Moreover, our method is able to synthesize dynamic contents only appearing at distant time (right, Fig. 10)", + "bbox": [ + 496, + 500, + 893, + 636 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Conclusion. We presented a new approach for space-time view synthesis from a monocular video depicting a complex dynamic scene. By representing a dynamic scene within a volumetric IBR framework, our approach overcomes limitations of recent methods that cannot model long videos with complex camera and object motion. We have shown that our method can synthesize photo-realistic novel views from in-the-wild dynamic videos, and can achieve significant improvements over prior state-of-the-art methods on the dynamic scene benchmarks.", + "bbox": [ + 496, + 662, + 893, + 813 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. Thanks to Andrew Liu, Richard Bowen and Lucy Chai for the fruitful discussions, and thanks to Rick Szeliski and Ricardo Martin-Brualla for helpful proofreading.", + "bbox": [ + 496, + 839, + 893, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "4280", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Aayush Bansal, Minh Vo, Yaser Sheikh, Deva Ramanan, and Srinivasa Narasimhan. 4D visualization of dynamic events from unconstrained multi-view videos. In Proc. Computer Vision and Pattern Recognition (CVPR), pages 5366-5375, 2020.", + "[2] Jonathan T Barron, Ben Mildenhall, Dor Verbin, Pratul P Srinivasan, and Peter Hedman. Mip-NeRF 360: Unbounded anti-aliased neural radiance fields. In Proc. 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Graphics, 33(4):156, 2014." + ], + "bbox": [ + 78, + 90, + 470, + 247 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "4284", + "bbox": [ + 482, + 945, + 516, + 955 + ], + "page_idx": 11 + } +] \ No newline at end of file diff --git a/2023/DynIBaR_ Neural Dynamic Image-Based Rendering/b5d1340a-3f6f-462f-9df3-03c14583f216_model.json b/2023/DynIBaR_ Neural Dynamic Image-Based Rendering/b5d1340a-3f6f-462f-9df3-03c14583f216_model.json new file mode 100644 index 0000000000000000000000000000000000000000..f2d28f44c57e29c98f49121469e89ce9d586c5dc --- /dev/null +++ b/2023/DynIBaR_ Neural Dynamic Image-Based Rendering/b5d1340a-3f6f-462f-9df3-03c14583f216_model.json @@ -0,0 +1,3007 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.221, + 0.131, + 0.75, + 0.154 + ], + "angle": 0, + "content": "DynIBaR: Neural Dynamic Image-Based Rendering" + }, + { + "type": "text", + "bbox": [ + 0.161, + 0.18, + 0.808, + 0.225 + ], + "angle": 0, + "content": "Zhengqi Li\\(^{1}\\), Qianqian Wang\\(^{1,2}\\), Forrester Cole\\(^{1}\\), Richard Tucker\\(^{1}\\), Noah Snavely\\(^{1}\\) \n\\(^{1}\\)Google Research Cornell Tech" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.277, + 0.668, + 0.482 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.679, + 0.277, + 0.889, + 0.481 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.487, + 0.896, + 0.57 + ], + "angle": 0, + "content": "Figure 1. Recent methods for synthesizing novel views from monocular videos of dynamic scenes-like HyperNeRF [50] and NSFF [35]–struggle to render high-quality views from long videos featuring complex camera and scene motion. We present a new approach that addresses these limitations, illustrated above via an application to 6DoF video stabilization, where we apply our approach and prior methods on a 30-second, shaky video clip, and compare novel views rendered along a smoothed camera path (left). On a dynamic scenes dataset (right) [75], our approach significantly improves rendering fidelity, as indicated by synthesized images and LPIPS errors computed on pixels corresponding to moving objects (yellow numbers). Please see the supplementary video for full results." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.589, + 0.314, + 0.604 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.63, + 0.474, + 0.903 + ], + "angle": 0, + "content": "We address the problem of synthesizing novel views from a monocular video depicting a complex dynamic scene. State-of-the-art methods based on temporally varying Neural Radiance Fields (aka dynamic NeRFs) have shown impressive results on this task. However, for long videos with complex object motions and uncontrolled camera trajectories, these methods can produce blurry or inaccurate renderings, hampering their use in real-world applications. Instead of encoding the entire dynamic scene within the weights of MLPs, we present a new approach that addresses these limitations by adopting a volumetric image-based rendering framework that synthesizes new viewpoints by aggregating features from nearby views in a scene motion-aware manner. Our system retains the advantages of prior methods in its ability to model complex scenes and view-dependent effects, but also enables synthesizing photo-realistic novel views from long videos featuring complex scene dynamics with unconstrained camera trajectories. We demonstrate signifi" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.59, + 0.895, + 0.651 + ], + "angle": 0, + "content": "cant improvements over state-of-the-art methods on dynamic scene datasets, and also apply our approach to in-the-wild videos with challenging camera and object motion, where prior methods fail to produce high-quality renderings." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.68, + 0.633, + 0.696 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.706, + 0.896, + 0.887 + ], + "angle": 0, + "content": "Computer vision methods can now produce free-viewpoint renderings of static 3D scenes with spectacular quality. What about moving scenes, like those featuring people or pets? Novel view synthesis from a monocular video of a dynamic scene is a much more challenging dynamic scene reconstruction problem. Recent work has made progress towards synthesizing novel views in both space and time, thanks to new time-varying neural volumetric representations like HyperNeRF [50] and Neural Scene Flow Fields (NSFF) [35], which encode spatiotemporally varying scene content volumetrically within a coordinate-based multi-layer perceptron (MLP)." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.888, + 0.892, + 0.902 + ], + "angle": 0, + "content": "However, these dynamic NeRF methods have limitations" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4273" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.212 + ], + "angle": 0, + "content": "that prevent their application to casual, in-the-wild videos. Local scene flow-based methods like NSFF struggle to scale to longer input videos captured with unconstrained camera motions: the NSFF paper only claims good performance for 1-second, forward-facing videos [35]. Methods like HyperNeRF that construct a canonical model are mostly constrained to object-centric scenes with controlled camera paths, and can fail on scenes with complex object motion." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.213, + 0.473, + 0.348 + ], + "angle": 0, + "content": "In this work, we present a new approach that is scalable to dynamic videos captured with 1) long time duration, 2) unbounded scenes, 3) uncontrolled camera trajectories, and 4) fast and complex object motion. Our approach retains the advantages of volumetric scene representations that can model intricate scene geometry with view-dependent effects, while significantly improving rendering fidelity for both static and dynamic scene content compared to recent methods [35, 50], as illustrated in Fig. 1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.348, + 0.473, + 0.483 + ], + "angle": 0, + "content": "We take inspiration from recent methods for rendering static scenes that synthesize novel images by aggregating local image features from nearby views along epipolar lines [39, 64, 70]. However, scenes that are in motion violate the epipolar constraints assumed by those methods. We instead propose to aggregate multi-view image features in scene motion-adjusted ray space, which allows us to correctly reason about spatio-temporally varying geometry and appearance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.485, + 0.473, + 0.666 + ], + "angle": 0, + "content": "We also encountered many efficiency and robustness challenges in scaling up aggregation-based methods to dynamic scenes. To efficiently model scene motion across multiple views, we model this motion using motion trajectory fields that span multiple frames, represented with learned basis functions. Furthermore, to achieve temporal coherence in our dynamic scene reconstruction, we introduce a new temporal photometric loss that operates in motion-adjusted ray space. Finally, to improve the quality of novel views, we propose to factor the scene into static and dynamic components through a new IBR-based motion segmentation technique within a Bayesian learning framework." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.666, + 0.473, + 0.831 + ], + "angle": 0, + "content": "On two dynamic scene benchmarks, we show that our approach can render highly detailed scene content and significantly improves upon the state-of-the-art, leading to an average reduction in LPIPS errors by over \\(50\\%\\) both across entire scenes, as well as on regions corresponding to dynamic objects. We also show that our method can be applied to inthe-wild videos with long duration, complex scene motion, and uncontrolled camera trajectories, where prior state-ofthe-art methods fail to produce high quality renderings. We hope that our work advances the applicability of dynamic view synthesis methods to real-world videos." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.845, + 0.22, + 0.86 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.472, + 0.903 + ], + "angle": 0, + "content": "Novel view synthesis. Classic image-based rendering (IBR) methods synthesize novel views by integrating pixel" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.212 + ], + "angle": 0, + "content": "information from input images [58], and can be categorized according to their dependence on explicit geometry. Light field or lumigraph rendering methods [9, 21, 26, 32] generate new views by filtering and interpolating sampled rays, without use of explicit geometric models. To handle sparser input views, many approaches [7, 14, 18, 23, 24, 26, 30, 52, 54, 55] leverage pre-computed proxy geometry such as depth maps or meshes to render novel views." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.213, + 0.897, + 0.44 + ], + "angle": 0, + "content": "Recently, neural representations have demonstrated high-quality novel view synthesis [12, 17, 38, 40, 46, 48, 59-62, 72, 81]. In particular, Neural Radiance Fields (NeRF) [46] achieves an unprecedented level of fidelity by encoding continuous scene radiance fields within multi-layer perceptrons (MLPs). Among all methods building on NeRF, IBRNet [70] is the most relevant to our work. IBRNet combines classical IBR techniques with volume rendering to produce a generalized IBR module that can render high-quality views without per-scene optimization. Our work extends this kind of volumetric IBR framework designed for static scenes [11, 64, 70] to more challenging dynamic scenes. Note that our focus is on synthesizing higher-quality novel views for long videos with complex camera and object motion, rather than on generalization across scenes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.448, + 0.895, + 0.522 + ], + "angle": 0, + "content": "Dynamic scene view synthesis. Our work is related to geometric reconstruction of dynamic scenes from RGBD [5, 15, 25, 47, 68, 83] or monocular videos [31, 44, 78, 80]. However, depth- or mesh-based representations struggle to model complex geometry and view-dependent effects." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.524, + 0.897, + 0.903 + ], + "angle": 0, + "content": "Most prior work on novel view synthesis for dynamic scenes requires multiple synchronized input videos [1, 3, 6, 27, 33, 63, 69, 76, 82], limiting their real-world applicability. Some methods [8, 13, 22, 51, 71] use domain knowledge such as template models to achieve high-quality results, but are restricted to specific categories [41, 56]. More recently, many works propose to synthesize novel views of dynamic scenes from a single camera. Yoon et al. [75] render novel views through explicit warping using depth maps obtained via single-view depth and multi-view stereo. However, this method fails to model complex scene geometry and to fill in realistic and consistent content at disocclusions. With advances in neural rendering, NeRF-based dynamic view synthesis methods have shown state-of-the-art results [16, 35, 53, 66, 74]. Some approaches, such as Nerfies [49] and HyperNeRF [50], represent scenes using a deformation field mapping each local observation to a canonical scene representation. These deformations are conditioned on time [53] or a per-frame latent code [49, 50, 66], and are parameterized as translations [53, 66] or rigid body motion fields [49, 50]. These methods can handle long videos, but are mostly limited to object-centric scenes with relatively small object motion and controlled camera paths. Other methods represent scenes as time-varying NeRFs [19, 20, 35, 67, 74]. In particular, NSFF uses neural scene flow fields that can" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4274" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.09, + 0.468, + 0.215 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.225, + 0.473, + 0.351 + ], + "angle": 0, + "content": "Figure 2. Rendering via motion-adjusted multi-view feature aggregation. Given a sampled location \\(\\mathbf{x}\\) at time \\(i\\) along a target ray \\(\\mathbf{r}\\), we estimate its motion trajectory, which determines the 3D correspondence of \\(\\mathbf{x}\\) at nearby time \\(j \\in \\mathcal{N}(i)\\), denoted \\(\\mathbf{x}_{i \\rightarrow j}\\). Each warped point is then projected into its corresponding source view. Image features \\(\\mathbf{f}_j\\) extracted along the projected curves are aggregated and fed to the ray transformer with time embedding \\(\\gamma(i)\\), producing per-sample color and density \\((\\mathbf{c}_i, \\sigma_i)\\). The final pixel color \\(\\hat{\\mathbf{C}}_i\\) is then synthesized by volume rendering \\((\\mathbf{c}_i, \\sigma_i)\\) along \\(\\mathbf{r}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.376, + 0.471, + 0.422 + ], + "angle": 0, + "content": "capture fast and complex 3D scene motion for in-the-wild videos [35]. However, this method only works well for short (1-2 second), forward-facing videos." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.435, + 0.384, + 0.453 + ], + "angle": 0, + "content": "3. Dynamic Image-Based Rendering" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.46, + 0.471, + 0.564 + ], + "angle": 0, + "content": "Given a monocular video of a dynamic scene with frames \\((I_1, I_2, \\ldots, I_N)\\) and known camera parameters \\((\\mathbf{P}_1, \\mathbf{P}_2, \\ldots, \\mathbf{P}_N)\\), our goal is to synthesize a novel viewpoint at any desired time within the video. Like many other approaches, we train per-video, first optimizing a model to reconstruct the input frames, then using this model to render novel views." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.566, + 0.47, + 0.656 + ], + "angle": 0, + "content": "Rather than encoding 3D color and density directly in the weights of an MLP as in recent dynamic NeRF methods, we integrate classical IBR ideas into a volumetric rendering framework. Compared to explicit surfaces, volumetric representations can more readily model complex scene geometry with view-dependent effects." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.657, + 0.471, + 0.792 + ], + "angle": 0, + "content": "The following sections introduce our methods for scene-motion-adjusted multi-view feature aggregation (Sec. 3.1), and enforcing temporal consistency via cross-time rendering in motion-adjusted ray space (Sec. 3.2). Our full system combines a static model and a dynamic model to produce a color at each pixel. Accurate scene factorization is achieved via segmentation masks derived from a separately trained motion segmentation module within a Bayesian learning framework (Sec. 3.3)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.802, + 0.396, + 0.819 + ], + "angle": 0, + "content": "3.1. Motion-adjusted feature aggregation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.471, + 0.901 + ], + "angle": 0, + "content": "We synthesize new views by aggregating features extracted from temporally nearby source views. To render an image at time \\(i\\), we first identify source views \\(I_{j}\\) within a temporal radius \\(r\\) frames of \\(i\\), \\(j \\in \\mathcal{N}(i) = [i - r, i + r]\\). For each source view, we extract a 2D feature map \\(F_{i}\\) through a" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.892, + 0.123 + ], + "angle": 0, + "content": "shared convolutional encoder network to form an input tuple \\(\\{I_j,\\mathbf{P}_j,F_j\\}\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.123, + 0.895, + 0.364 + ], + "angle": 0, + "content": "To predict the color and density of each point sampled along a target ray \\(\\mathbf{r}\\), we must aggregate source view features while accounting for scene motion. For a static scene, points along a target ray will lie along a corresponding epipolar line in a neighboring source view, hence we can aggregate potential correspondences by simply sampling along neighboring epipolar lines [64, 70]. However, moving scene elements violate epipolar constraints, leading to inconsistent feature aggregation if motion is not accounted for. Hence, we perform motion-adjusted feature aggregation, as shown in Fig. 3. To determine correspondence in dynamic scenes, one straightforward idea is to estimate a scene flow field via an MLP [35] to determine a given point's motion-adjusted 3D location at a nearby time. However, this strategy is computational infeasible in a volumetric IBR framework due to recursive unrolling of the MLPs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.371, + 0.895, + 0.446 + ], + "angle": 0, + "content": "Motion trajectory fields. Instead, we represent scene motion using motion trajectory fields described in terms of learned basis functions. For a given 3D point \\(\\mathbf{x}\\) along target ray \\(\\mathbf{r}\\) at time \\(i\\), we encode its trajectory coefficients with an MLP \\(G_{\\mathrm{MT}}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.585, + 0.453, + 0.892, + 0.471 + ], + "angle": 0, + "content": "\\[\n\\left\\{\\phi_ {i} ^ {l} (\\mathbf {x}) \\right\\} _ {l = 1} ^ {L} = G _ {\\mathrm {M T}} (\\gamma (\\mathbf {x}), \\gamma (i)), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.477, + 0.894, + 0.568 + ], + "angle": 0, + "content": "where \\(\\phi_i^l\\in \\mathcal{R}^3\\) are basis coefficients (with separate coefficients for \\(x,y,\\) and \\(z\\) using the motion basis described below) and \\(\\gamma\\) denotes positional encoding. We choose \\(L = 6\\) bases and 16 linearly increasing frequencies for the encoding \\(\\gamma\\) , based on the assumption that scene motion tends to be low frequency [80]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.568, + 0.894, + 0.659 + ], + "angle": 0, + "content": "We also introduce a global learnable motion basis \\(\\{h_i^l\\}_{l = 1}^L,h_i^l\\in \\mathcal{R}\\), spanning every time step \\(i\\) of the input video, which is optimized jointly with the MLP. The motion trajectory of \\(\\mathbf{x}\\) is then defined as \\(\\Gamma_{\\mathbf{x},i}(j) = \\sum_{l = 1}^{L}h_{j}^{l}\\phi_{i}^{l}(\\mathbf{x})\\) and thus, the relative displacement between \\(\\mathbf{x}\\) and its 3D correspondence \\(\\mathbf{x}_{i\\rightarrow j}\\) at time \\(j\\) is computed as" + }, + { + "type": "equation", + "bbox": [ + 0.599, + 0.667, + 0.891, + 0.684 + ], + "angle": 0, + "content": "\\[\n\\Delta_ {\\mathbf {x}, i} (j) = \\Gamma_ {\\mathbf {x}, i} (j) - \\Gamma_ {\\mathbf {x}, i} (i). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.895, + 0.825 + ], + "angle": 0, + "content": "With this motion trajectory representation, finding 3D correspondences for a query point \\(\\mathbf{x}\\) in neighboring views requires just a single MLP query, allowing efficient multi-view feature aggregation within our volume rendering framework. We initialize the basis \\(\\{h_i^l\\}_{l = 1}^L\\) with the DCT basis as proposed by Wang et al. [67], but fine-tune it along with other components during optimization, since we observe that a fixed DCT basis can fail to model a wide range of real-world motions (see third column of Fig. 4)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Using the estimated motion trajectory of \\(\\mathbf{x}\\) at time \\(i\\), we denote \\(\\mathbf{x}\\)'s corresponding 3D point at time \\(j\\) as \\(\\mathbf{x}_{i\\rightarrow j} = \\mathbf{x} + \\Delta_{\\mathbf{x},i}(j)\\). We project each warped point \\(\\mathbf{x}_{i\\rightarrow j}\\) into its source view \\(I_{j}\\) using camera parameters \\(\\mathbf{P}_j\\), and extract color and feature vector \\(\\mathbf{f}_j\\) at the projected 2D pixel location." + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4275" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.09, + 0.468, + 0.235 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.245, + 0.473, + 0.442 + ], + "angle": 0, + "content": "Figure 3. Temporal consistency via cross-time rendering. To enforce temporal consistency in a dynamic reconstruction, we render each frame \\(I_{i}\\) using the scene model from a nearby time \\(j\\), which we call cross-time rendering. A ray \\(\\mathbf{r}\\) from image \\(i\\) is instead rendered using a curved ray \\(\\mathbf{r}_{i\\rightarrow j}\\), i.e., \\(\\mathbf{r}\\) warped to time \\(j\\). That is, having computed the motion-adjusted point \\(\\mathbf{x}_{i\\rightarrow j} = \\mathbf{x} + \\Delta_{\\mathbf{x},i}(j)\\) at nearby time \\(j\\) from every sampled location along \\(\\mathbf{r}\\), we query \\(\\mathbf{x}_{i\\rightarrow j}\\) and time \\(j\\) via the MLP to predict its motion trajectory \\(\\Gamma_{\\mathbf{x}_{i\\rightarrow j},j}\\), along which we aggregate image features \\(\\mathbf{f}_k\\) extracted from source views within time \\(k\\in \\mathcal{N}(j)\\). The aggregated features along \\(\\mathbf{r}_{i\\rightarrow j}\\) are fed to the ray transformer with time embedding \\(\\gamma (j)\\) to produce per-sample color and density \\((\\mathbf{c}_j,\\sigma_j)\\) at time \\(j\\). A pixel color \\(\\hat{\\mathbf{C}}_{j\\rightarrow i}\\) is computed by volume rendering \\((\\mathbf{c}_j,\\sigma_j)\\), and then compared to the ground truth color \\(\\mathbf{C}_i\\) to form a reconstruction loss \\(\\mathcal{L}_{\\mathrm{pho}}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.468, + 0.472, + 0.619 + ], + "angle": 0, + "content": "The resulting set of source features across neighbor views \\( j \\) is fed to a shared MLP whose output features are aggregated through weighted average pooling [70] to produce a single feature vector at each 3D sample point along ray \\( \\mathbf{r} \\). A ray transformer network with time embedding \\( \\gamma(i) \\) then processes the sequence of aggregated features along the ray to predict per-sample colors and densities \\( (\\mathbf{c}_i, \\sigma_i) \\) (see Fig. 2). We then use standard NeRF volume rendering [4] to obtain a final pixel color \\( \\hat{\\mathbf{C}}_i(\\mathbf{r}) \\) for the ray from this sequence of colors and densities." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.633, + 0.47, + 0.65 + ], + "angle": 0, + "content": "3.2. Cross-time rendering for temporal consistency" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.658, + 0.473, + 0.854 + ], + "angle": 0, + "content": "If we optimize our dynamic scene representation by comparing \\(\\hat{\\mathbf{C}}_i\\) with \\(\\mathbf{C}_i\\) alone, the representation might overfit to the input images: it might perfectly reconstruct those views, but fail to render correct novel views. This can happen because the representation has the capacity to reconstruct completely separate models for each time instance, without utilizing or accurately reconstructing scene motion. Therefore, to recover a consistent scene with physically plausible motion, we enforce temporal coherence of the scene representation. One way to define temporal coherence in this context is that the scene at two neighboring times \\(i\\) and \\(j\\) should be consistent when taking scene motion into account [19, 35, 67]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.473, + 0.902 + ], + "angle": 0, + "content": "In particular, we enforce temporal photometric consistency in our optimized representation via cross-time rendering in motion-adjusted ray space, as shown in Fig. 3. The" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.894, + 0.168 + ], + "angle": 0, + "content": "idea is to render a view at time \\(i\\) but via some nearby time \\(j\\), which we refer to as cross-time rendering. For each nearby time \\(j \\in \\mathcal{N}(i)\\), rather than directly using points \\(\\mathbf{x}\\) along ray \\(\\mathbf{r}\\), we consider the points \\(\\mathbf{x}_{i \\to j}\\) along motion-adjusted ray \\(\\mathbf{r}_{i \\to j}\\) and treat them as if they lie along a ray at time \\(j\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.168, + 0.895, + 0.395 + ], + "angle": 0, + "content": "Specifically, having computed the motion-adjusted points \\(\\mathbf{x}_{i\\rightarrow j}\\), we query the MLP to predict the coefficients of new trajectories \\(\\{\\phi_j^l (\\mathbf{x}_{i\\rightarrow j})_{l = 1}^L = G_{\\mathrm{MT}}(\\mathbf{x}_{i\\rightarrow j},\\gamma (j))\\), and use these to compute corresponding 3D points \\((\\mathbf{x}_{i\\rightarrow j})_{j\\rightarrow k}\\) for images \\(k\\) in the temporal window \\(\\mathcal{N}(j)\\), using Eq. 2. These new 3D correspondences are then used to render a pixel color exactly as described for a \"straight\" ray \\(\\mathbf{r}_i\\) in Sec. 3.1, except now along the curved, motion-adjusted ray \\(\\mathbf{r}_{i\\rightarrow j}\\). That is, each point \\((\\mathbf{x}_{i\\rightarrow j})_{j\\rightarrow k}\\) is projected into its source view \\(I_{k}\\) and feature maps \\(F_{k}\\) with camera parameters \\(\\mathbf{P}_k\\) to extract an RGB color and image feature \\(\\mathbf{f}_k\\), and then these features are aggregated and input to the ray transformer with the time embedding \\(\\gamma (j)\\). The result is a sequence of colors and densities \\((\\mathbf{c}_j,\\sigma_j)\\) along \\(\\mathbf{r}_{i\\rightarrow j}\\) at time \\(j\\), which can be composited through volume rendering to form a color \\(\\hat{\\mathbf{C}}_{j\\rightarrow i}\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.397, + 0.894, + 0.427 + ], + "angle": 0, + "content": "We can then compare \\(\\hat{\\mathbf{C}}_{j\\rightarrow i}(\\mathbf{r})\\) with the target pixel \\(\\mathbf{C}_i(\\mathbf{r})\\) via a motion-disocclusion-aware RGB reconstruction loss:" + }, + { + "type": "equation", + "bbox": [ + 0.525, + 0.433, + 0.892, + 0.467 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {p h o}} = \\sum_ {\\mathbf {r}} \\sum_ {j \\in \\mathcal {N} (i)} \\hat {\\mathbf {W}} _ {j \\rightarrow i} (\\mathbf {r}) \\rho \\left(\\mathbf {C} _ {i} (\\mathbf {r}), \\hat {\\mathbf {C}} _ {j \\rightarrow i} (\\mathbf {r})\\right). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.473, + 0.895, + 0.626 + ], + "angle": 0, + "content": "We use a generalized Charbonnier loss [10] for the RGB loss \\(\\rho\\). \\(\\hat{\\mathbf{W}}_{j\\rightarrow i}(\\mathbf{r})\\) is a motion disocclusion weight computed by the difference of accumulated alpha weights between time \\(i\\) and \\(j\\) to address the motion disocclusion ambiguity described by NSFF [35] (see supplement for more details). Note that when \\(j = i\\), there is no scene motion-induced displacement, meaning \\(\\hat{\\mathbf{C}}_{j\\rightarrow i} = \\hat{\\mathbf{C}}_i\\) and no disocclusion weights are involved (\\(\\hat{\\mathbf{W}}_{j\\rightarrow i} = 1\\)). We show a comparison between our method with and without enforcing temporal consistency in the first column of Fig. 4." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.636, + 0.833, + 0.652 + ], + "angle": 0, + "content": "3.3. Combining static and dynamic models" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.895, + 0.854 + ], + "angle": 0, + "content": "As observed in NSFF, synthesizing novel views using a small temporal window is insufficient to recover complete and high-quality content for static scene regions, since the contents may only be observed in spatially distant frames due to uncontrolled camera paths. Therefore, we follow the ideas of NSFF [35], and model the entire scene using two separate representations. Dynamic content \\((\\mathbf{c}_i,\\sigma_i)\\) is represented with a time-varying model as above (used for cross-time rendering during optimization). Static content \\((\\mathbf{c},\\sigma)\\) is represented with a time-invariant model, which renders in the same way as the time-varying model, but aggregates multiview features without scene motion adjustment (i.e., along epipolar lines)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.895, + 0.901 + ], + "angle": 0, + "content": "The dynamic and static predictions are combined and rendered to a single output color \\(\\hat{\\mathbf{C}}_i^{\\mathrm{full}}\\) (or \\(\\hat{\\mathbf{C}}_{j\\rightarrow i}^{\\mathrm{full}}\\) during cross-time rendering) using the method for combining static and" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4276" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.174, + 0.233 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.105, + 0.234, + 0.15, + 0.243 + ], + "angle": 0, + "content": "(a) w/o TC" + }, + { + "type": "image", + "bbox": [ + 0.179, + 0.089, + 0.273, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.205, + 0.234, + 0.244, + 0.243 + ], + "angle": 0, + "content": "(b) w/ SF" + }, + { + "type": "image", + "bbox": [ + 0.276, + 0.089, + 0.371, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.288, + 0.234, + 0.359, + 0.243 + ], + "angle": 0, + "content": "(c) w/ DCT basis" + }, + { + "type": "image", + "bbox": [ + 0.374, + 0.089, + 0.47, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.403, + 0.234, + 0.438, + 0.244 + ], + "angle": 0, + "content": "(d) Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.252, + 0.473, + 0.364 + ], + "angle": 0, + "content": "Figure 4. Qualitative ablations. From left to right, we show rendered novel views (top) and depths (bottom) from our system (a) without enforcing temporal consistency, (b) aggregating image features with scene flow fields instead of motion trajectories, (c) representing motion trajectory with a fixed DCT basis instead of a learned one, and (d) with full configuration. Simpler configurations significantly degrade rendering quality as indicated by PSNR calculated over the regions of moving objects." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.39, + 0.47, + 0.437 + ], + "angle": 0, + "content": "transient models of NeRF-W [45]. Each model's color and density estimates can also be rendered separately, giving color \\(\\hat{\\mathbf{C}}^{\\mathrm{st}}\\) for static content and \\(\\hat{\\mathbf{C}}_i^{\\mathrm{dy}}\\) for dynamic content." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.437, + 0.47, + 0.484 + ], + "angle": 0, + "content": "When combining the two representations, we rewrite the photometric consistency term in Eq. 3 as a loss comparing \\(\\hat{\\mathbf{C}}_{j\\rightarrow i}^{\\mathrm{full}}(\\mathbf{r})\\) with target pixel \\(\\mathbf{C}_i(\\mathbf{r})\\):" + }, + { + "type": "equation", + "bbox": [ + 0.105, + 0.494, + 0.47, + 0.528 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {p h o}} = \\sum_ {\\mathbf {r}} \\sum_ {j \\in \\mathcal {N} (i)} \\hat {\\mathbf {W}} _ {j \\rightarrow i} (\\mathbf {r}) \\rho \\left(\\mathbf {C} _ {i} (\\mathbf {r}), \\hat {\\mathbf {C}} _ {j \\rightarrow i} ^ {\\text {f u l l}} (\\mathbf {r})\\right) \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.538, + 0.473, + 0.794 + ], + "angle": 0, + "content": "Image-based motion segmentation. In our framework, we observed that without any initialization, scene factorization tends to be dominated by either the time-invariant or the time-varying representation, a phenomena also observed in recent methods [28, 42]. To facilitate factorization, Gao et al. [19] initialize their system using masks from semantic segmentation, relying on the assumption that all moving objects are captured by a set of candidate semantic segmentation labels, and segmentation masks are temporally accurate. However, these assumptions do not hold in many real-world scenarios, as observed by Zhang et al. [79]. Instead, we propose a new motion segmentation module that produces segmentation masks for supervising our main two-component scene representation. Our idea is inspired by the Bayesian learning techniques proposed in recent work [45, 79], but integrated into a volumetric IBR representation for dynamic videos." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.473, + 0.902 + ], + "angle": 0, + "content": "In particular, before training our main two-component scene representation, we jointly train two lightweight models to obtain a motion segmentation mask \\( M_{i} \\) for each input frame \\( I_{i} \\). We model static scene content with an IBR-Net [70] that renders a pixel color \\( \\hat{\\mathbf{B}}^{\\mathrm{st}} \\) using volume rendering along each ray via feature aggregation along epipolar lines from nearby source views without considering scene" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.089, + 0.602, + 0.131 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.132, + 0.602, + 0.174 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.603, + 0.089, + 0.697, + 0.131 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.603, + 0.132, + 0.697, + 0.174 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.698, + 0.089, + 0.789, + 0.131 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.79, + 0.089, + 0.886, + 0.131 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.182, + 0.894, + 0.241 + ], + "angle": 0, + "content": "Figure 5. Motion segmentation. We show full rendering \\(\\hat{\\mathbf{B}}_i^{\\mathrm{full}}\\) (top) and motion segmentation overlaid with rendered dynamic content \\(\\alpha_i^{\\mathrm{dy}}\\odot \\hat{\\mathbf{B}}_i^{\\mathrm{dy}}\\) (bottom). Our approach segments challenging dynamic elements such as the moving shadow, swing, and swaying bushes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.263, + 0.895, + 0.323 + ], + "angle": 0, + "content": "motion; we model dynamic scene content with a 2D convolutional encoder-decoder network \\( D \\), which predicts a 2D opacity map \\( \\alpha_{i}^{\\mathrm{dy}} \\), confidence map \\( \\beta_{i}^{\\mathrm{dy}} \\), and RGB image \\( \\hat{\\mathbf{B}}_{i}^{\\mathrm{dy}} \\) from an input frame:" + }, + { + "type": "equation", + "bbox": [ + 0.616, + 0.324, + 0.892, + 0.344 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {B}} _ {i} ^ {\\mathrm {d y}}, \\boldsymbol {\\alpha} _ {i} ^ {\\mathrm {d y}}, \\boldsymbol {\\beta} _ {i} ^ {\\mathrm {d y}} = D (I _ {i}). \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.347, + 0.892, + 0.376 + ], + "angle": 0, + "content": "The full reconstructed image is then composited pixelwise from the outputs of the two models:" + }, + { + "type": "equation", + "bbox": [ + 0.525, + 0.379, + 0.892, + 0.399 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {B}} _ {i} ^ {\\text {f u l l}} (\\mathbf {r}) = \\boldsymbol {\\alpha} _ {i} ^ {\\mathrm {d y}} (\\mathbf {r}) \\hat {\\mathbf {B}} _ {i} ^ {\\mathrm {d y}} (\\mathbf {r}) + (1 - \\boldsymbol {\\alpha} _ {i} ^ {\\mathrm {d y}} (\\mathbf {r})) \\hat {\\mathbf {B}} ^ {\\mathrm {s t}} (\\mathbf {r}). \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.401, + 0.895, + 0.492 + ], + "angle": 0, + "content": "To segment moving objects, we assume the observed pixel color is uncertain in a heteroscedastic aleatoric manner, and model the observations in the video with a Cauchy distribution with time dependent confidence \\(\\beta_{i}^{\\mathrm{dy}}\\). By taking the negative log-likelihood of the observations, our segmentation loss is written as a weighted reconstruction loss:" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.494, + 0.892, + 0.536 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {s e g}} = \\sum_ {\\mathbf {r}} \\log \\left(\\beta_ {i} ^ {\\mathrm {d y}} (\\mathbf {r}) + \\frac {\\left| \\left| \\hat {\\mathbf {B}} _ {i} ^ {\\text {f u l l}} (\\mathbf {r}) - \\mathbf {C} _ {i} (\\mathbf {r}) \\right| \\right| ^ {2}}{\\beta_ {i} ^ {\\mathrm {d y}} (\\mathbf {r})}\\right). \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.538, + 0.895, + 0.658 + ], + "angle": 0, + "content": "By optimizing the two models using Eq. 7, we obtain a motion segmentation mask \\(M_{i}\\) by thresholding \\(\\alpha_{i}^{\\mathrm{dy}}\\) at 0.5. We do not require an alpha regularization loss as in NeRF-W [45] to avoid degeneracies, since we naturally include such an inductive basis by excluding skip connections from network \\(D\\), which leads \\(D\\) to converge more slowly than the static IBR model. We show our estimated motion segmentation masks overlaid on input images in Fig. 5." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.664, + 0.894, + 0.756 + ], + "angle": 0, + "content": "Supervision with segmentation masks. We initialize our main time-varying and time-invariant models with masks \\( M_{i} \\) as in Omnimatte [43], by applying a reconstruction loss to renderings from the time-varying model in dynamic regions, and to renderings from the time-invariant model in static regions:" + }, + { + "type": "equation", + "bbox": [ + 0.557, + 0.758, + 0.892, + 0.823 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\text {m a s k}} = \\sum_ {\\mathbf {r}} (1 - M _ {i}) (\\mathbf {r}) \\rho \\left(\\hat {\\mathbf {C}} ^ {\\mathrm {s t}} (\\mathbf {r}), \\mathbf {C} _ {i} (\\mathbf {r})\\right) \\\\ + \\sum_ {\\mathbf {r}} M _ {i} (\\mathbf {r}) \\rho \\left(\\hat {\\mathbf {C}} _ {i} ^ {\\mathrm {d y}} (\\mathbf {r}), \\mathbf {C} _ {i} (\\mathbf {r})\\right) \\tag {8} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.894, + 0.902 + ], + "angle": 0, + "content": "We perform morphological erosion and dilation on \\( M_{i} \\) to obtain masks of dynamic and static regions respectively in order to turn off the loss near mask boundaries. We supervise the system with \\( \\mathcal{L}_{\\mathrm{mask}} \\) and decay the weights by a factor of 5 for dynamic regions every 50K optimization steps." + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4277" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.091, + 0.228, + 0.108 + ], + "angle": 0, + "content": "3.4. Regularization" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.114, + 0.473, + 0.34 + ], + "angle": 0, + "content": "As noted in prior work, monocular reconstruction of complex dynamic scenes is highly ill-posed, and using photometric consistency alone is insufficient to avoid bad local minima during optimization [19, 35]. Therefore, we adopt regularization schemes used in prior work [2, 35, 73, 75], which consist of three main parts \\(\\mathcal{L}_{\\mathrm{reg}} = \\mathcal{L}_{\\mathrm{data}} + \\mathcal{L}_{\\mathrm{MT}} + \\mathcal{L}_{\\mathrm{cpt}}\\). \\(\\mathcal{L}_{\\mathrm{data}}\\) is a data-driven term consisting of \\(\\ell_{1}\\) monocular depth and optical flow consistency priors using the estimates from Zhang et al. [80] and RAFT [65]. \\(\\mathcal{L}_{\\mathrm{MT}}\\) is a motion trajectory regularization term that encourages estimated trajectory fields to be cycle-consistent and spatial-temporally smooth. \\(\\mathcal{L}_{\\mathrm{cpt}}\\) is a compactness prior that encourages the scene decomposition to be binary via an entropy loss, and mitigates floaters through distortion losses [2]. We refer readers to the supplement for more details." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.341, + 0.471, + 0.372 + ], + "angle": 0, + "content": "In summary, the final combined loss used to optimize our main representation for space-time view synthesis is:" + }, + { + "type": "equation", + "bbox": [ + 0.186, + 0.378, + 0.47, + 0.395 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {\\text {p h o}} + \\mathcal {L} _ {\\text {m a s k}} + \\mathcal {L} _ {\\text {r e g}}. \\tag {9}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.405, + 0.296, + 0.423 + ], + "angle": 0, + "content": "4. Implementation details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.431, + 0.473, + 0.612 + ], + "angle": 0, + "content": "Data. We conduct numerical evaluations on the Nvidia Dynamic Scene Dataset [75] and UCSD Dynamic Scenes Dataset [37]. Each dataset consists of eight forward-facing dynamic scenes recorded by synchronized multi-view cameras. We follow prior work [35] to derive a monocular video from each sequence, where each video contains \\(100\\sim 250\\) frames. We removed frames that lack large regions of moving objects. We follow the protocol from prior work [35] that uses held-out images per time instance for evaluation. We also tested the methods on in-the-wild monocular videos, which feature more challenging camera and object motions [20]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.614, + 0.473, + 0.901 + ], + "angle": 0, + "content": "View selection. For the time-varying, dynamic model we use a frame window radius of \\( r = 3 \\) for all experiments. For the time-invariant model representing static scene content, we use separate strategies for the dynamic scenes benchmarks and for in-the-wild videos. For the benchmarks, where camera viewpoints are located at discrete camera rig locations, we choose all nearby distinct viewpoints whose timestep is within 12 frames of the target time. For in-the-wild videos, naively choosing the nearest source views can lead to poor reconstruction due to insufficient camera baseline. Thus, to ensure that for any rendered pixel we have sufficient source views for computing its color, we select source views from distant frames. If we wish to select \\( N^{\\mathrm{vs}} \\) source views for the time-invariant model, we sub-sample every \\( \\frac{2r_{\\mathrm{max}}}{N^{\\mathrm{vs}}} \\) frames from the input video to build a candidate pool, where for a given target time \\( i \\), we only search source views within \\( [i - r_{\\mathrm{max}}, i + r_{\\mathrm{max}}] \\) frames. We estimate \\( r_{\\mathrm{max}}^{\\mathrm{max}} \\) using the method of Li et al. [34] based on SfM point可视ibility and camera relative baseline. We then construct a" + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.089, + 0.891, + 0.187 + ], + "angle": 0, + "content": "
MethodsFullDynamic Only
SSIM↑PSNR↑LPIPS↓SSIM↑PSNR↑LPIPS↓
Nerfies [49]0.60920.640.2040.45517.350.258
HyperNeRF [50]0.65420.900.1820.44617.560.242
DVS [19]0.92127.440.0700.77822.630.144
NSFF [35]0.92728.900.0620.78323.080.159
Ours0.95730.910.0270.82624.310.062
" + }, + { + "type": "table_caption", + "bbox": [ + 0.509, + 0.191, + 0.882, + 0.207 + ], + "angle": 0, + "content": "Table 1. Quantitative evaluation on the Nvidia dataset [75]." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.232, + 0.892, + 0.278 + ], + "angle": 0, + "content": "final set of source views for the model by choosing the top \\( N^{\\mathrm{vs}} \\) frames in the candidate pool that are the closest to the target view in terms of camera baseline. We set \\( N^{\\mathrm{vs}} = 16 \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.282, + 0.895, + 0.419 + ], + "angle": 0, + "content": "Global spatial coordinate embedding With local image feature aggregation alone, it is hard to determine density accurately on non-surface or occluded surface points due to inconsistent features from different source views, as described in NeuRay [39]. Therefore, to improve global reasoning for density prediction, we append a global spatial coordinate embedding as an input to the ray transformer, in addition to the time embedding, similar to the ideas from [64]. Please see supplement for more details." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.423, + 0.895, + 0.605 + ], + "angle": 0, + "content": "Handling degeneracy through virtual views. Prior work [35] observed that optimization can converge to bad local minimal if camera and object motions are close to colinear, or object motions are too fast to track. Inspired by [36], we synthesize images at eight randomly sampled nearby viewpoints for every input via depths estimated by [80]. During rendering, we randomly sample a virtual view as additional source image. We only apply this technique to in-the-wild videos since it improves optimization stability and rendering quality for such inputs, whereas we don't observe improvement on the benchmarks due to disentangled camera-object motions as described by [20]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.609, + 0.894, + 0.746 + ], + "angle": 0, + "content": "Time interpolation. Our approach also allows for time interpolation by performing scene motion-based splatting, as introduced by NSFF [35]. To render at a specified target fractional time, we predict the volumetric density and color at two nearby input times by aggregating local image features from their corresponding set of source views. The predicted color and density are then splatted and linearly blended via the scene flow derived from our motion trajectories, and weighted according to the target fractional time index." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.897, + 0.902 + ], + "angle": 0, + "content": "Setup. We estimate camera poses using COLMAP [57]. For each ray, we use a coarse-to-fine sampling strategy with 128 per-ray samples as in Wang et al. [70]. A separate model is trained from scratch for each scene using the Adam optimizer [29]. The network architecture for two main representations is a variant of that of IBRNet [70]. We reconstruct the entire scene in Euclidean space without special scene parameterization. Optimizing a full system on a 10 second video takes around two days using 8 Nvidia A100s, and rendering takes roughly 20 seconds for a \\(768 \\times 432\\) frame. We" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4278" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.177, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.093, + 0.223, + 0.165, + 0.232 + ], + "angle": 0, + "content": "Our rendered views" + }, + { + "type": "image", + "bbox": [ + 0.181, + 0.089, + 0.236, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.197, + 0.223, + 0.218, + 0.232 + ], + "angle": 0, + "content": "DVS" + }, + { + "type": "image", + "bbox": [ + 0.238, + 0.089, + 0.294, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.245, + 0.223, + 0.289, + 0.232 + ], + "angle": 0, + "content": "HyperNeRF" + }, + { + "type": "image", + "bbox": [ + 0.296, + 0.089, + 0.352, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.313, + 0.223, + 0.335, + 0.232 + ], + "angle": 0, + "content": "NSFF" + }, + { + "type": "image", + "bbox": [ + 0.354, + 0.089, + 0.41, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.373, + 0.224, + 0.392, + 0.233 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.412, + 0.089, + 0.468, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.434, + 0.223, + 0.447, + 0.232 + ], + "angle": 0, + "content": "GT" + }, + { + "type": "image_caption", + "bbox": [ + 0.082, + 0.242, + 0.465, + 0.257 + ], + "angle": 0, + "content": "Figure 6. Qualitative comparisons on the Nvidia dataset [75]." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.269, + 0.467, + 0.366 + ], + "angle": 0, + "content": "
MethodsFullDynamic Only
SSIM↑PSNR↑LPIPS↓SSIM↑PSNR↑LPIPS↓
Nerfies [49]0.82324.320.0960.59518.450.234
HyperNeRF [50]0.85925.100.0950.61819.260.212
DVS [19]0.94330.640.0750.86626.570.096
NSFF [35]0.95231.750.0340.85125.830.115
Ours0.98336.470.0140.90928.010.042
" + }, + { + "type": "table_caption", + "bbox": [ + 0.087, + 0.372, + 0.456, + 0.386 + ], + "angle": 0, + "content": "Table 2. Quantitative evaluation on the UCSD dataset [37]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.412, + 0.471, + 0.443 + ], + "angle": 0, + "content": "refer readers to the supplemental material for network architectures, hyper-parameters setting, and additional details." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.456, + 0.194, + 0.471 + ], + "angle": 0, + "content": "5. Evaluation" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.481, + 0.325, + 0.496 + ], + "angle": 0, + "content": "5.1. Baselines and error metrics" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.505, + 0.471, + 0.625 + ], + "angle": 0, + "content": "We compare our approach to state-of-the-art monocular view synthesis methods. Specifically, we compare to three recent canonical space-based methods, Nerfies [49], and HyperNeRF [50], and to two scene flow-based methods, NSFF [35] and Dynamic View Synthesis (DVS) from Gao et al. [19]. For fair comparisons, we use the same depth, optical flow and motion segmentation masks used for our approach as inputs to other methods." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.626, + 0.47, + 0.716 + ], + "angle": 0, + "content": "Following prior work [35], we report the rendering quality of each method with three standard error metrics: peak signal-to-noise ratio (PSNR), structural similarity (SSIM), and perceptual similarity via LPIPS [77], and calculate errors both over the entire scene (Full) and restricted to moving regions (Dynamic Only)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.727, + 0.295, + 0.743 + ], + "angle": 0, + "content": "5.2.Quantitative evaluation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.9 + ], + "angle": 0, + "content": "Quantitative results on the two benchmark datasets are shown in Table 1 and Table 2. Our approach significantly improves over prior state-of-the-art methods in terms of all error metrics. Notably, our approach improves PSNR over entire scene upon the second best methods by 2dB and 4dB on each of the two datasets. Our approach also reduces LPIPS error, a major indicator of perceptual quality compared with real images [77], by over \\(50\\%\\). These results suggest that our framework is much more effective at recovering highly detailed scene contents." + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.089, + 0.601, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.515, + 0.223, + 0.588, + 0.232 + ], + "angle": 0, + "content": "Our rendered views" + }, + { + "type": "image", + "bbox": [ + 0.603, + 0.089, + 0.659, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.62, + 0.223, + 0.64, + 0.232 + ], + "angle": 0, + "content": "DVS" + }, + { + "type": "image", + "bbox": [ + 0.66, + 0.089, + 0.717, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.666, + 0.223, + 0.711, + 0.234 + ], + "angle": 0, + "content": "HyperNeRF" + }, + { + "type": "image", + "bbox": [ + 0.72, + 0.089, + 0.774, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.735, + 0.223, + 0.758, + 0.232 + ], + "angle": 0, + "content": "NSFF" + }, + { + "type": "image", + "bbox": [ + 0.777, + 0.089, + 0.833, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.795, + 0.224, + 0.815, + 0.232 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.835, + 0.089, + 0.892, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.856, + 0.224, + 0.869, + 0.232 + ], + "angle": 0, + "content": "GT" + }, + { + "type": "image_caption", + "bbox": [ + 0.506, + 0.242, + 0.886, + 0.257 + ], + "angle": 0, + "content": "Figure 7. Qualitative comparisons on the UCSD dataset [37]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.284, + 0.895, + 0.632 + ], + "angle": 0, + "content": "Ablation study. We conduct an ablation study on the Nvidia Dynamic Scene Dataset to validate the effectiveness of our various proposed system components. We show comparisons between our full system and variants in Tab. 3: A) baseline IBRNet [70] with extra time embedding; B) without enforcing temporal consistency via cross-time rendering; C) using scene flow fields to aggregate image features within one time step; D) predicting multiple 3D scene flow vectors pointing to \\(2r\\) nearby times at each sample; E) without using a time-invariant static scene model; F) without masked reconstruction loss via estimated motion segmentation masks; and G) without regularization loss. For this ablation study, we train each model with 64 samples per ray. Without our motion trajectory representation and temporal consistency, view synthesis quality degrades significantly as shown in the first three rows of Tab. 3. Integrating a global spatial coordinate embedding further improves rendering quality. Combining static and dynamic models improves quality for static elements, as seen in metrics over full scenes. Finally, removing supervision from motion segmentation or regularization reduces overall rendering quality, demonstrating the value of proposed losses for avoiding bad local minimal during optimization." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.643, + 0.706, + 0.66 + ], + "angle": 0, + "content": "5.3. Qualitative evaluation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.668, + 0.895, + 0.819 + ], + "angle": 0, + "content": "Dynamic scenes dataset. We provide qualitative comparisons between our approach and three prior state-of-the-art methods [19, 35, 50] on the test views from two datasets in Fig. 6 and Fig.7. Prior dynamic-NeRF methods have difficulty rendering details of moving objects, as seen in the excessively blurred dynamic content including the texture of balloons, human faces, and clothing. In contrast, our approach synthesizes photo-realistic novel views of both static and dynamic scene content and which are closest to the ground truth images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.894, + 0.902 + ], + "angle": 0, + "content": "In-the-wild videos. We show qualitative comparisons on in-the-wild footage of complex dynamic scenes. We show comparisons with Dynamic-NeRF based methods in Fig. 8, and Fig. 9 shows comparisons with point cloud rendering using depths [80]. Our approach synthesizes photo-realistic" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4279" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.172, + 0.244 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.115, + 0.246, + 0.138, + 0.256 + ], + "angle": 0, + "content": "Input" + }, + { + "type": "image", + "bbox": [ + 0.173, + 0.089, + 0.348, + 0.245 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.248, + 0.248, + 0.271, + 0.257 + ], + "angle": 0, + "content": "DVS" + }, + { + "type": "image", + "bbox": [ + 0.349, + 0.089, + 0.528, + 0.245 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.413, + 0.246, + 0.464, + 0.257 + ], + "angle": 0, + "content": "HyperNeRF" + }, + { + "type": "image", + "bbox": [ + 0.53, + 0.089, + 0.709, + 0.245 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.607, + 0.246, + 0.632, + 0.256 + ], + "angle": 0, + "content": "NSFF" + }, + { + "type": "image", + "bbox": [ + 0.71, + 0.089, + 0.891, + 0.245 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.787, + 0.247, + 0.808, + 0.256 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.267, + 0.895, + 0.31 + ], + "angle": 0, + "content": "Figure 8. Qualitative comparisons on in-the-wild videos. We show results on 10-second videos of complex dynamic scenes. The leftmost column shows the start and end frames of each video; on the right we show novel views at intermediate times rendered from our approach and prior state-of-the-art methods [19,35,50]." + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.332, + 0.468, + 0.446 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.451, + 0.471, + 0.495 + ], + "angle": 0, + "content": "Figure 9. From left to right, We show inputs and corresponding novel views rendered from explicit depth warping with Zhang et al. [80], and from our approach." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.506, + 0.468, + 0.636 + ], + "angle": 0, + "content": "
MethodsFullDynamic Only
SSIM↑PSNR↑LPIPS↓SSIM↑PSNR↑LPIPS↓
A) [70]+time0.90525.330.0810.68320.090.122
B) w/o TC0.91127.570.0740.75122.160.104
C) w/ SF0.93529.420.0350.79722.410.095
D) w/ M-SF0.94729.590.0330.81422.970.084
E) w/o static rep.0.91928.190.0470.84024.010.071
F) w/o Lmask0.93029.950.0360.83524.300.063
G) w/o Lreg0.92129.460.0420.79522.190.080
Full0.95730.770.0280.83724.270.066
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.641, + 0.471, + 0.671 + ], + "angle": 0, + "content": "Table 3. Ablation study on the Nvidia Dataset. See Sec. 5.2 for detailed descriptions of each configuration." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.695, + 0.472, + 0.788 + ], + "angle": 0, + "content": "novel views, whereas prior dynamic-Nerf methods fail to recover high-quality details of both static and moving scene contents, such as the shirt wrinkles and the dog's fur in Fig. 8. On the other hand, explicit depth warping produces holes at regions near disocculusions and out of field of view. We refer readers to the supplementary video for full comparisons." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.8, + 0.32, + 0.816 + ], + "angle": 0, + "content": "6. Discussion and conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Limitations. Our method is limited to relatively small viewpoint changes compared with methods designed for static or quasi-static scene; Our method is not able to handle small fast moving object due to incorrect initial depth and optical flow estimates (left, Fig. 10). In addition, compared to" + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.332, + 0.632, + 0.39 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.632, + 0.332, + 0.761, + 0.39 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.762, + 0.332, + 0.892, + 0.39 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.396, + 0.895, + 0.468 + ], + "angle": 0, + "content": "Figure 10. Limitations. Our method might fail to model moving thin objects such as moving leash (left). Our method can fail to render dynamic contents only visible in distant frames (middle). The rendered static content can be unrealistic or blank if insufficient source views feature are aggregated for a given pixel (right)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.5, + 0.895, + 0.637 + ], + "angle": 0, + "content": "prior dynamic NeRF methods, the synthesized views are not strictly multi-view consistent, and rendering quality of static content depends on which source views are selected (middle, Fig. 10). Our approach is also sensitive to degenerate motion patterns from in-the-wild videos, in which object and camera motion is mostly colinear, but we show heuristics to handle such cases in the supplemental. Moreover, our method is able to synthesize dynamic contents only appearing at distant time (right, Fig. 10)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.663, + 0.895, + 0.814 + ], + "angle": 0, + "content": "Conclusion. We presented a new approach for space-time view synthesis from a monocular video depicting a complex dynamic scene. By representing a dynamic scene within a volumetric IBR framework, our approach overcomes limitations of recent methods that cannot model long videos with complex camera and object motion. We have shown that our method can synthesize photo-realistic novel views from in-the-wild dynamic videos, and can achieve significant improvements over prior state-of-the-art methods on the dynamic scene benchmarks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Acknowledgements. Thanks to Andrew Liu, Richard Bowen and Lucy Chai for the fruitful discussions, and thanks to Rick Szeliski and Ricardo Martin-Brualla for helpful proofreading." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4280" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.184 + ], + "angle": 0, + "content": "[1] Aayush Bansal, Minh Vo, Yaser Sheikh, Deva Ramanan, and Srinivasa Narasimhan. 4D visualization of dynamic events from unconstrained multi-view videos. In Proc. Computer Vision and Pattern Recognition (CVPR), pages 5366-5375, 2020." + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.187, + 0.472, + 0.243 + ], + "angle": 0, + "content": "[2] Jonathan T Barron, Ben Mildenhall, Dor Verbin, Pratul P Srinivasan, and Peter Hedman. 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Recent methods for synthesizing novel views from monocular videos of dynamic scenes-like HyperNeRF [50] and NSFF [35]–struggle to render high-quality views from long videos featuring complex camera and scene motion. We present a new approach that addresses these limitations, illustrated above via an application to 6DoF video stabilization, where we apply our approach and prior methods on a 30-second, shaky video clip, and compare novel views rendered along a smoothed camera path (left). On a dynamic scenes dataset (right) [75], our approach significantly improves rendering fidelity, as indicated by synthesized images and LPIPS errors computed on pixels corresponding to moving objects (yellow numbers). Please see the supplementary video for full results. + +![](images/0f605202fa0409d18adf9ef3673301e5e09a28d5f1dc1758e9d78287c3b365b3.jpg) + +# Abstract + +We address the problem of synthesizing novel views from a monocular video depicting a complex dynamic scene. State-of-the-art methods based on temporally varying Neural Radiance Fields (aka dynamic NeRFs) have shown impressive results on this task. However, for long videos with complex object motions and uncontrolled camera trajectories, these methods can produce blurry or inaccurate renderings, hampering their use in real-world applications. Instead of encoding the entire dynamic scene within the weights of MLPs, we present a new approach that addresses these limitations by adopting a volumetric image-based rendering framework that synthesizes new viewpoints by aggregating features from nearby views in a scene motion-aware manner. Our system retains the advantages of prior methods in its ability to model complex scenes and view-dependent effects, but also enables synthesizing photo-realistic novel views from long videos featuring complex scene dynamics with unconstrained camera trajectories. We demonstrate signifi + +cant improvements over state-of-the-art methods on dynamic scene datasets, and also apply our approach to in-the-wild videos with challenging camera and object motion, where prior methods fail to produce high-quality renderings. + +# 1. Introduction + +Computer vision methods can now produce free-viewpoint renderings of static 3D scenes with spectacular quality. What about moving scenes, like those featuring people or pets? Novel view synthesis from a monocular video of a dynamic scene is a much more challenging dynamic scene reconstruction problem. Recent work has made progress towards synthesizing novel views in both space and time, thanks to new time-varying neural volumetric representations like HyperNeRF [50] and Neural Scene Flow Fields (NSFF) [35], which encode spatiotemporally varying scene content volumetrically within a coordinate-based multi-layer perceptron (MLP). + +However, these dynamic NeRF methods have limitations + +that prevent their application to casual, in-the-wild videos. Local scene flow-based methods like NSFF struggle to scale to longer input videos captured with unconstrained camera motions: the NSFF paper only claims good performance for 1-second, forward-facing videos [35]. Methods like HyperNeRF that construct a canonical model are mostly constrained to object-centric scenes with controlled camera paths, and can fail on scenes with complex object motion. + +In this work, we present a new approach that is scalable to dynamic videos captured with 1) long time duration, 2) unbounded scenes, 3) uncontrolled camera trajectories, and 4) fast and complex object motion. Our approach retains the advantages of volumetric scene representations that can model intricate scene geometry with view-dependent effects, while significantly improving rendering fidelity for both static and dynamic scene content compared to recent methods [35, 50], as illustrated in Fig. 1. + +We take inspiration from recent methods for rendering static scenes that synthesize novel images by aggregating local image features from nearby views along epipolar lines [39, 64, 70]. However, scenes that are in motion violate the epipolar constraints assumed by those methods. We instead propose to aggregate multi-view image features in scene motion-adjusted ray space, which allows us to correctly reason about spatio-temporally varying geometry and appearance. + +We also encountered many efficiency and robustness challenges in scaling up aggregation-based methods to dynamic scenes. To efficiently model scene motion across multiple views, we model this motion using motion trajectory fields that span multiple frames, represented with learned basis functions. Furthermore, to achieve temporal coherence in our dynamic scene reconstruction, we introduce a new temporal photometric loss that operates in motion-adjusted ray space. Finally, to improve the quality of novel views, we propose to factor the scene into static and dynamic components through a new IBR-based motion segmentation technique within a Bayesian learning framework. + +On two dynamic scene benchmarks, we show that our approach can render highly detailed scene content and significantly improves upon the state-of-the-art, leading to an average reduction in LPIPS errors by over $50\%$ both across entire scenes, as well as on regions corresponding to dynamic objects. We also show that our method can be applied to inthe-wild videos with long duration, complex scene motion, and uncontrolled camera trajectories, where prior state-ofthe-art methods fail to produce high quality renderings. We hope that our work advances the applicability of dynamic view synthesis methods to real-world videos. + +# 2. Related Work + +Novel view synthesis. Classic image-based rendering (IBR) methods synthesize novel views by integrating pixel + +information from input images [58], and can be categorized according to their dependence on explicit geometry. Light field or lumigraph rendering methods [9, 21, 26, 32] generate new views by filtering and interpolating sampled rays, without use of explicit geometric models. To handle sparser input views, many approaches [7, 14, 18, 23, 24, 26, 30, 52, 54, 55] leverage pre-computed proxy geometry such as depth maps or meshes to render novel views. + +Recently, neural representations have demonstrated high-quality novel view synthesis [12, 17, 38, 40, 46, 48, 59-62, 72, 81]. In particular, Neural Radiance Fields (NeRF) [46] achieves an unprecedented level of fidelity by encoding continuous scene radiance fields within multi-layer perceptrons (MLPs). Among all methods building on NeRF, IBRNet [70] is the most relevant to our work. IBRNet combines classical IBR techniques with volume rendering to produce a generalized IBR module that can render high-quality views without per-scene optimization. Our work extends this kind of volumetric IBR framework designed for static scenes [11, 64, 70] to more challenging dynamic scenes. Note that our focus is on synthesizing higher-quality novel views for long videos with complex camera and object motion, rather than on generalization across scenes. + +Dynamic scene view synthesis. Our work is related to geometric reconstruction of dynamic scenes from RGBD [5, 15, 25, 47, 68, 83] or monocular videos [31, 44, 78, 80]. However, depth- or mesh-based representations struggle to model complex geometry and view-dependent effects. + +Most prior work on novel view synthesis for dynamic scenes requires multiple synchronized input videos [1, 3, 6, 27, 33, 63, 69, 76, 82], limiting their real-world applicability. Some methods [8, 13, 22, 51, 71] use domain knowledge such as template models to achieve high-quality results, but are restricted to specific categories [41, 56]. More recently, many works propose to synthesize novel views of dynamic scenes from a single camera. Yoon et al. [75] render novel views through explicit warping using depth maps obtained via single-view depth and multi-view stereo. However, this method fails to model complex scene geometry and to fill in realistic and consistent content at disocclusions. With advances in neural rendering, NeRF-based dynamic view synthesis methods have shown state-of-the-art results [16, 35, 53, 66, 74]. Some approaches, such as Nerfies [49] and HyperNeRF [50], represent scenes using a deformation field mapping each local observation to a canonical scene representation. These deformations are conditioned on time [53] or a per-frame latent code [49, 50, 66], and are parameterized as translations [53, 66] or rigid body motion fields [49, 50]. These methods can handle long videos, but are mostly limited to object-centric scenes with relatively small object motion and controlled camera paths. Other methods represent scenes as time-varying NeRFs [19, 20, 35, 67, 74]. In particular, NSFF uses neural scene flow fields that can + +![](images/87c90d518b08baa1383f2d6cf463dadae9fce64a13fea8dd9ce1256a36366b0b.jpg) +Figure 2. Rendering via motion-adjusted multi-view feature aggregation. Given a sampled location $\mathbf{x}$ at time $i$ along a target ray $\mathbf{r}$ , we estimate its motion trajectory, which determines the 3D correspondence of $\mathbf{x}$ at nearby time $j \in \mathcal{N}(i)$ , denoted $\mathbf{x}_{i \rightarrow j}$ . Each warped point is then projected into its corresponding source view. Image features $\mathbf{f}_j$ extracted along the projected curves are aggregated and fed to the ray transformer with time embedding $\gamma(i)$ , producing per-sample color and density $(\mathbf{c}_i, \sigma_i)$ . The final pixel color $\hat{\mathbf{C}}_i$ is then synthesized by volume rendering $(\mathbf{c}_i, \sigma_i)$ along $\mathbf{r}$ . + +capture fast and complex 3D scene motion for in-the-wild videos [35]. However, this method only works well for short (1-2 second), forward-facing videos. + +# 3. Dynamic Image-Based Rendering + +Given a monocular video of a dynamic scene with frames $(I_1, I_2, \ldots, I_N)$ and known camera parameters $(\mathbf{P}_1, \mathbf{P}_2, \ldots, \mathbf{P}_N)$ , our goal is to synthesize a novel viewpoint at any desired time within the video. Like many other approaches, we train per-video, first optimizing a model to reconstruct the input frames, then using this model to render novel views. + +Rather than encoding 3D color and density directly in the weights of an MLP as in recent dynamic NeRF methods, we integrate classical IBR ideas into a volumetric rendering framework. Compared to explicit surfaces, volumetric representations can more readily model complex scene geometry with view-dependent effects. + +The following sections introduce our methods for scene-motion-adjusted multi-view feature aggregation (Sec. 3.1), and enforcing temporal consistency via cross-time rendering in motion-adjusted ray space (Sec. 3.2). Our full system combines a static model and a dynamic model to produce a color at each pixel. Accurate scene factorization is achieved via segmentation masks derived from a separately trained motion segmentation module within a Bayesian learning framework (Sec. 3.3). + +# 3.1. Motion-adjusted feature aggregation + +We synthesize new views by aggregating features extracted from temporally nearby source views. To render an image at time $i$ , we first identify source views $I_{j}$ within a temporal radius $r$ frames of $i$ , $j \in \mathcal{N}(i) = [i - r, i + r]$ . For each source view, we extract a 2D feature map $F_{i}$ through a + +shared convolutional encoder network to form an input tuple $\{I_j,\mathbf{P}_j,F_j\}$ + +To predict the color and density of each point sampled along a target ray $\mathbf{r}$ , we must aggregate source view features while accounting for scene motion. For a static scene, points along a target ray will lie along a corresponding epipolar line in a neighboring source view, hence we can aggregate potential correspondences by simply sampling along neighboring epipolar lines [64, 70]. However, moving scene elements violate epipolar constraints, leading to inconsistent feature aggregation if motion is not accounted for. Hence, we perform motion-adjusted feature aggregation, as shown in Fig. 3. To determine correspondence in dynamic scenes, one straightforward idea is to estimate a scene flow field via an MLP [35] to determine a given point's motion-adjusted 3D location at a nearby time. However, this strategy is computational infeasible in a volumetric IBR framework due to recursive unrolling of the MLPs. + +Motion trajectory fields. Instead, we represent scene motion using motion trajectory fields described in terms of learned basis functions. For a given 3D point $\mathbf{x}$ along target ray $\mathbf{r}$ at time $i$ , we encode its trajectory coefficients with an MLP $G_{\mathrm{MT}}$ : + +$$ +\left\{\phi_ {i} ^ {l} (\mathbf {x}) \right\} _ {l = 1} ^ {L} = G _ {\mathrm {M T}} (\gamma (\mathbf {x}), \gamma (i)), \tag {1} +$$ + +where $\phi_i^l\in \mathcal{R}^3$ are basis coefficients (with separate coefficients for $x,y,$ and $z$ using the motion basis described below) and $\gamma$ denotes positional encoding. We choose $L = 6$ bases and 16 linearly increasing frequencies for the encoding $\gamma$ , based on the assumption that scene motion tends to be low frequency [80]. + +We also introduce a global learnable motion basis $\{h_i^l\}_{l = 1}^L,h_i^l\in \mathcal{R}$ , spanning every time step $i$ of the input video, which is optimized jointly with the MLP. The motion trajectory of $\mathbf{x}$ is then defined as $\Gamma_{\mathbf{x},i}(j) = \sum_{l = 1}^{L}h_{j}^{l}\phi_{i}^{l}(\mathbf{x})$ and thus, the relative displacement between $\mathbf{x}$ and its 3D correspondence $\mathbf{x}_{i\rightarrow j}$ at time $j$ is computed as + +$$ +\Delta_ {\mathbf {x}, i} (j) = \Gamma_ {\mathbf {x}, i} (j) - \Gamma_ {\mathbf {x}, i} (i). \tag {2} +$$ + +With this motion trajectory representation, finding 3D correspondences for a query point $\mathbf{x}$ in neighboring views requires just a single MLP query, allowing efficient multi-view feature aggregation within our volume rendering framework. We initialize the basis $\{h_i^l\}_{l = 1}^L$ with the DCT basis as proposed by Wang et al. [67], but fine-tune it along with other components during optimization, since we observe that a fixed DCT basis can fail to model a wide range of real-world motions (see third column of Fig. 4). + +Using the estimated motion trajectory of $\mathbf{x}$ at time $i$ , we denote $\mathbf{x}$ 's corresponding 3D point at time $j$ as $\mathbf{x}_{i\rightarrow j} = \mathbf{x} + \Delta_{\mathbf{x},i}(j)$ . We project each warped point $\mathbf{x}_{i\rightarrow j}$ into its source view $I_{j}$ using camera parameters $\mathbf{P}_j$ , and extract color and feature vector $\mathbf{f}_j$ at the projected 2D pixel location. + +![](images/8b9233be694e197a6021b471b2f2d1c3667ff80d110475c573bc5c9a6e2b9575.jpg) +Figure 3. Temporal consistency via cross-time rendering. To enforce temporal consistency in a dynamic reconstruction, we render each frame $I_{i}$ using the scene model from a nearby time $j$ , which we call cross-time rendering. A ray $\mathbf{r}$ from image $i$ is instead rendered using a curved ray $\mathbf{r}_{i\rightarrow j}$ , i.e., $\mathbf{r}$ warped to time $j$ . That is, having computed the motion-adjusted point $\mathbf{x}_{i\rightarrow j} = \mathbf{x} + \Delta_{\mathbf{x},i}(j)$ at nearby time $j$ from every sampled location along $\mathbf{r}$ , we query $\mathbf{x}_{i\rightarrow j}$ and time $j$ via the MLP to predict its motion trajectory $\Gamma_{\mathbf{x}_{i\rightarrow j},j}$ , along which we aggregate image features $\mathbf{f}_k$ extracted from source views within time $k\in \mathcal{N}(j)$ . The aggregated features along $\mathbf{r}_{i\rightarrow j}$ are fed to the ray transformer with time embedding $\gamma (j)$ to produce per-sample color and density $(\mathbf{c}_j,\sigma_j)$ at time $j$ . A pixel color $\hat{\mathbf{C}}_{j\rightarrow i}$ is computed by volume rendering $(\mathbf{c}_j,\sigma_j)$ , and then compared to the ground truth color $\mathbf{C}_i$ to form a reconstruction loss $\mathcal{L}_{\mathrm{pho}}$ . + +The resulting set of source features across neighbor views $j$ is fed to a shared MLP whose output features are aggregated through weighted average pooling [70] to produce a single feature vector at each 3D sample point along ray $\mathbf{r}$ . A ray transformer network with time embedding $\gamma(i)$ then processes the sequence of aggregated features along the ray to predict per-sample colors and densities $(\mathbf{c}_i, \sigma_i)$ (see Fig. 2). We then use standard NeRF volume rendering [4] to obtain a final pixel color $\hat{\mathbf{C}}_i(\mathbf{r})$ for the ray from this sequence of colors and densities. + +# 3.2. Cross-time rendering for temporal consistency + +If we optimize our dynamic scene representation by comparing $\hat{\mathbf{C}}_i$ with $\mathbf{C}_i$ alone, the representation might overfit to the input images: it might perfectly reconstruct those views, but fail to render correct novel views. This can happen because the representation has the capacity to reconstruct completely separate models for each time instance, without utilizing or accurately reconstructing scene motion. Therefore, to recover a consistent scene with physically plausible motion, we enforce temporal coherence of the scene representation. One way to define temporal coherence in this context is that the scene at two neighboring times $i$ and $j$ should be consistent when taking scene motion into account [19, 35, 67]. + +In particular, we enforce temporal photometric consistency in our optimized representation via cross-time rendering in motion-adjusted ray space, as shown in Fig. 3. The + +idea is to render a view at time $i$ but via some nearby time $j$ , which we refer to as cross-time rendering. For each nearby time $j \in \mathcal{N}(i)$ , rather than directly using points $\mathbf{x}$ along ray $\mathbf{r}$ , we consider the points $\mathbf{x}_{i \to j}$ along motion-adjusted ray $\mathbf{r}_{i \to j}$ and treat them as if they lie along a ray at time $j$ . + +Specifically, having computed the motion-adjusted points $\mathbf{x}_{i\rightarrow j}$ , we query the MLP to predict the coefficients of new trajectories $\{\phi_j^l (\mathbf{x}_{i\rightarrow j})_{l = 1}^L = G_{\mathrm{MT}}(\mathbf{x}_{i\rightarrow j},\gamma (j))$ , and use these to compute corresponding 3D points $(\mathbf{x}_{i\rightarrow j})_{j\rightarrow k}$ for images $k$ in the temporal window $\mathcal{N}(j)$ , using Eq. 2. These new 3D correspondences are then used to render a pixel color exactly as described for a "straight" ray $\mathbf{r}_i$ in Sec. 3.1, except now along the curved, motion-adjusted ray $\mathbf{r}_{i\rightarrow j}$ . That is, each point $(\mathbf{x}_{i\rightarrow j})_{j\rightarrow k}$ is projected into its source view $I_{k}$ and feature maps $F_{k}$ with camera parameters $\mathbf{P}_k$ to extract an RGB color and image feature $\mathbf{f}_k$ , and then these features are aggregated and input to the ray transformer with the time embedding $\gamma (j)$ . The result is a sequence of colors and densities $(\mathbf{c}_j,\sigma_j)$ along $\mathbf{r}_{i\rightarrow j}$ at time $j$ , which can be composited through volume rendering to form a color $\hat{\mathbf{C}}_{j\rightarrow i}$ . + +We can then compare $\hat{\mathbf{C}}_{j\rightarrow i}(\mathbf{r})$ with the target pixel $\mathbf{C}_i(\mathbf{r})$ via a motion-disocclusion-aware RGB reconstruction loss: + +$$ +\mathcal {L} _ {\mathrm {p h o}} = \sum_ {\mathbf {r}} \sum_ {j \in \mathcal {N} (i)} \hat {\mathbf {W}} _ {j \rightarrow i} (\mathbf {r}) \rho \left(\mathbf {C} _ {i} (\mathbf {r}), \hat {\mathbf {C}} _ {j \rightarrow i} (\mathbf {r})\right). \tag {3} +$$ + +We use a generalized Charbonnier loss [10] for the RGB loss $\rho$ . $\hat{\mathbf{W}}_{j\rightarrow i}(\mathbf{r})$ is a motion disocclusion weight computed by the difference of accumulated alpha weights between time $i$ and $j$ to address the motion disocclusion ambiguity described by NSFF [35] (see supplement for more details). Note that when $j = i$ , there is no scene motion-induced displacement, meaning $\hat{\mathbf{C}}_{j\rightarrow i} = \hat{\mathbf{C}}_i$ and no disocclusion weights are involved ( $\hat{\mathbf{W}}_{j\rightarrow i} = 1$ ). We show a comparison between our method with and without enforcing temporal consistency in the first column of Fig. 4. + +# 3.3. Combining static and dynamic models + +As observed in NSFF, synthesizing novel views using a small temporal window is insufficient to recover complete and high-quality content for static scene regions, since the contents may only be observed in spatially distant frames due to uncontrolled camera paths. Therefore, we follow the ideas of NSFF [35], and model the entire scene using two separate representations. Dynamic content $(\mathbf{c}_i,\sigma_i)$ is represented with a time-varying model as above (used for cross-time rendering during optimization). Static content $(\mathbf{c},\sigma)$ is represented with a time-invariant model, which renders in the same way as the time-varying model, but aggregates multiview features without scene motion adjustment (i.e., along epipolar lines). + +The dynamic and static predictions are combined and rendered to a single output color $\hat{\mathbf{C}}_i^{\mathrm{full}}$ (or $\hat{\mathbf{C}}_{j\rightarrow i}^{\mathrm{full}}$ during cross-time rendering) using the method for combining static and + +![](images/f00d932c889262daa8dee0efa234b05c984ee7804d3d5125c49942bab306af35.jpg) +(a) w/o TC + +![](images/109b70af9de32f69344a60a0164ac61035f3413b4851684825b4783a82590249.jpg) +(b) w/ SF + +![](images/9e788bb74bcafb3ba480a5e947ce50928ed63bb4ec66b9e5e303ed13eddbac35.jpg) +(c) w/ DCT basis + +![](images/dfd9e1a19fc0d530fe3ed4be67f11feca56c044d853878d5203c92aa72742768.jpg) +(d) Ours +Figure 4. Qualitative ablations. From left to right, we show rendered novel views (top) and depths (bottom) from our system (a) without enforcing temporal consistency, (b) aggregating image features with scene flow fields instead of motion trajectories, (c) representing motion trajectory with a fixed DCT basis instead of a learned one, and (d) with full configuration. Simpler configurations significantly degrade rendering quality as indicated by PSNR calculated over the regions of moving objects. + +transient models of NeRF-W [45]. Each model's color and density estimates can also be rendered separately, giving color $\hat{\mathbf{C}}^{\mathrm{st}}$ for static content and $\hat{\mathbf{C}}_i^{\mathrm{dy}}$ for dynamic content. + +When combining the two representations, we rewrite the photometric consistency term in Eq. 3 as a loss comparing $\hat{\mathbf{C}}_{j\rightarrow i}^{\mathrm{full}}(\mathbf{r})$ with target pixel $\mathbf{C}_i(\mathbf{r})$ : + +$$ +\mathcal {L} _ {\mathrm {p h o}} = \sum_ {\mathbf {r}} \sum_ {j \in \mathcal {N} (i)} \hat {\mathbf {W}} _ {j \rightarrow i} (\mathbf {r}) \rho \left(\mathbf {C} _ {i} (\mathbf {r}), \hat {\mathbf {C}} _ {j \rightarrow i} ^ {\text {f u l l}} (\mathbf {r})\right) \tag {4} +$$ + +Image-based motion segmentation. In our framework, we observed that without any initialization, scene factorization tends to be dominated by either the time-invariant or the time-varying representation, a phenomena also observed in recent methods [28, 42]. To facilitate factorization, Gao et al. [19] initialize their system using masks from semantic segmentation, relying on the assumption that all moving objects are captured by a set of candidate semantic segmentation labels, and segmentation masks are temporally accurate. However, these assumptions do not hold in many real-world scenarios, as observed by Zhang et al. [79]. Instead, we propose a new motion segmentation module that produces segmentation masks for supervising our main two-component scene representation. Our idea is inspired by the Bayesian learning techniques proposed in recent work [45, 79], but integrated into a volumetric IBR representation for dynamic videos. + +In particular, before training our main two-component scene representation, we jointly train two lightweight models to obtain a motion segmentation mask $M_{i}$ for each input frame $I_{i}$ . We model static scene content with an IBR-Net [70] that renders a pixel color $\hat{\mathbf{B}}^{\mathrm{st}}$ using volume rendering along each ray via feature aggregation along epipolar lines from nearby source views without considering scene + +![](images/4293e6e7f9e288c64fae755d71a7b6b757cfd16360545161584a7bf417145905.jpg) + +![](images/bd50b74c6baddecfcc2d12220e3e1018435063ce76898d035cf950fbf944d4c5.jpg) +Figure 5. Motion segmentation. We show full rendering $\hat{\mathbf{B}}_i^{\mathrm{full}}$ (top) and motion segmentation overlaid with rendered dynamic content $\alpha_i^{\mathrm{dy}}\odot \hat{\mathbf{B}}_i^{\mathrm{dy}}$ (bottom). Our approach segments challenging dynamic elements such as the moving shadow, swing, and swaying bushes. + +![](images/8b3b5c0611f6cb555a3f49eb3a63568b2dfc46ab9a257ba177719b17518de73b.jpg) + +![](images/2d5474edfc09460de47b49677a3ae598b08daed948249eb68f2f9e4594a6c004.jpg) + +![](images/2c5c5fc3033adf98524a590aa412bc396df3a23e3814ef563b46501a626c3ed0.jpg) + +![](images/ab65b0e5894ded0bcd7dc2bd4b29652abd673ab3ea3583c80cd24a42a1617bf5.jpg) + +motion; we model dynamic scene content with a 2D convolutional encoder-decoder network $D$ , which predicts a 2D opacity map $\alpha_{i}^{\mathrm{dy}}$ , confidence map $\beta_{i}^{\mathrm{dy}}$ , and RGB image $\hat{\mathbf{B}}_{i}^{\mathrm{dy}}$ from an input frame: + +$$ +\hat {\mathbf {B}} _ {i} ^ {\mathrm {d y}}, \boldsymbol {\alpha} _ {i} ^ {\mathrm {d y}}, \boldsymbol {\beta} _ {i} ^ {\mathrm {d y}} = D (I _ {i}). \tag {5} +$$ + +The full reconstructed image is then composited pixelwise from the outputs of the two models: + +$$ +\hat {\mathbf {B}} _ {i} ^ {\text {f u l l}} (\mathbf {r}) = \boldsymbol {\alpha} _ {i} ^ {\mathrm {d y}} (\mathbf {r}) \hat {\mathbf {B}} _ {i} ^ {\mathrm {d y}} (\mathbf {r}) + (1 - \boldsymbol {\alpha} _ {i} ^ {\mathrm {d y}} (\mathbf {r})) \hat {\mathbf {B}} ^ {\mathrm {s t}} (\mathbf {r}). \tag {6} +$$ + +To segment moving objects, we assume the observed pixel color is uncertain in a heteroscedastic aleatoric manner, and model the observations in the video with a Cauchy distribution with time dependent confidence $\beta_{i}^{\mathrm{dy}}$ . By taking the negative log-likelihood of the observations, our segmentation loss is written as a weighted reconstruction loss: + +$$ +\mathcal {L} _ {\mathrm {s e g}} = \sum_ {\mathbf {r}} \log \left(\beta_ {i} ^ {\mathrm {d y}} (\mathbf {r}) + \frac {\left| \left| \hat {\mathbf {B}} _ {i} ^ {\text {f u l l}} (\mathbf {r}) - \mathbf {C} _ {i} (\mathbf {r}) \right| \right| ^ {2}}{\beta_ {i} ^ {\mathrm {d y}} (\mathbf {r})}\right). \tag {7} +$$ + +By optimizing the two models using Eq. 7, we obtain a motion segmentation mask $M_{i}$ by thresholding $\alpha_{i}^{\mathrm{dy}}$ at 0.5. We do not require an alpha regularization loss as in NeRF-W [45] to avoid degeneracies, since we naturally include such an inductive basis by excluding skip connections from network $D$ , which leads $D$ to converge more slowly than the static IBR model. We show our estimated motion segmentation masks overlaid on input images in Fig. 5. + +Supervision with segmentation masks. We initialize our main time-varying and time-invariant models with masks $M_{i}$ as in Omnimatte [43], by applying a reconstruction loss to renderings from the time-varying model in dynamic regions, and to renderings from the time-invariant model in static regions: + +$$ +\begin{array}{l} \mathcal {L} _ {\text {m a s k}} = \sum_ {\mathbf {r}} (1 - M _ {i}) (\mathbf {r}) \rho \left(\hat {\mathbf {C}} ^ {\mathrm {s t}} (\mathbf {r}), \mathbf {C} _ {i} (\mathbf {r})\right) \\ + \sum_ {\mathbf {r}} M _ {i} (\mathbf {r}) \rho \left(\hat {\mathbf {C}} _ {i} ^ {\mathrm {d y}} (\mathbf {r}), \mathbf {C} _ {i} (\mathbf {r})\right) \tag {8} \\ \end{array} +$$ + +We perform morphological erosion and dilation on $M_{i}$ to obtain masks of dynamic and static regions respectively in order to turn off the loss near mask boundaries. We supervise the system with $\mathcal{L}_{\mathrm{mask}}$ and decay the weights by a factor of 5 for dynamic regions every 50K optimization steps. + +# 3.4. Regularization + +As noted in prior work, monocular reconstruction of complex dynamic scenes is highly ill-posed, and using photometric consistency alone is insufficient to avoid bad local minima during optimization [19, 35]. Therefore, we adopt regularization schemes used in prior work [2, 35, 73, 75], which consist of three main parts $\mathcal{L}_{\mathrm{reg}} = \mathcal{L}_{\mathrm{data}} + \mathcal{L}_{\mathrm{MT}} + \mathcal{L}_{\mathrm{cpt}}$ . $\mathcal{L}_{\mathrm{data}}$ is a data-driven term consisting of $\ell_{1}$ monocular depth and optical flow consistency priors using the estimates from Zhang et al. [80] and RAFT [65]. $\mathcal{L}_{\mathrm{MT}}$ is a motion trajectory regularization term that encourages estimated trajectory fields to be cycle-consistent and spatial-temporally smooth. $\mathcal{L}_{\mathrm{cpt}}$ is a compactness prior that encourages the scene decomposition to be binary via an entropy loss, and mitigates floaters through distortion losses [2]. We refer readers to the supplement for more details. + +In summary, the final combined loss used to optimize our main representation for space-time view synthesis is: + +$$ +\mathcal {L} = \mathcal {L} _ {\text {p h o}} + \mathcal {L} _ {\text {m a s k}} + \mathcal {L} _ {\text {r e g}}. \tag {9} +$$ + +# 4. Implementation details + +Data. We conduct numerical evaluations on the Nvidia Dynamic Scene Dataset [75] and UCSD Dynamic Scenes Dataset [37]. Each dataset consists of eight forward-facing dynamic scenes recorded by synchronized multi-view cameras. We follow prior work [35] to derive a monocular video from each sequence, where each video contains $100\sim 250$ frames. We removed frames that lack large regions of moving objects. We follow the protocol from prior work [35] that uses held-out images per time instance for evaluation. We also tested the methods on in-the-wild monocular videos, which feature more challenging camera and object motions [20]. + +View selection. For the time-varying, dynamic model we use a frame window radius of $r = 3$ for all experiments. For the time-invariant model representing static scene content, we use separate strategies for the dynamic scenes benchmarks and for in-the-wild videos. For the benchmarks, where camera viewpoints are located at discrete camera rig locations, we choose all nearby distinct viewpoints whose timestep is within 12 frames of the target time. For in-the-wild videos, naively choosing the nearest source views can lead to poor reconstruction due to insufficient camera baseline. Thus, to ensure that for any rendered pixel we have sufficient source views for computing its color, we select source views from distant frames. If we wish to select $N^{\mathrm{vs}}$ source views for the time-invariant model, we sub-sample every $\frac{2r_{\mathrm{max}}}{N^{\mathrm{vs}}}$ frames from the input video to build a candidate pool, where for a given target time $i$ , we only search source views within $[i - r_{\mathrm{max}}, i + r_{\mathrm{max}}]$ frames. We estimate $r_{\mathrm{max}}^{\mathrm{max}}$ using the method of Li et al. [34] based on SfM point可视ibility and camera relative baseline. We then construct a + +
MethodsFullDynamic Only
SSIM↑PSNR↑LPIPS↓SSIM↑PSNR↑LPIPS↓
Nerfies [49]0.60920.640.2040.45517.350.258
HyperNeRF [50]0.65420.900.1820.44617.560.242
DVS [19]0.92127.440.0700.77822.630.144
NSFF [35]0.92728.900.0620.78323.080.159
Ours0.95730.910.0270.82624.310.062
+ +Table 1. Quantitative evaluation on the Nvidia dataset [75]. + +final set of source views for the model by choosing the top $N^{\mathrm{vs}}$ frames in the candidate pool that are the closest to the target view in terms of camera baseline. We set $N^{\mathrm{vs}} = 16$ . + +Global spatial coordinate embedding With local image feature aggregation alone, it is hard to determine density accurately on non-surface or occluded surface points due to inconsistent features from different source views, as described in NeuRay [39]. Therefore, to improve global reasoning for density prediction, we append a global spatial coordinate embedding as an input to the ray transformer, in addition to the time embedding, similar to the ideas from [64]. Please see supplement for more details. + +Handling degeneracy through virtual views. Prior work [35] observed that optimization can converge to bad local minimal if camera and object motions are close to colinear, or object motions are too fast to track. Inspired by [36], we synthesize images at eight randomly sampled nearby viewpoints for every input via depths estimated by [80]. During rendering, we randomly sample a virtual view as additional source image. We only apply this technique to in-the-wild videos since it improves optimization stability and rendering quality for such inputs, whereas we don't observe improvement on the benchmarks due to disentangled camera-object motions as described by [20]. + +Time interpolation. Our approach also allows for time interpolation by performing scene motion-based splatting, as introduced by NSFF [35]. To render at a specified target fractional time, we predict the volumetric density and color at two nearby input times by aggregating local image features from their corresponding set of source views. The predicted color and density are then splatted and linearly blended via the scene flow derived from our motion trajectories, and weighted according to the target fractional time index. + +Setup. We estimate camera poses using COLMAP [57]. For each ray, we use a coarse-to-fine sampling strategy with 128 per-ray samples as in Wang et al. [70]. A separate model is trained from scratch for each scene using the Adam optimizer [29]. The network architecture for two main representations is a variant of that of IBRNet [70]. We reconstruct the entire scene in Euclidean space without special scene parameterization. Optimizing a full system on a 10 second video takes around two days using 8 Nvidia A100s, and rendering takes roughly 20 seconds for a $768 \times 432$ frame. We + +![](images/3d776eba96f1803c797b21b2807ece60d3cf77bfe48be57fefc53ddb3c199c6c.jpg) +Our rendered views + +![](images/593df20c052cd13a6a061df9745ee2bc9de0aec5ad036c67c24a13158ee22e02.jpg) +DVS + +![](images/54a68978a082babcb7b4bc5f0e0d03de32db745cee26c9f52c0db53b5ae981de.jpg) +HyperNeRF + +![](images/e4f452290da38fe2bd13ef41f4b52b39e01e91e0fe13b0bcaa08498db18a67d1.jpg) +NSFF +Figure 6. Qualitative comparisons on the Nvidia dataset [75]. + +![](images/74b19900d2dc88d78b363e564d081f2f8156bde25b05538f4ed7598a238abc1a.jpg) +Ours + +![](images/de37927ee5ffbf2bc82eb0f52b89928096d6b978f9b584b394debc7922cff216.jpg) +GT + +
MethodsFullDynamic Only
SSIM↑PSNR↑LPIPS↓SSIM↑PSNR↑LPIPS↓
Nerfies [49]0.82324.320.0960.59518.450.234
HyperNeRF [50]0.85925.100.0950.61819.260.212
DVS [19]0.94330.640.0750.86626.570.096
NSFF [35]0.95231.750.0340.85125.830.115
Ours0.98336.470.0140.90928.010.042
+ +Table 2. Quantitative evaluation on the UCSD dataset [37]. + +refer readers to the supplemental material for network architectures, hyper-parameters setting, and additional details. + +# 5. Evaluation + +# 5.1. Baselines and error metrics + +We compare our approach to state-of-the-art monocular view synthesis methods. Specifically, we compare to three recent canonical space-based methods, Nerfies [49], and HyperNeRF [50], and to two scene flow-based methods, NSFF [35] and Dynamic View Synthesis (DVS) from Gao et al. [19]. For fair comparisons, we use the same depth, optical flow and motion segmentation masks used for our approach as inputs to other methods. + +Following prior work [35], we report the rendering quality of each method with three standard error metrics: peak signal-to-noise ratio (PSNR), structural similarity (SSIM), and perceptual similarity via LPIPS [77], and calculate errors both over the entire scene (Full) and restricted to moving regions (Dynamic Only). + +# 5.2.Quantitative evaluation + +Quantitative results on the two benchmark datasets are shown in Table 1 and Table 2. Our approach significantly improves over prior state-of-the-art methods in terms of all error metrics. Notably, our approach improves PSNR over entire scene upon the second best methods by 2dB and 4dB on each of the two datasets. Our approach also reduces LPIPS error, a major indicator of perceptual quality compared with real images [77], by over $50\%$ . These results suggest that our framework is much more effective at recovering highly detailed scene contents. + +![](images/8d010bf52c01f35cffb791746740e39432e449402f60ccf0046c930b35030ab5.jpg) +Our rendered views +Figure 7. Qualitative comparisons on the UCSD dataset [37]. + +![](images/ff59b50d98d0184f5cfaf8254f4af5d228b4334a205379fc820f084edcadc8c7.jpg) +DVS + +![](images/47a517a517e98b78db2e93800f0b63091e03287affb5961ff81e39c77ed3c474.jpg) +HyperNeRF + +![](images/b3e8e6718a46b39ee11be7b34b1c4ab8c9d9135b313b4657310c49ad0cb7b52b.jpg) +NSFF + +![](images/c2a9e6be3f8b2b9cc71ed547d21fce4985d230e5e47b35bf13908a9b680a6947.jpg) +Ours + +![](images/6cd332f745c2acb1d1fe83a06d43fac2e4360e72710b07280bb8776d884f5d89.jpg) +GT + +Ablation study. We conduct an ablation study on the Nvidia Dynamic Scene Dataset to validate the effectiveness of our various proposed system components. We show comparisons between our full system and variants in Tab. 3: A) baseline IBRNet [70] with extra time embedding; B) without enforcing temporal consistency via cross-time rendering; C) using scene flow fields to aggregate image features within one time step; D) predicting multiple 3D scene flow vectors pointing to $2r$ nearby times at each sample; E) without using a time-invariant static scene model; F) without masked reconstruction loss via estimated motion segmentation masks; and G) without regularization loss. For this ablation study, we train each model with 64 samples per ray. Without our motion trajectory representation and temporal consistency, view synthesis quality degrades significantly as shown in the first three rows of Tab. 3. Integrating a global spatial coordinate embedding further improves rendering quality. Combining static and dynamic models improves quality for static elements, as seen in metrics over full scenes. Finally, removing supervision from motion segmentation or regularization reduces overall rendering quality, demonstrating the value of proposed losses for avoiding bad local minimal during optimization. + +# 5.3. Qualitative evaluation + +Dynamic scenes dataset. We provide qualitative comparisons between our approach and three prior state-of-the-art methods [19, 35, 50] on the test views from two datasets in Fig. 6 and Fig.7. Prior dynamic-NeRF methods have difficulty rendering details of moving objects, as seen in the excessively blurred dynamic content including the texture of balloons, human faces, and clothing. In contrast, our approach synthesizes photo-realistic novel views of both static and dynamic scene content and which are closest to the ground truth images. + +In-the-wild videos. We show qualitative comparisons on in-the-wild footage of complex dynamic scenes. We show comparisons with Dynamic-NeRF based methods in Fig. 8, and Fig. 9 shows comparisons with point cloud rendering using depths [80]. Our approach synthesizes photo-realistic + +![](images/8a0d628d664b461106331167aadfcb36ee07d14e56a2cf0c0c367f7706e61548.jpg) +Input + +![](images/3748e0049fa3f60d3ab0b2c29fe467a2f394770486f57710639cd0b87f926f1d.jpg) +DVS + +![](images/666f28fc07ce48329332469e73a6faea3d937de83d9d5b33de8957fcd1ca4246.jpg) +HyperNeRF +Figure 8. Qualitative comparisons on in-the-wild videos. We show results on 10-second videos of complex dynamic scenes. The leftmost column shows the start and end frames of each video; on the right we show novel views at intermediate times rendered from our approach and prior state-of-the-art methods [19,35,50]. + +![](images/49d02da58f0182bf12b36344f6f16551cad415c7f173e9e219634a1e5c0b8bda.jpg) +NSFF + +![](images/92cd4c156cccb001e58694bba8a13f0e09c4b08f54e11c1b677636931cf41b07.jpg) +Ours + +![](images/2df62ad10ade8370b6c816267cbfa910ac8450c9626d29c0edf41fcbd6103e12.jpg) +Figure 9. From left to right, We show inputs and corresponding novel views rendered from explicit depth warping with Zhang et al. [80], and from our approach. + +
MethodsFullDynamic Only
SSIM↑PSNR↑LPIPS↓SSIM↑PSNR↑LPIPS↓
A) [70]+time0.90525.330.0810.68320.090.122
B) w/o TC0.91127.570.0740.75122.160.104
C) w/ SF0.93529.420.0350.79722.410.095
D) w/ M-SF0.94729.590.0330.81422.970.084
E) w/o static rep.0.91928.190.0470.84024.010.071
F) w/o Lmask0.93029.950.0360.83524.300.063
G) w/o Lreg0.92129.460.0420.79522.190.080
Full0.95730.770.0280.83724.270.066
+ +Table 3. Ablation study on the Nvidia Dataset. See Sec. 5.2 for detailed descriptions of each configuration. + +novel views, whereas prior dynamic-Nerf methods fail to recover high-quality details of both static and moving scene contents, such as the shirt wrinkles and the dog's fur in Fig. 8. On the other hand, explicit depth warping produces holes at regions near disocculusions and out of field of view. We refer readers to the supplementary video for full comparisons. + +# 6. Discussion and conclusion + +Limitations. Our method is limited to relatively small viewpoint changes compared with methods designed for static or quasi-static scene; Our method is not able to handle small fast moving object due to incorrect initial depth and optical flow estimates (left, Fig. 10). In addition, compared to + +![](images/6a5c70a4cb23179dda7b619599307285d93c36e7fbeea198f7d704415474d980.jpg) +Figure 10. Limitations. Our method might fail to model moving thin objects such as moving leash (left). Our method can fail to render dynamic contents only visible in distant frames (middle). The rendered static content can be unrealistic or blank if insufficient source views feature are aggregated for a given pixel (right). + +![](images/d0c2038055b9eff8213e504c62f7355a1bc1ab38dba4f3bfdca32c65cc95a6b2.jpg) + +![](images/f2b4401b5ab9b67c28a5e317844551354d6ac3de52a8e0cd9f5e2e21635b0a54.jpg) + +prior dynamic NeRF methods, the synthesized views are not strictly multi-view consistent, and rendering quality of static content depends on which source views are selected (middle, Fig. 10). Our approach is also sensitive to degenerate motion patterns from in-the-wild videos, in which object and camera motion is mostly colinear, but we show heuristics to handle such cases in the supplemental. Moreover, our method is able to synthesize dynamic contents only appearing at distant time (right, Fig. 10) + +Conclusion. We presented a new approach for space-time view synthesis from a monocular video depicting a complex dynamic scene. By representing a dynamic scene within a volumetric IBR framework, our approach overcomes limitations of recent methods that cannot model long videos with complex camera and object motion. We have shown that our method can synthesize photo-realistic novel views from in-the-wild dynamic videos, and can achieve significant improvements over prior state-of-the-art methods on the dynamic scene benchmarks. + +Acknowledgements. Thanks to Andrew Liu, Richard Bowen and Lucy Chai for the fruitful discussions, and thanks to Rick Szeliski and Ricardo Martin-Brualla for helpful proofreading. + +# References + +[1] Aayush Bansal, Minh Vo, Yaser Sheikh, Deva Ramanan, and Srinivasa Narasimhan. 4D visualization of dynamic events from unconstrained multi-view videos. In Proc. 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Recent methods for synthesizing novel views from monocular videos of dynamic scenes-like HyperNeRF [50] and NSFF [35]–struggle to render high-quality views from long videos featuring complex camera and scene motion. We present a new approach that addresses these limitations, illustrated above via an application to 6DoF video stabilization, where we apply our approach and prior methods on a 30-second, shaky video clip, and compare novel views rendered along a smoothed camera path (left). On a dynamic scenes dataset (right) [75], our approach significantly improves rendering fidelity, as indicated by synthesized images and LPIPS errors computed on pixels corresponding to moving objects (yellow numbers). Please see the supplementary video for full results." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 415, + 219, + 544, + 380 + ], + "blocks": [ + { + "bbox": [ + 415, + 219, + 544, + 380 + ], + "lines": [ + { + "bbox": [ + 415, + 219, + 544, + 380 + ], + "spans": [ + { + "bbox": [ + 415, + 219, + 544, + 380 + ], + "type": "image", + "image_path": "0f605202fa0409d18adf9ef3673301e5e09a28d5f1dc1758e9d78287c3b365b3.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 143, + 466, + 192, + 478 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 466, + 192, + 478 + ], + "spans": [ + { + "bbox": [ + 143, + 466, + 192, + 478 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 498, + 290, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 498, + 290, + 715 + ], + "spans": [ + { + "bbox": [ + 45, + 498, + 290, + 715 + ], + "type": "text", + "content": "We address the problem of synthesizing novel views from a monocular video depicting a complex dynamic scene. State-of-the-art methods based on temporally varying Neural Radiance Fields (aka dynamic NeRFs) have shown impressive results on this task. However, for long videos with complex object motions and uncontrolled camera trajectories, these methods can produce blurry or inaccurate renderings, hampering their use in real-world applications. Instead of encoding the entire dynamic scene within the weights of MLPs, we present a new approach that addresses these limitations by adopting a volumetric image-based rendering framework that synthesizes new viewpoints by aggregating features from nearby views in a scene motion-aware manner. Our system retains the advantages of prior methods in its ability to model complex scenes and view-dependent effects, but also enables synthesizing photo-realistic novel views from long videos featuring complex scene dynamics with unconstrained camera trajectories. We demonstrate signifi" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 467, + 547, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 467, + 547, + 515 + ], + "spans": [ + { + "bbox": [ + 305, + 467, + 547, + 515 + ], + "type": "text", + "content": "cant improvements over state-of-the-art methods on dynamic scene datasets, and also apply our approach to in-the-wild videos with challenging camera and object motion, where prior methods fail to produce high-quality renderings." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 538, + 387, + 551 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 538, + 387, + 551 + ], + "spans": [ + { + "bbox": [ + 306, + 538, + 387, + 551 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 559, + 548, + 702 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 559, + 548, + 702 + ], + "spans": [ + { + "bbox": [ + 304, + 559, + 548, + 702 + ], + "type": "text", + "content": "Computer vision methods can now produce free-viewpoint renderings of static 3D scenes with spectacular quality. What about moving scenes, like those featuring people or pets? Novel view synthesis from a monocular video of a dynamic scene is a much more challenging dynamic scene reconstruction problem. Recent work has made progress towards synthesizing novel views in both space and time, thanks to new time-varying neural volumetric representations like HyperNeRF [50] and Neural Scene Flow Fields (NSFF) [35], which encode spatiotemporally varying scene content volumetrically within a coordinate-based multi-layer perceptron (MLP)." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 317, + 703, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 703, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 317, + 703, + 545, + 714 + ], + "type": "text", + "content": "However, these dynamic NeRF methods have limitations" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "4273" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "content": "that prevent their application to casual, in-the-wild videos. Local scene flow-based methods like NSFF struggle to scale to longer input videos captured with unconstrained camera motions: the NSFF paper only claims good performance for 1-second, forward-facing videos [35]. Methods like HyperNeRF that construct a canonical model are mostly constrained to object-centric scenes with controlled camera paths, and can fail on scenes with complex object motion." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 168, + 289, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 168, + 289, + 275 + ], + "spans": [ + { + "bbox": [ + 46, + 168, + 289, + 275 + ], + "type": "text", + "content": "In this work, we present a new approach that is scalable to dynamic videos captured with 1) long time duration, 2) unbounded scenes, 3) uncontrolled camera trajectories, and 4) fast and complex object motion. Our approach retains the advantages of volumetric scene representations that can model intricate scene geometry with view-dependent effects, while significantly improving rendering fidelity for both static and dynamic scene content compared to recent methods [35, 50], as illustrated in Fig. 1." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 275, + 289, + 382 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 275, + 289, + 382 + ], + "spans": [ + { + "bbox": [ + 46, + 275, + 289, + 382 + ], + "type": "text", + "content": "We take inspiration from recent methods for rendering static scenes that synthesize novel images by aggregating local image features from nearby views along epipolar lines [39, 64, 70]. However, scenes that are in motion violate the epipolar constraints assumed by those methods. We instead propose to aggregate multi-view image features in scene motion-adjusted ray space, which allows us to correctly reason about spatio-temporally varying geometry and appearance." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 384, + 289, + 527 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 384, + 289, + 527 + ], + "spans": [ + { + "bbox": [ + 46, + 384, + 289, + 527 + ], + "type": "text", + "content": "We also encountered many efficiency and robustness challenges in scaling up aggregation-based methods to dynamic scenes. To efficiently model scene motion across multiple views, we model this motion using motion trajectory fields that span multiple frames, represented with learned basis functions. Furthermore, to achieve temporal coherence in our dynamic scene reconstruction, we introduce a new temporal photometric loss that operates in motion-adjusted ray space. Finally, to improve the quality of novel views, we propose to factor the scene into static and dynamic components through a new IBR-based motion segmentation technique within a Bayesian learning framework." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 527, + 289, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 527, + 289, + 658 + ], + "spans": [ + { + "bbox": [ + 46, + 527, + 289, + 658 + ], + "type": "text", + "content": "On two dynamic scene benchmarks, we show that our approach can render highly detailed scene content and significantly improves upon the state-of-the-art, leading to an average reduction in LPIPS errors by over " + }, + { + "bbox": [ + 46, + 527, + 289, + 658 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 527, + 289, + 658 + ], + "type": "text", + "content": " both across entire scenes, as well as on regions corresponding to dynamic objects. We also show that our method can be applied to inthe-wild videos with long duration, complex scene motion, and uncontrolled camera trajectories, where prior state-ofthe-art methods fail to produce high quality renderings. We hope that our work advances the applicability of dynamic view synthesis methods to real-world videos." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 669, + 134, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 669, + 134, + 681 + ], + "spans": [ + { + "bbox": [ + 47, + 669, + 134, + 681 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "text", + "content": "Novel view synthesis. Classic image-based rendering (IBR) methods synthesize novel views by integrating pixel" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 547, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 167 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 167 + ], + "type": "text", + "content": "information from input images [58], and can be categorized according to their dependence on explicit geometry. Light field or lumigraph rendering methods [9, 21, 26, 32] generate new views by filtering and interpolating sampled rays, without use of explicit geometric models. To handle sparser input views, many approaches [7, 14, 18, 23, 24, 26, 30, 52, 54, 55] leverage pre-computed proxy geometry such as depth maps or meshes to render novel views." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 168, + 548, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 168, + 548, + 348 + ], + "spans": [ + { + "bbox": [ + 304, + 168, + 548, + 348 + ], + "type": "text", + "content": "Recently, neural representations have demonstrated high-quality novel view synthesis [12, 17, 38, 40, 46, 48, 59-62, 72, 81]. In particular, Neural Radiance Fields (NeRF) [46] achieves an unprecedented level of fidelity by encoding continuous scene radiance fields within multi-layer perceptrons (MLPs). Among all methods building on NeRF, IBRNet [70] is the most relevant to our work. IBRNet combines classical IBR techniques with volume rendering to produce a generalized IBR module that can render high-quality views without per-scene optimization. Our work extends this kind of volumetric IBR framework designed for static scenes [11, 64, 70] to more challenging dynamic scenes. Note that our focus is on synthesizing higher-quality novel views for long videos with complex camera and object motion, rather than on generalization across scenes." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 354, + 547, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 354, + 547, + 413 + ], + "spans": [ + { + "bbox": [ + 304, + 354, + 547, + 413 + ], + "type": "text", + "content": "Dynamic scene view synthesis. Our work is related to geometric reconstruction of dynamic scenes from RGBD [5, 15, 25, 47, 68, 83] or monocular videos [31, 44, 78, 80]. However, depth- or mesh-based representations struggle to model complex geometry and view-dependent effects." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 415, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 415, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 415, + 548, + 715 + ], + "type": "text", + "content": "Most prior work on novel view synthesis for dynamic scenes requires multiple synchronized input videos [1, 3, 6, 27, 33, 63, 69, 76, 82], limiting their real-world applicability. Some methods [8, 13, 22, 51, 71] use domain knowledge such as template models to achieve high-quality results, but are restricted to specific categories [41, 56]. More recently, many works propose to synthesize novel views of dynamic scenes from a single camera. Yoon et al. [75] render novel views through explicit warping using depth maps obtained via single-view depth and multi-view stereo. However, this method fails to model complex scene geometry and to fill in realistic and consistent content at disocclusions. With advances in neural rendering, NeRF-based dynamic view synthesis methods have shown state-of-the-art results [16, 35, 53, 66, 74]. Some approaches, such as Nerfies [49] and HyperNeRF [50], represent scenes using a deformation field mapping each local observation to a canonical scene representation. These deformations are conditioned on time [53] or a per-frame latent code [49, 50, 66], and are parameterized as translations [53, 66] or rigid body motion fields [49, 50]. These methods can handle long videos, but are mostly limited to object-centric scenes with relatively small object motion and controlled camera paths. Other methods represent scenes as time-varying NeRFs [19, 20, 35, 67, 74]. In particular, NSFF uses neural scene flow fields that can" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "4274" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 71, + 286, + 170 + ], + "blocks": [ + { + "bbox": [ + 48, + 71, + 286, + 170 + ], + "lines": [ + { + "bbox": [ + 48, + 71, + 286, + 170 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 286, + 170 + ], + "type": "image", + "image_path": "87c90d518b08baa1383f2d6cf463dadae9fce64a13fea8dd9ce1256a36366b0b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 178, + 289, + 277 + ], + "lines": [ + { + "bbox": [ + 46, + 178, + 289, + 277 + ], + "spans": [ + { + "bbox": [ + 46, + 178, + 289, + 277 + ], + "type": "text", + "content": "Figure 2. Rendering via motion-adjusted multi-view feature aggregation. Given a sampled location " + }, + { + "bbox": [ + 46, + 178, + 289, + 277 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 178, + 289, + 277 + ], + "type": "text", + "content": " at time " + }, + { + "bbox": [ + 46, + 178, + 289, + 277 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 178, + 289, + 277 + ], + "type": "text", + "content": " along a target ray " + }, + { + "bbox": [ + 46, + 178, + 289, + 277 + ], + "type": "inline_equation", + "content": "\\mathbf{r}" + }, + { + "bbox": [ + 46, + 178, + 289, + 277 + ], + "type": "text", + "content": ", we estimate its motion trajectory, which determines the 3D correspondence of " + }, + { + "bbox": [ + 46, + 178, + 289, + 277 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 178, + 289, + 277 + ], + "type": "text", + "content": " at nearby time " + }, + { + "bbox": [ + 46, + 178, + 289, + 277 + ], + "type": "inline_equation", + "content": "j \\in \\mathcal{N}(i)" + }, + { + "bbox": [ + 46, + 178, + 289, + 277 + ], + "type": "text", + "content": ", denoted " + }, + { + "bbox": [ + 46, + 178, + 289, + 277 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{i \\rightarrow j}" + }, + { + "bbox": [ + 46, + 178, + 289, + 277 + ], + "type": "text", + "content": ". Each warped point is then projected into its corresponding source view. Image features " + }, + { + "bbox": [ + 46, + 178, + 289, + 277 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_j" + }, + { + "bbox": [ + 46, + 178, + 289, + 277 + ], + "type": "text", + "content": " extracted along the projected curves are aggregated and fed to the ray transformer with time embedding " + }, + { + "bbox": [ + 46, + 178, + 289, + 277 + ], + "type": "inline_equation", + "content": "\\gamma(i)" + }, + { + "bbox": [ + 46, + 178, + 289, + 277 + ], + "type": "text", + "content": ", producing per-sample color and density " + }, + { + "bbox": [ + 46, + 178, + 289, + 277 + ], + "type": "inline_equation", + "content": "(\\mathbf{c}_i, \\sigma_i)" + }, + { + "bbox": [ + 46, + 178, + 289, + 277 + ], + "type": "text", + "content": ". The final pixel color " + }, + { + "bbox": [ + 46, + 178, + 289, + 277 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{C}}_i" + }, + { + "bbox": [ + 46, + 178, + 289, + 277 + ], + "type": "text", + "content": " is then synthesized by volume rendering " + }, + { + "bbox": [ + 46, + 178, + 289, + 277 + ], + "type": "inline_equation", + "content": "(\\mathbf{c}_i, \\sigma_i)" + }, + { + "bbox": [ + 46, + 178, + 289, + 277 + ], + "type": "text", + "content": " along " + }, + { + "bbox": [ + 46, + 178, + 289, + 277 + ], + "type": "inline_equation", + "content": "\\mathbf{r}" + }, + { + "bbox": [ + 46, + 178, + 289, + 277 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 297, + 288, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 297, + 288, + 334 + ], + "spans": [ + { + "bbox": [ + 46, + 297, + 288, + 334 + ], + "type": "text", + "content": "capture fast and complex 3D scene motion for in-the-wild videos [35]. However, this method only works well for short (1-2 second), forward-facing videos." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 344, + 235, + 358 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 344, + 235, + 358 + ], + "spans": [ + { + "bbox": [ + 47, + 344, + 235, + 358 + ], + "type": "text", + "content": "3. Dynamic Image-Based Rendering" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 364, + 288, + 446 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 364, + 288, + 446 + ], + "spans": [ + { + "bbox": [ + 46, + 364, + 288, + 446 + ], + "type": "text", + "content": "Given a monocular video of a dynamic scene with frames " + }, + { + "bbox": [ + 46, + 364, + 288, + 446 + ], + "type": "inline_equation", + "content": "(I_1, I_2, \\ldots, I_N)" + }, + { + "bbox": [ + 46, + 364, + 288, + 446 + ], + "type": "text", + "content": " and known camera parameters " + }, + { + "bbox": [ + 46, + 364, + 288, + 446 + ], + "type": "inline_equation", + "content": "(\\mathbf{P}_1, \\mathbf{P}_2, \\ldots, \\mathbf{P}_N)" + }, + { + "bbox": [ + 46, + 364, + 288, + 446 + ], + "type": "text", + "content": ", our goal is to synthesize a novel viewpoint at any desired time within the video. Like many other approaches, we train per-video, first optimizing a model to reconstruct the input frames, then using this model to render novel views." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 448, + 287, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 448, + 287, + 519 + ], + "spans": [ + { + "bbox": [ + 46, + 448, + 287, + 519 + ], + "type": "text", + "content": "Rather than encoding 3D color and density directly in the weights of an MLP as in recent dynamic NeRF methods, we integrate classical IBR ideas into a volumetric rendering framework. Compared to explicit surfaces, volumetric representations can more readily model complex scene geometry with view-dependent effects." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 520, + 288, + 627 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 520, + 288, + 627 + ], + "spans": [ + { + "bbox": [ + 46, + 520, + 288, + 627 + ], + "type": "text", + "content": "The following sections introduce our methods for scene-motion-adjusted multi-view feature aggregation (Sec. 3.1), and enforcing temporal consistency via cross-time rendering in motion-adjusted ray space (Sec. 3.2). Our full system combines a static model and a dynamic model to produce a color at each pixel. Accurate scene factorization is achieved via segmentation masks derived from a separately trained motion segmentation module within a Bayesian learning framework (Sec. 3.3)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 635, + 242, + 648 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 635, + 242, + 648 + ], + "spans": [ + { + "bbox": [ + 47, + 635, + 242, + 648 + ], + "type": "text", + "content": "3.1. Motion-adjusted feature aggregation" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 654, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 288, + 713 + ], + "type": "text", + "content": "We synthesize new views by aggregating features extracted from temporally nearby source views. To render an image at time " + }, + { + "bbox": [ + 46, + 654, + 288, + 713 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 654, + 288, + 713 + ], + "type": "text", + "content": ", we first identify source views " + }, + { + "bbox": [ + 46, + 654, + 288, + 713 + ], + "type": "inline_equation", + "content": "I_{j}" + }, + { + "bbox": [ + 46, + 654, + 288, + 713 + ], + "type": "text", + "content": " within a temporal radius " + }, + { + "bbox": [ + 46, + 654, + 288, + 713 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 654, + 288, + 713 + ], + "type": "text", + "content": " frames of " + }, + { + "bbox": [ + 46, + 654, + 288, + 713 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 654, + 288, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 654, + 288, + 713 + ], + "type": "inline_equation", + "content": "j \\in \\mathcal{N}(i) = [i - r, i + r]" + }, + { + "bbox": [ + 46, + 654, + 288, + 713 + ], + "type": "text", + "content": ". For each source view, we extract a 2D feature map " + }, + { + "bbox": [ + 46, + 654, + 288, + 713 + ], + "type": "inline_equation", + "content": "F_{i}" + }, + { + "bbox": [ + 46, + 654, + 288, + 713 + ], + "type": "text", + "content": " through a" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 72, + 545, + 97 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 545, + 97 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 545, + 97 + ], + "type": "text", + "content": "shared convolutional encoder network to form an input tuple " + }, + { + "bbox": [ + 306, + 72, + 545, + 97 + ], + "type": "inline_equation", + "content": "\\{I_j,\\mathbf{P}_j,F_j\\}" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 97, + 547, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 97, + 547, + 288 + ], + "spans": [ + { + "bbox": [ + 304, + 97, + 547, + 288 + ], + "type": "text", + "content": "To predict the color and density of each point sampled along a target ray " + }, + { + "bbox": [ + 304, + 97, + 547, + 288 + ], + "type": "inline_equation", + "content": "\\mathbf{r}" + }, + { + "bbox": [ + 304, + 97, + 547, + 288 + ], + "type": "text", + "content": ", we must aggregate source view features while accounting for scene motion. For a static scene, points along a target ray will lie along a corresponding epipolar line in a neighboring source view, hence we can aggregate potential correspondences by simply sampling along neighboring epipolar lines [64, 70]. However, moving scene elements violate epipolar constraints, leading to inconsistent feature aggregation if motion is not accounted for. Hence, we perform motion-adjusted feature aggregation, as shown in Fig. 3. To determine correspondence in dynamic scenes, one straightforward idea is to estimate a scene flow field via an MLP [35] to determine a given point's motion-adjusted 3D location at a nearby time. However, this strategy is computational infeasible in a volumetric IBR framework due to recursive unrolling of the MLPs." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 293, + 547, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 293, + 547, + 353 + ], + "spans": [ + { + "bbox": [ + 304, + 293, + 547, + 353 + ], + "type": "text", + "content": "Motion trajectory fields. Instead, we represent scene motion using motion trajectory fields described in terms of learned basis functions. For a given 3D point " + }, + { + "bbox": [ + 304, + 293, + 547, + 353 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 293, + 547, + 353 + ], + "type": "text", + "content": " along target ray " + }, + { + "bbox": [ + 304, + 293, + 547, + 353 + ], + "type": "inline_equation", + "content": "\\mathbf{r}" + }, + { + "bbox": [ + 304, + 293, + 547, + 353 + ], + "type": "text", + "content": " at time " + }, + { + "bbox": [ + 304, + 293, + 547, + 353 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 293, + 547, + 353 + ], + "type": "text", + "content": ", we encode its trajectory coefficients with an MLP " + }, + { + "bbox": [ + 304, + 293, + 547, + 353 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{MT}}" + }, + { + "bbox": [ + 304, + 293, + 547, + 353 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 358, + 358, + 545, + 373 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 358, + 545, + 373 + ], + "spans": [ + { + "bbox": [ + 358, + 358, + 545, + 373 + ], + "type": "interline_equation", + "content": "\\left\\{\\phi_ {i} ^ {l} (\\mathbf {x}) \\right\\} _ {l = 1} ^ {L} = G _ {\\mathrm {M T}} (\\gamma (\\mathbf {x}), \\gamma (i)), \\tag {1}", + "image_path": "14cfb628d0dd2353c45d9b09330656680e0ecac9f861b4bdac0dc1d6ebdd2d48.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 377, + 547, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 377, + 547, + 449 + ], + "spans": [ + { + "bbox": [ + 304, + 377, + 547, + 449 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 377, + 547, + 449 + ], + "type": "inline_equation", + "content": "\\phi_i^l\\in \\mathcal{R}^3" + }, + { + "bbox": [ + 304, + 377, + 547, + 449 + ], + "type": "text", + "content": " are basis coefficients (with separate coefficients for " + }, + { + "bbox": [ + 304, + 377, + 547, + 449 + ], + "type": "inline_equation", + "content": "x,y," + }, + { + "bbox": [ + 304, + 377, + 547, + 449 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 377, + 547, + 449 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 304, + 377, + 547, + 449 + ], + "type": "text", + "content": " using the motion basis described below) and " + }, + { + "bbox": [ + 304, + 377, + 547, + 449 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 304, + 377, + 547, + 449 + ], + "type": "text", + "content": " denotes positional encoding. We choose " + }, + { + "bbox": [ + 304, + 377, + 547, + 449 + ], + "type": "inline_equation", + "content": "L = 6" + }, + { + "bbox": [ + 304, + 377, + 547, + 449 + ], + "type": "text", + "content": " bases and 16 linearly increasing frequencies for the encoding " + }, + { + "bbox": [ + 304, + 377, + 547, + 449 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 304, + 377, + 547, + 449 + ], + "type": "text", + "content": " , based on the assumption that scene motion tends to be low frequency [80]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 449, + 547, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 547, + 521 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 547, + 521 + ], + "type": "text", + "content": "We also introduce a global learnable motion basis " + }, + { + "bbox": [ + 304, + 449, + 547, + 521 + ], + "type": "inline_equation", + "content": "\\{h_i^l\\}_{l = 1}^L,h_i^l\\in \\mathcal{R}" + }, + { + "bbox": [ + 304, + 449, + 547, + 521 + ], + "type": "text", + "content": ", spanning every time step " + }, + { + "bbox": [ + 304, + 449, + 547, + 521 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 449, + 547, + 521 + ], + "type": "text", + "content": " of the input video, which is optimized jointly with the MLP. The motion trajectory of " + }, + { + "bbox": [ + 304, + 449, + 547, + 521 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 449, + 547, + 521 + ], + "type": "text", + "content": " is then defined as " + }, + { + "bbox": [ + 304, + 449, + 547, + 521 + ], + "type": "inline_equation", + "content": "\\Gamma_{\\mathbf{x},i}(j) = \\sum_{l = 1}^{L}h_{j}^{l}\\phi_{i}^{l}(\\mathbf{x})" + }, + { + "bbox": [ + 304, + 449, + 547, + 521 + ], + "type": "text", + "content": " and thus, the relative displacement between " + }, + { + "bbox": [ + 304, + 449, + 547, + 521 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 449, + 547, + 521 + ], + "type": "text", + "content": " and its 3D correspondence " + }, + { + "bbox": [ + 304, + 449, + 547, + 521 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{i\\rightarrow j}" + }, + { + "bbox": [ + 304, + 449, + 547, + 521 + ], + "type": "text", + "content": " at time " + }, + { + "bbox": [ + 304, + 449, + 547, + 521 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 304, + 449, + 547, + 521 + ], + "type": "text", + "content": " is computed as" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 366, + 528, + 545, + 541 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 366, + 528, + 545, + 541 + ], + "spans": [ + { + "bbox": [ + 366, + 528, + 545, + 541 + ], + "type": "interline_equation", + "content": "\\Delta_ {\\mathbf {x}, i} (j) = \\Gamma_ {\\mathbf {x}, i} (j) - \\Gamma_ {\\mathbf {x}, i} (i). \\tag {2}", + "image_path": "8eb037e85f863ef2422f1af2982df8d3ab8cf8263674a2214e855df7c630fe96.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 545, + 547, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 547, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 547, + 653 + ], + "type": "text", + "content": "With this motion trajectory representation, finding 3D correspondences for a query point " + }, + { + "bbox": [ + 304, + 545, + 547, + 653 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 545, + 547, + 653 + ], + "type": "text", + "content": " in neighboring views requires just a single MLP query, allowing efficient multi-view feature aggregation within our volume rendering framework. We initialize the basis " + }, + { + "bbox": [ + 304, + 545, + 547, + 653 + ], + "type": "inline_equation", + "content": "\\{h_i^l\\}_{l = 1}^L" + }, + { + "bbox": [ + 304, + 545, + 547, + 653 + ], + "type": "text", + "content": " with the DCT basis as proposed by Wang et al. [67], but fine-tune it along with other components during optimization, since we observe that a fixed DCT basis can fail to model a wide range of real-world motions (see third column of Fig. 4)." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "type": "text", + "content": "Using the estimated motion trajectory of " + }, + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "type": "text", + "content": " at time " + }, + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "type": "text", + "content": ", we denote " + }, + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "type": "text", + "content": "'s corresponding 3D point at time " + }, + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{i\\rightarrow j} = \\mathbf{x} + \\Delta_{\\mathbf{x},i}(j)" + }, + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "type": "text", + "content": ". We project each warped point " + }, + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{i\\rightarrow j}" + }, + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "type": "text", + "content": " into its source view " + }, + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "type": "inline_equation", + "content": "I_{j}" + }, + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "type": "text", + "content": " using camera parameters " + }, + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_j" + }, + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "type": "text", + "content": ", and extract color and feature vector " + }, + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_j" + }, + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "type": "text", + "content": " at the projected 2D pixel location." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "4275" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 71, + 286, + 186 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 286, + 186 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 286, + 186 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 286, + 186 + ], + "type": "image", + "image_path": "8b9233be694e197a6021b471b2f2d1c3667ff80d110475c573bc5c9a6e2b9575.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "lines": [ + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "spans": [ + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "text", + "content": "Figure 3. Temporal consistency via cross-time rendering. To enforce temporal consistency in a dynamic reconstruction, we render each frame " + }, + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "inline_equation", + "content": "I_{i}" + }, + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "text", + "content": " using the scene model from a nearby time " + }, + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "text", + "content": ", which we call cross-time rendering. A ray " + }, + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "inline_equation", + "content": "\\mathbf{r}" + }, + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "text", + "content": " from image " + }, + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "text", + "content": " is instead rendered using a curved ray " + }, + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "inline_equation", + "content": "\\mathbf{r}_{i\\rightarrow j}" + }, + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "inline_equation", + "content": "\\mathbf{r}" + }, + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "text", + "content": " warped to time " + }, + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "text", + "content": ". That is, having computed the motion-adjusted point " + }, + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{i\\rightarrow j} = \\mathbf{x} + \\Delta_{\\mathbf{x},i}(j)" + }, + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "text", + "content": " at nearby time " + }, + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "text", + "content": " from every sampled location along " + }, + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "inline_equation", + "content": "\\mathbf{r}" + }, + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "text", + "content": ", we query " + }, + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{i\\rightarrow j}" + }, + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "text", + "content": " and time " + }, + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "text", + "content": " via the MLP to predict its motion trajectory " + }, + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "inline_equation", + "content": "\\Gamma_{\\mathbf{x}_{i\\rightarrow j},j}" + }, + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "text", + "content": ", along which we aggregate image features " + }, + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_k" + }, + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "text", + "content": " extracted from source views within time " + }, + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "inline_equation", + "content": "k\\in \\mathcal{N}(j)" + }, + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "text", + "content": ". The aggregated features along " + }, + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "inline_equation", + "content": "\\mathbf{r}_{i\\rightarrow j}" + }, + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "text", + "content": " are fed to the ray transformer with time embedding " + }, + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "inline_equation", + "content": "\\gamma (j)" + }, + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "text", + "content": " to produce per-sample color and density " + }, + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "inline_equation", + "content": "(\\mathbf{c}_j,\\sigma_j)" + }, + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "text", + "content": " at time " + }, + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "text", + "content": ". A pixel color " + }, + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{C}}_{j\\rightarrow i}" + }, + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "text", + "content": " is computed by volume rendering " + }, + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "inline_equation", + "content": "(\\mathbf{c}_j,\\sigma_j)" + }, + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "text", + "content": ", and then compared to the ground truth color " + }, + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_i" + }, + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "text", + "content": " to form a reconstruction loss " + }, + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{pho}}" + }, + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 370, + 288, + 490 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 370, + 288, + 490 + ], + "spans": [ + { + "bbox": [ + 46, + 370, + 288, + 490 + ], + "type": "text", + "content": "The resulting set of source features across neighbor views " + }, + { + "bbox": [ + 46, + 370, + 288, + 490 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 370, + 288, + 490 + ], + "type": "text", + "content": " is fed to a shared MLP whose output features are aggregated through weighted average pooling [70] to produce a single feature vector at each 3D sample point along ray " + }, + { + "bbox": [ + 46, + 370, + 288, + 490 + ], + "type": "inline_equation", + "content": "\\mathbf{r}" + }, + { + "bbox": [ + 46, + 370, + 288, + 490 + ], + "type": "text", + "content": ". A ray transformer network with time embedding " + }, + { + "bbox": [ + 46, + 370, + 288, + 490 + ], + "type": "inline_equation", + "content": "\\gamma(i)" + }, + { + "bbox": [ + 46, + 370, + 288, + 490 + ], + "type": "text", + "content": " then processes the sequence of aggregated features along the ray to predict per-sample colors and densities " + }, + { + "bbox": [ + 46, + 370, + 288, + 490 + ], + "type": "inline_equation", + "content": "(\\mathbf{c}_i, \\sigma_i)" + }, + { + "bbox": [ + 46, + 370, + 288, + 490 + ], + "type": "text", + "content": " (see Fig. 2). We then use standard NeRF volume rendering [4] to obtain a final pixel color " + }, + { + "bbox": [ + 46, + 370, + 288, + 490 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{C}}_i(\\mathbf{r})" + }, + { + "bbox": [ + 46, + 370, + 288, + 490 + ], + "type": "text", + "content": " for the ray from this sequence of colors and densities." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 501, + 287, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 501, + 287, + 514 + ], + "spans": [ + { + "bbox": [ + 47, + 501, + 287, + 514 + ], + "type": "text", + "content": "3.2. Cross-time rendering for temporal consistency" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 521, + 289, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 289, + 676 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 289, + 676 + ], + "type": "text", + "content": "If we optimize our dynamic scene representation by comparing " + }, + { + "bbox": [ + 46, + 521, + 289, + 676 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{C}}_i" + }, + { + "bbox": [ + 46, + 521, + 289, + 676 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 46, + 521, + 289, + 676 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_i" + }, + { + "bbox": [ + 46, + 521, + 289, + 676 + ], + "type": "text", + "content": " alone, the representation might overfit to the input images: it might perfectly reconstruct those views, but fail to render correct novel views. This can happen because the representation has the capacity to reconstruct completely separate models for each time instance, without utilizing or accurately reconstructing scene motion. Therefore, to recover a consistent scene with physically plausible motion, we enforce temporal coherence of the scene representation. One way to define temporal coherence in this context is that the scene at two neighboring times " + }, + { + "bbox": [ + 46, + 521, + 289, + 676 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 521, + 289, + 676 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 521, + 289, + 676 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 521, + 289, + 676 + ], + "type": "text", + "content": " should be consistent when taking scene motion into account [19, 35, 67]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 677, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 289, + 714 + ], + "type": "text", + "content": "In particular, we enforce temporal photometric consistency in our optimized representation via cross-time rendering in motion-adjusted ray space, as shown in Fig. 3. The" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "content": "idea is to render a view at time " + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "content": " but via some nearby time " + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "content": ", which we refer to as cross-time rendering. For each nearby time " + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "inline_equation", + "content": "j \\in \\mathcal{N}(i)" + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "content": ", rather than directly using points " + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "content": " along ray " + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "inline_equation", + "content": "\\mathbf{r}" + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "content": ", we consider the points " + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{i \\to j}" + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "content": " along motion-adjusted ray " + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "inline_equation", + "content": "\\mathbf{r}_{i \\to j}" + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "content": " and treat them as if they lie along a ray at time " + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 133, + 547, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 133, + 547, + 312 + ], + "spans": [ + { + "bbox": [ + 304, + 133, + 547, + 312 + ], + "type": "text", + "content": "Specifically, having computed the motion-adjusted points " + }, + { + "bbox": [ + 304, + 133, + 547, + 312 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{i\\rightarrow j}" + }, + { + "bbox": [ + 304, + 133, + 547, + 312 + ], + "type": "text", + "content": ", we query the MLP to predict the coefficients of new trajectories " + }, + { + "bbox": [ + 304, + 133, + 547, + 312 + ], + "type": "inline_equation", + "content": "\\{\\phi_j^l (\\mathbf{x}_{i\\rightarrow j})_{l = 1}^L = G_{\\mathrm{MT}}(\\mathbf{x}_{i\\rightarrow j},\\gamma (j))" + }, + { + "bbox": [ + 304, + 133, + 547, + 312 + ], + "type": "text", + "content": ", and use these to compute corresponding 3D points " + }, + { + "bbox": [ + 304, + 133, + 547, + 312 + ], + "type": "inline_equation", + "content": "(\\mathbf{x}_{i\\rightarrow j})_{j\\rightarrow k}" + }, + { + "bbox": [ + 304, + 133, + 547, + 312 + ], + "type": "text", + "content": " for images " + }, + { + "bbox": [ + 304, + 133, + 547, + 312 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 133, + 547, + 312 + ], + "type": "text", + "content": " in the temporal window " + }, + { + "bbox": [ + 304, + 133, + 547, + 312 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(j)" + }, + { + "bbox": [ + 304, + 133, + 547, + 312 + ], + "type": "text", + "content": ", using Eq. 2. These new 3D correspondences are then used to render a pixel color exactly as described for a \"straight\" ray " + }, + { + "bbox": [ + 304, + 133, + 547, + 312 + ], + "type": "inline_equation", + "content": "\\mathbf{r}_i" + }, + { + "bbox": [ + 304, + 133, + 547, + 312 + ], + "type": "text", + "content": " in Sec. 3.1, except now along the curved, motion-adjusted ray " + }, + { + "bbox": [ + 304, + 133, + 547, + 312 + ], + "type": "inline_equation", + "content": "\\mathbf{r}_{i\\rightarrow j}" + }, + { + "bbox": [ + 304, + 133, + 547, + 312 + ], + "type": "text", + "content": ". That is, each point " + }, + { + "bbox": [ + 304, + 133, + 547, + 312 + ], + "type": "inline_equation", + "content": "(\\mathbf{x}_{i\\rightarrow j})_{j\\rightarrow k}" + }, + { + "bbox": [ + 304, + 133, + 547, + 312 + ], + "type": "text", + "content": " is projected into its source view " + }, + { + "bbox": [ + 304, + 133, + 547, + 312 + ], + "type": "inline_equation", + "content": "I_{k}" + }, + { + "bbox": [ + 304, + 133, + 547, + 312 + ], + "type": "text", + "content": " and feature maps " + }, + { + "bbox": [ + 304, + 133, + 547, + 312 + ], + "type": "inline_equation", + "content": "F_{k}" + }, + { + "bbox": [ + 304, + 133, + 547, + 312 + ], + "type": "text", + "content": " with camera parameters " + }, + { + "bbox": [ + 304, + 133, + 547, + 312 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_k" + }, + { + "bbox": [ + 304, + 133, + 547, + 312 + ], + "type": "text", + "content": " to extract an RGB color and image feature " + }, + { + "bbox": [ + 304, + 133, + 547, + 312 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_k" + }, + { + "bbox": [ + 304, + 133, + 547, + 312 + ], + "type": "text", + "content": ", and then these features are aggregated and input to the ray transformer with the time embedding " + }, + { + "bbox": [ + 304, + 133, + 547, + 312 + ], + "type": "inline_equation", + "content": "\\gamma (j)" + }, + { + "bbox": [ + 304, + 133, + 547, + 312 + ], + "type": "text", + "content": ". The result is a sequence of colors and densities " + }, + { + "bbox": [ + 304, + 133, + 547, + 312 + ], + "type": "inline_equation", + "content": "(\\mathbf{c}_j,\\sigma_j)" + }, + { + "bbox": [ + 304, + 133, + 547, + 312 + ], + "type": "text", + "content": " along " + }, + { + "bbox": [ + 304, + 133, + 547, + 312 + ], + "type": "inline_equation", + "content": "\\mathbf{r}_{i\\rightarrow j}" + }, + { + "bbox": [ + 304, + 133, + 547, + 312 + ], + "type": "text", + "content": " at time " + }, + { + "bbox": [ + 304, + 133, + 547, + 312 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 304, + 133, + 547, + 312 + ], + "type": "text", + "content": ", which can be composited through volume rendering to form a color " + }, + { + "bbox": [ + 304, + 133, + 547, + 312 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{C}}_{j\\rightarrow i}" + }, + { + "bbox": [ + 304, + 133, + 547, + 312 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 314, + 547, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 314, + 547, + 338 + ], + "spans": [ + { + "bbox": [ + 305, + 314, + 547, + 338 + ], + "type": "text", + "content": "We can then compare " + }, + { + "bbox": [ + 305, + 314, + 547, + 338 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{C}}_{j\\rightarrow i}(\\mathbf{r})" + }, + { + "bbox": [ + 305, + 314, + 547, + 338 + ], + "type": "text", + "content": " with the target pixel " + }, + { + "bbox": [ + 305, + 314, + 547, + 338 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_i(\\mathbf{r})" + }, + { + "bbox": [ + 305, + 314, + 547, + 338 + ], + "type": "text", + "content": " via a motion-disocclusion-aware RGB reconstruction loss:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 321, + 342, + 545, + 369 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 342, + 545, + 369 + ], + "spans": [ + { + "bbox": [ + 321, + 342, + 545, + 369 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {p h o}} = \\sum_ {\\mathbf {r}} \\sum_ {j \\in \\mathcal {N} (i)} \\hat {\\mathbf {W}} _ {j \\rightarrow i} (\\mathbf {r}) \\rho \\left(\\mathbf {C} _ {i} (\\mathbf {r}), \\hat {\\mathbf {C}} _ {j \\rightarrow i} (\\mathbf {r})\\right). \\tag {3}", + "image_path": "45123eea568037afdbfc1d008cac33a80cf028bdbf60e184f2c3436f7743461d.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 374, + 547, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 374, + 547, + 495 + ], + "spans": [ + { + "bbox": [ + 304, + 374, + 547, + 495 + ], + "type": "text", + "content": "We use a generalized Charbonnier loss [10] for the RGB loss " + }, + { + "bbox": [ + 304, + 374, + 547, + 495 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 304, + 374, + 547, + 495 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 374, + 547, + 495 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{W}}_{j\\rightarrow i}(\\mathbf{r})" + }, + { + "bbox": [ + 304, + 374, + 547, + 495 + ], + "type": "text", + "content": " is a motion disocclusion weight computed by the difference of accumulated alpha weights between time " + }, + { + "bbox": [ + 304, + 374, + 547, + 495 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 374, + 547, + 495 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 374, + 547, + 495 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 304, + 374, + 547, + 495 + ], + "type": "text", + "content": " to address the motion disocclusion ambiguity described by NSFF [35] (see supplement for more details). Note that when " + }, + { + "bbox": [ + 304, + 374, + 547, + 495 + ], + "type": "inline_equation", + "content": "j = i" + }, + { + "bbox": [ + 304, + 374, + 547, + 495 + ], + "type": "text", + "content": ", there is no scene motion-induced displacement, meaning " + }, + { + "bbox": [ + 304, + 374, + 547, + 495 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{C}}_{j\\rightarrow i} = \\hat{\\mathbf{C}}_i" + }, + { + "bbox": [ + 304, + 374, + 547, + 495 + ], + "type": "text", + "content": " and no disocclusion weights are involved (" + }, + { + "bbox": [ + 304, + 374, + 547, + 495 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{W}}_{j\\rightarrow i} = 1" + }, + { + "bbox": [ + 304, + 374, + 547, + 495 + ], + "type": "text", + "content": "). We show a comparison between our method with and without enforcing temporal consistency in the first column of Fig. 4." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 503, + 509, + 516 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 503, + 509, + 516 + ], + "spans": [ + { + "bbox": [ + 305, + 503, + 509, + 516 + ], + "type": "text", + "content": "3.3. Combining static and dynamic models" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 521, + 547, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 547, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 547, + 676 + ], + "type": "text", + "content": "As observed in NSFF, synthesizing novel views using a small temporal window is insufficient to recover complete and high-quality content for static scene regions, since the contents may only be observed in spatially distant frames due to uncontrolled camera paths. Therefore, we follow the ideas of NSFF [35], and model the entire scene using two separate representations. Dynamic content " + }, + { + "bbox": [ + 304, + 521, + 547, + 676 + ], + "type": "inline_equation", + "content": "(\\mathbf{c}_i,\\sigma_i)" + }, + { + "bbox": [ + 304, + 521, + 547, + 676 + ], + "type": "text", + "content": " is represented with a time-varying model as above (used for cross-time rendering during optimization). Static content " + }, + { + "bbox": [ + 304, + 521, + 547, + 676 + ], + "type": "inline_equation", + "content": "(\\mathbf{c},\\sigma)" + }, + { + "bbox": [ + 304, + 521, + 547, + 676 + ], + "type": "text", + "content": " is represented with a time-invariant model, which renders in the same way as the time-varying model, but aggregates multiview features without scene motion adjustment (i.e., along epipolar lines)." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "text", + "content": "The dynamic and static predictions are combined and rendered to a single output color " + }, + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{C}}_i^{\\mathrm{full}}" + }, + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "text", + "content": " (or " + }, + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{C}}_{j\\rightarrow i}^{\\mathrm{full}}" + }, + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "text", + "content": " during cross-time rendering) using the method for combining static and" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "4276" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 106, + 184 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 106, + 184 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 106, + 184 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 106, + 184 + ], + "type": "image", + "image_path": "f00d932c889262daa8dee0efa234b05c984ee7804d3d5125c49942bab306af35.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 64, + 185, + 91, + 192 + ], + "lines": [ + { + "bbox": [ + 64, + 185, + 91, + 192 + ], + "spans": [ + { + "bbox": [ + 64, + 185, + 91, + 192 + ], + "type": "text", + "content": "(a) w/o TC" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 109, + 70, + 167, + 183 + ], + "blocks": [ + { + "bbox": [ + 109, + 70, + 167, + 183 + ], + "lines": [ + { + "bbox": [ + 109, + 70, + 167, + 183 + ], + "spans": [ + { + "bbox": [ + 109, + 70, + 167, + 183 + ], + "type": "image", + "image_path": "109b70af9de32f69344a60a0164ac61035f3413b4851684825b4783a82590249.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 125, + 185, + 149, + 192 + ], + "lines": [ + { + "bbox": [ + 125, + 185, + 149, + 192 + ], + "spans": [ + { + "bbox": [ + 125, + 185, + 149, + 192 + ], + "type": "text", + "content": "(b) w/ SF" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 168, + 70, + 227, + 183 + ], + "blocks": [ + { + "bbox": [ + 168, + 70, + 227, + 183 + ], + "lines": [ + { + "bbox": [ + 168, + 70, + 227, + 183 + ], + "spans": [ + { + "bbox": [ + 168, + 70, + 227, + 183 + ], + "type": "image", + "image_path": "9e788bb74bcafb3ba480a5e947ce50928ed63bb4ec66b9e5e303ed13eddbac35.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 176, + 185, + 219, + 192 + ], + "lines": [ + { + "bbox": [ + 176, + 185, + 219, + 192 + ], + "spans": [ + { + "bbox": [ + 176, + 185, + 219, + 192 + ], + "type": "text", + "content": "(c) w/ DCT basis" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 228, + 70, + 287, + 183 + ], + "blocks": [ + { + "bbox": [ + 228, + 70, + 287, + 183 + ], + "lines": [ + { + "bbox": [ + 228, + 70, + 287, + 183 + ], + "spans": [ + { + "bbox": [ + 228, + 70, + 287, + 183 + ], + "type": "image", + "image_path": "dfd9e1a19fc0d530fe3ed4be67f11feca56c044d853878d5203c92aa72742768.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 246, + 185, + 268, + 193 + ], + "lines": [ + { + "bbox": [ + 246, + 185, + 268, + 193 + ], + "spans": [ + { + "bbox": [ + 246, + 185, + 268, + 193 + ], + "type": "text", + "content": "(d) Ours" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 199, + 289, + 288 + ], + "lines": [ + { + "bbox": [ + 46, + 199, + 289, + 288 + ], + "spans": [ + { + "bbox": [ + 46, + 199, + 289, + 288 + ], + "type": "text", + "content": "Figure 4. Qualitative ablations. From left to right, we show rendered novel views (top) and depths (bottom) from our system (a) without enforcing temporal consistency, (b) aggregating image features with scene flow fields instead of motion trajectories, (c) representing motion trajectory with a fixed DCT basis instead of a learned one, and (d) with full configuration. Simpler configurations significantly degrade rendering quality as indicated by PSNR calculated over the regions of moving objects." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 308, + 287, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 308, + 287, + 346 + ], + "spans": [ + { + "bbox": [ + 46, + 308, + 287, + 346 + ], + "type": "text", + "content": "transient models of NeRF-W [45]. Each model's color and density estimates can also be rendered separately, giving color " + }, + { + "bbox": [ + 46, + 308, + 287, + 346 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{C}}^{\\mathrm{st}}" + }, + { + "bbox": [ + 46, + 308, + 287, + 346 + ], + "type": "text", + "content": " for static content and " + }, + { + "bbox": [ + 46, + 308, + 287, + 346 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{C}}_i^{\\mathrm{dy}}" + }, + { + "bbox": [ + 46, + 308, + 287, + 346 + ], + "type": "text", + "content": " for dynamic content." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 346, + 287, + 383 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 346, + 287, + 383 + ], + "spans": [ + { + "bbox": [ + 47, + 346, + 287, + 383 + ], + "type": "text", + "content": "When combining the two representations, we rewrite the photometric consistency term in Eq. 3 as a loss comparing " + }, + { + "bbox": [ + 47, + 346, + 287, + 383 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{C}}_{j\\rightarrow i}^{\\mathrm{full}}(\\mathbf{r})" + }, + { + "bbox": [ + 47, + 346, + 287, + 383 + ], + "type": "text", + "content": " with target pixel " + }, + { + "bbox": [ + 47, + 346, + 287, + 383 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_i(\\mathbf{r})" + }, + { + "bbox": [ + 47, + 346, + 287, + 383 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 64, + 391, + 287, + 418 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 391, + 287, + 418 + ], + "spans": [ + { + "bbox": [ + 64, + 391, + 287, + 418 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {p h o}} = \\sum_ {\\mathbf {r}} \\sum_ {j \\in \\mathcal {N} (i)} \\hat {\\mathbf {W}} _ {j \\rightarrow i} (\\mathbf {r}) \\rho \\left(\\mathbf {C} _ {i} (\\mathbf {r}), \\hat {\\mathbf {C}} _ {j \\rightarrow i} ^ {\\text {f u l l}} (\\mathbf {r})\\right) \\tag {4}", + "image_path": "cc87b77fc415d83f3be24f0621282b1cb04134be0074d0c9da0e89a683da7c78.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 426, + 289, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 426, + 289, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 289, + 628 + ], + "type": "text", + "content": "Image-based motion segmentation. In our framework, we observed that without any initialization, scene factorization tends to be dominated by either the time-invariant or the time-varying representation, a phenomena also observed in recent methods [28, 42]. To facilitate factorization, Gao et al. [19] initialize their system using masks from semantic segmentation, relying on the assumption that all moving objects are captured by a set of candidate semantic segmentation labels, and segmentation masks are temporally accurate. However, these assumptions do not hold in many real-world scenarios, as observed by Zhang et al. [79]. Instead, we propose a new motion segmentation module that produces segmentation masks for supervising our main two-component scene representation. Our idea is inspired by the Bayesian learning techniques proposed in recent work [45, 79], but integrated into a volumetric IBR representation for dynamic videos." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 630, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 289, + 714 + ], + "type": "text", + "content": "In particular, before training our main two-component scene representation, we jointly train two lightweight models to obtain a motion segmentation mask " + }, + { + "bbox": [ + 46, + 630, + 289, + 714 + ], + "type": "inline_equation", + "content": "M_{i}" + }, + { + "bbox": [ + 46, + 630, + 289, + 714 + ], + "type": "text", + "content": " for each input frame " + }, + { + "bbox": [ + 46, + 630, + 289, + 714 + ], + "type": "inline_equation", + "content": "I_{i}" + }, + { + "bbox": [ + 46, + 630, + 289, + 714 + ], + "type": "text", + "content": ". We model static scene content with an IBR-Net [70] that renders a pixel color " + }, + { + "bbox": [ + 46, + 630, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{B}}^{\\mathrm{st}}" + }, + { + "bbox": [ + 46, + 630, + 289, + 714 + ], + "type": "text", + "content": " using volume rendering along each ray via feature aggregation along epipolar lines from nearby source views without considering scene" + } + ] + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 310, + 70, + 368, + 103 + ], + "blocks": [ + { + "bbox": [ + 310, + 70, + 368, + 103 + ], + "lines": [ + { + "bbox": [ + 310, + 70, + 368, + 103 + ], + "spans": [ + { + "bbox": [ + 310, + 70, + 368, + 103 + ], + "type": "image", + "image_path": "4293e6e7f9e288c64fae755d71a7b6b757cfd16360545161584a7bf417145905.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 310, + 104, + 368, + 137 + ], + "blocks": [ + { + "bbox": [ + 310, + 104, + 368, + 137 + ], + "lines": [ + { + "bbox": [ + 310, + 104, + 368, + 137 + ], + "spans": [ + { + "bbox": [ + 310, + 104, + 368, + 137 + ], + "type": "image", + "image_path": "bd50b74c6baddecfcc2d12220e3e1018435063ce76898d035cf950fbf944d4c5.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 144, + 547, + 190 + ], + "lines": [ + { + "bbox": [ + 306, + 144, + 547, + 190 + ], + "spans": [ + { + "bbox": [ + 306, + 144, + 547, + 190 + ], + "type": "text", + "content": "Figure 5. Motion segmentation. We show full rendering " + }, + { + "bbox": [ + 306, + 144, + 547, + 190 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{B}}_i^{\\mathrm{full}}" + }, + { + "bbox": [ + 306, + 144, + 547, + 190 + ], + "type": "text", + "content": " (top) and motion segmentation overlaid with rendered dynamic content " + }, + { + "bbox": [ + 306, + 144, + 547, + 190 + ], + "type": "inline_equation", + "content": "\\alpha_i^{\\mathrm{dy}}\\odot \\hat{\\mathbf{B}}_i^{\\mathrm{dy}}" + }, + { + "bbox": [ + 306, + 144, + 547, + 190 + ], + "type": "text", + "content": " (bottom). Our approach segments challenging dynamic elements such as the moving shadow, swing, and swaying bushes." + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 369, + 70, + 426, + 103 + ], + "blocks": [ + { + "bbox": [ + 369, + 70, + 426, + 103 + ], + "lines": [ + { + "bbox": [ + 369, + 70, + 426, + 103 + ], + "spans": [ + { + "bbox": [ + 369, + 70, + 426, + 103 + ], + "type": "image", + "image_path": "8b3b5c0611f6cb555a3f49eb3a63568b2dfc46ab9a257ba177719b17518de73b.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 369, + 104, + 426, + 137 + ], + "blocks": [ + { + "bbox": [ + 369, + 104, + 426, + 137 + ], + "lines": [ + { + "bbox": [ + 369, + 104, + 426, + 137 + ], + "spans": [ + { + "bbox": [ + 369, + 104, + 426, + 137 + ], + "type": "image", + "image_path": "2d5474edfc09460de47b49677a3ae598b08daed948249eb68f2f9e4594a6c004.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 427, + 70, + 482, + 103 + ], + "blocks": [ + { + "bbox": [ + 427, + 70, + 482, + 103 + ], + "lines": [ + { + "bbox": [ + 427, + 70, + 482, + 103 + ], + "spans": [ + { + "bbox": [ + 427, + 70, + 482, + 103 + ], + "type": "image", + "image_path": "2c5c5fc3033adf98524a590aa412bc396df3a23e3814ef563b46501a626c3ed0.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + } + ], + "index": 18 + }, + { + "type": "image", + "bbox": [ + 483, + 70, + 542, + 103 + ], + "blocks": [ + { + "bbox": [ + 483, + 70, + 542, + 103 + ], + "lines": [ + { + "bbox": [ + 483, + 70, + 542, + 103 + ], + "spans": [ + { + "bbox": [ + 483, + 70, + 542, + 103 + ], + "type": "image", + "image_path": "ab65b0e5894ded0bcd7dc2bd4b29652abd673ab3ea3583c80cd24a42a1617bf5.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 208, + 547, + 255 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 208, + 547, + 255 + ], + "spans": [ + { + "bbox": [ + 304, + 208, + 547, + 255 + ], + "type": "text", + "content": "motion; we model dynamic scene content with a 2D convolutional encoder-decoder network " + }, + { + "bbox": [ + 304, + 208, + 547, + 255 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 208, + 547, + 255 + ], + "type": "text", + "content": ", which predicts a 2D opacity map " + }, + { + "bbox": [ + 304, + 208, + 547, + 255 + ], + "type": "inline_equation", + "content": "\\alpha_{i}^{\\mathrm{dy}}" + }, + { + "bbox": [ + 304, + 208, + 547, + 255 + ], + "type": "text", + "content": ", confidence map " + }, + { + "bbox": [ + 304, + 208, + 547, + 255 + ], + "type": "inline_equation", + "content": "\\beta_{i}^{\\mathrm{dy}}" + }, + { + "bbox": [ + 304, + 208, + 547, + 255 + ], + "type": "text", + "content": ", and RGB image " + }, + { + "bbox": [ + 304, + 208, + 547, + 255 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{B}}_{i}^{\\mathrm{dy}}" + }, + { + "bbox": [ + 304, + 208, + 547, + 255 + ], + "type": "text", + "content": " from an input frame:" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 376, + 256, + 545, + 272 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 376, + 256, + 545, + 272 + ], + "spans": [ + { + "bbox": [ + 376, + 256, + 545, + 272 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {B}} _ {i} ^ {\\mathrm {d y}}, \\boldsymbol {\\alpha} _ {i} ^ {\\mathrm {d y}}, \\boldsymbol {\\beta} _ {i} ^ {\\mathrm {d y}} = D (I _ {i}). \\tag {5}", + "image_path": "bae27556f45d76390fa804797ea41b6dfb08b7643d4968c7383402680b0a0cd1.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 274, + 545, + 297 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 274, + 545, + 297 + ], + "spans": [ + { + "bbox": [ + 304, + 274, + 545, + 297 + ], + "type": "text", + "content": "The full reconstructed image is then composited pixelwise from the outputs of the two models:" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 321, + 300, + 545, + 316 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 300, + 545, + 316 + ], + "spans": [ + { + "bbox": [ + 321, + 300, + 545, + 316 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {B}} _ {i} ^ {\\text {f u l l}} (\\mathbf {r}) = \\boldsymbol {\\alpha} _ {i} ^ {\\mathrm {d y}} (\\mathbf {r}) \\hat {\\mathbf {B}} _ {i} ^ {\\mathrm {d y}} (\\mathbf {r}) + (1 - \\boldsymbol {\\alpha} _ {i} ^ {\\mathrm {d y}} (\\mathbf {r})) \\hat {\\mathbf {B}} ^ {\\mathrm {s t}} (\\mathbf {r}). \\tag {6}", + "image_path": "41fc6590392c68fcd139928074f798d7e738940bc6e2699150e7c9386d55eac9.jpg" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 317, + 547, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 317, + 547, + 389 + ], + "spans": [ + { + "bbox": [ + 304, + 317, + 547, + 389 + ], + "type": "text", + "content": "To segment moving objects, we assume the observed pixel color is uncertain in a heteroscedastic aleatoric manner, and model the observations in the video with a Cauchy distribution with time dependent confidence " + }, + { + "bbox": [ + 304, + 317, + 547, + 389 + ], + "type": "inline_equation", + "content": "\\beta_{i}^{\\mathrm{dy}}" + }, + { + "bbox": [ + 304, + 317, + 547, + 389 + ], + "type": "text", + "content": ". By taking the negative log-likelihood of the observations, our segmentation loss is written as a weighted reconstruction loss:" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 315, + 391, + 545, + 424 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 391, + 545, + 424 + ], + "spans": [ + { + "bbox": [ + 315, + 391, + 545, + 424 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {s e g}} = \\sum_ {\\mathbf {r}} \\log \\left(\\beta_ {i} ^ {\\mathrm {d y}} (\\mathbf {r}) + \\frac {\\left| \\left| \\hat {\\mathbf {B}} _ {i} ^ {\\text {f u l l}} (\\mathbf {r}) - \\mathbf {C} _ {i} (\\mathbf {r}) \\right| \\right| ^ {2}}{\\beta_ {i} ^ {\\mathrm {d y}} (\\mathbf {r})}\\right). \\tag {7}", + "image_path": "a82200e9485991afddb6b25eeeaea1858f29de4b670944fec6fb226b484bd7c4.jpg" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 426, + 547, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 547, + 521 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 547, + 521 + ], + "type": "text", + "content": "By optimizing the two models using Eq. 7, we obtain a motion segmentation mask " + }, + { + "bbox": [ + 304, + 426, + 547, + 521 + ], + "type": "inline_equation", + "content": "M_{i}" + }, + { + "bbox": [ + 304, + 426, + 547, + 521 + ], + "type": "text", + "content": " by thresholding " + }, + { + "bbox": [ + 304, + 426, + 547, + 521 + ], + "type": "inline_equation", + "content": "\\alpha_{i}^{\\mathrm{dy}}" + }, + { + "bbox": [ + 304, + 426, + 547, + 521 + ], + "type": "text", + "content": " at 0.5. We do not require an alpha regularization loss as in NeRF-W [45] to avoid degeneracies, since we naturally include such an inductive basis by excluding skip connections from network " + }, + { + "bbox": [ + 304, + 426, + 547, + 521 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 426, + 547, + 521 + ], + "type": "text", + "content": ", which leads " + }, + { + "bbox": [ + 304, + 426, + 547, + 521 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 426, + 547, + 521 + ], + "type": "text", + "content": " to converge more slowly than the static IBR model. We show our estimated motion segmentation masks overlaid on input images in Fig. 5." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 304, + 525, + 547, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 525, + 547, + 598 + ], + "spans": [ + { + "bbox": [ + 304, + 525, + 547, + 598 + ], + "type": "text", + "content": "Supervision with segmentation masks. We initialize our main time-varying and time-invariant models with masks " + }, + { + "bbox": [ + 304, + 525, + 547, + 598 + ], + "type": "inline_equation", + "content": "M_{i}" + }, + { + "bbox": [ + 304, + 525, + 547, + 598 + ], + "type": "text", + "content": " as in Omnimatte [43], by applying a reconstruction loss to renderings from the time-varying model in dynamic regions, and to renderings from the time-invariant model in static regions:" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 340, + 600, + 545, + 651 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 340, + 600, + 545, + 651 + ], + "spans": [ + { + "bbox": [ + 340, + 600, + 545, + 651 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\text {m a s k}} = \\sum_ {\\mathbf {r}} (1 - M _ {i}) (\\mathbf {r}) \\rho \\left(\\hat {\\mathbf {C}} ^ {\\mathrm {s t}} (\\mathbf {r}), \\mathbf {C} _ {i} (\\mathbf {r})\\right) \\\\ + \\sum_ {\\mathbf {r}} M _ {i} (\\mathbf {r}) \\rho \\left(\\hat {\\mathbf {C}} _ {i} ^ {\\mathrm {d y}} (\\mathbf {r}), \\mathbf {C} _ {i} (\\mathbf {r})\\right) \\tag {8} \\\\ \\end{array}", + "image_path": "1bced7fd1ab5d78f37bca9a70408d87f088db71fd19bc12a7a60c4aaf4ec6feb.jpg" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 304, + 654, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 547, + 714 + ], + "type": "text", + "content": "We perform morphological erosion and dilation on " + }, + { + "bbox": [ + 304, + 654, + 547, + 714 + ], + "type": "inline_equation", + "content": "M_{i}" + }, + { + "bbox": [ + 304, + 654, + 547, + 714 + ], + "type": "text", + "content": " to obtain masks of dynamic and static regions respectively in order to turn off the loss near mask boundaries. We supervise the system with " + }, + { + "bbox": [ + 304, + 654, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{mask}}" + }, + { + "bbox": [ + 304, + 654, + 547, + 714 + ], + "type": "text", + "content": " and decay the weights by a factor of 5 for dynamic regions every 50K optimization steps." + } + ] + } + ], + "index": 30 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "4277" + } + ] + } + ], + "index": 31 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 139, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 139, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 139, + 85 + ], + "type": "text", + "content": "3.4. Regularization" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 90, + 289, + 269 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 90, + 289, + 269 + ], + "spans": [ + { + "bbox": [ + 46, + 90, + 289, + 269 + ], + "type": "text", + "content": "As noted in prior work, monocular reconstruction of complex dynamic scenes is highly ill-posed, and using photometric consistency alone is insufficient to avoid bad local minima during optimization [19, 35]. Therefore, we adopt regularization schemes used in prior work [2, 35, 73, 75], which consist of three main parts " + }, + { + "bbox": [ + 46, + 90, + 289, + 269 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{reg}} = \\mathcal{L}_{\\mathrm{data}} + \\mathcal{L}_{\\mathrm{MT}} + \\mathcal{L}_{\\mathrm{cpt}}" + }, + { + "bbox": [ + 46, + 90, + 289, + 269 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 90, + 289, + 269 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{data}}" + }, + { + "bbox": [ + 46, + 90, + 289, + 269 + ], + "type": "text", + "content": " is a data-driven term consisting of " + }, + { + "bbox": [ + 46, + 90, + 289, + 269 + ], + "type": "inline_equation", + "content": "\\ell_{1}" + }, + { + "bbox": [ + 46, + 90, + 289, + 269 + ], + "type": "text", + "content": " monocular depth and optical flow consistency priors using the estimates from Zhang et al. [80] and RAFT [65]. " + }, + { + "bbox": [ + 46, + 90, + 289, + 269 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{MT}}" + }, + { + "bbox": [ + 46, + 90, + 289, + 269 + ], + "type": "text", + "content": " is a motion trajectory regularization term that encourages estimated trajectory fields to be cycle-consistent and spatial-temporally smooth. " + }, + { + "bbox": [ + 46, + 90, + 289, + 269 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{cpt}}" + }, + { + "bbox": [ + 46, + 90, + 289, + 269 + ], + "type": "text", + "content": " is a compactness prior that encourages the scene decomposition to be binary via an entropy loss, and mitigates floaters through distortion losses [2]. We refer readers to the supplement for more details." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 270, + 288, + 294 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 270, + 288, + 294 + ], + "spans": [ + { + "bbox": [ + 47, + 270, + 288, + 294 + ], + "type": "text", + "content": "In summary, the final combined loss used to optimize our main representation for space-time view synthesis is:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 113, + 299, + 287, + 312 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 299, + 287, + 312 + ], + "spans": [ + { + "bbox": [ + 113, + 299, + 287, + 312 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {\\text {p h o}} + \\mathcal {L} _ {\\text {m a s k}} + \\mathcal {L} _ {\\text {r e g}}. \\tag {9}", + "image_path": "2e8792eb267e554ed1c8242d2131d38a19a08b45162aaf89a75018cd37d5afc0.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 320, + 181, + 335 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 320, + 181, + 335 + ], + "spans": [ + { + "bbox": [ + 47, + 320, + 181, + 335 + ], + "type": "text", + "content": "4. Implementation details" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 341, + 289, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 341, + 289, + 484 + ], + "spans": [ + { + "bbox": [ + 46, + 341, + 289, + 484 + ], + "type": "text", + "content": "Data. We conduct numerical evaluations on the Nvidia Dynamic Scene Dataset [75] and UCSD Dynamic Scenes Dataset [37]. Each dataset consists of eight forward-facing dynamic scenes recorded by synchronized multi-view cameras. We follow prior work [35] to derive a monocular video from each sequence, where each video contains " + }, + { + "bbox": [ + 46, + 341, + 289, + 484 + ], + "type": "inline_equation", + "content": "100\\sim 250" + }, + { + "bbox": [ + 46, + 341, + 289, + 484 + ], + "type": "text", + "content": " frames. We removed frames that lack large regions of moving objects. We follow the protocol from prior work [35] that uses held-out images per time instance for evaluation. We also tested the methods on in-the-wild monocular videos, which feature more challenging camera and object motions [20]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 486, + 289, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 486, + 289, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 486, + 289, + 713 + ], + "type": "text", + "content": "View selection. For the time-varying, dynamic model we use a frame window radius of " + }, + { + "bbox": [ + 46, + 486, + 289, + 713 + ], + "type": "inline_equation", + "content": "r = 3" + }, + { + "bbox": [ + 46, + 486, + 289, + 713 + ], + "type": "text", + "content": " for all experiments. For the time-invariant model representing static scene content, we use separate strategies for the dynamic scenes benchmarks and for in-the-wild videos. For the benchmarks, where camera viewpoints are located at discrete camera rig locations, we choose all nearby distinct viewpoints whose timestep is within 12 frames of the target time. For in-the-wild videos, naively choosing the nearest source views can lead to poor reconstruction due to insufficient camera baseline. Thus, to ensure that for any rendered pixel we have sufficient source views for computing its color, we select source views from distant frames. If we wish to select " + }, + { + "bbox": [ + 46, + 486, + 289, + 713 + ], + "type": "inline_equation", + "content": "N^{\\mathrm{vs}}" + }, + { + "bbox": [ + 46, + 486, + 289, + 713 + ], + "type": "text", + "content": " source views for the time-invariant model, we sub-sample every " + }, + { + "bbox": [ + 46, + 486, + 289, + 713 + ], + "type": "inline_equation", + "content": "\\frac{2r_{\\mathrm{max}}}{N^{\\mathrm{vs}}}" + }, + { + "bbox": [ + 46, + 486, + 289, + 713 + ], + "type": "text", + "content": " frames from the input video to build a candidate pool, where for a given target time " + }, + { + "bbox": [ + 46, + 486, + 289, + 713 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 486, + 289, + 713 + ], + "type": "text", + "content": ", we only search source views within " + }, + { + "bbox": [ + 46, + 486, + 289, + 713 + ], + "type": "inline_equation", + "content": "[i - r_{\\mathrm{max}}, i + r_{\\mathrm{max}}]" + }, + { + "bbox": [ + 46, + 486, + 289, + 713 + ], + "type": "text", + "content": " frames. We estimate " + }, + { + "bbox": [ + 46, + 486, + 289, + 713 + ], + "type": "inline_equation", + "content": "r_{\\mathrm{max}}^{\\mathrm{max}}" + }, + { + "bbox": [ + 46, + 486, + 289, + 713 + ], + "type": "text", + "content": " using the method of Li et al. [34] based on SfM point可视ibility and camera relative baseline. We then construct a" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 307, + 70, + 545, + 148 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 545, + 148 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 545, + 148 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 545, + 148 + ], + "type": "table", + "html": "
MethodsFullDynamic Only
SSIM↑PSNR↑LPIPS↓SSIM↑PSNR↑LPIPS↓
Nerfies [49]0.60920.640.2040.45517.350.258
HyperNeRF [50]0.65420.900.1820.44617.560.242
DVS [19]0.92127.440.0700.77822.630.144
NSFF [35]0.92728.900.0620.78323.080.159
Ours0.95730.910.0270.82624.310.062
", + "image_path": "d9ac34a35ea1d612ab91ffdb128ef06c12af5339b6ab8164fcd04ad8dda25d24.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 311, + 151, + 539, + 163 + ], + "lines": [ + { + "bbox": [ + 311, + 151, + 539, + 163 + ], + "spans": [ + { + "bbox": [ + 311, + 151, + 539, + 163 + ], + "type": "text", + "content": "Table 1. Quantitative evaluation on the Nvidia dataset [75]." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 183, + 545, + 220 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 183, + 545, + 220 + ], + "spans": [ + { + "bbox": [ + 305, + 183, + 545, + 220 + ], + "type": "text", + "content": "final set of source views for the model by choosing the top " + }, + { + "bbox": [ + 305, + 183, + 545, + 220 + ], + "type": "inline_equation", + "content": "N^{\\mathrm{vs}}" + }, + { + "bbox": [ + 305, + 183, + 545, + 220 + ], + "type": "text", + "content": " frames in the candidate pool that are the closest to the target view in terms of camera baseline. We set " + }, + { + "bbox": [ + 305, + 183, + 545, + 220 + ], + "type": "inline_equation", + "content": "N^{\\mathrm{vs}} = 16" + }, + { + "bbox": [ + 305, + 183, + 545, + 220 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 223, + 547, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 223, + 547, + 331 + ], + "spans": [ + { + "bbox": [ + 304, + 223, + 547, + 331 + ], + "type": "text", + "content": "Global spatial coordinate embedding With local image feature aggregation alone, it is hard to determine density accurately on non-surface or occluded surface points due to inconsistent features from different source views, as described in NeuRay [39]. Therefore, to improve global reasoning for density prediction, we append a global spatial coordinate embedding as an input to the ray transformer, in addition to the time embedding, similar to the ideas from [64]. Please see supplement for more details." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 335, + 547, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 335, + 547, + 479 + ], + "spans": [ + { + "bbox": [ + 304, + 335, + 547, + 479 + ], + "type": "text", + "content": "Handling degeneracy through virtual views. Prior work [35] observed that optimization can converge to bad local minimal if camera and object motions are close to colinear, or object motions are too fast to track. Inspired by [36], we synthesize images at eight randomly sampled nearby viewpoints for every input via depths estimated by [80]. During rendering, we randomly sample a virtual view as additional source image. We only apply this technique to in-the-wild videos since it improves optimization stability and rendering quality for such inputs, whereas we don't observe improvement on the benchmarks due to disentangled camera-object motions as described by [20]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 482, + 547, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 482, + 547, + 590 + ], + "spans": [ + { + "bbox": [ + 304, + 482, + 547, + 590 + ], + "type": "text", + "content": "Time interpolation. Our approach also allows for time interpolation by performing scene motion-based splatting, as introduced by NSFF [35]. To render at a specified target fractional time, we predict the volumetric density and color at two nearby input times by aggregating local image features from their corresponding set of source views. The predicted color and density are then splatted and linearly blended via the scene flow derived from our motion trajectories, and weighted according to the target fractional time index." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 594, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 548, + 714 + ], + "type": "text", + "content": "Setup. We estimate camera poses using COLMAP [57]. For each ray, we use a coarse-to-fine sampling strategy with 128 per-ray samples as in Wang et al. [70]. A separate model is trained from scratch for each scene using the Adam optimizer [29]. The network architecture for two main representations is a variant of that of IBRNet [70]. We reconstruct the entire scene in Euclidean space without special scene parameterization. Optimizing a full system on a 10 second video takes around two days using 8 Nvidia A100s, and rendering takes roughly 20 seconds for a " + }, + { + "bbox": [ + 304, + 594, + 548, + 714 + ], + "type": "inline_equation", + "content": "768 \\times 432" + }, + { + "bbox": [ + 304, + 594, + 548, + 714 + ], + "type": "text", + "content": " frame. We" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "4278" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 108, + 175 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 108, + 175 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 108, + 175 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 108, + 175 + ], + "type": "image", + "image_path": "3d776eba96f1803c797b21b2807ece60d3cf77bfe48be57fefc53ddb3c199c6c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 56, + 176, + 100, + 183 + ], + "lines": [ + { + "bbox": [ + 56, + 176, + 100, + 183 + ], + "spans": [ + { + "bbox": [ + 56, + 176, + 100, + 183 + ], + "type": "text", + "content": "Our rendered views" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 110, + 70, + 144, + 175 + ], + "blocks": [ + { + "bbox": [ + 110, + 70, + 144, + 175 + ], + "lines": [ + { + "bbox": [ + 110, + 70, + 144, + 175 + ], + "spans": [ + { + "bbox": [ + 110, + 70, + 144, + 175 + ], + "type": "image", + "image_path": "593df20c052cd13a6a061df9745ee2bc9de0aec5ad036c67c24a13158ee22e02.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 120, + 176, + 133, + 183 + ], + "lines": [ + { + "bbox": [ + 120, + 176, + 133, + 183 + ], + "spans": [ + { + "bbox": [ + 120, + 176, + 133, + 183 + ], + "type": "text", + "content": "DVS" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 145, + 70, + 179, + 175 + ], + "blocks": [ + { + "bbox": [ + 145, + 70, + 179, + 175 + ], + "lines": [ + { + "bbox": [ + 145, + 70, + 179, + 175 + ], + "spans": [ + { + "bbox": [ + 145, + 70, + 179, + 175 + ], + "type": "image", + "image_path": "54a68978a082babcb7b4bc5f0e0d03de32db745cee26c9f52c0db53b5ae981de.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 149, + 176, + 176, + 183 + ], + "lines": [ + { + "bbox": [ + 149, + 176, + 176, + 183 + ], + "spans": [ + { + "bbox": [ + 149, + 176, + 176, + 183 + ], + "type": "text", + "content": "HyperNeRF" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 181, + 70, + 215, + 175 + ], + "blocks": [ + { + "bbox": [ + 181, + 70, + 215, + 175 + ], + "lines": [ + { + "bbox": [ + 181, + 70, + 215, + 175 + ], + "spans": [ + { + "bbox": [ + 181, + 70, + 215, + 175 + ], + "type": "image", + "image_path": "e4f452290da38fe2bd13ef41f4b52b39e01e91e0fe13b0bcaa08498db18a67d1.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 191, + 176, + 205, + 183 + ], + "lines": [ + { + "bbox": [ + 191, + 176, + 205, + 183 + ], + "spans": [ + { + "bbox": [ + 191, + 176, + 205, + 183 + ], + "type": "text", + "content": "NSFF" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 50, + 191, + 284, + 203 + ], + "lines": [ + { + "bbox": [ + 50, + 191, + 284, + 203 + ], + "spans": [ + { + "bbox": [ + 50, + 191, + 284, + 203 + ], + "type": "text", + "content": "Figure 6. Qualitative comparisons on the Nvidia dataset [75]." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 216, + 70, + 250, + 175 + ], + "blocks": [ + { + "bbox": [ + 216, + 70, + 250, + 175 + ], + "lines": [ + { + "bbox": [ + 216, + 70, + 250, + 175 + ], + "spans": [ + { + "bbox": [ + 216, + 70, + 250, + 175 + ], + "type": "image", + "image_path": "74b19900d2dc88d78b363e564d081f2f8156bde25b05538f4ed7598a238abc1a.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 228, + 177, + 239, + 184 + ], + "lines": [ + { + "bbox": [ + 228, + 177, + 239, + 184 + ], + "spans": [ + { + "bbox": [ + 228, + 177, + 239, + 184 + ], + "type": "text", + "content": "Ours" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 252, + 70, + 286, + 175 + ], + "blocks": [ + { + "bbox": [ + 252, + 70, + 286, + 175 + ], + "lines": [ + { + "bbox": [ + 252, + 70, + 286, + 175 + ], + "spans": [ + { + "bbox": [ + 252, + 70, + 286, + 175 + ], + "type": "image", + "image_path": "de37927ee5ffbf2bc82eb0f52b89928096d6b978f9b584b394debc7922cff216.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 265, + 176, + 273, + 183 + ], + "lines": [ + { + "bbox": [ + 265, + 176, + 273, + 183 + ], + "spans": [ + { + "bbox": [ + 265, + 176, + 273, + 183 + ], + "type": "text", + "content": "GT" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 48, + 213, + 285, + 289 + ], + "blocks": [ + { + "bbox": [ + 48, + 213, + 285, + 289 + ], + "lines": [ + { + "bbox": [ + 48, + 213, + 285, + 289 + ], + "spans": [ + { + "bbox": [ + 48, + 213, + 285, + 289 + ], + "type": "table", + "html": "
MethodsFullDynamic Only
SSIM↑PSNR↑LPIPS↓SSIM↑PSNR↑LPIPS↓
Nerfies [49]0.82324.320.0960.59518.450.234
HyperNeRF [50]0.85925.100.0950.61819.260.212
DVS [19]0.94330.640.0750.86626.570.096
NSFF [35]0.95231.750.0340.85125.830.115
Ours0.98336.470.0140.90928.010.042
", + "image_path": "5860b7a9703bd64fcf57c8c05526ae470d7d49debeb07d7b8bffa4ad968a96eb.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "bbox": [ + 53, + 294, + 279, + 305 + ], + "lines": [ + { + "bbox": [ + 53, + 294, + 279, + 305 + ], + "spans": [ + { + "bbox": [ + 53, + 294, + 279, + 305 + ], + "type": "text", + "content": "Table 2. Quantitative evaluation on the UCSD dataset [37]." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 326, + 288, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 326, + 288, + 350 + ], + "spans": [ + { + "bbox": [ + 46, + 326, + 288, + 350 + ], + "type": "text", + "content": "refer readers to the supplemental material for network architectures, hyper-parameters setting, and additional details." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 47, + 361, + 118, + 373 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 361, + 118, + 373 + ], + "spans": [ + { + "bbox": [ + 47, + 361, + 118, + 373 + ], + "type": "text", + "content": "5. Evaluation" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 47, + 380, + 198, + 392 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 380, + 198, + 392 + ], + "spans": [ + { + "bbox": [ + 47, + 380, + 198, + 392 + ], + "type": "text", + "content": "5.1. Baselines and error metrics" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 46, + 399, + 288, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 399, + 288, + 495 + ], + "spans": [ + { + "bbox": [ + 46, + 399, + 288, + 495 + ], + "type": "text", + "content": "We compare our approach to state-of-the-art monocular view synthesis methods. Specifically, we compare to three recent canonical space-based methods, Nerfies [49], and HyperNeRF [50], and to two scene flow-based methods, NSFF [35] and Dynamic View Synthesis (DVS) from Gao et al. [19]. For fair comparisons, we use the same depth, optical flow and motion segmentation masks used for our approach as inputs to other methods." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 46, + 495, + 287, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 495, + 287, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 495, + 287, + 567 + ], + "type": "text", + "content": "Following prior work [35], we report the rendering quality of each method with three standard error metrics: peak signal-to-noise ratio (PSNR), structural similarity (SSIM), and perceptual similarity via LPIPS [77], and calculate errors both over the entire scene (Full) and restricted to moving regions (Dynamic Only)." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 47, + 575, + 180, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 575, + 180, + 588 + ], + "spans": [ + { + "bbox": [ + 47, + 575, + 180, + 588 + ], + "type": "text", + "content": "5.2.Quantitative evaluation" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 46, + 594, + 288, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 712 + ], + "type": "text", + "content": "Quantitative results on the two benchmark datasets are shown in Table 1 and Table 2. Our approach significantly improves over prior state-of-the-art methods in terms of all error metrics. Notably, our approach improves PSNR over entire scene upon the second best methods by 2dB and 4dB on each of the two datasets. Our approach also reduces LPIPS error, a major indicator of perceptual quality compared with real images [77], by over " + }, + { + "bbox": [ + 46, + 594, + 288, + 712 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 594, + 288, + 712 + ], + "type": "text", + "content": ". These results suggest that our framework is much more effective at recovering highly detailed scene contents." + } + ] + } + ], + "index": 21 + }, + { + "type": "image", + "bbox": [ + 307, + 70, + 367, + 175 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 367, + 175 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 367, + 175 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 367, + 175 + ], + "type": "image", + "image_path": "8d010bf52c01f35cffb791746740e39432e449402f60ccf0046c930b35030ab5.jpg" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 315, + 176, + 359, + 183 + ], + "lines": [ + { + "bbox": [ + 315, + 176, + 359, + 183 + ], + "spans": [ + { + "bbox": [ + 315, + 176, + 359, + 183 + ], + "type": "text", + "content": "Our rendered views" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 309, + 191, + 542, + 203 + ], + "lines": [ + { + "bbox": [ + 309, + 191, + 542, + 203 + ], + "spans": [ + { + "bbox": [ + 309, + 191, + 542, + 203 + ], + "type": "text", + "content": "Figure 7. Qualitative comparisons on the UCSD dataset [37]." + } + ] + } + ], + "index": 34, + "angle": 0, + "type": "image_caption" + } + ], + "index": 22 + }, + { + "type": "image", + "bbox": [ + 369, + 70, + 403, + 175 + ], + "blocks": [ + { + "bbox": [ + 369, + 70, + 403, + 175 + ], + "lines": [ + { + "bbox": [ + 369, + 70, + 403, + 175 + ], + "spans": [ + { + "bbox": [ + 369, + 70, + 403, + 175 + ], + "type": "image", + "image_path": "ff59b50d98d0184f5cfaf8254f4af5d228b4334a205379fc820f084edcadc8c7.jpg" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 379, + 176, + 391, + 183 + ], + "lines": [ + { + "bbox": [ + 379, + 176, + 391, + 183 + ], + "spans": [ + { + "bbox": [ + 379, + 176, + 391, + 183 + ], + "type": "text", + "content": "DVS" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_caption" + } + ], + "index": 24 + }, + { + "type": "image", + "bbox": [ + 403, + 70, + 438, + 175 + ], + "blocks": [ + { + "bbox": [ + 403, + 70, + 438, + 175 + ], + "lines": [ + { + "bbox": [ + 403, + 70, + 438, + 175 + ], + "spans": [ + { + "bbox": [ + 403, + 70, + 438, + 175 + ], + "type": "image", + "image_path": "47a517a517e98b78db2e93800f0b63091e03287affb5961ff81e39c77ed3c474.jpg" + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 407, + 176, + 435, + 185 + ], + "lines": [ + { + "bbox": [ + 407, + 176, + 435, + 185 + ], + "spans": [ + { + "bbox": [ + 407, + 176, + 435, + 185 + ], + "type": "text", + "content": "HyperNeRF" + } + ] + } + ], + "index": 27, + "angle": 0, + "type": "image_caption" + } + ], + "index": 26 + }, + { + "type": "image", + "bbox": [ + 440, + 70, + 473, + 175 + ], + "blocks": [ + { + "bbox": [ + 440, + 70, + 473, + 175 + ], + "lines": [ + { + "bbox": [ + 440, + 70, + 473, + 175 + ], + "spans": [ + { + "bbox": [ + 440, + 70, + 473, + 175 + ], + "type": "image", + "image_path": "b3e8e6718a46b39ee11be7b34b1c4ab8c9d9135b313b4657310c49ad0cb7b52b.jpg" + } + ] + } + ], + "index": 28, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 449, + 176, + 463, + 183 + ], + "lines": [ + { + "bbox": [ + 449, + 176, + 463, + 183 + ], + "spans": [ + { + "bbox": [ + 449, + 176, + 463, + 183 + ], + "type": "text", + "content": "NSFF" + } + ] + } + ], + "index": 29, + "angle": 0, + "type": "image_caption" + } + ], + "index": 28 + }, + { + "type": "image", + "bbox": [ + 475, + 70, + 509, + 175 + ], + "blocks": [ + { + "bbox": [ + 475, + 70, + 509, + 175 + ], + "lines": [ + { + "bbox": [ + 475, + 70, + 509, + 175 + ], + "spans": [ + { + "bbox": [ + 475, + 70, + 509, + 175 + ], + "type": "image", + "image_path": "c2a9e6be3f8b2b9cc71ed547d21fce4985d230e5e47b35bf13908a9b680a6947.jpg" + } + ] + } + ], + "index": 30, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 486, + 177, + 498, + 183 + ], + "lines": [ + { + "bbox": [ + 486, + 177, + 498, + 183 + ], + "spans": [ + { + "bbox": [ + 486, + 177, + 498, + 183 + ], + "type": "text", + "content": "Ours" + } + ] + } + ], + "index": 31, + "angle": 0, + "type": "image_caption" + } + ], + "index": 30 + }, + { + "type": "image", + "bbox": [ + 511, + 70, + 545, + 175 + ], + "blocks": [ + { + "bbox": [ + 511, + 70, + 545, + 175 + ], + "lines": [ + { + "bbox": [ + 511, + 70, + 545, + 175 + ], + "spans": [ + { + "bbox": [ + 511, + 70, + 545, + 175 + ], + "type": "image", + "image_path": "6cd332f745c2acb1d1fe83a06d43fac2e4360e72710b07280bb8776d884f5d89.jpg" + } + ] + } + ], + "index": 32, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 523, + 177, + 531, + 183 + ], + "lines": [ + { + "bbox": [ + 523, + 177, + 531, + 183 + ], + "spans": [ + { + "bbox": [ + 523, + 177, + 531, + 183 + ], + "type": "text", + "content": "GT" + } + ] + } + ], + "index": 33, + "angle": 0, + "type": "image_caption" + } + ], + "index": 32 + }, + { + "bbox": [ + 304, + 224, + 547, + 500 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 224, + 547, + 500 + ], + "spans": [ + { + "bbox": [ + 304, + 224, + 547, + 500 + ], + "type": "text", + "content": "Ablation study. We conduct an ablation study on the Nvidia Dynamic Scene Dataset to validate the effectiveness of our various proposed system components. We show comparisons between our full system and variants in Tab. 3: A) baseline IBRNet [70] with extra time embedding; B) without enforcing temporal consistency via cross-time rendering; C) using scene flow fields to aggregate image features within one time step; D) predicting multiple 3D scene flow vectors pointing to " + }, + { + "bbox": [ + 304, + 224, + 547, + 500 + ], + "type": "inline_equation", + "content": "2r" + }, + { + "bbox": [ + 304, + 224, + 547, + 500 + ], + "type": "text", + "content": " nearby times at each sample; E) without using a time-invariant static scene model; F) without masked reconstruction loss via estimated motion segmentation masks; and G) without regularization loss. For this ablation study, we train each model with 64 samples per ray. Without our motion trajectory representation and temporal consistency, view synthesis quality degrades significantly as shown in the first three rows of Tab. 3. Integrating a global spatial coordinate embedding further improves rendering quality. Combining static and dynamic models improves quality for static elements, as seen in metrics over full scenes. Finally, removing supervision from motion segmentation or regularization reduces overall rendering quality, demonstrating the value of proposed losses for avoiding bad local minimal during optimization." + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 306, + 509, + 432, + 522 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 509, + 432, + 522 + ], + "spans": [ + { + "bbox": [ + 306, + 509, + 432, + 522 + ], + "type": "text", + "content": "5.3. Qualitative evaluation" + } + ] + } + ], + "index": 36 + }, + { + "bbox": [ + 304, + 529, + 547, + 648 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 529, + 547, + 648 + ], + "spans": [ + { + "bbox": [ + 304, + 529, + 547, + 648 + ], + "type": "text", + "content": "Dynamic scenes dataset. We provide qualitative comparisons between our approach and three prior state-of-the-art methods [19, 35, 50] on the test views from two datasets in Fig. 6 and Fig.7. Prior dynamic-NeRF methods have difficulty rendering details of moving objects, as seen in the excessively blurred dynamic content including the texture of balloons, human faces, and clothing. In contrast, our approach synthesizes photo-realistic novel views of both static and dynamic scene content and which are closest to the ground truth images." + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 304, + 653, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 547, + 714 + ], + "type": "text", + "content": "In-the-wild videos. We show qualitative comparisons on in-the-wild footage of complex dynamic scenes. We show comparisons with Dynamic-NeRF based methods in Fig. 8, and Fig. 9 shows comparisons with point cloud rendering using depths [80]. Our approach synthesizes photo-realistic" + } + ] + } + ], + "index": 38 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "4279" + } + ] + } + ], + "index": 39 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 70, + 105, + 193 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 105, + 193 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 105, + 193 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 105, + 193 + ], + "type": "image", + "image_path": "8a0d628d664b461106331167aadfcb36ee07d14e56a2cf0c0c367f7706e61548.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 70, + 194, + 84, + 202 + ], + "lines": [ + { + "bbox": [ + 70, + 194, + 84, + 202 + ], + "spans": [ + { + "bbox": [ + 70, + 194, + 84, + 202 + ], + "type": "text", + "content": "Input" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 105, + 70, + 212, + 194 + ], + "blocks": [ + { + "bbox": [ + 105, + 70, + 212, + 194 + ], + "lines": [ + { + "bbox": [ + 105, + 70, + 212, + 194 + ], + "spans": [ + { + "bbox": [ + 105, + 70, + 212, + 194 + ], + "type": "image", + "image_path": "3748e0049fa3f60d3ab0b2c29fe467a2f394770486f57710639cd0b87f926f1d.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 151, + 196, + 165, + 203 + ], + "lines": [ + { + "bbox": [ + 151, + 196, + 165, + 203 + ], + "spans": [ + { + "bbox": [ + 151, + 196, + 165, + 203 + ], + "type": "text", + "content": "DVS" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 213, + 70, + 323, + 194 + ], + "blocks": [ + { + "bbox": [ + 213, + 70, + 323, + 194 + ], + "lines": [ + { + "bbox": [ + 213, + 70, + 323, + 194 + ], + "spans": [ + { + "bbox": [ + 213, + 70, + 323, + 194 + ], + "type": "image", + "image_path": "666f28fc07ce48329332469e73a6faea3d937de83d9d5b33de8957fcd1ca4246.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 252, + 194, + 283, + 203 + ], + "lines": [ + { + "bbox": [ + 252, + 194, + 283, + 203 + ], + "spans": [ + { + "bbox": [ + 252, + 194, + 283, + 203 + ], + "type": "text", + "content": "HyperNeRF" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 211, + 547, + 245 + ], + "lines": [ + { + "bbox": [ + 46, + 211, + 547, + 245 + ], + "spans": [ + { + "bbox": [ + 46, + 211, + 547, + 245 + ], + "type": "text", + "content": "Figure 8. Qualitative comparisons on in-the-wild videos. We show results on 10-second videos of complex dynamic scenes. The leftmost column shows the start and end frames of each video; on the right we show novel views at intermediate times rendered from our approach and prior state-of-the-art methods [19,35,50]." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 324, + 70, + 433, + 194 + ], + "blocks": [ + { + "bbox": [ + 324, + 70, + 433, + 194 + ], + "lines": [ + { + "bbox": [ + 324, + 70, + 433, + 194 + ], + "spans": [ + { + "bbox": [ + 324, + 70, + 433, + 194 + ], + "type": "image", + "image_path": "49d02da58f0182bf12b36344f6f16551cad415c7f173e9e219634a1e5c0b8bda.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 371, + 194, + 386, + 202 + ], + "lines": [ + { + "bbox": [ + 371, + 194, + 386, + 202 + ], + "spans": [ + { + "bbox": [ + 371, + 194, + 386, + 202 + ], + "type": "text", + "content": "NSFF" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 434, + 70, + 545, + 194 + ], + "blocks": [ + { + "bbox": [ + 434, + 70, + 545, + 194 + ], + "lines": [ + { + "bbox": [ + 434, + 70, + 545, + 194 + ], + "spans": [ + { + "bbox": [ + 434, + 70, + 545, + 194 + ], + "type": "image", + "image_path": "92cd4c156cccb001e58694bba8a13f0e09c4b08f54e11c1b677636931cf41b07.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 481, + 195, + 494, + 202 + ], + "lines": [ + { + "bbox": [ + 481, + 195, + 494, + 202 + ], + "spans": [ + { + "bbox": [ + 481, + 195, + 494, + 202 + ], + "type": "text", + "content": "Ours" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 48, + 262, + 286, + 353 + ], + "blocks": [ + { + "bbox": [ + 48, + 262, + 286, + 353 + ], + "lines": [ + { + "bbox": [ + 48, + 262, + 286, + 353 + ], + "spans": [ + { + "bbox": [ + 48, + 262, + 286, + 353 + ], + "type": "image", + "image_path": "2df62ad10ade8370b6c816267cbfa910ac8450c9626d29c0edf41fcbd6103e12.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 357, + 288, + 392 + ], + "lines": [ + { + "bbox": [ + 46, + 357, + 288, + 392 + ], + "spans": [ + { + "bbox": [ + 46, + 357, + 288, + 392 + ], + "type": "text", + "content": "Figure 9. From left to right, We show inputs and corresponding novel views rendered from explicit depth warping with Zhang et al. [80], and from our approach." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 48, + 400, + 286, + 503 + ], + "blocks": [ + { + "bbox": [ + 48, + 400, + 286, + 503 + ], + "lines": [ + { + "bbox": [ + 48, + 400, + 286, + 503 + ], + "spans": [ + { + "bbox": [ + 48, + 400, + 286, + 503 + ], + "type": "table", + "html": "
MethodsFullDynamic Only
SSIM↑PSNR↑LPIPS↓SSIM↑PSNR↑LPIPS↓
A) [70]+time0.90525.330.0810.68320.090.122
B) w/o TC0.91127.570.0740.75122.160.104
C) w/ SF0.93529.420.0350.79722.410.095
D) w/ M-SF0.94729.590.0330.81422.970.084
E) w/o static rep.0.91928.190.0470.84024.010.071
F) w/o Lmask0.93029.950.0360.83524.300.063
G) w/o Lreg0.92129.460.0420.79522.190.080
Full0.95730.770.0280.83724.270.066
", + "image_path": "f15eae0c6ff895243afe07c4b9edd8f8c8828863d7706e6844e38097361611c2.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 507, + 288, + 531 + ], + "lines": [ + { + "bbox": [ + 46, + 507, + 288, + 531 + ], + "spans": [ + { + "bbox": [ + 46, + 507, + 288, + 531 + ], + "type": "text", + "content": "Table 3. Ablation study on the Nvidia Dataset. See Sec. 5.2 for detailed descriptions of each configuration." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 550, + 288, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 550, + 288, + 624 + ], + "spans": [ + { + "bbox": [ + 46, + 550, + 288, + 624 + ], + "type": "text", + "content": "novel views, whereas prior dynamic-Nerf methods fail to recover high-quality details of both static and moving scene contents, such as the shirt wrinkles and the dog's fur in Fig. 8. On the other hand, explicit depth warping produces holes at regions near disocculusions and out of field of view. We refer readers to the supplementary video for full comparisons." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 47, + 633, + 195, + 646 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 633, + 195, + 646 + ], + "spans": [ + { + "bbox": [ + 47, + 633, + 195, + 646 + ], + "type": "text", + "content": "6. Discussion and conclusion" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 46, + 653, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 289, + 715 + ], + "type": "text", + "content": "Limitations. Our method is limited to relatively small viewpoint changes compared with methods designed for static or quasi-static scene; Our method is not able to handle small fast moving object due to incorrect initial depth and optical flow estimates (left, Fig. 10). In addition, compared to" + } + ] + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 306, + 262, + 386, + 308 + ], + "blocks": [ + { + "bbox": [ + 306, + 262, + 386, + 308 + ], + "lines": [ + { + "bbox": [ + 306, + 262, + 386, + 308 + ], + "spans": [ + { + "bbox": [ + 306, + 262, + 386, + 308 + ], + "type": "image", + "image_path": "6a5c70a4cb23179dda7b619599307285d93c36e7fbeea198f7d704415474d980.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 313, + 547, + 370 + ], + "lines": [ + { + "bbox": [ + 305, + 313, + 547, + 370 + ], + "spans": [ + { + "bbox": [ + 305, + 313, + 547, + 370 + ], + "type": "text", + "content": "Figure 10. Limitations. Our method might fail to model moving thin objects such as moving leash (left). Our method can fail to render dynamic contents only visible in distant frames (middle). The rendered static content can be unrealistic or blank if insufficient source views feature are aggregated for a given pixel (right)." + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "type": "image", + "bbox": [ + 386, + 262, + 465, + 308 + ], + "blocks": [ + { + "bbox": [ + 386, + 262, + 465, + 308 + ], + "lines": [ + { + "bbox": [ + 386, + 262, + 465, + 308 + ], + "spans": [ + { + "bbox": [ + 386, + 262, + 465, + 308 + ], + "type": "image", + "image_path": "d0c2038055b9eff8213e504c62f7355a1bc1ab38dba4f3bfdca32c65cc95a6b2.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + } + ], + "index": 19 + }, + { + "type": "image", + "bbox": [ + 466, + 262, + 545, + 308 + ], + "blocks": [ + { + "bbox": [ + 466, + 262, + 545, + 308 + ], + "lines": [ + { + "bbox": [ + 466, + 262, + 545, + 308 + ], + "spans": [ + { + "bbox": [ + 466, + 262, + 545, + 308 + ], + "type": "image", + "image_path": "f2b4401b5ab9b67c28a5e317844551354d6ac3de52a8e0cd9f5e2e21635b0a54.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_body" + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 396, + 547, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 396, + 547, + 504 + ], + "spans": [ + { + "bbox": [ + 304, + 396, + 547, + 504 + ], + "type": "text", + "content": "prior dynamic NeRF methods, the synthesized views are not strictly multi-view consistent, and rendering quality of static content depends on which source views are selected (middle, Fig. 10). Our approach is also sensitive to degenerate motion patterns from in-the-wild videos, in which object and camera motion is mostly colinear, but we show heuristics to handle such cases in the supplemental. Moreover, our method is able to synthesize dynamic contents only appearing at distant time (right, Fig. 10)" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 525, + 547, + 644 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 525, + 547, + 644 + ], + "spans": [ + { + "bbox": [ + 304, + 525, + 547, + 644 + ], + "type": "text", + "content": "Conclusion. We presented a new approach for space-time view synthesis from a monocular video depicting a complex dynamic scene. By representing a dynamic scene within a volumetric IBR framework, our approach overcomes limitations of recent methods that cannot model long videos with complex camera and object motion. We have shown that our method can synthesize photo-realistic novel views from in-the-wild dynamic videos, and can achieve significant improvements over prior state-of-the-art methods on the dynamic scene benchmarks." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": "Acknowledgements. Thanks to Andrew Liu, Richard Bowen and Lucy Chai for the fruitful discussions, and thanks to Rick Szeliski and Ricardo Martin-Brualla for helpful proofreading." + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4280" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "text", + "content": "[1] Aayush Bansal, Minh Vo, Yaser Sheikh, Deva Ramanan, and Srinivasa Narasimhan. 4D visualization of dynamic events from unconstrained multi-view videos. 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Local training on non-iid distributed data results in deflected local optimum, which causes the client models drift further away from each other and degrades the aggregated global model's performance. A natural solution is to gather all client data onto the server, such that the server has a global view of the entire data distribution. Unfortunately, this reduces to regular training, which compromises clients' privacy and conflicts with the purpose of FL. In this paper, we put forth an idea to collect and leverage global knowledge on the server without hindering data privacy. We unearth such knowledge from the dynamics of the global model's trajectory. Specifically, we first reserve a short trajectory of global model snapshots on the server. Then, we synthesize a small pseudo dataset such that the model trained on it mimics the dynamics of the reserved global model trajectory. Afterward, the synthesized data is used to help aggregate the deflected clients into the global model. We name our method DYNAFED, which enjoys the following advantages: 1) we do not rely on any external on-server dataset, which requires no additional cost for data collection; 2) the pseudo data can be synthesized in early communication rounds, which enables DYNAFED to take effect early for boosting the convergence and stabilizing training; 3) the pseudo data only needs to be synthesized once and can be directly utilized on the server to help aggregation in subsequent rounds. Experiments across extensive benchmarks are conducted to showcase the effectiveness of DYNAFED. We also provide insights and understanding of the underlying mechanism of our method.", + "bbox": [ + 76, + 316, + 473, + 771 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 78, + 799, + 209, + 814 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Federated learning (FL) has become a popular distributed training paradigm to alleviate the server's computational bur", + "bbox": [ + 76, + 824, + 470, + 854 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d7d9d55ad3fa1b56737a1f41227421e6262fe50cc431d280b3d298071dda1c37.jpg", + "image_caption": [ + "Figure 1. Illustration of DYNAFED. Firstly, we run the standard FedAvg for $L$ communication rounds and save the checkpoints to form a trajectory of the global model at the server. Then, we synthesize a pseudo dataset $\\mathcal{D}_{\\mathrm{syn}}$ , with which the network can be trained to mimic the dynamics of the global trajectory. In this way, the knowledge that captures the essential information about the global data distribution is transferred from the global dynamics to $\\mathcal{D}_{\\mathrm{syn}}$ . Afterward, $\\mathcal{D}_{\\mathrm{syn}}$ is adopted to help aggregate the deflected clients into the global model at the server." + ], + "image_footnote": [], + "bbox": [ + 506, + 285, + 888, + 539 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "den and preserve clients' data privacy [3, 23, 31, 45]. In the FL paradigm, the clients only have access to their private datasets, while the server is responsible for aggregating the clients' updates into a global model. The most prevalent approaches in FL are based on local-SGD [34] (also referred to as FedAvg), where the client model is updated locally for multiple steps before being sent and merged on the server. Such approaches save communication costs and perform well given the client data are iid-distributed. However, in real-world applications such as healthcare [22, 23, 36, 37] and bio-metrics [2], the client data usually demonstrates heterogeneity (highly non-iid), which deflects the local optimum from the global optimum [24, 32, 52] and makes the locally", + "bbox": [ + 496, + 703, + 895, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Joint first authors. Code is available at this link.", + "bbox": [ + 93, + 862, + 352, + 875 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "$\\dagger$ Correspondence to Weizhong Zhang (weizhongzhang@fudan.edu.cn) and Qifeng Chen (chenqifeng22@gmail.com)", + "bbox": [ + 78, + 875, + 468, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "12177", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "trained clients biased. Therefore, naively averaging the client models results in slow convergence and performance drop.", + "bbox": [ + 76, + 90, + 468, + 121 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To alleviate the difficulty of training under heterogeneity, a few lines of work have been frequently discussed. The first line attempts to modify the local training process, including imposing regularization on the client models [1,24,29,31] and data sharing or augmentation [35, 38, 48, 52]. However, these solutions have a high requirement for the server's control of local clients. An orthogonal line focuses on refining the global model in the server aggregation process [6, 33, 40, 44, 46]. The majority of these methods typically require a large external dataset on the server, then use it to align the outputs of the global model with that of the client ensemble [6, 15, 33, 44]. Unfortunately, such a large-scale task-related dataset is often hard to acquire in reality. To circumvent this limitation, a few data-free knowledge distillation (KD) approaches are recently proposed [50,53]. These methods attempt to transfer the knowledge contained in the global model to a generator, which is subsequently leveraged to produce pseudo data to either help local training at the clients [53] or finetune the global model at the server [50]. It is clear that these methods require a global model with reasonable performance to ensure the generation of helpful pseudo data. However, such requirement is hard to achieve in practice since the global model often performs poorly under heterogeneity, especially in the early rounds of training. Other solutions include personalized FL [16, 27, 30, 39], similarity clustering [4, 10, 13], meta learning [21, 28], etc.", + "bbox": [ + 75, + 125, + 472, + 517 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Even though the above-mentioned works propose techniques to alleviate the challenges posed by heterogeneity to some extent, they do not tackle the issue from its root cause: the data is unevenly scattered at different clients and is kept locally due to privacy concerns, which is also the main obstacle for training an accurate global model. Ideally, imagine if we can collect all the client data to the server, then training can be directly conducted at the server, and the heterogeneity issue no longer exists. However, this reduces to regular training and conflicts with the original purpose of FL to protect client privacy. We then raise a natural question: is it possible to derive the essential information about the global data distribution on the server to help training without compromising client privacy?", + "bbox": [ + 75, + 520, + 470, + 733 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Despite the global model typically performing poorly due to heterogeneity, the changes in its parameters are steered jointly by the data scattered at different clients. Therefore, the update dynamics of the global model contain knowledge about global data distribution. Driven by this intuition, we propose DYNAFED to explicitly unearth such knowledge hidden in the global dynamics and transfer it to a pseudo dataset $\\mathcal{D}_{\\mathrm{syn}}$ at the server. $\\mathcal{D}_{\\mathrm{syn}}$ can then approximate the global data distribution on the server to aid aggregation. More specifically, inspired by recent works in dataset condensation [5,41,51], we formulate the data synthesis process into a", + "bbox": [ + 75, + 734, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "learning problem, which minimizes the distance between the trajectory trained with $\\mathcal{D}_{\\mathrm{syn}}$ and the global model trajectory derived with $\\mathcal{D}$ . Fine-tuning the aggregated global model with $\\mathcal{D}_{\\mathrm{syn}}$ effectively alleviates the performance degradation caused by deflected clients. An appealing feature of our DYNAFED is that the data can be synthesized using just the global model's trajectory of the first few rounds, which enables $\\mathcal{D}_{\\mathrm{syn}}$ to take effect and help aggregation from early rounds. In addition, the synthesizing process only needs to be conducted once in practice, after which the derived $\\mathcal{D}_{\\mathrm{syn}}$ can be directly applied in subsequent rounds to help aggregate the deviated client models.", + "bbox": [ + 496, + 90, + 893, + 271 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Notably, our framework can be readily applied to the majority of FL approaches, since we rely on only the history of the global model's parameters for synthesizing $\\mathcal{D}_{\\mathrm{syn}}$ , which is available in the conventional setting of FedAvg-based methods. Furthermore, because we extract global knowledge using the global dynamics, rather than any client-specific information as in [12, 17, 18, 20, 47], the derived $\\mathcal{D}_{\\mathrm{syn}}$ comprises of information mixed with the entire global data distribution, thus prevents leakage of client privacy.", + "bbox": [ + 496, + 273, + 895, + 409 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our DYNAFED possesses the following advantages compared with previous approaches: 1) It leverages the knowledge of the global data distribution to alleviate the aggregation bias of the global model without depending on any external datasets; 2) DYNAFED is able to generate informative data in the early rounds of federated learning, which significantly helps convergence and stabilizes training in subsequent rounds; 3) Compared with [50, 53], which need to keep updating the generator throughout all communication rounds, the data synthesis process in our method only needs to be done once, which reduces the computational overhead. In summary, we make the following contributions:", + "bbox": [ + 496, + 409, + 895, + 592 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a practical approach named DYNAFED for tackling the heterogeneity problem, which extracts and exploits the hidden information from the global model's trajectory. In this way, the server can access the essential knowledge of the global data distribution to reinforce aggregation;", + "- We experimentally show the synthesized dataset helps stabilize training, boost convergence and achieve significant performance improvement under heterogeneity;", + "- We provide insights and detailed analysis into the working mechanisms of the proposed DYNAFED both experimentally and theoretically." + ], + "bbox": [ + 517, + 602, + 893, + 782 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 799, + 640, + 814 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Regularization-based Methods FedAvg [34] is the most widely used technique in FL, which periodically aggregates the local models to the global model in each communication round. FedProx [31] proposes to impose a proximal term during local training, such that the local model does not", + "bbox": [ + 496, + 824, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "12178", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "drift too far from its global initialization; Scaffold [24] introduces a control variate and variance reduction to alleviate the drift of local training. Moon [29] proposes to leverage the similarity between model representations to regularize the client local training. FedDyn [1] introduces the linear and quadratic penalty terms to correct the clients' objective during local training. These methods are orthogonal to our approach and can be jointly used.", + "bbox": [ + 75, + 90, + 472, + 212 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Data-Dependent Knowledge Distillation Methods This line of work attempts to distill client ensemble knowledge into the global model. [33] proposes to use an unlabeled external dataset on the server to match the global model's outputs with that of the client ensemble. On top of this, [6] further proposes to sample and combine higher-quality client models via a Bayesian model ensemble. Subsequently, some advanced techniques, such as pre-training [15] and weighted consensus distillation scheme [8] are proposed. These methods typically require a large amount of data following similar distribution as the task data, which is usually hard to acquire in practice. Besides, these methods need to conduct KD with a large dataset in every communication round, which introduces prohibitive computational overhead.", + "bbox": [ + 75, + 217, + 472, + 429 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Data-free Knowledge Distillation Methods Recently, a few works have proposed to perform KD in a data-free manner by synthesizing data with generative models [50,53]. [53] proposes to train a lightweight generator on the server, which produces a feature embedding conditioned on the class index. The generator is then sent to the clients to regularize local training. [50] trains a class conditional GAN [14] on the server, where the global model acts as the discriminator. The pseudo data is then used to finetune the global model. These methods all depend on the global model for training the generator. Unfortunately, the model performance is often poor under high data heterogeneity, which makes the quality of the pseudo data questionable. On the other hand, due to the use of update dynamics of the global model rather than an individual model, our method can synthesize high-quality data containing rich global information even if the global model performs poorly.", + "bbox": [ + 75, + 446, + 472, + 705 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Preliminary", + "text_level": 1, + "bbox": [ + 76, + 715, + 204, + 733 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Federated Learning. Suppose we have $M$ clients in a federated learning system. For each client $m \\in [M]$ , a private dataset $\\mathcal{D}_m = \\{(x_i, y_i)\\}_{i=1}^{|\\mathcal{D}_m|}$ is kept locally. The overall optimization goal of the FL system is to jointly train a global model which performs well on the combination of local data, denoted as $\\mathcal{D} = \\cup_{m=1}^{M} \\mathcal{D}_m$ , where $\\mathcal{D}$ is from a global distribution. Let $\\alpha_m = \\frac{|\\mathcal{D}_m|}{|\\mathcal{D}|}$ denote the portion of data samples on client $m$ . Let $\\boldsymbol{w} \\in \\mathbb{R}^d$ denote the model parameter to optimize, and $\\mathcal{L}_m(\\boldsymbol{w}, \\mathcal{D}_m) = \\frac{1}{|\\mathcal{D}_m|} \\sum_{\\xi \\in \\mathcal{D}_m} \\ell(\\boldsymbol{w}, \\xi)$ denote the empirical risk with the loss", + "bbox": [ + 75, + 741, + 472, + 905 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "function $\\ell (\\cdot ,\\cdot)$ . The optimization problem of a generic FL system can be formulated as follows:", + "bbox": [ + 496, + 90, + 893, + 121 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\boldsymbol {w}} \\mathcal {L} (\\boldsymbol {w}, \\mathcal {D}) = \\sum_ {m = 1} ^ {M} \\alpha_ {m} \\mathcal {L} _ {m} (\\boldsymbol {w}, \\mathcal {D} _ {m}). \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 128, + 893, + 167 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "FedAvg. The main-stream solutions of Eqn. 1 rely on local-SGD to reduce the communication cost of transferring gradients. FedAvg [34] is the most prevalent approach, which uses a weighted average to aggregate the locally trained models into a global model in each communication round. Typically, not all the clients participate in every communication round. Suppose $\\mathcal{M}^c\\subset [M]$ is the set of the participated clients in the $c$ -th round, and $P^{c} = \\sum_{m\\in \\mathcal{M}^{c}}\\alpha_{m}$ . The aggregation process for the global model $\\pmb{w}^{c + 1}$ at the end of $c$ -th communication round can be formulated as:", + "bbox": [ + 496, + 174, + 893, + 325 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {w} ^ {c + 1} = \\frac {1}{P ^ {c}} \\sum_ {m \\in \\mathcal {M} ^ {c}} \\alpha_ {m} \\boldsymbol {w} _ {m} ^ {c}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 607, + 330, + 892, + 362 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\pmb{w}_{m}^{c}$ denotes the client $m$ 's locally trained model. After the aggregation, the updated global model $\\pmb{w}^{c + 1}$ is then distributed to and client and utilized to initiate the $c + 1$ -th round of the training.", + "bbox": [ + 496, + 369, + 893, + 431 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Proposed Method", + "text_level": 1, + "bbox": [ + 498, + 443, + 671, + 460 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we introduce our proposed method DYNAFED. The overall framework is illustrated in Figure 1. Firstly, we collect a trajectory of the global model's updates in the early phase of federated training, with which we construct a synthetic dataset $\\mathcal{D}_{\\mathrm{syn}} = \\{\\pmb {X},\\pmb {y}\\}$ on the server side. Then, we utilize $\\mathcal{D}_{\\mathrm{syn}}$ to aid the server-side aggregation, which effectively helps recover the performance drop caused by deflected local models.", + "bbox": [ + 496, + 468, + 893, + 589 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Acquiring Global Knowledge by Data Synthesis", + "text_level": 1, + "bbox": [ + 498, + 598, + 890, + 614 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our goal is to construct a pseudo dataset $\\mathcal{D}_{\\mathrm{syn}}$ , which achieves a similar effect during training as the global dataset $\\mathcal{D}$ . In other words, the trajectory of a network trained with $\\mathcal{D}_{\\mathrm{syn}}$ should have similar dynamics with the trajectory trained with $\\mathcal{D}$ . To be precise, we denote the trajectory trained on $\\mathcal{D}$ as a sequence $\\{\\boldsymbol{w}^t\\}_{t=0}^L$ , where $L$ is the length of the trajectory. In order to reduce the number of unrolling steps during optimization, we align the trajectory in a segment-by-segment manner. Without loss of generality, we consider a segment from $\\boldsymbol{w}^t$ to $\\boldsymbol{w}^{t+s}$ , then the problem becomes the following: starting from $\\boldsymbol{w}^t$ , the network should arrive at a place close to $\\boldsymbol{w}^{t+s}$ after being trained for $s$ steps on $\\mathcal{D}_{\\mathrm{syn}}$ . We further formulate the data synthesis task into a learning problem as follows:", + "bbox": [ + 496, + 619, + 893, + 815 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\boldsymbol {X}, \\boldsymbol {y}} \\mathbb {E} _ {t \\sim U (1, L - s)} [ d (\\tilde {\\boldsymbol {w}}, \\boldsymbol {w} ^ {\\mathrm {t} + s}) ] \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 602, + 823, + 892, + 844 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\ns. t. \\tilde {\\boldsymbol {w}} = \\mathcal {A} (\\boldsymbol {X}, \\boldsymbol {y}, \\boldsymbol {w} ^ {\\mathrm {t}}, s) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 617, + 848, + 892, + 864 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the inner loop expressed by Eqn.4, we run the trainer $\\mathcal{A}(\\cdot)$ that trains a neural network initialized from $\\boldsymbol{w}^{\\mathrm{t}}$ on the synthetic", + "bbox": [ + 496, + 872, + 893, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "12179", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "dataset $\\mathcal{D}_{\\mathrm{syn}} = \\{\\pmb {X},\\pmb {y}\\}$ for $s$ steps, which arrives at $\\tilde{\\pmb{w}}$ . In the outer loop, we minimize the distance between $\\pmb{w}^{\\mathrm{t + s}}$ and $\\tilde{\\pmb{w}}$ , denoted as $d(\\tilde{\\pmb{w}},\\pmb{w}^{\\mathrm{t + s}})$ , by optimizing over $(\\pmb {X},\\pmb {y})$ . The expectation of the uniform distribution $U$ is adopted to take into account all the segments along the trajectory. $d(\\cdot ,\\cdot)$ is a general distance measure, which can take the form of euclidean distance or cosine distance, etc. During the optimization, we treat both $(\\pmb {X},\\pmb {y})$ to be learnable variables, where $\\pmb{X}$ is initialized with random noise, and $\\pmb{y}$ is initialized with equal probabilities over all labels. The detailed algorithm is shown in Algorithm 1.", + "bbox": [ + 75, + 90, + 472, + 231 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Algorithm 1 DataSyn", + "text_level": 1, + "bbox": [ + 78, + 244, + 225, + 260 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Require: Global trajectory $\\{\\pmb{w}^c\\}_1^L$ , learning rate $\\eta$ , training rounds $N$ , inner steps $s'$ .", + "bbox": [ + 78, + 265, + 468, + 294 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1: Randomly initialize $\\mathbf{X}_0$ and pair them with $\\mathbf{y}$ to form the synthetic dataset.", + "2: for training iteration $n = 1, 2 \\dots N$ do", + "3: Sample $t \\sim U(1, L - s)$ , then take $\\boldsymbol{w}^{\\mathrm{t}}$ and $\\boldsymbol{w}^{\\mathrm{t + s}}$ from the trajectory.", + "4: Get the trained parameters $\\tilde{\\boldsymbol{w}} = \\mathcal{A}(\\boldsymbol{X}_n, \\boldsymbol{y}_n, \\boldsymbol{w}^{\\mathrm{t}}, s')$", + "5: Calculate the distance $d(\\tilde{\\boldsymbol{w}}, \\boldsymbol{w}^{\\mathrm{t+s}})$ and obtain gradient w.r.t $\\boldsymbol{X}_n$ and $\\boldsymbol{y}_n$ as $\\nabla_{\\boldsymbol{X}_n} d(\\tilde{\\boldsymbol{w}}, \\boldsymbol{w}^{\\mathrm{t+s}})$ and $\\nabla_{\\boldsymbol{y}_n} d(\\tilde{\\boldsymbol{w}}, \\boldsymbol{w}^{\\mathrm{t+s}})$ .", + "6: Update $\\mathbf{X}_n$ and $\\mathbf{y}_n$ using gradient descent $\\mathbf{X}_{n+1} = \\mathbf{X}_n - \\eta \\nabla_{\\mathbf{X}_n} d(\\tilde{\\mathbf{w}}, \\mathbf{w}^{\\mathrm{t+s}})$ , $\\mathbf{y}_{n+1} = \\mathbf{y}_n - \\eta \\nabla_{\\mathbf{y}_n} d(\\tilde{\\mathbf{w}}, \\mathbf{w}^{\\mathrm{t+s}})$", + "7: end for" + ], + "bbox": [ + 84, + 295, + 468, + 445 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Output: Optimized synthetic data $\\mathcal{D}_{\\mathrm{syn}}$", + "bbox": [ + 101, + 446, + 341, + 460 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Note that since the size of $\\mathcal{D}_{\\mathrm{syn}}$ is much smaller than $\\mathcal{D}$ , the effective step size should have a different scale. Therefore, in Equation 4, we may increase the number of steps from $s$ to $s'$ to account for this scale mismatch.", + "bbox": [ + 75, + 479, + 468, + 535 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this way, the knowledge hidden in the dynamics of the global model can be transferred to $\\mathcal{D}_{\\mathrm{syn}}$ , which then acts as an approximation of the global data distribution to aid the server-side aggregation.", + "bbox": [ + 75, + 537, + 470, + 579 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Overall Algorithm of DynaFed", + "text_level": 1, + "bbox": [ + 76, + 585, + 349, + 602 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section, we present our DYNAFED that integrates the data synthesis process into the federated learning framework.", + "bbox": [ + 75, + 609, + 468, + 637 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Firstly, to construct the global trajectory on the server, we collect the global model's checkpoints from the first few communication rounds of FedAvg mainly considering the following two factors: 1) collecting a long trajectory induces prohibitive cost due to the expensive global communication, 2) the change in global model's parameters becomes insignificant during late rounds, which makes it difficult to extract knowledge from the dynamics.", + "bbox": [ + 75, + 637, + 468, + 733 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Note that although $\\mathcal{D}_{\\mathrm{syn}}$ contains rich global knowledge, it is not sufficient to replace the global data distribution $\\mathcal{D}$ due to the following reasons: 1) the objective in Eqn.3 can not be ideally solved due to the two-level optimization procedure, 2) to make the scale of the optimization problem acceptable, the size of $\\mathcal{D}_{\\mathrm{syn}}$ cannot be as large as $\\mathcal{D}$ , 3) there exists an inconsistency between the trainer $\\mathcal{A}(\\cdot)$ and the one that produces the global trajectory, i.e., FedAvg. Therefore, instead of simply conduct regular training with $\\mathcal{D}_{\\mathrm{syn}}$ , we leverage such $\\mathcal{D}_{\\mathrm{syn}}$ to help aggregation by finetuning the global model on the server side.", + "bbox": [ + 75, + 734, + 468, + 871 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The rundown of the entire algorithm is presented in Algorithm 2. Firstly, the global model's trajectory in the earliest $L$ rounds is", + "bbox": [ + 76, + 872, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Algorithm 2 DYNAFED", + "text_level": 1, + "bbox": [ + 500, + 90, + 663, + 104 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Require: Client data $\\mathcal{D}_m = \\{(x_i,y_i)\\}_{i = 1}^{|\\mathcal{D}_m|}$ , global parameters $\\boldsymbol{w}$ , client parameters $\\{\\boldsymbol{w}_m\\}_{m = 1}^{|\\mathcal{M}|}$ . Total communication rounds $C$ , local steps $T$ , data learning rate $\\eta$ , data training rounds $N$ , trajectory length $L$ , inner steps for data synthesis $s'$ .", + "bbox": [ + 500, + 109, + 893, + 170 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1: for communication round $c = 1,2\\ldots C$ do", + "2: Sample active clients $\\mathcal{M}^c$ randomly. Distribute $\\boldsymbol{w}^c$ to active clients and initialize their parameters." + ], + "bbox": [ + 508, + 171, + 890, + 212 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "3: for all users $m \\in \\mathcal{M}^c$ do", + "4: $\\{\\pmb{w}_m^c\\}_{m=1}^{|\\mathcal{M}^c|} \\gets \\text{LocalTrain}(\\pmb{w}^c, T)$", + "5: end for", + "6: Clients send updated $\\{\\pmb{w}_m^c\\}_{m=1}^{|\\mathcal{M}^c|}$ to server.", + "7: $\\pmb{w}^{c + 1}\\gets \\frac{1}{|\\mathcal{M}^c|}\\sum_{m\\in \\mathcal{M}^c}\\pmb{w}_m^c$", + "8: if $c = L$ then", + "9: $\\mathcal{D}_{\\mathrm{syn}}\\gets \\mathrm{DataSyn}(\\{\\pmb {w}^c\\}_{c = 1}^L,\\eta ,s',N)$", + "10:", + "11: else if $c > L$ then", + "12: $\\pmb{w}^{c + 1}\\gets$ Finetune $(\\mathcal{D}_{\\mathrm{syn}},\\pmb{w}^{c + 1})$", + "13: else", + "14: Add $\\pmb{w}^{c + 1}$ into trajectory list.", + "15: end if", + "16: end for" + ], + "bbox": [ + 504, + 213, + 795, + 404 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "collected and stored on the server. Then, the server executes the data synthesis procedure to generate the pseudo data $\\mathcal{D}_{\\mathrm{syn}}$ . In all subsequent rounds, $\\mathcal{D}_{\\mathrm{syn}}$ is leveraged on the server to help reduce the negative impact of deflected client models by finetuning the global model.", + "bbox": [ + 498, + 439, + 890, + 508 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our method enjoys the following appealing properties:", + "bbox": [ + 517, + 511, + 844, + 526 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- In contrast to data-dependent KD methods [6,33], DYNAFED extracts the knowledge of the global data distribution from the global model trajectory, which does not depend on any external datasets;", + "- Compared with data-free KD methods [50, 53], DYNAFED is able to synthesize informative pseudo data in the early rounds of federated learning without requiring the global model to be well trained, which significantly helps convergence and stabilizes training;", + "- The data synthesis only needs to be conducted once. Besides, since only a few samples are synthesized, refining the global model on the server requires negligible time." + ], + "bbox": [ + 519, + 537, + 890, + 704 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Remark 1. We emphasize that our DYNAFED does not raise privacy concerns given following reasons: 1) we rely on only the trajectory of the global model's parameters, which is available in the conventional setting of all FedAvg-based methods; 2) we keep $\\mathcal{D}_{\\text{syn}}$ at the server rather than sending it to the clients; 3) we extract global knowledge using the global dynamics, rather than any client-specific information as in [12, 17, 18, 20, 47], the derived $\\mathcal{D}_{\\text{syn}}$ comprises of information mixed with the entire global data distribution, thus prevents leakage of client privacy; 4) our DYNAFED shares a similar flavor as dataset condensation (DC) methods, which aims to generate informative pseudo data containing global knowledge, rather than real-looking data. The privacy-preserving ability of DC was also discussed in previous work [11].", + "bbox": [ + 496, + 720, + 893, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "12180", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "5. Theoretical Analysis", + "text_level": 1, + "bbox": [ + 76, + 89, + 272, + 107 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we present some insights to understand our data synthesis process from the neural tangent kernel (NTK) theory and also give the convergence results for DYNAfed. Detailed proofs are given in the appendix.", + "bbox": [ + 76, + 114, + 468, + 169 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In our data synthesis process, we align the segments (e.g., from $t$ to $t + s$ ) of the trajectories trained on $\\mathcal{D}$ and $\\mathcal{D}_{\\mathrm{syn}}$ for any $t$ . Essentially, those segments are the cumulative gradients calculated using $\\mathcal{D}$ and $\\mathcal{D}_{\\mathrm{syn}}$ , which approximate to $\\nabla \\mathcal{L}(\\boldsymbol{w}_t, \\mathcal{D}_{\\mathrm{syn}}) \\Delta t$ and $\\nabla \\mathcal{L}(\\boldsymbol{w}^t, \\mathcal{D}) \\Delta t$ . Therefore, we can expect $\\nabla \\mathcal{L}(\\boldsymbol{w}, \\mathcal{D}_{\\mathrm{syn}})$ would be close to $\\nabla \\mathcal{L}(\\boldsymbol{w}, \\mathcal{D})$ , which is verified by our experimental result (left of Figure.6). Given a sample $\\boldsymbol{x}$ , if continuous-time gradient descent is adopted as the training solver, the dynamics of neural network function trained on $\\mathcal{D}_{\\mathrm{syn}}$ and $\\mathcal{D}$ take the forms of", + "bbox": [ + 76, + 170, + 470, + 295 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{ \\begin{array}{l} \\frac {d f (\\boldsymbol {x} , \\boldsymbol {w} ^ {t})}{d t} = \\nabla_ {\\boldsymbol {w} ^ {t}} f (\\boldsymbol {x}, \\boldsymbol {w} ^ {t}) ^ {\\top} \\nabla \\mathcal {L} \\left(\\boldsymbol {w} ^ {t}, \\mathcal {D} _ {\\text {s y n}}\\right), \\\\ \\frac {d f (\\boldsymbol {x} , \\boldsymbol {w} ^ {t})}{d t} = \\nabla_ {\\boldsymbol {w} ^ {t}} f (\\boldsymbol {x}, \\boldsymbol {w} ^ {t}) ^ {\\top} \\nabla \\mathcal {L} \\left(\\boldsymbol {w} ^ {t}, \\mathcal {D}\\right). \\end{array} \\right. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 127, + 303, + 470, + 340 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "which is close to an ordinary differential equation according to the NTK theory [19]. Note that the right-hand sides of the two equations in (5) are close if $\\nabla \\mathcal{L}(\\boldsymbol{w}, \\mathcal{D}_{\\mathrm{syn}}) \\approx \\nabla \\mathcal{L}(\\boldsymbol{w}, \\mathcal{D})$ . In this case, the following lemma about the continuous dependence of differentiable equation shows that the neural functions $f(\\boldsymbol{x}, \\boldsymbol{w}^t)$ learned with pseudo data $\\mathcal{D}_{\\mathrm{syn}}$ are similar to that learned with real global data $\\mathcal{D}$ during the whole training process. This further indicates that $\\mathcal{D}_{\\mathrm{syn}}$ achieves similar effect as $\\mathcal{D}$ during training.", + "bbox": [ + 76, + 348, + 468, + 459 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Lemma 1 (Continuous Dependence [42]). Suppose $\\tilde{F}(t, f)$ and $F(t, f)$ are two continuous functions in a region $G$ satisfying", + "bbox": [ + 76, + 467, + 470, + 496 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\left| \\tilde {F} (t, f) - F (t, f) \\right| \\leq \\epsilon , \\forall (t, f) \\in G.\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 503, + 387, + 520 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Further, we assume $F(t,f)$ satisfy the $L_{F}$ -Lipschitz condition w.r.t., $f$ . Let $\\tilde{f}(t)$ and $f(t)$ be the solutions of initial problems,", + "bbox": [ + 76, + 529, + 468, + 556 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {d \\tilde {f}}{d t} = \\tilde {F} (t, \\tilde {f}) a n d \\frac {d f}{d t} = F (t, f),\n$$\n", + "text_format": "latex", + "bbox": [ + 169, + 565, + 375, + 594 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "with $\\tilde{f}(t_0) = f_0$ and $f(t_0) = f_0$ . Then, in a common region $|t - t_0| \\leq \\alpha$ , we have the following estimation:", + "bbox": [ + 76, + 602, + 468, + 632 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n| \\tilde {f} (t) - f (t) | \\leq \\frac {\\epsilon}{L _ {F}} \\left(e ^ {\\alpha L _ {F}} - 1\\right).\n$$\n", + "text_format": "latex", + "bbox": [ + 165, + 638, + 379, + 665 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To analyze the convergence of DYNAFED, we need to define some additional notations and rewrite our method as follows. Suppose with the $\\mathcal{D}_{\\mathrm{syn}}$ generated from the data synthesis process, in DYNAFED we run SGD for $\\tau_{1}$ and $\\tau_{2}$ iterations in each local training round and finetuning process, respectively. Let the sets $\\mathcal{I}$ and $\\mathcal{J}$ be", + "bbox": [ + 76, + 672, + 468, + 753 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {I} = \\left\\{t | t = k \\left(\\tau_ {1} + \\tau_ {2}\\right) + c, k = 0, 1, 2, \\dots , c \\in \\left[ \\tau_ {1} \\right] \\right\\},\n$$\n", + "text_format": "latex", + "bbox": [ + 104, + 763, + 437, + 779 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {J} = \\{t | t = k \\left(\\tau_ {1} + \\tau_ {2}\\right) + \\tau_ {1}, k = 0, 1, 2, \\dots \\}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 107, + 781, + 468, + 797 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $[\\tau_1] = \\{0, 1, \\dots, \\tau_1 - 1\\}$ . Therefore, when $t \\in \\mathcal{I}$ , we perform local training, while when $t \\notin \\mathcal{I}$ , we conduct finetuning. $\\mathcal{I}$ denotes the time index for aggregation. The detailed steps of DYNAFED can be rewritten as", + "bbox": [ + 76, + 805, + 470, + 859 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {v} _ {t + 1} ^ {m} = \\left\\{ \\begin{array}{l l} \\boldsymbol {w} _ {m} ^ {t} - \\eta_ {t} \\nabla \\ell (\\boldsymbol {w} _ {m} ^ {t}, \\xi_ {m} ^ {t}), & \\text {i f} t \\in \\mathcal {I} \\\\ \\boldsymbol {w} _ {m} ^ {t} - \\eta_ {t} \\nabla \\mathcal {L} (\\boldsymbol {w} _ {m} ^ {t}, \\mathcal {D} _ {\\text {s y n}}), & \\text {i f} t \\notin \\mathcal {I} \\end{array} , \\right.\n$$\n", + "text_format": "latex", + "bbox": [ + 127, + 867, + 418, + 902 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {w} _ {m} ^ {t + 1} = \\left\\{ \\begin{array}{l l} \\boldsymbol {v} _ {m} ^ {t + 1}, & \\text {i f} t + 1 \\notin \\mathcal {J} \\\\ \\sum_ {m = 1} ^ {M} \\alpha_ {m} \\boldsymbol {v} _ {m} ^ {t + 1}, & \\text {i f} t + 1 \\in \\mathcal {J} \\end{array} , \\right.\n$$\n", + "text_format": "latex", + "bbox": [ + 550, + 88, + 825, + 125 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\xi_m^t\\sim \\mathcal{D}_m$ . Based on the notations, we define a sequence:", + "bbox": [ + 500, + 133, + 872, + 148 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\bar {\\boldsymbol {w}} ^ {t} = \\sum_ {m = 1} ^ {M} \\alpha_ {m} \\boldsymbol {w} _ {m} ^ {t}.\n$$\n", + "text_format": "latex", + "bbox": [ + 635, + 148, + 756, + 184 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Hence, our algorithm is an integration of FedAvg and a biased GD. For $\\bar{\\boldsymbol{w}}^t$ , note that $\\bar{\\boldsymbol{w}}^t = \\boldsymbol{w}_1^t = \\dots = \\boldsymbol{w}_M^t$ in the finetuning process and we have the following convergence results:", + "bbox": [ + 498, + 186, + 893, + 227 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Theorem 1 (Convergence). For $\\tilde{L}$ -smooth, $\\mu$ -strongly convex loss functions $\\ell(\\cdot, \\cdot)$ . We assume $\\|\\nabla \\mathcal{L}(\\boldsymbol{w}, \\mathcal{D}_{\\mathrm{syn}}) - \\nabla \\mathcal{L}(\\boldsymbol{w}, \\mathcal{D})\\| \\leq \\delta\\|\\nabla \\mathcal{L}(\\boldsymbol{w}, \\mathcal{D})\\| + \\epsilon$ holds with two small non-negative scalars $\\delta$ and $\\epsilon$ . Let $\\eta_t = \\frac{c}{t}$ for a proper constant $c$ . Then, DYNAfed satisfies", + "bbox": [ + 498, + 237, + 892, + 292 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbb {E} \\mathcal {L} \\left(\\bar {\\boldsymbol {w}} ^ {T}, \\mathcal {D}\\right) - \\mathcal {L} \\left(\\boldsymbol {w} ^ {*}, \\mathcal {D}\\right) \\leq \\frac {C}{T}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 596, + 301, + 890, + 329 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{w}^*$ is the minimum of $\\mathcal{L}(\\mathbf{w},\\mathcal{D})$ and $C$ is a constant, whose detailed formula is given in the appendix.", + "bbox": [ + 498, + 337, + 890, + 364 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "More detailed discussions about the convergence result are given in the Appendix.", + "bbox": [ + 498, + 375, + 890, + 402 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "6. Experiments", + "text_level": 1, + "bbox": [ + 500, + 416, + 632, + 434 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Benchmark Datasets and Experimental Settings. We conduct experiments over four commonly used datasets: FashionMNIST [43], CIFAR10 [25], CINIC10 [9] and CIFAR100 [25]. Among them, FashionMNIST is a dataset containing grey-scale images of fashion products. CIFAR10 is an image classification dataset containing daily objects. CINIC10 is a dataset combining CIFAR10 and samples from similar classes that are downsampled from ImageNet [26]. These three datasets contain 10 classes. CIFAR100 contains the same data as CIFAR10, but categorizes the data into 100 classes. For each dataset, we mainly conduct experiments with heterogeneous client data distribution. We follow prior work [6, 33] to use Dirichlet distribution for simulating the non-IID data distribution, where the degree of heterogeneity is defined by $\\alpha$ , smaller $\\alpha$ value corresponds to more severe heterogeneity.", + "bbox": [ + 498, + 440, + 893, + 635 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "**Baseline Methods** We consider various state-of-the-art solutions against non-IID data distribution in the context of federated learning. Specifically, we compare with the following approaches 1) the vanilla aggregation strategy FedAVG [34]; 2) regularization-based strategies FedProx [31], Scaffold [24]; 3) data-dependent knowledge distillation strategies that need external dataset FedDF [33] and FedBE [6], ABAVG [44]; (4) data sharing [49] or data-free knowledge distillation [53] methods. Note that we do not compare with [50] since the code is not published. Please refer to Appendix for detailed settings of the baseline methods.", + "bbox": [ + 498, + 638, + 893, + 779 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Configurations Unless specified otherwise, we follow [?,7,15] and adopt the following default configurations throughout the experiments: we run 200 global communication rounds with local epoch set to 1. There are 80 clients in total, and the participation ratio in each round is set to $40\\%$ . Experiments using other participation ratios are in the Appendix. We report the global model's average performance in the last five rounds evaluated using the test split of the datasets. For the construction of global trajectory, we first run", + "bbox": [ + 498, + 789, + 893, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "12181", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/09df25c0d590f1123042c722f6e35097f53713f12d5f726a923d7559f35f7966.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Methodα = 0.01α = 0.04α = 0.16
FMNISTCIFAR10CINIC10FMNISTCIFAR10CINIC10FMNISTCIFAR10CINIC10
FedAVG74.50±1.3239.30±3.4231.60±5.5081.74±1.9851.19±2.8545.35±3.0089.54±1.5169.74±1.2955.40±2.05
FedProx76.88±1.8342.13±3.6432.56±4.5983.06±2.5358.93±2.1446.30±2.8789.53±1.1370.20±0.7457.78±2.08
Scaffold77.92±0.8742.04±2.2634.90±3.3482.25±1.3554.23±1.9046.22±2.1888.54±0.3268.57±0.9154.30±0.83
FedDF*72.36±2.0839.73±3.9831.97±4.3181.65±0.9754.20±2.9345.79±2.9589.70±0.9770.71±0.9455.78±1.02
FedBE*72.33±1.7938.36±3.7432.04±3.7381.31±1.2553.49±2.3645.50±2.8889.62±0.7570.23±0.7655.42±1.37
ABAVG*75.98±1.9939.95±1.3732.75±4.1884.88±1.8457.25±3.4247.39±3.3689.53±1.1270.55±2.4156.02±1.49
FedGen†75.59±1.1240.19±2.1432.59±3.2581.46±1.0856.60±1.2945.57±2.7089.95±0.8970.89±0.5455.34±1.13
FedMix†81.34±0.6850.48±1.2337.15±1.8184.23±0.5062.77±1.0750.22±1.4189.05±0.2470.33±0.5556.74±0.45
DynaFed†87.52±0.1565.53±0.3448.04±0.7089.45±0.1170.07±0.1255.43±0.2491.35±0.0774.69±0.1459.80±0.10
", + "bbox": [ + 81, + 79, + 893, + 244 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/d97420e46aa9dd4e99dbed5d0d019e19418c9e08cdb0c4dca79e3dc5b6e95d71.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 89, + 327, + 285, + 438 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c60f02cf13c2bab8a5b39a2480dd19f0e2f292e294e051483525c68d8c2965ac.jpg", + "image_caption": [ + "Figure 2. Visualization of global model's test performance on various datasets throughout the global communication rounds. We can see that the global model rapidly converges to a satisfactory test accuracy once $\\mathcal{D}_{\\mathrm{syn}}$ participates in refining the global model. Furthermore, $\\mathcal{D}_{\\mathrm{syn}}$ also helps reduce the fluctuation of model performances between communication rounds, which significantly boosts the training stability. DYNAFED requires less than $10\\%$ communication rounds to achieve comparable performance with the baseline methods." + ], + "image_footnote": [], + "bbox": [ + 86, + 440, + 281, + 549 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/48df3604cbbe66aef95c5e0257a689f926bf887cce17d1920597e857bd0e4a1a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 289, + 328, + 480, + 438 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e6e041f4c08e73411d9ed83e18275c3cc01ff161190504cbd1db236aeb050cb7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 289, + 440, + 478, + 549 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f3edfecc2ba679040b3672a6e2e4e71fa782b55731d10503396c2fc079c9a703.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 488, + 327, + 679, + 436 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0c3a3cc00b9c000b4a70a39e3da39938ac0c81e87a59273ab58f45bf71189ee6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 486, + 439, + 678, + 549 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/1ca2e50711a9dd072d7c1251247a94f697c50427e06aec1021ab841e42e3d54e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 686, + 328, + 879, + 436 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f63afb430a9ade5ef0ea098f1e1a3dc7078de4423886da1e5c893d9b88ef5e3b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 684, + 439, + 875, + 549 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/c23b25e2096d4c4532fa3dba1e6b5882d3d26d2e4779b43ecaa68c1fcb3d56c8.jpg", + "table_caption": [ + "Table 1. Comparison of test performances achieved by different FL methods with different degrees of data heterogeneity $\\alpha$ across multiple datasets. We report the mean test accuracy of last five communication rounds. *Methods assume the availability of proxy data. † Methods are based on data sharing or generation. We observe that our approach outperforms other methods by a large margin, and its advantage is more prominent on more challenging datasets with higher heterogeneity. Specifically, DYNAFED demonstrates relative improvement over the FedAvg baseline by $17.5\\%$ , $64.5\\%$ , $52.0\\%$ , and $82.2\\%$ on FMNIST, CIFAR10, CINIC10, and CIFAR100, respectively." + ], + "table_footnote": [], + "table_body": "
Methodα = 0.01α = 0.04α = 0.08α = 0.16
FedAVG16.54±2.1826.56±1.5334.54±1.0239.65±0.94
FedProx18.46±1.0528.58±1.4634.82±0.5440.98±0.49
Scaffold17.33±1.2128.46±1.1835.04±0.3540.57±0.33
FedDF*16.02±1.9426.94±1.2534.77±0.8839.76±0.44
FedBE*15.78±2.3428.03±0.3433.91±0.7939.45±0.79
ABAVG16.52±1.9829.14±0.5734.66±0.9841.00±0.23
FedGen†16.51 ±1.3227.03±1.1434.56±0.7839.96±0.58
FedMix†23.54±0.9632.18±0.5936.30±0.4241.09±0.14
DynaFed†30.14±0.1936.79±0.1240.02±0.0942.47±0.06
", + "bbox": [ + 84, + 630, + 464, + 765 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Comparison of test performances on CIFAR100 with different degrees of data heterogeneity $\\alpha$ .", + "bbox": [ + 75, + 767, + 468, + 796 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "FedAvg [34] and use the checkpoints from the first 20 communication rounds ( $L = 20$ ). We set the time difference $s$ between the start and end checkpoint to 5, and the target checkpoint is averaged with 2 checkpoints sampled between $\\boldsymbol{w}^{\\mathrm{t}}$ and $\\boldsymbol{w}^{\\mathrm{t+s}}$ . More details can be found in the Appendix.", + "bbox": [ + 75, + 830, + 472, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "6.1. Main Experiments with Data Heterogeneity", + "text_level": 1, + "bbox": [ + 500, + 642, + 870, + 659 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We demonstrate the superior performance of our DYNAFED by conducting experiments on heterogeneous client data across comprehensive datasets and various heterogeneity values $\\alpha$ . Specifically, we use three datasets with 10 classes (shown in Table 1): FashionMNIST [43], CIFAR10 [25] and CINIC10 [9], heterogeneity degree $\\alpha$ set to 0.01, 0.04 and 0.16; and CIFAR100 containing 100 classes, with $\\alpha$ values 0.01, 0.04, 0.08 and 0.16 (shown in Table 2). DYNAFED significantly boosts the convergence, stabilizes training, and brings considerable performance improvement compared with previous approaches. Specifically, with heterogeneity value $\\alpha = 0.01$ , DYNAFED demonstrates relative improvement over the FedAvg baseline by $17.5\\%$ , $64.5\\%$ , $52.0\\%$ , and $82.2\\%$ on FMNIST, CIFAR10, CINIC10, and CIFAR100, respectively.", + "bbox": [ + 496, + 664, + 893, + 844 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As demonstrated in Figure 2, the performance of DYNAfed is rapidly boosted as soon as the synthesized data starts refining the global model on the server. This verifies that DYNAfed does not depend on the global model's performance in data synthesis,", + "bbox": [ + 496, + 845, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "12182", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b7957d5521c001e863c38b4f52f642b407916e6d0a5e45b1f0cab694329a8be8.jpg", + "image_caption": [ + "Figure 3. Loss curves over each client's data throughout local training and finetuning. Each of the 3 colors represents the loss over one client's data. The stars are the global model's average losses over all client data after finetuning with $\\mathcal{D}_{\\mathrm{syn}}$ . During local training, the client losses quickly converge to near zero. However, due to deflection caused by heterogeneity, the losses over some clients' data dramatically increase after aggregation. Finetuning with $\\mathcal{D}_{\\mathrm{syn}}$ decreases those losses and reduces the aggregation bias." + ], + "image_footnote": [], + "bbox": [ + 83, + 90, + 464, + 205 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f30787b1a537c6acaf19908fe77f8bbacc07ce8168269156ff3f340c637479f9.jpg", + "image_caption": [ + "Figure 4. Visualization of learned synthetic data on 3 classes from CIFAR10 throughout the optimization process. In the beginning, the pixels are randomly initialized and contain little information. As the optimization goes on, some patterns emerge in the synthetic images but remain unrecognizable." + ], + "image_footnote": [], + "bbox": [ + 86, + 333, + 460, + 421 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "which is consistent with our analysis in Section 4. This characteristic enables faster convergence to achieve good performance with fewer communication rounds. As shown in Figure 2, DYNAfed requires less than $20\\%$ communication rounds to achieve comparable performance with the baseline methods.", + "bbox": [ + 75, + 508, + 470, + 580 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6.2. Detailed Analysis", + "text_level": 1, + "bbox": [ + 76, + 588, + 246, + 604 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We conduct a detailed analysis of DYNAFED and aim to provide answers to the following questions: (1) Does $\\mathcal{D}_{\\mathrm{syn}}$ contain information about global data distribution while protecting client privacy? (2) Can we leverage just the dynamics of the early rounds to synthesize $\\mathcal{D}_{\\mathrm{syn}}$ ? (3) How many pseudo samples do we need to synthesize to ensure effectiveness? (4) Does $\\mathcal{D}_{\\mathrm{syn}}$ still help convergence under more severe heterogeneity and longer local training?", + "bbox": [ + 75, + 611, + 470, + 709 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "$\\mathcal{D}_{\\mathrm{syn}}$ Contains Global Information and Preserves Privacy. We conduct experiment with CIFAR10 and set $\\alpha = 0.01$ , where client datasets are extremely non-iid. We track the losses calculated over each client's data throughout local training as well as the global model's finetuning. During local training, we calculate the client models' losses over their own datasets, i.e., $\\mathcal{L}_m(\\boldsymbol{w}_m, \\mathcal{D}_m)$ . During finetuning, we calculate the global model's losses over each client's dataset, i.e., $\\mathcal{L}_m(\\boldsymbol{w}, \\mathcal{D}_m)$ . To prevent cluttering, we randomly select 3 client datasets for illustration. The result is shown in Figure 3, each color represents the loss over one clients' dataset. We observe that the client models easily overfit during local training due to the extreme class imbalance. The deflected client models make the aggregated global model demonstrate high loss values over some", + "bbox": [ + 75, + 719, + 472, + 901 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/53d7fcfd11e3f7ed0eabe6224258ee31f95fd668e066cf384c19d22e37f2a42c.jpg", + "image_caption": [ + "Figure 5. Left: The test accuracy curves for different choices of trajectory length L on the CIFAR10 dataset with $\\alpha = 0.01$ . By leveraging the dynamics of the global model's trajectory in the first few rounds, e.g., $\\mathrm{L} \\in \\{10, 15, 20, 15\\}$ , the derived $\\mathcal{D}_{\\mathrm{syn}}$ already helps achieve faster convergence and stable training. In contrast, the FedGen approach only brings slight performance gain during the later phase of training due to the dependence on the global model's performance. Right: We show the performance of DYNAfed with different sizes of $\\mathcal{D}_{\\mathrm{syn}}$ for various $\\alpha$ . The performance gain is significant with just 150 synthesized samples." + ], + "image_footnote": [], + "bbox": [ + 506, + 90, + 687, + 229 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/512527f1baef093b440ced96309bc4d2179e53b61ec1aaa5921927d6a226f165.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 700, + 90, + 883, + 229 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "clients' data. Remarkably, we observe that finetuning with $\\mathcal{D}_{\\mathrm{syn}}$ is able to recover the global model to a reasonable state, which achieves small losses over all client datasets. This verifies that $\\mathcal{D}_{\\mathrm{syn}}$ contains information of the global data distribution. Furthermore, Figure 4 presents the synthesized data of CIFAR10, client-specific information can not be observed.", + "bbox": [ + 496, + 400, + 893, + 484 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "$\\mathcal{D}_{\\mathrm{syn}}$ Can be Learned with Early Trajectory. We conduct experiments with different choices of trajectory length $L$ in left of Figure 5. We observe that even if with $L = 10$ , the result is comparable with performance obtained with longer trajectory $L = 25$ . Compared with the baseline methods, DYNAfed achieves significant convergence speedup and performance boost. These results support our claim in Section 4 that our method can take effect early during training. By contrast, the data-free KD method FedGen [53] that trains a generator to produce pseudo data starts to show a slight improvement only in the late stage of training since it depends explicitly on the global model's performance when training the generator.", + "bbox": [ + 496, + 497, + 890, + 664 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "How the Size of $\\mathcal{D}_{\\mathrm{syn}}$ Impacts the Performance. As shown in the right of Figure 5, we conduct experiments with different sizes of $\\mathcal{D}_{\\mathrm{syn}}$ and various heterogeneity degrees $\\alpha$ . We find that a small $\\mathcal{D}_{\\mathrm{syn}}$ suffices for good performance, while larger $\\mathcal{D}_{\\mathrm{syn}}$ brings only marginal performance boost. This property not only saves the cost for synthesizing $\\mathcal{D}_{\\mathrm{syn}}$ , but also makes the finetuning of the global model more efficient.", + "bbox": [ + 496, + 676, + 890, + 776 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "$\\mathcal{D}_{\\mathrm{syn}}$ is Able to Mimic the Global Dynamics. In the left of Figure 6, we calculate the cosine distance between the target checkpoint $\\boldsymbol{w}^{\\mathrm{t+s}}$ and the parameters $\\tilde{\\boldsymbol{w}}$ trained from $\\boldsymbol{w}^{\\mathrm{t}}$ for $s'$ steps with $\\mathcal{D}_{\\mathrm{syn}}$ , a randomly sampled real dataset of the same size as $\\mathcal{D}_{\\mathrm{syn}}$ , and a dataset consisted of noisy pixels, respectively. We can see that in terms of mimicking the global trajectory, $\\mathcal{D}_{\\mathrm{syn}}$ not only significantly outperforms the noise dataset, but also achieves only half of the distance obtained with real dataset, which is not", + "bbox": [ + 496, + 787, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "12183", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/ac0eec6feb6bb418ee0499742140e9956b0b46bf00544b4454966b0f692e8e37.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Methodα = 0.01α = 0.04
5 epochs10 epochs5 epochs10 epochs
FedAVG33.23±3.5429.93±4.6250.28±2.1746.09±2.95
FedProx42.60±2.3042.86±2.8458.40±1.3554.30±1.98
Scaffold39.43±1.8636.52±2.0455.46±1.2550.05±1.57
FedDF*31.68±3.1639.85±3.7952.31±2.3850.90±2.53
FedBE*35.49±2.8834.19±3.3449.78±1.7951.34±1.90
ABAVG*37.87±2.5735.08±3.0356.81±1.9452.17±2.32
FedGen†35.64±2.5235.03±3.5857.60±1.5554.48±2.03
FedMix†47.36±1.2441.53±1.3760.74±0.9556.35±1.33
DynaFed†61.45±0.4659.04±0.6468.35±0.2066.30±0.34
", + "bbox": [ + 84, + 80, + 460, + 223 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/851582cf0b3de154e9086b213489703fff167174f7bfe46763fd1b5b544f8814.jpg", + "table_caption": [ + "Table 3. Test performances on CIFAR10 achieved by different FL algorithms under various degrees of data heterogeneity and local training epochs. Total communication rounds of 100 and 50 are set with local training epochs of 5 and 10, respectively. As can be seen, DYNAfed significantly surpasses other methods." + ], + "table_footnote": [], + "table_body": "
MethodCIFAR10CINIC10
α = 0.01α = 0.04α = 0.01α = 0.04
Acc = 0.45Acc = 0.55Acc = 0.33Acc = 0.45
FedAVG132.0±15.0117.0±8.0189.3±10.5138.7±5.6
FedProx113.3±16.4102.0±4.7156.7±7.0118.3±4.0
Scaffold105.0±10.4100.3±3.5158.0±5.4110.0±3.4
FedDF*145.7±13.1117.3±5.8180.7±5.0170.0±7.0
FedBE*165.0±12.7122.7±4.5185.3±14.6174.3±6.8
ABAVG*109.7±5.4110.7±5.0150.0±8.4127.0±5.8
FedGen†115.7±10.4110.3±5.7167.0±12.1128.3±5.5
FedMix†77.3±3.789.3±3.579.0±7.882.3±5.5
DynaFed†22.3±0.622.0±1.021.3±1.522.7±1.4
", + "bbox": [ + 78, + 297, + 480, + 450 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "accessible in FL setting. This verifies the ability of $\\mathcal{D}_{\\mathrm{syn}}$ to mimic global trajectory.", + "bbox": [ + 75, + 516, + 468, + 545 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "DYNAFED is Robust to Longer Local Training. Longer local training is generally required in FL to reduce the total number of global communication rounds. Under different heterogeneity degrees, we conduct experiments to evaluate the impact of longer local training epochs on DYNAFED. Specifically, we conduct experiments with total communication rounds of 100 and 50 with ocal training epochs of 5 and 10, respectively. The results are presented in Table 3, from which we observe the following: 1) DYNAFED consistently outperforms other methods by a large margin even with longer local training epochs; 2) the performance of DYNAFED is less sensitive to the length of local training, which benefits from the $\\mathcal{D}_{\\mathrm{syn}}$ containing information about the global data distribution. Therefore, DYNAFED is able to achieve similar performance with less global communication rounds, which is the major bottleneck in the efficiency of FL.", + "bbox": [ + 75, + 547, + 468, + 757 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We further conduct experiments on varying local epochs to measure the quality of $\\mathcal{D}_{\\mathrm{syn}}$ . Specifically, we use it to train a network from scratch and evaluate its test performance. Shown in right of Figure 6, the quality of $\\mathcal{D}_{\\mathrm{syn}}$ stays similar with longer local training and more severe heterogeneity. This further explains the superior performance of DYNAfed with longer local training.", + "bbox": [ + 75, + 758, + 468, + 842 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6.3. Architecture Generalization and Efficiency", + "text_level": 1, + "bbox": [ + 76, + 849, + 441, + 864 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To showcase the generalization ability of our approach over different network architecture choices, we conduct experiments on", + "bbox": [ + 76, + 872, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/3cd3a3592dc3ed41bf8cc1768f10547362d3d5bc93ea879059d94f4c866539e7.jpg", + "table_caption": [ + "Table 4. Comparison of the number of communication rounds to reach target accuracy. With the knowledge of global data distribution stored in $\\mathcal{D}_{\\mathrm{syn}}$ at the server, the convergence speed of our DYNAfed is significantly accelerated." + ], + "table_footnote": [], + "table_body": "
Methodα = 0.01α = 0.04
MLPConvNetMLPConvNet
FedAVG65.64±1.6974.51±1.3273.26±1.4981.74±1.98
FedProx68.09±1.4776.88±1.8379.83±1.7083.06±2.53
Scaffold67.60±1.5377.92±0.8778.09±1.3582.25±1.35
FedDF*64.59±1.7072.36±2.0877.20±1.5881.65±0.97
FedBE*65.97±1.6472.33±1.7975.42±1.3581.31±1.25
ABAVG*69.19±1.5075.98±1.9981.64±1.2084.44±1.84
FedGen†68.67±1.4575.59±1.1277.94±1.3856.60±1.08
FedMix†70.30±0.9281.34±0.6881.95±0.6484.23±0.50
DynaFed†73.89±0.2487.52±0.1583.54±0.4289.45±0.11
", + "bbox": [ + 506, + 79, + 883, + 223 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5. Performance comparison across different network architectures. We conduct the experiment on FMNIST dataset using MLP and ConvNet to demonstrate the generalization of DYNAfed for different network architectures.", + "bbox": [ + 496, + 226, + 895, + 281 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/efaff97bb181e00412c5e7a9a452f9a04285173a947750a6221dc3181ecd7445.jpg", + "image_caption": [ + "Figure 6. Left: the cosine distance between the target checkpoint $\\boldsymbol{w}^{\\mathrm{t + s}}$ and the parameters $\\tilde{\\boldsymbol{w}}$ obtained by training with different datasets from $\\boldsymbol{w}^{\\mathrm{t}}$ for $s^{\\prime}$ steps. We can see that the distance derived using $\\mathcal{D}_{\\mathrm{syn}}$ is constantly smaller compared with other data. Right: Test performances of a model trained from scratch using only $\\mathcal{D}_{\\mathrm{syn}}$ generated under various local epochs and client heterogeneity. The two plots together verify the quality of the generated $\\mathcal{D}_{\\mathrm{syn}}$ ." + ], + "image_footnote": [], + "bbox": [ + 506, + 286, + 687, + 425 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3a12a63d5d219cfdcab82e74f1b23df918c7a826e02303df5994161b36d455f6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 700, + 286, + 880, + 425 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "FMNIST using different network architectures. Specifically, we choose ConvNet and MLP following [34, 53]. As shown in Table 5, under various client data heterogeneity, our method demonstrates superior performances with both network architectures.", + "bbox": [ + 496, + 542, + 893, + 598 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Thanks to the rich knowledge of global data distribution contained in $\\mathcal{D}_{\\mathrm{syn}}$ , using it to refine the global model greatly boosts the convergence speed of training. As shown in Figure 2, as soon as $\\mathcal{D}_{\\mathrm{syn}}$ is used to refine the global model, its performance rapidly increases to a reasonable accuracy, which reduces many rounds of communication. In Table 4, we also quantitatively compare the convergence speed of different FL algorithms by showing the number of communication rounds needed to reach the highest test accuracy achievable by the baselines. As can be observed, our DYNAfed requires only less than $20\\%$ communication rounds to reach a target accuracy comparable to other methods.", + "bbox": [ + 496, + 598, + 893, + 750 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 763, + 617, + 780 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We propose DYNAFED to tackle the data heterogeneity issue, which synthesizes a pseudo dataset to extract the knowledge of the global data distribution from the dynamics of the global model's trajectory. Extensive experiments show that DYNAFED demonstrates relative improvement over the FedAvg baseline up to $82.2\\%$ on CIFAR100. Further, we believe our work is able to provide insights for extracting global information on the server side, which goes beyond tackling the data heterogeneity issue.", + "bbox": [ + 496, + 789, + 893, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "12184", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Durmus Alp Emre Acar, Yue Zhao, Ramon Matas Navarro, Matthew Mattina, Paul N Whatmough, and Venkatesh Saligrama. Federated learning based on dynamic regularization. arXiv preprint arXiv:2111.04263, 2021. 2, 3", + "[2] Divyansh Aggarwal, Jiayu Zhou, and Anil K Jain. Fedface: Collaborative learning of face recognition model. In 2021 IEEE International Joint Conference on Biometrics (IJCB), pages 1-8. 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PMLR, 2021. 2, 3, 4, 5, 7, 8" + ], + "bbox": [ + 501, + 92, + 893, + 757 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "12186", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/DynaFed_ Tackling Client Data Heterogeneity With Global Dynamics/ba56f7cd-e332-49dd-9060-cbf5c82b8082_model.json b/2023/DynaFed_ Tackling Client Data Heterogeneity With Global Dynamics/ba56f7cd-e332-49dd-9060-cbf5c82b8082_model.json new file mode 100644 index 0000000000000000000000000000000000000000..be35826fc690cf42fd000a5516e39ed3ddba1b1d --- /dev/null +++ b/2023/DynaFed_ Tackling Client Data Heterogeneity With Global Dynamics/ba56f7cd-e332-49dd-9060-cbf5c82b8082_model.json @@ -0,0 +1,2651 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.132, + 0.131, + 0.84, + 0.154 + ], + "angle": 0, + "content": "DYNAMICS" + }, + { + "type": "text", + "bbox": [ + 0.176, + 0.18, + 0.794, + 0.217 + ], + "angle": 0, + "content": "Renjie Pi\\(^{1*}\\) Weizhong Zhang\\(^{2*}\\) Yueqi Xie\\(^{1*}\\) Jiahui Gao\\(^{3}\\) Xiaoyu Wang\\(^{1}\\) Sunghun Kim\\(^{1}\\) Qifeng Chen\\(^{1\\dagger}\\)" + }, + { + "type": "text", + "bbox": [ + 0.265, + 0.218, + 0.706, + 0.234 + ], + "angle": 0, + "content": "1The Hong Kong University of Science and Technology" + }, + { + "type": "text", + "bbox": [ + 0.277, + 0.235, + 0.692, + 0.253 + ], + "angle": 0, + "content": "\\(^{2}\\)Fudan University \\(^{3}\\)The University of Hong Kong" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.287, + 0.314, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.318, + 0.474, + 0.772 + ], + "angle": 0, + "content": "The Federated Learning (FL) paradigm is known to face challenges under heterogeneous client data. Local training on non-iid distributed data results in deflected local optimum, which causes the client models drift further away from each other and degrades the aggregated global model's performance. A natural solution is to gather all client data onto the server, such that the server has a global view of the entire data distribution. Unfortunately, this reduces to regular training, which compromises clients' privacy and conflicts with the purpose of FL. In this paper, we put forth an idea to collect and leverage global knowledge on the server without hindering data privacy. We unearth such knowledge from the dynamics of the global model's trajectory. Specifically, we first reserve a short trajectory of global model snapshots on the server. Then, we synthesize a small pseudo dataset such that the model trained on it mimics the dynamics of the reserved global model trajectory. Afterward, the synthesized data is used to help aggregate the deflected clients into the global model. We name our method DYNAFED, which enjoys the following advantages: 1) we do not rely on any external on-server dataset, which requires no additional cost for data collection; 2) the pseudo data can be synthesized in early communication rounds, which enables DYNAFED to take effect early for boosting the convergence and stabilizing training; 3) the pseudo data only needs to be synthesized once and can be directly utilized on the server to help aggregation in subsequent rounds. Experiments across extensive benchmarks are conducted to showcase the effectiveness of DYNAFED. We also provide insights and understanding of the underlying mechanism of our method." + }, + { + "type": "title", + "bbox": [ + 0.079, + 0.8, + 0.21, + 0.815 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.825, + 0.471, + 0.856 + ], + "angle": 0, + "content": "Federated learning (FL) has become a popular distributed training paradigm to alleviate the server's computational bur" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.286, + 0.889, + 0.54 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.553, + 0.895, + 0.679 + ], + "angle": 0, + "content": "Figure 1. Illustration of DYNAFED. Firstly, we run the standard FedAvg for \\( L \\) communication rounds and save the checkpoints to form a trajectory of the global model at the server. Then, we synthesize a pseudo dataset \\( \\mathcal{D}_{\\mathrm{syn}} \\), with which the network can be trained to mimic the dynamics of the global trajectory. In this way, the knowledge that captures the essential information about the global data distribution is transferred from the global dynamics to \\( \\mathcal{D}_{\\mathrm{syn}} \\). Afterward, \\( \\mathcal{D}_{\\mathrm{syn}} \\) is adopted to help aggregate the deflected clients into the global model at the server." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.896, + 0.903 + ], + "angle": 0, + "content": "den and preserve clients' data privacy [3, 23, 31, 45]. In the FL paradigm, the clients only have access to their private datasets, while the server is responsible for aggregating the clients' updates into a global model. The most prevalent approaches in FL are based on local-SGD [34] (also referred to as FedAvg), where the client model is updated locally for multiple steps before being sent and merged on the server. Such approaches save communication costs and perform well given the client data are iid-distributed. However, in real-world applications such as healthcare [22, 23, 36, 37] and bio-metrics [2], the client data usually demonstrates heterogeneity (highly non-iid), which deflects the local optimum from the global optimum [24, 32, 52] and makes the locally" + }, + { + "type": "page_footnote", + "bbox": [ + 0.094, + 0.863, + 0.354, + 0.875 + ], + "angle": 0, + "content": "*Joint first authors. Code is available at this link." + }, + { + "type": "page_footnote", + "bbox": [ + 0.079, + 0.876, + 0.47, + 0.9 + ], + "angle": 0, + "content": "\\(\\dagger\\) Correspondence to Weizhong Zhang (weizhongzhang@fudan.edu.cn) and Qifeng Chen (chenqifeng22@gmail.com)" + }, + { + "type": "list", + "bbox": [ + 0.079, + 0.863, + 0.47, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12177" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.122 + ], + "angle": 0, + "content": "trained clients biased. Therefore, naively averaging the client models results in slow convergence and performance drop." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.125, + 0.473, + 0.518 + ], + "angle": 0, + "content": "To alleviate the difficulty of training under heterogeneity, a few lines of work have been frequently discussed. The first line attempts to modify the local training process, including imposing regularization on the client models [1,24,29,31] and data sharing or augmentation [35, 38, 48, 52]. However, these solutions have a high requirement for the server's control of local clients. An orthogonal line focuses on refining the global model in the server aggregation process [6, 33, 40, 44, 46]. The majority of these methods typically require a large external dataset on the server, then use it to align the outputs of the global model with that of the client ensemble [6, 15, 33, 44]. Unfortunately, such a large-scale task-related dataset is often hard to acquire in reality. To circumvent this limitation, a few data-free knowledge distillation (KD) approaches are recently proposed [50,53]. These methods attempt to transfer the knowledge contained in the global model to a generator, which is subsequently leveraged to produce pseudo data to either help local training at the clients [53] or finetune the global model at the server [50]. It is clear that these methods require a global model with reasonable performance to ensure the generation of helpful pseudo data. However, such requirement is hard to achieve in practice since the global model often performs poorly under heterogeneity, especially in the early rounds of training. Other solutions include personalized FL [16, 27, 30, 39], similarity clustering [4, 10, 13], meta learning [21, 28], etc." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.521, + 0.472, + 0.734 + ], + "angle": 0, + "content": "Even though the above-mentioned works propose techniques to alleviate the challenges posed by heterogeneity to some extent, they do not tackle the issue from its root cause: the data is unevenly scattered at different clients and is kept locally due to privacy concerns, which is also the main obstacle for training an accurate global model. Ideally, imagine if we can collect all the client data to the server, then training can be directly conducted at the server, and the heterogeneity issue no longer exists. However, this reduces to regular training and conflicts with the original purpose of FL to protect client privacy. We then raise a natural question: is it possible to derive the essential information about the global data distribution on the server to help training without compromising client privacy?" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Despite the global model typically performing poorly due to heterogeneity, the changes in its parameters are steered jointly by the data scattered at different clients. Therefore, the update dynamics of the global model contain knowledge about global data distribution. Driven by this intuition, we propose DYNAFED to explicitly unearth such knowledge hidden in the global dynamics and transfer it to a pseudo dataset \\( \\mathcal{D}_{\\mathrm{syn}} \\) at the server. \\( \\mathcal{D}_{\\mathrm{syn}} \\) can then approximate the global data distribution on the server to aid aggregation. More specifically, inspired by recent works in dataset condensation [5,41,51], we formulate the data synthesis process into a" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.272 + ], + "angle": 0, + "content": "learning problem, which minimizes the distance between the trajectory trained with \\(\\mathcal{D}_{\\mathrm{syn}}\\) and the global model trajectory derived with \\(\\mathcal{D}\\). Fine-tuning the aggregated global model with \\(\\mathcal{D}_{\\mathrm{syn}}\\) effectively alleviates the performance degradation caused by deflected clients. An appealing feature of our DYNAFED is that the data can be synthesized using just the global model's trajectory of the first few rounds, which enables \\(\\mathcal{D}_{\\mathrm{syn}}\\) to take effect and help aggregation from early rounds. In addition, the synthesizing process only needs to be conducted once in practice, after which the derived \\(\\mathcal{D}_{\\mathrm{syn}}\\) can be directly applied in subsequent rounds to help aggregate the deviated client models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.274, + 0.897, + 0.41 + ], + "angle": 0, + "content": "Notably, our framework can be readily applied to the majority of FL approaches, since we rely on only the history of the global model's parameters for synthesizing \\(\\mathcal{D}_{\\mathrm{syn}}\\), which is available in the conventional setting of FedAvg-based methods. Furthermore, because we extract global knowledge using the global dynamics, rather than any client-specific information as in [12, 17, 18, 20, 47], the derived \\(\\mathcal{D}_{\\mathrm{syn}}\\) comprises of information mixed with the entire global data distribution, thus prevents leakage of client privacy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.41, + 0.897, + 0.593 + ], + "angle": 0, + "content": "Our DYNAFED possesses the following advantages compared with previous approaches: 1) It leverages the knowledge of the global data distribution to alleviate the aggregation bias of the global model without depending on any external datasets; 2) DYNAFED is able to generate informative data in the early rounds of federated learning, which significantly helps convergence and stabilizes training in subsequent rounds; 3) Compared with [50, 53], which need to keep updating the generator throughout all communication rounds, the data synthesis process in our method only needs to be done once, which reduces the computational overhead. In summary, we make the following contributions:" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.603, + 0.892, + 0.693 + ], + "angle": 0, + "content": "- We propose a practical approach named DYNAFED for tackling the heterogeneity problem, which extracts and exploits the hidden information from the global model's trajectory. In this way, the server can access the essential knowledge of the global data distribution to reinforce aggregation;" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.694, + 0.894, + 0.739 + ], + "angle": 0, + "content": "- We experimentally show the synthesized dataset helps stabilize training, boost convergence and achieve significant performance improvement under heterogeneity;" + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.739, + 0.895, + 0.784 + ], + "angle": 0, + "content": "- We provide insights and detailed analysis into the working mechanisms of the proposed DYNAFED both experimentally and theoretically." + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.603, + 0.895, + 0.784 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.8, + 0.642, + 0.815 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Regularization-based Methods FedAvg [34] is the most widely used technique in FL, which periodically aggregates the local models to the global model in each communication round. FedProx [31] proposes to impose a proximal term during local training, such that the local model does not" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "12178" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.473, + 0.213 + ], + "angle": 0, + "content": "drift too far from its global initialization; Scaffold [24] introduces a control variate and variance reduction to alleviate the drift of local training. Moon [29] proposes to leverage the similarity between model representations to regularize the client local training. FedDyn [1] introduces the linear and quadratic penalty terms to correct the clients' objective during local training. These methods are orthogonal to our approach and can be jointly used." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.218, + 0.473, + 0.43 + ], + "angle": 0, + "content": "Data-Dependent Knowledge Distillation Methods This line of work attempts to distill client ensemble knowledge into the global model. [33] proposes to use an unlabeled external dataset on the server to match the global model's outputs with that of the client ensemble. On top of this, [6] further proposes to sample and combine higher-quality client models via a Bayesian model ensemble. Subsequently, some advanced techniques, such as pre-training [15] and weighted consensus distillation scheme [8] are proposed. These methods typically require a large amount of data following similar distribution as the task data, which is usually hard to acquire in practice. Besides, these methods need to conduct KD with a large dataset in every communication round, which introduces prohibitive computational overhead." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.447, + 0.473, + 0.706 + ], + "angle": 0, + "content": "Data-free Knowledge Distillation Methods Recently, a few works have proposed to perform KD in a data-free manner by synthesizing data with generative models [50,53]. [53] proposes to train a lightweight generator on the server, which produces a feature embedding conditioned on the class index. The generator is then sent to the clients to regularize local training. [50] trains a class conditional GAN [14] on the server, where the global model acts as the discriminator. The pseudo data is then used to finetune the global model. These methods all depend on the global model for training the generator. Unfortunately, the model performance is often poor under high data heterogeneity, which makes the quality of the pseudo data questionable. On the other hand, due to the use of update dynamics of the global model rather than an individual model, our method can synthesize high-quality data containing rich global information even if the global model performs poorly." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.717, + 0.205, + 0.734 + ], + "angle": 0, + "content": "3. Preliminary" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.742, + 0.473, + 0.906 + ], + "angle": 0, + "content": "Federated Learning. Suppose we have \\(M\\) clients in a federated learning system. For each client \\(m \\in [M]\\), a private dataset \\(\\mathcal{D}_m = \\{(x_i, y_i)\\}_{i=1}^{|\\mathcal{D}_m|}\\) is kept locally. The overall optimization goal of the FL system is to jointly train a global model which performs well on the combination of local data, denoted as \\(\\mathcal{D} = \\cup_{m=1}^{M} \\mathcal{D}_m\\), where \\(\\mathcal{D}\\) is from a global distribution. Let \\(\\alpha_m = \\frac{|\\mathcal{D}_m|}{|\\mathcal{D}|}\\) denote the portion of data samples on client \\(m\\). Let \\(\\boldsymbol{w} \\in \\mathbb{R}^d\\) denote the model parameter to optimize, and \\(\\mathcal{L}_m(\\boldsymbol{w}, \\mathcal{D}_m) = \\frac{1}{|\\mathcal{D}_m|} \\sum_{\\xi \\in \\mathcal{D}_m} \\ell(\\boldsymbol{w}, \\xi)\\) denote the empirical risk with the loss" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.091, + 0.894, + 0.122 + ], + "angle": 0, + "content": "function \\(\\ell (\\cdot ,\\cdot)\\) . The optimization problem of a generic FL system can be formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.577, + 0.13, + 0.894, + 0.168 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\boldsymbol {w}} \\mathcal {L} (\\boldsymbol {w}, \\mathcal {D}) = \\sum_ {m = 1} ^ {M} \\alpha_ {m} \\mathcal {L} _ {m} (\\boldsymbol {w}, \\mathcal {D} _ {m}). \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.175, + 0.895, + 0.326 + ], + "angle": 0, + "content": "FedAvg. The main-stream solutions of Eqn. 1 rely on local-SGD to reduce the communication cost of transferring gradients. FedAvg [34] is the most prevalent approach, which uses a weighted average to aggregate the locally trained models into a global model in each communication round. Typically, not all the clients participate in every communication round. Suppose \\(\\mathcal{M}^c\\subset [M]\\) is the set of the participated clients in the \\(c\\) -th round, and \\(P^{c} = \\sum_{m\\in \\mathcal{M}^{c}}\\alpha_{m}\\). The aggregation process for the global model \\(\\pmb{w}^{c + 1}\\) at the end of \\(c\\) -th communication round can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.608, + 0.331, + 0.893, + 0.363 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {w} ^ {c + 1} = \\frac {1}{P ^ {c}} \\sum_ {m \\in \\mathcal {M} ^ {c}} \\alpha_ {m} \\boldsymbol {w} _ {m} ^ {c}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.37, + 0.894, + 0.432 + ], + "angle": 0, + "content": "where \\(\\pmb{w}_{m}^{c}\\) denotes the client \\(m\\)'s locally trained model. After the aggregation, the updated global model \\(\\pmb{w}^{c + 1}\\) is then distributed to and client and utilized to initiate the \\(c + 1\\)-th round of the training." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.444, + 0.673, + 0.461 + ], + "angle": 0, + "content": "4. Proposed Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.469, + 0.895, + 0.59 + ], + "angle": 0, + "content": "In this section, we introduce our proposed method DYNAFED. The overall framework is illustrated in Figure 1. Firstly, we collect a trajectory of the global model's updates in the early phase of federated training, with which we construct a synthetic dataset \\(\\mathcal{D}_{\\mathrm{syn}} = \\{\\pmb {X},\\pmb {y}\\}\\) on the server side. Then, we utilize \\(\\mathcal{D}_{\\mathrm{syn}}\\) to aid the server-side aggregation, which effectively helps recover the performance drop caused by deflected local models." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.599, + 0.892, + 0.616 + ], + "angle": 0, + "content": "4.1. Acquiring Global Knowledge by Data Synthesis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.621, + 0.895, + 0.816 + ], + "angle": 0, + "content": "Our goal is to construct a pseudo dataset \\(\\mathcal{D}_{\\mathrm{syn}}\\), which achieves a similar effect during training as the global dataset \\(\\mathcal{D}\\). In other words, the trajectory of a network trained with \\(\\mathcal{D}_{\\mathrm{syn}}\\) should have similar dynamics with the trajectory trained with \\(\\mathcal{D}\\). To be precise, we denote the trajectory trained on \\(\\mathcal{D}\\) as a sequence \\(\\{\\boldsymbol{w}^t\\}_{t=0}^L\\), where \\(L\\) is the length of the trajectory. In order to reduce the number of unrolling steps during optimization, we align the trajectory in a segment-by-segment manner. Without loss of generality, we consider a segment from \\(\\boldsymbol{w}^t\\) to \\(\\boldsymbol{w}^{t+s}\\), then the problem becomes the following: starting from \\(\\boldsymbol{w}^t\\), the network should arrive at a place close to \\(\\boldsymbol{w}^{t+s}\\) after being trained for \\(s\\) steps on \\(\\mathcal{D}_{\\mathrm{syn}}\\). We further formulate the data synthesis task into a learning problem as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.604, + 0.824, + 0.893, + 0.845 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\boldsymbol {X}, \\boldsymbol {y}} \\mathbb {E} _ {t \\sim U (1, L - s)} [ d (\\tilde {\\boldsymbol {w}}, \\boldsymbol {w} ^ {\\mathrm {t} + s}) ] \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.618, + 0.849, + 0.893, + 0.866 + ], + "angle": 0, + "content": "\\[\ns. t. \\tilde {\\boldsymbol {w}} = \\mathcal {A} (\\boldsymbol {X}, \\boldsymbol {y}, \\boldsymbol {w} ^ {\\mathrm {t}}, s) \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.873, + 0.894, + 0.901 + ], + "angle": 0, + "content": "In the inner loop expressed by Eqn.4, we run the trainer \\(\\mathcal{A}(\\cdot)\\) that trains a neural network initialized from \\(\\boldsymbol{w}^{\\mathrm{t}}\\) on the synthetic" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "12179" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.232 + ], + "angle": 0, + "content": "dataset \\(\\mathcal{D}_{\\mathrm{syn}} = \\{\\pmb {X},\\pmb {y}\\}\\) for \\(s\\) steps, which arrives at \\(\\tilde{\\pmb{w}}\\). In the outer loop, we minimize the distance between \\(\\pmb{w}^{\\mathrm{t + s}}\\) and \\(\\tilde{\\pmb{w}}\\), denoted as \\(d(\\tilde{\\pmb{w}},\\pmb{w}^{\\mathrm{t + s}})\\), by optimizing over \\((\\pmb {X},\\pmb {y})\\). The expectation of the uniform distribution \\(U\\) is adopted to take into account all the segments along the trajectory. \\(d(\\cdot ,\\cdot)\\) is a general distance measure, which can take the form of euclidean distance or cosine distance, etc. During the optimization, we treat both \\((\\pmb {X},\\pmb {y})\\) to be learnable variables, where \\(\\pmb{X}\\) is initialized with random noise, and \\(\\pmb{y}\\) is initialized with equal probabilities over all labels. The detailed algorithm is shown in Algorithm 1." + }, + { + "type": "title", + "bbox": [ + 0.08, + 0.246, + 0.227, + 0.261 + ], + "angle": 0, + "content": "Algorithm 1 DataSyn" + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.266, + 0.469, + 0.295 + ], + "angle": 0, + "content": "Require: Global trajectory \\(\\{\\pmb{w}^c\\}_1^L\\), learning rate \\(\\eta\\), training rounds \\(N\\), inner steps \\(s'\\)." + }, + { + "type": "text", + "bbox": [ + 0.086, + 0.296, + 0.469, + 0.323 + ], + "angle": 0, + "content": "1: Randomly initialize \\( \\mathbf{X}_0 \\) and pair them with \\( \\mathbf{y} \\) to form the synthetic dataset." + }, + { + "type": "text", + "bbox": [ + 0.086, + 0.324, + 0.338, + 0.336 + ], + "angle": 0, + "content": "2: for training iteration \\( n = 1, 2 \\dots N \\) do" + }, + { + "type": "text", + "bbox": [ + 0.086, + 0.337, + 0.468, + 0.365 + ], + "angle": 0, + "content": "3: Sample \\( t \\sim U(1, L - s) \\), then take \\( \\boldsymbol{w}^{\\mathrm{t}} \\) and \\( \\boldsymbol{w}^{\\mathrm{t + s}} \\) from the trajectory." + }, + { + "type": "text", + "bbox": [ + 0.086, + 0.365, + 0.422, + 0.379 + ], + "angle": 0, + "content": "4: Get the trained parameters \\(\\tilde{\\boldsymbol{w}} = \\mathcal{A}(\\boldsymbol{X}_n, \\boldsymbol{y}_n, \\boldsymbol{w}^{\\mathrm{t}}, s')\\)" + }, + { + "type": "text", + "bbox": [ + 0.086, + 0.379, + 0.469, + 0.407 + ], + "angle": 0, + "content": "5: Calculate the distance \\(d(\\tilde{\\boldsymbol{w}}, \\boldsymbol{w}^{\\mathrm{t+s}})\\) and obtain gradient w.r.t \\(\\boldsymbol{X}_n\\) and \\(\\boldsymbol{y}_n\\) as \\(\\nabla_{\\boldsymbol{X}_n} d(\\tilde{\\boldsymbol{w}}, \\boldsymbol{w}^{\\mathrm{t+s}})\\) and \\(\\nabla_{\\boldsymbol{y}_n} d(\\tilde{\\boldsymbol{w}}, \\boldsymbol{w}^{\\mathrm{t+s}})\\)." + }, + { + "type": "text", + "bbox": [ + 0.086, + 0.407, + 0.468, + 0.435 + ], + "angle": 0, + "content": "6: Update \\( \\mathbf{X}_n \\) and \\( \\mathbf{y}_n \\) using gradient descent \\( \\mathbf{X}_{n+1} = \\mathbf{X}_n - \\eta \\nabla_{\\mathbf{X}_n} d(\\tilde{\\mathbf{w}}, \\mathbf{w}^{\\mathrm{t+s}}) \\), \\( \\mathbf{y}_{n+1} = \\mathbf{y}_n - \\eta \\nabla_{\\mathbf{y}_n} d(\\tilde{\\mathbf{w}}, \\mathbf{w}^{\\mathrm{t+s}}) \\)" + }, + { + "type": "text", + "bbox": [ + 0.086, + 0.435, + 0.153, + 0.446 + ], + "angle": 0, + "content": "7: end for" + }, + { + "type": "list", + "bbox": [ + 0.086, + 0.296, + 0.469, + 0.446 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.102, + 0.448, + 0.342, + 0.462 + ], + "angle": 0, + "content": "Output: Optimized synthetic data \\(\\mathcal{D}_{\\mathrm{syn}}\\)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.481, + 0.47, + 0.536 + ], + "angle": 0, + "content": "Note that since the size of \\( \\mathcal{D}_{\\mathrm{syn}} \\) is much smaller than \\( \\mathcal{D} \\), the effective step size should have a different scale. Therefore, in Equation 4, we may increase the number of steps from \\( s \\) to \\( s' \\) to account for this scale mismatch." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.538, + 0.472, + 0.58 + ], + "angle": 0, + "content": "In this way, the knowledge hidden in the dynamics of the global model can be transferred to \\(\\mathcal{D}_{\\mathrm{syn}}\\), which then acts as an approximation of the global data distribution to aid the server-side aggregation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.587, + 0.35, + 0.603 + ], + "angle": 0, + "content": "4.2. Overall Algorithm of DynaFed" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.61, + 0.469, + 0.638 + ], + "angle": 0, + "content": "In this section, we present our DYNAFED that integrates the data synthesis process into the federated learning framework." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.638, + 0.469, + 0.734 + ], + "angle": 0, + "content": "Firstly, to construct the global trajectory on the server, we collect the global model's checkpoints from the first few communication rounds of FedAvg mainly considering the following two factors: 1) collecting a long trajectory induces prohibitive cost due to the expensive global communication, 2) the change in global model's parameters becomes insignificant during late rounds, which makes it difficult to extract knowledge from the dynamics." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.469, + 0.872 + ], + "angle": 0, + "content": "Note that although \\(\\mathcal{D}_{\\mathrm{syn}}\\) contains rich global knowledge, it is not sufficient to replace the global data distribution \\(\\mathcal{D}\\) due to the following reasons: 1) the objective in Eqn.3 can not be ideally solved due to the two-level optimization procedure, 2) to make the scale of the optimization problem acceptable, the size of \\(\\mathcal{D}_{\\mathrm{syn}}\\) cannot be as large as \\(\\mathcal{D}\\), 3) there exists an inconsistency between the trainer \\(\\mathcal{A}(\\cdot)\\) and the one that produces the global trajectory, i.e., FedAvg. Therefore, instead of simply conduct regular training with \\(\\mathcal{D}_{\\mathrm{syn}}\\), we leverage such \\(\\mathcal{D}_{\\mathrm{syn}}\\) to help aggregation by finetuning the global model on the server side." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.873, + 0.469, + 0.901 + ], + "angle": 0, + "content": "The rundown of the entire algorithm is presented in Algorithm 2. Firstly, the global model's trajectory in the earliest \\( L \\) rounds is" + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.091, + 0.665, + 0.106 + ], + "angle": 0, + "content": "Algorithm 2 DYNAFED" + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.111, + 0.894, + 0.171 + ], + "angle": 0, + "content": "Require: Client data \\(\\mathcal{D}_m = \\{(x_i,y_i)\\}_{i = 1}^{|\\mathcal{D}_m|}\\), global parameters \\(\\boldsymbol{w}\\), client parameters \\(\\{\\boldsymbol{w}_m\\}_{m = 1}^{|\\mathcal{M}|}\\). Total communication rounds \\(C\\), local steps \\(T\\), data learning rate \\(\\eta\\), data training rounds \\(N\\), trajectory length \\(L\\), inner steps for data synthesis \\(s'\\)." + }, + { + "type": "text", + "bbox": [ + 0.509, + 0.172, + 0.788, + 0.184 + ], + "angle": 0, + "content": "1: for communication round \\( c = 1,2\\ldots C \\) do" + }, + { + "type": "text", + "bbox": [ + 0.509, + 0.185, + 0.892, + 0.213 + ], + "angle": 0, + "content": "2: Sample active clients \\(\\mathcal{M}^c\\) randomly. Distribute \\(\\boldsymbol{w}^c\\) to active clients and initialize their parameters." + }, + { + "type": "list", + "bbox": [ + 0.509, + 0.172, + 0.892, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.509, + 0.214, + 0.697, + 0.226 + ], + "angle": 0, + "content": "3: for all users \\(m \\in \\mathcal{M}^c\\) do" + }, + { + "type": "text", + "bbox": [ + 0.509, + 0.226, + 0.765, + 0.241 + ], + "angle": 0, + "content": "4: \\(\\{\\pmb{w}_m^c\\}_{m=1}^{|\\mathcal{M}^c|} \\gets \\text{LocalTrain}(\\pmb{w}^c, T)\\)" + }, + { + "type": "text", + "bbox": [ + 0.509, + 0.242, + 0.592, + 0.253 + ], + "angle": 0, + "content": "5: end for" + }, + { + "type": "text", + "bbox": [ + 0.509, + 0.253, + 0.797, + 0.269 + ], + "angle": 0, + "content": "6: Clients send updated \\(\\{\\pmb{w}_m^c\\}_{m=1}^{|\\mathcal{M}^c|}\\) to server." + }, + { + "type": "text", + "bbox": [ + 0.509, + 0.269, + 0.72, + 0.284 + ], + "angle": 0, + "content": "7: \\(\\pmb{w}^{c + 1}\\gets \\frac{1}{|\\mathcal{M}^c|}\\sum_{m\\in \\mathcal{M}^c}\\pmb{w}_m^c\\)" + }, + { + "type": "text", + "bbox": [ + 0.509, + 0.284, + 0.628, + 0.294 + ], + "angle": 0, + "content": "8: if \\( c = L \\) then" + }, + { + "type": "text", + "bbox": [ + 0.509, + 0.295, + 0.783, + 0.31 + ], + "angle": 0, + "content": "9: \\(\\mathcal{D}_{\\mathrm{syn}}\\gets \\mathrm{DataSyn}(\\{\\pmb {w}^c\\}_{c = 1}^L,\\eta ,s',N)\\)" + }, + { + "type": "text", + "bbox": [ + 0.508, + 0.311, + 0.522, + 0.321 + ], + "angle": 0, + "content": "10:" + }, + { + "type": "text", + "bbox": [ + 0.507, + 0.324, + 0.654, + 0.336 + ], + "angle": 0, + "content": "11: else if \\( c > L \\) then" + }, + { + "type": "text", + "bbox": [ + 0.507, + 0.337, + 0.748, + 0.351 + ], + "angle": 0, + "content": "12: \\(\\pmb{w}^{c + 1}\\gets\\) Finetune \\((\\mathcal{D}_{\\mathrm{syn}},\\pmb{w}^{c + 1})\\)" + }, + { + "type": "text", + "bbox": [ + 0.505, + 0.352, + 0.57, + 0.362 + ], + "angle": 0, + "content": "13: else" + }, + { + "type": "text", + "bbox": [ + 0.505, + 0.365, + 0.737, + 0.379 + ], + "angle": 0, + "content": "14: Add \\(\\pmb{w}^{c + 1}\\) into trajectory list." + }, + { + "type": "text", + "bbox": [ + 0.505, + 0.38, + 0.583, + 0.391 + ], + "angle": 0, + "content": "15: end if" + }, + { + "type": "text", + "bbox": [ + 0.505, + 0.394, + 0.576, + 0.405 + ], + "angle": 0, + "content": "16: end for" + }, + { + "type": "list", + "bbox": [ + 0.505, + 0.214, + 0.797, + 0.405 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.44, + 0.892, + 0.51 + ], + "angle": 0, + "content": "collected and stored on the server. Then, the server executes the data synthesis procedure to generate the pseudo data \\(\\mathcal{D}_{\\mathrm{syn}}\\). In all subsequent rounds, \\(\\mathcal{D}_{\\mathrm{syn}}\\) is leveraged on the server to help reduce the negative impact of deflected client models by finetuning the global model." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.512, + 0.846, + 0.527 + ], + "angle": 0, + "content": "Our method enjoys the following appealing properties:" + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.538, + 0.892, + 0.592 + ], + "angle": 0, + "content": "- In contrast to data-dependent KD methods [6,33], DYNAFED extracts the knowledge of the global data distribution from the global model trajectory, which does not depend on any external datasets;" + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.593, + 0.892, + 0.662 + ], + "angle": 0, + "content": "- Compared with data-free KD methods [50, 53], DYNAFED is able to synthesize informative pseudo data in the early rounds of federated learning without requiring the global model to be well trained, which significantly helps convergence and stabilizes training;" + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.663, + 0.892, + 0.705 + ], + "angle": 0, + "content": "- The data synthesis only needs to be conducted once. Besides, since only a few samples are synthesized, refining the global model on the server requires negligible time." + }, + { + "type": "list", + "bbox": [ + 0.52, + 0.538, + 0.892, + 0.705 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.721, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Remark 1. We emphasize that our DYNAFED does not raise privacy concerns given following reasons: 1) we rely on only the trajectory of the global model's parameters, which is available in the conventional setting of all FedAvg-based methods; 2) we keep \\(\\mathcal{D}_{\\text{syn}}\\) at the server rather than sending it to the clients; 3) we extract global knowledge using the global dynamics, rather than any client-specific information as in [12, 17, 18, 20, 47], the derived \\(\\mathcal{D}_{\\text{syn}}\\) comprises of information mixed with the entire global data distribution, thus prevents leakage of client privacy; 4) our DYNAFED shares a similar flavor as dataset condensation (DC) methods, which aims to generate informative pseudo data containing global knowledge, rather than real-looking data. The privacy-preserving ability of DC was also discussed in previous work [11]." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "12180" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.09, + 0.274, + 0.108 + ], + "angle": 0, + "content": "5. Theoretical Analysis" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.115, + 0.47, + 0.17 + ], + "angle": 0, + "content": "In this section, we present some insights to understand our data synthesis process from the neural tangent kernel (NTK) theory and also give the convergence results for DYNAfed. Detailed proofs are given in the appendix." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.171, + 0.471, + 0.296 + ], + "angle": 0, + "content": "In our data synthesis process, we align the segments (e.g., from \\(t\\) to \\(t + s\\)) of the trajectories trained on \\(\\mathcal{D}\\) and \\(\\mathcal{D}_{\\mathrm{syn}}\\) for any \\(t\\). Essentially, those segments are the cumulative gradients calculated using \\(\\mathcal{D}\\) and \\(\\mathcal{D}_{\\mathrm{syn}}\\), which approximate to \\(\\nabla \\mathcal{L}(\\boldsymbol{w}_t, \\mathcal{D}_{\\mathrm{syn}}) \\Delta t\\) and \\(\\nabla \\mathcal{L}(\\boldsymbol{w}^t, \\mathcal{D}) \\Delta t\\). Therefore, we can expect \\(\\nabla \\mathcal{L}(\\boldsymbol{w}, \\mathcal{D}_{\\mathrm{syn}})\\) would be close to \\(\\nabla \\mathcal{L}(\\boldsymbol{w}, \\mathcal{D})\\), which is verified by our experimental result (left of Figure.6). Given a sample \\(\\boldsymbol{x}\\), if continuous-time gradient descent is adopted as the training solver, the dynamics of neural network function trained on \\(\\mathcal{D}_{\\mathrm{syn}}\\) and \\(\\mathcal{D}\\) take the forms of" + }, + { + "type": "equation", + "bbox": [ + 0.129, + 0.304, + 0.472, + 0.342 + ], + "angle": 0, + "content": "\\[\n\\left\\{ \\begin{array}{l} \\frac {d f (\\boldsymbol {x} , \\boldsymbol {w} ^ {t})}{d t} = \\nabla_ {\\boldsymbol {w} ^ {t}} f (\\boldsymbol {x}, \\boldsymbol {w} ^ {t}) ^ {\\top} \\nabla \\mathcal {L} \\left(\\boldsymbol {w} ^ {t}, \\mathcal {D} _ {\\text {s y n}}\\right), \\\\ \\frac {d f (\\boldsymbol {x} , \\boldsymbol {w} ^ {t})}{d t} = \\nabla_ {\\boldsymbol {w} ^ {t}} f (\\boldsymbol {x}, \\boldsymbol {w} ^ {t}) ^ {\\top} \\nabla \\mathcal {L} \\left(\\boldsymbol {w} ^ {t}, \\mathcal {D}\\right). \\end{array} \\right. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.349, + 0.47, + 0.46 + ], + "angle": 0, + "content": "which is close to an ordinary differential equation according to the NTK theory [19]. Note that the right-hand sides of the two equations in (5) are close if \\(\\nabla \\mathcal{L}(\\boldsymbol{w}, \\mathcal{D}_{\\mathrm{syn}}) \\approx \\nabla \\mathcal{L}(\\boldsymbol{w}, \\mathcal{D})\\). In this case, the following lemma about the continuous dependence of differentiable equation shows that the neural functions \\(f(\\boldsymbol{x}, \\boldsymbol{w}^t)\\) learned with pseudo data \\(\\mathcal{D}_{\\mathrm{syn}}\\) are similar to that learned with real global data \\(\\mathcal{D}\\) during the whole training process. This further indicates that \\(\\mathcal{D}_{\\mathrm{syn}}\\) achieves similar effect as \\(\\mathcal{D}\\) during training." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.468, + 0.471, + 0.497 + ], + "angle": 0, + "content": "Lemma 1 (Continuous Dependence [42]). Suppose \\(\\tilde{F}(t, f)\\) and \\(F(t, f)\\) are two continuous functions in a region \\(G\\) satisfying" + }, + { + "type": "equation", + "bbox": [ + 0.158, + 0.505, + 0.388, + 0.521 + ], + "angle": 0, + "content": "\\[\n\\left| \\tilde {F} (t, f) - F (t, f) \\right| \\leq \\epsilon , \\forall (t, f) \\in G.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.53, + 0.47, + 0.558 + ], + "angle": 0, + "content": "Further, we assume \\( F(t,f) \\) satisfy the \\( L_{F} \\)-Lipschitz condition w.r.t., \\( f \\). Let \\( \\tilde{f}(t) \\) and \\( f(t) \\) be the solutions of initial problems," + }, + { + "type": "equation", + "bbox": [ + 0.17, + 0.566, + 0.376, + 0.595 + ], + "angle": 0, + "content": "\\[\n\\frac {d \\tilde {f}}{d t} = \\tilde {F} (t, \\tilde {f}) a n d \\frac {d f}{d t} = F (t, f),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.603, + 0.469, + 0.633 + ], + "angle": 0, + "content": "with \\(\\tilde{f}(t_0) = f_0\\) and \\(f(t_0) = f_0\\). Then, in a common region \\(|t - t_0| \\leq \\alpha\\), we have the following estimation:" + }, + { + "type": "equation", + "bbox": [ + 0.166, + 0.64, + 0.38, + 0.666 + ], + "angle": 0, + "content": "\\[\n| \\tilde {f} (t) - f (t) | \\leq \\frac {\\epsilon}{L _ {F}} \\left(e ^ {\\alpha L _ {F}} - 1\\right).\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.673, + 0.47, + 0.755 + ], + "angle": 0, + "content": "To analyze the convergence of DYNAFED, we need to define some additional notations and rewrite our method as follows. Suppose with the \\(\\mathcal{D}_{\\mathrm{syn}}\\) generated from the data synthesis process, in DYNAFED we run SGD for \\(\\tau_{1}\\) and \\(\\tau_{2}\\) iterations in each local training round and finetuning process, respectively. Let the sets \\(\\mathcal{I}\\) and \\(\\mathcal{J}\\) be" + }, + { + "type": "equation", + "bbox": [ + 0.106, + 0.765, + 0.438, + 0.78 + ], + "angle": 0, + "content": "\\[\n\\mathcal {I} = \\left\\{t | t = k \\left(\\tau_ {1} + \\tau_ {2}\\right) + c, k = 0, 1, 2, \\dots , c \\in \\left[ \\tau_ {1} \\right] \\right\\},\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.109, + 0.782, + 0.47, + 0.798 + ], + "angle": 0, + "content": "\\[\n\\mathcal {J} = \\{t | t = k \\left(\\tau_ {1} + \\tau_ {2}\\right) + \\tau_ {1}, k = 0, 1, 2, \\dots \\}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.806, + 0.471, + 0.861 + ], + "angle": 0, + "content": "where \\([\\tau_1] = \\{0, 1, \\dots, \\tau_1 - 1\\}\\). Therefore, when \\(t \\in \\mathcal{I}\\), we perform local training, while when \\(t \\notin \\mathcal{I}\\), we conduct finetuning. \\(\\mathcal{I}\\) denotes the time index for aggregation. The detailed steps of DYNAFED can be rewritten as" + }, + { + "type": "equation", + "bbox": [ + 0.129, + 0.868, + 0.419, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {v} _ {t + 1} ^ {m} = \\left\\{ \\begin{array}{l l} \\boldsymbol {w} _ {m} ^ {t} - \\eta_ {t} \\nabla \\ell (\\boldsymbol {w} _ {m} ^ {t}, \\xi_ {m} ^ {t}), & \\text {i f} t \\in \\mathcal {I} \\\\ \\boldsymbol {w} _ {m} ^ {t} - \\eta_ {t} \\nabla \\mathcal {L} (\\boldsymbol {w} _ {m} ^ {t}, \\mathcal {D} _ {\\text {s y n}}), & \\text {i f} t \\notin \\mathcal {I} \\end{array} , \\right.\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.551, + 0.089, + 0.826, + 0.126 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {w} _ {m} ^ {t + 1} = \\left\\{ \\begin{array}{l l} \\boldsymbol {v} _ {m} ^ {t + 1}, & \\text {i f} t + 1 \\notin \\mathcal {J} \\\\ \\sum_ {m = 1} ^ {M} \\alpha_ {m} \\boldsymbol {v} _ {m} ^ {t + 1}, & \\text {i f} t + 1 \\in \\mathcal {J} \\end{array} , \\right.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.135, + 0.874, + 0.15 + ], + "angle": 0, + "content": "where \\(\\xi_m^t\\sim \\mathcal{D}_m\\) . Based on the notations, we define a sequence:" + }, + { + "type": "equation", + "bbox": [ + 0.636, + 0.15, + 0.757, + 0.185 + ], + "angle": 0, + "content": "\\[\n\\bar {\\boldsymbol {w}} ^ {t} = \\sum_ {m = 1} ^ {M} \\alpha_ {m} \\boldsymbol {w} _ {m} ^ {t}.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.187, + 0.894, + 0.228 + ], + "angle": 0, + "content": "Hence, our algorithm is an integration of FedAvg and a biased GD. For \\(\\bar{\\boldsymbol{w}}^t\\), note that \\(\\bar{\\boldsymbol{w}}^t = \\boldsymbol{w}_1^t = \\dots = \\boldsymbol{w}_M^t\\) in the finetuning process and we have the following convergence results:" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.238, + 0.893, + 0.294 + ], + "angle": 0, + "content": "Theorem 1 (Convergence). For \\(\\tilde{L}\\)-smooth, \\(\\mu\\)-strongly convex loss functions \\(\\ell(\\cdot, \\cdot)\\). We assume \\(\\|\\nabla \\mathcal{L}(\\boldsymbol{w}, \\mathcal{D}_{\\mathrm{syn}}) - \\nabla \\mathcal{L}(\\boldsymbol{w}, \\mathcal{D})\\| \\leq \\delta\\|\\nabla \\mathcal{L}(\\boldsymbol{w}, \\mathcal{D})\\| + \\epsilon\\) holds with two small non-negative scalars \\(\\delta\\) and \\(\\epsilon\\). Let \\(\\eta_t = \\frac{c}{t}\\) for a proper constant \\(c\\). Then, DYNAfed satisfies" + }, + { + "type": "equation", + "bbox": [ + 0.597, + 0.303, + 0.892, + 0.33 + ], + "angle": 0, + "content": "\\[\n\\mathbb {E} \\mathcal {L} \\left(\\bar {\\boldsymbol {w}} ^ {T}, \\mathcal {D}\\right) - \\mathcal {L} \\left(\\boldsymbol {w} ^ {*}, \\mathcal {D}\\right) \\leq \\frac {C}{T}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.338, + 0.892, + 0.366 + ], + "angle": 0, + "content": "where \\(\\mathbf{w}^*\\) is the minimum of \\(\\mathcal{L}(\\mathbf{w},\\mathcal{D})\\) and \\(C\\) is a constant, whose detailed formula is given in the appendix." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.376, + 0.892, + 0.403 + ], + "angle": 0, + "content": "More detailed discussions about the convergence result are given in the Appendix." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.417, + 0.633, + 0.435 + ], + "angle": 0, + "content": "6. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.441, + 0.894, + 0.636 + ], + "angle": 0, + "content": "Benchmark Datasets and Experimental Settings. We conduct experiments over four commonly used datasets: FashionMNIST [43], CIFAR10 [25], CINIC10 [9] and CIFAR100 [25]. Among them, FashionMNIST is a dataset containing grey-scale images of fashion products. CIFAR10 is an image classification dataset containing daily objects. CINIC10 is a dataset combining CIFAR10 and samples from similar classes that are downsampled from ImageNet [26]. These three datasets contain 10 classes. CIFAR100 contains the same data as CIFAR10, but categorizes the data into 100 classes. For each dataset, we mainly conduct experiments with heterogeneous client data distribution. We follow prior work [6, 33] to use Dirichlet distribution for simulating the non-IID data distribution, where the degree of heterogeneity is defined by \\(\\alpha\\), smaller \\(\\alpha\\) value corresponds to more severe heterogeneity." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.64, + 0.894, + 0.78 + ], + "angle": 0, + "content": "**Baseline Methods** We consider various state-of-the-art solutions against non-IID data distribution in the context of federated learning. Specifically, we compare with the following approaches 1) the vanilla aggregation strategy FedAVG [34]; 2) regularization-based strategies FedProx [31], Scaffold [24]; 3) data-dependent knowledge distillation strategies that need external dataset FedDF [33] and FedBE [6], ABAVG [44]; (4) data sharing [49] or data-free knowledge distillation [53] methods. Note that we do not compare with [50] since the code is not published. Please refer to Appendix for detailed settings of the baseline methods." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.79, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Configurations Unless specified otherwise, we follow [?,7,15] and adopt the following default configurations throughout the experiments: we run 200 global communication rounds with local epoch set to 1. There are 80 clients in total, and the participation ratio in each round is set to \\(40\\%\\). Experiments using other participation ratios are in the Appendix. We report the global model's average performance in the last five rounds evaluated using the test split of the datasets. For the construction of global trajectory, we first run" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "12181" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.08, + 0.894, + 0.245 + ], + "angle": 0, + "content": "
Methodα = 0.01α = 0.04α = 0.16
FMNISTCIFAR10CINIC10FMNISTCIFAR10CINIC10FMNISTCIFAR10CINIC10
FedAVG74.50±1.3239.30±3.4231.60±5.5081.74±1.9851.19±2.8545.35±3.0089.54±1.5169.74±1.2955.40±2.05
FedProx76.88±1.8342.13±3.6432.56±4.5983.06±2.5358.93±2.1446.30±2.8789.53±1.1370.20±0.7457.78±2.08
Scaffold77.92±0.8742.04±2.2634.90±3.3482.25±1.3554.23±1.9046.22±2.1888.54±0.3268.57±0.9154.30±0.83
FedDF*72.36±2.0839.73±3.9831.97±4.3181.65±0.9754.20±2.9345.79±2.9589.70±0.9770.71±0.9455.78±1.02
FedBE*72.33±1.7938.36±3.7432.04±3.7381.31±1.2553.49±2.3645.50±2.8889.62±0.7570.23±0.7655.42±1.37
ABAVG*75.98±1.9939.95±1.3732.75±4.1884.88±1.8457.25±3.4247.39±3.3689.53±1.1270.55±2.4156.02±1.49
FedGen†75.59±1.1240.19±2.1432.59±3.2581.46±1.0856.60±1.2945.57±2.7089.95±0.8970.89±0.5455.34±1.13
FedMix†81.34±0.6850.48±1.2337.15±1.8184.23±0.5062.77±1.0750.22±1.4189.05±0.2470.33±0.5556.74±0.45
DynaFed†87.52±0.1565.53±0.3448.04±0.7089.45±0.1170.07±0.1255.43±0.2491.35±0.0774.69±0.1459.80±0.10
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.256, + 0.895, + 0.326 + ], + "angle": 0, + "content": "Table 1. Comparison of test performances achieved by different FL methods with different degrees of data heterogeneity \\(\\alpha\\) across multiple datasets. We report the mean test accuracy of last five communication rounds. *Methods assume the availability of proxy data. † Methods are based on data sharing or generation. We observe that our approach outperforms other methods by a large margin, and its advantage is more prominent on more challenging datasets with higher heterogeneity. Specifically, DYNAFED demonstrates relative improvement over the FedAvg baseline by \\(17.5\\%\\), \\(64.5\\%\\), \\(52.0\\%\\), and \\(82.2\\%\\) on FMNIST, CIFAR10, CINIC10, and CIFAR100, respectively." + }, + { + "type": "image", + "bbox": [ + 0.091, + 0.328, + 0.287, + 0.439 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.441, + 0.282, + 0.55 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.29, + 0.329, + 0.482, + 0.439 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.29, + 0.441, + 0.48, + 0.55 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.489, + 0.328, + 0.68, + 0.438 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.487, + 0.44, + 0.679, + 0.55 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.687, + 0.329, + 0.88, + 0.438 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.686, + 0.44, + 0.877, + 0.55 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.561, + 0.897, + 0.618 + ], + "angle": 0, + "content": "Figure 2. Visualization of global model's test performance on various datasets throughout the global communication rounds. We can see that the global model rapidly converges to a satisfactory test accuracy once \\(\\mathcal{D}_{\\mathrm{syn}}\\) participates in refining the global model. Furthermore, \\(\\mathcal{D}_{\\mathrm{syn}}\\) also helps reduce the fluctuation of model performances between communication rounds, which significantly boosts the training stability. DYNAFED requires less than \\(10\\%\\) communication rounds to achieve comparable performance with the baseline methods." + }, + { + "type": "table", + "bbox": [ + 0.085, + 0.631, + 0.465, + 0.766 + ], + "angle": 0, + "content": "
Methodα = 0.01α = 0.04α = 0.08α = 0.16
FedAVG16.54±2.1826.56±1.5334.54±1.0239.65±0.94
FedProx18.46±1.0528.58±1.4634.82±0.5440.98±0.49
Scaffold17.33±1.2128.46±1.1835.04±0.3540.57±0.33
FedDF*16.02±1.9426.94±1.2534.77±0.8839.76±0.44
FedBE*15.78±2.3428.03±0.3433.91±0.7939.45±0.79
ABAVG16.52±1.9829.14±0.5734.66±0.9841.00±0.23
FedGen†16.51 ±1.3227.03±1.1434.56±0.7839.96±0.58
FedMix†23.54±0.9632.18±0.5936.30±0.4241.09±0.14
DynaFed†30.14±0.1936.79±0.1240.02±0.0942.47±0.06
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.768, + 0.47, + 0.797 + ], + "angle": 0, + "content": "Table 2. Comparison of test performances on CIFAR100 with different degrees of data heterogeneity \\( \\alpha \\) ." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.831, + 0.473, + 0.903 + ], + "angle": 0, + "content": "FedAvg [34] and use the checkpoints from the first 20 communication rounds (\\(L = 20\\)). We set the time difference \\(s\\) between the start and end checkpoint to 5, and the target checkpoint is averaged with 2 checkpoints sampled between \\(\\boldsymbol{w}^{\\mathrm{t}}\\) and \\(\\boldsymbol{w}^{\\mathrm{t+s}}\\). More details can be found in the Appendix." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.643, + 0.871, + 0.66 + ], + "angle": 0, + "content": "6.1. Main Experiments with Data Heterogeneity" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.665, + 0.895, + 0.845 + ], + "angle": 0, + "content": "We demonstrate the superior performance of our DYNAFED by conducting experiments on heterogeneous client data across comprehensive datasets and various heterogeneity values \\(\\alpha\\). Specifically, we use three datasets with 10 classes (shown in Table 1): FashionMNIST [43], CIFAR10 [25] and CINIC10 [9], heterogeneity degree \\(\\alpha\\) set to 0.01, 0.04 and 0.16; and CIFAR100 containing 100 classes, with \\(\\alpha\\) values 0.01, 0.04, 0.08 and 0.16 (shown in Table 2). DYNAFED significantly boosts the convergence, stabilizes training, and brings considerable performance improvement compared with previous approaches. Specifically, with heterogeneity value \\(\\alpha = 0.01\\), DYNAFED demonstrates relative improvement over the FedAvg baseline by \\(17.5\\%\\), \\(64.5\\%\\), \\(52.0\\%\\), and \\(82.2\\%\\) on FMNIST, CIFAR10, CINIC10, and CIFAR100, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.846, + 0.895, + 0.903 + ], + "angle": 0, + "content": "As demonstrated in Figure 2, the performance of DYNAfed is rapidly boosted as soon as the synthesized data starts refining the global model on the server. This verifies that DYNAfed does not depend on the global model's performance in data synthesis," + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "12182" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.092, + 0.465, + 0.207 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.215, + 0.473, + 0.327 + ], + "angle": 0, + "content": "Figure 3. Loss curves over each client's data throughout local training and finetuning. Each of the 3 colors represents the loss over one client's data. The stars are the global model's average losses over all client data after finetuning with \\(\\mathcal{D}_{\\mathrm{syn}}\\). During local training, the client losses quickly converge to near zero. However, due to deflection caused by heterogeneity, the losses over some clients' data dramatically increase after aggregation. Finetuning with \\(\\mathcal{D}_{\\mathrm{syn}}\\) decreases those losses and reduces the aggregation bias." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.334, + 0.461, + 0.422 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.431, + 0.472, + 0.502 + ], + "angle": 0, + "content": "Figure 4. Visualization of learned synthetic data on 3 classes from CIFAR10 throughout the optimization process. In the beginning, the pixels are randomly initialized and contain little information. As the optimization goes on, some patterns emerge in the synthetic images but remain unrecognizable." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.51, + 0.472, + 0.581 + ], + "angle": 0, + "content": "which is consistent with our analysis in Section 4. This characteristic enables faster convergence to achieve good performance with fewer communication rounds. As shown in Figure 2, DYNAfed requires less than \\(20\\%\\) communication rounds to achieve comparable performance with the baseline methods." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.589, + 0.248, + 0.605 + ], + "angle": 0, + "content": "6.2. Detailed Analysis" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.612, + 0.471, + 0.71 + ], + "angle": 0, + "content": "We conduct a detailed analysis of DYNAFED and aim to provide answers to the following questions: (1) Does \\(\\mathcal{D}_{\\mathrm{syn}}\\) contain information about global data distribution while protecting client privacy? (2) Can we leverage just the dynamics of the early rounds to synthesize \\(\\mathcal{D}_{\\mathrm{syn}}\\)? (3) How many pseudo samples do we need to synthesize to ensure effectiveness? (4) Does \\(\\mathcal{D}_{\\mathrm{syn}}\\) still help convergence under more severe heterogeneity and longer local training?" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.473, + 0.902 + ], + "angle": 0, + "content": "\\(\\mathcal{D}_{\\mathrm{syn}}\\) Contains Global Information and Preserves Privacy. We conduct experiment with CIFAR10 and set \\(\\alpha = 0.01\\), where client datasets are extremely non-iid. We track the losses calculated over each client's data throughout local training as well as the global model's finetuning. During local training, we calculate the client models' losses over their own datasets, i.e., \\(\\mathcal{L}_m(\\boldsymbol{w}_m, \\mathcal{D}_m)\\). During finetuning, we calculate the global model's losses over each client's dataset, i.e., \\(\\mathcal{L}_m(\\boldsymbol{w}, \\mathcal{D}_m)\\). To prevent cluttering, we randomly select 3 client datasets for illustration. The result is shown in Figure 3, each color represents the loss over one clients' dataset. We observe that the client models easily overfit during local training due to the extreme class imbalance. The deflected client models make the aggregated global model demonstrate high loss values over some" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.092, + 0.688, + 0.231 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.702, + 0.092, + 0.885, + 0.231 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.246, + 0.895, + 0.386 + ], + "angle": 0, + "content": "Figure 5. Left: The test accuracy curves for different choices of trajectory length L on the CIFAR10 dataset with \\(\\alpha = 0.01\\). By leveraging the dynamics of the global model's trajectory in the first few rounds, e.g., \\(\\mathrm{L} \\in \\{10, 15, 20, 15\\}\\), the derived \\(\\mathcal{D}_{\\mathrm{syn}}\\) already helps achieve faster convergence and stable training. In contrast, the FedGen approach only brings slight performance gain during the later phase of training due to the dependence on the global model's performance. Right: We show the performance of DYNAfed with different sizes of \\(\\mathcal{D}_{\\mathrm{syn}}\\) for various \\(\\alpha\\). The performance gain is significant with just 150 synthesized samples." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.401, + 0.895, + 0.485 + ], + "angle": 0, + "content": "clients' data. Remarkably, we observe that finetuning with \\(\\mathcal{D}_{\\mathrm{syn}}\\) is able to recover the global model to a reasonable state, which achieves small losses over all client datasets. This verifies that \\(\\mathcal{D}_{\\mathrm{syn}}\\) contains information of the global data distribution. Furthermore, Figure 4 presents the synthesized data of CIFAR10, client-specific information can not be observed." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.498, + 0.892, + 0.665 + ], + "angle": 0, + "content": "\\(\\mathcal{D}_{\\mathrm{syn}}\\) Can be Learned with Early Trajectory. We conduct experiments with different choices of trajectory length \\(L\\) in left of Figure 5. We observe that even if with \\(L = 10\\), the result is comparable with performance obtained with longer trajectory \\(L = 25\\). Compared with the baseline methods, DYNAfed achieves significant convergence speedup and performance boost. These results support our claim in Section 4 that our method can take effect early during training. By contrast, the data-free KD method FedGen [53] that trains a generator to produce pseudo data starts to show a slight improvement only in the late stage of training since it depends explicitly on the global model's performance when training the generator." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.678, + 0.892, + 0.777 + ], + "angle": 0, + "content": "How the Size of \\( \\mathcal{D}_{\\mathrm{syn}} \\) Impacts the Performance. As shown in the right of Figure 5, we conduct experiments with different sizes of \\( \\mathcal{D}_{\\mathrm{syn}} \\) and various heterogeneity degrees \\( \\alpha \\). We find that a small \\( \\mathcal{D}_{\\mathrm{syn}} \\) suffices for good performance, while larger \\( \\mathcal{D}_{\\mathrm{syn}} \\) brings only marginal performance boost. This property not only saves the cost for synthesizing \\( \\mathcal{D}_{\\mathrm{syn}} \\), but also makes the finetuning of the global model more efficient." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.789, + 0.895, + 0.903 + ], + "angle": 0, + "content": "\\(\\mathcal{D}_{\\mathrm{syn}}\\) is Able to Mimic the Global Dynamics. In the left of Figure 6, we calculate the cosine distance between the target checkpoint \\(\\boldsymbol{w}^{\\mathrm{t+s}}\\) and the parameters \\(\\tilde{\\boldsymbol{w}}\\) trained from \\(\\boldsymbol{w}^{\\mathrm{t}}\\) for \\(s'\\) steps with \\(\\mathcal{D}_{\\mathrm{syn}}\\), a randomly sampled real dataset of the same size as \\(\\mathcal{D}_{\\mathrm{syn}}\\), and a dataset consisted of noisy pixels, respectively. We can see that in terms of mimicking the global trajectory, \\(\\mathcal{D}_{\\mathrm{syn}}\\) not only significantly outperforms the noise dataset, but also achieves only half of the distance obtained with real dataset, which is not" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12183" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.086, + 0.081, + 0.462, + 0.224 + ], + "angle": 0, + "content": "
Methodα = 0.01α = 0.04
5 epochs10 epochs5 epochs10 epochs
FedAVG33.23±3.5429.93±4.6250.28±2.1746.09±2.95
FedProx42.60±2.3042.86±2.8458.40±1.3554.30±1.98
Scaffold39.43±1.8636.52±2.0455.46±1.2550.05±1.57
FedDF*31.68±3.1639.85±3.7952.31±2.3850.90±2.53
FedBE*35.49±2.8834.19±3.3449.78±1.7951.34±1.90
ABAVG*37.87±2.5735.08±3.0356.81±1.9452.17±2.32
FedGen†35.64±2.5235.03±3.5857.60±1.5554.48±2.03
FedMix†47.36±1.2441.53±1.3760.74±0.9556.35±1.33
DynaFed†61.45±0.4659.04±0.6468.35±0.2066.30±0.34
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.227, + 0.474, + 0.297 + ], + "angle": 0, + "content": "Table 3. Test performances on CIFAR10 achieved by different FL algorithms under various degrees of data heterogeneity and local training epochs. Total communication rounds of 100 and 50 are set with local training epochs of 5 and 10, respectively. As can be seen, DYNAfed significantly surpasses other methods." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.298, + 0.481, + 0.451 + ], + "angle": 0, + "content": "
MethodCIFAR10CINIC10
α = 0.01α = 0.04α = 0.01α = 0.04
Acc = 0.45Acc = 0.55Acc = 0.33Acc = 0.45
FedAVG132.0±15.0117.0±8.0189.3±10.5138.7±5.6
FedProx113.3±16.4102.0±4.7156.7±7.0118.3±4.0
Scaffold105.0±10.4100.3±3.5158.0±5.4110.0±3.4
FedDF*145.7±13.1117.3±5.8180.7±5.0170.0±7.0
FedBE*165.0±12.7122.7±4.5185.3±14.6174.3±6.8
ABAVG*109.7±5.4110.7±5.0150.0±8.4127.0±5.8
FedGen†115.7±10.4110.3±5.7167.0±12.1128.3±5.5
FedMix†77.3±3.789.3±3.579.0±7.882.3±5.5
DynaFed†22.3±0.622.0±1.021.3±1.522.7±1.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.456, + 0.474, + 0.513 + ], + "angle": 0, + "content": "Table 4. Comparison of the number of communication rounds to reach target accuracy. With the knowledge of global data distribution stored in \\( \\mathcal{D}_{\\mathrm{syn}} \\) at the server, the convergence speed of our DYNAfed is significantly accelerated." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.517, + 0.47, + 0.546 + ], + "angle": 0, + "content": "accessible in FL setting. This verifies the ability of \\(\\mathcal{D}_{\\mathrm{syn}}\\) to mimic global trajectory." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.549, + 0.47, + 0.758 + ], + "angle": 0, + "content": "DYNAFED is Robust to Longer Local Training. Longer local training is generally required in FL to reduce the total number of global communication rounds. Under different heterogeneity degrees, we conduct experiments to evaluate the impact of longer local training epochs on DYNAFED. Specifically, we conduct experiments with total communication rounds of 100 and 50 with ocal training epochs of 5 and 10, respectively. The results are presented in Table 3, from which we observe the following: 1) DYNAFED consistently outperforms other methods by a large margin even with longer local training epochs; 2) the performance of DYNAFED is less sensitive to the length of local training, which benefits from the \\(\\mathcal{D}_{\\mathrm{syn}}\\) containing information about the global data distribution. Therefore, DYNAFED is able to achieve similar performance with less global communication rounds, which is the major bottleneck in the efficiency of FL." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.759, + 0.47, + 0.843 + ], + "angle": 0, + "content": "We further conduct experiments on varying local epochs to measure the quality of \\(\\mathcal{D}_{\\mathrm{syn}}\\). Specifically, we use it to train a network from scratch and evaluate its test performance. Shown in right of Figure 6, the quality of \\(\\mathcal{D}_{\\mathrm{syn}}\\) stays similar with longer local training and more severe heterogeneity. This further explains the superior performance of DYNAfed with longer local training." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.85, + 0.442, + 0.866 + ], + "angle": 0, + "content": "6.3. Architecture Generalization and Efficiency" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.873, + 0.47, + 0.901 + ], + "angle": 0, + "content": "To showcase the generalization ability of our approach over different network architecture choices, we conduct experiments on" + }, + { + "type": "table", + "bbox": [ + 0.508, + 0.08, + 0.885, + 0.224 + ], + "angle": 0, + "content": "
Methodα = 0.01α = 0.04
MLPConvNetMLPConvNet
FedAVG65.64±1.6974.51±1.3273.26±1.4981.74±1.98
FedProx68.09±1.4776.88±1.8379.83±1.7083.06±2.53
Scaffold67.60±1.5377.92±0.8778.09±1.3582.25±1.35
FedDF*64.59±1.7072.36±2.0877.20±1.5881.65±0.97
FedBE*65.97±1.6472.33±1.7975.42±1.3581.31±1.25
ABAVG*69.19±1.5075.98±1.9981.64±1.2084.44±1.84
FedGen†68.67±1.4575.59±1.1277.94±1.3856.60±1.08
FedMix†70.30±0.9281.34±0.6881.95±0.6484.23±0.50
DynaFed†73.89±0.2487.52±0.1583.54±0.4289.45±0.11
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.227, + 0.896, + 0.282 + ], + "angle": 0, + "content": "Table 5. Performance comparison across different network architectures. We conduct the experiment on FMNIST dataset using MLP and ConvNet to demonstrate the generalization of DYNAfed for different network architectures." + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.287, + 0.689, + 0.426 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.702, + 0.287, + 0.882, + 0.426 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.43, + 0.897, + 0.528 + ], + "angle": 0, + "content": "Figure 6. Left: the cosine distance between the target checkpoint \\(\\boldsymbol{w}^{\\mathrm{t + s}}\\) and the parameters \\(\\tilde{\\boldsymbol{w}}\\) obtained by training with different datasets from \\(\\boldsymbol{w}^{\\mathrm{t}}\\) for \\(s^{\\prime}\\) steps. We can see that the distance derived using \\(\\mathcal{D}_{\\mathrm{syn}}\\) is constantly smaller compared with other data. Right: Test performances of a model trained from scratch using only \\(\\mathcal{D}_{\\mathrm{syn}}\\) generated under various local epochs and client heterogeneity. The two plots together verify the quality of the generated \\(\\mathcal{D}_{\\mathrm{syn}}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.543, + 0.895, + 0.599 + ], + "angle": 0, + "content": "FMNIST using different network architectures. Specifically, we choose ConvNet and MLP following [34, 53]. As shown in Table 5, under various client data heterogeneity, our method demonstrates superior performances with both network architectures." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.895, + 0.751 + ], + "angle": 0, + "content": "Thanks to the rich knowledge of global data distribution contained in \\( \\mathcal{D}_{\\mathrm{syn}} \\), using it to refine the global model greatly boosts the convergence speed of training. As shown in Figure 2, as soon as \\( \\mathcal{D}_{\\mathrm{syn}} \\) is used to refine the global model, its performance rapidly increases to a reasonable accuracy, which reduces many rounds of communication. In Table 4, we also quantitatively compare the convergence speed of different FL algorithms by showing the number of communication rounds needed to reach the highest test accuracy achievable by the baselines. As can be observed, our DYNAfed requires only less than \\( 20\\% \\) communication rounds to reach a target accuracy comparable to other methods." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.765, + 0.619, + 0.781 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.79, + 0.895, + 0.901 + ], + "angle": 0, + "content": "We propose DYNAFED to tackle the data heterogeneity issue, which synthesizes a pseudo dataset to extract the knowledge of the global data distribution from the dynamics of the global model's trajectory. Extensive experiments show that DYNAFED demonstrates relative improvement over the FedAvg baseline up to \\(82.2\\%\\) on CIFAR100. Further, we believe our work is able to provide insights for extracting global information on the server side, which goes beyond tackling the data heterogeneity issue." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12184" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.471, + 0.17 + ], + "angle": 0, + "content": "[1] Durmus Alp Emre Acar, Yue Zhao, Ramon Matas Navarro, Matthew Mattina, Paul N Whatmough, and Venkatesh Saligrama. Federated learning based on dynamic regularization. arXiv preprint arXiv:2111.04263, 2021. 2, 3" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.171, + 0.472, + 0.227 + ], + "angle": 0, + "content": "[2] Divyansh Aggarwal, Jiayu Zhou, and Anil K Jain. Fedface: Collaborative learning of face recognition model. 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PMLR, 2021. 2, 3, 4, 5, 7, 8" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.894, + 0.758 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "12186" + } + ] +] \ No newline at end of file diff --git a/2023/DynaFed_ Tackling Client Data Heterogeneity With Global Dynamics/ba56f7cd-e332-49dd-9060-cbf5c82b8082_origin.pdf b/2023/DynaFed_ Tackling Client Data Heterogeneity With Global Dynamics/ba56f7cd-e332-49dd-9060-cbf5c82b8082_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..2451538f167d9f586acb09f1e4e2ca0a5613fa58 --- /dev/null +++ b/2023/DynaFed_ Tackling Client Data Heterogeneity With Global Dynamics/ba56f7cd-e332-49dd-9060-cbf5c82b8082_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:ed4ef948962d396d81d24fe9fd4a224b5f4cdcbcd1c35e1ee6b9de92833e24f9 +size 1126322 diff --git a/2023/DynaFed_ Tackling Client Data Heterogeneity With Global Dynamics/full.md b/2023/DynaFed_ Tackling Client Data Heterogeneity With Global Dynamics/full.md new file mode 100644 index 0000000000000000000000000000000000000000..c1eba9b63974e8f67e98f62e589b2dc653396fe1 --- /dev/null +++ b/2023/DynaFed_ Tackling Client Data Heterogeneity With Global Dynamics/full.md @@ -0,0 +1,377 @@ +# DYNAMICS + +Renjie Pi $^{1*}$ Weizhong Zhang $^{2*}$ Yueqi Xie $^{1*}$ Jiahui Gao $^{3}$ Xiaoyu Wang $^{1}$ Sunghun Kim $^{1}$ Qifeng Chen $^{1\dagger}$ + +1The Hong Kong University of Science and Technology + +$^{2}$ Fudan University $^{3}$ The University of Hong Kong + +# Abstract + +The Federated Learning (FL) paradigm is known to face challenges under heterogeneous client data. Local training on non-iid distributed data results in deflected local optimum, which causes the client models drift further away from each other and degrades the aggregated global model's performance. A natural solution is to gather all client data onto the server, such that the server has a global view of the entire data distribution. Unfortunately, this reduces to regular training, which compromises clients' privacy and conflicts with the purpose of FL. In this paper, we put forth an idea to collect and leverage global knowledge on the server without hindering data privacy. We unearth such knowledge from the dynamics of the global model's trajectory. Specifically, we first reserve a short trajectory of global model snapshots on the server. Then, we synthesize a small pseudo dataset such that the model trained on it mimics the dynamics of the reserved global model trajectory. Afterward, the synthesized data is used to help aggregate the deflected clients into the global model. We name our method DYNAFED, which enjoys the following advantages: 1) we do not rely on any external on-server dataset, which requires no additional cost for data collection; 2) the pseudo data can be synthesized in early communication rounds, which enables DYNAFED to take effect early for boosting the convergence and stabilizing training; 3) the pseudo data only needs to be synthesized once and can be directly utilized on the server to help aggregation in subsequent rounds. Experiments across extensive benchmarks are conducted to showcase the effectiveness of DYNAFED. We also provide insights and understanding of the underlying mechanism of our method. + +# 1. Introduction + +Federated learning (FL) has become a popular distributed training paradigm to alleviate the server's computational bur + +![](images/d7d9d55ad3fa1b56737a1f41227421e6262fe50cc431d280b3d298071dda1c37.jpg) +Figure 1. Illustration of DYNAFED. Firstly, we run the standard FedAvg for $L$ communication rounds and save the checkpoints to form a trajectory of the global model at the server. Then, we synthesize a pseudo dataset $\mathcal{D}_{\mathrm{syn}}$ , with which the network can be trained to mimic the dynamics of the global trajectory. In this way, the knowledge that captures the essential information about the global data distribution is transferred from the global dynamics to $\mathcal{D}_{\mathrm{syn}}$ . Afterward, $\mathcal{D}_{\mathrm{syn}}$ is adopted to help aggregate the deflected clients into the global model at the server. + +den and preserve clients' data privacy [3, 23, 31, 45]. In the FL paradigm, the clients only have access to their private datasets, while the server is responsible for aggregating the clients' updates into a global model. The most prevalent approaches in FL are based on local-SGD [34] (also referred to as FedAvg), where the client model is updated locally for multiple steps before being sent and merged on the server. Such approaches save communication costs and perform well given the client data are iid-distributed. However, in real-world applications such as healthcare [22, 23, 36, 37] and bio-metrics [2], the client data usually demonstrates heterogeneity (highly non-iid), which deflects the local optimum from the global optimum [24, 32, 52] and makes the locally + +trained clients biased. Therefore, naively averaging the client models results in slow convergence and performance drop. + +To alleviate the difficulty of training under heterogeneity, a few lines of work have been frequently discussed. The first line attempts to modify the local training process, including imposing regularization on the client models [1,24,29,31] and data sharing or augmentation [35, 38, 48, 52]. However, these solutions have a high requirement for the server's control of local clients. An orthogonal line focuses on refining the global model in the server aggregation process [6, 33, 40, 44, 46]. The majority of these methods typically require a large external dataset on the server, then use it to align the outputs of the global model with that of the client ensemble [6, 15, 33, 44]. Unfortunately, such a large-scale task-related dataset is often hard to acquire in reality. To circumvent this limitation, a few data-free knowledge distillation (KD) approaches are recently proposed [50,53]. These methods attempt to transfer the knowledge contained in the global model to a generator, which is subsequently leveraged to produce pseudo data to either help local training at the clients [53] or finetune the global model at the server [50]. It is clear that these methods require a global model with reasonable performance to ensure the generation of helpful pseudo data. However, such requirement is hard to achieve in practice since the global model often performs poorly under heterogeneity, especially in the early rounds of training. Other solutions include personalized FL [16, 27, 30, 39], similarity clustering [4, 10, 13], meta learning [21, 28], etc. + +Even though the above-mentioned works propose techniques to alleviate the challenges posed by heterogeneity to some extent, they do not tackle the issue from its root cause: the data is unevenly scattered at different clients and is kept locally due to privacy concerns, which is also the main obstacle for training an accurate global model. Ideally, imagine if we can collect all the client data to the server, then training can be directly conducted at the server, and the heterogeneity issue no longer exists. However, this reduces to regular training and conflicts with the original purpose of FL to protect client privacy. We then raise a natural question: is it possible to derive the essential information about the global data distribution on the server to help training without compromising client privacy? + +Despite the global model typically performing poorly due to heterogeneity, the changes in its parameters are steered jointly by the data scattered at different clients. Therefore, the update dynamics of the global model contain knowledge about global data distribution. Driven by this intuition, we propose DYNAFED to explicitly unearth such knowledge hidden in the global dynamics and transfer it to a pseudo dataset $\mathcal{D}_{\mathrm{syn}}$ at the server. $\mathcal{D}_{\mathrm{syn}}$ can then approximate the global data distribution on the server to aid aggregation. More specifically, inspired by recent works in dataset condensation [5,41,51], we formulate the data synthesis process into a + +learning problem, which minimizes the distance between the trajectory trained with $\mathcal{D}_{\mathrm{syn}}$ and the global model trajectory derived with $\mathcal{D}$ . Fine-tuning the aggregated global model with $\mathcal{D}_{\mathrm{syn}}$ effectively alleviates the performance degradation caused by deflected clients. An appealing feature of our DYNAFED is that the data can be synthesized using just the global model's trajectory of the first few rounds, which enables $\mathcal{D}_{\mathrm{syn}}$ to take effect and help aggregation from early rounds. In addition, the synthesizing process only needs to be conducted once in practice, after which the derived $\mathcal{D}_{\mathrm{syn}}$ can be directly applied in subsequent rounds to help aggregate the deviated client models. + +Notably, our framework can be readily applied to the majority of FL approaches, since we rely on only the history of the global model's parameters for synthesizing $\mathcal{D}_{\mathrm{syn}}$ , which is available in the conventional setting of FedAvg-based methods. Furthermore, because we extract global knowledge using the global dynamics, rather than any client-specific information as in [12, 17, 18, 20, 47], the derived $\mathcal{D}_{\mathrm{syn}}$ comprises of information mixed with the entire global data distribution, thus prevents leakage of client privacy. + +Our DYNAFED possesses the following advantages compared with previous approaches: 1) It leverages the knowledge of the global data distribution to alleviate the aggregation bias of the global model without depending on any external datasets; 2) DYNAFED is able to generate informative data in the early rounds of federated learning, which significantly helps convergence and stabilizes training in subsequent rounds; 3) Compared with [50, 53], which need to keep updating the generator throughout all communication rounds, the data synthesis process in our method only needs to be done once, which reduces the computational overhead. In summary, we make the following contributions: + +- We propose a practical approach named DYNAFED for tackling the heterogeneity problem, which extracts and exploits the hidden information from the global model's trajectory. In this way, the server can access the essential knowledge of the global data distribution to reinforce aggregation; +- We experimentally show the synthesized dataset helps stabilize training, boost convergence and achieve significant performance improvement under heterogeneity; +- We provide insights and detailed analysis into the working mechanisms of the proposed DYNAFED both experimentally and theoretically. + +# 2. Related Work + +Regularization-based Methods FedAvg [34] is the most widely used technique in FL, which periodically aggregates the local models to the global model in each communication round. FedProx [31] proposes to impose a proximal term during local training, such that the local model does not + +drift too far from its global initialization; Scaffold [24] introduces a control variate and variance reduction to alleviate the drift of local training. Moon [29] proposes to leverage the similarity between model representations to regularize the client local training. FedDyn [1] introduces the linear and quadratic penalty terms to correct the clients' objective during local training. These methods are orthogonal to our approach and can be jointly used. + +Data-Dependent Knowledge Distillation Methods This line of work attempts to distill client ensemble knowledge into the global model. [33] proposes to use an unlabeled external dataset on the server to match the global model's outputs with that of the client ensemble. On top of this, [6] further proposes to sample and combine higher-quality client models via a Bayesian model ensemble. Subsequently, some advanced techniques, such as pre-training [15] and weighted consensus distillation scheme [8] are proposed. These methods typically require a large amount of data following similar distribution as the task data, which is usually hard to acquire in practice. Besides, these methods need to conduct KD with a large dataset in every communication round, which introduces prohibitive computational overhead. + +Data-free Knowledge Distillation Methods Recently, a few works have proposed to perform KD in a data-free manner by synthesizing data with generative models [50,53]. [53] proposes to train a lightweight generator on the server, which produces a feature embedding conditioned on the class index. The generator is then sent to the clients to regularize local training. [50] trains a class conditional GAN [14] on the server, where the global model acts as the discriminator. The pseudo data is then used to finetune the global model. These methods all depend on the global model for training the generator. Unfortunately, the model performance is often poor under high data heterogeneity, which makes the quality of the pseudo data questionable. On the other hand, due to the use of update dynamics of the global model rather than an individual model, our method can synthesize high-quality data containing rich global information even if the global model performs poorly. + +# 3. Preliminary + +Federated Learning. Suppose we have $M$ clients in a federated learning system. For each client $m \in [M]$ , a private dataset $\mathcal{D}_m = \{(x_i, y_i)\}_{i=1}^{|\mathcal{D}_m|}$ is kept locally. The overall optimization goal of the FL system is to jointly train a global model which performs well on the combination of local data, denoted as $\mathcal{D} = \cup_{m=1}^{M} \mathcal{D}_m$ , where $\mathcal{D}$ is from a global distribution. Let $\alpha_m = \frac{|\mathcal{D}_m|}{|\mathcal{D}|}$ denote the portion of data samples on client $m$ . Let $\boldsymbol{w} \in \mathbb{R}^d$ denote the model parameter to optimize, and $\mathcal{L}_m(\boldsymbol{w}, \mathcal{D}_m) = \frac{1}{|\mathcal{D}_m|} \sum_{\xi \in \mathcal{D}_m} \ell(\boldsymbol{w}, \xi)$ denote the empirical risk with the loss + +function $\ell (\cdot ,\cdot)$ . The optimization problem of a generic FL system can be formulated as follows: + +$$ +\min _ {\boldsymbol {w}} \mathcal {L} (\boldsymbol {w}, \mathcal {D}) = \sum_ {m = 1} ^ {M} \alpha_ {m} \mathcal {L} _ {m} (\boldsymbol {w}, \mathcal {D} _ {m}). \tag {1} +$$ + +FedAvg. The main-stream solutions of Eqn. 1 rely on local-SGD to reduce the communication cost of transferring gradients. FedAvg [34] is the most prevalent approach, which uses a weighted average to aggregate the locally trained models into a global model in each communication round. Typically, not all the clients participate in every communication round. Suppose $\mathcal{M}^c\subset [M]$ is the set of the participated clients in the $c$ -th round, and $P^{c} = \sum_{m\in \mathcal{M}^{c}}\alpha_{m}$ . The aggregation process for the global model $\pmb{w}^{c + 1}$ at the end of $c$ -th communication round can be formulated as: + +$$ +\boldsymbol {w} ^ {c + 1} = \frac {1}{P ^ {c}} \sum_ {m \in \mathcal {M} ^ {c}} \alpha_ {m} \boldsymbol {w} _ {m} ^ {c}, \tag {2} +$$ + +where $\pmb{w}_{m}^{c}$ denotes the client $m$ 's locally trained model. After the aggregation, the updated global model $\pmb{w}^{c + 1}$ is then distributed to and client and utilized to initiate the $c + 1$ -th round of the training. + +# 4. Proposed Method + +In this section, we introduce our proposed method DYNAFED. The overall framework is illustrated in Figure 1. Firstly, we collect a trajectory of the global model's updates in the early phase of federated training, with which we construct a synthetic dataset $\mathcal{D}_{\mathrm{syn}} = \{\pmb {X},\pmb {y}\}$ on the server side. Then, we utilize $\mathcal{D}_{\mathrm{syn}}$ to aid the server-side aggregation, which effectively helps recover the performance drop caused by deflected local models. + +# 4.1. Acquiring Global Knowledge by Data Synthesis + +Our goal is to construct a pseudo dataset $\mathcal{D}_{\mathrm{syn}}$ , which achieves a similar effect during training as the global dataset $\mathcal{D}$ . In other words, the trajectory of a network trained with $\mathcal{D}_{\mathrm{syn}}$ should have similar dynamics with the trajectory trained with $\mathcal{D}$ . To be precise, we denote the trajectory trained on $\mathcal{D}$ as a sequence $\{\boldsymbol{w}^t\}_{t=0}^L$ , where $L$ is the length of the trajectory. In order to reduce the number of unrolling steps during optimization, we align the trajectory in a segment-by-segment manner. Without loss of generality, we consider a segment from $\boldsymbol{w}^t$ to $\boldsymbol{w}^{t+s}$ , then the problem becomes the following: starting from $\boldsymbol{w}^t$ , the network should arrive at a place close to $\boldsymbol{w}^{t+s}$ after being trained for $s$ steps on $\mathcal{D}_{\mathrm{syn}}$ . We further formulate the data synthesis task into a learning problem as follows: + +$$ +\min _ {\boldsymbol {X}, \boldsymbol {y}} \mathbb {E} _ {t \sim U (1, L - s)} [ d (\tilde {\boldsymbol {w}}, \boldsymbol {w} ^ {\mathrm {t} + s}) ] \tag {3} +$$ + +$$ +s. t. \tilde {\boldsymbol {w}} = \mathcal {A} (\boldsymbol {X}, \boldsymbol {y}, \boldsymbol {w} ^ {\mathrm {t}}, s) \tag {4} +$$ + +In the inner loop expressed by Eqn.4, we run the trainer $\mathcal{A}(\cdot)$ that trains a neural network initialized from $\boldsymbol{w}^{\mathrm{t}}$ on the synthetic + +dataset $\mathcal{D}_{\mathrm{syn}} = \{\pmb {X},\pmb {y}\}$ for $s$ steps, which arrives at $\tilde{\pmb{w}}$ . In the outer loop, we minimize the distance between $\pmb{w}^{\mathrm{t + s}}$ and $\tilde{\pmb{w}}$ , denoted as $d(\tilde{\pmb{w}},\pmb{w}^{\mathrm{t + s}})$ , by optimizing over $(\pmb {X},\pmb {y})$ . The expectation of the uniform distribution $U$ is adopted to take into account all the segments along the trajectory. $d(\cdot ,\cdot)$ is a general distance measure, which can take the form of euclidean distance or cosine distance, etc. During the optimization, we treat both $(\pmb {X},\pmb {y})$ to be learnable variables, where $\pmb{X}$ is initialized with random noise, and $\pmb{y}$ is initialized with equal probabilities over all labels. The detailed algorithm is shown in Algorithm 1. + +# Algorithm 1 DataSyn + +Require: Global trajectory $\{\pmb{w}^c\}_1^L$ , learning rate $\eta$ , training rounds $N$ , inner steps $s'$ . + +1: Randomly initialize $\mathbf{X}_0$ and pair them with $\mathbf{y}$ to form the synthetic dataset. +2: for training iteration $n = 1, 2 \dots N$ do +3: Sample $t \sim U(1, L - s)$ , then take $\boldsymbol{w}^{\mathrm{t}}$ and $\boldsymbol{w}^{\mathrm{t + s}}$ from the trajectory. +4: Get the trained parameters $\tilde{\boldsymbol{w}} = \mathcal{A}(\boldsymbol{X}_n, \boldsymbol{y}_n, \boldsymbol{w}^{\mathrm{t}}, s')$ +5: Calculate the distance $d(\tilde{\boldsymbol{w}}, \boldsymbol{w}^{\mathrm{t+s}})$ and obtain gradient w.r.t $\boldsymbol{X}_n$ and $\boldsymbol{y}_n$ as $\nabla_{\boldsymbol{X}_n} d(\tilde{\boldsymbol{w}}, \boldsymbol{w}^{\mathrm{t+s}})$ and $\nabla_{\boldsymbol{y}_n} d(\tilde{\boldsymbol{w}}, \boldsymbol{w}^{\mathrm{t+s}})$ . +6: Update $\mathbf{X}_n$ and $\mathbf{y}_n$ using gradient descent $\mathbf{X}_{n+1} = \mathbf{X}_n - \eta \nabla_{\mathbf{X}_n} d(\tilde{\mathbf{w}}, \mathbf{w}^{\mathrm{t+s}})$ , $\mathbf{y}_{n+1} = \mathbf{y}_n - \eta \nabla_{\mathbf{y}_n} d(\tilde{\mathbf{w}}, \mathbf{w}^{\mathrm{t+s}})$ +7: end for + +Output: Optimized synthetic data $\mathcal{D}_{\mathrm{syn}}$ + +Note that since the size of $\mathcal{D}_{\mathrm{syn}}$ is much smaller than $\mathcal{D}$ , the effective step size should have a different scale. Therefore, in Equation 4, we may increase the number of steps from $s$ to $s'$ to account for this scale mismatch. + +In this way, the knowledge hidden in the dynamics of the global model can be transferred to $\mathcal{D}_{\mathrm{syn}}$ , which then acts as an approximation of the global data distribution to aid the server-side aggregation. + +# 4.2. Overall Algorithm of DynaFed + +In this section, we present our DYNAFED that integrates the data synthesis process into the federated learning framework. + +Firstly, to construct the global trajectory on the server, we collect the global model's checkpoints from the first few communication rounds of FedAvg mainly considering the following two factors: 1) collecting a long trajectory induces prohibitive cost due to the expensive global communication, 2) the change in global model's parameters becomes insignificant during late rounds, which makes it difficult to extract knowledge from the dynamics. + +Note that although $\mathcal{D}_{\mathrm{syn}}$ contains rich global knowledge, it is not sufficient to replace the global data distribution $\mathcal{D}$ due to the following reasons: 1) the objective in Eqn.3 can not be ideally solved due to the two-level optimization procedure, 2) to make the scale of the optimization problem acceptable, the size of $\mathcal{D}_{\mathrm{syn}}$ cannot be as large as $\mathcal{D}$ , 3) there exists an inconsistency between the trainer $\mathcal{A}(\cdot)$ and the one that produces the global trajectory, i.e., FedAvg. Therefore, instead of simply conduct regular training with $\mathcal{D}_{\mathrm{syn}}$ , we leverage such $\mathcal{D}_{\mathrm{syn}}$ to help aggregation by finetuning the global model on the server side. + +The rundown of the entire algorithm is presented in Algorithm 2. Firstly, the global model's trajectory in the earliest $L$ rounds is + +# Algorithm 2 DYNAFED + +Require: Client data $\mathcal{D}_m = \{(x_i,y_i)\}_{i = 1}^{|\mathcal{D}_m|}$ , global parameters $\boldsymbol{w}$ , client parameters $\{\boldsymbol{w}_m\}_{m = 1}^{|\mathcal{M}|}$ . Total communication rounds $C$ , local steps $T$ , data learning rate $\eta$ , data training rounds $N$ , trajectory length $L$ , inner steps for data synthesis $s'$ . + +1: for communication round $c = 1,2\ldots C$ do +2: Sample active clients $\mathcal{M}^c$ randomly. Distribute $\boldsymbol{w}^c$ to active clients and initialize their parameters. + +3: for all users $m \in \mathcal{M}^c$ do +4: $\{\pmb{w}_m^c\}_{m=1}^{|\mathcal{M}^c|} \gets \text{LocalTrain}(\pmb{w}^c, T)$ +5: end for +6: Clients send updated $\{\pmb{w}_m^c\}_{m=1}^{|\mathcal{M}^c|}$ to server. +7: $\pmb{w}^{c + 1}\gets \frac{1}{|\mathcal{M}^c|}\sum_{m\in \mathcal{M}^c}\pmb{w}_m^c$ +8: if $c = L$ then +9: $\mathcal{D}_{\mathrm{syn}}\gets \mathrm{DataSyn}(\{\pmb {w}^c\}_{c = 1}^L,\eta ,s',N)$ +10: +11: else if $c > L$ then +12: $\pmb{w}^{c + 1}\gets$ Finetune $(\mathcal{D}_{\mathrm{syn}},\pmb{w}^{c + 1})$ +13: else +14: Add $\pmb{w}^{c + 1}$ into trajectory list. +15: end if +16: end for + +collected and stored on the server. Then, the server executes the data synthesis procedure to generate the pseudo data $\mathcal{D}_{\mathrm{syn}}$ . In all subsequent rounds, $\mathcal{D}_{\mathrm{syn}}$ is leveraged on the server to help reduce the negative impact of deflected client models by finetuning the global model. + +Our method enjoys the following appealing properties: + +- In contrast to data-dependent KD methods [6,33], DYNAFED extracts the knowledge of the global data distribution from the global model trajectory, which does not depend on any external datasets; +- Compared with data-free KD methods [50, 53], DYNAFED is able to synthesize informative pseudo data in the early rounds of federated learning without requiring the global model to be well trained, which significantly helps convergence and stabilizes training; +- The data synthesis only needs to be conducted once. Besides, since only a few samples are synthesized, refining the global model on the server requires negligible time. + +Remark 1. We emphasize that our DYNAFED does not raise privacy concerns given following reasons: 1) we rely on only the trajectory of the global model's parameters, which is available in the conventional setting of all FedAvg-based methods; 2) we keep $\mathcal{D}_{\text{syn}}$ at the server rather than sending it to the clients; 3) we extract global knowledge using the global dynamics, rather than any client-specific information as in [12, 17, 18, 20, 47], the derived $\mathcal{D}_{\text{syn}}$ comprises of information mixed with the entire global data distribution, thus prevents leakage of client privacy; 4) our DYNAFED shares a similar flavor as dataset condensation (DC) methods, which aims to generate informative pseudo data containing global knowledge, rather than real-looking data. The privacy-preserving ability of DC was also discussed in previous work [11]. + +# 5. Theoretical Analysis + +In this section, we present some insights to understand our data synthesis process from the neural tangent kernel (NTK) theory and also give the convergence results for DYNAfed. Detailed proofs are given in the appendix. + +In our data synthesis process, we align the segments (e.g., from $t$ to $t + s$ ) of the trajectories trained on $\mathcal{D}$ and $\mathcal{D}_{\mathrm{syn}}$ for any $t$ . Essentially, those segments are the cumulative gradients calculated using $\mathcal{D}$ and $\mathcal{D}_{\mathrm{syn}}$ , which approximate to $\nabla \mathcal{L}(\boldsymbol{w}_t, \mathcal{D}_{\mathrm{syn}}) \Delta t$ and $\nabla \mathcal{L}(\boldsymbol{w}^t, \mathcal{D}) \Delta t$ . Therefore, we can expect $\nabla \mathcal{L}(\boldsymbol{w}, \mathcal{D}_{\mathrm{syn}})$ would be close to $\nabla \mathcal{L}(\boldsymbol{w}, \mathcal{D})$ , which is verified by our experimental result (left of Figure.6). Given a sample $\boldsymbol{x}$ , if continuous-time gradient descent is adopted as the training solver, the dynamics of neural network function trained on $\mathcal{D}_{\mathrm{syn}}$ and $\mathcal{D}$ take the forms of + +$$ +\left\{ \begin{array}{l} \frac {d f (\boldsymbol {x} , \boldsymbol {w} ^ {t})}{d t} = \nabla_ {\boldsymbol {w} ^ {t}} f (\boldsymbol {x}, \boldsymbol {w} ^ {t}) ^ {\top} \nabla \mathcal {L} \left(\boldsymbol {w} ^ {t}, \mathcal {D} _ {\text {s y n}}\right), \\ \frac {d f (\boldsymbol {x} , \boldsymbol {w} ^ {t})}{d t} = \nabla_ {\boldsymbol {w} ^ {t}} f (\boldsymbol {x}, \boldsymbol {w} ^ {t}) ^ {\top} \nabla \mathcal {L} \left(\boldsymbol {w} ^ {t}, \mathcal {D}\right). \end{array} \right. \tag {5} +$$ + +which is close to an ordinary differential equation according to the NTK theory [19]. Note that the right-hand sides of the two equations in (5) are close if $\nabla \mathcal{L}(\boldsymbol{w}, \mathcal{D}_{\mathrm{syn}}) \approx \nabla \mathcal{L}(\boldsymbol{w}, \mathcal{D})$ . In this case, the following lemma about the continuous dependence of differentiable equation shows that the neural functions $f(\boldsymbol{x}, \boldsymbol{w}^t)$ learned with pseudo data $\mathcal{D}_{\mathrm{syn}}$ are similar to that learned with real global data $\mathcal{D}$ during the whole training process. This further indicates that $\mathcal{D}_{\mathrm{syn}}$ achieves similar effect as $\mathcal{D}$ during training. + +Lemma 1 (Continuous Dependence [42]). Suppose $\tilde{F}(t, f)$ and $F(t, f)$ are two continuous functions in a region $G$ satisfying + +$$ +\left| \tilde {F} (t, f) - F (t, f) \right| \leq \epsilon , \forall (t, f) \in G. +$$ + +Further, we assume $F(t,f)$ satisfy the $L_{F}$ -Lipschitz condition w.r.t., $f$ . Let $\tilde{f}(t)$ and $f(t)$ be the solutions of initial problems, + +$$ +\frac {d \tilde {f}}{d t} = \tilde {F} (t, \tilde {f}) a n d \frac {d f}{d t} = F (t, f), +$$ + +with $\tilde{f}(t_0) = f_0$ and $f(t_0) = f_0$ . Then, in a common region $|t - t_0| \leq \alpha$ , we have the following estimation: + +$$ +| \tilde {f} (t) - f (t) | \leq \frac {\epsilon}{L _ {F}} \left(e ^ {\alpha L _ {F}} - 1\right). +$$ + +To analyze the convergence of DYNAFED, we need to define some additional notations and rewrite our method as follows. Suppose with the $\mathcal{D}_{\mathrm{syn}}$ generated from the data synthesis process, in DYNAFED we run SGD for $\tau_{1}$ and $\tau_{2}$ iterations in each local training round and finetuning process, respectively. Let the sets $\mathcal{I}$ and $\mathcal{J}$ be + +$$ +\mathcal {I} = \left\{t | t = k \left(\tau_ {1} + \tau_ {2}\right) + c, k = 0, 1, 2, \dots , c \in \left[ \tau_ {1} \right] \right\}, +$$ + +$$ +\mathcal {J} = \{t | t = k \left(\tau_ {1} + \tau_ {2}\right) + \tau_ {1}, k = 0, 1, 2, \dots \}, \tag {6} +$$ + +where $[\tau_1] = \{0, 1, \dots, \tau_1 - 1\}$ . Therefore, when $t \in \mathcal{I}$ , we perform local training, while when $t \notin \mathcal{I}$ , we conduct finetuning. $\mathcal{I}$ denotes the time index for aggregation. The detailed steps of DYNAFED can be rewritten as + +$$ +\boldsymbol {v} _ {t + 1} ^ {m} = \left\{ \begin{array}{l l} \boldsymbol {w} _ {m} ^ {t} - \eta_ {t} \nabla \ell (\boldsymbol {w} _ {m} ^ {t}, \xi_ {m} ^ {t}), & \text {i f} t \in \mathcal {I} \\ \boldsymbol {w} _ {m} ^ {t} - \eta_ {t} \nabla \mathcal {L} (\boldsymbol {w} _ {m} ^ {t}, \mathcal {D} _ {\text {s y n}}), & \text {i f} t \notin \mathcal {I} \end{array} , \right. +$$ + +$$ +\boldsymbol {w} _ {m} ^ {t + 1} = \left\{ \begin{array}{l l} \boldsymbol {v} _ {m} ^ {t + 1}, & \text {i f} t + 1 \notin \mathcal {J} \\ \sum_ {m = 1} ^ {M} \alpha_ {m} \boldsymbol {v} _ {m} ^ {t + 1}, & \text {i f} t + 1 \in \mathcal {J} \end{array} , \right. +$$ + +where $\xi_m^t\sim \mathcal{D}_m$ . Based on the notations, we define a sequence: + +$$ +\bar {\boldsymbol {w}} ^ {t} = \sum_ {m = 1} ^ {M} \alpha_ {m} \boldsymbol {w} _ {m} ^ {t}. +$$ + +Hence, our algorithm is an integration of FedAvg and a biased GD. For $\bar{\boldsymbol{w}}^t$ , note that $\bar{\boldsymbol{w}}^t = \boldsymbol{w}_1^t = \dots = \boldsymbol{w}_M^t$ in the finetuning process and we have the following convergence results: + +Theorem 1 (Convergence). For $\tilde{L}$ -smooth, $\mu$ -strongly convex loss functions $\ell(\cdot, \cdot)$ . We assume $\|\nabla \mathcal{L}(\boldsymbol{w}, \mathcal{D}_{\mathrm{syn}}) - \nabla \mathcal{L}(\boldsymbol{w}, \mathcal{D})\| \leq \delta\|\nabla \mathcal{L}(\boldsymbol{w}, \mathcal{D})\| + \epsilon$ holds with two small non-negative scalars $\delta$ and $\epsilon$ . Let $\eta_t = \frac{c}{t}$ for a proper constant $c$ . Then, DYNAfed satisfies + +$$ +\mathbb {E} \mathcal {L} \left(\bar {\boldsymbol {w}} ^ {T}, \mathcal {D}\right) - \mathcal {L} \left(\boldsymbol {w} ^ {*}, \mathcal {D}\right) \leq \frac {C}{T}, \tag {7} +$$ + +where $\mathbf{w}^*$ is the minimum of $\mathcal{L}(\mathbf{w},\mathcal{D})$ and $C$ is a constant, whose detailed formula is given in the appendix. + +More detailed discussions about the convergence result are given in the Appendix. + +# 6. Experiments + +Benchmark Datasets and Experimental Settings. We conduct experiments over four commonly used datasets: FashionMNIST [43], CIFAR10 [25], CINIC10 [9] and CIFAR100 [25]. Among them, FashionMNIST is a dataset containing grey-scale images of fashion products. CIFAR10 is an image classification dataset containing daily objects. CINIC10 is a dataset combining CIFAR10 and samples from similar classes that are downsampled from ImageNet [26]. These three datasets contain 10 classes. CIFAR100 contains the same data as CIFAR10, but categorizes the data into 100 classes. For each dataset, we mainly conduct experiments with heterogeneous client data distribution. We follow prior work [6, 33] to use Dirichlet distribution for simulating the non-IID data distribution, where the degree of heterogeneity is defined by $\alpha$ , smaller $\alpha$ value corresponds to more severe heterogeneity. + +**Baseline Methods** We consider various state-of-the-art solutions against non-IID data distribution in the context of federated learning. Specifically, we compare with the following approaches 1) the vanilla aggregation strategy FedAVG [34]; 2) regularization-based strategies FedProx [31], Scaffold [24]; 3) data-dependent knowledge distillation strategies that need external dataset FedDF [33] and FedBE [6], ABAVG [44]; (4) data sharing [49] or data-free knowledge distillation [53] methods. Note that we do not compare with [50] since the code is not published. Please refer to Appendix for detailed settings of the baseline methods. + +Configurations Unless specified otherwise, we follow [?,7,15] and adopt the following default configurations throughout the experiments: we run 200 global communication rounds with local epoch set to 1. There are 80 clients in total, and the participation ratio in each round is set to $40\%$ . Experiments using other participation ratios are in the Appendix. We report the global model's average performance in the last five rounds evaluated using the test split of the datasets. For the construction of global trajectory, we first run + +
Methodα = 0.01α = 0.04α = 0.16
FMNISTCIFAR10CINIC10FMNISTCIFAR10CINIC10FMNISTCIFAR10CINIC10
FedAVG74.50±1.3239.30±3.4231.60±5.5081.74±1.9851.19±2.8545.35±3.0089.54±1.5169.74±1.2955.40±2.05
FedProx76.88±1.8342.13±3.6432.56±4.5983.06±2.5358.93±2.1446.30±2.8789.53±1.1370.20±0.7457.78±2.08
Scaffold77.92±0.8742.04±2.2634.90±3.3482.25±1.3554.23±1.9046.22±2.1888.54±0.3268.57±0.9154.30±0.83
FedDF*72.36±2.0839.73±3.9831.97±4.3181.65±0.9754.20±2.9345.79±2.9589.70±0.9770.71±0.9455.78±1.02
FedBE*72.33±1.7938.36±3.7432.04±3.7381.31±1.2553.49±2.3645.50±2.8889.62±0.7570.23±0.7655.42±1.37
ABAVG*75.98±1.9939.95±1.3732.75±4.1884.88±1.8457.25±3.4247.39±3.3689.53±1.1270.55±2.4156.02±1.49
FedGen†75.59±1.1240.19±2.1432.59±3.2581.46±1.0856.60±1.2945.57±2.7089.95±0.8970.89±0.5455.34±1.13
FedMix†81.34±0.6850.48±1.2337.15±1.8184.23±0.5062.77±1.0750.22±1.4189.05±0.2470.33±0.5556.74±0.45
DynaFed†87.52±0.1565.53±0.3448.04±0.7089.45±0.1170.07±0.1255.43±0.2491.35±0.0774.69±0.1459.80±0.10
+ +![](images/d97420e46aa9dd4e99dbed5d0d019e19418c9e08cdb0c4dca79e3dc5b6e95d71.jpg) + +![](images/c60f02cf13c2bab8a5b39a2480dd19f0e2f292e294e051483525c68d8c2965ac.jpg) +Figure 2. Visualization of global model's test performance on various datasets throughout the global communication rounds. We can see that the global model rapidly converges to a satisfactory test accuracy once $\mathcal{D}_{\mathrm{syn}}$ participates in refining the global model. Furthermore, $\mathcal{D}_{\mathrm{syn}}$ also helps reduce the fluctuation of model performances between communication rounds, which significantly boosts the training stability. DYNAFED requires less than $10\%$ communication rounds to achieve comparable performance with the baseline methods. + +![](images/48df3604cbbe66aef95c5e0257a689f926bf887cce17d1920597e857bd0e4a1a.jpg) + +![](images/e6e041f4c08e73411d9ed83e18275c3cc01ff161190504cbd1db236aeb050cb7.jpg) + +![](images/f3edfecc2ba679040b3672a6e2e4e71fa782b55731d10503396c2fc079c9a703.jpg) + +![](images/0c3a3cc00b9c000b4a70a39e3da39938ac0c81e87a59273ab58f45bf71189ee6.jpg) + +![](images/1ca2e50711a9dd072d7c1251247a94f697c50427e06aec1021ab841e42e3d54e.jpg) + +![](images/f63afb430a9ade5ef0ea098f1e1a3dc7078de4423886da1e5c893d9b88ef5e3b.jpg) + +Table 1. Comparison of test performances achieved by different FL methods with different degrees of data heterogeneity $\alpha$ across multiple datasets. We report the mean test accuracy of last five communication rounds. *Methods assume the availability of proxy data. † Methods are based on data sharing or generation. We observe that our approach outperforms other methods by a large margin, and its advantage is more prominent on more challenging datasets with higher heterogeneity. Specifically, DYNAFED demonstrates relative improvement over the FedAvg baseline by $17.5\%$ , $64.5\%$ , $52.0\%$ , and $82.2\%$ on FMNIST, CIFAR10, CINIC10, and CIFAR100, respectively. + +
Methodα = 0.01α = 0.04α = 0.08α = 0.16
FedAVG16.54±2.1826.56±1.5334.54±1.0239.65±0.94
FedProx18.46±1.0528.58±1.4634.82±0.5440.98±0.49
Scaffold17.33±1.2128.46±1.1835.04±0.3540.57±0.33
FedDF*16.02±1.9426.94±1.2534.77±0.8839.76±0.44
FedBE*15.78±2.3428.03±0.3433.91±0.7939.45±0.79
ABAVG16.52±1.9829.14±0.5734.66±0.9841.00±0.23
FedGen†16.51 ±1.3227.03±1.1434.56±0.7839.96±0.58
FedMix†23.54±0.9632.18±0.5936.30±0.4241.09±0.14
DynaFed†30.14±0.1936.79±0.1240.02±0.0942.47±0.06
+ +Table 2. Comparison of test performances on CIFAR100 with different degrees of data heterogeneity $\alpha$ . + +FedAvg [34] and use the checkpoints from the first 20 communication rounds ( $L = 20$ ). We set the time difference $s$ between the start and end checkpoint to 5, and the target checkpoint is averaged with 2 checkpoints sampled between $\boldsymbol{w}^{\mathrm{t}}$ and $\boldsymbol{w}^{\mathrm{t+s}}$ . More details can be found in the Appendix. + +# 6.1. Main Experiments with Data Heterogeneity + +We demonstrate the superior performance of our DYNAFED by conducting experiments on heterogeneous client data across comprehensive datasets and various heterogeneity values $\alpha$ . Specifically, we use three datasets with 10 classes (shown in Table 1): FashionMNIST [43], CIFAR10 [25] and CINIC10 [9], heterogeneity degree $\alpha$ set to 0.01, 0.04 and 0.16; and CIFAR100 containing 100 classes, with $\alpha$ values 0.01, 0.04, 0.08 and 0.16 (shown in Table 2). DYNAFED significantly boosts the convergence, stabilizes training, and brings considerable performance improvement compared with previous approaches. Specifically, with heterogeneity value $\alpha = 0.01$ , DYNAFED demonstrates relative improvement over the FedAvg baseline by $17.5\%$ , $64.5\%$ , $52.0\%$ , and $82.2\%$ on FMNIST, CIFAR10, CINIC10, and CIFAR100, respectively. + +As demonstrated in Figure 2, the performance of DYNAfed is rapidly boosted as soon as the synthesized data starts refining the global model on the server. This verifies that DYNAfed does not depend on the global model's performance in data synthesis, + +![](images/b7957d5521c001e863c38b4f52f642b407916e6d0a5e45b1f0cab694329a8be8.jpg) +Figure 3. Loss curves over each client's data throughout local training and finetuning. Each of the 3 colors represents the loss over one client's data. The stars are the global model's average losses over all client data after finetuning with $\mathcal{D}_{\mathrm{syn}}$ . During local training, the client losses quickly converge to near zero. However, due to deflection caused by heterogeneity, the losses over some clients' data dramatically increase after aggregation. Finetuning with $\mathcal{D}_{\mathrm{syn}}$ decreases those losses and reduces the aggregation bias. + +![](images/f30787b1a537c6acaf19908fe77f8bbacc07ce8168269156ff3f340c637479f9.jpg) +Figure 4. Visualization of learned synthetic data on 3 classes from CIFAR10 throughout the optimization process. In the beginning, the pixels are randomly initialized and contain little information. As the optimization goes on, some patterns emerge in the synthetic images but remain unrecognizable. + +which is consistent with our analysis in Section 4. This characteristic enables faster convergence to achieve good performance with fewer communication rounds. As shown in Figure 2, DYNAfed requires less than $20\%$ communication rounds to achieve comparable performance with the baseline methods. + +# 6.2. Detailed Analysis + +We conduct a detailed analysis of DYNAFED and aim to provide answers to the following questions: (1) Does $\mathcal{D}_{\mathrm{syn}}$ contain information about global data distribution while protecting client privacy? (2) Can we leverage just the dynamics of the early rounds to synthesize $\mathcal{D}_{\mathrm{syn}}$ ? (3) How many pseudo samples do we need to synthesize to ensure effectiveness? (4) Does $\mathcal{D}_{\mathrm{syn}}$ still help convergence under more severe heterogeneity and longer local training? + +$\mathcal{D}_{\mathrm{syn}}$ Contains Global Information and Preserves Privacy. We conduct experiment with CIFAR10 and set $\alpha = 0.01$ , where client datasets are extremely non-iid. We track the losses calculated over each client's data throughout local training as well as the global model's finetuning. During local training, we calculate the client models' losses over their own datasets, i.e., $\mathcal{L}_m(\boldsymbol{w}_m, \mathcal{D}_m)$ . During finetuning, we calculate the global model's losses over each client's dataset, i.e., $\mathcal{L}_m(\boldsymbol{w}, \mathcal{D}_m)$ . To prevent cluttering, we randomly select 3 client datasets for illustration. The result is shown in Figure 3, each color represents the loss over one clients' dataset. We observe that the client models easily overfit during local training due to the extreme class imbalance. The deflected client models make the aggregated global model demonstrate high loss values over some + +![](images/53d7fcfd11e3f7ed0eabe6224258ee31f95fd668e066cf384c19d22e37f2a42c.jpg) +Figure 5. Left: The test accuracy curves for different choices of trajectory length L on the CIFAR10 dataset with $\alpha = 0.01$ . By leveraging the dynamics of the global model's trajectory in the first few rounds, e.g., $\mathrm{L} \in \{10, 15, 20, 15\}$ , the derived $\mathcal{D}_{\mathrm{syn}}$ already helps achieve faster convergence and stable training. In contrast, the FedGen approach only brings slight performance gain during the later phase of training due to the dependence on the global model's performance. Right: We show the performance of DYNAfed with different sizes of $\mathcal{D}_{\mathrm{syn}}$ for various $\alpha$ . The performance gain is significant with just 150 synthesized samples. + +![](images/512527f1baef093b440ced96309bc4d2179e53b61ec1aaa5921927d6a226f165.jpg) + +clients' data. Remarkably, we observe that finetuning with $\mathcal{D}_{\mathrm{syn}}$ is able to recover the global model to a reasonable state, which achieves small losses over all client datasets. This verifies that $\mathcal{D}_{\mathrm{syn}}$ contains information of the global data distribution. Furthermore, Figure 4 presents the synthesized data of CIFAR10, client-specific information can not be observed. + +$\mathcal{D}_{\mathrm{syn}}$ Can be Learned with Early Trajectory. We conduct experiments with different choices of trajectory length $L$ in left of Figure 5. We observe that even if with $L = 10$ , the result is comparable with performance obtained with longer trajectory $L = 25$ . Compared with the baseline methods, DYNAfed achieves significant convergence speedup and performance boost. These results support our claim in Section 4 that our method can take effect early during training. By contrast, the data-free KD method FedGen [53] that trains a generator to produce pseudo data starts to show a slight improvement only in the late stage of training since it depends explicitly on the global model's performance when training the generator. + +How the Size of $\mathcal{D}_{\mathrm{syn}}$ Impacts the Performance. As shown in the right of Figure 5, we conduct experiments with different sizes of $\mathcal{D}_{\mathrm{syn}}$ and various heterogeneity degrees $\alpha$ . We find that a small $\mathcal{D}_{\mathrm{syn}}$ suffices for good performance, while larger $\mathcal{D}_{\mathrm{syn}}$ brings only marginal performance boost. This property not only saves the cost for synthesizing $\mathcal{D}_{\mathrm{syn}}$ , but also makes the finetuning of the global model more efficient. + +$\mathcal{D}_{\mathrm{syn}}$ is Able to Mimic the Global Dynamics. In the left of Figure 6, we calculate the cosine distance between the target checkpoint $\boldsymbol{w}^{\mathrm{t+s}}$ and the parameters $\tilde{\boldsymbol{w}}$ trained from $\boldsymbol{w}^{\mathrm{t}}$ for $s'$ steps with $\mathcal{D}_{\mathrm{syn}}$ , a randomly sampled real dataset of the same size as $\mathcal{D}_{\mathrm{syn}}$ , and a dataset consisted of noisy pixels, respectively. We can see that in terms of mimicking the global trajectory, $\mathcal{D}_{\mathrm{syn}}$ not only significantly outperforms the noise dataset, but also achieves only half of the distance obtained with real dataset, which is not + +
Methodα = 0.01α = 0.04
5 epochs10 epochs5 epochs10 epochs
FedAVG33.23±3.5429.93±4.6250.28±2.1746.09±2.95
FedProx42.60±2.3042.86±2.8458.40±1.3554.30±1.98
Scaffold39.43±1.8636.52±2.0455.46±1.2550.05±1.57
FedDF*31.68±3.1639.85±3.7952.31±2.3850.90±2.53
FedBE*35.49±2.8834.19±3.3449.78±1.7951.34±1.90
ABAVG*37.87±2.5735.08±3.0356.81±1.9452.17±2.32
FedGen†35.64±2.5235.03±3.5857.60±1.5554.48±2.03
FedMix†47.36±1.2441.53±1.3760.74±0.9556.35±1.33
DynaFed†61.45±0.4659.04±0.6468.35±0.2066.30±0.34
+ +Table 3. Test performances on CIFAR10 achieved by different FL algorithms under various degrees of data heterogeneity and local training epochs. Total communication rounds of 100 and 50 are set with local training epochs of 5 and 10, respectively. As can be seen, DYNAfed significantly surpasses other methods. + +
MethodCIFAR10CINIC10
α = 0.01α = 0.04α = 0.01α = 0.04
Acc = 0.45Acc = 0.55Acc = 0.33Acc = 0.45
FedAVG132.0±15.0117.0±8.0189.3±10.5138.7±5.6
FedProx113.3±16.4102.0±4.7156.7±7.0118.3±4.0
Scaffold105.0±10.4100.3±3.5158.0±5.4110.0±3.4
FedDF*145.7±13.1117.3±5.8180.7±5.0170.0±7.0
FedBE*165.0±12.7122.7±4.5185.3±14.6174.3±6.8
ABAVG*109.7±5.4110.7±5.0150.0±8.4127.0±5.8
FedGen†115.7±10.4110.3±5.7167.0±12.1128.3±5.5
FedMix†77.3±3.789.3±3.579.0±7.882.3±5.5
DynaFed†22.3±0.622.0±1.021.3±1.522.7±1.4
+ +accessible in FL setting. This verifies the ability of $\mathcal{D}_{\mathrm{syn}}$ to mimic global trajectory. + +DYNAFED is Robust to Longer Local Training. Longer local training is generally required in FL to reduce the total number of global communication rounds. Under different heterogeneity degrees, we conduct experiments to evaluate the impact of longer local training epochs on DYNAFED. Specifically, we conduct experiments with total communication rounds of 100 and 50 with ocal training epochs of 5 and 10, respectively. The results are presented in Table 3, from which we observe the following: 1) DYNAFED consistently outperforms other methods by a large margin even with longer local training epochs; 2) the performance of DYNAFED is less sensitive to the length of local training, which benefits from the $\mathcal{D}_{\mathrm{syn}}$ containing information about the global data distribution. Therefore, DYNAFED is able to achieve similar performance with less global communication rounds, which is the major bottleneck in the efficiency of FL. + +We further conduct experiments on varying local epochs to measure the quality of $\mathcal{D}_{\mathrm{syn}}$ . Specifically, we use it to train a network from scratch and evaluate its test performance. Shown in right of Figure 6, the quality of $\mathcal{D}_{\mathrm{syn}}$ stays similar with longer local training and more severe heterogeneity. This further explains the superior performance of DYNAfed with longer local training. + +# 6.3. Architecture Generalization and Efficiency + +To showcase the generalization ability of our approach over different network architecture choices, we conduct experiments on + +Table 4. Comparison of the number of communication rounds to reach target accuracy. With the knowledge of global data distribution stored in $\mathcal{D}_{\mathrm{syn}}$ at the server, the convergence speed of our DYNAfed is significantly accelerated. + +
Methodα = 0.01α = 0.04
MLPConvNetMLPConvNet
FedAVG65.64±1.6974.51±1.3273.26±1.4981.74±1.98
FedProx68.09±1.4776.88±1.8379.83±1.7083.06±2.53
Scaffold67.60±1.5377.92±0.8778.09±1.3582.25±1.35
FedDF*64.59±1.7072.36±2.0877.20±1.5881.65±0.97
FedBE*65.97±1.6472.33±1.7975.42±1.3581.31±1.25
ABAVG*69.19±1.5075.98±1.9981.64±1.2084.44±1.84
FedGen†68.67±1.4575.59±1.1277.94±1.3856.60±1.08
FedMix†70.30±0.9281.34±0.6881.95±0.6484.23±0.50
DynaFed†73.89±0.2487.52±0.1583.54±0.4289.45±0.11
+ +Table 5. Performance comparison across different network architectures. We conduct the experiment on FMNIST dataset using MLP and ConvNet to demonstrate the generalization of DYNAfed for different network architectures. + +![](images/efaff97bb181e00412c5e7a9a452f9a04285173a947750a6221dc3181ecd7445.jpg) +Figure 6. Left: the cosine distance between the target checkpoint $\boldsymbol{w}^{\mathrm{t + s}}$ and the parameters $\tilde{\boldsymbol{w}}$ obtained by training with different datasets from $\boldsymbol{w}^{\mathrm{t}}$ for $s^{\prime}$ steps. We can see that the distance derived using $\mathcal{D}_{\mathrm{syn}}$ is constantly smaller compared with other data. Right: Test performances of a model trained from scratch using only $\mathcal{D}_{\mathrm{syn}}$ generated under various local epochs and client heterogeneity. The two plots together verify the quality of the generated $\mathcal{D}_{\mathrm{syn}}$ . + +![](images/3a12a63d5d219cfdcab82e74f1b23df918c7a826e02303df5994161b36d455f6.jpg) + +FMNIST using different network architectures. Specifically, we choose ConvNet and MLP following [34, 53]. As shown in Table 5, under various client data heterogeneity, our method demonstrates superior performances with both network architectures. + +Thanks to the rich knowledge of global data distribution contained in $\mathcal{D}_{\mathrm{syn}}$ , using it to refine the global model greatly boosts the convergence speed of training. As shown in Figure 2, as soon as $\mathcal{D}_{\mathrm{syn}}$ is used to refine the global model, its performance rapidly increases to a reasonable accuracy, which reduces many rounds of communication. In Table 4, we also quantitatively compare the convergence speed of different FL algorithms by showing the number of communication rounds needed to reach the highest test accuracy achievable by the baselines. As can be observed, our DYNAfed requires only less than $20\%$ communication rounds to reach a target accuracy comparable to other methods. + +# 7. Conclusion + +We propose DYNAFED to tackle the data heterogeneity issue, which synthesizes a pseudo dataset to extract the knowledge of the global data distribution from the dynamics of the global model's trajectory. Extensive experiments show that DYNAFED demonstrates relative improvement over the FedAvg baseline up to $82.2\%$ on CIFAR100. 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PMLR, 2021. 2, 3, 4, 5, 7, 8 \ No newline at end of file diff --git a/2023/DynaFed_ Tackling Client Data Heterogeneity With Global Dynamics/images.zip b/2023/DynaFed_ Tackling Client Data Heterogeneity With Global Dynamics/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..d992d56359879e44fbf2b2d153cc12f5d6121ee6 --- /dev/null +++ b/2023/DynaFed_ Tackling Client Data Heterogeneity With Global Dynamics/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:f08eb0582574081197767dc7ab1b4cd5ed76bbebde05da0b19220c9a7b6fbcb1 +size 670458 diff --git a/2023/DynaFed_ Tackling Client Data Heterogeneity With Global Dynamics/layout.json b/2023/DynaFed_ Tackling Client Data Heterogeneity With Global Dynamics/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..f05d164e965af70688134434a9787df354fdb555 --- /dev/null +++ b/2023/DynaFed_ Tackling Client Data Heterogeneity With Global Dynamics/layout.json @@ -0,0 +1,13128 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 80, + 103, + 514, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 103, + 514, + 121 + ], + "spans": [ + { + "bbox": [ + 80, + 103, + 514, + 121 + ], + "type": "text", + "content": "DYNAMICS" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 107, + 142, + 485, + 171 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 142, + 485, + 171 + ], + "spans": [ + { + "bbox": [ + 107, + 142, + 485, + 171 + ], + "type": "text", + "content": "Renjie Pi" + }, + { + "bbox": [ + 107, + 142, + 485, + 171 + ], + "type": "inline_equation", + "content": "^{1*}" + }, + { + "bbox": [ + 107, + 142, + 485, + 171 + ], + "type": "text", + "content": " Weizhong Zhang" + }, + { + "bbox": [ + 107, + 142, + 485, + 171 + ], + "type": "inline_equation", + "content": "^{2*}" + }, + { + "bbox": [ + 107, + 142, + 485, + 171 + ], + "type": "text", + "content": " Yueqi Xie" + }, + { + "bbox": [ + 107, + 142, + 485, + 171 + ], + "type": "inline_equation", + "content": "^{1*}" + }, + { + "bbox": [ + 107, + 142, + 485, + 171 + ], + "type": "text", + "content": " Jiahui Gao" + }, + { + "bbox": [ + 107, + 142, + 485, + 171 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 107, + 142, + 485, + 171 + ], + "type": "text", + "content": " Xiaoyu Wang" + }, + { + "bbox": [ + 107, + 142, + 485, + 171 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 107, + 142, + 485, + 171 + ], + "type": "text", + "content": " Sunghun Kim" + }, + { + "bbox": [ + 107, + 142, + 485, + 171 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 107, + 142, + 485, + 171 + ], + "type": "text", + "content": " Qifeng Chen" + }, + { + "bbox": [ + 107, + 142, + 485, + 171 + ], + "type": "inline_equation", + "content": "^{1\\dagger}" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 162, + 172, + 432, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 162, + 172, + 432, + 185 + ], + "spans": [ + { + "bbox": [ + 162, + 172, + 432, + 185 + ], + "type": "text", + "content": "1The Hong Kong University of Science and Technology" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 169, + 186, + 423, + 200 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 169, + 186, + 423, + 200 + ], + "spans": [ + { + "bbox": [ + 169, + 186, + 423, + 200 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 169, + 186, + 423, + 200 + ], + "type": "text", + "content": "Fudan University " + }, + { + "bbox": [ + 169, + 186, + 423, + 200 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 169, + 186, + 423, + 200 + ], + "type": "text", + "content": "The University of Hong Kong" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 143, + 227, + 192, + 239 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 227, + 192, + 239 + ], + "spans": [ + { + "bbox": [ + 143, + 227, + 192, + 239 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 251, + 290, + 611 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 251, + 290, + 611 + ], + "spans": [ + { + "bbox": [ + 47, + 251, + 290, + 611 + ], + "type": "text", + "content": "The Federated Learning (FL) paradigm is known to face challenges under heterogeneous client data. Local training on non-iid distributed data results in deflected local optimum, which causes the client models drift further away from each other and degrades the aggregated global model's performance. A natural solution is to gather all client data onto the server, such that the server has a global view of the entire data distribution. Unfortunately, this reduces to regular training, which compromises clients' privacy and conflicts with the purpose of FL. In this paper, we put forth an idea to collect and leverage global knowledge on the server without hindering data privacy. We unearth such knowledge from the dynamics of the global model's trajectory. Specifically, we first reserve a short trajectory of global model snapshots on the server. Then, we synthesize a small pseudo dataset such that the model trained on it mimics the dynamics of the reserved global model trajectory. Afterward, the synthesized data is used to help aggregate the deflected clients into the global model. We name our method DYNAFED, which enjoys the following advantages: 1) we do not rely on any external on-server dataset, which requires no additional cost for data collection; 2) the pseudo data can be synthesized in early communication rounds, which enables DYNAFED to take effect early for boosting the convergence and stabilizing training; 3) the pseudo data only needs to be synthesized once and can be directly utilized on the server to help aggregation in subsequent rounds. Experiments across extensive benchmarks are conducted to showcase the effectiveness of DYNAFED. We also provide insights and understanding of the underlying mechanism of our method." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 48, + 633, + 128, + 645 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 633, + 128, + 645 + ], + "spans": [ + { + "bbox": [ + 48, + 633, + 128, + 645 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 653, + 288, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 653, + 288, + 677 + ], + "spans": [ + { + "bbox": [ + 47, + 653, + 288, + 677 + ], + "type": "text", + "content": "Federated learning (FL) has become a popular distributed training paradigm to alleviate the server's computational bur" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 310, + 226, + 544, + 427 + ], + "blocks": [ + { + "bbox": [ + 310, + 226, + 544, + 427 + ], + "lines": [ + { + "bbox": [ + 310, + 226, + 544, + 427 + ], + "spans": [ + { + "bbox": [ + 310, + 226, + 544, + 427 + ], + "type": "image", + "image_path": "d7d9d55ad3fa1b56737a1f41227421e6262fe50cc431d280b3d298071dda1c37.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 437, + 547, + 537 + ], + "lines": [ + { + "bbox": [ + 305, + 437, + 547, + 537 + ], + "spans": [ + { + "bbox": [ + 305, + 437, + 547, + 537 + ], + "type": "text", + "content": "Figure 1. Illustration of DYNAFED. Firstly, we run the standard FedAvg for " + }, + { + "bbox": [ + 305, + 437, + 547, + 537 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 305, + 437, + 547, + 537 + ], + "type": "text", + "content": " communication rounds and save the checkpoints to form a trajectory of the global model at the server. Then, we synthesize a pseudo dataset " + }, + { + "bbox": [ + 305, + 437, + 547, + 537 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 305, + 437, + 547, + 537 + ], + "type": "text", + "content": ", with which the network can be trained to mimic the dynamics of the global trajectory. In this way, the knowledge that captures the essential information about the global data distribution is transferred from the global dynamics to " + }, + { + "bbox": [ + 305, + 437, + 547, + 537 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 305, + 437, + 547, + 537 + ], + "type": "text", + "content": ". Afterward, " + }, + { + "bbox": [ + 305, + 437, + 547, + 537 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 305, + 437, + 547, + 537 + ], + "type": "text", + "content": " is adopted to help aggregate the deflected clients into the global model at the server." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 557, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 548, + 715 + ], + "type": "text", + "content": "den and preserve clients' data privacy [3, 23, 31, 45]. In the FL paradigm, the clients only have access to their private datasets, while the server is responsible for aggregating the clients' updates into a global model. The most prevalent approaches in FL are based on local-SGD [34] (also referred to as FedAvg), where the client model is updated locally for multiple steps before being sent and merged on the server. Such approaches save communication costs and perform well given the client data are iid-distributed. However, in real-world applications such as healthcare [22, 23, 36, 37] and bio-metrics [2], the client data usually demonstrates heterogeneity (highly non-iid), which deflects the local optimum from the global optimum [24, 32, 52] and makes the locally" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 57, + 683, + 216, + 693 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 683, + 216, + 693 + ], + "spans": [ + { + "bbox": [ + 57, + 683, + 216, + 693 + ], + "type": "text", + "content": "*Joint first authors. Code is available at this link." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 48, + 693, + 287, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 693, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 48, + 693, + 287, + 712 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 48, + 693, + 287, + 712 + ], + "type": "text", + "content": " Correspondence to Weizhong Zhang (weizhongzhang@fudan.edu.cn) and Qifeng Chen (chenqifeng22@gmail.com)" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12177" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": "trained clients biased. Therefore, naively averaging the client models results in slow convergence and performance drop." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 99, + 289, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 99, + 289, + 410 + ], + "spans": [ + { + "bbox": [ + 46, + 99, + 289, + 410 + ], + "type": "text", + "content": "To alleviate the difficulty of training under heterogeneity, a few lines of work have been frequently discussed. The first line attempts to modify the local training process, including imposing regularization on the client models [1,24,29,31] and data sharing or augmentation [35, 38, 48, 52]. However, these solutions have a high requirement for the server's control of local clients. An orthogonal line focuses on refining the global model in the server aggregation process [6, 33, 40, 44, 46]. The majority of these methods typically require a large external dataset on the server, then use it to align the outputs of the global model with that of the client ensemble [6, 15, 33, 44]. Unfortunately, such a large-scale task-related dataset is often hard to acquire in reality. To circumvent this limitation, a few data-free knowledge distillation (KD) approaches are recently proposed [50,53]. These methods attempt to transfer the knowledge contained in the global model to a generator, which is subsequently leveraged to produce pseudo data to either help local training at the clients [53] or finetune the global model at the server [50]. It is clear that these methods require a global model with reasonable performance to ensure the generation of helpful pseudo data. However, such requirement is hard to achieve in practice since the global model often performs poorly under heterogeneity, especially in the early rounds of training. Other solutions include personalized FL [16, 27, 30, 39], similarity clustering [4, 10, 13], meta learning [21, 28], etc." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 412, + 288, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 412, + 288, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 412, + 288, + 581 + ], + "type": "text", + "content": "Even though the above-mentioned works propose techniques to alleviate the challenges posed by heterogeneity to some extent, they do not tackle the issue from its root cause: the data is unevenly scattered at different clients and is kept locally due to privacy concerns, which is also the main obstacle for training an accurate global model. Ideally, imagine if we can collect all the client data to the server, then training can be directly conducted at the server, and the heterogeneity issue no longer exists. However, this reduces to regular training and conflicts with the original purpose of FL to protect client privacy. We then raise a natural question: is it possible to derive the essential information about the global data distribution on the server to help training without compromising client privacy?" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": "Despite the global model typically performing poorly due to heterogeneity, the changes in its parameters are steered jointly by the data scattered at different clients. Therefore, the update dynamics of the global model contain knowledge about global data distribution. Driven by this intuition, we propose DYNAFED to explicitly unearth such knowledge hidden in the global dynamics and transfer it to a pseudo dataset " + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": " at the server. " + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": " can then approximate the global data distribution on the server to aid aggregation. More specifically, inspired by recent works in dataset condensation [5,41,51], we formulate the data synthesis process into a" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 547, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 215 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 215 + ], + "type": "text", + "content": "learning problem, which minimizes the distance between the trajectory trained with " + }, + { + "bbox": [ + 304, + 72, + 547, + 215 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 304, + 72, + 547, + 215 + ], + "type": "text", + "content": " and the global model trajectory derived with " + }, + { + "bbox": [ + 304, + 72, + 547, + 215 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 304, + 72, + 547, + 215 + ], + "type": "text", + "content": ". Fine-tuning the aggregated global model with " + }, + { + "bbox": [ + 304, + 72, + 547, + 215 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 304, + 72, + 547, + 215 + ], + "type": "text", + "content": " effectively alleviates the performance degradation caused by deflected clients. An appealing feature of our DYNAFED is that the data can be synthesized using just the global model's trajectory of the first few rounds, which enables " + }, + { + "bbox": [ + 304, + 72, + 547, + 215 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 304, + 72, + 547, + 215 + ], + "type": "text", + "content": " to take effect and help aggregation from early rounds. In addition, the synthesizing process only needs to be conducted once in practice, after which the derived " + }, + { + "bbox": [ + 304, + 72, + 547, + 215 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 304, + 72, + 547, + 215 + ], + "type": "text", + "content": " can be directly applied in subsequent rounds to help aggregate the deviated client models." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 217, + 548, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 217, + 548, + 324 + ], + "spans": [ + { + "bbox": [ + 304, + 217, + 548, + 324 + ], + "type": "text", + "content": "Notably, our framework can be readily applied to the majority of FL approaches, since we rely on only the history of the global model's parameters for synthesizing " + }, + { + "bbox": [ + 304, + 217, + 548, + 324 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 304, + 217, + 548, + 324 + ], + "type": "text", + "content": ", which is available in the conventional setting of FedAvg-based methods. Furthermore, because we extract global knowledge using the global dynamics, rather than any client-specific information as in [12, 17, 18, 20, 47], the derived " + }, + { + "bbox": [ + 304, + 217, + 548, + 324 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 304, + 217, + 548, + 324 + ], + "type": "text", + "content": " comprises of information mixed with the entire global data distribution, thus prevents leakage of client privacy." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 324, + 548, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 324, + 548, + 469 + ], + "spans": [ + { + "bbox": [ + 304, + 324, + 548, + 469 + ], + "type": "text", + "content": "Our DYNAFED possesses the following advantages compared with previous approaches: 1) It leverages the knowledge of the global data distribution to alleviate the aggregation bias of the global model without depending on any external datasets; 2) DYNAFED is able to generate informative data in the early rounds of federated learning, which significantly helps convergence and stabilizes training in subsequent rounds; 3) Compared with [50, 53], which need to keep updating the generator throughout all communication rounds, the data synthesis process in our method only needs to be done once, which reduces the computational overhead. In summary, we make the following contributions:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 477, + 547, + 620 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 317, + 477, + 545, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 477, + 545, + 548 + ], + "spans": [ + { + "bbox": [ + 317, + 477, + 545, + 548 + ], + "type": "text", + "content": "- We propose a practical approach named DYNAFED for tackling the heterogeneity problem, which extracts and exploits the hidden information from the global model's trajectory. In this way, the server can access the essential knowledge of the global data distribution to reinforce aggregation;" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 317, + 549, + 547, + 585 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 549, + 547, + 585 + ], + "spans": [ + { + "bbox": [ + 317, + 549, + 547, + 585 + ], + "type": "text", + "content": "- We experimentally show the synthesized dataset helps stabilize training, boost convergence and achieve significant performance improvement under heterogeneity;" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 317, + 585, + 547, + 620 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 585, + 547, + 620 + ], + "spans": [ + { + "bbox": [ + 317, + 585, + 547, + 620 + ], + "type": "text", + "content": "- We provide insights and detailed analysis into the working mechanisms of the proposed DYNAFED both experimentally and theoretically." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 633, + 392, + 645 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 633, + 392, + 645 + ], + "spans": [ + { + "bbox": [ + 306, + 633, + 392, + 645 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "content": "Regularization-based Methods FedAvg [34] is the most widely used technique in FL, which periodically aggregates the local models to the global model in each communication round. FedProx [31] proposes to impose a proximal term during local training, such that the local model does not" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "12178" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": "drift too far from its global initialization; Scaffold [24] introduces a control variate and variance reduction to alleviate the drift of local training. Moon [29] proposes to leverage the similarity between model representations to regularize the client local training. FedDyn [1] introduces the linear and quadratic penalty terms to correct the clients' objective during local training. These methods are orthogonal to our approach and can be jointly used." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 172, + 289, + 340 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 172, + 289, + 340 + ], + "spans": [ + { + "bbox": [ + 46, + 172, + 289, + 340 + ], + "type": "text", + "content": "Data-Dependent Knowledge Distillation Methods This line of work attempts to distill client ensemble knowledge into the global model. [33] proposes to use an unlabeled external dataset on the server to match the global model's outputs with that of the client ensemble. On top of this, [6] further proposes to sample and combine higher-quality client models via a Bayesian model ensemble. Subsequently, some advanced techniques, such as pre-training [15] and weighted consensus distillation scheme [8] are proposed. These methods typically require a large amount of data following similar distribution as the task data, which is usually hard to acquire in practice. Besides, these methods need to conduct KD with a large dataset in every communication round, which introduces prohibitive computational overhead." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 354, + 289, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 354, + 289, + 559 + ], + "spans": [ + { + "bbox": [ + 46, + 354, + 289, + 559 + ], + "type": "text", + "content": "Data-free Knowledge Distillation Methods Recently, a few works have proposed to perform KD in a data-free manner by synthesizing data with generative models [50,53]. [53] proposes to train a lightweight generator on the server, which produces a feature embedding conditioned on the class index. The generator is then sent to the clients to regularize local training. [50] trains a class conditional GAN [14] on the server, where the global model acts as the discriminator. The pseudo data is then used to finetune the global model. These methods all depend on the global model for training the generator. Unfortunately, the model performance is often poor under high data heterogeneity, which makes the quality of the pseudo data questionable. On the other hand, due to the use of update dynamics of the global model rather than an individual model, our method can synthesize high-quality data containing rich global information even if the global model performs poorly." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 567, + 125, + 581 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 567, + 125, + 581 + ], + "spans": [ + { + "bbox": [ + 47, + 567, + 125, + 581 + ], + "type": "text", + "content": "3. Preliminary" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 587, + 289, + 717 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 587, + 289, + 717 + ], + "spans": [ + { + "bbox": [ + 46, + 587, + 289, + 717 + ], + "type": "text", + "content": "Federated Learning. Suppose we have " + }, + { + "bbox": [ + 46, + 587, + 289, + 717 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 587, + 289, + 717 + ], + "type": "text", + "content": " clients in a federated learning system. For each client " + }, + { + "bbox": [ + 46, + 587, + 289, + 717 + ], + "type": "inline_equation", + "content": "m \\in [M]" + }, + { + "bbox": [ + 46, + 587, + 289, + 717 + ], + "type": "text", + "content": ", a private dataset " + }, + { + "bbox": [ + 46, + 587, + 289, + 717 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_m = \\{(x_i, y_i)\\}_{i=1}^{|\\mathcal{D}_m|}" + }, + { + "bbox": [ + 46, + 587, + 289, + 717 + ], + "type": "text", + "content": " is kept locally. The overall optimization goal of the FL system is to jointly train a global model which performs well on the combination of local data, denoted as " + }, + { + "bbox": [ + 46, + 587, + 289, + 717 + ], + "type": "inline_equation", + "content": "\\mathcal{D} = \\cup_{m=1}^{M} \\mathcal{D}_m" + }, + { + "bbox": [ + 46, + 587, + 289, + 717 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 587, + 289, + 717 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 46, + 587, + 289, + 717 + ], + "type": "text", + "content": " is from a global distribution. Let " + }, + { + "bbox": [ + 46, + 587, + 289, + 717 + ], + "type": "inline_equation", + "content": "\\alpha_m = \\frac{|\\mathcal{D}_m|}{|\\mathcal{D}|}" + }, + { + "bbox": [ + 46, + 587, + 289, + 717 + ], + "type": "text", + "content": " denote the portion of data samples on client " + }, + { + "bbox": [ + 46, + 587, + 289, + 717 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 587, + 289, + 717 + ], + "type": "text", + "content": ". Let " + }, + { + "bbox": [ + 46, + 587, + 289, + 717 + ], + "type": "inline_equation", + "content": "\\boldsymbol{w} \\in \\mathbb{R}^d" + }, + { + "bbox": [ + 46, + 587, + 289, + 717 + ], + "type": "text", + "content": " denote the model parameter to optimize, and " + }, + { + "bbox": [ + 46, + 587, + 289, + 717 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_m(\\boldsymbol{w}, \\mathcal{D}_m) = \\frac{1}{|\\mathcal{D}_m|} \\sum_{\\xi \\in \\mathcal{D}_m} \\ell(\\boldsymbol{w}, \\xi)" + }, + { + "bbox": [ + 46, + 587, + 289, + 717 + ], + "type": "text", + "content": " denote the empirical risk with the loss" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 547, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 96 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 96 + ], + "type": "text", + "content": "function " + }, + { + "bbox": [ + 304, + 72, + 547, + 96 + ], + "type": "inline_equation", + "content": "\\ell (\\cdot ,\\cdot)" + }, + { + "bbox": [ + 304, + 72, + 547, + 96 + ], + "type": "text", + "content": " . The optimization problem of a generic FL system can be formulated as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 353, + 102, + 547, + 133 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 353, + 102, + 547, + 133 + ], + "spans": [ + { + "bbox": [ + 353, + 102, + 547, + 133 + ], + "type": "interline_equation", + "content": "\\min _ {\\boldsymbol {w}} \\mathcal {L} (\\boldsymbol {w}, \\mathcal {D}) = \\sum_ {m = 1} ^ {M} \\alpha_ {m} \\mathcal {L} _ {m} (\\boldsymbol {w}, \\mathcal {D} _ {m}). \\tag {1}", + "image_path": "d994bcf4dde0fbc504c53e854ead4e214ea4f67eaca34f6e26c91ff6d4d12224.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 138, + 547, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 138, + 547, + 258 + ], + "spans": [ + { + "bbox": [ + 304, + 138, + 547, + 258 + ], + "type": "text", + "content": "FedAvg. The main-stream solutions of Eqn. 1 rely on local-SGD to reduce the communication cost of transferring gradients. FedAvg [34] is the most prevalent approach, which uses a weighted average to aggregate the locally trained models into a global model in each communication round. Typically, not all the clients participate in every communication round. Suppose " + }, + { + "bbox": [ + 304, + 138, + 547, + 258 + ], + "type": "inline_equation", + "content": "\\mathcal{M}^c\\subset [M]" + }, + { + "bbox": [ + 304, + 138, + 547, + 258 + ], + "type": "text", + "content": " is the set of the participated clients in the " + }, + { + "bbox": [ + 304, + 138, + 547, + 258 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 138, + 547, + 258 + ], + "type": "text", + "content": " -th round, and " + }, + { + "bbox": [ + 304, + 138, + 547, + 258 + ], + "type": "inline_equation", + "content": "P^{c} = \\sum_{m\\in \\mathcal{M}^{c}}\\alpha_{m}" + }, + { + "bbox": [ + 304, + 138, + 547, + 258 + ], + "type": "text", + "content": ". The aggregation process for the global model " + }, + { + "bbox": [ + 304, + 138, + 547, + 258 + ], + "type": "inline_equation", + "content": "\\pmb{w}^{c + 1}" + }, + { + "bbox": [ + 304, + 138, + 547, + 258 + ], + "type": "text", + "content": " at the end of " + }, + { + "bbox": [ + 304, + 138, + 547, + 258 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 138, + 547, + 258 + ], + "type": "text", + "content": " -th communication round can be formulated as:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 372, + 262, + 546, + 287 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 372, + 262, + 546, + 287 + ], + "spans": [ + { + "bbox": [ + 372, + 262, + 546, + 287 + ], + "type": "interline_equation", + "content": "\\boldsymbol {w} ^ {c + 1} = \\frac {1}{P ^ {c}} \\sum_ {m \\in \\mathcal {M} ^ {c}} \\alpha_ {m} \\boldsymbol {w} _ {m} ^ {c}, \\tag {2}", + "image_path": "66d92d9b5a0111e2a4829f6b0dc97e304148d376a45c4cd5a52a445362d47080.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 293, + 547, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 293, + 547, + 342 + ], + "spans": [ + { + "bbox": [ + 304, + 293, + 547, + 342 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 293, + 547, + 342 + ], + "type": "inline_equation", + "content": "\\pmb{w}_{m}^{c}" + }, + { + "bbox": [ + 304, + 293, + 547, + 342 + ], + "type": "text", + "content": " denotes the client " + }, + { + "bbox": [ + 304, + 293, + 547, + 342 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 293, + 547, + 342 + ], + "type": "text", + "content": "'s locally trained model. After the aggregation, the updated global model " + }, + { + "bbox": [ + 304, + 293, + 547, + 342 + ], + "type": "inline_equation", + "content": "\\pmb{w}^{c + 1}" + }, + { + "bbox": [ + 304, + 293, + 547, + 342 + ], + "type": "text", + "content": " is then distributed to and client and utilized to initiate the " + }, + { + "bbox": [ + 304, + 293, + 547, + 342 + ], + "type": "inline_equation", + "content": "c + 1" + }, + { + "bbox": [ + 304, + 293, + 547, + 342 + ], + "type": "text", + "content": "-th round of the training." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 351, + 411, + 365 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 351, + 411, + 365 + ], + "spans": [ + { + "bbox": [ + 305, + 351, + 411, + 365 + ], + "type": "text", + "content": "4. Proposed Method" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 371, + 547, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 371, + 547, + 467 + ], + "spans": [ + { + "bbox": [ + 304, + 371, + 547, + 467 + ], + "type": "text", + "content": "In this section, we introduce our proposed method DYNAFED. The overall framework is illustrated in Figure 1. Firstly, we collect a trajectory of the global model's updates in the early phase of federated training, with which we construct a synthetic dataset " + }, + { + "bbox": [ + 304, + 371, + 547, + 467 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}} = \\{\\pmb {X},\\pmb {y}\\}" + }, + { + "bbox": [ + 304, + 371, + 547, + 467 + ], + "type": "text", + "content": " on the server side. Then, we utilize " + }, + { + "bbox": [ + 304, + 371, + 547, + 467 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 304, + 371, + 547, + 467 + ], + "type": "text", + "content": " to aid the server-side aggregation, which effectively helps recover the performance drop caused by deflected local models." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 474, + 545, + 487 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 474, + 545, + 487 + ], + "spans": [ + { + "bbox": [ + 305, + 474, + 545, + 487 + ], + "type": "text", + "content": "4.1. Acquiring Global Knowledge by Data Synthesis" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 491, + 547, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 491, + 547, + 646 + ], + "spans": [ + { + "bbox": [ + 304, + 491, + 547, + 646 + ], + "type": "text", + "content": "Our goal is to construct a pseudo dataset " + }, + { + "bbox": [ + 304, + 491, + 547, + 646 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 304, + 491, + 547, + 646 + ], + "type": "text", + "content": ", which achieves a similar effect during training as the global dataset " + }, + { + "bbox": [ + 304, + 491, + 547, + 646 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 304, + 491, + 547, + 646 + ], + "type": "text", + "content": ". In other words, the trajectory of a network trained with " + }, + { + "bbox": [ + 304, + 491, + 547, + 646 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 304, + 491, + 547, + 646 + ], + "type": "text", + "content": " should have similar dynamics with the trajectory trained with " + }, + { + "bbox": [ + 304, + 491, + 547, + 646 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 304, + 491, + 547, + 646 + ], + "type": "text", + "content": ". To be precise, we denote the trajectory trained on " + }, + { + "bbox": [ + 304, + 491, + 547, + 646 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 304, + 491, + 547, + 646 + ], + "type": "text", + "content": " as a sequence " + }, + { + "bbox": [ + 304, + 491, + 547, + 646 + ], + "type": "inline_equation", + "content": "\\{\\boldsymbol{w}^t\\}_{t=0}^L" + }, + { + "bbox": [ + 304, + 491, + 547, + 646 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 491, + 547, + 646 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 304, + 491, + 547, + 646 + ], + "type": "text", + "content": " is the length of the trajectory. In order to reduce the number of unrolling steps during optimization, we align the trajectory in a segment-by-segment manner. Without loss of generality, we consider a segment from " + }, + { + "bbox": [ + 304, + 491, + 547, + 646 + ], + "type": "inline_equation", + "content": "\\boldsymbol{w}^t" + }, + { + "bbox": [ + 304, + 491, + 547, + 646 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 491, + 547, + 646 + ], + "type": "inline_equation", + "content": "\\boldsymbol{w}^{t+s}" + }, + { + "bbox": [ + 304, + 491, + 547, + 646 + ], + "type": "text", + "content": ", then the problem becomes the following: starting from " + }, + { + "bbox": [ + 304, + 491, + 547, + 646 + ], + "type": "inline_equation", + "content": "\\boldsymbol{w}^t" + }, + { + "bbox": [ + 304, + 491, + 547, + 646 + ], + "type": "text", + "content": ", the network should arrive at a place close to " + }, + { + "bbox": [ + 304, + 491, + 547, + 646 + ], + "type": "inline_equation", + "content": "\\boldsymbol{w}^{t+s}" + }, + { + "bbox": [ + 304, + 491, + 547, + 646 + ], + "type": "text", + "content": " after being trained for " + }, + { + "bbox": [ + 304, + 491, + 547, + 646 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 491, + 547, + 646 + ], + "type": "text", + "content": " steps on " + }, + { + "bbox": [ + 304, + 491, + 547, + 646 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 304, + 491, + 547, + 646 + ], + "type": "text", + "content": ". We further formulate the data synthesis task into a learning problem as follows:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 369, + 652, + 546, + 669 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 369, + 652, + 546, + 669 + ], + "spans": [ + { + "bbox": [ + 369, + 652, + 546, + 669 + ], + "type": "interline_equation", + "content": "\\min _ {\\boldsymbol {X}, \\boldsymbol {y}} \\mathbb {E} _ {t \\sim U (1, L - s)} [ d (\\tilde {\\boldsymbol {w}}, \\boldsymbol {w} ^ {\\mathrm {t} + s}) ] \\tag {3}", + "image_path": "3f0b76941c4715e66591ff097caeec6e5220cadf3465b4bd87b7562718b76ea7.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 378, + 672, + 546, + 685 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 378, + 672, + 546, + 685 + ], + "spans": [ + { + "bbox": [ + 378, + 672, + 546, + 685 + ], + "type": "interline_equation", + "content": "s. t. \\tilde {\\boldsymbol {w}} = \\mathcal {A} (\\boldsymbol {X}, \\boldsymbol {y}, \\boldsymbol {w} ^ {\\mathrm {t}}, s) \\tag {4}", + "image_path": "414358c9e4ed2e6ec1df9924d14ee9eb2bb72b363215f81a4d46d36bd7d68173.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 691, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 691, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 691, + 547, + 713 + ], + "type": "text", + "content": "In the inner loop expressed by Eqn.4, we run the trainer " + }, + { + "bbox": [ + 304, + 691, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{A}(\\cdot)" + }, + { + "bbox": [ + 304, + 691, + 547, + 713 + ], + "type": "text", + "content": " that trains a neural network initialized from " + }, + { + "bbox": [ + 304, + 691, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\boldsymbol{w}^{\\mathrm{t}}" + }, + { + "bbox": [ + 304, + 691, + 547, + 713 + ], + "type": "text", + "content": " on the synthetic" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "12179" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 183 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 183 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 183 + ], + "type": "text", + "content": "dataset " + }, + { + "bbox": [ + 46, + 72, + 289, + 183 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}} = \\{\\pmb {X},\\pmb {y}\\}" + }, + { + "bbox": [ + 46, + 72, + 289, + 183 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 46, + 72, + 289, + 183 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 72, + 289, + 183 + ], + "type": "text", + "content": " steps, which arrives at " + }, + { + "bbox": [ + 46, + 72, + 289, + 183 + ], + "type": "inline_equation", + "content": "\\tilde{\\pmb{w}}" + }, + { + "bbox": [ + 46, + 72, + 289, + 183 + ], + "type": "text", + "content": ". In the outer loop, we minimize the distance between " + }, + { + "bbox": [ + 46, + 72, + 289, + 183 + ], + "type": "inline_equation", + "content": "\\pmb{w}^{\\mathrm{t + s}}" + }, + { + "bbox": [ + 46, + 72, + 289, + 183 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 72, + 289, + 183 + ], + "type": "inline_equation", + "content": "\\tilde{\\pmb{w}}" + }, + { + "bbox": [ + 46, + 72, + 289, + 183 + ], + "type": "text", + "content": ", denoted as " + }, + { + "bbox": [ + 46, + 72, + 289, + 183 + ], + "type": "inline_equation", + "content": "d(\\tilde{\\pmb{w}},\\pmb{w}^{\\mathrm{t + s}})" + }, + { + "bbox": [ + 46, + 72, + 289, + 183 + ], + "type": "text", + "content": ", by optimizing over " + }, + { + "bbox": [ + 46, + 72, + 289, + 183 + ], + "type": "inline_equation", + "content": "(\\pmb {X},\\pmb {y})" + }, + { + "bbox": [ + 46, + 72, + 289, + 183 + ], + "type": "text", + "content": ". The expectation of the uniform distribution " + }, + { + "bbox": [ + 46, + 72, + 289, + 183 + ], + "type": "inline_equation", + "content": "U" + }, + { + "bbox": [ + 46, + 72, + 289, + 183 + ], + "type": "text", + "content": " is adopted to take into account all the segments along the trajectory. " + }, + { + "bbox": [ + 46, + 72, + 289, + 183 + ], + "type": "inline_equation", + "content": "d(\\cdot ,\\cdot)" + }, + { + "bbox": [ + 46, + 72, + 289, + 183 + ], + "type": "text", + "content": " is a general distance measure, which can take the form of euclidean distance or cosine distance, etc. During the optimization, we treat both " + }, + { + "bbox": [ + 46, + 72, + 289, + 183 + ], + "type": "inline_equation", + "content": "(\\pmb {X},\\pmb {y})" + }, + { + "bbox": [ + 46, + 72, + 289, + 183 + ], + "type": "text", + "content": " to be learnable variables, where " + }, + { + "bbox": [ + 46, + 72, + 289, + 183 + ], + "type": "inline_equation", + "content": "\\pmb{X}" + }, + { + "bbox": [ + 46, + 72, + 289, + 183 + ], + "type": "text", + "content": " is initialized with random noise, and " + }, + { + "bbox": [ + 46, + 72, + 289, + 183 + ], + "type": "inline_equation", + "content": "\\pmb{y}" + }, + { + "bbox": [ + 46, + 72, + 289, + 183 + ], + "type": "text", + "content": " is initialized with equal probabilities over all labels. The detailed algorithm is shown in Algorithm 1." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 194, + 138, + 206 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 194, + 138, + 206 + ], + "spans": [ + { + "bbox": [ + 48, + 194, + 138, + 206 + ], + "type": "text", + "content": "Algorithm 1 DataSyn" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 48, + 210, + 287, + 233 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 210, + 287, + 233 + ], + "spans": [ + { + "bbox": [ + 48, + 210, + 287, + 233 + ], + "type": "text", + "content": "Require: Global trajectory " + }, + { + "bbox": [ + 48, + 210, + 287, + 233 + ], + "type": "inline_equation", + "content": "\\{\\pmb{w}^c\\}_1^L" + }, + { + "bbox": [ + 48, + 210, + 287, + 233 + ], + "type": "text", + "content": ", learning rate " + }, + { + "bbox": [ + 48, + 210, + 287, + 233 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 48, + 210, + 287, + 233 + ], + "type": "text", + "content": ", training rounds " + }, + { + "bbox": [ + 48, + 210, + 287, + 233 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 48, + 210, + 287, + 233 + ], + "type": "text", + "content": ", inner steps " + }, + { + "bbox": [ + 48, + 210, + 287, + 233 + ], + "type": "inline_equation", + "content": "s'" + }, + { + "bbox": [ + 48, + 210, + 287, + 233 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 52, + 234, + 287, + 353 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 52, + 234, + 287, + 255 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 234, + 287, + 255 + ], + "spans": [ + { + "bbox": [ + 52, + 234, + 287, + 255 + ], + "type": "text", + "content": "1: Randomly initialize " + }, + { + "bbox": [ + 52, + 234, + 287, + 255 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_0" + }, + { + "bbox": [ + 52, + 234, + 287, + 255 + ], + "type": "text", + "content": " and pair them with " + }, + { + "bbox": [ + 52, + 234, + 287, + 255 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 52, + 234, + 287, + 255 + ], + "type": "text", + "content": " to form the synthetic dataset." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 52, + 256, + 206, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 256, + 206, + 266 + ], + "spans": [ + { + "bbox": [ + 52, + 256, + 206, + 266 + ], + "type": "text", + "content": "2: for training iteration " + }, + { + "bbox": [ + 52, + 256, + 206, + 266 + ], + "type": "inline_equation", + "content": "n = 1, 2 \\dots N" + }, + { + "bbox": [ + 52, + 256, + 206, + 266 + ], + "type": "text", + "content": " do" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 52, + 266, + 286, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 266, + 286, + 289 + ], + "spans": [ + { + "bbox": [ + 52, + 266, + 286, + 289 + ], + "type": "text", + "content": "3: Sample " + }, + { + "bbox": [ + 52, + 266, + 286, + 289 + ], + "type": "inline_equation", + "content": "t \\sim U(1, L - s)" + }, + { + "bbox": [ + 52, + 266, + 286, + 289 + ], + "type": "text", + "content": ", then take " + }, + { + "bbox": [ + 52, + 266, + 286, + 289 + ], + "type": "inline_equation", + "content": "\\boldsymbol{w}^{\\mathrm{t}}" + }, + { + "bbox": [ + 52, + 266, + 286, + 289 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 52, + 266, + 286, + 289 + ], + "type": "inline_equation", + "content": "\\boldsymbol{w}^{\\mathrm{t + s}}" + }, + { + "bbox": [ + 52, + 266, + 286, + 289 + ], + "type": "text", + "content": " from the trajectory." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 52, + 289, + 258, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 289, + 258, + 300 + ], + "spans": [ + { + "bbox": [ + 52, + 289, + 258, + 300 + ], + "type": "text", + "content": "4: Get the trained parameters " + }, + { + "bbox": [ + 52, + 289, + 258, + 300 + ], + "type": "inline_equation", + "content": "\\tilde{\\boldsymbol{w}} = \\mathcal{A}(\\boldsymbol{X}_n, \\boldsymbol{y}_n, \\boldsymbol{w}^{\\mathrm{t}}, s')" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 52, + 300, + 287, + 322 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 300, + 287, + 322 + ], + "spans": [ + { + "bbox": [ + 52, + 300, + 287, + 322 + ], + "type": "text", + "content": "5: Calculate the distance " + }, + { + "bbox": [ + 52, + 300, + 287, + 322 + ], + "type": "inline_equation", + "content": "d(\\tilde{\\boldsymbol{w}}, \\boldsymbol{w}^{\\mathrm{t+s}})" + }, + { + "bbox": [ + 52, + 300, + 287, + 322 + ], + "type": "text", + "content": " and obtain gradient w.r.t " + }, + { + "bbox": [ + 52, + 300, + 287, + 322 + ], + "type": "inline_equation", + "content": "\\boldsymbol{X}_n" + }, + { + "bbox": [ + 52, + 300, + 287, + 322 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 52, + 300, + 287, + 322 + ], + "type": "inline_equation", + "content": "\\boldsymbol{y}_n" + }, + { + "bbox": [ + 52, + 300, + 287, + 322 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 52, + 300, + 287, + 322 + ], + "type": "inline_equation", + "content": "\\nabla_{\\boldsymbol{X}_n} d(\\tilde{\\boldsymbol{w}}, \\boldsymbol{w}^{\\mathrm{t+s}})" + }, + { + "bbox": [ + 52, + 300, + 287, + 322 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 52, + 300, + 287, + 322 + ], + "type": "inline_equation", + "content": "\\nabla_{\\boldsymbol{y}_n} d(\\tilde{\\boldsymbol{w}}, \\boldsymbol{w}^{\\mathrm{t+s}})" + }, + { + "bbox": [ + 52, + 300, + 287, + 322 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 52, + 322, + 286, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 322, + 286, + 344 + ], + "spans": [ + { + "bbox": [ + 52, + 322, + 286, + 344 + ], + "type": "text", + "content": "6: Update " + }, + { + "bbox": [ + 52, + 322, + 286, + 344 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_n" + }, + { + "bbox": [ + 52, + 322, + 286, + 344 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 52, + 322, + 286, + 344 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_n" + }, + { + "bbox": [ + 52, + 322, + 286, + 344 + ], + "type": "text", + "content": " using gradient descent " + }, + { + "bbox": [ + 52, + 322, + 286, + 344 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_{n+1} = \\mathbf{X}_n - \\eta \\nabla_{\\mathbf{X}_n} d(\\tilde{\\mathbf{w}}, \\mathbf{w}^{\\mathrm{t+s}})" + }, + { + "bbox": [ + 52, + 322, + 286, + 344 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 52, + 322, + 286, + 344 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_{n+1} = \\mathbf{y}_n - \\eta \\nabla_{\\mathbf{y}_n} d(\\tilde{\\mathbf{w}}, \\mathbf{w}^{\\mathrm{t+s}})" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 52, + 344, + 93, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 344, + 93, + 353 + ], + "spans": [ + { + "bbox": [ + 52, + 344, + 93, + 353 + ], + "type": "text", + "content": "7: end for" + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 62, + 354, + 209, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 354, + 209, + 365 + ], + "spans": [ + { + "bbox": [ + 62, + 354, + 209, + 365 + ], + "type": "text", + "content": "Output: Optimized synthetic data " + }, + { + "bbox": [ + 62, + 354, + 209, + 365 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 380, + 287, + 424 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 380, + 287, + 424 + ], + "spans": [ + { + "bbox": [ + 46, + 380, + 287, + 424 + ], + "type": "text", + "content": "Note that since the size of " + }, + { + "bbox": [ + 46, + 380, + 287, + 424 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 46, + 380, + 287, + 424 + ], + "type": "text", + "content": " is much smaller than " + }, + { + "bbox": [ + 46, + 380, + 287, + 424 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 46, + 380, + 287, + 424 + ], + "type": "text", + "content": ", the effective step size should have a different scale. Therefore, in Equation 4, we may increase the number of steps from " + }, + { + "bbox": [ + 46, + 380, + 287, + 424 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 380, + 287, + 424 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 380, + 287, + 424 + ], + "type": "inline_equation", + "content": "s'" + }, + { + "bbox": [ + 46, + 380, + 287, + 424 + ], + "type": "text", + "content": " to account for this scale mismatch." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 426, + 288, + 459 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 426, + 288, + 459 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 288, + 459 + ], + "type": "text", + "content": "In this way, the knowledge hidden in the dynamics of the global model can be transferred to " + }, + { + "bbox": [ + 46, + 426, + 288, + 459 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 46, + 426, + 288, + 459 + ], + "type": "text", + "content": ", which then acts as an approximation of the global data distribution to aid the server-side aggregation." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 464, + 214, + 477 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 464, + 214, + 477 + ], + "spans": [ + { + "bbox": [ + 47, + 464, + 214, + 477 + ], + "type": "text", + "content": "4.2. Overall Algorithm of DynaFed" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 483, + 287, + 505 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 483, + 287, + 505 + ], + "spans": [ + { + "bbox": [ + 46, + 483, + 287, + 505 + ], + "type": "text", + "content": "In this section, we present our DYNAFED that integrates the data synthesis process into the federated learning framework." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 505, + 287, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 505, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 505, + 287, + 581 + ], + "type": "text", + "content": "Firstly, to construct the global trajectory on the server, we collect the global model's checkpoints from the first few communication rounds of FedAvg mainly considering the following two factors: 1) collecting a long trajectory induces prohibitive cost due to the expensive global communication, 2) the change in global model's parameters becomes insignificant during late rounds, which makes it difficult to extract knowledge from the dynamics." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 46, + 582, + 287, + 690 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 690 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 690 + ], + "type": "text", + "content": "Note that although " + }, + { + "bbox": [ + 46, + 582, + 287, + 690 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 46, + 582, + 287, + 690 + ], + "type": "text", + "content": " contains rich global knowledge, it is not sufficient to replace the global data distribution " + }, + { + "bbox": [ + 46, + 582, + 287, + 690 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 46, + 582, + 287, + 690 + ], + "type": "text", + "content": " due to the following reasons: 1) the objective in Eqn.3 can not be ideally solved due to the two-level optimization procedure, 2) to make the scale of the optimization problem acceptable, the size of " + }, + { + "bbox": [ + 46, + 582, + 287, + 690 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 46, + 582, + 287, + 690 + ], + "type": "text", + "content": " cannot be as large as " + }, + { + "bbox": [ + 46, + 582, + 287, + 690 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 46, + 582, + 287, + 690 + ], + "type": "text", + "content": ", 3) there exists an inconsistency between the trainer " + }, + { + "bbox": [ + 46, + 582, + 287, + 690 + ], + "type": "inline_equation", + "content": "\\mathcal{A}(\\cdot)" + }, + { + "bbox": [ + 46, + 582, + 287, + 690 + ], + "type": "text", + "content": " and the one that produces the global trajectory, i.e., FedAvg. Therefore, instead of simply conduct regular training with " + }, + { + "bbox": [ + 46, + 582, + 287, + 690 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 46, + 582, + 287, + 690 + ], + "type": "text", + "content": ", we leverage such " + }, + { + "bbox": [ + 46, + 582, + 287, + 690 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 46, + 582, + 287, + 690 + ], + "type": "text", + "content": " to help aggregation by finetuning the global model on the server side." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 47, + 691, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 691, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 691, + 287, + 713 + ], + "type": "text", + "content": "The rundown of the entire algorithm is presented in Algorithm 2. Firstly, the global model's trajectory in the earliest " + }, + { + "bbox": [ + 47, + 691, + 287, + 713 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 47, + 691, + 287, + 713 + ], + "type": "text", + "content": " rounds is" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 72, + 406, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 406, + 83 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 406, + 83 + ], + "type": "text", + "content": "Algorithm 2 DYNAFED" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 87, + 547, + 135 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 87, + 547, + 135 + ], + "spans": [ + { + "bbox": [ + 306, + 87, + 547, + 135 + ], + "type": "text", + "content": "Require: Client data " + }, + { + "bbox": [ + 306, + 87, + 547, + 135 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_m = \\{(x_i,y_i)\\}_{i = 1}^{|\\mathcal{D}_m|}" + }, + { + "bbox": [ + 306, + 87, + 547, + 135 + ], + "type": "text", + "content": ", global parameters " + }, + { + "bbox": [ + 306, + 87, + 547, + 135 + ], + "type": "inline_equation", + "content": "\\boldsymbol{w}" + }, + { + "bbox": [ + 306, + 87, + 547, + 135 + ], + "type": "text", + "content": ", client parameters " + }, + { + "bbox": [ + 306, + 87, + 547, + 135 + ], + "type": "inline_equation", + "content": "\\{\\boldsymbol{w}_m\\}_{m = 1}^{|\\mathcal{M}|}" + }, + { + "bbox": [ + 306, + 87, + 547, + 135 + ], + "type": "text", + "content": ". Total communication rounds " + }, + { + "bbox": [ + 306, + 87, + 547, + 135 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 306, + 87, + 547, + 135 + ], + "type": "text", + "content": ", local steps " + }, + { + "bbox": [ + 306, + 87, + 547, + 135 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 306, + 87, + 547, + 135 + ], + "type": "text", + "content": ", data learning rate " + }, + { + "bbox": [ + 306, + 87, + 547, + 135 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 306, + 87, + 547, + 135 + ], + "type": "text", + "content": ", data training rounds " + }, + { + "bbox": [ + 306, + 87, + 547, + 135 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 306, + 87, + 547, + 135 + ], + "type": "text", + "content": ", trajectory length " + }, + { + "bbox": [ + 306, + 87, + 547, + 135 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 306, + 87, + 547, + 135 + ], + "type": "text", + "content": ", inner steps for data synthesis " + }, + { + "bbox": [ + 306, + 87, + 547, + 135 + ], + "type": "inline_equation", + "content": "s'" + }, + { + "bbox": [ + 306, + 87, + 547, + 135 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 311, + 136, + 545, + 168 + ], + "type": "list", + "angle": 0, + "index": 23, + "blocks": [ + { + "bbox": [ + 311, + 136, + 482, + 145 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 136, + 482, + 145 + ], + "spans": [ + { + "bbox": [ + 311, + 136, + 482, + 145 + ], + "type": "text", + "content": "1: for communication round " + }, + { + "bbox": [ + 311, + 136, + 482, + 145 + ], + "type": "inline_equation", + "content": "c = 1,2\\ldots C" + }, + { + "bbox": [ + 311, + 136, + 482, + 145 + ], + "type": "text", + "content": " do" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 311, + 146, + 545, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 146, + 545, + 168 + ], + "spans": [ + { + "bbox": [ + 311, + 146, + 545, + 168 + ], + "type": "text", + "content": "2: Sample active clients " + }, + { + "bbox": [ + 311, + 146, + 545, + 168 + ], + "type": "inline_equation", + "content": "\\mathcal{M}^c" + }, + { + "bbox": [ + 311, + 146, + 545, + 168 + ], + "type": "text", + "content": " randomly. Distribute " + }, + { + "bbox": [ + 311, + 146, + 545, + 168 + ], + "type": "inline_equation", + "content": "\\boldsymbol{w}^c" + }, + { + "bbox": [ + 311, + 146, + 545, + 168 + ], + "type": "text", + "content": " to active clients and initialize their parameters." + } + ] + } + ], + "index": 22 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 309, + 169, + 487, + 320 + ], + "type": "list", + "angle": 0, + "index": 38, + "blocks": [ + { + "bbox": [ + 311, + 169, + 426, + 178 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 169, + 426, + 178 + ], + "spans": [ + { + "bbox": [ + 311, + 169, + 426, + 178 + ], + "type": "text", + "content": "3: for all users " + }, + { + "bbox": [ + 311, + 169, + 426, + 178 + ], + "type": "inline_equation", + "content": "m \\in \\mathcal{M}^c" + }, + { + "bbox": [ + 311, + 169, + 426, + 178 + ], + "type": "text", + "content": " do" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 311, + 178, + 468, + 190 + ], + "type": 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"type": "inline_equation", + "content": "\\{\\pmb{w}_m^c\\}_{m=1}^{|\\mathcal{M}^c|}" + }, + { + "bbox": [ + 311, + 200, + 487, + 213 + ], + "type": "text", + "content": " to server." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 311, + 213, + 440, + 224 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 213, + 440, + 224 + ], + "spans": [ + { + "bbox": [ + 311, + 213, + 440, + 224 + ], + "type": "text", + "content": "7: " + }, + { + "bbox": [ + 311, + 213, + 440, + 224 + ], + "type": "inline_equation", + "content": "\\pmb{w}^{c + 1}\\gets \\frac{1}{|\\mathcal{M}^c|}\\sum_{m\\in \\mathcal{M}^c}\\pmb{w}_m^c" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 311, + 224, + 384, + 232 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 224, + 384, + 232 + ], + "spans": [ + { + "bbox": [ + 311, + 224, + 384, + 232 + ], + "type": "text", + "content": "8: if " + }, + { + "bbox": [ + 311, + 224, + 384, + 232 + ], + "type": "inline_equation", + "content": "c = L" + }, + { + "bbox": [ + 311, + 224, + 384, + 232 + ], + "type": "text", + "content": " then" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 311, + 233, + 479, + 245 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 233, + 479, + 245 + ], + "spans": [ + { + "bbox": [ + 311, + 233, + 479, + 245 + ], + "type": "text", + "content": "9: " + }, + { + "bbox": [ + 311, + 233, + 479, + 245 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}\\gets \\mathrm{DataSyn}(\\{\\pmb {w}^c\\}_{c = 1}^L,\\eta ,s',N)" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 310, + 246, + 319, + 254 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 246, + 319, + 254 + ], + "spans": [ + { + "bbox": [ + 310, + 246, + 319, + 254 + ], + "type": "text", + "content": "10:" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 310, + 256, + 400, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 256, + 400, + 266 + ], + "spans": [ + { + "bbox": [ + 310, + 256, + 400, + 266 + ], + "type": "text", + "content": "11: else if " + }, + { + "bbox": [ + 310, + 256, + 400, + 266 + ], + "type": "inline_equation", + "content": "c > L" + }, + { + "bbox": [ + 310, + 256, + 400, + 266 + ], + "type": "text", + "content": " then" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 310, + 266, + 457, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 266, + 457, + 277 + ], + "spans": [ + { + "bbox": [ + 310, + 266, + 457, + 277 + ], + "type": "text", + "content": "12: " + }, + { + "bbox": [ + 310, + 266, + 457, + 277 + ], + "type": "inline_equation", + "content": "\\pmb{w}^{c + 1}\\gets" + }, + { + "bbox": [ + 310, + 266, + 457, + 277 + ], + "type": "text", + "content": " Finetune " + }, + { + "bbox": [ + 310, + 266, + 457, + 277 + ], + "type": "inline_equation", + "content": "(\\mathcal{D}_{\\mathrm{syn}},\\pmb{w}^{c + 1})" + } + ] + 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Then, the server executes the data synthesis procedure to generate the pseudo data " + }, + { + "bbox": [ + 305, + 348, + 545, + 403 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 305, + 348, + 545, + 403 + ], + "type": "text", + "content": ". In all subsequent rounds, " + }, + { + "bbox": [ + 305, + 348, + 545, + 403 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 305, + 348, + 545, + 403 + ], + "type": "text", + "content": " is leveraged on the server to help reduce the negative impact of deflected client models by finetuning the global model." + } + ] + } + ], + "index": 39 + }, + { + "bbox": [ + 317, + 405, + 517, + 417 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 405, + 517, + 417 + ], + "spans": [ + { + "bbox": [ + 317, + 405, + 517, + 417 + ], + "type": "text", + "content": "Our method enjoys the following appealing properties:" + } + ] + } + ], + "index": 40 + }, + { + "bbox": [ + 318, + 426, + 545, + 558 + ], + "type": "list", + "angle": 0, + "index": 44, + "blocks": [ + { + "bbox": [ + 318, + 426, + 545, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 426, + 545, + 468 + ], + "spans": [ + { + "bbox": [ + 318, + 426, + 545, + 468 + ], + "type": "text", + "content": "- In contrast to data-dependent KD methods [6,33], DYNAFED extracts the knowledge of the global data distribution from the global model trajectory, which does not depend on any external datasets;" + } + ] + } + ], + "index": 41 + }, + { + "bbox": [ + 318, + 469, + 545, + 524 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 469, + 545, + 524 + ], + "spans": [ + { + "bbox": [ + 318, + 469, + 545, + 524 + ], + "type": "text", + "content": "- Compared with data-free KD methods [50, 53], DYNAFED is able to synthesize informative pseudo data in the early rounds of federated learning without requiring the global model to be well trained, which significantly helps convergence and stabilizes training;" + } + ] + } + ], + "index": 42 + }, + { + "bbox": [ + 318, + 525, + 545, + 558 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 525, + 545, + 558 + ], + "spans": [ + { + "bbox": [ + 318, + 525, + 545, + 558 + ], + "type": "text", + "content": "- The data synthesis only needs to be conducted once. Besides, since only a few samples are synthesized, refining the global model on the server requires negligible time." + } + ] + } + ], + "index": 43 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 304, + 571, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 571, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 571, + 547, + 713 + ], + "type": "text", + "content": "Remark 1. We emphasize that our DYNAFED does not raise privacy concerns given following reasons: 1) we rely on only the trajectory of the global model's parameters, which is available in the conventional setting of all FedAvg-based methods; 2) we keep " + }, + { + "bbox": [ + 304, + 571, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\text{syn}}" + }, + { + "bbox": [ + 304, + 571, + 547, + 713 + ], + "type": "text", + "content": " at the server rather than sending it to the clients; 3) we extract global knowledge using the global dynamics, rather than any client-specific information as in [12, 17, 18, 20, 47], the derived " + }, + { + "bbox": [ + 304, + 571, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\text{syn}}" + }, + { + "bbox": [ + 304, + 571, + 547, + 713 + ], + "type": "text", + "content": " comprises of information mixed with the entire global data distribution, thus prevents leakage of client privacy; 4) our DYNAFED shares a similar flavor as dataset condensation (DC) methods, which aims to generate informative pseudo data containing global knowledge, rather than real-looking data. The privacy-preserving ability of DC was also discussed in previous work [11]." + } + ] + } + ], + "index": 45 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "12180" + } + ] + } + ], + "index": 46 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 71, + 167, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 71, + 167, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 167, + 85 + ], + "type": "text", + "content": "5. Theoretical Analysis" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 91, + 287, + 134 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 91, + 287, + 134 + ], + "spans": [ + { + "bbox": [ + 47, + 91, + 287, + 134 + ], + "type": "text", + "content": "In this section, we present some insights to understand our data synthesis process from the neural tangent kernel (NTK) theory and also give the convergence results for DYNAfed. Detailed proofs are given in the appendix." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 135, + 288, + 234 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 135, + 288, + 234 + ], + "spans": [ + { + "bbox": [ + 47, + 135, + 288, + 234 + ], + "type": "text", + "content": "In our data synthesis process, we align the segments (e.g., from " + }, + { + "bbox": [ + 47, + 135, + 288, + 234 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 135, + 288, + 234 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 47, + 135, + 288, + 234 + ], + "type": "inline_equation", + "content": "t + s" + }, + { + "bbox": [ + 47, + 135, + 288, + 234 + ], + "type": "text", + "content": ") of the trajectories trained on " + }, + { + "bbox": [ + 47, + 135, + 288, + 234 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 47, + 135, + 288, + 234 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 135, + 288, + 234 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 47, + 135, + 288, + 234 + ], + "type": "text", + "content": " for any " + }, + { + "bbox": [ + 47, + 135, + 288, + 234 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 135, + 288, + 234 + ], + "type": "text", + "content": ". Essentially, those segments are the cumulative gradients calculated using " + }, + { + "bbox": [ + 47, + 135, + 288, + 234 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 47, + 135, + 288, + 234 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 135, + 288, + 234 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 47, + 135, + 288, + 234 + ], + "type": "text", + "content": ", which approximate to " + }, + { + "bbox": [ + 47, + 135, + 288, + 234 + ], + "type": "inline_equation", + "content": "\\nabla \\mathcal{L}(\\boldsymbol{w}_t, \\mathcal{D}_{\\mathrm{syn}}) \\Delta t" + }, + { + "bbox": [ + 47, + 135, + 288, + 234 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 135, + 288, + 234 + ], + "type": "inline_equation", + "content": "\\nabla \\mathcal{L}(\\boldsymbol{w}^t, \\mathcal{D}) \\Delta t" + }, + { + "bbox": [ + 47, + 135, + 288, + 234 + ], + "type": "text", + "content": ". Therefore, we can expect " + }, + { + "bbox": [ + 47, + 135, + 288, + 234 + ], + "type": "inline_equation", + "content": "\\nabla \\mathcal{L}(\\boldsymbol{w}, \\mathcal{D}_{\\mathrm{syn}})" + }, + { + "bbox": [ + 47, + 135, + 288, + 234 + ], + "type": "text", + "content": " would be close to " + }, + { + "bbox": [ + 47, + 135, + 288, + 234 + ], + "type": "inline_equation", + "content": "\\nabla \\mathcal{L}(\\boldsymbol{w}, \\mathcal{D})" + }, + { + "bbox": [ + 47, + 135, + 288, + 234 + ], + "type": "text", + "content": ", which is verified by our experimental result (left of Figure.6). Given a sample " + }, + { + "bbox": [ + 47, + 135, + 288, + 234 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}" + }, + { + "bbox": [ + 47, + 135, + 288, + 234 + ], + "type": "text", + "content": ", if continuous-time gradient descent is adopted as the training solver, the dynamics of neural network function trained on " + }, + { + "bbox": [ + 47, + 135, + 288, + 234 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 47, + 135, + 288, + 234 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 135, + 288, + 234 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 47, + 135, + 288, + 234 + ], + "type": "text", + "content": " take the forms of" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 78, + 240, + 288, + 270 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 240, + 288, + 270 + ], + "spans": [ + { + "bbox": [ + 78, + 240, + 288, + 270 + ], + "type": "interline_equation", + "content": "\\left\\{ \\begin{array}{l} \\frac {d f (\\boldsymbol {x} , \\boldsymbol {w} ^ {t})}{d t} = \\nabla_ {\\boldsymbol {w} ^ {t}} f (\\boldsymbol {x}, \\boldsymbol {w} ^ {t}) ^ {\\top} \\nabla \\mathcal {L} \\left(\\boldsymbol {w} ^ {t}, \\mathcal {D} _ {\\text {s y n}}\\right), \\\\ \\frac {d f (\\boldsymbol {x} , \\boldsymbol {w} ^ {t})}{d t} = \\nabla_ {\\boldsymbol {w} ^ {t}} f (\\boldsymbol {x}, \\boldsymbol {w} ^ {t}) ^ {\\top} \\nabla \\mathcal {L} \\left(\\boldsymbol {w} ^ {t}, \\mathcal {D}\\right). \\end{array} \\right. \\tag {5}", + "image_path": "46e6e2655324c8381829bfdc969d441aba5b937faa6c835f51164e07f42526b3.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 276, + 287, + 364 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 276, + 287, + 364 + ], + "spans": [ + { + "bbox": [ + 47, + 276, + 287, + 364 + ], + "type": "text", + "content": "which is close to an ordinary differential equation according to the NTK theory [19]. Note that the right-hand sides of the two equations in (5) are close if " + }, + { + "bbox": [ + 47, + 276, + 287, + 364 + ], + "type": "inline_equation", + "content": "\\nabla \\mathcal{L}(\\boldsymbol{w}, \\mathcal{D}_{\\mathrm{syn}}) \\approx \\nabla \\mathcal{L}(\\boldsymbol{w}, \\mathcal{D})" + }, + { + "bbox": [ + 47, + 276, + 287, + 364 + ], + "type": "text", + "content": ". In this case, the following lemma about the continuous dependence of differentiable equation shows that the neural functions " + }, + { + "bbox": [ + 47, + 276, + 287, + 364 + ], + "type": "inline_equation", + "content": "f(\\boldsymbol{x}, \\boldsymbol{w}^t)" + }, + { + "bbox": [ + 47, + 276, + 287, + 364 + ], + "type": "text", + "content": " learned with pseudo data " + }, + { + "bbox": [ + 47, + 276, + 287, + 364 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 47, + 276, + 287, + 364 + ], + "type": "text", + "content": " are similar to that learned with real global data " + }, + { + "bbox": [ + 47, + 276, + 287, + 364 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 47, + 276, + 287, + 364 + ], + "type": "text", + "content": " during the whole training process. This further indicates that " + }, + { + "bbox": [ + 47, + 276, + 287, + 364 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 47, + 276, + 287, + 364 + ], + "type": "text", + "content": " achieves similar effect as " + }, + { + "bbox": [ + 47, + 276, + 287, + 364 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 47, + 276, + 287, + 364 + ], + "type": "text", + "content": " during training." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 370, + 288, + 393 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 370, + 288, + 393 + ], + "spans": [ + { + "bbox": [ + 47, + 370, + 288, + 393 + ], + "type": "text", + "content": "Lemma 1 (Continuous Dependence [42]). Suppose " + }, + { + "bbox": [ + 47, + 370, + 288, + 393 + ], + "type": "inline_equation", + "content": "\\tilde{F}(t, f)" + }, + { + "bbox": [ + 47, + 370, + 288, + 393 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 370, + 288, + 393 + ], + "type": "inline_equation", + "content": "F(t, f)" + }, + { + "bbox": [ + 47, + 370, + 288, + 393 + ], + "type": "text", + "content": " are two continuous functions in a region " + }, + { + "bbox": [ + 47, + 370, + 288, + 393 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 47, + 370, + 288, + 393 + ], + "type": "text", + "content": " satisfying" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 96, + 399, + 237, + 412 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 399, + 237, + 412 + ], + "spans": [ + { + "bbox": [ + 96, + 399, + 237, + 412 + ], + "type": "interline_equation", + "content": "\\left| \\tilde {F} (t, f) - F (t, f) \\right| \\leq \\epsilon , \\forall (t, f) \\in G.", + "image_path": "ec878b61a0ee447bd8596f6374550594cbf07826547f23d547516e1694659930.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 419, + 287, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 419, + 287, + 441 + ], + "spans": [ + { + "bbox": [ + 47, + 419, + 287, + 441 + ], + "type": "text", + "content": "Further, we assume " + }, + { + "bbox": [ + 47, + 419, + 287, + 441 + ], + "type": "inline_equation", + "content": "F(t,f)" + }, + { + "bbox": [ + 47, + 419, + 287, + 441 + ], + "type": "text", + "content": " satisfy the " + }, + { + "bbox": [ + 47, + 419, + 287, + 441 + ], + "type": "inline_equation", + "content": "L_{F}" + }, + { + "bbox": [ + 47, + 419, + 287, + 441 + ], + "type": "text", + "content": "-Lipschitz condition w.r.t., " + }, + { + "bbox": [ + 47, + 419, + 287, + 441 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 47, + 419, + 287, + 441 + ], + "type": "text", + "content": ". Let " + }, + { + "bbox": [ + 47, + 419, + 287, + 441 + ], + "type": "inline_equation", + "content": "\\tilde{f}(t)" + }, + { + "bbox": [ + 47, + 419, + 287, + 441 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 419, + 287, + 441 + ], + "type": "inline_equation", + "content": "f(t)" + }, + { + "bbox": [ + 47, + 419, + 287, + 441 + ], + "type": "text", + "content": " be the solutions of initial problems," + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 104, + 448, + 230, + 471 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 448, + 230, + 471 + ], + "spans": [ + { + "bbox": [ + 104, + 448, + 230, + 471 + ], + "type": "interline_equation", + "content": "\\frac {d \\tilde {f}}{d t} = \\tilde {F} (t, \\tilde {f}) a n d \\frac {d f}{d t} = F (t, f),", + "image_path": "b9b5a49a79491633fb48a83b4fe98c635d010ff4a5ffba548581a2d6f6b7b6a6.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 477, + 287, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 477, + 287, + 501 + ], + "spans": [ + { + "bbox": [ + 47, + 477, + 287, + 501 + ], + "type": "text", + "content": "with " + }, + { + "bbox": [ + 47, + 477, + 287, + 501 + ], + "type": "inline_equation", + "content": "\\tilde{f}(t_0) = f_0" + }, + { + "bbox": [ + 47, + 477, + 287, + 501 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 477, + 287, + 501 + ], + "type": "inline_equation", + "content": "f(t_0) = f_0" + }, + { + "bbox": [ + 47, + 477, + 287, + 501 + ], + "type": "text", + "content": ". Then, in a common region " + }, + { + "bbox": [ + 47, + 477, + 287, + 501 + ], + "type": "inline_equation", + "content": "|t - t_0| \\leq \\alpha" + }, + { + "bbox": [ + 47, + 477, + 287, + 501 + ], + "type": "text", + "content": ", we have the following estimation:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 101, + 506, + 232, + 527 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 101, + 506, + 232, + 527 + ], + "spans": [ + { + "bbox": [ + 101, + 506, + 232, + 527 + ], + "type": "interline_equation", + "content": "| \\tilde {f} (t) - f (t) | \\leq \\frac {\\epsilon}{L _ {F}} \\left(e ^ {\\alpha L _ {F}} - 1\\right).", + "image_path": "297b501e89c53c3235e87a9b4246db5bc3671398cae9390be21978e01556c754.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 533, + 287, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 533, + 287, + 597 + ], + "spans": [ + { + "bbox": [ + 47, + 533, + 287, + 597 + ], + "type": "text", + "content": "To analyze the convergence of DYNAFED, we need to define some additional notations and rewrite our method as follows. Suppose with the " + }, + { + "bbox": [ + 47, + 533, + 287, + 597 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 47, + 533, + 287, + 597 + ], + "type": "text", + "content": " generated from the data synthesis process, in DYNAFED we run SGD for " + }, + { + "bbox": [ + 47, + 533, + 287, + 597 + ], + "type": "inline_equation", + "content": "\\tau_{1}" + }, + { + "bbox": [ + 47, + 533, + 287, + 597 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 533, + 287, + 597 + ], + "type": "inline_equation", + "content": "\\tau_{2}" + }, + { + "bbox": [ + 47, + 533, + 287, + 597 + ], + "type": "text", + "content": " iterations in each local training round and finetuning process, respectively. Let the sets " + }, + { + "bbox": [ + 47, + 533, + 287, + 597 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 47, + 533, + 287, + 597 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 533, + 287, + 597 + ], + "type": "inline_equation", + "content": "\\mathcal{J}" + }, + { + "bbox": [ + 47, + 533, + 287, + 597 + ], + "type": "text", + "content": " be" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 64, + 605, + 268, + 617 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 605, + 268, + 617 + ], + "spans": [ + { + "bbox": [ + 64, + 605, + 268, + 617 + ], + "type": "interline_equation", + "content": "\\mathcal {I} = \\left\\{t | t = k \\left(\\tau_ {1} + \\tau_ {2}\\right) + c, k = 0, 1, 2, \\dots , c \\in \\left[ \\tau_ {1} \\right] \\right\\},", + "image_path": "adc9f05f47b30cf2adb4a3c38f438b09bf09adca9020c25ea73121611aafbcb2.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 66, + 619, + 287, + 632 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 619, + 287, + 632 + ], + "spans": [ + { + "bbox": [ + 66, + 619, + 287, + 632 + ], + "type": "interline_equation", + "content": "\\mathcal {J} = \\{t | t = k \\left(\\tau_ {1} + \\tau_ {2}\\right) + \\tau_ {1}, k = 0, 1, 2, \\dots \\}, \\tag {6}", + "image_path": "665d1fe6ab27a29511b73a88b373db143a1c5b6101deffb289ed8ae236e67a65.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 638, + 288, + 681 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 638, + 288, + 681 + ], + "spans": [ + { + "bbox": [ + 47, + 638, + 288, + 681 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 638, + 288, + 681 + ], + "type": "inline_equation", + "content": "[\\tau_1] = \\{0, 1, \\dots, \\tau_1 - 1\\}" + }, + { + "bbox": [ + 47, + 638, + 288, + 681 + ], + "type": "text", + "content": ". Therefore, when " + }, + { + "bbox": [ + 47, + 638, + 288, + 681 + ], + "type": "inline_equation", + "content": "t \\in \\mathcal{I}" + }, + { + "bbox": [ + 47, + 638, + 288, + 681 + ], + "type": "text", + "content": ", we perform local training, while when " + }, + { + "bbox": [ + 47, + 638, + 288, + 681 + ], + "type": "inline_equation", + "content": "t \\notin \\mathcal{I}" + }, + { + "bbox": [ + 47, + 638, + 288, + 681 + ], + "type": "text", + "content": ", we conduct finetuning. " + }, + { + "bbox": [ + 47, + 638, + 288, + 681 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 47, + 638, + 288, + 681 + ], + "type": "text", + "content": " denotes the time index for aggregation. The detailed steps of DYNAFED can be rewritten as" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 78, + 687, + 256, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 687, + 256, + 715 + ], + "spans": [ + { + "bbox": [ + 78, + 687, + 256, + 715 + ], + "type": "interline_equation", + "content": "\\boldsymbol {v} _ {t + 1} ^ {m} = \\left\\{ \\begin{array}{l l} \\boldsymbol {w} _ {m} ^ {t} - \\eta_ {t} \\nabla \\ell (\\boldsymbol {w} _ {m} ^ {t}, \\xi_ {m} ^ {t}), & \\text {i f} t \\in \\mathcal {I} \\\\ \\boldsymbol {w} _ {m} ^ {t} - \\eta_ {t} \\nabla \\mathcal {L} (\\boldsymbol {w} _ {m} ^ {t}, \\mathcal {D} _ {\\text {s y n}}), & \\text {i f} t \\notin \\mathcal {I} \\end{array} , \\right.", + "image_path": "1606da08b67523cbd9f11f3e5870bea1d7d9d49dcbb234e2ea63edd78fa9a6e7.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 337, + 70, + 505, + 99 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 337, + 70, + 505, + 99 + ], + "spans": [ + { + "bbox": [ + 337, + 70, + 505, + 99 + ], + "type": "interline_equation", + "content": "\\boldsymbol {w} _ {m} ^ {t + 1} = \\left\\{ \\begin{array}{l l} \\boldsymbol {v} _ {m} ^ {t + 1}, & \\text {i f} t + 1 \\notin \\mathcal {J} \\\\ \\sum_ {m = 1} ^ {M} \\alpha_ {m} \\boldsymbol {v} _ {m} ^ {t + 1}, & \\text {i f} t + 1 \\in \\mathcal {J} \\end{array} , \\right.", + "image_path": "9aef5378dfec28cdc8db5be4229cda1df89a9fbf834fb1d24044a20c5c2e0631.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 106, + 534, + 118 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 106, + 534, + 118 + ], + "spans": [ + { + "bbox": [ + 306, + 106, + 534, + 118 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 106, + 534, + 118 + ], + "type": "inline_equation", + "content": "\\xi_m^t\\sim \\mathcal{D}_m" + }, + { + "bbox": [ + 306, + 106, + 534, + 118 + ], + "type": "text", + "content": " . Based on the notations, we define a sequence:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 389, + 118, + 463, + 146 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 389, + 118, + 463, + 146 + ], + "spans": [ + { + "bbox": [ + 389, + 118, + 463, + 146 + ], + "type": "interline_equation", + "content": "\\bar {\\boldsymbol {w}} ^ {t} = \\sum_ {m = 1} ^ {M} \\alpha_ {m} \\boldsymbol {w} _ {m} ^ {t}.", + "image_path": "ef2feffa45d50c96efa8350751ba7c47c3cfce4d0b95a4660ff387ae1d872e2c.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 148, + 547, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 148, + 547, + 180 + ], + "spans": [ + { + "bbox": [ + 305, + 148, + 547, + 180 + ], + "type": "text", + "content": "Hence, our algorithm is an integration of FedAvg and a biased GD. For " + }, + { + "bbox": [ + 305, + 148, + 547, + 180 + ], + "type": "inline_equation", + "content": "\\bar{\\boldsymbol{w}}^t" + }, + { + "bbox": [ + 305, + 148, + 547, + 180 + ], + "type": "text", + "content": ", note that " + }, + { + "bbox": [ + 305, + 148, + 547, + 180 + ], + "type": "inline_equation", + "content": "\\bar{\\boldsymbol{w}}^t = \\boldsymbol{w}_1^t = \\dots = \\boldsymbol{w}_M^t" + }, + { + "bbox": [ + 305, + 148, + 547, + 180 + ], + "type": "text", + "content": " in the finetuning process and we have the following convergence results:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 188, + 546, + 232 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 188, + 546, + 232 + ], + "spans": [ + { + "bbox": [ + 305, + 188, + 546, + 232 + ], + "type": "text", + "content": "Theorem 1 (Convergence). For " + }, + { + "bbox": [ + 305, + 188, + 546, + 232 + ], + "type": "inline_equation", + "content": "\\tilde{L}" + }, + { + "bbox": [ + 305, + 188, + 546, + 232 + ], + "type": "text", + "content": "-smooth, " + }, + { + "bbox": [ + 305, + 188, + 546, + 232 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 305, + 188, + 546, + 232 + ], + "type": "text", + "content": "-strongly convex loss functions " + }, + { + "bbox": [ + 305, + 188, + 546, + 232 + ], + "type": "inline_equation", + "content": "\\ell(\\cdot, \\cdot)" + }, + { + "bbox": [ + 305, + 188, + 546, + 232 + ], + "type": "text", + "content": ". We assume " + }, + { + "bbox": [ + 305, + 188, + 546, + 232 + ], + "type": "inline_equation", + "content": "\\|\\nabla \\mathcal{L}(\\boldsymbol{w}, \\mathcal{D}_{\\mathrm{syn}}) - \\nabla \\mathcal{L}(\\boldsymbol{w}, \\mathcal{D})\\| \\leq \\delta\\|\\nabla \\mathcal{L}(\\boldsymbol{w}, \\mathcal{D})\\| + \\epsilon" + }, + { + "bbox": [ + 305, + 188, + 546, + 232 + ], + "type": "text", + "content": " holds with two small non-negative scalars " + }, + { + "bbox": [ + 305, + 188, + 546, + 232 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 305, + 188, + 546, + 232 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 188, + 546, + 232 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 305, + 188, + 546, + 232 + ], + "type": "text", + "content": ". Let " + }, + { + "bbox": [ + 305, + 188, + 546, + 232 + ], + "type": "inline_equation", + "content": "\\eta_t = \\frac{c}{t}" + }, + { + "bbox": [ + 305, + 188, + 546, + 232 + ], + "type": "text", + "content": " for a proper constant " + }, + { + "bbox": [ + 305, + 188, + 546, + 232 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 305, + 188, + 546, + 232 + ], + "type": "text", + "content": ". Then, DYNAfed satisfies" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 365, + 239, + 545, + 261 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 239, + 545, + 261 + ], + "spans": [ + { + "bbox": [ + 365, + 239, + 545, + 261 + ], + "type": "interline_equation", + "content": "\\mathbb {E} \\mathcal {L} \\left(\\bar {\\boldsymbol {w}} ^ {T}, \\mathcal {D}\\right) - \\mathcal {L} \\left(\\boldsymbol {w} ^ {*}, \\mathcal {D}\\right) \\leq \\frac {C}{T}, \\tag {7}", + "image_path": "bb07b14e038f31a164ea4aaaee5816dbdb35f7585407629dd200f1edf12d4266.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 267, + 545, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 267, + 545, + 289 + ], + "spans": [ + { + "bbox": [ + 305, + 267, + 545, + 289 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 267, + 545, + 289 + ], + "type": "inline_equation", + "content": "\\mathbf{w}^*" + }, + { + "bbox": [ + 305, + 267, + 545, + 289 + ], + "type": "text", + "content": " is the minimum of " + }, + { + "bbox": [ + 305, + 267, + 545, + 289 + ], + "type": "inline_equation", + "content": "\\mathcal{L}(\\mathbf{w},\\mathcal{D})" + }, + { + "bbox": [ + 305, + 267, + 545, + 289 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 267, + 545, + 289 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 305, + 267, + 545, + 289 + ], + "type": "text", + "content": " is a constant, whose detailed formula is given in the appendix." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 305, + 297, + 545, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 297, + 545, + 319 + ], + "spans": [ + { + "bbox": [ + 305, + 297, + 545, + 319 + ], + "type": "text", + "content": "More detailed discussions about the convergence result are given in the Appendix." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 330, + 387, + 344 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 330, + 387, + 344 + ], + "spans": [ + { + "bbox": [ + 306, + 330, + 387, + 344 + ], + "type": "text", + "content": "6. Experiments" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 305, + 349, + 547, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 349, + 547, + 503 + ], + "spans": [ + { + "bbox": [ + 305, + 349, + 547, + 503 + ], + "type": "text", + "content": "Benchmark Datasets and Experimental Settings. We conduct experiments over four commonly used datasets: FashionMNIST [43], CIFAR10 [25], CINIC10 [9] and CIFAR100 [25]. Among them, FashionMNIST is a dataset containing grey-scale images of fashion products. CIFAR10 is an image classification dataset containing daily objects. CINIC10 is a dataset combining CIFAR10 and samples from similar classes that are downsampled from ImageNet [26]. These three datasets contain 10 classes. CIFAR100 contains the same data as CIFAR10, but categorizes the data into 100 classes. For each dataset, we mainly conduct experiments with heterogeneous client data distribution. We follow prior work [6, 33] to use Dirichlet distribution for simulating the non-IID data distribution, where the degree of heterogeneity is defined by " + }, + { + "bbox": [ + 305, + 349, + 547, + 503 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 305, + 349, + 547, + 503 + ], + "type": "text", + "content": ", smaller " + }, + { + "bbox": [ + 305, + 349, + 547, + 503 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 305, + 349, + 547, + 503 + ], + "type": "text", + "content": " value corresponds to more severe heterogeneity." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 305, + 506, + 547, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 506, + 547, + 617 + ], + "spans": [ + { + "bbox": [ + 305, + 506, + 547, + 617 + ], + "type": "text", + "content": "**Baseline Methods** We consider various state-of-the-art solutions against non-IID data distribution in the context of federated learning. Specifically, we compare with the following approaches 1) the vanilla aggregation strategy FedAVG [34]; 2) regularization-based strategies FedProx [31], Scaffold [24]; 3) data-dependent knowledge distillation strategies that need external dataset FedDF [33] and FedBE [6], ABAVG [44]; (4) data sharing [49] or data-free knowledge distillation [53] methods. Note that we do not compare with [50] since the code is not published. Please refer to Appendix for detailed settings of the baseline methods." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 305, + 625, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 625, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 625, + 547, + 713 + ], + "type": "text", + "content": "Configurations Unless specified otherwise, we follow [?,7,15] and adopt the following default configurations throughout the experiments: we run 200 global communication rounds with local epoch set to 1. There are 80 clients in total, and the participation ratio in each round is set to " + }, + { + "bbox": [ + 305, + 625, + 547, + 713 + ], + "type": "inline_equation", + "content": "40\\%" + }, + { + "bbox": [ + 305, + 625, + 547, + 713 + ], + "type": "text", + "content": ". Experiments using other participation ratios are in the Appendix. We report the global model's average performance in the last five rounds evaluated using the test split of the datasets. For the construction of global trajectory, we first run" + } + ] + } + ], + "index": 27 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12181" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 63, + 547, + 194 + ], + "blocks": [ + { + "bbox": [ + 50, + 63, + 547, + 194 + ], + "lines": [ + { + "bbox": [ + 50, + 63, + 547, + 194 + ], + "spans": [ + { + "bbox": [ + 50, + 63, + 547, + 194 + ], + "type": "table", + "html": "
Methodα = 0.01α = 0.04α = 0.16
FMNISTCIFAR10CINIC10FMNISTCIFAR10CINIC10FMNISTCIFAR10CINIC10
FedAVG74.50±1.3239.30±3.4231.60±5.5081.74±1.9851.19±2.8545.35±3.0089.54±1.5169.74±1.2955.40±2.05
FedProx76.88±1.8342.13±3.6432.56±4.5983.06±2.5358.93±2.1446.30±2.8789.53±1.1370.20±0.7457.78±2.08
Scaffold77.92±0.8742.04±2.2634.90±3.3482.25±1.3554.23±1.9046.22±2.1888.54±0.3268.57±0.9154.30±0.83
FedDF*72.36±2.0839.73±3.9831.97±4.3181.65±0.9754.20±2.9345.79±2.9589.70±0.9770.71±0.9455.78±1.02
FedBE*72.33±1.7938.36±3.7432.04±3.7381.31±1.2553.49±2.3645.50±2.8889.62±0.7570.23±0.7655.42±1.37
ABAVG*75.98±1.9939.95±1.3732.75±4.1884.88±1.8457.25±3.4247.39±3.3689.53±1.1270.55±2.4156.02±1.49
FedGen†75.59±1.1240.19±2.1432.59±3.2581.46±1.0856.60±1.2945.57±2.7089.95±0.8970.89±0.5455.34±1.13
FedMix†81.34±0.6850.48±1.2337.15±1.8184.23±0.5062.77±1.0750.22±1.4189.05±0.2470.33±0.5556.74±0.45
DynaFed†87.52±0.1565.53±0.3448.04±0.7089.45±0.1170.07±0.1255.43±0.2491.35±0.0774.69±0.1459.80±0.10
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Visualization of global model's test performance on various datasets throughout the global communication rounds. We can see that the global model rapidly converges to a satisfactory test accuracy once " + }, + { + "bbox": [ + 46, + 444, + 548, + 489 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 46, + 444, + 548, + 489 + ], + "type": "text", + "content": " participates in refining the global model. Furthermore, " + }, + { + "bbox": [ + 46, + 444, + 548, + 489 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 46, + 444, + 548, + 489 + ], + "type": "text", + "content": " also helps reduce the fluctuation of model performances between communication rounds, which significantly boosts the training stability. 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Comparison of test performances achieved by different FL methods with different degrees of data heterogeneity " + }, + { + "bbox": [ + 46, + 202, + 547, + 258 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 202, + 547, + 258 + ], + "type": "text", + "content": " across multiple datasets. We report the mean test accuracy of last five communication rounds. *Methods assume the availability of proxy data. † Methods are based on data sharing or generation. We observe that our approach outperforms other methods by a large margin, and its advantage is more prominent on more challenging datasets with higher heterogeneity. Specifically, DYNAFED demonstrates relative improvement over the FedAvg baseline by " + }, + { + "bbox": [ + 46, + 202, + 547, + 258 + ], + "type": "inline_equation", + "content": "17.5\\%" + }, + { + "bbox": [ + 46, + 202, + 547, + 258 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 202, + 547, + 258 + ], + "type": "inline_equation", + "content": "64.5\\%" + }, + { + "bbox": [ + 46, + 202, + 547, + 258 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 202, + 547, + 258 + ], + "type": "inline_equation", + "content": "52.0\\%" + }, + { + "bbox": [ + 46, + 202, + 547, + 258 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 202, + 547, + 258 + ], + "type": "inline_equation", + "content": "82.2\\%" + }, + { + "bbox": [ + 46, + 202, + 547, + 258 + ], + "type": "text", + "content": " on FMNIST, CIFAR10, CINIC10, and CIFAR100, respectively." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 52, + 499, + 284, + 606 + ], + "lines": [ + { + "bbox": [ + 52, + 499, + 284, + 606 + ], + "spans": [ + { + "bbox": [ + 52, + 499, + 284, + 606 + ], + "type": "table", + "html": "
Methodα = 0.01α = 0.04α = 0.08α = 0.16
FedAVG16.54±2.1826.56±1.5334.54±1.0239.65±0.94
FedProx18.46±1.0528.58±1.4634.82±0.5440.98±0.49
Scaffold17.33±1.2128.46±1.1835.04±0.3540.57±0.33
FedDF*16.02±1.9426.94±1.2534.77±0.8839.76±0.44
FedBE*15.78±2.3428.03±0.3433.91±0.7939.45±0.79
ABAVG16.52±1.9829.14±0.5734.66±0.9841.00±0.23
FedGen†16.51 ±1.3227.03±1.1434.56±0.7839.96±0.58
FedMix†23.54±0.9632.18±0.5936.30±0.4241.09±0.14
DynaFed†30.14±0.1936.79±0.1240.02±0.0942.47±0.06
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Comparison of test performances on CIFAR100 with different degrees of data heterogeneity " + }, + { + "bbox": [ + 46, + 608, + 287, + 631 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 608, + 287, + 631 + ], + "type": "text", + "content": " ." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 658, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 658, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 658, + 289, + 715 + ], + "type": "text", + "content": "FedAvg [34] and use the checkpoints from the first 20 communication rounds (" + }, + { + "bbox": [ + 46, + 658, + 289, + 715 + ], + "type": "inline_equation", + "content": "L = 20" + }, + { + "bbox": [ + 46, + 658, + 289, + 715 + ], + "type": "text", + "content": "). We set the time difference " + }, + { + "bbox": [ + 46, + 658, + 289, + 715 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 658, + 289, + 715 + ], + "type": "text", + "content": " between the start and end checkpoint to 5, and the target checkpoint is averaged with 2 checkpoints sampled between " + }, + { + "bbox": [ + 46, + 658, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\boldsymbol{w}^{\\mathrm{t}}" + }, + { + "bbox": [ + 46, + 658, + 289, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 658, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\boldsymbol{w}^{\\mathrm{t+s}}" + }, + { + "bbox": [ + 46, + 658, + 289, + 715 + ], + "type": "text", + "content": ". More details can be found in the Appendix." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 509, + 533, + 522 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 509, + 533, + 522 + ], + "spans": [ + { + "bbox": [ + 306, + 509, + 533, + 522 + ], + "type": "text", + "content": "6.1. Main Experiments with Data Heterogeneity" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 526, + 547, + 669 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 526, + 547, + 669 + ], + "spans": [ + { + "bbox": [ + 304, + 526, + 547, + 669 + ], + "type": "text", + "content": "We demonstrate the superior performance of our DYNAFED by conducting experiments on heterogeneous client data across comprehensive datasets and various heterogeneity values " + }, + { + "bbox": [ + 304, + 526, + 547, + 669 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 526, + 547, + 669 + ], + "type": "text", + "content": ". Specifically, we use three datasets with 10 classes (shown in Table 1): FashionMNIST [43], CIFAR10 [25] and CINIC10 [9], heterogeneity degree " + }, + { + "bbox": [ + 304, + 526, + 547, + 669 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 526, + 547, + 669 + ], + "type": "text", + "content": " set to 0.01, 0.04 and 0.16; and CIFAR100 containing 100 classes, with " + }, + { + "bbox": [ + 304, + 526, + 547, + 669 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 526, + 547, + 669 + ], + "type": "text", + "content": " values 0.01, 0.04, 0.08 and 0.16 (shown in Table 2). DYNAFED significantly boosts the convergence, stabilizes training, and brings considerable performance improvement compared with previous approaches. Specifically, with heterogeneity value " + }, + { + "bbox": [ + 304, + 526, + 547, + 669 + ], + "type": "inline_equation", + "content": "\\alpha = 0.01" + }, + { + "bbox": [ + 304, + 526, + 547, + 669 + ], + "type": "text", + "content": ", DYNAFED demonstrates relative improvement over the FedAvg baseline by " + }, + { + "bbox": [ + 304, + 526, + 547, + 669 + ], + "type": "inline_equation", + "content": "17.5\\%" + }, + { + "bbox": [ + 304, + 526, + 547, + 669 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 526, + 547, + 669 + ], + "type": "inline_equation", + "content": "64.5\\%" + }, + { + "bbox": [ + 304, + 526, + 547, + 669 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 526, + 547, + 669 + ], + "type": "inline_equation", + "content": "52.0\\%" + }, + { + "bbox": [ + 304, + 526, + 547, + 669 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 526, + 547, + 669 + ], + "type": "inline_equation", + "content": "82.2\\%" + }, + { + "bbox": [ + 304, + 526, + 547, + 669 + ], + "type": "text", + "content": " on FMNIST, CIFAR10, CINIC10, and CIFAR100, respectively." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 670, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 670, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 670, + 547, + 715 + ], + "type": "text", + "content": "As demonstrated in Figure 2, the performance of DYNAfed is rapidly boosted as soon as the synthesized data starts refining the global model on the server. This verifies that DYNAfed does not depend on the global model's performance in data synthesis," + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "12182" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 72, + 284, + 163 + ], + "blocks": [ + { + "bbox": [ + 51, + 72, + 284, + 163 + ], + "lines": [ + { + "bbox": [ + 51, + 72, + 284, + 163 + ], + "spans": [ + { + "bbox": [ + 51, + 72, + 284, + 163 + ], + "type": "image", + "image_path": "b7957d5521c001e863c38b4f52f642b407916e6d0a5e45b1f0cab694329a8be8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 170, + 289, + 258 + ], + "lines": [ + { + "bbox": [ + 46, + 170, + 289, + 258 + ], + "spans": [ + { + "bbox": [ + 46, + 170, + 289, + 258 + ], + "type": "text", + "content": "Figure 3. Loss curves over each client's data throughout local training and finetuning. Each of the 3 colors represents the loss over one client's data. The stars are the global model's average losses over all client data after finetuning with " + }, + { + "bbox": [ + 46, + 170, + 289, + 258 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 46, + 170, + 289, + 258 + ], + "type": "text", + "content": ". During local training, the client losses quickly converge to near zero. However, due to deflection caused by heterogeneity, the losses over some clients' data dramatically increase after aggregation. Finetuning with " + }, + { + "bbox": [ + 46, + 170, + 289, + 258 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 46, + 170, + 289, + 258 + ], + "type": "text", + "content": " decreases those losses and reduces the aggregation bias." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 53, + 264, + 282, + 334 + ], + "blocks": [ + { + "bbox": [ + 53, + 264, + 282, + 334 + ], + "lines": [ + { + "bbox": [ + 53, + 264, + 282, + 334 + ], + "spans": [ + { + "bbox": [ + 53, + 264, + 282, + 334 + ], + "type": "image", + "image_path": "f30787b1a537c6acaf19908fe77f8bbacc07ce8168269156ff3f340c637479f9.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 341, + 288, + 397 + ], + "lines": [ + { + "bbox": [ + 46, + 341, + 288, + 397 + ], + "spans": [ + { + "bbox": [ + 46, + 341, + 288, + 397 + ], + "type": "text", + "content": "Figure 4. Visualization of learned synthetic data on 3 classes from CIFAR10 throughout the optimization process. In the beginning, the pixels are randomly initialized and contain little information. As the optimization goes on, some patterns emerge in the synthetic images but remain unrecognizable." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 403, + 288, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 403, + 288, + 460 + ], + "spans": [ + { + "bbox": [ + 46, + 403, + 288, + 460 + ], + "type": "text", + "content": "which is consistent with our analysis in Section 4. This characteristic enables faster convergence to achieve good performance with fewer communication rounds. As shown in Figure 2, DYNAfed requires less than " + }, + { + "bbox": [ + 46, + 403, + 288, + 460 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 46, + 403, + 288, + 460 + ], + "type": "text", + "content": " communication rounds to achieve comparable performance with the baseline methods." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 466, + 151, + 479 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 466, + 151, + 479 + ], + "spans": [ + { + "bbox": [ + 47, + 466, + 151, + 479 + ], + "type": "text", + "content": "6.2. Detailed Analysis" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 484, + 288, + 562 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 484, + 288, + 562 + ], + "spans": [ + { + "bbox": [ + 46, + 484, + 288, + 562 + ], + "type": "text", + "content": "We conduct a detailed analysis of DYNAFED and aim to provide answers to the following questions: (1) Does " + }, + { + "bbox": [ + 46, + 484, + 288, + 562 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 46, + 484, + 288, + 562 + ], + "type": "text", + "content": " contain information about global data distribution while protecting client privacy? (2) Can we leverage just the dynamics of the early rounds to synthesize " + }, + { + "bbox": [ + 46, + 484, + 288, + 562 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 46, + 484, + 288, + 562 + ], + "type": "text", + "content": "? (3) How many pseudo samples do we need to synthesize to ensure effectiveness? (4) Does " + }, + { + "bbox": [ + 46, + 484, + 288, + 562 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 46, + 484, + 288, + 562 + ], + "type": "text", + "content": " still help convergence under more severe heterogeneity and longer local training?" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "type": "text", + "content": " Contains Global Information and Preserves Privacy. We conduct experiment with CIFAR10 and set " + }, + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\alpha = 0.01" + }, + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "type": "text", + "content": ", where client datasets are extremely non-iid. We track the losses calculated over each client's data throughout local training as well as the global model's finetuning. During local training, we calculate the client models' losses over their own datasets, i.e., " + }, + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_m(\\boldsymbol{w}_m, \\mathcal{D}_m)" + }, + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "type": "text", + "content": ". During finetuning, we calculate the global model's losses over each client's dataset, i.e., " + }, + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_m(\\boldsymbol{w}, \\mathcal{D}_m)" + }, + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "type": "text", + "content": ". To prevent cluttering, we randomly select 3 client datasets for illustration. The result is shown in Figure 3, each color represents the loss over one clients' dataset. We observe that the client models easily overfit during local training due to the extreme class imbalance. The deflected client models make the aggregated global model demonstrate high loss values over some" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 310, + 72, + 421, + 182 + ], + "blocks": [ + { + "bbox": [ + 310, + 72, + 421, + 182 + ], + "lines": [ + { + "bbox": [ + 310, + 72, + 421, + 182 + ], + "spans": [ + { + "bbox": [ + 310, + 72, + 421, + 182 + ], + "type": "image", + "image_path": "53d7fcfd11e3f7ed0eabe6224258ee31f95fd668e066cf384c19d22e37f2a42c.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 194, + 547, + 305 + ], + "lines": [ + { + "bbox": [ + 304, + 194, + 547, + 305 + ], + "spans": [ + { + "bbox": [ + 304, + 194, + 547, + 305 + ], + "type": "text", + "content": "Figure 5. Left: The test accuracy curves for different choices of trajectory length L on the CIFAR10 dataset with " + }, + { + "bbox": [ + 304, + 194, + 547, + 305 + ], + "type": "inline_equation", + "content": "\\alpha = 0.01" + }, + { + "bbox": [ + 304, + 194, + 547, + 305 + ], + "type": "text", + "content": ". By leveraging the dynamics of the global model's trajectory in the first few rounds, e.g., " + }, + { + "bbox": [ + 304, + 194, + 547, + 305 + ], + "type": "inline_equation", + "content": "\\mathrm{L} \\in \\{10, 15, 20, 15\\}" + }, + { + "bbox": [ + 304, + 194, + 547, + 305 + ], + "type": "text", + "content": ", the derived " + }, + { + "bbox": [ + 304, + 194, + 547, + 305 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 304, + 194, + 547, + 305 + ], + "type": "text", + "content": " already helps achieve faster convergence and stable training. In contrast, the FedGen approach only brings slight performance gain during the later phase of training due to the dependence on the global model's performance. Right: We show the performance of DYNAfed with different sizes of " + }, + { + "bbox": [ + 304, + 194, + 547, + 305 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 304, + 194, + 547, + 305 + ], + "type": "text", + "content": " for various " + }, + { + "bbox": [ + 304, + 194, + 547, + 305 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 194, + 547, + 305 + ], + "type": "text", + "content": ". The performance gain is significant with just 150 synthesized samples." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 429, + 72, + 541, + 182 + ], + "blocks": [ + { + "bbox": [ + 429, + 72, + 541, + 182 + ], + "lines": [ + { + "bbox": [ + 429, + 72, + 541, + 182 + ], + "spans": [ + { + "bbox": [ + 429, + 72, + 541, + 182 + ], + "type": "image", + "image_path": "512527f1baef093b440ced96309bc4d2179e53b61ec1aaa5921927d6a226f165.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 317, + 547, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 317, + 547, + 384 + ], + "spans": [ + { + "bbox": [ + 304, + 317, + 547, + 384 + ], + "type": "text", + "content": "clients' data. Remarkably, we observe that finetuning with " + }, + { + "bbox": [ + 304, + 317, + 547, + 384 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 304, + 317, + 547, + 384 + ], + "type": "text", + "content": " is able to recover the global model to a reasonable state, which achieves small losses over all client datasets. This verifies that " + }, + { + "bbox": [ + 304, + 317, + 547, + 384 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 304, + 317, + 547, + 384 + ], + "type": "text", + "content": " contains information of the global data distribution. Furthermore, Figure 4 presents the synthesized data of CIFAR10, client-specific information can not be observed." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 394, + 545, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 394, + 545, + 526 + ], + "spans": [ + { + "bbox": [ + 304, + 394, + 545, + 526 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 304, + 394, + 545, + 526 + ], + "type": "text", + "content": " Can be Learned with Early Trajectory. We conduct experiments with different choices of trajectory length " + }, + { + "bbox": [ + 304, + 394, + 545, + 526 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 304, + 394, + 545, + 526 + ], + "type": "text", + "content": " in left of Figure 5. We observe that even if with " + }, + { + "bbox": [ + 304, + 394, + 545, + 526 + ], + "type": "inline_equation", + "content": "L = 10" + }, + { + "bbox": [ + 304, + 394, + 545, + 526 + ], + "type": "text", + "content": ", the result is comparable with performance obtained with longer trajectory " + }, + { + "bbox": [ + 304, + 394, + 545, + 526 + ], + "type": "inline_equation", + "content": "L = 25" + }, + { + "bbox": [ + 304, + 394, + 545, + 526 + ], + "type": "text", + "content": ". Compared with the baseline methods, DYNAfed achieves significant convergence speedup and performance boost. These results support our claim in Section 4 that our method can take effect early during training. By contrast, the data-free KD method FedGen [53] that trains a generator to produce pseudo data starts to show a slight improvement only in the late stage of training since it depends explicitly on the global model's performance when training the generator." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 536, + 545, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 536, + 545, + 615 + ], + "spans": [ + { + "bbox": [ + 304, + 536, + 545, + 615 + ], + "type": "text", + "content": "How the Size of " + }, + { + "bbox": [ + 304, + 536, + 545, + 615 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 304, + 536, + 545, + 615 + ], + "type": "text", + "content": " Impacts the Performance. As shown in the right of Figure 5, we conduct experiments with different sizes of " + }, + { + "bbox": [ + 304, + 536, + 545, + 615 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 304, + 536, + 545, + 615 + ], + "type": "text", + "content": " and various heterogeneity degrees " + }, + { + "bbox": [ + 304, + 536, + 545, + 615 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 536, + 545, + 615 + ], + "type": "text", + "content": ". We find that a small " + }, + { + "bbox": [ + 304, + 536, + 545, + 615 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 304, + 536, + 545, + 615 + ], + "type": "text", + "content": " suffices for good performance, while larger " + }, + { + "bbox": [ + 304, + 536, + 545, + 615 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 304, + 536, + 545, + 615 + ], + "type": "text", + "content": " brings only marginal performance boost. This property not only saves the cost for synthesizing " + }, + { + "bbox": [ + 304, + 536, + 545, + 615 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 304, + 536, + 545, + 615 + ], + "type": "text", + "content": ", but also makes the finetuning of the global model more efficient." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 624, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 624, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 624, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 304, + 624, + 547, + 715 + ], + "type": "text", + "content": " is Able to Mimic the Global Dynamics. In the left of Figure 6, we calculate the cosine distance between the target checkpoint " + }, + { + "bbox": [ + 304, + 624, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\boldsymbol{w}^{\\mathrm{t+s}}" + }, + { + "bbox": [ + 304, + 624, + 547, + 715 + ], + "type": "text", + "content": " and the parameters " + }, + { + "bbox": [ + 304, + 624, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\tilde{\\boldsymbol{w}}" + }, + { + "bbox": [ + 304, + 624, + 547, + 715 + ], + "type": "text", + "content": " trained from " + }, + { + "bbox": [ + 304, + 624, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\boldsymbol{w}^{\\mathrm{t}}" + }, + { + "bbox": [ + 304, + 624, + 547, + 715 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 304, + 624, + 547, + 715 + ], + "type": "inline_equation", + "content": "s'" + }, + { + "bbox": [ + 304, + 624, + 547, + 715 + ], + "type": "text", + "content": " steps with " + }, + { + "bbox": [ + 304, + 624, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 304, + 624, + 547, + 715 + ], + "type": "text", + "content": ", a randomly sampled real dataset of the same size as " + }, + { + "bbox": [ + 304, + 624, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 304, + 624, + 547, + 715 + ], + "type": "text", + "content": ", and a dataset consisted of noisy pixels, respectively. We can see that in terms of mimicking the global trajectory, " + }, + { + "bbox": [ + 304, + 624, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 304, + 624, + 547, + 715 + ], + "type": "text", + "content": " not only significantly outperforms the noise dataset, but also achieves only half of the distance obtained with real dataset, which is not" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12183" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 52, + 64, + 282, + 177 + ], + "blocks": [ + { + "bbox": [ + 52, + 64, + 282, + 177 + ], + "lines": [ + { + "bbox": [ + 52, + 64, + 282, + 177 + ], + "spans": [ + { + "bbox": [ + 52, + 64, + 282, + 177 + ], + "type": "table", + "html": "
Methodα = 0.01α = 0.04
5 epochs10 epochs5 epochs10 epochs
FedAVG33.23±3.5429.93±4.6250.28±2.1746.09±2.95
FedProx42.60±2.3042.86±2.8458.40±1.3554.30±1.98
Scaffold39.43±1.8636.52±2.0455.46±1.2550.05±1.57
FedDF*31.68±3.1639.85±3.7952.31±2.3850.90±2.53
FedBE*35.49±2.8834.19±3.3449.78±1.7951.34±1.90
ABAVG*37.87±2.5735.08±3.0356.81±1.9452.17±2.32
FedGen†35.64±2.5235.03±3.5857.60±1.5554.48±2.03
FedMix†47.36±1.2441.53±1.3760.74±0.9556.35±1.33
DynaFed†61.45±0.4659.04±0.6468.35±0.2066.30±0.34
", + "image_path": "ac0eec6feb6bb418ee0499742140e9956b0b46bf00544b4454966b0f692e8e37.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 48, + 236, + 294, + 357 + ], + "blocks": [ + { + "bbox": [ + 46, + 179, + 290, + 235 + ], + "lines": [ + { + "bbox": [ + 46, + 179, + 290, + 235 + ], + "spans": [ + { + "bbox": [ + 46, + 179, + 290, + 235 + ], + "type": "text", + "content": "Table 3. Test performances on CIFAR10 achieved by different FL algorithms under various degrees of data heterogeneity and local training epochs. Total communication rounds of 100 and 50 are set with local training epochs of 5 and 10, respectively. As can be seen, DYNAfed significantly surpasses other methods." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 236, + 294, + 357 + ], + "lines": [ + { + "bbox": [ + 48, + 236, + 294, + 357 + ], + "spans": [ + { + "bbox": [ + 48, + 236, + 294, + 357 + ], + "type": "table", + "html": "
MethodCIFAR10CINIC10
α = 0.01α = 0.04α = 0.01α = 0.04
Acc = 0.45Acc = 0.55Acc = 0.33Acc = 0.45
FedAVG132.0±15.0117.0±8.0189.3±10.5138.7±5.6
FedProx113.3±16.4102.0±4.7156.7±7.0118.3±4.0
Scaffold105.0±10.4100.3±3.5158.0±5.4110.0±3.4
FedDF*145.7±13.1117.3±5.8180.7±5.0170.0±7.0
FedBE*165.0±12.7122.7±4.5185.3±14.6174.3±6.8
ABAVG*109.7±5.4110.7±5.0150.0±8.4127.0±5.8
FedGen†115.7±10.4110.3±5.7167.0±12.1128.3±5.5
FedMix†77.3±3.789.3±3.579.0±7.882.3±5.5
DynaFed†22.3±0.622.0±1.021.3±1.522.7±1.4
", + "image_path": "851582cf0b3de154e9086b213489703fff167174f7bfe46763fd1b5b544f8814.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 409, + 287, + 432 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 409, + 287, + 432 + ], + "spans": [ + { + "bbox": [ + 46, + 409, + 287, + 432 + ], + "type": "text", + "content": "accessible in FL setting. This verifies the ability of " + }, + { + "bbox": [ + 46, + 409, + 287, + 432 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 46, + 409, + 287, + 432 + ], + "type": "text", + "content": " to mimic global trajectory." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 434, + 287, + 600 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 434, + 287, + 600 + ], + "spans": [ + { + "bbox": [ + 46, + 434, + 287, + 600 + ], + "type": "text", + "content": "DYNAFED is Robust to Longer Local Training. Longer local training is generally required in FL to reduce the total number of global communication rounds. Under different heterogeneity degrees, we conduct experiments to evaluate the impact of longer local training epochs on DYNAFED. Specifically, we conduct experiments with total communication rounds of 100 and 50 with ocal training epochs of 5 and 10, respectively. The results are presented in Table 3, from which we observe the following: 1) DYNAFED consistently outperforms other methods by a large margin even with longer local training epochs; 2) the performance of DYNAFED is less sensitive to the length of local training, which benefits from the " + }, + { + "bbox": [ + 46, + 434, + 287, + 600 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 46, + 434, + 287, + 600 + ], + "type": "text", + "content": " containing information about the global data distribution. Therefore, DYNAFED is able to achieve similar performance with less global communication rounds, which is the major bottleneck in the efficiency of FL." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 601, + 287, + 667 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 601, + 287, + 667 + ], + "spans": [ + { + "bbox": [ + 46, + 601, + 287, + 667 + ], + "type": "text", + "content": "We further conduct experiments on varying local epochs to measure the quality of " + }, + { + "bbox": [ + 46, + 601, + 287, + 667 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 46, + 601, + 287, + 667 + ], + "type": "text", + "content": ". Specifically, we use it to train a network from scratch and evaluate its test performance. Shown in right of Figure 6, the quality of " + }, + { + "bbox": [ + 46, + 601, + 287, + 667 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 46, + 601, + 287, + 667 + ], + "type": "text", + "content": " stays similar with longer local training and more severe heterogeneity. This further explains the superior performance of DYNAfed with longer local training." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 673, + 270, + 685 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 673, + 270, + 685 + ], + "spans": [ + { + "bbox": [ + 47, + 673, + 270, + 685 + ], + "type": "text", + "content": "6.3. Architecture Generalization and Efficiency" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 691, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 691, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 691, + 287, + 713 + ], + "type": "text", + "content": "To showcase the generalization ability of our approach over different network architecture choices, we conduct experiments on" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 310, + 63, + 541, + 177 + ], + "blocks": [ + { + "bbox": [ + 46, + 361, + 290, + 406 + ], + "lines": [ + { + "bbox": [ + 46, + 361, + 290, + 406 + ], + "spans": [ + { + "bbox": [ + 46, + 361, + 290, + 406 + ], + "type": "text", + "content": "Table 4. Comparison of the number of communication rounds to reach target accuracy. With the knowledge of global data distribution stored in " + }, + { + "bbox": [ + 46, + 361, + 290, + 406 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 46, + 361, + 290, + 406 + ], + "type": "text", + "content": " at the server, the convergence speed of our DYNAfed is significantly accelerated." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 310, + 63, + 541, + 177 + ], + "lines": [ + { + "bbox": [ + 310, + 63, + 541, + 177 + ], + "spans": [ + { + "bbox": [ + 310, + 63, + 541, + 177 + ], + "type": "table", + "html": "
Methodα = 0.01α = 0.04
MLPConvNetMLPConvNet
FedAVG65.64±1.6974.51±1.3273.26±1.4981.74±1.98
FedProx68.09±1.4776.88±1.8379.83±1.7083.06±2.53
Scaffold67.60±1.5377.92±0.8778.09±1.3582.25±1.35
FedDF*64.59±1.7072.36±2.0877.20±1.5881.65±0.97
FedBE*65.97±1.6472.33±1.7975.42±1.3581.31±1.25
ABAVG*69.19±1.5075.98±1.9981.64±1.2084.44±1.84
FedGen†68.67±1.4575.59±1.1277.94±1.3856.60±1.08
FedMix†70.30±0.9281.34±0.6881.95±0.6484.23±0.50
DynaFed†73.89±0.2487.52±0.1583.54±0.4289.45±0.11
", + "image_path": "3cd3a3592dc3ed41bf8cc1768f10547362d3d5bc93ea879059d94f4c866539e7.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 179, + 548, + 223 + ], + "lines": [ + { + "bbox": [ + 304, + 179, + 548, + 223 + ], + "spans": [ + { + "bbox": [ + 304, + 179, + 548, + 223 + ], + "type": "text", + "content": "Table 5. Performance comparison across different network architectures. We conduct the experiment on FMNIST dataset using MLP and ConvNet to demonstrate the generalization of DYNAfed for different network architectures." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 310, + 227, + 421, + 337 + ], + "blocks": [ + { + "bbox": [ + 310, + 227, + 421, + 337 + ], + "lines": [ + { + "bbox": [ + 310, + 227, + 421, + 337 + ], + "spans": [ + { + "bbox": [ + 310, + 227, + 421, + 337 + ], + "type": "image", + "image_path": "efaff97bb181e00412c5e7a9a452f9a04285173a947750a6221dc3181ecd7445.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 340, + 548, + 418 + ], + "lines": [ + { + "bbox": [ + 304, + 340, + 548, + 418 + ], + "spans": [ + { + "bbox": [ + 304, + 340, + 548, + 418 + ], + "type": "text", + "content": "Figure 6. Left: the cosine distance between the target checkpoint " + }, + { + "bbox": [ + 304, + 340, + 548, + 418 + ], + "type": "inline_equation", + "content": "\\boldsymbol{w}^{\\mathrm{t + s}}" + }, + { + "bbox": [ + 304, + 340, + 548, + 418 + ], + "type": "text", + "content": " and the parameters " + }, + { + "bbox": [ + 304, + 340, + 548, + 418 + ], + "type": "inline_equation", + "content": "\\tilde{\\boldsymbol{w}}" + }, + { + "bbox": [ + 304, + 340, + 548, + 418 + ], + "type": "text", + "content": " obtained by training with different datasets from " + }, + { + "bbox": [ + 304, + 340, + 548, + 418 + ], + "type": "inline_equation", + "content": "\\boldsymbol{w}^{\\mathrm{t}}" + }, + { + "bbox": [ + 304, + 340, + 548, + 418 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 304, + 340, + 548, + 418 + ], + "type": "inline_equation", + "content": "s^{\\prime}" + }, + { + "bbox": [ + 304, + 340, + 548, + 418 + ], + "type": "text", + "content": " steps. We can see that the distance derived using " + }, + { + "bbox": [ + 304, + 340, + 548, + 418 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 304, + 340, + 548, + 418 + ], + "type": "text", + "content": " is constantly smaller compared with other data. Right: Test performances of a model trained from scratch using only " + }, + { + "bbox": [ + 304, + 340, + 548, + 418 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 304, + 340, + 548, + 418 + ], + "type": "text", + "content": " generated under various local epochs and client heterogeneity. The two plots together verify the quality of the generated " + }, + { + "bbox": [ + 304, + 340, + 548, + 418 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 304, + 340, + 548, + 418 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 429, + 227, + 539, + 337 + ], + "blocks": [ + { + "bbox": [ + 429, + 227, + 539, + 337 + ], + "lines": [ + { + "bbox": [ + 429, + 227, + 539, + 337 + ], + "spans": [ + { + "bbox": [ + 429, + 227, + 539, + 337 + ], + "type": "image", + "image_path": "3a12a63d5d219cfdcab82e74f1b23df918c7a826e02303df5994161b36d455f6.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 430, + 547, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 430, + 547, + 474 + ], + "spans": [ + { + "bbox": [ + 304, + 430, + 547, + 474 + ], + "type": "text", + "content": "FMNIST using different network architectures. Specifically, we choose ConvNet and MLP following [34, 53]. As shown in Table 5, under various client data heterogeneity, our method demonstrates superior performances with both network architectures." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 474, + 547, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 547, + 594 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 547, + 594 + ], + "type": "text", + "content": "Thanks to the rich knowledge of global data distribution contained in " + }, + { + "bbox": [ + 304, + 474, + 547, + 594 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 304, + 474, + 547, + 594 + ], + "type": "text", + "content": ", using it to refine the global model greatly boosts the convergence speed of training. As shown in Figure 2, as soon as " + }, + { + "bbox": [ + 304, + 474, + 547, + 594 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{syn}}" + }, + { + "bbox": [ + 304, + 474, + 547, + 594 + ], + "type": "text", + "content": " is used to refine the global model, its performance rapidly increases to a reasonable accuracy, which reduces many rounds of communication. In Table 4, we also quantitatively compare the convergence speed of different FL algorithms by showing the number of communication rounds needed to reach the highest test accuracy achievable by the baselines. As can be observed, our DYNAfed requires only less than " + }, + { + "bbox": [ + 304, + 474, + 547, + 594 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 304, + 474, + 547, + 594 + ], + "type": "text", + "content": " communication rounds to reach a target accuracy comparable to other methods." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 605, + 378, + 618 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 605, + 378, + 618 + ], + "spans": [ + { + "bbox": [ + 306, + 605, + 378, + 618 + ], + "type": "text", + "content": "7. Conclusion" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 625, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 625, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 625, + 547, + 713 + ], + "type": "text", + "content": "We propose DYNAFED to tackle the data heterogeneity issue, which synthesizes a pseudo dataset to extract the knowledge of the global data distribution from the dynamics of the global model's trajectory. Extensive experiments show that DYNAFED demonstrates relative improvement over the FedAvg baseline up to " + }, + { + "bbox": [ + 304, + 625, + 547, + 713 + ], + "type": "inline_equation", + "content": "82.2\\%" + }, + { + "bbox": [ + 304, + 625, + 547, + 713 + ], + "type": "text", + "content": " on CIFAR100. Further, we believe our work is able to provide insights for extracting global information on the server side, which goes beyond tackling the data heterogeneity issue." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12184" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 53, + 91, + 288, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 288, + 134 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 288, + 134 + ], + "type": "text", + "content": "[1] Durmus Alp Emre Acar, Yue Zhao, Ramon Matas Navarro, Matthew Mattina, Paul N Whatmough, and Venkatesh Saligrama. 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PMLR, 2021. 2, 3, 4, 5, 7, 8" + } + ] + } + ], + "index": 27 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "text", + "content": "12186" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/DynaMask_ Dynamic Mask Selection for Instance Segmentation/6de3482f-3d80-4aaa-a48e-484855bf3aa9_content_list.json b/2023/DynaMask_ Dynamic Mask Selection for Instance Segmentation/6de3482f-3d80-4aaa-a48e-484855bf3aa9_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..547591170b111c28b0f5bd12decd82a849a9b6c5 --- /dev/null +++ b/2023/DynaMask_ Dynamic Mask Selection for Instance Segmentation/6de3482f-3d80-4aaa-a48e-484855bf3aa9_content_list.json @@ -0,0 +1,1607 @@ +[ + { + "type": "text", + "text": "DynaMask: Dynamic Mask Selection for Instance Segmentation", + "text_level": 1, + "bbox": [ + 161, + 130, + 807, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Ruihuang Li,\\* Chenhang He,\\* Shuai Li, Yabin Zhang, Lei Zhang† The Hong Kong Polytechnic University", + "bbox": [ + 205, + 180, + 767, + 217 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{csrhli, csche, cslzhang}@comp.polyu.edu.hk", + "bbox": [ + 292, + 219, + 671, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 268, + 313, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The representative instance segmentation methods mostly segment different object instances with a mask of the fixed resolution, e.g., $28 \\times 28$ grid. However, a low-resolution mask loses rich details, while a high-resolution mask incurs quadratic computation overhead. It is a challenging task to predict the optimal binary mask for each instance. In this paper, we propose to dynamically select suitable masks for different object proposals. First, a dual-level Feature Pyramid Network (FPN) with adaptive feature aggregation is developed to gradually increase the mask grid resolution, ensuring high-quality segmentation of objects. Specifically, an efficient region-level top-down path (r-FPN) is introduced to incorporate complementary contextual and detailed information from different stages of image-level FPN (i-FPN). Then, to alleviate the increase of computation and memory costs caused by using large masks, we develop a Mask Switch Module (MSM) with negligible computational cost to select the most suitable mask resolution for each instance, achieving high efficiency while maintaining high segmentation accuracy. Without bells and whistles, the proposed method, namely DynaMask, brings consistent and noticeable performance improvements over other state-of-the-arts at a moderate computation overhead. The source code: https://github.com/lslrh/DynaMask.", + "bbox": [ + 76, + 300, + 473, + 662 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 690, + 209, + 705 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Instance segmentation (IS) is an important computer vision task, aiming at simultaneously predicting the class label and the binary mask for each instance of interest in an image. It works as the cornerstone of many downstream vision applications, such as autonomous driving, video surveillance, and robotics, to name a few. Recent years have witnessed the significant advances of deep convolutional neural networks (CNNs) based IS methods with a rich amount of training data as the rocket fuel [1, 10, 17, 25, 26]. Existing IS methods can be roughly divided into two ma", + "bbox": [ + 75, + 715, + 468, + 867 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/dbec4932b6e30d8c0989dd315998d63c80dd30a438930fb01719e1ef84492e09.jpg", + "image_caption": [ + "Figure 1. Dynamic mask selection results. Some \"hard\" samples with irregular shapes like \"person\" are assigned larger masks, while the \"easy\" ones like \"frisbee\" are assigned smaller ones." + ], + "image_footnote": [], + "bbox": [ + 532, + 267, + 859, + 448 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "jor categories: two-stage [6, 10, 17] and single-stage methods [1, 2, 26]. The former first detect a sparse set of proposals and then performs mask predictions based on them, while the latter directly predict classification scores and masks based on the pre-defined anchors. Generally speaking, two-stage methods could produce higher segmentation accuracy but cost more computational resources than single-stage methods.", + "bbox": [ + 496, + 505, + 892, + 626 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Among the many recently developed IS methods, the proposal-based two-stage methods [6, 10, 17], which follow a detection-and-segmentation paradigm, are still the top performers. These methods need to predict a binary grid mask of uniform resolution for all proposals, e.g., $28 \\times 28$ , and then upsample it to the original image size. For instance, Mask R-CNN [10] first generates a group of proposals with an object detector and then performs per pixel foreground/background segmentation on the Regions of Interest (RoIs) [24]. Despite achieving promising performance, the low-resolution mask of Mask R-CNN is insufficient to capture more detailed information, resulting in unsatisfactory predictions, especially over object boundaries. An intuitive solution to improve the segmentation quality is to adopt a larger mask. Nevertheless, high-resolution masks often generate excessive predictions on the smooth regions, resulting in high computational complexity.", + "bbox": [ + 496, + 627, + 893, + 883 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "It is difficult to segment different objects in an image", + "bbox": [ + 517, + 885, + 890, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*denotes the equal contribution, †denotes the corresponding author. This work is supported by the Hong Kong RGC RIF grant (R5001-18).", + "bbox": [ + 76, + 875, + 467, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "11279", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "with masks of the same resolution. Objects with irregular shapes and complicated boundaries demand more fine-grained masks to predict, referred to as \"hard\" samples, such as the \"person\" in Fig. 1. In comparison, the \"easy\" samples with regular shapes and fewer details can be efficiently segmented using coarser masks, like the \"frisbee\" in Fig. 1. Inspired by the above observations, we propose to adaptively adjust the mask size for each instance for better IS performance. Specifically, instead of using a uniform resolution for all instances, we assign high-resolution masks to \"hard\" objects and low-resolution masks to \"easy\" objects. In this way, the redundant computation for \"easy\" samples can be reduced while the accuracy of \"hard\" samples can be improved, achieving a balance between accuracy and speed. As shown in Tab. 1, however, directly predicting a high-resolution mask by Mask R-CNN [10] unexpectedly degrades the mask average precision (AP). This attributes to two main reasons. First, the RoI features of larger objects are extracted from higher pyramid levels, which are very coarse due to the downsampling operations [20]. Thus simply increasing the mask size of these RoIs will not bring extra useful information. Second, the mask head of Mask R-CNN is oversimplified, so it cannot make more precise predictions as the mask grid size increases.", + "bbox": [ + 76, + 90, + 472, + 453 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To overcome the above mentioned problems, we propose a dual-level FPN framework to gradually enlarge the mask grid. Specifically, in addition to traditional image-level FPN (i-FPN), a region-level FPN (r-FPN) is designed to achieve coarse-to-fine mask prediction. Wherein we construct information flows between i-FPN and r-FPN at different pyramid levels, aiming to incorporate complementary contextual and detailed information from multiple feature levels for high-quality segmentation. With the dual-level FPN, we present a data-dependent Mask Switch Module (MSM) with negligible computational cost to adaptively select masks for each instance. The overall approach, namely DynaMask, is evaluated on benchmark instance segmentation datasets to demonstrate its superiority over state-of-the-arts. The major contributions of this work are summarized as follows:", + "bbox": [ + 76, + 454, + 472, + 680 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- A dynamic mask selection method (DynaMask) is proposed to adaptively assign appropriate masks to different instances. Specifically, it assigns low-resolution masks to \"easy\" samples for efficiency while assigning high-resolution masks to \"hard\" samples for accuracy.", + "- A dual-level FPN framework is developed for IS. We construct direct information flows from i-FPN to r-FPN at multiple levels, facilitating complementary information aggregation from multiple pyramid levels.", + "- Extensive experiments demonstrate that DynaMask achieves a good trade-off between IS accuracy and efficiency, outperforming many state-of-the-art two-stage IS methods at a moderate computation overhead." + ], + "bbox": [ + 93, + 688, + 468, + 891 + ], + "page_idx": 1 + }, + { + "type": "table", + "img_path": "images/0ecdaa54fb186dcd7c63d2aad016e77283d7752d39db972398597b1bdb1e4cf5.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodResolutionAPFLOPs
Mask R-CNN [10]14×1432.90.2G
28×2834.70.5G
56×5633.82.0G
112×11232.58.0G
DynaMask14×1432.90.2G
28×2836.10.6G
56×5637.11.0G
112×11237.61.4G
", + "bbox": [ + 540, + 88, + 857, + 224 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Table 1. Mask AP and FLOPs with different mask resolutions. For Mask R-CNN, directly increasing the mask resolution will decrease the mask AP. While for our DynaMask, higher mask resolution results in better performance.", + "bbox": [ + 496, + 233, + 890, + 291 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 308, + 640, + 324 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Instance Segmentation. To date, most of the top-performing IS methods still follow the Mask R-CNN metaarchitecture [10]. These proposal-based approaches typically employ an object detector to localize each instance in bounding boxes. Then the instance-wise features are cropped and extracted from FPN features based on the detected bounding boxes by using RoI pooling/align [10, 24]. Finally, a compact segmentation head is deployed to obtain the desired object masks. Mask Scoring R-CNN [14] aligns the mask quality and score by using a branch to explicitly learn the quality of predicted masks. BMask R-CNN [6] leverages boundary details to improve mask localization ability. DCT-Mask [25] encodes high-resolution binary masks into compact vectors through the discrete cosine transform (DCT). PANet [22] constructs two feature pyramids for improving mask prediction.", + "bbox": [ + 496, + 335, + 890, + 578 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Some works [3, 17, 30] have been proposed to improve the mask quality by coarse-to-fine refinement. HTC [3] performs cascaded refinement on both detection and segmentation tasks and explores the reciprocal relationships between them. PointRend [17] and RefineMask [30] extract fine-grained features in a multi-stage manner. The former performs point-based predictions over the blurred areas, while the latter refines the entire RoI feature. Despite the promising segmentation results, multiple refinement stages inevitably increase the inference time and memory burden. In this paper, we dynamically select the suitable mask for each instance so that \"easy\" samples are assigned small masks (with fewer refinement stages) for efficiency, and \"hard\" samples are assigned large masks (with more refinement stages) for accuracy, achieving a balance between efficiency and accuracy.", + "bbox": [ + 496, + 580, + 890, + 823 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Dynamic Networks. Dynamic networks, which aim to adaptively adjust the network architecture according to the input feature, have been widely studied in recent years. Dynamic model compression methods either drop blocks [12, 23, 27] or prune channels [19, 29] for speeding", + "bbox": [ + 496, + 824, + 890, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "11280", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/b29b2729616c25008a941ebaf283eac79f37a0e1463997eb2cb14761f2b3ca4e.jpg", + "image_caption": [ + "Figure 2. The overall architecture of DynaMask. We propose a dual-level FPN framework to gradually increase the mask size and achieve higher-quality IS. The information flow is constructed between each level of image-level FPN (i-FPN) and region-level FPN (r-FPN), so that region-wise feature hierarchies $\\{L_{tiny}, L_{small}, L_{medium}, L_{large}\\}$ are constantly enhanced by incorporating complementary information from $\\{P2, P3, P4\\}$ of i-FPN, resulting in coarse-to-fine mask predictions. To reduce the computation and memory cost, a Mask Switch Module (MSM) is developed to predict the mask resolution for each instance with budgeted resource consumption. Specifically, MSM outputs four different switching states, corresponding to four different mask resolutions, i.e., $[14 \\times 14, 28 \\times 28, 56 \\times 56, 112 \\times 112]$ ." + ], + "image_footnote": [], + "bbox": [ + 119, + 90, + 851, + 280 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "up the inference. For instance, SkipNet [27] skips convolutional blocks through a reinforcement learning-based gating network. Huang et al. propose a multi-scale dense network with multiple classifiers for allocating different computations for \"easy\" and \"hard\" samples. Li et al. [18] adopt an end-to-end dynamic routing framework to alleviate the scale variance among inputs. DRNet [32] attempts to reduce the redundancy on the input resolution of modern CNNs.", + "bbox": [ + 75, + 387, + 468, + 507 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "However, employing dynamic masks at different resolutions for segmenting different instances has rarely been explored in the field of IS. Conventional methods [6, 10, 17] typically predict a fixed-size mask irrespective of the object type. This is sufficient for \"easy\" samples but produces over-smoothing predictions for \"hard\" samples over the fine-level details. In order to improve the segmentation performance without introducing many additional computation burdens, we devise a dynamic mask selection framework to adaptively allocate suitable masks to different objects according to their segmentation difficulties.", + "bbox": [ + 75, + 508, + 468, + 675 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Dynamic Mask Selection", + "text_level": 1, + "bbox": [ + 76, + 689, + 307, + 705 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The framework of DynaMask is illustrated in Fig. 2. A dual-level FPN architecture is first proposed for improving IS quality, and then a Mask Switch Module (MSM) is developed to dynamically allocate appropriate masks to each instance, so that the resource consumption can be reduced while maintaining superior IS performance. Our DynaMask produces high-quality segmentation with a moderate computation overhead.", + "bbox": [ + 75, + 714, + 468, + 835 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Dual-Level FPN", + "text_level": 1, + "bbox": [ + 76, + 845, + 236, + 861 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Original image-level FPN (i-FPN) [20] introduces a top-down path to propagate contextual semantic information", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "from higher layers to lower ones. Actually, the lower-level features contain more fine-grained details than higher-level ones, which are beneficial for high-quality segmentation, especially on boundary regions, but these information is not fully explored in Mask R-CNN [10]. In this work, we propose a region-level FPN (r-FPN) to integrate more detailed information from lower layers of i-FPN into region-wise feature hierarchies. The information flows from each level of i-FPN to r-FPN are shown in Fig. 2.", + "bbox": [ + 496, + 387, + 890, + 523 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Region-Level FPN. We follow the original i-FPN to define the layers producing feature maps of the same resolution as one network stage corresponding to one feature level. We use $\\{P_2, P_3, P_4, P_5\\}$ to denote different feature levels of i-FPN. The r-FPN starts from an RoI-Aligned region-wise feature, and it is gradually enhanced by fusing the complementary information from $\\{P_2, P_3, P_4\\}$ of i-FPN, resulting in top-down region-based feature hierarchies, denoted by $\\{L_{tiny}, L_{small}, L_{medium}, L_{large}\\}$ . From $L_{tiny}$ to $L_{large}$ , the spatial resolution is progressively increased by a factor of two. We design a Feature Aggregation Module (FAM) to integrate the r-FPN feature $L_r$ and the i-FPN feature $P_i$ .", + "bbox": [ + 496, + 530, + 892, + 712 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Feature Aggregation Module (FAM). There exists spatial misalignments between $L_{r}$ and $P_{i}$ due to the upsampling and RoI pooling [24] operations, which may degrade the segmentation performance on boundary areas. To overcome this limitation, we propose the FAM to adaptively aggregate multi-scale features. As show in Fig. 3, FAM contains two deformable convolutions [8, 13] which play different roles. The first one (Deform_Conv1) adjusts the positions of $L_{r}$ , making it better aligned to $P_{i}$ . Here we first concatenate $L_{r}$ with $P_{i}$ , and then pass the concatenated features through a $3 \\times 3$ Conv to obtain the offset map, denoted by $\\Delta_{o}$ . Finally, $L_{r}$ is aligned to $P_{i}$ with the learned offset $\\Delta_{o}$ . The", + "bbox": [ + 496, + 719, + 892, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "11281", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/01a40b0e210f07ddea80274f6b0d3fa40922e904296e3bf53b425c5cbe79ae55.jpg", + "image_caption": [ + "Figure 3. Feature Alignment Molecule (FAM). Deform_Conv1 adjusts the spatial positions of upsampled r-FPN feature $L_{r}$ and the cropped i-FPN feature $P_{i}$ . Deform_Conv2 attends to the salient parts of objects." + ], + "image_footnote": [], + "bbox": [ + 89, + 87, + 457, + 196 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "second one (Deform_Conv2) works like an attention mechanism, which attends to the salient parts of objects. The proposed FAM is plugged into different stages of r-FPN and it plays a key role in improving the mask prediction.", + "bbox": [ + 75, + 271, + 470, + 333 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Mask Switch Module (MSM)", + "text_level": 1, + "bbox": [ + 76, + 340, + 336, + 357 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The proposed dual-level FPN framework brings a significant performance improvement but at the price of expensive computation and memory burdens. Inspired by the fact that different instances require different mask grids to achieve accurate segmentation, we propose a novel method to adaptively adjust the mask grid resolution for different instances. Specifically, an MSM is developed to perform mask resolution prediction under a budgeted computation consumption, achieving a good trade-off between segmentation accuracy and efficiency.", + "bbox": [ + 75, + 364, + 468, + 515 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Optimal Mask Assignment. The MSM module is actually a lightweight classifier, denoted by $f_{MSM}(\\cdot)$ , which is illustrated in Fig. 4. It contains a channel-wise attention module [11], followed by a few convolutional layers and fully-connected layers. This classifier aims to find the optimal mask resolution from a collection of $K$ candidates, i.e., $[r^1, r^2, \\dots, r^K]$ , so that the instance could be accurately segmented with the minimal resource cost. Specifically, MSM takes the cropped region-wise RoI feature as input and outputs a probability vector $P = [p^1, \\dots, p^K]$ by taking a softmax operation. Each element of this vector represents the probability that the corresponding candidate resolution is selected:", + "bbox": [ + 75, + 515, + 470, + 710 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np ^ {k} = \\frac {\\exp \\left(f _ {M S M} ^ {k} (x)\\right)}{\\sum_ {k ^ {\\prime}} \\exp \\left(f _ {M S M} ^ {k ^ {\\prime}} (x)\\right)}, \\quad k \\in \\{1, \\dots , K \\}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 719, + 468, + 756 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $x$ is the input RoI feature fed to MSM. The candidate resolution of the largest probability is chosen as the switching state, which decides the resolution of mask grid to segment an object.", + "bbox": [ + 75, + 763, + 468, + 825 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Reparameterization with Gumbel-Softmax. The soft output $P$ of MSM should be transformed into a one-hot prediction, denoted by $Y = [y^{1},\\dots ,y^{K}]$ , $y^{k}\\in \\{0,1\\}$ . This process can be done by discrete sampling, which however is non-differentiable and does not support end-to-end training.", + "bbox": [ + 75, + 825, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To allow the gradient back-propagation for updating MSM, we introduce a reparameterization method [15], called the Gumbel-Softmax. Given a categorical distribution with class probabilities $P = [p^{1},\\dots ,p^{K}]$ , we can draw a group of masks through the rule $y =$ onehot $\\left(\\arg \\max_{k}(logp^{k} + g^{k})\\right)$ , where $\\{g^k\\}_{i = k}^K$ are i.i.d. samples drawn from the Gumbel(0,1) distribution, which is defined by $g = -\\log (-\\log (u))$ with $u\\sim \\text{Uniform}(0,1)$ . Then we use the Gumbel-softmax function as a continuous, differentiable approximation to the original softmax function:", + "bbox": [ + 496, + 90, + 893, + 258 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ny ^ {k} = \\frac {\\exp \\left(\\left(\\log p ^ {k} + g ^ {k}\\right) / \\tau\\right)}{\\sum_ {k ^ {\\prime}} \\exp \\left(\\left(\\log p ^ {k ^ {\\prime}} + g ^ {k ^ {\\prime}}\\right) / \\tau\\right)}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 268, + 890, + 308 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\tau$ denotes a temperature parameter. When $\\tau$ approaches 0, the Gumbel-softmax is close to one-hot.", + "bbox": [ + 496, + 316, + 890, + 348 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Objective Function", + "text_level": 1, + "bbox": [ + 498, + 358, + 683, + 375 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The proposed framework gradually enlarges the mask resolution by a factor of two to improve the segmentation performance. On the one hand, FAM adaptively aggregates complementary information from multiple stages of i-FPN and r-FPN to enhance the feature hierarchies. On the other hand, MSM dynamically allocates masks of different resolutions for different instances in an image, reducing resource costs without sacrificing accuracy. In this subsection, we elaborate on the loss function used to train the mask head.", + "bbox": [ + 496, + 382, + 890, + 531 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Mask Loss. Given a positive instance $x_{i}$ , we first predict its mask switching state $Y = [y^{1},\\dots ,y^{K}]$ by MSM, and obtain a group of mask prediction maps at $K$ different resolutions $\\{\\hat{m}_i^1,\\dots ,\\hat{m}_i^K\\}$ by passing this instance through different stages of r-FPN. We define the mask loss function as follows:", + "bbox": [ + 496, + 532, + 893, + 623 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {m a s k}} = \\sum_ {i = 1} ^ {N} \\sum_ {k = 1} ^ {K} y ^ {k} \\ell \\left(\\hat {m} _ {i} ^ {k}, m _ {i}\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 633, + 890, + 676 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\hat{m}_i^k$ denotes the $k$ -th mask prediction of $x_i$ , and $m_i$ represents its corresponding ground truth mask grid. $y^k$ is the indicator for whether the $k$ -th mask resolution is selected as the output resolution. $\\ell$ is defined as the binary cross-entropy loss in this paper.", + "bbox": [ + 496, + 686, + 890, + 763 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Edge Loss. In Eq. 3, we assume that the mask producing smaller loss should have higher quality, so that the most accurate mask could be selected by minimizing the mask loss. However, our empirical results show that the mask loss produced on different masks is very close, making it difficult to distinguish the mask quality. In comparison, as shown in Fig. 5, the edge loss produced by masks of different resolutions varies greatly, which could better reveal the mask quality. Given the output of MSM $Y = [y^{1},\\dots ,y^{K}]$", + "bbox": [ + 496, + 763, + 890, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "11282", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/be6e6f211d82e965e97da5142b5cc9cba3130d3ac20dfb002cffe881aafadbb1.jpg", + "image_caption": [ + "Figure 4. The Mask Switch Module (MSM), which is a CNN-based classifier and consists of a SE-block [11], two convolutional layers and two fully-connected layers." + ], + "image_footnote": [], + "bbox": [ + 130, + 99, + 834, + 205 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/2ac052ae07c5b19bf8f795b5182c206479c3969718c93cf6946b1b1e84219f71.jpg", + "image_caption": [ + "Figure 5. The predicted object edges using the masks of different resolutions. The edge loss computed on boundary regions could reflect the quality of mask." + ], + "image_footnote": [], + "bbox": [ + 117, + 251, + 429, + 359 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "and the edge maps of different resolutions, denoted by $\\{\\hat{e}_i^1,\\dots ,\\hat{e}_i^K\\}$ , the edge loss is defined as follows:", + "bbox": [ + 76, + 430, + 468, + 463 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {e d g e} = \\sum_ {i = 1} ^ {N} \\sum_ {k = 1} ^ {K} y ^ {k} \\ell \\left(\\hat {e} _ {i} ^ {k}, e _ {i}\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 477, + 468, + 518 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $e_i$ denotes the ground-truth edge, which is generated by first applying the Laplacian operator on the ground-truth mask $m_i$ to obtain a soft edge map, and then converting it into a binary edge map by thresholding [6]. Fig. 5 visualizes the object edges predicted by using masks of different resolutions. As can be seen, the edge loss could better reveal the quality of masks, i.e., higher-resolution masks produce edges closer to GT (smaller loss), while lower-resolution masks produce edges more different from GT (larger loss).", + "bbox": [ + 75, + 535, + 468, + 672 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Budget Constraint. By optimizing the edge loss in Eq. 4, the model tends to converge to a sub-optimal solution that all instances are segmented with the largest mask, i.e., $112 \\times 112$ , which incorporates more detailed information and hence has the minimal prediction loss. Actually, not all samples require the largest mask for segmentation. The redundant computations of segmenting the \"easy\" samples can be saved for efficiency. In order to reduce the computational cost and avoid the above mentioned sub-optimal solution, we propose to train the MSM with a budget constraint. Specifically, let $\\mathcal{C}$ denote the computational cost (e.g., FLOPs) corresponding to the selected mask resolution. We add a penalty to the model when the expectation of FLOPs computed on current batch data, denoted by $\\mathbb{E}(\\mathcal{C})$ , exceeds the target FLOPs, denoted by $\\mathcal{C}_t$ . The budget con", + "bbox": [ + 75, + 674, + 470, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "strain is defined as follows:", + "bbox": [ + 500, + 255, + 687, + 268 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {b u d g e t}} = \\max \\left(\\frac {\\mathbb {E} (\\mathcal {C})}{\\mathcal {C} _ {t}} - 1, 0\\right). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 280, + 890, + 313 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We further introduce an information entropy loss to balance the resolution predictions of MSM. Given a group of output probability vectors $P_{1}, P_{2}, \\dots, P_{N}$ , where $N$ is the number of instances of the current batch, the frequency of the $k$ -th resolution is calculated by: $f^{k} = \\frac{1}{N}\\sum_{i}p_{i}^{k}$ . Then the information entropy loss is defined as follows:", + "bbox": [ + 498, + 324, + 890, + 415 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {e n t r o p y}} = \\frac {1}{K} \\sum_ {k} f ^ {k} \\log f ^ {k}. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 598, + 428, + 890, + 464 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The above entropy loss tends to push each element $f^k$ to be $\\frac{1}{K}$ so that MSM could select different resolutions with similar probabilities.", + "bbox": [ + 498, + 478, + 890, + 523 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finally, the total objective function of the mask branch is obtained as follows:", + "bbox": [ + 498, + 525, + 890, + 555 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {\\text {m a s k}} + \\lambda_ {1} \\mathcal {L} _ {\\text {e d g e}} + \\lambda_ {2} \\mathcal {L} _ {\\text {r e g}}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 570, + 890, + 588 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\lambda_{1}$ and $\\lambda_{2}$ are the trade-off hyper-parameters. $\\mathcal{L}_{reg}$ denotes the regularization term which is obtained by combining the budget constraint in Eq. 5 and the information entropy loss in Eq. 6, i.e., $\\mathcal{L}_{reg} = \\mathcal{L}_{budget} + \\mathcal{L}_{entropy}$ .", + "bbox": [ + 498, + 599, + 890, + 662 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 676, + 633, + 695 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We perform extensive experiments on the benchmark instance segmentation datasets: COCO [21] and Cityscapes [7]. COCO [21] contains about 115k images (train2017) with instance-level annotations of 80 categories for training. We use the val2017 set (around 5k images) for the ablation study and the test-dev2017 set (about 20k images) for comparison with other methods. The Cityscapes dataset [7] contains 2975, 500, and 1525 images collected from 8 categories of urban scenes for training, validation, and testing, respectively. On both COCO and Cityscapes datasets, we use the standard mask AP as the evaluation metric, which computes the average precision over varying IoU thresholds (from 0.5 to 0.95).", + "bbox": [ + 496, + 704, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "11283", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/b9e5b9e3fd080b5c4bedf62d3e2b215354b24a55f150144ca00cebdeadd2b283.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 99, + 99, + 230, + 181 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/8625a4e7ec2055337dfbafa4b527333c3f10c18fec6e35d32db5b28aac33c9af.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 232, + 99, + 362, + 181 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/52c38f004f782417b85dfa9154621dd9b25865fbc0e5ccbddbea7220096a84da.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 362, + 99, + 493, + 181 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0432c9e88664b8d887225c73876329ba1fb0445cc7dfe66b127c7d0df0c9150a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 495, + 99, + 625, + 181 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/8d7eb519be6935e317be0ce286818f7c777750c3eece6685a7e335066e1043bc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 627, + 99, + 756, + 181 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/fce6755db42aa1817a10b704a932639b9962236a0e224bae0d51252e67df6f2c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 759, + 99, + 888, + 181 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/3386b64eff68f4cafbedcf7be316699a77f9360eaa7791913c7fcc57782cce29.jpg", + "image_caption": [ + "Figure 6. Example results of Mask R-CNN [10] (left), PointRend [17] (middle), and DynaMask (right), using ResNet-50-FPN as backbone." + ], + "image_footnote": [], + "bbox": [ + 99, + 186, + 230, + 267 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/1c56c9d89529b655375104a96b8225d767beea9ce9b701921f5f9dbcc9e083db.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 230, + 186, + 361, + 267 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e49251e4bd2e1b39e5cdb4747205c281a26d455987fe9d802997ca168a96e4a6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 362, + 186, + 493, + 267 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/7cd416729655ca19dc02a697cdd6d113cbf067d3983f3c53a655d61a9be5a9b0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 495, + 185, + 625, + 266 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/ebfddc63aa08d092f14818ea94a218311d62ec19c4c8e97111d996c447ebd72a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 627, + 185, + 756, + 266 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/6905a9d1f573026df2e082edf85d91d28ebde90f7da6aa8901683ca59a1de517.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 759, + 186, + 888, + 267 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Implementation Details", + "text_level": 1, + "bbox": [ + 76, + 310, + 294, + 325 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We adopt Mask R-CNN [10] as our baseline. The backbone is pre-trained on ImageNet. The hyper-parameters and loss functions are set the same as Mask R-CNN implemented in MMDetection [4] unless specified. The proposed MSM has four switching states, which correspond to four candidate resolutions, i.e., $[14 \\times 14, 28 \\times 28, 56 \\times 56, 112 \\times 112]$ . The hyper-parameter $\\lambda_{1}$ is set as 0.1. We first pretrain the model without MSM using mask loss at all resolutions for one epoch. The initial learning rate is 0.02, and the batch size is 16 on 8 GPUs. Then we train all modules for 12 epochs using SGD with the same initial learning rate and batch size and reduce the learning rate by a factor of 0.1 after 8 and 11 epochs, respectively. Multi-scale training is used with the shorter side randomly sampled from [640, 800], while for inference, the short side is resized to 800. In the ablation study, we use the standard $1 \\times$ training schedule and data augmentation defined in MMDetection [4].", + "bbox": [ + 75, + 333, + 473, + 604 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Main Results", + "text_level": 1, + "bbox": [ + 76, + 619, + 215, + 633 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparison with Mask R-CNN. We first compare the performance of DynaMask with the baseline Mask R-CNN on COCO by using ResNet-50 and ResNet-101 backbones. As shown in Tab. 2, our method outperforms Mask R-CNN by a large margin. The performance is improved by $2.9\\%$ AP and $2.8\\%$ AP with “ $1 \\times$ ” and “ $2 \\times$ ” schedules, respectively, when ResNet-50-FPN backbone is used. Particularly, DynaMask outperforms the baseline by $3.3\\%$ , and $3.6\\%$ with “ $1 \\times$ ” and “ $2 \\times$ ” schedules in terms of $\\mathrm{AP}_{75}$ , respectively. Similar observations can be obtained when ResNet-101-FPN is used as the backbone. This is because the proposed dual-level FPN structure incorporates complementary semantic and detailed information from multiple levels of FPN, resulting in more precise mask localization and higher-quality segmentation.", + "bbox": [ + 75, + 643, + 468, + 868 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparison with state-of-the-art methods. We then compare the segmentation performance of DynaMask with", + "bbox": [ + 75, + 869, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "many other state-of-the-art methods on COCO. The results are listed in Tab. 3. All models are trained on COCO train2017 and evaluated on COCO test-dev2017. Without bells and whistles, DynaMask surpasses these methods with visible margins. Furthermore, we compare our method with other representative two-stage IS methods on Cityscapes val set in Tab. 4. Our method outperforms Mask R-CNN [10] by $4.2\\%$ . Noticeably, its performance on large objects is $5.8\\%$ AP higher than Mask R-CNN. This is because DynaMask employs high-resolution masks to achieve high-quality segmentation on large and difficult objects. RefineMask [30] also produces outstanding performance since it refines the mask prediction with fine-grained features, but it costs many computations due to the multi-stage refinement.", + "bbox": [ + 496, + 310, + 892, + 536 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Visualizations of segmentation results. In Fig. 6, we visualize the segmentation results of DynaMask together with two representative methods: Mask R-CNN [10], and PointRend [17]. One can see that our method achieves finer and more accurate predictions around the objects' boundaries. This is because Dynamask introduces an r-FPN to fuse complementary information from multiple stages, so that difficult instances can be segmented with large masks which contain more fine-grained details. Mask R-CNN [10] employs a uniform coarse mask for prediction, while PointRend [17] makes point-wise refinement only at the blurred regions, which is not enough to capture sufficient details.", + "bbox": [ + 496, + 537, + 893, + 733 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 741, + 653, + 758 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Mask resolution prediction. To better understand how DynaMask selects suitable masks for different instances, we show the mask selection results in Fig. 7. As can be seen, the \"hard\" objects with irregular shapes and complex boundaries are assigned large masks, such as the \"potted plant\", \"person\", \"giraffe\", etc. On the contrary, the \"easy\" samples with regular shapes and less details are assigned small masks, such as the \"skis\", \"suitcase\", \"dining table\" and so on. It is worth mentioning that the choice of mask", + "bbox": [ + 496, + 763, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "11284", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/1d178b64cb5ffce4d57bd9078f03a1b38df17766a946850b45aec77ed6a8041a.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodBackboneSched.AP\\( AP_{50} \\)\\( AP_{75} \\)\\( AP_S \\)\\( AP_M \\)\\( AP_L \\)
Mask R-CNN [10]ResNet-50-FPN1×34.755.737.218.337.447.2
DynaMaskResNet-50-FPN1×37.657.440.520.740.450.3
Mask R-CNN [10]ResNet-50-FPN2×35.456.437.919.138.648.4
DynaMaskResNet-50-FPN2×38.258.141.520.540.852.7
Mask R-CNN [10]ResNet-101-FPN1×36.157.538.618.839.749.5
DynaMaskResNet-101-FPN1×38.758.841.820.941.852.4
Mask R-CNN [10]ResNet-101-FPN2×36.657.939.119.240.250.5
DynaMaskResNet-101-FPN2×39.059.142.220.942.153.3
", + "bbox": [ + 202, + 88, + 767, + 215 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/dd4aa37511c254ae234236839d62b8219c2f5e67c2914067398028fe4d1c0d03.jpg", + "table_caption": [ + "Table 2. Comparison with Mask R-CNN on COCO val2017." + ], + "table_footnote": [], + "table_body": "
MethodBackbonesched.AP\\( AP_{50} \\)\\( AP_{75} \\)\\( AP_S \\)\\( AP_M \\)\\( AP_L \\)
MEInst [31]ResNet-101-FPN3×33.956.235.419.836.142.3
Mask R-CNN [10]ResNet-101-FPN3×38.560.041.619.241.655.8
BMask R-CNN [6]ResNet-101-FPN1×37.759.340.616.839.954.6
TensorMask [5]ResNet-101-FPN6×37.159.339.417.439.151.6
Mask Scoring [14]ResNet-101-FPN18e38.358.841.517.840.454.4
ConDInst [26]ResNet-101-FPN3×39.160.942.021.541.750.9
BlendMask [2]ResNet-101-FPN3×38.460.741.318.241.553.3
PointRend [17]ResNeXt-101-FPN3×41.463.344.824.243.953.2
SOLOv2 [28]ResNet-101-FPN6×39.760.742.917.342.957.4
HTC [3]ResNet-101-FPN20e39.761.843.121.042.253.5
DCT-Mask†[25]ResNet-101-FPN3×40.161.243.622.742.751.8
RefineMask [30]ResNet-101-FPN3×39.4-----
Mask Transfiner†[16]ResNet-101-FPN3×40.7--23.142.853.8
QueryInst†[9]ResNet-101-FPN3×41.764.445.324.243.953.9
DynaMaskResNet-101-FPN3×39.661.442.921.242.453.2
DynaMask†ResNet-101-FPN3×41.362.545.222.843.454.0
DynaMask†ResNeXt-101-FPN3×42.062.946.323.444.054.8
", + "bbox": [ + 204, + 241, + 766, + 469 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Comparison with state-of-the-art methods for instance segmentation on COCO test-dev2017, † denotes multi-scale training.", + "bbox": [ + 76, + 472, + 890, + 487 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "size is independent of object size. For example, in the third image, the small but hard object \"potted plant\" is allocated a large mask, while the large but easy sample \"suitcase\" in the fifth image can be accurately segmented with a small mask. We provide quantitative analysis of the correlations between the predicted mask resolutions and the class in supplemental files.", + "bbox": [ + 75, + 501, + 470, + 606 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Influence of the budget constraint. In Tab. 5, we explore the influence of budget constraint on the model complexity (FLOPs). The average FLOPs are calculated by taking the average over all instances of the validation set. By tuning hyper-parameters $\\mathcal{C}_t$ and $\\lambda_2$ to different values, we get models of different computational costs. For example, the FLOPs are reduced by about $19\\%$ without sacrificing the segmentation performance by setting $\\mathcal{C}_t$ and $\\lambda_2$ to 1.0 and 0.4, respectively. This demonstrates that there exists much redundancy when using the large mask $(112 \\times 112)$ for all instances. Actually, many instances in COCO dataset can be efficiently segmented with smaller masks. Thus the redundant computation for easier samples can be reduced, while the accuracy of harder samples can be maintained by still using larger masks. By setting the target FLOPs $\\mathcal{C}_t$ to a smaller value (e.g., 0.4, 0.6, 0.8), more significant computation reduction can be achieved at a slight degradation of accuracy. For instance, by setting both $\\mathcal{C}_t$ and $\\lambda_2$ to 0.4, more than half of the FLOPs (around $54\\%$ ) are reduced while still", + "bbox": [ + 75, + 613, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "producing competitive segmentation results (36.8% AP).", + "bbox": [ + 496, + 501, + 872, + 516 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Speed comparison of different methods. To validate the efficiency of our model, we compare the model accuracy, FLOPs, and runtime of different two-stage IS methods in Tab. 6. Inference time is tested on one NVIDIA Titan RTX with the input size $800 \\times 1333$ . Compared to these methods, our DynaMask method achieves visible performance gain at a small amount of extra computational cost. Specifically, DynaMask $(\\mathcal{C}_t = 0.4)$ outperforms PointRend [17] and DCT-mask [25] by $1.2\\%$ AP and $0.3\\%$ AP, respectively, with comparable runtime. Though HTC [3] produces a similar segmentation result ( $0.2\\%$ lower AP) to DynaMask, it is two times slower than DynaMask because it performs hybrid cascade refinement on both detection and segmentation tasks, resulting in a large amount of memory and computation overhead.", + "bbox": [ + 496, + 518, + 890, + 744 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Influence of mask size. The Mask Switch Module (MSM) outputs four different candidate mask resolutions $[14 \\times 14, 28 \\times 28, 56 \\times 56, 112 \\times 112]$ . We choose one of them as the uniform output mask size and report the corresponding results in Tab. 7. As can be seen, models with larger mask resolutions could achieve higher segmentation performance, especially on large objects, but the computational cost also increases obviously. For example, the performance is improved by $3.2\\%$ , $4.2\\%$ , and $4.7\\%$ AP when the mask resolution is increased from $14 \\times 14$ to $28 \\times 28$ , $56 \\times 56$", + "bbox": [ + 496, + 750, + 892, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "11285", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7514bf444671cdbc4c22c023fa90b3edb1f436b3b15aa981d6c60b55dc269adc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 88, + 277, + 191 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/aa4c5fd8720176105b12bf4676a822b12fc42d82fd8e9f4581cefeb3176a86b5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 282, + 88, + 480, + 191 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9330e594aff21872f60c8c68d5501a5e7478d0eef8442f14255e5930f3be5b72.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 488, + 88, + 687, + 191 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/daf1f139fbb42a00f8172e813da7853924f9b11734b95667018c9674e1d4a5dd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 694, + 88, + 890, + 191 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d07a7ffb3fcb8d532d4511f20cd576c76921efc08bc25fc02322e798d8d6b541.jpg", + "image_caption": [ + "Figure 7. Mask selection results by DynaMask. Each color corresponds to a candidate resolution (red $\\rightarrow$ large, blue $\\rightarrow$ medium, green $\\rightarrow$ small, yellow $\\rightarrow$ tiny)." + ], + "image_footnote": [], + "bbox": [ + 78, + 193, + 277, + 297 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/72962a20700d150f9f54bf1f18fd2c2e06d99ccb16262c7a5ff47ac6d01a7358.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 282, + 193, + 480, + 297 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d35deea7549de6b96be10608a037c940d2d3358bee8af28347e232ed9a979b81.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 488, + 193, + 687, + 297 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/894c99410100a652210e9bff0d3e05a7881727871c31b372fcb2e5c7cc3f638f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 694, + 193, + 890, + 297 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/5d76936bd4e6e6fc2dfcb5ee1beac5a38616756f333d355ebd0e4b4bae1cbf5e.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodAPAPsAPMAPL
Mask R-CNN [10]33.812.031.551.8
PointRend [17]35.8---
BMask R-CNN [6]35.8---
RefineMask [30]37.614.634.058.1
DynaMask38.014.835.157.6
", + "bbox": [ + 81, + 329, + 372, + 411 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/aa13f96f2b94ce4cf96574424883d27f8af3c0701aa223805c3d6c9a50628e07.jpg", + "table_caption": [ + "Table 4. The results on Cityscapes val set with ResNet-50-FPN backbone." + ], + "table_footnote": [], + "table_body": "
Ctλ2FLOPsΔAP
1.00.31.27G-9%37.6
1.00.41.13G-19%37.6
1.00.51.06G-24%37.5
0.80.40.92G-34%37.4
0.60.40.83G-41%37.2
0.40.40.64G-54%36.8
", + "bbox": [ + 395, + 327, + 575, + 414 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/1d74413bb367227e99500e811661b398bc90942b1aa09572a27a35b6907fab46.jpg", + "table_caption": [ + "Table 5. The influence of the budget constraint." + ], + "table_footnote": [], + "table_body": "
MethodAPFLOPsFPS
Mask R-CNN [10]34.70.5G12.4
PointRend [17]35.60.9G9.4
DCT-Mask†[25]36.50.5G11.8
HTC [3]37.4-3.9
DynaMask37.61.4G8.3
DynaMask (Ct=0.4)36.80.64G11.2
", + "bbox": [ + 622, + 327, + 870, + 414 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/2439245b38b1194b4e3e6a8a64bb83e156b3c45e0769aee6b381d144d05c052c.jpg", + "table_caption": [ + "Table 6. Speed comparison of different methods on val set, †: multi-scale training." + ], + "table_footnote": [], + "table_body": "
Mask SizeFLOPsAP\\( {\\mathrm{{AP}}}_{50} \\)\\( {\\mathrm{{AP}}}_{75} \\)\\( {\\mathrm{{AP}}}_{\\mathrm{S}} \\)\\( {\\mathrm{{AP}}}_{\\mathrm{M}} \\)\\( {\\mathrm{{AP}}}_{\\mathrm{L}} \\)
\\( {14} \\times {14} \\)0.23G32.955.334.419.335.843.6
\\( {28} \\times {28} \\)0.62G36.157.138.720.439.248.2
\\( {56} \\times {56} \\)1.01G37.157.340.020.540.049.7
\\( {112} \\times {112} \\)1.40G37.657.440.520.740.450.3
", + "bbox": [ + 99, + 455, + 460, + 521 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "and $112 \\times 112$ , respectively. Nevertheless, the performance tends to saturate as the mask size increases further.", + "bbox": [ + 75, + 550, + 468, + 579 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Size-based mask selection method. We compare the performance and mask distributions of different mask selection methods in Tab. 8. The baseline is performed by using a uniform mask size $(28 \\times 28)$ for all objects. Size-based method denotes assigning masks according to the size of object. Specifically, we assign a mask $\\hat{m}_i^k$ to the instance of width $w$ and height $h$ by the following rule:", + "bbox": [ + 75, + 579, + 468, + 678 + ], + "page_idx": 7 + }, + { + "type": "equation", + "text": "\n$$\nk = \\left\\lfloor k _ {0} + \\log_ {2} \\left(\\sqrt {w h} / \\sqrt {w _ {0} h _ {0}}\\right) \\right\\rfloor , \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 165, + 688, + 468, + 712 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "where $w_{0}$ and $h_0$ denote the width and height of the input image, respectively. and $k_{0}$ denotes the index of the highest mask resolution $112 \\times 112$ , i.e., $k_{0} = 4$ . Intuitively, Eq. 8 means that the larger object will be assigned a higher-resolution mask. This conforms to our common sense, since the larger objects usually contain many details which need finer-grained masks to achieve high-quality prediction.", + "bbox": [ + 75, + 719, + 468, + 824 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "As can be seen from Tab. 8, the size-based method attains comparable performance with the baseline at a lower cost. Our DynaMask $(\\mathcal{C}_t = 0.4)$ outperforms the baseline by $0.7\\%$ AP and the size-based method by $0.9\\%$ AP at a slight extra computation cost, demonstrating that the", + "bbox": [ + 75, + 825, + 468, + 901 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/def46a5f8a630fffb58178609a8b0aeb3e59e63d4b79f30fd52b38f6ccb52d19.jpg", + "table_caption": [ + "Table 7. Performance of using different mask sizes." + ], + "table_footnote": [], + "table_body": "
Mask SizeFLOPsAPTinySmallMediumLarge
28×280.62G36.10100
Size-based0.56G35.947%32%14%8%
DynaMask (Ct=0.4)0.64G36.835%34%21%10%
DynaMask1.4G37.60001
", + "bbox": [ + 514, + 455, + 877, + 521 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 8. Comparison with size-based mask selection method.", + "bbox": [ + 514, + 521, + 877, + 534 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "proposed mask selection strategy could better partition different objects according to their segmentation difficulties and assign more suitable masks to achieve better performance. More analyses about the distribution of predicted mask scales can be found in supplemental materials.", + "bbox": [ + 498, + 550, + 890, + 627 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 638, + 617, + 652 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we proposed a simple yet effective method to improve instance segmentation performance at a small amount of computation and memory overhead. We devised a dual-level FPN structure for better exploring complementary contextual and detailed information from multiple pyramid levels. Specifically, in addition to traditional image-level FPN (i-FPN), we augmented a region-level top-down path (r-FPN) to gradually enlarge the mask size and incorporate more details from i-FPN. Furthermore, to reduce the computation and memory cost led by using large masks, we introduced a Mask Switch Module (MSM) to adaptively select suitable masks for each proposal so that the redundant computation for easy samples can be reduced by using smaller masks. Extensive experimental results demonstrated that our method achieved significant performance gains with moderate extra computation overhead.", + "bbox": [ + 496, + 657, + 892, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "11286", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Daniel Bolya, Chong Zhou, Fanyi Xiao, and Yong Jae Lee. Yolact: Real-time instance segmentation. In Proceedings of the IEEE/CVF international conference on computer vision, pages 9157-9166, 2019. 1", + "[2] Hao Chen, Kunyang Sun, Zhi Tian, Chunhua Shen, Yongming Huang, and Youliang Yan. Blendmask: Top-down meets bottom-up for instance segmentation. 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Advances in Neural Information Processing Systems, 34, 2021. 3" + ], + "bbox": [ + 78, + 90, + 467, + 457 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "11288", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/DynaMask_ Dynamic Mask Selection for Instance Segmentation/6de3482f-3d80-4aaa-a48e-484855bf3aa9_model.json b/2023/DynaMask_ Dynamic Mask Selection for Instance Segmentation/6de3482f-3d80-4aaa-a48e-484855bf3aa9_model.json new file mode 100644 index 0000000000000000000000000000000000000000..ed615e9501d8f8f8bfcb89328ce7696e0c20dec4 --- /dev/null +++ b/2023/DynaMask_ Dynamic Mask Selection for Instance Segmentation/6de3482f-3d80-4aaa-a48e-484855bf3aa9_model.json @@ -0,0 +1,1991 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.163, + 0.131, + 0.808, + 0.154 + ], + "angle": 0, + "content": "DynaMask: Dynamic Mask Selection for Instance Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.207, + 0.181, + 0.768, + 0.218 + ], + "angle": 0, + "content": "Ruihuang Li,\\* Chenhang He,\\* Shuai Li, Yabin Zhang, Lei Zhang† The Hong Kong Polytechnic University" + }, + { + "type": "text", + "bbox": [ + 0.294, + 0.22, + 0.673, + 0.234 + ], + "angle": 0, + "content": "{csrhli, csche, cslzhang}@comp.polyu.edu.hk" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.301, + 0.474, + 0.664 + ], + "angle": 0, + "content": "The representative instance segmentation methods mostly segment different object instances with a mask of the fixed resolution, e.g., \\(28 \\times 28\\) grid. However, a low-resolution mask loses rich details, while a high-resolution mask incurs quadratic computation overhead. It is a challenging task to predict the optimal binary mask for each instance. In this paper, we propose to dynamically select suitable masks for different object proposals. First, a dual-level Feature Pyramid Network (FPN) with adaptive feature aggregation is developed to gradually increase the mask grid resolution, ensuring high-quality segmentation of objects. Specifically, an efficient region-level top-down path (r-FPN) is introduced to incorporate complementary contextual and detailed information from different stages of image-level FPN (i-FPN). Then, to alleviate the increase of computation and memory costs caused by using large masks, we develop a Mask Switch Module (MSM) with negligible computational cost to select the most suitable mask resolution for each instance, achieving high efficiency while maintaining high segmentation accuracy. Without bells and whistles, the proposed method, namely DynaMask, brings consistent and noticeable performance improvements over other state-of-the-arts at a moderate computation overhead. The source code: https://github.com/lslrh/DynaMask." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.691, + 0.21, + 0.707 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.716, + 0.47, + 0.868 + ], + "angle": 0, + "content": "Instance segmentation (IS) is an important computer vision task, aiming at simultaneously predicting the class label and the binary mask for each instance of interest in an image. It works as the cornerstone of many downstream vision applications, such as autonomous driving, video surveillance, and robotics, to name a few. Recent years have witnessed the significant advances of deep convolutional neural networks (CNNs) based IS methods with a rich amount of training data as the rocket fuel [1, 10, 17, 25, 26]. Existing IS methods can be roughly divided into two ma" + }, + { + "type": "image", + "bbox": [ + 0.534, + 0.268, + 0.86, + 0.449 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.455, + 0.892, + 0.497 + ], + "angle": 0, + "content": "Figure 1. Dynamic mask selection results. Some \"hard\" samples with irregular shapes like \"person\" are assigned larger masks, while the \"easy\" ones like \"frisbee\" are assigned smaller ones." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.506, + 0.893, + 0.627 + ], + "angle": 0, + "content": "jor categories: two-stage [6, 10, 17] and single-stage methods [1, 2, 26]. The former first detect a sparse set of proposals and then performs mask predictions based on them, while the latter directly predict classification scores and masks based on the pre-defined anchors. Generally speaking, two-stage methods could produce higher segmentation accuracy but cost more computational resources than single-stage methods." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.628, + 0.895, + 0.885 + ], + "angle": 0, + "content": "Among the many recently developed IS methods, the proposal-based two-stage methods [6, 10, 17], which follow a detection-and-segmentation paradigm, are still the top performers. These methods need to predict a binary grid mask of uniform resolution for all proposals, e.g., \\(28 \\times 28\\), and then upsample it to the original image size. For instance, Mask R-CNN [10] first generates a group of proposals with an object detector and then performs per pixel foreground/background segmentation on the Regions of Interest (RoIs) [24]. Despite achieving promising performance, the low-resolution mask of Mask R-CNN is insufficient to capture more detailed information, resulting in unsatisfactory predictions, especially over object boundaries. An intuitive solution to improve the segmentation quality is to adopt a larger mask. Nevertheless, high-resolution masks often generate excessive predictions on the smooth regions, resulting in high computational complexity." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "It is difficult to segment different objects in an image" + }, + { + "type": "page_footnote", + "bbox": [ + 0.077, + 0.875, + 0.468, + 0.901 + ], + "angle": 0, + "content": "*denotes the equal contribution, †denotes the corresponding author. This work is supported by the Hong Kong RGC RIF grant (R5001-18)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11279" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.454 + ], + "angle": 0, + "content": "with masks of the same resolution. Objects with irregular shapes and complicated boundaries demand more fine-grained masks to predict, referred to as \"hard\" samples, such as the \"person\" in Fig. 1. In comparison, the \"easy\" samples with regular shapes and fewer details can be efficiently segmented using coarser masks, like the \"frisbee\" in Fig. 1. Inspired by the above observations, we propose to adaptively adjust the mask size for each instance for better IS performance. Specifically, instead of using a uniform resolution for all instances, we assign high-resolution masks to \"hard\" objects and low-resolution masks to \"easy\" objects. In this way, the redundant computation for \"easy\" samples can be reduced while the accuracy of \"hard\" samples can be improved, achieving a balance between accuracy and speed. As shown in Tab. 1, however, directly predicting a high-resolution mask by Mask R-CNN [10] unexpectedly degrades the mask average precision (AP). This attributes to two main reasons. First, the RoI features of larger objects are extracted from higher pyramid levels, which are very coarse due to the downsampling operations [20]. Thus simply increasing the mask size of these RoIs will not bring extra useful information. Second, the mask head of Mask R-CNN is oversimplified, so it cannot make more precise predictions as the mask grid size increases." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.455, + 0.473, + 0.681 + ], + "angle": 0, + "content": "To overcome the above mentioned problems, we propose a dual-level FPN framework to gradually enlarge the mask grid. Specifically, in addition to traditional image-level FPN (i-FPN), a region-level FPN (r-FPN) is designed to achieve coarse-to-fine mask prediction. Wherein we construct information flows between i-FPN and r-FPN at different pyramid levels, aiming to incorporate complementary contextual and detailed information from multiple feature levels for high-quality segmentation. With the dual-level FPN, we present a data-dependent Mask Switch Module (MSM) with negligible computational cost to adaptively select masks for each instance. The overall approach, namely DynaMask, is evaluated on benchmark instance segmentation datasets to demonstrate its superiority over state-of-the-arts. The major contributions of this work are summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.094, + 0.689, + 0.47, + 0.765 + ], + "angle": 0, + "content": "- A dynamic mask selection method (DynaMask) is proposed to adaptively assign appropriate masks to different instances. Specifically, it assigns low-resolution masks to \"easy\" samples for efficiency while assigning high-resolution masks to \"hard\" samples for accuracy." + }, + { + "type": "text", + "bbox": [ + 0.094, + 0.767, + 0.47, + 0.829 + ], + "angle": 0, + "content": "- A dual-level FPN framework is developed for IS. We construct direct information flows from i-FPN to r-FPN at multiple levels, facilitating complementary information aggregation from multiple pyramid levels." + }, + { + "type": "text", + "bbox": [ + 0.094, + 0.83, + 0.47, + 0.892 + ], + "angle": 0, + "content": "- Extensive experiments demonstrate that DynaMask achieves a good trade-off between IS accuracy and efficiency, outperforming many state-of-the-art two-stage IS methods at a moderate computation overhead." + }, + { + "type": "list", + "bbox": [ + 0.094, + 0.689, + 0.47, + 0.892 + ], + "angle": 0, + "content": null + }, + { + "type": "table", + "bbox": [ + 0.541, + 0.089, + 0.858, + 0.226 + ], + "angle": 0, + "content": "
MethodResolutionAPFLOPs
Mask R-CNN [10]14×1432.90.2G
28×2834.70.5G
56×5633.82.0G
112×11232.58.0G
DynaMask14×1432.90.2G
28×2836.10.6G
56×5637.11.0G
112×11237.61.4G
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.234, + 0.892, + 0.292 + ], + "angle": 0, + "content": "Table 1. Mask AP and FLOPs with different mask resolutions. For Mask R-CNN, directly increasing the mask resolution will decrease the mask AP. While for our DynaMask, higher mask resolution results in better performance." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.309, + 0.642, + 0.325 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.337, + 0.892, + 0.579 + ], + "angle": 0, + "content": "Instance Segmentation. To date, most of the top-performing IS methods still follow the Mask R-CNN metaarchitecture [10]. These proposal-based approaches typically employ an object detector to localize each instance in bounding boxes. Then the instance-wise features are cropped and extracted from FPN features based on the detected bounding boxes by using RoI pooling/align [10, 24]. Finally, a compact segmentation head is deployed to obtain the desired object masks. Mask Scoring R-CNN [14] aligns the mask quality and score by using a branch to explicitly learn the quality of predicted masks. BMask R-CNN [6] leverages boundary details to improve mask localization ability. DCT-Mask [25] encodes high-resolution binary masks into compact vectors through the discrete cosine transform (DCT). PANet [22] constructs two feature pyramids for improving mask prediction." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.581, + 0.892, + 0.824 + ], + "angle": 0, + "content": "Some works [3, 17, 30] have been proposed to improve the mask quality by coarse-to-fine refinement. HTC [3] performs cascaded refinement on both detection and segmentation tasks and explores the reciprocal relationships between them. PointRend [17] and RefineMask [30] extract fine-grained features in a multi-stage manner. The former performs point-based predictions over the blurred areas, while the latter refines the entire RoI feature. Despite the promising segmentation results, multiple refinement stages inevitably increase the inference time and memory burden. In this paper, we dynamically select the suitable mask for each instance so that \"easy\" samples are assigned small masks (with fewer refinement stages) for efficiency, and \"hard\" samples are assigned large masks (with more refinement stages) for accuracy, achieving a balance between efficiency and accuracy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Dynamic Networks. Dynamic networks, which aim to adaptively adjust the network architecture according to the input feature, have been widely studied in recent years. Dynamic model compression methods either drop blocks [12, 23, 27] or prune channels [19, 29] for speeding" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11280" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.12, + 0.092, + 0.852, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.29, + 0.892, + 0.377 + ], + "angle": 0, + "content": "Figure 2. The overall architecture of DynaMask. We propose a dual-level FPN framework to gradually increase the mask size and achieve higher-quality IS. The information flow is constructed between each level of image-level FPN (i-FPN) and region-level FPN (r-FPN), so that region-wise feature hierarchies \\(\\{L_{tiny}, L_{small}, L_{medium}, L_{large}\\}\\) are constantly enhanced by incorporating complementary information from \\(\\{P2, P3, P4\\}\\) of i-FPN, resulting in coarse-to-fine mask predictions. To reduce the computation and memory cost, a Mask Switch Module (MSM) is developed to predict the mask resolution for each instance with budgeted resource consumption. Specifically, MSM outputs four different switching states, corresponding to four different mask resolutions, i.e., \\([14 \\times 14, 28 \\times 28, 56 \\times 56, 112 \\times 112]\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.388, + 0.469, + 0.508 + ], + "angle": 0, + "content": "up the inference. For instance, SkipNet [27] skips convolutional blocks through a reinforcement learning-based gating network. Huang et al. propose a multi-scale dense network with multiple classifiers for allocating different computations for \"easy\" and \"hard\" samples. Li et al. [18] adopt an end-to-end dynamic routing framework to alleviate the scale variance among inputs. DRNet [32] attempts to reduce the redundancy on the input resolution of modern CNNs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.509, + 0.469, + 0.676 + ], + "angle": 0, + "content": "However, employing dynamic masks at different resolutions for segmenting different instances has rarely been explored in the field of IS. Conventional methods [6, 10, 17] typically predict a fixed-size mask irrespective of the object type. This is sufficient for \"easy\" samples but produces over-smoothing predictions for \"hard\" samples over the fine-level details. In order to improve the segmentation performance without introducing many additional computation burdens, we devise a dynamic mask selection framework to adaptively allocate suitable masks to different objects according to their segmentation difficulties." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.69, + 0.308, + 0.707 + ], + "angle": 0, + "content": "3. Dynamic Mask Selection" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.715, + 0.469, + 0.837 + ], + "angle": 0, + "content": "The framework of DynaMask is illustrated in Fig. 2. A dual-level FPN architecture is first proposed for improving IS quality, and then a Mask Switch Module (MSM) is developed to dynamically allocate appropriate masks to each instance, so that the resource consumption can be reduced while maintaining superior IS performance. Our DynaMask produces high-quality segmentation with a moderate computation overhead." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.847, + 0.238, + 0.862 + ], + "angle": 0, + "content": "3.1. Dual-Level FPN" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Original image-level FPN (i-FPN) [20] introduces a top-down path to propagate contextual semantic information" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.388, + 0.892, + 0.525 + ], + "angle": 0, + "content": "from higher layers to lower ones. Actually, the lower-level features contain more fine-grained details than higher-level ones, which are beneficial for high-quality segmentation, especially on boundary regions, but these information is not fully explored in Mask R-CNN [10]. In this work, we propose a region-level FPN (r-FPN) to integrate more detailed information from lower layers of i-FPN into region-wise feature hierarchies. The information flows from each level of i-FPN to r-FPN are shown in Fig. 2." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.531, + 0.893, + 0.713 + ], + "angle": 0, + "content": "Region-Level FPN. We follow the original i-FPN to define the layers producing feature maps of the same resolution as one network stage corresponding to one feature level. We use \\(\\{P_2, P_3, P_4, P_5\\}\\) to denote different feature levels of i-FPN. The r-FPN starts from an RoI-Aligned region-wise feature, and it is gradually enhanced by fusing the complementary information from \\(\\{P_2, P_3, P_4\\}\\) of i-FPN, resulting in top-down region-based feature hierarchies, denoted by \\(\\{L_{tiny}, L_{small}, L_{medium}, L_{large}\\}\\). From \\(L_{tiny}\\) to \\(L_{large}\\), the spatial resolution is progressively increased by a factor of two. We design a Feature Aggregation Module (FAM) to integrate the r-FPN feature \\(L_r\\) and the i-FPN feature \\(P_i\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Feature Aggregation Module (FAM). There exists spatial misalignments between \\( L_{r} \\) and \\( P_{i} \\) due to the upsampling and RoI pooling [24] operations, which may degrade the segmentation performance on boundary areas. To overcome this limitation, we propose the FAM to adaptively aggregate multi-scale features. As show in Fig. 3, FAM contains two deformable convolutions [8, 13] which play different roles. The first one (Deform_Conv1) adjusts the positions of \\( L_{r} \\), making it better aligned to \\( P_{i} \\). Here we first concatenate \\( L_{r} \\) with \\( P_{i} \\), and then pass the concatenated features through a \\( 3 \\times 3 \\) Conv to obtain the offset map, denoted by \\( \\Delta_{o} \\). Finally, \\( L_{r} \\) is aligned to \\( P_{i} \\) with the learned offset \\( \\Delta_{o} \\). The" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "11281" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.091, + 0.088, + 0.458, + 0.198 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.208, + 0.471, + 0.264 + ], + "angle": 0, + "content": "Figure 3. Feature Alignment Molecule (FAM). Deform_Conv1 adjusts the spatial positions of upsampled r-FPN feature \\( L_{r} \\) and the cropped i-FPN feature \\( P_{i} \\). Deform_Conv2 attends to the salient parts of objects." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.272, + 0.471, + 0.334 + ], + "angle": 0, + "content": "second one (Deform_Conv2) works like an attention mechanism, which attends to the salient parts of objects. The proposed FAM is plugged into different stages of r-FPN and it plays a key role in improving the mask prediction." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.342, + 0.338, + 0.358 + ], + "angle": 0, + "content": "3.2. Mask Switch Module (MSM)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.365, + 0.47, + 0.516 + ], + "angle": 0, + "content": "The proposed dual-level FPN framework brings a significant performance improvement but at the price of expensive computation and memory burdens. Inspired by the fact that different instances require different mask grids to achieve accurate segmentation, we propose a novel method to adaptively adjust the mask grid resolution for different instances. Specifically, an MSM is developed to perform mask resolution prediction under a budgeted computation consumption, achieving a good trade-off between segmentation accuracy and efficiency." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.516, + 0.471, + 0.712 + ], + "angle": 0, + "content": "Optimal Mask Assignment. The MSM module is actually a lightweight classifier, denoted by \\( f_{MSM}(\\cdot) \\), which is illustrated in Fig. 4. It contains a channel-wise attention module [11], followed by a few convolutional layers and fully-connected layers. This classifier aims to find the optimal mask resolution from a collection of \\( K \\) candidates, i.e., \\( [r^1, r^2, \\dots, r^K] \\), so that the instance could be accurately segmented with the minimal resource cost. Specifically, MSM takes the cropped region-wise RoI feature as input and outputs a probability vector \\( P = [p^1, \\dots, p^K] \\) by taking a softmax operation. Each element of this vector represents the probability that the corresponding candidate resolution is selected:" + }, + { + "type": "equation", + "bbox": [ + 0.103, + 0.72, + 0.47, + 0.757 + ], + "angle": 0, + "content": "\\[\np ^ {k} = \\frac {\\exp \\left(f _ {M S M} ^ {k} (x)\\right)}{\\sum_ {k ^ {\\prime}} \\exp \\left(f _ {M S M} ^ {k ^ {\\prime}} (x)\\right)}, \\quad k \\in \\{1, \\dots , K \\}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.469, + 0.826 + ], + "angle": 0, + "content": "where \\( x \\) is the input RoI feature fed to MSM. The candidate resolution of the largest probability is chosen as the switching state, which decides the resolution of mask grid to segment an object." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Reparameterization with Gumbel-Softmax. The soft output \\( P \\) of MSM should be transformed into a one-hot prediction, denoted by \\( Y = [y^{1},\\dots ,y^{K}] \\), \\( y^{k}\\in \\{0,1\\} \\). This process can be done by discrete sampling, which however is non-differentiable and does not support end-to-end training." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.26 + ], + "angle": 0, + "content": "To allow the gradient back-propagation for updating MSM, we introduce a reparameterization method [15], called the Gumbel-Softmax. Given a categorical distribution with class probabilities \\( P = [p^{1},\\dots ,p^{K}] \\), we can draw a group of masks through the rule \\( y = \\) onehot \\( \\left(\\arg \\max_{k}(logp^{k} + g^{k})\\right) \\), where \\( \\{g^k\\}_{i = k}^K \\) are i.i.d. samples drawn from the Gumbel(0,1) distribution, which is defined by \\( g = -\\log (-\\log (u)) \\) with \\( u\\sim \\text{Uniform}(0,1) \\). Then we use the Gumbel-softmax function as a continuous, differentiable approximation to the original softmax function:" + }, + { + "type": "equation", + "bbox": [ + 0.575, + 0.27, + 0.892, + 0.309 + ], + "angle": 0, + "content": "\\[\ny ^ {k} = \\frac {\\exp \\left(\\left(\\log p ^ {k} + g ^ {k}\\right) / \\tau\\right)}{\\sum_ {k ^ {\\prime}} \\exp \\left(\\left(\\log p ^ {k ^ {\\prime}} + g ^ {k ^ {\\prime}}\\right) / \\tau\\right)}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.318, + 0.892, + 0.349 + ], + "angle": 0, + "content": "where \\(\\tau\\) denotes a temperature parameter. When \\(\\tau\\) approaches 0, the Gumbel-softmax is close to one-hot." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.359, + 0.684, + 0.375 + ], + "angle": 0, + "content": "3.3. Objective Function" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.383, + 0.892, + 0.532 + ], + "angle": 0, + "content": "The proposed framework gradually enlarges the mask resolution by a factor of two to improve the segmentation performance. On the one hand, FAM adaptively aggregates complementary information from multiple stages of i-FPN and r-FPN to enhance the feature hierarchies. On the other hand, MSM dynamically allocates masks of different resolutions for different instances in an image, reducing resource costs without sacrificing accuracy. In this subsection, we elaborate on the loss function used to train the mask head." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.534, + 0.894, + 0.624 + ], + "angle": 0, + "content": "Mask Loss. Given a positive instance \\( x_{i} \\), we first predict its mask switching state \\( Y = [y^{1},\\dots ,y^{K}] \\) by MSM, and obtain a group of mask prediction maps at \\( K \\) different resolutions \\( \\{\\hat{m}_i^1,\\dots ,\\hat{m}_i^K\\} \\) by passing this instance through different stages of r-FPN. We define the mask loss function as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.588, + 0.634, + 0.892, + 0.677 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {m a s k}} = \\sum_ {i = 1} ^ {N} \\sum_ {k = 1} ^ {K} y ^ {k} \\ell \\left(\\hat {m} _ {i} ^ {k}, m _ {i}\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.688, + 0.892, + 0.765 + ], + "angle": 0, + "content": "where \\(\\hat{m}_i^k\\) denotes the \\(k\\)-th mask prediction of \\(x_i\\), and \\(m_i\\) represents its corresponding ground truth mask grid. \\(y^k\\) is the indicator for whether the \\(k\\)-th mask resolution is selected as the output resolution. \\(\\ell\\) is defined as the binary cross-entropy loss in this paper." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Edge Loss. In Eq. 3, we assume that the mask producing smaller loss should have higher quality, so that the most accurate mask could be selected by minimizing the mask loss. However, our empirical results show that the mask loss produced on different masks is very close, making it difficult to distinguish the mask quality. In comparison, as shown in Fig. 5, the edge loss produced by masks of different resolutions varies greatly, which could better reveal the mask quality. Given the output of MSM \\( Y = [y^{1},\\dots ,y^{K}] \\)" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11282" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.131, + 0.1, + 0.835, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.207, + 0.895, + 0.237 + ], + "angle": 0, + "content": "Figure 4. The Mask Switch Module (MSM), which is a CNN-based classifier and consists of a SE-block [11], two convolutional layers and two fully-connected layers." + }, + { + "type": "image", + "bbox": [ + 0.118, + 0.252, + 0.431, + 0.36 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.363, + 0.471, + 0.406 + ], + "angle": 0, + "content": "Figure 5. The predicted object edges using the masks of different resolutions. The edge loss computed on boundary regions could reflect the quality of mask." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.431, + 0.47, + 0.464 + ], + "angle": 0, + "content": "and the edge maps of different resolutions, denoted by \\(\\{\\hat{e}_i^1,\\dots ,\\hat{e}_i^K\\}\\), the edge loss is defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.176, + 0.478, + 0.47, + 0.52 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {e d g e} = \\sum_ {i = 1} ^ {N} \\sum_ {k = 1} ^ {K} y ^ {k} \\ell \\left(\\hat {e} _ {i} ^ {k}, e _ {i}\\right), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.536, + 0.47, + 0.673 + ], + "angle": 0, + "content": "where \\( e_i \\) denotes the ground-truth edge, which is generated by first applying the Laplacian operator on the ground-truth mask \\( m_i \\) to obtain a soft edge map, and then converting it into a binary edge map by thresholding [6]. Fig. 5 visualizes the object edges predicted by using masks of different resolutions. As can be seen, the edge loss could better reveal the quality of masks, i.e., higher-resolution masks produce edges closer to GT (smaller loss), while lower-resolution masks produce edges more different from GT (larger loss)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.675, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Budget Constraint. By optimizing the edge loss in Eq. 4, the model tends to converge to a sub-optimal solution that all instances are segmented with the largest mask, i.e., \\(112 \\times 112\\), which incorporates more detailed information and hence has the minimal prediction loss. Actually, not all samples require the largest mask for segmentation. The redundant computations of segmenting the \"easy\" samples can be saved for efficiency. In order to reduce the computational cost and avoid the above mentioned sub-optimal solution, we propose to train the MSM with a budget constraint. Specifically, let \\(\\mathcal{C}\\) denote the computational cost (e.g., FLOPs) corresponding to the selected mask resolution. We add a penalty to the model when the expectation of FLOPs computed on current batch data, denoted by \\(\\mathbb{E}(\\mathcal{C})\\), exceeds the target FLOPs, denoted by \\(\\mathcal{C}_t\\). The budget con" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.256, + 0.688, + 0.27 + ], + "angle": 0, + "content": "strain is defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.595, + 0.281, + 0.892, + 0.314 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {b u d g e t}} = \\max \\left(\\frac {\\mathbb {E} (\\mathcal {C})}{\\mathcal {C} _ {t}} - 1, 0\\right). \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.325, + 0.892, + 0.416 + ], + "angle": 0, + "content": "We further introduce an information entropy loss to balance the resolution predictions of MSM. Given a group of output probability vectors \\( P_{1}, P_{2}, \\dots, P_{N} \\), where \\( N \\) is the number of instances of the current batch, the frequency of the \\( k \\)-th resolution is calculated by: \\( f^{k} = \\frac{1}{N}\\sum_{i}p_{i}^{k} \\). Then the information entropy loss is defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.599, + 0.429, + 0.892, + 0.465 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {e n t r o p y}} = \\frac {1}{K} \\sum_ {k} f ^ {k} \\log f ^ {k}. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.479, + 0.892, + 0.525 + ], + "angle": 0, + "content": "The above entropy loss tends to push each element \\( f^k \\) to be \\( \\frac{1}{K} \\) so that MSM could select different resolutions with similar probabilities." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.526, + 0.892, + 0.556 + ], + "angle": 0, + "content": "Finally, the total objective function of the mask branch is obtained as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.567, + 0.571, + 0.891, + 0.589 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {\\text {m a s k}} + \\lambda_ {1} \\mathcal {L} _ {\\text {e d g e}} + \\lambda_ {2} \\mathcal {L} _ {\\text {r e g}}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.601, + 0.892, + 0.664 + ], + "angle": 0, + "content": "where \\(\\lambda_{1}\\) and \\(\\lambda_{2}\\) are the trade-off hyper-parameters. \\(\\mathcal{L}_{reg}\\) denotes the regularization term which is obtained by combining the budget constraint in Eq. 5 and the information entropy loss in Eq. 6, i.e., \\(\\mathcal{L}_{reg} = \\mathcal{L}_{budget} + \\mathcal{L}_{entropy}\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.678, + 0.634, + 0.696 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We perform extensive experiments on the benchmark instance segmentation datasets: COCO [21] and Cityscapes [7]. COCO [21] contains about 115k images (train2017) with instance-level annotations of 80 categories for training. We use the val2017 set (around 5k images) for the ablation study and the test-dev2017 set (about 20k images) for comparison with other methods. The Cityscapes dataset [7] contains 2975, 500, and 1525 images collected from 8 categories of urban scenes for training, validation, and testing, respectively. On both COCO and Cityscapes datasets, we use the standard mask AP as the evaluation metric, which computes the average precision over varying IoU thresholds (from 0.5 to 0.95)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11283" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.1, + 0.101, + 0.232, + 0.183 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.233, + 0.101, + 0.363, + 0.183 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.363, + 0.101, + 0.494, + 0.183 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.496, + 0.101, + 0.627, + 0.182 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.628, + 0.101, + 0.758, + 0.182 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.76, + 0.101, + 0.89, + 0.182 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.1, + 0.187, + 0.231, + 0.268 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.232, + 0.187, + 0.362, + 0.268 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.363, + 0.187, + 0.494, + 0.268 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.496, + 0.186, + 0.627, + 0.267 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.628, + 0.186, + 0.757, + 0.267 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.76, + 0.187, + 0.89, + 0.268 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.276, + 0.892, + 0.291 + ], + "angle": 0, + "content": "Figure 6. Example results of Mask R-CNN [10] (left), PointRend [17] (middle), and DynaMask (right), using ResNet-50-FPN as backbone." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.311, + 0.295, + 0.327 + ], + "angle": 0, + "content": "4.1. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.334, + 0.474, + 0.606 + ], + "angle": 0, + "content": "We adopt Mask R-CNN [10] as our baseline. The backbone is pre-trained on ImageNet. The hyper-parameters and loss functions are set the same as Mask R-CNN implemented in MMDetection [4] unless specified. The proposed MSM has four switching states, which correspond to four candidate resolutions, i.e., \\([14 \\times 14, 28 \\times 28, 56 \\times 56, 112 \\times 112]\\). The hyper-parameter \\(\\lambda_{1}\\) is set as 0.1. We first pretrain the model without MSM using mask loss at all resolutions for one epoch. The initial learning rate is 0.02, and the batch size is 16 on 8 GPUs. Then we train all modules for 12 epochs using SGD with the same initial learning rate and batch size and reduce the learning rate by a factor of 0.1 after 8 and 11 epochs, respectively. Multi-scale training is used with the shorter side randomly sampled from [640, 800], while for inference, the short side is resized to 800. In the ablation study, we use the standard \\(1 \\times\\) training schedule and data augmentation defined in MMDetection [4]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.62, + 0.216, + 0.634 + ], + "angle": 0, + "content": "4.2. Main Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.644, + 0.47, + 0.869 + ], + "angle": 0, + "content": "Comparison with Mask R-CNN. We first compare the performance of DynaMask with the baseline Mask R-CNN on COCO by using ResNet-50 and ResNet-101 backbones. As shown in Tab. 2, our method outperforms Mask R-CNN by a large margin. The performance is improved by \\(2.9\\%\\) AP and \\(2.8\\%\\) AP with “\\(1 \\times\\)” and “\\(2 \\times\\)” schedules, respectively, when ResNet-50-FPN backbone is used. Particularly, DynaMask outperforms the baseline by \\(3.3\\%\\), and \\(3.6\\%\\) with “\\(1 \\times\\)” and “\\(2 \\times\\)” schedules in terms of \\(\\mathrm{AP}_{75}\\), respectively. Similar observations can be obtained when ResNet-101-FPN is used as the backbone. This is because the proposed dual-level FPN structure incorporates complementary semantic and detailed information from multiple levels of FPN, resulting in more precise mask localization and higher-quality segmentation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Comparison with state-of-the-art methods. We then compare the segmentation performance of DynaMask with" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.311, + 0.893, + 0.537 + ], + "angle": 0, + "content": "many other state-of-the-art methods on COCO. The results are listed in Tab. 3. All models are trained on COCO train2017 and evaluated on COCO test-dev2017. Without bells and whistles, DynaMask surpasses these methods with visible margins. Furthermore, we compare our method with other representative two-stage IS methods on Cityscapes val set in Tab. 4. Our method outperforms Mask R-CNN [10] by \\(4.2\\%\\). Noticeably, its performance on large objects is \\(5.8\\%\\) AP higher than Mask R-CNN. This is because DynaMask employs high-resolution masks to achieve high-quality segmentation on large and difficult objects. RefineMask [30] also produces outstanding performance since it refines the mask prediction with fine-grained features, but it costs many computations due to the multi-stage refinement." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.538, + 0.895, + 0.734 + ], + "angle": 0, + "content": "Visualizations of segmentation results. In Fig. 6, we visualize the segmentation results of DynaMask together with two representative methods: Mask R-CNN [10], and PointRend [17]. One can see that our method achieves finer and more accurate predictions around the objects' boundaries. This is because Dynamask introduces an r-FPN to fuse complementary information from multiple stages, so that difficult instances can be segmented with large masks which contain more fine-grained details. Mask R-CNN [10] employs a uniform coarse mask for prediction, while PointRend [17] makes point-wise refinement only at the blurred regions, which is not enough to capture sufficient details." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.742, + 0.655, + 0.759 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Mask resolution prediction. To better understand how DynaMask selects suitable masks for different instances, we show the mask selection results in Fig. 7. As can be seen, the \"hard\" objects with irregular shapes and complex boundaries are assigned large masks, such as the \"potted plant\", \"person\", \"giraffe\", etc. On the contrary, the \"easy\" samples with regular shapes and less details are assigned small masks, such as the \"skis\", \"suitcase\", \"dining table\" and so on. It is worth mentioning that the choice of mask" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11284" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.204, + 0.089, + 0.768, + 0.217 + ], + "angle": 0, + "content": "
MethodBackboneSched.AP\\( AP_{50} \\)\\( AP_{75} \\)\\( AP_S \\)\\( AP_M \\)\\( AP_L \\)
Mask R-CNN [10]ResNet-50-FPN1×34.755.737.218.337.447.2
DynaMaskResNet-50-FPN1×37.657.440.520.740.450.3
Mask R-CNN [10]ResNet-50-FPN2×35.456.437.919.138.648.4
DynaMaskResNet-50-FPN2×38.258.141.520.540.852.7
Mask R-CNN [10]ResNet-101-FPN1×36.157.538.618.839.749.5
DynaMaskResNet-101-FPN1×38.758.841.820.941.852.4
Mask R-CNN [10]ResNet-101-FPN2×36.657.939.119.240.250.5
DynaMaskResNet-101-FPN2×39.059.142.220.942.153.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.298, + 0.22, + 0.672, + 0.234 + ], + "angle": 0, + "content": "Table 2. Comparison with Mask R-CNN on COCO val2017." + }, + { + "type": "table", + "bbox": [ + 0.205, + 0.242, + 0.767, + 0.47 + ], + "angle": 0, + "content": "
MethodBackbonesched.AP\\( AP_{50} \\)\\( AP_{75} \\)\\( AP_S \\)\\( AP_M \\)\\( AP_L \\)
MEInst [31]ResNet-101-FPN3×33.956.235.419.836.142.3
Mask R-CNN [10]ResNet-101-FPN3×38.560.041.619.241.655.8
BMask R-CNN [6]ResNet-101-FPN1×37.759.340.616.839.954.6
TensorMask [5]ResNet-101-FPN6×37.159.339.417.439.151.6
Mask Scoring [14]ResNet-101-FPN18e38.358.841.517.840.454.4
ConDInst [26]ResNet-101-FPN3×39.160.942.021.541.750.9
BlendMask [2]ResNet-101-FPN3×38.460.741.318.241.553.3
PointRend [17]ResNeXt-101-FPN3×41.463.344.824.243.953.2
SOLOv2 [28]ResNet-101-FPN6×39.760.742.917.342.957.4
HTC [3]ResNet-101-FPN20e39.761.843.121.042.253.5
DCT-Mask†[25]ResNet-101-FPN3×40.161.243.622.742.751.8
RefineMask [30]ResNet-101-FPN3×39.4-----
Mask Transfiner†[16]ResNet-101-FPN3×40.7--23.142.853.8
QueryInst†[9]ResNet-101-FPN3×41.764.445.324.243.953.9
DynaMaskResNet-101-FPN3×39.661.442.921.242.453.2
DynaMask†ResNet-101-FPN3×41.362.545.222.843.454.0
DynaMask†ResNeXt-101-FPN3×42.062.946.323.444.054.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.473, + 0.891, + 0.488 + ], + "angle": 0, + "content": "Table 3. Comparison with state-of-the-art methods for instance segmentation on COCO test-dev2017, † denotes multi-scale training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.502, + 0.471, + 0.607 + ], + "angle": 0, + "content": "size is independent of object size. For example, in the third image, the small but hard object \"potted plant\" is allocated a large mask, while the large but easy sample \"suitcase\" in the fifth image can be accurately segmented with a small mask. We provide quantitative analysis of the correlations between the predicted mask resolutions and the class in supplemental files." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.614, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Influence of the budget constraint. In Tab. 5, we explore the influence of budget constraint on the model complexity (FLOPs). The average FLOPs are calculated by taking the average over all instances of the validation set. By tuning hyper-parameters \\(\\mathcal{C}_t\\) and \\(\\lambda_2\\) to different values, we get models of different computational costs. For example, the FLOPs are reduced by about \\(19\\%\\) without sacrificing the segmentation performance by setting \\(\\mathcal{C}_t\\) and \\(\\lambda_2\\) to 1.0 and 0.4, respectively. This demonstrates that there exists much redundancy when using the large mask \\((112 \\times 112)\\) for all instances. Actually, many instances in COCO dataset can be efficiently segmented with smaller masks. Thus the redundant computation for easier samples can be reduced, while the accuracy of harder samples can be maintained by still using larger masks. By setting the target FLOPs \\(\\mathcal{C}_t\\) to a smaller value (e.g., 0.4, 0.6, 0.8), more significant computation reduction can be achieved at a slight degradation of accuracy. For instance, by setting both \\(\\mathcal{C}_t\\) and \\(\\lambda_2\\) to 0.4, more than half of the FLOPs (around \\(54\\%\\)) are reduced while still" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.502, + 0.874, + 0.517 + ], + "angle": 0, + "content": "producing competitive segmentation results (36.8% AP)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.52, + 0.892, + 0.746 + ], + "angle": 0, + "content": "Speed comparison of different methods. To validate the efficiency of our model, we compare the model accuracy, FLOPs, and runtime of different two-stage IS methods in Tab. 6. Inference time is tested on one NVIDIA Titan RTX with the input size \\(800 \\times 1333\\). Compared to these methods, our DynaMask method achieves visible performance gain at a small amount of extra computational cost. Specifically, DynaMask \\((\\mathcal{C}_t = 0.4)\\) outperforms PointRend [17] and DCT-mask [25] by \\(1.2\\%\\) AP and \\(0.3\\%\\) AP, respectively, with comparable runtime. Though HTC [3] produces a similar segmentation result (\\(0.2\\%\\) lower AP) to DynaMask, it is two times slower than DynaMask because it performs hybrid cascade refinement on both detection and segmentation tasks, resulting in a large amount of memory and computation overhead." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Influence of mask size. The Mask Switch Module (MSM) outputs four different candidate mask resolutions \\([14 \\times 14, 28 \\times 28, 56 \\times 56, 112 \\times 112]\\). We choose one of them as the uniform output mask size and report the corresponding results in Tab. 7. As can be seen, models with larger mask resolutions could achieve higher segmentation performance, especially on large objects, but the computational cost also increases obviously. For example, the performance is improved by \\(3.2\\%\\), \\(4.2\\%\\), and \\(4.7\\%\\) AP when the mask resolution is increased from \\(14 \\times 14\\) to \\(28 \\times 28\\), \\(56 \\times 56\\)" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11285" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.278, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.284, + 0.089, + 0.482, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.489, + 0.089, + 0.688, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.695, + 0.089, + 0.892, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.194, + 0.278, + 0.298 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.284, + 0.194, + 0.482, + 0.298 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.489, + 0.194, + 0.688, + 0.298 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.695, + 0.194, + 0.892, + 0.298 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.3, + 0.892, + 0.328 + ], + "angle": 0, + "content": "Figure 7. Mask selection results by DynaMask. Each color corresponds to a candidate resolution (red \\(\\rightarrow\\) large, blue \\(\\rightarrow\\) medium, green \\(\\rightarrow\\) small, yellow \\(\\rightarrow\\) tiny)." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.33, + 0.374, + 0.412 + ], + "angle": 0, + "content": "
MethodAPAPsAPMAPL
Mask R-CNN [10]33.812.031.551.8
PointRend [17]35.8---
BMask R-CNN [6]35.8---
RefineMask [30]37.614.634.058.1
DynaMask38.014.835.157.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.413, + 0.366, + 0.439 + ], + "angle": 0, + "content": "Table 4. The results on Cityscapes val set with ResNet-50-FPN backbone." + }, + { + "type": "table", + "bbox": [ + 0.396, + 0.328, + 0.576, + 0.415 + ], + "angle": 0, + "content": "
Ctλ2FLOPsΔAP
1.00.31.27G-9%37.6
1.00.41.13G-19%37.6
1.00.51.06G-24%37.5
0.80.40.92G-34%37.4
0.60.40.83G-41%37.2
0.40.40.64G-54%36.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.383, + 0.416, + 0.59, + 0.442 + ], + "angle": 0, + "content": "Table 5. The influence of the budget constraint." + }, + { + "type": "table", + "bbox": [ + 0.623, + 0.328, + 0.872, + 0.415 + ], + "angle": 0, + "content": "
MethodAPFLOPsFPS
Mask R-CNN [10]34.70.5G12.4
PointRend [17]35.60.9G9.4
DCT-Mask†[25]36.50.5G11.8
HTC [3]37.4-3.9
DynaMask37.61.4G8.3
DynaMask (Ct=0.4)36.80.64G11.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.605, + 0.416, + 0.892, + 0.443 + ], + "angle": 0, + "content": "Table 6. Speed comparison of different methods on val set, †: multi-scale training." + }, + { + "type": "table", + "bbox": [ + 0.101, + 0.457, + 0.462, + 0.522 + ], + "angle": 0, + "content": "
Mask SizeFLOPsAP\\( {\\mathrm{{AP}}}_{50} \\)\\( {\\mathrm{{AP}}}_{75} \\)\\( {\\mathrm{{AP}}}_{\\mathrm{S}} \\)\\( {\\mathrm{{AP}}}_{\\mathrm{M}} \\)\\( {\\mathrm{{AP}}}_{\\mathrm{L}} \\)
\\( {14} \\times {14} \\)0.23G32.955.334.419.335.843.6
\\( {28} \\times {28} \\)0.62G36.157.138.720.439.248.2
\\( {56} \\times {56} \\)1.01G37.157.340.020.540.049.7
\\( {112} \\times {112} \\)1.40G37.657.440.520.740.450.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.13, + 0.522, + 0.435, + 0.535 + ], + "angle": 0, + "content": "Table 7. Performance of using different mask sizes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.551, + 0.469, + 0.58 + ], + "angle": 0, + "content": "and \\(112 \\times 112\\), respectively. Nevertheless, the performance tends to saturate as the mask size increases further." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.58, + 0.47, + 0.679 + ], + "angle": 0, + "content": "Size-based mask selection method. We compare the performance and mask distributions of different mask selection methods in Tab. 8. The baseline is performed by using a uniform mask size \\((28 \\times 28)\\) for all objects. Size-based method denotes assigning masks according to the size of object. Specifically, we assign a mask \\(\\hat{m}_i^k\\) to the instance of width \\(w\\) and height \\(h\\) by the following rule:" + }, + { + "type": "equation", + "bbox": [ + 0.166, + 0.689, + 0.47, + 0.713 + ], + "angle": 0, + "content": "\\[\nk = \\left\\lfloor k _ {0} + \\log_ {2} \\left(\\sqrt {w h} / \\sqrt {w _ {0} h _ {0}}\\right) \\right\\rfloor , \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.469, + 0.825 + ], + "angle": 0, + "content": "where \\( w_{0} \\) and \\( h_0 \\) denote the width and height of the input image, respectively. and \\( k_{0} \\) denotes the index of the highest mask resolution \\( 112 \\times 112 \\), i.e., \\( k_{0} = 4 \\). Intuitively, Eq. 8 means that the larger object will be assigned a higher-resolution mask. This conforms to our common sense, since the larger objects usually contain many details which need finer-grained masks to achieve high-quality prediction." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.47, + 0.902 + ], + "angle": 0, + "content": "As can be seen from Tab. 8, the size-based method attains comparable performance with the baseline at a lower cost. Our DynaMask \\((\\mathcal{C}_t = 0.4)\\) outperforms the baseline by \\(0.7\\%\\) AP and the size-based method by \\(0.9\\%\\) AP at a slight extra computation cost, demonstrating that the" + }, + { + "type": "table", + "bbox": [ + 0.515, + 0.457, + 0.879, + 0.522 + ], + "angle": 0, + "content": "
Mask SizeFLOPsAPTinySmallMediumLarge
28×280.62G36.10100
Size-based0.56G35.947%32%14%8%
DynaMask (Ct=0.4)0.64G36.835%34%21%10%
DynaMask1.4G37.60001
" + }, + { + "type": "table_caption", + "bbox": [ + 0.515, + 0.522, + 0.879, + 0.535 + ], + "angle": 0, + "content": "Table 8. Comparison with size-based mask selection method." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.551, + 0.892, + 0.628 + ], + "angle": 0, + "content": "proposed mask selection strategy could better partition different objects according to their segmentation difficulties and assign more suitable masks to achieve better performance. More analyses about the distribution of predicted mask scales can be found in supplemental materials." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.639, + 0.619, + 0.654 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.893, + 0.901 + ], + "angle": 0, + "content": "In this work, we proposed a simple yet effective method to improve instance segmentation performance at a small amount of computation and memory overhead. We devised a dual-level FPN structure for better exploring complementary contextual and detailed information from multiple pyramid levels. Specifically, in addition to traditional image-level FPN (i-FPN), we augmented a region-level top-down path (r-FPN) to gradually enlarge the mask size and incorporate more details from i-FPN. Furthermore, to reduce the computation and memory cost led by using large masks, we introduced a Mask Switch Module (MSM) to adaptively select suitable masks for each proposal so that the redundant computation for easy samples can be reduced by using smaller masks. Extensive experimental results demonstrated that our method achieved significant performance gains with moderate extra computation overhead." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11286" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.473, + 0.171 + ], + "angle": 0, + "content": "[1] Daniel Bolya, Chong Zhou, Fanyi Xiao, and Yong Jae Lee. Yolact: Real-time instance segmentation. In Proceedings of the IEEE/CVF international conference on computer vision, pages 9157-9166, 2019. 1" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.173, + 0.472, + 0.243 + ], + "angle": 0, + "content": "[2] Hao Chen, Kunyang Sun, Zhi Tian, Chunhua Shen, Yongming Huang, and Youliang Yan. Blendmask: Top-down meets bottom-up for instance segmentation. 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However, a low-resolution mask loses rich details, while a high-resolution mask incurs quadratic computation overhead. It is a challenging task to predict the optimal binary mask for each instance. In this paper, we propose to dynamically select suitable masks for different object proposals. First, a dual-level Feature Pyramid Network (FPN) with adaptive feature aggregation is developed to gradually increase the mask grid resolution, ensuring high-quality segmentation of objects. Specifically, an efficient region-level top-down path (r-FPN) is introduced to incorporate complementary contextual and detailed information from different stages of image-level FPN (i-FPN). Then, to alleviate the increase of computation and memory costs caused by using large masks, we develop a Mask Switch Module (MSM) with negligible computational cost to select the most suitable mask resolution for each instance, achieving high efficiency while maintaining high segmentation accuracy. Without bells and whistles, the proposed method, namely DynaMask, brings consistent and noticeable performance improvements over other state-of-the-arts at a moderate computation overhead. The source code: https://github.com/lslrh/DynaMask. + +# 1. Introduction + +Instance segmentation (IS) is an important computer vision task, aiming at simultaneously predicting the class label and the binary mask for each instance of interest in an image. It works as the cornerstone of many downstream vision applications, such as autonomous driving, video surveillance, and robotics, to name a few. Recent years have witnessed the significant advances of deep convolutional neural networks (CNNs) based IS methods with a rich amount of training data as the rocket fuel [1, 10, 17, 25, 26]. Existing IS methods can be roughly divided into two ma + +![](images/dbec4932b6e30d8c0989dd315998d63c80dd30a438930fb01719e1ef84492e09.jpg) +Figure 1. Dynamic mask selection results. Some "hard" samples with irregular shapes like "person" are assigned larger masks, while the "easy" ones like "frisbee" are assigned smaller ones. + +jor categories: two-stage [6, 10, 17] and single-stage methods [1, 2, 26]. The former first detect a sparse set of proposals and then performs mask predictions based on them, while the latter directly predict classification scores and masks based on the pre-defined anchors. Generally speaking, two-stage methods could produce higher segmentation accuracy but cost more computational resources than single-stage methods. + +Among the many recently developed IS methods, the proposal-based two-stage methods [6, 10, 17], which follow a detection-and-segmentation paradigm, are still the top performers. These methods need to predict a binary grid mask of uniform resolution for all proposals, e.g., $28 \times 28$ , and then upsample it to the original image size. For instance, Mask R-CNN [10] first generates a group of proposals with an object detector and then performs per pixel foreground/background segmentation on the Regions of Interest (RoIs) [24]. Despite achieving promising performance, the low-resolution mask of Mask R-CNN is insufficient to capture more detailed information, resulting in unsatisfactory predictions, especially over object boundaries. An intuitive solution to improve the segmentation quality is to adopt a larger mask. Nevertheless, high-resolution masks often generate excessive predictions on the smooth regions, resulting in high computational complexity. + +It is difficult to segment different objects in an image + +with masks of the same resolution. Objects with irregular shapes and complicated boundaries demand more fine-grained masks to predict, referred to as "hard" samples, such as the "person" in Fig. 1. In comparison, the "easy" samples with regular shapes and fewer details can be efficiently segmented using coarser masks, like the "frisbee" in Fig. 1. Inspired by the above observations, we propose to adaptively adjust the mask size for each instance for better IS performance. Specifically, instead of using a uniform resolution for all instances, we assign high-resolution masks to "hard" objects and low-resolution masks to "easy" objects. In this way, the redundant computation for "easy" samples can be reduced while the accuracy of "hard" samples can be improved, achieving a balance between accuracy and speed. As shown in Tab. 1, however, directly predicting a high-resolution mask by Mask R-CNN [10] unexpectedly degrades the mask average precision (AP). This attributes to two main reasons. First, the RoI features of larger objects are extracted from higher pyramid levels, which are very coarse due to the downsampling operations [20]. Thus simply increasing the mask size of these RoIs will not bring extra useful information. Second, the mask head of Mask R-CNN is oversimplified, so it cannot make more precise predictions as the mask grid size increases. + +To overcome the above mentioned problems, we propose a dual-level FPN framework to gradually enlarge the mask grid. Specifically, in addition to traditional image-level FPN (i-FPN), a region-level FPN (r-FPN) is designed to achieve coarse-to-fine mask prediction. Wherein we construct information flows between i-FPN and r-FPN at different pyramid levels, aiming to incorporate complementary contextual and detailed information from multiple feature levels for high-quality segmentation. With the dual-level FPN, we present a data-dependent Mask Switch Module (MSM) with negligible computational cost to adaptively select masks for each instance. The overall approach, namely DynaMask, is evaluated on benchmark instance segmentation datasets to demonstrate its superiority over state-of-the-arts. The major contributions of this work are summarized as follows: + +- A dynamic mask selection method (DynaMask) is proposed to adaptively assign appropriate masks to different instances. Specifically, it assigns low-resolution masks to "easy" samples for efficiency while assigning high-resolution masks to "hard" samples for accuracy. +- A dual-level FPN framework is developed for IS. We construct direct information flows from i-FPN to r-FPN at multiple levels, facilitating complementary information aggregation from multiple pyramid levels. +- Extensive experiments demonstrate that DynaMask achieves a good trade-off between IS accuracy and efficiency, outperforming many state-of-the-art two-stage IS methods at a moderate computation overhead. + +
MethodResolutionAPFLOPs
Mask R-CNN [10]14×1432.90.2G
28×2834.70.5G
56×5633.82.0G
112×11232.58.0G
DynaMask14×1432.90.2G
28×2836.10.6G
56×5637.11.0G
112×11237.61.4G
+ +Table 1. Mask AP and FLOPs with different mask resolutions. For Mask R-CNN, directly increasing the mask resolution will decrease the mask AP. While for our DynaMask, higher mask resolution results in better performance. + +# 2. Related Work + +Instance Segmentation. To date, most of the top-performing IS methods still follow the Mask R-CNN metaarchitecture [10]. These proposal-based approaches typically employ an object detector to localize each instance in bounding boxes. Then the instance-wise features are cropped and extracted from FPN features based on the detected bounding boxes by using RoI pooling/align [10, 24]. Finally, a compact segmentation head is deployed to obtain the desired object masks. Mask Scoring R-CNN [14] aligns the mask quality and score by using a branch to explicitly learn the quality of predicted masks. BMask R-CNN [6] leverages boundary details to improve mask localization ability. DCT-Mask [25] encodes high-resolution binary masks into compact vectors through the discrete cosine transform (DCT). PANet [22] constructs two feature pyramids for improving mask prediction. + +Some works [3, 17, 30] have been proposed to improve the mask quality by coarse-to-fine refinement. HTC [3] performs cascaded refinement on both detection and segmentation tasks and explores the reciprocal relationships between them. PointRend [17] and RefineMask [30] extract fine-grained features in a multi-stage manner. The former performs point-based predictions over the blurred areas, while the latter refines the entire RoI feature. Despite the promising segmentation results, multiple refinement stages inevitably increase the inference time and memory burden. In this paper, we dynamically select the suitable mask for each instance so that "easy" samples are assigned small masks (with fewer refinement stages) for efficiency, and "hard" samples are assigned large masks (with more refinement stages) for accuracy, achieving a balance between efficiency and accuracy. + +Dynamic Networks. Dynamic networks, which aim to adaptively adjust the network architecture according to the input feature, have been widely studied in recent years. Dynamic model compression methods either drop blocks [12, 23, 27] or prune channels [19, 29] for speeding + +![](images/b29b2729616c25008a941ebaf283eac79f37a0e1463997eb2cb14761f2b3ca4e.jpg) +Figure 2. The overall architecture of DynaMask. We propose a dual-level FPN framework to gradually increase the mask size and achieve higher-quality IS. The information flow is constructed between each level of image-level FPN (i-FPN) and region-level FPN (r-FPN), so that region-wise feature hierarchies $\{L_{tiny}, L_{small}, L_{medium}, L_{large}\}$ are constantly enhanced by incorporating complementary information from $\{P2, P3, P4\}$ of i-FPN, resulting in coarse-to-fine mask predictions. To reduce the computation and memory cost, a Mask Switch Module (MSM) is developed to predict the mask resolution for each instance with budgeted resource consumption. Specifically, MSM outputs four different switching states, corresponding to four different mask resolutions, i.e., $[14 \times 14, 28 \times 28, 56 \times 56, 112 \times 112]$ . + +up the inference. For instance, SkipNet [27] skips convolutional blocks through a reinforcement learning-based gating network. Huang et al. propose a multi-scale dense network with multiple classifiers for allocating different computations for "easy" and "hard" samples. Li et al. [18] adopt an end-to-end dynamic routing framework to alleviate the scale variance among inputs. DRNet [32] attempts to reduce the redundancy on the input resolution of modern CNNs. + +However, employing dynamic masks at different resolutions for segmenting different instances has rarely been explored in the field of IS. Conventional methods [6, 10, 17] typically predict a fixed-size mask irrespective of the object type. This is sufficient for "easy" samples but produces over-smoothing predictions for "hard" samples over the fine-level details. In order to improve the segmentation performance without introducing many additional computation burdens, we devise a dynamic mask selection framework to adaptively allocate suitable masks to different objects according to their segmentation difficulties. + +# 3. Dynamic Mask Selection + +The framework of DynaMask is illustrated in Fig. 2. A dual-level FPN architecture is first proposed for improving IS quality, and then a Mask Switch Module (MSM) is developed to dynamically allocate appropriate masks to each instance, so that the resource consumption can be reduced while maintaining superior IS performance. Our DynaMask produces high-quality segmentation with a moderate computation overhead. + +# 3.1. Dual-Level FPN + +Original image-level FPN (i-FPN) [20] introduces a top-down path to propagate contextual semantic information + +from higher layers to lower ones. Actually, the lower-level features contain more fine-grained details than higher-level ones, which are beneficial for high-quality segmentation, especially on boundary regions, but these information is not fully explored in Mask R-CNN [10]. In this work, we propose a region-level FPN (r-FPN) to integrate more detailed information from lower layers of i-FPN into region-wise feature hierarchies. The information flows from each level of i-FPN to r-FPN are shown in Fig. 2. + +Region-Level FPN. We follow the original i-FPN to define the layers producing feature maps of the same resolution as one network stage corresponding to one feature level. We use $\{P_2, P_3, P_4, P_5\}$ to denote different feature levels of i-FPN. The r-FPN starts from an RoI-Aligned region-wise feature, and it is gradually enhanced by fusing the complementary information from $\{P_2, P_3, P_4\}$ of i-FPN, resulting in top-down region-based feature hierarchies, denoted by $\{L_{tiny}, L_{small}, L_{medium}, L_{large}\}$ . From $L_{tiny}$ to $L_{large}$ , the spatial resolution is progressively increased by a factor of two. We design a Feature Aggregation Module (FAM) to integrate the r-FPN feature $L_r$ and the i-FPN feature $P_i$ . + +Feature Aggregation Module (FAM). There exists spatial misalignments between $L_{r}$ and $P_{i}$ due to the upsampling and RoI pooling [24] operations, which may degrade the segmentation performance on boundary areas. To overcome this limitation, we propose the FAM to adaptively aggregate multi-scale features. As show in Fig. 3, FAM contains two deformable convolutions [8, 13] which play different roles. The first one (Deform_Conv1) adjusts the positions of $L_{r}$ , making it better aligned to $P_{i}$ . Here we first concatenate $L_{r}$ with $P_{i}$ , and then pass the concatenated features through a $3 \times 3$ Conv to obtain the offset map, denoted by $\Delta_{o}$ . Finally, $L_{r}$ is aligned to $P_{i}$ with the learned offset $\Delta_{o}$ . The + +![](images/01a40b0e210f07ddea80274f6b0d3fa40922e904296e3bf53b425c5cbe79ae55.jpg) +Figure 3. Feature Alignment Molecule (FAM). Deform_Conv1 adjusts the spatial positions of upsampled r-FPN feature $L_{r}$ and the cropped i-FPN feature $P_{i}$ . Deform_Conv2 attends to the salient parts of objects. + +second one (Deform_Conv2) works like an attention mechanism, which attends to the salient parts of objects. The proposed FAM is plugged into different stages of r-FPN and it plays a key role in improving the mask prediction. + +# 3.2. Mask Switch Module (MSM) + +The proposed dual-level FPN framework brings a significant performance improvement but at the price of expensive computation and memory burdens. Inspired by the fact that different instances require different mask grids to achieve accurate segmentation, we propose a novel method to adaptively adjust the mask grid resolution for different instances. Specifically, an MSM is developed to perform mask resolution prediction under a budgeted computation consumption, achieving a good trade-off between segmentation accuracy and efficiency. + +Optimal Mask Assignment. The MSM module is actually a lightweight classifier, denoted by $f_{MSM}(\cdot)$ , which is illustrated in Fig. 4. It contains a channel-wise attention module [11], followed by a few convolutional layers and fully-connected layers. This classifier aims to find the optimal mask resolution from a collection of $K$ candidates, i.e., $[r^1, r^2, \dots, r^K]$ , so that the instance could be accurately segmented with the minimal resource cost. Specifically, MSM takes the cropped region-wise RoI feature as input and outputs a probability vector $P = [p^1, \dots, p^K]$ by taking a softmax operation. Each element of this vector represents the probability that the corresponding candidate resolution is selected: + +$$ +p ^ {k} = \frac {\exp \left(f _ {M S M} ^ {k} (x)\right)}{\sum_ {k ^ {\prime}} \exp \left(f _ {M S M} ^ {k ^ {\prime}} (x)\right)}, \quad k \in \{1, \dots , K \}, \tag {1} +$$ + +where $x$ is the input RoI feature fed to MSM. The candidate resolution of the largest probability is chosen as the switching state, which decides the resolution of mask grid to segment an object. + +Reparameterization with Gumbel-Softmax. The soft output $P$ of MSM should be transformed into a one-hot prediction, denoted by $Y = [y^{1},\dots ,y^{K}]$ , $y^{k}\in \{0,1\}$ . This process can be done by discrete sampling, which however is non-differentiable and does not support end-to-end training. + +To allow the gradient back-propagation for updating MSM, we introduce a reparameterization method [15], called the Gumbel-Softmax. Given a categorical distribution with class probabilities $P = [p^{1},\dots ,p^{K}]$ , we can draw a group of masks through the rule $y =$ onehot $\left(\arg \max_{k}(logp^{k} + g^{k})\right)$ , where $\{g^k\}_{i = k}^K$ are i.i.d. samples drawn from the Gumbel(0,1) distribution, which is defined by $g = -\log (-\log (u))$ with $u\sim \text{Uniform}(0,1)$ . Then we use the Gumbel-softmax function as a continuous, differentiable approximation to the original softmax function: + +$$ +y ^ {k} = \frac {\exp \left(\left(\log p ^ {k} + g ^ {k}\right) / \tau\right)}{\sum_ {k ^ {\prime}} \exp \left(\left(\log p ^ {k ^ {\prime}} + g ^ {k ^ {\prime}}\right) / \tau\right)}, \tag {2} +$$ + +where $\tau$ denotes a temperature parameter. When $\tau$ approaches 0, the Gumbel-softmax is close to one-hot. + +# 3.3. Objective Function + +The proposed framework gradually enlarges the mask resolution by a factor of two to improve the segmentation performance. On the one hand, FAM adaptively aggregates complementary information from multiple stages of i-FPN and r-FPN to enhance the feature hierarchies. On the other hand, MSM dynamically allocates masks of different resolutions for different instances in an image, reducing resource costs without sacrificing accuracy. In this subsection, we elaborate on the loss function used to train the mask head. + +Mask Loss. Given a positive instance $x_{i}$ , we first predict its mask switching state $Y = [y^{1},\dots ,y^{K}]$ by MSM, and obtain a group of mask prediction maps at $K$ different resolutions $\{\hat{m}_i^1,\dots ,\hat{m}_i^K\}$ by passing this instance through different stages of r-FPN. We define the mask loss function as follows: + +$$ +\mathcal {L} _ {\text {m a s k}} = \sum_ {i = 1} ^ {N} \sum_ {k = 1} ^ {K} y ^ {k} \ell \left(\hat {m} _ {i} ^ {k}, m _ {i}\right), \tag {3} +$$ + +where $\hat{m}_i^k$ denotes the $k$ -th mask prediction of $x_i$ , and $m_i$ represents its corresponding ground truth mask grid. $y^k$ is the indicator for whether the $k$ -th mask resolution is selected as the output resolution. $\ell$ is defined as the binary cross-entropy loss in this paper. + +Edge Loss. In Eq. 3, we assume that the mask producing smaller loss should have higher quality, so that the most accurate mask could be selected by minimizing the mask loss. However, our empirical results show that the mask loss produced on different masks is very close, making it difficult to distinguish the mask quality. In comparison, as shown in Fig. 5, the edge loss produced by masks of different resolutions varies greatly, which could better reveal the mask quality. Given the output of MSM $Y = [y^{1},\dots ,y^{K}]$ + +![](images/be6e6f211d82e965e97da5142b5cc9cba3130d3ac20dfb002cffe881aafadbb1.jpg) +Figure 4. The Mask Switch Module (MSM), which is a CNN-based classifier and consists of a SE-block [11], two convolutional layers and two fully-connected layers. + +![](images/2ac052ae07c5b19bf8f795b5182c206479c3969718c93cf6946b1b1e84219f71.jpg) +Figure 5. The predicted object edges using the masks of different resolutions. The edge loss computed on boundary regions could reflect the quality of mask. + +and the edge maps of different resolutions, denoted by $\{\hat{e}_i^1,\dots ,\hat{e}_i^K\}$ , the edge loss is defined as follows: + +$$ +\mathcal {L} _ {e d g e} = \sum_ {i = 1} ^ {N} \sum_ {k = 1} ^ {K} y ^ {k} \ell \left(\hat {e} _ {i} ^ {k}, e _ {i}\right), \tag {4} +$$ + +where $e_i$ denotes the ground-truth edge, which is generated by first applying the Laplacian operator on the ground-truth mask $m_i$ to obtain a soft edge map, and then converting it into a binary edge map by thresholding [6]. Fig. 5 visualizes the object edges predicted by using masks of different resolutions. As can be seen, the edge loss could better reveal the quality of masks, i.e., higher-resolution masks produce edges closer to GT (smaller loss), while lower-resolution masks produce edges more different from GT (larger loss). + +Budget Constraint. By optimizing the edge loss in Eq. 4, the model tends to converge to a sub-optimal solution that all instances are segmented with the largest mask, i.e., $112 \times 112$ , which incorporates more detailed information and hence has the minimal prediction loss. Actually, not all samples require the largest mask for segmentation. The redundant computations of segmenting the "easy" samples can be saved for efficiency. In order to reduce the computational cost and avoid the above mentioned sub-optimal solution, we propose to train the MSM with a budget constraint. Specifically, let $\mathcal{C}$ denote the computational cost (e.g., FLOPs) corresponding to the selected mask resolution. We add a penalty to the model when the expectation of FLOPs computed on current batch data, denoted by $\mathbb{E}(\mathcal{C})$ , exceeds the target FLOPs, denoted by $\mathcal{C}_t$ . The budget con + +strain is defined as follows: + +$$ +\mathcal {L} _ {\text {b u d g e t}} = \max \left(\frac {\mathbb {E} (\mathcal {C})}{\mathcal {C} _ {t}} - 1, 0\right). \tag {5} +$$ + +We further introduce an information entropy loss to balance the resolution predictions of MSM. Given a group of output probability vectors $P_{1}, P_{2}, \dots, P_{N}$ , where $N$ is the number of instances of the current batch, the frequency of the $k$ -th resolution is calculated by: $f^{k} = \frac{1}{N}\sum_{i}p_{i}^{k}$ . Then the information entropy loss is defined as follows: + +$$ +\mathcal {L} _ {\text {e n t r o p y}} = \frac {1}{K} \sum_ {k} f ^ {k} \log f ^ {k}. \tag {6} +$$ + +The above entropy loss tends to push each element $f^k$ to be $\frac{1}{K}$ so that MSM could select different resolutions with similar probabilities. + +Finally, the total objective function of the mask branch is obtained as follows: + +$$ +\mathcal {L} _ {\text {t o t a l}} = \mathcal {L} _ {\text {m a s k}} + \lambda_ {1} \mathcal {L} _ {\text {e d g e}} + \lambda_ {2} \mathcal {L} _ {\text {r e g}}, \tag {7} +$$ + +where $\lambda_{1}$ and $\lambda_{2}$ are the trade-off hyper-parameters. $\mathcal{L}_{reg}$ denotes the regularization term which is obtained by combining the budget constraint in Eq. 5 and the information entropy loss in Eq. 6, i.e., $\mathcal{L}_{reg} = \mathcal{L}_{budget} + \mathcal{L}_{entropy}$ . + +# 4. Experiments + +We perform extensive experiments on the benchmark instance segmentation datasets: COCO [21] and Cityscapes [7]. COCO [21] contains about 115k images (train2017) with instance-level annotations of 80 categories for training. We use the val2017 set (around 5k images) for the ablation study and the test-dev2017 set (about 20k images) for comparison with other methods. The Cityscapes dataset [7] contains 2975, 500, and 1525 images collected from 8 categories of urban scenes for training, validation, and testing, respectively. On both COCO and Cityscapes datasets, we use the standard mask AP as the evaluation metric, which computes the average precision over varying IoU thresholds (from 0.5 to 0.95). + +![](images/b9e5b9e3fd080b5c4bedf62d3e2b215354b24a55f150144ca00cebdeadd2b283.jpg) + +![](images/8625a4e7ec2055337dfbafa4b527333c3f10c18fec6e35d32db5b28aac33c9af.jpg) + +![](images/52c38f004f782417b85dfa9154621dd9b25865fbc0e5ccbddbea7220096a84da.jpg) + +![](images/0432c9e88664b8d887225c73876329ba1fb0445cc7dfe66b127c7d0df0c9150a.jpg) + +![](images/8d7eb519be6935e317be0ce286818f7c777750c3eece6685a7e335066e1043bc.jpg) + +![](images/fce6755db42aa1817a10b704a932639b9962236a0e224bae0d51252e67df6f2c.jpg) + +![](images/3386b64eff68f4cafbedcf7be316699a77f9360eaa7791913c7fcc57782cce29.jpg) +Figure 6. Example results of Mask R-CNN [10] (left), PointRend [17] (middle), and DynaMask (right), using ResNet-50-FPN as backbone. + +![](images/1c56c9d89529b655375104a96b8225d767beea9ce9b701921f5f9dbcc9e083db.jpg) + +![](images/e49251e4bd2e1b39e5cdb4747205c281a26d455987fe9d802997ca168a96e4a6.jpg) + +![](images/7cd416729655ca19dc02a697cdd6d113cbf067d3983f3c53a655d61a9be5a9b0.jpg) + +![](images/ebfddc63aa08d092f14818ea94a218311d62ec19c4c8e97111d996c447ebd72a.jpg) + +![](images/6905a9d1f573026df2e082edf85d91d28ebde90f7da6aa8901683ca59a1de517.jpg) + +# 4.1. Implementation Details + +We adopt Mask R-CNN [10] as our baseline. The backbone is pre-trained on ImageNet. The hyper-parameters and loss functions are set the same as Mask R-CNN implemented in MMDetection [4] unless specified. The proposed MSM has four switching states, which correspond to four candidate resolutions, i.e., $[14 \times 14, 28 \times 28, 56 \times 56, 112 \times 112]$ . The hyper-parameter $\lambda_{1}$ is set as 0.1. We first pretrain the model without MSM using mask loss at all resolutions for one epoch. The initial learning rate is 0.02, and the batch size is 16 on 8 GPUs. Then we train all modules for 12 epochs using SGD with the same initial learning rate and batch size and reduce the learning rate by a factor of 0.1 after 8 and 11 epochs, respectively. Multi-scale training is used with the shorter side randomly sampled from [640, 800], while for inference, the short side is resized to 800. In the ablation study, we use the standard $1 \times$ training schedule and data augmentation defined in MMDetection [4]. + +# 4.2. Main Results + +Comparison with Mask R-CNN. We first compare the performance of DynaMask with the baseline Mask R-CNN on COCO by using ResNet-50 and ResNet-101 backbones. As shown in Tab. 2, our method outperforms Mask R-CNN by a large margin. The performance is improved by $2.9\%$ AP and $2.8\%$ AP with “ $1 \times$ ” and “ $2 \times$ ” schedules, respectively, when ResNet-50-FPN backbone is used. Particularly, DynaMask outperforms the baseline by $3.3\%$ , and $3.6\%$ with “ $1 \times$ ” and “ $2 \times$ ” schedules in terms of $\mathrm{AP}_{75}$ , respectively. Similar observations can be obtained when ResNet-101-FPN is used as the backbone. This is because the proposed dual-level FPN structure incorporates complementary semantic and detailed information from multiple levels of FPN, resulting in more precise mask localization and higher-quality segmentation. + +Comparison with state-of-the-art methods. We then compare the segmentation performance of DynaMask with + +many other state-of-the-art methods on COCO. The results are listed in Tab. 3. All models are trained on COCO train2017 and evaluated on COCO test-dev2017. Without bells and whistles, DynaMask surpasses these methods with visible margins. Furthermore, we compare our method with other representative two-stage IS methods on Cityscapes val set in Tab. 4. Our method outperforms Mask R-CNN [10] by $4.2\%$ . Noticeably, its performance on large objects is $5.8\%$ AP higher than Mask R-CNN. This is because DynaMask employs high-resolution masks to achieve high-quality segmentation on large and difficult objects. RefineMask [30] also produces outstanding performance since it refines the mask prediction with fine-grained features, but it costs many computations due to the multi-stage refinement. + +Visualizations of segmentation results. In Fig. 6, we visualize the segmentation results of DynaMask together with two representative methods: Mask R-CNN [10], and PointRend [17]. One can see that our method achieves finer and more accurate predictions around the objects' boundaries. This is because Dynamask introduces an r-FPN to fuse complementary information from multiple stages, so that difficult instances can be segmented with large masks which contain more fine-grained details. Mask R-CNN [10] employs a uniform coarse mask for prediction, while PointRend [17] makes point-wise refinement only at the blurred regions, which is not enough to capture sufficient details. + +# 4.3. Ablation Study + +Mask resolution prediction. To better understand how DynaMask selects suitable masks for different instances, we show the mask selection results in Fig. 7. As can be seen, the "hard" objects with irregular shapes and complex boundaries are assigned large masks, such as the "potted plant", "person", "giraffe", etc. On the contrary, the "easy" samples with regular shapes and less details are assigned small masks, such as the "skis", "suitcase", "dining table" and so on. It is worth mentioning that the choice of mask + +
MethodBackboneSched.AP\( AP_{50} \)\( AP_{75} \)\( AP_S \)\( AP_M \)\( AP_L \)
Mask R-CNN [10]ResNet-50-FPN1×34.755.737.218.337.447.2
DynaMaskResNet-50-FPN1×37.657.440.520.740.450.3
Mask R-CNN [10]ResNet-50-FPN2×35.456.437.919.138.648.4
DynaMaskResNet-50-FPN2×38.258.141.520.540.852.7
Mask R-CNN [10]ResNet-101-FPN1×36.157.538.618.839.749.5
DynaMaskResNet-101-FPN1×38.758.841.820.941.852.4
Mask R-CNN [10]ResNet-101-FPN2×36.657.939.119.240.250.5
DynaMaskResNet-101-FPN2×39.059.142.220.942.153.3
+ +Table 2. Comparison with Mask R-CNN on COCO val2017. + +
MethodBackbonesched.AP\( AP_{50} \)\( AP_{75} \)\( AP_S \)\( AP_M \)\( AP_L \)
MEInst [31]ResNet-101-FPN3×33.956.235.419.836.142.3
Mask R-CNN [10]ResNet-101-FPN3×38.560.041.619.241.655.8
BMask R-CNN [6]ResNet-101-FPN1×37.759.340.616.839.954.6
TensorMask [5]ResNet-101-FPN6×37.159.339.417.439.151.6
Mask Scoring [14]ResNet-101-FPN18e38.358.841.517.840.454.4
ConDInst [26]ResNet-101-FPN3×39.160.942.021.541.750.9
BlendMask [2]ResNet-101-FPN3×38.460.741.318.241.553.3
PointRend [17]ResNeXt-101-FPN3×41.463.344.824.243.953.2
SOLOv2 [28]ResNet-101-FPN6×39.760.742.917.342.957.4
HTC [3]ResNet-101-FPN20e39.761.843.121.042.253.5
DCT-Mask†[25]ResNet-101-FPN3×40.161.243.622.742.751.8
RefineMask [30]ResNet-101-FPN3×39.4-----
Mask Transfiner†[16]ResNet-101-FPN3×40.7--23.142.853.8
QueryInst†[9]ResNet-101-FPN3×41.764.445.324.243.953.9
DynaMaskResNet-101-FPN3×39.661.442.921.242.453.2
DynaMask†ResNet-101-FPN3×41.362.545.222.843.454.0
DynaMask†ResNeXt-101-FPN3×42.062.946.323.444.054.8
+ +Table 3. Comparison with state-of-the-art methods for instance segmentation on COCO test-dev2017, † denotes multi-scale training. + +size is independent of object size. For example, in the third image, the small but hard object "potted plant" is allocated a large mask, while the large but easy sample "suitcase" in the fifth image can be accurately segmented with a small mask. We provide quantitative analysis of the correlations between the predicted mask resolutions and the class in supplemental files. + +Influence of the budget constraint. In Tab. 5, we explore the influence of budget constraint on the model complexity (FLOPs). The average FLOPs are calculated by taking the average over all instances of the validation set. By tuning hyper-parameters $\mathcal{C}_t$ and $\lambda_2$ to different values, we get models of different computational costs. For example, the FLOPs are reduced by about $19\%$ without sacrificing the segmentation performance by setting $\mathcal{C}_t$ and $\lambda_2$ to 1.0 and 0.4, respectively. This demonstrates that there exists much redundancy when using the large mask $(112 \times 112)$ for all instances. Actually, many instances in COCO dataset can be efficiently segmented with smaller masks. Thus the redundant computation for easier samples can be reduced, while the accuracy of harder samples can be maintained by still using larger masks. By setting the target FLOPs $\mathcal{C}_t$ to a smaller value (e.g., 0.4, 0.6, 0.8), more significant computation reduction can be achieved at a slight degradation of accuracy. For instance, by setting both $\mathcal{C}_t$ and $\lambda_2$ to 0.4, more than half of the FLOPs (around $54\%$ ) are reduced while still + +producing competitive segmentation results (36.8% AP). + +Speed comparison of different methods. To validate the efficiency of our model, we compare the model accuracy, FLOPs, and runtime of different two-stage IS methods in Tab. 6. Inference time is tested on one NVIDIA Titan RTX with the input size $800 \times 1333$ . Compared to these methods, our DynaMask method achieves visible performance gain at a small amount of extra computational cost. Specifically, DynaMask $(\mathcal{C}_t = 0.4)$ outperforms PointRend [17] and DCT-mask [25] by $1.2\%$ AP and $0.3\%$ AP, respectively, with comparable runtime. Though HTC [3] produces a similar segmentation result ( $0.2\%$ lower AP) to DynaMask, it is two times slower than DynaMask because it performs hybrid cascade refinement on both detection and segmentation tasks, resulting in a large amount of memory and computation overhead. + +Influence of mask size. The Mask Switch Module (MSM) outputs four different candidate mask resolutions $[14 \times 14, 28 \times 28, 56 \times 56, 112 \times 112]$ . We choose one of them as the uniform output mask size and report the corresponding results in Tab. 7. As can be seen, models with larger mask resolutions could achieve higher segmentation performance, especially on large objects, but the computational cost also increases obviously. For example, the performance is improved by $3.2\%$ , $4.2\%$ , and $4.7\%$ AP when the mask resolution is increased from $14 \times 14$ to $28 \times 28$ , $56 \times 56$ + +![](images/7514bf444671cdbc4c22c023fa90b3edb1f436b3b15aa981d6c60b55dc269adc.jpg) + +![](images/aa4c5fd8720176105b12bf4676a822b12fc42d82fd8e9f4581cefeb3176a86b5.jpg) + +![](images/9330e594aff21872f60c8c68d5501a5e7478d0eef8442f14255e5930f3be5b72.jpg) + +![](images/daf1f139fbb42a00f8172e813da7853924f9b11734b95667018c9674e1d4a5dd.jpg) + +![](images/d07a7ffb3fcb8d532d4511f20cd576c76921efc08bc25fc02322e798d8d6b541.jpg) +Figure 7. Mask selection results by DynaMask. Each color corresponds to a candidate resolution (red $\rightarrow$ large, blue $\rightarrow$ medium, green $\rightarrow$ small, yellow $\rightarrow$ tiny). + +![](images/72962a20700d150f9f54bf1f18fd2c2e06d99ccb16262c7a5ff47ac6d01a7358.jpg) + +![](images/d35deea7549de6b96be10608a037c940d2d3358bee8af28347e232ed9a979b81.jpg) + +![](images/894c99410100a652210e9bff0d3e05a7881727871c31b372fcb2e5c7cc3f638f.jpg) + +
MethodAPAPsAPMAPL
Mask R-CNN [10]33.812.031.551.8
PointRend [17]35.8---
BMask R-CNN [6]35.8---
RefineMask [30]37.614.634.058.1
DynaMask38.014.835.157.6
+ +Table 4. The results on Cityscapes val set with ResNet-50-FPN backbone. + +
Ctλ2FLOPsΔAP
1.00.31.27G-9%37.6
1.00.41.13G-19%37.6
1.00.51.06G-24%37.5
0.80.40.92G-34%37.4
0.60.40.83G-41%37.2
0.40.40.64G-54%36.8
+ +Table 5. The influence of the budget constraint. + +
MethodAPFLOPsFPS
Mask R-CNN [10]34.70.5G12.4
PointRend [17]35.60.9G9.4
DCT-Mask†[25]36.50.5G11.8
HTC [3]37.4-3.9
DynaMask37.61.4G8.3
DynaMask (Ct=0.4)36.80.64G11.2
+ +Table 6. Speed comparison of different methods on val set, †: multi-scale training. + +
Mask SizeFLOPsAP\( {\mathrm{{AP}}}_{50} \)\( {\mathrm{{AP}}}_{75} \)\( {\mathrm{{AP}}}_{\mathrm{S}} \)\( {\mathrm{{AP}}}_{\mathrm{M}} \)\( {\mathrm{{AP}}}_{\mathrm{L}} \)
\( {14} \times {14} \)0.23G32.955.334.419.335.843.6
\( {28} \times {28} \)0.62G36.157.138.720.439.248.2
\( {56} \times {56} \)1.01G37.157.340.020.540.049.7
\( {112} \times {112} \)1.40G37.657.440.520.740.450.3
+ +and $112 \times 112$ , respectively. Nevertheless, the performance tends to saturate as the mask size increases further. + +Size-based mask selection method. We compare the performance and mask distributions of different mask selection methods in Tab. 8. The baseline is performed by using a uniform mask size $(28 \times 28)$ for all objects. Size-based method denotes assigning masks according to the size of object. Specifically, we assign a mask $\hat{m}_i^k$ to the instance of width $w$ and height $h$ by the following rule: + +$$ +k = \left\lfloor k _ {0} + \log_ {2} \left(\sqrt {w h} / \sqrt {w _ {0} h _ {0}}\right) \right\rfloor , \tag {8} +$$ + +where $w_{0}$ and $h_0$ denote the width and height of the input image, respectively. and $k_{0}$ denotes the index of the highest mask resolution $112 \times 112$ , i.e., $k_{0} = 4$ . Intuitively, Eq. 8 means that the larger object will be assigned a higher-resolution mask. This conforms to our common sense, since the larger objects usually contain many details which need finer-grained masks to achieve high-quality prediction. + +As can be seen from Tab. 8, the size-based method attains comparable performance with the baseline at a lower cost. Our DynaMask $(\mathcal{C}_t = 0.4)$ outperforms the baseline by $0.7\%$ AP and the size-based method by $0.9\%$ AP at a slight extra computation cost, demonstrating that the + +Table 7. Performance of using different mask sizes. + +
Mask SizeFLOPsAPTinySmallMediumLarge
28×280.62G36.10100
Size-based0.56G35.947%32%14%8%
DynaMask (Ct=0.4)0.64G36.835%34%21%10%
DynaMask1.4G37.60001
+ +Table 8. Comparison with size-based mask selection method. + +proposed mask selection strategy could better partition different objects according to their segmentation difficulties and assign more suitable masks to achieve better performance. More analyses about the distribution of predicted mask scales can be found in supplemental materials. + +# 5. Conclusion + +In this work, we proposed a simple yet effective method to improve instance segmentation performance at a small amount of computation and memory overhead. We devised a dual-level FPN structure for better exploring complementary contextual and detailed information from multiple pyramid levels. Specifically, in addition to traditional image-level FPN (i-FPN), we augmented a region-level top-down path (r-FPN) to gradually enlarge the mask size and incorporate more details from i-FPN. Furthermore, to reduce the computation and memory cost led by using large masks, we introduced a Mask Switch Module (MSM) to adaptively select suitable masks for each proposal so that the redundant computation for easy samples can be reduced by using smaller masks. Extensive experimental results demonstrated that our method achieved significant performance gains with moderate extra computation overhead. + +# References + +[1] Daniel Bolya, Chong Zhou, Fanyi Xiao, and Yong Jae Lee. Yolact: Real-time instance segmentation. In Proceedings of the IEEE/CVF international conference on computer vision, pages 9157-9166, 2019. 1 +[2] Hao Chen, Kunyang Sun, Zhi Tian, Chunhua Shen, Yongming Huang, and Youliang Yan. Blendmask: Top-down meets bottom-up for instance segmentation. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 8573-8581, 2020. 1, 7 +[3] Kai Chen, Jiangmiao Pang, Jiaqi Wang, Yu Xiong, Xiaoxiao Li, Shuyang Sun, Wansen Feng, Ziwei Liu, Jianping Shi, Wanli Ouyang, et al. Hybrid task cascade for instance segmentation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 4974-4983, 2019. 2, 7, 8 +[4] Kai Chen, Jiaqi Wang, Jiangmiao Pang, Yuhang Cao, Yu Xiong, Xiaoxiao Li, Shuyang Sun, Wansen Feng, Ziwei Liu, Jiarui Xu, et al. Mmdetection: Open mmlab detection toolbox and benchmark. arXiv preprint arXiv:1906.07155, 2019. 6 +[5] Xinlei Chen, Ross Girshick, Kaiming He, and Piotr Dólar. Tensormask: A foundation for dense object segmentation. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 2061-2069, 2019. 7 +[6] Tianheng Cheng, Xinggang Wang, Lichao Huang, and Wenyu Liu. Boundary-preserving mask r-cnn. In European conference on computer vision, pages 660-676. Springer, 2020. 1, 2, 3, 5, 7, 8 +[7] Marius Cordts, Mohamed Omran, Sebastian Ramos, Timo Rehfeld, Markus Enzweiler, Rodrigo Benenson, Uwe Franke, Stefan Roth, and Bernt Schiele. The cityscapes dataset for semantic urban scene understanding. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 3213-3223, 2016. 5 +[8] Jifeng Dai, Haozhi Qi, Yuwen Xiong, Yi Li, Guodong Zhang, Han Hu, and Yichen Wei. Deformable convolutional networks. In Proceedings of the IEEE international conference on computer vision, pages 764-773, 2017. 3 +[9] Yuxin Fang, Shusheng Yang, Xinggang Wang, Yu Li, Chen Fang, Ying Shan, Bin Feng, and Wenyu Liu. Instances as queries. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 6910-6919, 2021. 7 +[10] Kaiming He, Georgia Gkioxari, Piotr Dólar, and Ross Girshick. Mask r-cnn. In Proceedings of the IEEE international conference on computer vision, pages 2961-2969, 2017. 1, 2, 3, 6, 7, 8 +[11] Jie Hu, Li Shen, and Gang Sun. Squeeze-and-excitation networks. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 7132-7141, 2018. 4, 5 +[12] Gao Huang and Danlu Chen. Multi-scale dense networks for resource efficient image classification. *ICLR* 2018, 2018. 2 +[13] Shihua Huang, Zhichao Lu, Ran Cheng, and Cheng He. Fapn: Feature-aligned pyramid network for dense image prediction. In Proceedings of the IEEE/CVF international conference on computer vision, pages 864-873, 2021. 3 + +[14] Zhaojin Huang, Lichao Huang, Yongchao Gong, Chang Huang, and Xinggang Wang. Mask scoring r-cnn. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 6409-6418, 2019. 2, 7 +[15] Eric Jang, Shixiang Gu, and Ben Poole. Categorical reparameterization with gumbel-softmax. stat, 1050:5, 2017. 4 +[16] Lei Ke, Martin Danelljan, Xia Li, Yu-Wing Tai, Chi-Keung Tang, and Fisher Yu. Mask transfiner for high-quality instance segmentation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 4412–4421, 2022. 7 +[17] Alexander Kirillov, Yuxin Wu, Kaiming He, and Ross Girshick. Pointrend: Image segmentation as rendering. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 9799-9808, 2020. 1, 2, 3, 6, 7, 8 +[18] Yanwei Li, Lin Song, Yukang Chen, Zeming Li, Xiangyu Zhang, Xingang Wang, and Jian Sun. Learning dynamic routing for semantic segmentation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 8553-8562, 2020. 3 +[19] Ji Lin, Yongming Rao, Jiwen Lu, and Jie Zhou. Runtime neural pruning. Advances in neural information processing systems, 30, 2017. 2 +[20] Tsung-Yi Lin, Piotr Dólar, Ross Girshick, Kaiming He, Bharath Hariharan, and Serge Belongie. Feature pyramid networks for object detection. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 2117-2125, 2017. 2, 3 +[21] Tsung-Yi Lin, Michael Maire, Serge Belongie, James Hays, Pietro Perona, Deva Ramanan, Piotr Dólar, and C Lawrence Zitnick. Microsoft coco: Common objects in context. In European conference on computer vision, pages 740-755. Springer, 2014. 5 +[22] Shu Liu, Lu Qi, Haifang Qin, Jianping Shi, and Jiaya Jia. Path aggregation network for instance segmentation. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 8759-8768, 2018. 2 +[23] Ravi Teja Mullapudi, William R Mark, Noam Shazeer, and Kayvon Fatahalian. Hydranets: Specialized dynamic architectures for efficient inference. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 8080-8089, 2018. 2 +[24] Shaoqing Ren, Kaiming He, Ross Girshick, and Jian Sun. Faster r-cnn: Towards real-time object detection with region proposal networks. Advances in neural information processing systems, 28, 2015. 1, 2, 3 +[25] Xing Shen, Jirui Yang, Chunbo Wei, Bing Deng, Jianqiang Huang, Xian-Sheng Hua, Xiaoliang Cheng, and Kewei Liang. Dct-mask: Discrete cosine transform mask representation for instance segmentation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 8720-8729, 2021. 1, 2, 7, 8 +[26] Zhi Tian, Chunhua Shen, and Hao Chen. Conditional convolutions for instance segmentation. In European Conference on Computer Vision, pages 282-298. Springer, 2020. 1, 7 +[27] Xin Wang, Fisher Yu, Zi-Yi Dou, Trevor Darrell, and Joseph E Gonzalez. Skipnet: Learning dynamic routing in + +convolutional networks. In Proceedings of the European Conference on Computer Vision (ECCV), pages 409-424, 2018. 2, 3 +[28] Xinlong Wang, Rufeng Zhang, Tao Kong, Lei Li, and Chunhua Shen. Solov2: Dynamic and fast instance segmentation. Advances in Neural information processing systems, 33:17721-17732, 2020. 7 +[29] Zhonghui You, Kun Yan, Jinmian Ye, Meng Ma, and Ping Wang. Gate decorator: Global filter pruning method for accelerating deep convolutional neural networks. Advances in Neural Information Processing Systems, 32, 2019. 2 +[30] Gang Zhang, Xin Lu, Jingru Tan, Jianmin Li, Zhaoxiang Zhang, Quanquan Li, and Xiaolin Hu. Refinemask: Towards high-quality instance segmentation with fine-grained features. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 6861-6869, 2021. 2, 6, 7, 8 +[31] Rufeng Zhang, Zhi Tian, Chunhua Shen, Mingyu You, and Youliang Yan. Mask encoding for single shot instance segmentation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 10226-10235, 2020. 7 +[32] Mingjian Zhu, Kai Han, Enhua Wu, Qiulin Zhang, Ying Nie, Zhenzhong Lan, and Yunhe Wang. Dynamic resolution network. Advances in Neural Information Processing Systems, 34, 2021. 3 \ No newline at end of file diff --git a/2023/DynaMask_ Dynamic Mask Selection for Instance Segmentation/images.zip b/2023/DynaMask_ Dynamic Mask Selection for Instance Segmentation/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..1a0132c7025ba188b454dca98450aee0ec141eac --- /dev/null +++ b/2023/DynaMask_ Dynamic Mask Selection for Instance Segmentation/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:0f554c5d3422bba573853a3db52058d301883888ecd164fc792a395a40876998 +size 693962 diff --git a/2023/DynaMask_ Dynamic Mask Selection for Instance Segmentation/layout.json b/2023/DynaMask_ Dynamic Mask Selection for Instance Segmentation/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..46229aedc3348e1e276ac65df5050c1b9ac3eb5c --- /dev/null +++ b/2023/DynaMask_ Dynamic Mask Selection for Instance Segmentation/layout.json @@ -0,0 +1,8799 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 99, + 103, + 494, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 99, + 103, + 494, + 121 + ], + "spans": [ + { + "bbox": [ + 99, + 103, + 494, + 121 + ], + "type": "text", + "content": "DynaMask: Dynamic Mask Selection for Instance Segmentation" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 126, + 143, + 470, + 172 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 126, + 143, + 470, + 172 + ], + "spans": [ + { + "bbox": [ + 126, + 143, + 470, + 172 + ], + "type": "text", + "content": "Ruihuang Li,\\* Chenhang He,\\* Shuai Li, Yabin Zhang, Lei Zhang† The Hong Kong Polytechnic University" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 179, + 174, + 411, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 179, + 174, + 411, + 185 + ], + "spans": [ + { + "bbox": [ + 179, + 174, + 411, + 185 + ], + "type": "text", + "content": "{csrhli, csche, cslzhang}@comp.polyu.edu.hk" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "spans": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 238, + 290, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 238, + 290, + 525 + ], + "spans": [ + { + "bbox": [ + 47, + 238, + 290, + 525 + ], + "type": "text", + "content": "The representative instance segmentation methods mostly segment different object instances with a mask of the fixed resolution, e.g., " + }, + { + "bbox": [ + 47, + 238, + 290, + 525 + ], + "type": "inline_equation", + "content": "28 \\times 28" + }, + { + "bbox": [ + 47, + 238, + 290, + 525 + ], + "type": "text", + "content": " grid. However, a low-resolution mask loses rich details, while a high-resolution mask incurs quadratic computation overhead. It is a challenging task to predict the optimal binary mask for each instance. In this paper, we propose to dynamically select suitable masks for different object proposals. First, a dual-level Feature Pyramid Network (FPN) with adaptive feature aggregation is developed to gradually increase the mask grid resolution, ensuring high-quality segmentation of objects. Specifically, an efficient region-level top-down path (r-FPN) is introduced to incorporate complementary contextual and detailed information from different stages of image-level FPN (i-FPN). Then, to alleviate the increase of computation and memory costs caused by using large masks, we develop a Mask Switch Module (MSM) with negligible computational cost to select the most suitable mask resolution for each instance, achieving high efficiency while maintaining high segmentation accuracy. Without bells and whistles, the proposed method, namely DynaMask, brings consistent and noticeable performance improvements over other state-of-the-arts at a moderate computation overhead. The source code: https://github.com/lslrh/DynaMask." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 547, + 128, + 559 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 547, + 128, + 559 + ], + "spans": [ + { + "bbox": [ + 47, + 547, + 128, + 559 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 567, + 287, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 567, + 287, + 687 + ], + "spans": [ + { + "bbox": [ + 46, + 567, + 287, + 687 + ], + "type": "text", + "content": "Instance segmentation (IS) is an important computer vision task, aiming at simultaneously predicting the class label and the binary mask for each instance of interest in an image. It works as the cornerstone of many downstream vision applications, such as autonomous driving, video surveillance, and robotics, to name a few. Recent years have witnessed the significant advances of deep convolutional neural networks (CNNs) based IS methods with a rich amount of training data as the rocket fuel [1, 10, 17, 25, 26]. Existing IS methods can be roughly divided into two ma" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 326, + 212, + 526, + 355 + ], + "blocks": [ + { + "bbox": [ + 326, + 212, + 526, + 355 + ], + "lines": [ + { + "bbox": [ + 326, + 212, + 526, + 355 + ], + "spans": [ + { + "bbox": [ + 326, + 212, + 526, + 355 + ], + "type": "image", + "image_path": "dbec4932b6e30d8c0989dd315998d63c80dd30a438930fb01719e1ef84492e09.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 360, + 545, + 393 + ], + "lines": [ + { + "bbox": [ + 305, + 360, + 545, + 393 + ], + "spans": [ + { + "bbox": [ + 305, + 360, + 545, + 393 + ], + "type": "text", + "content": "Figure 1. Dynamic mask selection results. Some \"hard\" samples with irregular shapes like \"person\" are assigned larger masks, while the \"easy\" ones like \"frisbee\" are assigned smaller ones." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 400, + 546, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 400, + 546, + 496 + ], + "spans": [ + { + "bbox": [ + 304, + 400, + 546, + 496 + ], + "type": "text", + "content": "jor categories: two-stage [6, 10, 17] and single-stage methods [1, 2, 26]. The former first detect a sparse set of proposals and then performs mask predictions based on them, while the latter directly predict classification scores and masks based on the pre-defined anchors. Generally speaking, two-stage methods could produce higher segmentation accuracy but cost more computational resources than single-stage methods." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 497, + 547, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 497, + 547, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 497, + 547, + 700 + ], + "type": "text", + "content": "Among the many recently developed IS methods, the proposal-based two-stage methods [6, 10, 17], which follow a detection-and-segmentation paradigm, are still the top performers. These methods need to predict a binary grid mask of uniform resolution for all proposals, e.g., " + }, + { + "bbox": [ + 304, + 497, + 547, + 700 + ], + "type": "inline_equation", + "content": "28 \\times 28" + }, + { + "bbox": [ + 304, + 497, + 547, + 700 + ], + "type": "text", + "content": ", and then upsample it to the original image size. For instance, Mask R-CNN [10] first generates a group of proposals with an object detector and then performs per pixel foreground/background segmentation on the Regions of Interest (RoIs) [24]. Despite achieving promising performance, the low-resolution mask of Mask R-CNN is insufficient to capture more detailed information, resulting in unsatisfactory predictions, especially over object boundaries. An intuitive solution to improve the segmentation quality is to adopt a larger mask. Nevertheless, high-resolution masks often generate excessive predictions on the smooth regions, resulting in high computational complexity." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "text", + "content": "It is difficult to segment different objects in an image" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 693, + 286, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 286, + 713 + ], + "type": "text", + "content": "*denotes the equal contribution, †denotes the corresponding author. This work is supported by the Hong Kong RGC RIF grant (R5001-18)." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11279" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 359 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 359 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 359 + ], + "type": "text", + "content": "with masks of the same resolution. Objects with irregular shapes and complicated boundaries demand more fine-grained masks to predict, referred to as \"hard\" samples, such as the \"person\" in Fig. 1. In comparison, the \"easy\" samples with regular shapes and fewer details can be efficiently segmented using coarser masks, like the \"frisbee\" in Fig. 1. Inspired by the above observations, we propose to adaptively adjust the mask size for each instance for better IS performance. Specifically, instead of using a uniform resolution for all instances, we assign high-resolution masks to \"hard\" objects and low-resolution masks to \"easy\" objects. In this way, the redundant computation for \"easy\" samples can be reduced while the accuracy of \"hard\" samples can be improved, achieving a balance between accuracy and speed. As shown in Tab. 1, however, directly predicting a high-resolution mask by Mask R-CNN [10] unexpectedly degrades the mask average precision (AP). This attributes to two main reasons. First, the RoI features of larger objects are extracted from higher pyramid levels, which are very coarse due to the downsampling operations [20]. Thus simply increasing the mask size of these RoIs will not bring extra useful information. Second, the mask head of Mask R-CNN is oversimplified, so it cannot make more precise predictions as the mask grid size increases." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 360, + 289, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 360, + 289, + 539 + ], + "spans": [ + { + "bbox": [ + 47, + 360, + 289, + 539 + ], + "type": "text", + "content": "To overcome the above mentioned problems, we propose a dual-level FPN framework to gradually enlarge the mask grid. Specifically, in addition to traditional image-level FPN (i-FPN), a region-level FPN (r-FPN) is designed to achieve coarse-to-fine mask prediction. Wherein we construct information flows between i-FPN and r-FPN at different pyramid levels, aiming to incorporate complementary contextual and detailed information from multiple feature levels for high-quality segmentation. With the dual-level FPN, we present a data-dependent Mask Switch Module (MSM) with negligible computational cost to adaptively select masks for each instance. The overall approach, namely DynaMask, is evaluated on benchmark instance segmentation datasets to demonstrate its superiority over state-of-the-arts. The major contributions of this work are summarized as follows:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 57, + 545, + 287, + 706 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 57, + 545, + 287, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 545, + 287, + 605 + ], + "spans": [ + { + "bbox": [ + 57, + 545, + 287, + 605 + ], + "type": "text", + "content": "- A dynamic mask selection method (DynaMask) is proposed to adaptively assign appropriate masks to different instances. Specifically, it assigns low-resolution masks to \"easy\" samples for efficiency while assigning high-resolution masks to \"hard\" samples for accuracy." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 57, + 607, + 287, + 656 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 607, + 287, + 656 + ], + "spans": [ + { + "bbox": [ + 57, + 607, + 287, + 656 + ], + "type": "text", + "content": "- A dual-level FPN framework is developed for IS. We construct direct information flows from i-FPN to r-FPN at multiple levels, facilitating complementary information aggregation from multiple pyramid levels." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 57, + 657, + 287, + 706 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 657, + 287, + 706 + ], + "spans": [ + { + "bbox": [ + 57, + 657, + 287, + 706 + ], + "type": "text", + "content": "- Extensive experiments demonstrate that DynaMask achieves a good trade-off between IS accuracy and efficiency, outperforming many state-of-the-art two-stage IS methods at a moderate computation overhead." + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "type": "table", + "bbox": [ + 331, + 70, + 525, + 178 + ], + "blocks": [ + { + "bbox": [ + 331, + 70, + 525, + 178 + ], + "lines": [ + { + "bbox": [ + 331, + 70, + 525, + 178 + ], + "spans": [ + { + "bbox": [ + 331, + 70, + 525, + 178 + ], + "type": "table", + "html": "
MethodResolutionAPFLOPs
Mask R-CNN [10]14×1432.90.2G
28×2834.70.5G
56×5633.82.0G
112×11232.58.0G
DynaMask14×1432.90.2G
28×2836.10.6G
56×5637.11.0G
112×11237.61.4G
", + "image_path": "0ecdaa54fb186dcd7c63d2aad016e77283d7752d39db972398597b1bdb1e4cf5.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 185, + 545, + 231 + ], + "lines": [ + { + "bbox": [ + 304, + 185, + 545, + 231 + ], + "spans": [ + { + "bbox": [ + 304, + 185, + 545, + 231 + ], + "type": "text", + "content": "Table 1. Mask AP and FLOPs with different mask resolutions. For Mask R-CNN, directly increasing the mask resolution will decrease the mask AP. While for our DynaMask, higher mask resolution results in better performance." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 244, + 392, + 257 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 244, + 392, + 257 + ], + "spans": [ + { + "bbox": [ + 306, + 244, + 392, + 257 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 266, + 545, + 458 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 266, + 545, + 458 + ], + "spans": [ + { + "bbox": [ + 304, + 266, + 545, + 458 + ], + "type": "text", + "content": "Instance Segmentation. To date, most of the top-performing IS methods still follow the Mask R-CNN metaarchitecture [10]. These proposal-based approaches typically employ an object detector to localize each instance in bounding boxes. Then the instance-wise features are cropped and extracted from FPN features based on the detected bounding boxes by using RoI pooling/align [10, 24]. Finally, a compact segmentation head is deployed to obtain the desired object masks. Mask Scoring R-CNN [14] aligns the mask quality and score by using a branch to explicitly learn the quality of predicted masks. BMask R-CNN [6] leverages boundary details to improve mask localization ability. DCT-Mask [25] encodes high-resolution binary masks into compact vectors through the discrete cosine transform (DCT). PANet [22] constructs two feature pyramids for improving mask prediction." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 460, + 545, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 460, + 545, + 652 + ], + "spans": [ + { + "bbox": [ + 304, + 460, + 545, + 652 + ], + "type": "text", + "content": "Some works [3, 17, 30] have been proposed to improve the mask quality by coarse-to-fine refinement. HTC [3] performs cascaded refinement on both detection and segmentation tasks and explores the reciprocal relationships between them. PointRend [17] and RefineMask [30] extract fine-grained features in a multi-stage manner. The former performs point-based predictions over the blurred areas, while the latter refines the entire RoI feature. Despite the promising segmentation results, multiple refinement stages inevitably increase the inference time and memory burden. In this paper, we dynamically select the suitable mask for each instance so that \"easy\" samples are assigned small masks (with fewer refinement stages) for efficiency, and \"hard\" samples are assigned large masks (with more refinement stages) for accuracy, achieving a balance between efficiency and accuracy." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 653, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 715 + ], + "type": "text", + "content": "Dynamic Networks. Dynamic networks, which aim to adaptively adjust the network architecture according to the input feature, have been widely studied in recent years. Dynamic model compression methods either drop blocks [12, 23, 27] or prune channels [19, 29] for speeding" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "11280" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 73, + 72, + 521, + 222 + ], + "blocks": [ + { + "bbox": [ + 73, + 72, + 521, + 222 + ], + "lines": [ + { + "bbox": [ + 73, + 72, + 521, + 222 + ], + "spans": [ + { + "bbox": [ + 73, + 72, + 521, + 222 + ], + "type": "image", + "image_path": "b29b2729616c25008a941ebaf283eac79f37a0e1463997eb2cb14761f2b3ca4e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 229, + 545, + 298 + ], + "lines": [ + { + "bbox": [ + 45, + 229, + 545, + 298 + ], + "spans": [ + { + "bbox": [ + 45, + 229, + 545, + 298 + ], + "type": "text", + "content": "Figure 2. The overall architecture of DynaMask. We propose a dual-level FPN framework to gradually increase the mask size and achieve higher-quality IS. The information flow is constructed between each level of image-level FPN (i-FPN) and region-level FPN (r-FPN), so that region-wise feature hierarchies " + }, + { + "bbox": [ + 45, + 229, + 545, + 298 + ], + "type": "inline_equation", + "content": "\\{L_{tiny}, L_{small}, L_{medium}, L_{large}\\}" + }, + { + "bbox": [ + 45, + 229, + 545, + 298 + ], + "type": "text", + "content": " are constantly enhanced by incorporating complementary information from " + }, + { + "bbox": [ + 45, + 229, + 545, + 298 + ], + "type": "inline_equation", + "content": "\\{P2, P3, P4\\}" + }, + { + "bbox": [ + 45, + 229, + 545, + 298 + ], + "type": "text", + "content": " of i-FPN, resulting in coarse-to-fine mask predictions. To reduce the computation and memory cost, a Mask Switch Module (MSM) is developed to predict the mask resolution for each instance with budgeted resource consumption. Specifically, MSM outputs four different switching states, corresponding to four different mask resolutions, i.e., " + }, + { + "bbox": [ + 45, + 229, + 545, + 298 + ], + "type": "inline_equation", + "content": "[14 \\times 14, 28 \\times 28, 56 \\times 56, 112 \\times 112]" + }, + { + "bbox": [ + 45, + 229, + 545, + 298 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 307, + 287, + 402 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 307, + 287, + 402 + ], + "spans": [ + { + "bbox": [ + 46, + 307, + 287, + 402 + ], + "type": "text", + "content": "up the inference. For instance, SkipNet [27] skips convolutional blocks through a reinforcement learning-based gating network. Huang et al. propose a multi-scale dense network with multiple classifiers for allocating different computations for \"easy\" and \"hard\" samples. Li et al. [18] adopt an end-to-end dynamic routing framework to alleviate the scale variance among inputs. DRNet [32] attempts to reduce the redundancy on the input resolution of modern CNNs." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 403, + 287, + 535 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 403, + 287, + 535 + ], + "spans": [ + { + "bbox": [ + 46, + 403, + 287, + 535 + ], + "type": "text", + "content": "However, employing dynamic masks at different resolutions for segmenting different instances has rarely been explored in the field of IS. Conventional methods [6, 10, 17] typically predict a fixed-size mask irrespective of the object type. This is sufficient for \"easy\" samples but produces over-smoothing predictions for \"hard\" samples over the fine-level details. In order to improve the segmentation performance without introducing many additional computation burdens, we devise a dynamic mask selection framework to adaptively allocate suitable masks to different objects according to their segmentation difficulties." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 546, + 188, + 559 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 546, + 188, + 559 + ], + "spans": [ + { + "bbox": [ + 47, + 546, + 188, + 559 + ], + "type": "text", + "content": "3. Dynamic Mask Selection" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 566, + 287, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 566, + 287, + 662 + ], + "spans": [ + { + "bbox": [ + 46, + 566, + 287, + 662 + ], + "type": "text", + "content": "The framework of DynaMask is illustrated in Fig. 2. A dual-level FPN architecture is first proposed for improving IS quality, and then a Mask Switch Module (MSM) is developed to dynamically allocate appropriate masks to each instance, so that the resource consumption can be reduced while maintaining superior IS performance. Our DynaMask produces high-quality segmentation with a moderate computation overhead." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 670, + 145, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 670, + 145, + 682 + ], + "spans": [ + { + "bbox": [ + 47, + 670, + 145, + 682 + ], + "type": "text", + "content": "3.1. Dual-Level FPN" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "Original image-level FPN (i-FPN) [20] introduces a top-down path to propagate contextual semantic information" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 307, + 545, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 307, + 545, + 415 + ], + "spans": [ + { + "bbox": [ + 304, + 307, + 545, + 415 + ], + "type": "text", + "content": "from higher layers to lower ones. Actually, the lower-level features contain more fine-grained details than higher-level ones, which are beneficial for high-quality segmentation, especially on boundary regions, but these information is not fully explored in Mask R-CNN [10]. In this work, we propose a region-level FPN (r-FPN) to integrate more detailed information from lower layers of i-FPN into region-wise feature hierarchies. The information flows from each level of i-FPN to r-FPN are shown in Fig. 2." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 420, + 546, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 420, + 546, + 564 + ], + "spans": [ + { + "bbox": [ + 304, + 420, + 546, + 564 + ], + "type": "text", + "content": "Region-Level FPN. We follow the original i-FPN to define the layers producing feature maps of the same resolution as one network stage corresponding to one feature level. We use " + }, + { + "bbox": [ + 304, + 420, + 546, + 564 + ], + "type": "inline_equation", + "content": "\\{P_2, P_3, P_4, P_5\\}" + }, + { + "bbox": [ + 304, + 420, + 546, + 564 + ], + "type": "text", + "content": " to denote different feature levels of i-FPN. The r-FPN starts from an RoI-Aligned region-wise feature, and it is gradually enhanced by fusing the complementary information from " + }, + { + "bbox": [ + 304, + 420, + 546, + 564 + ], + "type": "inline_equation", + "content": "\\{P_2, P_3, P_4\\}" + }, + { + "bbox": [ + 304, + 420, + 546, + 564 + ], + "type": "text", + "content": " of i-FPN, resulting in top-down region-based feature hierarchies, denoted by " + }, + { + "bbox": [ + 304, + 420, + 546, + 564 + ], + "type": "inline_equation", + "content": "\\{L_{tiny}, L_{small}, L_{medium}, L_{large}\\}" + }, + { + "bbox": [ + 304, + 420, + 546, + 564 + ], + "type": "text", + "content": ". From " + }, + { + "bbox": [ + 304, + 420, + 546, + 564 + ], + "type": "inline_equation", + "content": "L_{tiny}" + }, + { + "bbox": [ + 304, + 420, + 546, + 564 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 420, + 546, + 564 + ], + "type": "inline_equation", + "content": "L_{large}" + }, + { + "bbox": [ + 304, + 420, + 546, + 564 + ], + "type": "text", + "content": ", the spatial resolution is progressively increased by a factor of two. We design a Feature Aggregation Module (FAM) to integrate the r-FPN feature " + }, + { + "bbox": [ + 304, + 420, + 546, + 564 + ], + "type": "inline_equation", + "content": "L_r" + }, + { + "bbox": [ + 304, + 420, + 546, + 564 + ], + "type": "text", + "content": " and the i-FPN feature " + }, + { + "bbox": [ + 304, + 420, + 546, + 564 + ], + "type": "inline_equation", + "content": "P_i" + }, + { + "bbox": [ + 304, + 420, + 546, + 564 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "content": "Feature Aggregation Module (FAM). There exists spatial misalignments between " + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "inline_equation", + "content": "L_{r}" + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "inline_equation", + "content": "P_{i}" + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "content": " due to the upsampling and RoI pooling [24] operations, which may degrade the segmentation performance on boundary areas. To overcome this limitation, we propose the FAM to adaptively aggregate multi-scale features. As show in Fig. 3, FAM contains two deformable convolutions [8, 13] which play different roles. The first one (Deform_Conv1) adjusts the positions of " + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "inline_equation", + "content": "L_{r}" + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "content": ", making it better aligned to " + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "inline_equation", + "content": "P_{i}" + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "content": ". Here we first concatenate " + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "inline_equation", + "content": "L_{r}" + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "inline_equation", + "content": "P_{i}" + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "content": ", and then pass the concatenated features through a " + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "content": " Conv to obtain the offset map, denoted by " + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\Delta_{o}" + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "content": ". Finally, " + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "inline_equation", + "content": "L_{r}" + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "content": " is aligned to " + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "inline_equation", + "content": "P_{i}" + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "content": " with the learned offset " + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\Delta_{o}" + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "content": ". The" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11281" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 55, + 69, + 280, + 156 + ], + "blocks": [ + { + "bbox": [ + 55, + 69, + 280, + 156 + ], + "lines": [ + { + "bbox": [ + 55, + 69, + 280, + 156 + ], + "spans": [ + { + "bbox": [ + 55, + 69, + 280, + 156 + ], + "type": "image", + "image_path": "01a40b0e210f07ddea80274f6b0d3fa40922e904296e3bf53b425c5cbe79ae55.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 164, + 288, + 209 + ], + "lines": [ + { + "bbox": [ + 46, + 164, + 288, + 209 + ], + "spans": [ + { + "bbox": [ + 46, + 164, + 288, + 209 + ], + "type": "text", + "content": "Figure 3. Feature Alignment Molecule (FAM). Deform_Conv1 adjusts the spatial positions of upsampled r-FPN feature " + }, + { + "bbox": [ + 46, + 164, + 288, + 209 + ], + "type": "inline_equation", + "content": "L_{r}" + }, + { + "bbox": [ + 46, + 164, + 288, + 209 + ], + "type": "text", + "content": " and the cropped i-FPN feature " + }, + { + "bbox": [ + 46, + 164, + 288, + 209 + ], + "type": "inline_equation", + "content": "P_{i}" + }, + { + "bbox": [ + 46, + 164, + 288, + 209 + ], + "type": "text", + "content": ". Deform_Conv2 attends to the salient parts of objects." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 215, + 288, + 264 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 215, + 288, + 264 + ], + "spans": [ + { + "bbox": [ + 46, + 215, + 288, + 264 + ], + "type": "text", + "content": "second one (Deform_Conv2) works like an attention mechanism, which attends to the salient parts of objects. The proposed FAM is plugged into different stages of r-FPN and it plays a key role in improving the mask prediction." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 270, + 206, + 283 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 270, + 206, + 283 + ], + "spans": [ + { + "bbox": [ + 47, + 270, + 206, + 283 + ], + "type": "text", + "content": "3.2. Mask Switch Module (MSM)" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 289, + 287, + 408 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 289, + 287, + 408 + ], + "spans": [ + { + "bbox": [ + 46, + 289, + 287, + 408 + ], + "type": "text", + "content": "The proposed dual-level FPN framework brings a significant performance improvement but at the price of expensive computation and memory burdens. Inspired by the fact that different instances require different mask grids to achieve accurate segmentation, we propose a novel method to adaptively adjust the mask grid resolution for different instances. Specifically, an MSM is developed to perform mask resolution prediction under a budgeted computation consumption, achieving a good trade-off between segmentation accuracy and efficiency." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 408, + 288, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 408, + 288, + 563 + ], + "spans": [ + { + "bbox": [ + 46, + 408, + 288, + 563 + ], + "type": "text", + "content": "Optimal Mask Assignment. The MSM module is actually a lightweight classifier, denoted by " + }, + { + "bbox": [ + 46, + 408, + 288, + 563 + ], + "type": "inline_equation", + "content": "f_{MSM}(\\cdot)" + }, + { + "bbox": [ + 46, + 408, + 288, + 563 + ], + "type": "text", + "content": ", which is illustrated in Fig. 4. It contains a channel-wise attention module [11], followed by a few convolutional layers and fully-connected layers. This classifier aims to find the optimal mask resolution from a collection of " + }, + { + "bbox": [ + 46, + 408, + 288, + 563 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 408, + 288, + 563 + ], + "type": "text", + "content": " candidates, i.e., " + }, + { + "bbox": [ + 46, + 408, + 288, + 563 + ], + "type": "inline_equation", + "content": "[r^1, r^2, \\dots, r^K]" + }, + { + "bbox": [ + 46, + 408, + 288, + 563 + ], + "type": "text", + "content": ", so that the instance could be accurately segmented with the minimal resource cost. Specifically, MSM takes the cropped region-wise RoI feature as input and outputs a probability vector " + }, + { + "bbox": [ + 46, + 408, + 288, + 563 + ], + "type": "inline_equation", + "content": "P = [p^1, \\dots, p^K]" + }, + { + "bbox": [ + 46, + 408, + 288, + 563 + ], + "type": "text", + "content": " by taking a softmax operation. Each element of this vector represents the probability that the corresponding candidate resolution is selected:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 63, + 570, + 287, + 599 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 570, + 287, + 599 + ], + "spans": [ + { + "bbox": [ + 63, + 570, + 287, + 599 + ], + "type": "interline_equation", + "content": "p ^ {k} = \\frac {\\exp \\left(f _ {M S M} ^ {k} (x)\\right)}{\\sum_ {k ^ {\\prime}} \\exp \\left(f _ {M S M} ^ {k ^ {\\prime}} (x)\\right)}, \\quad k \\in \\{1, \\dots , K \\}, \\tag {1}", + "image_path": "0412a014e78c283def552f2f47a0ebf4617159acccf623d28ace9886459292d1.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 605, + 287, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 654 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 654 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 605, + 287, + 654 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 605, + 287, + 654 + ], + "type": "text", + "content": " is the input RoI feature fed to MSM. The candidate resolution of the largest probability is chosen as the switching state, which decides the resolution of mask grid to segment an object." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "text", + "content": "Reparameterization with Gumbel-Softmax. The soft output " + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "text", + "content": " of MSM should be transformed into a one-hot prediction, denoted by " + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "inline_equation", + "content": "Y = [y^{1},\\dots ,y^{K}]" + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "inline_equation", + "content": "y^{k}\\in \\{0,1\\}" + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "text", + "content": ". This process can be done by discrete sampling, which however is non-differentiable and does not support end-to-end training." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "type": "text", + "content": "To allow the gradient back-propagation for updating MSM, we introduce a reparameterization method [15], called the Gumbel-Softmax. Given a categorical distribution with class probabilities " + }, + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "type": "inline_equation", + "content": "P = [p^{1},\\dots ,p^{K}]" + }, + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "type": "text", + "content": ", we can draw a group of masks through the rule " + }, + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "type": "inline_equation", + "content": "y =" + }, + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "type": "text", + "content": " onehot " + }, + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "type": "inline_equation", + "content": "\\left(\\arg \\max_{k}(logp^{k} + g^{k})\\right)" + }, + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "type": "inline_equation", + "content": "\\{g^k\\}_{i = k}^K" + }, + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "type": "text", + "content": " are i.i.d. samples drawn from the Gumbel(0,1) distribution, which is defined by " + }, + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "type": "inline_equation", + "content": "g = -\\log (-\\log (u))" + }, + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "type": "inline_equation", + "content": "u\\sim \\text{Uniform}(0,1)" + }, + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "type": "text", + "content": ". Then we use the Gumbel-softmax function as a continuous, differentiable approximation to the original softmax function:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 351, + 213, + 545, + 244 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 213, + 545, + 244 + ], + "spans": [ + { + "bbox": [ + 351, + 213, + 545, + 244 + ], + "type": "interline_equation", + "content": "y ^ {k} = \\frac {\\exp \\left(\\left(\\log p ^ {k} + g ^ {k}\\right) / \\tau\\right)}{\\sum_ {k ^ {\\prime}} \\exp \\left(\\left(\\log p ^ {k ^ {\\prime}} + g ^ {k ^ {\\prime}}\\right) / \\tau\\right)}, \\tag {2}", + "image_path": "8c4310cfb5ad3465b5a7d255e11285dac9b4cb8521db5908557469989beec44a.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 251, + 545, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 251, + 545, + 276 + ], + "spans": [ + { + "bbox": [ + 304, + 251, + 545, + 276 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 251, + 545, + 276 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 251, + 545, + 276 + ], + "type": "text", + "content": " denotes a temperature parameter. When " + }, + { + "bbox": [ + 304, + 251, + 545, + 276 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 251, + 545, + 276 + ], + "type": "text", + "content": " approaches 0, the Gumbel-softmax is close to one-hot." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 284, + 418, + 297 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 284, + 418, + 297 + ], + "spans": [ + { + "bbox": [ + 305, + 284, + 418, + 297 + ], + "type": "text", + "content": "3.3. Objective Function" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 303, + 545, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 303, + 545, + 421 + ], + "spans": [ + { + "bbox": [ + 304, + 303, + 545, + 421 + ], + "type": "text", + "content": "The proposed framework gradually enlarges the mask resolution by a factor of two to improve the segmentation performance. On the one hand, FAM adaptively aggregates complementary information from multiple stages of i-FPN and r-FPN to enhance the feature hierarchies. On the other hand, MSM dynamically allocates masks of different resolutions for different instances in an image, reducing resource costs without sacrificing accuracy. In this subsection, we elaborate on the loss function used to train the mask head." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 422, + 547, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 422, + 547, + 494 + ], + "spans": [ + { + "bbox": [ + 304, + 422, + 547, + 494 + ], + "type": "text", + "content": "Mask Loss. Given a positive instance " + }, + { + "bbox": [ + 304, + 422, + 547, + 494 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 304, + 422, + 547, + 494 + ], + "type": "text", + "content": ", we first predict its mask switching state " + }, + { + "bbox": [ + 304, + 422, + 547, + 494 + ], + "type": "inline_equation", + "content": "Y = [y^{1},\\dots ,y^{K}]" + }, + { + "bbox": [ + 304, + 422, + 547, + 494 + ], + "type": "text", + "content": " by MSM, and obtain a group of mask prediction maps at " + }, + { + "bbox": [ + 304, + 422, + 547, + 494 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 422, + 547, + 494 + ], + "type": "text", + "content": " different resolutions " + }, + { + "bbox": [ + 304, + 422, + 547, + 494 + ], + "type": "inline_equation", + "content": "\\{\\hat{m}_i^1,\\dots ,\\hat{m}_i^K\\}" + }, + { + "bbox": [ + 304, + 422, + 547, + 494 + ], + "type": "text", + "content": " by passing this instance through different stages of r-FPN. We define the mask loss function as follows:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 359, + 502, + 545, + 536 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 502, + 545, + 536 + ], + "spans": [ + { + "bbox": [ + 359, + 502, + 545, + 536 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {m a s k}} = \\sum_ {i = 1} ^ {N} \\sum_ {k = 1} ^ {K} y ^ {k} \\ell \\left(\\hat {m} _ {i} ^ {k}, m _ {i}\\right), \\tag {3}", + "image_path": "454cda8f5831bd3ca5acc568b906c073298889f43299f26abbce35f9a6a3aa2e.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 544, + 545, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 544, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 544, + 545, + 605 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 544, + 545, + 605 + ], + "type": "inline_equation", + "content": "\\hat{m}_i^k" + }, + { + "bbox": [ + 304, + 544, + 545, + 605 + ], + "type": "text", + "content": " denotes the " + }, + { + "bbox": [ + 304, + 544, + 545, + 605 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 544, + 545, + 605 + ], + "type": "text", + "content": "-th mask prediction of " + }, + { + "bbox": [ + 304, + 544, + 545, + 605 + ], + "type": "inline_equation", + "content": "x_i" + }, + { + "bbox": [ + 304, + 544, + 545, + 605 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 544, + 545, + 605 + ], + "type": "inline_equation", + "content": "m_i" + }, + { + "bbox": [ + 304, + 544, + 545, + 605 + ], + "type": "text", + "content": " represents its corresponding ground truth mask grid. " + }, + { + "bbox": [ + 304, + 544, + 545, + 605 + ], + "type": "inline_equation", + "content": "y^k" + }, + { + "bbox": [ + 304, + 544, + 545, + 605 + ], + "type": "text", + "content": " is the indicator for whether the " + }, + { + "bbox": [ + 304, + 544, + 545, + 605 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 544, + 545, + 605 + ], + "type": "text", + "content": "-th mask resolution is selected as the output resolution. " + }, + { + "bbox": [ + 304, + 544, + 545, + 605 + ], + "type": "inline_equation", + "content": "\\ell" + }, + { + "bbox": [ + 304, + 544, + 545, + 605 + ], + "type": "text", + "content": " is defined as the binary cross-entropy loss in this paper." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 605, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 715 + ], + "type": "text", + "content": "Edge Loss. In Eq. 3, we assume that the mask producing smaller loss should have higher quality, so that the most accurate mask could be selected by minimizing the mask loss. However, our empirical results show that the mask loss produced on different masks is very close, making it difficult to distinguish the mask quality. In comparison, as shown in Fig. 5, the edge loss produced by masks of different resolutions varies greatly, which could better reveal the mask quality. Given the output of MSM " + }, + { + "bbox": [ + 304, + 605, + 545, + 715 + ], + "type": "inline_equation", + "content": "Y = [y^{1},\\dots ,y^{K}]" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "11282" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 80, + 79, + 511, + 163 + ], + "blocks": [ + { + "bbox": [ + 80, + 79, + 511, + 163 + ], + "lines": [ + { + "bbox": [ + 80, + 79, + 511, + 163 + ], + "spans": [ + { + "bbox": [ + 80, + 79, + 511, + 163 + ], + "type": "image", + "image_path": "be6e6f211d82e965e97da5142b5cc9cba3130d3ac20dfb002cffe881aafadbb1.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 163, + 547, + 187 + ], + "lines": [ + { + "bbox": [ + 46, + 163, + 547, + 187 + ], + "spans": [ + { + "bbox": [ + 46, + 163, + 547, + 187 + ], + "type": "text", + "content": "Figure 4. The Mask Switch Module (MSM), which is a CNN-based classifier and consists of a SE-block [11], two convolutional layers and two fully-connected layers." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 72, + 199, + 263, + 285 + ], + "blocks": [ + { + "bbox": [ + 72, + 199, + 263, + 285 + ], + "lines": [ + { + "bbox": [ + 72, + 199, + 263, + 285 + ], + "spans": [ + { + "bbox": [ + 72, + 199, + 263, + 285 + ], + "type": "image", + "image_path": "2ac052ae07c5b19bf8f795b5182c206479c3969718c93cf6946b1b1e84219f71.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 287, + 288, + 321 + ], + "lines": [ + { + "bbox": [ + 46, + 287, + 288, + 321 + ], + "spans": [ + { + "bbox": [ + 46, + 287, + 288, + 321 + ], + "type": "text", + "content": "Figure 5. The predicted object edges using the masks of different resolutions. The edge loss computed on boundary regions could reflect the quality of mask." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 341, + 287, + 367 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 341, + 287, + 367 + ], + "spans": [ + { + "bbox": [ + 47, + 341, + 287, + 367 + ], + "type": "text", + "content": "and the edge maps of different resolutions, denoted by " + }, + { + "bbox": [ + 47, + 341, + 287, + 367 + ], + "type": "inline_equation", + "content": "\\{\\hat{e}_i^1,\\dots ,\\hat{e}_i^K\\}" + }, + { + "bbox": [ + 47, + 341, + 287, + 367 + ], + "type": "text", + "content": ", the edge loss is defined as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 107, + 378, + 287, + 411 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 378, + 287, + 411 + ], + "spans": [ + { + "bbox": [ + 107, + 378, + 287, + 411 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {e d g e} = \\sum_ {i = 1} ^ {N} \\sum_ {k = 1} ^ {K} y ^ {k} \\ell \\left(\\hat {e} _ {i} ^ {k}, e _ {i}\\right), \\tag {4}", + "image_path": "9e72870aab6b5379ce50078132b8e97b593c677ce471cff09828e56b9d4f2a59.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 424, + 287, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 424, + 287, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 424, + 287, + 533 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 424, + 287, + 533 + ], + "type": "inline_equation", + "content": "e_i" + }, + { + "bbox": [ + 46, + 424, + 287, + 533 + ], + "type": "text", + "content": " denotes the ground-truth edge, which is generated by first applying the Laplacian operator on the ground-truth mask " + }, + { + "bbox": [ + 46, + 424, + 287, + 533 + ], + "type": "inline_equation", + "content": "m_i" + }, + { + "bbox": [ + 46, + 424, + 287, + 533 + ], + "type": "text", + "content": " to obtain a soft edge map, and then converting it into a binary edge map by thresholding [6]. Fig. 5 visualizes the object edges predicted by using masks of different resolutions. As can be seen, the edge loss could better reveal the quality of masks, i.e., higher-resolution masks produce edges closer to GT (smaller loss), while lower-resolution masks produce edges more different from GT (larger loss)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 534, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 534, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 534, + 288, + 714 + ], + "type": "text", + "content": "Budget Constraint. By optimizing the edge loss in Eq. 4, the model tends to converge to a sub-optimal solution that all instances are segmented with the largest mask, i.e., " + }, + { + "bbox": [ + 46, + 534, + 288, + 714 + ], + "type": "inline_equation", + "content": "112 \\times 112" + }, + { + "bbox": [ + 46, + 534, + 288, + 714 + ], + "type": "text", + "content": ", which incorporates more detailed information and hence has the minimal prediction loss. Actually, not all samples require the largest mask for segmentation. The redundant computations of segmenting the \"easy\" samples can be saved for efficiency. In order to reduce the computational cost and avoid the above mentioned sub-optimal solution, we propose to train the MSM with a budget constraint. Specifically, let " + }, + { + "bbox": [ + 46, + 534, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 46, + 534, + 288, + 714 + ], + "type": "text", + "content": " denote the computational cost (e.g., FLOPs) corresponding to the selected mask resolution. We add a penalty to the model when the expectation of FLOPs computed on current batch data, denoted by " + }, + { + "bbox": [ + 46, + 534, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathbb{E}(\\mathcal{C})" + }, + { + "bbox": [ + 46, + 534, + 288, + 714 + ], + "type": "text", + "content": ", exceeds the target FLOPs, denoted by " + }, + { + "bbox": [ + 46, + 534, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_t" + }, + { + "bbox": [ + 46, + 534, + 288, + 714 + ], + "type": "text", + "content": ". The budget con" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 202, + 421, + 213 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 202, + 421, + 213 + ], + "spans": [ + { + "bbox": [ + 306, + 202, + 421, + 213 + ], + "type": "text", + "content": "strain is defined as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 364, + 222, + 545, + 248 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 222, + 545, + 248 + ], + "spans": [ + { + "bbox": [ + 364, + 222, + 545, + 248 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {b u d g e t}} = \\max \\left(\\frac {\\mathbb {E} (\\mathcal {C})}{\\mathcal {C} _ {t}} - 1, 0\\right). \\tag {5}", + "image_path": "15695ed75ec7f35a727d63cb65ec4472cfbf3a4a7df1f4d7312d582fe31973e3.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 257, + 545, + 329 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 257, + 545, + 329 + ], + "spans": [ + { + "bbox": [ + 305, + 257, + 545, + 329 + ], + "type": "text", + "content": "We further introduce an information entropy loss to balance the resolution predictions of MSM. Given a group of output probability vectors " + }, + { + "bbox": [ + 305, + 257, + 545, + 329 + ], + "type": "inline_equation", + "content": "P_{1}, P_{2}, \\dots, P_{N}" + }, + { + "bbox": [ + 305, + 257, + 545, + 329 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 305, + 257, + 545, + 329 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 305, + 257, + 545, + 329 + ], + "type": "text", + "content": " is the number of instances of the current batch, the frequency of the " + }, + { + "bbox": [ + 305, + 257, + 545, + 329 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 257, + 545, + 329 + ], + "type": "text", + "content": "-th resolution is calculated by: " + }, + { + "bbox": [ + 305, + 257, + 545, + 329 + ], + "type": "inline_equation", + "content": "f^{k} = \\frac{1}{N}\\sum_{i}p_{i}^{k}" + }, + { + "bbox": [ + 305, + 257, + 545, + 329 + ], + "type": "text", + "content": ". Then the information entropy loss is defined as follows:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 366, + 339, + 545, + 368 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 366, + 339, + 545, + 368 + ], + "spans": [ + { + "bbox": [ + 366, + 339, + 545, + 368 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {e n t r o p y}} = \\frac {1}{K} \\sum_ {k} f ^ {k} \\log f ^ {k}. \\tag {6}", + "image_path": "f89770e85df27ebdcb1eba5d1fb287e66f088ca35ab870f929a4bf5979765ec0.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 379, + 545, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 379, + 545, + 415 + ], + "spans": [ + { + "bbox": [ + 305, + 379, + 545, + 415 + ], + "type": "text", + "content": "The above entropy loss tends to push each element " + }, + { + "bbox": [ + 305, + 379, + 545, + 415 + ], + "type": "inline_equation", + "content": "f^k" + }, + { + "bbox": [ + 305, + 379, + 545, + 415 + ], + "type": "text", + "content": " to be " + }, + { + "bbox": [ + 305, + 379, + 545, + 415 + ], + "type": "inline_equation", + "content": "\\frac{1}{K}" + }, + { + "bbox": [ + 305, + 379, + 545, + 415 + ], + "type": "text", + "content": " so that MSM could select different resolutions with similar probabilities." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 416, + 545, + 440 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 416, + 545, + 440 + ], + "spans": [ + { + "bbox": [ + 305, + 416, + 545, + 440 + ], + "type": "text", + "content": "Finally, the total objective function of the mask branch is obtained as follows:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 347, + 452, + 545, + 466 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 452, + 545, + 466 + ], + "spans": [ + { + "bbox": [ + 347, + 452, + 545, + 466 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {\\text {m a s k}} + \\lambda_ {1} \\mathcal {L} _ {\\text {e d g e}} + \\lambda_ {2} \\mathcal {L} _ {\\text {r e g}}, \\tag {7}", + "image_path": "d53738b7de01d17173e74019f62ee65eb3d28a29c004565945ee01b339901bc8.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 475, + 545, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 475, + 545, + 525 + ], + "spans": [ + { + "bbox": [ + 305, + 475, + 545, + 525 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 475, + 545, + 525 + ], + "type": "inline_equation", + "content": "\\lambda_{1}" + }, + { + "bbox": [ + 305, + 475, + 545, + 525 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 475, + 545, + 525 + ], + "type": "inline_equation", + "content": "\\lambda_{2}" + }, + { + "bbox": [ + 305, + 475, + 545, + 525 + ], + "type": "text", + "content": " are the trade-off hyper-parameters. " + }, + { + "bbox": [ + 305, + 475, + 545, + 525 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{reg}" + }, + { + "bbox": [ + 305, + 475, + 545, + 525 + ], + "type": "text", + "content": " denotes the regularization term which is obtained by combining the budget constraint in Eq. 5 and the information entropy loss in Eq. 6, i.e., " + }, + { + "bbox": [ + 305, + 475, + 545, + 525 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{reg} = \\mathcal{L}_{budget} + \\mathcal{L}_{entropy}" + }, + { + "bbox": [ + 305, + 475, + 545, + 525 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 536, + 388, + 551 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 536, + 388, + 551 + ], + "spans": [ + { + "bbox": [ + 306, + 536, + 388, + 551 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": "We perform extensive experiments on the benchmark instance segmentation datasets: COCO [21] and Cityscapes [7]. COCO [21] contains about 115k images (train2017) with instance-level annotations of 80 categories for training. We use the val2017 set (around 5k images) for the ablation study and the test-dev2017 set (about 20k images) for comparison with other methods. The Cityscapes dataset [7] contains 2975, 500, and 1525 images collected from 8 categories of urban scenes for training, validation, and testing, respectively. On both COCO and Cityscapes datasets, we use the standard mask AP as the evaluation metric, which computes the average precision over varying IoU thresholds (from 0.5 to 0.95)." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11283" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 79, + 141, + 144 + ], + "blocks": [ + { + "bbox": [ + 61, + 79, + 141, + 144 + ], + "lines": [ + { + "bbox": [ + 61, + 79, + 141, + 144 + ], + "spans": [ + { + "bbox": [ + 61, + 79, + 141, + 144 + ], + "type": "image", + "image_path": "b9e5b9e3fd080b5c4bedf62d3e2b215354b24a55f150144ca00cebdeadd2b283.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 142, + 79, + 222, + 144 + ], + "blocks": [ + { + "bbox": [ + 142, + 79, + 222, + 144 + ], + "lines": [ + { + "bbox": [ + 142, + 79, + 222, + 144 + ], + "spans": [ + { + "bbox": [ + 142, + 79, + 222, + 144 + ], + "type": "image", + "image_path": "8625a4e7ec2055337dfbafa4b527333c3f10c18fec6e35d32db5b28aac33c9af.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 222, + 79, + 302, + 144 + ], + "blocks": [ + { + "bbox": [ + 222, + 79, + 302, + 144 + ], + "lines": [ + { + "bbox": [ + 222, + 79, + 302, + 144 + ], + "spans": [ + { + "bbox": [ + 222, + 79, + 302, + 144 + ], + "type": "image", + "image_path": "52c38f004f782417b85dfa9154621dd9b25865fbc0e5ccbddbea7220096a84da.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 303, + 79, + 383, + 144 + ], + "blocks": [ + { + "bbox": [ + 303, + 79, + 383, + 144 + ], + "lines": [ + { + "bbox": [ + 303, + 79, + 383, + 144 + ], + "spans": [ + { + "bbox": [ + 303, + 79, + 383, + 144 + ], + "type": "image", + "image_path": "0432c9e88664b8d887225c73876329ba1fb0445cc7dfe66b127c7d0df0c9150a.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 384, + 79, + 463, + 144 + ], + "blocks": [ + { + "bbox": [ + 384, + 79, + 463, + 144 + ], + "lines": [ + { + "bbox": [ + 384, + 79, + 463, + 144 + ], + "spans": [ + { + "bbox": [ + 384, + 79, + 463, + 144 + ], + "type": "image", + "image_path": "8d7eb519be6935e317be0ce286818f7c777750c3eece6685a7e335066e1043bc.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 465, + 79, + 544, + 144 + ], + "blocks": [ + { + "bbox": [ + 465, + 79, + 544, + 144 + ], + "lines": [ + { + "bbox": [ + 465, + 79, + 544, + 144 + ], + "spans": [ + { + "bbox": [ + 465, + 79, + 544, + 144 + ], + "type": "image", + "image_path": "fce6755db42aa1817a10b704a932639b9962236a0e224bae0d51252e67df6f2c.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 61, + 148, + 141, + 212 + ], + "blocks": [ + { + "bbox": [ + 61, + 148, + 141, + 212 + ], + "lines": [ + { + "bbox": [ + 61, + 148, + 141, + 212 + ], + "spans": [ + { + "bbox": [ + 61, + 148, + 141, + 212 + ], + "type": "image", + "image_path": "3386b64eff68f4cafbedcf7be316699a77f9360eaa7791913c7fcc57782cce29.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 218, + 545, + 230 + ], + "lines": [ + { + "bbox": [ + 46, + 218, + 545, + 230 + ], + "spans": [ + { + "bbox": [ + 46, + 218, + 545, + 230 + ], + "type": "text", + "content": "Figure 6. Example results of Mask R-CNN [10] (left), PointRend [17] (middle), and DynaMask (right), using ResNet-50-FPN as backbone." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 141, + 148, + 221, + 212 + ], + "blocks": [ + { + "bbox": [ + 141, + 148, + 221, + 212 + ], + "lines": [ + { + "bbox": [ + 141, + 148, + 221, + 212 + ], + "spans": [ + { + "bbox": [ + 141, + 148, + 221, + 212 + ], + "type": "image", + "image_path": "1c56c9d89529b655375104a96b8225d767beea9ce9b701921f5f9dbcc9e083db.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 222, + 148, + 302, + 212 + ], + "blocks": [ + { + "bbox": [ + 222, + 148, + 302, + 212 + ], + "lines": [ + { + "bbox": [ + 222, + 148, + 302, + 212 + ], + "spans": [ + { + "bbox": [ + 222, + 148, + 302, + 212 + ], + "type": "image", + "image_path": "e49251e4bd2e1b39e5cdb4747205c281a26d455987fe9d802997ca168a96e4a6.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 303, + 147, + 383, + 211 + ], + "blocks": [ + { + "bbox": [ + 303, + 147, + 383, + 211 + ], + "lines": [ + { + "bbox": [ + 303, + 147, + 383, + 211 + ], + "spans": [ + { + "bbox": [ + 303, + 147, + 383, + 211 + ], + "type": "image", + "image_path": "7cd416729655ca19dc02a697cdd6d113cbf067d3983f3c53a655d61a9be5a9b0.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 384, + 147, + 463, + 211 + ], + "blocks": [ + { + "bbox": [ + 384, + 147, + 463, + 211 + ], + "lines": [ + { + "bbox": [ + 384, + 147, + 463, + 211 + ], + "spans": [ + { + "bbox": [ + 384, + 147, + 463, + 211 + ], + "type": "image", + "image_path": "ebfddc63aa08d092f14818ea94a218311d62ec19c4c8e97111d996c447ebd72a.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 465, + 148, + 544, + 212 + ], + "blocks": [ + { + "bbox": [ + 465, + 148, + 544, + 212 + ], + "lines": [ + { + "bbox": [ + 465, + 148, + 544, + 212 + ], + "spans": [ + { + "bbox": [ + 465, + 148, + 544, + 212 + ], + "type": "image", + "image_path": "6905a9d1f573026df2e082edf85d91d28ebde90f7da6aa8901683ca59a1de517.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 246, + 180, + 258 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 246, + 180, + 258 + ], + "spans": [ + { + "bbox": [ + 47, + 246, + 180, + 258 + ], + "type": "text", + "content": "4.1. Implementation Details" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 264, + 290, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 264, + 290, + 479 + ], + "spans": [ + { + "bbox": [ + 46, + 264, + 290, + 479 + ], + "type": "text", + "content": "We adopt Mask R-CNN [10] as our baseline. The backbone is pre-trained on ImageNet. The hyper-parameters and loss functions are set the same as Mask R-CNN implemented in MMDetection [4] unless specified. The proposed MSM has four switching states, which correspond to four candidate resolutions, i.e., " + }, + { + "bbox": [ + 46, + 264, + 290, + 479 + ], + "type": "inline_equation", + "content": "[14 \\times 14, 28 \\times 28, 56 \\times 56, 112 \\times 112]" + }, + { + "bbox": [ + 46, + 264, + 290, + 479 + ], + "type": "text", + "content": ". The hyper-parameter " + }, + { + "bbox": [ + 46, + 264, + 290, + 479 + ], + "type": "inline_equation", + "content": "\\lambda_{1}" + }, + { + "bbox": [ + 46, + 264, + 290, + 479 + ], + "type": "text", + "content": " is set as 0.1. We first pretrain the model without MSM using mask loss at all resolutions for one epoch. The initial learning rate is 0.02, and the batch size is 16 on 8 GPUs. Then we train all modules for 12 epochs using SGD with the same initial learning rate and batch size and reduce the learning rate by a factor of 0.1 after 8 and 11 epochs, respectively. Multi-scale training is used with the shorter side randomly sampled from [640, 800], while for inference, the short side is resized to 800. In the ablation study, we use the standard " + }, + { + "bbox": [ + 46, + 264, + 290, + 479 + ], + "type": "inline_equation", + "content": "1 \\times" + }, + { + "bbox": [ + 46, + 264, + 290, + 479 + ], + "type": "text", + "content": " training schedule and data augmentation defined in MMDetection [4]." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 47, + 491, + 132, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 491, + 132, + 502 + ], + "spans": [ + { + "bbox": [ + 47, + 491, + 132, + 502 + ], + "type": "text", + "content": "4.2. Main Results" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 510, + 287, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 287, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 287, + 688 + ], + "type": "text", + "content": "Comparison with Mask R-CNN. We first compare the performance of DynaMask with the baseline Mask R-CNN on COCO by using ResNet-50 and ResNet-101 backbones. As shown in Tab. 2, our method outperforms Mask R-CNN by a large margin. The performance is improved by " + }, + { + "bbox": [ + 46, + 510, + 287, + 688 + ], + "type": "inline_equation", + "content": "2.9\\%" + }, + { + "bbox": [ + 46, + 510, + 287, + 688 + ], + "type": "text", + "content": " AP and " + }, + { + "bbox": [ + 46, + 510, + 287, + 688 + ], + "type": "inline_equation", + "content": "2.8\\%" + }, + { + "bbox": [ + 46, + 510, + 287, + 688 + ], + "type": "text", + "content": " AP with “" + }, + { + "bbox": [ + 46, + 510, + 287, + 688 + ], + "type": "inline_equation", + "content": "1 \\times" + }, + { + "bbox": [ + 46, + 510, + 287, + 688 + ], + "type": "text", + "content": "” and “" + }, + { + "bbox": [ + 46, + 510, + 287, + 688 + ], + "type": "inline_equation", + "content": "2 \\times" + }, + { + "bbox": [ + 46, + 510, + 287, + 688 + ], + "type": "text", + "content": "” schedules, respectively, when ResNet-50-FPN backbone is used. Particularly, DynaMask outperforms the baseline by " + }, + { + "bbox": [ + 46, + 510, + 287, + 688 + ], + "type": "inline_equation", + "content": "3.3\\%" + }, + { + "bbox": [ + 46, + 510, + 287, + 688 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 510, + 287, + 688 + ], + "type": "inline_equation", + "content": "3.6\\%" + }, + { + "bbox": [ + 46, + 510, + 287, + 688 + ], + "type": "text", + "content": " with “" + }, + { + "bbox": [ + 46, + 510, + 287, + 688 + ], + "type": "inline_equation", + "content": "1 \\times" + }, + { + "bbox": [ + 46, + 510, + 287, + 688 + ], + "type": "text", + "content": "” and “" + }, + { + "bbox": [ + 46, + 510, + 287, + 688 + ], + "type": "inline_equation", + "content": "2 \\times" + }, + { + "bbox": [ + 46, + 510, + 287, + 688 + ], + "type": "text", + "content": "” schedules in terms of " + }, + { + "bbox": [ + 46, + 510, + 287, + 688 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{75}" + }, + { + "bbox": [ + 46, + 510, + 287, + 688 + ], + "type": "text", + "content": ", respectively. Similar observations can be obtained when ResNet-101-FPN is used as the backbone. This is because the proposed dual-level FPN structure incorporates complementary semantic and detailed information from multiple levels of FPN, resulting in more precise mask localization and higher-quality segmentation." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "content": "Comparison with state-of-the-art methods. We then compare the segmentation performance of DynaMask with" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 246, + 546, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 246, + 546, + 425 + ], + "spans": [ + { + "bbox": [ + 304, + 246, + 546, + 425 + ], + "type": "text", + "content": "many other state-of-the-art methods on COCO. The results are listed in Tab. 3. All models are trained on COCO train2017 and evaluated on COCO test-dev2017. Without bells and whistles, DynaMask surpasses these methods with visible margins. Furthermore, we compare our method with other representative two-stage IS methods on Cityscapes val set in Tab. 4. Our method outperforms Mask R-CNN [10] by " + }, + { + "bbox": [ + 304, + 246, + 546, + 425 + ], + "type": "inline_equation", + "content": "4.2\\%" + }, + { + "bbox": [ + 304, + 246, + 546, + 425 + ], + "type": "text", + "content": ". Noticeably, its performance on large objects is " + }, + { + "bbox": [ + 304, + 246, + 546, + 425 + ], + "type": "inline_equation", + "content": "5.8\\%" + }, + { + "bbox": [ + 304, + 246, + 546, + 425 + ], + "type": "text", + "content": " AP higher than Mask R-CNN. This is because DynaMask employs high-resolution masks to achieve high-quality segmentation on large and difficult objects. RefineMask [30] also produces outstanding performance since it refines the mask prediction with fine-grained features, but it costs many computations due to the multi-stage refinement." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 426, + 547, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 547, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 547, + 581 + ], + "type": "text", + "content": "Visualizations of segmentation results. In Fig. 6, we visualize the segmentation results of DynaMask together with two representative methods: Mask R-CNN [10], and PointRend [17]. One can see that our method achieves finer and more accurate predictions around the objects' boundaries. This is because Dynamask introduces an r-FPN to fuse complementary information from multiple stages, so that difficult instances can be segmented with large masks which contain more fine-grained details. Mask R-CNN [10] employs a uniform coarse mask for prediction, while PointRend [17] makes point-wise refinement only at the blurred regions, which is not enough to capture sufficient details." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 587, + 400, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 587, + 400, + 601 + ], + "spans": [ + { + "bbox": [ + 306, + 587, + 400, + 601 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "type": "text", + "content": "Mask resolution prediction. To better understand how DynaMask selects suitable masks for different instances, we show the mask selection results in Fig. 7. As can be seen, the \"hard\" objects with irregular shapes and complex boundaries are assigned large masks, such as the \"potted plant\", \"person\", \"giraffe\", etc. On the contrary, the \"easy\" samples with regular shapes and less details are assigned small masks, such as the \"skis\", \"suitcase\", \"dining table\" and so on. It is worth mentioning that the choice of mask" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "11284" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 124, + 70, + 470, + 171 + ], + "blocks": [ + { + "bbox": [ + 124, + 70, + 470, + 171 + ], + "lines": [ + { + "bbox": [ + 124, + 70, + 470, + 171 + ], + "spans": [ + { + "bbox": [ + 124, + 70, + 470, + 171 + ], + "type": "table", + "html": "
MethodBackboneSched.AP\\( AP_{50} \\)\\( AP_{75} \\)\\( AP_S \\)\\( AP_M \\)\\( AP_L \\)
Mask R-CNN [10]ResNet-50-FPN1×34.755.737.218.337.447.2
DynaMaskResNet-50-FPN1×37.657.440.520.740.450.3
Mask R-CNN [10]ResNet-50-FPN2×35.456.437.919.138.648.4
DynaMaskResNet-50-FPN2×38.258.141.520.540.852.7
Mask R-CNN [10]ResNet-101-FPN1×36.157.538.618.839.749.5
DynaMaskResNet-101-FPN1×38.758.841.820.941.852.4
Mask R-CNN [10]ResNet-101-FPN2×36.657.939.119.240.250.5
DynaMaskResNet-101-FPN2×39.059.142.220.942.153.3
", + "image_path": "1d178b64cb5ffce4d57bd9078f03a1b38df17766a946850b45aec77ed6a8041a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 125, + 191, + 469, + 372 + ], + "blocks": [ + { + "bbox": [ + 182, + 174, + 411, + 185 + ], + "lines": [ + { + "bbox": [ + 182, + 174, + 411, + 185 + ], + "spans": [ + { + "bbox": [ + 182, + 174, + 411, + 185 + ], + "type": "text", + "content": "Table 2. Comparison with Mask R-CNN on COCO val2017." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 125, + 191, + 469, + 372 + ], + "lines": [ + { + "bbox": [ + 125, + 191, + 469, + 372 + ], + "spans": [ + { + "bbox": [ + 125, + 191, + 469, + 372 + ], + "type": "table", + "html": "
MethodBackbonesched.AP\\( AP_{50} \\)\\( AP_{75} \\)\\( AP_S \\)\\( AP_M \\)\\( AP_L \\)
MEInst [31]ResNet-101-FPN3×33.956.235.419.836.142.3
Mask R-CNN [10]ResNet-101-FPN3×38.560.041.619.241.655.8
BMask R-CNN [6]ResNet-101-FPN1×37.759.340.616.839.954.6
TensorMask [5]ResNet-101-FPN6×37.159.339.417.439.151.6
Mask Scoring [14]ResNet-101-FPN18e38.358.841.517.840.454.4
ConDInst [26]ResNet-101-FPN3×39.160.942.021.541.750.9
BlendMask [2]ResNet-101-FPN3×38.460.741.318.241.553.3
PointRend [17]ResNeXt-101-FPN3×41.463.344.824.243.953.2
SOLOv2 [28]ResNet-101-FPN6×39.760.742.917.342.957.4
HTC [3]ResNet-101-FPN20e39.761.843.121.042.253.5
DCT-Mask†[25]ResNet-101-FPN3×40.161.243.622.742.751.8
RefineMask [30]ResNet-101-FPN3×39.4-----
Mask Transfiner†[16]ResNet-101-FPN3×40.7--23.142.853.8
QueryInst†[9]ResNet-101-FPN3×41.764.445.324.243.953.9
DynaMaskResNet-101-FPN3×39.661.442.921.242.453.2
DynaMask†ResNet-101-FPN3×41.362.545.222.843.454.0
DynaMask†ResNeXt-101-FPN3×42.062.946.323.444.054.8
", + "image_path": "dd4aa37511c254ae234236839d62b8219c2f5e67c2914067398028fe4d1c0d03.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 374, + 545, + 386 + ], + "lines": [ + { + "bbox": [ + 47, + 374, + 545, + 386 + ], + "spans": [ + { + "bbox": [ + 47, + 374, + 545, + 386 + ], + "type": "text", + "content": "Table 3. Comparison with state-of-the-art methods for instance segmentation on COCO test-dev2017, † denotes multi-scale training." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 397, + 288, + 480 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 397, + 288, + 480 + ], + "spans": [ + { + "bbox": [ + 46, + 397, + 288, + 480 + ], + "type": "text", + "content": "size is independent of object size. For example, in the third image, the small but hard object \"potted plant\" is allocated a large mask, while the large but easy sample \"suitcase\" in the fifth image can be accurately segmented with a small mask. We provide quantitative analysis of the correlations between the predicted mask resolutions and the class in supplemental files." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 486, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 486, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 486, + 287, + 713 + ], + "type": "text", + "content": "Influence of the budget constraint. In Tab. 5, we explore the influence of budget constraint on the model complexity (FLOPs). The average FLOPs are calculated by taking the average over all instances of the validation set. By tuning hyper-parameters " + }, + { + "bbox": [ + 46, + 486, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_t" + }, + { + "bbox": [ + 46, + 486, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 486, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\lambda_2" + }, + { + "bbox": [ + 46, + 486, + 287, + 713 + ], + "type": "text", + "content": " to different values, we get models of different computational costs. For example, the FLOPs are reduced by about " + }, + { + "bbox": [ + 46, + 486, + 287, + 713 + ], + "type": "inline_equation", + "content": "19\\%" + }, + { + "bbox": [ + 46, + 486, + 287, + 713 + ], + "type": "text", + "content": " without sacrificing the segmentation performance by setting " + }, + { + "bbox": [ + 46, + 486, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_t" + }, + { + "bbox": [ + 46, + 486, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 486, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\lambda_2" + }, + { + "bbox": [ + 46, + 486, + 287, + 713 + ], + "type": "text", + "content": " to 1.0 and 0.4, respectively. This demonstrates that there exists much redundancy when using the large mask " + }, + { + "bbox": [ + 46, + 486, + 287, + 713 + ], + "type": "inline_equation", + "content": "(112 \\times 112)" + }, + { + "bbox": [ + 46, + 486, + 287, + 713 + ], + "type": "text", + "content": " for all instances. Actually, many instances in COCO dataset can be efficiently segmented with smaller masks. Thus the redundant computation for easier samples can be reduced, while the accuracy of harder samples can be maintained by still using larger masks. By setting the target FLOPs " + }, + { + "bbox": [ + 46, + 486, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_t" + }, + { + "bbox": [ + 46, + 486, + 287, + 713 + ], + "type": "text", + "content": " to a smaller value (e.g., 0.4, 0.6, 0.8), more significant computation reduction can be achieved at a slight degradation of accuracy. For instance, by setting both " + }, + { + "bbox": [ + 46, + 486, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_t" + }, + { + "bbox": [ + 46, + 486, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 486, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\lambda_2" + }, + { + "bbox": [ + 46, + 486, + 287, + 713 + ], + "type": "text", + "content": " to 0.4, more than half of the FLOPs (around " + }, + { + "bbox": [ + 46, + 486, + 287, + 713 + ], + "type": "inline_equation", + "content": "54\\%" + }, + { + "bbox": [ + 46, + 486, + 287, + 713 + ], + "type": "text", + "content": ") are reduced while still" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 397, + 534, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 397, + 534, + 409 + ], + "spans": [ + { + "bbox": [ + 304, + 397, + 534, + 409 + ], + "type": "text", + "content": "producing competitive segmentation results (36.8% AP)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 411, + 545, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 411, + 545, + 590 + ], + "spans": [ + { + "bbox": [ + 304, + 411, + 545, + 590 + ], + "type": "text", + "content": "Speed comparison of different methods. To validate the efficiency of our model, we compare the model accuracy, FLOPs, and runtime of different two-stage IS methods in Tab. 6. Inference time is tested on one NVIDIA Titan RTX with the input size " + }, + { + "bbox": [ + 304, + 411, + 545, + 590 + ], + "type": "inline_equation", + "content": "800 \\times 1333" + }, + { + "bbox": [ + 304, + 411, + 545, + 590 + ], + "type": "text", + "content": ". Compared to these methods, our DynaMask method achieves visible performance gain at a small amount of extra computational cost. Specifically, DynaMask " + }, + { + "bbox": [ + 304, + 411, + 545, + 590 + ], + "type": "inline_equation", + "content": "(\\mathcal{C}_t = 0.4)" + }, + { + "bbox": [ + 304, + 411, + 545, + 590 + ], + "type": "text", + "content": " outperforms PointRend [17] and DCT-mask [25] by " + }, + { + "bbox": [ + 304, + 411, + 545, + 590 + ], + "type": "inline_equation", + "content": "1.2\\%" + }, + { + "bbox": [ + 304, + 411, + 545, + 590 + ], + "type": "text", + "content": " AP and " + }, + { + "bbox": [ + 304, + 411, + 545, + 590 + ], + "type": "inline_equation", + "content": "0.3\\%" + }, + { + "bbox": [ + 304, + 411, + 545, + 590 + ], + "type": "text", + "content": " AP, respectively, with comparable runtime. Though HTC [3] produces a similar segmentation result (" + }, + { + "bbox": [ + 304, + 411, + 545, + 590 + ], + "type": "inline_equation", + "content": "0.2\\%" + }, + { + "bbox": [ + 304, + 411, + 545, + 590 + ], + "type": "text", + "content": " lower AP) to DynaMask, it is two times slower than DynaMask because it performs hybrid cascade refinement on both detection and segmentation tasks, resulting in a large amount of memory and computation overhead." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "text", + "content": "Influence of mask size. The Mask Switch Module (MSM) outputs four different candidate mask resolutions " + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "inline_equation", + "content": "[14 \\times 14, 28 \\times 28, 56 \\times 56, 112 \\times 112]" + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "text", + "content": ". We choose one of them as the uniform output mask size and report the corresponding results in Tab. 7. As can be seen, models with larger mask resolutions could achieve higher segmentation performance, especially on large objects, but the computational cost also increases obviously. For example, the performance is improved by " + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "inline_equation", + "content": "3.2\\%" + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "inline_equation", + "content": "4.2\\%" + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "inline_equation", + "content": "4.7\\%" + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "text", + "content": " AP when the mask resolution is increased from " + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "inline_equation", + "content": "14 \\times 14" + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "inline_equation", + "content": "28 \\times 28" + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "inline_equation", + "content": "56 \\times 56" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11285" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 170, + 152 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 170, + 152 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 170, + 152 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 170, + 152 + ], + "type": "image", + "image_path": "7514bf444671cdbc4c22c023fa90b3edb1f436b3b15aa981d6c60b55dc269adc.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 173, + 70, + 294, + 152 + ], + "blocks": [ + { + "bbox": [ + 173, + 70, + 294, + 152 + ], + "lines": [ + { + "bbox": [ + 173, + 70, + 294, + 152 + ], + "spans": [ + { + "bbox": [ + 173, + 70, + 294, + 152 + ], + "type": "image", + "image_path": "aa4c5fd8720176105b12bf4676a822b12fc42d82fd8e9f4581cefeb3176a86b5.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 299, + 70, + 421, + 152 + ], + "blocks": [ + { + "bbox": [ + 299, + 70, + 421, + 152 + ], + "lines": [ + { + "bbox": [ + 299, + 70, + 421, + 152 + ], + "spans": [ + { + "bbox": [ + 299, + 70, + 421, + 152 + ], + "type": "image", + "image_path": "9330e594aff21872f60c8c68d5501a5e7478d0eef8442f14255e5930f3be5b72.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 425, + 70, + 545, + 152 + ], + "blocks": [ + { + "bbox": [ + 425, + 70, + 545, + 152 + ], + "lines": [ + { + "bbox": [ + 425, + 70, + 545, + 152 + ], + "spans": [ + { + "bbox": [ + 425, + 70, + 545, + 152 + ], + "type": "image", + "image_path": "daf1f139fbb42a00f8172e813da7853924f9b11734b95667018c9674e1d4a5dd.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 48, + 153, + 170, + 236 + ], + "blocks": [ + { + "bbox": [ + 48, + 153, + 170, + 236 + ], + "lines": [ + { + "bbox": [ + 48, + 153, + 170, + 236 + ], + "spans": [ + { + "bbox": [ + 48, + 153, + 170, + 236 + ], + "type": "image", + "image_path": "d07a7ffb3fcb8d532d4511f20cd576c76921efc08bc25fc02322e798d8d6b541.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 237, + 545, + 259 + ], + "lines": [ + { + "bbox": [ + 47, + 237, + 545, + 259 + ], + "spans": [ + { + "bbox": [ + 47, + 237, + 545, + 259 + ], + "type": "text", + "content": "Figure 7. Mask selection results by DynaMask. Each color corresponds to a candidate resolution (red " + }, + { + "bbox": [ + 47, + 237, + 545, + 259 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 47, + 237, + 545, + 259 + ], + "type": "text", + "content": " large, blue " + }, + { + "bbox": [ + 47, + 237, + 545, + 259 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 47, + 237, + 545, + 259 + ], + "type": "text", + "content": " medium, green " + }, + { + "bbox": [ + 47, + 237, + 545, + 259 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 47, + 237, + 545, + 259 + ], + "type": "text", + "content": " small, yellow " + }, + { + "bbox": [ + 47, + 237, + 545, + 259 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 47, + 237, + 545, + 259 + ], + "type": "text", + "content": " tiny)." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 173, + 153, + 294, + 236 + ], + "blocks": [ + { + "bbox": [ + 173, + 153, + 294, + 236 + ], + "lines": [ + { + "bbox": [ + 173, + 153, + 294, + 236 + ], + "spans": [ + { + "bbox": [ + 173, + 153, + 294, + 236 + ], + "type": "image", + "image_path": "72962a20700d150f9f54bf1f18fd2c2e06d99ccb16262c7a5ff47ac6d01a7358.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 299, + 153, + 421, + 236 + ], + "blocks": [ + { + "bbox": [ + 299, + 153, + 421, + 236 + ], + "lines": [ + { + "bbox": [ + 299, + 153, + 421, + 236 + ], + "spans": [ + { + "bbox": [ + 299, + 153, + 421, + 236 + ], + "type": "image", + "image_path": "d35deea7549de6b96be10608a037c940d2d3358bee8af28347e232ed9a979b81.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 425, + 153, + 545, + 236 + ], + "blocks": [ + { + "bbox": [ + 425, + 153, + 545, + 236 + ], + "lines": [ + { + "bbox": [ + 425, + 153, + 545, + 236 + ], + "spans": [ + { + "bbox": [ + 425, + 153, + 545, + 236 + ], + "type": "image", + "image_path": "894c99410100a652210e9bff0d3e05a7881727871c31b372fcb2e5c7cc3f638f.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 50, + 261, + 228, + 326 + ], + "blocks": [ + { + "bbox": [ + 50, + 261, + 228, + 326 + ], + "lines": [ + { + "bbox": [ + 50, + 261, + 228, + 326 + ], + "spans": [ + { + "bbox": [ + 50, + 261, + 228, + 326 + ], + "type": "table", + "html": "
MethodAPAPsAPMAPL
Mask R-CNN [10]33.812.031.551.8
PointRend [17]35.8---
BMask R-CNN [6]35.8---
RefineMask [30]37.614.634.058.1
DynaMask38.014.835.157.6
", + "image_path": "5d76936bd4e6e6fc2dfcb5ee1beac5a38616756f333d355ebd0e4b4bae1cbf5e.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 242, + 259, + 352, + 328 + ], + "blocks": [ + { + "bbox": [ + 47, + 327, + 223, + 347 + ], + "lines": [ + { + "bbox": [ + 47, + 327, + 223, + 347 + ], + "spans": [ + { + "bbox": [ + 47, + 327, + 223, + 347 + ], + "type": "text", + "content": "Table 4. The results on Cityscapes val set with ResNet-50-FPN backbone." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 242, + 259, + 352, + 328 + ], + "lines": [ + { + "bbox": [ + 242, + 259, + 352, + 328 + ], + "spans": [ + { + "bbox": [ + 242, + 259, + 352, + 328 + ], + "type": "table", + "html": "
Ctλ2FLOPsΔAP
1.00.31.27G-9%37.6
1.00.41.13G-19%37.6
1.00.51.06G-24%37.5
0.80.40.92G-34%37.4
0.60.40.83G-41%37.2
0.40.40.64G-54%36.8
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MethodAPFLOPsFPS
Mask R-CNN [10]34.70.5G12.4
PointRend [17]35.60.9G9.4
DCT-Mask†[25]36.50.5G11.8
HTC [3]37.4-3.9
DynaMask37.61.4G8.3
DynaMask (Ct=0.4)36.80.64G11.2
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Mask SizeFLOPsAP\\( {\\mathrm{{AP}}}_{50} \\)\\( {\\mathrm{{AP}}}_{75} \\)\\( {\\mathrm{{AP}}}_{\\mathrm{S}} \\)\\( {\\mathrm{{AP}}}_{\\mathrm{M}} \\)\\( {\\mathrm{{AP}}}_{\\mathrm{L}} \\)
\\( {14} \\times {14} \\)0.23G32.955.334.419.335.843.6
\\( {28} \\times {28} \\)0.62G36.157.138.720.439.248.2
\\( {56} \\times {56} \\)1.01G37.157.340.020.540.049.7
\\( {112} \\times {112} \\)1.40G37.657.440.520.740.450.3
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Nevertheless, the performance tends to saturate as the mask size increases further." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 46, + 459, + 287, + 537 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 459, + 287, + 537 + ], + "spans": [ + { + "bbox": [ + 46, + 459, + 287, + 537 + ], + "type": "text", + "content": "Size-based mask selection method. We compare the performance and mask distributions of different mask selection methods in Tab. 8. The baseline is performed by using a uniform mask size " + }, + { + "bbox": [ + 46, + 459, + 287, + 537 + ], + "type": "inline_equation", + "content": "(28 \\times 28)" + }, + { + "bbox": [ + 46, + 459, + 287, + 537 + ], + "type": "text", + "content": " for all objects. Size-based method denotes assigning masks according to the size of object. Specifically, we assign a mask " + }, + { + "bbox": [ + 46, + 459, + 287, + 537 + ], + "type": "inline_equation", + "content": "\\hat{m}_i^k" + }, + { + "bbox": [ + 46, + 459, + 287, + 537 + ], + "type": "text", + "content": " to the instance of width " + }, + { + "bbox": [ + 46, + 459, + 287, + 537 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 46, + 459, + 287, + 537 + ], + "type": "text", + "content": " and height " + }, + { + "bbox": [ + 46, + 459, + 287, + 537 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 46, + 459, + 287, + 537 + ], + "type": "text", + "content": " by the following rule:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 101, + 545, + 287, + 564 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 101, + 545, + 287, + 564 + ], + "spans": [ + { + "bbox": [ + 101, + 545, + 287, + 564 + ], + "type": "interline_equation", + "content": "k = \\left\\lfloor k _ {0} + \\log_ {2} \\left(\\sqrt {w h} / \\sqrt {w _ {0} h _ {0}}\\right) \\right\\rfloor , \\tag {8}", + "image_path": "1ec91f99b0250ae5d4f6901fde6dd3863284cbd131a313ba0ad2d963b647e498.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 46, + 570, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 287, + 653 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 570, + 287, + 653 + ], + "type": "inline_equation", + "content": "w_{0}" + }, + { + "bbox": [ + 46, + 570, + 287, + 653 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 570, + 287, + 653 + ], + "type": "inline_equation", + "content": "h_0" + }, + { + "bbox": [ + 46, + 570, + 287, + 653 + ], + "type": "text", + "content": " denote the width and height of the input image, respectively. and " + }, + { + "bbox": [ + 46, + 570, + 287, + 653 + ], + "type": "inline_equation", + "content": "k_{0}" + }, + { + "bbox": [ + 46, + 570, + 287, + 653 + ], + "type": "text", + "content": " denotes the index of the highest mask resolution " + }, + { + "bbox": [ + 46, + 570, + 287, + 653 + ], + "type": "inline_equation", + "content": "112 \\times 112" + }, + { + "bbox": [ + 46, + 570, + 287, + 653 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 46, + 570, + 287, + 653 + ], + "type": "inline_equation", + "content": "k_{0} = 4" + }, + { + "bbox": [ + 46, + 570, + 287, + 653 + ], + "type": "text", + "content": ". Intuitively, Eq. 8 means that the larger object will be assigned a higher-resolution mask. This conforms to our common sense, since the larger objects usually contain many details which need finer-grained masks to achieve high-quality prediction." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "text", + "content": "As can be seen from Tab. 8, the size-based method attains comparable performance with the baseline at a lower cost. Our DynaMask " + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "inline_equation", + "content": "(\\mathcal{C}_t = 0.4)" + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "text", + "content": " outperforms the baseline by " + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "inline_equation", + "content": "0.7\\%" + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "text", + "content": " AP and the size-based method by " + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "inline_equation", + "content": "0.9\\%" + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "text", + "content": " AP at a slight extra computation cost, demonstrating that the" + } + ] + } + ], + "index": 21 + }, + { + "type": "table", + "bbox": [ + 315, + 361, + 537, + 413 + ], + "blocks": [ + { + "bbox": [ + 79, + 413, + 266, + 423 + ], + "lines": [ + { + "bbox": [ + 79, + 413, + 266, + 423 + ], + "spans": [ + { + "bbox": [ + 79, + 413, + 266, + 423 + ], + "type": "text", + "content": "Table 7. Performance of using different mask sizes." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 315, + 361, + 537, + 413 + ], + "lines": [ + { + "bbox": [ + 315, + 361, + 537, + 413 + ], + "spans": [ + { + "bbox": [ + 315, + 361, + 537, + 413 + ], + "type": "table", + "html": "
Mask SizeFLOPsAPTinySmallMediumLarge
28×280.62G36.10100
Size-based0.56G35.947%32%14%8%
DynaMask (Ct=0.4)0.64G36.835%34%21%10%
DynaMask1.4G37.60001
", + "image_path": "def46a5f8a630fffb58178609a8b0aeb3e59e63d4b79f30fd52b38f6ccb52d19.jpg" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "table_body" + } + ], + "index": 22 + }, + { + "bbox": [ + 315, + 413, + 537, + 423 + ], + "lines": [ + { + "bbox": [ + 315, + 413, + 537, + 423 + ], + "spans": [ + { + "bbox": [ + 315, + 413, + 537, + 423 + ], + "type": "text", + "content": "Table 8. Comparison with size-based mask selection method." + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 436, + 545, + 497 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 436, + 545, + 497 + ], + "spans": [ + { + "bbox": [ + 305, + 436, + 545, + 497 + ], + "type": "text", + "content": "proposed mask selection strategy could better partition different objects according to their segmentation difficulties and assign more suitable masks to achieve better performance. More analyses about the distribution of predicted mask scales can be found in supplemental materials." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 306, + 506, + 378, + 517 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 506, + 378, + 517 + ], + "spans": [ + { + "bbox": [ + 306, + 506, + 378, + 517 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 304, + 521, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 546, + 713 + ], + "type": "text", + "content": "In this work, we proposed a simple yet effective method to improve instance segmentation performance at a small amount of computation and memory overhead. We devised a dual-level FPN structure for better exploring complementary contextual and detailed information from multiple pyramid levels. Specifically, in addition to traditional image-level FPN (i-FPN), we augmented a region-level top-down path (r-FPN) to gradually enlarge the mask size and incorporate more details from i-FPN. Furthermore, to reduce the computation and memory cost led by using large masks, we introduced a Mask Switch Module (MSM) to adaptively select suitable masks for each proposal so that the redundant computation for easy samples can be reduced by using smaller masks. Extensive experimental results demonstrated that our method achieved significant performance gains with moderate extra computation overhead." + } + ] + } + ], + "index": 26 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "11286" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 289, + 714 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 289, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 289, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 289, + 135 + ], + "type": "text", + "content": "[1] Daniel Bolya, Chong Zhou, Fanyi Xiao, and Yong Jae Lee. 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However, gait recognition often suffers from multiple exterior factors in real scenes, such as carrying conditions, wearing overcoats, and diverse viewing angles. Recently, various deep learning-based gait recognition methods have achieved promising results, but they tend to extract one of the salient features using fixed-weighted convolutional networks, do not well consider the relationship within gait features in key regions, and ignore the aggregation of complete motion patterns. In this paper, we propose a new perspective that actual gait features include global motion patterns in multiple key regions, and each global motion pattern is composed of a series of local motion patterns. To this end, we propose a Dynamic Aggregation Network (DANet) to learn more discriminative gait features. Specifically, we create a dynamic attention mechanism between the features of neighboring pixels that not only adaptively focuses on key regions but also generates more expressive local motion patterns. In addition, we develop a self-attention mechanism to select representative local motion patterns and further learn robust global motion patterns. Extensive experiments on three popular public gait datasets, i.e., CASIA-B, OUMVLP, and Gait3D, demonstrate that the proposed method can provide substantial improvements over the current state-of-the-art methods.1", + "bbox": [ + 76, + 318, + 473, + 728 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 78, + 758, + 209, + 773 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Gait recognition aims to retrieve the same identity at a long distance, and has been widely used throughout social security [28], video surveillance [4, 15, 49], crime investigation [25], and so on. Compared with action recognition [17, 53, 54] and person re-identification [2, 55, 60, 61], the", + "bbox": [ + 76, + 785, + 468, + 863 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/48e30b2ab7fb6b9048838f1f6d317450e14c7af659cb84f8e96a905b7a3a4370.jpg", + "image_caption": [ + "Figure 1. The features of each pixel are mapped as a vector with both magnitude and phase components. The magnitude represents contextual information, while the phase direction is used to construct dynamic attention models for the key regions. The convolution operation is denoted by $*$ , and the blue circles in the diagrams represent the key regions learned by the dynamic attention." + ], + "image_footnote": [], + "bbox": [ + 506, + 284, + 885, + 494 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "gait recognition task is one of the most challenging fine-grained label classification problems. On the one hand, silhouette data is a binary image of a person suffering from the limitations of the segmentation algorithm [26, 62, 63], with occasional holes and broken edges. On the other hand, gait recognition is also impacted by various exterior factors in real scenes, such as carrying conditions, wearing coats, and diverse viewing angles. Different angles and clothing conditions will greatly change the silhouette appearance of the same person, resulting in the intra-class variance being much greater than inter-class. We ask: How to learn more robust features adaptively for each person under the influence of various external factors? We attempt to answer this question from the following perspectives:", + "bbox": [ + 496, + 611, + 893, + 823 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "(i) Local Motion Patterns. Gait, or the act of walking, is essentially the coordinated movement of body parts. In a gait sequence, we observe that each part has a unique representative motion pattern, and each motion pattern is composed of a set of localized sub-movements. Therefore, it", + "bbox": [ + 496, + 824, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding Authors", + "bbox": [ + 94, + 875, + 228, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "$^{1}$ Code available at https://github.com/XKMar/FastGait", + "bbox": [ + 94, + 887, + 455, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "22076", + "bbox": [ + 478, + 943, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/7ed8b20f48853835890a51fdae65039ae999623b1f4c97d32231b1c7f21329fd.jpg", + "image_caption": [ + "Figure 2. Comparison of the actual motion pattern with the Max-based method, Mean-based method, and Global Motion Pattern Aggregator (GMPA) module. The black curve represents a single periodic action that is affected by disturbances, whereas the green curve represents a synthesized periodic action consisting of distinct local motion patterns selected by the GMPA." + ], + "image_footnote": [], + "bbox": [ + 91, + 90, + 467, + 239 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "is critical to accurately locate the discriminative parts and obtain representative local motion patterns under the interference of various external factors. However, previous gait-based approaches [7, 8, 13, 14, 20, 24, 33] simply use convolutional networks with non-linear activation to model the dynamic movements. Once the network has been trained, the parameters and the non-linear function can only focus on the fixed patterns. To this end, we propose to encode the features of each pixel as a vector with magnitude and phase, as shown in Fig. 1, which allows learning the dynamic attention mapping functions among the neighboring pixel of focusing. By modeling the relationship, the network can further focus on local motion patterns in key regions.", + "bbox": [ + 75, + 356, + 468, + 551 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "(ii) Global Motion Patterns. Gait is a periodic movement. We assume that the actual motion pattern is a one-dimensional signal, as shown in Fig. 2, whereby the local motion patterns are the points on the signal. Therefore, it is essential to use a series of local motion patterns to further fit the actual motion patterns for obtaining discriminative gait features. However, recent gait-based methods [8,20,33] only use Max- or Mean-based methods to extract one of the significant local features. These methods are susceptible to disturbances and can not fit the actual motion patterns. According to the Nyquist-Shannon sampling theorem [37, 39] in signal processing theory, when a continuous signal is sampled at a frequency greater than twice the frequency of the signal, the information of the original signal is retained intact. In this regard, we propose to construct a global attention model and use it to dynamically select a preset number of distinguishable local motion patterns (green arrows), while excluding the effect of noise (red arrows). By selecting sufficient discriminative local motion patterns, the network can further obtain robust global motion patterns.", + "bbox": [ + 75, + 551, + 468, + 854 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Driven by this analysis, we propose a novel and effective Dynamic Aggregated Network (DANet) for gait recognition. As shown in Fig. 3, DANet consists of two", + "bbox": [ + 76, + 854, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "well-designed components, i.e., Local Conv-Mixing Block (LCMB) and Global Motion Patterns Aggregator (GMPA). Firstly, we encode the features of each pixel into the complex domain including magnitude and phase, where the magnitude term represents the contextual information and the phase term is used to establish the relationship between each vector. The local motion pattern is generated by aggregating the magnitude and phase of the vectors in the neighboring regions of focus. Secondly, we use the self-attentive mechanism in the GMPA model to dynamically select sufficient discriminative local motion patterns and further learn to fit the actual gait patterns. Finally, with our proposed modules, we obtain the most representative stable gait features for each person and outperform the state-of-the-art (SOTA) methods, especially under the most challenging condition of cross-dressing.", + "bbox": [ + 496, + 90, + 890, + 332 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our main contributions can be summarized as follows:", + "bbox": [ + 517, + 333, + 879, + 347 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a novel LCMB to extract the representative local motion patterns, which can dynamically model the relationships among the features of neighboring pixels and then accurately locate key regions.", + "- We design an effective GMPA to select the discriminative local motion patterns and then aggregate them to obtain a robust global representation. To the best of our knowledge, it is the first attempt to explore the potential of self-attention model in this task.", + "- Experimental results are illustrated to demonstrate the effectiveness of the proposed method, outperforming the SOTA method on CASIA-B [56], OUMVLP [41] and Gait3D [59] datasets. In addition, many rigorous ablation experiments on CASIA-B [56] further validated the effectiveness of each component in DANet." + ], + "bbox": [ + 517, + 359, + 890, + 607 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 500, + 633, + 648, + 648 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this section, we provide a brief overview of relevant research in the fields of gait recognition, local action modeling, and global action modeling.", + "bbox": [ + 496, + 657, + 890, + 703 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Gait Architectures. Gait recognition approaches mainly fall into two typical categories, i.e., model-based approaches and appearance-based approaches. Model-based approaches [1,3,27,29-31,44] attempt to explicitly fit human pose structures [10] to images. However, the predefined points are empirically designed and limited by the inaccuracy of estimation results for low-quality images. Therefore, the model-based methods are generally inferior to appearance-based methods in performance. Appearance-based approaches [7,8,13,18,20,21,24,32,33,43,47,51, 52, 58] are the mainstream frameworks for gait and have benefited from the quick growth of deep learning. It can be roughly divided into three classes, namely template-based", + "bbox": [ + 496, + 704, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "22077", + "bbox": [ + 478, + 943, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/c65902a1bfcfdf261891d12e69d680b19eecaee04f9dd85a11867b5aa44f080b.jpg", + "image_caption": [ + "Figure 3. The overview of the proposed DANet. Each stage contains the Local Conv-Mixing Block (LCMB), which utilizes a dynamic attention model to establish relationships among neighboring pixels of interest. The HP denotes Horizontal Pooling, GMPA represents Global Motion Pattern Aggregator, and $l$ indicates the number of last stages. In particular, the $\\mathrm{GMPA}_j$ module is responsible for aggregating the local motion patterns of the $j$ -th part and producing the final global motion patterns $v_{i}$ for recognition." + ], + "image_footnote": [], + "bbox": [ + 89, + 93, + 877, + 218 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "methods, set-based methods, and sequence-based methods. The template-based approaches [18, 36, 43, 47, 52, 57] extracted gait spatio-temporal features by compressing a sequence of gait silhouettes, e.g., Gait Energy Image (GEI), which inevitably destroyed the representation of discriminative local motion patterns in gait sequences. The set-based approaches [8,20,21,23] assumed that the appearance of a silhouette contained its position information, which could not construct local motion patterns using continuous frames. Recently some advanced sequence-based methods [7, 24, 32, 33, 51] used 3D convolutional (C3D) neural networks to extract gait features from the gait sequence and achieve SOTA results. Our approach belongs to the sequence-based method, in contrast to other methods, we propose to use variable-length frames as the input.", + "bbox": [ + 75, + 300, + 472, + 526 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Local Action Modeling. Local action modeling [14,24,32, 33] aims at building short-range spatio-temporal features, which have been shown to be beneficial for gait recognition in various literature. GaitPart [14] proposed a micro-motion capture module to model the short-range spatio-temporal features. MT3D [32] proposed multiple temporal-scale 3D convolutional layers to extract the small and large temporal-scale motion features. GaitGL [33] utilized a local temporal aggregation module to extract the local temporal information. 3DLocal [24] proposed a localization module to adaptively sample the local action features. In contrast to these strategies, we propose to map each pixel of the gait sequence to the complex-valued domain, using the phase term to encode the relationship between gait features. By fully exploiting the phase term, we construct a dynamic attention model among each pixel of the feature to extract local motion patterns in key regions.", + "bbox": [ + 75, + 532, + 468, + 789 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Global Action Modeling. Global action modeling, aiming at capturing long-range dependencies, has been demonstrated to be advantageous to a wide range of recognition tasks such as action recognition [6, 45, 48, 54] and person re-identification [9, 16, 19, 35, 40, 61]. Many attention-based approaches [12, 34, 46] built global relationships in the spatial dimension [5, 50] or channel dimension [22] with re", + "bbox": [ + 75, + 794, + 468, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "markable results. However, current state-of-the-art works [7, 8, 32, 33] in gait recognition still directly use Max- or Mean-based methods to extract global temporal features, which only focus on the most salient features. Different from these methods, we design an efficient global self-attention model to obtain a robust representation for each person, which can select discriminative local motion patterns, and further map them to global motion patterns.", + "bbox": [ + 496, + 300, + 893, + 421 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 498, + 435, + 635, + 453 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we first describe the overall architecture of our method in Sec. 3.1, and then introduce the proposed two novel well-designed modules, i.e., Local Conv-Mixing Block (LCMB) in Sec. 3.2 and Global Motion Pattern Aggregator (GMPA) in Sec. 3.3. Finally, we will discuss the joint loss functions in Sec. 3.4.", + "bbox": [ + 496, + 460, + 893, + 551 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Formulation and Motivation", + "text_level": 1, + "bbox": [ + 498, + 561, + 756, + 577 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Gait recognition aims to identify the same person under the influence of various external factors. Let $\\mathbf{X} \\in \\mathbb{R}^{T \\times H \\times W}$ denote silhouette data containing consecutive $T$ frames, where $T, H$ , and $W$ represent the temporal, height, and width dimensions of input frames. In our implementation, we sample variable-length frames $T \\in [20, 40]$ from a continuous sequence as the input. The extraction of gait features can be expressed as", + "bbox": [ + 496, + 585, + 893, + 707 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nf = \\mathcal {G} (\\mathcal {L} (\\mathbf {X})), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 643, + 719, + 890, + 736 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $f \\in \\mathbb{R}^{P \\times C}$ is the output features, $P$ is the number of horizontally sliced parts, $C$ is the feature channels, $\\mathcal{L}$ represents the local motion pattern extraction, and $\\mathcal{G}$ denotes the global motion pattern aggregation.", + "bbox": [ + 496, + 748, + 893, + 809 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To learn distinctive representation for each person, the previous C2D-based methods [8, 20] and C3D-based methods [32, 33] only use convolutional layers and non-linear functions to learn gait features. However, the trained network can only recognize certain movement patterns that are vulnerable to noise. In this work, we propose a novel", + "bbox": [ + 496, + 810, + 893, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "22078", + "bbox": [ + 478, + 943, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/e7f524e9b846da2fb31d19e2466bfc2ef044d4b7b89022658178f585e323ae6b.jpg", + "image_caption": [ + "Figure 4. The architecture of LCMB, where “ $\\odot$ ” represents Hadamard product, “ $\\oplus$ ” represents element-wise sum operation, and Mix denotes vector aggregation operation." + ], + "image_footnote": [], + "bbox": [ + 83, + 95, + 460, + 194 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "LCMB in the backbone of DANet, which enables the network to focus on the key regions and extract the local motion patterns by dynamically building the relationships among pixels. Furthermore, inspired by the Nyquist-Shannon sampling theorem [37, 39], we propose a new perspective that a complete gait pattern should contain many distinguishable local motion patterns. To this end, we developed an effective GMPA to select sufficient distinguishable local motion patterns while effectively excluding the interference of noise. The selected local motion patterns are then aggregated to generate a robust global motion pattern.", + "bbox": [ + 75, + 265, + 468, + 431 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Local Conv-Mixing Block", + "text_level": 1, + "bbox": [ + 76, + 439, + 310, + 455 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section, we provide a detailed description of the vector representation and vector aggregation in the Local Conv-Mixing Block (LCMB) module.", + "bbox": [ + 75, + 462, + 468, + 508 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Vector Representation. In the LCMB module, the input features are denoted as $\\mathbf{V} = [v_{1}, v_{2}, \\dots, v_{N}] \\in \\mathbb{R}^{N \\times C_{i}}$ , where $N$ is the number of pixels in the gait sequence, $C_{i}$ is the dimension of input features. As shown in Fig. 4, we obtain the magnitude $|v_{j}|$ and phase $\\theta_{j}$ of each vector by multiply with the learnable parameters $W^{m} \\in \\mathbb{R}^{C_{i} \\times C_{l}}$ and $W^{t} \\in \\mathbb{R}^{C_{i} \\times C_{l}}$ , separately, i.e.,", + "bbox": [ + 75, + 508, + 468, + 613 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left| v _ {j} \\right| = W ^ {m} v _ {j}, j = 1, 2, \\dots , N, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 165, + 622, + 467, + 640 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\theta_ {j} = \\max \\left(0, W ^ {t} v _ {j}\\right), j = 1, 2, \\dots , N, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 145, + 642, + 468, + 660 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the subscript $j$ is the feature of the $j$ -th pixel. The content of each vector is a real-value feature modeled by the magnitude term $|v_{j}|$ , while the relationship of each vector is modulated by the phase term $\\theta_{j}$ , using grouped convolutional layers with rectified linear activation ReLU. The complex vectors $\\tilde{v}_{j} \\in \\mathbb{C}^{C_{l}}$ modulated by the magnitude and phase terms using Euler's formula, i.e.,", + "bbox": [ + 75, + 667, + 468, + 773 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {v} _ {j} = \\overbrace {\\left| v _ {j} \\right| \\odot \\cos \\theta_ {j}} ^ {\\text {r e a l p a r t}} + \\overbrace {i \\left| v _ {j} \\right| \\odot \\sin \\theta_ {j}} ^ {\\text {i m a g i n a r y p a r t}}, j = 1, 2, \\dots , N, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 781, + 468, + 818 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $i$ is the imaginary unit satisfying $i^2 = -1$ , and $\\odot$ is element-wise multiplication.", + "bbox": [ + 75, + 824, + 468, + 854 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Vector Aggregation. After representing the features of each pixel as a vector, we further aggregate the local spatiotemporal domain of each vector as shown in Fig. 4. In", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/d31f78a244c95de98258e75cf85db2fbe09f95595b3ae2e917337375f83b02d8.jpg", + "image_caption": [ + "Figure 5. The architecture of GMPA and the feature maps are shown by their dimensions, where “ $\\otimes$ ” is matrix multiplication." + ], + "image_footnote": [], + "bbox": [ + 511, + 93, + 879, + 191 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "particular, the complex-value representation of the output $\\tilde{o}_j\\in \\mathbb{C}^{C_i}$ that aggregated by learnable convolution kernels $\\mathcal{K}\\in \\mathbb{R}^{C_i\\times C_l\\times K_t\\times K_s\\times K_s}$ , i.e.,", + "bbox": [ + 498, + 253, + 890, + 299 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {o} _ {j} = \\sum_ {m \\in \\mathcal {N} (j)} \\mathcal {K} [ j - m ] \\tilde {v} _ {m} + v _ {j}, j = 1, 2, \\dots , N, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 306, + 890, + 342 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{N}(j)$ denotes the neighboring pixels set of $j$ , and $\\tilde{v}_m$ represents the vector belong to the neighboring pixels of $\\tilde{v}_j$ . Following [42], we obtain the real-value output feature $o_j \\in \\mathbb{R}^{C_i}$ by summing the real and imaginary parts of $\\tilde{v}_j$ for convenient computation, i.e.,", + "bbox": [ + 498, + 352, + 890, + 429 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\no _ {j} = \\sum_ {m \\in \\mathcal {N} (j)} \\left(\\mathcal {K} [ j - m ] | v _ {m} | \\odot \\cos \\theta_ {m} + \\right. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 522, + 440, + 890, + 474 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left. \\mathcal {K} [ j - m ] \\left| v _ {m} \\right| \\odot \\sin \\theta_ {m}\\right) + v _ {j}, j = 1, 2, \\dots , N,\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 476, + 846, + 494 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $(\\cos \\theta_{m} + \\sin \\theta_{m})$ denotes the dynamic attention among the neighboring pixels of $j$ . To further comprehend the dynamic aggregation model, heatmaps showcasing the phase values are visualized in Fig. 6.", + "bbox": [ + 498, + 505, + 890, + 566 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Global Motion Patterns Aggregator", + "text_level": 1, + "bbox": [ + 500, + 575, + 808, + 590 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this part, we propose a new instantiation of the global action modeling framework for gait recognition named the global motion patterns aggregator (GMPA), which selects a preset number of distinguished local motion patterns and then utilizes an attention mechanism to aggregate query-specific global motion patterns of each query location. The GMPA adopts separate parameters for each part and models the global movement patterns of the corresponding part.", + "bbox": [ + 496, + 598, + 890, + 719 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Lower-order Global Motion Patterns. Gait data is affected by a number of variable factors, such as segmentation holes or broken edges, further impairing the actual movement pattern. To this end, we first propose to squeeze variable local motion patterns into a preset number of channel descriptors. Then, we utilize softmax to construct an attention map in the temporal dimension, and multiply the squeezed attention maps with the reshaped local motion pattern features to obtain the global low-order motion patterns. Formally, the global low-order motion patterns $\\tilde{\\mathbf{G}}\\in \\mathbb{R}^{P\\times C\\times M}$ are generated by local motion patterns $\\mathbf{L}\\in \\mathbb{R}^{P\\times T\\times C}$ and attention maps $\\mathbf{M}\\in \\mathbb{R}^{P\\times T\\times M}$ , and can", + "bbox": [ + 496, + 719, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "22079", + "bbox": [ + 478, + 943, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "be expressed as", + "bbox": [ + 76, + 90, + 184, + 104 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {M} = \\frac {\\exp \\left(W _ {1} \\mathbf {L} _ {i}\\right)}{\\sum_ {i = 1} ^ {T} \\exp \\left(W _ {1} \\mathbf {L} _ {i}\\right)}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 187, + 114, + 468, + 151 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {\\mathbf {G}} = \\mathbf {M} \\otimes \\mathbf {L}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 228, + 154, + 468, + 170 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $W_{1}\\in \\mathbb{R}^{P\\times C\\times M}$ is the weight of Separate $FC_{1}$ , $i$ is the index of frame, and $\\otimes$ denotes matrix multiplication.", + "bbox": [ + 75, + 181, + 468, + 212 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Higher-order Global Motion Patterns. To take advantage of the information aggregated in the low-order global motion patterns, we perform a further mapping aiming at fully capturing the high-order global motion patterns. In addition, we also introduce residual learning into GMPA to ease the training. Concretely, we further map the preset number of low-order global motion patterns $\\tilde{\\mathbf{G}}$ into a high-order global feature $\\mathbf{G}$ , i.e.,", + "bbox": [ + 75, + 212, + 468, + 333 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {G} = \\delta \\left(W _ {2} \\tilde {\\mathbf {G}}\\right) \\oplus \\mathbf {L}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 205, + 342, + 468, + 359 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $W_{2}\\in \\mathbb{R}^{P\\times M\\times 1}$ is the weight of Separate $FC_2$ , $\\delta$ represents the LeakyReLU activation function, and $\\oplus$ denotes the broadcast element-wise addition.", + "bbox": [ + 75, + 369, + 468, + 416 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Joint Loss", + "text_level": 1, + "bbox": [ + 76, + 425, + 192, + 440 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this work, there are two types of loss functions involved, i.e., triplet loss $\\mathcal{L}_{tp}$ and cross-entropy loss $\\mathcal{L}_{ce}$ , which constrain the features of each part separately. Formally, triplet loss $\\mathcal{L}_{tp}$ [11] can be expressed as:", + "bbox": [ + 75, + 449, + 468, + 508 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {t p} = \\frac {1}{N _ {t p}} \\overbrace {\\sum_ {p = 1} ^ {P} \\sum_ {i = 1} ^ {S} \\sum_ {a = 1} ^ {K} \\sum_ {s = 1} ^ {K} \\sum_ {j = 1} ^ {S} \\sum_ {n = 1} ^ {K}} ^ {\\text {p a r t s}} \\max (0, m + \\tag {10} \\\\ D \\big (\\mathcal {F} (x _ {a, i} ^ {p}), \\mathcal {F} (x _ {s, i} ^ {p}) \\big) - D \\big (\\mathcal {F} (x _ {a, i} ^ {p}), \\mathcal {F} (x _ {n, j} ^ {p}) \\big), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 518, + 468, + 612 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $P$ is the number of sliced parts horizontally on the gait features, $N_{tp}$ is a positive integer obtained by multiplying the non-zero terms in triplets with the number of parts, $(S, K)$ denotes the number of subjects with different identities and the number of samples per person, $m$ is the margin value, $D(f_1, f_2)$ represents the euclidean distance between two features, $\\mathcal{F}$ denotes the feature extraction model, and $x$ represents the input sequence. We retain the case where the anchor and positive labels are the same, in other words, our triplet loss function requires the distance between each anchor sample and the negative sample is greater than the margin, which is an important trick for gait recognition.", + "bbox": [ + 75, + 619, + 468, + 801 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Here, we propose to use the cross entropy loss $\\mathcal{L}_{ce}$ to constrain each part with the label smoothing. Formally,", + "bbox": [ + 75, + 801, + 468, + 830 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {c e} = - \\frac {1}{N _ {c e}} \\overbrace {\\sum_ {p = 1} ^ {P} \\sum_ {i = 1} ^ {S} \\sum_ {j = 1} ^ {K} \\sum_ {b = 1} ^ {B}} ^ {\\text {p a r t s}} q _ {i, j} ^ {p, b} \\log p _ {i, j} ^ {p, b}, \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 107, + 842, + 468, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $N_{ce}$ is a positive integer obtained by multiplying the mini-batch with the number of parts, $p$ is the distribution of predicted probabilities, and $q$ is the label of the mini-batch. In our experiments, the combined loss function $\\mathcal{L}_c$ can be expressed as:", + "bbox": [ + 496, + 90, + 890, + 166 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {c} = \\mathcal {L} _ {t p} + \\beta \\mathcal {L} _ {c e}, \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 632, + 181, + 890, + 198 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\beta$ is the hyper-parameter to balance the two terms and is set to 0.2 through the experiments.", + "bbox": [ + 496, + 212, + 890, + 242 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 498, + 258, + 633, + 277 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we evaluate our network on three typical gait datasets, i.e., CASIA-B [56], OUMVLP [41], and Gait3D [59], and provide the implementation details. Then, we compare our approach with the current state-of-the-art methods. Finally, we conduct comprehensive ablation studies to verify the effectiveness of the proposed method.", + "bbox": [ + 496, + 286, + 890, + 377 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Datasets and Implementation Details", + "text_level": 1, + "bbox": [ + 498, + 390, + 818, + 406 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "CASIA-B [56] is a widely used dataset for gait recognition. It contains 124 subjects, 3 different walking conditions, and 11 different camera viewpoints uniformly distributed in $[0^{\\circ}, 180^{\\circ}]$ . The different walking conditions include normal walking (NM), walking with bags (BG), and walking wearing a coat (CL). In summary, there are 110 sequences for each person, and each sequence has an uncertain length of frames. We take the first 74 subjects as the training set and the rest 50 subjects for the test. In the test phase, the first 4 normal walking conditions are taken as the gallery, and the rest are taken as the probe.", + "bbox": [ + 496, + 414, + 890, + 580 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "OUMVLP [41] has the largest number of sequences in the public gait dataset. It consists of 10,307 subjects, 2 different walking sequences (\"00-01\"), and 14 different camera viewpoints uniformly distributed in $[0^{\\circ}, 90^{\\circ}]$ and $[180^{\\circ}, 270^{\\circ}]$ . In general, each subject contains up to 28 sequences. According to the official split way, we take 5153 subjects as the training set and the rest of 5154 as the test set. In the test phase, the sequences of \"01\" are taken as the gallery, and the rest of \"00\" is taken as the probe.", + "bbox": [ + 496, + 580, + 890, + 717 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Gait3D [59] is a large-scale comprehensive dataset for gait recognition, containing silhouettes, 2D/3D human body pose, and 3D Mesh. Compared with the above datasets, Gait3D collected from more complex scenes in the wild is more challenging for the gait recognition task. It contains 4000 subjects, 25309 sequences, and 39 different camera viewpoints. Following the official splitting approach, we take 3000 subjects as the training set and the remaining 1000 subjects as the test set. In the testing phase, we calculate the similarity of one sequence of query set to all sequences in gallery set, and then report the average rank-1 and rank-5 recognition rates for all query sequences.", + "bbox": [ + 496, + 719, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "22080", + "bbox": [ + 478, + 943, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/d7375032eb2d21af516c00dcda5d10fc042eeab5aff38d20a247db5b332aae89.jpg", + "table_caption": [ + "Table 1. The performance comparisons on CASIA-B are reported with rank-1 accuracy $(\\%)$ , excluding the identical-view cases. The defaults input silhouette size is $64 \\times 44$ and $\" (* ) \"$ indicates that the input size is $128 \\times 88$ ." + ], + "table_footnote": [], + "table_body": "
MethodProbe ViewMean
0°18°36°54°72°90°108°126°134°162°180°
NMCNN-LB [52]82.690.396.194.390.187.489.994.094.791.378.589.9
GaitSet [8]90.897.999.496.993.691.795.097.898.996.885.895.0
GaitPart [14]94.198.699.398.594.092.395.998.499.297.890.496.2
GLN(*) [20]93.299.399.598.796.195.697.298.199.398.690.196.9
MT3D [32]95.798.299.097.595.193.996.198.699.298.292.096.7
GaitGL [33]96.098.399.097.996.995.497.098.999.398.894.097.4
LagrangeGait [7]95.798.199.198.396.495.297.599.099.398.994.997.5
DANet(ours)96.499.199.298.296.695.597.699.499.599.396.998.0
BGCNN-LB [52]64.280.682.776.964.863.168.076.982.275.461.372.4
GaitSet [8]83.891.291.888.883.381.084.190.092.294.479.087.2
GaitPart [14]89.194.896.795.188.394.989.093.596.193.885.891.5
GLN(*) [20]91.197.797.895.292.591.292.496.097.595.088.194.0
MT3D [32]91.095.497.594.292.386.991.295.697.396.486.693.0
GaitGL [33]92.696.696.895.593.589.392.296.598.296.991.594.5
LagrangeGait [7]94.296.296.895.894.389.591.796.898.097.090.994.6
DANet(ours)95.097.398.397.494.791.093.997.498.297.694.295.9
CLCNN-LB [52]37.757.266.661.155.254.655.259.158.948.839.454.0
GaitSet [8]61.475.480.777.372.170.171.573.573.568.450.070.4
GaitPart [14]70.785.586.983.377.172.576.982.283.880.266.578.7
GLN(*) [20]70.682.485.282.779.276.476.278.977.978.764.377.5
MT3D [32]76.087.689.885.081.275.781.084.585.482.268.181.5
GaitGL [33]76.690.090.387.184.579.084.187.087.384.469.583.6
LagrangeGait [7]77.490.693.290.284.780.385.287.789.386.671.085.1
DANet(ours)82.894.896.994.389.083.987.992.395.192.080.389.9
", + "bbox": [ + 98, + 141, + 870, + 537 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details. We implement our network in PyTorch [38] for all experiments. Following the preprocessing method mentioned in [8], we align and resize the input silhouettes to $64 \\times 44$ . During the training phase, the sampling module randomly selects [20, 40] sequences as the inputs. In the test phase, we utilize all silhouettes to obtain the gait feature. We train the model in an end-to-end manner with an optimizer of SGD and an initial learning rate of 0.1, which is reduced by a factor of 10 until convergence. The parameter $l$ in Fig. 3 indicates the number of stages, where $l = 0$ for CASIA-B and $l = 1$ for OUMVLP and Gait3D. (1) In CASIA-B, the model is trained for a total of 40K iterations with the step size set every 10K iterations, using a mini-batch size of (8, 16). The convolutional channels are set to (64, 128, 256), and the stride of the temporal pooling and spatial pooling modules are set to $m = 3$ and $n = 1$ , respectively. (2) In the case of OUMVLP and Gait3D, we consider that the number of sequences in OUMVLP is 20 times greater than that in CASIA-B, and the sequences in Gait3D are collected in the wild with more views. To account for these differences, we set the number of channels in four stages to (64, 128, 256, 512) and the training mini", + "bbox": [ + 75, + 563, + 472, + 895 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "batch size to (32, 16). The model is trained for a total of $200\\mathrm{K}$ iterations, with the step size set every $50\\mathrm{K}$ iterations. Additionally, the stride of spatial pooling is set to $n = 2$", + "bbox": [ + 498, + 563, + 890, + 609 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Comparison with State-of-the-art Methods", + "text_level": 1, + "bbox": [ + 498, + 619, + 864, + 635 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To verify the effectiveness of our method, several latest gait recognition methods are introduced for comparison, including CNN-LB [52], GaitSet [8], GaitPart [14], GLN [20], MT3D [32], GaitGL [33], and LagrangeGait [7]. Evaluation on CASIA-B. The performance comparison on CASIA-B is provided in Tab. 1, where the probe sequence is divided into three subsets according to the walking conditions. (1) Comparing with the template-based approach, i.e., CNN-LB [52], our method achieves significantly better results in all walking conditions and viewpoints. The possible reason is that the template-based approach directly compressing the gait sequence into a gait energy map would greatly compromise the temporal information in gait sequence. Once the temporal features are neglected, the motion pattern of the gait can not be adequately represented. (2) In contrast to the set-based methods, i.e., GaitSet [8] and GLN [20], the proposed method achieves higher recog", + "bbox": [ + 496, + 642, + 890, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "22081", + "bbox": [ + 478, + 943, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/32149ef8307644db68bca52147e72944053fa60e791078f6b4e098d156a34224.jpg", + "table_caption": [ + "Table 2. Rank-1 accuracy (%) on OUMVLP under all view angles, excluding the identical-views cases." + ], + "table_footnote": [], + "table_body": "
MethodProbe ViewMean
0°15°30°45°60°75°90°180°195°210°225°240°255°270°
GaitSet [8]79.587.989.990.288.188.787.881.786.789.089.387.287.886.287.1
GaitPart [14]82.688.990.891.089.789.989.585.288.190.090.189.089.188.288.7
GLN [20]83.890.091.091.290.390.089.485.389.190.590.689.689.388.589.2
GaitGL [33]84.990.291.191.591.190.890.388.588.690.390.489.689.588.889.7
LagrangeGait [7]85.990.691.391.591.291.090.688.989.290.590.689.989.889.290.0
CSTL [23]87.191.091.591.890.690.890.689.490.290.590.789.890.089.490.2
DANet(ours)87.791.391.691.891.791.491.190.490.390.790.990.590.389.990.7
", + "bbox": [ + 101, + 127, + 867, + 253 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "nition accuracy. This may be due to the fact that the set-based approach assumes that each silhouette contains positional information but ignores the motion patterns between sequences. We believe that motion patterns are the essential features of each person, and adequately expressing them is the key to identifying cross-views and cross-dressing conditions. (3) Compared to the sequence-based methods, i.e., GaitPart [14], MT3D [32], GaitGL [33], and LagrangeGait [7] our method exceeds GaitPart by $11.2\\%$ , MT3D by $8.4\\%$ , GaitGL by $6.3\\%$ , and LagrangeGait by $4.8\\%$ under the most challenging cross-dressing condition. The experimental results prove the effectiveness of our method and also confirm that the combination of LCMB and GMPA modules can extract more discriminating gait features.", + "bbox": [ + 75, + 279, + 468, + 489 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Evaluation on OUMVLP. To further demonstrate the effectiveness of our proposed method, as shown in Tab. 2, DANet is also evaluated on the largest gait datasets, i.e., OUMVLP. (1) Compared with other methods, the proposed method achieves the state-of-the-art performance under all cross-view conditions. The comparison results also demonstrate that the proposed method can also effectively obtain representative and stable global motion patterns on the large-scale dataset. (2) It is worth noting that some subjects had no sequences corresponding to the probes in the gallery because of missing sequences, therefore the recognition accuracy in the Tab. 2 is lower than the actual performance.", + "bbox": [ + 75, + 489, + 468, + 671 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Evaluation on Gait3D. The effectiveness of our method was further validated on a wild dataset, i.e., Gait3D. (1) We observe a significant degradation in rank-1 performance of all methods, i.e., GaitPart [14], GLN [20], and GaitGL [33], on the Gait3D dataset. The possible reason is that Gait3D contains more complex conditions, such as misaligned and occlusions in the silhouette data. (2) The experimental comparison results are illustrated in Tab. 3, which confirms that our proposed method is effective in extracting robust global motion patterns on the wild dataset.", + "bbox": [ + 75, + 671, + 470, + 821 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 832, + 232, + 848 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we provide an ablation study in DANet to gain a better understanding of the effect of different configurations on the LCMB and GMPA. All experiments in the", + "bbox": [ + 76, + 854, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/2a35f103e27acef8e79204300a11ca801ebcf656c08aaf39298014b96e1020d4.jpg", + "table_caption": [ + "Table 3. The performance comparisons on Gait3D are reported with rank-1 accuracy(%) and rank-5 accuracy(%)." + ], + "table_footnote": [], + "table_body": "
MethodsPublicationR-1(%)R-5(%)
GaitSet [8]AAAI 201936.758.3
GaitPart [14]CVPR 202028.247.6
GLN [20]ECCV 202031.452.9
GaitGL [33]ICCV 202129.748.5
SMPLGait [59]CVPR 202246.364.5
DANetOurs48.069.7
", + "bbox": [ + 527, + 316, + 861, + 436 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/68daf5563659faeebfde3cbe8b1c9e91ce84928435341118ab1665134422bbaa.jpg", + "table_caption": [ + "Table 4. The ablation study of the proposed modules on CASIA-B with rank-1 accuracy (\\%). Where the Conv. represents the convolutional layer, and the Aggr. denotes the aggregator." + ], + "table_footnote": [], + "table_body": "
MethodConv.Aggr.NMBGCL
GaitSet [8]C2DMax95.087.270.4
GaitPart [14]C2DMCM96.291.578.7
GaitGL [33]C3DGeM97.494.583.6
DANet(C2D)C2DGMPA97.894.584.3
DANet(C3D)C3DGMPA97.895.487.7
DANet(Max)LCMBMax97.895.686.9
DANet(Mean)LCMBMean97.495.087.1
DANet(Gem)LCMBGeM97.195.085.3
DANet(MCM)LCMBMCM97.594.885.4
DANetLCMBGMPA97.996.289.9
", + "bbox": [ + 508, + 508, + 877, + 696 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ablation study are performed on CASIA-B, excluding the identical-views cases.", + "bbox": [ + 498, + 715, + 888, + 744 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The Effectiveness of Local Conv-Mixing Block. As mentioned in Sec. 3.2, we design a novel Local Conv-Mixing Block (LCMB) module to effectively aggregate local motion patterns. (1) As shown in Tab. 4, compared with the benchmark approach, i.e., GaitSet [8], GaitPart [14], and GaitGL [33], the LCMB-based method achieves higher accuracy under the same conditions. (2) With other conditions remaining the same, we directly replace our LCMB with C2D or C3D convolutional layers. As shown in Tab. 4, our LCMB is significantly higher than the C2D or C3D convo", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "22082", + "bbox": [ + 478, + 943, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/fc977001f425ccee8bb6db55efc89d8b1c074c1267e207980c9758b55a593a33.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 84, + 90, + 341, + 189 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/836e493dd7b852d014bad2aac9871c6234c39fe684418072c76d2f4c7b339876.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 344, + 92, + 602, + 189 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/864523effda4aaefb0a049a12371b893b67a6dae6706d427e803bb6d46ab1ac0.jpg", + "image_caption": [ + "(c)" + ], + "image_footnote": [], + "bbox": [ + 604, + 92, + 857, + 189 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5b05872fd4e54b1212ec5b3ceb6eb69b3710da930e9638ecb5b3b52d57f9dcc9.jpg", + "image_caption": [ + "Figure 6. Visualization of attention maps (dash boxes) for phase values and corresponding positions (solid points) in the silhouettes of the same person, where \"J\" represents the face, \"H\" represents the hand, \"L\" represents the leg, and \"F\" represents the foot." + ], + "image_footnote": [], + "bbox": [ + 859, + 92, + 885, + 191 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "lutional methods, which demonstrates that the LCMB can effectively extract the local motion patterns of gait.", + "bbox": [ + 75, + 257, + 467, + 287 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The Effectiveness of Global Motion Patterns Aggregator. To demonstrate the effectiveness of GMPA, as shown in Tab. 4, we fully compare it with other aggregators, i.e., Max [8], MCM [14], GeM [33]. (1) The C2D and C3D convolutional layers combined with our GMPA module can significantly improve the performance. (2) In contrast to MCM, our GMPA focus on establishing a complete global motion pattern, which we believe is the essence of the actual motion of the gait. (3) Compared to Max- or Mean-based methods, the experimental results show that GMPA can effectively aggregate robust global motion patterns.", + "bbox": [ + 75, + 287, + 467, + 455 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Analysis of the Number of Lower-order Global Motion Patterns. The number of low-order global motion patterns $N_{patt}$ ( $M$ in GMPA module) selected in the GMPA module will directly affect the final feature representation. (1) As shown in Tab. 5, when $N_{patt} = 1$ or 8, the network cannot fit actual movement patterns due to insufficiently sampled low-order motion patterns. (2) The experimental results show that when $N_{patt} = 32$ , the network over-fits real motion pattern when the number of samples is excessive. Therefore, we adopt $N_{patt} = 16$ as the default parameter of DANet.", + "bbox": [ + 75, + 455, + 467, + 607 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Analysis of the Number of Horizontal Slice Parts. As shown in Tab. 5, we further analyze the effect of the number spatial parts $N_{part}$ ( $P$ in the Horizontal Pooling module). (1) In DANet, the experimental results rise as the number of $N_{part}$ increases. (2) The possible reason is that the LCMB and GMPA modules can effectively select the key regions and aggregate robust global motion patterns. As a result, the network expresses more sufficient global motion patterns when the number of $N_{part}$ increases.", + "bbox": [ + 75, + 607, + 467, + 744 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Visualization", + "text_level": 1, + "bbox": [ + 76, + 755, + 212, + 768 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To gain further insight into the local motion patterns of salient parts established by the phase term of the vector, as shown in Fig. 6, we visualize the heatmaps for the phase values and corresponding silhouettes of the same person. (1) In terms of the spatial dimension, the phase term of the vector can be effectively located in the key regions. (2) In terms of the temporal dimension, the phase terms of the vectors in the sequence move with the motion of the body parts,", + "bbox": [ + 75, + 779, + 467, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/462aae76a2f421547619a8ca33b1c5188c89353d215c0476645f8528df6c3987.jpg", + "table_caption": [ + "Table 5. Comparison of the number of spatial bins $N_{part}$ in HP and low-order global motion patterns $N_{patt}$ in GMPA." + ], + "table_footnote": [], + "table_body": "
NpattNpartNMBGCLMean
161697.594.485.792.5
163297.795.689.394.2
16497.895.686.993.4
86497.495.087.193.1
326497.594.788.593.6
166497.996.289.994.6
", + "bbox": [ + 531, + 294, + 854, + 430 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "precisely localizing the disappearance and appearance of hand movements and the alternate walking of the legs. (3) The visualization results show that, in contrast to the fixed parameters in the CNN, the phase term of the vector can dynamically distinguish the key regions.", + "bbox": [ + 496, + 449, + 890, + 525 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 547, + 617, + 563 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose a novel Dynamic Aggregated (DANet) for gait recognition, which consists of a serial of Local Conv-Mixing Block (LCMB) and Global Motion Pattern Aggregator (GMPA) to adaptively aggregate the robust discriminative global motion patterns. The proposed method can dynamically locate the key regions and extract the local motion patterns, and then adaptively select the distinguishing local motion patterns to further construct robust global motion patterns. The experimental results on three popular gait datasets, i.e., CASIA-B, OUMVLP, and Gait3D, verify the effectiveness of the proposed method and show great potential for practical applications. In the future, we will further investigate adaptive learning of the local and global motion patterns in the complex-valued domain to aggregate more representative gait features.", + "bbox": [ + 496, + 575, + 890, + 803 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Acknowledgement", + "text_level": 1, + "bbox": [ + 500, + 825, + 679, + 843 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported by National Natural Science Foundation of China (Grants No.62171038, No.61827901, No.62088101, No.62276031, and No.62276025).", + "bbox": [ + 498, + 854, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "22083", + "bbox": [ + 478, + 943, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Gunawan Ariyanto and Mark S Nixon. Model-based 3d gait biometrics. In international joint conference on biometrics, 2011. 2", + "[2] Shutao Bai, Bingpeng Ma, Hong Chang, Rui Huang, and Xilin Chen. Salient-to-broad transition for video person re-identification. 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Pattern recognition letters, 2006. 1" + ], + "bbox": [ + 501, + 92, + 890, + 659 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "22085", + "bbox": [ + 478, + 943, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Dynamic Aggregated Network for Gait Recognition/3a3ce788-5b5c-498f-8336-10d8bcc8bede_model.json b/2023/Dynamic Aggregated Network for Gait Recognition/3a3ce788-5b5c-498f-8336-10d8bcc8bede_model.json new file mode 100644 index 0000000000000000000000000000000000000000..1578e298569c83ab217538d2a826d551509777f2 --- /dev/null +++ b/2023/Dynamic Aggregated Network for Gait Recognition/3a3ce788-5b5c-498f-8336-10d8bcc8bede_model.json @@ -0,0 +1,2299 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.225, + 0.131, + 0.748, + 0.154 + ], + "angle": 0, + "content": "Dynamic Aggregated Network for Gait Recognition" + }, + { + "type": "text", + "bbox": [ + 0.146, + 0.18, + 0.823, + 0.218 + ], + "angle": 0, + "content": "Kang Ma\\(^{1}\\), Ying Fu\\(^{1*}\\), Dezhi Zheng\\(^{1*}\\), Chunshui Cao\\(^{2}\\), Xuecai Hu\\(^{2}\\), Yongzhen Huang\\(^{2,3}\\) \n\\(^{1}\\)Beijing Institute of Technology, \\(^{2}\\)WATRIX.AI, \\(^{3}\\)Beijing Normal University" + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.22, + 0.875, + 0.252 + ], + "angle": 0, + "content": "kangx.ma@gmail.com, {fuying, zhengdezhi}@bit.edu.cn, {chunshui.cao, xuecai.hu}@watrix.ai, huangyongzhen@bnu.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.287, + 0.314, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.319, + 0.474, + 0.729 + ], + "angle": 0, + "content": "Gait recognition is beneficial for a variety of applications, including video surveillance, crime scene investigation, and social security, to mention a few. However, gait recognition often suffers from multiple exterior factors in real scenes, such as carrying conditions, wearing overcoats, and diverse viewing angles. Recently, various deep learning-based gait recognition methods have achieved promising results, but they tend to extract one of the salient features using fixed-weighted convolutional networks, do not well consider the relationship within gait features in key regions, and ignore the aggregation of complete motion patterns. In this paper, we propose a new perspective that actual gait features include global motion patterns in multiple key regions, and each global motion pattern is composed of a series of local motion patterns. To this end, we propose a Dynamic Aggregation Network (DANet) to learn more discriminative gait features. Specifically, we create a dynamic attention mechanism between the features of neighboring pixels that not only adaptively focuses on key regions but also generates more expressive local motion patterns. In addition, we develop a self-attention mechanism to select representative local motion patterns and further learn robust global motion patterns. Extensive experiments on three popular public gait datasets, i.e., CASIA-B, OUMVLP, and Gait3D, demonstrate that the proposed method can provide substantial improvements over the current state-of-the-art methods.1" + }, + { + "type": "title", + "bbox": [ + 0.079, + 0.759, + 0.21, + 0.775 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.786, + 0.47, + 0.864 + ], + "angle": 0, + "content": "Gait recognition aims to retrieve the same identity at a long distance, and has been widely used throughout social security [28], video surveillance [4, 15, 49], crime investigation [25], and so on. Compared with action recognition [17, 53, 54] and person re-identification [2, 55, 60, 61], the" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.285, + 0.887, + 0.496 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.51, + 0.895, + 0.596 + ], + "angle": 0, + "content": "Figure 1. The features of each pixel are mapped as a vector with both magnitude and phase components. The magnitude represents contextual information, while the phase direction is used to construct dynamic attention models for the key regions. The convolution operation is denoted by \\(*\\), and the blue circles in the diagrams represent the key regions learned by the dynamic attention." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.612, + 0.895, + 0.824 + ], + "angle": 0, + "content": "gait recognition task is one of the most challenging fine-grained label classification problems. On the one hand, silhouette data is a binary image of a person suffering from the limitations of the segmentation algorithm [26, 62, 63], with occasional holes and broken edges. On the other hand, gait recognition is also impacted by various exterior factors in real scenes, such as carrying conditions, wearing coats, and diverse viewing angles. Different angles and clothing conditions will greatly change the silhouette appearance of the same person, resulting in the intra-class variance being much greater than inter-class. We ask: How to learn more robust features adaptively for each person under the influence of various external factors? We attempt to answer this question from the following perspectives:" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.895, + 0.903 + ], + "angle": 0, + "content": "(i) Local Motion Patterns. Gait, or the act of walking, is essentially the coordinated movement of body parts. In a gait sequence, we observe that each part has a unique representative motion pattern, and each motion pattern is composed of a set of localized sub-movements. Therefore, it" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.875, + 0.229, + 0.888 + ], + "angle": 0, + "content": "*Corresponding Authors" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.888, + 0.456, + 0.9 + ], + "angle": 0, + "content": "\\(^{1}\\)Code available at https://github.com/XKMar/FastGait" + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.875, + 0.456, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.944, + 0.521, + 0.956 + ], + "angle": 0, + "content": "22076" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.092, + 0.091, + 0.468, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.259, + 0.472, + 0.342 + ], + "angle": 0, + "content": "Figure 2. Comparison of the actual motion pattern with the Max-based method, Mean-based method, and Global Motion Pattern Aggregator (GMPA) module. The black curve represents a single periodic action that is affected by disturbances, whereas the green curve represents a synthesized periodic action consisting of distinct local motion patterns selected by the GMPA." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.357, + 0.47, + 0.553 + ], + "angle": 0, + "content": "is critical to accurately locate the discriminative parts and obtain representative local motion patterns under the interference of various external factors. However, previous gait-based approaches [7, 8, 13, 14, 20, 24, 33] simply use convolutional networks with non-linear activation to model the dynamic movements. Once the network has been trained, the parameters and the non-linear function can only focus on the fixed patterns. To this end, we propose to encode the features of each pixel as a vector with magnitude and phase, as shown in Fig. 1, which allows learning the dynamic attention mapping functions among the neighboring pixel of focusing. By modeling the relationship, the network can further focus on local motion patterns in key regions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.553, + 0.47, + 0.856 + ], + "angle": 0, + "content": "(ii) Global Motion Patterns. Gait is a periodic movement. We assume that the actual motion pattern is a one-dimensional signal, as shown in Fig. 2, whereby the local motion patterns are the points on the signal. Therefore, it is essential to use a series of local motion patterns to further fit the actual motion patterns for obtaining discriminative gait features. However, recent gait-based methods [8,20,33] only use Max- or Mean-based methods to extract one of the significant local features. These methods are susceptible to disturbances and can not fit the actual motion patterns. According to the Nyquist-Shannon sampling theorem [37, 39] in signal processing theory, when a continuous signal is sampled at a frequency greater than twice the frequency of the signal, the information of the original signal is retained intact. In this regard, we propose to construct a global attention model and use it to dynamically select a preset number of distinguishable local motion patterns (green arrows), while excluding the effect of noise (red arrows). By selecting sufficient discriminative local motion patterns, the network can further obtain robust global motion patterns." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Driven by this analysis, we propose a novel and effective Dynamic Aggregated Network (DANet) for gait recognition. As shown in Fig. 3, DANet consists of two" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.333 + ], + "angle": 0, + "content": "well-designed components, i.e., Local Conv-Mixing Block (LCMB) and Global Motion Patterns Aggregator (GMPA). Firstly, we encode the features of each pixel into the complex domain including magnitude and phase, where the magnitude term represents the contextual information and the phase term is used to establish the relationship between each vector. The local motion pattern is generated by aggregating the magnitude and phase of the vectors in the neighboring regions of focus. Secondly, we use the self-attentive mechanism in the GMPA model to dynamically select sufficient discriminative local motion patterns and further learn to fit the actual gait patterns. Finally, with our proposed modules, we obtain the most representative stable gait features for each person and outperform the state-of-the-art (SOTA) methods, especially under the most challenging condition of cross-dressing." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.334, + 0.88, + 0.348 + ], + "angle": 0, + "content": "Our main contributions can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.36, + 0.892, + 0.421 + ], + "angle": 0, + "content": "- We propose a novel LCMB to extract the representative local motion patterns, which can dynamically model the relationships among the features of neighboring pixels and then accurately locate key regions." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.431, + 0.892, + 0.506 + ], + "angle": 0, + "content": "- We design an effective GMPA to select the discriminative local motion patterns and then aggregate them to obtain a robust global representation. To the best of our knowledge, it is the first attempt to explore the potential of self-attention model in this task." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.518, + 0.892, + 0.608 + ], + "angle": 0, + "content": "- Experimental results are illustrated to demonstrate the effectiveness of the proposed method, outperforming the SOTA method on CASIA-B [56], OUMVLP [41] and Gait3D [59] datasets. In addition, many rigorous ablation experiments on CASIA-B [56] further validated the effectiveness of each component in DANet." + }, + { + "type": "list", + "bbox": [ + 0.519, + 0.36, + 0.892, + 0.608 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.634, + 0.65, + 0.649 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.892, + 0.704 + ], + "angle": 0, + "content": "In this section, we provide a brief overview of relevant research in the fields of gait recognition, local action modeling, and global action modeling." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Gait Architectures. Gait recognition approaches mainly fall into two typical categories, i.e., model-based approaches and appearance-based approaches. Model-based approaches [1,3,27,29-31,44] attempt to explicitly fit human pose structures [10] to images. However, the predefined points are empirically designed and limited by the inaccuracy of estimation results for low-quality images. Therefore, the model-based methods are generally inferior to appearance-based methods in performance. Appearance-based approaches [7,8,13,18,20,21,24,32,33,43,47,51, 52, 58] are the mainstream frameworks for gait and have benefited from the quick growth of deep learning. It can be roughly divided into three classes, namely template-based" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.944, + 0.521, + 0.956 + ], + "angle": 0, + "content": "22077" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.09, + 0.094, + 0.878, + 0.219 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.23, + 0.895, + 0.288 + ], + "angle": 0, + "content": "Figure 3. The overview of the proposed DANet. Each stage contains the Local Conv-Mixing Block (LCMB), which utilizes a dynamic attention model to establish relationships among neighboring pixels of interest. The HP denotes Horizontal Pooling, GMPA represents Global Motion Pattern Aggregator, and \\(l\\) indicates the number of last stages. In particular, the \\(\\mathrm{GMPA}_j\\) module is responsible for aggregating the local motion patterns of the \\(j\\)-th part and producing the final global motion patterns \\(v_{i}\\) for recognition." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.301, + 0.473, + 0.527 + ], + "angle": 0, + "content": "methods, set-based methods, and sequence-based methods. The template-based approaches [18, 36, 43, 47, 52, 57] extracted gait spatio-temporal features by compressing a sequence of gait silhouettes, e.g., Gait Energy Image (GEI), which inevitably destroyed the representation of discriminative local motion patterns in gait sequences. The set-based approaches [8,20,21,23] assumed that the appearance of a silhouette contained its position information, which could not construct local motion patterns using continuous frames. Recently some advanced sequence-based methods [7, 24, 32, 33, 51] used 3D convolutional (C3D) neural networks to extract gait features from the gait sequence and achieve SOTA results. Our approach belongs to the sequence-based method, in contrast to other methods, we propose to use variable-length frames as the input." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.533, + 0.47, + 0.79 + ], + "angle": 0, + "content": "Local Action Modeling. Local action modeling [14,24,32, 33] aims at building short-range spatio-temporal features, which have been shown to be beneficial for gait recognition in various literature. GaitPart [14] proposed a micro-motion capture module to model the short-range spatio-temporal features. MT3D [32] proposed multiple temporal-scale 3D convolutional layers to extract the small and large temporal-scale motion features. GaitGL [33] utilized a local temporal aggregation module to extract the local temporal information. 3DLocal [24] proposed a localization module to adaptively sample the local action features. In contrast to these strategies, we propose to map each pixel of the gait sequence to the complex-valued domain, using the phase term to encode the relationship between gait features. By fully exploiting the phase term, we construct a dynamic attention model among each pixel of the feature to extract local motion patterns in key regions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Global Action Modeling. Global action modeling, aiming at capturing long-range dependencies, has been demonstrated to be advantageous to a wide range of recognition tasks such as action recognition [6, 45, 48, 54] and person re-identification [9, 16, 19, 35, 40, 61]. Many attention-based approaches [12, 34, 46] built global relationships in the spatial dimension [5, 50] or channel dimension [22] with re" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.301, + 0.895, + 0.422 + ], + "angle": 0, + "content": "markable results. However, current state-of-the-art works [7, 8, 32, 33] in gait recognition still directly use Max- or Mean-based methods to extract global temporal features, which only focus on the most salient features. Different from these methods, we design an efficient global self-attention model to obtain a robust representation for each person, which can select discriminative local motion patterns, and further map them to global motion patterns." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.436, + 0.637, + 0.454 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.461, + 0.895, + 0.553 + ], + "angle": 0, + "content": "In this section, we first describe the overall architecture of our method in Sec. 3.1, and then introduce the proposed two novel well-designed modules, i.e., Local Conv-Mixing Block (LCMB) in Sec. 3.2 and Global Motion Pattern Aggregator (GMPA) in Sec. 3.3. Finally, we will discuss the joint loss functions in Sec. 3.4." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.563, + 0.757, + 0.578 + ], + "angle": 0, + "content": "3.1. Formulation and Motivation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.586, + 0.894, + 0.708 + ], + "angle": 0, + "content": "Gait recognition aims to identify the same person under the influence of various external factors. Let \\(\\mathbf{X} \\in \\mathbb{R}^{T \\times H \\times W}\\) denote silhouette data containing consecutive \\(T\\) frames, where \\(T, H\\), and \\(W\\) represent the temporal, height, and width dimensions of input frames. In our implementation, we sample variable-length frames \\(T \\in [20, 40]\\) from a continuous sequence as the input. The extraction of gait features can be expressed as" + }, + { + "type": "equation", + "bbox": [ + 0.645, + 0.72, + 0.892, + 0.737 + ], + "angle": 0, + "content": "\\[\nf = \\mathcal {G} (\\mathcal {L} (\\mathbf {X})), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.749, + 0.895, + 0.81 + ], + "angle": 0, + "content": "where \\( f \\in \\mathbb{R}^{P \\times C} \\) is the output features, \\( P \\) is the number of horizontally sliced parts, \\( C \\) is the feature channels, \\( \\mathcal{L} \\) represents the local motion pattern extraction, and \\( \\mathcal{G} \\) denotes the global motion pattern aggregation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.895, + 0.902 + ], + "angle": 0, + "content": "To learn distinctive representation for each person, the previous C2D-based methods [8, 20] and C3D-based methods [32, 33] only use convolutional layers and non-linear functions to learn gait features. However, the trained network can only recognize certain movement patterns that are vulnerable to noise. In this work, we propose a novel" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.944, + 0.521, + 0.956 + ], + "angle": 0, + "content": "22078" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.096, + 0.462, + 0.195 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.212, + 0.47, + 0.255 + ], + "angle": 0, + "content": "Figure 4. The architecture of LCMB, where “\\(\\odot\\)” represents Hadamard product, “\\(\\oplus\\)” represents element-wise sum operation, and Mix denotes vector aggregation operation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.266, + 0.47, + 0.432 + ], + "angle": 0, + "content": "LCMB in the backbone of DANet, which enables the network to focus on the key regions and extract the local motion patterns by dynamically building the relationships among pixels. Furthermore, inspired by the Nyquist-Shannon sampling theorem [37, 39], we propose a new perspective that a complete gait pattern should contain many distinguishable local motion patterns. To this end, we developed an effective GMPA to select sufficient distinguishable local motion patterns while effectively excluding the interference of noise. The selected local motion patterns are then aggregated to generate a robust global motion pattern." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.44, + 0.312, + 0.456 + ], + "angle": 0, + "content": "3.2. Local Conv-Mixing Block" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.463, + 0.47, + 0.509 + ], + "angle": 0, + "content": "In this section, we provide a detailed description of the vector representation and vector aggregation in the Local Conv-Mixing Block (LCMB) module." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.509, + 0.47, + 0.614 + ], + "angle": 0, + "content": "Vector Representation. In the LCMB module, the input features are denoted as \\(\\mathbf{V} = [v_{1}, v_{2}, \\dots, v_{N}] \\in \\mathbb{R}^{N \\times C_{i}}\\), where \\(N\\) is the number of pixels in the gait sequence, \\(C_{i}\\) is the dimension of input features. As shown in Fig. 4, we obtain the magnitude \\(|v_{j}|\\) and phase \\(\\theta_{j}\\) of each vector by multiply with the learnable parameters \\(W^{m} \\in \\mathbb{R}^{C_{i} \\times C_{l}}\\) and \\(W^{t} \\in \\mathbb{R}^{C_{i} \\times C_{l}}\\), separately, i.e.," + }, + { + "type": "equation", + "bbox": [ + 0.166, + 0.623, + 0.468, + 0.641 + ], + "angle": 0, + "content": "\\[\n\\left| v _ {j} \\right| = W ^ {m} v _ {j}, j = 1, 2, \\dots , N, \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.146, + 0.643, + 0.469, + 0.661 + ], + "angle": 0, + "content": "\\[\n\\theta_ {j} = \\max \\left(0, W ^ {t} v _ {j}\\right), j = 1, 2, \\dots , N, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.668, + 0.47, + 0.774 + ], + "angle": 0, + "content": "where the subscript \\(j\\) is the feature of the \\(j\\)-th pixel. The content of each vector is a real-value feature modeled by the magnitude term \\(|v_{j}|\\), while the relationship of each vector is modulated by the phase term \\(\\theta_{j}\\), using grouped convolutional layers with rectified linear activation ReLU. The complex vectors \\(\\tilde{v}_{j} \\in \\mathbb{C}^{C_{l}}\\) modulated by the magnitude and phase terms using Euler's formula, i.e.," + }, + { + "type": "equation", + "bbox": [ + 0.088, + 0.782, + 0.469, + 0.819 + ], + "angle": 0, + "content": "\\[\n\\tilde {v} _ {j} = \\overbrace {\\left| v _ {j} \\right| \\odot \\cos \\theta_ {j}} ^ {\\text {r e a l p a r t}} + \\overbrace {i \\left| v _ {j} \\right| \\odot \\sin \\theta_ {j}} ^ {\\text {i m a g i n a r y p a r t}}, j = 1, 2, \\dots , N, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.856 + ], + "angle": 0, + "content": "where \\(i\\) is the imaginary unit satisfying \\(i^2 = -1\\), and \\(\\odot\\) is element-wise multiplication." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Vector Aggregation. After representing the features of each pixel as a vector, we further aggregate the local spatiotemporal domain of each vector as shown in Fig. 4. In" + }, + { + "type": "image", + "bbox": [ + 0.512, + 0.094, + 0.88, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.212, + 0.892, + 0.24 + ], + "angle": 0, + "content": "Figure 5. The architecture of GMPA and the feature maps are shown by their dimensions, where “\\(\\otimes\\)” is matrix multiplication." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.254, + 0.892, + 0.3 + ], + "angle": 0, + "content": "particular, the complex-value representation of the output \\(\\tilde{o}_j\\in \\mathbb{C}^{C_i}\\) that aggregated by learnable convolution kernels \\(\\mathcal{K}\\in \\mathbb{R}^{C_i\\times C_l\\times K_t\\times K_s\\times K_s}\\) , i.e.," + }, + { + "type": "equation", + "bbox": [ + 0.52, + 0.308, + 0.892, + 0.343 + ], + "angle": 0, + "content": "\\[\n\\tilde {o} _ {j} = \\sum_ {m \\in \\mathcal {N} (j)} \\mathcal {K} [ j - m ] \\tilde {v} _ {m} + v _ {j}, j = 1, 2, \\dots , N, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.353, + 0.892, + 0.43 + ], + "angle": 0, + "content": "where \\(\\mathcal{N}(j)\\) denotes the neighboring pixels set of \\(j\\), and \\(\\tilde{v}_m\\) represents the vector belong to the neighboring pixels of \\(\\tilde{v}_j\\). Following [42], we obtain the real-value output feature \\(o_j \\in \\mathbb{R}^{C_i}\\) by summing the real and imaginary parts of \\(\\tilde{v}_j\\) for convenient computation, i.e.," + }, + { + "type": "equation", + "bbox": [ + 0.523, + 0.441, + 0.892, + 0.475 + ], + "angle": 0, + "content": "\\[\no _ {j} = \\sum_ {m \\in \\mathcal {N} (j)} \\left(\\mathcal {K} [ j - m ] | v _ {m} | \\odot \\cos \\theta_ {m} + \\right. \\tag {6}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.525, + 0.477, + 0.848, + 0.496 + ], + "angle": 0, + "content": "\\[\n\\left. \\mathcal {K} [ j - m ] \\left| v _ {m} \\right| \\odot \\sin \\theta_ {m}\\right) + v _ {j}, j = 1, 2, \\dots , N,\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.506, + 0.892, + 0.567 + ], + "angle": 0, + "content": "where \\((\\cos \\theta_{m} + \\sin \\theta_{m})\\) denotes the dynamic attention among the neighboring pixels of \\(j\\). To further comprehend the dynamic aggregation model, heatmaps showcasing the phase values are visualized in Fig. 6." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.576, + 0.809, + 0.592 + ], + "angle": 0, + "content": "3.3. Global Motion Patterns Aggregator" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.892, + 0.72 + ], + "angle": 0, + "content": "In this part, we propose a new instantiation of the global action modeling framework for gait recognition named the global motion patterns aggregator (GMPA), which selects a preset number of distinguished local motion patterns and then utilizes an attention mechanism to aggregate query-specific global motion patterns of each query location. The GMPA adopts separate parameters for each part and models the global movement patterns of the corresponding part." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Lower-order Global Motion Patterns. Gait data is affected by a number of variable factors, such as segmentation holes or broken edges, further impairing the actual movement pattern. To this end, we first propose to squeeze variable local motion patterns into a preset number of channel descriptors. Then, we utilize softmax to construct an attention map in the temporal dimension, and multiply the squeezed attention maps with the reshaped local motion pattern features to obtain the global low-order motion patterns. Formally, the global low-order motion patterns \\(\\tilde{\\mathbf{G}}\\in \\mathbb{R}^{P\\times C\\times M}\\) are generated by local motion patterns \\(\\mathbf{L}\\in \\mathbb{R}^{P\\times T\\times C}\\) and attention maps \\(\\mathbf{M}\\in \\mathbb{R}^{P\\times T\\times M}\\), and can" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.944, + 0.519, + 0.956 + ], + "angle": 0, + "content": "22079" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.186, + 0.106 + ], + "angle": 0, + "content": "be expressed as" + }, + { + "type": "equation", + "bbox": [ + 0.188, + 0.115, + 0.47, + 0.152 + ], + "angle": 0, + "content": "\\[\n\\mathbf {M} = \\frac {\\exp \\left(W _ {1} \\mathbf {L} _ {i}\\right)}{\\sum_ {i = 1} ^ {T} \\exp \\left(W _ {1} \\mathbf {L} _ {i}\\right)}, \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.229, + 0.155, + 0.469, + 0.171 + ], + "angle": 0, + "content": "\\[\n\\tilde {\\mathbf {G}} = \\mathbf {M} \\otimes \\mathbf {L}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.182, + 0.469, + 0.213 + ], + "angle": 0, + "content": "where \\(W_{1}\\in \\mathbb{R}^{P\\times C\\times M}\\) is the weight of Separate \\(FC_{1}\\), \\(i\\) is the index of frame, and \\(\\otimes\\) denotes matrix multiplication." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.213, + 0.469, + 0.334 + ], + "angle": 0, + "content": "Higher-order Global Motion Patterns. To take advantage of the information aggregated in the low-order global motion patterns, we perform a further mapping aiming at fully capturing the high-order global motion patterns. In addition, we also introduce residual learning into GMPA to ease the training. Concretely, we further map the preset number of low-order global motion patterns \\(\\tilde{\\mathbf{G}}\\) into a high-order global feature \\(\\mathbf{G}\\), i.e.," + }, + { + "type": "equation", + "bbox": [ + 0.207, + 0.343, + 0.469, + 0.361 + ], + "angle": 0, + "content": "\\[\n\\mathbf {G} = \\delta \\left(W _ {2} \\tilde {\\mathbf {G}}\\right) \\oplus \\mathbf {L}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.371, + 0.47, + 0.417 + ], + "angle": 0, + "content": "where \\(W_{2}\\in \\mathbb{R}^{P\\times M\\times 1}\\) is the weight of Separate \\(FC_2\\), \\(\\delta\\) represents the LeakyReLU activation function, and \\(\\oplus\\) denotes the broadcast element-wise addition." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.426, + 0.194, + 0.441 + ], + "angle": 0, + "content": "3.4. Joint Loss" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.45, + 0.47, + 0.51 + ], + "angle": 0, + "content": "In this work, there are two types of loss functions involved, i.e., triplet loss \\(\\mathcal{L}_{tp}\\) and cross-entropy loss \\(\\mathcal{L}_{ce}\\), which constrain the features of each part separately. Formally, triplet loss \\(\\mathcal{L}_{tp}\\) [11] can be expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.091, + 0.52, + 0.469, + 0.613 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {t p} = \\frac {1}{N _ {t p}} \\overbrace {\\sum_ {p = 1} ^ {P} \\sum_ {i = 1} ^ {S} \\sum_ {a = 1} ^ {K} \\sum_ {s = 1} ^ {K} \\sum_ {j = 1} ^ {S} \\sum_ {n = 1} ^ {K}} ^ {\\text {p a r t s}} \\max (0, m + \\tag {10} \\\\ D \\big (\\mathcal {F} (x _ {a, i} ^ {p}), \\mathcal {F} (x _ {s, i} ^ {p}) \\big) - D \\big (\\mathcal {F} (x _ {a, i} ^ {p}), \\mathcal {F} (x _ {n, j} ^ {p}) \\big), \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.621, + 0.469, + 0.802 + ], + "angle": 0, + "content": "where \\( P \\) is the number of sliced parts horizontally on the gait features, \\( N_{tp} \\) is a positive integer obtained by multiplying the non-zero terms in triplets with the number of parts, \\( (S, K) \\) denotes the number of subjects with different identities and the number of samples per person, \\( m \\) is the margin value, \\( D(f_1, f_2) \\) represents the euclidean distance between two features, \\( \\mathcal{F} \\) denotes the feature extraction model, and \\( x \\) represents the input sequence. We retain the case where the anchor and positive labels are the same, in other words, our triplet loss function requires the distance between each anchor sample and the negative sample is greater than the margin, which is an important trick for gait recognition." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.802, + 0.469, + 0.832 + ], + "angle": 0, + "content": "Here, we propose to use the cross entropy loss \\(\\mathcal{L}_{ce}\\) to constrain each part with the label smoothing. Formally," + }, + { + "type": "equation", + "bbox": [ + 0.108, + 0.843, + 0.469, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {c e} = - \\frac {1}{N _ {c e}} \\overbrace {\\sum_ {p = 1} ^ {P} \\sum_ {i = 1} ^ {S} \\sum_ {j = 1} ^ {K} \\sum_ {b = 1} ^ {B}} ^ {\\text {p a r t s}} q _ {i, j} ^ {p, b} \\log p _ {i, j} ^ {p, b}, \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.167 + ], + "angle": 0, + "content": "where \\(N_{ce}\\) is a positive integer obtained by multiplying the mini-batch with the number of parts, \\(p\\) is the distribution of predicted probabilities, and \\(q\\) is the label of the mini-batch. In our experiments, the combined loss function \\(\\mathcal{L}_c\\) can be expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.633, + 0.182, + 0.892, + 0.199 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {c} = \\mathcal {L} _ {t p} + \\beta \\mathcal {L} _ {c e}, \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.213, + 0.892, + 0.243 + ], + "angle": 0, + "content": "where \\(\\beta\\) is the hyper-parameter to balance the two terms and is set to 0.2 through the experiments." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.26, + 0.634, + 0.278 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.287, + 0.892, + 0.378 + ], + "angle": 0, + "content": "In this section, we evaluate our network on three typical gait datasets, i.e., CASIA-B [56], OUMVLP [41], and Gait3D [59], and provide the implementation details. Then, we compare our approach with the current state-of-the-art methods. Finally, we conduct comprehensive ablation studies to verify the effectiveness of the proposed method." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.391, + 0.82, + 0.407 + ], + "angle": 0, + "content": "4.1. Datasets and Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.415, + 0.892, + 0.581 + ], + "angle": 0, + "content": "CASIA-B [56] is a widely used dataset for gait recognition. It contains 124 subjects, 3 different walking conditions, and 11 different camera viewpoints uniformly distributed in \\([0^{\\circ}, 180^{\\circ}]\\). The different walking conditions include normal walking (NM), walking with bags (BG), and walking wearing a coat (CL). In summary, there are 110 sequences for each person, and each sequence has an uncertain length of frames. We take the first 74 subjects as the training set and the rest 50 subjects for the test. In the test phase, the first 4 normal walking conditions are taken as the gallery, and the rest are taken as the probe." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.582, + 0.892, + 0.718 + ], + "angle": 0, + "content": "OUMVLP [41] has the largest number of sequences in the public gait dataset. It consists of 10,307 subjects, 2 different walking sequences (\"00-01\"), and 14 different camera viewpoints uniformly distributed in \\([0^{\\circ}, 90^{\\circ}]\\) and \\([180^{\\circ}, 270^{\\circ}]\\). In general, each subject contains up to 28 sequences. According to the official split way, we take 5153 subjects as the training set and the rest of 5154 as the test set. In the test phase, the sequences of \"01\" are taken as the gallery, and the rest of \"00\" is taken as the probe." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Gait3D [59] is a large-scale comprehensive dataset for gait recognition, containing silhouettes, 2D/3D human body pose, and 3D Mesh. Compared with the above datasets, Gait3D collected from more complex scenes in the wild is more challenging for the gait recognition task. It contains 4000 subjects, 25309 sequences, and 39 different camera viewpoints. Following the official splitting approach, we take 3000 subjects as the training set and the remaining 1000 subjects as the test set. In the testing phase, we calculate the similarity of one sequence of query set to all sequences in gallery set, and then report the average rank-1 and rank-5 recognition rates for all query sequences." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.944, + 0.521, + 0.956 + ], + "angle": 0, + "content": "22080" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.892, + 0.118 + ], + "angle": 0, + "content": "Table 1. The performance comparisons on CASIA-B are reported with rank-1 accuracy \\((\\%)\\), excluding the identical-view cases. The defaults input silhouette size is \\(64 \\times 44\\) and \\(\" (* ) \"\\) indicates that the input size is \\(128 \\times 88\\)." + }, + { + "type": "table", + "bbox": [ + 0.099, + 0.142, + 0.872, + 0.538 + ], + "angle": 0, + "content": "
MethodProbe ViewMean
0°18°36°54°72°90°108°126°134°162°180°
NMCNN-LB [52]82.690.396.194.390.187.489.994.094.791.378.589.9
GaitSet [8]90.897.999.496.993.691.795.097.898.996.885.895.0
GaitPart [14]94.198.699.398.594.092.395.998.499.297.890.496.2
GLN(*) [20]93.299.399.598.796.195.697.298.199.398.690.196.9
MT3D [32]95.798.299.097.595.193.996.198.699.298.292.096.7
GaitGL [33]96.098.399.097.996.995.497.098.999.398.894.097.4
LagrangeGait [7]95.798.199.198.396.495.297.599.099.398.994.997.5
DANet(ours)96.499.199.298.296.695.597.699.499.599.396.998.0
BGCNN-LB [52]64.280.682.776.964.863.168.076.982.275.461.372.4
GaitSet [8]83.891.291.888.883.381.084.190.092.294.479.087.2
GaitPart [14]89.194.896.795.188.394.989.093.596.193.885.891.5
GLN(*) [20]91.197.797.895.292.591.292.496.097.595.088.194.0
MT3D [32]91.095.497.594.292.386.991.295.697.396.486.693.0
GaitGL [33]92.696.696.895.593.589.392.296.598.296.991.594.5
LagrangeGait [7]94.296.296.895.894.389.591.796.898.097.090.994.6
DANet(ours)95.097.398.397.494.791.093.997.498.297.694.295.9
CLCNN-LB [52]37.757.266.661.155.254.655.259.158.948.839.454.0
GaitSet [8]61.475.480.777.372.170.171.573.573.568.450.070.4
GaitPart [14]70.785.586.983.377.172.576.982.283.880.266.578.7
GLN(*) [20]70.682.485.282.779.276.476.278.977.978.764.377.5
MT3D [32]76.087.689.885.081.275.781.084.585.482.268.181.5
GaitGL [33]76.690.090.387.184.579.084.187.087.384.469.583.6
LagrangeGait [7]77.490.693.290.284.780.385.287.789.386.671.085.1
DANet(ours)82.894.896.994.389.083.987.992.395.192.080.389.9
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.564, + 0.473, + 0.896 + ], + "angle": 0, + "content": "Implementation Details. We implement our network in PyTorch [38] for all experiments. Following the preprocessing method mentioned in [8], we align and resize the input silhouettes to \\(64 \\times 44\\). During the training phase, the sampling module randomly selects [20, 40] sequences as the inputs. In the test phase, we utilize all silhouettes to obtain the gait feature. We train the model in an end-to-end manner with an optimizer of SGD and an initial learning rate of 0.1, which is reduced by a factor of 10 until convergence. The parameter \\(l\\) in Fig. 3 indicates the number of stages, where \\(l = 0\\) for CASIA-B and \\(l = 1\\) for OUMVLP and Gait3D. (1) In CASIA-B, the model is trained for a total of 40K iterations with the step size set every 10K iterations, using a mini-batch size of (8, 16). The convolutional channels are set to (64, 128, 256), and the stride of the temporal pooling and spatial pooling modules are set to \\(m = 3\\) and \\(n = 1\\), respectively. (2) In the case of OUMVLP and Gait3D, we consider that the number of sequences in OUMVLP is 20 times greater than that in CASIA-B, and the sequences in Gait3D are collected in the wild with more views. To account for these differences, we set the number of channels in four stages to (64, 128, 256, 512) and the training mini" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.564, + 0.892, + 0.61 + ], + "angle": 0, + "content": "batch size to (32, 16). The model is trained for a total of \\(200\\mathrm{K}\\) iterations, with the step size set every \\(50\\mathrm{K}\\) iterations. Additionally, the stride of spatial pooling is set to \\(n = 2\\)" + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.62, + 0.866, + 0.636 + ], + "angle": 0, + "content": "4.2. Comparison with State-of-the-art Methods" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.643, + 0.892, + 0.903 + ], + "angle": 0, + "content": "To verify the effectiveness of our method, several latest gait recognition methods are introduced for comparison, including CNN-LB [52], GaitSet [8], GaitPart [14], GLN [20], MT3D [32], GaitGL [33], and LagrangeGait [7]. Evaluation on CASIA-B. The performance comparison on CASIA-B is provided in Tab. 1, where the probe sequence is divided into three subsets according to the walking conditions. (1) Comparing with the template-based approach, i.e., CNN-LB [52], our method achieves significantly better results in all walking conditions and viewpoints. The possible reason is that the template-based approach directly compressing the gait sequence into a gait energy map would greatly compromise the temporal information in gait sequence. Once the temporal features are neglected, the motion pattern of the gait can not be adequately represented. (2) In contrast to the set-based methods, i.e., GaitSet [8] and GLN [20], the proposed method achieves higher recog" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.944, + 0.518, + 0.956 + ], + "angle": 0, + "content": "22081" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.18, + 0.089, + 0.79, + 0.104 + ], + "angle": 0, + "content": "Table 2. Rank-1 accuracy (%) on OUMVLP under all view angles, excluding the identical-views cases." + }, + { + "type": "table", + "bbox": [ + 0.102, + 0.128, + 0.868, + 0.254 + ], + "angle": 0, + "content": "
MethodProbe ViewMean
0°15°30°45°60°75°90°180°195°210°225°240°255°270°
GaitSet [8]79.587.989.990.288.188.787.881.786.789.089.387.287.886.287.1
GaitPart [14]82.688.990.891.089.789.989.585.288.190.090.189.089.188.288.7
GLN [20]83.890.091.091.290.390.089.485.389.190.590.689.689.388.589.2
GaitGL [33]84.990.291.191.591.190.890.388.588.690.390.489.689.588.889.7
LagrangeGait [7]85.990.691.391.591.291.090.688.989.290.590.689.989.889.290.0
CSTL [23]87.191.091.591.890.690.890.689.490.290.590.789.890.089.490.2
DANet(ours)87.791.391.691.891.791.491.190.490.390.790.990.590.389.990.7
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.28, + 0.47, + 0.49 + ], + "angle": 0, + "content": "nition accuracy. This may be due to the fact that the set-based approach assumes that each silhouette contains positional information but ignores the motion patterns between sequences. We believe that motion patterns are the essential features of each person, and adequately expressing them is the key to identifying cross-views and cross-dressing conditions. (3) Compared to the sequence-based methods, i.e., GaitPart [14], MT3D [32], GaitGL [33], and LagrangeGait [7] our method exceeds GaitPart by \\(11.2\\%\\), MT3D by \\(8.4\\%\\), GaitGL by \\(6.3\\%\\), and LagrangeGait by \\(4.8\\%\\) under the most challenging cross-dressing condition. The experimental results prove the effectiveness of our method and also confirm that the combination of LCMB and GMPA modules can extract more discriminating gait features." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.491, + 0.47, + 0.672 + ], + "angle": 0, + "content": "Evaluation on OUMVLP. To further demonstrate the effectiveness of our proposed method, as shown in Tab. 2, DANet is also evaluated on the largest gait datasets, i.e., OUMVLP. (1) Compared with other methods, the proposed method achieves the state-of-the-art performance under all cross-view conditions. The comparison results also demonstrate that the proposed method can also effectively obtain representative and stable global motion patterns on the large-scale dataset. (2) It is worth noting that some subjects had no sequences corresponding to the probes in the gallery because of missing sequences, therefore the recognition accuracy in the Tab. 2 is lower than the actual performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.672, + 0.471, + 0.822 + ], + "angle": 0, + "content": "Evaluation on Gait3D. The effectiveness of our method was further validated on a wild dataset, i.e., Gait3D. (1) We observe a significant degradation in rank-1 performance of all methods, i.e., GaitPart [14], GLN [20], and GaitGL [33], on the Gait3D dataset. The possible reason is that Gait3D contains more complex conditions, such as misaligned and occlusions in the silhouette data. (2) The experimental comparison results are illustrated in Tab. 3, which confirms that our proposed method is effective in extracting robust global motion patterns on the wild dataset." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.833, + 0.233, + 0.849 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.47, + 0.901 + ], + "angle": 0, + "content": "In this section, we provide an ablation study in DANet to gain a better understanding of the effect of different configurations on the LCMB and GMPA. All experiments in the" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.278, + 0.892, + 0.307 + ], + "angle": 0, + "content": "Table 3. The performance comparisons on Gait3D are reported with rank-1 accuracy(%) and rank-5 accuracy(%)." + }, + { + "type": "table", + "bbox": [ + 0.528, + 0.317, + 0.862, + 0.438 + ], + "angle": 0, + "content": "
MethodsPublicationR-1(%)R-5(%)
GaitSet [8]AAAI 201936.758.3
GaitPart [14]CVPR 202028.247.6
GLN [20]ECCV 202031.452.9
GaitGL [33]ICCV 202129.748.5
SMPLGait [59]CVPR 202246.364.5
DANetOurs48.069.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.456, + 0.892, + 0.499 + ], + "angle": 0, + "content": "Table 4. The ablation study of the proposed modules on CASIA-B with rank-1 accuracy (\\%). Where the Conv. represents the convolutional layer, and the Aggr. denotes the aggregator." + }, + { + "type": "table", + "bbox": [ + 0.509, + 0.509, + 0.879, + 0.698 + ], + "angle": 0, + "content": "
MethodConv.Aggr.NMBGCL
GaitSet [8]C2DMax95.087.270.4
GaitPart [14]C2DMCM96.291.578.7
GaitGL [33]C3DGeM97.494.583.6
DANet(C2D)C2DGMPA97.894.584.3
DANet(C3D)C3DGMPA97.895.487.7
DANet(Max)LCMBMax97.895.686.9
DANet(Mean)LCMBMean97.495.087.1
DANet(Gem)LCMBGeM97.195.085.3
DANet(MCM)LCMBMCM97.594.885.4
DANetLCMBGMPA97.996.289.9
" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.717, + 0.89, + 0.746 + ], + "angle": 0, + "content": "ablation study are performed on CASIA-B, excluding the identical-views cases." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The Effectiveness of Local Conv-Mixing Block. As mentioned in Sec. 3.2, we design a novel Local Conv-Mixing Block (LCMB) module to effectively aggregate local motion patterns. (1) As shown in Tab. 4, compared with the benchmark approach, i.e., GaitSet [8], GaitPart [14], and GaitGL [33], the LCMB-based method achieves higher accuracy under the same conditions. (2) With other conditions remaining the same, we directly replace our LCMB with C2D or C3D convolutional layers. As shown in Tab. 4, our LCMB is significantly higher than the C2D or C3D convo" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.944, + 0.521, + 0.956 + ], + "angle": 0, + "content": "22082" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.092, + 0.342, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.205, + 0.192, + 0.223, + 0.204 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.345, + 0.093, + 0.603, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.464, + 0.192, + 0.483, + 0.204 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.606, + 0.093, + 0.859, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.724, + 0.192, + 0.742, + 0.204 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image", + "bbox": [ + 0.861, + 0.093, + 0.886, + 0.192 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.216, + 0.894, + 0.245 + ], + "angle": 0, + "content": "Figure 6. Visualization of attention maps (dash boxes) for phase values and corresponding positions (solid points) in the silhouettes of the same person, where \"J\" represents the face, \"H\" represents the hand, \"L\" represents the leg, and \"F\" represents the foot." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.258, + 0.468, + 0.289 + ], + "angle": 0, + "content": "lutional methods, which demonstrates that the LCMB can effectively extract the local motion patterns of gait." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.289, + 0.468, + 0.456 + ], + "angle": 0, + "content": "The Effectiveness of Global Motion Patterns Aggregator. To demonstrate the effectiveness of GMPA, as shown in Tab. 4, we fully compare it with other aggregators, i.e., Max [8], MCM [14], GeM [33]. (1) The C2D and C3D convolutional layers combined with our GMPA module can significantly improve the performance. (2) In contrast to MCM, our GMPA focus on establishing a complete global motion pattern, which we believe is the essence of the actual motion of the gait. (3) Compared to Max- or Mean-based methods, the experimental results show that GMPA can effectively aggregate robust global motion patterns." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.456, + 0.468, + 0.608 + ], + "angle": 0, + "content": "Analysis of the Number of Lower-order Global Motion Patterns. The number of low-order global motion patterns \\( N_{patt} \\) (\\( M \\) in GMPA module) selected in the GMPA module will directly affect the final feature representation. (1) As shown in Tab. 5, when \\( N_{patt} = 1 \\) or 8, the network cannot fit actual movement patterns due to insufficiently sampled low-order motion patterns. (2) The experimental results show that when \\( N_{patt} = 32 \\), the network over-fits real motion pattern when the number of samples is excessive. Therefore, we adopt \\( N_{patt} = 16 \\) as the default parameter of DANet." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.608, + 0.468, + 0.745 + ], + "angle": 0, + "content": "Analysis of the Number of Horizontal Slice Parts. As shown in Tab. 5, we further analyze the effect of the number spatial parts \\( N_{part} \\) (\\( P \\) in the Horizontal Pooling module). (1) In DANet, the experimental results rise as the number of \\( N_{part} \\) increases. (2) The possible reason is that the LCMB and GMPA modules can effectively select the key regions and aggregate robust global motion patterns. As a result, the network expresses more sufficient global motion patterns when the number of \\( N_{part} \\) increases." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.756, + 0.214, + 0.77 + ], + "angle": 0, + "content": "4.4. Visualization" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.468, + 0.901 + ], + "angle": 0, + "content": "To gain further insight into the local motion patterns of salient parts established by the phase term of the vector, as shown in Fig. 6, we visualize the heatmaps for the phase values and corresponding silhouettes of the same person. (1) In terms of the spatial dimension, the phase term of the vector can be effectively located in the key regions. (2) In terms of the temporal dimension, the phase terms of the vectors in the sequence move with the motion of the body parts," + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.256, + 0.892, + 0.285 + ], + "angle": 0, + "content": "Table 5. Comparison of the number of spatial bins \\(N_{part}\\) in HP and low-order global motion patterns \\(N_{patt}\\) in GMPA." + }, + { + "type": "table", + "bbox": [ + 0.532, + 0.295, + 0.855, + 0.431 + ], + "angle": 0, + "content": "
NpattNpartNMBGCLMean
161697.594.485.792.5
163297.795.689.394.2
16497.895.686.993.4
86497.495.087.193.1
326497.594.788.593.6
166497.996.289.994.6
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.45, + 0.892, + 0.526 + ], + "angle": 0, + "content": "precisely localizing the disappearance and appearance of hand movements and the alternate walking of the legs. (3) The visualization results show that, in contrast to the fixed parameters in the CNN, the phase term of the vector can dynamically distinguish the key regions." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.548, + 0.619, + 0.564 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.577, + 0.892, + 0.804 + ], + "angle": 0, + "content": "In this paper, we propose a novel Dynamic Aggregated (DANet) for gait recognition, which consists of a serial of Local Conv-Mixing Block (LCMB) and Global Motion Pattern Aggregator (GMPA) to adaptively aggregate the robust discriminative global motion patterns. The proposed method can dynamically locate the key regions and extract the local motion patterns, and then adaptively select the distinguishing local motion patterns to further construct robust global motion patterns. The experimental results on three popular gait datasets, i.e., CASIA-B, OUMVLP, and Gait3D, verify the effectiveness of the proposed method and show great potential for practical applications. In the future, we will further investigate adaptive learning of the local and global motion patterns in the complex-valued domain to aggregate more representative gait features." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.827, + 0.68, + 0.844 + ], + "angle": 0, + "content": "6. Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "This work was supported by National Natural Science Foundation of China (Grants No.62171038, No.61827901, No.62088101, No.62276031, and No.62276025)." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.944, + 0.518, + 0.956 + ], + "angle": 0, + "content": "22083" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.468, + 0.156 + ], + "angle": 0, + "content": "[1] Gunawan Ariyanto and Mark S Nixon. Model-based 3d gait biometrics. In international joint conference on biometrics, 2011. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.159, + 0.468, + 0.2 + ], + "angle": 0, + "content": "[2] Shutao Bai, Bingpeng Ma, Hong Chang, Rui Huang, and Xilin Chen. 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However, gait recognition often suffers from multiple exterior factors in real scenes, such as carrying conditions, wearing overcoats, and diverse viewing angles. Recently, various deep learning-based gait recognition methods have achieved promising results, but they tend to extract one of the salient features using fixed-weighted convolutional networks, do not well consider the relationship within gait features in key regions, and ignore the aggregation of complete motion patterns. In this paper, we propose a new perspective that actual gait features include global motion patterns in multiple key regions, and each global motion pattern is composed of a series of local motion patterns. To this end, we propose a Dynamic Aggregation Network (DANet) to learn more discriminative gait features. Specifically, we create a dynamic attention mechanism between the features of neighboring pixels that not only adaptively focuses on key regions but also generates more expressive local motion patterns. In addition, we develop a self-attention mechanism to select representative local motion patterns and further learn robust global motion patterns. Extensive experiments on three popular public gait datasets, i.e., CASIA-B, OUMVLP, and Gait3D, demonstrate that the proposed method can provide substantial improvements over the current state-of-the-art methods.1 + +# 1. Introduction + +Gait recognition aims to retrieve the same identity at a long distance, and has been widely used throughout social security [28], video surveillance [4, 15, 49], crime investigation [25], and so on. Compared with action recognition [17, 53, 54] and person re-identification [2, 55, 60, 61], the + +![](images/48e30b2ab7fb6b9048838f1f6d317450e14c7af659cb84f8e96a905b7a3a4370.jpg) +Figure 1. The features of each pixel are mapped as a vector with both magnitude and phase components. The magnitude represents contextual information, while the phase direction is used to construct dynamic attention models for the key regions. The convolution operation is denoted by $*$ , and the blue circles in the diagrams represent the key regions learned by the dynamic attention. + +gait recognition task is one of the most challenging fine-grained label classification problems. On the one hand, silhouette data is a binary image of a person suffering from the limitations of the segmentation algorithm [26, 62, 63], with occasional holes and broken edges. On the other hand, gait recognition is also impacted by various exterior factors in real scenes, such as carrying conditions, wearing coats, and diverse viewing angles. Different angles and clothing conditions will greatly change the silhouette appearance of the same person, resulting in the intra-class variance being much greater than inter-class. We ask: How to learn more robust features adaptively for each person under the influence of various external factors? We attempt to answer this question from the following perspectives: + +(i) Local Motion Patterns. Gait, or the act of walking, is essentially the coordinated movement of body parts. In a gait sequence, we observe that each part has a unique representative motion pattern, and each motion pattern is composed of a set of localized sub-movements. Therefore, it + +![](images/7ed8b20f48853835890a51fdae65039ae999623b1f4c97d32231b1c7f21329fd.jpg) +Figure 2. Comparison of the actual motion pattern with the Max-based method, Mean-based method, and Global Motion Pattern Aggregator (GMPA) module. The black curve represents a single periodic action that is affected by disturbances, whereas the green curve represents a synthesized periodic action consisting of distinct local motion patterns selected by the GMPA. + +is critical to accurately locate the discriminative parts and obtain representative local motion patterns under the interference of various external factors. However, previous gait-based approaches [7, 8, 13, 14, 20, 24, 33] simply use convolutional networks with non-linear activation to model the dynamic movements. Once the network has been trained, the parameters and the non-linear function can only focus on the fixed patterns. To this end, we propose to encode the features of each pixel as a vector with magnitude and phase, as shown in Fig. 1, which allows learning the dynamic attention mapping functions among the neighboring pixel of focusing. By modeling the relationship, the network can further focus on local motion patterns in key regions. + +(ii) Global Motion Patterns. Gait is a periodic movement. We assume that the actual motion pattern is a one-dimensional signal, as shown in Fig. 2, whereby the local motion patterns are the points on the signal. Therefore, it is essential to use a series of local motion patterns to further fit the actual motion patterns for obtaining discriminative gait features. However, recent gait-based methods [8,20,33] only use Max- or Mean-based methods to extract one of the significant local features. These methods are susceptible to disturbances and can not fit the actual motion patterns. According to the Nyquist-Shannon sampling theorem [37, 39] in signal processing theory, when a continuous signal is sampled at a frequency greater than twice the frequency of the signal, the information of the original signal is retained intact. In this regard, we propose to construct a global attention model and use it to dynamically select a preset number of distinguishable local motion patterns (green arrows), while excluding the effect of noise (red arrows). By selecting sufficient discriminative local motion patterns, the network can further obtain robust global motion patterns. + +Driven by this analysis, we propose a novel and effective Dynamic Aggregated Network (DANet) for gait recognition. As shown in Fig. 3, DANet consists of two + +well-designed components, i.e., Local Conv-Mixing Block (LCMB) and Global Motion Patterns Aggregator (GMPA). Firstly, we encode the features of each pixel into the complex domain including magnitude and phase, where the magnitude term represents the contextual information and the phase term is used to establish the relationship between each vector. The local motion pattern is generated by aggregating the magnitude and phase of the vectors in the neighboring regions of focus. Secondly, we use the self-attentive mechanism in the GMPA model to dynamically select sufficient discriminative local motion patterns and further learn to fit the actual gait patterns. Finally, with our proposed modules, we obtain the most representative stable gait features for each person and outperform the state-of-the-art (SOTA) methods, especially under the most challenging condition of cross-dressing. + +Our main contributions can be summarized as follows: + +- We propose a novel LCMB to extract the representative local motion patterns, which can dynamically model the relationships among the features of neighboring pixels and then accurately locate key regions. +- We design an effective GMPA to select the discriminative local motion patterns and then aggregate them to obtain a robust global representation. To the best of our knowledge, it is the first attempt to explore the potential of self-attention model in this task. +- Experimental results are illustrated to demonstrate the effectiveness of the proposed method, outperforming the SOTA method on CASIA-B [56], OUMVLP [41] and Gait3D [59] datasets. In addition, many rigorous ablation experiments on CASIA-B [56] further validated the effectiveness of each component in DANet. + +# 2. Related Works + +In this section, we provide a brief overview of relevant research in the fields of gait recognition, local action modeling, and global action modeling. + +Gait Architectures. Gait recognition approaches mainly fall into two typical categories, i.e., model-based approaches and appearance-based approaches. Model-based approaches [1,3,27,29-31,44] attempt to explicitly fit human pose structures [10] to images. However, the predefined points are empirically designed and limited by the inaccuracy of estimation results for low-quality images. Therefore, the model-based methods are generally inferior to appearance-based methods in performance. Appearance-based approaches [7,8,13,18,20,21,24,32,33,43,47,51, 52, 58] are the mainstream frameworks for gait and have benefited from the quick growth of deep learning. It can be roughly divided into three classes, namely template-based + +![](images/c65902a1bfcfdf261891d12e69d680b19eecaee04f9dd85a11867b5aa44f080b.jpg) +Figure 3. The overview of the proposed DANet. Each stage contains the Local Conv-Mixing Block (LCMB), which utilizes a dynamic attention model to establish relationships among neighboring pixels of interest. The HP denotes Horizontal Pooling, GMPA represents Global Motion Pattern Aggregator, and $l$ indicates the number of last stages. In particular, the $\mathrm{GMPA}_j$ module is responsible for aggregating the local motion patterns of the $j$ -th part and producing the final global motion patterns $v_{i}$ for recognition. + +methods, set-based methods, and sequence-based methods. The template-based approaches [18, 36, 43, 47, 52, 57] extracted gait spatio-temporal features by compressing a sequence of gait silhouettes, e.g., Gait Energy Image (GEI), which inevitably destroyed the representation of discriminative local motion patterns in gait sequences. The set-based approaches [8,20,21,23] assumed that the appearance of a silhouette contained its position information, which could not construct local motion patterns using continuous frames. Recently some advanced sequence-based methods [7, 24, 32, 33, 51] used 3D convolutional (C3D) neural networks to extract gait features from the gait sequence and achieve SOTA results. Our approach belongs to the sequence-based method, in contrast to other methods, we propose to use variable-length frames as the input. + +Local Action Modeling. Local action modeling [14,24,32, 33] aims at building short-range spatio-temporal features, which have been shown to be beneficial for gait recognition in various literature. GaitPart [14] proposed a micro-motion capture module to model the short-range spatio-temporal features. MT3D [32] proposed multiple temporal-scale 3D convolutional layers to extract the small and large temporal-scale motion features. GaitGL [33] utilized a local temporal aggregation module to extract the local temporal information. 3DLocal [24] proposed a localization module to adaptively sample the local action features. In contrast to these strategies, we propose to map each pixel of the gait sequence to the complex-valued domain, using the phase term to encode the relationship between gait features. By fully exploiting the phase term, we construct a dynamic attention model among each pixel of the feature to extract local motion patterns in key regions. + +Global Action Modeling. Global action modeling, aiming at capturing long-range dependencies, has been demonstrated to be advantageous to a wide range of recognition tasks such as action recognition [6, 45, 48, 54] and person re-identification [9, 16, 19, 35, 40, 61]. Many attention-based approaches [12, 34, 46] built global relationships in the spatial dimension [5, 50] or channel dimension [22] with re + +markable results. However, current state-of-the-art works [7, 8, 32, 33] in gait recognition still directly use Max- or Mean-based methods to extract global temporal features, which only focus on the most salient features. Different from these methods, we design an efficient global self-attention model to obtain a robust representation for each person, which can select discriminative local motion patterns, and further map them to global motion patterns. + +# 3. Methodology + +In this section, we first describe the overall architecture of our method in Sec. 3.1, and then introduce the proposed two novel well-designed modules, i.e., Local Conv-Mixing Block (LCMB) in Sec. 3.2 and Global Motion Pattern Aggregator (GMPA) in Sec. 3.3. Finally, we will discuss the joint loss functions in Sec. 3.4. + +# 3.1. Formulation and Motivation + +Gait recognition aims to identify the same person under the influence of various external factors. Let $\mathbf{X} \in \mathbb{R}^{T \times H \times W}$ denote silhouette data containing consecutive $T$ frames, where $T, H$ , and $W$ represent the temporal, height, and width dimensions of input frames. In our implementation, we sample variable-length frames $T \in [20, 40]$ from a continuous sequence as the input. The extraction of gait features can be expressed as + +$$ +f = \mathcal {G} (\mathcal {L} (\mathbf {X})), \tag {1} +$$ + +where $f \in \mathbb{R}^{P \times C}$ is the output features, $P$ is the number of horizontally sliced parts, $C$ is the feature channels, $\mathcal{L}$ represents the local motion pattern extraction, and $\mathcal{G}$ denotes the global motion pattern aggregation. + +To learn distinctive representation for each person, the previous C2D-based methods [8, 20] and C3D-based methods [32, 33] only use convolutional layers and non-linear functions to learn gait features. However, the trained network can only recognize certain movement patterns that are vulnerable to noise. In this work, we propose a novel + +![](images/e7f524e9b846da2fb31d19e2466bfc2ef044d4b7b89022658178f585e323ae6b.jpg) +Figure 4. The architecture of LCMB, where “ $\odot$ ” represents Hadamard product, “ $\oplus$ ” represents element-wise sum operation, and Mix denotes vector aggregation operation. + +LCMB in the backbone of DANet, which enables the network to focus on the key regions and extract the local motion patterns by dynamically building the relationships among pixels. Furthermore, inspired by the Nyquist-Shannon sampling theorem [37, 39], we propose a new perspective that a complete gait pattern should contain many distinguishable local motion patterns. To this end, we developed an effective GMPA to select sufficient distinguishable local motion patterns while effectively excluding the interference of noise. The selected local motion patterns are then aggregated to generate a robust global motion pattern. + +# 3.2. Local Conv-Mixing Block + +In this section, we provide a detailed description of the vector representation and vector aggregation in the Local Conv-Mixing Block (LCMB) module. + +Vector Representation. In the LCMB module, the input features are denoted as $\mathbf{V} = [v_{1}, v_{2}, \dots, v_{N}] \in \mathbb{R}^{N \times C_{i}}$ , where $N$ is the number of pixels in the gait sequence, $C_{i}$ is the dimension of input features. As shown in Fig. 4, we obtain the magnitude $|v_{j}|$ and phase $\theta_{j}$ of each vector by multiply with the learnable parameters $W^{m} \in \mathbb{R}^{C_{i} \times C_{l}}$ and $W^{t} \in \mathbb{R}^{C_{i} \times C_{l}}$ , separately, i.e., + +$$ +\left| v _ {j} \right| = W ^ {m} v _ {j}, j = 1, 2, \dots , N, \tag {2} +$$ + +$$ +\theta_ {j} = \max \left(0, W ^ {t} v _ {j}\right), j = 1, 2, \dots , N, \tag {3} +$$ + +where the subscript $j$ is the feature of the $j$ -th pixel. The content of each vector is a real-value feature modeled by the magnitude term $|v_{j}|$ , while the relationship of each vector is modulated by the phase term $\theta_{j}$ , using grouped convolutional layers with rectified linear activation ReLU. The complex vectors $\tilde{v}_{j} \in \mathbb{C}^{C_{l}}$ modulated by the magnitude and phase terms using Euler's formula, i.e., + +$$ +\tilde {v} _ {j} = \overbrace {\left| v _ {j} \right| \odot \cos \theta_ {j}} ^ {\text {r e a l p a r t}} + \overbrace {i \left| v _ {j} \right| \odot \sin \theta_ {j}} ^ {\text {i m a g i n a r y p a r t}}, j = 1, 2, \dots , N, \tag {4} +$$ + +where $i$ is the imaginary unit satisfying $i^2 = -1$ , and $\odot$ is element-wise multiplication. + +Vector Aggregation. After representing the features of each pixel as a vector, we further aggregate the local spatiotemporal domain of each vector as shown in Fig. 4. In + +![](images/d31f78a244c95de98258e75cf85db2fbe09f95595b3ae2e917337375f83b02d8.jpg) +Figure 5. The architecture of GMPA and the feature maps are shown by their dimensions, where “ $\otimes$ ” is matrix multiplication. + +particular, the complex-value representation of the output $\tilde{o}_j\in \mathbb{C}^{C_i}$ that aggregated by learnable convolution kernels $\mathcal{K}\in \mathbb{R}^{C_i\times C_l\times K_t\times K_s\times K_s}$ , i.e., + +$$ +\tilde {o} _ {j} = \sum_ {m \in \mathcal {N} (j)} \mathcal {K} [ j - m ] \tilde {v} _ {m} + v _ {j}, j = 1, 2, \dots , N, \tag {5} +$$ + +where $\mathcal{N}(j)$ denotes the neighboring pixels set of $j$ , and $\tilde{v}_m$ represents the vector belong to the neighboring pixels of $\tilde{v}_j$ . Following [42], we obtain the real-value output feature $o_j \in \mathbb{R}^{C_i}$ by summing the real and imaginary parts of $\tilde{v}_j$ for convenient computation, i.e., + +$$ +o _ {j} = \sum_ {m \in \mathcal {N} (j)} \left(\mathcal {K} [ j - m ] | v _ {m} | \odot \cos \theta_ {m} + \right. \tag {6} +$$ + +$$ +\left. \mathcal {K} [ j - m ] \left| v _ {m} \right| \odot \sin \theta_ {m}\right) + v _ {j}, j = 1, 2, \dots , N, +$$ + +where $(\cos \theta_{m} + \sin \theta_{m})$ denotes the dynamic attention among the neighboring pixels of $j$ . To further comprehend the dynamic aggregation model, heatmaps showcasing the phase values are visualized in Fig. 6. + +# 3.3. Global Motion Patterns Aggregator + +In this part, we propose a new instantiation of the global action modeling framework for gait recognition named the global motion patterns aggregator (GMPA), which selects a preset number of distinguished local motion patterns and then utilizes an attention mechanism to aggregate query-specific global motion patterns of each query location. The GMPA adopts separate parameters for each part and models the global movement patterns of the corresponding part. + +Lower-order Global Motion Patterns. Gait data is affected by a number of variable factors, such as segmentation holes or broken edges, further impairing the actual movement pattern. To this end, we first propose to squeeze variable local motion patterns into a preset number of channel descriptors. Then, we utilize softmax to construct an attention map in the temporal dimension, and multiply the squeezed attention maps with the reshaped local motion pattern features to obtain the global low-order motion patterns. Formally, the global low-order motion patterns $\tilde{\mathbf{G}}\in \mathbb{R}^{P\times C\times M}$ are generated by local motion patterns $\mathbf{L}\in \mathbb{R}^{P\times T\times C}$ and attention maps $\mathbf{M}\in \mathbb{R}^{P\times T\times M}$ , and can + +be expressed as + +$$ +\mathbf {M} = \frac {\exp \left(W _ {1} \mathbf {L} _ {i}\right)}{\sum_ {i = 1} ^ {T} \exp \left(W _ {1} \mathbf {L} _ {i}\right)}, \tag {7} +$$ + +$$ +\tilde {\mathbf {G}} = \mathbf {M} \otimes \mathbf {L}, \tag {8} +$$ + +where $W_{1}\in \mathbb{R}^{P\times C\times M}$ is the weight of Separate $FC_{1}$ , $i$ is the index of frame, and $\otimes$ denotes matrix multiplication. + +Higher-order Global Motion Patterns. To take advantage of the information aggregated in the low-order global motion patterns, we perform a further mapping aiming at fully capturing the high-order global motion patterns. In addition, we also introduce residual learning into GMPA to ease the training. Concretely, we further map the preset number of low-order global motion patterns $\tilde{\mathbf{G}}$ into a high-order global feature $\mathbf{G}$ , i.e., + +$$ +\mathbf {G} = \delta \left(W _ {2} \tilde {\mathbf {G}}\right) \oplus \mathbf {L}, \tag {9} +$$ + +where $W_{2}\in \mathbb{R}^{P\times M\times 1}$ is the weight of Separate $FC_2$ , $\delta$ represents the LeakyReLU activation function, and $\oplus$ denotes the broadcast element-wise addition. + +# 3.4. Joint Loss + +In this work, there are two types of loss functions involved, i.e., triplet loss $\mathcal{L}_{tp}$ and cross-entropy loss $\mathcal{L}_{ce}$ , which constrain the features of each part separately. Formally, triplet loss $\mathcal{L}_{tp}$ [11] can be expressed as: + +$$ +\begin{array}{l} \mathcal {L} _ {t p} = \frac {1}{N _ {t p}} \overbrace {\sum_ {p = 1} ^ {P} \sum_ {i = 1} ^ {S} \sum_ {a = 1} ^ {K} \sum_ {s = 1} ^ {K} \sum_ {j = 1} ^ {S} \sum_ {n = 1} ^ {K}} ^ {\text {p a r t s}} \max (0, m + \tag {10} \\ D \big (\mathcal {F} (x _ {a, i} ^ {p}), \mathcal {F} (x _ {s, i} ^ {p}) \big) - D \big (\mathcal {F} (x _ {a, i} ^ {p}), \mathcal {F} (x _ {n, j} ^ {p}) \big), \\ \end{array} +$$ + +where $P$ is the number of sliced parts horizontally on the gait features, $N_{tp}$ is a positive integer obtained by multiplying the non-zero terms in triplets with the number of parts, $(S, K)$ denotes the number of subjects with different identities and the number of samples per person, $m$ is the margin value, $D(f_1, f_2)$ represents the euclidean distance between two features, $\mathcal{F}$ denotes the feature extraction model, and $x$ represents the input sequence. We retain the case where the anchor and positive labels are the same, in other words, our triplet loss function requires the distance between each anchor sample and the negative sample is greater than the margin, which is an important trick for gait recognition. + +Here, we propose to use the cross entropy loss $\mathcal{L}_{ce}$ to constrain each part with the label smoothing. Formally, + +$$ +\mathcal {L} _ {c e} = - \frac {1}{N _ {c e}} \overbrace {\sum_ {p = 1} ^ {P} \sum_ {i = 1} ^ {S} \sum_ {j = 1} ^ {K} \sum_ {b = 1} ^ {B}} ^ {\text {p a r t s}} q _ {i, j} ^ {p, b} \log p _ {i, j} ^ {p, b}, \tag {11} +$$ + +where $N_{ce}$ is a positive integer obtained by multiplying the mini-batch with the number of parts, $p$ is the distribution of predicted probabilities, and $q$ is the label of the mini-batch. In our experiments, the combined loss function $\mathcal{L}_c$ can be expressed as: + +$$ +\mathcal {L} _ {c} = \mathcal {L} _ {t p} + \beta \mathcal {L} _ {c e}, \tag {12} +$$ + +where $\beta$ is the hyper-parameter to balance the two terms and is set to 0.2 through the experiments. + +# 4. Experiments + +In this section, we evaluate our network on three typical gait datasets, i.e., CASIA-B [56], OUMVLP [41], and Gait3D [59], and provide the implementation details. Then, we compare our approach with the current state-of-the-art methods. Finally, we conduct comprehensive ablation studies to verify the effectiveness of the proposed method. + +# 4.1. Datasets and Implementation Details + +CASIA-B [56] is a widely used dataset for gait recognition. It contains 124 subjects, 3 different walking conditions, and 11 different camera viewpoints uniformly distributed in $[0^{\circ}, 180^{\circ}]$ . The different walking conditions include normal walking (NM), walking with bags (BG), and walking wearing a coat (CL). In summary, there are 110 sequences for each person, and each sequence has an uncertain length of frames. We take the first 74 subjects as the training set and the rest 50 subjects for the test. In the test phase, the first 4 normal walking conditions are taken as the gallery, and the rest are taken as the probe. + +OUMVLP [41] has the largest number of sequences in the public gait dataset. It consists of 10,307 subjects, 2 different walking sequences ("00-01"), and 14 different camera viewpoints uniformly distributed in $[0^{\circ}, 90^{\circ}]$ and $[180^{\circ}, 270^{\circ}]$ . In general, each subject contains up to 28 sequences. According to the official split way, we take 5153 subjects as the training set and the rest of 5154 as the test set. In the test phase, the sequences of "01" are taken as the gallery, and the rest of "00" is taken as the probe. + +Gait3D [59] is a large-scale comprehensive dataset for gait recognition, containing silhouettes, 2D/3D human body pose, and 3D Mesh. Compared with the above datasets, Gait3D collected from more complex scenes in the wild is more challenging for the gait recognition task. It contains 4000 subjects, 25309 sequences, and 39 different camera viewpoints. Following the official splitting approach, we take 3000 subjects as the training set and the remaining 1000 subjects as the test set. In the testing phase, we calculate the similarity of one sequence of query set to all sequences in gallery set, and then report the average rank-1 and rank-5 recognition rates for all query sequences. + +Table 1. The performance comparisons on CASIA-B are reported with rank-1 accuracy $(\%)$ , excluding the identical-view cases. The defaults input silhouette size is $64 \times 44$ and $" (* ) "$ indicates that the input size is $128 \times 88$ . + +
MethodProbe ViewMean
0°18°36°54°72°90°108°126°134°162°180°
NMCNN-LB [52]82.690.396.194.390.187.489.994.094.791.378.589.9
GaitSet [8]90.897.999.496.993.691.795.097.898.996.885.895.0
GaitPart [14]94.198.699.398.594.092.395.998.499.297.890.496.2
GLN(*) [20]93.299.399.598.796.195.697.298.199.398.690.196.9
MT3D [32]95.798.299.097.595.193.996.198.699.298.292.096.7
GaitGL [33]96.098.399.097.996.995.497.098.999.398.894.097.4
LagrangeGait [7]95.798.199.198.396.495.297.599.099.398.994.997.5
DANet(ours)96.499.199.298.296.695.597.699.499.599.396.998.0
BGCNN-LB [52]64.280.682.776.964.863.168.076.982.275.461.372.4
GaitSet [8]83.891.291.888.883.381.084.190.092.294.479.087.2
GaitPart [14]89.194.896.795.188.394.989.093.596.193.885.891.5
GLN(*) [20]91.197.797.895.292.591.292.496.097.595.088.194.0
MT3D [32]91.095.497.594.292.386.991.295.697.396.486.693.0
GaitGL [33]92.696.696.895.593.589.392.296.598.296.991.594.5
LagrangeGait [7]94.296.296.895.894.389.591.796.898.097.090.994.6
DANet(ours)95.097.398.397.494.791.093.997.498.297.694.295.9
CLCNN-LB [52]37.757.266.661.155.254.655.259.158.948.839.454.0
GaitSet [8]61.475.480.777.372.170.171.573.573.568.450.070.4
GaitPart [14]70.785.586.983.377.172.576.982.283.880.266.578.7
GLN(*) [20]70.682.485.282.779.276.476.278.977.978.764.377.5
MT3D [32]76.087.689.885.081.275.781.084.585.482.268.181.5
GaitGL [33]76.690.090.387.184.579.084.187.087.384.469.583.6
LagrangeGait [7]77.490.693.290.284.780.385.287.789.386.671.085.1
DANet(ours)82.894.896.994.389.083.987.992.395.192.080.389.9
+ +Implementation Details. We implement our network in PyTorch [38] for all experiments. Following the preprocessing method mentioned in [8], we align and resize the input silhouettes to $64 \times 44$ . During the training phase, the sampling module randomly selects [20, 40] sequences as the inputs. In the test phase, we utilize all silhouettes to obtain the gait feature. We train the model in an end-to-end manner with an optimizer of SGD and an initial learning rate of 0.1, which is reduced by a factor of 10 until convergence. The parameter $l$ in Fig. 3 indicates the number of stages, where $l = 0$ for CASIA-B and $l = 1$ for OUMVLP and Gait3D. (1) In CASIA-B, the model is trained for a total of 40K iterations with the step size set every 10K iterations, using a mini-batch size of (8, 16). The convolutional channels are set to (64, 128, 256), and the stride of the temporal pooling and spatial pooling modules are set to $m = 3$ and $n = 1$ , respectively. (2) In the case of OUMVLP and Gait3D, we consider that the number of sequences in OUMVLP is 20 times greater than that in CASIA-B, and the sequences in Gait3D are collected in the wild with more views. To account for these differences, we set the number of channels in four stages to (64, 128, 256, 512) and the training mini + +batch size to (32, 16). The model is trained for a total of $200\mathrm{K}$ iterations, with the step size set every $50\mathrm{K}$ iterations. Additionally, the stride of spatial pooling is set to $n = 2$ + +# 4.2. Comparison with State-of-the-art Methods + +To verify the effectiveness of our method, several latest gait recognition methods are introduced for comparison, including CNN-LB [52], GaitSet [8], GaitPart [14], GLN [20], MT3D [32], GaitGL [33], and LagrangeGait [7]. Evaluation on CASIA-B. The performance comparison on CASIA-B is provided in Tab. 1, where the probe sequence is divided into three subsets according to the walking conditions. (1) Comparing with the template-based approach, i.e., CNN-LB [52], our method achieves significantly better results in all walking conditions and viewpoints. The possible reason is that the template-based approach directly compressing the gait sequence into a gait energy map would greatly compromise the temporal information in gait sequence. Once the temporal features are neglected, the motion pattern of the gait can not be adequately represented. (2) In contrast to the set-based methods, i.e., GaitSet [8] and GLN [20], the proposed method achieves higher recog + +Table 2. Rank-1 accuracy (%) on OUMVLP under all view angles, excluding the identical-views cases. + +
MethodProbe ViewMean
0°15°30°45°60°75°90°180°195°210°225°240°255°270°
GaitSet [8]79.587.989.990.288.188.787.881.786.789.089.387.287.886.287.1
GaitPart [14]82.688.990.891.089.789.989.585.288.190.090.189.089.188.288.7
GLN [20]83.890.091.091.290.390.089.485.389.190.590.689.689.388.589.2
GaitGL [33]84.990.291.191.591.190.890.388.588.690.390.489.689.588.889.7
LagrangeGait [7]85.990.691.391.591.291.090.688.989.290.590.689.989.889.290.0
CSTL [23]87.191.091.591.890.690.890.689.490.290.590.789.890.089.490.2
DANet(ours)87.791.391.691.891.791.491.190.490.390.790.990.590.389.990.7
+ +nition accuracy. This may be due to the fact that the set-based approach assumes that each silhouette contains positional information but ignores the motion patterns between sequences. We believe that motion patterns are the essential features of each person, and adequately expressing them is the key to identifying cross-views and cross-dressing conditions. (3) Compared to the sequence-based methods, i.e., GaitPart [14], MT3D [32], GaitGL [33], and LagrangeGait [7] our method exceeds GaitPart by $11.2\%$ , MT3D by $8.4\%$ , GaitGL by $6.3\%$ , and LagrangeGait by $4.8\%$ under the most challenging cross-dressing condition. The experimental results prove the effectiveness of our method and also confirm that the combination of LCMB and GMPA modules can extract more discriminating gait features. + +Evaluation on OUMVLP. To further demonstrate the effectiveness of our proposed method, as shown in Tab. 2, DANet is also evaluated on the largest gait datasets, i.e., OUMVLP. (1) Compared with other methods, the proposed method achieves the state-of-the-art performance under all cross-view conditions. The comparison results also demonstrate that the proposed method can also effectively obtain representative and stable global motion patterns on the large-scale dataset. (2) It is worth noting that some subjects had no sequences corresponding to the probes in the gallery because of missing sequences, therefore the recognition accuracy in the Tab. 2 is lower than the actual performance. + +Evaluation on Gait3D. The effectiveness of our method was further validated on a wild dataset, i.e., Gait3D. (1) We observe a significant degradation in rank-1 performance of all methods, i.e., GaitPart [14], GLN [20], and GaitGL [33], on the Gait3D dataset. The possible reason is that Gait3D contains more complex conditions, such as misaligned and occlusions in the silhouette data. (2) The experimental comparison results are illustrated in Tab. 3, which confirms that our proposed method is effective in extracting robust global motion patterns on the wild dataset. + +# 4.3. Ablation Study + +In this section, we provide an ablation study in DANet to gain a better understanding of the effect of different configurations on the LCMB and GMPA. All experiments in the + +Table 3. The performance comparisons on Gait3D are reported with rank-1 accuracy(%) and rank-5 accuracy(%). + +
MethodsPublicationR-1(%)R-5(%)
GaitSet [8]AAAI 201936.758.3
GaitPart [14]CVPR 202028.247.6
GLN [20]ECCV 202031.452.9
GaitGL [33]ICCV 202129.748.5
SMPLGait [59]CVPR 202246.364.5
DANetOurs48.069.7
+ +Table 4. The ablation study of the proposed modules on CASIA-B with rank-1 accuracy (\%). Where the Conv. represents the convolutional layer, and the Aggr. denotes the aggregator. + +
MethodConv.Aggr.NMBGCL
GaitSet [8]C2DMax95.087.270.4
GaitPart [14]C2DMCM96.291.578.7
GaitGL [33]C3DGeM97.494.583.6
DANet(C2D)C2DGMPA97.894.584.3
DANet(C3D)C3DGMPA97.895.487.7
DANet(Max)LCMBMax97.895.686.9
DANet(Mean)LCMBMean97.495.087.1
DANet(Gem)LCMBGeM97.195.085.3
DANet(MCM)LCMBMCM97.594.885.4
DANetLCMBGMPA97.996.289.9
+ +ablation study are performed on CASIA-B, excluding the identical-views cases. + +The Effectiveness of Local Conv-Mixing Block. As mentioned in Sec. 3.2, we design a novel Local Conv-Mixing Block (LCMB) module to effectively aggregate local motion patterns. (1) As shown in Tab. 4, compared with the benchmark approach, i.e., GaitSet [8], GaitPart [14], and GaitGL [33], the LCMB-based method achieves higher accuracy under the same conditions. (2) With other conditions remaining the same, we directly replace our LCMB with C2D or C3D convolutional layers. As shown in Tab. 4, our LCMB is significantly higher than the C2D or C3D convo + +![](images/fc977001f425ccee8bb6db55efc89d8b1c074c1267e207980c9758b55a593a33.jpg) +(a) + +![](images/836e493dd7b852d014bad2aac9871c6234c39fe684418072c76d2f4c7b339876.jpg) +(b) + +![](images/864523effda4aaefb0a049a12371b893b67a6dae6706d427e803bb6d46ab1ac0.jpg) +(c) + +![](images/5b05872fd4e54b1212ec5b3ceb6eb69b3710da930e9638ecb5b3b52d57f9dcc9.jpg) +Figure 6. Visualization of attention maps (dash boxes) for phase values and corresponding positions (solid points) in the silhouettes of the same person, where "J" represents the face, "H" represents the hand, "L" represents the leg, and "F" represents the foot. + +lutional methods, which demonstrates that the LCMB can effectively extract the local motion patterns of gait. + +The Effectiveness of Global Motion Patterns Aggregator. To demonstrate the effectiveness of GMPA, as shown in Tab. 4, we fully compare it with other aggregators, i.e., Max [8], MCM [14], GeM [33]. (1) The C2D and C3D convolutional layers combined with our GMPA module can significantly improve the performance. (2) In contrast to MCM, our GMPA focus on establishing a complete global motion pattern, which we believe is the essence of the actual motion of the gait. (3) Compared to Max- or Mean-based methods, the experimental results show that GMPA can effectively aggregate robust global motion patterns. + +Analysis of the Number of Lower-order Global Motion Patterns. The number of low-order global motion patterns $N_{patt}$ ( $M$ in GMPA module) selected in the GMPA module will directly affect the final feature representation. (1) As shown in Tab. 5, when $N_{patt} = 1$ or 8, the network cannot fit actual movement patterns due to insufficiently sampled low-order motion patterns. (2) The experimental results show that when $N_{patt} = 32$ , the network over-fits real motion pattern when the number of samples is excessive. Therefore, we adopt $N_{patt} = 16$ as the default parameter of DANet. + +Analysis of the Number of Horizontal Slice Parts. As shown in Tab. 5, we further analyze the effect of the number spatial parts $N_{part}$ ( $P$ in the Horizontal Pooling module). (1) In DANet, the experimental results rise as the number of $N_{part}$ increases. (2) The possible reason is that the LCMB and GMPA modules can effectively select the key regions and aggregate robust global motion patterns. As a result, the network expresses more sufficient global motion patterns when the number of $N_{part}$ increases. + +# 4.4. Visualization + +To gain further insight into the local motion patterns of salient parts established by the phase term of the vector, as shown in Fig. 6, we visualize the heatmaps for the phase values and corresponding silhouettes of the same person. (1) In terms of the spatial dimension, the phase term of the vector can be effectively located in the key regions. (2) In terms of the temporal dimension, the phase terms of the vectors in the sequence move with the motion of the body parts, + +Table 5. Comparison of the number of spatial bins $N_{part}$ in HP and low-order global motion patterns $N_{patt}$ in GMPA. + +
NpattNpartNMBGCLMean
161697.594.485.792.5
163297.795.689.394.2
16497.895.686.993.4
86497.495.087.193.1
326497.594.788.593.6
166497.996.289.994.6
+ +precisely localizing the disappearance and appearance of hand movements and the alternate walking of the legs. (3) The visualization results show that, in contrast to the fixed parameters in the CNN, the phase term of the vector can dynamically distinguish the key regions. + +# 5. Conclusion + +In this paper, we propose a novel Dynamic Aggregated (DANet) for gait recognition, which consists of a serial of Local Conv-Mixing Block (LCMB) and Global Motion Pattern Aggregator (GMPA) to adaptively aggregate the robust discriminative global motion patterns. The proposed method can dynamically locate the key regions and extract the local motion patterns, and then adaptively select the distinguishing local motion patterns to further construct robust global motion patterns. The experimental results on three popular gait datasets, i.e., CASIA-B, OUMVLP, and Gait3D, verify the effectiveness of the proposed method and show great potential for practical applications. 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However, gait recognition often suffers from multiple exterior factors in real scenes, such as carrying conditions, wearing overcoats, and diverse viewing angles. Recently, various deep learning-based gait recognition methods have achieved promising results, but they tend to extract one of the salient features using fixed-weighted convolutional networks, do not well consider the relationship within gait features in key regions, and ignore the aggregation of complete motion patterns. In this paper, we propose a new perspective that actual gait features include global motion patterns in multiple key regions, and each global motion pattern is composed of a series of local motion patterns. To this end, we propose a Dynamic Aggregation Network (DANet) to learn more discriminative gait features. Specifically, we create a dynamic attention mechanism between the features of neighboring pixels that not only adaptively focuses on key regions but also generates more expressive local motion patterns. In addition, we develop a self-attention mechanism to select representative local motion patterns and further learn robust global motion patterns. Extensive experiments on three popular public gait datasets, i.e., CASIA-B, OUMVLP, and Gait3D, demonstrate that the proposed method can provide substantial improvements over the current state-of-the-art methods.1" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 48, + 601, + 128, + 613 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 601, + 128, + 613 + ], + "spans": [ + { + "bbox": [ + 48, + 601, + 128, + 613 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 622, + 287, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 622, + 287, + 684 + ], + "spans": [ + { + "bbox": [ + 47, + 622, + 287, + 684 + ], + "type": "text", + "content": "Gait recognition aims to retrieve the same identity at a long distance, and has been widely used throughout social security [28], video surveillance [4, 15, 49], crime investigation [25], and so on. Compared with action recognition [17, 53, 54] and person re-identification [2, 55, 60, 61], the" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 310, + 225, + 542, + 392 + ], + "blocks": [ + { + "bbox": [ + 310, + 225, + 542, + 392 + ], + "lines": [ + { + "bbox": [ + 310, + 225, + 542, + 392 + ], + "spans": [ + { + "bbox": [ + 310, + 225, + 542, + 392 + ], + "type": "image", + "image_path": "48e30b2ab7fb6b9048838f1f6d317450e14c7af659cb84f8e96a905b7a3a4370.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 403, + 547, + 472 + ], + "lines": [ + { + "bbox": [ + 305, + 403, + 547, + 472 + ], + "spans": [ + { + "bbox": [ + 305, + 403, + 547, + 472 + ], + "type": "text", + "content": "Figure 1. The features of each pixel are mapped as a vector with both magnitude and phase components. The magnitude represents contextual information, while the phase direction is used to construct dynamic attention models for the key regions. The convolution operation is denoted by " + }, + { + "bbox": [ + 305, + 403, + 547, + 472 + ], + "type": "inline_equation", + "content": "*" + }, + { + "bbox": [ + 305, + 403, + 547, + 472 + ], + "type": "text", + "content": ", and the blue circles in the diagrams represent the key regions learned by the dynamic attention." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 484, + 547, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 484, + 547, + 652 + ], + "spans": [ + { + "bbox": [ + 304, + 484, + 547, + 652 + ], + "type": "text", + "content": "gait recognition task is one of the most challenging fine-grained label classification problems. On the one hand, silhouette data is a binary image of a person suffering from the limitations of the segmentation algorithm [26, 62, 63], with occasional holes and broken edges. On the other hand, gait recognition is also impacted by various exterior factors in real scenes, such as carrying conditions, wearing coats, and diverse viewing angles. Different angles and clothing conditions will greatly change the silhouette appearance of the same person, resulting in the intra-class variance being much greater than inter-class. We ask: How to learn more robust features adaptively for each person under the influence of various external factors? We attempt to answer this question from the following perspectives:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "content": "(i) Local Motion Patterns. Gait, or the act of walking, is essentially the coordinated movement of body parts. In a gait sequence, we observe that each part has a unique representative motion pattern, and each motion pattern is composed of a set of localized sub-movements. Therefore, it" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 693, + 140, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 693, + 140, + 703 + ], + "spans": [ + { + "bbox": [ + 58, + 693, + 140, + 703 + ], + "type": "text", + "content": "*Corresponding Authors" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 58, + 703, + 279, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 703, + 279, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 703, + 279, + 712 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 58, + 703, + 279, + 712 + ], + "type": "text", + "content": "Code available at https://github.com/XKMar/FastGait" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 293, + 747, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 747, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 747, + 318, + 757 + ], + "type": "text", + "content": "22076" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 72, + 286, + 190 + ], + "blocks": [ + { + "bbox": [ + 56, + 72, + 286, + 190 + ], + "lines": [ + { + "bbox": [ + 56, + 72, + 286, + 190 + ], + "spans": [ + { + "bbox": [ + 56, + 72, + 286, + 190 + ], + "type": "image", + "image_path": "7ed8b20f48853835890a51fdae65039ae999623b1f4c97d32231b1c7f21329fd.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 205, + 288, + 270 + ], + "lines": [ + { + "bbox": [ + 46, + 205, + 288, + 270 + ], + "spans": [ + { + "bbox": [ + 46, + 205, + 288, + 270 + ], + "type": "text", + "content": "Figure 2. Comparison of the actual motion pattern with the Max-based method, Mean-based method, and Global Motion Pattern Aggregator (GMPA) module. The black curve represents a single periodic action that is affected by disturbances, whereas the green curve represents a synthesized periodic action consisting of distinct local motion patterns selected by the GMPA." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 282, + 287, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 282, + 287, + 437 + ], + "spans": [ + { + "bbox": [ + 46, + 282, + 287, + 437 + ], + "type": "text", + "content": "is critical to accurately locate the discriminative parts and obtain representative local motion patterns under the interference of various external factors. However, previous gait-based approaches [7, 8, 13, 14, 20, 24, 33] simply use convolutional networks with non-linear activation to model the dynamic movements. Once the network has been trained, the parameters and the non-linear function can only focus on the fixed patterns. To this end, we propose to encode the features of each pixel as a vector with magnitude and phase, as shown in Fig. 1, which allows learning the dynamic attention mapping functions among the neighboring pixel of focusing. By modeling the relationship, the network can further focus on local motion patterns in key regions." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 437, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 437, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 287, + 677 + ], + "type": "text", + "content": "(ii) Global Motion Patterns. Gait is a periodic movement. We assume that the actual motion pattern is a one-dimensional signal, as shown in Fig. 2, whereby the local motion patterns are the points on the signal. Therefore, it is essential to use a series of local motion patterns to further fit the actual motion patterns for obtaining discriminative gait features. However, recent gait-based methods [8,20,33] only use Max- or Mean-based methods to extract one of the significant local features. These methods are susceptible to disturbances and can not fit the actual motion patterns. According to the Nyquist-Shannon sampling theorem [37, 39] in signal processing theory, when a continuous signal is sampled at a frequency greater than twice the frequency of the signal, the information of the original signal is retained intact. In this regard, we propose to construct a global attention model and use it to dynamically select a preset number of distinguishable local motion patterns (green arrows), while excluding the effect of noise (red arrows). By selecting sufficient discriminative local motion patterns, the network can further obtain robust global motion patterns." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": "Driven by this analysis, we propose a novel and effective Dynamic Aggregated Network (DANet) for gait recognition. As shown in Fig. 3, DANet consists of two" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "type": "text", + "content": "well-designed components, i.e., Local Conv-Mixing Block (LCMB) and Global Motion Patterns Aggregator (GMPA). Firstly, we encode the features of each pixel into the complex domain including magnitude and phase, where the magnitude term represents the contextual information and the phase term is used to establish the relationship between each vector. The local motion pattern is generated by aggregating the magnitude and phase of the vectors in the neighboring regions of focus. Secondly, we use the self-attentive mechanism in the GMPA model to dynamically select sufficient discriminative local motion patterns and further learn to fit the actual gait patterns. Finally, with our proposed modules, we obtain the most representative stable gait features for each person and outperform the state-of-the-art (SOTA) methods, especially under the most challenging condition of cross-dressing." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 317, + 264, + 538, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 264, + 538, + 275 + ], + "spans": [ + { + "bbox": [ + 317, + 264, + 538, + 275 + ], + "type": "text", + "content": "Our main contributions can be summarized as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 285, + 545, + 481 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 317, + 285, + 545, + 333 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 285, + 545, + 333 + ], + "spans": [ + { + "bbox": [ + 317, + 285, + 545, + 333 + ], + "type": "text", + "content": "- We propose a novel LCMB to extract the representative local motion patterns, which can dynamically model the relationships among the features of neighboring pixels and then accurately locate key regions." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 317, + 341, + 545, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 341, + 545, + 400 + ], + "spans": [ + { + "bbox": [ + 317, + 341, + 545, + 400 + ], + "type": "text", + "content": "- We design an effective GMPA to select the discriminative local motion patterns and then aggregate them to obtain a robust global representation. To the best of our knowledge, it is the first attempt to explore the potential of self-attention model in this task." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 317, + 410, + 545, + 481 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 410, + 545, + 481 + ], + "spans": [ + { + "bbox": [ + 317, + 410, + 545, + 481 + ], + "type": "text", + "content": "- Experimental results are illustrated to demonstrate the effectiveness of the proposed method, outperforming the SOTA method on CASIA-B [56], OUMVLP [41] and Gait3D [59] datasets. In addition, many rigorous ablation experiments on CASIA-B [56] further validated the effectiveness of each component in DANet." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 502, + 397, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 502, + 397, + 514 + ], + "spans": [ + { + "bbox": [ + 306, + 502, + 397, + 514 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 521, + 545, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 545, + 557 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 545, + 557 + ], + "type": "text", + "content": "In this section, we provide a brief overview of relevant research in the fields of gait recognition, local action modeling, and global action modeling." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": "Gait Architectures. Gait recognition approaches mainly fall into two typical categories, i.e., model-based approaches and appearance-based approaches. Model-based approaches [1,3,27,29-31,44] attempt to explicitly fit human pose structures [10] to images. However, the predefined points are empirically designed and limited by the inaccuracy of estimation results for low-quality images. Therefore, the model-based methods are generally inferior to appearance-based methods in performance. Appearance-based approaches [7,8,13,18,20,21,24,32,33,43,47,51, 52, 58] are the mainstream frameworks for gait and have benefited from the quick growth of deep learning. It can be roughly divided into three classes, namely template-based" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 747, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 747, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 747, + 318, + 757 + ], + "type": "text", + "content": "22077" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 55, + 74, + 537, + 173 + ], + "blocks": [ + { + "bbox": [ + 55, + 74, + 537, + 173 + ], + "lines": [ + { + "bbox": [ + 55, + 74, + 537, + 173 + ], + "spans": [ + { + "bbox": [ + 55, + 74, + 537, + 173 + ], + "type": "image", + "image_path": "c65902a1bfcfdf261891d12e69d680b19eecaee04f9dd85a11867b5aa44f080b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 182, + 547, + 228 + ], + "lines": [ + { + "bbox": [ + 46, + 182, + 547, + 228 + ], + "spans": [ + { + "bbox": [ + 46, + 182, + 547, + 228 + ], + "type": "text", + "content": "Figure 3. The overview of the proposed DANet. Each stage contains the Local Conv-Mixing Block (LCMB), which utilizes a dynamic attention model to establish relationships among neighboring pixels of interest. The HP denotes Horizontal Pooling, GMPA represents Global Motion Pattern Aggregator, and " + }, + { + "bbox": [ + 46, + 182, + 547, + 228 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 182, + 547, + 228 + ], + "type": "text", + "content": " indicates the number of last stages. In particular, the " + }, + { + "bbox": [ + 46, + 182, + 547, + 228 + ], + "type": "inline_equation", + "content": "\\mathrm{GMPA}_j" + }, + { + "bbox": [ + 46, + 182, + 547, + 228 + ], + "type": "text", + "content": " module is responsible for aggregating the local motion patterns of the " + }, + { + "bbox": [ + 46, + 182, + 547, + 228 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 182, + 547, + 228 + ], + "type": "text", + "content": "-th part and producing the final global motion patterns " + }, + { + "bbox": [ + 46, + 182, + 547, + 228 + ], + "type": "inline_equation", + "content": "v_{i}" + }, + { + "bbox": [ + 46, + 182, + 547, + 228 + ], + "type": "text", + "content": " for recognition." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 238, + 289, + 417 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 238, + 289, + 417 + ], + "spans": [ + { + "bbox": [ + 46, + 238, + 289, + 417 + ], + "type": "text", + "content": "methods, set-based methods, and sequence-based methods. The template-based approaches [18, 36, 43, 47, 52, 57] extracted gait spatio-temporal features by compressing a sequence of gait silhouettes, e.g., Gait Energy Image (GEI), which inevitably destroyed the representation of discriminative local motion patterns in gait sequences. The set-based approaches [8,20,21,23] assumed that the appearance of a silhouette contained its position information, which could not construct local motion patterns using continuous frames. Recently some advanced sequence-based methods [7, 24, 32, 33, 51] used 3D convolutional (C3D) neural networks to extract gait features from the gait sequence and achieve SOTA results. Our approach belongs to the sequence-based method, in contrast to other methods, we propose to use variable-length frames as the input." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 422, + 287, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 422, + 287, + 625 + ], + "spans": [ + { + "bbox": [ + 46, + 422, + 287, + 625 + ], + "type": "text", + "content": "Local Action Modeling. Local action modeling [14,24,32, 33] aims at building short-range spatio-temporal features, which have been shown to be beneficial for gait recognition in various literature. GaitPart [14] proposed a micro-motion capture module to model the short-range spatio-temporal features. MT3D [32] proposed multiple temporal-scale 3D convolutional layers to extract the small and large temporal-scale motion features. GaitGL [33] utilized a local temporal aggregation module to extract the local temporal information. 3DLocal [24] proposed a localization module to adaptively sample the local action features. In contrast to these strategies, we propose to map each pixel of the gait sequence to the complex-valued domain, using the phase term to encode the relationship between gait features. By fully exploiting the phase term, we construct a dynamic attention model among each pixel of the feature to extract local motion patterns in key regions." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": "Global Action Modeling. Global action modeling, aiming at capturing long-range dependencies, has been demonstrated to be advantageous to a wide range of recognition tasks such as action recognition [6, 45, 48, 54] and person re-identification [9, 16, 19, 35, 40, 61]. Many attention-based approaches [12, 34, 46] built global relationships in the spatial dimension [5, 50] or channel dimension [22] with re" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 238, + 547, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 238, + 547, + 334 + ], + "spans": [ + { + "bbox": [ + 304, + 238, + 547, + 334 + ], + "type": "text", + "content": "markable results. However, current state-of-the-art works [7, 8, 32, 33] in gait recognition still directly use Max- or Mean-based methods to extract global temporal features, which only focus on the most salient features. Different from these methods, we design an efficient global self-attention model to obtain a robust representation for each person, which can select discriminative local motion patterns, and further map them to global motion patterns." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 345, + 389, + 359 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 345, + 389, + 359 + ], + "spans": [ + { + "bbox": [ + 305, + 345, + 389, + 359 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 365, + 547, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 365, + 547, + 437 + ], + "spans": [ + { + "bbox": [ + 304, + 365, + 547, + 437 + ], + "type": "text", + "content": "In this section, we first describe the overall architecture of our method in Sec. 3.1, and then introduce the proposed two novel well-designed modules, i.e., Local Conv-Mixing Block (LCMB) in Sec. 3.2 and Global Motion Pattern Aggregator (GMPA) in Sec. 3.3. Finally, we will discuss the joint loss functions in Sec. 3.4." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 445, + 463, + 457 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 445, + 463, + 457 + ], + "spans": [ + { + "bbox": [ + 305, + 445, + 463, + 457 + ], + "type": "text", + "content": "3.1. Formulation and Motivation" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 464, + 547, + 560 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 464, + 547, + 560 + ], + "spans": [ + { + "bbox": [ + 304, + 464, + 547, + 560 + ], + "type": "text", + "content": "Gait recognition aims to identify the same person under the influence of various external factors. Let " + }, + { + "bbox": [ + 304, + 464, + 547, + 560 + ], + "type": "inline_equation", + "content": "\\mathbf{X} \\in \\mathbb{R}^{T \\times H \\times W}" + }, + { + "bbox": [ + 304, + 464, + 547, + 560 + ], + "type": "text", + "content": " denote silhouette data containing consecutive " + }, + { + "bbox": [ + 304, + 464, + 547, + 560 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 464, + 547, + 560 + ], + "type": "text", + "content": " frames, where " + }, + { + "bbox": [ + 304, + 464, + 547, + 560 + ], + "type": "inline_equation", + "content": "T, H" + }, + { + "bbox": [ + 304, + 464, + 547, + 560 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 464, + 547, + 560 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 304, + 464, + 547, + 560 + ], + "type": "text", + "content": " represent the temporal, height, and width dimensions of input frames. In our implementation, we sample variable-length frames " + }, + { + "bbox": [ + 304, + 464, + 547, + 560 + ], + "type": "inline_equation", + "content": "T \\in [20, 40]" + }, + { + "bbox": [ + 304, + 464, + 547, + 560 + ], + "type": "text", + "content": " from a continuous sequence as the input. The extraction of gait features can be expressed as" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 394, + 570, + 545, + 583 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 394, + 570, + 545, + 583 + ], + "spans": [ + { + "bbox": [ + 394, + 570, + 545, + 583 + ], + "type": "interline_equation", + "content": "f = \\mathcal {G} (\\mathcal {L} (\\mathbf {X})), \\tag {1}", + "image_path": "d1a5f813e2aab27e89b8e564fdf4055a9a6c7242e9abc77070231b1308d0f3a1.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 593, + 547, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 593, + 547, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 593, + 547, + 641 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 593, + 547, + 641 + ], + "type": "inline_equation", + "content": "f \\in \\mathbb{R}^{P \\times C}" + }, + { + "bbox": [ + 304, + 593, + 547, + 641 + ], + "type": "text", + "content": " is the output features, " + }, + { + "bbox": [ + 304, + 593, + 547, + 641 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 593, + 547, + 641 + ], + "type": "text", + "content": " is the number of horizontally sliced parts, " + }, + { + "bbox": [ + 304, + 593, + 547, + 641 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 593, + 547, + 641 + ], + "type": "text", + "content": " is the feature channels, " + }, + { + "bbox": [ + 304, + 593, + 547, + 641 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 304, + 593, + 547, + 641 + ], + "type": "text", + "content": " represents the local motion pattern extraction, and " + }, + { + "bbox": [ + 304, + 593, + 547, + 641 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 304, + 593, + 547, + 641 + ], + "type": "text", + "content": " denotes the global motion pattern aggregation." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "type": "text", + "content": "To learn distinctive representation for each person, the previous C2D-based methods [8, 20] and C3D-based methods [32, 33] only use convolutional layers and non-linear functions to learn gait features. However, the trained network can only recognize certain movement patterns that are vulnerable to noise. In this work, we propose a novel" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 747, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 747, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 747, + 318, + 757 + ], + "type": "text", + "content": "22078" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 76, + 282, + 154 + ], + "blocks": [ + { + "bbox": [ + 51, + 76, + 282, + 154 + ], + "lines": [ + { + "bbox": [ + 51, + 76, + 282, + 154 + ], + "spans": [ + { + "bbox": [ + 51, + 76, + 282, + 154 + ], + "type": "image", + "image_path": "e7f524e9b846da2fb31d19e2466bfc2ef044d4b7b89022658178f585e323ae6b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 167, + 287, + 201 + ], + "lines": [ + { + "bbox": [ + 46, + 167, + 287, + 201 + ], + "spans": [ + { + "bbox": [ + 46, + 167, + 287, + 201 + ], + "type": "text", + "content": "Figure 4. The architecture of LCMB, where “" + }, + { + "bbox": [ + 46, + 167, + 287, + 201 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 46, + 167, + 287, + 201 + ], + "type": "text", + "content": "” represents Hadamard product, “" + }, + { + "bbox": [ + 46, + 167, + 287, + 201 + ], + "type": "inline_equation", + "content": "\\oplus" + }, + { + "bbox": [ + 46, + 167, + 287, + 201 + ], + "type": "text", + "content": "” represents element-wise sum operation, and Mix denotes vector aggregation operation." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 210, + 287, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 210, + 287, + 342 + ], + "spans": [ + { + "bbox": [ + 46, + 210, + 287, + 342 + ], + "type": "text", + "content": "LCMB in the backbone of DANet, which enables the network to focus on the key regions and extract the local motion patterns by dynamically building the relationships among pixels. Furthermore, inspired by the Nyquist-Shannon sampling theorem [37, 39], we propose a new perspective that a complete gait pattern should contain many distinguishable local motion patterns. To this end, we developed an effective GMPA to select sufficient distinguishable local motion patterns while effectively excluding the interference of noise. The selected local motion patterns are then aggregated to generate a robust global motion pattern." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 348, + 190, + 361 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 348, + 190, + 361 + ], + "spans": [ + { + "bbox": [ + 47, + 348, + 190, + 361 + ], + "type": "text", + "content": "3.2. Local Conv-Mixing Block" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 366, + 287, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 366, + 287, + 403 + ], + "spans": [ + { + "bbox": [ + 46, + 366, + 287, + 403 + ], + "type": "text", + "content": "In this section, we provide a detailed description of the vector representation and vector aggregation in the Local Conv-Mixing Block (LCMB) module." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 403, + 287, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 403, + 287, + 486 + ], + "spans": [ + { + "bbox": [ + 46, + 403, + 287, + 486 + ], + "type": "text", + "content": "Vector Representation. In the LCMB module, the input features are denoted as " + }, + { + "bbox": [ + 46, + 403, + 287, + 486 + ], + "type": "inline_equation", + "content": "\\mathbf{V} = [v_{1}, v_{2}, \\dots, v_{N}] \\in \\mathbb{R}^{N \\times C_{i}}" + }, + { + "bbox": [ + 46, + 403, + 287, + 486 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 403, + 287, + 486 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 403, + 287, + 486 + ], + "type": "text", + "content": " is the number of pixels in the gait sequence, " + }, + { + "bbox": [ + 46, + 403, + 287, + 486 + ], + "type": "inline_equation", + "content": "C_{i}" + }, + { + "bbox": [ + 46, + 403, + 287, + 486 + ], + "type": "text", + "content": " is the dimension of input features. As shown in Fig. 4, we obtain the magnitude " + }, + { + "bbox": [ + 46, + 403, + 287, + 486 + ], + "type": "inline_equation", + "content": "|v_{j}|" + }, + { + "bbox": [ + 46, + 403, + 287, + 486 + ], + "type": "text", + "content": " and phase " + }, + { + "bbox": [ + 46, + 403, + 287, + 486 + ], + "type": "inline_equation", + "content": "\\theta_{j}" + }, + { + "bbox": [ + 46, + 403, + 287, + 486 + ], + "type": "text", + "content": " of each vector by multiply with the learnable parameters " + }, + { + "bbox": [ + 46, + 403, + 287, + 486 + ], + "type": "inline_equation", + "content": "W^{m} \\in \\mathbb{R}^{C_{i} \\times C_{l}}" + }, + { + "bbox": [ + 46, + 403, + 287, + 486 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 403, + 287, + 486 + ], + "type": "inline_equation", + "content": "W^{t} \\in \\mathbb{R}^{C_{i} \\times C_{l}}" + }, + { + "bbox": [ + 46, + 403, + 287, + 486 + ], + "type": "text", + "content": ", separately, i.e.," + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 101, + 493, + 286, + 507 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 101, + 493, + 286, + 507 + ], + "spans": [ + { + "bbox": [ + 101, + 493, + 286, + 507 + ], + "type": "interline_equation", + "content": "\\left| v _ {j} \\right| = W ^ {m} v _ {j}, j = 1, 2, \\dots , N, \\tag {2}", + "image_path": "f2a156111bab09539ccc4391664933e1815f31c97dddb15c6ee7843d26201aaa.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 89, + 509, + 287, + 523 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 89, + 509, + 287, + 523 + ], + "spans": [ + { + "bbox": [ + 89, + 509, + 287, + 523 + ], + "type": "interline_equation", + "content": "\\theta_ {j} = \\max \\left(0, W ^ {t} v _ {j}\\right), j = 1, 2, \\dots , N, \\tag {3}", + "image_path": "10263ec8cd2c1e774dd377656f9cc65e995df767e35914bfe3ff6c34d174d8fc.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 529, + 287, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 529, + 287, + 613 + ], + "spans": [ + { + "bbox": [ + 46, + 529, + 287, + 613 + ], + "type": "text", + "content": "where the subscript " + }, + { + "bbox": [ + 46, + 529, + 287, + 613 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 529, + 287, + 613 + ], + "type": "text", + "content": " is the feature of the " + }, + { + "bbox": [ + 46, + 529, + 287, + 613 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 529, + 287, + 613 + ], + "type": "text", + "content": "-th pixel. The content of each vector is a real-value feature modeled by the magnitude term " + }, + { + "bbox": [ + 46, + 529, + 287, + 613 + ], + "type": "inline_equation", + "content": "|v_{j}|" + }, + { + "bbox": [ + 46, + 529, + 287, + 613 + ], + "type": "text", + "content": ", while the relationship of each vector is modulated by the phase term " + }, + { + "bbox": [ + 46, + 529, + 287, + 613 + ], + "type": "inline_equation", + "content": "\\theta_{j}" + }, + { + "bbox": [ + 46, + 529, + 287, + 613 + ], + "type": "text", + "content": ", using grouped convolutional layers with rectified linear activation ReLU. The complex vectors " + }, + { + "bbox": [ + 46, + 529, + 287, + 613 + ], + "type": "inline_equation", + "content": "\\tilde{v}_{j} \\in \\mathbb{C}^{C_{l}}" + }, + { + "bbox": [ + 46, + 529, + 287, + 613 + ], + "type": "text", + "content": " modulated by the magnitude and phase terms using Euler's formula, i.e.," + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 53, + 619, + 287, + 648 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 619, + 287, + 648 + ], + "spans": [ + { + "bbox": [ + 53, + 619, + 287, + 648 + ], + "type": "interline_equation", + "content": "\\tilde {v} _ {j} = \\overbrace {\\left| v _ {j} \\right| \\odot \\cos \\theta_ {j}} ^ {\\text {r e a l p a r t}} + \\overbrace {i \\left| v _ {j} \\right| \\odot \\sin \\theta_ {j}} ^ {\\text {i m a g i n a r y p a r t}}, j = 1, 2, \\dots , N, \\tag {4}", + "image_path": "b48c67debff1a8a3fbb5f89a3acade215bb69383b9570241d19c7ae610148700.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 653, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 677 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 653, + 287, + 677 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 653, + 287, + 677 + ], + "type": "text", + "content": " is the imaginary unit satisfying " + }, + { + "bbox": [ + 46, + 653, + 287, + 677 + ], + "type": "inline_equation", + "content": "i^2 = -1" + }, + { + "bbox": [ + 46, + 653, + 287, + 677 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 653, + 287, + 677 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 46, + 653, + 287, + 677 + ], + "type": "text", + "content": " is element-wise multiplication." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "Vector Aggregation. After representing the features of each pixel as a vector, we further aggregate the local spatiotemporal domain of each vector as shown in Fig. 4. In" + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 313, + 74, + 538, + 152 + ], + "blocks": [ + { + "bbox": [ + 313, + 74, + 538, + 152 + ], + "lines": [ + { + "bbox": [ + 313, + 74, + 538, + 152 + ], + "spans": [ + { + "bbox": [ + 313, + 74, + 538, + 152 + ], + "type": "image", + "image_path": "d31f78a244c95de98258e75cf85db2fbe09f95595b3ae2e917337375f83b02d8.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 167, + 545, + 190 + ], + "lines": [ + { + "bbox": [ + 305, + 167, + 545, + 190 + ], + "spans": [ + { + "bbox": [ + 305, + 167, + 545, + 190 + ], + "type": "text", + "content": "Figure 5. The architecture of GMPA and the feature maps are shown by their dimensions, where “" + }, + { + "bbox": [ + 305, + 167, + 545, + 190 + ], + "type": "inline_equation", + "content": "\\otimes" + }, + { + "bbox": [ + 305, + 167, + 545, + 190 + ], + "type": "text", + "content": "” is matrix multiplication." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 201, + 545, + 237 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 201, + 545, + 237 + ], + "spans": [ + { + "bbox": [ + 305, + 201, + 545, + 237 + ], + "type": "text", + "content": "particular, the complex-value representation of the output " + }, + { + "bbox": [ + 305, + 201, + 545, + 237 + ], + "type": "inline_equation", + "content": "\\tilde{o}_j\\in \\mathbb{C}^{C_i}" + }, + { + "bbox": [ + 305, + 201, + 545, + 237 + ], + "type": "text", + "content": " that aggregated by learnable convolution kernels " + }, + { + "bbox": [ + 305, + 201, + 545, + 237 + ], + "type": "inline_equation", + "content": "\\mathcal{K}\\in \\mathbb{R}^{C_i\\times C_l\\times K_t\\times K_s\\times K_s}" + }, + { + "bbox": [ + 305, + 201, + 545, + 237 + ], + "type": "text", + "content": " , i.e.," + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 318, + 243, + 545, + 271 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 243, + 545, + 271 + ], + "spans": [ + { + "bbox": [ + 318, + 243, + 545, + 271 + ], + "type": "interline_equation", + "content": "\\tilde {o} _ {j} = \\sum_ {m \\in \\mathcal {N} (j)} \\mathcal {K} [ j - m ] \\tilde {v} _ {m} + v _ {j}, j = 1, 2, \\dots , N, \\tag {5}", + "image_path": "b4bc0977fc9eec892cf05a25d493998aa159e5c3cee643b51794a3e54d2b45da.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 279, + 545, + 340 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 279, + 545, + 340 + ], + "spans": [ + { + "bbox": [ + 305, + 279, + 545, + 340 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 279, + 545, + 340 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(j)" + }, + { + "bbox": [ + 305, + 279, + 545, + 340 + ], + "type": "text", + "content": " denotes the neighboring pixels set of " + }, + { + "bbox": [ + 305, + 279, + 545, + 340 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 305, + 279, + 545, + 340 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 279, + 545, + 340 + ], + "type": "inline_equation", + "content": "\\tilde{v}_m" + }, + { + "bbox": [ + 305, + 279, + 545, + 340 + ], + "type": "text", + "content": " represents the vector belong to the neighboring pixels of " + }, + { + "bbox": [ + 305, + 279, + 545, + 340 + ], + "type": "inline_equation", + "content": "\\tilde{v}_j" + }, + { + "bbox": [ + 305, + 279, + 545, + 340 + ], + "type": "text", + "content": ". Following [42], we obtain the real-value output feature " + }, + { + "bbox": [ + 305, + 279, + 545, + 340 + ], + "type": "inline_equation", + "content": "o_j \\in \\mathbb{R}^{C_i}" + }, + { + "bbox": [ + 305, + 279, + 545, + 340 + ], + "type": "text", + "content": " by summing the real and imaginary parts of " + }, + { + "bbox": [ + 305, + 279, + 545, + 340 + ], + "type": "inline_equation", + "content": "\\tilde{v}_j" + }, + { + "bbox": [ + 305, + 279, + 545, + 340 + ], + "type": "text", + "content": " for convenient computation, i.e.," + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 320, + 349, + 545, + 376 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 349, + 545, + 376 + ], + "spans": [ + { + "bbox": [ + 320, + 349, + 545, + 376 + ], + "type": "interline_equation", + "content": "o _ {j} = \\sum_ {m \\in \\mathcal {N} (j)} \\left(\\mathcal {K} [ j - m ] | v _ {m} | \\odot \\cos \\theta_ {m} + \\right. \\tag {6}", + "image_path": "6600d3708034a2d4a2bc18973508140bda50800838ad642081f7adc09e980911.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 321, + 377, + 518, + 392 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 377, + 518, + 392 + ], + "spans": [ + { + "bbox": [ + 321, + 377, + 518, + 392 + ], + "type": "interline_equation", + "content": "\\left. \\mathcal {K} [ j - m ] \\left| v _ {m} \\right| \\odot \\sin \\theta_ {m}\\right) + v _ {j}, j = 1, 2, \\dots , N,", + "image_path": "f9a269cf3d0051eca51cd1df2e7803cc12dd3acf36eb1983ca157ef1889438a8.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 400, + 545, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 400, + 545, + 449 + ], + "spans": [ + { + "bbox": [ + 305, + 400, + 545, + 449 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 400, + 545, + 449 + ], + "type": "inline_equation", + "content": "(\\cos \\theta_{m} + \\sin \\theta_{m})" + }, + { + "bbox": [ + 305, + 400, + 545, + 449 + ], + "type": "text", + "content": " denotes the dynamic attention among the neighboring pixels of " + }, + { + "bbox": [ + 305, + 400, + 545, + 449 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 305, + 400, + 545, + 449 + ], + "type": "text", + "content": ". To further comprehend the dynamic aggregation model, heatmaps showcasing the phase values are visualized in Fig. 6." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 456, + 495, + 468 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 456, + 495, + 468 + ], + "spans": [ + { + "bbox": [ + 306, + 456, + 495, + 468 + ], + "type": "text", + "content": "3.3. Global Motion Patterns Aggregator" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 474, + 545, + 570 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 545, + 570 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 545, + 570 + ], + "type": "text", + "content": "In this part, we propose a new instantiation of the global action modeling framework for gait recognition named the global motion patterns aggregator (GMPA), which selects a preset number of distinguished local motion patterns and then utilizes an attention mechanism to aggregate query-specific global motion patterns of each query location. The GMPA adopts separate parameters for each part and models the global movement patterns of the corresponding part." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": "Lower-order Global Motion Patterns. Gait data is affected by a number of variable factors, such as segmentation holes or broken edges, further impairing the actual movement pattern. To this end, we first propose to squeeze variable local motion patterns into a preset number of channel descriptors. Then, we utilize softmax to construct an attention map in the temporal dimension, and multiply the squeezed attention maps with the reshaped local motion pattern features to obtain the global low-order motion patterns. Formally, the global low-order motion patterns " + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{G}}\\in \\mathbb{R}^{P\\times C\\times M}" + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": " are generated by local motion patterns " + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{L}\\in \\mathbb{R}^{P\\times T\\times C}" + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": " and attention maps " + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{M}\\in \\mathbb{R}^{P\\times T\\times M}" + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": ", and can" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 747, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 747, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 747, + 317, + 757 + ], + "type": "text", + "content": "22079" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 113, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 113, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 113, + 83 + ], + "type": "text", + "content": "be expressed as" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 115, + 91, + 287, + 120 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 91, + 287, + 120 + ], + "spans": [ + { + "bbox": [ + 115, + 91, + 287, + 120 + ], + "type": "interline_equation", + "content": "\\mathbf {M} = \\frac {\\exp \\left(W _ {1} \\mathbf {L} _ {i}\\right)}{\\sum_ {i = 1} ^ {T} \\exp \\left(W _ {1} \\mathbf {L} _ {i}\\right)}, \\tag {7}", + "image_path": "3dd4413fd7a96f2a9fcb02569ca55df7538f2e6a0ea00d80933b97ed51cfe0ca.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 140, + 122, + 287, + 135 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 140, + 122, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 140, + 122, + 287, + 135 + ], + "type": "interline_equation", + "content": "\\tilde {\\mathbf {G}} = \\mathbf {M} \\otimes \\mathbf {L}, \\tag {8}", + "image_path": "b4d2e0314929121923acf93eac9b0bf0515a8046582351ac7e633a67f68f7f8c.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 144, + 287, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 144, + 287, + 168 + ], + "spans": [ + { + "bbox": [ + 46, + 144, + 287, + 168 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 144, + 287, + 168 + ], + "type": "inline_equation", + "content": "W_{1}\\in \\mathbb{R}^{P\\times C\\times M}" + }, + { + "bbox": [ + 46, + 144, + 287, + 168 + ], + "type": "text", + "content": " is the weight of Separate " + }, + { + "bbox": [ + 46, + 144, + 287, + 168 + ], + "type": "inline_equation", + "content": "FC_{1}" + }, + { + "bbox": [ + 46, + 144, + 287, + 168 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 144, + 287, + 168 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 144, + 287, + 168 + ], + "type": "text", + "content": " is the index of frame, and " + }, + { + "bbox": [ + 46, + 144, + 287, + 168 + ], + "type": "inline_equation", + "content": "\\otimes" + }, + { + "bbox": [ + 46, + 144, + 287, + 168 + ], + "type": "text", + "content": " denotes matrix multiplication." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 168, + 287, + 264 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 168, + 287, + 264 + ], + "spans": [ + { + "bbox": [ + 46, + 168, + 287, + 264 + ], + "type": "text", + "content": "Higher-order Global Motion Patterns. To take advantage of the information aggregated in the low-order global motion patterns, we perform a further mapping aiming at fully capturing the high-order global motion patterns. In addition, we also introduce residual learning into GMPA to ease the training. Concretely, we further map the preset number of low-order global motion patterns " + }, + { + "bbox": [ + 46, + 168, + 287, + 264 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{G}}" + }, + { + "bbox": [ + 46, + 168, + 287, + 264 + ], + "type": "text", + "content": " into a high-order global feature " + }, + { + "bbox": [ + 46, + 168, + 287, + 264 + ], + "type": "inline_equation", + "content": "\\mathbf{G}" + }, + { + "bbox": [ + 46, + 168, + 287, + 264 + ], + "type": "text", + "content": ", i.e.," + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 126, + 271, + 287, + 285 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 126, + 271, + 287, + 285 + ], + "spans": [ + { + "bbox": [ + 126, + 271, + 287, + 285 + ], + "type": "interline_equation", + "content": "\\mathbf {G} = \\delta \\left(W _ {2} \\tilde {\\mathbf {G}}\\right) \\oplus \\mathbf {L}, \\tag {9}", + "image_path": "ec3ac2dd4b48dbc7599c9f4411bd5aeba95a78d9fb4cc5ae4f86f1772b11446e.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 293, + 287, + 330 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 293, + 287, + 330 + ], + "spans": [ + { + "bbox": [ + 46, + 293, + 287, + 330 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 293, + 287, + 330 + ], + "type": "inline_equation", + "content": "W_{2}\\in \\mathbb{R}^{P\\times M\\times 1}" + }, + { + "bbox": [ + 46, + 293, + 287, + 330 + ], + "type": "text", + "content": " is the weight of Separate " + }, + { + "bbox": [ + 46, + 293, + 287, + 330 + ], + "type": "inline_equation", + "content": "FC_2" + }, + { + "bbox": [ + 46, + 293, + 287, + 330 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 293, + 287, + 330 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 46, + 293, + 287, + 330 + ], + "type": "text", + "content": " represents the LeakyReLU activation function, and " + }, + { + "bbox": [ + 46, + 293, + 287, + 330 + ], + "type": "inline_equation", + "content": "\\oplus" + }, + { + "bbox": [ + 46, + 293, + 287, + 330 + ], + "type": "text", + "content": " denotes the broadcast element-wise addition." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 337, + 118, + 349 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 337, + 118, + 349 + ], + "spans": [ + { + "bbox": [ + 47, + 337, + 118, + 349 + ], + "type": "text", + "content": "3.4. Joint Loss" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 356, + 287, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 356, + 287, + 403 + ], + "spans": [ + { + "bbox": [ + 46, + 356, + 287, + 403 + ], + "type": "text", + "content": "In this work, there are two types of loss functions involved, i.e., triplet loss " + }, + { + "bbox": [ + 46, + 356, + 287, + 403 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{tp}" + }, + { + "bbox": [ + 46, + 356, + 287, + 403 + ], + "type": "text", + "content": " and cross-entropy loss " + }, + { + "bbox": [ + 46, + 356, + 287, + 403 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{ce}" + }, + { + "bbox": [ + 46, + 356, + 287, + 403 + ], + "type": "text", + "content": ", which constrain the features of each part separately. Formally, triplet loss " + }, + { + "bbox": [ + 46, + 356, + 287, + 403 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{tp}" + }, + { + "bbox": [ + 46, + 356, + 287, + 403 + ], + "type": "text", + "content": " [11] can be expressed as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 411, + 287, + 485 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 411, + 287, + 485 + ], + "spans": [ + { + "bbox": [ + 55, + 411, + 287, + 485 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {t p} = \\frac {1}{N _ {t p}} \\overbrace {\\sum_ {p = 1} ^ {P} \\sum_ {i = 1} ^ {S} \\sum_ {a = 1} ^ {K} \\sum_ {s = 1} ^ {K} \\sum_ {j = 1} ^ {S} \\sum_ {n = 1} ^ {K}} ^ {\\text {p a r t s}} \\max (0, m + \\tag {10} \\\\ D \\big (\\mathcal {F} (x _ {a, i} ^ {p}), \\mathcal {F} (x _ {s, i} ^ {p}) \\big) - D \\big (\\mathcal {F} (x _ {a, i} ^ {p}), \\mathcal {F} (x _ {n, j} ^ {p}) \\big), \\\\ \\end{array}", + "image_path": "11eac735b467018bb5a29bb72dc4dd7517851f8571b65f6583dd160f0c4c0b45.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 491, + 287, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 491, + 287, + 635 + ], + "spans": [ + { + "bbox": [ + 46, + 491, + 287, + 635 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 491, + 287, + 635 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 491, + 287, + 635 + ], + "type": "text", + "content": " is the number of sliced parts horizontally on the gait features, " + }, + { + "bbox": [ + 46, + 491, + 287, + 635 + ], + "type": "inline_equation", + "content": "N_{tp}" + }, + { + "bbox": [ + 46, + 491, + 287, + 635 + ], + "type": "text", + "content": " is a positive integer obtained by multiplying the non-zero terms in triplets with the number of parts, " + }, + { + "bbox": [ + 46, + 491, + 287, + 635 + ], + "type": "inline_equation", + "content": "(S, K)" + }, + { + "bbox": [ + 46, + 491, + 287, + 635 + ], + "type": "text", + "content": " denotes the number of subjects with different identities and the number of samples per person, " + }, + { + "bbox": [ + 46, + 491, + 287, + 635 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 491, + 287, + 635 + ], + "type": "text", + "content": " is the margin value, " + }, + { + "bbox": [ + 46, + 491, + 287, + 635 + ], + "type": "inline_equation", + "content": "D(f_1, f_2)" + }, + { + "bbox": [ + 46, + 491, + 287, + 635 + ], + "type": "text", + "content": " represents the euclidean distance between two features, " + }, + { + "bbox": [ + 46, + 491, + 287, + 635 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 46, + 491, + 287, + 635 + ], + "type": "text", + "content": " denotes the feature extraction model, and " + }, + { + "bbox": [ + 46, + 491, + 287, + 635 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 491, + 287, + 635 + ], + "type": "text", + "content": " represents the input sequence. We retain the case where the anchor and positive labels are the same, in other words, our triplet loss function requires the distance between each anchor sample and the negative sample is greater than the margin, which is an important trick for gait recognition." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 635, + 287, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 635, + 287, + 658 + ], + "spans": [ + { + "bbox": [ + 46, + 635, + 287, + 658 + ], + "type": "text", + "content": "Here, we propose to use the cross entropy loss " + }, + { + "bbox": [ + 46, + 635, + 287, + 658 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{ce}" + }, + { + "bbox": [ + 46, + 635, + 287, + 658 + ], + "type": "text", + "content": " to constrain each part with the label smoothing. Formally," + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 66, + 667, + 287, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 667, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 66, + 667, + 287, + 715 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {c e} = - \\frac {1}{N _ {c e}} \\overbrace {\\sum_ {p = 1} ^ {P} \\sum_ {i = 1} ^ {S} \\sum_ {j = 1} ^ {K} \\sum_ {b = 1} ^ {B}} ^ {\\text {p a r t s}} q _ {i, j} ^ {p, b} \\log p _ {i, j} ^ {p, b}, \\tag {11}", + "image_path": "4a7d92ca2bb5708748d0968bed8ea65f0abc18765c3d5a01afa4af8f717e466a.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "inline_equation", + "content": "N_{ce}" + }, + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "text", + "content": " is a positive integer obtained by multiplying the mini-batch with the number of parts, " + }, + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "text", + "content": " is the distribution of predicted probabilities, and " + }, + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "text", + "content": " is the label of the mini-batch. In our experiments, the combined loss function " + }, + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_c" + }, + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "text", + "content": " can be expressed as:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 387, + 144, + 545, + 157 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 387, + 144, + 545, + 157 + ], + "spans": [ + { + "bbox": [ + 387, + 144, + 545, + 157 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {c} = \\mathcal {L} _ {t p} + \\beta \\mathcal {L} _ {c e}, \\tag {12}", + "image_path": "7bd0f093d184e93ccec9681fc15d3b688264972c7c974e7600c15eeb2c304588.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 168, + 545, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 168, + 545, + 192 + ], + "spans": [ + { + "bbox": [ + 304, + 168, + 545, + 192 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 168, + 545, + 192 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 168, + 545, + 192 + ], + "type": "text", + "content": " is the hyper-parameter to balance the two terms and is set to 0.2 through the experiments." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 205, + 388, + 220 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 205, + 388, + 220 + ], + "spans": [ + { + "bbox": [ + 305, + 205, + 388, + 220 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 227, + 545, + 299 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 227, + 545, + 299 + ], + "spans": [ + { + "bbox": [ + 304, + 227, + 545, + 299 + ], + "type": "text", + "content": "In this section, we evaluate our network on three typical gait datasets, i.e., CASIA-B [56], OUMVLP [41], and Gait3D [59], and provide the implementation details. Then, we compare our approach with the current state-of-the-art methods. Finally, we conduct comprehensive ablation studies to verify the effectiveness of the proposed method." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 309, + 501, + 322 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 309, + 501, + 322 + ], + "spans": [ + { + "bbox": [ + 305, + 309, + 501, + 322 + ], + "type": "text", + "content": "4.1. Datasets and Implementation Details" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 328, + 545, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 328, + 545, + 460 + ], + "spans": [ + { + "bbox": [ + 304, + 328, + 545, + 460 + ], + "type": "text", + "content": "CASIA-B [56] is a widely used dataset for gait recognition. It contains 124 subjects, 3 different walking conditions, and 11 different camera viewpoints uniformly distributed in " + }, + { + "bbox": [ + 304, + 328, + 545, + 460 + ], + "type": "inline_equation", + "content": "[0^{\\circ}, 180^{\\circ}]" + }, + { + "bbox": [ + 304, + 328, + 545, + 460 + ], + "type": "text", + "content": ". The different walking conditions include normal walking (NM), walking with bags (BG), and walking wearing a coat (CL). In summary, there are 110 sequences for each person, and each sequence has an uncertain length of frames. We take the first 74 subjects as the training set and the rest 50 subjects for the test. In the test phase, the first 4 normal walking conditions are taken as the gallery, and the rest are taken as the probe." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 460, + 545, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 460, + 545, + 568 + ], + "spans": [ + { + "bbox": [ + 304, + 460, + 545, + 568 + ], + "type": "text", + "content": "OUMVLP [41] has the largest number of sequences in the public gait dataset. It consists of 10,307 subjects, 2 different walking sequences (\"00-01\"), and 14 different camera viewpoints uniformly distributed in " + }, + { + "bbox": [ + 304, + 460, + 545, + 568 + ], + "type": "inline_equation", + "content": "[0^{\\circ}, 90^{\\circ}]" + }, + { + "bbox": [ + 304, + 460, + 545, + 568 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 460, + 545, + 568 + ], + "type": "inline_equation", + "content": "[180^{\\circ}, 270^{\\circ}]" + }, + { + "bbox": [ + 304, + 460, + 545, + 568 + ], + "type": "text", + "content": ". In general, each subject contains up to 28 sequences. According to the official split way, we take 5153 subjects as the training set and the rest of 5154 as the test set. In the test phase, the sequences of \"01\" are taken as the gallery, and the rest of \"00\" is taken as the probe." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": "Gait3D [59] is a large-scale comprehensive dataset for gait recognition, containing silhouettes, 2D/3D human body pose, and 3D Mesh. Compared with the above datasets, Gait3D collected from more complex scenes in the wild is more challenging for the gait recognition task. It contains 4000 subjects, 25309 sequences, and 39 different camera viewpoints. Following the official splitting approach, we take 3000 subjects as the training set and the remaining 1000 subjects as the test set. In the testing phase, we calculate the similarity of one sequence of query set to all sequences in gallery set, and then report the average rank-1 and rank-5 recognition rates for all query sequences." + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 747, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 747, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 747, + 318, + 757 + ], + "type": "text", + "content": "22080" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 60, + 112, + 533, + 426 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 545, + 93 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 545, + 93 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 545, + 93 + ], + "type": "text", + "content": "Table 1. The performance comparisons on CASIA-B are reported with rank-1 accuracy " + }, + { + "bbox": [ + 47, + 70, + 545, + 93 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 47, + 70, + 545, + 93 + ], + "type": "text", + "content": ", excluding the identical-view cases. The defaults input silhouette size is " + }, + { + "bbox": [ + 47, + 70, + 545, + 93 + ], + "type": "inline_equation", + "content": "64 \\times 44" + }, + { + "bbox": [ + 47, + 70, + 545, + 93 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 70, + 545, + 93 + ], + "type": "inline_equation", + "content": "\" (* ) \"" + }, + { + "bbox": [ + 47, + 70, + 545, + 93 + ], + "type": "text", + "content": " indicates that the input size is " + }, + { + "bbox": [ + 47, + 70, + 545, + 93 + ], + "type": "inline_equation", + "content": "128 \\times 88" + }, + { + "bbox": [ + 47, + 70, + 545, + 93 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 60, + 112, + 533, + 426 + ], + "lines": [ + { + "bbox": [ + 60, + 112, + 533, + 426 + ], + "spans": [ + { + "bbox": [ + 60, + 112, + 533, + 426 + ], + "type": "table", + "html": "
MethodProbe ViewMean
0°18°36°54°72°90°108°126°134°162°180°
NMCNN-LB [52]82.690.396.194.390.187.489.994.094.791.378.589.9
GaitSet [8]90.897.999.496.993.691.795.097.898.996.885.895.0
GaitPart [14]94.198.699.398.594.092.395.998.499.297.890.496.2
GLN(*) [20]93.299.399.598.796.195.697.298.199.398.690.196.9
MT3D [32]95.798.299.097.595.193.996.198.699.298.292.096.7
GaitGL [33]96.098.399.097.996.995.497.098.999.398.894.097.4
LagrangeGait [7]95.798.199.198.396.495.297.599.099.398.994.997.5
DANet(ours)96.499.199.298.296.695.597.699.499.599.396.998.0
BGCNN-LB [52]64.280.682.776.964.863.168.076.982.275.461.372.4
GaitSet [8]83.891.291.888.883.381.084.190.092.294.479.087.2
GaitPart [14]89.194.896.795.188.394.989.093.596.193.885.891.5
GLN(*) [20]91.197.797.895.292.591.292.496.097.595.088.194.0
MT3D [32]91.095.497.594.292.386.991.295.697.396.486.693.0
GaitGL [33]92.696.696.895.593.589.392.296.598.296.991.594.5
LagrangeGait [7]94.296.296.895.894.389.591.796.898.097.090.994.6
DANet(ours)95.097.398.397.494.791.093.997.498.297.694.295.9
CLCNN-LB [52]37.757.266.661.155.254.655.259.158.948.839.454.0
GaitSet [8]61.475.480.777.372.170.171.573.573.568.450.070.4
GaitPart [14]70.785.586.983.377.172.576.982.283.880.266.578.7
GLN(*) [20]70.682.485.282.779.276.476.278.977.978.764.377.5
MT3D [32]76.087.689.885.081.275.781.084.585.482.268.181.5
GaitGL [33]76.690.090.387.184.579.084.187.087.384.469.583.6
LagrangeGait [7]77.490.693.290.284.780.385.287.789.386.671.085.1
DANet(ours)82.894.896.994.389.083.987.992.395.192.080.389.9
", + "image_path": "d7375032eb2d21af516c00dcda5d10fc042eeab5aff38d20a247db5b332aae89.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 446, + 289, + 709 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 446, + 289, + 709 + ], + "spans": [ + { + "bbox": [ + 46, + 446, + 289, + 709 + ], + "type": "text", + "content": "Implementation Details. We implement our network in PyTorch [38] for all experiments. Following the preprocessing method mentioned in [8], we align and resize the input silhouettes to " + }, + { + "bbox": [ + 46, + 446, + 289, + 709 + ], + "type": "inline_equation", + "content": "64 \\times 44" + }, + { + "bbox": [ + 46, + 446, + 289, + 709 + ], + "type": "text", + "content": ". During the training phase, the sampling module randomly selects [20, 40] sequences as the inputs. In the test phase, we utilize all silhouettes to obtain the gait feature. We train the model in an end-to-end manner with an optimizer of SGD and an initial learning rate of 0.1, which is reduced by a factor of 10 until convergence. The parameter " + }, + { + "bbox": [ + 46, + 446, + 289, + 709 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 446, + 289, + 709 + ], + "type": "text", + "content": " in Fig. 3 indicates the number of stages, where " + }, + { + "bbox": [ + 46, + 446, + 289, + 709 + ], + "type": "inline_equation", + "content": "l = 0" + }, + { + "bbox": [ + 46, + 446, + 289, + 709 + ], + "type": "text", + "content": " for CASIA-B and " + }, + { + "bbox": [ + 46, + 446, + 289, + 709 + ], + "type": "inline_equation", + "content": "l = 1" + }, + { + "bbox": [ + 46, + 446, + 289, + 709 + ], + "type": "text", + "content": " for OUMVLP and Gait3D. (1) In CASIA-B, the model is trained for a total of 40K iterations with the step size set every 10K iterations, using a mini-batch size of (8, 16). The convolutional channels are set to (64, 128, 256), and the stride of the temporal pooling and spatial pooling modules are set to " + }, + { + "bbox": [ + 46, + 446, + 289, + 709 + ], + "type": "inline_equation", + "content": "m = 3" + }, + { + "bbox": [ + 46, + 446, + 289, + 709 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 446, + 289, + 709 + ], + "type": "inline_equation", + "content": "n = 1" + }, + { + "bbox": [ + 46, + 446, + 289, + 709 + ], + "type": "text", + "content": ", respectively. (2) In the case of OUMVLP and Gait3D, we consider that the number of sequences in OUMVLP is 20 times greater than that in CASIA-B, and the sequences in Gait3D are collected in the wild with more views. To account for these differences, we set the number of channels in four stages to (64, 128, 256, 512) and the training mini" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 305, + 446, + 545, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 446, + 545, + 483 + ], + "spans": [ + { + "bbox": [ + 305, + 446, + 545, + 483 + ], + "type": "text", + "content": "batch size to (32, 16). The model is trained for a total of " + }, + { + "bbox": [ + 305, + 446, + 545, + 483 + ], + "type": "inline_equation", + "content": "200\\mathrm{K}" + }, + { + "bbox": [ + 305, + 446, + 545, + 483 + ], + "type": "text", + "content": " iterations, with the step size set every " + }, + { + "bbox": [ + 305, + 446, + 545, + 483 + ], + "type": "inline_equation", + "content": "50\\mathrm{K}" + }, + { + "bbox": [ + 305, + 446, + 545, + 483 + ], + "type": "text", + "content": " iterations. Additionally, the stride of spatial pooling is set to " + }, + { + "bbox": [ + 305, + 446, + 545, + 483 + ], + "type": "inline_equation", + "content": "n = 2" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 305, + 491, + 529, + 503 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 491, + 529, + 503 + ], + "spans": [ + { + "bbox": [ + 305, + 491, + 529, + 503 + ], + "type": "text", + "content": "4.2. Comparison with State-of-the-art Methods" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 509, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 509, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 509, + 545, + 715 + ], + "type": "text", + "content": "To verify the effectiveness of our method, several latest gait recognition methods are introduced for comparison, including CNN-LB [52], GaitSet [8], GaitPart [14], GLN [20], MT3D [32], GaitGL [33], and LagrangeGait [7]. Evaluation on CASIA-B. The performance comparison on CASIA-B is provided in Tab. 1, where the probe sequence is divided into three subsets according to the walking conditions. (1) Comparing with the template-based approach, i.e., CNN-LB [52], our method achieves significantly better results in all walking conditions and viewpoints. The possible reason is that the template-based approach directly compressing the gait sequence into a gait energy map would greatly compromise the temporal information in gait sequence. Once the temporal features are neglected, the motion pattern of the gait can not be adequately represented. (2) In contrast to the set-based methods, i.e., GaitSet [8] and GLN [20], the proposed method achieves higher recog" + } + ] + } + ], + "index": 5 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 747, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 747, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 747, + 317, + 757 + ], + "type": "text", + "content": "22081" + } + ] + } + ], + "index": 6 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 62, + 101, + 531, + 201 + ], + "blocks": [ + { + "bbox": [ + 110, + 70, + 483, + 82 + ], + "lines": [ + { + "bbox": [ + 110, + 70, + 483, + 82 + ], + "spans": [ + { + "bbox": [ + 110, + 70, + 483, + 82 + ], + "type": "text", + "content": "Table 2. Rank-1 accuracy (%) on OUMVLP under all view angles, excluding the identical-views cases." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 62, + 101, + 531, + 201 + ], + "lines": [ + { + "bbox": [ + 62, + 101, + 531, + 201 + ], + "spans": [ + { + "bbox": [ + 62, + 101, + 531, + 201 + ], + "type": "table", + "html": "
MethodProbe ViewMean
0°15°30°45°60°75°90°180°195°210°225°240°255°270°
GaitSet [8]79.587.989.990.288.188.787.881.786.789.089.387.287.886.287.1
GaitPart [14]82.688.990.891.089.789.989.585.288.190.090.189.089.188.288.7
GLN [20]83.890.091.091.290.390.089.485.389.190.590.689.689.388.589.2
GaitGL [33]84.990.291.191.591.190.890.388.588.690.390.489.689.588.889.7
LagrangeGait [7]85.990.691.391.591.291.090.688.989.290.590.689.989.889.290.0
CSTL [23]87.191.091.591.890.690.890.689.490.290.590.789.890.089.490.2
DANet(ours)87.791.391.691.891.791.491.190.490.390.790.990.590.389.990.7
", + "image_path": "32149ef8307644db68bca52147e72944053fa60e791078f6b4e098d156a34224.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 221, + 287, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 221, + 287, + 388 + ], + "spans": [ + { + "bbox": [ + 46, + 221, + 287, + 388 + ], + "type": "text", + "content": "nition accuracy. This may be due to the fact that the set-based approach assumes that each silhouette contains positional information but ignores the motion patterns between sequences. We believe that motion patterns are the essential features of each person, and adequately expressing them is the key to identifying cross-views and cross-dressing conditions. (3) Compared to the sequence-based methods, i.e., GaitPart [14], MT3D [32], GaitGL [33], and LagrangeGait [7] our method exceeds GaitPart by " + }, + { + "bbox": [ + 46, + 221, + 287, + 388 + ], + "type": "inline_equation", + "content": "11.2\\%" + }, + { + "bbox": [ + 46, + 221, + 287, + 388 + ], + "type": "text", + "content": ", MT3D by " + }, + { + "bbox": [ + 46, + 221, + 287, + 388 + ], + "type": "inline_equation", + "content": "8.4\\%" + }, + { + "bbox": [ + 46, + 221, + 287, + 388 + ], + "type": "text", + "content": ", GaitGL by " + }, + { + "bbox": [ + 46, + 221, + 287, + 388 + ], + "type": "inline_equation", + "content": "6.3\\%" + }, + { + "bbox": [ + 46, + 221, + 287, + 388 + ], + "type": "text", + "content": ", and LagrangeGait by " + }, + { + "bbox": [ + 46, + 221, + 287, + 388 + ], + "type": "inline_equation", + "content": "4.8\\%" + }, + { + "bbox": [ + 46, + 221, + 287, + 388 + ], + "type": "text", + "content": " under the most challenging cross-dressing condition. The experimental results prove the effectiveness of our method and also confirm that the combination of LCMB and GMPA modules can extract more discriminating gait features." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 388, + 287, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 388, + 287, + 532 + ], + "spans": [ + { + "bbox": [ + 46, + 388, + 287, + 532 + ], + "type": "text", + "content": "Evaluation on OUMVLP. To further demonstrate the effectiveness of our proposed method, as shown in Tab. 2, DANet is also evaluated on the largest gait datasets, i.e., OUMVLP. (1) Compared with other methods, the proposed method achieves the state-of-the-art performance under all cross-view conditions. The comparison results also demonstrate that the proposed method can also effectively obtain representative and stable global motion patterns on the large-scale dataset. (2) It is worth noting that some subjects had no sequences corresponding to the probes in the gallery because of missing sequences, therefore the recognition accuracy in the Tab. 2 is lower than the actual performance." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 532, + 288, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 532, + 288, + 651 + ], + "spans": [ + { + "bbox": [ + 46, + 532, + 288, + 651 + ], + "type": "text", + "content": "Evaluation on Gait3D. The effectiveness of our method was further validated on a wild dataset, i.e., Gait3D. (1) We observe a significant degradation in rank-1 performance of all methods, i.e., GaitPart [14], GLN [20], and GaitGL [33], on the Gait3D dataset. The possible reason is that Gait3D contains more complex conditions, such as misaligned and occlusions in the silhouette data. (2) The experimental comparison results are illustrated in Tab. 3, which confirms that our proposed method is effective in extracting robust global motion patterns on the wild dataset." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 659, + 142, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 659, + 142, + 672 + ], + "spans": [ + { + "bbox": [ + 47, + 659, + 142, + 672 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": "In this section, we provide an ablation study in DANet to gain a better understanding of the effect of different configurations on the LCMB and GMPA. All experiments in the" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 323, + 251, + 527, + 346 + ], + "blocks": [ + { + "bbox": [ + 305, + 220, + 545, + 243 + ], + "lines": [ + { + "bbox": [ + 305, + 220, + 545, + 243 + ], + "spans": [ + { + "bbox": [ + 305, + 220, + 545, + 243 + ], + "type": "text", + "content": "Table 3. The performance comparisons on Gait3D are reported with rank-1 accuracy(%) and rank-5 accuracy(%)." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 323, + 251, + 527, + 346 + ], + "lines": [ + { + "bbox": [ + 323, + 251, + 527, + 346 + ], + "spans": [ + { + "bbox": [ + 323, + 251, + 527, + 346 + ], + "type": "table", + "html": "
MethodsPublicationR-1(%)R-5(%)
GaitSet [8]AAAI 201936.758.3
GaitPart [14]CVPR 202028.247.6
GLN [20]ECCV 202031.452.9
GaitGL [33]ICCV 202129.748.5
SMPLGait [59]CVPR 202246.364.5
DANetOurs48.069.7
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MethodConv.Aggr.NMBGCL
GaitSet [8]C2DMax95.087.270.4
GaitPart [14]C2DMCM96.291.578.7
GaitGL [33]C3DGeM97.494.583.6
DANet(C2D)C2DGMPA97.894.584.3
DANet(C3D)C3DGMPA97.895.487.7
DANet(Max)LCMBMax97.895.686.9
DANet(Mean)LCMBMean97.495.087.1
DANet(Gem)LCMBGeM97.195.085.3
DANet(MCM)LCMBMCM97.594.885.4
DANetLCMBGMPA97.996.289.9
", + "image_path": "68daf5563659faeebfde3cbe8b1c9e91ce84928435341118ab1665134422bbaa.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 567, + 544, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 567, + 544, + 590 + ], + "spans": [ + { + "bbox": [ + 305, + 567, + 544, + 590 + ], + "type": "text", + "content": "ablation study are performed on CASIA-B, excluding the identical-views cases." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "The Effectiveness of Local Conv-Mixing Block. As mentioned in Sec. 3.2, we design a novel Local Conv-Mixing Block (LCMB) module to effectively aggregate local motion patterns. (1) As shown in Tab. 4, compared with the benchmark approach, i.e., GaitSet [8], GaitPart [14], and GaitGL [33], the LCMB-based method achieves higher accuracy under the same conditions. (2) With other conditions remaining the same, we directly replace our LCMB with C2D or C3D convolutional layers. As shown in Tab. 4, our LCMB is significantly higher than the C2D or C3D convo" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 747, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 747, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 747, + 318, + 757 + ], + "type": "text", + "content": "22082" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 72, + 209, + 150 + ], + "blocks": [ + { + "bbox": [ + 52, + 72, + 209, + 150 + ], + "lines": [ + { + "bbox": [ + 52, + 72, + 209, + 150 + ], + "spans": [ + { + "bbox": [ + 52, + 72, + 209, + 150 + ], + "type": "image", + "image_path": "fc977001f425ccee8bb6db55efc89d8b1c074c1267e207980c9758b55a593a33.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 125, + 152, + 136, + 161 + ], + "lines": [ + { + "bbox": [ + 125, + 152, + 136, + 161 + ], + "spans": [ + { + "bbox": [ + 125, + 152, + 136, + 161 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 211, + 73, + 369, + 150 + ], + "blocks": [ + { + "bbox": [ + 211, + 73, + 369, + 150 + ], + "lines": [ + { + "bbox": [ + 211, + 73, + 369, + 150 + ], + "spans": [ + { + "bbox": [ + 211, + 73, + 369, + 150 + ], + "type": "image", + "image_path": "836e493dd7b852d014bad2aac9871c6234c39fe684418072c76d2f4c7b339876.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 283, + 152, + 295, + 161 + ], + "lines": [ + { + "bbox": [ + 283, + 152, + 295, + 161 + ], + "spans": [ + { + "bbox": [ + 283, + 152, + 295, + 161 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 370, + 73, + 525, + 150 + ], + "blocks": [ + { + "bbox": [ + 370, + 73, + 525, + 150 + ], + "lines": [ + { + "bbox": [ + 370, + 73, + 525, + 150 + ], + "spans": [ + { + "bbox": [ + 370, + 73, + 525, + 150 + ], + "type": "image", + "image_path": "864523effda4aaefb0a049a12371b893b67a6dae6706d427e803bb6d46ab1ac0.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 443, + 152, + 454, + 161 + ], + "lines": [ + { + "bbox": [ + 443, + 152, + 454, + 161 + ], + "spans": [ + { + "bbox": [ + 443, + 152, + 454, + 161 + ], + "type": "text", + "content": "(c)" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 526, + 73, + 542, + 152 + ], + "blocks": [ + { + "bbox": [ + 526, + 73, + 542, + 152 + ], + "lines": [ + { + "bbox": [ + 526, + 73, + 542, + 152 + ], + "spans": [ + { + "bbox": [ + 526, + 73, + 542, + 152 + ], + "type": "image", + "image_path": "5b05872fd4e54b1212ec5b3ceb6eb69b3710da930e9638ecb5b3b52d57f9dcc9.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 171, + 547, + 194 + ], + "lines": [ + { + "bbox": [ + 46, + 171, + 547, + 194 + ], + "spans": [ + { + "bbox": [ + 46, + 171, + 547, + 194 + ], + "type": "text", + "content": "Figure 6. Visualization of attention maps (dash boxes) for phase values and corresponding positions (solid points) in the silhouettes of the same person, where \"J\" represents the face, \"H\" represents the hand, \"L\" represents the leg, and \"F\" represents the foot." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 204, + 286, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 204, + 286, + 228 + ], + "spans": [ + { + "bbox": [ + 46, + 204, + 286, + 228 + ], + "type": "text", + "content": "lutional methods, which demonstrates that the LCMB can effectively extract the local motion patterns of gait." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 228, + 286, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 228, + 286, + 361 + ], + "spans": [ + { + "bbox": [ + 46, + 228, + 286, + 361 + ], + "type": "text", + "content": "The Effectiveness of Global Motion Patterns Aggregator. To demonstrate the effectiveness of GMPA, as shown in Tab. 4, we fully compare it with other aggregators, i.e., Max [8], MCM [14], GeM [33]. (1) The C2D and C3D convolutional layers combined with our GMPA module can significantly improve the performance. (2) In contrast to MCM, our GMPA focus on establishing a complete global motion pattern, which we believe is the essence of the actual motion of the gait. (3) Compared to Max- or Mean-based methods, the experimental results show that GMPA can effectively aggregate robust global motion patterns." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 361, + 286, + 481 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 361, + 286, + 481 + ], + "spans": [ + { + "bbox": [ + 46, + 361, + 286, + 481 + ], + "type": "text", + "content": "Analysis of the Number of Lower-order Global Motion Patterns. The number of low-order global motion patterns " + }, + { + "bbox": [ + 46, + 361, + 286, + 481 + ], + "type": "inline_equation", + "content": "N_{patt}" + }, + { + "bbox": [ + 46, + 361, + 286, + 481 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 46, + 361, + 286, + 481 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 361, + 286, + 481 + ], + "type": "text", + "content": " in GMPA module) selected in the GMPA module will directly affect the final feature representation. (1) As shown in Tab. 5, when " + }, + { + "bbox": [ + 46, + 361, + 286, + 481 + ], + "type": "inline_equation", + "content": "N_{patt} = 1" + }, + { + "bbox": [ + 46, + 361, + 286, + 481 + ], + "type": "text", + "content": " or 8, the network cannot fit actual movement patterns due to insufficiently sampled low-order motion patterns. (2) The experimental results show that when " + }, + { + "bbox": [ + 46, + 361, + 286, + 481 + ], + "type": "inline_equation", + "content": "N_{patt} = 32" + }, + { + "bbox": [ + 46, + 361, + 286, + 481 + ], + "type": "text", + "content": ", the network over-fits real motion pattern when the number of samples is excessive. Therefore, we adopt " + }, + { + "bbox": [ + 46, + 361, + 286, + 481 + ], + "type": "inline_equation", + "content": "N_{patt} = 16" + }, + { + "bbox": [ + 46, + 361, + 286, + 481 + ], + "type": "text", + "content": " as the default parameter of DANet." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 481, + 286, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 481, + 286, + 590 + ], + "spans": [ + { + "bbox": [ + 46, + 481, + 286, + 590 + ], + "type": "text", + "content": "Analysis of the Number of Horizontal Slice Parts. As shown in Tab. 5, we further analyze the effect of the number spatial parts " + }, + { + "bbox": [ + 46, + 481, + 286, + 590 + ], + "type": "inline_equation", + "content": "N_{part}" + }, + { + "bbox": [ + 46, + 481, + 286, + 590 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 46, + 481, + 286, + 590 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 481, + 286, + 590 + ], + "type": "text", + "content": " in the Horizontal Pooling module). (1) In DANet, the experimental results rise as the number of " + }, + { + "bbox": [ + 46, + 481, + 286, + 590 + ], + "type": "inline_equation", + "content": "N_{part}" + }, + { + "bbox": [ + 46, + 481, + 286, + 590 + ], + "type": "text", + "content": " increases. (2) The possible reason is that the LCMB and GMPA modules can effectively select the key regions and aggregate robust global motion patterns. As a result, the network expresses more sufficient global motion patterns when the number of " + }, + { + "bbox": [ + 46, + 481, + 286, + 590 + ], + "type": "inline_equation", + "content": "N_{part}" + }, + { + "bbox": [ + 46, + 481, + 286, + 590 + ], + "type": "text", + "content": " increases." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 598, + 130, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 598, + 130, + 609 + ], + "spans": [ + { + "bbox": [ + 47, + 598, + 130, + 609 + ], + "type": "text", + "content": "4.4. Visualization" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "type": "text", + "content": "To gain further insight into the local motion patterns of salient parts established by the phase term of the vector, as shown in Fig. 6, we visualize the heatmaps for the phase values and corresponding silhouettes of the same person. (1) In terms of the spatial dimension, the phase term of the vector can be effectively located in the key regions. (2) In terms of the temporal dimension, the phase terms of the vectors in the sequence move with the motion of the body parts," + } + ] + } + ], + "index": 13 + }, + { + "type": "table", + "bbox": [ + 325, + 233, + 523, + 341 + ], + "blocks": [ + { + "bbox": [ + 305, + 202, + 545, + 225 + ], + "lines": [ + { + "bbox": [ + 305, + 202, + 545, + 225 + ], + "spans": [ + { + "bbox": [ + 305, + 202, + 545, + 225 + ], + "type": "text", + "content": "Table 5. Comparison of the number of spatial bins " + }, + { + "bbox": [ + 305, + 202, + 545, + 225 + ], + "type": "inline_equation", + "content": "N_{part}" + }, + { + "bbox": [ + 305, + 202, + 545, + 225 + ], + "type": "text", + "content": " in HP and low-order global motion patterns " + }, + { + "bbox": [ + 305, + 202, + 545, + 225 + ], + "type": "inline_equation", + "content": "N_{patt}" + }, + { + "bbox": [ + 305, + 202, + 545, + 225 + ], + "type": "text", + "content": " in GMPA." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 325, + 233, + 523, + 341 + ], + "lines": [ + { + "bbox": [ + 325, + 233, + 523, + 341 + ], + "spans": [ + { + "bbox": [ + 325, + 233, + 523, + 341 + ], + "type": "table", + "html": "
NpattNpartNMBGCLMean
161697.594.485.792.5
163297.795.689.394.2
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", + "image_path": "462aae76a2f421547619a8ca33b1c5188c89353d215c0476645f8528df6c3987.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_body" + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 356, + 545, + 416 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 356, + 545, + 416 + ], + "spans": [ + { + "bbox": [ + 304, + 356, + 545, + 416 + ], + "type": "text", + "content": "precisely localizing the disappearance and appearance of hand movements and the alternate walking of the legs. (3) The visualization results show that, in contrast to the fixed parameters in the CNN, the phase term of the vector can dynamically distinguish the key regions." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 434, + 378, + 446 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 434, + 378, + 446 + ], + "spans": [ + { + "bbox": [ + 306, + 434, + 378, + 446 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 456, + 545, + 636 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 456, + 545, + 636 + ], + "spans": [ + { + "bbox": [ + 304, + 456, + 545, + 636 + ], + "type": "text", + "content": "In this paper, we propose a novel Dynamic Aggregated (DANet) for gait recognition, which consists of a serial of Local Conv-Mixing Block (LCMB) and Global Motion Pattern Aggregator (GMPA) to adaptively aggregate the robust discriminative global motion patterns. The proposed method can dynamically locate the key regions and extract the local motion patterns, and then adaptively select the distinguishing local motion patterns to further construct robust global motion patterns. The experimental results on three popular gait datasets, i.e., CASIA-B, OUMVLP, and Gait3D, verify the effectiveness of the proposed method and show great potential for practical applications. In the future, we will further investigate adaptive learning of the local and global motion patterns in the complex-valued domain to aggregate more representative gait features." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 654, + 416, + 668 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 654, + 416, + 668 + ], + "spans": [ + { + "bbox": [ + 306, + 654, + 416, + 668 + ], + "type": "text", + "content": "6. Acknowledgement" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": "This work was supported by National Natural Science Foundation of China (Grants No.62171038, No.61827901, No.62088101, No.62276031, and No.62276025)." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 747, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 747, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 747, + 317, + 757 + ], + "type": "text", + "content": "22083" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 712 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 53, + 91, + 286, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 286, + 123 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 286, + 123 + ], + "type": "text", + "content": "[1] Gunawan Ariyanto and Mark S Nixon. 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Pattern recognition letters, 2006. 1" + } + ] + } + ], + "index": 30 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 747, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 747, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 747, + 317, + 757 + ], + "type": "text", + "content": "22085" + } + ] + } + ], + "index": 32 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Dynamic Coarse-To-Fine Learning for Oriented Tiny Object Detection/e9804a4f-6933-4148-ae33-ea1a17587f5f_content_list.json b/2023/Dynamic Coarse-To-Fine Learning for Oriented Tiny Object Detection/e9804a4f-6933-4148-ae33-ea1a17587f5f_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..1b6d3251b63ffafeeaa0b77b5f70df711f7df497 --- /dev/null +++ b/2023/Dynamic Coarse-To-Fine Learning for Oriented Tiny Object Detection/e9804a4f-6933-4148-ae33-ea1a17587f5f_content_list.json @@ -0,0 +1,2026 @@ +[ + { + "type": "text", + "text": "Dynamic Coarse-to-Fine Learning for Oriented Tiny Object Detection", + "text_level": 1, + "bbox": [ + 130, + 130, + 836, + 151 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Chang Xu $^{1}$ , Jian Ding $^{2}$ , Jinwang Wang $^{1}$ , Wen Yang $^{1*}$ , Huai Yu $^{1}$ , Lei Yu $^{1*}$ , Gui-Song Xia $^{2}$ $^{1}$ School of Electronic Information, Wuhan University \n $^{2}$ School of Computer Science, Wuhan University", + "bbox": [ + 122, + 179, + 843, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{xuchangeis, jian.ding, jwwangchn, yangwen, yuhuai, ly.wd, guisong.xia}@whu.edu.cn", + "bbox": [ + 145, + 236, + 815, + 251 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 286, + 310, + 301 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Detecting arbitrarily oriented tiny objects poses intense challenges to existing detectors, especially for label assignment. Despite the exploration of adaptive label assignment in recent oriented object detectors, the extreme geometry shape and limited feature of oriented tiny objects still induce severe mismatch and imbalance issues. Specifically, the position prior, positive sample feature, and instance are mismatched, and the learning of extreme-shaped objects is biased and unbalanced due to little proper feature supervision. To tackle these issues, we propose a dynamic prior along with the coarse-to-fine assigner, dubbed DCFL. For one thing, we model the prior, label assignment, and object representation all in a dynamic manner to alleviate the mismatch issue. For another, we leverage the coarse prior matching and finer posterior constraint to dynamically assign labels, providing appropriate and relatively balanced supervision for diverse instances. Extensive experiments on six datasets show substantial improvements to the baseline. Notably, we obtain the state-of-the-art performance for one-stage detectors on the DOTA-v1.5, DOTA-v2.0, and DIOR-R datasets under single-scale training and testing. Codes are available at https://github.com/Chasel-Tsui/mmrotate-dcfl.", + "bbox": [ + 75, + 319, + 470, + 664 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 696, + 207, + 712 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The oriented bounding box is a finer representation for object detection since the object's background region is greatly eradicated by introducing the rotation angle [55]. This advantage is pronounced in aerial images, where objects are in arbitrary orientations, resulting in the prosperity of corresponding object detection datasets [7, 11, 35, 55] and customized oriented object detectors [10, 17, 18, 60, 62]. Nevertheless, one ignorable fact is that there exist numerous tiny objects in aerial images. When oriented objects are tiny-sized, the challenges posed to existing object detec", + "bbox": [ + 75, + 723, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/1526adbf2c93c96dcfa12072377bb6d386b3ec3d5f7c421e32bd033545b8c174.jpg", + "image_caption": [ + "Figure 1. Comparisons of different learning paradigms for oriented object detection. $\\mathbf{M}^*$ means the matching function. Each box in the $2^{nd}$ row denotes a prior location. The $3^{rd}$ row are predictions of the RetinaNet and DCFL, where green, blue, and red boxes denote true positive, false positive, and false negative predictions. (a) RetinaNet, FCOS, and Rotated RPN statically assign labels between fixed priors and fixed gts. (b) Our proposed DCFL dynamically updates priors and gts, and dynamically assigns labels." + ], + "image_footnote": [], + "bbox": [ + 509, + 285, + 684, + 460 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4aa88e6d63773e986665faec731902ad01d8f794d719779be4287cd2dfb24f81.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 707, + 286, + 883, + 460 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tors are quite remarkable. Especially, the extreme geometry characteristics of oriented tiny objects hamper the accurate label assignment.", + "bbox": [ + 496, + 613, + 890, + 657 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Label assignment is a fundamental and crucial process in object detection [68], in which priors (box for anchor-based [30] and point for anchor-free detectors [50]) need to be assigned with appropriate labels to supervise the network training. In fact, there have been some works that lay a foundation for the effective label assignment of oriented objects, as shown in Fig. 1. Early works additionally preset anchors of different angles (e.g. Rotated RPN [36]) or refine high-quality anchors (e.g. $\\mathrm{S}^2\\mathrm{A}$ -Net [17]) based on the generic object detector, then a static rule (e.g. MaxIoU strategy [44]) is used to separate positive and negative (pos/neg) training samples. The derived prior boxes can thus cover more ground truth (gt) boxes and a considerable accuracy improvement can be expected. However, the static assignment cannot adaptively divide pos/neg samples according to the gt's shape and filter out low-quality samples, usually", + "bbox": [ + 496, + 659, + 890, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding Authors", + "bbox": [ + 94, + 886, + 227, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "7318", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d3f40233bf6fefa2613d355a9f0e50197da0c3f35aad322bf2c196f1870a309b.jpg", + "image_caption": [ + "Figure 2. The mismatch and imbalance issues. Each point in the left image denotes a prior location. The number in the pie-shaped bar chart denotes the mean number of positive samples assigned to each instance in a specific angle range." + ], + "image_footnote": [], + "bbox": [ + 83, + 93, + 465, + 224 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "leading to sub-optimal performance.", + "bbox": [ + 76, + 320, + 318, + 335 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recently, the exploration of adaptive label assignment [68] brings new insight to the community. For oriented object detection, DAL [38] defines a prediction-aware matching degree and utilizes it to reweight anchors, achieving dynamic sample learning. Besides, several studies [21,23,26] incorporate the shape information into detectors and propose shape-aware sampling and measurement.", + "bbox": [ + 75, + 337, + 468, + 444 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Despite the progress, the arbitrary orientation and extreme size of oriented tiny objects still pose a dilemma to the detector. As shown in Fig. 2, the mismatch and imbalance issues are particularly pronounced. For one thing, there is a mutual mismatch issue between the position prior, feature, and instance. Although some adaptive label assignment schemes may explore a better pos/neg division of the prior boxes or points, the sampled feature location behind the prior is still fixed and the derived prior is still static and uniformly located, most priors deviate from the tiny object's main body. The prior and feature themselves cannot well-match the extreme shapes of oriented tiny objects, no matter how we divide pos/neg samples. For another, the existing detectors tend to introduce bias and imbalance for oriented and tiny objects. More precisely, for anchor-based detectors, gt with shapes different from anchor boxes will yield low IoU [38, 59], leading to the lack of positive samples. In Fig. 2, we calculate the mean number of positive samples assigned to different gts with the RetinaNet and observe that there is an extreme lack of positive samples for gts with angles and scales far from predefined anchors. For anchor-free detectors, the static prior and its fixed stride limit the upper number of high-quality positive samples. Tiny objects only cover a limited number of feature points, and most of these points are away from the object's main body.", + "bbox": [ + 73, + 446, + 468, + 821 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "This motivates us to design a more dynamic and balanced learning pipeline for oriented tiny object detection. As shown in Fig. 1, we alleviate the mismatch issue by reformulating the prior, label assignment, and $gt$ representation all in a dynamic manner, which can be updated by", + "bbox": [ + 75, + 824, + 468, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "the Deep Neural Network (DNN). Simultaneously, we dynamically and progressively assign labels in a coarse-to-fine manner to seek balanced supervision for various instances.", + "bbox": [ + 498, + 90, + 890, + 136 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Specifically, we introduce a dynamic Prior Capturing Block (PCB) to learn the prior, which adaptively adjusts the prior location while retaining the physical meaning of prior [54]. The PCB is inspired by the paradigm of learnable proposals in the DETR [4] and Sparse R-CNN [48] which naturally avoids the mismatch issue between the predefined prior and feature. Compared to this paradigm, we introduce its flexibility for prior updates while keeping the fast-convergence ability of dense detectors [32, 54]. Based on the dynamic prior, we then select Cross-FPN-layer Coarse Positive Sample (CPS) candidates for further label assignment, and the CPS is realized by the Generalized Jensen-Shannon Divergence [39] (GJSD) between the $gt$ and the dynamic prior. The GJSD is able to enlarge the CPS to the object's nearby spatial locations and adjacent FPN layers, ensuring more candidates for extreme-shaped objects. After obtaining the CPS, we re-rank these candidates with predictions (posterior) and represent the $gt$ with a finer Dynamic Gaussian Mixture Model (DGMM), filtering out low-quality samples. All designs are incorporated into an end-to-end one-stage detector without additional branches.", + "bbox": [ + 496, + 137, + 892, + 455 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In short, our contributions are listed as follows: (1) We identify that there exist severe mismatch and imbalance issues in the current learning pipeline for oriented tiny object detection. (2) We design a Dynamic Coarse-to-Fine Learning (DCFL) scheme for oriented tiny object detection, which is the first to model the prior, label assignment, and $gt$ representation all in a dynamic manner. In the DCFL, we propose to use the GJSD to construct Coarse Positive Samples (CPS) and represent objects with a finer Dynamic Gaussian Mixture Model (DGMM), obtaining coarse-to-fine label assignment. (3) Extensive experiments on six datasets show promising results.", + "bbox": [ + 496, + 455, + 893, + 638 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 652, + 640, + 669 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Oriented Object Detection", + "text_level": 1, + "bbox": [ + 500, + 679, + 738, + 695 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Prior for Oriented Objects. Anchor, as a classic design in generic object detectors (e.g. Faster R-CNN [44], RetinaNet [30]), has facilitated object detection for a long time. Similarly, oriented object detection also benefits from the anchor design. Initially, rotated RPN [36] extends the RPN to the field of oriented object detection by tiling 54 anchors each location with preset angles and scales. Indeed, enumerating potential $gt$ shapes can notably improve the recall, apart from the sacks of additional computational cost. RoI Transformer [10] utilizes horizontal anchors and transforms the RPN-generated horizontal proposals to oriented proposals, reducing the number of rotated anchors. To save computation, the Oriented R-CNN [56] introduces an ori", + "bbox": [ + 496, + 704, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "7319", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ented RPN that directly predicts oriented proposals based on horizontal anchors. Recently, one-stage oriented object detectors gradually emerged, including anchor-based detectors [17, 60] with box prior and anchor-free detectors [26, 28] with point prior. Most of them retain the fixed prior design, except for the $\\mathrm{S}^2\\mathrm{A}$ -Net [17] which proposes to generate high-quality anchors.", + "bbox": [ + 75, + 90, + 468, + 196 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Label Assignment. ATSS [68] reveals that label assignment plays a pivotal role in the detectors' performance [14,24,37]. In the field of oriented object detection, DAL [38] observes inconsistency between the input prior IoU and the output predicted IoU, then defines a matching degree as the soft label that dynamically reweights anchors. Recently, SASM [21] introduces a shape-adaptive sample selection and measurement strategy to improve detection performance. Similarly, GGHL [23] proposes to fit the main body of the instance by a single 2-D Gaussian heatmap, then it divides and reweights samples in a dynamic manner. In addition, Oriented Reppoints [26] improves the RepPoints [65] by assessing the quality of points for more effective label assignment.", + "bbox": [ + 75, + 198, + 470, + 409 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Tiny Object Detection", + "text_level": 1, + "bbox": [ + 76, + 421, + 282, + 436 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Multi-scale Learning. Basically, one can use a multi-resolution image pyramid to obtain multi-scale learning. However, the vanilla image pyramid will bring much computation cost. Thus, some works [29, 33, 34, 42, 49, 69] reduce computation with the efficient Feature Pyramid Network (FPN). Unlike the FPN, TridentNet [27] introduces multi-branch detection heads of various receptive fields for multi-scale prediction. Moreover, one can normalize the scale of objects for scale-invariant object detection, for example, SNIP [46] and SNIPER [47] resize images and train objects within a certain scale range.", + "bbox": [ + 75, + 445, + 468, + 609 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Label Assignment. Tiny objects usually have low IoU with anchors or cover a limited number of feature points, thus suffering from the lack of positive samples. ATSS [68] slightly reconciles the number of positive samples for objects of different scales. NWD [57] designs a new metric to replace IoU, which can sample more positive samples for tiny objects. Recently, the RFLA [58] utilizes outliers to detect tiny objects for scale-balanced learning.", + "bbox": [ + 75, + 612, + 468, + 733 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Context Information. Tiny object lacks discriminative features, but objects are closely related to the surrounding context. Therefore, we can leverage the context information to enhance small object detection. Muti-Region CNN (MRCNN) [15] and Inside-Outside Network (ION) [3] are two representative works that exploit local and global context information. Recently, the Relation Network [22] and transformer-based detectors [4, 54, 72] reason about the association between instances via the attention mechanism.", + "bbox": [ + 75, + 734, + 468, + 868 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Feature Enhancement. The feature representation of small objects can be enhanced by super-resolution or GAN.", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "PGAN [25] first applies GAN to small object detection. Besides, Bai et al. [1] introduce the MT-GAN which trains an image-level super-resolution model to improve the RoI features of small objects. In addition, there are some other methods based on super-resolution including [2,8,40,43].", + "bbox": [ + 496, + 90, + 890, + 167 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "By contrast, our method simultaneously handles the prior mismatch and unbalanced learning via dynamically modeling the prior, label assignment, and $gt$ representation. Meanwhile, unlike the two-stage RoI-Transformer [10] or one-stage S²A-Net [17], we embed the dynamic prior inside the end-to-end one-stage detector without introducing any auxiliary branch.", + "bbox": [ + 496, + 167, + 890, + 272 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 284, + 589, + 299 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Overview. Given a set of dense prior $P \\in \\mathbb{R}^{W \\times H \\times C}$ ( $W \\times H$ is the feature map size, $C$ is the shape information number, each feature point has one prior for simplicity), object detectors remap the set $P$ into final detection results $D$ through the Deep Neural Network (DNN), which can be simplified as:", + "bbox": [ + 496, + 306, + 890, + 398 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nD = \\mathrm {D N N} _ {h} (P), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 637, + 398, + 890, + 415 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathrm{DNN}_h$ denotes the detection head. Detection results $D$ contain two parts: classification scores $D_{cls} \\in \\mathbb{R}^{W \\times H \\times A}$ ( $A$ is the class number) and box locations $D_{reg} \\in \\mathbb{R}^{W \\times H \\times B}$ ( $B$ is the box parameter number).", + "bbox": [ + 496, + 420, + 890, + 479 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To train the $\\mathrm{DNN}_h$ , we need to find a proper matching between the prior set $P$ and the $gt$ set $GT$ , and assign pos/neg labels to $P$ to supervise the network learning. For static assigners (e.g. RetinaNet [30]), the set of pos labels $G$ can be obtained via hand-crafted matching function $\\mathcal{M}_s$ :", + "bbox": [ + 496, + 479, + 890, + 556 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nG = \\mathcal {M} _ {s} (P, G T). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 632, + 564, + 890, + 579 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For dynamic assigners [14, 24, 38], they tend to simultaneously leverage the prior information $P$ and posterior information (predictions) $D$ , and then apply a prediction-aware mapping $\\mathcal{M}_d$ to get the set $G$ :", + "bbox": [ + 496, + 587, + 890, + 647 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nG = \\mathcal {M} _ {d} (P, D, G T). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 620, + 655, + 890, + 671 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "After the pos/neg label separation, the loss function can be summarized into two parts:", + "bbox": [ + 496, + 679, + 890, + 709 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\sum_ {i = 1} ^ {N _ {p o s}} \\mathcal {L} _ {p o s} \\left(D _ {i}, G _ {i}\\right) + \\sum_ {j = 1} ^ {N _ {n e g}} \\mathcal {L} _ {n e g} \\left(D _ {j}, y _ {j}\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 542, + 715, + 890, + 760 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $N_{pos}$ , $N_{neg}$ are the number of positive and negative samples respectively, $y_{j}$ denotes the negative label.", + "bbox": [ + 496, + 767, + 888, + 796 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "While in this work, we model the prior, label assignment, and $gt$ representation all in a dynamic manner to alleviate the mismatch issue. To begin with, the dynamic prior is reformulated to (\\~ denotes the dynamic item):", + "bbox": [ + 496, + 797, + 890, + 857 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {D} = \\mathrm {D N N} _ {h} (\\underbrace {\\mathrm {D N N} _ {p} (P)} _ {\\text {D y n a m i c P r i o r} \\tilde {P}}), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 602, + 864, + 890, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "7320", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$\\mathrm{DNN}_p$ is a learnable block incorporated within the detection head to update the prior. Then, the matching function is reformulated to a coarse-to-fine paradigm:", + "bbox": [ + 76, + 90, + 468, + 137 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {G} = \\mathcal {M} _ {d} \\left(\\mathcal {M} _ {s} (\\tilde {P}, G T), \\tilde {G T}\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 171, + 147, + 468, + 165 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the $\\tilde{G}T$ is a finer representation of an object with the Dynamic Gaussian Mixture Model (DGMM). In a nutshell, our final loss is modeled as:", + "bbox": [ + 76, + 176, + 468, + 220 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\sum_ {i = 1} ^ {\\tilde {N} _ {p o s}} \\mathcal {L} _ {p o s} \\left(\\tilde {D} _ {i}, \\tilde {G} _ {i}\\right) + \\sum_ {j = 1} ^ {\\tilde {N} _ {n e g}} \\mathcal {L} _ {n e g} \\left(\\tilde {D} _ {j}, y _ {j}\\right). \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 120, + 220, + 468, + 266 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1. Dynamic Prior", + "text_level": 1, + "bbox": [ + 76, + 275, + 227, + 291 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Inspired by the purely learnable paradigm of proposal updation in the DETR [4] and Sparse R-CNN [48], we propose to introduce more flexibility into the prior to mitigate the mismatch issue. Moreover, we retain the physical meaning of prior where each individual prior stands for a feature point, inheriting the fast convergence ability of dense detectors. The structure of the proposed Prior Capturing Block (PCB) is shown in Fig. 3, in which a dilated convolution is deployed to take the surrounding information into account, and then the Deformable Convolution Network (DCN) [9] is leveraged to capture the dynamic prior. Besides, we utilize the learned offsets from the regression branch to guide the feature extraction of the classification branch, leading to better alignment between the two tasks.", + "bbox": [ + 75, + 299, + 468, + 508 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The dynamic prior capturing process is as follows. First of all, we initialize each prior location $\\mathbf{p}(x,y)$ by each feature point's spatial location s (which is remapped to the image). In each iteration, we forward the network to capture the offset sets of each prior location $\\Delta \\mathbf{o}$ . Hence, the prior spatial location can be updated by:", + "bbox": [ + 75, + 510, + 468, + 599 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {\\mathbf {s}} = \\mathbf {s} + s t \\sum_ {i = 1} ^ {n} \\Delta \\mathbf {o} _ {i} / 2 n, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 601, + 468, + 638 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $st$ is the feature map's stride, $n$ is the number of offsets. Finally, we utilize the 2-D Gaussian distribution $\\mathcal{N}_p(\\boldsymbol{\\mu}_p, \\boldsymbol{\\Sigma}_p)$ which is demonstrated conducive to small objects [58,61] and oriented objects [61,63] to fit the prior spatial location. Concretely, the dynamic $\\tilde{\\mathbf{s}}$ serves as the Gaussian's mean vector $\\boldsymbol{\\mu}_p$ . We preset one prior which is square-shaped $(w, h, \\theta)$ as that in RetinaNet [30] on each feature point, then compute the co-variance matrix $\\boldsymbol{\\Sigma}_p$ by [64]:", + "bbox": [ + 75, + 638, + 468, + 760 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\Sigma} _ {p} = \\left[ \\begin{array}{c c} \\cos \\theta & - \\sin \\theta \\\\ \\sin \\theta & \\cos \\theta \\end{array} \\right] \\left[ \\begin{array}{c c} \\frac {w ^ {2}}{4} & 0 \\\\ 0 & \\frac {h ^ {2}}{4} \\end{array} \\right] \\left[ \\begin{array}{c c} \\cos \\theta & \\sin \\theta \\\\ - \\sin \\theta & \\cos \\theta \\end{array} \\right]. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 94, + 771, + 468, + 809 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Coarse Prior Matching", + "text_level": 1, + "bbox": [ + 76, + 816, + 290, + 832 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given a set of prior, one basic assignment rule is to specify a range of candidate true prediction samples for a specific $gt$ . Some adaptive strategies restrict the candidates of a given $gt$ inside a single FPN layer [14,23,68], while some", + "bbox": [ + 76, + 840, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "works release all layers as candidates [67, 71]. However, for oriented tiny objects, the former strict heuristic rule may lead to a sub-optimal layer selection and the latter loose one will induce the slow convergence issue [32].", + "bbox": [ + 496, + 90, + 890, + 151 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Hence, we propose Cross-FPN-layer Coarse Positive Sample (CPS) candidates, which narrows down the sample range compared to the all-FPN-layer manner while discarding the single-layer heuristic. In the CPS, we slightly expand the range of candidates to the $gt$ 's nearby spatial location and adjacent FPN layers, which warrants relatively diverse and sufficient candidates compared to the single-layer heuristic and alleviates the quantity imbalance issue.", + "bbox": [ + 496, + 151, + 890, + 271 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Specifically, the similarity measurement in constructing the CPS is realized with the Jensen-Shannon Divergence (JSD) [13], which inherits the scale invariance property of the Kullback-Leibler Divergence (KLD) [63] and can measure the $gt$ 's similarity with nearby non-overlapping priors [58, 63]. Moreover, it conquers KLD's drawback of asymmetry. However, the closed-form solution of the JSD between Gaussian distributions is unavailable [39], thus, we utilize the Generalized Jensen-Shannon Divergence (GJSD) [39] which yields a closed-form solution, as the substitute.", + "bbox": [ + 496, + 272, + 890, + 436 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For example, the GJSD between two Gaussian distributions $\\mathcal{N}_p(\\boldsymbol{\\mu}_p, \\boldsymbol{\\Sigma}_p)$ and $\\mathcal{N}_g(\\boldsymbol{\\mu}_g, \\boldsymbol{\\Sigma}_g)$ is defined by:", + "bbox": [ + 498, + 438, + 890, + 470 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {G J S D} \\left(\\mathcal {N} _ {p}, \\mathcal {N} _ {g}\\right) = (1 - \\alpha) \\mathrm {K L} \\left(\\mathcal {N} _ {\\alpha}, \\mathcal {N} _ {p}\\right) + \\alpha \\mathrm {K L} \\left(\\mathcal {N} _ {\\alpha}, \\mathcal {N} _ {g}\\right), \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 481, + 890, + 511 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where KL denotes the KLD, and $\\mathcal{N}_{\\alpha}(\\pmb{\\mu}_{\\alpha}, \\pmb{\\Sigma}_{\\alpha})$ is given by:", + "bbox": [ + 500, + 512, + 887, + 527 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\Sigma} _ {\\alpha} = \\left(\\boldsymbol {\\Sigma} _ {p} \\boldsymbol {\\Sigma} _ {g}\\right) _ {\\alpha} ^ {\\boldsymbol {\\Sigma}} = \\left((1 - \\alpha) \\boldsymbol {\\Sigma} _ {p} ^ {- 1} + \\alpha \\boldsymbol {\\Sigma} _ {g} ^ {- 1}\\right) ^ {- 1}, \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 521, + 539, + 890, + 560 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "and", + "bbox": [ + 500, + 571, + 527, + 583 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\boldsymbol {\\mu} _ {\\alpha} = \\left(\\boldsymbol {\\mu} _ {p} \\boldsymbol {\\mu} _ {g}\\right) _ {\\alpha} ^ {\\boldsymbol {\\mu}} \\\\ = \\boldsymbol {\\Sigma} _ {\\alpha} \\left((1 - \\alpha) \\boldsymbol {\\Sigma} _ {p} ^ {- 1} \\boldsymbol {\\mu} _ {p} + \\alpha \\boldsymbol {\\Sigma} _ {g} ^ {- 1} \\boldsymbol {\\mu} _ {g}\\right). \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 557, + 580, + 834, + 622 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "(12)", + "bbox": [ + 861, + 594, + 888, + 606 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Note that $\\alpha$ is a parameter that controls the weight of two distributions [39] in similarity measurement. In our work, the $\\mathcal{N}_p$ and $\\mathcal{N}_q$ contribute equally, thus $\\alpha$ is set to 0.5.", + "bbox": [ + 496, + 626, + 890, + 671 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Ultimately, for each $gt$ , we select $K$ priors which hold the top $K$ GJSD score with this $gt$ as the Coarse Positive Samples (CPS) and regard the remaining priors as negative samples, this coarse matching serves as the $\\mathcal{M}_s$ in Eq. 6. The ranking manner works together with the GJSD measurement to construct the Cross-FPN-layer CPS, eliminating the imbalance issue raised by the MaxIoU matching for outlier angles and scales, which will be analyzed in Sec. 5.", + "bbox": [ + 496, + 671, + 890, + 792 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Finer Dynamic Posterior Matching", + "text_level": 1, + "bbox": [ + 500, + 801, + 803, + 816 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Based on Coarse Positive Sample (CPS) candidates, we design a dynamic posterior (prediction) matching rule $\\mathcal{M}_d$ to filter out low-quality samples. The $\\mathcal{M}_d$ consists of two key components, namely a posterior re-ranking strategy and a Dynamic Gaussian Mixture Model (DGMM) constraint.", + "bbox": [ + 496, + 825, + 890, + 898 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "7321", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/dc573d6825887ef255c083e96a81d529d1824e4a6c745b3ce279f11d04cede5a.jpg", + "image_caption": [ + "Figure 3. The process of feature extraction and dynamic coarse-to-fine learning. PCB denotes the prior capturing block." + ], + "image_footnote": [], + "bbox": [ + 78, + 88, + 486, + 251 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/9002cf5257404920462cd97d3152015c0644aeafbe4c298b57ebe07f1c4b0464.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 490, + 88, + 883, + 251 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We re-rank the sample candidates in the CPS according to their predicted scores. In other words, we further refine the positive samples by their Possibility of becoming True predictions $(PT)$ [14], which is a linear combination of the predicted classification score and the location score with the $gt$ . We define the $PT$ of the $i^{th}$ sample $D_{i}$ as:", + "bbox": [ + 75, + 305, + 470, + 396 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nP T _ {i} = \\frac {1}{2} C l s (D _ {i}) + \\frac {1}{2} I o U (D _ {i}, g t _ {i}), \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 402, + 468, + 433 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $Cls$ is the predicted classification confidence and $IoU$ is the rotated IoU between the predicted location and its corresponding $gt$ location. We select candidates with $Q$ highest $PT$ as Medium Positive Sample (MPS) candidates.", + "bbox": [ + 75, + 441, + 468, + 500 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Following this, we filter out those samples too far away from the $gts$ with a finer instance representation, getting the Finer Positive Samples (FPS). Different from previous works which utilize the center probability map [53] or the single-Gaussian [23,64] for instance representation, we represent the instance by a finer DGMM. It consists of two components: one is centered on the geometry center and the other is centered on the semantic center of the object. Concretely, for a specific instance $gt_{i}$ , the geometry center $(cx_{i}, cy_{i})$ serves as the mean vector $\\mu_{i,1}$ of the first Gaussian, and the semantic center $(sx_{i}, sy_{i})$ , which is deduced by averaging the location of the samples in the MPS, serves as the $\\mu_{i,2}$ . That is to say, we parameterize the instance as:", + "bbox": [ + 75, + 500, + 468, + 684 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nD G M M _ {i} (s | x, y) = \\sum_ {m = 1} ^ {2} w _ {i, m} \\sqrt {2 \\pi | \\boldsymbol {\\Sigma} _ {i , m} |} \\mathcal {N} _ {i, m} \\left(\\boldsymbol {\\mu} _ {i, m}, \\boldsymbol {\\Sigma} _ {i, m}\\right), \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 686, + 468, + 733 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $w_{i,m}$ is the weight of each Gaussian with a summation of 1, $\\Sigma_{i,m}$ equals to the $gt$ 's $\\Sigma_g$ . Each sample in MPS has a DGMM score $DGMM(s|MPS)$ , we set negative masks to samples which have $DGMM(s|MPS) < e^{-g}$ with any $gt$ , the $g$ is adjustable.", + "bbox": [ + 75, + 734, + 468, + 810 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 821, + 209, + 838 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Datasets", + "text_level": 1, + "bbox": [ + 76, + 847, + 179, + 861 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Experiments are done on six datasets, i.e., DOTA-v1.0 [55]/v1.5/v2.0 [11], DIOR-R [7], VisDrone [12], and", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "MS COCO [31]. In ablation studies and analyses, we choose the large-scale DOTA-v2.0 train set for training and val set for evaluation, which contains a large number of tiny objects. To compare with other methods, we use trainval sets of DOTA-v1.0, DOTA-v1.5, DOTA-v2.0, and DIOR-R for training and their test sets for testing, we choose the VisDrone2019, MS COCO train set, val set for training and testing.", + "bbox": [ + 496, + 304, + 890, + 426 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Implementation Details", + "text_level": 1, + "bbox": [ + 498, + 435, + 718, + 452 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We conduct all the experiments on the computer with a single NVIDIA RTX 3090 GPU, and the batch size is set to 4. Models are built based on MMDetection [6] and MMRotate [70] with PyTorch [41]. The ImageNet [45] pre-trained models are used as the backbone. The Stochastic Gradient Descent (SGD) optimizer is used for training with a learning rate of 0.005, a momentum of 0.9, and a weight decay of 0.0001. The ResNet-50 [20] with FPN [29] is the default backbone if not specified. We use Focal loss [30] for classification and IoU loss [66] for regression. We only use random flipping as data augmentation for all experiments.", + "bbox": [ + 496, + 458, + 890, + 625 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For experiments on the DOTA-v1.0 and DOTA-v2.0, we follow the official settings of the DOTA-v2.0 benchmark [11], i.e., we crop images into patches of $1024 \\times 1024$ with overlaps of 200 and train the model for 12 epochs. For DOTA-v2.0, we reproduce one-stage state-of-the-art methods [17,21,26,38,50,60,63,68] with the same settings.", + "bbox": [ + 496, + 625, + 890, + 715 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For experiments on other datasets, we set the input size to $1024 \\times 1024$ (overlap 200), $800 \\times 800$ , $1333 \\times 800$ , and $1333 \\times 800$ for DOTA-v1.5, DIOR-R, VisDrone, and COCO respectively. We train the models for 40, 40, 12, and 12 epochs on the DOTA-v1.5, DIOR-R, COCO, and VisDrone as previous works do [16, 26]. The above settings are fixed unless otherwise specified.", + "bbox": [ + 496, + 715, + 890, + 821 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Main Results", + "text_level": 1, + "bbox": [ + 500, + 830, + 638, + 845 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Results on DOTA series. As shown in Tab. 1, our proposed method achieves the state-of-the-art performance of $57.66\\%$ mAP on the DOTA-v2.0 OBB benchmark un", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "7322", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/5b470d38085c0b67b4b2742a123a0ad9bf1a86810f458ff604d43d1a55dd3d76.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodBackbonePlaneBDBridgeGTFSVLVShipTCBCSTSBFRAHarborSPHCCCAirHelimAP
multi-stage:
FR OBB [44]R5071.6147.2039.2858.7035.5548.8851.5178.9758.3658.5536.1151.7343.5755.3357.073.5152.942.7947.31
FR OBB + DpR5071.5549.7440.3460.4040.7450.6756.5879.0358.2258.2434.7351.9544.3355.1053.147.2159.536.3848.77
MR [19]R5076.2049.9141.6160.0041.0850.7756.2478.0155.8557.4836.6251.6747.3955.7959.063.6460.268.9549.47
HTC* [5]R5077.6947.2541.1560.7141.7752.7958.8778.7455.2258.4938.5752.4849.5856.1854.094.2066.3811.9250.34
RT [10]R5071.8148.3945.8864.0242.0954.3959.9282.7063.2958.7141.0452.8253.3256.1857.9425.7163.728.7052.81
Oriented R-CNN [56]R5077.9550.2946.7365.2442.6154.5660.0279.0861.6959.4242.2656.8951.1156.1659.3325.8160.679.1753.28
one-stage:
DAL [38]R5071.2338.3638.6045.2435.4243.7556.0470.8450.8756.6320.2846.5333.4947.2912.150.8125.770.0038.52
SASM [21]R5070.3040.6237.0159.0340.2145.4644.6078.5849.3460.7329.8946.5742.9548.3128.131.8276.370.7444.53
RetinaNet-O [30]R5070.6347.2639.1255.0238.1040.5247.1677.7456.8652.1237.2251.7544.1553.1951.066.5864.287.4546.68
\\( R^3Det w/ KLD [63] \\)R5075.4450.9541.1661.6141.1145.7649.6578.5254.9760.7942.0753.2043.0849.5534.0936.2668.650.0647.26
FCOS-O [51]R5074.8447.5340.8357.4143.8947.7255.6678.6157.8663.0038.0252.3841.9153.2440.227.1565.517.4248.51
Oriented Rep [26]R5073.0246.6842.3763.0547.0650.2858.6478.8457.1266.7735.2150.7648.7751.6234.236.1764.665.8748.95
ATSS-O [68]R5077.4649.5542.1262.6145.1548.4051.7078.4359.3362.6539.1852.4342.9253.9842.705.9167.0910.6849.57
\\( S^2A-Net [17] \\)R5077.8451.3143.7262.5947.5150.5857.8680.7359.1165.3236.4352.6045.3652.4640.120.0062.8111.1149.86
one-stage:
DCFLR5075.7149.4044.6963.2346.4851.5555.5079.3059.9665.3941.8654.4247.0355.7250.4911.7569.017.7551.57
\\( S^2A-Net w/ DCFL \\)R5074.7953.2545.8165.4646.4953.2358.1081.5160.1366.4243.2455.0950.5255.5854.535.2368.7313.0652.84
DCFL†R5078.3053.0344.2460.1748.5655.4258.6678.2960.8965.9343.5455.8253.3360.0054.7630.9074.0115.6055.08
DCFL†ReR10179.4955.9750.1561.5949.0055.3359.3181.1866.5260.0652.8756.7157.8358.1360.3535.6678.6513.0357.66
", + "bbox": [ + 80, + 89, + 893, + 358 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/d1d8ced44cc06e0a65feec4c892dfa26fa7aa62ea1a8ae53734bdfaa914d3f0d.jpg", + "table_caption": [ + "Table 1. Main results on the DOTA-v2.0 OBB Task. We follow the official class abbreviations as the DOTA-v2.0 benchmark [11]. $\\dagger$ denotes training for 40 epochs. Note that this paper [63] reports $50.90\\%$ mAP for $\\mathrm{R}^3\\mathrm{Det}$ w/ KLD under 20 epochs, the ReR101 backbone is proposed by the ReDet [18]. The results in red and blue denote the best and second-best performance of each column." + ], + "table_footnote": [], + "table_body": "
MethodCFA [16]RetinaNet-O [30]R3Det [60]Oriented Rep [26]ATSS-O [68]
mAP69.6369.7970.1871.9472.29
Method KLD [63]S2A-Net [17]GGHL [23](3x)DCFLDCFL(3x)
mAP72.7673.9173.9874.2675.35
", + "bbox": [ + 80, + 422, + 468, + 474 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/f01e5c79846380873a54d326fca7a71359ea65fbf5c929045b55aeaa472f36e0.jpg", + "table_caption": [ + "Table 2. Comparison with one-stage detectors on the DOTA-v1.0 OBB Task. All results are based on the MMRotate [70] with 12 epochs except for GGHL [23]. 3x means training for 36 epochs." + ], + "table_footnote": [], + "table_body": "
MethodBackboneSVShipSTmAP
RetinaNet-O [30]R5044.5373.3159.9659.16
FR OBB [19]R5051.2879.3767.5062.00
CMR [19]R5051.6479.9967.5863.41
RT [10]R5052.0580.7268.2665.03
ReDet [18]ReR5052.3880.9268.6466.86
DCFLR5056.72 (+12.19)80.87 (+7.56)75.65 (+15.69)67.37 (+8.21)
DCFLReR10157.31 (+12.78)86.60 (+13.29)76.55 (+16.59)70.24 (+11.08)
", + "bbox": [ + 80, + 529, + 468, + 618 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/c0cee14f7bd89962072b94e1c492cd1c6d12a65c341a6edc910e88fe74214149.jpg", + "table_caption": [ + "Table 3. Main results on the DOTA-v1.5 OBB Task." + ], + "table_footnote": [], + "table_body": "
MethodRetinaNet-O [30]FR-OBB [44]RT [10]AOPG [7]
mAP57.5559.5463.8764.41
MethodGGHL [23]Oriented Rep [26]DCFLDCFL (ReR101)
mAP66.4866.7166.8071.03
", + "bbox": [ + 88, + 643, + 457, + 703 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/617fdfba6caa4504d19d80781728de61c9b8dcadda49e0942b89d70f590f80b6.jpg", + "table_caption": [ + "Table 4. Performance comparisons on the DIOR-R dataset." + ], + "table_footnote": [], + "table_body": "
MethodBackboneVEBRWM
RetinaNet-O [30]R5038.024.060.2
Oriented Rep [26]R5050.438.864.7
DCFLR5050.9 (+12.9)42.1 (+18.1)70.9 (+10.7)
", + "bbox": [ + 89, + 727, + 457, + 787 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "der single-scale training and testing. Besides, our model achieves $51.57\\%$ mAP without bells and whistles, surpassing all one-stage object detectors tested. The results on the DOTA-v1.0 [55] and DOTA-v1.5 are listed in Tab. 2, Tab. 3.", + "bbox": [ + 76, + 839, + 468, + 902 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/e88f0835a5b46b327a8c215e921879a6d7a9c5a230ed08b29a6ec485ad6ee8d9.jpg", + "table_caption": [ + "Table 5. Detection results of typical tiny objects on the DIOR-R dataset. VE, BR, and WM denote vehicle, bridge, and wind-mill." + ], + "table_footnote": [], + "table_body": "
DatasetVisDroneMS COCODOTA-v2.0 HBB
MethodRetinaNet [30]DCFLRetinaNetDCFLFCOS [58]DCFL
AP0.529.232.155.457.355.457.4
", + "bbox": [ + 503, + 421, + 890, + 477 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 6. Results of one-stage object detectors on HBB datasets.", + "bbox": [ + 506, + 481, + 883, + 494 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/af612884815b4307fcbca15cf0ea6bb11efe7f5db42eb3571e0ffb702806cc50.jpg", + "image_caption": [ + "Figure 4. Different ways of constructing the CPS. Yellow and orange denote the possible regions of CPS and MPS respectively." + ], + "image_footnote": [], + "bbox": [ + 519, + 498, + 870, + 574 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results also indicate that our DCFL is very effective for detecting tiny oriented objects on the tested datasets, such as small vehicles, ships, and storage tanks, where a boost of about 10 points can be expected compared to the baseline.", + "bbox": [ + 496, + 625, + 893, + 686 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results on DIOR-R. DIOR-R contains some tiny oriented objects, such as the vehicle, bridge, and windmill. The mAP and class-wise AP of tiny objects are in Tab. 4 and Tab. 5, we also achieve the state-of-the-art performance of $71.03\\%$ mAP and notable improvements on tiny objects.", + "bbox": [ + 496, + 686, + 893, + 761 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results on HBB Datasets. Moreover, we discard the angle to verify the versatility of the DCFL on the generic small object detection datasets VisDrone [12], MS COCO [31], and DOTA-v2.0 HBB [11]. In Tab. 6, our method gets a notable $\\mathrm{AP}_{0.5}$ boost compared to the baseline.", + "bbox": [ + 496, + 761, + 893, + 838 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 847, + 653, + 864 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Effects of Individual Strategy. We check the effectiveness of each proposed strategy in the proposed method. In", + "bbox": [ + 500, + 869, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "7323", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/c9a6cc24ef7673038e0936839a9ff0788cf455ea732a58a986b8b7ad5ca643b5.jpg", + "table_caption": [], + "table_footnote": [ + "(a) Individual effectiveness. CPS, MPS, and DGMM denote Coarse, Medium Sample Candidates and Dynamic Gaussian Mixture Model." + ], + "table_body": "
MethodCPSMPSDGMMmAP
baseline [30]51.70
DCFL✓✓53.41
✓✓57.20
✓✓✓59.15
", + "bbox": [ + 117, + 77, + 379, + 162 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/4451616804128918d8a534fb5b184656ecc120ebf03b052321476d3ec49c2981.jpg", + "table_caption": [], + "table_footnote": [ + "(b) Comparisons of different CPS. The FPN layer number varies for different strategies of getting the CPS." + ], + "table_body": "
StrategyMeasurementmAP
All-FPN-layerGaussian50.12
Single-FPN-layerGaussian56.72
Cross-FPN-layerKLD [63]57.82
Cross-FPN-layerGWD [61]58.55
Cross-FPN-layerGJSD59.15
", + "bbox": [ + 395, + 78, + 640, + 162 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/9ff4e41d251b8195e35a23bf3b1843cad0d2eb39cdb0d2ddf115515d13b9fee3.jpg", + "table_caption": [], + "table_footnote": [ + "(c) Effects of detailed designs in the PCB. DP denotes the dynamic prior. Guiding denotes reg guidescls." + ], + "table_body": "
DCNDilated ConvDPmAP
58.07
✓58.41
✓✓58.65
Separate✓✓58.71
Guiding✓✓59.15
", + "bbox": [ + 656, + 79, + 854, + 162 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/7f4bbbea4d1521766139f939c66ddf15d6cc62d0b6773cefad82d8c2b5f1f00e.jpg", + "table_caption": [], + "table_footnote": [ + "(d) Effects of parameters $K$ and $Q$ ." + ], + "table_body": "
K2420
Q20161281612108
mAP58.3158.1158.9559.0658.6658.7158.9258.28
K1612
Q12108610864
mAP59.1558.5758.9757.8458.7958.2557.0157.37
", + "bbox": [ + 184, + 200, + 584, + 299 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/0ba3a6c64c6bdec6b3027656098901541d433fbbb7061bedbd4fe3a3728b10ce.jpg", + "table_caption": [], + "table_footnote": [ + "(e) Effects of parameter $g$" + ], + "table_body": "
g1.21.0
mAP57.9158.20
g0.80.4
mAP59.1558.95
", + "bbox": [ + 599, + 200, + 790, + 299 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 7. Ablations. We train on DOTA-v2.0 train set, test on val set, and report mAP under IoU threshold 0.5.", + "bbox": [ + 129, + 325, + 836, + 340 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "all ablation experiments, we employ one prior for each feature point for fair comparisons. As seen in Tab. 7a, the baseline detector RetinaNet-OBB yields a result of $51.70\\%$ mAP. When we gradually apply the posterior re-ranked MPS and DGMM into the detector based on the CPS, the mAP improves progressively, verifying each design's effectiveness. Note that the CPS cannot be independently used since the samples in it are too coarse to serve as the final positive samples. Nevertheless, we compare some different ways of constructing the CPS to verify its superiority.", + "bbox": [ + 75, + 356, + 468, + 507 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparisons of Different CPS. The design of the CPS matters in the training pipeline. We show several paradigms of designing the CPS as shown in Fig. 7b, including limiting the CPS for a specific $gt$ within a single layer like FCOS [50], releasing all FPN layers as the CPS, like Objectbox [67]. We compare their performance in Tab. 7b. For fair comparisons, the number of samples in CPS is fixed at 16, and all other components are kept the same. For the Single-FPN-layer way, we group $gt$ onto different layers according to the scale division strategy in FCOS, then assign labels within each layer. For the All-FPN-layer way, we do not group $gt$ onto different layers, instead, we discard the prior scale information and directly measure the distance between Gaussian $gt$ and prior points. The results are shown in Tab. 7b, we can observe that neither of the above two ways will yield the best performance. By contrast, the distribution distances (KLD, GWD, GJSD) are able to construct the Cross-FPN-layer CPS, where the candidates are extended to adjacent layers besides the main layer. We can also see the GJSD gets the best performance of $59.15\\%$ mAP, mainly resulting from its property of scale-invariance [39, 63], symmetry [39], and ability to measure non-overlapping boxes [39] compared to other counterparts.", + "bbox": [ + 75, + 507, + 468, + 854 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Fixed Prior and Dynamic Prior. We conduct a finer group of ablation studies to verify the necessity of introducing the dynamic prior. As shown in Tab. 7c, if we disable the", + "bbox": [ + 76, + 854, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "dynamic prior by fixing the location of samples, a slight performance drop will be introduced. Hence, the prior should be adjusted accordingly when leveraging the dynamic sampling strategy to better capture the shape of objects.", + "bbox": [ + 496, + 356, + 890, + 416 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Detailed Design in PCB. For the PCB, it is made up of a dilated convolution and a guiding DCN, we slightly enlarge the receptive field with a dilation rate of 3. After that, we take advantage of the DCN to generate dynamic priors in a guiding manner. As shown in Tab. 7c, we can observe that the DCN can bring an improvement of $0.34\\mathrm{mAP}$ points and the dilated convolution can slightly enhance the mAP. We find that the application of the DCN [9] to the single regression branch will slightly deteriorate the accuracy (noted by Separate in Tab. 7c), which may cause mismatch issues between the two branches. Thus we utilize the offsets from the regression head to guide the offsets classification head for better alignment (noted by Guiding).", + "bbox": [ + 496, + 417, + 892, + 613 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effects of Parameters. The introduced three parameters are robust in a certain range. From Tab. 7d, we can see that a combination of $K = 16$ and $Q = 12$ gets the best performance. In Tab. 7e, we verify the threshold $e^{-g}$ in the DGMM, we empirically set $w_{i,1}$ to 0.7, then a threshold of $g = 0.8$ yields the highest mAP. Although making the CPS/MPS/FPS coarser and stricter will weaken the performance, the mAP only waves marginally. In other words, the coarse-to-fine assignment manner somewhat warrants the parameter selection's robustness since multiple parameters can attenuate the effects of an under-tuned one.", + "bbox": [ + 496, + 614, + 890, + 781 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5. Analysis", + "text_level": 1, + "bbox": [ + 500, + 797, + 596, + 814 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For a clearer dissection of why the proposed scheme works, we perform more meticulous analyses as follows.", + "bbox": [ + 500, + 824, + 890, + 853 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Reconciliation of imbalance problems. To delve into the imbalance issue, we calculate the mean predicted IoU and the mean positive sample number of $gt$ holding differ", + "bbox": [ + 500, + 854, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "7324", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0e4bacdce06e68bde739295fe670a8d4894c6c85c6052477375b664eb420dc0e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 96, + 88, + 251, + 205 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/64659c3fa9895d4bf2ea4632dce7a718cb144a7c8ef051f16746194de2c404f9.jpg", + "image_caption": [ + "Figure 5. Visualization analysis of the predicted results. The first row is the result of the RetinaNet-OBB while the second row is the result of the DCFL. TP, FN, and FP predictions are marked in green, red, and blue respectively." + ], + "image_footnote": [], + "bbox": [ + 96, + 205, + 250, + 323 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ffa40b98c0457b20a508f84e0b5265d1d54cc04b8c2ada738177f6cba764d2b3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 253, + 88, + 408, + 205 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/de0e5df3c32a3328d4385b9dc194742c7ea802d09efad95198e615648ce8eb28.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 253, + 205, + 406, + 321 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6d945039f1bfe7927f5a288c35cbc04b951f68f925ab12752b288e75bae9e60c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 408, + 88, + 562, + 205 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/181e26520d24adc5ba1d4f85ee3e7bd5a39758db9dbafcfe567d4eca78c28bb0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 408, + 205, + 560, + 321 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2b3248716472d496eb9403a39b8985df5349bf10405ecab2314fd28b70916bd2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 562, + 88, + 715, + 205 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/eb72422d1dbb7620540f324a29c940ada82c4654829d7c50086c528dcb5a767a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 562, + 205, + 715, + 321 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ba93afe185ddb684966bb1f880ab680e92bfae22bec54e97db321633c221d4b1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 717, + 88, + 867, + 205 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/293019a5b0140591e6aab307cdb110b75dd519fbace9cccbe663f8205fdeea7d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 717, + 205, + 867, + 321 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ec941bf00e2a0ec6ddf65e2dfeffba983900861c6516e6fbb33930e209a2b2cd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 96, + 368, + 269, + 474 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b72daa37ff7effa447c8aa374cd000eaaaf4cd30c2b556c9928796809f665595.jpg", + "image_caption": [ + "Figure 6. Statistical analysis of imbalance issues. The first and second columns show quality and quantity imbalance respectively." + ], + "image_footnote": [], + "bbox": [ + 96, + 476, + 271, + 563 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/fff6d3388249ba26e2ceaf88c50fd9d36aeef3a6d34eba834c5b81eb92f2ae74.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 295, + 368, + 439, + 474 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6118b619891aeb23f10a695a32464ce38b28c8b2f2a631bc65fe6abc4f5187dd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 295, + 478, + 442, + 563 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c6911e040344a6e266b391b463ecdaee753c19bc0278ebcee7054132b5edffb9.jpg", + "image_caption": [ + "Figure 7. Visualization of sampled dynamic priors." + ], + "image_footnote": [], + "bbox": [ + 96, + 603, + 447, + 636 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ent angles and different scales (absolute size). Results are shown in Fig. 6, which are from the models' last training epoch. Here we summarize two kinds of imbalance issues (quantity and quality imbalance) for RetinaNet: (1) The positive sample number assigned to each instance changes periodically w.r.t. its angle and scale, whereas objects with shapes (scale, angle) different from predefined priors will hold much fewer positive samples. (2) The predicted IoU changes periodically w.r.t. gt's scale while remaining invariant w.r.t. gt's angle. By contrast, DCFL remarkably reconciles the imbalance: (1) more positive samples are compensated to previously outlier angles and scales. (2) the samples' quality (predicted IoU) can also be improved and balanced across all angles and scales. The above results are the desired behavior of dynamic coarse-to-fine learning.", + "bbox": [ + 75, + 657, + 468, + 883 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Visualization. We visualize the predicted results and", + "bbox": [ + 96, + 885, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/cadc8fee4c085174fa29fdc367103df9d78c3d7fc985573149ddfbb727e23bbd.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodR3Det [60]S2A-Net [17]GA-RetinaNet [52]RetinaNet [30]DCFL
Params, GFLOPs42.0M, 337.338.6M, 197.937.4M, 206.936.5M, 217.336.1M, 157.8
", + "bbox": [ + 501, + 369, + 890, + 395 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 8. Comparison of params, GFLOPs with ${1024} \\times {1024}$ input.", + "bbox": [ + 500, + 398, + 890, + 412 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "positive samples in Fig. 5 and Fig. 7. We can see that the DCFL remarkably eliminates the False Negative and False Positive predictions, especially for the extreme-shaped oriented tiny objects. Fig. 7 shows that the proposed strategy is able to dynamically generate and sample priors that better fit the instance's main body, verifying the claims of dynamic modeling and mismatch alleviation in this work.", + "bbox": [ + 498, + 417, + 890, + 523 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Speed. We test the inference speed on DOTA-v2.0 val set with a single RTX3090 GPU, the FPS of the $\\mathrm{R}^3\\mathrm{Det}$ , $\\mathrm{S}^2\\mathrm{A}$ -Net, RetinaNet, and DCFL is 16.2, 18.9, 20.8, and 20.9. It indicates that our method is of high efficiency. Moreover, we provide the parameters and GLOPs in Tab. 8, where we can see that the DCFL is lighter.", + "bbox": [ + 498, + 523, + 890, + 614 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 623, + 617, + 638 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose a novel DCFL scheme for detecting oriented tiny objects. We identify that the mismatched feature prior and unbalanced positive samples are two obstacles hampering the label assignment for oriented tiny objects. To address these, we propose a dynamic prior to alleviate the mismatch issue and a coarse-to-fine assigner to mitigate the imbalance issue, where the prior, label assignment, and $gt$ representation are all reformulated in a dynamic manner. Extensive experiments and analyses show the convincing improvements brought by the DCFL.", + "bbox": [ + 496, + 648, + 890, + 800 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 500, + 814, + 658, + 830 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We thank the reviewers for their comments. This work was supported in parts by NSFC (62271355, 62271354) and the Fundamental Research Funds for the Central Universities (20420222kf1010).", + "bbox": [ + 498, + 839, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "7325", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Yancheng Bai, Yongqiang Zhang, Mingli Ding, and Bernard Ghanem. 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In International Conference on Learning Representations, 2021. 3" + ], + "bbox": [ + 501, + 92, + 890, + 375 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "7328", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Dynamic Coarse-To-Fine Learning for Oriented Tiny Object Detection/e9804a4f-6933-4148-ae33-ea1a17587f5f_model.json b/2023/Dynamic Coarse-To-Fine Learning for Oriented Tiny Object Detection/e9804a4f-6933-4148-ae33-ea1a17587f5f_model.json new file mode 100644 index 0000000000000000000000000000000000000000..bfdd0a07b36b02faf4fd081a822c1baa00706bca --- /dev/null +++ b/2023/Dynamic Coarse-To-Fine Learning for Oriented Tiny Object Detection/e9804a4f-6933-4148-ae33-ea1a17587f5f_model.json @@ -0,0 +1,2818 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.132, + 0.131, + 0.838, + 0.152 + ], + "angle": 0, + "content": "Dynamic Coarse-to-Fine Learning for Oriented Tiny Object Detection" + }, + { + "type": "text", + "bbox": [ + 0.123, + 0.18, + 0.844, + 0.234 + ], + "angle": 0, + "content": "Chang Xu\\(^{1}\\), Jian Ding\\(^{2}\\), Jinwang Wang\\(^{1}\\), Wen Yang\\(^{1*}\\), Huai Yu\\(^{1}\\), Lei Yu\\(^{1*}\\), Gui-Song Xia\\(^{2}\\) \n\\(^{1}\\) School of Electronic Information, Wuhan University \n\\(^{2}\\) School of Computer Science, Wuhan University" + }, + { + "type": "text", + "bbox": [ + 0.147, + 0.237, + 0.816, + 0.252 + ], + "angle": 0, + "content": "{xuchangeis, jian.ding, jwwangchn, yangwen, yuhuai, ly.wd, guisong.xia}@whu.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.287, + 0.312, + 0.302 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.32, + 0.471, + 0.665 + ], + "angle": 0, + "content": "Detecting arbitrarily oriented tiny objects poses intense challenges to existing detectors, especially for label assignment. Despite the exploration of adaptive label assignment in recent oriented object detectors, the extreme geometry shape and limited feature of oriented tiny objects still induce severe mismatch and imbalance issues. Specifically, the position prior, positive sample feature, and instance are mismatched, and the learning of extreme-shaped objects is biased and unbalanced due to little proper feature supervision. To tackle these issues, we propose a dynamic prior along with the coarse-to-fine assigner, dubbed DCFL. For one thing, we model the prior, label assignment, and object representation all in a dynamic manner to alleviate the mismatch issue. For another, we leverage the coarse prior matching and finer posterior constraint to dynamically assign labels, providing appropriate and relatively balanced supervision for diverse instances. Extensive experiments on six datasets show substantial improvements to the baseline. Notably, we obtain the state-of-the-art performance for one-stage detectors on the DOTA-v1.5, DOTA-v2.0, and DIOR-R datasets under single-scale training and testing. Codes are available at https://github.com/Chasel-Tsui/mmrotate-dcfl." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.698, + 0.208, + 0.713 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.724, + 0.469, + 0.875 + ], + "angle": 0, + "content": "The oriented bounding box is a finer representation for object detection since the object's background region is greatly eradicated by introducing the rotation angle [55]. This advantage is pronounced in aerial images, where objects are in arbitrary orientations, resulting in the prosperity of corresponding object detection datasets [7, 11, 35, 55] and customized oriented object detectors [10, 17, 18, 60, 62]. Nevertheless, one ignorable fact is that there exist numerous tiny objects in aerial images. When oriented objects are tiny-sized, the challenges posed to existing object detec" + }, + { + "type": "image", + "bbox": [ + 0.51, + 0.286, + 0.685, + 0.461 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.709, + 0.287, + 0.884, + 0.461 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.474, + 0.892, + 0.587 + ], + "angle": 0, + "content": "Figure 1. Comparisons of different learning paradigms for oriented object detection. \\( \\mathbf{M}^* \\) means the matching function. Each box in the \\( 2^{nd} \\) row denotes a prior location. The \\( 3^{rd} \\) row are predictions of the RetinaNet and DCFL, where green, blue, and red boxes denote true positive, false positive, and false negative predictions. (a) RetinaNet, FCOS, and Rotated RPN statically assign labels between fixed priors and fixed gts. (b) Our proposed DCFL dynamically updates priors and gts, and dynamically assigns labels." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.891, + 0.658 + ], + "angle": 0, + "content": "tors are quite remarkable. Especially, the extreme geometry characteristics of oriented tiny objects hamper the accurate label assignment." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Label assignment is a fundamental and crucial process in object detection [68], in which priors (box for anchor-based [30] and point for anchor-free detectors [50]) need to be assigned with appropriate labels to supervise the network training. In fact, there have been some works that lay a foundation for the effective label assignment of oriented objects, as shown in Fig. 1. Early works additionally preset anchors of different angles (e.g. Rotated RPN [36]) or refine high-quality anchors (e.g. \\(\\mathrm{S}^2\\mathrm{A}\\) -Net [17]) based on the generic object detector, then a static rule (e.g. MaxIoU strategy [44]) is used to separate positive and negative (pos/neg) training samples. The derived prior boxes can thus cover more ground truth (gt) boxes and a considerable accuracy improvement can be expected. However, the static assignment cannot adaptively divide pos/neg samples according to the gt's shape and filter out low-quality samples, usually" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.228, + 0.9 + ], + "angle": 0, + "content": "*Corresponding Authors" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7318" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.094, + 0.466, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.234, + 0.472, + 0.292 + ], + "angle": 0, + "content": "Figure 2. The mismatch and imbalance issues. Each point in the left image denotes a prior location. The number in the pie-shaped bar chart denotes the mean number of positive samples assigned to each instance in a specific angle range." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.321, + 0.32, + 0.336 + ], + "angle": 0, + "content": "leading to sub-optimal performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.338, + 0.469, + 0.445 + ], + "angle": 0, + "content": "Recently, the exploration of adaptive label assignment [68] brings new insight to the community. For oriented object detection, DAL [38] defines a prediction-aware matching degree and utilizes it to reweight anchors, achieving dynamic sample learning. Besides, several studies [21,23,26] incorporate the shape information into detectors and propose shape-aware sampling and measurement." + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.447, + 0.47, + 0.822 + ], + "angle": 0, + "content": "Despite the progress, the arbitrary orientation and extreme size of oriented tiny objects still pose a dilemma to the detector. As shown in Fig. 2, the mismatch and imbalance issues are particularly pronounced. For one thing, there is a mutual mismatch issue between the position prior, feature, and instance. Although some adaptive label assignment schemes may explore a better pos/neg division of the prior boxes or points, the sampled feature location behind the prior is still fixed and the derived prior is still static and uniformly located, most priors deviate from the tiny object's main body. The prior and feature themselves cannot well-match the extreme shapes of oriented tiny objects, no matter how we divide pos/neg samples. For another, the existing detectors tend to introduce bias and imbalance for oriented and tiny objects. More precisely, for anchor-based detectors, gt with shapes different from anchor boxes will yield low IoU [38, 59], leading to the lack of positive samples. In Fig. 2, we calculate the mean number of positive samples assigned to different gts with the RetinaNet and observe that there is an extreme lack of positive samples for gts with angles and scales far from predefined anchors. For anchor-free detectors, the static prior and its fixed stride limit the upper number of high-quality positive samples. Tiny objects only cover a limited number of feature points, and most of these points are away from the object's main body." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.903 + ], + "angle": 0, + "content": "This motivates us to design a more dynamic and balanced learning pipeline for oriented tiny object detection. As shown in Fig. 1, we alleviate the mismatch issue by reformulating the prior, label assignment, and \\( gt \\) representation all in a dynamic manner, which can be updated by" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.137 + ], + "angle": 0, + "content": "the Deep Neural Network (DNN). Simultaneously, we dynamically and progressively assign labels in a coarse-to-fine manner to seek balanced supervision for various instances." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.138, + 0.893, + 0.456 + ], + "angle": 0, + "content": "Specifically, we introduce a dynamic Prior Capturing Block (PCB) to learn the prior, which adaptively adjusts the prior location while retaining the physical meaning of prior [54]. The PCB is inspired by the paradigm of learnable proposals in the DETR [4] and Sparse R-CNN [48] which naturally avoids the mismatch issue between the predefined prior and feature. Compared to this paradigm, we introduce its flexibility for prior updates while keeping the fast-convergence ability of dense detectors [32, 54]. Based on the dynamic prior, we then select Cross-FPN-layer Coarse Positive Sample (CPS) candidates for further label assignment, and the CPS is realized by the Generalized Jensen-Shannon Divergence [39] (GJSD) between the \\( gt \\) and the dynamic prior. The GJSD is able to enlarge the CPS to the object's nearby spatial locations and adjacent FPN layers, ensuring more candidates for extreme-shaped objects. After obtaining the CPS, we re-rank these candidates with predictions (posterior) and represent the \\( gt \\) with a finer Dynamic Gaussian Mixture Model (DGMM), filtering out low-quality samples. All designs are incorporated into an end-to-end one-stage detector without additional branches." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.457, + 0.895, + 0.639 + ], + "angle": 0, + "content": "In short, our contributions are listed as follows: (1) We identify that there exist severe mismatch and imbalance issues in the current learning pipeline for oriented tiny object detection. (2) We design a Dynamic Coarse-to-Fine Learning (DCFL) scheme for oriented tiny object detection, which is the first to model the prior, label assignment, and \\( gt \\) representation all in a dynamic manner. In the DCFL, we propose to use the GJSD to construct Coarse Positive Samples (CPS) and represent objects with a finer Dynamic Gaussian Mixture Model (DGMM), obtaining coarse-to-fine label assignment. (3) Extensive experiments on six datasets show promising results." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.654, + 0.642, + 0.67 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.68, + 0.74, + 0.696 + ], + "angle": 0, + "content": "2.1. Oriented Object Detection" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Prior for Oriented Objects. Anchor, as a classic design in generic object detectors (e.g. Faster R-CNN [44], RetinaNet [30]), has facilitated object detection for a long time. Similarly, oriented object detection also benefits from the anchor design. Initially, rotated RPN [36] extends the RPN to the field of oriented object detection by tiling 54 anchors each location with preset angles and scales. Indeed, enumerating potential \\(gt\\) shapes can notably improve the recall, apart from the sacks of additional computational cost. RoI Transformer [10] utilizes horizontal anchors and transforms the RPN-generated horizontal proposals to oriented proposals, reducing the number of rotated anchors. To save computation, the Oriented R-CNN [56] introduces an ori" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7319" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.198 + ], + "angle": 0, + "content": "ented RPN that directly predicts oriented proposals based on horizontal anchors. Recently, one-stage oriented object detectors gradually emerged, including anchor-based detectors [17, 60] with box prior and anchor-free detectors [26, 28] with point prior. Most of them retain the fixed prior design, except for the \\(\\mathrm{S}^2\\mathrm{A}\\)-Net [17] which proposes to generate high-quality anchors." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.199, + 0.471, + 0.41 + ], + "angle": 0, + "content": "Label Assignment. ATSS [68] reveals that label assignment plays a pivotal role in the detectors' performance [14,24,37]. In the field of oriented object detection, DAL [38] observes inconsistency between the input prior IoU and the output predicted IoU, then defines a matching degree as the soft label that dynamically reweights anchors. Recently, SASM [21] introduces a shape-adaptive sample selection and measurement strategy to improve detection performance. Similarly, GGHL [23] proposes to fit the main body of the instance by a single 2-D Gaussian heatmap, then it divides and reweights samples in a dynamic manner. In addition, Oriented Reppoints [26] improves the RepPoints [65] by assessing the quality of points for more effective label assignment." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.422, + 0.283, + 0.437 + ], + "angle": 0, + "content": "2.2. Tiny Object Detection" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.446, + 0.469, + 0.611 + ], + "angle": 0, + "content": "Multi-scale Learning. Basically, one can use a multi-resolution image pyramid to obtain multi-scale learning. However, the vanilla image pyramid will bring much computation cost. Thus, some works [29, 33, 34, 42, 49, 69] reduce computation with the efficient Feature Pyramid Network (FPN). Unlike the FPN, TridentNet [27] introduces multi-branch detection heads of various receptive fields for multi-scale prediction. Moreover, one can normalize the scale of objects for scale-invariant object detection, for example, SNIP [46] and SNIPER [47] resize images and train objects within a certain scale range." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.613, + 0.469, + 0.734 + ], + "angle": 0, + "content": "Label Assignment. Tiny objects usually have low IoU with anchors or cover a limited number of feature points, thus suffering from the lack of positive samples. ATSS [68] slightly reconciles the number of positive samples for objects of different scales. NWD [57] designs a new metric to replace IoU, which can sample more positive samples for tiny objects. Recently, the RFLA [58] utilizes outliers to detect tiny objects for scale-balanced learning." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.469, + 0.869 + ], + "angle": 0, + "content": "Context Information. Tiny object lacks discriminative features, but objects are closely related to the surrounding context. Therefore, we can leverage the context information to enhance small object detection. Muti-Region CNN (MRCNN) [15] and Inside-Outside Network (ION) [3] are two representative works that exploit local and global context information. Recently, the Relation Network [22] and transformer-based detectors [4, 54, 72] reason about the association between instances via the attention mechanism." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Feature Enhancement. The feature representation of small objects can be enhanced by super-resolution or GAN." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.168 + ], + "angle": 0, + "content": "PGAN [25] first applies GAN to small object detection. Besides, Bai et al. [1] introduce the MT-GAN which trains an image-level super-resolution model to improve the RoI features of small objects. In addition, there are some other methods based on super-resolution including [2,8,40,43]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.168, + 0.892, + 0.273 + ], + "angle": 0, + "content": "By contrast, our method simultaneously handles the prior mismatch and unbalanced learning via dynamically modeling the prior, label assignment, and \\( gt \\) representation. Meanwhile, unlike the two-stage RoI-Transformer [10] or one-stage S²A-Net [17], we embed the dynamic prior inside the end-to-end one-stage detector without introducing any auxiliary branch." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.285, + 0.59, + 0.3 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.308, + 0.892, + 0.4 + ], + "angle": 0, + "content": "Overview. Given a set of dense prior \\( P \\in \\mathbb{R}^{W \\times H \\times C} \\) (\\( W \\times H \\) is the feature map size, \\( C \\) is the shape information number, each feature point has one prior for simplicity), object detectors remap the set \\( P \\) into final detection results \\( D \\) through the Deep Neural Network (DNN), which can be simplified as:" + }, + { + "type": "equation", + "bbox": [ + 0.638, + 0.4, + 0.891, + 0.416 + ], + "angle": 0, + "content": "\\[\nD = \\mathrm {D N N} _ {h} (P), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.421, + 0.892, + 0.481 + ], + "angle": 0, + "content": "where \\(\\mathrm{DNN}_h\\) denotes the detection head. Detection results \\(D\\) contain two parts: classification scores \\(D_{cls} \\in \\mathbb{R}^{W \\times H \\times A}\\) (\\(A\\) is the class number) and box locations \\(D_{reg} \\in \\mathbb{R}^{W \\times H \\times B}\\) (\\(B\\) is the box parameter number)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.481, + 0.892, + 0.557 + ], + "angle": 0, + "content": "To train the \\(\\mathrm{DNN}_h\\), we need to find a proper matching between the prior set \\(P\\) and the \\(gt\\) set \\(GT\\), and assign pos/neg labels to \\(P\\) to supervise the network learning. For static assigners (e.g. RetinaNet [30]), the set of pos labels \\(G\\) can be obtained via hand-crafted matching function \\(\\mathcal{M}_s\\):" + }, + { + "type": "equation", + "bbox": [ + 0.633, + 0.565, + 0.891, + 0.58 + ], + "angle": 0, + "content": "\\[\nG = \\mathcal {M} _ {s} (P, G T). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.588, + 0.891, + 0.648 + ], + "angle": 0, + "content": "For dynamic assigners [14, 24, 38], they tend to simultaneously leverage the prior information \\(P\\) and posterior information (predictions) \\(D\\), and then apply a prediction-aware mapping \\(\\mathcal{M}_d\\) to get the set \\(G\\):" + }, + { + "type": "equation", + "bbox": [ + 0.622, + 0.656, + 0.891, + 0.672 + ], + "angle": 0, + "content": "\\[\nG = \\mathcal {M} _ {d} (P, D, G T). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.68, + 0.891, + 0.71 + ], + "angle": 0, + "content": "After the pos/neg label separation, the loss function can be summarized into two parts:" + }, + { + "type": "equation", + "bbox": [ + 0.544, + 0.717, + 0.891, + 0.761 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\sum_ {i = 1} ^ {N _ {p o s}} \\mathcal {L} _ {p o s} \\left(D _ {i}, G _ {i}\\right) + \\sum_ {j = 1} ^ {N _ {n e g}} \\mathcal {L} _ {n e g} \\left(D _ {j}, y _ {j}\\right), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.768, + 0.89, + 0.797 + ], + "angle": 0, + "content": "where \\(N_{pos}\\), \\(N_{neg}\\) are the number of positive and negative samples respectively, \\(y_{j}\\) denotes the negative label." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.798, + 0.892, + 0.858 + ], + "angle": 0, + "content": "While in this work, we model the prior, label assignment, and \\( gt \\) representation all in a dynamic manner to alleviate the mismatch issue. To begin with, the dynamic prior is reformulated to (\\~ denotes the dynamic item):" + }, + { + "type": "equation", + "bbox": [ + 0.604, + 0.865, + 0.891, + 0.903 + ], + "angle": 0, + "content": "\\[\n\\tilde {D} = \\mathrm {D N N} _ {h} (\\underbrace {\\mathrm {D N N} _ {p} (P)} _ {\\text {D y n a m i c P r i o r} \\tilde {P}}), \\tag {5}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7320" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.138 + ], + "angle": 0, + "content": "\\(\\mathrm{DNN}_p\\) is a learnable block incorporated within the detection head to update the prior. Then, the matching function is reformulated to a coarse-to-fine paradigm:" + }, + { + "type": "equation", + "bbox": [ + 0.173, + 0.148, + 0.469, + 0.166 + ], + "angle": 0, + "content": "\\[\n\\tilde {G} = \\mathcal {M} _ {d} \\left(\\mathcal {M} _ {s} (\\tilde {P}, G T), \\tilde {G T}\\right), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.177, + 0.469, + 0.221 + ], + "angle": 0, + "content": "the \\(\\tilde{G}T\\) is a finer representation of an object with the Dynamic Gaussian Mixture Model (DGMM). In a nutshell, our final loss is modeled as:" + }, + { + "type": "equation", + "bbox": [ + 0.122, + 0.222, + 0.469, + 0.267 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\sum_ {i = 1} ^ {\\tilde {N} _ {p o s}} \\mathcal {L} _ {p o s} \\left(\\tilde {D} _ {i}, \\tilde {G} _ {i}\\right) + \\sum_ {j = 1} ^ {\\tilde {N} _ {n e g}} \\mathcal {L} _ {n e g} \\left(\\tilde {D} _ {j}, y _ {j}\\right). \\tag {7}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.276, + 0.228, + 0.292 + ], + "angle": 0, + "content": "3.1. Dynamic Prior" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.3, + 0.469, + 0.51 + ], + "angle": 0, + "content": "Inspired by the purely learnable paradigm of proposal updation in the DETR [4] and Sparse R-CNN [48], we propose to introduce more flexibility into the prior to mitigate the mismatch issue. Moreover, we retain the physical meaning of prior where each individual prior stands for a feature point, inheriting the fast convergence ability of dense detectors. The structure of the proposed Prior Capturing Block (PCB) is shown in Fig. 3, in which a dilated convolution is deployed to take the surrounding information into account, and then the Deformable Convolution Network (DCN) [9] is leveraged to capture the dynamic prior. Besides, we utilize the learned offsets from the regression branch to guide the feature extraction of the classification branch, leading to better alignment between the two tasks." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.511, + 0.469, + 0.601 + ], + "angle": 0, + "content": "The dynamic prior capturing process is as follows. First of all, we initialize each prior location \\(\\mathbf{p}(x,y)\\) by each feature point's spatial location s (which is remapped to the image). In each iteration, we forward the network to capture the offset sets of each prior location \\(\\Delta \\mathbf{o}\\). Hence, the prior spatial location can be updated by:" + }, + { + "type": "equation", + "bbox": [ + 0.19, + 0.602, + 0.469, + 0.64 + ], + "angle": 0, + "content": "\\[\n\\tilde {\\mathbf {s}} = \\mathbf {s} + s t \\sum_ {i = 1} ^ {n} \\Delta \\mathbf {o} _ {i} / 2 n, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.64, + 0.469, + 0.761 + ], + "angle": 0, + "content": "where \\(st\\) is the feature map's stride, \\(n\\) is the number of offsets. Finally, we utilize the 2-D Gaussian distribution \\(\\mathcal{N}_p(\\boldsymbol{\\mu}_p, \\boldsymbol{\\Sigma}_p)\\) which is demonstrated conducive to small objects [58,61] and oriented objects [61,63] to fit the prior spatial location. Concretely, the dynamic \\(\\tilde{\\mathbf{s}}\\) serves as the Gaussian's mean vector \\(\\boldsymbol{\\mu}_p\\). We preset one prior which is square-shaped \\((w, h, \\theta)\\) as that in RetinaNet [30] on each feature point, then compute the co-variance matrix \\(\\boldsymbol{\\Sigma}_p\\) by [64]:" + }, + { + "type": "equation", + "bbox": [ + 0.096, + 0.772, + 0.469, + 0.81 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\Sigma} _ {p} = \\left[ \\begin{array}{c c} \\cos \\theta & - \\sin \\theta \\\\ \\sin \\theta & \\cos \\theta \\end{array} \\right] \\left[ \\begin{array}{c c} \\frac {w ^ {2}}{4} & 0 \\\\ 0 & \\frac {h ^ {2}}{4} \\end{array} \\right] \\left[ \\begin{array}{c c} \\cos \\theta & \\sin \\theta \\\\ - \\sin \\theta & \\cos \\theta \\end{array} \\right]. \\tag {9}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.817, + 0.292, + 0.833 + ], + "angle": 0, + "content": "3.2. Coarse Prior Matching" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.841, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Given a set of prior, one basic assignment rule is to specify a range of candidate true prediction samples for a specific \\( gt \\). Some adaptive strategies restrict the candidates of a given \\( gt \\) inside a single FPN layer [14,23,68], while some" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.152 + ], + "angle": 0, + "content": "works release all layers as candidates [67, 71]. However, for oriented tiny objects, the former strict heuristic rule may lead to a sub-optimal layer selection and the latter loose one will induce the slow convergence issue [32]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.152, + 0.892, + 0.272 + ], + "angle": 0, + "content": "Hence, we propose Cross-FPN-layer Coarse Positive Sample (CPS) candidates, which narrows down the sample range compared to the all-FPN-layer manner while discarding the single-layer heuristic. In the CPS, we slightly expand the range of candidates to the \\( gt \\)'s nearby spatial location and adjacent FPN layers, which warrants relatively diverse and sufficient candidates compared to the single-layer heuristic and alleviates the quantity imbalance issue." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.273, + 0.892, + 0.437 + ], + "angle": 0, + "content": "Specifically, the similarity measurement in constructing the CPS is realized with the Jensen-Shannon Divergence (JSD) [13], which inherits the scale invariance property of the Kullback-Leibler Divergence (KLD) [63] and can measure the \\( gt \\)'s similarity with nearby non-overlapping priors [58, 63]. Moreover, it conquers KLD's drawback of asymmetry. However, the closed-form solution of the JSD between Gaussian distributions is unavailable [39], thus, we utilize the Generalized Jensen-Shannon Divergence (GJSD) [39] which yields a closed-form solution, as the substitute." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.439, + 0.892, + 0.471 + ], + "angle": 0, + "content": "For example, the GJSD between two Gaussian distributions \\(\\mathcal{N}_p(\\boldsymbol{\\mu}_p, \\boldsymbol{\\Sigma}_p)\\) and \\(\\mathcal{N}_g(\\boldsymbol{\\mu}_g, \\boldsymbol{\\Sigma}_g)\\) is defined by:" + }, + { + "type": "equation", + "bbox": [ + 0.501, + 0.482, + 0.891, + 0.512 + ], + "angle": 0, + "content": "\\[\n\\operatorname {G J S D} \\left(\\mathcal {N} _ {p}, \\mathcal {N} _ {g}\\right) = (1 - \\alpha) \\mathrm {K L} \\left(\\mathcal {N} _ {\\alpha}, \\mathcal {N} _ {p}\\right) + \\alpha \\mathrm {K L} \\left(\\mathcal {N} _ {\\alpha}, \\mathcal {N} _ {g}\\right), \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.513, + 0.888, + 0.529 + ], + "angle": 0, + "content": "where KL denotes the KLD, and \\(\\mathcal{N}_{\\alpha}(\\pmb{\\mu}_{\\alpha}, \\pmb{\\Sigma}_{\\alpha})\\) is given by:" + }, + { + "type": "equation", + "bbox": [ + 0.522, + 0.54, + 0.891, + 0.561 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\Sigma} _ {\\alpha} = \\left(\\boldsymbol {\\Sigma} _ {p} \\boldsymbol {\\Sigma} _ {g}\\right) _ {\\alpha} ^ {\\boldsymbol {\\Sigma}} = \\left((1 - \\alpha) \\boldsymbol {\\Sigma} _ {p} ^ {- 1} + \\alpha \\boldsymbol {\\Sigma} _ {g} ^ {- 1}\\right) ^ {- 1}, \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.572, + 0.529, + 0.584 + ], + "angle": 0, + "content": "and" + }, + { + "type": "equation", + "bbox": [ + 0.558, + 0.581, + 0.835, + 0.623 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\boldsymbol {\\mu} _ {\\alpha} = \\left(\\boldsymbol {\\mu} _ {p} \\boldsymbol {\\mu} _ {g}\\right) _ {\\alpha} ^ {\\boldsymbol {\\mu}} \\\\ = \\boldsymbol {\\Sigma} _ {\\alpha} \\left((1 - \\alpha) \\boldsymbol {\\Sigma} _ {p} ^ {- 1} \\boldsymbol {\\mu} _ {p} + \\alpha \\boldsymbol {\\Sigma} _ {g} ^ {- 1} \\boldsymbol {\\mu} _ {g}\\right). \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.862, + 0.595, + 0.89, + 0.607 + ], + "angle": 0, + "content": "(12)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.627, + 0.891, + 0.672 + ], + "angle": 0, + "content": "Note that \\(\\alpha\\) is a parameter that controls the weight of two distributions [39] in similarity measurement. In our work, the \\(\\mathcal{N}_p\\) and \\(\\mathcal{N}_q\\) contribute equally, thus \\(\\alpha\\) is set to 0.5." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.672, + 0.892, + 0.793 + ], + "angle": 0, + "content": "Ultimately, for each \\(gt\\), we select \\(K\\) priors which hold the top \\(K\\) GJSD score with this \\(gt\\) as the Coarse Positive Samples (CPS) and regard the remaining priors as negative samples, this coarse matching serves as the \\(\\mathcal{M}_s\\) in Eq. 6. The ranking manner works together with the GJSD measurement to construct the Cross-FPN-layer CPS, eliminating the imbalance issue raised by the MaxIoU matching for outlier angles and scales, which will be analyzed in Sec. 5." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.802, + 0.805, + 0.818 + ], + "angle": 0, + "content": "3.3. Finer Dynamic Posterior Matching" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Based on Coarse Positive Sample (CPS) candidates, we design a dynamic posterior (prediction) matching rule \\(\\mathcal{M}_d\\) to filter out low-quality samples. The \\(\\mathcal{M}_d\\) consists of two key components, namely a posterior re-ranking strategy and a Dynamic Gaussian Mixture Model (DGMM) constraint." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "7321" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.079, + 0.089, + 0.487, + 0.252 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.491, + 0.089, + 0.885, + 0.252 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.13, + 0.265, + 0.838, + 0.28 + ], + "angle": 0, + "content": "Figure 3. The process of feature extraction and dynamic coarse-to-fine learning. PCB denotes the prior capturing block." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.306, + 0.471, + 0.397 + ], + "angle": 0, + "content": "We re-rank the sample candidates in the CPS according to their predicted scores. In other words, we further refine the positive samples by their Possibility of becoming True predictions \\((PT)\\) [14], which is a linear combination of the predicted classification score and the location score with the \\(gt\\). We define the \\(PT\\) of the \\(i^{th}\\) sample \\(D_{i}\\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.149, + 0.404, + 0.47, + 0.434 + ], + "angle": 0, + "content": "\\[\nP T _ {i} = \\frac {1}{2} C l s (D _ {i}) + \\frac {1}{2} I o U (D _ {i}, g t _ {i}), \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.442, + 0.47, + 0.501 + ], + "angle": 0, + "content": "where \\( Cls \\) is the predicted classification confidence and \\( IoU \\) is the rotated IoU between the predicted location and its corresponding \\( gt \\) location. We select candidates with \\( Q \\) highest \\( PT \\) as Medium Positive Sample (MPS) candidates." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.501, + 0.47, + 0.685 + ], + "angle": 0, + "content": "Following this, we filter out those samples too far away from the \\( gts \\) with a finer instance representation, getting the Finer Positive Samples (FPS). Different from previous works which utilize the center probability map [53] or the single-Gaussian [23,64] for instance representation, we represent the instance by a finer DGMM. It consists of two components: one is centered on the geometry center and the other is centered on the semantic center of the object. Concretely, for a specific instance \\( gt_{i} \\), the geometry center \\( (cx_{i}, cy_{i}) \\) serves as the mean vector \\( \\mu_{i,1} \\) of the first Gaussian, and the semantic center \\( (sx_{i}, sy_{i}) \\), which is deduced by averaging the location of the samples in the MPS, serves as the \\( \\mu_{i,2} \\). That is to say, we parameterize the instance as:" + }, + { + "type": "equation", + "bbox": [ + 0.085, + 0.687, + 0.469, + 0.734 + ], + "angle": 0, + "content": "\\[\nD G M M _ {i} (s | x, y) = \\sum_ {m = 1} ^ {2} w _ {i, m} \\sqrt {2 \\pi | \\boldsymbol {\\Sigma} _ {i , m} |} \\mathcal {N} _ {i, m} \\left(\\boldsymbol {\\mu} _ {i, m}, \\boldsymbol {\\Sigma} _ {i, m}\\right), \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.47, + 0.811 + ], + "angle": 0, + "content": "where \\(w_{i,m}\\) is the weight of each Gaussian with a summation of 1, \\(\\Sigma_{i,m}\\) equals to the \\(gt\\)'s \\(\\Sigma_g\\). Each sample in MPS has a DGMM score \\(DGMM(s|MPS)\\), we set negative masks to samples which have \\(DGMM(s|MPS) < e^{-g}\\) with any \\(gt\\), the \\(g\\) is adjustable." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.823, + 0.21, + 0.839 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.848, + 0.18, + 0.862 + ], + "angle": 0, + "content": "4.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Experiments are done on six datasets, i.e., DOTA-v1.0 [55]/v1.5/v2.0 [11], DIOR-R [7], VisDrone [12], and" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.305, + 0.892, + 0.427 + ], + "angle": 0, + "content": "MS COCO [31]. In ablation studies and analyses, we choose the large-scale DOTA-v2.0 train set for training and val set for evaluation, which contains a large number of tiny objects. To compare with other methods, we use trainval sets of DOTA-v1.0, DOTA-v1.5, DOTA-v2.0, and DIOR-R for training and their test sets for testing, we choose the VisDrone2019, MS COCO train set, val set for training and testing." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.436, + 0.719, + 0.453 + ], + "angle": 0, + "content": "4.2. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.459, + 0.892, + 0.626 + ], + "angle": 0, + "content": "We conduct all the experiments on the computer with a single NVIDIA RTX 3090 GPU, and the batch size is set to 4. Models are built based on MMDetection [6] and MMRotate [70] with PyTorch [41]. The ImageNet [45] pre-trained models are used as the backbone. The Stochastic Gradient Descent (SGD) optimizer is used for training with a learning rate of 0.005, a momentum of 0.9, and a weight decay of 0.0001. The ResNet-50 [20] with FPN [29] is the default backbone if not specified. We use Focal loss [30] for classification and IoU loss [66] for regression. We only use random flipping as data augmentation for all experiments." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.626, + 0.892, + 0.717 + ], + "angle": 0, + "content": "For experiments on the DOTA-v1.0 and DOTA-v2.0, we follow the official settings of the DOTA-v2.0 benchmark [11], i.e., we crop images into patches of \\(1024 \\times 1024\\) with overlaps of 200 and train the model for 12 epochs. For DOTA-v2.0, we reproduce one-stage state-of-the-art methods [17,21,26,38,50,60,63,68] with the same settings." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.717, + 0.892, + 0.822 + ], + "angle": 0, + "content": "For experiments on other datasets, we set the input size to \\(1024 \\times 1024\\) (overlap 200), \\(800 \\times 800\\), \\(1333 \\times 800\\), and \\(1333 \\times 800\\) for DOTA-v1.5, DIOR-R, VisDrone, and COCO respectively. We train the models for 40, 40, 12, and 12 epochs on the DOTA-v1.5, DIOR-R, COCO, and VisDrone as previous works do [16, 26]. The above settings are fixed unless otherwise specified." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.832, + 0.64, + 0.847 + ], + "angle": 0, + "content": "4.3. Main Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Results on DOTA series. As shown in Tab. 1, our proposed method achieves the state-of-the-art performance of \\(57.66\\%\\) mAP on the DOTA-v2.0 OBB benchmark un" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7322" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.081, + 0.09, + 0.894, + 0.359 + ], + "angle": 0, + "content": "
MethodBackbonePlaneBDBridgeGTFSVLVShipTCBCSTSBFRAHarborSPHCCCAirHelimAP
multi-stage:
FR OBB [44]R5071.6147.2039.2858.7035.5548.8851.5178.9758.3658.5536.1151.7343.5755.3357.073.5152.942.7947.31
FR OBB + DpR5071.5549.7440.3460.4040.7450.6756.5879.0358.2258.2434.7351.9544.3355.1053.147.2159.536.3848.77
MR [19]R5076.2049.9141.6160.0041.0850.7756.2478.0155.8557.4836.6251.6747.3955.7959.063.6460.268.9549.47
HTC* [5]R5077.6947.2541.1560.7141.7752.7958.8778.7455.2258.4938.5752.4849.5856.1854.094.2066.3811.9250.34
RT [10]R5071.8148.3945.8864.0242.0954.3959.9282.7063.2958.7141.0452.8253.3256.1857.9425.7163.728.7052.81
Oriented R-CNN [56]R5077.9550.2946.7365.2442.6154.5660.0279.0861.6959.4242.2656.8951.1156.1659.3325.8160.679.1753.28
one-stage:
DAL [38]R5071.2338.3638.6045.2435.4243.7556.0470.8450.8756.6320.2846.5333.4947.2912.150.8125.770.0038.52
SASM [21]R5070.3040.6237.0159.0340.2145.4644.6078.5849.3460.7329.8946.5742.9548.3128.131.8276.370.7444.53
RetinaNet-O [30]R5070.6347.2639.1255.0238.1040.5247.1677.7456.8652.1237.2251.7544.1553.1951.066.5864.287.4546.68
\\( R^3Det w/ KLD [63] \\)R5075.4450.9541.1661.6141.1145.7649.6578.5254.9760.7942.0753.2043.0849.5534.0936.2668.650.0647.26
FCOS-O [51]R5074.8447.5340.8357.4143.8947.7255.6678.6157.8663.0038.0252.3841.9153.2440.227.1565.517.4248.51
Oriented Rep [26]R5073.0246.6842.3763.0547.0650.2858.6478.8457.1266.7735.2150.7648.7751.6234.236.1764.665.8748.95
ATSS-O [68]R5077.4649.5542.1262.6145.1548.4051.7078.4359.3362.6539.1852.4342.9253.9842.705.9167.0910.6849.57
\\( S^2A-Net [17] \\)R5077.8451.3143.7262.5947.5150.5857.8680.7359.1165.3236.4352.6045.3652.4640.120.0062.8111.1149.86
one-stage:
DCFLR5075.7149.4044.6963.2346.4851.5555.5079.3059.9665.3941.8654.4247.0355.7250.4911.7569.017.7551.57
\\( S^2A-Net w/ DCFL \\)R5074.7953.2545.8165.4646.4953.2358.1081.5160.1366.4243.2455.0950.5255.5854.535.2368.7313.0652.84
DCFL†R5078.3053.0344.2460.1748.5655.4258.6678.2960.8965.9343.5455.8253.3360.0054.7630.9074.0115.6055.08
DCFL†ReR10179.4955.9750.1561.5949.0055.3359.3181.1866.5260.0652.8756.7157.8358.1360.3535.6678.6513.0357.66
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.364, + 0.893, + 0.409 + ], + "angle": 0, + "content": "Table 1. Main results on the DOTA-v2.0 OBB Task. We follow the official class abbreviations as the DOTA-v2.0 benchmark [11]. \\(\\dagger\\) denotes training for 40 epochs. Note that this paper [63] reports \\(50.90\\%\\) mAP for \\(\\mathrm{R}^3\\mathrm{Det}\\) w/ KLD under 20 epochs, the ReR101 backbone is proposed by the ReDet [18]. The results in red and blue denote the best and second-best performance of each column." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.423, + 0.47, + 0.476 + ], + "angle": 0, + "content": "
MethodCFA [16]RetinaNet-O [30]R3Det [60]Oriented Rep [26]ATSS-O [68]
mAP69.6369.7970.1871.9472.29
Method KLD [63]S2A-Net [17]GGHL [23](3x)DCFLDCFL(3x)
mAP72.7673.9173.9874.2675.35
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.48, + 0.47, + 0.523 + ], + "angle": 0, + "content": "Table 2. Comparison with one-stage detectors on the DOTA-v1.0 OBB Task. All results are based on the MMRotate [70] with 12 epochs except for GGHL [23]. 3x means training for 36 epochs." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.53, + 0.47, + 0.619 + ], + "angle": 0, + "content": "
MethodBackboneSVShipSTmAP
RetinaNet-O [30]R5044.5373.3159.9659.16
FR OBB [19]R5051.2879.3767.5062.00
CMR [19]R5051.6479.9967.5863.41
RT [10]R5052.0580.7268.2665.03
ReDet [18]ReR5052.3880.9268.6466.86
DCFLR5056.72 (+12.19)80.87 (+7.56)75.65 (+15.69)67.37 (+8.21)
DCFLReR10157.31 (+12.78)86.60 (+13.29)76.55 (+16.59)70.24 (+11.08)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.118, + 0.625, + 0.428, + 0.637 + ], + "angle": 0, + "content": "Table 3. Main results on the DOTA-v1.5 OBB Task." + }, + { + "type": "table", + "bbox": [ + 0.089, + 0.645, + 0.458, + 0.704 + ], + "angle": 0, + "content": "
MethodRetinaNet-O [30]FR-OBB [44]RT [10]AOPG [7]
mAP57.5559.5463.8764.41
MethodGGHL [23]Oriented Rep [26]DCFLDCFL (ReR101)
mAP66.4866.7166.8071.03
" + }, + { + "type": "table_caption", + "bbox": [ + 0.098, + 0.707, + 0.449, + 0.721 + ], + "angle": 0, + "content": "Table 4. Performance comparisons on the DIOR-R dataset." + }, + { + "type": "table", + "bbox": [ + 0.09, + 0.728, + 0.458, + 0.788 + ], + "angle": 0, + "content": "
MethodBackboneVEBRWM
RetinaNet-O [30]R5038.024.060.2
Oriented Rep [26]R5050.438.864.7
DCFLR5050.9 (+12.9)42.1 (+18.1)70.9 (+10.7)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.793, + 0.47, + 0.822 + ], + "angle": 0, + "content": "Table 5. Detection results of typical tiny objects on the DIOR-R dataset. VE, BR, and WM denote vehicle, bridge, and wind-mill." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.84, + 0.47, + 0.903 + ], + "angle": 0, + "content": "der single-scale training and testing. Besides, our model achieves \\(51.57\\%\\) mAP without bells and whistles, surpassing all one-stage object detectors tested. The results on the DOTA-v1.0 [55] and DOTA-v1.5 are listed in Tab. 2, Tab. 3." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.422, + 0.892, + 0.478 + ], + "angle": 0, + "content": "
DatasetVisDroneMS COCODOTA-v2.0 HBB
MethodRetinaNet [30]DCFLRetinaNetDCFLFCOS [58]DCFL
AP0.529.232.155.457.355.457.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.507, + 0.482, + 0.884, + 0.496 + ], + "angle": 0, + "content": "Table 6. Results of one-stage object detectors on HBB datasets." + }, + { + "type": "image", + "bbox": [ + 0.52, + 0.499, + 0.872, + 0.575 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.586, + 0.892, + 0.616 + ], + "angle": 0, + "content": "Figure 4. Different ways of constructing the CPS. Yellow and orange denote the possible regions of CPS and MPS respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.626, + 0.894, + 0.687 + ], + "angle": 0, + "content": "Results also indicate that our DCFL is very effective for detecting tiny oriented objects on the tested datasets, such as small vehicles, ships, and storage tanks, where a boost of about 10 points can be expected compared to the baseline." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.687, + 0.894, + 0.762 + ], + "angle": 0, + "content": "Results on DIOR-R. DIOR-R contains some tiny oriented objects, such as the vehicle, bridge, and windmill. The mAP and class-wise AP of tiny objects are in Tab. 4 and Tab. 5, we also achieve the state-of-the-art performance of \\(71.03\\%\\) mAP and notable improvements on tiny objects." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.762, + 0.894, + 0.839 + ], + "angle": 0, + "content": "Results on HBB Datasets. Moreover, we discard the angle to verify the versatility of the DCFL on the generic small object detection datasets VisDrone [12], MS COCO [31], and DOTA-v2.0 HBB [11]. In Tab. 6, our method gets a notable \\(\\mathrm{AP}_{0.5}\\) boost compared to the baseline." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.848, + 0.655, + 0.865 + ], + "angle": 0, + "content": "4.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.894, + 0.903 + ], + "angle": 0, + "content": "Effects of Individual Strategy. We check the effectiveness of each proposed strategy in the proposed method. In" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7323" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.119, + 0.078, + 0.38, + 0.163 + ], + "angle": 0, + "content": "
MethodCPSMPSDGMMmAP
baseline [30]51.70
DCFL✓✓53.41
✓✓57.20
✓✓✓59.15
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.116, + 0.165, + 0.379, + 0.201 + ], + "angle": 0, + "content": "(a) Individual effectiveness. CPS, MPS, and DGMM denote Coarse, Medium Sample Candidates and Dynamic Gaussian Mixture Model." + }, + { + "type": "table", + "bbox": [ + 0.396, + 0.079, + 0.642, + 0.163 + ], + "angle": 0, + "content": "
StrategyMeasurementmAP
All-FPN-layerGaussian50.12
Single-FPN-layerGaussian56.72
Cross-FPN-layerKLD [63]57.82
Cross-FPN-layerGWD [61]58.55
Cross-FPN-layerGJSD59.15
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.393, + 0.165, + 0.641, + 0.201 + ], + "angle": 0, + "content": "(b) Comparisons of different CPS. The FPN layer number varies for different strategies of getting the CPS." + }, + { + "type": "table", + "bbox": [ + 0.658, + 0.08, + 0.855, + 0.163 + ], + "angle": 0, + "content": "
DCNDilated ConvDPmAP
58.07
✓58.41
✓✓58.65
Separate✓✓58.71
Guiding✓✓59.15
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.655, + 0.165, + 0.854, + 0.201 + ], + "angle": 0, + "content": "(c) Effects of detailed designs in the PCB. DP denotes the dynamic prior. Guiding denotes reg guidescls." + }, + { + "type": "table", + "bbox": [ + 0.185, + 0.202, + 0.586, + 0.3 + ], + "angle": 0, + "content": "
K2420
Q20161281612108
mAP58.3158.1158.9559.0658.6658.7158.9258.28
K1612
Q12108610864
mAP59.1558.5758.9757.8458.7958.2557.0157.37
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.283, + 0.302, + 0.482, + 0.315 + ], + "angle": 0, + "content": "(d) Effects of parameters \\(K\\) and \\(Q\\)." + }, + { + "type": "table", + "bbox": [ + 0.601, + 0.202, + 0.791, + 0.3 + ], + "angle": 0, + "content": "
g1.21.0
mAP57.9158.20
g0.80.4
mAP59.1558.95
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.619, + 0.302, + 0.767, + 0.315 + ], + "angle": 0, + "content": "(e) Effects of parameter \\(g\\)" + }, + { + "type": "table_caption", + "bbox": [ + 0.13, + 0.327, + 0.838, + 0.341 + ], + "angle": 0, + "content": "Table 7. Ablations. We train on DOTA-v2.0 train set, test on val set, and report mAP under IoU threshold 0.5." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.357, + 0.469, + 0.508 + ], + "angle": 0, + "content": "all ablation experiments, we employ one prior for each feature point for fair comparisons. As seen in Tab. 7a, the baseline detector RetinaNet-OBB yields a result of \\(51.70\\%\\) mAP. When we gradually apply the posterior re-ranked MPS and DGMM into the detector based on the CPS, the mAP improves progressively, verifying each design's effectiveness. Note that the CPS cannot be independently used since the samples in it are too coarse to serve as the final positive samples. Nevertheless, we compare some different ways of constructing the CPS to verify its superiority." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.508, + 0.469, + 0.856 + ], + "angle": 0, + "content": "Comparisons of Different CPS. The design of the CPS matters in the training pipeline. We show several paradigms of designing the CPS as shown in Fig. 7b, including limiting the CPS for a specific \\( gt \\) within a single layer like FCOS [50], releasing all FPN layers as the CPS, like Objectbox [67]. We compare their performance in Tab. 7b. For fair comparisons, the number of samples in CPS is fixed at 16, and all other components are kept the same. For the Single-FPN-layer way, we group \\( gt \\) onto different layers according to the scale division strategy in FCOS, then assign labels within each layer. For the All-FPN-layer way, we do not group \\( gt \\) onto different layers, instead, we discard the prior scale information and directly measure the distance between Gaussian \\( gt \\) and prior points. The results are shown in Tab. 7b, we can observe that neither of the above two ways will yield the best performance. By contrast, the distribution distances (KLD, GWD, GJSD) are able to construct the Cross-FPN-layer CPS, where the candidates are extended to adjacent layers besides the main layer. We can also see the GJSD gets the best performance of \\( 59.15\\% \\) mAP, mainly resulting from its property of scale-invariance [39, 63], symmetry [39], and ability to measure non-overlapping boxes [39] compared to other counterparts." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Fixed Prior and Dynamic Prior. We conduct a finer group of ablation studies to verify the necessity of introducing the dynamic prior. As shown in Tab. 7c, if we disable the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.357, + 0.892, + 0.417 + ], + "angle": 0, + "content": "dynamic prior by fixing the location of samples, a slight performance drop will be introduced. Hence, the prior should be adjusted accordingly when leveraging the dynamic sampling strategy to better capture the shape of objects." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.419, + 0.893, + 0.614 + ], + "angle": 0, + "content": "Detailed Design in PCB. For the PCB, it is made up of a dilated convolution and a guiding DCN, we slightly enlarge the receptive field with a dilation rate of 3. After that, we take advantage of the DCN to generate dynamic priors in a guiding manner. As shown in Tab. 7c, we can observe that the DCN can bring an improvement of \\(0.34\\mathrm{mAP}\\) points and the dilated convolution can slightly enhance the mAP. We find that the application of the DCN [9] to the single regression branch will slightly deteriorate the accuracy (noted by Separate in Tab. 7c), which may cause mismatch issues between the two branches. Thus we utilize the offsets from the regression head to guide the offsets classification head for better alignment (noted by Guiding)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.616, + 0.892, + 0.782 + ], + "angle": 0, + "content": "Effects of Parameters. The introduced three parameters are robust in a certain range. From Tab. 7d, we can see that a combination of \\( K = 16 \\) and \\( Q = 12 \\) gets the best performance. In Tab. 7e, we verify the threshold \\( e^{-g} \\) in the DGMM, we empirically set \\( w_{i,1} \\) to 0.7, then a threshold of \\( g = 0.8 \\) yields the highest mAP. Although making the CPS/MPS/FPS coarser and stricter will weaken the performance, the mAP only waves marginally. In other words, the coarse-to-fine assignment manner somewhat warrants the parameter selection's robustness since multiple parameters can attenuate the effects of an under-tuned one." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.798, + 0.597, + 0.815 + ], + "angle": 0, + "content": "5. Analysis" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.825, + 0.891, + 0.854 + ], + "angle": 0, + "content": "For a clearer dissection of why the proposed scheme works, we perform more meticulous analyses as follows." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Reconciliation of imbalance problems. To delve into the imbalance issue, we calculate the mean predicted IoU and the mean positive sample number of \\( gt \\) holding differ" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7324" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.098, + 0.089, + 0.252, + 0.207 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.098, + 0.207, + 0.251, + 0.324 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.254, + 0.089, + 0.409, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.254, + 0.207, + 0.408, + 0.323 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.41, + 0.089, + 0.563, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.409, + 0.207, + 0.562, + 0.323 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.563, + 0.089, + 0.717, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.563, + 0.207, + 0.717, + 0.323 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.718, + 0.089, + 0.869, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.718, + 0.207, + 0.869, + 0.323 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.328, + 0.892, + 0.357 + ], + "angle": 0, + "content": "Figure 5. Visualization analysis of the predicted results. The first row is the result of the RetinaNet-OBB while the second row is the result of the DCFL. TP, FN, and FP predictions are marked in green, red, and blue respectively." + }, + { + "type": "image", + "bbox": [ + 0.098, + 0.369, + 0.271, + 0.475 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.098, + 0.477, + 0.272, + 0.564 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.296, + 0.369, + 0.44, + 0.475 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.296, + 0.479, + 0.443, + 0.564 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.567, + 0.47, + 0.595 + ], + "angle": 0, + "content": "Figure 6. Statistical analysis of imbalance issues. The first and second columns show quality and quantity imbalance respectively." + }, + { + "type": "image", + "bbox": [ + 0.097, + 0.604, + 0.449, + 0.637 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.121, + 0.637, + 0.425, + 0.65 + ], + "angle": 0, + "content": "Figure 7. Visualization of sampled dynamic priors." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.658, + 0.47, + 0.884 + ], + "angle": 0, + "content": "ent angles and different scales (absolute size). Results are shown in Fig. 6, which are from the models' last training epoch. Here we summarize two kinds of imbalance issues (quantity and quality imbalance) for RetinaNet: (1) The positive sample number assigned to each instance changes periodically w.r.t. its angle and scale, whereas objects with shapes (scale, angle) different from predefined priors will hold much fewer positive samples. (2) The predicted IoU changes periodically w.r.t. gt's scale while remaining invariant w.r.t. gt's angle. By contrast, DCFL remarkably reconciles the imbalance: (1) more positive samples are compensated to previously outlier angles and scales. (2) the samples' quality (predicted IoU) can also be improved and balanced across all angles and scales. The above results are the desired behavior of dynamic coarse-to-fine learning." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Visualization. We visualize the predicted results and" + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.37, + 0.892, + 0.396 + ], + "angle": 0, + "content": "
MethodR3Det [60]S2A-Net [17]GA-RetinaNet [52]RetinaNet [30]DCFL
Params, GFLOPs42.0M, 337.338.6M, 197.937.4M, 206.936.5M, 217.336.1M, 157.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.399, + 0.892, + 0.413 + ], + "angle": 0, + "content": "Table 8. Comparison of params, GFLOPs with \\( {1024} \\times {1024} \\) input." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.418, + 0.892, + 0.524 + ], + "angle": 0, + "content": "positive samples in Fig. 5 and Fig. 7. We can see that the DCFL remarkably eliminates the False Negative and False Positive predictions, especially for the extreme-shaped oriented tiny objects. Fig. 7 shows that the proposed strategy is able to dynamically generate and sample priors that better fit the instance's main body, verifying the claims of dynamic modeling and mismatch alleviation in this work." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.525, + 0.892, + 0.616 + ], + "angle": 0, + "content": "Speed. We test the inference speed on DOTA-v2.0 val set with a single RTX3090 GPU, the FPS of the \\(\\mathrm{R}^3\\mathrm{Det}\\), \\(\\mathrm{S}^2\\mathrm{A}\\) -Net, RetinaNet, and DCFL is 16.2, 18.9, 20.8, and 20.9. It indicates that our method is of high efficiency. Moreover, we provide the parameters and GLOPs in Tab. 8, where we can see that the DCFL is lighter." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.624, + 0.619, + 0.639 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.649, + 0.892, + 0.801 + ], + "angle": 0, + "content": "In this paper, we propose a novel DCFL scheme for detecting oriented tiny objects. We identify that the mismatched feature prior and unbalanced positive samples are two obstacles hampering the label assignment for oriented tiny objects. To address these, we propose a dynamic prior to alleviate the mismatch issue and a coarse-to-fine assigner to mitigate the imbalance issue, where the prior, label assignment, and \\( gt \\) representation are all reformulated in a dynamic manner. Extensive experiments and analyses show the convincing improvements brought by the DCFL." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.815, + 0.66, + 0.832 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.892, + 0.9 + ], + "angle": 0, + "content": "We thank the reviewers for their comments. This work was supported in parts by NSFC (62271355, 62271354) and the Fundamental Research Funds for the Central Universities (20420222kf1010)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7325" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Yancheng Bai, Yongqiang Zhang, Mingli Ding, and Bernard Ghanem. Sod-mtgan: Small object detection via multi-task generative adversarial network. In European Conference on Computer Vision, pages 206-221. Springer, 2018. 3" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.173, + 0.47, + 0.228 + ], + "angle": 0, + "content": "[2] Syed Muhammad Arsalan Bashir and Yi Wang. 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In International Conference on Learning Representations, 2021. 3" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.375 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "7328" + } + ] +] \ No newline at end of file diff --git a/2023/Dynamic Coarse-To-Fine Learning for Oriented Tiny Object Detection/e9804a4f-6933-4148-ae33-ea1a17587f5f_origin.pdf b/2023/Dynamic Coarse-To-Fine Learning for Oriented Tiny Object Detection/e9804a4f-6933-4148-ae33-ea1a17587f5f_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..d9a2f5247a5fd9aa4c18cfb46780ed1d664fbb16 --- /dev/null +++ b/2023/Dynamic Coarse-To-Fine Learning for Oriented Tiny Object Detection/e9804a4f-6933-4148-ae33-ea1a17587f5f_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:154ef9f048bbd067b79bac01d0c647d097642adaa3886b91d65a0f5a3b9e3ae5 +size 3172717 diff --git a/2023/Dynamic Coarse-To-Fine Learning for Oriented Tiny Object Detection/full.md b/2023/Dynamic Coarse-To-Fine Learning for Oriented Tiny Object Detection/full.md new file mode 100644 index 0000000000000000000000000000000000000000..815059e29f76cda0b57669b1e37007912107034a --- /dev/null +++ b/2023/Dynamic Coarse-To-Fine Learning for Oriented Tiny Object Detection/full.md @@ -0,0 +1,421 @@ +# Dynamic Coarse-to-Fine Learning for Oriented Tiny Object Detection + +Chang Xu $^{1}$ , Jian Ding $^{2}$ , Jinwang Wang $^{1}$ , Wen Yang $^{1*}$ , Huai Yu $^{1}$ , Lei Yu $^{1*}$ , Gui-Song Xia $^{2}$ $^{1}$ School of Electronic Information, Wuhan University + $^{2}$ School of Computer Science, Wuhan University + +{xuchangeis, jian.ding, jwwangchn, yangwen, yuhuai, ly.wd, guisong.xia}@whu.edu.cn + +# Abstract + +Detecting arbitrarily oriented tiny objects poses intense challenges to existing detectors, especially for label assignment. Despite the exploration of adaptive label assignment in recent oriented object detectors, the extreme geometry shape and limited feature of oriented tiny objects still induce severe mismatch and imbalance issues. Specifically, the position prior, positive sample feature, and instance are mismatched, and the learning of extreme-shaped objects is biased and unbalanced due to little proper feature supervision. To tackle these issues, we propose a dynamic prior along with the coarse-to-fine assigner, dubbed DCFL. For one thing, we model the prior, label assignment, and object representation all in a dynamic manner to alleviate the mismatch issue. For another, we leverage the coarse prior matching and finer posterior constraint to dynamically assign labels, providing appropriate and relatively balanced supervision for diverse instances. Extensive experiments on six datasets show substantial improvements to the baseline. Notably, we obtain the state-of-the-art performance for one-stage detectors on the DOTA-v1.5, DOTA-v2.0, and DIOR-R datasets under single-scale training and testing. Codes are available at https://github.com/Chasel-Tsui/mmrotate-dcfl. + +# 1. Introduction + +The oriented bounding box is a finer representation for object detection since the object's background region is greatly eradicated by introducing the rotation angle [55]. This advantage is pronounced in aerial images, where objects are in arbitrary orientations, resulting in the prosperity of corresponding object detection datasets [7, 11, 35, 55] and customized oriented object detectors [10, 17, 18, 60, 62]. Nevertheless, one ignorable fact is that there exist numerous tiny objects in aerial images. When oriented objects are tiny-sized, the challenges posed to existing object detec + +![](images/1526adbf2c93c96dcfa12072377bb6d386b3ec3d5f7c421e32bd033545b8c174.jpg) +Figure 1. Comparisons of different learning paradigms for oriented object detection. $\mathbf{M}^*$ means the matching function. Each box in the $2^{nd}$ row denotes a prior location. The $3^{rd}$ row are predictions of the RetinaNet and DCFL, where green, blue, and red boxes denote true positive, false positive, and false negative predictions. (a) RetinaNet, FCOS, and Rotated RPN statically assign labels between fixed priors and fixed gts. (b) Our proposed DCFL dynamically updates priors and gts, and dynamically assigns labels. + +![](images/4aa88e6d63773e986665faec731902ad01d8f794d719779be4287cd2dfb24f81.jpg) + +tors are quite remarkable. Especially, the extreme geometry characteristics of oriented tiny objects hamper the accurate label assignment. + +Label assignment is a fundamental and crucial process in object detection [68], in which priors (box for anchor-based [30] and point for anchor-free detectors [50]) need to be assigned with appropriate labels to supervise the network training. In fact, there have been some works that lay a foundation for the effective label assignment of oriented objects, as shown in Fig. 1. Early works additionally preset anchors of different angles (e.g. Rotated RPN [36]) or refine high-quality anchors (e.g. $\mathrm{S}^2\mathrm{A}$ -Net [17]) based on the generic object detector, then a static rule (e.g. MaxIoU strategy [44]) is used to separate positive and negative (pos/neg) training samples. The derived prior boxes can thus cover more ground truth (gt) boxes and a considerable accuracy improvement can be expected. However, the static assignment cannot adaptively divide pos/neg samples according to the gt's shape and filter out low-quality samples, usually + +![](images/d3f40233bf6fefa2613d355a9f0e50197da0c3f35aad322bf2c196f1870a309b.jpg) +Figure 2. The mismatch and imbalance issues. Each point in the left image denotes a prior location. The number in the pie-shaped bar chart denotes the mean number of positive samples assigned to each instance in a specific angle range. + +leading to sub-optimal performance. + +Recently, the exploration of adaptive label assignment [68] brings new insight to the community. For oriented object detection, DAL [38] defines a prediction-aware matching degree and utilizes it to reweight anchors, achieving dynamic sample learning. Besides, several studies [21,23,26] incorporate the shape information into detectors and propose shape-aware sampling and measurement. + +Despite the progress, the arbitrary orientation and extreme size of oriented tiny objects still pose a dilemma to the detector. As shown in Fig. 2, the mismatch and imbalance issues are particularly pronounced. For one thing, there is a mutual mismatch issue between the position prior, feature, and instance. Although some adaptive label assignment schemes may explore a better pos/neg division of the prior boxes or points, the sampled feature location behind the prior is still fixed and the derived prior is still static and uniformly located, most priors deviate from the tiny object's main body. The prior and feature themselves cannot well-match the extreme shapes of oriented tiny objects, no matter how we divide pos/neg samples. For another, the existing detectors tend to introduce bias and imbalance for oriented and tiny objects. More precisely, for anchor-based detectors, gt with shapes different from anchor boxes will yield low IoU [38, 59], leading to the lack of positive samples. In Fig. 2, we calculate the mean number of positive samples assigned to different gts with the RetinaNet and observe that there is an extreme lack of positive samples for gts with angles and scales far from predefined anchors. For anchor-free detectors, the static prior and its fixed stride limit the upper number of high-quality positive samples. Tiny objects only cover a limited number of feature points, and most of these points are away from the object's main body. + +This motivates us to design a more dynamic and balanced learning pipeline for oriented tiny object detection. As shown in Fig. 1, we alleviate the mismatch issue by reformulating the prior, label assignment, and $gt$ representation all in a dynamic manner, which can be updated by + +the Deep Neural Network (DNN). Simultaneously, we dynamically and progressively assign labels in a coarse-to-fine manner to seek balanced supervision for various instances. + +Specifically, we introduce a dynamic Prior Capturing Block (PCB) to learn the prior, which adaptively adjusts the prior location while retaining the physical meaning of prior [54]. The PCB is inspired by the paradigm of learnable proposals in the DETR [4] and Sparse R-CNN [48] which naturally avoids the mismatch issue between the predefined prior and feature. Compared to this paradigm, we introduce its flexibility for prior updates while keeping the fast-convergence ability of dense detectors [32, 54]. Based on the dynamic prior, we then select Cross-FPN-layer Coarse Positive Sample (CPS) candidates for further label assignment, and the CPS is realized by the Generalized Jensen-Shannon Divergence [39] (GJSD) between the $gt$ and the dynamic prior. The GJSD is able to enlarge the CPS to the object's nearby spatial locations and adjacent FPN layers, ensuring more candidates for extreme-shaped objects. After obtaining the CPS, we re-rank these candidates with predictions (posterior) and represent the $gt$ with a finer Dynamic Gaussian Mixture Model (DGMM), filtering out low-quality samples. All designs are incorporated into an end-to-end one-stage detector without additional branches. + +In short, our contributions are listed as follows: (1) We identify that there exist severe mismatch and imbalance issues in the current learning pipeline for oriented tiny object detection. (2) We design a Dynamic Coarse-to-Fine Learning (DCFL) scheme for oriented tiny object detection, which is the first to model the prior, label assignment, and $gt$ representation all in a dynamic manner. In the DCFL, we propose to use the GJSD to construct Coarse Positive Samples (CPS) and represent objects with a finer Dynamic Gaussian Mixture Model (DGMM), obtaining coarse-to-fine label assignment. (3) Extensive experiments on six datasets show promising results. + +# 2. Related Work + +# 2.1. Oriented Object Detection + +Prior for Oriented Objects. Anchor, as a classic design in generic object detectors (e.g. Faster R-CNN [44], RetinaNet [30]), has facilitated object detection for a long time. Similarly, oriented object detection also benefits from the anchor design. Initially, rotated RPN [36] extends the RPN to the field of oriented object detection by tiling 54 anchors each location with preset angles and scales. Indeed, enumerating potential $gt$ shapes can notably improve the recall, apart from the sacks of additional computational cost. RoI Transformer [10] utilizes horizontal anchors and transforms the RPN-generated horizontal proposals to oriented proposals, reducing the number of rotated anchors. To save computation, the Oriented R-CNN [56] introduces an ori + +ented RPN that directly predicts oriented proposals based on horizontal anchors. Recently, one-stage oriented object detectors gradually emerged, including anchor-based detectors [17, 60] with box prior and anchor-free detectors [26, 28] with point prior. Most of them retain the fixed prior design, except for the $\mathrm{S}^2\mathrm{A}$ -Net [17] which proposes to generate high-quality anchors. + +Label Assignment. ATSS [68] reveals that label assignment plays a pivotal role in the detectors' performance [14,24,37]. In the field of oriented object detection, DAL [38] observes inconsistency between the input prior IoU and the output predicted IoU, then defines a matching degree as the soft label that dynamically reweights anchors. Recently, SASM [21] introduces a shape-adaptive sample selection and measurement strategy to improve detection performance. Similarly, GGHL [23] proposes to fit the main body of the instance by a single 2-D Gaussian heatmap, then it divides and reweights samples in a dynamic manner. In addition, Oriented Reppoints [26] improves the RepPoints [65] by assessing the quality of points for more effective label assignment. + +# 2.2. Tiny Object Detection + +Multi-scale Learning. Basically, one can use a multi-resolution image pyramid to obtain multi-scale learning. However, the vanilla image pyramid will bring much computation cost. Thus, some works [29, 33, 34, 42, 49, 69] reduce computation with the efficient Feature Pyramid Network (FPN). Unlike the FPN, TridentNet [27] introduces multi-branch detection heads of various receptive fields for multi-scale prediction. Moreover, one can normalize the scale of objects for scale-invariant object detection, for example, SNIP [46] and SNIPER [47] resize images and train objects within a certain scale range. + +Label Assignment. Tiny objects usually have low IoU with anchors or cover a limited number of feature points, thus suffering from the lack of positive samples. ATSS [68] slightly reconciles the number of positive samples for objects of different scales. NWD [57] designs a new metric to replace IoU, which can sample more positive samples for tiny objects. Recently, the RFLA [58] utilizes outliers to detect tiny objects for scale-balanced learning. + +Context Information. Tiny object lacks discriminative features, but objects are closely related to the surrounding context. Therefore, we can leverage the context information to enhance small object detection. Muti-Region CNN (MRCNN) [15] and Inside-Outside Network (ION) [3] are two representative works that exploit local and global context information. Recently, the Relation Network [22] and transformer-based detectors [4, 54, 72] reason about the association between instances via the attention mechanism. + +Feature Enhancement. The feature representation of small objects can be enhanced by super-resolution or GAN. + +PGAN [25] first applies GAN to small object detection. Besides, Bai et al. [1] introduce the MT-GAN which trains an image-level super-resolution model to improve the RoI features of small objects. In addition, there are some other methods based on super-resolution including [2,8,40,43]. + +By contrast, our method simultaneously handles the prior mismatch and unbalanced learning via dynamically modeling the prior, label assignment, and $gt$ representation. Meanwhile, unlike the two-stage RoI-Transformer [10] or one-stage S²A-Net [17], we embed the dynamic prior inside the end-to-end one-stage detector without introducing any auxiliary branch. + +# 3. Method + +Overview. Given a set of dense prior $P \in \mathbb{R}^{W \times H \times C}$ ( $W \times H$ is the feature map size, $C$ is the shape information number, each feature point has one prior for simplicity), object detectors remap the set $P$ into final detection results $D$ through the Deep Neural Network (DNN), which can be simplified as: + +$$ +D = \mathrm {D N N} _ {h} (P), \tag {1} +$$ + +where $\mathrm{DNN}_h$ denotes the detection head. Detection results $D$ contain two parts: classification scores $D_{cls} \in \mathbb{R}^{W \times H \times A}$ ( $A$ is the class number) and box locations $D_{reg} \in \mathbb{R}^{W \times H \times B}$ ( $B$ is the box parameter number). + +To train the $\mathrm{DNN}_h$ , we need to find a proper matching between the prior set $P$ and the $gt$ set $GT$ , and assign pos/neg labels to $P$ to supervise the network learning. For static assigners (e.g. RetinaNet [30]), the set of pos labels $G$ can be obtained via hand-crafted matching function $\mathcal{M}_s$ : + +$$ +G = \mathcal {M} _ {s} (P, G T). \tag {2} +$$ + +For dynamic assigners [14, 24, 38], they tend to simultaneously leverage the prior information $P$ and posterior information (predictions) $D$ , and then apply a prediction-aware mapping $\mathcal{M}_d$ to get the set $G$ : + +$$ +G = \mathcal {M} _ {d} (P, D, G T). \tag {3} +$$ + +After the pos/neg label separation, the loss function can be summarized into two parts: + +$$ +\mathcal {L} = \sum_ {i = 1} ^ {N _ {p o s}} \mathcal {L} _ {p o s} \left(D _ {i}, G _ {i}\right) + \sum_ {j = 1} ^ {N _ {n e g}} \mathcal {L} _ {n e g} \left(D _ {j}, y _ {j}\right), \tag {4} +$$ + +where $N_{pos}$ , $N_{neg}$ are the number of positive and negative samples respectively, $y_{j}$ denotes the negative label. + +While in this work, we model the prior, label assignment, and $gt$ representation all in a dynamic manner to alleviate the mismatch issue. To begin with, the dynamic prior is reformulated to (\~ denotes the dynamic item): + +$$ +\tilde {D} = \mathrm {D N N} _ {h} (\underbrace {\mathrm {D N N} _ {p} (P)} _ {\text {D y n a m i c P r i o r} \tilde {P}}), \tag {5} +$$ + +$\mathrm{DNN}_p$ is a learnable block incorporated within the detection head to update the prior. Then, the matching function is reformulated to a coarse-to-fine paradigm: + +$$ +\tilde {G} = \mathcal {M} _ {d} \left(\mathcal {M} _ {s} (\tilde {P}, G T), \tilde {G T}\right), \tag {6} +$$ + +the $\tilde{G}T$ is a finer representation of an object with the Dynamic Gaussian Mixture Model (DGMM). In a nutshell, our final loss is modeled as: + +$$ +\mathcal {L} = \sum_ {i = 1} ^ {\tilde {N} _ {p o s}} \mathcal {L} _ {p o s} \left(\tilde {D} _ {i}, \tilde {G} _ {i}\right) + \sum_ {j = 1} ^ {\tilde {N} _ {n e g}} \mathcal {L} _ {n e g} \left(\tilde {D} _ {j}, y _ {j}\right). \tag {7} +$$ + +# 3.1. Dynamic Prior + +Inspired by the purely learnable paradigm of proposal updation in the DETR [4] and Sparse R-CNN [48], we propose to introduce more flexibility into the prior to mitigate the mismatch issue. Moreover, we retain the physical meaning of prior where each individual prior stands for a feature point, inheriting the fast convergence ability of dense detectors. The structure of the proposed Prior Capturing Block (PCB) is shown in Fig. 3, in which a dilated convolution is deployed to take the surrounding information into account, and then the Deformable Convolution Network (DCN) [9] is leveraged to capture the dynamic prior. Besides, we utilize the learned offsets from the regression branch to guide the feature extraction of the classification branch, leading to better alignment between the two tasks. + +The dynamic prior capturing process is as follows. First of all, we initialize each prior location $\mathbf{p}(x,y)$ by each feature point's spatial location s (which is remapped to the image). In each iteration, we forward the network to capture the offset sets of each prior location $\Delta \mathbf{o}$ . Hence, the prior spatial location can be updated by: + +$$ +\tilde {\mathbf {s}} = \mathbf {s} + s t \sum_ {i = 1} ^ {n} \Delta \mathbf {o} _ {i} / 2 n, \tag {8} +$$ + +where $st$ is the feature map's stride, $n$ is the number of offsets. Finally, we utilize the 2-D Gaussian distribution $\mathcal{N}_p(\boldsymbol{\mu}_p, \boldsymbol{\Sigma}_p)$ which is demonstrated conducive to small objects [58,61] and oriented objects [61,63] to fit the prior spatial location. Concretely, the dynamic $\tilde{\mathbf{s}}$ serves as the Gaussian's mean vector $\boldsymbol{\mu}_p$ . We preset one prior which is square-shaped $(w, h, \theta)$ as that in RetinaNet [30] on each feature point, then compute the co-variance matrix $\boldsymbol{\Sigma}_p$ by [64]: + +$$ +\boldsymbol {\Sigma} _ {p} = \left[ \begin{array}{c c} \cos \theta & - \sin \theta \\ \sin \theta & \cos \theta \end{array} \right] \left[ \begin{array}{c c} \frac {w ^ {2}}{4} & 0 \\ 0 & \frac {h ^ {2}}{4} \end{array} \right] \left[ \begin{array}{c c} \cos \theta & \sin \theta \\ - \sin \theta & \cos \theta \end{array} \right]. \tag {9} +$$ + +# 3.2. Coarse Prior Matching + +Given a set of prior, one basic assignment rule is to specify a range of candidate true prediction samples for a specific $gt$ . Some adaptive strategies restrict the candidates of a given $gt$ inside a single FPN layer [14,23,68], while some + +works release all layers as candidates [67, 71]. However, for oriented tiny objects, the former strict heuristic rule may lead to a sub-optimal layer selection and the latter loose one will induce the slow convergence issue [32]. + +Hence, we propose Cross-FPN-layer Coarse Positive Sample (CPS) candidates, which narrows down the sample range compared to the all-FPN-layer manner while discarding the single-layer heuristic. In the CPS, we slightly expand the range of candidates to the $gt$ 's nearby spatial location and adjacent FPN layers, which warrants relatively diverse and sufficient candidates compared to the single-layer heuristic and alleviates the quantity imbalance issue. + +Specifically, the similarity measurement in constructing the CPS is realized with the Jensen-Shannon Divergence (JSD) [13], which inherits the scale invariance property of the Kullback-Leibler Divergence (KLD) [63] and can measure the $gt$ 's similarity with nearby non-overlapping priors [58, 63]. Moreover, it conquers KLD's drawback of asymmetry. However, the closed-form solution of the JSD between Gaussian distributions is unavailable [39], thus, we utilize the Generalized Jensen-Shannon Divergence (GJSD) [39] which yields a closed-form solution, as the substitute. + +For example, the GJSD between two Gaussian distributions $\mathcal{N}_p(\boldsymbol{\mu}_p, \boldsymbol{\Sigma}_p)$ and $\mathcal{N}_g(\boldsymbol{\mu}_g, \boldsymbol{\Sigma}_g)$ is defined by: + +$$ +\operatorname {G J S D} \left(\mathcal {N} _ {p}, \mathcal {N} _ {g}\right) = (1 - \alpha) \mathrm {K L} \left(\mathcal {N} _ {\alpha}, \mathcal {N} _ {p}\right) + \alpha \mathrm {K L} \left(\mathcal {N} _ {\alpha}, \mathcal {N} _ {g}\right), \tag {10} +$$ + +where KL denotes the KLD, and $\mathcal{N}_{\alpha}(\pmb{\mu}_{\alpha}, \pmb{\Sigma}_{\alpha})$ is given by: + +$$ +\boldsymbol {\Sigma} _ {\alpha} = \left(\boldsymbol {\Sigma} _ {p} \boldsymbol {\Sigma} _ {g}\right) _ {\alpha} ^ {\boldsymbol {\Sigma}} = \left((1 - \alpha) \boldsymbol {\Sigma} _ {p} ^ {- 1} + \alpha \boldsymbol {\Sigma} _ {g} ^ {- 1}\right) ^ {- 1}, \tag {11} +$$ + +and + +$$ +\begin{array}{l} \boldsymbol {\mu} _ {\alpha} = \left(\boldsymbol {\mu} _ {p} \boldsymbol {\mu} _ {g}\right) _ {\alpha} ^ {\boldsymbol {\mu}} \\ = \boldsymbol {\Sigma} _ {\alpha} \left((1 - \alpha) \boldsymbol {\Sigma} _ {p} ^ {- 1} \boldsymbol {\mu} _ {p} + \alpha \boldsymbol {\Sigma} _ {g} ^ {- 1} \boldsymbol {\mu} _ {g}\right). \\ \end{array} +$$ + +(12) + +Note that $\alpha$ is a parameter that controls the weight of two distributions [39] in similarity measurement. In our work, the $\mathcal{N}_p$ and $\mathcal{N}_q$ contribute equally, thus $\alpha$ is set to 0.5. + +Ultimately, for each $gt$ , we select $K$ priors which hold the top $K$ GJSD score with this $gt$ as the Coarse Positive Samples (CPS) and regard the remaining priors as negative samples, this coarse matching serves as the $\mathcal{M}_s$ in Eq. 6. The ranking manner works together with the GJSD measurement to construct the Cross-FPN-layer CPS, eliminating the imbalance issue raised by the MaxIoU matching for outlier angles and scales, which will be analyzed in Sec. 5. + +# 3.3. Finer Dynamic Posterior Matching + +Based on Coarse Positive Sample (CPS) candidates, we design a dynamic posterior (prediction) matching rule $\mathcal{M}_d$ to filter out low-quality samples. The $\mathcal{M}_d$ consists of two key components, namely a posterior re-ranking strategy and a Dynamic Gaussian Mixture Model (DGMM) constraint. + +![](images/dc573d6825887ef255c083e96a81d529d1824e4a6c745b3ce279f11d04cede5a.jpg) +Figure 3. The process of feature extraction and dynamic coarse-to-fine learning. PCB denotes the prior capturing block. + +![](images/9002cf5257404920462cd97d3152015c0644aeafbe4c298b57ebe07f1c4b0464.jpg) + +We re-rank the sample candidates in the CPS according to their predicted scores. In other words, we further refine the positive samples by their Possibility of becoming True predictions $(PT)$ [14], which is a linear combination of the predicted classification score and the location score with the $gt$ . We define the $PT$ of the $i^{th}$ sample $D_{i}$ as: + +$$ +P T _ {i} = \frac {1}{2} C l s (D _ {i}) + \frac {1}{2} I o U (D _ {i}, g t _ {i}), \tag {13} +$$ + +where $Cls$ is the predicted classification confidence and $IoU$ is the rotated IoU between the predicted location and its corresponding $gt$ location. We select candidates with $Q$ highest $PT$ as Medium Positive Sample (MPS) candidates. + +Following this, we filter out those samples too far away from the $gts$ with a finer instance representation, getting the Finer Positive Samples (FPS). Different from previous works which utilize the center probability map [53] or the single-Gaussian [23,64] for instance representation, we represent the instance by a finer DGMM. It consists of two components: one is centered on the geometry center and the other is centered on the semantic center of the object. Concretely, for a specific instance $gt_{i}$ , the geometry center $(cx_{i}, cy_{i})$ serves as the mean vector $\mu_{i,1}$ of the first Gaussian, and the semantic center $(sx_{i}, sy_{i})$ , which is deduced by averaging the location of the samples in the MPS, serves as the $\mu_{i,2}$ . That is to say, we parameterize the instance as: + +$$ +D G M M _ {i} (s | x, y) = \sum_ {m = 1} ^ {2} w _ {i, m} \sqrt {2 \pi | \boldsymbol {\Sigma} _ {i , m} |} \mathcal {N} _ {i, m} \left(\boldsymbol {\mu} _ {i, m}, \boldsymbol {\Sigma} _ {i, m}\right), \tag {14} +$$ + +where $w_{i,m}$ is the weight of each Gaussian with a summation of 1, $\Sigma_{i,m}$ equals to the $gt$ 's $\Sigma_g$ . Each sample in MPS has a DGMM score $DGMM(s|MPS)$ , we set negative masks to samples which have $DGMM(s|MPS) < e^{-g}$ with any $gt$ , the $g$ is adjustable. + +# 4. Experiments + +# 4.1. Datasets + +Experiments are done on six datasets, i.e., DOTA-v1.0 [55]/v1.5/v2.0 [11], DIOR-R [7], VisDrone [12], and + +MS COCO [31]. In ablation studies and analyses, we choose the large-scale DOTA-v2.0 train set for training and val set for evaluation, which contains a large number of tiny objects. To compare with other methods, we use trainval sets of DOTA-v1.0, DOTA-v1.5, DOTA-v2.0, and DIOR-R for training and their test sets for testing, we choose the VisDrone2019, MS COCO train set, val set for training and testing. + +# 4.2. Implementation Details + +We conduct all the experiments on the computer with a single NVIDIA RTX 3090 GPU, and the batch size is set to 4. Models are built based on MMDetection [6] and MMRotate [70] with PyTorch [41]. The ImageNet [45] pre-trained models are used as the backbone. The Stochastic Gradient Descent (SGD) optimizer is used for training with a learning rate of 0.005, a momentum of 0.9, and a weight decay of 0.0001. The ResNet-50 [20] with FPN [29] is the default backbone if not specified. We use Focal loss [30] for classification and IoU loss [66] for regression. We only use random flipping as data augmentation for all experiments. + +For experiments on the DOTA-v1.0 and DOTA-v2.0, we follow the official settings of the DOTA-v2.0 benchmark [11], i.e., we crop images into patches of $1024 \times 1024$ with overlaps of 200 and train the model for 12 epochs. For DOTA-v2.0, we reproduce one-stage state-of-the-art methods [17,21,26,38,50,60,63,68] with the same settings. + +For experiments on other datasets, we set the input size to $1024 \times 1024$ (overlap 200), $800 \times 800$ , $1333 \times 800$ , and $1333 \times 800$ for DOTA-v1.5, DIOR-R, VisDrone, and COCO respectively. We train the models for 40, 40, 12, and 12 epochs on the DOTA-v1.5, DIOR-R, COCO, and VisDrone as previous works do [16, 26]. The above settings are fixed unless otherwise specified. + +# 4.3. Main Results + +Results on DOTA series. As shown in Tab. 1, our proposed method achieves the state-of-the-art performance of $57.66\%$ mAP on the DOTA-v2.0 OBB benchmark un + +
MethodBackbonePlaneBDBridgeGTFSVLVShipTCBCSTSBFRAHarborSPHCCCAirHelimAP
multi-stage:
FR OBB [44]R5071.6147.2039.2858.7035.5548.8851.5178.9758.3658.5536.1151.7343.5755.3357.073.5152.942.7947.31
FR OBB + DpR5071.5549.7440.3460.4040.7450.6756.5879.0358.2258.2434.7351.9544.3355.1053.147.2159.536.3848.77
MR [19]R5076.2049.9141.6160.0041.0850.7756.2478.0155.8557.4836.6251.6747.3955.7959.063.6460.268.9549.47
HTC* [5]R5077.6947.2541.1560.7141.7752.7958.8778.7455.2258.4938.5752.4849.5856.1854.094.2066.3811.9250.34
RT [10]R5071.8148.3945.8864.0242.0954.3959.9282.7063.2958.7141.0452.8253.3256.1857.9425.7163.728.7052.81
Oriented R-CNN [56]R5077.9550.2946.7365.2442.6154.5660.0279.0861.6959.4242.2656.8951.1156.1659.3325.8160.679.1753.28
one-stage:
DAL [38]R5071.2338.3638.6045.2435.4243.7556.0470.8450.8756.6320.2846.5333.4947.2912.150.8125.770.0038.52
SASM [21]R5070.3040.6237.0159.0340.2145.4644.6078.5849.3460.7329.8946.5742.9548.3128.131.8276.370.7444.53
RetinaNet-O [30]R5070.6347.2639.1255.0238.1040.5247.1677.7456.8652.1237.2251.7544.1553.1951.066.5864.287.4546.68
\( R^3Det w/ KLD [63] \)R5075.4450.9541.1661.6141.1145.7649.6578.5254.9760.7942.0753.2043.0849.5534.0936.2668.650.0647.26
FCOS-O [51]R5074.8447.5340.8357.4143.8947.7255.6678.6157.8663.0038.0252.3841.9153.2440.227.1565.517.4248.51
Oriented Rep [26]R5073.0246.6842.3763.0547.0650.2858.6478.8457.1266.7735.2150.7648.7751.6234.236.1764.665.8748.95
ATSS-O [68]R5077.4649.5542.1262.6145.1548.4051.7078.4359.3362.6539.1852.4342.9253.9842.705.9167.0910.6849.57
\( S^2A-Net [17] \)R5077.8451.3143.7262.5947.5150.5857.8680.7359.1165.3236.4352.6045.3652.4640.120.0062.8111.1149.86
one-stage:
DCFLR5075.7149.4044.6963.2346.4851.5555.5079.3059.9665.3941.8654.4247.0355.7250.4911.7569.017.7551.57
\( S^2A-Net w/ DCFL \)R5074.7953.2545.8165.4646.4953.2358.1081.5160.1366.4243.2455.0950.5255.5854.535.2368.7313.0652.84
DCFL†R5078.3053.0344.2460.1748.5655.4258.6678.2960.8965.9343.5455.8253.3360.0054.7630.9074.0115.6055.08
DCFL†ReR10179.4955.9750.1561.5949.0055.3359.3181.1866.5260.0652.8756.7157.8358.1360.3535.6678.6513.0357.66
+ +Table 1. Main results on the DOTA-v2.0 OBB Task. We follow the official class abbreviations as the DOTA-v2.0 benchmark [11]. $\dagger$ denotes training for 40 epochs. Note that this paper [63] reports $50.90\%$ mAP for $\mathrm{R}^3\mathrm{Det}$ w/ KLD under 20 epochs, the ReR101 backbone is proposed by the ReDet [18]. The results in red and blue denote the best and second-best performance of each column. + +
MethodCFA [16]RetinaNet-O [30]R3Det [60]Oriented Rep [26]ATSS-O [68]
mAP69.6369.7970.1871.9472.29
Method KLD [63]S2A-Net [17]GGHL [23](3x)DCFLDCFL(3x)
mAP72.7673.9173.9874.2675.35
+ +Table 2. Comparison with one-stage detectors on the DOTA-v1.0 OBB Task. All results are based on the MMRotate [70] with 12 epochs except for GGHL [23]. 3x means training for 36 epochs. + +
MethodBackboneSVShipSTmAP
RetinaNet-O [30]R5044.5373.3159.9659.16
FR OBB [19]R5051.2879.3767.5062.00
CMR [19]R5051.6479.9967.5863.41
RT [10]R5052.0580.7268.2665.03
ReDet [18]ReR5052.3880.9268.6466.86
DCFLR5056.72 (+12.19)80.87 (+7.56)75.65 (+15.69)67.37 (+8.21)
DCFLReR10157.31 (+12.78)86.60 (+13.29)76.55 (+16.59)70.24 (+11.08)
+ +Table 3. Main results on the DOTA-v1.5 OBB Task. + +
MethodRetinaNet-O [30]FR-OBB [44]RT [10]AOPG [7]
mAP57.5559.5463.8764.41
MethodGGHL [23]Oriented Rep [26]DCFLDCFL (ReR101)
mAP66.4866.7166.8071.03
+ +Table 4. Performance comparisons on the DIOR-R dataset. + +
MethodBackboneVEBRWM
RetinaNet-O [30]R5038.024.060.2
Oriented Rep [26]R5050.438.864.7
DCFLR5050.9 (+12.9)42.1 (+18.1)70.9 (+10.7)
+ +der single-scale training and testing. Besides, our model achieves $51.57\%$ mAP without bells and whistles, surpassing all one-stage object detectors tested. The results on the DOTA-v1.0 [55] and DOTA-v1.5 are listed in Tab. 2, Tab. 3. + +Table 5. Detection results of typical tiny objects on the DIOR-R dataset. VE, BR, and WM denote vehicle, bridge, and wind-mill. + +
DatasetVisDroneMS COCODOTA-v2.0 HBB
MethodRetinaNet [30]DCFLRetinaNetDCFLFCOS [58]DCFL
AP0.529.232.155.457.355.457.4
+ +Table 6. Results of one-stage object detectors on HBB datasets. + +![](images/af612884815b4307fcbca15cf0ea6bb11efe7f5db42eb3571e0ffb702806cc50.jpg) +Figure 4. Different ways of constructing the CPS. Yellow and orange denote the possible regions of CPS and MPS respectively. + +Results also indicate that our DCFL is very effective for detecting tiny oriented objects on the tested datasets, such as small vehicles, ships, and storage tanks, where a boost of about 10 points can be expected compared to the baseline. + +Results on DIOR-R. DIOR-R contains some tiny oriented objects, such as the vehicle, bridge, and windmill. The mAP and class-wise AP of tiny objects are in Tab. 4 and Tab. 5, we also achieve the state-of-the-art performance of $71.03\%$ mAP and notable improvements on tiny objects. + +Results on HBB Datasets. Moreover, we discard the angle to verify the versatility of the DCFL on the generic small object detection datasets VisDrone [12], MS COCO [31], and DOTA-v2.0 HBB [11]. In Tab. 6, our method gets a notable $\mathrm{AP}_{0.5}$ boost compared to the baseline. + +# 4.4. Ablation Study + +Effects of Individual Strategy. We check the effectiveness of each proposed strategy in the proposed method. In + +
MethodCPSMPSDGMMmAP
baseline [30]51.70
DCFL✓✓53.41
✓✓57.20
✓✓✓59.15
+ +(a) Individual effectiveness. CPS, MPS, and DGMM denote Coarse, Medium Sample Candidates and Dynamic Gaussian Mixture Model. + +
StrategyMeasurementmAP
All-FPN-layerGaussian50.12
Single-FPN-layerGaussian56.72
Cross-FPN-layerKLD [63]57.82
Cross-FPN-layerGWD [61]58.55
Cross-FPN-layerGJSD59.15
+ +(b) Comparisons of different CPS. The FPN layer number varies for different strategies of getting the CPS. + +
DCNDilated ConvDPmAP
58.07
✓58.41
✓✓58.65
Separate✓✓58.71
Guiding✓✓59.15
+ +(c) Effects of detailed designs in the PCB. DP denotes the dynamic prior. Guiding denotes reg guidescls. + +
K2420
Q20161281612108
mAP58.3158.1158.9559.0658.6658.7158.9258.28
K1612
Q12108610864
mAP59.1558.5758.9757.8458.7958.2557.0157.37
+ +(d) Effects of parameters $K$ and $Q$ . + +
g1.21.0
mAP57.9158.20
g0.80.4
mAP59.1558.95
+ +(e) Effects of parameter $g$ + +Table 7. Ablations. We train on DOTA-v2.0 train set, test on val set, and report mAP under IoU threshold 0.5. + +all ablation experiments, we employ one prior for each feature point for fair comparisons. As seen in Tab. 7a, the baseline detector RetinaNet-OBB yields a result of $51.70\%$ mAP. When we gradually apply the posterior re-ranked MPS and DGMM into the detector based on the CPS, the mAP improves progressively, verifying each design's effectiveness. Note that the CPS cannot be independently used since the samples in it are too coarse to serve as the final positive samples. Nevertheless, we compare some different ways of constructing the CPS to verify its superiority. + +Comparisons of Different CPS. The design of the CPS matters in the training pipeline. We show several paradigms of designing the CPS as shown in Fig. 7b, including limiting the CPS for a specific $gt$ within a single layer like FCOS [50], releasing all FPN layers as the CPS, like Objectbox [67]. We compare their performance in Tab. 7b. For fair comparisons, the number of samples in CPS is fixed at 16, and all other components are kept the same. For the Single-FPN-layer way, we group $gt$ onto different layers according to the scale division strategy in FCOS, then assign labels within each layer. For the All-FPN-layer way, we do not group $gt$ onto different layers, instead, we discard the prior scale information and directly measure the distance between Gaussian $gt$ and prior points. The results are shown in Tab. 7b, we can observe that neither of the above two ways will yield the best performance. By contrast, the distribution distances (KLD, GWD, GJSD) are able to construct the Cross-FPN-layer CPS, where the candidates are extended to adjacent layers besides the main layer. We can also see the GJSD gets the best performance of $59.15\%$ mAP, mainly resulting from its property of scale-invariance [39, 63], symmetry [39], and ability to measure non-overlapping boxes [39] compared to other counterparts. + +Fixed Prior and Dynamic Prior. We conduct a finer group of ablation studies to verify the necessity of introducing the dynamic prior. As shown in Tab. 7c, if we disable the + +dynamic prior by fixing the location of samples, a slight performance drop will be introduced. Hence, the prior should be adjusted accordingly when leveraging the dynamic sampling strategy to better capture the shape of objects. + +Detailed Design in PCB. For the PCB, it is made up of a dilated convolution and a guiding DCN, we slightly enlarge the receptive field with a dilation rate of 3. After that, we take advantage of the DCN to generate dynamic priors in a guiding manner. As shown in Tab. 7c, we can observe that the DCN can bring an improvement of $0.34\mathrm{mAP}$ points and the dilated convolution can slightly enhance the mAP. We find that the application of the DCN [9] to the single regression branch will slightly deteriorate the accuracy (noted by Separate in Tab. 7c), which may cause mismatch issues between the two branches. Thus we utilize the offsets from the regression head to guide the offsets classification head for better alignment (noted by Guiding). + +Effects of Parameters. The introduced three parameters are robust in a certain range. From Tab. 7d, we can see that a combination of $K = 16$ and $Q = 12$ gets the best performance. In Tab. 7e, we verify the threshold $e^{-g}$ in the DGMM, we empirically set $w_{i,1}$ to 0.7, then a threshold of $g = 0.8$ yields the highest mAP. Although making the CPS/MPS/FPS coarser and stricter will weaken the performance, the mAP only waves marginally. In other words, the coarse-to-fine assignment manner somewhat warrants the parameter selection's robustness since multiple parameters can attenuate the effects of an under-tuned one. + +# 5. Analysis + +For a clearer dissection of why the proposed scheme works, we perform more meticulous analyses as follows. + +Reconciliation of imbalance problems. To delve into the imbalance issue, we calculate the mean predicted IoU and the mean positive sample number of $gt$ holding differ + +![](images/0e4bacdce06e68bde739295fe670a8d4894c6c85c6052477375b664eb420dc0e.jpg) + +![](images/64659c3fa9895d4bf2ea4632dce7a718cb144a7c8ef051f16746194de2c404f9.jpg) +Figure 5. Visualization analysis of the predicted results. The first row is the result of the RetinaNet-OBB while the second row is the result of the DCFL. TP, FN, and FP predictions are marked in green, red, and blue respectively. + +![](images/ffa40b98c0457b20a508f84e0b5265d1d54cc04b8c2ada738177f6cba764d2b3.jpg) + +![](images/de0e5df3c32a3328d4385b9dc194742c7ea802d09efad95198e615648ce8eb28.jpg) + +![](images/6d945039f1bfe7927f5a288c35cbc04b951f68f925ab12752b288e75bae9e60c.jpg) + +![](images/181e26520d24adc5ba1d4f85ee3e7bd5a39758db9dbafcfe567d4eca78c28bb0.jpg) + +![](images/2b3248716472d496eb9403a39b8985df5349bf10405ecab2314fd28b70916bd2.jpg) + +![](images/eb72422d1dbb7620540f324a29c940ada82c4654829d7c50086c528dcb5a767a.jpg) + +![](images/ba93afe185ddb684966bb1f880ab680e92bfae22bec54e97db321633c221d4b1.jpg) + +![](images/293019a5b0140591e6aab307cdb110b75dd519fbace9cccbe663f8205fdeea7d.jpg) + +![](images/ec941bf00e2a0ec6ddf65e2dfeffba983900861c6516e6fbb33930e209a2b2cd.jpg) + +![](images/b72daa37ff7effa447c8aa374cd000eaaaf4cd30c2b556c9928796809f665595.jpg) +Figure 6. Statistical analysis of imbalance issues. The first and second columns show quality and quantity imbalance respectively. + +![](images/fff6d3388249ba26e2ceaf88c50fd9d36aeef3a6d34eba834c5b81eb92f2ae74.jpg) + +![](images/6118b619891aeb23f10a695a32464ce38b28c8b2f2a631bc65fe6abc4f5187dd.jpg) + +![](images/c6911e040344a6e266b391b463ecdaee753c19bc0278ebcee7054132b5edffb9.jpg) +Figure 7. Visualization of sampled dynamic priors. + +ent angles and different scales (absolute size). Results are shown in Fig. 6, which are from the models' last training epoch. Here we summarize two kinds of imbalance issues (quantity and quality imbalance) for RetinaNet: (1) The positive sample number assigned to each instance changes periodically w.r.t. its angle and scale, whereas objects with shapes (scale, angle) different from predefined priors will hold much fewer positive samples. (2) The predicted IoU changes periodically w.r.t. gt's scale while remaining invariant w.r.t. gt's angle. By contrast, DCFL remarkably reconciles the imbalance: (1) more positive samples are compensated to previously outlier angles and scales. (2) the samples' quality (predicted IoU) can also be improved and balanced across all angles and scales. The above results are the desired behavior of dynamic coarse-to-fine learning. + +Visualization. We visualize the predicted results and + +
MethodR3Det [60]S2A-Net [17]GA-RetinaNet [52]RetinaNet [30]DCFL
Params, GFLOPs42.0M, 337.338.6M, 197.937.4M, 206.936.5M, 217.336.1M, 157.8
+ +Table 8. Comparison of params, GFLOPs with ${1024} \times {1024}$ input. + +positive samples in Fig. 5 and Fig. 7. We can see that the DCFL remarkably eliminates the False Negative and False Positive predictions, especially for the extreme-shaped oriented tiny objects. Fig. 7 shows that the proposed strategy is able to dynamically generate and sample priors that better fit the instance's main body, verifying the claims of dynamic modeling and mismatch alleviation in this work. + +Speed. We test the inference speed on DOTA-v2.0 val set with a single RTX3090 GPU, the FPS of the $\mathrm{R}^3\mathrm{Det}$ , $\mathrm{S}^2\mathrm{A}$ -Net, RetinaNet, and DCFL is 16.2, 18.9, 20.8, and 20.9. It indicates that our method is of high efficiency. Moreover, we provide the parameters and GLOPs in Tab. 8, where we can see that the DCFL is lighter. + +# 6. Conclusion + +In this paper, we propose a novel DCFL scheme for detecting oriented tiny objects. We identify that the mismatched feature prior and unbalanced positive samples are two obstacles hampering the label assignment for oriented tiny objects. To address these, we propose a dynamic prior to alleviate the mismatch issue and a coarse-to-fine assigner to mitigate the imbalance issue, where the prior, label assignment, and $gt$ representation are all reformulated in a dynamic manner. Extensive experiments and analyses show the convincing improvements brought by the DCFL. + +# Acknowledgement + +We thank the reviewers for their comments. This work was supported in parts by NSFC (62271355, 62271354) and the Fundamental Research Funds for the Central Universities (20420222kf1010). + +# References + +[1] Yancheng Bai, Yongqiang Zhang, Mingli Ding, and Bernard Ghanem. Sod-mtgan: Small object detection via multi-task generative adversarial network. In European Conference on Computer Vision, pages 206-221. Springer, 2018. 3 +[2] Syed Muhammad Arsalan Bashir and Yi Wang. 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Despite the exploration of adaptive label assignment in recent oriented object detectors, the extreme geometry shape and limited feature of oriented tiny objects still induce severe mismatch and imbalance issues. Specifically, the position prior, positive sample feature, and instance are mismatched, and the learning of extreme-shaped objects is biased and unbalanced due to little proper feature supervision. To tackle these issues, we propose a dynamic prior along with the coarse-to-fine assigner, dubbed DCFL. For one thing, we model the prior, label assignment, and object representation all in a dynamic manner to alleviate the mismatch issue. For another, we leverage the coarse prior matching and finer posterior constraint to dynamically assign labels, providing appropriate and relatively balanced supervision for diverse instances. Extensive experiments on six datasets show substantial improvements to the baseline. 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This advantage is pronounced in aerial images, where objects are in arbitrary orientations, resulting in the prosperity of corresponding object detection datasets [7, 11, 35, 55] and customized oriented object detectors [10, 17, 18, 60, 62]. Nevertheless, one ignorable fact is that there exist numerous tiny objects in aerial images. When oriented objects are tiny-sized, the challenges posed to existing object detec" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 312, + 226, + 419, + 365 + ], + "blocks": [ + { + "bbox": [ + 312, + 226, + 419, + 365 + ], + "lines": [ + { + "bbox": [ + 312, + 226, + 419, + 365 + ], + "spans": [ + { + "bbox": [ + 312, + 226, + 419, + 365 + ], + "type": "image", + "image_path": "1526adbf2c93c96dcfa12072377bb6d386b3ec3d5f7c421e32bd033545b8c174.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 375, + 545, + 464 + ], + "lines": [ + { + "bbox": [ + 305, + 375, + 545, + 464 + ], + "spans": [ + { + "bbox": [ + 305, + 375, + 545, + 464 + ], + "type": "text", + "content": "Figure 1. Comparisons of different learning paradigms for oriented object detection. " + }, + { + "bbox": [ + 305, + 375, + 545, + 464 + ], + "type": "inline_equation", + "content": "\\mathbf{M}^*" + }, + { + "bbox": [ + 305, + 375, + 545, + 464 + ], + "type": "text", + "content": " means the matching function. Each box in the " + }, + { + "bbox": [ + 305, + 375, + 545, + 464 + ], + "type": "inline_equation", + "content": "2^{nd}" + }, + { + "bbox": [ + 305, + 375, + 545, + 464 + ], + "type": "text", + "content": " row denotes a prior location. The " + }, + { + "bbox": [ + 305, + 375, + 545, + 464 + ], + "type": "inline_equation", + "content": "3^{rd}" + }, + { + "bbox": [ + 305, + 375, + 545, + 464 + ], + "type": "text", + "content": " row are predictions of the RetinaNet and DCFL, where green, blue, and red boxes denote true positive, false positive, and false negative predictions. (a) RetinaNet, FCOS, and Rotated RPN statically assign labels between fixed priors and fixed gts. (b) Our proposed DCFL dynamically updates priors and gts, and dynamically assigns labels." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 433, + 227, + 541, + 365 + ], + "blocks": [ + { + "bbox": [ + 433, + 227, + 541, + 365 + ], + "lines": [ + { + "bbox": [ + 433, + 227, + 541, + 365 + ], + "spans": [ + { + "bbox": [ + 433, + 227, + 541, + 365 + ], + "type": "image", + "image_path": "4aa88e6d63773e986665faec731902ad01d8f794d719779be4287cd2dfb24f81.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 486, + 545, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 545, + 521 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 545, + 521 + ], + "type": "text", + "content": "tors are quite remarkable. Especially, the extreme geometry characteristics of oriented tiny objects hamper the accurate label assignment." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "content": "Label assignment is a fundamental and crucial process in object detection [68], in which priors (box for anchor-based [30] and point for anchor-free detectors [50]) need to be assigned with appropriate labels to supervise the network training. In fact, there have been some works that lay a foundation for the effective label assignment of oriented objects, as shown in Fig. 1. Early works additionally preset anchors of different angles (e.g. Rotated RPN [36]) or refine high-quality anchors (e.g. " + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{S}^2\\mathrm{A}" + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "content": " -Net [17]) based on the generic object detector, then a static rule (e.g. MaxIoU strategy [44]) is used to separate positive and negative (pos/neg) training samples. The derived prior boxes can thus cover more ground truth (gt) boxes and a considerable accuracy improvement can be expected. However, the static assignment cannot adaptively divide pos/neg samples according to the gt's shape and filter out low-quality samples, usually" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 139, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 139, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 139, + 712 + ], + "type": "text", + "content": "*Corresponding Authors" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7318" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 74, + 285, + 178 + ], + "blocks": [ + { + "bbox": [ + 51, + 74, + 285, + 178 + ], + "lines": [ + { + "bbox": [ + 51, + 74, + 285, + 178 + ], + "spans": [ + { + "bbox": [ + 51, + 74, + 285, + 178 + ], + "type": "image", + "image_path": "d3f40233bf6fefa2613d355a9f0e50197da0c3f35aad322bf2c196f1870a309b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 185, + 288, + 231 + ], + "lines": [ + { + "bbox": [ + 46, + 185, + 288, + 231 + ], + "spans": [ + { + "bbox": [ + 46, + 185, + 288, + 231 + ], + "type": "text", + "content": "Figure 2. The mismatch and imbalance issues. Each point in the left image denotes a prior location. The number in the pie-shaped bar chart denotes the mean number of positive samples assigned to each instance in a specific angle range." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 254, + 195, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 254, + 195, + 266 + ], + "spans": [ + { + "bbox": [ + 47, + 254, + 195, + 266 + ], + "type": "text", + "content": "leading to sub-optimal performance." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 267, + 287, + 352 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 267, + 287, + 352 + ], + "spans": [ + { + "bbox": [ + 46, + 267, + 287, + 352 + ], + "type": "text", + "content": "Recently, the exploration of adaptive label assignment [68] brings new insight to the community. For oriented object detection, DAL [38] defines a prediction-aware matching degree and utilizes it to reweight anchors, achieving dynamic sample learning. Besides, several studies [21,23,26] incorporate the shape information into detectors and propose shape-aware sampling and measurement." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 354, + 287, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 354, + 287, + 651 + ], + "spans": [ + { + "bbox": [ + 45, + 354, + 287, + 651 + ], + "type": "text", + "content": "Despite the progress, the arbitrary orientation and extreme size of oriented tiny objects still pose a dilemma to the detector. As shown in Fig. 2, the mismatch and imbalance issues are particularly pronounced. For one thing, there is a mutual mismatch issue between the position prior, feature, and instance. Although some adaptive label assignment schemes may explore a better pos/neg division of the prior boxes or points, the sampled feature location behind the prior is still fixed and the derived prior is still static and uniformly located, most priors deviate from the tiny object's main body. The prior and feature themselves cannot well-match the extreme shapes of oriented tiny objects, no matter how we divide pos/neg samples. For another, the existing detectors tend to introduce bias and imbalance for oriented and tiny objects. More precisely, for anchor-based detectors, gt with shapes different from anchor boxes will yield low IoU [38, 59], leading to the lack of positive samples. In Fig. 2, we calculate the mean number of positive samples assigned to different gts with the RetinaNet and observe that there is an extreme lack of positive samples for gts with angles and scales far from predefined anchors. For anchor-free detectors, the static prior and its fixed stride limit the upper number of high-quality positive samples. Tiny objects only cover a limited number of feature points, and most of these points are away from the object's main body." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": "This motivates us to design a more dynamic and balanced learning pipeline for oriented tiny object detection. As shown in Fig. 1, we alleviate the mismatch issue by reformulating the prior, label assignment, and " + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "inline_equation", + "content": "gt" + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": " representation all in a dynamic manner, which can be updated by" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "text", + "content": "the Deep Neural Network (DNN). Simultaneously, we dynamically and progressively assign labels in a coarse-to-fine manner to seek balanced supervision for various instances." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 109, + 546, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 109, + 546, + 361 + ], + "spans": [ + { + "bbox": [ + 304, + 109, + 546, + 361 + ], + "type": "text", + "content": "Specifically, we introduce a dynamic Prior Capturing Block (PCB) to learn the prior, which adaptively adjusts the prior location while retaining the physical meaning of prior [54]. The PCB is inspired by the paradigm of learnable proposals in the DETR [4] and Sparse R-CNN [48] which naturally avoids the mismatch issue between the predefined prior and feature. Compared to this paradigm, we introduce its flexibility for prior updates while keeping the fast-convergence ability of dense detectors [32, 54]. Based on the dynamic prior, we then select Cross-FPN-layer Coarse Positive Sample (CPS) candidates for further label assignment, and the CPS is realized by the Generalized Jensen-Shannon Divergence [39] (GJSD) between the " + }, + { + "bbox": [ + 304, + 109, + 546, + 361 + ], + "type": "inline_equation", + "content": "gt" + }, + { + "bbox": [ + 304, + 109, + 546, + 361 + ], + "type": "text", + "content": " and the dynamic prior. The GJSD is able to enlarge the CPS to the object's nearby spatial locations and adjacent FPN layers, ensuring more candidates for extreme-shaped objects. After obtaining the CPS, we re-rank these candidates with predictions (posterior) and represent the " + }, + { + "bbox": [ + 304, + 109, + 546, + 361 + ], + "type": "inline_equation", + "content": "gt" + }, + { + "bbox": [ + 304, + 109, + 546, + 361 + ], + "type": "text", + "content": " with a finer Dynamic Gaussian Mixture Model (DGMM), filtering out low-quality samples. All designs are incorporated into an end-to-end one-stage detector without additional branches." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 361, + 547, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 361, + 547, + 506 + ], + "spans": [ + { + "bbox": [ + 304, + 361, + 547, + 506 + ], + "type": "text", + "content": "In short, our contributions are listed as follows: (1) We identify that there exist severe mismatch and imbalance issues in the current learning pipeline for oriented tiny object detection. (2) We design a Dynamic Coarse-to-Fine Learning (DCFL) scheme for oriented tiny object detection, which is the first to model the prior, label assignment, and " + }, + { + "bbox": [ + 304, + 361, + 547, + 506 + ], + "type": "inline_equation", + "content": "gt" + }, + { + "bbox": [ + 304, + 361, + 547, + 506 + ], + "type": "text", + "content": " representation all in a dynamic manner. In the DCFL, we propose to use the GJSD to construct Coarse Positive Samples (CPS) and represent objects with a finer Dynamic Gaussian Mixture Model (DGMM), obtaining coarse-to-fine label assignment. (3) Extensive experiments on six datasets show promising results." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 517, + 392, + 530 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 517, + 392, + 530 + ], + "spans": [ + { + "bbox": [ + 306, + 517, + 392, + 530 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 538, + 452, + 551 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 538, + 452, + 551 + ], + "spans": [ + { + "bbox": [ + 306, + 538, + 452, + 551 + ], + "type": "text", + "content": "2.1. Oriented Object Detection" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": "Prior for Oriented Objects. Anchor, as a classic design in generic object detectors (e.g. Faster R-CNN [44], RetinaNet [30]), has facilitated object detection for a long time. Similarly, oriented object detection also benefits from the anchor design. Initially, rotated RPN [36] extends the RPN to the field of oriented object detection by tiling 54 anchors each location with preset angles and scales. Indeed, enumerating potential " + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "gt" + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": " shapes can notably improve the recall, apart from the sacks of additional computational cost. RoI Transformer [10] utilizes horizontal anchors and transforms the RPN-generated horizontal proposals to oriented proposals, reducing the number of rotated anchors. To save computation, the Oriented R-CNN [56] introduces an ori" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7319" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "text", + "content": "ented RPN that directly predicts oriented proposals based on horizontal anchors. Recently, one-stage oriented object detectors gradually emerged, including anchor-based detectors [17, 60] with box prior and anchor-free detectors [26, 28] with point prior. Most of them retain the fixed prior design, except for the " + }, + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "inline_equation", + "content": "\\mathrm{S}^2\\mathrm{A}" + }, + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "text", + "content": "-Net [17] which proposes to generate high-quality anchors." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 157, + 288, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 157, + 288, + 324 + ], + "spans": [ + { + "bbox": [ + 46, + 157, + 288, + 324 + ], + "type": "text", + "content": "Label Assignment. ATSS [68] reveals that label assignment plays a pivotal role in the detectors' performance [14,24,37]. In the field of oriented object detection, DAL [38] observes inconsistency between the input prior IoU and the output predicted IoU, then defines a matching degree as the soft label that dynamically reweights anchors. Recently, SASM [21] introduces a shape-adaptive sample selection and measurement strategy to improve detection performance. Similarly, GGHL [23] proposes to fit the main body of the instance by a single 2-D Gaussian heatmap, then it divides and reweights samples in a dynamic manner. In addition, Oriented Reppoints [26] improves the RepPoints [65] by assessing the quality of points for more effective label assignment." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 334, + 173, + 346 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 334, + 173, + 346 + ], + "spans": [ + { + "bbox": [ + 47, + 334, + 173, + 346 + ], + "type": "text", + "content": "2.2. Tiny Object Detection" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 353, + 287, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 353, + 287, + 483 + ], + "spans": [ + { + "bbox": [ + 46, + 353, + 287, + 483 + ], + "type": "text", + "content": "Multi-scale Learning. Basically, one can use a multi-resolution image pyramid to obtain multi-scale learning. However, the vanilla image pyramid will bring much computation cost. Thus, some works [29, 33, 34, 42, 49, 69] reduce computation with the efficient Feature Pyramid Network (FPN). Unlike the FPN, TridentNet [27] introduces multi-branch detection heads of various receptive fields for multi-scale prediction. Moreover, one can normalize the scale of objects for scale-invariant object detection, for example, SNIP [46] and SNIPER [47] resize images and train objects within a certain scale range." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 485, + 287, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 485, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 485, + 287, + 581 + ], + "type": "text", + "content": "Label Assignment. Tiny objects usually have low IoU with anchors or cover a limited number of feature points, thus suffering from the lack of positive samples. ATSS [68] slightly reconciles the number of positive samples for objects of different scales. NWD [57] designs a new metric to replace IoU, which can sample more positive samples for tiny objects. Recently, the RFLA [58] utilizes outliers to detect tiny objects for scale-balanced learning." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 582, + 287, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 688 + ], + "type": "text", + "content": "Context Information. Tiny object lacks discriminative features, but objects are closely related to the surrounding context. Therefore, we can leverage the context information to enhance small object detection. Muti-Region CNN (MRCNN) [15] and Inside-Outside Network (ION) [3] are two representative works that exploit local and global context information. Recently, the Relation Network [22] and transformer-based detectors [4, 54, 72] reason about the association between instances via the attention mechanism." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "Feature Enhancement. The feature representation of small objects can be enhanced by super-resolution or GAN." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": "PGAN [25] first applies GAN to small object detection. Besides, Bai et al. [1] introduce the MT-GAN which trains an image-level super-resolution model to improve the RoI features of small objects. In addition, there are some other methods based on super-resolution including [2,8,40,43]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 133, + 545, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 133, + 545, + 216 + ], + "spans": [ + { + "bbox": [ + 304, + 133, + 545, + 216 + ], + "type": "text", + "content": "By contrast, our method simultaneously handles the prior mismatch and unbalanced learning via dynamically modeling the prior, label assignment, and " + }, + { + "bbox": [ + 304, + 133, + 545, + 216 + ], + "type": "inline_equation", + "content": "gt" + }, + { + "bbox": [ + 304, + 133, + 545, + 216 + ], + "type": "text", + "content": " representation. Meanwhile, unlike the two-stage RoI-Transformer [10] or one-stage S²A-Net [17], we embed the dynamic prior inside the end-to-end one-stage detector without introducing any auxiliary branch." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 225, + 361, + 237 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 225, + 361, + 237 + ], + "spans": [ + { + "bbox": [ + 306, + 225, + 361, + 237 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 243, + 545, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 243, + 545, + 316 + ], + "spans": [ + { + "bbox": [ + 304, + 243, + 545, + 316 + ], + "type": "text", + "content": "Overview. Given a set of dense prior " + }, + { + "bbox": [ + 304, + 243, + 545, + 316 + ], + "type": "inline_equation", + "content": "P \\in \\mathbb{R}^{W \\times H \\times C}" + }, + { + "bbox": [ + 304, + 243, + 545, + 316 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 304, + 243, + 545, + 316 + ], + "type": "inline_equation", + "content": "W \\times H" + }, + { + "bbox": [ + 304, + 243, + 545, + 316 + ], + "type": "text", + "content": " is the feature map size, " + }, + { + "bbox": [ + 304, + 243, + 545, + 316 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 243, + 545, + 316 + ], + "type": "text", + "content": " is the shape information number, each feature point has one prior for simplicity), object detectors remap the set " + }, + { + "bbox": [ + 304, + 243, + 545, + 316 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 243, + 545, + 316 + ], + "type": "text", + "content": " into final detection results " + }, + { + "bbox": [ + 304, + 243, + 545, + 316 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 243, + 545, + 316 + ], + "type": "text", + "content": " through the Deep Neural Network (DNN), which can be simplified as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 390, + 316, + 545, + 329 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 390, + 316, + 545, + 329 + ], + "spans": [ + { + "bbox": [ + 390, + 316, + 545, + 329 + ], + "type": "interline_equation", + "content": "D = \\mathrm {D N N} _ {h} (P), \\tag {1}", + "image_path": "64f38f0ba8b9e8251273d171498c9f766373b51a51231c14109527df2fca2001.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 333, + 545, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 333, + 545, + 380 + ], + "spans": [ + { + "bbox": [ + 304, + 333, + 545, + 380 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 333, + 545, + 380 + ], + "type": "inline_equation", + "content": "\\mathrm{DNN}_h" + }, + { + "bbox": [ + 304, + 333, + 545, + 380 + ], + "type": "text", + "content": " denotes the detection head. Detection results " + }, + { + "bbox": [ + 304, + 333, + 545, + 380 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 333, + 545, + 380 + ], + "type": "text", + "content": " contain two parts: classification scores " + }, + { + "bbox": [ + 304, + 333, + 545, + 380 + ], + "type": "inline_equation", + "content": "D_{cls} \\in \\mathbb{R}^{W \\times H \\times A}" + }, + { + "bbox": [ + 304, + 333, + 545, + 380 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 304, + 333, + 545, + 380 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 304, + 333, + 545, + 380 + ], + "type": "text", + "content": " is the class number) and box locations " + }, + { + "bbox": [ + 304, + 333, + 545, + 380 + ], + "type": "inline_equation", + "content": "D_{reg} \\in \\mathbb{R}^{W \\times H \\times B}" + }, + { + "bbox": [ + 304, + 333, + 545, + 380 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 304, + 333, + 545, + 380 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 304, + 333, + 545, + 380 + ], + "type": "text", + "content": " is the box parameter number)." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 380, + 545, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 380, + 545, + 441 + ], + "spans": [ + { + "bbox": [ + 304, + 380, + 545, + 441 + ], + "type": "text", + "content": "To train the " + }, + { + "bbox": [ + 304, + 380, + 545, + 441 + ], + "type": "inline_equation", + "content": "\\mathrm{DNN}_h" + }, + { + "bbox": [ + 304, + 380, + 545, + 441 + ], + "type": "text", + "content": ", we need to find a proper matching between the prior set " + }, + { + "bbox": [ + 304, + 380, + 545, + 441 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 380, + 545, + 441 + ], + "type": "text", + "content": " and the " + }, + { + "bbox": [ + 304, + 380, + 545, + 441 + ], + "type": "inline_equation", + "content": "gt" + }, + { + "bbox": [ + 304, + 380, + 545, + 441 + ], + "type": "text", + "content": " set " + }, + { + "bbox": [ + 304, + 380, + 545, + 441 + ], + "type": "inline_equation", + "content": "GT" + }, + { + "bbox": [ + 304, + 380, + 545, + 441 + ], + "type": "text", + "content": ", and assign pos/neg labels to " + }, + { + "bbox": [ + 304, + 380, + 545, + 441 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 380, + 545, + 441 + ], + "type": "text", + "content": " to supervise the network learning. For static assigners (e.g. RetinaNet [30]), the set of pos labels " + }, + { + "bbox": [ + 304, + 380, + 545, + 441 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 380, + 545, + 441 + ], + "type": "text", + "content": " can be obtained via hand-crafted matching function " + }, + { + "bbox": [ + 304, + 380, + 545, + 441 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_s" + }, + { + "bbox": [ + 304, + 380, + 545, + 441 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 387, + 447, + 545, + 459 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 387, + 447, + 545, + 459 + ], + "spans": [ + { + "bbox": [ + 387, + 447, + 545, + 459 + ], + "type": "interline_equation", + "content": "G = \\mathcal {M} _ {s} (P, G T). \\tag {2}", + "image_path": "f07fa9dcbb893cccb1bb40d2527b90aa868466407cea0da64243b79fee6fcb3e.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 465, + 545, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 465, + 545, + 513 + ], + "spans": [ + { + "bbox": [ + 304, + 465, + 545, + 513 + ], + "type": "text", + "content": "For dynamic assigners [14, 24, 38], they tend to simultaneously leverage the prior information " + }, + { + "bbox": [ + 304, + 465, + 545, + 513 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 465, + 545, + 513 + ], + "type": "text", + "content": " and posterior information (predictions) " + }, + { + "bbox": [ + 304, + 465, + 545, + 513 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 465, + 545, + 513 + ], + "type": "text", + "content": ", and then apply a prediction-aware mapping " + }, + { + "bbox": [ + 304, + 465, + 545, + 513 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_d" + }, + { + "bbox": [ + 304, + 465, + 545, + 513 + ], + "type": "text", + "content": " to get the set " + }, + { + "bbox": [ + 304, + 465, + 545, + 513 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 465, + 545, + 513 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 380, + 519, + 545, + 532 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 380, + 519, + 545, + 532 + ], + "spans": [ + { + "bbox": [ + 380, + 519, + 545, + 532 + ], + "type": "interline_equation", + "content": "G = \\mathcal {M} _ {d} (P, D, G T). \\tag {3}", + "image_path": "d7e9edb1d37f8f43b43841413c97c755fddda8c363a0650ac41b091297eb18f3.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 538, + 545, + 562 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 538, + 545, + 562 + ], + "spans": [ + { + "bbox": [ + 304, + 538, + 545, + 562 + ], + "type": "text", + "content": "After the pos/neg label separation, the loss function can be summarized into two parts:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 332, + 567, + 545, + 602 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 332, + 567, + 545, + 602 + ], + "spans": [ + { + "bbox": [ + 332, + 567, + 545, + 602 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\sum_ {i = 1} ^ {N _ {p o s}} \\mathcal {L} _ {p o s} \\left(D _ {i}, G _ {i}\\right) + \\sum_ {j = 1} ^ {N _ {n e g}} \\mathcal {L} _ {n e g} \\left(D _ {j}, y _ {j}\\right), \\tag {4}", + "image_path": "7427b1601fa1e5088d01ecf9a06b32083f794abfb06b885ee7a6069db091a7b8.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 608, + 544, + 631 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 608, + 544, + 631 + ], + "spans": [ + { + "bbox": [ + 304, + 608, + 544, + 631 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 608, + 544, + 631 + ], + "type": "inline_equation", + "content": "N_{pos}" + }, + { + "bbox": [ + 304, + 608, + 544, + 631 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 608, + 544, + 631 + ], + "type": "inline_equation", + "content": "N_{neg}" + }, + { + "bbox": [ + 304, + 608, + 544, + 631 + ], + "type": "text", + "content": " are the number of positive and negative samples respectively, " + }, + { + "bbox": [ + 304, + 608, + 544, + 631 + ], + "type": "inline_equation", + "content": "y_{j}" + }, + { + "bbox": [ + 304, + 608, + 544, + 631 + ], + "type": "text", + "content": " denotes the negative label." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 632, + 545, + 679 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 632, + 545, + 679 + ], + "spans": [ + { + "bbox": [ + 304, + 632, + 545, + 679 + ], + "type": "text", + "content": "While in this work, we model the prior, label assignment, and " + }, + { + "bbox": [ + 304, + 632, + 545, + 679 + ], + "type": "inline_equation", + "content": "gt" + }, + { + "bbox": [ + 304, + 632, + 545, + 679 + ], + "type": "text", + "content": " representation all in a dynamic manner to alleviate the mismatch issue. To begin with, the dynamic prior is reformulated to (\\~ denotes the dynamic item):" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 369, + 685, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 369, + 685, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 369, + 685, + 545, + 715 + ], + "type": "interline_equation", + "content": "\\tilde {D} = \\mathrm {D N N} _ {h} (\\underbrace {\\mathrm {D N N} _ {p} (P)} _ {\\text {D y n a m i c P r i o r} \\tilde {P}}), \\tag {5}", + "image_path": "02d65eb735febf354c57e615cc1adc996a36effa4ecf15738f0943233e12af08.jpg" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7320" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "inline_equation", + "content": "\\mathrm{DNN}_p" + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "text", + "content": " is a learnable block incorporated within the detection head to update the prior. Then, the matching function is reformulated to a coarse-to-fine paradigm:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 117, + 287, + 131 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 117, + 287, + 131 + ], + "spans": [ + { + "bbox": [ + 105, + 117, + 287, + 131 + ], + "type": "interline_equation", + "content": "\\tilde {G} = \\mathcal {M} _ {d} \\left(\\mathcal {M} _ {s} (\\tilde {P}, G T), \\tilde {G T}\\right), \\tag {6}", + "image_path": "1a43f2b482b9e4268b46d03d404fcb7221787b0cd8a1ce88b07377490fce8e3c.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 140, + 287, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 140, + 287, + 175 + ], + "spans": [ + { + "bbox": [ + 47, + 140, + 287, + 175 + ], + "type": "text", + "content": "the " + }, + { + "bbox": [ + 47, + 140, + 287, + 175 + ], + "type": "inline_equation", + "content": "\\tilde{G}T" + }, + { + "bbox": [ + 47, + 140, + 287, + 175 + ], + "type": "text", + "content": " is a finer representation of an object with the Dynamic Gaussian Mixture Model (DGMM). In a nutshell, our final loss is modeled as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 74, + 175, + 287, + 211 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 74, + 175, + 287, + 211 + ], + "spans": [ + { + "bbox": [ + 74, + 175, + 287, + 211 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\sum_ {i = 1} ^ {\\tilde {N} _ {p o s}} \\mathcal {L} _ {p o s} \\left(\\tilde {D} _ {i}, \\tilde {G} _ {i}\\right) + \\sum_ {j = 1} ^ {\\tilde {N} _ {n e g}} \\mathcal {L} _ {n e g} \\left(\\tilde {D} _ {j}, y _ {j}\\right). \\tag {7}", + "image_path": "f63fbbab934cd1b806931a11f96b1ca2b9bcb5c110bc4f772fd7fae82da1cc14.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 218, + 139, + 231 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 218, + 139, + 231 + ], + "spans": [ + { + "bbox": [ + 47, + 218, + 139, + 231 + ], + "type": "text", + "content": "3.1. Dynamic Prior" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 237, + 287, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 237, + 287, + 403 + ], + "spans": [ + { + "bbox": [ + 46, + 237, + 287, + 403 + ], + "type": "text", + "content": "Inspired by the purely learnable paradigm of proposal updation in the DETR [4] and Sparse R-CNN [48], we propose to introduce more flexibility into the prior to mitigate the mismatch issue. Moreover, we retain the physical meaning of prior where each individual prior stands for a feature point, inheriting the fast convergence ability of dense detectors. The structure of the proposed Prior Capturing Block (PCB) is shown in Fig. 3, in which a dilated convolution is deployed to take the surrounding information into account, and then the Deformable Convolution Network (DCN) [9] is leveraged to capture the dynamic prior. Besides, we utilize the learned offsets from the regression branch to guide the feature extraction of the classification branch, leading to better alignment between the two tasks." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 404, + 287, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 404, + 287, + 475 + ], + "spans": [ + { + "bbox": [ + 46, + 404, + 287, + 475 + ], + "type": "text", + "content": "The dynamic prior capturing process is as follows. First of all, we initialize each prior location " + }, + { + "bbox": [ + 46, + 404, + 287, + 475 + ], + "type": "inline_equation", + "content": "\\mathbf{p}(x,y)" + }, + { + "bbox": [ + 46, + 404, + 287, + 475 + ], + "type": "text", + "content": " by each feature point's spatial location s (which is remapped to the image). In each iteration, we forward the network to capture the offset sets of each prior location " + }, + { + "bbox": [ + 46, + 404, + 287, + 475 + ], + "type": "inline_equation", + "content": "\\Delta \\mathbf{o}" + }, + { + "bbox": [ + 46, + 404, + 287, + 475 + ], + "type": "text", + "content": ". Hence, the prior spatial location can be updated by:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 116, + 476, + 287, + 506 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 476, + 287, + 506 + ], + "spans": [ + { + "bbox": [ + 116, + 476, + 287, + 506 + ], + "type": "interline_equation", + "content": "\\tilde {\\mathbf {s}} = \\mathbf {s} + s t \\sum_ {i = 1} ^ {n} \\Delta \\mathbf {o} _ {i} / 2 n, \\tag {8}", + "image_path": "709977b1a147aa690204dd3f5073bb316ac92deffd496c9d5deed2e5d29d6648.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 506, + 287, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 506, + 287, + 602 + ], + "spans": [ + { + "bbox": [ + 46, + 506, + 287, + 602 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 506, + 287, + 602 + ], + "type": "inline_equation", + "content": "st" + }, + { + "bbox": [ + 46, + 506, + 287, + 602 + ], + "type": "text", + "content": " is the feature map's stride, " + }, + { + "bbox": [ + 46, + 506, + 287, + 602 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 506, + 287, + 602 + ], + "type": "text", + "content": " is the number of offsets. Finally, we utilize the 2-D Gaussian distribution " + }, + { + "bbox": [ + 46, + 506, + 287, + 602 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_p(\\boldsymbol{\\mu}_p, \\boldsymbol{\\Sigma}_p)" + }, + { + "bbox": [ + 46, + 506, + 287, + 602 + ], + "type": "text", + "content": " which is demonstrated conducive to small objects [58,61] and oriented objects [61,63] to fit the prior spatial location. Concretely, the dynamic " + }, + { + "bbox": [ + 46, + 506, + 287, + 602 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{s}}" + }, + { + "bbox": [ + 46, + 506, + 287, + 602 + ], + "type": "text", + "content": " serves as the Gaussian's mean vector " + }, + { + "bbox": [ + 46, + 506, + 287, + 602 + ], + "type": "inline_equation", + "content": "\\boldsymbol{\\mu}_p" + }, + { + "bbox": [ + 46, + 506, + 287, + 602 + ], + "type": "text", + "content": ". We preset one prior which is square-shaped " + }, + { + "bbox": [ + 46, + 506, + 287, + 602 + ], + "type": "inline_equation", + "content": "(w, h, \\theta)" + }, + { + "bbox": [ + 46, + 506, + 287, + 602 + ], + "type": "text", + "content": " as that in RetinaNet [30] on each feature point, then compute the co-variance matrix " + }, + { + "bbox": [ + 46, + 506, + 287, + 602 + ], + "type": "inline_equation", + "content": "\\boldsymbol{\\Sigma}_p" + }, + { + "bbox": [ + 46, + 506, + 287, + 602 + ], + "type": "text", + "content": " by [64]:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 58, + 611, + 287, + 641 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 611, + 287, + 641 + ], + "spans": [ + { + "bbox": [ + 58, + 611, + 287, + 641 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\Sigma} _ {p} = \\left[ \\begin{array}{c c} \\cos \\theta & - \\sin \\theta \\\\ \\sin \\theta & \\cos \\theta \\end{array} \\right] \\left[ \\begin{array}{c c} \\frac {w ^ {2}}{4} & 0 \\\\ 0 & \\frac {h ^ {2}}{4} \\end{array} \\right] \\left[ \\begin{array}{c c} \\cos \\theta & \\sin \\theta \\\\ - \\sin \\theta & \\cos \\theta \\end{array} \\right]. \\tag {9}", + "image_path": "80892738e993ea553dd07d4337c756d696fd5b444f929f3b489ec500e6ebe705.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 647, + 178, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 178, + 659 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 178, + 659 + ], + "type": "text", + "content": "3.2. Coarse Prior Matching" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 666, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 666, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 666, + 287, + 713 + ], + "type": "text", + "content": "Given a set of prior, one basic assignment rule is to specify a range of candidate true prediction samples for a specific " + }, + { + "bbox": [ + 47, + 666, + 287, + 713 + ], + "type": "inline_equation", + "content": "gt" + }, + { + "bbox": [ + 47, + 666, + 287, + 713 + ], + "type": "text", + "content": ". Some adaptive strategies restrict the candidates of a given " + }, + { + "bbox": [ + 47, + 666, + 287, + 713 + ], + "type": "inline_equation", + "content": "gt" + }, + { + "bbox": [ + 47, + 666, + 287, + 713 + ], + "type": "text", + "content": " inside a single FPN layer [14,23,68], while some" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": "works release all layers as candidates [67, 71]. However, for oriented tiny objects, the former strict heuristic rule may lead to a sub-optimal layer selection and the latter loose one will induce the slow convergence issue [32]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 120, + 545, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 120, + 545, + 215 + ], + "spans": [ + { + "bbox": [ + 304, + 120, + 545, + 215 + ], + "type": "text", + "content": "Hence, we propose Cross-FPN-layer Coarse Positive Sample (CPS) candidates, which narrows down the sample range compared to the all-FPN-layer manner while discarding the single-layer heuristic. In the CPS, we slightly expand the range of candidates to the " + }, + { + "bbox": [ + 304, + 120, + 545, + 215 + ], + "type": "inline_equation", + "content": "gt" + }, + { + "bbox": [ + 304, + 120, + 545, + 215 + ], + "type": "text", + "content": "'s nearby spatial location and adjacent FPN layers, which warrants relatively diverse and sufficient candidates compared to the single-layer heuristic and alleviates the quantity imbalance issue." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 216, + 545, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 216, + 545, + 346 + ], + "spans": [ + { + "bbox": [ + 304, + 216, + 545, + 346 + ], + "type": "text", + "content": "Specifically, the similarity measurement in constructing the CPS is realized with the Jensen-Shannon Divergence (JSD) [13], which inherits the scale invariance property of the Kullback-Leibler Divergence (KLD) [63] and can measure the " + }, + { + "bbox": [ + 304, + 216, + 545, + 346 + ], + "type": "inline_equation", + "content": "gt" + }, + { + "bbox": [ + 304, + 216, + 545, + 346 + ], + "type": "text", + "content": "'s similarity with nearby non-overlapping priors [58, 63]. Moreover, it conquers KLD's drawback of asymmetry. However, the closed-form solution of the JSD between Gaussian distributions is unavailable [39], thus, we utilize the Generalized Jensen-Shannon Divergence (GJSD) [39] which yields a closed-form solution, as the substitute." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 347, + 545, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 347, + 545, + 373 + ], + "spans": [ + { + "bbox": [ + 305, + 347, + 545, + 373 + ], + "type": "text", + "content": "For example, the GJSD between two Gaussian distributions " + }, + { + "bbox": [ + 305, + 347, + 545, + 373 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_p(\\boldsymbol{\\mu}_p, \\boldsymbol{\\Sigma}_p)" + }, + { + "bbox": [ + 305, + 347, + 545, + 373 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 347, + 545, + 373 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_g(\\boldsymbol{\\mu}_g, \\boldsymbol{\\Sigma}_g)" + }, + { + "bbox": [ + 305, + 347, + 545, + 373 + ], + "type": "text", + "content": " is defined by:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 381, + 545, + 405 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 381, + 545, + 405 + ], + "spans": [ + { + "bbox": [ + 306, + 381, + 545, + 405 + ], + "type": "interline_equation", + "content": "\\operatorname {G J S D} \\left(\\mathcal {N} _ {p}, \\mathcal {N} _ {g}\\right) = (1 - \\alpha) \\mathrm {K L} \\left(\\mathcal {N} _ {\\alpha}, \\mathcal {N} _ {p}\\right) + \\alpha \\mathrm {K L} \\left(\\mathcal {N} _ {\\alpha}, \\mathcal {N} _ {g}\\right), \\tag {10}", + "image_path": "a85792f560a6f88f82bc75a0f01d4a45f31ad1b718f04715463f3c0d8e7b361c.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 406, + 543, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 406, + 543, + 418 + ], + "spans": [ + { + "bbox": [ + 306, + 406, + 543, + 418 + ], + "type": "text", + "content": "where KL denotes the KLD, and " + }, + { + "bbox": [ + 306, + 406, + 543, + 418 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_{\\alpha}(\\pmb{\\mu}_{\\alpha}, \\pmb{\\Sigma}_{\\alpha})" + }, + { + "bbox": [ + 306, + 406, + 543, + 418 + ], + "type": "text", + "content": " is given by:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 319, + 427, + 545, + 444 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 427, + 545, + 444 + ], + "spans": [ + { + "bbox": [ + 319, + 427, + 545, + 444 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\Sigma} _ {\\alpha} = \\left(\\boldsymbol {\\Sigma} _ {p} \\boldsymbol {\\Sigma} _ {g}\\right) _ {\\alpha} ^ {\\boldsymbol {\\Sigma}} = \\left((1 - \\alpha) \\boldsymbol {\\Sigma} _ {p} ^ {- 1} + \\alpha \\boldsymbol {\\Sigma} _ {g} ^ {- 1}\\right) ^ {- 1}, \\tag {11}", + "image_path": "4678c0d0a9da35e3c6dddcdd6e861c3429bc3acb4bbe9150889669060edb8faa.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 453, + 323, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 453, + 323, + 462 + ], + "spans": [ + { + "bbox": [ + 306, + 453, + 323, + 462 + ], + "type": "text", + "content": "and" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 341, + 460, + 511, + 493 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 341, + 460, + 511, + 493 + ], + "spans": [ + { + "bbox": [ + 341, + 460, + 511, + 493 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\boldsymbol {\\mu} _ {\\alpha} = \\left(\\boldsymbol {\\mu} _ {p} \\boldsymbol {\\mu} _ {g}\\right) _ {\\alpha} ^ {\\boldsymbol {\\mu}} \\\\ = \\boldsymbol {\\Sigma} _ {\\alpha} \\left((1 - \\alpha) \\boldsymbol {\\Sigma} _ {p} ^ {- 1} \\boldsymbol {\\mu} _ {p} + \\alpha \\boldsymbol {\\Sigma} _ {g} ^ {- 1} \\boldsymbol {\\mu} _ {g}\\right). \\\\ \\end{array}", + "image_path": "a26e67993565d751557792835fee086caeae61fc11419591248cec739c1ed694.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 527, + 471, + 544, + 480 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 527, + 471, + 544, + 480 + ], + "spans": [ + { + "bbox": [ + 527, + 471, + 544, + 480 + ], + "type": "text", + "content": "(12)" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 496, + 545, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 496, + 545, + 532 + ], + "spans": [ + { + "bbox": [ + 304, + 496, + 545, + 532 + ], + "type": "text", + "content": "Note that " + }, + { + "bbox": [ + 304, + 496, + 545, + 532 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 496, + 545, + 532 + ], + "type": "text", + "content": " is a parameter that controls the weight of two distributions [39] in similarity measurement. In our work, the " + }, + { + "bbox": [ + 304, + 496, + 545, + 532 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_p" + }, + { + "bbox": [ + 304, + 496, + 545, + 532 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 496, + 545, + 532 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_q" + }, + { + "bbox": [ + 304, + 496, + 545, + 532 + ], + "type": "text", + "content": " contribute equally, thus " + }, + { + "bbox": [ + 304, + 496, + 545, + 532 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 496, + 545, + 532 + ], + "type": "text", + "content": " is set to 0.5." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 532, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 532, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 532, + 545, + 628 + ], + "type": "text", + "content": "Ultimately, for each " + }, + { + "bbox": [ + 304, + 532, + 545, + 628 + ], + "type": "inline_equation", + "content": "gt" + }, + { + "bbox": [ + 304, + 532, + 545, + 628 + ], + "type": "text", + "content": ", we select " + }, + { + "bbox": [ + 304, + 532, + 545, + 628 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 532, + 545, + 628 + ], + "type": "text", + "content": " priors which hold the top " + }, + { + "bbox": [ + 304, + 532, + 545, + 628 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 532, + 545, + 628 + ], + "type": "text", + "content": " GJSD score with this " + }, + { + "bbox": [ + 304, + 532, + 545, + 628 + ], + "type": "inline_equation", + "content": "gt" + }, + { + "bbox": [ + 304, + 532, + 545, + 628 + ], + "type": "text", + "content": " as the Coarse Positive Samples (CPS) and regard the remaining priors as negative samples, this coarse matching serves as the " + }, + { + "bbox": [ + 304, + 532, + 545, + 628 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_s" + }, + { + "bbox": [ + 304, + 532, + 545, + 628 + ], + "type": "text", + "content": " in Eq. 6. The ranking manner works together with the GJSD measurement to construct the Cross-FPN-layer CPS, eliminating the imbalance issue raised by the MaxIoU matching for outlier angles and scales, which will be analyzed in Sec. 5." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 635, + 492, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 635, + 492, + 647 + ], + "spans": [ + { + "bbox": [ + 306, + 635, + 492, + 647 + ], + "type": "text", + "content": "3.3. Finer Dynamic Posterior Matching" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 654, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 712 + ], + "type": "text", + "content": "Based on Coarse Positive Sample (CPS) candidates, we design a dynamic posterior (prediction) matching rule " + }, + { + "bbox": [ + 304, + 654, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_d" + }, + { + "bbox": [ + 304, + 654, + 545, + 712 + ], + "type": "text", + "content": " to filter out low-quality samples. The " + }, + { + "bbox": [ + 304, + 654, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_d" + }, + { + "bbox": [ + 304, + 654, + 545, + 712 + ], + "type": "text", + "content": " consists of two key components, namely a posterior re-ranking strategy and a Dynamic Gaussian Mixture Model (DGMM) constraint." + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "7321" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 70, + 298, + 199 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 298, + 199 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 298, + 199 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 298, + 199 + ], + "type": "image", + "image_path": "dc573d6825887ef255c083e96a81d529d1824e4a6c745b3ce279f11d04cede5a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 79, + 209, + 512, + 221 + ], + "lines": [ + { + "bbox": [ + 79, + 209, + 512, + 221 + ], + "spans": [ + { + "bbox": [ + 79, + 209, + 512, + 221 + ], + "type": "text", + "content": "Figure 3. The process of feature extraction and dynamic coarse-to-fine learning. PCB denotes the prior capturing block." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 300, + 70, + 541, + 199 + ], + "blocks": [ + { + "bbox": [ + 300, + 70, + 541, + 199 + ], + "lines": [ + { + "bbox": [ + 300, + 70, + 541, + 199 + ], + "spans": [ + { + "bbox": [ + 300, + 70, + 541, + 199 + ], + "type": "image", + "image_path": "9002cf5257404920462cd97d3152015c0644aeafbe4c298b57ebe07f1c4b0464.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 242, + 288, + 314 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 242, + 288, + 314 + ], + "spans": [ + { + "bbox": [ + 46, + 242, + 288, + 314 + ], + "type": "text", + "content": "We re-rank the sample candidates in the CPS according to their predicted scores. In other words, we further refine the positive samples by their Possibility of becoming True predictions " + }, + { + "bbox": [ + 46, + 242, + 288, + 314 + ], + "type": "inline_equation", + "content": "(PT)" + }, + { + "bbox": [ + 46, + 242, + 288, + 314 + ], + "type": "text", + "content": " [14], which is a linear combination of the predicted classification score and the location score with the " + }, + { + "bbox": [ + 46, + 242, + 288, + 314 + ], + "type": "inline_equation", + "content": "gt" + }, + { + "bbox": [ + 46, + 242, + 288, + 314 + ], + "type": "text", + "content": ". We define the " + }, + { + "bbox": [ + 46, + 242, + 288, + 314 + ], + "type": "inline_equation", + "content": "PT" + }, + { + "bbox": [ + 46, + 242, + 288, + 314 + ], + "type": "text", + "content": " of the " + }, + { + "bbox": [ + 46, + 242, + 288, + 314 + ], + "type": "inline_equation", + "content": "i^{th}" + }, + { + "bbox": [ + 46, + 242, + 288, + 314 + ], + "type": "text", + "content": " sample " + }, + { + "bbox": [ + 46, + 242, + 288, + 314 + ], + "type": "inline_equation", + "content": "D_{i}" + }, + { + "bbox": [ + 46, + 242, + 288, + 314 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 91, + 319, + 287, + 343 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 319, + 287, + 343 + ], + "spans": [ + { + "bbox": [ + 91, + 319, + 287, + 343 + ], + "type": "interline_equation", + "content": "P T _ {i} = \\frac {1}{2} C l s (D _ {i}) + \\frac {1}{2} I o U (D _ {i}, g t _ {i}), \\tag {13}", + "image_path": "ed449830f8b5bcfc61f2d2bc0fe6a13dec0d7f21318643298006c06f29b82c8f.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 350, + 287, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 350, + 287, + 396 + ], + "spans": [ + { + "bbox": [ + 46, + 350, + 287, + 396 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 350, + 287, + 396 + ], + "type": "inline_equation", + "content": "Cls" + }, + { + "bbox": [ + 46, + 350, + 287, + 396 + ], + "type": "text", + "content": " is the predicted classification confidence and " + }, + { + "bbox": [ + 46, + 350, + 287, + 396 + ], + "type": "inline_equation", + "content": "IoU" + }, + { + "bbox": [ + 46, + 350, + 287, + 396 + ], + "type": "text", + "content": " is the rotated IoU between the predicted location and its corresponding " + }, + { + "bbox": [ + 46, + 350, + 287, + 396 + ], + "type": "inline_equation", + "content": "gt" + }, + { + "bbox": [ + 46, + 350, + 287, + 396 + ], + "type": "text", + "content": " location. We select candidates with " + }, + { + "bbox": [ + 46, + 350, + 287, + 396 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 46, + 350, + 287, + 396 + ], + "type": "text", + "content": " highest " + }, + { + "bbox": [ + 46, + 350, + 287, + 396 + ], + "type": "inline_equation", + "content": "PT" + }, + { + "bbox": [ + 46, + 350, + 287, + 396 + ], + "type": "text", + "content": " as Medium Positive Sample (MPS) candidates." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 396, + 287, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 396, + 287, + 542 + ], + "spans": [ + { + "bbox": [ + 46, + 396, + 287, + 542 + ], + "type": "text", + "content": "Following this, we filter out those samples too far away from the " + }, + { + "bbox": [ + 46, + 396, + 287, + 542 + ], + "type": "inline_equation", + "content": "gts" + }, + { + "bbox": [ + 46, + 396, + 287, + 542 + ], + "type": "text", + "content": " with a finer instance representation, getting the Finer Positive Samples (FPS). Different from previous works which utilize the center probability map [53] or the single-Gaussian [23,64] for instance representation, we represent the instance by a finer DGMM. It consists of two components: one is centered on the geometry center and the other is centered on the semantic center of the object. Concretely, for a specific instance " + }, + { + "bbox": [ + 46, + 396, + 287, + 542 + ], + "type": "inline_equation", + "content": "gt_{i}" + }, + { + "bbox": [ + 46, + 396, + 287, + 542 + ], + "type": "text", + "content": ", the geometry center " + }, + { + "bbox": [ + 46, + 396, + 287, + 542 + ], + "type": "inline_equation", + "content": "(cx_{i}, cy_{i})" + }, + { + "bbox": [ + 46, + 396, + 287, + 542 + ], + "type": "text", + "content": " serves as the mean vector " + }, + { + "bbox": [ + 46, + 396, + 287, + 542 + ], + "type": "inline_equation", + "content": "\\mu_{i,1}" + }, + { + "bbox": [ + 46, + 396, + 287, + 542 + ], + "type": "text", + "content": " of the first Gaussian, and the semantic center " + }, + { + "bbox": [ + 46, + 396, + 287, + 542 + ], + "type": "inline_equation", + "content": "(sx_{i}, sy_{i})" + }, + { + "bbox": [ + 46, + 396, + 287, + 542 + ], + "type": "text", + "content": ", which is deduced by averaging the location of the samples in the MPS, serves as the " + }, + { + "bbox": [ + 46, + 396, + 287, + 542 + ], + "type": "inline_equation", + "content": "\\mu_{i,2}" + }, + { + "bbox": [ + 46, + 396, + 287, + 542 + ], + "type": "text", + "content": ". That is to say, we parameterize the instance as:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 52, + 544, + 287, + 581 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 544, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 52, + 544, + 287, + 581 + ], + "type": "interline_equation", + "content": "D G M M _ {i} (s | x, y) = \\sum_ {m = 1} ^ {2} w _ {i, m} \\sqrt {2 \\pi | \\boldsymbol {\\Sigma} _ {i , m} |} \\mathcal {N} _ {i, m} \\left(\\boldsymbol {\\mu} _ {i, m}, \\boldsymbol {\\Sigma} _ {i, m}\\right), \\tag {14}", + "image_path": "1bbfb8c39b8d8b39c9e633e5085558e51ac4c745c3479e019e4c72d13cafbfd7.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 582, + 287, + 642 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 642 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 642 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 582, + 287, + 642 + ], + "type": "inline_equation", + "content": "w_{i,m}" + }, + { + "bbox": [ + 46, + 582, + 287, + 642 + ], + "type": "text", + "content": " is the weight of each Gaussian with a summation of 1, " + }, + { + "bbox": [ + 46, + 582, + 287, + 642 + ], + "type": "inline_equation", + "content": "\\Sigma_{i,m}" + }, + { + "bbox": [ + 46, + 582, + 287, + 642 + ], + "type": "text", + "content": " equals to the " + }, + { + "bbox": [ + 46, + 582, + 287, + 642 + ], + "type": "inline_equation", + "content": "gt" + }, + { + "bbox": [ + 46, + 582, + 287, + 642 + ], + "type": "text", + "content": "'s " + }, + { + "bbox": [ + 46, + 582, + 287, + 642 + ], + "type": "inline_equation", + "content": "\\Sigma_g" + }, + { + "bbox": [ + 46, + 582, + 287, + 642 + ], + "type": "text", + "content": ". Each sample in MPS has a DGMM score " + }, + { + "bbox": [ + 46, + 582, + 287, + 642 + ], + "type": "inline_equation", + "content": "DGMM(s|MPS)" + }, + { + "bbox": [ + 46, + 582, + 287, + 642 + ], + "type": "text", + "content": ", we set negative masks to samples which have " + }, + { + "bbox": [ + 46, + 582, + 287, + 642 + ], + "type": "inline_equation", + "content": "DGMM(s|MPS) < e^{-g}" + }, + { + "bbox": [ + 46, + 582, + 287, + 642 + ], + "type": "text", + "content": " with any " + }, + { + "bbox": [ + 46, + 582, + 287, + 642 + ], + "type": "inline_equation", + "content": "gt" + }, + { + "bbox": [ + 46, + 582, + 287, + 642 + ], + "type": "text", + "content": ", the " + }, + { + "bbox": [ + 46, + 582, + 287, + 642 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 46, + 582, + 287, + 642 + ], + "type": "text", + "content": " is adjustable." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 651, + 128, + 664 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 651, + 128, + 664 + ], + "spans": [ + { + "bbox": [ + 47, + 651, + 128, + 664 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 671, + 110, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 110, + 682 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 110, + 682 + ], + "type": "text", + "content": "4.1. Datasets" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "Experiments are done on six datasets, i.e., DOTA-v1.0 [55]/v1.5/v2.0 [11], DIOR-R [7], VisDrone [12], and" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 241, + 545, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 241, + 545, + 338 + ], + "spans": [ + { + "bbox": [ + 304, + 241, + 545, + 338 + ], + "type": "text", + "content": "MS COCO [31]. In ablation studies and analyses, we choose the large-scale DOTA-v2.0 train set for training and val set for evaluation, which contains a large number of tiny objects. To compare with other methods, we use trainval sets of DOTA-v1.0, DOTA-v1.5, DOTA-v2.0, and DIOR-R for training and their test sets for testing, we choose the VisDrone2019, MS COCO train set, val set for training and testing." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 345, + 440, + 358 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 345, + 440, + 358 + ], + "spans": [ + { + "bbox": [ + 305, + 345, + 440, + 358 + ], + "type": "text", + "content": "4.2. Implementation Details" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 363, + 545, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 363, + 545, + 495 + ], + "spans": [ + { + "bbox": [ + 304, + 363, + 545, + 495 + ], + "type": "text", + "content": "We conduct all the experiments on the computer with a single NVIDIA RTX 3090 GPU, and the batch size is set to 4. Models are built based on MMDetection [6] and MMRotate [70] with PyTorch [41]. The ImageNet [45] pre-trained models are used as the backbone. The Stochastic Gradient Descent (SGD) optimizer is used for training with a learning rate of 0.005, a momentum of 0.9, and a weight decay of 0.0001. The ResNet-50 [20] with FPN [29] is the default backbone if not specified. We use Focal loss [30] for classification and IoU loss [66] for regression. We only use random flipping as data augmentation for all experiments." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 495, + 545, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 495, + 545, + 567 + ], + "spans": [ + { + "bbox": [ + 304, + 495, + 545, + 567 + ], + "type": "text", + "content": "For experiments on the DOTA-v1.0 and DOTA-v2.0, we follow the official settings of the DOTA-v2.0 benchmark [11], i.e., we crop images into patches of " + }, + { + "bbox": [ + 304, + 495, + 545, + 567 + ], + "type": "inline_equation", + "content": "1024 \\times 1024" + }, + { + "bbox": [ + 304, + 495, + 545, + 567 + ], + "type": "text", + "content": " with overlaps of 200 and train the model for 12 epochs. For DOTA-v2.0, we reproduce one-stage state-of-the-art methods [17,21,26,38,50,60,63,68] with the same settings." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 567, + 545, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 567, + 545, + 651 + ], + "spans": [ + { + "bbox": [ + 304, + 567, + 545, + 651 + ], + "type": "text", + "content": "For experiments on other datasets, we set the input size to " + }, + { + "bbox": [ + 304, + 567, + 545, + 651 + ], + "type": "inline_equation", + "content": "1024 \\times 1024" + }, + { + "bbox": [ + 304, + 567, + 545, + 651 + ], + "type": "text", + "content": " (overlap 200), " + }, + { + "bbox": [ + 304, + 567, + 545, + 651 + ], + "type": "inline_equation", + "content": "800 \\times 800" + }, + { + "bbox": [ + 304, + 567, + 545, + 651 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 567, + 545, + 651 + ], + "type": "inline_equation", + "content": "1333 \\times 800" + }, + { + "bbox": [ + 304, + 567, + 545, + 651 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 567, + 545, + 651 + ], + "type": "inline_equation", + "content": "1333 \\times 800" + }, + { + "bbox": [ + 304, + 567, + 545, + 651 + ], + "type": "text", + "content": " for DOTA-v1.5, DIOR-R, VisDrone, and COCO respectively. We train the models for 40, 40, 12, and 12 epochs on the DOTA-v1.5, DIOR-R, COCO, and VisDrone as previous works do [16, 26]. The above settings are fixed unless otherwise specified." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 658, + 391, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 658, + 391, + 670 + ], + "spans": [ + { + "bbox": [ + 306, + 658, + 391, + 670 + ], + "type": "text", + "content": "4.3. Main Results" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "Results on DOTA series. As shown in Tab. 1, our proposed method achieves the state-of-the-art performance of " + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "57.66\\%" + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": " mAP on the DOTA-v2.0 OBB benchmark un" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7322" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 71, + 547, + 284 + ], + "blocks": [ + { + "bbox": [ + 49, + 71, + 547, + 284 + ], + "lines": [ + { + "bbox": [ + 49, + 71, + 547, + 284 + ], + "spans": [ + { + "bbox": [ + 49, + 71, + 547, + 284 + ], + "type": "table", + "html": "
MethodBackbonePlaneBDBridgeGTFSVLVShipTCBCSTSBFRAHarborSPHCCCAirHelimAP
multi-stage:
FR OBB [44]R5071.6147.2039.2858.7035.5548.8851.5178.9758.3658.5536.1151.7343.5755.3357.073.5152.942.7947.31
FR OBB + DpR5071.5549.7440.3460.4040.7450.6756.5879.0358.2258.2434.7351.9544.3355.1053.147.2159.536.3848.77
MR [19]R5076.2049.9141.6160.0041.0850.7756.2478.0155.8557.4836.6251.6747.3955.7959.063.6460.268.9549.47
HTC* [5]R5077.6947.2541.1560.7141.7752.7958.8778.7455.2258.4938.5752.4849.5856.1854.094.2066.3811.9250.34
RT [10]R5071.8148.3945.8864.0242.0954.3959.9282.7063.2958.7141.0452.8253.3256.1857.9425.7163.728.7052.81
Oriented R-CNN [56]R5077.9550.2946.7365.2442.6154.5660.0279.0861.6959.4242.2656.8951.1156.1659.3325.8160.679.1753.28
one-stage:
DAL [38]R5071.2338.3638.6045.2435.4243.7556.0470.8450.8756.6320.2846.5333.4947.2912.150.8125.770.0038.52
SASM [21]R5070.3040.6237.0159.0340.2145.4644.6078.5849.3460.7329.8946.5742.9548.3128.131.8276.370.7444.53
RetinaNet-O [30]R5070.6347.2639.1255.0238.1040.5247.1677.7456.8652.1237.2251.7544.1553.1951.066.5864.287.4546.68
\\( R^3Det w/ KLD [63] \\)R5075.4450.9541.1661.6141.1145.7649.6578.5254.9760.7942.0753.2043.0849.5534.0936.2668.650.0647.26
FCOS-O [51]R5074.8447.5340.8357.4143.8947.7255.6678.6157.8663.0038.0252.3841.9153.2440.227.1565.517.4248.51
Oriented Rep [26]R5073.0246.6842.3763.0547.0650.2858.6478.8457.1266.7735.2150.7648.7751.6234.236.1764.665.8748.95
ATSS-O [68]R5077.4649.5542.1262.6145.1548.4051.7078.4359.3362.6539.1852.4342.9253.9842.705.9167.0910.6849.57
\\( S^2A-Net [17] \\)R5077.8451.3143.7262.5947.5150.5857.8680.7359.1165.3236.4352.6045.3652.4640.120.0062.8111.1149.86
one-stage:
DCFLR5075.7149.4044.6963.2346.4851.5555.5079.3059.9665.3941.8654.4247.0355.7250.4911.7569.017.7551.57
\\( S^2A-Net w/ DCFL \\)R5074.7953.2545.8165.4646.4953.2358.1081.5160.1366.4243.2455.0950.5255.5854.535.2368.7313.0652.84
DCFL†R5078.3053.0344.2460.1748.5655.4258.6678.2960.8965.9343.5455.8253.3360.0054.7630.9074.0115.6055.08
DCFL†ReR10179.4955.9750.1561.5949.0055.3359.3181.1866.5260.0652.8756.7157.8358.1360.3535.6678.6513.0357.66
", + "image_path": "5b470d38085c0b67b4b2742a123a0ad9bf1a86810f458ff604d43d1a55dd3d76.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 49, + 335, + 287, + 376 + ], + "blocks": [ + { + "bbox": [ + 46, + 288, + 546, + 323 + ], + "lines": [ + { + "bbox": [ + 46, + 288, + 546, + 323 + ], + "spans": [ + { + "bbox": [ + 46, + 288, + 546, + 323 + ], + "type": "text", + "content": "Table 1. Main results on the DOTA-v2.0 OBB Task. We follow the official class abbreviations as the DOTA-v2.0 benchmark [11]. " + }, + { + "bbox": [ + 46, + 288, + 546, + 323 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 46, + 288, + 546, + 323 + ], + "type": "text", + "content": " denotes training for 40 epochs. Note that this paper [63] reports " + }, + { + "bbox": [ + 46, + 288, + 546, + 323 + ], + "type": "inline_equation", + "content": "50.90\\%" + }, + { + "bbox": [ + 46, + 288, + 546, + 323 + ], + "type": "text", + "content": " mAP for " + }, + { + "bbox": [ + 46, + 288, + 546, + 323 + ], + "type": "inline_equation", + "content": "\\mathrm{R}^3\\mathrm{Det}" + }, + { + "bbox": [ + 46, + 288, + 546, + 323 + ], + "type": "text", + "content": " w/ KLD under 20 epochs, the ReR101 backbone is proposed by the ReDet [18]. The results in red and blue denote the best and second-best performance of each column." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 335, + 287, + 376 + ], + "lines": [ + { + "bbox": [ + 49, + 335, + 287, + 376 + ], + "spans": [ + { + "bbox": [ + 49, + 335, + 287, + 376 + ], + "type": "table", + "html": "
MethodCFA [16]RetinaNet-O [30]R3Det [60]Oriented Rep [26]ATSS-O [68]
mAP69.6369.7970.1871.9472.29
Method KLD [63]S2A-Net [17]GGHL [23](3x)DCFLDCFL(3x)
mAP72.7673.9173.9874.2675.35
", + "image_path": "d1d8ced44cc06e0a65feec4c892dfa26fa7aa62ea1a8ae53734bdfaa914d3f0d.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 49, + 419, + 287, + 490 + ], + "blocks": [ + { + "bbox": [ + 47, + 380, + 287, + 414 + ], + "lines": [ + { + "bbox": [ + 47, + 380, + 287, + 414 + ], + "spans": [ + { + "bbox": [ + 47, + 380, + 287, + 414 + ], + "type": "text", + "content": "Table 2. Comparison with one-stage detectors on the DOTA-v1.0 OBB Task. All results are based on the MMRotate [70] with 12 epochs except for GGHL [23]. 3x means training for 36 epochs." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 419, + 287, + 490 + ], + "lines": [ + { + "bbox": [ + 49, + 419, + 287, + 490 + ], + "spans": [ + { + "bbox": [ + 49, + 419, + 287, + 490 + ], + "type": "table", + "html": "
MethodBackboneSVShipSTmAP
RetinaNet-O [30]R5044.5373.3159.9659.16
FR OBB [19]R5051.2879.3767.5062.00
CMR [19]R5051.6479.9967.5863.41
RT [10]R5052.0580.7268.2665.03
ReDet [18]ReR5052.3880.9268.6466.86
DCFLR5056.72 (+12.19)80.87 (+7.56)75.65 (+15.69)67.37 (+8.21)
DCFLReR10157.31 (+12.78)86.60 (+13.29)76.55 (+16.59)70.24 (+11.08)
", + "image_path": "f01e5c79846380873a54d326fca7a71359ea65fbf5c929045b55aeaa472f36e0.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 54, + 510, + 280, + 557 + ], + "blocks": [ + { + "bbox": [ + 72, + 495, + 261, + 504 + ], + "lines": [ + { + "bbox": [ + 72, + 495, + 261, + 504 + ], + "spans": [ + { + "bbox": [ + 72, + 495, + 261, + 504 + ], + "type": "text", + "content": "Table 3. Main results on the DOTA-v1.5 OBB Task." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 54, + 510, + 280, + 557 + ], + "lines": [ + { + "bbox": [ + 54, + 510, + 280, + 557 + ], + "spans": [ + { + "bbox": [ + 54, + 510, + 280, + 557 + ], + "type": "table", + "html": "
MethodRetinaNet-O [30]FR-OBB [44]RT [10]AOPG [7]
mAP57.5559.5463.8764.41
MethodGGHL [23]Oriented Rep [26]DCFLDCFL (ReR101)
mAP66.4866.7166.8071.03
", + "image_path": "c0cee14f7bd89962072b94e1c492cd1c6d12a65c341a6edc910e88fe74214149.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 55, + 576, + 280, + 624 + ], + "blocks": [ + { + "bbox": [ + 59, + 559, + 274, + 571 + ], + "lines": [ + { + "bbox": [ + 59, + 559, + 274, + 571 + ], + "spans": [ + { + "bbox": [ + 59, + 559, + 274, + 571 + ], + "type": "text", + "content": "Table 4. Performance comparisons on the DIOR-R dataset." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 55, + 576, + 280, + 624 + ], + "lines": [ + { + "bbox": [ + 55, + 576, + 280, + 624 + ], + "spans": [ + { + "bbox": [ + 55, + 576, + 280, + 624 + ], + "type": "table", + "html": "
MethodBackboneVEBRWM
RetinaNet-O [30]R5038.024.060.2
Oriented Rep [26]R5050.438.864.7
DCFLR5050.9 (+12.9)42.1 (+18.1)70.9 (+10.7)
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DatasetVisDroneMS COCODOTA-v2.0 HBB
MethodRetinaNet [30]DCFLRetinaNetDCFLFCOS [58]DCFL
AP0.529.232.155.457.355.457.4
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MethodCPSMPSDGMMmAP
baseline [30]51.70
DCFL✓✓53.41
✓✓57.20
✓✓✓59.15
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StrategyMeasurementmAP
All-FPN-layerGaussian50.12
Single-FPN-layerGaussian56.72
Cross-FPN-layerKLD [63]57.82
Cross-FPN-layerGWD [61]58.55
Cross-FPN-layerGJSD59.15
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DCNDilated ConvDPmAP
58.07
✓58.41
✓✓58.65
Separate✓✓58.71
Guiding✓✓59.15
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K2420
Q20161281612108
mAP58.3158.1158.9559.0658.6658.7158.9258.28
K1612
Q12108610864
mAP59.1558.5758.9757.8458.7958.2557.0157.37
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g1.21.0
mAP57.9158.20
g0.80.4
mAP59.1558.95
", + "image_path": "0ba3a6c64c6bdec6b3027656098901541d433fbbb7061bedbd4fe3a3728b10ce.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 378, + 239, + 469, + 249 + ], + "lines": [ + { + "bbox": [ + 378, + 239, + 469, + 249 + ], + "spans": [ + { + "bbox": [ + 378, + 239, + 469, + 249 + ], + "type": "text", + "content": "(e) Effects of parameter " + }, + { + "bbox": [ + 378, + 239, + 469, + 249 + ], + "type": "inline_equation", + "content": "g" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 8 + }, + { + "bbox": [ + 79, + 258, + 512, + 270 + ], + "lines": [ + { + "bbox": [ + 79, + 258, + 512, + 270 + ], + "spans": [ + { + "bbox": [ + 79, + 258, + 512, + 270 + ], + "type": "text", + "content": "Table 7. Ablations. We train on DOTA-v2.0 train set, test on val set, and report mAP under IoU threshold 0.5." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 282, + 287, + 402 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 282, + 287, + 402 + ], + "spans": [ + { + "bbox": [ + 46, + 282, + 287, + 402 + ], + "type": "text", + "content": "all ablation experiments, we employ one prior for each feature point for fair comparisons. As seen in Tab. 7a, the baseline detector RetinaNet-OBB yields a result of " + }, + { + "bbox": [ + 46, + 282, + 287, + 402 + ], + "type": "inline_equation", + "content": "51.70\\%" + }, + { + "bbox": [ + 46, + 282, + 287, + 402 + ], + "type": "text", + "content": " mAP. When we gradually apply the posterior re-ranked MPS and DGMM into the detector based on the CPS, the mAP improves progressively, verifying each design's effectiveness. Note that the CPS cannot be independently used since the samples in it are too coarse to serve as the final positive samples. Nevertheless, we compare some different ways of constructing the CPS to verify its superiority." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 402, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 402, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 402, + 287, + 677 + ], + "type": "text", + "content": "Comparisons of Different CPS. The design of the CPS matters in the training pipeline. We show several paradigms of designing the CPS as shown in Fig. 7b, including limiting the CPS for a specific " + }, + { + "bbox": [ + 46, + 402, + 287, + 677 + ], + "type": "inline_equation", + "content": "gt" + }, + { + "bbox": [ + 46, + 402, + 287, + 677 + ], + "type": "text", + "content": " within a single layer like FCOS [50], releasing all FPN layers as the CPS, like Objectbox [67]. We compare their performance in Tab. 7b. For fair comparisons, the number of samples in CPS is fixed at 16, and all other components are kept the same. For the Single-FPN-layer way, we group " + }, + { + "bbox": [ + 46, + 402, + 287, + 677 + ], + "type": "inline_equation", + "content": "gt" + }, + { + "bbox": [ + 46, + 402, + 287, + 677 + ], + "type": "text", + "content": " onto different layers according to the scale division strategy in FCOS, then assign labels within each layer. For the All-FPN-layer way, we do not group " + }, + { + "bbox": [ + 46, + 402, + 287, + 677 + ], + "type": "inline_equation", + "content": "gt" + }, + { + "bbox": [ + 46, + 402, + 287, + 677 + ], + "type": "text", + "content": " onto different layers, instead, we discard the prior scale information and directly measure the distance between Gaussian " + }, + { + "bbox": [ + 46, + 402, + 287, + 677 + ], + "type": "inline_equation", + "content": "gt" + }, + { + "bbox": [ + 46, + 402, + 287, + 677 + ], + "type": "text", + "content": " and prior points. The results are shown in Tab. 7b, we can observe that neither of the above two ways will yield the best performance. By contrast, the distribution distances (KLD, GWD, GJSD) are able to construct the Cross-FPN-layer CPS, where the candidates are extended to adjacent layers besides the main layer. We can also see the GJSD gets the best performance of " + }, + { + "bbox": [ + 46, + 402, + 287, + 677 + ], + "type": "inline_equation", + "content": "59.15\\%" + }, + { + "bbox": [ + 46, + 402, + 287, + 677 + ], + "type": "text", + "content": " mAP, mainly resulting from its property of scale-invariance [39, 63], symmetry [39], and ability to measure non-overlapping boxes [39] compared to other counterparts." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": "Fixed Prior and Dynamic Prior. We conduct a finer group of ablation studies to verify the necessity of introducing the dynamic prior. As shown in Tab. 7c, if we disable the" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 282, + 545, + 330 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 282, + 545, + 330 + ], + "spans": [ + { + "bbox": [ + 304, + 282, + 545, + 330 + ], + "type": "text", + "content": "dynamic prior by fixing the location of samples, a slight performance drop will be introduced. Hence, the prior should be adjusted accordingly when leveraging the dynamic sampling strategy to better capture the shape of objects." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 331, + 546, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 331, + 546, + 486 + ], + "spans": [ + { + "bbox": [ + 304, + 331, + 546, + 486 + ], + "type": "text", + "content": "Detailed Design in PCB. For the PCB, it is made up of a dilated convolution and a guiding DCN, we slightly enlarge the receptive field with a dilation rate of 3. After that, we take advantage of the DCN to generate dynamic priors in a guiding manner. As shown in Tab. 7c, we can observe that the DCN can bring an improvement of " + }, + { + "bbox": [ + 304, + 331, + 546, + 486 + ], + "type": "inline_equation", + "content": "0.34\\mathrm{mAP}" + }, + { + "bbox": [ + 304, + 331, + 546, + 486 + ], + "type": "text", + "content": " points and the dilated convolution can slightly enhance the mAP. We find that the application of the DCN [9] to the single regression branch will slightly deteriorate the accuracy (noted by Separate in Tab. 7c), which may cause mismatch issues between the two branches. Thus we utilize the offsets from the regression head to guide the offsets classification head for better alignment (noted by Guiding)." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 487, + 545, + 619 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 487, + 545, + 619 + ], + "spans": [ + { + "bbox": [ + 304, + 487, + 545, + 619 + ], + "type": "text", + "content": "Effects of Parameters. The introduced three parameters are robust in a certain range. From Tab. 7d, we can see that a combination of " + }, + { + "bbox": [ + 304, + 487, + 545, + 619 + ], + "type": "inline_equation", + "content": "K = 16" + }, + { + "bbox": [ + 304, + 487, + 545, + 619 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 487, + 545, + 619 + ], + "type": "inline_equation", + "content": "Q = 12" + }, + { + "bbox": [ + 304, + 487, + 545, + 619 + ], + "type": "text", + "content": " gets the best performance. In Tab. 7e, we verify the threshold " + }, + { + "bbox": [ + 304, + 487, + 545, + 619 + ], + "type": "inline_equation", + "content": "e^{-g}" + }, + { + "bbox": [ + 304, + 487, + 545, + 619 + ], + "type": "text", + "content": " in the DGMM, we empirically set " + }, + { + "bbox": [ + 304, + 487, + 545, + 619 + ], + "type": "inline_equation", + "content": "w_{i,1}" + }, + { + "bbox": [ + 304, + 487, + 545, + 619 + ], + "type": "text", + "content": " to 0.7, then a threshold of " + }, + { + "bbox": [ + 304, + 487, + 545, + 619 + ], + "type": "inline_equation", + "content": "g = 0.8" + }, + { + "bbox": [ + 304, + 487, + 545, + 619 + ], + "type": "text", + "content": " yields the highest mAP. Although making the CPS/MPS/FPS coarser and stricter will weaken the performance, the mAP only waves marginally. In other words, the coarse-to-fine assignment manner somewhat warrants the parameter selection's robustness since multiple parameters can attenuate the effects of an under-tuned one." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 632, + 365, + 645 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 632, + 365, + 645 + ], + "spans": [ + { + "bbox": [ + 306, + 632, + 365, + 645 + ], + "type": "text", + "content": "5. Analysis" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 653, + 545, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 653, + 545, + 676 + ], + "spans": [ + { + "bbox": [ + 306, + 653, + 545, + 676 + ], + "type": "text", + "content": "For a clearer dissection of why the proposed scheme works, we perform more meticulous analyses as follows." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "type": "text", + "content": "Reconciliation of imbalance problems. To delve into the imbalance issue, we calculate the mean predicted IoU and the mean positive sample number of " + }, + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "gt" + }, + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "type": "text", + "content": " holding differ" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7324" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 59, + 70, + 154, + 163 + ], + "blocks": [ + { + "bbox": [ + 59, + 70, + 154, + 163 + ], + "lines": [ + { + "bbox": [ + 59, + 70, + 154, + 163 + ], + "spans": [ + { + "bbox": [ + 59, + 70, + 154, + 163 + ], + "type": "image", + "image_path": "0e4bacdce06e68bde739295fe670a8d4894c6c85c6052477375b664eb420dc0e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 59, + 163, + 153, + 256 + ], + "blocks": [ + { + "bbox": [ + 59, + 163, + 153, + 256 + ], + "lines": [ + { + "bbox": [ + 59, + 163, + 153, + 256 + ], + "spans": [ + { + "bbox": [ + 59, + 163, + 153, + 256 + ], + "type": "image", + "image_path": "64659c3fa9895d4bf2ea4632dce7a718cb144a7c8ef051f16746194de2c404f9.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 259, + 545, + 282 + ], + "lines": [ + { + "bbox": [ + 46, + 259, + 545, + 282 + ], + "spans": [ + { + "bbox": [ + 46, + 259, + 545, + 282 + ], + "type": "text", + "content": "Figure 5. Visualization analysis of the predicted results. The first row is the result of the RetinaNet-OBB while the second row is the result of the DCFL. TP, FN, and FP predictions are marked in green, red, and blue respectively." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 155, + 70, + 250, + 163 + ], + "blocks": [ + { + "bbox": [ + 155, + 70, + 250, + 163 + ], + "lines": [ + { + "bbox": [ + 155, + 70, + 250, + 163 + ], + "spans": [ + { + "bbox": [ + 155, + 70, + 250, + 163 + ], + "type": "image", + "image_path": "ffa40b98c0457b20a508f84e0b5265d1d54cc04b8c2ada738177f6cba764d2b3.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 155, + 163, + 249, + 255 + ], + "blocks": [ + { + "bbox": [ + 155, + 163, + 249, + 255 + ], + "lines": [ + { + "bbox": [ + 155, + 163, + 249, + 255 + ], + "spans": [ + { + "bbox": [ + 155, + 163, + 249, + 255 + ], + "type": "image", + "image_path": "de0e5df3c32a3328d4385b9dc194742c7ea802d09efad95198e615648ce8eb28.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 250, + 70, + 344, + 163 + ], + "blocks": [ + { + "bbox": [ + 250, + 70, + 344, + 163 + ], + "lines": [ + { + "bbox": [ + 250, + 70, + 344, + 163 + ], + "spans": [ + { + "bbox": [ + 250, + 70, + 344, + 163 + ], + "type": "image", + "image_path": "6d945039f1bfe7927f5a288c35cbc04b951f68f925ab12752b288e75bae9e60c.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 250, + 163, + 343, + 255 + ], + "blocks": [ + { + "bbox": [ + 250, + 163, + 343, + 255 + ], + "lines": [ + { + "bbox": [ + 250, + 163, + 343, + 255 + ], + "spans": [ + { + "bbox": [ + 250, + 163, + 343, + 255 + ], + "type": "image", + "image_path": "181e26520d24adc5ba1d4f85ee3e7bd5a39758db9dbafcfe567d4eca78c28bb0.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 344, + 70, + 438, + 163 + ], + "blocks": [ + { + "bbox": [ + 344, + 70, + 438, + 163 + ], + "lines": [ + { + "bbox": [ + 344, + 70, + 438, + 163 + ], + "spans": [ + { + "bbox": [ + 344, + 70, + 438, + 163 + ], + "type": "image", + "image_path": "2b3248716472d496eb9403a39b8985df5349bf10405ecab2314fd28b70916bd2.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 344, + 163, + 438, + 255 + ], + "blocks": [ + { + "bbox": [ + 344, + 163, + 438, + 255 + ], + "lines": [ + { + "bbox": [ + 344, + 163, + 438, + 255 + ], + "spans": [ + { + "bbox": [ + 344, + 163, + 438, + 255 + ], + "type": "image", + "image_path": "eb72422d1dbb7620540f324a29c940ada82c4654829d7c50086c528dcb5a767a.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 439, + 70, + 531, + 163 + ], + "blocks": [ + { + "bbox": [ + 439, + 70, + 531, + 163 + ], + "lines": [ + { + "bbox": [ + 439, + 70, + 531, + 163 + ], + "spans": [ + { + "bbox": [ + 439, + 70, + 531, + 163 + ], + "type": "image", + "image_path": "ba93afe185ddb684966bb1f880ab680e92bfae22bec54e97db321633c221d4b1.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 439, + 163, + 531, + 255 + ], + "blocks": [ + { + "bbox": [ + 439, + 163, + 531, + 255 + ], + "lines": [ + { + "bbox": [ + 439, + 163, + 531, + 255 + ], + "spans": [ + { + "bbox": [ + 439, + 163, + 531, + 255 + ], + "type": "image", + "image_path": "293019a5b0140591e6aab307cdb110b75dd519fbace9cccbe663f8205fdeea7d.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 59, + 292, + 165, + 376 + ], + "blocks": [ + { + "bbox": [ + 59, + 292, + 165, + 376 + ], + "lines": [ + { + "bbox": [ + 59, + 292, + 165, + 376 + ], + "spans": [ + { + "bbox": [ + 59, + 292, + 165, + 376 + ], + "type": "image", + "image_path": "ec941bf00e2a0ec6ddf65e2dfeffba983900861c6516e6fbb33930e209a2b2cd.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 59, + 377, + 166, + 446 + ], + "blocks": [ + { + "bbox": [ + 59, + 377, + 166, + 446 + ], + "lines": [ + { + "bbox": [ + 59, + 377, + 166, + 446 + ], + "spans": [ + { + "bbox": [ + 59, + 377, + 166, + 446 + ], + "type": "image", + "image_path": "b72daa37ff7effa447c8aa374cd000eaaaf4cd30c2b556c9928796809f665595.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 449, + 287, + 471 + ], + "lines": [ + { + "bbox": [ + 47, + 449, + 287, + 471 + ], + "spans": [ + { + "bbox": [ + 47, + 449, + 287, + 471 + ], + "type": "text", + "content": "Figure 6. Statistical analysis of imbalance issues. The first and second columns show quality and quantity imbalance respectively." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 181, + 292, + 269, + 376 + ], + "blocks": [ + { + "bbox": [ + 181, + 292, + 269, + 376 + ], + "lines": [ + { + "bbox": [ + 181, + 292, + 269, + 376 + ], + "spans": [ + { + "bbox": [ + 181, + 292, + 269, + 376 + ], + "type": "image", + "image_path": "fff6d3388249ba26e2ceaf88c50fd9d36aeef3a6d34eba834c5b81eb92f2ae74.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 181, + 379, + 271, + 446 + ], + "blocks": [ + { + "bbox": [ + 181, + 379, + 271, + 446 + ], + "lines": [ + { + "bbox": [ + 181, + 379, + 271, + 446 + ], + "spans": [ + { + "bbox": [ + 181, + 379, + 271, + 446 + ], + "type": "image", + "image_path": "6118b619891aeb23f10a695a32464ce38b28c8b2f2a631bc65fe6abc4f5187dd.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 59, + 478, + 274, + 504 + ], + "blocks": [ + { + "bbox": [ + 59, + 478, + 274, + 504 + ], + "lines": [ + { + "bbox": [ + 59, + 478, + 274, + 504 + ], + "spans": [ + { + "bbox": [ + 59, + 478, + 274, + 504 + ], + "type": "image", + "image_path": "c6911e040344a6e266b391b463ecdaee753c19bc0278ebcee7054132b5edffb9.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 74, + 504, + 260, + 514 + ], + "lines": [ + { + "bbox": [ + 74, + 504, + 260, + 514 + ], + "spans": [ + { + "bbox": [ + 74, + 504, + 260, + 514 + ], + "type": "text", + "content": "Figure 7. Visualization of sampled dynamic priors." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "bbox": [ + 46, + 521, + 287, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 700 + ], + "type": "text", + "content": "ent angles and different scales (absolute size). Results are shown in Fig. 6, which are from the models' last training epoch. Here we summarize two kinds of imbalance issues (quantity and quality imbalance) for RetinaNet: (1) The positive sample number assigned to each instance changes periodically w.r.t. its angle and scale, whereas objects with shapes (scale, angle) different from predefined priors will hold much fewer positive samples. (2) The predicted IoU changes periodically w.r.t. gt's scale while remaining invariant w.r.t. gt's angle. By contrast, DCFL remarkably reconciles the imbalance: (1) more positive samples are compensated to previously outlier angles and scales. (2) the samples' quality (predicted IoU) can also be improved and balanced across all angles and scales. The above results are the desired behavior of dynamic coarse-to-fine learning." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "type": "text", + "content": "Visualization. We visualize the predicted results and" + } + ] + } + ], + "index": 19 + }, + { + "type": "table", + "bbox": [ + 307, + 293, + 545, + 313 + ], + "blocks": [ + { + "bbox": [ + 307, + 293, + 545, + 313 + ], + "lines": [ + { + "bbox": [ + 307, + 293, + 545, + 313 + ], + "spans": [ + { + "bbox": [ + 307, + 293, + 545, + 313 + ], + "type": "table", + "html": "
MethodR3Det [60]S2A-Net [17]GA-RetinaNet [52]RetinaNet [30]DCFL
Params, GFLOPs42.0M, 337.338.6M, 197.937.4M, 206.936.5M, 217.336.1M, 157.8
", + "image_path": "cadc8fee4c085174fa29fdc367103df9d78c3d7fc985573149ddfbb727e23bbd.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "table_body" + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 316, + 545, + 327 + ], + "lines": [ + { + "bbox": [ + 306, + 316, + 545, + 327 + ], + "spans": [ + { + "bbox": [ + 306, + 316, + 545, + 327 + ], + "type": "text", + "content": "Table 8. Comparison of params, GFLOPs with " + }, + { + "bbox": [ + 306, + 316, + 545, + 327 + ], + "type": "inline_equation", + "content": "{1024} \\times {1024}" + }, + { + "bbox": [ + 306, + 316, + 545, + 327 + ], + "type": "text", + "content": " input." + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 331, + 545, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 331, + 545, + 415 + ], + "spans": [ + { + "bbox": [ + 305, + 331, + 545, + 415 + ], + "type": "text", + "content": "positive samples in Fig. 5 and Fig. 7. We can see that the DCFL remarkably eliminates the False Negative and False Positive predictions, especially for the extreme-shaped oriented tiny objects. Fig. 7 shows that the proposed strategy is able to dynamically generate and sample priors that better fit the instance's main body, verifying the claims of dynamic modeling and mismatch alleviation in this work." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 305, + 415, + 545, + 487 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 415, + 545, + 487 + ], + "spans": [ + { + "bbox": [ + 305, + 415, + 545, + 487 + ], + "type": "text", + "content": "Speed. We test the inference speed on DOTA-v2.0 val set with a single RTX3090 GPU, the FPS of the " + }, + { + "bbox": [ + 305, + 415, + 545, + 487 + ], + "type": "inline_equation", + "content": "\\mathrm{R}^3\\mathrm{Det}" + }, + { + "bbox": [ + 305, + 415, + 545, + 487 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 415, + 545, + 487 + ], + "type": "inline_equation", + "content": "\\mathrm{S}^2\\mathrm{A}" + }, + { + "bbox": [ + 305, + 415, + 545, + 487 + ], + "type": "text", + "content": " -Net, RetinaNet, and DCFL is 16.2, 18.9, 20.8, and 20.9. It indicates that our method is of high efficiency. Moreover, we provide the parameters and GLOPs in Tab. 8, where we can see that the DCFL is lighter." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 494, + 378, + 506 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 494, + 378, + 506 + ], + "spans": [ + { + "bbox": [ + 306, + 494, + 378, + 506 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 514, + 545, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 514, + 545, + 634 + ], + "spans": [ + { + "bbox": [ + 304, + 514, + 545, + 634 + ], + "type": "text", + "content": "In this paper, we propose a novel DCFL scheme for detecting oriented tiny objects. We identify that the mismatched feature prior and unbalanced positive samples are two obstacles hampering the label assignment for oriented tiny objects. To address these, we propose a dynamic prior to alleviate the mismatch issue and a coarse-to-fine assigner to mitigate the imbalance issue, where the prior, label assignment, and " + }, + { + "bbox": [ + 304, + 514, + 545, + 634 + ], + "type": "inline_equation", + "content": "gt" + }, + { + "bbox": [ + 304, + 514, + 545, + 634 + ], + "type": "text", + "content": " representation are all reformulated in a dynamic manner. Extensive experiments and analyses show the convincing improvements brought by the DCFL." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 306, + 645, + 403, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 645, + 403, + 658 + ], + "spans": [ + { + "bbox": [ + 306, + 645, + 403, + 658 + ], + "type": "text", + "content": "Acknowledgement" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 305, + 665, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 665, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 305, + 665, + 545, + 712 + ], + "type": "text", + "content": "We thank the reviewers for their comments. This work was supported in parts by NSFC (62271355, 62271354) and the Fundamental Research Funds for the Central Universities (20420222kf1010)." + } + ] + } + ], + "index": 27 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7325" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "text", + "content": "[1] Yancheng Bai, Yongqiang Zhang, Mingli Ding, and Bernard Ghanem. 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In International Conference on Learning Representations, 2021. 3" + } + ] + } + ], + "index": 19 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7328" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Dynamic Conceptional Contrastive Learning for Generalized Category Discovery/40efeb24-3451-4def-8441-e92b604d3421_content_list.json b/2023/Dynamic Conceptional Contrastive Learning for Generalized Category Discovery/40efeb24-3451-4def-8441-e92b604d3421_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..07e996c049e0e40f99a277e4ac2893c0d2cc99cf --- /dev/null +++ b/2023/Dynamic Conceptional Contrastive Learning for Generalized Category Discovery/40efeb24-3451-4def-8441-e92b604d3421_content_list.json @@ -0,0 +1,1631 @@ +[ + { + "type": "text", + "text": "Dynamic Conceptional Contrastive Learning for Generalized Category Discovery", + "text_level": 1, + "bbox": [ + 241, + 130, + 728, + 175 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Nan Pu Zhun Zhong* Nicu Sebe", + "bbox": [ + 339, + 203, + 629, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The Department of Information Engineering and Computer Science University of Trento, Trento, Italy", + "bbox": [ + 217, + 220, + 750, + 256 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{nan.pu, zhun.zhong, niculae.sebe}@unitn.it", + "bbox": [ + 292, + 258, + 671, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 308, + 313, + 325 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Generalized category discovery (GCD) is a recently proposed open-world problem, which aims to automatically cluster partially labeled data. The main challenge is that the unlabeled data contain instances that are not only from known categories of the labeled data but also from novel categories. This leads traditional novel category discovery (NCD) methods to be incapacitated for GCD, due to their assumption of unlabeled data are only from novel categories. One effective way for GCD is applying self-supervised learning to learn discriminate representation for unlabeled data. However, this manner largely ignores underlying relationships between instances of the same concepts (e.g., class, super-class, and sub-class), which results in inferior representation learning. In this paper, we propose a Dynamic Conceptional Contrastive Learning (DCCL) framework, which can effectively improve clustering accuracy by alternately estimating underlying visual conceptions and learning conceptual representation. In addition, we design a dynamic conception generation and update mechanism, which is able to ensure consistent conception learning and thus further facilitate the optimization of DCCL. Extensive experiments show that DCCL achieves new state-of-the-art performances on six generic and fine-grained visual recognition datasets, especially on fine-grained ones. For example, our method significantly surpasses the best competitor by $16.2\\%$ on the new classes for the CUB-200 dataset. Code is available at https://github.com/TPCD/DCCL", + "bbox": [ + 76, + 340, + 472, + 763 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 792, + 207, + 806 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Learning recognition models (e.g., image classification) from labeled data has been widely studied in the field of machine learning and deep learning [13, 18, 31]. In spite of their tremendous success, supervised learning techniques", + "bbox": [ + 76, + 816, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/7f5b2f9bafc25f8aebc5f7a4fd206915c9fc8f46a52372987cf6b31e436d2d0e.jpg", + "image_caption": [ + "Figure 1. Diagram of the proposed Dynamic Conceptional Contrastive Learning (DCCL). Samples from the conceptions should be close to each other. For example, samples from the same classes (bus) at the class level, samples belonging to the transportation (bus and bicycle) at the super-class level, and samples from trains with different colors at the sub-class level. Our DCCL potentially learns the underlying conceptions in unlabeled data and produces more discriminative representations." + ], + "image_footnote": [], + "bbox": [ + 501, + 316, + 890, + 487 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "rely heavily on huge annotated data, which is not suitable for open-world applications. Thus, the researchers recently have paid much effort on learning with label-imperfection data, such as semi-supervised learning [23, 33], self-supervised learning [12, 42], weakly-supervised learning [41,45], few-shot learning [32,38], open-set recognition [30] and learning with noisy labels [40], etc.", + "bbox": [ + 496, + 625, + 890, + 731 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, inspired by the fact that Humans can easily and automatically learn new knowledge with the guidance of previously learned knowledge, novel category discovery (NCD) [9, 11, 28, 44, 47] is introduced to automatically cluster unlabeled data of unseen categories with the help of knowledge from seen categories. However, the implementation of NCD is under a strong assumption that all the unlabeled instances belong to unseen categories, which is not practical in real-world applications. To address this limitation, Vaze et al. [35] extend NCD to the generalized category discovery (GCD) [35], where unlabeled images are", + "bbox": [ + 496, + 734, + 892, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 808, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding Author.", + "bbox": [ + 94, + 886, + 225, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "7579", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "from both novel and labeled categories.", + "bbox": [ + 76, + 90, + 339, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "GCD is a challenging open-world problem in that we need to 1) jointly distinguish the known and unknown classes and 2) discover the novel clusters without any annotations. To solve this problem, Vaze et al. [35] leverage the contrastive learning technique to learn discriminative representation for unlabeled data and use $k$ -means [21] to obtain final clustering results. In this method, the labeled data are fully exploited by supervised contrastive learning. However, self-supervised learning is applied to the unlabeled data, which enforces samples to be close to their augmentation counterparts while far away from others. As a consequence, the underlying relationships between samples of the same conceptions are largely overlooked and thus will lead to degraded representation learning. Intuitively, samples that belong to the same conceptions should be similar to each other in the feature space. The conceptions can be regarded as: classes, super-classes, sub-classes, etc. For example, as shown in Fig. 1, samples of the same class should be similar to each other, e.g., samples of the bus, samples of the bicycle. In addition, in the super-classes view, classes of the transportation, e.g., Bus and Bicycle, should belong to the same concept. Hence, the samples of transportation should be closer than that of other concepts (e.g., animals). Similarly, samples belong to the same sub-classes (e.g., red train) should be closer to that of other sub-classes (e.g., white train). Hence, embracing such conceptions and their relationships can greatly benefit the representation learning for unlabeled data, especially for unseen classes.", + "bbox": [ + 75, + 107, + 472, + 529 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Motivated by this, we propose a Dynamic Conceptional Contrastive Learning (DCCL) framework for GCD to effectively leverage the underlying relationships between unlabeled data for representation learning. Specifically, our DCCL includes two steps: Dynamic Conception Generation (DCG) and Dual-level Contrastive Learning (DCL). In DCG, we dynamically generate conceptions based on the hyper-parameter-free clustering method equipped with the proposed semi-supervised conceptual consolidation. In DCL, we propose to optimize the model with conception-level and instance-level contrastive learning objectives, where we maintain a dynamic memory to ensure comparing with the up-to-date conceptions. The DCG and DCL are alternately performed until the model converges.", + "bbox": [ + 75, + 530, + 472, + 741 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We summarize the contributions of this work as follows:", + "bbox": [ + 96, + 741, + 468, + 757 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a novel dynamic conceptionsal contrastive learning (DCCL) framework to effectively leverage the underlying relationships between unlabeled samples for learning discriminative representation for GCD.", + "- We introduce a novel dynamic conception generation and update mechanism to ensure consistent conception learning, which encourages the model to produce more discriminative representation." + ], + "bbox": [ + 94, + 768, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- Our DCCL approach consistently achieves superior performance over state-of-the-art GCD algorithms on both generic and fine-grained tasks.", + "bbox": [ + 517, + 90, + 893, + 137 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 171, + 640, + 186 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Novel Category Discovery", + "text_level": 1, + "bbox": [ + 500, + 198, + 735, + 215 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Novel category discovery [11] (NCD) tasks aim at discovering new categories by leveraging the knowledge of a set of labeled categories. RankStat [10] indicates that self-supervised pre-training is helpful for NCD. NCL [46] adopts contrastive learning to improve representation learning. UNO [9] proposes a unified objective for jointly learning on unlabeled and labeled data. Most recently, NCD has been extended to a generalized category discovery (GCD) [35], in which the unlabeled data include both labeled and unlabeled categories. Later, ORCA [3] defines an open-world semi-supervised learning task, which is similar to GCD. Although these definitions are relatively practical, most methods remain to assume that the class number of clustered data is known. Nevertheless, such prior knowledge is often not acquired in advance for real-world applications. To handle the drawback, DTC [11] and GCD [35] employed an independent algorithm to search the optimal class number, however, they did not associate clustering estimation with representation learning. Unlike these offline algorithms, we propose to jointly consider downstream clustering and representation learning. The experimental results show they are mutually beneficial for each other.", + "bbox": [ + 496, + 223, + 893, + 556 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Contrastive Learning based on Memory Buffer", + "text_level": 1, + "bbox": [ + 500, + 571, + 890, + 589 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Contrastive learning [5,6,22,37,43] (CL) has been shown to be significantly effective for representation learning in a self-supervised manner. MoCo [12] demonstrates that sampling positive-negative pairs from an instance-level buffer can benefit CL and reduce the impact of the size of the training batch. Then, instead of contrasting over all instances in a mini-batch, prototypical contrastive learning [20] (PCL) that contrasts the instance features with a set of prototypes, has been shown to provide comprehensive supervision. However, PCL still needs an instance-level memory buffer to yield the prototype set, which is not computation- and memory-efficient. Recently, SCL [14] propose a cluster-level momentum encoder but considers only three fixed numbers of classes during training, which is still limited compared to our dynamic method. Different from PCL and SCL that consider the fixed numbers of classes during the whole training process, our DCCL dynamically estimates the number of classes for different training stages in a efficient way, which encourages models to learn more discriminative representation.", + "bbox": [ + 496, + 598, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "7580", + "bbox": [ + 482, + 944, + 516, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/c5b5e59be55abcad8920c9da63691cc09d16dc1bf93567ac8283805f4061ad66.jpg", + "image_caption": [ + "Figure 2. (a) Overview of our DCCL framework. We first extract features and cluster the features to generate conceptual labels, then initialize conception representations by our DCG, and last learn representations by joint instance-level and conception-level objectives. During the training process, the DCG and dual-level representation learning are performed alternately, in which the conception buffer is updated every iteration to keep the consistency of the changing instance features and conceptual representations. (b) Illustration of the proposed conception consolidation. Without consolidating the relationships of conceptions by label information, Infomap tends to over-cluster data and thus provides the supervision that has a high risk to over-correct affinities between neighbor instances." + ], + "image_footnote": [], + "bbox": [ + 84, + 99, + 859, + 343 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Semi-Supervised Learning and Clustering", + "text_level": 1, + "bbox": [ + 76, + 440, + 434, + 458 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Semi-supervised learning (SSL) has been a long-standing research topic [39]. Different from GCD, SSL often assumes that the labeled and unlabeled data come from the same set of classes, in which consistency-based methods are the most effective methods for SSL, such as Mean-teacher [34], MixMatch [2], and FixMatch [33]. Consistency-based methods are the most effective methods for SSL, such as Mean-teacher [34], MixMatch [2], and FixMatch [33]. Moreover, semi-supervised classification is a relatively well-defined task, while the supervised information in semi-supervised clustering can take different forms [19], such as two instances are known to be must-linked in a relationship matrix or some cluster assignments are known beforehand. For instance, Basu et al. [1] proposed to initialize the clusters based on the data points for which cluster assignments are known. However, these methods can not adaptively assign the number of clusters for generating conceptions. To mitigate these limitations, we improve the classical InfoMap [27] to fully leverage both labeled and unlabeled data and dynamically produce varying conceptual labels for different contrastive learning epochs.", + "bbox": [ + 75, + 465, + 472, + 785 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Dynamic Conceptional Contrastive Learning", + "text_level": 1, + "bbox": [ + 76, + 801, + 470, + 837 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem Formulation", + "text_level": 1, + "bbox": [ + 76, + 845, + 279, + 861 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Generalized category discovery (GCD) aims at automatically categorizing unlabeled images in a dataset, where the", + "bbox": [ + 76, + 869, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "partial data are labeled and the remaining are unlabeled. The unlabeled images come from either labeled (known) classes or unlabeled (unknown) classes. This is a more realistic open-world setting than the common closed-set classification that assumes the labeled and unlabeled data belong to the same classes. Let the dataset be $\\mathcal{D} = \\mathcal{D}^L\\cup \\mathcal{D}^U$ where $\\mathcal{D}^L = \\{(\\mathbf{x}_i^L,\\mathbf{y}_i^L)\\}_{i = 1}^{M^L}\\in \\mathcal{X}\\times \\mathcal{Y}^L$ $L$ denotes the labeled subset and $\\mathcal{D}^U = \\{(\\mathbf{x}_i^U,\\mathbf{y}_i^U)\\}_{i = 1}^{M^U}\\in \\mathcal{X}\\times \\mathcal{Y}^U$ denotes the unlabeled subset with unknown $\\mathbf{y}_i^U\\in \\mathcal{V}^U$ . Only a subset of classes contains labeled instances, i.e., $\\mathcal{V}^L\\subset \\mathcal{V}^U$ The number of labeled classes $N^L$ can be directly calculated from the labeled data, while the number of unlabeled classes $N^U$ is not known during model training. Let $f$ and $h$ be a feature extractor and a MLP projection head. The extracted representation is defined as $\\mathbf{v}_i = f(\\mathbf{x}_i)$", + "bbox": [ + 496, + 440, + 893, + 674 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Overview", + "text_level": 1, + "bbox": [ + 500, + 681, + 609, + 695 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To tackle the problem of GCD, we propose a novel framework DCCL (see Fig. 2), to jointly learn representations using dual-level contrastive learning (DCL) and explore all possible relationships between labeled and unlabeled instances in a conceptionsal view. First, we extend the classical unsupervised clustering algorithm, Infomap [27], to a semi-supervised manner, which aims at dynamically generating reasonable conceptual representations and associating the labeled and unlabeled instances during representation learning. By alternately executing the dynamic conception generation (DCG) and DCL, DCL benefits from informative supervised information to generate higher-quality representations. Meanwhile, DCG gradually", + "bbox": [ + 496, + 703, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "7581", + "bbox": [ + 482, + 944, + 513, + 957 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "produces more comprehensive guidance based on a deeper understanding of conceptual relationships. DCG and DCL mutually benefit each other, thus resulting in a better representation for downstream clustering.", + "bbox": [ + 75, + 90, + 472, + 154 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Dynamic Conception Generation", + "text_level": 1, + "bbox": [ + 76, + 160, + 366, + 176 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Although the test-time semi-supervised $k$ -means [35] (SSK) succeeds in achieving considerable performance gain, it fails to jointly consider the representation learning and supervision information from semi-supervised clustering. Moreover, it is infeasible to directly perform SSK in each training epoch for assigning pseudo labels, because the real number of clusters is unknown during training. To overcome these drawbacks, we propose a dynamic conception generation (DCG) based on the hyper-parameter-free Infomap [27] algorithm. Specifically, we first propose a semi-supervised conceptual consolidation method to construct a similarity network, then execute the Infomap clustering algorithm on the constructed network to get conceptual label assignments, and finally calculate conception representation and initialize conceptual memory buffer.", + "bbox": [ + 75, + 183, + 468, + 410 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Conception Consolidation. In a given network, Infomap aims at partitioning semantic-similar sub-networks by the pattern of connections. To leverage the supervision from labeled data, we propose to enforce the similarity constraints into the networking, according to the labeled data that belong to the same category. Formally, we construct an adjacent matrix $\\mathcal{A}$ to represent the possible connection relationships among all instances. The weight of the edge of the $i$ -th and $j$ -th instances is given by:", + "bbox": [ + 75, + 410, + 468, + 546 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {A} _ {i j} = \\left\\{ \\begin{array}{l l} s _ {i} ^ {\\max }, & \\text {i f} \\mathbf {y} _ {i}, \\mathbf {y} _ {j} \\in \\mathcal {Y} ^ {L} \\text {a n d} \\mathbf {y} _ {i} = \\mathbf {y} _ {j} \\\\ s _ {i j}, & \\text {i f} \\mathbf {y} _ {i} \\text {o r} \\mathbf {y} _ {j} \\in \\mathcal {Y} ^ {U} \\text {a n d} s _ {i j} > \\tau^ {F} \\\\ 0, & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 556, + 468, + 612 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ns _ {i} ^ {\\text {m a x}} = \\underset {j} {\\arg \\max } \\left\\{s _ {i j} \\mid j \\in \\mathcal {D} \\right\\}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 165, + 619, + 468, + 647 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ns _ {i j} = \\left[ \\left(\\mathbf {v} _ {i} / \\| \\mathbf {v} _ {i} \\|\\right) \\cdot \\left(\\mathbf {v} _ {j} / \\| \\mathbf {v} _ {j} \\|\\right) + 1 \\right] / 2 \\in [ 0, 1 ], \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 119, + 651, + 468, + 670 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\cdot$ denotes dot product and $\\| \\cdot \\|$ is $l_{2}$ normalization. The $\\tau^{F}$ is a threshold to select high-confidence links. Through the conception consolidation illustrated in Fig. 2(b), we can establish a reliable relationship network with rich structural information for the subsequent clustering.", + "bbox": [ + 76, + 674, + 468, + 750 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Remark. We set the similarities of positive pairs with the maximal value of neighborhood similarities instead of 1. This is because we experimentally find that when imposing 1 for constraining positive pairs, Infomap tends to group all the labeled positive instances as an individual cluster.", + "bbox": [ + 76, + 750, + 468, + 824 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Entropy Minimization Clustering. In Infomap algorithm [26], the clustering problem is equivalent to minimizing the entropy that represents the minimum description length of the coding network. By solving the minimization objective, we acquire a conceptual label set", + "bbox": [ + 75, + 825, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1: Algorithm Pipeline of our DCCL" + ], + "code_body": "Input: Feature Extractor $f$ Projection Head $h$ Labeled data $\\mathcal{D}^L$ and Unlabeled data $\\mathcal{D}^U$ \nOutput: $f$ and $h$ \nfor $n = 1$ in [1,max_epoch] do if $n\\bmod\\tau^{I}==0$ then Extract features and construct adjacency matrix $\\mathcal{A}$ by Eq. (1), Eq. (2) and Eq. (3); Perform InfoMap [27] clustering to assign conceptual labels C; Initialize conceptual buffer by Eq. (4); \nend for $i = 1$ in [1,max_iteration] do Sample mini-batches from $\\mathcal{D}^L\\cup \\mathcal{D}^U$ Calculate overall optimization objective by Eq.(10); Update $f$ and $h$ by SGD [25]; Update conceptual buffer by Eq. (8); \nend", + "bbox": [ + 516, + 111, + 846, + 398 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\mathcal{C} = \\{\\mathbf{c}_i\\}_{i=1}^{M^L + M^U} \\in \\mathcal{V}^G$ for both labeled and unlabeled instances. Then, we combine the extracted feature vectors $\\mathcal{V}$ and corresponding conceptionsal labels to construct a generated feature dataset $\\mathcal{D}^G = \\{(\\mathbf{v}_i, \\mathbf{c}_i)\\}_{i=1}^{M^L + M^U} \\in \\mathcal{V} \\times \\mathcal{V}^G$ . $|\\mathcal{V}^G|$ denotes the number of estimated conceptions.", + "bbox": [ + 498, + 429, + 890, + 511 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Conceptional Memory Initialization. In this paper, our DCCL maintains a conception-level memory buffer that provides dynamic conceptual representations for dual-level contrastive learning, which is elaborated in Sec. 3.4. Here, we introduce the initialization of the conceptual memory buffer (CMB). We use the mean feature vector of the instances that share the same conceptual label to form a unique conceptual representation. Formally, the initial conceptual representation set is defined as:", + "bbox": [ + 498, + 511, + 892, + 647 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {U} = \\left\\{\\boldsymbol {\\mu} _ {k} \\right\\} _ {k = 1} ^ {K}, \\quad \\boldsymbol {\\mu} _ {k} = \\frac {1}{\\left| \\mathcal {D} _ {k} ^ {G} \\right|} \\sum_ {\\mathbf {v} _ {i} \\in \\mathcal {D} _ {k} ^ {G}} \\mathbf {v} _ {i}, \\quad K = | \\mathcal {Y} ^ {G} |, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 506, + 654, + 890, + 694 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{D}_k^G$ denotes the $k$ -th conception subset, i.e., if $\\mathbf{v}_i \\in \\mathcal{D}_k^G$ , $\\mathbf{c}_i = k$ . During whole training process, the initialization of CMB is executed every $\\tau^I$ epochs on center-cropped images. Thus, the number of conceptions $K$ is dynamically changing along with model training.", + "bbox": [ + 498, + 702, + 890, + 779 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Dual-Level Contrastive Learning", + "text_level": 1, + "bbox": [ + 500, + 786, + 790, + 803 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section, we first explain the proposed conception-level contrastive learning, then elaborate on the update of the conceptual memory buffer, and finally introduce the employed instance-level contrastive learning approach.", + "bbox": [ + 496, + 810, + 890, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Conception-Level Contrastive Learning. Based on the generated conceptual representations in Sec. 3.3, we", + "bbox": [ + 498, + 869, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "7582", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "propose to perform conception-level contrastive learning. Specifically, we first sample $N^C$ conception labels and a fixed number $N^I$ of instances for each conception label, resulting in a mini-batch $\\mathcal{B}^C$ with $N^C \\times N^I$ instances. Next, each instance representation is compared to all the conceptual representations. We pull the instance representation from its corresponding conceptual representation closer and push the instance representation away from other conceptual representations. Formally, we define the conceptual contrastive loss function as the following:", + "bbox": [ + 75, + 90, + 472, + 243 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {i} ^ {C} = - \\log \\frac {\\exp \\left(\\mathbf {v} _ {i} \\cdot \\boldsymbol {\\mu} _ {\\mathbf {c} _ {i}} / \\tau^ {C}\\right)}{\\sum_ {k = 1 , k \\neq \\mathbf {c} _ {i}} ^ {K} \\exp \\left(\\mathbf {v} _ {i} \\cdot \\boldsymbol {\\mu} _ {k} / \\tau^ {C}\\right)}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 129, + 253, + 468, + 294 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\tau^C$ is a temperature hyper-parameter to control the strength of the conception-level contrastive learning. In addition, in order to explicitly encourage learned representations with a large inter-conception margin, we propose a dispersion loss to further push the different conception representations away from each other. The loss function for the $m$ -th and the $n$ -th conceptions in $\\mathcal{B}^C$ is:", + "bbox": [ + 75, + 301, + 468, + 409 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} (m, n) = \\left[ \\tau^ {M} - \\left\\| \\frac {1}{\\left| \\mathcal {B} _ {m} ^ {C} \\right|} \\sum_ {\\mathbf {v} _ {i} \\in \\mathcal {B} _ {m} ^ {C}} \\mathbf {v} _ {i} \\right\\| \\cdot \\left\\| \\frac {1}{\\left| \\mathcal {B} _ {n} ^ {C} \\right|} \\sum_ {\\mathbf {v} _ {j} \\in \\mathcal {B} _ {n} ^ {C}} \\mathbf {v} _ {j} \\right\\| \\right] _ {+}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 419, + 468, + 470 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\tau^M$ is a threshold to filter the conception pairs with high uncertainty. We assume that two conception representations that are close tend to be highly entangled conceptions. Separating these conceptions has a high risk of overcorrect. We explore the impact of $\\tau^M$ in Sec. 4.4. The dispersion loss function over a mini-batch is defined as:", + "bbox": [ + 75, + 472, + 468, + 563 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} ^ {D} = \\frac {1}{N ^ {C}} \\sum_ {m = 1} ^ {N ^ {C}} \\frac {1}{N ^ {C}} \\sum_ {n = 1} ^ {N ^ {C}} \\mathcal {L} (m, n). \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 155, + 575, + 468, + 619 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Conceptional Memory Update. Different from [12, 20] that need to save all training instances, our CMB stores only the conception representations, which significantly reduces storage cost. Furthermore, the instance-wise update is easy to lead to an inconsistent update during each training iteration. To mitigate this drawback, we first adopt the resampling method as detailed in the previous section. Next, we propose to update the conception representation by each corresponding instance feature following a momentum update mechanism. The process is formulated as:", + "bbox": [ + 75, + 630, + 468, + 782 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\mu} _ {\\mathbf {c} _ {i}} \\leftarrow \\eta \\boldsymbol {\\mu} _ {\\mathbf {c} _ {i}} + (1 - \\eta) \\mathbf {v} _ {i}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 184, + 796, + 468, + 811 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\eta$ is the momentum updating factor.", + "bbox": [ + 76, + 824, + 357, + 839 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Remark. DCCL updates the memory buffer and computes the losses both at the conceptual level, which consistently updates the conceptual representation to maintain the conceptual consistency during the whole training process.", + "bbox": [ + 75, + 839, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Instance-Level Contrastive Learning. Inspired by [35], we combine supervised contrastive loss and self-supervised contrastive loss as an instance contrastive loss (ICL), to fine-tune the model. Formally, we assume $x_{i}$ and $\\hat{x}_i$ are two views (random augmentations) of the same image in a randomly-sampled mini-batch $\\mathcal{B}^I$ . Let $h$ be a MLP projection head. The extracted representation $\\mathbf{v}_i$ is further projected by $h$ to high-dimensional embedding space for instance-level contrastive learning. The loss function is:", + "bbox": [ + 496, + 90, + 890, + 227 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {i} ^ {I} = (\\lambda - 1) \\log \\frac {\\exp \\left(h \\left(\\mathbf {v} _ {i}\\right) \\cdot h \\left(\\hat {\\mathbf {v}} _ {i}\\right) / \\tau\\right)}{\\sum_ {j \\in \\mathcal {B} ^ {I} , j \\neq i} \\exp \\left(h \\left(\\mathbf {v} _ {i}\\right) \\cdot h \\left(\\mathbf {v} _ {j}\\right) / \\tau^ {S}\\right)} \\\\ \\frac {- \\lambda}{| \\mathcal {P} (i) |} \\sum_ {p \\in \\mathcal {P} (i)} \\log \\frac {\\exp \\left(h \\left(\\mathbf {v} _ {i} ^ {L}\\right) \\cdot h \\left(\\mathbf {v} _ {p} ^ {L}\\right) / \\tau\\right)}{\\sum_ {j \\in \\mathcal {B} ^ {L} , j \\neq i} \\exp \\left(h \\left(\\mathbf {v} _ {i} ^ {L}\\right) \\cdot h \\left(\\mathbf {v} _ {j} ^ {L}\\right) / \\tau^ {L}\\right)}, \\tag {9} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 503, + 236, + 890, + 327 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{B}^L$ donates the labeled subset within the mini-batch $\\mathcal{B}^I$ and $\\mathcal{B}^I = \\mathcal{B}^L\\cup \\mathcal{B}^U$ . $\\mathcal{P}(i)$ is the positive index set for the anchor image $i\\in \\mathcal{B}^L$ . $\\lambda$ is a trade-off factor to balance the contributions of self-supervised and supervised learning. For a fair comparison, we follow [35] and set $\\lambda$ to 0.35.", + "bbox": [ + 496, + 328, + 890, + 405 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Joint Optimization", + "text_level": 1, + "bbox": [ + 500, + 412, + 681, + 429 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "During the whole training process, we alternately perform dynamic conception generalization and dual-level contrastive representation learning, until the maximal training epoch. The pseudo-code of DCCL is elaborated in Algorithm 1. The overall objective over on mini-batch $\\mathcal{B}$ is given by the weighted sum of each loss function:", + "bbox": [ + 496, + 436, + 890, + 527 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {t o t a l}} = \\frac {1}{| \\mathcal {B} |} \\sum_ {i \\in \\mathcal {B}} \\mathcal {L} _ {i} ^ {I} + \\alpha \\frac {1}{| \\mathcal {B} |} \\sum_ {i \\in \\mathcal {B}} \\mathcal {L} _ {i} ^ {C} + \\beta \\mathcal {L} ^ {D}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 529, + 536, + 890, + 573 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\alpha$ and $\\beta$ are the weights to adjust the strengths of two loss functions. In all experiments, we use $l_{2}$ normalized feature vector $\\| \\mathbf{v}\\| _2$ for clustering evaluation.", + "bbox": [ + 496, + 582, + 890, + 628 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 641, + 633, + 657 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 500, + 666, + 689, + 681 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Data and Evaluation Metric. We evaluate DCCL on three generic image classification datasets, namely CIFAR-10 [17], CIFAR-100 [17] and ImageNet-100 [35]. ImageNet-100 denotes randomly sub-sampling 100 classes from the ImageNet [7] dataset. The dataset statistics and train-test splits are described in Tab. 1. We further evaluate DCCL on three more challenging fine-grained image classification datasets: CUB-200 [36], Stanford Cars [16], and Oxford-IIIT Pet [24]. The original training set of each fine-grained dataset is separated into labeled and unlabeled parts. We follow [35] sample a subset of half the classes as \"Old\" categories. $50\\%$ of instances of each labeled class are drawn to form the labeled set, and all the remaining data constitute the unlabeled set. For evaluation, we measure the clustering", + "bbox": [ + 496, + 688, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "7583", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/30fda43f35b294ad0cf56d19efbeb45944bdd6ba1a172adf96a64e6fbe813469.jpg", + "table_caption": [ + "Table 1. Statistics of the datasets and the splits for GCD. The first three are generic datasets while the last three are fine-grained datasets." + ], + "table_footnote": [], + "table_body": "
DatasetCIFAR10 [17]CIFAR100 [17]ImageNet-100 [7]CUB-200 [36]SCars [16]Pet [24]
Labelled# Classes580501009819
# Images12,50020,00031,8601,4982,000942
Unlabelled# Classes1010010020019637
# Images37,50030,00095,25544966,1442,738
", + "bbox": [ + 158, + 104, + 805, + 183 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/2a73ed0993064ac5a84bab6621a716d56c9d2f0e99caee980f2c5792e640caf6.jpg", + "table_caption": [ + "Table 2. Results on generic image recognition datasets." + ], + "table_footnote": [], + "table_body": "
MethodCIFAR10CIFAR100ImageNet-100
AllOldNewAllOldNewAllOldNew
k-means83.685.782.552.052.250.872.775.571.3
RankStats+46.819.260.558.277.619.337.161.624.8
UNO+68.698.353.869.580.647.270.395.057.9
GCD91.597.988.273.076.266.574.189.866.3
DCCL96.396.596.975.376.870.280.590.576.2
", + "bbox": [ + 78, + 210, + 467, + 304 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "accuracy by comparing the predicted label assignment with the ground truth, following the protocol in [35].", + "bbox": [ + 75, + 321, + 467, + 349 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details. We adopt the ViT-B-16 pretrained by DINO [4] as our backbone network. The output [CLS] token is used as the feature representation, which is also used for conception-level contrastive learning. Following [35], we project the representations by a projection head and use the projected embeddings for instance-level contrastive learning. We set the dimension of projected embeddings to 65,536 following [4]. At training time, we feed two views with random augmentations to the model. We only fine-tune the last block of the vision transformer with an initial learning rate of 0.01 and the head is trained with an initial learning rate of 0.1. All methods are trained for 200 epochs with a cosine annealing schedule. The size of the mini-batch is set to 128 with $N^C = 8$ and $N^I = 16$ . For a fair comparison, we follow [35] and set the temperatures of two supervised contrastive losses $\\tau^S$ , $\\tau^L$ and $\\tau^C$ to 0.07, 0.05 and 0.05, respectively. The $\\tau^F$ is empirically set to 0.6 for the fine-grained datasets and 0.7 for the generic datasets. Other hyper-parameters are discussed in Sec. 4.4. In testing, we first use the class number estimation algorithm [35] to predict the number of classes of the testing dataset, and then use semi-supervised $k$ -means for clustering evaluation. In dynamic conception generation, we adopt faiss [15] to accelerate the construction of relationship networks. Our experiments are conducted on RTX 3090 GPUs.", + "bbox": [ + 75, + 352, + 468, + 729 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Comparison with State-of-the-Art", + "text_level": 1, + "bbox": [ + 76, + 739, + 375, + 755 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To evaluate the performances of our DCCL, we conduct three group experiments by comparing our DCCL with three strong GCD baselines, including RankStats [10] and UNO [9] and the state-of-the-art GCD method [35].", + "bbox": [ + 75, + 763, + 468, + 824 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparison on Generic Datasets. As shown in Tab. 2, our DCCL is compared with other competitors on the generic image recognition datasets. Overall, the results in Tab. 2 show our DCCL consistently outperforms all others by a significant margin. Specifically, DCCL outperforms the", + "bbox": [ + 75, + 825, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/e6032995791ecfaa84051c26eae19040c5e492a570701ea9dc2c00517ec60e4b.jpg", + "table_caption": [ + "Table 3. Results on fine-grained datasets." + ], + "table_footnote": [], + "table_body": "
methodCUB-200Stanford-CarsOxford-Pet
AllOldNewAllOldNewAllOldNew
k-means34.338.932.112.810.613.877.170.180.7
RankStats+33.351.624.228.361.812.1---
UNO+35.149.028.135.570.518.6---
GCD51.356.648.739.057.629.980.285.177.6
DCCL63.560.864.943.155.736.288.188.288.0
", + "bbox": [ + 501, + 210, + 890, + 305 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "GCD method [35] by $4.8\\%$ on CIFAR-10, $2.3\\%$ on CIFAR-100, and $6.4\\%$ on ImageNet-100 for 'All' classes, and by $8.7\\%$ on CIFAR-10, $3.7\\%$ on CIFAR-100, and $9.9\\%$ on ImageNet-100 for 'Unseen' classes. These results experimentally demonstrate the generated dynamic conceptions provide effective supervision to learn better representations for unlabeled data. Moreover, $\\mathrm{UNO + }$ shows a strong accuracy on \"Old\" classes, but its accuracy when testing on \"New\" classes is relatively lower. This is because $\\mathrm{UNO + }$ trains the linear classifier on \"Old\" classes, thus resulting in an inevitable bias. On the contrary, our DCCL gets a relatively good balance on both the \"Old\" and \"Unseen\" classes, without bias to the labeled data.", + "bbox": [ + 496, + 320, + 890, + 515 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparison on Fine-Grained Datasets. In general, the differences between different classes in fine-grained datasets are subtle, which leads the fine-grained visual understanding to be more challenging for GCD. For verifying the effects of DCCL on fine-grained tasks, we compare our method with others on fine-grained image recognition datasets. The results in Tab. 3 show that DCCL consistently outperforms all other methods for \"All\" and \"New\" classes. Specifically, on CUB-200 and Oxford-Pet, DCCL achieves $12.2\\%$ and $7.9\\%$ improvement over the state-of-the-art for \"All\" classes. Especially for \"New\" classes, DCCL outperforms GCD by $16.2\\%$ on the CUB-200 dataset. These results demonstrate that our DCCL is efficient in capturing the conceptual information shared across different fine-grained classes, thereby generating precise and helpful supervision for representation learning.", + "bbox": [ + 496, + 518, + 890, + 762 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Visualization of Feature Distributions. To qualitatively explore the clustered features on Pets dataset [24], we visualize the t-SNE embeddings projected from the features extracted by pre-trained ViT [4], GCD [35], the DCCL without the proposed dispersion loss and our full DCCL method. As shown in Fig. 3, our features are more discriminative than the features from the pre-trained ViT and GCD. By comparing Fig. 3(c) and Fig. 3(d), the proposed dispersion loss effectively pushes cluster centers away from", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "7584", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/4567f3afdefab37e162b27a170ba870da9f1d3cc929cd46b6ac3dd3fe3d1be8a.jpg", + "image_caption": [ + "(a) DINO" + ], + "image_footnote": [], + "bbox": [ + 89, + 90, + 261, + 190 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d77f6169ef2e6e0faa5f854e06eb81b90e94ac7586d51127b15e7318e6ebb98a.jpg", + "image_caption": [ + "(b) GCD" + ], + "image_footnote": [], + "bbox": [ + 263, + 90, + 426, + 190 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3d98b8061f91a20b8e6f80820053dc8464f7f769cebf95fc4b50617b9c900b44.jpg", + "image_caption": [ + "(c) DCCL without $\\mathcal{L}^D$" + ], + "image_footnote": [], + "bbox": [ + 429, + 90, + 612, + 190 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3ad7218fd449650f66f514c33fe362170d3f029912b1fc4b922bd380a8e3a8ac.jpg", + "image_caption": [ + "(d) DCCL", + "(e) False Examples" + ], + "image_footnote": [], + "bbox": [ + 617, + 88, + 880, + 190 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/4d6dfd15659dab0619ec4a4ae152c80168646fbd98e41c9665522619bd473f2a.jpg", + "table_caption": [ + "Table 4. Effectiveness of each component of our DCCL. \"MU\" and \"CC\" denote the proposed momentum update by Eq. (8) and the conception consolidation proposed in Sec. 3.3, respectively." + ], + "table_footnote": [], + "table_body": "
IndexComponentCUB-200 [36]Pet [24]
\\( \\mathcal{L}^I \\)\\( \\mathcal{L}^C \\)\\( \\mathcal{L}^D \\)MUCCAllOldNewAllOldNew
a)✓51.356.648.780.285.177.6
b)✓54.952.355.481.680.781.0
c)✓✓57.754.058.183.581.180.3
d)✓✓✓59.553.360.884.383.184.5
e)✓✓✓✓60.159.460.785.886.884.6
f)✓✓✓✓✓63.560.864.988.188.288.0
", + "bbox": [ + 81, + 291, + 468, + 388 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "each other. A large inter-cluster margin not only improves cluster boundaries for \"Old\" and \"New\" categories, but also compacts intra-cluster distribution.", + "bbox": [ + 75, + 407, + 468, + 452 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Summary. The experimental results show that our DCCL achieves significant improvements on both generic and fine-grained datasets. Especially for discovering \"New\" categories in challenging fine-grained tasks, our dynamic conceptual contrastive learning succeeds in mining shared conceptions, which is especially beneficial for the generalized fine-grained new category discovery.", + "bbox": [ + 75, + 454, + 468, + 559 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Effectiveness Evaluation", + "text_level": 1, + "bbox": [ + 76, + 571, + 302, + 587 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To verify the effectiveness of each component in our DCCL, we conduct five experiments on both CUB-200 [36] and Pet [24] datasets, as shown in Tab. 4. Note that the configuration of the experiment a) is the same with GCD [35], which is the baseline method in our experiments.", + "bbox": [ + 75, + 595, + 468, + 672 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of Conceptional contrastive Learning. Based on the results of the experiment a) and b), we find that using only the conceptual contrastive learning can achieve competitive performance, compared to baseline method with only instance-level contrastive learning.", + "bbox": [ + 75, + 672, + 468, + 748 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of Conception-Level Momentum Updating. Comparing the experiment b) and c), we can find that consistent update of conceptual representations by the proposed momentum update can bring considerable improvements on both new and old classes. This implies that due to periodically generating conceptual representations, the conceptual labels are kept fixed within one training period, which leads to a severe sub-optimal problem, during conceptual contrastive learning. Thus, the proposed momentum update mitigates the problem to some extent.", + "bbox": [ + 75, + 750, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/17e7c9b9aa3f880318a8626fb573feef0fc574f6251f68ad5ee64347828f7124.jpg", + "image_caption": [ + "Figure 3. Visualization of features distributions of the unlabeled set of the Pet [24] dataset. (a)-(d) are the results generated from DINO [4], GCD [35], our DCCL without $\\mathcal{L}^D$ and full DCCL, in turn. (e) is a visualization of false samples that are easy to be incorrectly clustered." + ], + "image_footnote": [], + "bbox": [ + 504, + 250, + 696, + 349 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/95797e8f58b53b909892e359a3094592239b0b17d379945b87f1dc9341666d8b.jpg", + "image_caption": [ + "Figure 4. Impact of hyper-parameters. The clustering accuracy on \"All\" categories is reported." + ], + "image_footnote": [], + "bbox": [ + 504, + 351, + 696, + 450 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5b424a67fd25aa0010f1854957a9e4098f0209ce6e2f60e73620765304874c72.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 697, + 251, + 890, + 351 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/05f9656d48fc088005bc36d41aa4cd1b4a8a8eb536915ea4eab045b2ed9e51e1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 699, + 352, + 890, + 450 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of Dispersion Loss. The experiment d) in Tab. 4 shows that by adding the proposed dispersion loss, the model's performances on new classes acquire further improvements by $2.7\\%$ on \"New\" classes for the CUB-200 dataset. The improvements can be observed in Fig. 3(d).", + "bbox": [ + 498, + 484, + 890, + 561 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of Conception Consolidation. Without the proposed conception consolidation that considers labeled information to impose semi-supervised constraintsd, our DCCL suffers from a performance balance between the new and the old classes, as shown in Tab. 4 b), c) and d). In the experiment e) and f), our full method shows superior performance on all evaluation metrics, which experimentally demonstrates that our conception consolidation plays an essential role in rectifying the estimated latent conception relations between seen and unseen classes.", + "bbox": [ + 498, + 561, + 890, + 712 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Hyper-Parameter Analyses", + "text_level": 1, + "bbox": [ + 500, + 724, + 745, + 741 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we discuss the impact of the hyperparameters in our DCCL, including loss weights $(\\alpha$ and $\\beta)$ , the threshold parameter of dispersion loss $(\\tau^{M})$ , momentum updating factor $(\\eta)$ , and the frequency of DCG $(\\tau^{I})$ .", + "bbox": [ + 498, + 748, + 890, + 809 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Impact of loss weights and threshold parameters. For the evaluation of loss weights, we use the hold-off validation data to determine their values. Specifically, we first select the optimal $\\alpha$ to achieve the best accuracy on the \"All\" score, then we find the optimal $\\beta$ based on the selected $\\alpha$ . The impact of different values is shown in Fig. 4 (a)-(c).", + "bbox": [ + 498, + 810, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "7585", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/03a89caf92896da1c600a3aecd2d4b807675b83356498543c9d7be4e07039574.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 81, + 90, + 287, + 183 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2e369cfc5b95365d98be96fed357411ee6c3f700c32ee3fca9ac018841043b2e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 287, + 90, + 467, + 183 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/19affb57099820e1aaa7e1d71f312e508fa9a967e4f3c8af1bc058f5331c837c.jpg", + "image_caption": [ + "(b)", + "Figure 5. (a) visualizes the dynamics of DCG, which implies that our DCG adaptively estimates conceptual representation for different training stages. (b) illustrates the trend of performances on the CIFAR100 dataset, with varying the number of unlabeled classes. (c) is the comparison between the real number of classes in datasets and the estimated number of conceptions." + ], + "image_footnote": [], + "bbox": [ + 80, + 198, + 467, + 335 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Similarly, we choose the best $\\tau^M$ with the selected $\\alpha$ and $\\beta$ . Finally, our final model is obtained by using $\\alpha = 0.3$ , $\\beta = 0.1$ and $\\tau^M = 0.3$ .", + "bbox": [ + 75, + 441, + 468, + 484 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Impact of Update Rates. The impact of updating factor of CMB is illustrated in in Fig. 4 (d). The more smooth running average can obtain better performance. Considering the balance between computational consumption and performance, we thus set $\\tau^I = 5$ and $\\eta = 0.9$ in all experiments.", + "bbox": [ + 75, + 487, + 470, + 564 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Further Investigation of DCG", + "text_level": 1, + "bbox": [ + 76, + 574, + 341, + 589 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To explore our dynamic conception generation (DCG), we conduct two group experiments and the experimental results are shown in Fig. 5 and Tab. 5. From the Fig. 5 (a) we find that in the initial training stage, our DCG tends to generate fewer conceptions than at the convergence stage. This is because in the beginning, the model could not understand fine-grained classes well. Thus, DCG generates coarse-grained supervision like super-class, which has a low risk to over-correct. Later, with the growth of feature discriminability, DCG builds elaborate conceptual relationships to further refine the learned representations.", + "bbox": [ + 75, + 598, + 468, + 763 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "From the Fig. 5 (c), we find that the number of conceptions estimated by DCCL is close to the ground truth of the number of classes in the corresponding dataset. However, it is worth noting that the conception representations in this paper are not equivalent to the cluster centers. The DCG aims to adaptively generate proper conceptual representations that are beneficial for contrastive learning, instead of predicting the real number of classes within a dataset. Furthermore, we try to directly replace our DGC with semi-", + "bbox": [ + 75, + 765, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/1200fc22c12d60556e0bfc10a2e0922edee6cc6d16598c8fb6e6a028ba94b519.jpg", + "table_caption": [ + "Table 5. Comparison of different clustering methods for DCG." + ], + "table_footnote": [], + "table_body": "
Clustering MethodCUB-200 [36]
AllOldNew
k-means [21]54.153.453.3
SSK [35]55.955.154.2
FINCH [29]55.856.155.4
DBSCAN [8]60.554.759.8
InfoMap [27]61.455.262.7
DCG (Ours)63.560.864.9
", + "bbox": [ + 547, + 104, + 841, + 250 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "supervised $k$ -means [35] (SSK) with the prior of known $k$ . From the results in Tab. 5, SSK fails to generate effective latent conceptions, even leading to worse clustering.", + "bbox": [ + 496, + 266, + 890, + 310 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Discussion. Based on the comparison in Fig. 5 (b), we notice that when training on generic datasets, our DCG tends to generate more conceptions than the actual number of dataset classes, while generating fewer conceptions on fine-grained datasets. A possible explanation is that due to large inter-class differences in generic datasets, learning more sub-classes conceptions enables models to gain discriminability. Similarly, since fine-grained classes share more common attributes or conceptions, such super-class information can significantly benefit fine-grained GCD.", + "bbox": [ + 496, + 311, + 892, + 462 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.6. Evaluation with Different Split Protocols", + "text_level": 1, + "bbox": [ + 498, + 473, + 849, + 489 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To explore the effects of DCCL under strict annotation limitation, we propose to test models on varying splits of CIFAR100 [17]. We visualize the accuracy of \"All\" classes in Fig. 5 (b), which indicates that our DCCL has stronger robustness when only a few labeled classes are available. Meanwhile, with the growth of the number of unlabeled classes, GCD expresses a severe performance degradation.", + "bbox": [ + 496, + 496, + 890, + 603 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 617, + 617, + 633 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose to cope with the generalized category discovery (GCD) from the perspective of mining underlying relationships between known and unknown categories. To implement this idea, we propose a dynamic conceptual contrastive learning framework to alternately explore latent conceptual relationships and perform conceptual contrastive learning. This mechanism enables models to learn more discriminable representations. Furthermore, to mitigate the inconsistency of updating conception representations during the training process, we propose a conception-level momentum update to facilitate the model toward better optimization. Extensive experimental results show that our DCCL achieves a new state-of-the-art performance on GCD tasks.", + "bbox": [ + 496, + 643, + 892, + 853 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement This work has been supported by the EU H2020 project AI4Media (No. 951911) and by the PRIN project CREATIVE (Prot. 2020ZSL9F9).", + "bbox": [ + 498, + 854, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "7586", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Sugato Basu, Arindam Banerjee, and Raymond J. Mooney. Semi-supervised clustering by seeding. In Claude Sammut and Achim G. 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In CVPR, 2021. 1" + ], + "bbox": [ + 78, + 90, + 468, + 517 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "7588", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Dynamic Conceptional Contrastive Learning for Generalized Category Discovery/40efeb24-3451-4def-8441-e92b604d3421_model.json b/2023/Dynamic Conceptional Contrastive Learning for Generalized Category Discovery/40efeb24-3451-4def-8441-e92b604d3421_model.json new file mode 100644 index 0000000000000000000000000000000000000000..0dd4e16ec084a26684abed1472311dc7010c6e1e --- /dev/null +++ b/2023/Dynamic Conceptional Contrastive Learning for Generalized Category Discovery/40efeb24-3451-4def-8441-e92b604d3421_model.json @@ -0,0 +1,2222 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.809, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.242, + 0.131, + 0.73, + 0.176 + ], + "angle": 0, + "content": "Dynamic Conceptional Contrastive Learning for Generalized Category Discovery" + }, + { + "type": "text", + "bbox": [ + 0.34, + 0.204, + 0.63, + 0.222 + ], + "angle": 0, + "content": "Nan Pu Zhun Zhong* Nicu Sebe" + }, + { + "type": "text", + "bbox": [ + 0.218, + 0.222, + 0.751, + 0.257 + ], + "angle": 0, + "content": "The Department of Information Engineering and Computer Science University of Trento, Trento, Italy" + }, + { + "type": "text", + "bbox": [ + 0.293, + 0.26, + 0.672, + 0.275 + ], + "angle": 0, + "content": "{nan.pu, zhun.zhong, niculae.sebe}@unitn.it" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.309, + 0.314, + 0.326 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.342, + 0.473, + 0.765 + ], + "angle": 0, + "content": "Generalized category discovery (GCD) is a recently proposed open-world problem, which aims to automatically cluster partially labeled data. The main challenge is that the unlabeled data contain instances that are not only from known categories of the labeled data but also from novel categories. This leads traditional novel category discovery (NCD) methods to be incapacitated for GCD, due to their assumption of unlabeled data are only from novel categories. One effective way for GCD is applying self-supervised learning to learn discriminate representation for unlabeled data. However, this manner largely ignores underlying relationships between instances of the same concepts (e.g., class, super-class, and sub-class), which results in inferior representation learning. In this paper, we propose a Dynamic Conceptional Contrastive Learning (DCCL) framework, which can effectively improve clustering accuracy by alternately estimating underlying visual conceptions and learning conceptual representation. In addition, we design a dynamic conception generation and update mechanism, which is able to ensure consistent conception learning and thus further facilitate the optimization of DCCL. Extensive experiments show that DCCL achieves new state-of-the-art performances on six generic and fine-grained visual recognition datasets, especially on fine-grained ones. For example, our method significantly surpasses the best competitor by \\(16.2\\%\\) on the new classes for the CUB-200 dataset. Code is available at https://github.com/TPCD/DCCL" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.793, + 0.208, + 0.808 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.818, + 0.47, + 0.879 + ], + "angle": 0, + "content": "Learning recognition models (e.g., image classification) from labeled data has been widely studied in the field of machine learning and deep learning [13, 18, 31]. In spite of their tremendous success, supervised learning techniques" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.318, + 0.892, + 0.488 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.491, + 0.893, + 0.603 + ], + "angle": 0, + "content": "Figure 1. Diagram of the proposed Dynamic Conceptional Contrastive Learning (DCCL). Samples from the conceptions should be close to each other. For example, samples from the same classes (bus) at the class level, samples belonging to the transportation (bus and bicycle) at the super-class level, and samples from trains with different colors at the sub-class level. Our DCCL potentially learns the underlying conceptions in unlabeled data and produces more discriminative representations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.625, + 0.892, + 0.732 + ], + "angle": 0, + "content": "rely heavily on huge annotated data, which is not suitable for open-world applications. Thus, the researchers recently have paid much effort on learning with label-imperfection data, such as semi-supervised learning [23, 33], self-supervised learning [12, 42], weakly-supervised learning [41,45], few-shot learning [32,38], open-set recognition [30] and learning with noisy labels [40], etc." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Recently, inspired by the fact that Humans can easily and automatically learn new knowledge with the guidance of previously learned knowledge, novel category discovery (NCD) [9, 11, 28, 44, 47] is introduced to automatically cluster unlabeled data of unseen categories with the help of knowledge from seen categories. However, the implementation of NCD is under a strong assumption that all the unlabeled instances belong to unseen categories, which is not practical in real-world applications. To address this limitation, Vaze et al. [35] extend NCD to the generalized category discovery (GCD) [35], where unlabeled images are" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.227, + 0.9 + ], + "angle": 0, + "content": "*Corresponding Author." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7579" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.34, + 0.106 + ], + "angle": 0, + "content": "from both novel and labeled categories." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.108, + 0.473, + 0.53 + ], + "angle": 0, + "content": "GCD is a challenging open-world problem in that we need to 1) jointly distinguish the known and unknown classes and 2) discover the novel clusters without any annotations. To solve this problem, Vaze et al. [35] leverage the contrastive learning technique to learn discriminative representation for unlabeled data and use \\( k \\)-means [21] to obtain final clustering results. In this method, the labeled data are fully exploited by supervised contrastive learning. However, self-supervised learning is applied to the unlabeled data, which enforces samples to be close to their augmentation counterparts while far away from others. As a consequence, the underlying relationships between samples of the same conceptions are largely overlooked and thus will lead to degraded representation learning. Intuitively, samples that belong to the same conceptions should be similar to each other in the feature space. The conceptions can be regarded as: classes, super-classes, sub-classes, etc. For example, as shown in Fig. 1, samples of the same class should be similar to each other, e.g., samples of the bus, samples of the bicycle. In addition, in the super-classes view, classes of the transportation, e.g., Bus and Bicycle, should belong to the same concept. Hence, the samples of transportation should be closer than that of other concepts (e.g., animals). Similarly, samples belong to the same sub-classes (e.g., red train) should be closer to that of other sub-classes (e.g., white train). Hence, embracing such conceptions and their relationships can greatly benefit the representation learning for unlabeled data, especially for unseen classes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.531, + 0.473, + 0.742 + ], + "angle": 0, + "content": "Motivated by this, we propose a Dynamic Conceptional Contrastive Learning (DCCL) framework for GCD to effectively leverage the underlying relationships between unlabeled data for representation learning. Specifically, our DCCL includes two steps: Dynamic Conception Generation (DCG) and Dual-level Contrastive Learning (DCL). In DCG, we dynamically generate conceptions based on the hyper-parameter-free clustering method equipped with the proposed semi-supervised conceptual consolidation. In DCL, we propose to optimize the model with conception-level and instance-level contrastive learning objectives, where we maintain a dynamic memory to ensure comparing with the up-to-date conceptions. The DCG and DCL are alternately performed until the model converges." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.742, + 0.47, + 0.758 + ], + "angle": 0, + "content": "We summarize the contributions of this work as follows:" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.769, + 0.47, + 0.83 + ], + "angle": 0, + "content": "- We propose a novel dynamic conceptionsal contrastive learning (DCCL) framework to effectively leverage the underlying relationships between unlabeled samples for learning discriminative representation for GCD." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.84, + 0.471, + 0.902 + ], + "angle": 0, + "content": "- We introduce a novel dynamic conception generation and update mechanism to ensure consistent conception learning, which encourages the model to produce more discriminative representation." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.769, + 0.471, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.092, + 0.895, + 0.138 + ], + "angle": 0, + "content": "- Our DCCL approach consistently achieves superior performance over state-of-the-art GCD algorithms on both generic and fine-grained tasks." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.172, + 0.642, + 0.187 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.199, + 0.736, + 0.216 + ], + "angle": 0, + "content": "2.1. Novel Category Discovery" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.224, + 0.895, + 0.558 + ], + "angle": 0, + "content": "Novel category discovery [11] (NCD) tasks aim at discovering new categories by leveraging the knowledge of a set of labeled categories. RankStat [10] indicates that self-supervised pre-training is helpful for NCD. NCL [46] adopts contrastive learning to improve representation learning. UNO [9] proposes a unified objective for jointly learning on unlabeled and labeled data. Most recently, NCD has been extended to a generalized category discovery (GCD) [35], in which the unlabeled data include both labeled and unlabeled categories. Later, ORCA [3] defines an open-world semi-supervised learning task, which is similar to GCD. Although these definitions are relatively practical, most methods remain to assume that the class number of clustered data is known. Nevertheless, such prior knowledge is often not acquired in advance for real-world applications. To handle the drawback, DTC [11] and GCD [35] employed an independent algorithm to search the optimal class number, however, they did not associate clustering estimation with representation learning. Unlike these offline algorithms, we propose to jointly consider downstream clustering and representation learning. The experimental results show they are mutually beneficial for each other." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.573, + 0.892, + 0.59 + ], + "angle": 0, + "content": "2.2. Contrastive Learning based on Memory Buffer" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Contrastive learning [5,6,22,37,43] (CL) has been shown to be significantly effective for representation learning in a self-supervised manner. MoCo [12] demonstrates that sampling positive-negative pairs from an instance-level buffer can benefit CL and reduce the impact of the size of the training batch. Then, instead of contrasting over all instances in a mini-batch, prototypical contrastive learning [20] (PCL) that contrasts the instance features with a set of prototypes, has been shown to provide comprehensive supervision. However, PCL still needs an instance-level memory buffer to yield the prototype set, which is not computation- and memory-efficient. Recently, SCL [14] propose a cluster-level momentum encoder but considers only three fixed numbers of classes during training, which is still limited compared to our dynamic method. Different from PCL and SCL that consider the fixed numbers of classes during the whole training process, our DCCL dynamically estimates the number of classes for different training stages in a efficient way, which encourages models to learn more discriminative representation." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.517, + 0.957 + ], + "angle": 0, + "content": "7580" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.101, + 0.86, + 0.344 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.345, + 0.895, + 0.43 + ], + "angle": 0, + "content": "Figure 2. (a) Overview of our DCCL framework. We first extract features and cluster the features to generate conceptual labels, then initialize conception representations by our DCG, and last learn representations by joint instance-level and conception-level objectives. During the training process, the DCG and dual-level representation learning are performed alternately, in which the conception buffer is updated every iteration to keep the consistency of the changing instance features and conceptual representations. (b) Illustration of the proposed conception consolidation. Without consolidating the relationships of conceptions by label information, Infomap tends to over-cluster data and thus provides the supervision that has a high risk to over-correct affinities between neighbor instances." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.441, + 0.436, + 0.459 + ], + "angle": 0, + "content": "2.3. Semi-Supervised Learning and Clustering" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.466, + 0.473, + 0.786 + ], + "angle": 0, + "content": "Semi-supervised learning (SSL) has been a long-standing research topic [39]. Different from GCD, SSL often assumes that the labeled and unlabeled data come from the same set of classes, in which consistency-based methods are the most effective methods for SSL, such as Mean-teacher [34], MixMatch [2], and FixMatch [33]. Consistency-based methods are the most effective methods for SSL, such as Mean-teacher [34], MixMatch [2], and FixMatch [33]. Moreover, semi-supervised classification is a relatively well-defined task, while the supervised information in semi-supervised clustering can take different forms [19], such as two instances are known to be must-linked in a relationship matrix or some cluster assignments are known beforehand. For instance, Basu et al. [1] proposed to initialize the clusters based on the data points for which cluster assignments are known. However, these methods can not adaptively assign the number of clusters for generating conceptions. To mitigate these limitations, we improve the classical InfoMap [27] to fully leverage both labeled and unlabeled data and dynamically produce varying conceptual labels for different contrastive learning epochs." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.802, + 0.471, + 0.838 + ], + "angle": 0, + "content": "3. Dynamic Conceptional Contrastive Learning" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.846, + 0.281, + 0.862 + ], + "angle": 0, + "content": "3.1. Problem Formulation" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Generalized category discovery (GCD) aims at automatically categorizing unlabeled images in a dataset, where the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.441, + 0.895, + 0.675 + ], + "angle": 0, + "content": "partial data are labeled and the remaining are unlabeled. The unlabeled images come from either labeled (known) classes or unlabeled (unknown) classes. This is a more realistic open-world setting than the common closed-set classification that assumes the labeled and unlabeled data belong to the same classes. Let the dataset be \\(\\mathcal{D} = \\mathcal{D}^L\\cup \\mathcal{D}^U\\) where \\(\\mathcal{D}^L = \\{(\\mathbf{x}_i^L,\\mathbf{y}_i^L)\\}_{i = 1}^{M^L}\\in \\mathcal{X}\\times \\mathcal{Y}^L\\) \\(L\\) denotes the labeled subset and \\(\\mathcal{D}^U = \\{(\\mathbf{x}_i^U,\\mathbf{y}_i^U)\\}_{i = 1}^{M^U}\\in \\mathcal{X}\\times \\mathcal{Y}^U\\) denotes the unlabeled subset with unknown \\(\\mathbf{y}_i^U\\in \\mathcal{V}^U\\) . Only a subset of classes contains labeled instances, i.e., \\(\\mathcal{V}^L\\subset \\mathcal{V}^U\\) The number of labeled classes \\(N^L\\) can be directly calculated from the labeled data, while the number of unlabeled classes \\(N^U\\) is not known during model training. Let \\(f\\) and \\(h\\) be a feature extractor and a MLP projection head. The extracted representation is defined as \\(\\mathbf{v}_i = f(\\mathbf{x}_i)\\)" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.682, + 0.611, + 0.696 + ], + "angle": 0, + "content": "3.2. Overview" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.895, + 0.903 + ], + "angle": 0, + "content": "To tackle the problem of GCD, we propose a novel framework DCCL (see Fig. 2), to jointly learn representations using dual-level contrastive learning (DCL) and explore all possible relationships between labeled and unlabeled instances in a conceptionsal view. First, we extend the classical unsupervised clustering algorithm, Infomap [27], to a semi-supervised manner, which aims at dynamically generating reasonable conceptual representations and associating the labeled and unlabeled instances during representation learning. By alternately executing the dynamic conception generation (DCG) and DCL, DCL benefits from informative supervised information to generate higher-quality representations. Meanwhile, DCG gradually" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.958 + ], + "angle": 0, + "content": "7581" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.155 + ], + "angle": 0, + "content": "produces more comprehensive guidance based on a deeper understanding of conceptual relationships. DCG and DCL mutually benefit each other, thus resulting in a better representation for downstream clustering." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.161, + 0.367, + 0.178 + ], + "angle": 0, + "content": "3.3. Dynamic Conception Generation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.184, + 0.47, + 0.411 + ], + "angle": 0, + "content": "Although the test-time semi-supervised \\( k \\)-means [35] (SSK) succeeds in achieving considerable performance gain, it fails to jointly consider the representation learning and supervision information from semi-supervised clustering. Moreover, it is infeasible to directly perform SSK in each training epoch for assigning pseudo labels, because the real number of clusters is unknown during training. To overcome these drawbacks, we propose a dynamic conception generation (DCG) based on the hyper-parameter-free Infomap [27] algorithm. Specifically, we first propose a semi-supervised conceptual consolidation method to construct a similarity network, then execute the Infomap clustering algorithm on the constructed network to get conceptual label assignments, and finally calculate conception representation and initialize conceptual memory buffer." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.411, + 0.47, + 0.547 + ], + "angle": 0, + "content": "Conception Consolidation. In a given network, Infomap aims at partitioning semantic-similar sub-networks by the pattern of connections. To leverage the supervision from labeled data, we propose to enforce the similarity constraints into the networking, according to the labeled data that belong to the same category. Formally, we construct an adjacent matrix \\(\\mathcal{A}\\) to represent the possible connection relationships among all instances. The weight of the edge of the \\(i\\)-th and \\(j\\)-th instances is given by:" + }, + { + "type": "equation", + "bbox": [ + 0.103, + 0.557, + 0.47, + 0.613 + ], + "angle": 0, + "content": "\\[\n\\mathcal {A} _ {i j} = \\left\\{ \\begin{array}{l l} s _ {i} ^ {\\max }, & \\text {i f} \\mathbf {y} _ {i}, \\mathbf {y} _ {j} \\in \\mathcal {Y} ^ {L} \\text {a n d} \\mathbf {y} _ {i} = \\mathbf {y} _ {j} \\\\ s _ {i j}, & \\text {i f} \\mathbf {y} _ {i} \\text {o r} \\mathbf {y} _ {j} \\in \\mathcal {Y} ^ {U} \\text {a n d} s _ {i j} > \\tau^ {F} \\\\ 0, & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.166, + 0.621, + 0.469, + 0.648 + ], + "angle": 0, + "content": "\\[\ns _ {i} ^ {\\text {m a x}} = \\underset {j} {\\arg \\max } \\left\\{s _ {i j} \\mid j \\in \\mathcal {D} \\right\\}, \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.12, + 0.652, + 0.469, + 0.671 + ], + "angle": 0, + "content": "\\[\ns _ {i j} = \\left[ \\left(\\mathbf {v} _ {i} / \\| \\mathbf {v} _ {i} \\|\\right) \\cdot \\left(\\mathbf {v} _ {j} / \\| \\mathbf {v} _ {j} \\|\\right) + 1 \\right] / 2 \\in [ 0, 1 ], \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.675, + 0.469, + 0.75 + ], + "angle": 0, + "content": "where \\(\\cdot\\) denotes dot product and \\(\\| \\cdot \\|\\) is \\(l_{2}\\) normalization. The \\(\\tau^{F}\\) is a threshold to select high-confidence links. Through the conception consolidation illustrated in Fig. 2(b), we can establish a reliable relationship network with rich structural information for the subsequent clustering." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.75, + 0.469, + 0.825 + ], + "angle": 0, + "content": "Remark. We set the similarities of positive pairs with the maximal value of neighborhood similarities instead of 1. This is because we experimentally find that when imposing 1 for constraining positive pairs, Infomap tends to group all the labeled positive instances as an individual cluster." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Entropy Minimization Clustering. In Infomap algorithm [26], the clustering problem is equivalent to minimizing the entropy that represents the minimum description length of the coding network. By solving the minimization objective, we acquire a conceptual label set" + }, + { + "type": "code_caption", + "bbox": [ + 0.51, + 0.095, + 0.827, + 0.11 + ], + "angle": 0, + "content": "Algorithm 1: Algorithm Pipeline of our DCCL" + }, + { + "type": "algorithm", + "bbox": [ + 0.517, + 0.112, + 0.848, + 0.399 + ], + "angle": 0, + "content": "Input: Feature Extractor \\(f\\) Projection Head \\(h\\) Labeled data \\(\\mathcal{D}^L\\) and Unlabeled data \\(\\mathcal{D}^U\\) \nOutput: \\(f\\) and \\(h\\) \nfor \\(n = 1\\) in [1,max_epoch] do if \\(n\\bmod\\tau^{I}==0\\) then Extract features and construct adjacency matrix \\(\\mathcal{A}\\) by Eq. (1), Eq. (2) and Eq. (3); Perform InfoMap [27] clustering to assign conceptual labels C; Initialize conceptual buffer by Eq. (4); \nend for \\(i = 1\\) in [1,max_iteration] do Sample mini-batches from \\(\\mathcal{D}^L\\cup \\mathcal{D}^U\\) Calculate overall optimization objective by Eq.(10); Update \\(f\\) and \\(h\\) by SGD [25]; Update conceptual buffer by Eq. (8); \nend" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.43, + 0.892, + 0.512 + ], + "angle": 0, + "content": "\\(\\mathcal{C} = \\{\\mathbf{c}_i\\}_{i=1}^{M^L + M^U} \\in \\mathcal{V}^G\\) for both labeled and unlabeled instances. Then, we combine the extracted feature vectors \\(\\mathcal{V}\\) and corresponding conceptionsal labels to construct a generated feature dataset \\(\\mathcal{D}^G = \\{(\\mathbf{v}_i, \\mathbf{c}_i)\\}_{i=1}^{M^L + M^U} \\in \\mathcal{V} \\times \\mathcal{V}^G\\). \\(|\\mathcal{V}^G|\\) denotes the number of estimated conceptions." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.512, + 0.893, + 0.648 + ], + "angle": 0, + "content": "Conceptional Memory Initialization. In this paper, our DCCL maintains a conception-level memory buffer that provides dynamic conceptual representations for dual-level contrastive learning, which is elaborated in Sec. 3.4. Here, we introduce the initialization of the conceptual memory buffer (CMB). We use the mean feature vector of the instances that share the same conceptual label to form a unique conceptual representation. Formally, the initial conceptual representation set is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.508, + 0.655, + 0.892, + 0.695 + ], + "angle": 0, + "content": "\\[\n\\mathcal {U} = \\left\\{\\boldsymbol {\\mu} _ {k} \\right\\} _ {k = 1} ^ {K}, \\quad \\boldsymbol {\\mu} _ {k} = \\frac {1}{\\left| \\mathcal {D} _ {k} ^ {G} \\right|} \\sum_ {\\mathbf {v} _ {i} \\in \\mathcal {D} _ {k} ^ {G}} \\mathbf {v} _ {i}, \\quad K = | \\mathcal {Y} ^ {G} |, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.703, + 0.892, + 0.78 + ], + "angle": 0, + "content": "where \\(\\mathcal{D}_k^G\\) denotes the \\(k\\)-th conception subset, i.e., if \\(\\mathbf{v}_i \\in \\mathcal{D}_k^G\\), \\(\\mathbf{c}_i = k\\). During whole training process, the initialization of CMB is executed every \\(\\tau^I\\) epochs on center-cropped images. Thus, the number of conceptions \\(K\\) is dynamically changing along with model training." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.787, + 0.791, + 0.804 + ], + "angle": 0, + "content": "3.4. Dual-Level Contrastive Learning" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.871 + ], + "angle": 0, + "content": "In this section, we first explain the proposed conception-level contrastive learning, then elaborate on the update of the conceptual memory buffer, and finally introduce the employed instance-level contrastive learning approach." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Conception-Level Contrastive Learning. Based on the generated conceptual representations in Sec. 3.3, we" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7582" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.244 + ], + "angle": 0, + "content": "propose to perform conception-level contrastive learning. Specifically, we first sample \\( N^C \\) conception labels and a fixed number \\( N^I \\) of instances for each conception label, resulting in a mini-batch \\( \\mathcal{B}^C \\) with \\( N^C \\times N^I \\) instances. Next, each instance representation is compared to all the conceptual representations. We pull the instance representation from its corresponding conceptual representation closer and push the instance representation away from other conceptual representations. Formally, we define the conceptual contrastive loss function as the following:" + }, + { + "type": "equation", + "bbox": [ + 0.13, + 0.255, + 0.47, + 0.295 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {i} ^ {C} = - \\log \\frac {\\exp \\left(\\mathbf {v} _ {i} \\cdot \\boldsymbol {\\mu} _ {\\mathbf {c} _ {i}} / \\tau^ {C}\\right)}{\\sum_ {k = 1 , k \\neq \\mathbf {c} _ {i}} ^ {K} \\exp \\left(\\mathbf {v} _ {i} \\cdot \\boldsymbol {\\mu} _ {k} / \\tau^ {C}\\right)}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.303, + 0.47, + 0.41 + ], + "angle": 0, + "content": "where \\(\\tau^C\\) is a temperature hyper-parameter to control the strength of the conception-level contrastive learning. In addition, in order to explicitly encourage learned representations with a large inter-conception margin, we propose a dispersion loss to further push the different conception representations away from each other. The loss function for the \\(m\\)-th and the \\(n\\)-th conceptions in \\(\\mathcal{B}^C\\) is:" + }, + { + "type": "equation", + "bbox": [ + 0.077, + 0.42, + 0.47, + 0.472 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} (m, n) = \\left[ \\tau^ {M} - \\left\\| \\frac {1}{\\left| \\mathcal {B} _ {m} ^ {C} \\right|} \\sum_ {\\mathbf {v} _ {i} \\in \\mathcal {B} _ {m} ^ {C}} \\mathbf {v} _ {i} \\right\\| \\cdot \\left\\| \\frac {1}{\\left| \\mathcal {B} _ {n} ^ {C} \\right|} \\sum_ {\\mathbf {v} _ {j} \\in \\mathcal {B} _ {n} ^ {C}} \\mathbf {v} _ {j} \\right\\| \\right] _ {+}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.473, + 0.47, + 0.564 + ], + "angle": 0, + "content": "where \\(\\tau^M\\) is a threshold to filter the conception pairs with high uncertainty. We assume that two conception representations that are close tend to be highly entangled conceptions. Separating these conceptions has a high risk of overcorrect. We explore the impact of \\(\\tau^M\\) in Sec. 4.4. The dispersion loss function over a mini-batch is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.156, + 0.577, + 0.47, + 0.62 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} ^ {D} = \\frac {1}{N ^ {C}} \\sum_ {m = 1} ^ {N ^ {C}} \\frac {1}{N ^ {C}} \\sum_ {n = 1} ^ {N ^ {C}} \\mathcal {L} (m, n). \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.631, + 0.47, + 0.783 + ], + "angle": 0, + "content": "Conceptional Memory Update. Different from [12, 20] that need to save all training instances, our CMB stores only the conception representations, which significantly reduces storage cost. Furthermore, the instance-wise update is easy to lead to an inconsistent update during each training iteration. To mitigate this drawback, we first adopt the resampling method as detailed in the previous section. Next, we propose to update the conception representation by each corresponding instance feature following a momentum update mechanism. The process is formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.185, + 0.797, + 0.469, + 0.813 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\mu} _ {\\mathbf {c} _ {i}} \\leftarrow \\eta \\boldsymbol {\\mu} _ {\\mathbf {c} _ {i}} + (1 - \\eta) \\mathbf {v} _ {i}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.825, + 0.359, + 0.84 + ], + "angle": 0, + "content": "where \\(\\eta\\) is the momentum updating factor." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.469, + 0.902 + ], + "angle": 0, + "content": "Remark. DCCL updates the memory buffer and computes the losses both at the conceptual level, which consistently updates the conceptual representation to maintain the conceptual consistency during the whole training process." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.228 + ], + "angle": 0, + "content": "Instance-Level Contrastive Learning. Inspired by [35], we combine supervised contrastive loss and self-supervised contrastive loss as an instance contrastive loss (ICL), to fine-tune the model. Formally, we assume \\( x_{i} \\) and \\( \\hat{x}_i \\) are two views (random augmentations) of the same image in a randomly-sampled mini-batch \\( \\mathcal{B}^I \\). Let \\( h \\) be a MLP projection head. The extracted representation \\( \\mathbf{v}_i \\) is further projected by \\( h \\) to high-dimensional embedding space for instance-level contrastive learning. The loss function is:" + }, + { + "type": "equation", + "bbox": [ + 0.504, + 0.237, + 0.891, + 0.328 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {i} ^ {I} = (\\lambda - 1) \\log \\frac {\\exp \\left(h \\left(\\mathbf {v} _ {i}\\right) \\cdot h \\left(\\hat {\\mathbf {v}} _ {i}\\right) / \\tau\\right)}{\\sum_ {j \\in \\mathcal {B} ^ {I} , j \\neq i} \\exp \\left(h \\left(\\mathbf {v} _ {i}\\right) \\cdot h \\left(\\mathbf {v} _ {j}\\right) / \\tau^ {S}\\right)} \\\\ \\frac {- \\lambda}{| \\mathcal {P} (i) |} \\sum_ {p \\in \\mathcal {P} (i)} \\log \\frac {\\exp \\left(h \\left(\\mathbf {v} _ {i} ^ {L}\\right) \\cdot h \\left(\\mathbf {v} _ {p} ^ {L}\\right) / \\tau\\right)}{\\sum_ {j \\in \\mathcal {B} ^ {L} , j \\neq i} \\exp \\left(h \\left(\\mathbf {v} _ {i} ^ {L}\\right) \\cdot h \\left(\\mathbf {v} _ {j} ^ {L}\\right) / \\tau^ {L}\\right)}, \\tag {9} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.329, + 0.892, + 0.406 + ], + "angle": 0, + "content": "where \\(\\mathcal{B}^L\\) donates the labeled subset within the mini-batch \\(\\mathcal{B}^I\\) and \\(\\mathcal{B}^I = \\mathcal{B}^L\\cup \\mathcal{B}^U\\). \\(\\mathcal{P}(i)\\) is the positive index set for the anchor image \\(i\\in \\mathcal{B}^L\\). \\(\\lambda\\) is a trade-off factor to balance the contributions of self-supervised and supervised learning. For a fair comparison, we follow [35] and set \\(\\lambda\\) to 0.35." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.414, + 0.682, + 0.43 + ], + "angle": 0, + "content": "3.5. Joint Optimization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.437, + 0.892, + 0.528 + ], + "angle": 0, + "content": "During the whole training process, we alternately perform dynamic conception generalization and dual-level contrastive representation learning, until the maximal training epoch. The pseudo-code of DCCL is elaborated in Algorithm 1. The overall objective over on mini-batch \\(\\mathcal{B}\\) is given by the weighted sum of each loss function:" + }, + { + "type": "equation", + "bbox": [ + 0.531, + 0.537, + 0.892, + 0.574 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {t o t a l}} = \\frac {1}{| \\mathcal {B} |} \\sum_ {i \\in \\mathcal {B}} \\mathcal {L} _ {i} ^ {I} + \\alpha \\frac {1}{| \\mathcal {B} |} \\sum_ {i \\in \\mathcal {B}} \\mathcal {L} _ {i} ^ {C} + \\beta \\mathcal {L} ^ {D}, \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.583, + 0.892, + 0.629 + ], + "angle": 0, + "content": "where \\(\\alpha\\) and \\(\\beta\\) are the weights to adjust the strengths of two loss functions. In all experiments, we use \\(l_{2}\\) normalized feature vector \\(\\| \\mathbf{v}\\| _2\\) for clustering evaluation." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.642, + 0.634, + 0.659 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.667, + 0.691, + 0.683 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Data and Evaluation Metric. We evaluate DCCL on three generic image classification datasets, namely CIFAR-10 [17], CIFAR-100 [17] and ImageNet-100 [35]. ImageNet-100 denotes randomly sub-sampling 100 classes from the ImageNet [7] dataset. The dataset statistics and train-test splits are described in Tab. 1. We further evaluate DCCL on three more challenging fine-grained image classification datasets: CUB-200 [36], Stanford Cars [16], and Oxford-IIIT Pet [24]. The original training set of each fine-grained dataset is separated into labeled and unlabeled parts. We follow [35] sample a subset of half the classes as \"Old\" categories. \\(50\\%\\) of instances of each labeled class are drawn to form the labeled set, and all the remaining data constitute the unlabeled set. For evaluation, we measure the clustering" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7583" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.08, + 0.089, + 0.885, + 0.104 + ], + "angle": 0, + "content": "Table 1. Statistics of the datasets and the splits for GCD. The first three are generic datasets while the last three are fine-grained datasets." + }, + { + "type": "table", + "bbox": [ + 0.16, + 0.105, + 0.807, + 0.184 + ], + "angle": 0, + "content": "
DatasetCIFAR10 [17]CIFAR100 [17]ImageNet-100 [7]CUB-200 [36]SCars [16]Pet [24]
Labelled# Classes580501009819
# Images12,50020,00031,8601,4982,000942
Unlabelled# Classes1010010020019637
# Images37,50030,00095,25544966,1442,738
" + }, + { + "type": "table_caption", + "bbox": [ + 0.109, + 0.197, + 0.437, + 0.21 + ], + "angle": 0, + "content": "Table 2. Results on generic image recognition datasets." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.211, + 0.468, + 0.305 + ], + "angle": 0, + "content": "
MethodCIFAR10CIFAR100ImageNet-100
AllOldNewAllOldNewAllOldNew
k-means83.685.782.552.052.250.872.775.571.3
RankStats+46.819.260.558.277.619.337.161.624.8
UNO+68.698.353.869.580.647.270.395.057.9
GCD91.597.988.273.076.266.574.189.866.3
DCCL96.396.596.975.376.870.280.590.576.2
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.322, + 0.468, + 0.351 + ], + "angle": 0, + "content": "accuracy by comparing the predicted label assignment with the ground truth, following the protocol in [35]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.353, + 0.47, + 0.73 + ], + "angle": 0, + "content": "Implementation Details. We adopt the ViT-B-16 pretrained by DINO [4] as our backbone network. The output [CLS] token is used as the feature representation, which is also used for conception-level contrastive learning. Following [35], we project the representations by a projection head and use the projected embeddings for instance-level contrastive learning. We set the dimension of projected embeddings to 65,536 following [4]. At training time, we feed two views with random augmentations to the model. We only fine-tune the last block of the vision transformer with an initial learning rate of 0.01 and the head is trained with an initial learning rate of 0.1. All methods are trained for 200 epochs with a cosine annealing schedule. The size of the mini-batch is set to 128 with \\( N^C = 8 \\) and \\( N^I = 16 \\). For a fair comparison, we follow [35] and set the temperatures of two supervised contrastive losses \\( \\tau^S \\), \\( \\tau^L \\) and \\( \\tau^C \\) to 0.07, 0.05 and 0.05, respectively. The \\( \\tau^F \\) is empirically set to 0.6 for the fine-grained datasets and 0.7 for the generic datasets. Other hyper-parameters are discussed in Sec. 4.4. In testing, we first use the class number estimation algorithm [35] to predict the number of classes of the testing dataset, and then use semi-supervised \\( k \\)-means for clustering evaluation. In dynamic conception generation, we adopt faiss [15] to accelerate the construction of relationship networks. Our experiments are conducted on RTX 3090 GPUs." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.741, + 0.376, + 0.756 + ], + "angle": 0, + "content": "4.2. Comparison with State-of-the-Art" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.469, + 0.825 + ], + "angle": 0, + "content": "To evaluate the performances of our DCCL, we conduct three group experiments by comparing our DCCL with three strong GCD baselines, including RankStats [10] and UNO [9] and the state-of-the-art GCD method [35]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Comparison on Generic Datasets. As shown in Tab. 2, our DCCL is compared with other competitors on the generic image recognition datasets. Overall, the results in Tab. 2 show our DCCL consistently outperforms all others by a significant margin. Specifically, DCCL outperforms the" + }, + { + "type": "table_caption", + "bbox": [ + 0.573, + 0.197, + 0.819, + 0.21 + ], + "angle": 0, + "content": "Table 3. Results on fine-grained datasets." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.211, + 0.892, + 0.306 + ], + "angle": 0, + "content": "
methodCUB-200Stanford-CarsOxford-Pet
AllOldNewAllOldNewAllOldNew
k-means34.338.932.112.810.613.877.170.180.7
RankStats+33.351.624.228.361.812.1---
UNO+35.149.028.135.570.518.6---
GCD51.356.648.739.057.629.980.285.177.6
DCCL63.560.864.943.155.736.288.188.288.0
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.321, + 0.892, + 0.516 + ], + "angle": 0, + "content": "GCD method [35] by \\(4.8\\%\\) on CIFAR-10, \\(2.3\\%\\) on CIFAR-100, and \\(6.4\\%\\) on ImageNet-100 for 'All' classes, and by \\(8.7\\%\\) on CIFAR-10, \\(3.7\\%\\) on CIFAR-100, and \\(9.9\\%\\) on ImageNet-100 for 'Unseen' classes. These results experimentally demonstrate the generated dynamic conceptions provide effective supervision to learn better representations for unlabeled data. Moreover, \\(\\mathrm{UNO + }\\) shows a strong accuracy on \"Old\" classes, but its accuracy when testing on \"New\" classes is relatively lower. This is because \\(\\mathrm{UNO + }\\) trains the linear classifier on \"Old\" classes, thus resulting in an inevitable bias. On the contrary, our DCCL gets a relatively good balance on both the \"Old\" and \"Unseen\" classes, without bias to the labeled data." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.52, + 0.892, + 0.763 + ], + "angle": 0, + "content": "Comparison on Fine-Grained Datasets. In general, the differences between different classes in fine-grained datasets are subtle, which leads the fine-grained visual understanding to be more challenging for GCD. For verifying the effects of DCCL on fine-grained tasks, we compare our method with others on fine-grained image recognition datasets. The results in Tab. 3 show that DCCL consistently outperforms all other methods for \"All\" and \"New\" classes. Specifically, on CUB-200 and Oxford-Pet, DCCL achieves \\(12.2\\%\\) and \\(7.9\\%\\) improvement over the state-of-the-art for \"All\" classes. Especially for \"New\" classes, DCCL outperforms GCD by \\(16.2\\%\\) on the CUB-200 dataset. These results demonstrate that our DCCL is efficient in capturing the conceptual information shared across different fine-grained classes, thereby generating precise and helpful supervision for representation learning." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Visualization of Feature Distributions. To qualitatively explore the clustered features on Pets dataset [24], we visualize the t-SNE embeddings projected from the features extracted by pre-trained ViT [4], GCD [35], the DCCL without the proposed dispersion loss and our full DCCL method. As shown in Fig. 3, our features are more discriminative than the features from the pre-trained ViT and GCD. By comparing Fig. 3(c) and Fig. 3(d), the proposed dispersion loss effectively pushes cluster centers away from" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7584" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.091, + 0.091, + 0.262, + 0.191 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.144, + 0.195, + 0.198, + 0.206 + ], + "angle": 0, + "content": "(a) DINO" + }, + { + "type": "image", + "bbox": [ + 0.264, + 0.091, + 0.427, + 0.191 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.312, + 0.195, + 0.362, + 0.206 + ], + "angle": 0, + "content": "(b) GCD" + }, + { + "type": "image", + "bbox": [ + 0.43, + 0.091, + 0.613, + 0.191 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.451, + 0.194, + 0.573, + 0.206 + ], + "angle": 0, + "content": "(c) DCCL without \\(\\mathcal{L}^D\\)" + }, + { + "type": "image", + "bbox": [ + 0.619, + 0.089, + 0.882, + 0.191 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.653, + 0.195, + 0.71, + 0.206 + ], + "angle": 0, + "content": "(d) DCCL" + }, + { + "type": "image_caption", + "bbox": [ + 0.776, + 0.195, + 0.88, + 0.206 + ], + "angle": 0, + "content": "(e) False Examples" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.208, + 0.892, + 0.237 + ], + "angle": 0, + "content": "Figure 3. Visualization of features distributions of the unlabeled set of the Pet [24] dataset. (a)-(d) are the results generated from DINO [4], GCD [35], our DCCL without \\(\\mathcal{L}^D\\) and full DCCL, in turn. (e) is a visualization of false samples that are easy to be incorrectly clustered." + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.248, + 0.47, + 0.29 + ], + "angle": 0, + "content": "Table 4. Effectiveness of each component of our DCCL. \"MU\" and \"CC\" denote the proposed momentum update by Eq. (8) and the conception consolidation proposed in Sec. 3.3, respectively." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.292, + 0.469, + 0.39 + ], + "angle": 0, + "content": "
IndexComponentCUB-200 [36]Pet [24]
\\( \\mathcal{L}^I \\)\\( \\mathcal{L}^C \\)\\( \\mathcal{L}^D \\)MUCCAllOldNewAllOldNew
a)✓51.356.648.780.285.177.6
b)✓54.952.355.481.680.781.0
c)✓✓57.754.058.183.581.180.3
d)✓✓✓59.553.360.884.383.184.5
e)✓✓✓✓60.159.460.785.886.884.6
f)✓✓✓✓✓63.560.864.988.188.288.0
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.409, + 0.469, + 0.453 + ], + "angle": 0, + "content": "each other. A large inter-cluster margin not only improves cluster boundaries for \"Old\" and \"New\" categories, but also compacts intra-cluster distribution." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.455, + 0.469, + 0.56 + ], + "angle": 0, + "content": "Summary. The experimental results show that our DCCL achieves significant improvements on both generic and fine-grained datasets. Especially for discovering \"New\" categories in challenging fine-grained tasks, our dynamic conceptual contrastive learning succeeds in mining shared conceptions, which is especially beneficial for the generalized fine-grained new category discovery." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.573, + 0.303, + 0.588 + ], + "angle": 0, + "content": "4.3. Effectiveness Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.597, + 0.469, + 0.673 + ], + "angle": 0, + "content": "To verify the effectiveness of each component in our DCCL, we conduct five experiments on both CUB-200 [36] and Pet [24] datasets, as shown in Tab. 4. Note that the configuration of the experiment a) is the same with GCD [35], which is the baseline method in our experiments." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.673, + 0.469, + 0.749 + ], + "angle": 0, + "content": "Effectiveness of Conceptional contrastive Learning. Based on the results of the experiment a) and b), we find that using only the conceptual contrastive learning can achieve competitive performance, compared to baseline method with only instance-level contrastive learning." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Effectiveness of Conception-Level Momentum Updating. Comparing the experiment b) and c), we can find that consistent update of conceptual representations by the proposed momentum update can bring considerable improvements on both new and old classes. This implies that due to periodically generating conceptual representations, the conceptual labels are kept fixed within one training period, which leads to a severe sub-optimal problem, during conceptual contrastive learning. Thus, the proposed momentum update mitigates the problem to some extent." + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.251, + 0.697, + 0.35 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.352, + 0.697, + 0.452 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.252, + 0.891, + 0.352 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.7, + 0.353, + 0.891, + 0.451 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.455, + 0.892, + 0.483 + ], + "angle": 0, + "content": "Figure 4. Impact of hyper-parameters. The clustering accuracy on \"All\" categories is reported." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.486, + 0.892, + 0.562 + ], + "angle": 0, + "content": "Effectiveness of Dispersion Loss. The experiment d) in Tab. 4 shows that by adding the proposed dispersion loss, the model's performances on new classes acquire further improvements by \\(2.7\\%\\) on \"New\" classes for the CUB-200 dataset. The improvements can be observed in Fig. 3(d)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.563, + 0.892, + 0.713 + ], + "angle": 0, + "content": "Effectiveness of Conception Consolidation. Without the proposed conception consolidation that considers labeled information to impose semi-supervised constraintsd, our DCCL suffers from a performance balance between the new and the old classes, as shown in Tab. 4 b), c) and d). In the experiment e) and f), our full method shows superior performance on all evaluation metrics, which experimentally demonstrates that our conception consolidation plays an essential role in rectifying the estimated latent conception relations between seen and unseen classes." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.725, + 0.746, + 0.742 + ], + "angle": 0, + "content": "4.4. Hyper-Parameter Analyses" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.749, + 0.891, + 0.81 + ], + "angle": 0, + "content": "In this section, we discuss the impact of the hyperparameters in our DCCL, including loss weights \\((\\alpha\\) and \\(\\beta)\\), the threshold parameter of dispersion loss \\((\\tau^{M})\\), momentum updating factor \\((\\eta)\\), and the frequency of DCG \\((\\tau^{I})\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.811, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Impact of loss weights and threshold parameters. For the evaluation of loss weights, we use the hold-off validation data to determine their values. Specifically, we first select the optimal \\(\\alpha\\) to achieve the best accuracy on the \"All\" score, then we find the optimal \\(\\beta\\) based on the selected \\(\\alpha\\). The impact of different values is shown in Fig. 4 (a)-(c)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7585" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.092, + 0.288, + 0.184 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.19, + 0.185, + 0.209, + 0.197 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.288, + 0.092, + 0.468, + 0.184 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.382, + 0.185, + 0.401, + 0.197 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.199, + 0.468, + 0.337 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.343, + 0.471, + 0.428 + ], + "angle": 0, + "content": "Figure 5. (a) visualizes the dynamics of DCG, which implies that our DCG adaptively estimates conceptual representation for different training stages. (b) illustrates the trend of performances on the CIFAR100 dataset, with varying the number of unlabeled classes. (c) is the comparison between the real number of classes in datasets and the estimated number of conceptions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.442, + 0.47, + 0.486 + ], + "angle": 0, + "content": "Similarly, we choose the best \\(\\tau^M\\) with the selected \\(\\alpha\\) and \\(\\beta\\). Finally, our final model is obtained by using \\(\\alpha = 0.3\\), \\(\\beta = 0.1\\) and \\(\\tau^M = 0.3\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.488, + 0.471, + 0.565 + ], + "angle": 0, + "content": "Impact of Update Rates. The impact of updating factor of CMB is illustrated in in Fig. 4 (d). The more smooth running average can obtain better performance. Considering the balance between computational consumption and performance, we thus set \\(\\tau^I = 5\\) and \\(\\eta = 0.9\\) in all experiments." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.575, + 0.342, + 0.59 + ], + "angle": 0, + "content": "4.5. Further Investigation of DCG" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.47, + 0.765 + ], + "angle": 0, + "content": "To explore our dynamic conception generation (DCG), we conduct two group experiments and the experimental results are shown in Fig. 5 and Tab. 5. From the Fig. 5 (a) we find that in the initial training stage, our DCG tends to generate fewer conceptions than at the convergence stage. This is because in the beginning, the model could not understand fine-grained classes well. Thus, DCG generates coarse-grained supervision like super-class, which has a low risk to over-correct. Later, with the growth of feature discriminability, DCG builds elaborate conceptual relationships to further refine the learned representations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.766, + 0.471, + 0.902 + ], + "angle": 0, + "content": "From the Fig. 5 (c), we find that the number of conceptions estimated by DCCL is close to the ground truth of the number of classes in the corresponding dataset. However, it is worth noting that the conception representations in this paper are not equivalent to the cluster centers. The DCG aims to adaptively generate proper conceptual representations that are beneficial for contrastive learning, instead of predicting the real number of classes within a dataset. Furthermore, we try to directly replace our DGC with semi-" + }, + { + "type": "table_caption", + "bbox": [ + 0.51, + 0.089, + 0.882, + 0.104 + ], + "angle": 0, + "content": "Table 5. Comparison of different clustering methods for DCG." + }, + { + "type": "table", + "bbox": [ + 0.549, + 0.105, + 0.842, + 0.25 + ], + "angle": 0, + "content": "
Clustering MethodCUB-200 [36]
AllOldNew
k-means [21]54.153.453.3
SSK [35]55.955.154.2
FINCH [29]55.856.155.4
DBSCAN [8]60.554.759.8
InfoMap [27]61.455.262.7
DCG (Ours)63.560.864.9
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.267, + 0.892, + 0.311 + ], + "angle": 0, + "content": "supervised \\(k\\)-means [35] (SSK) with the prior of known \\(k\\). From the results in Tab. 5, SSK fails to generate effective latent conceptions, even leading to worse clustering." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.312, + 0.893, + 0.463 + ], + "angle": 0, + "content": "Discussion. Based on the comparison in Fig. 5 (b), we notice that when training on generic datasets, our DCG tends to generate more conceptions than the actual number of dataset classes, while generating fewer conceptions on fine-grained datasets. A possible explanation is that due to large inter-class differences in generic datasets, learning more sub-classes conceptions enables models to gain discriminability. Similarly, since fine-grained classes share more common attributes or conceptions, such super-class information can significantly benefit fine-grained GCD." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.474, + 0.85, + 0.49 + ], + "angle": 0, + "content": "4.6. Evaluation with Different Split Protocols" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.497, + 0.892, + 0.604 + ], + "angle": 0, + "content": "To explore the effects of DCCL under strict annotation limitation, we propose to test models on varying splits of CIFAR100 [17]. We visualize the accuracy of \"All\" classes in Fig. 5 (b), which indicates that our DCCL has stronger robustness when only a few labeled classes are available. Meanwhile, with the growth of the number of unlabeled classes, GCD expresses a severe performance degradation." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.618, + 0.619, + 0.634 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.893, + 0.854 + ], + "angle": 0, + "content": "In this paper, we propose to cope with the generalized category discovery (GCD) from the perspective of mining underlying relationships between known and unknown categories. To implement this idea, we propose a dynamic conceptual contrastive learning framework to alternately explore latent conceptual relationships and perform conceptual contrastive learning. This mechanism enables models to learn more discriminable representations. Furthermore, to mitigate the inconsistency of updating conception representations during the training process, we propose a conception-level momentum update to facilitate the model toward better optimization. Extensive experimental results show that our DCCL achieves a new state-of-the-art performance on GCD tasks." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgement This work has been supported by the EU H2020 project AI4Media (No. 951911) and by the PRIN project CREATIVE (Prot. 2020ZSL9F9)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7586" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.157 + ], + "angle": 0, + "content": "[1] Sugato Basu, Arindam Banerjee, and Raymond J. Mooney. Semi-supervised clustering by seeding. In Claude Sammut and Achim G. 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In CVPR, 2021. 1" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.469, + 0.518 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.956 + ], + "angle": 0, + "content": "7588" + } + ] +] \ No newline at end of file diff --git a/2023/Dynamic Conceptional Contrastive Learning for Generalized Category Discovery/40efeb24-3451-4def-8441-e92b604d3421_origin.pdf b/2023/Dynamic Conceptional Contrastive Learning for Generalized Category Discovery/40efeb24-3451-4def-8441-e92b604d3421_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..959891049b84ce7da7a83daf33b07c7ed19e2245 --- /dev/null +++ b/2023/Dynamic Conceptional Contrastive Learning for Generalized Category Discovery/40efeb24-3451-4def-8441-e92b604d3421_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:85705dbcfa9df5801428b7a58c45012b9454a2f7841c248201196cecd228d790 +size 8777940 diff --git a/2023/Dynamic Conceptional Contrastive Learning for Generalized Category Discovery/full.md b/2023/Dynamic Conceptional Contrastive Learning for Generalized Category Discovery/full.md new file mode 100644 index 0000000000000000000000000000000000000000..8ce0a87443430194dee4c74c371def03786b05b8 --- /dev/null +++ b/2023/Dynamic Conceptional Contrastive Learning for Generalized Category Discovery/full.md @@ -0,0 +1,331 @@ +# Dynamic Conceptional Contrastive Learning for Generalized Category Discovery + +Nan Pu Zhun Zhong* Nicu Sebe + +The Department of Information Engineering and Computer Science University of Trento, Trento, Italy + +{nan.pu, zhun.zhong, niculae.sebe}@unitn.it + +# Abstract + +Generalized category discovery (GCD) is a recently proposed open-world problem, which aims to automatically cluster partially labeled data. The main challenge is that the unlabeled data contain instances that are not only from known categories of the labeled data but also from novel categories. This leads traditional novel category discovery (NCD) methods to be incapacitated for GCD, due to their assumption of unlabeled data are only from novel categories. One effective way for GCD is applying self-supervised learning to learn discriminate representation for unlabeled data. However, this manner largely ignores underlying relationships between instances of the same concepts (e.g., class, super-class, and sub-class), which results in inferior representation learning. In this paper, we propose a Dynamic Conceptional Contrastive Learning (DCCL) framework, which can effectively improve clustering accuracy by alternately estimating underlying visual conceptions and learning conceptual representation. In addition, we design a dynamic conception generation and update mechanism, which is able to ensure consistent conception learning and thus further facilitate the optimization of DCCL. Extensive experiments show that DCCL achieves new state-of-the-art performances on six generic and fine-grained visual recognition datasets, especially on fine-grained ones. For example, our method significantly surpasses the best competitor by $16.2\%$ on the new classes for the CUB-200 dataset. Code is available at https://github.com/TPCD/DCCL + +# 1. Introduction + +Learning recognition models (e.g., image classification) from labeled data has been widely studied in the field of machine learning and deep learning [13, 18, 31]. In spite of their tremendous success, supervised learning techniques + +![](images/7f5b2f9bafc25f8aebc5f7a4fd206915c9fc8f46a52372987cf6b31e436d2d0e.jpg) +Figure 1. Diagram of the proposed Dynamic Conceptional Contrastive Learning (DCCL). Samples from the conceptions should be close to each other. For example, samples from the same classes (bus) at the class level, samples belonging to the transportation (bus and bicycle) at the super-class level, and samples from trains with different colors at the sub-class level. Our DCCL potentially learns the underlying conceptions in unlabeled data and produces more discriminative representations. + +rely heavily on huge annotated data, which is not suitable for open-world applications. Thus, the researchers recently have paid much effort on learning with label-imperfection data, such as semi-supervised learning [23, 33], self-supervised learning [12, 42], weakly-supervised learning [41,45], few-shot learning [32,38], open-set recognition [30] and learning with noisy labels [40], etc. + +Recently, inspired by the fact that Humans can easily and automatically learn new knowledge with the guidance of previously learned knowledge, novel category discovery (NCD) [9, 11, 28, 44, 47] is introduced to automatically cluster unlabeled data of unseen categories with the help of knowledge from seen categories. However, the implementation of NCD is under a strong assumption that all the unlabeled instances belong to unseen categories, which is not practical in real-world applications. To address this limitation, Vaze et al. [35] extend NCD to the generalized category discovery (GCD) [35], where unlabeled images are + +from both novel and labeled categories. + +GCD is a challenging open-world problem in that we need to 1) jointly distinguish the known and unknown classes and 2) discover the novel clusters without any annotations. To solve this problem, Vaze et al. [35] leverage the contrastive learning technique to learn discriminative representation for unlabeled data and use $k$ -means [21] to obtain final clustering results. In this method, the labeled data are fully exploited by supervised contrastive learning. However, self-supervised learning is applied to the unlabeled data, which enforces samples to be close to their augmentation counterparts while far away from others. As a consequence, the underlying relationships between samples of the same conceptions are largely overlooked and thus will lead to degraded representation learning. Intuitively, samples that belong to the same conceptions should be similar to each other in the feature space. The conceptions can be regarded as: classes, super-classes, sub-classes, etc. For example, as shown in Fig. 1, samples of the same class should be similar to each other, e.g., samples of the bus, samples of the bicycle. In addition, in the super-classes view, classes of the transportation, e.g., Bus and Bicycle, should belong to the same concept. Hence, the samples of transportation should be closer than that of other concepts (e.g., animals). Similarly, samples belong to the same sub-classes (e.g., red train) should be closer to that of other sub-classes (e.g., white train). Hence, embracing such conceptions and their relationships can greatly benefit the representation learning for unlabeled data, especially for unseen classes. + +Motivated by this, we propose a Dynamic Conceptional Contrastive Learning (DCCL) framework for GCD to effectively leverage the underlying relationships between unlabeled data for representation learning. Specifically, our DCCL includes two steps: Dynamic Conception Generation (DCG) and Dual-level Contrastive Learning (DCL). In DCG, we dynamically generate conceptions based on the hyper-parameter-free clustering method equipped with the proposed semi-supervised conceptual consolidation. In DCL, we propose to optimize the model with conception-level and instance-level contrastive learning objectives, where we maintain a dynamic memory to ensure comparing with the up-to-date conceptions. The DCG and DCL are alternately performed until the model converges. + +We summarize the contributions of this work as follows: + +- We propose a novel dynamic conceptionsal contrastive learning (DCCL) framework to effectively leverage the underlying relationships between unlabeled samples for learning discriminative representation for GCD. +- We introduce a novel dynamic conception generation and update mechanism to ensure consistent conception learning, which encourages the model to produce more discriminative representation. + +- Our DCCL approach consistently achieves superior performance over state-of-the-art GCD algorithms on both generic and fine-grained tasks. + +# 2. Related Work + +# 2.1. Novel Category Discovery + +Novel category discovery [11] (NCD) tasks aim at discovering new categories by leveraging the knowledge of a set of labeled categories. RankStat [10] indicates that self-supervised pre-training is helpful for NCD. NCL [46] adopts contrastive learning to improve representation learning. UNO [9] proposes a unified objective for jointly learning on unlabeled and labeled data. Most recently, NCD has been extended to a generalized category discovery (GCD) [35], in which the unlabeled data include both labeled and unlabeled categories. Later, ORCA [3] defines an open-world semi-supervised learning task, which is similar to GCD. Although these definitions are relatively practical, most methods remain to assume that the class number of clustered data is known. Nevertheless, such prior knowledge is often not acquired in advance for real-world applications. To handle the drawback, DTC [11] and GCD [35] employed an independent algorithm to search the optimal class number, however, they did not associate clustering estimation with representation learning. Unlike these offline algorithms, we propose to jointly consider downstream clustering and representation learning. The experimental results show they are mutually beneficial for each other. + +# 2.2. Contrastive Learning based on Memory Buffer + +Contrastive learning [5,6,22,37,43] (CL) has been shown to be significantly effective for representation learning in a self-supervised manner. MoCo [12] demonstrates that sampling positive-negative pairs from an instance-level buffer can benefit CL and reduce the impact of the size of the training batch. Then, instead of contrasting over all instances in a mini-batch, prototypical contrastive learning [20] (PCL) that contrasts the instance features with a set of prototypes, has been shown to provide comprehensive supervision. However, PCL still needs an instance-level memory buffer to yield the prototype set, which is not computation- and memory-efficient. Recently, SCL [14] propose a cluster-level momentum encoder but considers only three fixed numbers of classes during training, which is still limited compared to our dynamic method. Different from PCL and SCL that consider the fixed numbers of classes during the whole training process, our DCCL dynamically estimates the number of classes for different training stages in a efficient way, which encourages models to learn more discriminative representation. + +![](images/c5b5e59be55abcad8920c9da63691cc09d16dc1bf93567ac8283805f4061ad66.jpg) +Figure 2. (a) Overview of our DCCL framework. We first extract features and cluster the features to generate conceptual labels, then initialize conception representations by our DCG, and last learn representations by joint instance-level and conception-level objectives. During the training process, the DCG and dual-level representation learning are performed alternately, in which the conception buffer is updated every iteration to keep the consistency of the changing instance features and conceptual representations. (b) Illustration of the proposed conception consolidation. Without consolidating the relationships of conceptions by label information, Infomap tends to over-cluster data and thus provides the supervision that has a high risk to over-correct affinities between neighbor instances. + +# 2.3. Semi-Supervised Learning and Clustering + +Semi-supervised learning (SSL) has been a long-standing research topic [39]. Different from GCD, SSL often assumes that the labeled and unlabeled data come from the same set of classes, in which consistency-based methods are the most effective methods for SSL, such as Mean-teacher [34], MixMatch [2], and FixMatch [33]. Consistency-based methods are the most effective methods for SSL, such as Mean-teacher [34], MixMatch [2], and FixMatch [33]. Moreover, semi-supervised classification is a relatively well-defined task, while the supervised information in semi-supervised clustering can take different forms [19], such as two instances are known to be must-linked in a relationship matrix or some cluster assignments are known beforehand. For instance, Basu et al. [1] proposed to initialize the clusters based on the data points for which cluster assignments are known. However, these methods can not adaptively assign the number of clusters for generating conceptions. To mitigate these limitations, we improve the classical InfoMap [27] to fully leverage both labeled and unlabeled data and dynamically produce varying conceptual labels for different contrastive learning epochs. + +# 3. Dynamic Conceptional Contrastive Learning + +# 3.1. Problem Formulation + +Generalized category discovery (GCD) aims at automatically categorizing unlabeled images in a dataset, where the + +partial data are labeled and the remaining are unlabeled. The unlabeled images come from either labeled (known) classes or unlabeled (unknown) classes. This is a more realistic open-world setting than the common closed-set classification that assumes the labeled and unlabeled data belong to the same classes. Let the dataset be $\mathcal{D} = \mathcal{D}^L\cup \mathcal{D}^U$ where $\mathcal{D}^L = \{(\mathbf{x}_i^L,\mathbf{y}_i^L)\}_{i = 1}^{M^L}\in \mathcal{X}\times \mathcal{Y}^L$ $L$ denotes the labeled subset and $\mathcal{D}^U = \{(\mathbf{x}_i^U,\mathbf{y}_i^U)\}_{i = 1}^{M^U}\in \mathcal{X}\times \mathcal{Y}^U$ denotes the unlabeled subset with unknown $\mathbf{y}_i^U\in \mathcal{V}^U$ . Only a subset of classes contains labeled instances, i.e., $\mathcal{V}^L\subset \mathcal{V}^U$ The number of labeled classes $N^L$ can be directly calculated from the labeled data, while the number of unlabeled classes $N^U$ is not known during model training. Let $f$ and $h$ be a feature extractor and a MLP projection head. The extracted representation is defined as $\mathbf{v}_i = f(\mathbf{x}_i)$ + +# 3.2. Overview + +To tackle the problem of GCD, we propose a novel framework DCCL (see Fig. 2), to jointly learn representations using dual-level contrastive learning (DCL) and explore all possible relationships between labeled and unlabeled instances in a conceptionsal view. First, we extend the classical unsupervised clustering algorithm, Infomap [27], to a semi-supervised manner, which aims at dynamically generating reasonable conceptual representations and associating the labeled and unlabeled instances during representation learning. By alternately executing the dynamic conception generation (DCG) and DCL, DCL benefits from informative supervised information to generate higher-quality representations. Meanwhile, DCG gradually + +produces more comprehensive guidance based on a deeper understanding of conceptual relationships. DCG and DCL mutually benefit each other, thus resulting in a better representation for downstream clustering. + +# 3.3. Dynamic Conception Generation + +Although the test-time semi-supervised $k$ -means [35] (SSK) succeeds in achieving considerable performance gain, it fails to jointly consider the representation learning and supervision information from semi-supervised clustering. Moreover, it is infeasible to directly perform SSK in each training epoch for assigning pseudo labels, because the real number of clusters is unknown during training. To overcome these drawbacks, we propose a dynamic conception generation (DCG) based on the hyper-parameter-free Infomap [27] algorithm. Specifically, we first propose a semi-supervised conceptual consolidation method to construct a similarity network, then execute the Infomap clustering algorithm on the constructed network to get conceptual label assignments, and finally calculate conception representation and initialize conceptual memory buffer. + +Conception Consolidation. In a given network, Infomap aims at partitioning semantic-similar sub-networks by the pattern of connections. To leverage the supervision from labeled data, we propose to enforce the similarity constraints into the networking, according to the labeled data that belong to the same category. Formally, we construct an adjacent matrix $\mathcal{A}$ to represent the possible connection relationships among all instances. The weight of the edge of the $i$ -th and $j$ -th instances is given by: + +$$ +\mathcal {A} _ {i j} = \left\{ \begin{array}{l l} s _ {i} ^ {\max }, & \text {i f} \mathbf {y} _ {i}, \mathbf {y} _ {j} \in \mathcal {Y} ^ {L} \text {a n d} \mathbf {y} _ {i} = \mathbf {y} _ {j} \\ s _ {i j}, & \text {i f} \mathbf {y} _ {i} \text {o r} \mathbf {y} _ {j} \in \mathcal {Y} ^ {U} \text {a n d} s _ {i j} > \tau^ {F} \\ 0, & \text {o t h e r w i s e} \end{array} \right. \tag {1} +$$ + +$$ +s _ {i} ^ {\text {m a x}} = \underset {j} {\arg \max } \left\{s _ {i j} \mid j \in \mathcal {D} \right\}, \tag {2} +$$ + +$$ +s _ {i j} = \left[ \left(\mathbf {v} _ {i} / \| \mathbf {v} _ {i} \|\right) \cdot \left(\mathbf {v} _ {j} / \| \mathbf {v} _ {j} \|\right) + 1 \right] / 2 \in [ 0, 1 ], \tag {3} +$$ + +where $\cdot$ denotes dot product and $\| \cdot \|$ is $l_{2}$ normalization. The $\tau^{F}$ is a threshold to select high-confidence links. Through the conception consolidation illustrated in Fig. 2(b), we can establish a reliable relationship network with rich structural information for the subsequent clustering. + +Remark. We set the similarities of positive pairs with the maximal value of neighborhood similarities instead of 1. This is because we experimentally find that when imposing 1 for constraining positive pairs, Infomap tends to group all the labeled positive instances as an individual cluster. + +Entropy Minimization Clustering. In Infomap algorithm [26], the clustering problem is equivalent to minimizing the entropy that represents the minimum description length of the coding network. By solving the minimization objective, we acquire a conceptual label set + +Algorithm 1: Algorithm Pipeline of our DCCL +Input: Feature Extractor $f$ Projection Head $h$ Labeled data $\mathcal{D}^L$ and Unlabeled data $\mathcal{D}^U$ +Output: $f$ and $h$ +for $n = 1$ in [1,max_epoch] do if $n\bmod\tau^{I}==0$ then Extract features and construct adjacency matrix $\mathcal{A}$ by Eq. (1), Eq. (2) and Eq. (3); Perform InfoMap [27] clustering to assign conceptual labels C; Initialize conceptual buffer by Eq. (4); +end for $i = 1$ in [1,max_iteration] do Sample mini-batches from $\mathcal{D}^L\cup \mathcal{D}^U$ Calculate overall optimization objective by Eq.(10); Update $f$ and $h$ by SGD [25]; Update conceptual buffer by Eq. (8); +end + +$\mathcal{C} = \{\mathbf{c}_i\}_{i=1}^{M^L + M^U} \in \mathcal{V}^G$ for both labeled and unlabeled instances. Then, we combine the extracted feature vectors $\mathcal{V}$ and corresponding conceptionsal labels to construct a generated feature dataset $\mathcal{D}^G = \{(\mathbf{v}_i, \mathbf{c}_i)\}_{i=1}^{M^L + M^U} \in \mathcal{V} \times \mathcal{V}^G$ . $|\mathcal{V}^G|$ denotes the number of estimated conceptions. + +Conceptional Memory Initialization. In this paper, our DCCL maintains a conception-level memory buffer that provides dynamic conceptual representations for dual-level contrastive learning, which is elaborated in Sec. 3.4. Here, we introduce the initialization of the conceptual memory buffer (CMB). We use the mean feature vector of the instances that share the same conceptual label to form a unique conceptual representation. Formally, the initial conceptual representation set is defined as: + +$$ +\mathcal {U} = \left\{\boldsymbol {\mu} _ {k} \right\} _ {k = 1} ^ {K}, \quad \boldsymbol {\mu} _ {k} = \frac {1}{\left| \mathcal {D} _ {k} ^ {G} \right|} \sum_ {\mathbf {v} _ {i} \in \mathcal {D} _ {k} ^ {G}} \mathbf {v} _ {i}, \quad K = | \mathcal {Y} ^ {G} |, \tag {4} +$$ + +where $\mathcal{D}_k^G$ denotes the $k$ -th conception subset, i.e., if $\mathbf{v}_i \in \mathcal{D}_k^G$ , $\mathbf{c}_i = k$ . During whole training process, the initialization of CMB is executed every $\tau^I$ epochs on center-cropped images. Thus, the number of conceptions $K$ is dynamically changing along with model training. + +# 3.4. Dual-Level Contrastive Learning + +In this section, we first explain the proposed conception-level contrastive learning, then elaborate on the update of the conceptual memory buffer, and finally introduce the employed instance-level contrastive learning approach. + +Conception-Level Contrastive Learning. Based on the generated conceptual representations in Sec. 3.3, we + +propose to perform conception-level contrastive learning. Specifically, we first sample $N^C$ conception labels and a fixed number $N^I$ of instances for each conception label, resulting in a mini-batch $\mathcal{B}^C$ with $N^C \times N^I$ instances. Next, each instance representation is compared to all the conceptual representations. We pull the instance representation from its corresponding conceptual representation closer and push the instance representation away from other conceptual representations. Formally, we define the conceptual contrastive loss function as the following: + +$$ +\mathcal {L} _ {i} ^ {C} = - \log \frac {\exp \left(\mathbf {v} _ {i} \cdot \boldsymbol {\mu} _ {\mathbf {c} _ {i}} / \tau^ {C}\right)}{\sum_ {k = 1 , k \neq \mathbf {c} _ {i}} ^ {K} \exp \left(\mathbf {v} _ {i} \cdot \boldsymbol {\mu} _ {k} / \tau^ {C}\right)}, \tag {5} +$$ + +where $\tau^C$ is a temperature hyper-parameter to control the strength of the conception-level contrastive learning. In addition, in order to explicitly encourage learned representations with a large inter-conception margin, we propose a dispersion loss to further push the different conception representations away from each other. The loss function for the $m$ -th and the $n$ -th conceptions in $\mathcal{B}^C$ is: + +$$ +\mathcal {L} (m, n) = \left[ \tau^ {M} - \left\| \frac {1}{\left| \mathcal {B} _ {m} ^ {C} \right|} \sum_ {\mathbf {v} _ {i} \in \mathcal {B} _ {m} ^ {C}} \mathbf {v} _ {i} \right\| \cdot \left\| \frac {1}{\left| \mathcal {B} _ {n} ^ {C} \right|} \sum_ {\mathbf {v} _ {j} \in \mathcal {B} _ {n} ^ {C}} \mathbf {v} _ {j} \right\| \right] _ {+}, \tag {6} +$$ + +where $\tau^M$ is a threshold to filter the conception pairs with high uncertainty. We assume that two conception representations that are close tend to be highly entangled conceptions. Separating these conceptions has a high risk of overcorrect. We explore the impact of $\tau^M$ in Sec. 4.4. The dispersion loss function over a mini-batch is defined as: + +$$ +\mathcal {L} ^ {D} = \frac {1}{N ^ {C}} \sum_ {m = 1} ^ {N ^ {C}} \frac {1}{N ^ {C}} \sum_ {n = 1} ^ {N ^ {C}} \mathcal {L} (m, n). \tag {7} +$$ + +Conceptional Memory Update. Different from [12, 20] that need to save all training instances, our CMB stores only the conception representations, which significantly reduces storage cost. Furthermore, the instance-wise update is easy to lead to an inconsistent update during each training iteration. To mitigate this drawback, we first adopt the resampling method as detailed in the previous section. Next, we propose to update the conception representation by each corresponding instance feature following a momentum update mechanism. The process is formulated as: + +$$ +\boldsymbol {\mu} _ {\mathbf {c} _ {i}} \leftarrow \eta \boldsymbol {\mu} _ {\mathbf {c} _ {i}} + (1 - \eta) \mathbf {v} _ {i}, \tag {8} +$$ + +where $\eta$ is the momentum updating factor. + +Remark. DCCL updates the memory buffer and computes the losses both at the conceptual level, which consistently updates the conceptual representation to maintain the conceptual consistency during the whole training process. + +Instance-Level Contrastive Learning. Inspired by [35], we combine supervised contrastive loss and self-supervised contrastive loss as an instance contrastive loss (ICL), to fine-tune the model. Formally, we assume $x_{i}$ and $\hat{x}_i$ are two views (random augmentations) of the same image in a randomly-sampled mini-batch $\mathcal{B}^I$ . Let $h$ be a MLP projection head. The extracted representation $\mathbf{v}_i$ is further projected by $h$ to high-dimensional embedding space for instance-level contrastive learning. The loss function is: + +$$ +\begin{array}{l} \mathcal {L} _ {i} ^ {I} = (\lambda - 1) \log \frac {\exp \left(h \left(\mathbf {v} _ {i}\right) \cdot h \left(\hat {\mathbf {v}} _ {i}\right) / \tau\right)}{\sum_ {j \in \mathcal {B} ^ {I} , j \neq i} \exp \left(h \left(\mathbf {v} _ {i}\right) \cdot h \left(\mathbf {v} _ {j}\right) / \tau^ {S}\right)} \\ \frac {- \lambda}{| \mathcal {P} (i) |} \sum_ {p \in \mathcal {P} (i)} \log \frac {\exp \left(h \left(\mathbf {v} _ {i} ^ {L}\right) \cdot h \left(\mathbf {v} _ {p} ^ {L}\right) / \tau\right)}{\sum_ {j \in \mathcal {B} ^ {L} , j \neq i} \exp \left(h \left(\mathbf {v} _ {i} ^ {L}\right) \cdot h \left(\mathbf {v} _ {j} ^ {L}\right) / \tau^ {L}\right)}, \tag {9} \\ \end{array} +$$ + +where $\mathcal{B}^L$ donates the labeled subset within the mini-batch $\mathcal{B}^I$ and $\mathcal{B}^I = \mathcal{B}^L\cup \mathcal{B}^U$ . $\mathcal{P}(i)$ is the positive index set for the anchor image $i\in \mathcal{B}^L$ . $\lambda$ is a trade-off factor to balance the contributions of self-supervised and supervised learning. For a fair comparison, we follow [35] and set $\lambda$ to 0.35. + +# 3.5. Joint Optimization + +During the whole training process, we alternately perform dynamic conception generalization and dual-level contrastive representation learning, until the maximal training epoch. The pseudo-code of DCCL is elaborated in Algorithm 1. The overall objective over on mini-batch $\mathcal{B}$ is given by the weighted sum of each loss function: + +$$ +\mathcal {L} _ {\text {t o t a l}} = \frac {1}{| \mathcal {B} |} \sum_ {i \in \mathcal {B}} \mathcal {L} _ {i} ^ {I} + \alpha \frac {1}{| \mathcal {B} |} \sum_ {i \in \mathcal {B}} \mathcal {L} _ {i} ^ {C} + \beta \mathcal {L} ^ {D}, \tag {10} +$$ + +where $\alpha$ and $\beta$ are the weights to adjust the strengths of two loss functions. In all experiments, we use $l_{2}$ normalized feature vector $\| \mathbf{v}\| _2$ for clustering evaluation. + +# 4. Experiments + +# 4.1. Experimental Setup + +Data and Evaluation Metric. We evaluate DCCL on three generic image classification datasets, namely CIFAR-10 [17], CIFAR-100 [17] and ImageNet-100 [35]. ImageNet-100 denotes randomly sub-sampling 100 classes from the ImageNet [7] dataset. The dataset statistics and train-test splits are described in Tab. 1. We further evaluate DCCL on three more challenging fine-grained image classification datasets: CUB-200 [36], Stanford Cars [16], and Oxford-IIIT Pet [24]. The original training set of each fine-grained dataset is separated into labeled and unlabeled parts. We follow [35] sample a subset of half the classes as "Old" categories. $50\%$ of instances of each labeled class are drawn to form the labeled set, and all the remaining data constitute the unlabeled set. For evaluation, we measure the clustering + +Table 1. Statistics of the datasets and the splits for GCD. The first three are generic datasets while the last three are fine-grained datasets. + +
DatasetCIFAR10 [17]CIFAR100 [17]ImageNet-100 [7]CUB-200 [36]SCars [16]Pet [24]
Labelled# Classes580501009819
# Images12,50020,00031,8601,4982,000942
Unlabelled# Classes1010010020019637
# Images37,50030,00095,25544966,1442,738
+ +Table 2. Results on generic image recognition datasets. + +
MethodCIFAR10CIFAR100ImageNet-100
AllOldNewAllOldNewAllOldNew
k-means83.685.782.552.052.250.872.775.571.3
RankStats+46.819.260.558.277.619.337.161.624.8
UNO+68.698.353.869.580.647.270.395.057.9
GCD91.597.988.273.076.266.574.189.866.3
DCCL96.396.596.975.376.870.280.590.576.2
+ +accuracy by comparing the predicted label assignment with the ground truth, following the protocol in [35]. + +Implementation Details. We adopt the ViT-B-16 pretrained by DINO [4] as our backbone network. The output [CLS] token is used as the feature representation, which is also used for conception-level contrastive learning. Following [35], we project the representations by a projection head and use the projected embeddings for instance-level contrastive learning. We set the dimension of projected embeddings to 65,536 following [4]. At training time, we feed two views with random augmentations to the model. We only fine-tune the last block of the vision transformer with an initial learning rate of 0.01 and the head is trained with an initial learning rate of 0.1. All methods are trained for 200 epochs with a cosine annealing schedule. The size of the mini-batch is set to 128 with $N^C = 8$ and $N^I = 16$ . For a fair comparison, we follow [35] and set the temperatures of two supervised contrastive losses $\tau^S$ , $\tau^L$ and $\tau^C$ to 0.07, 0.05 and 0.05, respectively. The $\tau^F$ is empirically set to 0.6 for the fine-grained datasets and 0.7 for the generic datasets. Other hyper-parameters are discussed in Sec. 4.4. In testing, we first use the class number estimation algorithm [35] to predict the number of classes of the testing dataset, and then use semi-supervised $k$ -means for clustering evaluation. In dynamic conception generation, we adopt faiss [15] to accelerate the construction of relationship networks. Our experiments are conducted on RTX 3090 GPUs. + +# 4.2. Comparison with State-of-the-Art + +To evaluate the performances of our DCCL, we conduct three group experiments by comparing our DCCL with three strong GCD baselines, including RankStats [10] and UNO [9] and the state-of-the-art GCD method [35]. + +Comparison on Generic Datasets. As shown in Tab. 2, our DCCL is compared with other competitors on the generic image recognition datasets. Overall, the results in Tab. 2 show our DCCL consistently outperforms all others by a significant margin. Specifically, DCCL outperforms the + +Table 3. Results on fine-grained datasets. + +
methodCUB-200Stanford-CarsOxford-Pet
AllOldNewAllOldNewAllOldNew
k-means34.338.932.112.810.613.877.170.180.7
RankStats+33.351.624.228.361.812.1---
UNO+35.149.028.135.570.518.6---
GCD51.356.648.739.057.629.980.285.177.6
DCCL63.560.864.943.155.736.288.188.288.0
+ +GCD method [35] by $4.8\%$ on CIFAR-10, $2.3\%$ on CIFAR-100, and $6.4\%$ on ImageNet-100 for 'All' classes, and by $8.7\%$ on CIFAR-10, $3.7\%$ on CIFAR-100, and $9.9\%$ on ImageNet-100 for 'Unseen' classes. These results experimentally demonstrate the generated dynamic conceptions provide effective supervision to learn better representations for unlabeled data. Moreover, $\mathrm{UNO + }$ shows a strong accuracy on "Old" classes, but its accuracy when testing on "New" classes is relatively lower. This is because $\mathrm{UNO + }$ trains the linear classifier on "Old" classes, thus resulting in an inevitable bias. On the contrary, our DCCL gets a relatively good balance on both the "Old" and "Unseen" classes, without bias to the labeled data. + +Comparison on Fine-Grained Datasets. In general, the differences between different classes in fine-grained datasets are subtle, which leads the fine-grained visual understanding to be more challenging for GCD. For verifying the effects of DCCL on fine-grained tasks, we compare our method with others on fine-grained image recognition datasets. The results in Tab. 3 show that DCCL consistently outperforms all other methods for "All" and "New" classes. Specifically, on CUB-200 and Oxford-Pet, DCCL achieves $12.2\%$ and $7.9\%$ improvement over the state-of-the-art for "All" classes. Especially for "New" classes, DCCL outperforms GCD by $16.2\%$ on the CUB-200 dataset. These results demonstrate that our DCCL is efficient in capturing the conceptual information shared across different fine-grained classes, thereby generating precise and helpful supervision for representation learning. + +Visualization of Feature Distributions. To qualitatively explore the clustered features on Pets dataset [24], we visualize the t-SNE embeddings projected from the features extracted by pre-trained ViT [4], GCD [35], the DCCL without the proposed dispersion loss and our full DCCL method. As shown in Fig. 3, our features are more discriminative than the features from the pre-trained ViT and GCD. By comparing Fig. 3(c) and Fig. 3(d), the proposed dispersion loss effectively pushes cluster centers away from + +![](images/4567f3afdefab37e162b27a170ba870da9f1d3cc929cd46b6ac3dd3fe3d1be8a.jpg) +(a) DINO + +![](images/d77f6169ef2e6e0faa5f854e06eb81b90e94ac7586d51127b15e7318e6ebb98a.jpg) +(b) GCD + +![](images/3d98b8061f91a20b8e6f80820053dc8464f7f769cebf95fc4b50617b9c900b44.jpg) +(c) DCCL without $\mathcal{L}^D$ + +![](images/3ad7218fd449650f66f514c33fe362170d3f029912b1fc4b922bd380a8e3a8ac.jpg) +(d) DCCL +(e) False Examples + +Table 4. Effectiveness of each component of our DCCL. "MU" and "CC" denote the proposed momentum update by Eq. (8) and the conception consolidation proposed in Sec. 3.3, respectively. + +
IndexComponentCUB-200 [36]Pet [24]
\( \mathcal{L}^I \)\( \mathcal{L}^C \)\( \mathcal{L}^D \)MUCCAllOldNewAllOldNew
a)✓51.356.648.780.285.177.6
b)✓54.952.355.481.680.781.0
c)✓✓57.754.058.183.581.180.3
d)✓✓✓59.553.360.884.383.184.5
e)✓✓✓✓60.159.460.785.886.884.6
f)✓✓✓✓✓63.560.864.988.188.288.0
+ +each other. A large inter-cluster margin not only improves cluster boundaries for "Old" and "New" categories, but also compacts intra-cluster distribution. + +Summary. The experimental results show that our DCCL achieves significant improvements on both generic and fine-grained datasets. Especially for discovering "New" categories in challenging fine-grained tasks, our dynamic conceptual contrastive learning succeeds in mining shared conceptions, which is especially beneficial for the generalized fine-grained new category discovery. + +# 4.3. Effectiveness Evaluation + +To verify the effectiveness of each component in our DCCL, we conduct five experiments on both CUB-200 [36] and Pet [24] datasets, as shown in Tab. 4. Note that the configuration of the experiment a) is the same with GCD [35], which is the baseline method in our experiments. + +Effectiveness of Conceptional contrastive Learning. Based on the results of the experiment a) and b), we find that using only the conceptual contrastive learning can achieve competitive performance, compared to baseline method with only instance-level contrastive learning. + +Effectiveness of Conception-Level Momentum Updating. Comparing the experiment b) and c), we can find that consistent update of conceptual representations by the proposed momentum update can bring considerable improvements on both new and old classes. This implies that due to periodically generating conceptual representations, the conceptual labels are kept fixed within one training period, which leads to a severe sub-optimal problem, during conceptual contrastive learning. Thus, the proposed momentum update mitigates the problem to some extent. + +![](images/17e7c9b9aa3f880318a8626fb573feef0fc574f6251f68ad5ee64347828f7124.jpg) +Figure 3. Visualization of features distributions of the unlabeled set of the Pet [24] dataset. (a)-(d) are the results generated from DINO [4], GCD [35], our DCCL without $\mathcal{L}^D$ and full DCCL, in turn. (e) is a visualization of false samples that are easy to be incorrectly clustered. + +![](images/95797e8f58b53b909892e359a3094592239b0b17d379945b87f1dc9341666d8b.jpg) +Figure 4. Impact of hyper-parameters. The clustering accuracy on "All" categories is reported. + +![](images/5b424a67fd25aa0010f1854957a9e4098f0209ce6e2f60e73620765304874c72.jpg) + +![](images/05f9656d48fc088005bc36d41aa4cd1b4a8a8eb536915ea4eab045b2ed9e51e1.jpg) + +Effectiveness of Dispersion Loss. The experiment d) in Tab. 4 shows that by adding the proposed dispersion loss, the model's performances on new classes acquire further improvements by $2.7\%$ on "New" classes for the CUB-200 dataset. The improvements can be observed in Fig. 3(d). + +Effectiveness of Conception Consolidation. Without the proposed conception consolidation that considers labeled information to impose semi-supervised constraintsd, our DCCL suffers from a performance balance between the new and the old classes, as shown in Tab. 4 b), c) and d). In the experiment e) and f), our full method shows superior performance on all evaluation metrics, which experimentally demonstrates that our conception consolidation plays an essential role in rectifying the estimated latent conception relations between seen and unseen classes. + +# 4.4. Hyper-Parameter Analyses + +In this section, we discuss the impact of the hyperparameters in our DCCL, including loss weights $(\alpha$ and $\beta)$ , the threshold parameter of dispersion loss $(\tau^{M})$ , momentum updating factor $(\eta)$ , and the frequency of DCG $(\tau^{I})$ . + +Impact of loss weights and threshold parameters. For the evaluation of loss weights, we use the hold-off validation data to determine their values. Specifically, we first select the optimal $\alpha$ to achieve the best accuracy on the "All" score, then we find the optimal $\beta$ based on the selected $\alpha$ . The impact of different values is shown in Fig. 4 (a)-(c). + +![](images/03a89caf92896da1c600a3aecd2d4b807675b83356498543c9d7be4e07039574.jpg) +(a) + +![](images/2e369cfc5b95365d98be96fed357411ee6c3f700c32ee3fca9ac018841043b2e.jpg) + +![](images/19affb57099820e1aaa7e1d71f312e508fa9a967e4f3c8af1bc058f5331c837c.jpg) +(b) +Figure 5. (a) visualizes the dynamics of DCG, which implies that our DCG adaptively estimates conceptual representation for different training stages. (b) illustrates the trend of performances on the CIFAR100 dataset, with varying the number of unlabeled classes. (c) is the comparison between the real number of classes in datasets and the estimated number of conceptions. + +Similarly, we choose the best $\tau^M$ with the selected $\alpha$ and $\beta$ . Finally, our final model is obtained by using $\alpha = 0.3$ , $\beta = 0.1$ and $\tau^M = 0.3$ . + +Impact of Update Rates. The impact of updating factor of CMB is illustrated in in Fig. 4 (d). The more smooth running average can obtain better performance. Considering the balance between computational consumption and performance, we thus set $\tau^I = 5$ and $\eta = 0.9$ in all experiments. + +# 4.5. Further Investigation of DCG + +To explore our dynamic conception generation (DCG), we conduct two group experiments and the experimental results are shown in Fig. 5 and Tab. 5. From the Fig. 5 (a) we find that in the initial training stage, our DCG tends to generate fewer conceptions than at the convergence stage. This is because in the beginning, the model could not understand fine-grained classes well. Thus, DCG generates coarse-grained supervision like super-class, which has a low risk to over-correct. Later, with the growth of feature discriminability, DCG builds elaborate conceptual relationships to further refine the learned representations. + +From the Fig. 5 (c), we find that the number of conceptions estimated by DCCL is close to the ground truth of the number of classes in the corresponding dataset. However, it is worth noting that the conception representations in this paper are not equivalent to the cluster centers. The DCG aims to adaptively generate proper conceptual representations that are beneficial for contrastive learning, instead of predicting the real number of classes within a dataset. Furthermore, we try to directly replace our DGC with semi- + +Table 5. Comparison of different clustering methods for DCG. + +
Clustering MethodCUB-200 [36]
AllOldNew
k-means [21]54.153.453.3
SSK [35]55.955.154.2
FINCH [29]55.856.155.4
DBSCAN [8]60.554.759.8
InfoMap [27]61.455.262.7
DCG (Ours)63.560.864.9
+ +supervised $k$ -means [35] (SSK) with the prior of known $k$ . From the results in Tab. 5, SSK fails to generate effective latent conceptions, even leading to worse clustering. + +Discussion. Based on the comparison in Fig. 5 (b), we notice that when training on generic datasets, our DCG tends to generate more conceptions than the actual number of dataset classes, while generating fewer conceptions on fine-grained datasets. A possible explanation is that due to large inter-class differences in generic datasets, learning more sub-classes conceptions enables models to gain discriminability. Similarly, since fine-grained classes share more common attributes or conceptions, such super-class information can significantly benefit fine-grained GCD. + +# 4.6. Evaluation with Different Split Protocols + +To explore the effects of DCCL under strict annotation limitation, we propose to test models on varying splits of CIFAR100 [17]. We visualize the accuracy of "All" classes in Fig. 5 (b), which indicates that our DCCL has stronger robustness when only a few labeled classes are available. Meanwhile, with the growth of the number of unlabeled classes, GCD expresses a severe performance degradation. + +# 5. Conclusion + +In this paper, we propose to cope with the generalized category discovery (GCD) from the perspective of mining underlying relationships between known and unknown categories. To implement this idea, we propose a dynamic conceptual contrastive learning framework to alternately explore latent conceptual relationships and perform conceptual contrastive learning. This mechanism enables models to learn more discriminable representations. Furthermore, to mitigate the inconsistency of updating conception representations during the training process, we propose a conception-level momentum update to facilitate the model toward better optimization. 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The caltech-ucsd birds-200-2011 dataset. 2011. 5, 6, 7, 8 +[37] Xiaohan Wang, Linchao Zhu, and Yi Yang. T2vlad: global-local sequence alignment for text-video retrieval. In CVPR, 2021. 2 + +[38] Yaqing Wang, Quanming Yao, James T Kwok, and Lionel M Ni. Generalizing from a few examples: A survey on few-shot learning. ACM computing surveys (csur), 2020. 1 +[39] Xiangli Yang, Zixing Song, Irwin King, and Zenglin Xu. A survey on deep semi-supervised learning. Arxiv, 2021. 3 +[40] Li Yi, Sheng Liu, Qi She, A Ian McLeod, and Boyu Wang. On learning contrastive representations for learning with noisy labels. In CVPR, 2022. 1 +[41] Hong-Xing Yu and Wei-Shi Zheng. Weakly supervised discriminative feature learning with state information for person identification. In CVPR, 2020. 1 +[42] Xiaohua Zhai, Avital Oliver, Alexander Kolesnikov, and Lucas Beyer. S4l: Self-supervised semi-supervised learning. In ICCV, 2019. 1 +[43] Shuai Zhao, Xiaohan Wang, Linchao Zhu, and Yi Yang. Slimmable networks for contrastive self-supervised learning. arXiv, 2022. 2 +[44] Yuyang Zhao, Zhun Zhong, Nicu Sebe, and Gim Hee Lee. Novel class discovery in semantic segmentation. In CVPR, 2022. 1 +[45] Mingkai Zheng, Fei Wang, Shan You, Chen Qian, Changshui Zhang, Xiaogang Wang, and Chang Xu. Weakly supervised contrastive learning. In ICCV, 2021. 1 +[46] Zhun Zhong, Enrico Fini, Subhankar Roy, Zhiming Luo, Elisa Ricci, and Nicu Sebe. Neighborhood contrastive learning for novel class discovery. In CVPR, 2021. 2 +[47] Zhun Zhong, Linchao Zhu, Zhiming Luo, Shaozi Li, Yi Yang, and Nicu Sebe. Openmix: Reviving known knowledge for discovering novel visual categories in an open world. In CVPR, 2021. 1 \ No newline at end of file diff --git a/2023/Dynamic Conceptional Contrastive Learning for Generalized Category Discovery/images.zip b/2023/Dynamic Conceptional Contrastive Learning for Generalized Category Discovery/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..e34526119ba8b3c1f73c49c08c9d38ed6c783a5b --- /dev/null +++ b/2023/Dynamic Conceptional Contrastive Learning for Generalized Category Discovery/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:c6eeaf392043677e776ef90c05d4b6241a7caacdd68522a705d6014c1cee8611 +size 481616 diff --git a/2023/Dynamic Conceptional Contrastive Learning for Generalized Category Discovery/layout.json b/2023/Dynamic Conceptional Contrastive Learning for Generalized Category Discovery/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..cb8e4b207698e76a308ab1a28401c2b52f8cff05 --- /dev/null +++ b/2023/Dynamic Conceptional Contrastive Learning for Generalized Category Discovery/layout.json @@ -0,0 +1,9104 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 148, + 103, + 446, + 139 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 148, + 103, + 446, + 139 + ], + "spans": [ + { + "bbox": [ + 148, + 103, + 446, + 139 + ], + "type": "text", + "content": "Dynamic Conceptional Contrastive Learning for Generalized Category Discovery" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 208, + 161, + 385, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 208, + 161, + 385, + 175 + ], + "spans": [ + { + "bbox": [ + 208, + 161, + 385, + 175 + ], + "type": "text", + "content": "Nan Pu Zhun Zhong* Nicu Sebe" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 133, + 175, + 459, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 133, + 175, + 459, + 203 + ], + "spans": [ + { + "bbox": [ + 133, + 175, + 459, + 203 + ], + "type": "text", + "content": "The Department of Information Engineering and Computer Science University of Trento, Trento, Italy" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 179, + 205, + 411, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 179, + 205, + 411, + 217 + ], + "spans": [ + { + "bbox": [ + 179, + 205, + 411, + 217 + ], + "type": "text", + "content": "{nan.pu, zhun.zhong, niculae.sebe}@unitn.it" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 143, + 244, + 192, + 258 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 244, + 192, + 258 + ], + "spans": [ + { + "bbox": [ + 143, + 244, + 192, + 258 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 270, + 289, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 270, + 289, + 605 + ], + "spans": [ + { + "bbox": [ + 47, + 270, + 289, + 605 + ], + "type": "text", + "content": "Generalized category discovery (GCD) is a recently proposed open-world problem, which aims to automatically cluster partially labeled data. The main challenge is that the unlabeled data contain instances that are not only from known categories of the labeled data but also from novel categories. This leads traditional novel category discovery (NCD) methods to be incapacitated for GCD, due to their assumption of unlabeled data are only from novel categories. One effective way for GCD is applying self-supervised learning to learn discriminate representation for unlabeled data. However, this manner largely ignores underlying relationships between instances of the same concepts (e.g., class, super-class, and sub-class), which results in inferior representation learning. In this paper, we propose a Dynamic Conceptional Contrastive Learning (DCCL) framework, which can effectively improve clustering accuracy by alternately estimating underlying visual conceptions and learning conceptual representation. In addition, we design a dynamic conception generation and update mechanism, which is able to ensure consistent conception learning and thus further facilitate the optimization of DCCL. Extensive experiments show that DCCL achieves new state-of-the-art performances on six generic and fine-grained visual recognition datasets, especially on fine-grained ones. For example, our method significantly surpasses the best competitor by " + }, + { + "bbox": [ + 47, + 270, + 289, + 605 + ], + "type": "inline_equation", + "content": "16.2\\%" + }, + { + "bbox": [ + 47, + 270, + 289, + 605 + ], + "type": "text", + "content": " on the new classes for the CUB-200 dataset. Code is available at https://github.com/TPCD/DCCL" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 628, + 127, + 639 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 628, + 127, + 639 + ], + "spans": [ + { + "bbox": [ + 47, + 628, + 127, + 639 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 647, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 287, + 696 + ], + "type": "text", + "content": "Learning recognition models (e.g., image classification) from labeled data has been widely studied in the field of machine learning and deep learning [13, 18, 31]. In spite of their tremendous success, supervised learning techniques" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 307, + 251, + 545, + 386 + ], + "blocks": [ + { + "bbox": [ + 307, + 251, + 545, + 386 + ], + "lines": [ + { + "bbox": [ + 307, + 251, + 545, + 386 + ], + "spans": [ + { + "bbox": [ + 307, + 251, + 545, + 386 + ], + "type": "image", + "image_path": "7f5b2f9bafc25f8aebc5f7a4fd206915c9fc8f46a52372987cf6b31e436d2d0e.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 388, + 546, + 477 + ], + "lines": [ + { + "bbox": [ + 305, + 388, + 546, + 477 + ], + "spans": [ + { + "bbox": [ + 305, + 388, + 546, + 477 + ], + "type": "text", + "content": "Figure 1. Diagram of the proposed Dynamic Conceptional Contrastive Learning (DCCL). Samples from the conceptions should be close to each other. For example, samples from the same classes (bus) at the class level, samples belonging to the transportation (bus and bicycle) at the super-class level, and samples from trains with different colors at the sub-class level. Our DCCL potentially learns the underlying conceptions in unlabeled data and produces more discriminative representations." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 495, + 545, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 495, + 545, + 579 + ], + "spans": [ + { + "bbox": [ + 304, + 495, + 545, + 579 + ], + "type": "text", + "content": "rely heavily on huge annotated data, which is not suitable for open-world applications. Thus, the researchers recently have paid much effort on learning with label-imperfection data, such as semi-supervised learning [23, 33], self-supervised learning [12, 42], weakly-supervised learning [41,45], few-shot learning [32,38], open-set recognition [30] and learning with noisy labels [40], etc." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "type": "text", + "content": "Recently, inspired by the fact that Humans can easily and automatically learn new knowledge with the guidance of previously learned knowledge, novel category discovery (NCD) [9, 11, 28, 44, 47] is introduced to automatically cluster unlabeled data of unseen categories with the help of knowledge from seen categories. However, the implementation of NCD is under a strong assumption that all the unlabeled instances belong to unseen categories, which is not practical in real-world applications. To address this limitation, Vaze et al. [35] extend NCD to the generalized category discovery (GCD) [35], where unlabeled images are" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 495, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 495, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 495, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 138, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 138, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 138, + 712 + ], + "type": "text", + "content": "*Corresponding Author." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7579" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 208, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 208, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 208, + 83 + ], + "type": "text", + "content": "from both novel and labeled categories." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 85, + 289, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 85, + 289, + 419 + ], + "spans": [ + { + "bbox": [ + 46, + 85, + 289, + 419 + ], + "type": "text", + "content": "GCD is a challenging open-world problem in that we need to 1) jointly distinguish the known and unknown classes and 2) discover the novel clusters without any annotations. To solve this problem, Vaze et al. [35] leverage the contrastive learning technique to learn discriminative representation for unlabeled data and use " + }, + { + "bbox": [ + 46, + 85, + 289, + 419 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 85, + 289, + 419 + ], + "type": "text", + "content": "-means [21] to obtain final clustering results. In this method, the labeled data are fully exploited by supervised contrastive learning. However, self-supervised learning is applied to the unlabeled data, which enforces samples to be close to their augmentation counterparts while far away from others. As a consequence, the underlying relationships between samples of the same conceptions are largely overlooked and thus will lead to degraded representation learning. Intuitively, samples that belong to the same conceptions should be similar to each other in the feature space. The conceptions can be regarded as: classes, super-classes, sub-classes, etc. For example, as shown in Fig. 1, samples of the same class should be similar to each other, e.g., samples of the bus, samples of the bicycle. In addition, in the super-classes view, classes of the transportation, e.g., Bus and Bicycle, should belong to the same concept. Hence, the samples of transportation should be closer than that of other concepts (e.g., animals). Similarly, samples belong to the same sub-classes (e.g., red train) should be closer to that of other sub-classes (e.g., white train). Hence, embracing such conceptions and their relationships can greatly benefit the representation learning for unlabeled data, especially for unseen classes." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 420, + 289, + 587 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 420, + 289, + 587 + ], + "spans": [ + { + "bbox": [ + 46, + 420, + 289, + 587 + ], + "type": "text", + "content": "Motivated by this, we propose a Dynamic Conceptional Contrastive Learning (DCCL) framework for GCD to effectively leverage the underlying relationships between unlabeled data for representation learning. Specifically, our DCCL includes two steps: Dynamic Conception Generation (DCG) and Dual-level Contrastive Learning (DCL). In DCG, we dynamically generate conceptions based on the hyper-parameter-free clustering method equipped with the proposed semi-supervised conceptual consolidation. In DCL, we propose to optimize the model with conception-level and instance-level contrastive learning objectives, where we maintain a dynamic memory to ensure comparing with the up-to-date conceptions. The DCG and DCL are alternately performed until the model converges." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 587, + 287, + 600 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 587, + 287, + 600 + ], + "spans": [ + { + "bbox": [ + 59, + 587, + 287, + 600 + ], + "type": "text", + "content": "We summarize the contributions of this work as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 609, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 59, + 609, + 287, + 657 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 609, + 287, + 657 + ], + "spans": [ + { + "bbox": [ + 59, + 609, + 287, + 657 + ], + "type": "text", + "content": "- We propose a novel dynamic conceptionsal contrastive learning (DCCL) framework to effectively leverage the underlying relationships between unlabeled samples for learning discriminative representation for GCD." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 58, + 665, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 665, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 58, + 665, + 288, + 714 + ], + "type": "text", + "content": "- We introduce a novel dynamic conception generation and update mechanism to ensure consistent conception learning, which encourages the model to produce more discriminative representation." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 317, + 72, + 547, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 72, + 547, + 109 + ], + "spans": [ + { + "bbox": [ + 317, + 72, + 547, + 109 + ], + "type": "text", + "content": "- Our DCCL approach consistently achieves superior performance over state-of-the-art GCD algorithms on both generic and fine-grained tasks." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 136, + 392, + 148 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 136, + 392, + 148 + ], + "spans": [ + { + "bbox": [ + 306, + 136, + 392, + 148 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 157, + 450, + 171 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 157, + 450, + 171 + ], + "spans": [ + { + "bbox": [ + 306, + 157, + 450, + 171 + ], + "type": "text", + "content": "2.1. Novel Category Discovery" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 177, + 547, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 177, + 547, + 441 + ], + "spans": [ + { + "bbox": [ + 304, + 177, + 547, + 441 + ], + "type": "text", + "content": "Novel category discovery [11] (NCD) tasks aim at discovering new categories by leveraging the knowledge of a set of labeled categories. RankStat [10] indicates that self-supervised pre-training is helpful for NCD. NCL [46] adopts contrastive learning to improve representation learning. UNO [9] proposes a unified objective for jointly learning on unlabeled and labeled data. Most recently, NCD has been extended to a generalized category discovery (GCD) [35], in which the unlabeled data include both labeled and unlabeled categories. Later, ORCA [3] defines an open-world semi-supervised learning task, which is similar to GCD. Although these definitions are relatively practical, most methods remain to assume that the class number of clustered data is known. Nevertheless, such prior knowledge is often not acquired in advance for real-world applications. To handle the drawback, DTC [11] and GCD [35] employed an independent algorithm to search the optimal class number, however, they did not associate clustering estimation with representation learning. Unlike these offline algorithms, we propose to jointly consider downstream clustering and representation learning. The experimental results show they are mutually beneficial for each other." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 453, + 545, + 467 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 453, + 545, + 467 + ], + "spans": [ + { + "bbox": [ + 306, + 453, + 545, + 467 + ], + "type": "text", + "content": "2.2. Contrastive Learning based on Memory Buffer" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 474, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 547, + 715 + ], + "type": "text", + "content": "Contrastive learning [5,6,22,37,43] (CL) has been shown to be significantly effective for representation learning in a self-supervised manner. MoCo [12] demonstrates that sampling positive-negative pairs from an instance-level buffer can benefit CL and reduce the impact of the size of the training batch. Then, instead of contrasting over all instances in a mini-batch, prototypical contrastive learning [20] (PCL) that contrasts the instance features with a set of prototypes, has been shown to provide comprehensive supervision. However, PCL still needs an instance-level memory buffer to yield the prototype set, which is not computation- and memory-efficient. Recently, SCL [14] propose a cluster-level momentum encoder but considers only three fixed numbers of classes during training, which is still limited compared to our dynamic method. Different from PCL and SCL that consider the fixed numbers of classes during the whole training process, our DCCL dynamically estimates the number of classes for different training stages in a efficient way, which encourages models to learn more discriminative representation." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "text", + "content": "7580" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 79, + 526, + 272 + ], + "blocks": [ + { + "bbox": [ + 52, + 79, + 526, + 272 + ], + "lines": [ + { + "bbox": [ + 52, + 79, + 526, + 272 + ], + "spans": [ + { + "bbox": [ + 52, + 79, + 526, + 272 + ], + "type": "image", + "image_path": "c5b5e59be55abcad8920c9da63691cc09d16dc1bf93567ac8283805f4061ad66.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 273, + 547, + 340 + ], + "lines": [ + { + "bbox": [ + 46, + 273, + 547, + 340 + ], + "spans": [ + { + "bbox": [ + 46, + 273, + 547, + 340 + ], + "type": "text", + "content": "Figure 2. (a) Overview of our DCCL framework. We first extract features and cluster the features to generate conceptual labels, then initialize conception representations by our DCG, and last learn representations by joint instance-level and conception-level objectives. During the training process, the DCG and dual-level representation learning are performed alternately, in which the conception buffer is updated every iteration to keep the consistency of the changing instance features and conceptual representations. (b) Illustration of the proposed conception consolidation. Without consolidating the relationships of conceptions by label information, Infomap tends to over-cluster data and thus provides the supervision that has a high risk to over-correct affinities between neighbor instances." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 349, + 266, + 363 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 349, + 266, + 363 + ], + "spans": [ + { + "bbox": [ + 47, + 349, + 266, + 363 + ], + "type": "text", + "content": "2.3. Semi-Supervised Learning and Clustering" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 369, + 289, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 369, + 289, + 622 + ], + "spans": [ + { + "bbox": [ + 46, + 369, + 289, + 622 + ], + "type": "text", + "content": "Semi-supervised learning (SSL) has been a long-standing research topic [39]. Different from GCD, SSL often assumes that the labeled and unlabeled data come from the same set of classes, in which consistency-based methods are the most effective methods for SSL, such as Mean-teacher [34], MixMatch [2], and FixMatch [33]. Consistency-based methods are the most effective methods for SSL, such as Mean-teacher [34], MixMatch [2], and FixMatch [33]. Moreover, semi-supervised classification is a relatively well-defined task, while the supervised information in semi-supervised clustering can take different forms [19], such as two instances are known to be must-linked in a relationship matrix or some cluster assignments are known beforehand. For instance, Basu et al. [1] proposed to initialize the clusters based on the data points for which cluster assignments are known. However, these methods can not adaptively assign the number of clusters for generating conceptions. To mitigate these limitations, we improve the classical InfoMap [27] to fully leverage both labeled and unlabeled data and dynamically produce varying conceptual labels for different contrastive learning epochs." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 635, + 288, + 663 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 635, + 288, + 663 + ], + "spans": [ + { + "bbox": [ + 47, + 635, + 288, + 663 + ], + "type": "text", + "content": "3. Dynamic Conceptional Contrastive Learning" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 670, + 171, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 670, + 171, + 682 + ], + "spans": [ + { + "bbox": [ + 47, + 670, + 171, + 682 + ], + "type": "text", + "content": "3.1. Problem Formulation" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "text", + "content": "Generalized category discovery (GCD) aims at automatically categorizing unlabeled images in a dataset, where the" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 349, + 547, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 349, + 547, + 534 + ], + "spans": [ + { + "bbox": [ + 304, + 349, + 547, + 534 + ], + "type": "text", + "content": "partial data are labeled and the remaining are unlabeled. The unlabeled images come from either labeled (known) classes or unlabeled (unknown) classes. This is a more realistic open-world setting than the common closed-set classification that assumes the labeled and unlabeled data belong to the same classes. Let the dataset be " + }, + { + "bbox": [ + 304, + 349, + 547, + 534 + ], + "type": "inline_equation", + "content": "\\mathcal{D} = \\mathcal{D}^L\\cup \\mathcal{D}^U" + }, + { + "bbox": [ + 304, + 349, + 547, + 534 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 349, + 547, + 534 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^L = \\{(\\mathbf{x}_i^L,\\mathbf{y}_i^L)\\}_{i = 1}^{M^L}\\in \\mathcal{X}\\times \\mathcal{Y}^L" + }, + { + "bbox": [ + 304, + 349, + 547, + 534 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 304, + 349, + 547, + 534 + ], + "type": "text", + "content": " denotes the labeled subset and " + }, + { + "bbox": [ + 304, + 349, + 547, + 534 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^U = \\{(\\mathbf{x}_i^U,\\mathbf{y}_i^U)\\}_{i = 1}^{M^U}\\in \\mathcal{X}\\times \\mathcal{Y}^U" + }, + { + "bbox": [ + 304, + 349, + 547, + 534 + ], + "type": "text", + "content": " denotes the unlabeled subset with unknown " + }, + { + "bbox": [ + 304, + 349, + 547, + 534 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_i^U\\in \\mathcal{V}^U" + }, + { + "bbox": [ + 304, + 349, + 547, + 534 + ], + "type": "text", + "content": " . Only a subset of classes contains labeled instances, i.e., " + }, + { + "bbox": [ + 304, + 349, + 547, + 534 + ], + "type": "inline_equation", + "content": "\\mathcal{V}^L\\subset \\mathcal{V}^U" + }, + { + "bbox": [ + 304, + 349, + 547, + 534 + ], + "type": "text", + "content": " The number of labeled classes " + }, + { + "bbox": [ + 304, + 349, + 547, + 534 + ], + "type": "inline_equation", + "content": "N^L" + }, + { + "bbox": [ + 304, + 349, + 547, + 534 + ], + "type": "text", + "content": " can be directly calculated from the labeled data, while the number of unlabeled classes " + }, + { + "bbox": [ + 304, + 349, + 547, + 534 + ], + "type": "inline_equation", + "content": "N^U" + }, + { + "bbox": [ + 304, + 349, + 547, + 534 + ], + "type": "text", + "content": " is not known during model training. Let " + }, + { + "bbox": [ + 304, + 349, + 547, + 534 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 349, + 547, + 534 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 349, + 547, + 534 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 304, + 349, + 547, + 534 + ], + "type": "text", + "content": " be a feature extractor and a MLP projection head. The extracted representation is defined as " + }, + { + "bbox": [ + 304, + 349, + 547, + 534 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_i = f(\\mathbf{x}_i)" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 540, + 373, + 551 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 540, + 373, + 551 + ], + "spans": [ + { + "bbox": [ + 306, + 540, + 373, + 551 + ], + "type": "text", + "content": "3.2. Overview" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 557, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 547, + 715 + ], + "type": "text", + "content": "To tackle the problem of GCD, we propose a novel framework DCCL (see Fig. 2), to jointly learn representations using dual-level contrastive learning (DCL) and explore all possible relationships between labeled and unlabeled instances in a conceptionsal view. First, we extend the classical unsupervised clustering algorithm, Infomap [27], to a semi-supervised manner, which aims at dynamically generating reasonable conceptual representations and associating the labeled and unlabeled instances during representation learning. By alternately executing the dynamic conception generation (DCG) and DCL, DCL benefits from informative supervised information to generate higher-quality representations. Meanwhile, DCG gradually" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 758 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 758 + ], + "type": "text", + "content": "7581" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 122 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 122 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 122 + ], + "type": "text", + "content": "produces more comprehensive guidance based on a deeper understanding of conceptual relationships. DCG and DCL mutually benefit each other, thus resulting in a better representation for downstream clustering." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 127, + 224, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 127, + 224, + 140 + ], + "spans": [ + { + "bbox": [ + 47, + 127, + 224, + 140 + ], + "type": "text", + "content": "3.3. Dynamic Conception Generation" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 145, + 287, + 325 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 145, + 287, + 325 + ], + "spans": [ + { + "bbox": [ + 46, + 145, + 287, + 325 + ], + "type": "text", + "content": "Although the test-time semi-supervised " + }, + { + "bbox": [ + 46, + 145, + 287, + 325 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 145, + 287, + 325 + ], + "type": "text", + "content": "-means [35] (SSK) succeeds in achieving considerable performance gain, it fails to jointly consider the representation learning and supervision information from semi-supervised clustering. Moreover, it is infeasible to directly perform SSK in each training epoch for assigning pseudo labels, because the real number of clusters is unknown during training. To overcome these drawbacks, we propose a dynamic conception generation (DCG) based on the hyper-parameter-free Infomap [27] algorithm. Specifically, we first propose a semi-supervised conceptual consolidation method to construct a similarity network, then execute the Infomap clustering algorithm on the constructed network to get conceptual label assignments, and finally calculate conception representation and initialize conceptual memory buffer." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 325, + 287, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 325, + 287, + 433 + ], + "spans": [ + { + "bbox": [ + 46, + 325, + 287, + 433 + ], + "type": "text", + "content": "Conception Consolidation. In a given network, Infomap aims at partitioning semantic-similar sub-networks by the pattern of connections. To leverage the supervision from labeled data, we propose to enforce the similarity constraints into the networking, according to the labeled data that belong to the same category. Formally, we construct an adjacent matrix " + }, + { + "bbox": [ + 46, + 325, + 287, + 433 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 46, + 325, + 287, + 433 + ], + "type": "text", + "content": " to represent the possible connection relationships among all instances. The weight of the edge of the " + }, + { + "bbox": [ + 46, + 325, + 287, + 433 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 325, + 287, + 433 + ], + "type": "text", + "content": "-th and " + }, + { + "bbox": [ + 46, + 325, + 287, + 433 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 325, + 287, + 433 + ], + "type": "text", + "content": "-th instances is given by:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 63, + 441, + 287, + 485 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 441, + 287, + 485 + ], + "spans": [ + { + "bbox": [ + 63, + 441, + 287, + 485 + ], + "type": "interline_equation", + "content": "\\mathcal {A} _ {i j} = \\left\\{ \\begin{array}{l l} s _ {i} ^ {\\max }, & \\text {i f} \\mathbf {y} _ {i}, \\mathbf {y} _ {j} \\in \\mathcal {Y} ^ {L} \\text {a n d} \\mathbf {y} _ {i} = \\mathbf {y} _ {j} \\\\ s _ {i j}, & \\text {i f} \\mathbf {y} _ {i} \\text {o r} \\mathbf {y} _ {j} \\in \\mathcal {Y} ^ {U} \\text {a n d} s _ {i j} > \\tau^ {F} \\\\ 0, & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {1}", + "image_path": "a5a84dc7efce275fe9fb2649b0647ba012473c4775531b789ef628a40b5e9b46.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 101, + 491, + 287, + 513 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 101, + 491, + 287, + 513 + ], + "spans": [ + { + "bbox": [ + 101, + 491, + 287, + 513 + ], + "type": "interline_equation", + "content": "s _ {i} ^ {\\text {m a x}} = \\underset {j} {\\arg \\max } \\left\\{s _ {i j} \\mid j \\in \\mathcal {D} \\right\\}, \\tag {2}", + "image_path": "0bae760506d6f6efeb240f564eaa9694b72b879f3c052be588f45b1b8a97cd72.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 73, + 516, + 287, + 531 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 73, + 516, + 287, + 531 + ], + "spans": [ + { + "bbox": [ + 73, + 516, + 287, + 531 + ], + "type": "interline_equation", + "content": "s _ {i j} = \\left[ \\left(\\mathbf {v} _ {i} / \\| \\mathbf {v} _ {i} \\|\\right) \\cdot \\left(\\mathbf {v} _ {j} / \\| \\mathbf {v} _ {j} \\|\\right) + 1 \\right] / 2 \\in [ 0, 1 ], \\tag {3}", + "image_path": "c10593ce03e2aa50b1d41b5c9ea0d91fade4ff8dffdba84399ed1405a47f6a61.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 534, + 287, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 534, + 287, + 594 + ], + "spans": [ + { + "bbox": [ + 47, + 534, + 287, + 594 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 534, + 287, + 594 + ], + "type": "inline_equation", + "content": "\\cdot" + }, + { + "bbox": [ + 47, + 534, + 287, + 594 + ], + "type": "text", + "content": " denotes dot product and " + }, + { + "bbox": [ + 47, + 534, + 287, + 594 + ], + "type": "inline_equation", + "content": "\\| \\cdot \\|" + }, + { + "bbox": [ + 47, + 534, + 287, + 594 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 47, + 534, + 287, + 594 + ], + "type": "inline_equation", + "content": "l_{2}" + }, + { + "bbox": [ + 47, + 534, + 287, + 594 + ], + "type": "text", + "content": " normalization. The " + }, + { + "bbox": [ + 47, + 534, + 287, + 594 + ], + "type": "inline_equation", + "content": "\\tau^{F}" + }, + { + "bbox": [ + 47, + 534, + 287, + 594 + ], + "type": "text", + "content": " is a threshold to select high-confidence links. Through the conception consolidation illustrated in Fig. 2(b), we can establish a reliable relationship network with rich structural information for the subsequent clustering." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 594, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 594, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 47, + 594, + 287, + 653 + ], + "type": "text", + "content": "Remark. We set the similarities of positive pairs with the maximal value of neighborhood similarities instead of 1. This is because we experimentally find that when imposing 1 for constraining positive pairs, Infomap tends to group all the labeled positive instances as an individual cluster." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "text", + "content": "Entropy Minimization Clustering. In Infomap algorithm [26], the clustering problem is equivalent to minimizing the entropy that represents the minimum description length of the coding network. By solving the minimization objective, we acquire a conceptual label set" + } + ] + } + ], + "index": 9 + }, + { + "type": "code", + "bbox": [ + 316, + 88, + 518, + 316 + ], + "blocks": [ + { + "bbox": [ + 312, + 75, + 506, + 87 + ], + "lines": [ + { + "bbox": [ + 312, + 75, + 506, + 87 + ], + "spans": [ + { + "bbox": [ + 312, + 75, + 506, + 87 + ], + "type": "text", + "content": "Algorithm 1: Algorithm Pipeline of our DCCL" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 316, + 88, + 518, + 316 + ], + "lines": [ + { + "bbox": [ + 316, + 88, + 518, + 316 + ], + "spans": [ + { + "bbox": [ + 316, + 88, + 518, + 316 + ], + "type": "text", + "content": "Input: Feature Extractor " + }, + { + "bbox": [ + 316, + 88, + 518, + 316 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 316, + 88, + 518, + 316 + ], + "type": "text", + "content": " Projection Head " + }, + { + "bbox": [ + 316, + 88, + 518, + 316 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 316, + 88, + 518, + 316 + ], + "type": "text", + "content": " Labeled data " + }, + { + "bbox": [ + 316, + 88, + 518, + 316 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^L" + }, + { + "bbox": [ + 316, + 88, + 518, + 316 + ], + "type": "text", + "content": " and Unlabeled data " + }, + { + "bbox": [ + 316, + 88, + 518, + 316 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^U" + }, + { + "bbox": [ + 316, + 88, + 518, + 316 + ], + "type": "text", + "content": " \nOutput: " + }, + { + "bbox": [ + 316, + 88, + 518, + 316 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 316, + 88, + 518, + 316 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 316, + 88, + 518, + 316 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 316, + 88, + 518, + 316 + ], + "type": "text", + "content": " \nfor " + }, + { + "bbox": [ + 316, + 88, + 518, + 316 + ], + "type": "inline_equation", + "content": "n = 1" + }, + { + "bbox": [ + 316, + 88, + 518, + 316 + ], + "type": "text", + "content": " in [1,max_epoch] do if " + }, + { + "bbox": [ + 316, + 88, + 518, + 316 + ], + "type": "inline_equation", + "content": "n\\bmod\\tau^{I}==0" + }, + { + "bbox": [ + 316, + 88, + 518, + 316 + ], + "type": "text", + "content": " then Extract features and construct adjacency matrix " + }, + { + "bbox": [ + 316, + 88, + 518, + 316 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 316, + 88, + 518, + 316 + ], + "type": "text", + "content": " by Eq. (1), Eq. (2) and Eq. (3); Perform InfoMap [27] clustering to assign conceptual labels C; Initialize conceptual buffer by Eq. (4); \nend for " + }, + { + "bbox": [ + 316, + 88, + 518, + 316 + ], + "type": "inline_equation", + "content": "i = 1" + }, + { + "bbox": [ + 316, + 88, + 518, + 316 + ], + "type": "text", + "content": " in [1,max_iteration] do Sample mini-batches from " + }, + { + "bbox": [ + 316, + 88, + 518, + 316 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^L\\cup \\mathcal{D}^U" + }, + { + "bbox": [ + 316, + 88, + 518, + 316 + ], + "type": "text", + "content": " Calculate overall optimization objective by Eq.(10); Update " + }, + { + "bbox": [ + 316, + 88, + 518, + 316 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 316, + 88, + 518, + 316 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 316, + 88, + 518, + 316 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 316, + 88, + 518, + 316 + ], + "type": "text", + "content": " by SGD [25]; Update conceptual buffer by Eq. (8); \nend" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "code_body" + } + ], + "index": 11, + "sub_type": "algorithm" + }, + { + "bbox": [ + 305, + 340, + 545, + 405 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 340, + 545, + 405 + ], + "spans": [ + { + "bbox": [ + 305, + 340, + 545, + 405 + ], + "type": "inline_equation", + "content": "\\mathcal{C} = \\{\\mathbf{c}_i\\}_{i=1}^{M^L + M^U} \\in \\mathcal{V}^G" + }, + { + "bbox": [ + 305, + 340, + 545, + 405 + ], + "type": "text", + "content": " for both labeled and unlabeled instances. Then, we combine the extracted feature vectors " + }, + { + "bbox": [ + 305, + 340, + 545, + 405 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 305, + 340, + 545, + 405 + ], + "type": "text", + "content": " and corresponding conceptionsal labels to construct a generated feature dataset " + }, + { + "bbox": [ + 305, + 340, + 545, + 405 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^G = \\{(\\mathbf{v}_i, \\mathbf{c}_i)\\}_{i=1}^{M^L + M^U} \\in \\mathcal{V} \\times \\mathcal{V}^G" + }, + { + "bbox": [ + 305, + 340, + 545, + 405 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 305, + 340, + 545, + 405 + ], + "type": "inline_equation", + "content": "|\\mathcal{V}^G|" + }, + { + "bbox": [ + 305, + 340, + 545, + 405 + ], + "type": "text", + "content": " denotes the number of estimated conceptions." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 405, + 546, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 405, + 546, + 513 + ], + "spans": [ + { + "bbox": [ + 305, + 405, + 546, + 513 + ], + "type": "text", + "content": "Conceptional Memory Initialization. In this paper, our DCCL maintains a conception-level memory buffer that provides dynamic conceptual representations for dual-level contrastive learning, which is elaborated in Sec. 3.4. Here, we introduce the initialization of the conceptual memory buffer (CMB). We use the mean feature vector of the instances that share the same conceptual label to form a unique conceptual representation. Formally, the initial conceptual representation set is defined as:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 310, + 518, + 545, + 550 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 518, + 545, + 550 + ], + "spans": [ + { + "bbox": [ + 310, + 518, + 545, + 550 + ], + "type": "interline_equation", + "content": "\\mathcal {U} = \\left\\{\\boldsymbol {\\mu} _ {k} \\right\\} _ {k = 1} ^ {K}, \\quad \\boldsymbol {\\mu} _ {k} = \\frac {1}{\\left| \\mathcal {D} _ {k} ^ {G} \\right|} \\sum_ {\\mathbf {v} _ {i} \\in \\mathcal {D} _ {k} ^ {G}} \\mathbf {v} _ {i}, \\quad K = | \\mathcal {Y} ^ {G} |, \\tag {4}", + "image_path": "615493b50702fcbe39b1567e7ffe4ce8eb10488b6ddd550b039fdffb9b6de043.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 556, + 545, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 556, + 545, + 617 + ], + "spans": [ + { + "bbox": [ + 305, + 556, + 545, + 617 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 556, + 545, + 617 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_k^G" + }, + { + "bbox": [ + 305, + 556, + 545, + 617 + ], + "type": "text", + "content": " denotes the " + }, + { + "bbox": [ + 305, + 556, + 545, + 617 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 556, + 545, + 617 + ], + "type": "text", + "content": "-th conception subset, i.e., if " + }, + { + "bbox": [ + 305, + 556, + 545, + 617 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_i \\in \\mathcal{D}_k^G" + }, + { + "bbox": [ + 305, + 556, + 545, + 617 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 556, + 545, + 617 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_i = k" + }, + { + "bbox": [ + 305, + 556, + 545, + 617 + ], + "type": "text", + "content": ". During whole training process, the initialization of CMB is executed every " + }, + { + "bbox": [ + 305, + 556, + 545, + 617 + ], + "type": "inline_equation", + "content": "\\tau^I" + }, + { + "bbox": [ + 305, + 556, + 545, + 617 + ], + "type": "text", + "content": " epochs on center-cropped images. Thus, the number of conceptions " + }, + { + "bbox": [ + 305, + 556, + 545, + 617 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 305, + 556, + 545, + 617 + ], + "type": "text", + "content": " is dynamically changing along with model training." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 623, + 484, + 636 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 623, + 484, + 636 + ], + "spans": [ + { + "bbox": [ + 306, + 623, + 484, + 636 + ], + "type": "text", + "content": "3.4. Dual-Level Contrastive Learning" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 642, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 689 + ], + "type": "text", + "content": "In this section, we first explain the proposed conception-level contrastive learning, then elaborate on the update of the conceptual memory buffer, and finally introduce the employed instance-level contrastive learning approach." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": "Conception-Level Contrastive Learning. Based on the generated conceptual representations in Sec. 3.3, we" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7582" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": "propose to perform conception-level contrastive learning. Specifically, we first sample " + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "N^C" + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": " conception labels and a fixed number " + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "N^I" + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": " of instances for each conception label, resulting in a mini-batch " + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "\\mathcal{B}^C" + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "N^C \\times N^I" + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": " instances. Next, each instance representation is compared to all the conceptual representations. We pull the instance representation from its corresponding conceptual representation closer and push the instance representation away from other conceptual representations. Formally, we define the conceptual contrastive loss function as the following:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 79, + 201, + 287, + 233 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 79, + 201, + 287, + 233 + ], + "spans": [ + { + "bbox": [ + 79, + 201, + 287, + 233 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {i} ^ {C} = - \\log \\frac {\\exp \\left(\\mathbf {v} _ {i} \\cdot \\boldsymbol {\\mu} _ {\\mathbf {c} _ {i}} / \\tau^ {C}\\right)}{\\sum_ {k = 1 , k \\neq \\mathbf {c} _ {i}} ^ {K} \\exp \\left(\\mathbf {v} _ {i} \\cdot \\boldsymbol {\\mu} _ {k} / \\tau^ {C}\\right)}, \\tag {5}", + "image_path": "5d9f919d0b33254234a6e90beabab7c8b8adebc64b65f5504a444f3ec23c5721.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 239, + 287, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 239, + 287, + 324 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 287, + 324 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 239, + 287, + 324 + ], + "type": "inline_equation", + "content": "\\tau^C" + }, + { + "bbox": [ + 46, + 239, + 287, + 324 + ], + "type": "text", + "content": " is a temperature hyper-parameter to control the strength of the conception-level contrastive learning. In addition, in order to explicitly encourage learned representations with a large inter-conception margin, we propose a dispersion loss to further push the different conception representations away from each other. The loss function for the " + }, + { + "bbox": [ + 46, + 239, + 287, + 324 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 239, + 287, + 324 + ], + "type": "text", + "content": "-th and the " + }, + { + "bbox": [ + 46, + 239, + 287, + 324 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 239, + 287, + 324 + ], + "type": "text", + "content": "-th conceptions in " + }, + { + "bbox": [ + 46, + 239, + 287, + 324 + ], + "type": "inline_equation", + "content": "\\mathcal{B}^C" + }, + { + "bbox": [ + 46, + 239, + 287, + 324 + ], + "type": "text", + "content": " is:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 332, + 287, + 373 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 332, + 287, + 373 + ], + "spans": [ + { + "bbox": [ + 47, + 332, + 287, + 373 + ], + "type": "interline_equation", + "content": "\\mathcal {L} (m, n) = \\left[ \\tau^ {M} - \\left\\| \\frac {1}{\\left| \\mathcal {B} _ {m} ^ {C} \\right|} \\sum_ {\\mathbf {v} _ {i} \\in \\mathcal {B} _ {m} ^ {C}} \\mathbf {v} _ {i} \\right\\| \\cdot \\left\\| \\frac {1}{\\left| \\mathcal {B} _ {n} ^ {C} \\right|} \\sum_ {\\mathbf {v} _ {j} \\in \\mathcal {B} _ {n} ^ {C}} \\mathbf {v} _ {j} \\right\\| \\right] _ {+}, \\tag {6}", + "image_path": "565b35f10e268ec5147131e694385673951cdcea7ed68102f2371b711c7d653f.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 374, + 287, + 446 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 374, + 287, + 446 + ], + "spans": [ + { + "bbox": [ + 46, + 374, + 287, + 446 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 374, + 287, + 446 + ], + "type": "inline_equation", + "content": "\\tau^M" + }, + { + "bbox": [ + 46, + 374, + 287, + 446 + ], + "type": "text", + "content": " is a threshold to filter the conception pairs with high uncertainty. We assume that two conception representations that are close tend to be highly entangled conceptions. Separating these conceptions has a high risk of overcorrect. We explore the impact of " + }, + { + "bbox": [ + 46, + 374, + 287, + 446 + ], + "type": "inline_equation", + "content": "\\tau^M" + }, + { + "bbox": [ + 46, + 374, + 287, + 446 + ], + "type": "text", + "content": " in Sec. 4.4. The dispersion loss function over a mini-batch is defined as:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 95, + 456, + 287, + 491 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 95, + 456, + 287, + 491 + ], + "spans": [ + { + "bbox": [ + 95, + 456, + 287, + 491 + ], + "type": "interline_equation", + "content": "\\mathcal {L} ^ {D} = \\frac {1}{N ^ {C}} \\sum_ {m = 1} ^ {N ^ {C}} \\frac {1}{N ^ {C}} \\sum_ {n = 1} ^ {N ^ {C}} \\mathcal {L} (m, n). \\tag {7}", + "image_path": "86047d0d144b9f694011b97a9bf02f4d15b81488c432c22989e508047b2c3e3a.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 499, + 287, + 620 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 499, + 287, + 620 + ], + "spans": [ + { + "bbox": [ + 46, + 499, + 287, + 620 + ], + "type": "text", + "content": "Conceptional Memory Update. Different from [12, 20] that need to save all training instances, our CMB stores only the conception representations, which significantly reduces storage cost. Furthermore, the instance-wise update is easy to lead to an inconsistent update during each training iteration. To mitigate this drawback, we first adopt the resampling method as detailed in the previous section. Next, we propose to update the conception representation by each corresponding instance feature following a momentum update mechanism. The process is formulated as:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 113, + 631, + 287, + 643 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 631, + 287, + 643 + ], + "spans": [ + { + "bbox": [ + 113, + 631, + 287, + 643 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\mu} _ {\\mathbf {c} _ {i}} \\leftarrow \\eta \\boldsymbol {\\mu} _ {\\mathbf {c} _ {i}} + (1 - \\eta) \\mathbf {v} _ {i}, \\tag {8}", + "image_path": "b314bd4a9939f99faffcece037c0586d5f29611c8ffed41fac0984d39ed166b7.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 653, + 219, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 653, + 219, + 665 + ], + "spans": [ + { + "bbox": [ + 47, + 653, + 219, + 665 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 653, + 219, + 665 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 47, + 653, + 219, + 665 + ], + "type": "text", + "content": " is the momentum updating factor." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": "Remark. DCCL updates the memory buffer and computes the losses both at the conceptual level, which consistently updates the conceptual representation to maintain the conceptual consistency during the whole training process." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "content": "Instance-Level Contrastive Learning. Inspired by [35], we combine supervised contrastive loss and self-supervised contrastive loss as an instance contrastive loss (ICL), to fine-tune the model. Formally, we assume " + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "inline_equation", + "content": "\\hat{x}_i" + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "content": " are two views (random augmentations) of the same image in a randomly-sampled mini-batch " + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "inline_equation", + "content": "\\mathcal{B}^I" + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "content": ". Let " + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "content": " be a MLP projection head. The extracted representation " + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_i" + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "content": " is further projected by " + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "content": " to high-dimensional embedding space for instance-level contrastive learning. The loss function is:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 308, + 187, + 545, + 259 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 187, + 545, + 259 + ], + "spans": [ + { + "bbox": [ + 308, + 187, + 545, + 259 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {i} ^ {I} = (\\lambda - 1) \\log \\frac {\\exp \\left(h \\left(\\mathbf {v} _ {i}\\right) \\cdot h \\left(\\hat {\\mathbf {v}} _ {i}\\right) / \\tau\\right)}{\\sum_ {j \\in \\mathcal {B} ^ {I} , j \\neq i} \\exp \\left(h \\left(\\mathbf {v} _ {i}\\right) \\cdot h \\left(\\mathbf {v} _ {j}\\right) / \\tau^ {S}\\right)} \\\\ \\frac {- \\lambda}{| \\mathcal {P} (i) |} \\sum_ {p \\in \\mathcal {P} (i)} \\log \\frac {\\exp \\left(h \\left(\\mathbf {v} _ {i} ^ {L}\\right) \\cdot h \\left(\\mathbf {v} _ {p} ^ {L}\\right) / \\tau\\right)}{\\sum_ {j \\in \\mathcal {B} ^ {L} , j \\neq i} \\exp \\left(h \\left(\\mathbf {v} _ {i} ^ {L}\\right) \\cdot h \\left(\\mathbf {v} _ {j} ^ {L}\\right) / \\tau^ {L}\\right)}, \\tag {9} \\\\ \\end{array}", + "image_path": "4719ecfe2a9303c16ee9a753b7574e20a1607abfd4aad45e7994860338ca0233.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 260, + 545, + 321 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 260, + 545, + 321 + ], + "spans": [ + { + "bbox": [ + 304, + 260, + 545, + 321 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 260, + 545, + 321 + ], + "type": "inline_equation", + "content": "\\mathcal{B}^L" + }, + { + "bbox": [ + 304, + 260, + 545, + 321 + ], + "type": "text", + "content": " donates the labeled subset within the mini-batch " + }, + { + "bbox": [ + 304, + 260, + 545, + 321 + ], + "type": "inline_equation", + "content": "\\mathcal{B}^I" + }, + { + "bbox": [ + 304, + 260, + 545, + 321 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 260, + 545, + 321 + ], + "type": "inline_equation", + "content": "\\mathcal{B}^I = \\mathcal{B}^L\\cup \\mathcal{B}^U" + }, + { + "bbox": [ + 304, + 260, + 545, + 321 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 260, + 545, + 321 + ], + "type": "inline_equation", + "content": "\\mathcal{P}(i)" + }, + { + "bbox": [ + 304, + 260, + 545, + 321 + ], + "type": "text", + "content": " is the positive index set for the anchor image " + }, + { + "bbox": [ + 304, + 260, + 545, + 321 + ], + "type": "inline_equation", + "content": "i\\in \\mathcal{B}^L" + }, + { + "bbox": [ + 304, + 260, + 545, + 321 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 260, + 545, + 321 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 260, + 545, + 321 + ], + "type": "text", + "content": " is a trade-off factor to balance the contributions of self-supervised and supervised learning. For a fair comparison, we follow [35] and set " + }, + { + "bbox": [ + 304, + 260, + 545, + 321 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 260, + 545, + 321 + ], + "type": "text", + "content": " to 0.35." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 327, + 417, + 340 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 327, + 417, + 340 + ], + "spans": [ + { + "bbox": [ + 306, + 327, + 417, + 340 + ], + "type": "text", + "content": "3.5. Joint Optimization" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 346, + 545, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 346, + 545, + 418 + ], + "spans": [ + { + "bbox": [ + 304, + 346, + 545, + 418 + ], + "type": "text", + "content": "During the whole training process, we alternately perform dynamic conception generalization and dual-level contrastive representation learning, until the maximal training epoch. The pseudo-code of DCCL is elaborated in Algorithm 1. The overall objective over on mini-batch " + }, + { + "bbox": [ + 304, + 346, + 545, + 418 + ], + "type": "inline_equation", + "content": "\\mathcal{B}" + }, + { + "bbox": [ + 304, + 346, + 545, + 418 + ], + "type": "text", + "content": " is given by the weighted sum of each loss function:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 324, + 425, + 545, + 454 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 425, + 545, + 454 + ], + "spans": [ + { + "bbox": [ + 324, + 425, + 545, + 454 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {t o t a l}} = \\frac {1}{| \\mathcal {B} |} \\sum_ {i \\in \\mathcal {B}} \\mathcal {L} _ {i} ^ {I} + \\alpha \\frac {1}{| \\mathcal {B} |} \\sum_ {i \\in \\mathcal {B}} \\mathcal {L} _ {i} ^ {C} + \\beta \\mathcal {L} ^ {D}, \\tag {10}", + "image_path": "1d865cc5f01736ee8006187f6af714c3b35c567466897f855de70f0ecdd96661.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 461, + 545, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 461, + 545, + 498 + ], + "spans": [ + { + "bbox": [ + 304, + 461, + 545, + 498 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 461, + 545, + 498 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 461, + 545, + 498 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 461, + 545, + 498 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 461, + 545, + 498 + ], + "type": "text", + "content": " are the weights to adjust the strengths of two loss functions. In all experiments, we use " + }, + { + "bbox": [ + 304, + 461, + 545, + 498 + ], + "type": "inline_equation", + "content": "l_{2}" + }, + { + "bbox": [ + 304, + 461, + 545, + 498 + ], + "type": "text", + "content": " normalized feature vector " + }, + { + "bbox": [ + 304, + 461, + 545, + 498 + ], + "type": "inline_equation", + "content": "\\| \\mathbf{v}\\| _2" + }, + { + "bbox": [ + 304, + 461, + 545, + 498 + ], + "type": "text", + "content": " for clustering evaluation." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 508, + 388, + 521 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 508, + 388, + 521 + ], + "spans": [ + { + "bbox": [ + 306, + 508, + 388, + 521 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 528, + 422, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 528, + 422, + 540 + ], + "spans": [ + { + "bbox": [ + 306, + 528, + 422, + 540 + ], + "type": "text", + "content": "4.1. Experimental Setup" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": "Data and Evaluation Metric. We evaluate DCCL on three generic image classification datasets, namely CIFAR-10 [17], CIFAR-100 [17] and ImageNet-100 [35]. ImageNet-100 denotes randomly sub-sampling 100 classes from the ImageNet [7] dataset. The dataset statistics and train-test splits are described in Tab. 1. We further evaluate DCCL on three more challenging fine-grained image classification datasets: CUB-200 [36], Stanford Cars [16], and Oxford-IIIT Pet [24]. The original training set of each fine-grained dataset is separated into labeled and unlabeled parts. We follow [35] sample a subset of half the classes as \"Old\" categories. " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": " of instances of each labeled class are drawn to form the labeled set, and all the remaining data constitute the unlabeled set. For evaluation, we measure the clustering" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7583" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 97, + 83, + 493, + 145 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 541, + 82 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 541, + 82 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 541, + 82 + ], + "type": "text", + "content": "Table 1. Statistics of the datasets and the splits for GCD. The first three are generic datasets while the last three are fine-grained datasets." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 97, + 83, + 493, + 145 + ], + "lines": [ + { + "bbox": [ + 97, + 83, + 493, + 145 + ], + "spans": [ + { + "bbox": [ + 97, + 83, + 493, + 145 + ], + "type": "table", + "html": "
DatasetCIFAR10 [17]CIFAR100 [17]ImageNet-100 [7]CUB-200 [36]SCars [16]Pet [24]
Labelled# Classes580501009819
# Images12,50020,00031,8601,4982,000942
Unlabelled# Classes1010010020019637
# Images37,50030,00095,25544966,1442,738
", + "image_path": "30fda43f35b294ad0cf56d19efbeb45944bdd6ba1a172adf96a64e6fbe813469.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 48, + 167, + 286, + 241 + ], + "blocks": [ + { + "bbox": [ + 66, + 156, + 267, + 166 + ], + "lines": [ + { + "bbox": [ + 66, + 156, + 267, + 166 + ], + "spans": [ + { + "bbox": [ + 66, + 156, + 267, + 166 + ], + "type": "text", + "content": "Table 2. Results on generic image recognition datasets." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 167, + 286, + 241 + ], + "lines": [ + { + "bbox": [ + 48, + 167, + 286, + 241 + ], + "spans": [ + { + "bbox": [ + 48, + 167, + 286, + 241 + ], + "type": "table", + "html": "
MethodCIFAR10CIFAR100ImageNet-100
AllOldNewAllOldNewAllOldNew
k-means83.685.782.552.052.250.872.775.571.3
RankStats+46.819.260.558.277.619.337.161.624.8
UNO+68.698.353.869.580.647.270.395.057.9
GCD91.597.988.273.076.266.574.189.866.3
DCCL96.396.596.975.376.870.280.590.576.2
", + "image_path": "2a73ed0993064ac5a84bab6621a716d56c9d2f0e99caee980f2c5792e640caf6.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 255, + 286, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 255, + 286, + 277 + ], + "spans": [ + { + "bbox": [ + 46, + 255, + 286, + 277 + ], + "type": "text", + "content": "accuracy by comparing the predicted label assignment with the ground truth, following the protocol in [35]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 279, + 287, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 279, + 287, + 578 + ], + "spans": [ + { + "bbox": [ + 46, + 279, + 287, + 578 + ], + "type": "text", + "content": "Implementation Details. We adopt the ViT-B-16 pretrained by DINO [4] as our backbone network. The output [CLS] token is used as the feature representation, which is also used for conception-level contrastive learning. Following [35], we project the representations by a projection head and use the projected embeddings for instance-level contrastive learning. We set the dimension of projected embeddings to 65,536 following [4]. At training time, we feed two views with random augmentations to the model. We only fine-tune the last block of the vision transformer with an initial learning rate of 0.01 and the head is trained with an initial learning rate of 0.1. All methods are trained for 200 epochs with a cosine annealing schedule. The size of the mini-batch is set to 128 with " + }, + { + "bbox": [ + 46, + 279, + 287, + 578 + ], + "type": "inline_equation", + "content": "N^C = 8" + }, + { + "bbox": [ + 46, + 279, + 287, + 578 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 279, + 287, + 578 + ], + "type": "inline_equation", + "content": "N^I = 16" + }, + { + "bbox": [ + 46, + 279, + 287, + 578 + ], + "type": "text", + "content": ". For a fair comparison, we follow [35] and set the temperatures of two supervised contrastive losses " + }, + { + "bbox": [ + 46, + 279, + 287, + 578 + ], + "type": "inline_equation", + "content": "\\tau^S" + }, + { + "bbox": [ + 46, + 279, + 287, + 578 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 279, + 287, + 578 + ], + "type": "inline_equation", + "content": "\\tau^L" + }, + { + "bbox": [ + 46, + 279, + 287, + 578 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 279, + 287, + 578 + ], + "type": "inline_equation", + "content": "\\tau^C" + }, + { + "bbox": [ + 46, + 279, + 287, + 578 + ], + "type": "text", + "content": " to 0.07, 0.05 and 0.05, respectively. The " + }, + { + "bbox": [ + 46, + 279, + 287, + 578 + ], + "type": "inline_equation", + "content": "\\tau^F" + }, + { + "bbox": [ + 46, + 279, + 287, + 578 + ], + "type": "text", + "content": " is empirically set to 0.6 for the fine-grained datasets and 0.7 for the generic datasets. Other hyper-parameters are discussed in Sec. 4.4. In testing, we first use the class number estimation algorithm [35] to predict the number of classes of the testing dataset, and then use semi-supervised " + }, + { + "bbox": [ + 46, + 279, + 287, + 578 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 279, + 287, + 578 + ], + "type": "text", + "content": "-means for clustering evaluation. In dynamic conception generation, we adopt faiss [15] to accelerate the construction of relationship networks. Our experiments are conducted on RTX 3090 GPUs." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 586, + 230, + 598 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 586, + 230, + 598 + ], + "spans": [ + { + "bbox": [ + 47, + 586, + 230, + 598 + ], + "type": "text", + "content": "4.2. Comparison with State-of-the-Art" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 605, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 653 + ], + "type": "text", + "content": "To evaluate the performances of our DCCL, we conduct three group experiments by comparing our DCCL with three strong GCD baselines, including RankStats [10] and UNO [9] and the state-of-the-art GCD method [35]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "content": "Comparison on Generic Datasets. As shown in Tab. 2, our DCCL is compared with other competitors on the generic image recognition datasets. Overall, the results in Tab. 2 show our DCCL consistently outperforms all others by a significant margin. Specifically, DCCL outperforms the" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 307, + 167, + 545, + 242 + ], + "blocks": [ + { + "bbox": [ + 350, + 156, + 501, + 166 + ], + "lines": [ + { + "bbox": [ + 350, + 156, + 501, + 166 + ], + "spans": [ + { + "bbox": [ + 350, + 156, + 501, + 166 + ], + "type": "text", + "content": "Table 3. Results on fine-grained datasets." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 167, + 545, + 242 + ], + "lines": [ + { + "bbox": [ + 307, + 167, + 545, + 242 + ], + "spans": [ + { + "bbox": [ + 307, + 167, + 545, + 242 + ], + "type": "table", + "html": "
methodCUB-200Stanford-CarsOxford-Pet
AllOldNewAllOldNewAllOldNew
k-means34.338.932.112.810.613.877.170.180.7
RankStats+33.351.624.228.361.812.1---
UNO+35.149.028.135.570.518.6---
GCD51.356.648.739.057.629.980.285.177.6
DCCL63.560.864.943.155.736.288.188.288.0
", + "image_path": "e6032995791ecfaa84051c26eae19040c5e492a570701ea9dc2c00517ec60e4b.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 254, + 545, + 408 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 254, + 545, + 408 + ], + "spans": [ + { + "bbox": [ + 304, + 254, + 545, + 408 + ], + "type": "text", + "content": "GCD method [35] by " + }, + { + "bbox": [ + 304, + 254, + 545, + 408 + ], + "type": "inline_equation", + "content": "4.8\\%" + }, + { + "bbox": [ + 304, + 254, + 545, + 408 + ], + "type": "text", + "content": " on CIFAR-10, " + }, + { + "bbox": [ + 304, + 254, + 545, + 408 + ], + "type": "inline_equation", + "content": "2.3\\%" + }, + { + "bbox": [ + 304, + 254, + 545, + 408 + ], + "type": "text", + "content": " on CIFAR-100, and " + }, + { + "bbox": [ + 304, + 254, + 545, + 408 + ], + "type": "inline_equation", + "content": "6.4\\%" + }, + { + "bbox": [ + 304, + 254, + 545, + 408 + ], + "type": "text", + "content": " on ImageNet-100 for 'All' classes, and by " + }, + { + "bbox": [ + 304, + 254, + 545, + 408 + ], + "type": "inline_equation", + "content": "8.7\\%" + }, + { + "bbox": [ + 304, + 254, + 545, + 408 + ], + "type": "text", + "content": " on CIFAR-10, " + }, + { + "bbox": [ + 304, + 254, + 545, + 408 + ], + "type": "inline_equation", + "content": "3.7\\%" + }, + { + "bbox": [ + 304, + 254, + 545, + 408 + ], + "type": "text", + "content": " on CIFAR-100, and " + }, + { + "bbox": [ + 304, + 254, + 545, + 408 + ], + "type": "inline_equation", + "content": "9.9\\%" + }, + { + "bbox": [ + 304, + 254, + 545, + 408 + ], + "type": "text", + "content": " on ImageNet-100 for 'Unseen' classes. These results experimentally demonstrate the generated dynamic conceptions provide effective supervision to learn better representations for unlabeled data. Moreover, " + }, + { + "bbox": [ + 304, + 254, + 545, + 408 + ], + "type": "inline_equation", + "content": "\\mathrm{UNO + }" + }, + { + "bbox": [ + 304, + 254, + 545, + 408 + ], + "type": "text", + "content": " shows a strong accuracy on \"Old\" classes, but its accuracy when testing on \"New\" classes is relatively lower. This is because " + }, + { + "bbox": [ + 304, + 254, + 545, + 408 + ], + "type": "inline_equation", + "content": "\\mathrm{UNO + }" + }, + { + "bbox": [ + 304, + 254, + 545, + 408 + ], + "type": "text", + "content": " trains the linear classifier on \"Old\" classes, thus resulting in an inevitable bias. On the contrary, our DCCL gets a relatively good balance on both the \"Old\" and \"Unseen\" classes, without bias to the labeled data." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 411, + 545, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 411, + 545, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 411, + 545, + 604 + ], + "type": "text", + "content": "Comparison on Fine-Grained Datasets. In general, the differences between different classes in fine-grained datasets are subtle, which leads the fine-grained visual understanding to be more challenging for GCD. For verifying the effects of DCCL on fine-grained tasks, we compare our method with others on fine-grained image recognition datasets. The results in Tab. 3 show that DCCL consistently outperforms all other methods for \"All\" and \"New\" classes. Specifically, on CUB-200 and Oxford-Pet, DCCL achieves " + }, + { + "bbox": [ + 304, + 411, + 545, + 604 + ], + "type": "inline_equation", + "content": "12.2\\%" + }, + { + "bbox": [ + 304, + 411, + 545, + 604 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 411, + 545, + 604 + ], + "type": "inline_equation", + "content": "7.9\\%" + }, + { + "bbox": [ + 304, + 411, + 545, + 604 + ], + "type": "text", + "content": " improvement over the state-of-the-art for \"All\" classes. Especially for \"New\" classes, DCCL outperforms GCD by " + }, + { + "bbox": [ + 304, + 411, + 545, + 604 + ], + "type": "inline_equation", + "content": "16.2\\%" + }, + { + "bbox": [ + 304, + 411, + 545, + 604 + ], + "type": "text", + "content": " on the CUB-200 dataset. These results demonstrate that our DCCL is efficient in capturing the conceptual information shared across different fine-grained classes, thereby generating precise and helpful supervision for representation learning." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "Visualization of Feature Distributions. To qualitatively explore the clustered features on Pets dataset [24], we visualize the t-SNE embeddings projected from the features extracted by pre-trained ViT [4], GCD [35], the DCCL without the proposed dispersion loss and our full DCCL method. As shown in Fig. 3, our features are more discriminative than the features from the pre-trained ViT and GCD. By comparing Fig. 3(c) and Fig. 3(d), the proposed dispersion loss effectively pushes cluster centers away from" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "7584" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 55, + 72, + 160, + 151 + ], + "blocks": [ + { + "bbox": [ + 55, + 72, + 160, + 151 + ], + "lines": [ + { + "bbox": [ + 55, + 72, + 160, + 151 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 160, + 151 + ], + "type": "image", + "image_path": "4567f3afdefab37e162b27a170ba870da9f1d3cc929cd46b6ac3dd3fe3d1be8a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 88, + 154, + 121, + 163 + ], + "lines": [ + { + "bbox": [ + 88, + 154, + 121, + 163 + ], + "spans": [ + { + "bbox": [ + 88, + 154, + 121, + 163 + ], + "type": "text", + "content": "(a) DINO" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 161, + 72, + 261, + 151 + ], + "blocks": [ + { + "bbox": [ + 161, + 72, + 261, + 151 + ], + "lines": [ + { + "bbox": [ + 161, + 72, + 261, + 151 + ], + "spans": [ + { + "bbox": [ + 161, + 72, + 261, + 151 + ], + "type": "image", + "image_path": "d77f6169ef2e6e0faa5f854e06eb81b90e94ac7586d51127b15e7318e6ebb98a.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 190, + 154, + 221, + 163 + ], + "lines": [ + { + "bbox": [ + 190, + 154, + 221, + 163 + ], + "spans": [ + { + "bbox": [ + 190, + 154, + 221, + 163 + ], + "type": "text", + "content": "(b) GCD" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 263, + 72, + 375, + 151 + ], + "blocks": [ + { + "bbox": [ + 263, + 72, + 375, + 151 + ], + "lines": [ + { + "bbox": [ + 263, + 72, + 375, + 151 + ], + "spans": [ + { + "bbox": [ + 263, + 72, + 375, + 151 + ], + "type": "image", + "image_path": "3d98b8061f91a20b8e6f80820053dc8464f7f769cebf95fc4b50617b9c900b44.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 276, + 153, + 350, + 163 + ], + "lines": [ + { + "bbox": [ + 276, + 153, + 350, + 163 + ], + "spans": [ + { + "bbox": [ + 276, + 153, + 350, + 163 + ], + "type": "text", + "content": "(c) DCCL without " + }, + { + "bbox": [ + 276, + 153, + 350, + 163 + ], + "type": "inline_equation", + "content": "\\mathcal{L}^D" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 378, + 70, + 539, + 151 + ], + "blocks": [ + { + "bbox": [ + 378, + 70, + 539, + 151 + ], + "lines": [ + { + "bbox": [ + 378, + 70, + 539, + 151 + ], + "spans": [ + { + "bbox": [ + 378, + 70, + 539, + 151 + ], + "type": "image", + "image_path": "3ad7218fd449650f66f514c33fe362170d3f029912b1fc4b922bd380a8e3a8ac.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 399, + 154, + 434, + 163 + ], + "lines": [ + { + "bbox": [ + 399, + 154, + 434, + 163 + ], + "spans": [ + { + "bbox": [ + 399, + 154, + 434, + 163 + ], + "type": "text", + "content": "(d) DCCL" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 474, + 154, + 538, + 163 + ], + "lines": [ + { + "bbox": [ + 474, + 154, + 538, + 163 + ], + "spans": [ + { + "bbox": [ + 474, + 154, + 538, + 163 + ], + "type": "text", + "content": "(e) False Examples" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 50, + 231, + 287, + 308 + ], + "blocks": [ + { + "bbox": [ + 47, + 196, + 287, + 229 + ], + "lines": [ + { + "bbox": [ + 47, + 196, + 287, + 229 + ], + "spans": [ + { + "bbox": [ + 47, + 196, + 287, + 229 + ], + "type": "text", + "content": "Table 4. Effectiveness of each component of our DCCL. \"MU\" and \"CC\" denote the proposed momentum update by Eq. (8) and the conception consolidation proposed in Sec. 3.3, respectively." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 231, + 287, + 308 + ], + "lines": [ + { + "bbox": [ + 50, + 231, + 287, + 308 + ], + "spans": [ + { + "bbox": [ + 50, + 231, + 287, + 308 + ], + "type": "table", + "html": "
IndexComponentCUB-200 [36]Pet [24]
\\( \\mathcal{L}^I \\)\\( \\mathcal{L}^C \\)\\( \\mathcal{L}^D \\)MUCCAllOldNewAllOldNew
a)✓51.356.648.780.285.177.6
b)✓54.952.355.481.680.781.0
c)✓✓57.754.058.183.581.180.3
d)✓✓✓59.553.360.884.383.184.5
e)✓✓✓✓60.159.460.785.886.884.6
f)✓✓✓✓✓63.560.864.988.188.288.0
", + "image_path": "4d6dfd15659dab0619ec4a4ae152c80168646fbd98e41c9665522619bd473f2a.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 323, + 287, + 358 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 323, + 287, + 358 + ], + "spans": [ + { + "bbox": [ + 46, + 323, + 287, + 358 + ], + "type": "text", + "content": "each other. A large inter-cluster margin not only improves cluster boundaries for \"Old\" and \"New\" categories, but also compacts intra-cluster distribution." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 360, + 287, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 360, + 287, + 443 + ], + "spans": [ + { + "bbox": [ + 46, + 360, + 287, + 443 + ], + "type": "text", + "content": "Summary. The experimental results show that our DCCL achieves significant improvements on both generic and fine-grained datasets. Especially for discovering \"New\" categories in challenging fine-grained tasks, our dynamic conceptual contrastive learning succeeds in mining shared conceptions, which is especially beneficial for the generalized fine-grained new category discovery." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 453, + 185, + 465 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 453, + 185, + 465 + ], + "spans": [ + { + "bbox": [ + 47, + 453, + 185, + 465 + ], + "type": "text", + "content": "4.3. Effectiveness Evaluation" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 472, + 287, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 472, + 287, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 472, + 287, + 533 + ], + "type": "text", + "content": "To verify the effectiveness of each component in our DCCL, we conduct five experiments on both CUB-200 [36] and Pet [24] datasets, as shown in Tab. 4. Note that the configuration of the experiment a) is the same with GCD [35], which is the baseline method in our experiments." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 533, + 287, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 287, + 593 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 287, + 593 + ], + "type": "text", + "content": "Effectiveness of Conceptional contrastive Learning. Based on the results of the experiment a) and b), we find that using only the conceptual contrastive learning can achieve competitive performance, compared to baseline method with only instance-level contrastive learning." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "text", + "content": "Effectiveness of Conception-Level Momentum Updating. Comparing the experiment b) and c), we can find that consistent update of conceptual representations by the proposed momentum update can bring considerable improvements on both new and old classes. This implies that due to periodically generating conceptual representations, the conceptual labels are kept fixed within one training period, which leads to a severe sub-optimal problem, during conceptual contrastive learning. Thus, the proposed momentum update mitigates the problem to some extent." + } + ] + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 309, + 198, + 426, + 277 + ], + "blocks": [ + { + "bbox": [ + 46, + 164, + 545, + 187 + ], + "lines": [ + { + "bbox": [ + 46, + 164, + 545, + 187 + ], + "spans": [ + { + "bbox": [ + 46, + 164, + 545, + 187 + ], + "type": "text", + "content": "Figure 3. Visualization of features distributions of the unlabeled set of the Pet [24] dataset. (a)-(d) are the results generated from DINO [4], GCD [35], our DCCL without " + }, + { + "bbox": [ + 46, + 164, + 545, + 187 + ], + "type": "inline_equation", + "content": "\\mathcal{L}^D" + }, + { + "bbox": [ + 46, + 164, + 545, + 187 + ], + "type": "text", + "content": " and full DCCL, in turn. (e) is a visualization of false samples that are easy to be incorrectly clustered." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 309, + 198, + 426, + 277 + ], + "lines": [ + { + "bbox": [ + 309, + 198, + 426, + 277 + ], + "spans": [ + { + "bbox": [ + 309, + 198, + 426, + 277 + ], + "type": "image", + "image_path": "17e7c9b9aa3f880318a8626fb573feef0fc574f6251f68ad5ee64347828f7124.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + } + ], + "index": 18 + }, + { + "type": "image", + "bbox": [ + 309, + 278, + 426, + 357 + ], + "blocks": [ + { + "bbox": [ + 309, + 278, + 426, + 357 + ], + "lines": [ + { + "bbox": [ + 309, + 278, + 426, + 357 + ], + "spans": [ + { + "bbox": [ + 309, + 278, + 426, + 357 + ], + "type": "image", + "image_path": "95797e8f58b53b909892e359a3094592239b0b17d379945b87f1dc9341666d8b.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 360, + 545, + 382 + ], + "lines": [ + { + "bbox": [ + 306, + 360, + 545, + 382 + ], + "spans": [ + { + "bbox": [ + 306, + 360, + 545, + 382 + ], + "type": "text", + "content": "Figure 4. Impact of hyper-parameters. The clustering accuracy on \"All\" categories is reported." + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + } + ], + "index": 19 + }, + { + "type": "image", + "bbox": [ + 427, + 199, + 545, + 278 + ], + "blocks": [ + { + "bbox": [ + 427, + 199, + 545, + 278 + ], + "lines": [ + { + "bbox": [ + 427, + 199, + 545, + 278 + ], + "spans": [ + { + "bbox": [ + 427, + 199, + 545, + 278 + ], + "type": "image", + "image_path": "5b424a67fd25aa0010f1854957a9e4098f0209ce6e2f60e73620765304874c72.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_body" + } + ], + "index": 20 + }, + { + "type": "image", + "bbox": [ + 428, + 279, + 545, + 357 + ], + "blocks": [ + { + "bbox": [ + 428, + 279, + 545, + 357 + ], + "lines": [ + { + "bbox": [ + 428, + 279, + 545, + 357 + ], + "spans": [ + { + "bbox": [ + 428, + 279, + 545, + 357 + ], + "type": "image", + "image_path": "05f9656d48fc088005bc36d41aa4cd1b4a8a8eb536915ea4eab045b2ed9e51e1.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 384, + 545, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 384, + 545, + 445 + ], + "spans": [ + { + "bbox": [ + 305, + 384, + 545, + 445 + ], + "type": "text", + "content": "Effectiveness of Dispersion Loss. The experiment d) in Tab. 4 shows that by adding the proposed dispersion loss, the model's performances on new classes acquire further improvements by " + }, + { + "bbox": [ + 305, + 384, + 545, + 445 + ], + "type": "inline_equation", + "content": "2.7\\%" + }, + { + "bbox": [ + 305, + 384, + 545, + 445 + ], + "type": "text", + "content": " on \"New\" classes for the CUB-200 dataset. The improvements can be observed in Fig. 3(d)." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 305, + 445, + 545, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 445, + 545, + 564 + ], + "spans": [ + { + "bbox": [ + 305, + 445, + 545, + 564 + ], + "type": "text", + "content": "Effectiveness of Conception Consolidation. Without the proposed conception consolidation that considers labeled information to impose semi-supervised constraintsd, our DCCL suffers from a performance balance between the new and the old classes, as shown in Tab. 4 b), c) and d). In the experiment e) and f), our full method shows superior performance on all evaluation metrics, which experimentally demonstrates that our conception consolidation plays an essential role in rectifying the estimated latent conception relations between seen and unseen classes." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 306, + 574, + 456, + 587 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 574, + 456, + 587 + ], + "spans": [ + { + "bbox": [ + 306, + 574, + 456, + 587 + ], + "type": "text", + "content": "4.4. Hyper-Parameter Analyses" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 305, + 593, + 545, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 593, + 545, + 641 + ], + "spans": [ + { + "bbox": [ + 305, + 593, + 545, + 641 + ], + "type": "text", + "content": "In this section, we discuss the impact of the hyperparameters in our DCCL, including loss weights " + }, + { + "bbox": [ + 305, + 593, + 545, + 641 + ], + "type": "inline_equation", + "content": "(\\alpha" + }, + { + "bbox": [ + 305, + 593, + 545, + 641 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 593, + 545, + 641 + ], + "type": "inline_equation", + "content": "\\beta)" + }, + { + "bbox": [ + 305, + 593, + 545, + 641 + ], + "type": "text", + "content": ", the threshold parameter of dispersion loss " + }, + { + "bbox": [ + 305, + 593, + 545, + 641 + ], + "type": "inline_equation", + "content": "(\\tau^{M})" + }, + { + "bbox": [ + 305, + 593, + 545, + 641 + ], + "type": "text", + "content": ", momentum updating factor " + }, + { + "bbox": [ + 305, + 593, + 545, + 641 + ], + "type": "inline_equation", + "content": "(\\eta)" + }, + { + "bbox": [ + 305, + 593, + 545, + 641 + ], + "type": "text", + "content": ", and the frequency of DCG " + }, + { + "bbox": [ + 305, + 593, + 545, + 641 + ], + "type": "inline_equation", + "content": "(\\tau^{I})" + }, + { + "bbox": [ + 305, + 593, + 545, + 641 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 305, + 642, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 642, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 642, + 545, + 713 + ], + "type": "text", + "content": "Impact of loss weights and threshold parameters. For the evaluation of loss weights, we use the hold-off validation data to determine their values. Specifically, we first select the optimal " + }, + { + "bbox": [ + 305, + 642, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 305, + 642, + 545, + 713 + ], + "type": "text", + "content": " to achieve the best accuracy on the \"All\" score, then we find the optimal " + }, + { + "bbox": [ + 305, + 642, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 305, + 642, + 545, + 713 + ], + "type": "text", + "content": " based on the selected " + }, + { + "bbox": [ + 305, + 642, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 305, + 642, + 545, + 713 + ], + "type": "text", + "content": ". The impact of different values is shown in Fig. 4 (a)-(c)." + } + ] + } + ], + "index": 27 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7585" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 72, + 176, + 145 + ], + "blocks": [ + { + "bbox": [ + 50, + 72, + 176, + 145 + ], + "lines": [ + { + "bbox": [ + 50, + 72, + 176, + 145 + ], + "spans": [ + { + "bbox": [ + 50, + 72, + 176, + 145 + ], + "type": "image", + "image_path": "03a89caf92896da1c600a3aecd2d4b807675b83356498543c9d7be4e07039574.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 116, + 146, + 127, + 156 + ], + "lines": [ + { + "bbox": [ + 116, + 146, + 127, + 156 + ], + "spans": [ + { + "bbox": [ + 116, + 146, + 127, + 156 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 176, + 72, + 286, + 145 + ], + "blocks": [ + { + "bbox": [ + 176, + 72, + 286, + 145 + ], + "lines": [ + { + "bbox": [ + 176, + 72, + 286, + 145 + ], + "spans": [ + { + "bbox": [ + 176, + 72, + 286, + 145 + ], + "type": "image", + "image_path": "2e369cfc5b95365d98be96fed357411ee6c3f700c32ee3fca9ac018841043b2e.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 49, + 157, + 286, + 266 + ], + "blocks": [ + { + "bbox": [ + 233, + 146, + 245, + 156 + ], + "lines": [ + { + "bbox": [ + 233, + 146, + 245, + 156 + ], + "spans": [ + { + "bbox": [ + 233, + 146, + 245, + 156 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 49, + 157, + 286, + 266 + ], + "lines": [ + { + "bbox": [ + 49, + 157, + 286, + 266 + ], + "spans": [ + { + "bbox": [ + 49, + 157, + 286, + 266 + ], + "type": "image", + "image_path": "19affb57099820e1aaa7e1d71f312e508fa9a967e4f3c8af1bc058f5331c837c.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 271, + 288, + 338 + ], + "lines": [ + { + "bbox": [ + 46, + 271, + 288, + 338 + ], + "spans": [ + { + "bbox": [ + 46, + 271, + 288, + 338 + ], + "type": "text", + "content": "Figure 5. (a) visualizes the dynamics of DCG, which implies that our DCG adaptively estimates conceptual representation for different training stages. (b) illustrates the trend of performances on the CIFAR100 dataset, with varying the number of unlabeled classes. (c) is the comparison between the real number of classes in datasets and the estimated number of conceptions." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 350, + 287, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 350, + 287, + 384 + ], + "spans": [ + { + "bbox": [ + 46, + 350, + 287, + 384 + ], + "type": "text", + "content": "Similarly, we choose the best " + }, + { + "bbox": [ + 46, + 350, + 287, + 384 + ], + "type": "inline_equation", + "content": "\\tau^M" + }, + { + "bbox": [ + 46, + 350, + 287, + 384 + ], + "type": "text", + "content": " with the selected " + }, + { + "bbox": [ + 46, + 350, + 287, + 384 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 350, + 287, + 384 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 350, + 287, + 384 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 350, + 287, + 384 + ], + "type": "text", + "content": ". Finally, our final model is obtained by using " + }, + { + "bbox": [ + 46, + 350, + 287, + 384 + ], + "type": "inline_equation", + "content": "\\alpha = 0.3" + }, + { + "bbox": [ + 46, + 350, + 287, + 384 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 350, + 287, + 384 + ], + "type": "inline_equation", + "content": "\\beta = 0.1" + }, + { + "bbox": [ + 46, + 350, + 287, + 384 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 350, + 287, + 384 + ], + "type": "inline_equation", + "content": "\\tau^M = 0.3" + }, + { + "bbox": [ + 46, + 350, + 287, + 384 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 386, + 288, + 447 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 386, + 288, + 447 + ], + "spans": [ + { + "bbox": [ + 46, + 386, + 288, + 447 + ], + "type": "text", + "content": "Impact of Update Rates. The impact of updating factor of CMB is illustrated in in Fig. 4 (d). The more smooth running average can obtain better performance. Considering the balance between computational consumption and performance, we thus set " + }, + { + "bbox": [ + 46, + 386, + 288, + 447 + ], + "type": "inline_equation", + "content": "\\tau^I = 5" + }, + { + "bbox": [ + 46, + 386, + 288, + 447 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 386, + 288, + 447 + ], + "type": "inline_equation", + "content": "\\eta = 0.9" + }, + { + "bbox": [ + 46, + 386, + 288, + 447 + ], + "type": "text", + "content": " in all experiments." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 455, + 209, + 467 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 455, + 209, + 467 + ], + "spans": [ + { + "bbox": [ + 47, + 455, + 209, + 467 + ], + "type": "text", + "content": "4.5. Further Investigation of DCG" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 474, + 287, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 287, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 287, + 605 + ], + "type": "text", + "content": "To explore our dynamic conception generation (DCG), we conduct two group experiments and the experimental results are shown in Fig. 5 and Tab. 5. From the Fig. 5 (a) we find that in the initial training stage, our DCG tends to generate fewer conceptions than at the convergence stage. This is because in the beginning, the model could not understand fine-grained classes well. Thus, DCG generates coarse-grained supervision like super-class, which has a low risk to over-correct. Later, with the growth of feature discriminability, DCG builds elaborate conceptual relationships to further refine the learned representations." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 606, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 606, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 606, + 288, + 714 + ], + "type": "text", + "content": "From the Fig. 5 (c), we find that the number of conceptions estimated by DCCL is close to the ground truth of the number of classes in the corresponding dataset. However, it is worth noting that the conception representations in this paper are not equivalent to the cluster centers. The DCG aims to adaptively generate proper conceptual representations that are beneficial for contrastive learning, instead of predicting the real number of classes within a dataset. Furthermore, we try to directly replace our DGC with semi-" + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 335, + 83, + 515, + 198 + ], + "blocks": [ + { + "bbox": [ + 312, + 70, + 539, + 82 + ], + "lines": [ + { + "bbox": [ + 312, + 70, + 539, + 82 + ], + "spans": [ + { + "bbox": [ + 312, + 70, + 539, + 82 + ], + "type": "text", + "content": "Table 5. Comparison of different clustering methods for DCG." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 335, + 83, + 515, + 198 + ], + "lines": [ + { + "bbox": [ + 335, + 83, + 515, + 198 + ], + "spans": [ + { + "bbox": [ + 335, + 83, + 515, + 198 + ], + "type": "table", + "html": "
Clustering MethodCUB-200 [36]
AllOldNew
k-means [21]54.153.453.3
SSK [35]55.955.154.2
FINCH [29]55.856.155.4
DBSCAN [8]60.554.759.8
InfoMap [27]61.455.262.7
DCG (Ours)63.560.864.9
", + "image_path": "1200fc22c12d60556e0bfc10a2e0922edee6cc6d16598c8fb6e6a028ba94b519.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 211, + 545, + 246 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 211, + 545, + 246 + ], + "spans": [ + { + "bbox": [ + 304, + 211, + 545, + 246 + ], + "type": "text", + "content": "supervised " + }, + { + "bbox": [ + 304, + 211, + 545, + 246 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 211, + 545, + 246 + ], + "type": "text", + "content": "-means [35] (SSK) with the prior of known " + }, + { + "bbox": [ + 304, + 211, + 545, + 246 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 211, + 545, + 246 + ], + "type": "text", + "content": ". From the results in Tab. 5, SSK fails to generate effective latent conceptions, even leading to worse clustering." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 247, + 546, + 366 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 247, + 546, + 366 + ], + "spans": [ + { + "bbox": [ + 304, + 247, + 546, + 366 + ], + "type": "text", + "content": "Discussion. Based on the comparison in Fig. 5 (b), we notice that when training on generic datasets, our DCG tends to generate more conceptions than the actual number of dataset classes, while generating fewer conceptions on fine-grained datasets. A possible explanation is that due to large inter-class differences in generic datasets, learning more sub-classes conceptions enables models to gain discriminability. Similarly, since fine-grained classes share more common attributes or conceptions, such super-class information can significantly benefit fine-grained GCD." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 375, + 520, + 388 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 375, + 520, + 388 + ], + "spans": [ + { + "bbox": [ + 305, + 375, + 520, + 388 + ], + "type": "text", + "content": "4.6. Evaluation with Different Split Protocols" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 393, + 545, + 478 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 393, + 545, + 478 + ], + "spans": [ + { + "bbox": [ + 304, + 393, + 545, + 478 + ], + "type": "text", + "content": "To explore the effects of DCCL under strict annotation limitation, we propose to test models on varying splits of CIFAR100 [17]. We visualize the accuracy of \"All\" classes in Fig. 5 (b), which indicates that our DCCL has stronger robustness when only a few labeled classes are available. Meanwhile, with the growth of the number of unlabeled classes, GCD expresses a severe performance degradation." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 489, + 378, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 489, + 378, + 502 + ], + "spans": [ + { + "bbox": [ + 306, + 489, + 378, + 502 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 510, + 546, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 546, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 546, + 676 + ], + "type": "text", + "content": "In this paper, we propose to cope with the generalized category discovery (GCD) from the perspective of mining underlying relationships between known and unknown categories. To implement this idea, we propose a dynamic conceptual contrastive learning framework to alternately explore latent conceptual relationships and perform conceptual contrastive learning. This mechanism enables models to learn more discriminable representations. Furthermore, to mitigate the inconsistency of updating conception representations during the training process, we propose a conception-level momentum update to facilitate the model toward better optimization. Extensive experimental results show that our DCCL achieves a new state-of-the-art performance on GCD tasks." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgement This work has been supported by the EU H2020 project AI4Media (No. 951911) and by the PRIN project CREATIVE (Prot. 2020ZSL9F9)." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7586" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 19, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "text", + "content": "[1] Sugato Basu, Arindam Banerjee, and Raymond J. 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Recently, masked attention [8] is proposed to restrict each query to only attend to the foreground regions predicted by the preceding decoder block for easier optimization. Although promising, it relies on the learnable parameterized positional queries which tend to encode the dataset statistics, leading to inaccurate localization for distinct individual queries. In this paper, we propose a simple yet effective query design for semantic segmentation termed Dynamic Focus-aware Positional Queries (DFPQ), which dynamically generates positional queries conditioned on the cross-attention scores from the preceding decoder block and the positional encodings for the corresponding image features, simultaneously. Therefore, our DFPQ preserves rich localization information for the target segments and provides accurate and fine-grained positional priors. In addition, we propose to efficiently deal with high-resolution cross-attention by only aggregating the contextual tokens based on the low-resolution cross-attention scores to perform local relation aggregation. Extensive experiments on ADE20K and Cityscapes show that with the two modifications on Mask2former, our framework achieves SOTA performance and outperforms Mask2former by clear margins of $1.1\\%$ , $1.9\\%$ , and $1.1\\%$ single-scale mIoU with ResNet-50, Swin-T, and Swin-B backbones on the ADE20K validation set, respectively. Source code is available at https://github.com/ziplab/FASeg.", + "bbox": [ + 76, + 313, + 472, + 751 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 777, + 209, + 792 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Semantic segmentation aims at assigning each pixel in an image with a semantic class label. As the end-to-end Detection Transformer (DETR) [3,42,49,58] is revolutionizing the paradigm of the object detection task, recent segmentors [2,8,9,54] follow DETR to learn a set of queries repre", + "bbox": [ + 75, + 803, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "senting the class prototypes or target segments and achieve state-of-the-art performance on semantic segmentation.", + "bbox": [ + 500, + 282, + 890, + 313 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In DETR-like frameworks, providing the queries with meaningful positional priors and encourage each query to concentrate on specific regions is essential to learn representative queries [28, 43, 49, 58]. In this spirit, masked attention [8] is proposed, which restricts each query to only attend to a foreground region predicted by the previous decoder block with binary masks. Although promising, the positional priors in masked attention may be inaccurate and deteriorate performance for two reasons. First, each query comprises a content query that contains semantic information and a positional query that provides positional information for the likely locations of the target segments. However, masked attention still relies on positional queries that are randomly initialized learnable parameters [3, 40] (Figure 1 (a)), which tend to encode the average statistics across the dataset and cannot reflect the segments with large location variances. Second, since each query only attends to the predicted foreground regions, inaccurate predictions lead to error accumulation across the decoder blocks, especially during an early training stage.", + "bbox": [ + 496, + 316, + 892, + 619 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To this end, recent detectors propose to dynamically encode the anchor points into the positional queries to guide queries concentrating around the anchor positions [28, 30, 43] (Figure 1 (b)). The anchor-based query design mitigates the mentioned issues as the positional queries are dynamically generated for each target object, thus providing more accurate positional priors. In addition, it avoids restricting the queries to only attend to the foreground regions with binary masks to mitigate the error accumulation issue. However, the anchor-based queries cannot describe the fine-grained positional priors for semantic segmentation, which has details, edges, and boundaries [5, 6].", + "bbox": [ + 496, + 625, + 893, + 805 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Motivated by the observations that attention scores imply the salient regions for token pruning [24, 26], self-supervised learning [4], and semantic segmentation [34,56], in this paper, we propose a simple yet effective query design for semantic segmentation, dubbed Dynamic Focus-aware Positional Queries (DFPQ), which dynamically generates", + "bbox": [ + 496, + 810, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "†Corresponding author. E-mail: bohan.zhuang@gmail.com", + "bbox": [ + 94, + 886, + 419, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "11299", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/7a070ea939ca957a32e48bf79f5c2fa8bb15c0e2cfbc0466f930038ad8de672c.jpg", + "image_caption": [ + "Figure 1. (a) The original randomly initialized positional queries [3] as learnable network parameters, where the positional queries are shared among the Transformer decoder blocks and tend to encode dataset statistics modelling the likely positions for the semantic regions, which leads to inaccurate localization. (b) The anchor-based positional queries [43] are conditional on the bounding box coordinates to give each query positional priors around the anchor. However, the anchor points cannot describe semantic regions, thus still sub-optimal for semantic segmentation. (c) Our dynamic focus-aware queries for semantic segmentation are dynamically generated from the cross-attention scores of the preceding decoder block to provide accurate and fine-grained positional priors, facilitating locating and refining the target segments progressively." + ], + "image_footnote": [], + "bbox": [ + 86, + 89, + 370, + 227 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/0c68d443e4abcba8d3329900f0549ac73c1be31aa4d7ba44c106755857c94a85.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 375, + 88, + 638, + 227 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/71ca13a8e82ab46be2918b56cfa27a40b859eac058d76c6be962badb60f75baa.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 640, + 88, + 888, + 227 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "the positional queries conditioned on the cross-attention scores of the preceding decoder block and the positional encodings for the corresponding image features, simultaneously (Figure 1 (c)). In this way, our DFPQ preserves the localization information of the target segments, thereby providing accurate and fine-grained positional priors and facilitating progressively locating and refining the target segments. When implementing the positional encodings with more powerful ones like [10], our DFPQ is further empowered with higher capacity to encode the neighbourhood information for the target segments. Compared to the anchor-based positional queries [28,43], our DFPQ can cover fine-grained locations for the segmentation details, edges, and boundaries which include rich segmentation cues.", + "bbox": [ + 75, + 354, + 467, + 564 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In addition, we propose an efficient method named High-Resolution Cross-Attention (HRCA) to mine details for segmenting small regions from the high-resolution feature maps $(1/4 \\times 1/4$ of the original image size). Considering performing cross-attention on high-resolution feature maps requires a formidable amount of memory footprints and computational complexity, e.g., 11G extra floating-point operations with an input resolution of $512 \\times 512$ , we propose to encode token affinity only on the informative areas of high-resolution feature maps that are indicated important in the low-resolution counterparts. In this way, fine-grained details are learned efficiently with affordable memory and computations.", + "bbox": [ + 75, + 565, + 467, + 760 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our main contributions can be summarized as follows:", + "bbox": [ + 96, + 761, + 457, + 775 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We make the pioneering attempt to present a simple yet effective query formulation for semantic segmentation, which provides accurate and fine-grained positional priors to localize the target segments, and mitigates the error accumulation problem while being lightweight with little extra computation.", + "- We propose an efficient high-resolution cross-attention layer to enrich the segmentation details, which dis" + ], + "bbox": [ + 94, + 777, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "cards the semantically unimportant regions for any target segments in the high-resolution feature maps with affordable memory footprint and computational cost.", + "bbox": [ + 529, + 354, + 890, + 398 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- Extensive experiments on ADE20K and Cityscapes datasets demonstrate that simply incorporating our DFPQ and HRCA into Mask2former [8] achieves significant performance gain and outperforms the SOTA methods. For instance, our FASeg outperforms SOTA methods by $1.1\\%$ , $1.3\\%$ , and $0.9\\%$ single-scale mIoU on the ADE20K [57] validation set with ResNet-50, Swin-T, and Swin-B backbones, respectively.", + "bbox": [ + 517, + 402, + 890, + 523 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 534, + 638, + 549 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Semantic segmentation with Transformers. The recent segmentors with Transformers [25, 36, 50, 54] have pushed the horizon for semantic segmentation. In general, these segmentors consist of three modules: a backbone, a neck, and a head. Correspondingly, the recent advances can be roughly split into three orthogonal categories. The first category [14, 46, 48, 50, 52, 53] aims at learning more representative features by improving the backbone, mostly by improving the self-attention mechanism in Transformers. For example, focal self-attention [48] combines both fine-grained and coarse-grained features in a backbone self-attention layer. To provide better multi-scale features with neck, the second category [22, 23, 34, 34, 45] improves the feature pyramid network (FPN) [27] or pyramid scene parsing (PSP) [55] structure. For instance, SegFormer [45] simplifies FPN under the Transformer backbone to achieve a better accuracy-efficiency trade-off, and SegDeformer [34] adds external memory tokens to preserve the global information. The third category implements the head with Transformer and conduct set prediction following the DETR-like end-to-end framework [3]. In DETR-like framework, target segments are represented by a set of queries. Considering the importance of providing positional priors for", + "bbox": [ + 496, + 553, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "11300", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "the queries [28, 30, 43], masked attention [8] is proposed to restrict the cross-attention only to the local features. Our work also aims at providing better positional priors. In contrast to [8], we follow the recent detectors [28, 43] to provide accurate positional priors with dynamic positional queries rather than the learnable parameterized positional queries [3]. Differently, our DFPQ provides fine-grained positional priors that can cover the locations for fine segmentation details, edges, and boundaries. Very recent work [25] proposes a versatile multi-task head structure to share the mutual information among the segmentation and detection tasks, which however, is not directly comparable to our work.", + "bbox": [ + 75, + 90, + 472, + 286 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Positional encodings for Transformers. Both self-attention and cross-attention for Transformers are permutation-equivalent. Therefore, Positional Encodings (PE) play an essential role in introducing the order of the sequence. In general, the positional encodings include: absolute PE that is generated with sinusoidal functions [35, 40] or being entirely learnable parameters [19, 29]; relative PE that encodes distances between the input tokens [12, 32]; and conditional PE, which is dynamically generated, e.g., PEG [10] generates positional encodings with depth-wise convolution conditioned on the local neighbourhood information. In the same spirit, our DFPQ is also dynamically generated by exploring the idea of conditional encoding [38, 47], thus delivering higher segmentation accuracy. Differently, our DFPQ is tailored specifically for DETR-style semantic segmentation to learn positional priors for each target segment. In addition, since our DFPQ is conditional on the PE for the image features, implementing it with the more powerful PEs [10, 19] can further boost the representational capability of our DFPQ. We investigate the effect of different PE strategies in Section 4.2.", + "bbox": [ + 75, + 287, + 472, + 618 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "When solely pre-training Transformer backbones, the positional encodings are generally seen as a part of the feature embeddings and directly be combined with patch features after patchifying the image [15,39]. Differently, in the cross-attention layers of DETR-like frameworks, both the image features and the object queries require additional positional information to provide positional priors for aggregating the query-specific context, which we refer the readers to Section 3.1 for details. Recent detectors [28,43] encode anchor positions into positional queries. In contrast, we design a novel positional query formulation for semantic segmentation to reflect regions of interest instead of anchor points to preserve fine segmentation details.", + "bbox": [ + 75, + 619, + 472, + 816 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 821, + 169, + 837 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminary: Cross-attention in DETR", + "text_level": 1, + "bbox": [ + 76, + 847, + 410, + 863 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Before introducing our DFPQ, we first revisit the cross-attention layers in DETR-like frameworks [3]. Cross", + "bbox": [ + 76, + 869, + 468, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "attention layer is a basic module that updates the object queries by aggregating the image context. Since the cross-attention layer is permutation-invariant, both queries and keys require positional information, which introduces the order and provides positional priors to encourage high attention scores for positionally important regions. Specifically, with $N$ , $D$ , $H$ and $W$ respectively denoting the number of queries, the hidden dimensions, the height, and the width of the image features, we have the image features $\\pmb{K}_c$ and their positional encodings $\\pmb{K}_p$ and get keys $\\pmb{K} = \\pmb{K}_c + \\pmb{K}_p$ , where $\\pmb{K} \\in \\mathbb{R}^{HW \\times D}$ . We also have the object queries $\\pmb{Q} \\in \\mathbb{R}^{N \\times D}$ , where each query consists of a content query $\\pmb{Q}_c$ and a positional query $\\pmb{Q}_p$ .", + "bbox": [ + 496, + 90, + 890, + 287 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Then, the cross-attention operation can be formulated as", + "bbox": [ + 517, + 287, + 890, + 301 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {C r s - A t t e n t i o n} (\\boldsymbol {Q}, \\boldsymbol {K}, \\boldsymbol {V}) = \\operatorname {s o f t m a x} \\left(\\frac {\\boldsymbol {Q} \\boldsymbol {K} ^ {T}}{\\sqrt {D}}\\right) \\boldsymbol {V}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 509, + 321, + 890, + 364 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{V} \\in \\mathbb{R}^{HW \\times D}$ is also the image features in the DETR-like frameworks [3,9,54] and we omit all the linear projections and bias terms for simplicity. From Eq. (1), we can interpret the cross-attention as aggregating image context based on the dot-product similarity between $Q$ and $K$ . Since both the content parts and the positional parts for $Q$ and $K$ contribute to calculating the attention scores, similarities for both parts are considered. Therefore, content similarity contributes to mining the correlation between the object queries and the image features, while positional similarity provides positional priors for each target segment.", + "bbox": [ + 496, + 369, + 890, + 537 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Dynamic Focus-aware Positional Queries", + "text_level": 1, + "bbox": [ + 500, + 545, + 851, + 561 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this work, we aim to develop positional queries that provide effective positional priors under DETR-like frameworks for semantic segmentation. We argue that generating positional queries conditioned on cross-attention scores has three good properties. First, the cross-attention scores indicate the areas with rich context and may directly reflect the localization information for the target segments [4, 56]. Therefore, when stacking several decoder blocks with cross-attention layers in DETR-like frameworks, the localization information in the preceding block is helpful for progressively locating the target segments in the later blocks, especially when the blocks handle features at different scales [8, 23]. Second, cross-attention scores are dynamically generated. In contrast to the content-agnostic positional queries as learnable parameters in [3], which tend to encode statistics across the dataset and limit models' generalization capability, cross-attention scores are conditional on each target segment reflecting the specific contextual locations, thereby being more accurate. Finally, the cross-attention scores can cover fine-grained segmentation details, edges, and boundaries instead of encoding only a single center or anchor point alike [28, 43].", + "bbox": [ + 496, + 568, + 890, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "11301", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/9524ebe954325f01faa6b81ec81b4445197e664cd4c8e531560348aae0755ab6.jpg", + "image_caption": [ + "Figure 2. (a) Cross-attention with our dynamic focus-aware positional queries (DFPQ). \"pos\" is short for positional. We show generating DFPQ in the dashed box, where we multiply the positional encodings for the image features with the cross-attention scores of the preceding decoder block followed by a projection function $h$ to get DFPQ. Here we omit the bias terms for simplicity. (b) The overall framework for our FASeg is built upon Mask2former [8], which employs a Backbone to encode images, a Pixel Decoder to fuse the features under different resolutions, and a Transformer Decoder to learn the representation for each target segment. We first apply our DFPQ in each decoder block to provide more accurate positional priors (marked with blue arrows). Then, we further propose to incorporate our high-resolution cross-attention (HRCA) layers to model the cross-attention between the queries and the high-resolution feature maps (marked with red arrows). Here \"Top-k\" selects the top-k pixels indicated by the cross-attention scores of the previous Transformer decoder block." + ], + "image_footnote": [], + "bbox": [ + 86, + 88, + 459, + 314 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/bef652ff03ec48175ac721a89d41d77cc5fa7bcf52aa97c9619ff9f1eb32518a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 462, + 88, + 883, + 314 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Therefore, we propose to generate the positional queries conditional on the cross-attention scores of the preceding decoder block and the positional encodings for the corresponding image features, simultaneously, as shown in Figure 2 (a). Specifically, since the positional encodings $\\mathbf{K}_p$ for the image features preserve the positional information, we form our DFPQ by aggregating $\\mathbf{K}_p$ as indicated by the cross-attention scores $\\mathbf{A}$ in the cross-attention layer of the preceding decoder block, which can be formulated as", + "bbox": [ + 75, + 450, + 468, + 585 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {Q} _ {p} ^ {t} = h \\left(\\boldsymbol {A} ^ {t - 1} \\boldsymbol {K} _ {p} ^ {t - 1} + \\boldsymbol {B}\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 597, + 468, + 617 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $t$ is the index of the $t$ -th Transformer decoder block, $\\mathbf{A}^{t-1} \\in \\mathbb{R}^{N \\times HW}$ is the cross-attention scores from the $(t-1)$ -th Transformer decoder block, $\\mathbf{B} \\in \\mathbb{R}^{N \\times D}$ is learnable network parameters, and $h$ is a two-layered MLP with ReLU non-linearity in between. Note that the bias term $\\mathbf{B}$ is the original randomly initialized learnable positional queries, which we employ to stable the training in an early training stage. In this way, we dynamically generate DFPQ to provide positional priors for the target segments. It can also cover the fine-grained segmentation cues that are not restricted by anchor points.", + "bbox": [ + 75, + 628, + 468, + 792 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Note that as our DFPQ directly aggregates the positional information, implementing DFPQ with different $K_{p}$ leads to distinct behaviours. When implementing $K_{p}$ with the absolute sinusoidal function, the resulting DFPQ reflects an anchor point alike [28,43] instead of the target areas. In this case, we implement $K_{p}$ with conditional positional encodings [10] to further encode the neighbourhood information", + "bbox": [ + 75, + 795, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "and preserve the implicit positional priors for localizing the target segments. We empirically investigate the effect of different positional encodings in Section 4.2.", + "bbox": [ + 498, + 450, + 890, + 494 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Efficient High-resolution Cross-attention", + "text_level": 1, + "bbox": [ + 500, + 503, + 848, + 518 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As demonstrated by the prior arts [23, 38], high-resolution image features are important for segmenting small regions. However, modelling cross-attention between object queries and high-resolution image features requires an unbearable amount of memory footprints and computational cost. In this case, we propose an efficient High-Resolution Cross-Attention (HRCA) layer to mine details from high-resolution feature maps with affordable memory burden. Specifically, we first select the top-k pixels from the low-resolution image features with the highest cross-attention scores for all object queries. We then map these areas to the high-resolution feature map positions in a top-down manner and only perform cross-attention on these positions. Formally, we first get the low-resolution cross-attention scores $\\mathbf{A}_l$ , and then derive its high-resolution counterpart $\\mathbf{A}_h = f(\\mathbf{A}_l)$ with bilinear upsampling operation $f(\\cdot)$ . We next include the top-k pixels in $\\mathbf{A}_h$ with the highest scores into set $\\Omega$ , and the efficient HRCA can be formulated as", + "bbox": [ + 496, + 527, + 890, + 813 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {H R C A} (\\boldsymbol {Q}, \\boldsymbol {K}, \\boldsymbol {V}, \\Omega) = \\operatorname {s o f t m a x} \\left(\\frac {\\boldsymbol {Q} \\boldsymbol {K} ^ {\\prime T}}{\\sqrt {D}}\\right) \\boldsymbol {V} ^ {\\prime}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 820, + 890, + 861 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\pmb{K}^{\\prime} = g(\\pmb {K},\\Omega),\\pmb{V}^{\\prime} = g(\\pmb {V},\\Omega)$ and $g$ is the indexing operation. In this way, we only perform cross-attention", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "11302", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "on the informative areas for high-resolution feature maps, thereby saving considerable resource consumption.", + "bbox": [ + 75, + 90, + 467, + 119 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our HRCA is closely related to the previous sparse attention methods [1, 37, 41, 51] that only attend to a part of the entire sequence. Differently, our HRCA is specialized to the DETR-like frameworks, which determines the informative pixels based on their contribution to the target segments instead of the other pixels. One similar work to our HRCA is the RCDA module [43], which is a representative sparse cross-attention method that decouples cross-attention into a row-wise and column-wise attention to reduce the memory and computation cost. We include the comparison between our HRCA and RCDA [43] in Section 4.2.", + "bbox": [ + 75, + 121, + 467, + 286 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Focus-aware Segmentation Framework", + "text_level": 1, + "bbox": [ + 76, + 295, + 413, + 311 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We first briefly introduce Mask2former [8], which consists of backbone, neck, and head as introduced in Section 2 with the neck and head named \"Pixel Decoder\" and \"Transformer Decoder\", respectively. In Mask2former, Pixel Decoder fuses the features at multiple scales following [27,58]. Transformer Decoder cascades three blocks which model the cross-attention between the object queries and the image features of $1/32 \\times 1/32$ , $1/16 \\times 1/16$ , and $1/8 \\times 1/8$ of the original image resolution, respectively. The Transformer Decoder is repeated three times. We refer readers to [8,9] for more details.", + "bbox": [ + 75, + 318, + 467, + 484 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We develop our FASeg upon the Mask2former [8] framework by simply incorporating our DFPQ and HRCA. The overview of our FASeg is depicted in Figure 2 (b). We first provide more accurate and fine-grained positional priors for Mask2former with DFPQ (Section 3.2). We apply DFPQ in the cross-attention layers for each decoder block to provide good positional priors for aggregating the contextual image features to locate target segments. In this way, we progressively localize the target segments as we go deeper in the decoder blocks. Since there are no cross-attention scores before the first Transformer decoder block, we obtain the DFPQ for the first block by performing average pooling on the predicted foreground mask from the auxiliary prediction head as introduced in [8]. Next, we employ HRCA (Section 3.3) to enrich the segmentation details with affordable peak-time memory footprints and computational complexity. We add a fourth decoder block equipped with HRCA to model cross-attention on the high-resolution feature maps after the cascaded three decoder blocks that are already in Mask2former in a top-down manner. With the two simple modifications, our FASeg achieves solid performance gain over the original Mask2former (See Section 4.1).", + "bbox": [ + 75, + 484, + 467, + 816 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 830, + 207, + 845 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation details. Unless otherwise specified, we adopt the same training settings and implementation details as in Mask2former [8]. For our efficient HRCA in", + "bbox": [ + 75, + 854, + 467, + 900 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/8f9936d2fddda83c74e757237833327ba6df024258866c3c3327776fbdb12a87.jpg", + "table_caption": [ + "Table 1. Performance comparisons with the state-of-the-art semantic segmentation methods on ADE20K val [57] with 150 categories. #P and #F indicate the number of parameters (M) and FLOPs (G). We report both single-scale (s.s.) and multi-scale (m.s.) inference results." + ], + "table_footnote": [], + "table_body": "
MethodBackbonemIoUs.s.s. (%)mIoU m.s. (%)#P#F
UperNet [44]R5042.1-67238
DeepLab V3+ [6]R5044.044.944177
SenFormer [2]R5044.745.2144179
Maskformer [9]R5044.546.74153
PFD [31]R5045.648.37461
Mask2former [8]R5047.249.24471
FASeg (ours)R5048.349.35172
UperNet [44]Swin-T44.446.160236
SenFormer [2]Swin-T46.0-144179
Maskformer [9]Swin-T46.748.84255
PFD [31]Swin-T48.349.67465
Mask2former [8]Swin-T47.749.64774
FASeg (ours)Swin-T49.651.35475
SenFormer [2]Swin-B51.8-204242
Maskformer [9]Swin-B52.753.9102195
PFD [31]Swin-B54.155.3123206
Mask2former [8]Swin-B53.955.1107223
FASeg (ours)Swin-B55.056.0113225
UperNet [44]Swin-L52.153.5234647
SenFormer [2]Swin-L53.154.2314546
Maskformer [9]Swin-L54.155.6212375
PFD [31]Swin-L56.057.2242385
Mask2former [8]Swin-L56.157.3215403
FASeg (ours)Swin-L56.357.7222405
", + "bbox": [ + 501, + 162, + 890, + 503 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/3ae7675995e29f1b624a352f96e1928fa55da9ac4c759eaf056315f3a5b76bd6.jpg", + "table_caption": [ + "Table 2. Performance comparisons with the state-of-the-art semantic segmentation methods on Cityscapes val [11]. We report single-scale (s.s.) inference results. #P and #F indicate the number of parameters (M) and FLOPs (G)." + ], + "table_footnote": [], + "table_body": "
MethodBackbonemIoU s.s. (%)#P#F
Maskformer [9]R5078.541405
Senformer [2]R5078.81441,317
DeepLab V3+ [2]R5079.0--
Mask2former [8]R5079.444526
Maskformer [9]R10179.160561
Mask2former [8]R10180.167628
SenFormer [2]R10180.31621,473
FASeg (ours)R5080.567533
", + "bbox": [ + 501, + 575, + 890, + 702 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Section 3.3, we select $|\\Omega| = \\lfloor HW/32 \\rfloor$ from the low-resolution feature maps $(1/32 \\times 1/32$ of the original image size). By default, we train our models with a batch size of 16 on 8 NVIDIA V100 GPUs. We adopt ResNet [21] and Swin Transformer [29] pre-trained backbones. For ResNet [21], we use the ResNet-50 (R50) variant. For Swin Transformer [29], we use the Swin-T, Swin-B, and Swin-L backbones where Swin-B and Swin-L are pre-trained on ImageNet-22k [13]. Unless specified, we adopt all training settings the same as the default settings of FASeg with R50 [21] backbone on ADE20K val [57] with 150 categories for ablation experiments. We conduct the main", + "bbox": [ + 496, + 719, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "11303", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "experiments and ablation studies with the same seeds as Mask2former to seek fair comparisons.", + "bbox": [ + 75, + 90, + 468, + 119 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. We conduct our experiments on ADE20K [57] and Cityscapes [11]. ADE20K [57] is one of the most challenging large-scale datasets for semantic segmentation, which covers 150 fine-grained semantic concepts, where the training set and validation set contain 20,210 and 2,000 images, respectively. Cityscapes [11] is an urban street-view dataset with high-resolution images from 50 cities with 19 semantic classes, which consists of 2,975 images for the training set and 2,725 images for the validation set.", + "bbox": [ + 75, + 122, + 467, + 258 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation metrics. We use single-scale (s.s.) and multiscale (m.s.) mean Intersection over Union (mIoU) [17] as the evaluation metric. We also compare models in terms of their model size (number of parameters) and computational complexity with Floating-point Operations (FLOPs) to evaluate the efficiency of these models. For ablation studies on HRCA, we also show the training-time GPU memory consumption. For ADE20K [57] and Cityscapes [11], we calculate FLOPs with fixed $512 \\times 512$ and $1024 \\times 2048$ image size, respectively.", + "bbox": [ + 75, + 260, + 467, + 411 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Compared methods. We compare our method with the SOTA semantic segmentation methods, including DeepLab V3+ [6], UperNet [44], Maskformer [9], SenFormer [2], PFD [31] and Mask2former [8]. Among them, SenFormer [2], PFD [31] and Mask2former [8] are the recent Transformer-based segmentors, where PFD learns a hierarchy of latent queries to enrich the multi-scale information and SenFormer ensembles the multi-scale predictions. We refer the readers to Section 2 for more details.", + "bbox": [ + 75, + 412, + 467, + 547 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Main Results", + "text_level": 1, + "bbox": [ + 76, + 561, + 215, + 575 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare our FASeg with state-of-the-art semantic segmentation methods on ADE20K val [57] and Cityscapes val [11]. The results are reported in Tables 1 and 2. We observe that on ADE20K val (Table 1), with affordable number of extra parameters and FLOPs, our FASeg consistently outperforms the SOTA methods. Specifically, FASeg achieves $48.3\\%$ , $49.6\\%$ , $55.0\\%$ , and $56.3\\%$ mIoU for single-scale inference, outperforming the SOTA methods by $1.1\\%$ , $1.3\\%$ , $0.9\\%$ , and $0.2\\%$ on R50, Swin-T, Swin-B, and Swin-L backbones, respectively. The solid performance gain demonstrates the superiority of our FASeg framework. Our FASeg has more improvements with the smaller backbones (e.g., R50, Swin-T, and Swin-B). We conjecture that localizing the contextual features with smaller backbones under inferior representational capability is challenging. Nevertheless, our DFPQ provides more accurate positional priors, which ease the localization difficulty and lead to better results. For the comparisons on Cityscapes val in Table 2, we observe that with the R50 backbone, our FASeg outperforms all the SOTA methods under desirable numbers of parameters and FLOPs. Surprisingly, FASeg even", + "bbox": [ + 75, + 583, + 467, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/fc2b78eb35791b993ca567b164ef0a2d276668d2e15b3bf2ed4d80870bb80d93.jpg", + "table_caption": [ + "Table 3. Effect of the positional encodings $\\mathbf{K}_p$ for the image features on ADE20K val [57] with 150 categories." + ], + "table_footnote": [], + "table_body": "
KpMask2former [8] \nmIoU s.s. (%)FASeg \nmIoU s.s. (%)
Sinusoidal [3]47.246.9
Learnable absolute [19]47.047.5
Conditional [10]47.348.3
", + "bbox": [ + 501, + 121, + 887, + 195 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/2a9ca121df2ece509363f09aa1312d3c616e31e25aba37f27384b4104ed1b882.jpg", + "table_caption": [ + "Table 4. Ablation study for FASeg on ADE20K val [57] and Cityscapes val [11]. #P and #F indicate the number of parameters (M) and FLOPs (G) evaluated on ${512} \\times {512}$ images." + ], + "table_footnote": [], + "table_body": "
DFPQHRCAADE20K val\nmIoU s.s. (%)Cityscapes val\nmIoU s.s. (%)#P#F
47.279.44471
✓47.780.04471
✓47.679.85072
✓✓48.380.55172
", + "bbox": [ + 501, + 244, + 887, + 327 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/cec784044ff0c038fa6ddc3b50349d5ce418016ac6f0376228a6217c97b5fbd7.jpg", + "table_caption": [ + "Table 5. Performance comparisons between DFPQ and other positional queries variants on ADE20K val [57] with 150 categories." + ], + "table_footnote": [], + "table_body": "
MethodmIoU s.s.(%)
Learnable positional queries46.9
Pre-defined grid anchor positional queries46.6
Dynamic anchor positional queries47.0
Dynamic foreground positional queries47.8
DFPQ48.3
", + "bbox": [ + 506, + 361, + 877, + 448 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "outperforms the SOTA methods employing the R101 backbone, which demonstrates the effectiveness of our FASeg. To further investigate the flexibility and potential of our main contribution DFPQ, we show more experiments on instance segmentation in the supplementary material.", + "bbox": [ + 496, + 460, + 890, + 535 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We next show some qualitative results in Figure 3 and find that our FASeg provides more accurate predictions with finer details. The improved segmentation results again show the superiority of our DFPQ and HRCA. We include more qualitative results in the supplementary material.", + "bbox": [ + 496, + 536, + 890, + 611 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Ablation Study", + "text_level": 1, + "bbox": [ + 498, + 619, + 653, + 636 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Effect of $K_{p}$ . We investigate the effect of the positional encodings $K_{p}$ for the image features on ADE20k val with R50 backbone. The results are reported in Table 3. We observe that different $K_{p}$ have similar performance for Mask2former [8]. However, more powerful $K_{p}$ leads to much higher performance for our FASeg. For instance, FASeg with conditional positional encodings [10] outperforms Mask2former counterpart and FASeg with sinusoidal positional encodings [3] by $1.0\\%$ and $1.4\\%$ mIoU, respectively. The reason is that compared to Mask2former, our FASeg additionally aggregates $K_{p}$ to get DFPQ as explained in Section 3.2. Therefore, more powerful $K_{p}$ leads to higher representational capability of DFPQ that boosts the performance. We also find that with sinusoidal positional encodings, FASeg has even lower performance than Mask2former as the DFPQ aggregated from sinusoidal positional encodings reflects a single anchor point which can-", + "bbox": [ + 496, + 643, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "11304", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "not cover the fine-grained segmentation cues.", + "bbox": [ + 76, + 90, + 377, + 104 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of DFPQ and HRCA. We investigate the effectiveness of our DFPQ and HRCA on ADE20k val and Cityscapes val with the ResNet-50 backbone. The results are reported in Table 4. We observe that both DFPQ and HRCA gain clear margins from the vanilla Mask2former [8]. To be specific, integrating DFPQ on Mask2former boosts the performance by $0.5\\%$ and $0.6\\%$ mIoU on ADE20k val and Cityscapes val, respectively, with barely any extra parameter and computational cost. It is indicated that DFPQ is lightweight and contributes largely on the performance gain. Employing HRCA on Mask2former leads to $0.4\\%$ mIoU gain on both datasets, which however, has 6M more parameters and 1G higher FLOPs. The additional parameters and FLOPs are brought by the extra decoder layers handling high-resolution image features. Finally, our FASeg with both DFPQ and HRCA improves $1.1\\%$ mIoU for both ADE20k val and Cityscapes val, demonstrating the superiority of our FASeg.", + "bbox": [ + 75, + 108, + 468, + 381 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "DFPQ vs. other positional queries. We investigate the effectiveness of our DFPQ and compare it with other learnable query variants on ADE20K val [57]. The results are presented in Table 5. Here we adopt all the other settings the same as our FASeg with the R50 backbone and only differ the positional queries for all the competitors. Specifically, we compare with four settings: 1) learnable parameterized positional queries that are randomly initialized [3]; 2) positional queries as the pre-defined grid anchor points akin to [43]; 3) positional queries dynamically generated from the center of the foreground masks predicted by the previous layer similar to [28]; 4) positional queries dynamically generated from the entire predicted foreground masks. We find that our DFPQ outperforms all the competitors by large margins. For example, our DFPQ achieves $1.7\\%$ and $1.3\\%$ higher mIoU than the pre-defined grid and dynamic anchor positional queries, respectively. It is suggested that our DFPQ better suits semantic segmentation than the other positional query variants. We also visualize cross-attention maps among the different positional queries in Figure 4. We observe that our DFPQ (Figure 4 (c)) helps generate more compact and consistent cross-attention maps focusing on the target segments than the learnable parameterized positional queries (Figure 4 (a)) and dynamic anchor positional queries (Figure 4 (b)).", + "bbox": [ + 75, + 383, + 470, + 761 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "HRCA vs. other efficient cross-attention methods. We investigate the effectiveness of our HRCA and compare it with other cross-attention methods on ADE20k val. The results are reported in Table 6. For a fair comparison, we only replace HRCA for the other efficient cross-attention methods on our FASeg with the R50 backbone. We compare with three baselines: 1) the vanilla cross-attention that models the entire high-resolution features; 2) our HRCA with randomly sampled top-k pixels to form set $\\Omega$ that $|\\Omega|$", + "bbox": [ + 75, + 763, + 468, + 902 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/481313fccca020077f41d58d3db836cf4ced24e7d4756053c42ba4b5c51956ee.jpg", + "image_caption": [ + "GT" + ], + "image_footnote": [], + "bbox": [ + 503, + 101, + 627, + 152 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b58ba05f4cdda9506b2581ddc32db368b05abbc09f74678547f65663a1700fc3.jpg", + "image_caption": [ + "Mask2former" + ], + "image_footnote": [], + "bbox": [ + 630, + 101, + 761, + 152 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/81852ee119ddd22f46cb043c9e538f913af77bb995ad91dfeae8c6ca4d6e793a.jpg", + "image_caption": [ + "FASeg" + ], + "image_footnote": [], + "bbox": [ + 764, + 101, + 888, + 152 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/902b7511332beebe34c6b185fd6620dd09eaf954f8a0a656c9db0cea2f777111.jpg", + "image_caption": [ + "Figure 3. Qualitative results on the ADE20K val [57]. Compared to Mask2former [8], our FASeg predicts masks with finer details and yields more accurate predictions." + ], + "image_footnote": [], + "bbox": [ + 503, + 152, + 627, + 226 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ddc8e3734bad60cffa4d149c4da1e5bd2f65f1f7bc01ff5d8dc3ae34b6b322b2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 629, + 152, + 761, + 226 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/08149fe0ea425113bf2371722d79f1a6b1bc474c076b5004f7755b8f934e9425.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 764, + 152, + 888, + 226 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 6. Performance comparisons between our HRCA and other efficient cross-attention methods on ADE20K val [57] with 150 categories. #F denotes the number of FLOPs (G). The training memory footprint (M) and FLOPs are measured under $512 \\times 512$ image resolutions with a batch size of 4 on a single GPU.", + "bbox": [ + 498, + 273, + 892, + 343 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/bcfa7c501da5de30ef0f8a01f1f7fd39e6080687daf21a6b29187db4c68c5357.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodmIoU s.s. (%)Training Memory (M)#F
Vanilla47.37,45183
Random Ω46.76,34372
RCDA47.56,08272
HRCA48.36,34372
", + "bbox": [ + 501, + 348, + 887, + 422 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/0d5706d076f4596c5e35e9f05fd951bd342667a00d4111d0df8b10dbefa21fe1.jpg", + "table_caption": [ + "Table 7. Effect of $|\\Omega |$ in our efficient HRCA on ADE20K val [57] with 150 categories. #F indicates the number of FLOPs (G)." + ], + "table_footnote": [], + "table_body": "
|Ω|mIoU s.s. (%)Training memory (M)#F
HW47.37,45183
[HW/16]47.76,38172
[HW/32]48.36,34372
[HW/64]48.06,31771
", + "bbox": [ + 501, + 460, + 885, + 536 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "is the same as HRCA; 3) RCDA [43] that the cross-attention is decoupled to a row-wise and column-wise attention as introduced in Section 3.3. We empirically find that compared with the vanilla cross-attention, our HRCA achieves $1.0\\%$ mIoU gain while exhibiting 1,108M lower training-time GPU memory and 11G lower FLOPs. Our HRCA also outperforms the two efficient cross-attention methods by large margins. For example, HRCA achieves $0.8\\%$ higher mIoU than RCDA with marginally increased training-time memory. The results demonstrate the superiority of our HRCA for efficiently identifying and utilizing contextual tokens in high-resolution features.", + "bbox": [ + 496, + 551, + 890, + 733 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effect of $|\\Omega|$ in HRCA. We then investigate how $|\\Omega|$ affects the performance, memory consumption and computational complexity on FASeg with R50 backbone on ADE20k val. The results are reported in Table 7. $|\\Omega|$ determines the number of contextual tokens used in attention as introduced in Section 3.3. Here we measure the memory consumption by the training-time memory with a batch size of 4 on a single GPU. In the vanilla cross-attention layers, cross-attention attends to the entire feature maps from the encoder, in which case $|\\Omega| = HW$ . We observe that our HRCA outperforms the vanilla cross-attention by a signifi", + "bbox": [ + 496, + 734, + 892, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "11305", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/44a565ca7c50ea089c93678b618ebc45e8463e0c9d5befd59e2951b750796786.jpg", + "image_caption": [ + "Figure 4. Visualizations of the cross-attention maps for learnable positional queries ([3,8]), dynamic anchor positional queries (alike [28]) and our DFPQ. We show the visualizations for the normalized cross-attention maps in the last three decoder blocks and indicate the target segments in the red boxes. The cross-attention maps with the learnable positional queries and the dynamic anchor positional queries are often scattered without a clear focus and mix up different segments, while the cross-attention maps with DFPQ are more compact and consistent to reflect the target segments." + ], + "image_footnote": [], + "bbox": [ + 80, + 89, + 893, + 364 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/d4a2a5f076e0129c826204dc38d8b5dca511223007a2793ce5c8bf850431aa4a.jpg", + "table_caption": [ + "Table 8. Effect of applying HRCA to other high-resolution feature scales for FASeg with Swin-B Backbone on ADE20K val [57] with 150 categories." + ], + "table_footnote": [], + "table_body": "
1/4 × 1/41/8 × 1/8mIoU s.s. (%)Training Memory (M)
✓55.020,418
✓✓54.919,898
✓54.817,817
", + "bbox": [ + 78, + 498, + 468, + 554 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "cant margin. We conjecture that the sparse property [16, 18] has reduced the redundancy in high-resolution feature maps in our HRCA and leads to higher performance and efficiency. Since our HRCA achieves the highest performance when $|\\Omega| = \\lfloor HW/32 \\rfloor$ , we set $|\\Omega| = \\lfloor HW/32 \\rfloor$ by default for all the other experiments.", + "bbox": [ + 75, + 556, + 468, + 647 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of applying HRCA to other high-resolution feature scales. By default, HRCA is applied only to the high-resolution $1/4 \\times 1/4$ feature scale. We explore applying HRCA to $1/8 \\times 1/8$ and both $1/4 \\times 1/4$ and $1/8 \\times 1/8$ feature scales for FASeg with Swin-B backbone on ADE20k val. We measure the training-time memory consumption with a batch size of 4 on a single GPU and report the results in Table 8. We find that the performance only fluctuates within $0.2\\%$ mIoU. In particular, modeling the cross-attention only on the $1/8 \\times 1/8$ feature scale with HRCA saves more than 2,000M training-time memory, suggesting the potential for extending HRCA to more high-resolution features to alleviate the memory burden.", + "bbox": [ + 75, + 648, + 470, + 844 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 852, + 194, + 867 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we have explored providing positional priors with positional queries for the DETR-style semantic", + "bbox": [ + 75, + 869, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "segmentation. Specifically, we have proposed to dynamically generate the positional queries conditioned on the cross-attention scores of the preceding decoder block and the positional encodings for the corresponding image features, simultaneously. We have found that our novel query design delivers more accurate and fine-grained positional priors facilitating localizing the target segments progressively. To mitigate the training-time memory cost when modeling cross-attention on high-resolution feature maps, we have presented an efficient approach to only aggregate the contextual tokens from the high-resolution feature maps, which is shown to learn low-level details with affordable memory and computations. Finally, we have conducted extensive experiments to demonstrate the effectiveness of our proposed framework on the semantic segmentation task and its potential to be extended to other segmentation tasks.", + "bbox": [ + 496, + 454, + 890, + 696 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations and societal impact. Although our HRCA enriches the segmentation details with affordable memory and computations, it still requires more parameters. To this end, we will explore slimming [7, 20] or reusing [33] these blocks to save parameters. Another potential future direction is to explore the explainability of the positional priors generated by our DFPQ. Our technical innovations do not appear to have any negative societal impacts. However, the trained model may deliver unstable or biased predictions with training data that is not reviewed properly.", + "bbox": [ + 496, + 696, + 890, + 847 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement. Dr Jing Zhang was supported by Australian Research Council Projects in part by FL170100117 and IH180100002.", + "bbox": [ + 496, + 847, + 890, + 890 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "11306", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Iz Beltagy, Matthew E. Peters, and Arman Cohan. Longformer: The long-document transformer. arXiv:2004.05150, 2020. 5", + "[2] Walid Bousselham, Guillaume Thibault, Lucas Pagano, Archana Machireddy, Joe Gray, Young Hwan Chang, and Xubo Song. Efficient self-ensemble framework for semantic segmentation. arXiv preprint arXiv:2111.13280, 2021. 1, 5, 6", + "[3] Nicolas Carion, Francisco Massa, Gabriel Synnaeve, Nicolas Usunier, Alexander Kirillov, and Sergey Zagoruyko. 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In ICLR, 2021. 1, 5" + ], + "bbox": [ + 501, + 92, + 890, + 657 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "11308", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Dynamic Focus-Aware Positional Queries for Semantic Segmentation/0da0c2f9-7cdb-4694-a9e6-89d455ec6130_model.json b/2023/Dynamic Focus-Aware Positional Queries for Semantic Segmentation/0da0c2f9-7cdb-4694-a9e6-89d455ec6130_model.json new file mode 100644 index 0000000000000000000000000000000000000000..5ae2ba2c2ad90acf02279be0a14996475d74ab99 --- /dev/null +++ b/2023/Dynamic Focus-Aware Positional Queries for Semantic Segmentation/0da0c2f9-7cdb-4694-a9e6-89d455ec6130_model.json @@ -0,0 +1,2057 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.139, + 0.131, + 0.833, + 0.154 + ], + "angle": 0, + "content": "Dynamic Focus-aware Positional Queries for Semantic Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.267, + 0.18, + 0.686, + 0.218 + ], + "angle": 0, + "content": "Haoyu He\\(^{1}\\) Jianfei Cai\\(^{1}\\) Zizheng Pan\\(^{1}\\) Jing Liu\\(^{1}\\) Jing Zhang\\(^{2}\\) Dacheng Tao\\(^{2}\\) Bohan Zhuang\\(^{1\\dagger}\\)" + }, + { + "type": "text", + "bbox": [ + 0.245, + 0.224, + 0.725, + 0.244 + ], + "angle": 0, + "content": "1 ZIP Lab, Monash University 2 The University of Sydney" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.282, + 0.314, + 0.298 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.314, + 0.473, + 0.752 + ], + "angle": 0, + "content": "The DETR-like segmentors have underpinned the most recent breakthroughs in semantic segmentation, which end-to-end train a set of queries representing the class prototypes or target segments. Recently, masked attention [8] is proposed to restrict each query to only attend to the foreground regions predicted by the preceding decoder block for easier optimization. Although promising, it relies on the learnable parameterized positional queries which tend to encode the dataset statistics, leading to inaccurate localization for distinct individual queries. In this paper, we propose a simple yet effective query design for semantic segmentation termed Dynamic Focus-aware Positional Queries (DFPQ), which dynamically generates positional queries conditioned on the cross-attention scores from the preceding decoder block and the positional encodings for the corresponding image features, simultaneously. Therefore, our DFPQ preserves rich localization information for the target segments and provides accurate and fine-grained positional priors. In addition, we propose to efficiently deal with high-resolution cross-attention by only aggregating the contextual tokens based on the low-resolution cross-attention scores to perform local relation aggregation. Extensive experiments on ADE20K and Cityscapes show that with the two modifications on Mask2former, our framework achieves SOTA performance and outperforms Mask2former by clear margins of \\(1.1\\%\\), \\(1.9\\%\\), and \\(1.1\\%\\) single-scale mIoU with ResNet-50, Swin-T, and Swin-B backbones on the ADE20K validation set, respectively. Source code is available at https://github.com/ziplab/FASeg." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.779, + 0.21, + 0.794 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.804, + 0.47, + 0.88 + ], + "angle": 0, + "content": "Semantic segmentation aims at assigning each pixel in an image with a semantic class label. As the end-to-end Detection Transformer (DETR) [3,42,49,58] is revolutionizing the paradigm of the object detection task, recent segmentors [2,8,9,54] follow DETR to learn a set of queries repre" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.283, + 0.892, + 0.314 + ], + "angle": 0, + "content": "senting the class prototypes or target segments and achieve state-of-the-art performance on semantic segmentation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.318, + 0.893, + 0.621 + ], + "angle": 0, + "content": "In DETR-like frameworks, providing the queries with meaningful positional priors and encourage each query to concentrate on specific regions is essential to learn representative queries [28, 43, 49, 58]. In this spirit, masked attention [8] is proposed, which restricts each query to only attend to a foreground region predicted by the previous decoder block with binary masks. Although promising, the positional priors in masked attention may be inaccurate and deteriorate performance for two reasons. First, each query comprises a content query that contains semantic information and a positional query that provides positional information for the likely locations of the target segments. However, masked attention still relies on positional queries that are randomly initialized learnable parameters [3, 40] (Figure 1 (a)), which tend to encode the average statistics across the dataset and cannot reflect the segments with large location variances. Second, since each query only attends to the predicted foreground regions, inaccurate predictions lead to error accumulation across the decoder blocks, especially during an early training stage." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.625, + 0.895, + 0.806 + ], + "angle": 0, + "content": "To this end, recent detectors propose to dynamically encode the anchor points into the positional queries to guide queries concentrating around the anchor positions [28, 30, 43] (Figure 1 (b)). The anchor-based query design mitigates the mentioned issues as the positional queries are dynamically generated for each target object, thus providing more accurate positional priors. In addition, it avoids restricting the queries to only attend to the foreground regions with binary masks to mitigate the error accumulation issue. However, the anchor-based queries cannot describe the fine-grained positional priors for semantic segmentation, which has details, edges, and boundaries [5, 6]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Motivated by the observations that attention scores imply the salient regions for token pruning [24, 26], self-supervised learning [4], and semantic segmentation [34,56], in this paper, we propose a simple yet effective query design for semantic segmentation, dubbed Dynamic Focus-aware Positional Queries (DFPQ), which dynamically generates" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.421, + 0.901 + ], + "angle": 0, + "content": "†Corresponding author. E-mail: bohan.zhuang@gmail.com" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "11299" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.09, + 0.372, + 0.228 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.376, + 0.089, + 0.64, + 0.228 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.642, + 0.089, + 0.889, + 0.228 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.237, + 0.892, + 0.333 + ], + "angle": 0, + "content": "Figure 1. (a) The original randomly initialized positional queries [3] as learnable network parameters, where the positional queries are shared among the Transformer decoder blocks and tend to encode dataset statistics modelling the likely positions for the semantic regions, which leads to inaccurate localization. (b) The anchor-based positional queries [43] are conditional on the bounding box coordinates to give each query positional priors around the anchor. However, the anchor points cannot describe semantic regions, thus still sub-optimal for semantic segmentation. (c) Our dynamic focus-aware queries for semantic segmentation are dynamically generated from the cross-attention scores of the preceding decoder block to provide accurate and fine-grained positional priors, facilitating locating and refining the target segments progressively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.355, + 0.468, + 0.565 + ], + "angle": 0, + "content": "the positional queries conditioned on the cross-attention scores of the preceding decoder block and the positional encodings for the corresponding image features, simultaneously (Figure 1 (c)). In this way, our DFPQ preserves the localization information of the target segments, thereby providing accurate and fine-grained positional priors and facilitating progressively locating and refining the target segments. When implementing the positional encodings with more powerful ones like [10], our DFPQ is further empowered with higher capacity to encode the neighbourhood information for the target segments. Compared to the anchor-based positional queries [28,43], our DFPQ can cover fine-grained locations for the segmentation details, edges, and boundaries which include rich segmentation cues." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.566, + 0.468, + 0.761 + ], + "angle": 0, + "content": "In addition, we propose an efficient method named High-Resolution Cross-Attention (HRCA) to mine details for segmenting small regions from the high-resolution feature maps \\((1/4 \\times 1/4\\) of the original image size). Considering performing cross-attention on high-resolution feature maps requires a formidable amount of memory footprints and computational complexity, e.g., 11G extra floating-point operations with an input resolution of \\(512 \\times 512\\), we propose to encode token affinity only on the informative areas of high-resolution feature maps that are indicated important in the low-resolution counterparts. In this way, fine-grained details are learned efficiently with affordable memory and computations." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.762, + 0.458, + 0.776 + ], + "angle": 0, + "content": "Our main contributions can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.778, + 0.468, + 0.868 + ], + "angle": 0, + "content": "- We make the pioneering attempt to present a simple yet effective query formulation for semantic segmentation, which provides accurate and fine-grained positional priors to localize the target segments, and mitigates the error accumulation problem while being lightweight with little extra computation." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.871, + 0.468, + 0.901 + ], + "angle": 0, + "content": "- We propose an efficient high-resolution cross-attention layer to enrich the segmentation details, which dis" + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.778, + 0.468, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.531, + 0.355, + 0.891, + 0.4 + ], + "angle": 0, + "content": "cards the semantically unimportant regions for any target segments in the high-resolution feature maps with affordable memory footprint and computational cost." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.403, + 0.892, + 0.525 + ], + "angle": 0, + "content": "- Extensive experiments on ADE20K and Cityscapes datasets demonstrate that simply incorporating our DFPQ and HRCA into Mask2former [8] achieves significant performance gain and outperforms the SOTA methods. For instance, our FASeg outperforms SOTA methods by \\(1.1\\%\\), \\(1.3\\%\\), and \\(0.9\\%\\) single-scale mIoU on the ADE20K [57] validation set with ResNet-50, Swin-T, and Swin-B backbones, respectively." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.535, + 0.64, + 0.55 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.554, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Semantic segmentation with Transformers. The recent segmentors with Transformers [25, 36, 50, 54] have pushed the horizon for semantic segmentation. In general, these segmentors consist of three modules: a backbone, a neck, and a head. Correspondingly, the recent advances can be roughly split into three orthogonal categories. The first category [14, 46, 48, 50, 52, 53] aims at learning more representative features by improving the backbone, mostly by improving the self-attention mechanism in Transformers. For example, focal self-attention [48] combines both fine-grained and coarse-grained features in a backbone self-attention layer. To provide better multi-scale features with neck, the second category [22, 23, 34, 34, 45] improves the feature pyramid network (FPN) [27] or pyramid scene parsing (PSP) [55] structure. For instance, SegFormer [45] simplifies FPN under the Transformer backbone to achieve a better accuracy-efficiency trade-off, and SegDeformer [34] adds external memory tokens to preserve the global information. The third category implements the head with Transformer and conduct set prediction following the DETR-like end-to-end framework [3]. In DETR-like framework, target segments are represented by a set of queries. Considering the importance of providing positional priors for" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11300" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.287 + ], + "angle": 0, + "content": "the queries [28, 30, 43], masked attention [8] is proposed to restrict the cross-attention only to the local features. Our work also aims at providing better positional priors. In contrast to [8], we follow the recent detectors [28, 43] to provide accurate positional priors with dynamic positional queries rather than the learnable parameterized positional queries [3]. Differently, our DFPQ provides fine-grained positional priors that can cover the locations for fine segmentation details, edges, and boundaries. Very recent work [25] proposes a versatile multi-task head structure to share the mutual information among the segmentation and detection tasks, which however, is not directly comparable to our work." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.288, + 0.473, + 0.619 + ], + "angle": 0, + "content": "Positional encodings for Transformers. Both self-attention and cross-attention for Transformers are permutation-equivalent. Therefore, Positional Encodings (PE) play an essential role in introducing the order of the sequence. In general, the positional encodings include: absolute PE that is generated with sinusoidal functions [35, 40] or being entirely learnable parameters [19, 29]; relative PE that encodes distances between the input tokens [12, 32]; and conditional PE, which is dynamically generated, e.g., PEG [10] generates positional encodings with depth-wise convolution conditioned on the local neighbourhood information. In the same spirit, our DFPQ is also dynamically generated by exploring the idea of conditional encoding [38, 47], thus delivering higher segmentation accuracy. Differently, our DFPQ is tailored specifically for DETR-style semantic segmentation to learn positional priors for each target segment. In addition, since our DFPQ is conditional on the PE for the image features, implementing it with the more powerful PEs [10, 19] can further boost the representational capability of our DFPQ. We investigate the effect of different PE strategies in Section 4.2." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.62, + 0.473, + 0.817 + ], + "angle": 0, + "content": "When solely pre-training Transformer backbones, the positional encodings are generally seen as a part of the feature embeddings and directly be combined with patch features after patchifying the image [15,39]. Differently, in the cross-attention layers of DETR-like frameworks, both the image features and the object queries require additional positional information to provide positional priors for aggregating the query-specific context, which we refer the readers to Section 3.1 for details. Recent detectors [28,43] encode anchor positions into positional queries. In contrast, we design a novel positional query formulation for semantic segmentation to reflect regions of interest instead of anchor points to preserve fine segmentation details." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.822, + 0.17, + 0.838 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.848, + 0.411, + 0.864 + ], + "angle": 0, + "content": "3.1. Preliminary: Cross-attention in DETR" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Before introducing our DFPQ, we first revisit the cross-attention layers in DETR-like frameworks [3]. Cross" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.289 + ], + "angle": 0, + "content": "attention layer is a basic module that updates the object queries by aggregating the image context. Since the cross-attention layer is permutation-invariant, both queries and keys require positional information, which introduces the order and provides positional priors to encourage high attention scores for positionally important regions. Specifically, with \\(N\\), \\(D\\), \\(H\\) and \\(W\\) respectively denoting the number of queries, the hidden dimensions, the height, and the width of the image features, we have the image features \\(\\pmb{K}_c\\) and their positional encodings \\(\\pmb{K}_p\\) and get keys \\(\\pmb{K} = \\pmb{K}_c + \\pmb{K}_p\\), where \\(\\pmb{K} \\in \\mathbb{R}^{HW \\times D}\\). We also have the object queries \\(\\pmb{Q} \\in \\mathbb{R}^{N \\times D}\\), where each query consists of a content query \\(\\pmb{Q}_c\\) and a positional query \\(\\pmb{Q}_p\\)." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.289, + 0.892, + 0.303 + ], + "angle": 0, + "content": "Then, the cross-attention operation can be formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.51, + 0.323, + 0.892, + 0.365 + ], + "angle": 0, + "content": "\\[\n\\operatorname {C r s - A t t e n t i o n} (\\boldsymbol {Q}, \\boldsymbol {K}, \\boldsymbol {V}) = \\operatorname {s o f t m a x} \\left(\\frac {\\boldsymbol {Q} \\boldsymbol {K} ^ {T}}{\\sqrt {D}}\\right) \\boldsymbol {V}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.371, + 0.892, + 0.538 + ], + "angle": 0, + "content": "where \\(\\mathbf{V} \\in \\mathbb{R}^{HW \\times D}\\) is also the image features in the DETR-like frameworks [3,9,54] and we omit all the linear projections and bias terms for simplicity. From Eq. (1), we can interpret the cross-attention as aggregating image context based on the dot-product similarity between \\(Q\\) and \\(K\\). Since both the content parts and the positional parts for \\(Q\\) and \\(K\\) contribute to calculating the attention scores, similarities for both parts are considered. Therefore, content similarity contributes to mining the correlation between the object queries and the image features, while positional similarity provides positional priors for each target segment." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.546, + 0.852, + 0.562 + ], + "angle": 0, + "content": "3.2. Dynamic Focus-aware Positional Queries" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.569, + 0.892, + 0.903 + ], + "angle": 0, + "content": "In this work, we aim to develop positional queries that provide effective positional priors under DETR-like frameworks for semantic segmentation. We argue that generating positional queries conditioned on cross-attention scores has three good properties. First, the cross-attention scores indicate the areas with rich context and may directly reflect the localization information for the target segments [4, 56]. Therefore, when stacking several decoder blocks with cross-attention layers in DETR-like frameworks, the localization information in the preceding block is helpful for progressively locating the target segments in the later blocks, especially when the blocks handle features at different scales [8, 23]. Second, cross-attention scores are dynamically generated. In contrast to the content-agnostic positional queries as learnable parameters in [3], which tend to encode statistics across the dataset and limit models' generalization capability, cross-attention scores are conditional on each target segment reflecting the specific contextual locations, thereby being more accurate. Finally, the cross-attention scores can cover fine-grained segmentation details, edges, and boundaries instead of encoding only a single center or anchor point alike [28, 43]." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "11301" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.089, + 0.46, + 0.315 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.464, + 0.089, + 0.885, + 0.315 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.325, + 0.892, + 0.436 + ], + "angle": 0, + "content": "Figure 2. (a) Cross-attention with our dynamic focus-aware positional queries (DFPQ). \"pos\" is short for positional. We show generating DFPQ in the dashed box, where we multiply the positional encodings for the image features with the cross-attention scores of the preceding decoder block followed by a projection function \\( h \\) to get DFPQ. Here we omit the bias terms for simplicity. (b) The overall framework for our FASeg is built upon Mask2former [8], which employs a Backbone to encode images, a Pixel Decoder to fuse the features under different resolutions, and a Transformer Decoder to learn the representation for each target segment. We first apply our DFPQ in each decoder block to provide more accurate positional priors (marked with blue arrows). Then, we further propose to incorporate our high-resolution cross-attention (HRCA) layers to model the cross-attention between the queries and the high-resolution feature maps (marked with red arrows). Here \"Top-k\" selects the top-k pixels indicated by the cross-attention scores of the previous Transformer decoder block." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.451, + 0.47, + 0.587 + ], + "angle": 0, + "content": "Therefore, we propose to generate the positional queries conditional on the cross-attention scores of the preceding decoder block and the positional encodings for the corresponding image features, simultaneously, as shown in Figure 2 (a). Specifically, since the positional encodings \\( \\mathbf{K}_p \\) for the image features preserve the positional information, we form our DFPQ by aggregating \\( \\mathbf{K}_p \\) as indicated by the cross-attention scores \\( \\mathbf{A} \\) in the cross-attention layer of the preceding decoder block, which can be formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.18, + 0.598, + 0.47, + 0.618 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {Q} _ {p} ^ {t} = h \\left(\\boldsymbol {A} ^ {t - 1} \\boldsymbol {K} _ {p} ^ {t - 1} + \\boldsymbol {B}\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.469, + 0.794 + ], + "angle": 0, + "content": "where \\(t\\) is the index of the \\(t\\)-th Transformer decoder block, \\(\\mathbf{A}^{t-1} \\in \\mathbb{R}^{N \\times HW}\\) is the cross-attention scores from the \\((t-1)\\)-th Transformer decoder block, \\(\\mathbf{B} \\in \\mathbb{R}^{N \\times D}\\) is learnable network parameters, and \\(h\\) is a two-layered MLP with ReLU non-linearity in between. Note that the bias term \\(\\mathbf{B}\\) is the original randomly initialized learnable positional queries, which we employ to stable the training in an early training stage. In this way, we dynamically generate DFPQ to provide positional priors for the target segments. It can also cover the fine-grained segmentation cues that are not restricted by anchor points." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Note that as our DFPQ directly aggregates the positional information, implementing DFPQ with different \\( K_{p} \\) leads to distinct behaviours. When implementing \\( K_{p} \\) with the absolute sinusoidal function, the resulting DFPQ reflects an anchor point alike [28,43] instead of the target areas. In this case, we implement \\( K_{p} \\) with conditional positional encodings [10] to further encode the neighbourhood information" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.451, + 0.892, + 0.496 + ], + "angle": 0, + "content": "and preserve the implicit positional priors for localizing the target segments. We empirically investigate the effect of different positional encodings in Section 4.2." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.505, + 0.849, + 0.52 + ], + "angle": 0, + "content": "3.3. Efficient High-resolution Cross-attention" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.528, + 0.892, + 0.814 + ], + "angle": 0, + "content": "As demonstrated by the prior arts [23, 38], high-resolution image features are important for segmenting small regions. However, modelling cross-attention between object queries and high-resolution image features requires an unbearable amount of memory footprints and computational cost. In this case, we propose an efficient High-Resolution Cross-Attention (HRCA) layer to mine details from high-resolution feature maps with affordable memory burden. Specifically, we first select the top-k pixels from the low-resolution image features with the highest cross-attention scores for all object queries. We then map these areas to the high-resolution feature map positions in a top-down manner and only perform cross-attention on these positions. Formally, we first get the low-resolution cross-attention scores \\( \\mathbf{A}_l \\), and then derive its high-resolution counterpart \\( \\mathbf{A}_h = f(\\mathbf{A}_l) \\) with bilinear upsampling operation \\( f(\\cdot) \\). We next include the top-k pixels in \\( \\mathbf{A}_h \\) with the highest scores into set \\( \\Omega \\), and the efficient HRCA can be formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.521, + 0.821, + 0.892, + 0.862 + ], + "angle": 0, + "content": "\\[\n\\operatorname {H R C A} (\\boldsymbol {Q}, \\boldsymbol {K}, \\boldsymbol {V}, \\Omega) = \\operatorname {s o f t m a x} \\left(\\frac {\\boldsymbol {Q} \\boldsymbol {K} ^ {\\prime T}}{\\sqrt {D}}\\right) \\boldsymbol {V} ^ {\\prime}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.87, + 0.892, + 0.901 + ], + "angle": 0, + "content": "where \\(\\pmb{K}^{\\prime} = g(\\pmb {K},\\Omega),\\pmb{V}^{\\prime} = g(\\pmb {V},\\Omega)\\) and \\(g\\) is the indexing operation. In this way, we only perform cross-attention" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11302" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.468, + 0.121 + ], + "angle": 0, + "content": "on the informative areas for high-resolution feature maps, thereby saving considerable resource consumption." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.122, + 0.468, + 0.287 + ], + "angle": 0, + "content": "Our HRCA is closely related to the previous sparse attention methods [1, 37, 41, 51] that only attend to a part of the entire sequence. Differently, our HRCA is specialized to the DETR-like frameworks, which determines the informative pixels based on their contribution to the target segments instead of the other pixels. One similar work to our HRCA is the RCDA module [43], which is a representative sparse cross-attention method that decouples cross-attention into a row-wise and column-wise attention to reduce the memory and computation cost. We include the comparison between our HRCA and RCDA [43] in Section 4.2." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.296, + 0.414, + 0.312 + ], + "angle": 0, + "content": "3.4. Focus-aware Segmentation Framework" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.319, + 0.468, + 0.485 + ], + "angle": 0, + "content": "We first briefly introduce Mask2former [8], which consists of backbone, neck, and head as introduced in Section 2 with the neck and head named \"Pixel Decoder\" and \"Transformer Decoder\", respectively. In Mask2former, Pixel Decoder fuses the features at multiple scales following [27,58]. Transformer Decoder cascades three blocks which model the cross-attention between the object queries and the image features of \\(1/32 \\times 1/32\\), \\(1/16 \\times 1/16\\), and \\(1/8 \\times 1/8\\) of the original image resolution, respectively. The Transformer Decoder is repeated three times. We refer readers to [8,9] for more details." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.486, + 0.468, + 0.818 + ], + "angle": 0, + "content": "We develop our FASeg upon the Mask2former [8] framework by simply incorporating our DFPQ and HRCA. The overview of our FASeg is depicted in Figure 2 (b). We first provide more accurate and fine-grained positional priors for Mask2former with DFPQ (Section 3.2). We apply DFPQ in the cross-attention layers for each decoder block to provide good positional priors for aggregating the contextual image features to locate target segments. In this way, we progressively localize the target segments as we go deeper in the decoder blocks. Since there are no cross-attention scores before the first Transformer decoder block, we obtain the DFPQ for the first block by performing average pooling on the predicted foreground mask from the auxiliary prediction head as introduced in [8]. Next, we employ HRCA (Section 3.3) to enrich the segmentation details with affordable peak-time memory footprints and computational complexity. We add a fourth decoder block equipped with HRCA to model cross-attention on the high-resolution feature maps after the cascaded three decoder blocks that are already in Mask2former in a top-down manner. With the two simple modifications, our FASeg achieves solid performance gain over the original Mask2former (See Section 4.1)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.831, + 0.208, + 0.847 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Implementation details. Unless otherwise specified, we adopt the same training settings and implementation details as in Mask2former [8]. For our efficient HRCA in" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.09, + 0.892, + 0.159 + ], + "angle": 0, + "content": "Table 1. Performance comparisons with the state-of-the-art semantic segmentation methods on ADE20K val [57] with 150 categories. #P and #F indicate the number of parameters (M) and FLOPs (G). We report both single-scale (s.s.) and multi-scale (m.s.) inference results." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.164, + 0.892, + 0.505 + ], + "angle": 0, + "content": "
MethodBackbonemIoUs.s.s. (%)mIoU m.s. (%)#P#F
UperNet [44]R5042.1-67238
DeepLab V3+ [6]R5044.044.944177
SenFormer [2]R5044.745.2144179
Maskformer [9]R5044.546.74153
PFD [31]R5045.648.37461
Mask2former [8]R5047.249.24471
FASeg (ours)R5048.349.35172
UperNet [44]Swin-T44.446.160236
SenFormer [2]Swin-T46.0-144179
Maskformer [9]Swin-T46.748.84255
PFD [31]Swin-T48.349.67465
Mask2former [8]Swin-T47.749.64774
FASeg (ours)Swin-T49.651.35475
SenFormer [2]Swin-B51.8-204242
Maskformer [9]Swin-B52.753.9102195
PFD [31]Swin-B54.155.3123206
Mask2former [8]Swin-B53.955.1107223
FASeg (ours)Swin-B55.056.0113225
UperNet [44]Swin-L52.153.5234647
SenFormer [2]Swin-L53.154.2314546
Maskformer [9]Swin-L54.155.6212375
PFD [31]Swin-L56.057.2242385
Mask2former [8]Swin-L56.157.3215403
FASeg (ours)Swin-L56.357.7222405
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.517, + 0.892, + 0.572 + ], + "angle": 0, + "content": "Table 2. Performance comparisons with the state-of-the-art semantic segmentation methods on Cityscapes val [11]. We report single-scale (s.s.) inference results. #P and #F indicate the number of parameters (M) and FLOPs (G)." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.577, + 0.891, + 0.703 + ], + "angle": 0, + "content": "
MethodBackbonemIoU s.s. (%)#P#F
Maskformer [9]R5078.541405
Senformer [2]R5078.81441,317
DeepLab V3+ [2]R5079.0--
Mask2former [8]R5079.444526
Maskformer [9]R10179.160561
Mask2former [8]R10180.167628
SenFormer [2]R10180.31621,473
FASeg (ours)R5080.567533
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Section 3.3, we select \\( |\\Omega| = \\lfloor HW/32 \\rfloor \\) from the low-resolution feature maps \\( (1/32 \\times 1/32 \\) of the original image size). By default, we train our models with a batch size of 16 on 8 NVIDIA V100 GPUs. We adopt ResNet [21] and Swin Transformer [29] pre-trained backbones. For ResNet [21], we use the ResNet-50 (R50) variant. For Swin Transformer [29], we use the Swin-T, Swin-B, and Swin-L backbones where Swin-B and Swin-L are pre-trained on ImageNet-22k [13]. Unless specified, we adopt all training settings the same as the default settings of FASeg with R50 [21] backbone on ADE20K val [57] with 150 categories for ablation experiments. We conduct the main" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "11303" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.121 + ], + "angle": 0, + "content": "experiments and ablation studies with the same seeds as Mask2former to seek fair comparisons." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.123, + 0.468, + 0.259 + ], + "angle": 0, + "content": "Datasets. We conduct our experiments on ADE20K [57] and Cityscapes [11]. ADE20K [57] is one of the most challenging large-scale datasets for semantic segmentation, which covers 150 fine-grained semantic concepts, where the training set and validation set contain 20,210 and 2,000 images, respectively. Cityscapes [11] is an urban street-view dataset with high-resolution images from 50 cities with 19 semantic classes, which consists of 2,975 images for the training set and 2,725 images for the validation set." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.261, + 0.468, + 0.412 + ], + "angle": 0, + "content": "Evaluation metrics. We use single-scale (s.s.) and multiscale (m.s.) mean Intersection over Union (mIoU) [17] as the evaluation metric. We also compare models in terms of their model size (number of parameters) and computational complexity with Floating-point Operations (FLOPs) to evaluate the efficiency of these models. For ablation studies on HRCA, we also show the training-time GPU memory consumption. For ADE20K [57] and Cityscapes [11], we calculate FLOPs with fixed \\( 512 \\times 512 \\) and \\( 1024 \\times 2048 \\) image size, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.413, + 0.468, + 0.549 + ], + "angle": 0, + "content": "Compared methods. We compare our method with the SOTA semantic segmentation methods, including DeepLab V3+ [6], UperNet [44], Maskformer [9], SenFormer [2], PFD [31] and Mask2former [8]. Among them, SenFormer [2], PFD [31] and Mask2former [8] are the recent Transformer-based segmentors, where PFD learns a hierarchy of latent queries to enrich the multi-scale information and SenFormer ensembles the multi-scale predictions. We refer the readers to Section 2 for more details." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.562, + 0.216, + 0.576 + ], + "angle": 0, + "content": "4.1. Main Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.584, + 0.468, + 0.901 + ], + "angle": 0, + "content": "We compare our FASeg with state-of-the-art semantic segmentation methods on ADE20K val [57] and Cityscapes val [11]. The results are reported in Tables 1 and 2. We observe that on ADE20K val (Table 1), with affordable number of extra parameters and FLOPs, our FASeg consistently outperforms the SOTA methods. Specifically, FASeg achieves \\(48.3\\%\\), \\(49.6\\%\\), \\(55.0\\%\\), and \\(56.3\\%\\) mIoU for single-scale inference, outperforming the SOTA methods by \\(1.1\\%\\), \\(1.3\\%\\), \\(0.9\\%\\), and \\(0.2\\%\\) on R50, Swin-T, Swin-B, and Swin-L backbones, respectively. The solid performance gain demonstrates the superiority of our FASeg framework. Our FASeg has more improvements with the smaller backbones (e.g., R50, Swin-T, and Swin-B). We conjecture that localizing the contextual features with smaller backbones under inferior representational capability is challenging. Nevertheless, our DFPQ provides more accurate positional priors, which ease the localization difficulty and lead to better results. For the comparisons on Cityscapes val in Table 2, we observe that with the R50 backbone, our FASeg outperforms all the SOTA methods under desirable numbers of parameters and FLOPs. Surprisingly, FASeg even" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.089, + 0.892, + 0.118 + ], + "angle": 0, + "content": "Table 3. Effect of the positional encodings \\( \\mathbf{K}_p \\) for the image features on ADE20K val [57] with 150 categories." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.122, + 0.888, + 0.196 + ], + "angle": 0, + "content": "
KpMask2former [8] \nmIoU s.s. (%)FASeg \nmIoU s.s. (%)
Sinusoidal [3]47.246.9
Learnable absolute [19]47.047.5
Conditional [10]47.348.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.199, + 0.892, + 0.242 + ], + "angle": 0, + "content": "Table 4. Ablation study for FASeg on ADE20K val [57] and Cityscapes val [11]. #P and #F indicate the number of parameters (M) and FLOPs (G) evaluated on \\( {512} \\times {512} \\) images." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.246, + 0.888, + 0.328 + ], + "angle": 0, + "content": "
DFPQHRCAADE20K val\nmIoU s.s. (%)Cityscapes val\nmIoU s.s. (%)#P#F
47.279.44471
✓47.780.04471
✓47.679.85072
✓✓48.380.55172
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.33, + 0.892, + 0.358 + ], + "angle": 0, + "content": "Table 5. Performance comparisons between DFPQ and other positional queries variants on ADE20K val [57] with 150 categories." + }, + { + "type": "table", + "bbox": [ + 0.508, + 0.362, + 0.878, + 0.449 + ], + "angle": 0, + "content": "
MethodmIoU s.s.(%)
Learnable positional queries46.9
Pre-defined grid anchor positional queries46.6
Dynamic anchor positional queries47.0
Dynamic foreground positional queries47.8
DFPQ48.3
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.461, + 0.892, + 0.536 + ], + "angle": 0, + "content": "outperforms the SOTA methods employing the R101 backbone, which demonstrates the effectiveness of our FASeg. To further investigate the flexibility and potential of our main contribution DFPQ, we show more experiments on instance segmentation in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.537, + 0.892, + 0.612 + ], + "angle": 0, + "content": "We next show some qualitative results in Figure 3 and find that our FASeg provides more accurate predictions with finer details. The improved segmentation results again show the superiority of our DFPQ and HRCA. We include more qualitative results in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.621, + 0.654, + 0.637 + ], + "angle": 0, + "content": "4.2. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Effect of \\( K_{p} \\). We investigate the effect of the positional encodings \\( K_{p} \\) for the image features on ADE20k val with R50 backbone. The results are reported in Table 3. We observe that different \\( K_{p} \\) have similar performance for Mask2former [8]. However, more powerful \\( K_{p} \\) leads to much higher performance for our FASeg. For instance, FASeg with conditional positional encodings [10] outperforms Mask2former counterpart and FASeg with sinusoidal positional encodings [3] by \\( 1.0\\% \\) and \\( 1.4\\% \\) mIoU, respectively. The reason is that compared to Mask2former, our FASeg additionally aggregates \\( K_{p} \\) to get DFPQ as explained in Section 3.2. Therefore, more powerful \\( K_{p} \\) leads to higher representational capability of DFPQ that boosts the performance. We also find that with sinusoidal positional encodings, FASeg has even lower performance than Mask2former as the DFPQ aggregated from sinusoidal positional encodings reflects a single anchor point which can-" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11304" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.378, + 0.106 + ], + "angle": 0, + "content": "not cover the fine-grained segmentation cues." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.109, + 0.47, + 0.382 + ], + "angle": 0, + "content": "Effectiveness of DFPQ and HRCA. We investigate the effectiveness of our DFPQ and HRCA on ADE20k val and Cityscapes val with the ResNet-50 backbone. The results are reported in Table 4. We observe that both DFPQ and HRCA gain clear margins from the vanilla Mask2former [8]. To be specific, integrating DFPQ on Mask2former boosts the performance by \\(0.5\\%\\) and \\(0.6\\%\\) mIoU on ADE20k val and Cityscapes val, respectively, with barely any extra parameter and computational cost. It is indicated that DFPQ is lightweight and contributes largely on the performance gain. Employing HRCA on Mask2former leads to \\(0.4\\%\\) mIoU gain on both datasets, which however, has 6M more parameters and 1G higher FLOPs. The additional parameters and FLOPs are brought by the extra decoder layers handling high-resolution image features. Finally, our FASeg with both DFPQ and HRCA improves \\(1.1\\%\\) mIoU for both ADE20k val and Cityscapes val, demonstrating the superiority of our FASeg." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.385, + 0.471, + 0.762 + ], + "angle": 0, + "content": "DFPQ vs. other positional queries. We investigate the effectiveness of our DFPQ and compare it with other learnable query variants on ADE20K val [57]. The results are presented in Table 5. Here we adopt all the other settings the same as our FASeg with the R50 backbone and only differ the positional queries for all the competitors. Specifically, we compare with four settings: 1) learnable parameterized positional queries that are randomly initialized [3]; 2) positional queries as the pre-defined grid anchor points akin to [43]; 3) positional queries dynamically generated from the center of the foreground masks predicted by the previous layer similar to [28]; 4) positional queries dynamically generated from the entire predicted foreground masks. We find that our DFPQ outperforms all the competitors by large margins. For example, our DFPQ achieves \\(1.7\\%\\) and \\(1.3\\%\\) higher mIoU than the pre-defined grid and dynamic anchor positional queries, respectively. It is suggested that our DFPQ better suits semantic segmentation than the other positional query variants. We also visualize cross-attention maps among the different positional queries in Figure 4. We observe that our DFPQ (Figure 4 (c)) helps generate more compact and consistent cross-attention maps focusing on the target segments than the learnable parameterized positional queries (Figure 4 (a)) and dynamic anchor positional queries (Figure 4 (b))." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.47, + 0.903 + ], + "angle": 0, + "content": "HRCA vs. other efficient cross-attention methods. We investigate the effectiveness of our HRCA and compare it with other cross-attention methods on ADE20k val. The results are reported in Table 6. For a fair comparison, we only replace HRCA for the other efficient cross-attention methods on our FASeg with the R50 backbone. We compare with three baselines: 1) the vanilla cross-attention that models the entire high-resolution features; 2) our HRCA with randomly sampled top-k pixels to form set \\(\\Omega\\) that \\(|\\Omega|\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.556, + 0.093, + 0.575, + 0.102 + ], + "angle": 0, + "content": "GT" + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.102, + 0.629, + 0.153 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.665, + 0.093, + 0.728, + 0.102 + ], + "angle": 0, + "content": "Mask2former" + }, + { + "type": "image", + "bbox": [ + 0.631, + 0.102, + 0.762, + 0.153 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.812, + 0.093, + 0.845, + 0.102 + ], + "angle": 0, + "content": "FASeg" + }, + { + "type": "image", + "bbox": [ + 0.765, + 0.102, + 0.89, + 0.153 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.153, + 0.629, + 0.227 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.63, + 0.153, + 0.762, + 0.227 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.765, + 0.153, + 0.89, + 0.227 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.229, + 0.892, + 0.271 + ], + "angle": 0, + "content": "Figure 3. Qualitative results on the ADE20K val [57]. Compared to Mask2former [8], our FASeg predicts masks with finer details and yields more accurate predictions." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.274, + 0.893, + 0.344 + ], + "angle": 0, + "content": "Table 6. Performance comparisons between our HRCA and other efficient cross-attention methods on ADE20K val [57] with 150 categories. #F denotes the number of FLOPs (G). The training memory footprint (M) and FLOPs are measured under \\(512 \\times 512\\) image resolutions with a batch size of 4 on a single GPU." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.349, + 0.888, + 0.424 + ], + "angle": 0, + "content": "
MethodmIoU s.s. (%)Training Memory (M)#F
Vanilla47.37,45183
Random Ω46.76,34372
RCDA47.56,08272
HRCA48.36,34372
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.428, + 0.892, + 0.456 + ], + "angle": 0, + "content": "Table 7. Effect of \\( |\\Omega | \\) in our efficient HRCA on ADE20K val [57] with 150 categories. #F indicates the number of FLOPs (G)." + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.461, + 0.887, + 0.537 + ], + "angle": 0, + "content": "
|Ω|mIoU s.s. (%)Training memory (M)#F
HW47.37,45183
[HW/16]47.76,38172
[HW/32]48.36,34372
[HW/64]48.06,31771
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.553, + 0.892, + 0.734 + ], + "angle": 0, + "content": "is the same as HRCA; 3) RCDA [43] that the cross-attention is decoupled to a row-wise and column-wise attention as introduced in Section 3.3. We empirically find that compared with the vanilla cross-attention, our HRCA achieves \\(1.0\\%\\) mIoU gain while exhibiting 1,108M lower training-time GPU memory and 11G lower FLOPs. Our HRCA also outperforms the two efficient cross-attention methods by large margins. For example, HRCA achieves \\(0.8\\%\\) higher mIoU than RCDA with marginally increased training-time memory. The results demonstrate the superiority of our HRCA for efficiently identifying and utilizing contextual tokens in high-resolution features." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Effect of \\( |\\Omega| \\) in HRCA. We then investigate how \\( |\\Omega| \\) affects the performance, memory consumption and computational complexity on FASeg with R50 backbone on ADE20k val. The results are reported in Table 7. \\( |\\Omega| \\) determines the number of contextual tokens used in attention as introduced in Section 3.3. Here we measure the memory consumption by the training-time memory with a batch size of 4 on a single GPU. In the vanilla cross-attention layers, cross-attention attends to the entire feature maps from the encoder, in which case \\( |\\Omega| = HW \\). We observe that our HRCA outperforms the vanilla cross-attention by a signifi" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11305" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.09, + 0.894, + 0.366 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.371, + 0.893, + 0.442 + ], + "angle": 0, + "content": "Figure 4. Visualizations of the cross-attention maps for learnable positional queries ([3,8]), dynamic anchor positional queries (alike [28]) and our DFPQ. We show the visualizations for the normalized cross-attention maps in the last three decoder blocks and indicate the target segments in the red boxes. The cross-attention maps with the learnable positional queries and the dynamic anchor positional queries are often scattered without a clear focus and mix up different segments, while the cross-attention maps with DFPQ are more compact and consistent to reflect the target segments." + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.453, + 0.471, + 0.495 + ], + "angle": 0, + "content": "Table 8. Effect of applying HRCA to other high-resolution feature scales for FASeg with Swin-B Backbone on ADE20K val [57] with 150 categories." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.499, + 0.47, + 0.555 + ], + "angle": 0, + "content": "
1/4 × 1/41/8 × 1/8mIoU s.s. (%)Training Memory (M)
✓55.020,418
✓✓54.919,898
✓54.817,817
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.558, + 0.47, + 0.648 + ], + "angle": 0, + "content": "cant margin. We conjecture that the sparse property [16, 18] has reduced the redundancy in high-resolution feature maps in our HRCA and leads to higher performance and efficiency. Since our HRCA achieves the highest performance when \\( |\\Omega| = \\lfloor HW/32 \\rfloor \\), we set \\( |\\Omega| = \\lfloor HW/32 \\rfloor \\) by default for all the other experiments." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.649, + 0.471, + 0.845 + ], + "angle": 0, + "content": "Effect of applying HRCA to other high-resolution feature scales. By default, HRCA is applied only to the high-resolution \\(1/4 \\times 1/4\\) feature scale. We explore applying HRCA to \\(1/8 \\times 1/8\\) and both \\(1/4 \\times 1/4\\) and \\(1/8 \\times 1/8\\) feature scales for FASeg with Swin-B backbone on ADE20k val. We measure the training-time memory consumption with a batch size of 4 on a single GPU and report the results in Table 8. We find that the performance only fluctuates within \\(0.2\\%\\) mIoU. In particular, modeling the cross-attention only on the \\(1/8 \\times 1/8\\) feature scale with HRCA saves more than 2,000M training-time memory, suggesting the potential for extending HRCA to more high-resolution features to alleviate the memory burden." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.853, + 0.196, + 0.868 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.47, + 0.901 + ], + "angle": 0, + "content": "In this paper, we have explored providing positional priors with positional queries for the DETR-style semantic" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.455, + 0.892, + 0.697 + ], + "angle": 0, + "content": "segmentation. Specifically, we have proposed to dynamically generate the positional queries conditioned on the cross-attention scores of the preceding decoder block and the positional encodings for the corresponding image features, simultaneously. We have found that our novel query design delivers more accurate and fine-grained positional priors facilitating localizing the target segments progressively. To mitigate the training-time memory cost when modeling cross-attention on high-resolution feature maps, we have presented an efficient approach to only aggregate the contextual tokens from the high-resolution feature maps, which is shown to learn low-level details with affordable memory and computations. Finally, we have conducted extensive experiments to demonstrate the effectiveness of our proposed framework on the semantic segmentation task and its potential to be extended to other segmentation tasks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.697, + 0.892, + 0.848 + ], + "angle": 0, + "content": "Limitations and societal impact. Although our HRCA enriches the segmentation details with affordable memory and computations, it still requires more parameters. To this end, we will explore slimming [7, 20] or reusing [33] these blocks to save parameters. Another potential future direction is to explore the explainability of the positional priors generated by our DFPQ. Our technical innovations do not appear to have any negative societal impacts. However, the trained model may deliver unstable or biased predictions with training data that is not reviewed properly." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.848, + 0.892, + 0.891 + ], + "angle": 0, + "content": "Acknowledgement. Dr Jing Zhang was supported by Australian Research Council Projects in part by FL170100117 and IH180100002." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11306" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.155 + ], + "angle": 0, + "content": "[1] Iz Beltagy, Matthew E. Peters, and Arman Cohan. 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In ICLR, 2021. 1, 5" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.658 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.956 + ], + "angle": 0, + "content": "11308" + } + ] +] \ No newline at end of file diff --git a/2023/Dynamic Focus-Aware Positional Queries for Semantic Segmentation/0da0c2f9-7cdb-4694-a9e6-89d455ec6130_origin.pdf b/2023/Dynamic Focus-Aware Positional Queries for Semantic Segmentation/0da0c2f9-7cdb-4694-a9e6-89d455ec6130_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..431d38b0cf6ce720ed251e1f24ff52683b3bdb84 --- /dev/null +++ b/2023/Dynamic Focus-Aware Positional Queries for Semantic Segmentation/0da0c2f9-7cdb-4694-a9e6-89d455ec6130_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:6189fb259498f0d014976b7aeb935aee9e11c75b4fd76567695decd42853bbd0 +size 4423870 diff --git a/2023/Dynamic Focus-Aware Positional Queries for Semantic Segmentation/full.md b/2023/Dynamic Focus-Aware Positional Queries for Semantic Segmentation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..c289d40587ed5ee8b47badd57c6656f52766f52b --- /dev/null +++ b/2023/Dynamic Focus-Aware Positional Queries for Semantic Segmentation/full.md @@ -0,0 +1,280 @@ +# Dynamic Focus-aware Positional Queries for Semantic Segmentation + +Haoyu He $^{1}$ Jianfei Cai $^{1}$ Zizheng Pan $^{1}$ Jing Liu $^{1}$ Jing Zhang $^{2}$ Dacheng Tao $^{2}$ Bohan Zhuang $^{1\dagger}$ + +1 ZIP Lab, Monash University 2 The University of Sydney + +# Abstract + +The DETR-like segmentors have underpinned the most recent breakthroughs in semantic segmentation, which end-to-end train a set of queries representing the class prototypes or target segments. Recently, masked attention [8] is proposed to restrict each query to only attend to the foreground regions predicted by the preceding decoder block for easier optimization. Although promising, it relies on the learnable parameterized positional queries which tend to encode the dataset statistics, leading to inaccurate localization for distinct individual queries. In this paper, we propose a simple yet effective query design for semantic segmentation termed Dynamic Focus-aware Positional Queries (DFPQ), which dynamically generates positional queries conditioned on the cross-attention scores from the preceding decoder block and the positional encodings for the corresponding image features, simultaneously. Therefore, our DFPQ preserves rich localization information for the target segments and provides accurate and fine-grained positional priors. In addition, we propose to efficiently deal with high-resolution cross-attention by only aggregating the contextual tokens based on the low-resolution cross-attention scores to perform local relation aggregation. Extensive experiments on ADE20K and Cityscapes show that with the two modifications on Mask2former, our framework achieves SOTA performance and outperforms Mask2former by clear margins of $1.1\%$ , $1.9\%$ , and $1.1\%$ single-scale mIoU with ResNet-50, Swin-T, and Swin-B backbones on the ADE20K validation set, respectively. Source code is available at https://github.com/ziplab/FASeg. + +# 1. Introduction + +Semantic segmentation aims at assigning each pixel in an image with a semantic class label. As the end-to-end Detection Transformer (DETR) [3,42,49,58] is revolutionizing the paradigm of the object detection task, recent segmentors [2,8,9,54] follow DETR to learn a set of queries repre + +senting the class prototypes or target segments and achieve state-of-the-art performance on semantic segmentation. + +In DETR-like frameworks, providing the queries with meaningful positional priors and encourage each query to concentrate on specific regions is essential to learn representative queries [28, 43, 49, 58]. In this spirit, masked attention [8] is proposed, which restricts each query to only attend to a foreground region predicted by the previous decoder block with binary masks. Although promising, the positional priors in masked attention may be inaccurate and deteriorate performance for two reasons. First, each query comprises a content query that contains semantic information and a positional query that provides positional information for the likely locations of the target segments. However, masked attention still relies on positional queries that are randomly initialized learnable parameters [3, 40] (Figure 1 (a)), which tend to encode the average statistics across the dataset and cannot reflect the segments with large location variances. Second, since each query only attends to the predicted foreground regions, inaccurate predictions lead to error accumulation across the decoder blocks, especially during an early training stage. + +To this end, recent detectors propose to dynamically encode the anchor points into the positional queries to guide queries concentrating around the anchor positions [28, 30, 43] (Figure 1 (b)). The anchor-based query design mitigates the mentioned issues as the positional queries are dynamically generated for each target object, thus providing more accurate positional priors. In addition, it avoids restricting the queries to only attend to the foreground regions with binary masks to mitigate the error accumulation issue. However, the anchor-based queries cannot describe the fine-grained positional priors for semantic segmentation, which has details, edges, and boundaries [5, 6]. + +Motivated by the observations that attention scores imply the salient regions for token pruning [24, 26], self-supervised learning [4], and semantic segmentation [34,56], in this paper, we propose a simple yet effective query design for semantic segmentation, dubbed Dynamic Focus-aware Positional Queries (DFPQ), which dynamically generates + +![](images/7a070ea939ca957a32e48bf79f5c2fa8bb15c0e2cfbc0466f930038ad8de672c.jpg) +Figure 1. (a) The original randomly initialized positional queries [3] as learnable network parameters, where the positional queries are shared among the Transformer decoder blocks and tend to encode dataset statistics modelling the likely positions for the semantic regions, which leads to inaccurate localization. (b) The anchor-based positional queries [43] are conditional on the bounding box coordinates to give each query positional priors around the anchor. However, the anchor points cannot describe semantic regions, thus still sub-optimal for semantic segmentation. (c) Our dynamic focus-aware queries for semantic segmentation are dynamically generated from the cross-attention scores of the preceding decoder block to provide accurate and fine-grained positional priors, facilitating locating and refining the target segments progressively. + +![](images/0c68d443e4abcba8d3329900f0549ac73c1be31aa4d7ba44c106755857c94a85.jpg) + +![](images/71ca13a8e82ab46be2918b56cfa27a40b859eac058d76c6be962badb60f75baa.jpg) + +the positional queries conditioned on the cross-attention scores of the preceding decoder block and the positional encodings for the corresponding image features, simultaneously (Figure 1 (c)). In this way, our DFPQ preserves the localization information of the target segments, thereby providing accurate and fine-grained positional priors and facilitating progressively locating and refining the target segments. When implementing the positional encodings with more powerful ones like [10], our DFPQ is further empowered with higher capacity to encode the neighbourhood information for the target segments. Compared to the anchor-based positional queries [28,43], our DFPQ can cover fine-grained locations for the segmentation details, edges, and boundaries which include rich segmentation cues. + +In addition, we propose an efficient method named High-Resolution Cross-Attention (HRCA) to mine details for segmenting small regions from the high-resolution feature maps $(1/4 \times 1/4$ of the original image size). Considering performing cross-attention on high-resolution feature maps requires a formidable amount of memory footprints and computational complexity, e.g., 11G extra floating-point operations with an input resolution of $512 \times 512$ , we propose to encode token affinity only on the informative areas of high-resolution feature maps that are indicated important in the low-resolution counterparts. In this way, fine-grained details are learned efficiently with affordable memory and computations. + +Our main contributions can be summarized as follows: + +- We make the pioneering attempt to present a simple yet effective query formulation for semantic segmentation, which provides accurate and fine-grained positional priors to localize the target segments, and mitigates the error accumulation problem while being lightweight with little extra computation. +- We propose an efficient high-resolution cross-attention layer to enrich the segmentation details, which dis + +cards the semantically unimportant regions for any target segments in the high-resolution feature maps with affordable memory footprint and computational cost. + +- Extensive experiments on ADE20K and Cityscapes datasets demonstrate that simply incorporating our DFPQ and HRCA into Mask2former [8] achieves significant performance gain and outperforms the SOTA methods. For instance, our FASeg outperforms SOTA methods by $1.1\%$ , $1.3\%$ , and $0.9\%$ single-scale mIoU on the ADE20K [57] validation set with ResNet-50, Swin-T, and Swin-B backbones, respectively. + +# 2. Related Work + +Semantic segmentation with Transformers. The recent segmentors with Transformers [25, 36, 50, 54] have pushed the horizon for semantic segmentation. In general, these segmentors consist of three modules: a backbone, a neck, and a head. Correspondingly, the recent advances can be roughly split into three orthogonal categories. The first category [14, 46, 48, 50, 52, 53] aims at learning more representative features by improving the backbone, mostly by improving the self-attention mechanism in Transformers. For example, focal self-attention [48] combines both fine-grained and coarse-grained features in a backbone self-attention layer. To provide better multi-scale features with neck, the second category [22, 23, 34, 34, 45] improves the feature pyramid network (FPN) [27] or pyramid scene parsing (PSP) [55] structure. For instance, SegFormer [45] simplifies FPN under the Transformer backbone to achieve a better accuracy-efficiency trade-off, and SegDeformer [34] adds external memory tokens to preserve the global information. The third category implements the head with Transformer and conduct set prediction following the DETR-like end-to-end framework [3]. In DETR-like framework, target segments are represented by a set of queries. Considering the importance of providing positional priors for + +the queries [28, 30, 43], masked attention [8] is proposed to restrict the cross-attention only to the local features. Our work also aims at providing better positional priors. In contrast to [8], we follow the recent detectors [28, 43] to provide accurate positional priors with dynamic positional queries rather than the learnable parameterized positional queries [3]. Differently, our DFPQ provides fine-grained positional priors that can cover the locations for fine segmentation details, edges, and boundaries. Very recent work [25] proposes a versatile multi-task head structure to share the mutual information among the segmentation and detection tasks, which however, is not directly comparable to our work. + +Positional encodings for Transformers. Both self-attention and cross-attention for Transformers are permutation-equivalent. Therefore, Positional Encodings (PE) play an essential role in introducing the order of the sequence. In general, the positional encodings include: absolute PE that is generated with sinusoidal functions [35, 40] or being entirely learnable parameters [19, 29]; relative PE that encodes distances between the input tokens [12, 32]; and conditional PE, which is dynamically generated, e.g., PEG [10] generates positional encodings with depth-wise convolution conditioned on the local neighbourhood information. In the same spirit, our DFPQ is also dynamically generated by exploring the idea of conditional encoding [38, 47], thus delivering higher segmentation accuracy. Differently, our DFPQ is tailored specifically for DETR-style semantic segmentation to learn positional priors for each target segment. In addition, since our DFPQ is conditional on the PE for the image features, implementing it with the more powerful PEs [10, 19] can further boost the representational capability of our DFPQ. We investigate the effect of different PE strategies in Section 4.2. + +When solely pre-training Transformer backbones, the positional encodings are generally seen as a part of the feature embeddings and directly be combined with patch features after patchifying the image [15,39]. Differently, in the cross-attention layers of DETR-like frameworks, both the image features and the object queries require additional positional information to provide positional priors for aggregating the query-specific context, which we refer the readers to Section 3.1 for details. Recent detectors [28,43] encode anchor positions into positional queries. In contrast, we design a novel positional query formulation for semantic segmentation to reflect regions of interest instead of anchor points to preserve fine segmentation details. + +# 3. Method + +# 3.1. Preliminary: Cross-attention in DETR + +Before introducing our DFPQ, we first revisit the cross-attention layers in DETR-like frameworks [3]. Cross + +attention layer is a basic module that updates the object queries by aggregating the image context. Since the cross-attention layer is permutation-invariant, both queries and keys require positional information, which introduces the order and provides positional priors to encourage high attention scores for positionally important regions. Specifically, with $N$ , $D$ , $H$ and $W$ respectively denoting the number of queries, the hidden dimensions, the height, and the width of the image features, we have the image features $\pmb{K}_c$ and their positional encodings $\pmb{K}_p$ and get keys $\pmb{K} = \pmb{K}_c + \pmb{K}_p$ , where $\pmb{K} \in \mathbb{R}^{HW \times D}$ . We also have the object queries $\pmb{Q} \in \mathbb{R}^{N \times D}$ , where each query consists of a content query $\pmb{Q}_c$ and a positional query $\pmb{Q}_p$ . + +Then, the cross-attention operation can be formulated as + +$$ +\operatorname {C r s - A t t e n t i o n} (\boldsymbol {Q}, \boldsymbol {K}, \boldsymbol {V}) = \operatorname {s o f t m a x} \left(\frac {\boldsymbol {Q} \boldsymbol {K} ^ {T}}{\sqrt {D}}\right) \boldsymbol {V}, \tag {1} +$$ + +where $\mathbf{V} \in \mathbb{R}^{HW \times D}$ is also the image features in the DETR-like frameworks [3,9,54] and we omit all the linear projections and bias terms for simplicity. From Eq. (1), we can interpret the cross-attention as aggregating image context based on the dot-product similarity between $Q$ and $K$ . Since both the content parts and the positional parts for $Q$ and $K$ contribute to calculating the attention scores, similarities for both parts are considered. Therefore, content similarity contributes to mining the correlation between the object queries and the image features, while positional similarity provides positional priors for each target segment. + +# 3.2. Dynamic Focus-aware Positional Queries + +In this work, we aim to develop positional queries that provide effective positional priors under DETR-like frameworks for semantic segmentation. We argue that generating positional queries conditioned on cross-attention scores has three good properties. First, the cross-attention scores indicate the areas with rich context and may directly reflect the localization information for the target segments [4, 56]. Therefore, when stacking several decoder blocks with cross-attention layers in DETR-like frameworks, the localization information in the preceding block is helpful for progressively locating the target segments in the later blocks, especially when the blocks handle features at different scales [8, 23]. Second, cross-attention scores are dynamically generated. In contrast to the content-agnostic positional queries as learnable parameters in [3], which tend to encode statistics across the dataset and limit models' generalization capability, cross-attention scores are conditional on each target segment reflecting the specific contextual locations, thereby being more accurate. Finally, the cross-attention scores can cover fine-grained segmentation details, edges, and boundaries instead of encoding only a single center or anchor point alike [28, 43]. + +![](images/9524ebe954325f01faa6b81ec81b4445197e664cd4c8e531560348aae0755ab6.jpg) +Figure 2. (a) Cross-attention with our dynamic focus-aware positional queries (DFPQ). "pos" is short for positional. We show generating DFPQ in the dashed box, where we multiply the positional encodings for the image features with the cross-attention scores of the preceding decoder block followed by a projection function $h$ to get DFPQ. Here we omit the bias terms for simplicity. (b) The overall framework for our FASeg is built upon Mask2former [8], which employs a Backbone to encode images, a Pixel Decoder to fuse the features under different resolutions, and a Transformer Decoder to learn the representation for each target segment. We first apply our DFPQ in each decoder block to provide more accurate positional priors (marked with blue arrows). Then, we further propose to incorporate our high-resolution cross-attention (HRCA) layers to model the cross-attention between the queries and the high-resolution feature maps (marked with red arrows). Here "Top-k" selects the top-k pixels indicated by the cross-attention scores of the previous Transformer decoder block. + +![](images/bef652ff03ec48175ac721a89d41d77cc5fa7bcf52aa97c9619ff9f1eb32518a.jpg) + +Therefore, we propose to generate the positional queries conditional on the cross-attention scores of the preceding decoder block and the positional encodings for the corresponding image features, simultaneously, as shown in Figure 2 (a). Specifically, since the positional encodings $\mathbf{K}_p$ for the image features preserve the positional information, we form our DFPQ by aggregating $\mathbf{K}_p$ as indicated by the cross-attention scores $\mathbf{A}$ in the cross-attention layer of the preceding decoder block, which can be formulated as + +$$ +\boldsymbol {Q} _ {p} ^ {t} = h \left(\boldsymbol {A} ^ {t - 1} \boldsymbol {K} _ {p} ^ {t - 1} + \boldsymbol {B}\right), \tag {2} +$$ + +where $t$ is the index of the $t$ -th Transformer decoder block, $\mathbf{A}^{t-1} \in \mathbb{R}^{N \times HW}$ is the cross-attention scores from the $(t-1)$ -th Transformer decoder block, $\mathbf{B} \in \mathbb{R}^{N \times D}$ is learnable network parameters, and $h$ is a two-layered MLP with ReLU non-linearity in between. Note that the bias term $\mathbf{B}$ is the original randomly initialized learnable positional queries, which we employ to stable the training in an early training stage. In this way, we dynamically generate DFPQ to provide positional priors for the target segments. It can also cover the fine-grained segmentation cues that are not restricted by anchor points. + +Note that as our DFPQ directly aggregates the positional information, implementing DFPQ with different $K_{p}$ leads to distinct behaviours. When implementing $K_{p}$ with the absolute sinusoidal function, the resulting DFPQ reflects an anchor point alike [28,43] instead of the target areas. In this case, we implement $K_{p}$ with conditional positional encodings [10] to further encode the neighbourhood information + +and preserve the implicit positional priors for localizing the target segments. We empirically investigate the effect of different positional encodings in Section 4.2. + +# 3.3. Efficient High-resolution Cross-attention + +As demonstrated by the prior arts [23, 38], high-resolution image features are important for segmenting small regions. However, modelling cross-attention between object queries and high-resolution image features requires an unbearable amount of memory footprints and computational cost. In this case, we propose an efficient High-Resolution Cross-Attention (HRCA) layer to mine details from high-resolution feature maps with affordable memory burden. Specifically, we first select the top-k pixels from the low-resolution image features with the highest cross-attention scores for all object queries. We then map these areas to the high-resolution feature map positions in a top-down manner and only perform cross-attention on these positions. Formally, we first get the low-resolution cross-attention scores $\mathbf{A}_l$ , and then derive its high-resolution counterpart $\mathbf{A}_h = f(\mathbf{A}_l)$ with bilinear upsampling operation $f(\cdot)$ . We next include the top-k pixels in $\mathbf{A}_h$ with the highest scores into set $\Omega$ , and the efficient HRCA can be formulated as + +$$ +\operatorname {H R C A} (\boldsymbol {Q}, \boldsymbol {K}, \boldsymbol {V}, \Omega) = \operatorname {s o f t m a x} \left(\frac {\boldsymbol {Q} \boldsymbol {K} ^ {\prime T}}{\sqrt {D}}\right) \boldsymbol {V} ^ {\prime}, \tag {3} +$$ + +where $\pmb{K}^{\prime} = g(\pmb {K},\Omega),\pmb{V}^{\prime} = g(\pmb {V},\Omega)$ and $g$ is the indexing operation. In this way, we only perform cross-attention + +on the informative areas for high-resolution feature maps, thereby saving considerable resource consumption. + +Our HRCA is closely related to the previous sparse attention methods [1, 37, 41, 51] that only attend to a part of the entire sequence. Differently, our HRCA is specialized to the DETR-like frameworks, which determines the informative pixels based on their contribution to the target segments instead of the other pixels. One similar work to our HRCA is the RCDA module [43], which is a representative sparse cross-attention method that decouples cross-attention into a row-wise and column-wise attention to reduce the memory and computation cost. We include the comparison between our HRCA and RCDA [43] in Section 4.2. + +# 3.4. Focus-aware Segmentation Framework + +We first briefly introduce Mask2former [8], which consists of backbone, neck, and head as introduced in Section 2 with the neck and head named "Pixel Decoder" and "Transformer Decoder", respectively. In Mask2former, Pixel Decoder fuses the features at multiple scales following [27,58]. Transformer Decoder cascades three blocks which model the cross-attention between the object queries and the image features of $1/32 \times 1/32$ , $1/16 \times 1/16$ , and $1/8 \times 1/8$ of the original image resolution, respectively. The Transformer Decoder is repeated three times. We refer readers to [8,9] for more details. + +We develop our FASeg upon the Mask2former [8] framework by simply incorporating our DFPQ and HRCA. The overview of our FASeg is depicted in Figure 2 (b). We first provide more accurate and fine-grained positional priors for Mask2former with DFPQ (Section 3.2). We apply DFPQ in the cross-attention layers for each decoder block to provide good positional priors for aggregating the contextual image features to locate target segments. In this way, we progressively localize the target segments as we go deeper in the decoder blocks. Since there are no cross-attention scores before the first Transformer decoder block, we obtain the DFPQ for the first block by performing average pooling on the predicted foreground mask from the auxiliary prediction head as introduced in [8]. Next, we employ HRCA (Section 3.3) to enrich the segmentation details with affordable peak-time memory footprints and computational complexity. We add a fourth decoder block equipped with HRCA to model cross-attention on the high-resolution feature maps after the cascaded three decoder blocks that are already in Mask2former in a top-down manner. With the two simple modifications, our FASeg achieves solid performance gain over the original Mask2former (See Section 4.1). + +# 4. Experiments + +Implementation details. Unless otherwise specified, we adopt the same training settings and implementation details as in Mask2former [8]. For our efficient HRCA in + +Table 1. Performance comparisons with the state-of-the-art semantic segmentation methods on ADE20K val [57] with 150 categories. #P and #F indicate the number of parameters (M) and FLOPs (G). We report both single-scale (s.s.) and multi-scale (m.s.) inference results. + +
MethodBackbonemIoUs.s.s. (%)mIoU m.s. (%)#P#F
UperNet [44]R5042.1-67238
DeepLab V3+ [6]R5044.044.944177
SenFormer [2]R5044.745.2144179
Maskformer [9]R5044.546.74153
PFD [31]R5045.648.37461
Mask2former [8]R5047.249.24471
FASeg (ours)R5048.349.35172
UperNet [44]Swin-T44.446.160236
SenFormer [2]Swin-T46.0-144179
Maskformer [9]Swin-T46.748.84255
PFD [31]Swin-T48.349.67465
Mask2former [8]Swin-T47.749.64774
FASeg (ours)Swin-T49.651.35475
SenFormer [2]Swin-B51.8-204242
Maskformer [9]Swin-B52.753.9102195
PFD [31]Swin-B54.155.3123206
Mask2former [8]Swin-B53.955.1107223
FASeg (ours)Swin-B55.056.0113225
UperNet [44]Swin-L52.153.5234647
SenFormer [2]Swin-L53.154.2314546
Maskformer [9]Swin-L54.155.6212375
PFD [31]Swin-L56.057.2242385
Mask2former [8]Swin-L56.157.3215403
FASeg (ours)Swin-L56.357.7222405
+ +Table 2. Performance comparisons with the state-of-the-art semantic segmentation methods on Cityscapes val [11]. We report single-scale (s.s.) inference results. #P and #F indicate the number of parameters (M) and FLOPs (G). + +
MethodBackbonemIoU s.s. (%)#P#F
Maskformer [9]R5078.541405
Senformer [2]R5078.81441,317
DeepLab V3+ [2]R5079.0--
Mask2former [8]R5079.444526
Maskformer [9]R10179.160561
Mask2former [8]R10180.167628
SenFormer [2]R10180.31621,473
FASeg (ours)R5080.567533
+ +Section 3.3, we select $|\Omega| = \lfloor HW/32 \rfloor$ from the low-resolution feature maps $(1/32 \times 1/32$ of the original image size). By default, we train our models with a batch size of 16 on 8 NVIDIA V100 GPUs. We adopt ResNet [21] and Swin Transformer [29] pre-trained backbones. For ResNet [21], we use the ResNet-50 (R50) variant. For Swin Transformer [29], we use the Swin-T, Swin-B, and Swin-L backbones where Swin-B and Swin-L are pre-trained on ImageNet-22k [13]. Unless specified, we adopt all training settings the same as the default settings of FASeg with R50 [21] backbone on ADE20K val [57] with 150 categories for ablation experiments. We conduct the main + +experiments and ablation studies with the same seeds as Mask2former to seek fair comparisons. + +Datasets. We conduct our experiments on ADE20K [57] and Cityscapes [11]. ADE20K [57] is one of the most challenging large-scale datasets for semantic segmentation, which covers 150 fine-grained semantic concepts, where the training set and validation set contain 20,210 and 2,000 images, respectively. Cityscapes [11] is an urban street-view dataset with high-resolution images from 50 cities with 19 semantic classes, which consists of 2,975 images for the training set and 2,725 images for the validation set. + +Evaluation metrics. We use single-scale (s.s.) and multiscale (m.s.) mean Intersection over Union (mIoU) [17] as the evaluation metric. We also compare models in terms of their model size (number of parameters) and computational complexity with Floating-point Operations (FLOPs) to evaluate the efficiency of these models. For ablation studies on HRCA, we also show the training-time GPU memory consumption. For ADE20K [57] and Cityscapes [11], we calculate FLOPs with fixed $512 \times 512$ and $1024 \times 2048$ image size, respectively. + +Compared methods. We compare our method with the SOTA semantic segmentation methods, including DeepLab V3+ [6], UperNet [44], Maskformer [9], SenFormer [2], PFD [31] and Mask2former [8]. Among them, SenFormer [2], PFD [31] and Mask2former [8] are the recent Transformer-based segmentors, where PFD learns a hierarchy of latent queries to enrich the multi-scale information and SenFormer ensembles the multi-scale predictions. We refer the readers to Section 2 for more details. + +# 4.1. Main Results + +We compare our FASeg with state-of-the-art semantic segmentation methods on ADE20K val [57] and Cityscapes val [11]. The results are reported in Tables 1 and 2. We observe that on ADE20K val (Table 1), with affordable number of extra parameters and FLOPs, our FASeg consistently outperforms the SOTA methods. Specifically, FASeg achieves $48.3\%$ , $49.6\%$ , $55.0\%$ , and $56.3\%$ mIoU for single-scale inference, outperforming the SOTA methods by $1.1\%$ , $1.3\%$ , $0.9\%$ , and $0.2\%$ on R50, Swin-T, Swin-B, and Swin-L backbones, respectively. The solid performance gain demonstrates the superiority of our FASeg framework. Our FASeg has more improvements with the smaller backbones (e.g., R50, Swin-T, and Swin-B). We conjecture that localizing the contextual features with smaller backbones under inferior representational capability is challenging. Nevertheless, our DFPQ provides more accurate positional priors, which ease the localization difficulty and lead to better results. For the comparisons on Cityscapes val in Table 2, we observe that with the R50 backbone, our FASeg outperforms all the SOTA methods under desirable numbers of parameters and FLOPs. Surprisingly, FASeg even + +Table 3. Effect of the positional encodings $\mathbf{K}_p$ for the image features on ADE20K val [57] with 150 categories. + +
KpMask2former [8] +mIoU s.s. (%)FASeg +mIoU s.s. (%)
Sinusoidal [3]47.246.9
Learnable absolute [19]47.047.5
Conditional [10]47.348.3
+ +Table 4. Ablation study for FASeg on ADE20K val [57] and Cityscapes val [11]. #P and #F indicate the number of parameters (M) and FLOPs (G) evaluated on ${512} \times {512}$ images. + +
DFPQHRCAADE20K val +mIoU s.s. (%)Cityscapes val +mIoU s.s. (%)#P#F
47.279.44471
✓47.780.04471
✓47.679.85072
✓✓48.380.55172
+ +Table 5. Performance comparisons between DFPQ and other positional queries variants on ADE20K val [57] with 150 categories. + +
MethodmIoU s.s.(%)
Learnable positional queries46.9
Pre-defined grid anchor positional queries46.6
Dynamic anchor positional queries47.0
Dynamic foreground positional queries47.8
DFPQ48.3
+ +outperforms the SOTA methods employing the R101 backbone, which demonstrates the effectiveness of our FASeg. To further investigate the flexibility and potential of our main contribution DFPQ, we show more experiments on instance segmentation in the supplementary material. + +We next show some qualitative results in Figure 3 and find that our FASeg provides more accurate predictions with finer details. The improved segmentation results again show the superiority of our DFPQ and HRCA. We include more qualitative results in the supplementary material. + +# 4.2. Ablation Study + +Effect of $K_{p}$ . We investigate the effect of the positional encodings $K_{p}$ for the image features on ADE20k val with R50 backbone. The results are reported in Table 3. We observe that different $K_{p}$ have similar performance for Mask2former [8]. However, more powerful $K_{p}$ leads to much higher performance for our FASeg. For instance, FASeg with conditional positional encodings [10] outperforms Mask2former counterpart and FASeg with sinusoidal positional encodings [3] by $1.0\%$ and $1.4\%$ mIoU, respectively. The reason is that compared to Mask2former, our FASeg additionally aggregates $K_{p}$ to get DFPQ as explained in Section 3.2. Therefore, more powerful $K_{p}$ leads to higher representational capability of DFPQ that boosts the performance. We also find that with sinusoidal positional encodings, FASeg has even lower performance than Mask2former as the DFPQ aggregated from sinusoidal positional encodings reflects a single anchor point which can- + +not cover the fine-grained segmentation cues. + +Effectiveness of DFPQ and HRCA. We investigate the effectiveness of our DFPQ and HRCA on ADE20k val and Cityscapes val with the ResNet-50 backbone. The results are reported in Table 4. We observe that both DFPQ and HRCA gain clear margins from the vanilla Mask2former [8]. To be specific, integrating DFPQ on Mask2former boosts the performance by $0.5\%$ and $0.6\%$ mIoU on ADE20k val and Cityscapes val, respectively, with barely any extra parameter and computational cost. It is indicated that DFPQ is lightweight and contributes largely on the performance gain. Employing HRCA on Mask2former leads to $0.4\%$ mIoU gain on both datasets, which however, has 6M more parameters and 1G higher FLOPs. The additional parameters and FLOPs are brought by the extra decoder layers handling high-resolution image features. Finally, our FASeg with both DFPQ and HRCA improves $1.1\%$ mIoU for both ADE20k val and Cityscapes val, demonstrating the superiority of our FASeg. + +DFPQ vs. other positional queries. We investigate the effectiveness of our DFPQ and compare it with other learnable query variants on ADE20K val [57]. The results are presented in Table 5. Here we adopt all the other settings the same as our FASeg with the R50 backbone and only differ the positional queries for all the competitors. Specifically, we compare with four settings: 1) learnable parameterized positional queries that are randomly initialized [3]; 2) positional queries as the pre-defined grid anchor points akin to [43]; 3) positional queries dynamically generated from the center of the foreground masks predicted by the previous layer similar to [28]; 4) positional queries dynamically generated from the entire predicted foreground masks. We find that our DFPQ outperforms all the competitors by large margins. For example, our DFPQ achieves $1.7\%$ and $1.3\%$ higher mIoU than the pre-defined grid and dynamic anchor positional queries, respectively. It is suggested that our DFPQ better suits semantic segmentation than the other positional query variants. We also visualize cross-attention maps among the different positional queries in Figure 4. We observe that our DFPQ (Figure 4 (c)) helps generate more compact and consistent cross-attention maps focusing on the target segments than the learnable parameterized positional queries (Figure 4 (a)) and dynamic anchor positional queries (Figure 4 (b)). + +HRCA vs. other efficient cross-attention methods. We investigate the effectiveness of our HRCA and compare it with other cross-attention methods on ADE20k val. The results are reported in Table 6. For a fair comparison, we only replace HRCA for the other efficient cross-attention methods on our FASeg with the R50 backbone. We compare with three baselines: 1) the vanilla cross-attention that models the entire high-resolution features; 2) our HRCA with randomly sampled top-k pixels to form set $\Omega$ that $|\Omega|$ + +![](images/481313fccca020077f41d58d3db836cf4ced24e7d4756053c42ba4b5c51956ee.jpg) +GT + +![](images/b58ba05f4cdda9506b2581ddc32db368b05abbc09f74678547f65663a1700fc3.jpg) +Mask2former + +![](images/81852ee119ddd22f46cb043c9e538f913af77bb995ad91dfeae8c6ca4d6e793a.jpg) +FASeg + +![](images/902b7511332beebe34c6b185fd6620dd09eaf954f8a0a656c9db0cea2f777111.jpg) +Figure 3. Qualitative results on the ADE20K val [57]. Compared to Mask2former [8], our FASeg predicts masks with finer details and yields more accurate predictions. + +![](images/ddc8e3734bad60cffa4d149c4da1e5bd2f65f1f7bc01ff5d8dc3ae34b6b322b2.jpg) + +![](images/08149fe0ea425113bf2371722d79f1a6b1bc474c076b5004f7755b8f934e9425.jpg) + +Table 6. Performance comparisons between our HRCA and other efficient cross-attention methods on ADE20K val [57] with 150 categories. #F denotes the number of FLOPs (G). The training memory footprint (M) and FLOPs are measured under $512 \times 512$ image resolutions with a batch size of 4 on a single GPU. + +
MethodmIoU s.s. (%)Training Memory (M)#F
Vanilla47.37,45183
Random Ω46.76,34372
RCDA47.56,08272
HRCA48.36,34372
+ +Table 7. Effect of $|\Omega |$ in our efficient HRCA on ADE20K val [57] with 150 categories. #F indicates the number of FLOPs (G). + +
|Ω|mIoU s.s. (%)Training memory (M)#F
HW47.37,45183
[HW/16]47.76,38172
[HW/32]48.36,34372
[HW/64]48.06,31771
+ +is the same as HRCA; 3) RCDA [43] that the cross-attention is decoupled to a row-wise and column-wise attention as introduced in Section 3.3. We empirically find that compared with the vanilla cross-attention, our HRCA achieves $1.0\%$ mIoU gain while exhibiting 1,108M lower training-time GPU memory and 11G lower FLOPs. Our HRCA also outperforms the two efficient cross-attention methods by large margins. For example, HRCA achieves $0.8\%$ higher mIoU than RCDA with marginally increased training-time memory. The results demonstrate the superiority of our HRCA for efficiently identifying and utilizing contextual tokens in high-resolution features. + +Effect of $|\Omega|$ in HRCA. We then investigate how $|\Omega|$ affects the performance, memory consumption and computational complexity on FASeg with R50 backbone on ADE20k val. The results are reported in Table 7. $|\Omega|$ determines the number of contextual tokens used in attention as introduced in Section 3.3. Here we measure the memory consumption by the training-time memory with a batch size of 4 on a single GPU. In the vanilla cross-attention layers, cross-attention attends to the entire feature maps from the encoder, in which case $|\Omega| = HW$ . We observe that our HRCA outperforms the vanilla cross-attention by a signifi + +![](images/44a565ca7c50ea089c93678b618ebc45e8463e0c9d5befd59e2951b750796786.jpg) +Figure 4. Visualizations of the cross-attention maps for learnable positional queries ([3,8]), dynamic anchor positional queries (alike [28]) and our DFPQ. We show the visualizations for the normalized cross-attention maps in the last three decoder blocks and indicate the target segments in the red boxes. The cross-attention maps with the learnable positional queries and the dynamic anchor positional queries are often scattered without a clear focus and mix up different segments, while the cross-attention maps with DFPQ are more compact and consistent to reflect the target segments. + +Table 8. Effect of applying HRCA to other high-resolution feature scales for FASeg with Swin-B Backbone on ADE20K val [57] with 150 categories. + +
1/4 × 1/41/8 × 1/8mIoU s.s. (%)Training Memory (M)
✓55.020,418
✓✓54.919,898
✓54.817,817
+ +cant margin. We conjecture that the sparse property [16, 18] has reduced the redundancy in high-resolution feature maps in our HRCA and leads to higher performance and efficiency. Since our HRCA achieves the highest performance when $|\Omega| = \lfloor HW/32 \rfloor$ , we set $|\Omega| = \lfloor HW/32 \rfloor$ by default for all the other experiments. + +Effect of applying HRCA to other high-resolution feature scales. By default, HRCA is applied only to the high-resolution $1/4 \times 1/4$ feature scale. We explore applying HRCA to $1/8 \times 1/8$ and both $1/4 \times 1/4$ and $1/8 \times 1/8$ feature scales for FASeg with Swin-B backbone on ADE20k val. We measure the training-time memory consumption with a batch size of 4 on a single GPU and report the results in Table 8. We find that the performance only fluctuates within $0.2\%$ mIoU. In particular, modeling the cross-attention only on the $1/8 \times 1/8$ feature scale with HRCA saves more than 2,000M training-time memory, suggesting the potential for extending HRCA to more high-resolution features to alleviate the memory burden. + +# 5. Conclusion + +In this paper, we have explored providing positional priors with positional queries for the DETR-style semantic + +segmentation. Specifically, we have proposed to dynamically generate the positional queries conditioned on the cross-attention scores of the preceding decoder block and the positional encodings for the corresponding image features, simultaneously. We have found that our novel query design delivers more accurate and fine-grained positional priors facilitating localizing the target segments progressively. To mitigate the training-time memory cost when modeling cross-attention on high-resolution feature maps, we have presented an efficient approach to only aggregate the contextual tokens from the high-resolution feature maps, which is shown to learn low-level details with affordable memory and computations. Finally, we have conducted extensive experiments to demonstrate the effectiveness of our proposed framework on the semantic segmentation task and its potential to be extended to other segmentation tasks. + +Limitations and societal impact. Although our HRCA enriches the segmentation details with affordable memory and computations, it still requires more parameters. To this end, we will explore slimming [7, 20] or reusing [33] these blocks to save parameters. Another potential future direction is to explore the explainability of the positional priors generated by our DFPQ. Our technical innovations do not appear to have any negative societal impacts. However, the trained model may deliver unstable or biased predictions with training data that is not reviewed properly. + +Acknowledgement. Dr Jing Zhang was supported by Australian Research Council Projects in part by FL170100117 and IH180100002. + +# References + +[1] Iz Beltagy, Matthew E. Peters, and Arman Cohan. Longformer: The long-document transformer. arXiv:2004.05150, 2020. 5 +[2] Walid Bousselham, Guillaume Thibault, Lucas Pagano, Archana Machireddy, Joe Gray, Young Hwan Chang, and Xubo Song. Efficient self-ensemble framework for semantic segmentation. arXiv preprint arXiv:2111.13280, 2021. 1, 5, 6 +[3] Nicolas Carion, Francisco Massa, Gabriel Synnaeve, Nicolas Usunier, Alexander Kirillov, and Sergey Zagoruyko. End-to-end object detection with transformers. In ECCV, pages 213-229, 2020. 1, 2, 3, 6, 7, 8 +[4] Mathilde Caron, Hugo Touvron, Ishan Misra, Herve Jégou, Julien Mairal, Piotr Bojanowski, and Armand Joulin. Emerging properties in self-supervised vision transformers. 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Recently, masked attention [8] is proposed to restrict each query to only attend to the foreground regions predicted by the preceding decoder block for easier optimization. Although promising, it relies on the learnable parameterized positional queries which tend to encode the dataset statistics, leading to inaccurate localization for distinct individual queries. In this paper, we propose a simple yet effective query design for semantic segmentation termed Dynamic Focus-aware Positional Queries (DFPQ), which dynamically generates positional queries conditioned on the cross-attention scores from the preceding decoder block and the positional encodings for the corresponding image features, simultaneously. Therefore, our DFPQ preserves rich localization information for the target segments and provides accurate and fine-grained positional priors. In addition, we propose to efficiently deal with high-resolution cross-attention by only aggregating the contextual tokens based on the low-resolution cross-attention scores to perform local relation aggregation. Extensive experiments on ADE20K and Cityscapes show that with the two modifications on Mask2former, our framework achieves SOTA performance and outperforms Mask2former by clear margins of " + }, + { + "bbox": [ + 47, + 248, + 289, + 595 + ], + "type": "inline_equation", + "content": "1.1\\%" + }, + { + "bbox": [ + 47, + 248, + 289, + 595 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 248, + 289, + 595 + ], + "type": "inline_equation", + "content": "1.9\\%" + }, + { + "bbox": [ + 47, + 248, + 289, + 595 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 248, + 289, + 595 + ], + "type": "inline_equation", + "content": "1.1\\%" + }, + { + "bbox": [ + 47, + 248, + 289, + 595 + ], + "type": "text", + "content": " single-scale mIoU with ResNet-50, Swin-T, and Swin-B backbones on the ADE20K validation set, respectively. Source code is available at https://github.com/ziplab/FASeg." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 616, + 128, + 628 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 616, + 128, + 628 + ], + "spans": [ + { + "bbox": [ + 47, + 616, + 128, + 628 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 636, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 636, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 636, + 287, + 696 + ], + "type": "text", + "content": "Semantic segmentation aims at assigning each pixel in an image with a semantic class label. As the end-to-end Detection Transformer (DETR) [3,42,49,58] is revolutionizing the paradigm of the object detection task, recent segmentors [2,8,9,54] follow DETR to learn a set of queries repre" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 224, + 545, + 248 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 224, + 545, + 248 + ], + "spans": [ + { + "bbox": [ + 306, + 224, + 545, + 248 + ], + "type": "text", + "content": "senting the class prototypes or target segments and achieve state-of-the-art performance on semantic segmentation." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 251, + 546, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 251, + 546, + 491 + ], + "spans": [ + { + "bbox": [ + 304, + 251, + 546, + 491 + ], + "type": "text", + "content": "In DETR-like frameworks, providing the queries with meaningful positional priors and encourage each query to concentrate on specific regions is essential to learn representative queries [28, 43, 49, 58]. In this spirit, masked attention [8] is proposed, which restricts each query to only attend to a foreground region predicted by the previous decoder block with binary masks. Although promising, the positional priors in masked attention may be inaccurate and deteriorate performance for two reasons. First, each query comprises a content query that contains semantic information and a positional query that provides positional information for the likely locations of the target segments. However, masked attention still relies on positional queries that are randomly initialized learnable parameters [3, 40] (Figure 1 (a)), which tend to encode the average statistics across the dataset and cannot reflect the segments with large location variances. Second, since each query only attends to the predicted foreground regions, inaccurate predictions lead to error accumulation across the decoder blocks, especially during an early training stage." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 495, + 547, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 495, + 547, + 638 + ], + "spans": [ + { + "bbox": [ + 304, + 495, + 547, + 638 + ], + "type": "text", + "content": "To this end, recent detectors propose to dynamically encode the anchor points into the positional queries to guide queries concentrating around the anchor positions [28, 30, 43] (Figure 1 (b)). The anchor-based query design mitigates the mentioned issues as the positional queries are dynamically generated for each target object, thus providing more accurate positional priors. In addition, it avoids restricting the queries to only attend to the foreground regions with binary masks to mitigate the error accumulation issue. However, the anchor-based queries cannot describe the fine-grained positional priors for semantic segmentation, which has details, edges, and boundaries [5, 6]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "text", + "content": "Motivated by the observations that attention scores imply the salient regions for token pruning [24, 26], self-supervised learning [4], and semantic segmentation [34,56], in this paper, we propose a simple yet effective query design for semantic segmentation, dubbed Dynamic Focus-aware Positional Queries (DFPQ), which dynamically generates" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 257, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 257, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 257, + 713 + ], + "type": "text", + "content": "†Corresponding author. E-mail: bohan.zhuang@gmail.com" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "11299" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 71, + 227, + 180 + ], + "blocks": [ + { + "bbox": [ + 53, + 71, + 227, + 180 + ], + "lines": [ + { + "bbox": [ + 53, + 71, + 227, + 180 + ], + "spans": [ + { + "bbox": [ + 53, + 71, + 227, + 180 + ], + "type": "image", + "image_path": "7a070ea939ca957a32e48bf79f5c2fa8bb15c0e2cfbc0466f930038ad8de672c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 187, + 545, + 263 + ], + "lines": [ + { + "bbox": [ + 46, + 187, + 545, + 263 + ], + "spans": [ + { + "bbox": [ + 46, + 187, + 545, + 263 + ], + "type": "text", + "content": "Figure 1. (a) The original randomly initialized positional queries [3] as learnable network parameters, where the positional queries are shared among the Transformer decoder blocks and tend to encode dataset statistics modelling the likely positions for the semantic regions, which leads to inaccurate localization. (b) The anchor-based positional queries [43] are conditional on the bounding box coordinates to give each query positional priors around the anchor. However, the anchor points cannot describe semantic regions, thus still sub-optimal for semantic segmentation. (c) Our dynamic focus-aware queries for semantic segmentation are dynamically generated from the cross-attention scores of the preceding decoder block to provide accurate and fine-grained positional priors, facilitating locating and refining the target segments progressively." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 230, + 70, + 391, + 180 + ], + "blocks": [ + { + "bbox": [ + 230, + 70, + 391, + 180 + ], + "lines": [ + { + "bbox": [ + 230, + 70, + 391, + 180 + ], + "spans": [ + { + "bbox": [ + 230, + 70, + 391, + 180 + ], + "type": "image", + "image_path": "0c68d443e4abcba8d3329900f0549ac73c1be31aa4d7ba44c106755857c94a85.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 392, + 70, + 544, + 180 + ], + "blocks": [ + { + "bbox": [ + 392, + 70, + 544, + 180 + ], + "lines": [ + { + "bbox": [ + 392, + 70, + 544, + 180 + ], + "spans": [ + { + "bbox": [ + 392, + 70, + 544, + 180 + ], + "type": "image", + "image_path": "71ca13a8e82ab46be2918b56cfa27a40b859eac058d76c6be962badb60f75baa.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 281, + 286, + 447 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 281, + 286, + 447 + ], + "spans": [ + { + "bbox": [ + 46, + 281, + 286, + 447 + ], + "type": "text", + "content": "the positional queries conditioned on the cross-attention scores of the preceding decoder block and the positional encodings for the corresponding image features, simultaneously (Figure 1 (c)). In this way, our DFPQ preserves the localization information of the target segments, thereby providing accurate and fine-grained positional priors and facilitating progressively locating and refining the target segments. When implementing the positional encodings with more powerful ones like [10], our DFPQ is further empowered with higher capacity to encode the neighbourhood information for the target segments. Compared to the anchor-based positional queries [28,43], our DFPQ can cover fine-grained locations for the segmentation details, edges, and boundaries which include rich segmentation cues." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 448, + 286, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 448, + 286, + 602 + ], + "spans": [ + { + "bbox": [ + 46, + 448, + 286, + 602 + ], + "type": "text", + "content": "In addition, we propose an efficient method named High-Resolution Cross-Attention (HRCA) to mine details for segmenting small regions from the high-resolution feature maps " + }, + { + "bbox": [ + 46, + 448, + 286, + 602 + ], + "type": "inline_equation", + "content": "(1/4 \\times 1/4" + }, + { + "bbox": [ + 46, + 448, + 286, + 602 + ], + "type": "text", + "content": " of the original image size). Considering performing cross-attention on high-resolution feature maps requires a formidable amount of memory footprints and computational complexity, e.g., 11G extra floating-point operations with an input resolution of " + }, + { + "bbox": [ + 46, + 448, + 286, + 602 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 46, + 448, + 286, + 602 + ], + "type": "text", + "content": ", we propose to encode token affinity only on the informative areas of high-resolution feature maps that are indicated important in the low-resolution counterparts. In this way, fine-grained details are learned efficiently with affordable memory and computations." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 59, + 603, + 280, + 614 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 603, + 280, + 614 + ], + "spans": [ + { + "bbox": [ + 59, + 603, + 280, + 614 + ], + "type": "text", + "content": "Our main contributions can be summarized as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 58, + 616, + 286, + 713 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 58, + 616, + 286, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 616, + 286, + 687 + ], + "spans": [ + { + "bbox": [ + 58, + 616, + 286, + 687 + ], + "type": "text", + "content": "- We make the pioneering attempt to present a simple yet effective query formulation for semantic segmentation, which provides accurate and fine-grained positional priors to localize the target segments, and mitigates the error accumulation problem while being lightweight with little extra computation." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 58, + 689, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 689, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 689, + 286, + 713 + ], + "type": "text", + "content": "- We propose an efficient high-resolution cross-attention layer to enrich the segmentation details, which dis" + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 324, + 281, + 545, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 281, + 545, + 316 + ], + "spans": [ + { + "bbox": [ + 324, + 281, + 545, + 316 + ], + "type": "text", + "content": "cards the semantically unimportant regions for any target segments in the high-resolution feature maps with affordable memory footprint and computational cost." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 317, + 319, + 545, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 319, + 545, + 415 + ], + "spans": [ + { + "bbox": [ + 317, + 319, + 545, + 415 + ], + "type": "text", + "content": "- Extensive experiments on ADE20K and Cityscapes datasets demonstrate that simply incorporating our DFPQ and HRCA into Mask2former [8] achieves significant performance gain and outperforms the SOTA methods. For instance, our FASeg outperforms SOTA methods by " + }, + { + "bbox": [ + 317, + 319, + 545, + 415 + ], + "type": "inline_equation", + "content": "1.1\\%" + }, + { + "bbox": [ + 317, + 319, + 545, + 415 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 317, + 319, + 545, + 415 + ], + "type": "inline_equation", + "content": "1.3\\%" + }, + { + "bbox": [ + 317, + 319, + 545, + 415 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 317, + 319, + 545, + 415 + ], + "type": "inline_equation", + "content": "0.9\\%" + }, + { + "bbox": [ + 317, + 319, + 545, + 415 + ], + "type": "text", + "content": " single-scale mIoU on the ADE20K [57] validation set with ResNet-50, Swin-T, and Swin-B backbones, respectively." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 423, + 391, + 435 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 423, + 391, + 435 + ], + "spans": [ + { + "bbox": [ + 306, + 423, + 391, + 435 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 438, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 438, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 438, + 545, + 713 + ], + "type": "text", + "content": "Semantic segmentation with Transformers. The recent segmentors with Transformers [25, 36, 50, 54] have pushed the horizon for semantic segmentation. In general, these segmentors consist of three modules: a backbone, a neck, and a head. Correspondingly, the recent advances can be roughly split into three orthogonal categories. The first category [14, 46, 48, 50, 52, 53] aims at learning more representative features by improving the backbone, mostly by improving the self-attention mechanism in Transformers. For example, focal self-attention [48] combines both fine-grained and coarse-grained features in a backbone self-attention layer. To provide better multi-scale features with neck, the second category [22, 23, 34, 34, 45] improves the feature pyramid network (FPN) [27] or pyramid scene parsing (PSP) [55] structure. For instance, SegFormer [45] simplifies FPN under the Transformer backbone to achieve a better accuracy-efficiency trade-off, and SegDeformer [34] adds external memory tokens to preserve the global information. The third category implements the head with Transformer and conduct set prediction following the DETR-like end-to-end framework [3]. In DETR-like framework, target segments are represented by a set of queries. Considering the importance of providing positional priors for" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11300" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 227 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 227 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 227 + ], + "type": "text", + "content": "the queries [28, 30, 43], masked attention [8] is proposed to restrict the cross-attention only to the local features. Our work also aims at providing better positional priors. In contrast to [8], we follow the recent detectors [28, 43] to provide accurate positional priors with dynamic positional queries rather than the learnable parameterized positional queries [3]. Differently, our DFPQ provides fine-grained positional priors that can cover the locations for fine segmentation details, edges, and boundaries. Very recent work [25] proposes a versatile multi-task head structure to share the mutual information among the segmentation and detection tasks, which however, is not directly comparable to our work." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 228, + 289, + 490 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 228, + 289, + 490 + ], + "spans": [ + { + "bbox": [ + 46, + 228, + 289, + 490 + ], + "type": "text", + "content": "Positional encodings for Transformers. Both self-attention and cross-attention for Transformers are permutation-equivalent. Therefore, Positional Encodings (PE) play an essential role in introducing the order of the sequence. In general, the positional encodings include: absolute PE that is generated with sinusoidal functions [35, 40] or being entirely learnable parameters [19, 29]; relative PE that encodes distances between the input tokens [12, 32]; and conditional PE, which is dynamically generated, e.g., PEG [10] generates positional encodings with depth-wise convolution conditioned on the local neighbourhood information. In the same spirit, our DFPQ is also dynamically generated by exploring the idea of conditional encoding [38, 47], thus delivering higher segmentation accuracy. Differently, our DFPQ is tailored specifically for DETR-style semantic segmentation to learn positional priors for each target segment. In addition, since our DFPQ is conditional on the PE for the image features, implementing it with the more powerful PEs [10, 19] can further boost the representational capability of our DFPQ. We investigate the effect of different PE strategies in Section 4.2." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 491, + 289, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 491, + 289, + 647 + ], + "spans": [ + { + "bbox": [ + 46, + 491, + 289, + 647 + ], + "type": "text", + "content": "When solely pre-training Transformer backbones, the positional encodings are generally seen as a part of the feature embeddings and directly be combined with patch features after patchifying the image [15,39]. Differently, in the cross-attention layers of DETR-like frameworks, both the image features and the object queries require additional positional information to provide positional priors for aggregating the query-specific context, which we refer the readers to Section 3.1 for details. Recent detectors [28,43] encode anchor positions into positional queries. In contrast, we design a novel positional query formulation for semantic segmentation to reflect regions of interest instead of anchor points to preserve fine segmentation details." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 651, + 104, + 663 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 651, + 104, + 663 + ], + "spans": [ + { + "bbox": [ + 47, + 651, + 104, + 663 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 671, + 251, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 251, + 684 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 251, + 684 + ], + "type": "text", + "content": "3.1. Preliminary: Cross-attention in DETR" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "content": "Before introducing our DFPQ, we first revisit the cross-attention layers in DETR-like frameworks [3]. Cross" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "content": "attention layer is a basic module that updates the object queries by aggregating the image context. Since the cross-attention layer is permutation-invariant, both queries and keys require positional information, which introduces the order and provides positional priors to encourage high attention scores for positionally important regions. Specifically, with " + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "content": " respectively denoting the number of queries, the hidden dimensions, the height, and the width of the image features, we have the image features " + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "inline_equation", + "content": "\\pmb{K}_c" + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "content": " and their positional encodings " + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "inline_equation", + "content": "\\pmb{K}_p" + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "content": " and get keys " + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "inline_equation", + "content": "\\pmb{K} = \\pmb{K}_c + \\pmb{K}_p" + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "inline_equation", + "content": "\\pmb{K} \\in \\mathbb{R}^{HW \\times D}" + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "content": ". We also have the object queries " + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "inline_equation", + "content": "\\pmb{Q} \\in \\mathbb{R}^{N \\times D}" + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "content": ", where each query consists of a content query " + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "inline_equation", + "content": "\\pmb{Q}_c" + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "content": " and a positional query " + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "inline_equation", + "content": "\\pmb{Q}_p" + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 228, + 545, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 228, + 545, + 239 + ], + "spans": [ + { + "bbox": [ + 317, + 228, + 545, + 239 + ], + "type": "text", + "content": "Then, the cross-attention operation can be formulated as" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 312, + 255, + 545, + 289 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 255, + 545, + 289 + ], + "spans": [ + { + "bbox": [ + 312, + 255, + 545, + 289 + ], + "type": "interline_equation", + "content": "\\operatorname {C r s - A t t e n t i o n} (\\boldsymbol {Q}, \\boldsymbol {K}, \\boldsymbol {V}) = \\operatorname {s o f t m a x} \\left(\\frac {\\boldsymbol {Q} \\boldsymbol {K} ^ {T}}{\\sqrt {D}}\\right) \\boldsymbol {V}, \\tag {1}", + "image_path": "466d430ec47b6657a7d8fbd384ab80211268c15b478fbd6cc0385239c1e8e97c.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 293, + 545, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 293, + 545, + 426 + ], + "spans": [ + { + "bbox": [ + 304, + 293, + 545, + 426 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 293, + 545, + 426 + ], + "type": "inline_equation", + "content": "\\mathbf{V} \\in \\mathbb{R}^{HW \\times D}" + }, + { + "bbox": [ + 304, + 293, + 545, + 426 + ], + "type": "text", + "content": " is also the image features in the DETR-like frameworks [3,9,54] and we omit all the linear projections and bias terms for simplicity. From Eq. (1), we can interpret the cross-attention as aggregating image context based on the dot-product similarity between " + }, + { + "bbox": [ + 304, + 293, + 545, + 426 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 304, + 293, + 545, + 426 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 293, + 545, + 426 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 293, + 545, + 426 + ], + "type": "text", + "content": ". Since both the content parts and the positional parts for " + }, + { + "bbox": [ + 304, + 293, + 545, + 426 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 304, + 293, + 545, + 426 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 293, + 545, + 426 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 293, + 545, + 426 + ], + "type": "text", + "content": " contribute to calculating the attention scores, similarities for both parts are considered. Therefore, content similarity contributes to mining the correlation between the object queries and the image features, while positional similarity provides positional priors for each target segment." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 432, + 521, + 445 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 432, + 521, + 445 + ], + "spans": [ + { + "bbox": [ + 306, + 432, + 521, + 445 + ], + "type": "text", + "content": "3.2. Dynamic Focus-aware Positional Queries" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 450, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 450, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 450, + 545, + 715 + ], + "type": "text", + "content": "In this work, we aim to develop positional queries that provide effective positional priors under DETR-like frameworks for semantic segmentation. We argue that generating positional queries conditioned on cross-attention scores has three good properties. First, the cross-attention scores indicate the areas with rich context and may directly reflect the localization information for the target segments [4, 56]. Therefore, when stacking several decoder blocks with cross-attention layers in DETR-like frameworks, the localization information in the preceding block is helpful for progressively locating the target segments in the later blocks, especially when the blocks handle features at different scales [8, 23]. Second, cross-attention scores are dynamically generated. In contrast to the content-agnostic positional queries as learnable parameters in [3], which tend to encode statistics across the dataset and limit models' generalization capability, cross-attention scores are conditional on each target segment reflecting the specific contextual locations, thereby being more accurate. Finally, the cross-attention scores can cover fine-grained segmentation details, edges, and boundaries instead of encoding only a single center or anchor point alike [28, 43]." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11301" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 70, + 281, + 249 + ], + "blocks": [ + { + "bbox": [ + 53, + 70, + 281, + 249 + ], + "lines": [ + { + "bbox": [ + 53, + 70, + 281, + 249 + ], + "spans": [ + { + "bbox": [ + 53, + 70, + 281, + 249 + ], + "type": "image", + "image_path": "9524ebe954325f01faa6b81ec81b4445197e664cd4c8e531560348aae0755ab6.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 257, + 545, + 345 + ], + "lines": [ + { + "bbox": [ + 46, + 257, + 545, + 345 + ], + "spans": [ + { + "bbox": [ + 46, + 257, + 545, + 345 + ], + "type": "text", + "content": "Figure 2. (a) Cross-attention with our dynamic focus-aware positional queries (DFPQ). \"pos\" is short for positional. We show generating DFPQ in the dashed box, where we multiply the positional encodings for the image features with the cross-attention scores of the preceding decoder block followed by a projection function " + }, + { + "bbox": [ + 46, + 257, + 545, + 345 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 46, + 257, + 545, + 345 + ], + "type": "text", + "content": " to get DFPQ. Here we omit the bias terms for simplicity. (b) The overall framework for our FASeg is built upon Mask2former [8], which employs a Backbone to encode images, a Pixel Decoder to fuse the features under different resolutions, and a Transformer Decoder to learn the representation for each target segment. We first apply our DFPQ in each decoder block to provide more accurate positional priors (marked with blue arrows). Then, we further propose to incorporate our high-resolution cross-attention (HRCA) layers to model the cross-attention between the queries and the high-resolution feature maps (marked with red arrows). Here \"Top-k\" selects the top-k pixels indicated by the cross-attention scores of the previous Transformer decoder block." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 283, + 70, + 541, + 249 + ], + "blocks": [ + { + "bbox": [ + 283, + 70, + 541, + 249 + ], + "lines": [ + { + "bbox": [ + 283, + 70, + 541, + 249 + ], + "spans": [ + { + "bbox": [ + 283, + 70, + 541, + 249 + ], + "type": "image", + "image_path": "bef652ff03ec48175ac721a89d41d77cc5fa7bcf52aa97c9619ff9f1eb32518a.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 357, + 287, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 357, + 287, + 464 + ], + "spans": [ + { + "bbox": [ + 46, + 357, + 287, + 464 + ], + "type": "text", + "content": "Therefore, we propose to generate the positional queries conditional on the cross-attention scores of the preceding decoder block and the positional encodings for the corresponding image features, simultaneously, as shown in Figure 2 (a). Specifically, since the positional encodings " + }, + { + "bbox": [ + 46, + 357, + 287, + 464 + ], + "type": "inline_equation", + "content": "\\mathbf{K}_p" + }, + { + "bbox": [ + 46, + 357, + 287, + 464 + ], + "type": "text", + "content": " for the image features preserve the positional information, we form our DFPQ by aggregating " + }, + { + "bbox": [ + 46, + 357, + 287, + 464 + ], + "type": "inline_equation", + "content": "\\mathbf{K}_p" + }, + { + "bbox": [ + 46, + 357, + 287, + 464 + ], + "type": "text", + "content": " as indicated by the cross-attention scores " + }, + { + "bbox": [ + 46, + 357, + 287, + 464 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 46, + 357, + 287, + 464 + ], + "type": "text", + "content": " in the cross-attention layer of the preceding decoder block, which can be formulated as" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 110, + 473, + 287, + 489 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 473, + 287, + 489 + ], + "spans": [ + { + "bbox": [ + 110, + 473, + 287, + 489 + ], + "type": "interline_equation", + "content": "\\boldsymbol {Q} _ {p} ^ {t} = h \\left(\\boldsymbol {A} ^ {t - 1} \\boldsymbol {K} _ {p} ^ {t - 1} + \\boldsymbol {B}\\right), \\tag {2}", + "image_path": "a13a7c0ecb21178d5005e2f4b37b8bc27b6c31a72c3eb519953b785e24545d16.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 498, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 287, + 628 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 498, + 287, + 628 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 498, + 287, + 628 + ], + "type": "text", + "content": " is the index of the " + }, + { + "bbox": [ + 46, + 498, + 287, + 628 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 498, + 287, + 628 + ], + "type": "text", + "content": "-th Transformer decoder block, " + }, + { + "bbox": [ + 46, + 498, + 287, + 628 + ], + "type": "inline_equation", + "content": "\\mathbf{A}^{t-1} \\in \\mathbb{R}^{N \\times HW}" + }, + { + "bbox": [ + 46, + 498, + 287, + 628 + ], + "type": "text", + "content": " is the cross-attention scores from the " + }, + { + "bbox": [ + 46, + 498, + 287, + 628 + ], + "type": "inline_equation", + "content": "(t-1)" + }, + { + "bbox": [ + 46, + 498, + 287, + 628 + ], + "type": "text", + "content": "-th Transformer decoder block, " + }, + { + "bbox": [ + 46, + 498, + 287, + 628 + ], + "type": "inline_equation", + "content": "\\mathbf{B} \\in \\mathbb{R}^{N \\times D}" + }, + { + "bbox": [ + 46, + 498, + 287, + 628 + ], + "type": "text", + "content": " is learnable network parameters, and " + }, + { + "bbox": [ + 46, + 498, + 287, + 628 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 46, + 498, + 287, + 628 + ], + "type": "text", + "content": " is a two-layered MLP with ReLU non-linearity in between. Note that the bias term " + }, + { + "bbox": [ + 46, + 498, + 287, + 628 + ], + "type": "inline_equation", + "content": "\\mathbf{B}" + }, + { + "bbox": [ + 46, + 498, + 287, + 628 + ], + "type": "text", + "content": " is the original randomly initialized learnable positional queries, which we employ to stable the training in an early training stage. In this way, we dynamically generate DFPQ to provide positional priors for the target segments. It can also cover the fine-grained segmentation cues that are not restricted by anchor points." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "content": "Note that as our DFPQ directly aggregates the positional information, implementing DFPQ with different " + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "inline_equation", + "content": "K_{p}" + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "content": " leads to distinct behaviours. When implementing " + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "inline_equation", + "content": "K_{p}" + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "content": " with the absolute sinusoidal function, the resulting DFPQ reflects an anchor point alike [28,43] instead of the target areas. In this case, we implement " + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "inline_equation", + "content": "K_{p}" + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "content": " with conditional positional encodings [10] to further encode the neighbourhood information" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 357, + 545, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 357, + 545, + 392 + ], + "spans": [ + { + "bbox": [ + 305, + 357, + 545, + 392 + ], + "type": "text", + "content": "and preserve the implicit positional priors for localizing the target segments. We empirically investigate the effect of different positional encodings in Section 4.2." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 399, + 519, + 411 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 399, + 519, + 411 + ], + "spans": [ + { + "bbox": [ + 306, + 399, + 519, + 411 + ], + "type": "text", + "content": "3.3. Efficient High-resolution Cross-attention" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 418, + 545, + 644 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 418, + 545, + 644 + ], + "spans": [ + { + "bbox": [ + 304, + 418, + 545, + 644 + ], + "type": "text", + "content": "As demonstrated by the prior arts [23, 38], high-resolution image features are important for segmenting small regions. However, modelling cross-attention between object queries and high-resolution image features requires an unbearable amount of memory footprints and computational cost. In this case, we propose an efficient High-Resolution Cross-Attention (HRCA) layer to mine details from high-resolution feature maps with affordable memory burden. Specifically, we first select the top-k pixels from the low-resolution image features with the highest cross-attention scores for all object queries. We then map these areas to the high-resolution feature map positions in a top-down manner and only perform cross-attention on these positions. Formally, we first get the low-resolution cross-attention scores " + }, + { + "bbox": [ + 304, + 418, + 545, + 644 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_l" + }, + { + "bbox": [ + 304, + 418, + 545, + 644 + ], + "type": "text", + "content": ", and then derive its high-resolution counterpart " + }, + { + "bbox": [ + 304, + 418, + 545, + 644 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_h = f(\\mathbf{A}_l)" + }, + { + "bbox": [ + 304, + 418, + 545, + 644 + ], + "type": "text", + "content": " with bilinear upsampling operation " + }, + { + "bbox": [ + 304, + 418, + 545, + 644 + ], + "type": "inline_equation", + "content": "f(\\cdot)" + }, + { + "bbox": [ + 304, + 418, + 545, + 644 + ], + "type": "text", + "content": ". We next include the top-k pixels in " + }, + { + "bbox": [ + 304, + 418, + 545, + 644 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_h" + }, + { + "bbox": [ + 304, + 418, + 545, + 644 + ], + "type": "text", + "content": " with the highest scores into set " + }, + { + "bbox": [ + 304, + 418, + 545, + 644 + ], + "type": "inline_equation", + "content": "\\Omega" + }, + { + "bbox": [ + 304, + 418, + 545, + 644 + ], + "type": "text", + "content": ", and the efficient HRCA can be formulated as" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 318, + 650, + 545, + 682 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 650, + 545, + 682 + ], + "spans": [ + { + "bbox": [ + 318, + 650, + 545, + 682 + ], + "type": "interline_equation", + "content": "\\operatorname {H R C A} (\\boldsymbol {Q}, \\boldsymbol {K}, \\boldsymbol {V}, \\Omega) = \\operatorname {s o f t m a x} \\left(\\frac {\\boldsymbol {Q} \\boldsymbol {K} ^ {\\prime T}}{\\sqrt {D}}\\right) \\boldsymbol {V} ^ {\\prime}, \\tag {3}", + "image_path": "8ab8c05dc149fcbbe7610228b7df870321d57be80199598c070266beb3785647.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\pmb{K}^{\\prime} = g(\\pmb {K},\\Omega),\\pmb{V}^{\\prime} = g(\\pmb {V},\\Omega)" + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": " is the indexing operation. In this way, we only perform cross-attention" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "11302" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 286, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 286, + 95 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 286, + 95 + ], + "type": "text", + "content": "on the informative areas for high-resolution feature maps, thereby saving considerable resource consumption." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 96, + 286, + 227 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 96, + 286, + 227 + ], + "spans": [ + { + "bbox": [ + 46, + 96, + 286, + 227 + ], + "type": "text", + "content": "Our HRCA is closely related to the previous sparse attention methods [1, 37, 41, 51] that only attend to a part of the entire sequence. Differently, our HRCA is specialized to the DETR-like frameworks, which determines the informative pixels based on their contribution to the target segments instead of the other pixels. One similar work to our HRCA is the RCDA module [43], which is a representative sparse cross-attention method that decouples cross-attention into a row-wise and column-wise attention to reduce the memory and computation cost. We include the comparison between our HRCA and RCDA [43] in Section 4.2." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 234, + 253, + 247 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 234, + 253, + 247 + ], + "spans": [ + { + "bbox": [ + 47, + 234, + 253, + 247 + ], + "type": "text", + "content": "3.4. Focus-aware Segmentation Framework" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 252, + 286, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 252, + 286, + 384 + ], + "spans": [ + { + "bbox": [ + 46, + 252, + 286, + 384 + ], + "type": "text", + "content": "We first briefly introduce Mask2former [8], which consists of backbone, neck, and head as introduced in Section 2 with the neck and head named \"Pixel Decoder\" and \"Transformer Decoder\", respectively. In Mask2former, Pixel Decoder fuses the features at multiple scales following [27,58]. Transformer Decoder cascades three blocks which model the cross-attention between the object queries and the image features of " + }, + { + "bbox": [ + 46, + 252, + 286, + 384 + ], + "type": "inline_equation", + "content": "1/32 \\times 1/32" + }, + { + "bbox": [ + 46, + 252, + 286, + 384 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 252, + 286, + 384 + ], + "type": "inline_equation", + "content": "1/16 \\times 1/16" + }, + { + "bbox": [ + 46, + 252, + 286, + 384 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 252, + 286, + 384 + ], + "type": "inline_equation", + "content": "1/8 \\times 1/8" + }, + { + "bbox": [ + 46, + 252, + 286, + 384 + ], + "type": "text", + "content": " of the original image resolution, respectively. The Transformer Decoder is repeated three times. We refer readers to [8,9] for more details." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 384, + 286, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 384, + 286, + 647 + ], + "spans": [ + { + "bbox": [ + 46, + 384, + 286, + 647 + ], + "type": "text", + "content": "We develop our FASeg upon the Mask2former [8] framework by simply incorporating our DFPQ and HRCA. The overview of our FASeg is depicted in Figure 2 (b). We first provide more accurate and fine-grained positional priors for Mask2former with DFPQ (Section 3.2). We apply DFPQ in the cross-attention layers for each decoder block to provide good positional priors for aggregating the contextual image features to locate target segments. In this way, we progressively localize the target segments as we go deeper in the decoder blocks. Since there are no cross-attention scores before the first Transformer decoder block, we obtain the DFPQ for the first block by performing average pooling on the predicted foreground mask from the auxiliary prediction head as introduced in [8]. Next, we employ HRCA (Section 3.3) to enrich the segmentation details with affordable peak-time memory footprints and computational complexity. We add a fourth decoder block equipped with HRCA to model cross-attention on the high-resolution feature maps after the cascaded three decoder blocks that are already in Mask2former in a top-down manner. With the two simple modifications, our FASeg achieves solid performance gain over the original Mask2former (See Section 4.1)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 658, + 127, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 127, + 670 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 127, + 670 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "text", + "content": "Implementation details. Unless otherwise specified, we adopt the same training settings and implementation details as in Mask2former [8]. For our efficient HRCA in" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 307, + 129, + 545, + 399 + ], + "blocks": [ + { + "bbox": [ + 305, + 71, + 545, + 125 + ], + "lines": [ + { + "bbox": [ + 305, + 71, + 545, + 125 + ], + "spans": [ + { + "bbox": [ + 305, + 71, + 545, + 125 + ], + "type": "text", + "content": "Table 1. Performance comparisons with the state-of-the-art semantic segmentation methods on ADE20K val [57] with 150 categories. #P and #F indicate the number of parameters (M) and FLOPs (G). We report both single-scale (s.s.) and multi-scale (m.s.) inference results." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 129, + 545, + 399 + ], + "lines": [ + { + "bbox": [ + 307, + 129, + 545, + 399 + ], + "spans": [ + { + "bbox": [ + 307, + 129, + 545, + 399 + ], + "type": "table", + "html": "
MethodBackbonemIoUs.s.s. (%)mIoU m.s. (%)#P#F
UperNet [44]R5042.1-67238
DeepLab V3+ [6]R5044.044.944177
SenFormer [2]R5044.745.2144179
Maskformer [9]R5044.546.74153
PFD [31]R5045.648.37461
Mask2former [8]R5047.249.24471
FASeg (ours)R5048.349.35172
UperNet [44]Swin-T44.446.160236
SenFormer [2]Swin-T46.0-144179
Maskformer [9]Swin-T46.748.84255
PFD [31]Swin-T48.349.67465
Mask2former [8]Swin-T47.749.64774
FASeg (ours)Swin-T49.651.35475
SenFormer [2]Swin-B51.8-204242
Maskformer [9]Swin-B52.753.9102195
PFD [31]Swin-B54.155.3123206
Mask2former [8]Swin-B53.955.1107223
FASeg (ours)Swin-B55.056.0113225
UperNet [44]Swin-L52.153.5234647
SenFormer [2]Swin-L53.154.2314546
Maskformer [9]Swin-L54.155.6212375
PFD [31]Swin-L56.057.2242385
Mask2former [8]Swin-L56.157.3215403
FASeg (ours)Swin-L56.357.7222405
", + "image_path": "8f9936d2fddda83c74e757237833327ba6df024258866c3c3327776fbdb12a87.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 307, + 456, + 545, + 556 + ], + "blocks": [ + { + "bbox": [ + 305, + 409, + 545, + 453 + ], + "lines": [ + { + "bbox": [ + 305, + 409, + 545, + 453 + ], + "spans": [ + { + "bbox": [ + 305, + 409, + 545, + 453 + ], + "type": "text", + "content": "Table 2. Performance comparisons with the state-of-the-art semantic segmentation methods on Cityscapes val [11]. We report single-scale (s.s.) inference results. #P and #F indicate the number of parameters (M) and FLOPs (G)." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 456, + 545, + 556 + ], + "lines": [ + { + "bbox": [ + 307, + 456, + 545, + 556 + ], + "spans": [ + { + "bbox": [ + 307, + 456, + 545, + 556 + ], + "type": "table", + "html": "
MethodBackbonemIoU s.s. (%)#P#F
Maskformer [9]R5078.541405
Senformer [2]R5078.81441,317
DeepLab V3+ [2]R5079.0--
Mask2former [8]R5079.444526
Maskformer [9]R10179.160561
Mask2former [8]R10180.167628
SenFormer [2]R10180.31621,473
FASeg (ours)R5080.567533
", + "image_path": "3ae7675995e29f1b624a352f96e1928fa55da9ac4c759eaf056315f3a5b76bd6.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": "Section 3.3, we select " + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "inline_equation", + "content": "|\\Omega| = \\lfloor HW/32 \\rfloor" + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": " from the low-resolution feature maps " + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "inline_equation", + "content": "(1/32 \\times 1/32" + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": " of the original image size). By default, we train our models with a batch size of 16 on 8 NVIDIA V100 GPUs. We adopt ResNet [21] and Swin Transformer [29] pre-trained backbones. For ResNet [21], we use the ResNet-50 (R50) variant. For Swin Transformer [29], we use the Swin-T, Swin-B, and Swin-L backbones where Swin-B and Swin-L are pre-trained on ImageNet-22k [13]. Unless specified, we adopt all training settings the same as the default settings of FASeg with R50 [21] backbone on ADE20K val [57] with 150 categories for ablation experiments. We conduct the main" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "11303" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": "experiments and ablation studies with the same seeds as Mask2former to seek fair comparisons." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 97, + 286, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 97, + 286, + 205 + ], + "spans": [ + { + "bbox": [ + 46, + 97, + 286, + 205 + ], + "type": "text", + "content": "Datasets. We conduct our experiments on ADE20K [57] and Cityscapes [11]. ADE20K [57] is one of the most challenging large-scale datasets for semantic segmentation, which covers 150 fine-grained semantic concepts, where the training set and validation set contain 20,210 and 2,000 images, respectively. Cityscapes [11] is an urban street-view dataset with high-resolution images from 50 cities with 19 semantic classes, which consists of 2,975 images for the training set and 2,725 images for the validation set." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 206, + 286, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 206, + 286, + 326 + ], + "spans": [ + { + "bbox": [ + 46, + 206, + 286, + 326 + ], + "type": "text", + "content": "Evaluation metrics. We use single-scale (s.s.) and multiscale (m.s.) mean Intersection over Union (mIoU) [17] as the evaluation metric. We also compare models in terms of their model size (number of parameters) and computational complexity with Floating-point Operations (FLOPs) to evaluate the efficiency of these models. For ablation studies on HRCA, we also show the training-time GPU memory consumption. For ADE20K [57] and Cityscapes [11], we calculate FLOPs with fixed " + }, + { + "bbox": [ + 46, + 206, + 286, + 326 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 46, + 206, + 286, + 326 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 206, + 286, + 326 + ], + "type": "inline_equation", + "content": "1024 \\times 2048" + }, + { + "bbox": [ + 46, + 206, + 286, + 326 + ], + "type": "text", + "content": " image size, respectively." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 327, + 286, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 327, + 286, + 434 + ], + "spans": [ + { + "bbox": [ + 46, + 327, + 286, + 434 + ], + "type": "text", + "content": "Compared methods. We compare our method with the SOTA semantic segmentation methods, including DeepLab V3+ [6], UperNet [44], Maskformer [9], SenFormer [2], PFD [31] and Mask2former [8]. Among them, SenFormer [2], PFD [31] and Mask2former [8] are the recent Transformer-based segmentors, where PFD learns a hierarchy of latent queries to enrich the multi-scale information and SenFormer ensembles the multi-scale predictions. We refer the readers to Section 2 for more details." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 445, + 132, + 456 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 445, + 132, + 456 + ], + "spans": [ + { + "bbox": [ + 47, + 445, + 132, + 456 + ], + "type": "text", + "content": "4.1. Main Results" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 462, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 462, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 462, + 286, + 713 + ], + "type": "text", + "content": "We compare our FASeg with state-of-the-art semantic segmentation methods on ADE20K val [57] and Cityscapes val [11]. The results are reported in Tables 1 and 2. We observe that on ADE20K val (Table 1), with affordable number of extra parameters and FLOPs, our FASeg consistently outperforms the SOTA methods. Specifically, FASeg achieves " + }, + { + "bbox": [ + 46, + 462, + 286, + 713 + ], + "type": "inline_equation", + "content": "48.3\\%" + }, + { + "bbox": [ + 46, + 462, + 286, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 462, + 286, + 713 + ], + "type": "inline_equation", + "content": "49.6\\%" + }, + { + "bbox": [ + 46, + 462, + 286, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 462, + 286, + 713 + ], + "type": "inline_equation", + "content": "55.0\\%" + }, + { + "bbox": [ + 46, + 462, + 286, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 462, + 286, + 713 + ], + "type": "inline_equation", + "content": "56.3\\%" + }, + { + "bbox": [ + 46, + 462, + 286, + 713 + ], + "type": "text", + "content": " mIoU for single-scale inference, outperforming the SOTA methods by " + }, + { + "bbox": [ + 46, + 462, + 286, + 713 + ], + "type": "inline_equation", + "content": "1.1\\%" + }, + { + "bbox": [ + 46, + 462, + 286, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 462, + 286, + 713 + ], + "type": "inline_equation", + "content": "1.3\\%" + }, + { + "bbox": [ + 46, + 462, + 286, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 462, + 286, + 713 + ], + "type": "inline_equation", + "content": "0.9\\%" + }, + { + "bbox": [ + 46, + 462, + 286, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 462, + 286, + 713 + ], + "type": "inline_equation", + "content": "0.2\\%" + }, + { + "bbox": [ + 46, + 462, + 286, + 713 + ], + "type": "text", + "content": " on R50, Swin-T, Swin-B, and Swin-L backbones, respectively. The solid performance gain demonstrates the superiority of our FASeg framework. Our FASeg has more improvements with the smaller backbones (e.g., R50, Swin-T, and Swin-B). We conjecture that localizing the contextual features with smaller backbones under inferior representational capability is challenging. Nevertheless, our DFPQ provides more accurate positional priors, which ease the localization difficulty and lead to better results. For the comparisons on Cityscapes val in Table 2, we observe that with the R50 backbone, our FASeg outperforms all the SOTA methods under desirable numbers of parameters and FLOPs. Surprisingly, FASeg even" + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 307, + 96, + 543, + 155 + ], + "blocks": [ + { + "bbox": [ + 305, + 70, + 545, + 93 + ], + "lines": [ + { + "bbox": [ + 305, + 70, + 545, + 93 + ], + "spans": [ + { + "bbox": [ + 305, + 70, + 545, + 93 + ], + "type": "text", + "content": "Table 3. Effect of the positional encodings " + }, + { + "bbox": [ + 305, + 70, + 545, + 93 + ], + "type": "inline_equation", + "content": "\\mathbf{K}_p" + }, + { + "bbox": [ + 305, + 70, + 545, + 93 + ], + "type": "text", + "content": " for the image features on ADE20K val [57] with 150 categories." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 96, + 543, + 155 + ], + "lines": [ + { + "bbox": [ + 307, + 96, + 543, + 155 + ], + "spans": [ + { + "bbox": [ + 307, + 96, + 543, + 155 + ], + "type": "table", + "html": "
KpMask2former [8] \nmIoU s.s. (%)FASeg \nmIoU s.s. (%)
Sinusoidal [3]47.246.9
Learnable absolute [19]47.047.5
Conditional [10]47.348.3
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DFPQHRCAADE20K val\nmIoU s.s. (%)Cityscapes val\nmIoU s.s. (%)#P#F
47.279.44471
✓47.780.04471
✓47.679.85072
✓✓48.380.55172
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MethodmIoU s.s.(%)
Learnable positional queries46.9
Pre-defined grid anchor positional queries46.6
Dynamic anchor positional queries47.0
Dynamic foreground positional queries47.8
DFPQ48.3
", + "image_path": "cec784044ff0c038fa6ddc3b50349d5ce418016ac6f0376228a6217c97b5fbd7.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 365, + 545, + 424 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 365, + 545, + 424 + ], + "spans": [ + { + "bbox": [ + 304, + 365, + 545, + 424 + ], + "type": "text", + "content": "outperforms the SOTA methods employing the R101 backbone, which demonstrates the effectiveness of our FASeg. To further investigate the flexibility and potential of our main contribution DFPQ, we show more experiments on instance segmentation in the supplementary material." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 425, + 545, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 425, + 545, + 484 + ], + "spans": [ + { + "bbox": [ + 304, + 425, + 545, + 484 + ], + "type": "text", + "content": "We next show some qualitative results in Figure 3 and find that our FASeg provides more accurate predictions with finer details. The improved segmentation results again show the superiority of our DFPQ and HRCA. We include more qualitative results in the supplementary material." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 491, + 400, + 504 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 491, + 400, + 504 + ], + "spans": [ + { + "bbox": [ + 305, + 491, + 400, + 504 + ], + "type": "text", + "content": "4.2. Ablation Study" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": "Effect of " + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "inline_equation", + "content": "K_{p}" + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": ". We investigate the effect of the positional encodings " + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "inline_equation", + "content": "K_{p}" + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": " for the image features on ADE20k val with R50 backbone. The results are reported in Table 3. We observe that different " + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "inline_equation", + "content": "K_{p}" + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": " have similar performance for Mask2former [8]. However, more powerful " + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "inline_equation", + "content": "K_{p}" + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": " leads to much higher performance for our FASeg. For instance, FASeg with conditional positional encodings [10] outperforms Mask2former counterpart and FASeg with sinusoidal positional encodings [3] by " + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "inline_equation", + "content": "1.0\\%" + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "inline_equation", + "content": "1.4\\%" + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": " mIoU, respectively. The reason is that compared to Mask2former, our FASeg additionally aggregates " + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "inline_equation", + "content": "K_{p}" + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": " to get DFPQ as explained in Section 3.2. Therefore, more powerful " + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "inline_equation", + "content": "K_{p}" + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": " leads to higher representational capability of DFPQ that boosts the performance. We also find that with sinusoidal positional encodings, FASeg has even lower performance than Mask2former as the DFPQ aggregated from sinusoidal positional encodings reflects a single anchor point which can-" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "11304" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 231, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 231, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 231, + 83 + ], + "type": "text", + "content": "not cover the fine-grained segmentation cues." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 86, + 287, + 302 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 86, + 287, + 302 + ], + "spans": [ + { + "bbox": [ + 46, + 86, + 287, + 302 + ], + "type": "text", + "content": "Effectiveness of DFPQ and HRCA. We investigate the effectiveness of our DFPQ and HRCA on ADE20k val and Cityscapes val with the ResNet-50 backbone. The results are reported in Table 4. We observe that both DFPQ and HRCA gain clear margins from the vanilla Mask2former [8]. To be specific, integrating DFPQ on Mask2former boosts the performance by " + }, + { + "bbox": [ + 46, + 86, + 287, + 302 + ], + "type": "inline_equation", + "content": "0.5\\%" + }, + { + "bbox": [ + 46, + 86, + 287, + 302 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 86, + 287, + 302 + ], + "type": "inline_equation", + "content": "0.6\\%" + }, + { + "bbox": [ + 46, + 86, + 287, + 302 + ], + "type": "text", + "content": " mIoU on ADE20k val and Cityscapes val, respectively, with barely any extra parameter and computational cost. It is indicated that DFPQ is lightweight and contributes largely on the performance gain. Employing HRCA on Mask2former leads to " + }, + { + "bbox": [ + 46, + 86, + 287, + 302 + ], + "type": "inline_equation", + "content": "0.4\\%" + }, + { + "bbox": [ + 46, + 86, + 287, + 302 + ], + "type": "text", + "content": " mIoU gain on both datasets, which however, has 6M more parameters and 1G higher FLOPs. The additional parameters and FLOPs are brought by the extra decoder layers handling high-resolution image features. Finally, our FASeg with both DFPQ and HRCA improves " + }, + { + "bbox": [ + 46, + 86, + 287, + 302 + ], + "type": "inline_equation", + "content": "1.1\\%" + }, + { + "bbox": [ + 46, + 86, + 287, + 302 + ], + "type": "text", + "content": " mIoU for both ADE20k val and Cityscapes val, demonstrating the superiority of our FASeg." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 304, + 288, + 603 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 304, + 288, + 603 + ], + "spans": [ + { + "bbox": [ + 46, + 304, + 288, + 603 + ], + "type": "text", + "content": "DFPQ vs. other positional queries. We investigate the effectiveness of our DFPQ and compare it with other learnable query variants on ADE20K val [57]. The results are presented in Table 5. Here we adopt all the other settings the same as our FASeg with the R50 backbone and only differ the positional queries for all the competitors. Specifically, we compare with four settings: 1) learnable parameterized positional queries that are randomly initialized [3]; 2) positional queries as the pre-defined grid anchor points akin to [43]; 3) positional queries dynamically generated from the center of the foreground masks predicted by the previous layer similar to [28]; 4) positional queries dynamically generated from the entire predicted foreground masks. We find that our DFPQ outperforms all the competitors by large margins. For example, our DFPQ achieves " + }, + { + "bbox": [ + 46, + 304, + 288, + 603 + ], + "type": "inline_equation", + "content": "1.7\\%" + }, + { + "bbox": [ + 46, + 304, + 288, + 603 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 304, + 288, + 603 + ], + "type": "inline_equation", + "content": "1.3\\%" + }, + { + "bbox": [ + 46, + 304, + 288, + 603 + ], + "type": "text", + "content": " higher mIoU than the pre-defined grid and dynamic anchor positional queries, respectively. It is suggested that our DFPQ better suits semantic segmentation than the other positional query variants. We also visualize cross-attention maps among the different positional queries in Figure 4. We observe that our DFPQ (Figure 4 (c)) helps generate more compact and consistent cross-attention maps focusing on the target segments than the learnable parameterized positional queries (Figure 4 (a)) and dynamic anchor positional queries (Figure 4 (b))." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "text", + "content": "HRCA vs. other efficient cross-attention methods. We investigate the effectiveness of our HRCA and compare it with other cross-attention methods on ADE20k val. The results are reported in Table 6. For a fair comparison, we only replace HRCA for the other efficient cross-attention methods on our FASeg with the R50 backbone. We compare with three baselines: 1) the vanilla cross-attention that models the entire high-resolution features; 2) our HRCA with randomly sampled top-k pixels to form set " + }, + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\Omega" + }, + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "text", + "content": " that " + }, + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "inline_equation", + "content": "|\\Omega|" + } + ] + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 308, + 80, + 384, + 121 + ], + "blocks": [ + { + "bbox": [ + 340, + 73, + 351, + 80 + ], + "lines": [ + { + "bbox": [ + 340, + 73, + 351, + 80 + ], + "spans": [ + { + "bbox": [ + 340, + 73, + 351, + 80 + ], + "type": "text", + "content": "GT" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 308, + 80, + 384, + 121 + ], + "lines": [ + { + "bbox": [ + 308, + 80, + 384, + 121 + ], + "spans": [ + { + "bbox": [ + 308, + 80, + 384, + 121 + ], + "type": "image", + "image_path": "481313fccca020077f41d58d3db836cf4ced24e7d4756053c42ba4b5c51956ee.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 386, + 80, + 466, + 121 + ], + "blocks": [ + { + "bbox": [ + 406, + 73, + 445, + 80 + ], + "lines": [ + { + "bbox": [ + 406, + 73, + 445, + 80 + ], + "spans": [ + { + "bbox": [ + 406, + 73, + 445, + 80 + ], + "type": "text", + "content": "Mask2former" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 386, + 80, + 466, + 121 + ], + "lines": [ + { + "bbox": [ + 386, + 80, + 466, + 121 + ], + "spans": [ + { + "bbox": [ + 386, + 80, + 466, + 121 + ], + "type": "image", + "image_path": "b58ba05f4cdda9506b2581ddc32db368b05abbc09f74678547f65663a1700fc3.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 468, + 80, + 544, + 121 + ], + "blocks": [ + { + "bbox": [ + 496, + 73, + 517, + 80 + ], + "lines": [ + { + "bbox": [ + 496, + 73, + 517, + 80 + ], + "spans": [ + { + "bbox": [ + 496, + 73, + 517, + 80 + ], + "type": "text", + "content": "FASeg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 468, + 80, + 544, + 121 + ], + "lines": [ + { + "bbox": [ + 468, + 80, + 544, + 121 + ], + "spans": [ + { + "bbox": [ + 468, + 80, + 544, + 121 + ], + "type": "image", + "image_path": "81852ee119ddd22f46cb043c9e538f913af77bb995ad91dfeae8c6ca4d6e793a.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 308, + 121, + 384, + 179 + ], + "blocks": [ + { + "bbox": [ + 308, + 121, + 384, + 179 + ], + "lines": [ + { + "bbox": [ + 308, + 121, + 384, + 179 + ], + "spans": [ + { + "bbox": [ + 308, + 121, + 384, + 179 + ], + "type": "image", + "image_path": "902b7511332beebe34c6b185fd6620dd09eaf954f8a0a656c9db0cea2f777111.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 181, + 545, + 214 + ], + "lines": [ + { + "bbox": [ + 305, + 181, + 545, + 214 + ], + "spans": [ + { + "bbox": [ + 305, + 181, + 545, + 214 + ], + "type": "text", + "content": "Figure 3. Qualitative results on the ADE20K val [57]. Compared to Mask2former [8], our FASeg predicts masks with finer details and yields more accurate predictions." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 385, + 121, + 466, + 179 + ], + "blocks": [ + { + "bbox": [ + 385, + 121, + 466, + 179 + ], + "lines": [ + { + "bbox": [ + 385, + 121, + 466, + 179 + ], + "spans": [ + { + "bbox": [ + 385, + 121, + 466, + 179 + ], + "type": "image", + "image_path": "ddc8e3734bad60cffa4d149c4da1e5bd2f65f1f7bc01ff5d8dc3ae34b6b322b2.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 468, + 121, + 544, + 179 + ], + "blocks": [ + { + "bbox": [ + 468, + 121, + 544, + 179 + ], + "lines": [ + { + "bbox": [ + 468, + 121, + 544, + 179 + ], + "spans": [ + { + "bbox": [ + 468, + 121, + 544, + 179 + ], + "type": "image", + "image_path": "08149fe0ea425113bf2371722d79f1a6b1bc474c076b5004f7755b8f934e9425.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 217, + 546, + 272 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 217, + 546, + 272 + ], + "spans": [ + { + "bbox": [ + 305, + 217, + 546, + 272 + ], + "type": "text", + "content": "Table 6. Performance comparisons between our HRCA and other efficient cross-attention methods on ADE20K val [57] with 150 categories. #F denotes the number of FLOPs (G). The training memory footprint (M) and FLOPs are measured under " + }, + { + "bbox": [ + 305, + 217, + 546, + 272 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 305, + 217, + 546, + 272 + ], + "type": "text", + "content": " image resolutions with a batch size of 4 on a single GPU." + } + ] + } + ], + "index": 14 + }, + { + "type": "table", + "bbox": [ + 307, + 276, + 543, + 335 + ], + "blocks": [ + { + "bbox": [ + 307, + 276, + 543, + 335 + ], + "lines": [ + { + "bbox": [ + 307, + 276, + 543, + 335 + ], + "spans": [ + { + "bbox": [ + 307, + 276, + 543, + 335 + ], + "type": "table", + "html": "
MethodmIoU s.s. (%)Training Memory (M)#F
Vanilla47.37,45183
Random Ω46.76,34372
RCDA47.56,08272
HRCA48.36,34372
", + "image_path": "bcfa7c501da5de30ef0f8a01f1f7fd39e6080687daf21a6b29187db4c68c5357.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_body" + } + ], + "index": 15 + }, + { + "type": "table", + "bbox": [ + 307, + 365, + 542, + 425 + ], + "blocks": [ + { + "bbox": [ + 306, + 338, + 545, + 361 + ], + "lines": [ + { + "bbox": [ + 306, + 338, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 306, + 338, + 545, + 361 + ], + "type": "text", + "content": "Table 7. Effect of " + }, + { + "bbox": [ + 306, + 338, + 545, + 361 + ], + "type": "inline_equation", + "content": "|\\Omega |" + }, + { + "bbox": [ + 306, + 338, + 545, + 361 + ], + "type": "text", + "content": " in our efficient HRCA on ADE20K val [57] with 150 categories. #F indicates the number of FLOPs (G)." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 365, + 542, + 425 + ], + "lines": [ + { + "bbox": [ + 307, + 365, + 542, + 425 + ], + "spans": [ + { + "bbox": [ + 307, + 365, + 542, + 425 + ], + "type": "table", + "html": "
|Ω|mIoU s.s. (%)Training memory (M)#F
HW47.37,45183
[HW/16]47.76,38172
[HW/32]48.36,34372
[HW/64]48.06,31771
", + "image_path": "0d5706d076f4596c5e35e9f05fd951bd342667a00d4111d0df8b10dbefa21fe1.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "table_body" + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 437, + 545, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 545, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 545, + 581 + ], + "type": "text", + "content": "is the same as HRCA; 3) RCDA [43] that the cross-attention is decoupled to a row-wise and column-wise attention as introduced in Section 3.3. We empirically find that compared with the vanilla cross-attention, our HRCA achieves " + }, + { + "bbox": [ + 304, + 437, + 545, + 581 + ], + "type": "inline_equation", + "content": "1.0\\%" + }, + { + "bbox": [ + 304, + 437, + 545, + 581 + ], + "type": "text", + "content": " mIoU gain while exhibiting 1,108M lower training-time GPU memory and 11G lower FLOPs. Our HRCA also outperforms the two efficient cross-attention methods by large margins. For example, HRCA achieves " + }, + { + "bbox": [ + 304, + 437, + 545, + 581 + ], + "type": "inline_equation", + "content": "0.8\\%" + }, + { + "bbox": [ + 304, + 437, + 545, + 581 + ], + "type": "text", + "content": " higher mIoU than RCDA with marginally increased training-time memory. The results demonstrate the superiority of our HRCA for efficiently identifying and utilizing contextual tokens in high-resolution features." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "type": "text", + "content": "Effect of " + }, + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "type": "inline_equation", + "content": "|\\Omega|" + }, + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "type": "text", + "content": " in HRCA. We then investigate how " + }, + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "type": "inline_equation", + "content": "|\\Omega|" + }, + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "type": "text", + "content": " affects the performance, memory consumption and computational complexity on FASeg with R50 backbone on ADE20k val. The results are reported in Table 7. " + }, + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "type": "inline_equation", + "content": "|\\Omega|" + }, + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "type": "text", + "content": " determines the number of contextual tokens used in attention as introduced in Section 3.3. Here we measure the memory consumption by the training-time memory with a batch size of 4 on a single GPU. In the vanilla cross-attention layers, cross-attention attends to the entire feature maps from the encoder, in which case " + }, + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "type": "inline_equation", + "content": "|\\Omega| = HW" + }, + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "type": "text", + "content": ". We observe that our HRCA outperforms the vanilla cross-attention by a signifi" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "11305" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 71, + 547, + 289 + ], + "blocks": [ + { + "bbox": [ + 49, + 71, + 547, + 289 + ], + "lines": [ + { + "bbox": [ + 49, + 71, + 547, + 289 + ], + "spans": [ + { + "bbox": [ + 49, + 71, + 547, + 289 + ], + "type": "image", + "image_path": "44a565ca7c50ea089c93678b618ebc45e8463e0c9d5befd59e2951b750796786.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 293, + 546, + 350 + ], + "lines": [ + { + "bbox": [ + 46, + 293, + 546, + 350 + ], + "spans": [ + { + "bbox": [ + 46, + 293, + 546, + 350 + ], + "type": "text", + "content": "Figure 4. Visualizations of the cross-attention maps for learnable positional queries ([3,8]), dynamic anchor positional queries (alike [28]) and our DFPQ. We show the visualizations for the normalized cross-attention maps in the last three decoder blocks and indicate the target segments in the red boxes. The cross-attention maps with the learnable positional queries and the dynamic anchor positional queries are often scattered without a clear focus and mix up different segments, while the cross-attention maps with DFPQ are more compact and consistent to reflect the target segments." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 48, + 395, + 287, + 439 + ], + "blocks": [ + { + "bbox": [ + 46, + 358, + 288, + 392 + ], + "lines": [ + { + "bbox": [ + 46, + 358, + 288, + 392 + ], + "spans": [ + { + "bbox": [ + 46, + 358, + 288, + 392 + ], + "type": "text", + "content": "Table 8. Effect of applying HRCA to other high-resolution feature scales for FASeg with Swin-B Backbone on ADE20K val [57] with 150 categories." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 395, + 287, + 439 + ], + "lines": [ + { + "bbox": [ + 48, + 395, + 287, + 439 + ], + "spans": [ + { + "bbox": [ + 48, + 395, + 287, + 439 + ], + "type": "table", + "html": "
1/4 × 1/41/8 × 1/8mIoU s.s. (%)Training Memory (M)
✓55.020,418
✓✓54.919,898
✓54.817,817
", + "image_path": "d4a2a5f076e0129c826204dc38d8b5dca511223007a2793ce5c8bf850431aa4a.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 441, + 287, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 441, + 287, + 513 + ], + "spans": [ + { + "bbox": [ + 46, + 441, + 287, + 513 + ], + "type": "text", + "content": "cant margin. We conjecture that the sparse property [16, 18] has reduced the redundancy in high-resolution feature maps in our HRCA and leads to higher performance and efficiency. Since our HRCA achieves the highest performance when " + }, + { + "bbox": [ + 46, + 441, + 287, + 513 + ], + "type": "inline_equation", + "content": "|\\Omega| = \\lfloor HW/32 \\rfloor" + }, + { + "bbox": [ + 46, + 441, + 287, + 513 + ], + "type": "text", + "content": ", we set " + }, + { + "bbox": [ + 46, + 441, + 287, + 513 + ], + "type": "inline_equation", + "content": "|\\Omega| = \\lfloor HW/32 \\rfloor" + }, + { + "bbox": [ + 46, + 441, + 287, + 513 + ], + "type": "text", + "content": " by default for all the other experiments." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 514, + 288, + 669 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 514, + 288, + 669 + ], + "spans": [ + { + "bbox": [ + 46, + 514, + 288, + 669 + ], + "type": "text", + "content": "Effect of applying HRCA to other high-resolution feature scales. By default, HRCA is applied only to the high-resolution " + }, + { + "bbox": [ + 46, + 514, + 288, + 669 + ], + "type": "inline_equation", + "content": "1/4 \\times 1/4" + }, + { + "bbox": [ + 46, + 514, + 288, + 669 + ], + "type": "text", + "content": " feature scale. We explore applying HRCA to " + }, + { + "bbox": [ + 46, + 514, + 288, + 669 + ], + "type": "inline_equation", + "content": "1/8 \\times 1/8" + }, + { + "bbox": [ + 46, + 514, + 288, + 669 + ], + "type": "text", + "content": " and both " + }, + { + "bbox": [ + 46, + 514, + 288, + 669 + ], + "type": "inline_equation", + "content": "1/4 \\times 1/4" + }, + { + "bbox": [ + 46, + 514, + 288, + 669 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 514, + 288, + 669 + ], + "type": "inline_equation", + "content": "1/8 \\times 1/8" + }, + { + "bbox": [ + 46, + 514, + 288, + 669 + ], + "type": "text", + "content": " feature scales for FASeg with Swin-B backbone on ADE20k val. We measure the training-time memory consumption with a batch size of 4 on a single GPU and report the results in Table 8. We find that the performance only fluctuates within " + }, + { + "bbox": [ + 46, + 514, + 288, + 669 + ], + "type": "inline_equation", + "content": "0.2\\%" + }, + { + "bbox": [ + 46, + 514, + 288, + 669 + ], + "type": "text", + "content": " mIoU. In particular, modeling the cross-attention only on the " + }, + { + "bbox": [ + 46, + 514, + 288, + 669 + ], + "type": "inline_equation", + "content": "1/8 \\times 1/8" + }, + { + "bbox": [ + 46, + 514, + 288, + 669 + ], + "type": "text", + "content": " feature scale with HRCA saves more than 2,000M training-time memory, suggesting the potential for extending HRCA to more high-resolution features to alleviate the memory burden." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 675, + 119, + 687 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 675, + 119, + 687 + ], + "spans": [ + { + "bbox": [ + 47, + 675, + 119, + 687 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "content": "In this paper, we have explored providing positional priors with positional queries for the DETR-style semantic" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 360, + 545, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 360, + 545, + 552 + ], + "spans": [ + { + "bbox": [ + 304, + 360, + 545, + 552 + ], + "type": "text", + "content": "segmentation. Specifically, we have proposed to dynamically generate the positional queries conditioned on the cross-attention scores of the preceding decoder block and the positional encodings for the corresponding image features, simultaneously. We have found that our novel query design delivers more accurate and fine-grained positional priors facilitating localizing the target segments progressively. To mitigate the training-time memory cost when modeling cross-attention on high-resolution feature maps, we have presented an efficient approach to only aggregate the contextual tokens from the high-resolution feature maps, which is shown to learn low-level details with affordable memory and computations. Finally, we have conducted extensive experiments to demonstrate the effectiveness of our proposed framework on the semantic segmentation task and its potential to be extended to other segmentation tasks." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 552, + 545, + 671 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 552, + 545, + 671 + ], + "spans": [ + { + "bbox": [ + 304, + 552, + 545, + 671 + ], + "type": "text", + "content": "Limitations and societal impact. Although our HRCA enriches the segmentation details with affordable memory and computations, it still requires more parameters. To this end, we will explore slimming [7, 20] or reusing [33] these blocks to save parameters. Another potential future direction is to explore the explainability of the positional priors generated by our DFPQ. Our technical innovations do not appear to have any negative societal impacts. However, the trained model may deliver unstable or biased predictions with training data that is not reviewed properly." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 671, + 545, + 705 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 671, + 545, + 705 + ], + "spans": [ + { + "bbox": [ + 304, + 671, + 545, + 705 + ], + "type": "text", + "content": "Acknowledgement. Dr Jing Zhang was supported by Australian Research Council Projects in part by FL170100117 and IH180100002." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "11306" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 122 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 122 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 122 + ], + "type": "text", + "content": "[1] Iz Beltagy, Matthew E. 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Among various attacks, targeted attacks aim at misleading victim models to output adversary-desired predictions, which are more challenging and threatening than untargeted ones. Existing targeted attacks can be roughly divided into instance-specific and instance-agnostic attacks. Instance-specific attacks craft adversarial examples via iterative gradient updating on the specific instance. In contrast, instance-agnostic attacks learn a universal perturbation or a generative model on the global dataset to perform attacks. However, they rely too much on the classification boundary of substitute models, ignoring the realistic distribution of the target class, which may result in limited targeted attack performance. And there is no attempt to simultaneously combine the information of the specific instance and the global dataset. To deal with these limitations, we first conduct an analysis via a causal graph and propose to craft transferable targeted adversarial examples by injecting target patterns. Based on this analysis, we introduce a generative attack model composed of a cross-attention guided convolution module and a pattern injection module. Concretely, the former adopts a dynamic convolution kernel and a static convolution kernel for the specific instance and the global dataset, respectively, which can inherit the advantages of both instance-specific and instance-agnostic attacks. And the pattern injection module utilizes a pattern prototype to encode target patterns, which can guide the generation of targeted adversarial examples. Besides, we also provide rigorous theoretical analysis to guarantee the effectiveness of our method. Extensive experiments demonstrate that our method shows superior performance than 10 existing adversarial attacks against 13 models.", + "bbox": [ + 75, + 294, + 472, + 792 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 810, + 209, + 825 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "With the encouraging progress of deep neural networks (DNNs) in various fields [6, 19, 16, 44, 42], recent studies", + "bbox": [ + 76, + 835, + 468, + 866 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b6ccc82cec6d3f316c9a2ef583a8e7e302f91efe28bb8a7134069e1876f4ef0d.jpg", + "image_caption": [ + "Figure 1. Visualization comparison between adversarial examples generated by our method (a) and the instance-specific method MIM [9] (b). Our perturbations (a) not only show an underlying dependency with the input instance, but also have strong semantic patterns or styles of the target class (\"Hippopotamus\"). In contrast, the perturbations generated by MIM perform like random noises. The adversarial examples are generated against ResNet-152, and labels are predicted by another unknown model (VGG-16)." + ], + "image_footnote": [], + "bbox": [ + 506, + 268, + 888, + 445 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "[36, 29, 28, 38] have corroborated that adversarial examples generated with small-magnitude perturbations can mislead the DNNs to make incorrect predictions. Due to the vulnerability of DNNs, adversarial attacks expose a security threat to real application systems based on deep neural networks, especially in some sensitive fields such as autonomous driving [27], face verification and financial systems [43], to name a few. Therefore, adversarial attacks have become a research hotspot over the past decade [2, 48, 35, 3, 33], which are significant in demonstrating the adversarial robustness and stability of deep learning models.", + "bbox": [ + 496, + 597, + 890, + 763 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To further understand adversarial examples, there are tremendous works [1, 48, 33, 4, 36, 38] focusing on adversarial attacks. Recently, it has been found that adversarial examples possess an intriguing property of transferability, which indicates that adversarial examples generated for a white-box model can also mislead another black-box model. Due to this inherent property, black-box attacks become workable in real-world scenarios where attackers cannot access the attacked model. Extensive methods, such as", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* Equal Contribution † Corresponding Author", + "bbox": [ + 99, + 875, + 233, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "16404", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "MIM [9], DIM [53] and CD-AP [40], have made an impressive performance of boosting the transferability for untargeted attacks, which mislead the model to make an incorrect classification without specifying a target class. However, targeted attacks are more challenging compared with untargeted attacks, making the model output the adversary-desired target class. It is claimed in recent works [14, 55] that transferable targeted attacks are more worthy of study because attackers can directly control the unknown model to output the desired prediction, which can expose huge threats to data privacy and security. Therefore, it is of great significance to develop transferable targeted attacks.", + "bbox": [ + 75, + 90, + 472, + 272 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Existing methods of transferable targeted attacks can be roughly categorized into instance-specific [9, 14, 13, 54, 50, 34, 31] and instance-agnostic [52, 35, 27, 40, 39] attacks. Specifically, almost all instance-specific attacks craft adversarial examples via iterative gradient updating, where attackers can only take advantage of the specific input instance, the white-box model and the target class label. Instance-specific attacks rely on optimizing the classification score of the adversary-desired class label to perturb the specific instance, which ignore the global data distribution. As a result, they inevitably lead to adversarial examples over-fitting the white-box model and result in modest transferability of targeted attacks. On the other hand, via learning a universal perturbation [37] or a generative attack model [52, 55], instance-agnostic attacks optimize adversarial perturbations on the global data distribution rather than the specific instance. To a certain extent, they can alleviate the problem of data-specific over-fitting and lead to more transferable targeted adversarial examples. However, taking the generative attack methods as an example, they suffer from two limitations. (1) Most generative attacks [52, 40, 35] still rely on the target label and the classification boundary information of white-box models rather than the realistic data distribution of the target class. Consequently, it is claimed that most generative attacks still have the possibility of over-fitting the white-box model, which may result in limited performance of transferable targeted attacks. (2) Another limitation is that existing generative attacks [39, 55, 27] apply the same network weights to every input instance in the test dataset. Nevertheless, it is considered that the shared network weights cannot stimulate the best attack performance of generative models [39, 55, 55]. Thus these aforementioned limitations have become the bottleneck of developing transferable targeted attacks, to a certain extent.", + "bbox": [ + 75, + 275, + 472, + 805 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address the aforementioned limitations, in this paper we construct a causal graph to formulate the prediction process of classifiers, and analyze the origin of adversarial examples. Based on this analysis, we propose to generate targeted adversarial examples via injecting the specific pattern or style of the target class. To this end, we intro", + "bbox": [ + 75, + 810, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "duce a generative attack model, which can not only inject pattern or style information of the target class to improve transferable targeted attacks, but also learn specialized convolutional kernels for each input instance. Specifically, we designed a cross-attention guided convolution module and a pattern injection module in the proposed generative attack model. (1) The cross-attention guided convolution module consists of a static convolutional kernel and a dynamic convolutional kernel that is computed according to the input instance. Consequently, this static and dynamic mixup module can not only encode the global information of the dataset, but also learn specialized convolutional kernels for each input instance. This paradigm makes our generative model inherit the advantages of both instance-specific and instance-agnostic attacks. (2) The pattern injection module is designed to model the pattern or style information of the target class and guide the generation of targeted adversarial examples. Concretely, we propose a pattern prototype to learn a global pattern representation over images from the target class, and use the prototype to guide the generation of more transferable targeted adversarial examples. And the generated adversarial images of our method are presented in Figure 1. It is observed that our generated perturbations (as shown in Figure 1(a)) pose strong semantic patterns or styles of the target class and show an underlying dependency on the input instance. In contrast, the perturbations (as presented in Figure 1(b)) generated by MIM [9] perform like random noises. Finally, to further understand our method, we provide rigorous theoretical analysis to guarantee the effectiveness of our method, as shown in Section 3.4, where we derive a concise conclusion based on the problem of Gaussian binary classification.", + "bbox": [ + 496, + 90, + 893, + 574 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, the main contributions of this paper are three-fold: (1) We propose a dynamic generative model to craft transferable targeted adversarial examples, which can not only inject pattern or style information of the target class to improve transferable targeted attacks, but also learn specialized convolutional kernels for each input instance. Besides, our method inherits the advantages of both instancespecific and instance-agnostic attacks, and to the best of our knowledge, we are the first to bridge them. (2) We state that injecting the specific pattern or style of the target class can improve the transferability of targeted adversarial examples, and we provide a comprehensive theoretical analysis to verify the rationality of this statement. (3) Extensive experimental results demonstrate that our method significantly boosts the transferability of targeted adversarial examples over 10 existing methods against 13 models.", + "bbox": [ + 496, + 574, + 895, + 816 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 829, + 640, + 845 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Instance-specific Attacks. As the pioneering work [48] exposes the vulnerability of neural networks, many recent methods [54, 17, 3, 11, 29] utilize gradient-based optimization.", + "bbox": [ + 496, + 854, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "16405", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "tion to generate input-dependent adversarial examples. To further boost the transferability of the adversarial example, several works have been proposed by various strategies to optimize the gradient update process. MIM [9] introduces a momentum term during the iterative gradient updating. DIM [53] improves the transferability via integrating diverse input patterns for optimizing, and TIM [10] performs a convolution operation on the gradient that is applicable to any gradient-based attack methods. Besides, some recent works [5, 18, 20] propose to ensemble multiple pre-trained substitute models to craft more transferable adversarial examples. However, these methods pose modest transferability under the targeted attacks setting, because they rely too much on the target label and the classification boundary information of white-box models. Meanwhile, among these methods, they all face the problem of data-specific overfitting, because of ignoring the global data distribution. To overcome these limitations, in this paper, we propose a dynamic generative model to craft more transferable targeted adversarial examples, which can not only encode the global dataset, but also adapt to the specific instance.", + "bbox": [ + 76, + 90, + 472, + 407 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Instance-agnostic Attacks. Distinguished from instance-specific attacks, instance-agnostic attacks learn a universal perturbation [37] or a generative function [35, 27, 51, 41, 55, 40, 39] to craft adversarial examples. Compared with the universal perturbation, the latter is more flexible and has drawn more attention in recent years. Xiao et al. [52] first explore generating adversarial examples with GANs [16], which can consider the whole dataset instead of the specific input instance. CD-AP [40] and TTP [39] exploit generative models to craft more transferable adversarial examples. Recently, Yang et al. [55] boost the transferability of targeted adversarial examples with hierarchical generative networks. To a certain extent, these methods lead to more general and transferable adversarial examples because of alleviating the data-specific over-fitting problem. However, they also suffer from some limitations. First, existing generative attack methods [52, 57, 55, 40, 39] apply the same network weights to each input instance, which may limit the transferability of adversarial examples. And the second is that most of them also rely too much on the target label and the classification boundary of white-box models, ignoring the realistic data distribution of the target class. Motivated by these, in this paper, we propose a dynamic generative attack model, which can not only inject pattern or style information of the target class to improve transferable targeted attacks, but also learn specialized convolutional kernels for each input instance.", + "bbox": [ + 76, + 407, + 472, + 816 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 829, + 169, + 845 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we present the overall scheme of our proposed method, including some preliminaries, motivations, network architectures and theoretical analyses.", + "bbox": [ + 76, + 854, + 468, + 902 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/04c827378fe801b8e8c4dab075e5ac53b2f799071b7b53b7b5187757821b6231.jpg", + "image_caption": [ + "Figure 2. The casual graph of model inference. Each node is a random variable, where $C, S, \\mathbf{x}, \\mathbf{y}$ and $\\theta$ represent content, style or pattern, the input image, the prediction label, and model parameters, respectively. In order to achieve good performance, the model will learn the statistical correlation between the style $S$ and the label $\\mathbf{y}$ ." + ], + "image_footnote": [], + "bbox": [ + 511, + 104, + 684, + 229 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminaries and Motivation", + "text_level": 1, + "bbox": [ + 500, + 247, + 763, + 263 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We denote the clean image as $\\pmb{x} \\in \\mathcal{X}$ , and the attacked model parameterized by $\\theta$ is denoted as $f: \\mathcal{X} \\to \\mathcal{Y}$ . The goal of target attacks is to generate an adversarial perturbation $\\delta$ that can make the model misclassify the input $\\pmb{x}_{adv} = \\pmb{x} + \\delta$ to the predefined class $\\pmb{y}_t$ , which can be formulated as $f(\\pmb{x}_{adv}) = \\pmb{y}_t \\neq f(\\pmb{x})$ . To gain insights into the origin of targeted adversarial examples, we construct a casual graph $\\mathcal{G}$ to formulate the inference of deep learning models, as shown in Figure 2. For the input images $\\pmb{x}$ , we propose to group the whole causes of $\\pmb{x}$ into two categories, content-related cause $C$ and content-independent cause $S$ that can be dubbed as style or pattern cause. This indicates that $C \\rightarrow x \\gets S$ , and $C \\bot S$ . According to human visual intuition, only the content variable $C$ is relevant to the prediction class $y$ . Consequently, we can use the Law of total probability to expand the prediction $P_{\\theta}(\\pmb{y} \\mid \\pmb{x})$ as:", + "bbox": [ + 496, + 271, + 893, + 513 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nP _ {\\theta} (\\boldsymbol {y} \\mid \\boldsymbol {x}) = \\sum_ {s \\in \\mathbb {S}} P _ {\\theta} (s \\mid \\boldsymbol {x}) P _ {\\theta} (\\boldsymbol {y} \\mid \\boldsymbol {x}, s). \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 565, + 522, + 890, + 547 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "But several recent works [56] and Equation (1) imply that deep learning models can learn not only the dependencies between the content $C$ and the label $y$ , but also the statistical correlation between the style $S$ and the label $y$ (i.e., $P_{\\theta}(\\boldsymbol{y} \\mid \\boldsymbol{x}, s)$ ). This phenomenon indicates that deep learning models can capture some detailed texture patterns and style features to achieve good performance, and the output prediction $P_{\\theta}(\\boldsymbol{y} \\mid \\boldsymbol{x})$ will change with the statistical correlation between $\\boldsymbol{y}$ and $S$ (i.e., $P_{\\theta}(\\boldsymbol{y} \\mid \\boldsymbol{x}, s)$ ). And this property certainly offers attackers an opportunity to generate adversarial examples for misleading the model. Therefore, the inference of targeted adversarial examples can be formulated as:", + "bbox": [ + 496, + 558, + 893, + 752 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nP _ {\\theta} \\left(\\boldsymbol {y} _ {t} \\mid \\boldsymbol {x} _ {a d v}\\right) = \\sum_ {s \\in \\mathbb {S}} P _ {\\theta} (s \\mid \\boldsymbol {x} _ {a d v}) P _ {\\theta} \\left(\\boldsymbol {y} _ {t} \\mid \\boldsymbol {x} _ {a d v}, s\\right). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 761, + 890, + 787 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Inspired by Figure 2 and the aforementioned Equation (2), we first propose to exploit the statistical correlation between $\\mathbf{y}_t$ and $S$ (i.e., $P_{\\theta}(\\mathbf{y}_t \\mid \\mathbf{x}_{adv}, s))^1$ , via injecting the specific", + "bbox": [ + 496, + 796, + 893, + 844 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "1The statistical correlation between $\\mathbf{y}_t$ and $S$ (i.e., $P_{\\theta}(\\mathbf{y}_t \\mid \\mathbf{x}_{adv}, s)$ reflects that the model learns some non-robust features. According to the analysis of [24] and [55], the transferability of adversarial examples may arise from non-robust features, such as texture patterns or styles.", + "bbox": [ + 496, + 849, + 893, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "16406", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/5515ccc87363ed233b737da7d7dd3a3d5ddbdf8aa8e2f88d16454a79c9c7d4f1.jpg", + "image_caption": [ + "Figure 3. The architecture of our dynamic generative attack model, which is composed of a cross-attention guided convolution module (denoted as \"Dy_Conv\") and a pattern injection module. The cross-attention guided convolution module consists of a static convolutional kernel and a dynamic convolutional kernel that is computed according to the input instance. For the pattern injection, the pattern prototype $\\pmb{p}_t = \\{\\gamma_t,\\beta_t\\}$ encodes the patterns or styles of the target class, and the \"AdaCN\" layer performs an affine operation to inject $\\pmb{p}_t$ into the generation of adversarial examples. Similar to [25], we introduce $\\pmb{p}_t^{\\mathrm{running}}$ via the EMA updating based on $\\pmb{p}_t$ ." + ], + "image_footnote": [], + "bbox": [ + 155, + 79, + 816, + 327 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "style or pattern of images from the given target class $\\mathbf{y}_t$ to generate targeted transferable adversarial examples.", + "bbox": [ + 75, + 422, + 470, + 453 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To this end, we propose a generative model to craft targeted adversarial examples by injecting the pattern of the target class. Besides, we design a cross-attention guided dynamic convolution module in the generator, which makes our generative model inherit the advantages of both instance-specific and instance-agnostic attacks. Therefore, the formulation of our method can be denoted as", + "bbox": [ + 75, + 453, + 470, + 559 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {x} _ {a d v} = \\operatorname {c l i p} \\left\\{\\operatorname {P r o j} \\left(\\mathcal {W} * G _ {\\theta (\\boldsymbol {x})} (\\boldsymbol {x}, p _ {t}), - \\varepsilon , \\varepsilon\\right) + \\boldsymbol {x} \\right\\}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 119, + 569, + 468, + 585 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\varepsilon$ is the perturbation budget, $\\mathcal{W}$ is a smoothing operator with fixed weights, $p_t$ represents the semantic pattern or style of the target class, and Proj is a projection operation.", + "bbox": [ + 75, + 590, + 468, + 638 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Network Architecture", + "text_level": 1, + "bbox": [ + 76, + 643, + 282, + 659 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Specifically, our generative model is illustrated in Figure 3, which is composed of two modules: ① a cross attention-guided dynamic convolution module (corresponding to \"Dy_Conv\" in the ResBlock of Figure 3), ② a pattern injection module. And the detailed pipeline of our approach is presented in Algorithm 1. In the next section, we mainly describe the two designed modules in detail.", + "bbox": [ + 75, + 667, + 468, + 773 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Cross-attention guided dynamic convolution module. Considering that not only the global dataset needs to be modeled, but also specialized convolution kernels need to be learned for each input, we design a cross-attention guided convolution module. To achieve this goal, as shown in Figure 4, we propose a static and a dynamic convolution kernel parameterized with $W$ and $\\Delta W$ , respectively2. Thus", + "bbox": [ + 75, + 773, + 470, + 878 + ], + "page_idx": 3 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1: Dynamic Generative Targeted Attack" + ], + "code_body": "Input: A white-box model $f$ , training data $\\mathcal{X}$ , target samples $\\mathcal{X}_t$ , perturbation budget $\\epsilon$ , training epoch $T$ . Output: Generative attack model $G_{\\theta}$ . \n1 for $t \\gets 0$ to $T$ do \n2 Sample mini-batches $\\pmb{x} \\sim \\mathcal{X}$ and $\\pmb{x}_t \\sim \\mathcal{X}_t$ . \n3 Get the augmented mini-batches $\\pmb{x}'$ from $\\pmb{x}$ . \n4 Feed $\\pmb{x}$ , $\\pmb{x}'$ and $\\pmb{x}_t$ into the generator to get adversarial examples $\\pmb{x}_{adv}$ and $\\pmb{x}_{adv}'$ , where $\\pmb{x}_t$ is used for extracting and injecting target patterns $p_t$ . \n5 Update $p_t^{\\text{running}}$ based on $p_t$ via EMA updating. \n6 Forward pass $\\pmb{x}_{adv}$ , $\\pmb{x}_{adv}'$ and $\\pmb{x}_t$ through $f$ . \n7 Compute losses $L_{attack}$ , and backward for updating $G_{\\theta}$ . \n8 return Converged generator $G_{\\theta}$ .", + "bbox": [ + 506, + 443, + 890, + 650 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the designed module is formulated as:", + "bbox": [ + 500, + 679, + 751, + 695 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {X} _ {l} = \\operatorname {c o n v} \\left(\\boldsymbol {X} _ {l - 1}; W + \\Delta W\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 604, + 704, + 890, + 718 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $X_{l}$ is the output of layer $l$ . To get dynamic convolution kernels, we design a series of learnable kernels $(N\\times C_{in}\\times C_{out}\\times k^2)^3$ and attention queries $\\pmb {q}\\in R^{N\\times C_{in}}$ , which indicate the attention weight of each kernel. For the layer $l$ , we compute attention weights via performing cross-attention between attention queries $\\pmb{q}$ and the input $\\pmb{X}_{l - 1}\\in R^{C_{in}\\times H\\times W}$ , which can be indicated as:", + "bbox": [ + 496, + 726, + 893, + 830 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\na t t = \\operatorname {s o f t m a x} \\left(\\frac {Q K ^ {\\top}}{\\sqrt {d _ {k}}}\\right) V, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 604, + 840, + 890, + 868 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "2Note that we ignore bias terms for the sake of brevity", + "bbox": [ + 94, + 886, + 383, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "$^3 N$ indicates the number of learnable kernels, $k$ represents the kernel size, $C_{in}$ and $C_{out}$ are the number of input and output channels.", + "bbox": [ + 500, + 875, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "16407", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/76c702c3d176794366de9bc03834ef4564c0c526ede8b2a8ad8c18d647ee2059.jpg", + "image_caption": [ + "Figure 4. The illustration of the proposed cross-attention guided dynamic convolution module, which is composed of a static convolution kernel $W$ and a dynamic convolution kernel $\\Delta W$ ." + ], + "image_footnote": [], + "bbox": [ + 89, + 88, + 450, + 250 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $att \\in R^{N \\times C_{in}}$ , $Q = qW^{q}$ , $K = X_{l-1}^{\\top}W^{k}$ and $V = X_{l-1}^{\\top}W^{v}$ . Then we can get the attention weight $\\alpha = [\\alpha_{1}, \\alpha_{2}, \\dots, \\alpha_{N}] \\in R^{1 \\times N}$ by conducting the average pooling on $att$ , and each element in $\\alpha$ indicates the weight of corresponding kernels. Therefore, the dynamic convolution kernels are implemented as $\\Delta W = \\alpha_{1} * W_{1} + \\alpha_{2} * W_{2} + \\dots + \\alpha_{N} * W_{N}$ . Benefiting from this dynamic and static mixup convolution operation, our proposed generative attack model can inherit the advantages of both instance-specific and instance-agnostic attacks.", + "bbox": [ + 75, + 309, + 468, + 464 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Pattern injection module. First, to encode target patterns and styles during the generation of adversarial examples, we design a pattern prototype $\\pmb{p}_t = \\{\\gamma_t, \\beta_t\\}$ , which is extracted from the features of target samples, as shown in Figure 3. Following [25], we introduce $\\pmb{p}_t^{\\text{running}}$ to model patterns of the global samples for the target class. Note that we update $\\pmb{p}_t^{\\text{running}}$ during each training iteration, which can be indicated as $\\pmb{p}_t^{\\text{running}} = \\lambda \\pmb{p}_t + (1 - \\lambda) \\pmb{p}_t^{\\text{running}}$ . Then we propose an adaptive class normalization (corresponding to \"AdaCN\" in Figure 3) to inject $\\pmb{p}_t$ into the generation of target adversarial examples. Similar to [23], the AdaCN module exploits the learned $\\pmb{p}_t = \\{\\gamma_t, \\beta_t\\}$ to perform an affine operation for injecting target patterns or styles:", + "bbox": [ + 75, + 465, + 470, + 662 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {A d a C N} (\\boldsymbol {X}) = \\gamma_ {t} \\left(\\frac {\\boldsymbol {X} - \\mu (\\boldsymbol {X})}{\\sigma (\\boldsymbol {X})}\\right) + \\beta_ {t}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 155, + 674, + 468, + 703 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\pmb{p}_t = \\{\\pmb{\\gamma}_t, \\pmb{\\beta}_t\\}$ is the target pattern prototype. Note that Equation (6) represents pattern injection during training, and it is necessary to replace $\\pmb{p}_t = \\{\\pmb{\\gamma}_t, \\pmb{\\beta}_t\\}$ with $\\pmb{p}_t^{\\mathrm{running}} = \\{\\pmb{\\gamma}_t^{\\mathrm{running}}, \\pmb{\\beta}_t^{\\mathrm{running}}\\}$ during inference.", + "bbox": [ + 75, + 715, + 468, + 779 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Objective Function", + "text_level": 1, + "bbox": [ + 76, + 789, + 261, + 806 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To lead the victim model to misclassify adversarial examples as the target class, it is necessary to make the output distribution of adversarial examples $f(\\boldsymbol{x}_{adv}), f(\\boldsymbol{x}_{adv}')$ and target samples $f(\\boldsymbol{x}_t)$ consistent. Thus we define the loss", + "bbox": [ + 75, + 813, + 468, + 875 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "function as follows:", + "bbox": [ + 500, + 90, + 633, + 104 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} \\quad = D _ {K L} \\left(f \\left(\\boldsymbol {x} _ {a d v}\\right) \\| f \\left(\\boldsymbol {x} _ {t}\\right)\\right) + D _ {K L} \\left(f \\left(\\boldsymbol {x} _ {t}\\right) \\| f \\left(\\boldsymbol {x} _ {a d v}\\right)\\right) \\tag {7} \\\\ \\mathcal {L} _ {a u g} = D _ {K L} \\left(f (\\boldsymbol {x} _ {a d v} ^ {\\prime}) \\| f (\\boldsymbol {x} _ {t})\\right) + D _ {K L} \\left(f (\\boldsymbol {x} _ {t}) \\| f (\\boldsymbol {x} _ {a d v} ^ {\\prime})\\right) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 522, + 118, + 890, + 148 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Besides, similar to [39], we also introduce a local similarity loss. For a batch of generated adversarial examples $\\{\\pmb{x}_{adv}^i\\}_{i=1}^n$ , $\\{\\pmb{x}_{adv}^{j,i}\\}_{i=1}^n$ and target samples $\\{\\pmb{x}_t^i\\}_{i=1}^n$ , the similarity matrix can be computed as $S_{i,j} = \\frac{f(\\pmb{x}_{adv}^i) \\cdot f(\\pmb{x}_{adv}^{j,i})}{\\|f(\\pmb{x}_{adv}^i)\\| \\|f(\\pmb{x}_{adv}^{j,j})\\|}$ and $S_{i,j}^t = \\frac{f(\\pmb{x}_t^i) \\cdot f(\\pmb{x}_t^j)}{\\|f(\\pmb{x}_t^i)\\| \\|f(\\pmb{x}_t^j)\\|}$ . Hence, we can get the local similarity loss as:", + "bbox": [ + 500, + 160, + 890, + 262 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {s i m} = \\sum_ {i, j} \\overline {{\\mathcal {S}}} _ {i, j} ^ {t} \\log \\frac {\\overline {{\\mathcal {S}}} _ {i , j} ^ {t}}{\\overline {{\\mathcal {S}}} _ {i , j}} + \\sum_ {i, j} \\overline {{\\mathcal {S}}} _ {i, j} \\log \\frac {\\overline {{\\mathcal {S}}} _ {i , j}}{\\overline {{\\mathcal {S}}} _ {i , j} ^ {t}}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 542, + 275, + 890, + 319 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\overline{\\mathcal{S}}_{i,j} = \\frac{\\exp(\\mathcal{S}_{i,j})}{\\sum_k\\exp(\\mathcal{S}_{i,k})}$ and $\\overline{\\mathcal{S}}_{i,j}^t = \\frac{\\exp(\\mathcal{S}_{i,j}^t)}{\\sum_k\\exp(\\mathcal{S}_{i,k}^t)}$ . Finally, the total objective function can be formulated as:", + "bbox": [ + 498, + 330, + 890, + 373 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {a t t a c k}} = \\mathcal {L} + \\mathcal {L} _ {\\text {a u g}} + \\mathcal {L} _ {\\text {s i m}}. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 596, + 387, + 890, + 402 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Theoretical Analyses", + "text_level": 1, + "bbox": [ + 500, + 426, + 694, + 443 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In order to further explain the insights of our method, we consider a concrete setting that allows us to theoretically investigate why our method is effective for boosting target attacks. Please refer to the Supplementary Material for comprehensive proofs of the following theorem.", + "bbox": [ + 496, + 452, + 890, + 527 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Setup. We consider a simple problem of maximum likelihood classification, similar to that of [24], between two Gaussian distributions.", + "bbox": [ + 496, + 527, + 890, + 571 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {X} _ {s} \\sim N \\left(\\boldsymbol {\\mu} _ {s}, \\boldsymbol {\\Sigma} _ {s}\\right), \\quad \\mathcal {X} _ {t} \\sim N \\left(\\boldsymbol {\\mu} _ {t}, \\boldsymbol {\\Sigma} _ {t}\\right), \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 547, + 585, + 890, + 603 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\pmb{\\Sigma}_s, \\pmb{\\Sigma}_t = \\mathrm{diag}\\left\\{\\sigma_{s_1}^2, \\dots, \\sigma_{s_n}^2\\right\\}$ , $\\mathrm{diag}\\left\\{\\sigma_{t_1}^2, \\dots, \\sigma_{t_n}^2\\right\\}$ , respectively. To simplify the following derivation, we introduce a mapping and a translation operation to transform the model into a standard Gaussian binary classification model, which can be denoted as:", + "bbox": [ + 496, + 614, + 890, + 691 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {F} _ {s} = \\boldsymbol {A} \\mathcal {X} _ {s} - \\frac {\\boldsymbol {A} \\boldsymbol {\\mu} _ {s} + \\boldsymbol {\\mu} _ {t}}{2} \\sim N (- \\boldsymbol {\\mu}, \\boldsymbol {\\Sigma}), \\tag {11} \\\\ \\mathcal {F} _ {t} = \\boldsymbol {E} \\mathcal {X} _ {t} - \\frac {\\boldsymbol {A} \\mu_ {s} + \\mu_ {t}}{2} \\sim N (\\boldsymbol {\\mu}, \\boldsymbol {\\Sigma}), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 565, + 705, + 890, + 742 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where the mapping matrix $\\mathbf{A} = \\mathrm{diag}\\left\\{\\frac{\\sigma_{t_1}}{\\sigma_{s_1}},\\frac{\\sigma_{t_2}}{\\sigma_{s_2}}\\dots ,\\frac{\\sigma_{t_n}}{\\sigma_{s_n}}\\right\\}$ , $\\mathbf{E}$ is the identity matrix and $\\pmb {\\mu} = \\frac{-\\pmb{A}\\pmb{\\mu}_s + \\pmb{\\mu}_t}{2},\\pmb {\\Sigma} = \\pmb{\\Sigma}_t$ . To perform targeted attacks against this model with a given sample $x_{s}\\in \\mathcal{X}_{s}$ and the target label $t$ , where $A\\pmb {x}_s - \\frac{A\\pmb{\\mu}_s + \\pmb{\\mu}_t}{2} = f_s\\in \\mathcal{F}_s$ and $f_{s} + \\delta^{\\star} = A(x_{s} + \\delta) - \\frac{A\\mu_{s} + \\mu_{t}}{2}$ we aim to solve the following optimization problem:", + "bbox": [ + 498, + 750, + 890, + 852 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\delta} = \\boldsymbol {A} ^ {- 1} \\boldsymbol {\\delta} ^ {\\star}, \\quad \\boldsymbol {\\delta} ^ {\\star} = \\underset {\\| \\boldsymbol {\\delta} ^ {\\prime} \\| _ {2} ^ {2} \\leqslant \\varepsilon^ {2}} {\\operatorname {a r g m a x}} \\left(\\boldsymbol {f} _ {s} + \\boldsymbol {\\delta} ^ {\\prime}\\right) ^ {\\top} \\boldsymbol {\\Sigma} ^ {- 1} \\boldsymbol {\\mu}. \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 537, + 876, + 890, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "${}^{4}{W}_{1},{W}_{2}\\cdots {W}_{N}$ are the learnable kernels.", + "bbox": [ + 93, + 885, + 328, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "16408", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/78bb888f4e912ee8f33e77f1f3cf04fdec3cc72482f8c7ed246f3e63fadb8af9.jpg", + "table_caption": [ + "Table 1. The attack success rates against normally trained models on ImageNet NeurIPS validation set, and the perturbation budget $\\ell_{\\infty} \\leq 16/255$ . Note that the results are averaged on 8 different target classes." + ], + "table_footnote": [], + "table_body": "
Subsite ModelMethodInc-v3Inc-v4Inc-Res-v2Res152Densenet-121GoogleNetVgg-16
Inc-v3MIM99.900.801.000.400.200.200.30
TI-MIM98.500.500.500.300.200.400.40
SI-MIM99.801.502.000.800.700.700.50
DIM95.602.700.500.801.100.400.80
TI-DIM96.001.101.200.500.500.500.80
SI-DIM90.203.804.402.002.201.701.40
CD-AP94.2057.6060.1037.1041.6032.3041.70
TTP91.3746.0439.3716.4033.4725.8025.73
C-GSP93.4066.9066.6041.6046.4040.0045.00
GAP86.9045.0634.4834.4841.7426.8934.34
Ours94.6367.9555.0350.5047.3847.6748.11
Res152MIM0.500.400.6099.700.300.300.20
TI-MIM0.300.300.3096.500.300.400.30
SI-MIM1.301.201.6099.501.001.400.70
DIM2.302.203.0092.300.200.800.70
TI-DIM0.800.701.0090.600.600.800.50
SI-DIM4.204.805.4090.504.203.602.00
CD-AP33.3043.7042.7096.6053.8036.6034.10
TTP62.0349.2038.7095.1282.9665.0962.82
C-GSP37.7047.6045.1093.2064.2041.7045.90
GAP30.9931.4320.4884.8658.3529.8939.70
Ours66.8353.6247.6196.4886.6168.2969.58
Vgg-16MIM0.260.470.200.350.400.3490.24
TI-MIM0.430.630.340.551.450.6489.13
SI-MIM0.350.570.420.310.560.5290.89
DIM0.751.300.551.001.881.0397.70
TI-DIM0.230.380.170.290.480.3593.71
SI-DIM0.871.120.700.951.891.5591.42
CD-AP5.328.944.879.3314.023.1996.82
TTP22.5117.149.6822.6840.8722.4197.59
C-GSP9.429.603.0111.7632.2813.3396.81
GAP3.115.261.505.0811.232.7093.00
Ours28.1821.789.5625.2746.5523.7093.00
", + "bbox": [ + 217, + 128, + 750, + 494 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Taking advantage of the method of Lagrange multipliers, we can easily get the optimal solution as follows:", + "bbox": [ + 76, + 520, + 468, + 551 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{r l} \\delta^ {\\star} & = \\frac {1}{\\lambda} \\Sigma^ {- 1} \\boldsymbol {\\mu}, \\\\ s & = \\Sigma^ {- 1} [ A ^ {- 1} (A (\\quad , \\quad , \\quad , \\quad) ] \\end{array} \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 568, + 468, + 593 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\delta} = \\frac {\\hat {\\boldsymbol {\\Sigma}} ^ {- 1}}{2 \\lambda} \\left[ \\boldsymbol {A} ^ {- 1} \\left(\\boldsymbol {A} \\left(\\boldsymbol {x} _ {s} - \\boldsymbol {\\mu} _ {s}\\right) + \\boldsymbol {\\mu} _ {t}\\right) - \\boldsymbol {x} _ {s} \\right]. \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 583, + 468, + 604 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Going a step further, we rewrite the solution of $\\delta$ into a more concise formula as:", + "bbox": [ + 76, + 625, + 468, + 655 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\delta} = C _ {1} \\left[ \\left( \\begin{array}{c c c} \\frac {\\sigma_ {t _ {1}}}{\\sigma_ {s _ {1}}} & & \\\\ & \\ddots & \\\\ & & \\frac {\\sigma_ {t _ {n}}}{\\sigma_ {s _ {n}}} \\end{array} \\right) \\left(\\boldsymbol {x} _ {s} - \\boldsymbol {\\mu} _ {s}\\right) + \\boldsymbol {\\mu} _ {t} \\right] - C _ {2} \\boldsymbol {x} _ {s}, \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 690, + 468, + 757 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $C_1 = \\frac{\\Sigma^{-1}A^{-1}}{2\\lambda}$ and $C_2 = \\frac{\\Sigma^{-1}}{2\\lambda}$ . In fact, note that the item of represents target pattern or style injection, which is consistent with the previous works [23, 26]. Therefore, the formulation of Equation (14) shows a close underlying correlation between the optimal targeted adversarial perturbation and the embedding of target pattern or style, which also theoretically guarantees the effectiveness of our proposed generative model for targeted attacks.", + "bbox": [ + 76, + 773, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 518, + 633, + 535 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we conduct extensive experiments to demonstrate the effectiveness of our method for targeted attacks under various settings. Please feel free to get more experimental results in our Supplementary Material.", + "bbox": [ + 498, + 545, + 892, + 607 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 500, + 617, + 689, + 633 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Dataset. Following [55], we perform training on ImageNet [7] training set, and evaluate on ImageNet-NeurIPS (1k) proposed by NeurIPS 2017 adversarial competition [30].", + "bbox": [ + 498, + 642, + 893, + 686 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Victim Models. We consider 13 attacked models in our experiments. The normally trained models include Inception-v3 (Inc-v3) [47], Inception-v4 (Inc-v4) [45], DenseNet-121 [22], GoogleNet [46], ResNet-152 (Res-152) [19], and VGG16 (Vgg-16) [44] and Inception-ResNet (Inc-Res-v2) [45]. Besides, we also consider several models with robust training mechanisms, including adv-Inception-v3 (Adv-Inc-v3) [17], ens-adv-Inception-ResNet-v2 (Ens-Adv-IncRes-v2) [18] and ResNet-50 trained with various robust training tricks [21, 15].", + "bbox": [ + 498, + 688, + 890, + 838 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baseline Attacks. To illustrate the effectiveness of our method, we compare it with instance-specific attacks and instance-agnostic attacks. Instance-specific attacks mainly include MIM [9], DIM [53], SIM [32] and TIM [10], while", + "bbox": [ + 498, + 839, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "16409", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. The attack success rates against robust models on ImageNet NeurIPS validation set. The perturbation budget $\\ell_{\\infty} \\leq 16/255$ . Adv-Inc-v3 [29] and Ens-Adv-IncRes-v2 [49] are trained with the adversarial training mechanism. Res50_SIN (stylized ImageNet), Res50_SIN_IN (mixture of stylized ImageNet and Nature ImageNet) and Res50_SIN_fine_IN (mixture of stylized ImageNet and Nature ImageNet with finetuning tricks) are trained with auxiliary dataset [15], and Res50_Augmix [21] is trained with the state-of-the-art data augmentation approach. Note that the results are averaged on 8 different target classes.", + "bbox": [ + 75, + 75, + 893, + 148 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/4d9a7dd27f0645f00cd9502f86ce1acdbccf089df1848aeafa9b83dcd779e372.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Subsite ModelMethodAdv-Inc-v3Ens-IncRes-v2Res50_SINRes50_SIN_INRes50_SIN_fine_INRes50_AugMix
Res152MIM0.190.150.281.582.750.78
TI-MIM0.610.730.502.514.751.76
SI-MIM0.240.240.390.660.840.36
DIM0.630.370.948.5014.223.77
TI-DIM0.230.300.280.761.490.49
SI-DIM0.710.710.752.733.891.37
CD-AP3.776.487.0963.7276.7949.67
TTP27.9926.0824.6172.4774.5170.96
GAP5.724.517.3371.0483.6452.07
Ours31.1030.0727.7077.1380.5576.78
VGG16MIM0.140.150.160.400.340.19
TI-MIM0.260.240.200.450.570.28
SI-MIM0.280.200.210.490.250.14
DIM0.220.160.270.930.990.49
TI-DIM0.140.190.210.350.340.21
SI-DIM0.500.360.330.800.690.26
CD-AP0.360.340.354.6310.203.60
TTP3.753.202.6627.8032.7016.57
GAP0.300.520.424.528.923.35
Ours4.143.222.6630.1638.1017.95
", + "bbox": [ + 156, + 157, + 810, + 398 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/27526b296dfac3020fb371480d3ee4ef4707b685d318541607b39cb280af87f9.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 81, + 421, + 261, + 551 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c5baa04f5376891c990c7585a774bcbf29672695c0b37a3ad4f58cf05d34eac3.jpg", + "image_caption": [ + "(b)", + "Figure 5. Attack success rates of targeted adversarial examples generated by various generative attack methods against different input process defense methods. Figure (a) displays the results against various input smooth methods (including gaussian, medium and average smoothing). Figure (b) shows the results against JPEG compression (the JPEG quality factor varies from 70 to 90). Here, the substitute model is Res-152 and the target model is Vgg-16." + ], + "image_footnote": [], + "bbox": [ + 274, + 422, + 455, + 554 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "instance-agnostic attacks include CD-AP [40], TTP [39], GAP [41] and C-GSP [55]. In our experiments, the perturbation size $\\varepsilon = 16 / 255$ , the decay factor $\\mu_0$ is 1 in MIM, the transform probability is 0.7 in DIM, and the kernel size is 15 in TIM. And other hyper-parameters follow the default settings provided in their original works.", + "bbox": [ + 75, + 681, + 468, + 773 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Comparison with State-of-the-art Methods", + "text_level": 1, + "bbox": [ + 76, + 785, + 441, + 801 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Attack Normally Trained Models. To evaluate the performance of our method, we first perform targeted adversarial attacks to compare the transferability across normally trained models of adversarial examples generated by various methods, including 6 iterative instance-specific attack methods and 5 instance-agnostic attack methods. As shown", + "bbox": [ + 75, + 809, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "in Table 1, our dynamic generative attack method reaches the best transferability on 16 out of 18 various black-box cases. Furthermore, the attack success rate of our method against normally trained models is $65.42\\%$ on average with the substitute model as Res-152, which outperforms the best of baselines [39] by $5.28\\%$ on average. Another interesting discovery is that iterative instance-specific attack methods can reach better performance under the setting of white-box attacks, while generative attack methods show more transferability when adapting the adversarial examples to a black-box model. Among these generative methods, our method can still generate targeted adversarial examples with higher transferability than others.", + "bbox": [ + 496, + 422, + 893, + 619 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Attack Models with Robust Training Mechanisms. To comprehensively verify the effectiveness of our method, we compare the transferability of our approach with baselines against several robust models, which are trained with various robust training strategies. As presented in Table 2, although the attack success rate against these robust models is relatively low, our method is still able to outperform baseline methods. Our generative attack method achieves the best performance of targeted transferable adversarial attacks on 11 over 12 cases. And regarding Res-152 as the substitute model, our method outperforms the best of baselines [39] by $4.45\\%$ on average. Compared with normally trained models, models with adversarial or robust training strategies are difficult to attack successfully, which indicates they are more robust than normal models.", + "bbox": [ + 496, + 623, + 895, + 851 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Attack Models with Input Process Defense. Another widely used and simple defense method is Input Process, which leverages image processing techniques to remove", + "bbox": [ + 498, + 854, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "16410", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/02657f5b2009007f81625b8fb5da157bdd6854afa234b6f86b9709b71cdd564f.jpg", + "image_caption": [ + "Figure 6. Visualization results of adversarial examples generated by our proposed method. The 1st, 2nd and 3rd rows show clean images, adversarial perturbations and adversarial examples, respectively. And (a), (b) and (c) display the results of different target classes (French bulldog, Fire engine and Street sign), which indicate that different target classes lead to different patterns or texture styles of the generated perturbations and adversarial images. Please refer to our Supplementary Material for more qualitative examples." + ], + "image_footnote": [], + "bbox": [ + 145, + 70, + 823, + 284 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6c49253a6a03b5a3957d19de54ee2cbedacf77992c3ab3178a4a7c1df9fea5ac.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 81, + 356, + 272, + 469 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f0f4a1a912ac4e7095b741ca813ab8ad4cf6713ab4201b4bc53de02848f3d2d4.jpg", + "image_caption": [ + "(b)", + "Figure 7. Ablation studies. (a) Effect of the number of target samples. (b) Effect of the number of learnable convolution kernels. Note that the substitute model is Res-152, while victim models include Vgg-16, GoogleNet and Inc-v3." + ], + "image_footnote": [], + "bbox": [ + 274, + 356, + 460, + 469 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "the adversary perturbation before feeding into target models. To further understand our method, we also evaluate the targeted adversarial examples crafted by various generative attacks against several image processing based defense methods, namely, JPEG compression [12] and Smooth [8]. As presented in Figure 5, our method consistently outperforms the two existing generative attacks against both JPEG compression and various smoothing defense methods. For example, our method achieves an attack success rate of $54.77\\%$ , when the JPEG quality is 70, while TTP [39] and C-GSP [55] just reach $54.06\\%$ and $40.04\\%$ , respectively.", + "bbox": [ + 75, + 547, + 472, + 715 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Visualization and Ablation Studies", + "text_level": 1, + "bbox": [ + 76, + 724, + 379, + 739 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Visualization. To vividly demonstrate the working mechanism of our method, we visualize several adversarial examples and perturbations with different target classes. As shown in Figure 6, there is an underlying dependency between the generated perturbations and input instances, where the perturbations are mainly concentrated on the semantical part of the input images. Besides, for different target classes, our method tends to generate perturbations with different texture patterns, which also verifies the effectiveness of our designed pattern injection module.", + "bbox": [ + 75, + 750, + 468, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ablation Studies. To look deeper into our proposed method, in this section, we present a series of ablation studies. As shown in Figure 7, we vary the number of target samples and convolution kernels to verify the effectiveness of our method. As presented in Figure 7(a), the performance of our method continues to grow until the number of target samples reaches 1000. Besides, in Figure 7(b), when the number of kernels is greater than 4, our performance reaches a plateau, which means that it is sufficient to reach an impressive attack success rate by learning 4 kernels in each designed dynamic convolution module.", + "bbox": [ + 496, + 356, + 893, + 522 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 541, + 617, + 556 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we first construct a causal graph to expose the origin of targeted adversarial examples, which motivates us to inject target patterns or styles for generating transferable target adversarial examples. Then we introduce a dynamic generative attack model composed of a cross-attention guided convolution module and a pattern injection module. Our generative attack model can not only inject pattern or style information of the target class to improve transferable targeted attacks, but also learn specialized convolutional kernels for each input instance, which inherits the advantages of both instance-specific and instance-agnostic attacks. Moreover, we also provide rigorous theoretical analysis to guarantee the effectiveness of our method, and extensive experiments demonstrate that our method performs better than state-of-the-art targeted attack methods.", + "bbox": [ + 496, + 569, + 890, + 796 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Acknowledgement", + "text_level": 1, + "bbox": [ + 500, + 804, + 679, + 821 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was partially supported by the National Nature Science Foundation of China (Grant 62022078, Grant 62021002), and National Defense Basic Scientific Research Program (Grant JCKY2022911B002).", + "bbox": [ + 496, + 830, + 890, + 887 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "16411", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] N. Akhtar and A. Mian. Threat of adversarial attacks on deep learning in computer vision: A survey. IEEE Access, 6:14410-14430, 2018. 1", + "[2] Maksym Andriushchenko, Francesco Croce, Nicolas Flammarion, and Matthias Hein. 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IEEE, 2019. 3", + "bbox": [ + 78, + 90, + 470, + 148 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "16414", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Dynamic Generative Targeted Attacks With Pattern Injection/03048e96-e108-4f0d-8eee-8c14ea87df56_model.json b/2023/Dynamic Generative Targeted Attacks With Pattern Injection/03048e96-e108-4f0d-8eee-8c14ea87df56_model.json new file mode 100644 index 0000000000000000000000000000000000000000..bfba3db6395c208f1292f16cc3a0ee66a5fbac99 --- /dev/null +++ b/2023/Dynamic Generative Targeted Attacks With Pattern Injection/03048e96-e108-4f0d-8eee-8c14ea87df56_model.json @@ -0,0 +1,2092 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.178, + 0.131, + 0.793, + 0.154 + ], + "angle": 0, + "content": "Dynamic Generative Targeted Attacks with Pattern Injection" + }, + { + "type": "text", + "bbox": [ + 0.166, + 0.18, + 0.832, + 0.235 + ], + "angle": 0, + "content": "Weiwei Feng\\(^{1,\\ast}\\), Nanqing Xu\\(^{1,\\ast}\\), Tianzhu Zhang\\(^{1,2,\\dagger}\\), Yongdong Zhang\\(^{1}\\) \n\\(^{1}\\) University of Science and Technology of China, \\(^{2}\\) Deep Space Exploration Lab \nngww@mail.ustc.edu.cn, xnq@mail.ustc.edu.cn, {tzzhang, zhyd73}@ustc.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.295, + 0.473, + 0.794 + ], + "angle": 0, + "content": "Adversarial attacks can evaluate model robustness and have been of great concern in recent years. Among various attacks, targeted attacks aim at misleading victim models to output adversary-desired predictions, which are more challenging and threatening than untargeted ones. Existing targeted attacks can be roughly divided into instance-specific and instance-agnostic attacks. Instance-specific attacks craft adversarial examples via iterative gradient updating on the specific instance. In contrast, instance-agnostic attacks learn a universal perturbation or a generative model on the global dataset to perform attacks. However, they rely too much on the classification boundary of substitute models, ignoring the realistic distribution of the target class, which may result in limited targeted attack performance. And there is no attempt to simultaneously combine the information of the specific instance and the global dataset. To deal with these limitations, we first conduct an analysis via a causal graph and propose to craft transferable targeted adversarial examples by injecting target patterns. Based on this analysis, we introduce a generative attack model composed of a cross-attention guided convolution module and a pattern injection module. Concretely, the former adopts a dynamic convolution kernel and a static convolution kernel for the specific instance and the global dataset, respectively, which can inherit the advantages of both instance-specific and instance-agnostic attacks. And the pattern injection module utilizes a pattern prototype to encode target patterns, which can guide the generation of targeted adversarial examples. Besides, we also provide rigorous theoretical analysis to guarantee the effectiveness of our method. Extensive experiments demonstrate that our method shows superior performance than 10 existing adversarial attacks against 13 models." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.811, + 0.21, + 0.827 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.837, + 0.47, + 0.867 + ], + "angle": 0, + "content": "With the encouraging progress of deep neural networks (DNNs) in various fields [6, 19, 16, 44, 42], recent studies" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.269, + 0.889, + 0.446 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.459, + 0.892, + 0.57 + ], + "angle": 0, + "content": "Figure 1. Visualization comparison between adversarial examples generated by our method (a) and the instance-specific method MIM [9] (b). Our perturbations (a) not only show an underlying dependency with the input instance, but also have strong semantic patterns or styles of the target class (\"Hippopotamus\"). In contrast, the perturbations generated by MIM perform like random noises. The adversarial examples are generated against ResNet-152, and labels are predicted by another unknown model (VGG-16)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.598, + 0.892, + 0.764 + ], + "angle": 0, + "content": "[36, 29, 28, 38] have corroborated that adversarial examples generated with small-magnitude perturbations can mislead the DNNs to make incorrect predictions. Due to the vulnerability of DNNs, adversarial attacks expose a security threat to real application systems based on deep neural networks, especially in some sensitive fields such as autonomous driving [27], face verification and financial systems [43], to name a few. Therefore, adversarial attacks have become a research hotspot over the past decade [2, 48, 35, 3, 33], which are significant in demonstrating the adversarial robustness and stability of deep learning models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "To further understand adversarial examples, there are tremendous works [1, 48, 33, 4, 36, 38] focusing on adversarial attacks. Recently, it has been found that adversarial examples possess an intriguing property of transferability, which indicates that adversarial examples generated for a white-box model can also mislead another black-box model. Due to this inherent property, black-box attacks become workable in real-world scenarios where attackers cannot access the attacked model. Extensive methods, such as" + }, + { + "type": "page_footnote", + "bbox": [ + 0.101, + 0.875, + 0.235, + 0.901 + ], + "angle": 0, + "content": "* Equal Contribution † Corresponding Author" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "16404" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.473, + 0.273 + ], + "angle": 0, + "content": "MIM [9], DIM [53] and CD-AP [40], have made an impressive performance of boosting the transferability for untargeted attacks, which mislead the model to make an incorrect classification without specifying a target class. However, targeted attacks are more challenging compared with untargeted attacks, making the model output the adversary-desired target class. It is claimed in recent works [14, 55] that transferable targeted attacks are more worthy of study because attackers can directly control the unknown model to output the desired prediction, which can expose huge threats to data privacy and security. Therefore, it is of great significance to develop transferable targeted attacks." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.276, + 0.473, + 0.806 + ], + "angle": 0, + "content": "Existing methods of transferable targeted attacks can be roughly categorized into instance-specific [9, 14, 13, 54, 50, 34, 31] and instance-agnostic [52, 35, 27, 40, 39] attacks. Specifically, almost all instance-specific attacks craft adversarial examples via iterative gradient updating, where attackers can only take advantage of the specific input instance, the white-box model and the target class label. Instance-specific attacks rely on optimizing the classification score of the adversary-desired class label to perturb the specific instance, which ignore the global data distribution. As a result, they inevitably lead to adversarial examples over-fitting the white-box model and result in modest transferability of targeted attacks. On the other hand, via learning a universal perturbation [37] or a generative attack model [52, 55], instance-agnostic attacks optimize adversarial perturbations on the global data distribution rather than the specific instance. To a certain extent, they can alleviate the problem of data-specific over-fitting and lead to more transferable targeted adversarial examples. However, taking the generative attack methods as an example, they suffer from two limitations. (1) Most generative attacks [52, 40, 35] still rely on the target label and the classification boundary information of white-box models rather than the realistic data distribution of the target class. Consequently, it is claimed that most generative attacks still have the possibility of over-fitting the white-box model, which may result in limited performance of transferable targeted attacks. (2) Another limitation is that existing generative attacks [39, 55, 27] apply the same network weights to every input instance in the test dataset. Nevertheless, it is considered that the shared network weights cannot stimulate the best attack performance of generative models [39, 55, 55]. Thus these aforementioned limitations have become the bottleneck of developing transferable targeted attacks, to a certain extent." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.473, + 0.903 + ], + "angle": 0, + "content": "To address the aforementioned limitations, in this paper we construct a causal graph to formulate the prediction process of classifiers, and analyze the origin of adversarial examples. Based on this analysis, we propose to generate targeted adversarial examples via injecting the specific pattern or style of the target class. To this end, we intro" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.575 + ], + "angle": 0, + "content": "duce a generative attack model, which can not only inject pattern or style information of the target class to improve transferable targeted attacks, but also learn specialized convolutional kernels for each input instance. Specifically, we designed a cross-attention guided convolution module and a pattern injection module in the proposed generative attack model. (1) The cross-attention guided convolution module consists of a static convolutional kernel and a dynamic convolutional kernel that is computed according to the input instance. Consequently, this static and dynamic mixup module can not only encode the global information of the dataset, but also learn specialized convolutional kernels for each input instance. This paradigm makes our generative model inherit the advantages of both instance-specific and instance-agnostic attacks. (2) The pattern injection module is designed to model the pattern or style information of the target class and guide the generation of targeted adversarial examples. Concretely, we propose a pattern prototype to learn a global pattern representation over images from the target class, and use the prototype to guide the generation of more transferable targeted adversarial examples. And the generated adversarial images of our method are presented in Figure 1. It is observed that our generated perturbations (as shown in Figure 1(a)) pose strong semantic patterns or styles of the target class and show an underlying dependency on the input instance. In contrast, the perturbations (as presented in Figure 1(b)) generated by MIM [9] perform like random noises. Finally, to further understand our method, we provide rigorous theoretical analysis to guarantee the effectiveness of our method, as shown in Section 3.4, where we derive a concise conclusion based on the problem of Gaussian binary classification." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.575, + 0.896, + 0.817 + ], + "angle": 0, + "content": "In summary, the main contributions of this paper are three-fold: (1) We propose a dynamic generative model to craft transferable targeted adversarial examples, which can not only inject pattern or style information of the target class to improve transferable targeted attacks, but also learn specialized convolutional kernels for each input instance. Besides, our method inherits the advantages of both instancespecific and instance-agnostic attacks, and to the best of our knowledge, we are the first to bridge them. (2) We state that injecting the specific pattern or style of the target class can improve the transferability of targeted adversarial examples, and we provide a comprehensive theoretical analysis to verify the rationality of this statement. (3) Extensive experimental results demonstrate that our method significantly boosts the transferability of targeted adversarial examples over 10 existing methods against 13 models." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.83, + 0.642, + 0.847 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Instance-specific Attacks. As the pioneering work [48] exposes the vulnerability of neural networks, many recent methods [54, 17, 3, 11, 29] utilize gradient-based optimization." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16405" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.408 + ], + "angle": 0, + "content": "tion to generate input-dependent adversarial examples. To further boost the transferability of the adversarial example, several works have been proposed by various strategies to optimize the gradient update process. MIM [9] introduces a momentum term during the iterative gradient updating. DIM [53] improves the transferability via integrating diverse input patterns for optimizing, and TIM [10] performs a convolution operation on the gradient that is applicable to any gradient-based attack methods. Besides, some recent works [5, 18, 20] propose to ensemble multiple pre-trained substitute models to craft more transferable adversarial examples. However, these methods pose modest transferability under the targeted attacks setting, because they rely too much on the target label and the classification boundary information of white-box models. Meanwhile, among these methods, they all face the problem of data-specific overfitting, because of ignoring the global data distribution. To overcome these limitations, in this paper, we propose a dynamic generative model to craft more transferable targeted adversarial examples, which can not only encode the global dataset, but also adapt to the specific instance." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.409, + 0.473, + 0.817 + ], + "angle": 0, + "content": "Instance-agnostic Attacks. Distinguished from instance-specific attacks, instance-agnostic attacks learn a universal perturbation [37] or a generative function [35, 27, 51, 41, 55, 40, 39] to craft adversarial examples. Compared with the universal perturbation, the latter is more flexible and has drawn more attention in recent years. Xiao et al. [52] first explore generating adversarial examples with GANs [16], which can consider the whole dataset instead of the specific input instance. CD-AP [40] and TTP [39] exploit generative models to craft more transferable adversarial examples. Recently, Yang et al. [55] boost the transferability of targeted adversarial examples with hierarchical generative networks. To a certain extent, these methods lead to more general and transferable adversarial examples because of alleviating the data-specific over-fitting problem. However, they also suffer from some limitations. First, existing generative attack methods [52, 57, 55, 40, 39] apply the same network weights to each input instance, which may limit the transferability of adversarial examples. And the second is that most of them also rely too much on the target label and the classification boundary of white-box models, ignoring the realistic data distribution of the target class. Motivated by these, in this paper, we propose a dynamic generative attack model, which can not only inject pattern or style information of the target class to improve transferable targeted attacks, but also learn specialized convolutional kernels for each input instance." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.83, + 0.17, + 0.846 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.47, + 0.903 + ], + "angle": 0, + "content": "In this section, we present the overall scheme of our proposed method, including some preliminaries, motivations, network architectures and theoretical analyses." + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.106, + 0.685, + 0.231 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.69, + 0.083, + 0.895, + 0.237 + ], + "angle": 0, + "content": "Figure 2. The casual graph of model inference. Each node is a random variable, where \\( C, S, \\mathbf{x}, \\mathbf{y} \\) and \\( \\theta \\) represent content, style or pattern, the input image, the prediction label, and model parameters, respectively. In order to achieve good performance, the model will learn the statistical correlation between the style \\( S \\) and the label \\( \\mathbf{y} \\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.248, + 0.764, + 0.264 + ], + "angle": 0, + "content": "3.1. Preliminaries and Motivation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.272, + 0.895, + 0.515 + ], + "angle": 0, + "content": "We denote the clean image as \\( \\pmb{x} \\in \\mathcal{X} \\), and the attacked model parameterized by \\( \\theta \\) is denoted as \\( f: \\mathcal{X} \\to \\mathcal{Y} \\). The goal of target attacks is to generate an adversarial perturbation \\( \\delta \\) that can make the model misclassify the input \\( \\pmb{x}_{adv} = \\pmb{x} + \\delta \\) to the predefined class \\( \\pmb{y}_t \\), which can be formulated as \\( f(\\pmb{x}_{adv}) = \\pmb{y}_t \\neq f(\\pmb{x}) \\). To gain insights into the origin of targeted adversarial examples, we construct a casual graph \\( \\mathcal{G} \\) to formulate the inference of deep learning models, as shown in Figure 2. For the input images \\( \\pmb{x} \\), we propose to group the whole causes of \\( \\pmb{x} \\) into two categories, content-related cause \\( C \\) and content-independent cause \\( S \\) that can be dubbed as style or pattern cause. This indicates that \\( C \\rightarrow x \\gets S \\), and \\( C \\bot S \\). According to human visual intuition, only the content variable \\( C \\) is relevant to the prediction class \\( y \\). Consequently, we can use the Law of total probability to expand the prediction \\( P_{\\theta}(\\pmb{y} \\mid \\pmb{x}) \\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.566, + 0.523, + 0.892, + 0.549 + ], + "angle": 0, + "content": "\\[\nP _ {\\theta} (\\boldsymbol {y} \\mid \\boldsymbol {x}) = \\sum_ {s \\in \\mathbb {S}} P _ {\\theta} (s \\mid \\boldsymbol {x}) P _ {\\theta} (\\boldsymbol {y} \\mid \\boldsymbol {x}, s). \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.559, + 0.895, + 0.753 + ], + "angle": 0, + "content": "But several recent works [56] and Equation (1) imply that deep learning models can learn not only the dependencies between the content \\( C \\) and the label \\( y \\), but also the statistical correlation between the style \\( S \\) and the label \\( y \\) (i.e., \\( P_{\\theta}(\\boldsymbol{y} \\mid \\boldsymbol{x}, s) \\)). This phenomenon indicates that deep learning models can capture some detailed texture patterns and style features to achieve good performance, and the output prediction \\( P_{\\theta}(\\boldsymbol{y} \\mid \\boldsymbol{x}) \\) will change with the statistical correlation between \\( \\boldsymbol{y} \\) and \\( S \\) (i.e., \\( P_{\\theta}(\\boldsymbol{y} \\mid \\boldsymbol{x}, s) \\)). And this property certainly offers attackers an opportunity to generate adversarial examples for misleading the model. Therefore, the inference of targeted adversarial examples can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.519, + 0.762, + 0.892, + 0.789 + ], + "angle": 0, + "content": "\\[\nP _ {\\theta} \\left(\\boldsymbol {y} _ {t} \\mid \\boldsymbol {x} _ {a d v}\\right) = \\sum_ {s \\in \\mathbb {S}} P _ {\\theta} (s \\mid \\boldsymbol {x} _ {a d v}) P _ {\\theta} \\left(\\boldsymbol {y} _ {t} \\mid \\boldsymbol {x} _ {a d v}, s\\right). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.797, + 0.895, + 0.845 + ], + "angle": 0, + "content": "Inspired by Figure 2 and the aforementioned Equation (2), we first propose to exploit the statistical correlation between \\(\\mathbf{y}_t\\) and \\(S\\) (i.e., \\(P_{\\theta}(\\mathbf{y}_t \\mid \\mathbf{x}_{adv}, s))^1\\), via injecting the specific" + }, + { + "type": "page_footnote", + "bbox": [ + 0.498, + 0.851, + 0.895, + 0.901 + ], + "angle": 0, + "content": "1The statistical correlation between \\( \\mathbf{y}_t \\) and \\( S \\) (i.e., \\( P_{\\theta}(\\mathbf{y}_t \\mid \\mathbf{x}_{adv}, s) \\) reflects that the model learns some non-robust features. According to the analysis of [24] and [55], the transferability of adversarial examples may arise from non-robust features, such as texture patterns or styles." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "16406" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.156, + 0.08, + 0.817, + 0.328 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.34, + 0.895, + 0.412 + ], + "angle": 0, + "content": "Figure 3. The architecture of our dynamic generative attack model, which is composed of a cross-attention guided convolution module (denoted as \"Dy_Conv\") and a pattern injection module. The cross-attention guided convolution module consists of a static convolutional kernel and a dynamic convolutional kernel that is computed according to the input instance. For the pattern injection, the pattern prototype \\(\\pmb{p}_t = \\{\\gamma_t,\\beta_t\\}\\) encodes the patterns or styles of the target class, and the \"AdaCN\" layer performs an affine operation to inject \\(\\pmb{p}_t\\) into the generation of adversarial examples. Similar to [25], we introduce \\(\\pmb{p}_t^{\\mathrm{running}}\\) via the EMA updating based on \\(\\pmb{p}_t\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.424, + 0.471, + 0.454 + ], + "angle": 0, + "content": "style or pattern of images from the given target class \\(\\mathbf{y}_t\\) to generate targeted transferable adversarial examples." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.454, + 0.472, + 0.56 + ], + "angle": 0, + "content": "To this end, we propose a generative model to craft targeted adversarial examples by injecting the pattern of the target class. Besides, we design a cross-attention guided dynamic convolution module in the generator, which makes our generative model inherit the advantages of both instance-specific and instance-agnostic attacks. Therefore, the formulation of our method can be denoted as" + }, + { + "type": "equation", + "bbox": [ + 0.12, + 0.57, + 0.47, + 0.587 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {x} _ {a d v} = \\operatorname {c l i p} \\left\\{\\operatorname {P r o j} \\left(\\mathcal {W} * G _ {\\theta (\\boldsymbol {x})} (\\boldsymbol {x}, p _ {t}), - \\varepsilon , \\varepsilon\\right) + \\boldsymbol {x} \\right\\}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.592, + 0.47, + 0.639 + ], + "angle": 0, + "content": "where \\(\\varepsilon\\) is the perturbation budget, \\(\\mathcal{W}\\) is a smoothing operator with fixed weights, \\(p_t\\) represents the semantic pattern or style of the target class, and Proj is a projection operation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.645, + 0.283, + 0.66 + ], + "angle": 0, + "content": "3.2. Network Architecture" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.668, + 0.47, + 0.774 + ], + "angle": 0, + "content": "Specifically, our generative model is illustrated in Figure 3, which is composed of two modules: ① a cross attention-guided dynamic convolution module (corresponding to \"Dy_Conv\" in the ResBlock of Figure 3), ② a pattern injection module. And the detailed pipeline of our approach is presented in Algorithm 1. In the next section, we mainly describe the two designed modules in detail." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.774, + 0.471, + 0.88 + ], + "angle": 0, + "content": "Cross-attention guided dynamic convolution module. Considering that not only the global dataset needs to be modeled, but also specialized convolution kernels need to be learned for each input, we design a cross-attention guided convolution module. To achieve this goal, as shown in Figure 4, we propose a static and a dynamic convolution kernel parameterized with \\( W \\) and \\( \\Delta W \\), respectively2. Thus" + }, + { + "type": "code_caption", + "bbox": [ + 0.512, + 0.427, + 0.85, + 0.442 + ], + "angle": 0, + "content": "Algorithm 1: Dynamic Generative Targeted Attack" + }, + { + "type": "algorithm", + "bbox": [ + 0.508, + 0.444, + 0.892, + 0.651 + ], + "angle": 0, + "content": "Input: A white-box model \\(f\\), training data \\(\\mathcal{X}\\), target samples \\(\\mathcal{X}_t\\), perturbation budget \\(\\epsilon\\), training epoch \\(T\\). Output: Generative attack model \\(G_{\\theta}\\). \n1 for \\(t \\gets 0\\) to \\(T\\) do \n2 Sample mini-batches \\(\\pmb{x} \\sim \\mathcal{X}\\) and \\(\\pmb{x}_t \\sim \\mathcal{X}_t\\). \n3 Get the augmented mini-batches \\(\\pmb{x}'\\) from \\(\\pmb{x}\\). \n4 Feed \\(\\pmb{x}\\), \\(\\pmb{x}'\\) and \\(\\pmb{x}_t\\) into the generator to get adversarial examples \\(\\pmb{x}_{adv}\\) and \\(\\pmb{x}_{adv}'\\), where \\(\\pmb{x}_t\\) is used for extracting and injecting target patterns \\(p_t\\). \n5 Update \\(p_t^{\\text{running}}\\) based on \\(p_t\\) via EMA updating. \n6 Forward pass \\(\\pmb{x}_{adv}\\), \\(\\pmb{x}_{adv}'\\) and \\(\\pmb{x}_t\\) through \\(f\\). \n7 Compute losses \\(L_{attack}\\), and backward for updating \\(G_{\\theta}\\). \n8 return Converged generator \\(G_{\\theta}\\)." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.68, + 0.753, + 0.696 + ], + "angle": 0, + "content": "the designed module is formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.606, + 0.705, + 0.892, + 0.719 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {X} _ {l} = \\operatorname {c o n v} \\left(\\boldsymbol {X} _ {l - 1}; W + \\Delta W\\right), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.727, + 0.894, + 0.832 + ], + "angle": 0, + "content": "where \\(X_{l}\\) is the output of layer \\(l\\). To get dynamic convolution kernels, we design a series of learnable kernels \\((N\\times C_{in}\\times C_{out}\\times k^2)^3\\) and attention queries \\(\\pmb {q}\\in R^{N\\times C_{in}}\\), which indicate the attention weight of each kernel. For the layer \\(l\\), we compute attention weights via performing cross-attention between attention queries \\(\\pmb{q}\\) and the input \\(\\pmb{X}_{l - 1}\\in R^{C_{in}\\times H\\times W}\\), which can be indicated as:" + }, + { + "type": "equation", + "bbox": [ + 0.606, + 0.842, + 0.892, + 0.869 + ], + "angle": 0, + "content": "\\[\na t t = \\operatorname {s o f t m a x} \\left(\\frac {Q K ^ {\\top}}{\\sqrt {d _ {k}}}\\right) V, \\tag {5}\n\\]" + }, + { + "type": "page_footnote", + "bbox": [ + 0.095, + 0.887, + 0.384, + 0.901 + ], + "angle": 0, + "content": "2Note that we ignore bias terms for the sake of brevity" + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.875, + 0.892, + 0.901 + ], + "angle": 0, + "content": "\\( ^3 N \\) indicates the number of learnable kernels, \\( k \\) represents the kernel size, \\( C_{in} \\) and \\( C_{out} \\) are the number of input and output channels." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16407" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.091, + 0.089, + 0.452, + 0.25 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.254, + 0.47, + 0.296 + ], + "angle": 0, + "content": "Figure 4. The illustration of the proposed cross-attention guided dynamic convolution module, which is composed of a static convolution kernel \\( W \\) and a dynamic convolution kernel \\( \\Delta W \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.31, + 0.47, + 0.465 + ], + "angle": 0, + "content": "where \\(att \\in R^{N \\times C_{in}}\\), \\(Q = qW^{q}\\), \\(K = X_{l-1}^{\\top}W^{k}\\) and \\(V = X_{l-1}^{\\top}W^{v}\\). Then we can get the attention weight \\(\\alpha = [\\alpha_{1}, \\alpha_{2}, \\dots, \\alpha_{N}] \\in R^{1 \\times N}\\) by conducting the average pooling on \\(att\\), and each element in \\(\\alpha\\) indicates the weight of corresponding kernels. Therefore, the dynamic convolution kernels are implemented as \\(\\Delta W = \\alpha_{1} * W_{1} + \\alpha_{2} * W_{2} + \\dots + \\alpha_{N} * W_{N}\\). Benefiting from this dynamic and static mixup convolution operation, our proposed generative attack model can inherit the advantages of both instance-specific and instance-agnostic attacks." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.467, + 0.471, + 0.664 + ], + "angle": 0, + "content": "Pattern injection module. First, to encode target patterns and styles during the generation of adversarial examples, we design a pattern prototype \\( \\pmb{p}_t = \\{\\gamma_t, \\beta_t\\} \\), which is extracted from the features of target samples, as shown in Figure 3. Following [25], we introduce \\( \\pmb{p}_t^{\\text{running}} \\) to model patterns of the global samples for the target class. Note that we update \\( \\pmb{p}_t^{\\text{running}} \\) during each training iteration, which can be indicated as \\( \\pmb{p}_t^{\\text{running}} = \\lambda \\pmb{p}_t + (1 - \\lambda) \\pmb{p}_t^{\\text{running}} \\). Then we propose an adaptive class normalization (corresponding to \"AdaCN\" in Figure 3) to inject \\( \\pmb{p}_t \\) into the generation of target adversarial examples. Similar to [23], the AdaCN module exploits the learned \\( \\pmb{p}_t = \\{\\gamma_t, \\beta_t\\} \\) to perform an affine operation for injecting target patterns or styles:" + }, + { + "type": "equation", + "bbox": [ + 0.156, + 0.675, + 0.47, + 0.704 + ], + "angle": 0, + "content": "\\[\n\\operatorname {A d a C N} (\\boldsymbol {X}) = \\gamma_ {t} \\left(\\frac {\\boldsymbol {X} - \\mu (\\boldsymbol {X})}{\\sigma (\\boldsymbol {X})}\\right) + \\beta_ {t}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.716, + 0.469, + 0.78 + ], + "angle": 0, + "content": "where \\(\\pmb{p}_t = \\{\\pmb{\\gamma}_t, \\pmb{\\beta}_t\\}\\) is the target pattern prototype. Note that Equation (6) represents pattern injection during training, and it is necessary to replace \\(\\pmb{p}_t = \\{\\pmb{\\gamma}_t, \\pmb{\\beta}_t\\}\\) with \\(\\pmb{p}_t^{\\mathrm{running}} = \\{\\pmb{\\gamma}_t^{\\mathrm{running}}, \\pmb{\\beta}_t^{\\mathrm{running}}\\}\\) during inference." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.79, + 0.262, + 0.807 + ], + "angle": 0, + "content": "3.3. Objective Function" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.814, + 0.47, + 0.876 + ], + "angle": 0, + "content": "To lead the victim model to misclassify adversarial examples as the target class, it is necessary to make the output distribution of adversarial examples \\( f(\\boldsymbol{x}_{adv}), f(\\boldsymbol{x}_{adv}') \\) and target samples \\( f(\\boldsymbol{x}_t) \\) consistent. Thus we define the loss" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.634, + 0.105 + ], + "angle": 0, + "content": "function as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.523, + 0.119, + 0.891, + 0.149 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} \\quad = D _ {K L} \\left(f \\left(\\boldsymbol {x} _ {a d v}\\right) \\| f \\left(\\boldsymbol {x} _ {t}\\right)\\right) + D _ {K L} \\left(f \\left(\\boldsymbol {x} _ {t}\\right) \\| f \\left(\\boldsymbol {x} _ {a d v}\\right)\\right) \\tag {7} \\\\ \\mathcal {L} _ {a u g} = D _ {K L} \\left(f (\\boldsymbol {x} _ {a d v} ^ {\\prime}) \\| f (\\boldsymbol {x} _ {t})\\right) + D _ {K L} \\left(f (\\boldsymbol {x} _ {t}) \\| f (\\boldsymbol {x} _ {a d v} ^ {\\prime})\\right) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.161, + 0.892, + 0.263 + ], + "angle": 0, + "content": "Besides, similar to [39], we also introduce a local similarity loss. For a batch of generated adversarial examples \\(\\{\\pmb{x}_{adv}^i\\}_{i=1}^n\\), \\(\\{\\pmb{x}_{adv}^{j,i}\\}_{i=1}^n\\) and target samples \\(\\{\\pmb{x}_t^i\\}_{i=1}^n\\), the similarity matrix can be computed as \\(S_{i,j} = \\frac{f(\\pmb{x}_{adv}^i) \\cdot f(\\pmb{x}_{adv}^{j,i})}{\\|f(\\pmb{x}_{adv}^i)\\| \\|f(\\pmb{x}_{adv}^{j,j})\\|}\\) and \\(S_{i,j}^t = \\frac{f(\\pmb{x}_t^i) \\cdot f(\\pmb{x}_t^j)}{\\|f(\\pmb{x}_t^i)\\| \\|f(\\pmb{x}_t^j)\\|}\\). Hence, we can get the local similarity loss as:" + }, + { + "type": "equation", + "bbox": [ + 0.543, + 0.276, + 0.891, + 0.32 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {s i m} = \\sum_ {i, j} \\overline {{\\mathcal {S}}} _ {i, j} ^ {t} \\log \\frac {\\overline {{\\mathcal {S}}} _ {i , j} ^ {t}}{\\overline {{\\mathcal {S}}} _ {i , j}} + \\sum_ {i, j} \\overline {{\\mathcal {S}}} _ {i, j} \\log \\frac {\\overline {{\\mathcal {S}}} _ {i , j}}{\\overline {{\\mathcal {S}}} _ {i , j} ^ {t}}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.332, + 0.891, + 0.374 + ], + "angle": 0, + "content": "where \\(\\overline{\\mathcal{S}}_{i,j} = \\frac{\\exp(\\mathcal{S}_{i,j})}{\\sum_k\\exp(\\mathcal{S}_{i,k})}\\) and \\(\\overline{\\mathcal{S}}_{i,j}^t = \\frac{\\exp(\\mathcal{S}_{i,j}^t)}{\\sum_k\\exp(\\mathcal{S}_{i,k}^t)}\\). Finally, the total objective function can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.597, + 0.388, + 0.891, + 0.404 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {a t t a c k}} = \\mathcal {L} + \\mathcal {L} _ {\\text {a u g}} + \\mathcal {L} _ {\\text {s i m}}. \\tag {9}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.428, + 0.696, + 0.444 + ], + "angle": 0, + "content": "3.4. Theoretical Analyses" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.453, + 0.892, + 0.528 + ], + "angle": 0, + "content": "In order to further explain the insights of our method, we consider a concrete setting that allows us to theoretically investigate why our method is effective for boosting target attacks. Please refer to the Supplementary Material for comprehensive proofs of the following theorem." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.529, + 0.892, + 0.573 + ], + "angle": 0, + "content": "Setup. We consider a simple problem of maximum likelihood classification, similar to that of [24], between two Gaussian distributions." + }, + { + "type": "equation", + "bbox": [ + 0.548, + 0.587, + 0.891, + 0.604 + ], + "angle": 0, + "content": "\\[\n\\mathcal {X} _ {s} \\sim N \\left(\\boldsymbol {\\mu} _ {s}, \\boldsymbol {\\Sigma} _ {s}\\right), \\quad \\mathcal {X} _ {t} \\sim N \\left(\\boldsymbol {\\mu} _ {t}, \\boldsymbol {\\Sigma} _ {t}\\right), \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.616, + 0.892, + 0.693 + ], + "angle": 0, + "content": "where \\(\\pmb{\\Sigma}_s, \\pmb{\\Sigma}_t = \\mathrm{diag}\\left\\{\\sigma_{s_1}^2, \\dots, \\sigma_{s_n}^2\\right\\}\\), \\(\\mathrm{diag}\\left\\{\\sigma_{t_1}^2, \\dots, \\sigma_{t_n}^2\\right\\}\\), respectively. To simplify the following derivation, we introduce a mapping and a translation operation to transform the model into a standard Gaussian binary classification model, which can be denoted as:" + }, + { + "type": "equation", + "bbox": [ + 0.566, + 0.707, + 0.891, + 0.743 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {F} _ {s} = \\boldsymbol {A} \\mathcal {X} _ {s} - \\frac {\\boldsymbol {A} \\boldsymbol {\\mu} _ {s} + \\boldsymbol {\\mu} _ {t}}{2} \\sim N (- \\boldsymbol {\\mu}, \\boldsymbol {\\Sigma}), \\tag {11} \\\\ \\mathcal {F} _ {t} = \\boldsymbol {E} \\mathcal {X} _ {t} - \\frac {\\boldsymbol {A} \\mu_ {s} + \\mu_ {t}}{2} \\sim N (\\boldsymbol {\\mu}, \\boldsymbol {\\Sigma}), \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.751, + 0.892, + 0.853 + ], + "angle": 0, + "content": "where the mapping matrix \\( \\mathbf{A} = \\mathrm{diag}\\left\\{\\frac{\\sigma_{t_1}}{\\sigma_{s_1}},\\frac{\\sigma_{t_2}}{\\sigma_{s_2}}\\dots ,\\frac{\\sigma_{t_n}}{\\sigma_{s_n}}\\right\\} \\), \\( \\mathbf{E} \\) is the identity matrix and \\( \\pmb {\\mu} = \\frac{-\\pmb{A}\\pmb{\\mu}_s + \\pmb{\\mu}_t}{2},\\pmb {\\Sigma} = \\pmb{\\Sigma}_t \\). To perform targeted attacks against this model with a given sample \\( x_{s}\\in \\mathcal{X}_{s} \\) and the target label \\( t \\), where \\( A\\pmb {x}_s - \\frac{A\\pmb{\\mu}_s + \\pmb{\\mu}_t}{2} = f_s\\in \\mathcal{F}_s \\) and \\( f_{s} + \\delta^{\\star} = A(x_{s} + \\delta) - \\frac{A\\mu_{s} + \\mu_{t}}{2} \\) we aim to solve the following optimization problem:" + }, + { + "type": "equation", + "bbox": [ + 0.538, + 0.877, + 0.891, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\delta} = \\boldsymbol {A} ^ {- 1} \\boldsymbol {\\delta} ^ {\\star}, \\quad \\boldsymbol {\\delta} ^ {\\star} = \\underset {\\| \\boldsymbol {\\delta} ^ {\\prime} \\| _ {2} ^ {2} \\leqslant \\varepsilon^ {2}} {\\operatorname {a r g m a x}} \\left(\\boldsymbol {f} _ {s} + \\boldsymbol {\\delta} ^ {\\prime}\\right) ^ {\\top} \\boldsymbol {\\Sigma} ^ {- 1} \\boldsymbol {\\mu}. \\tag {12}\n\\]" + }, + { + "type": "page_footnote", + "bbox": [ + 0.094, + 0.886, + 0.329, + 0.901 + ], + "angle": 0, + "content": "\\( {}^{4}{W}_{1},{W}_{2}\\cdots {W}_{N} \\) are the learnable kernels." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16408" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.895, + 0.119 + ], + "angle": 0, + "content": "Table 1. The attack success rates against normally trained models on ImageNet NeurIPS validation set, and the perturbation budget \\(\\ell_{\\infty} \\leq 16/255\\). Note that the results are averaged on 8 different target classes." + }, + { + "type": "table", + "bbox": [ + 0.218, + 0.13, + 0.751, + 0.496 + ], + "angle": 0, + "content": "
Subsite ModelMethodInc-v3Inc-v4Inc-Res-v2Res152Densenet-121GoogleNetVgg-16
Inc-v3MIM99.900.801.000.400.200.200.30
TI-MIM98.500.500.500.300.200.400.40
SI-MIM99.801.502.000.800.700.700.50
DIM95.602.700.500.801.100.400.80
TI-DIM96.001.101.200.500.500.500.80
SI-DIM90.203.804.402.002.201.701.40
CD-AP94.2057.6060.1037.1041.6032.3041.70
TTP91.3746.0439.3716.4033.4725.8025.73
C-GSP93.4066.9066.6041.6046.4040.0045.00
GAP86.9045.0634.4834.4841.7426.8934.34
Ours94.6367.9555.0350.5047.3847.6748.11
Res152MIM0.500.400.6099.700.300.300.20
TI-MIM0.300.300.3096.500.300.400.30
SI-MIM1.301.201.6099.501.001.400.70
DIM2.302.203.0092.300.200.800.70
TI-DIM0.800.701.0090.600.600.800.50
SI-DIM4.204.805.4090.504.203.602.00
CD-AP33.3043.7042.7096.6053.8036.6034.10
TTP62.0349.2038.7095.1282.9665.0962.82
C-GSP37.7047.6045.1093.2064.2041.7045.90
GAP30.9931.4320.4884.8658.3529.8939.70
Ours66.8353.6247.6196.4886.6168.2969.58
Vgg-16MIM0.260.470.200.350.400.3490.24
TI-MIM0.430.630.340.551.450.6489.13
SI-MIM0.350.570.420.310.560.5290.89
DIM0.751.300.551.001.881.0397.70
TI-DIM0.230.380.170.290.480.3593.71
SI-DIM0.871.120.700.951.891.5591.42
CD-AP5.328.944.879.3314.023.1996.82
TTP22.5117.149.6822.6840.8722.4197.59
C-GSP9.429.603.0111.7632.2813.3396.81
GAP3.115.261.505.0811.232.7093.00
Ours28.1821.789.5625.2746.5523.7093.00
" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.521, + 0.47, + 0.552 + ], + "angle": 0, + "content": "Taking advantage of the method of Lagrange multipliers, we can easily get the optimal solution as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.101, + 0.569, + 0.469, + 0.594 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{r l} \\delta^ {\\star} & = \\frac {1}{\\lambda} \\Sigma^ {- 1} \\boldsymbol {\\mu}, \\\\ s & = \\Sigma^ {- 1} [ A ^ {- 1} (A (\\quad , \\quad , \\quad , \\quad) ] \\end{array} \\tag {13}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.104, + 0.584, + 0.469, + 0.606 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\delta} = \\frac {\\hat {\\boldsymbol {\\Sigma}} ^ {- 1}}{2 \\lambda} \\left[ \\boldsymbol {A} ^ {- 1} \\left(\\boldsymbol {A} \\left(\\boldsymbol {x} _ {s} - \\boldsymbol {\\mu} _ {s}\\right) + \\boldsymbol {\\mu} _ {t}\\right) - \\boldsymbol {x} _ {s} \\right]. \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.626, + 0.47, + 0.656 + ], + "angle": 0, + "content": "Going a step further, we rewrite the solution of \\(\\delta\\) into a more concise formula as:" + }, + { + "type": "equation", + "bbox": [ + 0.092, + 0.691, + 0.47, + 0.758 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\delta} = C _ {1} \\left[ \\left( \\begin{array}{c c c} \\frac {\\sigma_ {t _ {1}}}{\\sigma_ {s _ {1}}} & & \\\\ & \\ddots & \\\\ & & \\frac {\\sigma_ {t _ {n}}}{\\sigma_ {s _ {n}}} \\end{array} \\right) \\left(\\boldsymbol {x} _ {s} - \\boldsymbol {\\mu} _ {s}\\right) + \\boldsymbol {\\mu} _ {t} \\right] - C _ {2} \\boldsymbol {x} _ {s}, \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.775, + 0.471, + 0.903 + ], + "angle": 0, + "content": "where \\(C_1 = \\frac{\\Sigma^{-1}A^{-1}}{2\\lambda}\\) and \\(C_2 = \\frac{\\Sigma^{-1}}{2\\lambda}\\). In fact, note that the item of represents target pattern or style injection, which is consistent with the previous works [23, 26]. Therefore, the formulation of Equation (14) shows a close underlying correlation between the optimal targeted adversarial perturbation and the embedding of target pattern or style, which also theoretically guarantees the effectiveness of our proposed generative model for targeted attacks." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.519, + 0.634, + 0.536 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.546, + 0.893, + 0.608 + ], + "angle": 0, + "content": "In this section, we conduct extensive experiments to demonstrate the effectiveness of our method for targeted attacks under various settings. Please feel free to get more experimental results in our Supplementary Material." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.618, + 0.691, + 0.635 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.643, + 0.894, + 0.688 + ], + "angle": 0, + "content": "Dataset. Following [55], we perform training on ImageNet [7] training set, and evaluate on ImageNet-NeurIPS (1k) proposed by NeurIPS 2017 adversarial competition [30]." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.689, + 0.892, + 0.839 + ], + "angle": 0, + "content": "Victim Models. We consider 13 attacked models in our experiments. The normally trained models include Inception-v3 (Inc-v3) [47], Inception-v4 (Inc-v4) [45], DenseNet-121 [22], GoogleNet [46], ResNet-152 (Res-152) [19], and VGG16 (Vgg-16) [44] and Inception-ResNet (Inc-Res-v2) [45]. Besides, we also consider several models with robust training mechanisms, including adv-Inception-v3 (Adv-Inc-v3) [17], ens-adv-Inception-ResNet-v2 (Ens-Adv-IncRes-v2) [18] and ResNet-50 trained with various robust training tricks [21, 15]." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Baseline Attacks. To illustrate the effectiveness of our method, we compare it with instance-specific attacks and instance-agnostic attacks. Instance-specific attacks mainly include MIM [9], DIM [53], SIM [32] and TIM [10], while" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "16409" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.077, + 0.895, + 0.149 + ], + "angle": 0, + "content": "Table 2. The attack success rates against robust models on ImageNet NeurIPS validation set. The perturbation budget \\(\\ell_{\\infty} \\leq 16/255\\). Adv-Inc-v3 [29] and Ens-Adv-IncRes-v2 [49] are trained with the adversarial training mechanism. Res50_SIN (stylized ImageNet), Res50_SIN_IN (mixture of stylized ImageNet and Nature ImageNet) and Res50_SIN_fine_IN (mixture of stylized ImageNet and Nature ImageNet with finetuning tricks) are trained with auxiliary dataset [15], and Res50_Augmix [21] is trained with the state-of-the-art data augmentation approach. Note that the results are averaged on 8 different target classes." + }, + { + "type": "table", + "bbox": [ + 0.158, + 0.158, + 0.812, + 0.4 + ], + "angle": 0, + "content": "
Subsite ModelMethodAdv-Inc-v3Ens-IncRes-v2Res50_SINRes50_SIN_INRes50_SIN_fine_INRes50_AugMix
Res152MIM0.190.150.281.582.750.78
TI-MIM0.610.730.502.514.751.76
SI-MIM0.240.240.390.660.840.36
DIM0.630.370.948.5014.223.77
TI-DIM0.230.300.280.761.490.49
SI-DIM0.710.710.752.733.891.37
CD-AP3.776.487.0963.7276.7949.67
TTP27.9926.0824.6172.4774.5170.96
GAP5.724.517.3371.0483.6452.07
Ours31.1030.0727.7077.1380.5576.78
VGG16MIM0.140.150.160.400.340.19
TI-MIM0.260.240.200.450.570.28
SI-MIM0.280.200.210.490.250.14
DIM0.220.160.270.930.990.49
TI-DIM0.140.190.210.350.340.21
SI-DIM0.500.360.330.800.690.26
CD-AP0.360.340.354.6310.203.60
TTP3.753.202.6627.8032.7016.57
GAP0.300.520.424.528.923.35
Ours4.143.222.6630.1638.1017.95
" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.422, + 0.262, + 0.553 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.16, + 0.556, + 0.174, + 0.565 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.276, + 0.424, + 0.457, + 0.555 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.371, + 0.556, + 0.385, + 0.565 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.566, + 0.473, + 0.678 + ], + "angle": 0, + "content": "Figure 5. Attack success rates of targeted adversarial examples generated by various generative attack methods against different input process defense methods. Figure (a) displays the results against various input smooth methods (including gaussian, medium and average smoothing). Figure (b) shows the results against JPEG compression (the JPEG quality factor varies from 70 to 90). Here, the substitute model is Res-152 and the target model is Vgg-16." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.683, + 0.47, + 0.775 + ], + "angle": 0, + "content": "instance-agnostic attacks include CD-AP [40], TTP [39], GAP [41] and C-GSP [55]. In our experiments, the perturbation size \\(\\varepsilon = 16 / 255\\), the decay factor \\(\\mu_0\\) is 1 in MIM, the transform probability is 0.7 in DIM, and the kernel size is 15 in TIM. And other hyper-parameters follow the default settings provided in their original works." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.786, + 0.442, + 0.803 + ], + "angle": 0, + "content": "4.2. Comparison with State-of-the-art Methods" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Attack Normally Trained Models. To evaluate the performance of our method, we first perform targeted adversarial attacks to compare the transferability across normally trained models of adversarial examples generated by various methods, including 6 iterative instance-specific attack methods and 5 instance-agnostic attack methods. As shown" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.424, + 0.895, + 0.621 + ], + "angle": 0, + "content": "in Table 1, our dynamic generative attack method reaches the best transferability on 16 out of 18 various black-box cases. Furthermore, the attack success rate of our method against normally trained models is \\(65.42\\%\\) on average with the substitute model as Res-152, which outperforms the best of baselines [39] by \\(5.28\\%\\) on average. Another interesting discovery is that iterative instance-specific attack methods can reach better performance under the setting of white-box attacks, while generative attack methods show more transferability when adapting the adversarial examples to a black-box model. Among these generative methods, our method can still generate targeted adversarial examples with higher transferability than others." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.624, + 0.896, + 0.852 + ], + "angle": 0, + "content": "Attack Models with Robust Training Mechanisms. To comprehensively verify the effectiveness of our method, we compare the transferability of our approach with baselines against several robust models, which are trained with various robust training strategies. As presented in Table 2, although the attack success rate against these robust models is relatively low, our method is still able to outperform baseline methods. Our generative attack method achieves the best performance of targeted transferable adversarial attacks on 11 over 12 cases. And regarding Res-152 as the substitute model, our method outperforms the best of baselines [39] by \\(4.45\\%\\) on average. Compared with normally trained models, models with adversarial or robust training strategies are difficult to attack successfully, which indicates they are more robust than normal models." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Attack Models with Input Process Defense. Another widely used and simple defense method is Input Process, which leverages image processing techniques to remove" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "16410" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.147, + 0.071, + 0.825, + 0.285 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.287, + 0.895, + 0.345 + ], + "angle": 0, + "content": "Figure 6. Visualization results of adversarial examples generated by our proposed method. The 1st, 2nd and 3rd rows show clean images, adversarial perturbations and adversarial examples, respectively. And (a), (b) and (c) display the results of different target classes (French bulldog, Fire engine and Street sign), which indicate that different target classes lead to different patterns or texture styles of the generated perturbations and adversarial images. Please refer to our Supplementary Material for more qualitative examples." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.357, + 0.273, + 0.47 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.181, + 0.473, + 0.195, + 0.482 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.276, + 0.357, + 0.462, + 0.47 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.375, + 0.472, + 0.389, + 0.482 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.483, + 0.47, + 0.539 + ], + "angle": 0, + "content": "Figure 7. Ablation studies. (a) Effect of the number of target samples. (b) Effect of the number of learnable convolution kernels. Note that the substitute model is Res-152, while victim models include Vgg-16, GoogleNet and Inc-v3." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.548, + 0.473, + 0.716 + ], + "angle": 0, + "content": "the adversary perturbation before feeding into target models. To further understand our method, we also evaluate the targeted adversarial examples crafted by various generative attacks against several image processing based defense methods, namely, JPEG compression [12] and Smooth [8]. As presented in Figure 5, our method consistently outperforms the two existing generative attacks against both JPEG compression and various smoothing defense methods. For example, our method achieves an attack success rate of \\(54.77\\%\\), when the JPEG quality is 70, while TTP [39] and C-GSP [55] just reach \\(54.06\\%\\) and \\(40.04\\%\\), respectively." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.726, + 0.38, + 0.74 + ], + "angle": 0, + "content": "4.3. Visualization and Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Visualization. To vividly demonstrate the working mechanism of our method, we visualize several adversarial examples and perturbations with different target classes. As shown in Figure 6, there is an underlying dependency between the generated perturbations and input instances, where the perturbations are mainly concentrated on the semantical part of the input images. Besides, for different target classes, our method tends to generate perturbations with different texture patterns, which also verifies the effectiveness of our designed pattern injection module." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.357, + 0.895, + 0.523 + ], + "angle": 0, + "content": "Ablation Studies. To look deeper into our proposed method, in this section, we present a series of ablation studies. As shown in Figure 7, we vary the number of target samples and convolution kernels to verify the effectiveness of our method. As presented in Figure 7(a), the performance of our method continues to grow until the number of target samples reaches 1000. Besides, in Figure 7(b), when the number of kernels is greater than 4, our performance reaches a plateau, which means that it is sufficient to reach an impressive attack success rate by learning 4 kernels in each designed dynamic convolution module." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.542, + 0.619, + 0.558 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.57, + 0.892, + 0.797 + ], + "angle": 0, + "content": "In this paper, we first construct a causal graph to expose the origin of targeted adversarial examples, which motivates us to inject target patterns or styles for generating transferable target adversarial examples. Then we introduce a dynamic generative attack model composed of a cross-attention guided convolution module and a pattern injection module. Our generative attack model can not only inject pattern or style information of the target class to improve transferable targeted attacks, but also learn specialized convolutional kernels for each input instance, which inherits the advantages of both instance-specific and instance-agnostic attacks. Moreover, we also provide rigorous theoretical analysis to guarantee the effectiveness of our method, and extensive experiments demonstrate that our method performs better than state-of-the-art targeted attack methods." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.805, + 0.681, + 0.822 + ], + "angle": 0, + "content": "6. Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.831, + 0.892, + 0.888 + ], + "angle": 0, + "content": "This work was partially supported by the National Nature Science Foundation of China (Grant 62022078, Grant 62021002), and National Defense Basic Scientific Research Program (Grant JCKY2022911B002)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "16411" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.469, + 0.156 + ], + "angle": 0, + "content": "[1] N. Akhtar and A. Mian. Threat of adversarial attacks on deep learning in computer vision: A survey. 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IEEE, 2019. 3" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "16414" + } + ] +] \ No newline at end of file diff --git a/2023/Dynamic Generative Targeted Attacks With Pattern Injection/03048e96-e108-4f0d-8eee-8c14ea87df56_origin.pdf b/2023/Dynamic Generative Targeted Attacks With Pattern Injection/03048e96-e108-4f0d-8eee-8c14ea87df56_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..296e597468278b2bb49e0c5f9c79827e77f78723 --- /dev/null +++ b/2023/Dynamic Generative Targeted Attacks With Pattern Injection/03048e96-e108-4f0d-8eee-8c14ea87df56_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:8cf62faba7eebd885ec37ef89a0462ca551d8172e6050d9c5d4ee604e36dde15 +size 3198974 diff --git a/2023/Dynamic Generative Targeted Attacks With Pattern Injection/full.md b/2023/Dynamic Generative Targeted Attacks With Pattern Injection/full.md new file mode 100644 index 0000000000000000000000000000000000000000..36fc49b2815d8579f11e3893c20aef874ad824bc --- /dev/null +++ b/2023/Dynamic Generative Targeted Attacks With Pattern Injection/full.md @@ -0,0 +1,306 @@ +# Dynamic Generative Targeted Attacks with Pattern Injection + +Weiwei Feng $^{1,\ast}$ , Nanqing Xu $^{1,\ast}$ , Tianzhu Zhang $^{1,2,\dagger}$ , Yongdong Zhang $^{1}$ $^{1}$ University of Science and Technology of China, $^{2}$ Deep Space Exploration Lab +ngww@mail.ustc.edu.cn, xnq@mail.ustc.edu.cn, {tzzhang, zhyd73}@ustc.edu.cn + +# Abstract + +Adversarial attacks can evaluate model robustness and have been of great concern in recent years. Among various attacks, targeted attacks aim at misleading victim models to output adversary-desired predictions, which are more challenging and threatening than untargeted ones. Existing targeted attacks can be roughly divided into instance-specific and instance-agnostic attacks. Instance-specific attacks craft adversarial examples via iterative gradient updating on the specific instance. In contrast, instance-agnostic attacks learn a universal perturbation or a generative model on the global dataset to perform attacks. However, they rely too much on the classification boundary of substitute models, ignoring the realistic distribution of the target class, which may result in limited targeted attack performance. And there is no attempt to simultaneously combine the information of the specific instance and the global dataset. To deal with these limitations, we first conduct an analysis via a causal graph and propose to craft transferable targeted adversarial examples by injecting target patterns. Based on this analysis, we introduce a generative attack model composed of a cross-attention guided convolution module and a pattern injection module. Concretely, the former adopts a dynamic convolution kernel and a static convolution kernel for the specific instance and the global dataset, respectively, which can inherit the advantages of both instance-specific and instance-agnostic attacks. And the pattern injection module utilizes a pattern prototype to encode target patterns, which can guide the generation of targeted adversarial examples. Besides, we also provide rigorous theoretical analysis to guarantee the effectiveness of our method. Extensive experiments demonstrate that our method shows superior performance than 10 existing adversarial attacks against 13 models. + +# 1. Introduction + +With the encouraging progress of deep neural networks (DNNs) in various fields [6, 19, 16, 44, 42], recent studies + +![](images/b6ccc82cec6d3f316c9a2ef583a8e7e302f91efe28bb8a7134069e1876f4ef0d.jpg) +Figure 1. Visualization comparison between adversarial examples generated by our method (a) and the instance-specific method MIM [9] (b). Our perturbations (a) not only show an underlying dependency with the input instance, but also have strong semantic patterns or styles of the target class ("Hippopotamus"). In contrast, the perturbations generated by MIM perform like random noises. The adversarial examples are generated against ResNet-152, and labels are predicted by another unknown model (VGG-16). + +[36, 29, 28, 38] have corroborated that adversarial examples generated with small-magnitude perturbations can mislead the DNNs to make incorrect predictions. Due to the vulnerability of DNNs, adversarial attacks expose a security threat to real application systems based on deep neural networks, especially in some sensitive fields such as autonomous driving [27], face verification and financial systems [43], to name a few. Therefore, adversarial attacks have become a research hotspot over the past decade [2, 48, 35, 3, 33], which are significant in demonstrating the adversarial robustness and stability of deep learning models. + +To further understand adversarial examples, there are tremendous works [1, 48, 33, 4, 36, 38] focusing on adversarial attacks. Recently, it has been found that adversarial examples possess an intriguing property of transferability, which indicates that adversarial examples generated for a white-box model can also mislead another black-box model. Due to this inherent property, black-box attacks become workable in real-world scenarios where attackers cannot access the attacked model. Extensive methods, such as + +MIM [9], DIM [53] and CD-AP [40], have made an impressive performance of boosting the transferability for untargeted attacks, which mislead the model to make an incorrect classification without specifying a target class. However, targeted attacks are more challenging compared with untargeted attacks, making the model output the adversary-desired target class. It is claimed in recent works [14, 55] that transferable targeted attacks are more worthy of study because attackers can directly control the unknown model to output the desired prediction, which can expose huge threats to data privacy and security. Therefore, it is of great significance to develop transferable targeted attacks. + +Existing methods of transferable targeted attacks can be roughly categorized into instance-specific [9, 14, 13, 54, 50, 34, 31] and instance-agnostic [52, 35, 27, 40, 39] attacks. Specifically, almost all instance-specific attacks craft adversarial examples via iterative gradient updating, where attackers can only take advantage of the specific input instance, the white-box model and the target class label. Instance-specific attacks rely on optimizing the classification score of the adversary-desired class label to perturb the specific instance, which ignore the global data distribution. As a result, they inevitably lead to adversarial examples over-fitting the white-box model and result in modest transferability of targeted attacks. On the other hand, via learning a universal perturbation [37] or a generative attack model [52, 55], instance-agnostic attacks optimize adversarial perturbations on the global data distribution rather than the specific instance. To a certain extent, they can alleviate the problem of data-specific over-fitting and lead to more transferable targeted adversarial examples. However, taking the generative attack methods as an example, they suffer from two limitations. (1) Most generative attacks [52, 40, 35] still rely on the target label and the classification boundary information of white-box models rather than the realistic data distribution of the target class. Consequently, it is claimed that most generative attacks still have the possibility of over-fitting the white-box model, which may result in limited performance of transferable targeted attacks. (2) Another limitation is that existing generative attacks [39, 55, 27] apply the same network weights to every input instance in the test dataset. Nevertheless, it is considered that the shared network weights cannot stimulate the best attack performance of generative models [39, 55, 55]. Thus these aforementioned limitations have become the bottleneck of developing transferable targeted attacks, to a certain extent. + +To address the aforementioned limitations, in this paper we construct a causal graph to formulate the prediction process of classifiers, and analyze the origin of adversarial examples. Based on this analysis, we propose to generate targeted adversarial examples via injecting the specific pattern or style of the target class. To this end, we intro + +duce a generative attack model, which can not only inject pattern or style information of the target class to improve transferable targeted attacks, but also learn specialized convolutional kernels for each input instance. Specifically, we designed a cross-attention guided convolution module and a pattern injection module in the proposed generative attack model. (1) The cross-attention guided convolution module consists of a static convolutional kernel and a dynamic convolutional kernel that is computed according to the input instance. Consequently, this static and dynamic mixup module can not only encode the global information of the dataset, but also learn specialized convolutional kernels for each input instance. This paradigm makes our generative model inherit the advantages of both instance-specific and instance-agnostic attacks. (2) The pattern injection module is designed to model the pattern or style information of the target class and guide the generation of targeted adversarial examples. Concretely, we propose a pattern prototype to learn a global pattern representation over images from the target class, and use the prototype to guide the generation of more transferable targeted adversarial examples. And the generated adversarial images of our method are presented in Figure 1. It is observed that our generated perturbations (as shown in Figure 1(a)) pose strong semantic patterns or styles of the target class and show an underlying dependency on the input instance. In contrast, the perturbations (as presented in Figure 1(b)) generated by MIM [9] perform like random noises. Finally, to further understand our method, we provide rigorous theoretical analysis to guarantee the effectiveness of our method, as shown in Section 3.4, where we derive a concise conclusion based on the problem of Gaussian binary classification. + +In summary, the main contributions of this paper are three-fold: (1) We propose a dynamic generative model to craft transferable targeted adversarial examples, which can not only inject pattern or style information of the target class to improve transferable targeted attacks, but also learn specialized convolutional kernels for each input instance. Besides, our method inherits the advantages of both instancespecific and instance-agnostic attacks, and to the best of our knowledge, we are the first to bridge them. (2) We state that injecting the specific pattern or style of the target class can improve the transferability of targeted adversarial examples, and we provide a comprehensive theoretical analysis to verify the rationality of this statement. (3) Extensive experimental results demonstrate that our method significantly boosts the transferability of targeted adversarial examples over 10 existing methods against 13 models. + +# 2. Related Work + +Instance-specific Attacks. As the pioneering work [48] exposes the vulnerability of neural networks, many recent methods [54, 17, 3, 11, 29] utilize gradient-based optimization. + +tion to generate input-dependent adversarial examples. To further boost the transferability of the adversarial example, several works have been proposed by various strategies to optimize the gradient update process. MIM [9] introduces a momentum term during the iterative gradient updating. DIM [53] improves the transferability via integrating diverse input patterns for optimizing, and TIM [10] performs a convolution operation on the gradient that is applicable to any gradient-based attack methods. Besides, some recent works [5, 18, 20] propose to ensemble multiple pre-trained substitute models to craft more transferable adversarial examples. However, these methods pose modest transferability under the targeted attacks setting, because they rely too much on the target label and the classification boundary information of white-box models. Meanwhile, among these methods, they all face the problem of data-specific overfitting, because of ignoring the global data distribution. To overcome these limitations, in this paper, we propose a dynamic generative model to craft more transferable targeted adversarial examples, which can not only encode the global dataset, but also adapt to the specific instance. + +Instance-agnostic Attacks. Distinguished from instance-specific attacks, instance-agnostic attacks learn a universal perturbation [37] or a generative function [35, 27, 51, 41, 55, 40, 39] to craft adversarial examples. Compared with the universal perturbation, the latter is more flexible and has drawn more attention in recent years. Xiao et al. [52] first explore generating adversarial examples with GANs [16], which can consider the whole dataset instead of the specific input instance. CD-AP [40] and TTP [39] exploit generative models to craft more transferable adversarial examples. Recently, Yang et al. [55] boost the transferability of targeted adversarial examples with hierarchical generative networks. To a certain extent, these methods lead to more general and transferable adversarial examples because of alleviating the data-specific over-fitting problem. However, they also suffer from some limitations. First, existing generative attack methods [52, 57, 55, 40, 39] apply the same network weights to each input instance, which may limit the transferability of adversarial examples. And the second is that most of them also rely too much on the target label and the classification boundary of white-box models, ignoring the realistic data distribution of the target class. Motivated by these, in this paper, we propose a dynamic generative attack model, which can not only inject pattern or style information of the target class to improve transferable targeted attacks, but also learn specialized convolutional kernels for each input instance. + +# 3. Method + +In this section, we present the overall scheme of our proposed method, including some preliminaries, motivations, network architectures and theoretical analyses. + +![](images/04c827378fe801b8e8c4dab075e5ac53b2f799071b7b53b7b5187757821b6231.jpg) +Figure 2. The casual graph of model inference. Each node is a random variable, where $C, S, \mathbf{x}, \mathbf{y}$ and $\theta$ represent content, style or pattern, the input image, the prediction label, and model parameters, respectively. In order to achieve good performance, the model will learn the statistical correlation between the style $S$ and the label $\mathbf{y}$ . + +# 3.1. Preliminaries and Motivation + +We denote the clean image as $\pmb{x} \in \mathcal{X}$ , and the attacked model parameterized by $\theta$ is denoted as $f: \mathcal{X} \to \mathcal{Y}$ . The goal of target attacks is to generate an adversarial perturbation $\delta$ that can make the model misclassify the input $\pmb{x}_{adv} = \pmb{x} + \delta$ to the predefined class $\pmb{y}_t$ , which can be formulated as $f(\pmb{x}_{adv}) = \pmb{y}_t \neq f(\pmb{x})$ . To gain insights into the origin of targeted adversarial examples, we construct a casual graph $\mathcal{G}$ to formulate the inference of deep learning models, as shown in Figure 2. For the input images $\pmb{x}$ , we propose to group the whole causes of $\pmb{x}$ into two categories, content-related cause $C$ and content-independent cause $S$ that can be dubbed as style or pattern cause. This indicates that $C \rightarrow x \gets S$ , and $C \bot S$ . According to human visual intuition, only the content variable $C$ is relevant to the prediction class $y$ . Consequently, we can use the Law of total probability to expand the prediction $P_{\theta}(\pmb{y} \mid \pmb{x})$ as: + +$$ +P _ {\theta} (\boldsymbol {y} \mid \boldsymbol {x}) = \sum_ {s \in \mathbb {S}} P _ {\theta} (s \mid \boldsymbol {x}) P _ {\theta} (\boldsymbol {y} \mid \boldsymbol {x}, s). \tag {1} +$$ + +But several recent works [56] and Equation (1) imply that deep learning models can learn not only the dependencies between the content $C$ and the label $y$ , but also the statistical correlation between the style $S$ and the label $y$ (i.e., $P_{\theta}(\boldsymbol{y} \mid \boldsymbol{x}, s)$ ). This phenomenon indicates that deep learning models can capture some detailed texture patterns and style features to achieve good performance, and the output prediction $P_{\theta}(\boldsymbol{y} \mid \boldsymbol{x})$ will change with the statistical correlation between $\boldsymbol{y}$ and $S$ (i.e., $P_{\theta}(\boldsymbol{y} \mid \boldsymbol{x}, s)$ ). And this property certainly offers attackers an opportunity to generate adversarial examples for misleading the model. Therefore, the inference of targeted adversarial examples can be formulated as: + +$$ +P _ {\theta} \left(\boldsymbol {y} _ {t} \mid \boldsymbol {x} _ {a d v}\right) = \sum_ {s \in \mathbb {S}} P _ {\theta} (s \mid \boldsymbol {x} _ {a d v}) P _ {\theta} \left(\boldsymbol {y} _ {t} \mid \boldsymbol {x} _ {a d v}, s\right). \tag {2} +$$ + +Inspired by Figure 2 and the aforementioned Equation (2), we first propose to exploit the statistical correlation between $\mathbf{y}_t$ and $S$ (i.e., $P_{\theta}(\mathbf{y}_t \mid \mathbf{x}_{adv}, s))^1$ , via injecting the specific + +![](images/5515ccc87363ed233b737da7d7dd3a3d5ddbdf8aa8e2f88d16454a79c9c7d4f1.jpg) +Figure 3. The architecture of our dynamic generative attack model, which is composed of a cross-attention guided convolution module (denoted as "Dy_Conv") and a pattern injection module. The cross-attention guided convolution module consists of a static convolutional kernel and a dynamic convolutional kernel that is computed according to the input instance. For the pattern injection, the pattern prototype $\pmb{p}_t = \{\gamma_t,\beta_t\}$ encodes the patterns or styles of the target class, and the "AdaCN" layer performs an affine operation to inject $\pmb{p}_t$ into the generation of adversarial examples. Similar to [25], we introduce $\pmb{p}_t^{\mathrm{running}}$ via the EMA updating based on $\pmb{p}_t$ . + +style or pattern of images from the given target class $\mathbf{y}_t$ to generate targeted transferable adversarial examples. + +To this end, we propose a generative model to craft targeted adversarial examples by injecting the pattern of the target class. Besides, we design a cross-attention guided dynamic convolution module in the generator, which makes our generative model inherit the advantages of both instance-specific and instance-agnostic attacks. Therefore, the formulation of our method can be denoted as + +$$ +\boldsymbol {x} _ {a d v} = \operatorname {c l i p} \left\{\operatorname {P r o j} \left(\mathcal {W} * G _ {\theta (\boldsymbol {x})} (\boldsymbol {x}, p _ {t}), - \varepsilon , \varepsilon\right) + \boldsymbol {x} \right\}, \tag {3} +$$ + +where $\varepsilon$ is the perturbation budget, $\mathcal{W}$ is a smoothing operator with fixed weights, $p_t$ represents the semantic pattern or style of the target class, and Proj is a projection operation. + +# 3.2. Network Architecture + +Specifically, our generative model is illustrated in Figure 3, which is composed of two modules: ① a cross attention-guided dynamic convolution module (corresponding to "Dy_Conv" in the ResBlock of Figure 3), ② a pattern injection module. And the detailed pipeline of our approach is presented in Algorithm 1. In the next section, we mainly describe the two designed modules in detail. + +Cross-attention guided dynamic convolution module. Considering that not only the global dataset needs to be modeled, but also specialized convolution kernels need to be learned for each input, we design a cross-attention guided convolution module. To achieve this goal, as shown in Figure 4, we propose a static and a dynamic convolution kernel parameterized with $W$ and $\Delta W$ , respectively2. Thus + +Algorithm 1: Dynamic Generative Targeted Attack +Input: A white-box model $f$ , training data $\mathcal{X}$ , target samples $\mathcal{X}_t$ , perturbation budget $\epsilon$ , training epoch $T$ . Output: Generative attack model $G_{\theta}$ . +1 for $t \gets 0$ to $T$ do +2 Sample mini-batches $\pmb{x} \sim \mathcal{X}$ and $\pmb{x}_t \sim \mathcal{X}_t$ . +3 Get the augmented mini-batches $\pmb{x}'$ from $\pmb{x}$ . +4 Feed $\pmb{x}$ , $\pmb{x}'$ and $\pmb{x}_t$ into the generator to get adversarial examples $\pmb{x}_{adv}$ and $\pmb{x}_{adv}'$ , where $\pmb{x}_t$ is used for extracting and injecting target patterns $p_t$ . +5 Update $p_t^{\text{running}}$ based on $p_t$ via EMA updating. +6 Forward pass $\pmb{x}_{adv}$ , $\pmb{x}_{adv}'$ and $\pmb{x}_t$ through $f$ . +7 Compute losses $L_{attack}$ , and backward for updating $G_{\theta}$ . +8 return Converged generator $G_{\theta}$ . + +the designed module is formulated as: + +$$ +\boldsymbol {X} _ {l} = \operatorname {c o n v} \left(\boldsymbol {X} _ {l - 1}; W + \Delta W\right), \tag {4} +$$ + +where $X_{l}$ is the output of layer $l$ . To get dynamic convolution kernels, we design a series of learnable kernels $(N\times C_{in}\times C_{out}\times k^2)^3$ and attention queries $\pmb {q}\in R^{N\times C_{in}}$ , which indicate the attention weight of each kernel. For the layer $l$ , we compute attention weights via performing cross-attention between attention queries $\pmb{q}$ and the input $\pmb{X}_{l - 1}\in R^{C_{in}\times H\times W}$ , which can be indicated as: + +$$ +a t t = \operatorname {s o f t m a x} \left(\frac {Q K ^ {\top}}{\sqrt {d _ {k}}}\right) V, \tag {5} +$$ + +![](images/76c702c3d176794366de9bc03834ef4564c0c526ede8b2a8ad8c18d647ee2059.jpg) +Figure 4. The illustration of the proposed cross-attention guided dynamic convolution module, which is composed of a static convolution kernel $W$ and a dynamic convolution kernel $\Delta W$ . + +where $att \in R^{N \times C_{in}}$ , $Q = qW^{q}$ , $K = X_{l-1}^{\top}W^{k}$ and $V = X_{l-1}^{\top}W^{v}$ . Then we can get the attention weight $\alpha = [\alpha_{1}, \alpha_{2}, \dots, \alpha_{N}] \in R^{1 \times N}$ by conducting the average pooling on $att$ , and each element in $\alpha$ indicates the weight of corresponding kernels. Therefore, the dynamic convolution kernels are implemented as $\Delta W = \alpha_{1} * W_{1} + \alpha_{2} * W_{2} + \dots + \alpha_{N} * W_{N}$ . Benefiting from this dynamic and static mixup convolution operation, our proposed generative attack model can inherit the advantages of both instance-specific and instance-agnostic attacks. + +Pattern injection module. First, to encode target patterns and styles during the generation of adversarial examples, we design a pattern prototype $\pmb{p}_t = \{\gamma_t, \beta_t\}$ , which is extracted from the features of target samples, as shown in Figure 3. Following [25], we introduce $\pmb{p}_t^{\text{running}}$ to model patterns of the global samples for the target class. Note that we update $\pmb{p}_t^{\text{running}}$ during each training iteration, which can be indicated as $\pmb{p}_t^{\text{running}} = \lambda \pmb{p}_t + (1 - \lambda) \pmb{p}_t^{\text{running}}$ . Then we propose an adaptive class normalization (corresponding to "AdaCN" in Figure 3) to inject $\pmb{p}_t$ into the generation of target adversarial examples. Similar to [23], the AdaCN module exploits the learned $\pmb{p}_t = \{\gamma_t, \beta_t\}$ to perform an affine operation for injecting target patterns or styles: + +$$ +\operatorname {A d a C N} (\boldsymbol {X}) = \gamma_ {t} \left(\frac {\boldsymbol {X} - \mu (\boldsymbol {X})}{\sigma (\boldsymbol {X})}\right) + \beta_ {t}, \tag {6} +$$ + +where $\pmb{p}_t = \{\pmb{\gamma}_t, \pmb{\beta}_t\}$ is the target pattern prototype. Note that Equation (6) represents pattern injection during training, and it is necessary to replace $\pmb{p}_t = \{\pmb{\gamma}_t, \pmb{\beta}_t\}$ with $\pmb{p}_t^{\mathrm{running}} = \{\pmb{\gamma}_t^{\mathrm{running}}, \pmb{\beta}_t^{\mathrm{running}}\}$ during inference. + +# 3.3. Objective Function + +To lead the victim model to misclassify adversarial examples as the target class, it is necessary to make the output distribution of adversarial examples $f(\boldsymbol{x}_{adv}), f(\boldsymbol{x}_{adv}')$ and target samples $f(\boldsymbol{x}_t)$ consistent. Thus we define the loss + +function as follows: + +$$ +\begin{array}{l} \mathcal {L} \quad = D _ {K L} \left(f \left(\boldsymbol {x} _ {a d v}\right) \| f \left(\boldsymbol {x} _ {t}\right)\right) + D _ {K L} \left(f \left(\boldsymbol {x} _ {t}\right) \| f \left(\boldsymbol {x} _ {a d v}\right)\right) \tag {7} \\ \mathcal {L} _ {a u g} = D _ {K L} \left(f (\boldsymbol {x} _ {a d v} ^ {\prime}) \| f (\boldsymbol {x} _ {t})\right) + D _ {K L} \left(f (\boldsymbol {x} _ {t}) \| f (\boldsymbol {x} _ {a d v} ^ {\prime})\right) \\ \end{array} +$$ + +Besides, similar to [39], we also introduce a local similarity loss. For a batch of generated adversarial examples $\{\pmb{x}_{adv}^i\}_{i=1}^n$ , $\{\pmb{x}_{adv}^{j,i}\}_{i=1}^n$ and target samples $\{\pmb{x}_t^i\}_{i=1}^n$ , the similarity matrix can be computed as $S_{i,j} = \frac{f(\pmb{x}_{adv}^i) \cdot f(\pmb{x}_{adv}^{j,i})}{\|f(\pmb{x}_{adv}^i)\| \|f(\pmb{x}_{adv}^{j,j})\|}$ and $S_{i,j}^t = \frac{f(\pmb{x}_t^i) \cdot f(\pmb{x}_t^j)}{\|f(\pmb{x}_t^i)\| \|f(\pmb{x}_t^j)\|}$ . Hence, we can get the local similarity loss as: + +$$ +\mathcal {L} _ {s i m} = \sum_ {i, j} \overline {{\mathcal {S}}} _ {i, j} ^ {t} \log \frac {\overline {{\mathcal {S}}} _ {i , j} ^ {t}}{\overline {{\mathcal {S}}} _ {i , j}} + \sum_ {i, j} \overline {{\mathcal {S}}} _ {i, j} \log \frac {\overline {{\mathcal {S}}} _ {i , j}}{\overline {{\mathcal {S}}} _ {i , j} ^ {t}}, \tag {8} +$$ + +where $\overline{\mathcal{S}}_{i,j} = \frac{\exp(\mathcal{S}_{i,j})}{\sum_k\exp(\mathcal{S}_{i,k})}$ and $\overline{\mathcal{S}}_{i,j}^t = \frac{\exp(\mathcal{S}_{i,j}^t)}{\sum_k\exp(\mathcal{S}_{i,k}^t)}$ . Finally, the total objective function can be formulated as: + +$$ +\mathcal {L} _ {\text {a t t a c k}} = \mathcal {L} + \mathcal {L} _ {\text {a u g}} + \mathcal {L} _ {\text {s i m}}. \tag {9} +$$ + +# 3.4. Theoretical Analyses + +In order to further explain the insights of our method, we consider a concrete setting that allows us to theoretically investigate why our method is effective for boosting target attacks. Please refer to the Supplementary Material for comprehensive proofs of the following theorem. + +Setup. We consider a simple problem of maximum likelihood classification, similar to that of [24], between two Gaussian distributions. + +$$ +\mathcal {X} _ {s} \sim N \left(\boldsymbol {\mu} _ {s}, \boldsymbol {\Sigma} _ {s}\right), \quad \mathcal {X} _ {t} \sim N \left(\boldsymbol {\mu} _ {t}, \boldsymbol {\Sigma} _ {t}\right), \tag {10} +$$ + +where $\pmb{\Sigma}_s, \pmb{\Sigma}_t = \mathrm{diag}\left\{\sigma_{s_1}^2, \dots, \sigma_{s_n}^2\right\}$ , $\mathrm{diag}\left\{\sigma_{t_1}^2, \dots, \sigma_{t_n}^2\right\}$ , respectively. To simplify the following derivation, we introduce a mapping and a translation operation to transform the model into a standard Gaussian binary classification model, which can be denoted as: + +$$ +\begin{array}{l} \mathcal {F} _ {s} = \boldsymbol {A} \mathcal {X} _ {s} - \frac {\boldsymbol {A} \boldsymbol {\mu} _ {s} + \boldsymbol {\mu} _ {t}}{2} \sim N (- \boldsymbol {\mu}, \boldsymbol {\Sigma}), \tag {11} \\ \mathcal {F} _ {t} = \boldsymbol {E} \mathcal {X} _ {t} - \frac {\boldsymbol {A} \mu_ {s} + \mu_ {t}}{2} \sim N (\boldsymbol {\mu}, \boldsymbol {\Sigma}), \\ \end{array} +$$ + +where the mapping matrix $\mathbf{A} = \mathrm{diag}\left\{\frac{\sigma_{t_1}}{\sigma_{s_1}},\frac{\sigma_{t_2}}{\sigma_{s_2}}\dots ,\frac{\sigma_{t_n}}{\sigma_{s_n}}\right\}$ , $\mathbf{E}$ is the identity matrix and $\pmb {\mu} = \frac{-\pmb{A}\pmb{\mu}_s + \pmb{\mu}_t}{2},\pmb {\Sigma} = \pmb{\Sigma}_t$ . To perform targeted attacks against this model with a given sample $x_{s}\in \mathcal{X}_{s}$ and the target label $t$ , where $A\pmb {x}_s - \frac{A\pmb{\mu}_s + \pmb{\mu}_t}{2} = f_s\in \mathcal{F}_s$ and $f_{s} + \delta^{\star} = A(x_{s} + \delta) - \frac{A\mu_{s} + \mu_{t}}{2}$ we aim to solve the following optimization problem: + +$$ +\boldsymbol {\delta} = \boldsymbol {A} ^ {- 1} \boldsymbol {\delta} ^ {\star}, \quad \boldsymbol {\delta} ^ {\star} = \underset {\| \boldsymbol {\delta} ^ {\prime} \| _ {2} ^ {2} \leqslant \varepsilon^ {2}} {\operatorname {a r g m a x}} \left(\boldsymbol {f} _ {s} + \boldsymbol {\delta} ^ {\prime}\right) ^ {\top} \boldsymbol {\Sigma} ^ {- 1} \boldsymbol {\mu}. \tag {12} +$$ + +Table 1. The attack success rates against normally trained models on ImageNet NeurIPS validation set, and the perturbation budget $\ell_{\infty} \leq 16/255$ . Note that the results are averaged on 8 different target classes. + +
Subsite ModelMethodInc-v3Inc-v4Inc-Res-v2Res152Densenet-121GoogleNetVgg-16
Inc-v3MIM99.900.801.000.400.200.200.30
TI-MIM98.500.500.500.300.200.400.40
SI-MIM99.801.502.000.800.700.700.50
DIM95.602.700.500.801.100.400.80
TI-DIM96.001.101.200.500.500.500.80
SI-DIM90.203.804.402.002.201.701.40
CD-AP94.2057.6060.1037.1041.6032.3041.70
TTP91.3746.0439.3716.4033.4725.8025.73
C-GSP93.4066.9066.6041.6046.4040.0045.00
GAP86.9045.0634.4834.4841.7426.8934.34
Ours94.6367.9555.0350.5047.3847.6748.11
Res152MIM0.500.400.6099.700.300.300.20
TI-MIM0.300.300.3096.500.300.400.30
SI-MIM1.301.201.6099.501.001.400.70
DIM2.302.203.0092.300.200.800.70
TI-DIM0.800.701.0090.600.600.800.50
SI-DIM4.204.805.4090.504.203.602.00
CD-AP33.3043.7042.7096.6053.8036.6034.10
TTP62.0349.2038.7095.1282.9665.0962.82
C-GSP37.7047.6045.1093.2064.2041.7045.90
GAP30.9931.4320.4884.8658.3529.8939.70
Ours66.8353.6247.6196.4886.6168.2969.58
Vgg-16MIM0.260.470.200.350.400.3490.24
TI-MIM0.430.630.340.551.450.6489.13
SI-MIM0.350.570.420.310.560.5290.89
DIM0.751.300.551.001.881.0397.70
TI-DIM0.230.380.170.290.480.3593.71
SI-DIM0.871.120.700.951.891.5591.42
CD-AP5.328.944.879.3314.023.1996.82
TTP22.5117.149.6822.6840.8722.4197.59
C-GSP9.429.603.0111.7632.2813.3396.81
GAP3.115.261.505.0811.232.7093.00
Ours28.1821.789.5625.2746.5523.7093.00
+ +Taking advantage of the method of Lagrange multipliers, we can easily get the optimal solution as follows: + +$$ +\begin{array}{r l} \delta^ {\star} & = \frac {1}{\lambda} \Sigma^ {- 1} \boldsymbol {\mu}, \\ s & = \Sigma^ {- 1} [ A ^ {- 1} (A (\quad , \quad , \quad , \quad) ] \end{array} \tag {13} +$$ + +$$ +\boldsymbol {\delta} = \frac {\hat {\boldsymbol {\Sigma}} ^ {- 1}}{2 \lambda} \left[ \boldsymbol {A} ^ {- 1} \left(\boldsymbol {A} \left(\boldsymbol {x} _ {s} - \boldsymbol {\mu} _ {s}\right) + \boldsymbol {\mu} _ {t}\right) - \boldsymbol {x} _ {s} \right]. \tag {13} +$$ + +Going a step further, we rewrite the solution of $\delta$ into a more concise formula as: + +$$ +\boldsymbol {\delta} = C _ {1} \left[ \left( \begin{array}{c c c} \frac {\sigma_ {t _ {1}}}{\sigma_ {s _ {1}}} & & \\ & \ddots & \\ & & \frac {\sigma_ {t _ {n}}}{\sigma_ {s _ {n}}} \end{array} \right) \left(\boldsymbol {x} _ {s} - \boldsymbol {\mu} _ {s}\right) + \boldsymbol {\mu} _ {t} \right] - C _ {2} \boldsymbol {x} _ {s}, \tag {14} +$$ + +where $C_1 = \frac{\Sigma^{-1}A^{-1}}{2\lambda}$ and $C_2 = \frac{\Sigma^{-1}}{2\lambda}$ . In fact, note that the item of represents target pattern or style injection, which is consistent with the previous works [23, 26]. Therefore, the formulation of Equation (14) shows a close underlying correlation between the optimal targeted adversarial perturbation and the embedding of target pattern or style, which also theoretically guarantees the effectiveness of our proposed generative model for targeted attacks. + +# 4. Experiments + +In this section, we conduct extensive experiments to demonstrate the effectiveness of our method for targeted attacks under various settings. Please feel free to get more experimental results in our Supplementary Material. + +# 4.1. Experimental Setup + +Dataset. Following [55], we perform training on ImageNet [7] training set, and evaluate on ImageNet-NeurIPS (1k) proposed by NeurIPS 2017 adversarial competition [30]. + +Victim Models. We consider 13 attacked models in our experiments. The normally trained models include Inception-v3 (Inc-v3) [47], Inception-v4 (Inc-v4) [45], DenseNet-121 [22], GoogleNet [46], ResNet-152 (Res-152) [19], and VGG16 (Vgg-16) [44] and Inception-ResNet (Inc-Res-v2) [45]. Besides, we also consider several models with robust training mechanisms, including adv-Inception-v3 (Adv-Inc-v3) [17], ens-adv-Inception-ResNet-v2 (Ens-Adv-IncRes-v2) [18] and ResNet-50 trained with various robust training tricks [21, 15]. + +Baseline Attacks. To illustrate the effectiveness of our method, we compare it with instance-specific attacks and instance-agnostic attacks. Instance-specific attacks mainly include MIM [9], DIM [53], SIM [32] and TIM [10], while + +Table 2. The attack success rates against robust models on ImageNet NeurIPS validation set. The perturbation budget $\ell_{\infty} \leq 16/255$ . Adv-Inc-v3 [29] and Ens-Adv-IncRes-v2 [49] are trained with the adversarial training mechanism. Res50_SIN (stylized ImageNet), Res50_SIN_IN (mixture of stylized ImageNet and Nature ImageNet) and Res50_SIN_fine_IN (mixture of stylized ImageNet and Nature ImageNet with finetuning tricks) are trained with auxiliary dataset [15], and Res50_Augmix [21] is trained with the state-of-the-art data augmentation approach. Note that the results are averaged on 8 different target classes. + +
Subsite ModelMethodAdv-Inc-v3Ens-IncRes-v2Res50_SINRes50_SIN_INRes50_SIN_fine_INRes50_AugMix
Res152MIM0.190.150.281.582.750.78
TI-MIM0.610.730.502.514.751.76
SI-MIM0.240.240.390.660.840.36
DIM0.630.370.948.5014.223.77
TI-DIM0.230.300.280.761.490.49
SI-DIM0.710.710.752.733.891.37
CD-AP3.776.487.0963.7276.7949.67
TTP27.9926.0824.6172.4774.5170.96
GAP5.724.517.3371.0483.6452.07
Ours31.1030.0727.7077.1380.5576.78
VGG16MIM0.140.150.160.400.340.19
TI-MIM0.260.240.200.450.570.28
SI-MIM0.280.200.210.490.250.14
DIM0.220.160.270.930.990.49
TI-DIM0.140.190.210.350.340.21
SI-DIM0.500.360.330.800.690.26
CD-AP0.360.340.354.6310.203.60
TTP3.753.202.6627.8032.7016.57
GAP0.300.520.424.528.923.35
Ours4.143.222.6630.1638.1017.95
+ +![](images/27526b296dfac3020fb371480d3ee4ef4707b685d318541607b39cb280af87f9.jpg) +(a) + +![](images/c5baa04f5376891c990c7585a774bcbf29672695c0b37a3ad4f58cf05d34eac3.jpg) +(b) +Figure 5. Attack success rates of targeted adversarial examples generated by various generative attack methods against different input process defense methods. Figure (a) displays the results against various input smooth methods (including gaussian, medium and average smoothing). Figure (b) shows the results against JPEG compression (the JPEG quality factor varies from 70 to 90). Here, the substitute model is Res-152 and the target model is Vgg-16. + +instance-agnostic attacks include CD-AP [40], TTP [39], GAP [41] and C-GSP [55]. In our experiments, the perturbation size $\varepsilon = 16 / 255$ , the decay factor $\mu_0$ is 1 in MIM, the transform probability is 0.7 in DIM, and the kernel size is 15 in TIM. And other hyper-parameters follow the default settings provided in their original works. + +# 4.2. Comparison with State-of-the-art Methods + +Attack Normally Trained Models. To evaluate the performance of our method, we first perform targeted adversarial attacks to compare the transferability across normally trained models of adversarial examples generated by various methods, including 6 iterative instance-specific attack methods and 5 instance-agnostic attack methods. As shown + +in Table 1, our dynamic generative attack method reaches the best transferability on 16 out of 18 various black-box cases. Furthermore, the attack success rate of our method against normally trained models is $65.42\%$ on average with the substitute model as Res-152, which outperforms the best of baselines [39] by $5.28\%$ on average. Another interesting discovery is that iterative instance-specific attack methods can reach better performance under the setting of white-box attacks, while generative attack methods show more transferability when adapting the adversarial examples to a black-box model. Among these generative methods, our method can still generate targeted adversarial examples with higher transferability than others. + +Attack Models with Robust Training Mechanisms. To comprehensively verify the effectiveness of our method, we compare the transferability of our approach with baselines against several robust models, which are trained with various robust training strategies. As presented in Table 2, although the attack success rate against these robust models is relatively low, our method is still able to outperform baseline methods. Our generative attack method achieves the best performance of targeted transferable adversarial attacks on 11 over 12 cases. And regarding Res-152 as the substitute model, our method outperforms the best of baselines [39] by $4.45\%$ on average. Compared with normally trained models, models with adversarial or robust training strategies are difficult to attack successfully, which indicates they are more robust than normal models. + +Attack Models with Input Process Defense. Another widely used and simple defense method is Input Process, which leverages image processing techniques to remove + +![](images/02657f5b2009007f81625b8fb5da157bdd6854afa234b6f86b9709b71cdd564f.jpg) +Figure 6. Visualization results of adversarial examples generated by our proposed method. The 1st, 2nd and 3rd rows show clean images, adversarial perturbations and adversarial examples, respectively. And (a), (b) and (c) display the results of different target classes (French bulldog, Fire engine and Street sign), which indicate that different target classes lead to different patterns or texture styles of the generated perturbations and adversarial images. Please refer to our Supplementary Material for more qualitative examples. + +![](images/6c49253a6a03b5a3957d19de54ee2cbedacf77992c3ab3178a4a7c1df9fea5ac.jpg) +(a) + +![](images/f0f4a1a912ac4e7095b741ca813ab8ad4cf6713ab4201b4bc53de02848f3d2d4.jpg) +(b) +Figure 7. Ablation studies. (a) Effect of the number of target samples. (b) Effect of the number of learnable convolution kernels. Note that the substitute model is Res-152, while victim models include Vgg-16, GoogleNet and Inc-v3. + +the adversary perturbation before feeding into target models. To further understand our method, we also evaluate the targeted adversarial examples crafted by various generative attacks against several image processing based defense methods, namely, JPEG compression [12] and Smooth [8]. As presented in Figure 5, our method consistently outperforms the two existing generative attacks against both JPEG compression and various smoothing defense methods. For example, our method achieves an attack success rate of $54.77\%$ , when the JPEG quality is 70, while TTP [39] and C-GSP [55] just reach $54.06\%$ and $40.04\%$ , respectively. + +# 4.3. Visualization and Ablation Studies + +Visualization. To vividly demonstrate the working mechanism of our method, we visualize several adversarial examples and perturbations with different target classes. As shown in Figure 6, there is an underlying dependency between the generated perturbations and input instances, where the perturbations are mainly concentrated on the semantical part of the input images. Besides, for different target classes, our method tends to generate perturbations with different texture patterns, which also verifies the effectiveness of our designed pattern injection module. + +Ablation Studies. To look deeper into our proposed method, in this section, we present a series of ablation studies. As shown in Figure 7, we vary the number of target samples and convolution kernels to verify the effectiveness of our method. As presented in Figure 7(a), the performance of our method continues to grow until the number of target samples reaches 1000. Besides, in Figure 7(b), when the number of kernels is greater than 4, our performance reaches a plateau, which means that it is sufficient to reach an impressive attack success rate by learning 4 kernels in each designed dynamic convolution module. + +# 5. Conclusion + +In this paper, we first construct a causal graph to expose the origin of targeted adversarial examples, which motivates us to inject target patterns or styles for generating transferable target adversarial examples. Then we introduce a dynamic generative attack model composed of a cross-attention guided convolution module and a pattern injection module. Our generative attack model can not only inject pattern or style information of the target class to improve transferable targeted attacks, but also learn specialized convolutional kernels for each input instance, which inherits the advantages of both instance-specific and instance-agnostic attacks. Moreover, we also provide rigorous theoretical analysis to guarantee the effectiveness of our method, and extensive experiments demonstrate that our method performs better than state-of-the-art targeted attack methods. + +# 6. Acknowledgement + +This work was partially supported by the National Nature Science Foundation of China (Grant 62022078, Grant 62021002), and National Defense Basic Scientific Research Program (Grant JCKY2022911B002). + +# References + +[1] N. Akhtar and A. Mian. Threat of adversarial attacks on deep learning in computer vision: A survey. IEEE Access, 6:14410-14430, 2018. 1 +[2] Maksym Andriushchenko, Francesco Croce, Nicolas Flammarion, and Matthias Hein. 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Among various attacks, targeted attacks aim at misleading victim models to output adversary-desired predictions, which are more challenging and threatening than untargeted ones. Existing targeted attacks can be roughly divided into instance-specific and instance-agnostic attacks. Instance-specific attacks craft adversarial examples via iterative gradient updating on the specific instance. In contrast, instance-agnostic attacks learn a universal perturbation or a generative model on the global dataset to perform attacks. However, they rely too much on the classification boundary of substitute models, ignoring the realistic distribution of the target class, which may result in limited targeted attack performance. And there is no attempt to simultaneously combine the information of the specific instance and the global dataset. To deal with these limitations, we first conduct an analysis via a causal graph and propose to craft transferable targeted adversarial examples by injecting target patterns. Based on this analysis, we introduce a generative attack model composed of a cross-attention guided convolution module and a pattern injection module. Concretely, the former adopts a dynamic convolution kernel and a static convolution kernel for the specific instance and the global dataset, respectively, which can inherit the advantages of both instance-specific and instance-agnostic attacks. And the pattern injection module utilizes a pattern prototype to encode target patterns, which can guide the generation of targeted adversarial examples. Besides, we also provide rigorous theoretical analysis to guarantee the effectiveness of our method. Extensive experiments demonstrate that our method shows superior performance than 10 existing adversarial attacks against 13 models." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 642, + 128, + 654 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 642, + 128, + 654 + ], + "spans": [ + { + "bbox": [ + 47, + 642, + 128, + 654 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 662, + 287, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 662, + 287, + 686 + ], + "spans": [ + { + "bbox": [ + 47, + 662, + 287, + 686 + ], + "type": "text", + "content": "With the encouraging progress of deep neural networks (DNNs) in various fields [6, 19, 16, 44, 42], recent studies" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 310, + 213, + 544, + 353 + ], + "blocks": [ + { + "bbox": [ + 310, + 213, + 544, + 353 + ], + "lines": [ + { + "bbox": [ + 310, + 213, + 544, + 353 + ], + "spans": [ + { + "bbox": [ + 310, + 213, + 544, + 353 + ], + "type": "image", + "image_path": "b6ccc82cec6d3f316c9a2ef583a8e7e302f91efe28bb8a7134069e1876f4ef0d.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 363, + 545, + 451 + ], + "lines": [ + { + "bbox": [ + 304, + 363, + 545, + 451 + ], + "spans": [ + { + "bbox": [ + 304, + 363, + 545, + 451 + ], + "type": "text", + "content": "Figure 1. Visualization comparison between adversarial examples generated by our method (a) and the instance-specific method MIM [9] (b). Our perturbations (a) not only show an underlying dependency with the input instance, but also have strong semantic patterns or styles of the target class (\"Hippopotamus\"). In contrast, the perturbations generated by MIM perform like random noises. The adversarial examples are generated against ResNet-152, and labels are predicted by another unknown model (VGG-16)." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 473, + 545, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 473, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 473, + 545, + 605 + ], + "type": "text", + "content": "[36, 29, 28, 38] have corroborated that adversarial examples generated with small-magnitude perturbations can mislead the DNNs to make incorrect predictions. Due to the vulnerability of DNNs, adversarial attacks expose a security threat to real application systems based on deep neural networks, especially in some sensitive fields such as autonomous driving [27], face verification and financial systems [43], to name a few. Therefore, adversarial attacks have become a research hotspot over the past decade [2, 48, 35, 3, 33], which are significant in demonstrating the adversarial robustness and stability of deep learning models." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "To further understand adversarial examples, there are tremendous works [1, 48, 33, 4, 36, 38] focusing on adversarial attacks. Recently, it has been found that adversarial examples possess an intriguing property of transferability, which indicates that adversarial examples generated for a white-box model can also mislead another black-box model. Due to this inherent property, black-box attacks become workable in real-world scenarios where attackers cannot access the attacked model. Extensive methods, such as" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 61, + 693, + 143, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 693, + 143, + 713 + ], + "spans": [ + { + "bbox": [ + 61, + 693, + 143, + 713 + ], + "type": "text", + "content": "* Equal Contribution † Corresponding Author" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "16404" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "content": "MIM [9], DIM [53] and CD-AP [40], have made an impressive performance of boosting the transferability for untargeted attacks, which mislead the model to make an incorrect classification without specifying a target class. However, targeted attacks are more challenging compared with untargeted attacks, making the model output the adversary-desired target class. It is claimed in recent works [14, 55] that transferable targeted attacks are more worthy of study because attackers can directly control the unknown model to output the desired prediction, which can expose huge threats to data privacy and security. Therefore, it is of great significance to develop transferable targeted attacks." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 218, + 289, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 218, + 289, + 638 + ], + "spans": [ + { + "bbox": [ + 46, + 218, + 289, + 638 + ], + "type": "text", + "content": "Existing methods of transferable targeted attacks can be roughly categorized into instance-specific [9, 14, 13, 54, 50, 34, 31] and instance-agnostic [52, 35, 27, 40, 39] attacks. Specifically, almost all instance-specific attacks craft adversarial examples via iterative gradient updating, where attackers can only take advantage of the specific input instance, the white-box model and the target class label. Instance-specific attacks rely on optimizing the classification score of the adversary-desired class label to perturb the specific instance, which ignore the global data distribution. As a result, they inevitably lead to adversarial examples over-fitting the white-box model and result in modest transferability of targeted attacks. On the other hand, via learning a universal perturbation [37] or a generative attack model [52, 55], instance-agnostic attacks optimize adversarial perturbations on the global data distribution rather than the specific instance. To a certain extent, they can alleviate the problem of data-specific over-fitting and lead to more transferable targeted adversarial examples. However, taking the generative attack methods as an example, they suffer from two limitations. (1) Most generative attacks [52, 40, 35] still rely on the target label and the classification boundary information of white-box models rather than the realistic data distribution of the target class. Consequently, it is claimed that most generative attacks still have the possibility of over-fitting the white-box model, which may result in limited performance of transferable targeted attacks. (2) Another limitation is that existing generative attacks [39, 55, 27] apply the same network weights to every input instance in the test dataset. Nevertheless, it is considered that the shared network weights cannot stimulate the best attack performance of generative models [39, 55, 55]. Thus these aforementioned limitations have become the bottleneck of developing transferable targeted attacks, to a certain extent." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 642, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 289, + 715 + ], + "type": "text", + "content": "To address the aforementioned limitations, in this paper we construct a causal graph to formulate the prediction process of classifiers, and analyze the origin of adversarial examples. Based on this analysis, we propose to generate targeted adversarial examples via injecting the specific pattern or style of the target class. To this end, we intro" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 304, + 72, + 547, + 455 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 455 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 455 + ], + "type": "text", + "content": "duce a generative attack model, which can not only inject pattern or style information of the target class to improve transferable targeted attacks, but also learn specialized convolutional kernels for each input instance. Specifically, we designed a cross-attention guided convolution module and a pattern injection module in the proposed generative attack model. (1) The cross-attention guided convolution module consists of a static convolutional kernel and a dynamic convolutional kernel that is computed according to the input instance. Consequently, this static and dynamic mixup module can not only encode the global information of the dataset, but also learn specialized convolutional kernels for each input instance. This paradigm makes our generative model inherit the advantages of both instance-specific and instance-agnostic attacks. (2) The pattern injection module is designed to model the pattern or style information of the target class and guide the generation of targeted adversarial examples. Concretely, we propose a pattern prototype to learn a global pattern representation over images from the target class, and use the prototype to guide the generation of more transferable targeted adversarial examples. And the generated adversarial images of our method are presented in Figure 1. It is observed that our generated perturbations (as shown in Figure 1(a)) pose strong semantic patterns or styles of the target class and show an underlying dependency on the input instance. In contrast, the perturbations (as presented in Figure 1(b)) generated by MIM [9] perform like random noises. Finally, to further understand our method, we provide rigorous theoretical analysis to guarantee the effectiveness of our method, as shown in Section 3.4, where we derive a concise conclusion based on the problem of Gaussian binary classification." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 455, + 548, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 455, + 548, + 647 + ], + "spans": [ + { + "bbox": [ + 304, + 455, + 548, + 647 + ], + "type": "text", + "content": "In summary, the main contributions of this paper are three-fold: (1) We propose a dynamic generative model to craft transferable targeted adversarial examples, which can not only inject pattern or style information of the target class to improve transferable targeted attacks, but also learn specialized convolutional kernels for each input instance. Besides, our method inherits the advantages of both instancespecific and instance-agnostic attacks, and to the best of our knowledge, we are the first to bridge them. (2) We state that injecting the specific pattern or style of the target class can improve the transferability of targeted adversarial examples, and we provide a comprehensive theoretical analysis to verify the rationality of this statement. (3) Extensive experimental results demonstrate that our method significantly boosts the transferability of targeted adversarial examples over 10 existing methods against 13 models." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 657, + 392, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 657, + 392, + 670 + ], + "spans": [ + { + "bbox": [ + 306, + 657, + 392, + 670 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "content": "Instance-specific Attacks. As the pioneering work [48] exposes the vulnerability of neural networks, many recent methods [54, 17, 3, 11, 29] utilize gradient-based optimization." + } + ] + } + ], + "index": 6 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16405" + } + ] + } + ], + "index": 7 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 323 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 323 + ], + "type": "text", + "content": "tion to generate input-dependent adversarial examples. To further boost the transferability of the adversarial example, several works have been proposed by various strategies to optimize the gradient update process. MIM [9] introduces a momentum term during the iterative gradient updating. DIM [53] improves the transferability via integrating diverse input patterns for optimizing, and TIM [10] performs a convolution operation on the gradient that is applicable to any gradient-based attack methods. Besides, some recent works [5, 18, 20] propose to ensemble multiple pre-trained substitute models to craft more transferable adversarial examples. However, these methods pose modest transferability under the targeted attacks setting, because they rely too much on the target label and the classification boundary information of white-box models. Meanwhile, among these methods, they all face the problem of data-specific overfitting, because of ignoring the global data distribution. To overcome these limitations, in this paper, we propose a dynamic generative model to craft more transferable targeted adversarial examples, which can not only encode the global dataset, but also adapt to the specific instance." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 323, + 289, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 323, + 289, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 323, + 289, + 647 + ], + "type": "text", + "content": "Instance-agnostic Attacks. Distinguished from instance-specific attacks, instance-agnostic attacks learn a universal perturbation [37] or a generative function [35, 27, 51, 41, 55, 40, 39] to craft adversarial examples. Compared with the universal perturbation, the latter is more flexible and has drawn more attention in recent years. Xiao et al. [52] first explore generating adversarial examples with GANs [16], which can consider the whole dataset instead of the specific input instance. CD-AP [40] and TTP [39] exploit generative models to craft more transferable adversarial examples. Recently, Yang et al. [55] boost the transferability of targeted adversarial examples with hierarchical generative networks. To a certain extent, these methods lead to more general and transferable adversarial examples because of alleviating the data-specific over-fitting problem. However, they also suffer from some limitations. First, existing generative attack methods [52, 57, 55, 40, 39] apply the same network weights to each input instance, which may limit the transferability of adversarial examples. And the second is that most of them also rely too much on the target label and the classification boundary of white-box models, ignoring the realistic data distribution of the target class. Motivated by these, in this paper, we propose a dynamic generative attack model, which can not only inject pattern or style information of the target class to improve transferable targeted attacks, but also learn specialized convolutional kernels for each input instance." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 657, + 104, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 657, + 104, + 670 + ], + "spans": [ + { + "bbox": [ + 47, + 657, + 104, + 670 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "content": "In this section, we present the overall scheme of our proposed method, including some preliminaries, motivations, network architectures and theoretical analyses." + } + ] + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 313, + 83, + 419, + 182 + ], + "blocks": [ + { + "bbox": [ + 313, + 83, + 419, + 182 + ], + "lines": [ + { + "bbox": [ + 313, + 83, + 419, + 182 + ], + "spans": [ + { + "bbox": [ + 313, + 83, + 419, + 182 + ], + "type": "image", + "image_path": "04c827378fe801b8e8c4dab075e5ac53b2f799071b7b53b7b5187757821b6231.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 422, + 65, + 547, + 187 + ], + "lines": [ + { + "bbox": [ + 422, + 65, + 547, + 187 + ], + "spans": [ + { + "bbox": [ + 422, + 65, + 547, + 187 + ], + "type": "text", + "content": "Figure 2. The casual graph of model inference. Each node is a random variable, where " + }, + { + "bbox": [ + 422, + 65, + 547, + 187 + ], + "type": "inline_equation", + "content": "C, S, \\mathbf{x}, \\mathbf{y}" + }, + { + "bbox": [ + 422, + 65, + 547, + 187 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 422, + 65, + 547, + 187 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 422, + 65, + 547, + 187 + ], + "type": "text", + "content": " represent content, style or pattern, the input image, the prediction label, and model parameters, respectively. In order to achieve good performance, the model will learn the statistical correlation between the style " + }, + { + "bbox": [ + 422, + 65, + 547, + 187 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 422, + 65, + 547, + 187 + ], + "type": "text", + "content": " and the label " + }, + { + "bbox": [ + 422, + 65, + 547, + 187 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 422, + 65, + 547, + 187 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 196, + 467, + 209 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 196, + 467, + 209 + ], + "spans": [ + { + "bbox": [ + 306, + 196, + 467, + 209 + ], + "type": "text", + "content": "3.1. Preliminaries and Motivation" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 215, + 547, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 215, + 547, + 407 + ], + "spans": [ + { + "bbox": [ + 304, + 215, + 547, + 407 + ], + "type": "text", + "content": "We denote the clean image as " + }, + { + "bbox": [ + 304, + 215, + 547, + 407 + ], + "type": "inline_equation", + "content": "\\pmb{x} \\in \\mathcal{X}" + }, + { + "bbox": [ + 304, + 215, + 547, + 407 + ], + "type": "text", + "content": ", and the attacked model parameterized by " + }, + { + "bbox": [ + 304, + 215, + 547, + 407 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 215, + 547, + 407 + ], + "type": "text", + "content": " is denoted as " + }, + { + "bbox": [ + 304, + 215, + 547, + 407 + ], + "type": "inline_equation", + "content": "f: \\mathcal{X} \\to \\mathcal{Y}" + }, + { + "bbox": [ + 304, + 215, + 547, + 407 + ], + "type": "text", + "content": ". The goal of target attacks is to generate an adversarial perturbation " + }, + { + "bbox": [ + 304, + 215, + 547, + 407 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 304, + 215, + 547, + 407 + ], + "type": "text", + "content": " that can make the model misclassify the input " + }, + { + "bbox": [ + 304, + 215, + 547, + 407 + ], + "type": "inline_equation", + "content": "\\pmb{x}_{adv} = \\pmb{x} + \\delta" + }, + { + "bbox": [ + 304, + 215, + 547, + 407 + ], + "type": "text", + "content": " to the predefined class " + }, + { + "bbox": [ + 304, + 215, + 547, + 407 + ], + "type": "inline_equation", + "content": "\\pmb{y}_t" + }, + { + "bbox": [ + 304, + 215, + 547, + 407 + ], + "type": "text", + "content": ", which can be formulated as " + }, + { + "bbox": [ + 304, + 215, + 547, + 407 + ], + "type": "inline_equation", + "content": "f(\\pmb{x}_{adv}) = \\pmb{y}_t \\neq f(\\pmb{x})" + }, + { + "bbox": [ + 304, + 215, + 547, + 407 + ], + "type": "text", + "content": ". To gain insights into the origin of targeted adversarial examples, we construct a casual graph " + }, + { + "bbox": [ + 304, + 215, + 547, + 407 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 304, + 215, + 547, + 407 + ], + "type": "text", + "content": " to formulate the inference of deep learning models, as shown in Figure 2. For the input images " + }, + { + "bbox": [ + 304, + 215, + 547, + 407 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 304, + 215, + 547, + 407 + ], + "type": "text", + "content": ", we propose to group the whole causes of " + }, + { + "bbox": [ + 304, + 215, + 547, + 407 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 304, + 215, + 547, + 407 + ], + "type": "text", + "content": " into two categories, content-related cause " + }, + { + "bbox": [ + 304, + 215, + 547, + 407 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 215, + 547, + 407 + ], + "type": "text", + "content": " and content-independent cause " + }, + { + "bbox": [ + 304, + 215, + 547, + 407 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 215, + 547, + 407 + ], + "type": "text", + "content": " that can be dubbed as style or pattern cause. This indicates that " + }, + { + "bbox": [ + 304, + 215, + 547, + 407 + ], + "type": "inline_equation", + "content": "C \\rightarrow x \\gets S" + }, + { + "bbox": [ + 304, + 215, + 547, + 407 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 215, + 547, + 407 + ], + "type": "inline_equation", + "content": "C \\bot S" + }, + { + "bbox": [ + 304, + 215, + 547, + 407 + ], + "type": "text", + "content": ". According to human visual intuition, only the content variable " + }, + { + "bbox": [ + 304, + 215, + 547, + 407 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 215, + 547, + 407 + ], + "type": "text", + "content": " is relevant to the prediction class " + }, + { + "bbox": [ + 304, + 215, + 547, + 407 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 215, + 547, + 407 + ], + "type": "text", + "content": ". Consequently, we can use the Law of total probability to expand the prediction " + }, + { + "bbox": [ + 304, + 215, + 547, + 407 + ], + "type": "inline_equation", + "content": "P_{\\theta}(\\pmb{y} \\mid \\pmb{x})" + }, + { + "bbox": [ + 304, + 215, + 547, + 407 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 346, + 414, + 545, + 434 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 346, + 414, + 545, + 434 + ], + "spans": [ + { + "bbox": [ + 346, + 414, + 545, + 434 + ], + "type": "interline_equation", + "content": "P _ {\\theta} (\\boldsymbol {y} \\mid \\boldsymbol {x}) = \\sum_ {s \\in \\mathbb {S}} P _ {\\theta} (s \\mid \\boldsymbol {x}) P _ {\\theta} (\\boldsymbol {y} \\mid \\boldsymbol {x}, s). \\tag {1}", + "image_path": "08d701ebea26bec7c74b74cbe3fa81c53181d08a945f6d15409089b34bed5824.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 442, + 547, + 596 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 442, + 547, + 596 + ], + "spans": [ + { + "bbox": [ + 304, + 442, + 547, + 596 + ], + "type": "text", + "content": "But several recent works [56] and Equation (1) imply that deep learning models can learn not only the dependencies between the content " + }, + { + "bbox": [ + 304, + 442, + 547, + 596 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 442, + 547, + 596 + ], + "type": "text", + "content": " and the label " + }, + { + "bbox": [ + 304, + 442, + 547, + 596 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 442, + 547, + 596 + ], + "type": "text", + "content": ", but also the statistical correlation between the style " + }, + { + "bbox": [ + 304, + 442, + 547, + 596 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 442, + 547, + 596 + ], + "type": "text", + "content": " and the label " + }, + { + "bbox": [ + 304, + 442, + 547, + 596 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 442, + 547, + 596 + ], + "type": "text", + "content": " (i.e., " + }, + { + "bbox": [ + 304, + 442, + 547, + 596 + ], + "type": "inline_equation", + "content": "P_{\\theta}(\\boldsymbol{y} \\mid \\boldsymbol{x}, s)" + }, + { + "bbox": [ + 304, + 442, + 547, + 596 + ], + "type": "text", + "content": "). This phenomenon indicates that deep learning models can capture some detailed texture patterns and style features to achieve good performance, and the output prediction " + }, + { + "bbox": [ + 304, + 442, + 547, + 596 + ], + "type": "inline_equation", + "content": "P_{\\theta}(\\boldsymbol{y} \\mid \\boldsymbol{x})" + }, + { + "bbox": [ + 304, + 442, + 547, + 596 + ], + "type": "text", + "content": " will change with the statistical correlation between " + }, + { + "bbox": [ + 304, + 442, + 547, + 596 + ], + "type": "inline_equation", + "content": "\\boldsymbol{y}" + }, + { + "bbox": [ + 304, + 442, + 547, + 596 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 442, + 547, + 596 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 442, + 547, + 596 + ], + "type": "text", + "content": " (i.e., " + }, + { + "bbox": [ + 304, + 442, + 547, + 596 + ], + "type": "inline_equation", + "content": "P_{\\theta}(\\boldsymbol{y} \\mid \\boldsymbol{x}, s)" + }, + { + "bbox": [ + 304, + 442, + 547, + 596 + ], + "type": "text", + "content": "). And this property certainly offers attackers an opportunity to generate adversarial examples for misleading the model. Therefore, the inference of targeted adversarial examples can be formulated as:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 317, + 603, + 545, + 624 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 603, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 317, + 603, + 545, + 624 + ], + "type": "interline_equation", + "content": "P _ {\\theta} \\left(\\boldsymbol {y} _ {t} \\mid \\boldsymbol {x} _ {a d v}\\right) = \\sum_ {s \\in \\mathbb {S}} P _ {\\theta} (s \\mid \\boldsymbol {x} _ {a d v}) P _ {\\theta} \\left(\\boldsymbol {y} _ {t} \\mid \\boldsymbol {x} _ {a d v}, s\\right). \\tag {2}", + "image_path": "6951442623750475c0f0c0f76a46ba0c3b5df8433d9321d631034f7eac2aef33.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 631, + 547, + 669 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 631, + 547, + 669 + ], + "spans": [ + { + "bbox": [ + 304, + 631, + 547, + 669 + ], + "type": "text", + "content": "Inspired by Figure 2 and the aforementioned Equation (2), we first propose to exploit the statistical correlation between " + }, + { + "bbox": [ + 304, + 631, + 547, + 669 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_t" + }, + { + "bbox": [ + 304, + 631, + 547, + 669 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 631, + 547, + 669 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 631, + 547, + 669 + ], + "type": "text", + "content": " (i.e., " + }, + { + "bbox": [ + 304, + 631, + 547, + 669 + ], + "type": "inline_equation", + "content": "P_{\\theta}(\\mathbf{y}_t \\mid \\mathbf{x}_{adv}, s))^1" + }, + { + "bbox": [ + 304, + 631, + 547, + 669 + ], + "type": "text", + "content": ", via injecting the specific" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 304, + 673, + 547, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 673, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 673, + 547, + 713 + ], + "type": "text", + "content": "1The statistical correlation between " + }, + { + "bbox": [ + 304, + 673, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_t" + }, + { + "bbox": [ + 304, + 673, + 547, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 673, + 547, + 713 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 673, + 547, + 713 + ], + "type": "text", + "content": " (i.e., " + }, + { + "bbox": [ + 304, + 673, + 547, + 713 + ], + "type": "inline_equation", + "content": "P_{\\theta}(\\mathbf{y}_t \\mid \\mathbf{x}_{adv}, s)" + }, + { + "bbox": [ + 304, + 673, + 547, + 713 + ], + "type": "text", + "content": " reflects that the model learns some non-robust features. According to the analysis of [24] and [55], the transferability of adversarial examples may arise from non-robust features, such as texture patterns or styles." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "16406" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 95, + 63, + 500, + 259 + ], + "blocks": [ + { + "bbox": [ + 95, + 63, + 500, + 259 + ], + "lines": [ + { + "bbox": [ + 95, + 63, + 500, + 259 + ], + "spans": [ + { + "bbox": [ + 95, + 63, + 500, + 259 + ], + "type": "image", + "image_path": "5515ccc87363ed233b737da7d7dd3a3d5ddbdf8aa8e2f88d16454a79c9c7d4f1.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 269, + 547, + 326 + ], + "lines": [ + { + "bbox": [ + 46, + 269, + 547, + 326 + ], + "spans": [ + { + "bbox": [ + 46, + 269, + 547, + 326 + ], + "type": "text", + "content": "Figure 3. The architecture of our dynamic generative attack model, which is composed of a cross-attention guided convolution module (denoted as \"Dy_Conv\") and a pattern injection module. The cross-attention guided convolution module consists of a static convolutional kernel and a dynamic convolutional kernel that is computed according to the input instance. For the pattern injection, the pattern prototype " + }, + { + "bbox": [ + 46, + 269, + 547, + 326 + ], + "type": "inline_equation", + "content": "\\pmb{p}_t = \\{\\gamma_t,\\beta_t\\}" + }, + { + "bbox": [ + 46, + 269, + 547, + 326 + ], + "type": "text", + "content": " encodes the patterns or styles of the target class, and the \"AdaCN\" layer performs an affine operation to inject " + }, + { + "bbox": [ + 46, + 269, + 547, + 326 + ], + "type": "inline_equation", + "content": "\\pmb{p}_t" + }, + { + "bbox": [ + 46, + 269, + 547, + 326 + ], + "type": "text", + "content": " into the generation of adversarial examples. Similar to [25], we introduce " + }, + { + "bbox": [ + 46, + 269, + 547, + 326 + ], + "type": "inline_equation", + "content": "\\pmb{p}_t^{\\mathrm{running}}" + }, + { + "bbox": [ + 46, + 269, + 547, + 326 + ], + "type": "text", + "content": " via the EMA updating based on " + }, + { + "bbox": [ + 46, + 269, + 547, + 326 + ], + "type": "inline_equation", + "content": "\\pmb{p}_t" + }, + { + "bbox": [ + 46, + 269, + 547, + 326 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 335, + 288, + 359 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 335, + 288, + 359 + ], + "spans": [ + { + "bbox": [ + 46, + 335, + 288, + 359 + ], + "type": "text", + "content": "style or pattern of images from the given target class " + }, + { + "bbox": [ + 46, + 335, + 288, + 359 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_t" + }, + { + "bbox": [ + 46, + 335, + 288, + 359 + ], + "type": "text", + "content": " to generate targeted transferable adversarial examples." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 359, + 288, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 359, + 288, + 443 + ], + "spans": [ + { + "bbox": [ + 46, + 359, + 288, + 443 + ], + "type": "text", + "content": "To this end, we propose a generative model to craft targeted adversarial examples by injecting the pattern of the target class. Besides, we design a cross-attention guided dynamic convolution module in the generator, which makes our generative model inherit the advantages of both instance-specific and instance-agnostic attacks. Therefore, the formulation of our method can be denoted as" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 73, + 451, + 287, + 464 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 73, + 451, + 287, + 464 + ], + "spans": [ + { + "bbox": [ + 73, + 451, + 287, + 464 + ], + "type": "interline_equation", + "content": "\\boldsymbol {x} _ {a d v} = \\operatorname {c l i p} \\left\\{\\operatorname {P r o j} \\left(\\mathcal {W} * G _ {\\theta (\\boldsymbol {x})} (\\boldsymbol {x}, p _ {t}), - \\varepsilon , \\varepsilon\\right) + \\boldsymbol {x} \\right\\}, \\tag {3}", + "image_path": "2e054d25b4f3cecd92cafb014078aefa57d8fc9dc742581f23afcdf669a59358.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 468, + 287, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 468, + 287, + 506 + ], + "spans": [ + { + "bbox": [ + 46, + 468, + 287, + 506 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 468, + 287, + 506 + ], + "type": "inline_equation", + "content": "\\varepsilon" + }, + { + "bbox": [ + 46, + 468, + 287, + 506 + ], + "type": "text", + "content": " is the perturbation budget, " + }, + { + "bbox": [ + 46, + 468, + 287, + 506 + ], + "type": "inline_equation", + "content": "\\mathcal{W}" + }, + { + "bbox": [ + 46, + 468, + 287, + 506 + ], + "type": "text", + "content": " is a smoothing operator with fixed weights, " + }, + { + "bbox": [ + 46, + 468, + 287, + 506 + ], + "type": "inline_equation", + "content": "p_t" + }, + { + "bbox": [ + 46, + 468, + 287, + 506 + ], + "type": "text", + "content": " represents the semantic pattern or style of the target class, and Proj is a projection operation." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 510, + 173, + 522 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 510, + 173, + 522 + ], + "spans": [ + { + "bbox": [ + 47, + 510, + 173, + 522 + ], + "type": "text", + "content": "3.2. Network Architecture" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 529, + 287, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 529, + 287, + 613 + ], + "spans": [ + { + "bbox": [ + 46, + 529, + 287, + 613 + ], + "type": "text", + "content": "Specifically, our generative model is illustrated in Figure 3, which is composed of two modules: ① a cross attention-guided dynamic convolution module (corresponding to \"Dy_Conv\" in the ResBlock of Figure 3), ② a pattern injection module. And the detailed pipeline of our approach is presented in Algorithm 1. In the next section, we mainly describe the two designed modules in detail." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 613, + 288, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 613, + 288, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 613, + 288, + 696 + ], + "type": "text", + "content": "Cross-attention guided dynamic convolution module. Considering that not only the global dataset needs to be modeled, but also specialized convolution kernels need to be learned for each input, we design a cross-attention guided convolution module. To achieve this goal, as shown in Figure 4, we propose a static and a dynamic convolution kernel parameterized with " + }, + { + "bbox": [ + 46, + 613, + 288, + 696 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 46, + 613, + 288, + 696 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 613, + 288, + 696 + ], + "type": "inline_equation", + "content": "\\Delta W" + }, + { + "bbox": [ + 46, + 613, + 288, + 696 + ], + "type": "text", + "content": ", respectively2. Thus" + } + ] + } + ], + "index": 8 + }, + { + "type": "code", + "bbox": [ + 310, + 351, + 545, + 515 + ], + "blocks": [ + { + "bbox": [ + 313, + 338, + 520, + 350 + ], + "lines": [ + { + "bbox": [ + 313, + 338, + 520, + 350 + ], + "spans": [ + { + "bbox": [ + 313, + 338, + 520, + 350 + ], + "type": "text", + "content": "Algorithm 1: Dynamic Generative Targeted Attack" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "lines": [ + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "spans": [ + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "text", + "content": "Input: A white-box model " + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "text", + "content": ", training data " + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "text", + "content": ", target samples " + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "inline_equation", + "content": "\\mathcal{X}_t" + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "text", + "content": ", perturbation budget " + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "text", + "content": ", training epoch " + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "text", + "content": ". Output: Generative attack model " + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "inline_equation", + "content": "G_{\\theta}" + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "text", + "content": ". \n1 for " + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "inline_equation", + "content": "t \\gets 0" + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "text", + "content": " do \n2 Sample mini-batches " + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "inline_equation", + "content": "\\pmb{x} \\sim \\mathcal{X}" + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "inline_equation", + "content": "\\pmb{x}_t \\sim \\mathcal{X}_t" + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "text", + "content": ". \n3 Get the augmented mini-batches " + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "inline_equation", + "content": "\\pmb{x}'" + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "text", + "content": ". \n4 Feed " + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "inline_equation", + "content": "\\pmb{x}'" + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "inline_equation", + "content": "\\pmb{x}_t" + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "text", + "content": " into the generator to get adversarial examples " + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "inline_equation", + "content": "\\pmb{x}_{adv}" + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "inline_equation", + "content": "\\pmb{x}_{adv}'" + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "inline_equation", + "content": "\\pmb{x}_t" + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "text", + "content": " is used for extracting and injecting target patterns " + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "inline_equation", + "content": "p_t" + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "text", + "content": ". \n5 Update " + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "inline_equation", + "content": "p_t^{\\text{running}}" + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "text", + "content": " based on " + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "inline_equation", + "content": "p_t" + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "text", + "content": " via EMA updating. \n6 Forward pass " + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "inline_equation", + "content": "\\pmb{x}_{adv}" + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "inline_equation", + "content": "\\pmb{x}_{adv}'" + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "inline_equation", + "content": "\\pmb{x}_t" + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "text", + "content": " through " + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "text", + "content": ". \n7 Compute losses " + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "inline_equation", + "content": "L_{attack}" + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "text", + "content": ", and backward for updating " + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "inline_equation", + "content": "G_{\\theta}" + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "text", + "content": ". \n8 return Converged generator " + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "inline_equation", + "content": "G_{\\theta}" + }, + { + "bbox": [ + 310, + 351, + 545, + 515 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "code_body" + } + ], + "index": 10, + "sub_type": "algorithm" + }, + { + "bbox": [ + 306, + 538, + 460, + 551 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 538, + 460, + 551 + ], + "spans": [ + { + "bbox": [ + 306, + 538, + 460, + 551 + ], + "type": "text", + "content": "the designed module is formulated as:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 370, + 558, + 545, + 569 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 370, + 558, + 545, + 569 + ], + "spans": [ + { + "bbox": [ + 370, + 558, + 545, + 569 + ], + "type": "interline_equation", + "content": "\\boldsymbol {X} _ {l} = \\operatorname {c o n v} \\left(\\boldsymbol {X} _ {l - 1}; W + \\Delta W\\right), \\tag {4}", + "image_path": "ef308bd3e110820700bf01ef2e47f5f095ebd35a07e7dc746c5a8b00fa6939bf.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 575, + 547, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 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To get dynamic convolution kernels, we design a series of learnable kernels " + }, + { + "bbox": [ + 304, + 575, + 547, + 658 + ], + "type": "inline_equation", + "content": "(N\\times C_{in}\\times C_{out}\\times k^2)^3" + }, + { + "bbox": [ + 304, + 575, + 547, + 658 + ], + "type": "text", + "content": " and attention queries " + }, + { + "bbox": [ + 304, + 575, + 547, + 658 + ], + "type": "inline_equation", + "content": "\\pmb {q}\\in R^{N\\times C_{in}}" + }, + { + "bbox": [ + 304, + 575, + 547, + 658 + ], + "type": "text", + "content": ", which indicate the attention weight of each kernel. For the layer " + }, + { + "bbox": [ + 304, + 575, + 547, + 658 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 575, + 547, + 658 + ], + "type": "text", + "content": ", we compute attention weights via performing cross-attention between attention queries " + }, + { + "bbox": [ + 304, + 575, + 547, + 658 + ], + "type": "inline_equation", + "content": "\\pmb{q}" + }, + { + "bbox": [ + 304, + 575, + 547, + 658 + ], + "type": "text", + "content": " and the input " + }, + { + "bbox": [ + 304, + 575, + 547, + 658 + ], + "type": "inline_equation", + "content": "\\pmb{X}_{l - 1}\\in R^{C_{in}\\times H\\times W}" + }, + { + "bbox": [ + 304, + 575, + 547, + 658 + ], + "type": "text", + "content": ", which can be indicated as:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 370, + 666, + 545, + 688 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 370, + 666, + 545, + 688 + ], + "spans": [ + { + "bbox": [ + 370, + 666, + 545, + 688 + ], + "type": "interline_equation", + "content": "a t t = \\operatorname {s o f t m a x} \\left(\\frac {Q K ^ {\\top}}{\\sqrt {d _ {k}}}\\right) V, \\tag {5}", + "image_path": "fda7fd31076b81d5d7060aba52ac179d2641ad31e13511b4a7662fcebf7c7a08.jpg" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 58, + 702, + 235, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 235, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 235, + 713 + ], + "type": "text", + "content": "2Note that we ignore bias terms for the sake of brevity" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "inline_equation", + "content": "^3 N" + }, + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "text", + "content": " indicates the number of learnable kernels, " + }, + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "text", + "content": " represents the kernel size, " + }, + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "inline_equation", + "content": "C_{in}" + }, + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "inline_equation", + "content": "C_{out}" + }, + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "text", + "content": " are the number of input and output channels." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16407" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 55, + 70, + 276, + 198 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 276, + 198 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 276, + 198 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 276, + 198 + ], + "type": "image", + "image_path": "76c702c3d176794366de9bc03834ef4564c0c526ede8b2a8ad8c18d647ee2059.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 201, + 287, + 234 + ], + "lines": [ + { + "bbox": [ + 46, + 201, + 287, + 234 + ], + "spans": [ + { + "bbox": [ + 46, + 201, + 287, + 234 + ], + "type": "text", + "content": "Figure 4. The illustration of the proposed cross-attention guided dynamic convolution module, which is composed of a static convolution kernel " + }, + { + "bbox": [ + 46, + 201, + 287, + 234 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 46, + 201, + 287, + 234 + ], + "type": "text", + "content": " and a dynamic convolution kernel " + }, + { + "bbox": [ + 46, + 201, + 287, + 234 + ], + "type": "inline_equation", + "content": "\\Delta W" + }, + { + "bbox": [ + 46, + 201, + 287, + 234 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 245, + 287, + 368 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 245, + 287, + 368 + ], + "spans": [ + { + "bbox": [ + 46, + 245, + 287, + 368 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 245, + 287, + 368 + ], + "type": "inline_equation", + "content": "att \\in R^{N \\times C_{in}}" + }, + { + "bbox": [ + 46, + 245, + 287, + 368 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 245, + 287, + 368 + ], + "type": "inline_equation", + "content": "Q = qW^{q}" + }, + { + "bbox": [ + 46, + 245, + 287, + 368 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 245, + 287, + 368 + ], + "type": "inline_equation", + "content": "K = X_{l-1}^{\\top}W^{k}" + }, + { + "bbox": [ + 46, + 245, + 287, + 368 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 245, + 287, + 368 + ], + "type": "inline_equation", + "content": "V = X_{l-1}^{\\top}W^{v}" + }, + { + "bbox": [ + 46, + 245, + 287, + 368 + ], + "type": "text", + "content": ". Then we can get the attention weight " + }, + { + "bbox": [ + 46, + 245, + 287, + 368 + ], + "type": "inline_equation", + "content": "\\alpha = [\\alpha_{1}, \\alpha_{2}, \\dots, \\alpha_{N}] \\in R^{1 \\times N}" + }, + { + "bbox": [ + 46, + 245, + 287, + 368 + ], + "type": "text", + "content": " by conducting the average pooling on " + }, + { + "bbox": [ + 46, + 245, + 287, + 368 + ], + "type": "inline_equation", + "content": "att" + }, + { + "bbox": [ + 46, + 245, + 287, + 368 + ], + "type": "text", + "content": ", and each element in " + }, + { + "bbox": [ + 46, + 245, + 287, + 368 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 245, + 287, + 368 + ], + "type": "text", + "content": " indicates the weight of corresponding kernels. Therefore, the dynamic convolution kernels are implemented as " + }, + { + "bbox": [ + 46, + 245, + 287, + 368 + ], + "type": "inline_equation", + "content": "\\Delta W = \\alpha_{1} * W_{1} + \\alpha_{2} * W_{2} + \\dots + \\alpha_{N} * W_{N}" + }, + { + "bbox": [ + 46, + 245, + 287, + 368 + ], + "type": "text", + "content": ". Benefiting from this dynamic and static mixup convolution operation, our proposed generative attack model can inherit the advantages of both instance-specific and instance-agnostic attacks." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 369, + 288, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 369, + 288, + 525 + ], + "spans": [ + { + "bbox": [ + 46, + 369, + 288, + 525 + ], + "type": "text", + "content": "Pattern injection module. First, to encode target patterns and styles during the generation of adversarial examples, we design a pattern prototype " + }, + { + "bbox": [ + 46, + 369, + 288, + 525 + ], + "type": "inline_equation", + "content": "\\pmb{p}_t = \\{\\gamma_t, \\beta_t\\}" + }, + { + "bbox": [ + 46, + 369, + 288, + 525 + ], + "type": "text", + "content": ", which is extracted from the features of target samples, as shown in Figure 3. Following [25], we introduce " + }, + { + "bbox": [ + 46, + 369, + 288, + 525 + ], + "type": "inline_equation", + "content": "\\pmb{p}_t^{\\text{running}}" + }, + { + "bbox": [ + 46, + 369, + 288, + 525 + ], + "type": "text", + "content": " to model patterns of the global samples for the target class. Note that we update " + }, + { + "bbox": [ + 46, + 369, + 288, + 525 + ], + "type": "inline_equation", + "content": "\\pmb{p}_t^{\\text{running}}" + }, + { + "bbox": [ + 46, + 369, + 288, + 525 + ], + "type": "text", + "content": " during each training iteration, which can be indicated as " + }, + { + "bbox": [ + 46, + 369, + 288, + 525 + ], + "type": "inline_equation", + "content": "\\pmb{p}_t^{\\text{running}} = \\lambda \\pmb{p}_t + (1 - \\lambda) \\pmb{p}_t^{\\text{running}}" + }, + { + "bbox": [ + 46, + 369, + 288, + 525 + ], + "type": "text", + "content": ". Then we propose an adaptive class normalization (corresponding to \"AdaCN\" in Figure 3) to inject " + }, + { + "bbox": [ + 46, + 369, + 288, + 525 + ], + "type": "inline_equation", + "content": "\\pmb{p}_t" + }, + { + "bbox": [ + 46, + 369, + 288, + 525 + ], + "type": "text", + "content": " into the generation of target adversarial examples. Similar to [23], the AdaCN module exploits the learned " + }, + { + "bbox": [ + 46, + 369, + 288, + 525 + ], + "type": "inline_equation", + "content": "\\pmb{p}_t = \\{\\gamma_t, \\beta_t\\}" + }, + { + "bbox": [ + 46, + 369, + 288, + 525 + ], + "type": "text", + "content": " to perform an affine operation for injecting target patterns or styles:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 95, + 534, + 287, + 557 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 95, + 534, + 287, + 557 + ], + "spans": [ + { + "bbox": [ + 95, + 534, + 287, + 557 + ], + "type": "interline_equation", + "content": "\\operatorname {A d a C N} (\\boldsymbol {X}) = \\gamma_ {t} \\left(\\frac {\\boldsymbol {X} - \\mu (\\boldsymbol {X})}{\\sigma (\\boldsymbol {X})}\\right) + \\beta_ {t}, \\tag {6}", + "image_path": "47670185ffa993bb4d64a0000bf29db053649cfa0dfafa9c64380b04de14a06b.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 567, + 287, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 567, + 287, + 617 + ], + "spans": [ + { + "bbox": [ + 46, + 567, + 287, + 617 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 567, + 287, + 617 + ], + "type": "inline_equation", + "content": "\\pmb{p}_t = \\{\\pmb{\\gamma}_t, \\pmb{\\beta}_t\\}" + }, + { + "bbox": [ + 46, + 567, + 287, + 617 + ], + "type": "text", + "content": " is the target pattern prototype. Note that Equation (6) represents pattern injection during training, and it is necessary to replace " + }, + { + "bbox": [ + 46, + 567, + 287, + 617 + ], + "type": "inline_equation", + "content": "\\pmb{p}_t = \\{\\pmb{\\gamma}_t, \\pmb{\\beta}_t\\}" + }, + { + "bbox": [ + 46, + 567, + 287, + 617 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 46, + 567, + 287, + 617 + ], + "type": "inline_equation", + "content": "\\pmb{p}_t^{\\mathrm{running}} = \\{\\pmb{\\gamma}_t^{\\mathrm{running}}, \\pmb{\\beta}_t^{\\mathrm{running}}\\}" + }, + { + "bbox": [ + 46, + 567, + 287, + 617 + ], + "type": "text", + "content": " during inference." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 625, + 160, + 639 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 625, + 160, + 639 + ], + "spans": [ + { + "bbox": [ + 47, + 625, + 160, + 639 + ], + "type": "text", + "content": "3.3. Objective Function" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 644, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 644, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 644, + 287, + 693 + ], + "type": "text", + "content": "To lead the victim model to misclassify adversarial examples as the target class, it is necessary to make the output distribution of adversarial examples " + }, + { + "bbox": [ + 46, + 644, + 287, + 693 + ], + "type": "inline_equation", + "content": "f(\\boldsymbol{x}_{adv}), f(\\boldsymbol{x}_{adv}')" + }, + { + "bbox": [ + 46, + 644, + 287, + 693 + ], + "type": "text", + "content": " and target samples " + }, + { + "bbox": [ + 46, + 644, + 287, + 693 + ], + "type": "inline_equation", + "content": "f(\\boldsymbol{x}_t)" + }, + { + "bbox": [ + 46, + 644, + 287, + 693 + ], + "type": "text", + "content": " consistent. Thus we define the loss" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 72, + 388, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 388, + 83 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 388, + 83 + ], + "type": "text", + "content": "function as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 320, + 94, + 545, + 118 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 94, + 545, + 118 + ], + "spans": [ + { + "bbox": [ + 320, + 94, + 545, + 118 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} \\quad = D _ {K L} \\left(f \\left(\\boldsymbol {x} _ {a d v}\\right) \\| f \\left(\\boldsymbol {x} _ {t}\\right)\\right) + D _ {K L} \\left(f \\left(\\boldsymbol {x} _ {t}\\right) \\| f \\left(\\boldsymbol {x} _ {a d v}\\right)\\right) \\tag {7} \\\\ \\mathcal {L} _ {a u g} = D _ {K L} \\left(f (\\boldsymbol {x} _ {a d v} ^ {\\prime}) \\| f (\\boldsymbol {x} _ {t})\\right) + D _ {K L} \\left(f (\\boldsymbol {x} _ {t}) \\| f (\\boldsymbol {x} _ {a d v} ^ {\\prime})\\right) \\\\ \\end{array}", + "image_path": "9ca843f4362646470398ef91c866b5ab51d841268c4c28d560039239b644576d.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 127, + 545, + 208 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 127, + 545, + 208 + ], + "spans": [ + { + "bbox": [ + 306, + 127, + 545, + 208 + ], + "type": "text", + "content": "Besides, similar to [39], we also introduce a local similarity loss. For a batch of generated adversarial examples " + }, + { + "bbox": [ + 306, + 127, + 545, + 208 + ], + "type": "inline_equation", + "content": "\\{\\pmb{x}_{adv}^i\\}_{i=1}^n" + }, + { + "bbox": [ + 306, + 127, + 545, + 208 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 306, + 127, + 545, + 208 + ], + "type": "inline_equation", + "content": "\\{\\pmb{x}_{adv}^{j,i}\\}_{i=1}^n" + }, + { + "bbox": [ + 306, + 127, + 545, + 208 + ], + "type": "text", + "content": " and target samples " + }, + { + "bbox": [ + 306, + 127, + 545, + 208 + ], + "type": "inline_equation", + "content": "\\{\\pmb{x}_t^i\\}_{i=1}^n" + }, + { + "bbox": [ + 306, + 127, + 545, + 208 + ], + "type": "text", + "content": ", the similarity matrix can be computed as " + }, + { + "bbox": [ + 306, + 127, + 545, + 208 + ], + "type": "inline_equation", + "content": "S_{i,j} = \\frac{f(\\pmb{x}_{adv}^i) \\cdot f(\\pmb{x}_{adv}^{j,i})}{\\|f(\\pmb{x}_{adv}^i)\\| \\|f(\\pmb{x}_{adv}^{j,j})\\|}" + }, + { + "bbox": [ + 306, + 127, + 545, + 208 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 127, + 545, + 208 + ], + "type": "inline_equation", + "content": "S_{i,j}^t = \\frac{f(\\pmb{x}_t^i) \\cdot f(\\pmb{x}_t^j)}{\\|f(\\pmb{x}_t^i)\\| \\|f(\\pmb{x}_t^j)\\|}" + }, + { + "bbox": [ + 306, + 127, + 545, + 208 + ], + "type": "text", + "content": ". Hence, we can get the local similarity loss as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 332, + 218, + 545, + 253 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 332, + 218, + 545, + 253 + ], + "spans": [ + { + "bbox": [ + 332, + 218, + 545, + 253 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {s i m} = \\sum_ {i, j} \\overline {{\\mathcal {S}}} _ {i, j} ^ {t} \\log \\frac {\\overline {{\\mathcal {S}}} _ {i , j} ^ {t}}{\\overline {{\\mathcal {S}}} _ {i , j}} + \\sum_ {i, j} \\overline {{\\mathcal {S}}} _ {i, j} \\log \\frac {\\overline {{\\mathcal {S}}} _ {i , j}}{\\overline {{\\mathcal {S}}} _ {i , j} ^ {t}}, \\tag {8}", + "image_path": "9c7fd235587c48fd2f34ea2140ce88fc508b42cc074c45ab25ffa8b9ca2af395.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 262, + 545, + 296 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 262, + 545, + 296 + ], + "spans": [ + { + "bbox": [ + 305, + 262, + 545, + 296 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 262, + 545, + 296 + ], + "type": "inline_equation", + "content": "\\overline{\\mathcal{S}}_{i,j} = \\frac{\\exp(\\mathcal{S}_{i,j})}{\\sum_k\\exp(\\mathcal{S}_{i,k})}" + }, + { + "bbox": [ + 305, + 262, + 545, + 296 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 262, + 545, + 296 + ], + "type": "inline_equation", + "content": "\\overline{\\mathcal{S}}_{i,j}^t = \\frac{\\exp(\\mathcal{S}_{i,j}^t)}{\\sum_k\\exp(\\mathcal{S}_{i,k}^t)}" + }, + { + "bbox": [ + 305, + 262, + 545, + 296 + ], + "type": "text", + "content": ". Finally, the total objective function can be formulated as:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 365, + 307, + 545, + 319 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 307, + 545, + 319 + ], + "spans": [ + { + "bbox": [ + 365, + 307, + 545, + 319 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {a t t a c k}} = \\mathcal {L} + \\mathcal {L} _ {\\text {a u g}} + \\mathcal {L} _ {\\text {s i m}}. \\tag {9}", + "image_path": "efed4423d0f72667fb21706e6f62c8f4186f4d2e2cc63410d16d181e3ecfdd15.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 338, + 425, + 351 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 338, + 425, + 351 + ], + "spans": [ + { + "bbox": [ + 306, + 338, + 425, + 351 + ], + "type": "text", + "content": "3.4. Theoretical Analyses" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 358, + 545, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 358, + 545, + 418 + ], + "spans": [ + { + "bbox": [ + 304, + 358, + 545, + 418 + ], + "type": "text", + "content": "In order to further explain the insights of our method, we consider a concrete setting that allows us to theoretically investigate why our method is effective for boosting target attacks. Please refer to the Supplementary Material for comprehensive proofs of the following theorem." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 418, + 545, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 418, + 545, + 453 + ], + "spans": [ + { + "bbox": [ + 304, + 418, + 545, + 453 + ], + "type": "text", + "content": "Setup. We consider a simple problem of maximum likelihood classification, similar to that of [24], between two Gaussian distributions." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 335, + 464, + 545, + 478 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 335, + 464, + 545, + 478 + ], + "spans": [ + { + "bbox": [ + 335, + 464, + 545, + 478 + ], + "type": "interline_equation", + "content": "\\mathcal {X} _ {s} \\sim N \\left(\\boldsymbol {\\mu} _ {s}, \\boldsymbol {\\Sigma} _ {s}\\right), \\quad \\mathcal {X} _ {t} \\sim N \\left(\\boldsymbol {\\mu} _ {t}, \\boldsymbol {\\Sigma} _ {t}\\right), \\tag {10}", + "image_path": "18a3436b4ea0d175b65b5647779bcaf78a721ccfab37926f9a013428d69c9ab3.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 487, + 545, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 487, + 545, + 548 + ], + "spans": [ + { + "bbox": [ + 304, + 487, + 545, + 548 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 487, + 545, + 548 + ], + "type": "inline_equation", + "content": "\\pmb{\\Sigma}_s, \\pmb{\\Sigma}_t = \\mathrm{diag}\\left\\{\\sigma_{s_1}^2, \\dots, \\sigma_{s_n}^2\\right\\}" + }, + { + "bbox": [ + 304, + 487, + 545, + 548 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 487, + 545, + 548 + ], + "type": "inline_equation", + "content": "\\mathrm{diag}\\left\\{\\sigma_{t_1}^2, \\dots, \\sigma_{t_n}^2\\right\\}" + }, + { + "bbox": [ + 304, + 487, + 545, + 548 + ], + "type": "text", + "content": ", respectively. To simplify the following derivation, we introduce a mapping and a translation operation to transform the model into a standard Gaussian binary classification model, which can be denoted as:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 346, + 559, + 545, + 588 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 346, + 559, + 545, + 588 + ], + "spans": [ + { + "bbox": [ + 346, + 559, + 545, + 588 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {F} _ {s} = \\boldsymbol {A} \\mathcal {X} _ {s} - \\frac {\\boldsymbol {A} \\boldsymbol {\\mu} _ {s} + \\boldsymbol {\\mu} _ {t}}{2} \\sim N (- \\boldsymbol {\\mu}, \\boldsymbol {\\Sigma}), \\tag {11} \\\\ \\mathcal {F} _ {t} = \\boldsymbol {E} \\mathcal {X} _ {t} - \\frac {\\boldsymbol {A} \\mu_ {s} + \\mu_ {t}}{2} \\sim N (\\boldsymbol {\\mu}, \\boldsymbol {\\Sigma}), \\\\ \\end{array}", + "image_path": "503beb8746315cbd68a614b800972a3fcd2d2171c2809802dd364c6167942423.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 594, + 545, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 594, + 545, + 675 + ], + "spans": [ + { + "bbox": [ + 305, + 594, + 545, + 675 + ], + "type": "text", + "content": "where the mapping matrix " + }, + { + "bbox": [ + 305, + 594, + 545, + 675 + ], + "type": "inline_equation", + "content": "\\mathbf{A} = \\mathrm{diag}\\left\\{\\frac{\\sigma_{t_1}}{\\sigma_{s_1}},\\frac{\\sigma_{t_2}}{\\sigma_{s_2}}\\dots ,\\frac{\\sigma_{t_n}}{\\sigma_{s_n}}\\right\\}" + }, + { + "bbox": [ + 305, + 594, + 545, + 675 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 594, + 545, + 675 + ], + "type": "inline_equation", + "content": "\\mathbf{E}" + }, + { + "bbox": [ + 305, + 594, + 545, + 675 + ], + "type": "text", + "content": " is the identity matrix and " + }, + { + "bbox": [ + 305, + 594, + 545, + 675 + ], + "type": "inline_equation", + "content": "\\pmb {\\mu} = \\frac{-\\pmb{A}\\pmb{\\mu}_s + \\pmb{\\mu}_t}{2},\\pmb {\\Sigma} = \\pmb{\\Sigma}_t" + }, + { + "bbox": [ + 305, + 594, + 545, + 675 + ], + "type": "text", + "content": ". To perform targeted attacks against this model with a given sample " + }, + { + "bbox": [ + 305, + 594, + 545, + 675 + ], + "type": "inline_equation", + "content": "x_{s}\\in \\mathcal{X}_{s}" + }, + { + "bbox": [ + 305, + 594, + 545, + 675 + ], + "type": "text", + "content": " and the target label " + }, + { + "bbox": [ + 305, + 594, + 545, + 675 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 305, + 594, + 545, + 675 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 305, + 594, + 545, + 675 + ], + "type": "inline_equation", + "content": "A\\pmb {x}_s - \\frac{A\\pmb{\\mu}_s + \\pmb{\\mu}_t}{2} = f_s\\in \\mathcal{F}_s" + }, + { + "bbox": [ + 305, + 594, + 545, + 675 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 594, + 545, + 675 + ], + "type": "inline_equation", + "content": "f_{s} + \\delta^{\\star} = A(x_{s} + \\delta) - \\frac{A\\mu_{s} + \\mu_{t}}{2}" + }, + { + "bbox": [ + 305, + 594, + 545, + 675 + ], + "type": "text", + "content": " we aim to solve the following optimization problem:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 329, + 694, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 694, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 329, + 694, + 545, + 715 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\delta} = \\boldsymbol {A} ^ {- 1} \\boldsymbol {\\delta} ^ {\\star}, \\quad \\boldsymbol {\\delta} ^ {\\star} = \\underset {\\| \\boldsymbol {\\delta} ^ {\\prime} \\| _ {2} ^ {2} \\leqslant \\varepsilon^ {2}} {\\operatorname {a r g m a x}} \\left(\\boldsymbol {f} _ {s} + \\boldsymbol {\\delta} ^ {\\prime}\\right) ^ {\\top} \\boldsymbol {\\Sigma} ^ {- 1} \\boldsymbol {\\mu}. \\tag {12}", + "image_path": "ebc235cc5b0e6f791d9148b5d997b0e6e5c530afc12252ab56c765b593c2fc17.jpg" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 57, + 701, + 201, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 701, + 201, + 713 + ], + "spans": [ + { + "bbox": [ + 57, + 701, + 201, + 713 + ], + "type": "inline_equation", + "content": "{}^{4}{W}_{1},{W}_{2}\\cdots {W}_{N}" + }, + { + "bbox": [ + 57, + 701, + 201, + 713 + ], + "type": "text", + "content": " are the learnable kernels." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16408" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 133, + 102, + 459, + 392 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 547, + 94 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 547, + 94 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 547, + 94 + ], + "type": "text", + "content": "Table 1. The attack success rates against normally trained models on ImageNet NeurIPS validation set, and the perturbation budget " + }, + { + "bbox": [ + 47, + 70, + 547, + 94 + ], + "type": "inline_equation", + "content": "\\ell_{\\infty} \\leq 16/255" + }, + { + "bbox": [ + 47, + 70, + 547, + 94 + ], + "type": "text", + "content": ". Note that the results are averaged on 8 different target classes." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 133, + 102, + 459, + 392 + ], + "lines": [ + { + "bbox": [ + 133, + 102, + 459, + 392 + ], + "spans": [ + { + "bbox": [ + 133, + 102, + 459, + 392 + ], + "type": "table", + "html": "
Subsite ModelMethodInc-v3Inc-v4Inc-Res-v2Res152Densenet-121GoogleNetVgg-16
Inc-v3MIM99.900.801.000.400.200.200.30
TI-MIM98.500.500.500.300.200.400.40
SI-MIM99.801.502.000.800.700.700.50
DIM95.602.700.500.801.100.400.80
TI-DIM96.001.101.200.500.500.500.80
SI-DIM90.203.804.402.002.201.701.40
CD-AP94.2057.6060.1037.1041.6032.3041.70
TTP91.3746.0439.3716.4033.4725.8025.73
C-GSP93.4066.9066.6041.6046.4040.0045.00
GAP86.9045.0634.4834.4841.7426.8934.34
Ours94.6367.9555.0350.5047.3847.6748.11
Res152MIM0.500.400.6099.700.300.300.20
TI-MIM0.300.300.3096.500.300.400.30
SI-MIM1.301.201.6099.501.001.400.70
DIM2.302.203.0092.300.200.800.70
TI-DIM0.800.701.0090.600.600.800.50
SI-DIM4.204.805.4090.504.203.602.00
CD-AP33.3043.7042.7096.6053.8036.6034.10
TTP62.0349.2038.7095.1282.9665.0962.82
C-GSP37.7047.6045.1093.2064.2041.7045.90
GAP30.9931.4320.4884.8658.3529.8939.70
Ours66.8353.6247.6196.4886.6168.2969.58
Vgg-16MIM0.260.470.200.350.400.3490.24
TI-MIM0.430.630.340.551.450.6489.13
SI-MIM0.350.570.420.310.560.5290.89
DIM0.751.300.551.001.881.0397.70
TI-DIM0.230.380.170.290.480.3593.71
SI-DIM0.871.120.700.951.891.5591.42
CD-AP5.328.944.879.3314.023.1996.82
TTP22.5117.149.6822.6840.8722.4197.59
C-GSP9.429.603.0111.7632.2813.3396.81
GAP3.115.261.505.0811.232.7093.00
Ours28.1821.789.5625.2746.5523.7093.00
", + "image_path": "78bb888f4e912ee8f33e77f1f3cf04fdec3cc72482f8c7ed246f3e63fadb8af9.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 412, + 287, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 412, + 287, + 437 + ], + "spans": [ + { + "bbox": [ + 47, + 412, + 287, + 437 + ], + "type": "text", + "content": "Taking advantage of the method of Lagrange multipliers, we can easily get the optimal solution as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 61, + 450, + 287, + 470 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 450, + 287, + 470 + ], + "spans": [ + { + "bbox": [ + 61, + 450, + 287, + 470 + ], + "type": "interline_equation", + "content": "\\begin{array}{r l} \\delta^ {\\star} & = \\frac {1}{\\lambda} \\Sigma^ {- 1} \\boldsymbol {\\mu}, \\\\ s & = \\Sigma^ {- 1} [ A ^ {- 1} (A (\\quad , \\quad , \\quad , \\quad) ] \\end{array} \\tag {13}", + "image_path": "425a9699fff241113a062eef88fe542ae769febda5db7ef3393c075fa0b16b49.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 63, + 462, + 287, + 479 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 462, + 287, + 479 + ], + "spans": [ + { + "bbox": [ + 63, + 462, + 287, + 479 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\delta} = \\frac {\\hat {\\boldsymbol {\\Sigma}} ^ {- 1}}{2 \\lambda} \\left[ \\boldsymbol {A} ^ {- 1} \\left(\\boldsymbol {A} \\left(\\boldsymbol {x} _ {s} - \\boldsymbol {\\mu} _ {s}\\right) + \\boldsymbol {\\mu} _ {t}\\right) - \\boldsymbol {x} _ {s} \\right]. \\tag {13}", + "image_path": "5928941916731af2d9acf9278f6c2f79f9a5e4fd45755dbc47c6fadce294f5de.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 495, + 287, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 495, + 287, + 519 + ], + "spans": [ + { + "bbox": [ + 47, + 495, + 287, + 519 + ], + "type": "text", + "content": "Going a step further, we rewrite the solution of " + }, + { + "bbox": [ + 47, + 495, + 287, + 519 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 47, + 495, + 287, + 519 + ], + "type": "text", + "content": " into a more concise formula as:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 56, + 547, + 287, + 600 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 547, + 287, + 600 + ], + "spans": [ + { + "bbox": [ + 56, + 547, + 287, + 600 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\delta} = C _ {1} \\left[ \\left( \\begin{array}{c c c} \\frac {\\sigma_ {t _ {1}}}{\\sigma_ {s _ {1}}} & & \\\\ & \\ddots & \\\\ & & \\frac {\\sigma_ {t _ {n}}}{\\sigma_ {s _ {n}}} \\end{array} \\right) \\left(\\boldsymbol {x} _ {s} - \\boldsymbol {\\mu} _ {s}\\right) + \\boldsymbol {\\mu} _ {t} \\right] - C _ {2} \\boldsymbol {x} _ {s}, \\tag {14}", + "image_path": "8a56e41d2868a7226a22e0319856820f992b7ffb9b6c09a96ed7dee6e23027e9.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 613, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 613, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 613, + 288, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 613, + 288, + 715 + ], + "type": "inline_equation", + "content": "C_1 = \\frac{\\Sigma^{-1}A^{-1}}{2\\lambda}" + }, + { + "bbox": [ + 47, + 613, + 288, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 613, + 288, + 715 + ], + "type": "inline_equation", + "content": "C_2 = \\frac{\\Sigma^{-1}}{2\\lambda}" + }, + { + "bbox": [ + 47, + 613, + 288, + 715 + ], + "type": "text", + "content": ". In fact, note that the item of represents target pattern or style injection, which is consistent with the previous works [23, 26]. Therefore, the formulation of Equation (14) shows a close underlying correlation between the optimal targeted adversarial perturbation and the embedding of target pattern or style, which also theoretically guarantees the effectiveness of our proposed generative model for targeted attacks." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 411, + 388, + 424 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 411, + 388, + 424 + ], + "spans": [ + { + "bbox": [ + 306, + 411, + 388, + 424 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 432, + 546, + 481 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 432, + 546, + 481 + ], + "spans": [ + { + "bbox": [ + 305, + 432, + 546, + 481 + ], + "type": "text", + "content": "In this section, we conduct extensive experiments to demonstrate the effectiveness of our method for targeted attacks under various settings. Please feel free to get more experimental results in our Supplementary Material." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 489, + 422, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 489, + 422, + 502 + ], + "spans": [ + { + "bbox": [ + 306, + 489, + 422, + 502 + ], + "type": "text", + "content": "4.1. Experimental Setup" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 509, + 547, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 509, + 547, + 544 + ], + "spans": [ + { + "bbox": [ + 305, + 509, + 547, + 544 + ], + "type": "text", + "content": "Dataset. Following [55], we perform training on ImageNet [7] training set, and evaluate on ImageNet-NeurIPS (1k) proposed by NeurIPS 2017 adversarial competition [30]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 545, + 545, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 545, + 545, + 664 + ], + "spans": [ + { + "bbox": [ + 305, + 545, + 545, + 664 + ], + "type": "text", + "content": "Victim Models. We consider 13 attacked models in our experiments. The normally trained models include Inception-v3 (Inc-v3) [47], Inception-v4 (Inc-v4) [45], DenseNet-121 [22], GoogleNet [46], ResNet-152 (Res-152) [19], and VGG16 (Vgg-16) [44] and Inception-ResNet (Inc-Res-v2) [45]. Besides, we also consider several models with robust training mechanisms, including adv-Inception-v3 (Adv-Inc-v3) [17], ens-adv-Inception-ResNet-v2 (Ens-Adv-IncRes-v2) [18] and ResNet-50 trained with various robust training tricks [21, 15]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 665, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 665, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 665, + 547, + 713 + ], + "type": "text", + "content": "Baseline Attacks. To illustrate the effectiveness of our method, we compare it with instance-specific attacks and instance-agnostic attacks. Instance-specific attacks mainly include MIM [9], DIM [53], SIM [32] and TIM [10], while" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "16409" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 60, + 547, + 118 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 60, + 547, + 118 + ], + "spans": [ + { + "bbox": [ + 46, + 60, + 547, + 118 + ], + "type": "text", + "content": "Table 2. The attack success rates against robust models on ImageNet NeurIPS validation set. The perturbation budget " + }, + { + "bbox": [ + 46, + 60, + 547, + 118 + ], + "type": "inline_equation", + "content": "\\ell_{\\infty} \\leq 16/255" + }, + { + "bbox": [ + 46, + 60, + 547, + 118 + ], + "type": "text", + "content": ". Adv-Inc-v3 [29] and Ens-Adv-IncRes-v2 [49] are trained with the adversarial training mechanism. Res50_SIN (stylized ImageNet), Res50_SIN_IN (mixture of stylized ImageNet and Nature ImageNet) and Res50_SIN_fine_IN (mixture of stylized ImageNet and Nature ImageNet with finetuning tricks) are trained with auxiliary dataset [15], and Res50_Augmix [21] is trained with the state-of-the-art data augmentation approach. Note that the results are averaged on 8 different target classes." + } + ] + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 96, + 125, + 496, + 316 + ], + "blocks": [ + { + "bbox": [ + 96, + 125, + 496, + 316 + ], + "lines": [ + { + "bbox": [ + 96, + 125, + 496, + 316 + ], + "spans": [ + { + "bbox": [ + 96, + 125, + 496, + 316 + ], + "type": "table", + "html": "
Subsite ModelMethodAdv-Inc-v3Ens-IncRes-v2Res50_SINRes50_SIN_INRes50_SIN_fine_INRes50_AugMix
Res152MIM0.190.150.281.582.750.78
TI-MIM0.610.730.502.514.751.76
SI-MIM0.240.240.390.660.840.36
DIM0.630.370.948.5014.223.77
TI-DIM0.230.300.280.761.490.49
SI-DIM0.710.710.752.733.891.37
CD-AP3.776.487.0963.7276.7949.67
TTP27.9926.0824.6172.4774.5170.96
GAP5.724.517.3371.0483.6452.07
Ours31.1030.0727.7077.1380.5576.78
VGG16MIM0.140.150.160.400.340.19
TI-MIM0.260.240.200.450.570.28
SI-MIM0.280.200.210.490.250.14
DIM0.220.160.270.930.990.49
TI-DIM0.140.190.210.350.340.21
SI-DIM0.500.360.330.800.690.26
CD-AP0.360.340.354.6310.203.60
TTP3.753.202.6627.8032.7016.57
GAP0.300.520.424.528.923.35
Ours4.143.222.6630.1638.1017.95
", + "image_path": "4d9a7dd27f0645f00cd9502f86ce1acdbccf089df1848aeafa9b83dcd779e372.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 50, + 334, + 160, + 437 + ], + "blocks": [ + { + "bbox": [ + 50, + 334, + 160, + 437 + ], + "lines": [ + { + "bbox": [ + 50, + 334, + 160, + 437 + ], + "spans": [ + { + "bbox": [ + 50, + 334, + 160, + 437 + ], + "type": "image", + "image_path": "27526b296dfac3020fb371480d3ee4ef4707b685d318541607b39cb280af87f9.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 97, + 440, + 106, + 447 + ], + "lines": [ + { + "bbox": [ + 97, + 440, + 106, + 447 + ], + "spans": [ + { + "bbox": [ + 97, + 440, + 106, + 447 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 168, + 335, + 279, + 439 + ], + "blocks": [ + { + "bbox": [ + 168, + 335, + 279, + 439 + ], + "lines": [ + { + "bbox": [ + 168, + 335, + 279, + 439 + ], + "spans": [ + { + "bbox": [ + 168, + 335, + 279, + 439 + ], + "type": "image", + "image_path": "c5baa04f5376891c990c7585a774bcbf29672695c0b37a3ad4f58cf05d34eac3.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 227, + 440, + 235, + 447 + ], + "lines": [ + { + "bbox": [ + 227, + 440, + 235, + 447 + ], + "spans": [ + { + "bbox": [ + 227, + 440, + 235, + 447 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 448, + 289, + 536 + ], + "lines": [ + { + "bbox": [ + 46, + 448, + 289, + 536 + ], + "spans": [ + { + "bbox": [ + 46, + 448, + 289, + 536 + ], + "type": "text", + "content": "Figure 5. Attack success rates of targeted adversarial examples generated by various generative attack methods against different input process defense methods. Figure (a) displays the results against various input smooth methods (including gaussian, medium and average smoothing). Figure (b) shows the results against JPEG compression (the JPEG quality factor varies from 70 to 90). Here, the substitute model is Res-152 and the target model is Vgg-16." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 540, + 287, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 540, + 287, + 613 + ], + "spans": [ + { + "bbox": [ + 46, + 540, + 287, + 613 + ], + "type": "text", + "content": "instance-agnostic attacks include CD-AP [40], TTP [39], GAP [41] and C-GSP [55]. In our experiments, the perturbation size " + }, + { + "bbox": [ + 46, + 540, + 287, + 613 + ], + "type": "inline_equation", + "content": "\\varepsilon = 16 / 255" + }, + { + "bbox": [ + 46, + 540, + 287, + 613 + ], + "type": "text", + "content": ", the decay factor " + }, + { + "bbox": [ + 46, + 540, + 287, + 613 + ], + "type": "inline_equation", + "content": "\\mu_0" + }, + { + "bbox": [ + 46, + 540, + 287, + 613 + ], + "type": "text", + "content": " is 1 in MIM, the transform probability is 0.7 in DIM, and the kernel size is 15 in TIM. And other hyper-parameters follow the default settings provided in their original works." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 622, + 270, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 622, + 270, + 635 + ], + "spans": [ + { + "bbox": [ + 47, + 622, + 270, + 635 + ], + "type": "text", + "content": "4.2. Comparison with State-of-the-art Methods" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "text", + "content": "Attack Normally Trained Models. To evaluate the performance of our method, we first perform targeted adversarial attacks to compare the transferability across normally trained models of adversarial examples generated by various methods, including 6 iterative instance-specific attack methods and 5 instance-agnostic attack methods. As shown" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 335, + 547, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 335, + 547, + 491 + ], + "spans": [ + { + "bbox": [ + 304, + 335, + 547, + 491 + ], + "type": "text", + "content": "in Table 1, our dynamic generative attack method reaches the best transferability on 16 out of 18 various black-box cases. Furthermore, the attack success rate of our method against normally trained models is " + }, + { + "bbox": [ + 304, + 335, + 547, + 491 + ], + "type": "inline_equation", + "content": "65.42\\%" + }, + { + "bbox": [ + 304, + 335, + 547, + 491 + ], + "type": "text", + "content": " on average with the substitute model as Res-152, which outperforms the best of baselines [39] by " + }, + { + "bbox": [ + 304, + 335, + 547, + 491 + ], + "type": "inline_equation", + "content": "5.28\\%" + }, + { + "bbox": [ + 304, + 335, + 547, + 491 + ], + "type": "text", + "content": " on average. Another interesting discovery is that iterative instance-specific attack methods can reach better performance under the setting of white-box attacks, while generative attack methods show more transferability when adapting the adversarial examples to a black-box model. Among these generative methods, our method can still generate targeted adversarial examples with higher transferability than others." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 494, + 548, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 494, + 548, + 674 + ], + "spans": [ + { + "bbox": [ + 304, + 494, + 548, + 674 + ], + "type": "text", + "content": "Attack Models with Robust Training Mechanisms. To comprehensively verify the effectiveness of our method, we compare the transferability of our approach with baselines against several robust models, which are trained with various robust training strategies. As presented in Table 2, although the attack success rate against these robust models is relatively low, our method is still able to outperform baseline methods. Our generative attack method achieves the best performance of targeted transferable adversarial attacks on 11 over 12 cases. And regarding Res-152 as the substitute model, our method outperforms the best of baselines [39] by " + }, + { + "bbox": [ + 304, + 494, + 548, + 674 + ], + "type": "inline_equation", + "content": "4.45\\%" + }, + { + "bbox": [ + 304, + 494, + 548, + 674 + ], + "type": "text", + "content": " on average. Compared with normally trained models, models with adversarial or robust training strategies are difficult to attack successfully, which indicates they are more robust than normal models." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "content": "Attack Models with Input Process Defense. Another widely used and simple defense method is Input Process, which leverages image processing techniques to remove" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "16410" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 89, + 56, + 504, + 225 + ], + "blocks": [ + { + "bbox": [ + 89, + 56, + 504, + 225 + ], + "lines": [ + { + "bbox": [ + 89, + 56, + 504, + 225 + ], + "spans": [ + { + "bbox": [ + 89, + 56, + 504, + 225 + ], + "type": "image", + "image_path": "02657f5b2009007f81625b8fb5da157bdd6854afa234b6f86b9709b71cdd564f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 227, + 547, + 273 + ], + "lines": [ + { + "bbox": [ + 46, + 227, + 547, + 273 + ], + "spans": [ + { + "bbox": [ + 46, + 227, + 547, + 273 + ], + "type": "text", + "content": "Figure 6. Visualization results of adversarial examples generated by our proposed method. The 1st, 2nd and 3rd rows show clean images, adversarial perturbations and adversarial examples, respectively. And (a), (b) and (c) display the results of different target classes (French bulldog, Fire engine and Street sign), which indicate that different target classes lead to different patterns or texture styles of the generated perturbations and adversarial images. Please refer to our Supplementary Material for more qualitative examples." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 50, + 282, + 167, + 372 + ], + "blocks": [ + { + "bbox": [ + 50, + 282, + 167, + 372 + ], + "lines": [ + { + "bbox": [ + 50, + 282, + 167, + 372 + ], + "spans": [ + { + "bbox": [ + 50, + 282, + 167, + 372 + ], + "type": "image", + "image_path": "6c49253a6a03b5a3957d19de54ee2cbedacf77992c3ab3178a4a7c1df9fea5ac.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 110, + 374, + 119, + 381 + ], + "lines": [ + { + "bbox": [ + 110, + 374, + 119, + 381 + ], + "spans": [ + { + "bbox": [ + 110, + 374, + 119, + 381 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 168, + 282, + 282, + 372 + ], + "blocks": [ + { + "bbox": [ + 168, + 282, + 282, + 372 + ], + "lines": [ + { + "bbox": [ + 168, + 282, + 282, + 372 + ], + "spans": [ + { + "bbox": [ + 168, + 282, + 282, + 372 + ], + "type": "image", + "image_path": "f0f4a1a912ac4e7095b741ca813ab8ad4cf6713ab4201b4bc53de02848f3d2d4.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 229, + 373, + 238, + 381 + ], + "lines": [ + { + "bbox": [ + 229, + 373, + 238, + 381 + ], + "spans": [ + { + "bbox": [ + 229, + 373, + 238, + 381 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 382, + 287, + 426 + ], + "lines": [ + { + "bbox": [ + 46, + 382, + 287, + 426 + ], + "spans": [ + { + "bbox": [ + 46, + 382, + 287, + 426 + ], + "type": "text", + "content": "Figure 7. Ablation studies. (a) Effect of the number of target samples. (b) Effect of the number of learnable convolution kernels. Note that the substitute model is Res-152, while victim models include Vgg-16, GoogleNet and Inc-v3." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 434, + 289, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 434, + 289, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 434, + 289, + 567 + ], + "type": "text", + "content": "the adversary perturbation before feeding into target models. To further understand our method, we also evaluate the targeted adversarial examples crafted by various generative attacks against several image processing based defense methods, namely, JPEG compression [12] and Smooth [8]. As presented in Figure 5, our method consistently outperforms the two existing generative attacks against both JPEG compression and various smoothing defense methods. For example, our method achieves an attack success rate of " + }, + { + "bbox": [ + 46, + 434, + 289, + 567 + ], + "type": "inline_equation", + "content": "54.77\\%" + }, + { + "bbox": [ + 46, + 434, + 289, + 567 + ], + "type": "text", + "content": ", when the JPEG quality is 70, while TTP [39] and C-GSP [55] just reach " + }, + { + "bbox": [ + 46, + 434, + 289, + 567 + ], + "type": "inline_equation", + "content": "54.06\\%" + }, + { + "bbox": [ + 46, + 434, + 289, + 567 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 434, + 289, + 567 + ], + "type": "inline_equation", + "content": "40.04\\%" + }, + { + "bbox": [ + 46, + 434, + 289, + 567 + ], + "type": "text", + "content": ", respectively." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 574, + 232, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 574, + 232, + 586 + ], + "spans": [ + { + "bbox": [ + 47, + 574, + 232, + 586 + ], + "type": "text", + "content": "4.3. Visualization and Ablation Studies" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 594, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 715 + ], + "type": "text", + "content": "Visualization. To vividly demonstrate the working mechanism of our method, we visualize several adversarial examples and perturbations with different target classes. As shown in Figure 6, there is an underlying dependency between the generated perturbations and input instances, where the perturbations are mainly concentrated on the semantical part of the input images. Besides, for different target classes, our method tends to generate perturbations with different texture patterns, which also verifies the effectiveness of our designed pattern injection module." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 282, + 547, + 414 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 282, + 547, + 414 + ], + "spans": [ + { + "bbox": [ + 304, + 282, + 547, + 414 + ], + "type": "text", + "content": "Ablation Studies. To look deeper into our proposed method, in this section, we present a series of ablation studies. As shown in Figure 7, we vary the number of target samples and convolution kernels to verify the effectiveness of our method. As presented in Figure 7(a), the performance of our method continues to grow until the number of target samples reaches 1000. Besides, in Figure 7(b), when the number of kernels is greater than 4, our performance reaches a plateau, which means that it is sufficient to reach an impressive attack success rate by learning 4 kernels in each designed dynamic convolution module." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 429, + 378, + 441 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 429, + 378, + 441 + ], + "spans": [ + { + "bbox": [ + 306, + 429, + 378, + 441 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 451, + 545, + 631 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 451, + 545, + 631 + ], + "spans": [ + { + "bbox": [ + 304, + 451, + 545, + 631 + ], + "type": "text", + "content": "In this paper, we first construct a causal graph to expose the origin of targeted adversarial examples, which motivates us to inject target patterns or styles for generating transferable target adversarial examples. Then we introduce a dynamic generative attack model composed of a cross-attention guided convolution module and a pattern injection module. Our generative attack model can not only inject pattern or style information of the target class to improve transferable targeted attacks, but also learn specialized convolutional kernels for each input instance, which inherits the advantages of both instance-specific and instance-agnostic attacks. Moreover, we also provide rigorous theoretical analysis to guarantee the effectiveness of our method, and extensive experiments demonstrate that our method performs better than state-of-the-art targeted attack methods." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 637, + 416, + 651 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 637, + 416, + 651 + ], + "spans": [ + { + "bbox": [ + 306, + 637, + 416, + 651 + ], + "type": "text", + "content": "6. Acknowledgement" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 658, + 545, + 703 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 658, + 545, + 703 + ], + "spans": [ + { + "bbox": [ + 304, + 658, + 545, + 703 + ], + "type": "text", + "content": "This work was partially supported by the National Nature Science Foundation of China (Grant 62022078, Grant 62021002), and National Defense Basic Scientific Research Program (Grant JCKY2022911B002)." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16411" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "type": "text", + "content": "[1] N. 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IEEE, 2019. 3" + } + ] + } + ], + "index": 0 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "text", + "content": "16414" + } + ] + } + ], + "index": 1 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Dynamic Graph Enhanced Contrastive Learning for Chest X-Ray Report Generation/7bbdab16-5f4c-46f9-abdb-480a53791847_content_list.json b/2023/Dynamic Graph Enhanced Contrastive Learning for Chest X-Ray Report Generation/7bbdab16-5f4c-46f9-abdb-480a53791847_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..f7b14b32285e9d7b733781634d8395ffb1a5894a --- /dev/null +++ b/2023/Dynamic Graph Enhanced Contrastive Learning for Chest X-Ray Report Generation/7bbdab16-5f4c-46f9-abdb-480a53791847_content_list.json @@ -0,0 +1,1542 @@ +[ + { + "type": "text", + "text": "Dynamic Graph Enhanced Contrastive Learning for Chest X-ray Report Generation", + "text_level": 1, + "bbox": [ + 117, + 128, + 852, + 174 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Mingjie Li $^{1}$ Bingqian Lin $^{2}$ Zicong Chen $^{5}$ Haokun Lin $^{2}$ Xiaodan Liang $^{2,3,4}$ Xiaojun Chang $^{1*}$", + "bbox": [ + 98, + 202, + 877, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ ReLER, AAII, University of Technology Sydney $^{2}$ School of ISE, Sun Yat-Sen University $^{3}$ Department of Computer Vision, Mohamed bin Zayed University of Artificial Intelligence", + "bbox": [ + 127, + 220, + 843, + 256 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{4}$ Peng Cheng National Lab $^{5}$ The University of Hong Kong", + "bbox": [ + 251, + 256, + 718, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 308, + 313, + 325 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Automatic radiology reporting has great clinical potential to relieve radiologists from heavy workloads and improve diagnosis interpretation. Recently, researchers have enhanced data-driven neural networks with medical knowledge graphs to eliminate the severe visual and textual bias in this task. The structures of such graphs are exploited by using the clinical dependencies formed by the disease topic tags via general knowledge and usually do not update during the training process. Consequently, the fixed graphs can not guarantee the most appropriate scope of knowledge and limit the effectiveness. To address the limitation, we propose a knowledge graph with Dynamic structure and nodes to facilitate chest X-ray report generation with Contrastive Learning, named DCL. In detail, the fundamental structure of our graph is pre-constructed from general knowledge. Then we explore specific knowledge extracted from the retrieved reports to add additional nodes or redefine their relations in a bottom-up manner. Each image feature is integrated with its very own updated graph before being fed into the decoder module for report generation. Finally, this paper introduces Image-Report Contrastive and Image-Report Matching losses to better represent visual features and textual information. Evaluated on IU-Xray and MIMIC-CXR datasets, our DCL outperforms previous state-of-the-art models on these two benchmarks.", + "bbox": [ + 76, + 340, + 473, + 720 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 728, + 209, + 744 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, automatic report generation has received growing attentions from both machine learning and automatic medicine fields. It aims to generate semantically coherent and informative reports to describe the referring examination images, such as Chest X-Ray [8, 18], Lung CT Scan [26] or funds angiography [23]. Such techniques have great clinical potential in relieving junior radiologists from heavy workloads and reducing diagnosis errors by improv-", + "bbox": [ + 75, + 753, + 468, + 876 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0172bbe2ff52d24362741d5239404e42be5e169a4432cbc62aefea1e4a9c6982.jpg", + "image_caption": [ + "Ground Truth Report" + ], + "image_footnote": [], + "bbox": [ + 509, + 309, + 658, + 424 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "A single portable AP semi-upright view of the chest was obtained. Cardiomediastinal silhouette including moderate cardiomegaly is stable. An ICD device is also unchanged in position. Interval development of increased opacification in the right lower lung probably reflects asymmetric edema and a layering effusion...", + "bbox": [ + 661, + 339, + 877, + 417 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/bb4855157e79078ddbefd3e1153239bcc9205dd4f38ea965ae8b0a05b1c67f70.jpg", + "image_caption": [ + "Figure 1. An illustration of one sample from MIMIC-CXR [18] and the pre-constructed graph in [46], where the blue circle, orange boxes and black boxes refer to the global node, organ-level entities and key findings, respectively. The red dash line here represents the unconnected relation." + ], + "image_footnote": [], + "bbox": [ + 511, + 426, + 885, + 545 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ing the interpretation [7, 30].", + "bbox": [ + 500, + 628, + 691, + 642 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Witnessed the great progress in artificial intelligence, especially deep learning methods [12,25,39], researchers have proposed various data-driven neural networks for radiology reporting and achieved promising performances in metrics that measure descriptive accuracy [7, 44] and clinical correctness [11, 46]. Compared with the similar task generic image captioning [14], the key challenges in chest X-ray report generation (CRG) task are the severe visual and textual data bias [19, 26]. On the one hand, medical images are highly similar to each other due to the imaging methods and human tissues themselves. However, abnormal regions or lesions that should acquire more attentions usually locate at a small part and lack detailed annotations in existing CRG benchmarks. On the other hand, sentences that describe normal regions are likely to appear repeatedly among each dataset which disables the model to describe specific crucial abnormalities. Two concepts have been proved ef", + "bbox": [ + 496, + 643, + 892, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation.", + "bbox": [ + 236, + 1, + 810, + 21 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "Except for this watermark, it is identical to the accepted version:", + "bbox": [ + 294, + 16, + 753, + 27 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 292, + 30, + 753, + 45 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author. https://github.com/mlii0117/DCL", + "bbox": [ + 94, + 886, + 468, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "3334", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "fective in eliminating those bias.", + "bbox": [ + 76, + 90, + 294, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The first one is to integrate medical knowledge with ORG systems [24,30,44,46]. Zhang et al. [46] constructed a universal graph comprised of a global node, 7 organs/tissues and 20 findings (normal or disease keywords). Disease keyword nodes linked to the same organ are connected to each other and the root in the graph. This graph can enhance the relationships among findings and emphasize the disease keywords. Thus, it is also adopted in the following works [30, 44]. However, this graph is built from general knowledge and may be inappropriate in some cases. As the shown report in Fig. 1, it is observed that effusion should be suggestive of edema, however, such relationship is not modelled in the graph. Furthermore, some nodes like 'cicatrix' or 'hypoinflation' only appear very few times in two ORG benchmarks [8, 18]. Therefore, it is necessary to update the scope of knowledge for each case; In addition to the medical knowledge, recent works [5, 11, 31, 38, 43] utilize contrastive learning to improve the visual and textual representations by contrasting positive and negative pairs. They proposed various contrastive learning objectives to capture the abnormal regions from a chest X-Ray image. Since normal images usually dominate the dataset over abnormal ones [37], it is also crucial to recognize the normal or abnormal cases in the meantime.", + "bbox": [ + 76, + 109, + 472, + 470 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we propose a novel framework, named DCL, which exploits a dynamic graph integrating specific knowledge with general knowledge to enhance visual representations learned in a contrastive manner. We adopt the general knowledge with 28 entities from [46] as the fundamental structure of our graph, and the relationships are modelled in an adjacency matrix. Given a medical image, we first retrieve its semantically similar reports from the training set. Specific knowledge is extracted from those reports via RadGraph [17] and stored in triplets (). And we integrate those triplets with the pre-constructed graph by dynamically adding additional nodes or linking two entities. We utilize a graph encoder to propagate information over the updated graph for refining the node features, which are initialized by a pretrained SciBert [4]. Then the dedicated node features are attended to visual representations for report generation via a Transformer [39] decoder. Based on the dynamic graph, we introduce a contrastive learning objective, image-report contrastive loss to well represent the visual features and textual information. In addition, contrastive learning can help ensure the accuracy of the report retrieval procedure in the dynamic graph construction process. Image-report matching loss is also employed to further improve the performances.", + "bbox": [ + 76, + 474, + 472, + 853 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We evaluate our method on two benchmarks, IU-Xray [8] and MIMIC-CXR [18]. Experimental results demonstrate that our approach can either outperform or", + "bbox": [ + 76, + 854, + 470, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "match previous state-of-the-art (SOTA) methods in metrics that measure descriptive accuracy and clinical correctness. It indicates that leveraging dynamic graphs to enhance contrastive learning is helpful to generate high-quality reports.", + "bbox": [ + 496, + 90, + 890, + 151 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our main contributions are as follows:", + "bbox": [ + 517, + 152, + 854, + 167 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a novel framework that leverages a dynamic graph to enhance visual representations with contrastive learning paradigms for radiology reporting.", + "- Our proposed dynamic graph integrates both general and specific knowledge; The contrastive learning objective can improve visual and textual representations and dynamic graph accuracy.", + "- We conduct extensive experiments on two popular benchmarks to show the effectiveness of our approach, which achieves the SOTA performance on both language generation and clinical efficacy metrics." + ], + "bbox": [ + 517, + 178, + 890, + 368 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 383, + 640, + 398 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Medical Report Generation Meets Knowledge Graph", + "text_level": 1, + "bbox": [ + 500, + 407, + 890, + 440 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "When radiologists write reports, they will make inferences with their expert knowledge. Typically, a report contains many sections, e.g., impressions, finding, comparison and indication. Following the previous works, we combine the impressions and finding sections as the target for report generation. To endow the medical report generation systems with the capability to incorporate medical knowledge, various kinds of knowledge graphs have been explored and can be roughly divided into three groups. The first kind is proposed to emphasize the abnormal terminologies or disease keywords. Li et al. [20] collected abnormalities from MIMIC-CXR dataset, and utilized them as the node of their proposed abnormality graph. Edges here are the attention weights from source nodes to target nodes in the graph. Such graph is adopted in the following works [26, 48] as prior medical knowledge to enhance the generation procedure and can even facilitate the unsupervised learning framework [32]. Secondly, Zhang et al. [46] and Liu et al. [30] adopted a universal graph with 20 entities. Entities linked to the same organ are connected to each other in the graph. Such relationships are modelled into an adjacency matrix and utilized to propagate messages in a graph encoding module. Since this graph is pre-constructed with prior knowledge in a fixed structure, we found that it can not guarantee the appropriate scope of knowledge for some cases (e.g. missing or unconnected common entities). To tackle this challenge, Liu et al. [30] utilized the global representations from pre-retrieved reports from the training corpus to model domain-specific knowledge. In contrast, we aim to directly update the pre-constructed graph to", + "bbox": [ + 496, + 446, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "3335", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/f3b8b9302222eee942f3c237b61f49be92d3f12480fa0bb0c8eddc8656aca700.jpg", + "image_caption": [ + "Figure 2. Illustration of our proposed Dynamic graph enhanced Contrastive Learning approach (DCL). DCL contains two unimodal encoders, a multimodal encoder, a report decoder and three dynamic graph modules for construction, encoding and cross-modal attention, respectively. In addition to Report Generation (RG) loss, Image-Report Contrastive (IRC) loss and Image-Report Matching (IRM) loss are adopted for training DCL." + ], + "image_footnote": [], + "bbox": [ + 116, + 85, + 851, + 369 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "model the appropriate knowledge. In the last, Li et al. [24] constructed a clinical graph by extracting structural information from the training corpus via a NLP-rule-based algorithm. They restored a set of triplets for each case to model the domain-specific knowledge and replace the visual representations.", + "bbox": [ + 75, + 449, + 468, + 537 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our approach is based on the second category. Instead of using the fixed graph in [46], we dynamically update the graph by injecting new knowledge extracted from the retrieved reports for each case. As a result, the appropriate scope of knowledge for different cases can be activated to generate more high-quality reports.", + "bbox": [ + 75, + 541, + 470, + 633 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Contrastive Learning", + "text_level": 1, + "bbox": [ + 76, + 648, + 277, + 664 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The goal of contrastive learning is to improve representation learning by contrasting positive/negative or similar/dissimilar pairs. Inspired by the recent success of contrastive learning in vision-and-language pretraining tasks [21], some works have introduced it in the CRG systems. Yan et al. [43] developed a weakly supervised method to contrast target reports with incorrect ones by identifying \"hard\" negative samples. To detect the abnormal regions, Liu et al. [31] compared the referring image with known normal images via a contrastive attention mechanism. Other works [5, 42, 45] employed contrastive learning during the pretraining process to better represent visual features and textual information. All those works aimed to improve the expressiveness of both visual and textual representations and then facilitate radiology reporting. In our", + "bbox": [ + 75, + 674, + 470, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "work, contrastive learning can also improve the accuracy of the dynamic graph by training the model to retrieve the most semantically similar reports.", + "bbox": [ + 498, + 449, + 892, + 494 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 500, + 508, + 633, + 526 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we will introduce the detailed implementations of our proposed Dynamic graph enhanced Contrastive Learning approach (DCL). The overall structure of DCL is illustrated in Fig. 2, which contains four basic modules and three dynamic graph modules with three training objectives. We first describe the background of DCL and then introduce the dynamic graph modules and contrastive learning objectives, respectively.", + "bbox": [ + 496, + 534, + 890, + 655 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Background", + "text_level": 1, + "bbox": [ + 500, + 666, + 633, + 681 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Notation In this work, we aim to leverage dynamic graphs to enhance contrastive learning for radiology reporting. In the CRG task, the computer is asked to describe a given medical image $I$ with a free-text report $T = \\{y_{1}, y_{2}, \\ldots, y_{n}\\}$ . We denote the target report by $\\hat{T} = \\{\\hat{y}_{1}, \\hat{y}_{2}, \\ldots, \\hat{y}_{\\hat{n}}\\}$ . $n$ and $\\hat{n}$ represent the numbers of tokens in a report. Our dynamic graph, denoted by $G = \\{V, E\\}$ , where $V$ and $E$ are the sets of nodes and edges, respectively, is built on a pre-constructed graph $G_{pre}$ proposed in [46] and updated with specific knowledge $K_{I} = \\{k_{I}^{1}, \\ldots, k_{I}^{n_{K}}\\}$ extracted from retrieved reports $\\{T_{i}^{*}\\}_{i=1}^{n_{T}}$ . Each $k$ is stored in a triplet format, which consists of a subjective entity $e_{s}$ , an objective entity $e_{o}$ and their relation $r$ . $n_{T}$ and $n_{K}$ are the numbers of reports and triplets, respectively. All the", + "bbox": [ + 496, + 688, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "3336", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "triplets are acquired from the RadGraph [17].", + "bbox": [ + 76, + 90, + 377, + 104 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Typical CRG systems are encoder-decoder frameworks. The encoder is usually a CNN, e.g., ResNet [12] or DenseNet [15], encodes the given image $I$ to dense visual vectors $\\mathbf{f}_I$ . The decoder is usually a RNN (e.g., LSTM [13]) or a Transformer [39], which decodes $\\mathbf{f}_I$ to a report $T$ . In this work, we adopt the Transformer [39] as the backbone to generate the long and robust reports.", + "bbox": [ + 75, + 106, + 467, + 210 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Image Encoder Recently, visual Transformers have shown superior capabilities to represent images than CNNs. Thus, we only employ a ViT [10] pretrained on the ImageNet [9] as the image encoder to simplify the architecture. The input image will be divided into 196 patches, and a [CLS] token is further appended to the beginning of sequence before being fed into the encoder layers. The whole process of an encoder layer $\\mathbf{f}_e(\\cdot)$ can be written as follows:", + "bbox": [ + 75, + 212, + 467, + 332 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {f} _ {e} (x) = \\operatorname {L N} \\left(\\operatorname {F F N} \\left(e _ {\\text {a t t n}}\\right) + e _ {\\text {a t t n}}\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 338, + 467, + 354 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ne _ {a t t n} = \\operatorname {L N} (\\mathrm {M H A} (x) + x), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 158, + 358, + 467, + 373 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where FFN and LN denote the Feed Forward Network [39] and Layer Normalization operation [2], respectively. $x$ is the input of each encoder layer. MHA [39] (multi-head attention) divides a scaled dot-product attention into $n$ parallel heads and each head $\\mathrm{Att}(\\cdot)$ can be written as follows:", + "bbox": [ + 76, + 378, + 467, + 454 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {A t t} (x) = \\operatorname {s o f t m a x} \\left(\\frac {\\mathbf {Q} ^ {x} \\left(\\mathbf {K} ^ {x}\\right) ^ {\\top}}{\\sqrt {d}}\\right) \\mathbf {V} ^ {x}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 472, + 467, + 506 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $d = 768$ is the dimension of the embedding space and $\\{\\mathbf{Q},\\mathbf{K}^{*},\\mathbf{V}^{*}\\}$ are the packed $d$ -dimensional Query, Key, Value vectors, respectively. The final output is the encoded visual vectors $\\mathbf{f}_I$ , which will be used for report generation.", + "bbox": [ + 76, + 510, + 467, + 570 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Report Decoder Our report decoder consists of two Transformer decoder layers. The whole process of a decoder layer $\\mathbf{f}_d(\\cdot)$ can be written as follows:", + "bbox": [ + 76, + 571, + 467, + 614 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {f} _ {d} (\\mathbf {y}) = \\mathrm {L N} \\left(\\mathrm {F F N} \\left(e _ {c a}\\right) + e _ {c a}\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 150, + 622, + 467, + 638 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ne _ {c a} = \\mathrm {L N} \\left(\\mathrm {C A} \\left(e _ {\\text {a t t n}}, \\mathbf {f} _ {I}\\right) + e _ {\\text {a t t n}}\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 166, + 641, + 467, + 656 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ne _ {a t t n} = \\operatorname {L N} (\\operatorname {M M H A} (\\mathbf {y}) + \\mathbf {y})), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 661, + 467, + 676 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where MMHA and CA represent the masked multi-head self-attention and cross attention mechanism in [39]. $\\mathbf{y}$ is the input of decoder. A [Decode] token is added to the beginning of $\\mathbf{y}$ to signal the start while a [EOS] token is to signal its end. In Cross-attention sublayer, for each head, $\\{\\mathbf{Q},\\mathbf{K}^{*},\\mathbf{V}^{*}\\}$ comes from $\\mathbf{Q} = W_{q}*e_{attn}$ , $\\mathbf{K} = W_{k}*\\mathbf{f}_{I}$ , and $\\mathbf{V} = W_{v}*\\mathbf{f}_{I}$ , where $W_{*}$ are the learnable parameters. The $f_{d}(\\mathbf{y})$ will be sent to a Linear & Log-Softmax layer to get the output of target sentences. Notably, only token embedding is adopted during the decoding procedure. The entire auto-regressive generation process can be written as follows:", + "bbox": [ + 76, + 681, + 467, + 861 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np (T | I) = \\prod_ {t = 1} p \\left(y _ {t} \\mid y _ {1}, \\dots , y _ {t - 1}, I\\right). \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 866, + 467, + 896 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $y_{t}$ is the input token in time step $t$ .", + "bbox": [ + 500, + 90, + 772, + 106 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Typically, the report generation objective is the cross-entropy loss to compare the predicted token index sequence with the ground truth. Given the ground truth report $\\hat{T}$ , all the underlying modules are trained to maximize $p(\\mathbf{y} | I)$ by minimizing the following:", + "bbox": [ + 498, + 106, + 890, + 181 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {R G}} = - \\sum_ {t = 1} ^ {\\hat {n}} \\log p \\left(\\hat {y} _ {t} \\mid \\hat {y} _ {1}, \\dots , \\hat {y} _ {t - 1}, I\\right). \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 560, + 193, + 890, + 233 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Dynamic Graph", + "text_level": 1, + "bbox": [ + 500, + 243, + 660, + 258 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The chest knowledge graph $G_{pre}$ proposed in [46] has been widely integrated with CRG systems to emphasize the disease keywords and enhance their relationships. $G_{pre}$ consists of 27 entities and a root node referring to the global feature and an adjacency matrix $A = \\{e_{ij}\\}$ to represent the edges $V$ . Each node is a disease keyword and we set $e_{ij}$ to 1 when source node $n_i$ connects target node $n_j$ . Nodes linked to the same organ or tissue are connected to each other and the root. This graph is not updated during the training, and we found that it limits the effectiveness from two aspects. Firstly, those entities can not cover the most common disease keywords for all datasets because of the dataset bias; Secondly, entities linked to different organs can also affect each other clinically. To tackle those limitations, we propose a dynamic graph $G$ with dynamic structure and nodes and integrate it with visual features to generate high-quality reports. This process is illustrated in Fig. 3, and we will introduce the three key modules, i.e., dynamic graph construction, dynamic graph encoder, and graph attention in this section, respectively.", + "bbox": [ + 496, + 266, + 890, + 568 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Dynamic Graph Construction We construct our graph in a bottom-up manner, in which we first construct the fundamental structure from general knowledge and then add nodes or redefine their relationships according to specific knowledge. We extend $G_{pre}$ to our fundamental structure with 28 entities consisting of a global node represented by a [CLS] token, 7 organs or tissues, and 20 disease keywords. In addition to link criteria in $G_{pre}$ , every organ will connect to each other organ or tissue.", + "bbox": [ + 496, + 569, + 890, + 703 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To get the specific knowledge for each given image $I$ , we first retrieve the top- $n_T$ similar reports $\\{T_i^*\\}_{i=1}^{n_T}$ by calculating the similarity between the visual feature $\\mathbf{f}_I$ and representations of reports in queue $\\{\\mathbf{f}_{T^*}^i\\}_{i=1}^{n_Q}$ , where $n_Q$ is the length of the report queue. For each retrieved report, we extract anatomy and observation entities by Stanza [47]. Those entities are further utilized to quote the specific knowledge $K_I$ from RadGraph [17]. Each triplet $k$ in $K_I$ aims to depict the relationship between source and target entities. There are three kinds of relations in RadGraph, namely 'suggestive of', 'modify' and 'located at'. For a triplet whose only source entity $e_s$ or target entity $e_o$ is in the graph, we will add another entity in the triplet as an ad", + "bbox": [ + 496, + 704, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "3337", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "ditional node, and set their relation to 1 in the adjacency matrix $A$ . Note that if the relation is 'located at' and the entity needed to be added is the target entity $e_{o}$ , $e_{o}$ will be treated as an organ/tissue node. In this bottom-up manner, our dynamic graph is capable to exploit both general and specific knowledge.", + "bbox": [ + 75, + 90, + 468, + 181 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Dynamic Graph Encoder We propose a dynamic graph encoder to propagate information and learn dedicated node features in our dynamic graph. To this end, this module is built upon the standard Transformer encoder layer $\\mathbf{f}_G$ and conducted as (see Figure 3):", + "bbox": [ + 75, + 181, + 470, + 257 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {f} _ {G} = \\mathrm {L N} \\left(\\mathrm {F F N} \\left(e _ {r s a}\\right) + e _ {r s a}\\right), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 176, + 268, + 467, + 284 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\ne _ {r s a} = \\operatorname {L N} (\\operatorname {R S A} \\left(\\mathbf {f} _ {N}, A\\right) + \\mathbf {f} _ {N}), \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 166, + 287, + 468, + 303 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where RSA is an MMHA-like relational self-attention module to encode the structural information of a graph to the model. Concretely, we utilize adjacency matrix $A$ as a visible mask [24,33] to control the original MMHA. It promises that each node can only impact its linked nodes and enhance their relationships. $\\mathbf{f}_N$ is the initialized nodes representations and consists of entity embedding and level encoding. Previous works initialized representations randomly, which limits the effectiveness seriously [49]. Moreover, some additional nodes appear a few times during the training and hard to find the best embeddings. Therefore, we first adopt word embeddings $\\epsilon_{sci}$ from well-trained SciBert [4] to initialize each entity. For those entities consisting of one more word, e.g., 'foreign object', we calculate the average. Furthermore, we add level encoding $\\epsilon_l$ to demonstrate each node is the root, organ, or disease keyword. Thus, the structural information of our graph is well represented and encoded during message passing and propagation.", + "bbox": [ + 75, + 313, + 468, + 585 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Graph Attention Graph attention aims to integrate knowledge from dynamic graphs with visual features. Following [30], we utilize cross attention to achieve this goal. The whole process can be written as follows:", + "bbox": [ + 75, + 585, + 468, + 645 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {f} _ {\\bar {I}} = \\mathrm {L N} (\\mathrm {F F N} (e _ {g a}) + e _ {g a}), \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 657, + 467, + 672 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\ne _ {g a} = \\operatorname {L N} \\left(\\operatorname {C A} \\left(\\mathbf {f} _ {I}, \\mathbf {f} _ {G}\\right)\\right) + \\mathbf {f} _ {I}). \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 173, + 676, + 468, + 691 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In each head, Query comes from visual features $\\mathbf{f}_I$ while Key and Value come from the learned graph representations $\\mathbf{f}_G$ . Finally, we get the dynamic graph enhanced visual features $\\mathbf{f}_{\\hat{I}}$ . Notably, the first token in both $\\mathbf{f}_{\\hat{I}}$ and $\\mathbf{f}_G$ is [CLS] to aggregate visual and graph information.", + "bbox": [ + 75, + 702, + 468, + 777 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Contrastive Learning", + "text_level": 1, + "bbox": [ + 76, + 786, + 277, + 801 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Collecting paired image and text data is prohibitively expensive leading to a smaller size of CRG datasets compared with captioning datasets, like COCO [28]. It hinders the potential of existing data-driven CRG systems. In this section, we introduce the image-report contrastive loss used in our DCL, which can effectively improve the visual", + "bbox": [ + 75, + 809, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/ea6ed29b4b8fd7201931b6f6c67cd8e9724f068a6cc5d277b58feca0db3525ec.jpg", + "image_caption": [ + "Figure 3. illustration of our proposed dynamic graph construction, dynamic graph encoder (DGE), and graph attention (GA) modules. The structure of the pre-constructed graph can be found in Fig. 1." + ], + "image_footnote": [], + "bbox": [ + 519, + 88, + 874, + 284 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "and textual representations as well as ensure the report retrieval accuracy in the dynamic graph construction process. Moreover, inspired by recent vision-language pretraining works [21,22], we also adopt an image-report matching loss in the proposed method for further enhancing the representations to improve the performance.", + "bbox": [ + 498, + 351, + 890, + 441 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Image-Report Contrastive Loss (IRC) can activate radiology reporting by encouraging the positive image-report pairs to have similar representations in contrast to the negative pairs. A report encoder with the same architecture as an image encoder is utilized to extract textual representations $\\mathbf{f}_T$ referring to the positive or negative report. Then we calculate the similar between two [CLS] representations by $s = W_I(V_{cls})^t W_T(T_{cls})$ , where $W_I$ and $W_T$ are two learnable matrices. We also maintain two queues to store the most recent $M$ image-report representations from the momentum image and report encoders. After a Softmax activation, we can get the image-report similarity $f_m^{i2r}(I) = \\frac{\\exp s(I,T_m) / \\tau}{\\sum_{m=1}^M \\exp s(I,T_m) / \\tau}$ and the report-image similarity $f_m^{r2i}(T)$ , where $\\tau$ is a learnable temperature parameter. The IRC can be written as follows:", + "bbox": [ + 498, + 441, + 892, + 674 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {I R C}} = \\frac {1}{2} \\left(\\mathcal {L} _ {\\mathrm {c e}} (g (T), f (T)) + \\mathcal {L} _ {\\mathrm {c e}} (g (I), f (I))\\right), \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 681, + 890, + 710 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{\\mathrm{ce}}$ is the cross entropy loss and $g(I)$ is the ground truth of image-report similarity.", + "bbox": [ + 498, + 719, + 890, + 748 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Image-Report Matching Loss (IRM) is a binary classification task to predict whether the given image-report pair is positive (matched) or negative (unmatched). Different from IRC, we utilize a multimodal encoder to capture the multimodal representations via cross attention mechanism. Then [Encode] vector is projected to $d = 2$ with a linear layer to predict the probability $p^{itm}$ . The IRM is conducted as:", + "bbox": [ + 498, + 750, + 890, + 854 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {I R M}} = \\mathcal {L} _ {\\mathrm {c e}} \\left(g ^ {i t m}, p ^ {i t m}\\right). \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 609, + 878, + 890, + 897 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "3338", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finally, we calculate the sum of $\\mathcal{L}_{\\mathrm{RG}}$ , $\\mathcal{L}_{\\mathrm{IRC}}$ and $\\mathcal{L}_{\\mathrm{IRM}}$ as our total loss function. Notably, the multimodal encoder is only used during the training process to improve representation learning.", + "bbox": [ + 75, + 90, + 470, + 151 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 160, + 209, + 176 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Datasets, Evaluation Metrics and Settings", + "text_level": 1, + "bbox": [ + 76, + 178, + 431, + 194 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We evaluate our proposed DCL on two widely-used radiology reporting benchmarks, IU-Xray [8] and MIMIC-CXR [18]. We adopt the settings in [7,30] to split those two datasets and preprocess the reports for a fair comparison.", + "bbox": [ + 75, + 202, + 467, + 262 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "IU-Xray [8] has been widely used to evaluate the performance of radiology reporting systems. It contains 3,955 radiology reports and 7,470 chest xray images. Either frontal or frontal and lateral view images are associated with each report. Following [7, 20], we exclude those cases with only one image and finally get 2069/296/590 cases for training/validation/testing. By Stanza [47], 739 unique entities are extracted and utilized as dynamic node candidates.", + "bbox": [ + 75, + 263, + 467, + 383 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "MIMIC-CXR [18] is the largest radiology dataset to date, consisting of 368,960 chest X-ray images and 222,758 radiology reports and is splitted officially. Recently, various MIMIC-child datasets have been proposed by exploring structural radiology information, e.g., Chest Image Genome [41] and RadGraph [17]. In this work, we adopt RadGraph to update our dynamic structure. Classified by relation, RadGraph consists of 2,895,725 (suggestive of), 6,115,264 (located at) and 4,010,875 (modify) triplets.", + "bbox": [ + 75, + 383, + 467, + 520 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Natural Language Generation Metrics (NLG) are used to measure the descriptive accuracy of predicted reports. CIDEr [40] and BLEU [36] are two main NLG metrics used to measure the quality of predicted reports. BLEU is proposed for machine translation tasks and measures the word n-gram overlap between predictions and reports. Due to the textual bias in CRG datasets, CRG systems can achieve considerable BLEU values even when they just repeat the most frequent sentences. In contrast, CIDEr is tailored to evaluate captioning systems by rewarding topic terms (terminologies in CRG task) and penalizing frequent terms. Additionally, values of ROUGE-L [27] and METEOR [3] are also reported for comparison.", + "bbox": [ + 75, + 521, + 467, + 715 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Clinical Efficacy Metrics are recently proposed to capture and evaluate the clinical correctness of predicted reports. It first employs the CheXPert labeling tool proposed in [16] to label predicted reports and the ground truth reports in 14 different medical terminologies. Then classification measurements, i.e., F1-Score, Precision and Recall are calculated to evaluate how well the generated report describes the abnormalities. Since the provider of IU-Xray does not use CheXPert to build the labels, CE metrics are only reported on the MIMIC-CXR dataset [38, 44].", + "bbox": [ + 75, + 718, + 467, + 868 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Experimental Settings We use the same image encoder for different views images and concatenate visual tokens via", + "bbox": [ + 76, + 869, + 467, + 898 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/7407a8d427a25fa7fad2690310394273c65d47752003f30fb1585cc2b269d060.jpg", + "image_caption": [ + "Figure 4. Micro-average of receiver operating characteristic curve for clinical abnormalities predictions from the generated reports." + ], + "image_footnote": [], + "bbox": [ + 521, + 90, + 867, + 284 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "fusion operation for further process. Considering the domain gap between medical and generic texts, we employ a pretrained SciBert [4] to serve as a tokenizer and report encoder. The model is trained on 4 NVIDIA 2080 Ti GPUs with batch sizes 8 and 30 epochs. The checkpoint acquires the highest CIEDr metric is used for testing. The learning rate is set as 1e-4 and the optimizer is AdamW [34] with a weight decay of 0.02. The top 3 similar reports from the text queue $Q$ are retrieved. And the size of $Q$ is set as 65,536 and 1,380 for MIMIC-CXR and IU-Xray. The max length of specific knowledge is set as 90. For batch operation, the nodes in $G$ are padded to 50 with a [PAD] token. Note that, we project all encoded vectors by a linear transformation layer into the dimension of $d = 768$ .", + "bbox": [ + 496, + 338, + 890, + 549 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Main Results", + "text_level": 1, + "bbox": [ + 500, + 560, + 637, + 574 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Descriptive Accuracy In Tab. 1, we compare our DCL with a wide range of existing state-of-the-art CRG systems on two benchmarks. R2Gen [7] and CMN [6] have been widely used as baseline CRG models recently. KERP [20], MKG [46], PPKED [30] and MGSK [44] are proposed to integrate medical knowledge with typical CRG backbones. CA [31] and CMCL [29] employ contrastive learning and curriculum learning to improve performance. The performances of other baseline models, such as HRGP [19], M2TR [35] and TopDown [1] are also reported. Since we follow the same settings, we directly cite the results from original papers. As shown in Tab. 1, our DCL achieves the SOTA descriptive accuracy, which outperforms others in CIDEr and ROUGE-L metrics and matches their performances in BLEU-4 and METEOR metrics. Higher CIDEr values demonstrate that our model does not repeat frequent sentences in training set but generates reports with more accurate topics.", + "bbox": [ + 496, + 583, + 890, + 853 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Clinical Correctness We also evaluate our method by clinical efficacy (CE) metrics on the MIMIC-CXR dataset and compare the performances with other baseline models. Fol-", + "bbox": [ + 498, + 854, + 890, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "3339", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/16cb1acd91aa55ce9a6a37ff1d78e74687bc89ca8bdc8c12415da1ddce97b383.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Iu-Xray [8]MIMIC-CXR [18]
MethodsCIDErBLEU-4ROUGE-LMETEORMethodsCIDErBLEU-4ROUGE-LMETEOR
R2Gen [7]0.3980.1650.3710.187R2Gen [7]0.2530.1030.2770.142
KERP [20]0.2800.1620.339-CMN [6]-0.1060.2780.142
HRGP [19]0.3430.1510.322-TopDown [1]0.0730.0920.2670.129
MKG [46]0.3040.1470.367-M2TR [35]-0.1070.2720.145
PPKED [30]0.3510.1680.3760.190PPKED [30]0.2370.1060.2840.149
MGSK [44]0.3820.1780.381-MGSK [44]0.2030.1150.284-
CA [31]-0.1690.3810.193CA [31]-0.1090.2830.151
CMCL [29]-0.1620.3780.186CMCL [29]-0.0970.2810.133
Ours0.5860.1630.3830.193Ours0.2810.1090.2840.150
", + "bbox": [ + 81, + 88, + 893, + 280 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/28aeb635b1d1f8e9ad9c9e619668a89e38807259963ece838860e1592f332bb0.jpg", + "table_caption": [ + "Table 1. The performances of our proposed DCL compared with other state-of-the-art systems on IU-Xray and MIMIC-CXR dataset. The best results in each column are highlighted in bold. CIDEr [40] is proposed to evaluate captioning systems." + ], + "table_footnote": [], + "table_body": "
MethodsPrecisionRecallF1-score
TopDown [1]0.1660.1210.133
M2TR [35]0.2400.4280.308
R2Gen [7]0.3330.2730.276
MKSG [44]0.4580.3480.371
Ours w/o G0.2750.1850.194
Ours w/o LIRC0.4630.3370.359
Ours w/o LIRM0.4690.3530.372
Ours0.4710.3520.373
", + "bbox": [ + 101, + 327, + 444, + 486 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. The comparison of the clinical efficacy metrics on MIMIC-CXR dataset. The w/o is the abbreviation of without.", + "bbox": [ + 75, + 496, + 468, + 523 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "lowing official splitting, we directly cite the results from [44] for comparison. In Fig. 4, we show the micro-average of ROC for 14 chesty terminologies prediction and present the AUC scores. 'Pleural Effusion' and 'Pleural Other' achieve the highest AUCs (0.82). The experimental results in Tab. 2 reveal that our DCL significantly outperforms the previous models on three CE metrics. Compared with the current SOTA method MGSK [44] that also leverages general prior knowledge and specific knowledge from RadGraph [17], we make a performance-boosting. The improvement verifies the importance of our dynamic graph concepts and also demonstrates that our system can predict more accurate clinical information.", + "bbox": [ + 75, + 537, + 468, + 733 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 734, + 230, + 750 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we conduct ablation studies on IU-Xray and MIMIC-CXR datasets to investigate the contribution of each component in our proposed DCL. Tab. 3 presents the quantitative analysis of DCL on IU-Xray with measuring descriptive accuracy. And clinical correctness evaluation is reported in Tab. 2. Our base model only keeps the image encoder and report decoder and employs $\\mathcal{L}_{\\mathrm{RG}}$ .", + "bbox": [ + 75, + 750, + 468, + 854 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effect of Dynamic Graph Our dynamic graph is constructed in a bottom-up manner, that exploits general knowledge from $G_{pre}$ and specific knowledge $K_I$ extracted from", + "bbox": [ + 75, + 854, + 468, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "retrieved Top-3 similar reports. Comparing the base model with settings (a) and (b), our dynamic graph can boost the performance of base model, substantially. More specifically, leveraging the general knowledge only lead to an increase on all NLG metrics by $15.2\\%$ on CIDEr and $1.1\\%$ on BLEU-4. By integrating specific knowledge, our dynamic graph can further boost the performances, e.g. $0.535 \\rightarrow 0.557$ on CIDEr. It demonstrates the effectiveness and necessity of constructing dynamic graphs for each image. We hypothesize that this performance improvement may be due to that the dynamic knowledge can emphasize keywords when generating reports since dynamic nodes are from retrieved reports. It has been proved in Tab. 2, leveraging dynamic graph significantly improve the performances on all CE metrics, which means the generated reports can provide more accurate medical terminologies.", + "bbox": [ + 496, + 329, + 890, + 571 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effect of Contrastive Learning Sequentially, we evaluate the effectiveness of two introduced learning objectives, i.e., image report contrastive loss (IRC) and image report matching loss (IRM). The performances of settings (b,c) in Tab. 2 show that both IRC and IRM can boost the base model performances. It proves the importance of visual and textual representation qualities since severe data bias in CRG datasets will degenerate the representation capabilities seriously. However, comparing (c) and (d), it is observed that IRC brings more improvement than IRM. We speculate the reason is that IRC can straightly improve visual and textual representations by aligning similar pairs. In contrast, IRM works on multimodal representations and represents unimodal in an indirect manner.", + "bbox": [ + 496, + 570, + 890, + 779 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Choice of Parameter Initialization We employ a pretrained ViT [10] and SciBert [4] as image and report encoder in our implementation. It is worth noting that Transformers lack some of the inductive biases inherent to CNNs and therefore generalize bad with insufficient and unbalanced data [10]. Not surprisingly, comparing setting (f) and the full model, the performances drop steeply without pretrained ViT parameters. The performances of setting (e)", + "bbox": [ + 496, + 779, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "3340", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/a9994a6c9875bc414d96ddd2548ec1c9254f3e017380b37dce64d3ef04fd1246.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Settings\\(G_{pre}\\)\\(K_I\\)IRCIRMViT [10]SciBert [4]CIDErBLEU-4ROUGE-LMETEOR
Base✓✓0.3830.1330.2770.163
(a)✓✓✓0.5350.1440.3490.180
(b)✓✓✓✓0.5570.1500.3610.182
(c)✓✓✓✓✓0.5800.1610.3850.188
(d)✓✓✓✓✓0.5640.1550.3700.188
(e)✓✓✓✓✓0.5800.1580.3740.190
(f)✓✓✓✓✓0.5270.1580.3560.179
DCL✓✓✓✓✓✓0.5860.1630.3830.193
", + "bbox": [ + 109, + 88, + 861, + 271 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/98c0b82415d6aeb3d03901db95e9832e4d0907a5c42dc7e9a9431e92882dc6cd.jpg", + "table_caption": [ + "Table 3. Quantitative analysis of proposed method on IU-Xray dataset. The base model consists of an image encoder and a report decoder with report generation loss only." + ], + "table_footnote": [], + "table_body": "
ImageGround Truth ReportRetrieved Specific KnowledgeOursR2Gen
Lateral view somewhat limited due to overlying motion artifact lungs are low in volume there is no focal airspace the consolidation to suggest pneumonia a 1 2-cm calcified granuloma just below the medial aspect of the right hemidiaphragm is unchanged from prior study no pleural effusions or pulmonary edema there is no pneumothorax the inferior sternotomy wire is fractured but unchanged surgical clips and vascular markers in the thorax are related to prior cabg surgery.effusion located _ at pleural,vascular modify pulmonary, sternotomy suggestive _ of cabg,consolidation suggestive _ of effusion,effusion suggestive _ of consolidation,low modify effusion,low suggestive _ of effusion, low suggestive _ of consolidation,vascular modify chest,effusion suggestive _ of atelectasis,atelectasis modify lunglung volumes are low. there is no focal consolidation effusion or pneumothorax. airspace consolidation is noted within the left upper lobe compatible with pneumonia. borderline size of the cardiac silhouette without evidence of pulmonary edema, midline sternotomy wires and mediastinal clips are again noted.ap upright and lateral views of the chest provided . lung volumes are low limiting assessment . allowing for this there is no focal consolidation effusion or pneumothorax . the cardiomeiastinal silhouette is normal . imaged osseous structures are intact . no free air below the right hemidiaphragm is seen.
", + "bbox": [ + 81, + 309, + 888, + 415 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Figure 5. Illustrations of reports from ground truth, ours and R2Gen [7] and retrieved specific knowledge for one sample from MIMIC-CXR [18]. For better visualization, different colors highlight different medical entities.", + "bbox": [ + 75, + 425, + 892, + 455 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "demonstrate the effectiveness of pretrained SciBert. The improvement comes from two aspects. Firstly, it provides well pretrained parameters; Secondly, its tokenizer encodes each token (medical terminology) with a well pretrained embedding, which avoids Graph Transformers to propagate similar hidden states [49].", + "bbox": [ + 75, + 465, + 470, + 556 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Case Study", + "text_level": 1, + "bbox": [ + 76, + 564, + 200, + 580 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To further investigate the effectiveness of our method, we perform qualitative analysis on MIMIC-CXR [18] with their retrieved specific knowledge, and reports from ground truth, our model and R2Gen [7]. Entities extracted by Stanza [47] from the ground truth report have been highlighted with different colors. It is observed that some entities, e.g. cabg, consolidation, and sternotomy) are not included in the pre-constructed graph node lists. This observation proves our motivation for constructing knowledge graphs dynamically. We conduct the same operation on retrieved reports and use extracted entities to quote related triplets from RadGraph [17]. Those triplets are known as specific knowledge in this paper and shown in Fig. 5. Retrieved specific knowledge triplets $<$ sternotomy,suggestive_of,cabg> and $<$ consolidation,suggestive_of,effusion> demonstrate that the retrieved reports contain similar medical terminologies and clinical information. We speculate that IRC and IRM objectives bring such capabilities. Then the entities in our dynamic graph emphasize disease/organ keywords when generating reports and it is why our DCL can predict sen", + "bbox": [ + 75, + 583, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "tence \"airspace consolidation is noted within the left upper lobe compatible with pneumonia,\" but R2Gen can not.", + "bbox": [ + 496, + 465, + 892, + 496 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion and Discussion", + "text_level": 1, + "bbox": [ + 498, + 500, + 748, + 513 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we present a practical approach to leverage dynamic graph to enhance contrastive learning for radiology report generation. In which the dynamic graph is constructed in a bottom-up manner to integrate retrieved specific knowledge with general knowledge. Then contrastive learning is employed to improve visual and textual representations, which also promises the accuracy of our dynamic graph. Experiments on two popular benchmarks verify the effectiveness of our method in generating accurate and meaningful reports. More encouragingly, our approach can outperform or match existing SOTA methods in language generation and clinical efficacy metrics.", + "bbox": [ + 496, + 517, + 892, + 698 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitation and Future Work Retrieved reports can not be exactly the same as ground truth, and knowledge noises are involved during the dynamic graph construction process. It may guide the model to generate inaccurate sentences. In the future, we plan to propose a specific objective for the dynamic graph construction process to further improve the accuracy of dynamic graphs and the quality of predicted reports.", + "bbox": [ + 496, + 698, + 890, + 819 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements", + "text_level": 1, + "bbox": [ + 500, + 821, + 668, + 838 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was partially supported by \"Taishan Scholars Youth Expert Program\" of Shandong Province, and partially supported by National Key R&D Program of China under Grant No. 2020AAA0109700.", + "bbox": [ + 496, + 839, + 892, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "3341", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Peter Anderson, Xiaodong He, Chris Buehler, Damien Teney, Mark Johnson, Stephen Gould, and Lei Zhang. 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In Proceedings of the Conference on Neural Information Processing Systems, 2022. 5, 8" + ], + "bbox": [ + 501, + 92, + 893, + 880 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "3343", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Dynamic Graph Enhanced Contrastive Learning for Chest X-Ray Report Generation/7bbdab16-5f4c-46f9-abdb-480a53791847_model.json b/2023/Dynamic Graph Enhanced Contrastive Learning for Chest X-Ray Report Generation/7bbdab16-5f4c-46f9-abdb-480a53791847_model.json new file mode 100644 index 0000000000000000000000000000000000000000..8128d7b9351ce375408bae0649523609f96b60dd --- /dev/null +++ b/2023/Dynamic Graph Enhanced Contrastive Learning for Chest X-Ray Report Generation/7bbdab16-5f4c-46f9-abdb-480a53791847_model.json @@ -0,0 +1,2101 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.002, + 0.812, + 0.022 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation." + }, + { + "type": "header", + "bbox": [ + 0.295, + 0.017, + 0.754, + 0.028 + ], + "angle": 0, + "content": "Except for this watermark, it is identical to the accepted version:" + }, + { + "type": "header", + "bbox": [ + 0.294, + 0.031, + 0.754, + 0.046 + ], + "angle": 0, + "content": "the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.119, + 0.13, + 0.853, + 0.175 + ], + "angle": 0, + "content": "Dynamic Graph Enhanced Contrastive Learning for Chest X-ray Report Generation" + }, + { + "type": "text", + "bbox": [ + 0.099, + 0.203, + 0.878, + 0.222 + ], + "angle": 0, + "content": "Mingjie Li\\(^{1}\\) Bingqian Lin\\(^{2}\\) Zicong Chen\\(^{5}\\) Haokun Lin\\(^{2}\\) Xiaodan Liang\\(^{2,3,4}\\) Xiaojun Chang\\(^{1*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.128, + 0.222, + 0.844, + 0.257 + ], + "angle": 0, + "content": "\\(^{1}\\)ReLER, AAII, University of Technology Sydney \\(^{2}\\)School of ISE, Sun Yat-Sen University \\(^{3}\\)Department of Computer Vision, Mohamed bin Zayed University of Artificial Intelligence" + }, + { + "type": "text", + "bbox": [ + 0.253, + 0.257, + 0.72, + 0.275 + ], + "angle": 0, + "content": "\\(^{4}\\)Peng Cheng National Lab \\(^{5}\\)The University of Hong Kong" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.309, + 0.314, + 0.326 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.342, + 0.474, + 0.721 + ], + "angle": 0, + "content": "Automatic radiology reporting has great clinical potential to relieve radiologists from heavy workloads and improve diagnosis interpretation. Recently, researchers have enhanced data-driven neural networks with medical knowledge graphs to eliminate the severe visual and textual bias in this task. The structures of such graphs are exploited by using the clinical dependencies formed by the disease topic tags via general knowledge and usually do not update during the training process. Consequently, the fixed graphs can not guarantee the most appropriate scope of knowledge and limit the effectiveness. To address the limitation, we propose a knowledge graph with Dynamic structure and nodes to facilitate chest X-ray report generation with Contrastive Learning, named DCL. In detail, the fundamental structure of our graph is pre-constructed from general knowledge. Then we explore specific knowledge extracted from the retrieved reports to add additional nodes or redefine their relations in a bottom-up manner. Each image feature is integrated with its very own updated graph before being fed into the decoder module for report generation. Finally, this paper introduces Image-Report Contrastive and Image-Report Matching losses to better represent visual features and textual information. Evaluated on IU-Xray and MIMIC-CXR datasets, our DCL outperforms previous state-of-the-art models on these two benchmarks." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.729, + 0.21, + 0.745 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.755, + 0.47, + 0.877 + ], + "angle": 0, + "content": "Recently, automatic report generation has received growing attentions from both machine learning and automatic medicine fields. It aims to generate semantically coherent and informative reports to describe the referring examination images, such as Chest X-Ray [8, 18], Lung CT Scan [26] or funds angiography [23]. Such techniques have great clinical potential in relieving junior radiologists from heavy workloads and reducing diagnosis errors by improv-" + }, + { + "type": "image", + "bbox": [ + 0.511, + 0.31, + 0.659, + 0.425 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.662, + 0.312, + 0.771, + 0.324 + ], + "angle": 0, + "content": "Ground Truth Report" + }, + { + "type": "text", + "bbox": [ + 0.662, + 0.34, + 0.878, + 0.419 + ], + "angle": 0, + "content": "A single portable AP semi-upright view of the chest was obtained. Cardiomediastinal silhouette including moderate cardiomegaly is stable. An ICD device is also unchanged in position. Interval development of increased opacification in the right lower lung probably reflects asymmetric edema and a layering effusion..." + }, + { + "type": "image", + "bbox": [ + 0.512, + 0.428, + 0.887, + 0.546 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.557, + 0.893, + 0.626 + ], + "angle": 0, + "content": "Figure 1. An illustration of one sample from MIMIC-CXR [18] and the pre-constructed graph in [46], where the blue circle, orange boxes and black boxes refer to the global node, organ-level entities and key findings, respectively. The red dash line here represents the unconnected relation." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.629, + 0.692, + 0.643 + ], + "angle": 0, + "content": "ing the interpretation [7, 30]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.645, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Witnessed the great progress in artificial intelligence, especially deep learning methods [12,25,39], researchers have proposed various data-driven neural networks for radiology reporting and achieved promising performances in metrics that measure descriptive accuracy [7, 44] and clinical correctness [11, 46]. Compared with the similar task generic image captioning [14], the key challenges in chest X-ray report generation (CRG) task are the severe visual and textual data bias [19, 26]. On the one hand, medical images are highly similar to each other due to the imaging methods and human tissues themselves. However, abnormal regions or lesions that should acquire more attentions usually locate at a small part and lack detailed annotations in existing CRG benchmarks. On the other hand, sentences that describe normal regions are likely to appear repeatedly among each dataset which disables the model to describe specific crucial abnormalities. Two concepts have been proved ef" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.47, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author. https://github.com/mlii0117/DCL" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3334" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.078, + 0.092, + 0.295, + 0.106 + ], + "angle": 0, + "content": "fective in eliminating those bias." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.11, + 0.473, + 0.472 + ], + "angle": 0, + "content": "The first one is to integrate medical knowledge with ORG systems [24,30,44,46]. Zhang et al. [46] constructed a universal graph comprised of a global node, 7 organs/tissues and 20 findings (normal or disease keywords). Disease keyword nodes linked to the same organ are connected to each other and the root in the graph. This graph can enhance the relationships among findings and emphasize the disease keywords. Thus, it is also adopted in the following works [30, 44]. However, this graph is built from general knowledge and may be inappropriate in some cases. As the shown report in Fig. 1, it is observed that effusion should be suggestive of edema, however, such relationship is not modelled in the graph. Furthermore, some nodes like 'cicatrix' or 'hypoinflation' only appear very few times in two ORG benchmarks [8, 18]. Therefore, it is necessary to update the scope of knowledge for each case; In addition to the medical knowledge, recent works [5, 11, 31, 38, 43] utilize contrastive learning to improve the visual and textual representations by contrasting positive and negative pairs. They proposed various contrastive learning objectives to capture the abnormal regions from a chest X-Ray image. Since normal images usually dominate the dataset over abnormal ones [37], it is also crucial to recognize the normal or abnormal cases in the meantime." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.476, + 0.473, + 0.854 + ], + "angle": 0, + "content": "In this paper, we propose a novel framework, named DCL, which exploits a dynamic graph integrating specific knowledge with general knowledge to enhance visual representations learned in a contrastive manner. We adopt the general knowledge with 28 entities from [46] as the fundamental structure of our graph, and the relationships are modelled in an adjacency matrix. Given a medical image, we first retrieve its semantically similar reports from the training set. Specific knowledge is extracted from those reports via RadGraph [17] and stored in triplets (). And we integrate those triplets with the pre-constructed graph by dynamically adding additional nodes or linking two entities. We utilize a graph encoder to propagate information over the updated graph for refining the node features, which are initialized by a pretrained SciBert [4]. Then the dedicated node features are attended to visual representations for report generation via a Transformer [39] decoder. Based on the dynamic graph, we introduce a contrastive learning objective, image-report contrastive loss to well represent the visual features and textual information. In addition, contrastive learning can help ensure the accuracy of the report retrieval procedure in the dynamic graph construction process. Image-report matching loss is also employed to further improve the performances." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.472, + 0.903 + ], + "angle": 0, + "content": "We evaluate our method on two benchmarks, IU-Xray [8] and MIMIC-CXR [18]. Experimental results demonstrate that our approach can either outperform or" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.152 + ], + "angle": 0, + "content": "match previous state-of-the-art (SOTA) methods in metrics that measure descriptive accuracy and clinical correctness. It indicates that leveraging dynamic graphs to enhance contrastive learning is helpful to generate high-quality reports." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.153, + 0.856, + 0.168 + ], + "angle": 0, + "content": "In summary, our main contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.179, + 0.892, + 0.224 + ], + "angle": 0, + "content": "- We propose a novel framework that leverages a dynamic graph to enhance visual representations with contrastive learning paradigms for radiology reporting." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.237, + 0.892, + 0.297 + ], + "angle": 0, + "content": "- Our proposed dynamic graph integrates both general and specific knowledge; The contrastive learning objective can improve visual and textual representations and dynamic graph accuracy." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.309, + 0.892, + 0.369 + ], + "angle": 0, + "content": "- We conduct extensive experiments on two popular benchmarks to show the effectiveness of our approach, which achieves the SOTA performance on both language generation and clinical efficacy metrics." + }, + { + "type": "list", + "bbox": [ + 0.519, + 0.179, + 0.892, + 0.369 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.384, + 0.642, + 0.4 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.409, + 0.892, + 0.441 + ], + "angle": 0, + "content": "2.1. Medical Report Generation Meets Knowledge Graph" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.448, + 0.895, + 0.903 + ], + "angle": 0, + "content": "When radiologists write reports, they will make inferences with their expert knowledge. Typically, a report contains many sections, e.g., impressions, finding, comparison and indication. Following the previous works, we combine the impressions and finding sections as the target for report generation. To endow the medical report generation systems with the capability to incorporate medical knowledge, various kinds of knowledge graphs have been explored and can be roughly divided into three groups. The first kind is proposed to emphasize the abnormal terminologies or disease keywords. Li et al. [20] collected abnormalities from MIMIC-CXR dataset, and utilized them as the node of their proposed abnormality graph. Edges here are the attention weights from source nodes to target nodes in the graph. Such graph is adopted in the following works [26, 48] as prior medical knowledge to enhance the generation procedure and can even facilitate the unsupervised learning framework [32]. Secondly, Zhang et al. [46] and Liu et al. [30] adopted a universal graph with 20 entities. Entities linked to the same organ are connected to each other in the graph. Such relationships are modelled into an adjacency matrix and utilized to propagate messages in a graph encoding module. Since this graph is pre-constructed with prior knowledge in a fixed structure, we found that it can not guarantee the appropriate scope of knowledge for some cases (e.g. missing or unconnected common entities). To tackle this challenge, Liu et al. [30] utilized the global representations from pre-retrieved reports from the training corpus to model domain-specific knowledge. In contrast, we aim to directly update the pre-constructed graph to" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3335" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.117, + 0.087, + 0.852, + 0.371 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.381, + 0.895, + 0.437 + ], + "angle": 0, + "content": "Figure 2. Illustration of our proposed Dynamic graph enhanced Contrastive Learning approach (DCL). DCL contains two unimodal encoders, a multimodal encoder, a report decoder and three dynamic graph modules for construction, encoding and cross-modal attention, respectively. In addition to Report Generation (RG) loss, Image-Report Contrastive (IRC) loss and Image-Report Matching (IRM) loss are adopted for training DCL." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.45, + 0.47, + 0.539 + ], + "angle": 0, + "content": "model the appropriate knowledge. In the last, Li et al. [24] constructed a clinical graph by extracting structural information from the training corpus via a NLP-rule-based algorithm. They restored a set of triplets for each case to model the domain-specific knowledge and replace the visual representations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.542, + 0.471, + 0.634 + ], + "angle": 0, + "content": "Our approach is based on the second category. Instead of using the fixed graph in [46], we dynamically update the graph by injecting new knowledge extracted from the retrieved reports for each case. As a result, the appropriate scope of knowledge for different cases can be activated to generate more high-quality reports." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.649, + 0.279, + 0.665 + ], + "angle": 0, + "content": "2.2. Contrastive Learning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.675, + 0.471, + 0.901 + ], + "angle": 0, + "content": "The goal of contrastive learning is to improve representation learning by contrasting positive/negative or similar/dissimilar pairs. Inspired by the recent success of contrastive learning in vision-and-language pretraining tasks [21], some works have introduced it in the CRG systems. Yan et al. [43] developed a weakly supervised method to contrast target reports with incorrect ones by identifying \"hard\" negative samples. To detect the abnormal regions, Liu et al. [31] compared the referring image with known normal images via a contrastive attention mechanism. Other works [5, 42, 45] employed contrastive learning during the pretraining process to better represent visual features and textual information. All those works aimed to improve the expressiveness of both visual and textual representations and then facilitate radiology reporting. In our" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.45, + 0.893, + 0.495 + ], + "angle": 0, + "content": "work, contrastive learning can also improve the accuracy of the dynamic graph by training the model to retrieve the most semantically similar reports." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.51, + 0.634, + 0.527 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.535, + 0.892, + 0.656 + ], + "angle": 0, + "content": "In this section, we will introduce the detailed implementations of our proposed Dynamic graph enhanced Contrastive Learning approach (DCL). The overall structure of DCL is illustrated in Fig. 2, which contains four basic modules and three dynamic graph modules with three training objectives. We first describe the background of DCL and then introduce the dynamic graph modules and contrastive learning objectives, respectively." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.667, + 0.634, + 0.683 + ], + "angle": 0, + "content": "3.1. Background" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Notation In this work, we aim to leverage dynamic graphs to enhance contrastive learning for radiology reporting. In the CRG task, the computer is asked to describe a given medical image \\(I\\) with a free-text report \\(T = \\{y_{1}, y_{2}, \\ldots, y_{n}\\}\\). We denote the target report by \\(\\hat{T} = \\{\\hat{y}_{1}, \\hat{y}_{2}, \\ldots, \\hat{y}_{\\hat{n}}\\}\\). \\(n\\) and \\(\\hat{n}\\) represent the numbers of tokens in a report. Our dynamic graph, denoted by \\(G = \\{V, E\\}\\), where \\(V\\) and \\(E\\) are the sets of nodes and edges, respectively, is built on a pre-constructed graph \\(G_{pre}\\) proposed in [46] and updated with specific knowledge \\(K_{I} = \\{k_{I}^{1}, \\ldots, k_{I}^{n_{K}}\\}\\) extracted from retrieved reports \\(\\{T_{i}^{*}\\}_{i=1}^{n_{T}}\\). Each \\(k\\) is stored in a triplet format, which consists of a subjective entity \\(e_{s}\\), an objective entity \\(e_{o}\\) and their relation \\(r\\). \\(n_{T}\\) and \\(n_{K}\\) are the numbers of reports and triplets, respectively. All the" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "3336" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.379, + 0.106 + ], + "angle": 0, + "content": "triplets are acquired from the RadGraph [17]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.107, + 0.468, + 0.212 + ], + "angle": 0, + "content": "Typical CRG systems are encoder-decoder frameworks. The encoder is usually a CNN, e.g., ResNet [12] or DenseNet [15], encodes the given image \\(I\\) to dense visual vectors \\(\\mathbf{f}_I\\). The decoder is usually a RNN (e.g., LSTM [13]) or a Transformer [39], which decodes \\(\\mathbf{f}_I\\) to a report \\(T\\). In this work, we adopt the Transformer [39] as the backbone to generate the long and robust reports." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.213, + 0.468, + 0.333 + ], + "angle": 0, + "content": "Image Encoder Recently, visual Transformers have shown superior capabilities to represent images than CNNs. Thus, we only employ a ViT [10] pretrained on the ImageNet [9] as the image encoder to simplify the architecture. The input image will be divided into 196 patches, and a [CLS] token is further appended to the beginning of sequence before being fed into the encoder layers. The whole process of an encoder layer \\(\\mathbf{f}_e(\\cdot)\\) can be written as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.157, + 0.339, + 0.468, + 0.356 + ], + "angle": 0, + "content": "\\[\n\\mathbf {f} _ {e} (x) = \\operatorname {L N} \\left(\\operatorname {F F N} \\left(e _ {\\text {a t t n}}\\right) + e _ {\\text {a t t n}}\\right), \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.16, + 0.359, + 0.468, + 0.374 + ], + "angle": 0, + "content": "\\[\ne _ {a t t n} = \\operatorname {L N} (\\mathrm {M H A} (x) + x), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.38, + 0.468, + 0.455 + ], + "angle": 0, + "content": "where FFN and LN denote the Feed Forward Network [39] and Layer Normalization operation [2], respectively. \\(x\\) is the input of each encoder layer. MHA [39] (multi-head attention) divides a scaled dot-product attention into \\(n\\) parallel heads and each head \\(\\mathrm{Att}(\\cdot)\\) can be written as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.155, + 0.473, + 0.468, + 0.507 + ], + "angle": 0, + "content": "\\[\n\\operatorname {A t t} (x) = \\operatorname {s o f t m a x} \\left(\\frac {\\mathbf {Q} ^ {x} \\left(\\mathbf {K} ^ {x}\\right) ^ {\\top}}{\\sqrt {d}}\\right) \\mathbf {V} ^ {x}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.511, + 0.468, + 0.571 + ], + "angle": 0, + "content": "where \\(d = 768\\) is the dimension of the embedding space and \\(\\{\\mathbf{Q},\\mathbf{K}^{*},\\mathbf{V}^{*}\\}\\) are the packed \\(d\\)-dimensional Query, Key, Value vectors, respectively. The final output is the encoded visual vectors \\(\\mathbf{f}_I\\), which will be used for report generation." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.572, + 0.468, + 0.616 + ], + "angle": 0, + "content": "Report Decoder Our report decoder consists of two Transformer decoder layers. The whole process of a decoder layer \\(\\mathbf{f}_d(\\cdot)\\) can be written as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.151, + 0.623, + 0.468, + 0.639 + ], + "angle": 0, + "content": "\\[\n\\mathbf {f} _ {d} (\\mathbf {y}) = \\mathrm {L N} \\left(\\mathrm {F F N} \\left(e _ {c a}\\right) + e _ {c a}\\right), \\tag {4}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.167, + 0.642, + 0.468, + 0.657 + ], + "angle": 0, + "content": "\\[\ne _ {c a} = \\mathrm {L N} \\left(\\mathrm {C A} \\left(e _ {\\text {a t t n}}, \\mathbf {f} _ {I}\\right) + e _ {\\text {a t t n}}\\right), \\tag {5}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.155, + 0.662, + 0.468, + 0.677 + ], + "angle": 0, + "content": "\\[\ne _ {a t t n} = \\operatorname {L N} (\\operatorname {M M H A} (\\mathbf {y}) + \\mathbf {y})), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.682, + 0.468, + 0.862 + ], + "angle": 0, + "content": "where MMHA and CA represent the masked multi-head self-attention and cross attention mechanism in [39]. \\(\\mathbf{y}\\) is the input of decoder. A [Decode] token is added to the beginning of \\(\\mathbf{y}\\) to signal the start while a [EOS] token is to signal its end. In Cross-attention sublayer, for each head, \\(\\{\\mathbf{Q},\\mathbf{K}^{*},\\mathbf{V}^{*}\\}\\) comes from \\(\\mathbf{Q} = W_{q}*e_{attn}\\), \\(\\mathbf{K} = W_{k}*\\mathbf{f}_{I}\\), and \\(\\mathbf{V} = W_{v}*\\mathbf{f}_{I}\\), where \\(W_{*}\\) are the learnable parameters. The \\(f_{d}(\\mathbf{y})\\) will be sent to a Linear & Log-Softmax layer to get the output of target sentences. Notably, only token embedding is adopted during the decoding procedure. The entire auto-regressive generation process can be written as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.153, + 0.867, + 0.468, + 0.897 + ], + "angle": 0, + "content": "\\[\np (T | I) = \\prod_ {t = 1} p \\left(y _ {t} \\mid y _ {1}, \\dots , y _ {t - 1}, I\\right). \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.773, + 0.107 + ], + "angle": 0, + "content": "where \\(y_{t}\\) is the input token in time step \\(t\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.107, + 0.892, + 0.183 + ], + "angle": 0, + "content": "Typically, the report generation objective is the cross-entropy loss to compare the predicted token index sequence with the ground truth. Given the ground truth report \\(\\hat{T}\\), all the underlying modules are trained to maximize \\(p(\\mathbf{y} | I)\\) by minimizing the following:" + }, + { + "type": "equation", + "bbox": [ + 0.561, + 0.194, + 0.892, + 0.234 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {R G}} = - \\sum_ {t = 1} ^ {\\hat {n}} \\log p \\left(\\hat {y} _ {t} \\mid \\hat {y} _ {1}, \\dots , \\hat {y} _ {t - 1}, I\\right). \\tag {8}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.244, + 0.661, + 0.26 + ], + "angle": 0, + "content": "3.2. Dynamic Graph" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.267, + 0.892, + 0.569 + ], + "angle": 0, + "content": "The chest knowledge graph \\( G_{pre} \\) proposed in [46] has been widely integrated with CRG systems to emphasize the disease keywords and enhance their relationships. \\( G_{pre} \\) consists of 27 entities and a root node referring to the global feature and an adjacency matrix \\( A = \\{e_{ij}\\} \\) to represent the edges \\( V \\). Each node is a disease keyword and we set \\( e_{ij} \\) to 1 when source node \\( n_i \\) connects target node \\( n_j \\). Nodes linked to the same organ or tissue are connected to each other and the root. This graph is not updated during the training, and we found that it limits the effectiveness from two aspects. Firstly, those entities can not cover the most common disease keywords for all datasets because of the dataset bias; Secondly, entities linked to different organs can also affect each other clinically. To tackle those limitations, we propose a dynamic graph \\( G \\) with dynamic structure and nodes and integrate it with visual features to generate high-quality reports. This process is illustrated in Fig. 3, and we will introduce the three key modules, i.e., dynamic graph construction, dynamic graph encoder, and graph attention in this section, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.57, + 0.892, + 0.704 + ], + "angle": 0, + "content": "Dynamic Graph Construction We construct our graph in a bottom-up manner, in which we first construct the fundamental structure from general knowledge and then add nodes or redefine their relationships according to specific knowledge. We extend \\( G_{pre} \\) to our fundamental structure with 28 entities consisting of a global node represented by a [CLS] token, 7 organs or tissues, and 20 disease keywords. In addition to link criteria in \\( G_{pre} \\), every organ will connect to each other organ or tissue." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.892, + 0.901 + ], + "angle": 0, + "content": "To get the specific knowledge for each given image \\(I\\), we first retrieve the top-\\(n_T\\) similar reports \\(\\{T_i^*\\}_{i=1}^{n_T}\\) by calculating the similarity between the visual feature \\(\\mathbf{f}_I\\) and representations of reports in queue \\(\\{\\mathbf{f}_{T^*}^i\\}_{i=1}^{n_Q}\\), where \\(n_Q\\) is the length of the report queue. For each retrieved report, we extract anatomy and observation entities by Stanza [47]. Those entities are further utilized to quote the specific knowledge \\(K_I\\) from RadGraph [17]. Each triplet \\(k\\) in \\(K_I\\) aims to depict the relationship between source and target entities. There are three kinds of relations in RadGraph, namely 'suggestive of', 'modify' and 'located at'. For a triplet whose only source entity \\(e_s\\) or target entity \\(e_o\\) is in the graph, we will add another entity in the triplet as an ad" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3337" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.182 + ], + "angle": 0, + "content": "ditional node, and set their relation to 1 in the adjacency matrix \\( A \\). Note that if the relation is 'located at' and the entity needed to be added is the target entity \\( e_{o} \\), \\( e_{o} \\) will be treated as an organ/tissue node. In this bottom-up manner, our dynamic graph is capable to exploit both general and specific knowledge." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.183, + 0.471, + 0.258 + ], + "angle": 0, + "content": "Dynamic Graph Encoder We propose a dynamic graph encoder to propagate information and learn dedicated node features in our dynamic graph. To this end, this module is built upon the standard Transformer encoder layer \\(\\mathbf{f}_G\\) and conducted as (see Figure 3):" + }, + { + "type": "equation", + "bbox": [ + 0.177, + 0.269, + 0.468, + 0.285 + ], + "angle": 0, + "content": "\\[\n\\mathbf {f} _ {G} = \\mathrm {L N} \\left(\\mathrm {F F N} \\left(e _ {r s a}\\right) + e _ {r s a}\\right), \\tag {9}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.168, + 0.288, + 0.469, + 0.304 + ], + "angle": 0, + "content": "\\[\ne _ {r s a} = \\operatorname {L N} (\\operatorname {R S A} \\left(\\mathbf {f} _ {N}, A\\right) + \\mathbf {f} _ {N}), \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.314, + 0.47, + 0.586 + ], + "angle": 0, + "content": "where RSA is an MMHA-like relational self-attention module to encode the structural information of a graph to the model. Concretely, we utilize adjacency matrix \\(A\\) as a visible mask [24,33] to control the original MMHA. It promises that each node can only impact its linked nodes and enhance their relationships. \\(\\mathbf{f}_N\\) is the initialized nodes representations and consists of entity embedding and level encoding. Previous works initialized representations randomly, which limits the effectiveness seriously [49]. Moreover, some additional nodes appear a few times during the training and hard to find the best embeddings. Therefore, we first adopt word embeddings \\(\\epsilon_{sci}\\) from well-trained SciBert [4] to initialize each entity. For those entities consisting of one more word, e.g., 'foreign object', we calculate the average. Furthermore, we add level encoding \\(\\epsilon_l\\) to demonstrate each node is the root, organ, or disease keyword. Thus, the structural information of our graph is well represented and encoded during message passing and propagation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.586, + 0.47, + 0.646 + ], + "angle": 0, + "content": "Graph Attention Graph attention aims to integrate knowledge from dynamic graphs with visual features. Following [30], we utilize cross attention to achieve this goal. The whole process can be written as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.182, + 0.658, + 0.468, + 0.674 + ], + "angle": 0, + "content": "\\[\n\\mathbf {f} _ {\\bar {I}} = \\mathrm {L N} (\\mathrm {F F N} (e _ {g a}) + e _ {g a}), \\tag {11}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.174, + 0.677, + 0.469, + 0.693 + ], + "angle": 0, + "content": "\\[\ne _ {g a} = \\operatorname {L N} \\left(\\operatorname {C A} \\left(\\mathbf {f} _ {I}, \\mathbf {f} _ {G}\\right)\\right) + \\mathbf {f} _ {I}). \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.703, + 0.469, + 0.779 + ], + "angle": 0, + "content": "In each head, Query comes from visual features \\(\\mathbf{f}_I\\) while Key and Value come from the learned graph representations \\(\\mathbf{f}_G\\). Finally, we get the dynamic graph enhanced visual features \\(\\mathbf{f}_{\\hat{I}}\\). Notably, the first token in both \\(\\mathbf{f}_{\\hat{I}}\\) and \\(\\mathbf{f}_G\\) is [CLS] to aggregate visual and graph information." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.787, + 0.279, + 0.803 + ], + "angle": 0, + "content": "3.3. Contrastive Learning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Collecting paired image and text data is prohibitively expensive leading to a smaller size of CRG datasets compared with captioning datasets, like COCO [28]. It hinders the potential of existing data-driven CRG systems. In this section, we introduce the image-report contrastive loss used in our DCL, which can effectively improve the visual" + }, + { + "type": "image", + "bbox": [ + 0.521, + 0.089, + 0.875, + 0.285 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.3, + 0.892, + 0.342 + ], + "angle": 0, + "content": "Figure 3. illustration of our proposed dynamic graph construction, dynamic graph encoder (DGE), and graph attention (GA) modules. The structure of the pre-constructed graph can be found in Fig. 1." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.352, + 0.892, + 0.442 + ], + "angle": 0, + "content": "and textual representations as well as ensure the report retrieval accuracy in the dynamic graph construction process. Moreover, inspired by recent vision-language pretraining works [21,22], we also adopt an image-report matching loss in the proposed method for further enhancing the representations to improve the performance." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.443, + 0.893, + 0.675 + ], + "angle": 0, + "content": "Image-Report Contrastive Loss (IRC) can activate radiology reporting by encouraging the positive image-report pairs to have similar representations in contrast to the negative pairs. A report encoder with the same architecture as an image encoder is utilized to extract textual representations \\(\\mathbf{f}_T\\) referring to the positive or negative report. Then we calculate the similar between two [CLS] representations by \\(s = W_I(V_{cls})^t W_T(T_{cls})\\), where \\(W_I\\) and \\(W_T\\) are two learnable matrices. We also maintain two queues to store the most recent \\(M\\) image-report representations from the momentum image and report encoders. After a Softmax activation, we can get the image-report similarity \\(f_m^{i2r}(I) = \\frac{\\exp s(I,T_m) / \\tau}{\\sum_{m=1}^M \\exp s(I,T_m) / \\tau}\\) and the report-image similarity \\(f_m^{r2i}(T)\\), where \\(\\tau\\) is a learnable temperature parameter. The IRC can be written as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.52, + 0.682, + 0.891, + 0.711 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {I R C}} = \\frac {1}{2} \\left(\\mathcal {L} _ {\\mathrm {c e}} (g (T), f (T)) + \\mathcal {L} _ {\\mathrm {c e}} (g (I), f (I))\\right), \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.72, + 0.891, + 0.749 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{\\mathrm{ce}}\\) is the cross entropy loss and \\(g(I)\\) is the ground truth of image-report similarity." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.75, + 0.892, + 0.856 + ], + "angle": 0, + "content": "Image-Report Matching Loss (IRM) is a binary classification task to predict whether the given image-report pair is positive (matched) or negative (unmatched). Different from IRC, we utilize a multimodal encoder to capture the multimodal representations via cross attention mechanism. Then [Encode] vector is projected to \\( d = 2 \\) with a linear layer to predict the probability \\( p^{itm} \\). The IRM is conducted as:" + }, + { + "type": "equation", + "bbox": [ + 0.61, + 0.88, + 0.891, + 0.898 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {I R M}} = \\mathcal {L} _ {\\mathrm {c e}} \\left(g ^ {i t m}, p ^ {i t m}\\right). \\tag {14}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3338" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.152 + ], + "angle": 0, + "content": "Finally, we calculate the sum of \\(\\mathcal{L}_{\\mathrm{RG}}\\), \\(\\mathcal{L}_{\\mathrm{IRC}}\\) and \\(\\mathcal{L}_{\\mathrm{IRM}}\\) as our total loss function. Notably, the multimodal encoder is only used during the training process to improve representation learning." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.161, + 0.21, + 0.178 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.179, + 0.433, + 0.195 + ], + "angle": 0, + "content": "4.1. Datasets, Evaluation Metrics and Settings" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.203, + 0.468, + 0.263 + ], + "angle": 0, + "content": "We evaluate our proposed DCL on two widely-used radiology reporting benchmarks, IU-Xray [8] and MIMIC-CXR [18]. We adopt the settings in [7,30] to split those two datasets and preprocess the reports for a fair comparison." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.264, + 0.468, + 0.384 + ], + "angle": 0, + "content": "IU-Xray [8] has been widely used to evaluate the performance of radiology reporting systems. It contains 3,955 radiology reports and 7,470 chest xray images. Either frontal or frontal and lateral view images are associated with each report. Following [7, 20], we exclude those cases with only one image and finally get 2069/296/590 cases for training/validation/testing. By Stanza [47], 739 unique entities are extracted and utilized as dynamic node candidates." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.385, + 0.468, + 0.521 + ], + "angle": 0, + "content": "MIMIC-CXR [18] is the largest radiology dataset to date, consisting of 368,960 chest X-ray images and 222,758 radiology reports and is splitted officially. Recently, various MIMIC-child datasets have been proposed by exploring structural radiology information, e.g., Chest Image Genome [41] and RadGraph [17]. In this work, we adopt RadGraph to update our dynamic structure. Classified by relation, RadGraph consists of 2,895,725 (suggestive of), 6,115,264 (located at) and 4,010,875 (modify) triplets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.522, + 0.468, + 0.717 + ], + "angle": 0, + "content": "Natural Language Generation Metrics (NLG) are used to measure the descriptive accuracy of predicted reports. CIDEr [40] and BLEU [36] are two main NLG metrics used to measure the quality of predicted reports. BLEU is proposed for machine translation tasks and measures the word n-gram overlap between predictions and reports. Due to the textual bias in CRG datasets, CRG systems can achieve considerable BLEU values even when they just repeat the most frequent sentences. In contrast, CIDEr is tailored to evaluate captioning systems by rewarding topic terms (terminologies in CRG task) and penalizing frequent terms. Additionally, values of ROUGE-L [27] and METEOR [3] are also reported for comparison." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.719, + 0.468, + 0.869 + ], + "angle": 0, + "content": "Clinical Efficacy Metrics are recently proposed to capture and evaluate the clinical correctness of predicted reports. It first employs the CheXPert labeling tool proposed in [16] to label predicted reports and the ground truth reports in 14 different medical terminologies. Then classification measurements, i.e., F1-Score, Precision and Recall are calculated to evaluate how well the generated report describes the abnormalities. Since the provider of IU-Xray does not use CheXPert to build the labels, CE metrics are only reported on the MIMIC-CXR dataset [38, 44]." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.468, + 0.9 + ], + "angle": 0, + "content": "Experimental Settings We use the same image encoder for different views images and concatenate visual tokens via" + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.091, + 0.869, + 0.285 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.299, + 0.892, + 0.327 + ], + "angle": 0, + "content": "Figure 4. Micro-average of receiver operating characteristic curve for clinical abnormalities predictions from the generated reports." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.339, + 0.892, + 0.55 + ], + "angle": 0, + "content": "fusion operation for further process. Considering the domain gap between medical and generic texts, we employ a pretrained SciBert [4] to serve as a tokenizer and report encoder. The model is trained on 4 NVIDIA 2080 Ti GPUs with batch sizes 8 and 30 epochs. The checkpoint acquires the highest CIEDr metric is used for testing. The learning rate is set as 1e-4 and the optimizer is AdamW [34] with a weight decay of 0.02. The top 3 similar reports from the text queue \\( Q \\) are retrieved. And the size of \\( Q \\) is set as 65,536 and 1,380 for MIMIC-CXR and IU-Xray. The max length of specific knowledge is set as 90. For batch operation, the nodes in \\( G \\) are padded to 50 with a [PAD] token. Note that, we project all encoded vectors by a linear transformation layer into the dimension of \\( d = 768 \\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.561, + 0.638, + 0.575 + ], + "angle": 0, + "content": "4.2. Main Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.892, + 0.854 + ], + "angle": 0, + "content": "Descriptive Accuracy In Tab. 1, we compare our DCL with a wide range of existing state-of-the-art CRG systems on two benchmarks. R2Gen [7] and CMN [6] have been widely used as baseline CRG models recently. KERP [20], MKG [46], PPKED [30] and MGSK [44] are proposed to integrate medical knowledge with typical CRG backbones. CA [31] and CMCL [29] employ contrastive learning and curriculum learning to improve performance. The performances of other baseline models, such as HRGP [19], M2TR [35] and TopDown [1] are also reported. Since we follow the same settings, we directly cite the results from original papers. As shown in Tab. 1, our DCL achieves the SOTA descriptive accuracy, which outperforms others in CIDEr and ROUGE-L metrics and matches their performances in BLEU-4 and METEOR metrics. Higher CIDEr values demonstrate that our model does not repeat frequent sentences in training set but generates reports with more accurate topics." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Clinical Correctness We also evaluate our method by clinical efficacy (CE) metrics on the MIMIC-CXR dataset and compare the performances with other baseline models. Fol-" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "3339" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.894, + 0.281 + ], + "angle": 0, + "content": "
Iu-Xray [8]MIMIC-CXR [18]
MethodsCIDErBLEU-4ROUGE-LMETEORMethodsCIDErBLEU-4ROUGE-LMETEOR
R2Gen [7]0.3980.1650.3710.187R2Gen [7]0.2530.1030.2770.142
KERP [20]0.2800.1620.339-CMN [6]-0.1060.2780.142
HRGP [19]0.3430.1510.322-TopDown [1]0.0730.0920.2670.129
MKG [46]0.3040.1470.367-M2TR [35]-0.1070.2720.145
PPKED [30]0.3510.1680.3760.190PPKED [30]0.2370.1060.2840.149
MGSK [44]0.3820.1780.381-MGSK [44]0.2030.1150.284-
CA [31]-0.1690.3810.193CA [31]-0.1090.2830.151
CMCL [29]-0.1620.3780.186CMCL [29]-0.0970.2810.133
Ours0.5860.1630.3830.193Ours0.2810.1090.2840.150
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.29, + 0.893, + 0.319 + ], + "angle": 0, + "content": "Table 1. The performances of our proposed DCL compared with other state-of-the-art systems on IU-Xray and MIMIC-CXR dataset. The best results in each column are highlighted in bold. CIDEr [40] is proposed to evaluate captioning systems." + }, + { + "type": "table", + "bbox": [ + 0.102, + 0.328, + 0.446, + 0.487 + ], + "angle": 0, + "content": "
MethodsPrecisionRecallF1-score
TopDown [1]0.1660.1210.133
M2TR [35]0.2400.4280.308
R2Gen [7]0.3330.2730.276
MKSG [44]0.4580.3480.371
Ours w/o G0.2750.1850.194
Ours w/o LIRC0.4630.3370.359
Ours w/o LIRM0.4690.3530.372
Ours0.4710.3520.373
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.497, + 0.47, + 0.525 + ], + "angle": 0, + "content": "Table 2. The comparison of the clinical efficacy metrics on MIMIC-CXR dataset. The w/o is the abbreviation of without." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.539, + 0.47, + 0.734 + ], + "angle": 0, + "content": "lowing official splitting, we directly cite the results from [44] for comparison. In Fig. 4, we show the micro-average of ROC for 14 chesty terminologies prediction and present the AUC scores. 'Pleural Effusion' and 'Pleural Other' achieve the highest AUCs (0.82). The experimental results in Tab. 2 reveal that our DCL significantly outperforms the previous models on three CE metrics. Compared with the current SOTA method MGSK [44] that also leverages general prior knowledge and specific knowledge from RadGraph [17], we make a performance-boosting. The improvement verifies the importance of our dynamic graph concepts and also demonstrates that our system can predict more accurate clinical information." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.736, + 0.231, + 0.751 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.469, + 0.856 + ], + "angle": 0, + "content": "In this section, we conduct ablation studies on IU-Xray and MIMIC-CXR datasets to investigate the contribution of each component in our proposed DCL. Tab. 3 presents the quantitative analysis of DCL on IU-Xray with measuring descriptive accuracy. And clinical correctness evaluation is reported in Tab. 2. Our base model only keeps the image encoder and report decoder and employs \\(\\mathcal{L}_{\\mathrm{RG}}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.469, + 0.902 + ], + "angle": 0, + "content": "Effect of Dynamic Graph Our dynamic graph is constructed in a bottom-up manner, that exploits general knowledge from \\( G_{pre} \\) and specific knowledge \\( K_I \\) extracted from" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.33, + 0.892, + 0.572 + ], + "angle": 0, + "content": "retrieved Top-3 similar reports. Comparing the base model with settings (a) and (b), our dynamic graph can boost the performance of base model, substantially. More specifically, leveraging the general knowledge only lead to an increase on all NLG metrics by \\(15.2\\%\\) on CIDEr and \\(1.1\\%\\) on BLEU-4. By integrating specific knowledge, our dynamic graph can further boost the performances, e.g. \\(0.535 \\rightarrow 0.557\\) on CIDEr. It demonstrates the effectiveness and necessity of constructing dynamic graphs for each image. We hypothesize that this performance improvement may be due to that the dynamic knowledge can emphasize keywords when generating reports since dynamic nodes are from retrieved reports. It has been proved in Tab. 2, leveraging dynamic graph significantly improve the performances on all CE metrics, which means the generated reports can provide more accurate medical terminologies." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.571, + 0.892, + 0.78 + ], + "angle": 0, + "content": "Effect of Contrastive Learning Sequentially, we evaluate the effectiveness of two introduced learning objectives, i.e., image report contrastive loss (IRC) and image report matching loss (IRM). The performances of settings (b,c) in Tab. 2 show that both IRC and IRM can boost the base model performances. It proves the importance of visual and textual representation qualities since severe data bias in CRG datasets will degenerate the representation capabilities seriously. However, comparing (c) and (d), it is observed that IRC brings more improvement than IRM. We speculate the reason is that IRC can straightly improve visual and textual representations by aligning similar pairs. In contrast, IRM works on multimodal representations and represents unimodal in an indirect manner." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Choice of Parameter Initialization We employ a pretrained ViT [10] and SciBert [4] as image and report encoder in our implementation. It is worth noting that Transformers lack some of the inductive biases inherent to CNNs and therefore generalize bad with insufficient and unbalanced data [10]. Not surprisingly, comparing setting (f) and the full model, the performances drop steeply without pretrained ViT parameters. The performances of setting (e)" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "3340" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.11, + 0.089, + 0.862, + 0.272 + ], + "angle": 0, + "content": "
Settings\\(G_{pre}\\)\\(K_I\\)IRCIRMViT [10]SciBert [4]CIDErBLEU-4ROUGE-LMETEOR
Base✓✓0.3830.1330.2770.163
(a)✓✓✓0.5350.1440.3490.180
(b)✓✓✓✓0.5570.1500.3610.182
(c)✓✓✓✓✓0.5800.1610.3850.188
(d)✓✓✓✓✓0.5640.1550.3700.188
(e)✓✓✓✓✓0.5800.1580.3740.190
(f)✓✓✓✓✓0.5270.1580.3560.179
DCL✓✓✓✓✓✓0.5860.1630.3830.193
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.28, + 0.893, + 0.308 + ], + "angle": 0, + "content": "Table 3. Quantitative analysis of proposed method on IU-Xray dataset. The base model consists of an image encoder and a report decoder with report generation loss only." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.31, + 0.889, + 0.416 + ], + "angle": 0, + "content": "
ImageGround Truth ReportRetrieved Specific KnowledgeOursR2Gen
Lateral view somewhat limited due to overlying motion artifact lungs are low in volume there is no focal airspace the consolidation to suggest pneumonia a 1 2-cm calcified granuloma just below the medial aspect of the right hemidiaphragm is unchanged from prior study no pleural effusions or pulmonary edema there is no pneumothorax the inferior sternotomy wire is fractured but unchanged surgical clips and vascular markers in the thorax are related to prior cabg surgery.effusion located _ at pleural,vascular modify pulmonary, sternotomy suggestive _ of cabg,consolidation suggestive _ of effusion,effusion suggestive _ of consolidation,low modify effusion,low suggestive _ of effusion, low suggestive _ of consolidation,vascular modify chest,effusion suggestive _ of atelectasis,atelectasis modify lunglung volumes are low. there is no focal consolidation effusion or pneumothorax. airspace consolidation is noted within the left upper lobe compatible with pneumonia. borderline size of the cardiac silhouette without evidence of pulmonary edema, midline sternotomy wires and mediastinal clips are again noted.ap upright and lateral views of the chest provided . lung volumes are low limiting assessment . allowing for this there is no focal consolidation effusion or pneumothorax . the cardiomeiastinal silhouette is normal . imaged osseous structures are intact . no free air below the right hemidiaphragm is seen.
" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.426, + 0.893, + 0.456 + ], + "angle": 0, + "content": "Figure 5. Illustrations of reports from ground truth, ours and R2Gen [7] and retrieved specific knowledge for one sample from MIMIC-CXR [18]. For better visualization, different colors highlight different medical entities." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.466, + 0.471, + 0.557 + ], + "angle": 0, + "content": "demonstrate the effectiveness of pretrained SciBert. The improvement comes from two aspects. Firstly, it provides well pretrained parameters; Secondly, its tokenizer encodes each token (medical terminology) with a well pretrained embedding, which avoids Graph Transformers to propagate similar hidden states [49]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.565, + 0.201, + 0.581 + ], + "angle": 0, + "content": "4.4. Case Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.584, + 0.471, + 0.903 + ], + "angle": 0, + "content": "To further investigate the effectiveness of our method, we perform qualitative analysis on MIMIC-CXR [18] with their retrieved specific knowledge, and reports from ground truth, our model and R2Gen [7]. Entities extracted by Stanza [47] from the ground truth report have been highlighted with different colors. It is observed that some entities, e.g. cabg, consolidation, and sternotomy) are not included in the pre-constructed graph node lists. This observation proves our motivation for constructing knowledge graphs dynamically. We conduct the same operation on retrieved reports and use extracted entities to quote related triplets from RadGraph [17]. Those triplets are known as specific knowledge in this paper and shown in Fig. 5. Retrieved specific knowledge triplets \\(<\\) sternotomy,suggestive_of,cabg> and \\(<\\) consolidation,suggestive_of,effusion> demonstrate that the retrieved reports contain similar medical terminologies and clinical information. We speculate that IRC and IRM objectives bring such capabilities. Then the entities in our dynamic graph emphasize disease/organ keywords when generating reports and it is why our DCL can predict sen" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.467, + 0.893, + 0.497 + ], + "angle": 0, + "content": "tence \"airspace consolidation is noted within the left upper lobe compatible with pneumonia,\" but R2Gen can not." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.5, + 0.749, + 0.515 + ], + "angle": 0, + "content": "5. Conclusion and Discussion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.518, + 0.893, + 0.699 + ], + "angle": 0, + "content": "In this paper, we present a practical approach to leverage dynamic graph to enhance contrastive learning for radiology report generation. In which the dynamic graph is constructed in a bottom-up manner to integrate retrieved specific knowledge with general knowledge. Then contrastive learning is employed to improve visual and textual representations, which also promises the accuracy of our dynamic graph. Experiments on two popular benchmarks verify the effectiveness of our method in generating accurate and meaningful reports. More encouragingly, our approach can outperform or match existing SOTA methods in language generation and clinical efficacy metrics." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.699, + 0.892, + 0.82 + ], + "angle": 0, + "content": "Limitation and Future Work Retrieved reports can not be exactly the same as ground truth, and knowledge noises are involved during the dynamic graph construction process. It may guide the model to generate inaccurate sentences. In the future, we plan to propose a specific objective for the dynamic graph construction process to further improve the accuracy of dynamic graphs and the quality of predicted reports." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.823, + 0.669, + 0.839 + ], + "angle": 0, + "content": "Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.893, + 0.9 + ], + "angle": 0, + "content": "This work was partially supported by \"Taishan Scholars Youth Expert Program\" of Shandong Province, and partially supported by National Key R&D Program of China under Grant No. 2020AAA0109700." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "3341" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.198 + ], + "angle": 0, + "content": "[1] Peter Anderson, Xiaodong He, Chris Buehler, Damien Teney, Mark Johnson, Stephen Gould, and Lei Zhang. 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In Proceedings of the Conference on Neural Information Processing Systems, 2022. 5, 8" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.894, + 0.881 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3343" + } + ] +] \ No newline at end of file diff --git a/2023/Dynamic Graph Enhanced Contrastive Learning for Chest X-Ray Report Generation/7bbdab16-5f4c-46f9-abdb-480a53791847_origin.pdf b/2023/Dynamic Graph Enhanced Contrastive Learning for Chest X-Ray Report Generation/7bbdab16-5f4c-46f9-abdb-480a53791847_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..a134e9002ed318ab3862539f2959cf24def290ec --- /dev/null +++ b/2023/Dynamic Graph Enhanced Contrastive Learning for Chest X-Ray Report Generation/7bbdab16-5f4c-46f9-abdb-480a53791847_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:e65be62c13ae1b5ebe07dca53444b3896b161bfd641448053ab79b648ee2214e +size 3733514 diff --git a/2023/Dynamic Graph Enhanced Contrastive Learning for Chest X-Ray Report Generation/full.md b/2023/Dynamic Graph Enhanced Contrastive Learning for Chest X-Ray Report Generation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..78a1282402fcdab67f79578d2844de56edce0bf4 --- /dev/null +++ b/2023/Dynamic Graph Enhanced Contrastive Learning for Chest X-Ray Report Generation/full.md @@ -0,0 +1,311 @@ +# Dynamic Graph Enhanced Contrastive Learning for Chest X-ray Report Generation + +Mingjie Li $^{1}$ Bingqian Lin $^{2}$ Zicong Chen $^{5}$ Haokun Lin $^{2}$ Xiaodan Liang $^{2,3,4}$ Xiaojun Chang $^{1*}$ + +$^{1}$ ReLER, AAII, University of Technology Sydney $^{2}$ School of ISE, Sun Yat-Sen University $^{3}$ Department of Computer Vision, Mohamed bin Zayed University of Artificial Intelligence + +$^{4}$ Peng Cheng National Lab $^{5}$ The University of Hong Kong + +# Abstract + +Automatic radiology reporting has great clinical potential to relieve radiologists from heavy workloads and improve diagnosis interpretation. Recently, researchers have enhanced data-driven neural networks with medical knowledge graphs to eliminate the severe visual and textual bias in this task. The structures of such graphs are exploited by using the clinical dependencies formed by the disease topic tags via general knowledge and usually do not update during the training process. Consequently, the fixed graphs can not guarantee the most appropriate scope of knowledge and limit the effectiveness. To address the limitation, we propose a knowledge graph with Dynamic structure and nodes to facilitate chest X-ray report generation with Contrastive Learning, named DCL. In detail, the fundamental structure of our graph is pre-constructed from general knowledge. Then we explore specific knowledge extracted from the retrieved reports to add additional nodes or redefine their relations in a bottom-up manner. Each image feature is integrated with its very own updated graph before being fed into the decoder module for report generation. Finally, this paper introduces Image-Report Contrastive and Image-Report Matching losses to better represent visual features and textual information. Evaluated on IU-Xray and MIMIC-CXR datasets, our DCL outperforms previous state-of-the-art models on these two benchmarks. + +# 1. Introduction + +Recently, automatic report generation has received growing attentions from both machine learning and automatic medicine fields. It aims to generate semantically coherent and informative reports to describe the referring examination images, such as Chest X-Ray [8, 18], Lung CT Scan [26] or funds angiography [23]. Such techniques have great clinical potential in relieving junior radiologists from heavy workloads and reducing diagnosis errors by improv- + +![](images/0172bbe2ff52d24362741d5239404e42be5e169a4432cbc62aefea1e4a9c6982.jpg) +Ground Truth Report + +A single portable AP semi-upright view of the chest was obtained. Cardiomediastinal silhouette including moderate cardiomegaly is stable. An ICD device is also unchanged in position. Interval development of increased opacification in the right lower lung probably reflects asymmetric edema and a layering effusion... + +![](images/bb4855157e79078ddbefd3e1153239bcc9205dd4f38ea965ae8b0a05b1c67f70.jpg) +Figure 1. An illustration of one sample from MIMIC-CXR [18] and the pre-constructed graph in [46], where the blue circle, orange boxes and black boxes refer to the global node, organ-level entities and key findings, respectively. The red dash line here represents the unconnected relation. + +ing the interpretation [7, 30]. + +Witnessed the great progress in artificial intelligence, especially deep learning methods [12,25,39], researchers have proposed various data-driven neural networks for radiology reporting and achieved promising performances in metrics that measure descriptive accuracy [7, 44] and clinical correctness [11, 46]. Compared with the similar task generic image captioning [14], the key challenges in chest X-ray report generation (CRG) task are the severe visual and textual data bias [19, 26]. On the one hand, medical images are highly similar to each other due to the imaging methods and human tissues themselves. However, abnormal regions or lesions that should acquire more attentions usually locate at a small part and lack detailed annotations in existing CRG benchmarks. On the other hand, sentences that describe normal regions are likely to appear repeatedly among each dataset which disables the model to describe specific crucial abnormalities. Two concepts have been proved ef + +fective in eliminating those bias. + +The first one is to integrate medical knowledge with ORG systems [24,30,44,46]. Zhang et al. [46] constructed a universal graph comprised of a global node, 7 organs/tissues and 20 findings (normal or disease keywords). Disease keyword nodes linked to the same organ are connected to each other and the root in the graph. This graph can enhance the relationships among findings and emphasize the disease keywords. Thus, it is also adopted in the following works [30, 44]. However, this graph is built from general knowledge and may be inappropriate in some cases. As the shown report in Fig. 1, it is observed that effusion should be suggestive of edema, however, such relationship is not modelled in the graph. Furthermore, some nodes like 'cicatrix' or 'hypoinflation' only appear very few times in two ORG benchmarks [8, 18]. Therefore, it is necessary to update the scope of knowledge for each case; In addition to the medical knowledge, recent works [5, 11, 31, 38, 43] utilize contrastive learning to improve the visual and textual representations by contrasting positive and negative pairs. They proposed various contrastive learning objectives to capture the abnormal regions from a chest X-Ray image. Since normal images usually dominate the dataset over abnormal ones [37], it is also crucial to recognize the normal or abnormal cases in the meantime. + +In this paper, we propose a novel framework, named DCL, which exploits a dynamic graph integrating specific knowledge with general knowledge to enhance visual representations learned in a contrastive manner. We adopt the general knowledge with 28 entities from [46] as the fundamental structure of our graph, and the relationships are modelled in an adjacency matrix. Given a medical image, we first retrieve its semantically similar reports from the training set. Specific knowledge is extracted from those reports via RadGraph [17] and stored in triplets (). And we integrate those triplets with the pre-constructed graph by dynamically adding additional nodes or linking two entities. We utilize a graph encoder to propagate information over the updated graph for refining the node features, which are initialized by a pretrained SciBert [4]. Then the dedicated node features are attended to visual representations for report generation via a Transformer [39] decoder. Based on the dynamic graph, we introduce a contrastive learning objective, image-report contrastive loss to well represent the visual features and textual information. In addition, contrastive learning can help ensure the accuracy of the report retrieval procedure in the dynamic graph construction process. Image-report matching loss is also employed to further improve the performances. + +We evaluate our method on two benchmarks, IU-Xray [8] and MIMIC-CXR [18]. Experimental results demonstrate that our approach can either outperform or + +match previous state-of-the-art (SOTA) methods in metrics that measure descriptive accuracy and clinical correctness. It indicates that leveraging dynamic graphs to enhance contrastive learning is helpful to generate high-quality reports. + +In summary, our main contributions are as follows: + +- We propose a novel framework that leverages a dynamic graph to enhance visual representations with contrastive learning paradigms for radiology reporting. +- Our proposed dynamic graph integrates both general and specific knowledge; The contrastive learning objective can improve visual and textual representations and dynamic graph accuracy. +- We conduct extensive experiments on two popular benchmarks to show the effectiveness of our approach, which achieves the SOTA performance on both language generation and clinical efficacy metrics. + +# 2. Related Work + +# 2.1. Medical Report Generation Meets Knowledge Graph + +When radiologists write reports, they will make inferences with their expert knowledge. Typically, a report contains many sections, e.g., impressions, finding, comparison and indication. Following the previous works, we combine the impressions and finding sections as the target for report generation. To endow the medical report generation systems with the capability to incorporate medical knowledge, various kinds of knowledge graphs have been explored and can be roughly divided into three groups. The first kind is proposed to emphasize the abnormal terminologies or disease keywords. Li et al. [20] collected abnormalities from MIMIC-CXR dataset, and utilized them as the node of their proposed abnormality graph. Edges here are the attention weights from source nodes to target nodes in the graph. Such graph is adopted in the following works [26, 48] as prior medical knowledge to enhance the generation procedure and can even facilitate the unsupervised learning framework [32]. Secondly, Zhang et al. [46] and Liu et al. [30] adopted a universal graph with 20 entities. Entities linked to the same organ are connected to each other in the graph. Such relationships are modelled into an adjacency matrix and utilized to propagate messages in a graph encoding module. Since this graph is pre-constructed with prior knowledge in a fixed structure, we found that it can not guarantee the appropriate scope of knowledge for some cases (e.g. missing or unconnected common entities). To tackle this challenge, Liu et al. [30] utilized the global representations from pre-retrieved reports from the training corpus to model domain-specific knowledge. In contrast, we aim to directly update the pre-constructed graph to + +![](images/f3b8b9302222eee942f3c237b61f49be92d3f12480fa0bb0c8eddc8656aca700.jpg) +Figure 2. Illustration of our proposed Dynamic graph enhanced Contrastive Learning approach (DCL). DCL contains two unimodal encoders, a multimodal encoder, a report decoder and three dynamic graph modules for construction, encoding and cross-modal attention, respectively. In addition to Report Generation (RG) loss, Image-Report Contrastive (IRC) loss and Image-Report Matching (IRM) loss are adopted for training DCL. + +model the appropriate knowledge. In the last, Li et al. [24] constructed a clinical graph by extracting structural information from the training corpus via a NLP-rule-based algorithm. They restored a set of triplets for each case to model the domain-specific knowledge and replace the visual representations. + +Our approach is based on the second category. Instead of using the fixed graph in [46], we dynamically update the graph by injecting new knowledge extracted from the retrieved reports for each case. As a result, the appropriate scope of knowledge for different cases can be activated to generate more high-quality reports. + +# 2.2. Contrastive Learning + +The goal of contrastive learning is to improve representation learning by contrasting positive/negative or similar/dissimilar pairs. Inspired by the recent success of contrastive learning in vision-and-language pretraining tasks [21], some works have introduced it in the CRG systems. Yan et al. [43] developed a weakly supervised method to contrast target reports with incorrect ones by identifying "hard" negative samples. To detect the abnormal regions, Liu et al. [31] compared the referring image with known normal images via a contrastive attention mechanism. Other works [5, 42, 45] employed contrastive learning during the pretraining process to better represent visual features and textual information. All those works aimed to improve the expressiveness of both visual and textual representations and then facilitate radiology reporting. In our + +work, contrastive learning can also improve the accuracy of the dynamic graph by training the model to retrieve the most semantically similar reports. + +# 3. Methodology + +In this section, we will introduce the detailed implementations of our proposed Dynamic graph enhanced Contrastive Learning approach (DCL). The overall structure of DCL is illustrated in Fig. 2, which contains four basic modules and three dynamic graph modules with three training objectives. We first describe the background of DCL and then introduce the dynamic graph modules and contrastive learning objectives, respectively. + +# 3.1. Background + +Notation In this work, we aim to leverage dynamic graphs to enhance contrastive learning for radiology reporting. In the CRG task, the computer is asked to describe a given medical image $I$ with a free-text report $T = \{y_{1}, y_{2}, \ldots, y_{n}\}$ . We denote the target report by $\hat{T} = \{\hat{y}_{1}, \hat{y}_{2}, \ldots, \hat{y}_{\hat{n}}\}$ . $n$ and $\hat{n}$ represent the numbers of tokens in a report. Our dynamic graph, denoted by $G = \{V, E\}$ , where $V$ and $E$ are the sets of nodes and edges, respectively, is built on a pre-constructed graph $G_{pre}$ proposed in [46] and updated with specific knowledge $K_{I} = \{k_{I}^{1}, \ldots, k_{I}^{n_{K}}\}$ extracted from retrieved reports $\{T_{i}^{*}\}_{i=1}^{n_{T}}$ . Each $k$ is stored in a triplet format, which consists of a subjective entity $e_{s}$ , an objective entity $e_{o}$ and their relation $r$ . $n_{T}$ and $n_{K}$ are the numbers of reports and triplets, respectively. All the + +triplets are acquired from the RadGraph [17]. + +Typical CRG systems are encoder-decoder frameworks. The encoder is usually a CNN, e.g., ResNet [12] or DenseNet [15], encodes the given image $I$ to dense visual vectors $\mathbf{f}_I$ . The decoder is usually a RNN (e.g., LSTM [13]) or a Transformer [39], which decodes $\mathbf{f}_I$ to a report $T$ . In this work, we adopt the Transformer [39] as the backbone to generate the long and robust reports. + +Image Encoder Recently, visual Transformers have shown superior capabilities to represent images than CNNs. Thus, we only employ a ViT [10] pretrained on the ImageNet [9] as the image encoder to simplify the architecture. The input image will be divided into 196 patches, and a [CLS] token is further appended to the beginning of sequence before being fed into the encoder layers. The whole process of an encoder layer $\mathbf{f}_e(\cdot)$ can be written as follows: + +$$ +\mathbf {f} _ {e} (x) = \operatorname {L N} \left(\operatorname {F F N} \left(e _ {\text {a t t n}}\right) + e _ {\text {a t t n}}\right), \tag {1} +$$ + +$$ +e _ {a t t n} = \operatorname {L N} (\mathrm {M H A} (x) + x), \tag {2} +$$ + +where FFN and LN denote the Feed Forward Network [39] and Layer Normalization operation [2], respectively. $x$ is the input of each encoder layer. MHA [39] (multi-head attention) divides a scaled dot-product attention into $n$ parallel heads and each head $\mathrm{Att}(\cdot)$ can be written as follows: + +$$ +\operatorname {A t t} (x) = \operatorname {s o f t m a x} \left(\frac {\mathbf {Q} ^ {x} \left(\mathbf {K} ^ {x}\right) ^ {\top}}{\sqrt {d}}\right) \mathbf {V} ^ {x}, \tag {3} +$$ + +where $d = 768$ is the dimension of the embedding space and $\{\mathbf{Q},\mathbf{K}^{*},\mathbf{V}^{*}\}$ are the packed $d$ -dimensional Query, Key, Value vectors, respectively. The final output is the encoded visual vectors $\mathbf{f}_I$ , which will be used for report generation. + +Report Decoder Our report decoder consists of two Transformer decoder layers. The whole process of a decoder layer $\mathbf{f}_d(\cdot)$ can be written as follows: + +$$ +\mathbf {f} _ {d} (\mathbf {y}) = \mathrm {L N} \left(\mathrm {F F N} \left(e _ {c a}\right) + e _ {c a}\right), \tag {4} +$$ + +$$ +e _ {c a} = \mathrm {L N} \left(\mathrm {C A} \left(e _ {\text {a t t n}}, \mathbf {f} _ {I}\right) + e _ {\text {a t t n}}\right), \tag {5} +$$ + +$$ +e _ {a t t n} = \operatorname {L N} (\operatorname {M M H A} (\mathbf {y}) + \mathbf {y})), \tag {6} +$$ + +where MMHA and CA represent the masked multi-head self-attention and cross attention mechanism in [39]. $\mathbf{y}$ is the input of decoder. A [Decode] token is added to the beginning of $\mathbf{y}$ to signal the start while a [EOS] token is to signal its end. In Cross-attention sublayer, for each head, $\{\mathbf{Q},\mathbf{K}^{*},\mathbf{V}^{*}\}$ comes from $\mathbf{Q} = W_{q}*e_{attn}$ , $\mathbf{K} = W_{k}*\mathbf{f}_{I}$ , and $\mathbf{V} = W_{v}*\mathbf{f}_{I}$ , where $W_{*}$ are the learnable parameters. The $f_{d}(\mathbf{y})$ will be sent to a Linear & Log-Softmax layer to get the output of target sentences. Notably, only token embedding is adopted during the decoding procedure. The entire auto-regressive generation process can be written as follows: + +$$ +p (T | I) = \prod_ {t = 1} p \left(y _ {t} \mid y _ {1}, \dots , y _ {t - 1}, I\right). \tag {7} +$$ + +where $y_{t}$ is the input token in time step $t$ . + +Typically, the report generation objective is the cross-entropy loss to compare the predicted token index sequence with the ground truth. Given the ground truth report $\hat{T}$ , all the underlying modules are trained to maximize $p(\mathbf{y} | I)$ by minimizing the following: + +$$ +\mathcal {L} _ {\mathrm {R G}} = - \sum_ {t = 1} ^ {\hat {n}} \log p \left(\hat {y} _ {t} \mid \hat {y} _ {1}, \dots , \hat {y} _ {t - 1}, I\right). \tag {8} +$$ + +# 3.2. Dynamic Graph + +The chest knowledge graph $G_{pre}$ proposed in [46] has been widely integrated with CRG systems to emphasize the disease keywords and enhance their relationships. $G_{pre}$ consists of 27 entities and a root node referring to the global feature and an adjacency matrix $A = \{e_{ij}\}$ to represent the edges $V$ . Each node is a disease keyword and we set $e_{ij}$ to 1 when source node $n_i$ connects target node $n_j$ . Nodes linked to the same organ or tissue are connected to each other and the root. This graph is not updated during the training, and we found that it limits the effectiveness from two aspects. Firstly, those entities can not cover the most common disease keywords for all datasets because of the dataset bias; Secondly, entities linked to different organs can also affect each other clinically. To tackle those limitations, we propose a dynamic graph $G$ with dynamic structure and nodes and integrate it with visual features to generate high-quality reports. This process is illustrated in Fig. 3, and we will introduce the three key modules, i.e., dynamic graph construction, dynamic graph encoder, and graph attention in this section, respectively. + +Dynamic Graph Construction We construct our graph in a bottom-up manner, in which we first construct the fundamental structure from general knowledge and then add nodes or redefine their relationships according to specific knowledge. We extend $G_{pre}$ to our fundamental structure with 28 entities consisting of a global node represented by a [CLS] token, 7 organs or tissues, and 20 disease keywords. In addition to link criteria in $G_{pre}$ , every organ will connect to each other organ or tissue. + +To get the specific knowledge for each given image $I$ , we first retrieve the top- $n_T$ similar reports $\{T_i^*\}_{i=1}^{n_T}$ by calculating the similarity between the visual feature $\mathbf{f}_I$ and representations of reports in queue $\{\mathbf{f}_{T^*}^i\}_{i=1}^{n_Q}$ , where $n_Q$ is the length of the report queue. For each retrieved report, we extract anatomy and observation entities by Stanza [47]. Those entities are further utilized to quote the specific knowledge $K_I$ from RadGraph [17]. Each triplet $k$ in $K_I$ aims to depict the relationship between source and target entities. There are three kinds of relations in RadGraph, namely 'suggestive of', 'modify' and 'located at'. For a triplet whose only source entity $e_s$ or target entity $e_o$ is in the graph, we will add another entity in the triplet as an ad + +ditional node, and set their relation to 1 in the adjacency matrix $A$ . Note that if the relation is 'located at' and the entity needed to be added is the target entity $e_{o}$ , $e_{o}$ will be treated as an organ/tissue node. In this bottom-up manner, our dynamic graph is capable to exploit both general and specific knowledge. + +Dynamic Graph Encoder We propose a dynamic graph encoder to propagate information and learn dedicated node features in our dynamic graph. To this end, this module is built upon the standard Transformer encoder layer $\mathbf{f}_G$ and conducted as (see Figure 3): + +$$ +\mathbf {f} _ {G} = \mathrm {L N} \left(\mathrm {F F N} \left(e _ {r s a}\right) + e _ {r s a}\right), \tag {9} +$$ + +$$ +e _ {r s a} = \operatorname {L N} (\operatorname {R S A} \left(\mathbf {f} _ {N}, A\right) + \mathbf {f} _ {N}), \tag {10} +$$ + +where RSA is an MMHA-like relational self-attention module to encode the structural information of a graph to the model. Concretely, we utilize adjacency matrix $A$ as a visible mask [24,33] to control the original MMHA. It promises that each node can only impact its linked nodes and enhance their relationships. $\mathbf{f}_N$ is the initialized nodes representations and consists of entity embedding and level encoding. Previous works initialized representations randomly, which limits the effectiveness seriously [49]. Moreover, some additional nodes appear a few times during the training and hard to find the best embeddings. Therefore, we first adopt word embeddings $\epsilon_{sci}$ from well-trained SciBert [4] to initialize each entity. For those entities consisting of one more word, e.g., 'foreign object', we calculate the average. Furthermore, we add level encoding $\epsilon_l$ to demonstrate each node is the root, organ, or disease keyword. Thus, the structural information of our graph is well represented and encoded during message passing and propagation. + +Graph Attention Graph attention aims to integrate knowledge from dynamic graphs with visual features. Following [30], we utilize cross attention to achieve this goal. The whole process can be written as follows: + +$$ +\mathbf {f} _ {\bar {I}} = \mathrm {L N} (\mathrm {F F N} (e _ {g a}) + e _ {g a}), \tag {11} +$$ + +$$ +e _ {g a} = \operatorname {L N} \left(\operatorname {C A} \left(\mathbf {f} _ {I}, \mathbf {f} _ {G}\right)\right) + \mathbf {f} _ {I}). \tag {12} +$$ + +In each head, Query comes from visual features $\mathbf{f}_I$ while Key and Value come from the learned graph representations $\mathbf{f}_G$ . Finally, we get the dynamic graph enhanced visual features $\mathbf{f}_{\hat{I}}$ . Notably, the first token in both $\mathbf{f}_{\hat{I}}$ and $\mathbf{f}_G$ is [CLS] to aggregate visual and graph information. + +# 3.3. Contrastive Learning + +Collecting paired image and text data is prohibitively expensive leading to a smaller size of CRG datasets compared with captioning datasets, like COCO [28]. It hinders the potential of existing data-driven CRG systems. In this section, we introduce the image-report contrastive loss used in our DCL, which can effectively improve the visual + +![](images/ea6ed29b4b8fd7201931b6f6c67cd8e9724f068a6cc5d277b58feca0db3525ec.jpg) +Figure 3. illustration of our proposed dynamic graph construction, dynamic graph encoder (DGE), and graph attention (GA) modules. The structure of the pre-constructed graph can be found in Fig. 1. + +and textual representations as well as ensure the report retrieval accuracy in the dynamic graph construction process. Moreover, inspired by recent vision-language pretraining works [21,22], we also adopt an image-report matching loss in the proposed method for further enhancing the representations to improve the performance. + +Image-Report Contrastive Loss (IRC) can activate radiology reporting by encouraging the positive image-report pairs to have similar representations in contrast to the negative pairs. A report encoder with the same architecture as an image encoder is utilized to extract textual representations $\mathbf{f}_T$ referring to the positive or negative report. Then we calculate the similar between two [CLS] representations by $s = W_I(V_{cls})^t W_T(T_{cls})$ , where $W_I$ and $W_T$ are two learnable matrices. We also maintain two queues to store the most recent $M$ image-report representations from the momentum image and report encoders. After a Softmax activation, we can get the image-report similarity $f_m^{i2r}(I) = \frac{\exp s(I,T_m) / \tau}{\sum_{m=1}^M \exp s(I,T_m) / \tau}$ and the report-image similarity $f_m^{r2i}(T)$ , where $\tau$ is a learnable temperature parameter. The IRC can be written as follows: + +$$ +\mathcal {L} _ {\mathrm {I R C}} = \frac {1}{2} \left(\mathcal {L} _ {\mathrm {c e}} (g (T), f (T)) + \mathcal {L} _ {\mathrm {c e}} (g (I), f (I))\right), \tag {13} +$$ + +where $\mathcal{L}_{\mathrm{ce}}$ is the cross entropy loss and $g(I)$ is the ground truth of image-report similarity. + +Image-Report Matching Loss (IRM) is a binary classification task to predict whether the given image-report pair is positive (matched) or negative (unmatched). Different from IRC, we utilize a multimodal encoder to capture the multimodal representations via cross attention mechanism. Then [Encode] vector is projected to $d = 2$ with a linear layer to predict the probability $p^{itm}$ . The IRM is conducted as: + +$$ +\mathcal {L} _ {\mathrm {I R M}} = \mathcal {L} _ {\mathrm {c e}} \left(g ^ {i t m}, p ^ {i t m}\right). \tag {14} +$$ + +Finally, we calculate the sum of $\mathcal{L}_{\mathrm{RG}}$ , $\mathcal{L}_{\mathrm{IRC}}$ and $\mathcal{L}_{\mathrm{IRM}}$ as our total loss function. Notably, the multimodal encoder is only used during the training process to improve representation learning. + +# 4. Experiments + +# 4.1. Datasets, Evaluation Metrics and Settings + +We evaluate our proposed DCL on two widely-used radiology reporting benchmarks, IU-Xray [8] and MIMIC-CXR [18]. We adopt the settings in [7,30] to split those two datasets and preprocess the reports for a fair comparison. + +IU-Xray [8] has been widely used to evaluate the performance of radiology reporting systems. It contains 3,955 radiology reports and 7,470 chest xray images. Either frontal or frontal and lateral view images are associated with each report. Following [7, 20], we exclude those cases with only one image and finally get 2069/296/590 cases for training/validation/testing. By Stanza [47], 739 unique entities are extracted and utilized as dynamic node candidates. + +MIMIC-CXR [18] is the largest radiology dataset to date, consisting of 368,960 chest X-ray images and 222,758 radiology reports and is splitted officially. Recently, various MIMIC-child datasets have been proposed by exploring structural radiology information, e.g., Chest Image Genome [41] and RadGraph [17]. In this work, we adopt RadGraph to update our dynamic structure. Classified by relation, RadGraph consists of 2,895,725 (suggestive of), 6,115,264 (located at) and 4,010,875 (modify) triplets. + +Natural Language Generation Metrics (NLG) are used to measure the descriptive accuracy of predicted reports. CIDEr [40] and BLEU [36] are two main NLG metrics used to measure the quality of predicted reports. BLEU is proposed for machine translation tasks and measures the word n-gram overlap between predictions and reports. Due to the textual bias in CRG datasets, CRG systems can achieve considerable BLEU values even when they just repeat the most frequent sentences. In contrast, CIDEr is tailored to evaluate captioning systems by rewarding topic terms (terminologies in CRG task) and penalizing frequent terms. Additionally, values of ROUGE-L [27] and METEOR [3] are also reported for comparison. + +Clinical Efficacy Metrics are recently proposed to capture and evaluate the clinical correctness of predicted reports. It first employs the CheXPert labeling tool proposed in [16] to label predicted reports and the ground truth reports in 14 different medical terminologies. Then classification measurements, i.e., F1-Score, Precision and Recall are calculated to evaluate how well the generated report describes the abnormalities. Since the provider of IU-Xray does not use CheXPert to build the labels, CE metrics are only reported on the MIMIC-CXR dataset [38, 44]. + +Experimental Settings We use the same image encoder for different views images and concatenate visual tokens via + +![](images/7407a8d427a25fa7fad2690310394273c65d47752003f30fb1585cc2b269d060.jpg) +Figure 4. Micro-average of receiver operating characteristic curve for clinical abnormalities predictions from the generated reports. + +fusion operation for further process. Considering the domain gap between medical and generic texts, we employ a pretrained SciBert [4] to serve as a tokenizer and report encoder. The model is trained on 4 NVIDIA 2080 Ti GPUs with batch sizes 8 and 30 epochs. The checkpoint acquires the highest CIEDr metric is used for testing. The learning rate is set as 1e-4 and the optimizer is AdamW [34] with a weight decay of 0.02. The top 3 similar reports from the text queue $Q$ are retrieved. And the size of $Q$ is set as 65,536 and 1,380 for MIMIC-CXR and IU-Xray. The max length of specific knowledge is set as 90. For batch operation, the nodes in $G$ are padded to 50 with a [PAD] token. Note that, we project all encoded vectors by a linear transformation layer into the dimension of $d = 768$ . + +# 4.2. Main Results + +Descriptive Accuracy In Tab. 1, we compare our DCL with a wide range of existing state-of-the-art CRG systems on two benchmarks. R2Gen [7] and CMN [6] have been widely used as baseline CRG models recently. KERP [20], MKG [46], PPKED [30] and MGSK [44] are proposed to integrate medical knowledge with typical CRG backbones. CA [31] and CMCL [29] employ contrastive learning and curriculum learning to improve performance. The performances of other baseline models, such as HRGP [19], M2TR [35] and TopDown [1] are also reported. Since we follow the same settings, we directly cite the results from original papers. As shown in Tab. 1, our DCL achieves the SOTA descriptive accuracy, which outperforms others in CIDEr and ROUGE-L metrics and matches their performances in BLEU-4 and METEOR metrics. Higher CIDEr values demonstrate that our model does not repeat frequent sentences in training set but generates reports with more accurate topics. + +Clinical Correctness We also evaluate our method by clinical efficacy (CE) metrics on the MIMIC-CXR dataset and compare the performances with other baseline models. Fol- + +
Iu-Xray [8]MIMIC-CXR [18]
MethodsCIDErBLEU-4ROUGE-LMETEORMethodsCIDErBLEU-4ROUGE-LMETEOR
R2Gen [7]0.3980.1650.3710.187R2Gen [7]0.2530.1030.2770.142
KERP [20]0.2800.1620.339-CMN [6]-0.1060.2780.142
HRGP [19]0.3430.1510.322-TopDown [1]0.0730.0920.2670.129
MKG [46]0.3040.1470.367-M2TR [35]-0.1070.2720.145
PPKED [30]0.3510.1680.3760.190PPKED [30]0.2370.1060.2840.149
MGSK [44]0.3820.1780.381-MGSK [44]0.2030.1150.284-
CA [31]-0.1690.3810.193CA [31]-0.1090.2830.151
CMCL [29]-0.1620.3780.186CMCL [29]-0.0970.2810.133
Ours0.5860.1630.3830.193Ours0.2810.1090.2840.150
+ +Table 1. The performances of our proposed DCL compared with other state-of-the-art systems on IU-Xray and MIMIC-CXR dataset. The best results in each column are highlighted in bold. CIDEr [40] is proposed to evaluate captioning systems. + +
MethodsPrecisionRecallF1-score
TopDown [1]0.1660.1210.133
M2TR [35]0.2400.4280.308
R2Gen [7]0.3330.2730.276
MKSG [44]0.4580.3480.371
Ours w/o G0.2750.1850.194
Ours w/o LIRC0.4630.3370.359
Ours w/o LIRM0.4690.3530.372
Ours0.4710.3520.373
+ +Table 2. The comparison of the clinical efficacy metrics on MIMIC-CXR dataset. The w/o is the abbreviation of without. + +lowing official splitting, we directly cite the results from [44] for comparison. In Fig. 4, we show the micro-average of ROC for 14 chesty terminologies prediction and present the AUC scores. 'Pleural Effusion' and 'Pleural Other' achieve the highest AUCs (0.82). The experimental results in Tab. 2 reveal that our DCL significantly outperforms the previous models on three CE metrics. Compared with the current SOTA method MGSK [44] that also leverages general prior knowledge and specific knowledge from RadGraph [17], we make a performance-boosting. The improvement verifies the importance of our dynamic graph concepts and also demonstrates that our system can predict more accurate clinical information. + +# 4.3. Ablation Study + +In this section, we conduct ablation studies on IU-Xray and MIMIC-CXR datasets to investigate the contribution of each component in our proposed DCL. Tab. 3 presents the quantitative analysis of DCL on IU-Xray with measuring descriptive accuracy. And clinical correctness evaluation is reported in Tab. 2. Our base model only keeps the image encoder and report decoder and employs $\mathcal{L}_{\mathrm{RG}}$ . + +Effect of Dynamic Graph Our dynamic graph is constructed in a bottom-up manner, that exploits general knowledge from $G_{pre}$ and specific knowledge $K_I$ extracted from + +retrieved Top-3 similar reports. Comparing the base model with settings (a) and (b), our dynamic graph can boost the performance of base model, substantially. More specifically, leveraging the general knowledge only lead to an increase on all NLG metrics by $15.2\%$ on CIDEr and $1.1\%$ on BLEU-4. By integrating specific knowledge, our dynamic graph can further boost the performances, e.g. $0.535 \rightarrow 0.557$ on CIDEr. It demonstrates the effectiveness and necessity of constructing dynamic graphs for each image. We hypothesize that this performance improvement may be due to that the dynamic knowledge can emphasize keywords when generating reports since dynamic nodes are from retrieved reports. It has been proved in Tab. 2, leveraging dynamic graph significantly improve the performances on all CE metrics, which means the generated reports can provide more accurate medical terminologies. + +Effect of Contrastive Learning Sequentially, we evaluate the effectiveness of two introduced learning objectives, i.e., image report contrastive loss (IRC) and image report matching loss (IRM). The performances of settings (b,c) in Tab. 2 show that both IRC and IRM can boost the base model performances. It proves the importance of visual and textual representation qualities since severe data bias in CRG datasets will degenerate the representation capabilities seriously. However, comparing (c) and (d), it is observed that IRC brings more improvement than IRM. We speculate the reason is that IRC can straightly improve visual and textual representations by aligning similar pairs. In contrast, IRM works on multimodal representations and represents unimodal in an indirect manner. + +Choice of Parameter Initialization We employ a pretrained ViT [10] and SciBert [4] as image and report encoder in our implementation. It is worth noting that Transformers lack some of the inductive biases inherent to CNNs and therefore generalize bad with insufficient and unbalanced data [10]. Not surprisingly, comparing setting (f) and the full model, the performances drop steeply without pretrained ViT parameters. The performances of setting (e) + +
Settings\(G_{pre}\)\(K_I\)IRCIRMViT [10]SciBert [4]CIDErBLEU-4ROUGE-LMETEOR
Base✓✓0.3830.1330.2770.163
(a)✓✓✓0.5350.1440.3490.180
(b)✓✓✓✓0.5570.1500.3610.182
(c)✓✓✓✓✓0.5800.1610.3850.188
(d)✓✓✓✓✓0.5640.1550.3700.188
(e)✓✓✓✓✓0.5800.1580.3740.190
(f)✓✓✓✓✓0.5270.1580.3560.179
DCL✓✓✓✓✓✓0.5860.1630.3830.193
+ +Table 3. Quantitative analysis of proposed method on IU-Xray dataset. The base model consists of an image encoder and a report decoder with report generation loss only. + +
ImageGround Truth ReportRetrieved Specific KnowledgeOursR2Gen
Lateral view somewhat limited due to overlying motion artifact lungs are low in volume there is no focal airspace the consolidation to suggest pneumonia a 1 2-cm calcified granuloma just below the medial aspect of the right hemidiaphragm is unchanged from prior study no pleural effusions or pulmonary edema there is no pneumothorax the inferior sternotomy wire is fractured but unchanged surgical clips and vascular markers in the thorax are related to prior cabg surgery.effusion located _ at pleural,vascular modify pulmonary, sternotomy suggestive _ of cabg,consolidation suggestive _ of effusion,effusion suggestive _ of consolidation,low modify effusion,low suggestive _ of effusion, low suggestive _ of consolidation,vascular modify chest,effusion suggestive _ of atelectasis,atelectasis modify lunglung volumes are low. there is no focal consolidation effusion or pneumothorax. airspace consolidation is noted within the left upper lobe compatible with pneumonia. borderline size of the cardiac silhouette without evidence of pulmonary edema, midline sternotomy wires and mediastinal clips are again noted.ap upright and lateral views of the chest provided . lung volumes are low limiting assessment . allowing for this there is no focal consolidation effusion or pneumothorax . the cardiomeiastinal silhouette is normal . imaged osseous structures are intact . no free air below the right hemidiaphragm is seen.
+ +Figure 5. Illustrations of reports from ground truth, ours and R2Gen [7] and retrieved specific knowledge for one sample from MIMIC-CXR [18]. For better visualization, different colors highlight different medical entities. + +demonstrate the effectiveness of pretrained SciBert. The improvement comes from two aspects. Firstly, it provides well pretrained parameters; Secondly, its tokenizer encodes each token (medical terminology) with a well pretrained embedding, which avoids Graph Transformers to propagate similar hidden states [49]. + +# 4.4. Case Study + +To further investigate the effectiveness of our method, we perform qualitative analysis on MIMIC-CXR [18] with their retrieved specific knowledge, and reports from ground truth, our model and R2Gen [7]. Entities extracted by Stanza [47] from the ground truth report have been highlighted with different colors. It is observed that some entities, e.g. cabg, consolidation, and sternotomy) are not included in the pre-constructed graph node lists. This observation proves our motivation for constructing knowledge graphs dynamically. We conduct the same operation on retrieved reports and use extracted entities to quote related triplets from RadGraph [17]. Those triplets are known as specific knowledge in this paper and shown in Fig. 5. Retrieved specific knowledge triplets $<$ sternotomy,suggestive_of,cabg> and $<$ consolidation,suggestive_of,effusion> demonstrate that the retrieved reports contain similar medical terminologies and clinical information. We speculate that IRC and IRM objectives bring such capabilities. Then the entities in our dynamic graph emphasize disease/organ keywords when generating reports and it is why our DCL can predict sen + +tence "airspace consolidation is noted within the left upper lobe compatible with pneumonia," but R2Gen can not. + +# 5. Conclusion and Discussion + +In this paper, we present a practical approach to leverage dynamic graph to enhance contrastive learning for radiology report generation. In which the dynamic graph is constructed in a bottom-up manner to integrate retrieved specific knowledge with general knowledge. Then contrastive learning is employed to improve visual and textual representations, which also promises the accuracy of our dynamic graph. Experiments on two popular benchmarks verify the effectiveness of our method in generating accurate and meaningful reports. More encouragingly, our approach can outperform or match existing SOTA methods in language generation and clinical efficacy metrics. + +Limitation and Future Work Retrieved reports can not be exactly the same as ground truth, and knowledge noises are involved during the dynamic graph construction process. It may guide the model to generate inaccurate sentences. In the future, we plan to propose a specific objective for the dynamic graph construction process to further improve the accuracy of dynamic graphs and the quality of predicted reports. + +# Acknowledgements + +This work was partially supported by "Taishan Scholars Youth Expert Program" of Shandong Province, and partially supported by National Key R&D Program of China under Grant No. 2020AAA0109700. + +# References + +[1] Peter Anderson, Xiaodong He, Chris Buehler, Damien Teney, Mark Johnson, Stephen Gould, and Lei Zhang. Bottom-up and top-down attention for image captioning and visual question answering. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 6077-6086, 2018. 6, 7 +[2] Jimmy Lei Ba, Jamie Ryan Kiros, and Geoffrey E Hinton. Layer normalization. arXiv preprint arXiv:1607.06450, 2016. 4 +[3] Satanjeev Banerjee and Alon Lavie. Meteor: An automatic metric for mt evaluation with improved correlation with human judgments. 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"type": "text", + "content": "Automatic radiology reporting has great clinical potential to relieve radiologists from heavy workloads and improve diagnosis interpretation. Recently, researchers have enhanced data-driven neural networks with medical knowledge graphs to eliminate the severe visual and textual bias in this task. The structures of such graphs are exploited by using the clinical dependencies formed by the disease topic tags via general knowledge and usually do not update during the training process. Consequently, the fixed graphs can not guarantee the most appropriate scope of knowledge and limit the effectiveness. To address the limitation, we propose a knowledge graph with Dynamic structure and nodes to facilitate chest X-ray report generation with Contrastive Learning, named DCL. In detail, the fundamental structure of our graph is pre-constructed from general knowledge. Then we explore specific knowledge extracted from the retrieved reports to add additional nodes or redefine their relations in a bottom-up manner. Each image feature is integrated with its very own updated graph before being fed into the decoder module for report generation. Finally, this paper introduces Image-Report Contrastive and Image-Report Matching losses to better represent visual features and textual information. Evaluated on IU-Xray and MIMIC-CXR datasets, our DCL outperforms previous state-of-the-art models on these two benchmarks." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 577, + 128, + 590 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 577, + 128, + 590 + ], + "spans": [ + { + "bbox": [ + 47, + 577, + 128, + 590 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 597, + 287, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 597, + 287, + 694 + ], + "spans": [ + { + "bbox": [ + 46, + 597, + 287, + 694 + ], + "type": "text", + "content": "Recently, automatic report generation has received growing attentions from both machine learning and automatic medicine fields. It aims to generate semantically coherent and informative reports to describe the referring examination images, such as Chest X-Ray [8, 18], Lung CT Scan [26] or funds angiography [23]. Such techniques have great clinical potential in relieving junior radiologists from heavy workloads and reducing diagnosis errors by improv-" + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 312, + 245, + 403, + 336 + ], + "blocks": [ + { + "bbox": [ + 312, + 245, + 403, + 336 + ], + "lines": [ + { + "bbox": [ + 312, + 245, + 403, + 336 + ], + "spans": [ + { + "bbox": [ + 312, + 245, + 403, + 336 + ], + "type": "image", + "image_path": "0172bbe2ff52d24362741d5239404e42be5e169a4432cbc62aefea1e4a9c6982.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 405, + 247, + 471, + 256 + ], + "lines": [ + { + "bbox": [ + 405, + 247, + 471, + 256 + ], + "spans": [ + { + "bbox": [ + 405, + 247, + 471, + 256 + ], + "type": "text", + "content": "Ground Truth Report" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 405, + 269, + 537, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 405, + 269, + 537, + 331 + ], + "spans": [ + { + "bbox": [ + 405, + 269, + 537, + 331 + ], + "type": "text", + "content": "A single portable AP semi-upright view of the chest was obtained. Cardiomediastinal silhouette including moderate cardiomegaly is stable. An ICD device is also unchanged in position. Interval development of increased opacification in the right lower lung probably reflects asymmetric edema and a layering effusion..." + } + ] + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 313, + 338, + 542, + 432 + ], + "blocks": [ + { + "bbox": [ + 313, + 338, + 542, + 432 + ], + "lines": [ + { + "bbox": [ + 313, + 338, + 542, + 432 + ], + "spans": [ + { + "bbox": [ + 313, + 338, + 542, + 432 + ], + "type": "image", + "image_path": "bb4855157e79078ddbefd3e1153239bcc9205dd4f38ea965ae8b0a05b1c67f70.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 441, + 546, + 495 + ], + "lines": [ + { + "bbox": [ + 304, + 441, + 546, + 495 + ], + "spans": [ + { + "bbox": [ + 304, + 441, + 546, + 495 + ], + "type": "text", + "content": "Figure 1. An illustration of one sample from MIMIC-CXR [18] and the pre-constructed graph in [46], where the blue circle, orange boxes and black boxes refer to the global node, organ-level entities and key findings, respectively. The red dash line here represents the unconnected relation." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 498, + 423, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 498, + 423, + 509 + ], + "spans": [ + { + "bbox": [ + 306, + 498, + 423, + 509 + ], + "type": "text", + "content": "ing the interpretation [7, 30]." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 510, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 546, + 713 + ], + "type": "text", + "content": "Witnessed the great progress in artificial intelligence, especially deep learning methods [12,25,39], researchers have proposed various data-driven neural networks for radiology reporting and achieved promising performances in metrics that measure descriptive accuracy [7, 44] and clinical correctness [11, 46]. Compared with the similar task generic image captioning [14], the key challenges in chest X-ray report generation (CRG) task are the severe visual and textual data bias [19, 26]. On the one hand, medical images are highly similar to each other due to the imaging methods and human tissues themselves. However, abnormal regions or lesions that should acquire more attentions usually locate at a small part and lack detailed annotations in existing CRG benchmarks. On the other hand, sentences that describe normal regions are likely to appear repeatedly among each dataset which disables the model to describe specific crucial abnormalities. Two concepts have been proved ef" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 1, + 496, + 17 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 1, + 496, + 17 + ], + "spans": [ + { + "bbox": [ + 145, + 1, + 496, + 17 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 180, + 13, + 461, + 22 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 180, + 13, + 461, + 22 + ], + "spans": [ + { + "bbox": [ + 180, + 13, + 461, + 22 + ], + "type": "text", + "content": "Except for this watermark, it is identical to the accepted version:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 179, + 24, + 461, + 36 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 179, + 24, + 461, + 36 + ], + "spans": [ + { + "bbox": [ + 179, + 24, + 461, + 36 + ], + "type": "text", + "content": "the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 702, + 287, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 287, + 712 + ], + "type": "text", + "content": "*Corresponding author. https://github.com/mlii0117/DCL" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3334" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 180, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 180, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 180, + 83 + ], + "type": "text", + "content": "fective in eliminating those bias." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 87, + 289, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 87, + 289, + 373 + ], + "spans": [ + { + "bbox": [ + 47, + 87, + 289, + 373 + ], + "type": "text", + "content": "The first one is to integrate medical knowledge with ORG systems [24,30,44,46]. Zhang et al. [46] constructed a universal graph comprised of a global node, 7 organs/tissues and 20 findings (normal or disease keywords). Disease keyword nodes linked to the same organ are connected to each other and the root in the graph. This graph can enhance the relationships among findings and emphasize the disease keywords. Thus, it is also adopted in the following works [30, 44]. However, this graph is built from general knowledge and may be inappropriate in some cases. As the shown report in Fig. 1, it is observed that effusion should be suggestive of edema, however, such relationship is not modelled in the graph. Furthermore, some nodes like 'cicatrix' or 'hypoinflation' only appear very few times in two ORG benchmarks [8, 18]. Therefore, it is necessary to update the scope of knowledge for each case; In addition to the medical knowledge, recent works [5, 11, 31, 38, 43] utilize contrastive learning to improve the visual and textual representations by contrasting positive and negative pairs. They proposed various contrastive learning objectives to capture the abnormal regions from a chest X-Ray image. Since normal images usually dominate the dataset over abnormal ones [37], it is also crucial to recognize the normal or abnormal cases in the meantime." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 376, + 289, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 376, + 289, + 676 + ], + "spans": [ + { + "bbox": [ + 47, + 376, + 289, + 676 + ], + "type": "text", + "content": "In this paper, we propose a novel framework, named DCL, which exploits a dynamic graph integrating specific knowledge with general knowledge to enhance visual representations learned in a contrastive manner. We adopt the general knowledge with 28 entities from [46] as the fundamental structure of our graph, and the relationships are modelled in an adjacency matrix. Given a medical image, we first retrieve its semantically similar reports from the training set. Specific knowledge is extracted from those reports via RadGraph [17] and stored in triplets (). And we integrate those triplets with the pre-constructed graph by dynamically adding additional nodes or linking two entities. We utilize a graph encoder to propagate information over the updated graph for refining the node features, which are initialized by a pretrained SciBert [4]. Then the dedicated node features are attended to visual representations for report generation via a Transformer [39] decoder. Based on the dynamic graph, we introduce a contrastive learning objective, image-report contrastive loss to well represent the visual features and textual information. In addition, contrastive learning can help ensure the accuracy of the report retrieval procedure in the dynamic graph construction process. Image-report matching loss is also employed to further improve the performances." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "text", + "content": "We evaluate our method on two benchmarks, IU-Xray [8] and MIMIC-CXR [18]. Experimental results demonstrate that our approach can either outperform or" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": "match previous state-of-the-art (SOTA) methods in metrics that measure descriptive accuracy and clinical correctness. It indicates that leveraging dynamic graphs to enhance contrastive learning is helpful to generate high-quality reports." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 317, + 121, + 523, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 121, + 523, + 133 + ], + "spans": [ + { + "bbox": [ + 317, + 121, + 523, + 133 + ], + "type": "text", + "content": "In summary, our main contributions are as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 317, + 141, + 545, + 292 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 317, + 141, + 545, + 177 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 141, + 545, + 177 + ], + "spans": [ + { + "bbox": [ + 317, + 141, + 545, + 177 + ], + "type": "text", + "content": "- We propose a novel framework that leverages a dynamic graph to enhance visual representations with contrastive learning paradigms for radiology reporting." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 187, + 545, + 235 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 187, + 545, + 235 + ], + "spans": [ + { + "bbox": [ + 317, + 187, + 545, + 235 + ], + "type": "text", + "content": "- Our proposed dynamic graph integrates both general and specific knowledge; The contrastive learning objective can improve visual and textual representations and dynamic graph accuracy." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 317, + 244, + 545, + 292 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 244, + 545, + 292 + ], + "spans": [ + { + "bbox": [ + 317, + 244, + 545, + 292 + ], + "type": "text", + "content": "- We conduct extensive experiments on two popular benchmarks to show the effectiveness of our approach, which achieves the SOTA performance on both language generation and clinical efficacy metrics." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 304, + 392, + 316 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 304, + 392, + 316 + ], + "spans": [ + { + "bbox": [ + 306, + 304, + 392, + 316 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 323, + 545, + 349 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 323, + 545, + 349 + ], + "spans": [ + { + "bbox": [ + 306, + 323, + 545, + 349 + ], + "type": "text", + "content": "2.1. Medical Report Generation Meets Knowledge Graph" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 354, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 354, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 354, + 547, + 715 + ], + "type": "text", + "content": "When radiologists write reports, they will make inferences with their expert knowledge. Typically, a report contains many sections, e.g., impressions, finding, comparison and indication. Following the previous works, we combine the impressions and finding sections as the target for report generation. To endow the medical report generation systems with the capability to incorporate medical knowledge, various kinds of knowledge graphs have been explored and can be roughly divided into three groups. The first kind is proposed to emphasize the abnormal terminologies or disease keywords. Li et al. [20] collected abnormalities from MIMIC-CXR dataset, and utilized them as the node of their proposed abnormality graph. Edges here are the attention weights from source nodes to target nodes in the graph. Such graph is adopted in the following works [26, 48] as prior medical knowledge to enhance the generation procedure and can even facilitate the unsupervised learning framework [32]. Secondly, Zhang et al. [46] and Liu et al. [30] adopted a universal graph with 20 entities. Entities linked to the same organ are connected to each other in the graph. Such relationships are modelled into an adjacency matrix and utilized to propagate messages in a graph encoding module. Since this graph is pre-constructed with prior knowledge in a fixed structure, we found that it can not guarantee the appropriate scope of knowledge for some cases (e.g. missing or unconnected common entities). To tackle this challenge, Liu et al. [30] utilized the global representations from pre-retrieved reports from the training corpus to model domain-specific knowledge. In contrast, we aim to directly update the pre-constructed graph to" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3335" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 71, + 68, + 521, + 293 + ], + "blocks": [ + { + "bbox": [ + 71, + 68, + 521, + 293 + ], + "lines": [ + { + "bbox": [ + 71, + 68, + 521, + 293 + ], + "spans": [ + { + "bbox": [ + 71, + 68, + 521, + 293 + ], + "type": "image", + "image_path": "f3b8b9302222eee942f3c237b61f49be92d3f12480fa0bb0c8eddc8656aca700.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 301, + 547, + 346 + ], + "lines": [ + { + "bbox": [ + 46, + 301, + 547, + 346 + ], + "spans": [ + { + "bbox": [ + 46, + 301, + 547, + 346 + ], + "type": "text", + "content": "Figure 2. Illustration of our proposed Dynamic graph enhanced Contrastive Learning approach (DCL). DCL contains two unimodal encoders, a multimodal encoder, a report decoder and three dynamic graph modules for construction, encoding and cross-modal attention, respectively. In addition to Report Generation (RG) loss, Image-Report Contrastive (IRC) loss and Image-Report Matching (IRM) loss are adopted for training DCL." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 356, + 287, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 356, + 287, + 426 + ], + "spans": [ + { + "bbox": [ + 46, + 356, + 287, + 426 + ], + "type": "text", + "content": "model the appropriate knowledge. In the last, Li et al. [24] constructed a clinical graph by extracting structural information from the training corpus via a NLP-rule-based algorithm. They restored a set of triplets for each case to model the domain-specific knowledge and replace the visual representations." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 429, + 288, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 429, + 288, + 502 + ], + "spans": [ + { + "bbox": [ + 46, + 429, + 288, + 502 + ], + "type": "text", + "content": "Our approach is based on the second category. Instead of using the fixed graph in [46], we dynamically update the graph by injecting new knowledge extracted from the retrieved reports for each case. As a result, the appropriate scope of knowledge for different cases can be activated to generate more high-quality reports." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 514, + 170, + 526 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 514, + 170, + 526 + ], + "spans": [ + { + "bbox": [ + 47, + 514, + 170, + 526 + ], + "type": "text", + "content": "2.2. Contrastive Learning" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 534, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 534, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 534, + 288, + 713 + ], + "type": "text", + "content": "The goal of contrastive learning is to improve representation learning by contrasting positive/negative or similar/dissimilar pairs. Inspired by the recent success of contrastive learning in vision-and-language pretraining tasks [21], some works have introduced it in the CRG systems. Yan et al. [43] developed a weakly supervised method to contrast target reports with incorrect ones by identifying \"hard\" negative samples. To detect the abnormal regions, Liu et al. [31] compared the referring image with known normal images via a contrastive attention mechanism. Other works [5, 42, 45] employed contrastive learning during the pretraining process to better represent visual features and textual information. All those works aimed to improve the expressiveness of both visual and textual representations and then facilitate radiology reporting. In our" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 356, + 546, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 356, + 546, + 392 + ], + "spans": [ + { + "bbox": [ + 305, + 356, + 546, + 392 + ], + "type": "text", + "content": "work, contrastive learning can also improve the accuracy of the dynamic graph by training the model to retrieve the most semantically similar reports." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 403, + 388, + 417 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 403, + 388, + 417 + ], + "spans": [ + { + "bbox": [ + 306, + 403, + 388, + 417 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 423, + 545, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 423, + 545, + 519 + ], + "spans": [ + { + "bbox": [ + 304, + 423, + 545, + 519 + ], + "type": "text", + "content": "In this section, we will introduce the detailed implementations of our proposed Dynamic graph enhanced Contrastive Learning approach (DCL). The overall structure of DCL is illustrated in Fig. 2, which contains four basic modules and three dynamic graph modules with three training objectives. We first describe the background of DCL and then introduce the dynamic graph modules and contrastive learning objectives, respectively." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 528, + 388, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 528, + 388, + 540 + ], + "spans": [ + { + "bbox": [ + 306, + 528, + 388, + 540 + ], + "type": "text", + "content": "3.1. Background" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": "Notation In this work, we aim to leverage dynamic graphs to enhance contrastive learning for radiology reporting. In the CRG task, the computer is asked to describe a given medical image " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": " with a free-text report " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "T = \\{y_{1}, y_{2}, \\ldots, y_{n}\\}" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": ". We denote the target report by " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\hat{T} = \\{\\hat{y}_{1}, \\hat{y}_{2}, \\ldots, \\hat{y}_{\\hat{n}}\\}" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\hat{n}" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": " represent the numbers of tokens in a report. Our dynamic graph, denoted by " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "G = \\{V, E\\}" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": " are the sets of nodes and edges, respectively, is built on a pre-constructed graph " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "G_{pre}" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": " proposed in [46] and updated with specific knowledge " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "K_{I} = \\{k_{I}^{1}, \\ldots, k_{I}^{n_{K}}\\}" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": " extracted from retrieved reports " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\{T_{i}^{*}\\}_{i=1}^{n_{T}}" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": ". Each " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": " is stored in a triplet format, which consists of a subjective entity " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "e_{s}" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": ", an objective entity " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "e_{o}" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": " and their relation " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "n_{T}" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "n_{K}" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": " are the numbers of reports and triplets, respectively. All the" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3336" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 231, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 231, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 231, + 83 + ], + "type": "text", + "content": "triplets are acquired from the RadGraph [17]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 84, + 286, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 84, + 286, + 167 + ], + "spans": [ + { + "bbox": [ + 46, + 84, + 286, + 167 + ], + "type": "text", + "content": "Typical CRG systems are encoder-decoder frameworks. The encoder is usually a CNN, e.g., ResNet [12] or DenseNet [15], encodes the given image " + }, + { + "bbox": [ + 46, + 84, + 286, + 167 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 84, + 286, + 167 + ], + "type": "text", + "content": " to dense visual vectors " + }, + { + "bbox": [ + 46, + 84, + 286, + 167 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_I" + }, + { + "bbox": [ + 46, + 84, + 286, + 167 + ], + "type": "text", + "content": ". The decoder is usually a RNN (e.g., LSTM [13]) or a Transformer [39], which decodes " + }, + { + "bbox": [ + 46, + 84, + 286, + 167 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_I" + }, + { + "bbox": [ + 46, + 84, + 286, + 167 + ], + "type": "text", + "content": " to a report " + }, + { + "bbox": [ + 46, + 84, + 286, + 167 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 84, + 286, + 167 + ], + "type": "text", + "content": ". In this work, we adopt the Transformer [39] as the backbone to generate the long and robust reports." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 168, + 286, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 168, + 286, + 263 + ], + "spans": [ + { + "bbox": [ + 46, + 168, + 286, + 263 + ], + "type": "text", + "content": "Image Encoder Recently, visual Transformers have shown superior capabilities to represent images than CNNs. Thus, we only employ a ViT [10] pretrained on the ImageNet [9] as the image encoder to simplify the architecture. The input image will be divided into 196 patches, and a [CLS] token is further appended to the beginning of sequence before being fed into the encoder layers. The whole process of an encoder layer " + }, + { + "bbox": [ + 46, + 168, + 286, + 263 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_e(\\cdot)" + }, + { + "bbox": [ + 46, + 168, + 286, + 263 + ], + "type": "text", + "content": " can be written as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 96, + 268, + 286, + 281 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 268, + 286, + 281 + ], + "spans": [ + { + "bbox": [ + 96, + 268, + 286, + 281 + ], + "type": "interline_equation", + "content": "\\mathbf {f} _ {e} (x) = \\operatorname {L N} \\left(\\operatorname {F F N} \\left(e _ {\\text {a t t n}}\\right) + e _ {\\text {a t t n}}\\right), \\tag {1}", + "image_path": "c6e65f8956c50f7926d903ee9ef5d13f60182ee59ff691fe0f11ae4bdd7f68a6.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 97, + 284, + 286, + 296 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 284, + 286, + 296 + ], + "spans": [ + { + "bbox": [ + 97, + 284, + 286, + 296 + ], + "type": "interline_equation", + "content": "e _ {a t t n} = \\operatorname {L N} (\\mathrm {M H A} (x) + x), \\tag {2}", + "image_path": "efe2cc18138f70e02a1faa4cea5947e185e2c29b27827982781d1271404730d6.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 300, + 286, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 300, + 286, + 360 + ], + "spans": [ + { + "bbox": [ + 47, + 300, + 286, + 360 + ], + "type": "text", + "content": "where FFN and LN denote the Feed Forward Network [39] and Layer Normalization operation [2], respectively. " + }, + { + "bbox": [ + 47, + 300, + 286, + 360 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 47, + 300, + 286, + 360 + ], + "type": "text", + "content": " is the input of each encoder layer. MHA [39] (multi-head attention) divides a scaled dot-product attention into " + }, + { + "bbox": [ + 47, + 300, + 286, + 360 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 47, + 300, + 286, + 360 + ], + "type": "text", + "content": " parallel heads and each head " + }, + { + "bbox": [ + 47, + 300, + 286, + 360 + ], + "type": "inline_equation", + "content": "\\mathrm{Att}(\\cdot)" + }, + { + "bbox": [ + 47, + 300, + 286, + 360 + ], + "type": "text", + "content": " can be written as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 94, + 374, + 286, + 401 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 374, + 286, + 401 + ], + "spans": [ + { + "bbox": [ + 94, + 374, + 286, + 401 + ], + "type": "interline_equation", + "content": "\\operatorname {A t t} (x) = \\operatorname {s o f t m a x} \\left(\\frac {\\mathbf {Q} ^ {x} \\left(\\mathbf {K} ^ {x}\\right) ^ {\\top}}{\\sqrt {d}}\\right) \\mathbf {V} ^ {x}, \\tag {3}", + "image_path": "7b0520f951ddd33f8f5a567f05df78f9c76db22cf238920f57d384b1ef713e61.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 404, + 286, + 452 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 404, + 286, + 452 + ], + "spans": [ + { + "bbox": [ + 47, + 404, + 286, + 452 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 404, + 286, + 452 + ], + "type": "inline_equation", + "content": "d = 768" + }, + { + "bbox": [ + 47, + 404, + 286, + 452 + ], + "type": "text", + "content": " is the dimension of the embedding space and " + }, + { + "bbox": [ + 47, + 404, + 286, + 452 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{Q},\\mathbf{K}^{*},\\mathbf{V}^{*}\\}" + }, + { + "bbox": [ + 47, + 404, + 286, + 452 + ], + "type": "text", + "content": " are the packed " + }, + { + "bbox": [ + 47, + 404, + 286, + 452 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 47, + 404, + 286, + 452 + ], + "type": "text", + "content": "-dimensional Query, Key, Value vectors, respectively. The final output is the encoded visual vectors " + }, + { + "bbox": [ + 47, + 404, + 286, + 452 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_I" + }, + { + "bbox": [ + 47, + 404, + 286, + 452 + ], + "type": "text", + "content": ", which will be used for report generation." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 453, + 286, + 487 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 453, + 286, + 487 + ], + "spans": [ + { + "bbox": [ + 47, + 453, + 286, + 487 + ], + "type": "text", + "content": "Report Decoder Our report decoder consists of two Transformer decoder layers. The whole process of a decoder layer " + }, + { + "bbox": [ + 47, + 453, + 286, + 487 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_d(\\cdot)" + }, + { + "bbox": [ + 47, + 453, + 286, + 487 + ], + "type": "text", + "content": " can be written as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 92, + 493, + 286, + 506 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 92, + 493, + 286, + 506 + ], + "spans": [ + { + "bbox": [ + 92, + 493, + 286, + 506 + ], + "type": "interline_equation", + "content": "\\mathbf {f} _ {d} (\\mathbf {y}) = \\mathrm {L N} \\left(\\mathrm {F F N} \\left(e _ {c a}\\right) + e _ {c a}\\right), \\tag {4}", + "image_path": "a21e5d8214f32320472104aadc1d1def12a99f9fdda1abcfaa28c19237f5c663.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 102, + 508, + 286, + 520 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 508, + 286, + 520 + ], + "spans": [ + { + "bbox": [ + 102, + 508, + 286, + 520 + ], + "type": "interline_equation", + "content": "e _ {c a} = \\mathrm {L N} \\left(\\mathrm {C A} \\left(e _ {\\text {a t t n}}, \\mathbf {f} _ {I}\\right) + e _ {\\text {a t t n}}\\right), \\tag {5}", + "image_path": "7000cf5d4bb50bd0a8e4eede3f843d82f4a918ae7baf8d459715b32177de0827.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 94, + 524, + 286, + 536 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 524, + 286, + 536 + ], + "spans": [ + { + "bbox": [ + 94, + 524, + 286, + 536 + ], + "type": "interline_equation", + "content": "e _ {a t t n} = \\operatorname {L N} (\\operatorname {M M H A} (\\mathbf {y}) + \\mathbf {y})), \\tag {6}", + "image_path": "6b9a2cb18275b847886857635755761627b8e541e05ebf11c0cec1b708646f0a.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 540, + 286, + 682 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 540, + 286, + 682 + ], + "spans": [ + { + "bbox": [ + 47, + 540, + 286, + 682 + ], + "type": "text", + "content": "where MMHA and CA represent the masked multi-head self-attention and cross attention mechanism in [39]. " + }, + { + "bbox": [ + 47, + 540, + 286, + 682 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 47, + 540, + 286, + 682 + ], + "type": "text", + "content": " is the input of decoder. A [Decode] token is added to the beginning of " + }, + { + "bbox": [ + 47, + 540, + 286, + 682 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 47, + 540, + 286, + 682 + ], + "type": "text", + "content": " to signal the start while a [EOS] token is to signal its end. In Cross-attention sublayer, for each head, " + }, + { + "bbox": [ + 47, + 540, + 286, + 682 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{Q},\\mathbf{K}^{*},\\mathbf{V}^{*}\\}" + }, + { + "bbox": [ + 47, + 540, + 286, + 682 + ], + "type": "text", + "content": " comes from " + }, + { + "bbox": [ + 47, + 540, + 286, + 682 + ], + "type": "inline_equation", + "content": "\\mathbf{Q} = W_{q}*e_{attn}" + }, + { + "bbox": [ + 47, + 540, + 286, + 682 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 540, + 286, + 682 + ], + "type": "inline_equation", + "content": "\\mathbf{K} = W_{k}*\\mathbf{f}_{I}" + }, + { + "bbox": [ + 47, + 540, + 286, + 682 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 540, + 286, + 682 + ], + "type": "inline_equation", + "content": "\\mathbf{V} = W_{v}*\\mathbf{f}_{I}" + }, + { + "bbox": [ + 47, + 540, + 286, + 682 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 540, + 286, + 682 + ], + "type": "inline_equation", + "content": "W_{*}" + }, + { + "bbox": [ + 47, + 540, + 286, + 682 + ], + "type": "text", + "content": " are the learnable parameters. The " + }, + { + "bbox": [ + 47, + 540, + 286, + 682 + ], + "type": "inline_equation", + "content": "f_{d}(\\mathbf{y})" + }, + { + "bbox": [ + 47, + 540, + 286, + 682 + ], + "type": "text", + "content": " will be sent to a Linear & Log-Softmax layer to get the output of target sentences. Notably, only token embedding is adopted during the decoding procedure. The entire auto-regressive generation process can be written as follows:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 93, + 686, + 286, + 710 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 686, + 286, + 710 + ], + "spans": [ + { + "bbox": [ + 93, + 686, + 286, + 710 + ], + "type": "interline_equation", + "content": "p (T | I) = \\prod_ {t = 1} p \\left(y _ {t} \\mid y _ {1}, \\dots , y _ {t - 1}, I\\right). \\tag {7}", + "image_path": "fdd50e1b0e65fa65fecc7679fc196e3a20eb55c82a49f22097c57937f868b1cb.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 72, + 473, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 473, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 473, + 84 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 72, + 473, + 84 + ], + "type": "inline_equation", + "content": "y_{t}" + }, + { + "bbox": [ + 306, + 72, + 473, + 84 + ], + "type": "text", + "content": " is the input token in time step " + }, + { + "bbox": [ + 306, + 72, + 473, + 84 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 306, + 72, + 473, + 84 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 84, + 545, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 84, + 545, + 144 + ], + "spans": [ + { + "bbox": [ + 305, + 84, + 545, + 144 + ], + "type": "text", + "content": "Typically, the report generation objective is the cross-entropy loss to compare the predicted token index sequence with the ground truth. Given the ground truth report " + }, + { + "bbox": [ + 305, + 84, + 545, + 144 + ], + "type": "inline_equation", + "content": "\\hat{T}" + }, + { + "bbox": [ + 305, + 84, + 545, + 144 + ], + "type": "text", + "content": ", all the underlying modules are trained to maximize " + }, + { + "bbox": [ + 305, + 84, + 545, + 144 + ], + "type": "inline_equation", + "content": "p(\\mathbf{y} | I)" + }, + { + "bbox": [ + 305, + 84, + 545, + 144 + ], + "type": "text", + "content": " by minimizing the following:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 343, + 153, + 545, + 185 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 343, + 153, + 545, + 185 + ], + "spans": [ + { + "bbox": [ + 343, + 153, + 545, + 185 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {R G}} = - \\sum_ {t = 1} ^ {\\hat {n}} \\log p \\left(\\hat {y} _ {t} \\mid \\hat {y} _ {1}, \\dots , \\hat {y} _ {t - 1}, I\\right). \\tag {8}", + "image_path": "a13670fe5f47b9d21c4eac7ddea39823cf857e9896e39f9ce0e7c6e20b1e9768.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 193, + 404, + 205 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 193, + 404, + 205 + ], + "spans": [ + { + "bbox": [ + 306, + 193, + 404, + 205 + ], + "type": "text", + "content": "3.2. Dynamic Graph" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 211, + 545, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 211, + 545, + 450 + ], + "spans": [ + { + "bbox": [ + 304, + 211, + 545, + 450 + ], + "type": "text", + "content": "The chest knowledge graph " + }, + { + "bbox": [ + 304, + 211, + 545, + 450 + ], + "type": "inline_equation", + "content": "G_{pre}" + }, + { + "bbox": [ + 304, + 211, + 545, + 450 + ], + "type": "text", + "content": " proposed in [46] has been widely integrated with CRG systems to emphasize the disease keywords and enhance their relationships. " + }, + { + "bbox": [ + 304, + 211, + 545, + 450 + ], + "type": "inline_equation", + "content": "G_{pre}" + }, + { + "bbox": [ + 304, + 211, + 545, + 450 + ], + "type": "text", + "content": " consists of 27 entities and a root node referring to the global feature and an adjacency matrix " + }, + { + "bbox": [ + 304, + 211, + 545, + 450 + ], + "type": "inline_equation", + "content": "A = \\{e_{ij}\\}" + }, + { + "bbox": [ + 304, + 211, + 545, + 450 + ], + "type": "text", + "content": " to represent the edges " + }, + { + "bbox": [ + 304, + 211, + 545, + 450 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 304, + 211, + 545, + 450 + ], + "type": "text", + "content": ". Each node is a disease keyword and we set " + }, + { + "bbox": [ + 304, + 211, + 545, + 450 + ], + "type": "inline_equation", + "content": "e_{ij}" + }, + { + "bbox": [ + 304, + 211, + 545, + 450 + ], + "type": "text", + "content": " to 1 when source node " + }, + { + "bbox": [ + 304, + 211, + 545, + 450 + ], + "type": "inline_equation", + "content": "n_i" + }, + { + "bbox": [ + 304, + 211, + 545, + 450 + ], + "type": "text", + "content": " connects target node " + }, + { + "bbox": [ + 304, + 211, + 545, + 450 + ], + "type": "inline_equation", + "content": "n_j" + }, + { + "bbox": [ + 304, + 211, + 545, + 450 + ], + "type": "text", + "content": ". Nodes linked to the same organ or tissue are connected to each other and the root. This graph is not updated during the training, and we found that it limits the effectiveness from two aspects. Firstly, those entities can not cover the most common disease keywords for all datasets because of the dataset bias; Secondly, entities linked to different organs can also affect each other clinically. To tackle those limitations, we propose a dynamic graph " + }, + { + "bbox": [ + 304, + 211, + 545, + 450 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 211, + 545, + 450 + ], + "type": "text", + "content": " with dynamic structure and nodes and integrate it with visual features to generate high-quality reports. This process is illustrated in Fig. 3, and we will introduce the three key modules, i.e., dynamic graph construction, dynamic graph encoder, and graph attention in this section, respectively." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 451, + 545, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 451, + 545, + 557 + ], + "spans": [ + { + "bbox": [ + 304, + 451, + 545, + 557 + ], + "type": "text", + "content": "Dynamic Graph Construction We construct our graph in a bottom-up manner, in which we first construct the fundamental structure from general knowledge and then add nodes or redefine their relationships according to specific knowledge. We extend " + }, + { + "bbox": [ + 304, + 451, + 545, + 557 + ], + "type": "inline_equation", + "content": "G_{pre}" + }, + { + "bbox": [ + 304, + 451, + 545, + 557 + ], + "type": "text", + "content": " to our fundamental structure with 28 entities consisting of a global node represented by a [CLS] token, 7 organs or tissues, and 20 disease keywords. In addition to link criteria in " + }, + { + "bbox": [ + 304, + 451, + 545, + 557 + ], + "type": "inline_equation", + "content": "G_{pre}" + }, + { + "bbox": [ + 304, + 451, + 545, + 557 + ], + "type": "text", + "content": ", every organ will connect to each other organ or tissue." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": "To get the specific knowledge for each given image " + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": ", we first retrieve the top-" + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "n_T" + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": " similar reports " + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\{T_i^*\\}_{i=1}^{n_T}" + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": " by calculating the similarity between the visual feature " + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_I" + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": " and representations of reports in queue " + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{f}_{T^*}^i\\}_{i=1}^{n_Q}" + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "n_Q" + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": " is the length of the report queue. For each retrieved report, we extract anatomy and observation entities by Stanza [47]. Those entities are further utilized to quote the specific knowledge " + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "K_I" + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": " from RadGraph [17]. Each triplet " + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "K_I" + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": " aims to depict the relationship between source and target entities. There are three kinds of relations in RadGraph, namely 'suggestive of', 'modify' and 'located at'. For a triplet whose only source entity " + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "e_s" + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": " or target entity " + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "e_o" + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": " is in the graph, we will add another entity in the triplet as an ad" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3337" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "content": "ditional node, and set their relation to 1 in the adjacency matrix " + }, + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "content": ". Note that if the relation is 'located at' and the entity needed to be added is the target entity " + }, + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "inline_equation", + "content": "e_{o}" + }, + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "inline_equation", + "content": "e_{o}" + }, + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "content": " will be treated as an organ/tissue node. In this bottom-up manner, our dynamic graph is capable to exploit both general and specific knowledge." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 144, + 288, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 144, + 288, + 204 + ], + "spans": [ + { + "bbox": [ + 46, + 144, + 288, + 204 + ], + "type": "text", + "content": "Dynamic Graph Encoder We propose a dynamic graph encoder to propagate information and learn dedicated node features in our dynamic graph. To this end, this module is built upon the standard Transformer encoder layer " + }, + { + "bbox": [ + 46, + 144, + 288, + 204 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_G" + }, + { + "bbox": [ + 46, + 144, + 288, + 204 + ], + "type": "text", + "content": " and conducted as (see Figure 3):" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 108, + 213, + 286, + 225 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 213, + 286, + 225 + ], + "spans": [ + { + "bbox": [ + 108, + 213, + 286, + 225 + ], + "type": "interline_equation", + "content": "\\mathbf {f} _ {G} = \\mathrm {L N} \\left(\\mathrm {F F N} \\left(e _ {r s a}\\right) + e _ {r s a}\\right), \\tag {9}", + "image_path": "20447af1911f946a1b8436884a19b3fdaa56ac57fa944671565fd6e68f8aa686.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 102, + 228, + 287, + 240 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 228, + 287, + 240 + ], + "spans": [ + { + "bbox": [ + 102, + 228, + 287, + 240 + ], + "type": "interline_equation", + "content": "e _ {r s a} = \\operatorname {L N} (\\operatorname {R S A} \\left(\\mathbf {f} _ {N}, A\\right) + \\mathbf {f} _ {N}), \\tag {10}", + "image_path": "359cec729c6452b5821b98b5b7769dc6a739d30c839e10e7fcf9dc8b123b65cc.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 248, + 287, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 248, + 287, + 464 + ], + "spans": [ + { + "bbox": [ + 46, + 248, + 287, + 464 + ], + "type": "text", + "content": "where RSA is an MMHA-like relational self-attention module to encode the structural information of a graph to the model. Concretely, we utilize adjacency matrix " + }, + { + "bbox": [ + 46, + 248, + 287, + 464 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 248, + 287, + 464 + ], + "type": "text", + "content": " as a visible mask [24,33] to control the original MMHA. It promises that each node can only impact its linked nodes and enhance their relationships. " + }, + { + "bbox": [ + 46, + 248, + 287, + 464 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_N" + }, + { + "bbox": [ + 46, + 248, + 287, + 464 + ], + "type": "text", + "content": " is the initialized nodes representations and consists of entity embedding and level encoding. Previous works initialized representations randomly, which limits the effectiveness seriously [49]. Moreover, some additional nodes appear a few times during the training and hard to find the best embeddings. Therefore, we first adopt word embeddings " + }, + { + "bbox": [ + 46, + 248, + 287, + 464 + ], + "type": "inline_equation", + "content": "\\epsilon_{sci}" + }, + { + "bbox": [ + 46, + 248, + 287, + 464 + ], + "type": "text", + "content": " from well-trained SciBert [4] to initialize each entity. For those entities consisting of one more word, e.g., 'foreign object', we calculate the average. Furthermore, we add level encoding " + }, + { + "bbox": [ + 46, + 248, + 287, + 464 + ], + "type": "inline_equation", + "content": "\\epsilon_l" + }, + { + "bbox": [ + 46, + 248, + 287, + 464 + ], + "type": "text", + "content": " to demonstrate each node is the root, organ, or disease keyword. Thus, the structural information of our graph is well represented and encoded during message passing and propagation." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 464, + 287, + 511 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 464, + 287, + 511 + ], + "spans": [ + { + "bbox": [ + 46, + 464, + 287, + 511 + ], + "type": "text", + "content": "Graph Attention Graph attention aims to integrate knowledge from dynamic graphs with visual features. Following [30], we utilize cross attention to achieve this goal. The whole process can be written as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 111, + 521, + 286, + 533 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 521, + 286, + 533 + ], + "spans": [ + { + "bbox": [ + 111, + 521, + 286, + 533 + ], + "type": "interline_equation", + "content": "\\mathbf {f} _ {\\bar {I}} = \\mathrm {L N} (\\mathrm {F F N} (e _ {g a}) + e _ {g a}), \\tag {11}", + "image_path": "c25481fc46a494f4e14ca89f57a2fd36ca5087057d306b4b3b807c1c9c08774b.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 536, + 287, + 548 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 536, + 287, + 548 + ], + "spans": [ + { + "bbox": [ + 106, + 536, + 287, + 548 + ], + "type": "interline_equation", + "content": "e _ {g a} = \\operatorname {L N} \\left(\\operatorname {C A} \\left(\\mathbf {f} _ {I}, \\mathbf {f} _ {G}\\right)\\right) + \\mathbf {f} _ {I}). \\tag {12}", + "image_path": "840458f81730901c396e95ac3cbefe1ddeec0971b1defb1a740fc782b30ad3ec.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 556, + 287, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 556, + 287, + 616 + ], + "spans": [ + { + "bbox": [ + 46, + 556, + 287, + 616 + ], + "type": "text", + "content": "In each head, Query comes from visual features " + }, + { + "bbox": [ + 46, + 556, + 287, + 616 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_I" + }, + { + "bbox": [ + 46, + 556, + 287, + 616 + ], + "type": "text", + "content": " while Key and Value come from the learned graph representations " + }, + { + "bbox": [ + 46, + 556, + 287, + 616 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_G" + }, + { + "bbox": [ + 46, + 556, + 287, + 616 + ], + "type": "text", + "content": ". Finally, we get the dynamic graph enhanced visual features " + }, + { + "bbox": [ + 46, + 556, + 287, + 616 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{\\hat{I}}" + }, + { + "bbox": [ + 46, + 556, + 287, + 616 + ], + "type": "text", + "content": ". Notably, the first token in both " + }, + { + "bbox": [ + 46, + 556, + 287, + 616 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{\\hat{I}}" + }, + { + "bbox": [ + 46, + 556, + 287, + 616 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 556, + 287, + 616 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_G" + }, + { + "bbox": [ + 46, + 556, + 287, + 616 + ], + "type": "text", + "content": " is [CLS] to aggregate visual and graph information." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 623, + 170, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 623, + 170, + 635 + ], + "spans": [ + { + "bbox": [ + 47, + 623, + 170, + 635 + ], + "type": "text", + "content": "3.3. Contrastive Learning" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "text", + "content": "Collecting paired image and text data is prohibitively expensive leading to a smaller size of CRG datasets compared with captioning datasets, like COCO [28]. It hinders the potential of existing data-driven CRG systems. In this section, we introduce the image-report contrastive loss used in our DCL, which can effectively improve the visual" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 318, + 70, + 535, + 225 + ], + "blocks": [ + { + "bbox": [ + 318, + 70, + 535, + 225 + ], + "lines": [ + { + "bbox": [ + 318, + 70, + 535, + 225 + ], + "spans": [ + { + "bbox": [ + 318, + 70, + 535, + 225 + ], + "type": "image", + "image_path": "ea6ed29b4b8fd7201931b6f6c67cd8e9724f068a6cc5d277b58feca0db3525ec.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 237, + 545, + 270 + ], + "lines": [ + { + "bbox": [ + 305, + 237, + 545, + 270 + ], + "spans": [ + { + "bbox": [ + 305, + 237, + 545, + 270 + ], + "type": "text", + "content": "Figure 3. illustration of our proposed dynamic graph construction, dynamic graph encoder (DGE), and graph attention (GA) modules. The structure of the pre-constructed graph can be found in Fig. 1." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 278, + 545, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 278, + 545, + 350 + ], + "spans": [ + { + "bbox": [ + 305, + 278, + 545, + 350 + ], + "type": "text", + "content": "and textual representations as well as ensure the report retrieval accuracy in the dynamic graph construction process. Moreover, inspired by recent vision-language pretraining works [21,22], we also adopt an image-report matching loss in the proposed method for further enhancing the representations to improve the performance." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 350, + 546, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 350, + 546, + 534 + ], + "spans": [ + { + "bbox": [ + 305, + 350, + 546, + 534 + ], + "type": "text", + "content": "Image-Report Contrastive Loss (IRC) can activate radiology reporting by encouraging the positive image-report pairs to have similar representations in contrast to the negative pairs. A report encoder with the same architecture as an image encoder is utilized to extract textual representations " + }, + { + "bbox": [ + 305, + 350, + 546, + 534 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_T" + }, + { + "bbox": [ + 305, + 350, + 546, + 534 + ], + "type": "text", + "content": " referring to the positive or negative report. Then we calculate the similar between two [CLS] representations by " + }, + { + "bbox": [ + 305, + 350, + 546, + 534 + ], + "type": "inline_equation", + "content": "s = W_I(V_{cls})^t W_T(T_{cls})" + }, + { + "bbox": [ + 305, + 350, + 546, + 534 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 305, + 350, + 546, + 534 + ], + "type": "inline_equation", + "content": "W_I" + }, + { + "bbox": [ + 305, + 350, + 546, + 534 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 350, + 546, + 534 + ], + "type": "inline_equation", + "content": "W_T" + }, + { + "bbox": [ + 305, + 350, + 546, + 534 + ], + "type": "text", + "content": " are two learnable matrices. We also maintain two queues to store the most recent " + }, + { + "bbox": [ + 305, + 350, + 546, + 534 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 305, + 350, + 546, + 534 + ], + "type": "text", + "content": " image-report representations from the momentum image and report encoders. After a Softmax activation, we can get the image-report similarity " + }, + { + "bbox": [ + 305, + 350, + 546, + 534 + ], + "type": "inline_equation", + "content": "f_m^{i2r}(I) = \\frac{\\exp s(I,T_m) / \\tau}{\\sum_{m=1}^M \\exp s(I,T_m) / \\tau}" + }, + { + "bbox": [ + 305, + 350, + 546, + 534 + ], + "type": "text", + "content": " and the report-image similarity " + }, + { + "bbox": [ + 305, + 350, + 546, + 534 + ], + "type": "inline_equation", + "content": "f_m^{r2i}(T)" + }, + { + "bbox": [ + 305, + 350, + 546, + 534 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 305, + 350, + 546, + 534 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 305, + 350, + 546, + 534 + ], + "type": "text", + "content": " is a learnable temperature parameter. The IRC can be written as follows:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 318, + 540, + 545, + 563 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 540, + 545, + 563 + ], + "spans": [ + { + "bbox": [ + 318, + 540, + 545, + 563 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {I R C}} = \\frac {1}{2} \\left(\\mathcal {L} _ {\\mathrm {c e}} (g (T), f (T)) + \\mathcal {L} _ {\\mathrm {c e}} (g (I), f (I))\\right), \\tag {13}", + "image_path": "22255d8596aaa488fcdc85f6983c31d2668b3b3a02a48f1ea15fa59d85393a2d.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 570, + 545, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 570, + 545, + 593 + ], + "spans": [ + { + "bbox": [ + 305, + 570, + 545, + 593 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 570, + 545, + 593 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{ce}}" + }, + { + "bbox": [ + 305, + 570, + 545, + 593 + ], + "type": "text", + "content": " is the cross entropy loss and " + }, + { + "bbox": [ + 305, + 570, + 545, + 593 + ], + "type": "inline_equation", + "content": "g(I)" + }, + { + "bbox": [ + 305, + 570, + 545, + 593 + ], + "type": "text", + "content": " is the ground truth of image-report similarity." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 594, + 545, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 594, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 305, + 594, + 545, + 677 + ], + "type": "text", + "content": "Image-Report Matching Loss (IRM) is a binary classification task to predict whether the given image-report pair is positive (matched) or negative (unmatched). Different from IRC, we utilize a multimodal encoder to capture the multimodal representations via cross attention mechanism. Then [Encode] vector is projected to " + }, + { + "bbox": [ + 305, + 594, + 545, + 677 + ], + "type": "inline_equation", + "content": "d = 2" + }, + { + "bbox": [ + 305, + 594, + 545, + 677 + ], + "type": "text", + "content": " with a linear layer to predict the probability " + }, + { + "bbox": [ + 305, + 594, + 545, + 677 + ], + "type": "inline_equation", + "content": "p^{itm}" + }, + { + "bbox": [ + 305, + 594, + 545, + 677 + ], + "type": "text", + "content": ". The IRM is conducted as:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 373, + 696, + 545, + 711 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 373, + 696, + 545, + 711 + ], + "spans": [ + { + "bbox": [ + 373, + 696, + 545, + 711 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {I R M}} = \\mathcal {L} _ {\\mathrm {c e}} \\left(g ^ {i t m}, p ^ {i t m}\\right). \\tag {14}", + "image_path": "e93e4cc8507bc169939f6c2e9732abcc75cc1c51b37a556c90df5e9c521e8f32.jpg" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3338" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "type": "text", + "content": "Finally, we calculate the sum of " + }, + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{RG}}" + }, + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{IRC}}" + }, + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{IRM}}" + }, + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "type": "text", + "content": " as our total loss function. Notably, the multimodal encoder is only used during the training process to improve representation learning." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 127, + 128, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 127, + 128, + 140 + ], + "spans": [ + { + "bbox": [ + 47, + 127, + 128, + 140 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 141, + 264, + 154 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 141, + 264, + 154 + ], + "spans": [ + { + "bbox": [ + 47, + 141, + 264, + 154 + ], + "type": "text", + "content": "4.1. Datasets, Evaluation Metrics and Settings" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 160, + 286, + 208 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 160, + 286, + 208 + ], + "spans": [ + { + "bbox": [ + 46, + 160, + 286, + 208 + ], + "type": "text", + "content": "We evaluate our proposed DCL on two widely-used radiology reporting benchmarks, IU-Xray [8] and MIMIC-CXR [18]. We adopt the settings in [7,30] to split those two datasets and preprocess the reports for a fair comparison." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 209, + 286, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 209, + 286, + 304 + ], + "spans": [ + { + "bbox": [ + 46, + 209, + 286, + 304 + ], + "type": "text", + "content": "IU-Xray [8] has been widely used to evaluate the performance of radiology reporting systems. It contains 3,955 radiology reports and 7,470 chest xray images. Either frontal or frontal and lateral view images are associated with each report. Following [7, 20], we exclude those cases with only one image and finally get 2069/296/590 cases for training/validation/testing. By Stanza [47], 739 unique entities are extracted and utilized as dynamic node candidates." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 304, + 286, + 412 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 304, + 286, + 412 + ], + "spans": [ + { + "bbox": [ + 46, + 304, + 286, + 412 + ], + "type": "text", + "content": "MIMIC-CXR [18] is the largest radiology dataset to date, consisting of 368,960 chest X-ray images and 222,758 radiology reports and is splitted officially. Recently, various MIMIC-child datasets have been proposed by exploring structural radiology information, e.g., Chest Image Genome [41] and RadGraph [17]. In this work, we adopt RadGraph to update our dynamic structure. Classified by relation, RadGraph consists of 2,895,725 (suggestive of), 6,115,264 (located at) and 4,010,875 (modify) triplets." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 413, + 286, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 413, + 286, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 413, + 286, + 567 + ], + "type": "text", + "content": "Natural Language Generation Metrics (NLG) are used to measure the descriptive accuracy of predicted reports. CIDEr [40] and BLEU [36] are two main NLG metrics used to measure the quality of predicted reports. BLEU is proposed for machine translation tasks and measures the word n-gram overlap between predictions and reports. Due to the textual bias in CRG datasets, CRG systems can achieve considerable BLEU values even when they just repeat the most frequent sentences. In contrast, CIDEr is tailored to evaluate captioning systems by rewarding topic terms (terminologies in CRG task) and penalizing frequent terms. Additionally, values of ROUGE-L [27] and METEOR [3] are also reported for comparison." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 569, + 286, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 569, + 286, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 569, + 286, + 688 + ], + "type": "text", + "content": "Clinical Efficacy Metrics are recently proposed to capture and evaluate the clinical correctness of predicted reports. It first employs the CheXPert labeling tool proposed in [16] to label predicted reports and the ground truth reports in 14 different medical terminologies. Then classification measurements, i.e., F1-Score, Precision and Recall are calculated to evaluate how well the generated report describes the abnormalities. Since the provider of IU-Xray does not use CheXPert to build the labels, CE metrics are only reported on the MIMIC-CXR dataset [38, 44]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 689, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 286, + 712 + ], + "type": "text", + "content": "Experimental Settings We use the same image encoder for different views images and concatenate visual tokens via" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 319, + 72, + 531, + 225 + ], + "blocks": [ + { + "bbox": [ + 319, + 72, + 531, + 225 + ], + "lines": [ + { + "bbox": [ + 319, + 72, + 531, + 225 + ], + "spans": [ + { + "bbox": [ + 319, + 72, + 531, + 225 + ], + "type": "image", + "image_path": "7407a8d427a25fa7fad2690310394273c65d47752003f30fb1585cc2b269d060.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 236, + 545, + 258 + ], + "lines": [ + { + "bbox": [ + 305, + 236, + 545, + 258 + ], + "spans": [ + { + "bbox": [ + 305, + 236, + 545, + 258 + ], + "type": "text", + "content": "Figure 4. Micro-average of receiver operating characteristic curve for clinical abnormalities predictions from the generated reports." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 268, + 545, + 435 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 268, + 545, + 435 + ], + "spans": [ + { + "bbox": [ + 304, + 268, + 545, + 435 + ], + "type": "text", + "content": "fusion operation for further process. Considering the domain gap between medical and generic texts, we employ a pretrained SciBert [4] to serve as a tokenizer and report encoder. The model is trained on 4 NVIDIA 2080 Ti GPUs with batch sizes 8 and 30 epochs. The checkpoint acquires the highest CIEDr metric is used for testing. The learning rate is set as 1e-4 and the optimizer is AdamW [34] with a weight decay of 0.02. The top 3 similar reports from the text queue " + }, + { + "bbox": [ + 304, + 268, + 545, + 435 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 304, + 268, + 545, + 435 + ], + "type": "text", + "content": " are retrieved. And the size of " + }, + { + "bbox": [ + 304, + 268, + 545, + 435 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 304, + 268, + 545, + 435 + ], + "type": "text", + "content": " is set as 65,536 and 1,380 for MIMIC-CXR and IU-Xray. The max length of specific knowledge is set as 90. For batch operation, the nodes in " + }, + { + "bbox": [ + 304, + 268, + 545, + 435 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 268, + 545, + 435 + ], + "type": "text", + "content": " are padded to 50 with a [PAD] token. Note that, we project all encoded vectors by a linear transformation layer into the dimension of " + }, + { + "bbox": [ + 304, + 268, + 545, + 435 + ], + "type": "inline_equation", + "content": "d = 768" + }, + { + "bbox": [ + 304, + 268, + 545, + 435 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 444, + 390, + 455 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 444, + 390, + 455 + ], + "spans": [ + { + "bbox": [ + 306, + 444, + 390, + 455 + ], + "type": "text", + "content": "4.2. Main Results" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 462, + 545, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 545, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 545, + 676 + ], + "type": "text", + "content": "Descriptive Accuracy In Tab. 1, we compare our DCL with a wide range of existing state-of-the-art CRG systems on two benchmarks. R2Gen [7] and CMN [6] have been widely used as baseline CRG models recently. KERP [20], MKG [46], PPKED [30] and MGSK [44] are proposed to integrate medical knowledge with typical CRG backbones. CA [31] and CMCL [29] employ contrastive learning and curriculum learning to improve performance. The performances of other baseline models, such as HRGP [19], M2TR [35] and TopDown [1] are also reported. Since we follow the same settings, we directly cite the results from original papers. As shown in Tab. 1, our DCL achieves the SOTA descriptive accuracy, which outperforms others in CIDEr and ROUGE-L metrics and matches their performances in BLEU-4 and METEOR metrics. Higher CIDEr values demonstrate that our model does not repeat frequent sentences in training set but generates reports with more accurate topics." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 677, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 712 + ], + "type": "text", + "content": "Clinical Correctness We also evaluate our method by clinical efficacy (CE) metrics on the MIMIC-CXR dataset and compare the performances with other baseline models. Fol-" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3339" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 547, + 222 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 547, + 222 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 547, + 222 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 547, + 222 + ], + "type": "table", + "html": "
Iu-Xray [8]MIMIC-CXR [18]
MethodsCIDErBLEU-4ROUGE-LMETEORMethodsCIDErBLEU-4ROUGE-LMETEOR
R2Gen [7]0.3980.1650.3710.187R2Gen [7]0.2530.1030.2770.142
KERP [20]0.2800.1620.339-CMN [6]-0.1060.2780.142
HRGP [19]0.3430.1510.322-TopDown [1]0.0730.0920.2670.129
MKG [46]0.3040.1470.367-M2TR [35]-0.1070.2720.145
PPKED [30]0.3510.1680.3760.190PPKED [30]0.2370.1060.2840.149
MGSK [44]0.3820.1780.381-MGSK [44]0.2030.1150.284-
CA [31]-0.1690.3810.193CA [31]-0.1090.2830.151
CMCL [29]-0.1620.3780.186CMCL [29]-0.0970.2810.133
Ours0.5860.1630.3830.193Ours0.2810.1090.2840.150
", + "image_path": "16cb1acd91aa55ce9a6a37ff1d78e74687bc89ca8bdc8c12415da1ddce97b383.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 62, + 259, + 272, + 385 + ], + "blocks": [ + { + "bbox": [ + 46, + 229, + 546, + 252 + ], + "lines": [ + { + "bbox": [ + 46, + 229, + 546, + 252 + ], + "spans": [ + { + "bbox": [ + 46, + 229, + 546, + 252 + ], + "type": "text", + "content": "Table 1. The performances of our proposed DCL compared with other state-of-the-art systems on IU-Xray and MIMIC-CXR dataset. The best results in each column are highlighted in bold. CIDEr [40] is proposed to evaluate captioning systems." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 62, + 259, + 272, + 385 + ], + "lines": [ + { + "bbox": [ + 62, + 259, + 272, + 385 + ], + "spans": [ + { + "bbox": [ + 62, + 259, + 272, + 385 + ], + "type": "table", + "html": "
MethodsPrecisionRecallF1-score
TopDown [1]0.1660.1210.133
M2TR [35]0.2400.4280.308
R2Gen [7]0.3330.2730.276
MKSG [44]0.4580.3480.371
Ours w/o G0.2750.1850.194
Ours w/o LIRC0.4630.3370.359
Ours w/o LIRM0.4690.3530.372
Ours0.4710.3520.373
", + "image_path": "28aeb635b1d1f8e9ad9c9e619668a89e38807259963ece838860e1592f332bb0.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 393, + 287, + 415 + ], + "lines": [ + { + "bbox": [ + 46, + 393, + 287, + 415 + ], + "spans": [ + { + "bbox": [ + 46, + 393, + 287, + 415 + ], + "type": "text", + "content": "Table 2. The comparison of the clinical efficacy metrics on MIMIC-CXR dataset. The w/o is the abbreviation of without." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 426, + 287, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 426, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 287, + 581 + ], + "type": "text", + "content": "lowing official splitting, we directly cite the results from [44] for comparison. In Fig. 4, we show the micro-average of ROC for 14 chesty terminologies prediction and present the AUC scores. 'Pleural Effusion' and 'Pleural Other' achieve the highest AUCs (0.82). The experimental results in Tab. 2 reveal that our DCL significantly outperforms the previous models on three CE metrics. Compared with the current SOTA method MGSK [44] that also leverages general prior knowledge and specific knowledge from RadGraph [17], we make a performance-boosting. The improvement verifies the importance of our dynamic graph concepts and also demonstrates that our system can predict more accurate clinical information." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 582, + 141, + 594 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 582, + 141, + 594 + ], + "spans": [ + { + "bbox": [ + 47, + 582, + 141, + 594 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 594, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 677 + ], + "type": "text", + "content": "In this section, we conduct ablation studies on IU-Xray and MIMIC-CXR datasets to investigate the contribution of each component in our proposed DCL. Tab. 3 presents the quantitative analysis of DCL on IU-Xray with measuring descriptive accuracy. And clinical correctness evaluation is reported in Tab. 2. Our base model only keeps the image encoder and report decoder and employs " + }, + { + "bbox": [ + 46, + 594, + 287, + 677 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{RG}}" + }, + { + "bbox": [ + 46, + 594, + 287, + 677 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "content": "Effect of Dynamic Graph Our dynamic graph is constructed in a bottom-up manner, that exploits general knowledge from " + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "inline_equation", + "content": "G_{pre}" + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "content": " and specific knowledge " + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "inline_equation", + "content": "K_I" + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "content": " extracted from" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 261, + 545, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 261, + 545, + 453 + ], + "spans": [ + { + "bbox": [ + 304, + 261, + 545, + 453 + ], + "type": "text", + "content": "retrieved Top-3 similar reports. Comparing the base model with settings (a) and (b), our dynamic graph can boost the performance of base model, substantially. More specifically, leveraging the general knowledge only lead to an increase on all NLG metrics by " + }, + { + "bbox": [ + 304, + 261, + 545, + 453 + ], + "type": "inline_equation", + "content": "15.2\\%" + }, + { + "bbox": [ + 304, + 261, + 545, + 453 + ], + "type": "text", + "content": " on CIDEr and " + }, + { + "bbox": [ + 304, + 261, + 545, + 453 + ], + "type": "inline_equation", + "content": "1.1\\%" + }, + { + "bbox": [ + 304, + 261, + 545, + 453 + ], + "type": "text", + "content": " on BLEU-4. By integrating specific knowledge, our dynamic graph can further boost the performances, e.g. " + }, + { + "bbox": [ + 304, + 261, + 545, + 453 + ], + "type": "inline_equation", + "content": "0.535 \\rightarrow 0.557" + }, + { + "bbox": [ + 304, + 261, + 545, + 453 + ], + "type": "text", + "content": " on CIDEr. It demonstrates the effectiveness and necessity of constructing dynamic graphs for each image. We hypothesize that this performance improvement may be due to that the dynamic knowledge can emphasize keywords when generating reports since dynamic nodes are from retrieved reports. It has been proved in Tab. 2, leveraging dynamic graph significantly improve the performances on all CE metrics, which means the generated reports can provide more accurate medical terminologies." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 452, + 545, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 452, + 545, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 452, + 545, + 617 + ], + "type": "text", + "content": "Effect of Contrastive Learning Sequentially, we evaluate the effectiveness of two introduced learning objectives, i.e., image report contrastive loss (IRC) and image report matching loss (IRM). The performances of settings (b,c) in Tab. 2 show that both IRC and IRM can boost the base model performances. It proves the importance of visual and textual representation qualities since severe data bias in CRG datasets will degenerate the representation capabilities seriously. However, comparing (c) and (d), it is observed that IRC brings more improvement than IRM. We speculate the reason is that IRC can straightly improve visual and textual representations by aligning similar pairs. In contrast, IRM works on multimodal representations and represents unimodal in an indirect manner." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "Choice of Parameter Initialization We employ a pretrained ViT [10] and SciBert [4] as image and report encoder in our implementation. It is worth noting that Transformers lack some of the inductive biases inherent to CNNs and therefore generalize bad with insufficient and unbalanced data [10]. Not surprisingly, comparing setting (f) and the full model, the performances drop steeply without pretrained ViT parameters. 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", + "image_path": "a9994a6c9875bc414d96ddd2548ec1c9254f3e017380b37dce64d3ef04fd1246.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 50, + 245, + 544, + 329 + ], + "blocks": [ + { + "bbox": [ + 46, + 221, + 546, + 243 + ], + "lines": [ + { + "bbox": [ + 46, + 221, + 546, + 243 + ], + "spans": [ + { + "bbox": [ + 46, + 221, + 546, + 243 + ], + "type": "text", + "content": "Table 3. Quantitative analysis of proposed method on IU-Xray dataset. The base model consists of an image encoder and a report decoder with report generation loss only." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 245, + 544, + 329 + ], + "lines": [ + { + "bbox": [ + 50, + 245, + 544, + 329 + ], + "spans": [ + { + "bbox": [ + 50, + 245, + 544, + 329 + ], + "type": "table", + "html": "
ImageGround Truth ReportRetrieved Specific KnowledgeOursR2Gen
Lateral view somewhat limited due to overlying motion artifact lungs are low in volume there is no focal airspace the consolidation to suggest pneumonia a 1 2-cm calcified granuloma just below the medial aspect of the right hemidiaphragm is unchanged from prior study no pleural effusions or pulmonary edema there is no pneumothorax the inferior sternotomy wire is fractured but unchanged surgical clips and vascular markers in the thorax are related to prior cabg surgery.effusion located _ at pleural,vascular modify pulmonary, sternotomy suggestive _ of cabg,consolidation suggestive _ of effusion,effusion suggestive _ of consolidation,low modify effusion,low suggestive _ of effusion, low suggestive _ of consolidation,vascular modify chest,effusion suggestive _ of atelectasis,atelectasis modify lunglung volumes are low. there is no focal consolidation effusion or pneumothorax. airspace consolidation is noted within the left upper lobe compatible with pneumonia. borderline size of the cardiac silhouette without evidence of pulmonary edema, midline sternotomy wires and mediastinal clips are again noted.ap upright and lateral views of the chest provided . lung volumes are low limiting assessment . allowing for this there is no focal consolidation effusion or pneumothorax . the cardiomeiastinal silhouette is normal . imaged osseous structures are intact . no free air below the right hemidiaphragm is seen.
", + "image_path": "98c0b82415d6aeb3d03901db95e9832e4d0907a5c42dc7e9a9431e92882dc6cd.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 337, + 546, + 361 + ], + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 337, + 546, + 361 + ], + "spans": [ + { + "bbox": [ + 46, + 337, + 546, + 361 + ], + "type": "text", + "content": "Figure 5. Illustrations of reports from ground truth, ours and R2Gen [7] and retrieved specific knowledge for one sample from MIMIC-CXR [18]. For better visualization, different colors highlight different medical entities." + } + ] + } + ], + "index": 3, + "type": "text" + }, + { + "bbox": [ + 46, + 369, + 288, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 369, + 288, + 441 + ], + "spans": [ + { + "bbox": [ + 46, + 369, + 288, + 441 + ], + "type": "text", + "content": "demonstrate the effectiveness of pretrained SciBert. The improvement comes from two aspects. Firstly, it provides well pretrained parameters; Secondly, its tokenizer encodes each token (medical terminology) with a well pretrained embedding, which avoids Graph Transformers to propagate similar hidden states [49]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 447, + 123, + 460 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 447, + 123, + 460 + ], + "spans": [ + { + "bbox": [ + 47, + 447, + 123, + 460 + ], + "type": "text", + "content": "4.4. Case Study" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 462, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 462, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 462, + 288, + 715 + ], + "type": "text", + "content": "To further investigate the effectiveness of our method, we perform qualitative analysis on MIMIC-CXR [18] with their retrieved specific knowledge, and reports from ground truth, our model and R2Gen [7]. Entities extracted by Stanza [47] from the ground truth report have been highlighted with different colors. It is observed that some entities, e.g. cabg, consolidation, and sternotomy) are not included in the pre-constructed graph node lists. This observation proves our motivation for constructing knowledge graphs dynamically. We conduct the same operation on retrieved reports and use extracted entities to quote related triplets from RadGraph [17]. Those triplets are known as specific knowledge in this paper and shown in Fig. 5. Retrieved specific knowledge triplets " + }, + { + "bbox": [ + 46, + 462, + 288, + 715 + ], + "type": "inline_equation", + "content": "<" + }, + { + "bbox": [ + 46, + 462, + 288, + 715 + ], + "type": "text", + "content": " sternotomy,suggestive_of,cabg> and " + }, + { + "bbox": [ + 46, + 462, + 288, + 715 + ], + "type": "inline_equation", + "content": "<" + }, + { + "bbox": [ + 46, + 462, + 288, + 715 + ], + "type": "text", + "content": " consolidation,suggestive_of,effusion> demonstrate that the retrieved reports contain similar medical terminologies and clinical information. We speculate that IRC and IRM objectives bring such capabilities. Then the entities in our dynamic graph emphasize disease/organ keywords when generating reports and it is why our DCL can predict sen" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 369, + 546, + 393 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 369, + 546, + 393 + ], + "spans": [ + { + "bbox": [ + 304, + 369, + 546, + 393 + ], + "type": "text", + "content": "tence \"airspace consolidation is noted within the left upper lobe compatible with pneumonia,\" but R2Gen can not." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 396, + 458, + 407 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 396, + 458, + 407 + ], + "spans": [ + { + "bbox": [ + 305, + 396, + 458, + 407 + ], + "type": "text", + "content": "5. Conclusion and Discussion" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 410, + 546, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 410, + 546, + 553 + ], + "spans": [ + { + "bbox": [ + 304, + 410, + 546, + 553 + ], + "type": "text", + "content": "In this paper, we present a practical approach to leverage dynamic graph to enhance contrastive learning for radiology report generation. In which the dynamic graph is constructed in a bottom-up manner to integrate retrieved specific knowledge with general knowledge. Then contrastive learning is employed to improve visual and textual representations, which also promises the accuracy of our dynamic graph. Experiments on two popular benchmarks verify the effectiveness of our method in generating accurate and meaningful reports. More encouragingly, our approach can outperform or match existing SOTA methods in language generation and clinical efficacy metrics." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 553, + 545, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 553, + 545, + 649 + ], + "spans": [ + { + "bbox": [ + 304, + 553, + 545, + 649 + ], + "type": "text", + "content": "Limitation and Future Work Retrieved reports can not be exactly the same as ground truth, and knowledge noises are involved during the dynamic graph construction process. It may guide the model to generate inaccurate sentences. In the future, we plan to propose a specific objective for the dynamic graph construction process to further improve the accuracy of dynamic graphs and the quality of predicted reports." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 651, + 409, + 664 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 651, + 409, + 664 + ], + "spans": [ + { + "bbox": [ + 306, + 651, + 409, + 664 + ], + "type": "text", + "content": "Acknowledgements" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 665, + 546, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 546, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 546, + 712 + ], + "type": "text", + "content": "This work was partially supported by \"Taishan Scholars Youth Expert Program\" of Shandong Province, and partially supported by National Key R&D Program of China under Grant No. 2020AAA0109700." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "3341" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "type": "text", + "content": "[1] Peter Anderson, Xiaodong He, Chris Buehler, Damien Teney, Mark Johnson, Stephen Gould, and Lei Zhang. 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In Proceedings of the Conference on Neural Information Processing Systems, 2022. 5, 8" + } + ] + } + ], + "index": 26 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3343" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Dynamic Graph Learning With Content-Guided Spatial-Frequency Relation Reasoning for Deepfake Detection/0db433fe-2bb5-4d32-8dad-d6501909824f_content_list.json b/2023/Dynamic Graph Learning With Content-Guided Spatial-Frequency Relation Reasoning for Deepfake Detection/0db433fe-2bb5-4d32-8dad-d6501909824f_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..9b692f869e9360818ec6df0ff18899d0647353b2 --- /dev/null +++ b/2023/Dynamic Graph Learning With Content-Guided Spatial-Frequency Relation Reasoning for Deepfake Detection/0db433fe-2bb5-4d32-8dad-d6501909824f_content_list.json @@ -0,0 +1,1465 @@ +[ + { + "type": "text", + "text": "Dynamic Graph Learning with Content-guided Spatial-Frequency Relation Reasoning for Deepfake Detection", + "text_level": 1, + "bbox": [ + 105, + 161, + 863, + 204 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yuan Wang $^{1,2,4}$ Kun Yu $^{2}$ Chen Chen $^{1*}$ Xiyuan Hu $^{3}$ Silong Peng $^{1,4,5}$", + "bbox": [ + 193, + 226, + 771, + 245 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ Institute of Automation, Chinese Academy of Sciences $^{2}$ Alibaba Group", + "bbox": [ + 189, + 245, + 779, + 260 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{3}$ School of Computer Science and Engineering, Nanjing University of Science and Technology", + "bbox": [ + 112, + 260, + 855, + 277 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "4University of Chinese Academy of Sciences 5Beijing Visystem Co.Ltd", + "bbox": [ + 191, + 277, + 774, + 293 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{wangyuan2020, chen.chen}@ia.ac.cn yukun.yk@alibaba-inc.com xiyuan.hu@foxmail.com", + "bbox": [ + 112, + 296, + 852, + 309 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 340, + 312, + 355 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "With the springing up of face synthesis techniques, it is prominent in need to develop powerful face forgery detection methods due to security concerns. Some existing methods attempt to employ auxiliary frequency-aware information combined with CNN backbones to discover the forged clues. Due to the inadequate information interaction with image content, the extracted frequency features are thus spatially irrelevant, struggling to generalize well on increasingly realistic counterfeit types. To address this issue, we propose a Spatial-Frequency Dynamic Graph method to exploit the relation-aware features in spatial and frequency domains via dynamic graph learning. To this end, we introduce three well-designed components: 1) Content-guided Adaptive Frequency Extraction module to mine the content-adaptive forged frequency clues. 2) Multiple Domains Attention Map Learning module to enrich the spatial-frequency contextual features with multiscale attention maps. 3) Dynamic Graph Spatial-Frequency Feature Fusion Network to explore the high-order relation of spatial and frequency features. Extensive experiments on several benchmark show that our proposed method sustainably exceeds the state-of-the-arts by a considerable margin.", + "bbox": [ + 75, + 370, + 472, + 675 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 77, + 701, + 208, + 714 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent years have witnessed the continuous advances in deepfake creation [11, 27, 36]. Utilizing booming open-source tools such as Deepfakes [41], novices can readily manipulate the expression and identity of faces to generate visually untraceable videos. Face forgery technology has stimulated many applications [12, 14, 44, 46] with wide acceptance. These techniques can whereas be abused by ma", + "bbox": [ + 75, + 725, + 468, + 823 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/65a14129cd9a7343e4adbb1dab98573255871ae136ab6f7f0213a343d9f17953.jpg", + "image_caption": [ + "Figure 1. The motivation of our proposed approach. Our SFDG method (a) delves into the high-order relationships (b) of spatial and frequency domain via cross-domain graph reasoning (c)." + ], + "image_footnote": [], + "bbox": [ + 534, + 343, + 862, + 514 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "licious intentions to make pornographic movies, fake news and political rumors. In the circumstances, it is desperately in need to develop powerful forgery detection methods.", + "bbox": [ + 497, + 600, + 890, + 643 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Early face forgery detection methods [7,30,52] treat this challenge as vanilla dichotomy tasks in the prevailing view. They use off-the-shelf backbones to extract the global feature of faces and a binary classifier follow-up to identify the real and counterfeit faces. However, as the counterfeits become increasingly realistic, it is intractable for these methods to spot subtle and local forgery traces. One recent study [50] reformulates deepfake detection as a fine-grained classification task and designs a multi-attentional framework to extract local discriminative features from multiple attention maps. It is susceptible to common disturbances and the generalized features remain therefore poorly understood. Some other works resort to specific forgery patterns to encourage better classification such as DCT [24,28], SRM [25] and steganalysis features [45]. Although promising advances have been achieved by these previous works,", + "bbox": [ + 497, + 644, + 892, + 866 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 129, + 49, + 200, + 84 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 252, + 48, + 791, + 87 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Chen Chen is the corresponding author. This work is supported by the National Key R&D Program of China under Grant 2021YFF0602101, Alibaba Group through Alibaba Research Intern Program.", + "bbox": [ + 75, + 831, + 468, + 866 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "7278", + "bbox": [ + 468, + 885, + 500, + 897 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "they always extract frequency features with hand-crafted filter banks which are content-irrelevant, thus incapable to adapt the changes of complex scenarios. Moreover, they fuse multi-domain information via adding directly or attentional projection. However, these approaches devote little efforts to discover the high-order relation of spatial and frequency features and integrating them in a reasonable way.", + "bbox": [ + 75, + 125, + 468, + 223 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we provide seminal insights to exploit adaptive frequency features and delve into the interactions of spatial-frequency domains. To this end, we propose an adaptive extraction-multiscale enhancement-graph fusion paradigm for deepfake detection via dynamic graph learning, which prompts to excavate content-aware frequency clues and the high-order relation of multiple domains.", + "bbox": [ + 75, + 223, + 468, + 319 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Firstly, for adaptive frequency extraction, we tailor a Content-guided Adaptive Frequency Extraction (CAFÉ) module with coarse-grained DCT and fine-grained DCT to capture the local frequency cues guided by content-aware masks. Different from PEL [9] and F3Net [28], our customized frequency learning protocol provides potential for more combinations of frequency features, which is indispensable to spot complicated counterfeit patterns.", + "bbox": [ + 75, + 319, + 468, + 429 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To further enhance the representation of content-guided frequency features, we introduce a Multiple Domains Attention Map Learning (MDAML) module to generate multiscale spatial and frequency attention maps with high-level semantic features. Specifically, we first propose a MultiScale Attention Ensemble (MSAE) module, which produces multi-scale semantic attention maps with large receptive fields and endows rich contextual information to spatial and frequency domains. Moreover, an Attention Map Refinement Block (AMRB) is included in the MSAE module to refine the obtained semantic attention maps conducive to the following feature learning. In comparison with MADD [50] that merely emphasizes the spatial domain, we further introduce the semantic-relevant frequency attention map with rich semantic information retained for the subsequent spatial-frequency relation-discovery paradigm.", + "bbox": [ + 75, + 429, + 468, + 650 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Finally, to fully discover the spatial and frequency relationships, we propose a Dynamic Graph-based Spatial-Frequency Feature Fusion network (DG-SF $^3$ Net) to formulate the interaction of two domains via a graph-based relation discovery protocol. Specifically, DG-SF $^3$ Net is composed of two ingredients: Dynamic GCN [16] and Graph Information Interaction layers. The former constructs kNN-graph dynamically and performs graph convolution to reason high-order relationships in spatial and frequency domains, while the latter is designed to enhance the mutual relation with several graph-weighted MLP-Mixer [40] layers via channel-wise and node-wise interaction.", + "bbox": [ + 75, + 650, + 468, + 815 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The achievements, including contributions are threefold:", + "bbox": [ + 95, + 815, + 467, + 830 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "From a new perspective, we propose a novel SpatialFrequency Dynamic Graph (SFDG) framework, which", + "bbox": [ + 95, + 838, + 468, + 866 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "is qualified to exploit relation-aware spatial-frequency features to promote generalized forgery detection.", + "bbox": [ + 529, + 125, + 889, + 153 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- We first harness a CAFÉ module for content-aware frequency feature extraction, and then tailor an MDAML scheme to dig deeper into multiscale spatial-frequency attention maps with rich contextual understanding of forgeries. Finally, a seminal DG-SF3Net module is proposed to discover the multi-domain relationships with a graph-based relation-reasoning approach.", + "bbox": [ + 517, + 161, + 890, + 258 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- Our method achieves state-of-the-art performance on six benchmark datasets. The cross-dataset experiment and the perturbation analysis show the robustness and generalization ability of the proposed SFDG method.", + "bbox": [ + 517, + 266, + 890, + 321 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 499, + 332, + 648, + 346 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Over the past several years, with the remarkable progress of forgery creation techniques, increasing efforts have been made to boost the development of face forgery detection in computer vision communities. In this section, we briefly review previous works exploring the authenticity of faces.", + "bbox": [ + 497, + 355, + 890, + 423 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Rudimentary deepfake detection approaches base primarily on obvious counterfeit artifacts, which utilize handcrafted features to detect anomalies in spatial domain, e.g., inconsistent head pose [47] and unnatural eye blinding [21]. However, these traditional methods feel intractable to deal with the improved realistic deepfakes. With the overwhelming success of deep learning, some works [1,4,7] adopt off-the-shelf classification backbones to extract high-level semantic features for deepfake detection. Although considerable performances have been achieved on specific datasets, their vanilla structures would lead to catastrophic overfitting and lag behind the advanced face synthesis technology.", + "bbox": [ + 497, + 423, + 890, + 589 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To further exploit the essential forged clues, general deepfake detection [15, 20, 26, 34, 35] has been an area of intense investigation. Nguyen et al. [26] employ multi-task learning strategy to detect forged artifacts and locate manipulated regions simultaneously. Face X-ray [20] observes the specific blending step of face swapping and locates forgery boundary in a self-supervised manner. FReTAL [15] adopts the knowledge distillation to prevent catastrophic forgetting and enhance adaptability in different domains. DCL [35] performs dual-granularity contrastive learning to further improve the generalization. However, these approaches captures category-level differences instead of the intrinsic discrepancies between authentic and forged images.", + "bbox": [ + 497, + 590, + 890, + 769 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recently, other studies focus on mining specific forgery patterns, such as local texture, high-frequency noise, reconstruction residual and frequency clues. Among them, Zhao et al. [50] propose a fine-grained deepfake detection framework that aggregates the local texture and high-level semantic information into multiple attention maps. However, it fails to distinguish highly compressed videos with", + "bbox": [ + 497, + 769, + 890, + 866 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "7279", + "bbox": [ + 468, + 885, + 500, + 897 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/4f756507a3fb744590ae39856c3cef5c39a6c2050113dbf40bd29be759eb3c08.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 132, + 123, + 835, + 273 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/35ab0c4e7a12857f24ffbc12c86fd7064c6935e24b64d456ce117c85af0e68ac.jpg", + "image_caption": [ + "Figure 2. (a) Overview of the proposed Spatial-Frequency Dynamic Graph (SFDG) framework. (b) The Content-guided Adaptive Frequency Extraction (CAFÉ) module. (c) The Multiple Domains Attention map Learning (MDAML) network." + ], + "image_footnote": [], + "bbox": [ + 132, + 274, + 835, + 401 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "blurry texture. Luo et al. [25] utilize the high-pass filter SRM [8] to extract high-frequency noise guiding face forgery detection. RECCE [2] employs the reconstruction difference of authentic faces as guidance of forgery traces. $\\mathrm{F}^3\\mathrm{Net}$ [28] collaboratively mines the forged frequency clues with frequency-aware decomposition and local frequency statistics. However, the extracted frequency feature is coarse-grained, incapable of assembling discriminative feature patterns. To ameliorate this issue, PEL [9] learns the fine-grained frequency features using sliding window DCT combined with RGB images in a progressive enhancement learning fashion. Nevertheless, the fine-grained frequency is content-irrelevant and in compliance with the vanilla spatial-frequency fusion ethos, thus failing to achieve the utter information interaction of both domains.", + "bbox": [ + 75, + 471, + 468, + 678 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Different from existing studies, our proposed end-to-end SFDG approach excavates content-adaptive frequency clues and facilitates the comprehensive fusion of spatial and frequency features via dynamic graph learning.", + "bbox": [ + 75, + 678, + 468, + 733 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 77, + 745, + 168, + 758 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we propose a Spatial-Frequency Dynamic Graph (SFDG) framework, which consists of three major modules, i.e., Content-guided Adaptive Frequency Extraction (CAFÉ), Multiple Domains Attention Map Learning (MDAML), and Dynamic Graph Spatial Frequency Feature Fusion Network (DG-SF $^3$ Net). The primary idea of our approach is to exploit content-aware frequency features uti", + "bbox": [ + 75, + 769, + 468, + 866 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "lizing CAFÉ module. As limited context information do these features embrace, we present the MDAML module to generate high-level frequency attention maps in a multiscale learning manner. Beyond these improvements, we finally design a DG-F3Net to perform relation reasoning of spatial and frequency features via dynamic graph learning.", + "bbox": [ + 497, + 471, + 892, + 555 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Content-aware Frequency Extraction", + "text_level": 1, + "bbox": [ + 497, + 567, + 823, + 581 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Towards the frequency-aware face forgery detection, former studies generally use DCT to transform the input image into frequency domain. However, for the scarcity of spatial information in DCT process, the extracted frequency feature is presumably not compatible to the image content. To this end, we propose the CAFÉ module to fully exploit the forgery clues via content-aware frequency learning in order to handle complex or simple manipulated patterns adaptively. Without loss of generality, let $x^{s}\\in \\mathbb{R}^{3\\times H\\times W}$ denotes the RGB image, where $H$ and $W$ are the height and width of the input image. As shown in Fig. 2(b), we generate an attentional content mask $M^s$ using a UNet [29] submodule with the spatial information retained. We then propose a coarse-grained counterpart to partition the compact frequency spectrum into several bands. Specifically, we manually design $N_{f}$ binary filters $\\{f_i|i = 1,\\dots,N_f\\}$ to decompose the frequency domains into low, middle and high frequency bands. The low-frequency component lies on the top-left corner while the high-frequency response locates on the bottom-right corner [28]. As described, the", + "bbox": [ + 497, + 590, + 890, + 866 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "7280", + "bbox": [ + 468, + 885, + 500, + 897 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "coarse-grained process can be formulated as:", + "bbox": [ + 77, + 125, + 374, + 138 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nx _ {\\text {c o a r s e}} ^ {f, i} = \\mathcal {H} ^ {- 1} \\left[ \\mathcal {H} \\left(x ^ {s}\\right) \\odot f ^ {i} \\right], \\quad i = \\{1, 2, \\dots , N _ {f} \\}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 95, + 147, + 468, + 169 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\odot$ is the Hadamard product. $\\mathcal{H}$ and $\\mathcal{H}^{-1}$ represent the DCT and inverse DCT respectively. $x_{coarse}^{f}\\in \\mathbb{R}^{3N_{f}\\times H\\times W}$ is the extracted coarse frequency feature, which indicates global frequency information to some extent.", + "bbox": [ + 75, + 176, + 468, + 231 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Further, we design a fine-grained frequency extraction method to emphasize on the localized frequency features. Specifically, we slice $x^{s}$ via a sliding window to obtain a set of $l\\times l$ patches. $p_{m,n}\\in \\mathbb{R}^{3\\times l\\times l}$ denotes the patch sliced by the $(m$ -th, $n$ -th) sliding window. After performing DCT on each patch, we get the localized fine-grained frequency features $d_{m,n}^{f}\\in \\mathbb{R}^{3\\times l\\times l}$ . We repeat the channel of each $d_{m,n}^{f}$ to match the coarse-grained frequency features abovementioned. All localized patched are then gathered into a whole feature map $d^{f}\\in \\mathbb{R}^{3N_{f}\\times H\\times W}$ and go through several convolution Blocks composed by Conv2d, BN, and ReLU to form the output fine-grained frequency features $x_{fine}^{f}$ .", + "bbox": [ + 75, + 232, + 468, + 399 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Finally, we obtain the overall frequency head $x^{fh}$ through an adaptive frequency combine module guided by the learned content mask $M^s$ , which can be formulated as:", + "bbox": [ + 75, + 399, + 468, + 441 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nx ^ {f h} = \\left(1 - M ^ {s}\\right) \\odot x _ {f i n e} ^ {f} + M ^ {s} \\odot x _ {c o a r s e} ^ {f}. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 126, + 448, + 468, + 467 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The extracted frequency head $x^{fh} \\in \\mathbb{R}^{3N_f \\times H \\times W}$ will be fed into several stride convolution layers to obtain the final frequency feature $C_f$ channels $x^f$ with size of $H_f \\times W_f$ .", + "bbox": [ + 75, + 476, + 468, + 521 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Multiple Domains Attention Map Learning", + "text_level": 1, + "bbox": [ + 77, + 527, + 443, + 542 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To fully exploit the forged clues in spatial domain, we adopt EfficientNet-b4 as the backbone and further partition the entire network into low-level, mid-level and high-level layers, respectively. As shown in Fig. 2(c), to acquire spatial-frequency features with rich semantics, we further design a Multi-Scale Attention Ensemble (MSAE) module in spatial and frequency domains to generate multiscale attention maps and aggregate them with hierarchical feature pyramid. The MSAE includes light weighted ConvBlocks, which consist of several convolution layer, BN and non-linear activation layers ReLU, and certain global average layers to downsample the attention maps into multiple scales. With the multi-scale feature representation, we can obtain a sufficient receptive field and rich contextual information, which are of great significance for the deepfake detection task. Inspired by [48], we propose an Attention Map Refinement Block (AMRB) to get refined feature maps.", + "bbox": [ + 75, + 548, + 468, + 783 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As Fig. 2(c) shows, AMRB employs global average pooling to capture global context and uses a subsequent sigmoid layer to produce an attention vector that determines the feature distribution of attention maps in each scale. Finally, we upsample the refined multi-scale attention maps to the original size and add them spatially. We use AMRB in", + "bbox": [ + 75, + 783, + 468, + 866 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "both spatial and frequency streamline to acquire the multiscale spatial attention map $F^{s}$ and frequency feature map $F^{f}$ , which have $T_{s}$ and $T_{f}$ channels on behalf of the corresponding number of attention maps in these two domains.", + "bbox": [ + 499, + 125, + 890, + 181 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "After obtaining the refined multi-scale attention maps $F^{s}$ and $F^{f}$ , we perform Bilinear Attention Pooling (BAP) [23] to get the relation-aware feature matrix $P^{s}$ and $P^{f}$ respectively. As illustrated in Fig. 2(c), we use the Textural Feature Enhancement block [50] to capture the manipulated artifacts hidden in low-level layers. After the enhancement of the texture features, we get a textual feature map $F^{tex} \\in \\mathbb{R}^{C_{tex} \\times H_{tex} \\times W_{tex}}$ . For the spatial domain, we element-wisely multiply textural feature map $F^{tex}$ by each spatial attention map $F_{k}^{s}$ to obtain the partial textural feature maps $F_{k}^{tex}$ and compute the final spatial feature matrix employing BAP, which can be formulated as:", + "bbox": [ + 497, + 182, + 890, + 347 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np _ {k} ^ {\\mathrm {s}} = \\frac {\\sum_ {m = 1} ^ {H _ {t e x}} \\sum_ {n = 1} ^ {W _ {t e x}} F _ {k , m , n} ^ {t e x}}{\\left\\| \\sum_ {m = 1} ^ {H _ {t e x}} \\sum_ {n = 1} ^ {W _ {t e x}} F _ {k , m , n} ^ {t e x} \\right\\| _ {2}} \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 358, + 890, + 404 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The spatial attention vector $p_k^s \\in \\mathbb{R}^{1 \\times C_{tex}}$ is stacked together to get the texture-relevant spatial feature matrix $P^s \\in \\mathbb{R}^{T_s \\times N_s}$ . For the frequency domain, we perform the BAP with the frequency attention maps $F^f$ and the spatial feature after high-level backbone layers as shown in Fig. 2(a). Similar to Eq. 3, we can obtain the content-relevant frequency feature matrix $P^f \\in \\mathbb{R}^{T_f \\times N_f}$ . Finally, the learnt relation-aware feature matrices will be fed into the follow-up DG-SF $^3$ Net to collaboratively learn a comprehensive feature representation in a graph-based relation reasoning way.", + "bbox": [ + 497, + 415, + 890, + 554 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Dynamic Graph Learning", + "text_level": 1, + "bbox": [ + 499, + 565, + 737, + 580 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "After obtaining the spatial feature matrix $P^{s} \\in \\mathbb{R}^{T_{s} \\times N_{s}}$ and frequency feature matrix $P^{f} \\in \\mathbb{R}^{T_{f} \\times N_{f}}$ , we propose a novel DG-SF $^{3}$ Net to discover the comprehensive relation of them as shown in Fig. 3. Inspired by [19, 49, 51], we provide the intuition that there exists high-order relation of spatial and frequency features and Graph Convolution Network (GCN) performs tremendous potential in relation reasoning. As illustrated in Fig. 1(c), we confirm the above intuition by visualizing the correlation heatmap of spatial and frequency features. Therefore, we build a graph-based relation-discovery module to conduct reasoning with improved GCN to integrate spatial and frequency features.", + "bbox": [ + 497, + 586, + 890, + 752 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Firstly, we concatenate $P^s$ and $P^f$ in the channel dimension to get $V^{(0)} \\in \\mathbb{R}^{T^{(0)} \\times N^{(0)}}$ , where $T^{(0)} = T_s + T_f$ and $N^{(0)} = \\max(N_s, N_f)$ . We treat each column of $V^{(0)}$ as a node. As shown in the right bottom of Fig. 3, a dynamic GCN module is proposed to aggregate features based on their similarity. Different from original GCN, our model learns to dynamically design appropriate graph structures in each layer, rather than treating it as a fixed constant one.", + "bbox": [ + 497, + 752, + 890, + 866 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "7281", + "bbox": [ + 468, + 885, + 499, + 897 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/b45ef41ce2c3e17d9823bd660089fb3042a5ca43d1e7b5bd3e73ae343e7d320b.jpg", + "image_caption": [ + "Figure 3. The proposed Dynamic Graph Spatial-Frequency Feature Fusion Network (DG-SF $^3$ Net), which includes two modules: Dynamic Graph Convolution Network (DGCN) and Graph Information Interaction $(\\mathrm{GI}^2)$ layers." + ], + "image_footnote": [], + "bbox": [ + 137, + 123, + 831, + 313 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "At $t$ -th layer, we have a tailored sparse-connected graph $G^{(t)} = (V^{(t)},E^{(t)})$ for graph convolution, where the local neighbor of each center node $v_{i}^{(t)}$ can be defined as:", + "bbox": [ + 75, + 385, + 468, + 429 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {N} ^ {(t)} (i) = \\left\\{v _ {j i m} ^ {(t)} \\mid v _ {j i m} ^ {(t)} \\in k N N \\left(v _ {i} ^ {(t)}\\right), m = 1, \\dots , k \\right\\},\n$$\n", + "text_format": "latex", + "bbox": [ + 78, + 434, + 463, + 460 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $v_{j_{i1}}^{(t)}, \\ldots, v_{j_{ik}}^{(t)}$ are $k$ nodes closest to $v_{i}^{(t)}$ according to the Euclidean distance. After getting the localized kNN graph, we formulate the adjacency matrix $A^{(t)}$ based on $k$ neighbors attached to center node with self-loop added.", + "bbox": [ + 75, + 464, + 468, + 522 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "With this sparse-connected GCN, the node features can be updated with the message passing as follows:", + "bbox": [ + 75, + 522, + 468, + 551 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nV ^ {(t + 1)} = \\operatorname {R e L U} \\left(\\widetilde {D} ^ {(t) - \\frac {1}{2}} \\tilde {A} ^ {(t)} \\widetilde {D} ^ {(t) - \\frac {1}{2}} V ^ {(t)} W ^ {(t)}\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 95, + 555, + 468, + 579 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\tilde{D}^{(t)}\\in \\mathbb{R}^{T^{(t)}\\times T^{(t)}}$ is the degree matrix. $W^{(t)}\\in$ $\\mathbb{R}^{N^{(t)}\\times N^{(t + 1)}}$ is the learnable graph weight. In addition, the output channel is conforming with the input one.", + "bbox": [ + 75, + 584, + 468, + 630 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finally, we propose a Graph Information Interaction $(\\mathrm{GI}^2)$ component for the spatial-frequency feature interaction. The $\\mathrm{GI}^2$ component is composed of several MLP-Mixers [40] layers weighted by the graph adjacent matrix. Each of them leverages a channel-mixing MLP layer and a token-mixing MLP layer, which perform information interaction across all channels and node positions embedded in high-dimensional feature space. These two types of layers are interleaved to enable interaction of both input dimensions. Particularly, in order to highlight the localized features defined on the kNN graph abovementioned, we utilize the adjacent matrix derived from the first GCN layer to weight the feature of the token-mixing MLP.", + "bbox": [ + 75, + 631, + 468, + 811 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Loss Function", + "text_level": 1, + "bbox": [ + 77, + 817, + 221, + 830 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After dynamic graph learning, we obtain the semantic feature matrix $\\tilde{V} \\in \\mathbb{R}^{M \\times N}$ . Following MADD, we regard", + "bbox": [ + 75, + 838, + 468, + 866 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Region Independent Loss (RIL) with Cross Entropy (CE) loss as the loss function. The auxiliary RIL is defined as:", + "bbox": [ + 497, + 385, + 890, + 413 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {R I L} = \\sum_ {i = 1} ^ {B} \\sum_ {j = 1} ^ {M} \\operatorname {R e L U} \\left(\\left\\| \\tilde {V} _ {j} ^ {i} - c _ {j} ^ {t} \\right\\| _ {2} ^ {2} - m _ {i n} \\left(y _ {i}\\right)\\right) \\tag {5} \\\\ + \\sum_ {i \\neq j} ^ {M} \\mathrm {R e L U} \\left(m _ {o u t} - \\left\\| c _ {i} ^ {t} - c _ {j} ^ {t} \\right\\| _ {2} ^ {2}\\right) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 515, + 421, + 890, + 503 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$c \\in \\mathbb{R}^{M \\times N}$ are feature centers of $\\tilde{V}$ that can be updated iteratively during training. $B$ is the batch size, $M$ is the number of attention maps and $y_{i}$ is the label. $m_{in}$ and $m_{out}$ represent the margin of intra-class and inter-class.", + "bbox": [ + 497, + 511, + 890, + 568 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In conclusion, the total loss function $\\mathcal{L}$ of our proposed SFDG framework can be described as:", + "bbox": [ + 497, + 568, + 890, + 596 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\lambda_ {1} * \\mathcal {L} _ {C E} + \\lambda_ {2} * \\mathcal {L} _ {R I L} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 598, + 606, + 890, + 622 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\lambda_{1},\\lambda_{2}$ are hyper-parameters for balancing different terms. We set $\\lambda_1 = \\lambda_2 = 1$ in the following experiments.", + "bbox": [ + 497, + 630, + 890, + 659 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiment", + "text_level": 1, + "bbox": [ + 499, + 669, + 623, + 686 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 499, + 693, + 690, + 707 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. We appraise our proposed SFDG method and current state-of-the-art approaches on FaceForensics++ (FF++) [30], WildDeepfake [52], DFDC [5], Celeb-DF [22], DF-v1.0 [13] and DFD [6]. FF++ (low quality (LQ) and high quality (HQ) counterparts) is a widely-used benchmark dataset composed of 1000 real videos from YouTube and corresponding fake videos generated by four types of manipulated techniques: Deepfakes (DF) [41], Face2Face (F2F) [39], FaceSwap (FS) [17] and NeuralTextures (NT) [38]. WildDeepfake is a small real-scenario dataset including 7314 face sequences. Celeb-DF contains", + "bbox": [ + 497, + 713, + 890, + 866 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "7282", + "bbox": [ + 468, + 885, + 500, + 897 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/829c0e34d10d7ef582b05ef5a34acbe65538cf43bf09d8a4870de2da1e74c8e6.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodFF++ (LQ)FF++ (HQ)WildDeepfakeCeleb-DF
AccAUCAccAUCAccAUCAccAUC
Xception [4]86.8689.3095.7396.3079.9988.8697.9099.73
EfficientNet-b4 [37]86.6788.2096.6399.1882.3390.1298.1999.83
Add-Net [52]87.5091.0196.7897.7476.2586.1796.9399.55
SCL [18]89.0092.4096.6999.30————
MADD [50]88.6990.4097.6099.2982.6290.7197.9299.94
F3Net [28]90.4393.3097.5298.1080.6687.5395.9598.93
PEL [9]90.5294.2897.6399.3284.1491.62——
RECCE [2]91.0395.0297.0699.3283.2592.0298.5999.94
Local Relation [3]91.4795.2197.5999.46————
M2TR [43]92.3594.2298.2399.48————
SFDG (Xception)91.0894.4997.6199.4583.3692.1598.9599.94
SFDG (Ours)92.2895.9898.1999.5384.4192.5799.2299.96
", + "bbox": [ + 78, + 123, + 892, + 338 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Quantitative comparison in terms of Acc(%) and AUC(%) on FF++, WildDeepfake and Celeb-DF dataset. The red represents the best performance while the blue indicates the second-best results.", + "bbox": [ + 75, + 346, + 892, + 375 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "590 real videos and 5,639 high quality fake videos tampered with the improved deepfake methods. DFDC is a remarkable large-scale dataset with over 100,000 video clips. DFD and DF-v1.0 are two another large-scale publicly available datasets to evaluate the model's generalization ability.", + "bbox": [ + 75, + 397, + 470, + 467 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation Metrics. Following previous works [9, 28], we employ the commonly used Accuracy (Acc), Area Under the Receiver Operating Characteristic Curve (AUC) and Equal Error Rate (EER) as our evaluation metrics.", + "bbox": [ + 75, + 467, + 470, + 524 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details. Following the official split of FF++ dataset, we use 740 videos for training, 140 for validation and 140 remained for testing. We sample 50 frames per video at equal interval during training and validation phases, 20 frames in testing period. We use the remarkable DLIB [32] for face detection and alignment. We employ EfficientNet-b4 [37] pretrained on ImageNet [31] as the backbone of our network. We set $m_{out}$ to 0.2 and $m_{in}$ to [0.05,0.1] in Eq. 5. The whole network is trained with Adam optimizer with an initial learning rate of $1 \\times 10^{-4}$ , the weight decay of $1 \\times 10^{-5}$ . A step learning scheduler is used to reduce the learning rate half every 5 epochs.", + "bbox": [ + 75, + 524, + 470, + 692 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Experimental Results", + "text_level": 1, + "bbox": [ + 75, + 705, + 278, + 720 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Intra-testing. We compare our proposed method versus current state-of-the art approaches on the FF++ dataset under different quality settings (HQ and LQ), WildDeepfake and Celeb-DF datasets. As shown in Table 1, our method consistently achieves admirably performance on all quality settings and trumps all reference methods by a considerable margin. Specifically, in terms of Acc, our method achieves $92.28\\%$ and $98.19\\%$ on LQ and HQ settings respectively, with a remarkable improvement in comparison to PEL [9], i.e., $2.1\\%$ performance gain on LQ and $0.6\\%$ on HQ. Dif", + "bbox": [ + 75, + 728, + 468, + 866 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ferent from PEL which only utilizes fine-grained frequency features, our model extracts adaptive frequency features with a content mask providing rounded frequency representations. More importantly, we boost the information interaction between spatial and frequency domains via dynamic graph learning instead of vanilla convolution paradigm in PEL. Further, our method achieves a noteworthy performance compared with Local Relation [3] and M2TR [43], which introduce powerful priors of forgery masks. Instead, our SFDG only employs real/fake images as the input, but the AUC on both LQ and HQ settings surpass these two works strikingly. As discussed, these fruitful results give explanation of the effectiveness of our SFDG method.", + "bbox": [ + 497, + 397, + 892, + 577 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Cross-testing. To further appraise the generalization ability of our method on unseen manipulated types, we herein conduct cross-dataset experiments by training and testing on different datasets. Following PEL [9], we reimplement several state-of-the-art models for a fair comparison on $\\mathrm{FF}++$ (LQ) dataset and testing them on Celeb-DF, DFDC, DFD, DF-v1.0 and WildDeepfake dataset. Comparisons under AUC and EER metrics are detailedly shown in Table 2. It implicates that our SFDG method generally outperforms all competitors conspicuously on all testing datasets. Instead of overfitting with specific forged patterns as in most existing methods, SFDG explores the essential forgery with content-aware semantic attention maps and reasons about generalized forged cues via graph-based high-order relation discovery in spatial and frequency domains, which guarantees the superior generalization ability of our proposed method.", + "bbox": [ + 497, + 583, + 894, + 805 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Robustness. Considering the image quality will be deteriorated seriously by inevitable noise in video acquisition process, we further investigate the robustness of our SFDG model under several common perturbations. Specifically,", + "bbox": [ + 497, + 809, + 894, + 868 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "7283", + "bbox": [ + 468, + 885, + 500, + 897 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/fd79b09bf7273cee2e936c9a300a818efa6d2ad7b0ce6b8992631d49cf18ea39.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Training DataSetMethodTesting Dataset
Celeb-DFDFDWildDeepfakeDFDCDF-v1.0
AUCEER↓AUCEER↓AUCEER↓AUCEER↓AUCEER↓
FF++Xception [4]60.050.43265.430.39360.590.61955.650.46180.270.265
Ef-b4 [37]64.290.41983.170.23564.270.37660.120.42885.310.228
Add-Net [52]57.830.44457.160.45354.210.46251.600.548——
MADD [50]68.640.37174.180.32765.650.39763.020.41089.340.173
F3Net [28]67.950.36869.500.35460.490.43457.870.44282.270.246
PEL [9]69.180.35775.860.30867.390.38363.310.404——
SFDG (Ours)75.830.30388.000.19769.270.37773.640.33792.100.151
", + "bbox": [ + 100, + 122, + 868, + 266 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/7ca90be0c0cc2f01b6cccab7590d4fdbf2179026ca805c16aa718feacdcdf6ab.jpg", + "table_caption": [ + "Table 2. Cross-testing results in terms of AUC(%) and EER training on FF++ dataset. The bold indicates the best performance." + ], + "table_footnote": [], + "table_body": "
Method+GaussianNoise+SaltPepperNoise+GaussianBlur
ΔAcc(FF)ΔAcc(Wild)ΔAcc(FF)ΔAcc(Wild)ΔAcc(FF)ΔAcc(Wild)
Xception [4]-2.65%-0.98%-32.44%-27.80%-6.22%-12.71%
Add-Net [52]-41.51%-11.66%-11.28%-18.21%-11.28%-12.91%
F3Net [28]-9.86%-1.17%-31.08%-43.57%-11.08%-12.43%
MADD [50]-1.79%-0.99%-49.30%-29.47%-12.23%-14.86%
PEL [9]-0.10%-0.86%-9.39%-4.25%-7.41%-10.88%
SFDG (Ours)-0.10%-0.75%-10.10%-3.74%-3.76%-5.12%
", + "bbox": [ + 95, + 299, + 873, + 415 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "following PEL [9], we apply GaussianNoise, SaltPepperNoise and GaussianBlur to the FF++ (LQ) and WildDeepfake testing images, and adopt the decay of Acc to indicate the robustness of face forgery detection model. As shown in Table 3, a series of experiments throw light on that our method with the least performance decline is more robust to the perturbations abovementioned. We attribute it to the elaborate CAFÉ module which extracts the adaptive frequency features among multiple bands and acts as an image denoiser. We provide sufficient experiments results in terms of AUC in the supplementary materials.", + "bbox": [ + 75, + 461, + 468, + 612 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 75, + 623, + 228, + 638 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of Proposed Components. As shown in Table. 4, a series of ablation experiments on $\\mathrm{FF}++$ (LQ) benchmark have been conducted to verify the effectiveness of different components in our framework. Specifically, we develop the following variants: (a) the baseline model equipped with the MADD [50] pipeline, (b) the baseline model with the proposed CAFÉ module, (c) the proposed method w/o. DG-SF3Net, (d) the proposed method w/o. MDAML module. Comparing (a) and (b), we observe that the proposed CAFÉ module brings a considerable improvement of Acc and AUC metrics on FF++ (LQ) dataset. From variant (b) and (c), we empirically demonstrate that adding the MDAML module will bring $2.19\\%$ Acc and $1.52\\%$ AUC gains, which are attributed to the multi-scale contextual information and large receptive field of refined attention maps. When adding the DG-SF3Net module, as", + "bbox": [ + 75, + 644, + 468, + 866 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/0ed68d72808872486fe1324cc90cbade608d1506d808f6e556d8575d63f47be8.jpg", + "table_caption": [ + "Table 3. Robustness evaluation under three types of perturbations. Our SFDG performs admirably under several common perturbations." + ], + "table_footnote": [], + "table_body": "
IDCAFÉMDAMLDG -SF3NetAcc (LQ)AUC (LQ)
(a)88.6990.4
(b)✓89.5293.37
(c)✓✓91.4894.79
(d)✓✓92.0595.45
Ours✓✓✓92.2895.98
", + "bbox": [ + 502, + 459, + 889, + 562 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4. Ablation study on the FF++ (LQ) dataset.", + "bbox": [ + 544, + 571, + 845, + 584 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "shown in variant (c) and Ours, we observe a remarkable advance on both Acc and AUC metrics, which benefits from the dynamic graph learning protocol to reason about the relation-aware forged clues. Finally, the best performance is achieved when combining all components, with the Acc and AUC of $92.28\\%$ and $95.98\\%$ respectively.", + "bbox": [ + 497, + 612, + 890, + 697 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Setting of Hyper-parameters. During graph construction, the number of neighbor nodes $k$ is a hyperparameter which determines the structure and aggregated scope of GCNs [10]. As shown in Table 5, to further evaluate the effectiveness using different $k$ , we conduct a series of experiments on FF++ (LQ) and WildDeepfake datasets. From the experimental results, we conclude that too few neighbors can not guarantee the representative ability of the dynamic GCN module, thus degrades the information exchange of forged clues in spatial and frequency domains. Further, too many neighbors will tamper the regional separability of attention maps and tend to catastrophic overfitting. In our", + "bbox": [ + 497, + 698, + 892, + 866 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "7284", + "bbox": [ + 468, + 885, + 500, + 897 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3fac86f8c8abdefefe2d2823ea5216f0f13c786a96e76d763b90eb7031bae11c.jpg", + "image_caption": [ + "Figure 4. The Grad-CAM visualization for forged faces." + ], + "image_footnote": [], + "bbox": [ + 80, + 124, + 472, + 269 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/48c907c200be5b54ff87a56e2c7b864656a807e84e1ba95464eec2700146e073.jpg", + "image_caption": [ + "Figure 6. The visualization results of feature maps from MDAML module at different scales on FF++ and WildDeepfake datasets." + ], + "image_footnote": [], + "bbox": [ + 82, + 317, + 467, + 371 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/6259cadf37b5b3e3f6ae882b211ecd7f8c4f11a5d1c53d47f6bc7cd034c36f97.jpg", + "table_caption": [ + "Figure 5. The t-SNE feature visualization of the Ef-b4 and SFDG." + ], + "table_footnote": [ + "Table 5. Results in terms of Acc(%) and AUC(%) for different number of neighboring nodes in the graph construction." + ], + "table_body": "
#NeighborsFF++ (LQ)WildDeepfake
AccAUCAccAUC
592.1095.6082.0390.57
1092.2895.9884.4192.57
1592.2895.4983.5791.15
2092.0291.5981.4690.38
", + "bbox": [ + 80, + 421, + 467, + 509 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "work, we observe that our model achieves the best performance in terms of Acc and AUC when setting $k$ to 10.", + "bbox": [ + 77, + 570, + 468, + 598 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Visualization", + "text_level": 1, + "bbox": [ + 77, + 609, + 213, + 622 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Grad-CAM visualization. To better understand the internal mechanism of our method and explore interested regions for specific forged types, we supply the Grad-CAM [33] visualization on $\\mathrm{FF}++$ dataset. As shown in Fig. 4, the forgery artifacts in different domains locate on independent regions. Detailedly, the spatial branch focuses on the facial region with pronounced forgery traces, which are effortlessly discovered by CNN backbones in spatial domain. Conversely, the frequency streamline searches manipulated clues essentially concerned with a wider area, e.g., the background, hair or entire face. These regions are subtle and dynamically change according to the image content thus provides a generalized feature representation. Just as we have speculated, the frequency domain acts as the complementary to the spatial domain and these two domains contribute to each other via graph-based high-order relation discovery for exploiting comprehensive forged cues.", + "bbox": [ + 75, + 631, + 468, + 866 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/abd17e2b966a7429cc498f721ce870f517995fad195cc1d23e137c51e18092bf.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 510, + 125, + 884, + 239 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Attention Maps Visualization. We verify the effectiveness of our tailored MDAML module and visualize the results in Fig 6. We observe that feature maps with different scales highlight distinctive activated intensities. Detailedly, the large scale features with high resolution representation embrace richer and global manipulated traces, while the small scales concentrate on more localized salient feature around facial landmarks. Further, we aggregate the attention maps via hierarchical pyramid paradigm to exploit the essential discrepancy between authentic and counterfeit faces, which can resist the noise disturbance and visual compression.", + "bbox": [ + 497, + 313, + 892, + 465 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Feature Distribution Visualization. In this part, we investigate the discriminative ability of the proposed SFDG model. Leveraging the t-SNE [42] technique, we visualize the semantic feature distribution of the Ef-b4 [37] model and our SFDG on $\\mathrm{FF}++$ (LQ) and WildDeepfake dataset. As shown in Fig. 5, our approach encourages the samples of same class into a relatively compact feature space. To explain, our SFDG adequately captures the intrinsic discrepancy between genuine and forged faces in multiple domains through graph-based relationships discovery, thus improving the generalization ability of our method.", + "bbox": [ + 497, + 467, + 890, + 619 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 499, + 634, + 616, + 648 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose a novel Spatial-Frequency Dynamic Graph network that develops graph model to exploit relationships of spatial and frequency domains for spotting subtle forgery clues. Firstly, the Content-guided Adaptive Frequency Extraction module is proposed to mine the adaptive frequency clues via content-aware frequency learning. Further, a Multiple Domains Attention Map Learning scheme captures rich contextual information of spatial-frequency feature through multi-scale feature ensemble. Finally, Dynamic Graph based Spatial-Frequency Feature Fusion module performs relation reasoning of spatial and frequency domains via improved graph convolution. Extensive experiments and detailed visualizations on widely-used benchmarks confirm the effectiveness and generalizability of our SFDG method compared with other contenders.", + "bbox": [ + 497, + 657, + 890, + 866 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "7285", + "bbox": [ + 468, + 885, + 500, + 897 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 124, + 173, + 138 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Darius Afchar, Vincent Nozick, Junichi Yamagishi, and Isao Echizen. 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In Proceedings of the 28th ACM International Conference on Multimedia, pages 2382-2390, 2020. 1, 5, 6, 7" + ], + "bbox": [ + 502, + 125, + 890, + 858 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "7287", + "bbox": [ + 468, + 885, + 500, + 897 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Dynamic Graph Learning With Content-Guided Spatial-Frequency Relation Reasoning for Deepfake Detection/0db433fe-2bb5-4d32-8dad-d6501909824f_model.json b/2023/Dynamic Graph Learning With Content-Guided Spatial-Frequency Relation Reasoning for Deepfake Detection/0db433fe-2bb5-4d32-8dad-d6501909824f_model.json new file mode 100644 index 0000000000000000000000000000000000000000..be3f67535b7e14be90d5636d440f3960bd1777f0 --- /dev/null +++ b/2023/Dynamic Graph Learning With Content-Guided Spatial-Frequency Relation Reasoning for Deepfake Detection/0db433fe-2bb5-4d32-8dad-d6501909824f_model.json @@ -0,0 +1,2046 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.13, + 0.051, + 0.201, + 0.085 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.253, + 0.049, + 0.792, + 0.088 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.107, + 0.162, + 0.865, + 0.205 + ], + "angle": 0, + "content": "Dynamic Graph Learning with Content-guided Spatial-Frequency Relation Reasoning for Deepfake Detection" + }, + { + "type": "text", + "bbox": [ + 0.194, + 0.228, + 0.773, + 0.246 + ], + "angle": 0, + "content": "Yuan Wang\\(^{1,2,4}\\) Kun Yu\\(^{2}\\) Chen Chen\\(^{1*}\\) Xiyuan Hu\\(^{3}\\) Silong Peng\\(^{1,4,5}\\)" + }, + { + "type": "text", + "bbox": [ + 0.19, + 0.246, + 0.78, + 0.261 + ], + "angle": 0, + "content": "\\(^{1}\\)Institute of Automation, Chinese Academy of Sciences \\(^{2}\\)Alibaba Group" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.261, + 0.856, + 0.278 + ], + "angle": 0, + "content": "\\(^{3}\\)School of Computer Science and Engineering, Nanjing University of Science and Technology" + }, + { + "type": "text", + "bbox": [ + 0.192, + 0.278, + 0.776, + 0.294 + ], + "angle": 0, + "content": "4University of Chinese Academy of Sciences 5Beijing Visystem Co.Ltd" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.297, + 0.853, + 0.31 + ], + "angle": 0, + "content": "{wangyuan2020, chen.chen}@ia.ac.cn yukun.yk@alibaba-inc.com xiyuan.hu@foxmail.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.342, + 0.313, + 0.356 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.371, + 0.473, + 0.676 + ], + "angle": 0, + "content": "With the springing up of face synthesis techniques, it is prominent in need to develop powerful face forgery detection methods due to security concerns. Some existing methods attempt to employ auxiliary frequency-aware information combined with CNN backbones to discover the forged clues. Due to the inadequate information interaction with image content, the extracted frequency features are thus spatially irrelevant, struggling to generalize well on increasingly realistic counterfeit types. To address this issue, we propose a Spatial-Frequency Dynamic Graph method to exploit the relation-aware features in spatial and frequency domains via dynamic graph learning. To this end, we introduce three well-designed components: 1) Content-guided Adaptive Frequency Extraction module to mine the content-adaptive forged frequency clues. 2) Multiple Domains Attention Map Learning module to enrich the spatial-frequency contextual features with multiscale attention maps. 3) Dynamic Graph Spatial-Frequency Feature Fusion Network to explore the high-order relation of spatial and frequency features. Extensive experiments on several benchmark show that our proposed method sustainably exceeds the state-of-the-arts by a considerable margin." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.702, + 0.21, + 0.716 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.726, + 0.47, + 0.824 + ], + "angle": 0, + "content": "Recent years have witnessed the continuous advances in deepfake creation [11, 27, 36]. Utilizing booming open-source tools such as Deepfakes [41], novices can readily manipulate the expression and identity of faces to generate visually untraceable videos. Face forgery technology has stimulated many applications [12, 14, 44, 46] with wide acceptance. These techniques can whereas be abused by ma" + }, + { + "type": "image", + "bbox": [ + 0.536, + 0.344, + 0.863, + 0.515 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.535, + 0.893, + 0.575 + ], + "angle": 0, + "content": "Figure 1. The motivation of our proposed approach. Our SFDG method (a) delves into the high-order relationships (b) of spatial and frequency domain via cross-domain graph reasoning (c)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.602, + 0.891, + 0.644 + ], + "angle": 0, + "content": "licious intentions to make pornographic movies, fake news and political rumors. In the circumstances, it is desperately in need to develop powerful forgery detection methods." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.646, + 0.893, + 0.868 + ], + "angle": 0, + "content": "Early face forgery detection methods [7,30,52] treat this challenge as vanilla dichotomy tasks in the prevailing view. They use off-the-shelf backbones to extract the global feature of faces and a binary classifier follow-up to identify the real and counterfeit faces. However, as the counterfeits become increasingly realistic, it is intractable for these methods to spot subtle and local forgery traces. One recent study [50] reformulates deepfake detection as a fine-grained classification task and designs a multi-attentional framework to extract local discriminative features from multiple attention maps. It is susceptible to common disturbances and the generalized features remain therefore poorly understood. Some other works resort to specific forgery patterns to encourage better classification such as DCT [24,28], SRM [25] and steganalysis features [45]. Although promising advances have been achieved by these previous works," + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.832, + 0.47, + 0.867 + ], + "angle": 0, + "content": "*Chen Chen is the corresponding author. This work is supported by the National Key R&D Program of China under Grant 2021YFF0602101, Alibaba Group through Alibaba Research Intern Program." + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.887, + 0.502, + 0.898 + ], + "angle": 0, + "content": "7278" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.127, + 0.469, + 0.224 + ], + "angle": 0, + "content": "they always extract frequency features with hand-crafted filter banks which are content-irrelevant, thus incapable to adapt the changes of complex scenarios. Moreover, they fuse multi-domain information via adding directly or attentional projection. However, these approaches devote little efforts to discover the high-order relation of spatial and frequency features and integrating them in a reasonable way." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.224, + 0.469, + 0.32 + ], + "angle": 0, + "content": "In this paper, we provide seminal insights to exploit adaptive frequency features and delve into the interactions of spatial-frequency domains. To this end, we propose an adaptive extraction-multiscale enhancement-graph fusion paradigm for deepfake detection via dynamic graph learning, which prompts to excavate content-aware frequency clues and the high-order relation of multiple domains." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.32, + 0.469, + 0.43 + ], + "angle": 0, + "content": "Firstly, for adaptive frequency extraction, we tailor a Content-guided Adaptive Frequency Extraction (CAFÉ) module with coarse-grained DCT and fine-grained DCT to capture the local frequency cues guided by content-aware masks. Different from PEL [9] and F3Net [28], our customized frequency learning protocol provides potential for more combinations of frequency features, which is indispensable to spot complicated counterfeit patterns." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.431, + 0.469, + 0.651 + ], + "angle": 0, + "content": "To further enhance the representation of content-guided frequency features, we introduce a Multiple Domains Attention Map Learning (MDAML) module to generate multiscale spatial and frequency attention maps with high-level semantic features. Specifically, we first propose a MultiScale Attention Ensemble (MSAE) module, which produces multi-scale semantic attention maps with large receptive fields and endows rich contextual information to spatial and frequency domains. Moreover, an Attention Map Refinement Block (AMRB) is included in the MSAE module to refine the obtained semantic attention maps conducive to the following feature learning. In comparison with MADD [50] that merely emphasizes the spatial domain, we further introduce the semantic-relevant frequency attention map with rich semantic information retained for the subsequent spatial-frequency relation-discovery paradigm." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.652, + 0.469, + 0.816 + ], + "angle": 0, + "content": "Finally, to fully discover the spatial and frequency relationships, we propose a Dynamic Graph-based Spatial-Frequency Feature Fusion network (DG-SF\\(^3\\)Net) to formulate the interaction of two domains via a graph-based relation discovery protocol. Specifically, DG-SF\\(^3\\)Net is composed of two ingredients: Dynamic GCN [16] and Graph Information Interaction layers. The former constructs kNN-graph dynamically and performs graph convolution to reason high-order relationships in spatial and frequency domains, while the latter is designed to enhance the mutual relation with several graph-weighted MLP-Mixer [40] layers via channel-wise and node-wise interaction." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.817, + 0.468, + 0.831 + ], + "angle": 0, + "content": "The achievements, including contributions are threefold:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.839, + 0.469, + 0.867 + ], + "angle": 0, + "content": "From a new perspective, we propose a novel SpatialFrequency Dynamic Graph (SFDG) framework, which" + }, + { + "type": "text", + "bbox": [ + 0.531, + 0.127, + 0.89, + 0.154 + ], + "angle": 0, + "content": "is qualified to exploit relation-aware spatial-frequency features to promote generalized forgery detection." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.162, + 0.892, + 0.259 + ], + "angle": 0, + "content": "- We first harness a CAFÉ module for content-aware frequency feature extraction, and then tailor an MDAML scheme to dig deeper into multiscale spatial-frequency attention maps with rich contextual understanding of forgeries. Finally, a seminal DG-SF3Net module is proposed to discover the multi-domain relationships with a graph-based relation-reasoning approach." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.267, + 0.892, + 0.322 + ], + "angle": 0, + "content": "- Our method achieves state-of-the-art performance on six benchmark datasets. The cross-dataset experiment and the perturbation analysis show the robustness and generalization ability of the proposed SFDG method." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.333, + 0.65, + 0.347 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.356, + 0.892, + 0.424 + ], + "angle": 0, + "content": "Over the past several years, with the remarkable progress of forgery creation techniques, increasing efforts have been made to boost the development of face forgery detection in computer vision communities. In this section, we briefly review previous works exploring the authenticity of faces." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.425, + 0.892, + 0.59 + ], + "angle": 0, + "content": "Rudimentary deepfake detection approaches base primarily on obvious counterfeit artifacts, which utilize handcrafted features to detect anomalies in spatial domain, e.g., inconsistent head pose [47] and unnatural eye blinding [21]. However, these traditional methods feel intractable to deal with the improved realistic deepfakes. With the overwhelming success of deep learning, some works [1,4,7] adopt off-the-shelf classification backbones to extract high-level semantic features for deepfake detection. Although considerable performances have been achieved on specific datasets, their vanilla structures would lead to catastrophic overfitting and lag behind the advanced face synthesis technology." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.591, + 0.892, + 0.77 + ], + "angle": 0, + "content": "To further exploit the essential forged clues, general deepfake detection [15, 20, 26, 34, 35] has been an area of intense investigation. Nguyen et al. [26] employ multi-task learning strategy to detect forged artifacts and locate manipulated regions simultaneously. Face X-ray [20] observes the specific blending step of face swapping and locates forgery boundary in a self-supervised manner. FReTAL [15] adopts the knowledge distillation to prevent catastrophic forgetting and enhance adaptability in different domains. DCL [35] performs dual-granularity contrastive learning to further improve the generalization. However, these approaches captures category-level differences instead of the intrinsic discrepancies between authentic and forged images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.77, + 0.892, + 0.867 + ], + "angle": 0, + "content": "Recently, other studies focus on mining specific forgery patterns, such as local texture, high-frequency noise, reconstruction residual and frequency clues. Among them, Zhao et al. [50] propose a fine-grained deepfake detection framework that aggregates the local texture and high-level semantic information into multiple attention maps. However, it fails to distinguish highly compressed videos with" + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.887, + 0.502, + 0.898 + ], + "angle": 0, + "content": "7279" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.134, + 0.124, + 0.836, + 0.274 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.134, + 0.275, + 0.836, + 0.402 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.422, + 0.893, + 0.449 + ], + "angle": 0, + "content": "Figure 2. (a) Overview of the proposed Spatial-Frequency Dynamic Graph (SFDG) framework. (b) The Content-guided Adaptive Frequency Extraction (CAFÉ) module. (c) The Multiple Domains Attention map Learning (MDAML) network." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.472, + 0.47, + 0.679 + ], + "angle": 0, + "content": "blurry texture. Luo et al. [25] utilize the high-pass filter SRM [8] to extract high-frequency noise guiding face forgery detection. RECCE [2] employs the reconstruction difference of authentic faces as guidance of forgery traces. \\(\\mathrm{F}^3\\mathrm{Net}\\) [28] collaboratively mines the forged frequency clues with frequency-aware decomposition and local frequency statistics. However, the extracted frequency feature is coarse-grained, incapable of assembling discriminative feature patterns. To ameliorate this issue, PEL [9] learns the fine-grained frequency features using sliding window DCT combined with RGB images in a progressive enhancement learning fashion. Nevertheless, the fine-grained frequency is content-irrelevant and in compliance with the vanilla spatial-frequency fusion ethos, thus failing to achieve the utter information interaction of both domains." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.679, + 0.47, + 0.735 + ], + "angle": 0, + "content": "Different from existing studies, our proposed end-to-end SFDG approach excavates content-adaptive frequency clues and facilitates the comprehensive fusion of spatial and frequency features via dynamic graph learning." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.747, + 0.169, + 0.76 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.77, + 0.47, + 0.868 + ], + "angle": 0, + "content": "In this section, we propose a Spatial-Frequency Dynamic Graph (SFDG) framework, which consists of three major modules, i.e., Content-guided Adaptive Frequency Extraction (CAFÉ), Multiple Domains Attention Map Learning (MDAML), and Dynamic Graph Spatial Frequency Feature Fusion Network (DG-SF\\(^3\\)Net). The primary idea of our approach is to exploit content-aware frequency features uti" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.472, + 0.893, + 0.556 + ], + "angle": 0, + "content": "lizing CAFÉ module. As limited context information do these features embrace, we present the MDAML module to generate high-level frequency attention maps in a multiscale learning manner. Beyond these improvements, we finally design a DG-F3Net to perform relation reasoning of spatial and frequency features via dynamic graph learning." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.568, + 0.824, + 0.583 + ], + "angle": 0, + "content": "3.1. Content-aware Frequency Extraction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.591, + 0.892, + 0.868 + ], + "angle": 0, + "content": "Towards the frequency-aware face forgery detection, former studies generally use DCT to transform the input image into frequency domain. However, for the scarcity of spatial information in DCT process, the extracted frequency feature is presumably not compatible to the image content. To this end, we propose the CAFÉ module to fully exploit the forgery clues via content-aware frequency learning in order to handle complex or simple manipulated patterns adaptively. Without loss of generality, let \\(x^{s}\\in \\mathbb{R}^{3\\times H\\times W}\\) denotes the RGB image, where \\(H\\) and \\(W\\) are the height and width of the input image. As shown in Fig. 2(b), we generate an attentional content mask \\(M^s\\) using a UNet [29] submodule with the spatial information retained. We then propose a coarse-grained counterpart to partition the compact frequency spectrum into several bands. Specifically, we manually design \\(N_{f}\\) binary filters \\(\\{f_i|i = 1,\\dots,N_f\\}\\) to decompose the frequency domains into low, middle and high frequency bands. The low-frequency component lies on the top-left corner while the high-frequency response locates on the bottom-right corner [28]. As described, the" + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.887, + 0.502, + 0.898 + ], + "angle": 0, + "content": "7280" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.078, + 0.127, + 0.375, + 0.14 + ], + "angle": 0, + "content": "coarse-grained process can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.096, + 0.148, + 0.469, + 0.17 + ], + "angle": 0, + "content": "\\[\nx _ {\\text {c o a r s e}} ^ {f, i} = \\mathcal {H} ^ {- 1} \\left[ \\mathcal {H} \\left(x ^ {s}\\right) \\odot f ^ {i} \\right], \\quad i = \\{1, 2, \\dots , N _ {f} \\}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.177, + 0.469, + 0.232 + ], + "angle": 0, + "content": "where \\(\\odot\\) is the Hadamard product. \\(\\mathcal{H}\\) and \\(\\mathcal{H}^{-1}\\) represent the DCT and inverse DCT respectively. \\(x_{coarse}^{f}\\in \\mathbb{R}^{3N_{f}\\times H\\times W}\\) is the extracted coarse frequency feature, which indicates global frequency information to some extent." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.233, + 0.469, + 0.4 + ], + "angle": 0, + "content": "Further, we design a fine-grained frequency extraction method to emphasize on the localized frequency features. Specifically, we slice \\(x^{s}\\) via a sliding window to obtain a set of \\(l\\times l\\) patches. \\(p_{m,n}\\in \\mathbb{R}^{3\\times l\\times l}\\) denotes the patch sliced by the \\((m\\)-th, \\(n\\)-th) sliding window. After performing DCT on each patch, we get the localized fine-grained frequency features \\(d_{m,n}^{f}\\in \\mathbb{R}^{3\\times l\\times l}\\). We repeat the channel of each \\(d_{m,n}^{f}\\) to match the coarse-grained frequency features abovementioned. All localized patched are then gathered into a whole feature map \\(d^{f}\\in \\mathbb{R}^{3N_{f}\\times H\\times W}\\) and go through several convolution Blocks composed by Conv2d, BN, and ReLU to form the output fine-grained frequency features \\(x_{fine}^{f}\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.4, + 0.469, + 0.442 + ], + "angle": 0, + "content": "Finally, we obtain the overall frequency head \\( x^{fh} \\) through an adaptive frequency combine module guided by the learned content mask \\( M^s \\), which can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.127, + 0.45, + 0.469, + 0.469 + ], + "angle": 0, + "content": "\\[\nx ^ {f h} = \\left(1 - M ^ {s}\\right) \\odot x _ {f i n e} ^ {f} + M ^ {s} \\odot x _ {c o a r s e} ^ {f}. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.477, + 0.469, + 0.522 + ], + "angle": 0, + "content": "The extracted frequency head \\(x^{fh} \\in \\mathbb{R}^{3N_f \\times H \\times W}\\) will be fed into several stride convolution layers to obtain the final frequency feature \\(C_f\\) channels \\(x^f\\) with size of \\(H_f \\times W_f\\)." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.528, + 0.445, + 0.543 + ], + "angle": 0, + "content": "3.2. Multiple Domains Attention Map Learning" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.549, + 0.469, + 0.784 + ], + "angle": 0, + "content": "To fully exploit the forged clues in spatial domain, we adopt EfficientNet-b4 as the backbone and further partition the entire network into low-level, mid-level and high-level layers, respectively. As shown in Fig. 2(c), to acquire spatial-frequency features with rich semantics, we further design a Multi-Scale Attention Ensemble (MSAE) module in spatial and frequency domains to generate multiscale attention maps and aggregate them with hierarchical feature pyramid. The MSAE includes light weighted ConvBlocks, which consist of several convolution layer, BN and non-linear activation layers ReLU, and certain global average layers to downsample the attention maps into multiple scales. With the multi-scale feature representation, we can obtain a sufficient receptive field and rich contextual information, which are of great significance for the deepfake detection task. Inspired by [48], we propose an Attention Map Refinement Block (AMRB) to get refined feature maps." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.785, + 0.469, + 0.867 + ], + "angle": 0, + "content": "As Fig. 2(c) shows, AMRB employs global average pooling to capture global context and uses a subsequent sigmoid layer to produce an attention vector that determines the feature distribution of attention maps in each scale. Finally, we upsample the refined multi-scale attention maps to the original size and add them spatially. We use AMRB in" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.127, + 0.892, + 0.182 + ], + "angle": 0, + "content": "both spatial and frequency streamline to acquire the multiscale spatial attention map \\( F^{s} \\) and frequency feature map \\( F^{f} \\), which have \\( T_{s} \\) and \\( T_{f} \\) channels on behalf of the corresponding number of attention maps in these two domains." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.183, + 0.892, + 0.349 + ], + "angle": 0, + "content": "After obtaining the refined multi-scale attention maps \\( F^{s} \\) and \\( F^{f} \\), we perform Bilinear Attention Pooling (BAP) [23] to get the relation-aware feature matrix \\( P^{s} \\) and \\( P^{f} \\) respectively. As illustrated in Fig. 2(c), we use the Textural Feature Enhancement block [50] to capture the manipulated artifacts hidden in low-level layers. After the enhancement of the texture features, we get a textual feature map \\( F^{tex} \\in \\mathbb{R}^{C_{tex} \\times H_{tex} \\times W_{tex}} \\). For the spatial domain, we element-wisely multiply textural feature map \\( F^{tex} \\) by each spatial attention map \\( F_{k}^{s} \\) to obtain the partial textural feature maps \\( F_{k}^{tex} \\) and compute the final spatial feature matrix employing BAP, which can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.585, + 0.359, + 0.892, + 0.405 + ], + "angle": 0, + "content": "\\[\np _ {k} ^ {\\mathrm {s}} = \\frac {\\sum_ {m = 1} ^ {H _ {t e x}} \\sum_ {n = 1} ^ {W _ {t e x}} F _ {k , m , n} ^ {t e x}}{\\left\\| \\sum_ {m = 1} ^ {H _ {t e x}} \\sum_ {n = 1} ^ {W _ {t e x}} F _ {k , m , n} ^ {t e x} \\right\\| _ {2}} \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.416, + 0.892, + 0.555 + ], + "angle": 0, + "content": "The spatial attention vector \\(p_k^s \\in \\mathbb{R}^{1 \\times C_{tex}}\\) is stacked together to get the texture-relevant spatial feature matrix \\(P^s \\in \\mathbb{R}^{T_s \\times N_s}\\). For the frequency domain, we perform the BAP with the frequency attention maps \\(F^f\\) and the spatial feature after high-level backbone layers as shown in Fig. 2(a). Similar to Eq. 3, we can obtain the content-relevant frequency feature matrix \\(P^f \\in \\mathbb{R}^{T_f \\times N_f}\\). Finally, the learnt relation-aware feature matrices will be fed into the follow-up DG-SF\\(^3\\)Net to collaboratively learn a comprehensive feature representation in a graph-based relation reasoning way." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.566, + 0.738, + 0.581 + ], + "angle": 0, + "content": "3.3. Dynamic Graph Learning" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.587, + 0.892, + 0.753 + ], + "angle": 0, + "content": "After obtaining the spatial feature matrix \\( P^{s} \\in \\mathbb{R}^{T_{s} \\times N_{s}} \\) and frequency feature matrix \\( P^{f} \\in \\mathbb{R}^{T_{f} \\times N_{f}} \\), we propose a novel DG-SF\\(^{3}\\)Net to discover the comprehensive relation of them as shown in Fig. 3. Inspired by [19, 49, 51], we provide the intuition that there exists high-order relation of spatial and frequency features and Graph Convolution Network (GCN) performs tremendous potential in relation reasoning. As illustrated in Fig. 1(c), we confirm the above intuition by visualizing the correlation heatmap of spatial and frequency features. Therefore, we build a graph-based relation-discovery module to conduct reasoning with improved GCN to integrate spatial and frequency features." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.754, + 0.892, + 0.867 + ], + "angle": 0, + "content": "Firstly, we concatenate \\( P^s \\) and \\( P^f \\) in the channel dimension to get \\( V^{(0)} \\in \\mathbb{R}^{T^{(0)} \\times N^{(0)}} \\), where \\( T^{(0)} = T_s + T_f \\) and \\( N^{(0)} = \\max(N_s, N_f) \\). We treat each column of \\( V^{(0)} \\) as a node. As shown in the right bottom of Fig. 3, a dynamic GCN module is proposed to aggregate features based on their similarity. Different from original GCN, our model learns to dynamically design appropriate graph structures in each layer, rather than treating it as a fixed constant one." + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.887, + 0.5, + 0.898 + ], + "angle": 0, + "content": "7281" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.139, + 0.124, + 0.833, + 0.314 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.336, + 0.893, + 0.364 + ], + "angle": 0, + "content": "Figure 3. The proposed Dynamic Graph Spatial-Frequency Feature Fusion Network (DG-SF\\(^3\\)Net), which includes two modules: Dynamic Graph Convolution Network (DGCN) and Graph Information Interaction \\((\\mathrm{GI}^2)\\) layers." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.386, + 0.47, + 0.43 + ], + "angle": 0, + "content": "At \\(t\\)-th layer, we have a tailored sparse-connected graph \\(G^{(t)} = (V^{(t)},E^{(t)})\\) for graph convolution, where the local neighbor of each center node \\(v_{i}^{(t)}\\) can be defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.08, + 0.435, + 0.465, + 0.461 + ], + "angle": 0, + "content": "\\[\n\\mathcal {N} ^ {(t)} (i) = \\left\\{v _ {j i m} ^ {(t)} \\mid v _ {j i m} ^ {(t)} \\in k N N \\left(v _ {i} ^ {(t)}\\right), m = 1, \\dots , k \\right\\},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.465, + 0.469, + 0.523 + ], + "angle": 0, + "content": "where \\( v_{j_{i1}}^{(t)}, \\ldots, v_{j_{ik}}^{(t)} \\) are \\( k \\) nodes closest to \\( v_{i}^{(t)} \\) according to the Euclidean distance. After getting the localized kNN graph, we formulate the adjacency matrix \\( A^{(t)} \\) based on \\( k \\) neighbors attached to center node with self-loop added." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.523, + 0.469, + 0.552 + ], + "angle": 0, + "content": "With this sparse-connected GCN, the node features can be updated with the message passing as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.097, + 0.556, + 0.47, + 0.58 + ], + "angle": 0, + "content": "\\[\nV ^ {(t + 1)} = \\operatorname {R e L U} \\left(\\widetilde {D} ^ {(t) - \\frac {1}{2}} \\tilde {A} ^ {(t)} \\widetilde {D} ^ {(t) - \\frac {1}{2}} V ^ {(t)} W ^ {(t)}\\right), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.585, + 0.469, + 0.631 + ], + "angle": 0, + "content": "where \\(\\tilde{D}^{(t)}\\in \\mathbb{R}^{T^{(t)}\\times T^{(t)}}\\) is the degree matrix. \\(W^{(t)}\\in\\) \\(\\mathbb{R}^{N^{(t)}\\times N^{(t + 1)}}\\) is the learnable graph weight. In addition, the output channel is conforming with the input one." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.632, + 0.469, + 0.812 + ], + "angle": 0, + "content": "Finally, we propose a Graph Information Interaction \\((\\mathrm{GI}^2)\\) component for the spatial-frequency feature interaction. The \\(\\mathrm{GI}^2\\) component is composed of several MLP-Mixers [40] layers weighted by the graph adjacent matrix. Each of them leverages a channel-mixing MLP layer and a token-mixing MLP layer, which perform information interaction across all channels and node positions embedded in high-dimensional feature space. These two types of layers are interleaved to enable interaction of both input dimensions. Particularly, in order to highlight the localized features defined on the kNN graph abovementioned, we utilize the adjacent matrix derived from the first GCN layer to weight the feature of the token-mixing MLP." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.818, + 0.222, + 0.831 + ], + "angle": 0, + "content": "3.4. Loss Function" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.839, + 0.47, + 0.868 + ], + "angle": 0, + "content": "After dynamic graph learning, we obtain the semantic feature matrix \\(\\tilde{V} \\in \\mathbb{R}^{M \\times N}\\). Following MADD, we regard" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.386, + 0.892, + 0.414 + ], + "angle": 0, + "content": "Region Independent Loss (RIL) with Cross Entropy (CE) loss as the loss function. The auxiliary RIL is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.516, + 0.422, + 0.891, + 0.504 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {R I L} = \\sum_ {i = 1} ^ {B} \\sum_ {j = 1} ^ {M} \\operatorname {R e L U} \\left(\\left\\| \\tilde {V} _ {j} ^ {i} - c _ {j} ^ {t} \\right\\| _ {2} ^ {2} - m _ {i n} \\left(y _ {i}\\right)\\right) \\tag {5} \\\\ + \\sum_ {i \\neq j} ^ {M} \\mathrm {R e L U} \\left(m _ {o u t} - \\left\\| c _ {i} ^ {t} - c _ {j} ^ {t} \\right\\| _ {2} ^ {2}\\right) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.513, + 0.891, + 0.57 + ], + "angle": 0, + "content": "\\(c \\in \\mathbb{R}^{M \\times N}\\) are feature centers of \\(\\tilde{V}\\) that can be updated iteratively during training. \\(B\\) is the batch size, \\(M\\) is the number of attention maps and \\(y_{i}\\) is the label. \\(m_{in}\\) and \\(m_{out}\\) represent the margin of intra-class and inter-class." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.57, + 0.891, + 0.597 + ], + "angle": 0, + "content": "In conclusion, the total loss function \\(\\mathcal{L}\\) of our proposed SFDG framework can be described as:" + }, + { + "type": "equation", + "bbox": [ + 0.599, + 0.608, + 0.891, + 0.623 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\lambda_ {1} * \\mathcal {L} _ {C E} + \\lambda_ {2} * \\mathcal {L} _ {R I L} \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.631, + 0.891, + 0.66 + ], + "angle": 0, + "content": "where \\(\\lambda_{1},\\lambda_{2}\\) are hyper-parameters for balancing different terms. We set \\(\\lambda_1 = \\lambda_2 = 1\\) in the following experiments." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.671, + 0.625, + 0.687 + ], + "angle": 0, + "content": "4. Experiment" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.694, + 0.691, + 0.709 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.714, + 0.892, + 0.867 + ], + "angle": 0, + "content": "Datasets. We appraise our proposed SFDG method and current state-of-the-art approaches on FaceForensics++ (FF++) [30], WildDeepfake [52], DFDC [5], Celeb-DF [22], DF-v1.0 [13] and DFD [6]. FF++ (low quality (LQ) and high quality (HQ) counterparts) is a widely-used benchmark dataset composed of 1000 real videos from YouTube and corresponding fake videos generated by four types of manipulated techniques: Deepfakes (DF) [41], Face2Face (F2F) [39], FaceSwap (FS) [17] and NeuralTextures (NT) [38]. WildDeepfake is a small real-scenario dataset including 7314 face sequences. Celeb-DF contains" + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.887, + 0.502, + 0.898 + ], + "angle": 0, + "content": "7282" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.08, + 0.124, + 0.894, + 0.339 + ], + "angle": 0, + "content": "
MethodFF++ (LQ)FF++ (HQ)WildDeepfakeCeleb-DF
AccAUCAccAUCAccAUCAccAUC
Xception [4]86.8689.3095.7396.3079.9988.8697.9099.73
EfficientNet-b4 [37]86.6788.2096.6399.1882.3390.1298.1999.83
Add-Net [52]87.5091.0196.7897.7476.2586.1796.9399.55
SCL [18]89.0092.4096.6999.30————
MADD [50]88.6990.4097.6099.2982.6290.7197.9299.94
F3Net [28]90.4393.3097.5298.1080.6687.5395.9598.93
PEL [9]90.5294.2897.6399.3284.1491.62——
RECCE [2]91.0395.0297.0699.3283.2592.0298.5999.94
Local Relation [3]91.4795.2197.5999.46————
M2TR [43]92.3594.2298.2399.48————
SFDG (Xception)91.0894.4997.6199.4583.3692.1598.9599.94
SFDG (Ours)92.2895.9898.1999.5384.4192.5799.2299.96
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.347, + 0.893, + 0.376 + ], + "angle": 0, + "content": "Table 1. Quantitative comparison in terms of Acc(%) and AUC(%) on FF++, WildDeepfake and Celeb-DF dataset. The red represents the best performance while the blue indicates the second-best results." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.398, + 0.471, + 0.468 + ], + "angle": 0, + "content": "590 real videos and 5,639 high quality fake videos tampered with the improved deepfake methods. DFDC is a remarkable large-scale dataset with over 100,000 video clips. DFD and DF-v1.0 are two another large-scale publicly available datasets to evaluate the model's generalization ability." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.469, + 0.471, + 0.525 + ], + "angle": 0, + "content": "Evaluation Metrics. Following previous works [9, 28], we employ the commonly used Accuracy (Acc), Area Under the Receiver Operating Characteristic Curve (AUC) and Equal Error Rate (EER) as our evaluation metrics." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.525, + 0.471, + 0.693 + ], + "angle": 0, + "content": "Implementation Details. Following the official split of FF++ dataset, we use 740 videos for training, 140 for validation and 140 remained for testing. We sample 50 frames per video at equal interval during training and validation phases, 20 frames in testing period. We use the remarkable DLIB [32] for face detection and alignment. We employ EfficientNet-b4 [37] pretrained on ImageNet [31] as the backbone of our network. We set \\( m_{out} \\) to 0.2 and \\( m_{in} \\) to [0.05,0.1] in Eq. 5. The whole network is trained with Adam optimizer with an initial learning rate of \\( 1 \\times 10^{-4} \\), the weight decay of \\( 1 \\times 10^{-5} \\). A step learning scheduler is used to reduce the learning rate half every 5 epochs." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.706, + 0.28, + 0.721 + ], + "angle": 0, + "content": "4.2. Experimental Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.729, + 0.47, + 0.868 + ], + "angle": 0, + "content": "Intra-testing. We compare our proposed method versus current state-of-the art approaches on the FF++ dataset under different quality settings (HQ and LQ), WildDeepfake and Celeb-DF datasets. As shown in Table 1, our method consistently achieves admirably performance on all quality settings and trumps all reference methods by a considerable margin. Specifically, in terms of Acc, our method achieves \\(92.28\\%\\) and \\(98.19\\%\\) on LQ and HQ settings respectively, with a remarkable improvement in comparison to PEL [9], i.e., \\(2.1\\%\\) performance gain on LQ and \\(0.6\\%\\) on HQ. Dif" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.398, + 0.893, + 0.578 + ], + "angle": 0, + "content": "ferent from PEL which only utilizes fine-grained frequency features, our model extracts adaptive frequency features with a content mask providing rounded frequency representations. More importantly, we boost the information interaction between spatial and frequency domains via dynamic graph learning instead of vanilla convolution paradigm in PEL. Further, our method achieves a noteworthy performance compared with Local Relation [3] and M2TR [43], which introduce powerful priors of forgery masks. Instead, our SFDG only employs real/fake images as the input, but the AUC on both LQ and HQ settings surpass these two works strikingly. As discussed, these fruitful results give explanation of the effectiveness of our SFDG method." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.895, + 0.806 + ], + "angle": 0, + "content": "Cross-testing. To further appraise the generalization ability of our method on unseen manipulated types, we herein conduct cross-dataset experiments by training and testing on different datasets. Following PEL [9], we reimplement several state-of-the-art models for a fair comparison on \\(\\mathrm{FF}++\\) (LQ) dataset and testing them on Celeb-DF, DFDC, DFD, DF-v1.0 and WildDeepfake dataset. Comparisons under AUC and EER metrics are detailedly shown in Table 2. It implicates that our SFDG method generally outperforms all competitors conspicuously on all testing datasets. Instead of overfitting with specific forged patterns as in most existing methods, SFDG explores the essential forgery with content-aware semantic attention maps and reasons about generalized forged cues via graph-based high-order relation discovery in spatial and frequency domains, which guarantees the superior generalization ability of our proposed method." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.895, + 0.869 + ], + "angle": 0, + "content": "Robustness. Considering the image quality will be deteriorated seriously by inevitable noise in video acquisition process, we further investigate the robustness of our SFDG model under several common perturbations. Specifically," + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.887, + 0.502, + 0.898 + ], + "angle": 0, + "content": "7283" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.102, + 0.123, + 0.87, + 0.267 + ], + "angle": 0, + "content": "
Training DataSetMethodTesting Dataset
Celeb-DFDFDWildDeepfakeDFDCDF-v1.0
AUCEER↓AUCEER↓AUCEER↓AUCEER↓AUCEER↓
FF++Xception [4]60.050.43265.430.39360.590.61955.650.46180.270.265
Ef-b4 [37]64.290.41983.170.23564.270.37660.120.42885.310.228
Add-Net [52]57.830.44457.160.45354.210.46251.600.548——
MADD [50]68.640.37174.180.32765.650.39763.020.41089.340.173
F3Net [28]67.950.36869.500.35460.490.43457.870.44282.270.246
PEL [9]69.180.35775.860.30867.390.38363.310.404——
SFDG (Ours)75.830.30388.000.19769.270.37773.640.33792.100.151
" + }, + { + "type": "table_caption", + "bbox": [ + 0.109, + 0.276, + 0.859, + 0.289 + ], + "angle": 0, + "content": "Table 2. Cross-testing results in terms of AUC(%) and EER training on FF++ dataset. The bold indicates the best performance." + }, + { + "type": "table", + "bbox": [ + 0.097, + 0.3, + 0.875, + 0.416 + ], + "angle": 0, + "content": "
Method+GaussianNoise+SaltPepperNoise+GaussianBlur
ΔAcc(FF)ΔAcc(Wild)ΔAcc(FF)ΔAcc(Wild)ΔAcc(FF)ΔAcc(Wild)
Xception [4]-2.65%-0.98%-32.44%-27.80%-6.22%-12.71%
Add-Net [52]-41.51%-11.66%-11.28%-18.21%-11.28%-12.91%
F3Net [28]-9.86%-1.17%-31.08%-43.57%-11.08%-12.43%
MADD [50]-1.79%-0.99%-49.30%-29.47%-12.23%-14.86%
PEL [9]-0.10%-0.86%-9.39%-4.25%-7.41%-10.88%
SFDG (Ours)-0.10%-0.75%-10.10%-3.74%-3.76%-5.12%
" + }, + { + "type": "table_caption", + "bbox": [ + 0.084, + 0.425, + 0.884, + 0.438 + ], + "angle": 0, + "content": "Table 3. Robustness evaluation under three types of perturbations. Our SFDG performs admirably under several common perturbations." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.463, + 0.47, + 0.614 + ], + "angle": 0, + "content": "following PEL [9], we apply GaussianNoise, SaltPepperNoise and GaussianBlur to the FF++ (LQ) and WildDeepfake testing images, and adopt the decay of Acc to indicate the robustness of face forgery detection model. As shown in Table 3, a series of experiments throw light on that our method with the least performance decline is more robust to the perturbations abovementioned. We attribute it to the elaborate CAFÉ module which extracts the adaptive frequency features among multiple bands and acts as an image denoiser. We provide sufficient experiments results in terms of AUC in the supplementary materials." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.624, + 0.23, + 0.639 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.646, + 0.47, + 0.867 + ], + "angle": 0, + "content": "Effectiveness of Proposed Components. As shown in Table. 4, a series of ablation experiments on \\(\\mathrm{FF}++\\) (LQ) benchmark have been conducted to verify the effectiveness of different components in our framework. Specifically, we develop the following variants: (a) the baseline model equipped with the MADD [50] pipeline, (b) the baseline model with the proposed CAFÉ module, (c) the proposed method w/o. DG-SF3Net, (d) the proposed method w/o. MDAML module. Comparing (a) and (b), we observe that the proposed CAFÉ module brings a considerable improvement of Acc and AUC metrics on FF++ (LQ) dataset. From variant (b) and (c), we empirically demonstrate that adding the MDAML module will bring \\(2.19\\%\\) Acc and \\(1.52\\%\\) AUC gains, which are attributed to the multi-scale contextual information and large receptive field of refined attention maps. When adding the DG-SF3Net module, as" + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.46, + 0.89, + 0.564 + ], + "angle": 0, + "content": "
IDCAFÉMDAMLDG -SF3NetAcc (LQ)AUC (LQ)
(a)88.6990.4
(b)✓89.5293.37
(c)✓✓91.4894.79
(d)✓✓92.0595.45
Ours✓✓✓92.2895.98
" + }, + { + "type": "table_caption", + "bbox": [ + 0.545, + 0.572, + 0.846, + 0.585 + ], + "angle": 0, + "content": "Table 4. Ablation study on the FF++ (LQ) dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.892, + 0.698 + ], + "angle": 0, + "content": "shown in variant (c) and Ours, we observe a remarkable advance on both Acc and AUC metrics, which benefits from the dynamic graph learning protocol to reason about the relation-aware forged clues. Finally, the best performance is achieved when combining all components, with the Acc and AUC of \\(92.28\\%\\) and \\(95.98\\%\\) respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.699, + 0.893, + 0.867 + ], + "angle": 0, + "content": "Setting of Hyper-parameters. During graph construction, the number of neighbor nodes \\( k \\) is a hyperparameter which determines the structure and aggregated scope of GCNs [10]. As shown in Table 5, to further evaluate the effectiveness using different \\( k \\), we conduct a series of experiments on FF++ (LQ) and WildDeepfake datasets. From the experimental results, we conclude that too few neighbors can not guarantee the representative ability of the dynamic GCN module, thus degrades the information exchange of forged clues in spatial and frequency domains. Further, too many neighbors will tamper the regional separability of attention maps and tend to catastrophic overfitting. In our" + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.887, + 0.501, + 0.898 + ], + "angle": 0, + "content": "7284" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.125, + 0.473, + 0.27 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.105, + 0.289, + 0.441, + 0.302 + ], + "angle": 0, + "content": "Figure 4. The Grad-CAM visualization for forged faces." + }, + { + "type": "image", + "bbox": [ + 0.083, + 0.318, + 0.468, + 0.372 + ], + "angle": 0, + "content": null + }, + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.395, + 0.468, + 0.409 + ], + "angle": 0, + "content": "Figure 5. The t-SNE feature visualization of the Ef-b4 and SFDG." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.422, + 0.468, + 0.51 + ], + "angle": 0, + "content": "
#NeighborsFF++ (LQ)WildDeepfake
AccAUCAccAUC
592.1095.6082.0390.57
1092.2895.9884.4192.57
1592.2895.4983.5791.15
2092.0291.5981.4690.38
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.078, + 0.519, + 0.469, + 0.545 + ], + "angle": 0, + "content": "Table 5. Results in terms of Acc(%) and AUC(%) for different number of neighboring nodes in the graph construction." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.571, + 0.469, + 0.599 + ], + "angle": 0, + "content": "work, we observe that our model achieves the best performance in terms of Acc and AUC when setting \\( k \\) to 10." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.61, + 0.215, + 0.623 + ], + "angle": 0, + "content": "4.4. Visualization" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.632, + 0.47, + 0.867 + ], + "angle": 0, + "content": "Grad-CAM visualization. To better understand the internal mechanism of our method and explore interested regions for specific forged types, we supply the Grad-CAM [33] visualization on \\(\\mathrm{FF}++\\) dataset. As shown in Fig. 4, the forgery artifacts in different domains locate on independent regions. Detailedly, the spatial branch focuses on the facial region with pronounced forgery traces, which are effortlessly discovered by CNN backbones in spatial domain. Conversely, the frequency streamline searches manipulated clues essentially concerned with a wider area, e.g., the background, hair or entire face. These regions are subtle and dynamically change according to the image content thus provides a generalized feature representation. Just as we have speculated, the frequency domain acts as the complementary to the spatial domain and these two domains contribute to each other via graph-based high-order relation discovery for exploiting comprehensive forged cues." + }, + { + "type": "image", + "bbox": [ + 0.511, + 0.127, + 0.885, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.262, + 0.892, + 0.288 + ], + "angle": 0, + "content": "Figure 6. The visualization results of feature maps from MDAML module at different scales on FF++ and WildDeepfake datasets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.314, + 0.893, + 0.466 + ], + "angle": 0, + "content": "Attention Maps Visualization. We verify the effectiveness of our tailored MDAML module and visualize the results in Fig 6. We observe that feature maps with different scales highlight distinctive activated intensities. Detailedly, the large scale features with high resolution representation embrace richer and global manipulated traces, while the small scales concentrate on more localized salient feature around facial landmarks. Further, we aggregate the attention maps via hierarchical pyramid paradigm to exploit the essential discrepancy between authentic and counterfeit faces, which can resist the noise disturbance and visual compression." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.468, + 0.892, + 0.62 + ], + "angle": 0, + "content": "Feature Distribution Visualization. In this part, we investigate the discriminative ability of the proposed SFDG model. Leveraging the t-SNE [42] technique, we visualize the semantic feature distribution of the Ef-b4 [37] model and our SFDG on \\(\\mathrm{FF}++\\) (LQ) and WildDeepfake dataset. As shown in Fig. 5, our approach encourages the samples of same class into a relatively compact feature space. To explain, our SFDG adequately captures the intrinsic discrepancy between genuine and forged faces in multiple domains through graph-based relationships discovery, thus improving the generalization ability of our method." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.635, + 0.618, + 0.649 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.892, + 0.867 + ], + "angle": 0, + "content": "In this paper, we propose a novel Spatial-Frequency Dynamic Graph network that develops graph model to exploit relationships of spatial and frequency domains for spotting subtle forgery clues. Firstly, the Content-guided Adaptive Frequency Extraction module is proposed to mine the adaptive frequency clues via content-aware frequency learning. Further, a Multiple Domains Attention Map Learning scheme captures rich contextual information of spatial-frequency feature through multi-scale feature ensemble. Finally, Dynamic Graph based Spatial-Frequency Feature Fusion module performs relation reasoning of spatial and frequency domains via improved graph convolution. Extensive experiments and detailed visualizations on widely-used benchmarks confirm the effectiveness and generalizability of our SFDG method compared with other contenders." + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.887, + 0.501, + 0.898 + ], + "angle": 0, + "content": "7285" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.125, + 0.174, + 0.139 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.148, + 0.47, + 0.199 + ], + "angle": 0, + "content": "[1] Darius Afchar, Vincent Nozick, Junichi Yamagishi, and Isao Echizen. Mesonet: a compact facial video forgery detection network. 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In Proceedings of the 28th ACM International Conference on Multimedia, pages 2382-2390, 2020. 1, 5, 6, 7" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.127, + 0.892, + 0.859 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.887, + 0.501, + 0.898 + ], + "angle": 0, + "content": "7287" + } + ] +] \ No newline at end of file diff --git a/2023/Dynamic Graph Learning With Content-Guided Spatial-Frequency Relation Reasoning for Deepfake Detection/0db433fe-2bb5-4d32-8dad-d6501909824f_origin.pdf b/2023/Dynamic Graph Learning With Content-Guided Spatial-Frequency Relation Reasoning for Deepfake Detection/0db433fe-2bb5-4d32-8dad-d6501909824f_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..00a2febcbe902fcb330e2694466feb0bf4f62453 --- /dev/null +++ b/2023/Dynamic Graph Learning With Content-Guided Spatial-Frequency Relation Reasoning for Deepfake Detection/0db433fe-2bb5-4d32-8dad-d6501909824f_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:d668ad186209e9f76b02c91f5fe686b9ca3e0a2b5fc90d5f68b8c40634ff3ccf +size 1231717 diff --git a/2023/Dynamic Graph Learning With Content-Guided Spatial-Frequency Relation Reasoning for Deepfake Detection/full.md b/2023/Dynamic Graph Learning With Content-Guided Spatial-Frequency Relation Reasoning for Deepfake Detection/full.md new file mode 100644 index 0000000000000000000000000000000000000000..2828c06eb50ac17874a2ce7ddcaeb78d3e496d46 --- /dev/null +++ b/2023/Dynamic Graph Learning With Content-Guided Spatial-Frequency Relation Reasoning for Deepfake Detection/full.md @@ -0,0 +1,292 @@ +# Dynamic Graph Learning with Content-guided Spatial-Frequency Relation Reasoning for Deepfake Detection + +Yuan Wang $^{1,2,4}$ Kun Yu $^{2}$ Chen Chen $^{1*}$ Xiyuan Hu $^{3}$ Silong Peng $^{1,4,5}$ + +$^{1}$ Institute of Automation, Chinese Academy of Sciences $^{2}$ Alibaba Group + +$^{3}$ School of Computer Science and Engineering, Nanjing University of Science and Technology + +4University of Chinese Academy of Sciences 5Beijing Visystem Co.Ltd + +{wangyuan2020, chen.chen}@ia.ac.cn yukun.yk@alibaba-inc.com xiyuan.hu@foxmail.com + +# Abstract + +With the springing up of face synthesis techniques, it is prominent in need to develop powerful face forgery detection methods due to security concerns. Some existing methods attempt to employ auxiliary frequency-aware information combined with CNN backbones to discover the forged clues. Due to the inadequate information interaction with image content, the extracted frequency features are thus spatially irrelevant, struggling to generalize well on increasingly realistic counterfeit types. To address this issue, we propose a Spatial-Frequency Dynamic Graph method to exploit the relation-aware features in spatial and frequency domains via dynamic graph learning. To this end, we introduce three well-designed components: 1) Content-guided Adaptive Frequency Extraction module to mine the content-adaptive forged frequency clues. 2) Multiple Domains Attention Map Learning module to enrich the spatial-frequency contextual features with multiscale attention maps. 3) Dynamic Graph Spatial-Frequency Feature Fusion Network to explore the high-order relation of spatial and frequency features. Extensive experiments on several benchmark show that our proposed method sustainably exceeds the state-of-the-arts by a considerable margin. + +# 1. Introduction + +Recent years have witnessed the continuous advances in deepfake creation [11, 27, 36]. Utilizing booming open-source tools such as Deepfakes [41], novices can readily manipulate the expression and identity of faces to generate visually untraceable videos. Face forgery technology has stimulated many applications [12, 14, 44, 46] with wide acceptance. These techniques can whereas be abused by ma + +![](images/65a14129cd9a7343e4adbb1dab98573255871ae136ab6f7f0213a343d9f17953.jpg) +Figure 1. The motivation of our proposed approach. Our SFDG method (a) delves into the high-order relationships (b) of spatial and frequency domain via cross-domain graph reasoning (c). + +licious intentions to make pornographic movies, fake news and political rumors. In the circumstances, it is desperately in need to develop powerful forgery detection methods. + +Early face forgery detection methods [7,30,52] treat this challenge as vanilla dichotomy tasks in the prevailing view. They use off-the-shelf backbones to extract the global feature of faces and a binary classifier follow-up to identify the real and counterfeit faces. However, as the counterfeits become increasingly realistic, it is intractable for these methods to spot subtle and local forgery traces. One recent study [50] reformulates deepfake detection as a fine-grained classification task and designs a multi-attentional framework to extract local discriminative features from multiple attention maps. It is susceptible to common disturbances and the generalized features remain therefore poorly understood. Some other works resort to specific forgery patterns to encourage better classification such as DCT [24,28], SRM [25] and steganalysis features [45]. Although promising advances have been achieved by these previous works, + +they always extract frequency features with hand-crafted filter banks which are content-irrelevant, thus incapable to adapt the changes of complex scenarios. Moreover, they fuse multi-domain information via adding directly or attentional projection. However, these approaches devote little efforts to discover the high-order relation of spatial and frequency features and integrating them in a reasonable way. + +In this paper, we provide seminal insights to exploit adaptive frequency features and delve into the interactions of spatial-frequency domains. To this end, we propose an adaptive extraction-multiscale enhancement-graph fusion paradigm for deepfake detection via dynamic graph learning, which prompts to excavate content-aware frequency clues and the high-order relation of multiple domains. + +Firstly, for adaptive frequency extraction, we tailor a Content-guided Adaptive Frequency Extraction (CAFÉ) module with coarse-grained DCT and fine-grained DCT to capture the local frequency cues guided by content-aware masks. Different from PEL [9] and F3Net [28], our customized frequency learning protocol provides potential for more combinations of frequency features, which is indispensable to spot complicated counterfeit patterns. + +To further enhance the representation of content-guided frequency features, we introduce a Multiple Domains Attention Map Learning (MDAML) module to generate multiscale spatial and frequency attention maps with high-level semantic features. Specifically, we first propose a MultiScale Attention Ensemble (MSAE) module, which produces multi-scale semantic attention maps with large receptive fields and endows rich contextual information to spatial and frequency domains. Moreover, an Attention Map Refinement Block (AMRB) is included in the MSAE module to refine the obtained semantic attention maps conducive to the following feature learning. In comparison with MADD [50] that merely emphasizes the spatial domain, we further introduce the semantic-relevant frequency attention map with rich semantic information retained for the subsequent spatial-frequency relation-discovery paradigm. + +Finally, to fully discover the spatial and frequency relationships, we propose a Dynamic Graph-based Spatial-Frequency Feature Fusion network (DG-SF $^3$ Net) to formulate the interaction of two domains via a graph-based relation discovery protocol. Specifically, DG-SF $^3$ Net is composed of two ingredients: Dynamic GCN [16] and Graph Information Interaction layers. The former constructs kNN-graph dynamically and performs graph convolution to reason high-order relationships in spatial and frequency domains, while the latter is designed to enhance the mutual relation with several graph-weighted MLP-Mixer [40] layers via channel-wise and node-wise interaction. + +The achievements, including contributions are threefold: + +From a new perspective, we propose a novel SpatialFrequency Dynamic Graph (SFDG) framework, which + +is qualified to exploit relation-aware spatial-frequency features to promote generalized forgery detection. + +- We first harness a CAFÉ module for content-aware frequency feature extraction, and then tailor an MDAML scheme to dig deeper into multiscale spatial-frequency attention maps with rich contextual understanding of forgeries. Finally, a seminal DG-SF3Net module is proposed to discover the multi-domain relationships with a graph-based relation-reasoning approach. + +- Our method achieves state-of-the-art performance on six benchmark datasets. The cross-dataset experiment and the perturbation analysis show the robustness and generalization ability of the proposed SFDG method. + +# 2. Related Works + +Over the past several years, with the remarkable progress of forgery creation techniques, increasing efforts have been made to boost the development of face forgery detection in computer vision communities. In this section, we briefly review previous works exploring the authenticity of faces. + +Rudimentary deepfake detection approaches base primarily on obvious counterfeit artifacts, which utilize handcrafted features to detect anomalies in spatial domain, e.g., inconsistent head pose [47] and unnatural eye blinding [21]. However, these traditional methods feel intractable to deal with the improved realistic deepfakes. With the overwhelming success of deep learning, some works [1,4,7] adopt off-the-shelf classification backbones to extract high-level semantic features for deepfake detection. Although considerable performances have been achieved on specific datasets, their vanilla structures would lead to catastrophic overfitting and lag behind the advanced face synthesis technology. + +To further exploit the essential forged clues, general deepfake detection [15, 20, 26, 34, 35] has been an area of intense investigation. Nguyen et al. [26] employ multi-task learning strategy to detect forged artifacts and locate manipulated regions simultaneously. Face X-ray [20] observes the specific blending step of face swapping and locates forgery boundary in a self-supervised manner. FReTAL [15] adopts the knowledge distillation to prevent catastrophic forgetting and enhance adaptability in different domains. DCL [35] performs dual-granularity contrastive learning to further improve the generalization. However, these approaches captures category-level differences instead of the intrinsic discrepancies between authentic and forged images. + +Recently, other studies focus on mining specific forgery patterns, such as local texture, high-frequency noise, reconstruction residual and frequency clues. Among them, Zhao et al. [50] propose a fine-grained deepfake detection framework that aggregates the local texture and high-level semantic information into multiple attention maps. However, it fails to distinguish highly compressed videos with + +![](images/4f756507a3fb744590ae39856c3cef5c39a6c2050113dbf40bd29be759eb3c08.jpg) + +![](images/35ab0c4e7a12857f24ffbc12c86fd7064c6935e24b64d456ce117c85af0e68ac.jpg) +Figure 2. (a) Overview of the proposed Spatial-Frequency Dynamic Graph (SFDG) framework. (b) The Content-guided Adaptive Frequency Extraction (CAFÉ) module. (c) The Multiple Domains Attention map Learning (MDAML) network. + +blurry texture. Luo et al. [25] utilize the high-pass filter SRM [8] to extract high-frequency noise guiding face forgery detection. RECCE [2] employs the reconstruction difference of authentic faces as guidance of forgery traces. $\mathrm{F}^3\mathrm{Net}$ [28] collaboratively mines the forged frequency clues with frequency-aware decomposition and local frequency statistics. However, the extracted frequency feature is coarse-grained, incapable of assembling discriminative feature patterns. To ameliorate this issue, PEL [9] learns the fine-grained frequency features using sliding window DCT combined with RGB images in a progressive enhancement learning fashion. Nevertheless, the fine-grained frequency is content-irrelevant and in compliance with the vanilla spatial-frequency fusion ethos, thus failing to achieve the utter information interaction of both domains. + +Different from existing studies, our proposed end-to-end SFDG approach excavates content-adaptive frequency clues and facilitates the comprehensive fusion of spatial and frequency features via dynamic graph learning. + +# 3. Method + +In this section, we propose a Spatial-Frequency Dynamic Graph (SFDG) framework, which consists of three major modules, i.e., Content-guided Adaptive Frequency Extraction (CAFÉ), Multiple Domains Attention Map Learning (MDAML), and Dynamic Graph Spatial Frequency Feature Fusion Network (DG-SF $^3$ Net). The primary idea of our approach is to exploit content-aware frequency features uti + +lizing CAFÉ module. As limited context information do these features embrace, we present the MDAML module to generate high-level frequency attention maps in a multiscale learning manner. Beyond these improvements, we finally design a DG-F3Net to perform relation reasoning of spatial and frequency features via dynamic graph learning. + +# 3.1. Content-aware Frequency Extraction + +Towards the frequency-aware face forgery detection, former studies generally use DCT to transform the input image into frequency domain. However, for the scarcity of spatial information in DCT process, the extracted frequency feature is presumably not compatible to the image content. To this end, we propose the CAFÉ module to fully exploit the forgery clues via content-aware frequency learning in order to handle complex or simple manipulated patterns adaptively. Without loss of generality, let $x^{s}\in \mathbb{R}^{3\times H\times W}$ denotes the RGB image, where $H$ and $W$ are the height and width of the input image. As shown in Fig. 2(b), we generate an attentional content mask $M^s$ using a UNet [29] submodule with the spatial information retained. We then propose a coarse-grained counterpart to partition the compact frequency spectrum into several bands. Specifically, we manually design $N_{f}$ binary filters $\{f_i|i = 1,\dots,N_f\}$ to decompose the frequency domains into low, middle and high frequency bands. The low-frequency component lies on the top-left corner while the high-frequency response locates on the bottom-right corner [28]. As described, the + +coarse-grained process can be formulated as: + +$$ +x _ {\text {c o a r s e}} ^ {f, i} = \mathcal {H} ^ {- 1} \left[ \mathcal {H} \left(x ^ {s}\right) \odot f ^ {i} \right], \quad i = \{1, 2, \dots , N _ {f} \}, \tag {1} +$$ + +where $\odot$ is the Hadamard product. $\mathcal{H}$ and $\mathcal{H}^{-1}$ represent the DCT and inverse DCT respectively. $x_{coarse}^{f}\in \mathbb{R}^{3N_{f}\times H\times W}$ is the extracted coarse frequency feature, which indicates global frequency information to some extent. + +Further, we design a fine-grained frequency extraction method to emphasize on the localized frequency features. Specifically, we slice $x^{s}$ via a sliding window to obtain a set of $l\times l$ patches. $p_{m,n}\in \mathbb{R}^{3\times l\times l}$ denotes the patch sliced by the $(m$ -th, $n$ -th) sliding window. After performing DCT on each patch, we get the localized fine-grained frequency features $d_{m,n}^{f}\in \mathbb{R}^{3\times l\times l}$ . We repeat the channel of each $d_{m,n}^{f}$ to match the coarse-grained frequency features abovementioned. All localized patched are then gathered into a whole feature map $d^{f}\in \mathbb{R}^{3N_{f}\times H\times W}$ and go through several convolution Blocks composed by Conv2d, BN, and ReLU to form the output fine-grained frequency features $x_{fine}^{f}$ . + +Finally, we obtain the overall frequency head $x^{fh}$ through an adaptive frequency combine module guided by the learned content mask $M^s$ , which can be formulated as: + +$$ +x ^ {f h} = \left(1 - M ^ {s}\right) \odot x _ {f i n e} ^ {f} + M ^ {s} \odot x _ {c o a r s e} ^ {f}. \tag {2} +$$ + +The extracted frequency head $x^{fh} \in \mathbb{R}^{3N_f \times H \times W}$ will be fed into several stride convolution layers to obtain the final frequency feature $C_f$ channels $x^f$ with size of $H_f \times W_f$ . + +# 3.2. Multiple Domains Attention Map Learning + +To fully exploit the forged clues in spatial domain, we adopt EfficientNet-b4 as the backbone and further partition the entire network into low-level, mid-level and high-level layers, respectively. As shown in Fig. 2(c), to acquire spatial-frequency features with rich semantics, we further design a Multi-Scale Attention Ensemble (MSAE) module in spatial and frequency domains to generate multiscale attention maps and aggregate them with hierarchical feature pyramid. The MSAE includes light weighted ConvBlocks, which consist of several convolution layer, BN and non-linear activation layers ReLU, and certain global average layers to downsample the attention maps into multiple scales. With the multi-scale feature representation, we can obtain a sufficient receptive field and rich contextual information, which are of great significance for the deepfake detection task. Inspired by [48], we propose an Attention Map Refinement Block (AMRB) to get refined feature maps. + +As Fig. 2(c) shows, AMRB employs global average pooling to capture global context and uses a subsequent sigmoid layer to produce an attention vector that determines the feature distribution of attention maps in each scale. Finally, we upsample the refined multi-scale attention maps to the original size and add them spatially. We use AMRB in + +both spatial and frequency streamline to acquire the multiscale spatial attention map $F^{s}$ and frequency feature map $F^{f}$ , which have $T_{s}$ and $T_{f}$ channels on behalf of the corresponding number of attention maps in these two domains. + +After obtaining the refined multi-scale attention maps $F^{s}$ and $F^{f}$ , we perform Bilinear Attention Pooling (BAP) [23] to get the relation-aware feature matrix $P^{s}$ and $P^{f}$ respectively. As illustrated in Fig. 2(c), we use the Textural Feature Enhancement block [50] to capture the manipulated artifacts hidden in low-level layers. After the enhancement of the texture features, we get a textual feature map $F^{tex} \in \mathbb{R}^{C_{tex} \times H_{tex} \times W_{tex}}$ . For the spatial domain, we element-wisely multiply textural feature map $F^{tex}$ by each spatial attention map $F_{k}^{s}$ to obtain the partial textural feature maps $F_{k}^{tex}$ and compute the final spatial feature matrix employing BAP, which can be formulated as: + +$$ +p _ {k} ^ {\mathrm {s}} = \frac {\sum_ {m = 1} ^ {H _ {t e x}} \sum_ {n = 1} ^ {W _ {t e x}} F _ {k , m , n} ^ {t e x}}{\left\| \sum_ {m = 1} ^ {H _ {t e x}} \sum_ {n = 1} ^ {W _ {t e x}} F _ {k , m , n} ^ {t e x} \right\| _ {2}} \tag {3} +$$ + +The spatial attention vector $p_k^s \in \mathbb{R}^{1 \times C_{tex}}$ is stacked together to get the texture-relevant spatial feature matrix $P^s \in \mathbb{R}^{T_s \times N_s}$ . For the frequency domain, we perform the BAP with the frequency attention maps $F^f$ and the spatial feature after high-level backbone layers as shown in Fig. 2(a). Similar to Eq. 3, we can obtain the content-relevant frequency feature matrix $P^f \in \mathbb{R}^{T_f \times N_f}$ . Finally, the learnt relation-aware feature matrices will be fed into the follow-up DG-SF $^3$ Net to collaboratively learn a comprehensive feature representation in a graph-based relation reasoning way. + +# 3.3. Dynamic Graph Learning + +After obtaining the spatial feature matrix $P^{s} \in \mathbb{R}^{T_{s} \times N_{s}}$ and frequency feature matrix $P^{f} \in \mathbb{R}^{T_{f} \times N_{f}}$ , we propose a novel DG-SF $^{3}$ Net to discover the comprehensive relation of them as shown in Fig. 3. Inspired by [19, 49, 51], we provide the intuition that there exists high-order relation of spatial and frequency features and Graph Convolution Network (GCN) performs tremendous potential in relation reasoning. As illustrated in Fig. 1(c), we confirm the above intuition by visualizing the correlation heatmap of spatial and frequency features. Therefore, we build a graph-based relation-discovery module to conduct reasoning with improved GCN to integrate spatial and frequency features. + +Firstly, we concatenate $P^s$ and $P^f$ in the channel dimension to get $V^{(0)} \in \mathbb{R}^{T^{(0)} \times N^{(0)}}$ , where $T^{(0)} = T_s + T_f$ and $N^{(0)} = \max(N_s, N_f)$ . We treat each column of $V^{(0)}$ as a node. As shown in the right bottom of Fig. 3, a dynamic GCN module is proposed to aggregate features based on their similarity. Different from original GCN, our model learns to dynamically design appropriate graph structures in each layer, rather than treating it as a fixed constant one. + +![](images/b45ef41ce2c3e17d9823bd660089fb3042a5ca43d1e7b5bd3e73ae343e7d320b.jpg) +Figure 3. The proposed Dynamic Graph Spatial-Frequency Feature Fusion Network (DG-SF $^3$ Net), which includes two modules: Dynamic Graph Convolution Network (DGCN) and Graph Information Interaction $(\mathrm{GI}^2)$ layers. + +At $t$ -th layer, we have a tailored sparse-connected graph $G^{(t)} = (V^{(t)},E^{(t)})$ for graph convolution, where the local neighbor of each center node $v_{i}^{(t)}$ can be defined as: + +$$ +\mathcal {N} ^ {(t)} (i) = \left\{v _ {j i m} ^ {(t)} \mid v _ {j i m} ^ {(t)} \in k N N \left(v _ {i} ^ {(t)}\right), m = 1, \dots , k \right\}, +$$ + +where $v_{j_{i1}}^{(t)}, \ldots, v_{j_{ik}}^{(t)}$ are $k$ nodes closest to $v_{i}^{(t)}$ according to the Euclidean distance. After getting the localized kNN graph, we formulate the adjacency matrix $A^{(t)}$ based on $k$ neighbors attached to center node with self-loop added. + +With this sparse-connected GCN, the node features can be updated with the message passing as follows: + +$$ +V ^ {(t + 1)} = \operatorname {R e L U} \left(\widetilde {D} ^ {(t) - \frac {1}{2}} \tilde {A} ^ {(t)} \widetilde {D} ^ {(t) - \frac {1}{2}} V ^ {(t)} W ^ {(t)}\right), \tag {4} +$$ + +where $\tilde{D}^{(t)}\in \mathbb{R}^{T^{(t)}\times T^{(t)}}$ is the degree matrix. $W^{(t)}\in$ $\mathbb{R}^{N^{(t)}\times N^{(t + 1)}}$ is the learnable graph weight. In addition, the output channel is conforming with the input one. + +Finally, we propose a Graph Information Interaction $(\mathrm{GI}^2)$ component for the spatial-frequency feature interaction. The $\mathrm{GI}^2$ component is composed of several MLP-Mixers [40] layers weighted by the graph adjacent matrix. Each of them leverages a channel-mixing MLP layer and a token-mixing MLP layer, which perform information interaction across all channels and node positions embedded in high-dimensional feature space. These two types of layers are interleaved to enable interaction of both input dimensions. Particularly, in order to highlight the localized features defined on the kNN graph abovementioned, we utilize the adjacent matrix derived from the first GCN layer to weight the feature of the token-mixing MLP. + +# 3.4. Loss Function + +After dynamic graph learning, we obtain the semantic feature matrix $\tilde{V} \in \mathbb{R}^{M \times N}$ . Following MADD, we regard + +Region Independent Loss (RIL) with Cross Entropy (CE) loss as the loss function. The auxiliary RIL is defined as: + +$$ +\begin{array}{l} \mathcal {L} _ {R I L} = \sum_ {i = 1} ^ {B} \sum_ {j = 1} ^ {M} \operatorname {R e L U} \left(\left\| \tilde {V} _ {j} ^ {i} - c _ {j} ^ {t} \right\| _ {2} ^ {2} - m _ {i n} \left(y _ {i}\right)\right) \tag {5} \\ + \sum_ {i \neq j} ^ {M} \mathrm {R e L U} \left(m _ {o u t} - \left\| c _ {i} ^ {t} - c _ {j} ^ {t} \right\| _ {2} ^ {2}\right) \\ \end{array} +$$ + +$c \in \mathbb{R}^{M \times N}$ are feature centers of $\tilde{V}$ that can be updated iteratively during training. $B$ is the batch size, $M$ is the number of attention maps and $y_{i}$ is the label. $m_{in}$ and $m_{out}$ represent the margin of intra-class and inter-class. + +In conclusion, the total loss function $\mathcal{L}$ of our proposed SFDG framework can be described as: + +$$ +\mathcal {L} = \lambda_ {1} * \mathcal {L} _ {C E} + \lambda_ {2} * \mathcal {L} _ {R I L} \tag {6} +$$ + +where $\lambda_{1},\lambda_{2}$ are hyper-parameters for balancing different terms. We set $\lambda_1 = \lambda_2 = 1$ in the following experiments. + +# 4. Experiment + +# 4.1. Experimental Setup + +Datasets. We appraise our proposed SFDG method and current state-of-the-art approaches on FaceForensics++ (FF++) [30], WildDeepfake [52], DFDC [5], Celeb-DF [22], DF-v1.0 [13] and DFD [6]. FF++ (low quality (LQ) and high quality (HQ) counterparts) is a widely-used benchmark dataset composed of 1000 real videos from YouTube and corresponding fake videos generated by four types of manipulated techniques: Deepfakes (DF) [41], Face2Face (F2F) [39], FaceSwap (FS) [17] and NeuralTextures (NT) [38]. WildDeepfake is a small real-scenario dataset including 7314 face sequences. Celeb-DF contains + +
MethodFF++ (LQ)FF++ (HQ)WildDeepfakeCeleb-DF
AccAUCAccAUCAccAUCAccAUC
Xception [4]86.8689.3095.7396.3079.9988.8697.9099.73
EfficientNet-b4 [37]86.6788.2096.6399.1882.3390.1298.1999.83
Add-Net [52]87.5091.0196.7897.7476.2586.1796.9399.55
SCL [18]89.0092.4096.6999.30————
MADD [50]88.6990.4097.6099.2982.6290.7197.9299.94
F3Net [28]90.4393.3097.5298.1080.6687.5395.9598.93
PEL [9]90.5294.2897.6399.3284.1491.62——
RECCE [2]91.0395.0297.0699.3283.2592.0298.5999.94
Local Relation [3]91.4795.2197.5999.46————
M2TR [43]92.3594.2298.2399.48————
SFDG (Xception)91.0894.4997.6199.4583.3692.1598.9599.94
SFDG (Ours)92.2895.9898.1999.5384.4192.5799.2299.96
+ +Table 1. Quantitative comparison in terms of Acc(%) and AUC(%) on FF++, WildDeepfake and Celeb-DF dataset. The red represents the best performance while the blue indicates the second-best results. + +590 real videos and 5,639 high quality fake videos tampered with the improved deepfake methods. DFDC is a remarkable large-scale dataset with over 100,000 video clips. DFD and DF-v1.0 are two another large-scale publicly available datasets to evaluate the model's generalization ability. + +Evaluation Metrics. Following previous works [9, 28], we employ the commonly used Accuracy (Acc), Area Under the Receiver Operating Characteristic Curve (AUC) and Equal Error Rate (EER) as our evaluation metrics. + +Implementation Details. Following the official split of FF++ dataset, we use 740 videos for training, 140 for validation and 140 remained for testing. We sample 50 frames per video at equal interval during training and validation phases, 20 frames in testing period. We use the remarkable DLIB [32] for face detection and alignment. We employ EfficientNet-b4 [37] pretrained on ImageNet [31] as the backbone of our network. We set $m_{out}$ to 0.2 and $m_{in}$ to [0.05,0.1] in Eq. 5. The whole network is trained with Adam optimizer with an initial learning rate of $1 \times 10^{-4}$ , the weight decay of $1 \times 10^{-5}$ . A step learning scheduler is used to reduce the learning rate half every 5 epochs. + +# 4.2. Experimental Results + +Intra-testing. We compare our proposed method versus current state-of-the art approaches on the FF++ dataset under different quality settings (HQ and LQ), WildDeepfake and Celeb-DF datasets. As shown in Table 1, our method consistently achieves admirably performance on all quality settings and trumps all reference methods by a considerable margin. Specifically, in terms of Acc, our method achieves $92.28\%$ and $98.19\%$ on LQ and HQ settings respectively, with a remarkable improvement in comparison to PEL [9], i.e., $2.1\%$ performance gain on LQ and $0.6\%$ on HQ. Dif + +ferent from PEL which only utilizes fine-grained frequency features, our model extracts adaptive frequency features with a content mask providing rounded frequency representations. More importantly, we boost the information interaction between spatial and frequency domains via dynamic graph learning instead of vanilla convolution paradigm in PEL. Further, our method achieves a noteworthy performance compared with Local Relation [3] and M2TR [43], which introduce powerful priors of forgery masks. Instead, our SFDG only employs real/fake images as the input, but the AUC on both LQ and HQ settings surpass these two works strikingly. As discussed, these fruitful results give explanation of the effectiveness of our SFDG method. + +Cross-testing. To further appraise the generalization ability of our method on unseen manipulated types, we herein conduct cross-dataset experiments by training and testing on different datasets. Following PEL [9], we reimplement several state-of-the-art models for a fair comparison on $\mathrm{FF}++$ (LQ) dataset and testing them on Celeb-DF, DFDC, DFD, DF-v1.0 and WildDeepfake dataset. Comparisons under AUC and EER metrics are detailedly shown in Table 2. It implicates that our SFDG method generally outperforms all competitors conspicuously on all testing datasets. Instead of overfitting with specific forged patterns as in most existing methods, SFDG explores the essential forgery with content-aware semantic attention maps and reasons about generalized forged cues via graph-based high-order relation discovery in spatial and frequency domains, which guarantees the superior generalization ability of our proposed method. + +Robustness. Considering the image quality will be deteriorated seriously by inevitable noise in video acquisition process, we further investigate the robustness of our SFDG model under several common perturbations. Specifically, + +
Training DataSetMethodTesting Dataset
Celeb-DFDFDWildDeepfakeDFDCDF-v1.0
AUCEER↓AUCEER↓AUCEER↓AUCEER↓AUCEER↓
FF++Xception [4]60.050.43265.430.39360.590.61955.650.46180.270.265
Ef-b4 [37]64.290.41983.170.23564.270.37660.120.42885.310.228
Add-Net [52]57.830.44457.160.45354.210.46251.600.548——
MADD [50]68.640.37174.180.32765.650.39763.020.41089.340.173
F3Net [28]67.950.36869.500.35460.490.43457.870.44282.270.246
PEL [9]69.180.35775.860.30867.390.38363.310.404——
SFDG (Ours)75.830.30388.000.19769.270.37773.640.33792.100.151
+ +Table 2. Cross-testing results in terms of AUC(%) and EER training on FF++ dataset. The bold indicates the best performance. + +
Method+GaussianNoise+SaltPepperNoise+GaussianBlur
ΔAcc(FF)ΔAcc(Wild)ΔAcc(FF)ΔAcc(Wild)ΔAcc(FF)ΔAcc(Wild)
Xception [4]-2.65%-0.98%-32.44%-27.80%-6.22%-12.71%
Add-Net [52]-41.51%-11.66%-11.28%-18.21%-11.28%-12.91%
F3Net [28]-9.86%-1.17%-31.08%-43.57%-11.08%-12.43%
MADD [50]-1.79%-0.99%-49.30%-29.47%-12.23%-14.86%
PEL [9]-0.10%-0.86%-9.39%-4.25%-7.41%-10.88%
SFDG (Ours)-0.10%-0.75%-10.10%-3.74%-3.76%-5.12%
+ +following PEL [9], we apply GaussianNoise, SaltPepperNoise and GaussianBlur to the FF++ (LQ) and WildDeepfake testing images, and adopt the decay of Acc to indicate the robustness of face forgery detection model. As shown in Table 3, a series of experiments throw light on that our method with the least performance decline is more robust to the perturbations abovementioned. We attribute it to the elaborate CAFÉ module which extracts the adaptive frequency features among multiple bands and acts as an image denoiser. We provide sufficient experiments results in terms of AUC in the supplementary materials. + +# 4.3. Ablation Study + +Effectiveness of Proposed Components. As shown in Table. 4, a series of ablation experiments on $\mathrm{FF}++$ (LQ) benchmark have been conducted to verify the effectiveness of different components in our framework. Specifically, we develop the following variants: (a) the baseline model equipped with the MADD [50] pipeline, (b) the baseline model with the proposed CAFÉ module, (c) the proposed method w/o. DG-SF3Net, (d) the proposed method w/o. MDAML module. Comparing (a) and (b), we observe that the proposed CAFÉ module brings a considerable improvement of Acc and AUC metrics on FF++ (LQ) dataset. From variant (b) and (c), we empirically demonstrate that adding the MDAML module will bring $2.19\%$ Acc and $1.52\%$ AUC gains, which are attributed to the multi-scale contextual information and large receptive field of refined attention maps. When adding the DG-SF3Net module, as + +Table 3. Robustness evaluation under three types of perturbations. Our SFDG performs admirably under several common perturbations. + +
IDCAFÉMDAMLDG -SF3NetAcc (LQ)AUC (LQ)
(a)88.6990.4
(b)✓89.5293.37
(c)✓✓91.4894.79
(d)✓✓92.0595.45
Ours✓✓✓92.2895.98
+ +Table 4. Ablation study on the FF++ (LQ) dataset. + +shown in variant (c) and Ours, we observe a remarkable advance on both Acc and AUC metrics, which benefits from the dynamic graph learning protocol to reason about the relation-aware forged clues. Finally, the best performance is achieved when combining all components, with the Acc and AUC of $92.28\%$ and $95.98\%$ respectively. + +Setting of Hyper-parameters. During graph construction, the number of neighbor nodes $k$ is a hyperparameter which determines the structure and aggregated scope of GCNs [10]. As shown in Table 5, to further evaluate the effectiveness using different $k$ , we conduct a series of experiments on FF++ (LQ) and WildDeepfake datasets. From the experimental results, we conclude that too few neighbors can not guarantee the representative ability of the dynamic GCN module, thus degrades the information exchange of forged clues in spatial and frequency domains. Further, too many neighbors will tamper the regional separability of attention maps and tend to catastrophic overfitting. In our + +![](images/3fac86f8c8abdefefe2d2823ea5216f0f13c786a96e76d763b90eb7031bae11c.jpg) +Figure 4. The Grad-CAM visualization for forged faces. + +![](images/48c907c200be5b54ff87a56e2c7b864656a807e84e1ba95464eec2700146e073.jpg) +Figure 6. The visualization results of feature maps from MDAML module at different scales on FF++ and WildDeepfake datasets. + +Figure 5. The t-SNE feature visualization of the Ef-b4 and SFDG. + +
#NeighborsFF++ (LQ)WildDeepfake
AccAUCAccAUC
592.1095.6082.0390.57
1092.2895.9884.4192.57
1592.2895.4983.5791.15
2092.0291.5981.4690.38
+ +Table 5. Results in terms of Acc(%) and AUC(%) for different number of neighboring nodes in the graph construction. + +work, we observe that our model achieves the best performance in terms of Acc and AUC when setting $k$ to 10. + +# 4.4. Visualization + +Grad-CAM visualization. To better understand the internal mechanism of our method and explore interested regions for specific forged types, we supply the Grad-CAM [33] visualization on $\mathrm{FF}++$ dataset. As shown in Fig. 4, the forgery artifacts in different domains locate on independent regions. Detailedly, the spatial branch focuses on the facial region with pronounced forgery traces, which are effortlessly discovered by CNN backbones in spatial domain. Conversely, the frequency streamline searches manipulated clues essentially concerned with a wider area, e.g., the background, hair or entire face. These regions are subtle and dynamically change according to the image content thus provides a generalized feature representation. Just as we have speculated, the frequency domain acts as the complementary to the spatial domain and these two domains contribute to each other via graph-based high-order relation discovery for exploiting comprehensive forged cues. + +![](images/abd17e2b966a7429cc498f721ce870f517995fad195cc1d23e137c51e18092bf.jpg) + +Attention Maps Visualization. We verify the effectiveness of our tailored MDAML module and visualize the results in Fig 6. We observe that feature maps with different scales highlight distinctive activated intensities. Detailedly, the large scale features with high resolution representation embrace richer and global manipulated traces, while the small scales concentrate on more localized salient feature around facial landmarks. Further, we aggregate the attention maps via hierarchical pyramid paradigm to exploit the essential discrepancy between authentic and counterfeit faces, which can resist the noise disturbance and visual compression. + +Feature Distribution Visualization. In this part, we investigate the discriminative ability of the proposed SFDG model. Leveraging the t-SNE [42] technique, we visualize the semantic feature distribution of the Ef-b4 [37] model and our SFDG on $\mathrm{FF}++$ (LQ) and WildDeepfake dataset. As shown in Fig. 5, our approach encourages the samples of same class into a relatively compact feature space. To explain, our SFDG adequately captures the intrinsic discrepancy between genuine and forged faces in multiple domains through graph-based relationships discovery, thus improving the generalization ability of our method. + +# 5. Conclusion + +In this paper, we propose a novel Spatial-Frequency Dynamic Graph network that develops graph model to exploit relationships of spatial and frequency domains for spotting subtle forgery clues. Firstly, the Content-guided Adaptive Frequency Extraction module is proposed to mine the adaptive frequency clues via content-aware frequency learning. Further, a Multiple Domains Attention Map Learning scheme captures rich contextual information of spatial-frequency feature through multi-scale feature ensemble. Finally, Dynamic Graph based Spatial-Frequency Feature Fusion module performs relation reasoning of spatial and frequency domains via improved graph convolution. Extensive experiments and detailed visualizations on widely-used benchmarks confirm the effectiveness and generalizability of our SFDG method compared with other contenders. + +# References + +[1] Darius Afchar, Vincent Nozick, Junichi Yamagishi, and Isao Echizen. 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Reenactgan: Learning to reenact faces via boundary transfer. In Proceedings of the European Conference on Computer Vision, pages 603-619, 2018. 1 +[45] Xi Wu, Zhen Xie, YuTao Gao, and Yu Xiao. Sstnet: Detecting manipulated faces through spatial, steganalysis and temporal features. In 2020-2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pages 2952-2956. IEEE, 2020. 1 +[46] Yanbo Xu, Yueqin Yin, Liming Jiang, Qianyi Wu, Chengyao Zheng, Chen Change Loy, Bo Dai, and Wayne Wu. Transeditor: Transformer-based dual-space gan for highly controllable facial editing. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 7683-7692, 2022. 1 +[47] Xin Yang, Yuezun Li, and Siwei Lyu. Exposing deep fakes using inconsistent head poses. 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In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 15079-15088, 2021. 4 +[52] Bojia Zi, Minghao Chang, Jingjing Chen, Xingjun Ma, and Yu-Gang Jiang. Wilddeepfake: A challenging real-world dataset for deepfake detection. 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Some existing methods attempt to employ auxiliary frequency-aware information combined with CNN backbones to discover the forged clues. Due to the inadequate information interaction with image content, the extracted frequency features are thus spatially irrelevant, struggling to generalize well on increasingly realistic counterfeit types. To address this issue, we propose a Spatial-Frequency Dynamic Graph method to exploit the relation-aware features in spatial and frequency domains via dynamic graph learning. To this end, we introduce three well-designed components: 1) Content-guided Adaptive Frequency Extraction module to mine the content-adaptive forged frequency clues. 2) Multiple Domains Attention Map Learning module to enrich the spatial-frequency contextual features with multiscale attention maps. 3) Dynamic Graph Spatial-Frequency Feature Fusion Network to explore the high-order relation of spatial and frequency features. Extensive experiments on several benchmark show that our proposed method sustainably exceeds the state-of-the-arts by a considerable margin." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 591, + 124, + 602 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 591, + 124, + 602 + ], + "spans": [ + { + "bbox": [ + 46, + 591, + 124, + 602 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 45, + 611, + 279, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 611, + 279, + 693 + ], + "spans": [ + { + "bbox": [ + 45, + 611, + 279, + 693 + ], + "type": "text", + "content": "Recent years have witnessed the continuous advances in deepfake creation [11, 27, 36]. Utilizing booming open-source tools such as Deepfakes [41], novices can readily manipulate the expression and identity of faces to generate visually untraceable videos. Face forgery technology has stimulated many applications [12, 14, 44, 46] with wide acceptance. These techniques can whereas be abused by ma" + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 318, + 289, + 513, + 433 + ], + "blocks": [ + { + "bbox": [ + 318, + 289, + 513, + 433 + ], + "lines": [ + { + "bbox": [ + 318, + 289, + 513, + 433 + ], + "spans": [ + { + "bbox": [ + 318, + 289, + 513, + 433 + ], + "type": "image", + "image_path": "65a14129cd9a7343e4adbb1dab98573255871ae136ab6f7f0213a343d9f17953.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 296, + 450, + 531, + 484 + ], + "lines": [ + { + "bbox": [ + 296, + 450, + 531, + 484 + ], + "spans": [ + { + "bbox": [ + 296, + 450, + 531, + 484 + ], + "type": "text", + "content": "Figure 1. The motivation of our proposed approach. Our SFDG method (a) delves into the high-order relationships (b) of spatial and frequency domain via cross-domain graph reasoning (c)." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 296, + 506, + 530, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 506, + 530, + 542 + ], + "spans": [ + { + "bbox": [ + 296, + 506, + 530, + 542 + ], + "type": "text", + "content": "licious intentions to make pornographic movies, fake news and political rumors. In the circumstances, it is desperately in need to develop powerful forgery detection methods." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 296, + 543, + 531, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 543, + 531, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 543, + 531, + 730 + ], + "type": "text", + "content": "Early face forgery detection methods [7,30,52] treat this challenge as vanilla dichotomy tasks in the prevailing view. They use off-the-shelf backbones to extract the global feature of faces and a binary classifier follow-up to identify the real and counterfeit faces. However, as the counterfeits become increasingly realistic, it is intractable for these methods to spot subtle and local forgery traces. One recent study [50] reformulates deepfake detection as a fine-grained classification task and designs a multi-attentional framework to extract local discriminative features from multiple attention maps. It is susceptible to common disturbances and the generalized features remain therefore poorly understood. Some other works resort to specific forgery patterns to encourage better classification such as DCT [24,28], SRM [25] and steganalysis features [45]. Although promising advances have been achieved by these previous works," + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 77, + 42, + 119, + 71 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 42, + 119, + 71 + ], + "spans": [ + { + "bbox": [ + 77, + 42, + 119, + 71 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 150, + 41, + 471, + 74 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 150, + 41, + 471, + 74 + ], + "spans": [ + { + "bbox": [ + 150, + 41, + 471, + 74 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 700, + 279, + 730 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 700, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 700, + 279, + 730 + ], + "type": "text", + "content": "*Chen Chen is the corresponding author. This work is supported by the National Key R&D Program of China under Grant 2021YFF0602101, Alibaba Group through Alibaba Research Intern Program." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "text", + "content": "7278" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 45, + 106, + 279, + 188 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 106, + 279, + 188 + ], + "spans": [ + { + "bbox": [ + 45, + 106, + 279, + 188 + ], + "type": "text", + "content": "they always extract frequency features with hand-crafted filter banks which are content-irrelevant, thus incapable to adapt the changes of complex scenarios. Moreover, they fuse multi-domain information via adding directly or attentional projection. However, these approaches devote little efforts to discover the high-order relation of spatial and frequency features and integrating them in a reasonable way." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 188, + 279, + 269 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 188, + 279, + 269 + ], + "spans": [ + { + "bbox": [ + 45, + 188, + 279, + 269 + ], + "type": "text", + "content": "In this paper, we provide seminal insights to exploit adaptive frequency features and delve into the interactions of spatial-frequency domains. To this end, we propose an adaptive extraction-multiscale enhancement-graph fusion paradigm for deepfake detection via dynamic graph learning, which prompts to excavate content-aware frequency clues and the high-order relation of multiple domains." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 269, + 279, + 362 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 269, + 279, + 362 + ], + "spans": [ + { + "bbox": [ + 45, + 269, + 279, + 362 + ], + "type": "text", + "content": "Firstly, for adaptive frequency extraction, we tailor a Content-guided Adaptive Frequency Extraction (CAFÉ) module with coarse-grained DCT and fine-grained DCT to capture the local frequency cues guided by content-aware masks. Different from PEL [9] and F3Net [28], our customized frequency learning protocol provides potential for more combinations of frequency features, which is indispensable to spot complicated counterfeit patterns." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 362, + 279, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 362, + 279, + 548 + ], + "spans": [ + { + "bbox": [ + 45, + 362, + 279, + 548 + ], + "type": "text", + "content": "To further enhance the representation of content-guided frequency features, we introduce a Multiple Domains Attention Map Learning (MDAML) module to generate multiscale spatial and frequency attention maps with high-level semantic features. Specifically, we first propose a MultiScale Attention Ensemble (MSAE) module, which produces multi-scale semantic attention maps with large receptive fields and endows rich contextual information to spatial and frequency domains. Moreover, an Attention Map Refinement Block (AMRB) is included in the MSAE module to refine the obtained semantic attention maps conducive to the following feature learning. In comparison with MADD [50] that merely emphasizes the spatial domain, we further introduce the semantic-relevant frequency attention map with rich semantic information retained for the subsequent spatial-frequency relation-discovery paradigm." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 548, + 279, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 548, + 279, + 687 + ], + "spans": [ + { + "bbox": [ + 45, + 548, + 279, + 687 + ], + "type": "text", + "content": "Finally, to fully discover the spatial and frequency relationships, we propose a Dynamic Graph-based Spatial-Frequency Feature Fusion network (DG-SF" + }, + { + "bbox": [ + 45, + 548, + 279, + 687 + ], + "type": "inline_equation", + "content": "^3" + }, + { + "bbox": [ + 45, + 548, + 279, + 687 + ], + "type": "text", + "content": "Net) to formulate the interaction of two domains via a graph-based relation discovery protocol. Specifically, DG-SF" + }, + { + "bbox": [ + 45, + 548, + 279, + 687 + ], + "type": "inline_equation", + "content": "^3" + }, + { + "bbox": [ + 45, + 548, + 279, + 687 + ], + "type": "text", + "content": "Net is composed of two ingredients: Dynamic GCN [16] and Graph Information Interaction layers. The former constructs kNN-graph dynamically and performs graph convolution to reason high-order relationships in spatial and frequency domains, while the latter is designed to enhance the mutual relation with several graph-weighted MLP-Mixer [40] layers via channel-wise and node-wise interaction." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 57, + 687, + 278, + 699 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 687, + 278, + 699 + ], + "spans": [ + { + "bbox": [ + 57, + 687, + 278, + 699 + ], + "type": "text", + "content": "The achievements, including contributions are threefold:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 57, + 706, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 706, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 57, + 706, + 279, + 730 + ], + "type": "text", + "content": "From a new perspective, we propose a novel SpatialFrequency Dynamic Graph (SFDG) framework, which" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 315, + 106, + 529, + 129 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 106, + 529, + 129 + ], + "spans": [ + { + "bbox": [ + 315, + 106, + 529, + 129 + ], + "type": "text", + "content": "is qualified to exploit relation-aware spatial-frequency features to promote generalized forgery detection." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 308, + 136, + 530, + 218 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 136, + 530, + 218 + ], + "spans": [ + { + "bbox": [ + 308, + 136, + 530, + 218 + ], + "type": "text", + "content": "- We first harness a CAFÉ module for content-aware frequency feature extraction, and then tailor an MDAML scheme to dig deeper into multiscale spatial-frequency attention maps with rich contextual understanding of forgeries. Finally, a seminal DG-SF3Net module is proposed to discover the multi-domain relationships with a graph-based relation-reasoning approach." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 308, + 224, + 530, + 271 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 224, + 530, + 271 + ], + "spans": [ + { + "bbox": [ + 308, + 224, + 530, + 271 + ], + "type": "text", + "content": "- Our method achieves state-of-the-art performance on six benchmark datasets. The cross-dataset experiment and the perturbation analysis show the robustness and generalization ability of the proposed SFDG method." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 297, + 280, + 386, + 292 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 280, + 386, + 292 + ], + "spans": [ + { + "bbox": [ + 297, + 280, + 386, + 292 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 296, + 299, + 530, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 299, + 530, + 357 + ], + "spans": [ + { + "bbox": [ + 296, + 299, + 530, + 357 + ], + "type": "text", + "content": "Over the past several years, with the remarkable progress of forgery creation techniques, increasing efforts have been made to boost the development of face forgery detection in computer vision communities. In this section, we briefly review previous works exploring the authenticity of faces." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 296, + 357, + 530, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 357, + 530, + 496 + ], + "spans": [ + { + "bbox": [ + 296, + 357, + 530, + 496 + ], + "type": "text", + "content": "Rudimentary deepfake detection approaches base primarily on obvious counterfeit artifacts, which utilize handcrafted features to detect anomalies in spatial domain, e.g., inconsistent head pose [47] and unnatural eye blinding [21]. However, these traditional methods feel intractable to deal with the improved realistic deepfakes. With the overwhelming success of deep learning, some works [1,4,7] adopt off-the-shelf classification backbones to extract high-level semantic features for deepfake detection. Although considerable performances have been achieved on specific datasets, their vanilla structures would lead to catastrophic overfitting and lag behind the advanced face synthesis technology." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 296, + 497, + 530, + 648 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 497, + 530, + 648 + ], + "spans": [ + { + "bbox": [ + 296, + 497, + 530, + 648 + ], + "type": "text", + "content": "To further exploit the essential forged clues, general deepfake detection [15, 20, 26, 34, 35] has been an area of intense investigation. Nguyen et al. [26] employ multi-task learning strategy to detect forged artifacts and locate manipulated regions simultaneously. Face X-ray [20] observes the specific blending step of face swapping and locates forgery boundary in a self-supervised manner. FReTAL [15] adopts the knowledge distillation to prevent catastrophic forgetting and enhance adaptability in different domains. DCL [35] performs dual-granularity contrastive learning to further improve the generalization. However, these approaches captures category-level differences instead of the intrinsic discrepancies between authentic and forged images." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 296, + 648, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 648, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 648, + 530, + 730 + ], + "type": "text", + "content": "Recently, other studies focus on mining specific forgery patterns, such as local texture, high-frequency noise, reconstruction residual and frequency clues. Among them, Zhao et al. [50] propose a fine-grained deepfake detection framework that aggregates the local texture and high-level semantic information into multiple attention maps. However, it fails to distinguish highly compressed videos with" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "text", + "content": "7279" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 79, + 104, + 497, + 230 + ], + "blocks": [ + { + "bbox": [ + 79, + 104, + 497, + 230 + ], + "lines": [ + { + "bbox": [ + 79, + 104, + 497, + 230 + ], + "spans": [ + { + "bbox": [ + 79, + 104, + 497, + 230 + ], + "type": "image", + "image_path": "4f756507a3fb744590ae39856c3cef5c39a6c2050113dbf40bd29be759eb3c08.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 79, + 231, + 497, + 338 + ], + "blocks": [ + { + "bbox": [ + 79, + 231, + 497, + 338 + ], + "lines": [ + { + "bbox": [ + 79, + 231, + 497, + 338 + ], + "spans": [ + { + "bbox": [ + 79, + 231, + 497, + 338 + ], + "type": "image", + "image_path": "35ab0c4e7a12857f24ffbc12c86fd7064c6935e24b64d456ce117c85af0e68ac.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 355, + 531, + 378 + ], + "lines": [ + { + "bbox": [ + 45, + 355, + 531, + 378 + ], + "spans": [ + { + "bbox": [ + 45, + 355, + 531, + 378 + ], + "type": "text", + "content": "Figure 2. (a) Overview of the proposed Spatial-Frequency Dynamic Graph (SFDG) framework. (b) The Content-guided Adaptive Frequency Extraction (CAFÉ) module. (c) The Multiple Domains Attention map Learning (MDAML) network." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 397, + 279, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 397, + 279, + 571 + ], + "spans": [ + { + "bbox": [ + 45, + 397, + 279, + 571 + ], + "type": "text", + "content": "blurry texture. Luo et al. [25] utilize the high-pass filter SRM [8] to extract high-frequency noise guiding face forgery detection. RECCE [2] employs the reconstruction difference of authentic faces as guidance of forgery traces. " + }, + { + "bbox": [ + 45, + 397, + 279, + 571 + ], + "type": "inline_equation", + "content": "\\mathrm{F}^3\\mathrm{Net}" + }, + { + "bbox": [ + 45, + 397, + 279, + 571 + ], + "type": "text", + "content": " [28] collaboratively mines the forged frequency clues with frequency-aware decomposition and local frequency statistics. However, the extracted frequency feature is coarse-grained, incapable of assembling discriminative feature patterns. To ameliorate this issue, PEL [9] learns the fine-grained frequency features using sliding window DCT combined with RGB images in a progressive enhancement learning fashion. Nevertheless, the fine-grained frequency is content-irrelevant and in compliance with the vanilla spatial-frequency fusion ethos, thus failing to achieve the utter information interaction of both domains." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 571, + 279, + 618 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 571, + 279, + 618 + ], + "spans": [ + { + "bbox": [ + 45, + 571, + 279, + 618 + ], + "type": "text", + "content": "Different from existing studies, our proposed end-to-end SFDG approach excavates content-adaptive frequency clues and facilitates the comprehensive fusion of spatial and frequency features via dynamic graph learning." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 628, + 100, + 639 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 628, + 100, + 639 + ], + "spans": [ + { + "bbox": [ + 46, + 628, + 100, + 639 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 648, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 648, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 648, + 279, + 730 + ], + "type": "text", + "content": "In this section, we propose a Spatial-Frequency Dynamic Graph (SFDG) framework, which consists of three major modules, i.e., Content-guided Adaptive Frequency Extraction (CAFÉ), Multiple Domains Attention Map Learning (MDAML), and Dynamic Graph Spatial Frequency Feature Fusion Network (DG-SF" + }, + { + "bbox": [ + 45, + 648, + 279, + 730 + ], + "type": "inline_equation", + "content": "^3" + }, + { + "bbox": [ + 45, + 648, + 279, + 730 + ], + "type": "text", + "content": "Net). The primary idea of our approach is to exploit content-aware frequency features uti" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 296, + 397, + 531, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 397, + 531, + 468 + ], + "spans": [ + { + "bbox": [ + 296, + 397, + 531, + 468 + ], + "type": "text", + "content": "lizing CAFÉ module. As limited context information do these features embrace, we present the MDAML module to generate high-level frequency attention maps in a multiscale learning manner. Beyond these improvements, we finally design a DG-F3Net to perform relation reasoning of spatial and frequency features via dynamic graph learning." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 296, + 478, + 490, + 490 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 478, + 490, + 490 + ], + "spans": [ + { + "bbox": [ + 296, + 478, + 490, + 490 + ], + "type": "text", + "content": "3.1. Content-aware Frequency Extraction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 296, + 497, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 497, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 497, + 530, + 730 + ], + "type": "text", + "content": "Towards the frequency-aware face forgery detection, former studies generally use DCT to transform the input image into frequency domain. However, for the scarcity of spatial information in DCT process, the extracted frequency feature is presumably not compatible to the image content. To this end, we propose the CAFÉ module to fully exploit the forgery clues via content-aware frequency learning in order to handle complex or simple manipulated patterns adaptively. Without loss of generality, let " + }, + { + "bbox": [ + 296, + 497, + 530, + 730 + ], + "type": "inline_equation", + "content": "x^{s}\\in \\mathbb{R}^{3\\times H\\times W}" + }, + { + "bbox": [ + 296, + 497, + 530, + 730 + ], + "type": "text", + "content": " denotes the RGB image, where " + }, + { + "bbox": [ + 296, + 497, + 530, + 730 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 296, + 497, + 530, + 730 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 497, + 530, + 730 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 296, + 497, + 530, + 730 + ], + "type": "text", + "content": " are the height and width of the input image. As shown in Fig. 2(b), we generate an attentional content mask " + }, + { + "bbox": [ + 296, + 497, + 530, + 730 + ], + "type": "inline_equation", + "content": "M^s" + }, + { + "bbox": [ + 296, + 497, + 530, + 730 + ], + "type": "text", + "content": " using a UNet [29] submodule with the spatial information retained. We then propose a coarse-grained counterpart to partition the compact frequency spectrum into several bands. Specifically, we manually design " + }, + { + "bbox": [ + 296, + 497, + 530, + 730 + ], + "type": "inline_equation", + "content": "N_{f}" + }, + { + "bbox": [ + 296, + 497, + 530, + 730 + ], + "type": "text", + "content": " binary filters " + }, + { + "bbox": [ + 296, + 497, + 530, + 730 + ], + "type": "inline_equation", + "content": "\\{f_i|i = 1,\\dots,N_f\\}" + }, + { + "bbox": [ + 296, + 497, + 530, + 730 + ], + "type": "text", + "content": " to decompose the frequency domains into low, middle and high frequency bands. The low-frequency component lies on the top-left corner while the high-frequency response locates on the bottom-right corner [28]. As described, the" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "text", + "content": "7280" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 106, + 223, + 117 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 106, + 223, + 117 + ], + "spans": [ + { + "bbox": [ + 46, + 106, + 223, + 117 + ], + "type": "text", + "content": "coarse-grained process can be formulated as:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 124, + 279, + 143 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 124, + 279, + 143 + ], + "spans": [ + { + "bbox": [ + 57, + 124, + 279, + 143 + ], + "type": "interline_equation", + "content": "x _ {\\text {c o a r s e}} ^ {f, i} = \\mathcal {H} ^ {- 1} \\left[ \\mathcal {H} \\left(x ^ {s}\\right) \\odot f ^ {i} \\right], \\quad i = \\{1, 2, \\dots , N _ {f} \\}, \\tag {1}", + "image_path": "a932c9884845211ef7a5d2e470662a594d0fc4f592b0cab3086c9ffa35294e13.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 149, + 279, + 195 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 149, + 279, + 195 + ], + "spans": [ + { + "bbox": [ + 45, + 149, + 279, + 195 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 45, + 149, + 279, + 195 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 45, + 149, + 279, + 195 + ], + "type": "text", + "content": " is the Hadamard product. " + }, + { + "bbox": [ + 45, + 149, + 279, + 195 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 45, + 149, + 279, + 195 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 149, + 279, + 195 + ], + "type": "inline_equation", + "content": "\\mathcal{H}^{-1}" + }, + { + "bbox": [ + 45, + 149, + 279, + 195 + ], + "type": "text", + "content": " represent the DCT and inverse DCT respectively. " + }, + { + "bbox": [ + 45, + 149, + 279, + 195 + ], + "type": "inline_equation", + "content": "x_{coarse}^{f}\\in \\mathbb{R}^{3N_{f}\\times H\\times W}" + }, + { + "bbox": [ + 45, + 149, + 279, + 195 + ], + "type": "text", + "content": " is the extracted coarse frequency feature, which indicates global frequency information to some extent." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 196, + 279, + 336 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 196, + 279, + 336 + ], + "spans": [ + { + "bbox": [ + 45, + 196, + 279, + 336 + ], + "type": "text", + "content": "Further, we design a fine-grained frequency extraction method to emphasize on the localized frequency features. Specifically, we slice " + }, + { + "bbox": [ + 45, + 196, + 279, + 336 + ], + "type": "inline_equation", + "content": "x^{s}" + }, + { + "bbox": [ + 45, + 196, + 279, + 336 + ], + "type": "text", + "content": " via a sliding window to obtain a set of " + }, + { + "bbox": [ + 45, + 196, + 279, + 336 + ], + "type": "inline_equation", + "content": "l\\times l" + }, + { + "bbox": [ + 45, + 196, + 279, + 336 + ], + "type": "text", + "content": " patches. " + }, + { + "bbox": [ + 45, + 196, + 279, + 336 + ], + "type": "inline_equation", + "content": "p_{m,n}\\in \\mathbb{R}^{3\\times l\\times l}" + }, + { + "bbox": [ + 45, + 196, + 279, + 336 + ], + "type": "text", + "content": " denotes the patch sliced by the " + }, + { + "bbox": [ + 45, + 196, + 279, + 336 + ], + "type": "inline_equation", + "content": "(m" + }, + { + "bbox": [ + 45, + 196, + 279, + 336 + ], + "type": "text", + "content": "-th, " + }, + { + "bbox": [ + 45, + 196, + 279, + 336 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 45, + 196, + 279, + 336 + ], + "type": "text", + "content": "-th) sliding window. After performing DCT on each patch, we get the localized fine-grained frequency features " + }, + { + "bbox": [ + 45, + 196, + 279, + 336 + ], + "type": "inline_equation", + "content": "d_{m,n}^{f}\\in \\mathbb{R}^{3\\times l\\times l}" + }, + { + "bbox": [ + 45, + 196, + 279, + 336 + ], + "type": "text", + "content": ". We repeat the channel of each " + }, + { + "bbox": [ + 45, + 196, + 279, + 336 + ], + "type": "inline_equation", + "content": "d_{m,n}^{f}" + }, + { + "bbox": [ + 45, + 196, + 279, + 336 + ], + "type": "text", + "content": " to match the coarse-grained frequency features abovementioned. All localized patched are then gathered into a whole feature map " + }, + { + "bbox": [ + 45, + 196, + 279, + 336 + ], + "type": "inline_equation", + "content": "d^{f}\\in \\mathbb{R}^{3N_{f}\\times H\\times W}" + }, + { + "bbox": [ + 45, + 196, + 279, + 336 + ], + "type": "text", + "content": " and go through several convolution Blocks composed by Conv2d, BN, and ReLU to form the output fine-grained frequency features " + }, + { + "bbox": [ + 45, + 196, + 279, + 336 + ], + "type": "inline_equation", + "content": "x_{fine}^{f}" + }, + { + "bbox": [ + 45, + 196, + 279, + 336 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 336, + 279, + 372 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 336, + 279, + 372 + ], + "spans": [ + { + "bbox": [ + 45, + 336, + 279, + 372 + ], + "type": "text", + "content": "Finally, we obtain the overall frequency head " + }, + { + "bbox": [ + 45, + 336, + 279, + 372 + ], + "type": "inline_equation", + "content": "x^{fh}" + }, + { + "bbox": [ + 45, + 336, + 279, + 372 + ], + "type": "text", + "content": " through an adaptive frequency combine module guided by the learned content mask " + }, + { + "bbox": [ + 45, + 336, + 279, + 372 + ], + "type": "inline_equation", + "content": "M^s" + }, + { + "bbox": [ + 45, + 336, + 279, + 372 + ], + "type": "text", + "content": ", which can be formulated as:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 75, + 378, + 279, + 394 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 75, + 378, + 279, + 394 + ], + "spans": [ + { + "bbox": [ + 75, + 378, + 279, + 394 + ], + "type": "interline_equation", + "content": "x ^ {f h} = \\left(1 - M ^ {s}\\right) \\odot x _ {f i n e} ^ {f} + M ^ {s} \\odot x _ {c o a r s e} ^ {f}. \\tag {2}", + "image_path": "100d6de711604402853b320c62ab5aaad52fdcdcefb7ee2ce8e2511bc92b475f.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 401, + 279, + 439 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 401, + 279, + 439 + ], + "spans": [ + { + "bbox": [ + 45, + 401, + 279, + 439 + ], + "type": "text", + "content": "The extracted frequency head " + }, + { + "bbox": [ + 45, + 401, + 279, + 439 + ], + "type": "inline_equation", + "content": "x^{fh} \\in \\mathbb{R}^{3N_f \\times H \\times W}" + }, + { + "bbox": [ + 45, + 401, + 279, + 439 + ], + "type": "text", + "content": " will be fed into several stride convolution layers to obtain the final frequency feature " + }, + { + "bbox": [ + 45, + 401, + 279, + 439 + ], + "type": "inline_equation", + "content": "C_f" + }, + { + "bbox": [ + 45, + 401, + 279, + 439 + ], + "type": "text", + "content": " channels " + }, + { + "bbox": [ + 45, + 401, + 279, + 439 + ], + "type": "inline_equation", + "content": "x^f" + }, + { + "bbox": [ + 45, + 401, + 279, + 439 + ], + "type": "text", + "content": " with size of " + }, + { + "bbox": [ + 45, + 401, + 279, + 439 + ], + "type": "inline_equation", + "content": "H_f \\times W_f" + }, + { + "bbox": [ + 45, + 401, + 279, + 439 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 444, + 264, + 457 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 444, + 264, + 457 + ], + "spans": [ + { + "bbox": [ + 46, + 444, + 264, + 457 + ], + "type": "text", + "content": "3.2. Multiple Domains Attention Map Learning" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 462, + 279, + 660 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 462, + 279, + 660 + ], + "spans": [ + { + "bbox": [ + 45, + 462, + 279, + 660 + ], + "type": "text", + "content": "To fully exploit the forged clues in spatial domain, we adopt EfficientNet-b4 as the backbone and further partition the entire network into low-level, mid-level and high-level layers, respectively. As shown in Fig. 2(c), to acquire spatial-frequency features with rich semantics, we further design a Multi-Scale Attention Ensemble (MSAE) module in spatial and frequency domains to generate multiscale attention maps and aggregate them with hierarchical feature pyramid. The MSAE includes light weighted ConvBlocks, which consist of several convolution layer, BN and non-linear activation layers ReLU, and certain global average layers to downsample the attention maps into multiple scales. With the multi-scale feature representation, we can obtain a sufficient receptive field and rich contextual information, which are of great significance for the deepfake detection task. Inspired by [48], we propose an Attention Map Refinement Block (AMRB) to get refined feature maps." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 45, + 660, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 660, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 660, + 279, + 730 + ], + "type": "text", + "content": "As Fig. 2(c) shows, AMRB employs global average pooling to capture global context and uses a subsequent sigmoid layer to produce an attention vector that determines the feature distribution of attention maps in each scale. Finally, we upsample the refined multi-scale attention maps to the original size and add them spatially. We use AMRB in" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 297, + 106, + 530, + 153 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 106, + 530, + 153 + ], + "spans": [ + { + "bbox": [ + 297, + 106, + 530, + 153 + ], + "type": "text", + "content": "both spatial and frequency streamline to acquire the multiscale spatial attention map " + }, + { + "bbox": [ + 297, + 106, + 530, + 153 + ], + "type": "inline_equation", + "content": "F^{s}" + }, + { + "bbox": [ + 297, + 106, + 530, + 153 + ], + "type": "text", + "content": " and frequency feature map " + }, + { + "bbox": [ + 297, + 106, + 530, + 153 + ], + "type": "inline_equation", + "content": "F^{f}" + }, + { + "bbox": [ + 297, + 106, + 530, + 153 + ], + "type": "text", + "content": ", which have " + }, + { + "bbox": [ + 297, + 106, + 530, + 153 + ], + "type": "inline_equation", + "content": "T_{s}" + }, + { + "bbox": [ + 297, + 106, + 530, + 153 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 297, + 106, + 530, + 153 + ], + "type": "inline_equation", + "content": "T_{f}" + }, + { + "bbox": [ + 297, + 106, + 530, + 153 + ], + "type": "text", + "content": " channels on behalf of the corresponding number of attention maps in these two domains." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 296, + 154, + 530, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 154, + 530, + 293 + ], + "spans": [ + { + "bbox": [ + 296, + 154, + 530, + 293 + ], + "type": "text", + "content": "After obtaining the refined multi-scale attention maps " + }, + { + "bbox": [ + 296, + 154, + 530, + 293 + ], + "type": "inline_equation", + "content": "F^{s}" + }, + { + "bbox": [ + 296, + 154, + 530, + 293 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 154, + 530, + 293 + ], + "type": "inline_equation", + "content": "F^{f}" + }, + { + "bbox": [ + 296, + 154, + 530, + 293 + ], + "type": "text", + "content": ", we perform Bilinear Attention Pooling (BAP) [23] to get the relation-aware feature matrix " + }, + { + "bbox": [ + 296, + 154, + 530, + 293 + ], + "type": "inline_equation", + "content": "P^{s}" + }, + { + "bbox": [ + 296, + 154, + 530, + 293 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 154, + 530, + 293 + ], + "type": "inline_equation", + "content": "P^{f}" + }, + { + "bbox": [ + 296, + 154, + 530, + 293 + ], + "type": "text", + "content": " respectively. As illustrated in Fig. 2(c), we use the Textural Feature Enhancement block [50] to capture the manipulated artifacts hidden in low-level layers. After the enhancement of the texture features, we get a textual feature map " + }, + { + "bbox": [ + 296, + 154, + 530, + 293 + ], + "type": "inline_equation", + "content": "F^{tex} \\in \\mathbb{R}^{C_{tex} \\times H_{tex} \\times W_{tex}}" + }, + { + "bbox": [ + 296, + 154, + 530, + 293 + ], + "type": "text", + "content": ". For the spatial domain, we element-wisely multiply textural feature map " + }, + { + "bbox": [ + 296, + 154, + 530, + 293 + ], + "type": "inline_equation", + "content": "F^{tex}" + }, + { + "bbox": [ + 296, + 154, + 530, + 293 + ], + "type": "text", + "content": " by each spatial attention map " + }, + { + "bbox": [ + 296, + 154, + 530, + 293 + ], + "type": "inline_equation", + "content": "F_{k}^{s}" + }, + { + "bbox": [ + 296, + 154, + 530, + 293 + ], + "type": "text", + "content": " to obtain the partial textural feature maps " + }, + { + "bbox": [ + 296, + 154, + 530, + 293 + ], + "type": "inline_equation", + "content": "F_{k}^{tex}" + }, + { + "bbox": [ + 296, + 154, + 530, + 293 + ], + "type": "text", + "content": " and compute the final spatial feature matrix employing BAP, which can be formulated as:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 348, + 302, + 530, + 341 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 302, + 530, + 341 + ], + "spans": [ + { + "bbox": [ + 348, + 302, + 530, + 341 + ], + "type": "interline_equation", + "content": "p _ {k} ^ {\\mathrm {s}} = \\frac {\\sum_ {m = 1} ^ {H _ {t e x}} \\sum_ {n = 1} ^ {W _ {t e x}} F _ {k , m , n} ^ {t e x}}{\\left\\| \\sum_ {m = 1} ^ {H _ {t e x}} \\sum_ {n = 1} ^ {W _ {t e x}} F _ {k , m , n} ^ {t e x} \\right\\| _ {2}} \\tag {3}", + "image_path": "9d186382945fb47c362eb05e70a0d2576d6461cc439a2ef677917405e18fe599.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 296, + 350, + 530, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 350, + 530, + 467 + ], + "spans": [ + { + "bbox": [ + 296, + 350, + 530, + 467 + ], + "type": "text", + "content": "The spatial attention vector " + }, + { + "bbox": [ + 296, + 350, + 530, + 467 + ], + "type": "inline_equation", + "content": "p_k^s \\in \\mathbb{R}^{1 \\times C_{tex}}" + }, + { + "bbox": [ + 296, + 350, + 530, + 467 + ], + "type": "text", + "content": " is stacked together to get the texture-relevant spatial feature matrix " + }, + { + "bbox": [ + 296, + 350, + 530, + 467 + ], + "type": "inline_equation", + "content": "P^s \\in \\mathbb{R}^{T_s \\times N_s}" + }, + { + "bbox": [ + 296, + 350, + 530, + 467 + ], + "type": "text", + "content": ". For the frequency domain, we perform the BAP with the frequency attention maps " + }, + { + "bbox": [ + 296, + 350, + 530, + 467 + ], + "type": "inline_equation", + "content": "F^f" + }, + { + "bbox": [ + 296, + 350, + 530, + 467 + ], + "type": "text", + "content": " and the spatial feature after high-level backbone layers as shown in Fig. 2(a). Similar to Eq. 3, we can obtain the content-relevant frequency feature matrix " + }, + { + "bbox": [ + 296, + 350, + 530, + 467 + ], + "type": "inline_equation", + "content": "P^f \\in \\mathbb{R}^{T_f \\times N_f}" + }, + { + "bbox": [ + 296, + 350, + 530, + 467 + ], + "type": "text", + "content": ". Finally, the learnt relation-aware feature matrices will be fed into the follow-up DG-SF" + }, + { + "bbox": [ + 296, + 350, + 530, + 467 + ], + "type": "inline_equation", + "content": "^3" + }, + { + "bbox": [ + 296, + 350, + 530, + 467 + ], + "type": "text", + "content": "Net to collaboratively learn a comprehensive feature representation in a graph-based relation reasoning way." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 297, + 476, + 439, + 489 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 476, + 439, + 489 + ], + "spans": [ + { + "bbox": [ + 297, + 476, + 439, + 489 + ], + "type": "text", + "content": "3.3. Dynamic Graph Learning" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 296, + 494, + 530, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 494, + 530, + 634 + ], + "spans": [ + { + "bbox": [ + 296, + 494, + 530, + 634 + ], + "type": "text", + "content": "After obtaining the spatial feature matrix " + }, + { + "bbox": [ + 296, + 494, + 530, + 634 + ], + "type": "inline_equation", + "content": "P^{s} \\in \\mathbb{R}^{T_{s} \\times N_{s}}" + }, + { + "bbox": [ + 296, + 494, + 530, + 634 + ], + "type": "text", + "content": " and frequency feature matrix " + }, + { + "bbox": [ + 296, + 494, + 530, + 634 + ], + "type": "inline_equation", + "content": "P^{f} \\in \\mathbb{R}^{T_{f} \\times N_{f}}" + }, + { + "bbox": [ + 296, + 494, + 530, + 634 + ], + "type": "text", + "content": ", we propose a novel DG-SF" + }, + { + "bbox": [ + 296, + 494, + 530, + 634 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 296, + 494, + 530, + 634 + ], + "type": "text", + "content": "Net to discover the comprehensive relation of them as shown in Fig. 3. Inspired by [19, 49, 51], we provide the intuition that there exists high-order relation of spatial and frequency features and Graph Convolution Network (GCN) performs tremendous potential in relation reasoning. As illustrated in Fig. 1(c), we confirm the above intuition by visualizing the correlation heatmap of spatial and frequency features. Therefore, we build a graph-based relation-discovery module to conduct reasoning with improved GCN to integrate spatial and frequency features." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 296, + 634, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 634, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 634, + 530, + 730 + ], + "type": "text", + "content": "Firstly, we concatenate " + }, + { + "bbox": [ + 296, + 634, + 530, + 730 + ], + "type": "inline_equation", + "content": "P^s" + }, + { + "bbox": [ + 296, + 634, + 530, + 730 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 634, + 530, + 730 + ], + "type": "inline_equation", + "content": "P^f" + }, + { + "bbox": [ + 296, + 634, + 530, + 730 + ], + "type": "text", + "content": " in the channel dimension to get " + }, + { + "bbox": [ + 296, + 634, + 530, + 730 + ], + "type": "inline_equation", + "content": "V^{(0)} \\in \\mathbb{R}^{T^{(0)} \\times N^{(0)}}" + }, + { + "bbox": [ + 296, + 634, + 530, + 730 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 296, + 634, + 530, + 730 + ], + "type": "inline_equation", + "content": "T^{(0)} = T_s + T_f" + }, + { + "bbox": [ + 296, + 634, + 530, + 730 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 634, + 530, + 730 + ], + "type": "inline_equation", + "content": "N^{(0)} = \\max(N_s, N_f)" + }, + { + "bbox": [ + 296, + 634, + 530, + 730 + ], + "type": "text", + "content": ". We treat each column of " + }, + { + "bbox": [ + 296, + 634, + 530, + 730 + ], + "type": "inline_equation", + "content": "V^{(0)}" + }, + { + "bbox": [ + 296, + 634, + 530, + 730 + ], + "type": "text", + "content": " as a node. As shown in the right bottom of Fig. 3, a dynamic GCN module is proposed to aggregate features based on their similarity. Different from original GCN, our model learns to dynamically design appropriate graph structures in each layer, rather than treating it as a fixed constant one." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 746, + 297, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 746, + 297, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 746, + 297, + 756 + ], + "type": "text", + "content": "7281" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 82, + 104, + 495, + 264 + ], + "blocks": [ + { + "bbox": [ + 82, + 104, + 495, + 264 + ], + "lines": [ + { + "bbox": [ + 82, + 104, + 495, + 264 + ], + "spans": [ + { + "bbox": [ + 82, + 104, + 495, + 264 + ], + "type": "image", + "image_path": "b45ef41ce2c3e17d9823bd660089fb3042a5ca43d1e7b5bd3e73ae343e7d320b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 282, + 531, + 306 + ], + "lines": [ + { + "bbox": [ + 45, + 282, + 531, + 306 + ], + "spans": [ + { + "bbox": [ + 45, + 282, + 531, + 306 + ], + "type": "text", + "content": "Figure 3. The proposed Dynamic Graph Spatial-Frequency Feature Fusion Network (DG-SF" + }, + { + "bbox": [ + 45, + 282, + 531, + 306 + ], + "type": "inline_equation", + "content": "^3" + }, + { + "bbox": [ + 45, + 282, + 531, + 306 + ], + "type": "text", + "content": "Net), which includes two modules: Dynamic Graph Convolution Network (DGCN) and Graph Information Interaction " + }, + { + "bbox": [ + 45, + 282, + 531, + 306 + ], + "type": "inline_equation", + "content": "(\\mathrm{GI}^2)" + }, + { + "bbox": [ + 45, + 282, + 531, + 306 + ], + "type": "text", + "content": " layers." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 325, + 279, + 362 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 325, + 279, + 362 + ], + "spans": [ + { + "bbox": [ + 45, + 325, + 279, + 362 + ], + "type": "text", + "content": "At " + }, + { + "bbox": [ + 45, + 325, + 279, + 362 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 45, + 325, + 279, + 362 + ], + "type": "text", + "content": "-th layer, we have a tailored sparse-connected graph " + }, + { + "bbox": [ + 45, + 325, + 279, + 362 + ], + "type": "inline_equation", + "content": "G^{(t)} = (V^{(t)},E^{(t)})" + }, + { + "bbox": [ + 45, + 325, + 279, + 362 + ], + "type": "text", + "content": " for graph convolution, where the local neighbor of each center node " + }, + { + "bbox": [ + 45, + 325, + 279, + 362 + ], + "type": "inline_equation", + "content": "v_{i}^{(t)}" + }, + { + "bbox": [ + 45, + 325, + 279, + 362 + ], + "type": "text", + "content": " can be defined as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 366, + 276, + 388 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 366, + 276, + 388 + ], + "spans": [ + { + "bbox": [ + 47, + 366, + 276, + 388 + ], + "type": "interline_equation", + "content": "\\mathcal {N} ^ {(t)} (i) = \\left\\{v _ {j i m} ^ {(t)} \\mid v _ {j i m} ^ {(t)} \\in k N N \\left(v _ {i} ^ {(t)}\\right), m = 1, \\dots , k \\right\\},", + "image_path": "8cf6081ba99b5a44747c4365f8bc0c163d3d49bce252df114fa2251655d4766e.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 391, + 279, + 440 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 391, + 279, + 440 + ], + "spans": [ + { + "bbox": [ + 45, + 391, + 279, + 440 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 45, + 391, + 279, + 440 + ], + "type": "inline_equation", + "content": "v_{j_{i1}}^{(t)}, \\ldots, v_{j_{ik}}^{(t)}" + }, + { + "bbox": [ + 45, + 391, + 279, + 440 + ], + "type": "text", + "content": " are " + }, + { + "bbox": [ + 45, + 391, + 279, + 440 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 45, + 391, + 279, + 440 + ], + "type": "text", + "content": " nodes closest to " + }, + { + "bbox": [ + 45, + 391, + 279, + 440 + ], + "type": "inline_equation", + "content": "v_{i}^{(t)}" + }, + { + "bbox": [ + 45, + 391, + 279, + 440 + ], + "type": "text", + "content": " according to the Euclidean distance. After getting the localized kNN graph, we formulate the adjacency matrix " + }, + { + "bbox": [ + 45, + 391, + 279, + 440 + ], + "type": "inline_equation", + "content": "A^{(t)}" + }, + { + "bbox": [ + 45, + 391, + 279, + 440 + ], + "type": "text", + "content": " based on " + }, + { + "bbox": [ + 45, + 391, + 279, + 440 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 45, + 391, + 279, + 440 + ], + "type": "text", + "content": " neighbors attached to center node with self-loop added." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 440, + 279, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 440, + 279, + 464 + ], + "spans": [ + { + "bbox": [ + 45, + 440, + 279, + 464 + ], + "type": "text", + "content": "With this sparse-connected GCN, the node features can be updated with the message passing as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 57, + 468, + 279, + 488 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 468, + 279, + 488 + ], + "spans": [ + { + "bbox": [ + 57, + 468, + 279, + 488 + ], + "type": "interline_equation", + "content": "V ^ {(t + 1)} = \\operatorname {R e L U} \\left(\\widetilde {D} ^ {(t) - \\frac {1}{2}} \\tilde {A} ^ {(t)} \\widetilde {D} ^ {(t) - \\frac {1}{2}} V ^ {(t)} W ^ {(t)}\\right), \\tag {4}", + "image_path": "485e3849873489abf0e4928bfd676be3409df03f36ef195f3a9c3dd3d80c6320.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 492, + 279, + 531 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 492, + 279, + 531 + ], + "spans": [ + { + "bbox": [ + 45, + 492, + 279, + 531 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 45, + 492, + 279, + 531 + ], + "type": "inline_equation", + "content": "\\tilde{D}^{(t)}\\in \\mathbb{R}^{T^{(t)}\\times T^{(t)}}" + }, + { + "bbox": [ + 45, + 492, + 279, + 531 + ], + "type": "text", + "content": " is the degree matrix. " + }, + { + "bbox": [ + 45, + 492, + 279, + 531 + ], + "type": "inline_equation", + "content": "W^{(t)}\\in" + }, + { + "bbox": [ + 45, + 492, + 279, + 531 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{N^{(t)}\\times N^{(t + 1)}}" + }, + { + "bbox": [ + 45, + 492, + 279, + 531 + ], + "type": "text", + "content": " is the learnable graph weight. In addition, the output channel is conforming with the input one." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 532, + 279, + 683 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 532, + 279, + 683 + ], + "spans": [ + { + "bbox": [ + 45, + 532, + 279, + 683 + ], + "type": "text", + "content": "Finally, we propose a Graph Information Interaction " + }, + { + "bbox": [ + 45, + 532, + 279, + 683 + ], + "type": "inline_equation", + "content": "(\\mathrm{GI}^2)" + }, + { + "bbox": [ + 45, + 532, + 279, + 683 + ], + "type": "text", + "content": " component for the spatial-frequency feature interaction. The " + }, + { + "bbox": [ + 45, + 532, + 279, + 683 + ], + "type": "inline_equation", + "content": "\\mathrm{GI}^2" + }, + { + "bbox": [ + 45, + 532, + 279, + 683 + ], + "type": "text", + "content": " component is composed of several MLP-Mixers [40] layers weighted by the graph adjacent matrix. Each of them leverages a channel-mixing MLP layer and a token-mixing MLP layer, which perform information interaction across all channels and node positions embedded in high-dimensional feature space. These two types of layers are interleaved to enable interaction of both input dimensions. Particularly, in order to highlight the localized features defined on the kNN graph abovementioned, we utilize the adjacent matrix derived from the first GCN layer to weight the feature of the token-mixing MLP." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 688, + 132, + 699 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 688, + 132, + 699 + ], + "spans": [ + { + "bbox": [ + 46, + 688, + 132, + 699 + ], + "type": "text", + "content": "3.4. Loss Function" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 45, + 706, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 706, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 706, + 279, + 730 + ], + "type": "text", + "content": "After dynamic graph learning, we obtain the semantic feature matrix " + }, + { + "bbox": [ + 45, + 706, + 279, + 730 + ], + "type": "inline_equation", + "content": "\\tilde{V} \\in \\mathbb{R}^{M \\times N}" + }, + { + "bbox": [ + 45, + 706, + 279, + 730 + ], + "type": "text", + "content": ". Following MADD, we regard" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 296, + 325, + 530, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 325, + 530, + 348 + ], + "spans": [ + { + "bbox": [ + 296, + 325, + 530, + 348 + ], + "type": "text", + "content": "Region Independent Loss (RIL) with Cross Entropy (CE) loss as the loss function. The auxiliary RIL is defined as:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 307, + 355, + 530, + 424 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 355, + 530, + 424 + ], + "spans": [ + { + "bbox": [ + 307, + 355, + 530, + 424 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {R I L} = \\sum_ {i = 1} ^ {B} \\sum_ {j = 1} ^ {M} \\operatorname {R e L U} \\left(\\left\\| \\tilde {V} _ {j} ^ {i} - c _ {j} ^ {t} \\right\\| _ {2} ^ {2} - m _ {i n} \\left(y _ {i}\\right)\\right) \\tag {5} \\\\ + \\sum_ {i \\neq j} ^ {M} \\mathrm {R e L U} \\left(m _ {o u t} - \\left\\| c _ {i} ^ {t} - c _ {j} ^ {t} \\right\\| _ {2} ^ {2}\\right) \\\\ \\end{array}", + "image_path": "c2be63de4b92e1a0b2b7cc9a47fc2fe2fa4d95c73df63e360db7c3c87812399f.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 296, + 431, + 530, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 431, + 530, + 479 + ], + "spans": [ + { + "bbox": [ + 296, + 431, + 530, + 479 + ], + "type": "inline_equation", + "content": "c \\in \\mathbb{R}^{M \\times N}" + }, + { + "bbox": [ + 296, + 431, + 530, + 479 + ], + "type": "text", + "content": " are feature centers of " + }, + { + "bbox": [ + 296, + 431, + 530, + 479 + ], + "type": "inline_equation", + "content": "\\tilde{V}" + }, + { + "bbox": [ + 296, + 431, + 530, + 479 + ], + "type": "text", + "content": " that can be updated iteratively during training. " + }, + { + "bbox": [ + 296, + 431, + 530, + 479 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 296, + 431, + 530, + 479 + ], + "type": "text", + "content": " is the batch size, " + }, + { + "bbox": [ + 296, + 431, + 530, + 479 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 296, + 431, + 530, + 479 + ], + "type": "text", + "content": " is the number of attention maps and " + }, + { + "bbox": [ + 296, + 431, + 530, + 479 + ], + "type": "inline_equation", + "content": "y_{i}" + }, + { + "bbox": [ + 296, + 431, + 530, + 479 + ], + "type": "text", + "content": " is the label. " + }, + { + "bbox": [ + 296, + 431, + 530, + 479 + ], + "type": "inline_equation", + "content": "m_{in}" + }, + { + "bbox": [ + 296, + 431, + 530, + 479 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 431, + 530, + 479 + ], + "type": "inline_equation", + "content": "m_{out}" + }, + { + "bbox": [ + 296, + 431, + 530, + 479 + ], + "type": "text", + "content": " represent the margin of intra-class and inter-class." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 296, + 479, + 530, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 479, + 530, + 502 + ], + "spans": [ + { + "bbox": [ + 296, + 479, + 530, + 502 + ], + "type": "text", + "content": "In conclusion, the total loss function " + }, + { + "bbox": [ + 296, + 479, + 530, + 502 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 296, + 479, + 530, + 502 + ], + "type": "text", + "content": " of our proposed SFDG framework can be described as:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 356, + 511, + 530, + 524 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 356, + 511, + 530, + 524 + ], + "spans": [ + { + "bbox": [ + 356, + 511, + 530, + 524 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\lambda_ {1} * \\mathcal {L} _ {C E} + \\lambda_ {2} * \\mathcal {L} _ {R I L} \\tag {6}", + "image_path": "58d625b9e7b28c1864d7b811b7b574587d87e634f15d52b566614e098b754a28.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 296, + 531, + 530, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 531, + 530, + 555 + ], + "spans": [ + { + "bbox": [ + 296, + 531, + 530, + 555 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 296, + 531, + 530, + 555 + ], + "type": "inline_equation", + "content": "\\lambda_{1},\\lambda_{2}" + }, + { + "bbox": [ + 296, + 531, + 530, + 555 + ], + "type": "text", + "content": " are hyper-parameters for balancing different terms. We set " + }, + { + "bbox": [ + 296, + 531, + 530, + 555 + ], + "type": "inline_equation", + "content": "\\lambda_1 = \\lambda_2 = 1" + }, + { + "bbox": [ + 296, + 531, + 530, + 555 + ], + "type": "text", + "content": " in the following experiments." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 297, + 564, + 371, + 578 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 564, + 371, + 578 + ], + "spans": [ + { + "bbox": [ + 297, + 564, + 371, + 578 + ], + "type": "text", + "content": "4. Experiment" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 297, + 584, + 411, + 596 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 584, + 411, + 596 + ], + "spans": [ + { + "bbox": [ + 297, + 584, + 411, + 596 + ], + "type": "text", + "content": "4.1. Experimental Setup" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 296, + 601, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 601, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 601, + 530, + 730 + ], + "type": "text", + "content": "Datasets. We appraise our proposed SFDG method and current state-of-the-art approaches on FaceForensics++ (FF++) [30], WildDeepfake [52], DFDC [5], Celeb-DF [22], DF-v1.0 [13] and DFD [6]. FF++ (low quality (LQ) and high quality (HQ) counterparts) is a widely-used benchmark dataset composed of 1000 real videos from YouTube and corresponding fake videos generated by four types of manipulated techniques: Deepfakes (DF) [41], Face2Face (F2F) [39], FaceSwap (FS) [17] and NeuralTextures (NT) [38]. WildDeepfake is a small real-scenario dataset including 7314 face sequences. Celeb-DF contains" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "text", + "content": "7282" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 104, + 531, + 285 + ], + "blocks": [ + { + "bbox": [ + 47, + 104, + 531, + 285 + ], + "lines": [ + { + "bbox": [ + 47, + 104, + 531, + 285 + ], + "spans": [ + { + "bbox": [ + 47, + 104, + 531, + 285 + ], + "type": "table", + "html": "
MethodFF++ (LQ)FF++ (HQ)WildDeepfakeCeleb-DF
AccAUCAccAUCAccAUCAccAUC
Xception [4]86.8689.3095.7396.3079.9988.8697.9099.73
EfficientNet-b4 [37]86.6788.2096.6399.1882.3390.1298.1999.83
Add-Net [52]87.5091.0196.7897.7476.2586.1796.9399.55
SCL [18]89.0092.4096.6999.30————
MADD [50]88.6990.4097.6099.2982.6290.7197.9299.94
F3Net [28]90.4393.3097.5298.1080.6687.5395.9598.93
PEL [9]90.5294.2897.6399.3284.1491.62——
RECCE [2]91.0395.0297.0699.3283.2592.0298.5999.94
Local Relation [3]91.4795.2197.5999.46————
M2TR [43]92.3594.2298.2399.48————
SFDG (Xception)91.0894.4997.6199.4583.3692.1598.9599.94
SFDG (Ours)92.2895.9898.1999.5384.4192.5799.2299.96
", + "image_path": "829c0e34d10d7ef582b05ef5a34acbe65538cf43bf09d8a4870de2da1e74c8e6.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 292, + 531, + 316 + ], + "lines": [ + { + "bbox": [ + 45, + 292, + 531, + 316 + ], + "spans": [ + { + "bbox": [ + 45, + 292, + 531, + 316 + ], + "type": "text", + "content": "Table 1. Quantitative comparison in terms of Acc(%) and AUC(%) on FF++, WildDeepfake and Celeb-DF dataset. The red represents the best performance while the blue indicates the second-best results." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 45, + 335, + 280, + 394 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 335, + 280, + 394 + ], + "spans": [ + { + "bbox": [ + 45, + 335, + 280, + 394 + ], + "type": "text", + "content": "590 real videos and 5,639 high quality fake videos tampered with the improved deepfake methods. DFDC is a remarkable large-scale dataset with over 100,000 video clips. DFD and DF-v1.0 are two another large-scale publicly available datasets to evaluate the model's generalization ability." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 394, + 280, + 442 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 394, + 280, + 442 + ], + "spans": [ + { + "bbox": [ + 45, + 394, + 280, + 442 + ], + "type": "text", + "content": "Evaluation Metrics. Following previous works [9, 28], we employ the commonly used Accuracy (Acc), Area Under the Receiver Operating Characteristic Curve (AUC) and Equal Error Rate (EER) as our evaluation metrics." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 442, + 280, + 583 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 442, + 280, + 583 + ], + "spans": [ + { + "bbox": [ + 45, + 442, + 280, + 583 + ], + "type": "text", + "content": "Implementation Details. Following the official split of FF++ dataset, we use 740 videos for training, 140 for validation and 140 remained for testing. We sample 50 frames per video at equal interval during training and validation phases, 20 frames in testing period. We use the remarkable DLIB [32] for face detection and alignment. We employ EfficientNet-b4 [37] pretrained on ImageNet [31] as the backbone of our network. We set " + }, + { + "bbox": [ + 45, + 442, + 280, + 583 + ], + "type": "inline_equation", + "content": "m_{out}" + }, + { + "bbox": [ + 45, + 442, + 280, + 583 + ], + "type": "text", + "content": " to 0.2 and " + }, + { + "bbox": [ + 45, + 442, + 280, + 583 + ], + "type": "inline_equation", + "content": "m_{in}" + }, + { + "bbox": [ + 45, + 442, + 280, + 583 + ], + "type": "text", + "content": " to [0.05,0.1] in Eq. 5. The whole network is trained with Adam optimizer with an initial learning rate of " + }, + { + "bbox": [ + 45, + 442, + 280, + 583 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-4}" + }, + { + "bbox": [ + 45, + 442, + 280, + 583 + ], + "type": "text", + "content": ", the weight decay of " + }, + { + "bbox": [ + 45, + 442, + 280, + 583 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-5}" + }, + { + "bbox": [ + 45, + 442, + 280, + 583 + ], + "type": "text", + "content": ". A step learning scheduler is used to reduce the learning rate half every 5 epochs." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 594, + 166, + 607 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 594, + 166, + 607 + ], + "spans": [ + { + "bbox": [ + 45, + 594, + 166, + 607 + ], + "type": "text", + "content": "4.2. Experimental Results" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 613, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 613, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 613, + 279, + 730 + ], + "type": "text", + "content": "Intra-testing. We compare our proposed method versus current state-of-the art approaches on the FF++ dataset under different quality settings (HQ and LQ), WildDeepfake and Celeb-DF datasets. As shown in Table 1, our method consistently achieves admirably performance on all quality settings and trumps all reference methods by a considerable margin. Specifically, in terms of Acc, our method achieves " + }, + { + "bbox": [ + 45, + 613, + 279, + 730 + ], + "type": "inline_equation", + "content": "92.28\\%" + }, + { + "bbox": [ + 45, + 613, + 279, + 730 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 613, + 279, + 730 + ], + "type": "inline_equation", + "content": "98.19\\%" + }, + { + "bbox": [ + 45, + 613, + 279, + 730 + ], + "type": "text", + "content": " on LQ and HQ settings respectively, with a remarkable improvement in comparison to PEL [9], i.e., " + }, + { + "bbox": [ + 45, + 613, + 279, + 730 + ], + "type": "inline_equation", + "content": "2.1\\%" + }, + { + "bbox": [ + 45, + 613, + 279, + 730 + ], + "type": "text", + "content": " performance gain on LQ and " + }, + { + "bbox": [ + 45, + 613, + 279, + 730 + ], + "type": "inline_equation", + "content": "0.6\\%" + }, + { + "bbox": [ + 45, + 613, + 279, + 730 + ], + "type": "text", + "content": " on HQ. Dif" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 296, + 335, + 531, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 335, + 531, + 486 + ], + "spans": [ + { + "bbox": [ + 296, + 335, + 531, + 486 + ], + "type": "text", + "content": "ferent from PEL which only utilizes fine-grained frequency features, our model extracts adaptive frequency features with a content mask providing rounded frequency representations. More importantly, we boost the information interaction between spatial and frequency domains via dynamic graph learning instead of vanilla convolution paradigm in PEL. Further, our method achieves a noteworthy performance compared with Local Relation [3] and M2TR [43], which introduce powerful priors of forgery masks. Instead, our SFDG only employs real/fake images as the input, but the AUC on both LQ and HQ settings surpass these two works strikingly. As discussed, these fruitful results give explanation of the effectiveness of our SFDG method." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 296, + 491, + 532, + 678 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 491, + 532, + 678 + ], + "spans": [ + { + "bbox": [ + 296, + 491, + 532, + 678 + ], + "type": "text", + "content": "Cross-testing. To further appraise the generalization ability of our method on unseen manipulated types, we herein conduct cross-dataset experiments by training and testing on different datasets. Following PEL [9], we reimplement several state-of-the-art models for a fair comparison on " + }, + { + "bbox": [ + 296, + 491, + 532, + 678 + ], + "type": "inline_equation", + "content": "\\mathrm{FF}++" + }, + { + "bbox": [ + 296, + 491, + 532, + 678 + ], + "type": "text", + "content": " (LQ) dataset and testing them on Celeb-DF, DFDC, DFD, DF-v1.0 and WildDeepfake dataset. Comparisons under AUC and EER metrics are detailedly shown in Table 2. It implicates that our SFDG method generally outperforms all competitors conspicuously on all testing datasets. Instead of overfitting with specific forged patterns as in most existing methods, SFDG explores the essential forgery with content-aware semantic attention maps and reasons about generalized forged cues via graph-based high-order relation discovery in spatial and frequency domains, which guarantees the superior generalization ability of our proposed method." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 296, + 682, + 532, + 731 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 682, + 532, + 731 + ], + "spans": [ + { + "bbox": [ + 296, + 682, + 532, + 731 + ], + "type": "text", + "content": "Robustness. Considering the image quality will be deteriorated seriously by inevitable noise in video acquisition process, we further investigate the robustness of our SFDG model under several common perturbations. Specifically," + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "text", + "content": "7283" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 60, + 103, + 517, + 224 + ], + "blocks": [ + { + "bbox": [ + 60, + 103, + 517, + 224 + ], + "lines": [ + { + "bbox": [ + 60, + 103, + 517, + 224 + ], + "spans": [ + { + "bbox": [ + 60, + 103, + 517, + 224 + ], + "type": "table", + "html": "
Training DataSetMethodTesting Dataset
Celeb-DFDFDWildDeepfakeDFDCDF-v1.0
AUCEER↓AUCEER↓AUCEER↓AUCEER↓AUCEER↓
FF++Xception [4]60.050.43265.430.39360.590.61955.650.46180.270.265
Ef-b4 [37]64.290.41983.170.23564.270.37660.120.42885.310.228
Add-Net [52]57.830.44457.160.45354.210.46251.600.548——
MADD [50]68.640.37174.180.32765.650.39763.020.41089.340.173
F3Net [28]67.950.36869.500.35460.490.43457.870.44282.270.246
PEL [9]69.180.35775.860.30867.390.38363.310.404——
SFDG (Ours)75.830.30388.000.19769.270.37773.640.33792.100.151
", + "image_path": "fd79b09bf7273cee2e936c9a300a818efa6d2ad7b0ce6b8992631d49cf18ea39.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 57, + 252, + 520, + 350 + ], + "blocks": [ + { + "bbox": [ + 64, + 232, + 511, + 243 + ], + "lines": [ + { + "bbox": [ + 64, + 232, + 511, + 243 + ], + "spans": [ + { + "bbox": [ + 64, + 232, + 511, + 243 + ], + "type": "text", + "content": "Table 2. Cross-testing results in terms of AUC(%) and EER training on FF++ dataset. The bold indicates the best performance." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 57, + 252, + 520, + 350 + ], + "lines": [ + { + "bbox": [ + 57, + 252, + 520, + 350 + ], + "spans": [ + { + "bbox": [ + 57, + 252, + 520, + 350 + ], + "type": "table", + "html": "
Method+GaussianNoise+SaltPepperNoise+GaussianBlur
ΔAcc(FF)ΔAcc(Wild)ΔAcc(FF)ΔAcc(Wild)ΔAcc(FF)ΔAcc(Wild)
Xception [4]-2.65%-0.98%-32.44%-27.80%-6.22%-12.71%
Add-Net [52]-41.51%-11.66%-11.28%-18.21%-11.28%-12.91%
F3Net [28]-9.86%-1.17%-31.08%-43.57%-11.08%-12.43%
MADD [50]-1.79%-0.99%-49.30%-29.47%-12.23%-14.86%
PEL [9]-0.10%-0.86%-9.39%-4.25%-7.41%-10.88%
SFDG (Ours)-0.10%-0.75%-10.10%-3.74%-3.76%-5.12%
", + "image_path": "7ca90be0c0cc2f01b6cccab7590d4fdbf2179026ca805c16aa718feacdcdf6ab.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 389, + 279, + 516 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 389, + 279, + 516 + ], + "spans": [ + { + "bbox": [ + 45, + 389, + 279, + 516 + ], + "type": "text", + "content": "following PEL [9], we apply GaussianNoise, SaltPepperNoise and GaussianBlur to the FF++ (LQ) and WildDeepfake testing images, and adopt the decay of Acc to indicate the robustness of face forgery detection model. As shown in Table 3, a series of experiments throw light on that our method with the least performance decline is more robust to the perturbations abovementioned. We attribute it to the elaborate CAFÉ module which extracts the adaptive frequency features among multiple bands and acts as an image denoiser. We provide sufficient experiments results in terms of AUC in the supplementary materials." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 525, + 136, + 538 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 525, + 136, + 538 + ], + "spans": [ + { + "bbox": [ + 45, + 525, + 136, + 538 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 543, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 543, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 543, + 279, + 730 + ], + "type": "text", + "content": "Effectiveness of Proposed Components. As shown in Table. 4, a series of ablation experiments on " + }, + { + "bbox": [ + 45, + 543, + 279, + 730 + ], + "type": "inline_equation", + "content": "\\mathrm{FF}++" + }, + { + "bbox": [ + 45, + 543, + 279, + 730 + ], + "type": "text", + "content": " (LQ) benchmark have been conducted to verify the effectiveness of different components in our framework. Specifically, we develop the following variants: (a) the baseline model equipped with the MADD [50] pipeline, (b) the baseline model with the proposed CAFÉ module, (c) the proposed method w/o. DG-SF3Net, (d) the proposed method w/o. MDAML module. Comparing (a) and (b), we observe that the proposed CAFÉ module brings a considerable improvement of Acc and AUC metrics on FF++ (LQ) dataset. From variant (b) and (c), we empirically demonstrate that adding the MDAML module will bring " + }, + { + "bbox": [ + 45, + 543, + 279, + 730 + ], + "type": "inline_equation", + "content": "2.19\\%" + }, + { + "bbox": [ + 45, + 543, + 279, + 730 + ], + "type": "text", + "content": " Acc and " + }, + { + "bbox": [ + 45, + 543, + 279, + 730 + ], + "type": "inline_equation", + "content": "1.52\\%" + }, + { + "bbox": [ + 45, + 543, + 279, + 730 + ], + "type": "text", + "content": " AUC gains, which are attributed to the multi-scale contextual information and large receptive field of refined attention maps. When adding the DG-SF3Net module, as" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 299, + 387, + 529, + 474 + ], + "blocks": [ + { + "bbox": [ + 49, + 357, + 525, + 368 + ], + "lines": [ + { + "bbox": [ + 49, + 357, + 525, + 368 + ], + "spans": [ + { + "bbox": [ + 49, + 357, + 525, + 368 + ], + "type": "text", + "content": "Table 3. Robustness evaluation under three types of perturbations. Our SFDG performs admirably under several common perturbations." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 299, + 387, + 529, + 474 + ], + "lines": [ + { + "bbox": [ + 299, + 387, + 529, + 474 + ], + "spans": [ + { + "bbox": [ + 299, + 387, + 529, + 474 + ], + "type": "table", + "html": "
IDCAFÉMDAMLDG -SF3NetAcc (LQ)AUC (LQ)
(a)88.6990.4
(b)✓89.5293.37
(c)✓✓91.4894.79
(d)✓✓92.0595.45
Ours✓✓✓92.2895.98
", + "image_path": "0ed68d72808872486fe1324cc90cbade608d1506d808f6e556d8575d63f47be8.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 324, + 481, + 503, + 492 + ], + "lines": [ + { + "bbox": [ + 324, + 481, + 503, + 492 + ], + "spans": [ + { + "bbox": [ + 324, + 481, + 503, + 492 + ], + "type": "text", + "content": "Table 4. Ablation study on the FF++ (LQ) dataset." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 296, + 516, + 530, + 587 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 516, + 530, + 587 + ], + "spans": [ + { + "bbox": [ + 296, + 516, + 530, + 587 + ], + "type": "text", + "content": "shown in variant (c) and Ours, we observe a remarkable advance on both Acc and AUC metrics, which benefits from the dynamic graph learning protocol to reason about the relation-aware forged clues. Finally, the best performance is achieved when combining all components, with the Acc and AUC of " + }, + { + "bbox": [ + 296, + 516, + 530, + 587 + ], + "type": "inline_equation", + "content": "92.28\\%" + }, + { + "bbox": [ + 296, + 516, + 530, + 587 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 516, + 530, + 587 + ], + "type": "inline_equation", + "content": "95.98\\%" + }, + { + "bbox": [ + 296, + 516, + 530, + 587 + ], + "type": "text", + "content": " respectively." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 296, + 588, + 531, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 588, + 531, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 588, + 531, + 730 + ], + "type": "text", + "content": "Setting of Hyper-parameters. During graph construction, the number of neighbor nodes " + }, + { + "bbox": [ + 296, + 588, + 531, + 730 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 296, + 588, + 531, + 730 + ], + "type": "text", + "content": " is a hyperparameter which determines the structure and aggregated scope of GCNs [10]. As shown in Table 5, to further evaluate the effectiveness using different " + }, + { + "bbox": [ + 296, + 588, + 531, + 730 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 296, + 588, + 531, + 730 + ], + "type": "text", + "content": ", we conduct a series of experiments on FF++ (LQ) and WildDeepfake datasets. From the experimental results, we conclude that too few neighbors can not guarantee the representative ability of the dynamic GCN module, thus degrades the information exchange of forged clues in spatial and frequency domains. Further, too many neighbors will tamper the regional separability of attention maps and tend to catastrophic overfitting. In our" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "text", + "content": "7284" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 105, + 281, + 227 + ], + "blocks": [ + { + "bbox": [ + 48, + 105, + 281, + 227 + ], + "lines": [ + { + "bbox": [ + 48, + 105, + 281, + 227 + ], + "spans": [ + { + "bbox": [ + 48, + 105, + 281, + 227 + ], + "type": "image", + "image_path": "3fac86f8c8abdefefe2d2823ea5216f0f13c786a96e76d763b90eb7031bae11c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 62, + 243, + 262, + 254 + ], + "lines": [ + { + "bbox": [ + 62, + 243, + 262, + 254 + ], + "spans": [ + { + "bbox": [ + 62, + 243, + 262, + 254 + ], + "type": "text", + "content": "Figure 4. The Grad-CAM visualization for forged faces." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 49, + 267, + 278, + 313 + ], + "blocks": [ + { + "bbox": [ + 49, + 267, + 278, + 313 + ], + "lines": [ + { + "bbox": [ + 49, + 267, + 278, + 313 + ], + "spans": [ + { + "bbox": [ + 49, + 267, + 278, + 313 + ], + "type": "image", + "image_path": "48c907c200be5b54ff87a56e2c7b864656a807e84e1ba95464eec2700146e073.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 297, + 220, + 530, + 242 + ], + "lines": [ + { + "bbox": [ + 297, + 220, + 530, + 242 + ], + "spans": [ + { + "bbox": [ + 297, + 220, + 530, + 242 + ], + "type": "text", + "content": "Figure 6. The visualization results of feature maps from MDAML module at different scales on FF++ and WildDeepfake datasets." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 48, + 355, + 278, + 429 + ], + "blocks": [ + { + "bbox": [ + 46, + 332, + 278, + 344 + ], + "lines": [ + { + "bbox": [ + 46, + 332, + 278, + 344 + ], + "spans": [ + { + "bbox": [ + 46, + 332, + 278, + 344 + ], + "type": "text", + "content": "Figure 5. The t-SNE feature visualization of the Ef-b4 and SFDG." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 355, + 278, + 429 + ], + "lines": [ + { + "bbox": [ + 48, + 355, + 278, + 429 + ], + "spans": [ + { + "bbox": [ + 48, + 355, + 278, + 429 + ], + "type": "table", + "html": "
#NeighborsFF++ (LQ)WildDeepfake
AccAUCAccAUC
592.1095.6082.0390.57
1092.2895.9884.4192.57
1592.2895.4983.5791.15
2092.0291.5981.4690.38
", + "image_path": "6259cadf37b5b3e3f6ae882b211ecd7f8c4f11a5d1c53d47f6bc7cd034c36f97.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 46, + 436, + 279, + 458 + ], + "lines": [ + { + "bbox": [ + 46, + 436, + 279, + 458 + ], + "spans": [ + { + "bbox": [ + 46, + 436, + 279, + 458 + ], + "type": "text", + "content": "Table 5. Results in terms of Acc(%) and AUC(%) for different number of neighboring nodes in the graph construction." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 480, + 279, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 480, + 279, + 504 + ], + "spans": [ + { + "bbox": [ + 46, + 480, + 279, + 504 + ], + "type": "text", + "content": "work, we observe that our model achieves the best performance in terms of Acc and AUC when setting " + }, + { + "bbox": [ + 46, + 480, + 279, + 504 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 480, + 279, + 504 + ], + "type": "text", + "content": " to 10." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 513, + 127, + 524 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 513, + 127, + 524 + ], + "spans": [ + { + "bbox": [ + 46, + 513, + 127, + 524 + ], + "type": "text", + "content": "4.4. Visualization" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 532, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 532, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 532, + 279, + 730 + ], + "type": "text", + "content": "Grad-CAM visualization. To better understand the internal mechanism of our method and explore interested regions for specific forged types, we supply the Grad-CAM [33] visualization on " + }, + { + "bbox": [ + 45, + 532, + 279, + 730 + ], + "type": "inline_equation", + "content": "\\mathrm{FF}++" + }, + { + "bbox": [ + 45, + 532, + 279, + 730 + ], + "type": "text", + "content": " dataset. As shown in Fig. 4, the forgery artifacts in different domains locate on independent regions. Detailedly, the spatial branch focuses on the facial region with pronounced forgery traces, which are effortlessly discovered by CNN backbones in spatial domain. Conversely, the frequency streamline searches manipulated clues essentially concerned with a wider area, e.g., the background, hair or entire face. These regions are subtle and dynamically change according to the image content thus provides a generalized feature representation. Just as we have speculated, the frequency domain acts as the complementary to the spatial domain and these two domains contribute to each other via graph-based high-order relation discovery for exploiting comprehensive forged cues." + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 304, + 106, + 526, + 202 + ], + "blocks": [ + { + "bbox": [ + 304, + 106, + 526, + 202 + ], + "lines": [ + { + "bbox": [ + 304, + 106, + 526, + 202 + ], + "spans": [ + { + "bbox": [ + 304, + 106, + 526, + 202 + ], + "type": "image", + "image_path": "abd17e2b966a7429cc498f721ce870f517995fad195cc1d23e137c51e18092bf.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 296, + 264, + 531, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 264, + 531, + 392 + ], + "spans": [ + { + "bbox": [ + 296, + 264, + 531, + 392 + ], + "type": "text", + "content": "Attention Maps Visualization. We verify the effectiveness of our tailored MDAML module and visualize the results in Fig 6. We observe that feature maps with different scales highlight distinctive activated intensities. Detailedly, the large scale features with high resolution representation embrace richer and global manipulated traces, while the small scales concentrate on more localized salient feature around facial landmarks. Further, we aggregate the attention maps via hierarchical pyramid paradigm to exploit the essential discrepancy between authentic and counterfeit faces, which can resist the noise disturbance and visual compression." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 296, + 394, + 530, + 522 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 394, + 530, + 522 + ], + "spans": [ + { + "bbox": [ + 296, + 394, + 530, + 522 + ], + "type": "text", + "content": "Feature Distribution Visualization. In this part, we investigate the discriminative ability of the proposed SFDG model. Leveraging the t-SNE [42] technique, we visualize the semantic feature distribution of the Ef-b4 [37] model and our SFDG on " + }, + { + "bbox": [ + 296, + 394, + 530, + 522 + ], + "type": "inline_equation", + "content": "\\mathrm{FF}++" + }, + { + "bbox": [ + 296, + 394, + 530, + 522 + ], + "type": "text", + "content": " (LQ) and WildDeepfake dataset. As shown in Fig. 5, our approach encourages the samples of same class into a relatively compact feature space. To explain, our SFDG adequately captures the intrinsic discrepancy between genuine and forged faces in multiple domains through graph-based relationships discovery, thus improving the generalization ability of our method." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 297, + 534, + 367, + 546 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 534, + 367, + 546 + ], + "spans": [ + { + "bbox": [ + 297, + 534, + 367, + 546 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 296, + 554, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 554, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 554, + 530, + 730 + ], + "type": "text", + "content": "In this paper, we propose a novel Spatial-Frequency Dynamic Graph network that develops graph model to exploit relationships of spatial and frequency domains for spotting subtle forgery clues. Firstly, the Content-guided Adaptive Frequency Extraction module is proposed to mine the adaptive frequency clues via content-aware frequency learning. Further, a Multiple Domains Attention Map Learning scheme captures rich contextual information of spatial-frequency feature through multi-scale feature ensemble. Finally, Dynamic Graph based Spatial-Frequency Feature Fusion module performs relation reasoning of spatial and frequency domains via improved graph convolution. Extensive experiments and detailed visualizations on widely-used benchmarks confirm the effectiveness and generalizability of our SFDG method compared with other contenders." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "text", + "content": "7285" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 105, + 103, + 117 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 105, + 103, + 117 + ], + "spans": [ + { + "bbox": [ + 47, + 105, + 103, + 117 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 124, + 280, + 730 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 51, + 124, + 279, + 167 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 124, + 279, + 167 + ], + "spans": [ + { + "bbox": [ + 51, + 124, + 279, + 167 + ], + "type": "text", + "content": "[1] Darius Afchar, Vincent Nozick, Junichi Yamagishi, and Isao Echizen. 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In Proceedings of the 28th ACM International Conference on Multimedia, pages 2382-2390, 2020. 1, 5, 6, 7" + } + ] + } + ], + "index": 27 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "text", + "content": "7287" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Dynamic Inference With Grounding Based Vision and Language Models/605f806c-dc72-4654-be1c-1d10020323b9_content_list.json b/2023/Dynamic Inference With Grounding Based Vision and Language Models/605f806c-dc72-4654-be1c-1d10020323b9_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..2c66869c4275f04dc4c6d5ec82d495a634844e2b --- /dev/null +++ b/2023/Dynamic Inference With Grounding Based Vision and Language Models/605f806c-dc72-4654-be1c-1d10020323b9_content_list.json @@ -0,0 +1,1857 @@ +[ + { + "type": "text", + "text": "Dynamic Inference with Grounding Based Vision and Language Models", + "text_level": 1, + "bbox": [ + 122, + 130, + 846, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Burak Uzkent, Amanmeet Garg, Wentao Zhu, Keval Doshi, Jingru Yi, Xiaolong Wang, Mohamed Omar Amazon Prime Video", + "bbox": [ + 86, + 180, + 906, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{burauzke,amanmega,zhuwent,kcdos,jyijingr,xiaowanf,omarmk}@amazon.com", + "bbox": [ + 189, + 218, + 797, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 268, + 313, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Transformers have been recently utilized for vision and language tasks successfully. For example, recent image and language models with more than 200M parameters have been proposed to learn visual grounding in the pre-training step and show impressive results on downstream vision and language tasks. On the other hand, there exists a large amount of computational redundancy in these large models which skips their run-time efficiency. To address this problem, we propose dynamic inference for grounding based vision and language models conditioned on the input image-text pair. We first design an approach to dynamically skip multihead self-attention and feed forward network layers across two backbones and multimodal network. Additionally, we propose dynamic token pruning and fusion for two backbones. In particular, we remove redundant tokens at different levels of the backbones and fuse the image tokens with the language tokens in an adaptive manner. To learn policies for dynamic inference, we train agents using reinforcement learning. In this direction, we replace the CNN backbone in a recent grounding-based vision and language model, MDETR, with a vision transformer and call it ViTMDETR. Then, we apply our dynamic inference method to ViTMDETR, called D-ViTDMETR, and perform experiments on image-language tasks. Our results show that we can improve the run-time efficiency of the state-of-the-art models MDETR and GLIP by up to $\\sim 50\\%$ on Referring Expression Comprehension and Segmentation, and VQA with only maximum $\\sim 0.3\\%$ accuracy drop.", + "bbox": [ + 75, + 300, + 473, + 724 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 753, + 209, + 768 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Significant progress has been made in the development of image and language models attributed to: (1) emergence of transformers for different modalities [6, 13], and (2) large scale pre-training paradigms [4, 14, 17, 24, 29, 43, 44]. In particular, with the very large scale pre-training of image and language models, large number of parameters and computations are allocated for processing input image-text pair. Specifically, the number of parameters of recent vision and", + "bbox": [ + 75, + 779, + 470, + 902 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4754cd6cb827ea9bfdd884215b0d4bba8cd50fe8376c9f53bb85f74c83cd17d5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 511, + 272, + 687, + 406 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/5f8f92370dc977c82a820ba28526b69351a282632ac8fefd7c2040819e2f27ec.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 702, + 272, + 875, + 406 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c5983d4e14089244e8de323e77d9321f1fbcd9b27ce0bca98f56e582841e7c92.jpg", + "image_caption": [ + "Figure 1. Accuracy vs frames per second comparison of the large (Top Left) and small (Top Right) models and accuracy vs GLOPs comparison of the large (Bottom Left) and small (Bottom Right) models. D-ViTMDETR outperforms MDETR, GLIP and our ViT-MDETR model in both frames per second and GFLOPs metrics while maintaining high accuracy." + ], + "image_footnote": [], + "bbox": [ + 509, + 417, + 684, + 550 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c18d14a7b36d3f3291987293a9656a0215139c1cf4756ea97b22fbd8c1ffc877.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 700, + 417, + 872, + 550 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "language models can be more than 200M [14, 17, 44], resulting in low run-time efficiency. This problem with the single-modality transformers has been tackled by several studies before [27, 30, 37]. Such computational complexity is further amplified in multimodal networks often building on multiple transformer models. As a result, reducing the run-time complexity of the multimodal networks can be very beneficial for the downstream tasks. Existing methods including pruning [20], knowledge distillation [10, 33] and quantization [39] can potentially be extended toward this goal. However, they show significant performance drop ( $\\geq 1\\%$ ) at $\\geq 50\\%$ compression rates and these methods are mostly designed for parameter reduction not for run-time speed. As a result, we propose dynamic inference with the large image and language mod", + "bbox": [ + 496, + 672, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "2624", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "els mainly to achieve two goals: (1) drastically reduce runtime complexity, and (2) maintain their high accuracy. Towards these goals, in the first step, we analyze the classic architectural choices for the recent image and language models. A typical image and language model consists of a vision encoder (a CNN or a vision transformer), a text encoder (transformer), and a multimodal transformer (fusion network). Inspired by MDETR [14], we build a vision and language model consisting of vision and language transformer and DETR-like multimodal network and call it ViTMDETR. The transformer modules consist of a multi-head self attention (MSA) and feed forward network (FFN) blocks which are experimentally found to be computationally expensive modules in inference-time. It is also known that computationally complexity of transformer MSA module goes up quadratically w.r.t number of tokens. The number of tokens and the computational complexity gets further amplified with inclusion of multimodal inputs and related modules.", + "bbox": [ + 75, + 90, + 472, + 377 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "For these reasons, with our D-ViTMDETR model we propose to dynamically prune input tokens from multiple modalities across the transformer backbones and fuse vision tokens adaptively with the text tokens to improve the accuracy. This way, we can reduce the complexity quadratically. Additionally, we adaptively skip the computationally expensive MSA and FFN layers across the two backbones and the multimodal network to further improve run-time efficiency. To learn dynamic policies, we train decision networks using the policy-gradients based reinforcement learning algorithm and distill the knowledge from ViTMDETR to better optimize D-ViTMDETR.", + "bbox": [ + 75, + 378, + 472, + 559 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this research work, our contributions are as below:", + "bbox": [ + 96, + 560, + 447, + 574 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We introduce an MDETR-inspired transformer-based model ViTMDETR for grounding based vision and language tasks.", + "- We propose a novel method to learn dynamic token pruning and fusion actions to reduce computational complexity using reinforcement learning. Additionally, we train the same agents to learn MSA and FFN layer skipping throughout our vision and language model to further reduce complexity.", + "- For better optimization, we align the representations and predictions of D-ViTMDETR with the representations and predictions of the ViTMDETR model.", + "- We perform experiments with both our ViTMDETR and D-ViTMDETR models on several image and language benchmarks for Referring Expression Comprehension (REC) and Segmentation (RES), and VQA tasks. With our dynamic model, D-ViTMDETR, we can improve the run-time efficiency of the state-of-the-art models MDETR [14] and GLIP [17] by up to $\\sim 50\\%$ on Referring Expression Comprehension and" + ], + "bbox": [ + 96, + 584, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Segmentation, and VQA with only maximum $\\sim 0.3\\%$ accuracy drop as seen in Figure 1.", + "bbox": [ + 531, + 90, + 890, + 121 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 500, + 138, + 650, + 156 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Grounding Based Image and Language Models We can categorize existing grounding based image and language models into two categories: (1) two-stage and (2) single-stage. Two-stage methods [4, 24, 42] rely on off-the-shelf object detectors to get object proposals and then process the language query for the task of interest. On the other hand, single-stage methods [3, 5, 7, 14, 17, 40, 44] avoid using a separate off-the-shelf object detector and perform end-to-end training for detecting the referred object, reducing the computational complexity of the two-stage methods. The most recent vision and language models [5, 14, 17, 18, 38] utilize large-scale transformers to improve the accuracy of the previous models with CNN backbones [3, 40]. Other recent works [19, 29, 31] including CLIP [29] have developed image and language models trained on large-scale data with high-level image-to-text contrastive learning objective.", + "bbox": [ + 496, + 165, + 890, + 407 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Dynamic Inference with Transformers Dynamic inference with vision transformers have been mostly studied on single modality data. Wang et al. [35] proposed to leverage the redundancy in the image space to assign adaptive number of patches to each image. Other works [30,37,41] used adaptive number of tokens conditioned on the input. These studies exploit the redundancy on the input (image and tokens) to transformer encoders. On the other hand, depth-adaptive inference for transformers showed strong improvements [1,8,11,22]. Next, [27] performs conditional inference on the image space, in the attention heads and FFN components for the task of image recognition. However, there has been no dynamic method designed for multimodal tasks. Different from this studies, our study focuses on the vision and language models for the vision and language tasks. Since the amount of computation in the vision and language models will be drastically larger than the single-modality tasks, we can expect further gains by using dynamic inference on the vision and language models. In addition to MSA and FFN layer skipping across the backbones and multimodal network, we perform dynamic token pruning for text and vision tokens and adaptively fuse vision tokens with text tokens.", + "bbox": [ + 496, + 409, + 892, + 755 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Proposed Method", + "text_level": 1, + "bbox": [ + 500, + 773, + 671, + 791 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3.1. Building ViTMDETR", + "text_level": 1, + "bbox": [ + 500, + 800, + 702, + 816 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In our vision and language model, we have a vision encoder $f_{v}$ and text encoder $f_{t}$ parameterized by $\\theta_v$ and $\\theta_t$ that outputs representations $z_{v}\\in \\mathbb{R}^{v}$ and $z_{t}\\in \\mathbb{R}^{t}$ as", + "bbox": [ + 496, + 825, + 890, + 869 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\nz _ {v} ^ {i = N} = f _ {v} \\left(x _ {v}; \\theta_ {v}\\right), \\quad z _ {t} ^ {i = N} = f _ {t} \\left(x _ {t}; \\theta_ {t}\\right). \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 555, + 883, + 890, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "2625", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where $N$ represents the number of encoders. The modality-specific representations are then concatenated and passed to a third-stage multimodal network, $f_{m}$ , parameterized by $\\theta_{m}$ as", + "bbox": [ + 76, + 90, + 468, + 148 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nz _ {m} = f _ {m} \\left(\\left[ z _ {v} ^ {i = N}, z _ {t} ^ {i = N} \\right]; \\theta_ {m}\\right) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 148, + 468, + 169 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $z_{m}\\in \\mathbb{R}^{m}$ represents output of multimodal network. We then process $z_{m}$ with an MLP layer to get task-specific predictions, i.e., referring expression comprehension (REC) and VQA. Given this multimodal network with list of parameters $\\theta = [\\theta_v,\\theta_t,\\theta_m]$ , our goal is to introduce adaptivity in processing the modalities through vision and text backbones and multimodal network.", + "bbox": [ + 76, + 175, + 468, + 279 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Text Backbone The text transformer first projects raw language data to word embeddings and sums them with the positional embedding formulated as", + "bbox": [ + 76, + 281, + 468, + 325 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nz _ {t} ^ {i = 0} = e _ {t} \\left(x _ {t}\\right) + p _ {t} \\left(x _ {t}\\right) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 192, + 337, + 468, + 356 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where, for a given input token $x_{t}$ , $e_{t}$ and $p_{t}$ represent the word and positional embedding functions.", + "bbox": [ + 76, + 368, + 468, + 397 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Next, the transformer processes the input embeddings $z_{t}^{i = 0}$ by $N$ encoders where each encoder consists of MSA, layer norm (LN), GELU [9], and FFN layers. Operations in a transformer encoder can be formulated as", + "bbox": [ + 76, + 398, + 468, + 455 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nz _ {t} ^ {i} = M S A _ {t} \\left(L N _ {t} \\left(z _ {t} ^ {i}\\right)\\right) + z _ {t} ^ {i}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 468, + 468, + 487 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nz _ {t} ^ {i + 1} = F F N _ {t} \\left(L N _ {t} \\left(z _ {t} ^ {i}\\right)\\right) + z _ {t} ^ {i}. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 168, + 512, + 468, + 531 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We note that we can skip the MSA or FFN layers together with LN layer without any modification to the architecture. This will be useful for our dynamic inference method.", + "bbox": [ + 76, + 537, + 468, + 582 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Vision Backbone The vision transformer has a convolutional layer, $e_v$ , to divide the input image into patches and learn patch representations. Patch embedding is then summed with the positional embedding, $p_v$ as", + "bbox": [ + 76, + 584, + 468, + 643 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nz _ {v} ^ {i = 0} = e _ {v} \\left(x _ {v}\\right) + p _ {v} \\left(x _ {v}\\right). \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 186, + 654, + 468, + 672 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Next, the vision transformer processes the input embedding $z_{v}^{i = 0}$ by $N$ encoders with similar components to the text transformer encoder. We can formulate the operations in a vision transformer encoder as", + "bbox": [ + 76, + 685, + 468, + 743 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nz _ {v} ^ {i} = M S A _ {v} \\left(L N _ {v} \\left(z _ {v} ^ {i}\\right)\\right) + z _ {v} ^ {i}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 171, + 756, + 468, + 773 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nz _ {v} ^ {i + 1} = F F N _ {v} \\left(L N _ {v} \\left(z _ {v} ^ {i}\\right)\\right) + z _ {v} ^ {i}. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 165, + 800, + 468, + 818 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Similarly to the text transformer, we can skip the MSA or FFN layers without any modification to the architecture.", + "bbox": [ + 76, + 825, + 468, + 854 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Multimodal Transformer We then pass the concatenated representations $[z_t^{i=N}, z_v^{i=N}]$ to a multimodal transformer. MDETR uses a DETR-based transformer [2] to output", + "bbox": [ + 76, + 854, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "boundong box predictions for the given multimodal representations. For the REC task, we choose the bounding box predictions with the highest confidence score. For VQA, we do not output bounding boxes; instead, we output class probabilities for different answers. With DETR, we can use a different number of encoders and decoders on the input representations. In this study, we maintain the same structure with the DETR in the MDETR model for the multimodal transformer and use 6 encoders and 6 decoders with traditional transformer MSA and FFN layers on which we can perform skipping without any modification.", + "bbox": [ + 496, + 90, + 890, + 257 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Dynamic Token Pruning and Fusion", + "text_level": 1, + "bbox": [ + 500, + 266, + 813, + 281 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To achieve dynamic inference, we first propose an approach to prune redundant multimodal tokens and fuse tokens adaptively. We note that we only fuse selected vision tokens with the text tokens and process the fused vision tokens and text tokens with the text backbone. We follow this strategy as pre-trained language transformers are known to generalize to image modality [25]. In this direction, we place a decision network on after every two encoders of the backbones. The decision network provides output for the token pruning and fusion as", + "bbox": [ + 496, + 289, + 890, + 439 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\np _ {b}, s _ {b} = \\operatorname {s i g m o i d} \\left(f _ {d} \\left(\\left[ z _ {v} ^ {i}, z _ {t} ^ {i} \\right]; \\theta_ {d}\\right)\\right) \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 578, + 449, + 890, + 467 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $p_b$ represents the continuous predictions on token fusion and pruning across the two backbones whereas $\\theta_d$ represent the decision network parameters. On the other hand, $s_b$ represents the actions for MSA and FFN layer skipping that we detail in the next section. We use a single dense layer for the decision network. Note that the number of tokens from each backbone can get large depending on the size of the image and text. As a result, it can be very hard to optimize the decision network to provide actions for many tokens.", + "bbox": [ + 496, + 477, + 890, + 626 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/6bfb0d8583e3a26d0efa269197924fceb2b20951f7d10eadc7126b612bc02931.jpg", + "image_caption": [ + "Figure 2. Demonstration of action space for vision token pruning and fusion. We group each 16 neighboring tokens in a $64 \\times 64$ window and represent the window with two actions: (1) token pruning and (2) fusion. The actions are then applied to the tokens inside this window." + ], + "image_footnote": [], + "bbox": [ + 522, + 636, + 856, + 825 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "2626", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/8d3392447662aacd2a52ccc5e7ef7a771c3dcec2504d7a9532f59e587e23cd19.jpg", + "image_caption": [ + "Figure 3. Framework for combining the dynamic token fusion and pruning together with MSA and FFN layer skipping to get DViTMDETR model. We do not show layer skipping in the multimodal network for simplicity. By combining layer skipping together with token pruning and fusion, we tackle redundancy in both across the backbones and multimodal network and the input data." + ], + "image_footnote": [], + "bbox": [ + 98, + 87, + 872, + 332 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Reducing the Size of Action Space The amount of vision tokens can be very large especially for large size images given that each token covers $16 \\times 16$ pixels patch. Large action space can be a bottleneck for learning the decision network parameters. To simplify their training, we cluster the set of vision tokens by spatially grouping them as shown in Figure 2. More specifically, we divide the image into $M_v \\times M_v$ non-overlapping windows where each window is represented by $64 \\times 64$ pixels and take a single pruning and fusion action for all the patches in this window. Our action space for pruning and fusion then becomes $p_b \\in [0,1]^{2 * M_v * M_v + M_t}$ where $M_v * M_v$ and $M_t$ represent the number of vision token clusters and text tokens. Since, the number of text tokens is much smaller than the number of vision tokens, we do not modify their action space.", + "bbox": [ + 75, + 409, + 470, + 635 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Discrete Actions from Continuous Predictions In test time, we obtain discrete actions by using a piece-wise function as $\\mathbf{a}_{\\mathbf{p}}^{\\mathrm{j}} = 1$ if $p_b^j \\geq 0.5$ , otherwise $\\mathbf{a}_{\\mathbf{p}}^{\\mathrm{j}} = 0$ . For $\\mathbf{a}_{\\mathbf{p}}^{\\mathrm{j}} = 1$ we either prune or fuse the corresponding set of vision tokens in a spatial cluster and we keep the tokens for $\\mathbf{a}_{\\mathbf{p}}^{\\mathrm{j}} = 0$ . To avoid the conflicts between pruning and fusion, we prioritize pruning over fusion. In other words, if we decide to both prune and fuse a set of vision tokens in a cluster, we prune them and ignore fusion actions since pruning favors further computational efficiency.", + "bbox": [ + 75, + 637, + 468, + 787 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Dynamic MSA and FFN Layer Skipping", + "text_level": 1, + "bbox": [ + 76, + 799, + 423, + 816 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the next step, we propose a method to dynamically skip MSA and FFN layers in the image and language backbones, and multimodal transformer.", + "bbox": [ + 75, + 824, + 468, + 867 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Backbones For MSA and FFN layer skipping, we use the same decision network with the token pruning and fusion", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "actions from Eq. 9 where $s_b$ represents the continuous predictions of the decision network on which MSA and FFN layers should be skipped in the next two encoders of the language and text backbone. As a result, our action space for layer skipping can be represented as $s_b \\in [0,1]^8$ as we have 4 MSA and 4 FFN layers in two encoders across the two backbones.", + "bbox": [ + 496, + 409, + 890, + 513 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Multimodal Transformer Finally, we integrate a decision network before multimodal transformer as shown below.", + "bbox": [ + 498, + 513, + 890, + 544 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ns _ {f} = \\operatorname {s i g m o i d} \\left(f _ {m} \\left(\\left[ z _ {v} ^ {N}, z _ {t} ^ {N} \\right]; \\theta_ {m}\\right)\\right) \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 578, + 550, + 890, + 570 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $s_f$ represents the continuous predictions on skipping MSA and FFN layers in the multimodal network. Our action space in this case can be represented as $s_f \\in [0,1]^{24}$ as we have 12 MSA and 12 FFN layers in the 6 encoders and 6 decoders. We note that we have traditional MSA and FFN layers in these encoders and decoders.", + "bbox": [ + 496, + 574, + 890, + 662 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Discrete Actions from Continuous Predictions In test time, we obtain discrete actions by using a piece-wise function as $\\mathbf{a}_{\\mathbf{s}}^{\\mathrm{j}} = 1$ if $s_{s}^{j}\\geq 0.5$ , otherwise $\\mathbf{a}_{\\mathbf{s}}^{\\mathrm{j}} = 0$ . For $\\mathbf{a}_{\\mathbf{s}}^{\\mathrm{j}} = 1$ we skip the corresponding MSA or FFN layer and use the MSA or FFN layer for $\\mathbf{a}_{\\mathbf{s}}^{\\mathrm{j}} = 0$ . We note that we follow the same process to get actions $a_{m}$ for skipping MSA and FFN layers in the multimodal network after getting the predictions $s_f$ . We show the combination of the token pruning and fusion together with MSA and FFN layer skipping in Figure 3.", + "bbox": [ + 496, + 665, + 890, + 816 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Modeling the Reward and Policy Functions", + "text_level": 1, + "bbox": [ + 500, + 823, + 867, + 839 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4.1 Reward Function", + "text_level": 1, + "bbox": [ + 500, + 847, + 676, + 861 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Reward function is a critical component of our algorithm as it needs to reflect what we want to achieve with adaptive", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "2627", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "inference. In our method, our goal is to reduce the computational complexity in the inference time to increase run-time speed. As a result, we propose a dual reward function that consists of: (1) target task accuracy and (2) savings in computational complexity.", + "bbox": [ + 75, + 90, + 467, + 166 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Backbones For backbones, we formulate the reward function as", + "bbox": [ + 75, + 167, + 467, + 196 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {R} _ {b} = \\sigma * c (d, g) + (1 - \\sigma) * (\\mathcal {P} + \\mathcal {F} + \\mathcal {S}) \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 112, + 208, + 467, + 224 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $c$ represents the task accuracy given model predictions, $d$ , and ground truth, $g$ , whereas $\\mathcal{P}$ , and $\\mathcal{F}$ represent the ratio of pruned and fused tokens. $S$ represents the ratio of skipped MSA and FFN layers. We note that we assign same reward to skipping an MSA and an FFN layer. One can assign higher reward to MSA layer since it has more computational complexity. On the other hand, $\\sigma \\in [0,1]$ controls the trade-off between the task accuracy and computational efficiency obtained by the adaptive inference.", + "bbox": [ + 75, + 234, + 467, + 369 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Multimodal Network As we do not prune tokens for the multimodal network, we only consider skipping MSA and FFN layers. We formulate the reward function as", + "bbox": [ + 75, + 371, + 467, + 416 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {R} _ {f} = \\sigma * c (d, g) + (1 - \\sigma) S. \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 169, + 428, + 467, + 444 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4.2 Policy Functions", + "text_level": 1, + "bbox": [ + 76, + 460, + 246, + 474 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Backbones We model the policy function for the backbones as the multiplication of the probabilities of individual token pruning and fusion actions and repeat it for the layer skipping actions. We represent individual actions with an action-specific Bernoulli distribution. Next, we formulate the policy function for the decision networks for the backbones as", + "bbox": [ + 75, + 484, + 467, + 589 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\pi_ {d} \\left(\\mathbf {a} _ {\\mathbf {s}}, \\mathbf {a} _ {\\mathbf {p}} \\mid z _ {v} ^ {i}, z _ {t} ^ {i}\\right) = \\prod_ {j} s _ {b} ^ {j} ^ {\\mathbf {a} _ {\\mathbf {s}} ^ {\\mathrm {j}}} \\left(1 - s _ {b} ^ {j}\\right) ^ {1 - \\mathbf {a} _ {\\mathbf {s}} ^ {\\mathrm {j}}} + \\prod_ {j} p _ {b} ^ {j} ^ {\\mathbf {a} _ {\\mathbf {p}} ^ {\\mathrm {j}}} \\left(1 - p _ {b} ^ {j}\\right) ^ {1 - \\mathbf {a} _ {\\mathbf {p}} ^ {\\mathrm {j}}}. \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 612, + 467, + 657 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Multimodal Network Similar to the backbones, we model the policy function for the multimodal network as the multiplication of the probabilities of individual actions represented by Bernoulli distribution as", + "bbox": [ + 75, + 659, + 467, + 718 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\pi_ {m} \\left(\\mathbf {a} _ {\\mathbf {m}} \\mid z _ {v} ^ {N}, z _ {t} ^ {N}\\right) = \\prod_ {j} s _ {f} ^ {j \\mathbf {a} _ {\\mathbf {m}} ^ {\\mathrm {j}}} \\left(1 - s _ {f} ^ {j}\\right) ^ {1 - \\mathbf {a} _ {\\mathbf {m}} ^ {\\mathrm {j}}}. \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 114, + 729, + 467, + 766 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Training Procedure", + "text_level": 1, + "bbox": [ + 76, + 777, + 264, + 792 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Optimization", + "text_level": 1, + "bbox": [ + 76, + 801, + 215, + 816 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As we learn discrete actions, we cannot use the reparameterization trick to optimize the objective w.r.t. $\\theta_{d}$ . To optimize the parameters $\\theta_{d}$ , we need to use model-free reinforcement learning algorithms. Policy gradient [32] is suitable in our scenario as the number of unique actions the", + "bbox": [ + 75, + 825, + 467, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "policy network can choose increases exponentially with the number of tokens and MSA and FFN layers. Together with policy gradients we use the REINFORCE method [32] to optimize the objective w.r.t $\\theta_{d}$ and $\\theta_{m}$ as", + "bbox": [ + 496, + 90, + 890, + 151 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\underset {\\theta_ {d}, \\theta_ {m}} {\\arg \\max } J = \\mathcal {R} _ {b} \\nabla \\log_ {\\pi_ {\\theta_ {d}}} \\left(\\mathbf {a} _ {\\mathbf {s}}, \\mathbf {a} _ {\\mathbf {p}} \\mid z _ {v} ^ {i}, z _ {t} ^ {i}\\right) + \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 553, + 160, + 890, + 186 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {R} _ {f} \\nabla l o g _ {\\pi_ {\\theta_ {m}}} (\\mathbf {a _ {m}} | z _ {v} ^ {i = N}, z _ {t} ^ {i = N})\n$$\n", + "text_format": "latex", + "bbox": [ + 632, + 188, + 834, + 208 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\nabla log_{\\pi_{\\theta_d}}$ and $\\nabla log_{\\pi_{\\theta_m}}$ represent the log-likelihood of policy function for the backbones and multimodal network. Next, we substitute the policy functions with Eq. 13 and 14 and take its derivative w.r.t $\\theta_d$ and $\\theta_m$ for updating the weights.", + "bbox": [ + 496, + 215, + 890, + 290 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Pre-training the Decision Networks", + "text_level": 1, + "bbox": [ + 498, + 299, + 805, + 315 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After formulating the optimization steps, we pre-train the decision networks on the finetuning dataset while keeping the weights of the backbones and multimodal network frozen. By doing this, we can learn useful policies towards choosing the right decisions for token pruning and fusion together with adaptive layer skipping. To achieve it, we only optimize the objective shown in Eq. 15.", + "bbox": [ + 496, + 321, + 890, + 429 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Jointly Finetuning the Decision Networks, Backbones and Multimodal Network", + "text_level": 1, + "bbox": [ + 498, + 436, + 890, + 465 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In the previous step, we learned the parameters of the decision networks $\\theta_{d}$ by executing the decisions with the multimodal network and finding the reward value. Up until this step, the multimodal network has not been updated with the dynamic inference which results in accuracy drop. To avoid it, we propose joint-finetuning step where we finetune both the decision networks and backbones, and multimodal network jointly. As a result, the objective for the backbones and multimodal network parameters becomes:", + "bbox": [ + 496, + 474, + 890, + 609 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\underset {\\theta_ {v}, \\theta_ {t}, \\theta_ {m}} {\\arg \\min } L _ {t} = \\operatorname {T a k L o s s} (d, g | x _ {t}, y _ {t}, \\mathbf {a} _ {\\mathbf {s}}, \\mathbf {a} _ {\\mathbf {p}}, \\mathbf {a} _ {\\mathbf {m}}) \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 521, + 619, + 890, + 646 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "On the other hand, the objective for the decision networks remain similar to Eq. 15.", + "bbox": [ + 496, + 652, + 890, + 683 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.4. Distilling from ViTMDETR", + "text_level": 1, + "bbox": [ + 500, + 691, + 748, + 707 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To better optimize the model in the joint finetuning step, we make use of the original fixed model, ViTMDETR, that we started with. In this direction, we add an objective to align the ViTMDETR's representations with our dynamic model as", + "bbox": [ + 496, + 714, + 890, + 789 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\underset {\\theta_ {v} \\theta_ {t} \\theta_ {m}} {\\arg \\min } L _ {d} = \\| z _ {t} ^ {i = N} - \\hat {z} _ {t} ^ {i = N} \\| _ {1} + \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 580, + 797, + 890, + 825 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\| z _ {v} ^ {i = N} - \\hat {z} _ {v} ^ {i = N} \\| _ {1} + \\| z _ {m} - \\hat {z} _ {m} \\| _ {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 588, + 827, + 808, + 845 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\hat{z}_t^{i=N}$ , $\\hat{z}_v^{i=N}$ , and $\\hat{z}_m$ represent the outputs of ViTMDETR after the vision and text backbones and the multimodal network, respectively.", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "2628", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In addition to the representation alignment, we also change the ground truth predictions, $g$ , with the predictions of the ViTMDETR, $\\hat{g}$ , and the task loss becomes", + "bbox": [ + 75, + 90, + 470, + 137 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\underset {\\theta_ {v}, \\theta_ {t}, \\theta_ {m}} {\\arg \\min } L _ {t} = \\operatorname {T a k L o s s} \\left(d, \\hat {g} \\mid x _ {t}, y _ {t}, \\mathbf {a} _ {\\mathbf {s}}, \\mathbf {a} _ {\\mathbf {p}}, \\mathbf {a} _ {\\mathbf {m}}\\right) \\tag {18}\n$$\n", + "text_format": "latex", + "bbox": [ + 98, + 150, + 468, + 175 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our final objective for end-to-end training of the adaptive network then becomes a linear combination of the task loss $(\\mathcal{L}_t)$ and distillation loss $(\\mathcal{L}_d)$ objectives as", + "bbox": [ + 76, + 186, + 468, + 233 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\underset {\\theta_ {v}, \\theta_ {t}, \\theta_ {m}} {\\arg \\min } \\mathcal {L} = \\mathcal {L} _ {t} + \\mathcal {L} _ {d}. \\tag {19}\n$$\n", + "text_format": "latex", + "bbox": [ + 194, + 247, + 468, + 272 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 76, + 287, + 209, + 306 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Pre-training Dataset MDETR performs end-to-end pretraining for a language-conditioned bounding box detection task. To construct a pre-training dataset, it merges several independent vision and language datasets. These datasets are listed as MSCOCO [21], Flickr30k [28], and VisualGenome [16] as they have bounding box annotations of the objects mentioned in the language query. The task in this step is to accurately detect the bounding boxes of the objects mentioned in a language query. For example, given an input query of cat sitting next to a dog on the chair, the task would be to predict bounding boxes of a cat, a dog, and a chair in the image. We use the same pre-training dataset and objectives to MDETR [14] to pre-train ViTMDETR.", + "bbox": [ + 75, + 314, + 468, + 508 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Downstream Tasks/Datasets We finetune the pre-trained model end-to-end on vision and language tasks, including REC, RES and VQA. For REC, we use RefCOCO and RefCOCO+ [15], and RefCOCOg [26] benchmarks. The task in these datasets is to detect the bounding box of the object referred to the language expression. For RES task, we evaluate on the PhraseCut [36] dataset, where, the task is to segment the object associated with the language query. For the VQA, we use GQA benchmark [12].", + "bbox": [ + 75, + 511, + 468, + 647 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Metrics As the evaluation metric, for REC and RES tasks we compute the Jaccard index between predicted and ground-truth bounding boxes. If it is above 0.5, the prediction is considered correct. For the VQA, the task is to predict the correct answer from the given answer categories. We use the top-1 accuracy metric to evaluate models. Lastly, we measure the run-time efficiency in terms of frames per second on a single V100 GPU. Additionally, we use the GFLOPs metrics to evaluate the models.", + "bbox": [ + 75, + 647, + 470, + 782 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/df009ae54739fa4488072d156690bdd882076a8257f41cbe5f3756cebb061e70.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MDETRGLIPViTMDETR
Pre-training DatasetCOCO+COCO+COCO+
Flickr30k+VG (1.3M)Flickr30k+VG (1.3M)Flickr30k+VG (1.3M)
", + "bbox": [ + 78, + 830, + 447, + 869 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Pre-training dataset used in our experiments.", + "bbox": [ + 112, + 882, + 431, + 896 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details. We build our implementation following the official MDETR repository2. We first replace the CNN vision backbone with a transformer backbone, DeiT [33]. To implement DeiT, we use the timm library3. To utilize ImageNet pre-trained weights, we use $384 \\times 384$ pixels images in both training and test time. This way, our whole architecture mostly consists of transformer layers other than the patch embedding convolutional layer. For pre-training ViTMDETR, we use the batch size of 256 on 8 NVIDIA V100 GPUs. For the transfer learning tasks for ViTMDETR we use a batch size of 8 with 2 NVIDIA V100 GPUs. For D-ViTMDETR, we use batch size of 256 with 8 V100 GPUs in the transfer learning tasks. We note that our dynamic inference method benefits from large training batch size as it reduces the variance in the reward objective.", + "bbox": [ + 496, + 90, + 890, + 316 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baselines We compare our method to a number of baselines that we designed. Our first baseline represents Random MSA and FFN layer skipping, Random-LS, where we draw skipping probability from a uniform distribution and perform skipping if the sampled probability is higher than a pre-defined threshold. Additionally, we design another baseline, Random-TP+TF, that randomly prunes the tokens given a uniform distribution. Finally, we combine both baselines to get another baseline, Random-LS+TP+TF. In addition to the Random baselines, we develop Stochastic baselines where we decay the likelihood of survival of the tokens, and MSA and FFN layers with the increasing depth. We call this baseline Stochastic-LS+TP+TF.", + "bbox": [ + 496, + 318, + 890, + 513 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In addition to our baselines, we compare our models to MDETR [14] and GLIP [17] models. To be consistent with our set up, we pre-train both our ViTMDETR, and MDETR and GLIP in the same pre-training dataset consisting of 1.3M image-text pairs with ground truth bounding box annotations. as shown in Table 1. Also, we pre-train and finetune all the models on $384\\times 384$ pixels images. Finally, we apply our dynamic inference method to our ViTMDETR model in finetuning tasks and call it D-ViTMDETR.", + "bbox": [ + 496, + 515, + 890, + 651 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Results", + "text_level": 1, + "bbox": [ + 498, + 662, + 591, + 676 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Experiments on Large Model We first perform experiments on our large image and language model, ViTMDETR. This model contains two backbones: (1) DeiT-Base [33] with 86M parameters, (2) RoBERTa-Base [23] with 125M parameters and a multimodal network (DETR) with 18M parameters similar to [14], resulting in 229M parameters model. Next, after pre-training the model, we learn dynamic inference on the downstream tasks and report the results in the Table 2. As shown in the table, we can improve the run-time complexity of MDETR by $\\sim 50\\%$ while achieving $\\sim 1\\%$ higher accuracy. On the other hand, we perform additional ablation studies with the following two", + "bbox": [ + 496, + 680, + 890, + 863 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "$^{1}$ https://github.com/Lyken17/pytorch-OpCounter", + "bbox": [ + 94, + 792, + 354, + 806 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "$^{2}$ https://github.com/ashkamath/mdetr", + "bbox": [ + 517, + 875, + 715, + 887 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "3https://github.com/rwrightman/pytorch-image-models", + "bbox": [ + 517, + 887, + 805, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "2629", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/88f87f27bd80b769774c0df742e560b2b78edd6d875ad4ff7a17cce822c38d36.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
RefCOCORefCOCO+RefCOCOgGQAPhraseCut
valtestAtestBvaltestAtestBvaltestATest-DevTest-StdTestRun-Time Eff. (fps)GFLOPs
MDETR [14]87.088.682.577.281.571.076.977.162.162.057.22850
GLIP [17]87.789.583.078.082.772.477.678.362.662.2-2562
ViTMDETR87.689.383.378.082.572.677.878.162.362.057.52760
Random-LS83.986.179.775.778.968.073.875.158.258.454.13442
Random-TP+TF83.985.979.875.577.667.974.174.958.458.454.23245
Random-LS+TP+TF80.081.875.271.774.864.169.671.455.855.951.34132
Stochastic-LS+TP+TF83.185.078.874.678.067.072.474.357.057.153.64132
D-ViTMDETR-LS87.689.483.278.382.672.877.778.062.462.057.53442
D-ViTMDETR-TP+TF87.689.383.578.082.872.677.778.262.462.057.53245
D-ViTMDETR-LS+TP+TF87.489.283.278.182.572.477.477.761.961.657.341 (↑ 50%)32 (↓ 50%)
", + "bbox": [ + 98, + 88, + 870, + 234 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/619ab366132e252d4f5d853b358f49856306a47845965c61e193402515d859b8.jpg", + "table_caption": [ + "Table 2. Experiments on referring exprehension comprehension (REC) and Visual Question Answering (GQA) benchmarks on the large model we built. Note that ViTMDETR contains ${229M}$ parameters whereas MDETR and GLIP contains ${205M}$ and ${231M}$ parameters. D-ViTMDETR model is built on top of pre-trained ViTMDETR and only introduces $\\sim {1M}$ more parameters,resulting in ${230M}$ parameters." + ], + "table_footnote": [], + "table_body": "
RefCOCORefCOCO+RefCOCOgGQAPhraseCut
valtestAtestBvaltestAtestBvaltestATest-DevTest-StdTestRun-time Eff. (fps)GFLOPs
MDETR [14]83.985.479.775.079.569.474.674.958.858.654.54014
ViTMDETR84.185.780.075.279.869.874.674.858.858.954.74014
Random-LS81.882.477.171.977.867.072.572.655.856.149.04811
Random-TP+TF81.882.377.371.977.967.272.772.455.956.050.84610
Random-LS+TP+TF79.980.675.469.976.065.670.970.154.054.148.6559
Stochastic-LS+TP+TF80.981.776.170.576.966.471.470.954.855.048.9559
D-ViTMDETR-LS84.185.979.975.579.670.174.974.858.759.154.54811
D-ViTMDETR-TP+TF84.085.979.875.479.670.074.874.658.559.054.54610
D-ViTMDETR-LS+TP+TF83.885.779.675.279.569.974.774.458.358.854.255 (↑ 36%)9 (↓ 36%)
", + "bbox": [ + 96, + 301, + 870, + 439 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Experiments on referring exprehension comprehension (REC) and Visual Question Answering (GQA) benchmarks on the small models. Note that ViTMDETR and MDETR contain $80M$ and $80M$ parameters. D-ViTMDETR model is built on top of pre-trained ViTMDETR and only introduces $\\sim 1M$ more parameters, resulting in $81M$ parameters.", + "bbox": [ + 75, + 449, + 893, + 492 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "components of our method: (1) dynamic token pruning and fusion, (2) adaptive MSA and FFN layer skipping. With dynamic token pruning (TP) and fusion (TF) only, we can reduce the run-time complexity by $\\sim 20\\%$ . With adaptive layer skipping (LS), this number goes up to $\\sim 30\\%$ .", + "bbox": [ + 75, + 518, + 468, + 593 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Experiments on Small Model Next, we perform experiments on our small image and language model, ViTMDETR. This model contains the DeiT-Small vision backbone with 22M parameters and CLIP [29] text backbone with 40M parameters together with a multimodal network with 18M parameters resulting in 80M parameters image and language model. After pre-training this model, we learn dynamic inference on the finetuning tasks as shown in Table 3. As shown in the table, we can reduce the run-time complexity of MDETR by $\\sim 36\\%$ with no accuracy drop. On the other hand, in our ablation studies, with dynamic token pruning and fusion only, we can reduce the run-time complexity by $\\sim 15\\%$ . By adding dynamic layer skipping, this number goes up to $\\sim 36\\%$ .", + "bbox": [ + 75, + 594, + 470, + 806 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Ablation Studies", + "text_level": 1, + "bbox": [ + 76, + 816, + 241, + 830 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Impact of Knowledge Distillation In our ablation studies, we first perform experiments on the impact of knowledge distillation for the optimization of our adaptive model. We show the results in Table 4. As seen in the table, knowledge", + "bbox": [ + 75, + 839, + 468, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "distillation improves the accuracy of the dynamic model by around $\\sim 1\\%$ .", + "bbox": [ + 496, + 518, + 890, + 547 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Impact of Pretraining the Decision Networks Next, we perform experiments on the impact of pre-training the decision networks. We show the results in Table 5. As seen in the table, pre-training the decision networks is important to maintain the high accuracy of our dynamic model.", + "bbox": [ + 496, + 547, + 890, + 625 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Impact of Window Size for Spatial Clustering In our experiments, we set the window size to $64 \\times 64$ and learn single action for the vision tokens inside the window. We perform experiments with different window sizes and show the results in Table 6 and show that we get the best results with $64 \\times 64$ windows.", + "bbox": [ + 496, + 625, + 890, + 715 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Analyzing Learned Policies", + "text_level": 1, + "bbox": [ + 500, + 726, + 745, + 742 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Pruned Tokens Additionally, we visualize the pruned tokens by the decision network in Figure 4. As seen in the figure, the number of tokens that are pruned goes down w.r.t depth of the backbones. This makes sense since we have decreasing number of remaining tokens w.r.t. depth.", + "bbox": [ + 496, + 750, + 890, + 824 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Fused Tokens In the next step, we visualize the fusion policies learned by the decision network. In particular, we are interested in how many vision tokens are fused over the increasing number of layers in the backbones. We show the results in Figure 4. As we can see in the figure, the num", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "2630", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/57bf860b43e57696b7408b10dbbc27e675c053a730630f94530f3b20d04429d0.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
RefCOCORefCOCO+RefCOCOgGQAPhraseCut
valtestAtestBvaltestAtestBvaltestATest-DevTest-StdTest
ViTMDETR87.689.383.378.082.572.677.878.162.362.057.5
D-ViTMDETR (LS+TP+AF)86.988.482.377.281.371.577.077.460.860.655.9
D-ViTMDETR (LS+TP+AF) + KD87.489.283.278.182.572.477.477.761.961.657.3
", + "bbox": [ + 138, + 88, + 828, + 164 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/9bbca18b22596a094755bdeb905ea615e3d97266bf579c58ac19fb83aada060d.jpg", + "table_caption": [ + "Table 4. Ablation studies on the impact of knowledge distillation." + ], + "table_footnote": [], + "table_body": "
RefCOCORefCOCO+RefCOCOgGQAPhraseCut
valtestAtestBvaltestAtestBvaltestATest-DevTest-StdTest
Without Pre-training77.479.273.168.172.562.667.467.751.451.147.0
With Pre-training84.986.780.675.680.069.174.975.258.958.654.5
", + "bbox": [ + 138, + 200, + 828, + 272 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/cb8cda8fb1ff63128373105157144fd9fec8e0973782294a52819976a2d4e3ad.jpg", + "table_caption": [ + "Table 5. Ablation studies on the impact of pretraining the decision network." + ], + "table_footnote": [], + "table_body": "
Window SizeRefCOCORefCOCOgRefCOCO+
16x1684.574.873.0
32x3285.876.474.6
64x6487.478.177.4
128x12887.077.676.5
", + "bbox": [ + 120, + 319, + 426, + 395 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 6. Impact of window size on vision token clustering on the val split of RefCOCO, RefCOCOg, and RefCOCO+.", + "bbox": [ + 76, + 405, + 470, + 434 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ber of vision tokens that are fused with the text tokens goes down w.r.t depth of the backbones. On the other hand, we can see that on average we fuse $\\sim 30\\%$ of vision tokens with the language tokens across the processing in backbones.", + "bbox": [ + 76, + 448, + 468, + 510 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0fc6b8ea53001e7afd42cb1736d63092bafe3d946bc91a43d4ce63fcc5d4782b.jpg", + "image_caption": [ + "Figure 4. Probability of token pruning (Left) and fusion (Right) over depth for the RefCOCO experiments." + ], + "image_footnote": [], + "bbox": [ + 98, + 527, + 269, + 656 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7c90110b94026cce11efae2460aa75c4c9ce1d4fd818f79b42930f6ac7ed492c.jpg", + "image_caption": [ + "Figure 5. MSA and FFN layer skipping probability distribution in vision backbone (Top Left), text backbone (Top Right), and multimodal network (Bottom) that consists of 6 encoder and decoder layers. We show the results from RefCOCO experiments." + ], + "image_footnote": [], + "bbox": [ + 282, + 527, + 450, + 655 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Skipped MSA and FFN layers Next, we analyze the policies learned by the decision networks towards skipping MSA and FFN layers in both vision and text backbone as well as the multimodal network. We note that across the 12 encoders in the backbones, we learn decisions to potentially skip 20 MSA and FFN layers and 12 MSA and FFN layers in the multimodal network.", + "bbox": [ + 75, + 718, + 468, + 824 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "As seen in Figure 5, the skipping operations for MSA and FFN layers are distributed in a way that later MSA and FFN layers especially in the backbones are skipped with higher probability. This is similar to skipping operations with CNNs where shallow layers are more important than", + "bbox": [ + 75, + 824, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1a3fee95a39f4a1af15b44e97f130ac7d3c70845c9d80d4b421f0ca2632105a2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 537, + 324, + 689, + 441 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6adbab7be80a250563065530b44e7a3d5a20267d858e28f6a35532c298d386a7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 699, + 325, + 856, + 441 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b8f208a6c15fca4450033193d1e88e0c358e22e0caee5ba9907fcee8db590bea.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 537, + 450, + 692, + 566 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0b6331b5639caaabea3e334c5f5e5f5452ad2163611dd0be02333a1aa13219bb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 699, + 450, + 854, + 566 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "deep layers as they provide critical low-level abstraction of objects [34]. On the other hand, there is not a clear pattern with the skipping operations in the multimodal network.", + "bbox": [ + 498, + 665, + 893, + 712 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 724, + 619, + 739 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We propose a dynamic inference method for the vision and language models. Our method includes learning adaptive policies to skip MSA and FFN layers across vision and language backbones and multimodal network. Additionally, it dynamically prunes tokens from different modalities and fuse tokens at different stages of backbones. We then train our model on downstream vision and language tasks. In our experiments on REC, RES and VQA we show that we can improve the run-time complexity of MDETR, and GLIP by up to $\\sim 50\\%$ with only maximum $\\sim 0.3\\%$ accuracy drop.", + "bbox": [ + 496, + 750, + 893, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "2631", + "bbox": [ + 482, + 944, + 513, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Arian Bakhtiarnia, Qi Zhang, and Alexandros Iosifidis. Multi-exit vision transformer for dynamic inference. arXiv preprint arXiv:2106.15183, 2021. 2", + "[2] Nicolas Carion, Francisco Massa, Gabriel Synnaeve, Nicolas Usunier, Alexander Kirillov, and Sergey Zagoruyko. End-to-end object detection with transformers. In European Conference on Computer Vision, pages 213-229. 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Glipv2: Unifying localization and vision-language understanding. arXiv preprint arXiv:2206.05836, 2022.1, 2" + ], + "bbox": [ + 501, + 92, + 890, + 556 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "2633", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Dynamic Inference With Grounding Based Vision and Language Models/605f806c-dc72-4654-be1c-1d10020323b9_model.json b/2023/Dynamic Inference With Grounding Based Vision and Language Models/605f806c-dc72-4654-be1c-1d10020323b9_model.json new file mode 100644 index 0000000000000000000000000000000000000000..52d9178898837ceb24851e2a8718b3eb40c24506 --- /dev/null +++ b/2023/Dynamic Inference With Grounding Based Vision and Language Models/605f806c-dc72-4654-be1c-1d10020323b9_model.json @@ -0,0 +1,2365 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.123, + 0.131, + 0.848, + 0.154 + ], + "angle": 0, + "content": "Dynamic Inference with Grounding Based Vision and Language Models" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.181, + 0.907, + 0.216 + ], + "angle": 0, + "content": "Burak Uzkent, Amanmeet Garg, Wentao Zhu, Keval Doshi, Jingru Yi, Xiaolong Wang, Mohamed Omar Amazon Prime Video" + }, + { + "type": "text", + "bbox": [ + 0.19, + 0.219, + 0.799, + 0.234 + ], + "angle": 0, + "content": "{burauzke,amanmega,zhuwent,kcdos,jyijingr,xiaowanf,omarmk}@amazon.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.301, + 0.474, + 0.726 + ], + "angle": 0, + "content": "Transformers have been recently utilized for vision and language tasks successfully. For example, recent image and language models with more than 200M parameters have been proposed to learn visual grounding in the pre-training step and show impressive results on downstream vision and language tasks. On the other hand, there exists a large amount of computational redundancy in these large models which skips their run-time efficiency. To address this problem, we propose dynamic inference for grounding based vision and language models conditioned on the input image-text pair. We first design an approach to dynamically skip multihead self-attention and feed forward network layers across two backbones and multimodal network. Additionally, we propose dynamic token pruning and fusion for two backbones. In particular, we remove redundant tokens at different levels of the backbones and fuse the image tokens with the language tokens in an adaptive manner. To learn policies for dynamic inference, we train agents using reinforcement learning. In this direction, we replace the CNN backbone in a recent grounding-based vision and language model, MDETR, with a vision transformer and call it ViTMDETR. Then, we apply our dynamic inference method to ViTMDETR, called D-ViTDMETR, and perform experiments on image-language tasks. Our results show that we can improve the run-time efficiency of the state-of-the-art models MDETR and GLIP by up to \\(\\sim 50\\%\\) on Referring Expression Comprehension and Segmentation, and VQA with only maximum \\(\\sim 0.3\\%\\) accuracy drop." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.754, + 0.21, + 0.77 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Significant progress has been made in the development of image and language models attributed to: (1) emergence of transformers for different modalities [6, 13], and (2) large scale pre-training paradigms [4, 14, 17, 24, 29, 43, 44]. In particular, with the very large scale pre-training of image and language models, large number of parameters and computations are allocated for processing input image-text pair. Specifically, the number of parameters of recent vision and" + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.273, + 0.688, + 0.407 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.704, + 0.273, + 0.876, + 0.407 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.511, + 0.418, + 0.685, + 0.551 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.702, + 0.418, + 0.874, + 0.551 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.564, + 0.895, + 0.648 + ], + "angle": 0, + "content": "Figure 1. Accuracy vs frames per second comparison of the large (Top Left) and small (Top Right) models and accuracy vs GLOPs comparison of the large (Bottom Left) and small (Bottom Right) models. D-ViTMDETR outperforms MDETR, GLIP and our ViT-MDETR model in both frames per second and GFLOPs metrics while maintaining high accuracy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.674, + 0.895, + 0.903 + ], + "angle": 0, + "content": "language models can be more than 200M [14, 17, 44], resulting in low run-time efficiency. This problem with the single-modality transformers has been tackled by several studies before [27, 30, 37]. Such computational complexity is further amplified in multimodal networks often building on multiple transformer models. As a result, reducing the run-time complexity of the multimodal networks can be very beneficial for the downstream tasks. Existing methods including pruning [20], knowledge distillation [10, 33] and quantization [39] can potentially be extended toward this goal. However, they show significant performance drop (\\(\\geq 1\\%\\)) at \\(\\geq 50\\%\\) compression rates and these methods are mostly designed for parameter reduction not for run-time speed. As a result, we propose dynamic inference with the large image and language mod" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2624" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.378 + ], + "angle": 0, + "content": "els mainly to achieve two goals: (1) drastically reduce runtime complexity, and (2) maintain their high accuracy. Towards these goals, in the first step, we analyze the classic architectural choices for the recent image and language models. A typical image and language model consists of a vision encoder (a CNN or a vision transformer), a text encoder (transformer), and a multimodal transformer (fusion network). Inspired by MDETR [14], we build a vision and language model consisting of vision and language transformer and DETR-like multimodal network and call it ViTMDETR. The transformer modules consist of a multi-head self attention (MSA) and feed forward network (FFN) blocks which are experimentally found to be computationally expensive modules in inference-time. It is also known that computationally complexity of transformer MSA module goes up quadratically w.r.t number of tokens. The number of tokens and the computational complexity gets further amplified with inclusion of multimodal inputs and related modules." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.379, + 0.473, + 0.56 + ], + "angle": 0, + "content": "For these reasons, with our D-ViTMDETR model we propose to dynamically prune input tokens from multiple modalities across the transformer backbones and fuse vision tokens adaptively with the text tokens to improve the accuracy. This way, we can reduce the complexity quadratically. Additionally, we adaptively skip the computationally expensive MSA and FFN layers across the two backbones and the multimodal network to further improve run-time efficiency. To learn dynamic policies, we train decision networks using the policy-gradients based reinforcement learning algorithm and distill the knowledge from ViTMDETR to better optimize D-ViTMDETR." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.561, + 0.449, + 0.575 + ], + "angle": 0, + "content": "In this research work, our contributions are as below:" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.585, + 0.47, + 0.632 + ], + "angle": 0, + "content": "- We introduce an MDETR-inspired transformer-based model ViTMDETR for grounding based vision and language tasks." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.636, + 0.47, + 0.727 + ], + "angle": 0, + "content": "- We propose a novel method to learn dynamic token pruning and fusion actions to reduce computational complexity using reinforcement learning. Additionally, we train the same agents to learn MSA and FFN layer skipping throughout our vision and language model to further reduce complexity." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.731, + 0.47, + 0.775 + ], + "angle": 0, + "content": "- For better optimization, we align the representations and predictions of D-ViTMDETR with the representations and predictions of the ViTMDETR model." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.78, + 0.471, + 0.902 + ], + "angle": 0, + "content": "- We perform experiments with both our ViTMDETR and D-ViTMDETR models on several image and language benchmarks for Referring Expression Comprehension (REC) and Segmentation (RES), and VQA tasks. With our dynamic model, D-ViTMDETR, we can improve the run-time efficiency of the state-of-the-art models MDETR [14] and GLIP [17] by up to \\(\\sim 50\\%\\) on Referring Expression Comprehension and" + }, + { + "type": "list", + "bbox": [ + 0.097, + 0.585, + 0.471, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.532, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "Segmentation, and VQA with only maximum \\(\\sim 0.3\\%\\) accuracy drop as seen in Figure 1." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.14, + 0.651, + 0.157 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.166, + 0.892, + 0.409 + ], + "angle": 0, + "content": "Grounding Based Image and Language Models We can categorize existing grounding based image and language models into two categories: (1) two-stage and (2) single-stage. Two-stage methods [4, 24, 42] rely on off-the-shelf object detectors to get object proposals and then process the language query for the task of interest. On the other hand, single-stage methods [3, 5, 7, 14, 17, 40, 44] avoid using a separate off-the-shelf object detector and perform end-to-end training for detecting the referred object, reducing the computational complexity of the two-stage methods. The most recent vision and language models [5, 14, 17, 18, 38] utilize large-scale transformers to improve the accuracy of the previous models with CNN backbones [3, 40]. Other recent works [19, 29, 31] including CLIP [29] have developed image and language models trained on large-scale data with high-level image-to-text contrastive learning objective." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.41, + 0.893, + 0.756 + ], + "angle": 0, + "content": "Dynamic Inference with Transformers Dynamic inference with vision transformers have been mostly studied on single modality data. Wang et al. [35] proposed to leverage the redundancy in the image space to assign adaptive number of patches to each image. Other works [30,37,41] used adaptive number of tokens conditioned on the input. These studies exploit the redundancy on the input (image and tokens) to transformer encoders. On the other hand, depth-adaptive inference for transformers showed strong improvements [1,8,11,22]. Next, [27] performs conditional inference on the image space, in the attention heads and FFN components for the task of image recognition. However, there has been no dynamic method designed for multimodal tasks. Different from this studies, our study focuses on the vision and language models for the vision and language tasks. Since the amount of computation in the vision and language models will be drastically larger than the single-modality tasks, we can expect further gains by using dynamic inference on the vision and language models. In addition to MSA and FFN layer skipping across the backbones and multimodal network, we perform dynamic token pruning for text and vision tokens and adaptively fuse vision tokens with text tokens." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.775, + 0.673, + 0.792 + ], + "angle": 0, + "content": "3. Proposed Method" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.801, + 0.704, + 0.817 + ], + "angle": 0, + "content": "3.1. Building ViTMDETR" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.871 + ], + "angle": 0, + "content": "In our vision and language model, we have a vision encoder \\( f_{v} \\) and text encoder \\( f_{t} \\) parameterized by \\( \\theta_v \\) and \\( \\theta_t \\) that outputs representations \\( z_{v}\\in \\mathbb{R}^{v} \\) and \\( z_{t}\\in \\mathbb{R}^{t} \\) as" + }, + { + "type": "equation", + "bbox": [ + 0.557, + 0.884, + 0.892, + 0.903 + ], + "angle": 0, + "content": "\\[\nz _ {v} ^ {i = N} = f _ {v} \\left(x _ {v}; \\theta_ {v}\\right), \\quad z _ {t} ^ {i = N} = f _ {t} \\left(x _ {t}; \\theta_ {t}\\right). \\tag {1}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2625" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.15 + ], + "angle": 0, + "content": "where \\(N\\) represents the number of encoders. The modality-specific representations are then concatenated and passed to a third-stage multimodal network, \\(f_{m}\\), parameterized by \\(\\theta_{m}\\) as" + }, + { + "type": "equation", + "bbox": [ + 0.176, + 0.15, + 0.469, + 0.17 + ], + "angle": 0, + "content": "\\[\nz _ {m} = f _ {m} \\left(\\left[ z _ {v} ^ {i = N}, z _ {t} ^ {i = N} \\right]; \\theta_ {m}\\right) \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.176, + 0.469, + 0.28 + ], + "angle": 0, + "content": "where \\(z_{m}\\in \\mathbb{R}^{m}\\) represents output of multimodal network. We then process \\(z_{m}\\) with an MLP layer to get task-specific predictions, i.e., referring expression comprehension (REC) and VQA. Given this multimodal network with list of parameters \\(\\theta = [\\theta_v,\\theta_t,\\theta_m]\\), our goal is to introduce adaptivity in processing the modalities through vision and text backbones and multimodal network." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.282, + 0.469, + 0.327 + ], + "angle": 0, + "content": "Text Backbone The text transformer first projects raw language data to word embeddings and sums them with the positional embedding formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.193, + 0.338, + 0.469, + 0.357 + ], + "angle": 0, + "content": "\\[\nz _ {t} ^ {i = 0} = e _ {t} \\left(x _ {t}\\right) + p _ {t} \\left(x _ {t}\\right) \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.369, + 0.469, + 0.398 + ], + "angle": 0, + "content": "where, for a given input token \\( x_{t} \\), \\( e_{t} \\) and \\( p_{t} \\) represent the word and positional embedding functions." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.399, + 0.469, + 0.457 + ], + "angle": 0, + "content": "Next, the transformer processes the input embeddings \\( z_{t}^{i = 0} \\) by \\( N \\) encoders where each encoder consists of MSA, layer norm (LN), GELU [9], and FFN layers. Operations in a transformer encoder can be formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.175, + 0.469, + 0.469, + 0.488 + ], + "angle": 0, + "content": "\\[\nz _ {t} ^ {i} = M S A _ {t} \\left(L N _ {t} \\left(z _ {t} ^ {i}\\right)\\right) + z _ {t} ^ {i}, \\tag {4}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.169, + 0.513, + 0.469, + 0.532 + ], + "angle": 0, + "content": "\\[\nz _ {t} ^ {i + 1} = F F N _ {t} \\left(L N _ {t} \\left(z _ {t} ^ {i}\\right)\\right) + z _ {t} ^ {i}. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.539, + 0.469, + 0.583 + ], + "angle": 0, + "content": "We note that we can skip the MSA or FFN layers together with LN layer without any modification to the architecture. This will be useful for our dynamic inference method." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.585, + 0.469, + 0.644 + ], + "angle": 0, + "content": "Vision Backbone The vision transformer has a convolutional layer, \\( e_v \\), to divide the input image into patches and learn patch representations. Patch embedding is then summed with the positional embedding, \\( p_v \\) as" + }, + { + "type": "equation", + "bbox": [ + 0.187, + 0.655, + 0.469, + 0.673 + ], + "angle": 0, + "content": "\\[\nz _ {v} ^ {i = 0} = e _ {v} \\left(x _ {v}\\right) + p _ {v} \\left(x _ {v}\\right). \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.686, + 0.469, + 0.744 + ], + "angle": 0, + "content": "Next, the vision transformer processes the input embedding \\( z_{v}^{i = 0} \\) by \\( N \\) encoders with similar components to the text transformer encoder. We can formulate the operations in a vision transformer encoder as" + }, + { + "type": "equation", + "bbox": [ + 0.172, + 0.757, + 0.469, + 0.775 + ], + "angle": 0, + "content": "\\[\nz _ {v} ^ {i} = M S A _ {v} \\left(L N _ {v} \\left(z _ {v} ^ {i}\\right)\\right) + z _ {v} ^ {i}, \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.166, + 0.801, + 0.469, + 0.819 + ], + "angle": 0, + "content": "\\[\nz _ {v} ^ {i + 1} = F F N _ {v} \\left(L N _ {v} \\left(z _ {v} ^ {i}\\right)\\right) + z _ {v} ^ {i}. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.826, + 0.469, + 0.855 + ], + "angle": 0, + "content": "Similarly to the text transformer, we can skip the MSA or FFN layers without any modification to the architecture." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Multimodal Transformer We then pass the concatenated representations \\([z_t^{i=N}, z_v^{i=N}]\\) to a multimodal transformer. MDETR uses a DETR-based transformer [2] to output" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.258 + ], + "angle": 0, + "content": "boundong box predictions for the given multimodal representations. For the REC task, we choose the bounding box predictions with the highest confidence score. For VQA, we do not output bounding boxes; instead, we output class probabilities for different answers. With DETR, we can use a different number of encoders and decoders on the input representations. In this study, we maintain the same structure with the DETR in the MDETR model for the multimodal transformer and use 6 encoders and 6 decoders with traditional transformer MSA and FFN layers on which we can perform skipping without any modification." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.267, + 0.814, + 0.282 + ], + "angle": 0, + "content": "3.2. Dynamic Token Pruning and Fusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.29, + 0.892, + 0.44 + ], + "angle": 0, + "content": "To achieve dynamic inference, we first propose an approach to prune redundant multimodal tokens and fuse tokens adaptively. We note that we only fuse selected vision tokens with the text tokens and process the fused vision tokens and text tokens with the text backbone. We follow this strategy as pre-trained language transformers are known to generalize to image modality [25]. In this direction, we place a decision network on after every two encoders of the backbones. The decision network provides output for the token pruning and fusion as" + }, + { + "type": "equation", + "bbox": [ + 0.58, + 0.45, + 0.891, + 0.468 + ], + "angle": 0, + "content": "\\[\np _ {b}, s _ {b} = \\operatorname {s i g m o i d} \\left(f _ {d} \\left(\\left[ z _ {v} ^ {i}, z _ {t} ^ {i} \\right]; \\theta_ {d}\\right)\\right) \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.478, + 0.892, + 0.627 + ], + "angle": 0, + "content": "where \\( p_b \\) represents the continuous predictions on token fusion and pruning across the two backbones whereas \\( \\theta_d \\) represent the decision network parameters. On the other hand, \\( s_b \\) represents the actions for MSA and FFN layer skipping that we detail in the next section. We use a single dense layer for the decision network. Note that the number of tokens from each backbone can get large depending on the size of the image and text. As a result, it can be very hard to optimize the decision network to provide actions for many tokens." + }, + { + "type": "image", + "bbox": [ + 0.523, + 0.637, + 0.857, + 0.826 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.828, + 0.892, + 0.896 + ], + "angle": 0, + "content": "Figure 2. Demonstration of action space for vision token pruning and fusion. We group each 16 neighboring tokens in a \\(64 \\times 64\\) window and represent the window with two actions: (1) token pruning and (2) fusion. The actions are then applied to the tokens inside this window." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2626" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.099, + 0.088, + 0.873, + 0.333 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.341, + 0.895, + 0.385 + ], + "angle": 0, + "content": "Figure 3. Framework for combining the dynamic token fusion and pruning together with MSA and FFN layer skipping to get DViTMDETR model. We do not show layer skipping in the multimodal network for simplicity. By combining layer skipping together with token pruning and fusion, we tackle redundancy in both across the backbones and multimodal network and the input data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.41, + 0.471, + 0.636 + ], + "angle": 0, + "content": "Reducing the Size of Action Space The amount of vision tokens can be very large especially for large size images given that each token covers \\(16 \\times 16\\) pixels patch. Large action space can be a bottleneck for learning the decision network parameters. To simplify their training, we cluster the set of vision tokens by spatially grouping them as shown in Figure 2. More specifically, we divide the image into \\(M_v \\times M_v\\) non-overlapping windows where each window is represented by \\(64 \\times 64\\) pixels and take a single pruning and fusion action for all the patches in this window. Our action space for pruning and fusion then becomes \\(p_b \\in [0,1]^{2 * M_v * M_v + M_t}\\) where \\(M_v * M_v\\) and \\(M_t\\) represent the number of vision token clusters and text tokens. Since, the number of text tokens is much smaller than the number of vision tokens, we do not modify their action space." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.638, + 0.47, + 0.789 + ], + "angle": 0, + "content": "Discrete Actions from Continuous Predictions In test time, we obtain discrete actions by using a piece-wise function as \\(\\mathbf{a}_{\\mathbf{p}}^{\\mathrm{j}} = 1\\) if \\(p_b^j \\geq 0.5\\), otherwise \\(\\mathbf{a}_{\\mathbf{p}}^{\\mathrm{j}} = 0\\). For \\(\\mathbf{a}_{\\mathbf{p}}^{\\mathrm{j}} = 1\\) we either prune or fuse the corresponding set of vision tokens in a spatial cluster and we keep the tokens for \\(\\mathbf{a}_{\\mathbf{p}}^{\\mathrm{j}} = 0\\). To avoid the conflicts between pruning and fusion, we prioritize pruning over fusion. In other words, if we decide to both prune and fuse a set of vision tokens in a cluster, we prune them and ignore fusion actions since pruning favors further computational efficiency." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.8, + 0.424, + 0.817 + ], + "angle": 0, + "content": "3.3. Dynamic MSA and FFN Layer Skipping" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.469, + 0.868 + ], + "angle": 0, + "content": "In the next step, we propose a method to dynamically skip MSA and FFN layers in the image and language backbones, and multimodal transformer." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Backbones For MSA and FFN layer skipping, we use the same decision network with the token pruning and fusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.41, + 0.892, + 0.514 + ], + "angle": 0, + "content": "actions from Eq. 9 where \\( s_b \\) represents the continuous predictions of the decision network on which MSA and FFN layers should be skipped in the next two encoders of the language and text backbone. As a result, our action space for layer skipping can be represented as \\( s_b \\in [0,1]^8 \\) as we have 4 MSA and 4 FFN layers in two encoders across the two backbones." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.515, + 0.892, + 0.545 + ], + "angle": 0, + "content": "Multimodal Transformer Finally, we integrate a decision network before multimodal transformer as shown below." + }, + { + "type": "equation", + "bbox": [ + 0.579, + 0.551, + 0.892, + 0.571 + ], + "angle": 0, + "content": "\\[\ns _ {f} = \\operatorname {s i g m o i d} \\left(f _ {m} \\left(\\left[ z _ {v} ^ {N}, z _ {t} ^ {N} \\right]; \\theta_ {m}\\right)\\right) \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.575, + 0.892, + 0.664 + ], + "angle": 0, + "content": "where \\( s_f \\) represents the continuous predictions on skipping MSA and FFN layers in the multimodal network. Our action space in this case can be represented as \\( s_f \\in [0,1]^{24} \\) as we have 12 MSA and 12 FFN layers in the 6 encoders and 6 decoders. We note that we have traditional MSA and FFN layers in these encoders and decoders." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.666, + 0.892, + 0.817 + ], + "angle": 0, + "content": "Discrete Actions from Continuous Predictions In test time, we obtain discrete actions by using a piece-wise function as \\(\\mathbf{a}_{\\mathbf{s}}^{\\mathrm{j}} = 1\\) if \\(s_{s}^{j}\\geq 0.5\\), otherwise \\(\\mathbf{a}_{\\mathbf{s}}^{\\mathrm{j}} = 0\\). For \\(\\mathbf{a}_{\\mathbf{s}}^{\\mathrm{j}} = 1\\) we skip the corresponding MSA or FFN layer and use the MSA or FFN layer for \\(\\mathbf{a}_{\\mathbf{s}}^{\\mathrm{j}} = 0\\). We note that we follow the same process to get actions \\(a_{m}\\) for skipping MSA and FFN layers in the multimodal network after getting the predictions \\(s_f\\). We show the combination of the token pruning and fusion together with MSA and FFN layer skipping in Figure 3." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.824, + 0.868, + 0.84 + ], + "angle": 0, + "content": "3.4. Modeling the Reward and Policy Functions" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.848, + 0.677, + 0.862 + ], + "angle": 0, + "content": "3.4.1 Reward Function" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Reward function is a critical component of our algorithm as it needs to reflect what we want to achieve with adaptive" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2627" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.468, + 0.167 + ], + "angle": 0, + "content": "inference. In our method, our goal is to reduce the computational complexity in the inference time to increase run-time speed. As a result, we propose a dual reward function that consists of: (1) target task accuracy and (2) savings in computational complexity." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.168, + 0.468, + 0.197 + ], + "angle": 0, + "content": "Backbones For backbones, we formulate the reward function as" + }, + { + "type": "equation", + "bbox": [ + 0.114, + 0.209, + 0.468, + 0.226 + ], + "angle": 0, + "content": "\\[\n\\mathcal {R} _ {b} = \\sigma * c (d, g) + (1 - \\sigma) * (\\mathcal {P} + \\mathcal {F} + \\mathcal {S}) \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.236, + 0.468, + 0.37 + ], + "angle": 0, + "content": "where \\( c \\) represents the task accuracy given model predictions, \\( d \\), and ground truth, \\( g \\), whereas \\( \\mathcal{P} \\), and \\( \\mathcal{F} \\) represent the ratio of pruned and fused tokens. \\( S \\) represents the ratio of skipped MSA and FFN layers. We note that we assign same reward to skipping an MSA and an FFN layer. One can assign higher reward to MSA layer since it has more computational complexity. On the other hand, \\( \\sigma \\in [0,1] \\) controls the trade-off between the task accuracy and computational efficiency obtained by the adaptive inference." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.372, + 0.468, + 0.417 + ], + "angle": 0, + "content": "Multimodal Network As we do not prune tokens for the multimodal network, we only consider skipping MSA and FFN layers. We formulate the reward function as" + }, + { + "type": "equation", + "bbox": [ + 0.171, + 0.429, + 0.468, + 0.445 + ], + "angle": 0, + "content": "\\[\n\\mathcal {R} _ {f} = \\sigma * c (d, g) + (1 - \\sigma) S. \\tag {12}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.462, + 0.247, + 0.476 + ], + "angle": 0, + "content": "3.4.2 Policy Functions" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.485, + 0.468, + 0.59 + ], + "angle": 0, + "content": "Backbones We model the policy function for the backbones as the multiplication of the probabilities of individual token pruning and fusion actions and repeat it for the layer skipping actions. We represent individual actions with an action-specific Bernoulli distribution. Next, we formulate the policy function for the decision networks for the backbones as" + }, + { + "type": "equation", + "bbox": [ + 0.077, + 0.613, + 0.468, + 0.658 + ], + "angle": 0, + "content": "\\[\n\\pi_ {d} \\left(\\mathbf {a} _ {\\mathbf {s}}, \\mathbf {a} _ {\\mathbf {p}} \\mid z _ {v} ^ {i}, z _ {t} ^ {i}\\right) = \\prod_ {j} s _ {b} ^ {j} ^ {\\mathbf {a} _ {\\mathbf {s}} ^ {\\mathrm {j}}} \\left(1 - s _ {b} ^ {j}\\right) ^ {1 - \\mathbf {a} _ {\\mathbf {s}} ^ {\\mathrm {j}}} + \\prod_ {j} p _ {b} ^ {j} ^ {\\mathbf {a} _ {\\mathbf {p}} ^ {\\mathrm {j}}} \\left(1 - p _ {b} ^ {j}\\right) ^ {1 - \\mathbf {a} _ {\\mathbf {p}} ^ {\\mathrm {j}}}. \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.66, + 0.468, + 0.719 + ], + "angle": 0, + "content": "Multimodal Network Similar to the backbones, we model the policy function for the multimodal network as the multiplication of the probabilities of individual actions represented by Bernoulli distribution as" + }, + { + "type": "equation", + "bbox": [ + 0.115, + 0.731, + 0.468, + 0.767 + ], + "angle": 0, + "content": "\\[\n\\pi_ {m} \\left(\\mathbf {a} _ {\\mathbf {m}} \\mid z _ {v} ^ {N}, z _ {t} ^ {N}\\right) = \\prod_ {j} s _ {f} ^ {j \\mathbf {a} _ {\\mathbf {m}} ^ {\\mathrm {j}}} \\left(1 - s _ {f} ^ {j}\\right) ^ {1 - \\mathbf {a} _ {\\mathbf {m}} ^ {\\mathrm {j}}}. \\tag {14}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.778, + 0.266, + 0.794 + ], + "angle": 0, + "content": "4. Training Procedure" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.802, + 0.216, + 0.818 + ], + "angle": 0, + "content": "4.1. Optimization" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.468, + 0.901 + ], + "angle": 0, + "content": "As we learn discrete actions, we cannot use the reparameterization trick to optimize the objective w.r.t. \\(\\theta_{d}\\). To optimize the parameters \\(\\theta_{d}\\), we need to use model-free reinforcement learning algorithms. Policy gradient [32] is suitable in our scenario as the number of unique actions the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.152 + ], + "angle": 0, + "content": "policy network can choose increases exponentially with the number of tokens and MSA and FFN layers. Together with policy gradients we use the REINFORCE method [32] to optimize the objective w.r.t \\(\\theta_{d}\\) and \\(\\theta_{m}\\) as" + }, + { + "type": "equation", + "bbox": [ + 0.555, + 0.161, + 0.892, + 0.187 + ], + "angle": 0, + "content": "\\[\n\\underset {\\theta_ {d}, \\theta_ {m}} {\\arg \\max } J = \\mathcal {R} _ {b} \\nabla \\log_ {\\pi_ {\\theta_ {d}}} \\left(\\mathbf {a} _ {\\mathbf {s}}, \\mathbf {a} _ {\\mathbf {p}} \\mid z _ {v} ^ {i}, z _ {t} ^ {i}\\right) + \\tag {15}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.633, + 0.189, + 0.836, + 0.209 + ], + "angle": 0, + "content": "\\[\n\\mathcal {R} _ {f} \\nabla l o g _ {\\pi_ {\\theta_ {m}}} (\\mathbf {a _ {m}} | z _ {v} ^ {i = N}, z _ {t} ^ {i = N})\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.216, + 0.892, + 0.291 + ], + "angle": 0, + "content": "where \\(\\nabla log_{\\pi_{\\theta_d}}\\) and \\(\\nabla log_{\\pi_{\\theta_m}}\\) represent the log-likelihood of policy function for the backbones and multimodal network. Next, we substitute the policy functions with Eq. 13 and 14 and take its derivative w.r.t \\(\\theta_d\\) and \\(\\theta_m\\) for updating the weights." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.3, + 0.807, + 0.316 + ], + "angle": 0, + "content": "4.2. Pre-training the Decision Networks" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.323, + 0.892, + 0.43 + ], + "angle": 0, + "content": "After formulating the optimization steps, we pre-train the decision networks on the finetuning dataset while keeping the weights of the backbones and multimodal network frozen. By doing this, we can learn useful policies towards choosing the right decisions for token pruning and fusion together with adaptive layer skipping. To achieve it, we only optimize the objective shown in Eq. 15." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.437, + 0.892, + 0.467 + ], + "angle": 0, + "content": "4.3. Jointly Finetuning the Decision Networks, Backbones and Multimodal Network" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.476, + 0.892, + 0.611 + ], + "angle": 0, + "content": "In the previous step, we learned the parameters of the decision networks \\(\\theta_{d}\\) by executing the decisions with the multimodal network and finding the reward value. Up until this step, the multimodal network has not been updated with the dynamic inference which results in accuracy drop. To avoid it, we propose joint-finetuning step where we finetune both the decision networks and backbones, and multimodal network jointly. As a result, the objective for the backbones and multimodal network parameters becomes:" + }, + { + "type": "equation", + "bbox": [ + 0.522, + 0.621, + 0.891, + 0.647 + ], + "angle": 0, + "content": "\\[\n\\underset {\\theta_ {v}, \\theta_ {t}, \\theta_ {m}} {\\arg \\min } L _ {t} = \\operatorname {T a k L o s s} (d, g | x _ {t}, y _ {t}, \\mathbf {a} _ {\\mathbf {s}}, \\mathbf {a} _ {\\mathbf {p}}, \\mathbf {a} _ {\\mathbf {m}}) \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.654, + 0.892, + 0.684 + ], + "angle": 0, + "content": "On the other hand, the objective for the decision networks remain similar to Eq. 15." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.692, + 0.749, + 0.708 + ], + "angle": 0, + "content": "4.4. Distilling from ViTMDETR" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.715, + 0.892, + 0.79 + ], + "angle": 0, + "content": "To better optimize the model in the joint finetuning step, we make use of the original fixed model, ViTMDETR, that we started with. In this direction, we add an objective to align the ViTMDETR's representations with our dynamic model as" + }, + { + "type": "equation", + "bbox": [ + 0.581, + 0.798, + 0.891, + 0.826 + ], + "angle": 0, + "content": "\\[\n\\underset {\\theta_ {v} \\theta_ {t} \\theta_ {m}} {\\arg \\min } L _ {d} = \\| z _ {t} ^ {i = N} - \\hat {z} _ {t} ^ {i = N} \\| _ {1} + \\tag {17}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.589, + 0.828, + 0.809, + 0.847 + ], + "angle": 0, + "content": "\\[\n\\| z _ {v} ^ {i = N} - \\hat {z} _ {v} ^ {i = N} \\| _ {1} + \\| z _ {m} - \\hat {z} _ {m} \\| _ {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.855, + 0.892, + 0.901 + ], + "angle": 0, + "content": "where \\(\\hat{z}_t^{i=N}\\), \\(\\hat{z}_v^{i=N}\\), and \\(\\hat{z}_m\\) represent the outputs of ViTMDETR after the vision and text backbones and the multimodal network, respectively." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2628" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.138 + ], + "angle": 0, + "content": "In addition to the representation alignment, we also change the ground truth predictions, \\( g \\), with the predictions of the ViTMDETR, \\( \\hat{g} \\), and the task loss becomes" + }, + { + "type": "equation", + "bbox": [ + 0.099, + 0.151, + 0.47, + 0.176 + ], + "angle": 0, + "content": "\\[\n\\underset {\\theta_ {v}, \\theta_ {t}, \\theta_ {m}} {\\arg \\min } L _ {t} = \\operatorname {T a k L o s s} \\left(d, \\hat {g} \\mid x _ {t}, y _ {t}, \\mathbf {a} _ {\\mathbf {s}}, \\mathbf {a} _ {\\mathbf {p}}, \\mathbf {a} _ {\\mathbf {m}}\\right) \\tag {18}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.188, + 0.469, + 0.234 + ], + "angle": 0, + "content": "Our final objective for end-to-end training of the adaptive network then becomes a linear combination of the task loss \\((\\mathcal{L}_t)\\) and distillation loss \\((\\mathcal{L}_d)\\) objectives as" + }, + { + "type": "equation", + "bbox": [ + 0.195, + 0.248, + 0.469, + 0.273 + ], + "angle": 0, + "content": "\\[\n\\underset {\\theta_ {v}, \\theta_ {t}, \\theta_ {m}} {\\arg \\min } \\mathcal {L} = \\mathcal {L} _ {t} + \\mathcal {L} _ {d}. \\tag {19}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.289, + 0.21, + 0.308 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.315, + 0.47, + 0.51 + ], + "angle": 0, + "content": "Pre-training Dataset MDETR performs end-to-end pretraining for a language-conditioned bounding box detection task. To construct a pre-training dataset, it merges several independent vision and language datasets. These datasets are listed as MSCOCO [21], Flickr30k [28], and VisualGenome [16] as they have bounding box annotations of the objects mentioned in the language query. The task in this step is to accurately detect the bounding boxes of the objects mentioned in a language query. For example, given an input query of cat sitting next to a dog on the chair, the task would be to predict bounding boxes of a cat, a dog, and a chair in the image. We use the same pre-training dataset and objectives to MDETR [14] to pre-train ViTMDETR." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.512, + 0.47, + 0.648 + ], + "angle": 0, + "content": "Downstream Tasks/Datasets We finetune the pre-trained model end-to-end on vision and language tasks, including REC, RES and VQA. For REC, we use RefCOCO and RefCOCO+ [15], and RefCOCOg [26] benchmarks. The task in these datasets is to detect the bounding box of the object referred to the language expression. For RES task, we evaluate on the PhraseCut [36] dataset, where, the task is to segment the object associated with the language query. For the VQA, we use GQA benchmark [12]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.648, + 0.471, + 0.784 + ], + "angle": 0, + "content": "Metrics As the evaluation metric, for REC and RES tasks we compute the Jaccard index between predicted and ground-truth bounding boxes. If it is above 0.5, the prediction is considered correct. For the VQA, the task is to predict the correct answer from the given answer categories. We use the top-1 accuracy metric to evaluate models. Lastly, we measure the run-time efficiency in terms of frames per second on a single V100 GPU. Additionally, we use the GFLOPs metrics to evaluate the models." + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.793, + 0.356, + 0.807 + ], + "angle": 0, + "content": "\\(^{1}\\)https://github.com/Lyken17/pytorch-OpCounter" + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.832, + 0.449, + 0.871 + ], + "angle": 0, + "content": "
MDETRGLIPViTMDETR
Pre-training DatasetCOCO+COCO+COCO+
Flickr30k+VG (1.3M)Flickr30k+VG (1.3M)Flickr30k+VG (1.3M)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.114, + 0.883, + 0.432, + 0.897 + ], + "angle": 0, + "content": "Table 1. Pre-training dataset used in our experiments." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.318 + ], + "angle": 0, + "content": "Implementation Details. We build our implementation following the official MDETR repository2. We first replace the CNN vision backbone with a transformer backbone, DeiT [33]. To implement DeiT, we use the timm library3. To utilize ImageNet pre-trained weights, we use \\(384 \\times 384\\) pixels images in both training and test time. This way, our whole architecture mostly consists of transformer layers other than the patch embedding convolutional layer. For pre-training ViTMDETR, we use the batch size of 256 on 8 NVIDIA V100 GPUs. For the transfer learning tasks for ViTMDETR we use a batch size of 8 with 2 NVIDIA V100 GPUs. For D-ViTMDETR, we use batch size of 256 with 8 V100 GPUs in the transfer learning tasks. We note that our dynamic inference method benefits from large training batch size as it reduces the variance in the reward objective." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.319, + 0.892, + 0.514 + ], + "angle": 0, + "content": "Baselines We compare our method to a number of baselines that we designed. Our first baseline represents Random MSA and FFN layer skipping, Random-LS, where we draw skipping probability from a uniform distribution and perform skipping if the sampled probability is higher than a pre-defined threshold. Additionally, we design another baseline, Random-TP+TF, that randomly prunes the tokens given a uniform distribution. Finally, we combine both baselines to get another baseline, Random-LS+TP+TF. In addition to the Random baselines, we develop Stochastic baselines where we decay the likelihood of survival of the tokens, and MSA and FFN layers with the increasing depth. We call this baseline Stochastic-LS+TP+TF." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.516, + 0.892, + 0.652 + ], + "angle": 0, + "content": "In addition to our baselines, we compare our models to MDETR [14] and GLIP [17] models. To be consistent with our set up, we pre-train both our ViTMDETR, and MDETR and GLIP in the same pre-training dataset consisting of 1.3M image-text pairs with ground truth bounding box annotations. as shown in Table 1. Also, we pre-train and finetune all the models on \\(384\\times 384\\) pixels images. Finally, we apply our dynamic inference method to our ViTMDETR model in finetuning tasks and call it D-ViTMDETR." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.664, + 0.593, + 0.678 + ], + "angle": 0, + "content": "5.1. Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.681, + 0.892, + 0.864 + ], + "angle": 0, + "content": "Experiments on Large Model We first perform experiments on our large image and language model, ViTMDETR. This model contains two backbones: (1) DeiT-Base [33] with 86M parameters, (2) RoBERTa-Base [23] with 125M parameters and a multimodal network (DETR) with 18M parameters similar to [14], resulting in 229M parameters model. Next, after pre-training the model, we learn dynamic inference on the downstream tasks and report the results in the Table 2. As shown in the table, we can improve the run-time complexity of MDETR by \\(\\sim 50\\%\\) while achieving \\(\\sim 1\\%\\) higher accuracy. On the other hand, we perform additional ablation studies with the following two" + }, + { + "type": "page_footnote", + "bbox": [ + 0.518, + 0.875, + 0.717, + 0.888 + ], + "angle": 0, + "content": "\\(^{2}\\)https://github.com/ashkamath/mdetr" + }, + { + "type": "page_footnote", + "bbox": [ + 0.518, + 0.888, + 0.806, + 0.901 + ], + "angle": 0, + "content": "3https://github.com/rwrightman/pytorch-image-models" + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.875, + 0.806, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2629" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.099, + 0.089, + 0.872, + 0.235 + ], + "angle": 0, + "content": "
RefCOCORefCOCO+RefCOCOgGQAPhraseCut
valtestAtestBvaltestAtestBvaltestATest-DevTest-StdTestRun-Time Eff. (fps)GFLOPs
MDETR [14]87.088.682.577.281.571.076.977.162.162.057.22850
GLIP [17]87.789.583.078.082.772.477.678.362.662.2-2562
ViTMDETR87.689.383.378.082.572.677.878.162.362.057.52760
Random-LS83.986.179.775.778.968.073.875.158.258.454.13442
Random-TP+TF83.985.979.875.577.667.974.174.958.458.454.23245
Random-LS+TP+TF80.081.875.271.774.864.169.671.455.855.951.34132
Stochastic-LS+TP+TF83.185.078.874.678.067.072.474.357.057.153.64132
D-ViTMDETR-LS87.689.483.278.382.672.877.778.062.462.057.53442
D-ViTMDETR-TP+TF87.689.383.578.082.872.677.778.262.462.057.53245
D-ViTMDETR-LS+TP+TF87.489.283.278.182.572.477.477.761.961.657.341 (↑ 50%)32 (↓ 50%)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.246, + 0.894, + 0.29 + ], + "angle": 0, + "content": "Table 2. Experiments on referring exprehension comprehension (REC) and Visual Question Answering (GQA) benchmarks on the large model we built. Note that ViTMDETR contains \\( {229M} \\) parameters whereas MDETR and GLIP contains \\( {205M} \\) and \\( {231M} \\) parameters. D-ViTMDETR model is built on top of pre-trained ViTMDETR and only introduces \\( \\sim {1M} \\) more parameters,resulting in \\( {230M} \\) parameters." + }, + { + "type": "table", + "bbox": [ + 0.098, + 0.302, + 0.872, + 0.44 + ], + "angle": 0, + "content": "
RefCOCORefCOCO+RefCOCOgGQAPhraseCut
valtestAtestBvaltestAtestBvaltestATest-DevTest-StdTestRun-time Eff. (fps)GFLOPs
MDETR [14]83.985.479.775.079.569.474.674.958.858.654.54014
ViTMDETR84.185.780.075.279.869.874.674.858.858.954.74014
Random-LS81.882.477.171.977.867.072.572.655.856.149.04811
Random-TP+TF81.882.377.371.977.967.272.772.455.956.050.84610
Random-LS+TP+TF79.980.675.469.976.065.670.970.154.054.148.6559
Stochastic-LS+TP+TF80.981.776.170.576.966.471.470.954.855.048.9559
D-ViTMDETR-LS84.185.979.975.579.670.174.974.858.759.154.54811
D-ViTMDETR-TP+TF84.085.979.875.479.670.074.874.658.559.054.54610
D-ViTMDETR-LS+TP+TF83.885.779.675.279.569.974.774.458.358.854.255 (↑ 36%)9 (↓ 36%)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.45, + 0.895, + 0.493 + ], + "angle": 0, + "content": "Table 3. Experiments on referring exprehension comprehension (REC) and Visual Question Answering (GQA) benchmarks on the small models. Note that ViTMDETR and MDETR contain \\(80M\\) and \\(80M\\) parameters. D-ViTMDETR model is built on top of pre-trained ViTMDETR and only introduces \\(\\sim 1M\\) more parameters, resulting in \\(81M\\) parameters." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.519, + 0.47, + 0.594 + ], + "angle": 0, + "content": "components of our method: (1) dynamic token pruning and fusion, (2) adaptive MSA and FFN layer skipping. With dynamic token pruning (TP) and fusion (TF) only, we can reduce the run-time complexity by \\(\\sim 20\\%\\). With adaptive layer skipping (LS), this number goes up to \\(\\sim 30\\%\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.595, + 0.471, + 0.807 + ], + "angle": 0, + "content": "Experiments on Small Model Next, we perform experiments on our small image and language model, ViTMDETR. This model contains the DeiT-Small vision backbone with 22M parameters and CLIP [29] text backbone with 40M parameters together with a multimodal network with 18M parameters resulting in 80M parameters image and language model. After pre-training this model, we learn dynamic inference on the finetuning tasks as shown in Table 3. As shown in the table, we can reduce the run-time complexity of MDETR by \\(\\sim 36\\%\\) with no accuracy drop. On the other hand, in our ablation studies, with dynamic token pruning and fusion only, we can reduce the run-time complexity by \\(\\sim 15\\%\\). By adding dynamic layer skipping, this number goes up to \\(\\sim 36\\%\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.817, + 0.242, + 0.832 + ], + "angle": 0, + "content": "5.2. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Impact of Knowledge Distillation In our ablation studies, we first perform experiments on the impact of knowledge distillation for the optimization of our adaptive model. We show the results in Table 4. As seen in the table, knowledge" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.519, + 0.892, + 0.548 + ], + "angle": 0, + "content": "distillation improves the accuracy of the dynamic model by around \\(\\sim 1\\%\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.549, + 0.892, + 0.625 + ], + "angle": 0, + "content": "Impact of Pretraining the Decision Networks Next, we perform experiments on the impact of pre-training the decision networks. We show the results in Table 5. As seen in the table, pre-training the decision networks is important to maintain the high accuracy of our dynamic model." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.626, + 0.892, + 0.716 + ], + "angle": 0, + "content": "Impact of Window Size for Spatial Clustering In our experiments, we set the window size to \\(64 \\times 64\\) and learn single action for the vision tokens inside the window. We perform experiments with different window sizes and show the results in Table 6 and show that we get the best results with \\(64 \\times 64\\) windows." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.727, + 0.746, + 0.743 + ], + "angle": 0, + "content": "5.3. Analyzing Learned Policies" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.825 + ], + "angle": 0, + "content": "Pruned Tokens Additionally, we visualize the pruned tokens by the decision network in Figure 4. As seen in the figure, the number of tokens that are pruned goes down w.r.t depth of the backbones. This makes sense since we have decreasing number of remaining tokens w.r.t. depth." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Fused Tokens In the next step, we visualize the fusion policies learned by the decision network. In particular, we are interested in how many vision tokens are fused over the increasing number of layers in the backbones. We show the results in Figure 4. As we can see in the figure, the num" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2630" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.14, + 0.089, + 0.83, + 0.165 + ], + "angle": 0, + "content": "
RefCOCORefCOCO+RefCOCOgGQAPhraseCut
valtestAtestBvaltestAtestBvaltestATest-DevTest-StdTest
ViTMDETR87.689.383.378.082.572.677.878.162.362.057.5
D-ViTMDETR (LS+TP+AF)86.988.482.377.281.371.577.077.460.860.655.9
D-ViTMDETR (LS+TP+AF) + KD87.489.283.278.182.572.477.477.761.961.657.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.29, + 0.174, + 0.68, + 0.189 + ], + "angle": 0, + "content": "Table 4. Ablation studies on the impact of knowledge distillation." + }, + { + "type": "table", + "bbox": [ + 0.139, + 0.202, + 0.83, + 0.273 + ], + "angle": 0, + "content": "
RefCOCORefCOCO+RefCOCOgGQAPhraseCut
valtestAtestBvaltestAtestBvaltestATest-DevTest-StdTest
Without Pre-training77.479.273.168.172.562.667.467.751.451.147.0
With Pre-training84.986.780.675.680.069.174.975.258.958.654.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.26, + 0.282, + 0.71, + 0.297 + ], + "angle": 0, + "content": "Table 5. Ablation studies on the impact of pretraining the decision network." + }, + { + "type": "table", + "bbox": [ + 0.122, + 0.32, + 0.428, + 0.396 + ], + "angle": 0, + "content": "
Window SizeRefCOCORefCOCOgRefCOCO+
16x1684.574.873.0
32x3285.876.474.6
64x6487.478.177.4
128x12887.077.676.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.406, + 0.471, + 0.435 + ], + "angle": 0, + "content": "Table 6. Impact of window size on vision token clustering on the val split of RefCOCO, RefCOCOg, and RefCOCO+." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.449, + 0.47, + 0.511 + ], + "angle": 0, + "content": "ber of vision tokens that are fused with the text tokens goes down w.r.t depth of the backbones. On the other hand, we can see that on average we fuse \\(\\sim 30\\%\\) of vision tokens with the language tokens across the processing in backbones." + }, + { + "type": "image", + "bbox": [ + 0.099, + 0.528, + 0.27, + 0.657 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.284, + 0.528, + 0.451, + 0.656 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.673, + 0.47, + 0.703 + ], + "angle": 0, + "content": "Figure 4. Probability of token pruning (Left) and fusion (Right) over depth for the RefCOCO experiments." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.719, + 0.47, + 0.825 + ], + "angle": 0, + "content": "Skipped MSA and FFN layers Next, we analyze the policies learned by the decision networks towards skipping MSA and FFN layers in both vision and text backbone as well as the multimodal network. We note that across the 12 encoders in the backbones, we learn decisions to potentially skip 20 MSA and FFN layers and 12 MSA and FFN layers in the multimodal network." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.471, + 0.903 + ], + "angle": 0, + "content": "As seen in Figure 5, the skipping operations for MSA and FFN layers are distributed in a way that later MSA and FFN layers especially in the backbones are skipped with higher probability. This is similar to skipping operations with CNNs where shallow layers are more important than" + }, + { + "type": "image", + "bbox": [ + 0.539, + 0.325, + 0.691, + 0.442 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.7, + 0.326, + 0.857, + 0.442 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.539, + 0.452, + 0.693, + 0.567 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.7, + 0.452, + 0.856, + 0.567 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.585, + 0.895, + 0.643 + ], + "angle": 0, + "content": "Figure 5. MSA and FFN layer skipping probability distribution in vision backbone (Top Left), text backbone (Top Right), and multimodal network (Bottom) that consists of 6 encoder and decoder layers. We show the results from RefCOCO experiments." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.666, + 0.895, + 0.713 + ], + "angle": 0, + "content": "deep layers as they provide critical low-level abstraction of objects [34]. On the other hand, there is not a clear pattern with the skipping operations in the multimodal network." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.725, + 0.62, + 0.74 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.894, + 0.903 + ], + "angle": 0, + "content": "We propose a dynamic inference method for the vision and language models. Our method includes learning adaptive policies to skip MSA and FFN layers across vision and language backbones and multimodal network. Additionally, it dynamically prunes tokens from different modalities and fuse tokens at different stages of backbones. We then train our model on downstream vision and language tasks. In our experiments on REC, RES and VQA we show that we can improve the run-time complexity of MDETR, and GLIP by up to \\(\\sim 50\\%\\) with only maximum \\(\\sim 0.3\\%\\) accuracy drop." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.958 + ], + "angle": 0, + "content": "2631" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.157 + ], + "angle": 0, + "content": "[1] Arian Bakhtiarnia, Qi Zhang, and Alexandros Iosifidis. Multi-exit vision transformer for dynamic inference. arXiv preprint arXiv:2106.15183, 2021. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.157, + 0.472, + 0.225 + ], + "angle": 0, + "content": "[2] Nicolas Carion, Francisco Massa, Gabriel Synnaeve, Nicolas Usunier, Alexander Kirillov, and Sergey Zagoruyko. End-to-end object detection with transformers. 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For example, recent image and language models with more than 200M parameters have been proposed to learn visual grounding in the pre-training step and show impressive results on downstream vision and language tasks. On the other hand, there exists a large amount of computational redundancy in these large models which skips their run-time efficiency. To address this problem, we propose dynamic inference for grounding based vision and language models conditioned on the input image-text pair. We first design an approach to dynamically skip multihead self-attention and feed forward network layers across two backbones and multimodal network. Additionally, we propose dynamic token pruning and fusion for two backbones. In particular, we remove redundant tokens at different levels of the backbones and fuse the image tokens with the language tokens in an adaptive manner. To learn policies for dynamic inference, we train agents using reinforcement learning. In this direction, we replace the CNN backbone in a recent grounding-based vision and language model, MDETR, with a vision transformer and call it ViTMDETR. Then, we apply our dynamic inference method to ViTMDETR, called D-ViTDMETR, and perform experiments on image-language tasks. Our results show that we can improve the run-time efficiency of the state-of-the-art models MDETR and GLIP by up to $\sim 50\%$ on Referring Expression Comprehension and Segmentation, and VQA with only maximum $\sim 0.3\%$ accuracy drop. + +# 1. Introduction + +Significant progress has been made in the development of image and language models attributed to: (1) emergence of transformers for different modalities [6, 13], and (2) large scale pre-training paradigms [4, 14, 17, 24, 29, 43, 44]. In particular, with the very large scale pre-training of image and language models, large number of parameters and computations are allocated for processing input image-text pair. Specifically, the number of parameters of recent vision and + +![](images/4754cd6cb827ea9bfdd884215b0d4bba8cd50fe8376c9f53bb85f74c83cd17d5.jpg) + +![](images/5f8f92370dc977c82a820ba28526b69351a282632ac8fefd7c2040819e2f27ec.jpg) + +![](images/c5983d4e14089244e8de323e77d9321f1fbcd9b27ce0bca98f56e582841e7c92.jpg) +Figure 1. Accuracy vs frames per second comparison of the large (Top Left) and small (Top Right) models and accuracy vs GLOPs comparison of the large (Bottom Left) and small (Bottom Right) models. D-ViTMDETR outperforms MDETR, GLIP and our ViT-MDETR model in both frames per second and GFLOPs metrics while maintaining high accuracy. + +![](images/c18d14a7b36d3f3291987293a9656a0215139c1cf4756ea97b22fbd8c1ffc877.jpg) + +language models can be more than 200M [14, 17, 44], resulting in low run-time efficiency. This problem with the single-modality transformers has been tackled by several studies before [27, 30, 37]. Such computational complexity is further amplified in multimodal networks often building on multiple transformer models. As a result, reducing the run-time complexity of the multimodal networks can be very beneficial for the downstream tasks. Existing methods including pruning [20], knowledge distillation [10, 33] and quantization [39] can potentially be extended toward this goal. However, they show significant performance drop ( $\geq 1\%$ ) at $\geq 50\%$ compression rates and these methods are mostly designed for parameter reduction not for run-time speed. As a result, we propose dynamic inference with the large image and language mod + +els mainly to achieve two goals: (1) drastically reduce runtime complexity, and (2) maintain their high accuracy. Towards these goals, in the first step, we analyze the classic architectural choices for the recent image and language models. A typical image and language model consists of a vision encoder (a CNN or a vision transformer), a text encoder (transformer), and a multimodal transformer (fusion network). Inspired by MDETR [14], we build a vision and language model consisting of vision and language transformer and DETR-like multimodal network and call it ViTMDETR. The transformer modules consist of a multi-head self attention (MSA) and feed forward network (FFN) blocks which are experimentally found to be computationally expensive modules in inference-time. It is also known that computationally complexity of transformer MSA module goes up quadratically w.r.t number of tokens. The number of tokens and the computational complexity gets further amplified with inclusion of multimodal inputs and related modules. + +For these reasons, with our D-ViTMDETR model we propose to dynamically prune input tokens from multiple modalities across the transformer backbones and fuse vision tokens adaptively with the text tokens to improve the accuracy. This way, we can reduce the complexity quadratically. Additionally, we adaptively skip the computationally expensive MSA and FFN layers across the two backbones and the multimodal network to further improve run-time efficiency. To learn dynamic policies, we train decision networks using the policy-gradients based reinforcement learning algorithm and distill the knowledge from ViTMDETR to better optimize D-ViTMDETR. + +In this research work, our contributions are as below: + +- We introduce an MDETR-inspired transformer-based model ViTMDETR for grounding based vision and language tasks. +- We propose a novel method to learn dynamic token pruning and fusion actions to reduce computational complexity using reinforcement learning. Additionally, we train the same agents to learn MSA and FFN layer skipping throughout our vision and language model to further reduce complexity. +- For better optimization, we align the representations and predictions of D-ViTMDETR with the representations and predictions of the ViTMDETR model. +- We perform experiments with both our ViTMDETR and D-ViTMDETR models on several image and language benchmarks for Referring Expression Comprehension (REC) and Segmentation (RES), and VQA tasks. With our dynamic model, D-ViTMDETR, we can improve the run-time efficiency of the state-of-the-art models MDETR [14] and GLIP [17] by up to $\sim 50\%$ on Referring Expression Comprehension and + +Segmentation, and VQA with only maximum $\sim 0.3\%$ accuracy drop as seen in Figure 1. + +# 2. Related Works + +Grounding Based Image and Language Models We can categorize existing grounding based image and language models into two categories: (1) two-stage and (2) single-stage. Two-stage methods [4, 24, 42] rely on off-the-shelf object detectors to get object proposals and then process the language query for the task of interest. On the other hand, single-stage methods [3, 5, 7, 14, 17, 40, 44] avoid using a separate off-the-shelf object detector and perform end-to-end training for detecting the referred object, reducing the computational complexity of the two-stage methods. The most recent vision and language models [5, 14, 17, 18, 38] utilize large-scale transformers to improve the accuracy of the previous models with CNN backbones [3, 40]. Other recent works [19, 29, 31] including CLIP [29] have developed image and language models trained on large-scale data with high-level image-to-text contrastive learning objective. + +Dynamic Inference with Transformers Dynamic inference with vision transformers have been mostly studied on single modality data. Wang et al. [35] proposed to leverage the redundancy in the image space to assign adaptive number of patches to each image. Other works [30,37,41] used adaptive number of tokens conditioned on the input. These studies exploit the redundancy on the input (image and tokens) to transformer encoders. On the other hand, depth-adaptive inference for transformers showed strong improvements [1,8,11,22]. Next, [27] performs conditional inference on the image space, in the attention heads and FFN components for the task of image recognition. However, there has been no dynamic method designed for multimodal tasks. Different from this studies, our study focuses on the vision and language models for the vision and language tasks. Since the amount of computation in the vision and language models will be drastically larger than the single-modality tasks, we can expect further gains by using dynamic inference on the vision and language models. In addition to MSA and FFN layer skipping across the backbones and multimodal network, we perform dynamic token pruning for text and vision tokens and adaptively fuse vision tokens with text tokens. + +# 3. Proposed Method + +# 3.1. Building ViTMDETR + +In our vision and language model, we have a vision encoder $f_{v}$ and text encoder $f_{t}$ parameterized by $\theta_v$ and $\theta_t$ that outputs representations $z_{v}\in \mathbb{R}^{v}$ and $z_{t}\in \mathbb{R}^{t}$ as + +$$ +z _ {v} ^ {i = N} = f _ {v} \left(x _ {v}; \theta_ {v}\right), \quad z _ {t} ^ {i = N} = f _ {t} \left(x _ {t}; \theta_ {t}\right). \tag {1} +$$ + +where $N$ represents the number of encoders. The modality-specific representations are then concatenated and passed to a third-stage multimodal network, $f_{m}$ , parameterized by $\theta_{m}$ as + +$$ +z _ {m} = f _ {m} \left(\left[ z _ {v} ^ {i = N}, z _ {t} ^ {i = N} \right]; \theta_ {m}\right) \tag {2} +$$ + +where $z_{m}\in \mathbb{R}^{m}$ represents output of multimodal network. We then process $z_{m}$ with an MLP layer to get task-specific predictions, i.e., referring expression comprehension (REC) and VQA. Given this multimodal network with list of parameters $\theta = [\theta_v,\theta_t,\theta_m]$ , our goal is to introduce adaptivity in processing the modalities through vision and text backbones and multimodal network. + +Text Backbone The text transformer first projects raw language data to word embeddings and sums them with the positional embedding formulated as + +$$ +z _ {t} ^ {i = 0} = e _ {t} \left(x _ {t}\right) + p _ {t} \left(x _ {t}\right) \tag {3} +$$ + +where, for a given input token $x_{t}$ , $e_{t}$ and $p_{t}$ represent the word and positional embedding functions. + +Next, the transformer processes the input embeddings $z_{t}^{i = 0}$ by $N$ encoders where each encoder consists of MSA, layer norm (LN), GELU [9], and FFN layers. Operations in a transformer encoder can be formulated as + +$$ +z _ {t} ^ {i} = M S A _ {t} \left(L N _ {t} \left(z _ {t} ^ {i}\right)\right) + z _ {t} ^ {i}, \tag {4} +$$ + +$$ +z _ {t} ^ {i + 1} = F F N _ {t} \left(L N _ {t} \left(z _ {t} ^ {i}\right)\right) + z _ {t} ^ {i}. \tag {5} +$$ + +We note that we can skip the MSA or FFN layers together with LN layer without any modification to the architecture. This will be useful for our dynamic inference method. + +Vision Backbone The vision transformer has a convolutional layer, $e_v$ , to divide the input image into patches and learn patch representations. Patch embedding is then summed with the positional embedding, $p_v$ as + +$$ +z _ {v} ^ {i = 0} = e _ {v} \left(x _ {v}\right) + p _ {v} \left(x _ {v}\right). \tag {6} +$$ + +Next, the vision transformer processes the input embedding $z_{v}^{i = 0}$ by $N$ encoders with similar components to the text transformer encoder. We can formulate the operations in a vision transformer encoder as + +$$ +z _ {v} ^ {i} = M S A _ {v} \left(L N _ {v} \left(z _ {v} ^ {i}\right)\right) + z _ {v} ^ {i}, \tag {7} +$$ + +$$ +z _ {v} ^ {i + 1} = F F N _ {v} \left(L N _ {v} \left(z _ {v} ^ {i}\right)\right) + z _ {v} ^ {i}. \tag {8} +$$ + +Similarly to the text transformer, we can skip the MSA or FFN layers without any modification to the architecture. + +Multimodal Transformer We then pass the concatenated representations $[z_t^{i=N}, z_v^{i=N}]$ to a multimodal transformer. MDETR uses a DETR-based transformer [2] to output + +boundong box predictions for the given multimodal representations. For the REC task, we choose the bounding box predictions with the highest confidence score. For VQA, we do not output bounding boxes; instead, we output class probabilities for different answers. With DETR, we can use a different number of encoders and decoders on the input representations. In this study, we maintain the same structure with the DETR in the MDETR model for the multimodal transformer and use 6 encoders and 6 decoders with traditional transformer MSA and FFN layers on which we can perform skipping without any modification. + +# 3.2. Dynamic Token Pruning and Fusion + +To achieve dynamic inference, we first propose an approach to prune redundant multimodal tokens and fuse tokens adaptively. We note that we only fuse selected vision tokens with the text tokens and process the fused vision tokens and text tokens with the text backbone. We follow this strategy as pre-trained language transformers are known to generalize to image modality [25]. In this direction, we place a decision network on after every two encoders of the backbones. The decision network provides output for the token pruning and fusion as + +$$ +p _ {b}, s _ {b} = \operatorname {s i g m o i d} \left(f _ {d} \left(\left[ z _ {v} ^ {i}, z _ {t} ^ {i} \right]; \theta_ {d}\right)\right) \tag {9} +$$ + +where $p_b$ represents the continuous predictions on token fusion and pruning across the two backbones whereas $\theta_d$ represent the decision network parameters. On the other hand, $s_b$ represents the actions for MSA and FFN layer skipping that we detail in the next section. We use a single dense layer for the decision network. Note that the number of tokens from each backbone can get large depending on the size of the image and text. As a result, it can be very hard to optimize the decision network to provide actions for many tokens. + +![](images/6bfb0d8583e3a26d0efa269197924fceb2b20951f7d10eadc7126b612bc02931.jpg) +Figure 2. Demonstration of action space for vision token pruning and fusion. We group each 16 neighboring tokens in a $64 \times 64$ window and represent the window with two actions: (1) token pruning and (2) fusion. The actions are then applied to the tokens inside this window. + +![](images/8d3392447662aacd2a52ccc5e7ef7a771c3dcec2504d7a9532f59e587e23cd19.jpg) +Figure 3. Framework for combining the dynamic token fusion and pruning together with MSA and FFN layer skipping to get DViTMDETR model. We do not show layer skipping in the multimodal network for simplicity. By combining layer skipping together with token pruning and fusion, we tackle redundancy in both across the backbones and multimodal network and the input data. + +Reducing the Size of Action Space The amount of vision tokens can be very large especially for large size images given that each token covers $16 \times 16$ pixels patch. Large action space can be a bottleneck for learning the decision network parameters. To simplify their training, we cluster the set of vision tokens by spatially grouping them as shown in Figure 2. More specifically, we divide the image into $M_v \times M_v$ non-overlapping windows where each window is represented by $64 \times 64$ pixels and take a single pruning and fusion action for all the patches in this window. Our action space for pruning and fusion then becomes $p_b \in [0,1]^{2 * M_v * M_v + M_t}$ where $M_v * M_v$ and $M_t$ represent the number of vision token clusters and text tokens. Since, the number of text tokens is much smaller than the number of vision tokens, we do not modify their action space. + +Discrete Actions from Continuous Predictions In test time, we obtain discrete actions by using a piece-wise function as $\mathbf{a}_{\mathbf{p}}^{\mathrm{j}} = 1$ if $p_b^j \geq 0.5$ , otherwise $\mathbf{a}_{\mathbf{p}}^{\mathrm{j}} = 0$ . For $\mathbf{a}_{\mathbf{p}}^{\mathrm{j}} = 1$ we either prune or fuse the corresponding set of vision tokens in a spatial cluster and we keep the tokens for $\mathbf{a}_{\mathbf{p}}^{\mathrm{j}} = 0$ . To avoid the conflicts between pruning and fusion, we prioritize pruning over fusion. In other words, if we decide to both prune and fuse a set of vision tokens in a cluster, we prune them and ignore fusion actions since pruning favors further computational efficiency. + +# 3.3. Dynamic MSA and FFN Layer Skipping + +In the next step, we propose a method to dynamically skip MSA and FFN layers in the image and language backbones, and multimodal transformer. + +Backbones For MSA and FFN layer skipping, we use the same decision network with the token pruning and fusion + +actions from Eq. 9 where $s_b$ represents the continuous predictions of the decision network on which MSA and FFN layers should be skipped in the next two encoders of the language and text backbone. As a result, our action space for layer skipping can be represented as $s_b \in [0,1]^8$ as we have 4 MSA and 4 FFN layers in two encoders across the two backbones. + +Multimodal Transformer Finally, we integrate a decision network before multimodal transformer as shown below. + +$$ +s _ {f} = \operatorname {s i g m o i d} \left(f _ {m} \left(\left[ z _ {v} ^ {N}, z _ {t} ^ {N} \right]; \theta_ {m}\right)\right) \tag {10} +$$ + +where $s_f$ represents the continuous predictions on skipping MSA and FFN layers in the multimodal network. Our action space in this case can be represented as $s_f \in [0,1]^{24}$ as we have 12 MSA and 12 FFN layers in the 6 encoders and 6 decoders. We note that we have traditional MSA and FFN layers in these encoders and decoders. + +Discrete Actions from Continuous Predictions In test time, we obtain discrete actions by using a piece-wise function as $\mathbf{a}_{\mathbf{s}}^{\mathrm{j}} = 1$ if $s_{s}^{j}\geq 0.5$ , otherwise $\mathbf{a}_{\mathbf{s}}^{\mathrm{j}} = 0$ . For $\mathbf{a}_{\mathbf{s}}^{\mathrm{j}} = 1$ we skip the corresponding MSA or FFN layer and use the MSA or FFN layer for $\mathbf{a}_{\mathbf{s}}^{\mathrm{j}} = 0$ . We note that we follow the same process to get actions $a_{m}$ for skipping MSA and FFN layers in the multimodal network after getting the predictions $s_f$ . We show the combination of the token pruning and fusion together with MSA and FFN layer skipping in Figure 3. + +# 3.4. Modeling the Reward and Policy Functions + +# 3.4.1 Reward Function + +Reward function is a critical component of our algorithm as it needs to reflect what we want to achieve with adaptive + +inference. In our method, our goal is to reduce the computational complexity in the inference time to increase run-time speed. As a result, we propose a dual reward function that consists of: (1) target task accuracy and (2) savings in computational complexity. + +Backbones For backbones, we formulate the reward function as + +$$ +\mathcal {R} _ {b} = \sigma * c (d, g) + (1 - \sigma) * (\mathcal {P} + \mathcal {F} + \mathcal {S}) \tag {11} +$$ + +where $c$ represents the task accuracy given model predictions, $d$ , and ground truth, $g$ , whereas $\mathcal{P}$ , and $\mathcal{F}$ represent the ratio of pruned and fused tokens. $S$ represents the ratio of skipped MSA and FFN layers. We note that we assign same reward to skipping an MSA and an FFN layer. One can assign higher reward to MSA layer since it has more computational complexity. On the other hand, $\sigma \in [0,1]$ controls the trade-off between the task accuracy and computational efficiency obtained by the adaptive inference. + +Multimodal Network As we do not prune tokens for the multimodal network, we only consider skipping MSA and FFN layers. We formulate the reward function as + +$$ +\mathcal {R} _ {f} = \sigma * c (d, g) + (1 - \sigma) S. \tag {12} +$$ + +# 3.4.2 Policy Functions + +Backbones We model the policy function for the backbones as the multiplication of the probabilities of individual token pruning and fusion actions and repeat it for the layer skipping actions. We represent individual actions with an action-specific Bernoulli distribution. Next, we formulate the policy function for the decision networks for the backbones as + +$$ +\pi_ {d} \left(\mathbf {a} _ {\mathbf {s}}, \mathbf {a} _ {\mathbf {p}} \mid z _ {v} ^ {i}, z _ {t} ^ {i}\right) = \prod_ {j} s _ {b} ^ {j} ^ {\mathbf {a} _ {\mathbf {s}} ^ {\mathrm {j}}} \left(1 - s _ {b} ^ {j}\right) ^ {1 - \mathbf {a} _ {\mathbf {s}} ^ {\mathrm {j}}} + \prod_ {j} p _ {b} ^ {j} ^ {\mathbf {a} _ {\mathbf {p}} ^ {\mathrm {j}}} \left(1 - p _ {b} ^ {j}\right) ^ {1 - \mathbf {a} _ {\mathbf {p}} ^ {\mathrm {j}}}. \tag {13} +$$ + +Multimodal Network Similar to the backbones, we model the policy function for the multimodal network as the multiplication of the probabilities of individual actions represented by Bernoulli distribution as + +$$ +\pi_ {m} \left(\mathbf {a} _ {\mathbf {m}} \mid z _ {v} ^ {N}, z _ {t} ^ {N}\right) = \prod_ {j} s _ {f} ^ {j \mathbf {a} _ {\mathbf {m}} ^ {\mathrm {j}}} \left(1 - s _ {f} ^ {j}\right) ^ {1 - \mathbf {a} _ {\mathbf {m}} ^ {\mathrm {j}}}. \tag {14} +$$ + +# 4. Training Procedure + +# 4.1. Optimization + +As we learn discrete actions, we cannot use the reparameterization trick to optimize the objective w.r.t. $\theta_{d}$ . To optimize the parameters $\theta_{d}$ , we need to use model-free reinforcement learning algorithms. Policy gradient [32] is suitable in our scenario as the number of unique actions the + +policy network can choose increases exponentially with the number of tokens and MSA and FFN layers. Together with policy gradients we use the REINFORCE method [32] to optimize the objective w.r.t $\theta_{d}$ and $\theta_{m}$ as + +$$ +\underset {\theta_ {d}, \theta_ {m}} {\arg \max } J = \mathcal {R} _ {b} \nabla \log_ {\pi_ {\theta_ {d}}} \left(\mathbf {a} _ {\mathbf {s}}, \mathbf {a} _ {\mathbf {p}} \mid z _ {v} ^ {i}, z _ {t} ^ {i}\right) + \tag {15} +$$ + +$$ +\mathcal {R} _ {f} \nabla l o g _ {\pi_ {\theta_ {m}}} (\mathbf {a _ {m}} | z _ {v} ^ {i = N}, z _ {t} ^ {i = N}) +$$ + +where $\nabla log_{\pi_{\theta_d}}$ and $\nabla log_{\pi_{\theta_m}}$ represent the log-likelihood of policy function for the backbones and multimodal network. Next, we substitute the policy functions with Eq. 13 and 14 and take its derivative w.r.t $\theta_d$ and $\theta_m$ for updating the weights. + +# 4.2. Pre-training the Decision Networks + +After formulating the optimization steps, we pre-train the decision networks on the finetuning dataset while keeping the weights of the backbones and multimodal network frozen. By doing this, we can learn useful policies towards choosing the right decisions for token pruning and fusion together with adaptive layer skipping. To achieve it, we only optimize the objective shown in Eq. 15. + +# 4.3. Jointly Finetuning the Decision Networks, Backbones and Multimodal Network + +In the previous step, we learned the parameters of the decision networks $\theta_{d}$ by executing the decisions with the multimodal network and finding the reward value. Up until this step, the multimodal network has not been updated with the dynamic inference which results in accuracy drop. To avoid it, we propose joint-finetuning step where we finetune both the decision networks and backbones, and multimodal network jointly. As a result, the objective for the backbones and multimodal network parameters becomes: + +$$ +\underset {\theta_ {v}, \theta_ {t}, \theta_ {m}} {\arg \min } L _ {t} = \operatorname {T a k L o s s} (d, g | x _ {t}, y _ {t}, \mathbf {a} _ {\mathbf {s}}, \mathbf {a} _ {\mathbf {p}}, \mathbf {a} _ {\mathbf {m}}) \tag {16} +$$ + +On the other hand, the objective for the decision networks remain similar to Eq. 15. + +# 4.4. Distilling from ViTMDETR + +To better optimize the model in the joint finetuning step, we make use of the original fixed model, ViTMDETR, that we started with. In this direction, we add an objective to align the ViTMDETR's representations with our dynamic model as + +$$ +\underset {\theta_ {v} \theta_ {t} \theta_ {m}} {\arg \min } L _ {d} = \| z _ {t} ^ {i = N} - \hat {z} _ {t} ^ {i = N} \| _ {1} + \tag {17} +$$ + +$$ +\| z _ {v} ^ {i = N} - \hat {z} _ {v} ^ {i = N} \| _ {1} + \| z _ {m} - \hat {z} _ {m} \| _ {1} +$$ + +where $\hat{z}_t^{i=N}$ , $\hat{z}_v^{i=N}$ , and $\hat{z}_m$ represent the outputs of ViTMDETR after the vision and text backbones and the multimodal network, respectively. + +In addition to the representation alignment, we also change the ground truth predictions, $g$ , with the predictions of the ViTMDETR, $\hat{g}$ , and the task loss becomes + +$$ +\underset {\theta_ {v}, \theta_ {t}, \theta_ {m}} {\arg \min } L _ {t} = \operatorname {T a k L o s s} \left(d, \hat {g} \mid x _ {t}, y _ {t}, \mathbf {a} _ {\mathbf {s}}, \mathbf {a} _ {\mathbf {p}}, \mathbf {a} _ {\mathbf {m}}\right) \tag {18} +$$ + +Our final objective for end-to-end training of the adaptive network then becomes a linear combination of the task loss $(\mathcal{L}_t)$ and distillation loss $(\mathcal{L}_d)$ objectives as + +$$ +\underset {\theta_ {v}, \theta_ {t}, \theta_ {m}} {\arg \min } \mathcal {L} = \mathcal {L} _ {t} + \mathcal {L} _ {d}. \tag {19} +$$ + +# 5. Experiments + +Pre-training Dataset MDETR performs end-to-end pretraining for a language-conditioned bounding box detection task. To construct a pre-training dataset, it merges several independent vision and language datasets. These datasets are listed as MSCOCO [21], Flickr30k [28], and VisualGenome [16] as they have bounding box annotations of the objects mentioned in the language query. The task in this step is to accurately detect the bounding boxes of the objects mentioned in a language query. For example, given an input query of cat sitting next to a dog on the chair, the task would be to predict bounding boxes of a cat, a dog, and a chair in the image. We use the same pre-training dataset and objectives to MDETR [14] to pre-train ViTMDETR. + +Downstream Tasks/Datasets We finetune the pre-trained model end-to-end on vision and language tasks, including REC, RES and VQA. For REC, we use RefCOCO and RefCOCO+ [15], and RefCOCOg [26] benchmarks. The task in these datasets is to detect the bounding box of the object referred to the language expression. For RES task, we evaluate on the PhraseCut [36] dataset, where, the task is to segment the object associated with the language query. For the VQA, we use GQA benchmark [12]. + +Metrics As the evaluation metric, for REC and RES tasks we compute the Jaccard index between predicted and ground-truth bounding boxes. If it is above 0.5, the prediction is considered correct. For the VQA, the task is to predict the correct answer from the given answer categories. We use the top-1 accuracy metric to evaluate models. Lastly, we measure the run-time efficiency in terms of frames per second on a single V100 GPU. Additionally, we use the GFLOPs metrics to evaluate the models. + +
MDETRGLIPViTMDETR
Pre-training DatasetCOCO+COCO+COCO+
Flickr30k+VG (1.3M)Flickr30k+VG (1.3M)Flickr30k+VG (1.3M)
+ +Table 1. Pre-training dataset used in our experiments. + +Implementation Details. We build our implementation following the official MDETR repository2. We first replace the CNN vision backbone with a transformer backbone, DeiT [33]. To implement DeiT, we use the timm library3. To utilize ImageNet pre-trained weights, we use $384 \times 384$ pixels images in both training and test time. This way, our whole architecture mostly consists of transformer layers other than the patch embedding convolutional layer. For pre-training ViTMDETR, we use the batch size of 256 on 8 NVIDIA V100 GPUs. For the transfer learning tasks for ViTMDETR we use a batch size of 8 with 2 NVIDIA V100 GPUs. For D-ViTMDETR, we use batch size of 256 with 8 V100 GPUs in the transfer learning tasks. We note that our dynamic inference method benefits from large training batch size as it reduces the variance in the reward objective. + +Baselines We compare our method to a number of baselines that we designed. Our first baseline represents Random MSA and FFN layer skipping, Random-LS, where we draw skipping probability from a uniform distribution and perform skipping if the sampled probability is higher than a pre-defined threshold. Additionally, we design another baseline, Random-TP+TF, that randomly prunes the tokens given a uniform distribution. Finally, we combine both baselines to get another baseline, Random-LS+TP+TF. In addition to the Random baselines, we develop Stochastic baselines where we decay the likelihood of survival of the tokens, and MSA and FFN layers with the increasing depth. We call this baseline Stochastic-LS+TP+TF. + +In addition to our baselines, we compare our models to MDETR [14] and GLIP [17] models. To be consistent with our set up, we pre-train both our ViTMDETR, and MDETR and GLIP in the same pre-training dataset consisting of 1.3M image-text pairs with ground truth bounding box annotations. as shown in Table 1. Also, we pre-train and finetune all the models on $384\times 384$ pixels images. Finally, we apply our dynamic inference method to our ViTMDETR model in finetuning tasks and call it D-ViTMDETR. + +# 5.1. Results + +Experiments on Large Model We first perform experiments on our large image and language model, ViTMDETR. This model contains two backbones: (1) DeiT-Base [33] with 86M parameters, (2) RoBERTa-Base [23] with 125M parameters and a multimodal network (DETR) with 18M parameters similar to [14], resulting in 229M parameters model. Next, after pre-training the model, we learn dynamic inference on the downstream tasks and report the results in the Table 2. As shown in the table, we can improve the run-time complexity of MDETR by $\sim 50\%$ while achieving $\sim 1\%$ higher accuracy. On the other hand, we perform additional ablation studies with the following two + +
RefCOCORefCOCO+RefCOCOgGQAPhraseCut
valtestAtestBvaltestAtestBvaltestATest-DevTest-StdTestRun-Time Eff. (fps)GFLOPs
MDETR [14]87.088.682.577.281.571.076.977.162.162.057.22850
GLIP [17]87.789.583.078.082.772.477.678.362.662.2-2562
ViTMDETR87.689.383.378.082.572.677.878.162.362.057.52760
Random-LS83.986.179.775.778.968.073.875.158.258.454.13442
Random-TP+TF83.985.979.875.577.667.974.174.958.458.454.23245
Random-LS+TP+TF80.081.875.271.774.864.169.671.455.855.951.34132
Stochastic-LS+TP+TF83.185.078.874.678.067.072.474.357.057.153.64132
D-ViTMDETR-LS87.689.483.278.382.672.877.778.062.462.057.53442
D-ViTMDETR-TP+TF87.689.383.578.082.872.677.778.262.462.057.53245
D-ViTMDETR-LS+TP+TF87.489.283.278.182.572.477.477.761.961.657.341 (↑ 50%)32 (↓ 50%)
+ +Table 2. Experiments on referring exprehension comprehension (REC) and Visual Question Answering (GQA) benchmarks on the large model we built. Note that ViTMDETR contains ${229M}$ parameters whereas MDETR and GLIP contains ${205M}$ and ${231M}$ parameters. D-ViTMDETR model is built on top of pre-trained ViTMDETR and only introduces $\sim {1M}$ more parameters,resulting in ${230M}$ parameters. + +
RefCOCORefCOCO+RefCOCOgGQAPhraseCut
valtestAtestBvaltestAtestBvaltestATest-DevTest-StdTestRun-time Eff. (fps)GFLOPs
MDETR [14]83.985.479.775.079.569.474.674.958.858.654.54014
ViTMDETR84.185.780.075.279.869.874.674.858.858.954.74014
Random-LS81.882.477.171.977.867.072.572.655.856.149.04811
Random-TP+TF81.882.377.371.977.967.272.772.455.956.050.84610
Random-LS+TP+TF79.980.675.469.976.065.670.970.154.054.148.6559
Stochastic-LS+TP+TF80.981.776.170.576.966.471.470.954.855.048.9559
D-ViTMDETR-LS84.185.979.975.579.670.174.974.858.759.154.54811
D-ViTMDETR-TP+TF84.085.979.875.479.670.074.874.658.559.054.54610
D-ViTMDETR-LS+TP+TF83.885.779.675.279.569.974.774.458.358.854.255 (↑ 36%)9 (↓ 36%)
+ +Table 3. Experiments on referring exprehension comprehension (REC) and Visual Question Answering (GQA) benchmarks on the small models. Note that ViTMDETR and MDETR contain $80M$ and $80M$ parameters. D-ViTMDETR model is built on top of pre-trained ViTMDETR and only introduces $\sim 1M$ more parameters, resulting in $81M$ parameters. + +components of our method: (1) dynamic token pruning and fusion, (2) adaptive MSA and FFN layer skipping. With dynamic token pruning (TP) and fusion (TF) only, we can reduce the run-time complexity by $\sim 20\%$ . With adaptive layer skipping (LS), this number goes up to $\sim 30\%$ . + +Experiments on Small Model Next, we perform experiments on our small image and language model, ViTMDETR. This model contains the DeiT-Small vision backbone with 22M parameters and CLIP [29] text backbone with 40M parameters together with a multimodal network with 18M parameters resulting in 80M parameters image and language model. After pre-training this model, we learn dynamic inference on the finetuning tasks as shown in Table 3. As shown in the table, we can reduce the run-time complexity of MDETR by $\sim 36\%$ with no accuracy drop. On the other hand, in our ablation studies, with dynamic token pruning and fusion only, we can reduce the run-time complexity by $\sim 15\%$ . By adding dynamic layer skipping, this number goes up to $\sim 36\%$ . + +# 5.2. Ablation Studies + +Impact of Knowledge Distillation In our ablation studies, we first perform experiments on the impact of knowledge distillation for the optimization of our adaptive model. We show the results in Table 4. As seen in the table, knowledge + +distillation improves the accuracy of the dynamic model by around $\sim 1\%$ . + +Impact of Pretraining the Decision Networks Next, we perform experiments on the impact of pre-training the decision networks. We show the results in Table 5. As seen in the table, pre-training the decision networks is important to maintain the high accuracy of our dynamic model. + +Impact of Window Size for Spatial Clustering In our experiments, we set the window size to $64 \times 64$ and learn single action for the vision tokens inside the window. We perform experiments with different window sizes and show the results in Table 6 and show that we get the best results with $64 \times 64$ windows. + +# 5.3. Analyzing Learned Policies + +Pruned Tokens Additionally, we visualize the pruned tokens by the decision network in Figure 4. As seen in the figure, the number of tokens that are pruned goes down w.r.t depth of the backbones. This makes sense since we have decreasing number of remaining tokens w.r.t. depth. + +Fused Tokens In the next step, we visualize the fusion policies learned by the decision network. In particular, we are interested in how many vision tokens are fused over the increasing number of layers in the backbones. We show the results in Figure 4. As we can see in the figure, the num + +
RefCOCORefCOCO+RefCOCOgGQAPhraseCut
valtestAtestBvaltestAtestBvaltestATest-DevTest-StdTest
ViTMDETR87.689.383.378.082.572.677.878.162.362.057.5
D-ViTMDETR (LS+TP+AF)86.988.482.377.281.371.577.077.460.860.655.9
D-ViTMDETR (LS+TP+AF) + KD87.489.283.278.182.572.477.477.761.961.657.3
+ +Table 4. Ablation studies on the impact of knowledge distillation. + +
RefCOCORefCOCO+RefCOCOgGQAPhraseCut
valtestAtestBvaltestAtestBvaltestATest-DevTest-StdTest
Without Pre-training77.479.273.168.172.562.667.467.751.451.147.0
With Pre-training84.986.780.675.680.069.174.975.258.958.654.5
+ +Table 5. Ablation studies on the impact of pretraining the decision network. + +
Window SizeRefCOCORefCOCOgRefCOCO+
16x1684.574.873.0
32x3285.876.474.6
64x6487.478.177.4
128x12887.077.676.5
+ +Table 6. Impact of window size on vision token clustering on the val split of RefCOCO, RefCOCOg, and RefCOCO+. + +ber of vision tokens that are fused with the text tokens goes down w.r.t depth of the backbones. On the other hand, we can see that on average we fuse $\sim 30\%$ of vision tokens with the language tokens across the processing in backbones. + +![](images/0fc6b8ea53001e7afd42cb1736d63092bafe3d946bc91a43d4ce63fcc5d4782b.jpg) +Figure 4. Probability of token pruning (Left) and fusion (Right) over depth for the RefCOCO experiments. + +![](images/7c90110b94026cce11efae2460aa75c4c9ce1d4fd818f79b42930f6ac7ed492c.jpg) +Figure 5. MSA and FFN layer skipping probability distribution in vision backbone (Top Left), text backbone (Top Right), and multimodal network (Bottom) that consists of 6 encoder and decoder layers. We show the results from RefCOCO experiments. + +Skipped MSA and FFN layers Next, we analyze the policies learned by the decision networks towards skipping MSA and FFN layers in both vision and text backbone as well as the multimodal network. We note that across the 12 encoders in the backbones, we learn decisions to potentially skip 20 MSA and FFN layers and 12 MSA and FFN layers in the multimodal network. + +As seen in Figure 5, the skipping operations for MSA and FFN layers are distributed in a way that later MSA and FFN layers especially in the backbones are skipped with higher probability. This is similar to skipping operations with CNNs where shallow layers are more important than + +![](images/1a3fee95a39f4a1af15b44e97f130ac7d3c70845c9d80d4b421f0ca2632105a2.jpg) + +![](images/6adbab7be80a250563065530b44e7a3d5a20267d858e28f6a35532c298d386a7.jpg) + +![](images/b8f208a6c15fca4450033193d1e88e0c358e22e0caee5ba9907fcee8db590bea.jpg) + +![](images/0b6331b5639caaabea3e334c5f5e5f5452ad2163611dd0be02333a1aa13219bb.jpg) + +deep layers as they provide critical low-level abstraction of objects [34]. On the other hand, there is not a clear pattern with the skipping operations in the multimodal network. + +# 6. Conclusion + +We propose a dynamic inference method for the vision and language models. Our method includes learning adaptive policies to skip MSA and FFN layers across vision and language backbones and multimodal network. Additionally, it dynamically prunes tokens from different modalities and fuse tokens at different stages of backbones. We then train our model on downstream vision and language tasks. In our experiments on REC, RES and VQA we show that we can improve the run-time complexity of MDETR, and GLIP by up to $\sim 50\%$ with only maximum $\sim 0.3\%$ accuracy drop. + +# References + +[1] Arian Bakhtiarnia, Qi Zhang, and Alexandros Iosifidis. Multi-exit vision transformer for dynamic inference. arXiv preprint arXiv:2106.15183, 2021. 2 +[2] Nicolas Carion, Francisco Massa, Gabriel Synnaeve, Nicolas Usunier, Alexander Kirillov, and Sergey Zagoruyko. End-to-end object detection with transformers. In European Conference on Computer Vision, pages 213-229. Springer, 2020. 3 +[3] Xinpeng Chen, Lin Ma, Jingyuan Chen, Zequn Jie, Wei Liu, and Jiebo Luo. Real-time referring expression comprehension by single-stage grounding network. arXiv preprint arXiv:1812.03426, 2018. 2 +[4] Yen-Chun Chen, Linjie Li, Licheng Yu, Ahmed El Kholy, Faisal Ahmed, Zhe Gan, Yu Cheng, and Jingjing Liu. 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Glipv2: Unifying localization and vision-language understanding. arXiv preprint arXiv:2206.05836, 2022.1, 2 \ No newline at end of file diff --git a/2023/Dynamic Inference With Grounding Based Vision and Language Models/images.zip b/2023/Dynamic Inference With Grounding Based Vision and Language Models/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..a0e869eaefe150ac2c25bb7fefa16056a96d557f --- /dev/null +++ b/2023/Dynamic Inference With Grounding Based Vision and Language Models/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:f2e7850ac7e2f47ae87713a0bb42e4993417f342b33f092b46c2e0b6370f262c +size 618044 diff --git a/2023/Dynamic Inference With Grounding Based Vision and Language Models/layout.json b/2023/Dynamic Inference With Grounding Based Vision and Language Models/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..a8390a2c4830c672f3225d5cafa4ce78a2d5e75d --- /dev/null +++ b/2023/Dynamic Inference With Grounding Based Vision and Language Models/layout.json @@ -0,0 +1,9300 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 75, + 103, + 518, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 75, + 103, + 518, + 121 + ], + "spans": [ + { + "bbox": [ + 75, + 103, + 518, + 121 + ], + "type": "text", + "content": "Dynamic Inference with Grounding Based Vision and Language Models" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 53, + 143, + 555, + 171 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 143, + 555, + 171 + ], + "spans": [ + { + "bbox": [ + 53, + 143, + 555, + 171 + ], + "type": "text", + "content": "Burak Uzkent, Amanmeet Garg, Wentao Zhu, Keval Doshi, Jingru Yi, Xiaolong Wang, Mohamed Omar Amazon Prime Video" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 116, + 173, + 488, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 173, + 488, + 185 + ], + "spans": [ + { + "bbox": [ + 116, + 173, + 488, + 185 + ], + "type": "text", + "content": "{burauzke,amanmega,zhuwent,kcdos,jyijingr,xiaowanf,omarmk}@amazon.com" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "spans": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 238, + 290, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 238, + 290, + 574 + ], + "spans": [ + { + "bbox": [ + 46, + 238, + 290, + 574 + ], + "type": "text", + "content": "Transformers have been recently utilized for vision and language tasks successfully. For example, recent image and language models with more than 200M parameters have been proposed to learn visual grounding in the pre-training step and show impressive results on downstream vision and language tasks. On the other hand, there exists a large amount of computational redundancy in these large models which skips their run-time efficiency. To address this problem, we propose dynamic inference for grounding based vision and language models conditioned on the input image-text pair. We first design an approach to dynamically skip multihead self-attention and feed forward network layers across two backbones and multimodal network. Additionally, we propose dynamic token pruning and fusion for two backbones. In particular, we remove redundant tokens at different levels of the backbones and fuse the image tokens with the language tokens in an adaptive manner. To learn policies for dynamic inference, we train agents using reinforcement learning. 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Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "text", + "content": "Significant progress has been made in the development of image and language models attributed to: (1) emergence of transformers for different modalities [6, 13], and (2) large scale pre-training paradigms [4, 14, 17, 24, 29, 43, 44]. In particular, with the very large scale pre-training of image and language models, large number of parameters and computations are allocated for processing input image-text pair. 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Accuracy vs frames per second comparison of the large (Top Left) and small (Top Right) models and accuracy vs GLOPs comparison of the large (Bottom Left) and small (Bottom Right) models. D-ViTMDETR outperforms MDETR, GLIP and our ViT-MDETR model in both frames per second and GFLOPs metrics while maintaining high accuracy." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 429, + 331, + 534, + 436 + ], + "blocks": [ + { + "bbox": [ + 429, + 331, + 534, + 436 + ], + "lines": [ + { + "bbox": [ + 429, + 331, + 534, + 436 + ], + "spans": [ + { + "bbox": [ + 429, + 331, + 534, + 436 + ], + "type": "image", + "image_path": "c18d14a7b36d3f3291987293a9656a0215139c1cf4756ea97b22fbd8c1ffc877.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 533, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 547, + 715 + ], + "type": "text", + "content": "language models can be more than 200M [14, 17, 44], resulting in low run-time efficiency. This problem with the single-modality transformers has been tackled by several studies before [27, 30, 37]. Such computational complexity is further amplified in multimodal networks often building on multiple transformer models. As a result, reducing the run-time complexity of the multimodal networks can be very beneficial for the downstream tasks. Existing methods including pruning [20], knowledge distillation [10, 33] and quantization [39] can potentially be extended toward this goal. However, they show significant performance drop (" + }, + { + "bbox": [ + 304, + 533, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\geq 1\\%" + }, + { + "bbox": [ + 304, + 533, + 547, + 715 + ], + "type": "text", + "content": ") at " + }, + { + "bbox": [ + 304, + 533, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\geq 50\\%" + }, + { + "bbox": [ + 304, + 533, + 547, + 715 + ], + "type": "text", + "content": " compression rates and these methods are mostly designed for parameter reduction not for run-time speed. As a result, we propose dynamic inference with the large image and language mod" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2624" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 299 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 299 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 299 + ], + "type": "text", + "content": "els mainly to achieve two goals: (1) drastically reduce runtime complexity, and (2) maintain their high accuracy. Towards these goals, in the first step, we analyze the classic architectural choices for the recent image and language models. A typical image and language model consists of a vision encoder (a CNN or a vision transformer), a text encoder (transformer), and a multimodal transformer (fusion network). Inspired by MDETR [14], we build a vision and language model consisting of vision and language transformer and DETR-like multimodal network and call it ViTMDETR. The transformer modules consist of a multi-head self attention (MSA) and feed forward network (FFN) blocks which are experimentally found to be computationally expensive modules in inference-time. It is also known that computationally complexity of transformer MSA module goes up quadratically w.r.t number of tokens. The number of tokens and the computational complexity gets further amplified with inclusion of multimodal inputs and related modules." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 300, + 289, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 300, + 289, + 443 + ], + "spans": [ + { + "bbox": [ + 46, + 300, + 289, + 443 + ], + "type": "text", + "content": "For these reasons, with our D-ViTMDETR model we propose to dynamically prune input tokens from multiple modalities across the transformer backbones and fuse vision tokens adaptively with the text tokens to improve the accuracy. This way, we can reduce the complexity quadratically. Additionally, we adaptively skip the computationally expensive MSA and FFN layers across the two backbones and the multimodal network to further improve run-time efficiency. To learn dynamic policies, we train decision networks using the policy-gradients based reinforcement learning algorithm and distill the knowledge from ViTMDETR to better optimize D-ViTMDETR." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 59, + 444, + 274, + 455 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 444, + 274, + 455 + ], + "spans": [ + { + "bbox": [ + 59, + 444, + 274, + 455 + ], + "type": "text", + "content": "In this research work, our contributions are as below:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 463, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 59, + 463, + 287, + 500 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 463, + 287, + 500 + ], + "spans": [ + { + "bbox": [ + 59, + 463, + 287, + 500 + ], + "type": "text", + "content": "- We introduce an MDETR-inspired transformer-based model ViTMDETR for grounding based vision and language tasks." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 59, + 503, + 287, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 503, + 287, + 575 + ], + "spans": [ + { + "bbox": [ + 59, + 503, + 287, + 575 + ], + "type": "text", + "content": "- We propose a novel method to learn dynamic token pruning and fusion actions to reduce computational complexity using reinforcement learning. Additionally, we train the same agents to learn MSA and FFN layer skipping throughout our vision and language model to further reduce complexity." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 59, + 578, + 287, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 578, + 287, + 613 + ], + "spans": [ + { + "bbox": [ + 59, + 578, + 287, + 613 + ], + "type": "text", + "content": "- For better optimization, we align the representations and predictions of D-ViTMDETR with the representations and predictions of the ViTMDETR model." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 59, + 617, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 617, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 59, + 617, + 288, + 714 + ], + "type": "text", + "content": "- We perform experiments with both our ViTMDETR and D-ViTMDETR models on several image and language benchmarks for Referring Expression Comprehension (REC) and Segmentation (RES), and VQA tasks. With our dynamic model, D-ViTMDETR, we can improve the run-time efficiency of the state-of-the-art models MDETR [14] and GLIP [17] by up to " + }, + { + "bbox": [ + 59, + 617, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\sim 50\\%" + }, + { + "bbox": [ + 59, + 617, + 288, + 714 + ], + "type": "text", + "content": " on Referring Expression Comprehension and" + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 325, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 325, + 72, + 545, + 96 + ], + "type": "text", + "content": "Segmentation, and VQA with only maximum " + }, + { + "bbox": [ + 325, + 72, + 545, + 96 + ], + "type": "inline_equation", + "content": "\\sim 0.3\\%" + }, + { + "bbox": [ + 325, + 72, + 545, + 96 + ], + "type": "text", + "content": " accuracy drop as seen in Figure 1." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 110, + 398, + 124 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 110, + 398, + 124 + ], + "spans": [ + { + "bbox": [ + 306, + 110, + 398, + 124 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 131, + 545, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 131, + 545, + 323 + ], + "spans": [ + { + "bbox": [ + 304, + 131, + 545, + 323 + ], + "type": "text", + "content": "Grounding Based Image and Language Models We can categorize existing grounding based image and language models into two categories: (1) two-stage and (2) single-stage. Two-stage methods [4, 24, 42] rely on off-the-shelf object detectors to get object proposals and then process the language query for the task of interest. On the other hand, single-stage methods [3, 5, 7, 14, 17, 40, 44] avoid using a separate off-the-shelf object detector and perform end-to-end training for detecting the referred object, reducing the computational complexity of the two-stage methods. The most recent vision and language models [5, 14, 17, 18, 38] utilize large-scale transformers to improve the accuracy of the previous models with CNN backbones [3, 40]. Other recent works [19, 29, 31] including CLIP [29] have developed image and language models trained on large-scale data with high-level image-to-text contrastive learning objective." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 324, + 546, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 324, + 546, + 598 + ], + "spans": [ + { + "bbox": [ + 304, + 324, + 546, + 598 + ], + "type": "text", + "content": "Dynamic Inference with Transformers Dynamic inference with vision transformers have been mostly studied on single modality data. Wang et al. [35] proposed to leverage the redundancy in the image space to assign adaptive number of patches to each image. Other works [30,37,41] used adaptive number of tokens conditioned on the input. These studies exploit the redundancy on the input (image and tokens) to transformer encoders. On the other hand, depth-adaptive inference for transformers showed strong improvements [1,8,11,22]. Next, [27] performs conditional inference on the image space, in the attention heads and FFN components for the task of image recognition. However, there has been no dynamic method designed for multimodal tasks. Different from this studies, our study focuses on the vision and language models for the vision and language tasks. Since the amount of computation in the vision and language models will be drastically larger than the single-modality tasks, we can expect further gains by using dynamic inference on the vision and language models. In addition to MSA and FFN layer skipping across the backbones and multimodal network, we perform dynamic token pruning for text and vision tokens and adaptively fuse vision tokens with text tokens." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 613, + 411, + 627 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 613, + 411, + 627 + ], + "spans": [ + { + "bbox": [ + 306, + 613, + 411, + 627 + ], + "type": "text", + "content": "3. Proposed Method" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 634, + 430, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 634, + 430, + 647 + ], + "spans": [ + { + "bbox": [ + 306, + 634, + 430, + 647 + ], + "type": "text", + "content": "3.1. Building ViTMDETR" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 654, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 689 + ], + "type": "text", + "content": "In our vision and language model, we have a vision encoder " + }, + { + "bbox": [ + 304, + 654, + 545, + 689 + ], + "type": "inline_equation", + "content": "f_{v}" + }, + { + "bbox": [ + 304, + 654, + 545, + 689 + ], + "type": "text", + "content": " and text encoder " + }, + { + "bbox": [ + 304, + 654, + 545, + 689 + ], + "type": "inline_equation", + "content": "f_{t}" + }, + { + "bbox": [ + 304, + 654, + 545, + 689 + ], + "type": "text", + "content": " parameterized by " + }, + { + "bbox": [ + 304, + 654, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\theta_v" + }, + { + "bbox": [ + 304, + 654, + 545, + 689 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 654, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\theta_t" + }, + { + "bbox": [ + 304, + 654, + 545, + 689 + ], + "type": "text", + "content": " that outputs representations " + }, + { + "bbox": [ + 304, + 654, + 545, + 689 + ], + "type": "inline_equation", + "content": "z_{v}\\in \\mathbb{R}^{v}" + }, + { + "bbox": [ + 304, + 654, + 545, + 689 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 654, + 545, + 689 + ], + "type": "inline_equation", + "content": "z_{t}\\in \\mathbb{R}^{t}" + }, + { + "bbox": [ + 304, + 654, + 545, + 689 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 340, + 700, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 340, + 700, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 340, + 700, + 545, + 715 + ], + "type": "interline_equation", + "content": "z _ {v} ^ {i = N} = f _ {v} \\left(x _ {v}; \\theta_ {v}\\right), \\quad z _ {t} ^ {i = N} = f _ {t} \\left(x _ {t}; \\theta_ {t}\\right). \\tag {1}", + "image_path": "7d725056c7605d4456f03d2a49d75bab51cc20d87a3a6c08e1c358d977984952.jpg" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2625" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 118 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 118 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 118 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 72, + 287, + 118 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 47, + 72, + 287, + 118 + ], + "type": "text", + "content": " represents the number of encoders. The modality-specific representations are then concatenated and passed to a third-stage multimodal network, " + }, + { + "bbox": [ + 47, + 72, + 287, + 118 + ], + "type": "inline_equation", + "content": "f_{m}" + }, + { + "bbox": [ + 47, + 72, + 287, + 118 + ], + "type": "text", + "content": ", parameterized by " + }, + { + "bbox": [ + 47, + 72, + 287, + 118 + ], + "type": "inline_equation", + "content": "\\theta_{m}" + }, + { + "bbox": [ + 47, + 72, + 287, + 118 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 107, + 118, + 287, + 134 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 118, + 287, + 134 + ], + "spans": [ + { + "bbox": [ + 107, + 118, + 287, + 134 + ], + "type": "interline_equation", + "content": "z _ {m} = f _ {m} \\left(\\left[ z _ {v} ^ {i = N}, z _ {t} ^ {i = N} \\right]; \\theta_ {m}\\right) \\tag {2}", + "image_path": "3e699a9ed79cd33bde5e0a93da10c1201aa7ac34d02f3da81fae7e9db2cae1ea.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 139, + 287, + 221 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 139, + 287, + 221 + ], + "spans": [ + { + "bbox": [ + 47, + 139, + 287, + 221 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 139, + 287, + 221 + ], + "type": "inline_equation", + "content": "z_{m}\\in \\mathbb{R}^{m}" + }, + { + "bbox": [ + 47, + 139, + 287, + 221 + ], + "type": "text", + "content": " represents output of multimodal network. We then process " + }, + { + "bbox": [ + 47, + 139, + 287, + 221 + ], + "type": "inline_equation", + "content": "z_{m}" + }, + { + "bbox": [ + 47, + 139, + 287, + 221 + ], + "type": "text", + "content": " with an MLP layer to get task-specific predictions, i.e., referring expression comprehension (REC) and VQA. Given this multimodal network with list of parameters " + }, + { + "bbox": [ + 47, + 139, + 287, + 221 + ], + "type": "inline_equation", + "content": "\\theta = [\\theta_v,\\theta_t,\\theta_m]" + }, + { + "bbox": [ + 47, + 139, + 287, + 221 + ], + "type": "text", + "content": ", our goal is to introduce adaptivity in processing the modalities through vision and text backbones and multimodal network." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 223, + 287, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 223, + 287, + 258 + ], + "spans": [ + { + "bbox": [ + 47, + 223, + 287, + 258 + ], + "type": "text", + "content": "Text Backbone The text transformer first projects raw language data to word embeddings and sums them with the positional embedding formulated as" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 118, + 267, + 287, + 282 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 118, + 267, + 287, + 282 + ], + "spans": [ + { + "bbox": [ + 118, + 267, + 287, + 282 + ], + "type": "interline_equation", + "content": "z _ {t} ^ {i = 0} = e _ {t} \\left(x _ {t}\\right) + p _ {t} \\left(x _ {t}\\right) \\tag {3}", + "image_path": "ceb722cee15fce09b0db2f40dc5044abec68add800287d7cc63980adbfe9a104.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 292, + 287, + 315 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 292, + 287, + 315 + ], + "spans": [ + { + "bbox": [ + 47, + 292, + 287, + 315 + ], + "type": "text", + "content": "where, for a given input token " + }, + { + "bbox": [ + 47, + 292, + 287, + 315 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 47, + 292, + 287, + 315 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 292, + 287, + 315 + ], + "type": "inline_equation", + "content": "e_{t}" + }, + { + "bbox": [ + 47, + 292, + 287, + 315 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 292, + 287, + 315 + ], + "type": "inline_equation", + "content": "p_{t}" + }, + { + "bbox": [ + 47, + 292, + 287, + 315 + ], + "type": "text", + "content": " represent the word and positional embedding functions." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 316, + 287, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 316, + 287, + 361 + ], + "spans": [ + { + "bbox": [ + 47, + 316, + 287, + 361 + ], + "type": "text", + "content": "Next, the transformer processes the input embeddings " + }, + { + "bbox": [ + 47, + 316, + 287, + 361 + ], + "type": "inline_equation", + "content": "z_{t}^{i = 0}" + }, + { + "bbox": [ + 47, + 316, + 287, + 361 + ], + "type": "text", + "content": " by " + }, + { + "bbox": [ + 47, + 316, + 287, + 361 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 47, + 316, + 287, + 361 + ], + "type": "text", + "content": " encoders where each encoder consists of MSA, layer norm (LN), GELU [9], and FFN layers. Operations in a transformer encoder can be formulated as" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 107, + 371, + 287, + 386 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 371, + 287, + 386 + ], + "spans": [ + { + "bbox": [ + 107, + 371, + 287, + 386 + ], + "type": "interline_equation", + "content": "z _ {t} ^ {i} = M S A _ {t} \\left(L N _ {t} \\left(z _ {t} ^ {i}\\right)\\right) + z _ {t} ^ {i}, \\tag {4}", + "image_path": "78dd84c559b1db877897d343d574ed016297d8fde654b23585df49b5c5f3d95e.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 103, + 406, + 287, + 421 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 103, + 406, + 287, + 421 + ], + "spans": [ + { + "bbox": [ + 103, + 406, + 287, + 421 + ], + "type": "interline_equation", + "content": "z _ {t} ^ {i + 1} = F F N _ {t} \\left(L N _ {t} \\left(z _ {t} ^ {i}\\right)\\right) + z _ {t} ^ {i}. \\tag {5}", + "image_path": "ab139477435c1cda7f95cf7b86fa3acef5d8af969234e56b5396aaecf10ad7dc.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 426, + 287, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 426, + 287, + 461 + ], + "spans": [ + { + "bbox": [ + 47, + 426, + 287, + 461 + ], + "type": "text", + "content": "We note that we can skip the MSA or FFN layers together with LN layer without any modification to the architecture. This will be useful for our dynamic inference method." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 463, + 287, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 463, + 287, + 510 + ], + "spans": [ + { + "bbox": [ + 47, + 463, + 287, + 510 + ], + "type": "text", + "content": "Vision Backbone The vision transformer has a convolutional layer, " + }, + { + "bbox": [ + 47, + 463, + 287, + 510 + ], + "type": "inline_equation", + "content": "e_v" + }, + { + "bbox": [ + 47, + 463, + 287, + 510 + ], + "type": "text", + "content": ", to divide the input image into patches and learn patch representations. Patch embedding is then summed with the positional embedding, " + }, + { + "bbox": [ + 47, + 463, + 287, + 510 + ], + "type": "inline_equation", + "content": "p_v" + }, + { + "bbox": [ + 47, + 463, + 287, + 510 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 114, + 518, + 287, + 533 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 114, + 518, + 287, + 533 + ], + "spans": [ + { + "bbox": [ + 114, + 518, + 287, + 533 + ], + "type": "interline_equation", + "content": "z _ {v} ^ {i = 0} = e _ {v} \\left(x _ {v}\\right) + p _ {v} \\left(x _ {v}\\right). \\tag {6}", + "image_path": "0e93a44b6fd86e009345a4db1289a4110d666d37583e36f42206937509b899ca.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 543, + 287, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 543, + 287, + 589 + ], + "spans": [ + { + "bbox": [ + 47, + 543, + 287, + 589 + ], + "type": "text", + "content": "Next, the vision transformer processes the input embedding " + }, + { + "bbox": [ + 47, + 543, + 287, + 589 + ], + "type": "inline_equation", + "content": "z_{v}^{i = 0}" + }, + { + "bbox": [ + 47, + 543, + 287, + 589 + ], + "type": "text", + "content": " by " + }, + { + "bbox": [ + 47, + 543, + 287, + 589 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 47, + 543, + 287, + 589 + ], + "type": "text", + "content": " encoders with similar components to the text transformer encoder. We can formulate the operations in a vision transformer encoder as" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 599, + 287, + 613 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 599, + 287, + 613 + ], + "spans": [ + { + "bbox": [ + 105, + 599, + 287, + 613 + ], + "type": "interline_equation", + "content": "z _ {v} ^ {i} = M S A _ {v} \\left(L N _ {v} \\left(z _ {v} ^ {i}\\right)\\right) + z _ {v} ^ {i}, \\tag {7}", + "image_path": "1a970291f30303c58169a4c969f012e7684b5153039f3e5254267c575380d6dd.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 101, + 634, + 287, + 648 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 101, + 634, + 287, + 648 + ], + "spans": [ + { + "bbox": [ + 101, + 634, + 287, + 648 + ], + "type": "interline_equation", + "content": "z _ {v} ^ {i + 1} = F F N _ {v} \\left(L N _ {v} \\left(z _ {v} ^ {i}\\right)\\right) + z _ {v} ^ {i}. \\tag {8}", + "image_path": "e9d62f3a4e7816f876854b05351a8737d01102e4f5578b7a21be551bd742169e.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 47, + 654, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 654, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 47, + 654, + 287, + 677 + ], + "type": "text", + "content": "Similarly to the text transformer, we can skip the MSA or FFN layers without any modification to the architecture." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": "Multimodal Transformer We then pass the concatenated representations " + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "[z_t^{i=N}, z_v^{i=N}]" + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": " to a multimodal transformer. MDETR uses a DETR-based transformer [2] to output" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "content": "boundong box predictions for the given multimodal representations. For the REC task, we choose the bounding box predictions with the highest confidence score. For VQA, we do not output bounding boxes; instead, we output class probabilities for different answers. With DETR, we can use a different number of encoders and decoders on the input representations. In this study, we maintain the same structure with the DETR in the MDETR model for the multimodal transformer and use 6 encoders and 6 decoders with traditional transformer MSA and FFN layers on which we can perform skipping without any modification." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 211, + 498, + 223 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 211, + 498, + 223 + ], + "spans": [ + { + "bbox": [ + 306, + 211, + 498, + 223 + ], + "type": "text", + "content": "3.2. Dynamic Token Pruning and Fusion" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 229, + 545, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 229, + 545, + 348 + ], + "spans": [ + { + "bbox": [ + 304, + 229, + 545, + 348 + ], + "type": "text", + "content": "To achieve dynamic inference, we first propose an approach to prune redundant multimodal tokens and fuse tokens adaptively. We note that we only fuse selected vision tokens with the text tokens and process the fused vision tokens and text tokens with the text backbone. We follow this strategy as pre-trained language transformers are known to generalize to image modality [25]. In this direction, we place a decision network on after every two encoders of the backbones. The decision network provides output for the token pruning and fusion as" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 354, + 356, + 545, + 370 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 354, + 356, + 545, + 370 + ], + "spans": [ + { + "bbox": [ + 354, + 356, + 545, + 370 + ], + "type": "interline_equation", + "content": "p _ {b}, s _ {b} = \\operatorname {s i g m o i d} \\left(f _ {d} \\left(\\left[ z _ {v} ^ {i}, z _ {t} ^ {i} \\right]; \\theta_ {d}\\right)\\right) \\tag {9}", + "image_path": "ed99af68e01436f1a610ce27762feecf7ca21a96bcfa54a51b9cf6ab77e30c97.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 378, + 545, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 378, + 545, + 496 + ], + "spans": [ + { + "bbox": [ + 304, + 378, + 545, + 496 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 378, + 545, + 496 + ], + "type": "inline_equation", + "content": "p_b" + }, + { + "bbox": [ + 304, + 378, + 545, + 496 + ], + "type": "text", + "content": " represents the continuous predictions on token fusion and pruning across the two backbones whereas " + }, + { + "bbox": [ + 304, + 378, + 545, + 496 + ], + "type": "inline_equation", + "content": "\\theta_d" + }, + { + "bbox": [ + 304, + 378, + 545, + 496 + ], + "type": "text", + "content": " represent the decision network parameters. On the other hand, " + }, + { + "bbox": [ + 304, + 378, + 545, + 496 + ], + "type": "inline_equation", + "content": "s_b" + }, + { + "bbox": [ + 304, + 378, + 545, + 496 + ], + "type": "text", + "content": " represents the actions for MSA and FFN layer skipping that we detail in the next section. We use a single dense layer for the decision network. Note that the number of tokens from each backbone can get large depending on the size of the image and text. As a result, it can be very hard to optimize the decision network to provide actions for many tokens." + } + ] + } + ], + "index": 21 + }, + { + "type": "image", + "bbox": [ + 320, + 504, + 524, + 654 + ], + "blocks": [ + { + "bbox": [ + 320, + 504, + 524, + 654 + ], + "lines": [ + { + "bbox": [ + 320, + 504, + 524, + 654 + ], + "spans": [ + { + "bbox": [ + 320, + 504, + 524, + 654 + ], + "type": "image", + "image_path": "6bfb0d8583e3a26d0efa269197924fceb2b20951f7d10eadc7126b612bc02931.jpg" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 655, + 545, + 709 + ], + "lines": [ + { + "bbox": [ + 304, + 655, + 545, + 709 + ], + "spans": [ + { + "bbox": [ + 304, + 655, + 545, + 709 + ], + "type": "text", + "content": "Figure 2. Demonstration of action space for vision token pruning and fusion. We group each 16 neighboring tokens in a " + }, + { + "bbox": [ + 304, + 655, + 545, + 709 + ], + "type": "inline_equation", + "content": "64 \\times 64" + }, + { + "bbox": [ + 304, + 655, + 545, + 709 + ], + "type": "text", + "content": " window and represent the window with two actions: (1) token pruning and (2) fusion. The actions are then applied to the tokens inside this window." + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_caption" + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "2626" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 60, + 69, + 534, + 263 + ], + "blocks": [ + { + "bbox": [ + 60, + 69, + 534, + 263 + ], + "lines": [ + { + "bbox": [ + 60, + 69, + 534, + 263 + ], + "spans": [ + { + "bbox": [ + 60, + 69, + 534, + 263 + ], + "type": "image", + "image_path": "8d3392447662aacd2a52ccc5e7ef7a771c3dcec2504d7a9532f59e587e23cd19.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 270, + 547, + 304 + ], + "lines": [ + { + "bbox": [ + 46, + 270, + 547, + 304 + ], + "spans": [ + { + "bbox": [ + 46, + 270, + 547, + 304 + ], + "type": "text", + "content": "Figure 3. Framework for combining the dynamic token fusion and pruning together with MSA and FFN layer skipping to get DViTMDETR model. We do not show layer skipping in the multimodal network for simplicity. By combining layer skipping together with token pruning and fusion, we tackle redundancy in both across the backbones and multimodal network and the input data." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 324, + 288, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 324, + 288, + 503 + ], + "spans": [ + { + "bbox": [ + 46, + 324, + 288, + 503 + ], + "type": "text", + "content": "Reducing the Size of Action Space The amount of vision tokens can be very large especially for large size images given that each token covers " + }, + { + "bbox": [ + 46, + 324, + 288, + 503 + ], + "type": "inline_equation", + "content": "16 \\times 16" + }, + { + "bbox": [ + 46, + 324, + 288, + 503 + ], + "type": "text", + "content": " pixels patch. Large action space can be a bottleneck for learning the decision network parameters. To simplify their training, we cluster the set of vision tokens by spatially grouping them as shown in Figure 2. More specifically, we divide the image into " + }, + { + "bbox": [ + 46, + 324, + 288, + 503 + ], + "type": "inline_equation", + "content": "M_v \\times M_v" + }, + { + "bbox": [ + 46, + 324, + 288, + 503 + ], + "type": "text", + "content": " non-overlapping windows where each window is represented by " + }, + { + "bbox": [ + 46, + 324, + 288, + 503 + ], + "type": "inline_equation", + "content": "64 \\times 64" + }, + { + "bbox": [ + 46, + 324, + 288, + 503 + ], + "type": "text", + "content": " pixels and take a single pruning and fusion action for all the patches in this window. Our action space for pruning and fusion then becomes " + }, + { + "bbox": [ + 46, + 324, + 288, + 503 + ], + "type": "inline_equation", + "content": "p_b \\in [0,1]^{2 * M_v * M_v + M_t}" + }, + { + "bbox": [ + 46, + 324, + 288, + 503 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 46, + 324, + 288, + 503 + ], + "type": "inline_equation", + "content": "M_v * M_v" + }, + { + "bbox": [ + 46, + 324, + 288, + 503 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 324, + 288, + 503 + ], + "type": "inline_equation", + "content": "M_t" + }, + { + "bbox": [ + 46, + 324, + 288, + 503 + ], + "type": "text", + "content": " represent the number of vision token clusters and text tokens. Since, the number of text tokens is much smaller than the number of vision tokens, we do not modify their action space." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 505, + 287, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 505, + 287, + 624 + ], + "spans": [ + { + "bbox": [ + 46, + 505, + 287, + 624 + ], + "type": "text", + "content": "Discrete Actions from Continuous Predictions In test time, we obtain discrete actions by using a piece-wise function as " + }, + { + "bbox": [ + 46, + 505, + 287, + 624 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_{\\mathbf{p}}^{\\mathrm{j}} = 1" + }, + { + "bbox": [ + 46, + 505, + 287, + 624 + ], + "type": "text", + "content": " if " + }, + { + "bbox": [ + 46, + 505, + 287, + 624 + ], + "type": "inline_equation", + "content": "p_b^j \\geq 0.5" + }, + { + "bbox": [ + 46, + 505, + 287, + 624 + ], + "type": "text", + "content": ", otherwise " + }, + { + "bbox": [ + 46, + 505, + 287, + 624 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_{\\mathbf{p}}^{\\mathrm{j}} = 0" + }, + { + "bbox": [ + 46, + 505, + 287, + 624 + ], + "type": "text", + "content": ". For " + }, + { + "bbox": [ + 46, + 505, + 287, + 624 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_{\\mathbf{p}}^{\\mathrm{j}} = 1" + }, + { + "bbox": [ + 46, + 505, + 287, + 624 + ], + "type": "text", + "content": " we either prune or fuse the corresponding set of vision tokens in a spatial cluster and we keep the tokens for " + }, + { + "bbox": [ + 46, + 505, + 287, + 624 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_{\\mathbf{p}}^{\\mathrm{j}} = 0" + }, + { + "bbox": [ + 46, + 505, + 287, + 624 + ], + "type": "text", + "content": ". To avoid the conflicts between pruning and fusion, we prioritize pruning over fusion. In other words, if we decide to both prune and fuse a set of vision tokens in a cluster, we prune them and ignore fusion actions since pruning favors further computational efficiency." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 633, + 259, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 633, + 259, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 633, + 259, + 647 + ], + "type": "text", + "content": "3.3. Dynamic MSA and FFN Layer Skipping" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 653, + 287, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 687 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 687 + ], + "type": "text", + "content": "In the next step, we propose a method to dynamically skip MSA and FFN layers in the image and language backbones, and multimodal transformer." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "Backbones For MSA and FFN layer skipping, we use the same decision network with the token pruning and fusion" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 324, + 545, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 324, + 545, + 407 + ], + "spans": [ + { + "bbox": [ + 304, + 324, + 545, + 407 + ], + "type": "text", + "content": "actions from Eq. 9 where " + }, + { + "bbox": [ + 304, + 324, + 545, + 407 + ], + "type": "inline_equation", + "content": "s_b" + }, + { + "bbox": [ + 304, + 324, + 545, + 407 + ], + "type": "text", + "content": " represents the continuous predictions of the decision network on which MSA and FFN layers should be skipped in the next two encoders of the language and text backbone. As a result, our action space for layer skipping can be represented as " + }, + { + "bbox": [ + 304, + 324, + 545, + 407 + ], + "type": "inline_equation", + "content": "s_b \\in [0,1]^8" + }, + { + "bbox": [ + 304, + 324, + 545, + 407 + ], + "type": "text", + "content": " as we have 4 MSA and 4 FFN layers in two encoders across the two backbones." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 407, + 545, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 407, + 545, + 431 + ], + "spans": [ + { + "bbox": [ + 305, + 407, + 545, + 431 + ], + "type": "text", + "content": "Multimodal Transformer Finally, we integrate a decision network before multimodal transformer as shown below." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 354, + 436, + 545, + 452 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 354, + 436, + 545, + 452 + ], + "spans": [ + { + "bbox": [ + 354, + 436, + 545, + 452 + ], + "type": "interline_equation", + "content": "s _ {f} = \\operatorname {s i g m o i d} \\left(f _ {m} \\left(\\left[ z _ {v} ^ {N}, z _ {t} ^ {N} \\right]; \\theta_ {m}\\right)\\right) \\tag {10}", + "image_path": "2cf001f049b87bca4a57b62e6671a3e2c693fc051998cb06b864e7c588e4287a.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 455, + 545, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 455, + 545, + 525 + ], + "spans": [ + { + "bbox": [ + 304, + 455, + 545, + 525 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 455, + 545, + 525 + ], + "type": "inline_equation", + "content": "s_f" + }, + { + "bbox": [ + 304, + 455, + 545, + 525 + ], + "type": "text", + "content": " represents the continuous predictions on skipping MSA and FFN layers in the multimodal network. Our action space in this case can be represented as " + }, + { + "bbox": [ + 304, + 455, + 545, + 525 + ], + "type": "inline_equation", + "content": "s_f \\in [0,1]^{24}" + }, + { + "bbox": [ + 304, + 455, + 545, + 525 + ], + "type": "text", + "content": " as we have 12 MSA and 12 FFN layers in the 6 encoders and 6 decoders. We note that we have traditional MSA and FFN layers in these encoders and decoders." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 527, + 545, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 527, + 545, + 647 + ], + "spans": [ + { + "bbox": [ + 304, + 527, + 545, + 647 + ], + "type": "text", + "content": "Discrete Actions from Continuous Predictions In test time, we obtain discrete actions by using a piece-wise function as " + }, + { + "bbox": [ + 304, + 527, + 545, + 647 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_{\\mathbf{s}}^{\\mathrm{j}} = 1" + }, + { + "bbox": [ + 304, + 527, + 545, + 647 + ], + "type": "text", + "content": " if " + }, + { + "bbox": [ + 304, + 527, + 545, + 647 + ], + "type": "inline_equation", + "content": "s_{s}^{j}\\geq 0.5" + }, + { + "bbox": [ + 304, + 527, + 545, + 647 + ], + "type": "text", + "content": ", otherwise " + }, + { + "bbox": [ + 304, + 527, + 545, + 647 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_{\\mathbf{s}}^{\\mathrm{j}} = 0" + }, + { + "bbox": [ + 304, + 527, + 545, + 647 + ], + "type": "text", + "content": ". For " + }, + { + "bbox": [ + 304, + 527, + 545, + 647 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_{\\mathbf{s}}^{\\mathrm{j}} = 1" + }, + { + "bbox": [ + 304, + 527, + 545, + 647 + ], + "type": "text", + "content": " we skip the corresponding MSA or FFN layer and use the MSA or FFN layer for " + }, + { + "bbox": [ + 304, + 527, + 545, + 647 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_{\\mathbf{s}}^{\\mathrm{j}} = 0" + }, + { + "bbox": [ + 304, + 527, + 545, + 647 + ], + "type": "text", + "content": ". We note that we follow the same process to get actions " + }, + { + "bbox": [ + 304, + 527, + 545, + 647 + ], + "type": "inline_equation", + "content": "a_{m}" + }, + { + "bbox": [ + 304, + 527, + 545, + 647 + ], + "type": "text", + "content": " for skipping MSA and FFN layers in the multimodal network after getting the predictions " + }, + { + "bbox": [ + 304, + 527, + 545, + 647 + ], + "type": "inline_equation", + "content": "s_f" + }, + { + "bbox": [ + 304, + 527, + 545, + 647 + ], + "type": "text", + "content": ". We show the combination of the token pruning and fusion together with MSA and FFN layer skipping in Figure 3." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 652, + 531, + 665 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 652, + 531, + 665 + ], + "spans": [ + { + "bbox": [ + 306, + 652, + 531, + 665 + ], + "type": "text", + "content": "3.4. Modeling the Reward and Policy Functions" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 671, + 414, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 671, + 414, + 682 + ], + "spans": [ + { + "bbox": [ + 306, + 671, + 414, + 682 + ], + "type": "text", + "content": "3.4.1 Reward Function" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "Reward function is a critical component of our algorithm as it needs to reflect what we want to achieve with adaptive" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2627" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 286, + 132 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 286, + 132 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 286, + 132 + ], + "type": "text", + "content": "inference. In our method, our goal is to reduce the computational complexity in the inference time to increase run-time speed. As a result, we propose a dual reward function that consists of: (1) target task accuracy and (2) savings in computational complexity." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 133, + 286, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 133, + 286, + 156 + ], + "spans": [ + { + "bbox": [ + 46, + 133, + 286, + 156 + ], + "type": "text", + "content": "Backbones For backbones, we formulate the reward function as" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 69, + 165, + 286, + 178 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 165, + 286, + 178 + ], + "spans": [ + { + "bbox": [ + 69, + 165, + 286, + 178 + ], + "type": "interline_equation", + "content": "\\mathcal {R} _ {b} = \\sigma * c (d, g) + (1 - \\sigma) * (\\mathcal {P} + \\mathcal {F} + \\mathcal {S}) \\tag {11}", + "image_path": "3aa72c78d340fa23ed88b506b914f002fa626a88e4aed3fe63295bfd3d3c0f2a.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 186, + 286, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 186, + 286, + 293 + ], + "spans": [ + { + "bbox": [ + 46, + 186, + 286, + 293 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 186, + 286, + 293 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 186, + 286, + 293 + ], + "type": "text", + "content": " represents the task accuracy given model predictions, " + }, + { + "bbox": [ + 46, + 186, + 286, + 293 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 186, + 286, + 293 + ], + "type": "text", + "content": ", and ground truth, " + }, + { + "bbox": [ + 46, + 186, + 286, + 293 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 46, + 186, + 286, + 293 + ], + "type": "text", + "content": ", whereas " + }, + { + "bbox": [ + 46, + 186, + 286, + 293 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 46, + 186, + 286, + 293 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 186, + 286, + 293 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 46, + 186, + 286, + 293 + ], + "type": "text", + "content": " represent the ratio of pruned and fused tokens. " + }, + { + "bbox": [ + 46, + 186, + 286, + 293 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 186, + 286, + 293 + ], + "type": "text", + "content": " represents the ratio of skipped MSA and FFN layers. We note that we assign same reward to skipping an MSA and an FFN layer. One can assign higher reward to MSA layer since it has more computational complexity. On the other hand, " + }, + { + "bbox": [ + 46, + 186, + 286, + 293 + ], + "type": "inline_equation", + "content": "\\sigma \\in [0,1]" + }, + { + "bbox": [ + 46, + 186, + 286, + 293 + ], + "type": "text", + "content": " controls the trade-off between the task accuracy and computational efficiency obtained by the adaptive inference." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 294, + 286, + 330 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 294, + 286, + 330 + ], + "spans": [ + { + "bbox": [ + 46, + 294, + 286, + 330 + ], + "type": "text", + "content": "Multimodal Network As we do not prune tokens for the multimodal network, we only consider skipping MSA and FFN layers. We formulate the reward function as" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 104, + 339, + 286, + 352 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 339, + 286, + 352 + ], + "spans": [ + { + "bbox": [ + 104, + 339, + 286, + 352 + ], + "type": "interline_equation", + "content": "\\mathcal {R} _ {f} = \\sigma * c (d, g) + (1 - \\sigma) S. \\tag {12}", + "image_path": "9893404cdc30e2b657254550f8e748c1725ee0c1a6740de77428f44ed8e3fed8.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 365, + 151, + 376 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 365, + 151, + 376 + ], + "spans": [ + { + "bbox": [ + 47, + 365, + 151, + 376 + ], + "type": "text", + "content": "3.4.2 Policy Functions" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 384, + 286, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 384, + 286, + 467 + ], + "spans": [ + { + "bbox": [ + 46, + 384, + 286, + 467 + ], + "type": "text", + "content": "Backbones We model the policy function for the backbones as the multiplication of the probabilities of individual token pruning and fusion actions and repeat it for the layer skipping actions. We represent individual actions with an action-specific Bernoulli distribution. Next, we formulate the policy function for the decision networks for the backbones as" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 485, + 286, + 521 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 485, + 286, + 521 + ], + "spans": [ + { + "bbox": [ + 47, + 485, + 286, + 521 + ], + "type": "interline_equation", + "content": "\\pi_ {d} \\left(\\mathbf {a} _ {\\mathbf {s}}, \\mathbf {a} _ {\\mathbf {p}} \\mid z _ {v} ^ {i}, z _ {t} ^ {i}\\right) = \\prod_ {j} s _ {b} ^ {j} ^ {\\mathbf {a} _ {\\mathbf {s}} ^ {\\mathrm {j}}} \\left(1 - s _ {b} ^ {j}\\right) ^ {1 - \\mathbf {a} _ {\\mathbf {s}} ^ {\\mathrm {j}}} + \\prod_ {j} p _ {b} ^ {j} ^ {\\mathbf {a} _ {\\mathbf {p}} ^ {\\mathrm {j}}} \\left(1 - p _ {b} ^ {j}\\right) ^ {1 - \\mathbf {a} _ {\\mathbf {p}} ^ {\\mathrm {j}}}. \\tag {13}", + "image_path": "e136e943fb110ac19a2e33b30e0d45e14430738d3c299d0daeef456a6b9b8b22.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 522, + 286, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 522, + 286, + 569 + ], + "spans": [ + { + "bbox": [ + 46, + 522, + 286, + 569 + ], + "type": "text", + "content": "Multimodal Network Similar to the backbones, we model the policy function for the multimodal network as the multiplication of the probabilities of individual actions represented by Bernoulli distribution as" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 70, + 578, + 286, + 607 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 578, + 286, + 607 + ], + "spans": [ + { + "bbox": [ + 70, + 578, + 286, + 607 + ], + "type": "interline_equation", + "content": "\\pi_ {m} \\left(\\mathbf {a} _ {\\mathbf {m}} \\mid z _ {v} ^ {N}, z _ {t} ^ {N}\\right) = \\prod_ {j} s _ {f} ^ {j \\mathbf {a} _ {\\mathbf {m}} ^ {\\mathrm {j}}} \\left(1 - s _ {f} ^ {j}\\right) ^ {1 - \\mathbf {a} _ {\\mathbf {m}} ^ {\\mathrm {j}}}. \\tag {14}", + "image_path": "c467b4eab566ff25d0a9b88aaef9876f4541f8d810b6bab1b69c0cf55e305a00.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 616, + 162, + 628 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 616, + 162, + 628 + ], + "spans": [ + { + "bbox": [ + 47, + 616, + 162, + 628 + ], + "type": "text", + "content": "4. Training Procedure" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 635, + 132, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 635, + 132, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 635, + 132, + 647 + ], + "type": "text", + "content": "4.1. Optimization" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 654, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 286, + 713 + ], + "type": "text", + "content": "As we learn discrete actions, we cannot use the reparameterization trick to optimize the objective w.r.t. " + }, + { + "bbox": [ + 46, + 654, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\theta_{d}" + }, + { + "bbox": [ + 46, + 654, + 286, + 713 + ], + "type": "text", + "content": ". To optimize the parameters " + }, + { + "bbox": [ + 46, + 654, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\theta_{d}" + }, + { + "bbox": [ + 46, + 654, + 286, + 713 + ], + "type": "text", + "content": ", we need to use model-free reinforcement learning algorithms. Policy gradient [32] is suitable in our scenario as the number of unique actions the" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": "policy network can choose increases exponentially with the number of tokens and MSA and FFN layers. Together with policy gradients we use the REINFORCE method [32] to optimize the objective w.r.t " + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "\\theta_{d}" + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "\\theta_{m}" + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 339, + 127, + 545, + 148 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 339, + 127, + 545, + 148 + ], + "spans": [ + { + "bbox": [ + 339, + 127, + 545, + 148 + ], + "type": "interline_equation", + "content": "\\underset {\\theta_ {d}, \\theta_ {m}} {\\arg \\max } J = \\mathcal {R} _ {b} \\nabla \\log_ {\\pi_ {\\theta_ {d}}} \\left(\\mathbf {a} _ {\\mathbf {s}}, \\mathbf {a} _ {\\mathbf {p}} \\mid z _ {v} ^ {i}, z _ {t} ^ {i}\\right) + \\tag {15}", + "image_path": "b713f123098a51110f7a068782fd244fbf7d698ee8d1e526122e6dc72884ca34.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 387, + 149, + 511, + 165 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 387, + 149, + 511, + 165 + ], + "spans": [ + { + "bbox": [ + 387, + 149, + 511, + 165 + ], + "type": "interline_equation", + "content": "\\mathcal {R} _ {f} \\nabla l o g _ {\\pi_ {\\theta_ {m}}} (\\mathbf {a _ {m}} | z _ {v} ^ {i = N}, z _ {t} ^ {i = N})", + "image_path": "8057841bc4d9c173e4bef928d347599137f4589e44f3d63ae689a87897990c5d.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 171, + 545, + 230 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 171, + 545, + 230 + ], + "spans": [ + { + "bbox": [ + 304, + 171, + 545, + 230 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 171, + 545, + 230 + ], + "type": "inline_equation", + "content": "\\nabla log_{\\pi_{\\theta_d}}" + }, + { + "bbox": [ + 304, + 171, + 545, + 230 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 171, + 545, + 230 + ], + "type": "inline_equation", + "content": "\\nabla log_{\\pi_{\\theta_m}}" + }, + { + "bbox": [ + 304, + 171, + 545, + 230 + ], + "type": "text", + "content": " represent the log-likelihood of policy function for the backbones and multimodal network. Next, we substitute the policy functions with Eq. 13 and 14 and take its derivative w.r.t " + }, + { + "bbox": [ + 304, + 171, + 545, + 230 + ], + "type": "inline_equation", + "content": "\\theta_d" + }, + { + "bbox": [ + 304, + 171, + 545, + 230 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 171, + 545, + 230 + ], + "type": "inline_equation", + "content": "\\theta_m" + }, + { + "bbox": [ + 304, + 171, + 545, + 230 + ], + "type": "text", + "content": " for updating the weights." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 237, + 493, + 250 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 237, + 493, + 250 + ], + "spans": [ + { + "bbox": [ + 305, + 237, + 493, + 250 + ], + "type": "text", + "content": "4.2. Pre-training the Decision Networks" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 255, + 545, + 340 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 255, + 545, + 340 + ], + "spans": [ + { + "bbox": [ + 304, + 255, + 545, + 340 + ], + "type": "text", + "content": "After formulating the optimization steps, we pre-train the decision networks on the finetuning dataset while keeping the weights of the backbones and multimodal network frozen. By doing this, we can learn useful policies towards choosing the right decisions for token pruning and fusion together with adaptive layer skipping. To achieve it, we only optimize the objective shown in Eq. 15." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 346, + 545, + 369 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 346, + 545, + 369 + ], + "spans": [ + { + "bbox": [ + 305, + 346, + 545, + 369 + ], + "type": "text", + "content": "4.3. Jointly Finetuning the Decision Networks, Backbones and Multimodal Network" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 376, + 545, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 376, + 545, + 483 + ], + "spans": [ + { + "bbox": [ + 304, + 376, + 545, + 483 + ], + "type": "text", + "content": "In the previous step, we learned the parameters of the decision networks " + }, + { + "bbox": [ + 304, + 376, + 545, + 483 + ], + "type": "inline_equation", + "content": "\\theta_{d}" + }, + { + "bbox": [ + 304, + 376, + 545, + 483 + ], + "type": "text", + "content": " by executing the decisions with the multimodal network and finding the reward value. Up until this step, the multimodal network has not been updated with the dynamic inference which results in accuracy drop. To avoid it, we propose joint-finetuning step where we finetune both the decision networks and backbones, and multimodal network jointly. As a result, the objective for the backbones and multimodal network parameters becomes:" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 319, + 491, + 545, + 512 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 491, + 545, + 512 + ], + "spans": [ + { + "bbox": [ + 319, + 491, + 545, + 512 + ], + "type": "interline_equation", + "content": "\\underset {\\theta_ {v}, \\theta_ {t}, \\theta_ {m}} {\\arg \\min } L _ {t} = \\operatorname {T a k L o s s} (d, g | x _ {t}, y _ {t}, \\mathbf {a} _ {\\mathbf {s}}, \\mathbf {a} _ {\\mathbf {p}}, \\mathbf {a} _ {\\mathbf {m}}) \\tag {16}", + "image_path": "72a4b5bc16fa618cf7a6a13f6aae4cf4db81b523935a7193ff92f8c66779c092.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 517, + 545, + 541 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 517, + 545, + 541 + ], + "spans": [ + { + "bbox": [ + 304, + 517, + 545, + 541 + ], + "type": "text", + "content": "On the other hand, the objective for the decision networks remain similar to Eq. 15." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 548, + 458, + 560 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 548, + 458, + 560 + ], + "spans": [ + { + "bbox": [ + 306, + 548, + 458, + 560 + ], + "type": "text", + "content": "4.4. Distilling from ViTMDETR" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 566, + 545, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 566, + 545, + 625 + ], + "spans": [ + { + "bbox": [ + 304, + 566, + 545, + 625 + ], + "type": "text", + "content": "To better optimize the model in the joint finetuning step, we make use of the original fixed model, ViTMDETR, that we started with. In this direction, we add an objective to align the ViTMDETR's representations with our dynamic model as" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 355, + 632, + 545, + 654 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 355, + 632, + 545, + 654 + ], + "spans": [ + { + "bbox": [ + 355, + 632, + 545, + 654 + ], + "type": "interline_equation", + "content": "\\underset {\\theta_ {v} \\theta_ {t} \\theta_ {m}} {\\arg \\min } L _ {d} = \\| z _ {t} ^ {i = N} - \\hat {z} _ {t} ^ {i = N} \\| _ {1} + \\tag {17}", + "image_path": "b7d4a07e0d9b4f30ddb72b9ed543e5c4e0317d03d4a1c79fd6bd157515644e5e.jpg" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 360, + 655, + 495, + 670 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 360, + 655, + 495, + 670 + ], + "spans": [ + { + "bbox": [ + 360, + 655, + 495, + 670 + ], + "type": "interline_equation", + "content": "\\| z _ {v} ^ {i = N} - \\hat {z} _ {v} ^ {i = N} \\| _ {1} + \\| z _ {m} - \\hat {z} _ {m} \\| _ {1}", + "image_path": "b96b7c2c0968dcb4ed24faf981cc84e171c4f4f465c2cc0b86dc21acdcdeba85.jpg" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\hat{z}_t^{i=N}" + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\hat{z}_v^{i=N}" + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\hat{z}_m" + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": " represent the outputs of ViTMDETR after the vision and text backbones and the multimodal network, respectively." + } + ] + } + ], + "index": 28 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2628" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 109 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 109 + ], + "type": "text", + "content": "In addition to the representation alignment, we also change the ground truth predictions, " + }, + { + "bbox": [ + 46, + 72, + 288, + 109 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 46, + 72, + 288, + 109 + ], + "type": "text", + "content": ", with the predictions of the ViTMDETR, " + }, + { + "bbox": [ + 46, + 72, + 288, + 109 + ], + "type": "inline_equation", + "content": "\\hat{g}" + }, + { + "bbox": [ + 46, + 72, + 288, + 109 + ], + "type": "text", + "content": ", and the task loss becomes" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 60, + 119, + 287, + 139 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 60, + 119, + 287, + 139 + ], + "spans": [ + { + "bbox": [ + 60, + 119, + 287, + 139 + ], + "type": "interline_equation", + "content": "\\underset {\\theta_ {v}, \\theta_ {t}, \\theta_ {m}} {\\arg \\min } L _ {t} = \\operatorname {T a k L o s s} \\left(d, \\hat {g} \\mid x _ {t}, y _ {t}, \\mathbf {a} _ {\\mathbf {s}}, \\mathbf {a} _ {\\mathbf {p}}, \\mathbf {a} _ {\\mathbf {m}}\\right) \\tag {18}", + "image_path": "5123efd7fe1872a6b9c21c97b27e825f54e28e18192103159998245fe0e5d628.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 148, + 287, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 148, + 287, + 185 + ], + "spans": [ + { + "bbox": [ + 47, + 148, + 287, + 185 + ], + "type": "text", + "content": "Our final objective for end-to-end training of the adaptive network then becomes a linear combination of the task loss " + }, + { + "bbox": [ + 47, + 148, + 287, + 185 + ], + "type": "inline_equation", + "content": "(\\mathcal{L}_t)" + }, + { + "bbox": [ + 47, + 148, + 287, + 185 + ], + "type": "text", + "content": " and distillation loss " + }, + { + "bbox": [ + 47, + 148, + 287, + 185 + ], + "type": "inline_equation", + "content": "(\\mathcal{L}_d)" + }, + { + "bbox": [ + 47, + 148, + 287, + 185 + ], + "type": "text", + "content": " objectives as" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 119, + 196, + 287, + 216 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 119, + 196, + 287, + 216 + ], + "spans": [ + { + "bbox": [ + 119, + 196, + 287, + 216 + ], + "type": "interline_equation", + "content": "\\underset {\\theta_ {v}, \\theta_ {t}, \\theta_ {m}} {\\arg \\min } \\mathcal {L} = \\mathcal {L} _ {t} + \\mathcal {L} _ {d}. \\tag {19}", + "image_path": "a781a59624401b29969ba44c488485bc593a83a05f8c7451c33855cc3881d859.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 228, + 128, + 243 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 228, + 128, + 243 + ], + "spans": [ + { + "bbox": [ + 47, + 228, + 128, + 243 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 249, + 287, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 249, + 287, + 403 + ], + "spans": [ + { + "bbox": [ + 46, + 249, + 287, + 403 + ], + "type": "text", + "content": "Pre-training Dataset MDETR performs end-to-end pretraining for a language-conditioned bounding box detection task. To construct a pre-training dataset, it merges several independent vision and language datasets. These datasets are listed as MSCOCO [21], Flickr30k [28], and VisualGenome [16] as they have bounding box annotations of the objects mentioned in the language query. The task in this step is to accurately detect the bounding boxes of the objects mentioned in a language query. For example, given an input query of cat sitting next to a dog on the chair, the task would be to predict bounding boxes of a cat, a dog, and a chair in the image. We use the same pre-training dataset and objectives to MDETR [14] to pre-train ViTMDETR." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 405, + 287, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 405, + 287, + 513 + ], + "spans": [ + { + "bbox": [ + 46, + 405, + 287, + 513 + ], + "type": "text", + "content": "Downstream Tasks/Datasets We finetune the pre-trained model end-to-end on vision and language tasks, including REC, RES and VQA. For REC, we use RefCOCO and RefCOCO+ [15], and RefCOCOg [26] benchmarks. The task in these datasets is to detect the bounding box of the object referred to the language expression. For RES task, we evaluate on the PhraseCut [36] dataset, where, the task is to segment the object associated with the language query. For the VQA, we use GQA benchmark [12]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 513, + 288, + 620 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 513, + 288, + 620 + ], + "spans": [ + { + "bbox": [ + 46, + 513, + 288, + 620 + ], + "type": "text", + "content": "Metrics As the evaluation metric, for REC and RES tasks we compute the Jaccard index between predicted and ground-truth bounding boxes. If it is above 0.5, the prediction is considered correct. For the VQA, the task is to predict the correct answer from the given answer categories. We use the top-1 accuracy metric to evaluate models. Lastly, we measure the run-time efficiency in terms of frames per second on a single V100 GPU. Additionally, we use the GFLOPs metrics to evaluate the models." + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 48, + 658, + 274, + 689 + ], + "blocks": [ + { + "bbox": [ + 48, + 658, + 274, + 689 + ], + "lines": [ + { + "bbox": [ + 48, + 658, + 274, + 689 + ], + "spans": [ + { + "bbox": [ + 48, + 658, + 274, + 689 + ], + "type": "table", + "html": "
MDETRGLIPViTMDETR
Pre-training DatasetCOCO+COCO+COCO+
Flickr30k+VG (1.3M)Flickr30k+VG (1.3M)Flickr30k+VG (1.3M)
", + "image_path": "df009ae54739fa4488072d156690bdd882076a8257f41cbe5f3756cebb061e70.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 69, + 699, + 264, + 710 + ], + "lines": [ + { + "bbox": [ + 69, + 699, + 264, + 710 + ], + "spans": [ + { + "bbox": [ + 69, + 699, + 264, + 710 + ], + "type": "text", + "content": "Table 1. Pre-training dataset used in our experiments." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 72, + 545, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 251 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 251 + ], + "type": "text", + "content": "Implementation Details. We build our implementation following the official MDETR repository2. We first replace the CNN vision backbone with a transformer backbone, DeiT [33]. To implement DeiT, we use the timm library3. To utilize ImageNet pre-trained weights, we use " + }, + { + "bbox": [ + 304, + 72, + 545, + 251 + ], + "type": "inline_equation", + "content": "384 \\times 384" + }, + { + "bbox": [ + 304, + 72, + 545, + 251 + ], + "type": "text", + "content": " pixels images in both training and test time. This way, our whole architecture mostly consists of transformer layers other than the patch embedding convolutional layer. For pre-training ViTMDETR, we use the batch size of 256 on 8 NVIDIA V100 GPUs. For the transfer learning tasks for ViTMDETR we use a batch size of 8 with 2 NVIDIA V100 GPUs. For D-ViTMDETR, we use batch size of 256 with 8 V100 GPUs in the transfer learning tasks. We note that our dynamic inference method benefits from large training batch size as it reduces the variance in the reward objective." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 252, + 545, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 252, + 545, + 407 + ], + "spans": [ + { + "bbox": [ + 304, + 252, + 545, + 407 + ], + "type": "text", + "content": "Baselines We compare our method to a number of baselines that we designed. Our first baseline represents Random MSA and FFN layer skipping, Random-LS, where we draw skipping probability from a uniform distribution and perform skipping if the sampled probability is higher than a pre-defined threshold. Additionally, we design another baseline, Random-TP+TF, that randomly prunes the tokens given a uniform distribution. Finally, we combine both baselines to get another baseline, Random-LS+TP+TF. In addition to the Random baselines, we develop Stochastic baselines where we decay the likelihood of survival of the tokens, and MSA and FFN layers with the increasing depth. We call this baseline Stochastic-LS+TP+TF." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 408, + 545, + 516 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 408, + 545, + 516 + ], + "spans": [ + { + "bbox": [ + 304, + 408, + 545, + 516 + ], + "type": "text", + "content": "In addition to our baselines, we compare our models to MDETR [14] and GLIP [17] models. To be consistent with our set up, we pre-train both our ViTMDETR, and MDETR and GLIP in the same pre-training dataset consisting of 1.3M image-text pairs with ground truth bounding box annotations. as shown in Table 1. Also, we pre-train and finetune all the models on " + }, + { + "bbox": [ + 304, + 408, + 545, + 516 + ], + "type": "inline_equation", + "content": "384\\times 384" + }, + { + "bbox": [ + 304, + 408, + 545, + 516 + ], + "type": "text", + "content": " pixels images. Finally, we apply our dynamic inference method to our ViTMDETR model in finetuning tasks and call it D-ViTMDETR." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 525, + 362, + 536 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 525, + 362, + 536 + ], + "spans": [ + { + "bbox": [ + 305, + 525, + 362, + 536 + ], + "type": "text", + "content": "5.1. Results" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 539, + 545, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 539, + 545, + 684 + ], + "spans": [ + { + "bbox": [ + 304, + 539, + 545, + 684 + ], + "type": "text", + "content": "Experiments on Large Model We first perform experiments on our large image and language model, ViTMDETR. This model contains two backbones: (1) DeiT-Base [33] with 86M parameters, (2) RoBERTa-Base [23] with 125M parameters and a multimodal network (DETR) with 18M parameters similar to [14], resulting in 229M parameters model. Next, after pre-training the model, we learn dynamic inference on the downstream tasks and report the results in the Table 2. As shown in the table, we can improve the run-time complexity of MDETR by " + }, + { + "bbox": [ + 304, + 539, + 545, + 684 + ], + "type": "inline_equation", + "content": "\\sim 50\\%" + }, + { + "bbox": [ + 304, + 539, + 545, + 684 + ], + "type": "text", + "content": " while achieving " + }, + { + "bbox": [ + 304, + 539, + 545, + 684 + ], + "type": "inline_equation", + "content": "\\sim 1\\%" + }, + { + "bbox": [ + 304, + 539, + 545, + 684 + ], + "type": "text", + "content": " higher accuracy. On the other hand, we perform additional ablation studies with the following two" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 58, + 628, + 217, + 639 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 628, + 217, + 639 + ], + "spans": [ + { + "bbox": [ + 58, + 628, + 217, + 639 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 58, + 628, + 217, + 639 + ], + "type": "text", + "content": "https://github.com/Lyken17/pytorch-OpCounter" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 317, + 693, + 438, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 693, + 438, + 703 + ], + "spans": [ + { + "bbox": [ + 317, + 693, + 438, + 703 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 317, + 693, + 438, + 703 + ], + "type": "text", + "content": "https://github.com/ashkamath/mdetr" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 317, + 703, + 493, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 703, + 493, + 713 + ], + "spans": [ + { + "bbox": [ + 317, + 703, + 493, + 713 + ], + "type": "text", + "content": "3https://github.com/rwrightman/pytorch-image-models" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2629" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 60, + 70, + 533, + 186 + ], + "blocks": [ + { + "bbox": [ + 60, + 70, + 533, + 186 + ], + "lines": [ + { + "bbox": [ + 60, + 70, + 533, + 186 + ], + "spans": [ + { + "bbox": [ + 60, + 70, + 533, + 186 + ], + "type": "table", + "html": "
RefCOCORefCOCO+RefCOCOgGQAPhraseCut
valtestAtestBvaltestAtestBvaltestATest-DevTest-StdTestRun-Time Eff. (fps)GFLOPs
MDETR [14]87.088.682.577.281.571.076.977.162.162.057.22850
GLIP [17]87.789.583.078.082.772.477.678.362.662.2-2562
ViTMDETR87.689.383.378.082.572.677.878.162.362.057.52760
Random-LS83.986.179.775.778.968.073.875.158.258.454.13442
Random-TP+TF83.985.979.875.577.667.974.174.958.458.454.23245
Random-LS+TP+TF80.081.875.271.774.864.169.671.455.855.951.34132
Stochastic-LS+TP+TF83.185.078.874.678.067.072.474.357.057.153.64132
D-ViTMDETR-LS87.689.483.278.382.672.877.778.062.462.057.53442
D-ViTMDETR-TP+TF87.689.383.578.082.872.677.778.262.462.057.53245
D-ViTMDETR-LS+TP+TF87.489.283.278.182.572.477.477.761.961.657.341 (↑ 50%)32 (↓ 50%)
", + "image_path": "88f87f27bd80b769774c0df742e560b2b78edd6d875ad4ff7a17cce822c38d36.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 59, + 239, + 533, + 348 + ], + "blocks": [ + { + "bbox": [ + 46, + 194, + 547, + 229 + ], + "lines": [ + { + "bbox": [ + 46, + 194, + 547, + 229 + ], + "spans": [ + { + "bbox": [ + 46, + 194, + 547, + 229 + ], + "type": "text", + "content": "Table 2. Experiments on referring exprehension comprehension (REC) and Visual Question Answering (GQA) benchmarks on the large model we built. Note that ViTMDETR contains " + }, + { + "bbox": [ + 46, + 194, + 547, + 229 + ], + "type": "inline_equation", + "content": "{229M}" + }, + { + "bbox": [ + 46, + 194, + 547, + 229 + ], + "type": "text", + "content": " parameters whereas MDETR and GLIP contains " + }, + { + "bbox": [ + 46, + 194, + 547, + 229 + ], + "type": "inline_equation", + "content": "{205M}" + }, + { + "bbox": [ + 46, + 194, + 547, + 229 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 194, + 547, + 229 + ], + "type": "inline_equation", + "content": "{231M}" + }, + { + "bbox": [ + 46, + 194, + 547, + 229 + ], + "type": "text", + "content": " parameters. D-ViTMDETR model is built on top of pre-trained ViTMDETR and only introduces " + }, + { + "bbox": [ + 46, + 194, + 547, + 229 + ], + "type": "inline_equation", + "content": "\\sim {1M}" + }, + { + "bbox": [ + 46, + 194, + 547, + 229 + ], + "type": "text", + "content": " more parameters,resulting in " + }, + { + "bbox": [ + 46, + 194, + 547, + 229 + ], + "type": "inline_equation", + "content": "{230M}" + }, + { + "bbox": [ + 46, + 194, + 547, + 229 + ], + "type": "text", + "content": " parameters." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 59, + 239, + 533, + 348 + ], + "lines": [ + { + "bbox": [ + 59, + 239, + 533, + 348 + ], + "spans": [ + { + "bbox": [ + 59, + 239, + 533, + 348 + ], + "type": "table", + "html": "
RefCOCORefCOCO+RefCOCOgGQAPhraseCut
valtestAtestBvaltestAtestBvaltestATest-DevTest-StdTestRun-time Eff. (fps)GFLOPs
MDETR [14]83.985.479.775.079.569.474.674.958.858.654.54014
ViTMDETR84.185.780.075.279.869.874.674.858.858.954.74014
Random-LS81.882.477.171.977.867.072.572.655.856.149.04811
Random-TP+TF81.882.377.371.977.967.272.772.455.956.050.84610
Random-LS+TP+TF79.980.675.469.976.065.670.970.154.054.148.6559
Stochastic-LS+TP+TF80.981.776.170.576.966.471.470.954.855.048.9559
D-ViTMDETR-LS84.185.979.975.579.670.174.974.858.759.154.54811
D-ViTMDETR-TP+TF84.085.979.875.479.670.074.874.658.559.054.54610
D-ViTMDETR-LS+TP+TF83.885.779.675.279.569.974.774.458.358.854.255 (↑ 36%)9 (↓ 36%)
", + "image_path": "619ab366132e252d4f5d853b358f49856306a47845965c61e193402515d859b8.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 356, + 547, + 390 + ], + "lines": [ + { + "bbox": [ + 46, + 356, + 547, + 390 + ], + "spans": [ + { + "bbox": [ + 46, + 356, + 547, + 390 + ], + "type": "text", + "content": "Table 3. Experiments on referring exprehension comprehension (REC) and Visual Question Answering (GQA) benchmarks on the small models. Note that ViTMDETR and MDETR contain " + }, + { + "bbox": [ + 46, + 356, + 547, + 390 + ], + "type": "inline_equation", + "content": "80M" + }, + { + "bbox": [ + 46, + 356, + 547, + 390 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 356, + 547, + 390 + ], + "type": "inline_equation", + "content": "80M" + }, + { + "bbox": [ + 46, + 356, + 547, + 390 + ], + "type": "text", + "content": " parameters. D-ViTMDETR model is built on top of pre-trained ViTMDETR and only introduces " + }, + { + "bbox": [ + 46, + 356, + 547, + 390 + ], + "type": "inline_equation", + "content": "\\sim 1M" + }, + { + "bbox": [ + 46, + 356, + 547, + 390 + ], + "type": "text", + "content": " more parameters, resulting in " + }, + { + "bbox": [ + 46, + 356, + 547, + 390 + ], + "type": "inline_equation", + "content": "81M" + }, + { + "bbox": [ + 46, + 356, + 547, + 390 + ], + "type": "text", + "content": " parameters." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 411, + 287, + 470 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 411, + 287, + 470 + ], + "spans": [ + { + "bbox": [ + 46, + 411, + 287, + 470 + ], + "type": "text", + "content": "components of our method: (1) dynamic token pruning and fusion, (2) adaptive MSA and FFN layer skipping. With dynamic token pruning (TP) and fusion (TF) only, we can reduce the run-time complexity by " + }, + { + "bbox": [ + 46, + 411, + 287, + 470 + ], + "type": "inline_equation", + "content": "\\sim 20\\%" + }, + { + "bbox": [ + 46, + 411, + 287, + 470 + ], + "type": "text", + "content": ". With adaptive layer skipping (LS), this number goes up to " + }, + { + "bbox": [ + 46, + 411, + 287, + 470 + ], + "type": "inline_equation", + "content": "\\sim 30\\%" + }, + { + "bbox": [ + 46, + 411, + 287, + 470 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 471, + 288, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 471, + 288, + 639 + ], + "spans": [ + { + "bbox": [ + 46, + 471, + 288, + 639 + ], + "type": "text", + "content": "Experiments on Small Model Next, we perform experiments on our small image and language model, ViTMDETR. This model contains the DeiT-Small vision backbone with 22M parameters and CLIP [29] text backbone with 40M parameters together with a multimodal network with 18M parameters resulting in 80M parameters image and language model. After pre-training this model, we learn dynamic inference on the finetuning tasks as shown in Table 3. As shown in the table, we can reduce the run-time complexity of MDETR by " + }, + { + "bbox": [ + 46, + 471, + 288, + 639 + ], + "type": "inline_equation", + "content": "\\sim 36\\%" + }, + { + "bbox": [ + 46, + 471, + 288, + 639 + ], + "type": "text", + "content": " with no accuracy drop. On the other hand, in our ablation studies, with dynamic token pruning and fusion only, we can reduce the run-time complexity by " + }, + { + "bbox": [ + 46, + 471, + 288, + 639 + ], + "type": "inline_equation", + "content": "\\sim 15\\%" + }, + { + "bbox": [ + 46, + 471, + 288, + 639 + ], + "type": "text", + "content": ". By adding dynamic layer skipping, this number goes up to " + }, + { + "bbox": [ + 46, + 471, + 288, + 639 + ], + "type": "inline_equation", + "content": "\\sim 36\\%" + }, + { + "bbox": [ + 46, + 471, + 288, + 639 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 647, + 148, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 148, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 148, + 658 + ], + "type": "text", + "content": "5.2. Ablation Studies" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "type": "text", + "content": "Impact of Knowledge Distillation In our ablation studies, we first perform experiments on the impact of knowledge distillation for the optimization of our adaptive model. We show the results in Table 4. As seen in the table, knowledge" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 411, + 545, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 411, + 545, + 434 + ], + "spans": [ + { + "bbox": [ + 304, + 411, + 545, + 434 + ], + "type": "text", + "content": "distillation improves the accuracy of the dynamic model by around " + }, + { + "bbox": [ + 304, + 411, + 545, + 434 + ], + "type": "inline_equation", + "content": "\\sim 1\\%" + }, + { + "bbox": [ + 304, + 411, + 545, + 434 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 434, + 545, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 434, + 545, + 495 + ], + "spans": [ + { + "bbox": [ + 304, + 434, + 545, + 495 + ], + "type": "text", + "content": "Impact of Pretraining the Decision Networks Next, we perform experiments on the impact of pre-training the decision networks. We show the results in Table 5. As seen in the table, pre-training the decision networks is important to maintain the high accuracy of our dynamic model." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 495, + 545, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 495, + 545, + 567 + ], + "spans": [ + { + "bbox": [ + 304, + 495, + 545, + 567 + ], + "type": "text", + "content": "Impact of Window Size for Spatial Clustering In our experiments, we set the window size to " + }, + { + "bbox": [ + 304, + 495, + 545, + 567 + ], + "type": "inline_equation", + "content": "64 \\times 64" + }, + { + "bbox": [ + 304, + 495, + 545, + 567 + ], + "type": "text", + "content": " and learn single action for the vision tokens inside the window. We perform experiments with different window sizes and show the results in Table 6 and show that we get the best results with " + }, + { + "bbox": [ + 304, + 495, + 545, + 567 + ], + "type": "inline_equation", + "content": "64 \\times 64" + }, + { + "bbox": [ + 304, + 495, + 545, + 567 + ], + "type": "text", + "content": " windows." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 575, + 456, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 575, + 456, + 588 + ], + "spans": [ + { + "bbox": [ + 306, + 575, + 456, + 588 + ], + "type": "text", + "content": "5.3. Analyzing Learned Policies" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 594, + 545, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 653 + ], + "type": "text", + "content": "Pruned Tokens Additionally, we visualize the pruned tokens by the decision network in Figure 4. As seen in the figure, the number of tokens that are pruned goes down w.r.t depth of the backbones. This makes sense since we have decreasing number of remaining tokens w.r.t. depth." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "Fused Tokens In the next step, we visualize the fusion policies learned by the decision network. In particular, we are interested in how many vision tokens are fused over the increasing number of layers in the backbones. We show the results in Figure 4. As we can see in the figure, the num" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2630" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 85, + 70, + 507, + 130 + ], + "blocks": [ + { + "bbox": [ + 85, + 70, + 507, + 130 + ], + "lines": [ + { + "bbox": [ + 85, + 70, + 507, + 130 + ], + "spans": [ + { + "bbox": [ + 85, + 70, + 507, + 130 + ], + "type": "table", + "html": "
RefCOCORefCOCO+RefCOCOgGQAPhraseCut
valtestAtestBvaltestAtestBvaltestATest-DevTest-StdTest
ViTMDETR87.689.383.378.082.572.677.878.162.362.057.5
D-ViTMDETR (LS+TP+AF)86.988.482.377.281.371.577.077.460.860.655.9
D-ViTMDETR (LS+TP+AF) + KD87.489.283.278.182.572.477.477.761.961.657.3
", + "image_path": "57bf860b43e57696b7408b10dbbc27e675c053a730630f94530f3b20d04429d0.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 85, + 159, + 507, + 216 + ], + "blocks": [ + { + "bbox": [ + 177, + 137, + 416, + 149 + ], + "lines": [ + { + "bbox": [ + 177, + 137, + 416, + 149 + ], + "spans": [ + { + "bbox": [ + 177, + 137, + 416, + 149 + ], + "type": "text", + "content": "Table 4. Ablation studies on the impact of knowledge distillation." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 85, + 159, + 507, + 216 + ], + "lines": [ + { + "bbox": [ + 85, + 159, + 507, + 216 + ], + "spans": [ + { + "bbox": [ + 85, + 159, + 507, + 216 + ], + "type": "table", + "html": "
RefCOCORefCOCO+RefCOCOgGQAPhraseCut
valtestAtestBvaltestAtestBvaltestATest-DevTest-StdTest
Without Pre-training77.479.273.168.172.562.667.467.751.451.147.0
With Pre-training84.986.780.675.680.069.174.975.258.958.654.5
", + "image_path": "9bbca18b22596a094755bdeb905ea615e3d97266bf579c58ac19fb83aada060d.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 74, + 253, + 261, + 313 + ], + "blocks": [ + { + "bbox": [ + 159, + 223, + 434, + 235 + ], + "lines": [ + { + "bbox": [ + 159, + 223, + 434, + 235 + ], + "spans": [ + { + "bbox": [ + 159, + 223, + 434, + 235 + ], + "type": "text", + "content": "Table 5. Ablation studies on the impact of pretraining the decision network." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 74, + 253, + 261, + 313 + ], + "lines": [ + { + "bbox": [ + 74, + 253, + 261, + 313 + ], + "spans": [ + { + "bbox": [ + 74, + 253, + 261, + 313 + ], + "type": "table", + "html": "
Window SizeRefCOCORefCOCOgRefCOCO+
16x1684.574.873.0
32x3285.876.474.6
64x6487.478.177.4
128x12887.077.676.5
", + "image_path": "cb8cda8fb1ff63128373105157144fd9fec8e0973782294a52819976a2d4e3ad.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 321, + 288, + 344 + ], + "lines": [ + { + "bbox": [ + 47, + 321, + 288, + 344 + ], + "spans": [ + { + "bbox": [ + 47, + 321, + 288, + 344 + ], + "type": "text", + "content": "Table 6. Impact of window size on vision token clustering on the val split of RefCOCO, RefCOCOg, and RefCOCO+." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 355, + 287, + 404 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 355, + 287, + 404 + ], + "spans": [ + { + "bbox": [ + 47, + 355, + 287, + 404 + ], + "type": "text", + "content": "ber of vision tokens that are fused with the text tokens goes down w.r.t depth of the backbones. On the other hand, we can see that on average we fuse " + }, + { + "bbox": [ + 47, + 355, + 287, + 404 + ], + "type": "inline_equation", + "content": "\\sim 30\\%" + }, + { + "bbox": [ + 47, + 355, + 287, + 404 + ], + "type": "text", + "content": " of vision tokens with the language tokens across the processing in backbones." + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 60, + 418, + 165, + 520 + ], + "blocks": [ + { + "bbox": [ + 60, + 418, + 165, + 520 + ], + "lines": [ + { + "bbox": [ + 60, + 418, + 165, + 520 + ], + "spans": [ + { + "bbox": [ + 60, + 418, + 165, + 520 + ], + "type": "image", + "image_path": "0fc6b8ea53001e7afd42cb1736d63092bafe3d946bc91a43d4ce63fcc5d4782b.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 533, + 287, + 556 + ], + "lines": [ + { + "bbox": [ + 47, + 533, + 287, + 556 + ], + "spans": [ + { + "bbox": [ + 47, + 533, + 287, + 556 + ], + "type": "text", + "content": "Figure 4. Probability of token pruning (Left) and fusion (Right) over depth for the RefCOCO experiments." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 173, + 418, + 276, + 519 + ], + "blocks": [ + { + "bbox": [ + 173, + 418, + 276, + 519 + ], + "lines": [ + { + "bbox": [ + 173, + 418, + 276, + 519 + ], + "spans": [ + { + "bbox": [ + 173, + 418, + 276, + 519 + ], + "type": "image", + "image_path": "7c90110b94026cce11efae2460aa75c4c9ce1d4fd818f79b42930f6ac7ed492c.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 463, + 547, + 509 + ], + "lines": [ + { + "bbox": [ + 305, + 463, + 547, + 509 + ], + "spans": [ + { + "bbox": [ + 305, + 463, + 547, + 509 + ], + "type": "text", + "content": "Figure 5. MSA and FFN layer skipping probability distribution in vision backbone (Top Left), text backbone (Top Right), and multimodal network (Bottom) that consists of 6 encoder and decoder layers. We show the results from RefCOCO experiments." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 569, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 569, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 569, + 287, + 653 + ], + "type": "text", + "content": "Skipped MSA and FFN layers Next, we analyze the policies learned by the decision networks towards skipping MSA and FFN layers in both vision and text backbone as well as the multimodal network. We note that across the 12 encoders in the backbones, we learn decisions to potentially skip 20 MSA and FFN layers and 12 MSA and FFN layers in the multimodal network." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "content": "As seen in Figure 5, the skipping operations for MSA and FFN layers are distributed in a way that later MSA and FFN layers especially in the backbones are skipped with higher probability. This is similar to skipping operations with CNNs where shallow layers are more important than" + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 329, + 257, + 422, + 350 + ], + "blocks": [ + { + "bbox": [ + 329, + 257, + 422, + 350 + ], + "lines": [ + { + "bbox": [ + 329, + 257, + 422, + 350 + ], + "spans": [ + { + "bbox": [ + 329, + 257, + 422, + 350 + ], + "type": "image", + "image_path": "1a3fee95a39f4a1af15b44e97f130ac7d3c70845c9d80d4b421f0ca2632105a2.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 428, + 258, + 524, + 350 + ], + "blocks": [ + { + "bbox": [ + 428, + 258, + 524, + 350 + ], + "lines": [ + { + "bbox": [ + 428, + 258, + 524, + 350 + ], + "spans": [ + { + "bbox": [ + 428, + 258, + 524, + 350 + ], + "type": "image", + "image_path": "6adbab7be80a250563065530b44e7a3d5a20267d858e28f6a35532c298d386a7.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 329, + 357, + 424, + 449 + ], + "blocks": [ + { + "bbox": [ + 329, + 357, + 424, + 449 + ], + "lines": [ + { + "bbox": [ + 329, + 357, + 424, + 449 + ], + "spans": [ + { + "bbox": [ + 329, + 357, + 424, + 449 + ], + "type": "image", + "image_path": "b8f208a6c15fca4450033193d1e88e0c358e22e0caee5ba9907fcee8db590bea.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 428, + 357, + 523, + 449 + ], + "blocks": [ + { + "bbox": [ + 428, + 357, + 523, + 449 + ], + "lines": [ + { + "bbox": [ + 428, + 357, + 523, + 449 + ], + "spans": [ + { + "bbox": [ + 428, + 357, + 523, + 449 + ], + "type": "image", + "image_path": "0b6331b5639caaabea3e334c5f5e5f5452ad2163611dd0be02333a1aa13219bb.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 527, + 547, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 527, + 547, + 564 + ], + "spans": [ + { + "bbox": [ + 305, + 527, + 547, + 564 + ], + "type": "text", + "content": "deep layers as they provide critical low-level abstraction of objects [34]. On the other hand, there is not a clear pattern with the skipping operations in the multimodal network." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 574, + 379, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 574, + 379, + 586 + ], + "spans": [ + { + "bbox": [ + 306, + 574, + 379, + 586 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": "We propose a dynamic inference method for the vision and language models. Our method includes learning adaptive policies to skip MSA and FFN layers across vision and language backbones and multimodal network. Additionally, it dynamically prunes tokens from different modalities and fuse tokens at different stages of backbones. We then train our model on downstream vision and language tasks. In our experiments on REC, RES and VQA we show that we can improve the run-time complexity of MDETR, and GLIP by up to " + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\sim 50\\%" + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": " with only maximum " + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\sim 0.3\\%" + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": " accuracy drop." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 758 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 758 + ], + "type": "text", + "content": "2631" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "text", + "content": "[1] Arian Bakhtiarnia, Qi Zhang, and Alexandros Iosifidis. 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